LMFDB - Embedded newform 3.21.b.a.2.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,21,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, 21, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 21);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 21 $
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:	$7.60541295308$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 116898x^{4} + 3059043456x^{2} + 18153107947520 $ x^6 + 116898x^4 + 3059043456x^2 + 18153107947520
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{14}\cdot 3^{19}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.6
Root			$287.188i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.21.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)

$f(q)$	$=$	$q+1723.13i q^{2} +(-25942.2 + 53045.1i) q^{3} -1.92059e6 q^{4} +9.20415e6i q^{5} +(-9.14036e7 - 4.47017e7i) q^{6} +4.08861e8 q^{7} -1.50260e9i q^{8} +(-2.14079e9 - 2.75221e9i) q^{9} +O(q^{10})$	\(q+1723.13i q^{2} +(-25942.2 + 53045.1i) q^{3} -1.92059e6 q^{4} +9.20415e6i q^{5} +(-9.14036e7 - 4.47017e7i) q^{6} +4.08861e8 q^{7} -1.50260e9i q^{8} +(-2.14079e9 - 2.75221e9i) q^{9} -1.58599e10 q^{10} +1.86251e9i q^{11} +(4.98244e10 - 1.01878e11i) q^{12} +6.70490e10 q^{13} +7.04520e11i q^{14} +(-4.88236e11 - 2.38776e11i) q^{15} +5.75279e11 q^{16} +1.72456e12i q^{17} +(4.74242e12 - 3.68886e12i) q^{18} -8.30608e12 q^{19} -1.76774e13i q^{20} +(-1.06067e13 + 2.16881e13i) q^{21} -3.20934e12 q^{22} -1.84856e13i q^{23} +(7.97055e13 + 3.89807e13i) q^{24} +1.06510e13 q^{25} +1.15534e14i q^{26} +(2.01528e14 - 4.21602e13i) q^{27} -7.85255e14 q^{28} +1.25101e14i q^{29} +(4.11441e14 - 8.41293e14i) q^{30} +7.73973e14 q^{31} -5.84308e14i q^{32} +(-9.87969e13 - 4.83175e13i) q^{33} -2.97163e15 q^{34} +3.76322e15i q^{35} +(4.11159e15 + 5.28588e15i) q^{36} +3.58992e14 q^{37} -1.43124e16i q^{38} +(-1.73940e15 + 3.55663e15i) q^{39} +1.38301e16 q^{40} +1.14185e16i q^{41} +(-3.73713e16 - 1.82768e16i) q^{42} -9.36400e15 q^{43} -3.57712e15i q^{44} +(2.53318e16 - 1.97042e16i) q^{45} +3.18531e16 q^{46} +6.06257e16i q^{47} +(-1.49240e16 + 3.05158e16i) q^{48} +8.73749e16 q^{49} +1.83530e16i q^{50} +(-9.14795e16 - 4.47388e16i) q^{51} -1.28774e17 q^{52} -1.40322e17i q^{53} +(7.26474e16 + 3.47259e17i) q^{54} -1.71428e16 q^{55} -6.14353e17i q^{56} +(2.15478e17 - 4.40597e17i) q^{57} -2.15565e17 q^{58} +6.48312e17i q^{59} +(9.37702e17 + 4.58591e17i) q^{60} -1.26280e18 q^{61} +1.33365e18i q^{62} +(-8.75286e17 - 1.12527e18i) q^{63} +1.61006e18 q^{64} +6.17130e17i q^{65} +(8.32572e16 - 1.70240e17i) q^{66} +1.97861e18 q^{67} -3.31218e18i q^{68} +(9.80572e17 + 4.79557e17i) q^{69} -6.48451e18 q^{70} -1.85821e18i q^{71} +(-4.13547e18 + 3.21675e18i) q^{72} +2.65086e18 q^{73} +6.18589e17i q^{74} +(-2.76310e17 + 5.64983e17i) q^{75} +1.59526e19 q^{76} +7.61506e17i q^{77} +(-6.12852e18 - 2.99721e18i) q^{78} +3.40686e18 q^{79} +5.29496e18i q^{80} +(-2.99169e18 + 1.17838e19i) q^{81} -1.96756e19 q^{82} +1.78470e19i q^{83} +(2.03712e19 - 4.16540e19i) q^{84} -1.58731e19 q^{85} -1.61354e19i q^{86} +(-6.63600e18 - 3.24539e18i) q^{87} +2.79860e18 q^{88} -3.26076e19i q^{89} +(3.39528e19 + 4.36499e19i) q^{90} +2.74137e19 q^{91} +3.55033e19i q^{92} +(-2.00786e19 + 4.10555e19i) q^{93} -1.04466e20 q^{94} -7.64504e19i q^{95} +(3.09947e19 + 1.51582e19i) q^{96} +9.39298e19 q^{97} +1.50558e20i q^{98} +(5.12601e18 - 3.98724e18i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4122 q^{3} - 2125200 q^{4} - 96401232 q^{6} + 559607916 q^{7} - 1087483482 q^{9}+O(q^{10}) $ 6 * q - 4122 * q^3 - 2125200 * q^4 - 96401232 * q^6 + 559607916 * q^7 - 1087483482 * q^9	$ 6 q - 4122 q^{3} - 2125200 q^{4} - 96401232 q^{6} + 559607916 q^{7} - 1087483482 q^{9} - 10880304480 q^{10} + 63957886128 q^{12} + 17847879276 q^{13} - 487764624960 q^{15} - 317472843648 q^{16} + 9564155313120 q^{18} - 14958020195124 q^{19} + 25978999888044 q^{21} - 71051286019680 q^{22} + 294048705803904 q^{24} - 397204775017050 q^{25} + 10\!\cdots\!98 q^{27}+ \cdots - 17\!\cdots\!80 q^{99}+O(q^{100}) $ 6 * q - 4122 * q^3 - 2125200 * q^4 - 96401232 * q^6 + 559607916 * q^7 - 1087483482 * q^9 - 10880304480 * q^10 + 63957886128 * q^12 + 17847879276 * q^13 - 487764624960 * q^15 - 317472843648 * q^16 + 9564155313120 * q^18 - 14958020195124 * q^19 + 25978999888044 * q^21 - 71051286019680 * q^22 + 294048705803904 * q^24 - 397204775017050 * q^25 + 1077025592505798 * q^27 - 2034284889273504 * q^28 + 3061064118304800 * q^30 - 2182905165483348 * q^31 + 3811197222014400 * q^33 - 7566372644651136 * q^34 + 6910111676037744 * q^36 - 1934341462168404 * q^37 - 15813602040849876 * q^39 + 44482420967535360 * q^40 - 86552595699685920 * q^42 + 58194987502184076 * q^43 - 81854223046416000 * q^45 + 151411391218915776 * q^46 - 154489681080035712 * q^48 + 188165158287453522 * q^49 - 117657755976045312 * q^51 - 230547517796956704 * q^52 + 489800358305152272 * q^54 - 393208608470140800 * q^55 + 1211071992434087436 * q^57 - 1639827118548168480 * q^58 + 2591328282252814080 * q^60 - 2999109545381544468 * q^61 + 444547436097192876 * q^63 - 83569554960393216 * q^64 + 120735307117251360 * q^66 + 4488155969890198476 * q^67 - 3511312424189451648 * q^69 - 1812568842584740800 * q^70 - 10414532525611288320 * q^72 + 15738405804262597836 * q^73 - 20871070048457840250 * q^75 + 27275280223392575328 * q^76 - 13410777930056987040 * q^78 + 17679940751103803436 * q^79 - 13011625055229011514 * q^81 - 35403353112903693120 * q^82 + 60397598618988279264 * q^84 - 22576574831711316480 * q^85 + 17858271599894295360 * q^87 - 95000209108729447680 * q^88 + 179562325304911301280 * q^90 - 6461010485165713512 * q^91 - 24838278011742494484 * q^93 - 311754310853935072896 * q^94 + 184738040137761352704 * q^96 + 223240336245548394636 * q^97 - 178130031568853028480 * 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 $

$2$			1723.13i			1.68274i	0.540458	+	0.841371i	$0.318251\pi$
$2$			1723.13i			1.68274i	−0.540458	+	0.841371i	$0.681749\pi$
$3$	−25942.2	+	53045.1i	−0.439333	+	0.898324i
$3$	−25942.2	+	53045.1i	−0.439333	+	0.898324i
$4$	−1.92059e6			−1.83162
$5$			9.20415e6i			0.942505i	0.881998	+	0.471253i	$0.156198\pi$
$5$			9.20415e6i			0.942505i	−0.881998	+	0.471253i	$0.843802\pi$
$6$	−9.14036e7	−	4.47017e7i	−1.51165	−	0.739284i
$7$	4.08861e8			1.44742			0.723711	−	0.690103i	$-0.242435\pi$
$7$	4.08861e8			1.44742			0.723711	+	0.690103i	$0.242435\pi$
$8$		−	1.50260e9i		−	1.39940i
$9$	−2.14079e9	−	2.75221e9i	−0.613973	−	0.789327i
$10$	−1.58599e10			−1.58599
$11$			1.86251e9i			0.0718077i	0.999355	+	0.0359038i	$0.0114310\pi$
$11$			1.86251e9i			0.0718077i	−0.999355	+	0.0359038i	$0.988569\pi$
$12$	4.98244e10	−	1.01878e11i	0.804691	−	1.64539i
$13$	6.70490e10			0.486361			0.243181	−	0.969981i	$-0.421809\pi$
$13$	6.70490e10			0.486361			0.243181	+	0.969981i	$0.421809\pi$
$14$			7.04520e11i			2.43564i
$15$	−4.88236e11	−	2.38776e11i	−0.846675	−	0.414074i
$16$	5.75279e11			0.523214
$17$			1.72456e12i			0.855438i	0.903912	+	0.427719i	$0.140683\pi$
$17$			1.72456e12i			0.855438i	−0.903912	+	0.427719i	$0.859317\pi$
$18$	4.74242e12	−	3.68886e12i	1.32823	−	1.03316i
$19$	−8.30608e12			−1.35475			−0.677376	−	0.735637i	$-0.736883\pi$
$19$	−8.30608e12			−1.35475			−0.677376	+	0.735637i	$0.736883\pi$
$20$		−	1.76774e13i		−	1.72631i
$21$	−1.06067e13	+	2.16881e13i	−0.635900	+	1.30025i
$22$	−3.20934e12			−0.120834
$23$		−	1.84856e13i		−	0.446226i	−0.974793	−	0.223113i	$-0.928378\pi$
$23$		−	1.84856e13i		−	0.446226i	0.974793	−	0.223113i	$-0.0716220\pi$
$24$	7.97055e13	+	3.89807e13i	1.25712	+	0.614804i
$25$	1.06510e13			0.111684
$26$			1.15534e14i			0.818421i
$27$	2.01528e14	−	4.21602e13i	0.978810	−	0.204769i
$28$	−7.85255e14			−2.65113
$29$			1.25101e14i			0.297359i	0.988885	+	0.148679i	$0.0475023\pi$
$29$			1.25101e14i			0.297359i	−0.988885	+	0.148679i	$0.952498\pi$
$30$	4.11441e14	−	8.41293e14i	0.696779	−	1.42474i
$31$	7.73973e14			0.944298			0.472149	−	0.881519i	$-0.343478\pi$
$31$	7.73973e14			0.944298			0.472149	+	0.881519i	$0.343478\pi$
$32$		−	5.84308e14i		−	0.518970i
$33$	−9.87969e13	−	4.83175e13i	−0.0645066	−	0.0315475i
$34$	−2.97163e15			−1.43948
$35$			3.76322e15i			1.36420i
$36$	4.11159e15	+	5.28588e15i	1.12457	+	1.44575i
$37$	3.58992e14			0.0746565			0.0373282	−	0.999303i	$-0.488115\pi$
$37$	3.58992e14			0.0746565			0.0373282	+	0.999303i	$0.488115\pi$
$38$		−	1.43124e16i		−	2.27970i
$39$	−1.73940e15	+	3.55663e15i	−0.213675	+	0.436910i
$40$	1.38301e16			1.31894
$41$			1.14185e16i			0.850690i	0.905031	+	0.425345i	$0.139847\pi$
$41$			1.14185e16i			0.850690i	−0.905031	+	0.425345i	$0.860153\pi$
$42$	−3.73713e16	−	1.82768e16i	−2.18799	−	1.07006i
$43$	−9.36400e15			−0.433288			−0.216644	−	0.976251i	$-0.569511\pi$
$43$	−9.36400e15			−0.433288			−0.216644	+	0.976251i	$0.569511\pi$
$44$		−	3.57712e15i		−	0.131524i
$45$	2.53318e16	−	1.97042e16i	0.743945	−	0.578673i
$46$	3.18531e16			0.750884
$47$			6.06257e16i			1.15260i	0.817239	+	0.576300i	$0.195504\pi$
$47$			6.06257e16i			1.15260i	−0.817239	+	0.576300i	$0.804496\pi$
$48$	−1.49240e16	+	3.05158e16i	−0.229865	+	0.470015i
$49$	8.73749e16			1.09503
$50$			1.83530e16i			0.187935i
$51$	−9.14795e16	−	4.47388e16i	−0.768461	−	0.375822i
$52$	−1.28774e17			−0.890830
$53$		−	1.40322e17i		−	0.802356i	−0.916000	−	0.401178i	$-0.868601\pi$
$53$		−	1.40322e17i		−	0.802356i	0.916000	−	0.401178i	$-0.131399\pi$
$54$	7.26474e16	+	3.47259e17i	0.344574	+	1.64709i
$55$	−1.71428e16			−0.0676791
$56$		−	6.14353e17i		−	2.02553i
$57$	2.15478e17	−	4.40597e17i	0.595188	−	1.21701i
$58$	−2.15565e17			−0.500378
$59$			6.48312e17i			1.26842i	0.773160	+	0.634211i	$0.218675\pi$
$59$			6.48312e17i			1.26842i	−0.773160	+	0.634211i	$0.781325\pi$
$60$	9.37702e17	+	4.58591e17i	1.55079	+	0.758426i
$61$	−1.26280e18			−1.77025			−0.885127	−	0.465350i	$-0.845928\pi$
$61$	−1.26280e18			−1.77025			−0.885127	+	0.465350i	$0.845928\pi$
$62$			1.33365e18i			1.58901i
$63$	−8.75286e17	−	1.12527e18i	−0.888678	−	1.14249i
$64$	1.61006e18			1.39651
$65$			6.17130e17i			0.458398i
$66$	8.32572e16	−	1.70240e17i	0.0530863	−	0.108548i
$67$	1.97861e18			1.08545			0.542727	−	0.839909i	$-0.317392\pi$
$67$	1.97861e18			1.08545			0.542727	+	0.839909i	$0.317392\pi$
$68$		−	3.31218e18i		−	1.56684i
$69$	9.80572e17	+	4.79557e17i	0.400856	+	0.196042i
$70$	−6.48451e18			−2.29560
$71$		−	1.85821e18i		−	0.570836i	−0.958403	−	0.285418i	$-0.907868\pi$
$71$		−	1.85821e18i		−	0.570836i	0.958403	−	0.285418i	$-0.0921324\pi$
$72$	−4.13547e18	+	3.21675e18i	−1.10459	+	0.859196i
$73$	2.65086e18			0.616820			0.308410	−	0.951254i	$-0.400203\pi$
$73$	2.65086e18			0.616820			0.308410	+	0.951254i	$0.400203\pi$
$74$			6.18589e17i			0.125628i
$75$	−2.76310e17	+	5.64983e17i	−0.0490663	+	0.100328i
$76$	1.59526e19			2.48139
$77$			7.61506e17i			0.103936i
$78$	−6.12852e18	−	2.99721e18i	−0.735207	−	0.359559i
$79$	3.40686e18			0.359818			0.179909	−	0.983683i	$-0.442420\pi$
$79$	3.40686e18			0.359818			0.179909	+	0.983683i	$0.442420\pi$
$80$			5.29496e18i			0.493132i
$81$	−2.99169e18	+	1.17838e19i	−0.246074	+	0.969251i
$82$	−1.96756e19			−1.43149
$83$			1.78470e19i			1.15023i	0.818072	+	0.575116i	$0.195043\pi$
$83$			1.78470e19i			1.15023i	−0.818072	+	0.575116i	$0.804957\pi$
$84$	2.03712e19	−	4.16540e19i	1.16473	−	2.38157i
$85$	−1.58731e19			−0.806255
$86$		−	1.61354e19i		−	0.729112i
$87$	−6.63600e18	−	3.24539e18i	−0.267125	−	0.130640i
$88$	2.79860e18			0.100488
$89$		−	3.26076e19i		−	1.04573i	−0.852416	−	0.522864i	$-0.824864\pi$
$89$		−	3.26076e19i		−	1.04573i	0.852416	−	0.522864i	$-0.175136\pi$
$90$	3.39528e19	+	4.36499e19i	0.973757	+	1.25187i
$91$	2.74137e19			0.703970
$92$			3.55033e19i			0.817318i
$93$	−2.00786e19	+	4.10555e19i	−0.414861	+	0.848286i
$94$	−1.04466e20			−1.93953
$95$		−	7.64504e19i		−	1.27686i
$96$	3.09947e19	+	1.51582e19i	0.466203	+	0.228001i
$97$	9.39298e19			1.27375			0.636877	−	0.770965i	$-0.280226\pi$
$97$	9.39298e19			1.27375			0.636877	+	0.770965i	$0.280226\pi$
$98$			1.50558e20i			1.84265i
$99$	5.12601e18	−	3.98724e18i	0.0566797	−	0.0440880i
$100$	−2.04562e19			−0.204562
$101$		−	1.22451e20i		−	1.10853i	−0.832340	−	0.554265i	$-0.812999\pi$
$101$		−	1.22451e20i		−	1.10853i	0.832340	−	0.554265i	$-0.187001\pi$
$102$	7.70907e19	−	1.57631e20i	0.632412	−	1.29312i
$103$	−9.97412e19			−0.742168			−0.371084	−	0.928599i	$-0.621014\pi$
$103$	−9.97412e19			−0.742168			−0.371084	+	0.928599i	$0.621014\pi$
$104$		−	1.00748e20i		−	0.680616i
$105$	−1.99620e20	−	9.76261e19i	−1.22550	−	0.599339i
$106$	2.41793e20			1.35016
$107$			3.86242e20i			1.96346i	0.190285	+	0.981729i	$0.439059\pi$
$107$			3.86242e20i			1.96346i	−0.190285	+	0.981729i	$0.560941\pi$
$108$	−3.87054e20	+	8.09726e19i	−1.79281	+	0.375060i
$109$	7.59151e19			0.320674			0.160337	−	0.987062i	$-0.448742\pi$
$109$	7.59151e19			0.320674			0.160337	+	0.987062i	$0.448742\pi$
$110$		−	2.95392e19i		−	0.113886i
$111$	−9.31304e18	+	1.90428e19i	−0.0327991	+	0.0670657i
$112$	2.35209e20			0.757311
$113$		−	2.27492e20i		−	0.670165i	−0.942189	−	0.335082i	$-0.891236\pi$
$113$		−	2.27492e20i		−	0.670165i	0.942189	−	0.335082i	$-0.108764\pi$
$114$	7.59205e20	+	3.71296e20i	2.04791	+	1.00155i
$115$	1.70144e20			0.420571
$116$		−	2.40268e20i		−	0.544649i
$117$	−1.43538e20	−	1.84533e20i	−0.298613	−	0.383898i
$118$	−1.11712e21			−2.13443
$119$			7.05104e20i			1.23818i
$120$	−3.58784e20	+	7.33622e20i	−0.579456	+	1.18484i
$121$	6.69281e20			0.994844
$122$		−	2.17596e21i		−	2.97888i
$123$	−6.05697e20	−	2.96221e20i	−0.764196	−	0.373736i
$124$	−1.48649e21			−1.72960
$125$			9.75810e20i			1.04777i
$126$	1.93899e21	−	1.50823e21i	1.92251	−	1.49542i
$127$	1.94706e21			1.78378			0.891892	−	0.452249i	$-0.149378\pi$
$127$	1.94706e21			1.78378			0.891892	+	0.452249i	$0.149378\pi$
$128$			2.16165e21i			1.83099i
$129$	2.42922e20	−	4.96715e20i	0.190358	−	0.389233i
$130$	−1.06339e21			−0.771366
$131$		−	8.13569e20i		−	0.546615i	−0.961927	−	0.273308i	$-0.911882\pi$
$131$		−	8.13569e20i		−	0.546615i	0.961927	−	0.273308i	$-0.0881177\pi$
$132$	1.89749e20	+	9.27982e19i	0.118152	+	0.0577830i
$133$	−3.39603e21			−1.96090
$134$			3.40939e21i			1.82654i
$135$	3.88049e20	+	1.85490e21i	0.192996	+	0.922534i
$136$	2.59132e21			1.19710
$137$		−	1.88407e21i		−	0.808892i	−0.914562	−	0.404446i	$-0.867464\pi$
$137$		−	1.88407e21i		−	0.808892i	0.914562	−	0.404446i	$-0.132536\pi$
$138$	−8.26338e20	+	1.68965e21i	−0.329888	+	0.674537i
$139$	2.08132e21			0.773019			0.386510	−	0.922285i	$-0.373681\pi$
$139$	2.08132e21			0.773019			0.386510	+	0.922285i	$0.373681\pi$
$140$		−	7.22761e21i		−	2.49870i
$141$	−3.21590e21	−	1.57276e21i	−1.03541	−	0.506375i
$142$	3.20193e21			0.960570
$143$			1.24879e20i			0.0349245i
$144$	−1.23155e21	−	1.58329e21i	−0.321239	−	0.412987i
$145$	−1.15145e21			−0.280262
$146$			4.56777e21i			1.03795i
$147$	−2.26670e21	+	4.63482e21i	−0.481083	+	0.983692i
$148$	−6.89478e20			−0.136742
$149$		−	8.44507e21i		−	1.56582i	−0.622138	−	0.782908i	$-0.713736\pi$
$149$		−	8.44507e21i		−	1.56582i	0.622138	−	0.782908i	$-0.286264\pi$
$150$	−9.73537e20	−	4.76117e20i	−0.168826	−	0.0825659i
$151$	1.71634e20			0.0278506			0.0139253	−	0.999903i	$-0.495567\pi$
$151$	1.71634e20			0.0278506			0.0139253	+	0.999903i	$0.495567\pi$
$152$			1.24807e22i			1.89584i
$153$	4.74635e21	−	3.69192e21i	0.675221	−	0.525216i
$154$	−1.31217e21			−0.174897
$155$			7.12377e21i			0.890006i
$156$	3.34068e21	−	6.83083e21i	0.391371	−	0.800254i
$157$	5.82429e21			0.640098			0.320049	−	0.947401i	$-0.396301\pi$
$157$	5.82429e21			0.640098			0.320049	+	0.947401i	$0.396301\pi$
$158$			5.87045e21i			0.605481i
$159$	7.44341e21	+	3.64026e21i	0.720776	+	0.352502i
$160$	5.37806e21			0.489132
$161$		−	7.55804e21i		−	0.645878i
$162$	−2.03050e22	−	5.15507e21i	−1.63100	−	0.414080i
$163$	−8.71287e21			−0.658090			−0.329045	−	0.944314i	$-0.606727\pi$
$163$	−8.71287e21			−0.658090			−0.329045	+	0.944314i	$0.606727\pi$
$164$		−	2.19303e22i		−	1.55814i
$165$	4.44721e20	−	9.09342e20i	0.0297337	−	0.0607978i
$166$	−3.07527e22			−1.93554
$167$			1.36541e22i			0.809280i	0.914476	+	0.404640i	$0.132603\pi$
$167$			1.36541e22i			0.809280i	−0.914476	+	0.404640i	$0.867397\pi$
$168$	3.25885e22	+	1.59377e22i	1.81958	+	0.889881i
$169$	−1.45094e22			−0.763453
$170$		−	2.73514e22i		−	1.35672i
$171$	1.77816e22	+	2.28601e22i	0.831781	+	1.06934i
$172$	1.79844e22			0.793619
$173$		−	7.26725e21i		−	0.302628i	−0.988486	−	0.151314i	$-0.951650\pi$
$173$		−	7.26725e21i		−	0.302628i	0.988486	−	0.151314i	$-0.0483504\pi$
$174$	5.59223e21	−	1.14347e22i	0.219833	−	0.449502i
$175$	4.35477e21			0.161653
$176$			1.07146e21i			0.0375707i
$177$	−3.43898e22	−	1.68186e22i	−1.13945	−	0.557260i
$178$	5.61870e22			1.75969
$179$			6.52788e22i			1.93304i	0.256585	+	0.966522i	$0.417403\pi$
$179$			6.52788e22i			1.93304i	−0.256585	+	0.966522i	$0.582597\pi$
$180$	−4.86521e22	+	3.78437e22i	−1.36263	+	1.05991i
$181$	−1.71443e22			−0.454291			−0.227146	−	0.973861i	$-0.572939\pi$
$181$	−1.71443e22			−0.454291			−0.227146	+	0.973861i	$0.572939\pi$
$182$			4.72374e22i			1.18460i
$183$	3.27597e22	−	6.69853e22i	0.777731	−	1.59026i
$184$	−2.77764e22			−0.624451
$185$			3.30422e21i			0.0703641i
$186$	−7.07439e22	−	3.45979e22i	−1.42745	−	0.698104i
$187$	−3.21200e21			−0.0614270
$188$		−	1.16437e23i		−	2.11112i
$189$	8.23971e22	−	1.72376e22i	1.41675	−	0.296388i
$190$	1.31734e23			2.14863
$191$		−	8.45513e22i		−	1.30854i	−0.756262	−	0.654269i	$-0.772976\pi$
$191$		−	8.45513e22i		−	1.30854i	0.756262	−	0.654269i	$-0.227024\pi$
$192$	−4.17685e22	+	8.54059e22i	−0.613531	+	1.25451i
$193$	−2.74850e22			−0.383286			−0.191643	−	0.981465i	$-0.561382\pi$
$193$	−2.74850e22			−0.383286			−0.191643	+	0.981465i	$0.561382\pi$
$194$			1.61853e23i			2.14340i
$195$	−3.27357e22	−	1.60097e22i	−0.411790	−	0.201389i
$196$	−1.67812e23			−2.00568
$197$		−	4.22412e22i		−	0.479815i	−0.970796	−	0.239908i	$-0.922883\pi$
$197$		−	4.22412e22i		−	0.479815i	0.970796	−	0.239908i	$-0.0771172\pi$
$198$	6.87052e21	+	8.83278e21i	0.0741887	+	0.0953774i
$199$	3.19820e22			0.328379			0.164189	−	0.986429i	$-0.447499\pi$
$199$	3.19820e22			0.328379			0.164189	+	0.986429i	$0.447499\pi$
$200$		−	1.60041e22i		−	0.156290i
$201$	−5.13294e22	+	1.04955e23i	−0.476876	+	0.975089i
$202$	2.10998e23			1.86537
$203$			5.11489e22i			0.430404i
$204$	1.75695e23	+	8.59250e22i	1.40753	+	0.688364i
$205$	−1.05098e23			−0.801780
$206$		−	1.71867e23i		−	1.24888i
$207$	−5.08763e22	+	3.95738e22i	−0.352219	+	0.273971i
$208$	3.85719e22			0.254471
$209$		−	1.54701e22i		−	0.0972816i
$210$	1.68222e23	−	3.43972e23i	1.00853	−	2.06219i
$211$	−1.44571e23			−0.826524			−0.413262	−	0.910612i	$-0.635611\pi$
$211$	−1.44571e23			−0.826524			−0.413262	+	0.910612i	$0.635611\pi$
$212$			2.69502e23i			1.46961i
$213$	9.85691e22	+	4.82060e22i	0.512796	+	0.250787i
$214$	−6.65544e23			−3.30399
$215$		−	8.61877e22i		−	0.408376i
$216$	−6.33498e22	−	3.02816e23i	−0.286555	−	1.36975i
$217$	3.16447e23			1.36680
$218$			1.30811e23i			0.539611i
$219$	−6.87691e22	+	1.40615e23i	−0.270989	+	0.554104i
$220$	3.29243e22			0.123962
$221$			1.15630e23i			0.416052i
$222$	−3.28132e22	−	1.60476e22i	−0.112854	−	0.0551924i
$223$	4.18661e23			1.37662			0.688310	−	0.725417i	$-0.258353\pi$
$223$	4.18661e23			1.37662			0.688310	+	0.725417i	$0.258353\pi$
$224$		−	2.38901e23i		−	0.751168i
$225$	−2.28015e22	−	2.93138e22i	−0.0685707	−	0.0881549i
$226$	3.91998e23			1.12771
$227$		−	2.63499e23i		−	0.725305i	−0.931924	−	0.362653i	$-0.881871\pi$
$227$		−	2.63499e23i		−	0.725305i	0.931924	−	0.362653i	$-0.118129\pi$
$228$	−4.13845e23	+	8.46208e23i	−1.09016	+	2.22910i
$229$	6.30930e22			0.159084			0.0795420	−	0.996832i	$-0.474654\pi$
$229$	6.30930e22			0.159084			0.0795420	+	0.996832i	$0.474654\pi$
$230$			2.93180e23i			0.707712i
$231$	−4.03942e22	−	1.97551e22i	−0.0933682	−	0.0456625i
$232$	1.87976e23			0.416125
$233$			4.45602e23i			0.944904i	0.881356	+	0.472452i	$0.156631\pi$
$233$			4.45602e23i			0.944904i	−0.881356	+	0.472452i	$0.843369\pi$
$234$	3.17974e23	−	2.47334e23i	0.646002	−	0.502488i
$235$	−5.58008e23			−1.08633
$236$		−	1.24514e24i		−	2.32327i
$237$	−8.83813e22	+	1.80717e23i	−0.158080	+	0.323233i
$238$	−1.21499e24			−2.08354
$239$		−	5.27193e23i		−	0.866944i	−0.901167	−	0.433472i	$-0.857288\pi$
$239$		−	5.27193e23i		−	0.866944i	0.901167	−	0.433472i	$-0.142712\pi$
$240$	−2.80872e23	−	1.37363e23i	−0.442992	−	0.216649i
$241$	7.96863e23			1.20563			0.602814	−	0.797882i	$-0.294046\pi$
$241$	7.96863e23			1.20563			0.602814	+	0.797882i	$0.294046\pi$
$242$			1.15326e24i			1.67407i
$243$	−5.47464e23	−	4.64393e23i	−0.762593	−	0.646879i
$244$	2.42532e24			3.24243
$245$			8.04212e23i			1.03207i
$246$	5.10427e23	−	1.04369e24i	0.628902	−	1.28594i
$247$	−5.56915e23			−0.658899
$248$		−	1.16297e24i		−	1.32145i
$249$	−9.46699e23	−	4.62991e23i	−1.03328	−	0.505335i
$250$	−1.68144e24			−1.76312
$251$		−	2.91213e23i		−	0.293409i	−0.989180	−	0.146705i	$-0.953133\pi$
$251$		−	2.91213e23i		−	0.293409i	0.989180	−	0.146705i	$-0.0468667\pi$
$252$	1.68107e24	+	2.16119e24i	1.62772	+	2.09261i
$253$	3.44296e22			0.0320425
$254$			3.35503e24i			3.00165i
$255$	4.11783e23	−	8.41991e23i	0.354215	−	0.724279i
$256$	−2.03653e24			−1.68458
$257$			1.11473e23i			0.0886826i	0.999016	+	0.0443413i	$0.0141189\pi$
$257$			1.11473e23i			0.0886826i	−0.999016	+	0.0443413i	$0.985881\pi$
$258$	8.55903e23	+	4.18586e23i	0.654979	+	0.320323i
$259$	1.46778e23			0.108059
$260$		−	1.18526e24i		−	0.839612i
$261$	3.44305e23	−	2.67815e23i	0.234713	−	0.182570i
$262$	1.40188e24			0.919812
$263$		−	7.99006e23i		−	0.504652i	−0.967642	−	0.252326i	$-0.918804\pi$
$263$		−	7.99006e23i		−	0.504652i	0.967642	−	0.252326i	$-0.0811956\pi$
$264$	−7.26017e22	+	1.48452e23i	−0.0441476	+	0.0902707i
$265$	1.29155e24			0.756225
$266$		−	5.85179e24i		−	3.29969i
$267$	1.72967e24	+	8.45911e23i	0.939402	+	0.459422i
$268$	−3.80010e24			−1.98814
$269$			1.59234e24i			0.802625i	0.915941	+	0.401312i	$0.131446\pi$
$269$			1.59234e24i			0.802625i	−0.915941	+	0.401312i	$0.868554\pi$
$270$	−3.19623e24	+	6.68658e23i	−1.55239	+	0.324763i
$271$	1.78531e23			0.0835641			0.0417821	−	0.999127i	$-0.486696\pi$
$271$	1.78531e23			0.0835641			0.0417821	+	0.999127i	$0.486696\pi$
$272$			9.92103e23i			0.447577i
$273$	−7.11172e23	+	1.45417e24i	−0.309277	+	0.632393i
$274$	3.24649e24			1.36116
$275$			1.98375e22i			0.00801974i
$276$	−1.88328e24	−	9.21034e23i	−0.734216	−	0.359075i
$277$	−3.57234e24			−1.34324			−0.671622	−	0.740894i	$-0.734402\pi$
$277$	−3.57234e24			−1.34324			−0.671622	+	0.740894i	$0.734402\pi$
$278$			3.58638e24i			1.30079i
$279$	−1.65692e24	−	2.13014e24i	−0.579773	−	0.745360i
$280$	5.65460e24			1.90907
$281$		−	2.88988e23i		−	0.0941491i	−0.998891	−	0.0470746i	$-0.985010\pi$
$281$		−	2.88988e23i		−	0.0941491i	0.998891	−	0.0470746i	$-0.0149898\pi$
$282$	2.71007e24	−	5.54141e24i	0.852098	−	1.74232i
$283$	2.62274e24			0.795959			0.397980	−	0.917394i	$-0.369711\pi$
$283$	2.62274e24			0.795959			0.397980	+	0.917394i	$0.369711\pi$
$284$			3.56887e24i			1.04556i
$285$	4.05532e24	+	1.98329e24i	1.14704	+	0.560967i
$286$	−2.15183e23			−0.0587689
$287$			4.66859e24i			1.23131i
$288$	−1.60814e24	+	1.25088e24i	−0.409637	+	0.318633i
$289$	1.09013e24			0.268225
$290$		−	1.98409e24i		−	0.471609i
$291$	−2.43674e24	+	4.98252e24i	−0.559603	+	1.14424i
$292$	−5.09123e24			−1.12978
$293$		−	8.49833e24i		−	1.82246i	−0.411901	−	0.911229i	$-0.635135\pi$
$293$		−	8.49833e24i		−	1.82246i	0.411901	−	0.911229i	$-0.364865\pi$
$294$	−7.98638e24	−	3.90581e24i	−1.65530	−	0.809538i
$295$	−5.96716e24			−1.19549
$296$		−	5.39421e23i		−	0.104475i
$297$	7.85236e22	+	3.75348e23i	0.0147040	+	0.0702861i
$298$	1.45519e25			2.63486
$299$		−	1.23944e24i		−	0.217027i
$300$	5.30678e23	−	1.08510e24i	0.0898708	−	0.183763i
$301$	−3.82857e24			−0.627151
$302$			2.95748e23i			0.0468654i
$303$	6.49541e24	+	3.17664e24i	0.995819	+	0.487014i
$304$	−4.77831e24			−0.708825
$305$		−	1.16230e25i		−	1.66847i
$306$	6.36165e24	+	8.17857e24i	0.883803	+	1.13622i
$307$	−6.30421e23			−0.0847709			−0.0423854	−	0.999101i	$-0.513496\pi$
$307$	−6.30421e23			−0.0847709			−0.0423854	+	0.999101i	$0.513496\pi$
$308$		−	1.46254e24i		−	0.190371i
$309$	2.58750e24	−	5.29079e24i	0.326059	−	0.666708i
$310$	−1.22752e25			−1.49765
$311$			1.35822e25i			1.60460i	0.596922	+	0.802299i	$0.296390\pi$
$311$			1.35822e25i			1.60460i	−0.596922	+	0.802299i	$0.703610\pi$
$312$	5.34418e24	+	2.61362e24i	0.611413	+	0.299017i
$313$	2.58344e24			0.286256			0.143128	−	0.989704i	$-0.454284\pi$
$313$	2.58344e24			0.286256			0.143128	+	0.989704i	$0.454284\pi$
$314$			1.00360e25i			1.07712i
$315$	1.03572e25	−	8.05626e24i	1.07680	−	0.837584i
$316$	−6.54319e24			−0.659050
$317$			1.64877e24i			0.160904i	0.996758	+	0.0804520i	$0.0256364\pi$
$317$			1.64877e24i			0.160904i	−0.996758	+	0.0804520i	$0.974364\pi$
$318$	−6.27263e24	+	1.28259e25i	−0.593169	+	1.21288i
$319$	−2.33001e23			−0.0213526
$320$			1.48193e25i			1.31621i
$321$	−2.04883e25	−	1.00200e25i	−1.76382	−	0.862612i
$322$	1.30235e25			1.08685
$323$		−	1.43243e25i		−	1.15891i
$324$	5.74582e24	−	2.26319e25i	0.450715	−	1.77530i
$325$	7.14138e23			0.0543186
$326$		−	1.50134e25i		−	1.10740i
$327$	−1.96940e24	+	4.02693e24i	−0.140883	+	0.288069i
$328$	1.71574e25			1.19046
$329$			2.47875e25i			1.66830i
$330$	1.56691e24	+	7.66312e23i	0.102307	+	0.0500341i
$331$	−1.11021e24			−0.0703273			−0.0351636	−	0.999382i	$-0.511195\pi$
$331$	−1.11021e24			−0.0703273			−0.0351636	+	0.999382i	$0.511195\pi$
$332$		−	3.42769e25i		−	2.10679i
$333$	−7.68527e23	−	9.88023e23i	−0.0458371	−	0.0589284i
$334$	−2.35278e25			−1.36181
$335$			1.82114e25i			1.02305i
$336$	−6.10184e24	+	1.24767e25i	−0.332712	+	0.680311i
$337$	−1.54571e25			−0.818144			−0.409072	−	0.912502i	$-0.634147\pi$
$337$	−1.54571e25			−0.818144			−0.409072	+	0.912502i	$0.634147\pi$
$338$		−	2.50015e25i		−	1.28469i
$339$	1.20673e25	+	5.90163e24i	0.602025	+	0.294425i
$340$	3.04858e25			1.47675
$341$			1.44153e24i			0.0678078i
$342$	−3.93909e25	+	3.06399e25i	−1.79943	+	1.39967i
$343$	3.10026e24			0.137549
$344$			1.40703e25i			0.606345i
$345$	−4.41392e24	+	9.02533e24i	−0.184771	+	0.377809i
$346$	1.25224e25			0.509244
$347$		−	9.89938e22i		−	0.00391123i	−0.999998	−	0.00195561i	$-0.999378\pi$
$347$		−	9.89938e22i		−	0.00391123i	0.999998	−	0.00195561i	$-0.000622492\pi$
$348$	1.27451e25	+	6.23308e24i	0.489271	+	0.239282i
$349$	4.14951e25			1.54790			0.773949	−	0.633248i	$-0.218279\pi$
$349$	4.14951e25			1.54790			0.773949	+	0.633248i	$0.218279\pi$
$350$			7.50382e24i			0.272021i
$351$	1.35123e25	−	2.82680e24i	0.476056	−	0.0995919i
$352$	1.08828e24			0.0372660
$353$		−	3.72879e25i		−	1.24114i	−0.784151	−	0.620569i	$-0.786901\pi$
$353$		−	3.72879e25i		−	1.24114i	0.784151	−	0.620569i	$-0.213099\pi$
$354$	2.89806e25	−	5.92580e25i	0.937725	−	1.91741i
$355$	1.71033e25			0.538016
$356$			6.26259e25i			1.91538i
$357$	−3.74024e25	−	1.82919e25i	−1.11229	−	0.543973i
$358$	−1.12484e26			−3.25281
$359$			1.22381e25i			0.344168i	0.985082	+	0.172084i	$0.0550501\pi$
$359$			1.22381e25i			0.344168i	−0.985082	+	0.172084i	$0.944950\pi$
$360$	−2.96074e25	−	3.80635e25i	−0.809796	−	1.04108i
$361$	3.14009e25			0.835354
$362$		−	2.95418e25i		−	0.764455i
$363$	−1.73626e25	+	3.55021e25i	−0.437068	+	0.893692i
$364$	−5.26506e25			−1.28941
$365$			2.43989e25i			0.581356i
$366$	1.15424e26	+	5.64492e25i	2.67600	+	1.30872i
$367$	−3.49408e25			−0.788265			−0.394133	−	0.919054i	$-0.628955\pi$
$367$	−3.49408e25			−0.788265			−0.394133	+	0.919054i	$0.628955\pi$
$368$		−	1.06344e25i		−	0.233472i
$369$	3.14262e25	−	2.44447e25i	0.671473	−	0.522301i
$370$	−5.69359e24			−0.118405
$371$		−	5.73722e25i		−	1.16135i
$372$	3.85627e25	−	7.88510e25i	0.759868	−	1.55374i
$373$	1.89892e25			0.364266			0.182133	−	0.983274i	$-0.441700\pi$
$373$	1.89892e25			0.364266			0.182133	+	0.983274i	$0.441700\pi$
$374$		−	5.53469e24i		−	0.103366i
$375$	−5.17620e25	−	2.53146e25i	−0.941235	−	0.460319i
$376$	9.10960e25			1.61295
$377$			8.38790e24i			0.144624i
$378$	2.97027e25	+	1.41981e26i	0.498744	+	2.38403i
$379$	−8.33310e25			−1.36274			−0.681372	−	0.731937i	$-0.738617\pi$
$379$	−8.33310e25			−1.36274			−0.681372	+	0.731937i	$0.738617\pi$
$380$			1.46830e26i			2.33873i
$381$	−5.05110e25	+	1.03282e26i	−0.783675	+	1.60242i
$382$	1.45693e26			2.20193
$383$		−	7.32188e25i		−	1.07804i	−0.842293	−	0.539020i	$-0.818795\pi$
$383$		−	7.32188e25i		−	1.07804i	0.842293	−	0.539020i	$-0.181205\pi$
$384$	−1.14665e26	−	5.60779e25i	−1.64482	−	0.804414i
$385$	−7.00902e24			−0.0979602
$386$		−	4.73602e25i		−	0.644972i
$387$	2.00464e25	+	2.57717e25i	0.266027	+	0.342006i
$388$	−1.80401e26			−2.33304
$389$		−	2.93969e25i		−	0.370515i	−0.982690	−	0.185258i	$-0.940688\pi$
$389$		−	2.93969e25i		−	0.370515i	0.982690	−	0.185258i	$-0.0593119\pi$
$390$	2.75867e25	−	5.64079e25i	0.338887	−	0.692937i
$391$	3.18795e25			0.381719
$392$		−	1.31289e26i		−	1.53239i
$393$	4.31559e25	+	2.11058e25i	0.491038	+	0.240146i
$394$	7.27870e25			0.807406
$395$			3.13572e25i			0.339130i
$396$	−9.84499e24	+	7.65786e24i	−0.103816	+	0.0807524i
$397$	6.04021e25			0.621079			0.310540	−	0.950560i	$-0.399490\pi$
$397$	6.04021e25			0.621079			0.310540	+	0.950560i	$0.399490\pi$
$398$			5.51091e25i			0.552577i
$399$	8.81004e25	−	1.80143e26i	0.861487	−	1.76152i
$400$	6.12729e24			0.0584344
$401$			1.40497e25i			0.130684i	0.997863	+	0.0653422i	$0.0208139\pi$
$401$			1.40497e25i			0.130684i	−0.997863	+	0.0653422i	$0.979186\pi$
$402$	−1.80852e26	−	8.84470e25i	−1.64082	−	0.802459i
$403$	5.18942e25			0.459270
$404$			2.35178e26i			2.03041i
$405$	−1.08460e26	−	2.75360e25i	−0.913524	−	0.231927i
$406$	−8.81361e25			−0.724258
$407$			6.68625e23i			0.00536091i
$408$	−6.72244e25	+	1.37457e26i	−0.525927	+	1.07539i
$409$	6.45037e25			0.492438			0.246219	−	0.969214i	$-0.420812\pi$
$409$	6.45037e25			0.492438			0.246219	+	0.969214i	$0.420812\pi$
$410$		−	1.81097e26i		−	1.34919i
$411$	9.99406e25	+	4.88768e25i	0.726647	+	0.355373i
$412$	1.91562e26			1.35937
$413$			2.65069e26i			1.83594i
$414$	−6.81908e25	−	8.76664e25i	−0.461022	−	0.592693i
$415$	−1.64267e26			−1.08410
$416$		−	3.91773e25i		−	0.252407i
$417$	−5.39939e25	+	1.10404e26i	−0.339613	+	0.694422i
$418$	2.66570e25			0.163700
$419$			4.01739e25i			0.240882i	0.992721	+	0.120441i	$0.0384308\pi$
$419$			4.01739e25i			0.240882i	−0.992721	+	0.120441i	$0.961569\pi$
$420$	3.83390e26	+	1.87500e26i	2.24464	+	1.09776i
$421$	1.40111e26			0.801032			0.400516	−	0.916290i	$-0.368831\pi$
$421$	1.40111e26			0.801032			0.400516	+	0.916290i	$0.368831\pi$
$422$		−	2.49114e26i		−	1.39083i
$423$	1.66855e26	−	1.29787e26i	0.909778	−	0.707665i
$424$	−2.10848e26			−1.12282
$425$			1.83682e25i			0.0955384i
$426$	−8.30652e25	+	1.69847e26i	−0.422010	+	0.862903i
$427$	−5.16308e26			−2.56230
$428$		−	7.41814e26i		−	3.59631i
$429$	−6.62424e24	−	3.23964e24i	−0.0313735	−	0.0153435i
$430$	1.48512e26			0.687192
$431$			5.96092e25i			0.269489i	0.990880	+	0.134744i	$0.0430213\pi$
$431$			5.96092e25i			0.269489i	−0.990880	+	0.134744i	$0.956979\pi$
$432$	1.15935e26	−	2.42539e25i	0.512127	−	0.107138i
$433$	5.13196e25			0.221516			0.110758	−	0.993847i	$-0.464672\pi$
$433$	5.13196e25			0.221516			0.110758	+	0.993847i	$0.464672\pi$
$434$			5.45279e26i			2.29997i
$435$	2.98711e25	−	6.10788e25i	0.123129	−	0.251766i
$436$	−1.45802e26			−0.587352
$437$			1.53543e26i			0.604526i
$438$	−2.42298e26	−	1.18498e26i	−0.932415	−	0.456005i
$439$	−2.57791e25			−0.0969667			−0.0484834	−	0.998824i	$-0.515439\pi$
$439$	−2.57791e25			−0.0969667			−0.0484834	+	0.998824i	$0.515439\pi$
$440$			2.57587e25i			0.0947104i
$441$	−1.87051e26	−	2.40474e26i	−0.672319	−	0.864337i
$442$	−1.99245e26			−0.700108
$443$		−	3.77780e26i		−	1.29778i	−0.760881	−	0.648892i	$-0.775233\pi$
$443$		−	3.77780e26i		−	1.29778i	0.760881	−	0.648892i	$-0.224767\pi$
$444$	1.78866e25	−	3.65735e25i	0.0600754	−	0.122839i
$445$	3.00125e26			0.985603
$446$			7.21407e26i			2.31650i
$447$	4.47970e26	+	2.19084e26i	1.40661	+	0.687915i
$448$	6.58291e26			2.02133
$449$		−	3.84982e26i		−	1.15605i	−0.816019	−	0.578025i	$-0.803824\pi$
$449$		−	3.84982e26i		−	1.15605i	0.816019	−	0.578025i	$-0.196176\pi$
$450$	5.05114e25	−	3.92899e25i	0.148342	−	0.115387i
$451$	−2.12671e25			−0.0610861
$452$			4.36919e26i			1.22749i
$453$	−4.45257e24	+	9.10437e24i	−0.0122357	+	0.0250189i
$454$	4.54043e26			1.22050
$455$			2.52320e26i			0.663496i
$456$	−6.62040e26	−	3.23776e26i	−1.70308	−	0.832907i
$457$	−6.06043e26			−1.52525			−0.762626	−	0.646840i	$-0.776090\pi$
$457$	−6.06043e26			−1.52525			−0.762626	+	0.646840i	$0.776090\pi$
$458$			1.08717e26i			0.267697i
$459$	7.27077e25	+	3.47547e26i	0.175167	+	0.837312i
$460$	−3.26778e26			−0.770326
$461$		−	7.78719e26i		−	1.79627i	−0.439720	−	0.898135i	$-0.644922\pi$
$461$		−	7.78719e26i		−	1.79627i	0.439720	−	0.898135i	$-0.355078\pi$
$462$	3.40406e25	−	6.96043e25i	0.0768382	−	0.157115i
$463$	9.05508e25			0.200024			0.100012	−	0.994986i	$-0.468112\pi$
$463$	9.05508e25			0.200024			0.100012	+	0.994986i	$0.468112\pi$
$464$			7.19680e25i			0.155582i
$465$	−3.77881e26	−	1.84806e26i	−0.799514	−	0.391009i
$466$	−7.67829e26			−1.59003
$467$			3.11428e26i			0.631232i	0.948887	+	0.315616i	$0.102211\pi$
$467$			3.11428e26i			0.631232i	−0.948887	+	0.315616i	$0.897789\pi$
$468$	2.75678e26	+	3.54413e26i	0.546945	+	0.703156i
$469$	8.08975e26			1.57111
$470$		−	9.61520e26i		−	1.82801i
$471$	−1.51095e26	+	3.08951e26i	−0.281216	+	0.575016i
$472$	9.74152e26			1.77503
$473$		−	1.74405e25i		−	0.0311134i
$474$	−3.11399e26	−	1.52292e26i	−0.543918	−	0.266008i
$475$	−8.84678e25			−0.151304
$476$		−	1.35422e27i		−	2.26788i
$477$	−3.86196e26	+	3.00400e26i	−0.633322	+	0.492625i
$478$	9.08421e26			1.45884
$479$		−	5.46288e26i		−	0.859145i	−0.903032	−	0.429572i	$-0.858664\pi$
$479$		−	5.46288e26i		−	0.859145i	0.903032	−	0.429572i	$-0.141336\pi$
$480$	−1.39519e26	+	2.85280e26i	−0.214892	+	0.439399i
$481$	2.40701e25			0.0363100
$482$			1.37310e27i			2.02876i
$483$	4.00917e26	+	1.96072e26i	0.580208	+	0.283756i
$484$	−1.28542e27			−1.82218
$485$			8.64544e26i			1.20052i
$486$	8.00208e26	−	9.43350e26i	1.08853	−	1.28325i
$487$	−8.57420e26			−1.14263			−0.571313	−	0.820732i	$-0.693566\pi$
$487$	−8.57420e26			−1.14263			−0.571313	+	0.820732i	$0.693566\pi$
$488$			1.89748e27i			2.47730i
$489$	2.26031e26	−	4.62176e26i	0.289121	−	0.591178i
$490$	−1.38576e27			−1.73671
$491$			1.28943e27i			1.58337i	0.610927	+	0.791687i	$0.290797\pi$
$491$			1.28943e27i			1.58337i	−0.610927	+	0.791687i	$0.709203\pi$
$492$	1.16330e27	+	5.68921e26i	1.39972	+	0.684543i
$493$	−2.15744e26			−0.254372
$494$		−	9.59635e26i		−	1.10876i
$495$	3.66991e25	+	4.71806e25i	0.0415531	+	0.0534210i
$496$	4.45251e26			0.494069
$497$		−	7.59750e26i		−	0.826241i
$498$	7.97793e26	−	1.63128e27i	0.850348	−	1.73874i
$499$	1.33039e27			1.38987			0.694934	−	0.719074i	$-0.255434\pi$
$499$	1.33039e27			1.38987			0.694934	+	0.719074i	$0.255434\pi$
$500$		−	1.87413e27i		−	1.91911i
$501$	−7.24285e26	−	3.54218e26i	−0.726996	−	0.355544i
$502$	5.01798e26			0.493732
$503$			4.10286e26i			0.395737i	0.980229	+	0.197868i	$0.0634019\pi$
$503$			4.10286e26i			0.395737i	−0.980229	+	0.197868i	$0.936598\pi$
$504$	−1.69083e27	+	1.31520e27i	−1.59880	+	1.24362i
$505$	1.12705e27			1.04480
$506$			5.93265e25i			0.0539192i
$507$	3.76405e26	−	7.69653e26i	0.335410	−	0.685828i
$508$	−3.73951e27			−3.26721
$509$			1.02446e27i			0.877642i	0.898575	+	0.438821i	$0.144604\pi$
$509$			1.02446e27i			0.877642i	−0.898575	+	0.438821i	$0.855396\pi$
$510$	1.45086e27	+	7.09554e26i	1.21877	+	0.596052i
$511$	1.08383e27			0.892799
$512$		−	1.24254e27i		−	1.00372i
$513$	−1.67391e27	+	3.50186e26i	−1.32605	+	0.277412i
$514$	−1.92082e26			−0.149230
$515$		−	9.18033e26i		−	0.699497i
$516$	−4.66555e26	+	9.53987e26i	−0.348663	+	0.712927i
$517$	−1.12916e26			−0.0827655
$518$			2.52917e26i			0.181836i
$519$	3.85492e26	+	1.88528e26i	0.271858	+	0.132954i
$520$	9.27298e26			0.641484
$521$		−	2.36226e27i		−	1.60307i	−0.597951	−	0.801533i	$-0.704018\pi$
$521$		−	2.36226e27i		−	1.60307i	0.597951	−	0.801533i	$-0.295982\pi$
$522$	4.61480e26	+	5.93281e26i	0.307219	+	0.394962i
$523$	−1.49169e27			−0.974229			−0.487114	−	0.873338i	$-0.661951\pi$
$523$	−1.49169e27			−0.974229			−0.487114	+	0.873338i	$0.661951\pi$
$524$			1.56254e27i			1.00119i
$525$	−1.12972e26	+	2.30999e26i	−0.0710196	+	0.145217i
$526$	1.37679e27			0.849200
$527$			1.33476e27i			0.807789i
$528$	−5.68358e25	−	2.77960e25i	−0.0337507	−	0.0165061i
$529$	1.37444e27			0.800882
$530$			2.22550e27i			1.27253i
$531$	1.78429e27	−	1.38790e27i	1.00120	−	0.778777i
$532$	6.52239e27			3.59162
$533$			7.65601e26i			0.413743i
$534$	−1.45761e27	+	2.98045e27i	−0.773089	+	1.58077i
$535$	−3.55503e27			−1.85057
$536$		−	2.97305e27i		−	1.51899i
$537$	−3.46272e27	−	1.69347e27i	−1.73650	−	0.849250i
$538$	−2.74380e27			−1.35061
$539$			1.62736e26i			0.0786316i
$540$	−7.45284e26	−	3.56250e27i	−0.353496	−	1.68973i
$541$	8.26319e26			0.384747			0.192373	−	0.981322i	$-0.438382\pi$
$541$	8.26319e26			0.384747			0.192373	+	0.981322i	$0.438382\pi$
$542$			3.07631e26i			0.140617i
$543$	4.44761e26	−	9.09422e26i	0.199585	−	0.408101i
$544$	1.00767e27			0.443946
$545$			6.98734e26i			0.302237i
$546$	−2.50571e27	−	1.22544e27i	−1.06415	−	0.520434i
$547$	−1.57172e27			−0.655393			−0.327697	−	0.944783i	$-0.606272\pi$
$547$	−1.57172e27			−0.655393			−0.327697	+	0.944783i	$0.606272\pi$
$548$			3.61853e27i			1.48158i
$549$	2.70339e27	+	3.47549e27i	1.08689	+	1.39731i
$550$	−3.41826e25			−0.0134952
$551$		−	1.03910e27i		−	0.402848i
$552$	7.20581e26	−	1.47340e27i	0.274342	−	0.560959i
$553$	1.39293e27			0.520808
$554$		−	6.15560e27i		−	2.26033i
$555$	−1.75273e26	−	8.57186e25i	−0.0632098	−	0.0309133i
$556$	−3.99736e27			−1.41588
$557$			2.34811e27i			0.816894i	0.912782	+	0.408447i	$0.133930\pi$
$557$			2.34811e27i			0.816894i	−0.912782	+	0.408447i	$0.866070\pi$
$558$	3.67050e27	−	2.85508e27i	1.25425	−	0.975609i
$559$	−6.27847e26			−0.210735
$560$			2.16490e27i			0.713769i
$561$	8.33263e25	−	1.70381e26i	0.0269869	−	0.0551814i
$562$	4.97963e26			0.158429
$563$		−	3.06788e27i		−	0.958860i	−0.877580	−	0.479430i	$-0.840844\pi$
$563$		−	3.06788e27i		−	0.958860i	0.877580	−	0.479430i	$-0.159156\pi$
$564$	6.17644e27	+	3.02064e27i	1.89647	+	0.927487i
$565$	2.09387e27			0.631634
$566$			4.51932e27i			1.33939i
$567$	−1.22319e27	+	4.81795e27i	−0.356174	+	1.40291i
$568$	−2.79214e27			−0.798830
$569$		−	6.57800e27i		−	1.84915i	−0.381004	−	0.924573i	$-0.624422\pi$
$569$		−	6.57800e27i		−	1.84915i	0.381004	−	0.924573i	$-0.375578\pi$
$570$	−3.41746e27	+	6.98784e27i	−0.943963	+	1.93017i
$571$	1.50493e27			0.408466			0.204233	−	0.978922i	$-0.434530\pi$
$571$	1.50493e27			0.408466			0.204233	+	0.978922i	$0.434530\pi$
$572$		−	2.39842e26i		−	0.0639684i
$573$	4.48503e27	+	2.19344e27i	1.17549	+	0.574884i
$574$	−8.04457e27			−2.07197
$575$		−	1.96890e26i		−	0.0498362i
$576$	−3.44680e27	−	4.43123e27i	−0.857417	−	1.10230i
$577$	1.00748e27			0.246309			0.123154	−	0.992388i	$-0.460699\pi$
$577$	1.00748e27			0.246309			0.123154	+	0.992388i	$0.460699\pi$
$578$			1.87843e27i			0.451354i
$579$	7.13022e26	−	1.45795e27i	0.168390	−	0.344315i
$580$	2.21147e27			0.513334
$581$			7.29695e27i			1.66487i
$582$	−8.58552e27	−	4.19882e27i	−1.92547	−	0.941667i
$583$	2.61351e26			0.0576153
$584$		−	3.98318e27i		−	0.863180i
$585$	1.69847e27	−	1.32115e27i	0.361826	−	0.281444i
$586$	1.46437e28			3.06673
$587$		−	2.27974e27i		−	0.469358i	−0.972073	−	0.234679i	$-0.924596\pi$
$587$		−	2.27974e27i		−	0.469358i	0.972073	−	0.234679i	$-0.0754039\pi$
$588$	4.35340e27	−	8.90160e27i	0.881161	−	1.80175i
$589$	−6.42868e27			−1.27929
$590$		−	1.02822e28i		−	2.01171i
$591$	2.24069e27	+	1.09583e27i	0.431030	+	0.210799i
$592$	2.06521e26			0.0390613
$593$			5.61084e27i			1.04347i	0.853107	+	0.521736i	$0.174716\pi$
$593$			5.61084e27i			1.04347i	−0.853107	+	0.521736i	$0.825284\pi$
$594$	−6.46772e26	+	1.35306e26i	−0.118273	+	0.0247430i
$595$	−6.48989e27			−1.16699
$596$			1.62195e28i			2.86798i
$597$	−8.29683e26	+	1.69649e27i	−0.144268	+	0.294991i
$598$	2.13572e27			0.365201
$599$		−	6.23141e27i		−	1.04790i	−0.851750	−	0.523948i	$-0.824459\pi$
$599$		−	6.23141e27i		−	1.04790i	0.851750	−	0.523948i	$-0.175541\pi$
$600$	8.48942e26	+	4.15182e26i	0.140399	+	0.0686635i
$601$	−1.05722e28			−1.71957			−0.859786	−	0.510654i	$-0.829403\pi$
$601$	−1.05722e28			−1.71957			−0.859786	+	0.510654i	$0.829403\pi$
$602$		−	6.59712e27i		−	1.05533i
$603$	−4.23578e27	−	5.44555e27i	−0.666439	−	0.856778i
$604$	−3.29640e26			−0.0510117
$605$			6.16017e27i			0.937646i
$606$	−5.47375e27	+	1.11924e28i	−0.819519	+	1.67571i
$607$	4.24398e27			0.625009			0.312505	−	0.949916i	$-0.398832\pi$
$607$	4.24398e27			0.625009			0.312505	+	0.949916i	$0.398832\pi$
$608$			4.85331e27i			0.703075i
$609$	−2.71320e27	−	1.32691e27i	−0.386642	−	0.189091i
$610$	2.00279e28			2.80761
$611$			4.06490e27i			0.560580i
$612$	−9.11581e27	+	7.09068e27i	−1.23675	+	0.961996i
$613$	1.43883e28			1.92045			0.960226	−	0.279224i	$-0.0900772\pi$
$613$	1.43883e28			1.92045			0.960226	+	0.279224i	$0.0900772\pi$
$614$		−	1.08630e27i		−	0.142648i
$615$	2.72647e27	−	5.57493e27i	0.352248	−	0.720258i
$616$	1.14424e27			0.145448
$617$		−	2.65553e27i		−	0.332124i	−0.986115	−	0.166062i	$-0.946895\pi$
$617$		−	2.65553e27i		−	0.332124i	0.986115	−	0.166062i	$-0.0531051\pi$
$618$	9.11670e27	+	4.45860e27i	1.12190	+	0.548673i
$619$	8.61725e27			1.04343			0.521714	−	0.853121i	$-0.325293\pi$
$619$	8.61725e27			1.04343			0.521714	+	0.853121i	$0.325293\pi$
$620$		−	1.36819e28i		−	1.63015i
$621$	−7.79356e26	−	3.72537e27i	−0.0913735	−	0.436771i
$622$	−2.34039e28			−2.70013
$623$		−	1.33320e28i		−	1.51361i
$624$	−1.00064e27	+	2.04605e27i	−0.111797	+	0.228597i
$625$	−7.96575e27			−0.875843
$626$			4.45159e27i			0.481695i
$627$	8.20615e26	+	4.01329e26i	0.0873904	+	0.0427390i
$628$	−1.11861e28			−1.17242
$629$			6.19103e26i			0.0638640i
$630$	1.38820e28	+	1.78467e28i	1.40944	+	1.81198i
$631$	−5.34392e27			−0.534031			−0.267016	−	0.963692i	$-0.586038\pi$
$631$	−5.34392e27			−0.534031			−0.267016	+	0.963692i	$0.586038\pi$
$632$		−	5.11913e27i		−	0.503530i
$633$	3.75048e27	−	7.66877e27i	0.363119	−	0.742487i
$634$	−2.84104e27			−0.270760
$635$			1.79210e28i			1.68123i
$636$	−1.42958e28	−	6.99146e27i	−1.32019	−	0.645649i
$637$	5.85841e27			0.532580
$638$		−	4.01491e26i		−	0.0359310i
$639$	−5.11419e27	+	3.97804e27i	−0.450576	+	0.350478i
$640$	−1.98962e28			−1.72572
$641$		−	2.01527e28i		−	1.72089i	−0.509546	−	0.860444i	$-0.670186\pi$
$641$		−	2.01527e28i		−	1.72089i	0.509546	−	0.860444i	$-0.329814\pi$
$642$	1.72657e28	−	3.53039e28i	1.45155	−	2.96806i
$643$	−1.36349e27			−0.112861			−0.0564303	−	0.998407i	$-0.517972\pi$
$643$	−1.36349e27			−0.112861			−0.0564303	+	0.998407i	$0.517972\pi$
$644$			1.45159e28i			1.18300i
$645$	4.57184e27	+	2.23590e27i	0.366854	+	0.179413i
$646$	2.46826e28			1.95014
$647$			8.87248e27i			0.690243i	0.938558	+	0.345122i	$0.112162\pi$
$647$			8.87248e27i			0.690243i	−0.938558	+	0.345122i	$0.887838\pi$
$648$	1.77064e28	+	4.49531e27i	1.35637	+	0.344357i
$649$	−1.20748e27			−0.0910825
$650$			1.23055e27i			0.0914042i
$651$	−8.20933e27	+	1.67860e28i	−0.600479	+	1.22783i
$652$	1.67339e28			1.20537
$653$			1.50965e28i			1.07089i	0.844570	+	0.535445i	$0.179856\pi$
$653$			1.50965e28i			1.07089i	−0.844570	+	0.535445i	$0.820144\pi$
$654$	−6.93891e27	−	3.39353e27i	−0.484746	−	0.237069i
$655$	7.48822e27			0.515188
$656$			6.56884e27i			0.445093i
$657$	−5.67494e27	−	7.29574e27i	−0.378711	−	0.486873i
$658$	−4.27120e28			−2.80731
$659$			2.64396e28i			1.71159i	0.517314	+	0.855795i	$0.326932\pi$
$659$			2.64396e28i			1.71159i	−0.517314	+	0.855795i	$0.673068\pi$
$660$	−8.54129e26	+	1.74648e27i	−0.0544608	+	0.111358i
$661$	7.90201e27			0.496275			0.248138	−	0.968725i	$-0.420181\pi$
$661$	7.90201e27			0.496275			0.248138	+	0.968725i	$0.420181\pi$
$662$		−	1.91303e27i		−	0.118343i
$663$	−6.13361e27	−	2.99969e27i	−0.373750	−	0.182785i
$664$	2.68169e28			1.60964
$665$		−	3.12576e28i		−	1.84816i
$666$	1.70249e27	−	1.32427e27i	0.0991613	−	0.0771320i
$667$	2.31257e27			0.132689
$668$		−	2.62240e28i		−	1.48229i
$669$	−1.08610e28	+	2.22079e28i	−0.604795	+	1.23665i
$670$	−3.13806e28			−1.72152
$671$		−	2.35197e27i		−	0.127118i
$672$	1.26725e28	+	6.19760e27i	0.674792	+	0.330013i
$673$	−3.04590e28			−1.59796			−0.798978	−	0.601361i	$-0.794625\pi$
$673$	−3.04590e28			−1.59796			−0.798978	+	0.601361i	$0.794625\pi$
$674$		−	2.66346e28i		−	1.37673i
$675$	2.14647e27	−	4.49047e26i	0.109317	−	0.0228694i
$676$	2.78666e28			1.39836
$677$		−	1.31219e28i		−	0.648800i	−0.945920	−	0.324400i	$-0.894838\pi$
$677$		−	1.31219e28i		−	0.648800i	0.945920	−	0.324400i	$-0.105162\pi$
$678$	−1.01693e28	+	2.07936e28i	−0.495442	+	1.01305i
$679$	3.84042e28			1.84366
$680$			2.38509e28i			1.12828i
$681$	1.39774e28	+	6.83574e27i	0.651559	+	0.318651i
$682$	−2.48394e27			−0.114103
$683$		−	1.77441e28i		−	0.803243i	−0.915806	−	0.401622i	$-0.868447\pi$
$683$		−	1.77441e28i		−	0.803243i	0.915806	−	0.401622i	$-0.131553\pi$
$684$	−3.41512e28	−	4.39050e28i	−1.52351	−	1.95863i
$685$	1.73412e28			0.762385
$686$			5.34214e27i			0.231459i
$687$	−1.63677e27	+	3.34678e27i	−0.0698909	+	0.142909i
$688$	−5.38691e27			−0.226702
$689$		−	9.40846e27i		−	0.390235i
$690$	−1.55518e28	−	7.60574e27i	−0.635755	−	0.310921i
$691$	2.09145e28			0.842687			0.421344	−	0.906901i	$-0.361559\pi$
$691$	2.09145e28			0.842687			0.421344	+	0.906901i	$0.361559\pi$
$692$			1.39574e28i			0.554299i
$693$	2.09583e27	−	1.63022e27i	0.0820395	−	0.0638139i
$694$	1.70579e26			0.00658159
$695$			1.91568e28i			0.728575i
$696$	−4.87652e27	+	9.97124e27i	−0.182817	+	0.373815i
$697$	−1.96919e28			−0.727713
$698$			7.15013e28i			2.60471i
$699$	−2.36370e28	−	1.15599e28i	−0.848830	−	0.415128i
$700$	−8.36374e27			−0.296088
$701$			2.38448e28i			0.832174i	0.909325	+	0.416087i	$0.136599\pi$
$701$			2.38448e28i			0.832174i	−0.909325	+	0.416087i	$0.863401\pi$
$702$	4.87094e27	+	2.32834e28i	0.167587	+	0.801079i
$703$	−2.98182e27			−0.101141
$704$			2.99875e27i			0.100280i
$705$	1.44760e28	−	2.95996e28i	0.477261	−	0.975877i
$706$	6.42517e28			2.08852
$707$		−	5.00653e28i		−	1.60451i
$708$	6.60488e28	+	3.23017e28i	2.08705	+	1.02069i
$709$	−4.96631e28			−1.54729			−0.773645	−	0.633619i	$-0.781569\pi$
$709$	−4.96631e28			−1.54729			−0.773645	+	0.633619i	$0.781569\pi$
$710$			2.94711e28i			0.905342i
$711$	−7.29337e27	−	9.37640e27i	−0.220919	−	0.284014i
$712$	−4.89960e28			−1.46339
$713$		−	1.43074e28i		−	0.421371i
$714$	3.15194e28	−	6.44491e28i	0.915367	−	1.87169i
$715$	−1.14941e27			−0.0329165
$716$		−	1.25374e29i		−	3.54060i
$717$	2.79650e28	+	1.36765e28i	0.778796	+	0.380877i
$718$	−2.10879e28			−0.579146
$719$			5.28624e28i			1.43172i	0.698245	+	0.715859i	$0.253965\pi$
$719$			5.28624e28i			1.43172i	−0.698245	+	0.715859i	$0.746035\pi$
$720$	1.45729e28	−	1.13354e28i	0.389242	−	0.302769i
$721$	−4.07803e28			−1.07423
$722$			5.41078e28i			1.40569i
$723$	−2.06724e28	+	4.22697e28i	−0.529672	+	1.08304i
$724$	3.29272e28			0.832089
$725$			1.33245e27i			0.0332101i
$726$	−6.11747e28	−	2.99180e28i	−1.50385	−	0.735472i
$727$	4.61209e28			1.11829			0.559144	−	0.829071i	$-0.311130\pi$
$727$	4.61209e28			1.11829			0.559144	+	0.829071i	$0.311130\pi$
$728$		−	4.11918e28i		−	0.985138i
$729$	3.88362e28	−	1.69929e28i	0.916139	−	0.400861i
$730$	−4.20425e28			−0.978272
$731$		−	1.61488e28i		−	0.370651i
$732$	−6.29181e28	+	1.28651e29i	−1.42451	+	2.91276i
$733$	−4.87641e28			−1.08908			−0.544541	−	0.838734i	$-0.683296\pi$
$733$	−4.87641e28			−1.08908			−0.544541	+	0.838734i	$0.683296\pi$
$734$		−	6.02075e28i		−	1.32645i
$735$	−4.26596e28	−	2.08630e28i	−0.927135	−	0.453423i
$736$	−1.08013e28			−0.231578
$737$			3.68517e27i			0.0779439i
$738$	4.21213e28	+	5.41514e28i	0.878897	+	1.12992i
$739$	2.74292e27			0.0564636			0.0282318	−	0.999601i	$-0.491012\pi$
$739$	2.74292e27			0.0564636			0.0282318	+	0.999601i	$0.491012\pi$
$740$		−	6.34606e27i		−	0.128880i
$741$	1.44476e28	−	2.95416e28i	0.289476	−	0.591905i
$742$	9.88597e28			1.95425
$743$		−	2.97017e28i		−	0.579287i	−0.957135	−	0.289643i	$-0.906463\pi$
$743$		−	2.97017e28i		−	0.579287i	0.957135	−	0.289643i	$-0.0935367\pi$
$744$	6.16899e28	+	3.01700e28i	1.18709	+	0.580558i
$745$	7.77297e28			1.47579
$746$			3.27208e28i			0.612965i
$747$	4.91188e28	−	3.82068e28i	0.907909	−	0.706211i
$748$	6.16895e27			0.112511
$749$			1.57919e29i			2.84195i
$750$	4.36203e28	−	8.91925e28i	0.774598	−	1.58386i
$751$	−9.65151e28			−1.69120			−0.845601	−	0.533815i	$-0.820758\pi$
$751$	−9.65151e28			−1.69120			−0.845601	+	0.533815i	$0.820758\pi$
$752$			3.48767e28i			0.603055i
$753$	1.54475e28	+	7.55471e27i	0.263577	+	0.128904i
$754$	−1.44534e28			−0.243365
$755$			1.57975e27i			0.0262493i
$756$	−1.58251e29	+	3.31065e28i	−2.59495	+	0.542870i
$757$	7.99456e28			1.29371			0.646854	−	0.762614i	$-0.276084\pi$
$757$	7.99456e28			1.29371			0.646854	+	0.762614i	$0.276084\pi$
$758$		−	1.43590e29i		−	2.29315i
$759$	−8.93178e26	+	1.82632e27i	−0.0140773	+	0.0287845i
$760$	−1.14874e29			−1.78684
$761$			1.43886e28i			0.220888i	0.993882	+	0.110444i	$0.0352274\pi$
$761$			1.43886e28i			0.220888i	−0.993882	+	0.110444i	$0.964773\pi$
$762$	−1.77968e29	−	8.70369e28i	−2.69645	−	1.31872i
$763$	3.10387e28			0.464150
$764$			1.62389e29i			2.39675i
$765$	3.39810e28	+	4.36862e28i	0.495019	+	0.636399i
$766$	1.26165e29			1.81406
$767$			4.34687e28i			0.616912i
$768$	5.28320e28	−	1.08028e29i	0.740090	−	1.51330i
$769$	−7.56135e28			−1.04553			−0.522764	−	0.852477i	$-0.675099\pi$
$769$	−7.56135e28			−1.04553			−0.522764	+	0.852477i	$0.675099\pi$
$770$		−	1.20774e28i		−	0.164842i
$771$	−5.91310e27	−	2.89185e27i	−0.0796657	−	0.0389612i
$772$	5.27876e28			0.702035
$773$		−	1.23841e29i		−	1.62581i	−0.582397	−	0.812905i	$-0.697885\pi$
$773$		−	1.23841e29i		−	1.62581i	0.582397	−	0.812905i	$-0.302115\pi$
$774$	−4.44080e28	+	3.45424e28i	−0.575508	+	0.447655i
$775$	8.24357e27			0.105463
$776$		−	1.41139e29i		−	1.78250i
$777$	−3.80774e27	+	7.78585e27i	−0.0474741	+	0.0970724i
$778$	5.06547e28			0.623481
$779$		−	9.48431e28i		−	1.15247i
$780$	6.28720e28	+	3.07481e28i	0.754243	+	0.368869i
$781$	3.46093e27			0.0409904
$782$			5.49325e28i			0.642335i
$783$	5.27428e27	+	2.52114e28i	0.0608900	+	0.291058i
$784$	5.02650e28			0.572935
$785$			5.36077e28i			0.603296i
$786$	−3.63679e28	+	7.43631e28i	−0.404104	+	0.826289i
$787$	−2.58589e28			−0.283703			−0.141851	−	0.989888i	$-0.545305\pi$
$787$	−2.58589e28			−0.283703			−0.141851	+	0.989888i	$0.545305\pi$
$788$			8.11282e28i			0.878840i
$789$	4.23834e28	+	2.07279e28i	0.453342	+	0.221711i
$790$	−5.40325e28			−0.570669
$791$		−	9.30125e28i		−	0.970011i
$792$	−5.99121e27	−	7.70234e27i	−0.0616968	−	0.0793178i
$793$	−8.46694e28			−0.860983
$794$			1.04081e29i			1.04512i
$795$	−3.35055e28	+	6.85103e28i	−0.332235	+	0.679336i
$796$	−6.14245e28			−0.601465
$797$		−	1.00874e28i		−	0.0975428i	−0.998810	−	0.0487714i	$-0.984469\pi$
$797$		−	1.00874e28i		−	0.0975428i	0.998810	−	0.0487714i	$-0.0155306\pi$
$798$	3.10409e29	+	1.51808e29i	2.96419	+	1.44966i
$799$	−1.04553e29			−0.985977
$800$		−	6.22345e27i		−	0.0579604i
$801$	−8.97430e28	+	6.98060e28i	−0.825421	+	0.642048i
$802$	−2.42095e28			−0.219908
$803$			4.93725e27i			0.0442924i
$804$	9.85828e28	−	2.01577e29i	0.873455	−	1.78599i
$805$	6.95654e28			0.608743
$806$			8.94203e28i			0.772833i
$807$	−8.44658e28	−	4.13087e28i	−0.721017	−	0.352620i
$808$	−1.83994e29			−1.55128
$809$		−	6.71792e28i		−	0.559435i	−0.960082	−	0.279717i	$-0.909759\pi$
$809$		−	6.71792e28i		−	0.559435i	0.960082	−	0.279717i	$-0.0902408\pi$
$810$	4.74480e28	−	1.86891e29i	0.390273	−	1.53723i
$811$	1.71168e29			1.39063			0.695317	−	0.718703i	$-0.255264\pi$
$811$	1.71168e29			1.39063			0.695317	+	0.718703i	$0.255264\pi$
$812$		−	9.82363e28i		−	0.788336i
$813$	−4.63147e27	+	9.47018e27i	−0.0367125	+	0.0750677i
$814$	−1.15213e27			−0.00902103
$815$		−	8.01946e28i		−	0.620253i
$816$	−5.26262e28	−	2.57373e28i	−0.402069	−	0.196635i
$817$	7.77781e28			0.586998
$818$			1.11148e29i			0.828647i
$819$	−5.86871e28	−	7.54484e28i	−0.432219	−	0.555663i
$820$	2.01850e29			1.46856
$821$			2.49470e28i			0.179302i	0.995973	+	0.0896512i	$0.0285752\pi$
$821$			2.49470e28i			0.179302i	−0.995973	+	0.0896512i	$0.971425\pi$
$822$	−8.42210e28	+	1.72210e29i	−0.598001	+	1.22276i
$823$	7.30174e28			0.512186			0.256093	−	0.966652i	$-0.417565\pi$
$823$	7.30174e28			0.512186			0.256093	+	0.966652i	$0.417565\pi$
$824$			1.49871e29i			1.03859i
$825$	−1.05228e27	−	5.14628e26i	−0.00720433	−	0.00352334i
$826$	−4.56748e29			−3.08942
$827$		−	3.04135e28i		−	0.203241i	−0.994823	−	0.101621i	$-0.967597\pi$
$827$		−	3.04135e28i		−	0.203241i	0.994823	−	0.101621i	$-0.0324027\pi$
$828$	9.77127e28	−	7.60052e28i	0.645131	−	0.501811i
$829$	−8.88692e28			−0.579704			−0.289852	−	0.957072i	$-0.593606\pi$
$829$	−8.88692e28			−0.579704			−0.289852	+	0.957072i	$0.593606\pi$
$830$		−	2.83053e29i		−	1.82426i
$831$	9.26743e28	−	1.89495e29i	0.590132	−	1.20667i
$832$	1.07953e29			0.679206
$833$			1.50683e29i			0.936731i
$834$	−1.90240e29	−	9.30384e28i	−1.16853	−	0.571481i
$835$	−1.25675e29			−0.762751
$836$			2.97118e28i			0.178183i
$837$	1.55978e29	−	3.26308e28i	0.924288	−	0.193363i
$838$	−6.92248e28			−0.405342
$839$			2.68880e29i			1.55575i	0.628422	+	0.777873i	$0.283701\pi$
$839$			2.68880e29i			1.55575i	−0.628422	+	0.777873i	$0.716299\pi$
$840$	−1.46693e29	+	2.99949e29i	−0.838717	+	1.71496i
$841$	1.61344e29			0.911578
$842$			2.41428e29i			1.34793i
$843$	1.53294e28	+	7.49697e27i	0.0845764	+	0.0413628i
$844$	2.77661e29			1.51388
$845$		−	1.33547e29i		−	0.719558i
$846$	2.23640e29	+	2.87512e29i	1.19082	+	1.53092i
$847$	2.73643e29			1.43996
$848$		−	8.07244e28i		−	0.419804i
$849$	−6.80396e28	+	1.39124e29i	−0.349691	+	0.715029i
$850$	−3.16508e28			−0.160767
$851$		−	6.63619e27i		−	0.0333137i
$852$	−1.89311e29	−	9.25842e28i	−0.939248	−	0.459347i
$853$	−2.32359e29			−1.13938			−0.569690	−	0.821859i	$-0.692937\pi$
$853$	−2.32359e29			−1.13938			−0.569690	+	0.821859i	$0.692937\pi$
$854$		−	8.89665e29i		−	4.31170i
$855$	−2.10408e29	+	1.63664e29i	−1.00786	+	0.783958i
$856$	5.80366e29			2.74767
$857$		−	8.94927e28i		−	0.418774i	−0.977833	−	0.209387i	$-0.932853\pi$
$857$		−	8.94927e28i		−	0.418774i	0.977833	−	0.209387i	$-0.0671468\pi$
$858$	5.58231e27	−	1.14144e28i	0.0258191	−	0.0527935i
$859$	8.08812e28			0.369756			0.184878	−	0.982761i	$-0.440811\pi$
$859$	8.08812e28			0.369756			0.184878	+	0.982761i	$0.440811\pi$
$860$			1.65531e29i			0.747990i
$861$	−2.47646e29	−	1.21113e29i	−1.10611	−	0.540954i
$862$	−1.02714e29			−0.453480
$863$			2.86782e29i			1.25154i	0.780009	+	0.625768i	$0.215214\pi$
$863$			2.86782e29i			1.25154i	−0.780009	+	0.625768i	$0.784786\pi$
$864$	−2.46345e28	−	1.17755e29i	−0.106269	−	0.507973i
$865$	6.68888e28			0.285228
$866$			8.84303e28i			0.372754i
$867$	−2.82803e28	+	5.78261e28i	−0.117840	+	0.240953i
$868$	−6.07767e29			−2.50345
$869$			6.34529e27i			0.0258377i
$870$	1.05247e29	+	5.14717e28i	0.423658	+	0.207194i
$871$	1.32664e29			0.527923
$872$		−	1.14070e29i		−	0.448752i
$873$	−2.01084e29	−	2.58515e29i	−0.782051	−	1.00541i
$874$	−2.64574e29			−1.01726
$875$			3.98970e29i			1.51656i
$876$	1.32078e29	−	2.70065e29i	0.496350	−	1.01491i
$877$	−4.05215e29			−1.50553			−0.752766	−	0.658288i	$-0.771281\pi$
$877$	−4.05215e29			−1.50553			−0.752766	+	0.658288i	$0.771281\pi$
$878$		−	4.44207e28i		−	0.163170i
$879$	4.50795e29	+	2.20465e29i	1.63716	+	0.800666i
$880$	−9.86189e27			−0.0354106
$881$			1.61228e29i			0.572377i	0.958173	+	0.286188i	$0.0923883\pi$
$881$			1.61228e29i			0.572377i	−0.958173	+	0.286188i	$0.907612\pi$
$882$	4.14368e29	−	3.22314e29i	1.45446	−	1.13134i
$883$	−1.76808e29			−0.613613			−0.306806	−	0.951772i	$-0.599260\pi$
$883$	−1.76808e29			−0.613613			−0.306806	+	0.951772i	$0.599260\pi$
$884$		−	2.22078e29i		−	0.762050i
$885$	1.54801e29	−	3.16529e29i	0.525220	−	1.07394i
$886$	6.50964e29			2.18383
$887$		−	2.99748e29i		−	0.994305i	−0.867663	−	0.497153i	$-0.834379\pi$
$887$		−	2.99748e29i		−	0.994305i	0.867663	−	0.497153i	$-0.165621\pi$
$888$	2.86136e28	+	1.39937e28i	0.0938520	+	0.0458991i
$889$	7.96077e29			2.58189
$890$			5.17154e29i			1.65852i
$891$	−2.19475e28	−	5.57204e27i	−0.0695996	−	0.0176700i
$892$	−8.04078e29			−2.52145
$893$		−	5.03562e29i		−	1.56149i
$894$	−3.77509e29	+	7.71910e29i	−1.15758	+	2.36696i
$895$	−6.00836e29			−1.82190
$896$			8.83814e29i			2.65021i
$897$	6.57464e28	+	3.21538e28i	0.194961	+	0.0953473i
$898$	6.63373e29			1.94533
$899$			9.68248e28i			0.280795i
$900$	4.37925e28	+	5.62998e28i	0.125596	+	0.161466i
$901$	2.41994e29			0.686366
$902$		−	3.66459e28i		−	0.102792i
$903$	9.93215e28	−	2.03087e29i	0.275528	−	0.563385i
$904$	−3.41829e29			−0.937830
$905$		−	1.57799e29i		−	0.428172i
$906$	−1.56880e28	−	7.67234e27i	−0.0421003	−	0.0205895i
$907$	−4.03540e29			−1.07106			−0.535530	−	0.844516i	$-0.679888\pi$
$907$	−4.03540e29			−1.07106			−0.535530	+	0.844516i	$0.679888\pi$
$908$			5.06075e29i			1.32848i
$909$	−3.37010e29	+	2.62141e29i	−0.874993	+	0.680607i
$910$	−4.34780e29			−1.11649
$911$		−	4.68907e29i		−	1.19098i	−0.803365	−	0.595488i	$-0.796959\pi$
$911$		−	4.68907e29i		−	1.19098i	0.803365	−	0.595488i	$-0.203041\pi$
$912$	1.23960e29	−	2.53466e29i	0.311410	−	0.636755i
$913$	−3.32402e28			−0.0825954
$914$		−	1.04429e30i		−	2.56660i
$915$	6.16543e29	+	3.01525e29i	1.49883	+	0.733015i
$916$	−1.21176e29			−0.291382
$917$		−	3.32637e29i		−	0.791183i
$918$	−5.98869e29	+	1.25285e29i	−1.40898	+	0.294762i
$919$	3.01938e29			0.702688			0.351344	−	0.936246i	$-0.385725\pi$
$919$	3.01938e29			0.702688			0.351344	+	0.936246i	$0.385725\pi$
$920$		−	2.55658e29i		−	0.588548i
$921$	1.63545e28	−	3.34408e28i	0.0372427	−	0.0761517i
$922$	1.34183e30			3.02266
$923$		−	1.24591e29i		−	0.277633i
$924$	7.75808e28	+	3.79416e28i	0.171015	+	0.0836364i
$925$	3.82362e27			0.00833791
$926$			1.56031e29i			0.336589i
$927$	2.13525e29	+	2.74509e29i	0.455671	+	0.585813i
$928$	7.30975e28			0.154320
$929$			6.16284e29i			1.28713i	0.765390	+	0.643567i	$0.222546\pi$
$929$			6.16284e29i			1.28713i	−0.765390	+	0.643567i	$0.777454\pi$
$930$	3.18444e29	−	6.51138e29i	0.657967	−	1.34538i
$931$	−7.25743e29			−1.48349
$932$		−	8.55820e29i		−	1.73071i
$933$	−7.20470e29	−	3.52352e29i	−1.44145	−	0.704953i
$934$	−5.36631e29			−1.06220
$935$		−	2.95637e28i		−	0.0578953i
$936$	−2.77279e29	+	2.15680e29i	−0.537228	+	0.417880i
$937$	−6.87004e29			−1.31693			−0.658466	−	0.752610i	$-0.728794\pi$
$937$	−6.87004e29			−1.31693			−0.658466	+	0.752610i	$0.728794\pi$
$938$			1.39397e30i			2.64377i
$939$	−6.70200e28	+	1.37039e29i	−0.125762	+	0.257151i
$940$	1.07171e30			1.98975
$941$			4.31884e28i			0.0793360i	0.999213	+	0.0396680i	$0.0126300\pi$
$941$			4.31884e28i			0.0793360i	−0.999213	+	0.0396680i	$0.987370\pi$
$942$	−5.32361e29	−	2.60356e29i	−0.967603	−	0.473215i
$943$	2.11078e29			0.379600
$944$			3.72960e29i			0.663656i
$945$	1.58658e29	+	7.58395e29i	0.279347	+	1.33530i
$946$	3.00522e28			0.0523558
$947$			4.65994e29i			0.803305i	0.915792	+	0.401652i	$0.131564\pi$
$947$			4.65994e29i			0.803305i	−0.915792	+	0.401652i	$0.868436\pi$
$948$	1.69744e29	−	3.47084e29i	0.289543	−	0.592041i
$949$	1.77738e29			0.299997
$950$		−	1.52441e29i		−	0.254605i
$951$	−8.74591e28	−	4.27726e28i	−0.144544	−	0.0706904i
$952$	1.05949e30			1.73271
$953$			1.62814e29i			0.263490i	0.991284	+	0.131745i	$0.0420579\pi$
$953$			1.62814e29i			0.263490i	−0.991284	+	0.131745i	$0.957942\pi$
$954$	−5.17628e29	−	6.65466e29i	−0.828961	−	1.06572i
$955$	7.78223e29			1.23330
$956$			1.01252e30i			1.58791i
$957$	6.04456e27	−	1.23596e28i	0.00938092	−	0.0191816i
$958$	9.41324e29			1.44572
$959$		−	7.70321e29i		−	1.17081i
$960$	−7.86089e29	−	3.84444e29i	−1.18239	−	0.578256i
$961$	−7.27560e28			−0.108302
$962$			4.14758e28i			0.0611004i
$963$	1.06302e30	−	8.26863e29i	1.54981	−	1.20551i
$964$	−1.53045e30			−2.20825
$965$		−	2.52976e29i		−	0.361249i
$966$	−3.37857e29	+	6.90832e29i	−0.477487	+	0.976340i
$967$	−7.54565e29			−1.05544			−0.527718	−	0.849420i	$-0.676952\pi$
$967$	−7.54565e29			−1.05544			−0.527718	+	0.849420i	$0.676952\pi$
$968$		−	1.00566e30i		−	1.39219i
$969$	7.59835e29	+	3.71604e29i	1.04107	+	0.509146i
$970$	−1.48972e30			−2.02017
$971$			3.26311e29i			0.437964i	0.975729	+	0.218982i	$0.0702737\pi$
$971$			3.26311e29i			0.437964i	−0.975729	+	0.218982i	$0.929726\pi$
$972$	1.05146e30	+	8.91910e29i	1.39678	+	1.18484i
$973$	8.50969e29			1.11888
$974$		−	1.47744e30i		−	1.92274i
$975$	−1.85263e28	+	3.78816e28i	−0.0238640	+	0.0487957i
$976$	−7.26461e29			−0.926220
$977$			1.41414e30i			1.78463i	0.451418	+	0.892313i	$0.350918\pi$
$977$			1.41414e30i			1.78463i	−0.451418	+	0.892313i	$0.649082\pi$
$978$	7.96388e29	+	3.89480e29i	0.994800	+	0.486515i
$979$	6.07318e28			0.0750912
$980$		−	1.54456e30i		−	1.89036i
$981$	−1.62518e29	−	2.08935e29i	−0.196885	−	0.253116i
$982$	−2.22185e30			−2.66441
$983$		−	5.68076e29i		−	0.674329i	−0.941446	−	0.337164i	$-0.890532\pi$
$983$		−	5.68076e29i		−	0.674329i	0.941446	−	0.337164i	$-0.109468\pi$
$984$	−4.45101e29	+	9.10119e29i	−0.523008	+	1.06942i
$985$	3.88795e29			0.452229
$986$		−	3.71755e29i		−	0.428043i
$987$	−1.31486e30	−	6.43041e29i	−1.49867	−	0.732938i
$988$	1.06961e30			1.20685
$989$			1.73099e29i			0.193345i
$990$	−8.12982e28	+	6.32373e28i	−0.0898937	+	0.0699232i
$991$	−7.24543e29			−0.793100			−0.396550	−	0.918013i	$-0.629793\pi$
$991$	−7.24543e29			−0.793100			−0.396550	+	0.918013i	$0.629793\pi$
$992$		−	4.52239e29i		−	0.490062i
$993$	2.88012e28	−	5.88911e28i	0.0308971	−	0.0631767i
$994$	1.30915e30			1.39035
$995$			2.94367e29i			0.309499i
$996$	1.81822e30	+	8.89217e29i	1.89258	+	0.925581i
$997$	1.10479e30			1.13848			0.569241	−	0.822170i	$-0.307237\pi$
$997$	1.10479e30			1.13848			0.569241	+	0.822170i	$0.307237\pi$
$998$			2.29243e30i			2.33879i
$999$	7.23471e28	−	1.51352e28i	0.0730745	−	0.0152874i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.21.b.a.2.6	yes	6
3.2	odd	2	inner	3.21.b.a.2.1	✓	6
4.3	odd	2		48.21.e.c.17.3		6
12.11	even	2		48.21.e.c.17.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.21.b.a.2.1	✓	6	3.2	odd	2	inner
3.21.b.a.2.6	yes	6	1.1	even	1	trivial
48.21.e.c.17.3		6	4.3	odd	2
48.21.e.c.17.4		6	12.11	even	2

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:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1723.13i q^{2} +(-25942.2 + 53045.1i) q^{3} -1.92059e6 q^{4} +9.20415e6i q^{5} +(-9.14036e7 - 4.47017e7i) q^{6} +4.08861e8 q^{7} -1.50260e9i q^{8} +(-2.14079e9 - 2.75221e9i) q^{9} +O(q^{10})\)	\(q+1723.13i q^{2} +(-25942.2 + 53045.1i) q^{3} -1.92059e6 q^{4} +9.20415e6i q^{5} +(-9.14036e7 - 4.47017e7i) q^{6} +4.08861e8 q^{7} -1.50260e9i q^{8} +(-2.14079e9 - 2.75221e9i) q^{9} -1.58599e10 q^{10} +1.86251e9i q^{11} +(4.98244e10 - 1.01878e11i) q^{12} +6.70490e10 q^{13} +7.04520e11i q^{14} +(-4.88236e11 - 2.38776e11i) q^{15} +5.75279e11 q^{16} +1.72456e12i q^{17} +(4.74242e12 - 3.68886e12i) q^{18} -8.30608e12 q^{19} -1.76774e13i q^{20} +(-1.06067e13 + 2.16881e13i) q^{21} -3.20934e12 q^{22} -1.84856e13i q^{23} +(7.97055e13 + 3.89807e13i) q^{24} +1.06510e13 q^{25} +1.15534e14i q^{26} +(2.01528e14 - 4.21602e13i) q^{27} -7.85255e14 q^{28} +1.25101e14i q^{29} +(4.11441e14 - 8.41293e14i) q^{30} +7.73973e14 q^{31} -5.84308e14i q^{32} +(-9.87969e13 - 4.83175e13i) q^{33} -2.97163e15 q^{34} +3.76322e15i q^{35} +(4.11159e15 + 5.28588e15i) q^{36} +3.58992e14 q^{37} -1.43124e16i q^{38} +(-1.73940e15 + 3.55663e15i) q^{39} +1.38301e16 q^{40} +1.14185e16i q^{41} +(-3.73713e16 - 1.82768e16i) q^{42} -9.36400e15 q^{43} -3.57712e15i q^{44} +(2.53318e16 - 1.97042e16i) q^{45} +3.18531e16 q^{46} +6.06257e16i q^{47} +(-1.49240e16 + 3.05158e16i) q^{48} +8.73749e16 q^{49} +1.83530e16i q^{50} +(-9.14795e16 - 4.47388e16i) q^{51} -1.28774e17 q^{52} -1.40322e17i q^{53} +(7.26474e16 + 3.47259e17i) q^{54} -1.71428e16 q^{55} -6.14353e17i q^{56} +(2.15478e17 - 4.40597e17i) q^{57} -2.15565e17 q^{58} +6.48312e17i q^{59} +(9.37702e17 + 4.58591e17i) q^{60} -1.26280e18 q^{61} +1.33365e18i q^{62} +(-8.75286e17 - 1.12527e18i) q^{63} +1.61006e18 q^{64} +6.17130e17i q^{65} +(8.32572e16 - 1.70240e17i) q^{66} +1.97861e18 q^{67} -3.31218e18i q^{68} +(9.80572e17 + 4.79557e17i) q^{69} -6.48451e18 q^{70} -1.85821e18i q^{71} +(-4.13547e18 + 3.21675e18i) q^{72} +2.65086e18 q^{73} +6.18589e17i q^{74} +(-2.76310e17 + 5.64983e17i) q^{75} +1.59526e19 q^{76} +7.61506e17i q^{77} +(-6.12852e18 - 2.99721e18i) q^{78} +3.40686e18 q^{79} +5.29496e18i q^{80} +(-2.99169e18 + 1.17838e19i) q^{81} -1.96756e19 q^{82} +1.78470e19i q^{83} +(2.03712e19 - 4.16540e19i) q^{84} -1.58731e19 q^{85} -1.61354e19i q^{86} +(-6.63600e18 - 3.24539e18i) q^{87} +2.79860e18 q^{88} -3.26076e19i q^{89} +(3.39528e19 + 4.36499e19i) q^{90} +2.74137e19 q^{91} +3.55033e19i q^{92} +(-2.00786e19 + 4.10555e19i) q^{93} -1.04466e20 q^{94} -7.64504e19i q^{95} +(3.09947e19 + 1.51582e19i) q^{96} +9.39298e19 q^{97} +1.50558e20i q^{98} +(5.12601e18 - 3.98724e18i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4122 q^{3} - 2125200 q^{4} - 96401232 q^{6} + 559607916 q^{7} - 1087483482 q^{9}+O(q^{10}) \) 6 * q - 4122 * q^3 - 2125200 * q^4 - 96401232 * q^6 + 559607916 * q^7 - 1087483482 * q^9	\( 6 q - 4122 q^{3} - 2125200 q^{4} - 96401232 q^{6} + 559607916 q^{7} - 1087483482 q^{9} - 10880304480 q^{10} + 63957886128 q^{12} + 17847879276 q^{13} - 487764624960 q^{15} - 317472843648 q^{16} + 9564155313120 q^{18} - 14958020195124 q^{19} + 25978999888044 q^{21} - 71051286019680 q^{22} + 294048705803904 q^{24} - 397204775017050 q^{25} + 10\!\cdots\!98 q^{27}+ \cdots - 17\!\cdots\!80 q^{99}+O(q^{100}) \) 6 * q - 4122 * q^3 - 2125200 * q^4 - 96401232 * q^6 + 559607916 * q^7 - 1087483482 * q^9 - 10880304480 * q^10 + 63957886128 * q^12 + 17847879276 * q^13 - 487764624960 * q^15 - 317472843648 * q^16 + 9564155313120 * q^18 - 14958020195124 * q^19 + 25978999888044 * q^21 - 71051286019680 * q^22 + 294048705803904 * q^24 - 397204775017050 * q^25 + 1077025592505798 * q^27 - 2034284889273504 * q^28 + 3061064118304800 * q^30 - 2182905165483348 * q^31 + 3811197222014400 * q^33 - 7566372644651136 * q^34 + 6910111676037744 * q^36 - 1934341462168404 * q^37 - 15813602040849876 * q^39 + 44482420967535360 * q^40 - 86552595699685920 * q^42 + 58194987502184076 * q^43 - 81854223046416000 * q^45 + 151411391218915776 * q^46 - 154489681080035712 * q^48 + 188165158287453522 * q^49 - 117657755976045312 * q^51 - 230547517796956704 * q^52 + 489800358305152272 * q^54 - 393208608470140800 * q^55 + 1211071992434087436 * q^57 - 1639827118548168480 * q^58 + 2591328282252814080 * q^60 - 2999109545381544468 * q^61 + 444547436097192876 * q^63 - 83569554960393216 * q^64 + 120735307117251360 * q^66 + 4488155969890198476 * q^67 - 3511312424189451648 * q^69 - 1812568842584740800 * q^70 - 10414532525611288320 * q^72 + 15738405804262597836 * q^73 - 20871070048457840250 * q^75 + 27275280223392575328 * q^76 - 13410777930056987040 * q^78 + 17679940751103803436 * q^79 - 13011625055229011514 * q^81 - 35403353112903693120 * q^82 + 60397598618988279264 * q^84 - 22576574831711316480 * q^85 + 17858271599894295360 * q^87 - 95000209108729447680 * q^88 + 179562325304911301280 * q^90 - 6461010485165713512 * q^91 - 24838278011742494484 * q^93 - 311754310853935072896 * q^94 + 184738040137761352704 * q^96 + 223240336245548394636 * q^97 - 178130031568853028480 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more