LMFDB - Embedded newform 72.18.d.b.37.1

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			37.1
Root			$0.500000 + 58156.1i$ of defining polynomial
Character	$\chi$	$=$	72.37
Dual form			72.18.d.b.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-351.815 - 85.4288i) q^{2} +(116476. + 60110.3i) q^{4} -465248. i q^{5} +2.24795e7 q^{7} +(-3.58428e7 - 3.10981e7i) q^{8} +O(q^{10})$	\(q+(-351.815 - 85.4288i) q^{2} +(116476. + 60110.3i) q^{4} -465248. i q^{5} +2.24795e7 q^{7} +(-3.58428e7 - 3.10981e7i) q^{8} +(-3.97456e7 + 1.63681e8i) q^{10} +6.06148e8i q^{11} -2.12768e9i q^{13} +(-7.90864e9 - 1.92040e9i) q^{14} +(9.95338e9 + 1.40028e10i) q^{16} +5.45139e9 q^{17} -5.72346e9i q^{19} +(2.79662e10 - 5.41902e10i) q^{20} +(5.17825e10 - 2.13252e11i) q^{22} +1.30247e11 q^{23} +5.46483e11 q^{25} +(-1.81765e11 + 7.48551e11i) q^{26} +(2.61832e12 + 1.35125e12i) q^{28} -4.23568e11i q^{29} +3.83783e12 q^{31} +(-2.30551e12 - 5.77670e12i) q^{32} +(-1.91788e12 - 4.65706e11i) q^{34} -1.04586e13i q^{35} -2.39674e13i q^{37} +(-4.88948e11 + 2.01360e12i) q^{38} +(-1.44683e13 + 1.66758e13i) q^{40} +5.79528e12 q^{41} +4.00069e13i q^{43} +(-3.64357e13 + 7.06016e13i) q^{44} +(-4.58229e13 - 1.11268e13i) q^{46} +1.56837e14 q^{47} +2.72699e14 q^{49} +(-1.92261e14 - 4.66854e13i) q^{50} +(1.27896e14 - 2.47824e14i) q^{52} -6.45318e14i q^{53} +2.82010e14 q^{55} +(-8.05730e14 - 6.99071e14i) q^{56} +(-3.61849e13 + 1.49018e14i) q^{58} +8.37680e14i q^{59} +3.98624e14i q^{61} +(-1.35021e15 - 3.27862e14i) q^{62} +(3.17616e14 + 2.22929e15i) q^{64} -9.89901e14 q^{65} +5.22273e15i q^{67} +(6.34956e14 + 3.27685e14i) q^{68} +(-8.93463e14 + 3.67948e15i) q^{70} -5.50116e15 q^{71} +1.47400e15 q^{73} +(-2.04751e15 + 8.43211e15i) q^{74} +(3.44039e14 - 6.66645e14i) q^{76} +1.36259e16i q^{77} -1.94988e16 q^{79} +(6.51478e15 - 4.63079e15i) q^{80} +(-2.03887e15 - 4.95084e14i) q^{82} +3.36599e16i q^{83} -2.53625e15i q^{85} +(3.41774e15 - 1.40750e16i) q^{86} +(1.88501e16 - 2.17261e16i) q^{88} +1.09831e16 q^{89} -4.78293e16i q^{91} +(1.51706e16 + 7.82918e15i) q^{92} +(-5.51777e16 - 1.33984e16i) q^{94} -2.66283e15 q^{95} +6.57395e16 q^{97} +(-9.59397e16 - 2.32964e16i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−351.815	−	85.4288i	−0.971761	−	0.235966i
$2$	−351.815	−	85.4288i	−0.971761	−	0.235966i
$3$		0			0
$3$		0			0
$4$	116476.	+	60110.3i	0.888640	+	0.458605i
$5$		−	465248.i		−	0.532647i	−0.963884	−	0.266324i	$-0.914191\pi$
$5$		−	465248.i		−	0.532647i	0.963884	−	0.266324i	$-0.0858090\pi$
$6$		0			0
$7$	2.24795e7			1.47385			0.736926	−	0.675973i	$-0.236276\pi$
$7$	2.24795e7			1.47385			0.736926	+	0.675973i	$0.236276\pi$
$8$	−3.58428e7	−	3.10981e7i	−0.755331	−	0.655343i
$9$		0			0
$10$	−3.97456e7	+	1.63681e8i	−0.125687	+	0.517606i
$11$			6.06148e8i			0.852592i	0.904584	+	0.426296i	$0.140182\pi$
$11$			6.06148e8i			0.852592i	−0.904584	+	0.426296i	$0.859818\pi$
$12$		0			0
$13$		−	2.12768e9i		−	0.723417i	−0.932291	−	0.361708i	$-0.882194\pi$
$13$		−	2.12768e9i		−	0.723417i	0.932291	−	0.361708i	$-0.117806\pi$
$14$	−7.90864e9	−	1.92040e9i	−1.43223	−	0.347779i
$15$		0			0
$16$	9.95338e9	+	1.40028e10i	0.579363	+	0.815070i
$17$	5.45139e9			0.189536			0.0947680	−	0.995499i	$-0.469789\pi$
$17$	5.45139e9			0.189536			0.0947680	+	0.995499i	$0.469789\pi$
$18$		0			0
$19$		−	5.72346e9i		−	0.0773131i	−0.999253	−	0.0386565i	$-0.987692\pi$
$19$		−	5.72346e9i		−	0.0773131i	0.999253	−	0.0386565i	$-0.0123078\pi$
$20$	2.79662e10	−	5.41902e10i	0.244275	−	0.473332i
$21$		0			0
$22$	5.17825e10	−	2.13252e11i	0.201183	−	0.828515i
$23$	1.30247e11			0.346802			0.173401	−	0.984851i	$-0.444524\pi$
$23$	1.30247e11			0.346802			0.173401	+	0.984851i	$0.444524\pi$
$24$		0			0
$25$	5.46483e11			0.716287
$26$	−1.81765e11	+	7.48551e11i	−0.170702	+	0.702988i
$27$		0			0
$28$	2.61832e12	+	1.35125e12i	1.30972	+	0.675916i
$29$		−	4.23568e11i		−	0.157232i	−0.996905	−	0.0786159i	$-0.974950\pi$
$29$		−	4.23568e11i		−	0.157232i	0.996905	−	0.0786159i	$-0.0250501\pi$
$30$		0			0
$31$	3.83783e12			0.808187			0.404093	−	0.914718i	$-0.367587\pi$
$31$	3.83783e12			0.808187			0.404093	+	0.914718i	$0.367587\pi$
$32$	−2.30551e12	−	5.77670e12i	−0.370674	−	0.928763i
$33$		0			0
$34$	−1.91788e12	−	4.65706e11i	−0.184184	−	0.0447240i
$35$		−	1.04586e13i		−	0.785044i
$36$		0			0
$37$		−	2.39674e13i		−	1.12178i	−0.827891	−	0.560889i	$-0.810459\pi$
$37$		−	2.39674e13i		−	1.12178i	0.827891	−	0.560889i	$-0.189541\pi$
$38$	−4.88948e11	+	2.01360e12i	−0.0182432	+	0.0751299i
$39$		0			0
$40$	−1.44683e13	+	1.66758e13i	−0.349067	+	0.402325i
$41$	5.79528e12			0.113347			0.0566737	−	0.998393i	$-0.481951\pi$
$41$	5.79528e12			0.113347			0.0566737	+	0.998393i	$0.481951\pi$
$42$		0			0
$43$			4.00069e13i			0.521979i	0.965342	+	0.260989i	$0.0840488\pi$
$43$			4.00069e13i			0.521979i	−0.965342	+	0.260989i	$0.915951\pi$
$44$	−3.64357e13	+	7.06016e13i	−0.391003	+	0.757647i
$45$		0			0
$46$	−4.58229e13	−	1.11268e13i	−0.337008	−	0.0818333i
$47$	1.56837e14			0.960765			0.480382	−	0.877059i	$-0.340498\pi$
$47$	1.56837e14			0.960765			0.480382	+	0.877059i	$0.340498\pi$
$48$		0			0
$49$	2.72699e14			1.17224
$50$	−1.92261e14	−	4.66854e13i	−0.696060	−	0.169019i
$51$		0			0
$52$	1.27896e14	−	2.47824e14i	0.331763	−	0.642857i
$53$		−	6.45318e14i		−	1.42374i	−0.702314	−	0.711868i	$-0.747850\pi$
$53$		−	6.45318e14i		−	1.42374i	0.702314	−	0.711868i	$-0.252150\pi$
$54$		0			0
$55$	2.82010e14			0.454131
$56$	−8.05730e14	−	6.99071e14i	−1.11325	−	0.965880i
$57$		0			0
$58$	−3.61849e13	+	1.49018e14i	−0.0371013	+	0.152792i
$59$			8.37680e14i			0.742739i	0.928485	+	0.371369i	$0.121112\pi$
$59$			8.37680e14i			0.742739i	−0.928485	+	0.371369i	$0.878888\pi$
$60$		0			0
$61$			3.98624e14i			0.266232i	0.991100	+	0.133116i	$0.0424983\pi$
$61$			3.98624e14i			0.266232i	−0.991100	+	0.133116i	$0.957502\pi$
$62$	−1.35021e15	−	3.27862e14i	−0.785365	−	0.190705i
$63$		0			0
$64$	3.17616e14	+	2.22929e15i	0.141050	+	0.990002i
$65$	−9.89901e14			−0.385326
$66$		0			0
$67$			5.22273e15i			1.57131i	0.618665	+	0.785655i	$0.287674\pi$
$67$			5.22273e15i			1.57131i	−0.618665	+	0.785655i	$0.712326\pi$
$68$	6.34956e14	+	3.27685e14i	0.168429	+	0.0869222i
$69$		0			0
$70$	−8.93463e14	+	3.67948e15i	−0.185244	+	0.762875i
$71$	−5.50116e15			−1.01102			−0.505508	−	0.862822i	$-0.668695\pi$
$71$	−5.50116e15			−1.01102			−0.505508	+	0.862822i	$0.668695\pi$
$72$		0			0
$73$	1.47400e15			0.213921			0.106960	−	0.994263i	$-0.465888\pi$
$73$	1.47400e15			0.213921			0.106960	+	0.994263i	$0.465888\pi$
$74$	−2.04751e15	+	8.43211e15i	−0.264701	+	1.09010i
$75$		0			0
$76$	3.44039e14	−	6.66645e14i	0.0354562	−	0.0687035i
$77$			1.36259e16i			1.25659i
$78$		0			0
$79$	−1.94988e16			−1.44603			−0.723015	−	0.690833i	$-0.757244\pi$
$79$	−1.94988e16			−1.44603			−0.723015	+	0.690833i	$0.757244\pi$
$80$	6.51478e15	−	4.63079e15i	0.434145	−	0.308596i
$81$		0			0
$82$	−2.03887e15	−	4.95084e14i	−0.110147	−	0.0267461i
$83$			3.36599e16i			1.64040i	0.572078	+	0.820199i	$0.306138\pi$
$83$			3.36599e16i			1.64040i	−0.572078	+	0.820199i	$0.693862\pi$
$84$		0			0
$85$		−	2.53625e15i		−	0.100956i
$86$	3.41774e15	−	1.40750e16i	0.123169	−	0.507239i
$87$		0			0
$88$	1.88501e16	−	2.17261e16i	0.558740	−	0.643989i
$89$	1.09831e16			0.295740			0.147870	−	0.989007i	$-0.452758\pi$
$89$	1.09831e16			0.295740			0.147870	+	0.989007i	$0.452758\pi$
$90$		0			0
$91$		−	4.78293e16i		−	1.06621i
$92$	1.51706e16	+	7.82918e15i	0.308182	+	0.159045i
$93$		0			0
$94$	−5.51777e16	−	1.33984e16i	−0.933634	−	0.226708i
$95$	−2.66283e15			−0.0411806
$96$		0			0
$97$	6.57395e16			0.851660			0.425830	−	0.904803i	$-0.359982\pi$
$97$	6.57395e16			0.851660			0.425830	+	0.904803i	$0.359982\pi$
$98$	−9.59397e16	−	2.32964e16i	−1.13914	−	0.276609i
$99$		0			0
$100$	6.36521e16	+	3.28493e16i	0.636521	+	0.328493i
$101$			7.10748e16i			0.653106i	0.945179	+	0.326553i	$0.105887\pi$
$101$			7.10748e16i			0.653106i	−0.945179	+	0.326553i	$0.894113\pi$
$102$		0			0
$103$	−1.91977e17			−1.49325			−0.746624	−	0.665246i	$-0.768327\pi$
$103$	−1.91977e17			−1.49325			−0.746624	+	0.665246i	$0.768327\pi$
$104$	−6.61669e16	+	7.62622e16i	−0.474086	+	0.546419i
$105$		0			0
$106$	−5.51288e16	+	2.27033e17i	−0.335953	+	1.38353i
$107$			5.53132e16i			0.311220i	0.987819	+	0.155610i	$0.0497342\pi$
$107$			5.53132e16i			0.311220i	−0.987819	+	0.155610i	$0.950266\pi$
$108$		0			0
$109$		−	3.67908e17i		−	1.76854i	−0.466978	−	0.884269i	$-0.654657\pi$
$109$		−	3.67908e17i		−	1.76854i	0.466978	−	0.884269i	$-0.345343\pi$
$110$	−9.92152e16	−	2.40917e16i	−0.441307	−	0.107159i
$111$		0			0
$112$	2.23747e17	+	3.14776e17i	0.853895	+	1.20129i
$113$	3.48457e17			1.23306			0.616528	−	0.787333i	$-0.288539\pi$
$113$	3.48457e17			1.23306			0.616528	+	0.787333i	$0.288539\pi$
$114$		0			0
$115$		−	6.05972e16i		−	0.184723i
$116$	2.54608e16	−	4.93355e16i	0.0721073	−	0.139723i
$117$		0			0
$118$	7.15620e16	−	2.94708e17i	0.175261	−	0.721765i
$119$	1.22545e17			0.279348
$120$		0			0
$121$	1.38031e17			0.273088
$122$	3.40540e16	−	1.40242e17i	0.0628217	−	0.258714i
$123$		0			0
$124$	4.47015e17	+	2.30693e17i	0.718187	+	0.370639i
$125$		−	6.09207e17i		−	0.914176i
$126$		0			0
$127$	5.29745e17			0.694600			0.347300	−	0.937754i	$-0.387099\pi$
$127$	5.29745e17			0.694600			0.347300	+	0.937754i	$0.387099\pi$
$128$	7.87032e16	−	8.11431e17i	0.0965401	−	0.995329i
$129$		0			0
$130$	3.48262e17	+	8.45661e16i	0.374445	+	0.0909238i
$131$			1.11774e18i			1.12599i	0.826459	+	0.562996i	$0.190351\pi$
$131$			1.11774e18i			1.12599i	−0.826459	+	0.562996i	$0.809649\pi$
$132$		0			0
$133$		−	1.28661e17i		−	0.113948i
$134$	4.46171e17	−	1.83744e18i	0.370775	−	1.52694i
$135$		0			0
$136$	−1.95393e17	−	1.69528e17i	−0.143162	−	0.124211i
$137$	−6.75639e17			−0.465146			−0.232573	−	0.972579i	$-0.574715\pi$
$137$	−6.75639e17			−0.465146			−0.232573	+	0.972579i	$0.574715\pi$
$138$		0			0
$139$		−	1.43378e18i		−	0.872686i	−0.899780	−	0.436343i	$-0.856273\pi$
$139$		−	1.43378e18i		−	0.872686i	0.899780	−	0.436343i	$-0.143727\pi$
$140$	6.28668e17	−	1.21817e18i	0.360025	−	0.697622i
$141$		0			0
$142$	1.93539e18	+	4.69957e17i	0.982467	+	0.238565i
$143$	1.28969e18			0.616779
$144$		0			0
$145$	−1.97064e17			−0.0837491
$146$	−5.18575e17	−	1.25922e17i	−0.207880	−	0.0504780i
$147$		0			0
$148$	1.44069e18	−	2.79163e18i	0.514453	−	0.996857i
$149$		−	2.92569e18i		−	0.986608i	−0.869857	−	0.493304i	$-0.835789\pi$
$149$		−	2.92569e18i		−	0.986608i	0.869857	−	0.493304i	$-0.164211\pi$
$150$		0			0
$151$	3.38847e18			1.02023			0.510117	−	0.860105i	$-0.329602\pi$
$151$	3.38847e18			1.02023			0.510117	+	0.860105i	$0.329602\pi$
$152$	−1.77989e17	+	2.05145e17i	−0.0506666	+	0.0583970i
$153$		0			0
$154$	1.16405e18	−	4.79381e18i	0.296513	−	1.22111i
$155$		−	1.78555e18i		−	0.430479i
$156$		0			0
$157$		−	3.55208e18i		−	0.767954i	−0.923343	−	0.383977i	$-0.874554\pi$
$157$		−	3.55208e18i		−	0.767954i	0.923343	−	0.383977i	$-0.125446\pi$
$158$	6.85997e18	+	1.66576e18i	1.40520	+	0.341214i
$159$		0			0
$160$	−2.68760e18	+	1.07263e18i	−0.494703	+	0.197438i
$161$	2.92789e18			0.511134
$162$		0			0
$163$		−	6.81975e18i		−	1.07195i	−0.844234	−	0.535974i	$-0.819944\pi$
$163$		−	6.81975e18i		−	1.07195i	0.844234	−	0.535974i	$-0.180056\pi$
$164$	6.75010e17	+	3.48356e17i	0.100725	+	0.0519817i
$165$		0			0
$166$	2.87553e18	−	1.18421e19i	0.387078	−	1.59408i
$167$	1.29136e19			1.65180			0.825899	−	0.563819i	$-0.190668\pi$
$167$	1.29136e19			1.65180			0.825899	+	0.563819i	$0.190668\pi$
$168$		0			0
$169$	4.12338e18			0.476668
$170$	−2.16669e17	+	8.92292e17i	−0.0238221	+	0.0981050i
$171$		0			0
$172$	−2.40483e18	+	4.65984e18i	−0.239382	+	0.463851i
$173$		−	2.98078e18i		−	0.282448i	−0.989978	−	0.141224i	$-0.954896\pi$
$173$		−	2.98078e18i		−	0.282448i	0.989978	−	0.141224i	$-0.0451037\pi$
$174$		0			0
$175$	1.22847e19			1.05570
$176$	−8.48777e18	+	6.03322e18i	−0.694922	+	0.493960i
$177$		0			0
$178$	−3.86403e18	−	9.38274e17i	−0.287389	−	0.0697846i
$179$			4.00351e18i			0.283916i	0.989873	+	0.141958i	$0.0453398\pi$
$179$			4.00351e18i			0.283916i	−0.989873	+	0.141958i	$0.954660\pi$
$180$		0			0
$181$			2.28445e19i			1.47406i	0.675861	+	0.737029i	$0.263772\pi$
$181$			2.28445e19i			1.47406i	−0.675861	+	0.737029i	$0.736228\pi$
$182$	−4.08600e18	+	1.68271e19i	−0.251589	+	1.03610i
$183$		0			0
$184$	−4.66842e18	−	4.05043e18i	−0.261950	−	0.227274i
$185$	−1.11508e19			−0.597512
$186$		0			0
$187$			3.30435e18i			0.161597i
$188$	1.82677e19	+	9.42753e18i	0.853774	+	0.440612i
$189$		0			0
$190$	9.36824e17	+	2.27482e17i	0.0400177	+	0.00971722i
$191$	−3.05570e19			−1.24832			−0.624162	−	0.781295i	$-0.714559\pi$
$191$	−3.05570e19			−1.24832			−0.624162	+	0.781295i	$0.714559\pi$
$192$		0			0
$193$	2.24801e19			0.840547			0.420274	−	0.907397i	$-0.361934\pi$
$193$	2.24801e19			0.840547			0.420274	+	0.907397i	$0.361934\pi$
$194$	−2.31281e19	−	5.61604e18i	−0.827611	−	0.200963i
$195$		0			0
$196$	3.17629e19	+	1.63920e19i	1.04170	+	0.537596i
$197$		−	5.40141e19i		−	1.69646i	−0.529625	−	0.848232i	$-0.677667\pi$
$197$		−	5.40141e19i		−	1.69646i	0.529625	−	0.848232i	$-0.322333\pi$
$198$		0			0
$199$	−3.30197e18			−0.0951747			−0.0475874	−	0.998867i	$-0.515153\pi$
$199$	−3.30197e18			−0.0951747			−0.0475874	+	0.998867i	$0.515153\pi$
$200$	−1.95875e19	−	1.69946e19i	−0.541034	−	0.469414i
$201$		0			0
$202$	6.07183e18	−	2.50052e19i	0.154111	−	0.634663i
$203$		−	9.52162e18i		−	0.231737i
$204$		0			0
$205$		−	2.69624e18i		−	0.0603742i
$206$	6.75403e19	+	1.64003e19i	1.45108	+	0.352356i
$207$		0			0
$208$	2.97935e19	−	2.11776e19i	0.589635	−	0.419121i
$209$	3.46926e18			0.0659165
$210$		0			0
$211$		−	7.95957e19i		−	1.39473i	−0.716718	−	0.697363i	$-0.754357\pi$
$211$		−	7.95957e19i		−	1.39473i	0.716718	−	0.697363i	$-0.245643\pi$
$212$	3.87903e19	−	7.51640e19i	0.652932	−	1.26519i
$213$		0			0
$214$	4.72534e18	−	1.94600e19i	0.0734372	−	0.302431i
$215$	1.86131e19			0.278031
$216$		0			0
$217$	8.62727e19			1.19115
$218$	−3.14300e19	+	1.29436e20i	−0.417315	+	1.71860i
$219$		0			0
$220$	3.28473e19	+	1.69517e19i	0.403559	+	0.208267i
$221$		−	1.15988e19i		−	0.137113i
$222$		0			0
$223$	−7.18745e19			−0.787015			−0.393508	−	0.919321i	$-0.628739\pi$
$223$	−7.18745e19			−0.787015			−0.393508	+	0.919321i	$0.628739\pi$
$224$	−5.18267e19	−	1.29858e20i	−0.546318	−	1.36886i
$225$		0			0
$226$	−1.22593e20	−	2.97683e19i	−1.19824	−	0.290959i
$227$			1.07253e20i			1.00969i	0.863210	+	0.504845i	$0.168450\pi$
$227$			1.07253e20i			1.00969i	−0.863210	+	0.504845i	$0.831550\pi$
$228$		0			0
$229$			8.55186e19i			0.747238i	0.927582	+	0.373619i	$0.121883\pi$
$229$			8.55186e19i			0.747238i	−0.927582	+	0.373619i	$0.878117\pi$
$230$	−5.17674e18	+	2.13190e19i	−0.0435883	+	0.179507i
$231$		0			0
$232$	−1.31722e19	+	1.51819e19i	−0.103041	+	0.118762i
$233$	1.65020e20			1.24455			0.622273	−	0.782801i	$-0.286210\pi$
$233$	1.65020e20			1.24455			0.622273	+	0.782801i	$0.286210\pi$
$234$		0			0
$235$		−	7.29682e19i		−	0.511749i
$236$	−5.03532e19	+	9.75695e19i	−0.340624	+	0.660027i
$237$		0			0
$238$	−4.31131e19	−	1.04689e19i	−0.271460	−	0.0659166i
$239$	2.20002e20			1.33673			0.668367	−	0.743832i	$-0.266994\pi$
$239$	2.20002e20			1.33673			0.668367	+	0.743832i	$0.266994\pi$
$240$		0			0
$241$	1.65734e19			0.0938137			0.0469069	−	0.998899i	$-0.485064\pi$
$241$	1.65734e19			0.0938137			0.0469069	+	0.998899i	$0.485064\pi$
$242$	−4.85615e19	−	1.17919e19i	−0.265376	−	0.0644394i
$243$		0			0
$244$	−2.39614e19	+	4.64301e19i	−0.122095	+	0.236584i
$245$		−	1.26873e20i		−	0.624392i
$246$		0			0
$247$	−1.21777e19			−0.0559296
$248$	−1.37559e20	−	1.19349e20i	−0.610449	−	0.529640i
$249$		0			0
$250$	−5.20438e19	+	2.14328e20i	−0.215714	+	0.888361i
$251$			5.13762e19i			0.205843i	0.994690	+	0.102921i	$0.0328190\pi$
$251$			5.13762e19i			0.205843i	−0.994690	+	0.102921i	$0.967181\pi$
$252$		0			0
$253$			7.89490e19i			0.295680i
$254$	−1.86372e20	−	4.52554e19i	−0.674986	−	0.163902i
$255$		0			0
$256$	−9.70085e19	+	2.78750e20i	−0.328678	+	0.944442i
$257$	9.03372e19			0.296098			0.148049	−	0.988980i	$-0.452701\pi$
$257$	9.03372e19			0.296098			0.148049	+	0.988980i	$0.452701\pi$
$258$		0			0
$259$		−	5.38777e20i		−	1.65334i
$260$	−1.15300e20	−	5.95033e19i	−0.342416	−	0.176713i
$261$		0			0
$262$	9.54873e19	−	3.93239e20i	0.265696	−	1.09420i
$263$	1.92468e20			0.518484			0.259242	−	0.965812i	$-0.416527\pi$
$263$	1.92468e20			0.518484			0.259242	+	0.965812i	$0.416527\pi$
$264$		0			0
$265$	−3.00233e20			−0.758349
$266$	−1.09913e19	+	4.52648e19i	−0.0268879	+	0.110730i
$267$		0			0
$268$	−3.13940e20	+	6.08322e20i	−0.720611	+	1.39633i
$269$		−	5.40117e19i		−	0.120114i	−0.998195	−	0.0600569i	$-0.980872\pi$
$269$		−	5.40117e19i		−	0.120114i	0.998195	−	0.0600569i	$-0.0191282\pi$
$270$		0			0
$271$	6.53682e19			0.136498			0.0682492	−	0.997668i	$-0.478259\pi$
$271$	6.53682e19			0.136498			0.0682492	+	0.997668i	$0.478259\pi$
$272$	5.42598e19	+	7.63347e19i	0.109810	+	0.154485i
$273$		0			0
$274$	2.37700e20	+	5.77190e19i	0.452011	+	0.109759i
$275$			3.31250e20i			0.610700i
$276$		0			0
$277$			1.79771e20i			0.311632i	0.987786	+	0.155816i	$0.0498007\pi$
$277$			1.79771e20i			0.311632i	−0.987786	+	0.155816i	$0.950199\pi$
$278$	−1.22486e20	+	5.04427e20i	−0.205924	+	0.848043i
$279$		0			0
$280$	−3.25242e20	+	3.74865e20i	−0.514473	+	0.592968i
$281$	−5.43168e20			−0.833547			−0.416774	−	0.909010i	$-0.636839\pi$
$281$	−5.43168e20			−0.833547			−0.416774	+	0.909010i	$0.636839\pi$
$282$		0			0
$283$			7.08836e20i			1.02414i	0.858943	+	0.512072i	$0.171122\pi$
$283$			7.08836e20i			1.02414i	−0.858943	+	0.512072i	$0.828878\pi$
$284$	−6.40752e20	−	3.30676e20i	−0.898430	−	0.463657i
$285$		0			0
$286$	−4.53733e20	−	1.10177e20i	−0.599362	−	0.145539i
$287$	1.30275e20			0.167057
$288$		0			0
$289$	−7.97523e20			−0.964076
$290$	6.93303e19	+	1.68350e19i	0.0813842	+	0.0197619i
$291$		0			0
$292$	1.71685e20	+	8.86025e19i	0.190099	+	0.0981052i
$293$		−	1.02708e20i		−	0.110467i	−0.998473	−	0.0552334i	$-0.982410\pi$
$293$		−	1.02708e20i		−	0.110467i	0.998473	−	0.0552334i	$-0.0175903\pi$
$294$		0			0
$295$	3.89729e20			0.395618
$296$	−7.45342e20	+	8.59060e20i	−0.735150	+	0.847314i
$297$		0			0
$298$	−2.49938e20	+	1.02930e21i	−0.232806	+	0.958747i
$299$		−	2.77124e20i		−	0.250882i
$300$		0			0
$301$			8.99336e20i			0.769320i
$302$	−1.19211e21	−	2.89473e20i	−0.991423	−	0.240740i
$303$		0			0
$304$	8.01444e19	−	5.69677e19i	0.0630156	−	0.0447923i
$305$	1.85459e20			0.141808
$306$		0			0
$307$		−	6.24758e19i		−	0.0451893i	−0.999745	−	0.0225946i	$-0.992807\pi$
$307$		−	6.24758e19i		−	0.0451893i	0.999745	−	0.0225946i	$-0.00719271\pi$
$308$	−8.19059e20	+	1.58709e21i	−0.576281	+	1.11666i
$309$		0			0
$310$	−1.52537e20	+	6.28182e20i	−0.101578	+	0.418323i
$311$	6.19747e20			0.401561			0.200780	−	0.979636i	$-0.435652\pi$
$311$	6.19747e20			0.401561			0.200780	+	0.979636i	$0.435652\pi$
$312$		0			0
$313$	2.05658e21			1.26188			0.630942	−	0.775830i	$-0.282669\pi$
$313$	2.05658e21			1.26188			0.630942	+	0.775830i	$0.282669\pi$
$314$	−3.03450e20	+	1.24967e21i	−0.181211	+	0.746268i
$315$		0			0
$316$	−2.27114e21	−	1.17208e21i	−1.28500	−	0.663156i
$317$		−	2.76754e21i		−	1.52437i	−0.647361	−	0.762184i	$-0.724127\pi$
$317$		−	2.76754e21i		−	1.52437i	0.647361	−	0.762184i	$-0.275873\pi$
$318$		0			0
$319$	2.56745e20			0.134055
$320$	1.03717e21	−	1.47770e20i	0.527322	−	0.0751298i
$321$		0			0
$322$	−1.03008e21	−	2.50126e20i	−0.496701	−	0.120610i
$323$		−	3.12008e19i		−	0.0146536i
$324$		0			0
$325$		−	1.16274e21i		−	0.518174i
$326$	−5.82603e20	+	2.39929e21i	−0.252943	+	1.04168i
$327$		0			0
$328$	−2.07719e20	−	1.80222e20i	−0.0856148	−	0.0742815i
$329$	3.52563e21			1.41603
$330$		0			0
$331$			1.62038e21i			0.618128i	0.951041	+	0.309064i	$0.100016\pi$
$331$			1.62038e21i			0.618128i	−0.951041	+	0.309064i	$0.899984\pi$
$332$	−2.02331e21	+	3.92057e21i	−0.752295	+	1.45772i
$333$		0			0
$334$	−4.54319e21	−	1.10319e21i	−1.60515	−	0.389768i
$335$	2.42987e21			0.836954
$336$		0			0
$337$	7.17480e20			0.234939			0.117470	−	0.993076i	$-0.462522\pi$
$337$	7.17480e20			0.234939			0.117470	+	0.993076i	$0.462522\pi$
$338$	−1.45067e21	−	3.52255e20i	−0.463208	−	0.112477i
$339$		0			0
$340$	1.52455e20	−	2.95412e20i	0.0462989	−	0.0897134i
$341$			2.32630e21i			0.689053i
$342$		0			0
$343$	9.00726e20			0.253859
$344$	1.24414e21	−	1.43396e21i	0.342075	−	0.394267i
$345$		0			0
$346$	−2.54644e20	+	1.04868e21i	−0.0666480	+	0.274472i
$347$		−	6.16195e21i		−	1.57369i	−0.617154	−	0.786843i	$-0.711714\pi$
$347$		−	6.16195e21i		−	1.57369i	0.617154	−	0.786843i	$-0.288286\pi$
$348$		0			0
$349$		−	5.73892e21i		−	1.39577i	−0.716210	−	0.697885i	$-0.754125\pi$
$349$		−	5.73892e21i		−	1.39577i	0.716210	−	0.697885i	$-0.245875\pi$
$350$	−4.32194e21	−	1.04947e21i	−1.02589	−	0.249109i
$351$		0			0
$352$	3.50154e21	−	1.39748e21i	0.791856	−	0.316033i
$353$	7.35535e21			1.62375			0.811873	−	0.583834i	$-0.198448\pi$
$353$	7.35535e21			1.62375			0.811873	+	0.583834i	$0.198448\pi$
$354$		0			0
$355$			2.55941e21i			0.538515i
$356$	1.27927e21	+	6.60198e20i	0.262807	+	0.135628i
$357$		0			0
$358$	3.42015e20	−	1.40849e21i	0.0669945	−	0.275898i
$359$	1.38050e21			0.264079			0.132040	−	0.991244i	$-0.457847\pi$
$359$	1.38050e21			0.264079			0.132040	+	0.991244i	$0.457847\pi$
$360$		0			0
$361$	5.44763e21			0.994023
$362$	1.95158e21	−	8.03706e21i	0.347827	−	1.43243i
$363$		0			0
$364$	2.87504e21	−	5.57096e21i	0.488969	−	0.947477i
$365$		−	6.85776e20i		−	0.113944i
$366$		0			0
$367$	9.17912e21			1.45593			0.727963	−	0.685616i	$-0.240467\pi$
$367$	9.17912e21			1.45593			0.727963	+	0.685616i	$0.240467\pi$
$368$	1.29640e21	+	1.82382e21i	0.200924	+	0.282667i
$369$		0			0
$370$	3.92302e21	+	9.52600e20i	0.580639	+	0.140993i
$371$		−	1.45065e22i		−	2.09838i
$372$		0			0
$373$		−	3.68573e21i		−	0.509329i	−0.967029	−	0.254665i	$-0.918035\pi$
$373$		−	3.68573e21i		−	0.509329i	0.967029	−	0.254665i	$-0.0819651\pi$
$374$	2.82287e20	−	1.16252e21i	0.0381313	−	0.157033i
$375$		0			0
$376$	−5.62149e21	−	4.87734e21i	−0.725696	−	0.629631i
$377$	−9.01219e20			−0.113744
$378$		0			0
$379$		−	9.17543e21i		−	1.10712i	−0.832810	−	0.553558i	$-0.813270\pi$
$379$		−	9.17543e21i		−	1.10712i	0.832810	−	0.553558i	$-0.186730\pi$
$380$	−3.10155e20	−	1.60063e20i	−0.0365947	−	0.0188856i
$381$		0			0
$382$	1.07504e22	+	2.61045e21i	1.21307	+	0.294562i
$383$	7.23389e21			0.798329			0.399165	−	0.916879i	$-0.369300\pi$
$383$	7.23389e21			0.798329			0.399165	+	0.916879i	$0.369300\pi$
$384$		0			0
$385$	6.33944e21			0.669322
$386$	−7.90886e21	−	1.92045e21i	−0.816811	−	0.198340i
$387$		0			0
$388$	7.65706e21	+	3.95162e21i	0.756820	+	0.390576i
$389$			1.25731e21i			0.121583i	0.998150	+	0.0607914i	$0.0193624\pi$
$389$			1.25731e21i			0.121583i	−0.998150	+	0.0607914i	$0.980638\pi$
$390$		0			0
$391$	7.10027e20			0.0657314
$392$	−9.77431e21	−	8.48043e21i	−0.885431	−	0.768221i
$393$		0			0
$394$	−4.61436e21	+	1.90030e22i	−0.400308	+	1.64856i
$395$			9.07178e21i			0.770224i
$396$		0			0
$397$		−	1.07820e22i		−	0.876957i	−0.898742	−	0.438478i	$-0.855518\pi$
$397$		−	1.07820e22i		−	0.876957i	0.898742	−	0.438478i	$-0.144482\pi$
$398$	1.16168e21	+	2.82083e20i	0.0924871	+	0.0224580i
$399$		0			0
$400$	5.43935e21	+	7.65229e21i	0.414990	+	0.583824i
$401$	1.08434e22			0.809915			0.404957	−	0.914336i	$-0.367286\pi$
$401$	1.08434e22			0.809915			0.404957	+	0.914336i	$0.367286\pi$
$402$		0			0
$403$		−	8.16570e21i		−	0.584656i
$404$	−4.27233e21	+	8.27850e21i	−0.299518	+	0.580377i
$405$		0			0
$406$	−8.13420e20	+	3.34985e21i	−0.0546819	+	0.225193i
$407$	1.45278e22			0.956418
$408$		0			0
$409$	−2.32714e22			−1.46951			−0.734757	−	0.678330i	$-0.762704\pi$
$409$	−2.32714e22			−1.46951			−0.734757	+	0.678330i	$0.762704\pi$
$410$	−2.30337e20	+	9.48580e20i	−0.0142463	+	0.0586693i
$411$		0			0
$412$	−2.23606e22	−	1.15398e22i	−1.32696	−	0.684811i
$413$			1.88307e22i			1.09469i
$414$		0			0
$415$	1.56602e22			0.873754
$416$	−1.22910e22	+	4.90539e21i	−0.671883	+	0.268151i
$417$		0			0
$418$	−1.22054e21	−	2.96375e20i	−0.0640551	−	0.0155540i
$419$		−	2.64974e22i		−	1.36265i	−0.731980	−	0.681326i	$-0.761404\pi$
$419$		−	2.64974e22i		−	1.36265i	0.731980	−	0.681326i	$-0.238596\pi$
$420$		0			0
$421$		−	3.52910e21i		−	0.174288i	−0.996196	−	0.0871438i	$-0.972226\pi$
$421$		−	3.52910e21i		−	0.174288i	0.996196	−	0.0871438i	$-0.0277739\pi$
$422$	−6.79976e21	+	2.80030e22i	−0.329108	+	1.35534i
$423$		0			0
$424$	−2.00682e22	+	2.31300e22i	−0.933036	+	1.07539i
$425$	2.97910e21			0.135762
$426$		0			0
$427$			8.96089e21i			0.392387i
$428$	−3.32489e21	+	6.44266e21i	−0.142727	+	0.276562i
$429$		0			0
$430$	−6.54839e21	−	1.59010e21i	−0.270179	−	0.0656058i
$431$	1.62468e22			0.657220			0.328610	−	0.944466i	$-0.393420\pi$
$431$	1.62468e22			0.657220			0.328610	+	0.944466i	$0.393420\pi$
$432$		0			0
$433$	−2.11243e22			−0.821553			−0.410776	−	0.911736i	$-0.634742\pi$
$433$	−2.11243e22			−0.821553			−0.410776	+	0.911736i	$0.634742\pi$
$434$	−3.03521e22	−	7.37018e21i	−1.15751	−	0.281070i
$435$		0			0
$436$	2.21151e22	−	4.28524e22i	0.811060	−	1.57159i
$437$		−	7.45463e20i		−	0.0268123i
$438$		0			0
$439$	3.57810e22			1.23795			0.618977	−	0.785409i	$-0.287548\pi$
$439$	3.57810e22			1.23795			0.618977	+	0.785409i	$0.287548\pi$
$440$	−1.01080e22	−	8.76996e21i	−0.343019	−	0.297612i
$441$		0			0
$442$	−9.90875e20	+	4.08065e21i	−0.0323541	+	0.133242i
$443$			5.46996e22i			1.75207i	0.482245	+	0.876036i	$0.339822\pi$
$443$			5.46996e22i			1.75207i	−0.482245	+	0.876036i	$0.660178\pi$
$444$		0			0
$445$		−	5.10988e21i		−	0.157525i
$446$	2.52865e22	+	6.14015e21i	0.764791	+	0.185709i
$447$		0			0
$448$	7.13986e21	+	5.01134e22i	0.207887	+	1.45912i
$449$	−1.84591e22			−0.527371			−0.263686	−	0.964609i	$-0.584938\pi$
$449$	−1.84591e22			−0.527371			−0.263686	+	0.964609i	$0.584938\pi$
$450$		0			0
$451$			3.51280e21i			0.0966390i
$452$	4.05869e22	+	2.09459e22i	1.09574	+	0.565486i
$453$		0			0
$454$	9.16246e21	−	3.77331e22i	0.238252	−	0.981177i
$455$	−2.22525e22			−0.567914
$456$		0			0
$457$	2.92054e22			0.718085			0.359042	−	0.933321i	$-0.383103\pi$
$457$	2.92054e22			0.718085			0.359042	+	0.933321i	$0.383103\pi$
$458$	7.30575e21	−	3.00867e22i	0.176323	−	0.726137i
$459$		0			0
$460$	3.64251e21	−	7.05811e21i	0.0847149	−	0.164152i
$461$		−	4.03608e22i		−	0.921513i	−0.887527	−	0.460756i	$-0.847578\pi$
$461$		−	4.03608e22i		−	0.921513i	0.887527	−	0.460756i	$-0.152422\pi$
$462$		0			0
$463$	−6.51927e22			−1.43470			−0.717349	−	0.696714i	$-0.754644\pi$
$463$	−6.51927e22			−1.43470			−0.717349	+	0.696714i	$0.754644\pi$
$464$	5.93114e21	−	4.21593e21i	0.128155	−	0.0910943i
$465$		0			0
$466$	−5.80565e22	−	1.40974e22i	−1.20940	−	0.293670i
$467$			3.14842e21i			0.0644021i	0.999481	+	0.0322010i	$0.0102517\pi$
$467$			3.14842e21i			0.0644021i	−0.999481	+	0.0322010i	$0.989748\pi$
$468$		0			0
$469$			1.17405e23i			2.31588i
$470$	−6.23359e21	+	2.56713e22i	−0.120755	+	0.497298i
$471$		0			0
$472$	2.60503e22	−	3.00248e22i	0.486749	−	0.561013i
$473$	−2.42501e22			−0.445035
$474$		0			0
$475$		−	3.12777e21i		−	0.0553783i
$476$	1.42735e22	+	7.36620e21i	0.248240	+	0.128110i
$477$		0			0
$478$	−7.74001e22	−	1.87945e22i	−1.29899	−	0.315423i
$479$	−5.37771e22			−0.886637			−0.443318	−	0.896364i	$-0.646199\pi$
$479$	−5.37771e22			−0.886637			−0.443318	+	0.896364i	$0.646199\pi$
$480$		0			0
$481$	−5.09951e22			−0.811513
$482$	−5.83077e21	−	1.41584e21i	−0.0911645	−	0.0221368i
$483$		0			0
$484$	1.60773e22	+	8.29710e21i	0.242677	+	0.125239i
$485$		−	3.05852e22i		−	0.453635i
$486$		0			0
$487$	−1.62097e22			−0.232155			−0.116078	−	0.993240i	$-0.537032\pi$
$487$	−1.62097e22			−0.232155			−0.116078	+	0.993240i	$0.537032\pi$
$488$	1.23965e22	−	1.42878e22i	0.174473	−	0.201093i
$489$		0			0
$490$	−1.08386e22	+	4.46358e22i	−0.147335	+	0.606760i
$491$		−	3.89242e22i		−	0.520028i	−0.965605	−	0.260014i	$-0.916273\pi$
$491$		−	3.89242e22i		−	0.520028i	0.965605	−	0.260014i	$-0.0837273\pi$
$492$		0			0
$493$		−	2.30904e21i		−	0.0298011i
$494$	4.28430e21	+	1.04033e21i	0.0543502	+	0.0131975i
$495$		0			0
$496$	3.81994e22	+	5.37404e22i	0.468233	+	0.658729i
$497$	−1.23664e23			−1.49009
$498$		0			0
$499$			6.70841e22i			0.781205i	0.920560	+	0.390602i	$0.127733\pi$
$499$			6.70841e22i			0.781205i	−0.920560	+	0.390602i	$0.872267\pi$
$500$	3.66196e22	−	7.09579e22i	0.419246	−	0.812373i
$501$		0			0
$502$	4.38901e21	−	1.80749e22i	0.0485718	−	0.200030i
$503$	2.47633e22			0.269452			0.134726	−	0.990883i	$-0.456985\pi$
$503$	2.47633e22			0.269452			0.134726	+	0.990883i	$0.456985\pi$
$504$		0			0
$505$	3.30674e22			0.347875
$506$	6.74451e21	−	2.77754e22i	0.0697704	−	0.287330i
$507$		0			0
$508$	6.17024e22	+	3.18431e22i	0.617250	+	0.318547i
$509$		−	5.33536e22i		−	0.524883i	−0.964948	−	0.262441i	$-0.915472\pi$
$509$		−	5.33536e22i		−	0.524883i	0.964948	−	0.262441i	$-0.0845276\pi$
$510$		0			0
$511$	3.31348e22			0.315288
$512$	5.79424e22	−	8.97812e22i	0.542252	−	0.840216i
$513$		0			0
$514$	−3.17820e22	−	7.71740e21i	−0.287736	−	0.0698690i
$515$			8.93169e22i			0.795375i
$516$		0			0
$517$			9.50666e22i			0.819140i
$518$	−4.60271e22	+	1.89550e23i	−0.390131	+	1.60665i
$519$		0			0
$520$	3.54809e22	+	3.07841e22i	0.291049	+	0.252521i
$521$	2.10097e22			0.169551			0.0847754	−	0.996400i	$-0.472983\pi$
$521$	2.10097e22			0.169551			0.0847754	+	0.996400i	$0.472983\pi$
$522$		0			0
$523$		−	7.86323e22i		−	0.614238i	−0.951671	−	0.307119i	$-0.900635\pi$
$523$		−	7.86323e22i		−	0.614238i	0.951671	−	0.307119i	$-0.0993650\pi$
$524$	−6.71878e22	+	1.30190e23i	−0.516386	+	1.00060i
$525$		0			0
$526$	−6.77132e22	−	1.64423e22i	−0.503842	−	0.122344i
$527$	2.09215e22			0.153180
$528$		0			0
$529$	−1.24086e23			−0.879729
$530$	1.05627e23	+	2.56486e22i	0.736934	+	0.178944i
$531$		0			0
$532$	7.73383e21	−	1.49859e22i	0.0522572	−	0.101259i
$533$		−	1.23305e22i		−	0.0819974i
$534$		0			0
$535$	2.57344e22			0.165770
$536$	1.62417e23	−	1.87197e23i	1.02975	−	1.18686i
$537$		0			0
$538$	−4.61415e21	+	1.90021e22i	−0.0283428	+	0.116722i
$539$			1.65296e23i			0.999443i
$540$		0			0
$541$			8.46969e22i			0.496239i	0.968729	+	0.248120i	$0.0798126\pi$
$541$			8.46969e22i			0.496239i	−0.968729	+	0.248120i	$0.920187\pi$
$542$	−2.29975e22	−	5.58433e21i	−0.132644	−	0.0322090i
$543$		0			0
$544$	−1.25682e22	−	3.14911e22i	−0.0702560	−	0.176034i
$545$	−1.71169e23			−0.942007
$546$		0			0
$547$		−	3.22585e23i		−	1.72088i	−0.509548	−	0.860442i	$-0.670187\pi$
$547$		−	3.22585e23i		−	1.72088i	0.509548	−	0.860442i	$-0.329813\pi$
$548$	−7.86956e22	−	4.06128e22i	−0.413348	−	0.213318i
$549$		0			0
$550$	2.82983e22	−	1.16539e23i	0.144104	−	0.593455i
$551$	−2.42428e21			−0.0121561
$552$		0			0
$553$	−4.38324e23			−2.13123
$554$	1.53576e22	−	6.32462e22i	0.0735345	−	0.302832i
$555$		0			0
$556$	8.61852e22	−	1.67001e23i	0.400218	−	0.775504i
$557$			1.27684e23i			0.583937i	0.956428	+	0.291968i	$0.0943102\pi$
$557$			1.27684e23i			0.583937i	−0.956428	+	0.291968i	$0.905690\pi$
$558$		0			0
$559$	8.51220e22			0.377608
$560$	1.46449e23	−	1.04098e23i	0.639866	−	0.454825i
$561$		0			0
$562$	1.91095e23	+	4.64022e22i	0.810009	+	0.196689i
$563$			3.00272e23i			1.25370i	0.779141	+	0.626849i	$0.215656\pi$
$563$			3.00272e23i			1.25370i	−0.779141	+	0.626849i	$0.784344\pi$
$564$		0			0
$565$		−	1.62119e23i		−	0.656785i
$566$	6.05550e22	−	2.49379e23i	0.241663	−	0.995223i
$567$		0			0
$568$	1.97177e23	+	1.71076e23i	0.763652	+	0.662563i
$569$	−1.90009e23			−0.724969			−0.362485	−	0.931990i	$-0.618071\pi$
$569$	−1.90009e23			−0.724969			−0.362485	+	0.931990i	$0.618071\pi$
$570$		0			0
$571$			1.14724e23i			0.424862i	0.977176	+	0.212431i	$0.0681381\pi$
$571$			1.14724e23i			0.424862i	−0.977176	+	0.212431i	$0.931862\pi$
$572$	1.50218e23	+	7.75237e22i	0.548095	+	0.282858i
$573$		0			0
$574$	−4.58328e22	−	1.11293e22i	−0.162340	−	0.0394198i
$575$	7.11778e22			0.248409
$576$		0			0
$577$	−3.30120e23			−1.11861			−0.559303	−	0.828963i	$-0.688931\pi$
$577$	−3.30120e23			−1.11861			−0.559303	+	0.828963i	$0.688931\pi$
$578$	2.80581e23	+	6.81314e22i	0.936852	+	0.227489i
$579$		0			0
$580$	−2.29533e22	−	1.18456e22i	−0.0744228	−	0.0384078i
$581$			7.56660e23i			2.41771i
$582$		0			0
$583$	3.91159e23			1.21386
$584$	−5.28323e22	−	4.58386e22i	−0.161581	−	0.140192i
$585$		0			0
$586$	−8.77426e21	+	3.61344e22i	−0.0260664	+	0.107347i
$587$		−	4.63905e23i		−	1.35833i	−0.733985	−	0.679166i	$-0.762342\pi$
$587$		−	4.63905e23i		−	1.35833i	0.733985	−	0.679166i	$-0.237658\pi$
$588$		0			0
$589$		−	2.19657e22i		−	0.0624834i
$590$	−1.37113e23	−	3.32941e22i	−0.384446	−	0.0933523i
$591$		0			0
$592$	3.35611e23	−	2.38557e23i	0.914327	−	0.649916i
$593$	−6.61931e23			−1.77766			−0.888829	−	0.458240i	$-0.848480\pi$
$593$	−6.61931e23			−1.77766			−0.888829	+	0.458240i	$0.848480\pi$
$594$		0			0
$595$		−	5.70138e22i		−	0.148794i
$596$	1.75864e23	−	3.40772e23i	0.452463	−	0.876739i
$597$		0			0
$598$	−2.36744e22	+	9.74965e22i	−0.0591996	+	0.243797i
$599$	−3.11969e23			−0.769102			−0.384551	−	0.923104i	$-0.625644\pi$
$599$	−3.11969e23			−0.769102			−0.384551	+	0.923104i	$0.625644\pi$
$600$		0			0
$601$	−2.76234e22			−0.0661978			−0.0330989	−	0.999452i	$-0.510538\pi$
$601$	−2.76234e22			−0.0661978			−0.0330989	+	0.999452i	$0.510538\pi$
$602$	7.68292e22	−	3.16400e23i	0.181533	−	0.747595i
$603$		0			0
$604$	3.94675e23	+	2.03682e23i	0.906620	+	0.467884i
$605$		−	6.42189e22i		−	0.145459i
$606$		0			0
$607$	5.72816e23			1.26157			0.630785	−	0.775958i	$-0.282733\pi$
$607$	5.72816e23			1.26157			0.630785	+	0.775958i	$0.282733\pi$
$608$	−3.30627e22	+	1.31955e22i	−0.0718055	+	0.0286579i
$609$		0			0
$610$	−6.52474e22	−	1.58436e22i	−0.137803	−	0.0334618i
$611$		−	3.33700e23i		−	0.695033i
$612$		0			0
$613$			5.83184e23i			1.18139i	0.806896	+	0.590693i	$0.201146\pi$
$613$			5.83184e23i			1.18139i	−0.806896	+	0.590693i	$0.798854\pi$
$614$	−5.33723e21	+	2.19799e22i	−0.0106631	+	0.0439132i
$615$		0			0
$616$	4.23741e23	−	4.88392e23i	0.823501	−	0.949145i
$617$	5.87532e23			1.12618			0.563090	−	0.826396i	$-0.309612\pi$
$617$	5.87532e23			1.12618			0.563090	+	0.826396i	$0.309612\pi$
$618$		0			0
$619$			1.26636e23i			0.236150i	0.993005	+	0.118075i	$0.0376723\pi$
$619$			1.26636e23i			0.236150i	−0.993005	+	0.118075i	$0.962328\pi$
$620$	1.07330e23	−	2.07973e23i	0.197420	−	0.382541i
$621$		0			0
$622$	−2.18037e23	−	5.29443e22i	−0.390221	−	0.0947547i
$623$	2.46895e23			0.435878
$624$		0			0
$625$	1.33501e23			0.229353
$626$	−7.23537e23	−	1.75691e23i	−1.22625	−	0.297762i
$627$		0			0
$628$	2.13516e23	−	4.13731e23i	0.352188	−	0.682435i
$629$		−	1.30656e23i		−	0.212617i
$630$		0			0
$631$	9.95923e22			0.157753			0.0788763	−	0.996884i	$-0.474867\pi$
$631$	9.95923e22			0.157753			0.0788763	+	0.996884i	$0.474867\pi$
$632$	6.98891e23	+	6.06375e23i	1.09223	+	0.947646i
$633$		0			0
$634$	−2.36427e23	+	9.73661e23i	−0.359699	+	1.48132i
$635$		−	2.46463e23i		−	0.369977i
$636$		0			0
$637$		−	5.80218e23i		−	0.848019i
$638$	−9.03268e22	−	2.19334e22i	−0.130269	−	0.0316323i
$639$		0			0
$640$	−3.77517e23	−	3.66165e22i	−0.530160	−	0.0514218i
$641$	−8.64785e22			−0.119844			−0.0599218	−	0.998203i	$-0.519085\pi$
$641$	−8.64785e22			−0.119844			−0.0599218	+	0.998203i	$0.519085\pi$
$642$		0			0
$643$			5.63561e22i			0.0760585i	0.999277	+	0.0380292i	$0.0121080\pi$
$643$			5.63561e22i			0.0760585i	−0.999277	+	0.0380292i	$0.987892\pi$
$644$	3.41029e23	+	1.75996e23i	0.454215	+	0.234409i
$645$		0			0
$646$	−2.66545e21	+	1.09769e22i	−0.00345775	+	0.0142398i
$647$	8.85704e23			1.13397			0.566986	−	0.823728i	$-0.308110\pi$
$647$	8.85704e23			1.13397			0.566986	+	0.823728i	$0.308110\pi$
$648$		0			0
$649$	−5.07758e23			−0.633253
$650$	−9.93318e22	+	4.09071e23i	−0.122271	+	0.503541i
$651$		0			0
$652$	4.09937e23	−	7.94337e23i	0.491601	−	0.952577i
$653$		−	3.56939e23i		−	0.422505i	−0.977432	−	0.211252i	$-0.932246\pi$
$653$		−	3.56939e23i		−	0.422505i	0.977432	−	0.211252i	$-0.0677542\pi$
$654$		0			0
$655$	5.20028e23			0.599757
$656$	5.76826e22	+	8.11501e22i	0.0656693	+	0.0923860i
$657$		0			0
$658$	−1.24037e24	−	3.01190e23i	−1.37604	−	0.334134i
$659$		−	6.90655e23i		−	0.756372i	−0.925730	−	0.378186i	$-0.876548\pi$
$659$		−	6.90655e23i		−	0.756372i	0.925730	−	0.378186i	$-0.123452\pi$
$660$		0			0
$661$		−	1.43884e24i		−	1.53567i	−0.640645	−	0.767837i	$-0.721333\pi$
$661$		−	1.43884e24i		−	1.53567i	0.640645	−	0.767837i	$-0.278667\pi$
$662$	1.38427e23	−	5.70074e23i	0.145857	−	0.600673i
$663$		0			0
$664$	1.04676e24	−	1.20647e24i	1.07502	−	1.23904i
$665$	−5.98592e22			−0.0606942
$666$		0			0
$667$		−	5.51685e22i		−	0.0545282i
$668$	1.50412e24	+	7.76239e23i	1.46785	+	0.757523i
$669$		0			0
$670$	−8.54864e23	−	2.07581e23i	−0.813320	−	0.197493i
$671$	−2.41625e23			−0.226987
$672$		0			0
$673$	−1.28567e24			−1.17761			−0.588806	−	0.808275i	$-0.700402\pi$
$673$	−1.28567e24			−1.17761			−0.588806	+	0.808275i	$0.700402\pi$
$674$	−2.52420e23	−	6.12935e22i	−0.228305	−	0.0554377i
$675$		0			0
$676$	4.80274e23	+	2.47858e23i	0.423587	+	0.218603i
$677$		−	7.83643e23i		−	0.682519i	−0.939969	−	0.341259i	$-0.889147\pi$
$677$		−	7.83643e23i		−	0.682519i	0.939969	−	0.341259i	$-0.110853\pi$
$678$		0			0
$679$	1.47779e24			1.25522
$680$	−7.88726e22	+	9.09064e22i	−0.0661608	+	0.0762551i
$681$		0			0
$682$	1.98733e23	−	8.18426e23i	0.162593	−	0.669595i
$683$		−	7.52256e23i		−	0.607841i	−0.952697	−	0.303920i	$-0.901704\pi$
$683$		−	7.52256e23i		−	0.607841i	0.952697	−	0.303920i	$-0.0982957\pi$
$684$		0			0
$685$			3.14340e23i			0.247759i
$686$	−3.16889e23	−	7.69479e22i	−0.246690	−	0.0599021i
$687$		0			0
$688$	−5.60208e23	+	3.98204e23i	−0.425449	+	0.302415i
$689$	−1.37303e24			−1.02995
$690$		0			0
$691$			1.95452e24i			1.43046i	0.698888	+	0.715231i	$0.253679\pi$
$691$			1.95452e24i			1.43046i	−0.698888	+	0.715231i	$0.746321\pi$
$692$	1.79175e23	−	3.47189e23i	0.129532	−	0.250994i
$693$		0			0
$694$	−5.26408e23	+	2.16787e24i	−0.371336	+	1.52925i
$695$	−6.67066e23			−0.464834
$696$		0			0
$697$	3.15923e22			0.0214834
$698$	−4.90269e23	+	2.01904e24i	−0.329354	+	1.35636i
$699$		0			0
$700$	1.43087e24	+	7.38437e23i	0.938138	+	0.484150i
$701$			2.08668e24i			1.35162i	0.737078	+	0.675808i	$0.236205\pi$
$701$			2.08668e24i			1.35162i	−0.737078	+	0.675808i	$0.763795\pi$
$702$		0			0
$703$	−1.37177e23			−0.0867281
$704$	−1.35128e24	+	1.92522e23i	−0.844068	+	0.120258i
$705$		0			0
$706$	−2.58772e24	−	6.28358e23i	−1.57789	−	0.383149i
$707$			1.59773e24i			0.962583i
$708$		0			0
$709$			1.76067e24i			1.03558i	0.855508	+	0.517790i	$0.173245\pi$
$709$			1.76067e24i			1.03558i	−0.855508	+	0.517790i	$0.826755\pi$
$710$	2.18647e23	−	9.00438e23i	0.127071	−	0.523308i
$711$		0			0
$712$	−3.93666e23	−	3.41554e23i	−0.223382	−	0.193811i
$713$	4.99866e23			0.280280
$714$		0			0
$715$		−	6.00027e23i		−	0.328526i
$716$	−2.40652e23	+	4.66312e23i	−0.130205	+	0.252299i
$717$		0			0
$718$	−4.85682e23	−	1.17935e23i	−0.256622	−	0.0623137i
$719$	3.64140e24			1.90140			0.950698	−	0.310118i	$-0.100369\pi$
$719$	3.64140e24			1.90140			0.950698	+	0.310118i	$0.100369\pi$
$720$		0			0
$721$	−4.31555e24			−2.20083
$722$	−1.91656e24	−	4.65384e23i	−0.965953	−	0.234555i
$723$		0			0
$724$	−1.37319e24	+	2.66084e24i	−0.676010	+	1.30991i
$725$		−	2.31473e23i		−	0.112623i
$726$		0			0
$727$	2.16795e24			1.03040			0.515201	−	0.857069i	$-0.327717\pi$
$727$	2.16795e24			1.03040			0.515201	+	0.857069i	$0.327717\pi$
$728$	−1.48740e24	+	1.71434e24i	−0.698734	+	0.805341i
$729$		0			0
$730$	−5.85850e22	+	2.41266e23i	−0.0268870	+	0.110727i
$731$			2.18093e23i			0.0989338i
$732$		0			0
$733$			2.91223e24i			1.29075i	0.763866	+	0.645375i	$0.223299\pi$
$733$			2.91223e24i			1.29075i	−0.763866	+	0.645375i	$0.776701\pi$
$734$	−3.22935e24	−	7.84161e23i	−1.41481	−	0.343549i
$735$		0			0
$736$	−3.00285e23	−	7.52398e23i	−0.128550	−	0.322096i
$737$	−3.16575e24			−1.33969
$738$		0			0
$739$			2.56079e23i			0.105900i	0.998597	+	0.0529500i	$0.0168624\pi$
$739$			2.56079e23i			0.105900i	−0.998597	+	0.0529500i	$0.983138\pi$
$740$	−1.29880e24	−	6.70278e23i	−0.530973	−	0.274022i
$741$		0			0
$742$	−1.23927e24	+	5.10359e24i	−0.495145	+	2.03912i
$743$	1.24281e24			0.490907			0.245453	−	0.969408i	$-0.421063\pi$
$743$	1.24281e24			0.490907			0.245453	+	0.969408i	$0.421063\pi$
$744$		0			0
$745$	−1.36117e24			−0.525514
$746$	−3.14868e23	+	1.29670e24i	−0.120184	+	0.494947i
$747$		0			0
$748$	−1.98626e23	+	3.84877e23i	−0.0741091	+	0.143601i
$749$			1.24342e24i			0.458692i
$750$		0			0
$751$	4.22804e24			1.52475			0.762376	−	0.647134i	$-0.224032\pi$
$751$	4.22804e24			1.52475			0.762376	+	0.647134i	$0.224032\pi$
$752$	1.56106e24	+	2.19616e24i	0.556631	+	0.783090i
$753$		0			0
$754$	3.17063e23	+	7.69901e22i	0.110532	+	0.0268397i
$755$		−	1.57648e24i		−	0.543425i
$756$		0			0
$757$			1.18946e24i			0.400899i	0.979704	+	0.200449i	$0.0642402\pi$
$757$			1.18946e24i			0.400899i	−0.979704	+	0.200449i	$0.935760\pi$
$758$	−7.83846e23	+	3.22806e24i	−0.261242	+	1.07585i
$759$		0			0
$760$	9.54433e22	+	8.28090e22i	0.0311050	+	0.0269874i
$761$	5.41223e24			1.74424			0.872120	−	0.489291i	$-0.162745\pi$
$761$	5.41223e24			1.74424			0.872120	+	0.489291i	$0.162745\pi$
$762$		0			0
$763$		−	8.27041e24i		−	2.60656i
$764$	−3.55915e24	−	1.83679e24i	−1.10931	−	0.572487i
$765$		0			0
$766$	−2.54499e24	−	6.17982e23i	−0.775785	−	0.188378i
$767$	1.78232e24			0.537309
$768$		0			0
$769$	−2.19062e24			−0.645942			−0.322971	−	0.946409i	$-0.604682\pi$
$769$	−2.19062e24			−0.645942			−0.322971	+	0.946409i	$0.604682\pi$
$770$	−2.23031e24	−	5.41571e23i	−0.650421	−	0.157937i
$771$		0			0
$772$	2.61839e24	+	1.35129e24i	0.746944	+	0.385479i
$773$		−	1.32708e24i		−	0.374431i	−0.982319	−	0.187216i	$-0.940054\pi$
$773$		−	1.32708e24i		−	0.374431i	0.982319	−	0.187216i	$-0.0599463\pi$
$774$		0			0
$775$	2.09731e24			0.578893
$776$	−2.35629e24	−	2.04437e24i	−0.643285	−	0.558130i
$777$		0			0
$778$	1.07411e23	−	4.42342e23i	0.0286894	−	0.118149i
$779$		−	3.31690e22i		−	0.00876324i
$780$		0			0
$781$		−	3.33452e24i		−	0.861984i
$782$	−2.49798e23	−	6.06568e22i	−0.0638752	−	0.0155104i
$783$		0			0
$784$	2.71428e24	+	3.81855e24i	0.679153	+	0.955459i
$785$	−1.65260e24			−0.409049
$786$		0			0
$787$		−	2.81620e24i		−	0.682146i	−0.940037	−	0.341073i	$-0.889210\pi$
$787$		−	2.81620e24i		−	0.682146i	0.940037	−	0.341073i	$-0.110790\pi$
$788$	3.24681e24	−	6.29134e24i	0.778007	−	1.50755i
$789$		0			0
$790$	7.74991e23	−	3.19159e24i	0.181747	−	0.748474i
$791$	7.83316e24			1.81734
$792$		0			0
$793$	8.48146e23			0.192597
$794$	−9.21089e23	+	3.79326e24i	−0.206932	+	0.852193i
$795$		0			0
$796$	−3.84600e23	−	1.98482e23i	−0.0845761	−	0.0436476i
$797$		−	6.52060e24i		−	1.41870i	−0.704854	−	0.709352i	$-0.748988\pi$
$797$		−	6.52060e24i		−	1.41870i	0.704854	−	0.709352i	$-0.251012\pi$
$798$		0			0
$799$	8.54981e23			0.182100
$800$	−1.25992e24	−	3.15687e24i	−0.265509	−	0.665261i
$801$		0			0
$802$	−3.81488e24	−	9.26340e23i	−0.787044	−	0.191112i
$803$			8.93462e23i			0.182387i
$804$		0			0
$805$		−	1.36220e24i		−	0.272254i
$806$	−6.97585e23	+	2.87282e24i	−0.137959	+	0.568146i
$807$		0			0
$808$	2.21029e24	−	2.54752e24i	0.428009	−	0.493311i
$809$	−8.81198e23			−0.168854			−0.0844269	−	0.996430i	$-0.526906\pi$
$809$	−8.81198e23			−0.168854			−0.0844269	+	0.996430i	$0.526906\pi$
$810$		0			0
$811$			3.57272e24i			0.670381i	0.942150	+	0.335191i	$0.108801\pi$
$811$			3.57272e24i			0.670381i	−0.942150	+	0.335191i	$0.891199\pi$
$812$	5.72347e23	−	1.10904e24i	0.106276	−	0.205930i
$813$		0			0
$814$	−5.11111e24	−	1.24109e24i	−0.929410	−	0.225682i
$815$	−3.17288e24			−0.570971
$816$		0			0
$817$	2.28978e23			0.0403558
$818$	8.18722e24	+	1.98804e24i	1.42802	+	0.346755i
$819$		0			0
$820$	1.62072e23	−	3.14047e23i	0.0276879	−	0.0536509i
$821$			1.46618e24i			0.247896i	0.992289	+	0.123948i	$0.0395556\pi$
$821$			1.46618e24i			0.247896i	−0.992289	+	0.123948i	$0.960444\pi$
$822$		0			0
$823$	−2.89883e24			−0.480091			−0.240046	−	0.970762i	$-0.577162\pi$
$823$	−2.89883e24			−0.480091			−0.240046	+	0.970762i	$0.577162\pi$
$824$	6.88099e24	+	5.97011e24i	1.12790	+	0.978591i
$825$		0			0
$826$	1.60868e24	−	6.62491e24i	0.258309	−	1.06377i
$827$			4.06842e24i			0.646590i	0.946298	+	0.323295i	$0.104791\pi$
$827$			4.06842e24i			0.646590i	−0.946298	+	0.323295i	$0.895209\pi$
$828$		0			0
$829$			7.02644e24i			1.09401i	0.837129	+	0.547005i	$0.184232\pi$
$829$			7.02644e24i			1.09401i	−0.837129	+	0.547005i	$0.815768\pi$
$830$	−5.50951e24	−	1.33783e24i	−0.849081	−	0.206176i
$831$		0			0
$832$	4.74322e24	−	6.75786e23i	0.716184	−	0.102038i
$833$	1.48659e24			0.222182
$834$		0			0
$835$		−	6.00802e24i		−	0.879826i
$836$	4.04085e23	+	2.08538e23i	0.0585760	+	0.0302296i
$837$		0			0
$838$	−2.26364e24	+	9.32220e24i	−0.321539	+	1.32417i
$839$	3.75744e24			0.528342			0.264171	−	0.964476i	$-0.414902\pi$
$839$	3.75744e24			0.528342			0.264171	+	0.964476i	$0.414902\pi$
$840$		0			0
$841$	7.07774e24			0.975278
$842$	−3.01487e23	+	1.24159e24i	−0.0411259	+	0.169366i
$843$		0			0
$844$	4.78452e24	−	9.27097e24i	0.639628	−	1.23941i
$845$		−	1.91840e24i		−	0.253896i
$846$		0			0
$847$	3.10288e24			0.402491
$848$	9.03626e24	−	6.42310e24i	1.16044	−	0.824859i
$849$		0			0
$850$	−1.04809e24	−	2.54500e23i	−0.131928	−	0.0320352i
$851$		−	3.12169e24i		−	0.389034i
$852$		0			0
$853$		−	8.76545e24i		−	1.07080i	−0.844599	−	0.535399i	$-0.820161\pi$
$853$		−	8.76545e24i		−	1.07080i	0.844599	−	0.535399i	$-0.179839\pi$
$854$	7.65518e23	−	3.15258e24i	0.0925899	−	0.381306i
$855$		0			0
$856$	1.72014e24	−	1.98258e24i	0.203956	−	0.235074i
$857$	7.03954e24			0.826432			0.413216	−	0.910633i	$-0.364405\pi$
$857$	7.03954e24			0.826432			0.413216	+	0.910633i	$0.364405\pi$
$858$		0			0
$859$		−	5.42420e24i		−	0.624301i	−0.950033	−	0.312151i	$-0.898951\pi$
$859$		−	5.42420e24i		−	0.624301i	0.950033	−	0.312151i	$-0.101049\pi$
$860$	2.16798e24	+	1.11884e24i	0.247069	+	0.127506i
$861$		0			0
$862$	−5.71587e24	−	1.38794e24i	−0.638661	−	0.155082i
$863$	4.27768e24			0.473278			0.236639	−	0.971598i	$-0.423954\pi$
$863$	4.27768e24			0.473278			0.236639	+	0.971598i	$0.423954\pi$
$864$		0			0
$865$	−1.38680e24			−0.150445
$866$	7.43186e24	+	1.80462e24i	0.798353	+	0.193858i
$867$		0			0
$868$	1.00487e25	+	5.18588e24i	1.05850	+	0.546267i
$869$		−	1.18192e25i		−	1.23287i
$870$		0			0
$871$	1.11123e25			1.13671
$872$	−1.14412e25	+	1.31869e25i	−1.15900	+	1.33583i
$873$		0			0
$874$	−6.36840e22	+	2.62265e23i	−0.00632679	+	0.0260551i
$875$		−	1.36947e25i		−	1.34736i
$876$		0			0
$877$			1.78456e25i			1.72201i	0.508597	+	0.861005i	$0.330164\pi$
$877$			1.78456e25i			1.72201i	−0.508597	+	0.861005i	$0.669836\pi$
$878$	−1.25883e25	−	3.05673e24i	−1.20300	−	0.292115i
$879$		0			0
$880$	2.80695e24	+	3.94892e24i	0.263106	+	0.370148i
$881$	−2.01186e25			−1.86768			−0.933841	−	0.357688i	$-0.883565\pi$
$881$	−2.01186e25			−1.86768			−0.933841	+	0.357688i	$0.883565\pi$
$882$		0			0
$883$			9.33262e24i			0.849841i	0.905231	+	0.424921i	$0.139698\pi$
$883$			9.33262e24i			0.849841i	−0.905231	+	0.424921i	$0.860302\pi$
$884$	6.97209e23	−	1.35098e24i	0.0628809	−	0.121845i
$885$		0			0
$886$	4.67292e24	−	1.92441e25i	0.413429	−	1.70260i
$887$	−1.53656e25			−1.34647			−0.673237	−	0.739426i	$-0.735097\pi$
$887$	−1.53656e25			−1.34647			−0.673237	+	0.739426i	$0.735097\pi$
$888$		0			0
$889$	1.19084e25			1.02374
$890$	−4.36531e23	+	1.79773e24i	−0.0371706	+	0.153077i
$891$		0			0
$892$	−8.37164e24	−	4.32039e24i	−0.699373	−	0.360929i
$893$		−	8.97651e23i		−	0.0742797i
$894$		0			0
$895$	1.86262e24			0.151227
$896$	1.76921e24	−	1.82406e25i	0.142286	−	1.46697i
$897$		0			0
$898$	6.49419e24	+	1.57694e24i	0.512479	+	0.124442i
$899$		−	1.62558e24i		−	0.127073i
$900$		0			0
$901$		−	3.51788e24i		−	0.269849i
$902$	3.00094e23	−	1.23586e24i	0.0228035	−	0.0939101i
$903$		0			0
$904$	−1.24897e25	−	1.08364e25i	−0.931366	−	0.808076i
$905$	1.06284e25			0.785153
$906$		0			0
$907$			1.19285e25i			0.864818i	0.901678	+	0.432409i	$0.142336\pi$
$907$			1.19285e25i			0.864818i	−0.901678	+	0.432409i	$0.857664\pi$
$908$	−6.44698e24	+	1.24923e25i	−0.463049	+	0.897251i
$909$		0			0
$910$	7.82878e24	+	1.90101e24i	0.551877	+	0.134008i
$911$	−2.47178e24			−0.172625			−0.0863124	−	0.996268i	$-0.527508\pi$
$911$	−2.47178e24			−0.172625			−0.0863124	+	0.996268i	$0.527508\pi$
$912$		0			0
$913$	−2.04029e25			−1.39859
$914$	−1.02749e25	−	2.49498e24i	−0.697807	−	0.169443i
$915$		0			0
$916$	−5.14054e24	+	9.96085e24i	−0.342687	+	0.664025i
$917$			2.51263e25i			1.65955i
$918$		0			0
$919$	2.69765e24			0.174905			0.0874527	−	0.996169i	$-0.472127\pi$
$919$	2.69765e24			0.174905			0.0874527	+	0.996169i	$0.472127\pi$
$920$	−1.88446e24	+	2.17197e24i	−0.121057	+	0.139527i
$921$		0			0
$922$	−3.44797e24	+	1.41995e25i	−0.217446	+	0.895491i
$923$			1.17047e25i			0.731386i
$924$		0			0
$925$		−	1.30978e25i		−	0.803515i
$926$	2.29358e25	+	5.56933e24i	1.39418	+	0.338540i
$927$		0			0
$928$	−2.44683e24	+	9.76540e23i	−0.146031	+	0.0582817i
$929$	−1.73143e24			−0.102393			−0.0511967	−	0.998689i	$-0.516304\pi$
$929$	−1.73143e24			−0.102393			−0.0511967	+	0.998689i	$0.516304\pi$
$930$		0			0
$931$		−	1.56078e24i		−	0.0906296i
$932$	1.92208e25	+	9.91939e24i	1.10595	+	0.570755i
$933$		0			0
$934$	2.68966e23	−	1.10766e24i	0.0151967	−	0.0625834i
$935$	1.53734e24			0.0860741
$936$		0			0
$937$	−1.92274e25			−1.05714			−0.528572	−	0.848888i	$-0.677272\pi$
$937$	−1.92274e25			−1.05714			−0.528572	+	0.848888i	$0.677272\pi$
$938$	1.00297e25	−	4.13047e25i	0.546468	−	2.25048i
$939$		0			0
$940$	4.38614e24	−	8.49904e24i	0.234691	−	0.454761i
$941$			2.50201e25i			1.32671i	0.748303	+	0.663357i	$0.230869\pi$
$941$			2.50201e25i			1.32671i	−0.748303	+	0.663357i	$0.769131\pi$
$942$		0			0
$943$	7.54817e23			0.0393090
$944$	−1.17299e25	+	8.33774e24i	−0.605384	+	0.430315i
$945$		0			0
$946$	8.53155e24	+	2.07166e24i	0.432468	+	0.105013i
$947$			2.84634e25i			1.42992i	0.699165	+	0.714961i	$0.253555\pi$
$947$			2.84634e25i			1.42992i	−0.699165	+	0.714961i	$0.746445\pi$
$948$		0			0
$949$		−	3.13620e24i		−	0.154754i
$950$	−2.67202e23	+	1.10040e24i	−0.0130674	+	0.0538145i
$951$		0			0
$952$	−4.39235e24	−	3.81091e24i	−0.211000	−	0.183069i
$953$	−3.20703e25			−1.52691			−0.763455	−	0.645862i	$-0.776498\pi$
$953$	−3.20703e25			−1.52691			−0.763455	+	0.645862i	$0.776498\pi$
$954$		0			0
$955$			1.42166e25i			0.664916i
$956$	2.56249e25	+	1.32244e25i	1.18787	+	0.613033i
$957$		0			0
$958$	1.89196e25	+	4.59412e24i	0.861599	+	0.209216i
$959$	−1.51880e25			−0.685557
$960$		0			0
$961$	−7.82115e24			−0.346834
$962$	1.79409e25	+	4.35645e24i	0.788597	+	0.191489i
$963$		0			0
$964$	1.93040e24	+	9.96231e23i	0.0833666	+	0.0430234i
$965$		−	1.04589e25i		−	0.447715i
$966$		0			0
$967$	−4.41829e25			−1.85836			−0.929178	−	0.369633i	$-0.879483\pi$
$967$	−4.41829e25			−1.85836			−0.929178	+	0.369633i	$0.879483\pi$
$968$	−4.94743e24	−	4.29251e24i	−0.206272	−	0.178966i
$969$		0			0
$970$	−2.61286e24	+	1.07603e25i	−0.107042	+	0.440825i
$971$		−	5.97199e24i		−	0.242524i	−0.992621	−	0.121262i	$-0.961306\pi$
$971$		−	5.97199e24i		−	0.242524i	0.992621	−	0.121262i	$-0.0386942\pi$
$972$		0			0
$973$		−	3.22308e25i		−	1.28621i
$974$	5.70281e24	+	1.38477e24i	0.225599	+	0.0547807i
$975$		0			0
$976$	−5.58185e24	+	3.96766e24i	−0.216998	+	0.154245i
$977$	−1.23801e25			−0.477112			−0.238556	−	0.971129i	$-0.576674\pi$
$977$	−1.23801e25			−0.477112			−0.238556	+	0.971129i	$0.576674\pi$
$978$		0			0
$979$			6.65740e24i			0.252146i
$980$	7.62637e24	−	1.47776e25i	0.286349	−	0.554860i
$981$		0			0
$982$	−3.32525e24	+	1.36941e25i	−0.122709	+	0.505344i
$983$	−1.37346e25			−0.502471			−0.251235	−	0.967926i	$-0.580837\pi$
$983$	−1.37346e25			−0.502471			−0.251235	+	0.967926i	$0.580837\pi$
$984$		0			0
$985$	−2.51300e25			−0.903617
$986$	−1.97258e23	+	8.12354e23i	−0.00703204	+	0.0289595i
$987$		0			0
$988$	−1.41841e24	−	7.32006e23i	−0.0497013	−	0.0256496i
$989$			5.21078e24i			0.181023i
$990$		0			0
$991$	−3.74894e25			−1.28021			−0.640106	−	0.768286i	$-0.721110\pi$
$991$	−3.74894e25			−1.28021			−0.640106	+	0.768286i	$0.721110\pi$
$992$	−8.84815e24	−	2.21700e25i	−0.299574	−	0.750614i
$993$		0			0
$994$	4.35067e25	+	1.05644e25i	1.44801	+	0.351610i
$995$			1.53624e24i			0.0506946i
$996$		0			0
$997$			1.39329e25i			0.451993i	0.974128	+	0.225997i	$0.0725638\pi$
$997$			1.39329e25i			0.451993i	−0.974128	+	0.225997i	$0.927436\pi$
$998$	5.73091e24	−	2.36012e25i	0.184338	−	0.759144i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.18.d.b.37.1		16
3.2	odd	2		8.18.b.a.5.16	yes	16
8.5	even	2	inner	72.18.d.b.37.2		16
12.11	even	2		32.18.b.a.17.1		16
24.5	odd	2		8.18.b.a.5.15	✓	16
24.11	even	2		32.18.b.a.17.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.18.b.a.5.15	✓	16	24.5	odd	2
8.18.b.a.5.16	yes	16	3.2	odd	2
32.18.b.a.17.1		16	12.11	even	2
32.18.b.a.17.16		16	24.11	even	2
72.18.d.b.37.1		16	1.1	even	1	trivial
72.18.d.b.37.2		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)

\(f(q)\)	\(=\)	\(q+(-351.815 - 85.4288i) q^{2} +(116476. + 60110.3i) q^{4} -465248. i q^{5} +2.24795e7 q^{7} +(-3.58428e7 - 3.10981e7i) q^{8} +O(q^{10})\)	\(q+(-351.815 - 85.4288i) q^{2} +(116476. + 60110.3i) q^{4} -465248. i q^{5} +2.24795e7 q^{7} +(-3.58428e7 - 3.10981e7i) q^{8} +(-3.97456e7 + 1.63681e8i) q^{10} +6.06148e8i q^{11} -2.12768e9i q^{13} +(-7.90864e9 - 1.92040e9i) q^{14} +(9.95338e9 + 1.40028e10i) q^{16} +5.45139e9 q^{17} -5.72346e9i q^{19} +(2.79662e10 - 5.41902e10i) q^{20} +(5.17825e10 - 2.13252e11i) q^{22} +1.30247e11 q^{23} +5.46483e11 q^{25} +(-1.81765e11 + 7.48551e11i) q^{26} +(2.61832e12 + 1.35125e12i) q^{28} -4.23568e11i q^{29} +3.83783e12 q^{31} +(-2.30551e12 - 5.77670e12i) q^{32} +(-1.91788e12 - 4.65706e11i) q^{34} -1.04586e13i q^{35} -2.39674e13i q^{37} +(-4.88948e11 + 2.01360e12i) q^{38} +(-1.44683e13 + 1.66758e13i) q^{40} +5.79528e12 q^{41} +4.00069e13i q^{43} +(-3.64357e13 + 7.06016e13i) q^{44} +(-4.58229e13 - 1.11268e13i) q^{46} +1.56837e14 q^{47} +2.72699e14 q^{49} +(-1.92261e14 - 4.66854e13i) q^{50} +(1.27896e14 - 2.47824e14i) q^{52} -6.45318e14i q^{53} +2.82010e14 q^{55} +(-8.05730e14 - 6.99071e14i) q^{56} +(-3.61849e13 + 1.49018e14i) q^{58} +8.37680e14i q^{59} +3.98624e14i q^{61} +(-1.35021e15 - 3.27862e14i) q^{62} +(3.17616e14 + 2.22929e15i) q^{64} -9.89901e14 q^{65} +5.22273e15i q^{67} +(6.34956e14 + 3.27685e14i) q^{68} +(-8.93463e14 + 3.67948e15i) q^{70} -5.50116e15 q^{71} +1.47400e15 q^{73} +(-2.04751e15 + 8.43211e15i) q^{74} +(3.44039e14 - 6.66645e14i) q^{76} +1.36259e16i q^{77} -1.94988e16 q^{79} +(6.51478e15 - 4.63079e15i) q^{80} +(-2.03887e15 - 4.95084e14i) q^{82} +3.36599e16i q^{83} -2.53625e15i q^{85} +(3.41774e15 - 1.40750e16i) q^{86} +(1.88501e16 - 2.17261e16i) q^{88} +1.09831e16 q^{89} -4.78293e16i q^{91} +(1.51706e16 + 7.82918e15i) q^{92} +(-5.51777e16 - 1.33984e16i) q^{94} -2.66283e15 q^{95} +6.57395e16 q^{97} +(-9.59397e16 - 2.32964e16i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 270 q^{2} - 27436 q^{4} + 11529600 q^{7} - 24334920 q^{8}+O(q^{10}) \) 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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