LMFDB - Embedded newform 72.18.d.b.37.3

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			37.3
Root			$0.500000 + 82996.3i$ of defining polynomial
Character	$\chi$	$=$	72.37
Dual form			72.18.d.b.37.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-328.641 - 151.878i) q^{2} +(84938.1 + 99826.8i) q^{4} -663971. i q^{5} -1.66742e7 q^{7} +(-1.27527e7 - 4.57074e7i) q^{8} +O(q^{10})$	\(q+(-328.641 - 151.878i) q^{2} +(84938.1 + 99826.8i) q^{4} -663971. i q^{5} -1.66742e7 q^{7} +(-1.27527e7 - 4.57074e7i) q^{8} +(-1.00843e8 + 2.18208e8i) q^{10} -1.05479e9i q^{11} -9.19407e7i q^{13} +(5.47982e9 + 2.53244e9i) q^{14} +(-2.75091e9 + 1.69582e10i) q^{16} +1.98326e10 q^{17} +8.44846e10i q^{19} +(6.62821e10 - 5.63964e10i) q^{20} +(-1.60199e11 + 3.46647e11i) q^{22} +2.72263e10 q^{23} +3.22082e11 q^{25} +(-1.39638e10 + 3.02155e10i) q^{26} +(-1.41627e12 - 1.66453e12i) q^{28} +3.75013e12i q^{29} +5.36921e12 q^{31} +(3.47964e12 - 5.15536e12i) q^{32} +(-6.51781e12 - 3.01214e12i) q^{34} +1.10712e13i q^{35} -1.92294e13i q^{37} +(1.28314e13 - 2.77651e13i) q^{38} +(-3.03484e13 + 8.46739e12i) q^{40} -5.42400e13 q^{41} -3.96416e13i q^{43} +(1.05296e14 - 8.95918e13i) q^{44} +(-8.94769e12 - 4.13508e12i) q^{46} -4.48999e13 q^{47} +4.53979e13 q^{49} +(-1.05850e14 - 4.89172e13i) q^{50} +(9.17815e12 - 7.80927e12i) q^{52} +7.81803e14i q^{53} -7.00349e14 q^{55} +(2.12640e14 + 7.62134e14i) q^{56} +(5.69562e14 - 1.23245e15i) q^{58} -1.07092e15i q^{59} +1.92548e15i q^{61} +(-1.76454e15 - 8.15466e14i) q^{62} +(-1.92654e15 + 1.16578e15i) q^{64} -6.10460e13 q^{65} +3.68678e15i q^{67} +(1.68454e15 + 1.97982e15i) q^{68} +(1.68147e15 - 3.63844e15i) q^{70} +1.02421e16 q^{71} +1.25847e16 q^{73} +(-2.92052e15 + 6.31956e15i) q^{74} +(-8.43383e15 + 7.17596e15i) q^{76} +1.75877e16i q^{77} +3.24102e15 q^{79} +(1.12597e16 + 1.82652e15i) q^{80} +(1.78255e16 + 8.23787e15i) q^{82} +4.28316e15i q^{83} -1.31683e16i q^{85} +(-6.02070e15 + 1.30279e16i) q^{86} +(-4.82117e16 + 1.34514e16i) q^{88} -6.95255e16 q^{89} +1.53304e15i q^{91} +(2.31255e15 + 2.71792e15i) q^{92} +(1.47560e16 + 6.81931e15i) q^{94} +5.60953e16 q^{95} -7.74223e16 q^{97} +(-1.49196e16 - 6.89495e15i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−328.641	−	151.878i	−0.907752	−	0.419508i
$2$	−328.641	−	151.878i	−0.907752	−	0.419508i
$3$		0			0
$3$		0			0
$4$	84938.1	+	99826.8i	0.648026	+	0.761618i
$5$		−	663971.i		−	0.760158i	−0.924954	−	0.380079i	$-0.875897\pi$
$5$		−	663971.i		−	0.760158i	0.924954	−	0.380079i	$-0.124103\pi$
$6$		0			0
$7$	−1.66742e7			−1.09323			−0.546615	−	0.837384i	$-0.684084\pi$
$7$	−1.66742e7			−1.09323			−0.546615	+	0.837384i	$0.684084\pi$
$8$	−1.27527e7	−	4.57074e7i	−0.268742	−	0.963212i
$9$		0			0
$10$	−1.00843e8	+	2.18208e8i	−0.318892	+	0.690035i
$11$		−	1.05479e9i		−	1.48364i	−0.670600	−	0.741819i	$-0.733963\pi$
$11$		−	1.05479e9i		−	1.48364i	0.670600	−	0.741819i	$-0.266037\pi$
$12$		0			0
$13$		−	9.19407e7i		−	0.0312600i	−0.999878	−	0.0156300i	$-0.995025\pi$
$13$		−	9.19407e7i		−	0.0312600i	0.999878	−	0.0156300i	$-0.00497539\pi$
$14$	5.47982e9	+	2.53244e9i	0.992381	+	0.458618i
$15$		0			0
$16$	−2.75091e9	+	1.69582e10i	−0.160124	+	0.987097i
$17$	1.98326e10			0.689547			0.344773	−	0.938686i	$-0.387956\pi$
$17$	1.98326e10			0.689547			0.344773	+	0.938686i	$0.387956\pi$
$18$		0			0
$19$			8.44846e10i			1.14123i	0.821219	+	0.570613i	$0.193294\pi$
$19$			8.44846e10i			1.14123i	−0.821219	+	0.570613i	$0.806706\pi$
$20$	6.62821e10	−	5.63964e10i	0.578950	−	0.492602i
$21$		0			0
$22$	−1.60199e11	+	3.46647e11i	−0.622398	+	1.34677i
$23$	2.72263e10			0.0724941			0.0362470	−	0.999343i	$-0.488460\pi$
$23$	2.72263e10			0.0724941			0.0362470	+	0.999343i	$0.488460\pi$
$24$		0			0
$25$	3.22082e11			0.422160
$26$	−1.39638e10	+	3.02155e10i	−0.0131138	+	0.0283764i
$27$		0			0
$28$	−1.41627e12	−	1.66453e12i	−0.708441	−	0.832623i
$29$			3.75013e12i			1.39208i	0.718005	+	0.696038i	$0.245056\pi$
$29$			3.75013e12i			1.39208i	−0.718005	+	0.696038i	$0.754944\pi$
$30$		0			0
$31$	5.36921e12			1.13067			0.565336	−	0.824861i	$-0.308747\pi$
$31$	5.36921e12			1.13067			0.565336	+	0.824861i	$0.308747\pi$
$32$	3.47964e12	−	5.15536e12i	0.559448	−	0.828866i
$33$		0			0
$34$	−6.51781e12	−	3.01214e12i	−0.625937	−	0.289270i
$35$			1.10712e13i			0.831027i
$36$		0			0
$37$		−	1.92294e13i		−	0.900015i	−0.893025	−	0.450008i	$-0.851421\pi$
$37$		−	1.92294e13i		−	0.900015i	0.893025	−	0.450008i	$-0.148579\pi$
$38$	1.28314e13	−	2.77651e13i	0.478754	−	1.03595i
$39$		0			0
$40$	−3.03484e13	+	8.46739e12i	−0.732194	+	0.204287i
$41$	−5.42400e13			−1.06086			−0.530429	−	0.847730i	$-0.677969\pi$
$41$	−5.42400e13			−1.06086			−0.530429	+	0.847730i	$0.677969\pi$
$42$		0			0
$43$		−	3.96416e13i		−	0.517213i	−0.965983	−	0.258607i	$-0.916737\pi$
$43$		−	3.96416e13i		−	0.517213i	0.965983	−	0.258607i	$-0.0832634\pi$
$44$	1.05296e14	−	8.95918e13i	1.12996	−	0.961436i
$45$		0			0
$46$	−8.94769e12	−	4.13508e12i	−0.0658066	−	0.0304118i
$47$	−4.48999e13			−0.275051			−0.137526	−	0.990498i	$-0.543915\pi$
$47$	−4.48999e13			−0.275051			−0.137526	+	0.990498i	$0.543915\pi$
$48$		0			0
$49$	4.53979e13			0.195150
$50$	−1.05850e14	−	4.89172e13i	−0.383216	−	0.177099i
$51$		0			0
$52$	9.17815e12	−	7.80927e12i	0.0238082	−	0.0202573i
$53$			7.81803e14i			1.72485i	0.506181	+	0.862427i	$0.331057\pi$
$53$			7.81803e14i			1.72485i	−0.506181	+	0.862427i	$0.668943\pi$
$54$		0			0
$55$	−7.00349e14			−1.12780
$56$	2.12640e14	+	7.62134e14i	0.293797	+	1.05301i
$57$		0			0
$58$	5.69562e14	−	1.23245e15i	0.583987	−	1.26366i
$59$		−	1.07092e15i		−	0.949541i	−0.880110	−	0.474770i	$-0.842531\pi$
$59$		−	1.07092e15i		−	0.949541i	0.880110	−	0.474770i	$-0.157469\pi$
$60$		0			0
$61$			1.92548e15i			1.28599i	0.765872	+	0.642993i	$0.222308\pi$
$61$			1.92548e15i			1.28599i	−0.765872	+	0.642993i	$0.777692\pi$
$62$	−1.76454e15	−	8.15466e14i	−1.02637	−	0.474325i
$63$		0			0
$64$	−1.92654e15	+	1.16578e15i	−0.855555	+	0.517711i
$65$	−6.10460e13			−0.0237626
$66$		0			0
$67$			3.68678e15i			1.10920i	0.832116	+	0.554602i	$0.187129\pi$
$67$			3.68678e15i			1.10920i	−0.832116	+	0.554602i	$0.812871\pi$
$68$	1.68454e15	+	1.97982e15i	0.446845	+	0.525171i
$69$		0			0
$70$	1.68147e15	−	3.63844e15i	0.348622	−	0.754366i
$71$	1.02421e16			1.88232			0.941162	−	0.337957i	$-0.109736\pi$
$71$	1.02421e16			1.88232			0.941162	+	0.337957i	$0.109736\pi$
$72$		0			0
$73$	1.25847e16			1.82641			0.913204	−	0.407502i	$-0.133600\pi$
$73$	1.25847e16			1.82641			0.913204	+	0.407502i	$0.133600\pi$
$74$	−2.92052e15	+	6.31956e15i	−0.377564	+	0.816991i
$75$		0			0
$76$	−8.43383e15	+	7.17596e15i	−0.869179	+	0.739545i
$77$			1.75877e16i			1.62196i
$78$		0			0
$79$	3.24102e15			0.240354			0.120177	−	0.992752i	$-0.461654\pi$
$79$	3.24102e15			0.240354			0.120177	+	0.992752i	$0.461654\pi$
$80$	1.12597e16	+	1.82652e15i	0.750350	+	0.121720i
$81$		0			0
$82$	1.78255e16	+	8.23787e15i	0.962995	+	0.445038i
$83$			4.28316e15i			0.208737i	0.994539	+	0.104369i	$0.0332822\pi$
$83$			4.28316e15i			0.208737i	−0.994539	+	0.104369i	$0.966718\pi$
$84$		0			0
$85$		−	1.31683e16i		−	0.524165i
$86$	−6.02070e15	+	1.30279e16i	−0.216975	+	0.469501i
$87$		0			0
$88$	−4.82117e16	+	1.34514e16i	−1.42906	+	0.398716i
$89$	−6.95255e16			−1.87210			−0.936050	−	0.351868i	$-0.885547\pi$
$89$	−6.95255e16			−1.87210			−0.936050	+	0.351868i	$0.885547\pi$
$90$		0			0
$91$			1.53304e15i			0.0341744i
$92$	2.31255e15	+	2.71792e15i	0.0469781	+	0.0552128i
$93$		0			0
$94$	1.47560e16	+	6.81931e15i	0.249678	+	0.115386i
$95$	5.60953e16			0.867513
$96$		0			0
$97$	−7.74223e16			−1.00301			−0.501507	−	0.865154i	$-0.667221\pi$
$97$	−7.74223e16			−1.00301			−0.501507	+	0.865154i	$0.667221\pi$
$98$	−1.49196e16	−	6.89495e15i	−0.177148	−	0.0818671i
$99$		0			0
$100$	2.73571e16	+	3.21524e16i	0.273571	+	0.321524i
$101$		−	8.38662e16i		−	0.770646i	−0.922782	−	0.385323i	$-0.874090\pi$
$101$		−	8.38662e16i		−	0.770646i	0.922782	−	0.385323i	$-0.125910\pi$
$102$		0			0
$103$	8.10218e16			0.630210			0.315105	−	0.949057i	$-0.397960\pi$
$103$	8.10218e16			0.630210			0.315105	+	0.949057i	$0.397960\pi$
$104$	−4.20238e15	+	1.17249e15i	−0.0301101	+	0.00840089i
$105$		0			0
$106$	1.18739e17	−	2.56933e17i	0.723590	−	1.56574i
$107$			1.60731e17i			0.904351i	0.891929	+	0.452175i	$0.149352\pi$
$107$			1.60731e17i			0.904351i	−0.891929	+	0.452175i	$0.850648\pi$
$108$		0			0
$109$			1.05482e17i			0.507053i	0.967328	+	0.253526i	$0.0815905\pi$
$109$			1.05482e17i			0.507053i	−0.967328	+	0.253526i	$0.918410\pi$
$110$	2.30164e17	+	1.06368e17i	1.02376	+	0.473121i
$111$		0			0
$112$	4.58692e16	−	2.82764e17i	0.175052	−	1.07912i
$113$	1.30124e17			0.460458			0.230229	−	0.973136i	$-0.426052\pi$
$113$	1.30124e17			0.460458			0.230229	+	0.973136i	$0.426052\pi$
$114$		0			0
$115$		−	1.80775e16i		−	0.0551069i
$116$	−3.74363e17	+	3.18529e17i	−1.06023	+	0.902102i
$117$		0			0
$118$	−1.62649e17	+	3.51947e17i	−0.398340	+	0.861947i
$119$	−3.30692e17			−0.753833
$120$		0			0
$121$	−6.07133e17			−1.20118
$122$	2.92439e17	−	6.32794e17i	0.539481	−	1.16736i
$123$		0			0
$124$	4.56051e17	+	5.35991e17i	0.732705	+	0.861139i
$125$		−	7.20423e17i		−	1.08107i
$126$		0			0
$127$	1.12618e18			1.47664			0.738322	−	0.674448i	$-0.235619\pi$
$127$	1.12618e18			1.47664			0.738322	+	0.674448i	$0.235619\pi$
$128$	8.10197e17	−	9.05251e16i	0.993816	−	0.111041i
$129$		0			0
$130$	2.00622e16	+	9.27154e15i	0.0215705	+	0.00996859i
$131$		−	3.73512e17i		−	0.376269i	−0.982143	−	0.188134i	$-0.939756\pi$
$131$		−	3.73512e17i		−	0.376269i	0.982143	−	0.188134i	$-0.0602440\pi$
$132$		0			0
$133$		−	1.40871e18i		−	1.24762i
$134$	5.59941e17	−	1.21163e18i	0.465320	−	1.00688i
$135$		0			0
$136$	−2.52918e17	−	9.06497e17i	−0.185310	−	0.664180i
$137$	3.64355e17			0.250842			0.125421	−	0.992104i	$-0.459972\pi$
$137$	3.64355e17			0.250842			0.125421	+	0.992104i	$0.459972\pi$
$138$		0			0
$139$		−	2.51151e18i		−	1.52866i	−0.644828	−	0.764328i	$-0.723071\pi$
$139$		−	2.51151e18i		−	1.52866i	0.644828	−	0.764328i	$-0.276929\pi$
$140$	−1.10520e18	+	9.40364e17i	−0.632925	+	0.538527i
$141$		0			0
$142$	−3.36598e18	−	1.55555e18i	−1.70868	−	0.789649i
$143$	−9.69781e16			−0.0463786
$144$		0			0
$145$	2.48998e18			1.05820
$146$	−4.13585e18	−	1.91134e18i	−1.65793	−	0.766193i
$147$		0			0
$148$	1.91960e18	−	1.63330e18i	0.685468	−	0.583234i
$149$		−	2.83942e18i		−	0.957517i	−0.877947	−	0.478758i	$-0.841087\pi$
$149$		−	2.83942e18i		−	0.957517i	0.877947	−	0.478758i	$-0.158913\pi$
$150$		0			0
$151$	−2.74195e18			−0.825574			−0.412787	−	0.910828i	$-0.635445\pi$
$151$	−2.74195e18			−0.825574			−0.412787	+	0.910828i	$0.635445\pi$
$152$	3.86157e18	−	1.07740e18i	1.09924	−	0.306696i
$153$		0			0
$154$	2.67119e18	−	5.78006e18i	0.680423	−	1.47233i
$155$		−	3.56500e18i		−	0.859489i
$156$		0			0
$157$		−	3.26134e18i		−	0.705096i	−0.935794	−	0.352548i	$-0.885315\pi$
$157$		−	3.26134e18i		−	0.705096i	0.935794	−	0.352548i	$-0.114685\pi$
$158$	−1.06513e18	−	4.92239e17i	−0.218182	−	0.100830i
$159$		0			0
$160$	−3.42301e18	−	2.31038e18i	−0.630069	−	0.425269i
$161$	−4.53977e17			−0.0792526
$162$		0			0
$163$			7.80461e18i			1.22675i	0.789791	+	0.613376i	$0.210189\pi$
$163$			7.80461e18i			1.22675i	−0.789791	+	0.613376i	$0.789811\pi$
$164$	−4.60704e18	−	5.41461e18i	−0.687463	−	0.807968i
$165$		0			0
$166$	6.50518e17	−	1.40762e18i	0.0875670	−	0.189482i
$167$	8.54007e18			1.09237			0.546187	−	0.837663i	$-0.316079\pi$
$167$	8.54007e18			1.09237			0.546187	+	0.837663i	$0.316079\pi$
$168$		0			0
$169$	8.64196e18			0.999023
$170$	−1.99997e18	+	4.32764e18i	−0.219891	+	0.475811i
$171$		0			0
$172$	3.95730e18	−	3.36709e18i	0.393919	−	0.335168i
$173$		−	2.07391e18i		−	0.196516i	−0.995161	−	0.0982581i	$-0.968673\pi$
$173$		−	2.07391e18i		−	0.196516i	0.995161	−	0.0982581i	$-0.0313271\pi$
$174$		0			0
$175$	−5.37046e18			−0.461517
$176$	1.78873e19	+	2.90163e18i	1.46449	+	0.237566i
$177$		0			0
$178$	2.28489e19	+	1.05594e19i	1.69940	+	0.785360i
$179$			1.67289e19i			1.18636i	0.805071	+	0.593179i	$0.202127\pi$
$179$			1.67289e19i			1.18636i	−0.805071	+	0.593179i	$0.797873\pi$
$180$		0			0
$181$		−	3.02297e19i		−	1.95059i	−0.220907	−	0.975295i	$-0.570902\pi$
$181$		−	3.02297e19i		−	1.95059i	0.220907	−	0.975295i	$-0.429098\pi$
$182$	2.32835e17	−	5.03819e17i	0.0143364	−	0.0310219i
$183$		0			0
$184$	−3.47208e17	−	1.24445e18i	−0.0194822	−	0.0698272i
$185$	−1.27677e19			−0.684154
$186$		0			0
$187$		−	2.09192e19i		−	1.02304i
$188$	−3.81371e18	−	4.48221e18i	−0.178240	−	0.209484i
$189$		0			0
$190$	−1.84352e19	−	8.51965e18i	−0.787486	−	0.363928i
$191$	−1.22397e18			−0.0500019			−0.0250009	−	0.999687i	$-0.507959\pi$
$191$	−1.22397e18			−0.0500019			−0.0250009	+	0.999687i	$0.507959\pi$
$192$		0			0
$193$	−6.70836e18			−0.250830			−0.125415	−	0.992104i	$-0.540026\pi$
$193$	−6.70836e18			−0.250830			−0.125415	+	0.992104i	$0.540026\pi$
$194$	2.54442e19	+	1.17588e19i	0.910487	+	0.420772i
$195$		0			0
$196$	3.85601e18	+	4.53193e18i	0.126463	+	0.148630i
$197$			1.35900e19i			0.426832i	0.976961	+	0.213416i	$0.0684590\pi$
$197$			1.35900e19i			0.426832i	−0.976961	+	0.213416i	$0.931541\pi$
$198$		0			0
$199$	2.94272e19			0.848198			0.424099	−	0.905616i	$-0.360591\pi$
$199$	2.94272e19			0.848198			0.424099	+	0.905616i	$0.360591\pi$
$200$	−4.10741e18	−	1.47216e19i	−0.113452	−	0.406629i
$201$		0			0
$202$	−1.27374e19	+	2.75619e19i	−0.323292	+	0.699556i
$203$		−	6.25303e19i		−	1.52186i
$204$		0			0
$205$			3.60138e19i			0.806419i
$206$	−2.66271e19	−	1.23054e19i	−0.572074	−	0.264378i
$207$		0			0
$208$	1.55915e18	+	2.52921e17i	0.0308567	+	0.00500548i
$209$	8.91134e19			1.69317
$210$		0			0
$211$		−	7.34029e19i		−	1.28621i	−0.765777	−	0.643106i	$-0.777645\pi$
$211$		−	7.34029e19i		−	1.28621i	0.765777	−	0.643106i	$-0.222355\pi$
$212$	−7.80449e19	+	6.64049e19i	−1.31368	+	1.11775i
$213$		0			0
$214$	2.44115e19	−	5.28228e19i	0.379382	−	0.820926i
$215$	−2.63209e19			−0.393164
$216$		0			0
$217$	−8.95273e19			−1.23608
$218$	1.60204e19	−	3.46657e19i	0.212713	−	0.460278i
$219$		0			0
$220$	−5.94863e19	−	6.99136e19i	−0.730843	−	0.858952i
$221$		−	1.82342e18i		−	0.0215553i
$222$		0			0
$223$	7.73683e19			0.847172			0.423586	−	0.905856i	$-0.360771\pi$
$223$	7.73683e19			0.847172			0.423586	+	0.905856i	$0.360771\pi$
$224$	−5.80202e19	+	8.59614e19i	−0.611605	+	0.906140i
$225$		0			0
$226$	−4.27641e19	−	1.97630e19i	−0.417982	−	0.193166i
$227$		−	1.21923e20i		−	1.14780i	−0.818924	−	0.573902i	$-0.805429\pi$
$227$		−	1.21923e20i		−	1.14780i	0.818924	−	0.573902i	$-0.194571\pi$
$228$		0			0
$229$			1.42038e19i			0.124109i	0.998073	+	0.0620543i	$0.0197652\pi$
$229$			1.42038e19i			0.124109i	−0.998073	+	0.0620543i	$0.980235\pi$
$230$	−2.74557e18	+	5.94101e18i	−0.0231178	+	0.0500234i
$231$		0			0
$232$	1.71409e20	−	4.78241e19i	1.34087	−	0.374110i
$233$	7.02873e19			0.530092			0.265046	−	0.964236i	$-0.414613\pi$
$233$	7.02873e19			0.530092			0.265046	+	0.964236i	$0.414613\pi$
$234$		0			0
$235$			2.98122e19i			0.209082i
$236$	1.06906e20	−	9.09616e19i	0.723187	−	0.615327i
$237$		0			0
$238$	1.08679e20	+	5.02249e19i	0.684293	+	0.316239i
$239$	−4.12244e19			−0.250480			−0.125240	−	0.992126i	$-0.539970\pi$
$239$	−4.12244e19			−0.250480			−0.125240	+	0.992126i	$0.539970\pi$
$240$		0			0
$241$	9.34265e19			0.528841			0.264420	−	0.964408i	$-0.414819\pi$
$241$	9.34265e19			0.528841			0.264420	+	0.964408i	$0.414819\pi$
$242$	1.99529e20	+	9.22102e19i	1.09037	+	0.503904i
$243$		0			0
$244$	−1.92215e20	+	1.63547e20i	−0.979430	+	0.833353i
$245$		−	3.01429e19i		−	0.148345i
$246$		0			0
$247$	7.76758e18			0.0356748
$248$	−6.84717e19	−	2.45413e20i	−0.303859	−	1.08908i
$249$		0			0
$250$	−1.09416e20	+	2.36761e20i	−0.453516	+	0.981340i
$251$			8.23914e19i			0.330107i	0.986285	+	0.165054i	$0.0527797\pi$
$251$			8.23914e19i			0.330107i	−0.986285	+	0.165054i	$0.947220\pi$
$252$		0			0
$253$		−	2.87180e19i		−	0.107555i
$254$	−3.70109e20	−	1.71042e20i	−1.34043	−	0.619464i
$255$		0			0
$256$	−2.80013e20	−	9.33009e19i	−0.948721	−	0.316116i
$257$	−3.96731e20			−1.30036			−0.650182	−	0.759779i	$-0.725307\pi$
$257$	−3.96731e20			−1.30036			−0.650182	+	0.759779i	$0.725307\pi$
$258$		0			0
$259$			3.20634e20i			0.983923i
$260$	−5.18513e18	−	6.09402e18i	−0.0153988	−	0.0180980i
$261$		0			0
$262$	−5.67282e19	+	1.22751e20i	−0.157848	+	0.341559i
$263$	3.01079e20			0.811066			0.405533	−	0.914080i	$-0.367086\pi$
$263$	3.01079e20			0.811066			0.405533	+	0.914080i	$0.367086\pi$
$264$		0			0
$265$	5.19094e20			1.31116
$266$	−2.13952e20	+	4.62961e20i	−0.523387	+	1.13253i
$267$		0			0
$268$	−3.68039e20	+	3.13148e20i	−0.844790	+	0.718793i
$269$			7.99834e19i			0.177871i	0.996037	+	0.0889356i	$0.0283465\pi$
$269$			7.99834e19i			0.177871i	−0.996037	+	0.0889356i	$0.971653\pi$
$270$		0			0
$271$	−3.82151e20			−0.797986			−0.398993	−	0.916954i	$-0.630640\pi$
$271$	−3.82151e20			−0.797986			−0.398993	+	0.916954i	$0.630640\pi$
$272$	−5.45577e19	+	3.36325e20i	−0.110413	+	0.680650i
$273$		0			0
$274$	−1.19742e20	−	5.53375e19i	−0.227702	−	0.105230i
$275$		−	3.39729e20i		−	0.626332i
$276$		0			0
$277$		−	3.87625e20i		−	0.671945i	−0.941872	−	0.335972i	$-0.890935\pi$
$277$		−	3.87625e20i		−	0.671945i	0.941872	−	0.335972i	$-0.109065\pi$
$278$	−3.81444e20	+	8.25387e20i	−0.641283	+	1.38764i
$279$		0			0
$280$	5.06035e20	−	1.41187e20i	0.800455	−	0.223332i
$281$	5.68349e20			0.872190			0.436095	−	0.899901i	$-0.356361\pi$
$281$	5.68349e20			0.872190			0.436095	+	0.899901i	$0.356361\pi$
$282$		0			0
$283$			4.50897e20i			0.651467i	0.945462	+	0.325734i	$0.105611\pi$
$283$			4.50897e20i			0.651467i	−0.945462	+	0.325734i	$0.894389\pi$
$284$	8.69947e20	+	1.02244e21i	1.21979	+	1.43361i
$285$		0			0
$286$	3.18710e19	+	1.47288e19i	0.0421002	+	0.0194562i
$287$	9.04408e20			1.15976
$288$		0			0
$289$	−4.33908e20			−0.524525
$290$	−8.18309e20	−	3.78173e20i	−0.960581	−	0.443923i
$291$		0			0
$292$	1.06892e21	+	1.25629e21i	1.18356	+	1.39103i
$293$		−	1.51002e21i		−	1.62408i	−0.583602	−	0.812040i	$-0.698357\pi$
$293$		−	1.51002e21i		−	1.62408i	0.583602	−	0.812040i	$-0.301643\pi$
$294$		0			0
$295$	−7.11057e20			−0.721801
$296$	−8.78924e20	+	2.45225e20i	−0.866906	+	0.241872i
$297$		0			0
$298$	−4.31246e20	+	9.33150e20i	−0.401686	+	0.869187i
$299$		−	2.50321e18i		−	0.00226617i
$300$		0			0
$301$			6.60992e20i			0.565433i
$302$	9.01119e20	+	4.16443e20i	0.749416	+	0.346335i
$303$		0			0
$304$	−1.43271e21	−	2.32409e20i	−1.12650	−	0.182738i
$305$	1.27847e21			0.977553
$306$		0			0
$307$		−	7.15201e20i		−	0.517311i	−0.965970	−	0.258655i	$-0.916721\pi$
$307$		−	7.15201e20i		−	0.517311i	0.965970	−	0.258655i	$-0.0832794\pi$
$308$	−1.75573e21	+	1.49387e21i	−1.23531	+	1.05107i
$309$		0			0
$310$	−5.41445e20	+	1.17161e21i	−0.360562	+	0.780202i
$311$	−1.55199e21			−1.00560			−0.502801	−	0.864402i	$-0.667697\pi$
$311$	−1.55199e21			−1.00560			−0.502801	+	0.864402i	$0.667697\pi$
$312$		0			0
$313$	−7.03438e20			−0.431617			−0.215809	−	0.976436i	$-0.569239\pi$
$313$	−7.03438e20			−0.431617			−0.215809	+	0.976436i	$0.569239\pi$
$314$	−4.95325e20	+	1.07181e21i	−0.295793	+	0.640052i
$315$		0			0
$316$	2.75286e20	+	3.23540e20i	0.155756	+	0.183058i
$317$			2.05646e21i			1.13270i	0.824163	+	0.566352i	$0.191646\pi$
$317$			2.05646e21i			1.13270i	−0.824163	+	0.566352i	$0.808354\pi$
$318$		0			0
$319$	3.95559e21			2.06534
$320$	7.74046e20	+	1.27917e21i	0.393543	+	0.650357i
$321$		0			0
$322$	1.49195e20	+	6.89491e19i	0.0719417	+	0.0332471i
$323$			1.67555e21i			0.786929i
$324$		0			0
$325$		−	2.96125e19i		−	0.0131967i
$326$	1.18535e21	−	2.56492e21i	0.514632	−	1.11359i
$327$		0			0
$328$	6.91704e20	+	2.47917e21i	0.285097	+	1.02183i
$329$	7.48669e20			0.300694
$330$		0			0
$331$		−	7.03264e20i		−	0.268275i	−0.990963	−	0.134138i	$-0.957174\pi$
$331$		−	7.03264e20i		−	0.268275i	0.990963	−	0.134138i	$-0.0428264\pi$
$332$	−4.27574e20	+	3.63803e20i	−0.158978	+	0.135267i
$333$		0			0
$334$	−2.80662e21	−	1.29705e21i	−0.991605	−	0.458260i
$335$	2.44791e21			0.843170
$336$		0			0
$337$	8.84366e20			0.289586			0.144793	−	0.989462i	$-0.453748\pi$
$337$	8.84366e20			0.289586			0.144793	+	0.989462i	$0.453748\pi$
$338$	−2.84011e21	−	1.31252e21i	−0.906865	−	0.419098i
$339$		0			0
$340$	1.31455e21	−	1.11849e21i	0.399213	−	0.339672i
$341$		−	5.66339e21i		−	1.67751i
$342$		0			0
$343$	3.12195e21			0.879885
$344$	−1.81192e21	+	5.05536e20i	−0.498186	+	0.138997i
$345$		0			0
$346$	−3.14982e20	+	6.81573e20i	−0.0824401	+	0.178388i
$347$		−	5.48605e21i		−	1.40107i	−0.713620	−	0.700533i	$-0.752945\pi$
$347$		−	5.48605e21i		−	1.40107i	0.713620	−	0.700533i	$-0.247055\pi$
$348$		0			0
$349$		−	2.09596e19i		−	0.00509762i	−0.999997	−	0.00254881i	$-0.999189\pi$
$349$		−	2.09596e19i		−	0.00509762i	0.999997	−	0.00254881i	$-0.000811312\pi$
$350$	1.76495e21	+	8.15655e20i	0.418943	+	0.193610i
$351$		0			0
$352$	−5.43782e21	−	3.67029e21i	−1.22974	−	0.830018i
$353$	8.34131e20			0.184141			0.0920703	−	0.995753i	$-0.470652\pi$
$353$	8.34131e20			0.184141			0.0920703	+	0.995753i	$0.470652\pi$
$354$		0			0
$355$		−	6.80047e21i		−	1.43086i
$356$	−5.90536e21	−	6.94051e21i	−1.21317	−	1.42582i
$357$		0			0
$358$	2.54075e21	−	5.49780e21i	0.497687	−	1.07692i
$359$	7.98650e21			1.52775			0.763877	−	0.645361i	$-0.223293\pi$
$359$	7.98650e21			1.52775			0.763877	+	0.645361i	$0.223293\pi$
$360$		0			0
$361$	−1.65726e21			−0.302398
$362$	−4.59123e21	+	9.93473e21i	−0.818288	+	1.77065i
$363$		0			0
$364$	−1.53038e20	+	1.30213e20i	−0.0260278	+	0.0221459i
$365$		−	8.35586e21i		−	1.38836i
$366$		0			0
$367$	−4.95976e21			−0.786682			−0.393341	−	0.919393i	$-0.628681\pi$
$367$	−4.95976e21			−0.786682			−0.393341	+	0.919393i	$0.628681\pi$
$368$	−7.48971e19	+	4.61709e20i	−0.0116080	+	0.0715587i
$369$		0			0
$370$	4.19600e21	+	1.93914e21i	0.621042	+	0.287008i
$371$		−	1.30359e22i		−	1.88566i
$372$		0			0
$373$		−	1.32602e22i		−	1.83243i	−0.400692	−	0.916213i	$-0.631230\pi$
$373$		−	1.32602e22i		−	1.83243i	0.400692	−	0.916213i	$-0.368770\pi$
$374$	−3.17717e21	+	6.87491e21i	−0.429172	+	0.928664i
$375$		0			0
$376$	5.72593e20	+	2.05226e21i	0.0739178	+	0.264933i
$377$	3.44790e20			0.0435164
$378$		0			0
$379$		−	4.66066e21i		−	0.562360i	−0.959655	−	0.281180i	$-0.909274\pi$
$379$		−	4.66066e21i		−	0.562360i	0.959655	−	0.281180i	$-0.0907258\pi$
$380$	4.76463e21	+	5.59981e21i	0.562171	+	0.660713i
$381$		0			0
$382$	4.02246e20	+	1.85894e20i	0.0453893	+	0.0209762i
$383$	9.41823e21			1.03939			0.519696	−	0.854351i	$-0.326045\pi$
$383$	9.41823e21			1.03939			0.519696	+	0.854351i	$0.326045\pi$
$384$		0			0
$385$	1.16778e22			1.23294
$386$	2.20464e21	+	1.01885e21i	0.227691	+	0.105225i
$387$		0			0
$388$	−6.57611e21	−	7.72882e21i	−0.649979	−	0.763913i
$389$		−	2.84056e21i		−	0.274683i	−0.990524	−	0.137342i	$-0.956144\pi$
$389$		−	2.84056e21i		−	0.274683i	0.990524	−	0.137342i	$-0.0438558\pi$
$390$		0			0
$391$	5.39969e20			0.0499881
$392$	−5.78944e20	−	2.07502e21i	−0.0524451	−	0.187971i
$393$		0			0
$394$	2.06403e21	−	4.46624e21i	0.179059	−	0.387458i
$395$		−	2.15194e21i		−	0.182707i
$396$		0			0
$397$		−	6.92645e20i		−	0.0563367i	−0.999603	−	0.0281683i	$-0.991033\pi$
$397$		−	6.92645e20i		−	0.0563367i	0.999603	−	0.0281683i	$-0.00896745\pi$
$398$	−9.67098e21	−	4.46934e21i	−0.769953	−	0.355826i
$399$		0			0
$400$	−8.86019e20	+	5.46193e21i	−0.0675979	+	0.416713i
$401$	4.47868e21			0.334521			0.167260	−	0.985913i	$-0.446508\pi$
$401$	4.47868e21			0.334521			0.167260	+	0.985913i	$0.446508\pi$
$402$		0			0
$403$		−	4.93650e20i		−	0.0353448i
$404$	8.37209e21	−	7.12343e21i	0.586938	−	0.499399i
$405$		0			0
$406$	−9.49699e21	+	2.05500e22i	−0.638432	+	1.38147i
$407$	−2.02829e22			−1.33530
$408$		0			0
$409$	1.38245e22			0.872972			0.436486	−	0.899711i	$-0.356223\pi$
$409$	1.38245e22			0.872972			0.436486	+	0.899711i	$0.356223\pi$
$410$	5.46970e21	−	1.18356e22i	0.338299	−	0.732028i
$411$		0			0
$412$	6.88184e21	+	8.08815e21i	0.408393	+	0.479979i
$413$			1.78567e22i			1.03807i
$414$		0			0
$415$	2.84389e21			0.158673
$416$	−4.73988e20	−	3.19921e20i	−0.0259104	−	0.0174884i
$417$		0			0
$418$	−2.92863e22	−	1.35344e22i	−1.53697	−	0.710297i
$419$		−	4.06502e21i		−	0.209047i	−0.994522	−	0.104523i	$-0.966668\pi$
$419$		−	4.06502e21i		−	0.209047i	0.994522	−	0.104523i	$-0.0333317\pi$
$420$		0			0
$421$			8.16114e21i			0.403045i	0.979484	+	0.201522i	$0.0645888\pi$
$421$			8.16114e21i			0.403045i	−0.979484	+	0.201522i	$0.935411\pi$
$422$	−1.11483e22	+	2.41232e22i	−0.539576	+	1.16756i
$423$		0			0
$424$	3.57342e22	−	9.97007e21i	1.66140	−	0.463541i
$425$	6.38773e21			0.291099
$426$		0			0
$427$		−	3.21059e22i		−	1.40588i
$428$	−1.60452e22	+	1.36522e22i	−0.688770	+	0.586043i
$429$		0			0
$430$	8.65013e21	+	3.99757e21i	0.356895	+	0.164935i
$431$	9.79174e21			0.396098			0.198049	−	0.980192i	$-0.436539\pi$
$431$	9.79174e21			0.396098			0.198049	+	0.980192i	$0.436539\pi$
$432$		0			0
$433$	−2.60425e22			−1.01283			−0.506414	−	0.862290i	$-0.669029\pi$
$433$	−2.60425e22			−1.01283			−0.506414	+	0.862290i	$0.669029\pi$
$434$	2.94223e22	+	1.35972e22i	1.12206	+	0.518546i
$435$		0			0
$436$	−1.05299e22	+	8.95944e21i	−0.386181	+	0.328584i
$437$			2.30020e21i			0.0827321i
$438$		0			0
$439$	2.68066e22			0.927455			0.463727	−	0.885978i	$-0.346512\pi$
$439$	2.68066e22			0.927455			0.463727	+	0.885978i	$0.346512\pi$
$440$	8.93131e21	+	3.20112e22i	0.303087	+	1.08631i
$441$		0			0
$442$	−2.76938e20	+	5.99252e20i	−0.00904260	+	0.0195668i
$443$			6.73832e21i			0.215834i	0.994160	+	0.107917i	$0.0344181\pi$
$443$			6.73832e21i			0.215834i	−0.994160	+	0.107917i	$0.965582\pi$
$444$		0			0
$445$			4.61629e22i			1.42309i
$446$	−2.54264e22	−	1.17506e22i	−0.769022	−	0.355396i
$447$		0			0
$448$	3.21235e22	−	1.94385e22i	0.935318	−	0.565977i
$449$	3.12876e22			0.893878			0.446939	−	0.894564i	$-0.352514\pi$
$449$	3.12876e22			0.893878			0.446939	+	0.894564i	$0.352514\pi$
$450$		0			0
$451$			5.72118e22i			1.57393i
$452$	1.10525e22	+	1.29899e22i	0.298389	+	0.350693i
$453$		0			0
$454$	−1.85175e22	+	4.00691e22i	−0.481512	+	1.04192i
$455$	1.01789e21			0.0259779
$456$		0			0
$457$	−5.48338e22			−1.34822			−0.674110	−	0.738631i	$-0.735473\pi$
$457$	−5.48338e22			−1.34822			−0.674110	+	0.738631i	$0.735473\pi$
$458$	2.15724e21	−	4.66794e21i	0.0520645	−	0.112660i
$459$		0			0
$460$	1.80462e21	−	1.53547e21i	0.0419704	−	0.0357107i
$461$		−	6.78571e22i		−	1.54931i	−0.632386	−	0.774653i	$-0.717924\pi$
$461$		−	6.78571e22i		−	1.54931i	0.632386	−	0.774653i	$-0.282076\pi$
$462$		0			0
$463$	−1.64300e21			−0.0361576			−0.0180788	−	0.999837i	$-0.505755\pi$
$463$	−1.64300e21			−0.0361576			−0.0180788	+	0.999837i	$0.505755\pi$
$464$	−6.35954e22	−	1.03163e22i	−1.37411	−	0.222905i
$465$		0			0
$466$	−2.30993e22	−	1.06751e22i	−0.481192	−	0.222378i
$467$			4.77673e22i			0.977096i	0.872537	+	0.488548i	$0.162473\pi$
$467$			4.77673e22i			0.977096i	−0.872537	+	0.488548i	$0.837527\pi$
$468$		0			0
$469$		−	6.14740e22i		−	1.21261i
$470$	4.52782e21	−	9.79752e21i	0.0877117	−	0.189795i
$471$		0			0
$472$	−4.89489e22	+	1.36570e22i	−0.914609	+	0.255182i
$473$	−4.18136e22			−0.767357
$474$		0			0
$475$			2.72110e22i			0.481780i
$476$	−2.80884e22	−	3.30120e22i	−0.488504	−	0.574133i
$477$		0			0
$478$	1.35480e22	+	6.26109e21i	0.227373	+	0.105078i
$479$	5.48658e22			0.904585			0.452293	−	0.891870i	$-0.350606\pi$
$479$	5.48658e22			0.904585			0.452293	+	0.891870i	$0.350606\pi$
$480$		0			0
$481$	−1.76796e21			−0.0281345
$482$	−3.07038e22	−	1.41894e22i	−0.480056	−	0.221853i
$483$		0			0
$484$	−5.15687e22	−	6.06081e22i	−0.778396	−	0.914840i
$485$			5.14062e22i			0.762448i
$486$		0			0
$487$	1.26074e23			1.80564			0.902818	−	0.430022i	$-0.141494\pi$
$487$	1.26074e23			1.80564			0.902818	+	0.430022i	$0.141494\pi$
$488$	8.80089e22	−	2.45550e22i	1.23868	−	0.345599i
$489$		0			0
$490$	−4.57805e21	+	9.90620e21i	−0.0622320	+	0.134661i
$491$			1.93871e22i			0.259013i	0.991579	+	0.129506i	$0.0413393\pi$
$491$			1.93871e22i			0.259013i	−0.991579	+	0.129506i	$0.958661\pi$
$492$		0			0
$493$			7.43748e22i			0.959902i
$494$	−2.55275e21	−	1.17972e21i	−0.0323839	−	0.0149659i
$495$		0			0
$496$	−1.47702e22	+	9.10522e22i	−0.181048	+	1.11608i
$497$	−1.70779e23			−2.05781
$498$		0			0
$499$		−	8.94608e22i		−	1.04178i	−0.853622	−	0.520892i	$-0.825599\pi$
$499$		−	8.94608e22i		−	1.04178i	0.853622	−	0.520892i	$-0.174401\pi$
$500$	7.19175e22	−	6.11913e22i	0.823359	−	0.700559i
$501$		0			0
$502$	1.25134e22	−	2.70772e22i	0.138483	−	0.299655i
$503$	−3.84163e22			−0.418011			−0.209005	−	0.977914i	$-0.567023\pi$
$503$	−3.84163e22			−0.418011			−0.209005	+	0.977914i	$0.567023\pi$
$504$		0			0
$505$	−5.56847e22			−0.585813
$506$	−4.36164e21	+	9.43793e21i	−0.0451201	+	0.0976331i
$507$		0			0
$508$	9.56555e22	+	1.12423e23i	0.956904	+	1.12464i
$509$			1.79276e23i			1.76369i	0.471541	+	0.881844i	$0.343698\pi$
$509$			1.79276e23i			1.76369i	−0.471541	+	0.881844i	$0.656302\pi$
$510$		0			0
$511$	−2.09839e23			−1.99668
$512$	7.78534e22	+	7.31903e22i	0.728590	+	0.684950i
$513$		0			0
$514$	1.30382e23	+	6.02547e22i	1.18041	+	0.545513i
$515$		−	5.37961e22i		−	0.479059i
$516$		0			0
$517$			4.73599e22i			0.408076i
$518$	4.86972e22	−	1.05373e23i	0.412764	−	0.893158i
$519$		0			0
$520$	7.78498e20	+	2.79025e21i	0.00638601	+	0.0228884i
$521$	−6.78107e22			−0.547240			−0.273620	−	0.961838i	$-0.588221\pi$
$521$	−6.78107e22			−0.547240			−0.273620	+	0.961838i	$0.588221\pi$
$522$		0			0
$523$			2.09501e23i			1.63652i	0.574845	+	0.818262i	$0.305062\pi$
$523$			2.09501e23i			1.63652i	−0.574845	+	0.818262i	$0.694938\pi$
$524$	3.72865e22	−	3.17254e22i	0.286573	−	0.243832i
$525$		0			0
$526$	−9.89468e22	−	4.57272e22i	−0.736246	−	0.340248i
$527$	1.06485e23			0.779651
$528$		0			0
$529$	−1.40309e23			−0.994745
$530$	−1.70596e23	−	7.88390e22i	−1.19021	−	0.550043i
$531$		0			0
$532$	1.40627e23	−	1.19653e23i	0.950212	−	0.808492i
$533$			4.98687e21i			0.0331624i
$534$		0			0
$535$	1.06721e23			0.687450
$536$	1.68513e23	−	4.70162e22i	1.06840	−	0.298090i
$537$		0			0
$538$	1.21477e22	−	2.62858e22i	0.0746184	−	0.161463i
$539$		−	4.78852e22i		−	0.289532i
$540$		0			0
$541$			1.24185e23i			0.727600i	0.931477	+	0.363800i	$0.118521\pi$
$541$			1.24185e23i			0.727600i	−0.931477	+	0.363800i	$0.881479\pi$
$542$	1.25590e23	+	5.80403e22i	0.724374	+	0.334762i
$543$		0			0
$544$	6.90103e22	−	1.02244e23i	0.385765	−	0.571542i
$545$	7.00370e22			0.385440
$546$		0			0
$547$		−	1.22112e23i		−	0.651429i	−0.945468	−	0.325714i	$-0.894395\pi$
$547$		−	1.22112e23i		−	0.651429i	0.945468	−	0.325714i	$-0.105605\pi$
$548$	3.09476e22	+	3.63724e22i	0.162552	+	0.191046i
$549$		0			0
$550$	−5.15974e22	+	1.11649e23i	−0.262751	+	0.568554i
$551$	−3.16828e23			−1.58867
$552$		0			0
$553$	−5.40413e22			−0.262762
$554$	−5.88717e22	+	1.27389e23i	−0.281886	+	0.609959i
$555$		0			0
$556$	2.50716e23	−	2.13323e23i	1.16425	−	0.990609i
$557$			2.07273e23i			0.947924i	0.880545	+	0.473962i	$0.157177\pi$
$557$			2.07273e23i			0.947924i	−0.880545	+	0.473962i	$0.842823\pi$
$558$		0			0
$559$	−3.64468e21			−0.0161681
$560$	−1.87747e23	−	3.04558e22i	−0.820304	−	0.133067i
$561$		0			0
$562$	−1.86783e23	−	8.63197e22i	−0.791732	−	0.365891i
$563$			1.43541e23i			0.599314i	0.954047	+	0.299657i	$0.0968722\pi$
$563$			1.43541e23i			0.599314i	−0.954047	+	0.299657i	$0.903128\pi$
$564$		0			0
$565$		−	8.63985e22i		−	0.350021i
$566$	6.84813e22	−	1.48183e23i	0.273296	−	0.591370i
$567$		0			0
$568$	−1.30614e23	−	4.68141e23i	−0.505860	−	1.81308i
$569$	−1.29010e23			−0.492231			−0.246116	−	0.969240i	$-0.579154\pi$
$569$	−1.29010e23			−0.492231			−0.246116	+	0.969240i	$0.579154\pi$
$570$		0			0
$571$		−	2.64243e23i		−	0.978579i	−0.872121	−	0.489290i	$-0.837256\pi$
$571$		−	2.64243e23i		−	0.978579i	0.872121	−	0.489290i	$-0.162744\pi$
$572$	−8.23713e21	−	9.68101e21i	−0.0300545	−	0.0353228i
$573$		0			0
$574$	−2.97226e23	−	1.37360e23i	−1.05277	−	0.486529i
$575$	8.76912e21			0.0306041
$576$		0			0
$577$	−9.70397e22			−0.328818			−0.164409	−	0.986392i	$-0.552572\pi$
$577$	−9.70397e22			−0.328818			−0.164409	+	0.986392i	$0.552572\pi$
$578$	1.42600e23	+	6.59011e22i	0.476138	+	0.220042i
$579$		0			0
$580$	2.11494e23	+	2.48566e23i	0.685740	+	0.805943i
$581$		−	7.14182e22i		−	0.228198i
$582$		0			0
$583$	8.24637e23			2.55906
$584$	−1.60488e23	−	5.75214e23i	−0.490833	−	1.75922i
$585$		0			0
$586$	−2.29339e23	+	4.96254e23i	−0.681314	+	1.47426i
$587$			3.02349e23i			0.885288i	0.896697	+	0.442644i	$0.145959\pi$
$587$			3.02349e23i			0.885288i	−0.896697	+	0.442644i	$0.854041\pi$
$588$		0			0
$589$			4.53616e23i			1.29035i
$590$	2.33683e23	+	1.07994e23i	0.655216	+	0.302801i
$591$		0			0
$592$	3.26095e23	+	5.28982e22i	0.888402	+	0.144114i
$593$	3.18008e23			0.854030			0.427015	−	0.904245i	$-0.359565\pi$
$593$	3.18008e23			0.854030			0.427015	+	0.904245i	$0.359565\pi$
$594$		0			0
$595$			2.19570e23i			0.573032i
$596$	2.83450e23	−	2.41175e23i	0.729262	−	0.620496i
$597$		0			0
$598$	−3.80183e20	+	8.22657e20i	−0.000950675	+	0.00205712i
$599$	−3.24737e23			−0.800578			−0.400289	−	0.916389i	$-0.631090\pi$
$599$	−3.24737e23			−0.800578			−0.400289	+	0.916389i	$0.631090\pi$
$600$		0			0
$601$	−3.78448e23			−0.906929			−0.453464	−	0.891274i	$-0.649812\pi$
$601$	−3.78448e23			−0.906929			−0.453464	+	0.891274i	$0.649812\pi$
$602$	1.00390e23	−	2.17229e23i	0.237204	−	0.513273i
$603$		0			0
$604$	−2.32896e23	−	2.73721e23i	−0.534994	−	0.628772i
$605$			4.03118e23i			0.913087i
$606$		0			0
$607$	−2.72859e23			−0.600945			−0.300472	−	0.953791i	$-0.597144\pi$
$607$	−2.72859e23			−0.600945			−0.300472	+	0.953791i	$0.597144\pi$
$608$	4.35548e23	+	2.93976e23i	0.945924	+	0.638457i
$609$		0			0
$610$	−4.20156e23	−	1.94171e23i	−0.887375	−	0.410091i
$611$			4.12813e21i			0.00859811i
$612$		0			0
$613$		−	2.23929e23i		−	0.453625i	−0.973938	−	0.226813i	$-0.927169\pi$
$613$		−	2.23929e23i		−	0.453625i	0.973938	−	0.226813i	$-0.0728305\pi$
$614$	−1.08623e23	+	2.35044e23i	−0.217016	+	0.469590i
$615$		0			0
$616$	8.03891e23	−	2.24291e23i	1.56229	−	0.435888i
$617$	−9.37688e23			−1.79736			−0.898679	−	0.438608i	$-0.855472\pi$
$617$	−9.37688e23			−1.79736			−0.898679	+	0.438608i	$0.855472\pi$
$618$		0			0
$619$		−	8.46873e23i		−	1.57924i	−0.613597	−	0.789619i	$-0.710278\pi$
$619$		−	8.46873e23i		−	1.57924i	0.613597	−	0.789619i	$-0.289722\pi$
$620$	3.55883e23	−	3.02804e23i	0.654602	−	0.556971i
$621$		0			0
$622$	5.10048e23	+	2.35714e23i	0.912837	+	0.421858i
$623$	1.15928e24			2.04663
$624$		0			0
$625$	−2.32610e23			−0.399622
$626$	2.31179e23	+	1.06837e23i	0.391801	+	0.181067i
$627$		0			0
$628$	3.25569e23	−	2.77012e23i	0.537014	−	0.456921i
$629$		−	3.81368e23i		−	0.620603i
$630$		0			0
$631$	5.75474e23			0.911541			0.455771	−	0.890097i	$-0.349364\pi$
$631$	5.75474e23			0.911541			0.455771	+	0.890097i	$0.349364\pi$
$632$	−4.13316e22	−	1.48139e23i	−0.0645932	−	0.231512i
$633$		0			0
$634$	3.12331e23	−	6.75837e23i	0.475178	−	1.02821i
$635$		−	7.47750e23i		−	1.12248i
$636$		0			0
$637$		−	4.17392e21i		−	0.00610041i
$638$	−1.29997e24	−	6.00768e23i	−1.87481	−	0.866425i
$639$		0			0
$640$	−6.01060e22	−	5.37947e23i	−0.0844089	−	0.755457i
$641$	−4.70111e23			−0.651489			−0.325745	−	0.945458i	$-0.605615\pi$
$641$	−4.70111e23			−0.651489			−0.325745	+	0.945458i	$0.605615\pi$
$642$		0			0
$643$		−	1.44971e23i		−	0.195653i	−0.995203	−	0.0978266i	$-0.968811\pi$
$643$		−	1.44971e23i		−	0.195653i	0.995203	−	0.0978266i	$-0.0311891\pi$
$644$	−3.85599e22	−	4.53190e22i	−0.0513578	−	0.0603602i
$645$		0			0
$646$	2.54479e23	−	5.50655e23i	0.330123	−	0.714336i
$647$	−1.43169e23			−0.183300			−0.0916502	−	0.995791i	$-0.529214\pi$
$647$	−1.43169e23			−0.183300			−0.0916502	+	0.995791i	$0.529214\pi$
$648$		0			0
$649$	−1.12959e24			−1.40877
$650$	−4.49749e21	+	9.73188e21i	−0.00553613	+	0.0119794i
$651$		0			0
$652$	−7.79109e23	+	6.62909e23i	−0.934316	+	0.794967i
$653$			3.23785e23i			0.383260i	0.981467	+	0.191630i	$0.0613774\pi$
$653$			3.23785e23i			0.383260i	−0.981467	+	0.191630i	$0.938623\pi$
$654$		0			0
$655$	−2.48001e23			−0.286024
$656$	1.49209e23	−	9.19813e23i	0.169869	−	1.04717i
$657$		0			0
$658$	−2.46043e23	−	1.13706e23i	−0.272955	−	0.126143i
$659$		−	8.58094e23i		−	0.939742i	−0.882735	−	0.469871i	$-0.844300\pi$
$659$		−	8.58094e23i		−	0.939742i	0.882735	−	0.469871i	$-0.155700\pi$
$660$		0			0
$661$			7.30451e23i			0.779612i	0.920897	+	0.389806i	$0.127458\pi$
$661$			7.30451e23i			0.779612i	−0.920897	+	0.389806i	$0.872542\pi$
$662$	−1.06810e23	+	2.31121e23i	−0.112543	+	0.243527i
$663$		0			0
$664$	1.95772e23	−	5.46216e22i	0.201058	−	0.0560965i
$665$	−9.35343e23			−0.948390
$666$		0			0
$667$			1.02102e23i			0.100917i
$668$	7.25378e23	+	8.52528e23i	0.707887	+	0.831972i
$669$		0			0
$670$	−8.04485e23	−	3.71784e23i	−0.765389	−	0.353717i
$671$	2.03098e24			1.90794
$672$		0			0
$673$	−1.25481e23			−0.114934			−0.0574671	−	0.998347i	$-0.518302\pi$
$673$	−1.25481e23			−0.114934			−0.0574671	+	0.998347i	$0.518302\pi$
$674$	−2.90639e23	−	1.34316e23i	−0.262872	−	0.121484i
$675$		0			0
$676$	7.34032e23	+	8.62699e23i	0.647393	+	0.760874i
$677$			3.68442e22i			0.0320897i	0.999871	+	0.0160448i	$0.00510745\pi$
$677$			3.68442e22i			0.0320897i	−0.999871	+	0.0160448i	$0.994893\pi$
$678$		0			0
$679$	1.29095e24			1.09652
$680$	−6.01888e23	+	1.67930e23i	−0.504882	+	0.140865i
$681$		0			0
$682$	−8.60144e23	+	1.86122e24i	−0.703727	+	1.52276i
$683$			3.46565e23i			0.280033i	0.990149	+	0.140016i	$0.0447155\pi$
$683$			3.46565e23i			0.280033i	−0.990149	+	0.140016i	$0.955285\pi$
$684$		0			0
$685$		−	2.41921e23i		−	0.190679i
$686$	−1.02600e24	−	4.74156e23i	−0.798717	−	0.369119i
$687$		0			0
$688$	6.72251e23	+	1.09051e23i	0.510540	+	0.0828183i
$689$	7.18795e22			0.0539190
$690$		0			0
$691$		−	1.64173e24i		−	1.20154i	−0.799421	−	0.600771i	$-0.794860\pi$
$691$		−	1.64173e24i		−	1.20154i	0.799421	−	0.600771i	$-0.205140\pi$
$692$	2.07032e23	−	1.76154e23i	0.149670	−	0.127348i
$693$		0			0
$694$	−8.33210e23	+	1.80294e24i	−0.587759	+	1.27182i
$695$	−1.66757e24			−1.16202
$696$		0			0
$697$	−1.07572e24			−0.731511
$698$	−3.18331e21	+	6.88820e21i	−0.00213849	+	0.00462737i
$699$		0			0
$700$	−4.56157e23	−	5.36116e23i	−0.299075	−	0.351500i
$701$		−	1.08179e24i		−	0.700709i	−0.936617	−	0.350355i	$-0.886061\pi$
$701$		−	1.08179e24i		−	0.700709i	0.936617	−	0.350355i	$-0.113939\pi$
$702$		0			0
$703$	1.62458e24			1.02712
$704$	1.22965e24	+	2.03209e24i	0.768096	+	1.26933i
$705$		0			0
$706$	−2.74130e23	−	1.26686e23i	−0.167154	−	0.0772484i
$707$			1.39840e24i			0.842493i
$708$		0			0
$709$		−	1.54173e23i		−	0.0906808i	−0.998972	−	0.0453404i	$-0.985563\pi$
$709$		−	1.54173e23i		−	0.0906808i	0.998972	−	0.0453404i	$-0.0144372\pi$
$710$	−1.03284e24	+	2.23492e24i	−0.600258	+	1.29887i
$711$		0			0
$712$	8.86635e23	+	3.17783e24i	0.503112	+	1.80323i
$713$	1.46184e23			0.0819669
$714$		0			0
$715$			6.43906e22i			0.0352550i
$716$	−1.66999e24	+	1.42092e24i	−0.903552	+	0.768791i
$717$		0			0
$718$	−2.62469e24	−	1.21297e24i	−1.38682	−	0.640905i
$719$	1.87407e24			0.978565			0.489283	−	0.872125i	$-0.337259\pi$
$719$	1.87407e24			0.978565			0.489283	+	0.872125i	$0.337259\pi$
$720$		0			0
$721$	−1.35097e24			−0.688964
$722$	5.44644e23	+	2.51701e23i	0.274502	+	0.126858i
$723$		0			0
$724$	3.01773e24	−	2.56765e24i	1.48560	−	1.26403i
$725$			1.20785e24i			0.587679i
$726$		0			0
$727$	3.49121e24			1.65933			0.829667	−	0.558259i	$-0.188531\pi$
$727$	3.49121e24			1.65933			0.829667	+	0.558259i	$0.188531\pi$
$728$	7.00712e22	−	1.95503e22i	0.0329172	−	0.00918410i
$729$		0			0
$730$	−1.26907e24	+	2.74608e24i	−0.582428	+	1.26029i
$731$		−	7.86197e23i		−	0.356643i
$732$		0			0
$733$			4.17586e24i			1.85081i	0.378979	+	0.925405i	$0.376275\pi$
$733$			4.17586e24i			1.85081i	−0.378979	+	0.925405i	$0.623725\pi$
$734$	1.62998e24	+	7.53279e23i	0.714112	+	0.330019i
$735$		0			0
$736$	9.47378e22	−	1.40361e23i	0.0405566	−	0.0600878i
$737$	3.88877e24			1.64566
$738$		0			0
$739$			3.77789e24i			1.56233i	0.624327	+	0.781163i	$0.285373\pi$
$739$			3.77789e24i			1.56233i	−0.624327	+	0.781163i	$0.714627\pi$
$740$	−1.08447e24	−	1.27456e24i	−0.443350	−	0.521064i
$741$		0			0
$742$	−1.97987e24	+	4.28414e24i	−0.791050	+	1.71171i
$743$	2.48774e24			0.982651			0.491326	−	0.870976i	$-0.336513\pi$
$743$	2.48774e24			0.982651			0.491326	+	0.870976i	$0.336513\pi$
$744$		0			0
$745$	−1.88529e24			−0.727864
$746$	−2.01394e24	+	4.35786e24i	−0.768717	+	1.66339i
$747$		0			0
$748$	2.08830e24	−	1.77684e24i	0.779164	−	0.662955i
$749$		−	2.68005e24i		−	0.988663i
$750$		0			0
$751$	1.46920e22			0.00529836			0.00264918	−	0.999996i	$-0.499157\pi$
$751$	1.46920e22			0.00529836			0.00264918	+	0.999996i	$0.499157\pi$
$752$	1.23515e23	−	7.61421e23i	0.0440423	−	0.271502i
$753$		0			0
$754$	−1.13312e23	−	5.23660e22i	−0.0395021	−	0.0182555i
$755$			1.82058e24i			0.627567i
$756$		0			0
$757$			4.58159e24i			1.54419i	0.635506	+	0.772096i	$0.280792\pi$
$757$			4.58159e24i			1.54419i	−0.635506	+	0.772096i	$0.719208\pi$
$758$	−7.07853e23	+	1.53169e24i	−0.235914	+	0.510483i
$759$		0			0
$760$	−7.15364e23	−	2.56397e24i	−0.233137	−	0.835599i
$761$	−2.36360e24			−0.761736			−0.380868	−	0.924629i	$-0.624375\pi$
$761$	−2.36360e24			−0.761736			−0.380868	+	0.924629i	$0.624375\pi$
$762$		0			0
$763$		−	1.75883e24i		−	0.554325i
$764$	−1.03962e23	−	1.22185e23i	−0.0324025	−	0.0380823i
$765$		0			0
$766$	−3.09522e24	−	1.43042e24i	−0.943510	−	0.436033i
$767$	−9.84609e22			−0.0296827
$768$		0			0
$769$	−9.13423e23			−0.269338			−0.134669	−	0.990891i	$-0.542997\pi$
$769$	−9.13423e23			−0.269338			−0.134669	+	0.990891i	$0.542997\pi$
$770$	−3.83779e24	−	1.77359e24i	−1.11921	−	0.517229i
$771$		0			0
$772$	−5.69795e23	−	6.69674e23i	−0.162544	−	0.191036i
$773$			1.76234e24i			0.497238i	0.968601	+	0.248619i	$0.0799766\pi$
$773$			1.76234e24i			0.497238i	−0.968601	+	0.248619i	$0.920023\pi$
$774$		0			0
$775$	1.72933e24			0.477324
$776$	9.87341e23	+	3.53878e24i	0.269552	+	0.966114i
$777$		0			0
$778$	−4.31418e23	+	9.33524e23i	−0.115232	+	0.249344i
$779$		−	4.58244e24i		−	1.21068i
$780$		0			0
$781$		−	1.08033e25i		−	2.79268i
$782$	−1.77456e23	−	8.20094e22i	−0.0453767	−	0.0209704i
$783$		0			0
$784$	−1.24886e23	+	7.69867e23i	−0.0312482	+	0.192632i
$785$	−2.16543e24			−0.535985
$786$		0			0
$787$		−	3.12907e24i		−	0.757933i	−0.925410	−	0.378966i	$-0.876280\pi$
$787$		−	3.12907e24i		−	0.757933i	0.925410	−	0.378966i	$-0.123720\pi$
$788$	−1.35665e24	+	1.15431e24i	−0.325083	+	0.276598i
$789$		0			0
$790$	−3.26832e23	+	7.07216e23i	−0.0766470	+	0.165852i
$791$	−2.16971e24			−0.503387
$792$		0			0
$793$	1.77030e23			0.0402000
$794$	−1.05198e23	+	2.27632e23i	−0.0236337	+	0.0511397i
$795$		0			0
$796$	2.49949e24	+	2.93762e24i	0.549655	+	0.646003i
$797$			1.77982e24i			0.387241i	0.981077	+	0.193620i	$0.0620230\pi$
$797$			1.77982e24i			0.387241i	−0.981077	+	0.193620i	$0.937977\pi$
$798$		0			0
$799$	−8.90481e23			−0.189661
$800$	1.12073e24	−	1.66045e24i	0.236176	−	0.349914i
$801$		0			0
$802$	−1.47188e24	−	6.80214e23i	−0.303662	−	0.140334i
$803$		−	1.32742e25i		−	2.70973i
$804$		0			0
$805$			3.01427e23i			0.0602445i
$806$	−7.49745e22	+	1.62234e23i	−0.0148274	+	0.0320843i
$807$		0			0
$808$	−3.83331e24	+	1.06952e24i	−0.742296	+	0.207105i
$809$	−2.82672e23			−0.0541653			−0.0270826	−	0.999633i	$-0.508622\pi$
$809$	−2.82672e23			−0.0541653			−0.0270826	+	0.999633i	$0.508622\pi$
$810$		0			0
$811$		−	9.40519e24i		−	1.76478i	−0.470519	−	0.882390i	$-0.655933\pi$
$811$		−	9.40519e24i		−	1.76478i	0.470519	−	0.882390i	$-0.344067\pi$
$812$	6.24220e24	−	5.31121e24i	1.15908	−	0.986205i
$813$		0			0
$814$	6.66580e24	+	3.08053e24i	1.21212	+	0.560167i
$815$	5.18203e24			0.932525
$816$		0			0
$817$	3.34911e24			0.590258
$818$	−4.54329e24	−	2.09963e24i	−0.792442	−	0.366219i
$819$		0			0
$820$	−3.59514e24	+	3.05894e24i	−0.614183	+	0.522581i
$821$			2.44785e24i			0.413875i	0.978354	+	0.206937i	$0.0663496\pi$
$821$			2.44785e24i			0.413875i	−0.978354	+	0.206937i	$0.933650\pi$
$822$		0			0
$823$	2.44893e24			0.405581			0.202791	−	0.979222i	$-0.434999\pi$
$823$	2.44893e24			0.405581			0.202791	+	0.979222i	$0.434999\pi$
$824$	−1.03324e24	−	3.70330e24i	−0.169364	−	0.607026i
$825$		0			0
$826$	2.71204e24	−	5.86844e24i	0.435477	−	0.942306i
$827$		−	3.39629e24i		−	0.539769i	−0.962893	−	0.269885i	$-0.913014\pi$
$827$		−	3.39629e24i		−	0.539769i	0.962893	−	0.269885i	$-0.0869855\pi$
$828$		0			0
$829$			3.76176e24i			0.585703i	0.956158	+	0.292851i	$0.0946041\pi$
$829$			3.76176e24i			0.585703i	−0.956158	+	0.292851i	$0.905396\pi$
$830$	−9.34620e23	−	4.31925e23i	−0.144036	−	0.0665647i
$831$		0			0
$832$	1.07183e23	+	1.77127e23i	0.0161837	+	0.0267447i
$833$	9.00359e23			0.134565
$834$		0			0
$835$		−	5.67036e24i		−	0.830377i
$836$	7.56912e24	+	8.89591e24i	1.09722	+	1.28955i
$837$		0			0
$838$	−6.17387e23	+	1.33593e24i	−0.0876967	+	0.189762i
$839$	1.26128e25			1.77352			0.886758	−	0.462234i	$-0.152952\pi$
$839$	1.26128e25			1.77352			0.886758	+	0.462234i	$0.152952\pi$
$840$		0			0
$841$	−6.80632e24			−0.937877
$842$	1.23950e24	−	2.68209e24i	0.169080	−	0.365864i
$843$		0			0
$844$	7.32758e24	−	6.23471e24i	0.979602	−	0.833499i
$845$		−	5.73801e24i		−	0.759415i
$846$		0			0
$847$	1.01234e25			1.31317
$848$	−1.32580e25	−	2.15067e24i	−1.70260	−	0.276190i
$849$		0			0
$850$	−2.09927e24	−	9.70156e23i	−0.264246	−	0.122118i
$851$		−	5.23545e23i		−	0.0652458i
$852$		0			0
$853$			3.35040e24i			0.409289i	0.978836	+	0.204644i	$0.0656038\pi$
$853$			3.35040e24i			0.409289i	−0.978836	+	0.204644i	$0.934396\pi$
$854$	−4.87618e24	+	1.05513e25i	−0.589777	+	1.27619i
$855$		0			0
$856$	7.34659e24	−	2.04974e24i	0.871082	−	0.243037i
$857$	−7.08522e24			−0.831795			−0.415897	−	0.909412i	$-0.636532\pi$
$857$	−7.08522e24			−0.831795			−0.415897	+	0.909412i	$0.636532\pi$
$858$		0			0
$859$			8.34929e24i			0.960966i	0.877004	+	0.480483i	$0.159539\pi$
$859$			8.34929e24i			0.960966i	−0.877004	+	0.480483i	$0.840461\pi$
$860$	−2.23565e24	−	2.62753e24i	−0.254781	−	0.299441i
$861$		0			0
$862$	−3.21797e24	−	1.48715e24i	−0.359559	−	0.166166i
$863$	−6.81718e24			−0.754246			−0.377123	−	0.926163i	$-0.623087\pi$
$863$	−6.81718e24			−0.754246			−0.377123	+	0.926163i	$0.623087\pi$
$864$		0			0
$865$	−1.37702e24			−0.149383
$866$	8.55865e24	+	3.95529e24i	0.919397	+	0.424890i
$867$		0			0
$868$	−7.60428e24	−	8.93722e24i	−0.801014	−	0.941423i
$869$		−	3.41859e24i		−	0.356598i
$870$		0			0
$871$	3.38965e23			0.0346738
$872$	4.82131e24	−	1.34518e24i	0.488400	−	0.136267i
$873$		0			0
$874$	3.49351e23	−	7.55942e23i	0.0347068	−	0.0751002i
$875$			1.20125e25i			1.18185i
$876$		0			0
$877$		−	1.56397e25i		−	1.50914i	−0.656217	−	0.754572i	$-0.727844\pi$
$877$		−	1.56397e25i		−	1.50914i	0.656217	−	0.754572i	$-0.272156\pi$
$878$	−8.80974e24	−	4.07133e24i	−0.841899	−	0.389075i
$879$		0			0
$880$	1.92660e24	−	1.18767e25i	0.180588	−	1.11325i
$881$	1.62905e25			1.51230			0.756152	−	0.654396i	$-0.227077\pi$
$881$	1.62905e25			1.51230			0.756152	+	0.654396i	$0.227077\pi$
$882$		0			0
$883$			4.63346e24i			0.421929i	0.977494	+	0.210964i	$0.0676604\pi$
$883$			4.63346e24i			0.421929i	−0.977494	+	0.210964i	$0.932340\pi$
$884$	1.82027e23	−	1.54878e23i	0.0164169	−	0.0139684i
$885$		0			0
$886$	1.02340e24	−	2.21449e24i	0.0905441	−	0.195924i
$887$	1.40637e24			0.123239			0.0616197	−	0.998100i	$-0.480373\pi$
$887$	1.40637e24			0.123239			0.0616197	+	0.998100i	$0.480373\pi$
$888$		0			0
$889$	−1.87781e25			−1.61431
$890$	7.01113e24	−	1.51710e25i	0.596998	−	1.29181i
$891$		0			0
$892$	6.57152e24	+	7.72343e24i	0.548990	+	0.645222i
$893$		−	3.79335e24i		−	0.313896i
$894$		0			0
$895$	1.11075e25			0.901820
$896$	−1.35094e25	+	1.50943e24i	−1.08647	+	0.121394i
$897$		0			0
$898$	−1.02824e25	−	4.75190e24i	−0.811419	−	0.374989i
$899$			2.01352e25i			1.57398i
$900$		0			0
$901$			1.55052e25i			1.18937i
$902$	8.68921e24	−	1.88021e25i	0.660275	−	1.42874i
$903$		0			0
$904$	−1.65943e24	−	5.94763e24i	−0.123745	−	0.443519i
$905$	−2.00716e25			−1.48276
$906$		0			0
$907$		−	8.93640e24i		−	0.647889i	−0.946076	−	0.323945i	$-0.894991\pi$
$907$		−	8.93640e24i		−	0.647889i	0.946076	−	0.323945i	$-0.105009\pi$
$908$	1.21712e25	−	1.03559e25i	0.874188	−	0.743807i
$909$		0			0
$910$	−3.34521e23	−	1.54595e23i	−0.0235815	−	0.0108980i
$911$	−1.71271e25			−1.19613			−0.598064	−	0.801448i	$-0.704063\pi$
$911$	−1.71271e25			−1.19613			−0.598064	+	0.801448i	$0.704063\pi$
$912$		0			0
$913$	4.51783e24			0.309691
$914$	1.80207e25	+	8.32805e24i	1.22385	+	0.565589i
$915$		0			0
$916$	−1.41792e24	+	1.20644e24i	−0.0945233	+	0.0804256i
$917$			6.22800e24i			0.411348i
$918$		0			0
$919$	−1.92318e25			−1.24692			−0.623459	−	0.781856i	$-0.714273\pi$
$919$	−1.92318e25			−1.24692			−0.623459	+	0.781856i	$0.714273\pi$
$920$	−8.26275e23	+	2.30536e23i	−0.0530797	+	0.0148096i
$921$		0			0
$922$	−1.03060e25	+	2.23006e25i	−0.649946	+	1.40639i
$923$		−	9.41669e23i		−	0.0588415i
$924$		0			0
$925$		−	6.19343e24i		−	0.379950i
$926$	5.39958e23	+	2.49536e23i	0.0328221	+	0.0151684i
$927$		0			0
$928$	1.93333e25	+	1.30491e25i	1.15384	+	0.778794i
$929$	1.01792e25			0.601979			0.300989	−	0.953627i	$-0.402683\pi$
$929$	1.01792e25			0.601979			0.300989	+	0.953627i	$0.402683\pi$
$930$		0			0
$931$			3.83543e24i			0.222711i
$932$	5.97007e24	+	7.01656e24i	0.343514	+	0.403728i
$933$		0			0
$934$	7.25480e24	−	1.56983e25i	0.409899	−	0.886960i
$935$	−1.38897e25			−0.777670
$936$		0			0
$937$	2.57324e25			1.41480			0.707399	−	0.706815i	$-0.249869\pi$
$937$	2.57324e25			1.41480			0.707399	+	0.706815i	$0.249869\pi$
$938$	−9.33656e24	+	2.02029e25i	−0.508701	+	1.10075i
$939$		0			0
$940$	−2.97606e24	+	2.53219e24i	−0.159241	+	0.135491i
$941$			1.64698e25i			0.873327i	0.899625	+	0.436663i	$0.143840\pi$
$941$			1.64698e25i			0.873327i	−0.899625	+	0.436663i	$0.856160\pi$
$942$		0			0
$943$	−1.47676e24			−0.0769058
$944$	1.81608e25	+	2.94599e24i	0.937289	+	0.152044i
$945$		0			0
$946$	1.37417e25	+	6.35057e24i	0.696570	+	0.321912i
$947$			3.53295e25i			1.77485i	0.460949	+	0.887427i	$0.347509\pi$
$947$			3.53295e25i			1.77485i	−0.460949	+	0.887427i	$0.652491\pi$
$948$		0			0
$949$		−	1.15705e24i		−	0.0570936i
$950$	4.13275e24	−	8.94265e24i	0.202110	−	0.437336i
$951$		0			0
$952$	4.21721e24	+	1.51151e25i	0.202587	+	0.726101i
$953$	4.30929e24			0.205171			0.102585	−	0.994724i	$-0.467288\pi$
$953$	4.30929e24			0.205171			0.102585	+	0.994724i	$0.467288\pi$
$954$		0			0
$955$			8.12679e23i			0.0380093i
$956$	−3.50152e24	−	4.11530e24i	−0.162317	−	0.190770i
$957$		0			0
$958$	−1.80311e25	−	8.33291e24i	−0.821139	−	0.379481i
$959$	−6.07532e24			−0.274228
$960$		0			0
$961$	6.27834e24			0.278417
$962$	5.81025e23	+	2.68515e23i	0.0255392	+	0.0118027i
$963$		0			0
$964$	7.93547e24	+	9.32646e24i	0.342703	+	0.402775i
$965$			4.45415e24i			0.190670i
$966$		0			0
$967$	−2.86774e25			−1.20619			−0.603094	−	0.797670i	$-0.706066\pi$
$967$	−2.86774e25			−1.20619			−0.603094	+	0.797670i	$0.706066\pi$
$968$	7.74256e24	+	2.77505e25i	0.322808	+	1.15699i
$969$		0			0
$970$	7.80747e24	−	1.68942e25i	0.319853	−	0.692114i
$971$		−	3.16457e25i		−	1.28514i	−0.766225	−	0.642572i	$-0.777867\pi$
$971$		−	3.16457e25i		−	1.28514i	0.766225	−	0.642572i	$-0.222133\pi$
$972$		0			0
$973$			4.18775e25i			1.67117i
$974$	−4.14332e25	−	1.91479e25i	−1.63907	−	0.757479i
$975$		0			0
$976$	−3.26527e25	−	5.29683e24i	−1.26939	−	0.205917i
$977$	−3.66143e25			−1.41107			−0.705533	−	0.708677i	$-0.749292\pi$
$977$	−3.66143e25			−1.41107			−0.705533	+	0.708677i	$0.749292\pi$
$978$		0			0
$979$			7.33347e25i			2.77752i
$980$	3.00907e24	−	2.56028e24i	0.112982	−	0.0961315i
$981$		0			0
$982$	2.94448e24	−	6.37142e24i	0.108658	−	0.235119i
$983$	4.80762e25			1.75884			0.879418	−	0.476051i	$-0.157932\pi$
$983$	4.80762e25			1.75884			0.879418	+	0.476051i	$0.157932\pi$
$984$		0			0
$985$	9.02337e24			0.324460
$986$	1.12959e25	−	2.44426e25i	0.402687	−	0.871353i
$987$		0			0
$988$	6.59763e23	+	7.75412e23i	0.0231182	+	0.0271706i
$989$		−	1.07930e24i		−	0.0374949i
$990$		0			0
$991$	−2.82526e25			−0.964789			−0.482395	−	0.875954i	$-0.660233\pi$
$991$	−2.82526e25			−0.964789			−0.482395	+	0.875954i	$0.660233\pi$
$992$	1.86829e25	−	2.76802e25i	0.632551	−	0.937174i
$993$		0			0
$994$	5.61251e25	+	2.59376e25i	1.86798	+	0.863268i
$995$		−	1.95388e25i		−	0.644765i
$996$		0			0
$997$		−	2.70363e25i		−	0.877078i	−0.898712	−	0.438539i	$-0.855496\pi$
$997$		−	2.70363e25i		−	0.877078i	0.898712	−	0.438539i	$-0.144504\pi$
$998$	−1.35871e25	+	2.94005e25i	−0.437037	+	0.945682i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.18.d.b.37.3		16
3.2	odd	2		8.18.b.a.5.14	yes	16
8.5	even	2	inner	72.18.d.b.37.4		16
12.11	even	2		32.18.b.a.17.10		16
24.5	odd	2		8.18.b.a.5.13	✓	16
24.11	even	2		32.18.b.a.17.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.18.b.a.5.13	✓	16	24.5	odd	2
8.18.b.a.5.14	yes	16	3.2	odd	2
32.18.b.a.17.7		16	24.11	even	2
32.18.b.a.17.10		16	12.11	even	2
72.18.d.b.37.3		16	1.1	even	1	trivial
72.18.d.b.37.4		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)

\(f(q)\)	\(=\)	\(q+(-328.641 - 151.878i) q^{2} +(84938.1 + 99826.8i) q^{4} -663971. i q^{5} -1.66742e7 q^{7} +(-1.27527e7 - 4.57074e7i) q^{8} +O(q^{10})\)	\(q+(-328.641 - 151.878i) q^{2} +(84938.1 + 99826.8i) q^{4} -663971. i q^{5} -1.66742e7 q^{7} +(-1.27527e7 - 4.57074e7i) q^{8} +(-1.00843e8 + 2.18208e8i) q^{10} -1.05479e9i q^{11} -9.19407e7i q^{13} +(5.47982e9 + 2.53244e9i) q^{14} +(-2.75091e9 + 1.69582e10i) q^{16} +1.98326e10 q^{17} +8.44846e10i q^{19} +(6.62821e10 - 5.63964e10i) q^{20} +(-1.60199e11 + 3.46647e11i) q^{22} +2.72263e10 q^{23} +3.22082e11 q^{25} +(-1.39638e10 + 3.02155e10i) q^{26} +(-1.41627e12 - 1.66453e12i) q^{28} +3.75013e12i q^{29} +5.36921e12 q^{31} +(3.47964e12 - 5.15536e12i) q^{32} +(-6.51781e12 - 3.01214e12i) q^{34} +1.10712e13i q^{35} -1.92294e13i q^{37} +(1.28314e13 - 2.77651e13i) q^{38} +(-3.03484e13 + 8.46739e12i) q^{40} -5.42400e13 q^{41} -3.96416e13i q^{43} +(1.05296e14 - 8.95918e13i) q^{44} +(-8.94769e12 - 4.13508e12i) q^{46} -4.48999e13 q^{47} +4.53979e13 q^{49} +(-1.05850e14 - 4.89172e13i) q^{50} +(9.17815e12 - 7.80927e12i) q^{52} +7.81803e14i q^{53} -7.00349e14 q^{55} +(2.12640e14 + 7.62134e14i) q^{56} +(5.69562e14 - 1.23245e15i) q^{58} -1.07092e15i q^{59} +1.92548e15i q^{61} +(-1.76454e15 - 8.15466e14i) q^{62} +(-1.92654e15 + 1.16578e15i) q^{64} -6.10460e13 q^{65} +3.68678e15i q^{67} +(1.68454e15 + 1.97982e15i) q^{68} +(1.68147e15 - 3.63844e15i) q^{70} +1.02421e16 q^{71} +1.25847e16 q^{73} +(-2.92052e15 + 6.31956e15i) q^{74} +(-8.43383e15 + 7.17596e15i) q^{76} +1.75877e16i q^{77} +3.24102e15 q^{79} +(1.12597e16 + 1.82652e15i) q^{80} +(1.78255e16 + 8.23787e15i) q^{82} +4.28316e15i q^{83} -1.31683e16i q^{85} +(-6.02070e15 + 1.30279e16i) q^{86} +(-4.82117e16 + 1.34514e16i) q^{88} -6.95255e16 q^{89} +1.53304e15i q^{91} +(2.31255e15 + 2.71792e15i) q^{92} +(1.47560e16 + 6.81931e15i) q^{94} +5.60953e16 q^{95} -7.74223e16 q^{97} +(-1.49196e16 - 6.89495e15i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 270 q^{2} - 27436 q^{4} + 11529600 q^{7} - 24334920 q^{8}+O(q^{10}) \) 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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