LMFDB - Embedded newform 27.16.c.a.19.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [27,16,Mod(10,27)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("27.10"); S:= CuspForms(chi, 16); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 16, names="a")

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	27.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$38.5272463770$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			19.6
Character	$\chi$	$=$	27.19
Dual form			27.16.c.a.10.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-30.1976 + 52.3037i) q^{2} +(14560.2 + 25219.0i) q^{4} +(-62931.9 - 109001. i) q^{5} +(-2.04281e6 + 3.53826e6i) q^{7} -3.73776e6 q^{8} +7.60156e6 q^{10} +(3.00835e7 - 5.21061e7i) q^{11} +(5.90623e6 + 1.02299e7i) q^{13} +(-1.23376e8 - 2.13694e8i) q^{14} +(-3.64238e8 + 6.30879e8i) q^{16} -2.65805e9 q^{17} +2.33561e9 q^{19} +(1.83260e9 - 3.17416e9i) q^{20} +(1.81690e9 + 3.14696e9i) q^{22} +(8.95648e9 + 1.55131e10i) q^{23} +(7.33795e9 - 1.27097e10i) q^{25} -7.13415e8 q^{26} -1.18975e11 q^{28} +(-1.49932e10 + 2.59690e10i) q^{29} +(-5.73455e10 - 9.93254e10i) q^{31} +(-8.32376e10 - 1.44172e11i) q^{32} +(8.02666e10 - 1.39026e11i) q^{34} +5.14232e11 q^{35} +1.02630e11 q^{37} +(-7.05297e10 + 1.22161e11i) q^{38} +(2.35224e11 + 4.07420e11i) q^{40} +(-1.01906e12 - 1.76506e12i) q^{41} +(6.33169e11 - 1.09668e12i) q^{43} +1.75209e12 q^{44} -1.08186e12 q^{46} +(2.66170e12 - 4.61020e12i) q^{47} +(-5.97240e12 - 1.03445e13i) q^{49} +(4.43176e11 + 7.67604e11i) q^{50} +(-1.71992e11 + 2.97899e11i) q^{52} +4.91335e11 q^{53} -7.57284e12 q^{55} +(7.63555e12 - 1.32252e13i) q^{56} +(-9.05518e11 - 1.56840e12i) q^{58} +(4.33799e12 + 7.51363e12i) q^{59} +(1.40603e13 - 2.43532e13i) q^{61} +6.92678e12 q^{62} -1.38164e13 q^{64} +(7.43380e11 - 1.28757e12i) q^{65} +(5.72996e12 + 9.92457e12i) q^{67} +(-3.87018e13 - 6.70334e13i) q^{68} +(-1.55286e13 + 2.68963e13i) q^{70} -4.63738e13 q^{71} -2.03563e13 q^{73} +(-3.09916e12 + 5.36791e12i) q^{74} +(3.40070e13 + 5.89018e13i) q^{76} +(1.22910e14 + 2.12886e14i) q^{77} +(4.33752e13 - 7.51280e13i) q^{79} +9.16887e13 q^{80} +1.23092e14 q^{82} +(-5.62932e13 + 9.75026e13i) q^{83} +(1.67276e14 + 2.89731e14i) q^{85} +(3.82403e13 + 6.62342e13i) q^{86} +(-1.12445e14 + 1.94760e14i) q^{88} -7.18882e14 q^{89} -4.82613e13 q^{91} +(-2.60817e14 + 4.51748e14i) q^{92} +(1.60754e14 + 2.78433e14i) q^{94} +(-1.46984e14 - 2.54584e14i) q^{95} +(-1.42070e14 + 2.46072e14i) q^{97} +7.21407e14 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 129 q^{2} - 212993 q^{4} + 152655 q^{5} + 803705 q^{7} - 20162658 q^{8} + 65532 q^{10} + 60735990 q^{11} - 41509093 q^{13} - 215313024 q^{14} - 2952822785 q^{16} + 2121112242 q^{17} + 5670809246 q^{19}+ \cdots - 72\!\cdots\!90 q^{98}+O(q^{100}) $ 28 * q + 129 * q^2 - 212993 * q^4 + 152655 * q^5 + 803705 * q^7 - 20162658 * q^8 + 65532 * q^10 + 60735990 * q^11 - 41509093 * q^13 - 215313024 * q^14 - 2952822785 * q^16 + 2121112242 * q^17 + 5670809246 * q^19 + 1434155028 * q^20 + 7841223807 * q^22 + 49433203761 * q^23 - 59779497779 * q^25 - 28088907384 * q^26 - 103195803652 * q^28 + 152663830725 * q^29 - 13955906443 * q^31 + 779638216401 * q^32 - 15287791959 * q^34 - 2803990417206 * q^35 + 531598359836 * q^37 + 3598723579461 * q^38 - 1083028910664 * q^40 + 1656362316264 * q^41 + 2394872112236 * q^43 - 13185661781850 * q^44 + 1511321018232 * q^46 + 7686086213559 * q^47 - 7946464864203 * q^49 + 2177050903941 * q^50 + 1969798905818 * q^52 + 20778802614756 * q^53 - 21700105111626 * q^55 - 13789887516654 * q^56 + 15429496587216 * q^58 - 17132922121350 * q^59 - 17229834579991 * q^61 + 190512185539596 * q^62 + 11322374934466 * q^64 - 92170621979115 * q^65 - 19847122719016 * q^67 - 106742875854159 * q^68 - 85984052928798 * q^70 - 60954771085488 * q^71 + 206937948168362 * q^73 + 169102773629016 * q^74 - 274786877071699 * q^76 + 121510644149499 * q^77 + 137921083996235 * q^79 - 1189869535368192 * q^80 + 747645180639978 * q^82 + 243294491978445 * q^83 + 278537029457886 * q^85 + 1439527045654455 * q^86 + 8025917716587 * q^88 - 3513318445769832 * q^89 - 1924506955785338 * q^91 + 3448278918317022 * q^92 + 1100860396273032 * q^94 + 3375682767029028 * q^95 - 1883742033081100 * q^97 - 7254179697035790 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−30.1976	+	52.3037i	−0.166820	+	0.288940i	−0.937300	−	0.348524i	$-0.886683\pi$
$2$	−30.1976	+	52.3037i	−0.166820	+	0.288940i	0.770480	+	0.637464i	$0.220016\pi$
$3$		0			0
$3$		0			0
$4$	14560.2	+	25219.0i	0.444342	+	0.769624i
$5$	−62931.9	−	109001.i	−0.360243	−	0.623959i	0.627758	−	0.778409i	$-0.283973\pi$
$5$	−62931.9	−	109001.i	−0.360243	−	0.623959i	−0.988001	+	0.154450i	$0.950640\pi$
$6$		0			0
$7$	−2.04281e6	+	3.53826e6i	−0.937548	+	1.62388i	−0.167522	+	0.985868i	$0.553577\pi$
$7$	−2.04281e6	+	3.53826e6i	−0.937548	+	1.62388i	−0.770026	+	0.638013i	$0.779757\pi$
$8$	−3.73776e6			−0.630139
$9$		0			0
$10$	7.60156e6			0.240382
$11$	3.00835e7	−	5.21061e7i	0.465461	−	0.806202i	−0.533762	−	0.845635i	$-0.679222\pi$
$11$	3.00835e7	−	5.21061e7i	0.465461	−	0.806202i	0.999222	+	0.0394335i	$0.0125553\pi$
$12$		0			0
$13$	5.90623e6	+	1.02299e7i	0.0261057	+	0.0452164i	0.878783	−	0.477221i	$-0.158356\pi$
$13$	5.90623e6	+	1.02299e7i	0.0261057	+	0.0452164i	−0.852677	+	0.522438i	$0.825023\pi$
$14$	−1.23376e8	−	2.13694e8i	−0.312803	−	0.541790i
$15$		0			0
$16$	−3.64238e8	+	6.30879e8i	−0.339223	+	0.587551i
$17$	−2.65805e9			−1.57107			−0.785536	−	0.618816i	$-0.787613\pi$
$17$	−2.65805e9			−1.57107			−0.785536	+	0.618816i	$0.787613\pi$
$18$		0			0
$19$	2.33561e9			0.599443			0.299722	−	0.954027i	$-0.403106\pi$
$19$	2.33561e9			0.599443			0.299722	+	0.954027i	$0.403106\pi$
$20$	1.83260e9	−	3.17416e9i	0.320143	−	0.554503i
$21$		0			0
$22$	1.81690e9	+	3.14696e9i	0.155296	+	0.268980i
$23$	8.95648e9	+	1.55131e10i	0.548503	+	0.950035i	0.998377	+	0.0569429i	$0.0181353\pi$
$23$	8.95648e9	+	1.55131e10i	0.548503	+	0.950035i	−0.449875	+	0.893092i	$0.648531\pi$
$24$		0			0
$25$	7.33795e9	−	1.27097e10i	0.240450	−	0.416471i
$26$	−7.13415e8			−0.0174198
$27$		0			0
$28$	−1.18975e11			−1.66637
$29$	−1.49932e10	+	2.59690e10i	−0.161402	+	0.279557i	−0.935372	−	0.353666i	$-0.884935\pi$
$29$	−1.49932e10	+	2.59690e10i	−0.161402	+	0.279557i	0.773969	+	0.633223i	$0.218268\pi$
$30$		0			0
$31$	−5.73455e10	−	9.93254e10i	−0.374358	−	0.648407i	0.615873	−	0.787846i	$-0.288803\pi$
$31$	−5.73455e10	−	9.93254e10i	−0.374358	−	0.648407i	−0.990231	+	0.139439i	$0.955470\pi$
$32$	−8.32376e10	−	1.44172e11i	−0.428248	−	0.741747i
$33$		0			0
$34$	8.02666e10	−	1.39026e11i	0.262086	−	0.453946i
$35$	5.14232e11			1.35098
$36$		0			0
$37$	1.02630e11			0.177730			0.0888648	−	0.996044i	$-0.471676\pi$
$37$	1.02630e11			0.177730			0.0888648	+	0.996044i	$0.471676\pi$
$38$	−7.05297e10	+	1.22161e11i	−0.0999989	+	0.173203i
$39$		0			0
$40$	2.35224e11	+	4.07420e11i	0.227003	+	0.393181i
$41$	−1.01906e12	−	1.76506e12i	−0.817184	−	1.41540i	−0.907749	−	0.419514i	$-0.862201\pi$
$41$	−1.01906e12	−	1.76506e12i	−0.817184	−	1.41540i	0.0905650	−	0.995891i	$-0.471133\pi$
$42$		0			0
$43$	6.33169e11	−	1.09668e12i	0.355227	−	0.615272i	−0.631930	−	0.775026i	$-0.717737\pi$
$43$	6.33169e11	−	1.09668e12i	0.355227	−	0.615272i	0.987157	+	0.159754i	$0.0510701\pi$
$44$	1.75209e12			0.827296
$45$		0			0
$46$	−1.08186e12			−0.366004
$47$	2.66170e12	−	4.61020e12i	0.766346	−	1.32735i	−0.173186	−	0.984889i	$-0.555406\pi$
$47$	2.66170e12	−	4.61020e12i	0.766346	−	1.32735i	0.939532	−	0.342461i	$-0.111261\pi$
$48$		0			0
$49$	−5.97240e12	−	1.03445e13i	−1.25799	−	2.17891i
$50$	4.43176e11	+	7.67604e11i	0.0802235	+	0.138951i
$51$		0			0
$52$	−1.71992e11	+	2.97899e11i	−0.0231997	+	0.0401831i
$53$	4.91335e11			0.0574525			0.0287263	−	0.999587i	$-0.490855\pi$
$53$	4.91335e11			0.0574525			0.0287263	+	0.999587i	$0.490855\pi$
$54$		0			0
$55$	−7.57284e12			−0.670716
$56$	7.63555e12	−	1.32252e13i	0.590786	−	1.02327i
$57$		0			0
$58$	−9.05518e11	−	1.56840e12i	−0.0538502	−	0.0932712i
$59$	4.33799e12	+	7.51363e12i	0.226934	+	0.393061i	0.956898	−	0.290425i	$-0.0937966\pi$
$59$	4.33799e12	+	7.51363e12i	0.226934	+	0.393061i	−0.729964	+	0.683485i	$0.760463\pi$
$60$		0			0
$61$	1.40603e13	−	2.43532e13i	0.572824	−	0.992160i	−0.423451	−	0.905919i	$-0.639181\pi$
$61$	1.40603e13	−	2.43532e13i	0.572824	−	0.992160i	0.996274	−	0.0862406i	$-0.0274854\pi$
$62$	6.92678e12			0.249801
$63$		0			0
$64$	−1.38164e13			−0.392686
$65$	7.43380e11	−	1.28757e12i	0.0188088	−	0.0325778i
$66$		0			0
$67$	5.72996e12	+	9.92457e12i	0.115502	+	0.200056i	0.917980	−	0.396626i	$-0.129819\pi$
$67$	5.72996e12	+	9.92457e12i	0.115502	+	0.200056i	−0.802478	+	0.596681i	$0.796486\pi$
$68$	−3.87018e13	−	6.70334e13i	−0.698094	−	1.20913i
$69$		0			0
$70$	−1.55286e13	+	2.68963e13i	−0.225370	+	0.390352i
$71$	−4.63738e13			−0.605111			−0.302556	−	0.953132i	$-0.597840\pi$
$71$	−4.63738e13			−0.605111			−0.302556	+	0.953132i	$0.597840\pi$
$72$		0			0
$73$	−2.03563e13			−0.215664			−0.107832	−	0.994169i	$-0.534391\pi$
$73$	−2.03563e13			−0.215664			−0.107832	+	0.994169i	$0.534391\pi$
$74$	−3.09916e12	+	5.36791e12i	−0.0296488	+	0.0513532i
$75$		0			0
$76$	3.40070e13	+	5.89018e13i	0.266358	+	0.461346i
$77$	1.22910e14	+	2.12886e14i	0.872784	+	1.51171i
$78$		0			0
$79$	4.33752e13	−	7.51280e13i	0.254119	−	0.440148i	−0.710537	−	0.703660i	$-0.751548\pi$
$79$	4.33752e13	−	7.51280e13i	0.254119	−	0.440148i	0.964656	+	0.263513i	$0.0848810\pi$
$80$	9.16887e13			0.488811
$81$		0			0
$82$	1.23092e14			0.545289
$83$	−5.62932e13	+	9.75026e13i	−0.227704	+	0.394394i	−0.957127	−	0.289668i	$-0.906455\pi$
$83$	−5.62932e13	+	9.75026e13i	−0.227704	+	0.394394i	0.729424	+	0.684062i	$0.239788\pi$
$84$		0			0
$85$	1.67276e14	+	2.89731e14i	0.565968	+	0.980285i
$86$	3.82403e13	+	6.62342e13i	0.118518	+	0.205279i
$87$		0			0
$88$	−1.12445e14	+	1.94760e14i	−0.293305	+	0.508019i
$89$	−7.18882e14			−1.72279			−0.861396	−	0.507934i	$-0.830409\pi$
$89$	−7.18882e14			−1.72279			−0.861396	+	0.507934i	$0.830409\pi$
$90$		0			0
$91$	−4.82613e13			−0.0979014
$92$	−2.60817e14	+	4.51748e14i	−0.487446	+	0.844282i
$93$		0			0
$94$	1.60754e14	+	2.78433e14i	0.255683	+	0.442856i
$95$	−1.46984e14	−	2.54584e14i	−0.215945	−	0.374028i
$96$		0			0
$97$	−1.42070e14	+	2.46072e14i	−0.178531	+	0.309225i	−0.941378	−	0.337355i	$-0.890468\pi$
$97$	−1.42070e14	+	2.46072e14i	−0.178531	+	0.309225i	0.762847	+	0.646579i	$0.223801\pi$
$98$	7.21407e14			0.839431
$99$		0			0
$100$	4.27368e14			0.427368
$101$	8.47542e13	−	1.46799e14i	0.0786594	−	0.136242i	−0.824012	−	0.566572i	$-0.808269\pi$
$101$	8.47542e13	−	1.46799e14i	0.0786594	−	0.136242i	0.902672	+	0.430330i	$0.141603\pi$
$102$		0			0
$103$	−1.58415e14	−	2.74383e14i	−0.126916	−	0.219825i	0.795564	−	0.605869i	$-0.207175\pi$
$103$	−1.58415e14	−	2.74383e14i	−0.126916	−	0.219825i	−0.922480	+	0.386044i	$0.873841\pi$
$104$	−2.20761e13	−	3.82369e13i	−0.0164502	−	0.0284926i
$105$		0			0
$106$	−1.48371e13	+	2.56987e13i	−0.00958420	+	0.0166003i
$107$	−3.70048e14			−0.222782			−0.111391	−	0.993777i	$-0.535531\pi$
$107$	−3.70048e14			−0.222782			−0.111391	+	0.993777i	$0.535531\pi$
$108$		0			0
$109$	−9.62433e14			−0.504280			−0.252140	−	0.967691i	$-0.581134\pi$
$109$	−9.62433e14			−0.504280			−0.252140	+	0.967691i	$0.581134\pi$
$110$	2.28681e14	−	3.96088e14i	0.111889	−	0.193797i
$111$		0			0
$112$	−1.48814e15	−	2.57754e15i	−0.636076	−	1.10172i
$113$	1.47557e15	+	2.55576e15i	0.590027	+	1.02196i	0.994228	+	0.107287i	$0.0342163\pi$
$113$	1.47557e15	+	2.55576e15i	0.590027	+	1.02196i	−0.404201	+	0.914670i	$0.632450\pi$
$114$		0			0
$115$	1.12730e15	−	1.95254e15i	0.395189	−	0.684487i
$116$	−8.73219e14			−0.286872
$117$		0			0
$118$	−5.23987e14			−0.151428
$119$	5.42990e15	−	9.40487e15i	1.47296	−	2.55123i
$120$		0			0
$121$	2.78592e14	+	4.82536e14i	0.0666927	+	0.115515i
$122$	8.49174e14	+	1.47081e15i	0.191116	+	0.331023i
$123$		0			0
$124$	1.66993e15	−	2.89240e15i	0.332686	−	0.576229i
$125$	−5.68822e15			−1.06697
$126$		0			0
$127$	−3.44817e15			−0.574197			−0.287098	−	0.957901i	$-0.592691\pi$
$127$	−3.44817e15			−0.574197			−0.287098	+	0.957901i	$0.592691\pi$
$128$	3.14475e15	−	5.44687e15i	0.493755	−	0.855209i
$129$		0			0
$130$	4.48966e13	+	7.77631e13i	0.00627535	+	0.0108692i
$131$	−2.61435e15	−	4.52818e15i	−0.345007	−	0.597570i	0.640348	−	0.768085i	$-0.278790\pi$
$131$	−2.61435e15	−	4.52818e15i	−0.345007	−	0.597570i	−0.985355	+	0.170515i	$0.945457\pi$
$132$		0			0
$133$	−4.77122e15	+	8.26399e15i	−0.562007	+	0.973425i
$134$	−6.92123e14			−0.0770721
$135$		0			0
$136$	9.93515e15			0.989994
$137$	−5.47818e15	+	9.48848e15i	−0.516692	+	0.894937i	0.483120	+	0.875554i	$0.339503\pi$
$137$	−5.47818e15	+	9.48848e15i	−0.516692	+	0.894937i	−0.999812	+	0.0193829i	$0.993830\pi$
$138$		0			0
$139$	−6.16511e15	−	1.06783e16i	−0.521591	−	0.903422i	−0.999685	−	0.0251130i	$-0.992005\pi$
$139$	−6.16511e15	−	1.06783e16i	−0.521591	−	0.903422i	0.478094	−	0.878309i	$-0.341328\pi$
$140$	7.48733e15	+	1.29684e16i	0.600298	+	1.03975i
$141$		0			0
$142$	1.40038e15	−	2.42552e15i	0.100944	−	0.174841i
$143$	7.10720e14			0.0486047
$144$		0			0
$145$	3.77421e15			0.232576
$146$	6.14710e14	−	1.06471e15i	0.0359769	−	0.0623139i
$147$		0			0
$148$	1.49431e15	+	2.58822e15i	0.0789728	+	0.136785i
$149$	6.86129e15	+	1.18841e16i	0.344754	+	0.597131i	0.985309	−	0.170781i	$-0.0546291\pi$
$149$	6.86129e15	+	1.18841e16i	0.344754	+	0.597131i	−0.640555	+	0.767912i	$0.721296\pi$
$150$		0			0
$151$	−5.53932e15	+	9.59438e15i	−0.251843	+	0.436204i	−0.964033	−	0.265782i	$-0.914370\pi$
$151$	−5.53932e15	+	9.59438e15i	−0.251843	+	0.436204i	0.712191	+	0.701986i	$0.247703\pi$
$152$	−8.72995e15			−0.377733
$153$		0			0
$154$	−1.48463e16			−0.582389
$155$	−7.21772e15	+	1.25015e16i	−0.269720	+	0.467168i
$156$		0			0
$157$	2.67340e16	+	4.63046e16i	0.907437	+	1.57173i	0.817613	+	0.575769i	$0.195297\pi$
$157$	2.67340e16	+	4.63046e16i	0.907437	+	1.57173i	0.0898239	+	0.995958i	$0.471370\pi$
$158$	2.61965e15	+	4.53736e15i	0.0847842	+	0.146851i
$159$		0			0
$160$	−1.04766e16	+	1.81460e16i	−0.308546	+	0.534418i
$161$	−7.31857e16			−2.05699
$162$		0			0
$163$	2.54506e16			0.652064			0.326032	−	0.945359i	$-0.394288\pi$
$163$	2.54506e16			0.652064			0.326032	+	0.945359i	$0.394288\pi$
$164$	2.96754e16	−	5.13993e16i	0.726219	−	1.25785i
$165$		0			0
$166$	−3.39983e15	−	5.88868e15i	−0.0759708	−	0.131585i
$167$	3.12872e16	+	5.41910e16i	0.668334	+	1.15759i	0.978370	+	0.206863i	$0.0663254\pi$
$167$	3.12872e16	+	5.41910e16i	0.668334	+	1.15759i	−0.310036	+	0.950725i	$0.600341\pi$
$168$		0			0
$169$	2.55232e16	−	4.42074e16i	0.498637	−	0.863665i
$170$	−2.02053e16			−0.377658
$171$		0			0
$172$	3.68763e16			0.631370
$173$	1.82106e16	−	3.15417e16i	0.298524	−	0.517059i	−0.677275	−	0.735730i	$-0.736839\pi$
$173$	1.82106e16	−	3.15417e16i	0.298524	−	0.517059i	0.975798	+	0.218672i	$0.0701724\pi$
$174$		0			0
$175$	2.99801e16	+	5.19271e16i	0.450867	+	0.780924i
$176$	2.19151e16	+	3.79580e16i	0.315790	+	0.546964i
$177$		0			0
$178$	2.17085e16	−	3.76002e16i	0.287395	−	0.497783i
$179$	−5.71118e16			−0.724983			−0.362491	−	0.931987i	$-0.618074\pi$
$179$	−5.71118e16			−0.724983			−0.362491	+	0.931987i	$0.618074\pi$
$180$		0			0
$181$	−1.35199e17			−1.57900			−0.789502	−	0.613748i	$-0.789661\pi$
$181$	−1.35199e17			−1.57900			−0.789502	+	0.613748i	$0.789661\pi$
$182$	1.45737e15	−	2.52425e15i	0.0163319	−	0.0282876i
$183$		0			0
$184$	−3.34772e16	−	5.79842e16i	−0.345633	−	0.598654i
$185$	−6.45867e15	−	1.11867e16i	−0.0640258	−	0.110896i
$186$		0			0
$187$	−7.99634e16	+	1.38501e17i	−0.731272	+	1.26660i
$188$	1.55020e17			1.36208
$189$		0			0
$190$	1.77543e16			0.144096
$191$	7.91112e16	−	1.37025e17i	0.617288	−	1.06917i	−0.372691	−	0.927956i	$-0.621565\pi$
$191$	7.91112e16	−	1.37025e17i	0.617288	−	1.06917i	0.989978	−	0.141218i	$-0.0451019\pi$
$192$		0			0
$193$	−1.34353e17	−	2.32705e17i	−0.969540	−	1.67929i	−0.696887	−	0.717181i	$-0.745432\pi$
$193$	−1.34353e17	−	2.32705e17i	−0.969540	−	1.67929i	−0.272654	−	0.962112i	$-0.587901\pi$
$194$	−8.58032e15	−	1.48615e16i	−0.0595649	−	0.103169i
$195$		0			0
$196$	1.73919e17	−	3.01236e17i	1.11796	−	1.93636i
$197$	−7.23126e16			−0.447422			−0.223711	−	0.974656i	$-0.571817\pi$
$197$	−7.23126e16			−0.447422			−0.223711	+	0.974656i	$0.571817\pi$
$198$		0			0
$199$	−7.66993e16			−0.439940			−0.219970	−	0.975507i	$-0.570596\pi$
$199$	−7.66993e16			−0.439940			−0.219970	+	0.975507i	$0.570596\pi$
$200$	−2.74275e16	+	4.75058e16i	−0.151517	+	0.262435i
$201$		0			0
$202$	5.11874e15	+	8.86592e15i	0.0262439	+	0.0454557i
$203$	−6.12568e16	−	1.06100e17i	−0.302645	−	0.524197i
$204$		0			0
$205$	−1.28262e17	+	2.22157e17i	−0.588770	+	1.01978i
$206$	1.91350e16			0.0846884
$207$		0			0
$208$	−8.60509e15			−0.0354226
$209$	7.02633e16	−	1.21700e17i	0.279017	−	0.483272i
$210$		0			0
$211$	1.65432e17	+	2.86536e17i	0.611646	+	1.05940i	0.990963	+	0.134135i	$0.0428256\pi$
$211$	1.65432e17	+	2.86536e17i	0.611646	+	1.05940i	−0.379317	+	0.925267i	$0.623841\pi$
$212$	7.15395e15	+	1.23910e16i	0.0255286	+	0.0442168i
$213$		0			0
$214$	1.11745e16	−	1.93549e16i	0.0371643	−	0.0643705i
$215$	−1.59386e17			−0.511873
$216$		0			0
$217$	4.68585e17			1.40391
$218$	2.90631e16	−	5.03388e16i	0.0841238	−	0.145707i
$219$		0			0
$220$	−1.10262e17	−	1.90980e17i	−0.298028	−	0.516199i
$221$	−1.56991e16	−	2.71916e16i	−0.0410139	−	0.0710382i
$222$		0			0
$223$	2.03539e16	−	3.52541e16i	0.0497007	−	0.0860841i	−0.840105	−	0.542424i	$-0.817507\pi$
$223$	2.03539e16	−	3.52541e16i	0.0497007	−	0.0860841i	0.889805	+	0.456340i	$0.150840\pi$
$224$	6.80156e17			1.60601
$225$		0			0
$226$	−1.78235e17			−0.393712
$227$	−3.51405e17	+	6.08652e17i	−0.750956	+	1.30069i	0.196404	+	0.980523i	$0.437073\pi$
$227$	−3.51405e17	+	6.08652e17i	−0.750956	+	1.30069i	−0.947360	+	0.320170i	$0.896260\pi$
$228$		0			0
$229$	2.05335e16	+	3.55650e16i	0.0410862	+	0.0711635i	0.885837	−	0.463996i	$-0.153585\pi$
$229$	2.05335e16	+	3.55650e16i	0.0410862	+	0.0711635i	−0.844751	+	0.535160i	$0.820251\pi$
$230$	6.80832e16	+	1.17924e17i	0.131850	+	0.228372i
$231$		0			0
$232$	5.60411e16	−	9.70660e16i	0.101706	−	0.176160i
$233$	−4.65560e17			−0.818101			−0.409050	−	0.912512i	$-0.634140\pi$
$233$	−4.65560e17			−0.818101			−0.409050	+	0.912512i	$0.634140\pi$
$234$		0			0
$235$	−6.70023e17			−1.10428
$236$	−1.26324e17	+	2.18800e17i	−0.201673	+	0.349307i
$237$		0			0
$238$	3.27940e17	+	5.68008e17i	0.491436	+	0.851192i
$239$	−3.06509e17	−	5.30889e17i	−0.445102	−	0.770939i	0.552958	−	0.833209i	$-0.313499\pi$
$239$	−3.06509e17	−	5.30889e17i	−0.445102	−	0.770939i	−0.998059	+	0.0622707i	$0.980166\pi$
$240$		0			0
$241$	−4.79927e17	+	8.31257e17i	−0.654707	+	1.13399i	0.327260	+	0.944934i	$0.393875\pi$
$241$	−4.79927e17	+	8.31257e17i	−0.654707	+	1.13399i	−0.981967	+	0.189052i	$0.939459\pi$
$242$	−3.36512e16			−0.0445026
$243$		0			0
$244$	8.18884e17			1.01812
$245$	−7.51708e17	+	1.30200e18i	−0.906366	+	1.56987i
$246$		0			0
$247$	1.37947e16	+	2.38930e16i	0.0156489	+	0.0271047i
$248$	2.14344e17	+	3.71254e17i	0.235898	+	0.408586i
$249$		0			0
$250$	1.71770e17	−	2.97515e17i	0.177991	−	0.308290i
$251$	9.35854e17			0.941142			0.470571	−	0.882362i	$-0.344048\pi$
$251$	9.35854e17			0.941142			0.470571	+	0.882362i	$0.344048\pi$
$252$		0			0
$253$	1.07777e18			1.02123
$254$	1.04126e17	−	1.80352e17i	0.0957873	−	0.165908i
$255$		0			0
$256$	−3.64402e16	−	6.31162e16i	−0.0316068	−	0.0547446i
$257$	−3.05801e17	−	5.29663e17i	−0.257597	−	0.446170i	0.708001	−	0.706212i	$-0.249597\pi$
$257$	−3.05801e17	−	5.29663e17i	−0.257597	−	0.446170i	−0.965598	+	0.260041i	$0.916264\pi$
$258$		0			0
$259$	−2.09653e17	+	3.63130e17i	−0.166630	+	0.288612i
$260$	4.32951e16			0.0334302
$261$		0			0
$262$	3.15788e17			0.230216
$263$	7.75912e14	−	1.34392e15i	0.000549724	−	0.000952149i	−0.865750	−	0.500476i	$-0.833158\pi$
$263$	7.75912e14	−	1.34392e15i	0.000549724	−	0.000952149i	0.866300	+	0.499524i	$0.166492\pi$
$264$		0			0
$265$	−3.09207e16	−	5.35562e16i	−0.0206969	−	0.0358480i
$266$	−2.88158e17	−	4.99105e17i	−0.187508	−	0.324773i
$267$		0			0
$268$	−1.66859e17	+	2.89008e17i	−0.102645	+	0.177786i
$269$	−9.58357e17			−0.573304			−0.286652	−	0.958035i	$-0.592542\pi$
$269$	−9.58357e17			−0.573304			−0.286652	+	0.958035i	$0.592542\pi$
$270$		0			0
$271$	−2.86480e18			−1.62116			−0.810578	−	0.585631i	$-0.800847\pi$
$271$	−2.86480e18			−1.62116			−0.810578	+	0.585631i	$0.800847\pi$
$272$	9.68163e17	−	1.67691e18i	0.532944	−	0.923086i
$273$		0			0
$274$	−3.30855e17	−	5.73058e17i	−0.172389	−	0.298586i
$275$	−4.41502e17	−	7.64704e17i	−0.223840	−	0.387702i
$276$		0			0
$277$	1.44884e18	−	2.50946e18i	0.695700	−	1.20499i	−0.274244	−	0.961660i	$-0.588428\pi$
$277$	1.44884e18	−	2.50946e18i	0.695700	−	1.20499i	0.969944	−	0.243328i	$-0.0782390\pi$
$278$	7.44685e17			0.348046
$279$		0			0
$280$	−1.92208e18			−0.851306
$281$	−5.14159e17	+	8.90549e17i	−0.221717	+	0.384026i	−0.955330	−	0.295543i	$-0.904500\pi$
$281$	−5.14159e17	+	8.90549e17i	−0.221717	+	0.384026i	0.733612	+	0.679568i	$0.237833\pi$
$282$		0			0
$283$	−1.64158e18	−	2.84329e18i	−0.671217	−	1.16258i	−0.977559	−	0.210660i	$-0.932439\pi$
$283$	−1.64158e18	−	2.84329e18i	−0.671217	−	1.16258i	0.306342	−	0.951921i	$-0.400895\pi$
$284$	−6.75213e17	−	1.16950e18i	−0.268877	−	0.465708i
$285$		0			0
$286$	−2.14620e16	+	3.71733e16i	−0.00810821	+	0.0140438i
$287$	8.32698e18			3.06460
$288$		0			0
$289$	4.20281e18			1.46827
$290$	−1.13972e17	+	1.97405e17i	−0.0387983	+	0.0672006i
$291$		0			0
$292$	−2.96392e17	−	5.13366e17i	−0.0958286	−	0.165980i
$293$	−1.07377e18	−	1.85983e18i	−0.338381	−	0.586092i	0.645748	−	0.763551i	$-0.276546\pi$
$293$	−1.07377e18	−	1.85983e18i	−0.338381	−	0.586092i	−0.984128	+	0.177458i	$0.943212\pi$
$294$		0			0
$295$	5.45996e17	−	9.45693e17i	0.163503	−	0.283195i
$296$	−3.83605e17			−0.111994
$297$		0			0
$298$	−8.28777e17			−0.230047
$299$	−1.05798e17	+	1.83248e17i	−0.0286381	+	0.0496026i
$300$		0			0
$301$	2.58689e18	+	4.48063e18i	0.666085	+	1.15369i
$302$	−3.34548e17	−	5.79454e17i	−0.0840245	−	0.145535i
$303$		0			0
$304$	−8.50717e17	+	1.47349e18i	−0.203345	+	0.352204i
$305$	−3.53937e18			−0.825423
$306$		0			0
$307$	−5.28247e18			−1.17300			−0.586501	−	0.809948i	$-0.699495\pi$
$307$	−5.28247e18			−1.17300			−0.586501	+	0.809948i	$0.699495\pi$
$308$	−3.57919e18	+	6.19934e18i	−0.775630	+	1.34343i
$309$		0			0
$310$	−4.35915e17	−	7.55027e17i	−0.0899890	−	0.155866i
$311$	−1.12413e18	−	1.94706e18i	−0.226524	−	0.392352i	0.730251	−	0.683179i	$-0.239403\pi$
$311$	−1.12413e18	−	1.94706e18i	−0.226524	−	0.392352i	−0.956776	+	0.290827i	$0.906070\pi$
$312$		0			0
$313$	2.88449e17	−	4.99608e17i	0.0553970	−	0.0959505i	−0.836997	−	0.547207i	$-0.815691\pi$
$313$	2.88449e17	−	4.99608e17i	0.0553970	−	0.0959505i	0.892394	+	0.451257i	$0.149024\pi$
$314$	−3.22920e18			−0.605513
$315$		0			0
$316$	2.52621e18			0.451664
$317$	4.97239e18	−	8.61243e18i	0.868201	−	1.50377i	0.00436808	−	0.999990i	$-0.498610\pi$
$317$	4.97239e18	−	8.61243e18i	0.868201	−	1.50377i	0.863833	−	0.503778i	$-0.168057\pi$
$318$		0			0
$319$	9.02097e17	+	1.56248e18i	0.150253	+	0.260246i
$320$	8.69492e17	+	1.50600e18i	0.141462	+	0.245020i
$321$		0			0
$322$	2.21003e18	−	3.82789e18i	0.343146	−	0.594347i
$323$	−6.20817e18			−0.941769
$324$		0			0
$325$	1.73359e17			0.0251085
$326$	−7.68545e17	+	1.33116e18i	−0.108777	+	0.188407i
$327$		0			0
$328$	3.80899e18	+	6.59737e18i	0.514940	+	0.891902i
$329$	1.08747e19	+	1.88356e19i	1.43697	+	2.48891i
$330$		0			0
$331$	−4.83612e18	+	8.37641e18i	−0.610643	+	1.05766i	0.380489	+	0.924785i	$0.375756\pi$
$331$	−4.83612e18	+	8.37641e18i	−0.610643	+	1.05766i	−0.991132	+	0.132880i	$0.957578\pi$
$332$	−3.27856e18			−0.404714
$333$		0			0
$334$	−3.77919e18			−0.445964
$335$	7.21194e17	−	1.24914e18i	0.0832177	−	0.144137i
$336$		0			0
$337$	−4.88514e18	−	8.46130e18i	−0.539079	−	0.933712i	−0.998954	−	0.0457286i	$-0.985439\pi$
$337$	−4.88514e18	−	8.46130e18i	−0.539079	−	0.933712i	0.459875	−	0.887984i	$-0.347894\pi$
$338$	1.54148e18	+	2.66991e18i	0.166365	+	0.288152i
$339$		0			0
$340$	−4.87115e18	+	8.43708e18i	−0.502967	+	0.871165i
$341$	−6.90061e18			−0.696995
$342$		0			0
$343$	2.94052e19			2.84262
$344$	−2.36663e18	+	4.09913e18i	−0.223843	+	0.387707i
$345$		0			0
$346$	1.09983e18	+	1.90497e18i	0.0995993	+	0.172511i
$347$	3.89659e18	+	6.74908e18i	0.345313	+	0.598100i	0.985411	−	0.170194i	$-0.0544394\pi$
$347$	3.89659e18	+	6.74908e18i	0.345313	+	0.598100i	−0.640097	+	0.768294i	$0.721106\pi$
$348$		0			0
$349$	2.10783e18	−	3.65086e18i	0.178914	−	0.309888i	−0.762595	−	0.646876i	$-0.776075\pi$
$349$	2.10783e18	−	3.65086e18i	0.178914	−	0.309888i	0.941509	+	0.336988i	$0.109408\pi$
$350$	−3.62131e18			−0.300853
$351$		0			0
$352$	−1.00163e19			−0.797330
$353$	4.21138e18	−	7.29433e18i	0.328182	−	0.568428i	−0.653969	−	0.756521i	$-0.726897\pi$
$353$	4.21138e18	−	7.29433e18i	0.328182	−	0.568428i	0.982151	+	0.188093i	$0.0602308\pi$
$354$		0			0
$355$	2.91839e18	+	5.05480e18i	0.217987	+	0.377565i
$356$	−1.04671e19	−	1.81295e19i	−0.765509	−	1.32590i
$357$		0			0
$358$	1.72464e18	−	2.98716e18i	0.120941	−	0.209477i
$359$	1.15004e19			0.789778			0.394889	−	0.918729i	$-0.370783\pi$
$359$	1.15004e19			0.789778			0.394889	+	0.918729i	$0.370783\pi$
$360$		0			0
$361$	−9.72606e18			−0.640668
$362$	4.08267e18	−	7.07139e18i	0.263409	−	0.456237i
$363$		0			0
$364$	−7.02695e17	−	1.21710e18i	−0.0435018	−	0.0753472i
$365$	1.28106e18	+	2.21886e18i	0.0776914	+	0.134565i
$366$		0			0
$367$	5.75123e18	−	9.96142e18i	0.334784	−	0.579864i	−0.648659	−	0.761079i	$-0.724670\pi$
$367$	5.75123e18	−	9.96142e18i	0.334784	−	0.579864i	0.983443	+	0.181216i	$0.0580032\pi$
$368$	−1.30492e19			−0.744259
$369$		0			0
$370$	7.80144e17			0.0427230
$371$	−1.00371e18	+	1.73847e18i	−0.0538645	+	0.0932961i
$372$		0			0
$373$	−6.12919e18	−	1.06161e19i	−0.315927	−	0.547202i	0.663707	−	0.747993i	$-0.268982\pi$
$373$	−6.12919e18	−	1.06161e19i	−0.315927	−	0.547202i	−0.979634	+	0.200791i	$0.935649\pi$
$374$	−4.82940e18	−	8.36477e18i	−0.243981	−	0.422588i
$375$		0			0
$376$	−9.94879e18	+	1.72318e19i	−0.482905	+	0.836415i
$377$	−3.54214e17			−0.0168541
$378$		0			0
$379$	−1.54013e19			−0.704309			−0.352155	−	0.935942i	$-0.614551\pi$
$379$	−1.54013e19			−0.704309			−0.352155	+	0.935942i	$0.614551\pi$
$380$	4.28025e18	−	7.41360e18i	0.191907	−	0.332393i
$381$		0			0
$382$	4.77793e18	+	8.27562e18i	0.205951	+	0.356718i
$383$	8.38128e17	+	1.45168e18i	0.0354258	+	0.0613593i	0.883195	−	0.469007i	$-0.155388\pi$
$383$	8.38128e17	+	1.45168e18i	0.0354258	+	0.0613593i	−0.847769	+	0.530366i	$0.822055\pi$
$384$		0			0
$385$	1.54699e19	−	2.67947e19i	0.628828	−	1.08916i
$386$	1.62285e19			0.646953
$387$		0			0
$388$	−8.27426e18			−0.317316
$389$	1.84521e19	−	3.19599e19i	0.694102	−	1.20222i	−0.276381	−	0.961048i	$-0.589135\pi$
$389$	1.84521e19	−	3.19599e19i	0.694102	−	1.20222i	0.970483	−	0.241171i	$-0.0775315\pi$
$390$		0			0
$391$	−2.38068e19	−	4.12346e19i	−0.861738	−	1.49257i
$392$	2.23234e19	+	3.86652e19i	0.792710	+	1.37301i
$393$		0			0
$394$	2.18366e18	−	3.78222e18i	0.0746387	−	0.129278i
$395$	−1.09187e19			−0.366179
$396$		0			0
$397$	−3.49000e18			−0.112693			−0.0563464	−	0.998411i	$-0.517945\pi$
$397$	−3.49000e18			−0.112693			−0.0563464	+	0.998411i	$0.517945\pi$
$398$	2.31613e18	−	4.01166e18i	0.0733906	−	0.127116i
$399$		0			0
$400$	5.34552e18	+	9.25871e18i	0.163132	+	0.282553i
$401$	9.27342e18	+	1.60620e19i	0.277752	+	0.481080i	0.970826	−	0.239786i	$-0.0770773\pi$
$401$	9.27342e18	+	1.60620e19i	0.277752	+	0.481080i	−0.693074	+	0.720867i	$0.743744\pi$
$402$		0			0
$403$	6.77392e17	−	1.17328e18i	0.0195457	−	0.0338542i
$404$	4.93616e18			0.139807
$405$		0			0
$406$	7.39922e18			0.201949
$407$	3.08746e18	−	5.34763e18i	0.0827261	−	0.143286i
$408$		0			0
$409$	−9.46896e18	−	1.64007e19i	−0.244555	−	0.423582i	0.717451	−	0.696609i	$-0.245309\pi$
$409$	−9.46896e18	−	1.64007e19i	−0.244555	−	0.423582i	−0.962007	+	0.273026i	$0.911975\pi$
$410$	−7.74642e18	−	1.34172e19i	−0.196437	−	0.340238i
$411$		0			0
$412$	4.61311e18	−	7.99014e18i	0.112788	−	0.195355i
$413$	−3.54469e19			−0.851045
$414$		0			0
$415$	1.41705e19			0.328115
$416$	9.83242e17	−	1.70302e18i	0.0223594	−	0.0387276i
$417$		0			0
$418$	4.24356e18	+	7.35006e18i	0.0930911	+	0.161239i
$419$	−3.16496e19	−	5.48187e19i	−0.681966	−	1.18120i	−0.974380	−	0.224908i	$-0.927792\pi$
$419$	−3.16496e19	−	5.48187e19i	−0.681966	−	1.18120i	0.292414	−	0.956292i	$-0.405542\pi$
$420$		0			0
$421$	−4.08195e19	+	7.07015e19i	−0.848696	+	1.46999i	0.0336755	+	0.999433i	$0.489279\pi$
$421$	−4.08195e19	+	7.07015e19i	−0.848696	+	1.46999i	−0.882372	+	0.470553i	$0.844055\pi$
$422$	−1.99825e19			−0.408138
$423$		0			0
$424$	−1.83649e18			−0.0362031
$425$	−1.95046e19	+	3.37830e19i	−0.377764	+	0.654307i
$426$		0			0
$427$	5.74452e19	+	9.94980e19i	1.07410	+	1.86039i
$428$	−5.38797e18	−	9.33224e18i	−0.0989913	−	0.171458i
$429$		0			0
$430$	4.81307e18	−	8.33648e18i	0.0853904	−	0.147900i
$431$	5.26955e19			0.918744			0.459372	−	0.888244i	$-0.348075\pi$
$431$	5.26955e19			0.918744			0.459372	+	0.888244i	$0.348075\pi$
$432$		0			0
$433$	6.18330e19			1.04126			0.520632	−	0.853781i	$-0.325696\pi$
$433$	6.18330e19			1.04126			0.520632	+	0.853781i	$0.325696\pi$
$434$	−1.41501e19	+	2.45087e19i	−0.234200	+	0.405647i
$435$		0			0
$436$	−1.40132e19	−	2.42716e19i	−0.224073	−	0.388106i
$437$	2.09189e19	+	3.62325e19i	0.328796	+	0.569492i
$438$		0			0
$439$	2.95849e19	−	5.12425e19i	0.449351	−	0.778299i	−0.548993	−	0.835827i	$-0.684989\pi$
$439$	2.95849e19	−	5.12425e19i	0.449351	−	0.778299i	0.998344	+	0.0575281i	$0.0183219\pi$
$440$	2.83055e19			0.422644
$441$		0			0
$442$	1.89629e18			0.0273677
$443$	−4.02423e19	+	6.97018e19i	−0.571025	+	0.989045i	0.425436	+	0.904989i	$0.360121\pi$
$443$	−4.02423e19	+	6.97018e19i	−0.571025	+	0.989045i	−0.996461	+	0.0840562i	$0.973212\pi$
$444$		0			0
$445$	4.52406e19	+	7.83590e19i	0.620624	+	1.07495i
$446$	1.22928e18	+	2.12917e18i	0.0165821	+	0.0287210i
$447$		0			0
$448$	2.82243e19	−	4.88860e19i	0.368162	−	0.637675i
$449$	1.32316e19			0.169732			0.0848662	−	0.996392i	$-0.472954\pi$
$449$	1.32316e19			0.169732			0.0848662	+	0.996392i	$0.472954\pi$
$450$		0			0
$451$	−1.22627e20			−1.52147
$452$	−4.29693e19	+	7.44250e19i	−0.524348	+	0.908198i
$453$		0			0
$454$	−2.12232e19	−	3.67596e19i	−0.250548	−	0.433962i
$455$	3.03718e18	+	5.26054e18i	0.0352683	+	0.0610865i
$456$		0			0
$457$	−7.28419e19	+	1.26166e20i	−0.818483	+	1.41765i	0.0883169	+	0.996092i	$0.471851\pi$
$457$	−7.28419e19	+	1.26166e20i	−0.818483	+	1.41765i	−0.906800	+	0.421562i	$0.861482\pi$
$458$	−2.48024e18			−0.0274160
$459$		0			0
$460$	6.56547e19			0.702396
$461$	−2.27701e19	+	3.94390e19i	−0.239667	+	0.415115i	−0.960619	−	0.277870i	$-0.910372\pi$
$461$	−2.27701e19	+	3.94390e19i	−0.239667	+	0.415115i	0.720952	+	0.692985i	$0.243705\pi$
$462$		0			0
$463$	−1.94429e19	−	3.36760e19i	−0.198108	−	0.343134i	0.749807	−	0.661657i	$-0.230146\pi$
$463$	−1.94429e19	−	3.36760e19i	−0.198108	−	0.343134i	−0.947915	+	0.318523i	$0.896813\pi$
$464$	−1.09222e19	−	1.89178e19i	−0.109503	−	0.189665i
$465$		0			0
$466$	1.40588e19	−	2.43505e19i	0.136475	−	0.236382i
$467$	−1.23623e20			−1.18093			−0.590464	−	0.807064i	$-0.701055\pi$
$467$	−1.23623e20			−1.18093			−0.590464	+	0.807064i	$0.701055\pi$
$468$		0			0
$469$	−4.68209e19			−0.433155
$470$	2.02331e19	−	3.50447e19i	0.184216	−	0.319072i
$471$		0			0
$472$	−1.62144e19	−	2.80841e19i	−0.143000	−	0.247683i
$473$	−3.80959e19	−	6.59840e19i	−0.330689	−	0.572770i
$474$		0			0
$475$	1.71386e19	−	2.96849e19i	0.144136	−	0.249651i
$476$	3.16242e20			2.61799
$477$		0			0
$478$	3.70233e19			0.297007
$479$	2.96043e19	−	5.12762e19i	0.233797	−	0.404948i	−0.725125	−	0.688617i	$-0.758218\pi$
$479$	2.96043e19	−	5.12762e19i	0.233797	−	0.404948i	0.958922	+	0.283669i	$0.0915516\pi$
$480$		0			0
$481$	6.06154e17	+	1.04989e18i	0.00463975	+	0.00803629i
$482$	−2.89852e19	−	5.02039e19i	−0.218436	−	0.378342i
$483$		0			0
$484$	−8.11272e18	+	1.40516e19i	−0.0592688	+	0.102657i
$485$	3.57628e19			0.257258
$486$		0			0
$487$	−2.91549e19			−0.203350			−0.101675	−	0.994818i	$-0.532420\pi$
$487$	−2.91549e19			−0.203350			−0.101675	+	0.994818i	$0.532420\pi$
$488$	−5.25540e19	+	9.10263e19i	−0.360959	+	0.625199i
$489$		0			0
$490$	−4.53995e19	−	7.86343e19i	−0.302399	−	0.523771i
$491$	−9.61204e19	−	1.66485e20i	−0.630528	−	1.09211i	−0.987444	−	0.157970i	$-0.949505\pi$
$491$	−9.61204e19	−	1.66485e20i	−0.630528	−	1.09211i	0.356916	−	0.934136i	$-0.383828\pi$
$492$		0			0
$493$	3.98528e19	−	6.90270e19i	0.253575	−	0.439205i
$494$	−1.66626e18			−0.0104422
$495$		0			0
$496$	8.35497e19			0.507963
$497$	9.47331e19	−	1.64083e20i	0.567321	−	0.982629i
$498$		0			0
$499$	2.40099e19	+	4.15863e19i	0.139520	+	0.241655i	0.927315	−	0.374282i	$-0.122111\pi$
$499$	2.40099e19	+	4.15863e19i	0.139520	+	0.241655i	−0.787795	+	0.615937i	$0.788777\pi$
$500$	−8.28217e19	−	1.43451e20i	−0.474099	−	0.821164i
$501$		0			0
$502$	−2.82605e19	+	4.89486e19i	−0.157001	+	0.271933i
$503$	−1.16964e20			−0.640164			−0.320082	−	0.947390i	$-0.603710\pi$
$503$	−1.16964e20			−0.640164			−0.320082	+	0.947390i	$0.603710\pi$
$504$		0			0
$505$	−2.13350e19			−0.113346
$506$	−3.25460e19	+	5.63713e19i	−0.170360	+	0.295073i
$507$		0			0
$508$	−5.02061e19	−	8.69595e19i	−0.255140	−	0.441916i
$509$	7.81322e19	+	1.35329e20i	0.391243	+	0.677653i	0.992614	−	0.121317i	$-0.0387118\pi$
$509$	7.81322e19	+	1.35329e20i	0.391243	+	0.677653i	−0.601371	+	0.798970i	$0.705378\pi$
$510$		0			0
$511$	4.15841e19	−	7.20258e19i	0.202195	−	0.350212i
$512$	2.10496e20			1.00860
$513$		0			0
$514$	3.69378e19			0.171889
$515$	−1.99387e19	+	3.45348e19i	−0.0914413	+	0.158381i
$516$		0			0
$517$	−1.60146e20	−	2.77382e20i	−0.713408	−	1.23566i
$518$	−1.26620e19	−	2.19313e19i	−0.0555943	−	0.0962921i
$519$		0			0
$520$	−2.77858e18	+	4.81264e18i	−0.0118522	+	0.0205285i
$521$	2.60369e20			1.09473			0.547364	−	0.836894i	$-0.315631\pi$
$521$	2.60369e20			1.09473			0.547364	+	0.836894i	$0.315631\pi$
$522$		0			0
$523$	4.22701e19			0.172691			0.0863456	−	0.996265i	$-0.472481\pi$
$523$	4.22701e19			0.172691			0.0863456	+	0.996265i	$0.472481\pi$
$524$	7.61309e19	−	1.31863e20i	0.306603	−	0.531052i
$525$		0			0
$526$	4.68613e16	+	8.11662e16i	0.000183409	+	0.000317674i
$527$	1.52427e20	+	2.64012e20i	0.588143	+	1.01869i
$528$		0			0
$529$	−2.71196e19	+	4.69726e19i	−0.101711	+	0.176168i
$530$	3.73491e18			0.0138106
$531$		0			0
$532$	−2.77880e20			−0.998894
$533$	1.20376e19	−	2.08497e19i	0.0426663	−	0.0739002i
$534$		0			0
$535$	2.32878e19	+	4.03356e19i	0.0802555	+	0.139007i
$536$	−2.14172e19	−	3.70957e19i	−0.0727824	−	0.126063i
$537$		0			0
$538$	2.89400e19	−	5.01256e19i	0.0956383	−	0.165650i
$539$	−7.18682e20			−2.34218
$540$		0			0
$541$	4.19877e19			0.133089			0.0665445	−	0.997783i	$-0.478803\pi$
$541$	4.19877e19			0.133089			0.0665445	+	0.997783i	$0.478803\pi$
$542$	8.65100e19	−	1.49840e20i	0.270440	−	0.468417i
$543$		0			0
$544$	2.21250e20	+	3.83216e20i	0.672808	+	1.16534i
$545$	6.05677e19	+	1.04906e20i	0.181663	+	0.314650i
$546$		0			0
$547$	−2.50718e20	+	4.34257e20i	−0.731612	+	1.26719i	0.224582	+	0.974455i	$0.427898\pi$
$547$	−2.50718e20	+	4.34257e20i	−0.731612	+	1.26719i	−0.956194	+	0.292734i	$0.905435\pi$
$548$	−3.19054e20			−0.918353
$549$		0			0
$550$	5.33292e19			0.149364
$551$	−3.50183e19	+	6.06535e19i	−0.0967517	+	0.167579i
$552$		0			0
$553$	1.77215e20	+	3.06945e20i	0.476498	+	0.825319i
$554$	8.75028e19	+	1.51559e20i	0.232113	+	0.402031i
$555$		0			0
$556$	1.79531e20	−	3.10956e20i	0.463530	−	0.802857i
$557$	−3.32313e20			−0.846513			−0.423256	−	0.906010i	$-0.639113\pi$
$557$	−3.32313e20			−0.846513			−0.423256	+	0.906010i	$0.639113\pi$
$558$		0			0
$559$	1.49586e19			0.0370938
$560$	−1.87303e20	+	3.24418e20i	−0.458284	+	0.793771i
$561$		0			0
$562$	−3.10527e19	−	5.37848e19i	−0.0739736	−	0.128126i
$563$	2.04616e20	+	3.54405e20i	0.480979	+	0.833080i	0.999762	−	0.0218264i	$-0.00694810\pi$
$563$	2.04616e20	+	3.54405e20i	0.480979	+	0.833080i	−0.518783	+	0.854906i	$0.673615\pi$
$564$		0			0
$565$	1.85721e20	−	3.21678e20i	0.425106	−	0.736306i
$566$	1.98286e20			0.447888
$567$		0			0
$568$	1.73334e20			0.381304
$569$	−7.90826e19	+	1.36975e20i	−0.171688	+	0.297372i	−0.939010	−	0.343890i	$-0.888255\pi$
$569$	−7.90826e19	+	1.36975e20i	−0.171688	+	0.297372i	0.767322	+	0.641261i	$0.221589\pi$
$570$		0			0
$571$	2.14768e20	+	3.71989e20i	0.454150	+	0.786610i	0.998639	−	0.0521575i	$-0.0166098\pi$
$571$	2.14768e20	+	3.71989e20i	0.454150	+	0.786610i	−0.544489	+	0.838768i	$0.683276\pi$
$572$	1.03482e19	+	1.79237e19i	0.0215971	+	0.0374073i
$573$		0			0
$574$	−2.51455e20	+	4.35532e20i	−0.511235	+	0.885484i
$575$	2.62889e20			0.527550
$576$		0			0
$577$	5.03569e20			0.984557			0.492278	−	0.870438i	$-0.336164\pi$
$577$	5.03569e20			0.984557			0.492278	+	0.870438i	$0.336164\pi$
$578$	−1.26915e20	+	2.19822e20i	−0.244936	+	0.424241i
$579$		0			0
$580$	5.49533e19	+	9.51819e19i	0.103344	+	0.178996i
$581$	−2.29993e20	−	3.98359e20i	−0.426966	−	0.739527i
$582$		0			0
$583$	1.47811e19	−	2.56016e19i	0.0267419	−	0.0463183i
$584$	7.60869e19			0.135898
$585$		0			0
$586$	1.29701e20			0.225794
$587$	4.93403e20	−	8.54600e20i	0.848040	−	1.46885i	−0.0349149	−	0.999390i	$-0.511116\pi$
$587$	4.93403e20	−	8.54600e20i	0.848040	−	1.46885i	0.882955	−	0.469458i	$-0.155551\pi$
$588$		0			0
$589$	−1.33937e20	−	2.31985e20i	−0.224406	−	0.388683i
$590$	3.29755e19	+	5.71153e19i	0.0545508	+	0.0944848i
$591$		0			0
$592$	−3.73816e19	+	6.47468e19i	−0.0602899	+	0.104425i
$593$	−2.83452e19			−0.0451409			−0.0225704	−	0.999745i	$-0.507185\pi$
$593$	−2.83452e19			−0.0451409			−0.0225704	+	0.999745i	$0.507185\pi$
$594$		0			0
$595$	−1.36686e21			−2.12249
$596$	−1.99804e20	+	3.46070e20i	−0.306377	+	0.530661i
$597$		0			0
$598$	−6.38969e18	−	1.10673e19i	−0.00955479	−	0.0165494i
$599$	2.06362e20	+	3.57429e20i	0.304739	+	0.527823i	0.977203	−	0.212306i	$-0.0680975\pi$
$599$	2.06362e20	+	3.57429e20i	0.304739	+	0.527823i	−0.672464	+	0.740130i	$0.734764\pi$
$600$		0			0
$601$	2.81858e18	−	4.88192e18i	0.00405949	−	0.00703125i	−0.863989	−	0.503512i	$-0.832041\pi$
$601$	2.81858e18	−	4.88192e18i	0.00405949	−	0.00703125i	0.868048	+	0.496480i	$0.165374\pi$
$602$	−3.12472e20			−0.444464
$603$		0			0
$604$	−3.22615e20			−0.447617
$605$	3.50646e19	−	6.07337e19i	0.0480512	−	0.0832271i
$606$		0			0
$607$	−3.66530e20	−	6.34849e20i	−0.489998	−	0.848702i	0.509935	−	0.860213i	$-0.329669\pi$
$607$	−3.66530e20	−	6.34849e20i	−0.489998	−	0.848702i	−0.999934	+	0.0115107i	$0.996336\pi$
$608$	−1.94411e20	−	3.36729e20i	−0.256710	−	0.444635i
$609$		0			0
$610$	1.06880e20	−	1.85122e20i	0.137697	−	0.238498i
$611$	6.28824e19			0.0800240
$612$		0			0
$613$	9.93885e20			1.23419			0.617095	−	0.786888i	$-0.288309\pi$
$613$	9.93885e20			1.23419			0.617095	+	0.786888i	$0.288309\pi$
$614$	1.59518e20	−	2.76293e20i	0.195680	−	0.338927i
$615$		0			0
$616$	−4.59408e20	−	7.95718e20i	−0.549975	−	0.952585i
$617$	5.44990e20	+	9.43950e20i	0.644540	+	1.11638i	0.984408	+	0.175902i	$0.0562843\pi$
$617$	5.44990e20	+	9.43950e20i	0.644540	+	1.11638i	−0.339868	+	0.940473i	$0.610382\pi$
$618$		0			0
$619$	7.40888e20	−	1.28326e21i	0.855210	−	1.48127i	−0.0212393	−	0.999774i	$-0.506761\pi$
$619$	7.40888e20	−	1.28326e21i	0.855210	−	1.48127i	0.876450	−	0.481493i	$-0.159905\pi$
$620$	−4.20366e20			−0.479392
$621$		0			0
$622$	1.35784e20			0.151155
$623$	1.46854e21	−	2.54359e21i	1.61520	−	2.79761i
$624$		0			0
$625$	1.34034e20	+	2.32154e20i	0.143918	+	0.249273i
$626$	1.74209e19	+	3.01739e19i	0.0184826	+	0.0320128i
$627$		0			0
$628$	−7.78505e20	+	1.34841e21i	−0.806425	+	1.39677i
$629$	−2.72795e20			−0.279226
$630$		0			0
$631$	1.67989e20			0.167904			0.0839520	−	0.996470i	$-0.473246\pi$
$631$	1.67989e20			0.167904			0.0839520	+	0.996470i	$0.473246\pi$
$632$	−1.62126e20	+	2.80810e20i	−0.160131	+	0.277354i
$633$		0			0
$634$	3.00308e20	+	5.20148e20i	0.289666	+	0.501716i
$635$	2.17000e20	+	3.75855e20i	0.206850	+	0.358275i
$636$		0			0
$637$	7.05487e19	−	1.22194e20i	0.0656816	−	0.113764i
$638$	−1.08965e20			−0.100261
$639$		0			0
$640$	−7.91621e20			−0.711488
$641$	−3.89521e20	+	6.74670e20i	−0.346015	+	0.599316i	−0.985538	−	0.169456i	$-0.945799\pi$
$641$	−3.89521e20	+	6.74670e20i	−0.346015	+	0.599316i	0.639522	+	0.768772i	$0.279132\pi$
$642$		0			0
$643$	−5.14927e20	−	8.91879e20i	−0.446851	−	0.773969i	0.551328	−	0.834289i	$-0.314121\pi$
$643$	−5.14927e20	−	8.91879e20i	−0.446851	−	0.773969i	−0.998179	+	0.0603196i	$0.980788\pi$
$644$	−1.06560e21	−	1.84567e21i	−0.914008	−	1.58311i
$645$		0			0
$646$	1.87472e20	−	3.24710e20i	0.157105	−	0.272115i
$647$	−1.39120e21			−1.15241			−0.576206	−	0.817305i	$-0.695467\pi$
$647$	−1.39120e21			−1.15241			−0.576206	+	0.817305i	$0.695467\pi$
$648$		0			0
$649$	5.22008e20			0.422515
$650$	−5.23500e18	+	9.06729e18i	−0.00418858	+	0.00725483i
$651$		0			0
$652$	3.70566e20	+	6.41838e20i	0.289740	+	0.501844i
$653$	1.15096e21	+	1.99352e21i	0.889636	+	1.54089i	0.840307	+	0.542112i	$0.182375\pi$
$653$	1.15096e21	+	1.99352e21i	0.889636	+	1.54089i	0.0493291	+	0.998783i	$0.484292\pi$
$654$		0			0
$655$	−3.29051e20	+	5.69934e20i	−0.248573	+	0.430541i
$656$	1.48472e21			1.10883
$657$		0			0
$658$	−1.31356e21			−0.958861
$659$	8.02955e20	−	1.39076e21i	0.579496	−	1.00372i	−0.416041	−	0.909346i	$-0.636583\pi$
$659$	8.02955e20	−	1.39076e21i	0.579496	−	1.00372i	0.995537	−	0.0943707i	$-0.0300839\pi$
$660$		0			0
$661$	−3.15323e20	−	5.46155e20i	−0.222456	−	0.385305i	0.733097	−	0.680124i	$-0.238074\pi$
$661$	−3.15323e20	−	5.46155e20i	−0.222456	−	0.385305i	−0.955553	+	0.294819i	$0.904741\pi$
$662$	−2.92078e20	−	5.05894e20i	−0.203734	−	0.352878i
$663$		0			0
$664$	2.10410e20	−	3.64441e20i	0.143485	−	0.248523i
$665$	1.20105e21			0.809837
$666$		0			0
$667$	−5.37146e20			−0.354119
$668$	−9.11097e20	+	1.57807e21i	−0.593938	+	1.02873i
$669$		0			0
$670$	4.35566e19	+	7.54422e19i	0.0277647	+	0.0480898i
$671$	−8.45966e20	−	1.46526e21i	−0.533254	−	0.923623i
$672$		0			0
$673$	4.05868e20	−	7.02984e20i	0.250191	−	0.433343i	−0.713387	−	0.700770i	$-0.752840\pi$
$673$	4.05868e20	−	7.02984e20i	0.250191	−	0.433343i	0.963578	+	0.267427i	$0.0861733\pi$
$674$	5.90077e20			0.359716
$675$		0			0
$676$	1.48649e21			0.886262
$677$	−1.61236e21	+	2.79269e21i	−0.950707	+	1.64667i	−0.206807	+	0.978382i	$0.566307\pi$
$677$	−1.61236e21	+	2.79269e21i	−0.950707	+	1.64667i	−0.743900	+	0.668291i	$0.767026\pi$
$678$		0			0
$679$	−5.80444e20	−	1.00536e21i	−0.334763	−	0.579826i
$680$	−6.25238e20	−	1.08294e21i	−0.356639	−	0.617716i
$681$		0			0
$682$	2.08382e20	−	3.60928e20i	0.116272	−	0.201390i
$683$	1.31933e21			0.728114			0.364057	−	0.931377i	$-0.381391\pi$
$683$	1.31933e21			0.728114			0.364057	+	0.931377i	$0.381391\pi$
$684$		0			0
$685$	1.37901e21			0.744539
$686$	−8.87966e20	+	1.53800e21i	−0.474204	+	0.821346i
$687$		0			0
$688$	4.61248e20	+	7.98906e20i	0.241002	+	0.417429i
$689$	2.90194e18	+	5.02631e18i	0.00149984	+	0.00259780i
$690$		0			0
$691$	−1.22943e21	+	2.12944e21i	−0.621754	+	1.07691i	0.367405	+	0.930061i	$0.380246\pi$
$691$	−1.22943e21	+	2.12944e21i	−0.621754	+	1.07691i	−0.989159	+	0.146849i	$0.953087\pi$
$692$	1.06060e21			0.530588
$693$		0			0
$694$	−4.70669e20			−0.230420
$695$	−7.75964e20	+	1.34401e21i	−0.375799	+	0.650903i
$696$		0			0
$697$	2.70871e21	+	4.69162e21i	1.28386	+	2.22370i
$698$	1.27303e20	+	2.20494e20i	0.0596927	+	0.103391i
$699$		0			0
$700$	−8.73034e20	+	1.51214e21i	−0.400678	+	0.693995i
$701$	−1.42634e21			−0.647644			−0.323822	−	0.946118i	$-0.604968\pi$
$701$	−1.42634e21			−0.647644			−0.323822	+	0.946118i	$0.604968\pi$
$702$		0			0
$703$	2.39703e20			0.106539
$704$	−4.15645e20	+	7.19919e20i	−0.182780	+	0.316584i
$705$		0			0
$706$	2.54347e20	+	4.40542e20i	0.109494	+	0.189650i
$707$	3.46274e20	+	5.99764e20i	0.147494	+	0.255467i
$708$		0			0
$709$	1.03630e21	−	1.79493e21i	0.432155	−	0.748514i	−0.564904	−	0.825157i	$-0.691087\pi$
$709$	1.03630e21	−	1.79493e21i	0.432155	−	0.748514i	0.997059	+	0.0766430i	$0.0244202\pi$
$710$	−3.52513e20			−0.145458
$711$		0			0
$712$	2.68701e21			1.08560
$713$	1.02723e21	−	1.77921e21i	0.410673	−	0.711306i
$714$		0			0
$715$	−4.47269e19	−	7.74693e19i	−0.0175095	−	0.0303274i
$716$	−8.31559e20	−	1.44030e21i	−0.322141	−	0.557964i
$717$		0			0
$718$	−3.47284e20	+	6.01514e20i	−0.131750	+	0.228198i
$719$	−1.06103e21			−0.398348			−0.199174	−	0.979964i	$-0.563826\pi$
$719$	−1.06103e21			−0.398348			−0.199174	+	0.979964i	$0.563826\pi$
$720$		0			0
$721$	1.29445e21			0.475960
$722$	2.93703e20	−	5.08709e20i	0.106876	−	0.185114i
$723$		0			0
$724$	−1.96852e21	−	3.40958e21i	−0.701619	−	1.21524i
$725$	2.20039e20	+	3.81119e20i	0.0776184	+	0.134439i
$726$		0			0
$727$	−1.87262e21	+	3.24347e21i	−0.647054	+	1.12073i	0.336769	+	0.941587i	$0.390666\pi$
$727$	−1.87262e21	+	3.24347e21i	−0.647054	+	1.12073i	−0.983823	+	0.179143i	$0.942667\pi$
$728$	1.80389e20			0.0616915
$729$		0			0
$730$	−1.54740e20			−0.0518418
$731$	−1.68300e21	+	2.91503e21i	−0.558088	+	0.966636i
$732$		0			0
$733$	−1.60817e21	−	2.78543e21i	−0.522459	−	0.904926i	−0.999659	−	0.0261307i	$-0.991681\pi$
$733$	−1.60817e21	−	2.78543e21i	−0.522459	−	0.904926i	0.477199	−	0.878795i	$-0.341652\pi$
$734$	3.47346e20	+	6.01621e20i	0.111697	+	0.193465i
$735$		0			0
$736$	1.49103e21	−	2.58255e21i	0.469790	−	0.813700i
$737$	6.89508e20			0.215047
$738$		0			0
$739$	−4.58274e21			−1.40053			−0.700264	−	0.713884i	$-0.746934\pi$
$739$	−4.58274e21			−1.40053			−0.700264	+	0.713884i	$0.746934\pi$
$740$	1.88079e20	−	3.25763e20i	0.0568988	−	0.0985516i
$741$		0			0
$742$	−6.06190e19	−	1.04995e20i	−0.0179713	−	0.0311272i
$743$	−2.71748e21	−	4.70681e21i	−0.797535	−	1.38137i	−0.921217	−	0.389048i	$-0.872804\pi$
$743$	−2.71748e21	−	4.70681e21i	−0.797535	−	1.38137i	0.123683	−	0.992322i	$-0.460529\pi$
$744$		0			0
$745$	8.63588e20	−	1.49578e21i	0.248390	−	0.430224i
$746$	7.40346e20			0.210811
$747$		0			0
$748$	−4.65714e21			−1.29974
$749$	7.55939e20	−	1.30932e21i	0.208868	−	0.361771i
$750$		0			0
$751$	1.96608e21	+	3.40535e21i	0.532478	+	0.922279i	0.999281	+	0.0379178i	$0.0120725\pi$
$751$	1.96608e21	+	3.40535e21i	0.532478	+	0.922279i	−0.466803	+	0.884362i	$0.654594\pi$
$752$	1.93898e21	+	3.35842e21i	0.519924	+	0.900536i
$753$		0			0
$754$	1.06964e19	−	1.85267e19i	0.00281159	−	0.00486982i
$755$	1.39440e21			0.362898
$756$		0			0
$757$	−1.39623e21			−0.356235			−0.178118	−	0.984009i	$-0.557001\pi$
$757$	−1.39623e21			−0.356235			−0.178118	+	0.984009i	$0.557001\pi$
$758$	4.65082e20	−	8.05545e20i	0.117493	−	0.203503i
$759$		0			0
$760$	5.49392e20	+	9.51575e20i	0.136076	+	0.235690i
$761$	−4.95635e20	−	8.58464e20i	−0.121556	−	0.210541i	0.798825	−	0.601563i	$-0.205455\pi$
$761$	−4.95635e20	−	8.58464e20i	−0.121556	−	0.210541i	−0.920381	+	0.391022i	$0.872122\pi$
$762$		0			0
$763$	1.96607e21	−	3.40534e21i	0.472787	−	0.818891i
$764$	4.60750e21			1.09715
$765$		0			0
$766$	−1.01238e20			−0.0236389
$767$	−5.12424e19	+	8.87544e19i	−0.0118485	+	0.0205222i
$768$		0			0
$769$	−1.07945e21	−	1.86966e21i	−0.244768	−	0.423951i	0.717298	−	0.696766i	$-0.245379\pi$
$769$	−1.07945e21	−	1.86966e21i	−0.244768	−	0.423951i	−0.962066	+	0.272815i	$0.912045\pi$
$770$	9.34307e20	+	1.61827e21i	0.209802	+	0.363387i
$771$		0			0
$772$	3.91240e21	−	6.77648e21i	0.861616	−	1.49236i
$773$	4.60666e21			1.00471			0.502354	−	0.864662i	$-0.332468\pi$
$773$	4.60666e21			1.00471			0.502354	+	0.864662i	$0.332468\pi$
$774$		0			0
$775$	−1.68319e21			−0.360057
$776$	5.31022e20	−	9.19758e20i	0.112499	−	0.194855i
$777$		0			0
$778$	1.11441e21	+	1.93022e21i	0.231579	+	0.401107i
$779$	−2.38012e21	−	4.12249e21i	−0.489856	−	0.848455i
$780$		0			0
$781$	−1.39509e21	+	2.41636e21i	−0.281655	+	0.487842i
$782$	2.87563e21			0.575019
$783$		0			0
$784$	8.70149e21			1.70696
$785$	3.36484e21	−	5.82807e21i	0.653795	−	1.13241i
$786$		0			0
$787$	−4.94200e21	−	8.55979e21i	−0.942089	−	1.63175i	−0.761477	−	0.648191i	$-0.775526\pi$
$787$	−4.94200e21	−	8.55979e21i	−0.942089	−	1.63175i	−0.180612	−	0.983555i	$-0.557808\pi$
$788$	−1.05289e21	−	1.82365e21i	−0.198809	−	0.344347i
$789$		0			0
$790$	3.29719e20	−	5.71090e20i	0.0610858	−	0.105804i
$791$	−1.20573e22			−2.21272
$792$		0			0
$793$	3.32174e20			0.0598159
$794$	1.05389e20	−	1.82540e20i	0.0187994	−	0.0325615i
$795$		0			0
$796$	−1.11676e21	−	1.93428e21i	−0.195484	−	0.338588i
$797$	9.44066e20	+	1.63517e21i	0.163706	+	0.283547i	0.936195	−	0.351481i	$-0.114322\pi$
$797$	9.44066e20	+	1.63517e21i	0.163706	+	0.283547i	−0.772489	+	0.635028i	$0.780988\pi$
$798$		0			0
$799$	−7.07493e21	+	1.22541e22i	−1.20399	+	2.08536i
$800$	−2.44317e21			−0.411888
$801$		0			0
$802$	−1.12014e21			−0.185338
$803$	−6.12388e20	+	1.06069e21i	−0.100383	+	0.173868i
$804$		0			0
$805$	4.60572e21	+	7.97733e21i	0.741017	+	1.28348i
$806$	4.09112e19	+	7.08602e19i	0.00652122	+	0.0112951i
$807$		0			0
$808$	−3.16791e20	+	5.48698e20i	−0.0495664	+	0.0858515i
$809$	−5.89774e21			−0.914264			−0.457132	−	0.889399i	$-0.651123\pi$
$809$	−5.89774e21			−0.914264			−0.457132	+	0.889399i	$0.651123\pi$
$810$		0			0
$811$	4.05402e20			0.0616921			0.0308461	−	0.999524i	$-0.490180\pi$
$811$	4.05402e20			0.0616921			0.0308461	+	0.999524i	$0.490180\pi$
$812$	1.78382e21	−	3.08967e21i	0.268956	−	0.465846i
$813$		0			0
$814$	1.86467e20	+	3.22971e20i	0.0276007	+	0.0478057i
$815$	−1.60165e21	−	2.77414e21i	−0.234902	−	0.406861i
$816$		0			0
$817$	1.47884e21	−	2.56142e21i	0.212939	−	0.368821i
$818$	1.14376e21			0.163187
$819$		0			0
$820$	−7.47011e21			−1.04646
$821$	−1.37275e21	+	2.37768e21i	−0.190554	+	0.330049i	−0.945434	−	0.325814i	$-0.894362\pi$
$821$	−1.37275e21	+	2.37768e21i	−0.190554	+	0.330049i	0.754880	+	0.655863i	$0.227695\pi$
$822$		0			0
$823$	−1.27136e21	−	2.20205e21i	−0.173288	−	0.300144i	0.766280	−	0.642507i	$-0.222106\pi$
$823$	−1.27136e21	−	2.20205e21i	−0.173288	−	0.300144i	−0.939567	+	0.342364i	$0.888772\pi$
$824$	5.92117e20	+	1.02558e21i	0.0799748	+	0.138520i
$825$		0			0
$826$	1.07041e21	−	1.85400e21i	0.141971	−	0.245901i
$827$	2.76080e21			0.362864			0.181432	−	0.983403i	$-0.441927\pi$
$827$	2.76080e21			0.362864			0.181432	+	0.983403i	$0.441927\pi$
$828$		0			0
$829$	1.03335e22			1.33379			0.666895	−	0.745152i	$-0.267623\pi$
$829$	1.03335e22			1.33379			0.666895	+	0.745152i	$0.267623\pi$
$830$	−4.27916e20	+	7.41171e20i	−0.0547359	+	0.0948054i
$831$		0			0
$832$	−8.16029e19	−	1.41340e20i	−0.0102513	−	0.0177558i
$833$	1.58749e22	+	2.74962e22i	1.97640	+	3.42322i
$834$		0			0
$835$	3.93792e21	−	6.82069e21i	0.481525	−	0.834026i
$836$	4.09219e21			0.495917
$837$		0			0
$838$	3.82296e21			0.455061
$839$	−2.54647e21	+	4.41062e21i	−0.300417	+	0.520337i	−0.976230	−	0.216736i	$-0.930459\pi$
$839$	−2.54647e21	+	4.41062e21i	−0.300417	+	0.520337i	0.675814	+	0.737072i	$0.263792\pi$
$840$		0			0
$841$	3.86500e21	+	6.69438e21i	0.447898	+	0.775783i
$842$	−2.46530e21	−	4.27003e21i	−0.283158	−	0.490445i
$843$		0			0
$844$	−4.81744e21	+	8.34405e21i	−0.543561	+	0.941474i
$845$	−6.42489e21			−0.718522
$846$		0			0
$847$	−2.27645e21			−0.250111
$848$	−1.78963e20	+	3.09973e20i	−0.0194892	+	0.0337563i
$849$		0			0
$850$	−1.17798e21	−	2.04033e21i	−0.126037	−	0.218302i
$851$	9.19200e20	+	1.59210e21i	0.0974851	+	0.168849i
$852$		0			0
$853$	−4.66263e21	+	8.07591e21i	−0.485862	+	0.841538i	−0.999868	−	0.0162486i	$-0.994828\pi$
$853$	−4.66263e21	+	8.07591e21i	−0.485862	+	0.841538i	0.514006	+	0.857787i	$0.328161\pi$
$854$	−6.93882e21			−0.716723
$855$		0			0
$856$	1.38315e21			0.140383
$857$	−5.26915e21	+	9.12644e21i	−0.530133	+	0.918217i	0.469249	+	0.883066i	$0.344525\pi$
$857$	−5.26915e21	+	9.12644e21i	−0.530133	+	0.918217i	−0.999382	+	0.0351509i	$0.988809\pi$
$858$		0			0
$859$	−6.41079e20	−	1.11038e21i	−0.0633815	−	0.109780i	0.832593	−	0.553885i	$-0.186855\pi$
$859$	−6.41079e20	−	1.11038e21i	−0.0633815	−	0.109780i	−0.895975	+	0.444105i	$0.853522\pi$
$860$	−2.32070e21	−	4.01956e21i	−0.227447	−	0.393949i
$861$		0			0
$862$	−1.59128e21	+	2.75617e21i	−0.153264	+	0.265462i
$863$	−1.31224e22			−1.25295			−0.626474	−	0.779443i	$-0.715502\pi$
$863$	−1.31224e22			−1.25295			−0.626474	+	0.779443i	$0.715502\pi$
$864$		0			0
$865$	−4.58412e21			−0.430165
$866$	−1.86721e21	+	3.23409e21i	−0.173703	+	0.300863i
$867$		0			0
$868$	6.82270e21	+	1.18173e22i	0.623819	+	1.08049i
$869$	−2.60975e21	−	4.52022e21i	−0.236565	−	0.409743i
$870$		0			0
$871$	−6.76849e19	+	1.17234e20i	−0.00603053	+	0.0104452i
$872$	3.59734e21			0.317767
$873$		0			0
$874$	−2.52679e21			−0.219399
$875$	1.16200e22	−	2.01264e22i	1.00033	−	1.73263i
$876$		0			0
$877$	−2.74874e21	−	4.76095e21i	−0.232614	−	0.402900i	0.725962	−	0.687734i	$-0.241395\pi$
$877$	−2.74874e21	−	4.76095e21i	−0.232614	−	0.402900i	−0.958577	+	0.284835i	$0.908061\pi$
$878$	1.78678e21	+	3.09480e21i	0.149921	+	0.259671i
$879$		0			0
$880$	2.75832e21	−	4.77754e21i	0.227522	−	0.394080i
$881$	2.95621e21			0.241778			0.120889	−	0.992666i	$-0.461426\pi$
$881$	2.95621e21			0.241778			0.120889	+	0.992666i	$0.461426\pi$
$882$		0			0
$883$	1.03794e22			0.834580			0.417290	−	0.908773i	$-0.362980\pi$
$883$	1.03794e22			0.834580			0.417290	+	0.908773i	$0.362980\pi$
$884$	4.57163e20	−	7.91830e20i	0.0364485	−	0.0631306i
$885$		0			0
$886$	−2.43044e21	−	4.20965e21i	−0.190516	−	0.329984i
$887$	−9.84283e21	−	1.70483e22i	−0.765055	−	1.32511i	−0.940217	−	0.340575i	$-0.889378\pi$
$887$	−9.84283e21	−	1.70483e22i	−0.765055	−	1.32511i	0.175162	−	0.984540i	$-0.443955\pi$
$888$		0			0
$889$	7.04397e21	−	1.22005e22i	0.538337	−	0.932427i
$890$	−5.46462e21			−0.414129
$891$		0			0
$892$	1.18543e21			0.0883365
$893$	6.21669e21	−	1.07676e22i	0.459381	−	0.795672i
$894$		0			0
$895$	3.59415e21	+	6.22525e21i	0.261170	+	0.452360i
$896$	1.28483e22	+	2.22539e22i	0.925839	+	1.60360i
$897$		0			0
$898$	−3.99562e20	+	6.92062e20i	−0.0283147	+	0.0490425i
$899$	3.43918e21			0.241689
$900$		0			0
$901$	−1.30599e21			−0.0902621
$902$	3.70304e21	−	6.41386e21i	0.253811	−	0.439613i
$903$		0			0
$904$	−5.51533e21	−	9.55283e21i	−0.371799	−	0.643975i
$905$	8.50831e21	+	1.47368e22i	0.568825	+	0.985234i
$906$		0			0
$907$	−9.75556e20	+	1.68971e21i	−0.0641501	+	0.111111i	−0.896317	−	0.443414i	$-0.853767\pi$
$907$	−9.75556e20	+	1.68971e21i	−0.0641501	+	0.111111i	0.832167	+	0.554526i	$0.187100\pi$
$908$	−2.04661e22			−1.33473
$909$		0			0
$910$	−3.66861e20			−0.0235338
$911$	1.01824e22	−	1.76365e22i	0.647835	−	1.12208i	−0.335804	−	0.941932i	$-0.609008\pi$
$911$	1.01824e22	−	1.76365e22i	0.647835	−	1.12208i	0.983639	−	0.180151i	$-0.0576585\pi$
$912$		0			0
$913$	3.38699e21	+	5.86644e21i	0.211974	+	0.367150i
$914$	−4.39929e21	−	7.61980e21i	−0.273078	−	0.472985i
$915$		0			0
$916$	−5.97944e20	+	1.03567e21i	−0.0365127	+	0.0632419i
$917$	2.13625e22			1.29384
$918$		0			0
$919$	−2.69737e22			−1.60722			−0.803609	−	0.595158i	$-0.797089\pi$
$919$	−2.69737e22			−1.60722			−0.803609	+	0.595158i	$0.797089\pi$
$920$	−4.21356e21	+	7.29811e21i	−0.249024	+	0.431322i
$921$		0			0
$922$	−1.37520e21	−	2.38192e21i	−0.0799623	−	0.138499i
$923$	−2.73895e20	−	4.74399e20i	−0.0157969	−	0.0273610i
$924$		0			0
$925$	7.53091e20	−	1.30439e21i	0.0427350	−	0.0740193i
$926$	2.34851e21			0.132193
$927$		0			0
$928$	4.99200e21			0.276481
$929$	−2.60653e21	+	4.51464e21i	−0.143200	+	0.248030i	−0.928700	−	0.370832i	$-0.879073\pi$
$929$	−2.60653e21	+	4.51464e21i	−0.143200	+	0.248030i	0.785500	+	0.618862i	$0.212406\pi$
$930$		0			0
$931$	−1.39492e22	−	2.41607e22i	−0.754096	−	1.30613i
$932$	−6.77866e21	−	1.17410e22i	−0.363517	−	0.629630i
$933$		0			0
$934$	3.73312e21	−	6.46595e21i	0.197002	−	0.341217i
$935$	2.01290e22			1.05374
$936$		0			0
$937$	3.05737e21			0.157507			0.0787537	−	0.996894i	$-0.474906\pi$
$937$	3.05737e21			0.157507			0.0787537	+	0.996894i	$0.474906\pi$
$938$	1.41388e21	−	2.44891e21i	0.0722588	−	0.125156i
$939$		0			0
$940$	−9.75568e21	−	1.68973e22i	−0.490680	−	0.849883i
$941$	−4.83303e20	−	8.37104e20i	−0.0241155	−	0.0417693i	0.853716	−	0.520739i	$-0.174344\pi$
$941$	−4.83303e20	−	8.37104e20i	−0.0241155	−	0.0417693i	−0.877831	+	0.478970i	$0.841010\pi$
$942$		0			0
$943$	1.82543e22	−	3.16175e22i	0.896455	−	1.55271i
$944$	−6.32025e21			−0.307924
$945$		0			0
$946$	4.60161e21			0.220661
$947$	−1.25395e22	+	2.17191e22i	−0.596564	+	1.03328i	0.396760	+	0.917922i	$0.370134\pi$
$947$	−1.25395e22	+	2.17191e22i	−0.596564	+	1.03328i	−0.993324	+	0.115357i	$0.963199\pi$
$948$		0			0
$949$	−1.20229e20	−	2.08243e20i	−0.00563005	−	0.00975154i
$950$	1.03509e21	+	1.79282e21i	0.0480894	+	0.0832934i
$951$		0			0
$952$	−2.02957e22	+	3.51531e22i	−0.928167	+	1.60763i
$953$	1.90817e22			0.865804			0.432902	−	0.901441i	$-0.357490\pi$
$953$	1.90817e22			0.865804			0.432902	+	0.901441i	$0.357490\pi$
$954$		0			0
$955$	−1.99145e22			−0.889495
$956$	8.92568e21	−	1.54597e22i	0.395555	−	0.685122i
$957$		0			0
$958$	1.78796e21	+	3.09683e21i	0.0780038	+	0.135107i
$959$	−2.23818e22	−	3.87664e22i	−0.968847	−	1.67809i
$960$		0			0
$961$	5.15561e21	−	8.92978e21i	0.219712	−	0.380553i
$962$	−7.32175e19			−0.00309601
$963$		0			0
$964$	−2.79513e22			−1.16366
$965$	−1.69101e22	+	2.92892e22i	−0.698540	+	1.20991i
$966$		0			0
$967$	1.63752e22	+	2.83627e22i	0.666022	+	1.15358i	0.979007	+	0.203826i	$0.0653377\pi$
$967$	1.63752e22	+	2.83627e22i	0.666022	+	1.15358i	−0.312985	+	0.949758i	$0.601329\pi$
$968$	−1.04131e21	−	1.80360e21i	−0.0420257	−	0.0727906i
$969$		0			0
$970$	−1.07995e21	+	1.87053e21i	−0.0429157	+	0.0743321i
$971$	3.53904e22			1.39554			0.697768	−	0.716324i	$-0.254177\pi$
$971$	3.53904e22			1.39554			0.697768	+	0.716324i	$0.254177\pi$
$972$		0			0
$973$	5.03767e22			1.95607
$974$	8.80407e20	−	1.52491e21i	0.0339228	−	0.0587560i
$975$		0			0
$976$	1.02426e22	+	1.77407e22i	0.388630	+	0.673127i
$977$	−1.63624e22	−	2.83406e22i	−0.616082	−	1.06709i	−0.990194	−	0.139702i	$-0.955386\pi$
$977$	−1.63624e22	−	2.83406e22i	−0.616082	−	1.06709i	0.374111	−	0.927384i	$-0.377948\pi$
$978$		0			0
$979$	−2.16265e22	+	3.74582e22i	−0.801892	+	1.38892i
$980$	−4.37801e22			−1.61095
$981$		0			0
$982$	1.16104e22			0.420737
$983$	−2.39235e22	+	4.14367e22i	−0.860346	+	1.49016i	0.0112484	+	0.999937i	$0.496419\pi$
$983$	−2.39235e22	+	4.14367e22i	−0.860346	+	1.49016i	−0.871595	+	0.490227i	$0.836914\pi$
$984$		0			0
$985$	4.55077e21	+	7.88216e21i	0.161181	+	0.279173i
$986$	2.40691e21	+	4.16889e21i	0.0846025	+	0.146536i
$987$		0			0
$988$	−4.01706e20	+	6.95775e20i	−0.0139069	+	0.0240875i
$989$	2.26839e22			0.779373
$990$		0			0
$991$	−1.02329e21			−0.0346296			−0.0173148	−	0.999850i	$-0.505512\pi$
$991$	−1.02329e21			−0.0346296			−0.0173148	+	0.999850i	$0.505512\pi$
$992$	−9.54661e21	+	1.65352e22i	−0.320636	+	0.555357i
$993$		0			0
$994$	5.72142e21	+	9.90978e21i	0.189280	+	0.327843i
$995$	4.82683e21	+	8.36032e21i	0.158485	+	0.274505i
$996$		0			0
$997$	2.10812e22	−	3.65136e22i	0.681838	−	1.18098i	−0.292582	−	0.956240i	$-0.594514\pi$
$997$	2.10812e22	−	3.65136e22i	0.681838	−	1.18098i	0.974420	−	0.224737i	$-0.0721522\pi$
$998$	−2.90016e21			−0.0930985
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.16.c.a.19.6		28
3.2	odd	2		9.16.c.a.7.9	yes	28
9.2	odd	6		81.16.a.e.1.6		14
9.4	even	3	inner	27.16.c.a.10.6		28
9.5	odd	6		9.16.c.a.4.9	✓	28
9.7	even	3		81.16.a.c.1.9		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.16.c.a.4.9	✓	28	9.5	odd	6
9.16.c.a.7.9	yes	28	3.2	odd	2
27.16.c.a.10.6		28	9.4	even	3	inner
27.16.c.a.19.6		28	1.1	even	1	trivial
81.16.a.c.1.9		14	9.7	even	3
81.16.a.e.1.6		14	9.2	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	27.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-30.1976 + 52.3037i) q^{2} +(14560.2 + 25219.0i) q^{4} +(-62931.9 - 109001. i) q^{5} +(-2.04281e6 + 3.53826e6i) q^{7} -3.73776e6 q^{8} +7.60156e6 q^{10} +(3.00835e7 - 5.21061e7i) q^{11} +(5.90623e6 + 1.02299e7i) q^{13} +(-1.23376e8 - 2.13694e8i) q^{14} +(-3.64238e8 + 6.30879e8i) q^{16} -2.65805e9 q^{17} +2.33561e9 q^{19} +(1.83260e9 - 3.17416e9i) q^{20} +(1.81690e9 + 3.14696e9i) q^{22} +(8.95648e9 + 1.55131e10i) q^{23} +(7.33795e9 - 1.27097e10i) q^{25} -7.13415e8 q^{26} -1.18975e11 q^{28} +(-1.49932e10 + 2.59690e10i) q^{29} +(-5.73455e10 - 9.93254e10i) q^{31} +(-8.32376e10 - 1.44172e11i) q^{32} +(8.02666e10 - 1.39026e11i) q^{34} +5.14232e11 q^{35} +1.02630e11 q^{37} +(-7.05297e10 + 1.22161e11i) q^{38} +(2.35224e11 + 4.07420e11i) q^{40} +(-1.01906e12 - 1.76506e12i) q^{41} +(6.33169e11 - 1.09668e12i) q^{43} +1.75209e12 q^{44} -1.08186e12 q^{46} +(2.66170e12 - 4.61020e12i) q^{47} +(-5.97240e12 - 1.03445e13i) q^{49} +(4.43176e11 + 7.67604e11i) q^{50} +(-1.71992e11 + 2.97899e11i) q^{52} +4.91335e11 q^{53} -7.57284e12 q^{55} +(7.63555e12 - 1.32252e13i) q^{56} +(-9.05518e11 - 1.56840e12i) q^{58} +(4.33799e12 + 7.51363e12i) q^{59} +(1.40603e13 - 2.43532e13i) q^{61} +6.92678e12 q^{62} -1.38164e13 q^{64} +(7.43380e11 - 1.28757e12i) q^{65} +(5.72996e12 + 9.92457e12i) q^{67} +(-3.87018e13 - 6.70334e13i) q^{68} +(-1.55286e13 + 2.68963e13i) q^{70} -4.63738e13 q^{71} -2.03563e13 q^{73} +(-3.09916e12 + 5.36791e12i) q^{74} +(3.40070e13 + 5.89018e13i) q^{76} +(1.22910e14 + 2.12886e14i) q^{77} +(4.33752e13 - 7.51280e13i) q^{79} +9.16887e13 q^{80} +1.23092e14 q^{82} +(-5.62932e13 + 9.75026e13i) q^{83} +(1.67276e14 + 2.89731e14i) q^{85} +(3.82403e13 + 6.62342e13i) q^{86} +(-1.12445e14 + 1.94760e14i) q^{88} -7.18882e14 q^{89} -4.82613e13 q^{91} +(-2.60817e14 + 4.51748e14i) q^{92} +(1.60754e14 + 2.78433e14i) q^{94} +(-1.46984e14 - 2.54584e14i) q^{95} +(-1.42070e14 + 2.46072e14i) q^{97} +7.21407e14 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 129 q^{2} - 212993 q^{4} + 152655 q^{5} + 803705 q^{7} - 20162658 q^{8} + 65532 q^{10} + 60735990 q^{11} - 41509093 q^{13} - 215313024 q^{14} - 2952822785 q^{16} + 2121112242 q^{17} + 5670809246 q^{19}+ \cdots - 72\!\cdots\!90 q^{98}+O(q^{100}) \) 28 * q + 129 * q^2 - 212993 * q^4 + 152655 * q^5 + 803705 * q^7 - 20162658 * q^8 + 65532 * q^10 + 60735990 * q^11 - 41509093 * q^13 - 215313024 * q^14 - 2952822785 * q^16 + 2121112242 * q^17 + 5670809246 * q^19 + 1434155028 * q^20 + 7841223807 * q^22 + 49433203761 * q^23 - 59779497779 * q^25 - 28088907384 * q^26 - 103195803652 * q^28 + 152663830725 * q^29 - 13955906443 * q^31 + 779638216401 * q^32 - 15287791959 * q^34 - 2803990417206 * q^35 + 531598359836 * q^37 + 3598723579461 * q^38 - 1083028910664 * q^40 + 1656362316264 * q^41 + 2394872112236 * q^43 - 13185661781850 * q^44 + 1511321018232 * q^46 + 7686086213559 * q^47 - 7946464864203 * q^49 + 2177050903941 * q^50 + 1969798905818 * q^52 + 20778802614756 * q^53 - 21700105111626 * q^55 - 13789887516654 * q^56 + 15429496587216 * q^58 - 17132922121350 * q^59 - 17229834579991 * q^61 + 190512185539596 * q^62 + 11322374934466 * q^64 - 92170621979115 * q^65 - 19847122719016 * q^67 - 106742875854159 * q^68 - 85984052928798 * q^70 - 60954771085488 * q^71 + 206937948168362 * q^73 + 169102773629016 * q^74 - 274786877071699 * q^76 + 121510644149499 * q^77 + 137921083996235 * q^79 - 1189869535368192 * q^80 + 747645180639978 * q^82 + 243294491978445 * q^83 + 278537029457886 * q^85 + 1439527045654455 * q^86 + 8025917716587 * q^88 - 3513318445769832 * q^89 - 1924506955785338 * q^91 + 3448278918317022 * q^92 + 1100860396273032 * q^94 + 3375682767029028 * q^95 - 1883742033081100 * q^97 - 7254179697035790 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more