LMFDB - Embedded newform 126.9.n.b.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,9,Mod(19,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("126.19");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	126.n (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:	$51.3297048677$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{10}\cdot 7^{3} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.2
Root			$-10.5605 + 18.2913i$ of defining polynomial
Character	$\chi$	$=$	126.19
Dual form			126.9.n.b.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.65685 + 9.79796i) q^{2} +(-64.0000 - 110.851i) q^{4} +(-372.872 - 215.278i) q^{5} +(-1545.60 + 1837.37i) q^{7} +1448.15 q^{8} +O(q^{10})$	\(q+(-5.65685 + 9.79796i) q^{2} +(-64.0000 - 110.851i) q^{4} +(-372.872 - 215.278i) q^{5} +(-1545.60 + 1837.37i) q^{7} +1448.15 q^{8} +(4218.56 - 2435.59i) q^{10} +(5184.46 + 8979.75i) q^{11} +24214.7i q^{13} +(-9259.29 - 25537.4i) q^{14} +(-8192.00 + 14189.0i) q^{16} +(91515.8 - 52836.7i) q^{17} +(185178. + 106912. i) q^{19} +55111.1i q^{20} -117311. q^{22} +(16748.4 - 29009.1i) q^{23} +(-102624. - 177749. i) q^{25} +(-237255. - 136979. i) q^{26} +(302593. + 53739.4i) q^{28} -745053. q^{29} +(271844. - 156949. i) q^{31} +(-92681.9 - 160530. i) q^{32} +1.19556e6i q^{34} +(971854. - 352372. i) q^{35} +(-1.10934e6 + 1.92144e6i) q^{37} +(-2.09505e6 + 1.20958e6i) q^{38} +(-539976. - 311755. i) q^{40} +2.59102e6i q^{41} -4.49763e6 q^{43} +(663611. - 1.14941e6i) q^{44} +(189486. + 328200. i) q^{46} +(-1.61857e6 - 934482. i) q^{47} +(-987071. - 5.67967e6i) q^{49} +2.32210e6 q^{50} +(2.68423e6 - 1.54974e6i) q^{52} +(3.31278e6 + 5.73790e6i) q^{53} -4.46440e6i q^{55} +(-2.23826e6 + 2.66080e6i) q^{56} +(4.21466e6 - 7.30000e6i) q^{58} +(-4.50172e6 + 2.59907e6i) q^{59} +(-2.00074e7 - 1.15513e7i) q^{61} +3.55136e6i q^{62} +2.09715e6 q^{64} +(5.21289e6 - 9.02900e6i) q^{65} +(-5.75872e6 - 9.97440e6i) q^{67} +(-1.17140e7 - 6.76310e6i) q^{68} +(-2.04511e6 + 1.15155e7i) q^{70} -259882. q^{71} +(-7.31936e6 + 4.22584e6i) q^{73} +(-1.25508e7 - 2.17386e7i) q^{74} -2.73696e7i q^{76} +(-2.45122e7 - 4.35328e6i) q^{77} +(-285853. + 495111. i) q^{79} +(6.10913e6 - 3.52711e6i) q^{80} +(-2.53867e7 - 1.46570e7i) q^{82} -6.46856e7i q^{83} -4.54982e7 q^{85} +(2.54424e7 - 4.40676e7i) q^{86} +(7.50791e6 + 1.30041e7i) q^{88} +(-1.52515e7 - 8.80544e6i) q^{89} +(-4.44915e7 - 3.74262e7i) q^{91} -4.28759e6 q^{92} +(1.83120e7 - 1.05725e7i) q^{94} +(-4.60318e7 - 7.97293e7i) q^{95} -7.31853e7i q^{97} +(6.12329e7 + 2.24578e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 768 q^{4} - 1674 q^{5} - 1308 q^{7}+O(q^{10}) $ 12 * q - 768 * q^4 - 1674 * q^5 - 1308 * q^7	$ 12 q - 768 q^{4} - 1674 q^{5} - 1308 q^{7} + 17664 q^{10} - 10302 q^{11} - 56832 q^{14} - 98304 q^{16} - 173178 q^{17} + 405978 q^{19} - 941568 q^{22} - 158934 q^{23} + 838668 q^{25} - 1958400 q^{26} - 255744 q^{28} + 4355256 q^{29} + 4520250 q^{31} + 5270790 q^{35} + 134214 q^{37} - 1278720 q^{38} - 2260992 q^{40} - 12961896 q^{43} - 1318656 q^{44} + 2345472 q^{46} - 18385002 q^{47} - 3659172 q^{49} - 2970624 q^{50} - 3369984 q^{52} + 16540506 q^{53} - 4325376 q^{56} + 9176064 q^{58} - 31163922 q^{59} - 85390158 q^{61} + 25165824 q^{64} + 46506264 q^{65} - 37750362 q^{67} + 22166784 q^{68} + 92031744 q^{70} - 45506424 q^{71} + 9414786 q^{73} - 58837248 q^{74} + 100614066 q^{77} + 59730294 q^{79} + 27426816 q^{80} - 93259776 q^{82} - 64652220 q^{85} + 15144960 q^{86} + 60260352 q^{88} - 323014482 q^{89} - 266861424 q^{91} + 40687104 q^{92} - 443440128 q^{94} + 175918350 q^{95} - 472166400 q^{98}+O(q^{100}) $ 12 * q - 768 * q^4 - 1674 * q^5 - 1308 * q^7 + 17664 * q^10 - 10302 * q^11 - 56832 * q^14 - 98304 * q^16 - 173178 * q^17 + 405978 * q^19 - 941568 * q^22 - 158934 * q^23 + 838668 * q^25 - 1958400 * q^26 - 255744 * q^28 + 4355256 * q^29 + 4520250 * q^31 + 5270790 * q^35 + 134214 * q^37 - 1278720 * q^38 - 2260992 * q^40 - 12961896 * q^43 - 1318656 * q^44 + 2345472 * q^46 - 18385002 * q^47 - 3659172 * q^49 - 2970624 * q^50 - 3369984 * q^52 + 16540506 * q^53 - 4325376 * q^56 + 9176064 * q^58 - 31163922 * q^59 - 85390158 * q^61 + 25165824 * q^64 + 46506264 * q^65 - 37750362 * q^67 + 22166784 * q^68 + 92031744 * q^70 - 45506424 * q^71 + 9414786 * q^73 - 58837248 * q^74 + 100614066 * q^77 + 59730294 * q^79 + 27426816 * q^80 - 93259776 * q^82 - 64652220 * q^85 + 15144960 * q^86 + 60260352 * q^88 - 323014482 * q^89 - 266861424 * q^91 + 40687104 * q^92 - 443440128 * q^94 + 175918350 * q^95 - 472166400 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$		0			0
$3$		0			0
$4$	−64.0000	−	110.851i	−0.250000	−	0.433013i
$5$	−372.872	−	215.278i	−0.596595	−	0.344444i	0.171106	−	0.985253i	$-0.445266\pi$
$5$	−372.872	−	215.278i	−0.596595	−	0.344444i	−0.767701	+	0.640808i	$0.778599\pi$
$6$		0			0
$7$	−1545.60	+	1837.37i	−0.643730	+	0.765253i
$7$	−1545.60	+	1837.37i	−0.643730	+	0.765253i
$8$	1448.15			0.353553
$9$		0			0
$10$	4218.56	−	2435.59i	0.421856	−	0.243559i
$11$	5184.46	+	8979.75i	0.354106	+	0.613329i	0.986965	−	0.160938i	$-0.0514519\pi$
$11$	5184.46	+	8979.75i	0.354106	+	0.613329i	−0.632859	+	0.774267i	$0.718119\pi$
$12$		0			0
$13$			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
$15$		0			0
$16$	−8192.00	+	14189.0i	−0.125000	+	0.216506i
$17$	91515.8	−	52836.7i	1.09572	−	0.632616i	0.160628	−	0.987015i	$-0.448648\pi$
$17$	91515.8	−	52836.7i	1.09572	−	0.632616i	0.935094	+	0.354399i	$0.115315\pi$
$18$		0			0
$19$	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
$21$		0			0
$22$	−117311.			−0.500781
$23$	16748.4	−	29009.1i	0.0598496	−	0.103663i	−0.834548	−	0.550935i	$-0.814271\pi$
$23$	16748.4	−	29009.1i	0.0598496	−	0.103663i	0.894398	+	0.447272i	$0.147605\pi$
$24$		0			0
$25$	−102624.	−	177749.i	−0.262716	−	0.455038i
$26$	−237255.	−	136979.i	−0.519185	−	0.299751i
$27$		0			0
$28$	302593.	+	53739.4i	0.492297	+	0.0874300i
$29$	−745053.			−1.05340			−0.526702	−	0.850050i	$-0.676572\pi$
$29$	−745053.			−1.05340			−0.526702	+	0.850050i	$0.676572\pi$
$30$		0			0
$31$	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
$33$		0			0
$34$			1.19556e6i			0.894653i
$35$	971854.	−	352372.i	0.647633	−	0.234817i
$36$		0			0
$37$	−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
$39$		0			0
$40$	−539976.	−	311755.i	−0.210928	−	0.121779i
$41$			2.59102e6i			0.916928i	0.888713	+	0.458464i	$0.151600\pi$
$41$			2.59102e6i			0.916928i	−0.888713	+	0.458464i	$0.848400\pi$
$42$		0			0
$43$	−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
$45$		0			0
$46$	189486.	+	328200.i	0.0423201	+	0.0733005i
$47$	−1.61857e6	−	934482.i	−0.331696	−	0.191505i	0.324898	−	0.945749i	$-0.394670\pi$
$47$	−1.61857e6	−	934482.i	−0.331696	−	0.191505i	−0.656594	+	0.754244i	$0.728003\pi$
$48$		0			0
$49$	−987071.	−	5.67967e6i	−0.171224	−	0.985232i
$50$	2.32210e6			0.371537
$51$		0			0
$52$	2.68423e6	−	1.54974e6i	0.367119	−	0.211956i
$53$	3.31278e6	+	5.73790e6i	0.419845	+	0.727192i	0.995924	−	0.0902018i	$-0.0287512\pi$
$53$	3.31278e6	+	5.73790e6i	0.419845	+	0.727192i	−0.576079	+	0.817394i	$0.695418\pi$
$54$		0			0
$55$		−	4.46440e6i		−	0.487879i
$56$	−2.23826e6	+	2.66080e6i	−0.227593	+	0.270558i
$57$		0			0
$58$	4.21466e6	−	7.30000e6i	0.372435	−	0.645076i
$59$	−4.50172e6	+	2.59907e6i	−0.371510	+	0.214491i	−0.674118	−	0.738624i	$-0.735476\pi$
$59$	−4.50172e6	+	2.59907e6i	−0.371510	+	0.214491i	0.302608	+	0.953115i	$0.402143\pi$
$60$		0			0
$61$	−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
$63$		0			0
$64$	2.09715e6			0.125000
$65$	5.21289e6	−	9.02900e6i	0.292029	−	0.505808i
$66$		0			0
$67$	−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
$69$		0			0
$70$	−2.04511e6	+	1.15155e7i	−0.0851774	+	0.479613i
$71$	−259882.			−0.0102269			−0.00511343	−	0.999987i	$-0.501628\pi$
$71$	−259882.			−0.0102269			−0.00511343	+	0.999987i	$0.501628\pi$
$72$		0			0
$73$	−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
$75$		0			0
$76$		−	2.73696e7i		−	0.820378i
$77$	−2.45122e7	−	4.35328e6i	−0.697300	−	0.123838i
$78$		0			0
$79$	−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
$81$		0			0
$82$	−2.53867e7	−	1.46570e7i	−0.561501	−	0.324183i
$83$		−	6.46856e7i		−	1.36300i	−0.731819	−	0.681499i	$-0.761328\pi$
$83$		−	6.46856e7i		−	1.36300i	0.731819	−	0.681499i	$-0.238672\pi$
$84$		0			0
$85$	−4.54982e7			−0.871603
$86$	2.54424e7	−	4.40676e7i	0.465120	−	0.805611i
$87$		0			0
$88$	7.50791e6	+	1.30041e7i	0.125195	+	0.216845i
$89$	−1.52515e7	−	8.80544e6i	−0.243081	−	0.140343i	0.373511	−	0.927626i	$-0.378154\pi$
$89$	−1.52515e7	−	8.80544e6i	−0.243081	−	0.140343i	−0.616592	+	0.787283i	$0.711487\pi$
$90$		0			0
$91$	−4.44915e7	−	3.74262e7i	−0.648801	−	0.545770i
$92$	−4.28759e6			−0.0598496
$93$		0			0
$94$	1.83120e7	−	1.05725e7i	0.234545	−	0.135414i
$95$	−4.60318e7	−	7.97293e7i	−0.565149	−	0.978867i
$96$		0			0
$97$		−	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
$99$		0			0
$100$	−1.31358e7	+	2.27519e7i	−0.131358	+	0.227519i
$101$	−1.06141e8	+	6.12803e7i	−1.01999	+	0.588892i	−0.914101	−	0.405486i	$-0.867102\pi$
$101$	−1.06141e8	+	6.12803e7i	−1.01999	+	0.588892i	−0.105889	+	0.994378i	$0.533769\pi$
$102$		0			0
$103$	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
$105$		0			0
$106$	−7.49596e7			−0.593750
$107$	5.57798e7	−	9.66135e7i	0.425541	−	0.737059i	−0.570929	−	0.820999i	$-0.693417\pi$
$107$	5.57798e7	−	9.66135e7i	0.425541	−	0.737059i	0.996471	+	0.0839398i	$0.0267503\pi$
$108$		0			0
$109$	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
$111$		0			0
$112$	−1.34089e7	−	3.69821e7i	−0.0852159	−	0.235028i
$113$	−1.70571e8			−1.04614			−0.523072	−	0.852289i	$-0.675214\pi$
$113$	−1.70571e8			−1.04614			−0.523072	+	0.852289i	$0.675214\pi$
$114$		0			0
$115$	−1.24900e7	+	7.21111e6i	−0.0714120	+	0.0412297i
$116$	4.76834e7	+	8.25900e7i	0.263351	+	0.456137i
$117$		0			0
$118$		−	5.88102e7i		−	0.303336i
$119$	−4.43658e7	+	2.49813e8i	−0.221238	+	1.24574i
$120$		0			0
$121$	5.34221e7	−	9.25298e7i	0.249218	−	0.431658i
$122$	2.26358e8	−	1.30688e8i	1.02178	−	0.589924i
$123$		0			0
$124$	−3.47960e7	−	2.00895e7i	−0.147178	−	0.0849733i
$125$			2.56556e8i			1.05085i
$126$		0			0
$127$	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
$129$		0			0
$130$	5.89772e7	+	1.02151e8i	0.206495	+	0.357661i
$131$	−1.85525e8	−	1.07113e8i	−0.629965	−	0.363711i	0.150773	−	0.988568i	$-0.451824\pi$
$131$	−1.85525e8	−	1.07113e8i	−0.629965	−	0.363711i	−0.780739	+	0.624858i	$0.785157\pi$
$132$		0			0
$133$	−4.82648e8	+	1.74997e8i	−1.54250	+	0.559274i
$134$	1.30305e8			0.404149
$135$		0			0
$136$	1.32529e8	−	7.65157e7i	0.387396	−	0.223663i
$137$	1.80095e8	+	3.11933e8i	0.511232	+	0.885480i	0.999915	+	0.0130188i	$0.00414412\pi$
$137$	1.80095e8	+	3.11933e8i	0.511232	+	0.885480i	−0.488683	+	0.872461i	$0.662523\pi$
$138$		0			0
$139$		−	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
$141$		0			0
$142$	1.47011e6	−	2.54631e6i	0.00361574	−	0.00626265i
$143$	−2.17442e8	+	1.25540e8i	−0.519996	+	0.300220i
$144$		0			0
$145$	2.77809e8	+	1.60393e8i	0.628456	+	0.362839i
$146$		−	9.56197e7i		−	0.210444i
$147$		0			0
$148$	2.83992e8			0.591914
$149$	1.53733e8	−	2.66273e8i	0.311905	−	0.540235i	−0.666870	−	0.745174i	$-0.732366\pi$
$149$	1.53733e8	−	2.66273e8i	0.311905	−	0.540235i	0.978775	+	0.204939i	$0.0656996\pi$
$150$		0			0
$151$	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
$153$		0			0
$154$	1.81315e8	−	2.15544e8i	0.322368	−	0.383224i
$155$	−1.35151e8			−0.234149
$156$		0			0
$157$	−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
$159$		0			0
$160$			7.98094e7i			0.121779i
$161$	2.74142e7	+	7.56093e7i	0.0408011	+	0.112531i
$162$		0			0
$163$	−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
$165$		0			0
$166$	6.33787e8	+	3.65917e8i	0.834663	+	0.481893i
$167$			9.61875e8i			1.23667i	0.785916	+	0.618334i	$0.212192\pi$
$167$			9.61875e8i			1.23667i	−0.785916	+	0.618334i	$0.787808\pi$
$168$		0			0
$169$	2.29377e8			0.281192
$170$	2.57377e8	−	4.45790e8i	0.308158	−	0.533746i
$171$		0			0
$172$	2.87848e8	+	4.98568e8i	0.328889	+	0.569653i
$173$	−1.14482e8	−	6.60964e7i	−0.127807	−	0.0737893i	0.434733	−	0.900559i	$-0.356843\pi$
$173$	−1.14482e8	−	6.60964e7i	−0.127807	−	0.0737893i	−0.562540	+	0.826770i	$0.690176\pi$
$174$		0			0
$175$	4.85206e8	+	8.61707e7i	0.517337	+	0.0918771i
$176$	−1.69884e8			−0.177053
$177$		0			0
$178$	1.72551e8	−	9.96222e7i	0.171885	−	0.0992376i
$179$	−4.55563e8	−	7.89058e8i	−0.443748	−	0.768594i	0.554216	−	0.832373i	$-0.313018\pi$
$179$	−4.55563e8	−	7.89058e8i	−0.443748	−	0.768594i	−0.997964	+	0.0637788i	$0.979685\pi$
$180$		0			0
$181$		−	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
$183$		0			0
$184$	2.42543e7	−	4.20096e7i	0.0211600	−	0.0366503i
$185$	8.27286e8	−	4.77634e8i	0.706266	−	0.407763i
$186$		0			0
$187$	9.48921e8	+	5.47860e8i	0.776003	+	0.448026i
$188$			2.39227e8i			0.191505i
$189$		0			0
$190$	1.04158e9			0.799242
$191$	3.64929e8	−	6.32076e8i	0.274205	−	0.474937i	−0.695729	−	0.718304i	$-0.744919\pi$
$191$	3.64929e8	−	6.32076e8i	0.274205	−	0.474937i	0.969934	+	0.243367i	$0.0782520\pi$
$192$		0			0
$193$	−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
$195$		0			0
$196$	−5.66426e8	+	4.72917e8i	−0.383812	+	0.320450i
$197$	−2.58982e9			−1.71951			−0.859754	−	0.510709i	$-0.829383\pi$
$197$	−2.58982e9			−1.71951			−0.859754	+	0.510709i	$0.829383\pi$
$198$		0			0
$199$	−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
$201$		0			0
$202$		−	1.38662e9i		−	0.832819i
$203$	1.15155e9	−	1.36894e9i	0.678108	−	0.806121i
$204$		0			0
$205$	5.57789e8	−	9.66118e8i	0.315831	−	0.547035i
$206$	−2.77551e8	+	1.60244e8i	−0.154126	+	0.0889844i
$207$		0			0
$208$	−3.43582e8	−	1.98367e8i	−0.183560	−	0.105978i
$209$			2.21714e9i			1.16200i
$210$		0			0
$211$	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
$213$		0			0
$214$	6.31076e8	+	1.09306e9i	0.300903	+	0.521180i
$215$	1.67704e9	+	9.68240e8i	0.784855	+	0.453137i
$216$		0			0
$217$	−1.31787e8	+	7.42059e8i	−0.0594337	+	0.334657i
$218$	−1.50763e8			−0.0667527
$219$		0			0
$220$	−4.94884e8	+	2.85721e8i	−0.211258	+	0.121970i
$221$	1.27943e9	+	2.21603e9i	0.536347	+	0.928981i
$222$		0			0
$223$		−	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
$225$		0			0
$226$	9.64895e8	−	1.67125e9i	0.369868	−	0.640630i
$227$	−3.60245e9	+	2.07987e9i	−1.35673	+	0.783310i	−0.989182	−	0.146693i	$-0.953137\pi$
$227$	−3.60245e9	+	2.07987e9i	−1.35673	+	0.783310i	−0.367551	+	0.930003i	$0.619804\pi$
$228$		0			0
$229$	−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
$231$		0			0
$232$	−1.07895e9			−0.372435
$233$	1.05874e9	−	1.83378e9i	0.359223	−	0.622192i	−0.628608	−	0.777722i	$-0.716375\pi$
$233$	1.05874e9	−	1.83378e9i	0.359223	−	0.622192i	0.987831	+	0.155530i	$0.0497085\pi$
$234$		0			0
$235$	4.02346e8	+	6.96884e8i	0.131925	+	0.228502i
$236$	5.76220e8	+	3.32681e8i	0.185755	+	0.107246i
$237$		0			0
$238$	−2.19668e9	−	1.84785e9i	−0.684636	−	0.575915i
$239$	−3.66705e9			−1.12389			−0.561947	−	0.827173i	$-0.689947\pi$
$239$	−3.66705e9			−1.12389			−0.561947	+	0.827173i	$0.689947\pi$
$240$		0			0
$241$	−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
$243$		0			0
$244$			2.95713e9i			0.834279i
$245$	−8.54655e8	+	2.33028e9i	−0.237206	+	0.646762i
$246$		0			0
$247$	−2.58886e9	+	4.48403e9i	−0.695537	+	1.20471i
$248$	3.93672e8	−	2.27287e8i	0.104071	−	0.0600852i
$249$		0			0
$250$	−2.51372e9	−	1.45130e9i	−0.643513	−	0.371533i
$251$		−	4.21322e9i		−	1.06150i	−0.847529	−	0.530749i	$-0.821911\pi$
$251$		−	4.21322e9i		−	1.06150i	0.847529	−	0.530749i	$-0.178089\pi$
$252$		0			0
$253$	3.47326e8			0.0847724
$254$	−7.23982e8	+	1.25397e9i	−0.173937	+	0.301268i
$255$		0			0
$256$	−1.34218e8	−	2.32472e8i	−0.0312500	−	0.0541266i
$257$	−9.63051e8	−	5.56018e8i	−0.220758	−	0.127455i	0.385543	−	0.922690i	$-0.374014\pi$
$257$	−9.63051e8	−	5.56018e8i	−0.220758	−	0.127455i	−0.606301	+	0.795235i	$0.707347\pi$
$258$		0			0
$259$	−1.81580e9	−	5.00804e9i	−0.403524	−	1.11293i
$260$	−1.33450e9			−0.292029
$261$		0			0
$262$	2.09897e9	−	1.21184e9i	0.445453	−	0.257182i
$263$	−4.03552e9	−	6.98973e9i	−0.843483	−	1.46096i	−0.886932	−	0.461900i	$-0.847168\pi$
$263$	−4.03552e9	−	6.98973e9i	−0.843483	−	1.46096i	0.0434485	−	0.999056i	$-0.486166\pi$
$264$		0			0
$265$		−	2.85267e9i		−	0.578453i
$266$	1.01565e9	−	5.71890e9i	0.202871	−	1.14232i
$267$		0			0
$268$	−7.37116e8	+	1.27672e9i	−0.142888	+	0.247490i
$269$	−1.71619e9	+	9.90840e8i	−0.327759	+	0.189232i	−0.654846	−	0.755762i	$-0.727266\pi$
$269$	−1.71619e9	+	9.90840e8i	−0.327759	+	0.189232i	0.327087	+	0.944994i	$0.393933\pi$
$270$		0			0
$271$	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
$273$		0			0
$274$	−4.07507e9			−0.722992
$275$	1.06410e9	−	1.84307e9i	0.186059	−	0.322263i
$276$		0			0
$277$	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
$279$		0			0
$280$	1.40740e9	−	5.10290e8i	0.228973	−	0.0830203i
$281$	6.27601e9			1.00660			0.503302	−	0.864111i	$-0.332118\pi$
$281$	6.27601e9			1.00660			0.503302	+	0.864111i	$0.332118\pi$
$282$		0			0
$283$	−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
$285$		0			0
$286$		−	2.84066e9i		−	0.424575i
$287$	−4.76066e9	−	4.00467e9i	−0.701681	−	0.590254i
$288$		0			0
$289$	2.09555e9	−	3.62960e9i	0.300405	−	0.520317i
$290$	−3.14305e9	+	1.81464e9i	−0.444385	+	0.256566i
$291$		0			0
$292$	9.36878e8	+	5.40907e8i	0.128870	+	0.0744031i
$293$			4.83891e9i			0.656564i	0.944580	+	0.328282i	$0.106470\pi$
$293$			4.83891e9i			0.656564i	−0.944580	+	0.328282i	$0.893530\pi$
$294$		0			0
$295$	2.23809e9			0.295521
$296$	−1.60650e9	+	2.78254e9i	−0.209273	+	0.362472i
$297$		0			0
$298$	1.73929e9	+	3.01254e9i	0.220550	+	0.382004i
$299$	7.02447e8	+	4.05558e8i	0.0878878	+	0.0507420i
$300$		0			0
$301$	6.95152e9	−	8.26382e9i	0.846864	−	1.00673i
$302$	−9.06099e9			−1.08930
$303$		0			0
$304$	−3.03395e9	+	1.75165e9i	−0.355234	+	0.205095i
$305$	4.97347e9	+	8.61431e9i	0.574726	+	0.995454i
$306$		0			0
$307$		−	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
$309$		0			0
$310$	7.64528e8	−	1.32420e9i	0.0827840	−	0.143386i
$311$	−1.97836e7	+	1.14220e7i	−0.00211477	+	0.00122096i	−0.501057	−	0.865414i	$-0.667055\pi$
$311$	−1.97836e7	+	1.14220e7i	−0.00211477	+	0.00122096i	0.498942	+	0.866635i	$0.333722\pi$
$312$		0			0
$313$	−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
$315$		0			0
$316$	7.31783e7			0.00733895
$317$	9.21516e9	−	1.59611e10i	0.912569	−	1.58062i	0.102147	−	0.994769i	$-0.467429\pi$
$317$	9.21516e9	−	1.59611e10i	0.912569	−	1.58062i	0.810422	−	0.585846i	$-0.199238\pi$
$318$		0			0
$319$	−3.86270e9	−	6.69039e9i	−0.373017	−	0.646084i
$320$	−7.81969e8	−	4.51470e8i	−0.0745744	−	0.0430555i
$321$		0			0
$322$	−8.95895e8	−	1.59107e8i	−0.0833362	−	0.0148002i
$323$	2.25956e10			2.07594
$324$		0			0
$325$	4.30415e9	−	2.48500e9i	0.385792	−	0.222737i
$326$	−5.41350e9	−	9.37646e9i	−0.479301	−	0.830173i
$327$		0			0
$328$			3.75220e9i			0.324183i
$329$	4.21865e9	−	1.52959e9i	0.360072	−	0.130554i
$330$		0			0
$331$	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
$333$		0			0
$334$	−9.42441e9	−	5.44119e9i	−0.757301	−	0.437228i
$335$			4.95890e9i			0.393737i
$336$		0			0
$337$	−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
$339$		0			0
$340$	2.91189e9	+	5.04354e9i	0.217901	+	0.377415i
$341$	2.81873e9	+	1.62740e9i	0.208466	+	0.120358i
$342$		0			0
$343$	1.19613e10	+	6.96485e9i	0.864174	+	0.503194i
$344$	−6.51327e9			−0.465120
$345$		0			0
$346$	1.29522e9	−	7.47796e8i	0.0903731	−	0.0521769i
$347$	5.55696e9	+	9.62493e9i	0.383283	+	0.663865i	0.991529	−	0.129883i	$-0.0414602\pi$
$347$	5.55696e9	+	9.62493e9i	0.383283	+	0.663865i	−0.608247	+	0.793748i	$0.708127\pi$
$348$		0			0
$349$			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
$351$		0			0
$352$	9.61012e8	−	1.66452e9i	0.0625977	−	0.108422i
$353$	−8.28960e9	+	4.78600e9i	−0.533869	+	0.308229i	−0.742590	−	0.669746i	$-0.766403\pi$
$353$	−8.28960e9	+	4.78600e9i	−0.533869	+	0.308229i	0.208722	+	0.977975i	$0.433070\pi$
$354$		0			0
$355$	9.69026e7	+	5.59467e7i	0.00610129	+	0.00352258i
$356$			2.25419e9i			0.140343i
$357$		0			0
$358$	1.03082e10			0.627554
$359$	6.29146e9	−	1.08971e10i	0.378768	−	0.656046i	−0.612115	−	0.790769i	$-0.709681\pi$
$359$	6.29146e9	−	1.08971e10i	0.378768	−	0.656046i	0.990883	+	0.134723i	$0.0430144\pi$
$360$		0			0
$361$	1.43688e10	+	2.48875e10i	0.846040	+	1.46538i
$362$	3.18390e9	+	1.83822e9i	0.185406	+	0.107044i
$363$		0			0
$364$	−1.30128e9	+	7.32721e9i	−0.0741254	+	0.417381i
$365$	3.63891e9			0.205022
$366$		0			0
$367$	−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
$369$		0			0
$370$			1.08076e10i			0.576664i
$371$	−1.56629e10	−	2.78166e9i	−0.826753	−	0.146828i
$372$		0			0
$373$	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
$375$		0			0
$376$	−2.34394e9	−	1.35327e9i	−0.117272	−	0.0677072i
$377$		−	1.80413e10i		−	0.893103i
$378$		0			0
$379$	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
$381$		0			0
$382$	4.12870e9	+	7.15112e9i	0.193892	+	0.335831i
$383$	4.72608e9	+	2.72860e9i	0.219637	+	0.126808i	0.605782	−	0.795630i	$-0.292860\pi$
$383$	4.72608e9	+	2.72860e9i	0.219637	+	0.126808i	−0.386145	+	0.922438i	$0.626194\pi$
$384$		0			0
$385$	8.20276e9	+	6.90015e9i	0.373351	+	0.314062i
$386$	2.25609e10			1.01626
$387$		0			0
$388$	−8.11268e9	+	4.68386e9i	−0.357962	+	0.206670i
$389$	2.14316e10	+	3.71207e10i	0.935959	+	1.62113i	0.772915	+	0.634510i	$0.218798\pi$
$389$	2.14316e10	+	3.71207e10i	0.935959	+	1.62113i	0.163044	+	0.986619i	$0.447869\pi$
$390$		0			0
$391$		−	3.53972e9i		−	0.151447i
$392$	−1.42943e9	−	8.22504e9i	−0.0605367	−	0.348332i
$393$		0			0
$394$	1.46502e10	−	2.53749e10i	0.607938	−	1.05298i
$395$	2.13173e8	−	1.23075e8i	0.00875677	−	0.00505572i
$396$		0			0
$397$	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
$399$		0			0
$400$	3.36277e9			0.131358
$401$	−4.83802e9	+	8.37970e9i	−0.187107	+	0.324079i	−0.944285	−	0.329130i	$-0.893244\pi$
$401$	−4.83802e9	+	8.37970e9i	−0.187107	+	0.324079i	0.757177	+	0.653209i	$0.226578\pi$
$402$		0			0
$403$	3.80048e9	+	6.58263e9i	0.144085	+	0.249563i
$404$	1.35860e10	+	7.84388e9i	0.509995	+	0.294446i
$405$		0			0
$406$	6.89866e9	+	1.90267e10i	0.253899	+	0.700261i
$407$	−2.30054e10			−0.838401
$408$		0			0
$409$	−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
$411$		0			0
$412$		−	3.62592e9i		−	0.125843i
$413$	2.18238e9	−	1.22884e10i	0.0750119	−	0.422373i
$414$		0			0
$415$	−1.39254e10	+	2.41195e10i	−0.469477	+	0.813159i
$416$	3.88719e9	−	2.24427e9i	0.129796	−	0.0749379i
$417$		0			0
$418$	−2.17234e10	−	1.25420e10i	−0.711578	−	0.410830i
$419$		−	5.87657e9i		−	0.190664i	−0.995446	−	0.0953318i	$-0.969609\pi$
$419$		−	5.87657e9i		−	0.190664i	0.995446	−	0.0953318i	$-0.0303912\pi$
$420$		0			0
$421$	−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
$423$		0			0
$424$	4.79741e9	+	8.30936e9i	0.148438	+	0.257101i
$425$	−1.87833e10	−	1.08446e10i	−0.575728	−	0.332397i
$426$		0			0
$427$	5.21474e10	−	1.89075e10i	1.56863	−	0.568751i
$428$	−1.42796e10			−0.425541
$429$		0			0
$430$	−1.89735e10	+	1.09544e10i	−0.554977	+	0.320416i
$431$	2.01398e10	+	3.48832e10i	0.583642	+	1.01090i	0.995043	+	0.0994434i	$0.0317062\pi$
$431$	2.01398e10	+	3.48832e10i	0.583642	+	1.01090i	−0.411401	+	0.911454i	$0.634960\pi$
$432$		0			0
$433$		−	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
$435$		0			0
$436$	8.52844e8	−	1.47717e9i	0.0236006	−	0.0408775i
$437$	6.20286e9	−	3.58122e9i	0.170085	−	0.0981987i
$438$		0			0
$439$	−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
$441$		0			0
$442$	−2.89501e10			−0.758510
$443$	1.64102e9	−	2.84233e9i	0.0426088	−	0.0738006i	−0.843935	−	0.536446i	$-0.819766\pi$
$443$	1.64102e9	−	2.84233e9i	0.0426088	−	0.0738006i	0.886543	+	0.462646i	$0.153100\pi$
$444$		0			0
$445$	3.79123e9	+	6.56660e9i	0.0966808	+	0.167456i
$446$	2.75789e10	+	1.59227e10i	0.697007	+	0.402417i
$447$		0			0
$448$	−3.24135e9	+	3.85325e9i	−0.0804662	+	0.0956566i
$449$	1.42212e10			0.349906			0.174953	−	0.984577i	$-0.444023\pi$
$449$	1.42212e10			0.349906			0.174953	+	0.984577i	$0.444023\pi$
$450$		0			0
$451$	−2.32667e10	+	1.34330e10i	−0.562379	+	0.324689i
$452$	1.09165e10	+	1.89080e10i	0.261536	+	0.452994i
$453$		0			0
$454$		−	4.70622e10i		−	1.10777i
$455$	8.53260e9	+	2.35332e10i	0.199084	+	0.549080i
$456$		0			0
$457$	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
$459$		0			0
$460$	1.59872e9	+	9.23022e8i	0.0357060	+	0.0206149i
$461$		−	2.00621e10i		−	0.444193i	−0.975025	−	0.222097i	$-0.928710\pi$
$461$		−	2.00621e10i		−	0.444193i	0.975025	−	0.222097i	$-0.0712901\pi$
$462$		0			0
$463$	−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
$465$		0			0
$466$	1.19782e10	+	2.07469e10i	0.254009	+	0.439956i
$467$	−6.34957e10	−	3.66593e10i	−1.33499	−	0.770755i	−0.348927	−	0.937150i	$-0.613454\pi$
$467$	−6.34957e10	−	3.66593e10i	−1.33499	−	0.770755i	−0.986059	+	0.166395i	$0.946787\pi$
$468$		0			0
$469$	2.72273e10	+	4.83547e9i	0.562748	+	0.0999418i
$470$	−9.10406e9			−0.186571
$471$		0			0
$472$	−6.51918e9	+	3.76385e9i	−0.131349	+	0.0758341i
$473$	−2.33178e10	−	4.03876e10i	−0.465847	−	0.806870i
$474$		0			0
$475$		−	4.38869e10i		−	0.862106i
$476$	3.05315e10	−	1.10700e10i	0.594730	−	0.215636i
$477$		0			0
$478$	2.07440e10	−	3.59296e10i	0.397356	−	0.688242i
$479$	−6.54555e10	+	3.77908e10i	−1.24338	+	0.717867i	−0.969781	−	0.243977i	$-0.921548\pi$
$479$	−6.54555e10	+	3.77908e10i	−1.24338	+	0.717867i	−0.273600	+	0.961843i	$0.588215\pi$
$480$		0			0
$481$	−4.65271e10	−	2.68624e10i	−0.869212	−	0.501840i
$482$		−	1.94823e10i		−	0.360955i
$483$		0			0
$484$	−1.36761e10			−0.249218
$485$	−1.57552e10	+	2.72887e10i	−0.284745	+	0.493192i
$486$		0			0
$487$	−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
$489$		0			0
$490$	−1.79974e10	−	2.15559e10i	−0.312194	−	0.373923i
$491$	1.03557e10			0.178178			0.0890890	−	0.996024i	$-0.471604\pi$
$491$	1.03557e10			0.178178			0.0890890	+	0.996024i	$0.471604\pi$
$492$		0			0
$493$	−6.81841e10	+	3.93661e10i	−1.15424	+	0.666400i
$494$	−2.92896e10	−	5.07310e10i	−0.491819	−	0.851856i
$495$		0			0
$496$			5.14291e9i			0.0849733i
$497$	4.01672e8	−	4.77499e8i	0.00658333	−	0.00782613i
$498$		0			0
$499$	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
$501$		0			0
$502$	4.12810e10	+	2.38336e10i	0.650032	+	0.375296i
$503$		−	5.95396e10i		−	0.930109i	−0.885282	−	0.465055i	$-0.846035\pi$
$503$		−	5.95396e10i		−	0.930109i	0.885282	−	0.465055i	$-0.153965\pi$
$504$		0			0
$505$	5.27691e10			0.811362
$506$	−1.96477e9	+	3.40308e9i	−0.0299716	+	0.0519123i
$507$		0			0
$508$	−8.19092e9	−	1.41871e10i	−0.122992	−	0.213029i
$509$	4.81846e9	+	2.78194e9i	0.0717856	+	0.0414455i	0.535463	−	0.844559i	$-0.320137\pi$
$509$	4.81846e9	+	2.78194e9i	0.0717856	+	0.0414455i	−0.463678	+	0.886004i	$0.653470\pi$
$510$		0			0
$511$	3.54834e9	−	1.99798e10i	0.0520405	−	0.293027i
$512$	3.03700e9			0.0441942
$513$		0			0
$514$	1.08957e10	−	6.29062e9i	0.156100	−	0.0901241i
$515$	−6.09827e9	−	1.05625e10i	−0.0866918	−	0.150155i
$516$		0			0
$517$		−	1.93792e10i		−	0.271252i
$518$	5.93403e10	+	1.05386e10i	0.824197	+	0.146374i
$519$		0			0
$520$	7.54908e9	−	1.30754e10i	0.103248	−	0.178830i
$521$	6.49808e10	−	3.75167e10i	0.881930	−	0.509183i	0.0106360	−	0.999943i	$-0.496614\pi$
$521$	6.49808e10	−	3.75167e10i	0.881930	−	0.509183i	0.871294	+	0.490761i	$0.163281\pi$
$522$		0			0
$523$	−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
$525$		0			0
$526$	9.13134e10			1.19287
$527$	1.65854e10	−	2.87267e10i	0.215022	−	0.372428i
$528$		0			0
$529$	3.85945e10	+	6.68476e10i	0.492836	+	0.853617i
$530$	2.79503e10	+	1.61371e10i	0.354228	+	0.204514i
$531$		0			0
$532$	5.02881e10	+	4.23023e10i	0.627797	+	0.528102i
$533$	−6.27408e10			−0.777394
$534$		0			0
$535$	−4.15974e10	+	2.40163e10i	−0.507752	+	0.293151i
$536$	−8.33952e9	−	1.44445e10i	−0.101037	−	0.175002i
$537$		0			0
$538$		−	2.24202e10i		−	0.267614i
$539$	4.58846e10	−	3.83097e10i	0.543640	−	0.453893i
$540$		0			0
$541$	−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
$543$		0			0
$544$	−1.69637e10	−	9.79401e9i	−0.193698	−	0.111832i
$545$		−	5.73745e9i		−	0.0650329i
$546$		0			0
$547$	−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
$549$		0			0
$550$	1.20389e10	+	2.08519e10i	0.131563	+	0.227874i
$551$	−1.37967e11	−	7.96555e10i	−1.49682	−	0.864190i
$552$		0			0
$553$	−4.67891e8	−	1.29046e9i	−0.00500316	−	0.0137989i
$554$	−1.49589e10			−0.158804
$555$		0			0
$556$	−1.53272e10	+	8.84918e9i	−0.160385	+	0.0925985i
$557$	6.08743e10	+	1.05437e11i	0.632431	+	1.09540i	0.987053	+	0.160393i	$0.0512762\pi$
$557$	6.08743e10	+	1.05437e11i	0.632431	+	1.09540i	−0.354622	+	0.935010i	$0.615390\pi$
$558$		0			0
$559$		−	1.08909e11i		−	1.11536i
$560$	−2.96164e9	+	1.66762e10i	−0.0301148	+	0.169569i
$561$		0			0
$562$	−3.55025e10	+	6.14921e10i	−0.355888	+	0.616416i
$563$	−1.23249e11	+	7.11577e10i	−1.22673	+	0.708253i	−0.966344	−	0.257252i	$-0.917183\pi$
$563$	−1.23249e11	+	7.11577e10i	−1.22673	+	0.708253i	−0.260385	+	0.965505i	$0.583850\pi$
$564$		0			0
$565$	6.36011e10	+	3.67201e10i	0.624124	+	0.360338i
$566$		−	1.10337e11i		−	1.07512i
$567$		0			0
$568$	−3.76349e8			−0.00361574
$569$	−9.57798e10	+	1.65895e11i	−0.913745	+	1.58265i	−0.105016	+	0.994471i	$0.533489\pi$
$569$	−9.57798e10	+	1.65895e11i	−0.913745	+	1.58265i	−0.808729	+	0.588181i	$0.799844\pi$
$570$		0			0
$571$	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
$573$		0			0
$574$	6.61679e10	−	2.39910e10i	0.609537	−	0.221004i
$575$	−6.87511e9			−0.0628939
$576$		0			0
$577$	−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
$579$		0			0
$580$		−	4.10607e10i		−	0.362839i
$581$	1.18852e11	+	9.99778e10i	1.04304	+	0.877403i
$582$		0			0
$583$	−3.43499e10	+	5.94958e10i	−0.297339	+	0.515006i
$584$	−1.05996e10	+	6.11966e9i	−0.0911248	+	0.0526110i
$585$		0			0
$586$	−4.74114e10	−	2.73730e10i	−0.402062	−	0.232130i
$587$			1.08603e11i			0.914726i	0.889280	+	0.457363i	$0.151206\pi$
$587$			1.08603e11i			0.914726i	−0.889280	+	0.457363i	$0.848794\pi$
$588$		0			0
$589$	6.71193e10			0.557682
$590$	−1.26605e10	+	2.19287e10i	−0.104483	+	0.180969i
$591$		0			0
$592$	−1.81755e10	−	3.14808e10i	−0.147979	−	0.256306i
$593$	1.02644e11	+	5.92618e10i	0.830073	+	0.479243i	0.853878	−	0.520474i	$-0.174245\pi$
$593$	1.02644e11	+	5.92618e10i	0.830073	+	0.479243i	−0.0238046	+	0.999717i	$0.507578\pi$
$594$		0			0
$595$	7.03219e10	−	8.35972e10i	0.561077	−	0.666997i
$596$	−3.93557e10			−0.311905
$597$		0			0
$598$	−7.94728e9	+	4.58836e9i	−0.0621461	+	0.0358800i
$599$	−1.01445e11	−	1.75708e11i	−0.787996	−	1.36485i	−0.927193	−	0.374585i	$-0.877785\pi$
$599$	−1.01445e11	−	1.75708e11i	−0.787996	−	1.36485i	0.139196	−	0.990265i	$-0.455548\pi$
$600$		0			0
$601$		−	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
$603$		0			0
$604$	5.12567e10	−	8.87792e10i	0.385126	−	0.667058i
$605$	−3.98392e10	+	2.30012e10i	−0.297365	+	0.171684i
$606$		0			0
$607$	−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
$609$		0			0
$610$	−1.12537e11			−0.812785
$611$	2.26282e10	−	3.91933e10i	0.162363	−	0.281220i
$612$		0			0
$613$	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
$615$		0			0
$616$	−3.54975e10	−	6.30422e9i	−0.246533	−	0.0437833i
$617$	9.80871e10			0.676817			0.338408	−	0.940999i	$-0.390111\pi$
$617$	9.80871e10			0.676817			0.338408	+	0.940999i	$0.390111\pi$
$618$		0			0
$619$	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
$621$		0			0
$622$		−	2.58451e8i		−	0.00172670i
$623$	3.97515e10	−	1.44130e10i	0.263877	−	0.0956757i
$624$		0			0
$625$	1.51435e10	−	2.62293e10i	0.0992443	−	0.171896i
$626$	2.32998e9	−	1.34521e9i	0.0151724	−	0.00875980i
$627$		0			0
$628$	2.75359e10	+	1.58979e10i	0.177036	+	0.102212i
$629$			2.34456e11i			1.49782i
$630$		0			0
$631$	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
$633$		0			0
$634$	1.04258e11	+	1.80579e11i	0.645284	+	1.11766i
$635$	−4.77213e10	−	2.75519e10i	−0.293507	−	0.169456i
$636$		0			0
$637$	1.37532e11	−	2.39017e10i	0.835305	−	0.145168i
$638$	8.74029e10			0.527525
$639$		0			0
$640$	8.84697e9	−	5.10780e9i	0.0527321	−	0.0304449i
$641$	5.30434e10	+	9.18739e10i	0.314195	+	0.544202i	0.979266	−	0.202578i	$-0.0649320\pi$
$641$	5.30434e10	+	9.18739e10i	0.314195	+	0.544202i	−0.665071	+	0.746780i	$0.731599\pi$
$642$		0			0
$643$			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
$645$		0			0
$646$	−1.27820e11	+	2.21391e11i	−0.733954	+	1.27125i
$647$	2.34397e11	−	1.35329e11i	1.33763	−	0.772279i	0.351172	−	0.936311i	$-0.385783\pi$
$647$	2.34397e11	−	1.35329e11i	1.33763	−	0.772279i	0.986455	+	0.164032i	$0.0524500\pi$
$648$		0			0
$649$	−4.66780e10	−	2.69495e10i	−0.263107	−	0.151905i
$650$			5.62292e10i			0.314998i
$651$		0			0
$652$	1.22494e11			0.677834
$653$	1.34684e11	−	2.33279e11i	0.740734	−	1.28299i	−0.211427	−	0.977394i	$-0.567811\pi$
$653$	1.34684e11	−	2.33279e11i	0.740734	−	1.28299i	0.952161	−	0.305596i	$-0.0988556\pi$
$654$		0			0
$655$	4.61180e10	+	7.98787e10i	0.250556	+	0.433976i
$656$	−3.67639e10	−	2.12256e10i	−0.198521	−	0.114616i
$657$		0			0
$658$	−8.87746e9	+	4.99868e10i	−0.0473571	+	0.266656i
$659$	−3.10763e11			−1.64774			−0.823868	−	0.566781i	$-0.808188\pi$
$659$	−3.10763e11			−1.64774			−0.823868	+	0.566781i	$0.808188\pi$
$660$		0			0
$661$	−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
$663$		0			0
$664$		−	9.36748e10i		−	0.481893i
$665$	2.17639e11	+	3.86518e10i	1.11288	+	0.197644i
$666$		0			0
$667$	−1.24784e10	+	2.16133e10i	−0.0630459	+	0.109199i
$668$	1.06625e11	−	6.15600e10i	0.535493	−	0.309167i
$669$		0			0
$670$	−4.85871e10	−	2.80518e10i	−0.241114	−	0.139207i
$671$		−	2.39549e11i		−	1.18169i
$672$		0			0
$673$	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
$675$		0			0
$676$	−1.46801e10	−	2.54268e10i	−0.0702981	−	0.121760i
$677$	−3.19960e11	−	1.84729e11i	−1.52314	−	0.879388i	−0.999625	−	0.0273741i	$-0.991285\pi$
$677$	−3.19960e11	−	1.84729e11i	−1.52314	−	0.879388i	−0.523519	−	0.852014i	$-0.675381\pi$
$678$		0			0
$679$	1.34469e11	+	1.13115e11i	0.632618	+	0.532158i
$680$	−6.58885e10			−0.308158
$681$		0			0
$682$	−3.18903e10	+	1.84119e10i	−0.147408	+	0.0851061i
$683$	2.14512e10	+	3.71546e10i	0.0985755	+	0.170738i	0.911095	−	0.412196i	$-0.135238\pi$
$683$	2.14512e10	+	3.71546e10i	0.0985755	+	0.170738i	−0.812520	+	0.582934i	$0.801905\pi$
$684$		0			0
$685$		−	1.55081e11i		−	0.704364i
$686$	−1.35905e11	+	7.77969e10i	−0.613674	+	0.351290i
$687$		0			0
$688$	3.68446e10	−	6.38167e10i	0.164445	−	0.284827i
$689$	−1.38942e11	+	8.02180e10i	−0.616532	+	0.355955i
$690$		0			0
$691$	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
$693$		0			0
$694$	−1.25740e11			−0.542044
$695$	−2.97661e10	+	5.15564e10i	−0.127580	+	0.220975i
$696$		0			0
$697$	1.36901e11	+	2.37119e11i	0.580063	+	1.00470i
$698$	−2.05628e11	−	1.18719e11i	−0.866284	−	0.500149i
$699$		0			0
$700$	−2.15010e10	−	5.93006e10i	−0.0895503	−	0.246983i
$701$	4.62669e11			1.91601			0.958006	−	0.286748i	$-0.0925742\pi$
$701$	4.62669e11			1.91601			0.958006	+	0.286748i	$0.0925742\pi$
$702$		0			0
$703$	−4.10851e11	+	2.37205e11i	−1.68215	+	0.971187i
$704$	1.08726e10	+	1.88319e10i	0.0442632	+	0.0766662i
$705$		0			0
$706$		−	1.08295e11i		−	0.435902i
$707$	5.14557e10	−	2.89734e11i	0.205947	−	1.15964i
$708$		0			0
$709$	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
$711$		0			0
$712$	−2.20865e10	−	1.27516e10i	−0.0859423	−	0.0496188i
$713$		−	1.05146e10i		−	0.0406850i
$714$		0			0
$715$	1.08104e11			0.413636
$716$	−5.83121e10	+	1.00999e11i	−0.221874	+	0.384297i
$717$		0			0
$718$	7.11798e10	+	1.23287e11i	0.267830	+	0.463895i
$719$	−8.22291e9	−	4.74750e9i	−0.0307687	−	0.0177643i	0.484537	−	0.874771i	$-0.338988\pi$
$719$	−8.22291e9	−	4.74750e9i	−0.0307687	−	0.0177643i	−0.515305	+	0.857007i	$0.672322\pi$
$720$		0			0
$721$	−6.39411e10	+	2.31836e10i	−0.236613	+	0.0857905i
$722$	−3.25128e11			−1.19648
$723$		0			0
$724$	−3.60217e10	+	2.07971e10i	−0.131102	+	0.0756918i
$725$	7.64599e10	+	1.32432e11i	0.276746	+	0.479339i
$726$		0			0
$727$		−	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
$729$		0			0
$730$	−2.05848e10	+	3.56539e10i	−0.0724862	+	0.125550i
$731$	−4.11604e11	+	2.37640e11i	−1.44149	+	0.832242i
$732$		0			0
$733$	−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
$735$		0			0
$736$	−6.20909e9			−0.0211600
$737$	5.97118e10	−	1.03424e11i	0.202390	−	0.350550i
$738$		0			0
$739$	−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
$741$		0			0
$742$	1.15857e11	−	1.37729e11i	0.382215	−	0.454369i
$743$	2.65800e11			0.872167			0.436084	−	0.899906i	$-0.356365\pi$
$743$	2.65800e11			0.872167			0.436084	+	0.899906i	$0.356365\pi$
$744$		0			0
$745$	−1.14645e11	+	6.61906e10i	−0.372162	+	0.214868i
$746$	6.14879e9	+	1.06500e10i	0.0198534	+	0.0343871i
$747$		0			0
$748$		−	1.40252e11i		−	0.448026i
$749$	9.13019e10	+	2.51814e11i	0.290103	+	0.800114i
$750$		0			0
$751$	−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
$753$		0			0
$754$	1.76768e11	+	1.02057e11i	0.546911	+	0.315759i
$755$		−	3.44826e11i		−	1.06124i
$756$		0			0
$757$	−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
$759$		0			0
$760$	−6.66611e10	−	1.15460e11i	−0.199810	−	0.346082i
$761$	4.17660e11	+	2.41136e11i	1.24533	+	0.718990i	0.970174	−	0.242410i	$-0.0779378\pi$
$761$	4.17660e11	+	2.41136e11i	1.24533	+	0.718990i	0.275154	+	0.961400i	$0.411271\pi$
$762$		0			0
$763$	−3.15021e10	−	5.59464e9i	−0.0929481	−	0.0165072i
$764$	−9.34219e10			−0.274205
$765$		0			0
$766$	−5.34695e10	+	3.08706e10i	−0.155307	+	0.0896665i
$767$	−6.29357e10	−	1.09008e11i	−0.181851	−	0.314975i
$768$		0			0
$769$			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
$771$		0			0
$772$	−1.27623e11	+	2.21050e11i	−0.359303	+	0.622332i
$773$	2.35305e11	−	1.35853e11i	0.659041	−	0.380497i	−0.132871	−	0.991133i	$-0.542419\pi$
$773$	2.35305e11	−	1.35853e11i	0.659041	−	0.380497i	0.791911	+	0.610636i	$0.209086\pi$
$774$		0			0
$775$	−5.57952e10	−	3.22134e10i	−0.154664	−	0.0892954i
$776$		−	1.05984e11i		−	0.292275i
$777$		0			0
$778$	−4.84942e11			−1.32365
$779$	−2.77012e11	+	4.79799e11i	−0.752227	+	1.30290i
$780$		0			0
$781$	−1.34735e9	−	2.33367e9i	−0.00362139	−	0.00627243i
$782$	3.46820e10	+	2.00237e10i	0.0927421	+	0.0535447i
$783$		0			0
$784$	8.86747e10	+	3.25223e10i	0.234712	+	0.0860830i
$785$	1.06952e11			0.281650
$786$		0			0
$787$	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
$789$		0			0
$790$			2.78488e9i			0.00714987i
$791$	2.63634e11	−	3.13402e11i	0.673434	−	0.800564i
$792$		0			0
$793$	2.79712e11	−	4.84475e11i	0.707323	−	1.22512i
$794$	−4.11708e11	+	2.37700e11i	−1.03588	+	0.598063i
$795$		0			0
$796$	2.17593e11	+	1.25627e11i	0.541991	+	0.312919i
$797$			6.69693e11i			1.65975i	0.557949	+	0.829875i	$0.311588\pi$
$797$			6.69693e11i			1.65975i	−0.557949	+	0.829875i	$0.688412\pi$
$798$		0			0
$799$	−1.97500e11			−0.484596
$800$	−1.90227e10	+	3.29483e10i	−0.0464421	+	0.0804401i
$801$		0			0
$802$	−5.47360e10	−	9.48055e10i	−0.132305	−	0.229158i
$803$	−7.58939e10	−	4.38174e10i	−0.182534	−	0.105386i
$804$		0			0
$805$	6.05501e9	−	3.40942e10i	0.0144189	−	0.0811891i
$806$	−8.59951e10			−0.203767
$807$		0			0
$808$	−1.53708e11	+	8.87434e10i	−0.360621	+	0.208205i
$809$	−1.92597e10	−	3.33588e10i	−0.0449631	−	0.0778783i	0.842668	−	0.538433i	$-0.180984\pi$
$809$	−1.92597e10	−	3.33588e10i	−0.0449631	−	0.0778783i	−0.887631	+	0.460555i	$0.847650\pi$
$810$		0			0
$811$		−	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
$813$		0			0
$814$	1.30138e11	−	2.25406e11i	0.296420	−	0.513414i
$815$	3.56831e11	−	2.06017e11i	0.808784	−	0.466952i
$816$		0			0
$817$	−8.32862e11	−	4.80853e11i	−1.86932	−	1.07925i
$818$		−	1.41019e10i		−	0.0314966i
$819$		0			0
$820$	−1.42794e11			−0.315831
$821$	5.17118e10	−	8.95675e10i	0.113820	−	0.197141i	−0.803488	−	0.595321i	$-0.797025\pi$
$821$	5.17118e10	−	8.95675e10i	0.113820	−	0.197141i	0.917307	+	0.398180i	$0.130358\pi$
$822$		0			0
$823$	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
$825$		0			0
$826$	1.08056e11	+	9.08967e10i	0.232129	+	0.195267i
$827$	−3.92102e11			−0.838256			−0.419128	−	0.907927i	$-0.637664\pi$
$827$	−3.92102e11			−0.838256			−0.419128	+	0.907927i	$0.637664\pi$
$828$		0			0
$829$	−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
$831$		0			0
$832$			5.07820e10i			0.105978i
$833$	−3.90427e11	−	4.67626e11i	−0.810887	−	0.971222i
$834$		0			0
$835$	2.07070e11	−	3.58656e11i	0.425963	−	0.737790i
$836$	2.45772e11	−	1.41897e11i	0.503162	−	0.290501i
$837$		0			0
$838$	5.75784e10	+	3.32429e10i	0.116757	+	0.0674098i
$839$		−	3.44859e11i		−	0.695975i	−0.937499	−	0.347988i	$-0.886865\pi$
$839$		−	3.44859e11i		−	0.695975i	0.937499	−	0.347988i	$-0.113135\pi$
$840$		0			0
$841$	5.48574e10			0.109661
$842$	1.66975e11	−	2.89210e11i	0.332203	−	0.575393i
$843$		0			0
$844$	−7.29882e10	−	1.26419e11i	−0.143841	−	0.249140i
$845$	−8.55284e10	−	4.93798e10i	−0.167758	−	0.0968552i
$846$		0			0
$847$	8.74427e10	+	2.41170e11i	0.169899	+	0.468586i
$848$	−1.08553e11			−0.209922
$849$		0			0
$850$	2.12509e11	−	1.22692e11i	0.407101	−	0.235040i
$851$	3.71594e10	+	6.43620e10i	0.0708517	+	0.122719i
$852$		0			0
$853$			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
$855$		0			0
$856$	8.07778e10	−	1.39911e11i	0.150452	−	0.260590i
$857$	−7.44252e11	+	4.29694e11i	−1.37974	+	0.796592i	−0.992128	−	0.125231i	$-0.960033\pi$
$857$	−7.44252e11	+	4.29694e11i	−1.37974	+	0.796592i	−0.387611	+	0.921823i	$0.626700\pi$
$858$		0			0
$859$	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
$861$		0			0
$862$	−4.55712e11			−0.825395
$863$	1.24085e11	−	2.14922e11i	0.223706	−	0.387470i	−0.732225	−	0.681063i	$-0.761518\pi$
$863$	1.24085e11	−	2.14922e11i	0.223706	−	0.387470i	0.955930	+	0.293594i	$0.0948512\pi$
$864$		0			0
$865$	2.84582e10	+	4.92910e10i	0.0508326	+	0.0880447i
$866$	4.36900e11	+	2.52244e11i	0.776802	+	0.448487i
$867$		0			0
$868$	9.06925e10	−	3.28830e10i	0.159769	−	0.0579286i
$869$	−5.92797e9			−0.0103951
$870$		0			0
$871$	2.41527e11	−	1.39446e11i	0.419656	−	0.242289i
$872$	9.64883e9	+	1.67123e10i	0.0166882	+	0.0289048i
$873$		0			0
$874$			8.10338e10i			0.138874i
$875$	−4.71389e11	−	3.96532e11i	−0.804168	−	0.676466i
$876$		0			0
$877$	−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
$879$		0			0
$880$	6.33452e10	+	3.65723e10i	0.105629	+	0.0609849i
$881$		−	4.19437e11i		−	0.696246i	−0.937449	−	0.348123i	$-0.886819\pi$
$881$		−	4.19437e11i		−	0.696246i	0.937449	−	0.348123i	$-0.113181\pi$
$882$		0			0
$883$	−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
$885$		0			0
$886$	1.85660e10	+	3.21573e10i	0.0301290	+	0.0521849i
$887$	3.17793e11	+	1.83478e11i	0.513393	+	0.296407i	0.734227	−	0.678904i	$-0.237545\pi$
$887$	3.17793e11	+	1.83478e11i	0.513393	+	0.296407i	−0.220835	+	0.975311i	$0.570878\pi$
$888$		0			0
$889$	−1.97810e11	+	2.35153e11i	−0.316695	+	0.376481i
$890$	−8.57858e10			−0.136727
$891$		0			0
$892$	−3.12019e11	+	1.80144e11i	−0.492858	+	0.284552i
$893$	−1.99816e11	−	3.46091e11i	−0.314213	−	0.544232i
$894$		0			0
$895$			3.92290e11i			0.611386i
$896$	−1.94181e10	−	5.35559e10i	−0.0301284	−	0.0830950i
$897$		0			0
$898$	−8.04473e10	+	1.39339e11i	−0.123710	+	0.214273i
$899$	−2.02538e11	+	1.16935e11i	−0.310076	+	0.179022i
$900$		0			0
$901$	6.06343e11	+	3.50072e11i	0.920066	+	0.531201i
$902$		−	3.03955e11i		−	0.459180i
$903$		0			0
$904$	−2.47013e11			−0.369868
$905$	−6.99556e10	+	1.21167e11i	−0.104287	+	0.180630i
$906$		0			0
$907$	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
$909$		0			0
$910$	−2.78845e11	−	4.95218e10i	−0.406628	−	0.0722156i
$911$	6.36440e11			0.924026			0.462013	−	0.886873i	$-0.347127\pi$
$911$	6.36440e11			0.924026			0.462013	+	0.886873i	$0.347127\pi$
$912$		0			0
$913$	5.80861e11	−	3.35360e11i	0.835967	−	0.482646i
$914$	1.01112e11	+	1.75130e11i	0.144883	+	0.250944i
$915$		0			0
$916$			3.33580e10i			0.0473825i
$917$	4.83552e11	−	1.75325e11i	0.683858	−	0.247951i
$918$		0			0
$919$	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
$921$		0			0
$922$	1.96567e11	+	1.13488e11i	0.272012	+	0.157046i
$923$		−	6.29297e9i		−	0.00867059i
$924$		0			0
$925$	4.55379e11			0.622022
$926$	3.40643e11	−	5.90011e11i	0.463293	−	0.802447i
$927$		0			0
$928$	6.90529e10	+	1.19603e11i	0.0931087	+	0.161269i
$929$	3.95158e11	+	2.28145e11i	0.530528	+	0.306300i	0.741231	−	0.671250i	$-0.234242\pi$
$929$	3.95158e11	+	2.28145e11i	0.530528	+	0.306300i	−0.210704	+	0.977550i	$0.567575\pi$
$930$		0			0
$931$	4.24444e11	−	1.15728e12i	0.564965	−	1.54042i
$932$	−2.71036e11			−0.359223
$933$		0			0
$934$	7.18372e11	−	4.14752e11i	0.943978	−	0.545006i
$935$	−2.35884e11	−	4.08563e11i	−0.308640	−	0.534580i
$936$		0			0
$937$			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
$939$		0			0
$940$	5.15003e10	−	8.92012e10i	0.0659627	−	0.114251i
$941$	−3.09132e11	+	1.78478e11i	−0.394263	+	0.227628i	−0.684006	−	0.729477i	$-0.739764\pi$
$941$	−3.09132e11	+	1.78478e11i	−0.394263	+	0.227628i	0.289743	+	0.957105i	$0.406430\pi$
$942$		0			0
$943$	7.51630e10	+	4.33954e10i	0.0950511	+	0.0548778i
$944$		−	8.51662e10i		−	0.107246i
$945$		0			0
$946$	5.27622e11			0.658807
$947$	−6.86199e11	+	1.18853e12i	−0.853199	+	1.47778i	0.0251070	+	0.999685i	$0.492007\pi$
$947$	−6.86199e11	+	1.18853e12i	−0.853199	+	1.47778i	−0.878306	+	0.478099i	$0.841326\pi$
$948$		0			0
$949$	−1.02327e11	−	1.77236e11i	−0.126162	−	0.218518i
$950$	4.30002e11	+	2.48262e11i	0.527930	+	0.304801i
$951$		0			0
$952$	−6.42485e10	+	3.61767e11i	−0.0782196	+	0.440435i
$953$	1.05746e12			1.28201			0.641004	−	0.767537i	$-0.278518\pi$
$953$	1.05746e12			1.28201			0.641004	+	0.767537i	$0.278518\pi$
$954$		0			0
$955$	−2.72144e11	+	1.57122e11i	−0.327179	+	0.188897i
$956$	2.34691e11	+	4.06497e11i	0.280973	+	0.486660i
$957$		0			0
$958$		−	8.55108e11i		−	1.01522i
$959$	−8.51490e11	−	1.51221e11i	−1.00671	−	0.178788i
$960$		0			0
$961$	−3.77179e11	+	6.53294e11i	−0.442236	+	0.765976i
$962$	5.26394e11	−	3.03914e11i	0.614626	−	0.354854i
$963$		0			0
$964$	1.90887e11	+	1.10209e11i	0.221039	+	0.127617i
$965$			8.58578e11i			0.990080i
$966$		0			0
$967$	−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
$969$		0			0
$970$	−1.78249e11	−	3.08737e11i	−0.201345	−	0.348740i
$971$	6.47768e11	+	3.73989e11i	0.728690	+	0.420709i	0.817943	−	0.575300i	$-0.195115\pi$
$971$	6.47768e11	+	3.73989e11i	0.728690	+	0.420709i	−0.0892528	+	0.996009i	$0.528448\pi$
$972$		0			0
$973$	2.54051e11	+	2.13707e11i	0.283445	+	0.238434i
$974$	4.13184e11			0.459100
$975$		0			0
$976$	3.27802e11	−	1.89256e11i	0.361253	−	0.208570i
$977$	1.55722e11	+	2.69719e11i	0.170912	+	0.296029i	0.938739	−	0.344629i	$-0.111995\pi$
$977$	1.55722e11	+	2.69719e11i	0.170912	+	0.296029i	−0.767827	+	0.640657i	$0.778662\pi$
$978$		0			0
$979$		−	1.82606e11i		−	0.198785i
$980$	3.13013e11	−	5.43986e10i	0.339358	−	0.0589771i
$981$		0			0
$982$	−5.85808e10	+	1.01465e11i	−0.0629954	+	0.109111i
$983$	−1.53075e12	+	8.83778e11i	−1.63942	+	0.946518i	−0.658383	+	0.752683i	$0.728759\pi$
$983$	−1.53075e12	+	8.83778e11i	−1.63942	+	0.946518i	−0.981034	+	0.193835i	$0.937907\pi$
$984$		0			0
$985$	9.65670e11	+	5.57530e11i	1.02585	+	0.592275i
$986$		−	8.90754e11i		−	0.942432i
$987$		0			0
$988$	6.62748e11			0.695537
$989$	−7.53281e10	+	1.30472e11i	−0.0787357	+	0.136374i
$990$		0			0
$991$	−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
$993$		0			0
$994$	2.40632e9	+	6.63671e9i	0.00246495	+	0.00679841i
$995$	8.45149e11			0.862265
$996$		0			0
$997$	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
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.9.n.b.19.2		12
3.2	odd	2		14.9.d.a.5.6	yes	12
7.3	odd	6	inner	126.9.n.b.73.2		12
12.11	even	2		112.9.s.c.33.1		12
21.2	odd	6		98.9.b.c.97.6		12
21.5	even	6		98.9.b.c.97.1		12
21.11	odd	6		98.9.d.b.31.4		12
21.17	even	6		14.9.d.a.3.6	✓	12
21.20	even	2		98.9.d.b.19.4		12
84.59	odd	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	21.17	even	6
14.9.d.a.5.6	yes	12	3.2	odd	2
98.9.b.c.97.1		12	21.5	even	6
98.9.b.c.97.6		12	21.2	odd	6
98.9.d.b.19.4		12	21.20	even	2
98.9.d.b.31.4		12	21.11	odd	6
112.9.s.c.17.1		12	84.59	odd	6
112.9.s.c.33.1		12	12.11	even	2
126.9.n.b.19.2		12	1.1	even	1	trivial
126.9.n.b.73.2		12	7.3	odd	6	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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	126.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.65685 + 9.79796i) q^{2} +(-64.0000 - 110.851i) q^{4} +(-372.872 - 215.278i) q^{5} +(-1545.60 + 1837.37i) q^{7} +1448.15 q^{8} +O(q^{10})\)	\(q+(-5.65685 + 9.79796i) q^{2} +(-64.0000 - 110.851i) q^{4} +(-372.872 - 215.278i) q^{5} +(-1545.60 + 1837.37i) q^{7} +1448.15 q^{8} +(4218.56 - 2435.59i) q^{10} +(5184.46 + 8979.75i) q^{11} +24214.7i q^{13} +(-9259.29 - 25537.4i) q^{14} +(-8192.00 + 14189.0i) q^{16} +(91515.8 - 52836.7i) q^{17} +(185178. + 106912. i) q^{19} +55111.1i q^{20} -117311. q^{22} +(16748.4 - 29009.1i) q^{23} +(-102624. - 177749. i) q^{25} +(-237255. - 136979. i) q^{26} +(302593. + 53739.4i) q^{28} -745053. q^{29} +(271844. - 156949. i) q^{31} +(-92681.9 - 160530. i) q^{32} +1.19556e6i q^{34} +(971854. - 352372. i) q^{35} +(-1.10934e6 + 1.92144e6i) q^{37} +(-2.09505e6 + 1.20958e6i) q^{38} +(-539976. - 311755. i) q^{40} +2.59102e6i q^{41} -4.49763e6 q^{43} +(663611. - 1.14941e6i) q^{44} +(189486. + 328200. i) q^{46} +(-1.61857e6 - 934482. i) q^{47} +(-987071. - 5.67967e6i) q^{49} +2.32210e6 q^{50} +(2.68423e6 - 1.54974e6i) q^{52} +(3.31278e6 + 5.73790e6i) q^{53} -4.46440e6i q^{55} +(-2.23826e6 + 2.66080e6i) q^{56} +(4.21466e6 - 7.30000e6i) q^{58} +(-4.50172e6 + 2.59907e6i) q^{59} +(-2.00074e7 - 1.15513e7i) q^{61} +3.55136e6i q^{62} +2.09715e6 q^{64} +(5.21289e6 - 9.02900e6i) q^{65} +(-5.75872e6 - 9.97440e6i) q^{67} +(-1.17140e7 - 6.76310e6i) q^{68} +(-2.04511e6 + 1.15155e7i) q^{70} -259882. q^{71} +(-7.31936e6 + 4.22584e6i) q^{73} +(-1.25508e7 - 2.17386e7i) q^{74} -2.73696e7i q^{76} +(-2.45122e7 - 4.35328e6i) q^{77} +(-285853. + 495111. i) q^{79} +(6.10913e6 - 3.52711e6i) q^{80} +(-2.53867e7 - 1.46570e7i) q^{82} -6.46856e7i q^{83} -4.54982e7 q^{85} +(2.54424e7 - 4.40676e7i) q^{86} +(7.50791e6 + 1.30041e7i) q^{88} +(-1.52515e7 - 8.80544e6i) q^{89} +(-4.44915e7 - 3.74262e7i) q^{91} -4.28759e6 q^{92} +(1.83120e7 - 1.05725e7i) q^{94} +(-4.60318e7 - 7.97293e7i) q^{95} -7.31853e7i q^{97} +(6.12329e7 + 2.24578e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 768 q^{4} - 1674 q^{5} - 1308 q^{7}+O(q^{10}) \) 12 * q - 768 * q^4 - 1674 * q^5 - 1308 * q^7	\( 12 q - 768 q^{4} - 1674 q^{5} - 1308 q^{7} + 17664 q^{10} - 10302 q^{11} - 56832 q^{14} - 98304 q^{16} - 173178 q^{17} + 405978 q^{19} - 941568 q^{22} - 158934 q^{23} + 838668 q^{25} - 1958400 q^{26} - 255744 q^{28} + 4355256 q^{29} + 4520250 q^{31} + 5270790 q^{35} + 134214 q^{37} - 1278720 q^{38} - 2260992 q^{40} - 12961896 q^{43} - 1318656 q^{44} + 2345472 q^{46} - 18385002 q^{47} - 3659172 q^{49} - 2970624 q^{50} - 3369984 q^{52} + 16540506 q^{53} - 4325376 q^{56} + 9176064 q^{58} - 31163922 q^{59} - 85390158 q^{61} + 25165824 q^{64} + 46506264 q^{65} - 37750362 q^{67} + 22166784 q^{68} + 92031744 q^{70} - 45506424 q^{71} + 9414786 q^{73} - 58837248 q^{74} + 100614066 q^{77} + 59730294 q^{79} + 27426816 q^{80} - 93259776 q^{82} - 64652220 q^{85} + 15144960 q^{86} + 60260352 q^{88} - 323014482 q^{89} - 266861424 q^{91} + 40687104 q^{92} - 443440128 q^{94} + 175918350 q^{95} - 472166400 q^{98}+O(q^{100}) \) 12 * q - 768 * q^4 - 1674 * q^5 - 1308 * q^7 + 17664 * q^10 - 10302 * q^11 - 56832 * q^14 - 98304 * q^16 - 173178 * q^17 + 405978 * q^19 - 941568 * q^22 - 158934 * q^23 + 838668 * q^25 - 1958400 * q^26 - 255744 * q^28 + 4355256 * q^29 + 4520250 * q^31 + 5270790 * q^35 + 134214 * q^37 - 1278720 * q^38 - 2260992 * q^40 - 12961896 * q^43 - 1318656 * q^44 + 2345472 * q^46 - 18385002 * q^47 - 3659172 * q^49 - 2970624 * q^50 - 3369984 * q^52 + 16540506 * q^53 - 4325376 * q^56 + 9176064 * q^58 - 31163922 * q^59 - 85390158 * q^61 + 25165824 * q^64 + 46506264 * q^65 - 37750362 * q^67 + 22166784 * q^68 + 92031744 * q^70 - 45506424 * q^71 + 9414786 * q^73 - 58837248 * q^74 + 100614066 * q^77 + 59730294 * q^79 + 27426816 * q^80 - 93259776 * q^82 - 64652220 * q^85 + 15144960 * q^86 + 60260352 * q^88 - 323014482 * q^89 - 266861424 * q^91 + 40687104 * q^92 - 443440128 * q^94 + 175918350 * q^95 - 472166400 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more