LMFDB - Embedded newform 3.17.b.a.2.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,17,Mod(2,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 17, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 17);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 17 $
Character orbit:	$[\chi]$	$=$	3.b (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:	$4.86973631570$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3814x^{2} + 2981440 $ x^4 + 3814*x^2 + 2981440
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{6}\cdot 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.4
Root			$52.1196i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.17.b.a.2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+312.717i q^{2} +(-5369.70 + 3770.02i) q^{3} -32256.2 q^{4} -276758. i q^{5} +(-1.17895e6 - 1.67920e6i) q^{6} -7.10881e6 q^{7} +1.04072e7i q^{8} +(1.46206e7 - 4.04878e7i) q^{9} +O(q^{10})$	\(q+312.717i q^{2} +(-5369.70 + 3770.02i) q^{3} -32256.2 q^{4} -276758. i q^{5} +(-1.17895e6 - 1.67920e6i) q^{6} -7.10881e6 q^{7} +1.04072e7i q^{8} +(1.46206e7 - 4.04878e7i) q^{9} +8.65472e7 q^{10} +3.43468e8i q^{11} +(1.73206e8 - 1.21607e8i) q^{12} -7.14909e8 q^{13} -2.22305e9i q^{14} +(1.04338e9 + 1.48611e9i) q^{15} -5.36845e9 q^{16} +6.74629e8i q^{17} +(1.26612e10 + 4.57212e9i) q^{18} +4.70347e9 q^{19} +8.92717e9i q^{20} +(3.81722e10 - 2.68004e10i) q^{21} -1.07408e11 q^{22} +4.47377e10i q^{23} +(-3.92353e10 - 5.58834e10i) q^{24} +7.59927e10 q^{25} -2.23564e11i q^{26} +(7.41314e10 + 2.72527e11i) q^{27} +2.29303e11 q^{28} +3.75138e11i q^{29} +(-4.64732e11 + 3.26285e11i) q^{30} +6.58929e11 q^{31} -9.96762e11i q^{32} +(-1.29488e12 - 1.84432e12i) q^{33} -2.10968e11 q^{34} +1.96742e12i q^{35} +(-4.71605e11 + 1.30598e12i) q^{36} +3.89028e11 q^{37} +1.47086e12i q^{38} +(3.83885e12 - 2.69522e12i) q^{39} +2.88027e12 q^{40} -4.14027e12i q^{41} +(8.38094e12 + 1.19371e13i) q^{42} -1.68426e13 q^{43} -1.10790e13i q^{44} +(-1.12053e13 - 4.04638e12i) q^{45} -1.39903e13 q^{46} +9.08356e12i q^{47} +(2.88269e13 - 2.02392e13i) q^{48} +1.73022e13 q^{49} +2.37642e13i q^{50} +(-2.54336e12 - 3.62255e12i) q^{51} +2.30602e13 q^{52} +4.32802e13i q^{53} +(-8.52240e13 + 2.31822e13i) q^{54} +9.50576e13 q^{55} -7.39826e13i q^{56} +(-2.52562e13 + 1.77322e13i) q^{57} -1.17312e14 q^{58} -2.07085e14i q^{59} +(-3.36556e13 - 4.79362e13i) q^{60} +1.10641e14 q^{61} +2.06059e14i q^{62} +(-1.03935e14 + 2.87820e14i) q^{63} -4.01216e13 q^{64} +1.97857e14i q^{65} +(5.76750e14 - 4.04932e14i) q^{66} +1.61981e14 q^{67} -2.17610e13i q^{68} +(-1.68662e14 - 2.40228e14i) q^{69} -6.15247e14 q^{70} +8.06506e13i q^{71} +(4.21363e14 + 1.52159e14i) q^{72} -8.85416e14 q^{73} +1.21656e14i q^{74} +(-4.08058e14 + 2.86494e14i) q^{75} -1.51716e14 q^{76} -2.44165e15i q^{77} +(8.42843e14 + 1.20047e15i) q^{78} +2.35142e15 q^{79} +1.48576e15i q^{80} +(-1.42550e15 - 1.18391e15i) q^{81} +1.29474e15 q^{82} +3.93339e15i q^{83} +(-1.23129e15 + 8.64477e14i) q^{84} +1.86709e14 q^{85} -5.26696e15i q^{86} +(-1.41428e15 - 2.01438e15i) q^{87} -3.57453e15 q^{88} +3.56666e15i q^{89} +(1.26537e15 - 3.50410e15i) q^{90} +5.08215e15 q^{91} -1.44307e15i q^{92} +(-3.53825e15 + 2.48418e15i) q^{93} -2.84059e15 q^{94} -1.30172e15i q^{95} +(3.75781e15 + 5.35231e15i) q^{96} -1.51341e15 q^{97} +5.41071e15i q^{98} +(1.39062e16 + 5.02171e15i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2052 q^{3} - 12464 q^{4} - 403056 q^{6} - 3141544 q^{7} + 18618660 q^{9}+O(q^{10}) $ 4 * q - 2052 * q^3 - 12464 * q^4 - 403056 * q^6 - 3141544 * q^7 + 18618660 * q^9	$ 4 q - 2052 q^{3} - 12464 q^{4} - 403056 q^{6} - 3141544 q^{7} + 18618660 q^{9} - 18646560 q^{10} + 572494608 q^{12} - 1580730424 q^{13} + 6829958880 q^{15} - 14561268608 q^{16} + 42304978080 q^{18} - 56117116360 q^{19} + 124455437064 q^{21} - 173545812000 q^{22} + 100515572352 q^{24} - 8074048700 q^{25} - 317983667652 q^{27} + 746852001056 q^{28} - 1762329117600 q^{30} + 2471781156248 q^{31} - 3610697951520 q^{33} + 2721261612672 q^{34} - 1219654126512 q^{36} + 370563213896 q^{37} + 7022170227384 q^{39} - 11795287092480 q^{40} + 27587883687840 q^{42} - 28065022062664 q^{43} + 18795326443200 q^{45} - 43994579504832 q^{46} + 41041959355008 q^{48} + 29478262537164 q^{49} - 82841575222656 q^{51} + 42193089120416 q^{52} - 107063660756304 q^{54} + 290253653236800 q^{55} - 335129108488344 q^{57} + 8796421982880 q^{58} + 56126440892160 q^{60} + 362269793083208 q^{61} - 266698363786344 q^{63} - 653949742779392 q^{64} + 13\!\cdots\!80 q^{66}+ \cdots + 18\!\cdots\!60 q^{99}+O(q^{100}) $ 4 * q - 2052 * q^3 - 12464 * q^4 - 403056 * q^6 - 3141544 * q^7 + 18618660 * q^9 - 18646560 * q^10 + 572494608 * q^12 - 1580730424 * q^13 + 6829958880 * q^15 - 14561268608 * q^16 + 42304978080 * q^18 - 56117116360 * q^19 + 124455437064 * q^21 - 173545812000 * q^22 + 100515572352 * q^24 - 8074048700 * q^25 - 317983667652 * q^27 + 746852001056 * q^28 - 1762329117600 * q^30 + 2471781156248 * q^31 - 3610697951520 * q^33 + 2721261612672 * q^34 - 1219654126512 * q^36 + 370563213896 * q^37 + 7022170227384 * q^39 - 11795287092480 * q^40 + 27587883687840 * q^42 - 28065022062664 * q^43 + 18795326443200 * q^45 - 43994579504832 * q^46 + 41041959355008 * q^48 + 29478262537164 * q^49 - 82841575222656 * q^51 + 42193089120416 * q^52 - 107063660756304 * q^54 + 290253653236800 * q^55 - 335129108488344 * q^57 + 8796421982880 * q^58 + 56126440892160 * q^60 + 362269793083208 * q^61 - 266698363786344 * q^63 - 653949742779392 * q^64 + 1332768950045280 * q^66 - 26774405363464 * q^67 + 58823173290816 * q^69 - 2292362286177600 * q^70 + 2397649754476800 * q^72 + 317628887539976 * q^73 - 1511365865026500 * q^75 - 2008642200508384 * q^76 + 1538179445855520 * q^78 + 4794017165184920 * q^79 - 6444192852054396 * q^81 + 1589112481320000 * q^82 - 1210523902199136 * q^84 + 7999994092573440 * q^85 - 8850169595242080 * q^87 - 3370289894104320 * q^88 + 3549134645307360 * q^90 + 9328538231657008 * q^91 - 2064207396761784 * q^93 - 12859596129667968 * q^94 + 15507630559798272 * q^96 - 13833795002601784 * q^97 + 18943177097338560 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$			312.717i			1.22155i	0.791803	+	0.610776i	$0.209143\pi$
$2$			312.717i			1.22155i	−0.791803	+	0.610776i	$0.790857\pi$
$3$	−5369.70	+	3770.02i	−0.818427	+	0.574611i
$3$	−5369.70	+	3770.02i	−0.818427	+	0.574611i
$4$	−32256.2			−0.492190
$5$		−	276758.i		−	0.708501i	−0.935150	−	0.354251i	$-0.884736\pi$
$5$		−	276758.i		−	0.708501i	0.935150	−	0.354251i	$-0.115264\pi$
$6$	−1.17895e6	−	1.67920e6i	−0.701917	−	0.999751i
$7$	−7.10881e6			−1.23314			−0.616570	−	0.787300i	$-0.711478\pi$
$7$	−7.10881e6			−1.23314			−0.616570	+	0.787300i	$0.711478\pi$
$8$			1.04072e7i			0.620316i
$9$	1.46206e7	−	4.04878e7i	0.339645	−	0.940554i
$10$	8.65472e7			0.865472
$11$			3.43468e8i			1.60230i	0.598462	+	0.801151i	$0.295779\pi$
$11$			3.43468e8i			1.60230i	−0.598462	+	0.801151i	$0.704221\pi$
$12$	1.73206e8	−	1.21607e8i	0.402822	−	0.282818i
$13$	−7.14909e8			−0.876403			−0.438201	−	0.898877i	$-0.644384\pi$
$13$	−7.14909e8			−0.876403			−0.438201	+	0.898877i	$0.644384\pi$
$14$		−	2.22305e9i		−	1.50635i
$15$	1.04338e9	+	1.48611e9i	0.407112	+	0.579857i
$16$	−5.36845e9			−1.24994
$17$			6.74629e8i			0.0967105i	0.998830	+	0.0483552i	$0.0153980\pi$
$17$			6.74629e8i			0.0967105i	−0.998830	+	0.0483552i	$0.984602\pi$
$18$	1.26612e10	+	4.57212e9i	1.14894	+	0.414894i
$19$	4.70347e9			0.276942			0.138471	−	0.990366i	$-0.455781\pi$
$19$	4.70347e9			0.276942			0.138471	+	0.990366i	$0.455781\pi$
$20$			8.92717e9i			0.348718i
$21$	3.81722e10	−	2.68004e10i	1.00924	−	0.708576i
$22$	−1.07408e11			−1.95730
$23$			4.47377e10i			0.571283i	0.958337	+	0.285641i	$0.0922066\pi$
$23$			4.47377e10i			0.571283i	−0.958337	+	0.285641i	$0.907793\pi$
$24$	−3.92353e10	−	5.58834e10i	−0.356440	−	0.507683i
$25$	7.59927e10			0.498026
$26$		−	2.23564e11i		−	1.07057i
$27$	7.41314e10	+	2.72527e11i	0.262477	+	0.964938i
$28$	2.29303e11			0.606940
$29$			3.75138e11i			0.749906i	0.927044	+	0.374953i	$0.122341\pi$
$29$			3.75138e11i			0.749906i	−0.927044	+	0.374953i	$0.877659\pi$
$30$	−4.64732e11	+	3.26285e11i	−0.708325	+	0.497309i
$31$	6.58929e11			0.772583			0.386291	−	0.922377i	$-0.373756\pi$
$31$	6.58929e11			0.772583			0.386291	+	0.922377i	$0.373756\pi$
$32$		−	9.96762e11i		−	0.906550i
$33$	−1.29488e12	−	1.84432e12i	−0.920700	−	1.31137i
$34$	−2.10968e11			−0.118137
$35$			1.96742e12i			0.873682i
$36$	−4.71605e11	+	1.30598e12i	−0.167170	+	0.462932i
$37$	3.89028e11			0.110756			0.0553779	−	0.998465i	$-0.482364\pi$
$37$	3.89028e11			0.110756			0.0553779	+	0.998465i	$0.482364\pi$
$38$			1.47086e12i			0.338299i
$39$	3.83885e12	−	2.69522e12i	0.717272	−	0.503590i
$40$	2.88027e12			0.439495
$41$		−	4.14027e12i		−	0.518511i	−0.965809	−	0.259256i	$-0.916523\pi$
$41$		−	4.14027e12i		−	0.518511i	0.965809	−	0.259256i	$-0.0834772\pi$
$42$	8.38094e12	+	1.19371e13i	0.865562	+	1.23283i
$43$	−1.68426e13			−1.44099			−0.720494	−	0.693461i	$-0.756085\pi$
$43$	−1.68426e13			−1.44099			−0.720494	+	0.693461i	$0.756085\pi$
$44$		−	1.10790e13i		−	0.788638i
$45$	−1.12053e13	−	4.04638e12i	−0.666384	−	0.240639i
$46$	−1.39903e13			−0.697852
$47$			9.08356e12i			0.381481i	0.981640	+	0.190741i	$0.0610889\pi$
$47$			9.08356e12i			0.381481i	−0.981640	+	0.190741i	$0.938911\pi$
$48$	2.88269e13	−	2.02392e13i	1.02298	−	0.718228i
$49$	1.73022e13			0.520635
$50$			2.37642e13i			0.608365i
$51$	−2.54336e12	−	3.62255e12i	−0.0555709	−	0.0791504i
$52$	2.30602e13			0.431357
$53$			4.32802e13i			0.695155i	0.937651	+	0.347578i	$0.112996\pi$
$53$			4.32802e13i			0.695155i	−0.937651	+	0.347578i	$0.887004\pi$
$54$	−8.52240e13	+	2.31822e13i	−1.17872	+	0.320630i
$55$	9.50576e13			1.13523
$56$		−	7.39826e13i		−	0.764937i
$57$	−2.52562e13	+	1.77322e13i	−0.226657	+	0.159134i
$58$	−1.17312e14			−0.916049
$59$		−	2.07085e14i		−	1.41037i	−0.709024	−	0.705185i	$-0.750864\pi$
$59$		−	2.07085e14i		−	1.41037i	0.709024	−	0.705185i	$-0.249136\pi$
$60$	−3.36556e13	−	4.79362e13i	−0.200377	−	0.285400i
$61$	1.10641e14			0.577136			0.288568	−	0.957459i	$-0.406821\pi$
$61$	1.10641e14			0.577136			0.288568	+	0.957459i	$0.406821\pi$
$62$			2.06059e14i			0.943751i
$63$	−1.03935e14	+	2.87820e14i	−0.418830	+	1.15983i
$64$	−4.01216e13			−0.142541
$65$			1.97857e14i			0.620933i
$66$	5.76750e14	−	4.04932e14i	1.60190	−	1.12468i
$67$	1.61981e14			0.398901			0.199451	−	0.979908i	$-0.436084\pi$
$67$	1.61981e14			0.398901			0.199451	+	0.979908i	$0.436084\pi$
$68$		−	2.17610e13i		−	0.0476000i
$69$	−1.68662e14	−	2.40228e14i	−0.328265	−	0.467553i
$70$	−6.15247e14			−1.06725
$71$			8.06506e13i			0.124894i	0.998048	+	0.0624469i	$0.0198904\pi$
$71$			8.06506e13i			0.124894i	−0.998048	+	0.0624469i	$0.980110\pi$
$72$	4.21363e14	+	1.52159e14i	0.583440	+	0.210687i
$73$	−8.85416e14			−1.09790			−0.548952	−	0.835854i	$-0.684973\pi$
$73$	−8.85416e14			−1.09790			−0.548952	+	0.835854i	$0.684973\pi$
$74$			1.21656e14i			0.135294i
$75$	−4.08058e14	+	2.86494e14i	−0.407598	+	0.286171i
$76$	−1.51716e14			−0.136308
$77$		−	2.44165e15i		−	1.97586i
$78$	8.42843e14	+	1.20047e15i	0.615162	+	0.876185i
$79$	2.35142e15			1.54993			0.774967	−	0.632002i	$-0.217766\pi$
$79$	2.35142e15			1.54993			0.774967	+	0.632002i	$0.217766\pi$
$80$			1.48576e15i			0.885584i
$81$	−1.42550e15	−	1.18391e15i	−0.769282	−	0.638909i
$82$	1.29474e15			0.633389
$83$			3.93339e15i			1.74640i	0.487365	+	0.873198i	$0.337958\pi$
$83$			3.93339e15i			1.74640i	−0.487365	+	0.873198i	$0.662042\pi$
$84$	−1.23129e15	+	8.64477e14i	−0.496736	+	0.348754i
$85$	1.86709e14			0.0685195
$86$		−	5.26696e15i		−	1.76024i
$87$	−1.41428e15	−	2.01438e15i	−0.430904	−	0.613743i
$88$	−3.57453e15			−0.993934
$89$			3.56666e15i			0.906028i	0.891503	+	0.453014i	$0.149651\pi$
$89$			3.56666e15i			0.906028i	−0.891503	+	0.453014i	$0.850349\pi$
$90$	1.26537e15	−	3.50410e15i	0.293953	−	0.814023i
$91$	5.08215e15			1.08073
$92$		−	1.44307e15i		−	0.281180i
$93$	−3.53825e15	+	2.48418e15i	−0.632303	+	0.443934i
$94$	−2.84059e15			−0.465999
$95$		−	1.30172e15i		−	0.196214i
$96$	3.75781e15	+	5.35231e15i	0.520913	+	0.741945i
$97$	−1.51341e15			−0.193100			−0.0965502	−	0.995328i	$-0.530781\pi$
$97$	−1.51341e15			−0.193100			−0.0965502	+	0.995328i	$0.530781\pi$
$98$			5.41071e15i			0.635983i
$99$	1.39062e16	+	5.02171e15i	1.50705	+	0.544214i
$100$	−2.45124e15			−0.245124
$101$		−	1.00976e16i		−	0.932499i	−0.884653	−	0.466249i	$-0.845605\pi$
$101$		−	1.00976e16i		−	0.932499i	0.884653	−	0.466249i	$-0.154395\pi$
$102$	1.13284e15	−	7.95354e14i	0.0966864	−	0.0678827i
$103$	−2.41924e15			−0.190977			−0.0954884	−	0.995431i	$-0.530441\pi$
$103$	−2.41924e15			−0.190977			−0.0954884	+	0.995431i	$0.530441\pi$
$104$		−	7.44018e15i		−	0.543647i
$105$	−7.41722e15	−	1.05645e16i	−0.502027	−	0.715045i
$106$	−1.35345e16			−0.849169
$107$			1.15781e16i			0.673857i	0.941530	+	0.336929i	$0.109388\pi$
$107$			1.15781e16i			0.673857i	−0.941530	+	0.336929i	$0.890612\pi$
$108$	−2.39120e15	−	8.79068e15i	−0.129189	−	0.474933i
$109$	−1.26180e16			−0.633253			−0.316627	−	0.948550i	$-0.602550\pi$
$109$	−1.26180e16			−0.633253			−0.316627	+	0.948550i	$0.602550\pi$
$110$			2.97262e16i			1.38675i
$111$	−2.08896e15	+	1.46664e15i	−0.0906456	+	0.0636415i
$112$	3.81633e16			1.54135
$113$		−	2.03120e16i		−	0.764057i	−0.924151	−	0.382029i	$-0.875226\pi$
$113$		−	2.03120e16i		−	0.764057i	0.924151	−	0.382029i	$-0.124774\pi$
$114$	−5.54516e15	−	7.89805e15i	−0.194390	−	0.276873i
$115$	1.23815e16			0.404755
$116$		−	1.21005e16i		−	0.369096i
$117$	−1.04524e16	+	2.89450e16i	−0.297666	+	0.824304i
$118$	6.47591e16			1.72284
$119$		−	4.79581e15i		−	0.119258i
$120$	−1.54662e16	+	1.08587e16i	−0.359694	+	0.252538i
$121$	−7.20203e16			−1.56737
$122$			3.45995e16i			0.705003i
$123$	1.56089e16	+	2.22320e16i	0.297942	+	0.424364i
$124$	−2.12545e16			−0.380258
$125$		−	6.32616e16i		−	1.06135i
$126$	−9.00062e16	−	3.25023e16i	−1.41680	−	0.511623i
$127$	5.69808e16			0.841974			0.420987	−	0.907067i	$-0.361684\pi$
$127$	5.69808e16			0.841974			0.420987	+	0.907067i	$0.361684\pi$
$128$		−	7.78705e16i		−	1.08067i
$129$	9.04395e16	−	6.34968e16i	1.17934	−	0.828007i
$130$	−6.18733e16			−0.758502
$131$			1.29909e17i			1.49786i	0.662651	+	0.748928i	$0.269431\pi$
$131$			1.29909e17i			1.49786i	−0.662651	+	0.748928i	$0.730569\pi$
$132$	4.17679e16	+	5.94907e16i	0.453160	+	0.645442i
$133$	−3.34360e16			−0.341509
$134$			5.06542e16i			0.487279i
$135$	7.54241e16	−	2.05165e16i	0.683660	−	0.185966i
$136$	−7.02098e15			−0.0599911
$137$			1.41617e17i			1.14117i	0.821238	+	0.570586i	$0.193284\pi$
$137$			1.41617e17i			1.14117i	−0.821238	+	0.570586i	$0.806716\pi$
$138$	7.51235e16	−	5.27436e16i	0.571141	−	0.400993i
$139$	−3.68618e16			−0.264520			−0.132260	−	0.991215i	$-0.542223\pi$
$139$	−3.68618e16			−0.264520			−0.132260	+	0.991215i	$0.542223\pi$
$140$		−	6.34615e16i		−	0.430018i
$141$	−3.42452e16	−	4.87760e16i	−0.219203	−	0.312214i
$142$	−2.52208e16			−0.152564
$143$		−	2.45548e17i		−	1.40426i
$144$	−7.84900e16	+	2.17356e17i	−0.424536	+	1.17563i
$145$	1.03822e17			0.531309
$146$		−	2.76885e17i		−	1.34115i
$147$	−9.29077e16	+	6.52297e16i	−0.426102	+	0.299162i
$148$	−1.25486e16			−0.0545130
$149$			3.06216e17i			1.26049i	0.776398	+	0.630243i	$0.217045\pi$
$149$			3.06216e17i			1.26049i	−0.776398	+	0.630243i	$0.782955\pi$
$150$	−8.95917e16	−	1.27607e17i	−0.349573	−	0.497902i
$151$	−4.71608e17			−1.74488			−0.872440	−	0.488721i	$-0.837463\pi$
$151$	−4.71608e17			−1.74488			−0.872440	+	0.488721i	$0.837463\pi$
$152$			4.89498e16i			0.171792i
$153$	2.73142e16	+	9.86349e15i	0.0909614	+	0.0328472i
$154$	7.63545e17			2.41362
$155$		−	1.82364e17i		−	0.547376i
$156$	−1.23827e17	+	8.69376e16i	−0.353034	+	0.247862i
$157$	5.59035e17			1.51440			0.757202	−	0.653181i	$-0.226566\pi$
$157$	5.59035e17			1.51440			0.757202	+	0.653181i	$0.226566\pi$
$158$			7.35330e17i			1.89333i
$159$	−1.63167e17	−	2.32401e17i	−0.399444	−	0.568934i
$160$	−2.75862e17			−0.642292
$161$		−	3.18032e17i		−	0.704472i
$162$	3.70230e17	−	4.45777e17i	0.780461	−	0.939719i
$163$	2.34231e17			0.470050			0.235025	−	0.971989i	$-0.424483\pi$
$163$	2.34231e17			0.470050			0.235025	+	0.971989i	$0.424483\pi$
$164$			1.33549e17i			0.255206i
$165$	−5.10430e17	+	3.58369e17i	−0.929105	+	0.652317i
$166$	−1.23004e18			−2.13331
$167$		−	4.08862e17i		−	0.675842i	−0.941175	−	0.337921i	$-0.890276\pi$
$167$		−	4.08862e17i		−	0.675842i	0.941175	−	0.337921i	$-0.109724\pi$
$168$	2.78916e17	+	3.97264e17i	0.439541	+	0.626045i
$169$	−1.54322e17			−0.231918
$170$			5.83872e16i			0.0837002i
$171$	6.87675e16	−	1.90433e17i	0.0940621	−	0.260479i
$172$	5.43277e17			0.709241
$173$		−	2.03093e16i		−	0.0253119i	−0.999920	−	0.0126560i	$-0.995971\pi$
$173$		−	2.03093e16i		−	0.0253119i	0.999920	−	0.0126560i	$-0.00402863\pi$
$174$	6.29931e17	−	4.42269e17i	0.749719	−	0.526372i
$175$	−5.40218e17			−0.614136
$176$		−	1.84389e18i		−	2.00278i
$177$	7.80715e17	+	1.11198e18i	0.810413	+	1.15428i
$178$	−1.11536e18			−1.10676
$179$			1.38776e18i			1.31671i	0.752709	+	0.658354i	$0.228747\pi$
$179$			1.38776e18i			1.31671i	−0.752709	+	0.658354i	$0.771253\pi$
$180$	3.61441e17	+	1.30521e17i	0.327988	+	0.118440i
$181$	2.00744e18			1.74267			0.871334	−	0.490691i	$-0.163256\pi$
$181$	2.00744e18			1.74267			0.871334	+	0.490691i	$0.163256\pi$
$182$			1.58928e18i			1.32017i
$183$	−5.94110e17	+	4.17120e17i	−0.472344	+	0.331629i
$184$	−4.65593e17			−0.354376
$185$		−	1.07667e17i		−	0.0784707i
$186$	−7.76845e17	−	1.10647e18i	−0.542289	−	0.772391i
$187$	−2.31713e17			−0.154959
$188$		−	2.93001e17i		−	0.187761i
$189$	−5.26986e17	−	1.93734e18i	−0.323671	−	1.18990i
$190$	4.07072e17			0.239686
$191$		−	7.92402e17i		−	0.447382i	−0.974660	−	0.223691i	$-0.928189\pi$
$191$		−	7.92402e17i		−	0.447382i	0.974660	−	0.223691i	$-0.0718107\pi$
$192$	2.15441e17	−	1.51259e17i	0.116659	−	0.0819053i
$193$	−2.85892e17			−0.148506			−0.0742528	−	0.997239i	$-0.523657\pi$
$193$	−2.85892e17			−0.148506			−0.0742528	+	0.997239i	$0.523657\pi$
$194$		−	4.73270e17i		−	0.235882i
$195$	−7.45925e17	−	1.06243e18i	−0.356795	−	0.508188i
$196$	−5.58104e17			−0.256251
$197$			1.08139e18i			0.476707i	0.971178	+	0.238353i	$0.0766077\pi$
$197$			1.08139e18i			0.476707i	−0.971178	+	0.238353i	$0.923392\pi$
$198$	−1.57038e18	+	4.34872e18i	−0.664786	+	1.84094i
$199$	1.96655e18			0.799613			0.399806	−	0.916600i	$-0.369077\pi$
$199$	1.96655e18			0.799613			0.399806	+	0.916600i	$0.369077\pi$
$200$			7.90869e17i			0.308933i
$201$	−8.69788e17	+	6.10671e17i	−0.326471	+	0.229213i
$202$	3.15770e18			1.13910
$203$		−	2.66678e18i		−	0.924739i
$204$	8.20393e16	+	1.16850e17i	0.0273514	+	0.0389571i
$205$	−1.14586e18			−0.367366
$206$		−	7.56538e17i		−	0.233288i
$207$	1.81133e18	+	6.54093e17i	0.537322	+	0.194033i
$208$	3.83795e18			1.09545
$209$			1.61549e18i			0.443745i
$210$	3.30369e18	−	2.31949e18i	0.873464	−	0.613252i
$211$	−5.56143e18			−1.41556			−0.707778	−	0.706435i	$-0.750302\pi$
$211$	−5.56143e18			−1.41556			−0.707778	+	0.706435i	$0.750302\pi$
$212$		−	1.39605e18i		−	0.342149i
$213$	−3.04054e17	−	4.33069e17i	−0.0717653	−	0.102216i
$214$	−3.62068e18			−0.823152
$215$			4.66132e18i			1.02094i
$216$	−2.83624e18	+	7.71498e17i	−0.598567	+	0.162819i
$217$	−4.68420e18			−0.952703
$218$		−	3.94586e18i		−	0.773552i
$219$	4.75442e18	−	3.33804e18i	0.898554	−	0.630867i
$220$	−3.06619e18			−0.558751
$221$		−	4.82298e17i		−	0.0847573i
$222$	−4.58645e17	−	6.53255e17i	−0.0777414	−	0.110728i
$223$	8.62389e17			0.141015			0.0705074	−	0.997511i	$-0.477538\pi$
$223$	8.62389e17			0.141015			0.0705074	+	0.997511i	$0.477538\pi$
$224$			7.08579e18i			1.11790i
$225$	1.11106e18	−	3.07677e18i	0.169152	−	0.468420i
$226$	6.35193e18			0.933336
$227$		−	2.61451e18i		−	0.370837i	−0.982660	−	0.185418i	$-0.940636\pi$
$227$		−	2.61451e18i		−	0.370837i	0.982660	−	0.185418i	$-0.0593641\pi$
$228$	8.14669e17	−	5.71972e17i	0.111558	−	0.0783242i
$229$	5.58270e18			0.738176			0.369088	−	0.929394i	$-0.379670\pi$
$229$	5.58270e18			0.738176			0.369088	+	0.929394i	$0.379670\pi$
$230$			3.87192e18i			0.494429i
$231$	9.20505e18	+	1.31109e19i	1.13535	+	1.61710i
$232$	−3.90412e18			−0.465179
$233$		−	1.35764e19i		−	1.56293i	−0.623952	−	0.781463i	$-0.714474\pi$
$233$		−	1.35764e19i		−	1.56293i	0.623952	−	0.781463i	$-0.285526\pi$
$234$	−9.05162e18	−	3.26865e18i	−1.00693	−	0.363615i
$235$	2.51395e18			0.270280
$236$			6.67978e18i			0.694170i
$237$	−1.26264e19	+	8.86490e18i	−1.26851	+	0.890609i
$238$	1.49973e18			0.145679
$239$			8.32183e18i			0.781692i	0.920456	+	0.390846i	$0.127818\pi$
$239$			8.32183e18i			0.781692i	−0.920456	+	0.390846i	$0.872182\pi$
$240$	−5.60136e18	−	7.97810e18i	−0.508866	−	0.724785i
$241$	3.38184e18			0.297178			0.148589	−	0.988899i	$-0.452527\pi$
$241$	3.38184e18			0.297178			0.148589	+	0.988899i	$0.452527\pi$
$242$		−	2.25220e19i		−	1.91463i
$243$	1.21179e19	+	9.83099e17i	0.996725	+	0.0808625i
$244$	−3.56887e18			−0.284061
$245$		−	4.78853e18i		−	0.368870i
$246$	−6.95234e18	+	4.88118e18i	−0.518382	+	0.363952i
$247$	−3.36255e18			−0.242713
$248$			6.85759e18i			0.479246i
$249$	−1.48290e19	−	2.11211e19i	−1.00350	−	1.42930i
$250$	1.97830e19			1.29650
$251$			1.37972e19i			0.875789i	0.899026	+	0.437895i	$0.144276\pi$
$251$			1.37972e19i			0.875789i	−0.899026	+	0.437895i	$0.855724\pi$
$252$	3.35255e18	−	9.28397e18i	0.206144	−	0.570859i
$253$	−1.53660e19			−0.915368
$254$			1.78189e19i			1.02852i
$255$	−1.00257e18	+	7.03897e17i	−0.0560782	+	0.0393720i
$256$	2.17221e19			1.17756
$257$			1.93378e19i			1.01611i	0.861324	+	0.508057i	$0.169636\pi$
$257$			1.93378e19i			1.01611i	−0.861324	+	0.508057i	$0.830364\pi$
$258$	1.98566e19	+	2.82820e19i	1.01145	+	1.44063i
$259$	−2.76552e18			−0.136578
$260$		−	6.38211e18i		−	0.305617i
$261$	1.51885e19	+	5.48474e18i	0.705327	+	0.254702i
$262$	−4.06249e19			−1.82971
$263$		−	4.15307e19i		−	1.81436i	−0.420741	−	0.907181i	$-0.638230\pi$
$263$		−	4.15307e19i		−	1.81436i	0.420741	−	0.907181i	$-0.361770\pi$
$264$	1.91941e19	−	1.34760e19i	0.813462	−	0.571125i
$265$	1.19781e19			0.492519
$266$		−	1.04560e19i		−	0.417171i
$267$	−1.34464e19	−	1.91519e19i	−0.520613	−	0.741518i
$268$	−5.22488e18			−0.196335
$269$		−	4.45503e18i		−	0.162492i	−0.996694	−	0.0812460i	$-0.974110\pi$
$269$		−	4.45503e18i		−	0.162492i	0.996694	−	0.0812460i	$-0.0258899\pi$
$270$	6.41586e18	+	2.35864e19i	0.227167	+	0.835127i
$271$	−1.72748e19			−0.593827			−0.296913	−	0.954904i	$-0.595957\pi$
$271$	−1.72748e19			−0.593827			−0.296913	+	0.954904i	$0.595957\pi$
$272$		−	3.62171e18i		−	0.120882i
$273$	−2.72896e19	+	1.91598e19i	−0.884497	+	0.620998i
$274$	−4.42862e19			−1.39400
$275$			2.61010e19i			0.797988i
$276$	5.44040e18	+	7.74884e18i	0.161569	+	0.230125i
$277$	5.05204e19			1.45757			0.728784	−	0.684744i	$-0.240086\pi$
$277$	5.05204e19			1.45757			0.728784	+	0.684744i	$0.240086\pi$
$278$		−	1.15273e19i		−	0.323125i
$279$	9.63395e18	−	2.66786e19i	0.262404	−	0.726656i
$280$	−2.04753e19			−0.541959
$281$		−	2.72214e18i		−	0.0700260i	−0.999387	−	0.0350130i	$-0.988853\pi$
$281$		−	2.72214e18i		−	0.0700260i	0.999387	−	0.0350130i	$-0.0111473\pi$
$282$	1.52531e19	−	1.07091e19i	0.381386	−	0.267768i
$283$	−3.84294e18			−0.0934054			−0.0467027	−	0.998909i	$-0.514871\pi$
$283$	−3.84294e18			−0.0934054			−0.0467027	+	0.998909i	$0.514871\pi$
$284$		−	2.60148e18i		−	0.0614715i
$285$	4.90752e18	+	6.98986e18i	0.112747	+	0.160587i
$286$	7.67872e19			1.71538
$287$			2.94324e19i			0.639397i
$288$	−4.03567e19	−	1.45733e19i	−0.852659	−	0.307905i
$289$	4.82061e19			0.990647
$290$			3.24671e19i			0.649022i
$291$	8.12657e18	−	5.70559e18i	0.158039	−	0.110958i
$292$	2.85601e19			0.540378
$293$			4.00496e19i			0.737322i	0.929564	+	0.368661i	$0.120184\pi$
$293$			4.00496e19i			0.737322i	−0.929564	+	0.368661i	$0.879816\pi$
$294$	−2.03985e19	−	2.90539e19i	−0.365442	−	0.520505i
$295$	−5.73125e19			−0.999249
$296$			4.04868e18i			0.0687036i
$297$	−9.36042e19	+	2.54617e19i	−1.54612	+	0.420568i
$298$	−9.57592e19			−1.53975
$299$		−	3.19834e19i		−	0.500674i
$300$	1.31624e19	−	9.24121e18i	0.200616	−	0.140851i
$301$	1.19731e20			1.77694
$302$		−	1.47480e20i		−	2.13146i
$303$	3.80683e19	+	5.42212e19i	0.535824	+	0.763182i
$304$	−2.52503e19			−0.346161
$305$		−	3.06209e19i		−	0.408902i
$306$	−3.08448e18	+	8.54163e18i	−0.0401246	+	0.111114i
$307$	−8.00171e19			−1.01409			−0.507044	−	0.861920i	$-0.669262\pi$
$307$	−8.00171e19			−1.01409			−0.507044	+	0.861920i	$0.669262\pi$
$308$			7.87582e19i			0.972501i
$309$	1.29906e19	−	9.12058e18i	0.156301	−	0.109737i
$310$	5.70284e19			0.668649
$311$		−	1.25107e20i		−	1.42955i	−0.699355	−	0.714775i	$-0.746529\pi$
$311$		−	1.25107e20i		−	1.42955i	0.699355	−	0.714775i	$-0.253471\pi$
$312$	2.80496e19	+	3.99515e19i	0.312385	+	0.444935i
$313$	4.69482e19			0.509641			0.254820	−	0.966988i	$-0.417984\pi$
$313$	4.69482e19			0.509641			0.254820	+	0.966988i	$0.417984\pi$
$314$			1.74820e20i			1.84992i
$315$	7.96565e19	+	2.87649e19i	0.821744	+	0.296742i
$316$	−7.58478e19			−0.762863
$317$			5.48514e19i			0.537915i	0.963152	+	0.268957i	$0.0866791\pi$
$317$			5.48514e19i			0.537915i	−0.963152	+	0.268957i	$0.913321\pi$
$318$	7.26760e19	−	5.10252e19i	0.694983	−	0.487941i
$319$	−1.28848e20			−1.20158
$320$			1.11040e19i			0.100990i
$321$	−4.36498e19	−	6.21710e19i	−0.387206	−	0.551503i
$322$	9.94541e19			0.860549
$323$			3.17309e18i			0.0267832i
$324$	4.59811e19	+	3.81885e19i	0.378633	+	0.314465i
$325$	−5.43278e19			−0.436471
$326$			7.32482e19i			0.574191i
$327$	6.77547e19	−	4.75700e19i	0.518271	−	0.363874i
$328$	4.30886e19			0.321641
$329$		−	6.45733e19i		−	0.470420i
$330$	−1.12068e20	−	1.59620e20i	−0.796840	−	1.13495i
$331$	−1.44398e20			−1.00216			−0.501081	−	0.865401i	$-0.667064\pi$
$331$	−1.44398e20			−1.00216			−0.501081	+	0.865401i	$0.667064\pi$
$332$		−	1.26876e20i		−	0.859560i
$333$	5.68782e18	−	1.57509e19i	0.0376177	−	0.104172i
$334$	1.27858e20			0.825576
$335$		−	4.48295e19i		−	0.282622i
$336$	−2.04925e20	+	1.43876e20i	−1.26148	+	0.885676i
$337$	−1.23577e20			−0.742846			−0.371423	−	0.928464i	$-0.621130\pi$
$337$	−1.23577e20			−0.742846			−0.371423	+	0.928464i	$0.621130\pi$
$338$		−	4.82592e19i		−	0.283300i
$339$	7.65768e19	+	1.09070e20i	0.439035	+	0.625325i
$340$	−6.02253e18			−0.0337246
$341$			2.26321e20i			1.23791i
$342$	5.95516e19	+	2.15048e19i	0.318189	+	0.114902i
$343$	1.13248e20			0.591125
$344$		−	1.75283e20i		−	0.893868i
$345$	−6.64851e19	+	4.66787e19i	−0.331262	+	0.232576i
$346$	6.35106e18			0.0309198
$347$			2.90213e20i			1.38064i	0.723504	+	0.690320i	$0.242530\pi$
$347$			2.90213e20i			1.38064i	−0.723504	+	0.690320i	$0.757470\pi$
$348$	4.56192e19	+	6.49761e19i	0.212087	+	0.302078i
$349$	4.26107e20			1.93604			0.968021	−	0.250869i	$-0.0807164\pi$
$349$	4.26107e20			1.93604			0.968021	+	0.250869i	$0.0807164\pi$
$350$		−	1.68935e20i		−	0.750199i
$351$	−5.29972e19	−	1.94832e20i	−0.230036	−	0.845675i
$352$	3.42356e20			1.45257
$353$		−	3.04382e20i		−	1.26247i	−0.775591	−	0.631236i	$-0.782548\pi$
$353$		−	3.04382e20i		−	1.26247i	0.775591	−	0.631236i	$-0.217452\pi$
$354$	−3.47737e20	+	2.44143e20i	−1.41002	+	0.989962i
$355$	2.23207e19			0.0884874
$356$		−	1.15047e20i		−	0.445938i
$357$	1.80803e19	+	2.57520e19i	0.0685267	+	0.0976036i
$358$	−4.33976e20			−1.60843
$359$			6.70999e19i			0.243202i	0.992579	+	0.121601i	$0.0388028\pi$
$359$			6.70999e19i			0.243202i	−0.992579	+	0.121601i	$0.961197\pi$
$360$	4.21114e19	−	1.16616e20i	0.149272	−	0.413368i
$361$	−2.66319e20			−0.923303
$362$			6.27762e20i			2.12876i
$363$	3.86727e20	−	2.71518e20i	1.28278	−	0.900629i
$364$	−1.63931e20			−0.531924
$365$			2.45046e20i			0.777866i
$366$	−1.30441e20	−	1.85789e20i	−0.405102	−	0.576993i
$367$	−1.14079e20			−0.346639			−0.173320	−	0.984866i	$-0.555449\pi$
$367$	−1.14079e20			−0.346639			−0.173320	+	0.984866i	$0.555449\pi$
$368$		−	2.40172e20i		−	0.714069i
$369$	−1.67630e20	−	6.05333e19i	−0.487688	−	0.176110i
$370$	3.36692e19			0.0958561
$371$		−	3.07670e20i		−	0.857224i
$372$	1.14130e20	−	8.01301e19i	0.311213	−	0.218500i
$373$	−8.72192e19			−0.232778			−0.116389	−	0.993204i	$-0.537132\pi$
$373$	−8.72192e19			−0.232778			−0.116389	+	0.993204i	$0.537132\pi$
$374$		−	7.24608e19i		−	0.189291i
$375$	2.38497e20	+	3.39696e20i	0.609865	+	0.868640i
$376$	−9.45342e19			−0.236639
$377$		−	2.68189e20i		−	0.657220i
$378$	6.05841e20	−	1.64798e20i	1.45353	−	0.395382i
$379$	4.07877e20			0.958111			0.479056	−	0.877785i	$-0.340979\pi$
$379$	4.07877e20			0.958111			0.479056	+	0.877785i	$0.340979\pi$
$380$			4.19886e19i			0.0965746i
$381$	−3.05970e20	+	2.14819e20i	−0.689094	+	0.483807i
$382$	2.47798e20			0.546501
$383$			9.15624e20i			1.97755i	0.149422	+	0.988774i	$0.452259\pi$
$383$			9.15624e20i			1.97755i	−0.149422	+	0.988774i	$0.547741\pi$
$384$	2.93574e20	+	4.18141e20i	0.620965	+	0.884450i
$385$	−6.75746e20			−1.39990
$386$		−	8.94033e19i		−	0.181407i
$387$	−2.46249e20	+	6.81917e20i	−0.489425	+	1.35533i
$388$	4.88169e19			0.0950422
$389$		−	9.02288e20i		−	1.72087i	−0.509559	−	0.860436i	$-0.670191\pi$
$389$		−	9.02288e20i		−	1.72087i	0.509559	−	0.860436i	$-0.329809\pi$
$390$	3.32241e20	−	2.33264e20i	0.620778	−	0.435843i
$391$	−3.01814e19			−0.0552490
$392$			1.80067e20i			0.322958i
$393$	−4.89761e20	−	6.97574e20i	−0.860684	−	1.22589i
$394$	−3.38169e20			−0.582322
$395$		−	6.50775e20i		−	1.09813i
$396$	−4.48562e20	−	1.61981e20i	−0.741756	−	0.267857i
$397$	1.05321e21			1.70684			0.853419	−	0.521226i	$-0.174525\pi$
$397$	1.05321e21			1.70684			0.853419	+	0.521226i	$0.174525\pi$
$398$			6.14973e20i			0.976769i
$399$	1.79541e20	−	1.26055e20i	0.279500	−	0.196234i
$400$	−4.07963e20			−0.622502
$401$		−	2.31809e20i		−	0.346717i	−0.984859	−	0.173358i	$-0.944538\pi$
$401$		−	2.31809e20i		−	0.346717i	0.984859	−	0.173358i	$-0.0554619\pi$
$402$	−1.90967e20	−	2.71998e20i	−0.279995	−	0.398802i
$403$	−4.71074e20			−0.677094
$404$			3.25711e20i			0.458967i
$405$	−3.27657e20	+	3.94518e20i	−0.452668	+	0.545038i
$406$	8.33949e20			1.12962
$407$			1.33618e20i			0.177464i
$408$	3.77005e19	−	2.64692e19i	0.0490983	−	0.0344715i
$409$	−2.32833e19			−0.0297343			−0.0148671	−	0.999889i	$-0.504733\pi$
$409$	−2.32833e19			−0.0297343			−0.0148671	+	0.999889i	$0.504733\pi$
$410$		−	3.58329e20i		−	0.448757i
$411$	−5.33900e20	−	7.60442e20i	−0.655730	−	0.933966i
$412$	7.80354e19			0.0939970
$413$			1.47213e21i			1.73918i
$414$	−2.04546e20	+	5.66434e20i	−0.237022	+	0.656367i
$415$	1.08860e21			1.23732
$416$			7.12594e20i			0.794503i
$417$	1.97937e20	−	1.38970e20i	0.216490	−	0.151996i
$418$	−5.05191e20			−0.542058
$419$		−	3.12205e20i		−	0.328645i	−0.986407	−	0.164323i	$-0.947456\pi$
$419$		−	3.12205e20i		−	0.328645i	0.986407	−	0.164323i	$-0.0525438\pi$
$420$	2.39251e20	+	3.40769e20i	0.247093	+	0.351938i
$421$	1.66124e21			1.68336			0.841679	−	0.539978i	$-0.181567\pi$
$421$	1.66124e21			1.68336			0.841679	+	0.539978i	$0.181567\pi$
$422$		−	1.73916e21i		−	1.72918i
$423$	3.67773e20	+	1.32807e20i	0.358803	+	0.129568i
$424$	−4.50424e20			−0.431216
$425$			5.12669e19i			0.0481643i
$426$	1.35428e20	−	9.50831e19i	0.124863	−	0.0876651i
$427$	−7.86528e20			−0.711690
$428$		−	3.73466e20i		−	0.331666i
$429$	9.25721e20	+	1.31852e21i	0.806904	+	1.14929i
$430$	−1.45768e21			−1.24713
$431$			1.02197e20i			0.0858259i	0.999079	+	0.0429129i	$0.0136638\pi$
$431$			1.02197e20i			0.0858259i	−0.999079	+	0.0429129i	$0.986336\pi$
$432$	−3.97970e20	−	1.46305e21i	−0.328081	−	1.20611i
$433$	−2.16790e21			−1.75443			−0.877216	−	0.480096i	$-0.840602\pi$
$433$	−2.16790e21			−1.75443			−0.877216	+	0.480096i	$0.840602\pi$
$434$		−	1.46483e21i		−	1.16378i
$435$	−5.57495e20	+	3.91413e20i	−0.434838	+	0.305296i
$436$	4.07007e20			0.311681
$437$			2.10422e20i			0.158212i
$438$	1.04386e21	+	1.48679e21i	0.770638	+	1.09763i
$439$	−7.18216e20			−0.520641			−0.260321	−	0.965522i	$-0.583828\pi$
$439$	−7.18216e20			−0.520641			−0.260321	+	0.965522i	$0.583828\pi$
$440$			9.89281e20i			0.704203i
$441$	2.52969e20	−	7.00528e20i	0.176831	−	0.489685i
$442$	1.50823e20			0.103536
$443$		−	2.80285e20i		−	0.188960i	−0.995527	−	0.0944802i	$-0.969881\pi$
$443$		−	2.80285e20i		−	0.188960i	0.995527	−	0.0944802i	$-0.0301189\pi$
$444$	6.73819e19	−	4.73083e19i	0.0446149	−	0.0313237i
$445$	9.87103e20			0.641922
$446$			2.69684e20i			0.172257i
$447$	−1.15444e21	−	1.64429e21i	−0.724289	−	1.03162i
$448$	2.85217e20			0.175772
$449$			1.90690e21i			1.15440i	0.816603	+	0.577200i	$0.195855\pi$
$449$			1.90690e21i			1.15440i	−0.816603	+	0.577200i	$0.804145\pi$
$450$	9.62161e20	+	3.47448e20i	0.572200	+	0.206628i
$451$	1.42205e21			0.830812
$452$			6.55189e20i			0.376062i
$453$	2.53239e21	−	1.77797e21i	1.42806	−	1.00263i
$454$	8.17602e20			0.452997
$455$		−	1.40653e21i		−	0.765697i
$456$	−1.84542e20	−	2.62846e20i	−0.0987133	−	0.140599i
$457$	−1.24426e21			−0.654005			−0.327002	−	0.945024i	$-0.606038\pi$
$457$	−1.24426e21			−0.654005			−0.327002	+	0.945024i	$0.606038\pi$
$458$			1.74581e21i			0.901721i
$459$	−1.83855e20	+	5.00112e19i	−0.0933196	+	0.0253843i
$460$	−3.99381e20			−0.199216
$461$			1.67655e21i			0.821879i	0.911663	+	0.410940i	$0.134799\pi$
$461$			1.67655e21i			0.821879i	−0.911663	+	0.410940i	$0.865201\pi$
$462$	−4.10001e21	+	2.87858e21i	−1.97537	+	1.38689i
$463$	−2.07466e21			−0.982422			−0.491211	−	0.871041i	$-0.663446\pi$
$463$	−2.07466e21			−0.982422			−0.491211	+	0.871041i	$0.663446\pi$
$464$		−	2.01391e21i		−	0.937336i
$465$	6.87517e20	+	9.79240e20i	0.314528	+	0.447987i
$466$	4.24559e21			1.90920
$467$		−	1.45238e21i		−	0.642016i	−0.947076	−	0.321008i	$-0.895978\pi$
$467$		−	1.45238e21i		−	0.642016i	0.947076	−	0.321008i	$-0.104022\pi$
$468$	3.37155e20	−	9.33657e20i	0.146508	−	0.405715i
$469$	−1.15149e21			−0.491901
$470$			7.86156e20i			0.330161i
$471$	−3.00185e21	+	2.10757e21i	−1.23943	+	0.870193i
$472$	2.15517e21			0.874875
$473$		−	5.78487e21i		−	2.30890i
$474$	−2.77221e21	−	3.94850e21i	−1.08793	−	1.54955i
$475$	3.57429e20			0.137924
$476$			1.54694e20i			0.0586974i
$477$	1.75232e21	+	6.32782e20i	0.653831	+	0.236106i
$478$	−2.60238e21			−0.954878
$479$			5.43994e20i			0.196295i	0.995172	+	0.0981477i	$0.0312918\pi$
$479$			5.43994e20i			0.196295i	−0.995172	+	0.0981477i	$0.968708\pi$
$480$	1.48130e21	−	1.04001e21i	0.525669	−	0.369068i
$481$	−2.78119e20			−0.0970668
$482$			1.05756e21i			0.363019i
$483$	1.19899e21	+	1.70774e21i	0.404797	+	0.576559i
$484$	2.32310e21			0.771446
$485$			4.18849e20i			0.136812i
$486$	−3.07432e20	+	3.78946e21i	−0.0987778	+	1.21755i
$487$	8.43207e20			0.266503			0.133252	−	0.991082i	$-0.457458\pi$
$487$	8.43207e20			0.266503			0.133252	+	0.991082i	$0.457458\pi$
$488$			1.15146e21i			0.358007i
$489$	−1.25775e21	+	8.83057e20i	−0.384702	+	0.270096i
$490$	1.49746e21			0.450595
$491$			6.07036e21i			1.79706i	0.438911	+	0.898530i	$0.355364\pi$
$491$			6.07036e21i			1.79706i	−0.438911	+	0.898530i	$0.644636\pi$
$492$	−5.03484e20	−	7.17120e20i	−0.146644	−	0.208868i
$493$	−2.53079e20			−0.0725237
$494$		−	1.05153e21i		−	0.296487i
$495$	1.38980e21	−	3.84867e21i	0.385577	−	1.06775i
$496$	−3.53743e21			−0.965682
$497$		−	5.73330e20i		−	0.154012i
$498$	6.60495e21	−	4.63728e21i	1.74596	−	1.22583i
$499$	1.14493e21			0.297834			0.148917	−	0.988850i	$-0.452421\pi$
$499$	1.14493e21			0.297834			0.148917	+	0.988850i	$0.452421\pi$
$500$			2.04058e21i			0.522388i
$501$	1.54142e21	+	2.19547e21i	0.388346	+	0.553127i
$502$	−4.31461e21			−1.06982
$503$		−	4.27994e21i		−	1.04446i	−0.852803	−	0.522232i	$-0.825099\pi$
$503$		−	4.27994e21i		−	1.04446i	0.852803	−	0.522232i	$-0.174901\pi$
$504$	−2.99539e21	−	1.08167e21i	−0.719464	−	0.259807i
$505$	−2.79460e21			−0.660677
$506$		−	4.80520e21i		−	1.11817i
$507$	8.28663e20	−	5.81797e20i	0.189808	−	0.133262i
$508$	−1.83798e21			−0.414412
$509$			4.76935e21i			1.05856i	0.848446	+	0.529282i	$0.177539\pi$
$509$			4.76935e21i			1.05856i	−0.848446	+	0.529282i	$0.822461\pi$
$510$	−2.20121e20	−	3.13522e20i	−0.0480950	−	0.0685025i
$511$	6.29425e21			1.35387
$512$			1.68955e21i			0.357775i
$513$	3.48674e20	+	1.28182e21i	0.0726911	+	0.267232i
$514$	−6.04727e21			−1.24124
$515$			6.69544e20i			0.135307i
$516$	−2.91723e21	+	2.04816e21i	−0.580462	+	0.407537i
$517$	−3.11991e21			−0.611248
$518$		−	8.64827e20i		−	0.166837i
$519$	7.65663e19	+	1.09055e20i	0.0145445	+	0.0207160i
$520$	−2.05913e21			−0.385175
$521$		−	6.64803e21i		−	1.22459i	−0.790629	−	0.612295i	$-0.790246\pi$
$521$		−	6.64803e21i		−	1.22459i	0.790629	−	0.612295i	$-0.209754\pi$
$522$	−1.71517e21	+	4.74970e21i	−0.311132	+	0.861593i
$523$	−5.95294e20			−0.106345			−0.0531727	−	0.998585i	$-0.516933\pi$
$523$	−5.95294e20			−0.106345			−0.0531727	+	0.998585i	$0.516933\pi$
$524$		−	4.19038e21i		−	0.737231i
$525$	2.90081e21	−	2.03663e21i	0.502625	−	0.352889i
$526$	1.29874e22			2.21634
$527$			4.44533e20i			0.0747169i
$528$	6.95150e21	+	9.90112e21i	1.15082	+	1.63913i
$529$	4.13115e21			0.673636
$530$			3.74578e21i			0.601637i
$531$	−8.38441e21	−	3.02771e21i	−1.32653	−	0.479025i
$532$	1.07852e21			0.168087
$533$			2.95992e21i			0.454425i
$534$	5.98913e21	−	4.20492e21i	0.905803	−	0.635957i
$535$	3.20434e21			0.477429
$536$			1.68576e21i			0.247445i
$537$	−5.23187e21	−	7.45184e21i	−0.756594	−	1.07763i
$538$	1.39316e21			0.198492
$539$			5.94275e21i			0.834214i
$540$	−2.43290e21	+	6.61783e20i	−0.336491	+	0.0915305i
$541$	−6.55475e21			−0.893260			−0.446630	−	0.894719i	$-0.647376\pi$
$541$	−6.55475e21			−0.893260			−0.446630	+	0.894719i	$0.647376\pi$
$542$		−	5.40214e21i		−	0.725390i
$543$	−1.07794e22	+	7.56810e21i	−1.42625	+	1.00136i
$544$	6.72445e20			0.0876729
$545$			3.49213e21i			0.448661i
$546$	−5.99161e21	−	8.53394e21i	−0.758581	−	1.08046i
$547$	1.34210e22			1.67451			0.837253	−	0.546816i	$-0.184160\pi$
$547$	1.34210e22			1.67451			0.837253	+	0.546816i	$0.184160\pi$
$548$		−	4.56803e21i		−	0.561674i
$549$	1.61764e21	−	4.47962e21i	0.196022	−	0.542828i
$550$	−8.16225e21			−0.974784
$551$			1.76445e21i			0.207681i
$552$	2.50010e21	−	1.75530e21i	0.290031	−	0.203628i
$553$	−1.67158e22			−1.91129
$554$			1.57986e22i			1.78050i
$555$	4.05906e20	+	5.78138e20i	0.0450901	+	0.0642225i
$556$	1.18902e21			0.130194
$557$		−	1.06083e22i		−	1.14500i	−0.819905	−	0.572500i	$-0.805974\pi$
$557$		−	1.06083e22i		−	1.14500i	0.819905	−	0.572500i	$-0.194026\pi$
$558$	8.34285e21	+	3.01270e21i	0.887648	+	0.320540i
$559$	1.20409e22			1.26289
$560$		−	1.05620e22i		−	1.09205i
$561$	1.24423e21	−	8.73563e20i	0.126823	−	0.0890413i
$562$	8.51259e20			0.0855404
$563$		−	1.02060e22i		−	1.01109i	−0.862801	−	0.505544i	$-0.831292\pi$
$563$		−	1.02060e22i		−	1.01109i	0.862801	−	0.505544i	$-0.168708\pi$
$564$	1.10462e21	+	1.57333e21i	0.107890	+	0.153669i
$565$	−5.62153e21			−0.541336
$566$		−	1.20175e21i		−	0.114100i
$567$	1.01336e22	+	8.41620e21i	0.948633	+	0.787864i
$568$	−8.39345e20			−0.0774736
$569$			1.29597e22i			1.17950i	0.807587	+	0.589749i	$0.200773\pi$
$569$			1.29597e22i			1.17950i	−0.807587	+	0.589749i	$0.799227\pi$
$570$	−2.18585e21	+	1.53467e21i	−0.196165	+	0.137726i
$571$	−2.34308e21			−0.207347			−0.103673	−	0.994611i	$-0.533060\pi$
$571$	−2.34308e21			−0.207347			−0.103673	+	0.994611i	$0.533060\pi$
$572$			7.92045e21i			0.691164i
$573$	2.98737e21	+	4.25496e21i	0.257071	+	0.366150i
$574$	−9.20403e21			−0.781057
$575$			3.39974e21i			0.284514i
$576$	−5.86602e20	+	1.62443e21i	−0.0484132	+	0.134067i
$577$	1.87414e22			1.52544			0.762720	−	0.646729i	$-0.223864\pi$
$577$	1.87414e22			1.52544			0.762720	+	0.646729i	$0.223864\pi$
$578$			1.50749e22i			1.21013i
$579$	1.53515e21	−	1.07782e21i	0.121541	−	0.0853329i
$580$	−3.34892e21			−0.261505
$581$		−	2.79617e22i		−	2.15355i
$582$	1.78424e21	+	2.54132e21i	0.135541	+	0.193052i
$583$	−1.48653e22			−1.11385
$584$		−	9.21468e21i		−	0.681047i
$585$	8.01078e21	+	2.89279e21i	0.584021	+	0.210897i
$586$	−1.25242e22			−0.900677
$587$			3.32847e21i			0.236124i	0.993006	+	0.118062i	$0.0376681\pi$
$587$			3.32847e21i			0.236124i	−0.993006	+	0.118062i	$0.962332\pi$
$588$	2.99685e21	−	2.10406e21i	0.209723	−	0.147245i
$589$	3.09925e21			0.213961
$590$		−	1.79226e22i		−	1.22063i
$591$	−4.07685e21	−	5.80672e21i	−0.273921	−	0.390150i
$592$	−2.08847e21			−0.138438
$593$			1.79460e22i			1.17363i	0.809722	+	0.586814i	$0.199618\pi$
$593$			1.79460e22i			1.17363i	−0.809722	+	0.586814i	$0.800382\pi$
$594$	−7.96233e21	−	2.92717e22i	−0.513746	−	1.88867i
$595$	−1.32728e21			−0.0844942
$596$		−	9.87737e21i		−	0.620399i
$597$	−1.05598e22	+	7.41392e21i	−0.654424	+	0.459466i
$598$	1.00018e22			0.611600
$599$			5.13326e21i			0.309727i	0.987936	+	0.154863i	$0.0494938\pi$
$599$			5.13326e21i			0.309727i	−0.987936	+	0.154863i	$0.950506\pi$
$600$	−2.98159e21	−	4.24673e21i	−0.177516	−	0.252839i
$601$	−2.68398e21			−0.157682			−0.0788411	−	0.996887i	$-0.525122\pi$
$601$	−2.68398e21			−0.157682			−0.0788411	+	0.996887i	$0.525122\pi$
$602$			3.74418e22i			2.17063i
$603$	2.36826e21	−	6.55824e21i	0.135485	−	0.375188i
$604$	1.52123e22			0.858813
$605$			1.99322e22i			1.11049i
$606$	−1.69559e22	+	1.19046e22i	−0.932267	+	0.654537i
$607$	−9.52751e21			−0.516975			−0.258488	−	0.966015i	$-0.583224\pi$
$607$	−9.52751e21			−0.516975			−0.258488	+	0.966015i	$0.583224\pi$
$608$		−	4.68824e21i		−	0.251062i
$609$	1.00538e22	+	1.43198e22i	0.531365	+	0.756831i
$610$	9.57569e21			0.499495
$611$		−	6.49391e21i		−	0.334331i
$612$	−8.81052e20	−	3.18158e20i	−0.0447703	−	0.0161671i
$613$	2.23921e22			1.12308			0.561541	−	0.827449i	$-0.310209\pi$
$613$	2.23921e22			1.12308			0.561541	+	0.827449i	$0.310209\pi$
$614$		−	2.50227e22i		−	1.23876i
$615$	6.15290e21	−	4.31990e21i	0.300662	−	0.211092i
$616$	2.54106e22			1.22566
$617$		−	1.75829e22i		−	0.837162i	−0.908179	−	0.418581i	$-0.862528\pi$
$617$		−	1.75829e22i		−	0.837162i	0.908179	−	0.418581i	$-0.137472\pi$
$618$	2.85216e21	+	4.06238e21i	0.134050	+	0.190929i
$619$	−2.16013e22			−1.00220			−0.501101	−	0.865389i	$-0.667071\pi$
$619$	−2.16013e22			−1.00220			−0.501101	+	0.865389i	$0.667071\pi$
$620$			5.88237e21i			0.269413i
$621$	−1.21922e22	+	3.31647e21i	−0.551253	+	0.149949i
$622$	3.91232e22			1.74627
$623$		−	2.53547e22i		−	1.11726i
$624$	−2.06086e22	+	1.44692e22i	−0.896546	+	0.629457i
$625$	−5.91261e21			−0.253945
$626$			1.46815e22i			0.622553i
$627$	−6.09042e21	−	8.67469e21i	−0.254981	−	0.363173i
$628$	−1.80323e22			−0.745375
$629$			2.62449e20i			0.0107113i
$630$	−8.99529e21	+	2.49100e22i	−0.362486	+	1.00380i
$631$	−2.28393e22			−0.908757			−0.454379	−	0.890809i	$-0.650139\pi$
$631$	−2.28393e22			−0.908757			−0.454379	+	0.890809i	$0.650139\pi$
$632$			2.44716e22i			0.961449i
$633$	2.98632e22	−	2.09667e22i	1.15853	−	0.813393i
$634$	−1.71530e22			−0.657091
$635$		−	1.57699e22i		−	0.596540i
$636$	5.26315e21	+	7.49639e21i	0.196602	+	0.280024i
$637$	−1.23695e22			−0.456286
$638$		−	4.02929e22i		−	1.46779i
$639$	3.26536e21	+	1.17916e21i	0.117469	+	0.0424196i
$640$	−2.15513e22			−0.765657
$641$			2.43535e22i			0.854470i	0.904141	+	0.427235i	$0.140512\pi$
$641$			2.43535e22i			0.854470i	−0.904141	+	0.427235i	$0.859488\pi$
$642$	1.94420e22	−	1.36500e22i	0.673690	−	0.472992i
$643$	−3.79348e22			−1.29822			−0.649112	−	0.760693i	$-0.724859\pi$
$643$	−3.79348e22			−1.29822			−0.649112	+	0.760693i	$0.724859\pi$
$644$			1.02585e22i			0.346734i
$645$	−1.75733e22	−	2.50299e22i	−0.586644	−	0.835567i
$646$	−9.92281e20			−0.0327171
$647$			1.51186e22i			0.492354i	0.969225	+	0.246177i	$0.0791744\pi$
$647$			1.51186e22i			0.492354i	−0.969225	+	0.246177i	$0.920826\pi$
$648$	1.23212e22	−	1.48354e22i	0.396325	−	0.477198i
$649$	7.11271e22			2.25984
$650$		−	1.69893e22i		−	0.533173i
$651$	2.51527e22	−	1.76595e22i	0.779718	−	0.547433i
$652$	−7.55541e21			−0.231354
$653$			3.13376e22i			0.947896i	0.880553	+	0.473948i	$0.157172\pi$
$653$			3.13376e22i			0.947896i	−0.880553	+	0.473948i	$0.842828\pi$
$654$	1.48760e22	+	2.11881e22i	0.444491	+	0.633096i
$655$	3.59535e22			1.06123
$656$			2.22268e22i			0.648107i
$657$	−1.29453e22	+	3.58485e22i	−0.372898	+	1.03264i
$658$	2.01932e22			0.574642
$659$			2.15993e22i			0.607235i	0.952794	+	0.303617i	$0.0981945\pi$
$659$			2.15993e22i			0.607235i	−0.952794	+	0.303617i	$0.901806\pi$
$660$	1.64645e22	−	1.15596e22i	0.457297	−	0.321064i
$661$	−5.48959e22			−1.50636			−0.753179	−	0.657815i	$-0.771481\pi$
$661$	−5.48959e22			−1.50636			−0.753179	+	0.657815i	$0.771481\pi$
$662$		−	4.51558e22i		−	1.22419i
$663$	1.81827e21	+	2.58980e21i	0.0487025	+	0.0693677i
$664$	−4.09355e22			−1.08332
$665$			9.25370e21i			0.241959i
$666$	4.92557e21	+	1.77868e21i	0.127251	+	0.0459520i
$667$	−1.67828e22			−0.428408
$668$			1.31883e22i			0.332643i
$669$	−4.63077e21	+	3.25123e21i	−0.115410	+	0.0810286i
$670$	1.40190e22			0.345238
$671$			3.80017e22i			0.924747i
$672$	−2.67136e22	−	3.80486e22i	−0.642359	−	0.914922i
$673$	2.63360e22			0.625791			0.312896	−	0.949787i	$-0.398701\pi$
$673$	2.63360e22			0.625791			0.312896	+	0.949787i	$0.398701\pi$
$674$		−	3.86447e22i		−	0.907426i
$675$	5.63344e21	+	2.07101e22i	0.130721	+	0.480564i
$676$	4.97784e21			0.114148
$677$		−	8.67255e22i		−	1.96534i	−0.185365	−	0.982670i	$-0.559347\pi$
$677$		−	8.67255e22i		−	1.96534i	0.185365	−	0.982670i	$-0.440653\pi$
$678$	−3.41079e22	+	2.39469e22i	−0.763867	+	0.536305i
$679$	1.07586e22			0.238120
$680$			1.94312e21i			0.0425037i
$681$	9.85675e21	+	1.40391e22i	0.213087	+	0.303503i
$682$	−7.07745e22			−1.51217
$683$		−	5.07014e22i		−	1.07067i	−0.844641	−	0.535333i	$-0.820186\pi$
$683$		−	5.07014e22i		−	1.07067i	0.844641	−	0.535333i	$-0.179814\pi$
$684$	−2.21818e21	+	6.14263e21i	−0.0462965	+	0.128205i
$685$	3.91937e22			0.808522
$686$			3.54147e22i			0.722090i
$687$	−2.99774e22	+	2.10469e22i	−0.604143	+	0.424164i
$688$	9.04184e22			1.80115
$689$		−	3.09414e22i		−	0.609236i
$690$	−1.45972e22	−	2.07911e22i	−0.284104	−	0.404654i
$691$	6.54722e22			1.25960			0.629800	−	0.776758i	$-0.283137\pi$
$691$	6.54722e22			1.25960			0.629800	+	0.776758i	$0.283137\pi$
$692$			6.55099e20i			0.0124583i
$693$	−9.88567e22	−	3.56984e22i	−1.85841	−	0.671092i
$694$	−9.07546e22			−1.68653
$695$			1.02018e22i			0.187413i
$696$	2.09640e22	−	1.47186e22i	0.380715	−	0.267297i
$697$	2.79315e21			0.0501455
$698$			1.33251e23i			2.36498i
$699$	5.11834e22	+	7.29014e22i	0.898074	+	1.27914i
$700$	1.74254e22			0.302272
$701$			1.53086e21i			0.0262537i	0.999914	+	0.0131269i	$0.00417853\pi$
$701$			1.53086e21i			0.0262537i	−0.999914	+	0.0131269i	$0.995821\pi$
$702$	6.09274e22	−	1.65731e22i	1.03304	−	0.281001i
$703$	1.82978e21			0.0306730
$704$		−	1.37805e22i		−	0.228393i
$705$	−1.34992e22	+	9.47764e21i	−0.221204	+	0.155306i
$706$	9.51857e22			1.54218
$707$			7.17821e22i			1.14990i
$708$	−2.51829e22	−	3.58684e22i	−0.398878	−	0.568128i
$709$	1.08542e22			0.169991			0.0849956	−	0.996381i	$-0.472912\pi$
$709$	1.08542e22			0.169991			0.0849956	+	0.996381i	$0.472912\pi$
$710$			6.98008e21i			0.108092i
$711$	3.43792e22	−	9.52037e22i	0.526428	−	1.45780i
$712$	−3.71189e22			−0.562024
$713$			2.94790e22i			0.441363i
$714$	−8.05311e21	+	5.65402e21i	−0.119228	+	0.0837089i
$715$	−6.79575e22			−0.994922
$716$		−	4.47638e22i		−	0.648071i
$717$	−3.13735e22	−	4.46857e22i	−0.449169	−	0.639758i
$718$	−2.09833e22			−0.297083
$719$		−	1.17168e23i		−	1.64051i	−0.571997	−	0.820256i	$-0.693831\pi$
$719$		−	1.17168e23i		−	1.64051i	0.571997	−	0.820256i	$-0.306169\pi$
$720$	6.01552e22	+	2.17228e22i	0.832939	+	0.300784i
$721$	1.71979e22			0.235501
$722$		−	8.32825e22i		−	1.12786i
$723$	−1.81595e22	+	1.27496e22i	−0.243219	+	0.170762i
$724$	−6.47524e22			−0.857724
$725$			2.85077e22i			0.373472i
$726$	8.49084e22	+	1.20936e23i	1.10017	+	1.56698i
$727$	−6.75278e22			−0.865381			−0.432691	−	0.901542i	$-0.642436\pi$
$727$	−6.75278e22			−0.865381			−0.432691	+	0.901542i	$0.642436\pi$
$728$			5.28908e22i			0.670393i
$729$	−6.87755e22	+	4.04056e22i	−0.862211	+	0.506549i
$730$	−7.66302e22			−0.950205
$731$		−	1.13625e22i		−	0.139359i
$732$	1.91637e22	−	1.34547e22i	0.232483	−	0.163225i
$733$	−8.14391e22			−0.977240			−0.488620	−	0.872497i	$-0.662500\pi$
$733$	−8.14391e22			−0.977240			−0.488620	+	0.872497i	$0.662500\pi$
$734$		−	3.56745e22i		−	0.423438i
$735$	1.80529e22	+	2.57130e22i	0.211957	+	0.301894i
$736$	4.45929e22			0.517897
$737$			5.56352e22i			0.639160i
$738$	1.89298e22	−	5.24209e22i	0.215127	−	0.595736i
$739$	2.72207e22			0.306016			0.153008	−	0.988225i	$-0.451104\pi$
$739$	2.72207e22			0.306016			0.153008	+	0.988225i	$0.451104\pi$
$740$			3.47292e21i			0.0386225i
$741$	1.80559e22	−	1.26769e22i	0.198643	−	0.139465i
$742$	9.62139e22			1.04714
$743$		−	1.77551e22i		−	0.191167i	−0.995421	−	0.0955833i	$-0.969528\pi$
$743$		−	1.77551e22i		−	0.191167i	0.995421	−	0.0955833i	$-0.0304716\pi$
$744$	−2.58533e22	−	3.68232e22i	−0.275380	−	0.392227i
$745$	8.47479e22			0.893056
$746$		−	2.72750e22i		−	0.284350i
$747$	1.59254e23	+	5.75086e22i	1.64258	+	0.593155i
$748$	7.47419e21			0.0762695
$749$		−	8.23067e22i		−	0.830961i
$750$	−1.06229e23	+	7.45823e22i	−1.06109	+	0.744982i
$751$	−2.88558e22			−0.285177			−0.142588	−	0.989782i	$-0.545543\pi$
$751$	−2.88558e22			−0.285177			−0.142588	+	0.989782i	$0.545543\pi$
$752$		−	4.87646e22i		−	0.476828i
$753$	−5.20155e22	−	7.40865e22i	−0.503238	−	0.716770i
$754$	8.38674e22			0.802828
$755$			1.30521e23i			1.23625i
$756$	1.69986e22	+	6.24913e22i	0.159308	+	0.585659i
$757$	−5.88768e22			−0.545981			−0.272990	−	0.962017i	$-0.588013\pi$
$757$	−5.88768e22			−0.545981			−0.272990	+	0.962017i	$0.588013\pi$
$758$			1.27550e23i			1.17038i
$759$	8.25106e22	−	5.79300e22i	0.749162	−	0.525980i
$760$	1.35473e22			0.121715
$761$			4.74458e22i			0.421814i	0.977506	+	0.210907i	$0.0676417\pi$
$761$			4.74458e22i			0.421814i	−0.977506	+	0.210907i	$0.932358\pi$
$762$	−6.71776e22	−	9.56821e22i	−0.590996	−	0.841765i
$763$	8.96987e22			0.780890
$764$			2.55599e22i			0.220197i
$765$	2.72980e21	−	7.55943e21i	0.0232723	−	0.0644463i
$766$	−2.86331e23			−2.41568
$767$			1.48047e23i			1.23605i
$768$	−1.16641e23	+	8.18926e22i	−0.963743	+	0.676636i
$769$	1.15591e23			0.945176			0.472588	−	0.881283i	$-0.343320\pi$
$769$	1.15591e23			0.945176			0.472588	+	0.881283i	$0.343320\pi$
$770$		−	2.11318e23i		−	1.71005i
$771$	−7.29039e22	−	1.03838e23i	−0.583870	−	0.831615i
$772$	9.22178e21			0.0730931
$773$		−	6.88499e22i		−	0.540091i	−0.962848	−	0.270046i	$-0.912961\pi$
$773$		−	6.88499e22i		−	0.540091i	0.962848	−	0.270046i	$-0.0870388\pi$
$774$	−2.13247e23	−	7.70062e22i	−1.65560	−	0.597858i
$775$	5.00738e22			0.384766
$776$		−	1.57503e22i		−	0.119783i
$777$	1.48500e22	−	1.04261e22i	0.111779	−	0.0784789i
$778$	2.82161e23			2.10213
$779$		−	1.94736e22i		−	0.143598i
$780$	2.40607e22	+	3.42700e22i	0.175611	+	0.250125i
$781$	−2.77009e22			−0.200118
$782$		−	9.43824e21i		−	0.0674896i
$783$	−1.02235e23	+	2.78095e22i	−0.723613	+	0.196833i
$784$	−9.28861e22			−0.650762
$785$		−	1.54718e23i		−	1.07296i
$786$	2.18144e23	−	1.53157e23i	1.49748	−	1.05137i
$787$	−1.50748e23			−1.02436			−0.512181	−	0.858877i	$-0.671162\pi$
$787$	−1.50748e23			−1.02436			−0.512181	+	0.858877i	$0.671162\pi$
$788$		−	3.48814e22i		−	0.234631i
$789$	1.56572e23	+	2.23008e23i	1.04255	+	1.48492i
$790$	2.03509e23			1.34142
$791$			1.44394e23i			0.942190i
$792$	−5.22618e22	+	1.44725e23i	−0.337585	+	0.934848i
$793$	−7.90984e22			−0.505804
$794$			3.29358e23i			2.08499i
$795$	−6.43190e22	+	4.51579e22i	−0.403090	+	0.283006i
$796$	−6.34333e22			−0.393562
$797$		−	8.61549e22i		−	0.529192i	−0.964359	−	0.264596i	$-0.914761\pi$
$797$		−	8.61549e22i		−	0.529192i	0.964359	−	0.264596i	$-0.0852387\pi$
$798$	3.94194e22	+	5.61457e22i	0.239711	+	0.341424i
$799$	−6.12803e21			−0.0368932
$800$		−	7.57467e22i		−	0.451485i
$801$	1.44406e23	+	5.21467e22i	0.852168	+	0.307728i
$802$	7.24906e22			0.423533
$803$		−	3.04112e23i		−	1.75917i
$804$	2.80561e22	−	1.96979e22i	0.160686	−	0.112816i
$805$	−8.80180e22			−0.499119
$806$		−	1.47313e23i		−	0.827106i
$807$	1.67955e22	+	2.39221e22i	0.0933696	+	0.132988i
$808$	1.05088e23			0.578444
$809$			2.92416e23i			1.59372i	0.604161	+	0.796862i	$0.293508\pi$
$809$			2.92416e23i			1.59372i	−0.604161	+	0.796862i	$0.706492\pi$
$810$	−1.23373e23	−	1.02464e23i	−0.665792	−	0.552958i
$811$	−1.92966e23			−1.03113			−0.515564	−	0.856851i	$-0.672418\pi$
$811$	−1.92966e23			−1.03113			−0.515564	+	0.856851i	$0.672418\pi$
$812$			8.60202e22i			0.455148i
$813$	9.27607e22	−	6.51265e22i	0.486004	−	0.341219i
$814$	−4.17848e22			−0.216782
$815$		−	6.48255e22i		−	0.333031i
$816$	1.36539e22	+	1.94475e22i	0.0694602	+	0.0989332i
$817$	−7.92184e22			−0.399070
$818$		−	7.28108e21i		−	0.0363220i
$819$	7.43041e22	−	2.05765e23i	0.367064	−	1.01648i
$820$	3.69609e22			0.180814
$821$			1.31465e23i			0.636892i	0.947941	+	0.318446i	$0.103161\pi$
$821$			1.31465e23i			0.636892i	−0.947941	+	0.318446i	$0.896839\pi$
$822$	2.37803e23	−	1.66960e23i	1.14089	−	0.801009i
$823$	1.51869e22			0.0721556			0.0360778	−	0.999349i	$-0.488514\pi$
$823$	1.51869e22			0.0721556			0.0360778	+	0.999349i	$0.488514\pi$
$824$		−	2.51774e22i		−	0.118466i
$825$	−9.84014e22	−	1.40155e23i	−0.458532	−	0.653095i
$826$	−4.60360e23			−2.12450
$827$		−	2.24491e23i		−	1.02602i	−0.858383	−	0.513009i	$-0.828531\pi$
$827$		−	2.24491e23i		−	1.02602i	0.858383	−	0.513009i	$-0.171469\pi$
$828$	−5.84266e22	−	2.10985e22i	−0.264465	−	0.0955014i
$829$	8.92207e22			0.399972			0.199986	−	0.979799i	$-0.435910\pi$
$829$	8.92207e22			0.399972			0.199986	+	0.979799i	$0.435910\pi$
$830$			3.40424e23i			1.51146i
$831$	−2.71279e23	+	1.90463e23i	−1.19291	+	0.837534i
$832$	2.86833e22			0.124923
$833$			1.16726e22i			0.0503508i
$834$	4.34583e22	+	6.18983e22i	0.185671	+	0.264454i
$835$	−1.13156e23			−0.478835
$836$		−	5.21095e22i		−	0.218407i
$837$	4.88473e22	+	1.79576e23i	0.202786	+	0.745495i
$838$	9.76319e22			0.401458
$839$		−	3.14887e23i		−	1.28250i	−0.767331	−	0.641252i	$-0.778416\pi$
$839$		−	3.14887e23i		−	1.28250i	0.767331	−	0.641252i	$-0.221584\pi$
$840$	1.09946e23	−	7.71923e22i	0.443554	−	0.311415i
$841$	1.09518e23			0.437641
$842$			5.19500e23i			2.05631i
$843$	1.02625e22	+	1.46170e22i	0.0402377	+	0.0573111i
$844$	1.79391e23			0.696723
$845$			4.27099e22i			0.164314i
$846$	−4.15311e22	+	1.15009e23i	−0.158274	+	0.438297i
$847$	5.11979e23			1.93279
$848$		−	2.32347e23i		−	0.868902i
$849$	2.06354e22	−	1.44880e22i	0.0764455	−	0.0536717i
$850$	−1.60320e22			−0.0588352
$851$			1.74042e22i			0.0632729i
$852$	9.80764e21	+	1.39692e22i	0.0353222	+	0.0503099i
$853$	4.24442e23			1.51435			0.757174	−	0.653213i	$-0.226580\pi$
$853$	4.24442e23			1.51435			0.757174	+	0.653213i	$0.226580\pi$
$854$		−	2.45961e23i		−	0.869367i
$855$	−5.27038e22	−	1.90320e22i	−0.184550	−	0.0666431i
$856$	−1.20496e23			−0.418005
$857$		−	1.01944e23i		−	0.350359i	−0.984536	−	0.175180i	$-0.943949\pi$
$857$		−	1.01944e23i		−	0.350359i	0.984536	−	0.175180i	$-0.0560506\pi$
$858$	−4.12324e23	+	2.89489e23i	−1.40391	+	0.985676i
$859$	−3.39798e23			−1.14624			−0.573120	−	0.819472i	$-0.694267\pi$
$859$	−3.39798e23			−1.14624			−0.573120	+	0.819472i	$0.694267\pi$
$860$		−	1.50356e23i		−	0.502498i
$861$	−1.10961e23	−	1.58043e23i	−0.367404	−	0.523300i
$862$	−3.19587e22			−0.104841
$863$			2.27685e23i			0.740028i	0.929026	+	0.370014i	$0.120647\pi$
$863$			2.27685e23i			0.740028i	−0.929026	+	0.370014i	$0.879353\pi$
$864$	2.71645e23	−	7.38914e22i	0.874765	−	0.237949i
$865$	−5.62076e21			−0.0179335
$866$		−	6.77941e23i		−	2.14313i
$867$	−2.58852e23	+	1.81738e23i	−0.810772	+	0.569236i
$868$	1.51094e23			0.468911
$869$			8.07636e23i			2.48346i
$870$	−1.22402e23	−	1.74339e23i	−0.372935	−	0.531177i
$871$	−1.15802e23			−0.349598
$872$		−	1.31317e23i		−	0.392817i
$873$	−2.21270e22	+	6.12746e22i	−0.0655856	+	0.181621i
$874$	−6.58027e22			−0.193265
$875$			4.49714e23i			1.30880i
$876$	−1.53359e23	+	1.07672e23i	−0.442260	+	0.310507i
$877$	−3.55043e22			−0.101458			−0.0507288	−	0.998712i	$-0.516154\pi$
$877$	−3.55043e22			−0.101458			−0.0507288	+	0.998712i	$0.516154\pi$
$878$		−	2.24599e23i		−	0.635991i
$879$	−1.50988e23	−	2.15054e23i	−0.423673	−	0.603444i
$880$	−5.10311e23			−1.41897
$881$		−	5.58469e23i		−	1.53883i	−0.638747	−	0.769417i	$-0.720547\pi$
$881$		−	5.58469e23i		−	1.53883i	0.638747	−	0.769417i	$-0.279453\pi$
$882$	2.19067e23	+	7.91078e22i	0.598176	+	0.216008i
$883$	5.61513e23			1.51941			0.759704	−	0.650269i	$-0.225344\pi$
$883$	5.61513e23			1.51941			0.759704	+	0.650269i	$0.225344\pi$
$884$			1.55571e22i			0.0417168i
$885$	3.07751e23	−	2.16069e23i	0.817812	−	0.574179i
$886$	8.76502e22			0.230825
$887$			2.60967e22i			0.0681076i	0.999420	+	0.0340538i	$0.0108418\pi$
$887$			2.60967e22i			0.0681076i	−0.999420	+	0.0340538i	$0.989158\pi$
$888$	−1.52636e22	−	2.17402e22i	−0.0394778	−	0.0562289i
$889$	−4.05066e23			−1.03827
$890$			3.08684e23i			0.784142i
$891$	4.06635e23	−	4.89612e23i	1.02373	−	1.23262i
$892$	−2.78174e22			−0.0694061
$893$			4.27242e22i			0.105648i
$894$	5.14198e23	−	3.61014e23i	1.26017	−	0.884757i
$895$	3.84073e23			0.932889
$896$			5.53567e23i			1.33262i
$897$	1.20578e23	+	1.71741e23i	0.287693	+	0.409765i
$898$	−5.96320e23			−1.41016
$899$			2.47189e23i			0.579364i
$900$	−3.58386e22	+	9.92450e22i	−0.0832550	+	0.230552i
$901$	−2.91980e22			−0.0672288
$902$			4.44700e23i			1.01488i
$903$	−6.42917e23	+	4.51387e23i	−1.45430	+	1.02105i
$904$	2.11391e23			0.473957
$905$		−	5.55576e23i		−	1.23468i
$906$	5.56003e23	+	7.91923e23i	1.22476	+	1.74445i
$907$	4.66455e23			1.01848			0.509238	−	0.860626i	$-0.329927\pi$
$907$	4.66455e23			1.01848			0.509238	+	0.860626i	$0.329927\pi$
$908$			8.43341e22i			0.182522i
$909$	−4.08830e23	−	1.47633e23i	−0.877065	−	0.316719i
$910$	4.39846e23			0.935339
$911$		−	6.96041e22i		−	0.146719i	−0.997306	−	0.0733597i	$-0.976628\pi$
$911$		−	6.96041e22i		−	0.146719i	0.997306	−	0.0733597i	$-0.0233721\pi$
$912$	1.35587e23	−	9.51942e22i	0.283307	−	0.198908i
$913$	−1.35099e24			−2.79825
$914$		−	3.89101e23i		−	0.798901i
$915$	1.15441e23	+	1.64425e23i	0.234959	+	0.334656i
$916$	−1.80077e23			−0.363323
$917$		−	9.23501e23i		−	1.84707i
$918$	−1.56394e22	−	5.74945e22i	−0.0310083	−	0.113995i
$919$	1.90324e23			0.374084			0.187042	−	0.982352i	$-0.440110\pi$
$919$	1.90324e23			0.374084			0.187042	+	0.982352i	$0.440110\pi$
$920$			1.28857e23i			0.251076i
$921$	4.29668e23	−	3.01666e23i	0.829957	−	0.582706i
$922$	−5.24285e23			−1.00397
$923$		−	5.76578e22i		−	0.109457i
$924$	−2.96920e23	−	4.22908e23i	−0.558809	−	0.795921i
$925$	2.95633e22			0.0551593
$926$		−	6.48781e23i		−	1.20008i
$927$	−3.53707e22	+	9.79495e22i	−0.0648644	+	0.179624i
$928$	3.73923e23			0.679827
$929$		−	3.31139e22i		−	0.0596877i	−0.999555	−	0.0298438i	$-0.990499\pi$
$929$		−	3.31139e22i		−	0.0596877i	0.999555	−	0.0298438i	$-0.00950100\pi$
$930$	−3.06226e23	+	2.14998e23i	−0.547240	+	0.384213i
$931$	8.13804e22			0.144186
$932$			4.37924e23i			0.769257i
$933$	4.71657e23	+	6.71788e23i	0.821435	+	1.16998i
$934$	4.54185e23			0.784256
$935$			6.41286e22i			0.109789i
$936$	−3.01236e23	−	1.08780e23i	−0.511329	−	0.184647i
$937$	−7.97266e23			−1.34180			−0.670898	−	0.741550i	$-0.734091\pi$
$937$	−7.97266e23			−1.34180			−0.670898	+	0.741550i	$0.734091\pi$
$938$		−	3.60091e23i		−	0.600883i
$939$	−2.52098e23	+	1.76996e23i	−0.417104	+	0.292845i
$940$	−8.10905e22			−0.133029
$941$			8.32522e23i			1.35419i	0.735897	+	0.677094i	$0.236761\pi$
$941$			8.32522e23i			1.35419i	−0.735897	+	0.677094i	$0.763239\pi$
$942$	−6.59075e23	−	9.38731e23i	−1.06299	−	1.51403i
$943$	1.85226e23			0.296217
$944$			1.11173e24i			1.76288i
$945$	−5.36176e23	+	1.45848e23i	−0.843049	+	0.229322i
$946$	1.80903e24			2.82044
$947$			7.14569e20i			0.00110470i	1.00000		0.000552350i	$0.000175818\pi$
$947$			7.14569e20i			0.00110470i	−1.00000		0.000552350i	$0.999824\pi$
$948$	4.07280e23	−	2.85948e23i	0.624347	−	0.438349i
$949$	6.32991e23			0.962206
$950$			1.11774e23i			0.168482i
$951$	−2.06791e23	−	2.94535e23i	−0.309091	−	0.440244i
$952$	4.99108e22			0.0739774
$953$			6.28939e23i			0.924412i	0.886773	+	0.462206i	$0.152942\pi$
$953$			6.28939e23i			0.924412i	−0.886773	+	0.462206i	$0.847058\pi$
$954$	−1.97882e23	+	5.47980e23i	−0.288416	+	0.798689i
$955$	−2.19304e23			−0.316971
$956$		−	2.68431e23i		−	0.384741i
$957$	6.91873e23	−	4.85758e23i	0.983402	−	0.690438i
$958$	−1.70116e23			−0.239785
$959$		−	1.00673e24i		−	1.40723i
$960$	−4.18623e22	−	5.96251e22i	−0.0580300	−	0.0826531i
$961$	−2.93236e23			−0.403116
$962$		−	8.69728e22i		−	0.118572i
$963$	4.68772e23	+	1.69279e23i	0.633799	+	0.228872i
$964$	−1.09085e23			−0.146268
$965$			7.91229e22i			0.105216i
$966$	−5.34039e23	+	3.74944e23i	−0.704297	+	0.494481i
$967$	7.80856e23			1.02131			0.510657	−	0.859784i	$-0.329402\pi$
$967$	7.80856e23			1.02131			0.510657	+	0.859784i	$0.329402\pi$
$968$		−	7.49528e23i		−	0.972266i
$969$	−1.19626e22	−	1.70386e22i	−0.0153899	−	0.0219201i
$970$	−1.30982e23			−0.167123
$971$			1.10738e24i			1.40134i	0.713486	+	0.700669i	$0.247115\pi$
$971$			1.10738e24i			1.40134i	−0.713486	+	0.700669i	$0.752885\pi$
$972$	−3.90876e23	−	3.17110e22i	−0.490579	−	0.0397998i
$973$	2.62043e23			0.326190
$974$			2.63685e23i			0.325548i
$975$	2.91724e23	−	2.04817e23i	0.357220	−	0.250801i
$976$	−5.93972e23			−0.721385
$977$		−	1.41210e24i		−	1.70102i	−0.525956	−	0.850512i	$-0.676292\pi$
$977$		−	1.41210e24i		−	1.70102i	0.525956	−	0.850512i	$-0.323708\pi$
$978$	−2.76147e23	−	3.93321e23i	−0.329936	−	0.469933i
$979$	−1.22503e24			−1.45173
$980$			1.54460e23i			0.181555i
$981$	−1.84482e23	+	5.10873e23i	−0.215081	+	0.595608i
$982$	−1.89831e24			−2.19520
$983$			3.91385e23i			0.448928i	0.974482	+	0.224464i	$0.0720630\pi$
$983$			3.91385e23i			0.448928i	−0.974482	+	0.224464i	$0.927937\pi$
$984$	−2.31373e23	+	1.62445e23i	−0.263240	+	0.184818i
$985$	2.99283e23			0.337747
$986$		−	7.91421e22i		−	0.0885916i
$987$	2.43443e23	+	3.46739e23i	0.270308	+	0.385004i
$988$	1.08463e23			0.119461
$989$		−	7.53498e23i		−	0.823212i
$990$	1.20355e24	+	4.34615e23i	1.30431	+	0.471002i
$991$	4.73437e23			0.508947			0.254474	−	0.967080i	$-0.418098\pi$
$991$	4.73437e23			0.508947			0.254474	+	0.967080i	$0.418098\pi$
$992$		−	6.56796e23i		−	0.700385i
$993$	7.75375e23	−	5.44384e23i	0.820196	−	0.575853i
$994$	1.79290e23			0.188133
$995$		−	5.44258e23i		−	0.566527i
$996$	4.78326e23	+	6.81288e23i	0.493912	+	0.703487i
$997$	−4.33201e23			−0.443739			−0.221870	−	0.975076i	$-0.571216\pi$
$997$	−4.33201e23			−0.443739			−0.221870	+	0.975076i	$0.571216\pi$
$998$			3.58039e23i			0.363819i
$999$	2.88392e22	+	1.06021e23i	0.0290709	+	0.106873i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.17.b.a.2.4	yes	4
3.2	odd	2	inner	3.17.b.a.2.1	✓	4
4.3	odd	2		48.17.e.b.17.3		4
5.2	odd	4		75.17.d.b.74.2		8
5.3	odd	4		75.17.d.b.74.7		8
5.4	even	2		75.17.c.d.26.1		4
12.11	even	2		48.17.e.b.17.4		4
15.2	even	4		75.17.d.b.74.8		8
15.8	even	4		75.17.d.b.74.1		8
15.14	odd	2		75.17.c.d.26.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.17.b.a.2.1	✓	4	3.2	odd	2	inner
3.17.b.a.2.4	yes	4	1.1	even	1	trivial
48.17.e.b.17.3		4	4.3	odd	2
48.17.e.b.17.4		4	12.11	even	2
75.17.c.d.26.1		4	5.4	even	2
75.17.c.d.26.4		4	15.14	odd	2
75.17.d.b.74.1		8	15.8	even	4
75.17.d.b.74.2		8	5.2	odd	4
75.17.d.b.74.7		8	5.3	odd	4
75.17.d.b.74.8		8	15.2	even	4

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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+312.717i q^{2} +(-5369.70 + 3770.02i) q^{3} -32256.2 q^{4} -276758. i q^{5} +(-1.17895e6 - 1.67920e6i) q^{6} -7.10881e6 q^{7} +1.04072e7i q^{8} +(1.46206e7 - 4.04878e7i) q^{9} +O(q^{10})\)	\(q+312.717i q^{2} +(-5369.70 + 3770.02i) q^{3} -32256.2 q^{4} -276758. i q^{5} +(-1.17895e6 - 1.67920e6i) q^{6} -7.10881e6 q^{7} +1.04072e7i q^{8} +(1.46206e7 - 4.04878e7i) q^{9} +8.65472e7 q^{10} +3.43468e8i q^{11} +(1.73206e8 - 1.21607e8i) q^{12} -7.14909e8 q^{13} -2.22305e9i q^{14} +(1.04338e9 + 1.48611e9i) q^{15} -5.36845e9 q^{16} +6.74629e8i q^{17} +(1.26612e10 + 4.57212e9i) q^{18} +4.70347e9 q^{19} +8.92717e9i q^{20} +(3.81722e10 - 2.68004e10i) q^{21} -1.07408e11 q^{22} +4.47377e10i q^{23} +(-3.92353e10 - 5.58834e10i) q^{24} +7.59927e10 q^{25} -2.23564e11i q^{26} +(7.41314e10 + 2.72527e11i) q^{27} +2.29303e11 q^{28} +3.75138e11i q^{29} +(-4.64732e11 + 3.26285e11i) q^{30} +6.58929e11 q^{31} -9.96762e11i q^{32} +(-1.29488e12 - 1.84432e12i) q^{33} -2.10968e11 q^{34} +1.96742e12i q^{35} +(-4.71605e11 + 1.30598e12i) q^{36} +3.89028e11 q^{37} +1.47086e12i q^{38} +(3.83885e12 - 2.69522e12i) q^{39} +2.88027e12 q^{40} -4.14027e12i q^{41} +(8.38094e12 + 1.19371e13i) q^{42} -1.68426e13 q^{43} -1.10790e13i q^{44} +(-1.12053e13 - 4.04638e12i) q^{45} -1.39903e13 q^{46} +9.08356e12i q^{47} +(2.88269e13 - 2.02392e13i) q^{48} +1.73022e13 q^{49} +2.37642e13i q^{50} +(-2.54336e12 - 3.62255e12i) q^{51} +2.30602e13 q^{52} +4.32802e13i q^{53} +(-8.52240e13 + 2.31822e13i) q^{54} +9.50576e13 q^{55} -7.39826e13i q^{56} +(-2.52562e13 + 1.77322e13i) q^{57} -1.17312e14 q^{58} -2.07085e14i q^{59} +(-3.36556e13 - 4.79362e13i) q^{60} +1.10641e14 q^{61} +2.06059e14i q^{62} +(-1.03935e14 + 2.87820e14i) q^{63} -4.01216e13 q^{64} +1.97857e14i q^{65} +(5.76750e14 - 4.04932e14i) q^{66} +1.61981e14 q^{67} -2.17610e13i q^{68} +(-1.68662e14 - 2.40228e14i) q^{69} -6.15247e14 q^{70} +8.06506e13i q^{71} +(4.21363e14 + 1.52159e14i) q^{72} -8.85416e14 q^{73} +1.21656e14i q^{74} +(-4.08058e14 + 2.86494e14i) q^{75} -1.51716e14 q^{76} -2.44165e15i q^{77} +(8.42843e14 + 1.20047e15i) q^{78} +2.35142e15 q^{79} +1.48576e15i q^{80} +(-1.42550e15 - 1.18391e15i) q^{81} +1.29474e15 q^{82} +3.93339e15i q^{83} +(-1.23129e15 + 8.64477e14i) q^{84} +1.86709e14 q^{85} -5.26696e15i q^{86} +(-1.41428e15 - 2.01438e15i) q^{87} -3.57453e15 q^{88} +3.56666e15i q^{89} +(1.26537e15 - 3.50410e15i) q^{90} +5.08215e15 q^{91} -1.44307e15i q^{92} +(-3.53825e15 + 2.48418e15i) q^{93} -2.84059e15 q^{94} -1.30172e15i q^{95} +(3.75781e15 + 5.35231e15i) q^{96} -1.51341e15 q^{97} +5.41071e15i q^{98} +(1.39062e16 + 5.02171e15i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2052 q^{3} - 12464 q^{4} - 403056 q^{6} - 3141544 q^{7} + 18618660 q^{9}+O(q^{10}) \) 4 * q - 2052 * q^3 - 12464 * q^4 - 403056 * q^6 - 3141544 * q^7 + 18618660 * q^9	\( 4 q - 2052 q^{3} - 12464 q^{4} - 403056 q^{6} - 3141544 q^{7} + 18618660 q^{9} - 18646560 q^{10} + 572494608 q^{12} - 1580730424 q^{13} + 6829958880 q^{15} - 14561268608 q^{16} + 42304978080 q^{18} - 56117116360 q^{19} + 124455437064 q^{21} - 173545812000 q^{22} + 100515572352 q^{24} - 8074048700 q^{25} - 317983667652 q^{27} + 746852001056 q^{28} - 1762329117600 q^{30} + 2471781156248 q^{31} - 3610697951520 q^{33} + 2721261612672 q^{34} - 1219654126512 q^{36} + 370563213896 q^{37} + 7022170227384 q^{39} - 11795287092480 q^{40} + 27587883687840 q^{42} - 28065022062664 q^{43} + 18795326443200 q^{45} - 43994579504832 q^{46} + 41041959355008 q^{48} + 29478262537164 q^{49} - 82841575222656 q^{51} + 42193089120416 q^{52} - 107063660756304 q^{54} + 290253653236800 q^{55} - 335129108488344 q^{57} + 8796421982880 q^{58} + 56126440892160 q^{60} + 362269793083208 q^{61} - 266698363786344 q^{63} - 653949742779392 q^{64} + 13\!\cdots\!80 q^{66}+ \cdots + 18\!\cdots\!60 q^{99}+O(q^{100}) \) 4 * q - 2052 * q^3 - 12464 * q^4 - 403056 * q^6 - 3141544 * q^7 + 18618660 * q^9 - 18646560 * q^10 + 572494608 * q^12 - 1580730424 * q^13 + 6829958880 * q^15 - 14561268608 * q^16 + 42304978080 * q^18 - 56117116360 * q^19 + 124455437064 * q^21 - 173545812000 * q^22 + 100515572352 * q^24 - 8074048700 * q^25 - 317983667652 * q^27 + 746852001056 * q^28 - 1762329117600 * q^30 + 2471781156248 * q^31 - 3610697951520 * q^33 + 2721261612672 * q^34 - 1219654126512 * q^36 + 370563213896 * q^37 + 7022170227384 * q^39 - 11795287092480 * q^40 + 27587883687840 * q^42 - 28065022062664 * q^43 + 18795326443200 * q^45 - 43994579504832 * q^46 + 41041959355008 * q^48 + 29478262537164 * q^49 - 82841575222656 * q^51 + 42193089120416 * q^52 - 107063660756304 * q^54 + 290253653236800 * q^55 - 335129108488344 * q^57 + 8796421982880 * q^58 + 56126440892160 * q^60 + 362269793083208 * q^61 - 266698363786344 * q^63 - 653949742779392 * q^64 + 1332768950045280 * q^66 - 26774405363464 * q^67 + 58823173290816 * q^69 - 2292362286177600 * q^70 + 2397649754476800 * q^72 + 317628887539976 * q^73 - 1511365865026500 * q^75 - 2008642200508384 * q^76 + 1538179445855520 * q^78 + 4794017165184920 * q^79 - 6444192852054396 * q^81 + 1589112481320000 * q^82 - 1210523902199136 * q^84 + 7999994092573440 * q^85 - 8850169595242080 * q^87 - 3370289894104320 * q^88 + 3549134645307360 * q^90 + 9328538231657008 * q^91 - 2064207396761784 * q^93 - 12859596129667968 * q^94 + 15507630559798272 * q^96 - 13833795002601784 * q^97 + 18943177097338560 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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