LMFDB - Embedded newform 3.21.b.a.2.3

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			2.3
Root			$-92.1239i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.21.b.a.2.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-552.743i q^{2} +(-32781.6 + 49113.6i) q^{3} +743051. q^{4} -1.06933e7i q^{5} +(2.71472e7 + 1.81198e7i) q^{6} -3.45566e8 q^{7} -9.90310e8i q^{8} +(-1.33751e9 - 3.22005e9i) q^{9} +O(q^{10})$	\(q-552.743i q^{2} +(-32781.6 + 49113.6i) q^{3} +743051. q^{4} -1.06933e7i q^{5} +(2.71472e7 + 1.81198e7i) q^{6} -3.45566e8 q^{7} -9.90310e8i q^{8} +(-1.33751e9 - 3.22005e9i) q^{9} -5.91067e9 q^{10} -3.65746e10i q^{11} +(-2.43584e10 + 3.64939e10i) q^{12} +3.21302e10 q^{13} +1.91009e11i q^{14} +(5.25189e11 + 3.50545e11i) q^{15} +2.31758e11 q^{16} -4.71982e11i q^{17} +(-1.77986e12 + 7.39302e11i) q^{18} -3.83696e12 q^{19} -7.94569e12i q^{20} +(1.13282e13 - 1.69720e13i) q^{21} -2.02164e13 q^{22} +5.00426e13i q^{23} +(4.86377e13 + 3.24640e13i) q^{24} -1.89800e13 q^{25} -1.77598e13i q^{26} +(2.01994e14 + 3.98683e13i) q^{27} -2.56773e14 q^{28} -1.30583e14i q^{29} +(1.93761e14 - 2.90295e14i) q^{30} -1.26738e15 q^{31} -1.16652e15i q^{32} +(1.79631e15 + 1.19898e15i) q^{33} -2.60885e14 q^{34} +3.69525e15i q^{35} +(-9.93841e14 - 2.39266e15i) q^{36} +5.32197e15 q^{37} +2.12085e15i q^{38} +(-1.05328e15 + 1.57803e15i) q^{39} -1.05897e16 q^{40} -8.65225e15i q^{41} +(-9.38117e15 - 6.26160e15i) q^{42} +2.40530e16 q^{43} -2.71768e16i q^{44} +(-3.44331e16 + 1.43025e16i) q^{45} +2.76607e16 q^{46} +6.90144e16i q^{47} +(-7.59740e15 + 1.13825e16i) q^{48} +3.96237e16 q^{49} +1.04911e16i q^{50} +(2.31807e16 + 1.54723e16i) q^{51} +2.38744e16 q^{52} -1.83322e17i q^{53} +(2.20370e16 - 1.11651e17i) q^{54} -3.91105e17 q^{55} +3.42218e17i q^{56} +(1.25782e17 - 1.88447e17i) q^{57} -7.21789e16 q^{58} -5.32186e17i q^{59} +(3.90242e17 + 2.60473e17i) q^{60} +1.46387e17 q^{61} +7.00533e17i q^{62} +(4.62199e17 + 1.11274e18i) q^{63} -4.01769e17 q^{64} -3.43579e17i q^{65} +(6.62726e17 - 9.92900e17i) q^{66} -1.09645e18 q^{67} -3.50706e17i q^{68} +(-2.45778e18 - 1.64048e18i) q^{69} +2.04253e18 q^{70} -2.88787e17i q^{71} +(-3.18885e18 + 1.32455e18i) q^{72} +4.12612e18 q^{73} -2.94169e18i q^{74} +(6.22196e17 - 9.32178e17i) q^{75} -2.85105e18 q^{76} +1.26390e19i q^{77} +(8.72247e17 + 5.82194e17i) q^{78} +1.16564e19 q^{79} -2.47826e18i q^{80} +(-8.57978e18 + 8.61372e18i) q^{81} -4.78247e18 q^{82} -1.45849e19i q^{83} +(8.41744e18 - 1.26111e19i) q^{84} -5.04706e18 q^{85} -1.32951e19i q^{86} +(6.41340e18 + 4.28072e18i) q^{87} -3.62202e19 q^{88} +4.87444e18i q^{89} +(7.90561e18 + 1.90327e19i) q^{90} -1.11031e19 q^{91} +3.71842e19i q^{92} +(4.15466e19 - 6.22454e19i) q^{93} +3.81472e19 q^{94} +4.10299e19i q^{95} +(5.72919e19 + 3.82404e19i) q^{96} -3.51635e19 q^{97} -2.19017e19i q^{98} +(-1.17772e20 + 4.89191e19i) 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 $

$2$		−	552.743i		−	0.539789i	−0.962890	−	0.269894i	$-0.913011\pi$
$2$		−	552.743i		−	0.539789i	0.962890	−	0.269894i	$-0.0869887\pi$
$3$	−32781.6	+	49113.6i	−0.555160	+	0.831744i
$3$	−32781.6	+	49113.6i	−0.555160	+	0.831744i
$4$	743051.			0.708628
$5$		−	1.06933e7i		−	1.09500i	−0.836806	−	0.547499i	$-0.815580\pi$
$5$		−	1.06933e7i		−	1.09500i	0.836806	−	0.547499i	$-0.184420\pi$
$6$	2.71472e7	+	1.81198e7i	0.448966	+	0.299669i
$7$	−3.45566e8			−1.22335			−0.611675	−	0.791109i	$-0.709504\pi$
$7$	−3.45566e8			−1.22335			−0.611675	+	0.791109i	$0.709504\pi$
$8$		−	9.90310e8i		−	0.922298i
$9$	−1.33751e9	−	3.22005e9i	−0.383595	−	0.923501i
$10$	−5.91067e9			−0.591067
$11$		−	3.65746e10i		−	1.41011i	−0.709153	−	0.705055i	$-0.750922\pi$
$11$		−	3.65746e10i		−	1.41011i	0.709153	−	0.705055i	$-0.249078\pi$
$12$	−2.43584e10	+	3.64939e10i	−0.393402	+	0.589397i
$13$	3.21302e10			0.233067			0.116533	−	0.993187i	$-0.462822\pi$
$13$	3.21302e10			0.233067			0.116533	+	0.993187i	$0.462822\pi$
$14$			1.91009e11i			0.660350i
$15$	5.25189e11	+	3.50545e11i	0.910757	+	0.607899i
$16$	2.31758e11			0.210782
$17$		−	4.71982e11i		−	0.234119i	−0.993125	−	0.117059i	$-0.962653\pi$
$17$		−	4.71982e11i		−	0.234119i	0.993125	−	0.117059i	$-0.0373468\pi$
$18$	−1.77986e12	+	7.39302e11i	−0.498495	+	0.207060i
$19$	−3.83696e12			−0.625822			−0.312911	−	0.949782i	$-0.601304\pi$
$19$	−3.83696e12			−0.625822			−0.312911	+	0.949782i	$0.601304\pi$
$20$		−	7.94569e12i		−	0.775946i
$21$	1.13282e13	−	1.69720e13i	0.679155	−	1.01751i
$22$	−2.02164e13			−0.761161
$23$			5.00426e13i			1.20799i	0.796990	+	0.603993i	$0.206424\pi$
$23$			5.00426e13i			1.20799i	−0.796990	+	0.603993i	$0.793576\pi$
$24$	4.86377e13	+	3.24640e13i	0.767116	+	0.512023i
$25$	−1.89800e13			−0.199020
$26$		−	1.77598e13i		−	0.125807i
$27$	2.01994e14	+	3.98683e13i	0.981073	+	0.193638i
$28$	−2.56773e14			−0.866901
$29$		−	1.30583e14i		−	0.310389i	−0.987884	−	0.155195i	$-0.950400\pi$
$29$		−	1.30583e14i		−	0.310389i	0.987884	−	0.155195i	$-0.0496004\pi$
$30$	1.93761e14	−	2.90295e14i	0.328137	−	0.491616i
$31$	−1.26738e15			−1.54628			−0.773140	−	0.634235i	$-0.781315\pi$
$31$	−1.26738e15			−1.54628			−0.773140	+	0.634235i	$0.781315\pi$
$32$		−	1.16652e15i		−	1.03608i
$33$	1.79631e15	+	1.19898e15i	1.17285	+	0.782836i
$34$	−2.60885e14			−0.126375
$35$			3.69525e15i			1.33957i
$36$	−9.93841e14	−	2.39266e15i	−0.271826	−	0.654419i
$37$	5.32197e15			1.10677			0.553383	−	0.832927i	$-0.313337\pi$
$37$	5.32197e15			1.10677			0.553383	+	0.832927i	$0.313337\pi$
$38$			2.12085e15i			0.337811i
$39$	−1.05328e15	+	1.57803e15i	−0.129389	+	0.193852i
$40$	−1.05897e16			−1.00991
$41$		−	8.65225e15i		−	0.644600i	−0.946638	−	0.322300i	$-0.895544\pi$
$41$		−	8.65225e15i		−	0.644600i	0.946638	−	0.322300i	$-0.104456\pi$
$42$	−9.38117e15	−	6.26160e15i	−0.549242	−	0.366600i
$43$	2.40530e16			1.11297			0.556487	−	0.830857i	$-0.312149\pi$
$43$	2.40530e16			1.11297			0.556487	+	0.830857i	$0.312149\pi$
$44$		−	2.71768e16i		−	0.999244i
$45$	−3.44331e16	+	1.43025e16i	−1.01123	+	0.420036i
$46$	2.76607e16			0.652057
$47$			6.90144e16i			1.31208i	0.754725	+	0.656041i	$0.227770\pi$
$47$			6.90144e16i			1.31208i	−0.754725	+	0.656041i	$0.772230\pi$
$48$	−7.59740e15	+	1.13825e16i	−0.117018	+	0.175317i
$49$	3.96237e16			0.496585
$50$			1.04911e16i			0.107429i
$51$	2.31807e16	+	1.54723e16i	0.194727	+	0.129973i
$52$	2.38744e16			0.165158
$53$		−	1.83322e17i		−	1.04823i	−0.851649	−	0.524113i	$-0.824397\pi$
$53$		−	1.83322e17i		−	1.04823i	0.851649	−	0.524113i	$-0.175603\pi$
$54$	2.20370e16	−	1.11651e17i	0.104524	−	0.529572i
$55$	−3.91105e17			−1.54407
$56$			3.42218e17i			1.12829i
$57$	1.25782e17	−	1.88447e17i	0.347431	−	0.520523i
$58$	−7.21789e16			−0.167544
$59$		−	5.32186e17i		−	1.04122i	−0.853794	−	0.520611i	$-0.825704\pi$
$59$		−	5.32186e17i		−	1.04122i	0.853794	−	0.520611i	$-0.174296\pi$
$60$	3.90242e17	+	2.60473e17i	0.645389	+	0.430774i
$61$	1.46387e17			0.205212			0.102606	−	0.994722i	$-0.467282\pi$
$61$	1.46387e17			0.205212			0.102606	+	0.994722i	$0.467282\pi$
$62$			7.00533e17i			0.834665i
$63$	4.62199e17	+	1.11274e18i	0.469271	+	1.12977i
$64$	−4.01769e17			−0.348479
$65$		−	3.43579e17i		−	0.255208i
$66$	6.62726e17	−	9.92900e17i	0.422566	−	0.633091i
$67$	−1.09645e18			−0.601505			−0.300752	−	0.953702i	$-0.597238\pi$
$67$	−1.09645e18			−0.601505			−0.300752	+	0.953702i	$0.597238\pi$
$68$		−	3.50706e17i		−	0.165903i
$69$	−2.45778e18	−	1.64048e18i	−1.00473	−	0.670625i
$70$	2.04253e18			0.723082
$71$		−	2.88787e17i		−	0.0887143i	−0.999016	−	0.0443572i	$-0.985876\pi$
$71$		−	2.88787e17i		−	0.0887143i	0.999016	−	0.0443572i	$-0.0141240\pi$
$72$	−3.18885e18	+	1.32455e18i	−0.851743	+	0.353789i
$73$	4.12612e18			0.960094			0.480047	−	0.877243i	$-0.340620\pi$
$73$	4.12612e18			0.960094			0.480047	+	0.877243i	$0.340620\pi$
$74$		−	2.94169e18i		−	0.597419i
$75$	6.22196e17	−	9.32178e17i	0.110488	−	0.165534i
$76$	−2.85105e18			−0.443475
$77$			1.26390e19i			1.72506i
$78$	8.72247e17	+	5.82194e17i	0.104639	+	0.0698429i
$79$	1.16564e19			1.23110			0.615551	−	0.788097i	$-0.288934\pi$
$79$	1.16564e19			1.23110			0.615551	+	0.788097i	$0.288934\pi$
$80$		−	2.47826e18i		−	0.230806i
$81$	−8.57978e18	+	8.61372e18i	−0.705709	+	0.708501i
$82$	−4.78247e18			−0.347948
$83$		−	1.45849e19i		−	0.939991i	−0.882669	−	0.469996i	$-0.844255\pi$
$83$		−	1.45849e19i		−	0.939991i	0.882669	−	0.469996i	$-0.155745\pi$
$84$	8.41744e18	−	1.26111e19i	0.481268	−	0.721039i
$85$	−5.04706e18			−0.256359
$86$		−	1.32951e19i		−	0.600770i
$87$	6.41340e18	+	4.28072e18i	0.258164	+	0.172316i
$88$	−3.62202e19			−1.30054
$89$			4.87444e18i			0.156324i	0.996941	+	0.0781618i	$0.0249051\pi$
$89$			4.87444e18i			0.156324i	−0.996941	+	0.0781618i	$0.975095\pi$
$90$	7.90561e18	+	1.90327e19i	0.226731	+	0.545851i
$91$	−1.11031e19			−0.285122
$92$			3.71842e19i			0.856013i
$93$	4.15466e19	−	6.22454e19i	0.858433	−	1.28611i
$94$	3.81472e19			0.708247
$95$			4.10299e19i			0.685274i
$96$	5.72919e19	+	3.82404e19i	0.861750	+	0.575188i
$97$	−3.51635e19			−0.476842			−0.238421	−	0.971162i	$-0.576630\pi$
$97$	−3.51635e19			−0.476842			−0.238421	+	0.971162i	$0.576630\pi$
$98$		−	2.19017e19i		−	0.268051i
$99$	−1.17772e20	+	4.89191e19i	−1.30224	+	0.540912i
$100$	−1.41031e19			−0.141031
$101$		−	8.72743e19i		−	0.790083i	−0.918663	−	0.395041i	$-0.870730\pi$
$101$		−	8.72743e19i		−	0.790083i	0.918663	−	0.395041i	$-0.129270\pi$
$102$	8.55223e18	−	1.28130e19i	0.0701581	−	0.105111i
$103$	1.15743e20			0.861233			0.430617	−	0.902535i	$-0.358296\pi$
$103$	1.15743e20			0.861233			0.430617	+	0.902535i	$0.358296\pi$
$104$		−	3.18189e19i		−	0.214957i
$105$	−1.81487e20	−	1.21136e20i	−1.11418	−	0.743673i
$106$	−1.01330e20			−0.565821
$107$		−	9.49283e19i		−	0.482567i	−0.970455	−	0.241284i	$-0.922432\pi$
$107$		−	9.49283e19i		−	0.482567i	0.970455	−	0.241284i	$-0.0775684\pi$
$108$	1.50092e20	+	2.96242e19i	0.695216	+	0.137217i
$109$	2.70267e20			1.14164			0.570818	−	0.821077i	$-0.306626\pi$
$109$	2.70267e20			1.14164			0.570818	+	0.821077i	$0.306626\pi$
$110$			2.16181e20i			0.833470i
$111$	−1.74463e20	+	2.61382e20i	−0.614432	+	0.920545i
$112$	−8.00876e19			−0.257861
$113$			1.64159e20i			0.483593i	0.970327	+	0.241797i	$0.0777366\pi$
$113$			1.64159e20i			0.483593i	−0.970327	+	0.241797i	$0.922263\pi$
$114$	−1.04163e20	−	6.95250e19i	−0.280973	−	0.187539i
$115$	5.35123e20			1.32274
$116$		−	9.70297e19i		−	0.219951i
$117$	−4.29746e19	−	1.03461e20i	−0.0894033	−	0.215238i
$118$	−2.94162e20			−0.562040
$119$			1.63101e20i			0.286409i
$120$	3.47148e20	−	5.20100e20i	0.560664	−	0.839990i
$121$	−6.64953e20			−0.988411
$122$		−	8.09142e19i		−	0.110771i
$123$	4.24943e20	+	2.83635e20i	0.536142	+	0.357856i
$124$	−9.41724e20			−1.09574
$125$		−	8.16836e20i		−	0.877071i
$126$	6.15060e20	−	2.55478e20i	0.609834	−	0.253307i
$127$	1.17599e20			0.107737			0.0538687	−	0.998548i	$-0.482845\pi$
$127$	1.17599e20			0.107737			0.0538687	+	0.998548i	$0.482845\pi$
$128$		−	1.00111e21i		−	0.847971i
$129$	−7.88497e20	+	1.18133e21i	−0.617878	+	0.925708i
$130$	−1.89911e20			−0.137758
$131$			2.60615e21i			1.75100i	0.483217	+	0.875501i	$0.339468\pi$
$131$			2.60615e21i			1.75100i	−0.483217	+	0.875501i	$0.660532\pi$
$132$	1.33475e21	+	8.90900e20i	0.831115	+	0.554740i
$133$	1.32592e21			0.765599
$134$			6.06053e20i			0.324685i
$135$	4.26325e20	−	2.15999e21i	0.212033	−	1.07427i
$136$	−4.67408e20			−0.215927
$137$		−	2.75121e21i		−	1.18119i	−0.806969	−	0.590594i	$-0.798894\pi$
$137$		−	2.75121e21i		−	1.18119i	0.806969	−	0.590594i	$-0.201106\pi$
$138$	−9.06764e20	+	1.35852e21i	−0.361996	+	0.542344i
$139$	9.79968e20			0.363969			0.181984	−	0.983301i	$-0.441748\pi$
$139$	9.79968e20			0.363969			0.181984	+	0.983301i	$0.441748\pi$
$140$			2.74576e21i			0.949254i
$141$	−3.38955e21	−	2.26240e21i	−1.09132	−	0.728415i
$142$	−1.59625e20			−0.0478870
$143$		−	1.17515e21i		−	0.328650i
$144$	−3.09979e20	−	7.46272e20i	−0.0808552	−	0.194658i
$145$	−1.39637e21			−0.339875
$146$		−	2.28069e21i		−	0.518248i
$147$	−1.29893e21	+	1.94606e21i	−0.275684	+	0.413032i
$148$	3.95450e21			0.784285
$149$		−	2.71172e21i		−	0.502785i	−0.967885	−	0.251393i	$-0.919111\pi$
$149$		−	2.71172e21i		−	0.502785i	0.967885	−	0.251393i	$-0.0808886\pi$
$150$	−5.15255e20	−	3.43915e20i	−0.0893532	−	0.0596401i
$151$	4.08914e21			0.663533			0.331767	−	0.943362i	$-0.392355\pi$
$151$	4.08914e21			0.663533			0.331767	+	0.943362i	$0.392355\pi$
$152$			3.79978e21i			0.577194i
$153$	−1.51981e21	+	6.31282e20i	−0.216209	+	0.0898068i
$154$	6.98610e21			0.931167
$155$			1.35525e22i			1.69317i
$156$	−7.82642e20	+	1.17256e21i	−0.0916889	+	0.137369i
$157$	−9.50745e21			−1.04488			−0.522441	−	0.852675i	$-0.674979\pi$
$157$	−9.50745e21			−1.04488			−0.522441	+	0.852675i	$0.674979\pi$
$158$		−	6.44301e21i		−	0.664535i
$159$	9.00359e21	+	6.00958e21i	0.871856	+	0.581933i
$160$	−1.24740e22			−1.13450
$161$		−	1.72930e22i		−	1.47779i
$162$	4.76118e21	+	4.74242e21i	0.382441	+	0.380934i
$163$	2.30907e21			0.174406			0.0872028	−	0.996191i	$-0.472207\pi$
$163$	2.30907e21			0.174406			0.0872028	+	0.996191i	$0.472207\pi$
$164$		−	6.42906e21i		−	0.456782i
$165$	1.28211e22	−	1.92086e22i	0.857204	−	1.28427i
$166$	−8.06173e21			−0.507397
$167$			1.73165e22i			1.02635i	0.858284	+	0.513176i	$0.171531\pi$
$167$			1.73165e22i			1.02635i	−0.858284	+	0.513176i	$0.828469\pi$
$168$	−1.68075e22	−	1.12184e22i	−0.938451	−	0.626383i
$169$	−1.79726e22			−0.945680
$170$			2.78973e21i			0.138380i
$171$	5.13198e21	+	1.23552e22i	0.240062	+	0.577947i
$172$	1.78726e22			0.788684
$173$			1.29232e22i			0.538159i	0.963118	+	0.269080i	$0.0867195\pi$
$173$			1.29232e22i			0.538159i	−0.963118	+	0.269080i	$0.913281\pi$
$174$	2.36614e21	−	3.54497e21i	0.0930140	−	0.139354i
$175$	6.55885e21			0.243471
$176$		−	8.47645e21i		−	0.297227i
$177$	2.61376e22	+	1.74459e22i	0.866030	+	0.578045i
$178$	2.69431e21			0.0843816
$179$			6.02343e21i			0.178367i	0.996015	+	0.0891833i	$0.0284257\pi$
$179$			6.02343e21i			0.178367i	−0.996015	+	0.0891833i	$0.971574\pi$
$180$	−2.55855e22	+	1.06275e22i	−0.716588	+	0.297649i
$181$	−1.70381e21			−0.0451476			−0.0225738	−	0.999745i	$-0.507186\pi$
$181$	−1.70381e21			−0.0451476			−0.0225738	+	0.999745i	$0.507186\pi$
$182$			6.13718e21i			0.153906i
$183$	−4.79879e21	+	7.18958e21i	−0.113925	+	0.170684i
$184$	4.95577e22			1.11412
$185$		−	5.69097e22i		−	1.21191i
$186$	−3.44057e22	−	2.29646e22i	−0.694227	−	0.463372i
$187$	−1.72626e22			−0.330133
$188$			5.12812e22i			0.929779i
$189$	−6.98024e22	−	1.37771e22i	−1.20020	−	0.236887i
$190$	2.26790e22			0.369903
$191$		−	8.81963e22i		−	1.36495i	−0.730909	−	0.682475i	$-0.760904\pi$
$191$		−	8.81963e22i		−	1.36495i	0.730909	−	0.682475i	$-0.239096\pi$
$192$	1.31707e22	−	1.97324e22i	0.193462	−	0.289846i
$193$	−3.66704e22			−0.511378			−0.255689	−	0.966759i	$-0.582302\pi$
$193$	−3.66704e22			−0.511378			−0.255689	+	0.966759i	$0.582302\pi$
$194$			1.94364e22i			0.257394i
$195$	1.68744e22	+	1.12631e22i	0.212267	+	0.141681i
$196$	2.94424e22			0.351894
$197$			8.56301e22i			0.972667i	0.873773	+	0.486334i	$0.161666\pi$
$197$			8.56301e22i			0.972667i	−0.873773	+	0.486334i	$0.838334\pi$
$198$	2.70397e22	+	6.50978e22i	0.291978	+	0.702933i
$199$	7.36551e22			0.756261			0.378131	−	0.925752i	$-0.376567\pi$
$199$	7.36551e22			0.756261			0.378131	+	0.925752i	$0.376567\pi$
$200$			1.87961e22i			0.183556i
$201$	3.59433e22	−	5.38504e22i	0.333931	−	0.500298i
$202$	−4.82403e22			−0.426478
$203$			4.51250e22i			0.379715i
$204$	1.72245e22	+	1.14967e22i	0.137989	+	0.0921028i
$205$	−9.25214e22			−0.705836
$206$		−	6.39759e22i		−	0.464884i
$207$	1.61140e23	−	6.69327e22i	1.11558	−	0.463377i
$208$	7.44643e21			0.0491264
$209$			1.40335e23i			0.882478i
$210$	−6.69574e22	+	1.00316e23i	−0.401426	+	0.601419i
$211$	−2.81227e23			−1.60780			−0.803902	−	0.594762i	$-0.797246\pi$
$211$	−2.81227e23			−1.60780			−0.803902	+	0.594762i	$0.797246\pi$
$212$		−	1.36217e23i		−	0.742803i
$213$	1.41834e22	+	9.46690e21i	0.0737876	+	0.0492506i
$214$	−5.24710e22			−0.260484
$215$		−	2.57207e23i		−	1.21870i
$216$	3.94820e22	−	2.00037e23i	0.178592	−	0.904842i
$217$	4.37962e23			1.89164
$218$		−	1.49388e23i		−	0.616242i
$219$	−1.35261e23	+	2.02649e23i	−0.533005	+	0.798552i
$220$	−2.90611e23			−1.09417
$221$		−	1.51649e22i		−	0.0545653i
$222$	1.44477e23	+	9.64333e22i	0.496900	+	0.331663i
$223$	−1.37448e23			−0.451949			−0.225974	−	0.974133i	$-0.572557\pi$
$223$	−1.37448e23			−0.451949			−0.225974	+	0.974133i	$0.572557\pi$
$224$			4.03109e23i			1.26748i
$225$	2.53860e22	+	6.11166e22i	0.0763431	+	0.183795i
$226$	9.07378e22			0.261038
$227$			6.72239e23i			1.85040i	0.379482	+	0.925199i	$0.376102\pi$
$227$			6.72239e23i			1.85040i	−0.379482	+	0.925199i	$0.623898\pi$
$228$	9.34621e22	−	1.40026e23i	0.246200	−	0.368858i
$229$	6.42550e23			1.62014			0.810069	−	0.586334i	$-0.199429\pi$
$229$	6.42550e23			1.62014			0.810069	+	0.586334i	$0.199429\pi$
$230$		−	2.95786e23i		−	0.714001i
$231$	−6.20745e23	−	4.14325e23i	−1.43481	−	0.957683i
$232$	−1.29318e23			−0.286271
$233$		−	2.73046e22i		−	0.0578998i	−0.999581	−	0.0289499i	$-0.990784\pi$
$233$		−	2.73046e22i		−	0.0578998i	0.999581	−	0.0289499i	$-0.00921632\pi$
$234$	−5.71874e22	+	2.37539e22i	−0.116183	+	0.0482589i
$235$	7.37994e23			1.43673
$236$		−	3.95441e23i		−	0.737840i
$237$	−3.82116e23	+	5.72489e23i	−0.683458	+	1.02396i
$238$	9.01530e22			0.154600
$239$		−	5.46081e23i		−	0.898004i	−0.893531	−	0.449002i	$-0.851780\pi$
$239$		−	5.46081e23i		−	0.898004i	0.893531	−	0.449002i	$-0.148220\pi$
$240$	1.21717e23	+	8.12415e22i	0.191972	+	0.128134i
$241$	−1.21732e24			−1.84176			−0.920880	−	0.389845i	$-0.872529\pi$
$241$	−1.21732e24			−1.84176			−0.920880	+	0.389845i	$0.872529\pi$
$242$			3.67549e23i			0.533533i
$243$	−1.41792e23	−	7.03756e23i	−0.197510	−	0.980301i
$244$	1.08773e23			0.145419
$245$		−	4.23709e23i		−	0.543760i
$246$	1.56777e23	−	2.34885e23i	0.193167	−	0.289403i
$247$	−1.23282e23			−0.145858
$248$			1.25509e24i			1.42613i
$249$	7.16320e23	+	4.78118e23i	0.781832	+	0.521845i
$250$	−4.51501e23			−0.473433
$251$		−	1.26988e24i		−	1.27945i	−0.768603	−	0.639727i	$-0.779048\pi$
$251$		−	1.26988e24i		−	1.27945i	0.768603	−	0.639727i	$-0.220952\pi$
$252$	3.43438e23	+	8.26822e23i	0.332539	+	0.800584i
$253$	1.83029e24			1.70339
$254$		−	6.50021e22i		−	0.0581555i
$255$	1.65451e23	−	2.47880e23i	0.142320	−	0.213225i
$256$	−9.74641e23			−0.806204
$257$			2.02041e24i			1.60734i	0.595073	+	0.803672i	$0.297123\pi$
$257$			2.02041e24i			1.60734i	−0.595073	+	0.803672i	$0.702877\pi$
$258$	6.52973e23	+	4.35836e23i	0.499687	+	0.333523i
$259$	−1.83909e24			−1.35396
$260$		−	2.55297e23i		−	0.180847i
$261$	−4.20484e23	+	1.74656e23i	−0.286645	+	0.119064i
$262$	1.44053e24			0.945171
$263$		−	8.92819e23i		−	0.563905i	−0.959428	−	0.281952i	$-0.909018\pi$
$263$		−	8.92819e23i		−	0.563905i	0.959428	−	0.281952i	$-0.0909820\pi$
$264$	1.18736e24	−	1.77891e24i	0.722008	−	1.08172i
$265$	−1.96032e24			−1.14781
$266$		−	7.32895e23i		−	0.413262i
$267$	−2.39401e23	−	1.59792e23i	−0.130021	−	0.0867845i
$268$	−8.14715e23			−0.426243
$269$			2.64918e23i			0.133533i	0.997769	+	0.0667664i	$0.0212682\pi$
$269$			2.64918e23i			0.133533i	−0.997769	+	0.0667664i	$0.978732\pi$
$270$	−1.19392e24	−	2.35649e23i	−0.579880	−	0.114453i
$271$	1.50540e24			0.704626			0.352313	−	0.935882i	$-0.385395\pi$
$271$	1.50540e24			0.704626			0.352313	+	0.935882i	$0.385395\pi$
$272$		−	1.09385e23i		−	0.0493481i
$273$	3.63978e23	−	5.45315e23i	0.158288	−	0.237149i
$274$	−1.52072e24			−0.637591
$275$			6.94187e23i			0.280640i
$276$	−1.82625e24	−	1.21896e24i	−0.711983	−	0.475224i
$277$	2.35534e24			0.885637			0.442818	−	0.896611i	$-0.353979\pi$
$277$	2.35534e24			0.885637			0.442818	+	0.896611i	$0.353979\pi$
$278$		−	5.41671e23i		−	0.196466i
$279$	1.69513e24	+	4.08101e24i	0.593146	+	1.42799i
$280$	3.65945e24			1.23548
$281$		−	5.53085e23i		−	0.180189i	−0.995933	−	0.0900946i	$-0.971283\pi$
$281$		−	5.53085e23i		−	0.180189i	0.995933	−	0.0900946i	$-0.0287169\pi$
$282$	−1.25053e24	+	1.87355e24i	−0.393190	+	0.589080i
$283$	1.17330e21			0.000356079			0.000178039	−	1.00000i	$-0.499943\pi$
$283$	1.17330e21			0.000356079			0.000178039		1.00000i	$0.499943\pi$
$284$		−	2.14583e23i		−	0.0628655i
$285$	−2.01513e24	−	1.34503e24i	−0.569972	−	0.380436i
$286$	−6.49557e23			−0.177401
$287$			2.98992e24i			0.788572i
$288$	−3.75625e24	+	1.56023e24i	−0.956818	+	0.397434i
$289$	3.84146e24			0.945188
$290$			7.71833e23i			0.183461i
$291$	1.15272e24	−	1.72701e24i	0.264723	−	0.396610i
$292$	3.06592e24			0.680350
$293$		−	8.47619e23i		−	0.181771i	−0.995861	−	0.0908855i	$-0.971030\pi$
$293$		−	8.47619e23i		−	0.181771i	0.995861	−	0.0908855i	$-0.0289697\pi$
$294$	1.07567e24	+	7.17974e23i	0.222950	+	0.148811i
$295$	−5.69085e24			−1.14014
$296$		−	5.27040e24i		−	1.02077i
$297$	1.45817e24	−	7.38786e24i	0.273051	−	1.38342i
$298$	−1.49889e24			−0.271398
$299$			1.60788e24i			0.281541i
$300$	4.62323e23	−	6.92656e23i	0.0782949	−	0.117302i
$301$	−8.31190e24			−1.36156
$302$		−	2.26025e24i		−	0.358168i
$303$	4.28636e24	+	2.86099e24i	0.657146	+	0.438622i
$304$	−8.89244e23			−0.131912
$305$		−	1.56536e24i		−	0.224707i
$306$	3.48937e23	+	8.40062e23i	0.0484767	+	0.116707i
$307$	1.78041e24			0.239406			0.119703	−	0.992810i	$-0.461806\pi$
$307$	1.78041e24			0.239406			0.119703	+	0.992810i	$0.461806\pi$
$308$			9.39138e24i			1.22243i
$309$	−3.79423e24	+	5.68454e24i	−0.478122	+	0.716325i
$310$	7.49104e24			0.913956
$311$			7.30176e23i			0.0862629i	0.999069	+	0.0431314i	$0.0137334\pi$
$311$			7.30176e23i			0.0862629i	−0.999069	+	0.0431314i	$0.986267\pi$
$312$	1.56274e24	+	1.04308e24i	0.178789	+	0.119336i
$313$	−9.23471e24			−1.02325			−0.511623	−	0.859210i	$-0.670955\pi$
$313$	−9.23471e24			−1.02325			−0.511623	+	0.859210i	$0.670955\pi$
$314$			5.25518e24i			0.564016i
$315$	1.18989e25	−	4.94245e24i	1.23709	−	0.513851i
$316$	8.66131e24			0.872394
$317$		−	9.87080e24i		−	0.963296i	−0.876365	−	0.481648i	$-0.840038\pi$
$317$		−	9.87080e24i		−	0.963296i	0.876365	−	0.481648i	$-0.159962\pi$
$318$	3.32176e24	−	4.97668e24i	0.314121	−	0.470618i
$319$	−4.77602e24			−0.437683
$320$			4.29626e24i			0.381584i
$321$	4.66227e24	+	3.11190e24i	0.401372	+	0.267902i
$322$	−9.55861e24			−0.797694
$323$			1.81097e24i			0.146517i
$324$	−6.37521e24	+	6.40043e24i	−0.500086	+	0.502064i
$325$	−6.09833e23			−0.0463850
$326$		−	1.27632e24i		−	0.0941421i
$327$	−8.85979e24	+	1.32738e25i	−0.633791	+	0.949549i
$328$	−8.56841e24			−0.594513
$329$		−	2.38490e25i		−	1.60514i
$330$	−1.06174e25	−	7.08675e24i	−0.693233	−	0.462709i
$331$	1.56796e25			0.993242			0.496621	−	0.867968i	$-0.334574\pi$
$331$	1.56796e25			0.993242			0.496621	+	0.867968i	$0.334574\pi$
$332$		−	1.08374e25i		−	0.666105i
$333$	−7.11821e24	−	1.71370e25i	−0.424550	−	1.02210i
$334$	9.57160e24			0.554013
$335$			1.17247e25i			0.658647i
$336$	2.62540e24	−	3.93340e24i	0.143154	−	0.214474i
$337$	1.33149e25			0.704758			0.352379	−	0.935857i	$-0.385373\pi$
$337$	1.33149e25			0.704758			0.352379	+	0.935857i	$0.385373\pi$
$338$			9.93424e24i			0.510467i
$339$	−8.06244e24	−	5.38140e24i	−0.402225	−	0.268471i
$340$	−3.75022e24			−0.181664
$341$			4.63538e25i			2.18043i
$342$	6.82925e24	−	2.83667e24i	0.311969	−	0.129583i
$343$	1.38809e25			0.615852
$344$		−	2.38199e25i		−	1.02649i
$345$	−1.75422e25	+	2.62818e25i	−0.734333	+	1.10018i
$346$	7.14324e24			0.290492
$347$			1.00812e25i			0.398306i	0.979968	+	0.199153i	$0.0638191\pi$
$347$			1.00812e25i			0.398306i	−0.979968	+	0.199153i	$0.936181\pi$
$348$	4.76548e24	+	3.18079e24i	0.182942	+	0.122108i
$349$	2.15629e25			0.804366			0.402183	−	0.915559i	$-0.368252\pi$
$349$	2.15629e25			0.804366			0.402183	+	0.915559i	$0.368252\pi$
$350$		−	3.62536e24i		−	0.131423i
$351$	6.49012e24	+	1.28098e24i	0.228656	+	0.0451306i
$352$	−4.26650e25			−1.46098
$353$		−	1.13565e25i		−	0.378004i	−0.981977	−	0.189002i	$-0.939475\pi$
$353$		−	1.13565e25i		−	0.378004i	0.981977	−	0.189002i	$-0.0605253\pi$
$354$	9.64312e24	−	1.44474e25i	0.312022	−	0.467473i
$355$	−3.08809e24			−0.0971420
$356$			3.62195e24i			0.110775i
$357$	−8.01048e24	−	5.34672e24i	−0.238219	−	0.159003i
$358$	3.32941e24			0.0962803
$359$		−	3.62007e25i		−	1.01806i	−0.860749	−	0.509029i	$-0.830005\pi$
$359$		−	3.62007e25i		−	1.01806i	0.860749	−	0.509029i	$-0.169995\pi$
$360$	1.41639e25	+	3.40994e25i	0.387398	+	0.932657i
$361$	−2.28677e25			−0.608347
$362$			9.41768e23i			0.0243702i
$363$	2.17983e25	−	3.26583e25i	0.548726	−	0.822104i
$364$	−8.25018e24			−0.202046
$365$		−	4.41220e25i		−	1.05130i
$366$	3.97399e24	+	2.65250e24i	0.0921332	+	0.0614957i
$367$	−4.06485e25			−0.917030			−0.458515	−	0.888687i	$-0.651619\pi$
$367$	−4.06485e25			−0.917030			−0.458515	+	0.888687i	$0.651619\pi$
$368$			1.15978e25i			0.254622i
$369$	−2.78607e25	+	1.15725e25i	−0.595289	+	0.247266i
$370$	−3.14564e25			−0.654173
$371$			6.33498e25i			1.28235i
$372$	3.08713e25	−	4.62515e25i	0.608310	−	0.911373i
$373$	5.83808e25			1.11991			0.559953	−	0.828524i	$-0.310819\pi$
$373$	5.83808e25			1.11991			0.559953	+	0.828524i	$0.310819\pi$
$374$			9.54177e24i			0.178202i
$375$	4.01178e25	+	2.67772e25i	0.729499	+	0.486915i
$376$	6.83456e25			1.21013
$377$		−	4.19566e24i		−	0.0723414i
$378$	−7.61523e24	+	3.85828e25i	−0.127869	+	0.647852i
$379$	−1.09915e26			−1.79749			−0.898744	−	0.438474i	$-0.855519\pi$
$379$	−1.09915e26			−1.79749			−0.898744	+	0.438474i	$0.855519\pi$
$380$			3.04873e25i			0.485604i
$381$	−3.85509e24	+	5.77572e24i	−0.0598115	+	0.0896100i
$382$	−4.87499e25			−0.736784
$383$		−	1.45398e25i		−	0.214078i	−0.994255	−	0.107039i	$-0.965863\pi$
$383$		−	1.45398e25i		−	0.214078i	0.994255	−	0.107039i	$-0.0341370\pi$
$384$	4.91680e25	+	3.28179e25i	0.705294	+	0.470759i
$385$	1.35153e26			1.88893
$386$			2.02693e25i			0.276036i
$387$	−3.21712e25	−	7.74519e25i	−0.426931	−	1.02783i
$388$	−2.61282e25			−0.337904
$389$			3.14489e25i			0.396378i	0.980164	+	0.198189i	$0.0635060\pi$
$389$			3.14489e25i			0.396378i	−0.980164	+	0.198189i	$0.936494\pi$
$390$	6.22560e24	−	9.32723e24i	0.0764778	−	0.114579i
$391$	2.36192e25			0.282812
$392$		−	3.92397e25i		−	0.458000i
$393$	−1.27998e26	−	8.54339e25i	−1.45638	−	0.972086i
$394$	4.73315e25			0.525034
$395$		−	1.24646e26i		−	1.34805i
$396$	−8.75107e25	+	3.63493e25i	−0.922803	+	0.383305i
$397$	7.19118e24			0.0739427			0.0369713	−	0.999316i	$-0.488229\pi$
$397$	7.19118e24			0.0739427			0.0369713	+	0.999316i	$0.488229\pi$
$398$		−	4.07123e25i		−	0.408221i
$399$	−4.34659e25	+	6.51208e25i	−0.425030	+	0.636782i
$400$	−4.39877e24			−0.0419499
$401$			1.83735e26i			1.70903i	0.519431	+	0.854513i	$0.326144\pi$
$401$			1.83735e26i			1.70903i	−0.519431	+	0.854513i	$0.673856\pi$
$402$	−2.97655e25	−	1.98674e25i	−0.270055	−	0.180252i
$403$	−4.07211e25			−0.360387
$404$		−	6.48492e25i		−	0.559875i
$405$	9.21094e25	+	9.17465e25i	0.775807	+	0.772750i
$406$	2.49426e25			0.204966
$407$		−	1.94649e26i		−	1.56066i
$408$	1.53224e25	−	2.29561e25i	0.119874	−	0.179596i
$409$	9.90993e25			0.756550			0.378275	−	0.925693i	$-0.376517\pi$
$409$	9.90993e25			0.756550			0.378275	+	0.925693i	$0.376517\pi$
$410$			5.11406e25i			0.381002i
$411$	1.35122e26	+	9.01893e25i	0.982445	+	0.655748i
$412$	8.60026e25			0.610294
$413$			1.83906e26i			1.27378i
$414$	−3.69966e25	−	8.90690e25i	−0.250126	−	0.602175i
$415$	−1.55962e26			−1.02929
$416$		−	3.74805e25i		−	0.241475i
$417$	−3.21250e25	+	4.81298e25i	−0.202061	+	0.302729i
$418$	7.75694e25			0.476351
$419$			1.28332e26i			0.769473i	0.923026	+	0.384737i	$0.125708\pi$
$419$			1.28332e26i			0.769473i	−0.923026	+	0.384737i	$0.874292\pi$
$420$	−1.34854e26	−	9.00105e25i	−0.789536	−	0.526988i
$421$	2.24799e24			0.0128521			0.00642605	−	0.999979i	$-0.497955\pi$
$421$	2.24799e24			0.0128521			0.00642605	+	0.999979i	$0.497955\pi$
$422$			1.55447e26i			0.867874i
$423$	2.22230e26	−	9.23077e25i	1.21171	−	0.503308i
$424$	−1.81545e26			−0.966777
$425$			8.95823e24i			0.0465943i
$426$	5.23277e24	−	7.83976e24i	0.0265849	−	0.0398297i
$427$	−5.05862e25			−0.251046
$428$		−	7.05365e25i		−	0.341961i
$429$	5.77160e25	+	3.85234e25i	0.273352	+	0.182453i
$430$	−1.42169e26			−0.657842
$431$		−	3.71594e26i		−	1.67995i	−0.542627	−	0.839973i	$-0.682570\pi$
$431$		−	3.71594e26i		−	1.67995i	0.542627	−	0.839973i	$-0.317430\pi$
$432$	4.68137e25	+	9.23980e24i	0.206793	+	0.0408155i
$433$	−2.54165e26			−1.09708			−0.548538	−	0.836126i	$-0.684815\pi$
$433$	−2.54165e26			−1.09708			−0.548538	+	0.836126i	$0.684815\pi$
$434$		−	2.42081e26i		−	1.02109i
$435$	4.57752e25	−	6.85807e25i	0.188685	−	0.282689i
$436$	2.00822e26			0.808996
$437$		−	1.92011e26i		−	0.755984i
$438$	1.12013e26	+	7.47647e25i	0.431049	+	0.287710i
$439$	−2.48115e25			−0.0933273			−0.0466636	−	0.998911i	$-0.514859\pi$
$439$	−2.48115e25			−0.0933273			−0.0466636	+	0.998911i	$0.514859\pi$
$440$			3.87315e26i			1.42409i
$441$	−5.29972e25	−	1.27590e26i	−0.190488	−	0.458597i
$442$	−8.38229e24			−0.0294537
$443$			5.15223e26i			1.76994i	0.465652	+	0.884968i	$0.345820\pi$
$443$			5.15223e26i			1.76994i	−0.465652	+	0.884968i	$0.654180\pi$
$444$	−1.29635e26	+	1.94220e26i	−0.435404	+	0.652324i
$445$	5.21240e25			0.171174
$446$			7.59734e25i			0.243957i
$447$	1.33183e26	+	8.88947e25i	0.418189	+	0.279126i
$448$	1.38838e26			0.426312
$449$		−	4.14551e26i		−	1.24484i	−0.782682	−	0.622422i	$-0.786149\pi$
$449$		−	4.14551e26i		−	1.24484i	0.782682	−	0.622422i	$-0.213851\pi$
$450$	3.37818e25	−	1.40320e25i	0.0992106	−	0.0412091i
$451$	−3.16453e26			−0.908957
$452$			1.21978e26i			0.342688i
$453$	−1.34049e26	+	2.00833e26i	−0.368367	+	0.551890i
$454$	3.71576e26			0.998824
$455$			1.18729e26i			0.312208i
$456$	−1.86621e26	−	1.24563e26i	−0.480078	−	0.320435i
$457$	6.14547e26			1.54665			0.773327	−	0.634007i	$-0.218591\pi$
$457$	6.14547e26			1.54665			0.773327	+	0.634007i	$0.218591\pi$
$458$		−	3.55165e26i		−	0.874532i
$459$	1.88171e25	−	9.53376e25i	0.0453343	−	0.229688i
$460$	3.97623e26			0.937332
$461$			2.58856e25i			0.0597103i	0.999554	+	0.0298552i	$0.00950461\pi$
$461$			2.58856e25i			0.0597103i	−0.999554	+	0.0298552i	$0.990495\pi$
$462$	−2.29016e26	+	3.43113e26i	−0.516946	+	0.774492i
$463$	−6.27233e26			−1.38554			−0.692770	−	0.721158i	$-0.743610\pi$
$463$	−6.27233e26			−1.38554			−0.692770	+	0.721158i	$0.743610\pi$
$464$		−	3.02636e25i		−	0.0654246i
$465$	−6.65611e26	−	4.44272e26i	−1.40829	−	0.939982i
$466$	−1.50924e25			−0.0312536
$467$			5.47076e26i			1.10886i	0.832229	+	0.554432i	$0.187065\pi$
$467$			5.47076e26i			1.10886i	−0.832229	+	0.554432i	$0.812935\pi$
$468$	−3.19323e25	−	7.68767e25i	−0.0633537	−	0.152523i
$469$	3.78895e26			0.735851
$470$		−	4.07921e26i		−	0.775529i
$471$	3.11670e26	−	4.66945e26i	0.580077	−	0.869075i
$472$	−5.27029e26			−0.960317
$473$		−	8.79729e26i		−	1.56941i
$474$	3.16439e26	+	2.11212e26i	0.552723	+	0.368923i
$475$	7.28255e25			0.124551
$476$			1.21192e26i			0.202958i
$477$	−5.90305e26	+	2.45195e26i	−0.968039	+	0.402095i
$478$	−3.01843e26			−0.484732
$479$			8.05796e26i			1.26727i	0.773631	+	0.633636i	$0.218438\pi$
$479$			8.05796e26i			1.26727i	−0.773631	+	0.633636i	$0.781562\pi$
$480$	4.08917e26	−	6.12642e26i	0.629829	−	0.943614i
$481$	1.70996e26			0.257950
$482$			6.72864e26i			0.994161i
$483$	8.49324e26	+	5.66894e26i	1.22914	+	0.820409i
$484$	−4.94094e26			−0.700416
$485$			3.76015e26i			0.522141i
$486$	−3.88997e26	+	7.83746e25i	−0.529155	+	0.106614i
$487$	1.21044e27			1.61308			0.806538	−	0.591182i	$-0.201338\pi$
$487$	1.21044e27			1.61308			0.806538	+	0.591182i	$0.201338\pi$
$488$		−	1.44968e26i		−	0.189267i
$489$	−7.56949e25	+	1.13407e26i	−0.0968229	+	0.145061i
$490$	−2.34203e26			−0.293515
$491$		−	1.27713e27i		−	1.56827i	−0.620592	−	0.784134i	$-0.713107\pi$
$491$		−	1.27713e27i		−	1.56827i	0.620592	−	0.784134i	$-0.286893\pi$
$492$	3.15754e26	+	2.10755e26i	0.379926	+	0.253587i
$493$	−6.16328e25			−0.0726679
$494$			6.81435e25i			0.0787326i
$495$	5.23108e26	+	1.25938e27i	0.592297	+	1.42595i
$496$	−2.93724e26			−0.325929
$497$			9.97949e25i			0.108529i
$498$	2.64277e26	−	3.95941e26i	0.281686	−	0.422024i
$499$	−6.88524e26			−0.719306			−0.359653	−	0.933086i	$-0.617105\pi$
$499$	−6.88524e26			−0.719306			−0.359653	+	0.933086i	$0.617105\pi$
$500$		−	6.06951e26i		−	0.621518i
$501$	−8.50478e26	−	5.67664e26i	−0.853661	−	0.569789i
$502$	−7.01916e26			−0.690634
$503$			9.01072e26i			0.869120i	0.900643	+	0.434560i	$0.143096\pi$
$503$			9.01072e26i			0.869120i	−0.900643	+	0.434560i	$0.856904\pi$
$504$	1.10196e27	−	4.57721e26i	1.04198	−	0.432808i
$505$	−9.33253e26			−0.865139
$506$		−	1.01168e27i		−	0.919472i
$507$	5.89172e26	−	8.82700e26i	0.525003	−	0.786563i
$508$	8.73821e25			0.0763458
$509$			1.38451e27i			1.18609i	0.805168	+	0.593047i	$0.202075\pi$
$509$			1.38451e27i			1.18609i	−0.805168	+	0.593047i	$0.797925\pi$
$510$	−1.37014e26	−	9.14519e25i	−0.115097	−	0.0768230i
$511$	−1.42585e27			−1.17453
$512$		−	5.11010e26i		−	0.412791i
$513$	−7.75043e26	−	1.52973e26i	−0.613977	−	0.121183i
$514$	1.11677e27			0.867626
$515$		−	1.23767e27i		−	0.943049i
$516$	−5.85893e26	+	8.77788e26i	−0.437846	+	0.655983i
$517$	2.52417e27			1.85018
$518$			1.01655e27i			0.730853i
$519$	−6.34708e26	−	4.23645e26i	−0.447610	−	0.298764i
$520$	−3.40250e26			−0.235377
$521$		−	1.26875e27i		−	0.860994i	−0.902592	−	0.430497i	$-0.858338\pi$
$521$		−	1.26875e27i		−	0.860994i	0.902592	−	0.430497i	$-0.141662\pi$
$522$	9.65402e25	+	2.32420e26i	0.0642693	+	0.154728i
$523$	2.36185e27			1.54254			0.771268	−	0.636511i	$-0.219623\pi$
$523$	2.36185e27			1.54254			0.771268	+	0.636511i	$0.219623\pi$
$524$			1.93650e27i			1.24081i
$525$	−2.15010e26	+	3.22129e26i	−0.135165	+	0.202506i
$526$	−4.93500e26			−0.304389
$527$			5.98178e26i			0.362013i
$528$	4.16310e26	+	2.77872e26i	0.247216	+	0.165008i
$529$	−7.88109e26			−0.459229
$530$			1.08355e27i			0.619572i
$531$	−1.71367e27	+	7.11806e26i	−0.961570	+	0.399408i
$532$	9.85227e26			0.542525
$533$		−	2.77999e26i		−	0.150235i
$534$	−8.83240e25	+	1.32327e26i	−0.0468453	+	0.0701839i
$535$	−1.01510e27			−0.528410
$536$			1.08582e27i			0.554767i
$537$	−2.95833e26	−	1.97458e26i	−0.148355	−	0.0990220i
$538$	1.46431e26			0.0720795
$539$		−	1.44922e27i		−	0.700240i
$540$	3.16781e26	−	1.60498e27i	0.150253	−	0.761260i
$541$	4.12895e27			1.92250			0.961251	−	0.275674i	$-0.0889010\pi$
$541$	4.12895e27			1.92250			0.961251	+	0.275674i	$0.0889010\pi$
$542$		−	8.32099e26i		−	0.380349i
$543$	5.58536e25	−	8.36802e25i	0.0250641	−	0.0375512i
$544$	−5.50575e26			−0.242565
$545$		−	2.89005e27i		−	1.25009i
$546$	−3.01419e26	−	2.01187e26i	−0.128010	−	0.0854423i
$547$	−3.82135e27			−1.59347			−0.796735	−	0.604329i	$-0.793441\pi$
$547$	−3.82135e27			−1.59347			−0.796735	+	0.604329i	$0.793441\pi$
$548$		−	2.04429e27i		−	0.837023i
$549$	−1.95794e26	−	4.71372e26i	−0.0787184	−	0.189514i
$550$	3.83708e26			0.151486
$551$			5.01041e26i			0.194248i
$552$	−1.62458e27	+	2.43396e27i	−0.618516	+	0.926665i
$553$	−4.02806e27			−1.50607
$554$		−	1.30190e27i		−	0.478057i
$555$	2.79504e27	+	1.86559e27i	1.00799	+	0.672801i
$556$	7.28166e26			0.257918
$557$			4.26263e27i			1.48295i	0.670983	+	0.741473i	$0.265873\pi$
$557$			4.26263e27i			1.48295i	−0.670983	+	0.741473i	$0.734127\pi$
$558$	2.25575e27	−	9.36973e26i	0.770814	−	0.320173i
$559$	7.72829e26			0.259397
$560$			8.56404e26i			0.282357i
$561$	5.65895e26	−	8.47827e26i	0.183277	−	0.274586i
$562$	−3.05714e26			−0.0972641
$563$			1.02656e27i			0.320848i	0.987048	+	0.160424i	$0.0512861\pi$
$563$			1.02656e27i			0.320848i	−0.987048	+	0.160424i	$0.948714\pi$
$564$	−2.51861e27	−	1.68108e27i	−0.773337	−	0.516176i
$565$	1.75541e27			0.529533
$566$		−	6.48536e23i		−	0.000192207i
$567$	2.96488e27	−	2.97661e27i	0.863330	−	0.866745i
$568$	−2.85988e26			−0.0818210
$569$			4.08303e27i			1.14778i	0.818931	+	0.573892i	$0.194567\pi$
$569$			4.08303e27i			1.14778i	−0.818931	+	0.573892i	$0.805433\pi$
$570$	−7.43454e26	+	1.11385e27i	−0.205355	+	0.307664i
$571$	−1.45290e27			−0.394344			−0.197172	−	0.980369i	$-0.563176\pi$
$571$	−1.45290e27			−0.394344			−0.197172	+	0.980369i	$0.563176\pi$
$572$		−	8.73197e26i		−	0.232891i
$573$	4.33164e27	+	2.89122e27i	1.13529	+	0.757765i
$574$	1.65266e27			0.425662
$575$		−	9.49810e26i		−	0.240413i
$576$	5.37372e26	+	1.29372e27i	0.133675	+	0.321821i
$577$	−1.73801e27			−0.424908			−0.212454	−	0.977171i	$-0.568146\pi$
$577$	−1.73801e27			−0.424908			−0.212454	+	0.977171i	$0.568146\pi$
$578$		−	2.12334e27i		−	0.510202i
$579$	1.20211e27	−	1.80102e27i	0.283897	−	0.425336i
$580$	−1.03757e27			−0.240845
$581$			5.04006e27i			1.14994i
$582$	−9.54591e26	−	6.37156e26i	−0.214086	−	0.142895i
$583$	−6.70492e27			−1.47811
$584$		−	4.08614e27i		−	0.885493i
$585$	−1.10634e27	+	4.59542e26i	−0.235685	+	0.0978964i
$586$	−4.68516e26			−0.0981179
$587$		−	6.60188e27i		−	1.35921i	−0.733578	−	0.679606i	$-0.762151\pi$
$587$		−	6.60188e27i		−	1.35921i	0.733578	−	0.679606i	$-0.237849\pi$
$588$	−9.65170e26	+	1.44602e27i	−0.195358	+	0.292686i
$589$	4.86286e27			0.967696
$590$			3.14558e27i			0.615432i
$591$	−4.20561e27	−	2.80709e27i	−0.809010	−	0.539986i
$592$	1.23341e27			0.233287
$593$		−	7.02277e27i		−	1.30605i	−0.757334	−	0.653027i	$-0.773499\pi$
$593$		−	7.02277e27i		−	1.30605i	0.757334	−	0.653027i	$-0.226501\pi$
$594$	−4.08359e27	−	8.05993e26i	−0.746755	−	0.147390i
$595$	1.74409e27			0.313617
$596$		−	2.01495e27i		−	0.356288i
$597$	−2.41453e27	+	3.61747e27i	−0.419846	+	0.629015i
$598$	8.88746e26			0.151973
$599$			1.50131e27i			0.252466i	0.992001	+	0.126233i	$0.0402887\pi$
$599$			1.50131e27i			0.252466i	−0.992001	+	0.126233i	$0.959711\pi$
$600$	−9.23145e26	−	6.16167e26i	−0.152671	−	0.101903i
$601$	9.04979e27			1.47195			0.735976	−	0.677007i	$-0.236723\pi$
$601$	9.04979e27			1.47195			0.735976	+	0.677007i	$0.236723\pi$
$602$			4.59435e27i			0.734952i
$603$	1.46651e27	+	3.53061e27i	0.230734	+	0.555491i
$604$	3.03844e27			0.470198
$605$			7.11057e27i			1.08231i
$606$	1.58140e27	−	2.36926e27i	0.236763	−	0.354720i
$607$	−6.10925e26			−0.0899707			−0.0449853	−	0.998988i	$-0.514324\pi$
$607$	−6.10925e26			−0.0899707			−0.0449853	+	0.998988i	$0.514324\pi$
$608$			4.47588e27i			0.648399i
$609$	−2.21625e27	−	1.47927e27i	−0.315825	−	0.210802i
$610$	−8.65243e26			−0.121294
$611$			2.21745e27i			0.305803i
$612$	−1.12929e27	+	4.69075e26i	−0.153212	+	0.0636397i
$613$	−9.02654e27			−1.20480			−0.602402	−	0.798193i	$-0.705790\pi$
$613$	−9.02654e27			−1.20480			−0.602402	+	0.798193i	$0.705790\pi$
$614$		−	9.84109e26i		−	0.129229i
$615$	3.03300e27	−	4.54406e27i	0.391852	−	0.587074i
$616$	1.25165e28			1.59102
$617$		−	1.43266e28i		−	1.79180i	−0.444253	−	0.895902i	$-0.646531\pi$
$617$		−	1.43266e28i		−	1.79180i	0.444253	−	0.895902i	$-0.353469\pi$
$618$	3.14209e27	+	2.09724e27i	0.386664	+	0.258085i
$619$	1.97740e25			0.00239436			0.00119718	−	0.999999i	$-0.499619\pi$
$619$	1.97740e25			0.00239436			0.00119718	+	0.999999i	$0.499619\pi$
$620$			1.00702e28i			1.19983i
$621$	−1.99512e27	+	1.01083e28i	−0.233912	+	1.18512i
$622$	4.03600e26			0.0465637
$623$		−	1.68444e27i		−	0.191238i
$624$	−2.44106e26	+	3.65721e26i	−0.0272730	+	0.0408606i
$625$	−1.05448e28			−1.15941
$626$			5.10442e27i			0.552336i
$627$	−6.89237e27	−	4.60042e27i	−0.733995	−	0.489916i
$628$	−7.06452e27			−0.740433
$629$		−	2.51188e27i		−	0.259114i
$630$	−2.73191e27	−	6.57704e27i	−0.277371	−	0.667767i
$631$	8.07369e27			0.806823			0.403412	−	0.915019i	$-0.367824\pi$
$631$	8.07369e27			0.806823			0.403412	+	0.915019i	$0.367824\pi$
$632$		−	1.15435e28i		−	1.13544i
$633$	9.21909e27	−	1.38121e28i	0.892588	−	1.33728i
$634$	−5.45602e27			−0.519976
$635$		−	1.25753e27i		−	0.117972i
$636$	6.69013e27	+	4.46543e27i	0.617822	+	0.412374i
$637$	1.27312e27			0.115738
$638$			2.63992e27i			0.236256i
$639$	−9.29908e26	+	3.86256e26i	−0.0819278	+	0.0340304i
$640$	−1.07052e28			−0.928526
$641$			5.88611e27i			0.502630i	0.967905	+	0.251315i	$0.0808630\pi$
$641$			5.88611e27i			0.502630i	−0.967905	+	0.251315i	$0.919137\pi$
$642$	1.72008e27	−	2.57704e27i	0.144610	−	0.216656i
$643$	−9.35352e26			−0.0774222			−0.0387111	−	0.999250i	$-0.512325\pi$
$643$	−9.35352e26			−0.0774222			−0.0387111	+	0.999250i	$0.512325\pi$
$644$		−	1.28496e28i		−	1.04720i
$645$	1.26324e28	+	8.43166e27i	1.01365	+	0.676575i
$646$	1.00100e27			0.0790880
$647$			7.23899e27i			0.563165i	0.959537	+	0.281582i	$0.0908593\pi$
$647$			7.23899e27i			0.563165i	−0.959537	+	0.281582i	$0.909141\pi$
$648$	8.53025e27	+	8.49664e27i	0.653449	+	0.650874i
$649$	−1.94645e28			−1.46824
$650$			3.37081e26i			0.0250381i
$651$	−1.43571e28	+	2.15099e28i	−1.05016	+	1.57336i
$652$	1.71575e27			0.123589
$653$			3.92965e27i			0.278755i	0.990239	+	0.139377i	$0.0445101\pi$
$653$			3.92965e27i			0.278755i	−0.990239	+	0.139377i	$0.955490\pi$
$654$	7.33700e27	+	4.89719e27i	0.512556	+	0.342113i
$655$	2.78684e28			1.91734
$656$		−	2.00523e27i		−	0.135870i
$657$	−5.51875e27	−	1.32863e28i	−0.368287	−	0.886648i
$658$	−1.31824e28			−0.866434
$659$			2.07410e28i			1.34269i	0.741147	+	0.671343i	$0.234282\pi$
$659$			2.07410e28i			1.34269i	−0.741147	+	0.671343i	$0.765718\pi$
$660$	9.52669e27	−	1.42729e28i	0.607439	−	0.910069i
$661$	1.98121e28			1.24427			0.622136	−	0.782909i	$-0.286265\pi$
$661$	1.98121e28			1.24427			0.622136	+	0.782909i	$0.286265\pi$
$662$		−	8.66680e27i		−	0.536141i
$663$	7.44803e26	+	4.97130e26i	0.0453843	+	0.0302925i
$664$	−1.44436e28			−0.866952
$665$		−	1.41785e28i		−	0.838329i
$666$	−9.47238e27	+	3.93455e27i	−0.551717	+	0.229167i
$667$	6.53471e27			0.374946
$668$			1.28671e28i			0.727302i
$669$	4.50576e27	−	6.75056e27i	0.250904	−	0.375906i
$670$	6.48073e27			0.355530
$671$		−	5.35403e27i		−	0.289372i
$672$	−1.97981e28	−	1.32146e28i	−1.05422	−	0.703656i
$673$	−8.53248e26			−0.0447636			−0.0223818	−	0.999749i	$-0.507125\pi$
$673$	−8.53248e26			−0.0447636			−0.0223818	+	0.999749i	$0.507125\pi$
$674$		−	7.35974e27i		−	0.380420i
$675$	−3.83386e27	−	7.56702e26i	−0.195253	−	0.0385378i
$676$	−1.33546e28			−0.670136
$677$			1.67889e27i			0.0830111i	0.999138	+	0.0415056i	$0.0132154\pi$
$677$			1.67889e27i			0.0830111i	−0.999138	+	0.0415056i	$0.986785\pi$
$678$	−2.97453e27	+	4.45646e27i	−0.144918	+	0.217117i
$679$	1.21513e28			0.583345
$680$			4.99816e27i			0.236440i
$681$	−3.30161e28	−	2.20371e28i	−1.53906	−	1.02727i
$682$	2.56217e28			1.17697
$683$		−	1.41957e27i		−	0.0642612i	−0.999484	−	0.0321306i	$-0.989771\pi$
$683$		−	1.41957e27i		−	0.0642612i	0.999484	−	0.0321306i	$-0.0102292\pi$
$684$	3.81332e27	+	9.18053e27i	0.170115	+	0.409550i
$685$	−2.94197e28			−1.29340
$686$		−	7.67258e27i		−	0.332430i
$687$	−2.10638e28	+	3.15580e28i	−0.899436	+	1.34754i
$688$	5.57447e27			0.234595
$689$		−	5.89017e27i		−	0.244307i
$690$	1.45271e28	+	9.69633e27i	0.593866	+	0.396384i
$691$	2.92875e28			1.18005			0.590027	−	0.807384i	$-0.299117\pi$
$691$	2.92875e28			1.18005			0.590027	+	0.807384i	$0.299117\pi$
$692$			9.60263e27i			0.381355i
$693$	4.06981e28	−	1.69048e28i	1.59309	−	0.661724i
$694$	5.57231e27			0.215001
$695$		−	1.04791e28i		−	0.398545i
$696$	4.23924e27	−	6.35126e27i	0.158926	−	0.238104i
$697$	−4.08370e27			−0.150913
$698$		−	1.19188e28i		−	0.434188i
$699$	1.34103e27	+	8.95090e26i	0.0481578	+	0.0321436i
$700$	4.87356e27			0.172531
$701$			3.58407e28i			1.25083i	0.780294	+	0.625413i	$0.215069\pi$
$701$			3.58407e28i			1.25083i	−0.780294	+	0.625413i	$0.784931\pi$
$702$	7.08053e26	−	3.58737e27i	0.0243610	−	0.123426i
$703$	−2.04202e28			−0.692638
$704$			1.46946e28i			0.491394i
$705$	−2.41926e28	+	3.62456e28i	−0.797613	+	1.19499i
$706$	−6.27722e27			−0.204042
$707$			3.01590e28i			0.966548i
$708$	1.94216e28	+	1.29632e28i	0.613694	+	0.409619i
$709$	1.27965e28			0.398685			0.199343	−	0.979930i	$-0.436119\pi$
$709$	1.27965e28			0.398685			0.199343	+	0.979930i	$0.436119\pi$
$710$			1.70692e27i			0.0524361i
$711$	−1.55906e28	−	3.75342e28i	−0.472245	−	1.13692i
$712$	4.82720e27			0.144177
$713$		−	6.34228e28i		−	1.86788i
$714$	−2.95536e27	+	4.42774e27i	−0.0858279	+	0.128588i
$715$	−1.25663e28			−0.359871
$716$			4.47572e27i			0.126396i
$717$	2.68200e28	+	1.79014e28i	0.746909	+	0.498536i
$718$	−2.00097e28			−0.549536
$719$		−	5.14712e28i		−	1.39404i	−0.717052	−	0.697020i	$-0.754509\pi$
$719$		−	5.14712e28i		−	1.39404i	0.717052	−	0.697020i	$-0.245491\pi$
$720$	−7.98014e27	+	3.31471e27i	−0.213150	+	0.0885362i
$721$	−3.99967e28			−1.05359
$722$			1.26400e28i			0.328379i
$723$	3.99056e28	−	5.97869e28i	1.02247	−	1.53187i
$724$	−1.26602e27			−0.0319929
$725$			2.47847e27i			0.0617736i
$726$	−1.80516e28	−	1.20488e28i	−0.443763	−	0.296196i
$727$	−1.87882e28			−0.455555			−0.227778	−	0.973713i	$-0.573146\pi$
$727$	−1.87882e28			−0.455555			−0.227778	+	0.973713i	$0.573146\pi$
$728$			1.09955e28i			0.262968i
$729$	3.92122e28	+	1.61063e28i	0.925009	+	0.379946i
$730$	−2.43882e28			−0.567480
$731$		−	1.13526e28i		−	0.260568i
$732$	−3.56574e27	+	5.34222e27i	−0.0807308	+	0.120951i
$733$	−6.45505e28			−1.44165			−0.720825	−	0.693117i	$-0.756237\pi$
$733$	−6.45505e28			−1.44165			−0.720825	+	0.693117i	$0.756237\pi$
$734$			2.24682e28i			0.495003i
$735$	2.08099e28	+	1.38899e28i	0.452269	+	0.301874i
$736$	5.83756e28			1.25156
$737$			4.01021e28i			0.848188i
$738$	6.39662e27	+	1.53998e28i	0.133471	+	0.321330i
$739$	6.92709e28			1.42596			0.712979	−	0.701186i	$-0.247346\pi$
$739$	6.92709e28			1.42596			0.712979	+	0.701186i	$0.247346\pi$
$740$		−	4.22868e28i		−	0.858791i
$741$	4.04139e27	−	6.05484e27i	0.0809747	−	0.121317i
$742$	3.50162e28			0.692197
$743$			8.70498e28i			1.69777i	0.528576	+	0.848886i	$0.322726\pi$
$743$			8.70498e28i			1.69777i	−0.528576	+	0.848886i	$0.677274\pi$
$744$	−6.16422e28	−	4.11440e28i	−1.18618	−	0.791731i
$745$	−2.89974e28			−0.550549
$746$		−	3.22696e28i		−	0.604513i
$747$	−4.69643e28	+	1.95076e28i	−0.868083	+	0.360576i
$748$	−1.28270e28			−0.233942
$749$			3.28040e28i			0.590349i
$750$	1.48009e28	−	2.21748e28i	0.262831	−	0.393775i
$751$	2.75904e28			0.483458			0.241729	−	0.970344i	$-0.422286\pi$
$751$	2.75904e28			0.483458			0.241729	+	0.970344i	$0.422286\pi$
$752$			1.59946e28i			0.276564i
$753$	6.23683e28	+	4.16286e28i	1.06418	+	0.710301i
$754$	−2.31912e27			−0.0390491
$755$		−	4.37266e28i		−	0.726567i
$756$	−5.18667e28	−	1.02371e28i	−0.850493	−	0.167865i
$757$	1.04629e29			1.69315			0.846574	−	0.532271i	$-0.178661\pi$
$757$	1.04629e29			1.69315			0.846574	+	0.532271i	$0.178661\pi$
$758$			6.07549e28i			0.970263i
$759$	−5.99999e28	+	8.98922e28i	−0.945655	+	1.41679i
$760$	4.06323e28			0.632026
$761$		−	1.14700e29i		−	1.76082i	−0.474210	−	0.880412i	$-0.657266\pi$
$761$		−	1.14700e29i		−	1.76082i	0.474210	−	0.880412i	$-0.342734\pi$
$762$	3.19249e27	+	2.13088e27i	0.0483704	+	0.0322856i
$763$	−9.33951e28			−1.39662
$764$		−	6.55343e28i		−	0.967242i
$765$	6.75051e27	+	1.62518e28i	0.0983383	+	0.236748i
$766$	−8.03680e27			−0.115557
$767$		−	1.70993e28i		−	0.242674i
$768$	3.19503e28	−	4.78682e28i	0.447572	−	0.670555i
$769$	9.16230e27			0.126690			0.0633448	−	0.997992i	$-0.479823\pi$
$769$	9.16230e27			0.126690			0.0633448	+	0.997992i	$0.479823\pi$
$770$		−	7.47047e28i		−	1.01963i
$771$	−9.92298e28	−	6.62324e28i	−1.33690	−	0.892333i
$772$	−2.72480e28			−0.362377
$773$			7.07996e28i			0.929471i	0.885450	+	0.464735i	$0.153851\pi$
$773$			7.07996e28i			0.929471i	−0.885450	+	0.464735i	$0.846149\pi$
$774$	−4.28110e28	+	1.77824e28i	−0.554812	+	0.230453i
$775$	2.40548e28			0.307741
$776$			3.48227e28i			0.439790i
$777$	6.02885e28	−	9.03246e28i	0.751665	−	1.12615i
$778$	1.73832e28			0.213961
$779$			3.31983e28i			0.403405i
$780$	1.25386e28	+	8.36905e27i	0.150419	+	0.100399i
$781$	−1.05623e28			−0.125097
$782$		−	1.30554e28i		−	0.152659i
$783$	5.20612e27	−	2.63770e28i	0.0601031	−	0.304514i
$784$	9.18310e27			0.104672
$785$			1.01666e29i			1.14414i
$786$	−4.72230e28	+	7.07498e28i	−0.524721	+	0.786140i
$787$	−3.83619e27			−0.0420874			−0.0210437	−	0.999779i	$-0.506699\pi$
$787$	−3.83619e27			−0.0420874			−0.0210437	+	0.999779i	$0.506699\pi$
$788$			6.36275e28i			0.689259i
$789$	4.38496e28	+	2.92681e28i	0.469024	+	0.313057i
$790$	−6.88972e28			−0.727664
$791$		−	5.67278e28i		−	0.591604i
$792$	4.84450e28	+	1.16631e29i	0.498882	+	1.20105i
$793$	4.70343e27			0.0478281
$794$		−	3.97488e27i		−	0.0399134i
$795$	6.42625e28	−	9.62785e28i	0.637216	−	0.954680i
$796$	5.47294e28			0.535908
$797$			9.63071e27i			0.0931268i	0.998915	+	0.0465634i	$0.0148270\pi$
$797$			9.63071e27i			0.0931268i	−0.998915	+	0.0465634i	$0.985173\pi$
$798$	3.59951e28	+	2.40255e28i	0.343728	+	0.229426i
$799$	3.25735e28			0.307183
$800$			2.21405e28i			0.206200i
$801$	1.56959e28	−	6.51963e27i	0.144365	−	0.0599650i
$802$	1.01558e29			0.922512
$803$		−	1.50911e29i		−	1.35384i
$804$	2.67077e28	−	4.00136e28i	0.236633	−	0.354525i
$805$	−1.84920e29			−1.61818
$806$			2.25083e28i			0.194533i
$807$	−1.30111e28	−	8.68443e27i	−0.111065	−	0.0741321i
$808$	−8.64286e28			−0.728692
$809$			1.51922e29i			1.26513i	0.774507	+	0.632565i	$0.217998\pi$
$809$			1.51922e29i			1.26513i	−0.774507	+	0.632565i	$0.782002\pi$
$810$	5.07123e28	−	5.09129e28i	0.417122	−	0.418772i
$811$	5.57248e28			0.452731			0.226365	−	0.974042i	$-0.427316\pi$
$811$	5.57248e28			0.452731			0.226365	+	0.974042i	$0.427316\pi$
$812$			3.35302e28i			0.269076i
$813$	−4.93494e28	+	7.39356e28i	−0.391180	+	0.586068i
$814$	−1.07591e29			−0.842427
$815$		−	2.46916e28i		−	0.190974i
$816$	5.37232e27	+	3.58583e27i	0.0410450	+	0.0273961i
$817$	−9.22903e28			−0.696523
$818$		−	5.47765e28i		−	0.408377i
$819$	1.48506e28	+	3.57526e28i	0.109372	+	0.263311i
$820$	−6.87481e28			−0.500175
$821$		−	1.94189e29i		−	1.39570i	−0.716243	−	0.697851i	$-0.754140\pi$
$821$		−	1.94189e29i		−	1.39570i	0.716243	−	0.697851i	$-0.245860\pi$
$822$	4.98515e28	−	7.46879e28i	0.353965	−	0.530312i
$823$	−2.07933e29			−1.45856			−0.729281	−	0.684214i	$-0.760145\pi$
$823$	−2.07933e29			−1.45856			−0.729281	+	0.684214i	$0.760145\pi$
$824$		−	1.14621e29i		−	0.794314i
$825$	−3.40941e28	−	2.27566e28i	−0.233421	−	0.155800i
$826$	1.01653e29			0.687572
$827$		−	2.69913e28i		−	0.180372i	−0.995925	−	0.0901858i	$-0.971254\pi$
$827$		−	2.69913e28i		−	0.180372i	0.995925	−	0.0901858i	$-0.0287461\pi$
$828$	1.19735e29	−	4.97344e28i	0.790529	−	0.328362i
$829$	2.72581e29			1.77808			0.889039	−	0.457832i	$-0.151374\pi$
$829$	2.72581e29			1.77808			0.889039	+	0.457832i	$0.151374\pi$
$830$			8.62068e28i			0.555598i
$831$	−7.72118e28	+	1.15679e29i	−0.491670	+	0.736623i
$832$	−1.29089e28			−0.0812190
$833$		−	1.87017e28i		−	0.116260i
$834$	2.66034e28	+	1.77569e28i	0.163409	+	0.109070i
$835$	1.85171e29			1.12385
$836$			1.04276e29i			0.625349i
$837$	−2.56003e29	−	5.05281e28i	−1.51701	−	0.299419i
$838$	7.09345e28			0.415353
$839$			3.03655e28i			0.175696i	0.996134	+	0.0878478i	$0.0279989\pi$
$839$			3.03655e28i			0.175696i	−0.996134	+	0.0878478i	$0.972001\pi$
$840$	−1.19963e29	+	1.79729e29i	−0.685888	+	1.02760i
$841$	1.59943e29			0.903659
$842$		−	1.24256e27i		−	0.00693742i
$843$	2.71640e28	+	1.81310e28i	0.149871	+	0.100034i
$844$	−2.08966e29			−1.13934
$845$			1.92187e29i			1.03552i
$846$	−5.10225e28	−	1.22836e29i	−0.271680	−	0.654067i
$847$	2.29785e29			1.20917
$848$		−	4.24862e28i		−	0.220948i
$849$	−3.84628e25	+	5.76252e25i	−0.000197681	+	0.000296166i
$850$	4.95160e27			0.0251511
$851$			2.66326e29i			1.33696i
$852$	1.05390e28	+	7.03439e27i	0.0522880	+	0.0349004i
$853$	6.99358e28			0.342933			0.171467	−	0.985190i	$-0.445149\pi$
$853$	6.99358e28			0.342933			0.171467	+	0.985190i	$0.445149\pi$
$854$			2.79612e28i			0.135512i
$855$	1.32118e29	−	5.48780e28i	0.632851	−	0.262868i
$856$	−9.40084e28			−0.445071
$857$			1.65881e28i			0.0776228i	0.999247	+	0.0388114i	$0.0123571\pi$
$857$			1.65881e28i			0.0776228i	−0.999247	+	0.0388114i	$0.987643\pi$
$858$	2.12935e28	−	3.19021e28i	0.0984861	−	0.147553i
$859$	−1.17402e29			−0.536715			−0.268357	−	0.963319i	$-0.586481\pi$
$859$	−1.17402e29			−0.536715			−0.268357	+	0.963319i	$0.586481\pi$
$860$		−	1.91118e29i		−	0.863608i
$861$	−1.46846e29	−	9.80146e28i	−0.655890	−	0.437783i
$862$	−2.05396e29			−0.906816
$863$		−	1.57424e29i		−	0.687012i	−0.939150	−	0.343506i	$-0.888385\pi$
$863$		−	1.57424e29i		−	0.687012i	0.939150	−	0.343506i	$-0.111615\pi$
$864$	4.65071e28	−	2.35630e29i	0.200624	−	1.01647i
$865$	1.38193e29			0.589283
$866$			1.40488e29i			0.592189i
$867$	−1.25929e29	+	1.88668e29i	−0.524731	+	0.786155i
$868$	3.25428e29			1.34047
$869$		−	4.26329e29i		−	1.73599i
$870$	−3.79075e28	−	2.53019e28i	−0.152592	−	0.101850i
$871$	−3.52291e28			−0.140191
$872$		−	2.67648e29i		−	1.05293i
$873$	4.70316e28	+	1.13228e29i	0.182914	+	0.440364i
$874$	−1.06133e29			−0.408071
$875$			2.82271e29i			1.07297i
$876$	−1.00506e29	+	1.50578e29i	−0.377703	+	0.565877i
$877$	−2.26173e29			−0.840321			−0.420161	−	0.907450i	$-0.638026\pi$
$877$	−2.26173e29			−0.840321			−0.420161	+	0.907450i	$0.638026\pi$
$878$			1.37144e28i			0.0503770i
$879$	4.16297e28	+	2.77863e28i	0.151187	+	0.100912i
$880$	−9.06416e28			−0.325462
$881$			9.68944e27i			0.0343985i	0.999852	+	0.0171993i	$0.00547496\pi$
$881$			9.68944e27i			0.0343985i	−0.999852	+	0.0171993i	$0.994525\pi$
$882$	−7.05247e28	+	2.92939e28i	−0.247546	+	0.102823i
$883$	−2.40944e29			−0.836197			−0.418098	−	0.908402i	$-0.637303\pi$
$883$	−2.40944e29			−0.836197			−0.418098	+	0.908402i	$0.637303\pi$
$884$		−	1.12683e28i		−	0.0386665i
$885$	1.86555e29	−	2.79498e29i	0.632958	−	0.948301i
$886$	2.84786e29			0.955391
$887$			1.60350e29i			0.531902i	0.963987	+	0.265951i	$0.0856860\pi$
$887$			1.60350e29i			0.531902i	−0.963987	+	0.265951i	$0.914314\pi$
$888$	2.58849e29	+	1.72772e29i	0.849017	+	0.566689i
$889$	−4.06383e28			−0.131801
$890$		−	2.88112e28i		−	0.0923977i
$891$	3.15044e29	+	3.13802e29i	0.999065	+	0.995128i
$892$	−1.02131e29			−0.320264
$893$		−	2.64805e29i		−	0.821130i
$894$	4.91360e28	−	7.36158e28i	0.150669	−	0.225733i
$895$	6.44106e28			0.195311
$896$			3.45949e29i			1.03737i
$897$	−7.89689e28	−	5.27090e28i	−0.234170	−	0.156300i
$898$	−2.29140e29			−0.671952
$899$			1.65498e29i			0.479949i
$900$	1.88631e28	+	4.54128e28i	0.0540989	+	0.130243i
$901$	−8.65245e28			−0.245409
$902$			1.74917e29i			0.490645i
$903$	2.72478e29	−	4.08228e29i	0.755881	−	1.13247i
$904$	1.62568e29			0.446017
$905$			1.82194e28i			0.0494365i
$906$	1.11009e29	+	7.40945e28i	0.297904	+	0.198840i
$907$	1.18958e28			0.0315733			0.0157867	−	0.999875i	$-0.494975\pi$
$907$	1.18958e28			0.0315733			0.0157867	+	0.999875i	$0.494975\pi$
$908$			4.99508e29i			1.31124i
$909$	−2.81028e29	+	1.16731e29i	−0.729642	+	0.303072i
$910$	6.56269e28			0.168526
$911$		−	8.34864e28i		−	0.212047i	−0.994364	−	0.106023i	$-0.966188\pi$
$911$		−	8.34864e28i		−	0.212047i	0.994364	−	0.106023i	$-0.0338119\pi$
$912$	2.91509e28	−	4.36740e28i	0.0732324	−	0.109717i
$913$	−5.33439e29			−1.32549
$914$		−	3.39687e29i		−	0.834866i
$915$	7.68806e28	+	5.13151e28i	0.186898	+	0.124748i
$916$	4.77447e29			1.14808
$917$		−	9.00597e29i		−	2.14209i
$918$	−5.26973e28	−	1.04010e28i	−0.123983	−	0.0244709i
$919$	−1.72161e29			−0.400663			−0.200332	−	0.979728i	$-0.564202\pi$
$919$	−1.72161e29			−0.400663			−0.200332	+	0.979728i	$0.564202\pi$
$920$		−	5.29937e29i		−	1.21996i
$921$	−5.83647e28	+	8.74423e28i	−0.132909	+	0.199125i
$922$	1.43081e28			0.0322310
$923$		−	9.27879e27i		−	0.0206764i
$924$	−4.61245e29	−	3.07865e29i	−1.01674	−	0.678641i
$925$	−1.01011e29			−0.220268
$926$			3.46699e29i			0.747899i
$927$	−1.54807e29	−	3.72697e29i	−0.330365	−	0.795350i
$928$	−1.52327e29			−0.321587
$929$			8.89331e29i			1.85740i	0.370826	+	0.928702i	$0.379075\pi$
$929$			8.89331e29i			1.85740i	−0.370826	+	0.928702i	$0.620925\pi$
$930$	−2.45569e29	+	3.67912e29i	−0.507391	+	0.760177i
$931$	−1.52034e29			−0.310774
$932$		−	2.02887e28i		−	0.0410294i
$933$	−3.58616e28	−	2.39364e28i	−0.0717486	−	0.0478897i
$934$	3.02392e29			0.598552
$935$			1.84594e29i			0.361495i
$936$	−1.02458e29	+	4.25582e28i	−0.198513	+	0.0824565i
$937$	8.72185e29			1.67191			0.835955	−	0.548799i	$-0.184915\pi$
$937$	8.72185e29			1.67191			0.835955	+	0.548799i	$0.184915\pi$
$938$		−	2.09431e29i		−	0.397204i
$939$	3.02729e29	−	4.53550e29i	0.568065	−	0.851078i
$940$	5.48367e29			1.01811
$941$			3.06082e29i			0.562266i	0.959669	+	0.281133i	$0.0907102\pi$
$941$			3.06082e29i			0.562266i	−0.959669	+	0.281133i	$0.909290\pi$
$942$	−2.58101e29	−	1.72273e29i	−0.469116	−	0.313119i
$943$	4.32981e29			0.778668
$944$		−	1.23338e29i		−	0.219471i
$945$	−1.47324e29	+	7.46420e29i	−0.259391	+	1.31421i
$946$	−4.86265e29			−0.847152
$947$		−	5.13321e29i		−	0.884890i	−0.896796	−	0.442445i	$-0.854111\pi$
$947$		−	5.13321e29i		−	0.884890i	0.896796	−	0.442445i	$-0.145889\pi$
$948$	−2.83932e29	+	4.25388e29i	−0.484318	+	0.725608i
$949$	1.32573e29			0.223766
$950$		−	4.02538e28i		−	0.0672312i
$951$	4.84791e29	+	3.23581e29i	0.801216	+	0.534783i
$952$	1.61520e29			0.264155
$953$		−	1.54534e29i		−	0.250090i	−0.992151	−	0.125045i	$-0.960092\pi$
$953$		−	1.54534e29i		−	0.250090i	0.992151	−	0.125045i	$-0.0399075\pi$
$954$	1.35530e29	+	3.26287e29i	0.217046	+	0.522536i
$955$	−9.43113e29			−1.49462
$956$		−	4.05766e29i		−	0.636351i
$957$	1.56566e29	−	2.34568e29i	0.242984	−	0.364040i
$958$	4.45399e29			0.684059
$959$			9.50726e29i			1.44501i
$960$	−2.11005e29	−	1.40838e29i	−0.317380	−	0.211840i
$961$	9.34450e29			1.39098
$962$		−	9.45171e28i		−	0.139239i
$963$	−3.05674e29	+	1.26968e29i	−0.445651	+	0.185110i
$964$	−9.04528e29			−1.30512
$965$			3.92129e29i			0.559958i
$966$	3.13347e29	−	4.69458e29i	0.442847	−	0.663477i
$967$	−7.41045e29			−1.03652			−0.518262	−	0.855222i	$-0.673421\pi$
$967$	−7.41045e29			−1.03652			−0.518262	+	0.855222i	$0.673421\pi$
$968$			6.58510e29i			0.911609i
$969$	−8.89435e28	−	5.93667e28i	−0.121864	−	0.0813401i
$970$	2.07840e29			0.281846
$971$		−	9.81619e29i		−	1.31750i	−0.752362	−	0.658750i	$-0.771085\pi$
$971$		−	9.81619e29i		−	1.31750i	0.752362	−	0.658750i	$-0.228915\pi$
$972$	−1.05359e29	−	5.22926e29i	−0.139961	−	0.694669i
$973$	−3.38644e29			−0.445261
$974$		−	6.69065e29i		−	0.870720i
$975$	1.99913e28	−	2.99511e28i	0.0257511	−	0.0385804i
$976$	3.39262e28			0.0432551
$977$			2.50288e29i			0.315860i	0.987450	+	0.157930i	$0.0504820\pi$
$977$			2.50288e29i			0.315860i	−0.987450	+	0.157930i	$0.949518\pi$
$978$	6.26848e28	+	4.18399e28i	0.0783021	+	0.0522639i
$979$	1.78281e29			0.220433
$980$		−	3.14837e29i		−	0.385324i
$981$	−3.61486e29	−	8.70273e29i	−0.437926	−	1.05430i
$982$	−7.05925e29			−0.846533
$983$		−	9.63827e29i		−	1.14410i	−0.820219	−	0.572050i	$-0.806148\pi$
$983$		−	9.63827e29i		−	1.14410i	0.820219	−	0.572050i	$-0.193852\pi$
$984$	2.80886e29	−	4.20826e29i	0.330050	−	0.494483i
$985$	9.15672e29			1.06507
$986$			3.40671e28i			0.0392253i
$987$	1.17131e30	+	7.81810e29i	1.33506	+	0.891107i
$988$	−9.16050e28			−0.103359
$989$			1.20368e30i			1.34446i
$990$	6.96112e29	−	2.89145e29i	0.769711	−	0.319715i
$991$	−1.48037e30			−1.62045			−0.810223	−	0.586121i	$-0.800654\pi$
$991$	−1.48037e30			−1.62045			−0.810223	+	0.586121i	$0.800654\pi$
$992$			1.47842e30i			1.60206i
$993$	−5.14003e29	+	7.70082e29i	−0.551408	+	0.826123i
$994$	5.51610e28			0.0585825
$995$		−	7.87618e29i		−	0.828104i
$996$	5.32262e29	+	3.55266e29i	0.554028	+	0.369794i
$997$	−5.34930e29			−0.551246			−0.275623	−	0.961266i	$-0.588884\pi$
$997$	−5.34930e29			−0.551246			−0.275623	+	0.961266i	$0.588884\pi$
$998$			3.80577e29i			0.388273i
$999$	1.07501e30	+	2.12178e29i	1.08582	+	0.214312i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.21.b.a.2.3	✓	6
3.2	odd	2	inner	3.21.b.a.2.4	yes	6
4.3	odd	2		48.21.e.c.17.5		6
12.11	even	2		48.21.e.c.17.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.21.b.a.2.3	✓	6	1.1	even	1	trivial
3.21.b.a.2.4	yes	6	3.2	odd	2	inner
48.21.e.c.17.5		6	4.3	odd	2
48.21.e.c.17.6		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)

\(f(q)\)	\(=\)	\(q-552.743i q^{2} +(-32781.6 + 49113.6i) q^{3} +743051. q^{4} -1.06933e7i q^{5} +(2.71472e7 + 1.81198e7i) q^{6} -3.45566e8 q^{7} -9.90310e8i q^{8} +(-1.33751e9 - 3.22005e9i) q^{9} +O(q^{10})\)	\(q-552.743i q^{2} +(-32781.6 + 49113.6i) q^{3} +743051. q^{4} -1.06933e7i q^{5} +(2.71472e7 + 1.81198e7i) q^{6} -3.45566e8 q^{7} -9.90310e8i q^{8} +(-1.33751e9 - 3.22005e9i) q^{9} -5.91067e9 q^{10} -3.65746e10i q^{11} +(-2.43584e10 + 3.64939e10i) q^{12} +3.21302e10 q^{13} +1.91009e11i q^{14} +(5.25189e11 + 3.50545e11i) q^{15} +2.31758e11 q^{16} -4.71982e11i q^{17} +(-1.77986e12 + 7.39302e11i) q^{18} -3.83696e12 q^{19} -7.94569e12i q^{20} +(1.13282e13 - 1.69720e13i) q^{21} -2.02164e13 q^{22} +5.00426e13i q^{23} +(4.86377e13 + 3.24640e13i) q^{24} -1.89800e13 q^{25} -1.77598e13i q^{26} +(2.01994e14 + 3.98683e13i) q^{27} -2.56773e14 q^{28} -1.30583e14i q^{29} +(1.93761e14 - 2.90295e14i) q^{30} -1.26738e15 q^{31} -1.16652e15i q^{32} +(1.79631e15 + 1.19898e15i) q^{33} -2.60885e14 q^{34} +3.69525e15i q^{35} +(-9.93841e14 - 2.39266e15i) q^{36} +5.32197e15 q^{37} +2.12085e15i q^{38} +(-1.05328e15 + 1.57803e15i) q^{39} -1.05897e16 q^{40} -8.65225e15i q^{41} +(-9.38117e15 - 6.26160e15i) q^{42} +2.40530e16 q^{43} -2.71768e16i q^{44} +(-3.44331e16 + 1.43025e16i) q^{45} +2.76607e16 q^{46} +6.90144e16i q^{47} +(-7.59740e15 + 1.13825e16i) q^{48} +3.96237e16 q^{49} +1.04911e16i q^{50} +(2.31807e16 + 1.54723e16i) q^{51} +2.38744e16 q^{52} -1.83322e17i q^{53} +(2.20370e16 - 1.11651e17i) q^{54} -3.91105e17 q^{55} +3.42218e17i q^{56} +(1.25782e17 - 1.88447e17i) q^{57} -7.21789e16 q^{58} -5.32186e17i q^{59} +(3.90242e17 + 2.60473e17i) q^{60} +1.46387e17 q^{61} +7.00533e17i q^{62} +(4.62199e17 + 1.11274e18i) q^{63} -4.01769e17 q^{64} -3.43579e17i q^{65} +(6.62726e17 - 9.92900e17i) q^{66} -1.09645e18 q^{67} -3.50706e17i q^{68} +(-2.45778e18 - 1.64048e18i) q^{69} +2.04253e18 q^{70} -2.88787e17i q^{71} +(-3.18885e18 + 1.32455e18i) q^{72} +4.12612e18 q^{73} -2.94169e18i q^{74} +(6.22196e17 - 9.32178e17i) q^{75} -2.85105e18 q^{76} +1.26390e19i q^{77} +(8.72247e17 + 5.82194e17i) q^{78} +1.16564e19 q^{79} -2.47826e18i q^{80} +(-8.57978e18 + 8.61372e18i) q^{81} -4.78247e18 q^{82} -1.45849e19i q^{83} +(8.41744e18 - 1.26111e19i) q^{84} -5.04706e18 q^{85} -1.32951e19i q^{86} +(6.41340e18 + 4.28072e18i) q^{87} -3.62202e19 q^{88} +4.87444e18i q^{89} +(7.90561e18 + 1.90327e19i) q^{90} -1.11031e19 q^{91} +3.71842e19i q^{92} +(4.15466e19 - 6.22454e19i) q^{93} +3.81472e19 q^{94} +4.10299e19i q^{95} +(5.72919e19 + 3.82404e19i) q^{96} -3.51635e19 q^{97} -2.19017e19i q^{98} +(-1.17772e20 + 4.89191e19i) 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

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