LMFDB - Embedded newform 74.8.b.a.73.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,8,Mod(73,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("74.73");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	74.b (of order $2$, degree $1$, 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:	$23.1164918858$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			73.6
Character	$\chi$	$=$	74.73
Dual form			74.8.b.a.73.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-8.00000i q^{2} -28.7630 q^{3} -64.0000 q^{4} -436.339i q^{5} +230.104i q^{6} -218.580 q^{7} +512.000i q^{8} -1359.69 q^{9} -3490.71 q^{10} -1840.96 q^{11} +1840.83 q^{12} -12931.9i q^{13} +1748.64i q^{14} +12550.4i q^{15} +4096.00 q^{16} -30366.5i q^{17} +10877.5i q^{18} +33038.6i q^{19} +27925.7i q^{20} +6287.04 q^{21} +14727.7i q^{22} +64290.0i q^{23} -14726.7i q^{24} -112267. q^{25} -103456. q^{26} +102014. q^{27} +13989.2 q^{28} +174982. i q^{29} +100404. q^{30} +151461. i q^{31} -32768.0i q^{32} +52951.6 q^{33} -242932. q^{34} +95375.3i q^{35} +87020.0 q^{36} +(300206. + 69342.0i) q^{37} +264308. q^{38} +371962. i q^{39} +223406. q^{40} +409900. q^{41} -50296.3i q^{42} -787574. i q^{43} +117821. q^{44} +593285. i q^{45} +514320. q^{46} -295655. q^{47} -117813. q^{48} -775766. q^{49} +898136. i q^{50} +873434. i q^{51} +827645. i q^{52} -1.21561e6 q^{53} -816108. i q^{54} +803282. i q^{55} -111913. i q^{56} -950289. i q^{57} +1.39986e6 q^{58} +1.57556e6i q^{59} -803229. i q^{60} -1.82097e6i q^{61} +1.21169e6 q^{62} +297201. q^{63} -262144. q^{64} -5.64272e6 q^{65} -423612. i q^{66} +1.79212e6 q^{67} +1.94346e6i q^{68} -1.84918e6i q^{69} +763002. q^{70} -4.65562e6 q^{71} -696160. i q^{72} +3.86406e6 q^{73} +(554736. - 2.40165e6i) q^{74} +3.22914e6 q^{75} -2.11447e6i q^{76} +402398. q^{77} +2.97570e6 q^{78} +1.92310e6i q^{79} -1.78725e6i q^{80} +39416.7 q^{81} -3.27920e6i q^{82} -6.01597e6 q^{83} -402371. q^{84} -1.32501e7 q^{85} -6.30059e6 q^{86} -5.03302e6i q^{87} -942571. i q^{88} -3.90896e6i q^{89} +4.74628e6 q^{90} +2.82667e6i q^{91} -4.11456e6i q^{92} -4.35649e6i q^{93} +2.36524e6i q^{94} +1.44160e7 q^{95} +942507. i q^{96} -5.70113e6i q^{97} +6.20612e6i q^{98} +2.50313e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 106 q^{3} - 1536 q^{4} + 104 q^{7} + 17554 q^{9} + 1136 q^{10} + 366 q^{11} + 6784 q^{12} + 98304 q^{16} - 239820 q^{21} - 675570 q^{25} + 97008 q^{26} + 338780 q^{27} - 6656 q^{28} + 350400 q^{30}+ \cdots - 53279900 q^{99}+O(q^{100}) $ 24 * q - 106 * q^3 - 1536 * q^4 + 104 * q^7 + 17554 * q^9 + 1136 * q^10 + 366 * q^11 + 6784 * q^12 + 98304 * q^16 - 239820 * q^21 - 675570 * q^25 + 97008 * q^26 + 338780 * q^27 - 6656 * q^28 + 350400 * q^30 - 763792 * q^33 + 713632 * q^34 - 1123456 * q^36 + 41652 * q^37 - 30816 * q^38 - 72704 * q^40 + 1729722 * q^41 - 23424 * q^44 - 488496 * q^46 + 114756 * q^47 - 434176 * q^48 + 4003056 * q^49 - 1115964 * q^53 - 2075632 * q^58 + 3248208 * q^62 - 2350900 * q^63 - 6291456 * q^64 - 5246556 * q^65 - 2717994 * q^67 - 5649440 * q^70 + 10643280 * q^71 - 10450370 * q^73 - 1064064 * q^74 - 17737980 * q^75 + 11665236 * q^77 + 8431856 * q^78 + 47300176 * q^81 + 555912 * q^83 + 15348480 * q^84 - 4853096 * q^85 - 12070464 * q^86 + 32064160 * q^90 - 58516956 * q^95 - 53279900 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$-1$

Coefficient data

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

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

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

$2$		−	8.00000i		−	0.707107i
$2$		−	8.00000i		−	0.707107i
$3$	−28.7630			−0.615050			−0.307525	−	0.951540i	$-0.599501\pi$
$3$	−28.7630			−0.615050			−0.307525	+	0.951540i	$0.599501\pi$
$4$	−64.0000			−0.500000
$5$		−	436.339i		−	1.56109i	−0.625097	−	0.780547i	$-0.714940\pi$
$5$		−	436.339i		−	1.56109i	0.625097	−	0.780547i	$-0.285060\pi$
$6$			230.104i			0.434906i
$7$	−218.580			−0.240862			−0.120431	−	0.992722i	$-0.538428\pi$
$7$	−218.580			−0.240862			−0.120431	+	0.992722i	$0.538428\pi$
$8$			512.000i			0.353553i
$9$	−1359.69			−0.621713
$10$	−3490.71			−1.10386
$11$	−1840.96			−0.417032			−0.208516	−	0.978019i	$-0.566863\pi$
$11$	−1840.96			−0.417032			−0.208516	+	0.978019i	$0.566863\pi$
$12$	1840.83			0.307525
$13$		−	12931.9i		−	1.63253i	−0.577675	−	0.816267i	$-0.696040\pi$
$13$		−	12931.9i		−	1.63253i	0.577675	−	0.816267i	$-0.303960\pi$
$14$			1748.64i			0.170315i
$15$			12550.4i			0.960152i
$16$	4096.00			0.250000
$17$		−	30366.5i		−	1.49908i	−0.661961	−	0.749538i	$-0.730276\pi$
$17$		−	30366.5i		−	1.49908i	0.661961	−	0.749538i	$-0.269724\pi$
$18$			10877.5i			0.439618i
$19$			33038.6i			1.10505i	0.833495	+	0.552527i	$0.186336\pi$
$19$			33038.6i			1.10505i	−0.833495	+	0.552527i	$0.813664\pi$
$20$			27925.7i			0.780547i
$21$	6287.04			0.148142
$22$			14727.7i			0.294886i
$23$			64290.0i			1.10178i	0.834577	+	0.550891i	$0.185712\pi$
$23$			64290.0i			1.10178i	−0.834577	+	0.550891i	$0.814288\pi$
$24$		−	14726.7i		−	0.217453i
$25$	−112267.			−1.43702
$26$	−103456.			−1.15438
$27$	102014.			0.997435
$28$	13989.2			0.120431
$29$			174982.i			1.33230i	0.745819	+	0.666149i	$0.232058\pi$
$29$			174982.i			1.33230i	−0.745819	+	0.666149i	$0.767942\pi$
$30$	100404.			0.678930
$31$			151461.i			0.913136i	0.889688	+	0.456568i	$0.150922\pi$
$31$			151461.i			0.913136i	−0.889688	+	0.456568i	$0.849078\pi$
$32$		−	32768.0i		−	0.176777i
$33$	52951.6			0.256496
$34$	−242932.			−1.06001
$35$			95375.3i			0.376008i
$36$	87020.0			0.310857
$37$	300206.	+	69342.0i	0.974346	+	0.225056i
$37$	300206.	+	69342.0i	0.974346	+	0.225056i
$38$	264308.			0.781391
$39$			371962.i			1.00409i
$40$	223406.			0.551930
$41$	409900.			0.928826			0.464413	−	0.885619i	$-0.346265\pi$
$41$	409900.			0.928826			0.464413	+	0.885619i	$0.346265\pi$
$42$		−	50296.3i		−	0.104752i
$43$		−	787574.i		−	1.51061i	−0.655374	−	0.755304i	$-0.727489\pi$
$43$		−	787574.i		−	1.51061i	0.655374	−	0.755304i	$-0.272511\pi$
$44$	117821.			0.208516
$45$			593285.i			0.970554i
$46$	514320.			0.779078
$47$	−295655.			−0.415377			−0.207688	−	0.978195i	$-0.566594\pi$
$47$	−295655.			−0.415377			−0.207688	+	0.978195i	$0.566594\pi$
$48$	−117813.			−0.153763
$49$	−775766.			−0.941986
$50$			898136.i			1.01612i
$51$			873434.i			0.922007i
$52$			827645.i			0.816267i
$53$	−1.21561e6			−1.12157			−0.560786	−	0.827961i	$-0.689501\pi$
$53$	−1.21561e6			−1.12157			−0.560786	+	0.827961i	$0.689501\pi$
$54$		−	816108.i		−	0.705293i
$55$			803282.i			0.651027i
$56$		−	111913.i		−	0.0851576i
$57$		−	950289.i		−	0.679663i
$58$	1.39986e6			0.942076
$59$			1.57556e6i			0.998740i	0.866389	+	0.499370i	$0.166435\pi$
$59$			1.57556e6i			0.998740i	−0.866389	+	0.499370i	$0.833565\pi$
$60$		−	803229.i		−	0.480076i
$61$		−	1.82097e6i		−	1.02719i	−0.858034	−	0.513593i	$-0.828314\pi$
$61$		−	1.82097e6i		−	1.02719i	0.858034	−	0.513593i	$-0.171686\pi$
$62$	1.21169e6			0.645685
$63$	297201.			0.149747
$64$	−262144.			−0.125000
$65$	−5.64272e6			−2.54854
$66$		−	423612.i		−	0.181370i
$67$	1.79212e6			0.727957			0.363978	−	0.931407i	$-0.381418\pi$
$67$	1.79212e6			0.727957			0.363978	+	0.931407i	$0.381418\pi$
$68$			1.94346e6i			0.749538i
$69$		−	1.84918e6i		−	0.677651i
$70$	763002.			0.265878
$71$	−4.65562e6			−1.54374			−0.771869	−	0.635781i	$-0.780678\pi$
$71$	−4.65562e6			−1.54374			−0.771869	+	0.635781i	$0.780678\pi$
$72$		−	696160.i		−	0.219809i
$73$	3.86406e6			1.16256			0.581278	−	0.813705i	$-0.302553\pi$
$73$	3.86406e6			1.16256			0.581278	+	0.813705i	$0.302553\pi$
$74$	554736.	−	2.40165e6i	0.159138	−	0.688967i
$75$	3.22914e6			0.883838
$76$		−	2.11447e6i		−	0.552527i
$77$	402398.			0.100447
$78$	2.97570e6			0.709999
$79$			1.92310e6i			0.438841i	0.975630	+	0.219420i	$0.0704166\pi$
$79$			1.92310e6i			0.438841i	−0.975630	+	0.219420i	$0.929583\pi$
$80$		−	1.78725e6i		−	0.390274i
$81$	39416.7			0.00824105
$82$		−	3.27920e6i		−	0.656779i
$83$	−6.01597e6			−1.15487			−0.577434	−	0.816438i	$-0.695946\pi$
$83$	−6.01597e6			−1.15487			−0.577434	+	0.816438i	$0.695946\pi$
$84$	−402371.			−0.0740711
$85$	−1.32501e7			−2.34020
$86$	−6.30059e6			−1.06816
$87$		−	5.03302e6i		−	0.819429i
$88$		−	942571.i		−	0.147443i
$89$		−	3.90896e6i		−	0.587755i	−0.955843	−	0.293878i	$-0.905054\pi$
$89$		−	3.90896e6i		−	0.587755i	0.955843	−	0.293878i	$-0.0949458\pi$
$90$	4.74628e6			0.686285
$91$			2.82667e6i			0.393215i
$92$		−	4.11456e6i		−	0.550891i
$93$		−	4.35649e6i		−	0.561625i
$94$			2.36524e6i			0.293716i
$95$	1.44160e7			1.72509
$96$			942507.i			0.108727i
$97$		−	5.70113e6i		−	0.634249i	−0.948384	−	0.317125i	$-0.897283\pi$
$97$		−	5.70113e6i		−	0.634249i	0.948384	−	0.317125i	$-0.102717\pi$
$98$			6.20612e6i			0.666084i
$99$	2.50313e6			0.259274
$100$	7.18509e6			0.718509
$101$	3.70887e6			0.358193			0.179096	−	0.983832i	$-0.442683\pi$
$101$	3.70887e6			0.358193			0.179096	+	0.983832i	$0.442683\pi$
$102$	6.98747e6			0.651958
$103$		−	2.14896e7i		−	1.93775i	−0.247548	−	0.968876i	$-0.579625\pi$
$103$		−	2.14896e7i		−	1.93775i	0.247548	−	0.968876i	$-0.420375\pi$
$104$	6.62116e6			0.577188
$105$		−	2.74328e6i		−	0.231264i
$106$			9.72485e6i			0.793071i
$107$	−9.52504e6			−0.751664			−0.375832	−	0.926688i	$-0.622643\pi$
$107$	−9.52504e6			−0.751664			−0.375832	+	0.926688i	$0.622643\pi$
$108$	−6.52887e6			−0.498717
$109$			1.53128e7i			1.13256i	0.824211	+	0.566282i	$0.191619\pi$
$109$			1.53128e7i			1.13256i	−0.824211	+	0.566282i	$0.808381\pi$
$110$	6.42626e6			0.460345
$111$	−8.63483e6	−	1.99449e6i	−0.599271	−	0.138421i
$112$	−895306.			−0.0602155
$113$			1.43479e7i			0.935432i	0.883879	+	0.467716i	$0.154923\pi$
$113$			1.43479e7i			0.935432i	−0.883879	+	0.467716i	$0.845077\pi$
$114$	−7.60232e6			−0.480595
$115$	2.80522e7			1.71999
$116$		−	1.11989e7i		−	0.666149i
$117$			1.75834e7i			1.01497i
$118$	1.26045e7			0.706216
$119$			6.63753e6i			0.361071i
$120$	−6.42583e6			−0.339465
$121$	−1.60980e7			−0.826084
$122$	−1.45678e7			−0.726330
$123$	−1.17900e7			−0.571275
$124$		−	9.69352e6i		−	0.456568i
$125$			1.48975e7i			0.682226i
$126$		−	2.37761e6i		−	0.105887i
$127$	−2.88879e7			−1.25142			−0.625709	−	0.780057i	$-0.715190\pi$
$127$	−2.88879e7			−1.25142			−0.625709	+	0.780057i	$0.715190\pi$
$128$			2.09715e6i			0.0883883i
$129$			2.26530e7i			0.929100i
$130$			4.51417e7i			1.80209i
$131$			4.47719e7i			1.74003i	0.493029	+	0.870013i	$0.335890\pi$
$131$			4.47719e7i			1.74003i	−0.493029	+	0.870013i	$0.664110\pi$
$132$	−3.38890e6			−0.128248
$133$		−	7.22158e6i		−	0.266165i
$134$		−	1.43370e7i		−	0.514743i
$135$		−	4.45125e7i		−	1.55709i
$136$	1.55477e7			0.530004
$137$	−1.82661e7			−0.606910			−0.303455	−	0.952846i	$-0.598140\pi$
$137$	−1.82661e7			−0.606910			−0.303455	+	0.952846i	$0.598140\pi$
$138$	−1.47934e7			−0.479172
$139$	1.09171e7			0.344789			0.172395	−	0.985028i	$-0.444850\pi$
$139$	1.09171e7			0.344789			0.172395	+	0.985028i	$0.444850\pi$
$140$		−	6.10402e6i		−	0.188004i
$141$	8.50393e6			0.255477
$142$			3.72450e7i			1.09159i
$143$			2.38072e7i			0.680819i
$144$	−5.56928e6			−0.155428
$145$	7.63516e7			2.07984
$146$		−	3.09125e7i		−	0.822052i
$147$	2.23134e7			0.579368
$148$	−1.92132e7	−	4.43789e6i	−0.487173	−	0.112528i
$149$	−1.26851e6			−0.0314153			−0.0157077	−	0.999877i	$-0.505000\pi$
$149$	−1.26851e6			−0.0314153			−0.0157077	+	0.999877i	$0.505000\pi$
$150$		−	2.58331e7i		−	0.624968i
$151$	1.77132e7			0.418675			0.209337	−	0.977843i	$-0.432869\pi$
$151$	1.77132e7			0.418675			0.209337	+	0.977843i	$0.432869\pi$
$152$	−1.69157e7			−0.390696
$153$			4.12890e7i			0.931996i
$154$		−	3.21918e6i		−	0.0710269i
$155$	6.60885e7			1.42549
$156$		−	2.38056e7i		−	0.502045i
$157$	−5.87990e7			−1.21261			−0.606305	−	0.795232i	$-0.707349\pi$
$157$	−5.87990e7			−1.21261			−0.606305	+	0.795232i	$0.707349\pi$
$158$	1.53848e7			0.310307
$159$	3.49645e7			0.689823
$160$	−1.42980e7			−0.275965
$161$		−	1.40525e7i		−	0.265377i
$162$		−	315333.i		−	0.00582730i
$163$		−	1.26762e7i		−	0.229262i	−0.993408	−	0.114631i	$-0.963431\pi$
$163$		−	1.26762e7i		−	0.229262i	0.993408	−	0.114631i	$-0.0365686\pi$
$164$	−2.62336e7			−0.464413
$165$		−	2.31048e7i		−	0.400414i
$166$			4.81277e7i			0.816615i
$167$		−	9.36878e7i		−	1.55659i	−0.627896	−	0.778297i	$-0.716084\pi$
$167$		−	9.36878e7i		−	1.55659i	0.627896	−	0.778297i	$-0.283916\pi$
$168$			3.21896e6i			0.0523762i
$169$	−1.04487e8			−1.66517
$170$			1.06001e8i			1.65477i
$171$		−	4.49221e7i		−	0.687027i
$172$			5.04048e7i			0.755304i
$173$	4.88075e7			0.716680			0.358340	−	0.933591i	$-0.383343\pi$
$173$	4.88075e7			0.716680			0.358340	+	0.933591i	$0.383343\pi$
$174$	−4.02642e7			−0.579424
$175$	2.45394e7			0.346123
$176$	−7.54056e6			−0.104258
$177$		−	4.53179e7i		−	0.614275i
$178$	−3.12717e7			−0.415606
$179$			2.42184e7i			0.315617i	0.987470	+	0.157808i	$0.0504429\pi$
$179$			2.42184e7i			0.315617i	−0.987470	+	0.157808i	$0.949557\pi$
$180$		−	3.79702e7i		−	0.485277i
$181$	1.16754e8			1.46351			0.731754	−	0.681569i	$-0.238702\pi$
$181$	1.16754e8			1.46351			0.731754	+	0.681569i	$0.238702\pi$
$182$	2.26134e7			0.278045
$183$			5.23767e7i			0.631771i
$184$	−3.29165e7			−0.389539
$185$	3.02566e7	−	1.30992e8i	0.351333	−	1.52105i
$186$	−3.48519e7			−0.397128
$187$			5.59035e7i			0.625163i
$188$	1.89219e7			0.207688
$189$	−2.22982e7			−0.240244
$190$		−	1.15328e8i		−	1.21983i
$191$		−	1.10950e8i		−	1.15216i	−0.817394	−	0.576079i	$-0.804582\pi$
$191$		−	1.10950e8i		−	1.15216i	0.817394	−	0.576079i	$-0.195418\pi$
$192$	7.54006e6			0.0768813
$193$			1.19713e8i			1.19864i	0.800508	+	0.599321i	$0.204563\pi$
$193$			1.19713e8i			1.19864i	−0.800508	+	0.599321i	$0.795437\pi$
$194$	−4.56091e7			−0.448482
$195$	1.62302e8			1.56748
$196$	4.96490e7			0.470993
$197$	−9.15350e7			−0.853013			−0.426506	−	0.904485i	$-0.640256\pi$
$197$	−9.15350e7			−0.853013			−0.426506	+	0.904485i	$0.640256\pi$
$198$		−	2.00250e7i		−	0.183335i
$199$			9.98548e7i			0.898221i	0.893476	+	0.449110i	$0.148259\pi$
$199$			9.98548e7i			0.898221i	−0.893476	+	0.449110i	$0.851741\pi$
$200$		−	5.74807e7i		−	0.508062i
$201$	−5.15469e7			−0.447730
$202$		−	2.96710e7i		−	0.253280i
$203$		−	3.82477e7i		−	0.320900i
$204$		−	5.58998e7i		−	0.461004i
$205$		−	1.78856e8i		−	1.44999i
$206$	−1.71917e8			−1.37020
$207$		−	8.74143e7i		−	0.684993i
$208$		−	5.29693e7i		−	0.408134i
$209$		−	6.08226e7i		−	0.460843i
$210$	−2.19463e7			−0.163528
$211$	3.14648e7			0.230588			0.115294	−	0.993331i	$-0.463219\pi$
$211$	3.14648e7			0.230588			0.115294	+	0.993331i	$0.463219\pi$
$212$	7.77988e7			0.560786
$213$	1.33910e8			0.949476
$214$			7.62003e7i			0.531507i
$215$	−3.43650e8			−2.35820
$216$			5.22309e7i			0.352646i
$217$		−	3.31065e7i		−	0.219940i
$218$	1.22503e8			0.800844
$219$	−1.11142e8			−0.715031
$220$		−	5.14101e7i		−	0.325513i
$221$	−3.92698e8			−2.44729
$222$	−1.59559e7	+	6.90787e7i	−0.0978781	+	0.423749i
$223$	1.79751e8			1.08544			0.542718	−	0.839915i	$-0.317395\pi$
$223$	1.79751e8			1.08544			0.542718	+	0.839915i	$0.317395\pi$
$224$			7.16245e6i			0.0425788i
$225$	1.52648e8			0.893413
$226$	1.14783e8			0.661450
$227$			2.38058e8i			1.35080i	0.737451	+	0.675401i	$0.236029\pi$
$227$			2.38058e8i			1.35080i	−0.737451	+	0.675401i	$0.763971\pi$
$228$			6.08185e7i			0.339832i
$229$	−8.07491e7			−0.444338			−0.222169	−	0.975008i	$-0.571314\pi$
$229$	−8.07491e7			−0.444338			−0.222169	+	0.975008i	$0.571314\pi$
$230$		−	2.24418e8i		−	1.21621i
$231$	−1.15742e7			−0.0617800
$232$	−8.95909e7			−0.471038
$233$	−2.38358e8			−1.23448			−0.617241	−	0.786774i	$-0.711750\pi$
$233$	−2.38358e8			−1.23448			−0.617241	+	0.786774i	$0.711750\pi$
$234$	1.40667e8			0.717691
$235$			1.29006e8i			0.648442i
$236$		−	1.00836e8i		−	0.499370i
$237$		−	5.53142e7i		−	0.269909i
$238$	5.31002e7			0.255315
$239$			5.17075e7i			0.244997i	0.992469	+	0.122499i	$0.0390907\pi$
$239$			5.17075e7i			0.244997i	−0.992469	+	0.122499i	$0.960909\pi$
$240$			5.14066e7i			0.240038i
$241$			1.59716e8i			0.735004i	0.930023	+	0.367502i	$0.119787\pi$
$241$			1.59716e8i			0.735004i	−0.930023	+	0.367502i	$0.880213\pi$
$242$			1.28784e8i			0.584130i
$243$	−2.24237e8			−1.00250
$244$			1.16542e8i			0.513593i
$245$			3.38497e8i			1.47053i
$246$			9.43198e7i			0.403952i
$247$	4.27253e8			1.80404
$248$	−7.75482e7			−0.322842
$249$	1.73038e8			0.710301
$250$	1.19180e8			0.482406
$251$		−	6.61845e7i		−	0.264179i	−0.991238	−	0.132089i	$-0.957831\pi$
$251$		−	6.61845e7i		−	0.264179i	0.991238	−	0.132089i	$-0.0421686\pi$
$252$	−1.90209e7			−0.0748736
$253$		−	1.18355e8i		−	0.459479i
$254$			2.31103e8i			0.884886i
$255$	3.81113e8			1.43934
$256$	1.67772e7			0.0625000
$257$		−	7.17539e7i		−	0.263682i	−0.991271	−	0.131841i	$-0.957911\pi$
$257$		−	7.17539e7i		−	0.263682i	0.991271	−	0.131841i	$-0.0420888\pi$
$258$	1.81224e8			0.656973
$259$	−6.56191e7	−	1.51568e7i	−0.234683	−	0.0542074i
$260$	3.61134e8			1.27427
$261$		−	2.37921e8i		−	0.828307i
$262$	3.58175e8			1.23038
$263$	7.59401e6			0.0257410			0.0128705	−	0.999917i	$-0.495903\pi$
$263$	7.59401e6			0.0257410			0.0128705	+	0.999917i	$0.495903\pi$
$264$			2.71112e7i			0.0906849i
$265$			5.30417e8i			1.75088i
$266$	−5.77727e7			−0.188207
$267$			1.12434e8i			0.361499i
$268$	−1.14696e8			−0.363978
$269$	1.82568e8			0.571862			0.285931	−	0.958250i	$-0.407697\pi$
$269$	1.82568e8			0.571862			0.285931	+	0.958250i	$0.407697\pi$
$270$	−3.56100e8			−1.10103
$271$	−4.66628e8			−1.42422			−0.712111	−	0.702067i	$-0.752261\pi$
$271$	−4.66628e8			−1.42422			−0.712111	+	0.702067i	$0.752261\pi$
$272$		−	1.24381e8i		−	0.374769i
$273$		−	8.13037e7i		−	0.241847i
$274$			1.46129e8i			0.429150i
$275$	2.06679e8			0.599282
$276$			1.18347e8i			0.338826i
$277$			2.68840e8i			0.760001i	0.924986	+	0.380000i	$0.124076\pi$
$277$			2.68840e8i			0.760001i	−0.924986	+	0.380000i	$0.875924\pi$
$278$		−	8.73364e7i		−	0.243803i
$279$		−	2.05940e8i		−	0.567709i
$280$	−4.88321e7			−0.132939
$281$		−	1.29698e8i		−	0.348707i	−0.984683	−	0.174354i	$-0.944216\pi$
$281$		−	1.29698e8i		−	0.348707i	0.984683	−	0.174354i	$-0.0557835\pi$
$282$		−	6.80314e7i		−	0.180650i
$283$			2.36416e8i			0.620046i	0.950729	+	0.310023i	$0.100337\pi$
$283$			2.36416e8i			0.620046i	−0.950729	+	0.310023i	$0.899663\pi$
$284$	2.97960e8			0.771869
$285$	−4.14649e8			−1.06102
$286$	1.90457e8			0.481412
$287$	−8.95962e7			−0.223719
$288$			4.45542e7i			0.109904i
$289$	−5.11787e8			−1.24723
$290$		−	6.10813e8i		−	1.47067i
$291$			1.63982e8i			0.390095i
$292$	−2.47300e8			−0.581278
$293$	−3.90253e8			−0.906377			−0.453189	−	0.891415i	$-0.649714\pi$
$293$	−3.90253e8			−0.906377			−0.453189	+	0.891415i	$0.649714\pi$
$294$		−	1.78507e8i		−	0.409675i
$295$	6.87478e8			1.55913
$296$	−3.55031e7	+	1.53705e8i	−0.0795692	+	0.344483i
$297$	−1.87803e8			−0.415962
$298$			1.01481e7i			0.0222140i
$299$	8.31395e8			1.79870
$300$	−2.06665e8			−0.441919
$301$			1.72148e8i			0.363848i
$302$		−	1.41705e8i		−	0.296048i
$303$	−1.06678e8			−0.220306
$304$			1.35326e8i			0.276263i
$305$	−7.94562e8			−1.60353
$306$	3.30312e8			0.659021
$307$	−6.71676e8			−1.32488			−0.662438	−	0.749117i	$-0.730478\pi$
$307$	−6.71676e8			−1.32488			−0.662438	+	0.749117i	$0.730478\pi$
$308$	−2.57534e7			−0.0502236
$309$			6.18106e8i			1.19181i
$310$		−	5.28708e8i		−	1.00798i
$311$		−	9.56792e8i		−	1.80367i	−0.432084	−	0.901833i	$-0.642222\pi$
$311$		−	9.56792e8i		−	1.80367i	0.432084	−	0.901833i	$-0.357778\pi$
$312$	−1.90445e8			−0.354999
$313$		−	1.79700e8i		−	0.331240i	−0.986190	−	0.165620i	$-0.947038\pi$
$313$		−	1.79700e8i		−	0.331240i	0.986190	−	0.165620i	$-0.0529625\pi$
$314$			4.70392e8i			0.857445i
$315$		−	1.29681e8i		−	0.233769i
$316$		−	1.23078e8i		−	0.219420i
$317$	−1.12099e8			−0.197648			−0.0988242	−	0.995105i	$-0.531508\pi$
$317$	−1.12099e8			−0.197648			−0.0988242	+	0.995105i	$0.531508\pi$
$318$		−	2.79716e8i		−	0.487779i
$319$		−	3.22135e8i		−	0.555611i
$320$			1.14384e8i			0.195137i
$321$	2.73969e8			0.462311
$322$	−1.12420e8			−0.187650
$323$	1.00327e9			1.65656
$324$	−2.52267e6			−0.00412052
$325$			1.45183e9i			2.34598i
$326$	−1.01410e8			−0.162113
$327$		−	4.40444e8i		−	0.696584i
$328$			2.09869e8i			0.328390i
$329$	6.46243e7			0.100048
$330$	−1.84839e8			−0.283135
$331$		−	3.25801e8i		−	0.493804i	−0.969040	−	0.246902i	$-0.920587\pi$
$331$		−	3.25801e8i		−	0.493804i	0.969040	−	0.246902i	$-0.0794125\pi$
$332$	3.85022e8			0.577434
$333$	−4.08186e8	−	9.42834e7i	−0.605764	−	0.139920i
$334$	−7.49502e8			−1.10068
$335$		−	7.81973e8i		−	1.13641i
$336$	2.57517e7			0.0370355
$337$	1.02095e9			1.45311			0.726557	−	0.687106i	$-0.241119\pi$
$337$	1.02095e9			1.45311			0.726557	+	0.687106i	$0.241119\pi$
$338$			8.35894e8i			1.17745i
$339$		−	4.12688e8i		−	0.575338i
$340$	8.48007e8			1.17010
$341$		−	2.78834e8i		−	0.380807i
$342$	−3.59377e8			−0.485801
$343$	3.49578e8			0.467750
$344$	4.03238e8			0.534081
$345$	−8.06868e8			−1.05788
$346$		−	3.90460e8i		−	0.506769i
$347$		−	1.70646e8i		−	0.219252i	−0.993973	−	0.109626i	$-0.965035\pi$
$347$		−	1.70646e8i		−	0.219252i	0.993973	−	0.109626i	$-0.0349653\pi$
$348$			3.22113e8i			0.409715i
$349$	−1.45367e9			−1.83054			−0.915268	−	0.402846i	$-0.868021\pi$
$349$	−1.45367e9			−1.83054			−0.915268	+	0.402846i	$0.868021\pi$
$350$		−	1.96315e8i		−	0.244746i
$351$		−	1.31923e9i		−	1.62835i
$352$			6.03245e7i			0.0737216i
$353$		−	9.61016e8i		−	1.16284i	−0.813604	−	0.581419i	$-0.802498\pi$
$353$		−	9.61016e8i		−	1.16284i	0.813604	−	0.581419i	$-0.197502\pi$
$354$	−3.62543e8			−0.434358
$355$			2.03143e9i			2.40992i
$356$			2.50174e8i			0.293878i
$357$		−	1.90916e8i		−	0.222076i
$358$	1.93747e8			0.223175
$359$	−9.30279e8			−1.06116			−0.530582	−	0.847634i	$-0.678027\pi$
$359$	−9.30279e8			−1.06116			−0.530582	+	0.847634i	$0.678027\pi$
$360$	−3.03762e8			−0.343143
$361$	−1.97675e8			−0.221144
$362$		−	9.34028e8i		−	1.03486i
$363$	4.63029e8			0.508083
$364$		−	1.80907e8i		−	0.196608i
$365$		−	1.68604e9i		−	1.81486i
$366$	4.19014e8			0.446729
$367$	1.15126e9			1.21574			0.607871	−	0.794036i	$-0.292024\pi$
$367$	1.15126e9			1.21574			0.607871	+	0.794036i	$0.292024\pi$
$368$			2.63332e8i			0.275446i
$369$	−5.57336e8			−0.577464
$370$	−1.04793e9	−	2.42053e8i	−1.07554	−	0.248430i
$371$	2.65708e8			0.270144
$372$			2.78815e8i			0.280812i
$373$	−2.06569e8			−0.206103			−0.103052	−	0.994676i	$-0.532861\pi$
$373$	−2.06569e8			−0.206103			−0.103052	+	0.994676i	$0.532861\pi$
$374$	4.47228e8			0.442057
$375$		−	4.28497e8i		−	0.419603i
$376$		−	1.51375e8i		−	0.146858i
$377$	2.26286e9			2.17502
$378$			1.78385e8i			0.169878i
$379$	−4.39269e8			−0.414470			−0.207235	−	0.978291i	$-0.566446\pi$
$379$	−4.39269e8			−0.414470			−0.207235	+	0.978291i	$0.566446\pi$
$380$	−9.22625e8			−0.862547
$381$	8.30903e8			0.769685
$382$	−8.87604e8			−0.814699
$383$			7.09553e8i			0.645341i	0.946511	+	0.322670i	$0.104581\pi$
$383$			7.09553e8i			0.645341i	−0.946511	+	0.322670i	$0.895419\pi$
$384$		−	6.03205e7i		−	0.0543633i
$385$		−	1.75582e8i		−	0.156808i
$386$	9.57702e8			0.847569
$387$			1.07085e9i			0.939166i
$388$			3.64872e8i			0.317125i
$389$			8.64007e8i			0.744207i	0.928191	+	0.372103i	$0.121363\pi$
$389$			8.64007e8i			0.744207i	−0.928191	+	0.372103i	$0.878637\pi$
$390$		−	1.29841e9i		−	1.10838i
$391$	1.95226e9			1.65166
$392$		−	3.97192e8i		−	0.333042i
$393$		−	1.28778e9i		−	1.07020i
$394$			7.32280e8i			0.603171i
$395$	8.39124e8			0.685072
$396$	−1.60200e8			−0.129637
$397$	−1.34008e9			−1.07489			−0.537446	−	0.843298i	$-0.680611\pi$
$397$	−1.34008e9			−1.07489			−0.537446	+	0.843298i	$0.680611\pi$
$398$	7.98838e8			0.635138
$399$			2.07715e8i			0.163705i
$400$	−4.59846e8			−0.359254
$401$			1.06440e9i			0.824325i	0.911110	+	0.412163i	$0.135226\pi$
$401$			1.06440e9i			0.824325i	−0.911110	+	0.412163i	$0.864774\pi$
$402$			4.12375e8i			0.316593i
$403$	1.95869e9			1.49073
$404$	−2.37368e8			−0.179096
$405$		−	1.71990e7i		−	0.0128651i
$406$	−3.05982e8			−0.226910
$407$	−5.52666e8	−	1.27656e8i	−0.406334	−	0.0938555i
$408$	−4.47198e8			−0.325979
$409$			4.76556e8i			0.344415i	0.985061	+	0.172207i	$0.0550900\pi$
$409$			4.76556e8i			0.344415i	−0.985061	+	0.172207i	$0.944910\pi$
$410$	−1.43084e9			−1.02530
$411$	5.25389e8			0.373280
$412$			1.37533e9i			0.968876i
$413$		−	3.44386e8i		−	0.240559i
$414$	−6.99314e8			−0.484363
$415$			2.62500e9i			1.80286i
$416$	−4.23754e8			−0.288594
$417$	−3.14008e8			−0.212063
$418$	−4.86581e8			−0.325865
$419$	5.54660e8			0.368365			0.184182	−	0.982892i	$-0.441036\pi$
$419$	5.54660e8			0.368365			0.184182	+	0.982892i	$0.441036\pi$
$420$			1.75570e8i			0.115632i
$421$		−	9.45381e8i		−	0.617475i	−0.951147	−	0.308737i	$-0.900094\pi$
$421$		−	9.45381e8i		−	0.617475i	0.951147	−	0.308737i	$-0.0999065\pi$
$422$		−	2.51718e8i		−	0.163050i
$423$	4.01998e8			0.258245
$424$		−	6.22390e8i		−	0.396536i
$425$			3.40916e9i			2.15420i
$426$		−	1.07128e9i		−	0.671381i
$427$			3.98029e8i			0.247410i
$428$	6.09603e8			0.375832
$429$		−	6.84767e8i		−	0.418738i
$430$			2.74920e9i			1.66750i
$431$		−	3.43105e8i		−	0.206423i	−0.994659	−	0.103211i	$-0.967088\pi$
$431$		−	3.43105e8i		−	0.206423i	0.994659	−	0.103211i	$-0.0329118\pi$
$432$	4.17847e8			0.249359
$433$	1.81746e9			1.07587			0.537933	−	0.842988i	$-0.319205\pi$
$433$	1.81746e9			1.07587			0.537933	+	0.842988i	$0.319205\pi$
$434$	−2.64852e8			−0.155521
$435$	−2.19611e9			−1.27921
$436$		−	9.80022e8i		−	0.566282i
$437$	−2.12405e9			−1.21753
$438$			8.89138e8i			0.505603i
$439$			2.60960e9i			1.47214i	0.676907	+	0.736068i	$0.263320\pi$
$439$			2.60960e9i			1.47214i	−0.676907	+	0.736068i	$0.736680\pi$
$440$	−4.11281e8			−0.230173
$441$	1.05480e9			0.585645
$442$			3.14159e9i			1.73050i
$443$	−9.37318e8			−0.512241			−0.256120	−	0.966645i	$-0.582444\pi$
$443$	−9.37318e8			−0.512241			−0.256120	+	0.966645i	$0.582444\pi$
$444$	5.52629e8	+	1.27647e8i	0.299636	+	0.0692103i
$445$	−1.70563e9			−0.917541
$446$		−	1.43801e9i		−	0.767520i
$447$	3.64861e7			0.0193220
$448$	5.72996e7			0.0301077
$449$			7.81078e8i			0.407223i	0.979052	+	0.203611i	$0.0652679\pi$
$449$			7.81078e8i			0.407223i	−0.979052	+	0.203611i	$0.934732\pi$
$450$		−	1.22118e9i		−	0.631738i
$451$	−7.54609e8			−0.387350
$452$		−	9.18262e8i		−	0.467716i
$453$	−5.09484e8			−0.257506
$454$	1.90446e9			0.955161
$455$	1.23339e9			0.613847
$456$	4.86548e8			0.240297
$457$		−	2.36363e9i		−	1.15844i	−0.815172	−	0.579219i	$-0.803358\pi$
$457$		−	2.36363e9i		−	1.15844i	0.815172	−	0.579219i	$-0.196642\pi$
$458$			6.45993e8i			0.314194i
$459$		−	3.09780e9i		−	1.49523i
$460$	−1.79534e9			−0.859993
$461$			9.03045e8i			0.429295i	0.976692	+	0.214648i	$0.0688603\pi$
$461$			9.03045e8i			0.429295i	−0.976692	+	0.214648i	$0.931140\pi$
$462$			9.25934e7i			0.0436851i
$463$			3.74807e9i			1.75499i	0.479587	+	0.877494i	$0.340787\pi$
$463$			3.74807e9i			1.75499i	−0.479587	+	0.877494i	$0.659213\pi$
$464$			7.16727e8i			0.333074i
$465$	−1.90091e9			−0.876749
$466$			1.90687e9i			0.872911i
$467$		−	3.57109e9i		−	1.62253i	−0.584680	−	0.811264i	$-0.698780\pi$
$467$		−	3.57109e9i		−	1.62253i	0.584680	−	0.811264i	$-0.301220\pi$
$468$		−	1.12534e9i		−	0.507484i
$469$	−3.91723e8			−0.175337
$470$	1.03205e9			0.458518
$471$	1.69124e9			0.745816
$472$	−8.06686e8			−0.353108
$473$			1.44989e9i			0.629972i
$474$	−4.42514e8			−0.190855
$475$		−	3.70914e9i		−	1.58798i
$476$		−	4.24802e8i		−	0.180535i
$477$	1.65284e9			0.697296
$478$	4.13660e8			0.173239
$479$		−	2.27997e9i		−	0.947884i	−0.880556	−	0.473942i	$-0.842831\pi$
$479$		−	2.27997e9i		−	0.947884i	0.880556	−	0.473942i	$-0.157169\pi$
$480$	4.11253e8			0.169732
$481$	8.96727e8	−	3.88225e9i	0.367411	−	1.59065i
$482$	1.27773e9			0.519726
$483$			4.04194e8i			0.163220i
$484$	1.03027e9			0.413042
$485$	−2.48763e9			−0.990123
$486$			1.79390e9i			0.708877i
$487$			4.56730e9i			1.79188i	0.444176	+	0.895939i	$0.353496\pi$
$487$			4.56730e9i			1.79188i	−0.444176	+	0.895939i	$0.646504\pi$
$488$	9.32338e8			0.363165
$489$			3.64606e8i			0.141008i
$490$	2.70798e9			1.03982
$491$	−3.07909e9			−1.17392			−0.586959	−	0.809617i	$-0.699675\pi$
$491$	−3.07909e9			−1.17392			−0.586959	+	0.809617i	$0.699675\pi$
$492$	7.54558e8			0.285637
$493$	5.31360e9			1.99722
$494$		−	3.41802e9i		−	1.27565i
$495$		−	1.09221e9i		−	0.404752i
$496$			6.20385e8i			0.228284i
$497$	1.01763e9			0.371828
$498$		−	1.38430e9i		−	0.502259i
$499$		−	1.58219e9i		−	0.570040i	−0.958522	−	0.285020i	$-0.908000\pi$
$499$		−	1.58219e9i		−	0.570040i	0.958522	−	0.285020i	$-0.0920003\pi$
$500$		−	9.53439e8i		−	0.341113i
$501$			2.69475e9i			0.957383i
$502$	−5.29476e8			−0.186803
$503$			1.70666e9i			0.597941i	0.954262	+	0.298971i	$0.0966432\pi$
$503$			1.70666e9i			0.597941i	−0.954262	+	0.298971i	$0.903357\pi$
$504$			1.52167e8i			0.0529436i
$505$		−	1.61833e9i		−	0.559173i
$506$	−9.46841e8			−0.324900
$507$	3.00536e9			1.02416
$508$	1.84882e9			0.625709
$509$	−9.57264e8			−0.321751			−0.160875	−	0.986975i	$-0.551432\pi$
$509$	−9.57264e8			−0.321751			−0.160875	+	0.986975i	$0.551432\pi$
$510$		−	3.04891e9i		−	1.01777i
$511$	−8.44609e8			−0.280016
$512$		−	1.34218e8i		−	0.0441942i
$513$			3.37038e9i			1.10222i
$514$	−5.74032e8			−0.186451
$515$	−9.37676e9			−3.02501
$516$		−	1.44979e9i		−	0.464550i
$517$	5.44288e8			0.173225
$518$	−1.21254e8	+	5.24953e8i	−0.0383304	+	0.165946i
$519$	−1.40385e9			−0.440794
$520$		−	2.88907e9i		−	0.901045i
$521$	−5.57028e9			−1.72562			−0.862809	−	0.505530i	$-0.831297\pi$
$521$	−5.57028e9			−1.72562			−0.862809	+	0.505530i	$0.831297\pi$
$522$	−1.90337e9			−0.585702
$523$		−	2.23662e9i		−	0.683652i	−0.939763	−	0.341826i	$-0.888955\pi$
$523$		−	2.23662e9i		−	0.683652i	0.939763	−	0.341826i	$-0.111045\pi$
$524$		−	2.86540e9i		−	0.870013i
$525$	−7.05827e8			−0.212883
$526$		−	6.07521e7i		−	0.0182017i
$527$	4.59935e9			1.36886
$528$	2.16890e8			0.0641239
$529$	−7.28375e8			−0.213924
$530$	4.24333e9			1.23806
$531$		−	2.14227e9i		−	0.620930i
$532$			4.62181e8i			0.133083i
$533$		−	5.30081e9i		−	1.51634i
$534$	8.99469e8			0.255618
$535$			4.15615e9i			1.17342i
$536$			9.17566e8i			0.257372i
$537$		−	6.96596e8i		−	0.194120i
$538$		−	1.46054e9i		−	0.404367i
$539$	1.42815e9			0.392838
$540$			2.84880e9i			0.778545i
$541$		−	4.43925e9i		−	1.20537i	−0.797980	−	0.602683i	$-0.794098\pi$
$541$		−	4.43925e9i		−	1.20537i	0.797980	−	0.602683i	$-0.205902\pi$
$542$			3.73302e9i			1.00708i
$543$	−3.35819e9			−0.900130
$544$	−9.95050e8			−0.265002
$545$	6.68159e9			1.76804
$546$	−6.50429e8			−0.171012
$547$		−	4.17743e9i		−	1.09132i	−0.838005	−	0.545662i	$-0.816278\pi$
$547$		−	4.17743e9i		−	1.09132i	0.838005	−	0.545662i	$-0.183722\pi$
$548$	1.16903e9			0.303455
$549$			2.47595e9i			0.638615i
$550$		−	1.65343e9i		−	0.423757i
$551$	−5.78116e9			−1.47226
$552$	9.46778e8			0.239586
$553$		−	4.20352e8i		−	0.105700i
$554$	2.15072e9			0.537402
$555$	−8.70273e8	+	3.76772e9i	−0.216088	+	0.935520i
$556$	−6.98691e8			−0.172395
$557$			5.93601e9i			1.45546i	0.685862	+	0.727732i	$0.259426\pi$
$557$			5.93601e9i			1.45546i	−0.685862	+	0.727732i	$0.740574\pi$
$558$	−1.64752e9			−0.401431
$559$	−1.01849e10			−2.46612
$560$			3.90657e8i			0.0940021i
$561$		−	1.60795e9i		−	0.384507i
$562$	−1.03758e9			−0.246573
$563$			1.57174e9i			0.371193i	0.982626	+	0.185597i	$0.0594218\pi$
$563$			1.57174e9i			0.371193i	−0.982626	+	0.185597i	$0.940578\pi$
$564$	−5.44251e8			−0.127739
$565$	6.26053e9			1.46030
$566$	1.89133e9			0.438439
$567$	−8.61571e6			−0.00198495
$568$		−	2.38368e9i		−	0.545794i
$569$			3.01120e9i			0.685246i	0.939473	+	0.342623i	$0.111315\pi$
$569$			3.01120e9i			0.685246i	−0.939473	+	0.342623i	$0.888685\pi$
$570$			3.31719e9i			0.750254i
$571$	7.33216e8			0.164818			0.0824091	−	0.996599i	$-0.473739\pi$
$571$	7.33216e8			0.164818			0.0824091	+	0.996599i	$0.473739\pi$
$572$		−	1.52366e9i		−	0.340410i
$573$			3.19127e9i			0.708635i
$574$			7.16769e8i			0.158193i
$575$		−	7.21764e9i		−	1.58328i
$576$	3.56434e8			0.0777142
$577$		−	5.37612e9i		−	1.16507i	−0.812804	−	0.582537i	$-0.802060\pi$
$577$		−	5.37612e9i		−	1.16507i	0.812804	−	0.582537i	$-0.197940\pi$
$578$			4.09430e9i			0.881926i
$579$		−	3.44330e9i		−	0.737225i
$580$	−4.88651e9			−1.03992
$581$	1.31497e9			0.278164
$582$	1.31186e9			0.275839
$583$	2.23788e9			0.467732
$584$			1.97840e9i			0.411026i
$585$	7.67233e9			1.58446
$586$			3.12202e9i			0.640906i
$587$		−	2.99981e8i		−	0.0612153i	−0.999531	−	0.0306077i	$-0.990256\pi$
$587$		−	2.99981e8i		−	0.0612153i	0.999531	−	0.0306077i	$-0.00974425\pi$
$588$	−1.42806e9			−0.289684
$589$	−5.00406e9			−1.00906
$590$		−	5.49983e9i		−	1.10247i
$591$	2.63283e9			0.524646
$592$	1.22964e9	+	2.84025e8i	0.243586	+	0.0562639i
$593$	−2.79615e9			−0.550642			−0.275321	−	0.961352i	$-0.588784\pi$
$593$	−2.79615e9			−0.550642			−0.275321	+	0.961352i	$0.588784\pi$
$594$			1.50242e9i			0.294130i
$595$	2.89622e9			0.563665
$596$	8.11845e7			0.0157077
$597$		−	2.87213e9i		−	0.552451i
$598$		−	6.65116e9i		−	1.27187i
$599$	−2.36453e9			−0.449521			−0.224761	−	0.974414i	$-0.572160\pi$
$599$	−2.36453e9			−0.449521			−0.224761	+	0.974414i	$0.572160\pi$
$600$			1.65332e9i			0.312484i
$601$	3.28860e9			0.617946			0.308973	−	0.951071i	$-0.400015\pi$
$601$	3.28860e9			0.617946			0.308973	+	0.951071i	$0.400015\pi$
$602$	1.37719e9			0.257280
$603$	−2.43673e9			−0.452581
$604$	−1.13364e9			−0.209337
$605$			7.02421e9i			1.28960i
$606$			8.53427e8i			0.155780i
$607$		−	6.04149e8i		−	0.109644i	−0.998496	−	0.0548218i	$-0.982541\pi$
$607$		−	6.04149e8i		−	0.109644i	0.998496	−	0.0548218i	$-0.0174591\pi$
$608$	1.08261e9			0.195348
$609$			1.10012e9i			0.197369i
$610$			6.35649e9i			1.13387i
$611$			3.82339e9i			0.678117i
$612$		−	2.64249e9i		−	0.465998i
$613$	4.36468e9			0.765316			0.382658	−	0.923890i	$-0.375009\pi$
$613$	4.36468e9			0.765316			0.382658	+	0.923890i	$0.375009\pi$
$614$			5.37340e9i			0.936829i
$615$			5.14443e9i			0.891814i
$616$			2.06028e8i			0.0355134i
$617$	−6.38337e9			−1.09409			−0.547043	−	0.837104i	$-0.684247\pi$
$617$	−6.38337e9			−1.09409			−0.547043	+	0.837104i	$0.684247\pi$
$618$	4.94485e9			0.842740
$619$	−9.91019e9			−1.67944			−0.839720	−	0.543019i	$-0.817281\pi$
$619$	−9.91019e9			−1.67944			−0.839720	+	0.543019i	$0.817281\pi$
$620$	−4.22966e9			−0.712746
$621$			6.55845e9i			1.09896i
$622$	−7.65434e9			−1.27538
$623$			8.54423e8i			0.141568i
$624$			1.52356e9i			0.251023i
$625$	−2.27050e9			−0.371998
$626$	−1.43760e9			−0.234222
$627$			1.74944e9i			0.283441i
$628$	3.76314e9			0.606305
$629$	2.10567e9	−	9.11621e9i	0.337376	−	1.46062i
$630$	−1.03744e9			−0.165300
$631$		−	2.21176e9i		−	0.350457i	−0.984528	−	0.175229i	$-0.943934\pi$
$631$		−	2.21176e9i		−	0.350457i	0.984528	−	0.175229i	$-0.0560664\pi$
$632$	−9.84627e8			−0.155154
$633$	−9.05023e8			−0.141823
$634$			8.96790e8i			0.139759i
$635$			1.26049e10i			1.95358i
$636$	−2.23773e9			−0.344911
$637$			1.00322e10i			1.53782i
$638$	−2.57708e9			−0.392876
$639$	6.33019e9			0.959763
$640$	9.15070e8			0.137983
$641$	1.11059e10			1.66553			0.832765	−	0.553627i	$-0.186757\pi$
$641$	1.11059e10			1.66553			0.832765	+	0.553627i	$0.186757\pi$
$642$		−	2.19175e9i		−	0.326903i
$643$			5.30577e9i			0.787064i	0.919311	+	0.393532i	$0.128747\pi$
$643$			5.30577e9i			0.787064i	−0.919311	+	0.393532i	$0.871253\pi$
$644$			8.99362e8i			0.132689i
$645$	9.88441e9			1.45041
$646$		−	8.02613e9i		−	1.17137i
$647$		−	6.79329e9i		−	0.986087i	−0.870005	−	0.493044i	$-0.835884\pi$
$647$		−	6.79329e9i		−	0.986087i	0.870005	−	0.493044i	$-0.164116\pi$
$648$			2.01813e7i			0.00291365i
$649$		−	2.90054e9i		−	0.416507i
$650$	1.16146e10			1.65886
$651$			9.52243e8i			0.135274i
$652$			8.11277e8i			0.114631i
$653$		−	2.34434e9i		−	0.329477i	−0.986337	−	0.164739i	$-0.947322\pi$
$653$		−	2.34434e9i		−	0.329477i	0.986337	−	0.164739i	$-0.0526780\pi$
$654$	−3.52355e9			−0.492559
$655$	1.95357e10			2.71635
$656$	1.67895e9			0.232207
$657$	−5.25392e9			−0.722777
$658$		−	5.16995e8i		−	0.0707449i
$659$	4.06443e9			0.553224			0.276612	−	0.960982i	$-0.410788\pi$
$659$	4.06443e9			0.553224			0.276612	+	0.960982i	$0.410788\pi$
$660$			1.47871e9i			0.200207i
$661$		−	9.48531e9i		−	1.27746i	−0.769432	−	0.638729i	$-0.779461\pi$
$661$		−	9.48531e9i		−	1.27746i	0.769432	−	0.638729i	$-0.220539\pi$
$662$	−2.60641e9			−0.349172
$663$	1.12952e10			1.50521
$664$		−	3.08017e9i		−	0.408307i
$665$	−3.15106e9			−0.415510
$666$	−7.54267e8	+	3.26549e9i	−0.0989385	+	0.428340i
$667$	−1.12496e10			−1.46790
$668$			5.99602e9i			0.778297i
$669$	−5.17019e9			−0.667598
$670$	−6.25579e9			−0.803563
$671$			3.35233e9i			0.428369i
$672$		−	2.06014e8i		−	0.0261881i
$673$	1.24228e10			1.57097			0.785484	−	0.618882i	$-0.212414\pi$
$673$	1.24228e10			1.57097			0.785484	+	0.618882i	$0.212414\pi$
$674$		−	8.16760e9i		−	1.02751i
$675$	−1.14528e10			−1.43333
$676$	6.68715e9			0.832584
$677$	3.71661e9			0.460349			0.230174	−	0.973149i	$-0.426070\pi$
$677$	3.71661e9			0.460349			0.230174	+	0.973149i	$0.426070\pi$
$678$	−3.30150e9			−0.406825
$679$			1.24616e9i			0.152767i
$680$		−	6.78406e9i		−	0.827386i
$681$		−	6.84726e9i		−	0.830810i
$682$	−2.23067e9			−0.269271
$683$			1.01237e10i			1.21581i	0.794008	+	0.607907i	$0.207991\pi$
$683$			1.01237e10i			1.21581i	−0.794008	+	0.607907i	$0.792009\pi$
$684$			2.87501e9i			0.343513i
$685$			7.97022e9i			0.947444i
$686$		−	2.79662e9i		−	0.330750i
$687$	2.32259e9			0.273290
$688$		−	3.22590e9i		−	0.377652i
$689$			1.57202e10i			1.83100i
$690$			6.45494e9i			0.748033i
$691$	−4.47449e9			−0.515905			−0.257953	−	0.966158i	$-0.583048\pi$
$691$	−4.47449e9			−0.515905			−0.257953	+	0.966158i	$0.583048\pi$
$692$	−3.12368e9			−0.358340
$693$	−5.47135e8			−0.0624494
$694$	−1.36517e9			−0.155034
$695$		−	4.76354e9i		−	0.538249i
$696$	2.57691e9			0.289712
$697$		−	1.24472e10i		−	1.39238i
$698$			1.16294e10i			1.29438i
$699$	6.85591e9			0.759268
$700$	−1.57052e9			−0.173061
$701$		−	7.55194e9i		−	0.828029i	−0.910270	−	0.414015i	$-0.864126\pi$
$701$		−	7.55194e9i		−	0.828029i	0.910270	−	0.414015i	$-0.135874\pi$
$702$	−1.05539e10			−1.15141
$703$	−2.29096e9	+	9.91837e9i	−0.248699	+	1.07670i
$704$	4.82596e8			0.0521290
$705$		−	3.71060e9i		−	0.398825i
$706$	−7.68813e9			−0.822251
$707$	−8.10687e8			−0.0862750
$708$			2.90034e9i			0.307138i
$709$		−	1.16486e10i		−	1.22747i	−0.789511	−	0.613737i	$-0.789666\pi$
$709$		−	1.16486e10i		−	1.22747i	0.789511	−	0.613737i	$-0.210334\pi$
$710$	1.62515e10			1.70407
$711$		−	2.61481e9i		−	0.272833i
$712$	2.00139e9			0.207803
$713$	−9.73744e9			−1.00608
$714$	−1.52732e9			−0.157032
$715$	1.03880e10			1.06282
$716$		−	1.54998e9i		−	0.157808i
$717$		−	1.48727e9i		−	0.150686i
$718$			7.44223e9i			0.750356i
$719$	−1.79202e10			−1.79801			−0.899004	−	0.437940i	$-0.855708\pi$
$719$	−1.79202e10			−1.79801			−0.899004	+	0.437940i	$0.855708\pi$
$720$			2.43010e9i			0.242638i
$721$			4.69721e9i			0.466731i
$722$			1.58140e9i			0.156373i
$723$		−	4.59393e9i		−	0.452064i
$724$	−7.47222e9			−0.731754
$725$		−	1.96447e10i		−	1.91453i
$726$		−	3.70423e9i		−	0.359269i
$727$		−	1.09431e10i		−	1.05626i	−0.849164	−	0.528130i	$-0.822893\pi$
$727$		−	1.09431e10i		−	1.05626i	0.849164	−	0.528130i	$-0.177107\pi$
$728$	−1.44726e9			−0.139023
$729$	6.36354e9			0.608349
$730$	−1.34883e10			−1.28330
$731$	−2.39159e10			−2.26452
$732$		−	3.35211e9i		−	0.315885i
$733$	−9.29078e8			−0.0871341			−0.0435670	−	0.999051i	$-0.513872\pi$
$733$	−9.29078e8			−0.0871341			−0.0435670	+	0.999051i	$0.513872\pi$
$734$		−	9.21006e9i		−	0.859659i
$735$		−	9.73620e9i		−	0.904449i
$736$	2.10665e9			0.194769
$737$	−3.29922e9			−0.303581
$738$			4.45869e9i			0.408329i
$739$	1.02307e10			0.932498			0.466249	−	0.884653i	$-0.345605\pi$
$739$	1.02307e10			0.932498			0.466249	+	0.884653i	$0.345605\pi$
$740$	−1.93642e9	+	8.38346e9i	−0.175667	+	0.760523i
$741$	−1.22891e10			−1.10957
$742$		−	2.12566e9i		−	0.191021i
$743$	−1.88814e10			−1.68878			−0.844390	−	0.535730i	$-0.820037\pi$
$743$	−1.88814e10			−1.68878			−0.844390	+	0.535730i	$0.820037\pi$
$744$	2.23052e9			0.198564
$745$			5.53500e8i			0.0490423i
$746$			1.65256e9i			0.145737i
$747$	8.17983e9			0.717997
$748$		−	3.57782e9i		−	0.312582i
$749$	2.08199e9			0.181047
$750$	−3.42798e9			−0.296704
$751$	5.17118e9			0.445502			0.222751	−	0.974875i	$-0.428496\pi$
$751$	5.17118e9			0.445502			0.222751	+	0.974875i	$0.428496\pi$
$752$	−1.21100e9			−0.103844
$753$			1.90367e9i			0.162483i
$754$		−	1.81029e10i		−	1.53797i
$755$		−	7.72894e9i		−	0.653591i
$756$	1.42708e9			0.120122
$757$		−	2.05037e10i		−	1.71790i	−0.512061	−	0.858949i	$-0.671118\pi$
$757$		−	2.05037e10i		−	1.71790i	0.512061	−	0.858949i	$-0.328882\pi$
$758$			3.51415e9i			0.293074i
$759$			3.40425e9i			0.282602i
$760$			7.38100e9i			0.609913i
$761$	1.60081e10			1.31672			0.658361	−	0.752703i	$-0.271250\pi$
$761$	1.60081e10			1.31672			0.658361	+	0.752703i	$0.271250\pi$
$762$		−	6.64722e9i		−	0.544249i
$763$		−	3.34709e9i		−	0.272792i
$764$			7.10083e9i			0.576079i
$765$	1.80160e10			1.45493
$766$	5.67642e9			0.456325
$767$	2.03750e10			1.63048
$768$	−4.82564e8			−0.0384406
$769$			5.80747e9i			0.460516i	0.973130	+	0.230258i	$0.0739571\pi$
$769$			5.80747e9i			0.460516i	−0.973130	+	0.230258i	$0.926043\pi$
$770$	−1.40465e9			−0.110880
$771$			2.06386e9i			0.162177i
$772$		−	7.66162e9i		−	0.599321i
$773$	1.82075e9			0.141783			0.0708913	−	0.997484i	$-0.477416\pi$
$773$	1.82075e9			0.141783			0.0708913	+	0.997484i	$0.477416\pi$
$774$	8.56684e9			0.664090
$775$		−	1.70041e10i		−	1.31219i
$776$	2.91898e9			0.224241
$777$	1.88741e9	+	4.35956e8i	0.144342	+	0.0333402i
$778$	6.91206e9			0.526234
$779$			1.35425e10i			1.02640i
$780$	−1.03873e10			−0.783740
$781$	8.57081e9			0.643788
$782$		−	1.56181e10i		−	1.16790i
$783$			1.78506e10i			1.32888i
$784$	−3.17754e9			−0.235496
$785$			2.56563e10i			1.89300i
$786$	−1.03022e10			−0.756748
$787$	−5.84261e9			−0.427263			−0.213632	−	0.976914i	$-0.568529\pi$
$787$	−5.84261e9			−0.427263			−0.213632	+	0.976914i	$0.568529\pi$
$788$	5.85824e9			0.426506
$789$	−2.18427e8			−0.0158320
$790$		−	6.71299e9i		−	0.484419i
$791$		−	3.13616e9i		−	0.225310i
$792$			1.28160e9i			0.0916674i
$793$	−2.35487e10			−1.67692
$794$			1.07207e10i			0.760063i
$795$		−	1.52564e10i		−	1.07688i
$796$		−	6.39071e9i		−	0.449110i
$797$			9.50130e9i			0.664782i	0.943142	+	0.332391i	$0.107855\pi$
$797$			9.50130e9i			0.664782i	−0.943142	+	0.332391i	$0.892145\pi$
$798$	1.66172e9			0.115757
$799$			8.97800e9i			0.622681i
$800$			3.67876e9i			0.254031i
$801$			5.31497e9i			0.365415i
$802$	8.51518e9			0.582886
$803$	−7.11358e9			−0.484823
$804$	3.29900e9			0.223865
$805$	−6.13167e9			−0.414279
$806$		−	1.56695e10i		−	1.05410i
$807$	−5.25120e9			−0.351724
$808$			1.89894e9i			0.126640i
$809$		−	1.24098e10i		−	0.824033i	−0.911176	−	0.412017i	$-0.864825\pi$
$809$		−	1.24098e10i		−	0.824033i	0.911176	−	0.412017i	$-0.135175\pi$
$810$	−1.37592e8			−0.00909697
$811$	−8.02356e9			−0.528195			−0.264097	−	0.964496i	$-0.585074\pi$
$811$	−8.02356e9			−0.528195			−0.264097	+	0.964496i	$0.585074\pi$
$812$			2.44785e9i			0.160450i
$813$	1.34216e10			0.875968
$814$	−1.02125e9	+	4.42133e9i	−0.0663658	+	0.287321i
$815$	−5.53113e9			−0.357900
$816$			3.57758e9i			0.230502i
$817$	2.60203e10			1.66930
$818$	3.81245e9			0.243538
$819$		−	3.84339e9i		−	0.244467i
$820$			1.14468e10i			0.724993i
$821$	−9.82788e9			−0.619811			−0.309905	−	0.950767i	$-0.600297\pi$
$821$	−9.82788e9			−0.619811			−0.309905	+	0.950767i	$0.600297\pi$
$822$		−	4.20311e9i		−	0.263949i
$823$	9.98150e8			0.0624161			0.0312080	−	0.999513i	$-0.490065\pi$
$823$	9.98150e8			0.0624161			0.0312080	+	0.999513i	$0.490065\pi$
$824$	1.10027e10			0.685099
$825$	−5.94471e9			−0.368589
$826$	−2.75509e9			−0.170101
$827$		−	4.41382e9i		−	0.271359i	−0.990753	−	0.135680i	$-0.956678\pi$
$827$		−	4.41382e9i		−	0.271359i	0.990753	−	0.135680i	$-0.0433218\pi$
$828$			5.59451e9i			0.342496i
$829$			3.57418e9i			0.217889i	0.994048	+	0.108944i	$0.0347471\pi$
$829$			3.57418e9i			0.217889i	−0.994048	+	0.108944i	$0.965253\pi$
$830$	2.10000e10			1.27481
$831$		−	7.73264e9i		−	0.467438i
$832$			3.39003e9i			0.204067i
$833$			2.35573e10i			1.41211i
$834$			2.51206e9i			0.149951i
$835$	−4.08797e10			−2.42999
$836$			3.89265e9i			0.230421i
$837$			1.54511e10i			0.910794i
$838$		−	4.43728e9i		−	0.260473i
$839$	2.87912e10			1.68304			0.841518	−	0.540230i	$-0.181663\pi$
$839$	2.87912e10			1.68304			0.841518	+	0.540230i	$0.181663\pi$
$840$	1.40456e9			0.0817642
$841$	−1.33689e10			−0.775016
$842$	−7.56304e9			−0.436621
$843$			3.73051e9i			0.214472i
$844$	−2.01375e9			−0.115294
$845$			4.55917e10i			2.59948i
$846$		−	3.21598e9i		−	0.182607i
$847$	3.51872e9			0.198972
$848$	−4.97912e9			−0.280393
$849$		−	6.80004e9i		−	0.381359i
$850$	2.72733e10			1.52325
$851$	−4.45799e9	+	1.93002e10i	−0.247962	+	1.07352i
$852$	−8.57023e9			−0.474738
$853$			1.88255e10i			1.03854i	0.854609	+	0.519272i	$0.173797\pi$
$853$			1.88255e10i			1.03854i	−0.854609	+	0.519272i	$0.826203\pi$
$854$	3.18423e9			0.174945
$855$	−1.96013e10			−1.07251
$856$		−	4.87682e9i		−	0.265753i
$857$		−	1.95251e10i		−	1.05964i	−0.848109	−	0.529822i	$-0.822259\pi$
$857$		−	1.95251e10i		−	1.05964i	0.848109	−	0.529822i	$-0.177741\pi$
$858$	−5.47813e9			−0.296092
$859$		−	6.73950e9i		−	0.362787i	−0.983411	−	0.181393i	$-0.941939\pi$
$859$		−	6.73950e9i		−	0.362787i	0.983411	−	0.181393i	$-0.0580607\pi$
$860$	2.19936e10			1.17910
$861$	2.57706e9			0.137598
$862$	−2.74484e9			−0.145963
$863$	3.99553e9			0.211610			0.105805	−	0.994387i	$-0.466258\pi$
$863$	3.99553e9			0.211610			0.105805	+	0.994387i	$0.466258\pi$
$864$		−	3.34278e9i		−	0.176323i
$865$		−	2.12966e10i		−	1.11881i
$866$		−	1.45397e10i		−	0.760752i
$867$	1.47206e10			0.767110
$868$			2.11881e9i			0.109970i
$869$		−	3.54035e9i		−	0.183011i
$870$			1.75688e10i			0.904536i
$871$		−	2.31756e10i		−	1.18841i
$872$	−7.84018e9			−0.400422
$873$			7.75176e9i			0.394321i
$874$			1.69924e10i			0.860923i
$875$		−	3.25630e9i		−	0.164322i
$876$	7.11310e9			0.357515
$877$	2.14868e10			1.07566			0.537829	−	0.843054i	$-0.319245\pi$
$877$	2.14868e10			1.07566			0.537829	+	0.843054i	$0.319245\pi$
$878$	2.08768e10			1.04096
$879$	1.12249e10			0.557467
$880$			3.29024e9i			0.162757i
$881$	−1.61700e10			−0.796700			−0.398350	−	0.917234i	$-0.630417\pi$
$881$	−1.61700e10			−0.796700			−0.398350	+	0.917234i	$0.630417\pi$
$882$		−	8.43839e9i		−	0.414114i
$883$			1.22901e10i			0.600747i	0.953822	+	0.300373i	$0.0971113\pi$
$883$			1.22901e10i			0.600747i	−0.953822	+	0.300373i	$0.902889\pi$
$884$	2.51327e10			1.22365
$885$	−1.97740e10			−0.958942
$886$			7.49854e9i			0.362209i
$887$	−2.13630e10			−1.02785			−0.513925	−	0.857835i	$-0.671809\pi$
$887$	−2.13630e10			−1.02785			−0.513925	+	0.857835i	$0.671809\pi$
$888$	1.02118e9	−	4.42104e9i	0.0489391	−	0.211874i
$889$	6.31432e9			0.301419
$890$			1.36451e10i			0.648800i
$891$	−7.25644e7			−0.00343678
$892$	−1.15041e10			−0.542718
$893$		−	9.76800e9i		−	0.459014i
$894$		−	2.91889e8i		−	0.0136627i
$895$	1.05674e10			0.492708
$896$		−	4.58397e8i		−	0.0212894i
$897$	−2.39134e10			−1.10629
$898$	6.24862e9			0.287950
$899$	−2.65030e10			−1.21657
$900$	−9.76947e9			−0.446707
$901$			3.69137e10i			1.68132i
$902$			6.03687e9i			0.273898i
$903$		−	4.95151e9i		−	0.223785i
$904$	−7.34610e9			−0.330725
$905$		−	5.09441e10i		−	2.28467i
$906$			4.07587e9i			0.182084i
$907$			1.30045e10i			0.578721i	0.957220	+	0.289360i	$0.0934426\pi$
$907$			1.30045e10i			0.578721i	−0.957220	+	0.289360i	$0.906557\pi$
$908$		−	1.52357e10i		−	0.675401i
$909$	−5.04290e9			−0.222693
$910$		−	9.86710e9i		−	0.434055i
$911$		−	2.85983e10i		−	1.25322i	−0.779334	−	0.626608i	$-0.784443\pi$
$911$		−	2.85983e10i		−	1.25322i	0.779334	−	0.626608i	$-0.215557\pi$
$912$		−	3.89239e9i		−	0.169916i
$913$	1.10751e10			0.481617
$914$	−1.89090e10			−0.819139
$915$	2.28540e10			0.986254
$916$	5.16794e9			0.222169
$917$		−	9.78626e9i		−	0.419106i
$918$	−2.47824e10			−1.05729
$919$			1.77617e10i			0.754883i	0.926033	+	0.377441i	$0.123196\pi$
$919$			1.77617e10i			0.754883i	−0.926033	+	0.377441i	$0.876804\pi$
$920$			1.43627e10i			0.608107i
$921$	1.93194e10			0.814865
$922$	7.22436e9			0.303557
$923$			6.02063e10i			2.52021i
$924$	7.40747e8			0.0308900
$925$	−3.37032e10	−	7.78481e9i	−1.40015	−	0.323409i
$926$	2.99846e10			1.24096
$927$			2.92191e10i			1.20473i
$928$	5.73382e9			0.235519
$929$	−2.45214e10			−1.00344			−0.501719	−	0.865031i	$-0.667299\pi$
$929$	−2.45214e10			−1.00344			−0.501719	+	0.865031i	$0.667299\pi$
$930$			1.52073e10i			0.619955i
$931$		−	2.56302e10i		−	1.04094i
$932$	1.52549e10			0.617241
$933$			2.75203e10i			1.10935i
$934$	−2.85687e10			−1.14730
$935$	2.43929e10			0.975939
$936$	−9.00270e9			−0.358845
$937$	−2.41898e10			−0.960601			−0.480300	−	0.877104i	$-0.659472\pi$
$937$	−2.41898e10			−0.960601			−0.480300	+	0.877104i	$0.659472\pi$
$938$			3.13378e9i			0.123982i
$939$			5.16871e9i			0.203729i
$940$		−	8.25637e9i		−	0.324221i
$941$	1.50456e9			0.0588636			0.0294318	−	0.999567i	$-0.490630\pi$
$941$	1.50456e9			0.0588636			0.0294318	+	0.999567i	$0.490630\pi$
$942$		−	1.35299e10i		−	0.527371i
$943$			2.63525e10i			1.02336i
$944$			6.45349e9i			0.249685i
$945$			9.72957e9i			0.375044i
$946$	1.15991e10			0.445458
$947$			1.65709e10i			0.634045i	0.948418	+	0.317023i	$0.102683\pi$
$947$			1.65709e10i			0.634045i	−0.948418	+	0.317023i	$0.897317\pi$
$948$			3.54011e9i			0.134955i
$949$		−	4.99699e10i		−	1.89791i
$950$	−2.96731e10			−1.12287
$951$	3.22430e9			0.121564
$952$	−3.39842e9			−0.127658
$953$	1.84240e10			0.689540			0.344770	−	0.938687i	$-0.387957\pi$
$953$	1.84240e10			0.689540			0.344770	+	0.938687i	$0.387957\pi$
$954$		−	1.32227e10i		−	0.493063i
$955$	−4.84120e10			−1.79863
$956$		−	3.30928e9i		−	0.122499i
$957$			9.26558e9i			0.341728i
$958$	−1.82398e10			−0.670255
$959$	3.99262e9			0.146182
$960$		−	3.29002e9i		−	0.120019i
$961$	4.57211e9			0.166182
$962$	−3.10580e10	−	7.17381e9i	−1.12476	−	0.259799i
$963$	1.29511e10			0.467320
$964$		−	1.02218e10i		−	0.367502i
$965$	5.22354e10			1.87120
$966$	3.23355e9			0.115414
$967$		−	4.43490e10i		−	1.57722i	−0.614896	−	0.788608i	$-0.710802\pi$
$967$		−	4.43490e10i		−	1.57722i	0.614896	−	0.788608i	$-0.289198\pi$
$968$		−	8.24220e9i		−	0.292065i
$969$	−2.88570e10			−1.01887
$970$			1.99010e10i			0.700123i
$971$	−7.02253e9			−0.246165			−0.123082	−	0.992396i	$-0.539278\pi$
$971$	−7.02253e9			−0.246165			−0.123082	+	0.992396i	$0.539278\pi$
$972$	1.43512e10			0.501252
$973$	−2.38626e9			−0.0830466
$974$	3.65384e10			1.26705
$975$		−	4.17591e10i		−	1.44289i
$976$		−	7.45870e9i		−	0.256796i
$977$			2.56143e10i			0.878721i	0.898311	+	0.439361i	$0.144795\pi$
$977$			2.56143e10i			0.878721i	−0.898311	+	0.439361i	$0.855205\pi$
$978$	2.91685e9			0.0997076
$979$			7.19623e9i			0.245113i
$980$		−	2.16638e10i		−	0.735264i
$981$		−	2.08207e10i		−	0.704131i
$982$			2.46327e10i			0.830085i
$983$	3.79136e10			1.27309			0.636544	−	0.771241i	$-0.280364\pi$
$983$	3.79136e10			1.27309			0.636544	+	0.771241i	$0.280364\pi$
$984$		−	6.03647e9i		−	0.201976i
$985$			3.99403e10i			1.33163i
$986$		−	4.25088e10i		−	1.41224i
$987$	−1.85879e9			−0.0615348
$988$	−2.73442e10			−0.902019
$989$	5.06331e10			1.66436
$990$	−8.73770e9			−0.286203
$991$		−	3.80017e10i		−	1.24035i	−0.784463	−	0.620176i	$-0.787061\pi$
$991$		−	3.80017e10i		−	1.24035i	0.784463	−	0.620176i	$-0.212939\pi$
$992$	4.96308e9			0.161421
$993$			9.37103e9i			0.303714i
$994$		−	8.14103e9i		−	0.262922i
$995$	4.35706e10			1.40221
$996$	−1.10744e10			−0.355151
$997$		−	4.32069e10i		−	1.38077i	−0.723444	−	0.690383i	$-0.757442\pi$
$997$		−	4.32069e10i		−	1.38077i	0.723444	−	0.690383i	$-0.242558\pi$
$998$	−1.26575e10			−0.403079
$999$	3.06251e10	+	7.07382e9i	0.971847	+	0.224478i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.8.b.a.73.6	✓	24
37.36	even	2	inner	74.8.b.a.73.18	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.8.b.a.73.6	✓	24	1.1	even	1	trivial
74.8.b.a.73.18	yes	24	37.36	even	2	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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	74.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-8.00000i q^{2} -28.7630 q^{3} -64.0000 q^{4} -436.339i q^{5} +230.104i q^{6} -218.580 q^{7} +512.000i q^{8} -1359.69 q^{9} -3490.71 q^{10} -1840.96 q^{11} +1840.83 q^{12} -12931.9i q^{13} +1748.64i q^{14} +12550.4i q^{15} +4096.00 q^{16} -30366.5i q^{17} +10877.5i q^{18} +33038.6i q^{19} +27925.7i q^{20} +6287.04 q^{21} +14727.7i q^{22} +64290.0i q^{23} -14726.7i q^{24} -112267. q^{25} -103456. q^{26} +102014. q^{27} +13989.2 q^{28} +174982. i q^{29} +100404. q^{30} +151461. i q^{31} -32768.0i q^{32} +52951.6 q^{33} -242932. q^{34} +95375.3i q^{35} +87020.0 q^{36} +(300206. + 69342.0i) q^{37} +264308. q^{38} +371962. i q^{39} +223406. q^{40} +409900. q^{41} -50296.3i q^{42} -787574. i q^{43} +117821. q^{44} +593285. i q^{45} +514320. q^{46} -295655. q^{47} -117813. q^{48} -775766. q^{49} +898136. i q^{50} +873434. i q^{51} +827645. i q^{52} -1.21561e6 q^{53} -816108. i q^{54} +803282. i q^{55} -111913. i q^{56} -950289. i q^{57} +1.39986e6 q^{58} +1.57556e6i q^{59} -803229. i q^{60} -1.82097e6i q^{61} +1.21169e6 q^{62} +297201. q^{63} -262144. q^{64} -5.64272e6 q^{65} -423612. i q^{66} +1.79212e6 q^{67} +1.94346e6i q^{68} -1.84918e6i q^{69} +763002. q^{70} -4.65562e6 q^{71} -696160. i q^{72} +3.86406e6 q^{73} +(554736. - 2.40165e6i) q^{74} +3.22914e6 q^{75} -2.11447e6i q^{76} +402398. q^{77} +2.97570e6 q^{78} +1.92310e6i q^{79} -1.78725e6i q^{80} +39416.7 q^{81} -3.27920e6i q^{82} -6.01597e6 q^{83} -402371. q^{84} -1.32501e7 q^{85} -6.30059e6 q^{86} -5.03302e6i q^{87} -942571. i q^{88} -3.90896e6i q^{89} +4.74628e6 q^{90} +2.82667e6i q^{91} -4.11456e6i q^{92} -4.35649e6i q^{93} +2.36524e6i q^{94} +1.44160e7 q^{95} +942507. i q^{96} -5.70113e6i q^{97} +6.20612e6i q^{98} +2.50313e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 106 q^{3} - 1536 q^{4} + 104 q^{7} + 17554 q^{9} + 1136 q^{10} + 366 q^{11} + 6784 q^{12} + 98304 q^{16} - 239820 q^{21} - 675570 q^{25} + 97008 q^{26} + 338780 q^{27} - 6656 q^{28} + 350400 q^{30}+ \cdots - 53279900 q^{99}+O(q^{100}) \) 24 * q - 106 * q^3 - 1536 * q^4 + 104 * q^7 + 17554 * q^9 + 1136 * q^10 + 366 * q^11 + 6784 * q^12 + 98304 * q^16 - 239820 * q^21 - 675570 * q^25 + 97008 * q^26 + 338780 * q^27 - 6656 * q^28 + 350400 * q^30 - 763792 * q^33 + 713632 * q^34 - 1123456 * q^36 + 41652 * q^37 - 30816 * q^38 - 72704 * q^40 + 1729722 * q^41 - 23424 * q^44 - 488496 * q^46 + 114756 * q^47 - 434176 * q^48 + 4003056 * q^49 - 1115964 * q^53 - 2075632 * q^58 + 3248208 * q^62 - 2350900 * q^63 - 6291456 * q^64 - 5246556 * q^65 - 2717994 * q^67 - 5649440 * q^70 + 10643280 * q^71 - 10450370 * q^73 - 1064064 * q^74 - 17737980 * q^75 + 11665236 * q^77 + 8431856 * q^78 + 47300176 * q^81 + 555912 * q^83 + 15348480 * q^84 - 4853096 * q^85 - 12070464 * q^86 + 32064160 * q^90 - 58516956 * q^95 - 53279900 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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