LMFDB - Embedded newform 72.18.d.b.37.16

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			37.16
Root			$0.500000 - 83132.4i$ of defining polynomial
Character	$\chi$	$=$	72.37
Dual form			72.18.d.b.37.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(362.025 + 3.13586i) q^{2} +(131052. + 2270.52i) q^{4} +665059. i q^{5} -7.57536e6 q^{7} +(4.74371e7 + 1.23295e6i) q^{8} +O(q^{10})$	\(q+(362.025 + 3.13586i) q^{2} +(131052. + 2270.52i) q^{4} +665059. i q^{5} -7.57536e6 q^{7} +(4.74371e7 + 1.23295e6i) q^{8} +(-2.08553e6 + 2.40768e8i) q^{10} +1.97863e8i q^{11} -4.74981e9i q^{13} +(-2.74247e9 - 2.37553e7i) q^{14} +(1.71696e10 + 5.95115e8i) q^{16} -3.37447e10 q^{17} +1.00829e11i q^{19} +(-1.51003e9 + 8.71575e10i) q^{20} +(-6.20471e8 + 7.16313e10i) q^{22} -3.16250e11 q^{23} +3.20636e11 q^{25} +(1.48948e10 - 1.71955e12i) q^{26} +(-9.92769e11 - 1.72000e10i) q^{28} +3.54291e12i q^{29} +2.76965e11 q^{31} +(6.21394e12 + 2.69288e11i) q^{32} +(-1.22164e13 - 1.05819e11i) q^{34} -5.03806e12i q^{35} +2.12889e13i q^{37} +(-3.16187e11 + 3.65027e13i) q^{38} +(-8.19983e11 + 3.15485e13i) q^{40} -8.47798e13 q^{41} -1.38239e14i q^{43} +(-4.49252e11 + 2.59304e13i) q^{44} +(-1.14490e14 - 9.91717e11i) q^{46} -8.21469e13 q^{47} -1.75244e14 q^{49} +(1.16078e14 + 1.00547e12i) q^{50} +(1.07846e13 - 6.22474e14i) q^{52} +3.16386e14i q^{53} -1.31590e14 q^{55} +(-3.59353e14 - 9.34003e12i) q^{56} +(-1.11101e13 + 1.28262e15i) q^{58} -3.29635e14i q^{59} -6.60732e14i q^{61} +(1.00268e14 + 8.68526e11i) q^{62} +(2.24876e15 + 1.16975e14i) q^{64} +3.15891e15 q^{65} -3.64311e15i q^{67} +(-4.42232e15 - 7.66181e13i) q^{68} +(1.57987e13 - 1.82390e15i) q^{70} -9.19058e15 q^{71} -5.44264e15 q^{73} +(-6.67591e13 + 7.70712e15i) q^{74} +(-2.28935e14 + 1.32139e16i) q^{76} -1.49888e15i q^{77} +1.06400e16 q^{79} +(-3.95786e14 + 1.14188e16i) q^{80} +(-3.06924e16 - 2.65858e14i) q^{82} +9.38898e15i q^{83} -2.24422e16i q^{85} +(4.33498e14 - 5.00459e16i) q^{86} +(-2.43955e14 + 9.38604e15i) q^{88} -2.24169e16 q^{89} +3.59815e16i q^{91} +(-4.14453e16 - 7.18053e14i) q^{92} +(-2.97392e16 - 2.57601e14i) q^{94} -6.70573e16 q^{95} -4.00962e16 q^{97} +(-6.34429e16 - 5.49543e14i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	362.025	+	3.13586i	0.999962	+	0.00866168i
$2$	362.025	+	3.13586i	0.999962	+	0.00866168i
$3$		0			0
$3$		0			0
$4$	131052.	+	2270.52i	0.999850	+	0.0173227i
$5$			665059.i			0.761404i	0.924698	+	0.380702i	$0.124318\pi$
$5$			665059.i			0.761404i	−0.924698	+	0.380702i	$0.875682\pi$
$6$		0			0
$7$	−7.57536e6			−0.496672			−0.248336	−	0.968674i	$-0.579884\pi$
$7$	−7.57536e6			−0.496672			−0.248336	+	0.968674i	$0.579884\pi$
$8$	4.74371e7	+	1.23295e6i	0.999662	+	0.0259824i
$9$		0			0
$10$	−2.08553e6	+	2.40768e8i	−0.00659504	+	0.761375i
$11$			1.97863e8i			0.278308i	0.990271	+	0.139154i	$0.0444384\pi$
$11$			1.97863e8i			0.278308i	−0.990271	+	0.139154i	$0.955562\pi$
$12$		0			0
$13$		−	4.74981e9i		−	1.61495i	−0.589905	−	0.807473i	$-0.700835\pi$
$13$		−	4.74981e9i		−	1.61495i	0.589905	−	0.807473i	$-0.299165\pi$
$14$	−2.74247e9	−	2.37553e7i	−0.496654	−	0.00430202i
$15$		0			0
$16$	1.71696e10	+	5.95115e8i	0.999400	+	0.0346402i
$17$	−3.37447e10			−1.17325			−0.586624	−	0.809859i	$-0.699543\pi$
$17$	−3.37447e10			−1.17325			−0.586624	+	0.809859i	$0.699543\pi$
$18$		0			0
$19$			1.00829e11i			1.36201i	0.732278	+	0.681005i	$0.238457\pi$
$19$			1.00829e11i			1.36201i	−0.732278	+	0.681005i	$0.761543\pi$
$20$	−1.51003e9	+	8.71575e10i	−0.0131896	+	0.761290i
$21$		0			0
$22$	−6.20471e8	+	7.16313e10i	−0.00241062	+	0.278298i
$23$	−3.16250e11			−0.842062			−0.421031	−	0.907046i	$-0.638332\pi$
$23$	−3.16250e11			−0.842062			−0.421031	+	0.907046i	$0.638332\pi$
$24$		0			0
$25$	3.20636e11			0.420264
$26$	1.48948e10	−	1.71955e12i	0.0139881	−	1.61489i
$27$		0			0
$28$	−9.92769e11	−	1.72000e10i	−0.496598	−	0.00860371i
$29$			3.54291e12i			1.31516i	0.753386	+	0.657578i	$0.228419\pi$
$29$			3.54291e12i			1.31516i	−0.753386	+	0.657578i	$0.771581\pi$
$30$		0			0
$31$	2.76965e11			0.0583245			0.0291623	−	0.999575i	$-0.490716\pi$
$31$	2.76965e11			0.0583245			0.0291623	+	0.999575i	$0.490716\pi$
$32$	6.21394e12	+	2.69288e11i	0.999062	+	0.0432954i
$33$		0			0
$34$	−1.22164e13	−	1.05819e11i	−1.17320	−	0.0101623i
$35$		−	5.03806e12i		−	0.378168i
$36$		0			0
$37$			2.12889e13i			0.996412i	0.867059	+	0.498206i	$0.166008\pi$
$37$			2.12889e13i			0.996412i	−0.867059	+	0.498206i	$0.833992\pi$
$38$	−3.16187e11	+	3.65027e13i	−0.0117973	+	1.36196i
$39$		0			0
$40$	−8.19983e11	+	3.15485e13i	−0.0197831	+	0.761147i
$41$	−8.47798e13			−1.65817			−0.829086	−	0.559121i	$-0.811139\pi$
$41$	−8.47798e13			−1.65817			−0.829086	+	0.559121i	$0.811139\pi$
$42$		0			0
$43$		−	1.38239e14i		−	1.80363i	−0.432122	−	0.901815i	$-0.642235\pi$
$43$		−	1.38239e14i		−	1.80363i	0.432122	−	0.901815i	$-0.357765\pi$
$44$	−4.49252e11	+	2.59304e13i	−0.00482106	+	0.278267i
$45$		0			0
$46$	−1.14490e14	−	9.91717e11i	−0.842030	−	0.00729367i
$47$	−8.21469e13			−0.503221			−0.251611	−	0.967829i	$-0.580960\pi$
$47$	−8.21469e13			−0.503221			−0.251611	+	0.967829i	$0.580960\pi$
$48$		0			0
$49$	−1.75244e14			−0.753317
$50$	1.16078e14	+	1.00547e12i	0.420248	+	0.00364019i
$51$		0			0
$52$	1.07846e13	−	6.22474e14i	0.0279752	−	1.61470i
$53$			3.16386e14i			0.698028i	0.937118	+	0.349014i	$0.113483\pi$
$53$			3.16386e14i			0.698028i	−0.937118	+	0.349014i	$0.886517\pi$
$54$		0			0
$55$	−1.31590e14			−0.211905
$56$	−3.59353e14	−	9.34003e12i	−0.496505	−	0.0129048i
$57$		0			0
$58$	−1.11101e13	+	1.28262e15i	−0.0113915	+	1.31511i
$59$		−	3.29635e14i		−	0.292275i	−0.989264	−	0.146138i	$-0.953316\pi$
$59$		−	3.29635e14i		−	0.292275i	0.989264	−	0.146138i	$-0.0466842\pi$
$60$		0			0
$61$		−	6.60732e14i		−	0.441288i	−0.975354	−	0.220644i	$-0.929184\pi$
$61$		−	6.60732e14i		−	0.441288i	0.975354	−	0.220644i	$-0.0708159\pi$
$62$	1.00268e14	+	8.68526e11i	0.0583223	+	0.000505189i
$63$		0			0
$64$	2.24876e15	+	1.16975e14i	0.998650	+	0.0519474i
$65$	3.15891e15			1.22963
$66$		0			0
$67$		−	3.64311e15i		−	1.09607i	−0.836457	−	0.548033i	$-0.815377\pi$
$67$		−	3.64311e15i		−	1.09607i	0.836457	−	0.548033i	$-0.184623\pi$
$68$	−4.42232e15	−	7.66181e13i	−1.17307	−	0.0203238i
$69$		0			0
$70$	1.57987e13	−	1.82390e15i	0.00327557	−	0.378154i
$71$	−9.19058e15			−1.68907			−0.844534	−	0.535502i	$-0.820122\pi$
$71$	−9.19058e15			−1.68907			−0.844534	+	0.535502i	$0.820122\pi$
$72$		0			0
$73$	−5.44264e15			−0.789888			−0.394944	−	0.918705i	$-0.629236\pi$
$73$	−5.44264e15			−0.789888			−0.394944	+	0.918705i	$0.629236\pi$
$74$	−6.67591e13	+	7.70712e15i	−0.00863060	+	0.996374i
$75$		0			0
$76$	−2.28935e14	+	1.32139e16i	−0.0235937	+	1.36181i
$77$		−	1.49888e15i		−	0.138228i
$78$		0			0
$79$	1.06400e16			0.789059			0.394529	−	0.918883i	$-0.370908\pi$
$79$	1.06400e16			0.789059			0.394529	+	0.918883i	$0.370908\pi$
$80$	−3.95786e14	+	1.14188e16i	−0.0263752	+	0.760947i
$81$		0			0
$82$	−3.06924e16	−	2.65858e14i	−1.65811	−	0.0143626i
$83$			9.38898e15i			0.457567i	0.973477	+	0.228783i	$0.0734748\pi$
$83$			9.38898e15i			0.457567i	−0.973477	+	0.228783i	$0.926525\pi$
$84$		0			0
$85$		−	2.24422e16i		−	0.893316i
$86$	4.33498e14	−	5.00459e16i	0.0156225	−	1.80356i
$87$		0			0
$88$	−2.43955e14	+	9.38604e15i	−0.00723113	+	0.278214i
$89$	−2.24169e16			−0.603616			−0.301808	−	0.953369i	$-0.597590\pi$
$89$	−2.24169e16			−0.603616			−0.301808	+	0.953369i	$0.597590\pi$
$90$		0			0
$91$			3.59815e16i			0.802099i
$92$	−4.14453e16	−	7.18053e14i	−0.841936	−	0.0145868i
$93$		0			0
$94$	−2.97392e16	−	2.57601e14i	−0.503203	−	0.00435874i
$95$	−6.70573e16			−1.03704
$96$		0			0
$97$	−4.00962e16			−0.519450			−0.259725	−	0.965683i	$-0.583632\pi$
$97$	−4.00962e16			−0.519450			−0.259725	+	0.965683i	$0.583632\pi$
$98$	−6.34429e16	−	5.49543e14i	−0.753288	−	0.00652499i
$99$		0			0
$100$	4.20201e16	+	7.28011e14i	0.420201	+	0.00728011i
$101$		−	3.80297e16i		−	0.349455i	−0.984617	−	0.174728i	$-0.944096\pi$
$101$		−	3.80297e16i		−	0.349455i	0.984617	−	0.174728i	$-0.0559045\pi$
$102$		0			0
$103$	−2.07629e17			−1.61500			−0.807498	−	0.589870i	$-0.799179\pi$
$103$	−2.07629e17			−1.61500			−0.807498	+	0.589870i	$0.799179\pi$
$104$	5.85627e15	−	2.25317e17i	0.0419602	−	1.61440i
$105$		0			0
$106$	−9.92144e14	+	1.14540e17i	−0.00604609	+	0.698001i
$107$			1.68191e17i			0.946325i	0.880975	+	0.473162i	$0.156888\pi$
$107$			1.68191e17i			0.946325i	−0.880975	+	0.473162i	$0.843112\pi$
$108$		0			0
$109$		−	4.08973e15i		−	0.0196593i	−0.999952	−	0.00982967i	$-0.996871\pi$
$109$		−	4.08973e15i		−	0.0196593i	0.999952	−	0.00982967i	$-0.00312893\pi$
$110$	−4.76390e16	−	4.12650e14i	−0.211897	−	0.00183545i
$111$		0			0
$112$	−1.30066e17	−	4.50821e15i	−0.496374	−	0.0172048i
$113$	−2.83148e16			−0.100195			−0.0500976	−	0.998744i	$-0.515953\pi$
$113$	−2.83148e16			−0.100195			−0.0500976	+	0.998744i	$0.515953\pi$
$114$		0			0
$115$		−	2.10325e17i		−	0.641149i
$116$	−8.04426e15	+	4.64307e17i	−0.0227821	+	1.31496i
$117$		0			0
$118$	1.03369e15	−	1.19336e17i	0.00253159	−	0.292264i
$119$	2.55628e17			0.582720
$120$		0			0
$121$	4.66297e17			0.922544
$122$	2.07197e15	−	2.39202e17i	0.00382229	−	0.441271i
$123$		0			0
$124$	3.62970e16	+	6.28856e14i	0.0583158	+	0.00101034i
$125$			7.20642e17i			1.08139i
$126$		0			0
$127$	−1.04849e17			−0.137478			−0.0687388	−	0.997635i	$-0.521898\pi$
$127$	−1.04849e17			−0.137478			−0.0687388	+	0.997635i	$0.521898\pi$
$128$	8.13741e17	+	4.93997e16i	0.998162	+	0.0605954i
$129$		0			0
$130$	1.14360e18	+	9.90590e15i	1.22958	+	0.0106506i
$131$			7.82237e17i			0.788011i	0.919108	+	0.394005i	$0.128911\pi$
$131$			7.82237e17i			0.788011i	−0.919108	+	0.394005i	$0.871089\pi$
$132$		0			0
$133$		−	7.63817e17i		−	0.676473i
$134$	1.14243e16	−	1.31890e18i	0.00949377	−	1.09602i
$135$		0			0
$136$	−1.60075e18	−	4.16055e16i	−1.17285	−	0.0304839i
$137$	−6.27442e17			−0.431965			−0.215983	−	0.976397i	$-0.569295\pi$
$137$	−6.27442e17			−0.431965			−0.215983	+	0.976397i	$0.569295\pi$
$138$		0			0
$139$			2.57262e17i			0.156585i	0.996930	+	0.0782924i	$0.0249468\pi$
$139$			2.57262e17i			0.156585i	−0.996930	+	0.0782924i	$0.975053\pi$
$140$	1.14390e16	−	6.60250e17i	0.00655090	−	0.378112i
$141$		0			0
$142$	−3.32722e18	−	2.88204e16i	−1.68900	−	0.0146302i
$143$	9.39811e17			0.449453
$144$		0			0
$145$	−2.35625e18			−1.00137
$146$	−1.97037e18	−	1.70674e16i	−0.789859	−	0.00684176i
$147$		0			0
$148$	−4.83370e16	+	2.78996e18i	−0.0172606	+	0.996262i
$149$		−	5.12586e18i		−	1.72855i	−0.503016	−	0.864277i	$-0.667776\pi$
$149$		−	5.12586e18i		−	1.72855i	0.503016	−	0.864277i	$-0.332224\pi$
$150$		0			0
$151$	−1.51399e18			−0.455848			−0.227924	−	0.973679i	$-0.573194\pi$
$151$	−1.51399e18			−0.455848			−0.227924	+	0.973679i	$0.573194\pi$
$152$	−1.24317e17	+	4.78304e18i	−0.0353884	+	1.36155i
$153$		0			0
$154$	4.70029e15	−	5.42633e17i	0.00119729	−	0.138223i
$155$			1.84198e17i			0.0444085i
$156$		0			0
$157$		−	6.31795e18i		−	1.36593i	−0.730450	−	0.682966i	$-0.760690\pi$
$157$		−	6.31795e18i		−	1.36593i	0.730450	−	0.682966i	$-0.239310\pi$
$158$	3.85193e18	+	3.33654e16i	0.789029	+	0.00683458i
$159$		0			0
$160$	−1.79092e17	+	4.13264e18i	−0.0329653	+	0.760690i
$161$	2.39571e18			0.418229
$162$		0			0
$163$			7.62696e18i			1.19883i	0.800439	+	0.599414i	$0.204600\pi$
$163$			7.62696e18i			1.19883i	−0.800439	+	0.599414i	$0.795400\pi$
$164$	−1.11106e19	−	1.92494e17i	−1.65792	−	0.0287240i
$165$		0			0
$166$	−2.94426e16	+	3.39905e18i	−0.00396330	+	0.457550i
$167$	−7.60518e18			−0.972791			−0.486396	−	0.873739i	$-0.661689\pi$
$167$	−7.60518e18			−0.972791			−0.486396	+	0.873739i	$0.661689\pi$
$168$		0			0
$169$	−1.39103e19			−1.60805
$170$	7.03757e16	−	8.12465e18i	0.00773762	−	0.893282i
$171$		0			0
$172$	3.13874e17	−	1.81165e19i	0.0312438	−	1.80336i
$173$			9.85927e18i			0.934228i	0.884197	+	0.467114i	$0.154706\pi$
$173$			9.85927e18i			0.934228i	−0.884197	+	0.467114i	$0.845294\pi$
$174$		0			0
$175$	−2.42893e18			−0.208734
$176$	−1.17751e17	+	3.39722e18i	−0.00964067	+	0.278141i
$177$		0			0
$178$	−8.11549e18	−	7.02964e16i	−0.603593	−	0.00522833i
$179$		−	1.05371e19i		−	0.747257i	−0.927578	−	0.373628i	$-0.878114\pi$
$179$		−	1.05371e19i		−	0.747257i	0.927578	−	0.373628i	$-0.121886\pi$
$180$		0			0
$181$			2.64819e19i			1.70876i	0.519649	+	0.854380i	$0.326063\pi$
$181$			2.64819e19i			1.70876i	−0.519649	+	0.854380i	$0.673937\pi$
$182$	−1.12833e17	+	1.30262e19i	−0.00694753	+	0.802069i
$183$		0			0
$184$	−1.50020e19	−	3.89920e17i	−0.841778	−	0.0218788i
$185$	−1.41584e19			−0.758672
$186$		0			0
$187$		−	6.67682e18i		−	0.326525i
$188$	−1.07655e19	−	1.86516e17i	−0.503146	−	0.00871716i
$189$		0			0
$190$	−2.42764e19	−	2.10283e17i	−1.03700	−	0.00898251i
$191$	−2.32908e19			−0.951484			−0.475742	−	0.879585i	$-0.657820\pi$
$191$	−2.32908e19			−0.951484			−0.475742	+	0.879585i	$0.657820\pi$
$192$		0			0
$193$	−2.61228e17			−0.00976748			−0.00488374	−	0.999988i	$-0.501555\pi$
$193$	−2.61228e17			−0.00976748			−0.00488374	+	0.999988i	$0.501555\pi$
$194$	−1.45158e19	−	1.25736e17i	−0.519431	−	0.00449931i
$195$		0			0
$196$	−2.29662e19	−	3.97896e17i	−0.753204	−	0.0130495i
$197$		−	6.46253e18i		−	0.202974i	−0.994837	−	0.101487i	$-0.967640\pi$
$197$		−	6.46253e18i		−	0.202974i	0.994837	−	0.101487i	$-0.0323600\pi$
$198$		0			0
$199$	−1.82250e19			−0.525311			−0.262655	−	0.964890i	$-0.584598\pi$
$199$	−1.82250e19			−0.525311			−0.262655	+	0.964890i	$0.584598\pi$
$200$	1.52100e19	+	3.95328e17i	0.420122	+	0.0109195i
$201$		0			0
$202$	1.19256e17	−	1.37677e19i	0.00302687	−	0.349442i
$203$		−	2.68388e19i		−	0.653202i
$204$		0			0
$205$		−	5.63836e19i		−	1.26254i
$206$	−7.51669e19	−	6.51096e17i	−1.61494	−	0.0139886i
$207$		0			0
$208$	2.82668e18	−	8.15522e19i	0.0559421	−	1.61398i
$209$	−1.99503e19			−0.379059
$210$		0			0
$211$			7.73859e19i			1.35600i	0.735060	+	0.678002i	$0.237154\pi$
$211$			7.73859e19i			1.35600i	−0.735060	+	0.678002i	$0.762846\pi$
$212$	−7.18362e17	+	4.14631e19i	−0.0120917	+	0.697923i
$213$		0			0
$214$	−5.27424e17	+	6.08893e19i	−0.00819677	+	0.946289i
$215$	9.19369e19			1.37329
$216$		0			0
$217$	−2.09811e18			−0.0289682
$218$	1.28248e16	−	1.48058e18i	0.000170283	−	0.0196586i
$219$		0			0
$220$	−1.72452e19	−	2.98779e17i	−0.211873	−	0.00367077i
$221$			1.60281e20i			1.89473i
$222$		0			0
$223$	−1.34556e20			−1.47337			−0.736685	−	0.676236i	$-0.763610\pi$
$223$	−1.34556e20			−1.47337			−0.736685	+	0.676236i	$0.763610\pi$
$224$	−4.70729e19	−	2.03995e18i	−0.496207	−	0.0215036i
$225$		0			0
$226$	−1.02507e19	−	8.87915e16i	−0.100192	−	0.000867860i
$227$		−	7.95558e19i		−	0.748949i	−0.927237	−	0.374474i	$-0.877823\pi$
$227$		−	7.95558e19i		−	0.748949i	0.927237	−	0.374474i	$-0.122177\pi$
$228$		0			0
$229$		−	3.46397e19i		−	0.302673i	−0.988482	−	0.151336i	$-0.951642\pi$
$229$		−	3.46397e19i		−	0.302673i	0.988482	−	0.151336i	$-0.0483576\pi$
$230$	6.59550e17	−	7.61429e19i	0.00555343	−	0.641125i
$231$		0			0
$232$	−4.36823e18	+	1.68066e20i	−0.0341710	+	1.31471i
$233$	1.21528e20			0.916538			0.458269	−	0.888814i	$-0.348470\pi$
$233$	1.21528e20			0.916538			0.458269	+	0.888814i	$0.348470\pi$
$234$		0			0
$235$		−	5.46325e19i		−	0.383155i
$236$	7.48445e17	−	4.31995e19i	0.00506300	−	0.292231i
$237$		0			0
$238$	9.25438e19	+	8.01616e17i	0.582698	+	0.00504733i
$239$	2.25849e19			0.137226			0.0686129	−	0.997643i	$-0.478143\pi$
$239$	2.25849e19			0.137226			0.0686129	+	0.997643i	$0.478143\pi$
$240$		0			0
$241$	2.85622e20			1.61677			0.808383	−	0.588657i	$-0.200343\pi$
$241$	2.85622e20			1.61677			0.808383	+	0.588657i	$0.200343\pi$
$242$	1.68811e20	+	1.46225e18i	0.922510	+	0.00799079i
$243$		0			0
$244$	1.50021e18	−	8.65905e19i	0.00764430	−	0.441222i
$245$		−	1.16548e20i		−	0.573578i
$246$		0			0
$247$	4.78920e20			2.19957
$248$	1.31384e19	+	3.41484e17i	0.0583048	+	0.00151541i
$249$		0			0
$250$	−2.25983e18	+	2.60890e20i	−0.00936670	+	1.08135i
$251$		−	1.47186e20i		−	0.589713i	−0.955541	−	0.294857i	$-0.904728\pi$
$251$		−	1.47186e20i		−	0.589713i	0.955541	−	0.294857i	$-0.0952719\pi$
$252$		0			0
$253$		−	6.25741e19i		−	0.234353i
$254$	−3.79579e19	−	3.28792e17i	−0.137472	−	0.00119079i
$255$		0			0
$256$	2.94440e20	+	2.04357e19i	0.997600	+	0.0692389i
$257$	3.49632e20			1.14599			0.572993	−	0.819560i	$-0.305782\pi$
$257$	3.49632e20			1.14599			0.572993	+	0.819560i	$0.305782\pi$
$258$		0			0
$259$		−	1.61271e20i		−	0.494890i
$260$	4.13982e20	+	7.17237e18i	1.22944	+	0.0213005i
$261$		0			0
$262$	−2.45299e18	+	2.83189e20i	−0.00682550	+	0.787981i
$263$	2.56287e20			0.690402			0.345201	−	0.938529i	$-0.387811\pi$
$263$	2.56287e20			0.690402			0.345201	+	0.938529i	$0.387811\pi$
$264$		0			0
$265$	−2.10415e20			−0.531481
$266$	2.39523e18	−	2.76521e20i	0.00585939	−	0.676448i
$267$		0			0
$268$	8.27177e18	−	4.77438e20i	0.0189868	−	1.09590i
$269$			6.85596e20i			1.52466i	0.647187	+	0.762331i	$0.275945\pi$
$269$			6.85596e20i			1.52466i	−0.647187	+	0.762331i	$0.724055\pi$
$270$		0			0
$271$	5.06814e20			1.05830			0.529151	−	0.848528i	$-0.322511\pi$
$271$	5.06814e20			1.05830			0.529151	+	0.848528i	$0.322511\pi$
$272$	−5.79382e20	−	2.00820e19i	−1.17254	−	0.0406416i
$273$		0			0
$274$	−2.27150e20	−	1.96757e18i	−0.431949	−	0.00374154i
$275$			6.34419e19i			0.116963i
$276$		0			0
$277$		−	5.87639e20i		−	1.01867i	−0.860569	−	0.509334i	$-0.829892\pi$
$277$		−	5.87639e20i		−	1.01867i	0.860569	−	0.509334i	$-0.170108\pi$
$278$	−8.06738e17	+	9.31352e19i	−0.00135629	+	0.156579i
$279$		0			0
$280$	6.21167e18	−	2.38991e20i	0.00982574	−	0.378041i
$281$	5.24336e20			0.804647			0.402324	−	0.915498i	$-0.368203\pi$
$281$	5.24336e20			0.804647			0.402324	+	0.915498i	$0.368203\pi$
$282$		0			0
$283$			7.51546e20i			1.08585i	0.839780	+	0.542927i	$0.182684\pi$
$283$			7.51546e20i			1.08585i	−0.839780	+	0.542927i	$0.817316\pi$
$284$	−1.20445e21	−	2.08674e19i	−1.68881	−	0.0292592i
$285$		0			0
$286$	3.40235e20	+	2.94712e18i	0.449436	+	0.00389302i
$287$	6.42237e20			0.823568
$288$		0			0
$289$	3.11465e20			0.376511
$290$	−8.53020e20	−	7.38887e18i	−1.00133	−	0.00867351i
$291$		0			0
$292$	−7.13271e20	−	1.23576e19i	−0.789770	−	0.0136830i
$293$		−	7.51033e20i		−	0.807764i	−0.914811	−	0.403882i	$-0.867661\pi$
$293$		−	7.51033e20i		−	0.807764i	0.914811	−	0.403882i	$-0.132339\pi$
$294$		0			0
$295$	2.19227e20			0.222539
$296$	−2.62481e19	+	1.00988e21i	−0.0258892	+	0.996075i
$297$		0			0
$298$	1.60740e19	−	1.85569e21i	0.0149722	−	1.72849i
$299$			1.50213e21i			1.35988i
$300$		0			0
$301$			1.04721e21i			0.895813i
$302$	−5.48104e20	−	4.74768e18i	−0.455831	−	0.00394841i
$303$		0			0
$304$	−6.00049e19	+	1.73119e21i	−0.0471804	+	1.36119i
$305$	4.39426e20			0.335998
$306$		0			0
$307$			5.89249e19i			0.0426209i	0.999773	+	0.0213105i	$0.00678384\pi$
$307$			5.89249e19i			0.0426209i	−0.999773	+	0.0213105i	$0.993216\pi$
$308$	3.40325e18	−	1.96432e20i	0.00239449	−	0.138207i
$309$		0			0
$310$	−5.77621e17	+	6.66844e19i	−0.000384653	+	0.0444069i
$311$	9.05717e20			0.586853			0.293427	−	0.955982i	$-0.405204\pi$
$311$	9.05717e20			0.586853			0.293427	+	0.955982i	$0.405204\pi$
$312$		0			0
$313$	2.51738e21			1.54462			0.772311	−	0.635245i	$-0.219101\pi$
$313$	2.51738e21			1.54462			0.772311	+	0.635245i	$0.219101\pi$
$314$	1.98122e19	−	2.28726e21i	0.0118313	−	1.36588i
$315$		0			0
$316$	1.39439e21	+	2.41583e19i	0.788940	+	0.0136686i
$317$		−	1.88675e21i		−	1.03923i	−0.854401	−	0.519614i	$-0.826076\pi$
$317$		−	1.88675e21i		−	1.03923i	0.854401	−	0.519614i	$-0.173924\pi$
$318$		0			0
$319$	−7.01010e20			−0.366019
$320$	−7.77953e19	+	1.49556e21i	−0.0395529	+	0.760376i
$321$		0			0
$322$	8.67307e20	+	7.51262e18i	0.418213	+	0.00362257i
$323$		−	3.40245e21i		−	1.59798i
$324$		0			0
$325$		−	1.52296e21i		−	0.678704i
$326$	−2.39171e19	+	2.76115e21i	−0.0103839	+	1.19878i
$327$		0			0
$328$	−4.02171e21	−	1.04529e20i	−1.65761	−	0.0430834i
$329$	6.22292e20			0.249936
$330$		0			0
$331$			1.03084e21i			0.393236i	0.980480	+	0.196618i	$0.0629959\pi$
$331$			1.03084e21i			0.393236i	−0.980480	+	0.196618i	$0.937004\pi$
$332$	−2.13179e19	+	1.23045e21i	−0.00792630	+	0.457498i
$333$		0			0
$334$	−2.75327e21	−	2.38488e19i	−0.972755	−	0.00842601i
$335$	2.42288e21			0.834549
$336$		0			0
$337$	2.14822e21			0.703435			0.351717	−	0.936106i	$-0.385598\pi$
$337$	2.14822e21			0.703435			0.351717	+	0.936106i	$0.385598\pi$
$338$	−5.03588e21	−	4.36208e19i	−1.60799	−	0.0139284i
$339$		0			0
$340$	5.09556e19	−	2.94110e21i	0.0154747	−	0.893181i
$341$			5.48012e19i			0.0162322i
$342$		0			0
$343$	3.08980e21			0.870824
$344$	1.70441e20	−	6.55764e21i	0.0468627	−	1.80302i
$345$		0			0
$346$	−3.09173e19	+	3.56930e21i	−0.00809199	+	0.934193i
$347$			4.67482e21i			1.19389i	0.802282	+	0.596945i	$0.203619\pi$
$347$			4.67482e21i			1.19389i	−0.802282	+	0.596945i	$0.796381\pi$
$348$		0			0
$349$			4.72313e21i			1.14872i	0.818603	+	0.574360i	$0.194749\pi$
$349$			4.72313e21i			1.14872i	−0.818603	+	0.574360i	$0.805251\pi$
$350$	−8.79335e20	−	7.61680e18i	−0.208726	−	0.00180798i
$351$		0			0
$352$	−5.32820e19	+	1.22951e21i	−0.0120495	+	0.278047i
$353$	4.29922e21			0.949084			0.474542	−	0.880233i	$-0.342614\pi$
$353$	4.29922e21			0.949084			0.474542	+	0.880233i	$0.342614\pi$
$354$		0			0
$355$		−	6.11228e21i		−	1.28606i
$356$	−2.93779e21	−	5.08981e19i	−0.603525	−	0.0104563i
$357$		0			0
$358$	3.30429e19	−	3.81469e21i	0.00647250	−	0.747229i
$359$	5.26993e21			1.00810			0.504048	−	0.863675i	$-0.331843\pi$
$359$	5.26993e21			1.00810			0.504048	+	0.863675i	$0.331843\pi$
$360$		0			0
$361$	−4.68613e21			−0.855073
$362$	−8.30436e19	+	9.58710e21i	−0.0148007	+	1.70870i
$363$		0			0
$364$	−8.16969e19	+	4.71546e21i	−0.0138945	+	0.801979i
$365$		−	3.61968e21i		−	0.601424i
$366$		0			0
$367$	−7.39416e21			−1.17281			−0.586405	−	0.810018i	$-0.699457\pi$
$367$	−7.39416e21			−1.17281			−0.586405	+	0.810018i	$0.699457\pi$
$368$	−5.42987e21	−	1.88205e20i	−0.841557	−	0.0291692i
$369$		0			0
$370$	−5.12569e21	−	4.43988e19i	−0.758643	−	0.00657137i
$371$		−	2.39674e21i		−	0.346691i
$372$		0			0
$373$			3.45714e21i			0.477740i	0.971052	+	0.238870i	$0.0767769\pi$
$373$			3.45714e21i			0.477740i	−0.971052	+	0.238870i	$0.923223\pi$
$374$	2.09376e19	−	2.41718e21i	0.00282825	−	0.326512i
$375$		0			0
$376$	−3.89681e21	−	1.01283e20i	−0.503052	−	0.0130749i
$377$	1.68282e22			2.12391
$378$		0			0
$379$		−	3.17249e21i		−	0.382795i	−0.981513	−	0.191398i	$-0.938698\pi$
$379$		−	3.17249e21i		−	0.382795i	0.981513	−	0.191398i	$-0.0613020\pi$
$380$	−8.78802e21	−	1.52255e20i	−1.03688	−	0.0179644i
$381$		0			0
$382$	−8.43187e21	−	7.30369e19i	−0.951448	−	0.00824145i
$383$	−3.27971e21			−0.361947			−0.180974	−	0.983488i	$-0.557925\pi$
$383$	−3.27971e21			−0.361947			−0.180974	+	0.983488i	$0.557925\pi$
$384$		0			0
$385$	9.96845e20			0.105247
$386$	−9.45711e19	−	8.19175e17i	−0.00976711	−	8.46028e-5i
$387$		0			0
$388$	−5.25471e21	−	9.10394e19i	−0.519372	−	0.00899829i
$389$			1.09936e22i			1.06308i	0.847032	+	0.531542i	$0.178387\pi$
$389$			1.09936e22i			1.06308i	−0.847032	+	0.531542i	$0.821613\pi$
$390$		0			0
$391$	1.06718e22			0.987947
$392$	−8.31309e21	−	2.16067e20i	−0.753062	−	0.0195730i
$393$		0			0
$394$	2.02656e19	−	2.33960e21i	0.00175809	−	0.202966i
$395$			7.07620e21i			0.600792i
$396$		0			0
$397$		−	9.01100e21i		−	0.732915i	−0.930435	−	0.366458i	$-0.880570\pi$
$397$		−	9.01100e21i		−	0.732915i	0.930435	−	0.366458i	$-0.119430\pi$
$398$	−6.59791e21	−	5.71511e19i	−0.525291	−	0.00455008i
$399$		0			0
$400$	5.50518e21	+	1.90815e20i	0.420012	+	0.0145580i
$401$	−1.05004e22			−0.784296			−0.392148	−	0.919902i	$-0.628268\pi$
$401$	−1.05004e22			−0.784296			−0.392148	+	0.919902i	$0.628268\pi$
$402$		0			0
$403$		−	1.31553e21i		−	0.0941910i
$404$	8.63473e19	−	4.98388e21i	0.00605351	−	0.349403i
$405$		0			0
$406$	8.41629e19	−	9.71633e21i	0.00565783	−	0.653177i
$407$	−4.21228e21			−0.277310
$408$		0			0
$409$	5.86541e21			0.370382			0.185191	−	0.982703i	$-0.440710\pi$
$409$	5.86541e21			0.370382			0.185191	+	0.982703i	$0.440710\pi$
$410$	1.76811e20	−	2.04123e22i	0.0109357	−	1.26249i
$411$		0			0
$412$	−2.72103e22	−	4.71426e20i	−1.61475	−	0.0279761i
$413$			2.49711e21i			0.145165i
$414$		0			0
$415$	−6.24423e21			−0.348393
$416$	1.27907e21	−	2.95151e22i	0.0699198	−	1.61343i
$417$		0			0
$418$	−7.22252e21	−	6.25615e19i	−0.379045	−	0.00328329i
$419$			5.02281e21i			0.258302i	0.991625	+	0.129151i	$0.0412252\pi$
$419$			5.02281e21i			0.258302i	−0.991625	+	0.129151i	$0.958775\pi$
$420$		0			0
$421$			1.55885e22i			0.769848i	0.922948	+	0.384924i	$0.125772\pi$
$421$			1.55885e22i			0.769848i	−0.922948	+	0.384924i	$0.874228\pi$
$422$	−2.42672e20	+	2.80156e22i	−0.0117453	+	1.35595i
$423$		0			0
$424$	−3.90088e20	+	1.50084e22i	−0.0181365	+	0.697792i
$425$	−1.08198e22			−0.493074
$426$		0			0
$427$			5.00528e21i			0.219175i
$428$	−3.81881e20	+	2.20418e22i	−0.0163929	+	0.946183i
$429$		0			0
$430$	3.32834e22	+	2.88301e20i	1.37324	+	0.0118950i
$431$	2.78561e22			1.12684			0.563421	−	0.826170i	$-0.309485\pi$
$431$	2.78561e22			1.12684			0.563421	+	0.826170i	$0.309485\pi$
$432$		0			0
$433$	−1.24470e21			−0.0484079			−0.0242040	−	0.999707i	$-0.507705\pi$
$433$	−1.24470e21			−0.0484079			−0.0242040	+	0.999707i	$0.507705\pi$
$434$	−7.59570e20	−	6.57940e18i	−0.0289671	−	0.000250913i
$435$		0			0
$436$	9.28581e18	−	5.35968e20i	0.000340553	−	0.0196564i
$437$		−	3.18872e22i		−	1.14690i
$438$		0			0
$439$	−2.09614e22			−0.725224			−0.362612	−	0.931940i	$-0.618115\pi$
$439$	−2.09614e22			−0.725224			−0.362612	+	0.931940i	$0.618115\pi$
$440$	−6.24227e21	−	1.62244e20i	−0.211834	−	0.00550581i
$441$		0			0
$442$	−5.02619e20	+	5.80257e22i	−0.0164116	+	1.89466i
$443$		−	1.11978e22i		−	0.358674i	−0.983788	−	0.179337i	$-0.942605\pi$
$443$		−	1.11978e22i		−	0.358674i	0.983788	−	0.179337i	$-0.0573952\pi$
$444$		0			0
$445$		−	1.49086e22i		−	0.459596i
$446$	−4.87127e22	−	4.21950e20i	−1.47332	−	0.0127619i
$447$		0			0
$448$	−1.70352e22	−	8.86128e20i	−0.496002	−	0.0258008i
$449$	1.44200e22			0.411975			0.205987	−	0.978555i	$-0.433959\pi$
$449$	1.44200e22			0.411975			0.205987	+	0.978555i	$0.433959\pi$
$450$		0			0
$451$		−	1.67748e22i		−	0.461483i
$452$	−3.71072e21	−	6.42895e19i	−0.100180	−	0.00173565i
$453$		0			0
$454$	2.49476e20	−	2.88012e22i	0.00648716	−	0.748921i
$455$	−2.39298e22			−0.610721
$456$		0			0
$457$	2.99851e22			0.737254			0.368627	−	0.929577i	$-0.379828\pi$
$457$	2.99851e22			0.737254			0.368627	+	0.929577i	$0.379828\pi$
$458$	1.08626e20	−	1.25405e22i	0.00262165	−	0.302661i
$459$		0			0
$460$	4.77548e20	−	2.75636e22i	0.0111064	−	0.641053i
$461$			4.32706e22i			0.987950i	0.869476	+	0.493975i	$0.164456\pi$
$461$			4.32706e22i			0.987950i	−0.869476	+	0.493975i	$0.835544\pi$
$462$		0			0
$463$	−1.79925e22			−0.395962			−0.197981	−	0.980206i	$-0.563438\pi$
$463$	−1.79925e22			−0.395962			−0.197981	+	0.980206i	$0.563438\pi$
$464$	−2.10844e21	+	6.08302e22i	−0.0455573	+	1.31437i
$465$		0			0
$466$	4.39961e22	+	3.81095e20i	0.916504	+	0.00793876i
$467$		−	5.53566e22i		−	1.13234i	−0.824289	−	0.566169i	$-0.808425\pi$
$467$		−	5.53566e22i		−	1.13234i	0.824289	−	0.566169i	$-0.191575\pi$
$468$		0			0
$469$			2.75979e22i			0.544386i
$470$	1.71320e20	−	1.97783e22i	0.00331877	−	0.383140i
$471$		0			0
$472$	4.06424e20	−	1.56370e22i	0.00759402	−	0.292176i
$473$	2.73523e22			0.501965
$474$		0			0
$475$			3.23295e22i			0.572404i
$476$	3.35007e22	+	5.80410e20i	0.582632	+	0.0100943i
$477$		0			0
$478$	8.17630e21	+	7.08232e19i	0.137221	+	0.00118861i
$479$	1.18108e22			0.194727			0.0973637	−	0.995249i	$-0.468959\pi$
$479$	1.18108e22			0.194727			0.0973637	+	0.995249i	$0.468959\pi$
$480$		0			0
$481$	1.01118e23			1.60915
$482$	1.03402e23	+	8.95672e20i	1.61670	+	0.0140039i
$483$		0			0
$484$	6.11094e22	+	1.05874e21i	0.922406	+	0.0159810i
$485$		−	2.66664e22i		−	0.395511i
$486$		0			0
$487$	2.16692e22			0.310347			0.155173	−	0.987887i	$-0.450406\pi$
$487$	2.16692e22			0.310347			0.155173	+	0.987887i	$0.450406\pi$
$488$	8.14649e20	−	3.13432e22i	0.0114657	−	0.441139i
$489$		0			0
$490$	3.65478e20	−	4.21933e22i	0.00496815	−	0.573557i
$491$			1.30265e23i			1.74034i	0.492749	+	0.870172i	$0.335992\pi$
$491$			1.30265e23i			1.74034i	−0.492749	+	0.870172i	$0.664008\pi$
$492$		0			0
$493$		−	1.19555e23i		−	1.54300i
$494$	1.73381e23	+	1.50183e21i	2.19949	+	0.0190520i
$495$		0			0
$496$	4.75537e21	+	1.64826e20i	0.0582895	+	0.00202038i
$497$	6.96220e22			0.838913
$498$		0			0
$499$			5.17276e22i			0.602376i	0.953565	+	0.301188i	$0.0973832\pi$
$499$			5.17276e22i			0.602376i	−0.953565	+	0.301188i	$0.902617\pi$
$500$	−1.63623e21	+	9.44418e22i	−0.0187327	+	1.08123i
$501$		0			0
$502$	4.61556e20	−	5.32852e22i	0.00510791	−	0.589691i
$503$	−1.07219e23			−1.16665			−0.583327	−	0.812237i	$-0.698249\pi$
$503$	−1.07219e23			−1.16665			−0.583327	+	0.812237i	$0.698249\pi$
$504$		0			0
$505$	2.52920e22			0.266076
$506$	1.96224e20	−	2.26534e22i	0.00202989	−	0.234344i
$507$		0			0
$508$	−1.37407e22	−	2.38062e20i	−0.137457	−	0.00238148i
$509$		−	1.48328e23i		−	1.45922i	−0.683861	−	0.729612i	$-0.739701\pi$
$509$		−	1.48328e23i		−	1.45922i	0.683861	−	0.729612i	$-0.260299\pi$
$510$		0			0
$511$	4.12300e22			0.392316
$512$	1.06530e23	+	8.32156e21i	0.996963	+	0.0778772i
$513$		0			0
$514$	1.26576e23	+	1.09640e21i	1.14594	+	0.00992617i
$515$		−	1.38086e23i		−	1.22966i
$516$		0			0
$517$		−	1.62538e22i		−	0.140051i
$518$	5.05725e20	−	5.83842e22i	0.00428658	−	0.494872i
$519$		0			0
$520$	1.49849e23	+	3.89477e21i	1.22921	+	0.0319487i
$521$	−7.01242e22			−0.565910			−0.282955	−	0.959133i	$-0.591315\pi$
$521$	−7.01242e22			−0.565910			−0.282955	+	0.959133i	$0.591315\pi$
$522$		0			0
$523$			2.14598e23i			1.67634i	0.545410	+	0.838169i	$0.316374\pi$
$523$			2.14598e23i			1.67634i	−0.545410	+	0.838169i	$0.683626\pi$
$524$	−1.77609e21	+	1.02514e23i	−0.0136505	+	0.787893i
$525$		0			0
$526$	9.27822e22	+	8.03680e20i	0.690376	+	0.00598005i
$527$	−9.34612e21			−0.0684291
$528$		0			0
$529$	−4.10359e22			−0.290932
$530$	−7.61757e22	−	6.59834e20i	−0.531461	−	0.00460352i
$531$		0			0
$532$	1.73426e21	−	1.00100e23i	0.0117183	−	0.676371i
$533$			4.02688e23i			2.67786i
$534$		0			0
$535$	−1.11857e23			−0.720536
$536$	4.49177e21	−	1.72819e23i	0.0284785	−	1.09570i
$537$		0			0
$538$	−2.14993e21	+	2.48203e23i	−0.0132061	+	1.52460i
$539$		−	3.46743e22i		−	0.209654i
$540$		0			0
$541$			1.34761e23i			0.789565i	0.918775	+	0.394783i	$0.129180\pi$
$541$			1.34761e23i			0.789565i	−0.918775	+	0.394783i	$0.870820\pi$
$542$	1.83479e23	+	1.58930e21i	1.05826	+	0.00916667i
$543$		0			0
$544$	−2.09688e23	−	9.08704e21i	−1.17215	−	0.0507963i
$545$	2.71991e21			0.0149687
$546$		0			0
$547$		−	2.17960e23i		−	1.16274i	−0.813638	−	0.581372i	$-0.802516\pi$
$547$		−	2.17960e23i		−	1.16274i	0.813638	−	0.581372i	$-0.197484\pi$
$548$	−8.22277e22	−	1.42462e21i	−0.431900	−	0.00748281i
$549$		0			0
$550$	−1.98945e20	+	2.29676e22i	−0.00101310	+	0.116959i
$551$	−3.57229e23			−1.79126
$552$		0			0
$553$	−8.06015e22			−0.391904
$554$	1.84276e21	−	2.12740e23i	0.00882337	−	1.01863i
$555$		0			0
$556$	−5.84119e20	+	3.37148e22i	−0.00271247	+	0.156561i
$557$		−	7.39588e22i		−	0.338237i	−0.985596	−	0.169118i	$-0.945908\pi$
$557$		−	7.39588e22i		−	0.338237i	0.985596	−	0.169118i	$-0.0540920\pi$
$558$		0			0
$559$	−6.56608e23			−2.91277
$560$	2.99822e21	−	8.65013e22i	0.0130998	−	0.377941i
$561$		0			0
$562$	1.89823e23	+	1.64424e21i	0.804617	+	0.00696960i
$563$		−	6.46778e21i		−	0.0270044i	−0.999909	−	0.0135022i	$-0.995702\pi$
$563$		−	6.46778e21i		−	0.0270044i	0.999909	−	0.0135022i	$-0.00429801\pi$
$564$		0			0
$565$		−	1.88310e22i		−	0.0762891i
$566$	−2.35675e21	+	2.72079e23i	−0.00940532	+	1.08581i
$567$		0			0
$568$	−4.35975e23	−	1.13315e22i	−1.68850	−	0.0438861i
$569$	−3.40211e23			−1.29806			−0.649029	−	0.760764i	$-0.724824\pi$
$569$	−3.40211e23			−1.29806			−0.649029	+	0.760764i	$0.724824\pi$
$570$		0			0
$571$		−	4.01054e23i		−	1.48524i	−0.669715	−	0.742619i	$-0.733584\pi$
$571$		−	4.01054e23i		−	1.48524i	0.669715	−	0.742619i	$-0.266416\pi$
$572$	1.23164e23	+	2.13386e21i	0.449385	+	0.00778575i
$573$		0			0
$574$	2.32506e23	+	2.01397e21i	0.823537	+	0.00713348i
$575$	−1.01401e23			−0.353888
$576$		0			0
$577$	1.92304e23			0.651619			0.325810	−	0.945435i	$-0.394363\pi$
$577$	1.92304e23			0.651619			0.325810	+	0.945435i	$0.394363\pi$
$578$	1.12758e23	+	9.76711e20i	0.376496	+	0.00326121i
$579$		0			0
$580$	−3.08791e23	−	5.34991e21i	−1.00122	−	0.0173464i
$581$		−	7.11249e22i		−	0.227261i
$582$		0			0
$583$	−6.26010e22			−0.194267
$584$	−2.58183e23	−	6.71050e21i	−0.789622	−	0.0205232i
$585$		0			0
$586$	2.35514e21	−	2.71893e23i	0.00699659	−	0.807733i
$587$		−	1.13316e23i		−	0.331793i	−0.986143	−	0.165896i	$-0.946948\pi$
$587$		−	1.13316e23i		−	0.331793i	0.986143	−	0.165896i	$-0.0530517\pi$
$588$		0			0
$589$			2.79262e22i			0.0794386i
$590$	7.93657e22	+	6.87466e20i	0.222531	+	0.00192757i
$591$		0			0
$592$	−1.26693e22	+	3.65521e23i	−0.0345159	+	0.995814i
$593$	−4.06278e23			−1.09108			−0.545542	−	0.838084i	$-0.683676\pi$
$593$	−4.06278e23			−1.09108			−0.545542	+	0.838084i	$0.683676\pi$
$594$		0			0
$595$			1.70008e23i			0.443685i
$596$	1.16384e22	−	6.71755e23i	0.0299433	−	1.72830i
$597$		0			0
$598$	−4.71047e21	+	5.43808e23i	−0.0117789	+	1.35983i
$599$	−5.15444e23			−1.27073			−0.635365	−	0.772212i	$-0.719150\pi$
$599$	−5.15444e23			−1.27073			−0.635365	+	0.772212i	$0.719150\pi$
$600$		0			0
$601$	3.97639e23			0.952918			0.476459	−	0.879197i	$-0.341920\pi$
$601$	3.97639e23			0.952918			0.476459	+	0.879197i	$0.341920\pi$
$602$	−3.28390e21	+	3.79115e23i	−0.00775925	+	0.895780i
$603$		0			0
$604$	−1.98413e23	−	3.43756e21i	−0.455780	−	0.00789653i
$605$			3.10115e23i			0.702429i
$606$		0			0
$607$	−6.76629e23			−1.49021			−0.745104	−	0.666948i	$-0.767600\pi$
$607$	−6.76629e23			−1.49021			−0.745104	+	0.666948i	$0.767600\pi$
$608$	−2.71521e22	+	6.26547e23i	−0.0589688	+	1.36073i
$609$		0			0
$610$	1.59083e23	+	1.37798e21i	0.335986	+	0.00291031i
$611$			3.90182e23i			0.812675i
$612$		0			0
$613$		−	6.69956e23i		−	1.35716i	−0.734525	−	0.678582i	$-0.762595\pi$
$613$		−	6.69956e23i		−	1.35716i	0.734525	−	0.678582i	$-0.237405\pi$
$614$	−1.84781e20	+	2.13323e22i	−0.000369169	+	0.0426193i
$615$		0			0
$616$	1.84804e21	−	7.11026e22i	0.00359150	−	0.138181i
$617$	2.38236e23			0.456649			0.228325	−	0.973585i	$-0.426675\pi$
$617$	2.38236e23			0.456649			0.228325	+	0.973585i	$0.426675\pi$
$618$		0			0
$619$			1.75944e23i			0.328099i	0.986452	+	0.164049i	$0.0524556\pi$
$619$			1.75944e23i			0.328099i	−0.986452	+	0.164049i	$0.947544\pi$
$620$	−4.18227e20	+	2.41396e22i	−0.000769276	+	0.0444019i
$621$		0			0
$622$	3.27892e23	+	2.84021e21i	0.586831	+	0.00508314i
$623$	1.69816e23			0.299799
$624$		0			0
$625$	−2.34643e23			−0.403114
$626$	9.11355e23	+	7.89416e21i	1.54456	+	0.0133790i
$627$		0			0
$628$	1.43451e22	−	8.27982e23i	0.0236617	−	1.36573i
$629$		−	7.18388e23i		−	1.16904i
$630$		0			0
$631$	−5.34532e23			−0.846689			−0.423344	−	0.905969i	$-0.639144\pi$
$631$	−5.34532e23			−0.846689			−0.423344	+	0.905969i	$0.639144\pi$
$632$	5.04729e23	+	1.31185e22i	0.788792	+	0.0205017i
$633$		0			0
$634$	5.91659e21	−	6.83051e23i	0.00900146	−	1.03919i
$635$		−	6.97306e22i		−	0.104676i
$636$		0			0
$637$			8.32378e23i			1.21657i
$638$	−2.53783e23	−	2.19827e21i	−0.366005	−	0.00317034i
$639$		0			0
$640$	−3.28537e22	+	5.41185e23i	−0.0461376	+	0.760005i
$641$	1.21663e24			1.68603			0.843017	−	0.537887i	$-0.180777\pi$
$641$	1.21663e24			1.68603			0.843017	+	0.537887i	$0.180777\pi$
$642$		0			0
$643$			2.18465e23i			0.294842i	0.989074	+	0.147421i	$0.0470972\pi$
$643$			2.18465e23i			0.294842i	−0.989074	+	0.147421i	$0.952903\pi$
$644$	3.13963e23	+	5.43951e21i	0.418166	+	0.00724486i
$645$		0			0
$646$	1.06696e22	−	1.23177e24i	0.0138412	−	1.59792i
$647$	−1.14703e24			−1.46855			−0.734275	−	0.678852i	$-0.762478\pi$
$647$	−1.14703e24			−1.46855			−0.734275	+	0.678852i	$0.762478\pi$
$648$		0			0
$649$	6.52226e22			0.0813426
$650$	4.77580e21	−	5.51350e23i	0.00587872	−	0.678678i
$651$		0			0
$652$	−1.73172e22	+	9.99531e23i	−0.0207670	+	1.19865i
$653$			1.50867e23i			0.178580i	0.996006	+	0.0892898i	$0.0284597\pi$
$653$			1.50867e23i			0.178580i	−0.996006	+	0.0892898i	$0.971540\pi$
$654$		0			0
$655$	−5.20234e23			−0.599995
$656$	−1.45563e24	−	5.04537e22i	−1.65718	−	0.0574395i
$657$		0			0
$658$	2.25285e23	+	1.95142e21i	0.249927	+	0.00216487i
$659$			1.33218e24i			1.45894i	0.684013	+	0.729470i	$0.260233\pi$
$659$			1.33218e24i			1.45894i	−0.684013	+	0.729470i	$0.739767\pi$
$660$		0			0
$661$			1.50165e24i			1.60272i	0.598183	+	0.801359i	$0.295889\pi$
$661$			1.50165e24i			1.60272i	−0.598183	+	0.801359i	$0.704111\pi$
$662$	−3.23257e21	+	3.73190e23i	−0.00340609	+	0.393221i
$663$		0			0
$664$	−1.15761e22	+	4.45386e23i	−0.0118887	+	0.457413i
$665$	5.07983e23			0.515069
$666$		0			0
$667$		−	1.12045e24i		−	1.10744i
$668$	−9.96677e23	−	1.72677e22i	−0.972645	−	0.0168514i
$669$		0			0
$670$	8.77145e23	+	7.59783e21i	0.834517	+	0.00722860i
$671$	1.30734e23			0.122814
$672$		0			0
$673$	1.95354e24			1.78935			0.894673	−	0.446722i	$-0.147409\pi$
$673$	1.95354e24			1.78935			0.894673	+	0.446722i	$0.147409\pi$
$674$	7.77708e23	+	6.73651e21i	0.703408	+	0.00609293i
$675$		0			0
$676$	−1.82298e24	−	3.15837e22i	−1.60781	−	0.0278558i
$677$		−	1.79219e24i		−	1.56092i	−0.625208	−	0.780458i	$-0.714986\pi$
$677$		−	1.79219e24i		−	1.56092i	0.625208	−	0.780458i	$-0.285014\pi$
$678$		0			0
$679$	3.03743e23			0.257997
$680$	2.76701e22	−	1.06459e24i	0.0232105	−	0.893014i
$681$		0			0
$682$	−1.71849e20	+	1.98394e22i	−0.000140598	+	0.0162316i
$683$		−	2.23745e24i		−	1.80791i	−0.427628	−	0.903955i	$-0.640651\pi$
$683$		−	2.23745e24i		−	1.80791i	0.427628	−	0.903955i	$-0.359349\pi$
$684$		0			0
$685$		−	4.17286e23i		−	0.328900i
$686$	1.11858e24	+	9.68919e21i	0.870791	+	0.00754280i
$687$		0			0
$688$	8.22678e22	−	2.37350e24i	0.0624782	−	1.80255i
$689$	1.50278e24			1.12728
$690$		0			0
$691$			1.07548e24i			0.787114i	0.919300	+	0.393557i	$0.128756\pi$
$691$			1.07548e24i			0.787114i	−0.919300	+	0.393557i	$0.871244\pi$
$692$	−2.23857e22	+	1.29208e24i	−0.0161834	+	0.934088i
$693$		0			0
$694$	−1.46596e22	+	1.69240e24i	−0.0103411	+	1.19384i
$695$	−1.71094e23			−0.119224
$696$		0			0
$697$	2.86087e24			1.94545
$698$	−1.48111e22	+	1.70989e24i	−0.00994985	+	1.14868i
$699$		0			0
$700$	−3.18317e23	−	5.51495e21i	−0.208702	−	0.00361583i
$701$			4.83049e23i			0.312887i	0.987687	+	0.156444i	$0.0500030\pi$
$701$			4.83049e23i			0.312887i	−0.987687	+	0.156444i	$0.949997\pi$
$702$		0			0
$703$	−2.14654e24			−1.35712
$704$	−2.31450e22	+	4.44946e23i	−0.0144574	+	0.277933i
$705$		0			0
$706$	1.55642e24	+	1.34818e22i	0.949048	+	0.00822066i
$707$			2.88089e23i			0.173565i
$708$		0			0
$709$		−	6.46817e23i		−	0.380442i	−0.981741	−	0.190221i	$-0.939080\pi$
$709$		−	6.46817e23i		−	0.380442i	0.981741	−	0.190221i	$-0.0609204\pi$
$710$	1.91673e22	−	2.21280e24i	0.0111395	−	1.28601i
$711$		0			0
$712$	−1.06339e24	−	2.76389e22i	−0.603412	−	0.0156834i
$713$	−8.75904e22			−0.0491129
$714$		0			0
$715$			6.25030e23i			0.342215i
$716$	2.39247e22	−	1.38091e24i	0.0129445	−	0.747145i
$717$		0			0
$718$	1.90785e24	+	1.65258e22i	1.00806	+	0.00873181i
$719$	2.08660e24			1.08954			0.544770	−	0.838586i	$-0.316617\pi$
$719$	2.08660e24			1.08954			0.544770	+	0.838586i	$0.316617\pi$
$720$		0			0
$721$	1.57286e24			0.802124
$722$	−1.69650e24	−	1.46951e22i	−0.855041	−	0.00740637i
$723$		0			0
$724$	−6.01277e22	+	3.47051e24i	−0.0296003	+	1.70850i
$725$			1.13599e24i			0.552713i
$726$		0			0
$727$	2.50710e24			1.19160			0.595799	−	0.803134i	$-0.296836\pi$
$727$	2.50710e24			1.19160			0.595799	+	0.803134i	$0.296836\pi$
$728$	−4.43634e22	+	1.70686e24i	−0.0208405	+	0.801828i
$729$		0			0
$730$	1.13508e22	−	1.31041e24i	0.00520934	−	0.601401i
$731$			4.66482e24i			2.11611i
$732$		0			0
$733$		−	2.50202e24i		−	1.10894i	−0.832205	−	0.554469i	$-0.812921\pi$
$733$		−	2.50202e24i		−	1.10894i	0.832205	−	0.554469i	$-0.187079\pi$
$734$	−2.67687e24	−	2.31871e22i	−1.17277	−	0.0101585i
$735$		0			0
$736$	−1.96516e24	−	8.51623e22i	−0.841272	−	0.0364574i
$737$	7.20836e23			0.305044
$738$		0			0
$739$		−	1.98150e24i		−	0.819440i	−0.912211	−	0.409720i	$-0.865626\pi$
$739$		−	1.98150e24i		−	0.819440i	0.912211	−	0.409720i	$-0.134374\pi$
$740$	−1.85549e24	−	3.21469e22i	−0.758558	−	0.0131423i
$741$		0			0
$742$	7.51585e21	−	8.67680e23i	0.00300293	−	0.346678i
$743$	1.48113e24			0.585043			0.292521	−	0.956259i	$-0.405506\pi$
$743$	1.48113e24			0.585043			0.292521	+	0.956259i	$0.405506\pi$
$744$		0			0
$745$	3.40900e24			1.31613
$746$	−1.08411e22	+	1.25157e24i	−0.00413803	+	0.477722i
$747$		0			0
$748$	1.51599e22	−	8.75013e23i	0.00565629	−	0.326476i
$749$		−	1.27411e24i		−	0.470013i
$750$		0			0
$751$	−5.06055e24			−1.82498			−0.912490	−	0.409100i	$-0.865843\pi$
$751$	−5.06055e24			−1.82498			−0.912490	+	0.409100i	$0.865843\pi$
$752$	−1.41043e24	−	4.88868e22i	−0.502919	−	0.0174317i
$753$		0			0
$754$	6.09222e24	+	5.27709e22i	2.12383	+	0.0183966i
$755$		−	1.00690e24i		−	0.347085i
$756$		0			0
$757$			1.15475e23i			0.0389200i	0.999811	+	0.0194600i	$0.00619470\pi$
$757$			1.15475e23i			0.0389200i	−0.999811	+	0.0194600i	$0.993805\pi$
$758$	9.94849e21	−	1.14852e24i	0.00331565	−	0.382781i
$759$		0			0
$760$	−3.18101e24	−	8.26782e22i	−1.03669	−	0.0269448i
$761$	3.07347e24			0.990510			0.495255	−	0.868748i	$-0.335075\pi$
$761$	3.07347e24			0.990510			0.495255	+	0.868748i	$0.335075\pi$
$762$		0			0
$763$			3.09811e22i			0.00976425i
$764$	−3.05232e24	−	5.28824e22i	−0.951341	−	0.0164823i
$765$		0			0
$766$	−1.18734e24	−	1.02847e22i	−0.361934	−	0.00313507i
$767$	−1.56571e24			−0.472008
$768$		0			0
$769$	1.56828e24			0.462434			0.231217	−	0.972902i	$-0.425729\pi$
$769$	1.56828e24			0.462434			0.231217	+	0.972902i	$0.425729\pi$
$770$	3.60883e23	+	3.12597e21i	0.105243	+	0.000911619i
$771$		0			0
$772$	−3.42345e22	−	5.93124e20i	−0.00976601	−	0.000169199i
$773$			3.06812e24i			0.865659i	0.901476	+	0.432830i	$0.142485\pi$
$773$			3.06812e24i			0.865659i	−0.901476	+	0.432830i	$0.857515\pi$
$774$		0			0
$775$	8.88051e22			0.0245117
$776$	−1.90205e24	−	4.94366e22i	−0.519275	−	0.0134966i
$777$		0			0
$778$	−3.44744e22	+	3.97995e24i	−0.00920810	+	1.06304i
$779$		−	8.54827e24i		−	2.25845i
$780$		0			0
$781$		−	1.81847e24i		−	0.470082i
$782$	3.86345e24	+	3.34652e22i	0.987910	+	0.00855729i
$783$		0			0
$784$	−3.00887e24	−	1.04291e23i	−0.752865	−	0.0260951i
$785$	4.20181e24			1.04003
$786$		0			0
$787$		−	7.03196e23i		−	0.170330i	−0.996367	−	0.0851650i	$-0.972858\pi$
$787$		−	7.03196e23i		−	0.170330i	0.996367	−	0.0851650i	$-0.0271417\pi$
$788$	1.46733e22	−	8.46930e23i	0.00351606	−	0.202943i
$789$		0			0
$790$	−2.21900e22	+	2.56176e24i	−0.00520387	+	0.600770i
$791$	2.14495e23			0.0497642
$792$		0			0
$793$	−3.13835e24			−0.712656
$794$	2.82573e22	−	3.26221e24i	0.00634828	−	0.732888i
$795$		0			0
$796$	−2.38843e24	−	4.13803e22i	−0.525232	−	0.00909981i
$797$			4.69599e24i			1.02172i	0.859664	+	0.510859i	$0.170673\pi$
$797$			4.69599e24i			1.02172i	−0.859664	+	0.510859i	$0.829327\pi$
$798$		0			0
$799$	2.77202e24			0.590403
$800$	1.99241e24	+	8.63434e22i	0.419870	+	0.0181955i
$801$		0			0
$802$	−3.80142e24	−	3.29279e22i	−0.784267	−	0.00679333i
$803$		−	1.07690e24i		−	0.219832i
$804$		0			0
$805$			1.59329e24i			0.318441i
$806$	4.12534e21	−	4.76256e23i	0.000815852	−	0.0941874i
$807$		0			0
$808$	4.68887e22	−	1.80402e24i	0.00907970	−	0.349337i
$809$	4.37783e24			0.838873			0.419436	−	0.907785i	$-0.362228\pi$
$809$	4.37783e24			0.838873			0.419436	+	0.907785i	$0.362228\pi$
$810$		0			0
$811$			8.61180e24i			1.61591i	0.589245	+	0.807954i	$0.299425\pi$
$811$			8.61180e24i			1.61591i	−0.589245	+	0.807954i	$0.700575\pi$
$812$	6.09382e22	−	3.51729e24i	0.0113152	−	0.653104i
$813$		0			0
$814$	−1.52495e24	−	1.32091e22i	−0.277299	−	0.00240197i
$815$	−5.07238e24			−0.912793
$816$		0			0
$817$	1.39385e25			2.45656
$818$	2.12343e24	+	1.83931e22i	0.370369	+	0.00320814i
$819$		0			0
$820$	1.28020e23	−	7.38920e24i	0.0218706	−	1.26235i
$821$			4.09648e24i			0.692619i	0.938120	+	0.346309i	$0.112565\pi$
$821$			4.09648e24i			0.692619i	−0.938120	+	0.346309i	$0.887435\pi$
$822$		0			0
$823$	−4.02308e24			−0.666284			−0.333142	−	0.942877i	$-0.608109\pi$
$823$	−4.02308e24			−0.666284			−0.333142	+	0.942877i	$0.608109\pi$
$824$	−9.84932e24	−	2.55996e23i	−1.61445	−	0.0419616i
$825$		0			0
$826$	−7.83059e21	+	9.04015e23i	−0.00125737	+	0.145160i
$827$			6.80277e24i			1.08116i	0.841294	+	0.540579i	$0.181795\pi$
$827$			6.80277e24i			1.08116i	−0.841294	+	0.540579i	$0.818205\pi$
$828$		0			0
$829$			9.06827e24i			1.41192i	0.708251	+	0.705961i	$0.249485\pi$
$829$			9.06827e24i			1.41192i	−0.708251	+	0.705961i	$0.750515\pi$
$830$	−2.26057e24	−	1.95810e22i	−0.348380	−	0.00301767i
$831$		0			0
$832$	5.55610e23	−	1.06812e25i	0.0838922	−	1.61277i
$833$	5.91357e24			0.883827
$834$		0			0
$835$		−	5.05790e24i		−	0.740687i
$836$	−2.61454e24	−	4.52977e22i	−0.379002	−	0.00656633i
$837$		0			0
$838$	−1.57509e22	+	1.81838e24i	−0.00223733	+	0.258292i
$839$	2.26281e24			0.318179			0.159090	−	0.987264i	$-0.449144\pi$
$839$	2.26281e24			0.318179			0.159090	+	0.987264i	$0.449144\pi$
$840$		0			0
$841$	−5.29508e24			−0.729637
$842$	−4.88833e22	+	5.64341e24i	−0.00666818	+	0.769819i
$843$		0			0
$844$	−1.75707e23	+	1.01416e25i	−0.0234897	+	1.35580i
$845$		−	9.25117e24i		−	1.22438i
$846$		0			0
$847$	−3.53237e24			−0.458202
$848$	−1.88286e23	+	5.43221e24i	−0.0241798	+	0.697609i
$849$		0			0
$850$	−3.91703e24	−	3.39293e22i	−0.493055	−	0.00427085i
$851$		−	6.73262e24i		−	0.839040i
$852$		0			0
$853$		−	9.22743e24i		−	1.12723i	−0.826036	−	0.563617i	$-0.809409\pi$
$853$		−	9.22743e24i		−	1.12723i	0.826036	−	0.563617i	$-0.190591\pi$
$854$	−1.56959e22	+	1.81204e24i	−0.00189843	+	0.219167i
$855$		0			0
$856$	−2.07371e23	+	7.97849e24i	−0.0245878	+	0.946005i
$857$	−4.23968e24			−0.497733			−0.248867	−	0.968538i	$-0.580058\pi$
$857$	−4.23968e24			−0.497733			−0.248867	+	0.968538i	$0.580058\pi$
$858$		0			0
$859$		−	2.28165e24i		−	0.262608i	−0.991342	−	0.131304i	$-0.958084\pi$
$859$		−	2.28165e24i		−	0.262608i	0.991342	−	0.131304i	$-0.0419164\pi$
$860$	1.20485e25	+	2.08745e23i	1.37309	+	0.0237891i
$861$		0			0
$862$	1.00846e25	+	8.73528e22i	1.12680	+	0.00976034i
$863$	1.03258e25			1.14244			0.571220	−	0.820797i	$-0.306470\pi$
$863$	1.03258e25			1.14244			0.571220	+	0.820797i	$0.306470\pi$
$864$		0			0
$865$	−6.55700e24			−0.711325
$866$	−4.50612e23	−	3.90320e21i	−0.0484061	−	0.000419294i
$867$		0			0
$868$	−2.74963e23	−	4.76381e21i	−0.0289638	−	0.000501807i
$869$			2.10525e24i			0.219602i
$870$		0			0
$871$	−1.73041e25			−1.77009
$872$	5.04242e21	−	1.94005e23i	0.000510798	−	0.0196527i
$873$		0			0
$874$	9.99940e22	−	1.15440e25i	0.00993406	−	1.14685i
$875$		−	5.45912e24i		−	0.537099i
$876$		0			0
$877$		−	1.49582e24i		−	0.144338i	−0.997392	−	0.0721692i	$-0.977008\pi$
$877$		−	1.49582e24i		−	0.144338i	0.997392	−	0.0721692i	$-0.0229921\pi$
$878$	−7.58855e24	−	6.57321e22i	−0.725196	−	0.00628166i
$879$		0			0
$880$	−2.25935e24	−	7.83114e22i	−0.211778	−	0.00734044i
$881$	−9.02128e24			−0.837477			−0.418739	−	0.908107i	$-0.637528\pi$
$881$	−9.02128e24			−0.837477			−0.418739	+	0.908107i	$0.637528\pi$
$882$		0			0
$883$			5.61859e24i			0.511636i	0.966725	+	0.255818i	$0.0823448\pi$
$883$			5.61859e24i			0.511636i	−0.966725	+	0.255818i	$0.917655\pi$
$884$	−3.63922e23	+	2.10052e25i	−0.0328219	+	1.89445i
$885$		0			0
$886$	3.51146e22	−	4.05387e24i	0.00310672	−	0.358660i
$887$	−1.48729e25			−1.30330			−0.651649	−	0.758521i	$-0.725922\pi$
$887$	−1.48729e25			−1.30330			−0.651649	+	0.758521i	$0.725922\pi$
$888$		0			0
$889$	7.94267e23			0.0682813
$890$	4.67512e22	−	5.39728e24i	0.00398087	−	0.459578i
$891$		0			0
$892$	−1.76339e25	−	3.05513e23i	−1.47315	−	0.0255228i
$893$		−	8.28280e24i		−	0.685393i
$894$		0			0
$895$	7.00778e24			0.568964
$896$	−6.16438e24	−	3.74221e23i	−0.495760	−	0.0300961i
$897$		0			0
$898$	5.22039e24	+	4.52191e22i	0.411959	+	0.00356839i
$899$			9.81264e23i			0.0767059i
$900$		0			0
$901$		−	1.06764e25i		−	0.818959i
$902$	5.26034e22	−	6.07288e24i	0.00399722	−	0.461466i
$903$		0			0
$904$	−1.34317e24	−	3.49107e22i	−0.100161	−	0.00260332i
$905$	−1.76120e25			−1.30106
$906$		0			0
$907$			1.26650e25i			0.918215i	0.888381	+	0.459107i	$0.151831\pi$
$907$			1.26650e25i			0.918215i	−0.888381	+	0.459107i	$0.848169\pi$
$908$	1.80633e23	−	1.04260e25i	0.0129738	−	0.748836i
$909$		0			0
$910$	−8.66321e24	−	7.50407e22i	−0.610698	−	0.00528987i
$911$	−2.22052e25			−1.55077			−0.775387	−	0.631487i	$-0.782445\pi$
$911$	−2.22052e25			−1.55077			−0.775387	+	0.631487i	$0.782445\pi$
$912$		0			0
$913$	−1.85773e24			−0.127345
$914$	1.08553e25	+	9.40291e22i	0.737227	+	0.00638586i
$915$		0			0
$916$	7.86503e22	−	4.53962e24i	0.00524311	−	0.302627i
$917$		−	5.92572e24i		−	0.391383i
$918$		0			0
$919$	−2.34055e25			−1.51753			−0.758763	−	0.651367i	$-0.774196\pi$
$919$	−2.34055e25			−1.51753			−0.758763	+	0.651367i	$0.774196\pi$
$920$	2.59320e23	−	9.97721e24i	0.0166586	−	0.640933i
$921$		0			0
$922$	−1.35691e23	+	1.56650e25i	−0.00855731	+	0.987912i
$923$			4.36536e25i			2.72775i
$924$		0			0
$925$			6.82599e24i			0.418756i
$926$	−6.51374e24	−	5.64221e22i	−0.395947	−	0.00342970i
$927$		0			0
$928$	−9.54063e23	+	2.20155e25i	−0.0569402	+	1.31392i
$929$	−6.30561e24			−0.372901			−0.186450	−	0.982464i	$-0.559698\pi$
$929$	−6.30561e24			−0.372901			−0.186450	+	0.982464i	$0.559698\pi$
$930$		0			0
$931$		−	1.76697e25i		−	1.02603i
$932$	1.59265e25	+	2.75932e23i	0.916401	+	0.0158769i
$933$		0			0
$934$	1.73591e23	−	2.00405e25i	0.00980795	−	1.13229i
$935$	4.44048e24			0.248617
$936$		0			0
$937$	−8.24230e23			−0.0453171			−0.0226586	−	0.999743i	$-0.507213\pi$
$937$	−8.24230e23			−0.0453171			−0.0226586	+	0.999743i	$0.507213\pi$
$938$	−8.65432e22	+	9.99113e24i	−0.00471529	+	0.544365i
$939$		0			0
$940$	1.24044e23	−	7.15972e24i	0.00663728	−	0.383097i
$941$		−	6.73452e24i		−	0.357104i	−0.983930	−	0.178552i	$-0.942859\pi$
$941$		−	6.73452e24i		−	0.357104i	0.983930	−	0.178552i	$-0.0571413\pi$
$942$		0			0
$943$	2.68116e25			1.39628
$944$	1.96171e23	−	5.65970e24i	0.0101245	−	0.292100i
$945$		0			0
$946$	9.90221e24	+	8.57730e22i	0.501947	+	0.00434787i
$947$		−	2.19407e25i		−	1.10224i	−0.834426	−	0.551119i	$-0.814201\pi$
$947$		−	2.19407e25i		−	1.10224i	0.834426	−	0.551119i	$-0.185799\pi$
$948$		0			0
$949$			2.58515e25i			1.27563i
$950$	−1.01381e23	+	1.17041e25i	−0.00495798	+	0.572383i
$951$		0			0
$952$	1.21263e25	+	3.15177e23i	0.582523	+	0.0151405i
$953$	−1.04120e25			−0.495727			−0.247864	−	0.968795i	$-0.579728\pi$
$953$	−1.04120e25			−0.495727			−0.247864	+	0.968795i	$0.579728\pi$
$954$		0			0
$955$		−	1.54898e25i		−	0.724464i
$956$	2.95980e24	+	5.12795e22i	0.137205	+	0.00237712i
$957$		0			0
$958$	4.27580e24	+	3.70370e22i	0.194720	+	0.00168667i
$959$	4.75310e24			0.214545
$960$		0			0
$961$	−2.24734e25			−0.996598
$962$	3.66074e25	+	3.17093e23i	1.60909	+	0.0139380i
$963$		0			0
$964$	3.74315e25	+	6.48512e23i	1.61652	+	0.0280068i
$965$		−	1.73732e23i		−	0.00743700i
$966$		0			0
$967$	2.11036e25			0.887630			0.443815	−	0.896118i	$-0.353625\pi$
$967$	2.11036e25			0.887630			0.443815	+	0.896118i	$0.353625\pi$
$968$	2.21198e25	+	5.74921e23i	0.922233	+	0.0239700i
$969$		0			0
$970$	8.36221e22	−	9.65389e24i	0.00342579	−	0.395497i
$971$			6.24704e24i			0.253694i	0.991922	+	0.126847i	$0.0404858\pi$
$971$			6.24704e24i			0.253694i	−0.991922	+	0.126847i	$0.959514\pi$
$972$		0			0
$973$		−	1.94885e24i		−	0.0777713i
$974$	7.84480e24	+	6.79517e22i	0.310335	+	0.00268812i
$975$		0			0
$976$	3.93211e23	−	1.13445e25i	0.0152863	−	0.441023i
$977$	1.86564e25			0.718992			0.359496	−	0.933147i	$-0.382949\pi$
$977$	1.86564e25			0.718992			0.359496	+	0.933147i	$0.382949\pi$
$978$		0			0
$979$		−	4.43547e24i		−	0.167991i
$980$	2.64625e23	−	1.52739e25i	0.00993593	−	0.573492i
$981$		0			0
$982$	−4.08493e23	+	4.71592e25i	−0.0150743	+	1.74028i
$983$	2.39881e25			0.877589			0.438794	−	0.898588i	$-0.355406\pi$
$983$	2.39881e25			0.877589			0.438794	+	0.898588i	$0.355406\pi$
$984$		0			0
$985$	4.29797e24			0.154545
$986$	3.74907e23	−	4.32817e25i	0.0133650	−	1.54295i
$987$		0			0
$988$	6.27635e25	+	1.08740e24i	2.19924	+	0.0381026i
$989$			4.37180e25i			1.51877i
$990$		0			0
$991$	2.85777e25			0.975889			0.487945	−	0.872875i	$-0.337747\pi$
$991$	2.85777e25			0.975889			0.487945	+	0.872875i	$0.337747\pi$
$992$	1.72105e24	+	7.45834e22i	0.0582698	+	0.00252518i
$993$		0			0
$994$	2.52049e25	+	2.18325e23i	0.838882	+	0.00726640i
$995$		−	1.21207e25i		−	0.399974i
$996$		0			0
$997$			1.00050e25i			0.324571i	0.986744	+	0.162285i	$0.0518865\pi$
$997$			1.00050e25i			0.324571i	−0.986744	+	0.162285i	$0.948113\pi$
$998$	−1.62211e23	+	1.87267e25i	−0.00521759	+	0.602353i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.18.d.b.37.16		16
3.2	odd	2		8.18.b.a.5.1	✓	16
8.5	even	2	inner	72.18.d.b.37.15		16
12.11	even	2		32.18.b.a.17.3		16
24.5	odd	2		8.18.b.a.5.2	yes	16
24.11	even	2		32.18.b.a.17.14		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.18.b.a.5.1	✓	16	3.2	odd	2
8.18.b.a.5.2	yes	16	24.5	odd	2
32.18.b.a.17.3		16	12.11	even	2
32.18.b.a.17.14		16	24.11	even	2
72.18.d.b.37.15		16	8.5	even	2	inner
72.18.d.b.37.16		16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	72.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(362.025 + 3.13586i) q^{2} +(131052. + 2270.52i) q^{4} +665059. i q^{5} -7.57536e6 q^{7} +(4.74371e7 + 1.23295e6i) q^{8} +O(q^{10})\)	\(q+(362.025 + 3.13586i) q^{2} +(131052. + 2270.52i) q^{4} +665059. i q^{5} -7.57536e6 q^{7} +(4.74371e7 + 1.23295e6i) q^{8} +(-2.08553e6 + 2.40768e8i) q^{10} +1.97863e8i q^{11} -4.74981e9i q^{13} +(-2.74247e9 - 2.37553e7i) q^{14} +(1.71696e10 + 5.95115e8i) q^{16} -3.37447e10 q^{17} +1.00829e11i q^{19} +(-1.51003e9 + 8.71575e10i) q^{20} +(-6.20471e8 + 7.16313e10i) q^{22} -3.16250e11 q^{23} +3.20636e11 q^{25} +(1.48948e10 - 1.71955e12i) q^{26} +(-9.92769e11 - 1.72000e10i) q^{28} +3.54291e12i q^{29} +2.76965e11 q^{31} +(6.21394e12 + 2.69288e11i) q^{32} +(-1.22164e13 - 1.05819e11i) q^{34} -5.03806e12i q^{35} +2.12889e13i q^{37} +(-3.16187e11 + 3.65027e13i) q^{38} +(-8.19983e11 + 3.15485e13i) q^{40} -8.47798e13 q^{41} -1.38239e14i q^{43} +(-4.49252e11 + 2.59304e13i) q^{44} +(-1.14490e14 - 9.91717e11i) q^{46} -8.21469e13 q^{47} -1.75244e14 q^{49} +(1.16078e14 + 1.00547e12i) q^{50} +(1.07846e13 - 6.22474e14i) q^{52} +3.16386e14i q^{53} -1.31590e14 q^{55} +(-3.59353e14 - 9.34003e12i) q^{56} +(-1.11101e13 + 1.28262e15i) q^{58} -3.29635e14i q^{59} -6.60732e14i q^{61} +(1.00268e14 + 8.68526e11i) q^{62} +(2.24876e15 + 1.16975e14i) q^{64} +3.15891e15 q^{65} -3.64311e15i q^{67} +(-4.42232e15 - 7.66181e13i) q^{68} +(1.57987e13 - 1.82390e15i) q^{70} -9.19058e15 q^{71} -5.44264e15 q^{73} +(-6.67591e13 + 7.70712e15i) q^{74} +(-2.28935e14 + 1.32139e16i) q^{76} -1.49888e15i q^{77} +1.06400e16 q^{79} +(-3.95786e14 + 1.14188e16i) q^{80} +(-3.06924e16 - 2.65858e14i) q^{82} +9.38898e15i q^{83} -2.24422e16i q^{85} +(4.33498e14 - 5.00459e16i) q^{86} +(-2.43955e14 + 9.38604e15i) q^{88} -2.24169e16 q^{89} +3.59815e16i q^{91} +(-4.14453e16 - 7.18053e14i) q^{92} +(-2.97392e16 - 2.57601e14i) q^{94} -6.70573e16 q^{95} -4.00962e16 q^{97} +(-6.34429e16 - 5.49543e14i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 270 q^{2} - 27436 q^{4} + 11529600 q^{7} - 24334920 q^{8}+O(q^{10}) \) 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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