LMFDB - Embedded newform 48.8.k.a.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,8,Mod(11,48)]

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, 1, 2]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("48.11");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	48.k (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:	$14.9944812232$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.5
Character	$\chi$	$=$	48.11
Dual form			48.8.k.a.35.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10.8871 + 3.07743i) q^{2} +(22.4120 - 41.0451i) q^{3} +(109.059 - 67.0087i) q^{4} +(-78.5897 + 78.5897i) q^{5} +(-117.689 + 515.835i) q^{6} -861.367 q^{7} +(-981.123 + 1065.15i) q^{8} +(-1182.40 - 1839.81i) q^{9} +O(q^{10})$	\(q+(-10.8871 + 3.07743i) q^{2} +(22.4120 - 41.0451i) q^{3} +(109.059 - 67.0087i) q^{4} +(-78.5897 + 78.5897i) q^{5} +(-117.689 + 515.835i) q^{6} -861.367 q^{7} +(-981.123 + 1065.15i) q^{8} +(-1182.40 - 1839.81i) q^{9} +(613.761 - 1097.47i) q^{10} +(2056.62 + 2056.62i) q^{11} +(-306.151 - 5978.13i) q^{12} +(2103.41 - 2103.41i) q^{13} +(9377.81 - 2650.80i) q^{14} +(1464.37 + 4987.07i) q^{15} +(7403.68 - 14615.8i) q^{16} +31038.4i q^{17} +(18534.9 + 16391.4i) q^{18} +(-26598.3 - 26598.3i) q^{19} +(-3304.71 + 13837.1i) q^{20} +(-19305.0 + 35354.9i) q^{21} +(-28719.8 - 16061.6i) q^{22} +55236.2i q^{23} +(21730.4 + 64142.5i) q^{24} +65772.3i q^{25} +(-16427.0 + 29373.2i) q^{26} +(-102015. + 7298.17i) q^{27} +(-93939.8 + 57719.1i) q^{28} +(68856.8 + 68856.8i) q^{29} +(-31290.1 - 49788.4i) q^{30} +160973. i q^{31} +(-35625.7 + 181908. i) q^{32} +(130507. - 38321.3i) q^{33} +(-95518.4 - 337919. i) q^{34} +(67694.6 - 67694.6i) q^{35} +(-252235. - 121416. i) q^{36} +(270757. + 270757. i) q^{37} +(371433. + 207724. i) q^{38} +(-39193.1 - 133476. i) q^{39} +(-6603.83 - 160816. i) q^{40} -420443. q^{41} +(101373. - 444323. i) q^{42} +(67975.3 - 67975.3i) q^{43} +(362104. + 86481.3i) q^{44} +(237515. + 51665.0i) q^{45} +(-169986. - 601364. i) q^{46} +312531. q^{47} +(-433975. - 631454. i) q^{48} -81589.4 q^{49} +(-202410. - 716071. i) q^{50} +(1.27397e6 + 695632. i) q^{51} +(88448.9 - 370343. i) q^{52} +(-281866. + 281866. i) q^{53} +(1.08819e6 - 393400. i) q^{54} -323258. q^{55} +(845107. - 917487. i) q^{56} +(-1.68785e6 + 495609. i) q^{57} +(-961554. - 537751. i) q^{58} +(-1.58314e6 - 1.58314e6i) q^{59} +(493880. + 445759. i) q^{60} +(-1.63251e6 + 1.63251e6i) q^{61} +(-495383. - 1.75253e6i) q^{62} +(1.01848e6 + 1.58475e6i) q^{63} +(-171947. - 2.09009e6i) q^{64} +330613. i q^{65} +(-1.30292e6 + 818835. i) q^{66} +(1.24121e6 + 1.24121e6i) q^{67} +(2.07984e6 + 3.38501e6i) q^{68} +(2.26718e6 + 1.23795e6i) q^{69} +(-528674. + 945324. i) q^{70} +2.85228e6i q^{71} +(3.11976e6 + 545636. i) q^{72} -4.91160e6i q^{73} +(-3.78100e6 - 2.11453e6i) q^{74} +(2.69963e6 + 1.47409e6i) q^{75} +(-4.68309e6 - 1.11846e6i) q^{76} +(-1.77151e6 - 1.77151e6i) q^{77} +(837465. + 1.33256e6i) q^{78} -2.34370e6i q^{79} +(566797. + 1.73050e6i) q^{80} +(-1.98681e6 + 4.35079e6i) q^{81} +(4.57741e6 - 1.29388e6i) q^{82} +(6.24674e6 - 6.24674e6i) q^{83} +(263708. + 5.14937e6i) q^{84} +(-2.43930e6 - 2.43930e6i) q^{85} +(-530866. + 949245. i) q^{86} +(4.36945e6 - 1.28302e6i) q^{87} +(-4.20841e6 + 172816. i) q^{88} -7.35013e6 q^{89} +(-2.74485e6 + 168450. i) q^{90} +(-1.81181e6 + 1.81181e6i) q^{91} +(3.70131e6 + 6.02400e6i) q^{92} +(6.60716e6 + 3.60773e6i) q^{93} +(-3.40256e6 + 961791. i) q^{94} +4.18070e6 q^{95} +(6.66799e6 + 5.53919e6i) q^{96} -9.60307e6 q^{97} +(888274. - 251085. i) q^{98} +(1.35203e6 - 6.21554e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 2 q^{3} - 4 q^{4} + 172 q^{6} - 8 q^{7}+O(q^{10}) $ 108 * q - 2 * q^3 - 4 * q^4 + 172 * q^6 - 8 * q^7	$ 108 q - 2 q^{3} - 4 q^{4} + 172 q^{6} - 8 q^{7} - 6504 q^{10} + 12016 q^{12} - 4 q^{13} - 55280 q^{16} + 21172 q^{18} - 60588 q^{19} - 4376 q^{21} - 212744 q^{22} - 317304 q^{24} + 238042 q^{27} + 219736 q^{28} - 503852 q^{30} - 4 q^{33} - 364856 q^{34} + 867620 q^{36} - 4 q^{37} - 283948 q^{39} + 390392 q^{40} - 3022344 q^{42} + 752844 q^{43} - 156252 q^{45} - 1166824 q^{46} + 358320 q^{48} + 9882508 q^{49} + 1121592 q^{51} - 4458688 q^{52} + 203816 q^{54} + 4191000 q^{55} + 4975544 q^{58} - 4390240 q^{60} - 2279892 q^{61} + 4781432 q^{64} + 1457476 q^{66} + 1552540 q^{67} + 4372 q^{69} - 9366152 q^{70} - 1660280 q^{72} - 886066 q^{75} - 6569272 q^{76} - 13616772 q^{78} - 4 q^{81} + 11560256 q^{82} - 10944176 q^{84} + 7846496 q^{85} - 40789116 q^{87} + 24614816 q^{88} + 25746032 q^{90} - 1590680 q^{91} - 14495396 q^{93} - 6995856 q^{94} - 13927736 q^{96} - 8 q^{97} - 4701076 q^{99}+O(q^{100}) $ 108 * q - 2 * q^3 - 4 * q^4 + 172 * q^6 - 8 * q^7 - 6504 * q^10 + 12016 * q^12 - 4 * q^13 - 55280 * q^16 + 21172 * q^18 - 60588 * q^19 - 4376 * q^21 - 212744 * q^22 - 317304 * q^24 + 238042 * q^27 + 219736 * q^28 - 503852 * q^30 - 4 * q^33 - 364856 * q^34 + 867620 * q^36 - 4 * q^37 - 283948 * q^39 + 390392 * q^40 - 3022344 * q^42 + 752844 * q^43 - 156252 * q^45 - 1166824 * q^46 + 358320 * q^48 + 9882508 * q^49 + 1121592 * q^51 - 4458688 * q^52 + 203816 * q^54 + 4191000 * q^55 + 4975544 * q^58 - 4390240 * q^60 - 2279892 * q^61 + 4781432 * q^64 + 1457476 * q^66 + 1552540 * q^67 + 4372 * q^69 - 9366152 * q^70 - 1660280 * q^72 - 886066 * q^75 - 6569272 * q^76 - 13616772 * q^78 - 4 * q^81 + 11560256 * q^82 - 10944176 * q^84 + 7846496 * q^85 - 40789116 * q^87 + 24614816 * q^88 + 25746032 * q^90 - 1590680 * q^91 - 14495396 * q^93 - 6995856 * q^94 - 13927736 * q^96 - 8 * q^97 - 4701076 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−10.8871	+	3.07743i	−0.962295	+	0.272009i
$2$	−10.8871	+	3.07743i	−0.962295	+	0.272009i
$3$	22.4120	−	41.0451i	0.479244	−	0.877682i
$3$	22.4120	−	41.0451i	0.479244	−	0.877682i
$4$	109.059	−	67.0087i	0.852022	−	0.523505i
$5$	−78.5897	+	78.5897i	−0.281171	+	0.281171i	−0.833576	−	0.552405i	$-0.813710\pi$
$5$	−78.5897	+	78.5897i	−0.281171	+	0.281171i	0.552405	+	0.833576i	$0.313710\pi$
$6$	−117.689	+	515.835i	−0.222436	+	0.974947i
$7$	−861.367			−0.949173			−0.474586	−	0.880209i	$-0.657402\pi$
$7$	−861.367			−0.949173			−0.474586	+	0.880209i	$0.657402\pi$
$8$	−981.123	+	1065.15i	−0.677499	+	0.735524i
$9$	−1182.40	−	1839.81i	−0.540651	−	0.841247i
$10$	613.761	−	1097.47i	0.194088	−	0.347050i
$11$	2056.62	+	2056.62i	0.465886	+	0.465886i	0.900579	−	0.434693i	$-0.143143\pi$
$11$	2056.62	+	2056.62i	0.465886	+	0.465886i	−0.434693	+	0.900579i	$0.643143\pi$
$12$	−306.151	−	5978.13i	−0.0511448	−	0.998691i
$13$	2103.41	−	2103.41i	0.265536	−	0.265536i	−0.561763	−	0.827298i	$-0.689877\pi$
$13$	2103.41	−	2103.41i	0.265536	−	0.265536i	0.827298	+	0.561763i	$0.189877\pi$
$14$	9377.81	−	2650.80i	0.913384	−	0.258183i
$15$	1464.37	+	4987.07i	0.112029	+	0.381528i
$16$	7403.68	−	14615.8i	0.451885	−	0.892076i
$17$			31038.4i			1.53224i	0.642695	+	0.766122i	$0.277816\pi$
$17$			31038.4i			1.53224i	−0.642695	+	0.766122i	$0.722184\pi$
$18$	18534.9	+	16391.4i	0.749092	+	0.662466i
$19$	−26598.3	−	26598.3i	−0.889643	−	0.889643i	0.104845	−	0.994489i	$-0.466565\pi$
$19$	−26598.3	−	26598.3i	−0.889643	−	0.889643i	−0.994489	+	0.104845i	$0.966565\pi$
$20$	−3304.71	+	13837.1i	−0.0923695	+	0.386758i
$21$	−19305.0	+	35354.9i	−0.454885	+	0.833072i
$22$	−28719.8	−	16061.6i	−0.575045	−	0.321595i
$23$			55236.2i			0.946622i	0.880895	+	0.473311i	$0.156941\pi$
$23$			55236.2i			0.946622i	−0.880895	+	0.473311i	$0.843059\pi$
$24$	21730.4	+	64142.5i	0.320869	+	0.947124i
$25$			65772.3i			0.841886i
$26$	−16427.0	+	29373.2i	−0.183295	+	0.327751i
$27$	−102015.	+	7298.17i	−0.997451	+	0.0713577i
$28$	−93939.8	+	57719.1i	−0.808716	+	0.496897i
$29$	68856.8	+	68856.8i	0.524269	+	0.524269i	0.918858	−	0.394589i	$-0.129113\pi$
$29$	68856.8	+	68856.8i	0.524269	+	0.524269i	−0.394589	+	0.918858i	$0.629113\pi$
$30$	−31290.1	−	49788.4i	−0.211584	−	0.336669i
$31$			160973.i			0.970482i	0.874381	+	0.485241i	$0.161268\pi$
$31$			160973.i			0.970482i	−0.874381	+	0.485241i	$0.838732\pi$
$32$	−35625.7	+	181908.i	−0.192194	+	0.981357i
$33$	130507.	−	38321.3i	0.632173	−	0.185627i
$34$	−95518.4	−	337919.i	−0.416784	−	1.47447i
$35$	67694.6	−	67694.6i	0.266880	−	0.266880i
$36$	−252235.	−	121416.i	−0.901044	−	0.433727i
$37$	270757.	+	270757.i	0.878768	+	0.878768i	0.993407	−	0.114639i	$-0.0365713\pi$
$37$	270757.	+	270757.i	0.878768	+	0.878768i	−0.114639	+	0.993407i	$0.536571\pi$
$38$	371433.	+	207724.i	1.09809	+	0.614108i
$39$	−39193.1	−	133476.i	−0.105800	−	0.360312i
$40$	−6603.83	−	160816.i	−0.0163150	−	0.397301i
$41$	−420443.			−0.952716			−0.476358	−	0.879251i	$-0.658043\pi$
$41$	−420443.			−0.952716			−0.476358	+	0.879251i	$0.658043\pi$
$42$	101373.	−	444323.i	0.211131	−	0.925393i
$43$	67975.3	−	67975.3i	0.130380	−	0.130380i	−0.638905	−	0.769285i	$-0.720612\pi$
$43$	67975.3	−	67975.3i	0.130380	−	0.130380i	0.769285	+	0.638905i	$0.220612\pi$
$44$	362104.	+	86481.3i	0.640839	+	0.153052i
$45$	237515.	+	51665.0i	0.388550	+	0.0845187i
$46$	−169986.	−	601364.i	−0.257489	−	0.910929i
$47$	312531.			0.439087			0.219543	−	0.975603i	$-0.429543\pi$
$47$	312531.			0.439087			0.219543	+	0.975603i	$0.429543\pi$
$48$	−433975.	−	631454.i	−0.566397	−	0.824133i
$49$	−81589.4			−0.0990712
$50$	−202410.	−	716071.i	−0.229000	−	0.810142i
$51$	1.27397e6	+	695632.i	1.34482	+	0.734318i
$52$	88448.9	−	370343.i	0.0872330	−	0.365251i
$53$	−281866.	+	281866.i	−0.260062	+	0.260062i	−0.825079	−	0.565017i	$-0.808870\pi$
$53$	−281866.	+	281866.i	−0.260062	+	0.260062i	0.565017	+	0.825079i	$0.308870\pi$
$54$	1.08819e6	−	393400.i	0.940432	−	0.339983i
$55$	−323258.			−0.261987
$56$	845107.	−	917487.i	0.643063	−	0.698139i
$57$	−1.68785e6	+	495609.i	−1.20718	+	0.354468i
$58$	−961554.	−	537751.i	−0.647107	−	0.361895i
$59$	−1.58314e6	−	1.58314e6i	−1.00355	−	1.00355i	−0.999994	−	0.00355260i	$-0.998869\pi$
$59$	−1.58314e6	−	1.58314e6i	−1.00355	−	1.00355i	−0.00355260	−	0.999994i	$-0.501131\pi$
$60$	493880.	+	445759.i	0.295183	+	0.266423i
$61$	−1.63251e6	+	1.63251e6i	−0.920875	+	0.920875i	−0.997091	−	0.0762168i	$-0.975716\pi$
$61$	−1.63251e6	+	1.63251e6i	−0.920875	+	0.920875i	0.0762168	+	0.997091i	$0.475716\pi$
$62$	−495383.	−	1.75253e6i	−0.263979	−	0.933889i
$63$	1.01848e6	+	1.58475e6i	0.513171	+	0.798489i
$64$	−171947.	−	2.09009e6i	−0.0819907	−	0.996633i
$65$			330613.i			0.149322i
$66$	−1.30292e6	+	818835.i	−0.557844	+	0.350584i
$67$	1.24121e6	+	1.24121e6i	0.504177	+	0.504177i	0.912733	−	0.408556i	$-0.133968\pi$
$67$	1.24121e6	+	1.24121e6i	0.504177	+	0.504177i	−0.408556	+	0.912733i	$0.633968\pi$
$68$	2.07984e6	+	3.38501e6i	0.802138	+	1.30551i
$69$	2.26718e6	+	1.23795e6i	0.830833	+	0.453663i
$70$	−528674.	+	945324.i	−0.184223	+	0.329411i
$71$			2.85228e6i			0.945775i	0.881123	+	0.472888i	$0.156788\pi$
$71$			2.85228e6i			0.945775i	−0.881123	+	0.472888i	$0.843212\pi$
$72$	3.11976e6	+	545636.i	0.985048	+	0.172282i
$73$		−	4.91160e6i		−	1.47772i	−0.673857	−	0.738862i	$-0.735363\pi$
$73$		−	4.91160e6i		−	1.47772i	0.673857	−	0.738862i	$-0.264637\pi$
$74$	−3.78100e6	−	2.11453e6i	−1.08467	−	0.606601i
$75$	2.69963e6	+	1.47409e6i	0.738908	+	0.403468i
$76$	−4.68309e6	−	1.11846e6i	−1.22373	−	0.292263i
$77$	−1.77151e6	−	1.77151e6i	−0.442206	−	0.442206i
$78$	837465.	+	1.33256e6i	0.199818	+	0.317948i
$79$		−	2.34370e6i		−	0.534820i	−0.963583	−	0.267410i	$-0.913832\pi$
$79$		−	2.34370e6i		−	0.534820i	0.963583	−	0.267410i	$-0.0861678\pi$
$80$	566797.	+	1.73050e6i	0.123769	+	0.377883i
$81$	−1.98681e6	+	4.35079e6i	−0.415392	+	0.909642i
$82$	4.57741e6	−	1.29388e6i	0.916794	−	0.259147i
$83$	6.24674e6	−	6.24674e6i	1.19917	−	1.19917i	0.224752	−	0.974416i	$-0.427843\pi$
$83$	6.24674e6	−	6.24674e6i	1.19917	−	1.19917i	0.974416	−	0.224752i	$-0.0721571\pi$
$84$	263708.	+	5.14937e6i	0.0485452	+	0.947930i
$85$	−2.43930e6	−	2.43930e6i	−0.430822	−	0.430822i
$86$	−530866.	+	949245.i	−0.0899996	+	0.160929i
$87$	4.36945e6	−	1.28302e6i	0.711393	−	0.208889i
$88$	−4.20841e6	+	172816.i	−0.658308	+	0.0270331i
$89$	−7.35013e6			−1.10517			−0.552586	−	0.833456i	$-0.686359\pi$
$89$	−7.35013e6			−1.10517			−0.552586	+	0.833456i	$0.686359\pi$
$90$	−2.74485e6	+	168450.i	−0.396889	+	0.0243569i
$91$	−1.81181e6	+	1.81181e6i	−0.252039	+	0.252039i
$92$	3.70131e6	+	6.02400e6i	0.495562	+	0.806543i
$93$	6.60716e6	+	3.60773e6i	0.851774	+	0.465097i
$94$	−3.40256e6	+	961791.i	−0.422531	+	0.119435i
$95$	4.18070e6			0.500284
$96$	6.66799e6	+	5.53919e6i	0.769212	+	0.638994i
$97$	−9.60307e6			−1.06834			−0.534169	−	0.845377i	$-0.679376\pi$
$97$	−9.60307e6			−1.06834			−0.534169	+	0.845377i	$0.679376\pi$
$98$	888274.	−	251085.i	0.0953357	−	0.0269482i
$99$	1.35203e6	−	6.21554e6i	0.140043	−	0.643807i
$100$	4.40732e6	+	7.17306e6i	0.440732	+	0.717306i
$101$	−1.17915e7	+	1.17915e7i	−1.13879	+	1.13879i	−0.150120	+	0.988668i	$0.547966\pi$
$101$	−1.17915e7	+	1.17915e7i	−1.13879	+	1.13879i	−0.988668	+	0.150120i	$0.952034\pi$
$102$	−1.60107e7	−	3.65287e6i	−1.49386	−	0.340827i
$103$	−2.81302e6			−0.253655			−0.126827	−	0.991925i	$-0.540479\pi$
$103$	−2.81302e6			−0.253655			−0.126827	+	0.991925i	$0.540479\pi$
$104$	176748.	+	4.30416e6i	0.0154077	+	0.375208i
$105$	−1.26136e6	−	4.29570e6i	−0.106335	−	0.362136i
$106$	2.20129e6	−	3.93613e6i	0.179517	−	0.320996i
$107$	−3.36641e6	−	3.36641e6i	−0.265659	−	0.265659i	0.561690	−	0.827348i	$-0.310152\pi$
$107$	−3.36641e6	−	3.36641e6i	−0.265659	−	0.265659i	−0.827348	+	0.561690i	$0.810152\pi$
$108$	−1.06366e7	+	7.63183e6i	−0.812494	+	0.582969i
$109$	8.97239e6	−	8.97239e6i	0.663614	−	0.663614i	−0.292616	−	0.956230i	$-0.594526\pi$
$109$	8.97239e6	−	8.97239e6i	0.663614	−	0.663614i	0.956230	+	0.292616i	$0.0945259\pi$
$110$	3.51935e6	−	994804.i	0.252109	−	0.0712628i
$111$	1.71815e7	−	5.04505e6i	1.19242	−	0.350135i
$112$	−6.37729e6	+	1.25896e7i	−0.428917	+	0.846735i
$113$			4.24556e6i			0.276796i	0.990377	+	0.138398i	$0.0441954\pi$
$113$			4.24556e6i			0.276796i	−0.990377	+	0.138398i	$0.955805\pi$
$114$	1.68506e7	−	1.05900e7i	1.06524	−	0.669466i
$115$	−4.34100e6	−	4.34100e6i	−0.266163	−	0.266163i
$116$	1.21234e7	+	2.89544e6i	0.721146	+	0.172231i
$117$	−6.35696e6	−	1.38279e6i	−0.366943	−	0.0798188i
$118$	2.21078e7	+	1.23638e7i	1.23868	+	0.692734i
$119$		−	2.67354e7i		−	1.45436i
$120$	−6.74872e6	−	3.33316e6i	−0.356523	−	0.176085i
$121$		−	1.10278e7i		−	0.565900i
$122$	1.27494e7	−	2.27972e7i	0.635667	−	1.13664i
$123$	−9.42297e6	+	1.72571e7i	−0.456583	+	0.836182i
$124$	1.07866e7	+	1.75555e7i	0.508052	+	0.826872i
$125$	−1.13088e7	−	1.13088e7i	−0.517885	−	0.517885i
$126$	−1.59653e7	−	1.41190e7i	−0.711018	−	0.628794i
$127$		−	2.70743e7i		−	1.17286i	−0.810002	−	0.586428i	$-0.800534\pi$
$127$		−	2.70743e7i		−	1.17286i	0.810002	−	0.586428i	$-0.199466\pi$
$128$	8.30411e6	+	2.22259e7i	0.349992	+	0.936753i
$129$	−1.26659e6	−	4.31352e6i	−0.0519485	−	0.176916i
$130$	−1.01744e6	−	3.59942e6i	−0.0406168	−	0.143692i
$131$	3.21164e6	−	3.21164e6i	0.124818	−	0.124818i	−0.641938	−	0.766756i	$-0.721869\pi$
$131$	3.21164e6	−	3.21164e6i	0.124818	−	0.124818i	0.766756	+	0.641938i	$0.221869\pi$
$132$	1.16651e7	−	1.29244e7i	0.441449	−	0.489104i
$133$	2.29109e7	+	2.29109e7i	0.844425	+	0.844425i
$134$	−1.73329e7	−	9.69347e6i	−0.622308	−	0.348026i
$135$	7.44378e6	−	8.59090e6i	0.260390	−	0.300518i
$136$	−3.30606e7	−	3.04525e7i	−1.12700	−	1.03809i
$137$	2.06203e6			0.0685131			0.0342566	−	0.999413i	$-0.489094\pi$
$137$	2.06203e6			0.0685131			0.0342566	+	0.999413i	$0.489094\pi$
$138$	−2.84928e7	−	6.50069e6i	−0.922907	−	0.210563i
$139$	−1.87334e7	+	1.87334e7i	−0.591651	+	0.591651i	−0.938077	−	0.346426i	$-0.887395\pi$
$139$	−1.87334e7	+	1.87334e7i	−0.591651	+	0.591651i	0.346426	+	0.938077i	$0.387395\pi$
$140$	2.84657e6	−	1.19188e7i	0.0876746	−	0.367101i
$141$	7.00444e6	−	1.28279e7i	0.210429	−	0.385378i
$142$	−8.77768e6	−	3.10531e7i	−0.257259	−	0.910115i
$143$	8.65184e6			0.247419
$144$	−3.56444e7	+	3.66042e6i	−0.994768	+	0.102156i
$145$	−1.08229e7			−0.294818
$146$	1.51151e7	+	5.34732e7i	0.401954	+	1.42201i
$147$	−1.82858e6	+	3.34885e6i	−0.0474792	+	0.0869530i
$148$	4.76716e7	+	1.13854e7i	1.20877	+	0.288690i
$149$	−3.67528e7	+	3.67528e7i	−0.910204	+	0.910204i	−0.996288	−	0.0860842i	$-0.972565\pi$
$149$	−3.67528e7	+	3.67528e7i	−0.910204	+	0.910204i	0.0860842	+	0.996288i	$0.472565\pi$
$150$	−3.39276e7	−	7.74067e6i	−0.820794	−	0.187266i
$151$	7.12099e7			1.68314			0.841572	−	0.540145i	$-0.181630\pi$
$151$	7.12099e7			1.68314			0.841572	+	0.540145i	$0.181630\pi$
$152$	5.44274e7	−	2.23503e6i	1.25709	−	0.0516216i
$153$	5.71046e7	−	3.66999e7i	1.28900	−	0.828409i
$154$	2.47383e7	+	1.38349e7i	0.545817	+	0.305249i
$155$	−1.26508e7	−	1.26508e7i	−0.272871	−	0.272871i
$156$	−1.32184e7	−	1.19305e7i	−0.278769	−	0.251607i
$157$	−4.15337e7	+	4.15337e7i	−0.856549	+	0.856549i	−0.990930	−	0.134381i	$-0.957095\pi$
$157$	−4.15337e7	+	4.15337e7i	−0.856549	+	0.856549i	0.134381	+	0.990930i	$0.457095\pi$
$158$	7.21257e6	+	2.55162e7i	0.145476	+	0.514654i
$159$	5.25204e6	+	1.78864e7i	0.103619	+	0.352885i
$160$	−1.14963e7	−	1.70959e7i	−0.221890	−	0.329968i
$161$		−	4.75787e7i		−	0.898508i
$162$	8.24139e6	−	5.34819e7i	0.152299	−	0.988334i
$163$	4.02600e7	+	4.02600e7i	0.728143	+	0.728143i	0.970250	−	0.242107i	$-0.0778384\pi$
$163$	4.02600e7	+	4.02600e7i	0.728143	+	0.728143i	−0.242107	+	0.970250i	$0.577838\pi$
$164$	−4.58530e7	+	2.81733e7i	−0.811736	+	0.498752i
$165$	−7.24486e6	+	1.32682e7i	−0.125556	+	0.229941i
$166$	−4.87851e7	+	8.72329e7i	−0.827769	+	1.48014i
$167$			2.29117e7i			0.380670i	0.981719	+	0.190335i	$0.0609575\pi$
$167$			2.29117e7i			0.380670i	−0.981719	+	0.190335i	$0.939043\pi$
$168$	−1.87178e7	−	5.52503e7i	−0.304560	−	0.898984i
$169$			5.38998e7i			0.858982i
$170$	3.40637e7	+	1.90502e7i	0.531766	+	0.297391i
$171$	−1.74858e7	+	8.03856e7i	−0.267423	+	1.22940i
$172$	2.85838e6	−	1.19682e7i	0.0428321	−	0.179342i
$173$	−1.62717e7	−	1.62717e7i	−0.238931	−	0.238931i	0.577476	−	0.816407i	$-0.304038\pi$
$173$	−1.62717e7	−	1.62717e7i	−0.238931	−	0.238931i	−0.816407	+	0.577476i	$0.804038\pi$
$174$	−4.36224e7	+	2.74150e7i	−0.627751	+	0.394518i
$175$		−	5.66541e7i		−	0.799095i
$176$	4.52857e7	−	1.48326e7i	0.626133	−	0.205079i
$177$	−1.00462e8	+	2.94988e7i	−1.36174	+	0.399851i
$178$	8.00218e7	−	2.26195e7i	1.06350	−	0.300617i
$179$	−9.45028e7	+	9.45028e7i	−1.23157	+	1.23157i	−0.268210	+	0.963361i	$0.586432\pi$
$179$	−9.45028e7	+	9.45028e7i	−1.23157	+	1.23157i	−0.963361	+	0.268210i	$0.913568\pi$
$180$	2.93651e7	−	1.02810e7i	0.375299	−	0.131396i
$181$	1.05245e8	+	1.05245e8i	1.31925	+	1.31925i	0.914368	+	0.404884i	$0.132688\pi$
$181$	1.05245e8	+	1.05245e8i	1.31925	+	1.31925i	0.404884	+	0.914368i	$0.367312\pi$
$182$	1.41497e7	−	2.53011e7i	0.173979	−	0.311093i
$183$	3.04187e7	+	1.03594e8i	0.366912	+	1.24956i
$184$	−5.88350e7	−	5.41935e7i	−0.696263	−	0.641335i
$185$	−4.25575e7			−0.494168
$186$	−8.30355e7	−	1.89447e7i	−0.946168	−	0.215870i
$187$	−6.38342e7	+	6.38342e7i	−0.713851	+	0.713851i
$188$	3.40843e7	−	2.09423e7i	0.374112	−	0.229864i
$189$	8.78725e7	−	6.28641e6i	0.946753	−	0.0677308i
$190$	−4.55158e7	+	1.28658e7i	−0.481420	+	0.136082i
$191$	−1.47432e8			−1.53100			−0.765501	−	0.643434i	$-0.777509\pi$
$191$	−1.47432e8			−1.53100			−0.765501	+	0.643434i	$0.777509\pi$
$192$	−8.96417e7	−	3.97855e7i	−0.914020	−	0.405668i
$193$	−7.54605e7			−0.755561			−0.377780	−	0.925895i	$-0.623313\pi$
$193$	−7.54605e7			−0.755561			−0.377780	+	0.925895i	$0.623313\pi$
$194$	1.04550e8	−	2.95527e7i	1.02806	−	0.290597i
$195$	1.35700e7	+	7.40970e6i	0.131057	+	0.0715615i
$196$	−8.89805e6	+	5.46720e6i	−0.0844109	+	0.0518643i
$197$	1.09546e8	−	1.09546e8i	1.02086	−	1.02086i	0.0210793	−	0.999778i	$-0.493290\pi$
$197$	1.09546e8	−	1.09546e8i	1.02086	−	1.02086i	0.999778	−	0.0210793i	$-0.00671025\pi$
$198$	4.40819e6	+	7.18301e7i	0.0403582	+	0.657625i
$199$	6.78676e7			0.610487			0.305244	−	0.952274i	$-0.401262\pi$
$199$	6.78676e7			0.610487			0.305244	+	0.952274i	$0.401262\pi$
$200$	−7.00575e7	−	6.45307e7i	−0.619227	−	0.570377i
$201$	7.87636e7	−	2.31276e7i	0.684131	−	0.200884i
$202$	9.20877e7	−	1.64662e8i	0.786089	−	1.40561i
$203$	−5.93110e7	−	5.93110e7i	−0.497621	−	0.497621i
$204$	1.85552e8	−	9.50243e6i	1.53024	−	0.0783663i
$205$	3.30425e7	−	3.30425e7i	0.267876	−	0.267876i
$206$	3.06257e7	−	8.65688e6i	0.244091	−	0.0689963i
$207$	1.01624e8	−	6.53116e7i	0.796343	−	0.511792i
$208$	−1.51700e7	−	4.63160e7i	−0.116887	−	0.356869i
$209$		−	1.09405e8i		−	0.828945i
$210$	2.69523e7	+	4.28861e7i	0.200830	+	0.319557i
$211$	−9.02208e7	−	9.02208e7i	−0.661177	−	0.661177i	0.294480	−	0.955658i	$-0.404853\pi$
$211$	−9.02208e7	−	9.02208e7i	−0.661177	−	0.661177i	−0.955658	+	0.294480i	$0.904853\pi$
$212$	−1.18525e7	+	4.96275e7i	−0.0854349	+	0.357723i
$213$	1.17072e8	+	6.39253e7i	0.830090	+	0.453257i
$214$	4.70104e7	+	2.62906e7i	0.327903	+	0.183380i
$215$			1.06843e7i			0.0733182i
$216$	9.23157e7	−	1.15822e8i	0.623286	−	0.781994i
$217$		−	1.38657e8i		−	0.921155i
$218$	−7.00716e7	+	1.25295e8i	−0.458083	+	0.819101i
$219$	−2.01597e8	−	1.10079e8i	−1.29697	−	0.708190i
$220$	−3.52542e7	+	2.16611e7i	−0.223219	+	0.137152i
$221$	6.52865e7	+	6.52865e7i	0.406865	+	0.406865i
$222$	−1.71531e8	+	1.07801e8i	−1.05222	+	0.661282i
$223$		−	2.34082e8i		−	1.41352i	−0.707456	−	0.706758i	$-0.750157\pi$
$223$		−	2.34082e8i		−	1.41352i	0.707456	−	0.706758i	$-0.249843\pi$
$224$	3.06869e7	−	1.56690e8i	0.182425	−	0.931477i
$225$	1.21008e8	−	7.77695e7i	0.708234	−	0.455167i
$226$	−1.30654e7	−	4.62219e7i	−0.0752911	−	0.266360i
$227$	1.05597e8	−	1.05597e8i	0.599186	−	0.599186i	−0.340910	−	0.940096i	$-0.610735\pi$
$227$	1.05597e8	−	1.05597e8i	0.599186	−	0.599186i	0.940096	+	0.340910i	$0.110735\pi$
$228$	−1.50865e8	+	1.67151e8i	−0.842978	+	0.933979i
$229$	2.15688e8	+	2.15688e8i	1.18687	+	1.18687i	0.977929	+	0.208939i	$0.0670009\pi$
$229$	2.15688e8	+	2.15688e8i	1.18687	+	1.18687i	0.208939	+	0.977929i	$0.432999\pi$
$230$	6.06201e7	+	3.39019e7i	0.328525	+	0.183728i
$231$	−1.12415e8	+	3.30087e7i	−0.600041	+	0.176192i
$232$	−1.40900e8	+	5.78599e6i	−0.740803	+	0.0304207i
$233$	1.26332e8			0.654287			0.327143	−	0.944975i	$-0.393914\pi$
$233$	1.26332e8			0.654287			0.327143	+	0.944975i	$0.393914\pi$
$234$	7.34644e7	−	4.50848e6i	0.374819	−	0.0230025i
$235$	−2.45617e7	+	2.45617e7i	−0.123458	+	0.123458i
$236$	−2.78740e8	−	6.65714e7i	−1.38041	−	0.329682i
$237$	−9.61975e7	−	5.25271e7i	−0.469402	−	0.256309i
$238$	8.22764e7	+	2.91072e8i	0.395600	+	1.39953i
$239$	2.22421e7			0.105386			0.0526930	−	0.998611i	$-0.483220\pi$
$239$	2.22421e7			0.105386			0.0526930	+	0.998611i	$0.483220\pi$
$240$	8.37317e7	+	1.55198e7i	0.390976	+	0.0724680i
$241$	−1.91561e8			−0.881553			−0.440776	−	0.897617i	$-0.645297\pi$
$241$	−1.91561e8			−0.881553			−0.440776	+	0.897617i	$0.645297\pi$
$242$	3.39372e7	+	1.20061e8i	0.153930	+	0.544563i
$243$	1.34050e8	+	1.79059e8i	0.599302	+	0.800523i
$244$	−6.86472e7	+	2.87431e8i	−0.302523	+	1.26669i
$245$	6.41208e6	−	6.41208e6i	0.0278559	−	0.0278559i
$246$	4.94814e7	−	2.16879e8i	0.211919	−	0.928848i
$247$	−1.11894e8			−0.472464
$248$	−1.71461e8	−	1.57934e8i	−0.713812	−	0.657500i
$249$	−1.16396e8	−	3.96400e8i	−0.477795	−	1.62718i
$250$	1.57923e8	+	8.83186e7i	0.639227	+	0.357489i
$251$	−1.54777e7	−	1.54777e7i	−0.0617802	−	0.0617802i	0.675542	−	0.737322i	$-0.263910\pi$
$251$	−1.54777e7	−	1.54777e7i	−0.0617802	−	0.0617802i	−0.737322	+	0.675542i	$0.763910\pi$
$252$	2.17267e8	+	1.04584e8i	0.855246	+	0.411682i
$253$	−1.13600e8	+	1.13600e8i	−0.441018	+	0.441018i
$254$	8.33192e7	+	2.94761e8i	0.319027	+	1.12863i
$255$	−1.54791e8	+	4.54517e7i	−0.584594	+	0.171656i
$256$	−1.58807e8	−	2.16421e8i	−0.591601	−	0.806231i
$257$		−	2.72768e7i		−	0.100237i	−0.998743	−	0.0501184i	$-0.984040\pi$
$257$		−	2.72768e7i		−	0.100237i	0.998743	−	0.0501184i	$-0.0159599\pi$
$258$	2.70641e7	+	4.30639e7i	0.0981125	+	0.156115i
$259$	−2.33221e8	−	2.33221e8i	−0.834102	−	0.834102i
$260$	2.21539e7	+	3.60563e7i	0.0781707	+	0.127226i
$261$	4.52666e7	−	2.08100e8i	0.157593	−	0.724486i
$262$	−2.50819e7	+	4.48491e7i	−0.0861601	+	0.154063i
$263$			5.03430e8i			1.70645i	0.521541	+	0.853226i	$0.325357\pi$
$263$			5.03430e8i			1.70645i	−0.521541	+	0.853226i	$0.674643\pi$
$264$	−8.72257e7	+	1.76608e8i	−0.291763	+	0.590740i
$265$		−	4.43035e7i		−	0.146244i
$266$	−3.19940e8	−	1.78927e8i	−1.04228	−	0.582895i
$267$	−1.64731e8	+	3.01687e8i	−0.529647	+	0.969990i
$268$	2.18537e8	+	5.21931e7i	0.693510	+	0.165631i
$269$	2.43614e8	+	2.43614e8i	0.763077	+	0.763077i	0.976877	−	0.213800i	$-0.0685841\pi$
$269$	2.43614e8	+	2.43614e8i	0.763077	+	0.763077i	−0.213800	+	0.976877i	$0.568584\pi$
$270$	−5.46034e7	+	1.16438e8i	−0.168829	+	0.360015i
$271$		−	6.10841e8i		−	1.86438i	−0.361964	−	0.932192i	$-0.617894\pi$
$271$		−	6.10841e8i		−	1.86438i	0.361964	−	0.932192i	$-0.382106\pi$
$272$	4.53650e8	+	2.29798e8i	1.36688	+	0.692397i
$273$	3.37597e7	+	1.14972e8i	0.100422	+	0.341998i
$274$	−2.24496e7	+	6.34576e6i	−0.0659298	+	0.0186362i
$275$	−1.35269e8	+	1.35269e8i	−0.392223	+	0.392223i
$276$	3.30210e8	−	1.69106e7i	0.945383	−	0.0484148i
$277$	−1.37382e8	−	1.37382e8i	−0.388375	−	0.388375i	0.485732	−	0.874108i	$-0.338553\pi$
$277$	−1.37382e8	−	1.37382e8i	−0.388375	−	0.388375i	−0.874108	+	0.485732i	$0.838553\pi$
$278$	1.46303e8	−	2.61604e8i	0.408409	−	0.730277i
$279$	2.96159e8	−	1.90335e8i	0.816415	−	0.524692i
$280$	5.68833e6	+	1.38522e8i	0.0154857	+	0.377107i
$281$	2.69831e8			0.725471			0.362735	−	0.931892i	$-0.381843\pi$
$281$	2.69831e8			0.725471			0.362735	+	0.931892i	$0.381843\pi$
$282$	−3.67814e7	+	1.61214e8i	−0.0976689	+	0.428086i
$283$	2.86458e8	−	2.86458e8i	0.751291	−	0.751291i	−0.223429	−	0.974720i	$-0.571725\pi$
$283$	2.86458e8	−	2.86458e8i	0.751291	−	0.751291i	0.974720	+	0.223429i	$0.0717250\pi$
$284$	1.91127e8	+	3.11066e8i	0.495118	+	0.805822i
$285$	9.36978e7	−	1.71597e8i	0.239758	−	0.439090i
$286$	−9.41937e7	+	2.66254e7i	−0.238090	+	0.0673000i
$287$	3.62156e8			0.904292
$288$	3.76800e8	−	1.49544e8i	0.929473	−	0.368890i
$289$	−5.53042e8			−1.34777
$290$	1.17830e8	−	3.33066e7i	0.283702	−	0.0801931i
$291$	−2.15224e8	+	3.94159e8i	−0.511994	+	0.937662i
$292$	−3.29120e8	−	5.35654e8i	−0.773596	−	1.25905i
$293$	−3.54532e8	+	3.54532e8i	−0.823414	+	0.823414i	−0.986596	−	0.163182i	$-0.947824\pi$
$293$	−3.54532e8	+	3.54532e8i	−0.823414	+	0.823414i	0.163182	+	0.986596i	$0.447824\pi$
$294$	9.60216e6	−	4.20866e7i	0.0220370	−	0.0965892i
$295$	2.48837e8			0.564336
$296$	−5.54044e8	+	2.27515e7i	−1.24172	+	0.0509906i
$297$	−2.24816e8	−	1.94797e8i	−0.497943	−	0.431454i
$298$	2.87028e8	−	5.13236e8i	0.628301	−	1.12347i
$299$	1.16185e8	+	1.16185e8i	0.251362	+	0.251362i
$300$	3.93196e8	−	2.01363e7i	0.840784	−	0.0430581i
$301$	−5.85517e7	+	5.85517e7i	−0.123753	+	0.123753i
$302$	−7.75271e8	+	2.19143e8i	−1.61968	+	0.457830i
$303$	2.19712e8	+	7.48252e8i	0.453737	+	1.54525i
$304$	−5.85680e8	+	1.91829e8i	−1.19565	+	0.391614i
$305$		−	2.56596e8i		−	0.517846i
$306$	−5.08764e8	+	5.75292e8i	−1.01506	+	1.14779i
$307$	1.92073e8	+	1.92073e8i	0.378864	+	0.378864i	0.870692	−	0.491829i	$-0.163671\pi$
$307$	1.92073e8	+	1.92073e8i	0.378864	+	0.378864i	−0.491829	+	0.870692i	$0.663671\pi$
$308$	−3.11905e8	−	7.44922e7i	−0.608267	−	0.145272i
$309$	−6.30455e7	+	1.15461e8i	−0.121562	+	0.222628i
$310$	1.76663e8	+	9.87991e7i	0.336806	+	0.188359i
$311$		−	4.64984e8i		−	0.876549i	−0.898841	−	0.438275i	$-0.855590\pi$
$311$		−	4.64984e8i		−	0.876549i	0.898841	−	0.438275i	$-0.144410\pi$
$312$	1.80626e8	+	8.92102e7i	0.336697	+	0.166293i
$313$			1.06122e9i			1.95613i	0.208290	+	0.978067i	$0.433210\pi$
$313$			1.06122e9i			1.95613i	−0.208290	+	0.978067i	$0.566790\pi$
$314$	3.24366e8	−	5.80000e8i	0.591264	−	1.05724i
$315$	−2.04587e8	−	4.45026e7i	−0.368801	−	0.0802229i
$316$	−1.57048e8	−	2.55602e8i	−0.279981	−	0.455679i
$317$	−3.35242e8	−	3.35242e8i	−0.591086	−	0.591086i	0.346839	−	0.937925i	$-0.387255\pi$
$317$	−3.35242e8	−	3.35242e8i	−0.591086	−	0.591086i	−0.937925	+	0.346839i	$0.887255\pi$
$318$	−1.12224e8	−	1.78569e8i	−0.195700	−	0.311394i
$319$			2.83225e8i			0.488499i
$320$	1.77773e8	+	1.50746e8i	0.303278	+	0.257171i
$321$	−2.13623e8	+	6.27267e7i	−0.360479	+	0.105849i
$322$	1.46420e8	+	5.17995e8i	0.244402	+	0.864629i
$323$	8.25567e8	−	8.25567e8i	1.36315	−	1.36315i
$324$	7.48615e7	+	6.07626e8i	0.122279	+	0.992496i
$325$	1.38346e8	+	1.38346e8i	0.223551	+	0.223551i
$326$	−5.62212e8	−	3.14418e8i	−0.898750	−	0.502627i
$327$	−1.67184e8	−	5.69362e8i	−0.264409	−	0.900474i
$328$	4.12506e8	−	4.47836e8i	0.645464	−	0.700746i
$329$	−2.69204e8			−0.416769
$330$	3.80439e7	−	1.66748e8i	0.0582755	−	0.255424i
$331$	−3.39175e8	+	3.39175e8i	−0.514074	+	0.514074i	−0.915772	−	0.401698i	$-0.868420\pi$
$331$	−3.39175e8	+	3.39175e8i	−0.514074	+	0.514074i	0.401698	+	0.915772i	$0.368420\pi$
$332$	2.62677e8	−	1.09985e9i	0.393947	−	1.64949i
$333$	1.77997e8	−	8.18286e8i	0.264154	−	1.21437i
$334$	−7.05090e7	−	2.49442e8i	−0.103546	−	0.366317i
$335$	−1.95092e8			−0.283520
$336$	3.73812e8	+	5.43914e8i	0.537608	+	0.782244i
$337$	1.22452e9			1.74286			0.871428	−	0.490523i	$-0.163194\pi$
$337$	1.22452e9			1.74286			0.871428	+	0.490523i	$0.163194\pi$
$338$	−1.65873e8	−	5.86814e8i	−0.233651	−	0.826594i
$339$	1.74260e8	+	9.51515e7i	0.242939	+	0.132653i
$340$	−4.29481e8	−	1.02573e8i	−0.592608	−	0.141533i
$341$	−3.31060e8	+	3.31060e8i	−0.452134	+	0.452134i
$342$	−5.70111e7	−	9.28979e8i	−0.0770669	−	1.25578i
$343$	7.79651e8			1.04321
$344$	5.71192e6	+	1.39096e8i	0.00756532	+	0.184230i
$345$	−2.75467e8	+	8.08863e7i	−0.361163	+	0.106049i
$346$	2.27228e8	+	1.27077e8i	0.294913	+	0.164931i
$347$	8.28058e8	+	8.28058e8i	1.06392	+	1.06392i	0.997813	+	0.0661042i	$0.0210570\pi$
$347$	8.28058e8	+	8.28058e8i	1.06392	+	1.06392i	0.0661042	+	0.997813i	$0.478943\pi$
$348$	3.90555e8	−	4.32716e8i	0.496769	−	0.550396i
$349$	−3.10525e8	+	3.10525e8i	−0.391028	+	0.391028i	−0.875054	−	0.484026i	$-0.839174\pi$
$349$	−3.10525e8	+	3.10525e8i	−0.391028	+	0.391028i	0.484026	+	0.875054i	$0.339174\pi$
$350$	1.74349e8	+	6.16800e8i	0.217361	+	0.768965i
$351$	−1.99229e8	+	2.29931e8i	−0.245911	+	0.283807i
$352$	−4.47384e8	+	3.00847e8i	−0.546741	+	0.367660i
$353$			7.72354e8i			0.934555i	0.884111	+	0.467278i	$0.154765\pi$
$353$			7.72354e8i			0.934555i	−0.884111	+	0.467278i	$0.845235\pi$
$354$	1.00296e9	−	6.30321e8i	1.20163	−	0.755179i
$355$	−2.24160e8	−	2.24160e8i	−0.265925	−	0.265925i
$356$	−8.01597e8	+	4.92523e8i	−0.941632	+	0.578564i
$357$	−1.09736e9	−	5.99195e8i	−1.27647	−	0.696994i
$358$	7.38038e8	−	1.31969e9i	0.850136	−	1.52013i
$359$		−	9.61747e8i		−	1.09706i	−0.836131	−	0.548530i	$-0.815188\pi$
$359$		−	9.61747e8i		−	1.09706i	0.836131	−	0.548530i	$-0.184812\pi$
$360$	−2.88062e8	+	2.02299e8i	−0.325407	+	0.228526i
$361$			5.21064e8i			0.582930i
$362$	−1.46970e9	−	8.21934e8i	−1.62836	−	0.910661i
$363$	−4.52637e8	−	2.47155e8i	−0.496681	−	0.271204i
$364$	−7.61870e7	+	3.19001e8i	−0.0827992	+	0.346687i
$365$	3.86001e8	+	3.86001e8i	0.415493	+	0.415493i
$366$	−6.49976e8	−	1.03423e9i	−0.692968	−	1.10264i
$367$			6.74234e8i			0.711999i	0.934486	+	0.355999i	$0.115860\pi$
$367$			6.74234e8i			0.711999i	−0.934486	+	0.355999i	$0.884140\pi$
$368$	8.07321e8	+	4.08951e8i	0.844459	+	0.427764i
$369$	4.97134e8	+	7.73534e8i	0.515087	+	0.801470i
$370$	4.63328e8	−	1.30967e8i	0.475535	−	0.134418i
$371$	2.42790e8	−	2.42790e8i	0.246844	−	0.246844i
$372$	9.62319e8	−	4.92821e7i	0.969212	−	0.0496351i
$373$	1.92632e8	+	1.92632e8i	0.192197	+	0.192197i	0.796645	−	0.604448i	$-0.206606\pi$
$373$	1.92632e8	+	1.92632e8i	0.192197	+	0.192197i	−0.604448	+	0.796645i	$0.706606\pi$
$374$	4.98525e8	−	8.91415e8i	0.492761	−	0.881109i
$375$	−7.17627e8	+	2.10719e8i	−0.702731	+	0.206345i
$376$	−3.06631e8	+	3.32893e8i	−0.297481	+	0.322959i
$377$	2.89668e8			0.278424
$378$	−9.37333e8	+	3.38862e8i	−0.892632	+	0.322702i
$379$	1.18197e9	−	1.18197e9i	1.11524	−	1.11524i	0.122815	−	0.992430i	$-0.460808\pi$
$379$	1.18197e9	−	1.18197e9i	1.11524	−	1.11524i	0.992430	−	0.122815i	$-0.0391923\pi$
$380$	4.55942e8	−	2.80143e8i	0.426253	−	0.261901i
$381$	−1.11127e9	−	6.06790e8i	−1.02939	−	0.562083i
$382$	1.60511e9	−	4.53712e8i	1.47328	−	0.416446i
$383$	−4.65447e8			−0.423325			−0.211663	−	0.977343i	$-0.567888\pi$
$383$	−4.65447e8			−0.423325			−0.211663	+	0.977343i	$0.567888\pi$
$384$	1.09838e9	+	1.57284e8i	0.989902	+	0.141751i
$385$	2.78444e8			0.248671
$386$	8.21548e8	−	2.32224e8i	0.727072	−	0.205519i
$387$	−2.05436e8	−	4.46871e7i	−0.180172	−	0.0391917i
$388$	−1.04730e9	+	6.43489e8i	−0.910249	+	0.559281i
$389$	−4.37821e8	+	4.37821e8i	−0.377115	+	0.377115i	−0.870060	−	0.492946i	$-0.835920\pi$
$389$	−4.37821e8	+	4.37821e8i	−0.377115	+	0.377115i	0.492946	+	0.870060i	$0.335920\pi$
$390$	−1.70542e8	−	3.89094e7i	−0.145581	−	0.0332146i
$391$	−1.71444e9			−1.45046
$392$	8.00492e7	−	8.69051e7i	0.0671206	−	0.0728692i
$393$	−5.98428e7	−	2.03801e8i	−0.0497323	−	0.169369i
$394$	−8.55521e8	+	1.52976e9i	−0.704683	+	1.26005i
$395$	1.84191e8	+	1.84191e8i	0.150376	+	0.150376i
$396$	−2.69044e8	−	7.68457e8i	−0.217716	−	0.621851i
$397$	−4.88304e8	+	4.88304e8i	−0.391673	+	0.391673i	−0.875283	−	0.483611i	$-0.839325\pi$
$397$	−4.88304e8	+	4.88304e8i	−0.391673	+	0.391673i	0.483611	+	0.875283i	$0.339325\pi$
$398$	−7.38883e8	+	2.08858e8i	−0.587469	+	0.166058i
$399$	1.45386e9	−	4.26901e8i	1.14582	−	0.336451i
$400$	9.61314e8	+	4.86957e8i	0.751026	+	0.380435i
$401$		−	1.72497e8i		−	0.133591i	−0.997767	−	0.0667953i	$-0.978723\pi$
$401$		−	1.72497e8i		−	0.133591i	0.997767	−	0.0667953i	$-0.0212774\pi$
$402$	−7.86335e8	+	4.94182e8i	−0.603693	+	0.379399i
$403$	3.38593e8	+	3.38593e8i	0.257697	+	0.257697i
$404$	−4.95834e8	+	2.07609e9i	−0.374112	+	1.56643i
$405$	−1.85785e8	−	4.98070e8i	−0.138969	−	0.372561i
$406$	8.28251e8	+	4.63201e8i	0.614216	+	0.343501i
$407$			1.11369e9i			0.818811i
$408$	−1.99088e9	+	6.74476e8i	−1.45122	+	0.491650i
$409$		−	4.73098e8i		−	0.341916i	−0.985278	−	0.170958i	$-0.945314\pi$
$409$		−	4.73098e8i		−	0.341916i	0.985278	−	0.170958i	$-0.0546862\pi$
$410$	−2.58052e8	+	4.61423e8i	−0.184911	+	0.330640i
$411$	4.62143e7	−	8.46364e7i	0.0328345	−	0.0601327i
$412$	−3.06785e8	+	1.88497e8i	−0.216120	+	0.132790i
$413$	1.36367e9	+	1.36367e9i	0.952539	+	0.952539i
$414$	−9.05401e8	+	1.02380e9i	−0.627105	+	0.709107i
$415$			9.81858e8i			0.674342i
$416$	3.07692e8	+	4.57563e8i	0.209551	+	0.311619i
$417$	3.49063e8	+	1.18877e9i	0.235737	+	0.802827i
$418$	3.36686e8	+	1.19111e9i	0.225480	+	0.797689i
$419$	5.55982e6	−	5.55982e6i	0.00369242	−	0.00369242i	−0.705258	−	0.708951i	$-0.749169\pi$
$419$	5.55982e6	−	5.55982e6i	0.00369242	−	0.00369242i	0.708951	+	0.705258i	$0.249169\pi$
$420$	−4.25412e8	−	3.83962e8i	−0.280180	−	0.252881i
$421$	−1.65641e9	−	1.65641e9i	−1.08188	−	1.08188i	−0.996334	−	0.0855462i	$-0.972736\pi$
$421$	−1.65641e9	−	1.65641e9i	−1.08188	−	1.08188i	−0.0855462	−	0.996334i	$-0.527264\pi$
$422$	1.25989e9	+	7.04597e8i	0.816094	+	0.456402i
$423$	−3.69538e8	−	5.74996e8i	−0.237393	−	0.369380i
$424$	−2.36850e7	−	5.76776e8i	−0.0150901	−	0.367474i
$425$	−2.04147e9			−1.28997
$426$	−1.47130e9	−	3.35681e8i	−0.922081	−	0.210375i
$427$	1.40619e9	−	1.40619e9i	0.874069	−	0.874069i
$428$	−5.92715e8	−	1.41558e8i	−0.365421	−	0.0872734i
$429$	1.93905e8	−	3.55116e8i	0.118574	−	0.217155i
$430$	−3.28802e7	−	1.16321e8i	−0.0199432	−	0.0705538i
$431$	−5.37326e8			−0.323271			−0.161636	−	0.986851i	$-0.551677\pi$
$431$	−5.37326e8			−0.323271			−0.161636	+	0.986851i	$0.551677\pi$
$432$	−6.48619e8	+	1.54506e9i	−0.387076	+	0.922048i
$433$	6.20776e8			0.367474			0.183737	−	0.982975i	$-0.441180\pi$
$433$	6.20776e8			0.367474			0.183737	+	0.982975i	$0.441180\pi$
$434$	4.26707e8	+	1.50958e9i	0.250562	+	0.886422i
$435$	−2.42562e8	+	4.44226e8i	−0.141290	+	0.258757i
$436$	3.77291e8	−	1.57975e9i	0.218009	−	0.912819i
$437$	1.46919e9	−	1.46919e9i	0.842156	−	0.842156i
$438$	2.53358e9	+	5.78041e8i	1.44070	+	0.328700i
$439$	−8.19543e8			−0.462323			−0.231162	−	0.972915i	$-0.574253\pi$
$439$	−8.19543e8			−0.462323			−0.231162	+	0.972915i	$0.574253\pi$
$440$	3.17156e8	−	3.44319e8i	0.177496	−	0.192698i
$441$	9.64716e7	+	1.50109e8i	0.0535630	+	0.0833433i
$442$	−9.11697e8	−	5.09868e8i	−0.502195	−	0.280853i
$443$	1.09814e9	+	1.09814e9i	0.600129	+	0.600129i	0.940347	−	0.340218i	$-0.110501\pi$
$443$	1.09814e9	+	1.09814e9i	0.600129	+	0.600129i	−0.340218	+	0.940347i	$0.610501\pi$
$444$	1.53573e9	−	1.70152e9i	0.832673	−	0.922562i
$445$	5.77645e8	−	5.77645e8i	0.310742	−	0.310742i
$446$	7.20370e8	+	2.54848e9i	0.384489	+	1.36022i
$447$	6.84819e8	+	2.33223e9i	0.362660	+	1.23508i
$448$	1.48110e8	+	1.80034e9i	0.0778234	+	0.945977i
$449$		−	3.13950e9i		−	1.63681i	−0.574643	−	0.818404i	$-0.694859\pi$
$449$		−	3.13950e9i		−	1.63681i	0.574643	−	0.818404i	$-0.305141\pi$
$450$	−1.07810e9	+	1.21908e9i	−0.557720	+	0.630650i
$451$	−8.64692e8	−	8.64692e8i	−0.443857	−	0.443857i
$452$	2.84489e8	+	4.63016e8i	0.144904	+	0.235837i
$453$	1.59596e9	−	2.92282e9i	0.806636	−	1.47727i
$454$	−8.24681e8	+	1.47462e9i	−0.413609	+	0.739577i
$455$		−	2.84779e8i		−	0.141732i
$456$	1.12809e9	−	2.28407e9i	0.557143	−	1.12806i
$457$			1.97703e9i			0.968963i	0.874801	+	0.484482i	$0.160992\pi$
$457$			1.97703e9i			0.968963i	−0.874801	+	0.484482i	$0.839008\pi$
$458$	−3.01199e9	−	1.68446e9i	−1.46495	−	0.819278i
$459$	−2.26524e8	−	3.16638e9i	−0.109337	−	1.52834i
$460$	−7.64309e8	−	1.82540e8i	−0.366114	−	0.0874390i
$461$	3.80220e8	+	3.80220e8i	0.180751	+	0.180751i	0.791683	−	0.610932i	$-0.209205\pi$
$461$	3.80220e8	+	3.80220e8i	0.180751	+	0.180751i	−0.610932	+	0.791683i	$0.709205\pi$
$462$	1.12229e9	−	7.05317e8i	0.529491	−	0.332765i
$463$		−	2.83309e9i		−	1.32656i	−0.748371	−	0.663281i	$-0.769164\pi$
$463$		−	2.83309e9i		−	1.32656i	0.748371	−	0.663281i	$-0.230836\pi$
$464$	1.51619e9	−	4.96602e8i	0.704597	−	0.230779i
$465$	−8.02785e8	+	2.35724e8i	−0.370266	+	0.108722i
$466$	−1.37539e9	+	3.88778e8i	−0.629617	+	0.177972i
$467$	2.42370e8	−	2.42370e8i	0.110121	−	0.110121i	−0.649899	−	0.760020i	$-0.725189\pi$
$467$	2.42370e8	−	2.42370e8i	0.110121	−	0.110121i	0.760020	+	0.649899i	$0.225189\pi$
$468$	−7.85941e8	+	2.75166e8i	−0.354429	+	0.124089i
$469$	−1.06914e9	−	1.06914e9i	−0.478551	−	0.478551i
$470$	1.91819e8	−	3.42993e8i	0.0852216	−	0.152385i
$471$	7.73903e8	+	2.63561e9i	0.341282	+	1.16227i
$472$	3.23954e9	−	1.33030e8i	1.41803	−	0.0582308i
$473$	2.79599e8			0.121485
$474$	1.20896e9	+	2.75828e8i	0.521421	+	0.118963i
$475$	1.74943e9	−	1.74943e9i	0.748978	−	0.748978i
$476$	−1.79151e9	−	2.91574e9i	−0.761367	−	1.23915i
$477$	8.51859e8	+	1.85299e8i	0.359379	+	0.0781736i
$478$	−2.42152e8	+	6.84485e7i	−0.101412	+	0.0286659i
$479$	−4.65214e9			−1.93410			−0.967050	−	0.254587i	$-0.918060\pi$
$479$	−4.65214e9			−1.93410			−0.967050	+	0.254587i	$0.918060\pi$
$480$	−9.59358e8	+	8.87126e7i	−0.395947	+	0.0366135i
$481$	1.13903e9			0.466688
$482$	2.08555e9	−	5.89516e8i	0.848314	−	0.239790i
$483$	−1.95287e9	−	1.06633e9i	−0.788604	−	0.430604i
$484$	−7.38958e8	−	1.20268e9i	−0.296252	−	0.482160i
$485$	7.54702e8	−	7.54702e8i	0.300386	−	0.300386i
$486$	−2.01046e9	−	1.53690e9i	−0.794455	−	0.607323i
$487$	−2.09815e9			−0.823164			−0.411582	−	0.911373i	$-0.635024\pi$
$487$	−2.09815e9			−0.823164			−0.411582	+	0.911373i	$0.635024\pi$
$488$	−1.37178e8	−	3.34056e9i	−0.0534338	−	1.30122i
$489$	2.55478e9	−	7.50169e8i	0.988036	−	0.290120i
$490$	−5.00764e7	+	8.95419e7i	−0.0192286	+	0.0343827i
$491$	−1.37423e9	−	1.37423e9i	−0.523930	−	0.523930i	0.394826	−	0.918756i	$-0.370805\pi$
$491$	−1.37423e9	−	1.37423e9i	−0.523930	−	0.523930i	−0.918756	+	0.394826i	$0.870805\pi$
$492$	1.28719e8	+	2.51346e9i	0.0487265	+	0.951469i
$493$	−2.13720e9	+	2.13720e9i	−0.803307	+	0.803307i
$494$	1.21821e9	−	3.44346e8i	0.454649	−	0.128514i
$495$	3.82222e8	+	5.94733e8i	0.141644	+	0.220396i
$496$	2.35275e9	+	1.19179e9i	0.865744	+	0.438546i
$497$		−	2.45686e9i		−	0.897704i
$498$	2.48711e9	+	3.95745e9i	0.902387	+	1.43586i
$499$	2.77701e8	+	2.77701e8i	0.100052	+	0.100052i	0.755361	−	0.655309i	$-0.227462\pi$
$499$	2.77701e8	+	2.77701e8i	0.100052	+	0.100052i	−0.655309	+	0.755361i	$0.727462\pi$
$500$	−1.99112e9	−	4.75539e8i	−0.712365	−	0.170134i
$501$	9.40412e8	+	5.13496e8i	0.334108	+	0.182434i
$502$	2.16140e8	+	1.20876e8i	0.0762556	+	0.0426460i
$503$			1.76493e9i			0.618358i	0.951004	+	0.309179i	$0.100054\pi$
$503$			1.76493e9i			0.618358i	−0.951004	+	0.309179i	$0.899946\pi$
$504$	−2.68726e9	−	4.69993e8i	−0.934980	−	0.163525i
$505$		−	1.85337e9i		−	0.640388i
$506$	8.87181e8	−	1.58637e9i	0.304429	−	0.544350i
$507$	2.21233e9	+	1.20800e9i	0.753913	+	0.411661i
$508$	−1.81421e9	−	2.95269e9i	−0.613996	−	0.999299i
$509$	−4.75326e8	−	4.75326e8i	−0.159764	−	0.159764i	0.622698	−	0.782462i	$-0.286036\pi$
$509$	−4.75326e8	−	4.75326e8i	−0.159764	−	0.159764i	−0.782462	+	0.622698i	$0.786036\pi$
$510$	1.54535e9	−	9.71195e8i	0.515860	−	0.324199i
$511$			4.23070e9i			1.40262i
$512$	2.39497e9	+	1.86749e9i	0.788596	+	0.614912i
$513$	2.90755e9	+	2.51931e9i	0.950858	+	0.823892i
$514$	8.39423e7	+	2.96965e8i	0.0272653	+	0.0964573i
$515$	2.21075e8	−	2.21075e8i	0.0713204	−	0.0713204i
$516$	−4.27176e8	−	3.85555e8i	−0.136878	−	0.123541i
$517$	6.42757e8	+	6.42757e8i	0.204564	+	0.204564i
$518$	3.25683e9	+	1.82139e9i	1.02954	+	0.575769i
$519$	−1.03256e9	+	3.03193e8i	−0.324212	+	0.0951993i
$520$	−3.52153e8	−	3.24372e8i	−0.109830	−	0.101165i
$521$	−1.17929e9			−0.365333			−0.182667	−	0.983175i	$-0.558473\pi$
$521$	−1.17929e9			−0.365333			−0.182667	+	0.983175i	$0.558473\pi$
$522$	1.47589e8	+	2.40491e9i	0.0454157	+	0.740036i
$523$	−2.59444e9	+	2.59444e9i	−0.793028	+	0.793028i	−0.981985	−	0.188958i	$-0.939489\pi$
$523$	−2.59444e9	+	2.59444e9i	−0.793028	+	0.793028i	0.188958	+	0.981985i	$0.439489\pi$
$524$	1.35050e8	−	5.65465e8i	0.0410049	−	0.171691i
$525$	−2.32538e9	−	1.26973e9i	−0.701351	−	0.382961i
$526$	−1.54927e9	−	5.48091e9i	−0.464170	−	1.64211i
$527$	−4.99634e9			−1.48701
$528$	4.06138e8	−	2.19118e9i	0.120076	−	0.647828i
$529$	3.53784e8			0.103907
$530$	1.36341e8	+	4.82338e8i	0.0397796	+	0.140730i
$531$	−1.04076e9	+	4.78458e9i	−0.301662	+	1.38680i
$532$	4.03386e9	+	9.63407e8i	1.16153	+	0.277408i
$533$	−8.84365e8	+	8.84365e8i	−0.252980	+	0.252980i
$534$	8.65028e8	−	3.79145e9i	0.245831	−	1.07749i
$535$	5.29130e8			0.149391
$536$	−2.53986e9	+	1.04298e8i	−0.712414	+	0.0292549i
$537$	1.76088e9	+	5.99688e9i	0.490705	+	1.67115i
$538$	−3.40195e9	−	1.90255e9i	−0.941869	−	0.526742i
$539$	−1.67798e8	−	1.67798e8i	−0.0461559	−	0.0461559i
$540$	2.36145e8	−	1.43571e9i	0.0645358	−	0.392364i
$541$	2.53203e9	−	2.53203e9i	0.687509	−	0.687509i	−0.274172	−	0.961681i	$-0.588404\pi$
$541$	2.53203e9	−	2.53203e9i	0.687509	−	0.687509i	0.961681	+	0.274172i	$0.0884036\pi$
$542$	1.87982e9	+	6.65030e9i	0.507129	+	1.79409i
$543$	6.67857e9	−	1.96105e9i	1.79013	−	0.525641i
$544$	−5.64613e9	−	1.10577e9i	−1.50368	−	0.294488i
$545$			1.41027e9i			0.373178i
$546$	−7.21365e8	−	1.14782e9i	−0.189662	−	0.301787i
$547$	−5.16073e8	−	5.16073e8i	−0.134820	−	0.134820i	0.636476	−	0.771296i	$-0.280391\pi$
$547$	−5.16073e8	−	5.16073e8i	−0.134820	−	0.134820i	−0.771296	+	0.636476i	$0.780391\pi$
$548$	2.24883e8	−	1.38174e8i	0.0583747	−	0.0358670i
$549$	4.93378e9	+	1.07321e9i	1.27255	+	0.276811i
$550$	1.05641e9	−	1.88897e9i	0.270746	−	0.484122i
$551$		−	3.66294e9i		−	0.932824i
$552$	−3.54299e9	+	1.20030e9i	−0.896568	+	0.303742i
$553$			2.01879e9i			0.507637i
$554$	1.91848e9	+	1.07291e9i	0.479373	+	0.268090i
$555$	−9.53798e8	+	1.74678e9i	−0.236827	+	0.433722i
$556$	−7.87745e8	+	3.29835e9i	−0.194368	+	0.813833i
$557$	2.30815e8	+	2.30815e8i	0.0565941	+	0.0565941i	0.734837	−	0.678243i	$-0.237258\pi$
$557$	2.30815e8	+	2.30815e8i	0.0565941	+	0.0565941i	−0.678243	+	0.734837i	$0.737258\pi$
$558$	−2.63858e9	+	2.98361e9i	−0.642911	+	0.726980i
$559$		−	2.85960e8i		−	0.0692411i
$560$	−4.88220e8	−	1.49060e9i	−0.117478	−	0.358676i
$561$	1.18943e9	+	4.05073e9i	0.284426	+	0.968643i
$562$	−2.93769e9	+	8.30386e8i	−0.698117	+	0.197334i
$563$	7.15659e8	−	7.15659e8i	0.169016	−	0.169016i	−0.617531	−	0.786547i	$-0.711867\pi$
$563$	7.15659e8	−	7.15659e8i	0.169016	−	0.169016i	0.786547	+	0.617531i	$0.211867\pi$
$564$	−9.56816e7	−	1.86835e9i	−0.0224570	−	0.438512i
$565$	−3.33657e8	−	3.33657e8i	−0.0778271	−	0.0778271i
$566$	−2.23715e9	+	4.00026e9i	−0.518606	+	0.927322i
$567$	1.71137e9	−	3.74763e9i	0.394279	−	0.863408i
$568$	−3.03811e9	−	2.79844e9i	−0.695640	−	0.640762i
$569$	1.53741e9			0.349863			0.174931	−	0.984581i	$-0.444030\pi$
$569$	1.53741e9			0.349863			0.174931	+	0.984581i	$0.444030\pi$
$570$	−4.92022e8	+	2.15655e9i	−0.111281	+	0.487750i
$571$	−1.56729e9	+	1.56729e9i	−0.352308	+	0.352308i	−0.860968	−	0.508660i	$-0.830141\pi$
$571$	−1.56729e9	+	1.56729e9i	−0.352308	+	0.352308i	0.508660	+	0.860968i	$0.330141\pi$
$572$	9.43560e8	−	5.79748e8i	0.210806	−	0.129525i
$573$	−3.30425e9	+	6.05138e9i	−0.733723	+	1.34373i
$574$	−3.94284e9	+	1.11451e9i	−0.870196	+	0.245975i
$575$	−3.63302e9			−0.796948
$576$	−3.64205e9	+	2.78768e9i	−0.794086	+	0.607805i
$577$	−3.26392e8			−0.0707334			−0.0353667	−	0.999374i	$-0.511260\pi$
$577$	−3.26392e8			−0.0707334			−0.0353667	+	0.999374i	$0.511260\pi$
$578$	6.02104e9	−	1.70195e9i	1.29695	−	0.366605i
$579$	−1.69122e9	+	3.09729e9i	−0.362098	+	0.663142i
$580$	−1.18033e9	+	7.25226e8i	−0.251192	+	0.154339i
$581$	−5.38074e9	+	5.38074e9i	−1.13822	+	1.13822i
$582$	1.13017e9	−	4.95360e9i	0.237637	−	1.04157i
$583$	−1.15938e9			−0.242319
$584$	5.23161e9	+	4.81889e9i	1.08690	+	1.00116i
$585$	6.08264e8	−	3.90918e8i	0.125616	−	0.0807310i
$586$	2.76878e9	−	4.95088e9i	0.568391	−	1.01634i
$587$	2.93135e9	+	2.93135e9i	0.598183	+	0.598183i	0.939829	−	0.341646i	$-0.110984\pi$
$587$	2.93135e9	+	2.93135e9i	0.598183	+	0.598183i	−0.341646	+	0.939829i	$0.610984\pi$
$588$	2.49787e7	+	4.87752e8i	0.00506697	+	0.0989415i
$589$	4.28161e9	−	4.28161e9i	0.863382	−	0.863382i
$590$	−2.70912e9	+	7.65778e8i	−0.543058	+	0.153504i
$591$	−2.04118e9	−	6.95148e9i	−0.406749	−	1.38523i
$592$	5.96193e9	−	1.95273e9i	1.18103	−	0.386826i
$593$		−	7.65039e9i		−	1.50658i	−0.657688	−	0.753290i	$-0.728466\pi$
$593$		−	7.65039e9i		−	1.50658i	0.657688	−	0.753290i	$-0.271534\pi$
$594$	3.04707e9	+	1.42892e9i	0.596527	+	0.279741i
$595$	2.10113e9	+	2.10113e9i	0.408925	+	0.408925i
$596$	−1.54546e9	+	6.47098e9i	−0.299018	+	1.25201i
$597$	1.52105e9	−	2.78563e9i	0.292572	−	0.535814i
$598$	−1.62247e9	−	9.07366e8i	−0.310257	−	0.173512i
$599$			5.00928e9i			0.952317i	0.879359	+	0.476159i	$0.157971\pi$
$599$			5.00928e9i			0.952317i	−0.879359	+	0.476159i	$0.842029\pi$
$600$	−4.21880e9	+	1.42926e9i	−0.797370	+	0.270135i
$601$		−	3.57061e9i		−	0.670938i	−0.942051	−	0.335469i	$-0.891105\pi$
$601$		−	3.57061e9i		−	0.670938i	0.942051	−	0.335469i	$-0.108895\pi$
$602$	4.57271e8	−	8.17648e8i	0.0854252	−	0.152749i
$603$	8.15974e8	−	3.75120e9i	0.151553	−	0.696721i
$604$	7.76608e9	−	4.77168e9i	1.43408	−	0.881135i
$605$	8.66671e8	+	8.66671e8i	0.159115	+	0.159115i
$606$	−4.69472e9	−	7.47017e9i	−0.856950	−	1.36357i
$607$			5.41356e9i			0.982477i	0.871025	+	0.491238i	$0.163456\pi$
$607$			5.41356e9i			0.982477i	−0.871025	+	0.491238i	$0.836544\pi$
$608$	5.78602e9	−	3.89086e9i	1.04404	−	0.702074i
$609$	−3.76371e9	+	1.10515e9i	−0.675235	+	0.198272i
$610$	7.89656e8	+	2.79360e9i	0.140859	+	0.498321i
$611$	6.57381e8	−	6.57381e8i	0.116593	−	0.116593i
$612$	3.76855e9	−	7.82896e9i	0.664576	−	1.38062i
$613$	1.89300e9	+	1.89300e9i	0.331925	+	0.331925i	0.853317	−	0.521392i	$-0.174587\pi$
$613$	1.89300e9	+	1.89300e9i	0.331925	+	0.331925i	−0.521392	+	0.853317i	$0.674587\pi$
$614$	−2.68222e9	−	1.50003e9i	−0.467633	−	0.261524i
$615$	−6.15684e8	−	2.09678e9i	−0.106732	−	0.363488i
$616$	3.62499e9	−	1.48858e8i	0.624848	−	0.0256591i
$617$	5.52510e9			0.946983			0.473491	−	0.880798i	$-0.342993\pi$
$617$	5.52510e9			0.946983			0.473491	+	0.880798i	$0.342993\pi$
$618$	3.31062e8	−	1.45106e9i	0.0564221	−	0.247300i
$619$	−5.60197e9	+	5.60197e9i	−0.949344	+	0.949344i	−0.998777	−	0.0494337i	$-0.984258\pi$
$619$	−5.60197e9	+	5.60197e9i	−0.949344	+	0.949344i	0.0494337	+	0.998777i	$0.484258\pi$
$620$	−2.22740e9	−	5.31970e8i	−0.375342	−	0.0896429i
$621$	−4.03124e8	−	5.63493e9i	−0.0675488	−	0.944209i
$622$	1.43095e9	+	5.06233e9i	0.238429	+	0.843499i
$623$	6.33116e9			1.04900
$624$	−2.24104e9	−	4.15379e8i	−0.369235	−	0.0684381i
$625$	−3.36095e9			−0.550657
$626$	−3.26582e9	−	1.15536e10i	−0.532086	−	1.88238i
$627$	−4.49055e9	−	2.45199e9i	−0.727550	−	0.397266i
$628$	−1.74650e9	+	7.31274e9i	−0.281391	+	1.17821i
$629$	−8.40387e9	+	8.40387e9i	−1.34649	+	1.34649i
$630$	2.36432e9	−	1.45097e8i	0.376716	−	0.0231189i
$631$	1.25335e10			1.98595			0.992976	−	0.118315i	$-0.0377491\pi$
$631$	1.25335e10			1.98595			0.992976	+	0.118315i	$0.0377491\pi$
$632$	2.49640e9	+	2.29946e9i	0.393373	+	0.362340i
$633$	−5.72515e9	+	1.68109e9i	−0.897168	+	0.263438i
$634$	4.68150e9	+	2.61814e9i	0.729580	+	0.408018i
$635$	2.12776e9	+	2.12776e9i	0.329773	+	0.329773i
$636$	1.77133e9	+	1.59874e9i	0.273023	+	0.246421i
$637$	−1.71616e8	+	1.71616e8i	−0.0263069	+	0.0263069i
$638$	−8.71603e8	−	3.08350e9i	−0.132876	−	0.470080i
$639$	5.24764e9	−	3.37255e9i	0.795630	−	0.511335i
$640$	−2.39935e9	−	1.09411e9i	−0.361795	−	0.164980i
$641$		−	6.61031e9i		−	0.991332i	−0.868513	−	0.495666i	$-0.834924\pi$
$641$		−	6.61031e9i		−	0.991332i	0.868513	−	0.495666i	$-0.165076\pi$
$642$	2.13270e9	−	1.34032e9i	0.318095	−	0.199911i
$643$	−1.24226e9	−	1.24226e9i	−0.184279	−	0.184279i	0.608939	−	0.793217i	$-0.291596\pi$
$643$	−1.24226e9	−	1.24226e9i	−0.184279	−	0.184279i	−0.793217	+	0.608939i	$0.791596\pi$
$644$	−3.18818e9	−	5.18888e9i	−0.470374	−	0.765549i
$645$	4.38539e8	+	2.39457e8i	0.0643501	+	0.0351373i
$646$	−6.44743e9	+	1.15287e10i	−0.940963	+	1.68254i
$647$		−	1.72497e9i		−	0.250390i	−0.992132	−	0.125195i	$-0.960044\pi$
$647$		−	1.72497e9i		−	0.250390i	0.992132	−	0.125195i	$-0.0399557\pi$
$648$	−2.68495e9	−	6.38492e9i	−0.387636	−	0.921813i
$649$		−	6.51184e9i		−	0.935076i
$650$	−1.93194e9	−	1.08044e9i	−0.275929	−	0.154314i
$651$	−5.69119e9	−	3.10758e9i	−0.808481	−	0.441457i
$652$	7.08847e9	+	1.69294e9i	1.00158	+	0.239208i
$653$	1.43922e9	+	1.43922e9i	0.202269	+	0.202269i	0.800972	−	0.598702i	$-0.204317\pi$
$653$	1.43922e9	+	1.43922e9i	0.202269	+	0.202269i	−0.598702	+	0.800972i	$0.704317\pi$
$654$	3.57232e9	+	5.68422e9i	0.499376	+	0.794600i
$655$			5.04803e8i			0.0701904i
$656$	−3.11282e9	+	6.14510e9i	−0.430518	+	0.849896i
$657$	−9.03640e9	+	5.80750e9i	−1.24313	+	0.798933i
$658$	2.93085e9	−	8.28455e8i	0.401055	−	0.113365i
$659$	6.97772e9	−	6.97772e9i	0.949761	−	0.949761i	−0.0490360	−	0.998797i	$-0.515615\pi$
$659$	6.97772e9	−	6.97772e9i	0.949761	−	0.949761i	0.998797	+	0.0490360i	$0.0156149\pi$
$660$	9.89658e7	+	1.93248e9i	0.0133993	+	0.261644i
$661$	−4.45580e9	−	4.45580e9i	−0.600095	−	0.600095i	0.340242	−	0.940338i	$-0.389491\pi$
$661$	−4.45580e9	−	4.45580e9i	−0.600095	−	0.600095i	−0.940338	+	0.340242i	$0.889491\pi$
$662$	2.64885e9	−	4.73642e9i	0.354858	−	0.634523i
$663$	4.14289e9	−	1.21649e9i	0.552086	−	0.162111i
$664$	5.24909e8	+	1.27825e10i	0.0695818	+	1.69445i
$665$	−3.60112e9			−0.474856
$666$	5.80345e8	+	9.45655e9i	0.0761248	+	1.24043i
$667$	−3.80339e9	+	3.80339e9i	−0.496284	+	0.496284i
$668$	1.53528e9	+	2.49872e9i	0.199283	+	0.324340i
$669$	−9.60792e9	−	5.24624e9i	−1.24062	−	0.677418i
$670$	2.12400e9	−	6.00383e8i	0.272830	−	0.0771199i
$671$	−6.71489e9			−0.858045
$672$	−5.74359e9	−	4.77127e9i	−0.730115	−	0.606516i
$673$	−7.21452e9			−0.912336			−0.456168	−	0.889894i	$-0.650778\pi$
$673$	−7.21452e9			−0.912336			−0.456168	+	0.889894i	$0.650778\pi$
$674$	−1.33315e10	+	3.76838e9i	−1.67714	+	0.474072i
$675$	−4.80018e8	−	6.70977e9i	−0.0600751	−	0.839740i
$676$	3.61176e9	+	5.87826e9i	0.449681	+	0.731872i
$677$	5.92623e9	−	5.92623e9i	0.734037	−	0.734037i	−0.237380	−	0.971417i	$-0.576289\pi$
$677$	5.92623e9	−	5.92623e9i	0.734037	−	0.734037i	0.971417	+	0.237380i	$0.0762885\pi$
$678$	−2.19001e9	−	4.99655e8i	−0.269862	−	0.0615696i
$679$	8.27177e9			1.01404
$680$	4.99147e9	−	2.04972e8i	0.608762	−	0.0249985i
$681$	−1.96760e9	−	6.70089e9i	−0.238739	−	0.813050i
$682$	2.58548e9	−	4.62311e9i	0.312102	−	0.558070i
$683$	−1.36830e9	−	1.36830e9i	−0.164327	−	0.164327i	0.620154	−	0.784480i	$-0.287070\pi$
$683$	−1.36830e9	−	1.36830e9i	−0.164327	−	0.164327i	−0.784480	+	0.620154i	$0.787070\pi$
$684$	3.47955e9	+	9.93846e9i	0.415745	+	1.18747i
$685$	−1.62055e8	+	1.62055e8i	−0.0192639	+	0.0192639i
$686$	−8.48816e9	+	2.39932e9i	−1.00387	+	0.283762i
$687$	1.36870e10	−	4.01894e9i	1.61049	−	0.472894i
$688$	−4.90245e8	−	1.49678e9i	−0.0573923	−	0.175226i
$689$			1.18576e9i			0.138112i
$690$	2.75012e9	−	1.72835e9i	0.318699	−	0.200290i
$691$	7.12035e9	+	7.12035e9i	0.820972	+	0.820972i	0.986247	−	0.165276i	$-0.0528514\pi$
$691$	7.12035e9	+	7.12035e9i	0.820972	+	0.820972i	−0.165276	+	0.986247i	$0.552851\pi$
$692$	−2.86493e9	−	6.84230e8i	−0.328656	−	0.0784930i
$693$	−1.16459e9	+	5.35386e9i	−0.132925	+	0.611084i
$694$	−1.15635e10	−	6.46688e9i	−1.31320	−	0.734407i
$695$		−	2.94451e9i		−	0.332710i
$696$	−2.92036e9	+	5.91293e9i	−0.328326	+	0.664769i
$697$		−	1.30499e10i		−	1.45979i
$698$	2.42510e9	−	4.33634e9i	0.269921	−	0.482647i
$699$	2.83136e9	−	5.18532e9i	0.313563	−	0.574256i
$700$	−3.79632e9	−	6.17864e9i	−0.418330	−	0.680847i
$701$	9.52588e9	+	9.52588e9i	1.04446	+	1.04446i	0.998965	+	0.0454957i	$0.0144867\pi$
$701$	9.52588e9	+	9.52588e9i	1.04446	+	1.04446i	0.0454957	+	0.998965i	$0.485513\pi$
$702$	1.46143e9	−	3.11640e9i	0.159441	−	0.339995i
$703$		−	1.44034e10i		−	1.56358i
$704$	3.94489e9	−	4.65215e9i	0.426119	−	0.502516i
$705$	4.57661e8	+	1.55861e9i	0.0491906	+	0.167524i
$706$	−2.37686e9	−	8.40871e9i	−0.254207	−	0.899318i
$707$	1.01568e10	−	1.01568e10i	1.08091	−	1.08091i
$708$	−8.97954e9	+	9.94891e9i	−0.950907	+	1.05356i
$709$	1.10715e10	+	1.10715e10i	1.16666	+	1.16666i	0.982987	+	0.183677i	$0.0588001\pi$
$709$	1.10715e10	+	1.10715e10i	1.16666	+	1.16666i	0.183677	+	0.982987i	$0.441200\pi$
$710$	3.13029e9	+	1.75062e9i	0.328232	+	0.183564i
$711$	−4.31196e9	+	2.77120e9i	−0.449916	+	0.289151i
$712$	7.21138e9	−	7.82901e9i	0.748753	−	0.812881i
$713$	−8.89155e9			−0.918679
$714$	1.37911e10	+	3.14646e9i	1.41793	+	0.323503i
$715$	−6.79945e8	+	6.79945e8i	−0.0695669	+	0.0695669i
$716$	−3.97386e9	+	1.66389e10i	−0.404592	+	1.69406i
$717$	4.98490e8	−	9.12930e8i	0.0505056	−	0.0924954i
$718$	2.95971e9	+	1.04707e10i	0.298410	+	1.05570i
$719$	1.11655e10			1.12029			0.560143	−	0.828396i	$-0.310746\pi$
$719$	1.11655e10			1.12029			0.560143	+	0.828396i	$0.310746\pi$
$720$	2.51361e9	−	3.08895e9i	0.250977	−	0.308423i
$721$	2.42305e9			0.240762
$722$	−1.60354e9	−	5.67289e9i	−0.158562	−	0.560950i
$723$	−4.29328e9	+	7.86266e9i	−0.422479	+	0.773723i
$724$	1.85303e10	+	4.42559e9i	1.81467	+	0.433397i
$725$	−4.52887e9	+	4.52887e9i	−0.441374	+	0.441374i
$726$	5.68852e9	+	1.29785e9i	0.551723	+	0.125877i
$727$	−1.71898e10			−1.65921			−0.829605	−	0.558351i	$-0.811434\pi$
$727$	−1.71898e10			−1.65921			−0.829605	+	0.558351i	$0.811434\pi$
$728$	−1.52245e8	−	3.70746e9i	−0.0146246	−	0.356137i
$729$	1.03538e10	−	1.48905e9i	0.989816	−	0.142352i
$730$	−5.39034e9	−	3.01455e9i	−0.512845	−	0.286809i
$731$	2.10984e9	+	2.10984e9i	0.199774	+	0.199774i
$732$	1.02591e10	+	9.25955e9i	0.966767	+	0.872571i
$733$	6.11207e9	−	6.11207e9i	0.573224	−	0.573224i	−0.359804	−	0.933028i	$-0.617157\pi$
$733$	6.11207e9	−	6.11207e9i	0.573224	−	0.573224i	0.933028	+	0.359804i	$0.117157\pi$
$734$	−2.07491e9	−	7.34047e9i	−0.193670	−	0.685153i
$735$	−1.19477e8	−	4.06892e8i	−0.0110989	−	0.0377984i
$736$	−1.00479e10	−	1.96783e9i	−0.928974	−	0.181935i
$737$			5.10539e9i			0.469778i
$738$	−7.79285e9	−	6.89167e9i	−0.713673	−	0.631142i
$739$	1.71480e9	+	1.71480e9i	0.156299	+	0.156299i	0.780925	−	0.624625i	$-0.214748\pi$
$739$	1.71480e9	+	1.71480e9i	0.156299	+	0.156299i	−0.624625	+	0.780925i	$0.714748\pi$
$740$	−4.64127e9	+	2.85172e9i	−0.421042	+	0.258699i
$741$	−2.50777e9	+	4.59271e9i	−0.226425	+	0.414673i
$742$	−1.89612e9	+	3.39046e9i	−0.170393	+	0.304680i
$743$			7.40444e9i			0.662264i	0.943584	+	0.331132i	$0.107431\pi$
$743$			7.40444e9i			0.662264i	−0.943584	+	0.331132i	$0.892569\pi$
$744$	−1.03252e10	+	3.49801e9i	−0.919166	+	0.311398i
$745$		−	5.77678e9i		−	0.511846i
$746$	−2.69002e9	−	1.50440e9i	−0.237230	−	0.132671i
$747$	−1.88790e10	−	4.10662e9i	−1.65713	−	0.360465i
$748$	−2.68424e9	+	1.12391e10i	−0.234512	+	0.981922i
$749$	2.89972e9	+	2.89972e9i	0.252156	+	0.252156i
$750$	7.16442e9	−	4.50257e9i	0.620107	−	0.389714i
$751$		−	4.06286e8i		−	0.0350020i	−0.999847	−	0.0175010i	$-0.994429\pi$
$751$		−	4.06286e8i		−	0.0350020i	0.999847	−	0.0175010i	$-0.00557102\pi$
$752$	2.31388e9	−	4.56788e9i	0.198417	−	0.391699i
$753$	−9.82173e8	+	2.88399e8i	−0.0838312	+	0.0246156i
$754$	−3.15366e9	+	8.91434e8i	−0.267926	+	0.0757337i
$755$	−5.59637e9	+	5.59637e9i	−0.473251	+	0.473251i
$756$	9.16203e9	−	6.57381e9i	0.771197	−	0.553338i
$757$	1.83531e9	+	1.83531e9i	0.153771	+	0.153771i	0.779800	−	0.626029i	$-0.215321\pi$
$757$	1.83531e9	+	1.83531e9i	0.153771	+	0.153771i	−0.626029	+	0.779800i	$0.715321\pi$
$758$	−9.23085e9	+	1.65057e10i	−0.769838	+	1.37655i
$759$	2.11672e9	+	7.20873e9i	0.175719	+	0.598429i
$760$	−4.10178e9	+	4.45308e9i	−0.338942	+	0.367971i
$761$	−6.68973e9			−0.550253			−0.275126	−	0.961408i	$-0.588720\pi$
$761$	−6.68973e9			−0.550253			−0.275126	+	0.961408i	$0.588720\pi$
$762$	1.39659e10	+	3.18634e9i	1.14347	+	0.260886i
$763$	−7.72852e9	+	7.72852e9i	−0.629884	+	0.629884i
$764$	−1.60788e10	+	9.87924e9i	−1.30445	+	0.801488i
$765$	−1.60360e9	+	7.37207e9i	−0.129503	+	0.595353i
$766$	5.06737e9	−	1.43238e9i	0.407364	−	0.115148i
$767$	−6.65999e9			−0.532954
$768$	−1.24422e10	+	1.66781e9i	−0.991135	+	0.132856i
$769$	−6.32149e9			−0.501276			−0.250638	−	0.968081i	$-0.580640\pi$
$769$	−6.32149e9			−0.501276			−0.250638	+	0.968081i	$0.580640\pi$
$770$	−3.03145e9	+	8.56891e8i	−0.239295	+	0.0676407i
$771$	−1.11958e9	−	6.11327e8i	−0.0879760	−	0.0480378i
$772$	−8.22964e9	+	5.05651e9i	−0.643755	+	0.395540i
$773$	−1.41556e9	+	1.41556e9i	−0.110230	+	0.110230i	−0.760070	−	0.649841i	$-0.774836\pi$
$773$	−1.41556e9	+	1.41556e9i	−0.110230	+	0.110230i	0.649841	+	0.760070i	$0.274836\pi$
$774$	2.37413e9	−	1.45699e8i	0.184039	−	0.0112944i
$775$	−1.05876e10			−0.817035
$776$	9.42179e9	−	1.02287e10i	0.723798	−	0.785789i
$777$	−1.47996e10	+	4.34564e9i	−1.13181	+	0.332338i
$778$	3.41925e9	−	6.11398e9i	0.260317	−	0.465474i
$779$	1.11831e10	+	1.11831e10i	0.847578	+	0.847578i
$780$	1.97645e9	−	1.01217e8i	0.149126	−	0.00763703i
$781$	−5.86606e9	+	5.86606e9i	−0.440623	+	0.440623i
$782$	1.86654e10	−	5.27608e9i	1.39577	−	0.394537i
$783$	−7.52697e9	−	6.52191e9i	−0.560343	−	0.485522i
$784$	−6.04062e8	+	1.19249e9i	−0.0447687	+	0.0883791i
$785$		−	6.52825e9i		−	0.481673i
$786$	1.27870e9	+	2.03465e9i	0.0939269	+	0.149455i
$787$	3.02454e9	+	3.02454e9i	0.221181	+	0.221181i	0.808996	−	0.587814i	$-0.200012\pi$
$787$	3.02454e9	+	3.02454e9i	0.221181	+	0.221181i	−0.587814	+	0.808996i	$0.700012\pi$
$788$	4.60644e9	−	1.92875e10i	0.335369	−	1.40422i
$789$	2.06634e10	+	1.12829e10i	1.49772	+	0.817806i
$790$	−2.57214e9	−	1.43847e9i	−0.185609	−	0.103802i
$791$		−	3.65699e9i		−	0.262728i
$792$	5.29399e9	+	7.53833e9i	0.378656	+	0.539184i
$793$			6.86767e9i			0.489050i
$794$	3.81350e9	−	6.81894e9i	0.270366	−	0.483443i
$795$	−1.81844e9	−	9.92931e8i	−0.128356	−	0.0700864i
$796$	7.40156e9	−	4.54772e9i	0.520149	−	0.319593i
$797$	1.01048e10	+	1.01048e10i	0.707008	+	0.707008i	0.965905	−	0.258897i	$-0.0833591\pi$
$797$	1.01048e10	+	1.01048e10i	0.707008	+	0.707008i	−0.258897	+	0.965905i	$0.583359\pi$
$798$	−1.45146e10	+	9.12187e9i	−1.01110	+	0.635439i
$799$			9.70045e9i			0.672788i
$800$	−1.19645e10	−	2.34319e9i	−0.826191	−	0.161805i
$801$	8.69083e9	+	1.35228e10i	0.597513	+	0.929723i
$802$	5.30846e8	+	1.87799e9i	0.0363378	+	0.128554i
$803$	1.01013e10	−	1.01013e10i	0.688451	−	0.688451i
$804$	7.04012e9	−	7.80011e9i	0.477731	−	0.529303i
$805$	3.73919e9	+	3.73919e9i	0.252634	+	0.252634i
$806$	−4.72830e9	−	2.64431e9i	−0.318077	−	0.177885i
$807$	1.54590e10	−	4.53928e9i	1.03544	−	0.304039i
$808$	−9.90828e8	−	2.41286e10i	−0.0660783	−	1.60913i
$809$	7.84965e9			0.521231			0.260616	−	0.965443i	$-0.416075\pi$
$809$	7.84965e9			0.521231			0.260616	+	0.965443i	$0.416075\pi$
$810$	3.55543e9	+	4.85081e9i	0.235069	+	0.320713i
$811$	−5.16082e9	+	5.16082e9i	−0.339739	+	0.339739i	−0.856269	−	0.516530i	$-0.827223\pi$
$811$	−5.16082e9	+	5.16082e9i	−0.339739	+	0.339739i	0.516530	+	0.856269i	$0.327223\pi$
$812$	−1.04427e10	−	2.49404e9i	−0.684492	−	0.163477i
$813$	−2.50720e10	−	1.36902e10i	−1.63634	−	0.893494i
$814$	−3.42730e9	−	1.21249e10i	−0.222724	−	0.787938i
$815$	−6.32803e9			−0.409465
$816$	1.95993e10	−	1.34699e10i	1.26277	−	0.867858i
$817$	−3.61605e9			−0.231984
$818$	1.45592e9	+	5.15067e9i	0.0930041	+	0.329024i
$819$	5.47567e9	+	1.19109e9i	0.348292	+	0.0757618i
$820$	1.38944e9	−	5.81771e9i	0.0880020	−	0.368471i
$821$	3.89689e9	−	3.89689e9i	0.245763	−	0.245763i	−0.573466	−	0.819229i	$-0.694402\pi$
$821$	3.89689e9	−	3.89689e9i	0.245763	−	0.245763i	0.819229	+	0.573466i	$0.194402\pi$
$822$	−2.42678e8	+	1.06367e9i	−0.0152398	+	0.0667967i
$823$	2.39068e10			1.49494			0.747469	−	0.664297i	$-0.231269\pi$
$823$	2.39068e10			1.49494			0.747469	+	0.664297i	$0.231269\pi$
$824$	2.75992e9	−	2.99630e9i	0.171851	−	0.186569i
$825$	2.52048e9	+	8.58376e9i	0.156277	+	0.532217i
$826$	−1.90430e10	−	1.06498e10i	−1.17572	−	0.657524i
$827$	−9.59322e9	−	9.59322e9i	−0.589787	−	0.589787i	0.347787	−	0.937574i	$-0.386933\pi$
$827$	−9.59322e9	−	9.59322e9i	−0.589787	−	0.589787i	−0.937574	+	0.347787i	$0.886933\pi$
$828$	6.70656e9	−	1.39325e10i	0.410576	−	0.852948i
$829$	7.87710e9	−	7.87710e9i	0.480204	−	0.480204i	−0.424993	−	0.905197i	$-0.639723\pi$
$829$	7.87710e9	−	7.87710e9i	0.480204	−	0.480204i	0.905197	+	0.424993i	$0.139723\pi$
$830$	−3.02160e9	−	1.06896e10i	−0.183427	−	0.648916i
$831$	−8.71788e9	+	2.55986e9i	−0.526996	+	0.154744i
$832$	−4.75800e9	−	4.03465e9i	−0.286413	−	0.242870i
$833$		−	2.53240e9i		−	0.151801i
$834$	−7.45864e9	−	1.18681e10i	−0.445224	−	0.708434i
$835$	−1.80062e9	−	1.80062e9i	−0.107033	−	0.107033i
$836$	−7.33109e9	−	1.19316e10i	−0.433957	−	0.706279i
$837$	−1.17481e9	−	1.64217e10i	−0.0692514	−	0.968008i
$838$	−4.34205e7	+	7.76404e7i	−0.00254883	+	0.00455757i
$839$			1.79273e10i			1.04797i	0.851728	+	0.523984i	$0.175555\pi$
$839$			1.79273e10i			1.04797i	−0.851728	+	0.523984i	$0.824445\pi$
$840$	5.81313e9	+	2.87107e9i	0.338402	+	0.167135i
$841$		−	7.76736e9i		−	0.450285i
$842$	2.31310e10	+	1.29360e10i	1.33537	+	0.746807i
$843$	6.04746e9	−	1.10753e10i	0.347677	−	0.636733i
$844$	−1.58850e10	−	3.79380e9i	−0.909468	−	0.217208i
$845$	−4.23597e9	−	4.23597e9i	−0.241521	−	0.241521i
$846$	5.79271e9	+	5.12283e9i	0.328916	+	0.290880i
$847$			9.49898e9i			0.537137i
$848$	2.03285e9	+	6.20654e9i	0.114477	+	0.349513i
$849$	−5.33761e9	−	1.81778e10i	−0.299343	−	1.01945i
$850$	2.22257e10	−	6.28247e9i	1.24134	−	0.350884i
$851$	−1.49556e10	+	1.49556e10i	−0.831861	+	0.831861i
$852$	1.70513e10	−	8.73228e8i	0.944537	−	0.0483715i
$853$	−7.09528e9	−	7.09528e9i	−0.391425	−	0.391425i	0.483770	−	0.875195i	$-0.339267\pi$
$853$	−7.09528e9	−	7.09528e9i	−0.391425	−	0.391425i	−0.875195	+	0.483770i	$0.839267\pi$
$854$	−1.09819e10	+	1.96368e10i	−0.603358	+	1.07887i
$855$	−4.94328e9	−	7.69168e9i	−0.270479	−	0.420862i
$856$	6.88860e9	−	2.82877e8i	0.375381	−	0.0154149i
$857$	3.48368e10			1.89062			0.945312	−	0.326167i	$-0.105757\pi$
$857$	3.48368e10			1.89062			0.945312	+	0.326167i	$0.105757\pi$
$858$	−1.01822e9	+	4.46292e9i	−0.0550349	+	0.241220i
$859$	1.63259e10	−	1.63259e10i	0.878820	−	0.878820i	−0.114593	−	0.993413i	$-0.536556\pi$
$859$	1.63259e10	−	1.63259e10i	0.878820	−	0.878820i	0.993413	+	0.114593i	$0.0365563\pi$
$860$	7.15942e8	+	1.16522e9i	0.0383825	+	0.0624688i
$861$	8.11664e9	−	1.48647e10i	0.433376	−	0.793681i
$862$	5.84993e9	−	1.65358e9i	0.311082	−	0.0879326i
$863$	2.42695e9			0.128536			0.0642678	−	0.997933i	$-0.479529\pi$
$863$	2.42695e9			0.128536			0.0642678	+	0.997933i	$0.479529\pi$
$864$	2.30677e9	−	1.88174e10i	0.121676	−	0.992570i
$865$	2.55758e9			0.134361
$866$	−6.75846e9	+	1.91039e9i	−0.353619	+	0.0999562i
$867$	−1.23948e10	+	2.26997e10i	−0.645910	+	1.18291i
$868$	−9.29122e9	−	1.51218e10i	−0.482229	−	0.784844i
$869$	4.82011e9	−	4.82011e9i	0.249165	−	0.249165i
$870$	1.27373e9	−	5.58281e9i	0.0655783	−	0.287432i
$871$	5.22155e9			0.267754
$872$	7.53943e8	+	1.83600e10i	0.0385062	+	0.937701i
$873$	1.13547e10	+	1.76678e10i	0.577599	+	0.898737i
$874$	−1.14739e10	+	2.05166e10i	−0.581328	+	1.03948i
$875$	9.74107e9	+	9.74107e9i	0.491562	+	0.491562i
$876$	−2.93622e10	+	1.50369e9i	−1.47579	+	0.0755779i
$877$	−1.28812e10	+	1.28812e10i	−0.644849	+	0.644849i	−0.951744	−	0.306894i	$-0.900710\pi$
$877$	−1.28812e10	+	1.28812e10i	−0.644849	+	0.644849i	0.306894	+	0.951744i	$0.400710\pi$
$878$	8.92246e9	−	2.52208e9i	0.444891	−	0.125756i
$879$	6.60603e9	+	2.24976e10i	0.328080	+	1.11731i
$880$	−2.39330e9	+	4.72467e9i	−0.118388	+	0.233713i
$881$		−	3.54808e10i		−	1.74815i	−0.485793	−	0.874074i	$-0.661469\pi$
$881$		−	3.54808e10i		−	1.74815i	0.485793	−	0.874074i	$-0.338531\pi$
$882$	−1.51225e9	−	1.33737e9i	−0.0742135	−	0.0656313i
$883$	−1.71024e10	−	1.71024e10i	−0.835978	−	0.835978i	0.152349	−	0.988327i	$-0.451316\pi$
$883$	−1.71024e10	−	1.71024e10i	−0.835978	−	0.835978i	−0.988327	+	0.152349i	$0.951316\pi$
$884$	1.14948e10	+	2.74531e9i	0.559654	+	0.133662i
$885$	5.57693e9	−	1.02135e10i	0.270454	−	0.495308i
$886$	−1.53350e10	−	8.57614e9i	−0.740741	−	0.414261i
$887$		−	6.94261e9i		−	0.334033i	−0.985954	−	0.167017i	$-0.946587\pi$
$887$		−	6.94261e9i		−	0.334033i	0.985954	−	0.167017i	$-0.0534134\pi$
$888$	−1.14834e10	+	2.32507e10i	−0.550332	+	1.11427i
$889$			2.33209e10i			1.11324i
$890$	−4.51123e9	+	8.06655e9i	−0.214501	+	0.383551i
$891$	−1.30340e10	+	4.86181e9i	−0.617315	+	0.230264i
$892$	−1.56855e10	−	2.55287e10i	−0.739983	−	1.20435i
$893$	−8.31278e9	−	8.31278e9i	−0.390630	−	0.390630i
$894$	−1.46330e10	−	2.32838e10i	−0.684938	−	1.08986i
$895$		−	1.48539e10i		−	0.692564i
$896$	−7.15289e9	−	1.91447e10i	−0.332203	−	0.889140i
$897$	7.37274e9	−	2.16488e9i	0.341079	−	0.100152i
$898$	9.66158e9	+	3.41801e10i	0.445226	+	1.57509i
$899$	−1.10841e10	+	1.10841e10i	−0.508793	+	0.508793i
$900$	7.98581e9	−	1.65901e10i	0.365149	−	0.758576i
$901$	−8.74867e9	−	8.74867e9i	−0.398479	−	0.398479i
$902$	1.20750e10	+	6.75298e9i	0.547855	+	0.306388i
$903$	1.09100e9	+	3.71552e9i	0.0493081	+	0.167924i
$904$	−4.52217e9	−	4.16542e9i	−0.203590	−	0.187529i
$905$	−1.65424e10			−0.741871
$906$	−8.38062e9	+	3.67326e10i	−0.374393	+	1.64098i
$907$	−1.10779e9	+	1.10779e9i	−0.0492981	+	0.0492981i	−0.731326	−	0.682028i	$-0.761098\pi$
$907$	−1.10779e9	+	1.10779e9i	−0.0492981	+	0.0492981i	0.682028	+	0.731326i	$0.261098\pi$
$908$	4.44038e9	−	1.85922e10i	0.196843	−	0.824196i
$909$	3.56363e10	+	7.75174e9i	1.57369	+	0.342315i
$910$	8.76387e8	+	3.10043e9i	0.0385524	+	0.136388i
$911$	−3.62995e10			−1.59069			−0.795347	−	0.606155i	$-0.792711\pi$
$911$	−3.62995e10			−1.59069			−0.795347	+	0.606155i	$0.792711\pi$
$912$	−5.25259e9	+	2.83386e10i	−0.229293	+	1.23707i
$913$	2.56943e10			1.11735
$914$	−6.08418e9	−	2.15242e10i	−0.263566	−	0.932428i
$915$	−1.05320e10	−	5.75084e9i	−0.454504	−	0.248175i
$916$	3.79757e10	+	9.06974e9i	1.63257	+	0.389906i
$917$	−2.76640e9	+	2.76640e9i	−0.118474	+	0.118474i
$918$	1.22105e10	+	3.37757e10i	0.520936	+	1.44097i
$919$	−2.02263e10			−0.859629			−0.429815	−	0.902917i	$-0.641421\pi$
$919$	−2.02263e10			−0.859629			−0.429815	+	0.902917i	$0.641421\pi$
$920$	8.88288e9	−	3.64771e8i	0.376094	−	0.0154441i
$921$	1.21884e10	−	3.57893e9i	0.514090	−	0.150954i
$922$	−5.30960e9	−	2.96940e9i	−0.223102	−	0.124770i
$923$	5.99952e9	+	5.99952e9i	0.251137	+	0.251137i
$924$	−1.00479e10	+	1.11326e10i	−0.419011	+	0.464244i
$925$	−1.78083e10	+	1.78083e10i	−0.739822	+	0.739822i
$926$	8.71864e9	+	3.08442e10i	0.360836	+	1.27654i
$927$	3.32613e9	+	5.17542e9i	0.137139	+	0.213386i
$928$	−1.49787e10	+	1.00725e10i	−0.615256	+	0.413734i
$929$			2.45239e10i			1.00354i	0.865001	+	0.501771i	$0.167318\pi$
$929$			2.45239e10i			1.00354i	−0.865001	+	0.501771i	$0.832682\pi$
$930$	8.01459e9	−	5.03687e9i	0.326732	−	0.205339i
$931$	2.17014e9	+	2.17014e9i	0.0881380	+	0.0881380i
$932$	1.37776e10	−	8.46535e9i	0.557467	−	0.342523i
$933$	−1.90853e10	−	1.04212e10i	−0.769331	−	0.420080i
$934$	−1.89284e9	+	3.38459e9i	−0.0760150	+	0.135923i
$935$		−	1.00334e10i		−	0.401428i
$936$	7.70984e9	−	5.41444e9i	0.307312	−	0.215818i
$937$			1.83588e10i			0.729049i	0.931194	+	0.364524i	$0.118768\pi$
$937$			1.83588e10i			0.729049i	−0.931194	+	0.364524i	$0.881232\pi$
$938$	1.49300e10	+	8.34963e9i	0.590677	+	0.330337i
$939$	4.35577e10	+	2.37840e10i	1.71686	+	0.937465i
$940$	−1.03282e9	+	4.32452e9i	−0.0405582	+	0.169820i
$941$	−3.65009e9	−	3.65009e9i	−0.142804	−	0.142804i	0.632091	−	0.774895i	$-0.282197\pi$
$941$	−3.65009e9	−	3.65009e9i	−0.142804	−	0.142804i	−0.774895	+	0.632091i	$0.782197\pi$
$942$	−1.65365e10	−	2.63126e10i	−0.644562	−	1.02562i
$943$		−	2.32237e10i		−	0.901862i
$944$	−3.48599e10	+	1.14178e10i	−1.34873	+	0.441753i
$945$	−6.41182e9	+	7.39992e9i	−0.247156	+	0.285243i
$946$	−3.04403e9	+	8.60445e8i	−0.116904	+	0.0330449i
$947$	−2.60596e9	+	2.60596e9i	−0.0997110	+	0.0997110i	−0.755203	−	0.655492i	$-0.772462\pi$
$947$	−2.60596e9	+	2.60596e9i	−0.0997110	+	0.0997110i	0.655492	+	0.755203i	$0.272462\pi$
$948$	−1.40110e10	+	7.17527e8i	−0.534120	+	0.0273533i
$949$	−1.03311e10	−	1.03311e10i	−0.392388	−	0.392388i
$950$	−1.36625e10	+	2.44300e10i	−0.517009	+	0.924466i
$951$	−2.12735e10	+	6.24660e9i	−0.802060	+	0.235511i
$952$	2.84773e10	+	2.62308e10i	1.06972	+	0.985330i
$953$	1.72403e10			0.645236			0.322618	−	0.946529i	$-0.395437\pi$
$953$	1.72403e10			0.645236			0.322618	+	0.946529i	$0.395437\pi$
$954$	−9.84454e9	+	6.04156e8i	−0.367093	+	0.0225284i
$955$	1.15867e10	−	1.15867e10i	0.430473	−	0.430473i
$956$	2.42570e9	−	1.49041e9i	0.0897913	−	0.0551701i
$957$	1.16250e10	+	6.34763e9i	0.428747	+	0.234110i
$958$	5.06485e10	−	1.43166e10i	1.86117	−	0.526092i
$959$	−1.77617e9			−0.0650308
$960$	1.01716e10	−	3.91818e9i	0.371058	−	0.142934i
$961$	1.60028e9			0.0581654
$962$	−1.24007e10	+	3.50528e9i	−0.449092	+	0.126943i
$963$	−2.21309e9	+	1.01740e10i	−0.0798558	+	0.367113i
$964$	−2.08915e10	+	1.28363e10i	−0.751103	+	0.461498i
$965$	5.93042e9	−	5.93042e9i	0.212442	−	0.212442i
$966$	2.45427e10	+	5.59948e9i	0.875998	+	0.199861i
$967$	−3.19435e10			−1.13603			−0.568016	−	0.823018i	$-0.692289\pi$
$967$	−3.19435e10			−1.13603			−0.568016	+	0.823018i	$0.692289\pi$
$968$	1.17463e10	+	1.08196e10i	0.416233	+	0.383397i
$969$	−1.53829e10	−	5.23881e10i	−0.543131	−	1.84969i
$970$	−5.89399e9	+	1.05391e10i	−0.207352	+	0.370767i
$971$	−1.16257e10	−	1.16257e10i	−0.407522	−	0.407522i	0.473351	−	0.880874i	$-0.343044\pi$
$971$	−1.16257e10	−	1.16257e10i	−0.407522	−	0.407522i	−0.880874	+	0.473351i	$0.843044\pi$
$972$	2.66179e10	+	1.05454e10i	0.929697	+	0.368325i
$973$	1.61364e10	−	1.61364e10i	0.561579	−	0.561579i
$974$	2.28429e10	−	6.45692e9i	0.792126	−	0.223908i
$975$	8.77906e9	−	2.57782e9i	0.303342	−	0.0890711i
$976$	1.17738e10	+	3.59469e10i	0.405361	+	1.23762i
$977$			2.29869e10i			0.788587i	0.918984	+	0.394294i	$0.129011\pi$
$977$			2.29869e10i			0.788587i	−0.918984	+	0.394294i	$0.870989\pi$
$978$	−2.55056e10	+	1.60293e10i	−0.871867	+	0.547936i
$979$	−1.51164e10	−	1.51164e10i	−0.514885	−	0.514885i
$980$	2.69629e8	−	1.12896e9i	0.00915116	−	0.0383166i
$981$	−2.71164e10	−	5.89847e9i	−0.917046	−	0.199479i
$982$	1.91905e10	+	1.07323e10i	0.646689	+	0.361662i
$983$		−	2.00888e10i		−	0.674553i	−0.941406	−	0.337277i	$-0.890494\pi$
$983$		−	2.00888e10i		−	0.674553i	0.941406	−	0.337277i	$-0.109506\pi$
$984$	−9.13638e9	−	2.69683e10i	−0.305697	−	0.902340i
$985$			1.72184e10i			0.574071i
$986$	1.66909e10	−	2.98451e10i	0.554512	−	0.991525i
$987$	−6.03340e9	+	1.10495e10i	−0.199734	+	0.365791i
$988$	−1.22031e10	+	7.49788e9i	−0.402550	+	0.247337i
$989$	3.75470e9	+	3.75470e9i	0.123421	+	0.123421i
$990$	−5.99154e9	−	5.29867e9i	−0.196253	−	0.173558i
$991$			1.59138e9i			0.0519415i	0.999663	+	0.0259708i	$0.00826768\pi$
$991$			1.59138e9i			0.0519415i	−0.999663	+	0.0259708i	$0.991732\pi$
$992$	−2.92823e10	−	5.73479e9i	−0.952389	−	0.186520i
$993$	6.31988e9	+	2.15231e10i	0.204827	+	0.697560i
$994$	7.56081e9	+	2.67481e10i	0.244183	+	0.863856i
$995$	−5.33369e9	+	5.33369e9i	−0.171651	+	0.171651i
$996$	−3.92563e10	−	3.54314e10i	−1.25893	−	1.13627i
$997$	−9.78083e9	−	9.78083e9i	−0.312567	−	0.312567i	0.533337	−	0.845903i	$-0.320938\pi$
$997$	−9.78083e9	−	9.78083e9i	−0.312567	−	0.312567i	−0.845903	+	0.533337i	$0.820938\pi$
$998$	−3.87797e9	−	2.16876e9i	−0.123495	−	0.0690645i
$999$	−2.95974e10	−	2.56453e10i	−0.939235	−	0.813821i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.8.k.a.11.5	✓	108
3.2	odd	2	inner	48.8.k.a.11.50	yes	108
16.3	odd	4	inner	48.8.k.a.35.50	yes	108
48.35	even	4	inner	48.8.k.a.35.5	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.8.k.a.11.5	✓	108	1.1	even	1	trivial
48.8.k.a.11.50	yes	108	3.2	odd	2	inner
48.8.k.a.35.5	yes	108	48.35	even	4	inner
48.8.k.a.35.50	yes	108	16.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	48.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-10.8871 + 3.07743i) q^{2} +(22.4120 - 41.0451i) q^{3} +(109.059 - 67.0087i) q^{4} +(-78.5897 + 78.5897i) q^{5} +(-117.689 + 515.835i) q^{6} -861.367 q^{7} +(-981.123 + 1065.15i) q^{8} +(-1182.40 - 1839.81i) q^{9} +O(q^{10})\)	\(q+(-10.8871 + 3.07743i) q^{2} +(22.4120 - 41.0451i) q^{3} +(109.059 - 67.0087i) q^{4} +(-78.5897 + 78.5897i) q^{5} +(-117.689 + 515.835i) q^{6} -861.367 q^{7} +(-981.123 + 1065.15i) q^{8} +(-1182.40 - 1839.81i) q^{9} +(613.761 - 1097.47i) q^{10} +(2056.62 + 2056.62i) q^{11} +(-306.151 - 5978.13i) q^{12} +(2103.41 - 2103.41i) q^{13} +(9377.81 - 2650.80i) q^{14} +(1464.37 + 4987.07i) q^{15} +(7403.68 - 14615.8i) q^{16} +31038.4i q^{17} +(18534.9 + 16391.4i) q^{18} +(-26598.3 - 26598.3i) q^{19} +(-3304.71 + 13837.1i) q^{20} +(-19305.0 + 35354.9i) q^{21} +(-28719.8 - 16061.6i) q^{22} +55236.2i q^{23} +(21730.4 + 64142.5i) q^{24} +65772.3i q^{25} +(-16427.0 + 29373.2i) q^{26} +(-102015. + 7298.17i) q^{27} +(-93939.8 + 57719.1i) q^{28} +(68856.8 + 68856.8i) q^{29} +(-31290.1 - 49788.4i) q^{30} +160973. i q^{31} +(-35625.7 + 181908. i) q^{32} +(130507. - 38321.3i) q^{33} +(-95518.4 - 337919. i) q^{34} +(67694.6 - 67694.6i) q^{35} +(-252235. - 121416. i) q^{36} +(270757. + 270757. i) q^{37} +(371433. + 207724. i) q^{38} +(-39193.1 - 133476. i) q^{39} +(-6603.83 - 160816. i) q^{40} -420443. q^{41} +(101373. - 444323. i) q^{42} +(67975.3 - 67975.3i) q^{43} +(362104. + 86481.3i) q^{44} +(237515. + 51665.0i) q^{45} +(-169986. - 601364. i) q^{46} +312531. q^{47} +(-433975. - 631454. i) q^{48} -81589.4 q^{49} +(-202410. - 716071. i) q^{50} +(1.27397e6 + 695632. i) q^{51} +(88448.9 - 370343. i) q^{52} +(-281866. + 281866. i) q^{53} +(1.08819e6 - 393400. i) q^{54} -323258. q^{55} +(845107. - 917487. i) q^{56} +(-1.68785e6 + 495609. i) q^{57} +(-961554. - 537751. i) q^{58} +(-1.58314e6 - 1.58314e6i) q^{59} +(493880. + 445759. i) q^{60} +(-1.63251e6 + 1.63251e6i) q^{61} +(-495383. - 1.75253e6i) q^{62} +(1.01848e6 + 1.58475e6i) q^{63} +(-171947. - 2.09009e6i) q^{64} +330613. i q^{65} +(-1.30292e6 + 818835. i) q^{66} +(1.24121e6 + 1.24121e6i) q^{67} +(2.07984e6 + 3.38501e6i) q^{68} +(2.26718e6 + 1.23795e6i) q^{69} +(-528674. + 945324. i) q^{70} +2.85228e6i q^{71} +(3.11976e6 + 545636. i) q^{72} -4.91160e6i q^{73} +(-3.78100e6 - 2.11453e6i) q^{74} +(2.69963e6 + 1.47409e6i) q^{75} +(-4.68309e6 - 1.11846e6i) q^{76} +(-1.77151e6 - 1.77151e6i) q^{77} +(837465. + 1.33256e6i) q^{78} -2.34370e6i q^{79} +(566797. + 1.73050e6i) q^{80} +(-1.98681e6 + 4.35079e6i) q^{81} +(4.57741e6 - 1.29388e6i) q^{82} +(6.24674e6 - 6.24674e6i) q^{83} +(263708. + 5.14937e6i) q^{84} +(-2.43930e6 - 2.43930e6i) q^{85} +(-530866. + 949245. i) q^{86} +(4.36945e6 - 1.28302e6i) q^{87} +(-4.20841e6 + 172816. i) q^{88} -7.35013e6 q^{89} +(-2.74485e6 + 168450. i) q^{90} +(-1.81181e6 + 1.81181e6i) q^{91} +(3.70131e6 + 6.02400e6i) q^{92} +(6.60716e6 + 3.60773e6i) q^{93} +(-3.40256e6 + 961791. i) q^{94} +4.18070e6 q^{95} +(6.66799e6 + 5.53919e6i) q^{96} -9.60307e6 q^{97} +(888274. - 251085. i) q^{98} +(1.35203e6 - 6.21554e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 2 q^{3} - 4 q^{4} + 172 q^{6} - 8 q^{7}+O(q^{10}) \) 108 * q - 2 * q^3 - 4 * q^4 + 172 * q^6 - 8 * q^7	\( 108 q - 2 q^{3} - 4 q^{4} + 172 q^{6} - 8 q^{7} - 6504 q^{10} + 12016 q^{12} - 4 q^{13} - 55280 q^{16} + 21172 q^{18} - 60588 q^{19} - 4376 q^{21} - 212744 q^{22} - 317304 q^{24} + 238042 q^{27} + 219736 q^{28} - 503852 q^{30} - 4 q^{33} - 364856 q^{34} + 867620 q^{36} - 4 q^{37} - 283948 q^{39} + 390392 q^{40} - 3022344 q^{42} + 752844 q^{43} - 156252 q^{45} - 1166824 q^{46} + 358320 q^{48} + 9882508 q^{49} + 1121592 q^{51} - 4458688 q^{52} + 203816 q^{54} + 4191000 q^{55} + 4975544 q^{58} - 4390240 q^{60} - 2279892 q^{61} + 4781432 q^{64} + 1457476 q^{66} + 1552540 q^{67} + 4372 q^{69} - 9366152 q^{70} - 1660280 q^{72} - 886066 q^{75} - 6569272 q^{76} - 13616772 q^{78} - 4 q^{81} + 11560256 q^{82} - 10944176 q^{84} + 7846496 q^{85} - 40789116 q^{87} + 24614816 q^{88} + 25746032 q^{90} - 1590680 q^{91} - 14495396 q^{93} - 6995856 q^{94} - 13927736 q^{96} - 8 q^{97} - 4701076 q^{99}+O(q^{100}) \) 108 * q - 2 * q^3 - 4 * q^4 + 172 * q^6 - 8 * q^7 - 6504 * q^10 + 12016 * q^12 - 4 * q^13 - 55280 * q^16 + 21172 * q^18 - 60588 * q^19 - 4376 * q^21 - 212744 * q^22 - 317304 * q^24 + 238042 * q^27 + 219736 * q^28 - 503852 * q^30 - 4 * q^33 - 364856 * q^34 + 867620 * q^36 - 4 * q^37 - 283948 * q^39 + 390392 * q^40 - 3022344 * q^42 + 752844 * q^43 - 156252 * q^45 - 1166824 * q^46 + 358320 * q^48 + 9882508 * q^49 + 1121592 * q^51 - 4458688 * q^52 + 203816 * q^54 + 4191000 * q^55 + 4975544 * q^58 - 4390240 * q^60 - 2279892 * q^61 + 4781432 * q^64 + 1457476 * q^66 + 1552540 * q^67 + 4372 * q^69 - 9366152 * q^70 - 1660280 * q^72 - 886066 * q^75 - 6569272 * q^76 - 13616772 * q^78 - 4 * q^81 + 11560256 * q^82 - 10944176 * q^84 + 7846496 * q^85 - 40789116 * q^87 + 24614816 * q^88 + 25746032 * q^90 - 1590680 * q^91 - 14495396 * q^93 - 6995856 * q^94 - 13927736 * q^96 - 8 * q^97 - 4701076 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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