LMFDB - Embedded newform 36.17.d.d.19.5

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			19.5
Root			$159.117 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	36.19
Dual form			36.17.d.d.19.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-196.501 - 164.084i) q^{2} +(11689.0 + 64485.1i) q^{4} +45026.4 q^{5} +3.24149e6i q^{7} +(8.28406e6 - 1.45894e7i) q^{8} +O(q^{10})$	\(q+(-196.501 - 164.084i) q^{2} +(11689.0 + 64485.1i) q^{4} +45026.4 q^{5} +3.24149e6i q^{7} +(8.28406e6 - 1.45894e7i) q^{8} +(-8.84773e6 - 7.38811e6i) q^{10} -2.75960e7i q^{11} -6.92488e8 q^{13} +(5.31875e8 - 6.36954e8i) q^{14} +(-4.02170e9 + 1.50754e9i) q^{16} -2.60696e9 q^{17} -1.17841e10i q^{19} +(5.26316e8 + 2.90354e9i) q^{20} +(-4.52806e9 + 5.42264e9i) q^{22} -3.87992e9i q^{23} -1.50561e11 q^{25} +(1.36074e11 + 1.13626e11i) q^{26} +(-2.09028e11 + 3.78899e10i) q^{28} +6.46281e11 q^{29} +9.55575e11i q^{31} +(1.03763e12 + 3.63663e11i) q^{32} +(5.12270e11 + 4.27761e11i) q^{34} +1.45953e11i q^{35} +6.34959e12 q^{37} +(-1.93358e12 + 2.31558e12i) q^{38} +(3.73002e11 - 6.56907e11i) q^{40} -1.16356e13 q^{41} +1.79375e13i q^{43} +(1.77953e12 - 3.22571e11i) q^{44} +(-6.36633e11 + 7.62408e11i) q^{46} -3.29643e13i q^{47} +2.27257e13 q^{49} +(2.95852e13 + 2.47045e13i) q^{50} +(-8.09452e12 - 4.46552e13i) q^{52} -5.59722e12 q^{53} -1.24255e12i q^{55} +(4.72912e13 + 2.68527e13i) q^{56} +(-1.26995e14 - 1.06044e14i) q^{58} -1.93936e14i q^{59} -1.41886e13 q^{61} +(1.56794e14 - 1.87771e14i) q^{62} +(-1.44224e14 - 2.41718e14i) q^{64} -3.11803e13 q^{65} -3.51753e14i q^{67} +(-3.04729e13 - 1.68110e14i) q^{68} +(2.39484e13 - 2.86798e13i) q^{70} -8.84835e14i q^{71} +1.70546e14 q^{73} +(-1.24770e15 - 1.04186e15i) q^{74} +(7.59898e14 - 1.37745e14i) q^{76} +8.94522e13 q^{77} -1.50351e15i q^{79} +(-1.81083e14 + 6.78791e13i) q^{80} +(2.28641e15 + 1.90922e15i) q^{82} +4.88125e14i q^{83} -1.17382e14 q^{85} +(2.94326e15 - 3.52474e15i) q^{86} +(-4.02609e14 - 2.28607e14i) q^{88} +7.27333e15 q^{89} -2.24469e15i q^{91} +(2.50197e14 - 4.53526e13i) q^{92} +(-5.40891e15 + 6.47752e15i) q^{94} -5.30595e14i q^{95} -1.59239e15 q^{97} +(-4.46562e15 - 3.72892e15i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−196.501	−	164.084i	−0.767581	−	0.640952i
$2$	−196.501	−	164.084i	−0.767581	−	0.640952i
$3$		0			0
$3$		0			0
$4$	11689.0	+	64485.1i	0.178361	+	0.983965i
$5$	45026.4			0.115268			0.0576338	−	0.998338i	$-0.481644\pi$
$5$	45026.4			0.115268			0.0576338	+	0.998338i	$0.481644\pi$
$6$		0			0
$7$			3.24149e6i			0.562289i	0.959665	+	0.281145i	$0.0907141\pi$
$7$			3.24149e6i			0.562289i	−0.959665	+	0.281145i	$0.909286\pi$
$8$	8.28406e6	−	1.45894e7i	0.493768	−	0.869593i
$9$		0			0
$10$	−8.84773e6	−	7.38811e6i	−0.0884773	−	0.0738811i
$11$		−	2.75960e7i		−	0.128738i	−0.997926	−	0.0643688i	$-0.979497\pi$
$11$		−	2.75960e7i		−	0.128738i	0.997926	−	0.0643688i	$-0.0205034\pi$
$12$		0			0
$13$	−6.92488e8			−0.848917			−0.424459	−	0.905447i	$-0.639536\pi$
$13$	−6.92488e8			−0.848917			−0.424459	+	0.905447i	$0.639536\pi$
$14$	5.31875e8	−	6.36954e8i	0.360401	−	0.431602i
$15$		0			0
$16$	−4.02170e9	+	1.50754e9i	−0.936375	+	0.351001i
$17$	−2.60696e9			−0.373718			−0.186859	−	0.982387i	$-0.559831\pi$
$17$	−2.60696e9			−0.373718			−0.186859	+	0.982387i	$0.559831\pi$
$18$		0			0
$19$		−	1.17841e10i		−	0.693852i	−0.937892	−	0.346926i	$-0.887225\pi$
$19$		−	1.17841e10i		−	0.693852i	0.937892	−	0.346926i	$-0.112775\pi$
$20$	5.26316e8	+	2.90354e9i	0.0205592	+	0.113419i
$21$		0			0
$22$	−4.52806e9	+	5.42264e9i	−0.0825146	+	0.0988165i
$23$		−	3.87992e9i		−	0.0495451i	−0.999693	−	0.0247725i	$-0.992114\pi$
$23$		−	3.87992e9i		−	0.0495451i	0.999693	−	0.0247725i	$-0.00788615\pi$
$24$		0			0
$25$	−1.50561e11			−0.986713
$26$	1.36074e11	+	1.13626e11i	0.651612	+	0.544115i
$27$		0			0
$28$	−2.09028e11	+	3.78899e10i	−0.553273	+	0.100290i
$29$	6.46281e11			1.29193			0.645963	−	0.763369i	$-0.276456\pi$
$29$	6.46281e11			1.29193			0.645963	+	0.763369i	$0.276456\pi$
$30$		0			0
$31$			9.55575e11i			1.12040i	0.828359	+	0.560198i	$0.189275\pi$
$31$			9.55575e11i			1.12040i	−0.828359	+	0.560198i	$0.810725\pi$
$32$	1.03763e12	+	3.63663e11i	0.943718	+	0.330750i
$33$		0			0
$34$	5.12270e11	+	4.27761e11i	0.286859	+	0.239535i
$35$			1.45953e11i			0.0648138i
$36$		0			0
$37$	6.34959e12			1.80772			0.903861	−	0.427826i	$-0.140720\pi$
$37$	6.34959e12			1.80772			0.903861	+	0.427826i	$0.140720\pi$
$38$	−1.93358e12	+	2.31558e12i	−0.444726	+	0.532588i
$39$		0			0
$40$	3.73002e11	−	6.56907e11i	0.0569156	−	0.100236i
$41$	−1.16356e13			−1.45720			−0.728600	−	0.684939i	$-0.759829\pi$
$41$	−1.16356e13			−1.45720			−0.728600	+	0.684939i	$0.759829\pi$
$42$		0			0
$43$			1.79375e13i			1.53467i	0.641246	+	0.767335i	$0.278418\pi$
$43$			1.79375e13i			1.53467i	−0.641246	+	0.767335i	$0.721582\pi$
$44$	1.77953e12	−	3.22571e11i	0.126673	−	0.0229617i
$45$		0			0
$46$	−6.36633e11	+	7.62408e11i	−0.0317560	+	0.0380299i
$47$		−	3.29643e13i		−	1.38440i	−0.721706	−	0.692200i	$-0.756642\pi$
$47$		−	3.29643e13i		−	1.38440i	0.721706	−	0.692200i	$-0.243358\pi$
$48$		0			0
$49$	2.27257e13			0.683831
$50$	2.95852e13	+	2.47045e13i	0.757382	+	0.632436i
$51$		0			0
$52$	−8.09452e12	−	4.46552e13i	−0.151413	−	0.835305i
$53$	−5.59722e12			−0.0899013			−0.0449506	−	0.998989i	$-0.514313\pi$
$53$	−5.59722e12			−0.0899013			−0.0449506	+	0.998989i	$0.514313\pi$
$54$		0			0
$55$		−	1.24255e12i		−	0.0148393i
$56$	4.72912e13	+	2.68527e13i	0.488963	+	0.277641i
$57$		0			0
$58$	−1.26995e14	−	1.06044e14i	−0.991657	−	0.828062i
$59$		−	1.93936e14i		−	1.32082i	−0.750906	−	0.660409i	$-0.770383\pi$
$59$		−	1.93936e14i		−	1.32082i	0.750906	−	0.660409i	$-0.229617\pi$
$60$		0			0
$61$	−1.41886e13			−0.0740117			−0.0370058	−	0.999315i	$-0.511782\pi$
$61$	−1.41886e13			−0.0740117			−0.0370058	+	0.999315i	$0.511782\pi$
$62$	1.56794e14	−	1.87771e14i	0.718120	−	0.859994i
$63$		0			0
$64$	−1.44224e14	−	2.41718e14i	−0.512385	−	0.858756i
$65$	−3.11803e13			−0.0978527
$66$		0			0
$67$		−	3.51753e14i		−	0.866242i	−0.901336	−	0.433121i	$-0.857412\pi$
$67$		−	3.51753e14i		−	0.866242i	0.901336	−	0.433121i	$-0.142588\pi$
$68$	−3.04729e13	−	1.68110e14i	−0.0666565	−	0.367725i
$69$		0			0
$70$	2.39484e13	−	2.86798e13i	0.0415425	−	0.0497498i
$71$		−	8.84835e14i		−	1.37024i	−0.728432	−	0.685119i	$-0.759750\pi$
$71$		−	8.84835e14i		−	1.37024i	0.728432	−	0.685119i	$-0.240250\pi$
$72$		0			0
$73$	1.70546e14			0.211475			0.105737	−	0.994394i	$-0.466280\pi$
$73$	1.70546e14			0.211475			0.105737	+	0.994394i	$0.466280\pi$
$74$	−1.24770e15	−	1.04186e15i	−1.38757	−	1.15866i
$75$		0			0
$76$	7.59898e14	−	1.37745e14i	0.682727	−	0.123756i
$77$	8.94522e13			0.0723878
$78$		0			0
$79$		−	1.50351e15i		−	0.991037i	−0.868597	−	0.495519i	$-0.834978\pi$
$79$		−	1.50351e15i		−	0.991037i	0.868597	−	0.495519i	$-0.165022\pi$
$80$	−1.81083e14	+	6.78791e13i	−0.107934	+	0.0404591i
$81$		0			0
$82$	2.28641e15	+	1.90922e15i	1.11852	+	0.933996i
$83$			4.88125e14i			0.216724i	0.994112	+	0.108362i	$0.0345605\pi$
$83$			4.88125e14i			0.216724i	−0.994112	+	0.108362i	$0.965439\pi$
$84$		0			0
$85$	−1.17382e14			−0.0430776
$86$	2.94326e15	−	3.52474e15i	0.983650	−	1.17798i
$87$		0			0
$88$	−4.02609e14	−	2.28607e14i	−0.111949	−	0.0635666i
$89$	7.27333e15			1.84762			0.923811	−	0.382849i	$-0.125057\pi$
$89$	7.27333e15			1.84762			0.923811	+	0.382849i	$0.125057\pi$
$90$		0			0
$91$		−	2.24469e15i		−	0.477337i
$92$	2.50197e14	−	4.53526e13i	0.0487506	−	0.00883689i
$93$		0			0
$94$	−5.40891e15	+	6.47752e15i	−0.887334	+	1.06264i
$95$		−	5.30595e14i		−	0.0799787i
$96$		0			0
$97$	−1.59239e15			−0.203178			−0.101589	−	0.994826i	$-0.532393\pi$
$97$	−1.59239e15			−0.203178			−0.101589	+	0.994826i	$0.532393\pi$
$98$	−4.46562e15	−	3.72892e15i	−0.524895	−	0.438303i
$99$		0			0
$100$	−1.75991e15	−	9.70892e15i	−0.175991	−	0.970892i
$101$	−7.05130e15			−0.651176			−0.325588	−	0.945512i	$-0.605562\pi$
$101$	−7.05130e15			−0.651176			−0.325588	+	0.945512i	$0.605562\pi$
$102$		0			0
$103$		−	3.22497e15i		−	0.254582i	−0.991865	−	0.127291i	$-0.959372\pi$
$103$		−	3.22497e15i		−	0.254582i	0.991865	−	0.127291i	$-0.0406282\pi$
$104$	−5.73661e15	+	1.01030e16i	−0.419169	+	0.738213i
$105$		0			0
$106$	1.09986e15	+	9.18414e14i	0.0690065	+	0.0576224i
$107$		−	1.41542e16i		−	0.823785i	−0.911233	−	0.411892i	$-0.864868\pi$
$107$		−	1.41542e16i		−	0.823785i	0.911233	−	0.411892i	$-0.135132\pi$
$108$		0			0
$109$	2.21392e16			1.11109			0.555546	−	0.831486i	$-0.312509\pi$
$109$	2.21392e16			1.11109			0.555546	+	0.831486i	$0.312509\pi$
$110$	−2.03883e14	+	2.44162e14i	−0.00951127	+	0.0113903i
$111$		0			0
$112$	−4.88667e15	−	1.30363e16i	−0.197364	−	0.526514i
$113$	−1.02991e16			−0.387411			−0.193705	−	0.981060i	$-0.562051\pi$
$113$	−1.02991e16			−0.387411			−0.193705	+	0.981060i	$0.562051\pi$
$114$		0			0
$115$		−	1.74699e14i		−	0.00571095i
$116$	7.55440e15	+	4.16755e16i	0.230429	+	1.27121i
$117$		0			0
$118$	−3.18218e16	+	3.81086e16i	−0.846581	+	1.01383i
$119$		−	8.45044e15i		−	0.210138i
$120$		0			0
$121$	4.51882e16			0.983427
$122$	2.78807e15	+	2.32812e15i	0.0568099	+	0.0474379i
$123$		0			0
$124$	−6.16204e16	+	1.11698e16i	−1.10243	+	0.199834i
$125$	−1.36497e16			−0.229004
$126$		0			0
$127$			2.78419e15i			0.0411404i	0.999788	+	0.0205702i	$0.00654816\pi$
$127$			2.78419e15i			0.0411404i	−0.999788	+	0.0205702i	$0.993452\pi$
$128$	−1.13220e16	+	7.11626e16i	−0.157124	+	0.987579i
$129$		0			0
$130$	6.12694e15	+	5.11617e15i	0.0751099	+	0.0627189i
$131$			8.46988e16i			0.976577i	0.872682	+	0.488289i	$0.162379\pi$
$131$			8.46988e16i			0.976577i	−0.872682	+	0.488289i	$0.837621\pi$
$132$		0			0
$133$	3.81979e16			0.390146
$134$	−5.77170e16	+	6.91197e16i	−0.555220	+	0.664911i
$135$		0			0
$136$	−2.15963e16	+	3.80339e16i	−0.184530	+	0.324983i
$137$	1.59917e17			1.28863			0.644317	−	0.764758i	$-0.277142\pi$
$137$	1.59917e17			1.28863			0.644317	+	0.764758i	$0.277142\pi$
$138$		0			0
$139$		−	4.46000e15i		−	0.0320049i	−0.999872	−	0.0160024i	$-0.994906\pi$
$139$		−	4.46000e15i		−	0.0320049i	0.999872	−	0.0160024i	$-0.00509395\pi$
$140$	−9.41177e15	+	1.70605e15i	−0.0637745	+	0.0115602i
$141$		0			0
$142$	−1.45187e17	+	1.73871e17i	−0.878256	+	1.05177i
$143$			1.91099e16i			0.109288i
$144$		0			0
$145$	2.90997e16			0.148917
$146$	−3.35124e16	−	2.79838e16i	−0.162324	−	0.135545i
$147$		0			0
$148$	7.42206e16	+	4.09454e17i	0.322426	+	1.77874i
$149$	1.63558e17			0.673259			0.336629	−	0.941637i	$-0.390713\pi$
$149$	1.63558e17			0.673259			0.336629	+	0.941637i	$0.390713\pi$
$150$		0			0
$151$		−	4.45986e17i		−	1.65008i	−0.565074	−	0.825041i	$-0.691152\pi$
$151$		−	4.45986e17i		−	1.65008i	0.565074	−	0.825041i	$-0.308848\pi$
$152$	−1.71922e17	−	9.76201e16i	−0.603369	−	0.342602i
$153$		0			0
$154$	−1.75774e16	−	1.46777e16i	−0.0555635	−	0.0463971i
$155$			4.30262e16i			0.129145i
$156$		0			0
$157$	6.72606e17			1.82206			0.911031	−	0.412337i	$-0.135288\pi$
$157$	6.72606e17			1.82206			0.911031	+	0.412337i	$0.135288\pi$
$158$	−2.46702e17	+	2.95441e17i	−0.635208	+	0.760701i
$159$		0			0
$160$	4.67208e16	+	1.63745e16i	0.108780	+	0.0381248i
$161$	1.25767e16			0.0278587
$162$		0			0
$163$		−	6.97357e17i		−	1.39944i	−0.714417	−	0.699720i	$-0.753308\pi$
$163$		−	6.97357e17i		−	1.39944i	0.714417	−	0.699720i	$-0.246692\pi$
$164$	−1.36009e17	−	7.50326e17i	−0.259907	−	1.43383i
$165$		0			0
$166$	8.00934e16	−	9.59169e16i	0.138909	−	0.166353i
$167$		−	1.02388e18i		−	1.69246i	−0.532818	−	0.846230i	$-0.678867\pi$
$167$		−	1.02388e18i		−	1.69246i	0.532818	−	0.846230i	$-0.321133\pi$
$168$		0			0
$169$	−1.85877e17			−0.279340
$170$	2.30657e16	+	1.92605e16i	0.0330655	+	0.0276107i
$171$		0			0
$172$	−1.15670e18	+	2.09673e17i	−1.51006	+	0.273725i
$173$	4.70521e17			0.586423			0.293211	−	0.956048i	$-0.405276\pi$
$173$	4.70521e17			0.586423			0.293211	+	0.956048i	$0.405276\pi$
$174$		0			0
$175$		−	4.88040e17i		−	0.554818i
$176$	4.16021e16	+	1.10983e17i	0.0451870	+	0.120547i
$177$		0			0
$178$	−1.42921e18	−	1.19343e18i	−1.41820	−	1.18424i
$179$		−	1.41139e18i		−	1.33913i	−0.742755	−	0.669564i	$-0.766481\pi$
$179$		−	1.41139e18i		−	1.33913i	0.742755	−	0.669564i	$-0.233519\pi$
$180$		0			0
$181$	5.45235e17			0.473320			0.236660	−	0.971592i	$-0.423947\pi$
$181$	5.45235e17			0.473320			0.236660	+	0.971592i	$0.423947\pi$
$182$	−3.68317e17	+	4.41083e17i	−0.305950	+	0.366395i
$183$		0			0
$184$	−5.66056e16	−	3.21415e16i	−0.0430841	−	0.0244638i
$185$	2.85899e17			0.208372
$186$		0			0
$187$			7.19419e16i			0.0481115i
$188$	2.12571e18	−	3.85322e17i	1.36220	−	0.246922i
$189$		0			0
$190$	−8.70621e16	+	1.04262e17i	−0.0512626	+	0.0613902i
$191$		−	5.83418e17i		−	0.329392i	−0.986344	−	0.164696i	$-0.947336\pi$
$191$		−	5.83418e17i		−	0.329392i	0.986344	−	0.164696i	$-0.0526643\pi$
$192$		0			0
$193$	3.06897e18			1.59417			0.797083	−	0.603870i	$-0.206375\pi$
$193$	3.06897e18			1.59417			0.797083	+	0.603870i	$0.206375\pi$
$194$	3.12907e17	+	2.61286e17i	0.155956	+	0.130227i
$195$		0			0
$196$	2.65642e17	+	1.46547e18i	0.121968	+	0.672866i
$197$	−1.15460e18			−0.508982			−0.254491	−	0.967075i	$-0.581908\pi$
$197$	−1.15460e18			−0.508982			−0.254491	+	0.967075i	$0.581908\pi$
$198$		0			0
$199$			1.38254e18i			0.562149i	0.959686	+	0.281075i	$0.0906909\pi$
$199$			1.38254e18i			0.562149i	−0.959686	+	0.281075i	$0.909309\pi$
$200$	−1.24725e18	+	2.19658e18i	−0.487208	+	0.858039i
$201$		0			0
$202$	1.38559e18	+	1.15700e18i	0.499830	+	0.417373i
$203$			2.09491e18i			0.726436i
$204$		0			0
$205$	−5.23911e17			−0.167968
$206$	−5.29165e17	+	6.33709e17i	−0.163175	+	0.195412i
$207$		0			0
$208$	2.78498e18	−	1.04395e18i	0.794905	−	0.297971i
$209$	−3.25194e17			−0.0893249
$210$		0			0
$211$			1.48026e18i			0.376771i	0.982095	+	0.188385i	$0.0603254\pi$
$211$			1.48026e18i			0.376771i	−0.982095	+	0.188385i	$0.939675\pi$
$212$	−6.54262e16	−	3.60938e17i	−0.0160348	−	0.0884597i
$213$		0			0
$214$	−2.32247e18	+	2.78130e18i	−0.528007	+	0.632321i
$215$			8.07663e17i			0.176898i
$216$		0			0
$217$	−3.09748e18			−0.629987
$218$	−4.35037e18	−	3.63268e18i	−0.852853	−	0.712157i
$219$		0			0
$220$	8.01261e16	−	1.45242e16i	0.0146013	−	0.00264674i
$221$	1.80529e18			0.317255
$222$		0			0
$223$		−	6.05000e17i		−	0.0989274i	−0.998776	−	0.0494637i	$-0.984249\pi$
$223$		−	6.05000e17i		−	0.0989274i	0.998776	−	0.0494637i	$-0.0157512\pi$
$224$	−1.17881e18	+	3.36346e18i	−0.185977	+	0.530643i
$225$		0			0
$226$	2.02378e18	+	1.68991e18i	0.297369	+	0.248312i
$227$			1.25176e19i			1.77547i	0.460356	+	0.887734i	$0.347722\pi$
$227$			1.25176e19i			1.77547i	−0.460356	+	0.887734i	$0.652278\pi$
$228$		0			0
$229$	−1.23160e19			−1.62849			−0.814245	−	0.580521i	$-0.802849\pi$
$229$	−1.23160e19			−1.62849			−0.814245	+	0.580521i	$0.802849\pi$
$230$	−2.86653e16	+	3.43285e16i	−0.00366044	+	0.00438361i
$231$		0			0
$232$	5.35383e18	−	9.42882e18i	0.637912	−	1.12345i
$233$	−1.37425e18			−0.158205			−0.0791024	−	0.996866i	$-0.525205\pi$
$233$	−1.37425e18			−0.158205			−0.0791024	+	0.996866i	$0.525205\pi$
$234$		0			0
$235$		−	1.48427e18i		−	0.159577i
$236$	1.25060e19	−	2.26693e18i	1.29964	−	0.235582i
$237$		0			0
$238$	−1.38658e18	+	1.66052e18i	−0.134688	+	0.161298i
$239$			9.58646e18i			0.900482i	0.892907	+	0.450241i	$0.148662\pi$
$239$			9.58646e18i			0.900482i	−0.892907	+	0.450241i	$0.851338\pi$
$240$		0			0
$241$	−8.84376e18			−0.777142			−0.388571	−	0.921419i	$-0.627031\pi$
$241$	−8.84376e18			−0.777142			−0.388571	+	0.921419i	$0.627031\pi$
$242$	−8.87951e18	−	7.41465e18i	−0.754859	−	0.630329i
$243$		0			0
$244$	−1.65851e17	−	9.14953e17i	−0.0132008	−	0.0728249i
$245$	1.02326e18			0.0788236
$246$		0			0
$247$			8.16033e18i			0.589023i
$248$	1.39412e19	+	7.91604e18i	0.974289	+	0.553216i
$249$		0			0
$250$	2.68217e18	+	2.23969e18i	0.175779	+	0.146781i
$251$		−	1.29171e19i		−	0.819928i	−0.912102	−	0.409964i	$-0.865541\pi$
$251$		−	1.29171e19i		−	0.819928i	0.912102	−	0.409964i	$-0.134459\pi$
$252$		0			0
$253$	−1.07071e17			−0.00637831
$254$	4.56840e17	−	5.47095e17i	0.0263690	−	0.0315786i
$255$		0			0
$256$	1.39014e19	−	1.21257e19i	0.753596	−	0.657338i
$257$	−2.12187e19			−1.11495			−0.557474	−	0.830195i	$-0.688229\pi$
$257$	−2.12187e19			−1.11495			−0.557474	+	0.830195i	$0.688229\pi$
$258$		0			0
$259$			2.05821e19i			1.01646i
$260$	−3.64467e17	−	2.01066e18i	−0.0174531	−	0.0962837i
$261$		0			0
$262$	1.38977e19	−	1.66434e19i	0.625939	−	0.749602i
$263$		−	1.52461e19i		−	0.666060i	−0.942916	−	0.333030i	$-0.891929\pi$
$263$		−	1.52461e19i		−	0.666060i	0.942916	−	0.333030i	$-0.108071\pi$
$264$		0			0
$265$	−2.52023e17			−0.0103627
$266$	−7.50592e18	−	6.26766e18i	−0.299468	−	0.250065i
$267$		0			0
$268$	2.26828e19	−	4.11165e18i	0.852352	−	0.154503i
$269$	−2.80251e19			−1.02218			−0.511092	−	0.859526i	$-0.670759\pi$
$269$	−2.80251e19			−1.02218			−0.511092	+	0.859526i	$0.670759\pi$
$270$		0			0
$271$			4.19385e19i			1.44165i	0.693119	+	0.720824i	$0.256236\pi$
$271$			4.19385e19i			1.44165i	−0.693119	+	0.720824i	$0.743764\pi$
$272$	1.04844e19	−	3.93010e18i	0.349940	−	0.131175i
$273$		0			0
$274$	−3.14238e19	−	2.62398e19i	−0.989131	−	0.825953i
$275$			4.15487e18i			0.127027i
$276$		0			0
$277$	2.75902e19			0.796006			0.398003	−	0.917384i	$-0.369703\pi$
$277$	2.75902e19			0.796006			0.398003	+	0.917384i	$0.369703\pi$
$278$	−7.31813e17	+	8.76393e17i	−0.0205136	+	0.0245663i
$279$		0			0
$280$	2.12935e18	+	1.20908e18i	0.0563616	+	0.0320030i
$281$	1.24012e19			0.319017			0.159508	−	0.987197i	$-0.449009\pi$
$281$	1.24012e19			0.319017			0.159508	+	0.987197i	$0.449009\pi$
$282$		0			0
$283$		−	2.72260e19i		−	0.661748i	−0.943675	−	0.330874i	$-0.892656\pi$
$283$		−	2.72260e19i		−	0.661748i	0.943675	−	0.330874i	$-0.107344\pi$
$284$	5.70587e19	−	1.03429e19i	1.34827	−	0.244396i
$285$		0			0
$286$	3.13563e18	−	3.75511e18i	0.0700481	−	0.0838870i
$287$		−	3.77167e19i		−	0.819368i
$288$		0			0
$289$	−4.18649e19			−0.860335
$290$	−5.71812e18	−	4.77479e18i	−0.114306	−	0.0954488i
$291$		0			0
$292$	1.99352e18	+	1.09977e19i	0.0377187	+	0.208084i
$293$	7.20983e19			1.32735			0.663673	−	0.748023i	$-0.268997\pi$
$293$	7.20983e19			1.32735			0.663673	+	0.748023i	$0.268997\pi$
$294$		0			0
$295$		−	8.73226e18i		−	0.152248i
$296$	5.26004e19	−	9.26364e19i	0.892596	−	1.57198i
$297$		0			0
$298$	−3.21393e19	−	2.68372e19i	−0.516781	−	0.431527i
$299$			2.68680e18i			0.0420597i
$300$		0			0
$301$	−5.81443e19			−0.862929
$302$	−7.31790e19	+	8.76365e19i	−1.05762	+	1.26657i
$303$		0			0
$304$	1.77650e19	+	4.73921e19i	0.243543	+	0.649706i
$305$	−6.38861e17			−0.00853116
$306$		0			0
$307$		−	1.20412e20i		−	1.52603i	−0.646383	−	0.763013i	$-0.723719\pi$
$307$		−	1.20412e20i		−	1.52603i	0.646383	−	0.763013i	$-0.276281\pi$
$308$	1.04561e18	+	5.76834e18i	0.0129111	+	0.0712270i
$309$		0			0
$310$	7.05989e18	−	8.45467e18i	0.0827760	−	0.0991295i
$311$			5.06945e19i			0.579266i	0.957138	+	0.289633i	$0.0935332\pi$
$311$			5.06945e19i			0.579266i	−0.957138	+	0.289633i	$0.906467\pi$
$312$		0			0
$313$	4.30599e18			0.0467432			0.0233716	−	0.999727i	$-0.492560\pi$
$313$	4.30599e18			0.0467432			0.0233716	+	0.999727i	$0.492560\pi$
$314$	−1.32167e20	−	1.10364e20i	−1.39858	−	1.16785i
$315$		0			0
$316$	9.69542e19	−	1.75746e19i	0.975146	−	0.176762i
$317$	−9.98544e19			−0.979249			−0.489624	−	0.871934i	$-0.662866\pi$
$317$	−9.98544e19			−0.979249			−0.489624	+	0.871934i	$0.662866\pi$
$318$		0			0
$319$		−	1.78348e19i		−	0.166319i
$320$	−6.49388e18	−	1.08837e19i	−0.0590615	−	0.0989868i
$321$		0			0
$322$	−2.47133e18	−	2.06364e18i	−0.0213838	−	0.0178561i
$323$			3.07207e19i			0.259305i
$324$		0			0
$325$	1.04261e20			0.837638
$326$	−1.14425e20	+	1.37031e20i	−0.896975	+	1.07418i
$327$		0			0
$328$	−9.63903e19	+	1.69756e20i	−0.719520	+	1.26717i
$329$	1.06853e20			0.778433
$330$		0			0
$331$		−	3.89785e19i		−	0.270521i	−0.990810	−	0.135260i	$-0.956813\pi$
$331$		−	3.89785e19i		−	0.270521i	0.990810	−	0.135260i	$-0.0431871\pi$
$332$	−3.14768e19	+	5.70571e18i	−0.213249	+	0.0386550i
$333$		0			0
$334$	−1.68002e20	+	2.01194e20i	−1.08479	+	1.29910i
$335$		−	1.58382e19i		−	0.0998498i
$336$		0			0
$337$	1.58332e20			0.951767			0.475883	−	0.879508i	$-0.342128\pi$
$337$	1.58332e20			0.951767			0.475883	+	0.879508i	$0.342128\pi$
$338$	3.65250e19	+	3.04994e19i	0.214416	+	0.179043i
$339$		0			0
$340$	−1.37209e18	−	7.56942e18i	−0.00768334	−	0.0423868i
$341$	2.63701e19			0.144237
$342$		0			0
$343$			1.81389e20i			0.946800i
$344$	2.61697e20	+	1.48596e20i	1.33454	+	0.757772i
$345$		0			0
$346$	−9.24578e19	−	7.72049e19i	−0.450127	−	0.375869i
$347$			3.30940e20i			1.57439i	0.616701	+	0.787197i	$0.288469\pi$
$347$			3.30940e20i			1.57439i	−0.616701	+	0.787197i	$0.711531\pi$
$348$		0			0
$349$	1.03699e20			0.471164			0.235582	−	0.971854i	$-0.424300\pi$
$349$	1.03699e20			0.471164			0.235582	+	0.971854i	$0.424300\pi$
$350$	−8.00794e19	+	9.59002e19i	−0.355612	+	0.425868i
$351$		0			0
$352$	1.00357e19	−	2.86345e19i	0.0425799	−	0.121492i
$353$	1.73945e20			0.721465			0.360733	−	0.932669i	$-0.382527\pi$
$353$	1.73945e20			0.721465			0.360733	+	0.932669i	$0.382527\pi$
$354$		0			0
$355$		−	3.98410e19i		−	0.157944i
$356$	8.50182e19	+	4.69022e20i	0.329543	+	1.81800i
$357$		0			0
$358$	−2.31586e20	+	2.77339e20i	−0.858317	+	1.02789i
$359$		−	5.26548e20i		−	1.90846i	−0.299079	−	0.954228i	$-0.596679\pi$
$359$		−	5.26548e20i		−	1.90846i	0.299079	−	0.954228i	$-0.403321\pi$
$360$		0			0
$361$	1.49577e20			0.518569
$362$	−1.07139e20	−	8.94642e19i	−0.363312	−	0.303376i
$363$		0			0
$364$	1.44749e20	−	2.62383e19i	0.469683	−	0.0851381i
$365$	7.67907e18			0.0243762
$366$		0			0
$367$			1.15856e20i			0.352039i	0.984387	+	0.176019i	$0.0563222\pi$
$367$			1.15856e20i			0.352039i	−0.984387	+	0.176019i	$0.943678\pi$
$368$	5.84914e18	+	1.56039e19i	0.0173904	+	0.0463928i
$369$		0			0
$370$	−5.61794e19	−	4.69114e19i	−0.159942	−	0.133556i
$371$		−	1.81433e19i		−	0.0505505i
$372$		0			0
$373$	1.79070e20			0.477916			0.238958	−	0.971030i	$-0.423194\pi$
$373$	1.79070e20			0.477916			0.238958	+	0.971030i	$0.423194\pi$
$374$	1.18045e19	−	1.41366e19i	0.0308372	−	0.0369295i
$375$		0			0
$376$	−4.80929e20	−	2.73079e20i	−1.20387	−	0.683573i
$377$	−4.47542e20			−1.09674
$378$		0			0
$379$		−	5.63500e20i		−	1.32367i	−0.749649	−	0.661836i	$-0.769778\pi$
$379$		−	5.63500e20i		−	1.32367i	0.749649	−	0.661836i	$-0.230222\pi$
$380$	3.42155e19	−	6.20215e18i	0.0786963	−	0.0142651i
$381$		0			0
$382$	−9.57294e19	+	1.14642e20i	−0.211124	+	0.252835i
$383$		−	3.70048e20i		−	0.799222i	−0.916685	−	0.399611i	$-0.869145\pi$
$383$		−	3.70048e20i		−	0.799222i	0.916685	−	0.399611i	$-0.130855\pi$
$384$		0			0
$385$	4.02771e18			0.00834397
$386$	−6.03054e20	−	5.03568e20i	−1.22365	−	1.02178i
$387$		0			0
$388$	−1.86136e19	−	1.02686e20i	−0.0362390	−	0.199920i
$389$	1.44538e20			0.275666			0.137833	−	0.990455i	$-0.455986\pi$
$389$	1.44538e20			0.275666			0.137833	+	0.990455i	$0.455986\pi$
$390$		0			0
$391$			1.01148e19i			0.0185159i
$392$	1.88261e20	−	3.31553e20i	0.337654	−	0.594655i
$393$		0			0
$394$	2.26880e20	+	1.89451e20i	0.390685	+	0.326233i
$395$		−	6.76978e19i		−	0.114235i
$396$		0			0
$397$	−8.04793e19			−0.130425			−0.0652124	−	0.997871i	$-0.520772\pi$
$397$	−8.04793e19			−0.130425			−0.0652124	+	0.997871i	$0.520772\pi$
$398$	2.26852e20	−	2.71669e20i	0.360311	−	0.431495i
$399$		0			0
$400$	6.05509e20	−	2.26976e20i	0.923934	−	0.346338i
$401$	1.41133e20			0.211093			0.105546	−	0.994414i	$-0.466341\pi$
$401$	1.41133e20			0.211093			0.105546	+	0.994414i	$0.466341\pi$
$402$		0			0
$403$		−	6.61724e20i		−	0.951123i
$404$	−8.24229e19	−	4.54704e20i	−0.116144	−	0.640734i
$405$		0			0
$406$	3.43741e20	−	4.11651e20i	0.465611	−	0.557598i
$407$		−	1.75223e20i		−	0.232722i
$408$		0			0
$409$	1.27269e20			0.162531			0.0812654	−	0.996693i	$-0.474104\pi$
$409$	1.27269e20			0.162531			0.0812654	+	0.996693i	$0.474104\pi$
$410$	1.02949e20	+	8.59653e19i	0.128929	+	0.107660i
$411$		0			0
$412$	2.07963e20	−	3.76968e19i	0.250500	−	0.0454074i
$413$	6.28642e20			0.742682
$414$		0			0
$415$			2.19785e19i			0.0249812i
$416$	−7.18546e20	−	2.51832e20i	−0.801139	−	0.280779i
$417$		0			0
$418$	6.39009e19	+	5.33591e19i	0.0685641	+	0.0572530i
$419$			1.22983e21i			1.29459i	0.762240	+	0.647295i	$0.224100\pi$
$419$			1.22983e21i			1.29459i	−0.762240	+	0.647295i	$0.775900\pi$
$420$		0			0
$421$	−1.70492e21			−1.72762			−0.863810	−	0.503818i	$-0.831928\pi$
$421$	−1.70492e21			−1.72762			−0.863810	+	0.503818i	$0.831928\pi$
$422$	2.42886e20	−	2.90871e20i	0.241492	−	0.289202i
$423$		0			0
$424$	−4.63677e19	+	8.16599e19i	−0.0443904	+	0.0781775i
$425$	3.92506e20			0.368752
$426$		0			0
$427$		−	4.59921e19i		−	0.0416160i
$428$	9.12733e20	−	1.65448e20i	0.810575	−	0.146931i
$429$		0			0
$430$	1.32524e20	−	1.58706e20i	0.113383	−	0.135783i
$431$		−	1.28885e21i		−	1.08239i	−0.840896	−	0.541197i	$-0.817971\pi$
$431$		−	1.28885e21i		−	1.08239i	0.840896	−	0.541197i	$-0.182029\pi$
$432$		0			0
$433$	−1.15744e21			−0.936686			−0.468343	−	0.883547i	$-0.655149\pi$
$433$	−1.15744e21			−0.936686			−0.468343	+	0.883547i	$0.655149\pi$
$434$	6.08658e20	+	5.08247e20i	0.483566	+	0.403791i
$435$		0			0
$436$	2.58786e20	+	1.42765e21i	0.198175	+	1.09328i
$437$	−4.57214e19			−0.0343770
$438$		0			0
$439$			2.49135e21i			1.80600i	0.429639	+	0.903001i	$0.358641\pi$
$439$			2.49135e21i			1.80600i	−0.429639	+	0.903001i	$0.641359\pi$
$440$	−1.81280e19	−	1.02934e19i	−0.0129041	−	0.00732717i
$441$		0			0
$442$	−3.54741e20	−	2.96219e20i	−0.243519	−	0.203346i
$443$			2.09067e21i			1.40947i	0.709472	+	0.704734i	$0.248934\pi$
$443$			2.09067e21i			1.40947i	−0.709472	+	0.704734i	$0.751066\pi$
$444$		0			0
$445$	3.27492e20			0.212971
$446$	−9.92707e19	+	1.18883e20i	−0.0634078	+	0.0759348i
$447$		0			0
$448$	7.83526e20	−	4.67499e20i	0.482869	−	0.288109i
$449$	−2.29386e21			−1.38866			−0.694331	−	0.719656i	$-0.744300\pi$
$449$	−2.29386e21			−1.38866			−0.694331	+	0.719656i	$0.744300\pi$
$450$		0			0
$451$			3.21097e20i			0.187596i
$452$	−1.20386e20	−	6.64138e20i	−0.0690988	−	0.381198i
$453$		0			0
$454$	2.05393e21	−	2.45971e21i	1.13799	−	1.36282i
$455$		−	1.01070e20i		−	0.0550215i
$456$		0			0
$457$	1.45139e21			0.762876			0.381438	−	0.924394i	$-0.375429\pi$
$457$	1.45139e21			0.762876			0.381438	+	0.924394i	$0.375429\pi$
$458$	2.42010e21	+	2.02085e21i	1.25000	+	1.04378i
$459$		0			0
$460$	1.12655e19	−	2.04207e18i	0.00561937	−	0.00101861i
$461$	−2.70680e21			−1.32693			−0.663466	−	0.748207i	$-0.730915\pi$
$461$	−2.70680e21			−1.32693			−0.663466	+	0.748207i	$0.730915\pi$
$462$		0			0
$463$			2.77293e21i			1.31308i	0.754291	+	0.656540i	$0.227981\pi$
$463$			2.77293e21i			1.31308i	−0.754291	+	0.656540i	$0.772019\pi$
$464$	−2.59915e21	+	9.74294e20i	−1.20973	+	0.453467i
$465$		0			0
$466$	2.70042e20	+	2.25493e20i	0.121435	+	0.101402i
$467$			1.65320e21i			0.730785i	0.930853	+	0.365393i	$0.119065\pi$
$467$			1.65320e21i			0.730785i	−0.930853	+	0.365393i	$0.880935\pi$
$468$		0			0
$469$	1.14020e21			0.487079
$470$	−2.43544e20	+	2.91660e20i	−0.102281	+	0.122488i
$471$		0			0
$472$	−2.82941e21	−	1.60658e21i	−1.14857	−	0.652179i
$473$	4.95005e20			0.197570
$474$		0			0
$475$			1.77422e21i			0.684633i
$476$	5.44928e20	−	9.87775e19i	0.206768	−	0.0374803i
$477$		0			0
$478$	1.57298e21	−	1.88375e21i	0.577166	−	0.691193i
$479$		−	9.34864e20i		−	0.337337i	−0.985673	−	0.168669i	$-0.946053\pi$
$479$		−	9.34864e20i		−	0.337337i	0.985673	−	0.168669i	$-0.0539468\pi$
$480$		0			0
$481$	−4.39701e21			−1.53461
$482$	1.73780e21	+	1.45112e21i	0.596520	+	0.498111i
$483$		0			0
$484$	5.28206e20	+	2.91397e21i	0.175405	+	0.967658i
$485$	−7.16999e19			−0.0234199
$486$		0			0
$487$			1.25840e20i			0.0397729i	0.999802	+	0.0198864i	$0.00633047\pi$
$487$			1.25840e20i			0.0397729i	−0.999802	+	0.0198864i	$0.993670\pi$
$488$	−1.17539e20	+	2.07002e20i	−0.0365446	+	0.0643601i
$489$		0			0
$490$	−2.01071e20	−	1.67900e20i	−0.0605035	−	0.0505221i
$491$		−	1.35029e21i		−	0.399737i	−0.979823	−	0.199868i	$-0.935949\pi$
$491$		−	1.35029e21i		−	0.399737i	0.979823	−	0.199868i	$-0.0640515\pi$
$492$		0			0
$493$	−1.68483e21			−0.482815
$494$	1.33898e21	−	1.60351e21i	0.377536	−	0.452123i
$495$		0			0
$496$	−1.44057e21	−	3.84304e21i	−0.393260	−	1.04911i
$497$	2.86818e21			0.770470
$498$		0			0
$499$		−	5.21112e21i		−	1.35559i	−0.735253	−	0.677793i	$-0.762937\pi$
$499$		−	5.21112e21i		−	1.35559i	0.735253	−	0.677793i	$-0.237063\pi$
$500$	−1.59552e20	−	8.80202e20i	−0.0408453	−	0.225332i
$501$		0			0
$502$	−2.11949e21	+	2.53822e21i	−0.525535	+	0.629361i
$503$			3.67581e21i			0.897036i	0.893774	+	0.448518i	$0.148048\pi$
$503$			3.67581e21i			0.897036i	−0.893774	+	0.448518i	$0.851952\pi$
$504$		0			0
$505$	−3.17495e20			−0.0750595
$506$	2.10394e19	+	1.75685e19i	0.00489587	+	0.00408819i
$507$		0			0
$508$	−1.79539e20	+	3.25445e19i	−0.0404807	+	0.00733783i
$509$	−3.70215e21			−0.821698			−0.410849	−	0.911703i	$-0.634768\pi$
$509$	−3.70215e21			−0.821698			−0.410849	+	0.911703i	$0.634768\pi$
$510$		0			0
$511$			5.52822e20i			0.118910i
$512$	−4.72127e21	+	1.01722e20i	−0.999768	+	0.0215405i
$513$		0			0
$514$	4.16950e21	+	3.48165e21i	0.855812	+	0.714628i
$515$		−	1.45209e20i		−	0.0293451i
$516$		0			0
$517$	−9.09686e20			−0.178224
$518$	3.37719e21	−	4.04440e21i	0.651504	−	0.780217i
$519$		0			0
$520$	−2.58299e20	+	4.54900e20i	−0.0483166	+	0.0850921i
$521$	4.65046e21			0.856631			0.428316	−	0.903629i	$-0.359107\pi$
$521$	4.65046e21			0.856631			0.428316	+	0.903629i	$0.359107\pi$
$522$		0			0
$523$		−	7.31101e21i		−	1.30606i	−0.757331	−	0.653031i	$-0.773497\pi$
$523$		−	7.31101e21i		−	1.30606i	0.757331	−	0.653031i	$-0.226503\pi$
$524$	−5.46181e21	+	9.90047e20i	−0.960918	+	0.174183i
$525$		0			0
$526$	−2.50164e21	+	2.99587e21i	−0.426913	+	0.511255i
$527$		−	2.49115e21i		−	0.418712i
$528$		0			0
$529$	6.11756e21			0.997545
$530$	4.95227e19	+	4.13529e19i	0.00795422	+	0.00664200i
$531$		0			0
$532$	4.46497e20	+	2.46320e21i	0.0695866	+	0.383890i
$533$	8.05753e21			1.23704
$534$		0			0
$535$		−	6.37311e20i		−	0.0949557i
$536$	−5.13185e21	−	2.91394e21i	−0.753279	−	0.427723i
$537$		0			0
$538$	5.50696e21	+	4.59847e21i	0.784609	+	0.655171i
$539$		−	6.27139e20i		−	0.0880347i
$540$		0			0
$541$	8.52511e21			1.16178			0.580888	−	0.813984i	$-0.302706\pi$
$541$	8.52511e21			1.16178			0.580888	+	0.813984i	$0.302706\pi$
$542$	6.88143e21	−	8.24095e21i	0.924027	−	1.10658i
$543$		0			0
$544$	−2.70506e21	−	9.48057e20i	−0.352684	−	0.123607i
$545$	9.96849e20			0.128073
$546$		0			0
$547$			7.69610e21i			0.960223i	0.877208	+	0.480111i	$0.159404\pi$
$547$			7.69610e21i			0.960223i	−0.877208	+	0.480111i	$0.840596\pi$
$548$	1.86927e21	+	1.03123e22i	0.229842	+	1.26797i
$549$		0			0
$550$	6.81747e20	−	8.16436e20i	0.0814183	−	0.0975036i
$551$		−	7.61583e21i		−	0.896405i
$552$		0			0
$553$	4.87361e21			0.557250
$554$	−5.42149e21	−	4.52710e21i	−0.610999	−	0.510202i
$555$		0			0
$556$	2.87604e20	−	5.21331e19i	0.0314917	−	0.00570841i
$557$	4.62948e21			0.499678			0.249839	−	0.968287i	$-0.419622\pi$
$557$	4.62948e21			0.499678			0.249839	+	0.968287i	$0.419622\pi$
$558$		0			0
$559$		−	1.24215e22i		−	1.30281i
$560$	−2.20029e20	−	5.86977e20i	−0.0227497	−	0.0606900i
$561$		0			0
$562$	−2.43685e21	−	2.03484e21i	−0.244871	−	0.204475i
$563$		−	8.89108e21i		−	0.880820i	−0.897797	−	0.440410i	$-0.854833\pi$
$563$		−	8.89108e21i		−	0.880820i	0.897797	−	0.440410i	$-0.145167\pi$
$564$		0			0
$565$	−4.63731e20			−0.0446559
$566$	−4.46735e21	+	5.34993e21i	−0.424149	+	0.507945i
$567$		0			0
$568$	−1.29092e22	−	7.33003e21i	−1.19155	−	0.676580i
$569$	−1.92778e22			−1.75452			−0.877261	−	0.480014i	$-0.840632\pi$
$569$	−1.92778e22			−1.75452			−0.877261	+	0.480014i	$0.840632\pi$
$570$		0			0
$571$		−	9.49922e21i		−	0.840619i	−0.907381	−	0.420309i	$-0.861922\pi$
$571$		−	9.49922e21i		−	0.840619i	0.907381	−	0.420309i	$-0.138078\pi$
$572$	−1.23231e21	+	2.23377e20i	−0.107535	+	0.0194926i
$573$		0			0
$574$	−6.18871e21	+	7.41137e21i	−0.525176	+	0.628931i
$575$			5.84163e20i			0.0488868i
$576$		0			0
$577$	3.93866e20			0.0320584			0.0160292	−	0.999872i	$-0.494898\pi$
$577$	3.93866e20			0.0320584			0.0160292	+	0.999872i	$0.494898\pi$
$578$	8.22649e21	+	6.86935e21i	0.660377	+	0.551434i
$579$		0			0
$580$	3.40148e20	+	1.87650e21i	0.0265610	+	0.146529i
$581$	−1.58225e21			−0.121861
$582$		0			0
$583$			1.54461e20i			0.0115737i
$584$	1.41281e21	−	2.48815e21i	0.104419	−	0.183897i
$585$		0			0
$586$	−1.41674e22	−	1.18302e22i	−1.01885	−	0.850766i
$587$		−	1.14484e22i		−	0.812156i	−0.913838	−	0.406078i	$-0.866896\pi$
$587$		−	1.14484e22i		−	0.812156i	0.913838	−	0.406078i	$-0.133104\pi$
$588$		0			0
$589$	1.12606e22			0.777389
$590$	−1.43282e21	+	1.71590e21i	−0.0975835	+	0.116862i
$591$		0			0
$592$	−2.55361e22	+	9.57225e21i	−1.69271	+	0.634513i
$593$	2.05167e22			1.34175			0.670874	−	0.741572i	$-0.265919\pi$
$593$	2.05167e22			1.34175			0.670874	+	0.741572i	$0.265919\pi$
$594$		0			0
$595$		−	3.80493e20i		−	0.0242221i
$596$	1.91184e21	+	1.05471e22i	0.120083	+	0.662463i
$597$		0			0
$598$	4.40860e20	−	5.27958e20i	0.0269582	−	0.0322842i
$599$		−	5.38868e20i		−	0.0325138i	−0.999868	−	0.0162569i	$-0.994825\pi$
$599$		−	5.38868e20i		−	0.0325138i	0.999868	−	0.0162569i	$-0.00517496\pi$
$600$		0			0
$601$	−5.44089e21			−0.319650			−0.159825	−	0.987145i	$-0.551093\pi$
$601$	−5.44089e21			−0.319650			−0.159825	+	0.987145i	$0.551093\pi$
$602$	1.14254e22	+	9.54053e21i	0.662368	+	0.553096i
$603$		0			0
$604$	2.87594e22	−	5.21314e21i	1.62362	−	0.294309i
$605$	2.03466e21			0.113357
$606$		0			0
$607$			5.75755e21i			0.312412i	0.987724	+	0.156206i	$0.0499264\pi$
$607$			5.75755e21i			0.312412i	−0.987724	+	0.156206i	$0.950074\pi$
$608$	4.28544e21	−	1.22275e22i	0.229492	−	0.654801i
$609$		0			0
$610$	1.25537e20	+	1.04827e20i	0.00654835	+	0.00546806i
$611$			2.28274e22i			1.17524i
$612$		0			0
$613$	−9.14430e21			−0.458635			−0.229317	−	0.973352i	$-0.573649\pi$
$613$	−9.14430e21			−0.458635			−0.229317	+	0.973352i	$0.573649\pi$
$614$	−1.97576e22	+	2.36610e22i	−0.978109	+	1.17135i
$615$		0			0
$616$	7.41027e20	−	1.30505e21i	0.0357428	−	0.0629479i
$617$	−1.03301e22			−0.491841			−0.245920	−	0.969290i	$-0.579090\pi$
$617$	−1.03301e22			−0.491841			−0.245920	+	0.969290i	$0.579090\pi$
$618$		0			0
$619$			4.25685e22i			1.97498i	0.157681	+	0.987490i	$0.449598\pi$
$619$			4.25685e22i			1.97498i	−0.157681	+	0.987490i	$0.550402\pi$
$620$	−2.77455e21	+	5.02934e20i	−0.127075	+	0.0230345i
$621$		0			0
$622$	8.31815e21	−	9.96151e21i	0.371282	−	0.444633i
$623$			2.35764e22i			1.03890i
$624$		0			0
$625$	2.23591e22			0.960317
$626$	−8.46131e20	−	7.06544e20i	−0.0358792	−	0.0299602i
$627$		0			0
$628$	7.86211e21	+	4.33731e22i	0.324984	+	1.79285i
$629$	−1.65531e22			−0.675578
$630$		0			0
$631$		−	2.86017e22i		−	1.13804i	−0.822324	−	0.569020i	$-0.807323\pi$
$631$		−	2.86017e22i		−	1.13804i	0.822324	−	0.569020i	$-0.192677\pi$
$632$	−2.19353e22	−	1.24552e22i	−0.861800	−	0.489343i
$633$		0			0
$634$	1.96215e22	+	1.63845e22i	0.751652	+	0.627651i
$635$			1.25362e20i			0.00474216i
$636$		0			0
$637$	−1.57373e22			−0.580516
$638$	−2.92640e21	+	3.50455e21i	−0.106603	+	0.127664i
$639$		0			0
$640$	−5.09789e20	+	3.20420e21i	−0.0181113	+	0.113836i
$641$	5.68766e21			0.199558			0.0997791	−	0.995010i	$-0.468186\pi$
$641$	5.68766e21			0.199558			0.0997791	+	0.995010i	$0.468186\pi$
$642$		0			0
$643$			9.58453e21i			0.328007i	0.986460	+	0.164003i	$0.0524408\pi$
$643$			9.58453e21i			0.328007i	−0.986460	+	0.164003i	$0.947559\pi$
$644$	1.47010e20	+	8.11012e20i	0.00496889	+	0.0274120i
$645$		0			0
$646$	5.04077e21	−	6.03664e21i	0.166202	−	0.199038i
$647$			4.46026e22i			1.45253i	0.687414	+	0.726266i	$0.258746\pi$
$647$			4.46026e22i			1.45253i	−0.687414	+	0.726266i	$0.741254\pi$
$648$		0			0
$649$	−5.35188e21			−0.170039
$650$	−2.04874e22	−	1.71076e22i	−0.642955	−	0.536886i
$651$		0			0
$652$	4.49692e22	−	8.15144e21i	1.37700	−	0.249605i
$653$	4.48623e21			0.135699			0.0678494	−	0.997696i	$-0.478386\pi$
$653$	4.48623e21			0.135699			0.0678494	+	0.997696i	$0.478386\pi$
$654$		0			0
$655$			3.81368e21i			0.112568i
$656$	4.67950e22	−	1.75412e22i	1.36449	−	0.511479i
$657$		0			0
$658$	−2.09968e22	−	1.75329e22i	−0.597511	−	0.498939i
$659$		−	5.30196e21i		−	0.149057i	−0.997219	−	0.0745286i	$-0.976255\pi$
$659$		−	5.30196e21i		−	0.149057i	0.997219	−	0.0745286i	$-0.0237452\pi$
$660$		0			0
$661$	−5.01176e22			−1.37524			−0.687620	−	0.726070i	$-0.741345\pi$
$661$	−5.01176e22			−1.37524			−0.687620	+	0.726070i	$0.741345\pi$
$662$	−6.39573e21	+	7.65929e21i	−0.173391	+	0.207647i
$663$		0			0
$664$	7.12143e21	+	4.04366e21i	0.188461	+	0.107011i
$665$	1.71992e21			0.0449712
$666$		0			0
$667$		−	2.50752e21i		−	0.0640085i
$668$	6.60252e22	−	1.19682e22i	1.66532	−	0.301868i
$669$		0			0
$670$	−2.59879e21	+	3.11221e21i	−0.0639989	+	0.0766428i
$671$			3.91549e20i			0.00952808i
$672$		0			0
$673$	−7.45742e22			−1.77202			−0.886009	−	0.463668i	$-0.846533\pi$
$673$	−7.45742e22			−1.77202			−0.886009	+	0.463668i	$0.846533\pi$
$674$	−3.11124e22	−	2.59798e22i	−0.730558	−	0.610037i
$675$		0			0
$676$	−2.17273e21	−	1.19863e22i	−0.0498232	−	0.274861i
$677$	1.34138e22			0.303979			0.151989	−	0.988382i	$-0.451432\pi$
$677$	1.34138e22			0.303979			0.151989	+	0.988382i	$0.451432\pi$
$678$		0			0
$679$		−	5.16172e21i		−	0.114245i
$680$	−9.72402e20	+	1.71253e21i	−0.0212704	+	0.0374600i
$681$		0			0
$682$	−5.18174e21	−	4.32691e21i	−0.110714	−	0.0924490i
$683$		−	6.68422e22i		−	1.41151i	−0.708454	−	0.705757i	$-0.750607\pi$
$683$		−	6.68422e22i		−	1.41151i	0.708454	−	0.705757i	$-0.249393\pi$
$684$		0			0
$685$	7.20049e21			0.148538
$686$	2.97630e22	−	3.56431e22i	0.606854	−	0.726746i
$687$		0			0
$688$	−2.70415e22	−	7.21394e22i	−0.538671	−	1.43703i
$689$	3.87601e21			0.0763187
$690$		0			0
$691$			7.61674e22i			1.46536i	0.680572	+	0.732681i	$0.261731\pi$
$691$			7.61674e22i			1.46536i	−0.680572	+	0.732681i	$0.738269\pi$
$692$	5.49994e21	+	3.03416e22i	0.104595	+	0.577019i
$693$		0			0
$694$	5.43019e22	−	6.50300e22i	1.00911	−	1.20848i
$695$		−	2.00818e20i		−	0.00368913i
$696$		0			0
$697$	3.03337e22			0.544582
$698$	−2.03770e22	−	1.70154e22i	−0.361657	−	0.301994i
$699$		0			0
$700$	3.14713e22	−	5.70472e21i	0.545922	−	0.0989577i
$701$	−6.67032e22			−1.14394			−0.571969	−	0.820275i	$-0.693820\pi$
$701$	−6.67032e22			−1.14394			−0.571969	+	0.820275i	$0.693820\pi$
$702$		0			0
$703$		−	7.48241e22i		−	1.25429i
$704$	−6.67047e21	+	3.98000e21i	−0.110554	+	0.0659633i
$705$		0			0
$706$	−3.41804e22	−	2.85416e22i	−0.553783	−	0.462425i
$707$		−	2.28567e22i		−	0.366149i
$708$		0			0
$709$	6.94725e22			1.08803			0.544017	−	0.839074i	$-0.316903\pi$
$709$	6.94725e22			1.08803			0.544017	+	0.839074i	$0.316903\pi$
$710$	−6.53726e21	+	7.82878e21i	−0.101235	+	0.121235i
$711$		0			0
$712$	6.02527e22	−	1.06113e23i	0.912297	−	1.60668i
$713$	3.70756e21			0.0555101
$714$		0			0
$715$			8.60452e20i			0.0125973i
$716$	9.10135e22	−	1.64978e22i	1.31766	−	0.238848i
$717$		0			0
$718$	−8.63980e22	+	1.03467e23i	−1.22323	+	1.46489i
$719$		−	7.93076e22i		−	1.11041i	−0.831713	−	0.555205i	$-0.812640\pi$
$719$		−	7.93076e22i		−	1.11041i	0.831713	−	0.555205i	$-0.187360\pi$
$720$		0			0
$721$	1.04537e22			0.143149
$722$	−2.93919e22	−	2.45431e22i	−0.398044	−	0.332378i
$723$		0			0
$724$	6.37327e21	+	3.51596e22i	0.0844217	+	0.465731i
$725$	−9.73044e22			−1.27476
$726$		0			0
$727$			1.18224e23i			1.51506i	0.652802	+	0.757528i	$0.273593\pi$
$727$			1.18224e23i			1.51506i	−0.652802	+	0.757528i	$0.726407\pi$
$728$	−3.27486e22	−	1.85951e22i	−0.415089	−	0.235694i
$729$		0			0
$730$	−1.50894e21	−	1.26001e21i	−0.0187107	−	0.0156240i
$731$		−	4.67625e22i		−	0.573534i
$732$		0			0
$733$	−7.24896e22			−0.869849			−0.434925	−	0.900467i	$-0.643225\pi$
$733$	−7.24896e22			−0.869849			−0.434925	+	0.900467i	$0.643225\pi$
$734$	1.90101e22	−	2.27658e22i	0.225640	−	0.270218i
$735$		0			0
$736$	1.41099e21	−	4.02592e21i	0.0163870	−	0.0467566i
$737$	−9.70699e21			−0.111518
$738$		0			0
$739$		−	4.36734e21i		−	0.0490978i	−0.999699	−	0.0245489i	$-0.992185\pi$
$739$		−	4.36734e21i		−	0.0490978i	0.999699	−	0.0245489i	$-0.00781494\pi$
$740$	3.34189e21	+	1.84363e22i	0.0371653	+	0.205031i
$741$		0			0
$742$	−2.97703e21	+	3.56518e21i	−0.0324005	+	0.0388016i
$743$			1.41363e23i			1.52204i	0.648728	+	0.761020i	$0.275301\pi$
$743$			1.41363e23i			1.52204i	−0.648728	+	0.761020i	$0.724699\pi$
$744$		0			0
$745$	7.36444e21			0.0776050
$746$	−3.51873e22	−	2.93824e22i	−0.366839	−	0.306321i
$747$		0			0
$748$	−4.63918e21	+	8.40932e20i	−0.0473401	+	0.00858120i
$749$	4.58805e22			0.463205
$750$		0			0
$751$		−	8.90798e22i		−	0.880358i	−0.897910	−	0.440179i	$-0.854915\pi$
$751$		−	8.90798e22i		−	0.880358i	0.897910	−	0.440179i	$-0.145085\pi$
$752$	4.96950e22	+	1.32573e23i	0.485926	+	1.29632i
$753$		0			0
$754$	8.79422e22	+	7.34343e22i	0.841835	+	0.702956i
$755$		−	2.00811e22i		−	0.190201i
$756$		0			0
$757$	4.63034e22			0.429384			0.214692	−	0.976682i	$-0.431125\pi$
$757$	4.63034e22			0.429384			0.214692	+	0.976682i	$0.431125\pi$
$758$	−9.24612e22	+	1.10728e23i	−0.848410	+	1.01602i
$759$		0			0
$760$	−7.74104e21	−	4.39548e21i	−0.0695490	−	0.0394910i
$761$	1.56378e23			1.39026			0.695132	−	0.718882i	$-0.255346\pi$
$761$	1.56378e23			1.39026			0.695132	+	0.718882i	$0.255346\pi$
$762$		0			0
$763$			7.17639e22i			0.624755i
$764$	3.76218e22	−	6.81959e21i	0.324110	−	0.0587505i
$765$		0			0
$766$	−6.07188e22	+	7.27146e22i	−0.512263	+	0.613467i
$767$			1.34299e23i			1.12127i
$768$		0			0
$769$	2.59960e22			0.212567			0.106283	−	0.994336i	$-0.466105\pi$
$769$	2.59960e22			0.212567			0.106283	+	0.994336i	$0.466105\pi$
$770$	−7.91449e20	−	6.60882e20i	−0.00640467	−	0.00534809i
$771$		0			0
$772$	3.58733e22	+	1.97903e23i	0.284336	+	1.56860i
$773$	1.28175e23			1.00546			0.502732	−	0.864442i	$-0.332328\pi$
$773$	1.28175e23			1.00546			0.502732	+	0.864442i	$0.332328\pi$
$774$		0			0
$775$		−	1.43872e23i		−	1.10551i
$776$	−1.31915e22	+	2.32320e22i	−0.100323	+	0.176682i
$777$		0			0
$778$	−2.84017e22	−	2.37163e22i	−0.211596	−	0.176689i
$779$			1.37115e23i			1.01108i
$780$		0			0
$781$	−2.44180e22			−0.176401
$782$	1.65968e21	−	1.98757e21i	0.0118678	−	0.0142124i
$783$		0			0
$784$	−9.13959e22	+	3.42599e22i	−0.640322	+	0.240025i
$785$	3.02850e22			0.210025
$786$		0			0
$787$		−	3.96418e22i		−	0.269374i	−0.990888	−	0.134687i	$-0.956997\pi$
$787$		−	3.96418e22i		−	0.269374i	0.990888	−	0.134687i	$-0.0430029\pi$
$788$	−1.34962e22	−	7.44547e22i	−0.0907823	−	0.500821i
$789$		0			0
$790$	−1.11081e22	+	1.33027e22i	−0.0732189	+	0.0876843i
$791$		−	3.33844e22i		−	0.217837i
$792$		0			0
$793$	9.82542e21			0.0628298
$794$	1.58142e22	+	1.32054e22i	0.100112	+	0.0835961i
$795$		0			0
$796$	−8.91530e22	+	1.61605e22i	−0.553135	+	0.100265i
$797$	−2.13798e21			−0.0131322			−0.00656609	−	0.999978i	$-0.502090\pi$
$797$	−2.13798e21			−0.0131322			−0.00656609	+	0.999978i	$0.502090\pi$
$798$		0			0
$799$			8.59369e22i			0.517375i
$800$	−1.56226e23	−	5.47533e22i	−0.931180	−	0.326355i
$801$		0			0
$802$	−2.77327e22	−	2.31576e22i	−0.162031	−	0.135300i
$803$		−	4.70639e21i		−	0.0272247i
$804$		0			0
$805$	5.66285e20			0.00321120
$806$	−1.08578e23	+	1.30029e23i	−0.609624	+	0.730064i
$807$		0			0
$808$	−5.84134e22	+	1.02874e23i	−0.321530	+	0.566258i
$809$	−1.44463e23			−0.787351			−0.393675	−	0.919250i	$-0.628797\pi$
$809$	−1.44463e23			−0.787351			−0.393675	+	0.919250i	$0.628797\pi$
$810$		0			0
$811$		−	3.08751e23i		−	1.64984i	−0.565249	−	0.824920i	$-0.691220\pi$
$811$		−	3.08751e23i		−	1.64984i	0.565249	−	0.824920i	$-0.308780\pi$
$812$	−1.35091e23	+	2.44875e22i	−0.714788	+	0.129568i
$813$		0			0
$814$	−2.87513e22	+	3.44315e22i	−0.149164	+	0.178633i
$815$		−	3.13995e22i		−	0.161310i
$816$		0			0
$817$	2.11377e23			1.06483
$818$	−2.50084e22	−	2.08827e22i	−0.124755	−	0.104174i
$819$		0			0
$820$	−6.12402e21	−	3.37845e22i	−0.0299589	−	0.165275i
$821$	−1.09914e23			−0.532484			−0.266242	−	0.963906i	$-0.585782\pi$
$821$	−1.09914e23			−0.532484			−0.266242	+	0.963906i	$0.585782\pi$
$822$		0			0
$823$		−	7.16721e22i		−	0.340527i	−0.985399	−	0.170263i	$-0.945538\pi$
$823$		−	7.16721e22i		−	0.340527i	0.985399	−	0.170263i	$-0.0544618\pi$
$824$	−4.70503e22	−	2.67159e22i	−0.221383	−	0.125705i
$825$		0			0
$826$	−1.23529e23	−	1.03150e23i	−0.570069	−	0.476024i
$827$		−	2.00338e23i		−	0.915628i	−0.889048	−	0.457814i	$-0.848633\pi$
$827$		−	2.00338e23i		−	0.915628i	0.889048	−	0.457814i	$-0.151367\pi$
$828$		0			0
$829$	1.46109e23			0.654999			0.327499	−	0.944851i	$-0.393794\pi$
$829$	1.46109e23			0.654999			0.327499	+	0.944851i	$0.393794\pi$
$830$	3.60632e21	−	4.31880e21i	0.0160118	−	0.0191751i
$831$		0			0
$832$	9.98731e22	+	1.67387e23i	0.434973	+	0.729012i
$833$	−5.92451e22			−0.255560
$834$		0			0
$835$		−	4.61018e22i		−	0.195086i
$836$	−3.80121e21	−	2.09702e22i	−0.0159320	−	0.0878926i
$837$		0			0
$838$	2.01795e23	−	2.41662e23i	0.829770	−	0.993702i
$839$		−	2.64414e23i		−	1.07693i	−0.842647	−	0.538466i	$-0.819004\pi$
$839$		−	2.64414e23i		−	1.07693i	0.842647	−	0.538466i	$-0.180996\pi$
$840$		0			0
$841$	1.67433e23			0.669071
$842$	3.35019e23	+	2.79750e23i	1.32609	+	1.10732i
$843$		0			0
$844$	−9.54545e22	+	1.73028e22i	−0.370729	+	0.0672011i
$845$	−8.36939e21			−0.0321988
$846$		0			0
$847$			1.46477e23i			0.552970i
$848$	2.25104e22	−	8.43803e21i	0.0841813	−	0.0315555i
$849$		0			0
$850$	−7.71277e22	−	6.44039e22i	−0.283047	−	0.236353i
$851$		−	2.46359e22i		−	0.0895637i
$852$		0			0
$853$	−1.71142e23			−0.610609			−0.305305	−	0.952255i	$-0.598758\pi$
$853$	−1.71142e23			−0.610609			−0.305305	+	0.952255i	$0.598758\pi$
$854$	−7.54655e21	+	9.03748e21i	−0.0266739	+	0.0319436i
$855$		0			0
$856$	−2.06500e23	−	1.17254e23i	−0.716358	−	0.406759i
$857$	4.71695e23			1.62112			0.810559	−	0.585657i	$-0.199164\pi$
$857$	4.71695e23			1.62112			0.810559	+	0.585657i	$0.199164\pi$
$858$		0			0
$859$			1.89722e23i			0.639988i	0.947420	+	0.319994i	$0.103681\pi$
$859$			1.89722e23i			0.639988i	−0.947420	+	0.319994i	$0.896319\pi$
$860$	−5.20823e22	+	9.44081e21i	−0.174061	+	0.0315516i
$861$		0			0
$862$	−2.11480e23	+	2.53260e23i	−0.693762	+	0.830824i
$863$		−	1.25778e23i		−	0.408806i	−0.978887	−	0.204403i	$-0.934475\pi$
$863$		−	1.25778e23i		−	0.408806i	0.978887	−	0.204403i	$-0.0655254\pi$
$864$		0			0
$865$	2.11859e22			0.0675956
$866$	2.27437e23	+	1.89916e23i	0.718982	+	0.600371i
$867$		0			0
$868$	−3.62066e22	−	1.99742e23i	−0.112365	−	0.619885i
$869$	−4.14910e22			−0.127584
$870$		0			0
$871$			2.43585e23i			0.735368i
$872$	1.83402e23	−	3.22997e23i	0.548622	−	0.966198i
$873$		0			0
$874$	8.98428e21	+	7.50213e21i	0.0263871	+	0.0220340i
$875$		−	4.42453e22i		−	0.128766i
$876$		0			0
$877$	−1.17923e22			−0.0336977			−0.0168489	−	0.999858i	$-0.505363\pi$
$877$	−1.17923e22			−0.0336977			−0.0168489	+	0.999858i	$0.505363\pi$
$878$	4.08790e23	−	4.89551e23i	1.15756	−	1.38625i
$879$		0			0
$880$	1.87319e21	+	4.99717e21i	0.00520861	+	0.0138951i
$881$	3.20332e22			0.0882661			0.0441330	−	0.999026i	$-0.485947\pi$
$881$	3.20332e22			0.0882661			0.0441330	+	0.999026i	$0.485947\pi$
$882$		0			0
$883$		−	1.83970e23i		−	0.497808i	−0.968528	−	0.248904i	$-0.919930\pi$
$883$		−	1.83970e23i		−	0.497808i	0.968528	−	0.248904i	$-0.0800704\pi$
$884$	2.11021e22	+	1.16414e23i	0.0565859	+	0.312168i
$885$		0			0
$886$	3.43045e23	−	4.10818e23i	0.903401	−	1.08188i
$887$		−	1.11278e23i		−	0.290416i	−0.989401	−	0.145208i	$-0.953615\pi$
$887$		−	1.11278e23i		−	0.290416i	0.989401	−	0.145208i	$-0.0463851\pi$
$888$		0			0
$889$	−9.02490e21			−0.0231328
$890$	−6.43524e22	−	5.37361e22i	−0.163473	−	0.136504i
$891$		0			0
$892$	3.90135e22	−	7.07187e21i	0.0973412	−	0.0176448i
$893$	−3.88455e23			−0.960569
$894$		0			0
$895$		−	6.35497e22i		−	0.154358i
$896$	−2.30672e23	−	3.67001e22i	−0.555305	−	0.0883492i
$897$		0			0
$898$	4.50745e23	+	3.76386e23i	1.06591	+	0.890066i
$899$			6.17570e23i			1.44747i
$900$		0			0
$901$	1.45918e22			0.0335977
$902$	5.26869e22	−	6.30959e22i	0.120240	−	0.143995i
$903$		0			0
$904$	−8.53183e22	+	1.50257e23i	−0.191291	+	0.336890i
$905$	2.45500e22			0.0545585
$906$		0			0
$907$		−	7.45124e22i		−	0.162693i	−0.996686	−	0.0813467i	$-0.974078\pi$
$907$		−	7.45124e22i		−	0.162693i	0.996686	−	0.0813467i	$-0.0259221\pi$
$908$	−8.07197e23	+	1.46318e23i	−1.74700	+	0.316674i
$909$		0			0
$910$	−1.65840e22	+	1.98604e22i	−0.0352662	+	0.0422335i
$911$		−	6.10002e23i		−	1.28583i	−0.765936	−	0.642916i	$-0.777724\pi$
$911$		−	6.10002e23i		−	1.28583i	0.765936	−	0.642916i	$-0.222276\pi$
$912$		0			0
$913$	1.34703e22			0.0279005
$914$	−2.85199e23	−	2.38149e23i	−0.585569	−	0.488967i
$915$		0			0
$916$	−1.43962e23	−	7.94198e23i	−0.290459	−	1.60238i
$917$	−2.74550e23			−0.549119
$918$		0			0
$919$			2.84863e23i			0.559901i	0.960014	+	0.279951i	$0.0903181\pi$
$919$			2.84863e23i			0.559901i	−0.960014	+	0.279951i	$0.909682\pi$
$920$	−2.54875e21	−	1.44722e21i	−0.00496620	−	0.00281989i
$921$		0			0
$922$	5.31888e23	+	4.44142e23i	1.01853	+	0.850499i
$923$			6.12738e23i			1.16322i
$924$		0			0
$925$	−9.55997e23			−1.78370
$926$	4.54993e23	−	5.44883e23i	0.841621	−	1.00789i
$927$		0			0
$928$	6.70600e23	+	2.35029e23i	1.21921	+	0.427304i
$929$	2.66657e23			0.480649			0.240324	−	0.970693i	$-0.422746\pi$
$929$	2.66657e23			0.480649			0.240324	+	0.970693i	$0.422746\pi$
$930$		0			0
$931$		−	2.67802e23i		−	0.474478i
$932$	−1.60637e22	−	8.86190e22i	−0.0282175	−	0.155668i
$933$		0			0
$934$	2.71263e23	−	3.24854e23i	0.468398	−	0.560937i
$935$			3.23929e21i			0.00554570i
$936$		0			0
$937$	−6.92827e23			−1.16603			−0.583013	−	0.812463i	$-0.698126\pi$
$937$	−6.92827e23			−1.16603			−0.583013	+	0.812463i	$0.698126\pi$
$938$	−2.24051e23	−	1.87089e23i	−0.373872	−	0.312194i
$939$		0			0
$940$	9.57132e22	−	1.73497e22i	0.157018	−	0.0284622i
$941$	−5.28516e23			−0.859689			−0.429845	−	0.902903i	$-0.641432\pi$
$941$	−5.28516e23			−0.859689			−0.429845	+	0.902903i	$0.641432\pi$
$942$		0			0
$943$			4.51454e22i			0.0721971i
$944$	2.92367e23	+	7.79954e23i	0.463609	+	1.23678i
$945$		0			0
$946$	−9.72688e22	−	8.12223e22i	−0.151651	−	0.126633i
$947$			6.74753e23i			1.04315i	0.853207	+	0.521573i	$0.174655\pi$
$947$			6.74753e23i			1.04315i	−0.853207	+	0.521573i	$0.825345\pi$
$948$		0			0
$949$	−1.18101e23			−0.179524
$950$	2.91120e23	−	3.48635e23i	0.438817	−	0.525511i
$951$		0			0
$952$	−1.23286e23	−	7.00040e22i	−0.182734	−	0.103759i
$953$	7.56472e23			1.11186			0.555929	−	0.831229i	$-0.312362\pi$
$953$	7.56472e23			1.11186			0.555929	+	0.831229i	$0.312362\pi$
$954$		0			0
$955$		−	2.62692e22i		−	0.0379682i
$956$	−6.18185e23	+	1.12057e23i	−0.886043	+	0.160611i
$957$		0			0
$958$	−1.53396e23	+	1.83701e23i	−0.216217	+	0.258934i
$959$			5.18368e23i			0.724585i
$960$		0			0
$961$	−1.85701e23			−0.255286
$962$	8.64016e23	+	7.21478e23i	1.17793	+	0.983609i
$963$		0			0
$964$	−1.03375e23	−	5.70291e23i	−0.138612	−	0.764681i
$965$	1.38185e23			0.183756
$966$		0			0
$967$			1.04571e24i			1.36773i	0.729608	+	0.683866i	$0.239703\pi$
$967$			1.04571e24i			1.36773i	−0.729608	+	0.683866i	$0.760297\pi$
$968$	3.74342e23	−	6.59267e23i	0.485585	−	0.855181i
$969$		0			0
$970$	1.40891e22	+	1.17648e22i	0.0179766	+	0.0150110i
$971$			1.34646e23i			0.170388i	0.996364	+	0.0851941i	$0.0271510\pi$
$971$			1.34646e23i			0.170388i	−0.996364	+	0.0851941i	$0.972849\pi$
$972$		0			0
$973$	1.44570e22			0.0179960
$974$	2.06483e22	−	2.47277e22i	0.0254925	−	0.0305289i
$975$		0			0
$976$	5.70622e22	−	2.13898e22i	0.0693027	−	0.0259782i
$977$	−1.14732e24			−1.38207			−0.691034	−	0.722822i	$-0.742844\pi$
$977$	−1.14732e24			−1.38207			−0.691034	+	0.722822i	$0.742844\pi$
$978$		0			0
$979$		−	2.00715e23i		−	0.237858i
$980$	1.19609e22	+	6.59849e22i	0.0140590	+	0.0775597i
$981$		0			0
$982$	−2.21560e23	+	2.65332e23i	−0.256212	+	0.306830i
$983$			1.23621e23i			0.141796i	0.997484	+	0.0708980i	$0.0225865\pi$
$983$			1.23621e23i			0.141796i	−0.997484	+	0.0708980i	$0.977414\pi$
$984$		0			0
$985$	−5.19876e22			−0.0586692
$986$	3.31071e23	+	2.76454e23i	0.370600	+	0.309462i
$987$		0			0
$988$	−5.26220e23	+	9.53865e22i	−0.579578	+	0.105058i
$989$	6.95963e22			0.0760354
$990$		0			0
$991$			1.00814e24i			1.08376i	0.840456	+	0.541879i	$0.182287\pi$
$991$			1.00814e24i			1.08376i	−0.840456	+	0.541879i	$0.817713\pi$
$992$	−3.47508e23	+	9.91533e23i	−0.370571	+	1.05734i
$993$		0			0
$994$	−5.63600e23	−	4.70622e23i	−0.591398	−	0.493834i
$995$			6.22506e22i			0.0647976i
$996$		0			0
$997$	9.03998e23			0.925990			0.462995	−	0.886361i	$-0.346775\pi$
$997$	9.03998e23			0.925990			0.462995	+	0.886361i	$0.346775\pi$
$998$	−8.55060e23	+	1.02399e24i	−0.868865	+	1.04052i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.17.d.d.19.5		16
3.2	odd	2		12.17.d.a.7.12	yes	16
4.3	odd	2	inner	36.17.d.d.19.6		16
12.11	even	2		12.17.d.a.7.11	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.17.d.a.7.11	✓	16	12.11	even	2
12.17.d.a.7.12	yes	16	3.2	odd	2
36.17.d.d.19.5		16	1.1	even	1	trivial
36.17.d.d.19.6		16	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	36.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-196.501 - 164.084i) q^{2} +(11689.0 + 64485.1i) q^{4} +45026.4 q^{5} +3.24149e6i q^{7} +(8.28406e6 - 1.45894e7i) q^{8} +O(q^{10})\)	\(q+(-196.501 - 164.084i) q^{2} +(11689.0 + 64485.1i) q^{4} +45026.4 q^{5} +3.24149e6i q^{7} +(8.28406e6 - 1.45894e7i) q^{8} +(-8.84773e6 - 7.38811e6i) q^{10} -2.75960e7i q^{11} -6.92488e8 q^{13} +(5.31875e8 - 6.36954e8i) q^{14} +(-4.02170e9 + 1.50754e9i) q^{16} -2.60696e9 q^{17} -1.17841e10i q^{19} +(5.26316e8 + 2.90354e9i) q^{20} +(-4.52806e9 + 5.42264e9i) q^{22} -3.87992e9i q^{23} -1.50561e11 q^{25} +(1.36074e11 + 1.13626e11i) q^{26} +(-2.09028e11 + 3.78899e10i) q^{28} +6.46281e11 q^{29} +9.55575e11i q^{31} +(1.03763e12 + 3.63663e11i) q^{32} +(5.12270e11 + 4.27761e11i) q^{34} +1.45953e11i q^{35} +6.34959e12 q^{37} +(-1.93358e12 + 2.31558e12i) q^{38} +(3.73002e11 - 6.56907e11i) q^{40} -1.16356e13 q^{41} +1.79375e13i q^{43} +(1.77953e12 - 3.22571e11i) q^{44} +(-6.36633e11 + 7.62408e11i) q^{46} -3.29643e13i q^{47} +2.27257e13 q^{49} +(2.95852e13 + 2.47045e13i) q^{50} +(-8.09452e12 - 4.46552e13i) q^{52} -5.59722e12 q^{53} -1.24255e12i q^{55} +(4.72912e13 + 2.68527e13i) q^{56} +(-1.26995e14 - 1.06044e14i) q^{58} -1.93936e14i q^{59} -1.41886e13 q^{61} +(1.56794e14 - 1.87771e14i) q^{62} +(-1.44224e14 - 2.41718e14i) q^{64} -3.11803e13 q^{65} -3.51753e14i q^{67} +(-3.04729e13 - 1.68110e14i) q^{68} +(2.39484e13 - 2.86798e13i) q^{70} -8.84835e14i q^{71} +1.70546e14 q^{73} +(-1.24770e15 - 1.04186e15i) q^{74} +(7.59898e14 - 1.37745e14i) q^{76} +8.94522e13 q^{77} -1.50351e15i q^{79} +(-1.81083e14 + 6.78791e13i) q^{80} +(2.28641e15 + 1.90922e15i) q^{82} +4.88125e14i q^{83} -1.17382e14 q^{85} +(2.94326e15 - 3.52474e15i) q^{86} +(-4.02609e14 - 2.28607e14i) q^{88} +7.27333e15 q^{89} -2.24469e15i q^{91} +(2.50197e14 - 4.53526e13i) q^{92} +(-5.40891e15 + 6.47752e15i) q^{94} -5.30595e14i q^{95} -1.59239e15 q^{97} +(-4.46562e15 - 3.72892e15i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 186 q^{2} + 136588 q^{4} - 354144 q^{5} - 14683680 q^{8}+O(q^{10}) \) 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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