LMFDB - Embedded newform 45.16.b.b.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,16,Mod(19,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("45.19");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	45.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$64.2120772950$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 29397x^{4} + 153469728x^{2} + 65015354624 $ x^6 + 29397x^4 + 153469728x^2 + 65015354624
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{4}\cdot 5^{6} $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.3
Root			$-21.5470i$ of defining polynomial
Character	$\chi$	$=$	45.19
Dual form			45.16.b.b.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-43.0940i q^{2} +30910.9 q^{4} +(160365. + 69286.1i) q^{5} +1.29717e6i q^{7} -2.74418e6i q^{8} +O(q^{10})$	\(q-43.0940i q^{2} +30910.9 q^{4} +(160365. + 69286.1i) q^{5} +1.29717e6i q^{7} -2.74418e6i q^{8} +(2.98581e6 - 6.91078e6i) q^{10} +2.48560e7 q^{11} -1.64842e8i q^{13} +5.59000e7 q^{14} +8.94631e8 q^{16} -2.49651e9i q^{17} +3.47974e9 q^{19} +(4.95704e9 + 2.14170e9i) q^{20} -1.07114e9i q^{22} -1.39929e10i q^{23} +(2.09165e10 + 2.22222e10i) q^{25} -7.10369e9 q^{26} +4.00966e10i q^{28} -7.33587e10 q^{29} +6.63708e9 q^{31} -1.28474e11i q^{32} -1.07584e11 q^{34} +(-8.98755e10 + 2.08020e11i) q^{35} +8.47925e11i q^{37} -1.49956e11i q^{38} +(1.90133e11 - 4.40071e11i) q^{40} +7.77655e11 q^{41} -2.03959e12i q^{43} +7.68321e11 q^{44} -6.03008e11 q^{46} +3.83108e12i q^{47} +3.06492e12 q^{49} +(9.57641e11 - 9.01373e11i) q^{50} -5.09541e12i q^{52} +2.49472e12i q^{53} +(3.98604e12 + 1.72217e12i) q^{55} +3.55965e12 q^{56} +3.16132e12i q^{58} -1.33880e12 q^{59} +7.16455e12 q^{61} -2.86018e11i q^{62} +2.37788e13 q^{64} +(1.14213e13 - 2.64349e13i) q^{65} +6.61388e12i q^{67} -7.71693e13i q^{68} +(8.96442e12 + 3.87309e12i) q^{70} -1.42046e13 q^{71} -5.85350e13i q^{73} +3.65405e13 q^{74} +1.07562e14 q^{76} +3.22423e13i q^{77} +2.48505e14 q^{79} +(1.43468e14 + 6.19855e13i) q^{80} -3.35122e13i q^{82} +6.66100e13i q^{83} +(1.72973e14 - 4.00353e14i) q^{85} -8.78941e13 q^{86} -6.82092e13i q^{88} +5.07426e14 q^{89} +2.13827e14 q^{91} -4.32532e14i q^{92} +1.65096e14 q^{94} +(5.58029e14 + 2.41097e14i) q^{95} -1.18734e15i q^{97} -1.32080e14i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 38568 q^{4} + 238350 q^{5}+O(q^{10}) $ 6 * q - 38568 * q^4 + 238350 * q^5	$ 6 q - 38568 q^{4} + 238350 q^{5} - 48274200 q^{10} + 108590088 q^{11} - 663751704 q^{14} + 1155522336 q^{16} - 3630995640 q^{19} - 2533753800 q^{20} + 18250878750 q^{25} + 81970953168 q^{26} - 286168468740 q^{29} - 276236748288 q^{31} - 127784939136 q^{34} - 1171274911800 q^{35} + 4214283852000 q^{40} + 6153278882388 q^{41} - 8250173021664 q^{44} - 23334602656488 q^{46} + 11613390856242 q^{49} - 23694218070000 q^{50} + 33977390365800 q^{55} + 59280484297440 q^{56} - 14903258326680 q^{59} - 11352061428588 q^{61} + 73265851251072 q^{64} + 50675287275600 q^{65} - 156447825521400 q^{70} - 131693145807312 q^{71} + 353606797863216 q^{74} + 959127540575520 q^{76} - 26081853939360 q^{79} + 552945514077600 q^{80} - 548221025491200 q^{85} - 598387757484072 q^{86} - 59269690709820 q^{89} + 821206462566672 q^{91} - 308164835928456 q^{94} - 232287694599000 q^{95}+O(q^{100}) $ 6 * q - 38568 * q^4 + 238350 * q^5 - 48274200 * q^10 + 108590088 * q^11 - 663751704 * q^14 + 1155522336 * q^16 - 3630995640 * q^19 - 2533753800 * q^20 + 18250878750 * q^25 + 81970953168 * q^26 - 286168468740 * q^29 - 276236748288 * q^31 - 127784939136 * q^34 - 1171274911800 * q^35 + 4214283852000 * q^40 + 6153278882388 * q^41 - 8250173021664 * q^44 - 23334602656488 * q^46 + 11613390856242 * q^49 - 23694218070000 * q^50 + 33977390365800 * q^55 + 59280484297440 * q^56 - 14903258326680 * q^59 - 11352061428588 * q^61 + 73265851251072 * q^64 + 50675287275600 * q^65 - 156447825521400 * q^70 - 131693145807312 * q^71 + 353606797863216 * q^74 + 959127540575520 * q^76 - 26081853939360 * q^79 + 552945514077600 * q^80 - 548221025491200 * q^85 - 598387757484072 * q^86 - 59269690709820 * q^89 + 821206462566672 * q^91 - 308164835928456 * q^94 - 232287694599000 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	43.0940i		−	0.238063i	−0.992890	−	0.119031i	$-0.962021\pi$
$2$		−	43.0940i		−	0.238063i	0.992890	−	0.119031i	$-0.0379789\pi$
$3$		0			0
$3$		0			0
$4$	30910.9			0.943326
$5$	160365.	+	69286.1i	0.917984	+	0.396617i
$5$	160365.	+	69286.1i	0.917984	+	0.396617i
$6$		0			0
$7$			1.29717e6i			0.595333i	0.954670	+	0.297667i	$0.0962084\pi$
$7$			1.29717e6i			0.595333i	−0.954670	+	0.297667i	$0.903792\pi$
$8$		−	2.74418e6i		−	0.462634i
$9$		0			0
$10$	2.98581e6	−	6.91078e6i	0.0944197	−	0.218538i
$11$	2.48560e7			0.384579			0.192290	−	0.981338i	$-0.438409\pi$
$11$	2.48560e7			0.384579			0.192290	+	0.981338i	$0.438409\pi$
$12$		0			0
$13$		−	1.64842e8i		−	0.728606i	−0.931281	−	0.364303i	$-0.881307\pi$
$13$		−	1.64842e8i		−	0.728606i	0.931281	−	0.364303i	$-0.118693\pi$
$14$	5.59000e7			0.141727
$15$		0			0
$16$	8.94631e8			0.833190
$17$		−	2.49651e9i		−	1.47559i	−0.675024	−	0.737795i	$-0.735867\pi$
$17$		−	2.49651e9i		−	1.47559i	0.675024	−	0.737795i	$-0.264133\pi$
$18$		0			0
$19$	3.47974e9			0.893088			0.446544	−	0.894762i	$-0.352655\pi$
$19$	3.47974e9			0.893088			0.446544	+	0.894762i	$0.352655\pi$
$20$	4.95704e9	+	2.14170e9i	0.865959	+	0.374139i
$21$		0			0
$22$		−	1.07114e9i		−	0.0915540i
$23$		−	1.39929e10i		−	0.856934i	−0.903557	−	0.428467i	$-0.859054\pi$
$23$		−	1.39929e10i		−	0.856934i	0.903557	−	0.428467i	$-0.140946\pi$
$24$		0			0
$25$	2.09165e10	+	2.22222e10i	0.685390	+	0.728176i
$26$	−7.10369e9			−0.173454
$27$		0			0
$28$			4.00966e10i			0.561593i
$29$	−7.33587e10			−0.789709			−0.394854	−	0.918744i	$-0.629205\pi$
$29$	−7.33587e10			−0.789709			−0.394854	+	0.918744i	$0.629205\pi$
$30$		0			0
$31$	6.63708e9			0.0433276			0.0216638	−	0.999765i	$-0.493104\pi$
$31$	6.63708e9			0.0433276			0.0216638	+	0.999765i	$0.493104\pi$
$32$		−	1.28474e11i		−	0.660985i
$33$		0			0
$34$	−1.07584e11			−0.351283
$35$	−8.98755e10	+	2.08020e11i	−0.236119	+	0.546506i
$36$		0			0
$37$			8.47925e11i			1.46840i	0.678933	+	0.734201i	$0.262443\pi$
$37$			8.47925e11i			1.46840i	−0.678933	+	0.734201i	$0.737557\pi$
$38$		−	1.49956e11i		−	0.212611i
$39$		0			0
$40$	1.90133e11	−	4.40071e11i	0.183488	−	0.424690i
$41$	7.77655e11			0.623603			0.311801	−	0.950147i	$-0.399068\pi$
$41$	7.77655e11			0.623603			0.311801	+	0.950147i	$0.399068\pi$
$42$		0			0
$43$		−	2.03959e12i		−	1.14427i	−0.820158	−	0.572137i	$-0.806115\pi$
$43$		−	2.03959e12i		−	1.14427i	0.820158	−	0.572137i	$-0.193885\pi$
$44$	7.68321e11			0.362784
$45$		0			0
$46$	−6.03008e11			−0.204004
$47$			3.83108e12i			1.10303i	0.834165	+	0.551514i	$0.185950\pi$
$47$			3.83108e12i			1.10303i	−0.834165	+	0.551514i	$0.814050\pi$
$48$		0			0
$49$	3.06492e12			0.645578
$50$	9.57641e11	−	9.01373e11i	0.173352	−	0.163166i
$51$		0			0
$52$		−	5.09541e12i		−	0.687313i
$53$			2.49472e12i			0.291711i	0.989306	+	0.145856i	$0.0465935\pi$
$53$			2.49472e12i			0.291711i	−0.989306	+	0.145856i	$0.953407\pi$
$54$		0			0
$55$	3.98604e12	+	1.72217e12i	0.353038	+	0.152531i
$56$	3.55965e12			0.275421
$57$		0			0
$58$			3.16132e12i			0.188000i
$59$	−1.33880e12			−0.0700365			−0.0350183	−	0.999387i	$-0.511149\pi$
$59$	−1.33880e12			−0.0700365			−0.0350183	+	0.999387i	$0.511149\pi$
$60$		0			0
$61$	7.16455e12			0.291887			0.145944	−	0.989293i	$-0.453378\pi$
$61$	7.16455e12			0.291887			0.145944	+	0.989293i	$0.453378\pi$
$62$		−	2.86018e11i		−	0.0103147i
$63$		0			0
$64$	2.37788e13			0.675834
$65$	1.14213e13	−	2.64349e13i	0.288977	−	0.668849i
$66$		0			0
$67$			6.61388e12i			0.133320i	0.997776	+	0.0666600i	$0.0212343\pi$
$67$			6.61388e12i			0.133320i	−0.997776	+	0.0666600i	$0.978766\pi$
$68$		−	7.71693e13i		−	1.39196i
$69$		0			0
$70$	8.96442e12	+	3.87309e12i	0.130103	+	0.0562112i
$71$	−1.42046e13			−0.185349			−0.0926746	−	0.995696i	$-0.529542\pi$
$71$	−1.42046e13			−0.185349			−0.0926746	+	0.995696i	$0.529542\pi$
$72$		0			0
$73$		−	5.85350e13i		−	0.620147i	−0.950713	−	0.310073i	$-0.899646\pi$
$73$		−	5.85350e13i		−	0.620147i	0.950713	−	0.310073i	$-0.100354\pi$
$74$	3.65405e13			0.349572
$75$		0			0
$76$	1.07562e14			0.842473
$77$			3.22423e13i			0.228953i
$78$		0			0
$79$	2.48505e14			1.45590			0.727950	−	0.685630i	$-0.240473\pi$
$79$	2.48505e14			1.45590			0.727950	+	0.685630i	$0.240473\pi$
$80$	1.43468e14	+	6.19855e13i	0.764856	+	0.330457i
$81$		0			0
$82$		−	3.35122e13i		−	0.148457i
$83$			6.66100e13i			0.269435i	0.990884	+	0.134717i	$0.0430127\pi$
$83$			6.66100e13i			0.269435i	−0.990884	+	0.134717i	$0.956987\pi$
$84$		0			0
$85$	1.72973e14	−	4.00353e14i	0.585244	−	1.35457i
$86$	−8.78941e13			−0.272409
$87$		0			0
$88$		−	6.82092e13i		−	0.177919i
$89$	5.07426e14			1.21604			0.608020	−	0.793922i	$-0.291964\pi$
$89$	5.07426e14			1.21604			0.608020	+	0.793922i	$0.291964\pi$
$90$		0			0
$91$	2.13827e14			0.433763
$92$		−	4.32532e14i		−	0.808369i
$93$		0			0
$94$	1.65096e14			0.262590
$95$	5.58029e14	+	2.41097e14i	0.819841	+	0.354214i
$96$		0			0
$97$		−	1.18734e15i		−	1.49206i	−0.665912	−	0.746030i	$-0.731957\pi$
$97$		−	1.18734e15i		−	1.49206i	0.665912	−	0.746030i	$-0.268043\pi$
$98$		−	1.32080e14i		−	0.153688i
$99$		0			0
$100$	6.46547e14	+	6.86907e14i	0.646547	+	0.686907i
$101$	−1.97970e14			−0.183734			−0.0918671	−	0.995771i	$-0.529283\pi$
$101$	−1.97970e14			−0.183734			−0.0918671	+	0.995771i	$0.529283\pi$
$102$		0			0
$103$			1.50015e15i			1.20186i	0.799301	+	0.600931i	$0.205203\pi$
$103$			1.50015e15i			1.20186i	−0.799301	+	0.600931i	$0.794797\pi$
$104$	−4.52355e14			−0.337077
$105$		0			0
$106$	1.07507e14			0.0694456
$107$			6.89575e14i			0.415148i	0.978219	+	0.207574i	$0.0665568\pi$
$107$			6.89575e14i			0.415148i	−0.978219	+	0.207574i	$0.933443\pi$
$108$		0			0
$109$	1.35369e15			0.709287			0.354644	−	0.935002i	$-0.384602\pi$
$109$	1.35369e15			0.709287			0.354644	+	0.935002i	$0.384602\pi$
$110$	7.42153e13	−	1.71774e14i	0.0363118	−	0.0840451i
$111$		0			0
$112$			1.16048e15i			0.496026i
$113$		−	2.28009e15i		−	0.911726i	−0.890050	−	0.455863i	$-0.849331\pi$
$113$		−	2.28009e15i		−	0.911726i	0.890050	−	0.455863i	$-0.150669\pi$
$114$		0			0
$115$	9.69510e14	−	2.24397e15i	0.339874	−	0.786652i
$116$	−2.26759e15			−0.744953
$117$		0			0
$118$			5.76941e13i			0.0166731i
$119$	3.23838e15			0.878468
$120$		0			0
$121$	−3.55943e15			−0.852099
$122$		−	3.08749e14i		−	0.0694875i
$123$		0			0
$124$	2.05158e14			0.0408720
$125$	1.81459e15	+	5.01288e15i	0.340371	+	0.940291i
$126$		0			0
$127$		−	2.82207e15i		−	0.469938i	−0.972003	−	0.234969i	$-0.924501\pi$
$127$		−	2.82207e15i		−	0.469938i	0.972003	−	0.234969i	$-0.0754988\pi$
$128$		−	5.23457e15i		−	0.821876i
$129$		0			0
$130$	−1.13919e15	−	4.92187e14i	−0.159228	−	0.0687947i
$131$	−6.54539e15			−0.863775			−0.431888	−	0.901927i	$-0.642152\pi$
$131$	−6.54539e15			−0.863775			−0.431888	+	0.901927i	$0.642152\pi$
$132$		0			0
$133$			4.51379e15i			0.531685i
$134$	2.85019e14			0.0317386
$135$		0			0
$136$	−6.85086e15			−0.682658
$137$			1.17625e16i			1.10941i	0.832046	+	0.554707i	$0.187170\pi$
$137$			1.17625e16i			1.10941i	−0.832046	+	0.554707i	$0.812830\pi$
$138$		0			0
$139$	−2.03768e16			−1.72395			−0.861976	−	0.506949i	$-0.830773\pi$
$139$	−2.03768e16			−1.72395			−0.861976	+	0.506949i	$0.830773\pi$
$140$	−2.77813e15	+	6.43010e15i	−0.222737	+	0.515534i
$141$		0			0
$142$			6.12132e14i			0.0441247i
$143$		−	4.09731e15i		−	0.280207i
$144$		0			0
$145$	−1.17642e16	−	5.08274e15i	−0.724940	−	0.313212i
$146$	−2.52251e15			−0.147634
$147$		0			0
$148$			2.62101e16i			1.38518i
$149$	−2.89572e16			−1.45499			−0.727493	−	0.686115i	$-0.759315\pi$
$149$	−2.89572e16			−1.45499			−0.727493	+	0.686115i	$0.759315\pi$
$150$		0			0
$151$	1.77226e13			0.000805748			0.000402874	−	1.00000i	$-0.499872\pi$
$151$	1.77226e13			0.000805748			0.000402874		1.00000i	$0.499872\pi$
$152$		−	9.54901e15i		−	0.413172i
$153$		0			0
$154$	1.38945e15			0.0545051
$155$	1.06436e15	+	4.59857e14i	0.0397740	+	0.0171844i
$156$		0			0
$157$			1.04137e16i			0.353475i	0.984258	+	0.176737i	$0.0565543\pi$
$157$			1.04137e16i			0.353475i	−0.984258	+	0.176737i	$0.943446\pi$
$158$		−	1.07091e16i		−	0.346596i
$159$		0			0
$160$	8.90149e15	−	2.06028e16i	0.262158	−	0.606774i
$161$	1.81510e16			0.510161
$162$		0			0
$163$			4.70622e16i			1.20577i	0.797827	+	0.602886i	$0.205983\pi$
$163$			4.70622e16i			1.20577i	−0.797827	+	0.602886i	$0.794017\pi$
$164$	2.40380e16			0.588261
$165$		0			0
$166$	2.87049e15			0.0641424
$167$			3.97751e16i			0.849646i	0.905276	+	0.424823i	$0.139664\pi$
$167$			3.97751e16i			0.849646i	−0.905276	+	0.424823i	$0.860336\pi$
$168$		0			0
$169$	2.40130e16			0.469134
$170$	−1.72528e16	−	7.45410e15i	−0.322472	−	0.139325i
$171$		0			0
$172$		−	6.30457e16i		−	1.07942i
$173$		−	6.30223e16i		−	1.03311i	−0.856253	−	0.516557i	$-0.827213\pi$
$173$		−	6.30223e16i		−	1.03311i	0.856253	−	0.516557i	$-0.172787\pi$
$174$		0			0
$175$	−2.88258e16	+	2.71321e16i	−0.433507	+	0.408036i
$176$	2.22369e16			0.320428
$177$		0			0
$178$		−	2.18670e16i		−	0.289494i
$179$	−2.10684e16			−0.267445			−0.133722	−	0.991019i	$-0.542693\pi$
$179$	−2.10684e16			−0.267445			−0.133722	+	0.991019i	$0.542693\pi$
$180$		0			0
$181$	1.74536e16			0.203843			0.101922	−	0.994792i	$-0.467501\pi$
$181$	1.74536e16			0.203843			0.101922	+	0.994792i	$0.467501\pi$
$182$		−	9.21466e15i		−	0.103263i
$183$		0			0
$184$	−3.83989e16			−0.396447
$185$	−5.87494e16	+	1.35978e17i	−0.582392	+	1.34797i
$186$		0			0
$187$		−	6.20531e16i		−	0.567482i
$188$			1.18422e17i			1.04052i
$189$		0			0
$190$	1.03898e16	−	2.40477e16i	0.0843251	−	0.195174i
$191$	1.82919e17			1.42728			0.713639	−	0.700514i	$-0.247046\pi$
$191$	1.82919e17			1.42728			0.713639	+	0.700514i	$0.247046\pi$
$192$		0			0
$193$		−	4.54299e16i		−	0.327840i	−0.986474	−	0.163920i	$-0.947586\pi$
$193$		−	4.54299e16i		−	0.327840i	0.986474	−	0.163920i	$-0.0524139\pi$
$194$	−5.11671e16			−0.355204
$195$		0			0
$196$	9.47396e16			0.608991
$197$		−	2.54430e17i		−	1.57425i	−0.616797	−	0.787123i	$-0.711570\pi$
$197$		−	2.54430e17i		−	1.57425i	0.616797	−	0.787123i	$-0.288430\pi$
$198$		0			0
$199$	1.75148e17			1.00463			0.502316	−	0.864684i	$-0.332482\pi$
$199$	1.75148e17			1.00463			0.502316	+	0.864684i	$0.332482\pi$
$200$	6.09815e16	−	5.73985e16i	0.336879	−	0.317085i
$201$		0			0
$202$			8.53133e15i			0.0437403i
$203$		−	9.51584e16i		−	0.470140i
$204$		0			0
$205$	1.24709e17	+	5.38807e16i	0.572457	+	0.247331i
$206$	6.46473e16			0.286119
$207$		0			0
$208$		−	1.47473e17i		−	0.607067i
$209$	8.64923e16			0.343463
$210$		0			0
$211$	3.58937e17			1.32709			0.663545	−	0.748137i	$-0.269051\pi$
$211$	3.58937e17			1.32709			0.663545	+	0.748137i	$0.269051\pi$
$212$			7.71141e16i			0.275179i
$213$		0			0
$214$	2.97165e16			0.0988313
$215$	1.41315e17	−	3.27080e17i	0.453838	−	1.05043i
$216$		0			0
$217$			8.60939e15i			0.0257943i
$218$		−	5.83361e16i		−	0.168855i
$219$		0			0
$220$	1.23212e17	+	5.32340e16i	0.333030	+	0.143886i
$221$	−4.11529e17			−1.07512
$222$		0			0
$223$		−	8.51111e16i		−	0.207826i	−0.994586	−	0.103913i	$-0.966864\pi$
$223$		−	8.51111e16i		−	0.207826i	0.994586	−	0.103913i	$-0.0331364\pi$
$224$	1.66653e17			0.393506
$225$		0			0
$226$	−9.82583e16			−0.217048
$227$			8.22273e16i			0.175720i	0.996133	+	0.0878602i	$0.0280029\pi$
$227$			8.22273e16i			0.175720i	−0.996133	+	0.0878602i	$0.971997\pi$
$228$		0			0
$229$	−3.91258e17			−0.782884			−0.391442	−	0.920203i	$-0.628024\pi$
$229$	−3.91258e17			−0.782884			−0.391442	+	0.920203i	$0.628024\pi$
$230$	−9.67015e16	−	4.17800e16i	−0.187273	−	0.0809115i
$231$		0			0
$232$			2.01309e17i			0.365346i
$233$			9.50055e17i			1.66947i	0.550650	+	0.834736i	$0.314380\pi$
$233$			9.50055e17i			1.66947i	−0.550650	+	0.834736i	$0.685620\pi$
$234$		0			0
$235$	−2.65440e17	+	6.14371e17i	−0.437480	+	1.01256i
$236$	−4.13834e16			−0.0660673
$237$		0			0
$238$		−	1.39555e17i		−	0.209131i
$239$	−3.05534e17			−0.443685			−0.221843	−	0.975082i	$-0.571207\pi$
$239$	−3.05534e17			−0.443685			−0.221843	+	0.975082i	$0.571207\pi$
$240$		0			0
$241$	−1.24585e18			−1.69956			−0.849780	−	0.527137i	$-0.823266\pi$
$241$	−1.24585e18			−1.69956			−0.849780	+	0.527137i	$0.823266\pi$
$242$			1.53390e17i			0.202853i
$243$		0			0
$244$	2.21463e17			0.275345
$245$	4.91507e17	+	2.12357e17i	0.592631	+	0.256047i
$246$		0			0
$247$		−	5.73606e17i		−	0.650709i
$248$		−	1.82133e16i		−	0.0200448i
$249$		0			0
$250$	2.16025e17	−	7.81977e16i	0.223848	−	0.0810297i
$251$	−3.78704e17			−0.380844			−0.190422	−	0.981702i	$-0.560986\pi$
$251$	−3.78704e17			−0.380844			−0.190422	+	0.981702i	$0.560986\pi$
$252$		0			0
$253$		−	3.47806e17i		−	0.329559i
$254$	−1.21614e17			−0.111875
$255$		0			0
$256$	5.53605e17			0.480176
$257$		−	6.98680e16i		−	0.0588545i	−0.999567	−	0.0294273i	$-0.990632\pi$
$257$		−	6.98680e16i		−	0.0588545i	0.999567	−	0.0294273i	$-0.00936834\pi$
$258$		0			0
$259$	−1.09990e18			−0.874188
$260$	3.53041e17	−	8.17127e17i	0.272600	−	0.630942i
$261$		0			0
$262$			2.82067e17i			0.205633i
$263$			6.94838e17i			0.492284i	0.969234	+	0.246142i	$0.0791629\pi$
$263$			6.94838e17i			0.492284i	−0.969234	+	0.246142i	$0.920837\pi$
$264$		0			0
$265$	−1.72849e17	+	4.00067e17i	−0.115698	+	0.267786i
$266$	1.94517e17			0.126574
$267$		0			0
$268$			2.04441e17i			0.125764i
$269$	−1.75703e18			−1.05108			−0.525542	−	0.850768i	$-0.676137\pi$
$269$	−1.75703e18			−1.05108			−0.525542	+	0.850768i	$0.676137\pi$
$270$		0			0
$271$	−1.86384e18			−1.05472			−0.527362	−	0.849641i	$-0.676819\pi$
$271$	−1.86384e18			−1.05472			−0.527362	+	0.849641i	$0.676819\pi$
$272$		−	2.23345e18i		−	1.22945i
$273$		0			0
$274$	5.06891e17			0.264110
$275$	5.19899e17	+	5.52354e17i	0.263587	+	0.280041i
$276$		0			0
$277$			3.28806e18i			1.57885i	0.613846	+	0.789425i	$0.289621\pi$
$277$			3.28806e18i			1.57885i	−0.613846	+	0.789425i	$0.710379\pi$
$278$			8.78118e17i			0.410409i
$279$		0			0
$280$	5.70844e17	+	2.46634e17i	0.252832	+	0.109237i
$281$	−2.41481e18			−1.04132			−0.520662	−	0.853763i	$-0.674315\pi$
$281$	−2.41481e18			−1.04132			−0.520662	+	0.853763i	$0.674315\pi$
$282$		0			0
$283$			1.11571e17i			0.0456199i	0.999740	+	0.0228099i	$0.00726126\pi$
$283$			1.11571e17i			0.0456199i	−0.999740	+	0.0228099i	$0.992739\pi$
$284$	−4.39076e17			−0.174845
$285$		0			0
$286$	−1.76569e17			−0.0667068
$287$			1.00875e18i			0.371251i
$288$		0			0
$289$	−3.37012e18			−1.17737
$290$	−2.19035e17	+	5.06966e17i	−0.0745640	+	0.172581i
$291$		0			0
$292$		−	1.80937e18i		−	0.585001i
$293$		−	2.59868e18i		−	0.818927i	−0.912327	−	0.409463i	$-0.865716\pi$
$293$		−	2.59868e18i		−	0.818927i	0.912327	−	0.409463i	$-0.134284\pi$
$294$		0			0
$295$	−2.14697e17	−	9.27600e16i	−0.0642924	−	0.0277777i
$296$	2.32686e18			0.679332
$297$		0			0
$298$			1.24788e18i			0.346378i
$299$	−2.30661e18			−0.624367
$300$		0			0
$301$	2.64569e18			0.681224
$302$		−	7.63735e14i		−	0.000191819i
$303$		0			0
$304$	3.11308e18			0.744112
$305$	1.14895e18	+	4.96404e17i	0.267948	+	0.115767i
$306$		0			0
$307$		−	7.96608e18i		−	1.76892i	−0.466621	−	0.884458i	$-0.654529\pi$
$307$		−	7.96608e18i		−	1.76892i	0.466621	−	0.884458i	$-0.345471\pi$
$308$			9.96640e17i			0.215977i
$309$		0			0
$310$	1.98171e16	−	4.58674e16i	0.00409097	−	0.00946871i
$311$	8.72923e18			1.75903			0.879515	−	0.475872i	$-0.157867\pi$
$311$	8.72923e18			1.75903			0.879515	+	0.475872i	$0.157867\pi$
$312$		0			0
$313$		−	3.04567e17i		−	0.0584926i	−0.999572	−	0.0292463i	$-0.990689\pi$
$313$		−	3.04567e17i		−	0.0584926i	0.999572	−	0.0292463i	$-0.00931071\pi$
$314$	4.48768e17			0.0841492
$315$		0			0
$316$	7.68151e18			1.37339
$317$			5.64109e18i			0.984961i	0.870324	+	0.492480i	$0.163910\pi$
$317$			5.64109e18i			0.984961i	−0.870324	+	0.492480i	$0.836090\pi$
$318$		0			0
$319$	−1.82340e18			−0.303706
$320$	3.81329e18	+	1.64754e18i	0.620405	+	0.268047i
$321$		0			0
$322$		−	7.82201e17i		−	0.121450i
$323$		−	8.68718e18i		−	1.31783i
$324$		0			0
$325$	3.66314e18	−	3.44791e18i	0.530553	−	0.499379i
$326$	2.02810e18			0.287050
$327$		0			0
$328$		−	2.13402e18i		−	0.288500i
$329$	−4.96954e18			−0.656670
$330$		0			0
$331$	6.05049e18			0.763978			0.381989	−	0.924167i	$-0.375239\pi$
$331$	6.05049e18			0.763978			0.381989	+	0.924167i	$0.375239\pi$
$332$			2.05898e18i			0.254165i
$333$		0			0
$334$	1.71407e18			0.202269
$335$	−4.58250e17	+	1.06064e18i	−0.0528770	+	0.122386i
$336$		0			0
$337$			1.58672e19i			1.75096i	0.483254	+	0.875480i	$0.339455\pi$
$337$			1.58672e19i			1.75096i	−0.483254	+	0.875480i	$0.660545\pi$
$338$		−	1.03482e18i		−	0.111683i
$339$		0			0
$340$	5.34676e18	−	1.23753e19i	0.552076	−	1.27780i
$341$	1.64971e17			0.0166629
$342$		0			0
$343$			1.01341e19i			0.979667i
$344$	−5.59700e18			−0.529380
$345$		0			0
$346$	−2.71588e18			−0.245946
$347$		−	5.47026e18i		−	0.484771i	−0.970180	−	0.242386i	$-0.922070\pi$
$347$		−	5.47026e18i		−	0.484771i	0.970180	−	0.242386i	$-0.0779299\pi$
$348$		0			0
$349$	−7.51980e18			−0.638287			−0.319143	−	0.947706i	$-0.603395\pi$
$349$	−7.51980e18			−0.638287			−0.319143	+	0.947706i	$0.603395\pi$
$350$	1.16923e18	+	1.24222e18i	0.0971381	+	0.103202i
$351$		0			0
$352$		−	3.19336e18i		−	0.254201i
$353$		−	3.96219e18i		−	0.308763i	−0.988011	−	0.154382i	$-0.950662\pi$
$353$		−	3.96219e18i		−	0.308763i	0.988011	−	0.154382i	$-0.0493385\pi$
$354$		0			0
$355$	−2.27792e18	−	9.84179e17i	−0.170148	−	0.0735126i
$356$	1.56850e19			1.14712
$357$		0			0
$358$			9.07921e17i			0.0636686i
$359$	−1.88540e19			−1.29478			−0.647390	−	0.762159i	$-0.724140\pi$
$359$	−1.88540e19			−1.29478			−0.647390	+	0.762159i	$0.724140\pi$
$360$		0			0
$361$	−3.07257e18			−0.202394
$362$		−	7.52146e17i		−	0.0485275i
$363$		0			0
$364$	6.60959e18			0.409180
$365$	4.05566e18	−	9.38699e18i	0.245961	−	0.569285i
$366$		0			0
$367$		−	1.02228e19i		−	0.595077i	−0.954710	−	0.297538i	$-0.903834\pi$
$367$		−	1.02228e19i		−	0.595077i	0.954710	−	0.297538i	$-0.0961656\pi$
$368$		−	1.25184e19i		−	0.713989i
$369$		0			0
$370$	5.85982e18	+	2.53175e18i	0.320901	+	0.138646i
$371$	−3.23607e18			−0.173665
$372$		0			0
$373$			1.86547e19i			0.961550i	0.876844	+	0.480775i	$0.159645\pi$
$373$			1.86547e19i			0.961550i	−0.876844	+	0.480775i	$0.840355\pi$
$374$	−2.67412e18			−0.135096
$375$		0			0
$376$	1.05131e19			0.510298
$377$			1.20926e19i			0.575386i
$378$		0			0
$379$	−3.62923e19			−1.65967			−0.829833	−	0.558012i	$-0.811564\pi$
$379$	−3.62923e19			−1.65967			−0.829833	+	0.558012i	$0.811564\pi$
$380$	1.72492e19	+	7.45253e18i	0.773377	+	0.334139i
$381$		0			0
$382$		−	7.88270e18i		−	0.339782i
$383$			3.39832e19i			1.43640i	0.695839	+	0.718198i	$0.255033\pi$
$383$			3.39832e19i			1.43640i	−0.695839	+	0.718198i	$0.744967\pi$
$384$		0			0
$385$	−2.23394e18	+	5.17055e18i	−0.0908065	+	0.210175i
$386$	−1.95776e18			−0.0780465
$387$		0			0
$388$		−	3.67017e19i		−	1.40750i
$389$	−4.43693e19			−1.66902			−0.834508	−	0.550996i	$-0.814248\pi$
$389$	−4.43693e19			−1.66902			−0.834508	+	0.550996i	$0.814248\pi$
$390$		0			0
$391$	−3.49333e19			−1.26448
$392$		−	8.41069e18i		−	0.298666i
$393$		0			0
$394$	−1.09644e19			−0.374769
$395$	3.98516e19	+	1.72179e19i	1.33649	+	0.577434i
$396$		0			0
$397$			1.44302e19i			0.465953i	0.972482	+	0.232977i	$0.0748466\pi$
$397$			1.44302e19i			0.465953i	−0.972482	+	0.232977i	$0.925153\pi$
$398$		−	7.54781e18i		−	0.239165i
$399$		0			0
$400$	1.87125e19	+	1.98806e19i	0.571061	+	0.606709i
$401$	−2.34827e19			−0.703339			−0.351669	−	0.936124i	$-0.614386\pi$
$401$	−2.34827e19			−0.703339			−0.351669	+	0.936124i	$0.614386\pi$
$402$		0			0
$403$		−	1.09407e18i		−	0.0315687i
$404$	−6.11945e18			−0.173321
$405$		0			0
$406$	−4.10075e18			−0.111923
$407$			2.10760e19i			0.564717i
$408$		0			0
$409$	−3.99167e19			−1.03093			−0.515466	−	0.856910i	$-0.672381\pi$
$409$	−3.99167e19			−1.03093			−0.515466	+	0.856910i	$0.672381\pi$
$410$	2.32193e18	−	5.37420e18i	0.0588804	−	0.136281i
$411$		0			0
$412$			4.63709e19i			1.13375i
$413$		−	1.73664e18i		−	0.0416951i
$414$		0			0
$415$	−4.61515e18	+	1.06819e19i	−0.106862	+	0.247337i
$416$	−2.11780e19			−0.481598
$417$		0			0
$418$		−	3.72729e18i		−	0.0817658i
$419$	−7.16449e19			−1.54376			−0.771881	−	0.635767i	$-0.780684\pi$
$419$	−7.16449e19			−1.54376			−0.771881	+	0.635767i	$0.780684\pi$
$420$		0			0
$421$	−6.22202e18			−0.129365			−0.0646823	−	0.997906i	$-0.520603\pi$
$421$	−6.22202e18			−0.129365			−0.0646823	+	0.997906i	$0.520603\pi$
$422$		−	1.54680e19i		−	0.315931i
$423$		0			0
$424$	6.84596e18			0.134955
$425$	5.54778e19	−	5.22181e19i	1.07449	−	1.01136i
$426$		0			0
$427$			9.29361e18i			0.173770i
$428$			2.13154e19i			0.391620i
$429$		0			0
$430$	−1.40952e19	−	6.08984e18i	−0.250067	−	0.108042i
$431$	4.93032e19			0.859598			0.429799	−	0.902925i	$-0.358584\pi$
$431$	4.93032e19			0.859598			0.429799	+	0.902925i	$0.358584\pi$
$432$		0			0
$433$		−	1.59414e19i		−	0.268453i	−0.990951	−	0.134226i	$-0.957145\pi$
$433$		−	1.59414e19i		−	0.268453i	0.990951	−	0.134226i	$-0.0428549\pi$
$434$	3.71013e17			0.00614067
$435$		0			0
$436$	4.18439e19			0.669089
$437$		−	4.86914e19i		−	0.765318i
$438$		0			0
$439$	−1.26174e19			−0.191640			−0.0958201	−	0.995399i	$-0.530547\pi$
$439$	−1.26174e19			−0.191640			−0.0958201	+	0.995399i	$0.530547\pi$
$440$	4.72595e18	−	1.09384e19i	0.0705658	−	0.163327i
$441$		0			0
$442$			1.77344e19i			0.255947i
$443$			7.89961e19i			1.12093i	0.828179	+	0.560464i	$0.189377\pi$
$443$			7.89961e19i			1.12093i	−0.828179	+	0.560464i	$0.810623\pi$
$444$		0			0
$445$	8.13735e19	+	3.51576e19i	1.11630	+	0.482301i
$446$	−3.66778e18			−0.0494756
$447$		0			0
$448$			3.08450e19i			0.402347i
$449$	−4.36438e19			−0.559854			−0.279927	−	0.960021i	$-0.590310\pi$
$449$	−4.36438e19			−0.559854			−0.279927	+	0.960021i	$0.590310\pi$
$450$		0			0
$451$	1.93294e19			0.239825
$452$		−	7.04798e19i		−	0.860055i
$453$		0			0
$454$	3.54350e18			0.0418325
$455$	3.42905e19	+	1.48153e19i	0.398188	+	0.172038i
$456$		0			0
$457$		−	1.00520e20i		−	1.12949i	−0.825266	−	0.564744i	$-0.808975\pi$
$457$		−	1.00520e20i		−	1.12949i	0.825266	−	0.564744i	$-0.191025\pi$
$458$			1.68609e19i			0.186376i
$459$		0			0
$460$	2.99684e19	−	6.93631e19i	0.320612	−	0.742070i
$461$	1.09258e20			1.15000			0.574999	−	0.818154i	$-0.305002\pi$
$461$	1.09258e20			1.15000			0.574999	+	0.818154i	$0.305002\pi$
$462$		0			0
$463$		−	1.81520e20i		−	1.84955i	−0.380510	−	0.924777i	$-0.624252\pi$
$463$		−	1.81520e20i		−	1.84955i	0.380510	−	0.924777i	$-0.375748\pi$
$464$	−6.56290e19			−0.657978
$465$		0			0
$466$	4.09416e19			0.397439
$467$			1.14048e20i			1.08946i	0.838611	+	0.544731i	$0.183368\pi$
$467$			1.14048e20i			1.08946i	−0.838611	+	0.544731i	$0.816632\pi$
$468$		0			0
$469$	−8.57930e18			−0.0793699
$470$	2.64757e19	+	1.14389e19i	0.241054	+	0.104148i
$471$		0			0
$472$			3.67390e18i			0.0324013i
$473$		−	5.06961e19i		−	0.440064i
$474$		0			0
$475$	7.27837e19	+	7.73272e19i	0.612114	+	0.650325i
$476$	1.00101e20			0.828682
$477$		0			0
$478$			1.31667e19i			0.105625i
$479$	−1.21110e20			−0.956451			−0.478226	−	0.878237i	$-0.658720\pi$
$479$	−1.21110e20			−0.956451			−0.478226	+	0.878237i	$0.658720\pi$
$480$		0			0
$481$	1.39774e20			1.06989
$482$			5.36885e19i			0.404602i
$483$		0			0
$484$	−1.10025e20			−0.803807
$485$	8.22660e19	−	1.90408e20i	0.591776	−	1.36969i
$486$		0			0
$487$		−	1.00069e20i		−	0.697963i	−0.937130	−	0.348982i	$-0.886528\pi$
$487$		−	1.00069e20i		−	0.697963i	0.937130	−	0.348982i	$-0.113472\pi$
$488$		−	1.96608e19i		−	0.135037i
$489$		0			0
$490$	9.15129e18	−	2.11810e19i	0.0609553	−	0.141083i
$491$	1.32724e20			0.870641			0.435321	−	0.900276i	$-0.356635\pi$
$491$	1.32724e20			0.870641			0.435321	+	0.900276i	$0.356635\pi$
$492$		0			0
$493$			1.83141e20i			1.16529i
$494$	−2.47190e19			−0.154910
$495$		0			0
$496$	5.93774e18			0.0361001
$497$		−	1.84257e19i		−	0.110345i
$498$		0			0
$499$	−9.34938e18			−0.0543286			−0.0271643	−	0.999631i	$-0.508648\pi$
$499$	−9.34938e18			−0.0543286			−0.0271643	+	0.999631i	$0.508648\pi$
$500$	5.60905e19	+	1.54953e20i	0.321081	+	0.887001i
$501$		0			0
$502$			1.63198e19i			0.0906647i
$503$		−	1.56622e20i		−	0.857223i	−0.903489	−	0.428612i	$-0.859003\pi$
$503$		−	1.56622e20i		−	0.857223i	0.903489	−	0.428612i	$-0.140997\pi$
$504$		0			0
$505$	−3.17476e19	−	1.37166e19i	−0.168665	−	0.0728720i
$506$	−1.49884e19			−0.0784558
$507$		0			0
$508$		−	8.72329e19i		−	0.443305i
$509$	−1.94050e20			−0.971698			−0.485849	−	0.874043i	$-0.661489\pi$
$509$	−1.94050e20			−0.971698			−0.485849	+	0.874043i	$0.661489\pi$
$510$		0			0
$511$	7.59296e19			0.369194
$512$		−	1.95384e20i		−	0.936188i
$513$		0			0
$514$	−3.01089e18			−0.0140111
$515$	−1.03939e20	+	2.40571e20i	−0.476678	+	1.10329i
$516$		0			0
$517$			9.52252e19i			0.424202i
$518$			4.73990e19i			0.208112i
$519$		0			0
$520$	−7.25421e19	−	3.13419e19i	−0.309432	−	0.133691i
$521$	6.43719e19			0.270653			0.135327	−	0.990801i	$-0.456792\pi$
$521$	6.43719e19			0.270653			0.135327	+	0.990801i	$0.456792\pi$
$522$		0			0
$523$			1.94571e20i			0.794904i	0.917623	+	0.397452i	$0.130105\pi$
$523$			1.94571e20i			0.794904i	−0.917623	+	0.397452i	$0.869895\pi$
$524$	−2.02324e20			−0.814822
$525$		0			0
$526$	2.99433e19			0.117194
$527$		−	1.65695e19i		−	0.0639337i
$528$		0			0
$529$	7.08352e19			0.265663
$530$	1.72405e19	+	7.44877e18i	0.0637500	+	0.0275433i
$531$		0			0
$532$			1.39525e20i			0.501552i
$533$		−	1.28190e20i		−	0.454360i
$534$		0			0
$535$	−4.77779e19	+	1.10584e20i	−0.164655	+	0.381099i
$536$	1.81497e19			0.0616784
$537$		0			0
$538$			7.57175e19i			0.250224i
$539$	7.61817e19			0.248276
$540$		0			0
$541$	1.81403e19			0.0574996			0.0287498	−	0.999587i	$-0.490847\pi$
$541$	1.81403e19			0.0574996			0.0287498	+	0.999587i	$0.490847\pi$
$542$			8.03202e19i			0.251090i
$543$		0			0
$544$	−3.20737e20			−0.975344
$545$	2.17086e20	+	9.37922e19i	0.651114	+	0.281315i
$546$		0			0
$547$		−	6.00592e20i		−	1.75257i	−0.481796	−	0.876283i	$-0.660015\pi$
$547$		−	6.00592e20i		−	1.75257i	0.481796	−	0.876283i	$-0.339985\pi$
$548$			3.63588e20i			1.04654i
$549$		0			0
$550$	2.38031e19	−	2.24045e19i	0.0666674	−	0.0627502i
$551$	−2.55269e20			−0.705279
$552$		0			0
$553$			3.22352e20i			0.866746i
$554$	1.41695e20			0.375866
$555$		0			0
$556$	−6.29866e20			−1.62625
$557$			2.29611e20i			0.584895i	0.956282	+	0.292447i	$0.0944697\pi$
$557$			2.29611e20i			0.584895i	−0.956282	+	0.292447i	$0.905530\pi$
$558$		0			0
$559$	−3.36210e20			−0.833725
$560$	−8.04054e19	+	1.86101e20i	−0.196732	+	0.455344i
$561$		0			0
$562$			1.04064e20i			0.247901i
$563$		−	5.26651e20i		−	1.23797i	−0.785403	−	0.618985i	$-0.787544\pi$
$563$		−	5.26651e20i		−	1.23797i	0.785403	−	0.618985i	$-0.212456\pi$
$564$		0			0
$565$	1.57979e20	−	3.65648e20i	0.361606	−	0.836950i
$566$	4.80805e18			0.0108604
$567$		0			0
$568$			3.89799e19i			0.0857488i
$569$	−5.86825e20			−1.27399			−0.636996	−	0.770868i	$-0.719823\pi$
$569$	−5.86825e20			−1.27399			−0.636996	+	0.770868i	$0.719823\pi$
$570$		0			0
$571$	−2.76080e20			−0.583800			−0.291900	−	0.956449i	$-0.594287\pi$
$571$	−2.76080e20			−0.583800			−0.291900	+	0.956449i	$0.594287\pi$
$572$		−	1.26652e20i		−	0.264326i
$573$		0			0
$574$	4.34709e19			0.0883811
$575$	3.10952e20	−	2.92681e20i	0.623999	−	0.587335i
$576$		0			0
$577$			1.42599e20i			0.278804i	0.990236	+	0.139402i	$0.0445180\pi$
$577$			1.42599e20i			0.278804i	−0.990236	+	0.139402i	$0.955482\pi$
$578$			1.45232e20i			0.280287i
$579$		0			0
$580$	−3.63642e20	−	1.57112e20i	−0.683855	−	0.295461i
$581$	−8.64042e19			−0.160404
$582$		0			0
$583$			6.20088e19i			0.112186i
$584$	−1.60630e20			−0.286901
$585$		0			0
$586$	−1.11987e20			−0.194956
$587$			7.48323e20i			1.28618i	0.765789	+	0.643092i	$0.222349\pi$
$587$			7.48323e20i			1.28618i	−0.765789	+	0.643092i	$0.777651\pi$
$588$		0			0
$589$	2.30953e19			0.0386953
$590$	−3.99740e18	+	9.25212e18i	−0.00661283	+	0.0153056i
$591$		0			0
$592$			7.58581e20i			1.22346i
$593$		−	3.21784e20i		−	0.512454i	−0.966617	−	0.256227i	$-0.917521\pi$
$593$		−	3.21784e20i		−	0.512454i	0.966617	−	0.256227i	$-0.0824794\pi$
$594$		0			0
$595$	5.19324e20	+	2.24375e20i	0.806420	+	0.348415i
$596$	−8.95092e20			−1.37253
$597$		0			0
$598$			9.94010e19i			0.148639i
$599$	1.08146e21			1.59702			0.798509	−	0.601983i	$-0.205623\pi$
$599$	1.08146e21			1.59702			0.798509	+	0.601983i	$0.205623\pi$
$600$		0			0
$601$	5.36803e20			0.773136			0.386568	−	0.922261i	$-0.373660\pi$
$601$	5.36803e20			0.773136			0.386568	+	0.922261i	$0.373660\pi$
$602$		−	1.14013e20i		−	0.162174i
$603$		0			0
$604$	5.47820e17			0.000760083
$605$	−5.70809e20	−	2.46619e20i	−0.782213	−	0.337957i
$606$		0			0
$607$		−	4.11434e20i		−	0.550029i	−0.961440	−	0.275014i	$-0.911317\pi$
$607$		−	4.11434e20i		−	0.550029i	0.961440	−	0.275014i	$-0.0886826\pi$
$608$		−	4.47057e20i		−	0.590318i
$609$		0			0
$610$	2.13920e19	−	4.95126e19i	0.0275599	−	0.0637885i
$611$	6.31522e20			0.803673
$612$		0			0
$613$		−	5.44101e20i		−	0.675656i	−0.941208	−	0.337828i	$-0.890308\pi$
$613$		−	5.44101e20i		−	0.675656i	0.941208	−	0.337828i	$-0.109692\pi$
$614$	−3.43290e20			−0.421113
$615$		0			0
$616$	8.84786e19			0.105921
$617$		−	4.65828e20i		−	0.550918i	−0.961313	−	0.275459i	$-0.911170\pi$
$617$		−	4.65828e20i		−	0.550918i	0.961313	−	0.275459i	$-0.0888298\pi$
$618$		0			0
$619$	1.51736e21			1.75150			0.875749	−	0.482767i	$-0.160368\pi$
$619$	1.51736e21			1.75150			0.875749	+	0.482767i	$0.160368\pi$
$620$	3.29002e19	+	1.42146e19i	0.0375199	+	0.0162105i
$621$		0			0
$622$		−	3.76177e20i		−	0.418759i
$623$			6.58215e20i			0.723948i
$624$		0			0
$625$	−5.63262e19	+	9.29618e20i	−0.0604798	+	0.998169i
$626$	−1.31250e19			−0.0139249
$627$		0			0
$628$			3.21897e20i			0.333442i
$629$	2.11685e21			2.16676
$630$		0			0
$631$	5.94310e20			0.594009			0.297004	−	0.954876i	$-0.404012\pi$
$631$	5.94310e20			0.594009			0.297004	+	0.954876i	$0.404012\pi$
$632$		−	6.81941e20i		−	0.673549i
$633$		0			0
$634$	2.43097e20			0.234482
$635$	1.95530e20	−	4.52563e20i	0.186385	−	0.431396i
$636$		0			0
$637$		−	5.05228e20i		−	0.470372i
$638$			7.85777e19i			0.0723010i
$639$		0			0
$640$	3.62683e20	−	8.39444e20i	0.325970	−	0.754469i
$641$	−9.48383e20			−0.842458			−0.421229	−	0.906954i	$-0.638401\pi$
$641$	−9.48383e20			−0.842458			−0.421229	+	0.906954i	$0.638401\pi$
$642$		0			0
$643$		−	2.15909e21i		−	1.87365i	−0.349800	−	0.936824i	$-0.613750\pi$
$643$		−	2.15909e21i		−	1.87365i	0.349800	−	0.936824i	$-0.386250\pi$
$644$	5.61065e20			0.481249
$645$		0			0
$646$	−3.74365e20			−0.313727
$647$		−	2.26989e20i		−	0.188028i	−0.995571	−	0.0940139i	$-0.970030\pi$
$647$		−	2.26989e20i		−	0.188028i	0.995571	−	0.0940139i	$-0.0299698\pi$
$648$		0			0
$649$	−3.32771e19			−0.0269346
$650$	−1.48584e20	−	1.57859e20i	−0.118884	−	0.126305i
$651$		0			0
$652$			1.45474e21i			1.13744i
$653$			2.12810e21i			1.64491i	0.568830	+	0.822455i	$0.307396\pi$
$653$			2.12810e21i			1.64491i	−0.568830	+	0.822455i	$0.692604\pi$
$654$		0			0
$655$	−1.04965e21	−	4.53504e20i	−0.792932	−	0.342588i
$656$	6.95714e20			0.519580
$657$		0			0
$658$			2.14157e20i			0.156329i
$659$	−3.97715e20			−0.287032			−0.143516	−	0.989648i	$-0.545841\pi$
$659$	−3.97715e20			−0.287032			−0.143516	+	0.989648i	$0.545841\pi$
$660$		0			0
$661$	1.97089e20			0.139044			0.0695218	−	0.997580i	$-0.477853\pi$
$661$	1.97089e20			0.139044			0.0695218	+	0.997580i	$0.477853\pi$
$662$		−	2.60740e20i		−	0.181875i
$663$		0			0
$664$	1.82790e20			0.124650
$665$	−3.12743e20	+	7.23855e20i	−0.210875	+	0.488078i
$666$		0			0
$667$			1.02650e21i			0.676729i
$668$			1.22949e21i			0.801493i
$669$		0			0
$670$	4.57071e19	+	1.97478e19i	0.0291355	+	0.0125880i
$671$	1.78082e20			0.112254
$672$		0			0
$673$		−	1.12563e21i		−	0.693876i	−0.937888	−	0.346938i	$-0.887221\pi$
$673$		−	1.12563e21i		−	0.693876i	0.937888	−	0.346938i	$-0.112779\pi$
$674$	6.83781e20			0.416839
$675$		0			0
$676$	7.42265e20			0.442546
$677$			2.01414e21i			1.18761i	0.804608	+	0.593806i	$0.202375\pi$
$677$			2.01414e21i			1.18761i	−0.804608	+	0.593806i	$0.797625\pi$
$678$		0			0
$679$	1.54017e21			0.888273
$680$	−1.09864e21	−	4.74669e20i	−0.626669	−	0.270753i
$681$		0			0
$682$		−	7.10926e18i		−	0.00396681i
$683$		−	2.93860e21i		−	1.62176i	−0.585215	−	0.810878i	$-0.698990\pi$
$683$		−	2.93860e21i		−	1.62176i	0.585215	−	0.810878i	$-0.301010\pi$
$684$		0			0
$685$	−8.14974e20	+	1.88629e21i	−0.440012	+	1.01842i
$686$	4.36718e20			0.233222
$687$		0			0
$688$		−	1.82468e21i		−	0.953398i
$689$	4.11235e20			0.212542
$690$		0			0
$691$	−1.85211e20			−0.0936661			−0.0468330	−	0.998903i	$-0.514913\pi$
$691$	−1.85211e20			−0.0936661			−0.0468330	+	0.998903i	$0.514913\pi$
$692$		−	1.94808e21i		−	0.974564i
$693$		0			0
$694$	−2.35735e20			−0.115406
$695$	−3.26773e21	−	1.41183e21i	−1.58256	−	0.683748i
$696$		0			0
$697$		−	1.94142e21i		−	0.920182i
$698$			3.24058e20i			0.151952i
$699$		0			0
$700$	−8.91032e20	+	8.38678e20i	−0.408939	+	0.384911i
$701$	1.53115e21			0.695236			0.347618	−	0.937636i	$-0.386991\pi$
$701$	1.53115e21			0.695236			0.347618	+	0.937636i	$0.386991\pi$
$702$		0			0
$703$			2.95056e21i			1.31141i
$704$	5.91046e20			0.259912
$705$		0			0
$706$	−1.70747e20			−0.0735050
$707$		−	2.56800e20i		−	0.109383i
$708$		0			0
$709$	−1.28361e19			−0.00535287			−0.00267643	−	0.999996i	$-0.500852\pi$
$709$	−1.28361e19			−0.00535287			−0.00267643	+	0.999996i	$0.500852\pi$
$710$	−4.24122e19	+	9.81646e19i	−0.0175006	+	0.0405058i
$711$		0			0
$712$		−	1.39247e21i		−	0.562581i
$713$		−	9.28717e19i		−	0.0371289i
$714$		0			0
$715$	2.83886e20	−	6.57066e20i	0.111135	−	0.257225i
$716$	−6.51244e20			−0.252288
$717$		0			0
$718$			8.12495e20i			0.308239i
$719$	3.14657e21			1.18133			0.590665	−	0.806917i	$-0.298866\pi$
$719$	3.14657e21			1.18133			0.590665	+	0.806917i	$0.298866\pi$
$720$		0			0
$721$	−1.94594e21			−0.715508
$722$			1.32409e20i			0.0481825i
$723$		0			0
$724$	5.39507e20			0.192291
$725$	−1.53440e21	−	1.63019e21i	−0.541259	−	0.575047i
$726$		0			0
$727$			4.52609e21i			1.56392i	0.623327	+	0.781962i	$0.285781\pi$
$727$			4.52609e21i			1.56392i	−0.623327	+	0.781962i	$0.714219\pi$
$728$		−	5.86780e20i		−	0.200673i
$729$		0			0
$730$	−4.04522e20	−	1.74775e20i	−0.135526	−	0.0585540i
$731$	−5.09186e21			−1.68848
$732$		0			0
$733$			2.68116e21i			0.871048i	0.900177	+	0.435524i	$0.143437\pi$
$733$			2.68116e21i			0.871048i	−0.900177	+	0.435524i	$0.856563\pi$
$734$	−4.40539e20			−0.141666
$735$		0			0
$736$	−1.79772e21			−0.566421
$737$			1.64395e20i			0.0512721i
$738$		0			0
$739$	−1.15277e21			−0.352298			−0.176149	−	0.984364i	$-0.556364\pi$
$739$	−1.15277e21			−0.352298			−0.176149	+	0.984364i	$0.556364\pi$
$740$	−1.81600e21	+	4.20320e21i	−0.549386	+	1.27157i
$741$		0			0
$742$			1.39455e20i			0.0413433i
$743$			2.64683e21i			0.776801i	0.921491	+	0.388400i	$0.126972\pi$
$743$			2.64683e21i			0.776801i	−0.921491	+	0.388400i	$0.873028\pi$
$744$		0			0
$745$	−4.64372e21	−	2.00633e21i	−1.33565	−	0.577072i
$746$	8.03905e20			0.228909
$747$		0			0
$748$		−	1.91812e21i		−	0.535320i
$749$	−8.94493e20			−0.247151
$750$		0			0
$751$	−4.36972e21			−1.18346			−0.591730	−	0.806136i	$-0.701555\pi$
$751$	−4.36972e21			−1.18346			−0.591730	+	0.806136i	$0.701555\pi$
$752$			3.42740e21i			0.919033i
$753$		0			0
$754$	5.21118e20			0.136978
$755$	2.84208e18	+	1.22793e18i	0.000739664	+	0.000319573i
$756$		0			0
$757$		−	7.25274e20i		−	0.185047i	−0.995710	−	0.0925237i	$-0.970507\pi$
$757$		−	7.25274e20i		−	0.185047i	0.995710	−	0.0925237i	$-0.0294934\pi$
$758$			1.56398e21i			0.395105i
$759$		0			0
$760$	6.61613e20	−	1.53133e21i	0.163871	−	0.379286i
$761$	−2.04957e21			−0.502665			−0.251333	−	0.967901i	$-0.580869\pi$
$761$	−2.04957e21			−0.502665			−0.251333	+	0.967901i	$0.580869\pi$
$762$		0			0
$763$			1.75597e21i			0.422262i
$764$	5.65419e21			1.34639
$765$		0			0
$766$	1.46447e21			0.341952
$767$			2.20690e20i			0.0510290i
$768$		0			0
$769$	−2.52209e21			−0.571891			−0.285945	−	0.958246i	$-0.592308\pi$
$769$	−2.52209e21			−0.571891			−0.285945	+	0.958246i	$0.592308\pi$
$770$	2.22819e20	+	9.62695e19i	0.0500349	+	0.0216176i
$771$		0			0
$772$		−	1.40428e21i		−	0.309260i
$773$		−	2.53203e21i		−	0.552233i	−0.961124	−	0.276117i	$-0.910952\pi$
$773$		−	2.53203e21i		−	0.552233i	0.961124	−	0.276117i	$-0.0890476\pi$
$774$		0			0
$775$	1.38824e20	+	1.47490e20i	0.0296963	+	0.0315501i
$776$	−3.25827e21			−0.690277
$777$		0			0
$778$			1.91205e21i			0.397330i
$779$	2.70603e21			0.556932
$780$		0			0
$781$	−3.53069e20			−0.0712815
$782$			1.50541e21i			0.301027i
$783$		0			0
$784$	2.74198e21			0.537890
$785$	−7.21525e20	+	1.67000e21i	−0.140194	+	0.324484i
$786$		0			0
$787$		−	1.39343e21i		−	0.265629i	−0.991141	−	0.132814i	$-0.957599\pi$
$787$		−	1.39343e21i		−	0.265629i	0.991141	−	0.132814i	$-0.0424014\pi$
$788$		−	7.86468e21i		−	1.48503i
$789$		0			0
$790$	7.41989e20	−	1.71736e21i	0.137466	−	0.318169i
$791$	2.95766e21			0.542781
$792$		0			0
$793$		−	1.18102e21i		−	0.212671i
$794$	6.21853e20			0.110926
$795$		0			0
$796$	5.41398e21			0.947695
$797$			9.55241e20i			0.165644i	0.996564	+	0.0828220i	$0.0263933\pi$
$797$			9.55241e20i			0.165644i	−0.996564	+	0.0828220i	$0.973607\pi$
$798$		0			0
$799$	9.56431e21			1.62762
$800$	2.85498e21	−	2.68723e21i	0.481313	−	0.453033i
$801$		0			0
$802$			1.01196e21i			0.167439i
$803$		−	1.45495e21i		−	0.238496i
$804$		0			0
$805$	2.91080e21	+	1.25762e21i	0.468320	+	0.202339i
$806$	−4.71478e19			−0.00751533
$807$		0			0
$808$			5.43266e20i			0.0850016i
$809$	9.73892e21			1.50972			0.754861	−	0.655885i	$-0.227704\pi$
$809$	9.73892e21			1.50972			0.754861	+	0.655885i	$0.227704\pi$
$810$		0			0
$811$	4.03949e20			0.0614711			0.0307355	−	0.999528i	$-0.490215\pi$
$811$	4.03949e20			0.0614711			0.0307355	+	0.999528i	$0.490215\pi$
$812$		−	2.94143e21i		−	0.443495i
$813$		0			0
$814$	9.08249e20			0.134438
$815$	−3.26076e21	+	7.54715e21i	−0.478230	+	1.10688i
$816$		0			0
$817$		−	7.09724e21i		−	1.02194i
$818$			1.72017e21i			0.245427i
$819$		0			0
$820$	3.85486e21	+	1.66550e21i	0.540014	+	0.233314i
$821$	−1.42068e22			−1.97207			−0.986034	−	0.166541i	$-0.946740\pi$
$821$	−1.42068e22			−1.97207			−0.986034	+	0.166541i	$0.946740\pi$
$822$		0			0
$823$			6.03911e21i			0.823141i	0.911378	+	0.411570i	$0.135020\pi$
$823$			6.03911e21i			0.823141i	−0.911378	+	0.411570i	$0.864980\pi$
$824$	4.11667e21			0.556022
$825$		0			0
$826$	−7.48387e19			−0.00992604
$827$		−	1.20995e22i		−	1.59029i	−0.606421	−	0.795144i	$-0.707395\pi$
$827$		−	1.20995e22i		−	1.59029i	0.606421	−	0.795144i	$-0.292605\pi$
$828$		0			0
$829$	−5.90195e21			−0.761792			−0.380896	−	0.924618i	$-0.624384\pi$
$829$	−5.90195e21			−0.761792			−0.380896	+	0.924618i	$0.624384\pi$
$830$	4.60327e20	+	1.98885e20i	0.0588818	+	0.0254400i
$831$		0			0
$832$		−	3.91974e21i		−	0.492417i
$833$		−	7.65160e21i		−	0.952610i
$834$		0			0
$835$	−2.75586e21	+	6.37855e21i	−0.336984	+	0.779962i
$836$	2.67355e21			0.323998
$837$		0			0
$838$			3.08746e21i			0.367512i
$839$	−1.29661e22			−1.52966			−0.764831	−	0.644231i	$-0.777178\pi$
$839$	−1.29661e22			−1.52966			−0.764831	+	0.644231i	$0.777178\pi$
$840$		0			0
$841$	−3.24768e21			−0.376360
$842$			2.68131e20i			0.0307969i
$843$		0			0
$844$	1.10951e22			1.25188
$845$	3.85086e21	+	1.66377e21i	0.430657	+	0.186066i
$846$		0			0
$847$		−	4.61717e21i		−	0.507283i
$848$			2.23186e21i			0.243051i
$849$		0			0
$850$	−2.25028e21	−	2.39076e21i	−0.240766	−	0.255796i
$851$	1.18649e22			1.25832
$852$		0			0
$853$		−	9.05799e21i		−	0.943874i	−0.881632	−	0.471937i	$-0.843555\pi$
$853$		−	9.05799e21i		−	0.943874i	0.881632	−	0.471937i	$-0.156445\pi$
$854$	4.00499e20			0.0413682
$855$		0			0
$856$	1.89232e21			0.192061
$857$			1.80435e22i			1.81536i	0.419660	+	0.907682i	$0.362149\pi$
$857$			1.80435e22i			1.81536i	−0.419660	+	0.907682i	$0.637851\pi$
$858$		0			0
$859$	−2.44689e21			−0.241916			−0.120958	−	0.992658i	$-0.538597\pi$
$859$	−2.44689e21			−0.241916			−0.120958	+	0.992658i	$0.538597\pi$
$860$	4.36819e21	−	1.01103e22i	0.428117	−	0.990894i
$861$		0			0
$862$		−	2.12467e21i		−	0.204638i
$863$			9.95152e21i			0.950185i	0.879936	+	0.475093i	$0.157585\pi$
$863$			9.95152e21i			0.950185i	−0.879936	+	0.475093i	$0.842415\pi$
$864$		0			0
$865$	4.36657e21	−	1.01066e22i	0.409750	−	0.948383i
$866$	−6.86979e20			−0.0639086
$867$		0			0
$868$			2.66124e20i			0.0243325i
$869$	6.17683e21			0.559909
$870$		0			0
$871$	1.09025e21			0.0971378
$872$		−	3.71478e21i		−	0.328140i
$873$		0			0
$874$	−2.09831e21			−0.182194
$875$	−6.50254e21	+	2.35382e21i	−0.559786	+	0.202634i
$876$		0			0
$877$			1.75476e22i			1.48498i	0.669855	+	0.742492i	$0.266356\pi$
$877$			1.75476e22i			1.48498i	−0.669855	+	0.742492i	$0.733644\pi$
$878$			5.43734e20i			0.0456224i
$879$		0			0
$880$	3.56603e21	+	1.54071e21i	0.294148	+	0.127087i
$881$	1.45628e22			1.19104			0.595520	−	0.803341i	$-0.296946\pi$
$881$	1.45628e22			1.19104			0.595520	+	0.803341i	$0.296946\pi$
$882$		0			0
$883$		−	1.28619e22i		−	1.03419i	−0.855928	−	0.517095i	$-0.827013\pi$
$883$		−	1.28619e22i		−	1.03419i	0.855928	−	0.517095i	$-0.172987\pi$
$884$	−1.27207e22			−1.01419
$885$		0			0
$886$	3.40425e21			0.266851
$887$		−	1.46337e22i		−	1.13743i	−0.822534	−	0.568716i	$-0.807440\pi$
$887$		−	1.46337e22i		−	1.13743i	0.822534	−	0.568716i	$-0.192560\pi$
$888$		0			0
$889$	3.66070e21			0.279770
$890$	1.51508e21	−	3.50671e21i	0.114818	−	0.265751i
$891$		0			0
$892$		−	2.63086e21i		−	0.196048i
$893$			1.33311e22i			0.985102i
$894$		0			0
$895$	−3.37864e21	−	1.45975e21i	−0.245510	−	0.106073i
$896$	6.79011e21			0.489290
$897$		0			0
$898$			1.88078e21i			0.133280i
$899$	−4.86888e20			−0.0342162
$900$		0			0
$901$	6.22809e21			0.430446
$902$		−	8.32980e20i		−	0.0570933i
$903$		0			0
$904$	−6.25698e21			−0.421795
$905$	2.79895e21	+	1.20929e21i	0.187125	+	0.0808476i
$906$		0			0
$907$			4.06427e21i			0.267256i	0.991032	+	0.133628i	$0.0426627\pi$
$907$			4.06427e21i			0.267256i	−0.991032	+	0.133628i	$0.957337\pi$
$908$			2.54172e21i			0.165762i
$909$		0			0
$910$	6.38448e20	−	1.47771e21i	0.0409558	−	0.0947937i
$911$	−6.36749e21			−0.405117			−0.202558	−	0.979270i	$-0.564926\pi$
$911$	−6.36749e21			−0.405117			−0.202558	+	0.979270i	$0.564926\pi$
$912$		0			0
$913$			1.65566e21i			0.103619i
$914$	−4.33181e21			−0.268889
$915$		0			0
$916$	−1.20942e22			−0.738515
$917$		−	8.49045e21i		−	0.514234i
$918$		0			0
$919$	−2.93596e22			−1.74938			−0.874690	−	0.484682i	$-0.838935\pi$
$919$	−2.93596e22			−1.74938			−0.874690	+	0.484682i	$0.838935\pi$
$920$	−6.15785e21	−	2.66051e21i	−0.363932	−	0.157237i
$921$		0			0
$922$		−	4.70837e21i		−	0.273772i
$923$			2.34151e21i			0.135046i
$924$		0			0
$925$	−1.88427e22	+	1.77356e22i	−1.06925	+	1.00643i
$926$	−7.82241e21			−0.440310
$927$		0			0
$928$			9.42472e21i			0.521986i
$929$	−3.30652e22			−1.81658			−0.908288	−	0.418347i	$-0.862610\pi$
$929$	−3.30652e22			−1.81658			−0.908288	+	0.418347i	$0.862610\pi$
$930$		0			0
$931$	1.06651e22			0.576558
$932$			2.93671e22i			1.57486i
$933$		0			0
$934$	4.91479e21			0.259360
$935$	4.29942e21	−	9.95117e21i	0.225073	−	0.520939i
$936$		0			0
$937$			3.47429e22i			1.78986i	0.446205	+	0.894931i	$0.352775\pi$
$937$			3.47429e22i			1.78986i	−0.446205	+	0.894931i	$0.647225\pi$
$938$			3.69716e20i			0.0188950i
$939$		0			0
$940$	−8.20500e21	+	1.89908e22i	−0.412686	+	0.955177i
$941$	2.80935e21			0.140179			0.0700897	−	0.997541i	$-0.477671\pi$
$941$	2.80935e21			0.140179			0.0700897	+	0.997541i	$0.477671\pi$
$942$		0			0
$943$		−	1.08816e22i		−	0.534387i
$944$	−1.19773e21			−0.0583538
$945$		0			0
$946$	−2.18470e21			−0.104763
$947$			9.11666e21i			0.433722i	0.976203	+	0.216861i	$0.0695818\pi$
$947$			9.11666e21i			0.433722i	−0.976203	+	0.216861i	$0.930418\pi$
$948$		0			0
$949$	−9.64903e21			−0.451842
$950$	3.33234e21	−	3.13654e21i	0.154818	−	0.145722i
$951$		0			0
$952$		−	8.88669e21i		−	0.406409i
$953$		−	1.41863e22i		−	0.643682i	−0.946794	−	0.321841i	$-0.895698\pi$
$953$		−	1.41863e22i		−	0.643682i	0.946794	−	0.321841i	$-0.104302\pi$
$954$		0			0
$955$	2.93338e22	+	1.26737e22i	1.31022	+	0.566082i
$956$	−9.44433e21			−0.418540
$957$		0			0
$958$			5.21910e21i			0.227695i
$959$	−1.52578e22			−0.660471
$960$		0			0
$961$	−2.34212e22			−0.998123
$962$		−	6.02340e21i		−	0.254700i
$963$		0			0
$964$	−3.85102e22			−1.60324
$965$	3.14766e21	−	7.28538e21i	0.130027	−	0.300952i
$966$		0			0
$967$		−	1.40091e22i		−	0.569785i	−0.958560	−	0.284892i	$-0.908042\pi$
$967$		−	1.40091e22i		−	0.569785i	0.958560	−	0.284892i	$-0.0919578\pi$
$968$			9.76770e21i			0.394210i
$969$		0			0
$970$	−8.20543e21	−	3.54517e21i	−0.326072	−	0.140880i
$971$	3.55233e22			1.40078			0.700388	−	0.713762i	$-0.253010\pi$
$971$	3.55233e22			1.40078			0.700388	+	0.713762i	$0.253010\pi$
$972$		0			0
$973$		−	2.64321e22i		−	1.02633i
$974$	−4.31237e21			−0.166159
$975$		0			0
$976$	6.40963e21			0.243198
$977$		−	2.18841e22i		−	0.823985i	−0.911187	−	0.411993i	$-0.864833\pi$
$977$		−	2.18841e22i		−	0.823985i	0.911187	−	0.411993i	$-0.135167\pi$
$978$		0			0
$979$	1.26126e22			0.467663
$980$	1.51929e22	+	6.56413e21i	0.559044	+	0.241536i
$981$		0			0
$982$		−	5.71962e21i		−	0.207267i
$983$			6.12627e21i			0.220315i	0.993914	+	0.110158i	$0.0351356\pi$
$983$			6.12627e21i			0.220315i	−0.993914	+	0.110158i	$0.964864\pi$
$984$		0			0
$985$	1.76285e22	−	4.08018e22i	0.624372	−	1.44513i
$986$	7.89226e21			0.277411
$987$		0			0
$988$		−	1.77307e22i		−	0.613831i
$989$	−2.85397e22			−0.980568
$990$		0			0
$991$	3.50331e22			1.18557			0.592784	−	0.805361i	$-0.298029\pi$
$991$	3.50331e22			1.18557			0.592784	+	0.805361i	$0.298029\pi$
$992$		−	8.52695e20i		−	0.0286389i
$993$		0			0
$994$	−7.94036e20			−0.0262689
$995$	2.80876e22	+	1.21353e22i	0.922236	+	0.398453i
$996$		0			0
$997$			3.84796e22i			1.24456i	0.782793	+	0.622282i	$0.213794\pi$
$997$			3.84796e22i			1.24456i	−0.782793	+	0.622282i	$0.786206\pi$
$998$			4.02902e20i			0.0129336i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.16.b.b.19.3		6
3.2	odd	2		5.16.b.a.4.4	yes	6
5.4	even	2	inner	45.16.b.b.19.4		6
12.11	even	2		80.16.c.a.49.1		6
15.2	even	4		25.16.a.f.1.3		6
15.8	even	4		25.16.a.f.1.4		6
15.14	odd	2		5.16.b.a.4.3	✓	6
60.59	even	2		80.16.c.a.49.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.16.b.a.4.3	✓	6	15.14	odd	2
5.16.b.a.4.4	yes	6	3.2	odd	2
25.16.a.f.1.3		6	15.2	even	4
25.16.a.f.1.4		6	15.8	even	4
45.16.b.b.19.3		6	1.1	even	1	trivial
45.16.b.b.19.4		6	5.4	even	2	inner
80.16.c.a.49.1		6	12.11	even	2
80.16.c.a.49.6		6	60.59	even	2

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	45.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-43.0940i q^{2} +30910.9 q^{4} +(160365. + 69286.1i) q^{5} +1.29717e6i q^{7} -2.74418e6i q^{8} +O(q^{10})\)	\(q-43.0940i q^{2} +30910.9 q^{4} +(160365. + 69286.1i) q^{5} +1.29717e6i q^{7} -2.74418e6i q^{8} +(2.98581e6 - 6.91078e6i) q^{10} +2.48560e7 q^{11} -1.64842e8i q^{13} +5.59000e7 q^{14} +8.94631e8 q^{16} -2.49651e9i q^{17} +3.47974e9 q^{19} +(4.95704e9 + 2.14170e9i) q^{20} -1.07114e9i q^{22} -1.39929e10i q^{23} +(2.09165e10 + 2.22222e10i) q^{25} -7.10369e9 q^{26} +4.00966e10i q^{28} -7.33587e10 q^{29} +6.63708e9 q^{31} -1.28474e11i q^{32} -1.07584e11 q^{34} +(-8.98755e10 + 2.08020e11i) q^{35} +8.47925e11i q^{37} -1.49956e11i q^{38} +(1.90133e11 - 4.40071e11i) q^{40} +7.77655e11 q^{41} -2.03959e12i q^{43} +7.68321e11 q^{44} -6.03008e11 q^{46} +3.83108e12i q^{47} +3.06492e12 q^{49} +(9.57641e11 - 9.01373e11i) q^{50} -5.09541e12i q^{52} +2.49472e12i q^{53} +(3.98604e12 + 1.72217e12i) q^{55} +3.55965e12 q^{56} +3.16132e12i q^{58} -1.33880e12 q^{59} +7.16455e12 q^{61} -2.86018e11i q^{62} +2.37788e13 q^{64} +(1.14213e13 - 2.64349e13i) q^{65} +6.61388e12i q^{67} -7.71693e13i q^{68} +(8.96442e12 + 3.87309e12i) q^{70} -1.42046e13 q^{71} -5.85350e13i q^{73} +3.65405e13 q^{74} +1.07562e14 q^{76} +3.22423e13i q^{77} +2.48505e14 q^{79} +(1.43468e14 + 6.19855e13i) q^{80} -3.35122e13i q^{82} +6.66100e13i q^{83} +(1.72973e14 - 4.00353e14i) q^{85} -8.78941e13 q^{86} -6.82092e13i q^{88} +5.07426e14 q^{89} +2.13827e14 q^{91} -4.32532e14i q^{92} +1.65096e14 q^{94} +(5.58029e14 + 2.41097e14i) q^{95} -1.18734e15i q^{97} -1.32080e14i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 38568 q^{4} + 238350 q^{5}+O(q^{10}) \) 6 * q - 38568 * q^4 + 238350 * q^5	\( 6 q - 38568 q^{4} + 238350 q^{5} - 48274200 q^{10} + 108590088 q^{11} - 663751704 q^{14} + 1155522336 q^{16} - 3630995640 q^{19} - 2533753800 q^{20} + 18250878750 q^{25} + 81970953168 q^{26} - 286168468740 q^{29} - 276236748288 q^{31} - 127784939136 q^{34} - 1171274911800 q^{35} + 4214283852000 q^{40} + 6153278882388 q^{41} - 8250173021664 q^{44} - 23334602656488 q^{46} + 11613390856242 q^{49} - 23694218070000 q^{50} + 33977390365800 q^{55} + 59280484297440 q^{56} - 14903258326680 q^{59} - 11352061428588 q^{61} + 73265851251072 q^{64} + 50675287275600 q^{65} - 156447825521400 q^{70} - 131693145807312 q^{71} + 353606797863216 q^{74} + 959127540575520 q^{76} - 26081853939360 q^{79} + 552945514077600 q^{80} - 548221025491200 q^{85} - 598387757484072 q^{86} - 59269690709820 q^{89} + 821206462566672 q^{91} - 308164835928456 q^{94} - 232287694599000 q^{95}+O(q^{100}) \) 6 * q - 38568 * q^4 + 238350 * q^5 - 48274200 * q^10 + 108590088 * q^11 - 663751704 * q^14 + 1155522336 * q^16 - 3630995640 * q^19 - 2533753800 * q^20 + 18250878750 * q^25 + 81970953168 * q^26 - 286168468740 * q^29 - 276236748288 * q^31 - 127784939136 * q^34 - 1171274911800 * q^35 + 4214283852000 * q^40 + 6153278882388 * q^41 - 8250173021664 * q^44 - 23334602656488 * q^46 + 11613390856242 * q^49 - 23694218070000 * q^50 + 33977390365800 * q^55 + 59280484297440 * q^56 - 14903258326680 * q^59 - 11352061428588 * q^61 + 73265851251072 * q^64 + 50675287275600 * q^65 - 156447825521400 * q^70 - 131693145807312 * q^71 + 353606797863216 * q^74 + 959127540575520 * q^76 - 26081853939360 * q^79 + 552945514077600 * q^80 - 548221025491200 * q^85 - 598387757484072 * q^86 - 59269690709820 * q^89 + 821206462566672 * q^91 - 308164835928456 * q^94 - 232287694599000 * q^95

Introduction

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