LMFDB - Embedded newform 36.17.d.d.19.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,17,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, 17, names="a")

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

chi := DirichletCharacter("36.19");

S:= CuspForms(chi, 17);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 17 $
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:	$58.4368357884$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 83552 x^{14} - 1250532 x^{13} + 2808691818 x^{12} + 87176344944 x^{11} + \cdots + 22\!\cdots\!21 $ x^16 - 4x^15 - 83552x^14 - 1250532x^13 + 2808691818x^12 + 87176344944x^11 - 47760450026156x^10 - 2100222815971876x^9 + 425922111405607783x^8 + 22882678437708043392x^7 - 1895650750656864990684x^6 - 113810021245037478984132x^5 + 3885062818618335391872478x^4 + 240157126218264232633038164x^3 - 3336663916697285979405987668x^2 - 149808504442972901044544769648*x + 2248422306669320127742190566821
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{113}\cdot 3^{52} $
Twist minimal:	no (minimal twist has level 12)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.16
Root			$-120.624 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	36.19
Dual form			36.17.d.d.19.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(254.964 + 23.0089i) q^{2} +(64477.2 + 11732.9i) q^{4} +363465. q^{5} +2.07768e6i q^{7} +(1.61694e7 + 4.47501e6i) q^{8} +O(q^{10})$	\(q+(254.964 + 23.0089i) q^{2} +(64477.2 + 11732.9i) q^{4} +363465. q^{5} +2.07768e6i q^{7} +(1.61694e7 + 4.47501e6i) q^{8} +(9.26704e7 + 8.36292e6i) q^{10} -4.00917e8i q^{11} +2.75836e8 q^{13} +(-4.78050e7 + 5.29733e8i) q^{14} +(4.01965e9 + 1.51300e9i) q^{16} +7.49616e9 q^{17} -1.26547e10i q^{19} +(2.34352e10 + 4.26449e9i) q^{20} +(9.22466e9 - 1.02219e11i) q^{22} +1.11334e11i q^{23} -2.04812e10 q^{25} +(7.03282e10 + 6.34667e9i) q^{26} +(-2.43771e10 + 1.33963e11i) q^{28} -4.40939e11 q^{29} -9.68295e11i q^{31} +(9.90052e11 + 4.78249e11i) q^{32} +(1.91125e12 + 1.72478e11i) q^{34} +7.55163e11i q^{35} +2.64747e12 q^{37} +(2.91170e11 - 3.22649e12i) q^{38} +(5.87701e12 + 1.62651e12i) q^{40} +7.96145e12 q^{41} -6.27235e12i q^{43} +(4.70391e12 - 2.58500e13i) q^{44} +(-2.56167e12 + 2.83861e13i) q^{46} +1.17525e13i q^{47} +2.89162e13 q^{49} +(-5.22196e12 - 4.71249e11i) q^{50} +(1.77851e13 + 3.23635e12i) q^{52} +5.56077e13 q^{53} -1.45719e14i q^{55} +(-9.29762e12 + 3.35948e13i) q^{56} +(-1.12423e14 - 1.01455e13i) q^{58} +2.82548e14i q^{59} -1.86371e14 q^{61} +(2.22794e13 - 2.46880e14i) q^{62} +(2.41424e14 + 1.44716e14i) q^{64} +1.00257e14 q^{65} +8.81821e13i q^{67} +(4.83331e14 + 8.79514e13i) q^{68} +(-1.73755e13 + 1.92539e14i) q^{70} -1.09310e15i q^{71} +5.03458e14 q^{73} +(6.75009e14 + 6.09153e13i) q^{74} +(1.48476e14 - 8.15939e14i) q^{76} +8.32977e14 q^{77} +1.56854e15i q^{79} +(1.46100e15 + 5.49924e14i) q^{80} +(2.02988e15 + 1.83184e14i) q^{82} -8.07330e14i q^{83} +2.72459e15 q^{85} +(1.44320e14 - 1.59922e15i) q^{86} +(1.79411e15 - 6.48259e15i) q^{88} +5.95350e15 q^{89} +5.73098e14i q^{91} +(-1.30626e15 + 7.17849e15i) q^{92} +(-2.70411e14 + 2.99645e15i) q^{94} -4.59954e15i q^{95} -2.50681e15 q^{97} +(7.37258e15 + 6.65329e14i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 186 q^{2} + 136588 q^{4} - 354144 q^{5} - 14683680 q^{8}+O(q^{10}) $ 16 * q + 186 * q^2 + 136588 * q^4 - 354144 * q^5 - 14683680 * q^8	$ 16 q + 186 q^{2} + 136588 q^{4} - 354144 q^{5} - 14683680 q^{8} - 49800172 q^{10} - 906419296 q^{13} + 806064072 q^{14} - 2108540816 q^{16} - 12240765600 q^{17} - 1002788712 q^{20} + 216706355928 q^{22} + 206381182512 q^{25} - 1054507182588 q^{26} - 1526063922288 q^{28} - 327679573728 q^{29} + 5158730488416 q^{32} + 9473293385948 q^{34} - 8149494749152 q^{37} - 23318999782920 q^{38} - 28671795971776 q^{40} + 25536724613472 q^{41} + 11442227373552 q^{44} + 9929654732736 q^{46} - 93287012964080 q^{49} + 133601044957998 q^{50} + 302261844234872 q^{52} + 86928436629792 q^{53} - 530930989929024 q^{56} - 189801665049916 q^{58} + 476028596468000 q^{61} + 419080420491096 q^{62} + 305944925720704 q^{64} + 12\!\cdots\!92 q^{65}+ \cdots + 33\!\cdots\!90 q^{98}+O(q^{100}) $ 16 * q + 186 * q^2 + 136588 * q^4 - 354144 * q^5 - 14683680 * q^8 - 49800172 * q^10 - 906419296 * q^13 + 806064072 * q^14 - 2108540816 * q^16 - 12240765600 * q^17 - 1002788712 * q^20 + 216706355928 * q^22 + 206381182512 * q^25 - 1054507182588 * q^26 - 1526063922288 * q^28 - 327679573728 * q^29 + 5158730488416 * q^32 + 9473293385948 * q^34 - 8149494749152 * q^37 - 23318999782920 * q^38 - 28671795971776 * q^40 + 25536724613472 * q^41 + 11442227373552 * q^44 + 9929654732736 * q^46 - 93287012964080 * q^49 + 133601044957998 * q^50 + 302261844234872 * q^52 + 86928436629792 * q^53 - 530930989929024 * q^56 - 189801665049916 * q^58 + 476028596468000 * q^61 + 419080420491096 * q^62 + 305944925720704 * q^64 + 1276571708976192 * q^65 + 1393626893610696 * q^68 + 1815049064679696 * q^70 - 368686901901280 * q^73 - 875633111941836 * q^74 - 4351002030861264 * q^76 + 81504772370688 * q^77 + 8190389938127328 * q^80 + 2390391408733340 * q^82 + 10085047677398464 * q^85 + 894939801424296 * q^86 + 669091386916800 * q^88 + 5711067674201568 * q^89 - 7708247605922304 * q^92 - 9487273535547696 * q^94 - 13564951560560608 * q^97 + 33011660914531290 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	254.964	+	23.0089i	0.995953	+	0.0898784i
$2$	254.964	+	23.0089i	0.995953	+	0.0898784i
$3$		0			0
$3$		0			0
$4$	64477.2	+	11732.9i	0.983844	+	0.179029i
$5$	363465.			0.930470			0.465235	−	0.885187i	$-0.345970\pi$
$5$	363465.			0.930470			0.465235	+	0.885187i	$0.345970\pi$
$6$		0			0
$7$			2.07768e6i			0.360408i	0.983629	+	0.180204i	$0.0576757\pi$
$7$			2.07768e6i			0.360408i	−0.983629	+	0.180204i	$0.942324\pi$
$8$	1.61694e7	+	4.47501e6i	0.963771	+	0.266731i
$9$		0			0
$10$	9.26704e7	+	8.36292e6i	0.926704	+	0.0836292i
$11$		−	4.00917e8i		−	1.87031i	−0.354240	−	0.935154i	$-0.615261\pi$
$11$		−	4.00917e8i		−	1.87031i	0.354240	−	0.935154i	$-0.384739\pi$
$12$		0			0
$13$	2.75836e8			0.338146			0.169073	−	0.985604i	$-0.445923\pi$
$13$	2.75836e8			0.338146			0.169073	+	0.985604i	$0.445923\pi$
$14$	−4.78050e7	+	5.29733e8i	−0.0323929	+	0.358949i
$15$		0			0
$16$	4.01965e9	+	1.51300e9i	0.935897	+	0.352274i
$17$	7.49616e9			1.07460			0.537301	−	0.843391i	$-0.319444\pi$
$17$	7.49616e9			1.07460			0.537301	+	0.843391i	$0.319444\pi$
$18$		0			0
$19$		−	1.26547e10i		−	0.745115i	−0.928009	−	0.372557i	$-0.878481\pi$
$19$		−	1.26547e10i		−	0.745115i	0.928009	−	0.372557i	$-0.121519\pi$
$20$	2.34352e10	+	4.26449e9i	0.915437	+	0.166581i
$21$		0			0
$22$	9.22466e9	−	1.02219e11i	0.168100	−	1.86274i
$23$			1.11334e11i			1.42169i	0.703350	+	0.710844i	$0.251687\pi$
$23$			1.11334e11i			1.42169i	−0.703350	+	0.710844i	$0.748313\pi$
$24$		0			0
$25$	−2.04812e10			−0.134225
$26$	7.03282e10	+	6.34667e9i	0.336777	+	0.0303920i
$27$		0			0
$28$	−2.43771e10	+	1.33963e11i	−0.0645235	+	0.354585i
$29$	−4.40939e11			−0.881443			−0.440722	−	0.897644i	$-0.645277\pi$
$29$	−4.40939e11			−0.881443			−0.440722	+	0.897644i	$0.645277\pi$
$30$		0			0
$31$		−	9.68295e11i		−	1.13531i	−0.823267	−	0.567654i	$-0.807851\pi$
$31$		−	9.68295e11i		−	1.13531i	0.823267	−	0.567654i	$-0.192149\pi$
$32$	9.90052e11	+	4.78249e11i	0.900447	+	0.434965i
$33$		0			0
$34$	1.91125e12	+	1.72478e11i	1.07025	+	0.0965835i
$35$			7.55163e11i			0.335348i
$36$		0			0
$37$	2.64747e12			0.753732			0.376866	−	0.926268i	$-0.377002\pi$
$37$	2.64747e12			0.753732			0.376866	+	0.926268i	$0.377002\pi$
$38$	2.91170e11	−	3.22649e12i	0.0669697	−	0.742099i
$39$		0			0
$40$	5.87701e12	+	1.62651e12i	0.896760	+	0.248185i
$41$	7.96145e12			0.997059			0.498530	−	0.866873i	$-0.333873\pi$
$41$	7.96145e12			0.997059			0.498530	+	0.866873i	$0.333873\pi$
$42$		0			0
$43$		−	6.27235e12i		−	0.536639i	−0.963330	−	0.268320i	$-0.913532\pi$
$43$		−	6.27235e12i		−	0.536639i	0.963330	−	0.268320i	$-0.0864684\pi$
$44$	4.70391e12	−	2.58500e13i	0.334840	−	1.84009i
$45$		0			0
$46$	−2.56167e12	+	2.83861e13i	−0.127779	+	1.41593i
$47$			1.17525e13i			0.493567i	0.969071	+	0.246783i	$0.0793736\pi$
$47$			1.17525e13i			0.493567i	−0.969071	+	0.246783i	$0.920626\pi$
$48$		0			0
$49$	2.89162e13			0.870106
$50$	−5.22196e12	−	4.71249e11i	−0.133682	−	0.0120640i
$51$		0			0
$52$	1.77851e13	+	3.23635e12i	0.332683	+	0.0605380i
$53$	5.56077e13			0.893157			0.446578	−	0.894745i	$-0.352642\pi$
$53$	5.56077e13			0.893157			0.446578	+	0.894745i	$0.352642\pi$
$54$		0			0
$55$		−	1.45719e14i		−	1.74027i
$56$	−9.29762e12	+	3.35948e13i	−0.0961319	+	0.347350i
$57$		0			0
$58$	−1.12423e14	−	1.01455e13i	−0.877876	−	0.0792227i
$59$			2.82548e14i			1.92431i	0.272498	+	0.962156i	$0.412150\pi$
$59$			2.82548e14i			1.92431i	−0.272498	+	0.962156i	$0.587850\pi$
$60$		0			0
$61$	−1.86371e14			−0.972162			−0.486081	−	0.873914i	$-0.661574\pi$
$61$	−1.86371e14			−0.972162			−0.486081	+	0.873914i	$0.661574\pi$
$62$	2.22794e13	−	2.46880e14i	0.102040	−	1.13071i
$63$		0			0
$64$	2.41424e14	+	1.44716e14i	0.857709	+	0.514135i
$65$	1.00257e14			0.314634
$66$		0			0
$67$			8.81821e13i			0.217161i	0.994088	+	0.108581i	$0.0346305\pi$
$67$			8.81821e13i			0.217161i	−0.994088	+	0.108581i	$0.965369\pi$
$68$	4.83331e14	+	8.79514e13i	1.05724	+	0.192385i
$69$		0			0
$70$	−1.73755e13	+	1.92539e14i	−0.0301406	+	0.333991i
$71$		−	1.09310e15i		−	1.69275i	−0.532586	−	0.846376i	$-0.678780\pi$
$71$		−	1.09310e15i		−	1.69275i	0.532586	−	0.846376i	$-0.321220\pi$
$72$		0			0
$73$	5.03458e14			0.624282			0.312141	−	0.950036i	$-0.398954\pi$
$73$	5.03458e14			0.624282			0.312141	+	0.950036i	$0.398954\pi$
$74$	6.75009e14	+	6.09153e13i	0.750682	+	0.0677443i
$75$		0			0
$76$	1.48476e14	−	8.15939e14i	0.133397	−	0.733076i
$77$	8.32977e14			0.674073
$78$		0			0
$79$			1.56854e15i			1.03390i	0.856015	+	0.516951i	$0.172933\pi$
$79$			1.56854e15i			1.03390i	−0.856015	+	0.516951i	$0.827067\pi$
$80$	1.46100e15	+	5.49924e14i	0.870824	+	0.327780i
$81$		0			0
$82$	2.02988e15	+	1.83184e14i	0.993024	+	0.0896142i
$83$		−	8.07330e14i		−	0.358448i	−0.983808	−	0.179224i	$-0.942641\pi$
$83$		−	8.07330e14i		−	0.358448i	0.983808	−	0.179224i	$-0.0573587\pi$
$84$		0			0
$85$	2.72459e15			0.999884
$86$	1.44320e14	−	1.59922e15i	0.0482323	−	0.534468i
$87$		0			0
$88$	1.79411e15	−	6.48259e15i	0.498870	−	1.80255i
$89$	5.95350e15			1.51235			0.756176	−	0.654369i	$-0.227066\pi$
$89$	5.95350e15			1.51235			0.756176	+	0.654369i	$0.227066\pi$
$90$		0			0
$91$			5.73098e14i			0.121870i
$92$	−1.30626e15	+	7.17849e15i	−0.254524	+	1.39872i
$93$		0			0
$94$	−2.70411e14	+	2.99645e15i	−0.0443610	+	0.491569i
$95$		−	4.59954e15i		−	0.693307i
$96$		0			0
$97$	−2.50681e15			−0.319851			−0.159926	−	0.987129i	$-0.551125\pi$
$97$	−2.50681e15			−0.319851			−0.159926	+	0.987129i	$0.551125\pi$
$98$	7.37258e15	+	6.65329e14i	0.866585	+	0.0782038i
$99$		0			0
$100$	−1.32057e15	−	2.40303e14i	−0.132057	−	0.0240303i
$101$	−3.45042e15			−0.318641			−0.159320	−	0.987227i	$-0.550930\pi$
$101$	−3.45042e15			−0.318641			−0.159320	+	0.987227i	$0.550930\pi$
$102$		0			0
$103$		−	1.20028e16i		−	0.947510i	−0.880657	−	0.473755i	$-0.842898\pi$
$103$		−	1.20028e16i		−	0.947510i	0.880657	−	0.473755i	$-0.157102\pi$
$104$	4.46010e15	+	1.23437e15i	0.325895	+	0.0901940i
$105$		0			0
$106$	1.41779e16	+	1.27947e15i	0.889542	+	0.0802755i
$107$			1.78228e16i			1.03730i	0.854985	+	0.518652i	$0.173566\pi$
$107$			1.78228e16i			1.03730i	−0.854985	+	0.518652i	$0.826434\pi$
$108$		0			0
$109$	−2.01473e16			−1.01113			−0.505563	−	0.862790i	$-0.668715\pi$
$109$	−2.01473e16			−1.01113			−0.505563	+	0.862790i	$0.668715\pi$
$110$	3.35284e15	−	3.71532e16i	0.156412	−	1.73322i
$111$		0			0
$112$	−3.14354e15	+	8.35153e15i	−0.126962	+	0.337304i
$113$	−4.97373e16			−1.87092			−0.935458	−	0.353438i	$-0.885012\pi$
$113$	−4.97373e16			−1.87092			−0.935458	+	0.353438i	$0.885012\pi$
$114$		0			0
$115$			4.04659e16i			1.32284i
$116$	−2.84305e16	−	5.17348e15i	−0.867202	−	0.157804i
$117$		0			0
$118$	−6.50111e15	+	7.20395e16i	−0.172954	+	1.91652i
$119$			1.55746e16i			0.387294i
$120$		0			0
$121$	−1.14785e17			−2.49805
$122$	−4.75178e16	−	4.28818e15i	−0.968227	−	0.0873764i
$123$		0			0
$124$	1.13609e16	−	6.24329e16i	0.203254	−	1.11697i
$125$	−6.29045e16			−1.05536
$126$		0			0
$127$		−	1.28707e17i		−	1.90183i	−0.309458	−	0.950913i	$-0.600148\pi$
$127$		−	1.28707e17i		−	1.90183i	0.309458	−	0.950913i	$-0.399852\pi$
$128$	5.82245e16	+	4.24523e16i	0.808028	+	0.589144i
$129$		0			0
$130$	2.55618e16	+	2.30679e15i	0.313361	+	0.0282789i
$131$			5.58699e16i			0.644180i	0.946709	+	0.322090i	$0.104385\pi$
$131$			5.58699e16i			0.644180i	−0.946709	+	0.322090i	$0.895615\pi$
$132$		0			0
$133$	2.62924e16			0.268545
$134$	−2.02897e15	+	2.24832e16i	−0.0195181	+	0.216282i
$135$		0			0
$136$	1.21208e17	+	3.35454e16i	1.03567	+	0.286630i
$137$	4.13685e16			0.333354			0.166677	−	0.986012i	$-0.446696\pi$
$137$	4.13685e16			0.333354			0.166677	+	0.986012i	$0.446696\pi$
$138$		0			0
$139$			1.23079e17i			0.883214i	0.897209	+	0.441607i	$0.145591\pi$
$139$			1.23079e17i			0.883214i	−0.897209	+	0.441607i	$0.854409\pi$
$140$	−8.86023e15	+	4.86908e16i	−0.0600372	+	0.329930i
$141$		0			0
$142$	2.51510e16	−	2.78701e17i	0.152142	−	1.68590i
$143$		−	1.10587e17i		−	0.632437i
$144$		0			0
$145$	−1.60266e17			−0.820156
$146$	1.28364e17	+	1.15840e16i	0.621755	+	0.0561095i
$147$		0			0
$148$	1.70701e17	+	3.10624e16i	0.741555	+	0.134940i
$149$	−3.17368e17			−1.30639			−0.653196	−	0.757189i	$-0.726572\pi$
$149$	−3.17368e17			−1.30639			−0.653196	+	0.757189i	$0.726572\pi$
$150$		0			0
$151$			3.69595e17i			1.36745i	0.729741	+	0.683723i	$0.239640\pi$
$151$			3.69595e17i			1.36745i	−0.729741	+	0.683723i	$0.760360\pi$
$152$	5.66299e16	−	2.04619e17i	0.198745	−	0.718120i
$153$		0			0
$154$	2.12379e17	+	1.91659e16i	0.671345	+	0.0605847i
$155$		−	3.51941e17i		−	1.05637i
$156$		0			0
$157$	−6.48205e17			−1.75596			−0.877981	−	0.478696i	$-0.841110\pi$
$157$	−6.48205e17			−1.75596			−0.877981	+	0.478696i	$0.841110\pi$
$158$	−3.60904e16	+	3.99921e17i	−0.0929255	+	1.02972i
$159$		0			0
$160$	3.59849e17	+	1.73827e17i	0.837839	+	0.404722i
$161$	−2.31316e17			−0.512387
$162$		0			0
$163$		−	3.08754e16i		−	0.0619601i	−0.999520	−	0.0309801i	$-0.990137\pi$
$163$		−	3.08754e16i		−	0.0619601i	0.999520	−	0.0309801i	$-0.00986284\pi$
$164$	5.13332e17	+	9.34106e16i	0.980951	+	0.178503i
$165$		0			0
$166$	1.85758e16	−	2.05840e17i	0.0322168	−	0.356997i
$167$			6.62760e16i			0.109553i	0.998499	+	0.0547765i	$0.0174446\pi$
$167$			6.62760e16i			0.109553i	−0.998499	+	0.0547765i	$0.982555\pi$
$168$		0			0
$169$	−5.89331e17			−0.885657
$170$	6.94672e17	+	6.26898e16i	0.995838	+	0.0898681i
$171$		0			0
$172$	7.35927e16	−	4.04423e17i	0.0960742	−	0.527969i
$173$	3.18033e17			0.396372			0.198186	−	0.980164i	$-0.436495\pi$
$173$	3.18033e17			0.396372			0.198186	+	0.980164i	$0.436495\pi$
$174$		0			0
$175$		−	4.25533e16i		−	0.0483759i
$176$	6.06590e17	−	1.61155e18i	0.658861	−	1.75042i
$177$		0			0
$178$	1.51793e18	+	1.36983e17i	1.50623	+	0.135928i
$179$			1.31547e18i			1.24812i	0.781378	+	0.624058i	$0.214517\pi$
$179$			1.31547e18i			1.24812i	−0.781378	+	0.624058i	$0.785483\pi$
$180$		0			0
$181$	4.11057e17			0.356840			0.178420	−	0.983954i	$-0.442901\pi$
$181$	4.11057e17			0.356840			0.178420	+	0.983954i	$0.442901\pi$
$182$	−1.31863e16	+	1.46119e17i	−0.0109535	+	0.121377i
$183$		0			0
$184$	−4.98219e17	+	1.80020e18i	−0.379208	+	1.37018i
$185$	9.62262e17			0.701325
$186$		0			0
$187$		−	3.00534e18i		−	2.00984i
$188$	−1.37890e17	+	7.57765e17i	−0.0883629	+	0.485593i
$189$		0			0
$190$	1.05830e17	−	1.17272e18i	0.0623133	−	0.690501i
$191$			3.17928e17i			0.179499i	0.995964	+	0.0897496i	$0.0286067\pi$
$191$			3.17928e17i			0.179499i	−0.995964	+	0.0897496i	$0.971393\pi$
$192$		0			0
$193$	−2.01229e18			−1.04528			−0.522640	−	0.852554i	$-0.675053\pi$
$193$	−2.01229e18			−1.04528			−0.522640	+	0.852554i	$0.675053\pi$
$194$	−6.39147e17	−	5.76790e16i	−0.318557	−	0.0287477i
$195$		0			0
$196$	1.86443e18	+	3.39270e17i	0.856049	+	0.155775i
$197$	6.87244e17			0.302957			0.151479	−	0.988461i	$-0.451597\pi$
$197$	6.87244e17			0.302957			0.151479	+	0.988461i	$0.451597\pi$
$198$		0			0
$199$			2.26181e18i			0.919670i	0.888004	+	0.459835i	$0.152091\pi$
$199$			2.26181e18i			0.919670i	−0.888004	+	0.459835i	$0.847909\pi$
$200$	−3.31168e17	−	9.16534e16i	−0.129363	−	0.0358021i
$201$		0			0
$202$	−8.79734e17	−	7.93904e16i	−0.317351	−	0.0286389i
$203$		−	9.16129e17i		−	0.317679i
$204$		0			0
$205$	2.89371e18			0.927734
$206$	2.76170e17	−	3.06027e18i	0.0851607	−	0.943675i
$207$		0			0
$208$	1.10876e18	+	4.17341e17i	0.316470	+	0.119120i
$209$	−5.07349e18			−1.39359
$210$		0			0
$211$			3.18768e18i			0.811363i	0.914015	+	0.405681i	$0.132966\pi$
$211$			3.18768e18i			0.811363i	−0.914015	+	0.405681i	$0.867034\pi$
$212$	3.58543e18	+	6.52437e17i	0.878727	+	0.159901i
$213$		0			0
$214$	−4.10083e17	+	4.54418e18i	−0.0932313	+	1.03311i
$215$		−	2.27978e18i		−	0.499327i
$216$		0			0
$217$	2.01180e18			0.409174
$218$	−5.13684e18	−	4.63567e17i	−1.00703	−	0.0908784i
$219$		0			0
$220$	1.70971e18	−	9.39557e18i	0.311559	−	1.71215i
$221$	2.06771e18			0.363372
$222$		0			0
$223$		−	1.67258e18i		−	0.273494i	−0.990606	−	0.136747i	$-0.956335\pi$
$223$		−	1.67258e18i		−	0.273494i	0.990606	−	0.136747i	$-0.0436647\pi$
$224$	−9.93648e17	+	2.05701e18i	−0.156765	+	0.324528i
$225$		0			0
$226$	−1.26812e19	−	1.14440e18i	−1.86334	−	0.168155i
$227$		−	1.18440e18i		−	0.167993i	−0.996466	−	0.0839966i	$-0.973232\pi$
$227$		−	1.18440e18i		−	0.167993i	0.996466	−	0.0839966i	$-0.0267685\pi$
$228$		0			0
$229$	−5.49562e18			−0.726663			−0.363332	−	0.931660i	$-0.618361\pi$
$229$	−5.49562e18			−0.726663			−0.363332	+	0.931660i	$0.618361\pi$
$230$	−9.31076e17	+	1.03173e19i	−0.118895	+	1.31748i
$231$		0			0
$232$	−7.12971e18	−	1.97320e18i	−0.849509	−	0.235108i
$233$	−1.00120e19			−1.15259			−0.576293	−	0.817243i	$-0.695501\pi$
$233$	−1.00120e19			−1.15259			−0.576293	+	0.817243i	$0.695501\pi$
$234$		0			0
$235$			4.27161e18i			0.459249i
$236$	−3.31509e18	+	1.82179e19i	−0.344508	+	1.89322i
$237$		0			0
$238$	−3.58354e17	+	3.97096e18i	−0.0348094	+	0.385727i
$239$		−	5.24204e17i		−	0.0492399i	−0.999697	−	0.0246200i	$-0.992162\pi$
$239$		−	5.24204e17i		−	0.0492399i	0.999697	−	0.0246200i	$-0.00783757\pi$
$240$		0			0
$241$	−2.53720e18			−0.222956			−0.111478	−	0.993767i	$-0.535558\pi$
$241$	−2.53720e18			−0.222956			−0.111478	+	0.993767i	$0.535558\pi$
$242$	−2.92660e19	−	2.64107e18i	−2.48794	−	0.224521i
$243$		0			0
$244$	−1.20166e19	−	2.18666e18i	−0.956455	−	0.174046i
$245$	1.05100e19			0.809608
$246$		0			0
$247$		−	3.49062e18i		−	0.251957i
$248$	4.33312e18	−	1.56567e19i	0.302822	−	1.09418i
$249$		0			0
$250$	−1.60384e19	−	1.44736e18i	−1.05109	−	0.0948544i
$251$			1.04227e19i			0.661593i	0.943702	+	0.330797i	$0.107317\pi$
$251$			1.04227e19i			0.661593i	−0.943702	+	0.330797i	$0.892683\pi$
$252$		0			0
$253$	4.46356e19			2.65900
$254$	2.96139e18	−	3.28155e19i	0.170933	−	1.89413i
$255$		0			0
$256$	1.38684e19	+	1.21635e19i	0.751806	+	0.659384i
$257$	2.66097e19			1.39822			0.699110	−	0.715014i	$-0.253580\pi$
$257$	2.66097e19			1.39822			0.699110	+	0.715014i	$0.253580\pi$
$258$		0			0
$259$			5.50059e18i			0.271651i
$260$	6.46427e18	+	1.17630e18i	0.309551	+	0.0563288i
$261$		0			0
$262$	−1.28550e18	+	1.42448e19i	−0.0578979	+	0.641573i
$263$		−	1.19002e19i		−	0.519884i	−0.965624	−	0.259942i	$-0.916297\pi$
$263$		−	1.19002e19i		−	0.519884i	0.965624	−	0.259942i	$-0.0837035\pi$
$264$		0			0
$265$	2.02114e19			0.831056
$266$	6.70361e18	+	6.04958e17i	0.267458	+	0.0241364i
$267$		0			0
$268$	−1.03463e18	+	5.68573e18i	−0.0388782	+	0.213653i
$269$	8.57790e18			0.312869			0.156435	−	0.987688i	$-0.450000\pi$
$269$	8.57790e18			0.312869			0.156435	+	0.987688i	$0.450000\pi$
$270$		0			0
$271$		−	3.85518e19i		−	1.32523i	−0.748961	−	0.662614i	$-0.769447\pi$
$271$		−	3.85518e19i		−	1.32523i	0.748961	−	0.662614i	$-0.230553\pi$
$272$	3.01319e19	+	1.13417e19i	1.00572	+	0.378554i
$273$		0			0
$274$	1.05475e19	+	9.51844e17i	0.332005	+	0.0299613i
$275$			8.21126e18i			0.251043i
$276$		0			0
$277$	9.47812e18			0.273454			0.136727	−	0.990609i	$-0.456342\pi$
$277$	9.47812e18			0.273454			0.136727	+	0.990609i	$0.456342\pi$
$278$	−2.83191e18	+	3.13807e19i	−0.0793819	+	0.879640i
$279$		0			0
$280$	−3.37936e18	+	1.22105e19i	−0.0894479	+	0.323199i
$281$	2.91956e19			0.751047			0.375523	−	0.926813i	$-0.377463\pi$
$281$	2.91956e19			0.751047			0.375523	+	0.926813i	$0.377463\pi$
$282$		0			0
$283$		−	4.76515e19i		−	1.15820i	−0.815255	−	0.579102i	$-0.803403\pi$
$283$		−	4.76515e19i		−	1.15820i	0.815255	−	0.579102i	$-0.196597\pi$
$284$	1.28252e19	−	7.04800e19i	0.303052	−	1.66540i
$285$		0			0
$286$	2.54449e18	−	2.81958e19i	0.0568424	−	0.629877i
$287$			1.65413e19i			0.359348i
$288$		0			0
$289$	7.53119e18			0.154768
$290$	−4.08620e19	−	3.68754e18i	−0.816837	−	0.0737144i
$291$		0			0
$292$	3.24616e19	+	5.90701e18i	0.614196	+	0.111765i
$293$	2.60757e19			0.480059			0.240029	−	0.970766i	$-0.422843\pi$
$293$	2.60757e19			0.480059			0.240029	+	0.970766i	$0.422843\pi$
$294$		0			0
$295$			1.02696e20i			1.79052i
$296$	4.28080e19	+	1.18474e19i	0.726425	+	0.201044i
$297$		0			0
$298$	−8.09174e19	−	7.30229e18i	−1.30110	−	0.117416i
$299$			3.07098e19i			0.480738i
$300$		0			0
$301$	1.30319e19			0.193409
$302$	−8.50397e18	+	9.42334e19i	−0.122904	+	1.36191i
$303$		0			0
$304$	1.91466e19	−	5.08674e19i	0.262484	−	0.697350i
$305$	−6.77391e19			−0.904567
$306$		0			0
$307$		−	3.72489e19i		−	0.472069i	−0.971745	−	0.236035i	$-0.924152\pi$
$307$		−	3.72489e19i		−	0.472069i	0.971745	−	0.236035i	$-0.0758479\pi$
$308$	5.37080e19	+	9.77321e18i	0.663183	+	0.120679i
$309$		0			0
$310$	8.09777e18	−	8.97323e19i	0.0949450	−	1.05210i
$311$		−	1.25152e20i		−	1.43006i	−0.699093	−	0.715031i	$-0.746413\pi$
$311$		−	1.25152e20i		−	1.43006i	0.699093	−	0.715031i	$-0.253587\pi$
$312$		0			0
$313$	−1.11292e20			−1.20812			−0.604059	−	0.796940i	$-0.706451\pi$
$313$	−1.11292e20			−1.20812			−0.604059	+	0.796940i	$0.706451\pi$
$314$	−1.65269e20	−	1.49145e19i	−1.74885	−	0.157823i
$315$		0			0
$316$	−1.84035e19	+	1.01135e20i	−0.185099	+	1.01720i
$317$	−1.09756e18			−0.0107635			−0.00538177	−	0.999986i	$-0.501713\pi$
$317$	−1.09756e18			−0.0107635			−0.00538177	+	0.999986i	$0.501713\pi$
$318$		0			0
$319$			1.76780e20i			1.64857i
$320$	8.77490e19	+	5.25993e19i	0.798073	+	0.478388i
$321$		0			0
$322$	−5.89772e19	−	5.32232e18i	−0.510313	−	0.0460526i
$323$		−	9.48616e19i		−	0.800701i
$324$		0			0
$325$	−5.64944e18			−0.0453878
$326$	7.10409e17	−	7.87212e18i	0.00556888	−	0.0617094i
$327$		0			0
$328$	1.28732e20	+	3.56275e19i	0.960937	+	0.265947i
$329$	−2.44178e19			−0.177885
$330$		0			0
$331$		−	9.28071e19i		−	0.644106i	−0.946722	−	0.322053i	$-0.895627\pi$
$331$		−	9.28071e19i		−	0.644106i	0.946722	−	0.322053i	$-0.104373\pi$
$332$	9.47230e18	−	5.20544e19i	0.0641728	−	0.352657i
$333$		0			0
$334$	−1.52494e18	+	1.68980e19i	−0.00984646	+	0.109110i
$335$			3.20511e19i			0.202062i
$336$		0			0
$337$	−2.54699e20			−1.53105			−0.765523	−	0.643409i	$-0.777519\pi$
$337$	−2.54699e20			−1.53105			−0.765523	+	0.643409i	$0.777519\pi$
$338$	−1.50258e20	−	1.35599e19i	−0.882073	−	0.0796015i
$339$		0			0
$340$	1.75674e20	+	3.19673e19i	0.983730	+	0.179009i
$341$	−3.88206e20			−2.12338
$342$		0			0
$343$			1.29126e20i			0.674000i
$344$	2.80688e19	−	1.01420e20i	0.143138	−	0.517198i
$345$		0			0
$346$	8.10869e19	+	7.31758e18i	0.394768	+	0.0356253i
$347$			3.33158e20i			1.58495i	0.609906	+	0.792474i	$0.291207\pi$
$347$			3.33158e20i			1.58495i	−0.609906	+	0.792474i	$0.708793\pi$
$348$		0			0
$349$	−1.77058e20			−0.804472			−0.402236	−	0.915536i	$-0.631767\pi$
$349$	−1.77058e20			−0.804472			−0.402236	+	0.915536i	$0.631767\pi$
$350$	9.79104e17	−	1.08496e19i	0.00434795	−	0.0481801i
$351$		0			0
$352$	1.91738e20	−	3.96929e20i	0.813519	−	1.68411i
$353$	−1.12220e20			−0.465448			−0.232724	−	0.972543i	$-0.574764\pi$
$353$	−1.12220e20			−0.465448			−0.232724	+	0.972543i	$0.574764\pi$
$354$		0			0
$355$		−	3.97304e20i		−	1.57505i
$356$	3.83865e20	+	6.98517e19i	1.48792	+	0.270755i
$357$		0			0
$358$	−3.02674e19	+	3.35396e20i	−0.112179	+	1.24306i
$359$			1.82387e20i			0.661055i	0.943796	+	0.330528i	$0.107227\pi$
$359$			1.82387e20i			0.661055i	−0.943796	+	0.330528i	$0.892773\pi$
$360$		0			0
$361$	1.28300e20			0.444804
$362$	1.04805e20	+	9.45797e18i	0.355396	+	0.0320723i
$363$		0			0
$364$	−6.72408e18	+	3.69517e19i	−0.0218184	+	0.119901i
$365$	1.82989e20			0.580875
$366$		0			0
$367$		−	3.87362e20i		−	1.17703i	−0.808486	−	0.588516i	$-0.799712\pi$
$367$		−	3.87362e20i		−	1.17703i	0.808486	−	0.588516i	$-0.200288\pi$
$368$	−1.68449e20	+	4.47523e20i	−0.500824	+	1.33055i
$369$		0			0
$370$	2.45342e20	+	2.21406e19i	0.698487	+	0.0630340i
$371$			1.15535e20i			0.321900i
$372$		0			0
$373$	−5.24390e20			−1.39954			−0.699768	−	0.714371i	$-0.746713\pi$
$373$	−5.24390e20			−1.39954			−0.699768	+	0.714371i	$0.746713\pi$
$374$	6.91495e19	−	7.66253e20i	0.180641	−	2.00170i
$375$		0			0
$376$	−5.25923e19	+	1.90030e20i	−0.131650	+	0.475685i
$377$	−1.21627e20			−0.298056
$378$		0			0
$379$			4.26070e20i			1.00085i	0.865781	+	0.500423i	$0.166822\pi$
$379$			4.26070e20i			1.00085i	−0.865781	+	0.500423i	$0.833178\pi$
$380$	5.39658e19	−	2.96565e20i	0.124122	−	0.682106i
$381$		0			0
$382$	−7.31518e18	+	8.10603e19i	−0.0161331	+	0.178773i
$383$		−	7.93640e20i		−	1.71409i	−0.515243	−	0.857044i	$-0.672298\pi$
$383$		−	7.93640e20i		−	1.71409i	0.515243	−	0.857044i	$-0.327702\pi$
$384$		0			0
$385$	3.02758e20			0.627205
$386$	−5.13062e20	−	4.63006e19i	−1.04105	−	0.0939481i
$387$		0			0
$388$	−1.61632e20	−	2.94121e19i	−0.314684	−	0.0572628i
$389$	3.22822e20			0.615695			0.307848	−	0.951436i	$-0.400391\pi$
$389$	3.22822e20			0.615695			0.307848	+	0.951436i	$0.400391\pi$
$390$		0			0
$391$			8.34576e20i			1.52775i
$392$	4.67557e20	+	1.29400e20i	0.838583	+	0.232084i
$393$		0			0
$394$	1.75223e20	+	1.58127e19i	0.301731	+	0.0272293i
$395$			5.70110e20i			0.962015i
$396$		0			0
$397$	−3.57851e20			−0.579933			−0.289966	−	0.957037i	$-0.593644\pi$
$397$	−3.57851e20			−0.579933			−0.289966	+	0.957037i	$0.593644\pi$
$398$	−5.20418e19	+	5.76681e20i	−0.0826585	+	0.915948i
$399$		0			0
$400$	−8.23271e19	−	3.09881e19i	−0.125621	−	0.0472841i
$401$	8.64609e20			1.29320			0.646599	−	0.762830i	$-0.276191\pi$
$401$	8.64609e20			1.29320			0.646599	+	0.762830i	$0.276191\pi$
$402$		0			0
$403$		−	2.67090e20i		−	0.383900i
$404$	−2.22474e20	−	4.04834e19i	−0.313493	−	0.0570461i
$405$		0			0
$406$	2.10791e19	−	2.33580e20i	0.0285525	−	0.316393i
$407$		−	1.06142e21i		−	1.40971i
$408$		0			0
$409$	1.07480e21			1.37259			0.686296	−	0.727322i	$-0.259236\pi$
$409$	1.07480e21			1.37259			0.686296	+	0.727322i	$0.259236\pi$
$410$	7.37790e20	+	6.65809e19i	0.923979	+	0.0833833i
$411$		0			0
$412$	1.40827e20	−	7.73905e20i	0.169632	−	0.932202i
$413$	−5.87043e20			−0.693537
$414$		0			0
$415$		−	2.93436e20i		−	0.333525i
$416$	2.73092e20	+	1.31918e20i	0.304482	+	0.147082i
$417$		0			0
$418$	−1.29356e21	−	1.16735e20i	−1.38795	−	0.125254i
$419$			3.64964e20i			0.384183i	0.981377	+	0.192091i	$0.0615270\pi$
$419$			3.64964e20i			0.384183i	−0.981377	+	0.192091i	$0.938473\pi$
$420$		0			0
$421$	3.34227e20			0.338676			0.169338	−	0.985558i	$-0.445837\pi$
$421$	3.34227e20			0.338676			0.169338	+	0.985558i	$0.445837\pi$
$422$	−7.33449e19	+	8.12743e20i	−0.0729240	+	0.808079i
$423$		0			0
$424$	8.99142e20	+	2.48845e20i	0.860799	+	0.238233i
$425$	−1.53530e20			−0.144239
$426$		0			0
$427$		−	3.87218e20i		−	0.350374i
$428$	−2.09113e20	+	1.14917e21i	−0.185708	+	1.02055i
$429$		0			0
$430$	5.24552e19	−	5.81261e20i	0.0448787	−	0.497306i
$431$		−	1.07898e21i		−	0.906143i	−0.891474	−	0.453072i	$-0.850328\pi$
$431$		−	1.07898e21i		−	0.906143i	0.891474	−	0.453072i	$-0.149672\pi$
$432$		0			0
$433$	5.72559e20			0.463358			0.231679	−	0.972792i	$-0.425578\pi$
$433$	5.72559e20			0.463358			0.231679	+	0.972792i	$0.425578\pi$
$434$	5.12938e20	+	4.62894e19i	0.407518	+	0.0367759i
$435$		0			0
$436$	−1.29904e21	−	2.36386e20i	−0.994789	−	0.181021i
$437$	1.40890e21			1.05932
$438$		0			0
$439$			2.13684e21i			1.54902i	0.632562	+	0.774510i	$0.282003\pi$
$439$			2.13684e21i			1.54902i	−0.632562	+	0.774510i	$0.717997\pi$
$440$	6.52095e20	−	2.35619e21i	0.464183	−	1.67722i
$441$		0			0
$442$	5.27191e20	+	4.75757e19i	0.361901	+	0.0326593i
$443$			1.95631e21i			1.31889i	0.751754	+	0.659444i	$0.229208\pi$
$443$			1.95631e21i			1.31889i	−0.751754	+	0.659444i	$0.770792\pi$
$444$		0			0
$445$	2.16389e21			1.40720
$446$	3.84842e19	−	4.26447e20i	0.0245812	−	0.272387i
$447$		0			0
$448$	−3.00674e20	+	5.01601e20i	−0.185298	+	0.309125i
$449$	1.11036e21			0.672193			0.336097	−	0.941828i	$-0.390893\pi$
$449$	1.11036e21			0.672193			0.336097	+	0.941828i	$0.390893\pi$
$450$		0			0
$451$		−	3.19188e21i		−	1.86481i
$452$	−3.20692e21	−	5.83561e20i	−1.84069	−	0.334949i
$453$		0			0
$454$	2.72517e19	−	3.01979e20i	0.0150990	−	0.167313i
$455$			2.08301e20i			0.113397i
$456$		0			0
$457$	4.76768e19			0.0250598			0.0125299	−	0.999921i	$-0.496012\pi$
$457$	4.76768e19			0.0250598			0.0125299	+	0.999921i	$0.496012\pi$
$458$	−1.40119e21	−	1.26448e20i	−0.723722	−	0.0653114i
$459$		0			0
$460$	−4.74781e20	+	2.60913e21i	−0.236827	+	1.30147i
$461$	−8.26966e20			−0.405397			−0.202698	−	0.979241i	$-0.564971\pi$
$461$	−8.26966e20			−0.405397			−0.202698	+	0.979241i	$0.564971\pi$
$462$		0			0
$463$		−	8.20408e20i		−	0.388492i	−0.980953	−	0.194246i	$-0.937774\pi$
$463$		−	8.20408e20i		−	0.388492i	0.980953	−	0.194246i	$-0.0622260\pi$
$464$	−1.77242e21	−	6.67142e20i	−0.824940	−	0.310509i
$465$		0			0
$466$	−2.55270e21	−	2.30365e20i	−1.14792	−	0.103593i
$467$			4.07930e20i			0.180323i	0.995927	+	0.0901615i	$0.0287383\pi$
$467$			4.07930e20i			0.180323i	−0.995927	+	0.0901615i	$0.971262\pi$
$468$		0			0
$469$	−1.83214e20			−0.0782665
$470$	−9.82849e19	+	1.08911e21i	−0.0412766	+	0.457390i
$471$		0			0
$472$	−1.26440e21	+	4.56862e21i	−0.513274	+	1.85460i
$473$	−2.51469e21			−1.00368
$474$		0			0
$475$			2.59183e20i			0.100013i
$476$	−1.82735e20	+	1.00421e21i	−0.0693371	+	0.381037i
$477$		0			0
$478$	1.20614e19	−	1.33653e20i	0.00442561	−	0.0490406i
$479$		−	1.33160e21i		−	0.480497i	−0.970711	−	0.240248i	$-0.922771\pi$
$479$		−	1.33160e21i		−	0.480497i	0.970711	−	0.240248i	$-0.0772289\pi$
$480$		0			0
$481$	7.30267e20			0.254871
$482$	−6.46895e20	−	5.83782e19i	−0.222053	−	0.0200389i
$483$		0			0
$484$	−7.40101e21	−	1.34676e21i	−2.45770	−	0.447225i
$485$	−9.11138e20			−0.297612
$486$		0			0
$487$			2.89682e21i			0.915565i	0.889064	+	0.457783i	$0.151356\pi$
$487$			2.89682e21i			0.915565i	−0.889064	+	0.457783i	$0.848644\pi$
$488$	−3.01350e21	−	8.34009e20i	−0.936941	−	0.259306i
$489$		0			0
$490$	2.67968e21	+	2.41824e20i	0.806331	+	0.0727663i
$491$			1.68428e21i			0.498612i	0.968425	+	0.249306i	$0.0802025\pi$
$491$			1.68428e21i			0.498612i	−0.968425	+	0.249306i	$0.919798\pi$
$492$		0			0
$493$	−3.30535e21			−0.947200
$494$	8.03153e19	−	8.89982e20i	0.0226455	−	0.250938i
$495$		0			0
$496$	1.46503e21	−	3.89220e21i	0.399940	−	1.06253i
$497$	2.27111e21			0.610080
$498$		0			0
$499$		−	3.33834e21i		−	0.868412i	−0.900814	−	0.434206i	$-0.857029\pi$
$499$		−	3.33834e21i		−	0.868412i	0.900814	−	0.434206i	$-0.142971\pi$
$500$	−4.05591e21	−	7.38051e20i	−1.03831	−	0.188941i
$501$		0			0
$502$	−2.39815e20	+	2.65742e21i	−0.0594630	+	0.658916i
$503$			4.84911e21i			1.18336i	0.806171	+	0.591682i	$0.201536\pi$
$503$			4.84911e21i			1.18336i	−0.806171	+	0.591682i	$0.798464\pi$
$504$		0			0
$505$	−1.25411e21			−0.296486
$506$	1.13805e22	+	1.02702e21i	2.64823	+	0.238986i
$507$		0			0
$508$	1.51010e21	−	8.29864e21i	0.340483	−	1.87110i
$509$	−2.89455e21			−0.642450			−0.321225	−	0.947003i	$-0.604095\pi$
$509$	−2.89455e21			−0.642450			−0.321225	+	0.947003i	$0.604095\pi$
$510$		0			0
$511$			1.04602e21i			0.224996i
$512$	3.25607e21	+	3.42035e21i	0.689499	+	0.724287i
$513$		0			0
$514$	6.78452e21	+	6.12260e20i	1.39256	+	0.125670i
$515$		−	4.36259e21i		−	0.881630i
$516$		0			0
$517$	4.71176e21			0.923122
$518$	−1.26562e20	+	1.40245e21i	−0.0244156	+	0.270551i
$519$		0			0
$520$	1.62109e21	+	4.48649e20i	0.303236	+	0.0839228i
$521$	4.09134e21			0.753640			0.376820	−	0.926286i	$-0.377017\pi$
$521$	4.09134e21			0.753640			0.376820	+	0.926286i	$0.377017\pi$
$522$		0			0
$523$			2.51392e21i			0.449095i	0.974463	+	0.224547i	$0.0720903\pi$
$523$			2.51392e21i			0.449095i	−0.974463	+	0.224547i	$0.927910\pi$
$524$	−6.55514e20	+	3.60233e21i	−0.115327	+	0.633773i
$525$		0			0
$526$	2.73809e20	−	3.03411e21i	0.0467264	−	0.517780i
$527$		−	7.25849e21i		−	1.22000i
$528$		0			0
$529$	−6.26260e21			−1.02120
$530$	5.15319e21	+	4.65042e20i	0.827692	+	0.0746940i
$531$		0			0
$532$	1.69526e21	+	3.08485e20i	0.264206	+	0.0480774i
$533$	2.19605e21			0.337151
$534$		0			0
$535$			6.47797e21i			0.965181i
$536$	−3.94615e20	+	1.42585e21i	−0.0579236	+	0.209294i
$537$		0			0
$538$	2.18705e21	+	1.97368e20i	0.311603	+	0.0281202i
$539$		−	1.15930e22i		−	1.62737i
$540$		0			0
$541$	8.56679e21			1.16746			0.583728	−	0.811950i	$-0.301594\pi$
$541$	8.56679e21			1.16746			0.583728	+	0.811950i	$0.301594\pi$
$542$	8.87034e20	−	9.82932e21i	0.119109	−	1.31986i
$543$		0			0
$544$	7.42159e21	+	3.58503e21i	0.967622	+	0.467414i
$545$	−7.32284e21			−0.940822
$546$		0			0
$547$		−	1.51571e21i		−	0.189111i	−0.995520	−	0.0945555i	$-0.969857\pi$
$547$		−	1.51571e21i		−	0.189111i	0.995520	−	0.0945555i	$-0.0301430\pi$
$548$	2.66733e21	+	4.85372e20i	0.327968	+	0.0596801i
$549$		0			0
$550$	−1.88932e20	+	2.09357e21i	−0.0225634	+	0.250027i
$551$			5.57995e21i			0.656776i
$552$		0			0
$553$	−3.25892e21			−0.372626
$554$	2.41658e21	+	2.18081e20i	0.272347	+	0.0245776i
$555$		0			0
$556$	−1.44407e21	+	7.93580e21i	−0.158121	+	0.868945i
$557$	1.03623e22			1.11845			0.559225	−	0.829016i	$-0.311099\pi$
$557$	1.03623e22			1.11845			0.559225	+	0.829016i	$0.311099\pi$
$558$		0			0
$559$		−	1.73014e21i		−	0.181462i
$560$	−1.14256e21	+	3.03549e21i	−0.118134	+	0.313852i
$561$		0			0
$562$	7.44383e21	+	6.71758e20i	0.748007	+	0.0675029i
$563$			1.91056e22i			1.89275i	0.323066	+	0.946376i	$0.395286\pi$
$563$			1.91056e22i			1.89275i	−0.323066	+	0.946376i	$0.604714\pi$
$564$		0			0
$565$	−1.80777e22			−1.74083
$566$	1.09641e21	−	1.21494e22i	0.104098	−	1.15352i
$567$		0			0
$568$	4.89163e21	−	1.76748e22i	0.451510	−	1.63142i
$569$	−2.42125e21			−0.220365			−0.110182	−	0.993911i	$-0.535144\pi$
$569$	−2.42125e21			−0.220365			−0.110182	+	0.993911i	$0.535144\pi$
$570$		0			0
$571$		−	6.12261e20i		−	0.0541811i	−0.999633	−	0.0270905i	$-0.991376\pi$
$571$		−	6.12261e20i		−	0.0541811i	0.999633	−	0.0270905i	$-0.00862424\pi$
$572$	1.29751e21	−	7.13036e21i	0.113225	−	0.622219i
$573$		0			0
$574$	−3.80597e20	+	4.21744e21i	−0.0322976	+	0.357893i
$575$		−	2.28025e21i		−	0.190827i
$576$		0			0
$577$	−1.52521e21			−0.124143			−0.0620715	−	0.998072i	$-0.519771\pi$
$577$	−1.52521e21			−0.124143			−0.0620715	+	0.998072i	$0.519771\pi$
$578$	1.92018e21	+	1.73284e20i	0.154142	+	0.0139103i
$579$		0			0
$580$	−1.03335e22	−	1.88038e21i	−0.806906	−	0.146832i
$581$	1.67737e21			0.129187
$582$		0			0
$583$		−	2.22941e22i		−	1.67048i
$584$	8.14062e21	+	2.25298e21i	0.601665	+	0.166515i
$585$		0			0
$586$	6.64835e21	+	5.99972e20i	0.478116	+	0.0431469i
$587$			1.08203e22i			0.767596i	0.923417	+	0.383798i	$0.125384\pi$
$587$			1.08203e22i			0.767596i	−0.923417	+	0.383798i	$0.874616\pi$
$588$		0			0
$589$	−1.22535e22			−0.845935
$590$	−2.36292e21	+	2.61838e22i	−0.160929	+	1.78327i
$591$		0			0
$592$	1.06419e22	+	4.00563e21i	0.705416	+	0.265520i
$593$	−6.66353e21			−0.435779			−0.217890	−	0.975973i	$-0.569917\pi$
$593$	−6.66353e21			−0.435779			−0.217890	+	0.975973i	$0.569917\pi$
$594$		0			0
$595$			5.66082e21i			0.360366i
$596$	−2.04630e22	−	3.72364e21i	−1.28528	−	0.233882i
$597$		0			0
$598$	−7.06599e20	+	7.82990e21i	−0.0432080	+	0.478792i
$599$		−	4.67643e21i		−	0.282163i	−0.989998	−	0.141081i	$-0.954942\pi$
$599$		−	4.67643e21i		−	0.282163i	0.989998	−	0.141081i	$-0.0450579\pi$
$600$		0			0
$601$	−1.96529e22			−1.15460			−0.577299	−	0.816533i	$-0.695893\pi$
$601$	−1.96529e22			−1.15460			−0.577299	+	0.816533i	$0.695893\pi$
$602$	3.32267e21	+	2.99850e20i	0.192626	+	0.0173833i
$603$		0			0
$604$	−4.33641e21	+	2.38304e22i	−0.244813	+	1.34535i
$605$	−4.17203e22			−2.32437
$606$		0			0
$607$		−	7.83703e21i		−	0.425248i	−0.977134	−	0.212624i	$-0.931799\pi$
$607$		−	7.83703e21i		−	0.425248i	0.977134	−	0.212624i	$-0.0682009\pi$
$608$	6.05210e21	−	1.25288e22i	0.324099	−	0.670936i
$609$		0			0
$610$	−1.72710e22	−	1.55860e21i	−0.900906	−	0.0813011i
$611$			3.24175e21i			0.166897i
$612$		0			0
$613$	2.09738e22			1.05195			0.525973	−	0.850501i	$-0.323701\pi$
$613$	2.09738e22			1.05195			0.525973	+	0.850501i	$0.323701\pi$
$614$	8.57055e20	−	9.49711e21i	0.0424289	−	0.470159i
$615$		0			0
$616$	1.34687e22	+	3.72758e21i	0.649652	+	0.179796i
$617$	−1.80800e22			−0.860827			−0.430414	−	0.902632i	$-0.641632\pi$
$617$	−1.80800e22			−0.860827			−0.430414	+	0.902632i	$0.641632\pi$
$618$		0			0
$619$			4.17757e22i			1.93820i	0.246672	+	0.969099i	$0.420663\pi$
$619$			4.17757e22i			1.93820i	−0.246672	+	0.969099i	$0.579337\pi$
$620$	4.12928e21	−	2.26922e22i	0.189121	−	1.03930i
$621$		0			0
$622$	2.87961e21	−	3.19093e22i	0.128532	−	1.42427i
$623$			1.23695e22i			0.545063i
$624$		0			0
$625$	−1.97384e22			−0.847758
$626$	−2.83754e22	−	2.56070e21i	−1.20323	−	0.108584i
$627$		0			0
$628$	−4.17944e22	−	7.60530e21i	−1.72759	−	0.314369i
$629$	1.98459e22			0.809962
$630$		0			0
$631$		−	1.75827e22i		−	0.699600i	−0.936824	−	0.349800i	$-0.886250\pi$
$631$		−	1.75827e22i		−	0.699600i	0.936824	−	0.349800i	$-0.113750\pi$
$632$	−7.01923e21	+	2.53624e22i	−0.275774	+	0.996444i
$633$		0			0
$634$	−2.79839e20	−	2.52537e19i	−0.0107200	−	0.000967409i
$635$		−	4.67803e22i		−	1.76959i
$636$		0			0
$637$	7.97612e21			0.294223
$638$	−4.06751e21	+	4.50725e22i	−0.148171	+	1.64190i
$639$		0			0
$640$	2.11626e22	+	1.54299e22i	0.751846	+	0.548181i
$641$	3.00851e22			1.05557			0.527786	−	0.849378i	$-0.323022\pi$
$641$	3.00851e22			1.05557			0.527786	+	0.849378i	$0.323022\pi$
$642$		0			0
$643$			2.10447e22i			0.720205i	0.932913	+	0.360102i	$0.117258\pi$
$643$			2.10447e22i			0.720205i	−0.932913	+	0.360102i	$0.882742\pi$
$644$	−1.49146e22	−	2.71400e21i	−0.504109	−	0.0917323i
$645$		0			0
$646$	2.18266e21	−	2.41863e22i	0.0719658	−	0.797460i
$647$		−	1.77979e21i		−	0.0579609i	−0.999580	−	0.0289804i	$-0.990774\pi$
$647$		−	1.77979e21i		−	0.0579609i	0.999580	−	0.0289804i	$-0.00922605\pi$
$648$		0			0
$649$	1.13278e23			3.59906
$650$	−1.44040e21	−	1.29987e20i	−0.0452041	−	0.00407938i
$651$		0			0
$652$	3.62258e20	−	1.99076e21i	0.0110927	−	0.0609591i
$653$	3.59385e22			1.08706			0.543531	−	0.839389i	$-0.317087\pi$
$653$	3.59385e22			1.08706			0.543531	+	0.839389i	$0.317087\pi$
$654$		0			0
$655$			2.03067e22i			0.599390i
$656$	3.20022e22	+	1.20457e22i	0.933145	+	0.351238i
$657$		0			0
$658$	−6.22566e21	−	5.61827e20i	−0.177165	−	0.0159880i
$659$		−	5.99046e22i		−	1.68413i	−0.539373	−	0.842067i	$-0.681339\pi$
$659$		−	5.99046e22i		−	1.68413i	0.539373	−	0.842067i	$-0.318661\pi$
$660$		0			0
$661$	−1.11504e22			−0.305970			−0.152985	−	0.988229i	$-0.548889\pi$
$661$	−1.11504e22			−0.305970			−0.152985	+	0.988229i	$0.548889\pi$
$662$	2.13539e21	−	2.36625e22i	0.0578913	−	0.641499i
$663$		0			0
$664$	3.61281e21	−	1.30540e22i	0.0956093	−	0.345462i
$665$	9.55636e21			0.249873
$666$		0			0
$667$		−	4.90914e22i		−	1.25314i
$668$	−7.77608e20	+	4.27329e21i	−0.0196132	+	0.107783i
$669$		0			0
$670$	−7.37460e20	+	8.17187e21i	−0.0181610	+	0.201244i
$671$			7.47192e22i			1.81824i
$672$		0			0
$673$	−3.02379e22			−0.718506			−0.359253	−	0.933240i	$-0.616969\pi$
$673$	−3.02379e22			−0.718506			−0.359253	+	0.933240i	$0.616969\pi$
$674$	−6.49390e22	−	5.86034e21i	−1.52485	−	0.137608i
$675$		0			0
$676$	−3.79984e22	−	6.91455e21i	−0.871349	−	0.158559i
$677$	−2.09689e21			−0.0475190			−0.0237595	−	0.999718i	$-0.507564\pi$
$677$	−2.09689e21			−0.0475190			−0.0237595	+	0.999718i	$0.507564\pi$
$678$		0			0
$679$		−	5.20835e21i		−	0.115277i
$680$	4.40550e22	+	1.21926e22i	0.963660	+	0.266700i
$681$		0			0
$682$	−9.89785e22	−	8.93219e21i	−2.11478	−	0.190846i
$683$			1.19210e22i			0.251736i	0.992047	+	0.125868i	$0.0401716\pi$
$683$			1.19210e22i			0.251736i	−0.992047	+	0.125868i	$0.959828\pi$
$684$		0			0
$685$	1.50360e22			0.310176
$686$	−2.97104e21	+	3.29224e22i	−0.0605781	+	0.671273i
$687$		0			0
$688$	9.49009e21	−	2.52126e22i	0.189044	−	0.502239i
$689$	1.53386e22			0.302017
$690$		0			0
$691$			1.75286e22i			0.337228i	0.985682	+	0.168614i	$0.0539292\pi$
$691$			1.75286e22i			0.337228i	−0.985682	+	0.168614i	$0.946071\pi$
$692$	2.05059e22	+	3.73144e21i	0.389968	+	0.0709622i
$693$		0			0
$694$	−7.66560e21	+	8.49434e22i	−0.142453	+	1.57853i
$695$			4.47349e22i			0.821804i
$696$		0			0
$697$	5.96803e22			1.07144
$698$	−4.51433e22	−	4.07390e21i	−0.801216	−	0.0723047i
$699$		0			0
$700$	4.99272e20	−	2.74372e21i	0.00866070	−	0.0475943i
$701$	−4.33851e22			−0.744040			−0.372020	−	0.928225i	$-0.621335\pi$
$701$	−4.33851e22			−0.744040			−0.372020	+	0.928225i	$0.621335\pi$
$702$		0			0
$703$		−	3.35029e22i		−	0.561617i
$704$	5.80193e22	−	9.67909e22i	0.961592	−	1.60418i
$705$		0			0
$706$	−2.86119e22	−	2.58205e21i	−0.463564	−	0.0418337i
$707$		−	7.16887e21i		−	0.114841i
$708$		0			0
$709$	−2.79315e22			−0.437445			−0.218723	−	0.975787i	$-0.570189\pi$
$709$	−2.79315e22			−0.437445			−0.218723	+	0.975787i	$0.570189\pi$
$710$	9.14151e21	−	1.01298e23i	0.141563	−	1.56868i
$711$		0			0
$712$	9.62646e22	+	2.66420e22i	1.45756	+	0.403391i
$713$	1.07804e23			1.61406
$714$		0			0
$715$		−	4.01946e22i		−	0.588464i
$716$	−1.54342e22	+	8.48175e22i	−0.223449	+	1.22795i
$717$		0			0
$718$	−4.19652e21	+	4.65020e22i	−0.0594146	+	0.658380i
$719$		−	3.16812e22i		−	0.443578i	−0.975095	−	0.221789i	$-0.928810\pi$
$719$		−	3.16812e22i		−	0.443578i	0.975095	−	0.221789i	$-0.0711896\pi$
$720$		0			0
$721$	2.49379e22			0.341490
$722$	3.27119e22	+	2.95204e21i	0.443004	+	0.0399783i
$723$		0			0
$724$	2.65038e22	+	4.82288e21i	0.351075	+	0.0638849i
$725$	9.03095e21			0.118312
$726$		0			0
$727$		−	4.87349e22i		−	0.624547i	−0.949992	−	0.312273i	$-0.898909\pi$
$727$		−	4.87349e22i		−	0.624547i	0.949992	−	0.312273i	$-0.101091\pi$
$728$	−2.56462e21	+	9.26665e21i	−0.0325066	+	0.117455i
$729$		0			0
$730$	4.66557e22	+	4.21038e21i	0.578524	+	0.0522082i
$731$		−	4.70185e22i		−	0.576673i
$732$		0			0
$733$	9.12805e22			1.09533			0.547666	−	0.836697i	$-0.315516\pi$
$733$	9.12805e22			1.09533			0.547666	+	0.836697i	$0.315516\pi$
$734$	8.91276e21	−	9.87633e22i	0.105790	−	1.17227i
$735$		0			0
$736$	−5.32453e22	+	1.10226e23i	−0.618385	+	1.28016i
$737$	3.53537e22			0.406158
$738$		0			0
$739$			1.46123e23i			1.64272i	0.570409	+	0.821361i	$0.306785\pi$
$739$			1.46123e23i			1.64272i	−0.570409	+	0.821361i	$0.693215\pi$
$740$	6.20440e22	+	1.12901e22i	0.689995	+	0.125558i
$741$		0			0
$742$	−2.65833e21	+	2.94572e22i	−0.0289319	+	0.320598i
$743$		−	3.89731e22i		−	0.419618i	−0.977742	−	0.209809i	$-0.932716\pi$
$743$		−	3.89731e22i		−	0.419618i	0.977742	−	0.209809i	$-0.0672842\pi$
$744$		0			0
$745$	−1.15352e23			−1.21556
$746$	−1.33701e23	−	1.20656e22i	−1.39387	−	0.125788i
$747$		0			0
$748$	3.52613e22	−	1.93776e23i	0.359820	−	1.97736i
$749$	−3.70301e22			−0.373852
$750$		0			0
$751$		−	5.23880e22i		−	0.517741i	−0.965912	−	0.258871i	$-0.916650\pi$
$751$		−	5.23880e22i		−	0.517741i	0.965912	−	0.258871i	$-0.0833503\pi$
$752$	−1.77815e22	+	4.72407e22i	−0.173871	+	0.461928i
$753$		0			0
$754$	−3.10104e22	−	2.79849e21i	−0.296850	−	0.0267888i
$755$			1.34335e23i			1.27237i
$756$		0			0
$757$	5.73502e22			0.531824			0.265912	−	0.963997i	$-0.414327\pi$
$757$	5.73502e22			0.531824			0.265912	+	0.963997i	$0.414327\pi$
$758$	−9.80338e21	+	1.08632e23i	−0.0899544	+	0.996794i
$759$		0			0
$760$	2.05830e22	−	7.43718e22i	0.184927	−	0.668189i
$761$	2.70367e22			0.240367			0.120184	−	0.992752i	$-0.461652\pi$
$761$	2.70367e22			0.240367			0.120184	+	0.992752i	$0.461652\pi$
$762$		0			0
$763$		−	4.18596e22i		−	0.364417i
$764$	−3.73021e21	+	2.04991e22i	−0.0321356	+	0.176599i
$765$		0			0
$766$	1.82608e22	−	2.02349e23i	0.154060	−	1.70715i
$767$			7.79368e22i			0.650698i
$768$		0			0
$769$	8.86749e22			0.725087			0.362543	−	0.931967i	$-0.381908\pi$
$769$	8.86749e22			0.725087			0.362543	+	0.931967i	$0.381908\pi$
$770$	7.71923e22	+	6.96612e21i	0.624667	+	0.0563722i
$771$		0			0
$772$	−1.29747e23	−	2.36100e22i	−1.02839	−	0.187136i
$773$	−1.84361e23			−1.44622			−0.723108	−	0.690735i	$-0.757287\pi$
$773$	−1.84361e23			−1.44622			−0.723108	+	0.690735i	$0.757287\pi$
$774$		0			0
$775$			1.98318e22i			0.152387i
$776$	−4.05336e22	−	1.12180e22i	−0.308263	−	0.0853143i
$777$		0			0
$778$	8.23079e22	+	7.42776e21i	0.613203	+	0.0553377i
$779$		−	1.00750e23i		−	0.742923i
$780$		0			0
$781$	−4.38243e23			−3.16597
$782$	−1.92027e22	+	2.12787e23i	−0.137312	+	1.52156i
$783$		0			0
$784$	1.16233e23	+	4.37503e22i	0.814330	+	0.306516i
$785$	−2.35600e23			−1.63387
$786$		0			0
$787$			1.34135e23i			0.911475i	0.890114	+	0.455738i	$0.150624\pi$
$787$			1.34135e23i			0.911475i	−0.890114	+	0.455738i	$0.849376\pi$
$788$	4.43116e22	+	8.06335e21i	0.298063	+	0.0542383i
$789$		0			0
$790$	−1.31176e22	+	1.45357e23i	−0.0864644	+	0.958121i
$791$		−	1.03338e23i		−	0.674292i
$792$		0			0
$793$	−5.14077e22			−0.328732
$794$	−9.12390e22	−	8.23374e21i	−0.577586	−	0.0521234i
$795$		0			0
$796$	−2.65376e22	+	1.45835e23i	−0.164648	+	0.904812i
$797$	4.43256e22			0.272263			0.136131	−	0.990691i	$-0.456533\pi$
$797$	4.43256e22			0.272263			0.136131	+	0.990691i	$0.456533\pi$
$798$		0			0
$799$			8.80983e22i			0.530387i
$800$	−2.02774e22	−	9.79511e21i	−0.120863	−	0.0583834i
$801$		0			0
$802$	2.20444e23	+	1.98937e22i	1.28796	+	0.116231i
$803$		−	2.01845e23i		−	1.16760i
$804$		0			0
$805$	−8.40752e22			−0.476761
$806$	6.14545e21	−	6.80984e22i	0.0345043	−	0.382346i
$807$		0			0
$808$	−5.57913e22	−	1.54407e22i	−0.307097	−	0.0849914i
$809$	−1.26634e23			−0.690182			−0.345091	−	0.938569i	$-0.612152\pi$
$809$	−1.26634e23			−0.690182			−0.345091	+	0.938569i	$0.612152\pi$
$810$		0			0
$811$			8.77902e21i			0.0469115i	0.999725	+	0.0234557i	$0.00746688\pi$
$811$			8.77902e21i			0.0469115i	−0.999725	+	0.0234557i	$0.992533\pi$
$812$	1.07488e22	−	5.90694e22i	0.0568738	−	0.312546i
$813$		0			0
$814$	2.44220e22	−	2.70623e23i	0.126703	−	1.40401i
$815$		−	1.12221e22i		−	0.0576521i
$816$		0			0
$817$	−7.93747e22			−0.399858
$818$	2.74035e23	+	2.47300e22i	1.36704	+	0.123366i
$819$		0			0
$820$	1.86578e23	+	3.39515e22i	0.912745	+	0.166092i
$821$	−1.71008e23			−0.828460			−0.414230	−	0.910172i	$-0.635949\pi$
$821$	−1.71008e23			−0.828460			−0.414230	+	0.910172i	$0.635949\pi$
$822$		0			0
$823$			5.26971e22i			0.250373i	0.992133	+	0.125187i	$0.0399530\pi$
$823$			5.26971e22i			0.250373i	−0.992133	+	0.125187i	$0.960047\pi$
$824$	5.37125e22	−	1.94078e23i	0.252730	−	0.913183i
$825$		0			0
$826$	−1.49675e23	−	1.35072e22i	−0.690730	−	0.0623340i
$827$			1.93464e23i			0.884213i	0.896963	+	0.442107i	$0.145769\pi$
$827$			1.93464e23i			0.884213i	−0.896963	+	0.442107i	$0.854231\pi$
$828$		0			0
$829$	−2.56991e23			−1.15208			−0.576040	−	0.817422i	$-0.695403\pi$
$829$	−2.56991e23			−1.15208			−0.576040	+	0.817422i	$0.695403\pi$
$830$	6.75164e21	−	7.48156e22i	0.0299767	−	0.332175i
$831$		0			0
$832$	6.65933e22	+	3.99179e22i	0.290031	+	0.173853i
$833$	2.16760e23			0.935017
$834$		0			0
$835$			2.40890e22i			0.101936i
$836$	−3.27124e23	−	5.95266e22i	−1.37108	−	0.249494i
$837$		0			0
$838$	−8.39741e21	+	9.30526e22i	−0.0345297	+	0.382628i
$839$			3.64356e23i			1.48399i	0.670407	+	0.741994i	$0.266120\pi$
$839$			3.64356e23i			1.48399i	−0.670407	+	0.741994i	$0.733880\pi$
$840$		0			0
$841$	−5.58195e22			−0.223058
$842$	8.52159e22	+	7.69019e21i	0.337306	+	0.0304397i
$843$		0			0
$844$	−3.74006e22	+	2.05533e23i	−0.145258	+	0.798254i
$845$	−2.14201e23			−0.824078
$846$		0			0
$847$		−	2.38486e23i		−	0.900318i
$848$	2.23523e23	+	8.41347e22i	0.835903	+	0.314636i
$849$		0			0
$850$	−3.91447e22	−	3.53256e21i	−0.143655	−	0.0129640i
$851$			2.94753e23i			1.07157i
$852$		0			0
$853$	3.22578e23			1.15091			0.575457	−	0.817832i	$-0.304824\pi$
$853$	3.22578e23			1.15091			0.575457	+	0.817832i	$0.304824\pi$
$854$	8.90945e21	−	9.87266e22i	0.0314911	−	0.348956i
$855$		0			0
$856$	−7.97572e22	+	2.88184e23i	−0.276681	+	0.999724i
$857$	2.36855e23			0.814021			0.407011	−	0.913423i	$-0.366571\pi$
$857$	2.36855e23			0.814021			0.407011	+	0.913423i	$0.366571\pi$
$858$		0			0
$859$		−	3.99298e23i		−	1.34695i	−0.739210	−	0.673475i	$-0.764801\pi$
$859$		−	3.99298e23i		−	1.34695i	0.739210	−	0.673475i	$-0.235199\pi$
$860$	2.67483e22	−	1.46994e23i	0.0893942	−	0.491260i
$861$		0			0
$862$	2.48262e22	−	2.75102e23i	0.0814427	−	0.902476i
$863$		−	3.41785e23i		−	1.11088i	−0.831557	−	0.555440i	$-0.812550\pi$
$863$		−	3.41785e23i		−	1.11088i	0.831557	−	0.555440i	$-0.187450\pi$
$864$		0			0
$865$	1.15594e23			0.368812
$866$	1.45982e23	+	1.31739e22i	0.461483	+	0.0416459i
$867$		0			0
$868$	1.29715e23	+	2.36042e22i	0.402563	+	0.0732541i
$869$	6.28855e23			1.93372
$870$		0			0
$871$			2.43238e22i			0.0734321i
$872$	−3.25770e23	−	9.01593e22i	−0.974493	−	0.269699i
$873$		0			0
$874$	3.59218e23	+	3.24171e22i	1.05503	+	0.0952101i
$875$		−	1.30695e23i		−	0.380361i
$876$		0			0
$877$	2.80711e23			0.802164			0.401082	−	0.916042i	$-0.368634\pi$
$877$	2.80711e23			0.802164			0.401082	+	0.916042i	$0.368634\pi$
$878$	−4.91664e22	+	5.44818e23i	−0.139223	+	1.54275i
$879$		0			0
$880$	2.20474e23	−	5.85740e23i	0.613050	−	1.62871i
$881$	1.47052e23			0.405195			0.202597	−	0.979262i	$-0.435062\pi$
$881$	1.47052e23			0.405195			0.202597	+	0.979262i	$0.435062\pi$
$882$		0			0
$883$		−	4.38492e23i		−	1.18652i	−0.805010	−	0.593261i	$-0.797840\pi$
$883$		−	4.38492e23i		−	1.18652i	0.805010	−	0.593261i	$-0.202160\pi$
$884$	1.33320e23	+	2.42602e22i	0.357501	+	0.0650542i
$885$		0			0
$886$	−4.50125e22	+	4.98788e23i	−0.118540	+	1.31355i
$887$		−	2.97487e23i		−	0.776388i	−0.921578	−	0.388194i	$-0.873099\pi$
$887$		−	2.97487e23i		−	0.776388i	0.921578	−	0.388194i	$-0.126901\pi$
$888$		0			0
$889$	2.67411e23			0.685433
$890$	5.51714e23	+	4.97887e22i	1.40150	+	0.126477i
$891$		0			0
$892$	1.96242e22	−	1.07843e23i	0.0489635	−	0.269075i
$893$	1.48724e23			0.367764
$894$		0			0
$895$			4.78125e23i			1.16133i
$896$	−8.82022e22	+	1.20972e23i	−0.212332	+	0.291219i
$897$		0			0
$898$	2.83102e23	+	2.55482e22i	0.669473	+	0.0604157i
$899$			4.26959e23i			1.00071i
$900$		0			0
$901$	4.16844e23			0.959787
$902$	7.34416e22	−	8.13814e23i	0.167606	−	1.85726i
$903$		0			0
$904$	−8.04221e23	−	2.22574e23i	−1.80313	−	0.499031i
$905$	1.49405e23			0.332029
$906$		0			0
$907$			2.39210e23i			0.522301i	0.965298	+	0.261150i	$0.0841019\pi$
$907$			2.39210e23i			0.522301i	−0.965298	+	0.261150i	$0.915898\pi$
$908$	1.38964e22	−	7.63668e22i	0.0300757	−	0.165279i
$909$		0			0
$910$	−4.79277e21	+	5.31092e22i	−0.0101919	+	0.112938i
$911$		−	1.25620e22i		−	0.0264796i	−0.999912	−	0.0132398i	$-0.995786\pi$
$911$		−	1.25620e22i		−	0.0264796i	0.999912	−	0.0132398i	$-0.00421449\pi$
$912$		0			0
$913$	−3.23673e23			−0.670409
$914$	1.21559e22	+	1.09699e21i	0.0249584	+	0.00225234i
$915$		0			0
$916$	−3.54342e23	−	6.44794e22i	−0.714923	−	0.130094i
$917$	−1.16080e23			−0.232167
$918$		0			0
$919$			6.42061e23i			1.26198i	0.775791	+	0.630990i	$0.217351\pi$
$919$			6.42061e23i			1.26198i	−0.775791	+	0.630990i	$0.782649\pi$
$920$	−1.81085e23	+	6.54309e23i	−0.352842	+	1.27491i
$921$		0			0
$922$	−2.10846e23	−	1.90276e22i	−0.403756	−	0.0364364i
$923$		−	3.01516e23i		−	0.572397i
$924$		0			0
$925$	−5.42233e22			−0.101170
$926$	1.88767e22	−	2.09174e23i	0.0349170	−	0.386919i
$927$		0			0
$928$	−4.36552e23	−	2.10879e23i	−0.793693	−	0.383397i
$929$	−4.46521e23			−0.804852			−0.402426	−	0.915452i	$-0.631833\pi$
$929$	−4.46521e23			−0.804852			−0.402426	+	0.915452i	$0.631833\pi$
$930$		0			0
$931$		−	3.65926e23i		−	0.648329i
$932$	−6.45545e23	−	1.17469e23i	−1.13396	−	0.206347i
$933$		0			0
$934$	−9.38602e21	+	1.04008e23i	−0.0162071	+	0.179593i
$935$		−	1.09234e24i		−	1.87009i
$936$		0			0
$937$	5.19426e23			0.874191			0.437096	−	0.899415i	$-0.356007\pi$
$937$	5.19426e23			0.874191			0.437096	+	0.899415i	$0.356007\pi$
$938$	−4.67129e22	−	4.21555e21i	−0.0779497	−	0.00703447i
$939$		0			0
$940$	−5.01182e22	+	2.75421e23i	−0.0822191	+	0.451829i
$941$	−1.04009e24			−1.69182			−0.845909	−	0.533327i	$-0.820941\pi$
$941$	−1.04009e24			−1.69182			−0.845909	+	0.533327i	$0.820941\pi$
$942$		0			0
$943$			8.86378e23i			1.41751i
$944$	−4.27496e23	+	1.13574e24i	−0.677885	+	1.80096i
$945$		0			0
$946$	−6.41156e23	−	5.78603e22i	−0.999619	−	0.0902093i
$947$		−	1.98252e22i		−	0.0306491i	−0.999883	−	0.0153245i	$-0.995122\pi$
$947$		−	1.98252e22i		−	0.0306491i	0.999883	−	0.0153245i	$-0.00487814\pi$
$948$		0			0
$949$	1.38872e23			0.211098
$950$	−5.96352e21	+	6.60824e22i	−0.00898904	+	0.0996086i
$951$		0			0
$952$	−6.96964e22	+	2.51832e23i	−0.103303	+	0.373263i
$953$	9.30478e23			1.36761			0.683806	−	0.729664i	$-0.260324\pi$
$953$	9.30478e23			1.36761			0.683806	+	0.729664i	$0.260324\pi$
$954$		0			0
$955$			1.15556e23i			0.167019i
$956$	6.15042e21	−	3.37992e22i	0.00881539	−	0.0484444i
$957$		0			0
$958$	3.06387e22	−	3.39510e23i	0.0431863	−	0.478552i
$959$			8.59505e22i			0.120143i
$960$		0			0
$961$	−2.10172e23			−0.288926
$962$	1.86192e23	+	1.68026e22i	0.253840	+	0.0229074i
$963$		0			0
$964$	−1.63592e23	−	2.97686e22i	−0.219354	−	0.0399156i
$965$	−7.31397e23			−0.972601
$966$		0			0
$967$		−	2.80402e23i		−	0.366749i	−0.983043	−	0.183374i	$-0.941298\pi$
$967$		−	2.80402e23i		−	0.366749i	0.983043	−	0.183374i	$-0.0587020\pi$
$968$	−1.85600e24	−	5.13663e23i	−2.40755	−	0.666309i
$969$		0			0
$970$	−2.32307e23	−	2.09643e22i	−0.296407	−	0.0267489i
$971$			1.51191e24i			1.91325i	0.291329	+	0.956623i	$0.405903\pi$
$971$			1.51191e24i			1.91325i	−0.291329	+	0.956623i	$0.594097\pi$
$972$		0			0
$973$	−2.55719e23			−0.318317
$974$	−6.66525e22	+	7.38584e23i	−0.0822896	+	0.911860i
$975$		0			0
$976$	−7.49144e23	−	2.81979e23i	−0.909843	−	0.342467i
$977$	9.63725e23			1.16090			0.580452	−	0.814294i	$-0.302876\pi$
$977$	9.63725e23			1.16090			0.580452	+	0.814294i	$0.302876\pi$
$978$		0			0
$979$		−	2.38686e24i		−	2.82856i
$980$	6.77656e23	+	1.23313e23i	0.796528	+	0.144944i
$981$		0			0
$982$	−3.87534e22	+	4.29431e23i	−0.0448145	+	0.496594i
$983$			5.76517e23i			0.661278i	0.943757	+	0.330639i	$0.107264\pi$
$983$			5.76517e23i			0.661278i	−0.943757	+	0.330639i	$0.892736\pi$
$984$		0			0
$985$	2.49789e23			0.281893
$986$	−8.42744e23	−	7.60523e22i	−0.943366	−	0.0851328i
$987$		0			0
$988$	4.09550e22	−	2.25065e23i	0.0451078	−	0.247887i
$989$	6.98325e23			0.762934
$990$		0			0
$991$		−	7.09157e23i		−	0.762348i	−0.924503	−	0.381174i	$-0.875520\pi$
$991$		−	7.09157e23i		−	0.762348i	0.924503	−	0.381174i	$-0.124480\pi$
$992$	4.63086e23	−	9.58662e23i	0.493820	−	1.02229i
$993$		0			0
$994$	5.79051e23	+	5.22557e22i	0.607611	+	0.0548331i
$995$			8.22089e23i			0.855725i
$996$		0			0
$997$	6.99549e23			0.716567			0.358284	−	0.933613i	$-0.383362\pi$
$997$	6.99549e23			0.716567			0.358284	+	0.933613i	$0.383362\pi$
$998$	7.68114e22	−	8.51155e23i	0.0780515	−	0.864897i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.17.d.d.19.16		16
3.2	odd	2		12.17.d.a.7.1	✓	16
4.3	odd	2	inner	36.17.d.d.19.15		16
12.11	even	2		12.17.d.a.7.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.17.d.a.7.1	✓	16	3.2	odd	2
12.17.d.a.7.2	yes	16	12.11	even	2
36.17.d.d.19.15		16	4.3	odd	2	inner
36.17.d.d.19.16		16	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	36.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(254.964 + 23.0089i) q^{2} +(64477.2 + 11732.9i) q^{4} +363465. q^{5} +2.07768e6i q^{7} +(1.61694e7 + 4.47501e6i) q^{8} +O(q^{10})\)	\(q+(254.964 + 23.0089i) q^{2} +(64477.2 + 11732.9i) q^{4} +363465. q^{5} +2.07768e6i q^{7} +(1.61694e7 + 4.47501e6i) q^{8} +(9.26704e7 + 8.36292e6i) q^{10} -4.00917e8i q^{11} +2.75836e8 q^{13} +(-4.78050e7 + 5.29733e8i) q^{14} +(4.01965e9 + 1.51300e9i) q^{16} +7.49616e9 q^{17} -1.26547e10i q^{19} +(2.34352e10 + 4.26449e9i) q^{20} +(9.22466e9 - 1.02219e11i) q^{22} +1.11334e11i q^{23} -2.04812e10 q^{25} +(7.03282e10 + 6.34667e9i) q^{26} +(-2.43771e10 + 1.33963e11i) q^{28} -4.40939e11 q^{29} -9.68295e11i q^{31} +(9.90052e11 + 4.78249e11i) q^{32} +(1.91125e12 + 1.72478e11i) q^{34} +7.55163e11i q^{35} +2.64747e12 q^{37} +(2.91170e11 - 3.22649e12i) q^{38} +(5.87701e12 + 1.62651e12i) q^{40} +7.96145e12 q^{41} -6.27235e12i q^{43} +(4.70391e12 - 2.58500e13i) q^{44} +(-2.56167e12 + 2.83861e13i) q^{46} +1.17525e13i q^{47} +2.89162e13 q^{49} +(-5.22196e12 - 4.71249e11i) q^{50} +(1.77851e13 + 3.23635e12i) q^{52} +5.56077e13 q^{53} -1.45719e14i q^{55} +(-9.29762e12 + 3.35948e13i) q^{56} +(-1.12423e14 - 1.01455e13i) q^{58} +2.82548e14i q^{59} -1.86371e14 q^{61} +(2.22794e13 - 2.46880e14i) q^{62} +(2.41424e14 + 1.44716e14i) q^{64} +1.00257e14 q^{65} +8.81821e13i q^{67} +(4.83331e14 + 8.79514e13i) q^{68} +(-1.73755e13 + 1.92539e14i) q^{70} -1.09310e15i q^{71} +5.03458e14 q^{73} +(6.75009e14 + 6.09153e13i) q^{74} +(1.48476e14 - 8.15939e14i) q^{76} +8.32977e14 q^{77} +1.56854e15i q^{79} +(1.46100e15 + 5.49924e14i) q^{80} +(2.02988e15 + 1.83184e14i) q^{82} -8.07330e14i q^{83} +2.72459e15 q^{85} +(1.44320e14 - 1.59922e15i) q^{86} +(1.79411e15 - 6.48259e15i) q^{88} +5.95350e15 q^{89} +5.73098e14i q^{91} +(-1.30626e15 + 7.17849e15i) q^{92} +(-2.70411e14 + 2.99645e15i) q^{94} -4.59954e15i q^{95} -2.50681e15 q^{97} +(7.37258e15 + 6.65329e14i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 186 q^{2} + 136588 q^{4} - 354144 q^{5} - 14683680 q^{8}+O(q^{10}) \) 16 * q + 186 * q^2 + 136588 * q^4 - 354144 * q^5 - 14683680 * q^8	\( 16 q + 186 q^{2} + 136588 q^{4} - 354144 q^{5} - 14683680 q^{8} - 49800172 q^{10} - 906419296 q^{13} + 806064072 q^{14} - 2108540816 q^{16} - 12240765600 q^{17} - 1002788712 q^{20} + 216706355928 q^{22} + 206381182512 q^{25} - 1054507182588 q^{26} - 1526063922288 q^{28} - 327679573728 q^{29} + 5158730488416 q^{32} + 9473293385948 q^{34} - 8149494749152 q^{37} - 23318999782920 q^{38} - 28671795971776 q^{40} + 25536724613472 q^{41} + 11442227373552 q^{44} + 9929654732736 q^{46} - 93287012964080 q^{49} + 133601044957998 q^{50} + 302261844234872 q^{52} + 86928436629792 q^{53} - 530930989929024 q^{56} - 189801665049916 q^{58} + 476028596468000 q^{61} + 419080420491096 q^{62} + 305944925720704 q^{64} + 12\!\cdots\!92 q^{65}+ \cdots + 33\!\cdots\!90 q^{98}+O(q^{100}) \) 16 * q + 186 * q^2 + 136588 * q^4 - 354144 * q^5 - 14683680 * q^8 - 49800172 * q^10 - 906419296 * q^13 + 806064072 * q^14 - 2108540816 * q^16 - 12240765600 * q^17 - 1002788712 * q^20 + 216706355928 * q^22 + 206381182512 * q^25 - 1054507182588 * q^26 - 1526063922288 * q^28 - 327679573728 * q^29 + 5158730488416 * q^32 + 9473293385948 * q^34 - 8149494749152 * q^37 - 23318999782920 * q^38 - 28671795971776 * q^40 + 25536724613472 * q^41 + 11442227373552 * q^44 + 9929654732736 * q^46 - 93287012964080 * q^49 + 133601044957998 * q^50 + 302261844234872 * q^52 + 86928436629792 * q^53 - 530930989929024 * q^56 - 189801665049916 * q^58 + 476028596468000 * q^61 + 419080420491096 * q^62 + 305944925720704 * q^64 + 1276571708976192 * q^65 + 1393626893610696 * q^68 + 1815049064679696 * q^70 - 368686901901280 * q^73 - 875633111941836 * q^74 - 4351002030861264 * q^76 + 81504772370688 * q^77 + 8190389938127328 * q^80 + 2390391408733340 * q^82 + 10085047677398464 * q^85 + 894939801424296 * q^86 + 669091386916800 * q^88 + 5711067674201568 * q^89 - 7708247605922304 * q^92 - 9487273535547696 * q^94 - 13564951560560608 * q^97 + 33011660914531290 * q^98

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