LMFDB - Embedded newform 36.9.d.b.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,9,Mod(19,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("36.19");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	36.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.6656299622$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-39}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 10 $ x^2 - x + 10
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 4)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.1
Root			$0.500000 + 3.12250i$ of defining polynomial
Character	$\chi$	$=$	36.19
Dual form			36.9.d.b.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(10.0000 - 12.4900i) q^{2} +(-56.0000 - 249.800i) q^{4} -610.000 q^{5} +1398.88i q^{7} +(-3680.00 - 1798.56i) q^{8} +(-6100.00 + 7618.90i) q^{10} +18485.2i q^{11} -5470.00 q^{13} +(17472.0 + 13988.8i) q^{14} +(-59264.0 + 27977.6i) q^{16} -73090.0 q^{17} -19484.4i q^{19} +(34160.0 + 152378. i) q^{20} +(230880. + 184852. i) q^{22} +237210. i q^{23} -18525.0 q^{25} +(-54700.0 + 68320.3i) q^{26} +(349440. - 78337.3i) q^{28} +128222. q^{29} -67945.6i q^{31} +(-243200. + 1.01998e6i) q^{32} +(-730900. + 912894. i) q^{34} -853317. i q^{35} -3.47203e6 q^{37} +(-243360. - 194844. i) q^{38} +(2.24480e6 + 1.09712e6i) q^{40} -2.14688e6 q^{41} -5.92815e6i q^{43} +(4.61760e6 - 1.03517e6i) q^{44} +(2.96275e6 + 2.37210e6i) q^{46} -7.62629e6i q^{47} +3.80794e6 q^{49} +(-185250. + 231377. i) q^{50} +(306320. + 1.36641e6i) q^{52} -824290. q^{53} -1.12760e7i q^{55} +(2.51597e6 - 5.14788e6i) q^{56} +(1.28222e6 - 1.60149e6i) q^{58} +3.72552e6i q^{59} -1.47461e7 q^{61} +(-848640. - 679456. i) q^{62} +(1.03076e7 + 1.32374e7i) q^{64} +3.33670e6 q^{65} +1.52567e7i q^{67} +(4.09304e6 + 1.82579e7i) q^{68} +(-1.06579e7 - 8.53317e6i) q^{70} +1.19604e6i q^{71} -5.72563e6 q^{73} +(-3.47203e7 + 4.33656e7i) q^{74} +(-4.86720e6 + 1.09113e6i) q^{76} -2.58586e7 q^{77} +3.59132e7i q^{79} +(3.61510e7 - 1.70663e7i) q^{80} +(-2.14688e7 + 2.68145e7i) q^{82} +5.19603e7i q^{83} +4.45849e7 q^{85} +(-7.40426e7 - 5.92815e7i) q^{86} +(3.32467e7 - 6.80255e7i) q^{88} +8.33242e7 q^{89} -7.65187e6i q^{91} +(5.92550e7 - 1.32838e7i) q^{92} +(-9.52524e7 - 7.62629e7i) q^{94} +1.18855e7i q^{95} +1.20619e8 q^{97} +(3.80794e7 - 4.75611e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 20 q^{2} - 112 q^{4} - 1220 q^{5} - 7360 q^{8} - 12200 q^{10} - 10940 q^{13} + 34944 q^{14} - 118528 q^{16} - 146180 q^{17} + 68320 q^{20} + 461760 q^{22} - 37050 q^{25} - 109400 q^{26} + 698880 q^{28}+ \cdots + 76158740 q^{98}+O(q^{100}) $ 2 * q + 20 * q^2 - 112 * q^4 - 1220 * q^5 - 7360 * q^8 - 12200 * q^10 - 10940 * q^13 + 34944 * q^14 - 118528 * q^16 - 146180 * q^17 + 68320 * q^20 + 461760 * q^22 - 37050 * q^25 - 109400 * q^26 + 698880 * q^28 + 256444 * q^29 - 486400 * q^32 - 1461800 * q^34 - 6944060 * q^37 - 486720 * q^38 + 4489600 * q^40 - 4293764 * q^41 + 9235200 * q^44 + 5925504 * q^46 + 7615874 * q^49 - 370500 * q^50 + 612640 * q^52 - 1648580 * q^53 + 5031936 * q^56 + 2564440 * q^58 - 29492156 * q^61 - 1697280 * q^62 + 20615168 * q^64 + 6673400 * q^65 + 8186080 * q^68 - 21315840 * q^70 - 11451260 * q^73 - 69440600 * q^74 - 9734400 * q^76 - 51717120 * q^77 + 72302080 * q^80 - 42937640 * q^82 + 89169800 * q^85 - 148085184 * q^86 + 66493440 * q^88 + 166648444 * q^89 + 118510080 * q^92 - 190504704 * q^94 + 241238020 * q^97 + 76158740 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	10.0000	−	12.4900i	0.625000	−	0.780625i
$2$	10.0000	−	12.4900i	0.625000	−	0.780625i
$3$		0			0
$3$		0			0
$4$	−56.0000	−	249.800i	−0.218750	−	0.975781i
$5$	−610.000			−0.976000			−0.488000	−	0.872844i	$-0.662273\pi$
$5$	−610.000			−0.976000			−0.488000	+	0.872844i	$0.662273\pi$
$6$		0			0
$7$			1398.88i			0.582624i	0.956628	+	0.291312i	$0.0940917\pi$
$7$			1398.88i			0.582624i	−0.956628	+	0.291312i	$0.905908\pi$
$8$	−3680.00	−	1798.56i	−0.898438	−	0.439101i
$9$		0			0
$10$	−6100.00	+	7618.90i	−0.610000	+	0.761890i
$11$			18485.2i			1.26256i	0.775554	+	0.631282i	$0.217471\pi$
$11$			18485.2i			1.26256i	−0.775554	+	0.631282i	$0.782529\pi$
$12$		0			0
$13$	−5470.00			−0.191520			−0.0957600	−	0.995404i	$-0.530528\pi$
$13$	−5470.00			−0.191520			−0.0957600	+	0.995404i	$0.530528\pi$
$14$	17472.0	+	13988.8i	0.454810	+	0.364140i
$15$		0			0
$16$	−59264.0	+	27977.6i	−0.904297	+	0.426904i
$17$	−73090.0			−0.875109			−0.437555	−	0.899192i	$-0.644155\pi$
$17$	−73090.0			−0.875109			−0.437555	+	0.899192i	$0.644155\pi$
$18$		0			0
$19$		−	19484.4i		−	0.149511i	−0.997202	−	0.0747554i	$-0.976182\pi$
$19$		−	19484.4i		−	0.149511i	0.997202	−	0.0747554i	$-0.0238176\pi$
$20$	34160.0	+	152378.i	0.213500	+	0.952362i
$21$		0			0
$22$	230880.	+	184852.i	0.985588	+	0.789102i
$23$			237210.i			0.847660i	0.905742	+	0.423830i	$0.139315\pi$
$23$			237210.i			0.847660i	−0.905742	+	0.423830i	$0.860685\pi$
$24$		0			0
$25$	−18525.0			−0.0474240
$26$	−54700.0	+	68320.3i	−0.119700	+	0.149505i
$27$		0			0
$28$	349440.	−	78337.3i	0.568513	−	0.127449i
$29$	128222.			0.181289			0.0906443	−	0.995883i	$-0.471107\pi$
$29$	128222.			0.181289			0.0906443	+	0.995883i	$0.471107\pi$
$30$		0			0
$31$		−	67945.6i		−	0.0735723i	−0.999323	−	0.0367862i	$-0.988288\pi$
$31$		−	67945.6i		−	0.0735723i	0.999323	−	0.0367862i	$-0.0117120\pi$
$32$	−243200.	+	1.01998e6i	−0.231934	+	0.972732i
$33$		0			0
$34$	−730900.	+	912894.i	−0.546943	+	0.683132i
$35$		−	853317.i		−	0.568641i
$36$		0			0
$37$	−3.47203e6			−1.85258			−0.926289	−	0.376813i	$-0.877020\pi$
$37$	−3.47203e6			−1.85258			−0.926289	+	0.376813i	$0.877020\pi$
$38$	−243360.	−	194844.i	−0.116712	−	0.0934442i
$39$		0			0
$40$	2.24480e6	+	1.09712e6i	0.876875	+	0.428563i
$41$	−2.14688e6			−0.759754			−0.379877	−	0.925037i	$-0.624034\pi$
$41$	−2.14688e6			−0.759754			−0.379877	+	0.925037i	$0.624034\pi$
$42$		0			0
$43$		−	5.92815e6i		−	1.73399i	−0.498321	−	0.866993i	$-0.666050\pi$
$43$		−	5.92815e6i		−	1.73399i	0.498321	−	0.866993i	$-0.333950\pi$
$44$	4.61760e6	−	1.03517e6i	1.23199	−	0.276186i
$45$		0			0
$46$	2.96275e6	+	2.37210e6i	0.661704	+	0.529787i
$47$		−	7.62629e6i		−	1.56287i	−0.623989	−	0.781433i	$-0.714489\pi$
$47$		−	7.62629e6i		−	1.56287i	0.623989	−	0.781433i	$-0.285511\pi$
$48$		0			0
$49$	3.80794e6			0.660550
$50$	−185250.	+	231377.i	−0.0296400	+	0.0370203i
$51$		0			0
$52$	306320.	+	1.36641e6i	0.0418950	+	0.186881i
$53$	−824290.			−0.104466			−0.0522332	−	0.998635i	$-0.516634\pi$
$53$	−824290.			−0.104466			−0.0522332	+	0.998635i	$0.516634\pi$
$54$		0			0
$55$		−	1.12760e7i		−	1.23226i
$56$	2.51597e6	−	5.14788e6i	0.255831	−	0.523451i
$57$		0			0
$58$	1.28222e6	−	1.60149e6i	0.113305	−	0.141518i
$59$			3.72552e6i			0.307453i	0.988113	+	0.153726i	$0.0491274\pi$
$59$			3.72552e6i			0.307453i	−0.988113	+	0.153726i	$0.950873\pi$
$60$		0			0
$61$	−1.47461e7			−1.06502			−0.532509	−	0.846424i	$-0.678751\pi$
$61$	−1.47461e7			−1.06502			−0.532509	+	0.846424i	$0.678751\pi$
$62$	−848640.	−	679456.i	−0.0574324	−	0.0459827i
$63$		0			0
$64$	1.03076e7	+	1.32374e7i	0.614380	+	0.789010i
$65$	3.33670e6			0.186923
$66$		0			0
$67$			1.52567e7i			0.757113i	0.925578	+	0.378557i	$0.123579\pi$
$67$			1.52567e7i			0.757113i	−0.925578	+	0.378557i	$0.876421\pi$
$68$	4.09304e6	+	1.82579e7i	0.191430	+	0.853915i
$69$		0			0
$70$	−1.06579e7	−	8.53317e6i	−0.443895	−	0.355400i
$71$			1.19604e6i			0.0470666i	0.999723	+	0.0235333i	$0.00749158\pi$
$71$			1.19604e6i			0.0470666i	−0.999723	+	0.0235333i	$0.992508\pi$
$72$		0			0
$73$	−5.72563e6			−0.201619			−0.100810	−	0.994906i	$-0.532143\pi$
$73$	−5.72563e6			−0.201619			−0.100810	+	0.994906i	$0.532143\pi$
$74$	−3.47203e7	+	4.33656e7i	−1.15786	+	1.44617i
$75$		0			0
$76$	−4.86720e6	+	1.09113e6i	−0.145890	+	0.0327055i
$77$	−2.58586e7			−0.735600
$78$		0			0
$79$			3.59132e7i			0.922032i	0.887392	+	0.461016i	$0.152515\pi$
$79$			3.59132e7i			0.922032i	−0.887392	+	0.461016i	$0.847485\pi$
$80$	3.61510e7	−	1.70663e7i	0.882594	−	0.416658i
$81$		0			0
$82$	−2.14688e7	+	2.68145e7i	−0.474846	+	0.593082i
$83$			5.19603e7i			1.09486i	0.836851	+	0.547431i	$0.184394\pi$
$83$			5.19603e7i			1.09486i	−0.836851	+	0.547431i	$0.815606\pi$
$84$		0			0
$85$	4.45849e7			0.854107
$86$	−7.40426e7	−	5.92815e7i	−1.35359	−	1.08374i
$87$		0			0
$88$	3.32467e7	−	6.80255e7i	0.554393	−	1.13433i
$89$	8.33242e7			1.32804			0.664020	−	0.747715i	$-0.268849\pi$
$89$	8.33242e7			1.32804			0.664020	+	0.747715i	$0.268849\pi$
$90$		0			0
$91$		−	7.65187e6i		−	0.111584i
$92$	5.92550e7	−	1.32838e7i	0.827130	−	0.185426i
$93$		0			0
$94$	−9.52524e7	−	7.62629e7i	−1.22001	−	0.976792i
$95$			1.18855e7i			0.145923i
$96$		0			0
$97$	1.20619e8			1.36248			0.681238	−	0.732062i	$-0.261442\pi$
$97$	1.20619e8			1.36248			0.681238	+	0.732062i	$0.261442\pi$
$98$	3.80794e7	−	4.75611e7i	0.412844	−	0.515641i
$99$		0			0
$100$	1.03740e6	+	4.62754e6i	0.0103740	+	0.0462754i
$101$	−2.77246e7			−0.266428			−0.133214	−	0.991087i	$-0.542530\pi$
$101$	−2.77246e7			−0.266428			−0.133214	+	0.991087i	$0.542530\pi$
$102$		0			0
$103$			1.04501e8i			0.928477i	0.885710	+	0.464238i	$0.153672\pi$
$103$			1.04501e8i			0.928477i	−0.885710	+	0.464238i	$0.846328\pi$
$104$	2.01296e7	+	9.83812e6i	0.172069	+	0.0840967i
$105$		0			0
$106$	−8.24290e6	+	1.02954e7i	−0.0652915	+	0.0815490i
$107$		−	1.00328e8i		−	0.765394i	−0.923874	−	0.382697i	$-0.874995\pi$
$107$		−	1.00328e8i		−	0.765394i	0.923874	−	0.382697i	$-0.125005\pi$
$108$		0			0
$109$	−5.90716e7			−0.418478			−0.209239	−	0.977865i	$-0.567099\pi$
$109$	−5.90716e7			−0.418478			−0.209239	+	0.977865i	$0.567099\pi$
$110$	−1.40837e8	−	1.12760e8i	−0.961934	−	0.770164i
$111$		0			0
$112$	−3.91373e7	−	8.29032e7i	−0.248724	−	0.526865i
$113$	−5.50849e7			−0.337846			−0.168923	−	0.985629i	$-0.554029\pi$
$113$	−5.50849e7			−0.337846			−0.168923	+	0.985629i	$0.554029\pi$
$114$		0			0
$115$		−	1.44698e8i		−	0.827316i
$116$	−7.18043e6	−	3.20298e7i	−0.0396569	−	0.176898i
$117$		0			0
$118$	4.65317e7	+	3.72552e7i	0.240005	+	0.192158i
$119$		−	1.02244e8i		−	0.509859i
$120$		0			0
$121$	−1.27344e8			−0.594067
$122$	−1.47461e8	+	1.84178e8i	−0.665637	+	0.831380i
$123$		0			0
$124$	−1.69728e7	+	3.80495e6i	−0.0717905	+	0.0160939i
$125$	2.49581e8			1.02229
$126$		0			0
$127$			2.57160e8i			0.988529i	0.869312	+	0.494264i	$0.164562\pi$
$127$			2.57160e8i			0.988529i	−0.869312	+	0.494264i	$0.835438\pi$
$128$	2.68411e8	+	3.63229e6i	0.999908	+	0.0135313i
$129$		0			0
$130$	3.33670e7	−	4.16754e7i	0.116827	−	0.145917i
$131$			3.12175e8i			1.06002i	0.847992	+	0.530009i	$0.177812\pi$
$131$			3.12175e8i			1.06002i	−0.847992	+	0.530009i	$0.822188\pi$
$132$		0			0
$133$	2.72563e7			0.0871085
$134$	1.90556e8	+	1.52567e8i	0.591021	+	0.473196i
$135$		0			0
$136$	2.68971e8	+	1.31457e8i	0.786231	+	0.384262i
$137$	−2.21980e8			−0.630132			−0.315066	−	0.949070i	$-0.602027\pi$
$137$	−2.21980e8			−0.630132			−0.315066	+	0.949070i	$0.602027\pi$
$138$		0			0
$139$		−	2.95030e8i		−	0.790328i	−0.918611	−	0.395164i	$-0.870688\pi$
$139$		−	2.95030e8i		−	0.790328i	0.918611	−	0.395164i	$-0.129312\pi$
$140$	−2.13158e8	+	4.77857e7i	−0.554869	+	0.124390i
$141$		0			0
$142$	1.49386e7	+	1.19604e7i	0.0367414	+	0.0294166i
$143$		−	1.01114e8i		−	0.241806i
$144$		0			0
$145$	−7.82154e7			−0.176938
$146$	−5.72563e7	+	7.15131e7i	−0.126012	+	0.157389i
$147$		0			0
$148$	1.94434e8	+	8.67313e8i	0.405252	+	1.80771i
$149$	−4.03603e8			−0.818859			−0.409429	−	0.912342i	$-0.634272\pi$
$149$	−4.03603e8			−0.818859			−0.409429	+	0.912342i	$0.634272\pi$
$150$		0			0
$151$		−	8.36985e8i		−	1.60994i	−0.593316	−	0.804970i	$-0.702181\pi$
$151$		−	8.36985e8i		−	1.60994i	0.593316	−	0.804970i	$-0.297819\pi$
$152$	−3.50438e7	+	7.17026e7i	−0.0656504	+	0.134326i
$153$		0			0
$154$	−2.58586e8	+	3.22973e8i	−0.459750	+	0.574227i
$155$			4.14468e7i			0.0718066i
$156$		0			0
$157$	−2.71319e8			−0.446561			−0.223281	−	0.974754i	$-0.571677\pi$
$157$	−2.71319e8			−0.446561			−0.223281	+	0.974754i	$0.571677\pi$
$158$	4.48556e8	+	3.59132e8i	0.719761	+	0.576270i
$159$		0			0
$160$	1.48352e8	−	6.22190e8i	0.226367	−	0.949386i
$161$	−3.31828e8			−0.493867
$162$		0			0
$163$			5.78509e8i			0.819520i	0.912193	+	0.409760i	$0.134388\pi$
$163$			5.78509e8i			0.819520i	−0.912193	+	0.409760i	$0.865612\pi$
$164$	1.20225e8	+	5.36291e8i	0.166196	+	0.741353i
$165$		0			0
$166$	6.48984e8	+	5.19603e8i	0.854676	+	0.684288i
$167$		−	4.68118e8i		−	0.601852i	−0.953647	−	0.300926i	$-0.902704\pi$
$167$		−	4.68118e8i		−	0.601852i	0.953647	−	0.300926i	$-0.0972958\pi$
$168$		0			0
$169$	−7.85810e8			−0.963320
$170$	4.45849e8	−	5.56865e8i	0.533817	−	0.666737i
$171$		0			0
$172$	−1.48085e9	+	3.31976e8i	−1.69199	+	0.379309i
$173$	2.06197e8			0.230196			0.115098	−	0.993354i	$-0.463282\pi$
$173$	2.06197e8			0.230196			0.115098	+	0.993354i	$0.463282\pi$
$174$		0			0
$175$		−	2.59142e7i		−	0.0276303i
$176$	−5.17171e8	−	1.09551e9i	−0.538994	−	1.14173i
$177$		0			0
$178$	8.33242e8	−	1.04072e9i	0.830025	−	1.03670i
$179$		−	1.41911e8i		−	0.138230i	−0.997609	−	0.0691152i	$-0.977982\pi$
$179$		−	1.41911e8i		−	0.138230i	0.997609	−	0.0691152i	$-0.0220176\pi$
$180$		0			0
$181$	4.82566e8			0.449616			0.224808	−	0.974403i	$-0.427824\pi$
$181$	4.82566e8			0.449616			0.224808	+	0.974403i	$0.427824\pi$
$182$	−9.55718e7	−	7.65187e7i	−0.0871053	−	0.0697400i
$183$		0			0
$184$	4.26636e8	−	8.72933e8i	0.372209	−	0.761569i
$185$	2.11794e9			1.80812
$186$		0			0
$187$		−	1.35108e9i		−	1.10488i
$188$	−1.90505e9	+	4.27072e8i	−1.52502	+	0.341877i
$189$		0			0
$190$	1.48450e8	+	1.18855e8i	0.113911	+	0.0912016i
$191$		−	9.92461e8i		−	0.745727i	−0.927886	−	0.372864i	$-0.878376\pi$
$191$		−	9.92461e8i		−	0.745727i	0.927886	−	0.372864i	$-0.121624\pi$
$192$		0			0
$193$	1.17593e9			0.847526			0.423763	−	0.905773i	$-0.360709\pi$
$193$	1.17593e9			0.847526			0.423763	+	0.905773i	$0.360709\pi$
$194$	1.20619e9	−	1.50653e9i	0.851547	−	1.06358i
$195$		0			0
$196$	−2.13244e8	−	9.51222e8i	−0.144495	−	0.644552i
$197$	−1.70538e9			−1.13229			−0.566144	−	0.824306i	$-0.691565\pi$
$197$	−1.70538e9			−1.13229			−0.566144	+	0.824306i	$0.691565\pi$
$198$		0			0
$199$			2.49036e9i			1.58800i	0.607919	+	0.793999i	$0.292004\pi$
$199$			2.49036e9i			1.58800i	−0.607919	+	0.793999i	$0.707996\pi$
$200$	6.81720e7	+	3.33183e7i	0.0426075	+	0.0208239i
$201$		0			0
$202$	−2.77246e8	+	3.46281e8i	−0.166518	+	0.207981i
$203$			1.79367e8i			0.105623i
$204$		0			0
$205$	1.30960e9			0.741519
$206$	1.30522e9	+	1.04501e9i	0.724792	+	0.580298i
$207$		0			0
$208$	3.24174e8	−	1.53037e8i	0.173191	−	0.0817606i
$209$	3.60173e8			0.188767
$210$		0			0
$211$			1.46774e9i			0.740491i	0.928934	+	0.370245i	$0.120726\pi$
$211$			1.46774e9i			0.740491i	−0.928934	+	0.370245i	$0.879274\pi$
$212$	4.61602e7	+	2.05908e8i	0.0228520	+	0.101936i
$213$		0			0
$214$	−1.25309e9	−	1.00328e9i	−0.597486	−	0.478371i
$215$			3.61617e9i			1.69237i
$216$		0			0
$217$	9.50477e7			0.0428650
$218$	−5.90716e8	+	7.37804e8i	−0.261549	+	0.326674i
$219$		0			0
$220$	−2.81674e9	+	6.31454e8i	−1.20242	+	0.269557i
$221$	3.99802e8			0.167601
$222$		0			0
$223$		−	1.47920e9i		−	0.598147i	−0.954230	−	0.299073i	$-0.903322\pi$
$223$		−	1.47920e9i		−	0.598147i	0.954230	−	0.299073i	$-0.0966776\pi$
$224$	−1.42683e9	−	3.40208e8i	−0.566737	−	0.135130i
$225$		0			0
$226$	−5.50849e8	+	6.88011e8i	−0.211154	+	0.263731i
$227$			7.50054e8i			0.282481i	0.989975	+	0.141241i	$0.0451091\pi$
$227$			7.50054e8i			0.282481i	−0.989975	+	0.141241i	$0.954891\pi$
$228$		0			0
$229$	−2.84784e9			−1.03556			−0.517778	−	0.855515i	$-0.673241\pi$
$229$	−2.84784e9			−1.03556			−0.517778	+	0.855515i	$0.673241\pi$
$230$	−1.80728e9	−	1.44698e9i	−0.645823	−	0.517073i
$231$		0			0
$232$	−4.71857e8	−	2.30615e8i	−0.162876	−	0.0796041i
$233$	−2.20621e8			−0.0748553			−0.0374276	−	0.999299i	$-0.511916\pi$
$233$	−2.20621e8			−0.0748553			−0.0374276	+	0.999299i	$0.511916\pi$
$234$		0			0
$235$			4.65204e9i			1.52536i
$236$	9.30634e8	−	2.08629e8i	0.300007	−	0.0672553i
$237$		0			0
$238$	−1.27703e9	−	1.02244e9i	−0.398009	−	0.318662i
$239$			4.04493e9i			1.23971i	0.784717	+	0.619855i	$0.212808\pi$
$239$			4.04493e9i			1.23971i	−0.784717	+	0.619855i	$0.787192\pi$
$240$		0			0
$241$	6.17983e9			1.83193			0.915964	−	0.401260i	$-0.131427\pi$
$241$	6.17983e9			1.83193			0.915964	+	0.401260i	$0.131427\pi$
$242$	−1.27344e9	+	1.59052e9i	−0.371292	+	0.463743i
$243$		0			0
$244$	8.25780e8	+	3.68357e9i	0.232973	+	1.03922i
$245$	−2.32284e9			−0.644696
$246$		0			0
$247$			1.06580e8i			0.0286343i
$248$	−1.22204e8	+	2.50040e8i	−0.0323057	+	0.0661001i
$249$		0			0
$250$	2.49582e9	−	3.11727e9i	0.638929	−	0.798022i
$251$		−	5.21367e9i		−	1.31356i	−0.754084	−	0.656778i	$-0.771919\pi$
$251$		−	5.21367e9i		−	1.31356i	0.754084	−	0.656778i	$-0.228081\pi$
$252$		0			0
$253$	−4.38487e9			−1.07022
$254$	3.21193e9	+	2.57160e9i	0.771670	+	0.617830i
$255$		0			0
$256$	2.72948e9	−	3.31613e9i	0.635506	−	0.772096i
$257$	6.13693e9			1.40676			0.703378	−	0.710816i	$-0.251674\pi$
$257$	6.13693e9			1.40676			0.703378	+	0.710816i	$0.251674\pi$
$258$		0			0
$259$		−	4.85695e9i		−	1.07936i
$260$	−1.86855e8	−	8.33507e8i	−0.0408895	−	0.182396i
$261$		0			0
$262$	3.89907e9	+	3.12175e9i	0.827477	+	0.662512i
$263$		−	6.96916e9i		−	1.45666i	−0.685228	−	0.728329i	$-0.740297\pi$
$263$		−	6.96916e9i		−	1.45666i	0.685228	−	0.728329i	$-0.259703\pi$
$264$		0			0
$265$	5.02817e8			0.101959
$266$	2.72563e8	−	3.40431e8i	0.0544428	−	0.0679991i
$267$		0			0
$268$	3.81112e9	−	8.54374e8i	0.738777	−	0.165619i
$269$	−2.70720e9			−0.517025			−0.258513	−	0.966008i	$-0.583232\pi$
$269$	−2.70720e9			−0.517025			−0.258513	+	0.966008i	$0.583232\pi$
$270$		0			0
$271$		−	7.99032e9i		−	1.48145i	−0.671808	−	0.740725i	$-0.734482\pi$
$271$		−	7.99032e9i		−	1.48145i	0.671808	−	0.740725i	$-0.265518\pi$
$272$	4.33161e9	−	2.04488e9i	0.791359	−	0.373588i
$273$		0			0
$274$	−2.21980e9	+	2.77253e9i	−0.393832	+	0.491897i
$275$		−	3.42438e8i		−	0.0598758i
$276$		0			0
$277$	−8.22965e9			−1.39786			−0.698928	−	0.715192i	$-0.746339\pi$
$277$	−8.22965e9			−1.39786			−0.698928	+	0.715192i	$0.746339\pi$
$278$	−3.68493e9	−	2.95030e9i	−0.616949	−	0.493955i
$279$		0			0
$280$	−1.53474e9	+	3.14020e9i	−0.249691	+	0.510888i
$281$	−3.08105e9			−0.494167			−0.247083	−	0.968994i	$-0.579472\pi$
$281$	−3.08105e9			−0.494167			−0.247083	+	0.968994i	$0.579472\pi$
$282$		0			0
$283$			1.17112e9i			0.182582i	0.995824	+	0.0912908i	$0.0290993\pi$
$283$			1.17112e9i			0.182582i	−0.995824	+	0.0912908i	$0.970901\pi$
$284$	2.98771e8	−	6.69784e7i	0.0459267	−	0.0102958i
$285$		0			0
$286$	−1.26291e9	−	1.01114e9i	−0.188760	−	0.151129i
$287$		−	3.00323e9i		−	0.442650i
$288$		0			0
$289$	−1.63361e9			−0.234184
$290$	−7.82154e8	+	9.76910e8i	−0.110586	+	0.138122i
$291$		0			0
$292$	3.20635e8	+	1.43026e9i	0.0441042	+	0.196736i
$293$	−4.80980e9			−0.652614			−0.326307	−	0.945264i	$-0.605804\pi$
$293$	−4.80980e9			−0.652614			−0.326307	+	0.945264i	$0.605804\pi$
$294$		0			0
$295$		−	2.27256e9i		−	0.300074i
$296$	1.27771e10	+	6.24465e9i	1.66443	+	0.813470i
$297$		0			0
$298$	−4.03603e9	+	5.04100e9i	−0.511787	+	0.639221i
$299$		−	1.29754e9i		−	0.162344i
$300$		0			0
$301$	8.29277e9			1.01026
$302$	−1.04539e10	−	8.36985e9i	−1.25676	−	1.00621i
$303$		0			0
$304$	5.45126e8	+	1.15472e9i	0.0638268	+	0.135202i
$305$	8.99511e9			1.03946
$306$		0			0
$307$		−	3.49176e9i		−	0.393089i	−0.980495	−	0.196545i	$-0.937028\pi$
$307$		−	3.49176e9i		−	0.393089i	0.980495	−	0.196545i	$-0.0629721\pi$
$308$	1.44808e9	+	6.45947e9i	0.160912	+	0.717784i
$309$		0			0
$310$	5.17670e8	+	4.14468e8i	0.0560540	+	0.0448791i
$311$			1.29807e10i			1.38757i	0.720182	+	0.693785i	$0.244058\pi$
$311$			1.29807e10i			1.38757i	−0.720182	+	0.693785i	$0.755942\pi$
$312$		0			0
$313$	−6.31165e9			−0.657606			−0.328803	−	0.944399i	$-0.606645\pi$
$313$	−6.31165e9			−0.657606			−0.328803	+	0.944399i	$0.606645\pi$
$314$	−2.71319e9	+	3.38877e9i	−0.279101	+	0.348597i
$315$		0			0
$316$	8.97112e9	−	2.01114e9i	0.899702	−	0.201695i
$317$	−1.65902e10			−1.64291			−0.821455	−	0.570273i	$-0.806837\pi$
$317$	−1.65902e10			−1.64291			−0.821455	+	0.570273i	$0.806837\pi$
$318$		0			0
$319$			2.37021e9i			0.228888i
$320$	−6.28763e9	−	8.07481e9i	−0.599635	−	0.770074i
$321$		0			0
$322$	−3.31828e9	+	4.14453e9i	−0.308667	+	0.385525i
$323$			1.42411e9i			0.130838i
$324$		0			0
$325$	1.01332e8			0.00908264
$326$	7.22557e9	+	5.78509e9i	0.639738	+	0.512200i
$327$		0			0
$328$	7.90053e9	+	3.86129e9i	0.682591	+	0.333609i
$329$	1.06683e10			0.910563
$330$		0			0
$331$			5.48640e9i			0.457062i	0.973537	+	0.228531i	$0.0733922\pi$
$331$			5.48640e9i			0.457062i	−0.973537	+	0.228531i	$0.926608\pi$
$332$	1.29797e10	−	2.90978e9i	1.06834	−	0.239501i
$333$		0			0
$334$	−5.84680e9	−	4.68118e9i	−0.469821	−	0.376158i
$335$		−	9.30657e9i		−	0.738942i
$336$		0			0
$337$	−3.56226e8			−0.0276189			−0.0138095	−	0.999905i	$-0.504396\pi$
$337$	−3.56226e8			−0.0276189			−0.0138095	+	0.999905i	$0.504396\pi$
$338$	−7.85810e9	+	9.81476e9i	−0.602075	+	0.751992i
$339$		0			0
$340$	−2.49675e9	−	1.11373e10i	−0.186836	−	0.833421i
$341$	1.25599e9			0.0928897
$342$		0			0
$343$			1.33911e10i			0.967476i
$344$	−1.06621e10	+	2.18156e10i	−0.761396	+	1.55788i
$345$		0			0
$346$	2.06197e9	−	2.57540e9i	0.143872	−	0.179697i
$347$			1.59731e10i			1.10172i	0.834599	+	0.550859i	$0.185700\pi$
$347$			1.59731e10i			1.10172i	−0.834599	+	0.550859i	$0.814300\pi$
$348$		0			0
$349$	1.03634e10			0.698553			0.349277	−	0.937020i	$-0.386427\pi$
$349$	1.03634e10			0.698553			0.349277	+	0.937020i	$0.386427\pi$
$350$	−3.23669e8	−	2.59142e8i	−0.0215689	−	0.0172690i
$351$		0			0
$352$	−1.88546e10	−	4.49560e9i	−1.22814	−	0.292831i
$353$	1.30979e10			0.843536			0.421768	−	0.906704i	$-0.361410\pi$
$353$	1.30979e10			0.843536			0.421768	+	0.906704i	$0.361410\pi$
$354$		0			0
$355$		−	7.29586e8i		−	0.0459370i
$356$	−4.66616e9	−	2.08144e10i	−0.290509	−	1.29588i
$357$		0			0
$358$	−1.77247e9	−	1.41911e9i	−0.107906	−	0.0863940i
$359$		−	3.31454e9i		−	0.199547i	−0.995010	−	0.0997737i	$-0.968188\pi$
$359$		−	3.31454e9i		−	0.199547i	0.995010	−	0.0997737i	$-0.0318119\pi$
$360$		0			0
$361$	1.66039e10			0.977647
$362$	4.82566e9	−	6.02724e9i	0.281010	−	0.350982i
$363$		0			0
$364$	−1.91144e9	+	4.28505e8i	−0.108882	+	0.0244090i
$365$	3.49263e9			0.196780
$366$		0			0
$367$			1.96628e10i			1.08388i	0.840418	+	0.541939i	$0.182309\pi$
$367$			1.96628e10i			1.08388i	−0.840418	+	0.541939i	$0.817691\pi$
$368$	−6.63656e9	−	1.40580e10i	−0.361870	−	0.766536i
$369$		0			0
$370$	2.11794e10	−	2.64530e10i	1.13007	−	1.41146i
$371$		−	1.15308e9i		−	0.0608646i
$372$		0			0
$373$	−2.10063e10			−1.08521			−0.542606	−	0.839987i	$-0.682562\pi$
$373$	−2.10063e10			−1.08521			−0.542606	+	0.839987i	$0.682562\pi$
$374$	−1.68750e10	−	1.35108e10i	−0.862498	−	0.690551i
$375$		0			0
$376$	−1.37163e10	+	2.80648e10i	−0.686257	+	1.40414i
$377$	−7.01374e8			−0.0347204
$378$		0			0
$379$			3.04816e9i			0.147734i	0.997268	+	0.0738670i	$0.0235340\pi$
$379$			3.04816e9i			0.147734i	−0.997268	+	0.0738670i	$0.976466\pi$
$380$	2.96899e9	−	6.65587e8i	0.142388	−	0.0319206i
$381$		0			0
$382$	−1.23958e10	−	9.92461e9i	−0.582133	−	0.466080i
$383$			2.23357e10i			1.03802i	0.854770	+	0.519008i	$0.173698\pi$
$383$			2.23357e10i			1.03802i	−0.854770	+	0.519008i	$0.826302\pi$
$384$		0			0
$385$	1.57737e10			0.717945
$386$	1.17593e10	−	1.46874e10i	0.529704	−	0.661599i
$387$		0			0
$388$	−6.75466e9	−	3.01306e10i	−0.298042	−	1.32948i
$389$	−3.13680e10			−1.36990			−0.684948	−	0.728592i	$-0.740175\pi$
$389$	−3.13680e10			−1.36990			−0.684948	+	0.728592i	$0.740175\pi$
$390$		0			0
$391$		−	1.73377e10i		−	0.741795i
$392$	−1.40132e10	−	6.84880e9i	−0.593463	−	0.290048i
$393$		0			0
$394$	−1.70538e10	+	2.13002e10i	−0.707680	+	0.883892i
$395$		−	2.19071e10i		−	0.899904i
$396$		0			0
$397$	7.65788e9			0.308281			0.154140	−	0.988049i	$-0.450739\pi$
$397$	7.65788e9			0.308281			0.154140	+	0.988049i	$0.450739\pi$
$398$	3.11046e10	+	2.49036e10i	1.23963	+	0.992499i
$399$		0			0
$400$	1.09787e9	−	5.18285e8i	0.0428854	−	0.0202455i
$401$	3.26120e10			1.26125			0.630623	−	0.776089i	$-0.282799\pi$
$401$	3.26120e10			1.26125			0.630623	+	0.776089i	$0.282799\pi$
$402$		0			0
$403$			3.71662e8i			0.0140906i
$404$	1.55258e9	+	6.92561e9i	0.0582812	+	0.259976i
$405$		0			0
$406$	2.24029e9	+	1.79367e9i	0.0824520	+	0.0660144i
$407$		−	6.41811e10i		−	2.33900i
$408$		0			0
$409$	2.26168e10			0.808236			0.404118	−	0.914707i	$-0.367578\pi$
$409$	2.26168e10			0.808236			0.404118	+	0.914707i	$0.367578\pi$
$410$	1.30960e10	−	1.63569e10i	0.463450	−	0.578848i
$411$		0			0
$412$	2.61043e10	−	5.85205e9i	0.905990	−	0.203104i
$413$	−5.21155e9			−0.179129
$414$		0			0
$415$		−	3.16958e10i		−	1.06858i
$416$	1.33030e9	−	5.57931e9i	0.0444199	−	0.186297i
$417$		0			0
$418$	3.60173e9	−	4.49856e9i	0.117979	−	0.147356i
$419$			4.94503e10i			1.60440i	0.597054	+	0.802201i	$0.296338\pi$
$419$			4.94503e10i			1.60440i	−0.597054	+	0.802201i	$0.703662\pi$
$420$		0			0
$421$	−3.34077e10			−1.06345			−0.531726	−	0.846916i	$-0.678457\pi$
$421$	−3.34077e10			−1.06345			−0.531726	+	0.846916i	$0.678457\pi$
$422$	1.83321e10	+	1.46774e10i	0.578045	+	0.462807i
$423$		0			0
$424$	3.03339e9	+	1.48253e9i	0.0938565	+	0.0458713i
$425$	1.35399e9			0.0415012
$426$		0			0
$427$		−	2.06280e10i		−	0.620505i
$428$	−2.50618e10	+	5.61834e9i	−0.746857	+	0.167430i
$429$		0			0
$430$	4.51660e10	+	3.61617e10i	1.32111	+	1.05773i
$431$			3.06956e10i			0.889544i	0.895644	+	0.444772i	$0.146715\pi$
$431$			3.06956e10i			0.889544i	−0.895644	+	0.444772i	$0.853285\pi$
$432$		0			0
$433$	2.88433e9			0.0820529			0.0410265	−	0.999158i	$-0.486937\pi$
$433$	2.88433e9			0.0820529			0.0410265	+	0.999158i	$0.486937\pi$
$434$	9.50477e8	−	1.18715e9i	0.0267906	−	0.0334615i
$435$		0			0
$436$	3.30801e9	+	1.47561e10i	0.0915421	+	0.408343i
$437$	4.62189e9			0.126734
$438$		0			0
$439$			6.92422e10i			1.86429i	0.362088	+	0.932144i	$0.382064\pi$
$439$			6.92422e10i			1.86429i	−0.362088	+	0.932144i	$0.617936\pi$
$440$	−2.02805e10	+	4.14956e10i	−0.541088	+	1.10711i
$441$		0			0
$442$	3.99802e9	−	4.99353e9i	0.104751	−	0.130833i
$443$		−	2.06609e10i		−	0.536455i	−0.963356	−	0.268228i	$-0.913562\pi$
$443$		−	2.06609e10i		−	0.536455i	0.963356	−	0.268228i	$-0.0864379\pi$
$444$		0			0
$445$	−5.08278e10			−1.29617
$446$	−1.84752e10	−	1.47920e10i	−0.466928	−	0.373842i
$447$		0			0
$448$	−1.85175e10	+	1.44191e10i	−0.459696	+	0.357952i
$449$	−2.11092e10			−0.519382			−0.259691	−	0.965692i	$-0.583621\pi$
$449$	−2.11092e10			−0.519382			−0.259691	+	0.965692i	$0.583621\pi$
$450$		0			0
$451$		−	3.96855e10i		−	0.959237i
$452$	3.08476e9	+	1.37602e10i	0.0739039	+	0.329664i
$453$		0			0
$454$	9.36818e9	+	7.50054e9i	0.220512	+	0.176551i
$455$			4.66764e9i			0.108906i
$456$		0			0
$457$	−2.06831e10			−0.474188			−0.237094	−	0.971487i	$-0.576195\pi$
$457$	−2.06831e10			−0.474188			−0.237094	+	0.971487i	$0.576195\pi$
$458$	−2.84784e10	+	3.55695e10i	−0.647223	+	0.808381i
$459$		0			0
$460$	−3.61456e10	+	8.10309e9i	−0.807279	+	0.180975i
$461$	−7.65072e10			−1.69394			−0.846971	−	0.531640i	$-0.821576\pi$
$461$	−7.65072e10			−1.69394			−0.846971	+	0.531640i	$0.821576\pi$
$462$		0			0
$463$			3.41303e9i			0.0742704i	0.999310	+	0.0371352i	$0.0118232\pi$
$463$			3.41303e9i			0.0742704i	−0.999310	+	0.0371352i	$0.988177\pi$
$464$	−7.59895e9	+	3.58734e9i	−0.163939	+	0.0773929i
$465$		0			0
$466$	−2.20621e9	+	2.75555e9i	−0.0467845	+	0.0584339i
$467$		−	1.92903e10i		−	0.405576i	−0.979223	−	0.202788i	$-0.935000\pi$
$467$		−	1.92903e10i		−	0.405576i	0.979223	−	0.202788i	$-0.0650002\pi$
$468$		0			0
$469$	−2.13423e10			−0.441112
$470$	5.81039e10	+	4.65204e10i	1.19073	+	0.953349i
$471$		0			0
$472$	6.70056e9	−	1.37099e10i	0.135003	−	0.276227i
$473$	1.09583e11			2.18927
$474$		0			0
$475$			3.60948e8i			0.00709040i
$476$	−2.55406e10	+	5.72567e9i	−0.497511	+	0.111532i
$477$		0			0
$478$	5.05212e10	+	4.04493e10i	0.967748	+	0.774818i
$479$			2.43887e10i			0.463282i	0.972801	+	0.231641i	$0.0744095\pi$
$479$			2.43887e10i			0.463282i	−0.972801	+	0.231641i	$0.925590\pi$
$480$		0			0
$481$	1.89920e10			0.354806
$482$	6.17983e10	−	7.71861e10i	1.14496	−	1.43005i
$483$		0			0
$484$	7.13124e9	+	3.18104e10i	0.129952	+	0.579679i
$485$	−7.35776e10			−1.32978
$486$		0			0
$487$		−	9.30801e10i		−	1.65478i	−0.561626	−	0.827391i	$-0.689824\pi$
$487$		−	9.30801e10i		−	1.65478i	0.561626	−	0.827391i	$-0.310176\pi$
$488$	5.42656e10	+	2.65217e10i	0.956853	+	0.467651i
$489$		0			0
$490$	−2.32284e10	+	2.90123e10i	−0.402935	+	0.503266i
$491$			2.12850e9i			0.0366225i	0.999832	+	0.0183113i	$0.00582898\pi$
$491$			2.12850e9i			0.0366225i	−0.999832	+	0.0183113i	$0.994171\pi$
$492$		0			0
$493$	−9.37175e9			−0.158647
$494$	1.33118e9	+	1.06580e9i	0.0223526	+	0.0178964i
$495$		0			0
$496$	1.90095e9	+	4.02673e9i	0.0314083	+	0.0665312i
$497$	−1.67312e9			−0.0274221
$498$		0			0
$499$			1.04101e10i			0.167901i	0.996470	+	0.0839503i	$0.0267537\pi$
$499$			1.04101e10i			0.167901i	−0.996470	+	0.0839503i	$0.973246\pi$
$500$	−1.39766e10	−	6.23454e10i	−0.223625	−	0.997527i
$501$		0			0
$502$	−6.51187e10	−	5.21367e10i	−1.02539	−	0.820973i
$503$		−	3.93019e10i		−	0.613962i	−0.951716	−	0.306981i	$-0.900681\pi$
$503$		−	3.93019e10i		−	0.613962i	0.951716	−	0.306981i	$-0.0993188\pi$
$504$		0			0
$505$	1.69120e10			0.260034
$506$	−4.38487e10	+	5.47670e10i	−0.668890	+	0.835444i
$507$		0			0
$508$	6.42387e10	−	1.44010e10i	0.964587	−	0.216241i
$509$	3.25113e10			0.484354			0.242177	−	0.970232i	$-0.422139\pi$
$509$	3.25113e10			0.484354			0.242177	+	0.970232i	$0.422139\pi$
$510$		0			0
$511$		−	8.00947e9i		−	0.117468i
$512$	−1.41237e10	−	6.72524e10i	−0.205526	−	0.978652i
$513$		0			0
$514$	6.13693e10	−	7.66503e10i	0.879223	−	1.09815i
$515$		−	6.37455e10i		−	0.906194i
$516$		0			0
$517$	1.40973e11			1.97322
$518$	−6.06633e10	−	4.85695e10i	−0.842572	−	0.674598i
$519$		0			0
$520$	−1.22791e10	−	6.00125e9i	−0.167939	−	0.0820783i
$521$	−1.84550e9			−0.0250475			−0.0125237	−	0.999922i	$-0.503987\pi$
$521$	−1.84550e9			−0.0250475			−0.0125237	+	0.999922i	$0.503987\pi$
$522$		0			0
$523$			6.23770e10i			0.833715i	0.908972	+	0.416858i	$0.136869\pi$
$523$			6.23770e10i			0.833715i	−0.908972	+	0.416858i	$0.863131\pi$
$524$	7.79814e10	−	1.74818e10i	1.03435	−	0.231879i
$525$		0			0
$526$	−8.70448e10	−	6.96916e10i	−1.13710	−	0.910411i
$527$			4.96614e9i			0.0643838i
$528$		0			0
$529$	2.20424e10			0.281473
$530$	5.02817e9	−	6.28018e9i	0.0637245	−	0.0795919i
$531$		0			0
$532$	−1.52635e9	−	6.80863e9i	−0.0190550	−	0.0849988i
$533$	1.17434e10			0.145508
$534$		0			0
$535$			6.11998e10i			0.747025i
$536$	2.74400e10	−	5.61446e10i	0.332449	−	0.680219i
$537$		0			0
$538$	−2.70720e10	+	3.38130e10i	−0.323141	+	0.403603i
$539$			7.03905e10i			0.833986i
$540$		0			0
$541$	−7.45917e10			−0.870766			−0.435383	−	0.900245i	$-0.643387\pi$
$541$	−7.45917e10			−0.870766			−0.435383	+	0.900245i	$0.643387\pi$
$542$	−9.97991e10	−	7.99032e10i	−1.15646	−	0.925907i
$543$		0			0
$544$	1.77755e10	−	7.45506e10i	0.202967	−	0.851246i
$545$	3.60337e10			0.408435
$546$		0			0
$547$			1.41531e9i			0.0158089i	0.999969	+	0.00790445i	$0.00251609\pi$
$547$			1.41531e9i			0.0158089i	−0.999969	+	0.00790445i	$0.997484\pi$
$548$	1.24309e10	+	5.54506e10i	0.137841	+	0.614871i
$549$		0			0
$550$	−4.27705e9	−	3.42438e9i	−0.0467405	−	0.0374224i
$551$		−	2.49833e9i		−	0.0271046i
$552$		0			0
$553$	−5.02383e10			−0.537198
$554$	−8.22965e10	+	1.02788e11i	−0.873660	+	1.09120i
$555$		0			0
$556$	−7.36985e10	+	1.65217e10i	−0.771187	+	0.172884i
$557$	1.37543e11			1.42895			0.714475	−	0.699661i	$-0.246666\pi$
$557$	1.37543e11			1.42895			0.714475	+	0.699661i	$0.246666\pi$
$558$		0			0
$559$			3.24270e10i			0.332093i
$560$	2.38737e10	+	5.05710e10i	0.242755	+	0.514220i
$561$		0			0
$562$	−3.08105e10	+	3.84823e10i	−0.308854	+	0.385759i
$563$			1.06415e11i			1.05918i	0.848255	+	0.529589i	$0.177654\pi$
$563$			1.06415e11i			1.05918i	−0.848255	+	0.529589i	$0.822346\pi$
$564$		0			0
$565$	3.36018e10			0.329738
$566$	1.46273e10	+	1.17112e10i	0.142528	+	0.114113i
$567$		0			0
$568$	2.15115e9	−	4.40143e9i	0.0206670	−	0.0422864i
$569$	−4.02429e10			−0.383919			−0.191960	−	0.981403i	$-0.561484\pi$
$569$	−4.02429e10			−0.383919			−0.191960	+	0.981403i	$0.561484\pi$
$570$		0			0
$571$			1.50341e11i			1.41427i	0.707077	+	0.707137i	$0.250014\pi$
$571$			1.50341e11i			1.41427i	−0.707077	+	0.707137i	$0.749986\pi$
$572$	−2.52583e10	+	5.66238e9i	−0.235950	+	0.0528951i
$573$		0			0
$574$	−3.75103e10	−	3.00323e10i	−0.345544	−	0.276657i
$575$		−	4.39432e9i		−	0.0401994i
$576$		0			0
$577$	4.96477e9			0.0447915			0.0223958	−	0.999749i	$-0.492871\pi$
$577$	4.96477e9			0.0447915			0.0223958	+	0.999749i	$0.492871\pi$
$578$	−1.63361e10	+	2.04038e10i	−0.146365	+	0.182810i
$579$		0			0
$580$	4.38006e9	+	1.95382e10i	0.0387051	+	0.172652i
$581$	−7.26862e10			−0.637892
$582$		0			0
$583$		−	1.52372e10i		−	0.131895i
$584$	2.10703e10	+	1.02979e10i	0.181142	+	0.0885313i
$585$		0			0
$586$	−4.80980e10	+	6.00743e10i	−0.407884	+	0.509446i
$587$		−	1.53440e11i		−	1.29237i	−0.763181	−	0.646185i	$-0.776363\pi$
$587$		−	1.53440e11i		−	1.29237i	0.763181	−	0.646185i	$-0.223637\pi$
$588$		0			0
$589$	−1.32388e9			−0.0109999
$590$	−2.83843e10	−	2.27256e10i	−0.234245	−	0.187546i
$591$		0			0
$592$	2.05766e11	−	9.71390e10i	1.67528	−	0.790873i
$593$	−2.06036e11			−1.66619			−0.833094	−	0.553131i	$-0.813433\pi$
$593$	−2.06036e11			−1.66619			−0.833094	+	0.553131i	$0.813433\pi$
$594$		0			0
$595$			6.23689e10i			0.497623i
$596$	2.26017e10	+	1.00820e11i	0.179125	+	0.799027i
$597$		0			0
$598$	−1.62063e10	−	1.29754e10i	−0.126730	−	0.101465i
$599$			2.30634e11i			1.79150i	0.444558	+	0.895750i	$0.353361\pi$
$599$			2.30634e11i			1.79150i	−0.444558	+	0.895750i	$0.646639\pi$
$600$		0			0
$601$	1.01422e11			0.777382			0.388691	−	0.921368i	$-0.372927\pi$
$601$	1.01422e11			0.777382			0.388691	+	0.921368i	$0.372927\pi$
$602$	8.29277e10	−	1.03577e11i	0.631413	−	0.788635i
$603$		0			0
$604$	−2.09079e11	+	4.68711e10i	−1.57095	+	0.352174i
$605$	7.76795e10			0.579809
$606$		0			0
$607$		−	1.97883e11i		−	1.45765i	−0.684700	−	0.728825i	$-0.740067\pi$
$607$		−	1.97883e11i		−	1.45765i	0.684700	−	0.728825i	$-0.259933\pi$
$608$	1.98738e10	+	4.73860e9i	0.145434	+	0.0346766i
$609$		0			0
$610$	8.99511e10	−	1.12349e11i	0.649661	−	0.811427i
$611$			4.17158e10i			0.299320i
$612$		0			0
$613$	1.27158e11			0.900538			0.450269	−	0.892893i	$-0.351328\pi$
$613$	1.27158e11			0.900538			0.450269	+	0.892893i	$0.351328\pi$
$614$	−4.36121e10	−	3.49176e10i	−0.306855	−	0.245681i
$615$		0			0
$616$	9.51595e10	+	4.65082e10i	0.660890	+	0.323003i
$617$	5.06702e10			0.349632			0.174816	−	0.984601i	$-0.444067\pi$
$617$	5.06702e10			0.349632			0.174816	+	0.984601i	$0.444067\pi$
$618$		0			0
$619$		−	7.06748e10i		−	0.481395i	−0.970600	−	0.240698i	$-0.922624\pi$
$619$		−	7.06748e10i		−	0.481395i	0.970600	−	0.240698i	$-0.0773762\pi$
$620$	1.03534e10	−	2.32102e9i	0.0700675	−	0.0157077i
$621$		0			0
$622$	1.62128e11	+	1.29807e11i	1.08317	+	0.867231i
$623$			1.16561e11i			0.773748i
$624$		0			0
$625$	−1.45008e11			−0.950327
$626$	−6.31165e10	+	7.88325e10i	−0.411004	+	0.513343i
$627$		0			0
$628$	1.51938e10	+	6.77754e10i	0.0976853	+	0.435746i
$629$	2.53771e11			1.62121
$630$		0			0
$631$			1.65273e11i			1.04252i	0.853399	+	0.521259i	$0.174537\pi$
$631$			1.65273e11i			1.04252i	−0.853399	+	0.521259i	$0.825463\pi$
$632$	6.45921e10	−	1.32161e11i	0.404866	−	0.828388i
$633$		0			0
$634$	−1.65902e11	+	2.07211e11i	−1.02682	+	1.28250i
$635$		−	1.56868e11i		−	0.964804i
$636$		0			0
$637$	−2.08294e10			−0.126508
$638$	2.96039e10	+	2.37021e10i	0.178676	+	0.143055i
$639$		0			0
$640$	−1.63731e11	−	2.21570e9i	−0.975911	−	0.0132066i
$641$	−1.12013e11			−0.663490			−0.331745	−	0.943369i	$-0.607637\pi$
$641$	−1.12013e11			−0.663490			−0.331745	+	0.943369i	$0.607637\pi$
$642$		0			0
$643$		−	2.65913e11i		−	1.55559i	−0.628518	−	0.777795i	$-0.716338\pi$
$643$		−	2.65913e11i		−	1.55559i	0.628518	−	0.777795i	$-0.283662\pi$
$644$	1.85824e10	+	8.28907e10i	0.108033	+	0.481906i
$645$		0			0
$646$	1.77872e10	+	1.42411e10i	0.102136	+	0.0817739i
$647$		−	2.71996e11i		−	1.55219i	−0.630614	−	0.776097i	$-0.717197\pi$
$647$		−	2.71996e11i		−	1.55219i	0.630614	−	0.776097i	$-0.282803\pi$
$648$		0			0
$649$	−6.88669e10			−0.388179
$650$	1.01332e9	−	1.26563e9i	0.00567665	−	0.00709013i
$651$		0			0
$652$	1.44511e11	−	3.23965e10i	0.799672	−	0.179270i
$653$	−3.03789e11			−1.67078			−0.835391	−	0.549656i	$-0.814759\pi$
$653$	−3.03789e11			−1.67078			−0.835391	+	0.549656i	$0.814759\pi$
$654$		0			0
$655$		−	1.90427e11i		−	1.03458i
$656$	1.27233e11	−	6.00646e10i	0.687043	−	0.324342i
$657$		0			0
$658$	1.06683e11	−	1.33247e11i	0.569102	−	0.710808i
$659$		−	4.18575e10i		−	0.221938i	−0.993824	−	0.110969i	$-0.964605\pi$
$659$		−	4.18575e10i		−	0.221938i	0.993824	−	0.110969i	$-0.0353954\pi$
$660$		0			0
$661$	−2.46529e11			−1.29141			−0.645703	−	0.763589i	$-0.723435\pi$
$661$	−2.46529e11			−1.29141			−0.645703	+	0.763589i	$0.723435\pi$
$662$	6.85251e10	+	5.48640e10i	0.356794	+	0.285664i
$663$		0			0
$664$	9.34537e10	−	1.91214e11i	0.480755	−	0.983665i
$665$	−1.66264e10			−0.0850179
$666$		0			0
$667$			3.04155e10i			0.153671i
$668$	−1.16936e11	+	2.62146e10i	−0.587276	+	0.131655i
$669$		0			0
$670$	−1.16239e11	−	9.30657e10i	−0.576837	−	0.461839i
$671$		−	2.72584e11i		−	1.34465i
$672$		0			0
$673$	−3.15336e11			−1.53714			−0.768569	−	0.639767i	$-0.779031\pi$
$673$	−3.15336e11			−1.53714			−0.768569	+	0.639767i	$0.779031\pi$
$674$	−3.56226e9	+	4.44927e9i	−0.0172618	+	0.0215600i
$675$		0			0
$676$	4.40053e10	+	1.96295e11i	0.210726	+	0.939989i
$677$	2.47236e10			0.117695			0.0588475	−	0.998267i	$-0.481257\pi$
$677$	2.47236e10			0.117695			0.0588475	+	0.998267i	$0.481257\pi$
$678$		0			0
$679$			1.68731e11i			0.793811i
$680$	−1.64072e11	−	8.01886e10i	−0.767361	−	0.375039i
$681$		0			0
$682$	1.25599e10	−	1.56873e10i	0.0580561	−	0.0725120i
$683$		−	7.20843e10i		−	0.331251i	−0.986189	−	0.165626i	$-0.947036\pi$
$683$		−	7.20843e10i		−	0.331251i	0.986189	−	0.165626i	$-0.0529644\pi$
$684$		0			0
$685$	1.35408e11			0.615009
$686$	1.67255e11	+	1.33911e11i	0.755235	+	0.604672i
$687$		0			0
$688$	1.65855e11	+	3.51326e11i	0.740246	+	1.56804i
$689$	4.50887e9			0.0200074
$690$		0			0
$691$		−	2.95424e11i		−	1.29578i	−0.761732	−	0.647892i	$-0.775651\pi$
$691$		−	2.95424e11i		−	1.29578i	0.761732	−	0.647892i	$-0.224349\pi$
$692$	−1.15470e10	−	5.15080e10i	−0.0503554	−	0.224621i
$693$		0			0
$694$	1.99503e11	+	1.59731e11i	0.860028	+	0.688573i
$695$			1.79968e11i			0.771360i
$696$		0			0
$697$	1.56916e11			0.664867
$698$	1.03634e11	−	1.29438e11i	0.436596	−	0.545308i
$699$		0			0
$700$	−6.47338e9	+	1.45120e9i	−0.0269612	+	0.00604414i
$701$	2.87925e11			1.19236			0.596180	−	0.802851i	$-0.296685\pi$
$701$	2.87925e11			1.19236			0.596180	+	0.802851i	$0.296685\pi$
$702$		0			0
$703$			6.76504e10i			0.276980i
$704$	−2.44696e11	+	1.90538e11i	−0.996176	+	0.775694i
$705$		0			0
$706$	1.30979e11	−	1.63593e11i	0.527210	−	0.658485i
$707$		−	3.87834e10i		−	0.155227i
$708$		0			0
$709$	2.51685e11			0.996030			0.498015	−	0.867168i	$-0.334062\pi$
$709$	2.51685e11			0.996030			0.498015	+	0.867168i	$0.334062\pi$
$710$	−9.11252e9	−	7.29586e9i	−0.0358596	−	0.0287106i
$711$		0			0
$712$	−3.06633e11	−	1.49864e11i	−1.19316	−	0.583144i
$713$	1.61174e10			0.0623643
$714$		0			0
$715$			6.16795e10i			0.236003i
$716$	−3.54493e10	+	7.94701e9i	−0.134883	+	0.0302379i
$717$		0			0
$718$	−4.13986e10	−	3.31454e10i	−0.155772	−	0.124717i
$719$			1.38856e11i			0.519574i	0.965666	+	0.259787i	$0.0836524\pi$
$719$			1.38856e11i			0.519574i	−0.965666	+	0.259787i	$0.916348\pi$
$720$		0			0
$721$	−1.46184e11			−0.540953
$722$	1.66039e11	−	2.07383e11i	0.611029	−	0.763175i
$723$		0			0
$724$	−2.70237e10	−	1.20545e11i	−0.0983536	−	0.438727i
$725$	−2.37531e9			−0.00859743
$726$		0			0
$727$		−	1.79083e11i		−	0.641088i	−0.947234	−	0.320544i	$-0.896134\pi$
$727$		−	1.79083e11i		−	0.641088i	0.947234	−	0.320544i	$-0.103866\pi$
$728$	−1.37623e10	+	2.81589e10i	−0.0489967	+	0.100251i
$729$		0			0
$730$	3.49263e10	−	4.36230e10i	0.122988	−	0.153612i
$731$			4.33289e11i			1.51743i
$732$		0			0
$733$	2.17618e11			0.753839			0.376920	−	0.926246i	$-0.376983\pi$
$733$	2.17618e11			0.753839			0.376920	+	0.926246i	$0.376983\pi$
$734$	2.45588e11	+	1.96628e11i	0.846101	+	0.677423i
$735$		0			0
$736$	−2.41950e11	−	5.76895e10i	−0.824546	−	0.196601i
$737$	−2.82023e11			−0.955904
$738$		0			0
$739$			4.84950e11i			1.62599i	0.582268	+	0.812997i	$0.302166\pi$
$739$			4.84950e11i			1.62599i	−0.582268	+	0.812997i	$0.697834\pi$
$740$	−1.18605e11	−	5.29061e11i	−0.395525	−	1.76433i
$741$		0			0
$742$	−1.44020e10	−	1.15308e10i	−0.0475124	−	0.0380404i
$743$		−	2.03509e11i		−	0.667771i	−0.942614	−	0.333886i	$-0.891640\pi$
$743$		−	2.03509e11i		−	0.667771i	0.942614	−	0.333886i	$-0.108360\pi$
$744$		0			0
$745$	2.46198e11			0.799206
$746$	−2.10063e11	+	2.62369e11i	−0.678258	+	0.847144i
$747$		0			0
$748$	−3.37500e11	+	7.56606e10i	−1.07812	+	0.241693i
$749$	1.40346e11			0.445937
$750$		0			0
$751$			2.34693e11i			0.737804i	0.929468	+	0.368902i	$0.120266\pi$
$751$			2.34693e11i			0.737804i	−0.929468	+	0.368902i	$0.879734\pi$
$752$	2.13365e11	+	4.51965e11i	0.667194	+	1.41330i
$753$		0			0
$754$	−7.01374e9	+	8.76016e9i	−0.0217002	+	0.0271036i
$755$			5.10561e11i			1.57130i
$756$		0			0
$757$	−3.84882e11			−1.17204			−0.586022	−	0.810295i	$-0.699307\pi$
$757$	−3.84882e11			−1.17204			−0.586022	+	0.810295i	$0.699307\pi$
$758$	3.80715e10	+	3.04816e10i	0.115325	+	0.0923338i
$759$		0			0
$760$	2.13767e10	−	4.37386e10i	0.0640748	−	0.131102i
$761$	−2.39209e11			−0.713244			−0.356622	−	0.934249i	$-0.616072\pi$
$761$	−2.39209e11			−0.713244			−0.356622	+	0.934249i	$0.616072\pi$
$762$		0			0
$763$		−	8.26340e10i		−	0.243815i
$764$	−2.47917e11	+	5.55778e10i	−0.727666	+	0.163128i
$765$		0			0
$766$	2.78972e11	+	2.23357e11i	0.810301	+	0.648760i
$767$		−	2.03786e10i		−	0.0588833i
$768$		0			0
$769$	2.08457e11			0.596089			0.298045	−	0.954552i	$-0.403666\pi$
$769$	2.08457e11			0.596089			0.298045	+	0.954552i	$0.403666\pi$
$770$	1.57737e11	−	1.97014e11i	0.448716	−	0.560446i
$771$		0			0
$772$	−6.58522e10	−	2.93748e11i	−0.185396	−	0.826999i
$773$	5.54469e10			0.155296			0.0776478	−	0.996981i	$-0.475259\pi$
$773$	5.54469e10			0.155296			0.0776478	+	0.996981i	$0.475259\pi$
$774$		0			0
$775$			1.25869e9i			0.00348909i
$776$	−4.43878e11	−	2.16940e11i	−1.22410	−	0.598265i
$777$		0			0
$778$	−3.13680e11	+	3.91786e11i	−0.856185	+	1.06938i
$779$			4.18307e10i			0.113591i
$780$		0			0
$781$	−2.21091e10			−0.0594246
$782$	−2.16548e11	−	1.73377e11i	−0.579064	−	0.463622i
$783$		0			0
$784$	−2.25674e11	+	1.06537e11i	−0.597333	+	0.281991i
$785$	1.65504e11			0.435844
$786$		0			0
$787$			4.05908e11i			1.05811i	0.848589	+	0.529053i	$0.177453\pi$
$787$			4.05908e11i			1.05811i	−0.848589	+	0.529053i	$0.822547\pi$
$788$	9.55014e10	+	4.26005e11i	0.247688	+	1.10487i
$789$		0			0
$790$	−2.73619e11	−	2.19071e11i	−0.702487	−	0.562440i
$791$		−	7.70572e10i		−	0.196837i
$792$		0			0
$793$	8.06610e10			0.203972
$794$	7.65788e10	−	9.56469e10i	0.192676	−	0.240652i
$795$		0			0
$796$	6.22092e11	−	1.39460e11i	1.54954	−	0.347375i
$797$	3.09015e11			0.765855			0.382927	−	0.923778i	$-0.374916\pi$
$797$	3.09015e11			0.765855			0.382927	+	0.923778i	$0.374916\pi$
$798$		0			0
$799$			5.57406e11i			1.36768i
$800$	4.50528e9	−	1.88952e10i	0.0109992	−	0.0461308i
$801$		0			0
$802$	3.26120e11	−	4.07324e11i	0.788279	−	0.984560i
$803$		−	1.05839e11i		−	0.254557i
$804$		0			0
$805$	2.02415e11			0.482014
$806$	4.64206e9	+	3.71662e9i	0.0109994	+	0.00880660i
$807$		0			0
$808$	1.02027e11	+	4.98644e10i	0.239369	+	0.116989i
$809$	−4.77958e11			−1.11582			−0.557912	−	0.829900i	$-0.688397\pi$
$809$	−4.77958e11			−1.11582			−0.557912	+	0.829900i	$0.688397\pi$
$810$		0			0
$811$		−	6.37503e11i		−	1.47366i	−0.676075	−	0.736832i	$-0.736321\pi$
$811$		−	6.37503e11i		−	1.47366i	0.676075	−	0.736832i	$-0.263679\pi$
$812$	4.48059e10	−	1.00446e10i	0.103065	−	0.0231050i
$813$		0			0
$814$	−8.01622e11	−	6.41811e11i	−1.82588	−	1.46187i
$815$		−	3.52890e11i		−	0.799851i
$816$		0			0
$817$	−1.15506e11			−0.259250
$818$	2.26168e11	−	2.82484e11i	0.505148	−	0.630929i
$819$		0			0
$820$	−7.33375e10	−	3.27137e11i	−0.162207	−	0.723561i
$821$	8.43824e11			1.85729			0.928644	−	0.370973i	$-0.120976\pi$
$821$	8.43824e11			1.85729			0.928644	+	0.370973i	$0.120976\pi$
$822$		0			0
$823$		−	2.60916e11i		−	0.568723i	−0.958717	−	0.284362i	$-0.908218\pi$
$823$		−	2.60916e11i		−	0.568723i	0.958717	−	0.284362i	$-0.0917817\pi$
$824$	1.87951e11	−	3.84563e11i	0.407696	−	0.834179i
$825$		0			0
$826$	−5.21155e10	+	6.50922e10i	−0.111956	+	0.139833i
$827$		−	2.78675e11i		−	0.595765i	−0.954602	−	0.297883i	$-0.903720\pi$
$827$		−	2.78675e11i		−	0.595765i	0.954602	−	0.297883i	$-0.0962804\pi$
$828$		0			0
$829$	4.75156e11			1.00605			0.503023	−	0.864273i	$-0.332221\pi$
$829$	4.75156e11			1.00605			0.503023	+	0.864273i	$0.332221\pi$
$830$	−3.95880e11	−	3.16958e11i	−0.834164	−	0.667865i
$831$		0			0
$832$	−5.63825e10	−	7.24086e10i	−0.117666	−	0.151111i
$833$	−2.78322e11			−0.578053
$834$		0			0
$835$			2.85552e11i			0.587408i
$836$	−2.01697e10	−	8.99711e10i	−0.0412928	−	0.184195i
$837$		0			0
$838$	6.17635e11	+	4.94503e11i	1.25244	+	1.00275i
$839$			3.35440e11i			0.676966i	0.940973	+	0.338483i	$0.109914\pi$
$839$			3.35440e11i			0.676966i	−0.940973	+	0.338483i	$0.890086\pi$
$840$		0			0
$841$	−4.83806e11			−0.967134
$842$	−3.34077e11	+	4.17262e11i	−0.664658	+	0.830157i
$843$		0			0
$844$	3.66642e11	−	8.21935e10i	0.722557	−	0.161982i
$845$	4.79344e11			0.940200
$846$		0			0
$847$		−	1.78138e11i		−	0.346117i
$848$	4.88507e10	−	2.30616e10i	0.0944686	−	0.0445971i
$849$		0			0
$850$	1.35399e10	−	1.69114e10i	0.0259382	−	0.0323968i
$851$		−	8.23600e11i		−	1.57036i
$852$		0			0
$853$	−9.75408e10			−0.184243			−0.0921213	−	0.995748i	$-0.529365\pi$
$853$	−9.75408e10			−0.184243			−0.0921213	+	0.995748i	$0.529365\pi$
$854$	−2.57643e11	−	2.06280e11i	−0.484382	−	0.387816i
$855$		0			0
$856$	−1.80445e11	+	3.69205e11i	−0.336086	+	0.687659i
$857$	7.94769e10			0.147339			0.0736695	−	0.997283i	$-0.476529\pi$
$857$	7.94769e10			0.147339			0.0736695	+	0.997283i	$0.476529\pi$
$858$		0			0
$859$		−	4.15618e11i		−	0.763347i	−0.924297	−	0.381673i	$-0.875348\pi$
$859$		−	4.15618e11i		−	0.763347i	0.924297	−	0.381673i	$-0.124652\pi$
$860$	9.03320e11	−	2.02506e11i	1.65138	−	0.370206i
$861$		0			0
$862$	3.83388e11	+	3.06956e11i	0.694400	+	0.555965i
$863$			4.80012e11i			0.865383i	0.901542	+	0.432692i	$0.142436\pi$
$863$			4.80012e11i			0.865383i	−0.901542	+	0.432692i	$0.857564\pi$
$864$		0			0
$865$	−1.25780e11			−0.224671
$866$	2.88433e10	−	3.60253e10i	0.0512831	−	0.0640525i
$867$		0			0
$868$	−5.32267e9	−	2.37429e10i	−0.00937671	−	0.0418268i
$869$	−6.63863e11			−1.16412
$870$		0			0
$871$		−	8.34540e10i		−	0.145002i
$872$	2.17383e11	+	1.06244e11i	0.375976	+	0.183754i
$873$		0			0
$874$	4.62189e10	−	5.77274e10i	0.0792089	−	0.0989319i
$875$			3.49134e11i			0.595608i
$876$		0			0
$877$	2.74155e11			0.463444			0.231722	−	0.972782i	$-0.425564\pi$
$877$	2.74155e11			0.463444			0.231722	+	0.972782i	$0.425564\pi$
$878$	8.64835e11	+	6.92422e11i	1.45531	+	1.16518i
$879$		0			0
$880$	3.15474e11	+	6.68259e11i	0.526058	+	1.11433i
$881$	−8.01838e11			−1.33101			−0.665507	−	0.746391i	$-0.731785\pi$
$881$	−8.01838e11			−1.33101			−0.665507	+	0.746391i	$0.731785\pi$
$882$		0			0
$883$		−	9.95008e11i		−	1.63676i	−0.574681	−	0.818378i	$-0.694874\pi$
$883$		−	9.95008e11i		−	1.63676i	0.574681	−	0.818378i	$-0.305126\pi$
$884$	−2.23889e10	−	9.98706e10i	−0.0366627	−	0.163542i
$885$		0			0
$886$	−2.58054e11	−	2.06609e11i	−0.418770	−	0.335284i
$887$		−	5.46038e11i		−	0.882122i	−0.897477	−	0.441061i	$-0.854602\pi$
$887$		−	5.46038e11i		−	0.882122i	0.897477	−	0.441061i	$-0.145398\pi$
$888$		0			0
$889$	−3.59736e11			−0.575940
$890$	−5.08278e11	+	6.34839e11i	−0.810105	+	1.01182i
$891$		0			0
$892$	−3.69504e11	+	8.28353e10i	−0.583660	+	0.130845i
$893$	−1.48594e11			−0.233665
$894$		0			0
$895$			8.65656e10i			0.134913i
$896$	−5.08114e9	+	3.75474e11i	−0.00788368	+	0.582570i
$897$		0			0
$898$	−2.11092e11	+	2.63654e11i	−0.324614	+	0.405442i
$899$		−	8.71212e9i		−	0.0133378i
$900$		0			0
$901$	6.02474e10			0.0914195
$902$	−4.95672e11	−	3.96855e11i	−0.748804	−	0.599523i
$903$		0			0
$904$	2.02713e11	+	9.90735e10i	0.303534	+	0.148349i
$905$	−2.94365e11			−0.438826
$906$		0			0
$907$			6.55018e11i			0.967886i	0.875100	+	0.483943i	$0.160796\pi$
$907$			6.55018e11i			0.967886i	−0.875100	+	0.483943i	$0.839204\pi$
$908$	1.87364e11	−	4.20030e10i	0.275640	−	0.0617927i
$909$		0			0
$910$	5.82988e10	+	4.66764e10i	0.0850147	+	0.0680663i
$911$			1.19425e11i			0.173389i	0.996235	+	0.0866943i	$0.0276304\pi$
$911$			1.19425e11i			0.173389i	−0.996235	+	0.0866943i	$0.972370\pi$
$912$		0			0
$913$	−9.60496e11			−1.38233
$914$	−2.06831e11	+	2.58332e11i	−0.296368	+	0.370163i
$915$		0			0
$916$	1.59479e11	+	7.11390e11i	0.226528	+	1.01048i
$917$	−4.36696e11			−0.617592
$918$		0			0
$919$			5.33989e10i			0.0748635i	0.999299	+	0.0374318i	$0.0119177\pi$
$919$			5.33989e10i			0.0748635i	−0.999299	+	0.0374318i	$0.988082\pi$
$920$	−2.60248e11	+	5.32489e11i	−0.363276	+	0.743292i
$921$		0			0
$922$	−7.65072e11	+	9.55574e11i	−1.05871	+	1.32233i
$923$		−	6.54235e9i		−	0.00901420i
$924$		0			0
$925$	6.43194e10			0.0878567
$926$	4.26287e10	+	3.41303e10i	0.0579773	+	0.0464190i
$927$		0			0
$928$	−3.11836e10	+	1.30784e11i	−0.0420469	+	0.176345i
$929$	6.30991e11			0.847150			0.423575	−	0.905861i	$-0.360775\pi$
$929$	6.30991e11			0.847150			0.423575	+	0.905861i	$0.360775\pi$
$930$		0			0
$931$		−	7.41953e10i		−	0.0987593i
$932$	1.23548e10	+	5.51110e10i	0.0163746	+	0.0730423i
$933$		0			0
$934$	−2.40936e11	−	1.92903e11i	−0.316603	−	0.253485i
$935$			8.24161e11i			1.07836i
$936$		0			0
$937$	−8.41436e11			−1.09160			−0.545799	−	0.837916i	$-0.683774\pi$
$937$	−8.41436e11			−1.09160			−0.545799	+	0.837916i	$0.683774\pi$
$938$	−2.13423e11	+	2.66565e11i	−0.275695	+	0.344343i
$939$		0			0
$940$	1.16208e12	−	2.60514e11i	1.48842	−	0.333672i
$941$	4.52935e11			0.577666			0.288833	−	0.957379i	$-0.406733\pi$
$941$	4.52935e11			0.577666			0.288833	+	0.957379i	$0.406733\pi$
$942$		0			0
$943$		−	5.09262e11i		−	0.644013i
$944$	−1.04231e11	−	2.20789e11i	−0.131253	−	0.278029i
$945$		0			0
$946$	1.09583e12	−	1.36869e12i	1.36829	−	1.70900i
$947$			1.00309e12i			1.24721i	0.781739	+	0.623605i	$0.214333\pi$
$947$			1.00309e12i			1.24721i	−0.781739	+	0.623605i	$0.785667\pi$
$948$		0			0
$949$	3.13192e10			0.0386141
$950$	4.50824e9	+	3.60948e9i	0.00553494	+	0.00443150i
$951$		0			0
$952$	−1.83892e11	+	3.76258e11i	−0.223880	+	0.458077i
$953$	1.39040e12			1.68565			0.842826	−	0.538186i	$-0.180890\pi$
$953$	1.39040e12			1.68565			0.842826	+	0.538186i	$0.180890\pi$
$954$		0			0
$955$			6.05401e11i			0.727830i
$956$	1.01042e12	−	2.26516e11i	1.20968	−	0.271186i
$957$		0			0
$958$	3.04614e11	+	2.43887e11i	0.361650	+	0.289551i
$959$		−	3.10523e11i		−	0.367130i
$960$		0			0
$961$	8.48274e11			0.994587
$962$	1.89920e11	−	2.37210e11i	0.221754	−	0.276970i
$963$		0			0
$964$	−3.46071e11	−	1.54372e12i	−0.400734	−	1.78756i
$965$	−7.17318e11			−0.827185
$966$		0			0
$967$		−	9.01843e11i		−	1.03140i	−0.856771	−	0.515698i	$-0.827533\pi$
$967$		−	9.01843e11i		−	1.03140i	0.856771	−	0.515698i	$-0.172467\pi$
$968$	4.68624e11	+	2.29035e11i	0.533732	+	0.260856i
$969$		0			0
$970$	−7.35776e11	+	9.18984e11i	−0.831110	+	1.03806i
$971$		−	1.28411e12i		−	1.44452i	−0.691621	−	0.722261i	$-0.743103\pi$
$971$		−	1.28411e12i		−	1.44452i	0.691621	−	0.722261i	$-0.256897\pi$
$972$		0			0
$973$	4.12712e11			0.460464
$974$	−1.16257e12	−	9.30801e11i	−1.29176	−	1.03424i
$975$		0			0
$976$	8.73912e11	−	4.12560e11i	0.963093	−	0.454661i
$977$	−1.20120e12			−1.31837			−0.659183	−	0.751983i	$-0.729098\pi$
$977$	−1.20120e12			−1.31837			−0.659183	+	0.751983i	$0.729098\pi$
$978$		0			0
$979$			1.54026e12i			1.67674i
$980$	1.30079e11	+	5.80246e11i	0.141027	+	0.629082i
$981$		0			0
$982$	2.65850e10	+	2.12850e10i	0.0285884	+	0.0228891i
$983$		−	3.77388e11i		−	0.404179i	−0.979367	−	0.202090i	$-0.935227\pi$
$983$		−	3.77388e11i		−	0.404179i	0.979367	−	0.202090i	$-0.0647733\pi$
$984$		0			0
$985$	1.04028e12			1.10511
$986$	−9.37175e10	+	1.17053e11i	−0.0991546	+	0.123844i
$987$		0			0
$988$	2.66236e10	−	5.96846e9i	0.0279408	−	0.00626375i
$989$	1.40622e12			1.46983
$990$		0			0
$991$		−	3.35563e11i		−	0.347920i	−0.984753	−	0.173960i	$-0.944344\pi$
$991$		−	3.35563e11i		−	0.347920i	0.984753	−	0.173960i	$-0.0556563\pi$
$992$	6.93033e10	+	1.65244e10i	0.0715661	+	0.0170639i
$993$		0			0
$994$	−1.67312e10	+	2.08972e10i	−0.0171388	+	0.0214064i
$995$		−	1.51912e12i		−	1.54989i
$996$		0			0
$997$	−1.03163e12			−1.04410			−0.522050	−	0.852915i	$-0.674833\pi$
$997$	−1.03163e12			−1.04410			−0.522050	+	0.852915i	$0.674833\pi$
$998$	1.30022e11	+	1.04101e11i	0.131067	+	0.104938i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.9.d.b.19.1		2
3.2	odd	2		4.9.b.b.3.2	yes	2
4.3	odd	2	inner	36.9.d.b.19.2		2
12.11	even	2		4.9.b.b.3.1	✓	2
15.2	even	4		100.9.d.b.99.1		4
15.8	even	4		100.9.d.b.99.4		4
15.14	odd	2		100.9.b.c.51.1		2
24.5	odd	2		64.9.c.b.63.1		2
24.11	even	2		64.9.c.b.63.2		2
48.5	odd	4		256.9.d.e.127.4		4
48.11	even	4		256.9.d.e.127.2		4
48.29	odd	4		256.9.d.e.127.1		4
48.35	even	4		256.9.d.e.127.3		4
60.23	odd	4		100.9.d.b.99.2		4
60.47	odd	4		100.9.d.b.99.3		4
60.59	even	2		100.9.b.c.51.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.9.b.b.3.1	✓	2	12.11	even	2
4.9.b.b.3.2	yes	2	3.2	odd	2
36.9.d.b.19.1		2	1.1	even	1	trivial
36.9.d.b.19.2		2	4.3	odd	2	inner
64.9.c.b.63.1		2	24.5	odd	2
64.9.c.b.63.2		2	24.11	even	2
100.9.b.c.51.1		2	15.14	odd	2
100.9.b.c.51.2		2	60.59	even	2
100.9.d.b.99.1		4	15.2	even	4
100.9.d.b.99.2		4	60.23	odd	4
100.9.d.b.99.3		4	60.47	odd	4
100.9.d.b.99.4		4	15.8	even	4
256.9.d.e.127.1		4	48.29	odd	4
256.9.d.e.127.2		4	48.11	even	4
256.9.d.e.127.3		4	48.35	even	4
256.9.d.e.127.4		4	48.5	odd	4

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:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	36.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(10.0000 - 12.4900i) q^{2} +(-56.0000 - 249.800i) q^{4} -610.000 q^{5} +1398.88i q^{7} +(-3680.00 - 1798.56i) q^{8} +(-6100.00 + 7618.90i) q^{10} +18485.2i q^{11} -5470.00 q^{13} +(17472.0 + 13988.8i) q^{14} +(-59264.0 + 27977.6i) q^{16} -73090.0 q^{17} -19484.4i q^{19} +(34160.0 + 152378. i) q^{20} +(230880. + 184852. i) q^{22} +237210. i q^{23} -18525.0 q^{25} +(-54700.0 + 68320.3i) q^{26} +(349440. - 78337.3i) q^{28} +128222. q^{29} -67945.6i q^{31} +(-243200. + 1.01998e6i) q^{32} +(-730900. + 912894. i) q^{34} -853317. i q^{35} -3.47203e6 q^{37} +(-243360. - 194844. i) q^{38} +(2.24480e6 + 1.09712e6i) q^{40} -2.14688e6 q^{41} -5.92815e6i q^{43} +(4.61760e6 - 1.03517e6i) q^{44} +(2.96275e6 + 2.37210e6i) q^{46} -7.62629e6i q^{47} +3.80794e6 q^{49} +(-185250. + 231377. i) q^{50} +(306320. + 1.36641e6i) q^{52} -824290. q^{53} -1.12760e7i q^{55} +(2.51597e6 - 5.14788e6i) q^{56} +(1.28222e6 - 1.60149e6i) q^{58} +3.72552e6i q^{59} -1.47461e7 q^{61} +(-848640. - 679456. i) q^{62} +(1.03076e7 + 1.32374e7i) q^{64} +3.33670e6 q^{65} +1.52567e7i q^{67} +(4.09304e6 + 1.82579e7i) q^{68} +(-1.06579e7 - 8.53317e6i) q^{70} +1.19604e6i q^{71} -5.72563e6 q^{73} +(-3.47203e7 + 4.33656e7i) q^{74} +(-4.86720e6 + 1.09113e6i) q^{76} -2.58586e7 q^{77} +3.59132e7i q^{79} +(3.61510e7 - 1.70663e7i) q^{80} +(-2.14688e7 + 2.68145e7i) q^{82} +5.19603e7i q^{83} +4.45849e7 q^{85} +(-7.40426e7 - 5.92815e7i) q^{86} +(3.32467e7 - 6.80255e7i) q^{88} +8.33242e7 q^{89} -7.65187e6i q^{91} +(5.92550e7 - 1.32838e7i) q^{92} +(-9.52524e7 - 7.62629e7i) q^{94} +1.18855e7i q^{95} +1.20619e8 q^{97} +(3.80794e7 - 4.75611e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 20 q^{2} - 112 q^{4} - 1220 q^{5} - 7360 q^{8} - 12200 q^{10} - 10940 q^{13} + 34944 q^{14} - 118528 q^{16} - 146180 q^{17} + 68320 q^{20} + 461760 q^{22} - 37050 q^{25} - 109400 q^{26} + 698880 q^{28}+ \cdots + 76158740 q^{98}+O(q^{100}) \) 2 * q + 20 * q^2 - 112 * q^4 - 1220 * q^5 - 7360 * q^8 - 12200 * q^10 - 10940 * q^13 + 34944 * q^14 - 118528 * q^16 - 146180 * q^17 + 68320 * q^20 + 461760 * q^22 - 37050 * q^25 - 109400 * q^26 + 698880 * q^28 + 256444 * q^29 - 486400 * q^32 - 1461800 * q^34 - 6944060 * q^37 - 486720 * q^38 + 4489600 * q^40 - 4293764 * q^41 + 9235200 * q^44 + 5925504 * q^46 + 7615874 * q^49 - 370500 * q^50 + 612640 * q^52 - 1648580 * q^53 + 5031936 * q^56 + 2564440 * q^58 - 29492156 * q^61 - 1697280 * q^62 + 20615168 * q^64 + 6673400 * q^65 + 8186080 * q^68 - 21315840 * q^70 - 11451260 * q^73 - 69440600 * q^74 - 9734400 * q^76 - 51717120 * q^77 + 72302080 * q^80 - 42937640 * q^82 + 89169800 * q^85 - 148085184 * q^86 + 66493440 * q^88 + 166648444 * q^89 + 118510080 * q^92 - 190504704 * q^94 + 241238020 * q^97 + 76158740 * q^98

Introduction

L-functions

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Database

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