LMFDB - Embedded newform 14.9.d.a.5.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,9,Mod(3,14)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(14, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("14.3");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	14.d (of order $6$, 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:	$5.70330054086$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 1771 x^{10} + 26038 x^{9} + 2442597 x^{8} + 26522276 x^{7} + 1175865280 x^{6} + \cdots + 36\!\cdots\!00 $ x^12 - 2x^11 + 1771x^10 + 26038x^9 + 2442597x^8 + 26522276x^7 + 1175865280x^6 + 6901058684x^5 + 370996492174x^4 + 1285719886320x^3 + 55526550982200x^2 - 240706289358000*x + 3600954063202500
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{4}\cdot 7^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.6
Root			$-10.5605 - 18.2913i$ of defining polynomial
Character	$\chi$	$=$	14.5
Dual form			14.9.d.a.3.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.65685 - 9.79796i) q^{2} +(126.451 - 73.0064i) q^{3} +(-64.0000 - 110.851i) q^{4} +(372.872 + 215.278i) q^{5} -1651.95i q^{6} +(-1545.60 + 1837.37i) q^{7} -1448.15 q^{8} +(7379.38 - 12781.5i) q^{9} +O(q^{10})$	\(q+(5.65685 - 9.79796i) q^{2} +(126.451 - 73.0064i) q^{3} +(-64.0000 - 110.851i) q^{4} +(372.872 + 215.278i) q^{5} -1651.95i q^{6} +(-1545.60 + 1837.37i) q^{7} -1448.15 q^{8} +(7379.38 - 12781.5i) q^{9} +(4218.56 - 2435.59i) q^{10} +(-5184.46 - 8979.75i) q^{11} +(-16185.7 - 9344.82i) q^{12} +24214.7i q^{13} +(9259.29 + 25537.4i) q^{14} +62866.6 q^{15} +(-8192.00 + 14189.0i) q^{16} +(-91515.8 + 52836.7i) q^{17} +(-83488.1 - 144606. i) q^{18} +(185178. + 106912. i) q^{19} -55111.1i q^{20} +(-61301.9 + 345176. i) q^{21} -117311. q^{22} +(-16748.4 + 29009.1i) q^{23} +(-183120. + 105725. i) q^{24} +(-102624. - 177749. i) q^{25} +(237255. + 136979. i) q^{26} -1.19698e6i q^{27} +(302593. + 53739.4i) q^{28} +745053. q^{29} +(355627. - 615965. i) q^{30} +(271844. - 156949. i) q^{31} +(92681.9 + 160530. i) q^{32} +(-1.31116e6 - 756998. i) q^{33} +1.19556e6i q^{34} +(-971854. + 352372. i) q^{35} -1.88912e6 q^{36} +(-1.10934e6 + 1.92144e6i) q^{37} +(2.09505e6 - 1.20958e6i) q^{38} +(1.76783e6 + 3.06197e6i) q^{39} +(-539976. - 311755. i) q^{40} -2.59102e6i q^{41} +(3.03524e6 + 2.55324e6i) q^{42} -4.49763e6 q^{43} +(-663611. + 1.14941e6i) q^{44} +(5.50312e6 - 3.17723e6i) q^{45} +(189486. + 328200. i) q^{46} +(1.61857e6 + 934482. i) q^{47} +2.39227e6i q^{48} +(-987071. - 5.67967e6i) q^{49} -2.32210e6 q^{50} +(-7.71483e6 + 1.33625e7i) q^{51} +(2.68423e6 - 1.54974e6i) q^{52} +(-3.31278e6 - 5.73790e6i) q^{53} +(-1.17279e7 - 6.77112e6i) q^{54} -4.46440e6i q^{55} +(2.23826e6 - 2.66080e6i) q^{56} +3.12212e7 q^{57} +(4.21466e6 - 7.30000e6i) q^{58} +(4.50172e6 - 2.59907e6i) q^{59} +(-4.02346e6 - 6.96884e6i) q^{60} +(-2.00074e7 - 1.15513e7i) q^{61} -3.55136e6i q^{62} +(1.20788e7 + 3.33136e7i) q^{63} +2.09715e6 q^{64} +(-5.21289e6 + 9.02900e6i) q^{65} +(-1.48341e7 + 8.56446e6i) q^{66} +(-5.75872e6 - 9.97440e6i) q^{67} +(1.17140e7 + 6.76310e6i) q^{68} +4.89096e6i q^{69} +(-2.04511e6 + 1.15155e7i) q^{70} +259882. q^{71} +(-1.06865e7 + 1.85095e7i) q^{72} +(-7.31936e6 + 4.22584e6i) q^{73} +(1.25508e7 + 2.17386e7i) q^{74} +(-2.59537e7 - 1.49843e7i) q^{75} -2.73696e7i q^{76} +(2.45122e7 + 4.35328e6i) q^{77} +4.00015e7 q^{78} +(-285853. + 495111. i) q^{79} +(-6.10913e6 + 3.52711e6i) q^{80} +(-3.89709e7 - 6.74996e7i) q^{81} +(-2.53867e7 - 1.46570e7i) q^{82} +6.46856e7i q^{83} +(4.21865e7 - 1.52959e7i) q^{84} -4.54982e7 q^{85} +(-2.54424e7 + 4.40676e7i) q^{86} +(9.42126e7 - 5.43936e7i) q^{87} +(7.50791e6 + 1.30041e7i) q^{88} +(1.52515e7 + 8.80544e6i) q^{89} -7.18925e7i q^{90} +(-4.44915e7 - 3.74262e7i) q^{91} +4.28759e6 q^{92} +(2.29166e7 - 3.96927e7i) q^{93} +(1.83120e7 - 1.05725e7i) q^{94} +(4.60318e7 + 7.97293e7i) q^{95} +(2.34394e7 + 1.35327e7i) q^{96} -7.31853e7i q^{97} +(-6.12329e7 - 2.24578e7i) q^{98} -1.53032e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 162 q^{3} - 768 q^{4} + 1674 q^{5} - 1308 q^{7} + 23604 q^{9}+O(q^{10}) $ 12 * q + 162 * q^3 - 768 * q^4 + 1674 * q^5 - 1308 * q^7 + 23604 * q^9	\( 12 q + 162 q^{3} - 768 q^{4} + 1674 q^{5} - 1308 q^{7} + 23604 q^{9} + 17664 q^{10} + 10302 q^{11} - 20736 q^{12} + 56832 q^{14} - 255468 q^{15} - 98304 q^{16} + 173178 q^{17} + 16896 q^{18} + 405978 q^{19} - 656910 q^{21} - 941568 q^{22} + 158934 q^{23} + 98304 q^{24} + 838668 q^{25} + 1958400 q^{26} - 255744 q^{28} - 4355256 q^{29} + 916992 q^{30} + 4520250 q^{31} + 4954482 q^{33} - 5270790 q^{35} - 6042624 q^{36} + 134214 q^{37} + 1278720 q^{38} + 1335384 q^{39} - 2260992 q^{40} + 6660096 q^{42} - 12961896 q^{43} + 1318656 q^{44} - 8415396 q^{45} + 2345472 q^{46} + 18385002 q^{47} - 3659172 q^{49} + 2970624 q^{50} - 2673894 q^{51} - 3369984 q^{52} - 16540506 q^{53} - 19646208 q^{54} + 4325376 q^{56} + 100263780 q^{57} + 9176064 q^{58} + 31163922 q^{59} + 16349952 q^{60} - 85390158 q^{61} + 4361988 q^{63} + 25165824 q^{64} - 46506264 q^{65} - 111873024 q^{66} - 37750362 q^{67} - 22166784 q^{68} + 92031744 q^{70} + 45506424 q^{71} + 2162688 q^{72} + 9414786 q^{73} + 58837248 q^{74} + 9837540 q^{75} - 100614066 q^{77} - 25463808 q^{78} + 59730294 q^{79} - 27426816 q^{80} - 89677422 q^{81} - 93259776 q^{82} + 122616576 q^{84} - 64652220 q^{85} - 15144960 q^{86} + 334229724 q^{87} + 60260352 q^{88} + 323014482 q^{89} - 266861424 q^{91} - 40687104 q^{92} - 11119662 q^{93} - 443440128 q^{94} - 175918350 q^{95} - 12582912 q^{96} + 472166400 q^{98} - 346906296 q^{99}+O(q^{100}) \) 12 * q + 162 * q^3 - 768 * q^4 + 1674 * q^5 - 1308 * q^7 + 23604 * q^9 + 17664 * q^10 + 10302 * q^11 - 20736 * q^12 + 56832 * q^14 - 255468 * q^15 - 98304 * q^16 + 173178 * q^17 + 16896 * q^18 + 405978 * q^19 - 656910 * q^21 - 941568 * q^22 + 158934 * q^23 + 98304 * q^24 + 838668 * q^25 + 1958400 * q^26 - 255744 * q^28 - 4355256 * q^29 + 916992 * q^30 + 4520250 * q^31 + 4954482 * q^33 - 5270790 * q^35 - 6042624 * q^36 + 134214 * q^37 + 1278720 * q^38 + 1335384 * q^39 - 2260992 * q^40 + 6660096 * q^42 - 12961896 * q^43 + 1318656 * q^44 - 8415396 * q^45 + 2345472 * q^46 + 18385002 * q^47 - 3659172 * q^49 + 2970624 * q^50 - 2673894 * q^51 - 3369984 * q^52 - 16540506 * q^53 - 19646208 * q^54 + 4325376 * q^56 + 100263780 * q^57 + 9176064 * q^58 + 31163922 * q^59 + 16349952 * q^60 - 85390158 * q^61 + 4361988 * q^63 + 25165824 * q^64 - 46506264 * q^65 - 111873024 * q^66 - 37750362 * q^67 - 22166784 * q^68 + 92031744 * q^70 + 45506424 * q^71 + 2162688 * q^72 + 9414786 * q^73 + 58837248 * q^74 + 9837540 * q^75 - 100614066 * q^77 - 25463808 * q^78 + 59730294 * q^79 - 27426816 * q^80 - 89677422 * q^81 - 93259776 * q^82 + 122616576 * q^84 - 64652220 * q^85 - 15144960 * q^86 + 334229724 * q^87 + 60260352 * q^88 + 323014482 * q^89 - 266861424 * q^91 - 40687104 * q^92 - 11119662 * q^93 - 443440128 * q^94 - 175918350 * q^95 - 12582912 * q^96 + 472166400 * q^98 - 346906296 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	5.65685	−	9.79796i	0.353553	−	0.612372i
$2$	5.65685	−	9.79796i	0.353553	−	0.612372i
$3$	126.451	−	73.0064i	1.56112	−	0.901314i	0.563977	−	0.825790i	$-0.309271\pi$
$3$	126.451	−	73.0064i	1.56112	−	0.901314i	0.997144	−	0.0755236i	$-0.0240628\pi$
$4$	−64.0000	−	110.851i	−0.250000	−	0.433013i
$5$	372.872	+	215.278i	0.596595	+	0.344444i	0.767701	−	0.640808i	$-0.221401\pi$
$5$	372.872	+	215.278i	0.596595	+	0.344444i	−0.171106	+	0.985253i	$0.554734\pi$
$6$		−	1651.95i		−	1.27465i
$7$	−1545.60	+	1837.37i	−0.643730	+	0.765253i
$7$	−1545.60	+	1837.37i	−0.643730	+	0.765253i
$8$	−1448.15			−0.353553
$9$	7379.38	−	12781.5i	1.12473	−	1.94810i
$10$	4218.56	−	2435.59i	0.421856	−	0.243559i
$11$	−5184.46	−	8979.75i	−0.354106	−	0.613329i	0.632859	−	0.774267i	$-0.281881\pi$
$11$	−5184.46	−	8979.75i	−0.354106	−	0.613329i	−0.986965	+	0.160938i	$0.948548\pi$
$12$	−16185.7	−	9344.82i	−0.780561	−	0.450657i
$13$			24214.7i			0.847825i	0.905703	+	0.423913i	$0.139344\pi$
$13$			24214.7i			0.847825i	−0.905703	+	0.423913i	$0.860656\pi$
$14$	9259.29	+	25537.4i	0.241027	+	0.664760i
$15$	62866.6			1.24181
$16$	−8192.00	+	14189.0i	−0.125000	+	0.216506i
$17$	−91515.8	+	52836.7i	−1.09572	+	0.632616i	−0.935094	−	0.354399i	$-0.884685\pi$
$17$	−91515.8	+	52836.7i	−1.09572	+	0.632616i	−0.160628	+	0.987015i	$0.551352\pi$
$18$	−83488.1	−	144606.i	−0.795307	−	1.37751i
$19$	185178.	+	106912.i	1.42094	+	0.820378i	0.996379	−	0.0850230i	$-0.0270964\pi$
$19$	185178.	+	106912.i	1.42094	+	0.820378i	0.424557	+	0.905401i	$0.360430\pi$
$20$		−	55111.1i		−	0.344444i
$21$	−61301.9	+	345176.i	−0.315207	+	1.77486i
$22$	−117311.			−0.500781
$23$	−16748.4	+	29009.1i	−0.0598496	+	0.103663i	−0.894398	−	0.447272i	$-0.852395\pi$
$23$	−16748.4	+	29009.1i	−0.0598496	+	0.103663i	0.834548	+	0.550935i	$0.185729\pi$
$24$	−183120.	+	105725.i	−0.551940	+	0.318663i
$25$	−102624.	−	177749.i	−0.262716	−	0.455038i
$26$	237255.	+	136979.i	0.519185	+	0.299751i
$27$		−	1.19698e6i		−	2.25232i
$28$	302593.	+	53739.4i	0.492297	+	0.0874300i
$29$	745053.			1.05340			0.526702	−	0.850050i	$-0.323428\pi$
$29$	745053.			1.05340			0.526702	+	0.850050i	$0.323428\pi$
$30$	355627.	−	615965.i	0.439046	−	0.760450i
$31$	271844.	−	156949.i	0.294356	−	0.169947i	−0.345549	−	0.938401i	$-0.612307\pi$
$31$	271844.	−	156949.i	0.294356	−	0.169947i	0.639905	+	0.768454i	$0.278974\pi$
$32$	92681.9	+	160530.i	0.0883883	+	0.153093i
$33$	−1.31116e6	−	756998.i	−1.10560	−	0.638321i
$34$			1.19556e6i			0.894653i
$35$	−971854.	+	352372.i	−0.647633	+	0.234817i
$36$	−1.88912e6			−1.12473
$37$	−1.10934e6	+	1.92144e6i	−0.591914	+	1.02523i	0.402060	+	0.915613i	$0.368294\pi$
$37$	−1.10934e6	+	1.92144e6i	−0.591914	+	1.02523i	−0.993974	+	0.109612i	$0.965039\pi$
$38$	2.09505e6	−	1.20958e6i	1.00475	−	0.580095i
$39$	1.76783e6	+	3.06197e6i	0.764157	+	1.32356i
$40$	−539976.	−	311755.i	−0.210928	−	0.121779i
$41$		−	2.59102e6i		−	0.916928i	−0.888713	−	0.458464i	$-0.848400\pi$
$41$		−	2.59102e6i		−	0.916928i	0.888713	−	0.458464i	$-0.151600\pi$
$42$	3.03524e6	+	2.55324e6i	0.975430	+	0.820530i
$43$	−4.49763e6			−1.31556			−0.657779	−	0.753211i	$-0.728504\pi$
$43$	−4.49763e6			−1.31556			−0.657779	+	0.753211i	$0.728504\pi$
$44$	−663611.	+	1.14941e6i	−0.177053	+	0.306665i
$45$	5.50312e6	−	3.17723e6i	1.34202	−	0.774816i
$46$	189486.	+	328200.i	0.0423201	+	0.0733005i
$47$	1.61857e6	+	934482.i	0.331696	+	0.191505i	0.656594	−	0.754244i	$-0.271997\pi$
$47$	1.61857e6	+	934482.i	0.331696	+	0.191505i	−0.324898	+	0.945749i	$0.605330\pi$
$48$			2.39227e6i			0.450657i
$49$	−987071.	−	5.67967e6i	−0.171224	−	0.985232i
$50$	−2.32210e6			−0.371537
$51$	−7.71483e6	+	1.33625e7i	−1.14037	+	1.97518i
$52$	2.68423e6	−	1.54974e6i	0.367119	−	0.211956i
$53$	−3.31278e6	−	5.73790e6i	−0.419845	−	0.727192i	0.576079	−	0.817394i	$-0.304582\pi$
$53$	−3.31278e6	−	5.73790e6i	−0.419845	−	0.727192i	−0.995924	+	0.0902018i	$0.971249\pi$
$54$	−1.17279e7	−	6.77112e6i	−1.37926	−	0.796317i
$55$		−	4.46440e6i		−	0.487879i
$56$	2.23826e6	−	2.66080e6i	0.227593	−	0.270558i
$57$	3.12212e7			2.95767
$58$	4.21466e6	−	7.30000e6i	0.372435	−	0.645076i
$59$	4.50172e6	−	2.59907e6i	0.371510	−	0.214491i	−0.302608	−	0.953115i	$-0.597857\pi$
$59$	4.50172e6	−	2.59907e6i	0.371510	−	0.214491i	0.674118	+	0.738624i	$0.264524\pi$
$60$	−4.02346e6	−	6.96884e6i	−0.310452	−	0.537719i
$61$	−2.00074e7	−	1.15513e7i	−1.44501	−	0.834279i	−0.446836	−	0.894616i	$-0.647449\pi$
$61$	−2.00074e7	−	1.15513e7i	−1.44501	−	0.834279i	−0.998178	+	0.0603367i	$0.980783\pi$
$62$		−	3.55136e6i		−	0.240341i
$63$	1.20788e7	+	3.33136e7i	0.766761	+	2.11475i
$64$	2.09715e6			0.125000
$65$	−5.21289e6	+	9.02900e6i	−0.292029	+	0.505808i
$66$	−1.48341e7	+	8.56446e6i	−0.781780	+	0.451361i
$67$	−5.75872e6	−	9.97440e6i	−0.285777	−	0.494980i	0.687021	−	0.726638i	$-0.258918\pi$
$67$	−5.75872e6	−	9.97440e6i	−0.285777	−	0.494980i	−0.972797	+	0.231658i	$0.925585\pi$
$68$	1.17140e7	+	6.76310e6i	0.547861	+	0.316308i
$69$			4.89096e6i			0.215773i
$70$	−2.04511e6	+	1.15155e7i	−0.0851774	+	0.479613i
$71$	259882.			0.0102269			0.00511343	−	0.999987i	$-0.498372\pi$
$71$	259882.			0.0102269			0.00511343	+	0.999987i	$0.498372\pi$
$72$	−1.06865e7	+	1.85095e7i	−0.397653	+	0.688756i
$73$	−7.31936e6	+	4.22584e6i	−0.257740	+	0.148806i	−0.623303	−	0.781980i	$-0.714210\pi$
$73$	−7.31936e6	+	4.22584e6i	−0.257740	+	0.148806i	0.365563	+	0.930787i	$0.380876\pi$
$74$	1.25508e7	+	2.17386e7i	0.418547	+	0.724944i
$75$	−2.59537e7	−	1.49843e7i	−0.820264	−	0.473579i
$76$		−	2.73696e7i		−	0.820378i
$77$	2.45122e7	+	4.35328e6i	0.697300	+	0.123838i
$78$	4.00015e7			1.08068
$79$	−285853.	+	495111.i	−0.00733895	+	0.0127114i	−0.869672	−	0.493631i	$-0.835669\pi$
$79$	−285853.	+	495111.i	−0.00733895	+	0.0127114i	0.862333	+	0.506342i	$0.169003\pi$
$80$	−6.10913e6	+	3.52711e6i	−0.149149	+	0.0861111i
$81$	−3.89709e7	−	6.74996e7i	−0.905317	−	1.56805i
$82$	−2.53867e7	−	1.46570e7i	−0.561501	−	0.324183i
$83$			6.46856e7i			1.36300i	0.731819	+	0.681499i	$0.238672\pi$
$83$			6.46856e7i			1.36300i	−0.731819	+	0.681499i	$0.761328\pi$
$84$	4.21865e7	−	1.52959e7i	0.847337	−	0.307225i
$85$	−4.54982e7			−0.871603
$86$	−2.54424e7	+	4.40676e7i	−0.465120	+	0.805611i
$87$	9.42126e7	−	5.43936e7i	1.64449	−	0.949448i
$88$	7.50791e6	+	1.30041e7i	0.125195	+	0.216845i
$89$	1.52515e7	+	8.80544e6i	0.243081	+	0.140343i	0.616592	−	0.787283i	$-0.288513\pi$
$89$	1.52515e7	+	8.80544e6i	0.243081	+	0.140343i	−0.373511	+	0.927626i	$0.621846\pi$
$90$		−	7.18925e7i		−	1.09576i
$91$	−4.44915e7	−	3.74262e7i	−0.648801	−	0.545770i
$92$	4.28759e6			0.0598496
$93$	2.29166e7	−	3.96927e7i	0.306350	−	0.530614i
$94$	1.83120e7	−	1.05725e7i	0.234545	−	0.135414i
$95$	4.60318e7	+	7.97293e7i	0.565149	+	0.978867i
$96$	2.34394e7	+	1.35327e7i	0.275970	+	0.159331i
$97$		−	7.31853e7i		−	0.826678i	−0.910577	−	0.413339i	$-0.864362\pi$
$97$		−	7.31853e7i		−	0.826678i	0.910577	−	0.413339i	$-0.135638\pi$
$98$	−6.12329e7	−	2.24578e7i	−0.663866	−	0.243479i
$99$	−1.53032e8			−1.59310
$100$	−1.31358e7	+	2.27519e7i	−0.131358	+	0.227519i
$101$	1.06141e8	−	6.12803e7i	1.01999	−	0.588892i	0.105889	−	0.994378i	$-0.466231\pi$
$101$	1.06141e8	−	6.12803e7i	1.01999	−	0.588892i	0.914101	+	0.405486i	$0.132898\pi$
$102$	8.72834e7	+	1.51179e8i	0.806364	+	1.39666i
$103$	2.45323e7	+	1.41637e7i	0.217966	+	0.125843i	0.605008	−	0.796219i	$-0.293170\pi$
$103$	2.45323e7	+	1.41637e7i	0.217966	+	0.125843i	−0.387042	+	0.922062i	$0.626503\pi$
$104$		−	3.50667e7i		−	0.299751i
$105$	−9.71664e7	+	1.15509e8i	−0.799390	+	0.950299i
$106$	−7.49596e7			−0.593750
$107$	−5.57798e7	+	9.66135e7i	−0.425541	+	0.737059i	−0.996471	−	0.0839398i	$-0.973250\pi$
$107$	−5.57798e7	+	9.66135e7i	−0.425541	+	0.737059i	0.570929	+	0.820999i	$0.306583\pi$
$108$	−1.32686e8	+	7.66065e7i	−0.975285	+	0.563081i
$109$	6.66285e6	+	1.15404e7i	0.0472013	+	0.0817550i	0.888661	−	0.458565i	$-0.151636\pi$
$109$	6.66285e6	+	1.15404e7i	0.0472013	+	0.0817550i	−0.841459	+	0.540320i	$0.818303\pi$
$110$	−4.37420e7	−	2.52544e7i	−0.298764	−	0.172491i
$111$			3.23957e8i			2.13400i
$112$	−1.34089e7	−	3.69821e7i	−0.0852159	−	0.235028i
$113$	1.70571e8			1.04614			0.523072	−	0.852289i	$-0.324786\pi$
$113$	1.70571e8			1.04614			0.523072	+	0.852289i	$0.324786\pi$
$114$	1.76614e8	−	3.05904e8i	1.04570	−	1.81120i
$115$	−1.24900e7	+	7.21111e6i	−0.0714120	+	0.0412297i
$116$	−4.76834e7	−	8.25900e7i	−0.263351	−	0.456137i
$117$	3.09499e8	+	1.78690e8i	1.65164	+	0.953577i
$118$		−	5.88102e7i		−	0.303336i
$119$	4.43658e7	−	2.49813e8i	0.221238	−	1.24574i
$120$	−9.10406e7			−0.439046
$121$	5.34221e7	−	9.25298e7i	0.249218	−	0.431658i
$122$	−2.26358e8	+	1.30688e8i	−1.02178	+	0.589924i
$123$	−1.89161e8	−	3.27636e8i	−0.826440	−	1.43144i
$124$	−3.47960e7	−	2.00895e7i	−0.147178	−	0.0849733i
$125$		−	2.56556e8i		−	1.05085i
$126$	3.94733e8	+	7.01031e7i	1.56611	+	0.278135i
$127$	1.27983e8			0.491969			0.245985	−	0.969274i	$-0.420889\pi$
$127$	1.27983e8			0.491969			0.245985	+	0.969274i	$0.420889\pi$
$128$	1.18633e7	−	2.05478e7i	0.0441942	−	0.0765466i
$129$	−5.68729e8	+	3.28356e8i	−2.05375	+	1.18573i
$130$	5.89772e7	+	1.02151e8i	0.206495	+	0.357661i
$131$	1.85525e8	+	1.07113e8i	0.629965	+	0.363711i	0.780739	−	0.624858i	$-0.214843\pi$
$131$	1.85525e8	+	1.07113e8i	0.629965	+	0.363711i	−0.150773	+	0.988568i	$0.548176\pi$
$132$			1.93792e8i			0.638321i
$133$	−4.82648e8	+	1.74997e8i	−1.54250	+	0.559274i
$134$	−1.30305e8			−0.404149
$135$	2.57682e8	−	4.46319e8i	0.775800	−	1.34373i
$136$	1.32529e8	−	7.65157e7i	0.387396	−	0.223663i
$137$	−1.80095e8	−	3.11933e8i	−0.511232	−	0.885480i	−0.999915	−	0.0130188i	$-0.995856\pi$
$137$	−1.80095e8	−	3.11933e8i	−0.511232	−	0.885480i	0.488683	−	0.872461i	$-0.337477\pi$
$138$	4.79214e7	+	2.76674e7i	0.132134	+	0.0762874i
$139$		−	1.38268e8i		−	0.370394i	−0.982701	−	0.185197i	$-0.940708\pi$
$139$		−	1.38268e8i		−	0.370394i	0.982701	−	0.185197i	$-0.0592923\pi$
$140$	1.01260e8	+	8.51795e7i	0.263587	+	0.221729i
$141$	2.72893e8			0.690424
$142$	1.47011e6	−	2.54631e6i	0.00361574	−	0.00626265i
$143$	2.17442e8	−	1.25540e8i	0.519996	−	0.300220i
$144$	1.20904e8	+	2.09411e8i	0.281183	+	0.487024i
$145$	2.77809e8	+	1.60393e8i	0.628456	+	0.362839i
$146$			9.56197e7i			0.210444i
$147$	−5.39468e8	−	6.46136e8i	−1.15530	−	1.38374i
$148$	2.83992e8			0.591914
$149$	−1.53733e8	+	2.66273e8i	−0.311905	+	0.540235i	−0.978775	−	0.204939i	$-0.934300\pi$
$149$	−1.53733e8	+	2.66273e8i	−0.311905	+	0.540235i	0.666870	+	0.745174i	$0.267634\pi$
$150$	−2.93632e8	+	1.69529e8i	−0.580014	+	0.334871i
$151$	4.00443e8	+	6.93588e8i	0.770252	+	1.33412i	0.937425	+	0.348189i	$0.113203\pi$
$151$	4.00443e8	+	6.93588e8i	0.770252	+	1.33412i	−0.167172	+	0.985928i	$0.553464\pi$
$152$	−2.68166e8	−	1.54826e8i	−0.502377	−	0.290047i
$153$			1.55961e9i			2.84610i
$154$	1.81315e8	−	2.15544e8i	0.322368	−	0.383224i
$155$	1.35151e8			0.234149
$156$	2.26282e8	−	3.91933e8i	0.382078	−	0.661779i
$157$	−2.15124e8	+	1.24202e8i	−0.354071	+	0.204423i	−0.666477	−	0.745526i	$-0.732199\pi$
$157$	−2.15124e8	+	1.24202e8i	−0.354071	+	0.204423i	0.312406	+	0.949949i	$0.398865\pi$
$158$	3.23405e6	+	5.60155e6i	0.00518942	+	0.00898834i
$159$	−8.37807e8	−	4.83708e8i	−1.31086	−	0.756824i
$160$			7.98094e7i			0.121779i
$161$	−2.74142e7	−	7.56093e7i	−0.0408011	−	0.112531i
$162$	−8.81811e8			−1.28031
$163$	−4.78491e8	+	8.28770e8i	−0.677834	+	1.17404i	0.297798	+	0.954629i	$0.403748\pi$
$163$	−4.78491e8	+	8.28770e8i	−0.677834	+	1.17404i	−0.975632	+	0.219413i	$0.929586\pi$
$164$	−2.87218e8	+	1.65825e8i	−0.397041	+	0.229232i
$165$	−3.25930e8	−	5.64527e8i	−0.439732	−	0.761638i
$166$	6.33787e8	+	3.65917e8i	0.834663	+	0.481893i
$167$		−	9.61875e8i		−	1.23667i	−0.785916	−	0.618334i	$-0.787808\pi$
$167$		−	9.61875e8i		−	1.23667i	0.785916	−	0.618334i	$-0.212192\pi$
$168$	8.87746e7	−	4.99868e8i	0.111443	−	0.627506i
$169$	2.29377e8			0.281192
$170$	−2.57377e8	+	4.45790e8i	−0.308158	+	0.533746i
$171$	2.73299e9	−	1.57789e9i	3.19635	−	1.84541i
$172$	2.87848e8	+	4.98568e8i	0.328889	+	0.569653i
$173$	1.14482e8	+	6.60964e7i	0.127807	+	0.0737893i	0.562540	−	0.826770i	$-0.309824\pi$
$173$	1.14482e8	+	6.60964e7i	0.127807	+	0.0737893i	−0.434733	+	0.900559i	$0.643157\pi$
$174$		−	1.23079e9i		−	1.34272i
$175$	4.85206e8	+	8.61707e7i	0.517337	+	0.0918771i
$176$	1.69884e8			0.177053
$177$	3.79497e8	−	6.57309e8i	0.386648	−	0.669694i
$178$	1.72551e8	−	9.96222e7i	0.171885	−	0.0992376i
$179$	4.55563e8	+	7.89058e8i	0.443748	+	0.768594i	0.997964	−	0.0637788i	$-0.0203152\pi$
$179$	4.55563e8	+	7.89058e8i	0.443748	+	0.768594i	−0.554216	+	0.832373i	$0.686982\pi$
$180$	−7.04400e8	−	4.06685e8i	−0.671010	−	0.387408i
$181$		−	3.24955e8i		−	0.302767i	−0.988475	−	0.151384i	$-0.951627\pi$
$181$		−	3.24955e8i		−	0.302767i	0.988475	−	0.151384i	$-0.0483729\pi$
$182$	−6.18382e8	+	2.24211e8i	−0.563600	+	0.204349i
$183$	−3.37328e9			−3.00779
$184$	2.42543e7	−	4.20096e7i	0.0211600	−	0.0366503i
$185$	−8.27286e8	+	4.77634e8i	−0.706266	+	0.407763i
$186$	−2.59272e8	−	4.49072e8i	−0.216622	−	0.375201i
$187$	9.48921e8	+	5.47860e8i	0.776003	+	0.448026i
$188$		−	2.39227e8i		−	0.191505i
$189$	2.19929e9	+	1.85004e9i	1.72360	+	1.44989i
$190$	1.04158e9			0.799242
$191$	−3.64929e8	+	6.32076e8i	−0.274205	+	0.474937i	−0.969934	−	0.243367i	$-0.921748\pi$
$191$	−3.64929e8	+	6.32076e8i	−0.274205	+	0.474937i	0.695729	+	0.718304i	$0.255081\pi$
$192$	2.65187e8	−	1.53106e8i	0.195140	−	0.112664i
$193$	−9.97059e8	−	1.72696e9i	−0.718607	−	1.24466i	−0.961552	−	0.274624i	$-0.911447\pi$
$193$	−9.97059e8	−	1.72696e9i	−0.718607	−	1.24466i	0.242945	−	0.970040i	$-0.421887\pi$
$194$	−7.17066e8	−	4.13998e8i	−0.506235	−	0.292275i
$195$			1.52230e9i			1.05284i
$196$	−5.66426e8	+	4.72917e8i	−0.383812	+	0.320450i
$197$	2.58982e9			1.71951			0.859754	−	0.510709i	$-0.170617\pi$
$197$	2.58982e9			1.71951			0.859754	+	0.510709i	$0.170617\pi$
$198$	−8.65682e8	+	1.49941e9i	−0.563245	+	0.975570i
$199$	−1.69994e9	+	9.81463e8i	−1.08398	+	0.625838i	−0.931968	−	0.362541i	$-0.881909\pi$
$199$	−1.69994e9	+	9.81463e8i	−1.08398	+	0.625838i	−0.152015	+	0.988378i	$0.548576\pi$
$200$	1.48615e8	+	2.57408e8i	0.0928842	+	0.160880i
$201$	−1.45639e9	−	8.40847e8i	−0.892264	−	0.515149i
$202$		−	1.38662e9i		−	0.832819i
$203$	−1.15155e9	+	1.36894e9i	−0.678108	+	0.806121i
$204$	1.97500e9			1.14037
$205$	5.57789e8	−	9.66118e8i	0.315831	−	0.547035i
$206$	2.77551e8	−	1.60244e8i	0.154126	−	0.0889844i
$207$	2.47185e8	+	4.28137e8i	0.134630	+	0.233186i
$208$	−3.43582e8	−	1.98367e8i	−0.183560	−	0.105978i
$209$		−	2.21714e9i		−	1.16200i
$210$	5.82100e8	+	1.60545e9i	0.299310	+	0.825506i
$211$	1.14044e9			0.575364			0.287682	−	0.957726i	$-0.407115\pi$
$211$	1.14044e9			0.575364			0.287682	+	0.957726i	$0.407115\pi$
$212$	−4.24035e8	+	7.34451e8i	−0.209922	+	0.363596i
$213$	3.28623e7	−	1.89730e7i	0.0159654	−	0.00921761i
$214$	6.31076e8	+	1.09306e9i	0.300903	+	0.521180i
$215$	−1.67704e9	−	9.68240e8i	−0.784855	−	0.453137i
$216$			1.73341e9i			0.796317i
$217$	−1.31787e8	+	7.42059e8i	−0.0594337	+	0.334657i
$218$	1.50763e8			0.0667527
$219$	−6.17026e8	+	1.06872e9i	−0.268242	+	0.464609i
$220$	−4.94884e8	+	2.85721e8i	−0.211258	+	0.121970i
$221$	−1.27943e9	−	2.21603e9i	−0.536347	−	0.928981i
$222$	3.17411e9	+	1.83258e9i	1.30680	+	0.754484i
$223$		−	2.81476e9i		−	1.13821i	−0.822266	−	0.569104i	$-0.807290\pi$
$223$		−	2.81476e9i		−	1.13821i	0.822266	−	0.569104i	$-0.192710\pi$
$224$	−4.38202e8	−	7.78229e7i	−0.174053	−	0.0309112i
$225$	−3.02919e9			−1.18194
$226$	9.64895e8	−	1.67125e9i	0.369868	−	0.640630i
$227$	3.60245e9	−	2.07987e9i	1.35673	−	0.783310i	0.367551	−	0.930003i	$-0.380196\pi$
$227$	3.60245e9	−	2.07987e9i	1.35673	−	0.783310i	0.989182	+	0.146693i	$0.0468631\pi$
$228$	−1.99816e9	−	3.46091e9i	−0.739418	−	1.28071i
$229$	−2.25694e8	−	1.30305e8i	−0.0820689	−	0.0473825i	0.458404	−	0.888744i	$-0.348421\pi$
$229$	−2.25694e8	−	1.30305e8i	−0.0820689	−	0.0473825i	−0.540473	+	0.841361i	$0.681755\pi$
$230$			1.63169e8i			0.0583077i
$231$	3.41741e9	−	1.23907e9i	1.20019	−	0.435161i
$232$	−1.07895e9			−0.372435
$233$	−1.05874e9	+	1.83378e9i	−0.359223	+	0.622192i	−0.987831	−	0.155530i	$-0.950292\pi$
$233$	−1.05874e9	+	1.83378e9i	−0.359223	+	0.622192i	0.628608	+	0.777722i	$0.283625\pi$
$234$	3.50159e9	−	2.02164e9i	1.16789	−	0.674281i
$235$	4.02346e8	+	6.96884e8i	0.131925	+	0.228502i
$236$	−5.76220e8	−	3.32681e8i	−0.185755	−	0.107246i
$237$			8.34763e7i			0.0264588i
$238$	−2.19668e9	−	1.84785e9i	−0.684636	−	0.575915i
$239$	3.66705e9			1.12389			0.561947	−	0.827173i	$-0.310053\pi$
$239$	3.66705e9			1.12389			0.561947	+	0.827173i	$0.310053\pi$
$240$	−5.15003e8	+	8.92012e8i	−0.155226	+	0.268860i
$241$	−1.49130e9	+	8.61005e8i	−0.442077	+	0.255233i	−0.704478	−	0.709725i	$-0.748819\pi$
$241$	−1.49130e9	+	8.61005e8i	−0.442077	+	0.255233i	0.262401	+	0.964959i	$0.415486\pi$
$242$	−6.04402e8	−	1.04686e9i	−0.176224	−	0.305229i
$243$	−3.05460e9	−	1.76357e9i	−0.876050	−	0.505788i
$244$			2.95713e9i			0.834279i
$245$	8.54655e8	−	2.33028e9i	0.237206	−	0.646762i
$246$	−4.28022e9			−1.16876
$247$	−2.58886e9	+	4.48403e9i	−0.695537	+	1.20471i
$248$	−3.93672e8	+	2.27287e8i	−0.104071	+	0.0600852i
$249$	4.72247e9	+	8.17955e9i	1.22849	+	2.12781i
$250$	−2.51372e9	−	1.45130e9i	−0.643513	−	0.371533i
$251$			4.21322e9i			1.06150i	0.847529	+	0.530749i	$0.178089\pi$
$251$			4.21322e9i			1.06150i	−0.847529	+	0.530749i	$0.821911\pi$
$252$	2.91982e9	−	3.47102e9i	0.724024	−	0.860705i
$253$	3.47326e8			0.0847724
$254$	7.23982e8	−	1.25397e9i	0.173937	−	0.301268i
$255$	−5.75329e9	+	3.32166e9i	−1.36068	+	0.785588i
$256$	−1.34218e8	−	2.32472e8i	−0.0312500	−	0.0541266i
$257$	9.63051e8	+	5.56018e8i	0.220758	+	0.127455i	0.606301	−	0.795235i	$-0.292653\pi$
$257$	9.63051e8	+	5.56018e8i	0.220758	+	0.127455i	−0.385543	+	0.922690i	$0.625986\pi$
$258$			7.42985e9i			1.67688i
$259$	−1.81580e9	−	5.00804e9i	−0.403524	−	1.11293i
$260$	1.33450e9			0.292029
$261$	5.49802e9	−	9.52286e9i	1.18480	−	2.05213i
$262$	2.09897e9	−	1.21184e9i	0.445453	−	0.257182i
$263$	4.03552e9	+	6.98973e9i	0.843483	+	1.46096i	0.886932	+	0.461900i	$0.152832\pi$
$263$	4.03552e9	+	6.98973e9i	0.843483	+	1.46096i	−0.0434485	+	0.999056i	$0.513834\pi$
$264$	1.89876e9	+	1.09625e9i	0.390890	+	0.225681i
$265$		−	2.85267e9i		−	0.578453i
$266$	−1.01565e9	+	5.71890e9i	−0.202871	+	1.14232i
$267$	2.57142e9			0.505973
$268$	−7.37116e8	+	1.27672e9i	−0.142888	+	0.247490i
$269$	1.71619e9	−	9.90840e8i	0.327759	−	0.189232i	−0.327087	−	0.944994i	$-0.606067\pi$
$269$	1.71619e9	−	9.90840e8i	0.327759	−	0.189232i	0.654846	+	0.755762i	$0.272734\pi$
$270$	−2.91534e9	−	5.04952e9i	−0.548573	−	0.950157i
$271$	1.33197e9	+	7.69016e8i	0.246955	+	0.142580i	0.618369	−	0.785888i	$-0.287794\pi$
$271$	1.33197e9	+	7.69016e8i	0.246955	+	0.142580i	−0.371414	+	0.928467i	$0.621127\pi$
$272$		−	1.73135e9i		−	0.316308i
$273$	−8.35834e9	−	1.48441e9i	−1.50477	−	0.267241i
$274$	−4.07507e9			−0.722992
$275$	−1.06410e9	+	1.84307e9i	−0.186059	+	0.322263i
$276$	5.42169e8	−	3.13021e8i	0.0934326	−	0.0539433i
$277$	6.61097e8	+	1.14505e9i	0.112291	+	0.194494i	0.916694	−	0.399590i	$-0.130848\pi$
$277$	6.61097e8	+	1.14505e9i	0.112291	+	0.194494i	−0.804402	+	0.594085i	$0.797514\pi$
$278$	−1.35475e9	−	7.82165e8i	−0.226819	−	0.130954i
$279$		−	4.63275e9i		−	0.764578i
$280$	1.40740e9	−	5.10290e8i	0.228973	−	0.0830203i
$281$	−6.27601e9			−1.00660			−0.503302	−	0.864111i	$-0.667882\pi$
$281$	−6.27601e9			−1.00660			−0.503302	+	0.864111i	$0.667882\pi$
$282$	1.54372e9	−	2.67379e9i	0.244102	−	0.422796i
$283$	−8.44593e9	+	4.87626e9i	−1.31675	+	0.760223i	−0.983204	−	0.182512i	$-0.941577\pi$
$283$	−8.44593e9	+	4.87626e9i	−1.31675	+	0.760223i	−0.333542	+	0.942735i	$0.608244\pi$
$284$	−1.66324e7	−	2.88082e7i	−0.00255671	−	0.00442836i
$285$	1.16415e10	+	6.72123e9i	1.76453	+	1.01875i
$286$		−	2.84066e9i		−	0.424575i
$287$	4.76066e9	+	4.00467e9i	0.701681	+	0.590254i
$288$	2.73574e9			0.397653
$289$	2.09555e9	−	3.62960e9i	0.300405	−	0.520317i
$290$	3.14305e9	−	1.81464e9i	0.444385	−	0.256566i
$291$	−5.34299e9	−	9.25434e9i	−0.745097	−	1.29055i
$292$	9.36878e8	+	5.40907e8i	0.128870	+	0.0744031i
$293$		−	4.83891e9i		−	0.656564i	−0.944580	−	0.328282i	$-0.893530\pi$
$293$		−	4.83891e9i		−	0.656564i	0.944580	−	0.328282i	$-0.106470\pi$
$294$	−9.38251e9	+	1.63059e9i	−1.25583	+	0.218250i
$295$	2.23809e9			0.295521
$296$	1.60650e9	−	2.78254e9i	0.209273	−	0.362472i
$297$	−1.07486e10	+	6.20568e9i	−1.38142	+	0.797561i
$298$	1.73929e9	+	3.01254e9i	0.220550	+	0.382004i
$299$	−7.02447e8	−	4.05558e8i	−0.0878878	−	0.0507420i
$300$			3.83599e9i			0.473579i
$301$	6.95152e9	−	8.26382e9i	0.846864	−	1.00673i
$302$	9.06099e9			1.08930
$303$	8.94771e9	−	1.54979e10i	1.06155	−	1.83866i
$304$	−3.03395e9	+	1.75165e9i	−0.355234	+	0.205095i
$305$	−4.97347e9	−	8.61431e9i	−0.574726	−	0.995454i
$306$	1.52810e10	+	8.82247e9i	1.74287	+	1.00625i
$307$		−	8.43073e8i		−	0.0949100i	−0.998873	−	0.0474550i	$-0.984889\pi$
$307$		−	8.43073e8i		−	0.0949100i	0.998873	−	0.0474550i	$-0.0151111\pi$
$308$	−1.08622e9	−	2.99582e9i	−0.120702	−	0.332899i
$309$	4.13617e9			0.453696
$310$	7.64528e8	−	1.32420e9i	0.0827840	−	0.143386i
$311$	1.97836e7	−	1.14220e7i	0.00211477	−	0.00122096i	−0.498942	−	0.866635i	$-0.666278\pi$
$311$	1.97836e7	−	1.14220e7i	0.00211477	−	0.00122096i	0.501057	+	0.865414i	$0.332945\pi$
$312$	−2.56009e9	−	4.43421e9i	−0.270170	−	0.467948i
$313$	−2.05943e8	−	1.18901e8i	−0.0214570	−	0.0123882i	0.489233	−	0.872153i	$-0.337277\pi$
$313$	−2.05943e8	−	1.18901e8i	−0.0214570	−	0.0123882i	−0.510690	+	0.859765i	$0.670610\pi$
$314$			2.81037e9i			0.289098i
$315$	−2.66785e9	+	1.50220e10i	−0.270969	+	1.52576i
$316$	7.31783e7			0.00733895
$317$	−9.21516e9	+	1.59611e10i	−0.912569	+	1.58062i	−0.102147	+	0.994769i	$0.532571\pi$
$317$	−9.21516e9	+	1.59611e10i	−0.912569	+	1.58062i	−0.810422	+	0.585846i	$0.800762\pi$
$318$	−9.47870e9	+	5.47253e9i	−0.926916	+	0.535155i
$319$	−3.86270e9	−	6.69039e9i	−0.373017	−	0.646084i
$320$	7.81969e8	+	4.51470e8i	0.0745744	+	0.0430555i
$321$			1.62891e10i			1.53419i
$322$	−8.95895e8	−	1.59107e8i	−0.0833362	−	0.0148002i
$323$	−2.25956e10			−2.07594
$324$	−4.98828e9	+	8.63995e9i	−0.452658	+	0.784027i
$325$	4.30415e9	−	2.48500e9i	0.385792	−	0.222737i
$326$	5.41350e9	+	9.37646e9i	0.479301	+	0.830173i
$327$	1.68504e9	+	9.72861e8i	0.147374	+	0.0850863i
$328$			3.75220e9i			0.324183i
$329$	−4.21865e9	+	1.52959e9i	−0.360072	+	0.130554i
$330$	−7.37495e9			−0.621875
$331$	9.29252e9	−	1.60951e10i	0.774144	−	1.34086i	−0.161131	−	0.986933i	$-0.551514\pi$
$331$	9.29252e9	−	1.60951e10i	0.774144	−	1.34086i	0.935274	−	0.353923i	$-0.115153\pi$
$332$	7.17048e9	−	4.13988e9i	0.590196	−	0.340750i
$333$	1.63725e10	+	2.83580e10i	1.33149	+	2.30621i
$334$	−9.42441e9	−	5.44119e9i	−0.757301	−	0.437228i
$335$		−	4.95890e9i		−	0.393737i
$336$	−4.39550e9	−	3.69749e9i	−0.344866	−	0.290101i
$337$	−1.81757e10			−1.40919			−0.704597	−	0.709608i	$-0.748872\pi$
$337$	−1.81757e10			−1.40919			−0.704597	+	0.709608i	$0.748872\pi$
$338$	1.29755e9	−	2.24743e9i	0.0994165	−	0.172195i
$339$	2.15688e10	−	1.24528e10i	1.63316	−	0.942904i
$340$	2.91189e9	+	5.04354e9i	0.217901	+	0.377415i
$341$	−2.81873e9	−	1.62740e9i	−0.208466	−	0.120358i
$342$		−	3.57037e10i		−	2.60981i
$343$	1.19613e10	+	6.96485e9i	0.864174	+	0.503194i
$344$	6.51327e9			0.465120
$345$	−1.05291e9	+	1.82370e9i	−0.0743219	+	0.128729i
$346$	1.29522e9	−	7.47796e8i	0.0903731	−	0.0521769i
$347$	−5.55696e9	−	9.62493e9i	−0.383283	−	0.663865i	0.608247	−	0.793748i	$-0.291873\pi$
$347$	−5.55696e9	−	9.62493e9i	−0.383283	−	0.663865i	−0.991529	+	0.129883i	$0.958540\pi$
$348$	−1.20592e10	−	6.96239e9i	−0.822246	−	0.474724i
$349$			2.09868e10i			1.41464i	0.706896	+	0.707318i	$0.250095\pi$
$349$			2.09868e10i			1.41464i	−0.706896	+	0.707318i	$0.749905\pi$
$350$	3.58903e9	−	4.26657e9i	0.239169	−	0.284320i
$351$	2.89845e10			1.90958
$352$	9.61012e8	−	1.66452e9i	0.0625977	−	0.108422i
$353$	8.28960e9	−	4.78600e9i	0.533869	−	0.308229i	−0.208722	−	0.977975i	$-0.566930\pi$
$353$	8.28960e9	−	4.78600e9i	0.533869	−	0.308229i	0.742590	+	0.669746i	$0.233597\pi$
$354$	−4.29352e9	−	7.43660e9i	−0.273401	−	0.473545i
$355$	9.69026e7	+	5.59467e7i	0.00610129	+	0.00352258i
$356$		−	2.25419e9i		−	0.140343i
$357$	−1.26278e10	−	3.48280e10i	−0.777421	−	2.14415i
$358$	1.03082e10			0.627554
$359$	−6.29146e9	+	1.08971e10i	−0.378768	+	0.656046i	−0.990883	−	0.134723i	$-0.956986\pi$
$359$	−6.29146e9	+	1.08971e10i	−0.378768	+	0.656046i	0.612115	+	0.790769i	$0.290319\pi$
$360$	−7.96938e9	+	4.60112e9i	−0.474476	+	0.273939i
$361$	1.43688e10	+	2.48875e10i	0.846040	+	1.46538i
$362$	−3.18390e9	−	1.83822e9i	−0.185406	−	0.107044i
$363$		−	1.56006e10i		−	0.898495i
$364$	−1.30128e9	+	7.32721e9i	−0.0741254	+	0.417381i
$365$	−3.63891e9			−0.205022
$366$	−1.90821e10	+	3.30512e10i	−1.06341	+	1.84189i
$367$	−6.13318e9	+	3.54099e9i	−0.338082	+	0.195191i	−0.659423	−	0.751772i	$-0.729199\pi$
$367$	−6.13318e9	+	3.54099e9i	−0.338082	+	0.195191i	0.321342	+	0.946963i	$0.395866\pi$
$368$	−2.74406e8	−	4.75284e8i	−0.0149624	−	0.0259157i
$369$	−3.31170e10	−	1.91201e10i	−1.78626	−	1.03130i
$370$			1.08076e10i			0.576664i
$371$	1.56629e10	+	2.78166e9i	0.826753	+	0.146828i
$372$	−5.86665e9			−0.306350
$373$	5.43482e8	−	9.41338e8i	0.0280769	−	0.0486307i	−0.851646	−	0.524118i	$-0.824395\pi$
$373$	5.43482e8	−	9.41338e8i	0.0280769	−	0.0486307i	0.879722	+	0.475488i	$0.157728\pi$
$374$	1.07358e10	−	6.19833e9i	0.548717	−	0.316802i
$375$	−1.87302e10	−	3.24417e10i	−0.947148	−	1.64051i
$376$	−2.34394e9	−	1.35327e9i	−0.117272	−	0.0677072i
$377$			1.80413e10i			0.893103i
$378$	3.05677e10	−	1.10832e10i	1.49725	−	0.542870i
$379$	1.27216e10			0.616575			0.308288	−	0.951293i	$-0.400244\pi$
$379$	1.27216e10			0.616575			0.308288	+	0.951293i	$0.400244\pi$
$380$	5.89206e9	−	1.02054e10i	0.282575	−	0.489434i
$381$	1.61836e10	−	9.34359e9i	0.768024	−	0.443419i
$382$	4.12870e9	+	7.15112e9i	0.193892	+	0.335831i
$383$	−4.72608e9	−	2.72860e9i	−0.219637	−	0.126808i	0.386145	−	0.922438i	$-0.373806\pi$
$383$	−4.72608e9	−	2.72860e9i	−0.219637	−	0.126808i	−0.605782	+	0.795630i	$0.707140\pi$
$384$		−	3.46438e9i		−	0.159331i
$385$	8.20276e9	+	6.90015e9i	0.373351	+	0.314062i
$386$	−2.25609e10			−1.01626
$387$	−3.31897e10	+	5.74863e10i	−1.47965	+	2.56283i
$388$	−8.11268e9	+	4.68386e9i	−0.357962	+	0.206670i
$389$	−2.14316e10	−	3.71207e10i	−0.935959	−	1.62113i	−0.772915	−	0.634510i	$-0.781202\pi$
$389$	−2.14316e10	−	3.71207e10i	−0.935959	−	1.62113i	−0.163044	−	0.986619i	$-0.552131\pi$
$390$	1.49154e10	+	8.61142e9i	0.644729	+	0.372234i
$391$		−	3.53972e9i		−	0.151447i
$392$	1.42943e9	+	8.22504e9i	0.0605367	+	0.348332i
$393$	3.12797e10			1.31127
$394$	1.46502e10	−	2.53749e10i	0.607938	−	1.05298i
$395$	−2.13173e8	+	1.23075e8i	−0.00875677	+	0.00505572i
$396$	9.79407e9	+	1.69638e10i	0.398275	+	0.689832i
$397$	3.63902e10	+	2.10099e10i	1.46495	+	0.845789i	0.999233	−	0.0391461i	$-0.0124638\pi$
$397$	3.63902e10	+	2.10099e10i	1.46495	+	0.845789i	0.465715	+	0.884935i	$0.345797\pi$
$398$			2.22080e10i			0.885068i
$399$	−4.82553e10	+	5.73649e10i	−1.90394	+	2.26337i
$400$	3.36277e9			0.131358
$401$	4.83802e9	−	8.37970e9i	0.187107	−	0.324079i	−0.757177	−	0.653209i	$-0.773422\pi$
$401$	4.83802e9	−	8.37970e9i	0.187107	−	0.324079i	0.944285	+	0.329130i	$0.106756\pi$
$402$	−1.64772e10	+	9.51310e9i	−0.630926	+	0.364265i
$403$	3.80048e9	+	6.58263e9i	0.144085	+	0.249563i
$404$	−1.35860e10	−	7.84388e9i	−0.509995	−	0.294446i
$405$		−	3.35583e10i		−	1.24733i
$406$	6.89866e9	+	1.90267e10i	0.253899	+	0.700261i
$407$	2.30054e10			0.838401
$408$	1.11723e10	−	1.93509e10i	0.403182	−	0.698331i
$409$	−1.07945e9	+	6.23220e8i	−0.0385753	+	0.0222714i	−0.519164	−	0.854675i	$-0.673756\pi$
$409$	−1.07945e9	+	6.23220e8i	−0.0385753	+	0.0222714i	0.480588	+	0.876946i	$0.340423\pi$
$410$	−6.31066e9	−	1.09304e10i	−0.223326	−	0.386812i
$411$	−4.55462e10	−	2.62961e10i	−1.59619	−	0.921561i
$412$		−	3.62592e9i		−	0.125843i
$413$	−2.18238e9	+	1.22884e10i	−0.0750119	+	0.422373i
$414$	5.59316e9			0.190395
$415$	−1.39254e10	+	2.41195e10i	−0.469477	+	0.813159i
$416$	−3.88719e9	+	2.24427e9i	−0.129796	+	0.0749379i
$417$	−1.00945e10	−	1.74842e10i	−0.333841	−	0.578230i
$418$	−2.17234e10	−	1.25420e10i	−0.711578	−	0.410830i
$419$			5.87657e9i			0.190664i	0.995446	+	0.0953318i	$0.0303912\pi$
$419$			5.87657e9i			0.190664i	−0.995446	+	0.0953318i	$0.969609\pi$
$420$	1.90230e10	+	3.37841e9i	0.611339	+	0.108571i
$421$	−2.95174e10			−0.939613			−0.469807	−	0.882769i	$-0.655676\pi$
$421$	−2.95174e10			−0.939613			−0.469807	+	0.882769i	$0.655676\pi$
$422$	6.45131e9	−	1.11740e10i	0.203422	−	0.352337i
$423$	2.38881e10	−	1.37918e10i	0.746139	−	0.430784i
$424$	4.79741e9	+	8.30936e9i	0.148438	+	0.257101i
$425$	1.87833e10	+	1.08446e10i	0.575728	+	0.332397i
$426$		−	4.29311e8i		−	0.0130357i
$427$	5.21474e10	−	1.89075e10i	1.56863	−	0.568751i
$428$	1.42796e10			0.425541
$429$	1.83305e10	−	3.17494e10i	0.541185	−	0.937359i
$430$	−1.89735e10	+	1.09544e10i	−0.554977	+	0.320416i
$431$	−2.01398e10	−	3.48832e10i	−0.583642	−	1.01090i	−0.995043	−	0.0994434i	$-0.968294\pi$
$431$	−2.01398e10	−	3.48832e10i	−0.583642	−	1.01090i	0.411401	−	0.911454i	$-0.365040\pi$
$432$	1.69839e10	+	9.80563e9i	0.487642	+	0.281540i
$433$		−	4.45909e10i		−	1.26851i	−0.773123	−	0.634256i	$-0.781307\pi$
$433$		−	4.45909e10i		−	1.26851i	0.773123	−	0.634256i	$-0.218693\pi$
$434$	6.52516e9	+	5.48896e9i	0.183921	+	0.154715i
$435$	4.68390e10			1.30813
$436$	8.52844e8	−	1.47717e9i	0.0236006	−	0.0408775i
$437$	−6.20286e9	+	3.58122e9i	−0.170085	+	0.0981987i
$438$	6.98086e9	+	1.20912e10i	0.189676	+	0.328528i
$439$	−2.26501e10	−	1.30771e10i	−0.609835	−	0.352088i	0.163066	−	0.986615i	$-0.447862\pi$
$439$	−2.26501e10	−	1.30771e10i	−0.609835	−	0.352088i	−0.772901	+	0.634527i	$0.781195\pi$
$440$			6.46514e9i			0.172491i
$441$	−7.98784e10	−	2.92962e10i	−2.11191	−	0.774563i
$442$	−2.89501e10			−0.758510
$443$	−1.64102e9	+	2.84233e9i	−0.0426088	+	0.0738006i	−0.886543	−	0.462646i	$-0.846900\pi$
$443$	−1.64102e9	+	2.84233e9i	−0.0426088	+	0.0738006i	0.843935	+	0.536446i	$0.180234\pi$
$444$	3.59110e10	−	2.07332e10i	0.924050	−	0.533501i
$445$	3.79123e9	+	6.56660e9i	0.0966808	+	0.167456i
$446$	−2.75789e10	−	1.59227e10i	−0.697007	−	0.402417i
$447$			4.48940e10i			1.12450i
$448$	−3.24135e9	+	3.85325e9i	−0.0804662	+	0.0956566i
$449$	−1.42212e10			−0.349906			−0.174953	−	0.984577i	$-0.555977\pi$
$449$	−1.42212e10			−0.349906			−0.174953	+	0.984577i	$0.555977\pi$
$450$	−1.71357e10	+	2.96799e10i	−0.417880	+	0.723789i
$451$	−2.32667e10	+	1.34330e10i	−0.562379	+	0.324689i
$452$	−1.09165e10	−	1.89080e10i	−0.261536	−	0.452994i
$453$	1.01273e11	+	5.84698e10i	2.40492	+	1.38848i
$454$		−	4.70622e10i		−	1.10777i
$455$	−8.53260e9	−	2.35332e10i	−0.199084	−	0.549080i
$456$	−4.52131e10			−1.04570
$457$	8.93708e9	−	1.54795e10i	0.204895	−	0.354888i	−0.745204	−	0.666836i	$-0.767648\pi$
$457$	8.93708e9	−	1.54795e10i	0.204895	−	0.354888i	0.950099	+	0.311948i	$0.100981\pi$
$458$	−2.55344e9	+	1.47423e9i	−0.0580315	+	0.0335045i
$459$	6.32443e10	+	1.09542e11i	1.42485	+	2.46792i
$460$	1.59872e9	+	9.23022e8i	0.0357060	+	0.0206149i
$461$			2.00621e10i			0.444193i	0.975025	+	0.222097i	$0.0712901\pi$
$461$			2.00621e10i			0.444193i	−0.975025	+	0.222097i	$0.928710\pi$
$462$	7.19138e9	−	4.04929e10i	0.157850	−	0.888814i
$463$	−6.02177e10			−1.31039			−0.655195	−	0.755460i	$-0.727414\pi$
$463$	−6.02177e10			−1.31039			−0.655195	+	0.755460i	$0.727414\pi$
$464$	−6.10347e9	+	1.05715e10i	−0.131676	+	0.228069i
$465$	1.70899e10	−	9.86687e9i	0.365534	−	0.211041i
$466$	1.19782e10	+	2.07469e10i	0.254009	+	0.439956i
$467$	6.34957e10	+	3.66593e10i	1.33499	+	0.770755i	0.986059	−	0.166395i	$-0.0532127\pi$
$467$	6.34957e10	+	3.66593e10i	1.33499	+	0.770755i	0.348927	+	0.937150i	$0.386546\pi$
$468$		−	4.57445e10i		−	0.953577i
$469$	2.72273e10	+	4.83547e9i	0.562748	+	0.0999418i
$470$	9.10406e9			0.186571
$471$	−1.81351e10	+	3.14109e10i	−0.368499	+	0.638259i
$472$	−6.51918e9	+	3.76385e9i	−0.131349	+	0.0758341i
$473$	2.33178e10	+	4.03876e10i	0.465847	+	0.806870i
$474$	8.17898e8	+	4.72214e8i	0.0162026	+	0.00935460i
$475$		−	4.38869e10i		−	0.862106i
$476$	−3.05315e10	+	1.10700e10i	−0.594730	+	0.215636i
$477$	−9.77849e10			−1.88885
$478$	2.07440e10	−	3.59296e10i	0.397356	−	0.688242i
$479$	6.54555e10	−	3.77908e10i	1.24338	−	0.717867i	0.273600	−	0.961843i	$-0.411785\pi$
$479$	6.54555e10	−	3.77908e10i	1.24338	−	0.717867i	0.969781	+	0.243977i	$0.0784521\pi$
$480$	5.82660e9	+	1.00920e10i	0.109762	+	0.190113i
$481$	−4.65271e10	−	2.68624e10i	−0.869212	−	0.501840i
$482$			1.94823e10i			0.360955i
$483$	−8.98651e9	−	7.55944e9i	−0.165121	−	0.138900i
$484$	−1.36761e10			−0.249218
$485$	1.57552e10	−	2.72887e10i	0.284745	−	0.493192i
$486$	−3.45588e10	+	1.99525e10i	−0.619461	+	0.357646i
$487$	−1.82603e10	−	3.16278e10i	−0.324633	−	0.562280i	0.656805	−	0.754060i	$-0.271907\pi$
$487$	−1.82603e10	−	3.16278e10i	−0.324633	−	0.562280i	−0.981438	+	0.191780i	$0.938574\pi$
$488$	2.89739e10	+	1.67281e10i	0.510890	+	0.294962i
$489$			1.39732e11i			2.44376i
$490$	−1.79974e10	−	2.15559e10i	−0.312194	−	0.373923i
$491$	−1.03557e10			−0.178178			−0.0890890	−	0.996024i	$-0.528396\pi$
$491$	−1.03557e10			−0.178178			−0.0890890	+	0.996024i	$0.528396\pi$
$492$	−2.42126e10	+	4.19375e10i	−0.413220	+	0.715718i
$493$	−6.81841e10	+	3.93661e10i	−1.15424	+	0.666400i
$494$	2.92896e10	+	5.07310e10i	0.491819	+	0.851856i
$495$	−5.70615e10	−	3.29445e10i	−0.950435	−	0.548734i
$496$			5.14291e9i			0.0849733i
$497$	−4.01672e8	+	4.77499e8i	−0.00658333	+	0.00782613i
$498$	1.06857e11			1.73735
$499$	2.55128e10	−	4.41895e10i	0.411487	−	0.712716i	−0.583566	−	0.812066i	$-0.698343\pi$
$499$	2.55128e10	−	4.41895e10i	0.411487	−	0.712716i	0.995053	+	0.0993496i	$0.0316762\pi$
$500$	−2.84395e10	+	1.64196e10i	−0.455033	+	0.262713i
$501$	−7.02231e10	−	1.21630e11i	−1.11463	−	1.93059i
$502$	4.12810e10	+	2.38336e10i	0.650032	+	0.375296i
$503$			5.95396e10i			0.930109i	0.885282	+	0.465055i	$0.153965\pi$
$503$			5.95396e10i			0.930109i	−0.885282	+	0.465055i	$0.846035\pi$
$504$	−1.74919e10	−	4.82433e10i	−0.271091	−	0.747678i
$505$	5.27691e10			0.811362
$506$	1.96477e9	−	3.40308e9i	0.0299716	−	0.0519123i
$507$	2.90050e10	−	1.67460e10i	0.438976	−	0.253443i
$508$	−8.19092e9	−	1.41871e10i	−0.122992	−	0.213029i
$509$	−4.81846e9	−	2.78194e9i	−0.0717856	−	0.0414455i	0.463678	−	0.886004i	$-0.346530\pi$
$509$	−4.81846e9	−	2.78194e9i	−0.0717856	−	0.0414455i	−0.535463	+	0.844559i	$0.679863\pi$
$510$			7.51607e10i			1.11099i
$511$	3.54834e9	−	1.99798e10i	0.0520405	−	0.293027i
$512$	−3.03700e9			−0.0441942
$513$	1.27972e11	−	2.21654e11i	1.84776	−	3.20041i
$514$	1.08957e10	−	6.29062e9i	0.156100	−	0.0901241i
$515$	6.09827e9	+	1.05625e10i	0.0866918	+	0.150155i
$516$	7.27973e10	+	4.20296e10i	1.02687	+	0.592865i
$517$		−	1.93792e10i		−	0.271252i
$518$	−5.93403e10	−	1.05386e10i	−0.824197	−	0.146374i
$519$	1.93019e10			0.266029
$520$	7.54908e9	−	1.30754e10i	0.103248	−	0.178830i
$521$	−6.49808e10	+	3.75167e10i	−0.881930	+	0.509183i	−0.871294	−	0.490761i	$-0.836719\pi$
$521$	−6.49808e10	+	3.75167e10i	−0.881930	+	0.509183i	−0.0106360	+	0.999943i	$0.503386\pi$
$522$	−6.22031e10	−	1.07739e11i	−0.837779	−	1.45108i
$523$	−9.91270e10	−	5.72310e10i	−1.32491	−	0.764935i	−0.340400	−	0.940281i	$-0.610562\pi$
$523$	−9.91270e10	−	5.72310e10i	−1.32491	−	0.764935i	−0.984507	+	0.175346i	$0.943896\pi$
$524$		−	2.74209e10i		−	0.363711i
$525$	6.76457e10	−	2.45268e10i	0.890436	−	0.322852i
$526$	9.13134e10			1.19287
$527$	−1.65854e10	+	2.87267e10i	−0.215022	+	0.372428i
$528$	2.14820e10	−	1.24027e10i	0.276401	−	0.159580i
$529$	3.85945e10	+	6.68476e10i	0.492836	+	0.853617i
$530$	−2.79503e10	−	1.61371e10i	−0.354228	−	0.204514i
$531$		−	7.67180e10i		−	0.964982i
$532$	5.02881e10	+	4.23023e10i	0.627797	+	0.528102i
$533$	6.27408e10			0.777394
$534$	1.45461e10	−	2.51946e10i	0.178888	−	0.309844i
$535$	−4.15974e10	+	2.40163e10i	−0.507752	+	0.293151i
$536$	8.33952e9	+	1.44445e10i	0.101037	+	0.175002i
$537$	1.15213e11	+	6.65181e10i	1.38549	+	0.799912i
$538$		−	2.24202e10i		−	0.267614i
$539$	−4.58846e10	+	3.83097e10i	−0.543640	+	0.453893i
$540$	−6.59667e10			−0.775800
$541$	−6.17433e10	+	1.06942e11i	−0.720776	+	1.24842i	0.239913	+	0.970794i	$0.422881\pi$
$541$	−6.17433e10	+	1.06942e11i	−0.720776	+	1.24842i	−0.960689	+	0.277627i	$0.910452\pi$
$542$	1.50696e10	−	8.70042e9i	0.174624	−	0.100819i
$543$	−2.37238e10	−	4.10908e10i	−0.272888	−	0.472657i
$544$	−1.69637e10	−	9.79401e9i	−0.193698	−	0.111832i
$545$			5.73745e9i			0.0650329i
$546$	−6.18261e10	+	7.34976e10i	−0.695666	+	0.826994i
$547$	−1.25965e11			−1.40702			−0.703509	−	0.710686i	$-0.748385\pi$
$547$	−1.25965e11			−1.40702			−0.703509	+	0.710686i	$0.748385\pi$
$548$	−2.30521e10	+	3.99274e10i	−0.255616	+	0.442740i
$549$	−2.95285e11	+	1.70483e11i	−3.25051	+	1.87668i
$550$	1.20389e10	+	2.08519e10i	0.131563	+	0.227874i
$551$	1.37967e11	+	7.96555e10i	1.49682	+	0.864190i
$552$		−	7.08286e9i		−	0.0762874i
$553$	−4.67891e8	−	1.29046e9i	−0.00500316	−	0.0137989i
$554$	1.49589e10			0.158804
$555$	−6.97406e10	+	1.20794e11i	−0.735045	+	1.27314i
$556$	−1.53272e10	+	8.84918e9i	−0.160385	+	0.0925985i
$557$	−6.08743e10	−	1.05437e11i	−0.632431	−	1.09540i	−0.987053	−	0.160393i	$-0.948724\pi$
$557$	−6.08743e10	−	1.05437e11i	−0.632431	−	1.09540i	0.354622	−	0.935010i	$-0.384610\pi$
$558$	−4.53915e10	−	2.62068e10i	−0.468207	−	0.270319i
$559$		−	1.08909e11i		−	1.11536i
$560$	2.96164e9	−	1.66762e10i	0.0301148	−	0.169569i
$561$	1.59989e11			1.61525
$562$	−3.55025e10	+	6.14921e10i	−0.355888	+	0.616416i
$563$	1.23249e11	−	7.11577e10i	1.22673	−	0.708253i	0.260385	−	0.965505i	$-0.416150\pi$
$563$	1.23249e11	−	7.11577e10i	1.22673	−	0.708253i	0.966344	+	0.257252i	$0.0828172\pi$
$564$	−1.74651e10	−	3.02505e10i	−0.172606	−	0.298962i
$565$	6.36011e10	+	3.67201e10i	0.624124	+	0.360338i
$566$			1.10337e11i			1.07512i
$567$	1.84255e11	+	3.27230e10i	1.78274	+	0.316607i
$568$	−3.76349e8			−0.00361574
$569$	9.57798e10	−	1.65895e11i	0.913745	−	1.58265i	0.105016	−	0.994471i	$-0.466511\pi$
$569$	9.57798e10	−	1.65895e11i	0.913745	−	1.58265i	0.808729	−	0.588181i	$-0.200156\pi$
$570$	1.31709e11	−	7.60420e10i	1.24771	−	0.720368i
$571$	8.11688e10	+	1.40589e11i	0.763563	+	1.32253i	0.941003	+	0.338398i	$0.109885\pi$
$571$	8.11688e10	+	1.40589e11i	0.763563	+	1.32253i	−0.177440	+	0.984132i	$0.556782\pi$
$572$	−2.78326e10	−	1.60692e10i	−0.259998	−	0.150110i
$573$			1.06569e11i			0.988579i
$574$	6.61679e10	−	2.39910e10i	0.609537	−	0.221004i
$575$	6.87511e9			0.0628939
$576$	1.54757e10	−	2.68046e10i	0.140592	−	0.243512i
$577$	−7.10164e10	+	4.10013e10i	−0.640701	+	0.369909i	−0.784884	−	0.619642i	$-0.787278\pi$
$577$	−7.10164e10	+	4.10013e10i	−0.640701	+	0.369909i	0.144184	+	0.989551i	$0.453944\pi$
$578$	−2.37085e10	−	4.10643e10i	−0.212418	−	0.367919i
$579$	−2.52158e11	−	1.45583e11i	−2.24367	−	1.29538i
$580$		−	4.10607e10i		−	0.362839i
$581$	−1.18852e11	−	9.99778e10i	−1.04304	−	0.877403i
$582$	−1.20898e11			−1.05373
$583$	−3.43499e10	+	5.94958e10i	−0.297339	+	0.515006i
$584$	1.05996e10	−	6.11966e9i	0.0911248	−	0.0526110i
$585$	7.69358e10	+	1.33257e11i	0.656909	+	1.13780i
$586$	−4.74114e10	−	2.73730e10i	−0.402062	−	0.232130i
$587$		−	1.08603e11i		−	0.914726i	−0.889280	−	0.457363i	$-0.848794\pi$
$587$		−	1.08603e11i		−	0.914726i	0.889280	−	0.457363i	$-0.151206\pi$
$588$	−3.70990e10	+	1.01153e11i	−0.310351	+	0.846197i
$589$	6.71193e10			0.557682
$590$	1.26605e10	−	2.19287e10i	0.104483	−	0.180969i
$591$	3.27484e11	−	1.89073e11i	2.68436	−	1.54982i
$592$	−1.81755e10	−	3.14808e10i	−0.147979	−	0.256306i
$593$	−1.02644e11	−	5.92618e10i	−0.830073	−	0.479243i	0.0238046	−	0.999717i	$-0.492422\pi$
$593$	−1.02644e11	−	5.92618e10i	−0.830073	−	0.479243i	−0.853878	+	0.520474i	$0.825755\pi$
$594$			1.40419e11i			1.12792i
$595$	7.03219e10	−	8.35972e10i	0.561077	−	0.666997i
$596$	3.93557e10			0.311905
$597$	−1.43306e11	+	2.48214e11i	−1.12815	+	1.95402i
$598$	−7.94728e9	+	4.58836e9i	−0.0621461	+	0.0358800i
$599$	1.01445e11	+	1.75708e11i	0.787996	+	1.36485i	0.927193	+	0.374585i	$0.122215\pi$
$599$	1.01445e11	+	1.75708e11i	0.787996	+	1.36485i	−0.139196	+	0.990265i	$0.544452\pi$
$600$	3.75849e10	+	2.16997e10i	0.290007	+	0.167436i
$601$		−	1.70028e11i		−	1.30323i	−0.758549	−	0.651616i	$-0.774091\pi$
$601$		−	1.70028e11i		−	1.30323i	0.758549	−	0.651616i	$-0.225909\pi$
$602$	−4.16449e10	−	1.14858e11i	−0.317085	−	0.874530i
$603$	−1.69983e11			−1.28569
$604$	5.12567e10	−	8.87792e10i	0.385126	−	0.667058i
$605$	3.98392e10	−	2.30012e10i	0.297365	−	0.171684i
$606$	−1.01232e11	−	1.75339e11i	−0.750631	−	1.30013i
$607$	−8.83230e10	−	5.09933e10i	−0.650607	−	0.375628i	0.138081	−	0.990421i	$-0.455906\pi$
$607$	−8.83230e10	−	5.09933e10i	−0.650607	−	0.375628i	−0.788689	+	0.614792i	$0.789240\pi$
$608$			3.96354e10i			0.290047i
$609$	−4.56731e10	+	2.57174e11i	−0.332041	+	1.86964i
$610$	−1.12537e11			−0.812785
$611$	−2.26282e10	+	3.91933e10i	−0.162363	+	0.281220i
$612$	1.72884e11	−	9.98148e10i	1.23240	−	0.711524i
$613$	1.15082e11	+	1.99328e11i	0.815016	+	1.41165i	0.909317	+	0.416105i	$0.136605\pi$
$613$	1.15082e11	+	1.99328e11i	0.815016	+	1.41165i	−0.0943009	+	0.995544i	$0.530062\pi$
$614$	−8.26040e9	−	4.76914e9i	−0.0581203	−	0.0335557i
$615$		−	1.62889e11i		−	1.13865i
$616$	−3.54975e10	−	6.30422e9i	−0.246533	−	0.0437833i
$617$	−9.80871e10			−0.676817			−0.338408	−	0.940999i	$-0.609889\pi$
$617$	−9.80871e10			−0.676817			−0.338408	+	0.940999i	$0.609889\pi$
$618$	2.33977e10	−	4.05261e10i	0.160406	−	0.277831i
$619$	6.66450e10	−	3.84775e10i	0.453947	−	0.262086i	−0.255549	−	0.966796i	$-0.582256\pi$
$619$	6.66450e10	−	3.84775e10i	0.453947	−	0.262086i	0.709496	+	0.704710i	$0.248923\pi$
$620$	−8.64964e9	−	1.49816e10i	−0.0585371	−	0.101389i
$621$	3.47232e10	+	2.00474e10i	0.233482	+	0.134801i
$622$		−	2.58451e8i		−	0.00172670i
$623$	−3.97515e10	+	1.44130e10i	−0.263877	+	0.0956757i
$624$	−5.79283e10			−0.382078
$625$	1.51435e10	−	2.62293e10i	0.0992443	−	0.171896i
$626$	−2.32998e9	+	1.34521e9i	−0.0151724	+	0.00875980i
$627$	−1.61865e11	−	2.80359e11i	−1.04733	−	1.81403i
$628$	2.75359e10	+	1.58979e10i	0.177036	+	0.102212i
$629$		−	2.34456e11i		−	1.49782i
$630$	1.32093e11	+	1.11117e11i	0.838530	+	0.705370i
$631$	1.72588e11			1.08866			0.544330	−	0.838871i	$-0.316784\pi$
$631$	1.72588e11			1.08866			0.544330	+	0.838871i	$0.316784\pi$
$632$	4.13959e8	−	7.16998e8i	0.00259471	−	0.00449417i
$633$	1.44210e11	−	8.32595e10i	0.898214	−	0.518584i
$634$	1.04258e11	+	1.80579e11i	0.645284	+	1.11766i
$635$	4.77213e10	+	2.75519e10i	0.293507	+	0.169456i
$636$			1.23829e11i			0.756824i
$637$	1.37532e11	−	2.39017e10i	0.835305	−	0.145168i
$638$	−8.74029e10			−0.527525
$639$	1.91776e9	−	3.32167e9i	0.0115025	−	0.0199229i
$640$	8.84697e9	−	5.10780e9i	0.0527321	−	0.0304449i
$641$	−5.30434e10	−	9.18739e10i	−0.314195	−	0.544202i	0.665071	−	0.746780i	$-0.268401\pi$
$641$	−5.30434e10	−	9.18739e10i	−0.314195	−	0.544202i	−0.979266	+	0.202578i	$0.935068\pi$
$642$	1.59600e11	+	9.21453e10i	0.939493	+	0.542417i
$643$			1.34796e11i			0.788560i	0.918990	+	0.394280i	$0.129006\pi$
$643$			1.34796e11i			0.788560i	−0.918990	+	0.394280i	$0.870994\pi$
$644$	−6.62687e9	+	7.87789e9i	−0.0385270	+	0.0458001i
$645$	−2.82751e11			−1.63367
$646$	−1.27820e11	+	2.21391e11i	−0.733954	+	1.27125i
$647$	−2.34397e11	+	1.35329e11i	−1.33763	+	0.772279i	−0.986455	−	0.164032i	$-0.947550\pi$
$647$	−2.34397e11	+	1.35329e11i	−1.33763	+	0.772279i	−0.351172	+	0.936311i	$0.614217\pi$
$648$	5.64359e10	+	9.77499e10i	0.320078	+	0.554391i
$649$	−4.66780e10	−	2.69495e10i	−0.263107	−	0.151905i
$650$		−	5.62292e10i		−	0.314998i
$651$	3.75105e10	+	1.03455e11i	0.208847	+	0.576008i
$652$	1.22494e11			0.677834
$653$	−1.34684e11	+	2.33279e11i	−0.740734	+	1.28299i	0.211427	+	0.977394i	$0.432189\pi$
$653$	−1.34684e11	+	2.33279e11i	−0.740734	+	1.28299i	−0.952161	+	0.305596i	$0.901144\pi$
$654$	1.90641e10	−	1.10067e10i	0.104209	−	0.0601651i
$655$	4.61180e10	+	7.98787e10i	0.250556	+	0.433976i
$656$	3.67639e10	+	2.12256e10i	0.198521	+	0.114616i
$657$			1.24736e11i			0.669469i
$658$	−8.87746e9	+	4.99868e10i	−0.0473571	+	0.266656i
$659$	3.10763e11			1.64774			0.823868	−	0.566781i	$-0.191812\pi$
$659$	3.10763e11			1.64774			0.823868	+	0.566781i	$0.191812\pi$
$660$	−4.17190e10	+	7.22594e10i	−0.219866	+	0.380819i
$661$	−1.18849e11	+	6.86177e10i	−0.622574	+	0.359443i	−0.777870	−	0.628425i	$-0.783700\pi$
$661$	−1.18849e11	+	6.86177e10i	−0.622574	+	0.359443i	0.155296	+	0.987868i	$0.450367\pi$
$662$	−1.05133e11	−	1.82096e11i	−0.547402	−	0.948129i
$663$	−3.23569e11	−	1.86813e11i	−1.67461	−	0.966835i
$664$		−	9.36748e10i		−	0.481893i
$665$	−2.17639e11	−	3.86518e10i	−1.11288	−	0.197644i
$666$	3.70468e11			1.88301
$667$	−1.24784e10	+	2.16133e10i	−0.0630459	+	0.109199i
$668$	−1.06625e11	+	6.15600e10i	−0.535493	+	0.309167i
$669$	−2.05495e11	−	3.55928e11i	−1.02588	−	1.77688i
$670$	−4.85871e10	−	2.80518e10i	−0.241114	−	0.139207i
$671$			2.39549e11i			1.18169i
$672$	−6.10925e10	+	2.21508e10i	−0.299579	+	0.108620i
$673$	3.25349e11			1.58595			0.792975	−	0.609254i	$-0.208531\pi$
$673$	3.25349e11			1.58595			0.792975	+	0.609254i	$0.208531\pi$
$674$	−1.02817e11	+	1.78084e11i	−0.498225	+	0.862952i
$675$	−2.12762e11	+	1.22838e11i	−1.02489	+	0.591722i
$676$	−1.46801e10	−	2.54268e10i	−0.0702981	−	0.121760i
$677$	3.19960e11	+	1.84729e11i	1.52314	+	0.879388i	0.999625	+	0.0273741i	$0.00871454\pi$
$677$	3.19960e11	+	1.84729e11i	1.52314	+	0.879388i	0.523519	+	0.852014i	$0.324619\pi$
$678$		−	2.81774e11i		−	1.33347i
$679$	1.34469e11	+	1.13115e11i	0.632618	+	0.532158i
$680$	6.58885e10			0.308158
$681$	3.03688e11	−	5.26004e11i	1.41202	−	2.44568i
$682$	−3.18903e10	+	1.84119e10i	−0.147408	+	0.0851061i
$683$	−2.14512e10	−	3.71546e10i	−0.0985755	−	0.170738i	0.812520	−	0.582934i	$-0.198095\pi$
$683$	−2.14512e10	−	3.71546e10i	−0.0985755	−	0.170738i	−0.911095	+	0.412196i	$0.864762\pi$
$684$	−3.49823e11	−	2.01971e11i	−1.59817	−	0.922706i
$685$		−	1.55081e11i		−	0.704364i
$686$	1.35905e11	−	7.77969e10i	0.613674	−	0.351290i
$687$	−3.80523e10			−0.170826
$688$	3.68446e10	−	6.38167e10i	0.164445	−	0.284827i
$689$	1.38942e11	−	8.02180e10i	0.616532	−	0.355955i
$690$	1.19124e10	+	2.06328e10i	0.0525535	+	0.0910253i
$691$	5.33699e10	+	3.08131e10i	0.234091	+	0.135152i	0.612458	−	0.790503i	$-0.290181\pi$
$691$	5.33699e10	+	3.08131e10i	0.234091	+	0.135152i	−0.378367	+	0.925656i	$0.623514\pi$
$692$		−	1.69207e10i		−	0.0737893i
$693$	2.36526e11	−	2.81177e11i	1.02553	−	1.21912i
$694$	−1.25740e11			−0.542044
$695$	2.97661e10	−	5.15564e10i	0.127580	−	0.220975i
$696$	−1.36434e11	+	7.87704e10i	−0.581416	+	0.335681i
$697$	1.36901e11	+	2.37119e11i	0.580063	+	1.00470i
$698$	2.05628e11	+	1.18719e11i	0.866284	+	0.500149i
$699$			3.09178e11i			1.29509i
$700$	−2.15010e10	−	5.93006e10i	−0.0895503	−	0.246983i
$701$	−4.62669e11			−1.91601			−0.958006	−	0.286748i	$-0.907426\pi$
$701$	−4.62669e11			−1.91601			−0.958006	+	0.286748i	$0.907426\pi$
$702$	1.63961e11	−	2.83989e11i	0.675137	−	1.16937i
$703$	−4.10851e11	+	2.37205e11i	−1.68215	+	0.971187i
$704$	−1.08726e10	−	1.88319e10i	−0.0442632	−	0.0766662i
$705$	1.01754e11	+	5.87477e10i	0.411903	+	0.237813i
$706$		−	1.08295e11i		−	0.435902i
$707$	−5.14557e10	+	2.89734e11i	−0.205947	+	1.15964i
$708$	−9.71513e10			−0.386648
$709$	2.10316e11	−	3.64278e11i	0.832314	−	1.44161i	−0.0638847	−	0.997957i	$-0.520349\pi$
$709$	2.10316e11	−	3.64278e11i	0.832314	−	1.44161i	0.896199	−	0.443653i	$-0.146318\pi$
$710$	1.09633e9	−	6.32965e8i	0.00431427	−	0.00249084i
$711$	4.21883e9	+	7.30723e9i	0.0165087	+	0.0285940i
$712$	−2.20865e10	−	1.27516e10i	−0.0859423	−	0.0496188i
$713$			1.05146e10i			0.0406850i
$714$	−4.12677e11	−	7.32899e10i	−1.58788	−	0.282001i
$715$	1.08104e11			0.413636
$716$	5.83121e10	−	1.00999e11i	0.221874	−	0.384297i
$717$	4.63702e11	−	2.67718e11i	1.75453	−	1.01298i
$718$	7.11798e10	+	1.23287e11i	0.267830	+	0.463895i
$719$	8.22291e9	+	4.74750e9i	0.0307687	+	0.0177643i	0.515305	−	0.857007i	$-0.327678\pi$
$719$	8.22291e9	+	4.74750e9i	0.0307687	+	0.0177643i	−0.484537	+	0.874771i	$0.661012\pi$
$720$			1.04111e11i			0.387408i
$721$	−6.39411e10	+	2.31836e10i	−0.236613	+	0.0857905i
$722$	3.25128e11			1.19648
$723$	−1.25718e11	+	2.17750e11i	−0.460091	+	0.796901i
$724$	−3.60217e10	+	2.07971e10i	−0.131102	+	0.0756918i
$725$	−7.64599e10	−	1.32432e11i	−0.276746	−	0.479339i
$726$	−1.52854e11	−	8.82505e10i	−0.550214	−	0.317666i
$727$		−	2.81762e10i		−	0.100866i	−0.998727	−	0.0504331i	$-0.983940\pi$
$727$		−	2.81762e10i		−	0.100866i	0.998727	−	0.0504331i	$-0.0160602\pi$
$728$	6.44305e10	+	5.41989e10i	0.229386	+	0.192959i
$729$	−3.63195e9			−0.0128597
$730$	−2.05848e10	+	3.56539e10i	−0.0724862	+	0.125550i
$731$	4.11604e11	−	2.37640e11i	1.44149	−	0.832242i
$732$	2.15890e11	+	3.73932e11i	0.751947	+	1.30241i
$733$	−2.72605e11	−	1.57389e11i	−0.944319	−	0.545203i	−0.0530071	−	0.998594i	$-0.516881\pi$
$733$	−2.72605e11	−	1.57389e11i	−0.944319	−	0.545203i	−0.891311	+	0.453392i	$0.850214\pi$
$734$			8.01235e10i			0.276042i
$735$	−6.20538e10	−	3.57062e11i	−0.212627	−	1.22347i
$736$	−6.20909e9			−0.0211600
$737$	−5.97118e10	+	1.03424e11i	−0.202390	+	0.350550i
$738$	−3.74676e11	+	2.16319e11i	−1.26308	+	0.729239i
$739$	−2.78805e11	−	4.82904e11i	−0.934808	−	1.61914i	−0.774976	−	0.631991i	$-0.782238\pi$
$739$	−2.78805e11	−	4.82904e11i	−0.934808	−	1.61914i	−0.159833	−	0.987144i	$-0.551095\pi$
$740$	1.05893e11	+	6.11371e10i	0.353133	+	0.203882i
$741$			7.56013e11i			2.50759i
$742$	1.15857e11	−	1.37729e11i	0.382215	−	0.454369i
$743$	−2.65800e11			−0.872167			−0.436084	−	0.899906i	$-0.643635\pi$
$743$	−2.65800e11			−0.872167			−0.436084	+	0.899906i	$0.643635\pi$
$744$	−3.31868e10	+	5.74812e10i	−0.108311	+	0.187601i
$745$	−1.14645e11	+	6.61906e10i	−0.372162	+	0.214868i
$746$	−6.14879e9	−	1.06500e10i	−0.0198534	−	0.0343871i
$747$	8.26776e11	+	4.77340e11i	2.65525	+	1.53301i
$748$		−	1.40252e11i		−	0.448026i
$749$	−9.13019e10	−	2.51814e11i	−0.290103	−	0.800114i
$750$	−4.23817e11			−1.33947
$751$	−6.39080e10	+	1.10692e11i	−0.200907	+	0.347981i	−0.948821	−	0.315814i	$-0.897722\pi$
$751$	−6.39080e10	+	1.10692e11i	−0.200907	+	0.347981i	0.747914	+	0.663796i	$0.231056\pi$
$752$	−2.65187e10	+	1.53106e10i	−0.0829240	+	0.0478762i
$753$	3.07592e11	+	5.32765e11i	0.956743	+	1.65713i
$754$	1.76768e11	+	1.02057e11i	0.546911	+	0.315759i
$755$			3.44826e11i			1.06124i
$756$	6.43248e10	−	3.62197e11i	0.196921	−	1.10881i
$757$	−1.39036e11			−0.423394			−0.211697	−	0.977335i	$-0.567899\pi$
$757$	−1.39036e11			−0.423394			−0.211697	+	0.977335i	$0.567899\pi$
$758$	7.19644e10	−	1.24646e11i	0.217992	−	0.377574i
$759$	4.39196e10	−	2.53570e10i	0.132340	−	0.0764066i
$760$	−6.66611e10	−	1.15460e11i	−0.199810	−	0.346082i
$761$	−4.17660e11	−	2.41136e11i	−1.24533	−	0.718990i	−0.275154	−	0.961400i	$-0.588729\pi$
$761$	−4.17660e11	−	2.41136e11i	−1.24533	−	0.718990i	−0.970174	+	0.242410i	$0.922062\pi$
$762$		−	2.11421e11i		−	0.627089i
$763$	−3.15021e10	−	5.59464e9i	−0.0929481	−	0.0165072i
$764$	9.34219e10			0.274205
$765$	−3.35749e11	+	5.81534e11i	−0.980321	+	1.69797i
$766$	−5.34695e10	+	3.08706e10i	−0.155307	+	0.0896665i
$767$	6.29357e10	+	1.09008e11i	0.181851	+	0.314975i
$768$	−3.39439e10	−	1.95975e10i	−0.0975701	−	0.0563321i
$769$			2.81913e11i			0.806139i	0.915169	+	0.403070i	$0.132057\pi$
$769$			2.81913e11i			0.806139i	−0.915169	+	0.403070i	$0.867943\pi$
$770$	1.14009e11	−	4.13371e10i	0.324323	−	0.117592i
$771$	1.62371e11			0.459507
$772$	−1.27623e11	+	2.21050e11i	−0.359303	+	0.622332i
$773$	−2.35305e11	+	1.35853e11i	−0.659041	+	0.380497i	−0.791911	−	0.610636i	$-0.790914\pi$
$773$	−2.35305e11	+	1.35853e11i	−0.659041	+	0.380497i	0.132871	+	0.991133i	$0.457581\pi$
$774$	3.75499e11	+	6.50383e11i	1.04627	+	1.81220i
$775$	−5.57952e10	−	3.22134e10i	−0.154664	−	0.0892954i
$776$			1.05984e11i			0.292275i
$777$	−5.95229e11	−	5.00706e11i	−1.63305	−	1.37372i
$778$	−4.84942e11			−1.32365
$779$	2.77012e11	−	4.79799e11i	0.752227	−	1.30290i
$780$	1.68749e11	−	9.74271e10i	0.455892	−	0.263209i
$781$	−1.34735e9	−	2.33367e9i	−0.00362139	−	0.00627243i
$782$	−3.46820e10	−	2.00237e10i	−0.0927421	−	0.0535447i
$783$		−	8.91811e11i		−	2.37261i
$784$	8.86747e10	+	3.25223e10i	0.234712	+	0.0860830i
$785$	−1.06952e11			−0.281650
$786$	1.76945e11	−	3.06477e11i	0.463604	−	0.802986i
$787$	1.52232e11	−	8.78913e10i	0.396833	−	0.229111i	−0.288284	−	0.957545i	$-0.593085\pi$
$787$	1.52232e11	−	8.78913e10i	0.396833	−	0.229111i	0.685116	+	0.728434i	$0.259751\pi$
$788$	−1.65748e11	−	2.87084e11i	−0.429877	−	0.744569i
$789$	1.02059e12	+	5.89238e11i	2.63356	+	1.52049i
$790$			2.78488e9i			0.00714987i
$791$	−2.63634e11	+	3.13402e11i	−0.673434	+	0.800564i
$792$	2.21615e11			0.563245
$793$	2.79712e11	−	4.84475e11i	0.707323	−	1.22512i
$794$	4.11708e11	−	2.37700e11i	1.03588	−	0.598063i
$795$	−2.08263e11	−	3.60722e11i	−0.521367	−	0.903035i
$796$	2.17593e11	+	1.25627e11i	0.541991	+	0.312919i
$797$		−	6.69693e11i		−	1.65975i	−0.557949	−	0.829875i	$-0.688412\pi$
$797$		−	6.69693e11i		−	1.65975i	0.557949	−	0.829875i	$-0.311588\pi$
$798$	2.89086e11	+	7.97309e11i	0.712878	+	1.96614i
$799$	−1.97500e11			−0.484596
$800$	1.90227e10	−	3.29483e10i	0.0464421	−	0.0804401i
$801$	2.25093e11	−	1.29957e11i	0.546804	−	0.315697i
$802$	−5.47360e10	−	9.48055e10i	−0.132305	−	0.229158i
$803$	7.58939e10	+	4.38174e10i	0.182534	+	0.105386i
$804$			2.15257e11i			0.515149i
$805$	6.05501e9	−	3.40942e10i	0.0144189	−	0.0811891i
$806$	8.59951e10			0.203767
$807$	1.44675e11	−	2.50585e11i	0.341115	−	0.590828i
$808$	−1.53708e11	+	8.87434e10i	−0.360621	+	0.208205i
$809$	1.92597e10	+	3.33588e10i	0.0449631	+	0.0778783i	0.887631	−	0.460555i	$-0.152350\pi$
$809$	1.92597e10	+	3.33588e10i	0.0449631	+	0.0778783i	−0.842668	+	0.538433i	$0.819016\pi$
$810$	−3.28803e11	−	1.89834e11i	−0.763827	−	0.440996i
$811$		−	5.03679e11i		−	1.16432i	−0.813076	−	0.582158i	$-0.802209\pi$
$811$		−	5.03679e11i		−	1.16432i	0.813076	−	0.582158i	$-0.197791\pi$
$812$	2.25448e11	+	4.00387e10i	0.518587	+	0.0920991i
$813$	2.24572e11			0.514037
$814$	1.30138e11	−	2.25406e11i	0.296420	−	0.513414i
$815$	−3.56831e11	+	2.06017e11i	−0.808784	+	0.466952i
$816$	−1.26400e11	−	2.18931e11i	−0.285093	−	0.493795i
$817$	−8.32862e11	−	4.80853e11i	−1.86932	−	1.07925i
$818$			1.41019e10i			0.0314966i
$819$	−8.06680e11	+	2.92484e11i	−1.79294	+	0.650079i
$820$	−1.42794e11			−0.315831
$821$	−5.17118e10	+	8.95675e10i	−0.113820	+	0.197141i	−0.917307	−	0.398180i	$-0.869642\pi$
$821$	−5.17118e10	+	8.95675e10i	−0.113820	+	0.197141i	0.803488	+	0.595321i	$0.202975\pi$
$822$	−5.15296e11	+	2.97507e11i	−1.12868	+	0.651642i
$823$	9.90121e10	+	1.71494e11i	0.215819	+	0.373809i	0.953525	−	0.301312i	$-0.0974247\pi$
$823$	9.90121e10	+	1.71494e11i	0.215819	+	0.373809i	−0.737707	+	0.675121i	$0.764091\pi$
$824$	−3.55266e10	−	2.05113e10i	−0.0770628	−	0.0444922i
$825$			3.10743e11i			0.670789i
$826$	1.08056e11	+	9.08967e10i	0.232129	+	0.195267i
$827$	3.92102e11			0.838256			0.419128	−	0.907927i	$-0.362336\pi$
$827$	3.92102e11			0.838256			0.419128	+	0.907927i	$0.362336\pi$
$828$	3.16397e10	−	5.48016e10i	0.0673149	−	0.116593i
$829$	−2.04284e10	+	1.17943e10i	−0.0432529	+	0.0249721i	−0.521471	−	0.853269i	$-0.674616\pi$
$829$	−2.04284e10	+	1.17943e10i	−0.0432529	+	0.0249721i	0.478218	+	0.878241i	$0.341283\pi$
$830$	1.57548e11	+	2.72881e11i	0.331971	+	0.574990i
$831$	1.67193e11	+	9.65287e10i	0.350601	+	0.202420i
$832$			5.07820e10i			0.105978i
$833$	3.90427e11	+	4.67626e11i	0.810887	+	0.971222i
$834$	−2.28412e11			−0.472123
$835$	2.07070e11	−	3.58656e11i	0.425963	−	0.737790i
$836$	−2.45772e11	+	1.41897e11i	−0.503162	+	0.290501i
$837$	−1.87865e11	−	3.25391e11i	−0.382775	−	0.662985i
$838$	5.75784e10	+	3.32429e10i	0.116757	+	0.0674098i
$839$			3.44859e11i			0.695975i	0.937499	+	0.347988i	$0.113135\pi$
$839$			3.44859e11i			0.695975i	−0.937499	+	0.347988i	$0.886865\pi$
$840$	1.40712e11	−	1.67275e11i	0.282627	−	0.335981i
$841$	5.48574e10			0.109661
$842$	−1.66975e11	+	2.89210e11i	−0.332203	+	0.575393i
$843$	−7.93607e11	+	4.58189e11i	−1.57143	+	0.907265i
$844$	−7.29882e10	−	1.26419e11i	−0.143841	−	0.249140i
$845$	8.55284e10	+	4.93798e10i	0.167758	+	0.0968552i
$846$		−	3.12073e11i		−	0.609220i
$847$	8.74427e10	+	2.41170e11i	0.169899	+	0.468586i
$848$	1.08553e11			0.209922
$849$	−7.11997e11	+	1.23321e12i	−1.37040	+	2.37360i
$850$	2.12509e11	−	1.22692e11i	0.407101	−	0.235040i
$851$	−3.71594e10	−	6.43620e10i	−0.0708517	−	0.122719i
$852$	−4.20637e9	−	2.42855e9i	−0.00798268	−	0.00460880i
$853$			5.28623e11i			0.998504i	0.866457	+	0.499252i	$0.166392\pi$
$853$			5.28623e11i			0.998504i	−0.866457	+	0.499252i	$0.833608\pi$
$854$	1.09736e11	−	6.17895e11i	0.206308	−	1.16167i
$855$	1.35874e12			2.54257
$856$	8.07778e10	−	1.39911e11i	0.150452	−	0.260590i
$857$	7.44252e11	−	4.29694e11i	1.37974	−	0.796592i	0.387611	−	0.921823i	$-0.373300\pi$
$857$	7.44252e11	−	4.29694e11i	1.37974	−	0.796592i	0.992128	+	0.125231i	$0.0399671\pi$
$858$	−2.07386e11	−	3.59203e11i	−0.382675	−	0.662813i
$859$	3.93275e11	+	2.27057e11i	0.722310	+	0.417026i	0.815602	−	0.578613i	$-0.196406\pi$
$859$	3.93275e11	+	2.27057e11i	0.722310	+	0.417026i	−0.0932924	+	0.995639i	$0.529739\pi$
$860$			2.47869e11i			0.453137i
$861$	8.94356e11	+	1.58834e11i	1.62741	+	0.289022i
$862$	−4.55712e11			−0.825395
$863$	−1.24085e11	+	2.14922e11i	−0.223706	+	0.387470i	−0.955930	−	0.293594i	$-0.905149\pi$
$863$	−1.24085e11	+	2.14922e11i	−0.223706	+	0.387470i	0.732225	+	0.681063i	$0.238482\pi$
$864$	1.92150e11	−	1.10938e11i	0.344815	−	0.199079i
$865$	2.84582e10	+	4.92910e10i	0.0508326	+	0.0880447i
$866$	−4.36900e11	−	2.52244e11i	−0.776802	−	0.448487i
$867$		−	6.11955e11i		−	1.08304i
$868$	9.06925e10	−	3.28830e10i	0.159769	−	0.0579286i
$869$	5.92797e9			0.0103951
$870$	2.64961e11	−	4.58926e11i	0.462493	−	0.801061i
$871$	2.41527e11	−	1.39446e11i	0.419656	−	0.242289i
$872$	−9.64883e9	−	1.67123e10i	−0.0166882	−	0.0289048i
$873$	−9.35414e11	−	5.40061e11i	−1.61045	−	0.929793i
$874$			8.10338e10i			0.138874i
$875$	4.71389e11	+	3.96532e11i	0.804168	+	0.676466i
$876$	1.57959e11			0.268242
$877$	−2.25994e11	+	3.91433e11i	−0.382031	+	0.661696i	−0.991352	−	0.131227i	$-0.958108\pi$
$877$	−2.25994e11	+	3.91433e11i	−0.382031	+	0.661696i	0.609322	+	0.792923i	$0.291442\pi$
$878$	−2.56257e11	+	1.47950e11i	−0.431219	+	0.248964i
$879$	−3.53272e11	−	6.11884e11i	−0.591770	−	1.02498i
$880$	6.33452e10	+	3.65723e10i	0.105629	+	0.0609849i
$881$			4.19437e11i			0.696246i	0.937449	+	0.348123i	$0.113181\pi$
$881$			4.19437e11i			0.696246i	−0.937449	+	0.348123i	$0.886819\pi$
$882$	−7.38903e11	+	6.16921e11i	−1.22099	+	1.01942i
$883$	−7.68167e11			−1.26361			−0.631805	−	0.775128i	$-0.717686\pi$
$883$	−7.68167e11			−1.26361			−0.631805	+	0.775128i	$0.717686\pi$
$884$	−1.63767e11	+	2.83652e11i	−0.268174	+	0.464490i
$885$	2.83008e11	−	1.63395e11i	0.461344	−	0.266357i
$886$	1.85660e10	+	3.21573e10i	0.0301290	+	0.0521849i
$887$	−3.17793e11	−	1.83478e11i	−0.513393	−	0.296407i	0.220835	−	0.975311i	$-0.429122\pi$
$887$	−3.17793e11	−	1.83478e11i	−0.513393	−	0.296407i	−0.734227	+	0.678904i	$0.762455\pi$
$888$		−	4.69139e11i		−	0.754484i
$889$	−1.97810e11	+	2.35153e11i	−0.316695	+	0.376481i
$890$	8.57858e10			0.136727
$891$	−4.04087e11	+	6.99899e11i	−0.641156	+	1.11051i
$892$	−3.12019e11	+	1.80144e11i	−0.492858	+	0.284552i
$893$	1.99816e11	+	3.46091e11i	0.314213	+	0.544232i
$894$	4.39870e11	+	2.53959e11i	0.688611	+	0.397570i
$895$			3.92290e11i			0.611386i
$896$	1.94181e10	+	5.35559e10i	0.0301284	+	0.0830950i
$897$	−1.18433e11			−0.182938
$898$	−8.04473e10	+	1.39339e11i	−0.123710	+	0.214273i
$899$	2.02538e11	−	1.16935e11i	0.310076	−	0.179022i
$900$	1.93868e11	+	3.35789e11i	0.295486	+	0.511796i
$901$	6.06343e11	+	3.50072e11i	0.920066	+	0.531201i
$902$			3.03955e11i			0.459180i
$903$	2.75713e11	−	1.55247e12i	0.414674	−	2.33492i
$904$	−2.47013e11			−0.369868
$905$	6.99556e10	−	1.21167e11i	0.104287	−	0.180630i
$906$	1.14577e12	−	6.61511e11i	1.70053	−	0.981802i
$907$	2.00812e11	+	3.47817e11i	0.296730	+	0.513951i	0.975386	−	0.220505i	$-0.0707707\pi$
$907$	2.00812e11	+	3.47817e11i	0.296730	+	0.513951i	−0.678656	+	0.734456i	$0.737437\pi$
$908$	−4.61113e11	−	2.66224e11i	−0.678366	−	0.391655i
$909$		−	1.80884e12i		−	2.64938i
$910$	−2.78845e11	−	4.95218e10i	−0.406628	−	0.0722156i
$911$	−6.36440e11			−0.924026			−0.462013	−	0.886873i	$-0.652873\pi$
$911$	−6.36440e11			−0.924026			−0.462013	+	0.886873i	$0.652873\pi$
$912$	−2.55764e11	+	4.42996e11i	−0.369709	+	0.640355i
$913$	5.80861e11	−	3.35360e11i	0.835967	−	0.482646i
$914$	−1.01112e11	−	1.75130e11i	−0.144883	−	0.250944i
$915$	−1.25780e12	−	7.26191e11i	−1.79443	−	1.03602i
$916$			3.33580e10i			0.0473825i
$917$	−4.83552e11	+	1.75325e11i	−0.683858	+	0.247951i
$918$	1.43105e12			2.01505
$919$	1.63464e11	−	2.83127e11i	0.229171	−	0.396935i	−0.728392	−	0.685161i	$-0.759732\pi$
$919$	1.63464e11	−	2.83127e11i	0.229171	−	0.396935i	0.957563	+	0.288225i	$0.0930652\pi$
$920$	1.80875e10	−	1.04428e10i	0.0252480	−	0.0145769i
$921$	−6.15498e10	−	1.06607e11i	−0.0855437	−	0.148166i
$922$	1.96567e11	+	1.13488e11i	0.272012	+	0.157046i
$923$			6.29297e9i			0.00867059i
$924$	−3.56067e11	−	2.99523e11i	−0.488477	−	0.410906i
$925$	4.55379e11			0.622022
$926$	−3.40643e11	+	5.90011e11i	−0.463293	+	0.802447i
$927$	3.62066e11	−	2.09039e11i	0.490308	−	0.283080i
$928$	6.90529e10	+	1.19603e11i	0.0931087	+	0.161269i
$929$	−3.95158e11	−	2.28145e11i	−0.530528	−	0.306300i	0.210704	−	0.977550i	$-0.432425\pi$
$929$	−3.95158e11	−	2.28145e11i	−0.530528	−	0.306300i	−0.741231	+	0.671250i	$0.765758\pi$
$930$		−	2.23262e11i		−	0.298458i
$931$	4.24444e11	−	1.15728e12i	0.564965	−	1.54042i
$932$	2.71036e11			0.359223
$933$	1.66776e9	−	2.88865e9i	0.00220094	−	0.00381214i
$934$	7.18372e11	−	4.14752e11i	0.943978	−	0.545006i
$935$	2.35884e11	+	4.08563e11i	0.308640	+	0.534580i
$936$	−4.48203e11	−	2.58770e11i	−0.583944	−	0.337140i
$937$			8.50941e11i			1.10393i	0.833868	+	0.551964i	$0.186122\pi$
$937$			8.50941e11i			1.10393i	−0.833868	+	0.551964i	$0.813878\pi$
$938$	2.01399e11	−	2.39419e11i	0.260163	−	0.309276i
$939$	−3.47222e10			−0.0446627
$940$	5.15003e10	−	8.92012e10i	0.0659627	−	0.114251i
$941$	3.09132e11	−	1.78478e11i	0.394263	−	0.227628i	−0.289743	−	0.957105i	$-0.593570\pi$
$941$	3.09132e11	−	1.78478e11i	0.394263	−	0.227628i	0.684006	+	0.729477i	$0.260236\pi$
$942$	2.05175e11	+	3.55374e11i	0.260568	+	0.451317i
$943$	7.51630e10	+	4.33954e10i	0.0950511	+	0.0548778i
$944$			8.51662e10i			0.107246i
$945$	4.21781e11	+	1.16329e12i	0.528884	+	1.45868i
$946$	5.27622e11			0.658807
$947$	6.86199e11	−	1.18853e12i	0.853199	−	1.47778i	−0.0251070	−	0.999685i	$-0.507993\pi$
$947$	6.86199e11	−	1.18853e12i	0.853199	−	1.47778i	0.878306	−	0.478099i	$-0.158674\pi$
$948$	9.25346e9	−	5.34249e9i	0.0114570	−	0.00661470i
$949$	−1.02327e11	−	1.77236e11i	−0.126162	−	0.218518i
$950$	−4.30002e11	−	2.48262e11i	−0.527930	−	0.304801i
$951$			2.69106e12i			3.29004i
$952$	−6.42485e10	+	3.61767e11i	−0.0782196	+	0.440435i
$953$	−1.05746e12			−1.28201			−0.641004	−	0.767537i	$-0.721482\pi$
$953$	−1.05746e12			−1.28201			−0.641004	+	0.767537i	$0.721482\pi$
$954$	−5.53155e11	+	9.58092e11i	−0.667810	+	1.15668i
$955$	−2.72144e11	+	1.57122e11i	−0.327179	+	0.188897i
$956$	−2.34691e11	−	4.06497e11i	−0.280973	−	0.486660i
$957$	−9.76883e11	−	5.64004e11i	−1.16465	−	0.672410i
$958$		−	8.55108e11i		−	1.01522i
$959$	8.51490e11	+	1.51221e11i	1.00671	+	0.178788i
$960$	1.31841e11			0.155226
$961$	−3.77179e11	+	6.53294e11i	−0.442236	+	0.765976i
$962$	−5.26394e11	+	3.03914e11i	−0.614626	+	0.354854i
$963$	8.23240e11	+	1.42589e12i	0.957241	+	1.65799i
$964$	1.90887e11	+	1.10209e11i	0.221039	+	0.127617i
$965$		−	8.58578e11i		−	0.990080i
$966$	−1.24902e11	+	4.52868e10i	−0.143437	+	0.0520072i
$967$	−6.68065e11			−0.764035			−0.382017	−	0.924155i	$-0.624771\pi$
$967$	−6.68065e11			−0.764035			−0.382017	+	0.924155i	$0.624771\pi$
$968$	−7.73635e10	+	1.33997e11i	−0.0881119	+	0.152614i
$969$	−2.85723e12	+	1.64962e12i	−3.24079	+	1.87107i
$970$	−1.78249e11	−	3.08737e11i	−0.201345	−	0.348740i
$971$	−6.47768e11	−	3.73989e11i	−0.728690	−	0.420709i	0.0892528	−	0.996009i	$-0.471552\pi$
$971$	−6.47768e11	−	3.73989e11i	−0.728690	−	0.420709i	−0.817943	+	0.575300i	$0.804885\pi$
$972$			4.51474e11i			0.505788i
$973$	2.54051e11	+	2.13707e11i	0.283445	+	0.238434i
$974$	−4.13184e11			−0.459100
$975$	3.62842e11	−	6.28461e11i	0.401513	−	0.695440i
$976$	3.27802e11	−	1.89256e11i	0.361253	−	0.208570i
$977$	−1.55722e11	−	2.69719e11i	−0.170912	−	0.296029i	0.767827	−	0.640657i	$-0.221338\pi$
$977$	−1.55722e11	−	2.69719e11i	−0.170912	−	0.296029i	−0.938739	+	0.344629i	$0.888005\pi$
$978$	1.36908e12	+	7.90441e11i	1.49649	+	0.864001i
$979$		−	1.82606e11i		−	0.198785i
$980$	−3.13013e11	+	5.43986e10i	−0.339358	+	0.0589771i
$981$	1.96671e11			0.212355
$982$	−5.85808e10	+	1.01465e11i	−0.0629954	+	0.109111i
$983$	1.53075e12	−	8.83778e11i	1.63942	−	0.946518i	0.658383	−	0.752683i	$-0.271241\pi$
$983$	1.53075e12	−	8.83778e11i	1.63942	−	0.946518i	0.981034	−	0.193835i	$-0.0620927\pi$
$984$	2.73934e11	+	4.74468e11i	0.292190	+	0.506089i
$985$	9.65670e11	+	5.57530e11i	1.02585	+	0.592275i
$986$			8.90754e11i			0.942432i
$987$	−4.21782e11	+	5.01406e11i	−0.444446	+	0.528349i
$988$	6.62748e11			0.695537
$989$	7.53281e10	−	1.30472e11i	0.0787357	−	0.136374i
$990$	−6.45577e11	+	3.72724e11i	−0.672059	+	0.388013i
$991$	−6.46277e11	−	1.11938e12i	−0.670076	−	1.16061i	−0.977882	−	0.209157i	$-0.932928\pi$
$991$	−6.46277e11	−	1.11938e12i	−0.670076	−	1.16061i	0.307806	−	0.951449i	$-0.400405\pi$
$992$	5.03900e10	+	2.90927e10i	0.0520353	+	0.0300426i
$993$		−	2.71366e12i		−	2.79099i
$994$	2.40632e9	+	6.63671e9i	0.00246495	+	0.00679841i
$995$	−8.45149e11			−0.862265
$996$	6.04476e11	−	1.04698e12i	0.614245	−	1.06390i
$997$	2.08366e11	−	1.20300e11i	0.210886	−	0.121755i	−0.390837	−	0.920460i	$-0.627814\pi$
$997$	2.08366e11	−	1.20300e11i	0.210886	−	0.121755i	0.601723	+	0.798705i	$0.294481\pi$
$998$	−2.88644e11	−	4.99947e11i	−0.290965	−	0.503967i
$999$	2.29992e12	+	1.32786e12i	2.30914	+	1.33318i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.9.d.a.5.6	yes	12
3.2	odd	2		126.9.n.b.19.2		12
4.3	odd	2		112.9.s.c.33.1		12
7.2	even	3		98.9.b.c.97.6		12
7.3	odd	6	inner	14.9.d.a.3.6	✓	12
7.4	even	3		98.9.d.b.31.4		12
7.5	odd	6		98.9.b.c.97.1		12
7.6	odd	2		98.9.d.b.19.4		12
21.17	even	6		126.9.n.b.73.2		12
28.3	even	6		112.9.s.c.17.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.9.d.a.3.6	✓	12	7.3	odd	6	inner
14.9.d.a.5.6	yes	12	1.1	even	1	trivial
98.9.b.c.97.1		12	7.5	odd	6
98.9.b.c.97.6		12	7.2	even	3
98.9.d.b.19.4		12	7.6	odd	2
98.9.d.b.31.4		12	7.4	even	3
112.9.s.c.17.1		12	28.3	even	6
112.9.s.c.33.1		12	4.3	odd	2
126.9.n.b.19.2		12	3.2	odd	2
126.9.n.b.73.2		12	21.17	even	6

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:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	14.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(5.65685 - 9.79796i) q^{2} +(126.451 - 73.0064i) q^{3} +(-64.0000 - 110.851i) q^{4} +(372.872 + 215.278i) q^{5} -1651.95i q^{6} +(-1545.60 + 1837.37i) q^{7} -1448.15 q^{8} +(7379.38 - 12781.5i) q^{9} +O(q^{10})\)	\(q+(5.65685 - 9.79796i) q^{2} +(126.451 - 73.0064i) q^{3} +(-64.0000 - 110.851i) q^{4} +(372.872 + 215.278i) q^{5} -1651.95i q^{6} +(-1545.60 + 1837.37i) q^{7} -1448.15 q^{8} +(7379.38 - 12781.5i) q^{9} +(4218.56 - 2435.59i) q^{10} +(-5184.46 - 8979.75i) q^{11} +(-16185.7 - 9344.82i) q^{12} +24214.7i q^{13} +(9259.29 + 25537.4i) q^{14} +62866.6 q^{15} +(-8192.00 + 14189.0i) q^{16} +(-91515.8 + 52836.7i) q^{17} +(-83488.1 - 144606. i) q^{18} +(185178. + 106912. i) q^{19} -55111.1i q^{20} +(-61301.9 + 345176. i) q^{21} -117311. q^{22} +(-16748.4 + 29009.1i) q^{23} +(-183120. + 105725. i) q^{24} +(-102624. - 177749. i) q^{25} +(237255. + 136979. i) q^{26} -1.19698e6i q^{27} +(302593. + 53739.4i) q^{28} +745053. q^{29} +(355627. - 615965. i) q^{30} +(271844. - 156949. i) q^{31} +(92681.9 + 160530. i) q^{32} +(-1.31116e6 - 756998. i) q^{33} +1.19556e6i q^{34} +(-971854. + 352372. i) q^{35} -1.88912e6 q^{36} +(-1.10934e6 + 1.92144e6i) q^{37} +(2.09505e6 - 1.20958e6i) q^{38} +(1.76783e6 + 3.06197e6i) q^{39} +(-539976. - 311755. i) q^{40} -2.59102e6i q^{41} +(3.03524e6 + 2.55324e6i) q^{42} -4.49763e6 q^{43} +(-663611. + 1.14941e6i) q^{44} +(5.50312e6 - 3.17723e6i) q^{45} +(189486. + 328200. i) q^{46} +(1.61857e6 + 934482. i) q^{47} +2.39227e6i q^{48} +(-987071. - 5.67967e6i) q^{49} -2.32210e6 q^{50} +(-7.71483e6 + 1.33625e7i) q^{51} +(2.68423e6 - 1.54974e6i) q^{52} +(-3.31278e6 - 5.73790e6i) q^{53} +(-1.17279e7 - 6.77112e6i) q^{54} -4.46440e6i q^{55} +(2.23826e6 - 2.66080e6i) q^{56} +3.12212e7 q^{57} +(4.21466e6 - 7.30000e6i) q^{58} +(4.50172e6 - 2.59907e6i) q^{59} +(-4.02346e6 - 6.96884e6i) q^{60} +(-2.00074e7 - 1.15513e7i) q^{61} -3.55136e6i q^{62} +(1.20788e7 + 3.33136e7i) q^{63} +2.09715e6 q^{64} +(-5.21289e6 + 9.02900e6i) q^{65} +(-1.48341e7 + 8.56446e6i) q^{66} +(-5.75872e6 - 9.97440e6i) q^{67} +(1.17140e7 + 6.76310e6i) q^{68} +4.89096e6i q^{69} +(-2.04511e6 + 1.15155e7i) q^{70} +259882. q^{71} +(-1.06865e7 + 1.85095e7i) q^{72} +(-7.31936e6 + 4.22584e6i) q^{73} +(1.25508e7 + 2.17386e7i) q^{74} +(-2.59537e7 - 1.49843e7i) q^{75} -2.73696e7i q^{76} +(2.45122e7 + 4.35328e6i) q^{77} +4.00015e7 q^{78} +(-285853. + 495111. i) q^{79} +(-6.10913e6 + 3.52711e6i) q^{80} +(-3.89709e7 - 6.74996e7i) q^{81} +(-2.53867e7 - 1.46570e7i) q^{82} +6.46856e7i q^{83} +(4.21865e7 - 1.52959e7i) q^{84} -4.54982e7 q^{85} +(-2.54424e7 + 4.40676e7i) q^{86} +(9.42126e7 - 5.43936e7i) q^{87} +(7.50791e6 + 1.30041e7i) q^{88} +(1.52515e7 + 8.80544e6i) q^{89} -7.18925e7i q^{90} +(-4.44915e7 - 3.74262e7i) q^{91} +4.28759e6 q^{92} +(2.29166e7 - 3.96927e7i) q^{93} +(1.83120e7 - 1.05725e7i) q^{94} +(4.60318e7 + 7.97293e7i) q^{95} +(2.34394e7 + 1.35327e7i) q^{96} -7.31853e7i q^{97} +(-6.12329e7 - 2.24578e7i) q^{98} -1.53032e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 162 q^{3} - 768 q^{4} + 1674 q^{5} - 1308 q^{7} + 23604 q^{9}+O(q^{10}) \) 12 * q + 162 * q^3 - 768 * q^4 + 1674 * q^5 - 1308 * q^7 + 23604 * q^9	\( 12 q + 162 q^{3} - 768 q^{4} + 1674 q^{5} - 1308 q^{7} + 23604 q^{9} + 17664 q^{10} + 10302 q^{11} - 20736 q^{12} + 56832 q^{14} - 255468 q^{15} - 98304 q^{16} + 173178 q^{17} + 16896 q^{18} + 405978 q^{19} - 656910 q^{21} - 941568 q^{22} + 158934 q^{23} + 98304 q^{24} + 838668 q^{25} + 1958400 q^{26} - 255744 q^{28} - 4355256 q^{29} + 916992 q^{30} + 4520250 q^{31} + 4954482 q^{33} - 5270790 q^{35} - 6042624 q^{36} + 134214 q^{37} + 1278720 q^{38} + 1335384 q^{39} - 2260992 q^{40} + 6660096 q^{42} - 12961896 q^{43} + 1318656 q^{44} - 8415396 q^{45} + 2345472 q^{46} + 18385002 q^{47} - 3659172 q^{49} + 2970624 q^{50} - 2673894 q^{51} - 3369984 q^{52} - 16540506 q^{53} - 19646208 q^{54} + 4325376 q^{56} + 100263780 q^{57} + 9176064 q^{58} + 31163922 q^{59} + 16349952 q^{60} - 85390158 q^{61} + 4361988 q^{63} + 25165824 q^{64} - 46506264 q^{65} - 111873024 q^{66} - 37750362 q^{67} - 22166784 q^{68} + 92031744 q^{70} + 45506424 q^{71} + 2162688 q^{72} + 9414786 q^{73} + 58837248 q^{74} + 9837540 q^{75} - 100614066 q^{77} - 25463808 q^{78} + 59730294 q^{79} - 27426816 q^{80} - 89677422 q^{81} - 93259776 q^{82} + 122616576 q^{84} - 64652220 q^{85} - 15144960 q^{86} + 334229724 q^{87} + 60260352 q^{88} + 323014482 q^{89} - 266861424 q^{91} - 40687104 q^{92} - 11119662 q^{93} - 443440128 q^{94} - 175918350 q^{95} - 12582912 q^{96} + 472166400 q^{98} - 346906296 q^{99}+O(q^{100}) \) 12 * q + 162 * q^3 - 768 * q^4 + 1674 * q^5 - 1308 * q^7 + 23604 * q^9 + 17664 * q^10 + 10302 * q^11 - 20736 * q^12 + 56832 * q^14 - 255468 * q^15 - 98304 * q^16 + 173178 * q^17 + 16896 * q^18 + 405978 * q^19 - 656910 * q^21 - 941568 * q^22 + 158934 * q^23 + 98304 * q^24 + 838668 * q^25 + 1958400 * q^26 - 255744 * q^28 - 4355256 * q^29 + 916992 * q^30 + 4520250 * q^31 + 4954482 * q^33 - 5270790 * q^35 - 6042624 * q^36 + 134214 * q^37 + 1278720 * q^38 + 1335384 * q^39 - 2260992 * q^40 + 6660096 * q^42 - 12961896 * q^43 + 1318656 * q^44 - 8415396 * q^45 + 2345472 * q^46 + 18385002 * q^47 - 3659172 * q^49 + 2970624 * q^50 - 2673894 * q^51 - 3369984 * q^52 - 16540506 * q^53 - 19646208 * q^54 + 4325376 * q^56 + 100263780 * q^57 + 9176064 * q^58 + 31163922 * q^59 + 16349952 * q^60 - 85390158 * q^61 + 4361988 * q^63 + 25165824 * q^64 - 46506264 * q^65 - 111873024 * q^66 - 37750362 * q^67 - 22166784 * q^68 + 92031744 * q^70 + 45506424 * q^71 + 2162688 * q^72 + 9414786 * q^73 + 58837248 * q^74 + 9837540 * q^75 - 100614066 * q^77 - 25463808 * q^78 + 59730294 * q^79 - 27426816 * q^80 - 89677422 * q^81 - 93259776 * q^82 + 122616576 * q^84 - 64652220 * q^85 - 15144960 * q^86 + 334229724 * q^87 + 60260352 * q^88 + 323014482 * q^89 - 266861424 * q^91 - 40687104 * q^92 - 11119662 * q^93 - 443440128 * q^94 - 175918350 * q^95 - 12582912 * q^96 + 472166400 * q^98 - 346906296 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more