LMFDB - Embedded newform 72.18.d.b.37.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,18,Mod(37,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("72.37");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	72.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:	$131.919902888$
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} - 8 x^{15} + 109505575668 x^{14} - 766539029536 x^{13} + \cdots + 23\!\cdots\!64 $ x^16 - 8x^15 + 109505575668x^14 - 766539029536x^13 + 4565100228876328094758x^12 - 27390601363292961184944x^11 + 92591127780943012435040881148284x^10 - 462955638653634549696621441749088x^9 + 977795346278604835725743703677218847007441x^8 - 3911181382336685511282464131494050715936008x^7 + 5486253005890750810105420612112386097148906843883912x^6 - 16458759003983117594082276228892502324980015032552768x^5 + 15550361362184906921502189748666544464631762598295918546369552x^4 - 31100722696938548840928895118996183700448942016456464597789824x^3 + 18096113985773341939458863826141502874171854160838520206186924390289152x^2 - 18096113970222980593732715905689044683436914121788987093981784054126592*x + 2314274244692410619337768589845007009310106660645582524080800163846193346084864
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{120}\cdot 3^{20}\cdot 7 $
Twist minimal:	no (minimal twist has level 8)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			37.13
Root			$0.500000 + 65608.9i$ of defining polynomial
Character	$\chi$	$=$	72.37
Dual form			72.18.d.b.37.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(257.790 - 254.197i) q^{2} +(1839.67 - 131059. i) q^{4} -524871. i q^{5} +1.57495e7 q^{7} +(-3.28406e7 - 3.42534e7i) q^{8} +O(q^{10})$	\(q+(257.790 - 254.197i) q^{2} +(1839.67 - 131059. i) q^{4} -524871. i q^{5} +1.57495e7 q^{7} +(-3.28406e7 - 3.42534e7i) q^{8} +(-1.33421e8 - 1.35307e8i) q^{10} +2.44791e8i q^{11} +2.66178e9i q^{13} +(4.06007e9 - 4.00348e9i) q^{14} +(-1.71731e10 - 4.82212e8i) q^{16} +2.82837e10 q^{17} +7.79642e10i q^{19} +(-6.87892e10 - 9.65592e8i) q^{20} +(6.22252e10 + 6.31047e10i) q^{22} +3.66576e11 q^{23} +4.87450e11 q^{25} +(6.76615e11 + 6.86180e11i) q^{26} +(2.89740e10 - 2.06412e12i) q^{28} +2.78648e11i q^{29} +3.68562e12 q^{31} +(-4.54964e12 + 4.24104e12i) q^{32} +(7.29127e12 - 7.18964e12i) q^{34} -8.26647e12i q^{35} +3.50209e13i q^{37} +(1.98183e13 + 2.00984e13i) q^{38} +(-1.79786e13 + 1.72371e13i) q^{40} +3.67533e13 q^{41} +1.25028e14i q^{43} +(3.20821e13 + 4.50335e11i) q^{44} +(9.44998e13 - 9.31826e13i) q^{46} -1.02087e14 q^{47} +1.54166e13 q^{49} +(1.25660e14 - 1.23908e14i) q^{50} +(3.48850e14 + 4.89680e12i) q^{52} +4.67637e14i q^{53} +1.28484e14 q^{55} +(-5.17223e14 - 5.39474e14i) q^{56} +(7.08315e13 + 7.18327e13i) q^{58} +4.08479e13i q^{59} -2.55846e15i q^{61} +(9.50117e14 - 9.36874e14i) q^{62} +(-9.47911e13 + 2.24980e15i) q^{64} +1.39709e15 q^{65} +2.46686e15i q^{67} +(5.20328e13 - 3.70684e15i) q^{68} +(-2.10131e15 - 2.13101e15i) q^{70} -1.09996e15 q^{71} -1.21919e16 q^{73} +(8.90221e15 + 9.02805e15i) q^{74} +(1.02179e16 + 1.43429e14i) q^{76} +3.85534e15i q^{77} +2.49946e16 q^{79} +(-2.53099e14 + 9.01367e15i) q^{80} +(9.47466e15 - 9.34259e15i) q^{82} -3.68875e16i q^{83} -1.48453e16i q^{85} +(3.17818e16 + 3.22311e16i) q^{86} +(8.38492e15 - 8.03908e15i) q^{88} +4.15487e16 q^{89} +4.19217e16i q^{91} +(6.74381e14 - 4.80432e16i) q^{92} +(-2.63170e16 + 2.59501e16i) q^{94} +4.09212e16 q^{95} +7.13708e15 q^{97} +(3.97426e15 - 3.91886e15i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 270 q^{2} - 27436 q^{4} + 11529600 q^{7} - 24334920 q^{8}+O(q^{10}) $ 16 * q - 270 * q^2 - 27436 * q^4 + 11529600 * q^7 - 24334920 * q^8	$ 16 q - 270 q^{2} - 27436 q^{4} + 11529600 q^{7} - 24334920 q^{8} + 131002712 q^{10} - 16363788528 q^{14} + 26500434192 q^{16} + 7489125600 q^{17} + 209445719856 q^{20} + 223126527100 q^{22} - 746845345920 q^{23} - 1809682431664 q^{25} - 2467726531080 q^{26} + 3220542267040 q^{28} - 318979758592 q^{31} - 1455647316000 q^{32} - 4461251980292 q^{34} - 24076283913900 q^{38} + 60626292962592 q^{40} - 7482251536032 q^{41} - 193654716236040 q^{44} - 195097141003568 q^{46} + 376698804821760 q^{47} + 127691292101520 q^{49} - 474997408872102 q^{50} - 272251877663120 q^{52} + 22\!\cdots\!52 q^{55}+ \cdots - 33\!\cdots\!90 q^{98}+O(q^{100}) $ 16 * q - 270 * q^2 - 27436 * q^4 + 11529600 * q^7 - 24334920 * q^8 + 131002712 * q^10 - 16363788528 * q^14 + 26500434192 * q^16 + 7489125600 * q^17 + 209445719856 * q^20 + 223126527100 * q^22 - 746845345920 * q^23 - 1809682431664 * q^25 - 2467726531080 * q^26 + 3220542267040 * q^28 - 318979758592 * q^31 - 1455647316000 * q^32 - 4461251980292 * q^34 - 24076283913900 * q^38 + 60626292962592 * q^40 - 7482251536032 * q^41 - 193654716236040 * q^44 - 195097141003568 * q^46 + 376698804821760 * q^47 + 127691292101520 * q^49 - 474997408872102 * q^50 - 272251877663120 * q^52 + 2209036687713152 * q^55 + 162767516076480 * q^56 - 623262610679960 * q^58 - 695695648144320 * q^62 + 1111931745501248 * q^64 - 2385987975356160 * q^65 - 5981109959771880 * q^68 - 10044559836180288 * q^70 - 9025926285576576 * q^71 + 11332002046118560 * q^73 - 11098735408189464 * q^74 + 5959440926938280 * q^76 - 45299671392008448 * q^79 - 1337342539452480 * q^80 + 15639739637081420 * q^82 + 14252032276026564 * q^86 - 66964872768837680 * q^88 + 69879174608766048 * q^89 - 57336249810701280 * q^92 - 192318922166254176 * q^94 - 93790444358203776 * q^95 + 95593398602180640 * q^97 - 339641261743253790 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	257.790	−	254.197i	0.712052	−	0.702127i
$2$	257.790	−	254.197i	0.712052	−	0.702127i
$3$		0			0
$3$		0			0
$4$	1839.67	−	131059.i	0.0140356	−	0.999901i
$5$		−	524871.i		−	0.600908i	−0.953796	−	0.300454i	$-0.902862\pi$
$5$		−	524871.i		−	0.600908i	0.953796	−	0.300454i	$-0.0971381\pi$
$6$		0			0
$7$	1.57495e7			1.03260			0.516302	−	0.856407i	$-0.327308\pi$
$7$	1.57495e7			1.03260			0.516302	+	0.856407i	$0.327308\pi$
$8$	−3.28406e7	−	3.42534e7i	−0.692064	−	0.721836i
$9$		0			0
$10$	−1.33421e8	−	1.35307e8i	−0.421913	−	0.427877i
$11$			2.44791e8i			0.344316i	0.985069	+	0.172158i	$0.0550740\pi$
$11$			2.44791e8i			0.344316i	−0.985069	+	0.172158i	$0.944926\pi$
$12$		0			0
$13$			2.66178e9i			0.905009i	0.891762	+	0.452504i	$0.149469\pi$
$13$			2.66178e9i			0.905009i	−0.891762	+	0.452504i	$0.850531\pi$
$14$	4.06007e9	−	4.00348e9i	0.735268	−	0.725019i
$15$		0			0
$16$	−1.71731e10	−	4.82212e8i	−0.999606	−	0.0280684i
$17$	2.82837e10			0.983379			0.491689	−	0.870771i	$-0.336380\pi$
$17$	2.82837e10			0.983379			0.491689	+	0.870771i	$0.336380\pi$
$18$		0			0
$19$			7.79642e10i			1.05315i	0.850129	+	0.526574i	$0.176524\pi$
$19$			7.79642e10i			1.05315i	−0.850129	+	0.526574i	$0.823476\pi$
$20$	−6.87892e10	−	9.65592e8i	−0.600849	−	0.00843410i
$21$		0			0
$22$	6.22252e10	+	6.31047e10i	0.241754	+	0.245171i
$23$	3.66576e11			0.976063			0.488031	−	0.872826i	$-0.337715\pi$
$23$	3.66576e11			0.976063			0.488031	+	0.872826i	$0.337715\pi$
$24$		0			0
$25$	4.87450e11			0.638910
$26$	6.76615e11	+	6.86180e11i	0.635431	+	0.644413i
$27$		0			0
$28$	2.89740e10	−	2.06412e12i	0.0144932	−	1.03250i
$29$			2.78648e11i			0.103436i	0.998662	+	0.0517181i	$0.0164697\pi$
$29$			2.78648e11i			0.103436i	−0.998662	+	0.0517181i	$0.983530\pi$
$30$		0			0
$31$	3.68562e12			0.776133			0.388067	−	0.921631i	$-0.373143\pi$
$31$	3.68562e12			0.776133			0.388067	+	0.921631i	$0.373143\pi$
$32$	−4.54964e12	+	4.24104e12i	−0.731479	+	0.681864i
$33$		0			0
$34$	7.29127e12	−	7.18964e12i	0.700216	−	0.690457i
$35$		−	8.26647e12i		−	0.620500i
$36$		0			0
$37$			3.50209e13i			1.63913i	0.572989	+	0.819563i	$0.305784\pi$
$37$			3.50209e13i			1.63913i	−0.572989	+	0.819563i	$0.694216\pi$
$38$	1.98183e13	+	2.00984e13i	0.739444	+	0.749896i
$39$		0			0
$40$	−1.79786e13	+	1.72371e13i	−0.433757	+	0.415866i
$41$	3.67533e13			0.718843			0.359422	−	0.933175i	$-0.382974\pi$
$41$	3.67533e13			0.718843			0.359422	+	0.933175i	$0.382974\pi$
$42$		0			0
$43$			1.25028e14i			1.63127i	0.578565	+	0.815636i	$0.303613\pi$
$43$			1.25028e14i			1.63127i	−0.578565	+	0.815636i	$0.696387\pi$
$44$	3.20821e13	+	4.50335e11i	0.344282	+	0.00483268i
$45$		0			0
$46$	9.44998e13	−	9.31826e13i	0.695007	−	0.685320i
$47$	−1.02087e14			−0.625370			−0.312685	−	0.949857i	$-0.601228\pi$
$47$	−1.02087e14			−0.625370			−0.312685	+	0.949857i	$0.601228\pi$
$48$		0			0
$49$	1.54166e13			0.0662709
$50$	1.25660e14	−	1.23908e14i	0.454937	−	0.448596i
$51$		0			0
$52$	3.48850e14	+	4.89680e12i	0.904920	+	0.0127023i
$53$			4.67637e14i			1.03173i	0.856671	+	0.515863i	$0.172528\pi$
$53$			4.67637e14i			1.03173i	−0.856671	+	0.515863i	$0.827472\pi$
$54$		0			0
$55$	1.28484e14			0.206902
$56$	−5.17223e14	−	5.39474e14i	−0.714628	−	0.745371i
$57$		0			0
$58$	7.08315e13	+	7.18327e13i	0.0726254	+	0.0736519i
$59$			4.08479e13i			0.0362183i	0.999836	+	0.0181092i	$0.00576464\pi$
$59$			4.08479e13i			0.0362183i	−0.999836	+	0.0181092i	$0.994235\pi$
$60$		0			0
$61$		−	2.55846e15i		−	1.70874i	−0.519669	−	0.854368i	$-0.673945\pi$
$61$		−	2.55846e15i		−	1.70874i	0.519669	−	0.854368i	$-0.326055\pi$
$62$	9.50117e14	−	9.36874e14i	0.552647	−	0.544944i
$63$		0			0
$64$	−9.47911e13	+	2.24980e15i	−0.0420957	+	0.999114i
$65$	1.39709e15			0.543827
$66$		0			0
$67$			2.46686e15i			0.742179i	0.928597	+	0.371090i	$0.121016\pi$
$67$			2.46686e15i			0.742179i	−0.928597	+	0.371090i	$0.878984\pi$
$68$	5.20328e13	−	3.70684e15i	0.0138023	−	0.983282i
$69$		0			0
$70$	−2.10131e15	−	2.13101e15i	−0.435670	−	0.441828i
$71$	−1.09996e15			−0.202153			−0.101077	−	0.994879i	$-0.532229\pi$
$71$	−1.09996e15			−0.202153			−0.101077	+	0.994879i	$0.532229\pi$
$72$		0			0
$73$	−1.21919e16			−1.76941			−0.884703	−	0.466154i	$-0.845639\pi$
$73$	−1.21919e16			−1.76941			−0.884703	+	0.466154i	$0.845639\pi$
$74$	8.90221e15	+	9.02805e15i	1.15087	+	1.16714i
$75$		0			0
$76$	1.02179e16	+	1.43429e14i	1.05304	+	0.0147816i
$77$			3.85534e15i			0.355542i
$78$		0			0
$79$	2.49946e16			1.85360			0.926801	−	0.375554i	$-0.122547\pi$
$79$	2.49946e16			1.85360			0.926801	+	0.375554i	$0.122547\pi$
$80$	−2.53099e14	+	9.01367e15i	−0.0168665	+	0.600671i
$81$		0			0
$82$	9.47466e15	−	9.34259e15i	0.511854	−	0.504719i
$83$		−	3.68875e16i		−	1.79769i	−0.438262	−	0.898847i	$-0.644406\pi$
$83$		−	3.68875e16i		−	1.79769i	0.438262	−	0.898847i	$-0.355594\pi$
$84$		0			0
$85$		−	1.48453e16i		−	0.590920i
$86$	3.17818e16	+	3.22311e16i	1.14536	+	1.16155i
$87$		0			0
$88$	8.38492e15	−	8.03908e15i	0.248540	−	0.238289i
$89$	4.15487e16			1.11877			0.559387	−	0.828907i	$-0.311037\pi$
$89$	4.15487e16			1.11877			0.559387	+	0.828907i	$0.311037\pi$
$90$		0			0
$91$			4.19217e16i			0.934516i
$92$	6.74381e14	−	4.80432e16i	0.0136996	−	0.975967i
$93$		0			0
$94$	−2.63170e16	+	2.59501e16i	−0.445296	+	0.439089i
$95$	4.09212e16			0.632845
$96$		0			0
$97$	7.13708e15			0.0924614			0.0462307	−	0.998931i	$-0.485279\pi$
$97$	7.13708e15			0.0924614			0.0462307	+	0.998931i	$0.485279\pi$
$98$	3.97426e15	−	3.91886e15i	0.0471883	−	0.0465305i
$99$		0			0
$100$	8.96748e14	−	6.38847e16i	0.00896748	−	0.638847i
$101$			2.76571e16i			0.254141i	0.991894	+	0.127070i	$0.0405574\pi$
$101$			2.76571e16i			0.254141i	−0.991894	+	0.127070i	$0.959443\pi$
$102$		0			0
$103$	1.40681e17			1.09426			0.547128	−	0.837049i	$-0.315721\pi$
$103$	1.40681e17			1.09426			0.547128	+	0.837049i	$0.315721\pi$
$104$	9.11748e16	−	8.74143e16i	0.653268	−	0.626324i
$105$		0			0
$106$	1.18872e17	+	1.20552e17i	0.724402	+	0.734642i
$107$			2.87686e17i			1.61867i	0.587350	+	0.809333i	$0.300171\pi$
$107$			2.87686e17i			1.61867i	−0.587350	+	0.809333i	$0.699829\pi$
$108$		0			0
$109$		−	1.61873e17i		−	0.778127i	−0.921211	−	0.389063i	$-0.872799\pi$
$109$		−	1.61873e17i		−	0.778127i	0.921211	−	0.389063i	$-0.127201\pi$
$110$	3.31219e16	−	3.26602e16i	0.147325	−	0.145272i
$111$		0			0
$112$	−2.70468e17	−	7.59460e15i	−1.03220	−	0.0289836i
$113$	−3.01267e17			−1.06607			−0.533033	−	0.846094i	$-0.678948\pi$
$113$	−3.01267e17			−1.06607			−0.533033	+	0.846094i	$0.678948\pi$
$114$		0			0
$115$		−	1.92405e17i		−	0.586524i
$116$	3.65193e16	+	5.12621e14i	0.103426	+	0.00145179i
$117$		0			0
$118$	1.03834e16	+	1.05302e16i	0.0254298	+	0.0257893i
$119$	4.45455e17			1.01544
$120$		0			0
$121$	4.45524e17			0.881446
$122$	−6.50353e17	−	6.59546e17i	−1.19975	−	1.21671i
$123$		0			0
$124$	6.78034e15	−	4.83034e17i	0.0108935	−	0.776057i
$125$		−	6.56293e17i		−	0.984834i
$126$		0			0
$127$	−3.10547e17			−0.407189			−0.203595	−	0.979055i	$-0.565262\pi$
$127$	−3.10547e17			−0.407189			−0.203595	+	0.979055i	$0.565262\pi$
$128$	5.47457e17	+	6.04073e17i	0.671530	+	0.740977i
$129$		0			0
$130$	3.60156e17	−	3.55136e17i	0.387233	−	0.381835i
$131$		−	1.23335e18i		−	1.24246i	−0.783629	−	0.621229i	$-0.786634\pi$
$131$		−	1.23335e18i		−	1.24246i	0.783629	−	0.621229i	$-0.213366\pi$
$132$		0			0
$133$			1.22790e18i			1.08749i
$134$	6.27069e17	+	6.35933e17i	0.521104	+	0.528470i
$135$		0			0
$136$	−9.28854e17	−	9.68814e17i	−0.680561	−	0.709838i
$137$	−1.77025e18			−1.21873			−0.609367	−	0.792888i	$-0.708576\pi$
$137$	−1.77025e18			−1.21873			−0.609367	+	0.792888i	$0.708576\pi$
$138$		0			0
$139$		−	1.75424e18i		−	1.06773i	−0.845569	−	0.533866i	$-0.820739\pi$
$139$		−	1.75424e18i		−	1.06773i	0.845569	−	0.533866i	$-0.179261\pi$
$140$	−1.08340e18	−	1.52076e16i	−0.620439	−	0.00870908i
$141$		0			0
$142$	−2.83559e17	+	2.79606e17i	−0.143944	+	0.141937i
$143$	−6.51579e17			−0.311609
$144$		0			0
$145$	1.46254e17			0.0621556
$146$	−3.14296e18	+	3.09915e18i	−1.25991	+	1.24235i
$147$		0			0
$148$	4.58981e18	+	6.44270e16i	1.63897	+	0.0230061i
$149$			2.24173e18i			0.755962i	0.925813	+	0.377981i	$0.123382\pi$
$149$			2.24173e18i			0.755962i	−0.925813	+	0.377981i	$0.876618\pi$
$150$		0			0
$151$	1.48795e18			0.448006			0.224003	−	0.974589i	$-0.428088\pi$
$151$	1.48795e18			0.448006			0.224003	+	0.974589i	$0.428088\pi$
$152$	2.67054e18	−	2.56039e18i	0.760201	−	0.728846i
$153$		0			0
$154$	9.80016e17	+	9.93869e17i	0.249636	+	0.253165i
$155$		−	1.93448e18i		−	0.466384i
$156$		0			0
$157$		−	5.36324e18i		−	1.15953i	−0.814785	−	0.579763i	$-0.803145\pi$
$157$		−	5.36324e18i		−	1.15953i	0.814785	−	0.579763i	$-0.196855\pi$
$158$	6.44337e18	−	6.35356e18i	1.31986	−	1.30146i
$159$		0			0
$160$	2.22600e18	+	2.38797e18i	0.409737	+	0.439551i
$161$	5.77340e18			1.00789
$162$		0			0
$163$		−	2.95894e18i		−	0.465095i	−0.972585	−	0.232547i	$-0.925294\pi$
$163$		−	2.95894e18i		−	0.465095i	0.972585	−	0.232547i	$-0.0747061\pi$
$164$	6.76141e16	−	4.81686e18i	0.0100894	−	0.718772i
$165$		0			0
$166$	−9.37670e18	−	9.50925e18i	−1.26221	−	1.28005i
$167$	1.14232e18			0.146116			0.0730579	−	0.997328i	$-0.476724\pi$
$167$	1.14232e18			0.146116			0.0730579	+	0.997328i	$0.476724\pi$
$168$		0			0
$169$	1.56537e18			0.180959
$170$	−3.77364e18	−	3.82698e18i	−0.414901	−	0.420765i
$171$		0			0
$172$	1.63861e19	+	2.30011e17i	1.63111	+	0.0228959i
$173$			1.13255e19i			1.07316i	0.843849	+	0.536581i	$0.180284\pi$
$173$			1.13255e19i			1.07316i	−0.843849	+	0.536581i	$0.819716\pi$
$174$		0			0
$175$	7.67709e18			0.659741
$176$	1.18041e17	−	4.20382e18i	0.00966442	−	0.344181i
$177$		0			0
$178$	1.07108e19	−	1.05616e19i	0.796625	−	0.785521i
$179$		−	8.80447e18i		−	0.624385i	−0.950019	−	0.312192i	$-0.898937\pi$
$179$		−	8.80447e18i		−	0.624385i	0.950019	−	0.312192i	$-0.101063\pi$
$180$		0			0
$181$		−	6.64994e18i		−	0.429092i	−0.976714	−	0.214546i	$-0.931173\pi$
$181$		−	6.64994e18i		−	0.429092i	0.976714	−	0.214546i	$-0.0688271\pi$
$182$	1.06564e19	+	1.08070e19i	0.656149	+	0.665424i
$183$		0			0
$184$	−1.20386e19	−	1.25565e19i	−0.675498	−	0.704558i
$185$	1.83815e19			0.984964
$186$		0			0
$187$			6.92360e18i			0.338593i
$188$	−1.87806e17	+	1.33794e19i	−0.00877744	+	0.625309i
$189$		0			0
$190$	1.05491e19	−	1.04020e19i	0.450618	−	0.444337i
$191$	1.48372e19			0.606135			0.303068	−	0.952969i	$-0.401989\pi$
$191$	1.48372e19			0.606135			0.303068	+	0.952969i	$0.401989\pi$
$192$		0			0
$193$	2.59123e19			0.968878			0.484439	−	0.874825i	$-0.339024\pi$
$193$	2.59123e19			0.968878			0.484439	+	0.874825i	$0.339024\pi$
$194$	1.83987e18	−	1.81422e18i	0.0658373	−	0.0649197i
$195$		0			0
$196$	2.83615e16	−	2.02049e18i	0.000930151	−	0.0662643i
$197$		−	5.49419e19i		−	1.72560i	−0.505543	−	0.862801i	$-0.668708\pi$
$197$		−	5.49419e19i		−	1.72560i	0.505543	−	0.862801i	$-0.331292\pi$
$198$		0			0
$199$	7.58694e18			0.218683			0.109342	−	0.994004i	$-0.465126\pi$
$199$	7.58694e18			0.218683			0.109342	+	0.994004i	$0.465126\pi$
$200$	−1.60081e19	−	1.66968e19i	−0.442166	−	0.461188i
$201$		0			0
$202$	7.03035e18	+	7.12973e18i	0.178439	+	0.180962i
$203$			4.38857e18i			0.106809i
$204$		0			0
$205$		−	1.92908e19i		−	0.431958i
$206$	3.62662e19	−	3.57607e19i	0.779167	−	0.768307i
$207$		0			0
$208$	1.28354e18	−	4.57109e19i	0.0254022	−	0.904652i
$209$	−1.90849e19			−0.362616
$210$		0			0
$211$		−	2.70658e19i		−	0.474264i	−0.971477	−	0.237132i	$-0.923793\pi$
$211$		−	2.70658e19i		−	0.474264i	0.971477	−	0.237132i	$-0.0762074\pi$
$212$	6.12881e19	+	8.60299e17i	1.03162	+	0.0144809i
$213$		0			0
$214$	7.31290e19	+	7.41627e19i	1.13651	+	1.15257i
$215$	6.56238e19			0.980244
$216$		0			0
$217$	5.80467e19			0.801438
$218$	−4.11477e19	−	4.17294e19i	−0.546344	−	0.554066i
$219$		0			0
$220$	2.36368e17	−	1.68390e19i	0.00290400	−	0.206882i
$221$			7.52849e19i			0.889966i
$222$		0			0
$223$	−6.99062e18			−0.0765463			−0.0382732	−	0.999267i	$-0.512186\pi$
$223$	−6.99062e18			−0.0765463			−0.0382732	+	0.999267i	$0.512186\pi$
$224$	−7.16545e19	+	6.67944e19i	−0.755328	+	0.704096i
$225$		0			0
$226$	−7.76636e19	+	7.65811e19i	−0.759094	+	0.748514i
$227$			1.78757e20i			1.68285i	0.540377	+	0.841423i	$0.318281\pi$
$227$			1.78757e20i			1.68285i	−0.540377	+	0.841423i	$0.681719\pi$
$228$		0			0
$229$			2.48507e19i			0.217139i	0.994089	+	0.108569i	$0.0346269\pi$
$229$			2.48507e19i			0.217139i	−0.994089	+	0.108569i	$0.965373\pi$
$230$	−4.89089e19	−	4.96002e19i	−0.411814	−	0.417635i
$231$		0			0
$232$	9.54463e18	−	9.15096e18i	0.0746640	−	0.0715844i
$233$	−1.18068e20			−0.890446			−0.445223	−	0.895420i	$-0.646876\pi$
$233$	−1.18068e20			−0.890446			−0.445223	+	0.895420i	$0.646876\pi$
$234$		0			0
$235$			5.35824e19i			0.375790i
$236$	5.35349e18	+	7.51469e16i	0.0362147	+	0.000508345i
$237$		0			0
$238$	1.14834e20	−	1.13233e20i	0.723046	−	0.712968i
$239$	−1.23287e20			−0.749092			−0.374546	−	0.927208i	$-0.622201\pi$
$239$	−1.23287e20			−0.749092			−0.374546	+	0.927208i	$0.622201\pi$
$240$		0			0
$241$	−2.67815e20			−1.51597			−0.757983	−	0.652275i	$-0.773815\pi$
$241$	−2.67815e20			−1.51597			−0.757983	+	0.652275i	$0.773815\pi$
$242$	1.14852e20	−	1.13251e20i	0.627635	−	0.618887i
$243$		0			0
$244$	−3.35309e20	−	4.70673e18i	−1.70857	−	0.0239831i
$245$		−	8.09174e18i		−	0.0398227i
$246$		0			0
$247$	−2.07523e20			−0.953109
$248$	−1.21038e20	−	1.26245e20i	−0.537134	−	0.560241i
$249$		0			0
$250$	−1.66828e20	−	1.69186e20i	−0.691478	−	0.701253i
$251$		−	1.11530e20i		−	0.446854i	−0.974721	−	0.223427i	$-0.928276\pi$
$251$		−	1.11530e20i		−	0.446854i	0.974721	−	0.223427i	$-0.0717244\pi$
$252$		0			0
$253$			8.97346e19i			0.336074i
$254$	−8.00561e19	+	7.89402e19i	−0.289940	+	0.285898i
$255$		0			0
$256$	2.94683e20	+	1.65621e19i	0.998424	+	0.0561147i
$257$	−2.70681e19			−0.0887209			−0.0443604	−	0.999016i	$-0.514125\pi$
$257$	−2.70681e19			−0.0887209			−0.0443604	+	0.999016i	$0.514125\pi$
$258$		0			0
$259$			5.51562e20i			1.69257i
$260$	2.57019e18	−	1.83101e20i	0.00763293	−	0.543773i
$261$		0			0
$262$	−3.13515e20	−	3.17946e20i	−0.872363	−	0.884694i
$263$	−5.28511e20			−1.42374			−0.711869	−	0.702312i	$-0.752151\pi$
$263$	−5.28511e20			−1.42374			−0.711869	+	0.702312i	$0.752151\pi$
$264$		0			0
$265$	2.45449e20			0.619972
$266$	3.12128e20	+	3.16540e20i	0.763553	+	0.774346i
$267$		0			0
$268$	3.23305e20	+	4.53822e18i	0.742106	+	0.0104169i
$269$			7.69627e20i			1.71153i	0.517361	+	0.855767i	$0.326915\pi$
$269$			7.69627e20i			1.71153i	−0.517361	+	0.855767i	$0.673085\pi$
$270$		0			0
$271$	−1.28273e18			−0.00267853			−0.00133927	−	0.999999i	$-0.500426\pi$
$271$	−1.28273e18			−0.00267853			−0.00133927	+	0.999999i	$0.500426\pi$
$272$	−4.85719e20	−	1.36387e19i	−0.982991	−	0.0276019i
$273$		0			0
$274$	−4.56352e20	+	4.49992e20i	−0.867802	+	0.855706i
$275$			1.19323e20i			0.219987i
$276$		0			0
$277$			7.28964e19i			0.126365i	0.998002	+	0.0631827i	$0.0201251\pi$
$277$			7.28964e19i			0.126365i	−0.998002	+	0.0631827i	$0.979875\pi$
$278$	−4.45922e20	−	4.52225e20i	−0.749684	−	0.760281i
$279$		0			0
$280$	−2.83155e20	+	2.71476e20i	−0.447899	+	0.429425i
$281$	7.35344e20			1.12846			0.564231	−	0.825617i	$-0.309173\pi$
$281$	7.35344e20			1.12846			0.564231	+	0.825617i	$0.309173\pi$
$282$		0			0
$283$			2.65211e19i			0.0383184i	0.999816	+	0.0191592i	$0.00609894\pi$
$283$			2.65211e19i			0.0383184i	−0.999816	+	0.0191592i	$0.993901\pi$
$284$	−2.02357e18	+	1.44160e20i	−0.00283734	+	0.202133i
$285$		0			0
$286$	−1.67971e20	+	1.65629e20i	−0.221882	+	0.218789i
$287$	5.78847e20			0.742280
$288$		0			0
$289$	−2.72714e19			−0.0329667
$290$	3.77029e19	−	3.71774e19i	0.0442580	−	0.0436411i
$291$		0			0
$292$	−2.24291e19	+	1.59786e21i	−0.0248347	+	1.76923i
$293$			1.14055e21i			1.22671i	0.789809	+	0.613353i	$0.210180\pi$
$293$			1.14055e21i			1.22671i	−0.789809	+	0.613353i	$0.789820\pi$
$294$		0			0
$295$	2.14399e19			0.0217639
$296$	1.19958e21	−	1.15011e21i	1.18318	−	1.13438i
$297$		0			0
$298$	5.69841e20	+	5.77896e20i	0.530781	+	0.538284i
$299$			9.75744e20i			0.883346i
$300$		0			0
$301$			1.96914e21i			1.68446i
$302$	3.83578e20	−	3.78232e20i	0.319003	−	0.314557i
$303$		0			0
$304$	3.75952e19	−	1.33889e21i	0.0295602	−	1.05273i
$305$	−1.34286e21			−1.02679
$306$		0			0
$307$		−	4.88182e20i		−	0.353107i	−0.984291	−	0.176553i	$-0.943505\pi$
$307$		−	4.88182e20i		−	0.353107i	0.984291	−	0.176553i	$-0.0564948\pi$
$308$	5.05277e20	+	7.09256e18i	0.355507	+	0.00499025i
$309$		0			0
$310$	−4.91738e20	−	4.98689e20i	−0.327461	−	0.332090i
$311$	1.56774e21			1.01581			0.507904	−	0.861414i	$-0.330420\pi$
$311$	1.56774e21			1.01581			0.507904	+	0.861414i	$0.330420\pi$
$312$		0			0
$313$	−6.34156e20			−0.389107			−0.194554	−	0.980892i	$-0.562326\pi$
$313$	−6.34156e20			−0.389107			−0.194554	+	0.980892i	$0.562326\pi$
$314$	−1.36332e21	−	1.38259e21i	−0.814135	−	0.825643i
$315$		0			0
$316$	4.59819e19	−	3.27577e21i	0.0260164	−	1.85342i
$317$			2.83832e20i			0.156335i	0.996940	+	0.0781677i	$0.0249070\pi$
$317$			2.83832e20i			0.156335i	−0.996940	+	0.0781677i	$0.975093\pi$
$318$		0			0
$319$	−6.82105e19			−0.0356148
$320$	1.18086e21	+	4.97531e19i	0.600375	+	0.0252956i
$321$		0			0
$322$	1.48833e21	−	1.46758e21i	0.717667	−	0.707664i
$323$			2.20512e21i			1.03564i
$324$		0			0
$325$			1.29748e21i			0.578219i
$326$	−7.52154e20	−	7.62786e20i	−0.326556	−	0.331172i
$327$		0			0
$328$	−1.20700e21	−	1.25893e21i	−0.497485	−	0.518887i
$329$	−1.60782e21			−0.645760
$330$		0			0
$331$			2.11311e21i			0.806089i	0.915180	+	0.403045i	$0.132048\pi$
$331$			2.11311e21i			0.806089i	−0.915180	+	0.403045i	$0.867952\pi$
$332$	−4.83445e21	−	6.78610e19i	−1.79752	−	0.0252317i
$333$		0			0
$334$	2.94478e20	−	2.90374e20i	0.104042	−	0.102592i
$335$	1.29478e21			0.445981
$336$		0			0
$337$	4.08155e20			0.133651			0.0668253	−	0.997765i	$-0.478713\pi$
$337$	4.08155e20			0.133651			0.0668253	+	0.997765i	$0.478713\pi$
$338$	4.03537e20	−	3.97912e20i	0.128852	−	0.127056i
$339$		0			0
$340$	−1.94561e21	−	2.73105e19i	−0.590862	−	0.00829391i
$341$			9.02207e20i			0.267235i
$342$		0			0
$343$	−3.42101e21			−0.964172
$344$	4.28265e21	−	4.10600e21i	1.17751	−	1.12894i
$345$		0			0
$346$	2.87891e21	+	2.91960e21i	0.753495	+	0.764146i
$347$			3.05313e21i			0.779732i	0.920872	+	0.389866i	$0.127479\pi$
$347$			3.05313e21i			0.779732i	−0.920872	+	0.389866i	$0.872521\pi$
$348$		0			0
$349$		−	8.48728e20i		−	0.206420i	−0.994660	−	0.103210i	$-0.967089\pi$
$349$		−	8.48728e20i		−	0.206420i	0.994660	−	0.103210i	$-0.0329114\pi$
$350$	1.97908e21	−	1.95149e21i	0.469770	−	0.463222i
$351$		0			0
$352$	−1.03817e21	−	1.11371e21i	−0.234777	−	0.251860i
$353$	5.04249e21			1.11317			0.556583	−	0.830792i	$-0.312112\pi$
$353$	5.04249e21			1.11317			0.556583	+	0.830792i	$0.312112\pi$
$354$		0			0
$355$			5.77337e20i			0.121475i
$356$	7.64360e19	−	5.44533e21i	0.0157026	−	1.11866i
$357$		0			0
$358$	−2.23807e21	−	2.26971e21i	−0.438397	−	0.444594i
$359$	−9.63686e21			−1.84346			−0.921728	−	0.387837i	$-0.873222\pi$
$359$	−9.63686e21			−1.84346			−0.921728	+	0.387837i	$0.873222\pi$
$360$		0			0
$361$	−5.98028e20			−0.109121
$362$	−1.69040e21	−	1.71429e21i	−0.301277	−	0.305536i
$363$		0			0
$364$	5.49421e21	+	7.71222e19i	0.934424	+	0.0131165i
$365$			6.39919e21i			1.06325i
$366$		0			0
$367$	8.52037e21			1.35144			0.675720	−	0.737158i	$-0.263833\pi$
$367$	8.52037e21			1.35144			0.675720	+	0.737158i	$0.263833\pi$
$368$	−6.29525e21	−	1.76767e20i	−0.975678	−	0.0273965i
$369$		0			0
$370$	4.73856e21	−	4.67251e21i	0.701345	−	0.691570i
$371$			7.36506e21i			1.06536i
$372$		0			0
$373$		−	5.97419e21i		−	0.825569i	−0.910829	−	0.412785i	$-0.864556\pi$
$373$		−	5.97419e21i		−	0.825569i	0.910829	−	0.412785i	$-0.135444\pi$
$374$	1.75996e21	+	1.78484e21i	0.237735	+	0.241096i
$375$		0			0
$376$	3.35259e21	+	3.49682e21i	0.432796	+	0.451415i
$377$	−7.41698e20			−0.0936107
$378$		0			0
$379$		−	1.72231e21i		−	0.207816i	−0.994587	−	0.103908i	$-0.966865\pi$
$379$		−	1.72231e21i		−	0.207816i	0.994587	−	0.103908i	$-0.0331347\pi$
$380$	7.52816e19	−	5.36309e21i	0.00888235	−	0.632783i
$381$		0			0
$382$	3.82490e21	−	3.77158e21i	0.431600	−	0.425584i
$383$	5.14304e21			0.567584			0.283792	−	0.958886i	$-0.408408\pi$
$383$	5.14304e21			0.567584			0.283792	+	0.958886i	$0.408408\pi$
$384$		0			0
$385$	2.02356e21			0.213648
$386$	6.67995e21	−	6.58684e21i	0.689892	−	0.680275i
$387$		0			0
$388$	1.31299e19	−	9.35379e20i	0.00129775	−	0.0924523i
$389$			1.71218e21i			0.165569i	0.996567	+	0.0827843i	$0.0263813\pi$
$389$			1.71218e21i			0.165569i	−0.996567	+	0.0827843i	$0.973619\pi$
$390$		0			0
$391$	1.03681e22			0.959839
$392$	−5.06291e20	−	5.28072e20i	−0.0458636	−	0.0478367i
$393$		0			0
$394$	−1.39661e22	−	1.41635e22i	−1.21159	−	1.22872i
$395$		−	1.31190e22i		−	1.11384i
$396$		0			0
$397$			5.61976e21i			0.457087i	0.973534	+	0.228543i	$0.0733962\pi$
$397$			5.61976e21i			0.457087i	−0.973534	+	0.228543i	$0.926604\pi$
$398$	1.95584e21	−	1.92858e21i	0.155714	−	0.153543i
$399$		0			0
$400$	−8.37102e21	−	2.35054e20i	−0.638658	−	0.0179332i
$401$	1.00601e22			0.751410			0.375705	−	0.926739i	$-0.377401\pi$
$401$	1.00601e22			0.751410			0.375705	+	0.926739i	$0.377401\pi$
$402$		0			0
$403$			9.81029e21i			0.702407i
$404$	3.62471e21	+	5.08800e19i	0.254116	+	0.00356702i
$405$		0			0
$406$	1.11556e21	+	1.13133e21i	0.0749932	+	0.0760533i
$407$	−8.57280e21			−0.564378
$408$		0			0
$409$	9.17274e21			0.579230			0.289615	−	0.957143i	$-0.406473\pi$
$409$	9.17274e21			0.579230			0.289615	+	0.957143i	$0.406473\pi$
$410$	−4.90366e21	−	4.97297e21i	−0.303290	−	0.307577i
$411$		0			0
$412$	2.58807e20	−	1.84375e22i	0.0153585	−	1.09415i
$413$			6.43335e20i			0.0373992i
$414$		0			0
$415$	−1.93612e22			−1.08025
$416$	−1.12887e22	−	1.21101e22i	−0.617093	−	0.661995i
$417$		0			0
$418$	−4.91991e21	+	4.85133e21i	−0.258202	+	0.254603i
$419$			1.93790e22i			0.996581i	0.867010	+	0.498291i	$0.166039\pi$
$419$			1.93790e22i			0.996581i	−0.867010	+	0.498291i	$0.833961\pi$
$420$		0			0
$421$			3.52568e22i			1.74118i	0.492006	+	0.870592i	$0.336264\pi$
$421$			3.52568e22i			1.74118i	−0.492006	+	0.870592i	$0.663736\pi$
$422$	−6.88005e21	−	6.97730e21i	−0.332994	−	0.337701i
$423$		0			0
$424$	1.60182e22	−	1.53575e22i	0.744737	−	0.714019i
$425$	1.37869e22			0.628290
$426$		0			0
$427$		−	4.02945e22i		−	1.76445i
$428$	3.77039e22	+	5.29249e20i	1.61851	+	0.0227189i
$429$		0			0
$430$	1.69172e22	−	1.66814e22i	0.697985	−	0.688256i
$431$	1.08535e22			0.439048			0.219524	−	0.975607i	$-0.429550\pi$
$431$	1.08535e22			0.439048			0.219524	+	0.975607i	$0.429550\pi$
$432$		0			0
$433$	3.41436e22			1.32789			0.663945	−	0.747781i	$-0.268881\pi$
$433$	3.41436e22			1.32789			0.663945	+	0.747781i	$0.268881\pi$
$434$	1.49639e22	−	1.47553e22i	0.570665	−	0.562711i
$435$		0			0
$436$	−2.12150e22	−	2.97794e20i	−0.778050	−	0.0109215i
$437$			2.85798e22i			1.02794i
$438$		0			0
$439$	−1.05534e22			−0.365126			−0.182563	−	0.983194i	$-0.558439\pi$
$439$	−1.05534e22			−0.365126			−0.182563	+	0.983194i	$0.558439\pi$
$440$	−4.21948e21	−	4.40101e21i	−0.143190	−	0.149350i
$441$		0			0
$442$	1.91372e22	+	1.94077e22i	0.624869	+	0.633702i
$443$			2.27118e22i			0.727478i	0.931501	+	0.363739i	$0.118500\pi$
$443$			2.27118e22i			0.727478i	−0.931501	+	0.363739i	$0.881500\pi$
$444$		0			0
$445$		−	2.18077e22i		−	0.672280i
$446$	−1.80211e21	+	1.77700e21i	−0.0545050	+	0.0537453i
$447$		0			0
$448$	−1.49291e21	+	3.54333e22i	−0.0434682	+	1.03169i
$449$	−2.63226e22			−0.752029			−0.376014	−	0.926614i	$-0.622706\pi$
$449$	−2.63226e22			−0.752029			−0.376014	+	0.926614i	$0.622706\pi$
$450$		0			0
$451$			8.99689e21i			0.247509i
$452$	−5.54232e20	+	3.94837e22i	−0.0149629	+	1.06596i
$453$		0			0
$454$	4.54396e22	+	4.60819e22i	1.18157	+	1.19827i
$455$	2.20035e22			0.561558
$456$		0			0
$457$	−7.36512e21			−0.181089			−0.0905445	−	0.995892i	$-0.528861\pi$
$457$	−7.36512e21			−0.181089			−0.0905445	+	0.995892i	$0.528861\pi$
$458$	6.31697e21	+	6.40627e21i	0.152459	+	0.154614i
$459$		0			0
$460$	−2.52165e22	−	3.53963e20i	−0.586466	−	0.00823221i
$461$		−	3.04360e22i		−	0.694912i	−0.937696	−	0.347456i	$-0.887046\pi$
$461$		−	3.04360e22i		−	0.694912i	0.937696	−	0.347456i	$-0.112954\pi$
$462$		0			0
$463$	−6.61609e22			−1.45600			−0.728002	−	0.685575i	$-0.759551\pi$
$463$	−6.61609e22			−1.45600			−0.728002	+	0.685575i	$0.759551\pi$
$464$	1.34367e20	−	4.78525e21i	0.00290329	−	0.103395i
$465$		0			0
$466$	−3.04368e22	+	3.00126e22i	−0.634044	+	0.625206i
$467$		−	6.69796e21i		−	0.137009i	−0.997651	−	0.0685045i	$-0.978177\pi$
$467$		−	6.69796e21i		−	0.137009i	0.997651	−	0.0685045i	$-0.0218228\pi$
$468$		0			0
$469$			3.88519e22i			0.766377i
$470$	1.36205e22	+	1.38130e22i	0.263852	+	0.267582i
$471$		0			0
$472$	1.39918e21	−	1.34147e21i	0.0261437	−	0.0250654i
$473$	−3.06058e22			−0.561674
$474$		0			0
$475$			3.80036e22i			0.672867i
$476$	8.19491e20	−	5.83809e22i	0.0142523	−	1.01534i
$477$		0			0
$478$	−3.17822e22	+	3.13392e22i	−0.533392	+	0.525958i
$479$	−6.94574e20			−0.0114516			−0.00572581	−	0.999984i	$-0.501823\pi$
$479$	−6.94574e20			−0.0114516			−0.00572581	+	0.999984i	$0.501823\pi$
$480$		0			0
$481$	−9.32177e22			−1.48342
$482$	−6.90400e22	+	6.80777e22i	−1.07945	+	1.06440i
$483$		0			0
$484$	8.19619e20	−	5.83900e22i	0.0123716	−	0.881359i
$485$		−	3.74605e21i		−	0.0555608i
$486$		0			0
$487$	9.69164e22			1.38804			0.694019	−	0.719957i	$-0.255838\pi$
$487$	9.69164e22			1.38804			0.694019	+	0.719957i	$0.255838\pi$
$488$	−8.76359e22	+	8.40213e22i	−1.23343	+	1.18255i
$489$		0			0
$490$	−2.05690e21	−	2.08597e21i	−0.0279606	−	0.0283558i
$491$		−	1.39521e23i		−	1.86400i	−0.362455	−	0.932001i	$-0.618061\pi$
$491$		−	1.39521e23i		−	1.86400i	0.362455	−	0.932001i	$-0.381939\pi$
$492$		0			0
$493$			7.88120e21i			0.101717i
$494$	−5.34974e22	+	5.27518e22i	−0.678663	+	0.669203i
$495$		0			0
$496$	−6.32935e22	−	1.77725e21i	−0.775827	−	0.0217848i
$497$	−1.73238e22			−0.208744
$498$		0			0
$499$		−	8.18187e21i		−	0.0952792i	−0.998865	−	0.0476396i	$-0.984830\pi$
$499$		−	8.18187e21i		−	0.0952792i	0.998865	−	0.0476396i	$-0.0151699\pi$
$500$	−8.60132e22	−	1.20737e21i	−0.984737	−	0.0138227i
$501$		0			0
$502$	−2.83506e22	−	2.87514e22i	−0.313748	−	0.318183i
$503$	−1.78323e23			−1.94034			−0.970172	−	0.242419i	$-0.922059\pi$
$503$	−1.78323e23			−1.94034			−0.970172	+	0.242419i	$0.922059\pi$
$504$		0			0
$505$	1.45164e22			0.152715
$506$	2.28103e22	+	2.31327e22i	0.235967	+	0.239302i
$507$		0			0
$508$	−5.71306e20	+	4.07001e22i	−0.00571514	+	0.407149i
$509$			5.61580e22i			0.552473i	0.961090	+	0.276236i	$0.0890872\pi$
$509$			5.61580e22i			0.552473i	−0.961090	+	0.276236i	$0.910913\pi$
$510$		0			0
$511$	−1.92017e23			−1.82710
$512$	8.01764e22	−	7.06380e22i	0.750330	−	0.661064i
$513$		0			0
$514$	−6.97789e21	+	6.88062e21i	−0.0631738	+	0.0622933i
$515$		−	7.38394e22i		−	0.657547i
$516$		0			0
$517$		−	2.49899e22i		−	0.215325i
$518$	1.40205e23	+	1.42187e23i	1.18840	+	1.20520i
$519$		0			0
$520$	−4.58812e22	−	4.78551e22i	−0.376363	−	0.392554i
$521$	1.17899e23			0.951458			0.475729	−	0.879592i	$-0.342184\pi$
$521$	1.17899e23			0.951458			0.475729	+	0.879592i	$0.342184\pi$
$522$		0			0
$523$		−	1.02181e21i		−	0.00798187i	−0.999992	−	0.00399093i	$-0.998730\pi$
$523$		−	1.02181e21i		−	0.00798187i	0.999992	−	0.00399093i	$-0.00127036\pi$
$524$	−1.61642e23	−	2.26897e21i	−1.24233	−	0.0174386i
$525$		0			0
$526$	−1.36245e23	+	1.34346e23i	−1.01378	+	0.999645i
$527$	1.04243e23			0.763233
$528$		0			0
$529$	−6.67183e21			−0.0473011
$530$	6.32744e22	−	6.23925e22i	0.441452	−	0.435299i
$531$		0			0
$532$	1.60927e23	+	2.25893e21i	1.08738	+	0.0152635i
$533$			9.78291e22i			0.650559i
$534$		0			0
$535$	1.50998e23			0.972669
$536$	8.44984e22	−	8.10132e22i	0.535732	−	0.513635i
$537$		0			0
$538$	1.95637e23	+	1.98402e23i	1.20171	+	1.21870i
$539$			3.77385e21i			0.0228181i
$540$		0			0
$541$		−	3.93089e22i		−	0.230311i	−0.993347	−	0.115155i	$-0.963263\pi$
$541$		−	3.93089e22i		−	0.230311i	0.993347	−	0.115155i	$-0.0367366\pi$
$542$	−3.30676e20	+	3.26067e20i	−0.00190726	+	0.00188067i
$543$		0			0
$544$	−1.28681e23	+	1.19952e23i	−0.719321	+	0.670531i
$545$	−8.49627e22			−0.467582
$546$		0			0
$547$		−	2.63090e23i		−	1.40350i	−0.712423	−	0.701750i	$-0.752402\pi$
$547$		−	2.63090e23i		−	1.40350i	0.712423	−	0.701750i	$-0.247598\pi$
$548$	−3.25668e21	+	2.32007e23i	−0.0171057	+	1.21861i
$549$		0			0
$550$	3.03316e22	+	3.07604e22i	0.154459	+	0.156642i
$551$	−2.17245e22			−0.108934
$552$		0			0
$553$	3.93653e23			1.91404
$554$	1.85300e22	+	1.87920e22i	0.0887245	+	0.0899786i
$555$		0			0
$556$	−2.29909e23	−	3.22722e21i	−1.06763	−	0.0149863i
$557$		−	2.45492e23i		−	1.12271i	−0.827574	−	0.561357i	$-0.810280\pi$
$557$		−	2.45492e23i		−	1.12271i	0.827574	−	0.561357i	$-0.189720\pi$
$558$		0			0
$559$	−3.32797e23			−1.47632
$560$	−3.98619e21	+	1.41961e23i	−0.0174164	+	0.620255i
$561$		0			0
$562$	1.89565e23	−	1.86922e23i	0.803523	−	0.792323i
$563$		−	1.65751e23i		−	0.692044i	−0.938226	−	0.346022i	$-0.887532\pi$
$563$		−	1.65751e23i		−	0.692044i	0.938226	−	0.346022i	$-0.112468\pi$
$564$		0			0
$565$			1.58126e23i			0.640607i
$566$	6.74160e21	+	6.83689e21i	0.0269044	+	0.0272847i
$567$		0			0
$568$	3.61233e22	+	3.76773e22i	0.139903	+	0.145922i
$569$	3.03432e23			1.15773			0.578866	−	0.815423i	$-0.303496\pi$
$569$	3.03432e23			1.15773			0.578866	+	0.815423i	$0.303496\pi$
$570$		0			0
$571$		−	4.28152e23i		−	1.58559i	−0.609489	−	0.792795i	$-0.708625\pi$
$571$		−	4.28152e23i		−	1.58559i	0.609489	−	0.792795i	$-0.291375\pi$
$572$	−1.19869e21	+	8.53953e22i	−0.00437362	+	0.311579i
$573$		0			0
$574$	1.49221e23	−	1.47141e23i	0.528542	−	0.521175i
$575$	1.78687e23			0.623616
$576$		0			0
$577$	4.78622e23			1.62180			0.810902	−	0.585182i	$-0.198977\pi$
$577$	4.78622e23			1.62180			0.810902	+	0.585182i	$0.198977\pi$
$578$	−7.03029e21	+	6.93230e21i	−0.0234740	+	0.0231468i
$579$		0			0
$580$	2.69060e20	−	1.91679e22i	0.000872391	−	0.0621495i
$581$		−	5.80961e23i		−	1.85631i
$582$		0			0
$583$	−1.14473e23			−0.355240
$584$	4.00390e23	+	4.17615e23i	1.22454	+	1.27722i
$585$		0			0
$586$	2.89925e23	+	2.94023e23i	0.861303	+	0.873478i
$587$		−	3.65842e23i		−	1.07120i	−0.844472	−	0.535599i	$-0.820086\pi$
$587$		−	3.65842e23i		−	1.07120i	0.844472	−	0.535599i	$-0.179914\pi$
$588$		0			0
$589$			2.87346e23i			0.817383i
$590$	5.52700e21	−	5.44996e21i	0.0154970	−	0.0152810i
$591$		0			0
$592$	1.68875e22	−	6.01417e23i	0.0460077	−	1.63848i
$593$	6.50994e22			0.174828			0.0874142	−	0.996172i	$-0.472140\pi$
$593$	6.50994e22			0.174828			0.0874142	+	0.996172i	$0.472140\pi$
$594$		0			0
$595$		−	2.33806e23i		−	0.610186i
$596$	2.93799e23	+	4.12405e21i	0.755888	+	0.0106104i
$597$		0			0
$598$	2.48031e23	+	2.51537e23i	0.620221	+	0.628988i
$599$	−7.03579e23			−1.73454			−0.867271	−	0.497837i	$-0.834128\pi$
$599$	−7.03579e23			−1.73454			−0.867271	+	0.497837i	$0.834128\pi$
$600$		0			0
$601$	1.22977e23			0.294707			0.147354	−	0.989084i	$-0.452924\pi$
$601$	1.22977e23			0.294707			0.147354	+	0.989084i	$0.452924\pi$
$602$	5.00548e23	+	5.07624e23i	1.18270	+	1.19942i
$603$		0			0
$604$	2.73734e21	−	1.95009e23i	0.00628802	−	0.447961i
$605$		−	2.33843e23i		−	0.529668i
$606$		0			0
$607$	−5.67018e23			−1.24880			−0.624400	−	0.781105i	$-0.714657\pi$
$607$	−5.67018e23			−1.24880			−0.624400	+	0.781105i	$0.714657\pi$
$608$	−3.30649e23	−	3.54709e23i	−0.718104	−	0.770356i
$609$		0			0
$610$	−3.46177e23	+	3.41351e23i	−0.731129	+	0.720938i
$611$		−	2.71732e23i		−	0.565966i
$612$		0			0
$613$		−	3.36503e23i		−	0.681672i	−0.940123	−	0.340836i	$-0.889290\pi$
$613$		−	3.36503e23i		−	0.681672i	0.940123	−	0.340836i	$-0.110710\pi$
$614$	−1.24094e23	−	1.25849e23i	−0.247926	−	0.251430i
$615$		0			0
$616$	1.32058e23	−	1.26612e23i	0.256643	−	0.246058i
$617$	2.04462e22			0.0391912			0.0195956	−	0.999808i	$-0.493762\pi$
$617$	2.04462e22			0.0391912			0.0195956	+	0.999808i	$0.493762\pi$
$618$		0			0
$619$		−	5.34254e23i		−	0.996270i	−0.867099	−	0.498135i	$-0.834018\pi$
$619$		−	5.34254e23i		−	0.996270i	0.867099	−	0.498135i	$-0.165982\pi$
$620$	−2.53531e23	−	3.55880e21i	−0.466338	−	0.00654598i
$621$		0			0
$622$	4.04149e23	−	3.98516e23i	0.723308	−	0.713226i
$623$	6.54371e23			1.15525
$624$		0			0
$625$	2.74250e22			0.0471158
$626$	−1.63479e23	+	1.61201e23i	−0.277064	+	0.273203i
$627$		0			0
$628$	−7.02902e23	−	9.86662e21i	−1.15941	−	0.0162746i
$629$			9.90521e23i			1.61188i
$630$		0			0
$631$	9.89627e23			1.56755			0.783776	−	0.621043i	$-0.213291\pi$
$631$	9.89627e23			1.56755			0.783776	+	0.621043i	$0.213291\pi$
$632$	−8.20838e23	−	8.56151e23i	−1.28281	−	1.33800i
$633$		0			0
$634$	7.21492e22	+	7.31691e22i	0.109767	+	0.111319i
$635$			1.62997e23i			0.244683i
$636$		0			0
$637$			4.10356e22i			0.0599757i
$638$	−1.75840e22	+	1.73389e22i	−0.0253596	+	0.0250061i
$639$		0			0
$640$	3.17061e23	−	2.87345e23i	0.445259	−	0.403528i
$641$	4.56767e23			0.632997			0.316498	−	0.948593i	$-0.397493\pi$
$641$	4.56767e23			0.632997			0.316498	+	0.948593i	$0.397493\pi$
$642$		0			0
$643$		−	1.63786e23i		−	0.221046i	−0.993874	−	0.110523i	$-0.964747\pi$
$643$		−	1.63786e23i		−	0.221046i	0.993874	−	0.110523i	$-0.0352526\pi$
$644$	1.06212e22	−	7.56656e23i	0.0141463	−	1.00779i
$645$		0			0
$646$	5.60534e23	+	5.68458e23i	0.727153	+	0.737432i
$647$	−1.41349e24			−1.80969			−0.904846	−	0.425738i	$-0.860014\pi$
$647$	−1.41349e24			−1.80969			−0.904846	+	0.425738i	$0.860014\pi$
$648$		0			0
$649$	−9.99921e21			−0.0124706
$650$	3.29816e23	+	3.34478e23i	0.405983	+	0.411722i
$651$		0			0
$652$	−3.87796e23	−	5.44348e21i	−0.465049	−	0.00652788i
$653$			8.79618e23i			1.04119i	0.853802	+	0.520597i	$0.174291\pi$
$653$			8.79618e23i			1.04119i	−0.853802	+	0.520597i	$0.825709\pi$
$654$		0			0
$655$	−6.47352e23			−0.746602
$656$	−6.31169e23	−	1.77229e22i	−0.718560	−	0.0201768i
$657$		0			0
$658$	−4.14479e23	+	4.08702e23i	−0.459814	+	0.453405i
$659$		−	4.40891e23i		−	0.482843i	−0.970420	−	0.241421i	$-0.922386\pi$
$659$		−	4.40891e23i		−	0.482843i	0.970420	−	0.241421i	$-0.0776136\pi$
$660$		0			0
$661$			7.35760e23i			0.785278i	0.919693	+	0.392639i	$0.128438\pi$
$661$			7.35760e23i			0.785278i	−0.919693	+	0.392639i	$0.871562\pi$
$662$	5.37145e23	+	5.44738e23i	0.565977	+	0.573977i
$663$		0			0
$664$	−1.26352e24	+	1.21141e24i	−1.29764	+	1.24412i
$665$	6.44488e23			0.653478
$666$		0			0
$667$			1.02146e23i			0.100960i
$668$	2.10149e21	−	1.49711e23i	0.00205082	−	0.146101i
$669$		0			0
$670$	3.33783e23	−	3.29130e23i	0.317562	−	0.313135i
$671$	6.26288e23			0.588346
$672$		0			0
$673$	−3.52911e23			−0.323249			−0.161625	−	0.986852i	$-0.551673\pi$
$673$	−3.52911e23			−0.323249			−0.161625	+	0.986852i	$0.551673\pi$
$674$	1.05218e23	−	1.03752e23i	0.0951662	−	0.0938397i
$675$		0			0
$676$	2.87977e21	−	2.05156e23i	0.00253986	−	0.180941i
$677$		−	7.93301e23i		−	0.690930i	−0.938432	−	0.345465i	$-0.887721\pi$
$677$		−	7.93301e23i		−	0.690930i	0.938432	−	0.345465i	$-0.112279\pi$
$678$		0			0
$679$	1.12405e23			0.0954760
$680$	−5.08502e23	+	4.87529e23i	−0.426547	+	0.408954i
$681$		0			0
$682$	2.29338e23	+	2.32580e23i	0.187633	+	0.190285i
$683$		−	8.06966e23i		−	0.652048i	−0.945362	−	0.326024i	$-0.894291\pi$
$683$		−	8.06966e23i		−	0.652048i	0.945362	−	0.326024i	$-0.105709\pi$
$684$		0			0
$685$			9.29152e23i			0.732347i
$686$	−8.81904e23	+	8.69612e23i	−0.686541	+	0.676971i
$687$		0			0
$688$	6.02901e22	−	2.14712e24i	0.0457872	−	1.63063i
$689$	−1.24474e24			−0.933720
$690$		0			0
$691$		−	3.75773e23i		−	0.275019i	−0.990500	−	0.137509i	$-0.956090\pi$
$691$		−	3.75773e23i		−	0.275019i	0.990500	−	0.137509i	$-0.0439097\pi$
$692$	1.48431e24	+	2.08352e22i	1.07306	+	0.0150625i
$693$		0			0
$694$	7.76098e23	+	7.87068e23i	0.547471	+	0.555210i
$695$	−9.20749e23			−0.641609
$696$		0			0
$697$	1.03952e24			0.706895
$698$	−2.15744e23	−	2.18794e23i	−0.144933	−	0.146982i
$699$		0			0
$700$	1.41233e22	−	1.00615e24i	0.00925985	−	0.659676i
$701$			1.69069e24i			1.09512i	0.836767	+	0.547559i	$0.184443\pi$
$701$			1.69069e24i			1.09512i	−0.836767	+	0.547559i	$0.815557\pi$
$702$		0			0
$703$	−2.73038e24			−1.72624
$704$	−5.50732e23	−	2.32040e22i	−0.344011	−	0.0144942i
$705$		0			0
$706$	1.29990e24	−	1.28179e24i	0.792632	−	0.781584i
$707$			4.35585e23i			0.262427i
$708$		0			0
$709$			1.96311e24i			1.15466i	0.816512	+	0.577328i	$0.195905\pi$
$709$			1.96311e24i			1.15466i	−0.816512	+	0.577328i	$0.804095\pi$
$710$	1.46757e23	+	1.48832e23i	0.0852911	+	0.0864968i
$711$		0			0
$712$	−1.36448e24	−	1.42318e24i	−0.774263	−	0.807571i
$713$	1.35106e24			0.757555
$714$		0			0
$715$			3.41995e23i			0.187248i
$716$	−1.15391e24	−	1.61973e22i	−0.624323	−	0.00876361i
$717$		0			0
$718$	−2.48429e24	+	2.44966e24i	−1.31264	+	1.29434i
$719$	7.24919e23			0.378525			0.189262	−	0.981927i	$-0.439390\pi$
$719$	7.24919e23			0.378525			0.189262	+	0.981927i	$0.439390\pi$
$720$		0			0
$721$	2.21566e24			1.12993
$722$	−1.54166e23	+	1.52017e23i	−0.0777001	+	0.0766171i
$723$		0			0
$724$	−8.71536e23	−	1.22337e22i	−0.429049	−	0.00602256i
$725$			1.35827e23i			0.0660864i
$726$		0			0
$727$	−3.57325e24			−1.69832			−0.849162	−	0.528132i	$-0.822893\pi$
$727$	−3.57325e24			−1.69832			−0.849162	+	0.528132i	$0.822893\pi$
$728$	1.43596e24	−	1.37673e24i	0.674568	−	0.646744i
$729$		0			0
$730$	1.62665e24	+	1.64965e24i	0.746537	+	0.757089i
$731$			3.53627e24i			1.60416i
$732$		0			0
$733$			3.87913e24i			1.71930i	0.510887	+	0.859648i	$0.329317\pi$
$733$			3.87913e24i			1.71930i	−0.510887	+	0.859648i	$0.670683\pi$
$734$	2.19647e24	−	2.16585e24i	0.962296	−	0.948883i
$735$		0			0
$736$	−1.66779e24	+	1.55467e24i	−0.713969	+	0.665542i
$737$	−6.03865e23			−0.255544
$738$		0			0
$739$		−	3.80051e24i		−	1.57168i	−0.618430	−	0.785840i	$-0.712231\pi$
$739$		−	3.80051e24i		−	1.57168i	0.618430	−	0.785840i	$-0.287769\pi$
$740$	3.38159e22	−	2.40906e24i	0.0138246	−	0.984867i
$741$		0			0
$742$	1.87218e24	+	1.89864e24i	0.748020	+	0.758594i
$743$	−9.34750e23			−0.369224			−0.184612	−	0.982811i	$-0.559103\pi$
$743$	−9.34750e23			−0.369224			−0.184612	+	0.982811i	$0.559103\pi$
$744$		0			0
$745$	1.17662e24			0.454264
$746$	−1.51862e24	−	1.54009e24i	−0.579655	−	0.587848i
$747$		0			0
$748$	9.07401e23	+	1.27372e22i	0.338560	+	0.00475236i
$749$			4.53092e24i			1.67144i
$750$		0			0
$751$	−1.14251e24			−0.412024			−0.206012	−	0.978549i	$-0.566049\pi$
$751$	−1.14251e24			−0.412024			−0.206012	+	0.978549i	$0.566049\pi$
$752$	1.75314e24	+	4.92274e22i	0.625124	+	0.0175532i
$753$		0			0
$754$	−1.91202e23	+	1.88537e23i	−0.0666557	+	0.0657266i
$755$		−	7.80981e23i		−	0.269210i
$756$		0			0
$757$			4.16361e24i			1.40331i	0.712515	+	0.701657i	$0.247556\pi$
$757$			4.16361e24i			1.40331i	−0.712515	+	0.701657i	$0.752444\pi$
$758$	−4.37807e23	−	4.43995e23i	−0.145913	−	0.147976i
$759$		0			0
$760$	−1.34388e24	−	1.40169e24i	−0.437969	−	0.456811i
$761$	2.67038e24			0.860606			0.430303	−	0.902685i	$-0.358407\pi$
$761$	2.67038e24			0.860606			0.430303	+	0.902685i	$0.358407\pi$
$762$		0			0
$763$		−	2.54943e24i		−	0.803496i
$764$	2.72957e22	−	1.94455e24i	0.00850746	−	0.606075i
$765$		0			0
$766$	1.32582e24	−	1.30734e24i	0.404149	−	0.398516i
$767$	−1.08728e23			−0.0327779
$768$		0			0
$769$	1.07347e24			0.316530			0.158265	−	0.987397i	$-0.449410\pi$
$769$	1.07347e24			0.316530			0.158265	+	0.987397i	$0.449410\pi$
$770$	5.21653e23	−	5.14382e23i	0.152129	−	0.150008i
$771$		0			0
$772$	4.76702e22	−	3.39605e24i	0.0135988	−	0.968783i
$773$			5.44288e24i			1.53569i	0.640637	+	0.767844i	$0.278670\pi$
$773$			5.44288e24i			1.53569i	−0.640637	+	0.767844i	$0.721330\pi$
$774$		0			0
$775$	1.79655e24			0.495879
$776$	−2.34386e23	−	2.44469e23i	−0.0639892	−	0.0667420i
$777$		0			0
$778$	4.35231e23	+	4.41384e23i	0.116250	+	0.117893i
$779$			2.86544e24i			0.757048i
$780$		0			0
$781$		−	2.69260e23i		−	0.0696046i
$782$	2.67281e24	−	2.63555e24i	0.683455	−	0.673929i
$783$		0			0
$784$	−2.64751e23	−	7.43408e21i	−0.0662447	−	0.00186012i
$785$	−2.81501e24			−0.696768
$786$		0			0
$787$			7.33278e24i			1.77617i	0.459683	+	0.888083i	$0.347963\pi$
$787$			7.33278e24i			1.77617i	−0.459683	+	0.888083i	$0.652037\pi$
$788$	−7.20064e24	−	1.01075e23i	−1.72543	−	0.0242199i
$789$		0			0
$790$	−3.33480e24	−	3.38194e24i	−0.782059	−	0.793114i
$791$	−4.74480e24			−1.10082
$792$		0			0
$793$	6.81004e24			1.54642
$794$	1.42853e24	+	1.44872e24i	0.320933	+	0.325469i
$795$		0			0
$796$	1.39575e22	−	9.94337e23i	0.00306935	−	0.218662i
$797$		−	5.04426e24i		−	1.09749i	−0.835989	−	0.548746i	$-0.815105\pi$
$797$		−	5.04426e24i		−	1.09749i	0.835989	−	0.548746i	$-0.184895\pi$
$798$		0			0
$799$	−2.88739e24			−0.614976
$800$	−2.21772e24	+	2.06729e24i	−0.467349	+	0.435650i
$801$		0			0
$802$	2.59341e24	−	2.55726e24i	0.535043	−	0.527585i
$803$		−	2.98447e24i		−	0.609236i
$804$		0			0
$805$		−	3.03029e24i		−	0.605647i
$806$	2.49375e24	+	2.52900e24i	0.493179	+	0.500150i
$807$		0			0
$808$	9.47349e23	−	9.08275e23i	0.183448	−	0.175882i
$809$	6.54648e24			1.25443			0.627214	−	0.778847i	$-0.284195\pi$
$809$	6.54648e24			1.25443			0.627214	+	0.778847i	$0.284195\pi$
$810$		0			0
$811$			1.96650e24i			0.368992i	0.982833	+	0.184496i	$0.0590652\pi$
$811$			1.96650e24i			0.368992i	−0.982833	+	0.184496i	$0.940935\pi$
$812$	5.75162e23	+	8.07353e21i	0.106798	+	0.00149912i
$813$		0			0
$814$	−2.20998e24	+	2.17918e24i	−0.401866	+	0.396265i
$815$	−1.55306e24			−0.279479
$816$		0			0
$817$	−9.74773e24			−1.71797
$818$	2.36464e24	−	2.33168e24i	0.412442	−	0.406693i
$819$		0			0
$820$	−2.52823e24	−	3.54887e22i	−0.431916	−	0.00606279i
$821$			3.48398e24i			0.589059i	0.955642	+	0.294529i	$0.0951629\pi$
$821$			3.48398e24i			0.589059i	−0.955642	+	0.294529i	$0.904837\pi$
$822$		0			0
$823$	−7.93327e23			−0.131387			−0.0656937	−	0.997840i	$-0.520926\pi$
$823$	−7.93327e23			−0.131387			−0.0656937	+	0.997840i	$0.520926\pi$
$824$	−4.62005e24	−	4.81880e24i	−0.757295	−	0.789874i
$825$		0			0
$826$	1.63534e23	+	1.65846e23i	0.0262590	+	0.0266301i
$827$		−	8.23961e24i		−	1.30951i	−0.755840	−	0.654756i	$-0.772771\pi$
$827$		−	8.23961e24i		−	1.30951i	0.755840	−	0.654756i	$-0.227229\pi$
$828$		0			0
$829$		−	2.42199e24i		−	0.377102i	−0.982063	−	0.188551i	$-0.939621\pi$
$829$		−	2.42199e24i		−	0.377102i	0.982063	−	0.188551i	$-0.0603791\pi$
$830$	−4.99113e24	+	4.92156e24i	−0.769193	+	0.758471i
$831$		0			0
$832$	−5.98847e24	−	2.52313e23i	−0.904207	−	0.0380970i
$833$	4.36039e23			0.0651693
$834$		0			0
$835$		−	5.99570e23i		−	0.0878021i
$836$	−3.51100e22	+	2.50125e24i	−0.00508953	+	0.362580i
$837$		0			0
$838$	4.92609e24	+	4.99572e24i	0.699726	+	0.709617i
$839$	3.72199e24			0.523358			0.261679	−	0.965155i	$-0.415724\pi$
$839$	3.72199e24			0.523358			0.261679	+	0.965155i	$0.415724\pi$
$840$		0			0
$841$	7.17950e24			0.989301
$842$	8.96216e24	+	9.08885e24i	1.22253	+	1.23981i
$843$		0			0
$844$	−3.54722e24	−	4.97923e22i	−0.474217	−	0.00665658i
$845$		−	8.21617e23i		−	0.108740i
$846$		0			0
$847$	7.01679e24			0.910185
$848$	2.25500e23	−	8.03078e24i	0.0289589	−	1.03132i
$849$		0			0
$850$	3.55413e24	−	3.50459e24i	0.447375	−	0.441140i
$851$			1.28378e25i			1.59989i
$852$		0			0
$853$		−	5.25914e24i		−	0.642463i	−0.947001	−	0.321231i	$-0.895903\pi$
$853$		−	5.25914e24i		−	0.642463i	0.947001	−	0.321231i	$-0.104097\pi$
$854$	−1.02427e25	−	1.03875e25i	−1.23887	−	1.25638i
$855$		0			0
$856$	9.85423e24	−	9.44779e24i	1.16841	−	1.12022i
$857$	−1.85443e23			−0.0217708			−0.0108854	−	0.999941i	$-0.503465\pi$
$857$	−1.85443e23			−0.0217708			−0.0108854	+	0.999941i	$0.503465\pi$
$858$		0			0
$859$		−	1.65533e25i		−	1.90521i	−0.304213	−	0.952604i	$-0.598393\pi$
$859$		−	1.65533e25i		−	1.90521i	0.304213	−	0.952604i	$-0.401607\pi$
$860$	1.20726e23	−	8.60059e24i	0.0137583	−	0.980148i
$861$		0			0
$862$	2.79792e24	−	2.75892e24i	0.312625	−	0.308267i
$863$	−9.72354e24			−1.07580			−0.537901	−	0.843008i	$-0.680783\pi$
$863$	−9.72354e24			−1.07580			−0.537901	+	0.843008i	$0.680783\pi$
$864$		0			0
$865$	5.94442e24			0.644871
$866$	8.80189e24	−	8.67920e24i	0.945527	−	0.932347i
$867$		0			0
$868$	1.06787e23	−	7.60755e24i	0.0112487	−	0.801359i
$869$			6.11846e24i			0.638225i
$870$		0			0
$871$	−6.56623e24			−0.671679
$872$	−5.54471e24	+	5.31602e24i	−0.561680	+	0.538513i
$873$		0			0
$874$	7.26491e24	+	7.36760e24i	0.721744	+	0.731946i
$875$		−	1.03363e25i		−	1.01694i
$876$		0			0
$877$			3.35429e24i			0.323671i	0.986818	+	0.161836i	$0.0517415\pi$
$877$			3.35429e24i			0.323671i	−0.986818	+	0.161836i	$0.948259\pi$
$878$	−2.72056e24	+	2.68264e24i	−0.259989	+	0.256365i
$879$		0			0
$880$	−2.20646e24	−	6.19564e22i	−0.206821	−	0.00580742i
$881$	−4.42293e24			−0.410597			−0.205298	−	0.978699i	$-0.565816\pi$
$881$	−4.42293e24			−0.410597			−0.205298	+	0.978699i	$0.565816\pi$
$882$		0			0
$883$		−	5.46478e24i		−	0.497630i	−0.968551	−	0.248815i	$-0.919959\pi$
$883$		−	5.46478e24i		−	0.497630i	0.968551	−	0.248815i	$-0.0800412\pi$
$884$	9.86677e24	+	1.38500e23i	0.889879	+	0.0124912i
$885$		0			0
$886$	5.77328e24	+	5.85488e24i	0.510782	+	0.518002i
$887$	2.15636e25			1.88960			0.944800	−	0.327646i	$-0.106255\pi$
$887$	2.15636e25			1.88960			0.944800	+	0.327646i	$0.106255\pi$
$888$		0			0
$889$	−4.89097e24			−0.420465
$890$	−5.54346e24	−	5.62182e24i	−0.472026	−	0.478698i
$891$		0			0
$892$	−1.28605e22	+	9.16185e23i	−0.00107437	+	0.0765388i
$893$		−	7.95910e24i		−	0.658608i
$894$		0			0
$895$	−4.62121e24			−0.375198
$896$	8.62219e24	+	9.51386e24i	0.693425	+	0.765136i
$897$		0			0
$898$	−6.78570e24	+	6.69112e24i	−0.535483	+	0.528020i
$899$			1.02699e24i			0.0802803i
$900$		0			0
$901$			1.32265e25i			1.01458i
$902$	2.28698e24	+	2.31931e24i	0.173783	+	0.176240i
$903$		0			0
$904$	9.89377e24	+	1.03194e25i	0.737786	+	0.769526i
$905$	−3.49036e24			−0.257844
$906$		0			0
$907$			2.01078e24i			0.145781i	0.997340	+	0.0728906i	$0.0232224\pi$
$907$			2.01078e24i			0.145781i	−0.997340	+	0.0728906i	$0.976778\pi$
$908$	2.34278e25	+	3.28855e23i	1.68268	+	0.0236197i
$909$		0			0
$910$	5.67228e24	−	5.59322e24i	0.399858	−	0.394285i
$911$	7.02829e24			0.490844			0.245422	−	0.969416i	$-0.421074\pi$
$911$	7.02829e24			0.490844			0.245422	+	0.969416i	$0.421074\pi$
$912$		0			0
$913$	9.02974e24			0.618976
$914$	−1.89866e24	+	1.87219e24i	−0.128945	+	0.127147i
$915$		0			0
$916$	3.25691e24	+	4.57171e22i	0.217117	+	0.00304767i
$917$		−	1.94247e25i		−	1.28297i
$918$		0			0
$919$	3.84448e24			0.249262			0.124631	−	0.992203i	$-0.460225\pi$
$919$	3.84448e24			0.249262			0.124631	+	0.992203i	$0.460225\pi$
$920$	−6.59054e24	+	6.31871e24i	−0.423374	+	0.405912i
$921$		0			0
$922$	−7.73675e24	−	7.84611e24i	−0.487916	−	0.494813i
$923$		−	2.92784e24i		−	0.182950i
$924$		0			0
$925$			1.70709e25i			1.04725i
$926$	−1.70556e25	+	1.68179e25i	−1.03675	+	1.02230i
$927$		0			0
$928$	−1.18176e24	−	1.26775e24i	−0.0705294	−	0.0756614i
$929$	−9.60876e23			−0.0568243			−0.0284121	−	0.999596i	$-0.509045\pi$
$929$	−9.60876e23			−0.0568243			−0.0284121	+	0.999596i	$0.509045\pi$
$930$		0			0
$931$			1.20194e24i			0.0697930i
$932$	−2.17207e23	+	1.54739e25i	−0.0124979	+	0.890358i
$933$		0			0
$934$	−1.70260e24	−	1.72667e24i	−0.0961977	−	0.0975575i
$935$	3.63400e24			0.203463
$936$		0			0
$937$	4.30409e24			0.236644			0.118322	−	0.992975i	$-0.462249\pi$
$937$	4.30409e24			0.236644			0.118322	+	0.992975i	$0.462249\pi$
$938$	9.87603e24	+	1.00156e25i	0.538094	+	0.545700i
$939$		0			0
$940$	7.02246e24	+	9.85740e22i	0.375753	+	0.00527443i
$941$		−	3.71907e24i		−	0.197207i	−0.995127	−	0.0986036i	$-0.968562\pi$
$941$		−	3.71907e24i		−	0.197207i	0.995127	−	0.0986036i	$-0.0314376\pi$
$942$		0			0
$943$	1.34729e25			0.701636
$944$	1.96974e22	−	7.01486e23i	0.00101659	−	0.0362040i
$945$		0			0
$946$	−7.88988e24	+	7.77991e24i	−0.399941	+	0.394366i
$947$		−	8.59929e24i		−	0.432004i	−0.976393	−	0.216002i	$-0.930698\pi$
$947$		−	8.59929e24i		−	0.432004i	0.976393	−	0.216002i	$-0.0693018\pi$
$948$		0			0
$949$		−	3.24521e25i		−	1.60133i
$950$	9.66041e24	+	9.79696e24i	0.472438	+	0.479116i
$951$		0			0
$952$	−1.46290e25	−	1.52583e25i	−0.702750	−	0.732982i
$953$	2.86348e25			1.36334			0.681671	−	0.731659i	$-0.261253\pi$
$953$	2.86348e25			1.36334			0.681671	+	0.731659i	$0.261253\pi$
$954$		0			0
$955$		−	7.78764e24i		−	0.364231i
$956$	−2.26808e23	+	1.61579e25i	−0.0105140	+	0.749018i
$957$		0			0
$958$	−1.79055e23	+	1.76559e23i	−0.00815415	+	0.00804049i
$959$	−2.78805e25			−1.25847
$960$		0			0
$961$	−8.96632e24			−0.397617
$962$	−2.40306e25	+	2.36957e25i	−1.05627	+	1.04155i
$963$		0			0
$964$	−4.92691e23	+	3.50995e25i	−0.0212775	+	1.51582i
$965$		−	1.36006e25i		−	0.582206i
$966$		0			0
$967$	−2.59564e25			−1.09174			−0.545870	−	0.837870i	$-0.683801\pi$
$967$	−2.59564e25			−1.09174			−0.545870	+	0.837870i	$0.683801\pi$
$968$	−1.46313e25	−	1.52607e25i	−0.610017	−	0.636260i
$969$		0			0
$970$	−9.52234e23	−	9.65694e23i	−0.0390107	−	0.0395622i
$971$		−	3.57955e25i		−	1.45367i	−0.686814	−	0.726833i	$-0.740991\pi$
$971$		−	3.57955e25i		−	1.45367i	0.686814	−	0.726833i	$-0.259009\pi$
$972$		0			0
$973$		−	2.76284e25i		−	1.10254i
$974$	2.49841e25	−	2.46359e25i	0.988355	−	0.974579i
$975$		0			0
$976$	−1.23372e24	+	4.39367e25i	−0.0479615	+	1.70806i
$977$	−2.92622e25			−1.12773			−0.563863	−	0.825869i	$-0.690685\pi$
$977$	−2.92622e25			−1.12773			−0.563863	+	0.825869i	$0.690685\pi$
$978$		0			0
$979$			1.01707e25i			0.385212i
$980$	−1.06050e24	−	1.48862e22i	−0.0398187	−	0.000558935i
$981$		0			0
$982$	−3.54658e25	−	3.59671e25i	−1.30877	−	1.32727i
$983$	−8.30763e24			−0.303929			−0.151964	−	0.988386i	$-0.548560\pi$
$983$	−8.30763e24			−0.303929			−0.151964	+	0.988386i	$0.548560\pi$
$984$		0			0
$985$	−2.88374e25			−1.03693
$986$	2.00338e24	+	2.03170e24i	0.0714182	+	0.0724277i
$987$		0			0
$988$	−3.81775e23	+	2.71978e25i	−0.0133774	+	0.953015i
$989$			4.58324e25i			1.59222i
$990$		0			0
$991$	3.41708e25			1.16689			0.583443	−	0.812154i	$-0.301705\pi$
$991$	3.41708e25			1.16689			0.583443	+	0.812154i	$0.301705\pi$
$992$	−1.67682e25	+	1.56309e25i	−0.567725	+	0.529217i
$993$		0			0
$994$	−4.46591e24	+	4.40366e24i	−0.148637	+	0.146565i
$995$		−	3.98217e24i		−	0.131408i
$996$		0			0
$997$			9.48702e24i			0.307766i	0.988089	+	0.153883i	$0.0491779\pi$
$997$			9.48702e24i			0.307766i	−0.988089	+	0.153883i	$0.950822\pi$
$998$	−2.07981e24	−	2.10921e24i	−0.0668981	−	0.0678437i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.18.d.b.37.13		16
3.2	odd	2		8.18.b.a.5.4	yes	16
8.5	even	2	inner	72.18.d.b.37.14		16
12.11	even	2		32.18.b.a.17.6		16
24.5	odd	2		8.18.b.a.5.3	✓	16
24.11	even	2		32.18.b.a.17.11		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.18.b.a.5.3	✓	16	24.5	odd	2
8.18.b.a.5.4	yes	16	3.2	odd	2
32.18.b.a.17.6		16	12.11	even	2
32.18.b.a.17.11		16	24.11	even	2
72.18.d.b.37.13		16	1.1	even	1	trivial
72.18.d.b.37.14		16	8.5	even	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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	72.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(257.790 - 254.197i) q^{2} +(1839.67 - 131059. i) q^{4} -524871. i q^{5} +1.57495e7 q^{7} +(-3.28406e7 - 3.42534e7i) q^{8} +O(q^{10})\)	\(q+(257.790 - 254.197i) q^{2} +(1839.67 - 131059. i) q^{4} -524871. i q^{5} +1.57495e7 q^{7} +(-3.28406e7 - 3.42534e7i) q^{8} +(-1.33421e8 - 1.35307e8i) q^{10} +2.44791e8i q^{11} +2.66178e9i q^{13} +(4.06007e9 - 4.00348e9i) q^{14} +(-1.71731e10 - 4.82212e8i) q^{16} +2.82837e10 q^{17} +7.79642e10i q^{19} +(-6.87892e10 - 9.65592e8i) q^{20} +(6.22252e10 + 6.31047e10i) q^{22} +3.66576e11 q^{23} +4.87450e11 q^{25} +(6.76615e11 + 6.86180e11i) q^{26} +(2.89740e10 - 2.06412e12i) q^{28} +2.78648e11i q^{29} +3.68562e12 q^{31} +(-4.54964e12 + 4.24104e12i) q^{32} +(7.29127e12 - 7.18964e12i) q^{34} -8.26647e12i q^{35} +3.50209e13i q^{37} +(1.98183e13 + 2.00984e13i) q^{38} +(-1.79786e13 + 1.72371e13i) q^{40} +3.67533e13 q^{41} +1.25028e14i q^{43} +(3.20821e13 + 4.50335e11i) q^{44} +(9.44998e13 - 9.31826e13i) q^{46} -1.02087e14 q^{47} +1.54166e13 q^{49} +(1.25660e14 - 1.23908e14i) q^{50} +(3.48850e14 + 4.89680e12i) q^{52} +4.67637e14i q^{53} +1.28484e14 q^{55} +(-5.17223e14 - 5.39474e14i) q^{56} +(7.08315e13 + 7.18327e13i) q^{58} +4.08479e13i q^{59} -2.55846e15i q^{61} +(9.50117e14 - 9.36874e14i) q^{62} +(-9.47911e13 + 2.24980e15i) q^{64} +1.39709e15 q^{65} +2.46686e15i q^{67} +(5.20328e13 - 3.70684e15i) q^{68} +(-2.10131e15 - 2.13101e15i) q^{70} -1.09996e15 q^{71} -1.21919e16 q^{73} +(8.90221e15 + 9.02805e15i) q^{74} +(1.02179e16 + 1.43429e14i) q^{76} +3.85534e15i q^{77} +2.49946e16 q^{79} +(-2.53099e14 + 9.01367e15i) q^{80} +(9.47466e15 - 9.34259e15i) q^{82} -3.68875e16i q^{83} -1.48453e16i q^{85} +(3.17818e16 + 3.22311e16i) q^{86} +(8.38492e15 - 8.03908e15i) q^{88} +4.15487e16 q^{89} +4.19217e16i q^{91} +(6.74381e14 - 4.80432e16i) q^{92} +(-2.63170e16 + 2.59501e16i) q^{94} +4.09212e16 q^{95} +7.13708e15 q^{97} +(3.97426e15 - 3.91886e15i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 270 q^{2} - 27436 q^{4} + 11529600 q^{7} - 24334920 q^{8}+O(q^{10}) \) 16 * q - 270 * q^2 - 27436 * q^4 + 11529600 * q^7 - 24334920 * q^8	\( 16 q - 270 q^{2} - 27436 q^{4} + 11529600 q^{7} - 24334920 q^{8} + 131002712 q^{10} - 16363788528 q^{14} + 26500434192 q^{16} + 7489125600 q^{17} + 209445719856 q^{20} + 223126527100 q^{22} - 746845345920 q^{23} - 1809682431664 q^{25} - 2467726531080 q^{26} + 3220542267040 q^{28} - 318979758592 q^{31} - 1455647316000 q^{32} - 4461251980292 q^{34} - 24076283913900 q^{38} + 60626292962592 q^{40} - 7482251536032 q^{41} - 193654716236040 q^{44} - 195097141003568 q^{46} + 376698804821760 q^{47} + 127691292101520 q^{49} - 474997408872102 q^{50} - 272251877663120 q^{52} + 22\!\cdots\!52 q^{55}+ \cdots - 33\!\cdots\!90 q^{98}+O(q^{100}) \) 16 * q - 270 * q^2 - 27436 * q^4 + 11529600 * q^7 - 24334920 * q^8 + 131002712 * q^10 - 16363788528 * q^14 + 26500434192 * q^16 + 7489125600 * q^17 + 209445719856 * q^20 + 223126527100 * q^22 - 746845345920 * q^23 - 1809682431664 * q^25 - 2467726531080 * q^26 + 3220542267040 * q^28 - 318979758592 * q^31 - 1455647316000 * q^32 - 4461251980292 * q^34 - 24076283913900 * q^38 + 60626292962592 * q^40 - 7482251536032 * q^41 - 193654716236040 * q^44 - 195097141003568 * q^46 + 376698804821760 * q^47 + 127691292101520 * q^49 - 474997408872102 * q^50 - 272251877663120 * q^52 + 2209036687713152 * q^55 + 162767516076480 * q^56 - 623262610679960 * q^58 - 695695648144320 * q^62 + 1111931745501248 * q^64 - 2385987975356160 * q^65 - 5981109959771880 * q^68 - 10044559836180288 * q^70 - 9025926285576576 * q^71 + 11332002046118560 * q^73 - 11098735408189464 * q^74 + 5959440926938280 * q^76 - 45299671392008448 * q^79 - 1337342539452480 * q^80 + 15639739637081420 * q^82 + 14252032276026564 * q^86 - 66964872768837680 * q^88 + 69879174608766048 * q^89 - 57336249810701280 * q^92 - 192318922166254176 * q^94 - 93790444358203776 * q^95 + 95593398602180640 * q^97 - 339641261743253790 * q^98

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