LMFDB - Embedded newform 6.27.b.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,27,Mod(5,6)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 27, names="a")

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

chi := DirichletCharacter("6.5");

S:= CuspForms(chi, 27);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 27 $
Character orbit:	$[\chi]$	$=$	6.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:	$25.6975752438$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 11609466 x^{6} - 3416571600 x^{5} + 38618090622117 x^{4} + \cdots + 60\!\cdots\!96 $ x^8 - 11609466x^6 - 3416571600x^5 + 38618090622117x^4 + 19832313245955600x^3 - 25659229618759655524x^2 - 8410094250198512820000x + 6059395276689883547331396
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{59}\cdot 3^{34}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.1
Root			$2468.36 + 1.41421i$ of defining polynomial
Character	$\chi$	$=$	6.5
Dual form			6.27.b.a.5.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5792.62i q^{2} +(-847324. + 1.35052e6i) q^{3} -3.35544e7 q^{4} +2.16695e9i q^{5} +(7.82305e9 + 4.90823e9i) q^{6} +1.32110e11 q^{7} +1.94368e11i q^{8} +(-1.10595e12 - 2.28866e12i) q^{9} +O(q^{10})$	\(q-5792.62i q^{2} +(-847324. + 1.35052e6i) q^{3} -3.35544e7 q^{4} +2.16695e9i q^{5} +(7.82305e9 + 4.90823e9i) q^{6} +1.32110e11 q^{7} +1.94368e11i q^{8} +(-1.10595e12 - 2.28866e12i) q^{9} +1.25523e13 q^{10} +4.60048e13i q^{11} +(2.84315e13 - 4.53160e13i) q^{12} -1.11326e14 q^{13} -7.65260e14i q^{14} +(-2.92651e15 - 1.83611e15i) q^{15} +1.12590e15 q^{16} -8.56222e13i q^{17} +(-1.32573e16 + 6.40634e15i) q^{18} +3.34097e16 q^{19} -7.27106e16i q^{20} +(-1.11940e17 + 1.78417e17i) q^{21} +2.66488e17 q^{22} +4.89326e17i q^{23} +(-2.62498e17 - 1.64693e17i) q^{24} -3.20554e18 q^{25} +6.44870e17i q^{26} +(4.02798e18 + 4.45630e17i) q^{27} -4.43286e18 q^{28} +1.94231e18i q^{29} +(-1.06359e19 + 1.69521e19i) q^{30} -4.29420e19 q^{31} -6.52191e18i q^{32} +(-6.21304e19 - 3.89810e19i) q^{33} -4.95977e17 q^{34} +2.86274e20i q^{35} +(3.71095e19 + 7.67947e19i) q^{36} +4.58957e19 q^{37} -1.93529e20i q^{38} +(9.43294e19 - 1.50348e20i) q^{39} -4.21185e20 q^{40} -7.96853e20i q^{41} +(1.03350e21 + 6.48424e20i) q^{42} -1.50994e21 q^{43} -1.54366e21i q^{44} +(4.95940e21 - 2.39653e21i) q^{45} +2.83448e21 q^{46} -2.64922e21i q^{47} +(-9.54003e20 + 1.52055e21i) q^{48} +8.06544e21 q^{49} +1.85685e22i q^{50} +(1.15635e20 + 7.25498e19i) q^{51} +3.73549e21 q^{52} -2.66174e22i q^{53} +(2.58136e21 - 2.33325e22i) q^{54} -9.96899e22 q^{55} +2.56779e22i q^{56} +(-2.83088e22 + 4.51205e22i) q^{57} +1.12511e22 q^{58} +2.34835e22i q^{59} +(9.81973e22 + 6.16095e22i) q^{60} -8.16232e22 q^{61} +2.48746e23i q^{62} +(-1.46106e23 - 3.02354e23i) q^{63} -3.77789e22 q^{64} -2.41238e23i q^{65} +(-2.25802e23 + 3.59898e23i) q^{66} +9.08244e23 q^{67} +2.87301e21i q^{68} +(-6.60845e23 - 4.14618e23i) q^{69} +1.65828e24 q^{70} -5.09949e23i q^{71} +(4.44842e23 - 2.14961e23i) q^{72} -1.03543e24 q^{73} -2.65856e23i q^{74} +(2.71613e24 - 4.32915e24i) q^{75} -1.12104e24 q^{76} +6.07767e24i q^{77} +(-8.70911e23 - 5.46414e23i) q^{78} -9.95558e23 q^{79} +2.43976e24i q^{80} +(-4.01484e24 + 5.06228e24i) q^{81} -4.61587e24 q^{82} -4.25058e23i q^{83} +(3.75607e24 - 5.98667e24i) q^{84} +1.85539e23 q^{85} +8.74653e24i q^{86} +(-2.62313e24 - 1.64577e24i) q^{87} -8.94186e24 q^{88} +3.18315e25i q^{89} +(-1.38822e25 - 2.87279e25i) q^{90} -1.47072e25 q^{91} -1.64191e25i q^{92} +(3.63858e25 - 5.79940e25i) q^{93} -1.53459e25 q^{94} +7.23969e25i q^{95} +(8.80798e24 + 5.52617e24i) q^{96} +6.67068e25 q^{97} -4.67200e25i q^{98} +(1.05289e26 - 5.08789e25i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2194920 q^{3} - 268435456 q^{4} + 8978890752 q^{6} + 183211263760 q^{7} - 4853931303096 q^{9}+O(q^{10}) $ 8 * q + 2194920 * q^3 - 268435456 * q^4 + 8978890752 * q^6 + 183211263760 * q^7 - 4853931303096 * q^9	$ 8 q + 2194920 q^{3} - 268435456 q^{4} + 8978890752 q^{6} + 183211263760 q^{7} - 4853931303096 q^{9} + 18696278507520 q^{10} - 73649293885440 q^{12} + 512429022548560 q^{13} - 10\!\cdots\!40 q^{15}+ \cdots + 49\!\cdots\!36 q^{99}+O(q^{100}) $ 8 * q + 2194920 * q^3 - 268435456 * q^4 + 8978890752 * q^6 + 183211263760 * q^7 - 4853931303096 * q^9 + 18696278507520 * q^10 - 73649293885440 * q^12 + 512429022548560 * q^13 - 1064426665559040 * q^15 + 9007199254740992 * q^16 - 1881283573186560 * q^18 + 13250502825732304 * q^19 - 376087240418977584 * q^21 + 428662713355468800 * q^22 - 301281579173412864 * q^24 - 5623831579932691000 * q^25 + 11144542948278241320 * q^27 - 6147549891468984320 * q^28 - 12961438025281044480 * q^30 - 31284409294003569776 * q^31 - 27135100230528798720 * q^33 - 98764413849435635712 * q^34 + 162870907842406121472 * q^36 - 884494012218278308400 * q^37 + 1550610890749922311440 * q^39 - 627343005833641328640 * q^40 + 2912220856097001308160 * q^42 - 5161357724259210085040 * q^43 + 20490779480380306513920 * q^45 - 10789778429003593678848 * q^46 + 2471260223527012270080 * q^48 - 29984991896355791854440 * q^49 + 55593505357359326429184 * q^51 - 17194264791932123217920 * q^52 + 6309825934293776793600 * q^54 - 76225105088113564293120 * q^55 + 66535314651975639764880 * q^57 - 142582792844514288599040 * q^58 + 35716232168487549665280 * q^60 + 235221054408754640644432 * q^61 - 635461358798759743298160 * q^63 - 302231454903657293676544 * q^64 - 1507842687345202066489344 * q^66 + 4218736573110688595120080 * q^67 - 2608639506957020943089664 * q^69 + 1864568339879729269309440 * q^70 + 63125401729205450833920 * q^72 + 1648536069669962768198800 * q^73 + 2584159434345978668025000 * q^75 - 444613096031842444771328 * q^76 - 313072373593422745436160 * q^78 - 9378866636279258011040624 * q^79 - 746539638785265647226744 * q^81 - 6997685112389596533227520 * q^82 + 12619393734706234851852288 * q^84 - 41457721476781794937282560 * q^85 + 55271553720839002987729920 * q^87 - 14383533866221569677721600 * q^88 + 32441993904208401898536960 * q^90 - 71633324581325574226388320 * q^91 + 18549099857564620426167120 * q^93 + 67962530415252490428088320 * q^94 + 10109332261226898153013248 * q^96 - 92292347027073928712964080 * q^97 + 4908019641378975318951936 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/6\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$-1$

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 $

$2$		−	5792.62i		−	0.707107i
$2$		−	5792.62i		−	0.707107i
$3$	−847324.	+	1.35052e6i	−0.531463	+	0.847081i
$3$	−847324.	+	1.35052e6i	−0.531463	+	0.847081i
$4$	−3.35544e7			−0.500000
$5$			2.16695e9i			1.77516i	0.460651	+	0.887581i	$0.347616\pi$
$5$			2.16695e9i			1.77516i	−0.460651	+	0.887581i	$0.652384\pi$
$6$	7.82305e9	+	4.90823e9i	0.598977	+	0.375801i
$7$	1.32110e11			1.36351			0.681757	−	0.731579i	$-0.261216\pi$
$7$	1.32110e11			1.36351			0.681757	+	0.731579i	$0.261216\pi$
$8$			1.94368e11i			0.353553i
$9$	−1.10595e12	−	2.28866e12i	−0.435093	−	0.900385i
$10$	1.25523e13			1.25523
$11$			4.60048e13i			1.33259i	0.745686	+	0.666297i	$0.232122\pi$
$11$			4.60048e13i			1.33259i	−0.745686	+	0.666297i	$0.767878\pi$
$12$	2.84315e13	−	4.53160e13i	0.265732	−	0.423541i
$13$	−1.11326e14			−0.367565			−0.183782	−	0.982967i	$-0.558834\pi$
$13$	−1.11326e14			−0.367565			−0.183782	+	0.982967i	$0.558834\pi$
$14$		−	7.65260e14i		−	0.964150i
$15$	−2.92651e15	−	1.83611e15i	−1.50371	−	0.943434i
$16$	1.12590e15			0.250000
$17$		−	8.56222e13i		−	0.00864471i	−0.999991	−	0.00432236i	$-0.998624\pi$
$17$		−	8.56222e13i		−	0.00864471i	0.999991	−	0.00432236i	$-0.00137585\pi$
$18$	−1.32573e16	+	6.40634e15i	−0.636669	+	0.307657i
$19$	3.34097e16			0.794466			0.397233	−	0.917718i	$-0.369970\pi$
$19$	3.34097e16			0.794466			0.397233	+	0.917718i	$0.369970\pi$
$20$		−	7.27106e16i		−	0.887581i
$21$	−1.11940e17	+	1.78417e17i	−0.724658	+	1.15501i
$22$	2.66488e17			0.942287
$23$			4.89326e17i			0.970815i	0.874288	+	0.485407i	$0.161329\pi$
$23$			4.89326e17i			0.970815i	−0.874288	+	0.485407i	$0.838671\pi$
$24$	−2.62498e17	−	1.64693e17i	−0.299488	−	0.187901i
$25$	−3.20554e18			−2.15120
$26$			6.44870e17i			0.259907i
$27$	4.02798e18	+	4.45630e17i	0.993936	+	0.109963i
$28$	−4.43286e18			−0.681757
$29$			1.94231e18i			0.189297i	0.995511	+	0.0946486i	$0.0301728\pi$
$29$			1.94231e18i			0.189297i	−0.995511	+	0.0946486i	$0.969827\pi$
$30$	−1.06359e19	+	1.69521e19i	−0.667109	+	1.06328i
$31$	−4.29420e19			−1.75865			−0.879326	−	0.476220i	$-0.842007\pi$
$31$	−4.29420e19			−1.75865			−0.879326	+	0.476220i	$0.842007\pi$
$32$		−	6.52191e18i		−	0.176777i
$33$	−6.21304e19	−	3.89810e19i	−1.12882	−	0.708225i
$34$	−4.95977e17			−0.00611274
$35$			2.86274e20i			2.42046i
$36$	3.71095e19	+	7.67947e19i	0.217547	+	0.450193i
$37$	4.58957e19			0.188430			0.0942149	−	0.995552i	$-0.469966\pi$
$37$	4.58957e19			0.188430			0.0942149	+	0.995552i	$0.469966\pi$
$38$		−	1.93529e20i		−	0.561772i
$39$	9.43294e19	−	1.50348e20i	0.195347	−	0.311357i
$40$	−4.21185e20			−0.627615
$41$		−	7.96853e20i		−	0.861367i	−0.902503	−	0.430684i	$-0.858272\pi$
$41$		−	7.96853e20i		−	0.861367i	0.902503	−	0.430684i	$-0.141728\pi$
$42$	1.03350e21	+	6.48424e20i	0.816713	+	0.512410i
$43$	−1.50994e21			−0.878761			−0.439380	−	0.898301i	$-0.644802\pi$
$43$	−1.50994e21			−0.878761			−0.439380	+	0.898301i	$0.644802\pi$
$44$		−	1.54366e21i		−	0.666297i
$45$	4.95940e21	−	2.39653e21i	1.59833	−	0.772361i
$46$	2.83448e21			0.686470
$47$		−	2.64922e21i		−	0.485116i	−0.970137	−	0.242558i	$-0.922014\pi$
$47$		−	2.64922e21i		−	0.485116i	0.970137	−	0.242558i	$-0.0779865\pi$
$48$	−9.54003e20	+	1.52055e21i	−0.132866	+	0.211770i
$49$	8.06544e21			0.859170
$50$			1.85685e22i			1.52113i
$51$	1.15635e20	+	7.25498e19i	0.00732277	+	0.00459435i
$52$	3.73549e21			0.183782
$53$		−	2.66174e22i		−	1.02230i	−0.859491	−	0.511151i	$-0.829219\pi$
$53$		−	2.66174e22i		−	1.02230i	0.859491	−	0.511151i	$-0.170781\pi$
$54$	2.58136e21	−	2.33325e22i	0.0777554	−	0.702819i
$55$	−9.96899e22			−2.36557
$56$			2.56779e22i			0.482075i
$57$	−2.83088e22	+	4.51205e22i	−0.422230	+	0.672977i
$58$	1.12511e22			0.133853
$59$			2.34835e22i			0.223710i	0.993725	+	0.111855i	$0.0356793\pi$
$59$			2.34835e22i			0.223710i	−0.993725	+	0.111855i	$0.964321\pi$
$60$	9.81973e22	+	6.16095e22i	0.751853	+	0.471717i
$61$	−8.16232e22			−0.504111			−0.252055	−	0.967713i	$-0.581106\pi$
$61$	−8.16232e22			−0.504111			−0.252055	+	0.967713i	$0.581106\pi$
$62$			2.48746e23i			1.24355i
$63$	−1.46106e23	−	3.02354e23i	−0.593256	−	1.22769i
$64$	−3.77789e22			−0.125000
$65$		−	2.41238e23i		−	0.652487i
$66$	−2.25802e23	+	3.59898e23i	−0.500791	+	0.798193i
$67$	9.08244e23			1.65665			0.828324	−	0.560250i	$-0.189295\pi$
$67$	9.08244e23			1.65665			0.828324	+	0.560250i	$0.189295\pi$
$68$			2.87301e21i			0.00432236i
$69$	−6.60845e23	−	4.14618e23i	−0.822359	−	0.515953i
$70$	1.65828e24			1.71152
$71$		−	5.09949e23i		−	0.437691i	−0.975759	−	0.218846i	$-0.929771\pi$
$71$		−	5.09949e23i		−	0.437691i	0.975759	−	0.218846i	$-0.0702291\pi$
$72$	4.44842e23	−	2.14961e23i	0.318334	−	0.153829i
$73$	−1.03543e24			−0.619334			−0.309667	−	0.950845i	$-0.600218\pi$
$73$	−1.03543e24			−0.619334			−0.309667	+	0.950845i	$0.600218\pi$
$74$		−	2.65856e23i		−	0.133240i
$75$	2.71613e24	−	4.32915e24i	1.14328	−	1.82224i
$76$	−1.12104e24			−0.397233
$77$			6.07767e24i			1.81701i
$78$	−8.70911e23	−	5.46414e23i	−0.220163	−	0.138131i
$79$	−9.95558e23			−0.213262			−0.106631	−	0.994299i	$-0.534006\pi$
$79$	−9.95558e23			−0.213262			−0.106631	+	0.994299i	$0.534006\pi$
$80$			2.43976e24i			0.443791i
$81$	−4.01484e24	+	5.06228e24i	−0.621388	+	0.783503i
$82$	−4.61587e24			−0.609079
$83$		−	4.25058e23i		−	0.0479108i	−0.999713	−	0.0239554i	$-0.992374\pi$
$83$		−	4.25058e23i		−	0.0479108i	0.999713	−	0.0239554i	$-0.00762596\pi$
$84$	3.75607e24	−	5.98667e24i	0.362329	−	0.577504i
$85$	1.85539e23			0.0153458
$86$			8.74653e24i			0.621378i
$87$	−2.62313e24	−	1.64577e24i	−0.160350	−	0.100605i
$88$	−8.94186e24			−0.471143
$89$			3.18315e25i			1.44806i	0.689768	+	0.724030i	$0.257712\pi$
$89$			3.18315e25i			1.44806i	−0.689768	+	0.724030i	$0.742288\pi$
$90$	−1.38822e25	−	2.87279e25i	−0.546142	−	1.13019i
$91$	−1.47072e25			−0.501179
$92$		−	1.64191e25i		−	0.485407i
$93$	3.63858e25	−	5.79940e25i	0.934659	−	1.48972i
$94$	−1.53459e25			−0.343029
$95$			7.23969e25i			1.41031i
$96$	8.80798e24	+	5.52617e24i	0.149744	+	0.0939504i
$97$	6.67068e25			0.991146			0.495573	−	0.868566i	$-0.334958\pi$
$97$	6.67068e25			0.991146			0.495573	+	0.868566i	$0.334958\pi$
$98$		−	4.67200e25i		−	0.607525i
$99$	1.05289e26	−	5.08789e25i	1.19985	−	0.579803i
$100$	1.07560e26			1.07560
$101$			1.59574e26i			1.40212i	0.713102	+	0.701060i	$0.247289\pi$
$101$			1.59574e26i			1.40212i	−0.713102	+	0.701060i	$0.752711\pi$
$102$	4.20253e23	−	6.69827e23i	0.00324870	−	0.00517798i
$103$	2.45508e25			0.167179			0.0835894	−	0.996500i	$-0.473362\pi$
$103$	2.45508e25			0.167179			0.0835894	+	0.996500i	$0.473362\pi$
$104$		−	2.16382e25i		−	0.129954i
$105$	−3.86619e26	−	2.42567e26i	−2.05032	−	1.28639i
$106$	−1.54184e26			−0.722877
$107$		−	2.17488e26i		−	0.902498i	−0.892398	−	0.451249i	$-0.850979\pi$
$107$		−	2.17488e26i		−	0.902498i	0.892398	−	0.451249i	$-0.149021\pi$
$108$	−1.35157e26	−	1.49529e25i	−0.496968	−	0.0549814i
$109$	2.04940e26			0.668469			0.334235	−	0.942490i	$-0.391522\pi$
$109$	2.04940e26			0.668469			0.334235	+	0.942490i	$0.391522\pi$
$110$			5.77465e26i			1.67271i
$111$	−3.88885e25	+	6.19831e25i	−0.100144	+	0.159615i
$112$	1.48742e26			0.340878
$113$			2.42708e26i			0.495524i	0.968821	+	0.247762i	$0.0796951\pi$
$113$			2.42708e26i			0.495524i	−0.968821	+	0.247762i	$0.920305\pi$
$114$	2.61366e26	+	1.63982e26i	0.475867	+	0.298561i
$115$	−1.06034e27			−1.72335
$116$		−	6.51731e25i		−	0.0946486i
$117$	1.23121e26	+	2.54788e26i	0.159925	+	0.330950i
$118$	1.36031e26			0.158187
$119$		−	1.13115e25i		−	0.0117872i
$120$	3.56880e26	−	5.68819e26i	0.333554	−	0.531641i
$121$	−9.24622e26			−0.775808
$122$			4.72812e26i			0.356460i
$123$	1.07617e27	+	6.75193e26i	0.729648	+	0.457785i
$124$	1.44089e27			0.879326
$125$		−	3.71723e27i		−	2.04357i
$126$	−1.75142e27	+	8.46338e26i	−0.868107	+	0.419495i
$127$	1.62309e27			0.725928			0.362964	−	0.931803i	$-0.381765\pi$
$127$	1.62309e27			0.725928			0.362964	+	0.931803i	$0.381765\pi$
$128$			2.18839e26i			0.0883883i
$129$	1.27941e27	−	2.03921e27i	0.467029	−	0.744382i
$130$	−1.39740e27			−0.461378
$131$		−	1.76590e27i		−	0.527762i	−0.964555	−	0.263881i	$-0.914997\pi$
$131$		−	1.76590e27i		−	0.527762i	0.964555	−	0.263881i	$-0.0850027\pi$
$132$	2.08475e27	+	1.30798e27i	0.564408	+	0.354113i
$133$	4.41373e27			1.08327
$134$		−	5.26111e27i		−	1.17143i
$135$	−9.65656e26	+	8.72841e27i	−0.195202	+	1.76440i
$136$	1.66422e25			0.00305637
$137$			6.38522e27i			1.06613i	0.846076	+	0.533063i	$0.178959\pi$
$137$			6.38522e27i			1.06613i	−0.846076	+	0.533063i	$0.821041\pi$
$138$	−2.40172e27	+	3.82802e27i	−0.364834	+	0.581496i
$139$	−1.11970e28			−1.54849			−0.774244	−	0.632888i	$-0.781870\pi$
$139$	−1.11970e28			−1.54849			−0.774244	+	0.632888i	$0.781870\pi$
$140$		−	9.60577e27i		−	1.21023i
$141$	3.57782e27	+	2.24475e27i	0.410933	+	0.257821i
$142$	−2.95394e27			−0.309494
$143$		−	5.12154e27i		−	0.489815i
$144$	−1.24519e27	−	2.57680e27i	−0.108773	−	0.225096i
$145$	−4.20888e27			−0.336033
$146$			5.99787e27i			0.437935i
$147$	−6.83405e27	+	1.08926e28i	−0.456618	+	0.727787i
$148$	−1.54000e27			−0.0942149
$149$			2.47696e28i			1.38834i	0.719810	+	0.694171i	$0.244229\pi$
$149$			2.47696e28i			1.38834i	−0.719810	+	0.694171i	$0.755771\pi$
$150$	−2.50771e28	−	1.57335e28i	−1.28852	−	0.808424i
$151$	3.37618e28			1.59120			0.795600	−	0.605822i	$-0.207156\pi$
$151$	3.37618e28			1.59120			0.795600	+	0.605822i	$0.207156\pi$
$152$			6.49377e27i			0.280886i
$153$	−1.95960e26	+	9.46938e25i	−0.00778357	+	0.00376126i
$154$	3.52056e28			1.28482
$155$		−	9.30529e28i		−	3.12189i
$156$	−3.16517e27	+	5.04485e27i	−0.0976736	+	0.155679i
$157$	−5.77304e28			−1.63949			−0.819745	−	0.572728i	$-0.805885\pi$
$157$	−5.77304e28			−1.63949			−0.819745	+	0.572728i	$0.805885\pi$
$158$			5.76689e27i			0.150799i
$159$	3.59474e28	+	2.25536e28i	0.865973	+	0.543316i
$160$	1.41326e28			0.313807
$161$			6.46446e28i			1.32372i
$162$	2.93238e28	+	2.32564e28i	0.554020	+	0.439388i
$163$	4.19752e28			0.732071			0.366036	−	0.930601i	$-0.380715\pi$
$163$	4.19752e28			0.732071			0.366036	+	0.930601i	$0.380715\pi$
$164$			2.67380e28i			0.430684i
$165$	8.44697e28	−	1.34633e29i	1.25721	−	2.00383i
$166$	−2.46220e27			−0.0338780
$167$			2.62865e28i			0.334517i	0.985913	+	0.167259i	$0.0534915\pi$
$167$			2.62865e28i			0.334517i	−0.985913	+	0.167259i	$0.946508\pi$
$168$	−3.46785e28	−	2.17575e28i	−0.408357	−	0.256205i
$169$	−7.93398e28			−0.864896
$170$		−	1.07476e27i		−	0.0108511i
$171$	−3.69494e28	−	7.64633e28i	−0.345667	−	0.715326i
$172$	5.06653e28			0.439380
$173$			5.48260e28i			0.440948i	0.975393	+	0.220474i	$0.0707604\pi$
$173$			5.48260e28i			0.440948i	−0.975393	+	0.220474i	$0.929240\pi$
$174$	−9.53329e27	+	1.51948e28i	−0.0711382	+	0.113385i
$175$	−4.23482e29			−2.93319
$176$			5.17968e28i			0.333149i
$177$	−3.17149e28	−	1.98981e28i	−0.189501	−	0.118894i
$178$	1.84388e29			1.02393
$179$			2.09787e29i			1.08315i	0.840652	+	0.541576i	$0.182172\pi$
$179$			2.09787e29i			1.08315i	−0.840652	+	0.541576i	$0.817828\pi$
$180$	−1.66410e29	+	8.04142e28i	−0.799165	+	0.386180i
$181$	2.93249e29			1.31043			0.655217	−	0.755440i	$-0.272577\pi$
$181$	2.93249e29			1.31043			0.655217	+	0.755440i	$0.272577\pi$
$182$			8.51935e28i			0.354387i
$183$	6.91613e28	−	1.10234e29i	0.267916	−	0.427023i
$184$	−9.51093e28			−0.343235
$185$			9.94535e28i			0.334493i
$186$	−3.35937e29	−	2.10769e29i	−1.05339	−	0.660904i
$187$	3.93903e27			0.0115199
$188$			8.88930e28i			0.242558i
$189$	5.32134e29	+	5.88720e28i	1.35525	+	0.149936i
$190$	4.19368e29			0.997237
$191$		−	1.37415e29i		−	0.305210i	−0.988287	−	0.152605i	$-0.951234\pi$
$191$		−	1.37415e29i		−	0.305210i	0.988287	−	0.152605i	$-0.0487662\pi$
$192$	3.20110e28	−	5.10212e28i	0.0664329	−	0.105885i
$193$	−2.81615e29			−0.546274			−0.273137	−	0.961975i	$-0.588061\pi$
$193$	−2.81615e29			−0.546274			−0.273137	+	0.961975i	$0.588061\pi$
$194$		−	3.86407e29i		−	0.700846i
$195$	3.25797e29	+	2.04407e29i	0.552709	+	0.346773i
$196$	−2.70631e29			−0.429585
$197$		−	7.21721e29i		−	1.07228i	−0.844129	−	0.536140i	$-0.819882\pi$
$197$		−	7.21721e29i		−	1.07228i	0.844129	−	0.536140i	$-0.180118\pi$
$198$	−2.94722e29	−	6.09900e29i	−0.409982	−	0.848421i
$199$	8.26647e28			0.107704			0.0538518	−	0.998549i	$-0.482850\pi$
$199$	8.26647e28			0.107704			0.0538518	+	0.998549i	$0.482850\pi$
$200$		−	6.23054e29i		−	0.760564i
$201$	−7.69577e29	+	1.22660e30i	−0.880448	+	1.40331i
$202$	9.24353e29			0.991448
$203$			2.56598e29i			0.258109i
$204$	−3.88005e27	−	2.43437e27i	−0.00366139	−	0.00229717i
$205$	1.72674e30			1.52907
$206$		−	1.42213e29i		−	0.118213i
$207$	1.11990e30	−	5.41169e29i	0.874107	−	0.422395i
$208$	−1.25342e29			−0.0918912
$209$			1.53700e30i			1.05870i
$210$	−1.40510e30	+	2.23954e30i	−0.909612	+	1.44980i
$211$	−2.60934e30			−1.58803			−0.794015	−	0.607898i	$-0.792013\pi$
$211$	−2.60934e30			−1.58803			−0.794015	+	0.607898i	$0.792013\pi$
$212$			8.93132e29i			0.511151i
$213$	6.88696e29	+	4.32092e29i	0.370760	+	0.232617i
$214$	−1.25983e30			−0.638162
$215$		−	3.27197e30i		−	1.55994i
$216$	−8.66162e28	+	7.82910e29i	−0.0388777	+	0.351409i
$217$	−5.67304e30			−2.39795
$218$		−	1.18714e30i		−	0.472679i
$219$	8.77347e29	−	1.39837e30i	0.329153	−	0.524626i
$220$	3.34504e30			1.18279
$221$			9.53200e27i			0.00317749i
$222$	3.59044e29	+	2.25266e29i	0.112865	+	0.0708122i
$223$	−3.06158e30			−0.907785			−0.453892	−	0.891056i	$-0.649965\pi$
$223$	−3.06158e30			−0.907785			−0.453892	+	0.891056i	$0.649965\pi$
$224$		−	8.61606e29i		−	0.241037i
$225$	3.54516e30	+	7.33639e30i	0.935973	+	1.93691i
$226$	1.40592e30			0.350388
$227$		−	4.46099e30i		−	1.04977i	−0.851172	−	0.524887i	$-0.824108\pi$
$227$		−	4.46099e30i		−	1.04977i	0.851172	−	0.524887i	$-0.175892\pi$
$228$	9.49886e29	−	1.51399e30i	0.211115	−	0.336489i
$229$	9.02152e30			1.89417			0.947083	−	0.320988i	$-0.104015\pi$
$229$	9.02152e30			1.89417			0.947083	+	0.320988i	$0.104015\pi$
$230$			6.14216e30i			1.21860i
$231$	−8.20802e30	−	5.14976e30i	−1.53916	−	0.965675i
$232$	−3.77523e29			−0.0669267
$233$		−	4.93963e30i		−	0.828070i	−0.910261	−	0.414035i	$-0.864119\pi$
$233$		−	4.93963e30i		−	0.828070i	0.910261	−	0.414035i	$-0.135881\pi$
$234$	1.47589e30	−	7.13193e29i	0.234017	−	0.113084i
$235$	5.74071e30			0.861159
$236$		−	7.87974e29i		−	0.111855i
$237$	8.43560e29	−	1.34452e30i	0.113341	−	0.180651i
$238$	−6.55233e28			−0.00833480
$239$			4.96308e30i			0.597831i	0.954280	+	0.298916i	$0.0966249\pi$
$239$			4.96308e30i			0.597831i	−0.954280	+	0.298916i	$0.903375\pi$
$240$	−3.29495e30	−	2.06727e30i	−0.375927	−	0.235858i
$241$	6.61076e30			0.714546			0.357273	−	0.934000i	$-0.383707\pi$
$241$	6.61076e30			0.714546			0.357273	+	0.934000i	$0.383707\pi$
$242$			5.35598e30i			0.548579i
$243$	−3.43484e30	−	9.71151e30i	−0.333446	−	0.942769i
$244$	2.73882e30			0.252055
$245$			1.74774e31i			1.52517i
$246$	3.91114e30	−	6.23383e30i	0.323703	−	0.515939i
$247$	−3.71937e30			−0.292018
$248$		−	8.34655e30i		−	0.621777i
$249$	5.74050e29	+	3.60162e29i	0.0405843	+	0.0254628i
$250$	−2.15325e31			−1.44502
$251$		−	4.30629e30i		−	0.274375i	−0.990545	−	0.137188i	$-0.956194\pi$
$251$		−	4.30629e30i		−	0.274375i	0.990545	−	0.137188i	$-0.0438063\pi$
$252$	4.90251e30	+	1.01453e31i	0.296628	+	0.613844i
$253$	−2.25113e31			−1.29370
$254$		−	9.40192e30i		−	0.513308i
$255$	−1.57212e29	+	2.50574e29i	−0.00815572	+	0.0129991i
$256$	1.26765e30			0.0625000
$257$			3.72487e31i			1.74574i	0.487950	+	0.872871i	$0.337745\pi$
$257$			3.72487e31i			1.74574i	−0.487950	+	0.872871i	$0.662255\pi$
$258$	−1.18124e31	−	7.41115e30i	−0.526357	−	0.330240i
$259$	6.06326e30			0.256927
$260$			8.09460e30i			0.326243i
$261$	4.44528e30	−	2.14809e30i	0.170441	−	0.0823619i
$262$	−1.02292e31			−0.373184
$263$			1.90375e31i			0.660975i	0.943810	+	0.330488i	$0.107213\pi$
$263$			1.90375e31i			0.660975i	−0.943810	+	0.330488i	$0.892787\pi$
$264$	7.57665e30	−	1.20762e31i	0.250395	−	0.399097i
$265$	5.76785e31			1.81475
$266$		−	2.55671e31i		−	0.765984i
$267$	−4.29891e31	−	2.69716e31i	−1.22663	−	0.769591i
$268$	−3.04756e31			−0.828324
$269$			4.99660e31i			1.29388i	0.762540	+	0.646941i	$0.223952\pi$
$269$			4.99660e31i			1.29388i	−0.762540	+	0.646941i	$0.776048\pi$
$270$	5.05604e31	+	5.59368e30i	1.24762	+	0.138028i
$271$	−1.52657e31			−0.359018			−0.179509	−	0.983756i	$-0.557451\pi$
$271$	−1.52657e31			−0.359018			−0.179509	+	0.983756i	$0.557451\pi$
$272$		−	9.64021e28i		−	0.00216118i
$273$	1.24618e31	−	1.98624e31i	0.266359	−	0.424540i
$274$	3.69871e31			0.753865
$275$		−	1.47470e32i		−	2.86668i
$276$	2.21743e31	+	1.39123e31i	0.411179	+	0.257976i
$277$	6.75420e31			1.19492			0.597458	−	0.801900i	$-0.296178\pi$
$277$	6.75420e31			1.19492			0.597458	+	0.801900i	$0.296178\pi$
$278$			6.48597e31i			1.09495i
$279$	4.74916e31	+	9.82795e31i	0.765178	+	1.58346i
$280$	−5.56426e31			−0.855761
$281$		−	7.98432e31i		−	1.17235i	−0.810186	−	0.586173i	$-0.800634\pi$
$281$		−	7.98432e31i		−	1.17235i	0.810186	−	0.586173i	$-0.199366\pi$
$282$	1.30030e31	−	2.07250e31i	0.182307	−	0.290573i
$283$	−7.97448e31			−1.06777			−0.533886	−	0.845556i	$-0.679269\pi$
$283$	−7.97448e31			−1.06777			−0.533886	+	0.845556i	$0.679269\pi$
$284$			1.71110e31i			0.218846i
$285$	−9.77736e31	−	6.13437e31i	−1.19464	−	0.749526i
$286$	−2.96671e31			−0.346351
$287$		−	1.05272e32i		−	1.17449i
$288$	−1.49264e31	+	7.21289e30i	−0.159167	+	0.0769143i
$289$	9.80933e31			0.999925
$290$			2.43804e31i			0.237611i
$291$	−5.65223e31	+	9.00890e31i	−0.526758	+	0.839581i
$292$	3.47434e31			0.309667
$293$			2.06820e32i			1.76325i	0.471950	+	0.881625i	$0.343550\pi$
$293$			2.06820e32i			1.76325i	−0.471950	+	0.881625i	$0.656450\pi$
$294$	6.30964e31	+	3.95870e31i	0.514623	+	0.322877i
$295$	−5.08874e31			−0.397122
$296$			8.92066e30i			0.0666200i
$297$	−2.05011e31	+	1.85306e32i	−0.146536	+	1.32451i
$298$	1.43481e32			0.981707
$299$		−	5.44748e31i		−	0.356837i
$300$	−9.11383e31	+	1.45262e32i	−0.571642	+	0.911121i
$301$	−1.99478e32			−1.19820
$302$		−	1.95569e32i		−	1.12515i
$303$	−2.15508e32	−	1.35211e32i	−1.18771	−	0.745175i
$304$	3.76159e31			0.198616
$305$		−	1.76873e32i		−	0.894878i
$306$	5.48525e29	+	1.13512e30i	0.00265961	+	0.00550382i
$307$	3.59427e32			1.67037			0.835184	−	0.549970i	$-0.185361\pi$
$307$	3.59427e32			1.67037			0.835184	+	0.549970i	$0.185361\pi$
$308$		−	2.03933e32i		−	0.908506i
$309$	−2.08025e31	+	3.31563e31i	−0.0888495	+	0.141614i
$310$	−5.39020e32			−2.20751
$311$			3.69751e31i			0.145219i	0.997360	+	0.0726096i	$0.0231327\pi$
$311$			3.69751e31i			0.145219i	−0.997360	+	0.0726096i	$0.976867\pi$
$312$	2.92229e31	+	1.83346e31i	0.110081	+	0.0690657i
$313$	−6.24238e31			−0.225566			−0.112783	−	0.993620i	$-0.535977\pi$
$313$	−6.24238e31			−0.225566			−0.112783	+	0.993620i	$0.535977\pi$
$314$			3.34410e32i			1.15929i
$315$	6.55184e32	−	3.16605e32i	2.17935	−	1.05312i
$316$	3.34054e31			0.106631
$317$			3.07828e32i			0.943056i	0.881851	+	0.471528i	$0.156297\pi$
$317$			3.07828e32i			0.943056i	−0.881851	+	0.471528i	$0.843703\pi$
$318$	1.30644e32	−	2.08229e32i	0.384183	−	0.612335i
$319$	−8.93555e31			−0.252256
$320$		−	8.18649e31i		−	0.221895i
$321$	2.93722e32	+	1.84283e32i	0.764489	+	0.479645i
$322$	3.74462e32			0.936011
$323$		−	2.86061e30i		−	0.00686793i
$324$	1.34716e32	−	1.69862e32i	0.310694	−	0.391752i
$325$	3.56860e32			0.790705
$326$		−	2.43146e32i		−	0.517653i
$327$	−1.73650e32	+	2.76775e32i	−0.355267	+	0.566248i
$328$	1.54883e32			0.304539
$329$		−	3.49987e32i		−	0.661462i
$330$	−7.79879e32	−	4.89301e32i	−1.41692	−	0.888985i
$331$	−2.74331e32			−0.479193			−0.239596	−	0.970873i	$-0.577015\pi$
$331$	−2.74331e32			−0.479193			−0.239596	+	0.970873i	$0.577015\pi$
$332$			1.42626e31i			0.0239554i
$333$	−5.07583e31	−	1.05040e32i	−0.0819845	−	0.169659i
$334$	1.52268e32			0.236540
$335$			1.96812e33i			2.94082i
$336$	−1.26033e32	+	2.00879e32i	−0.181164	+	0.288752i
$337$	−9.41671e32			−1.30230			−0.651149	−	0.758950i	$-0.725713\pi$
$337$	−9.41671e32			−1.30230			−0.651149	+	0.758950i	$0.725713\pi$
$338$			4.59585e32i			0.611574i
$339$	−3.27782e32	−	2.05653e32i	−0.419749	−	0.263353i
$340$	−6.22565e30			−0.00767288
$341$		−	1.97554e33i		−	2.34357i
$342$	−4.42923e32	+	2.14034e32i	−0.505812	+	0.244423i
$343$	−1.74654e32			−0.192023
$344$		−	2.93485e32i		−	0.310689i
$345$	8.98454e32	−	1.43202e33i	0.915900	−	1.45982i
$346$	3.17586e32			0.311797
$347$			1.35715e33i			1.28335i	0.766978	+	0.641673i	$0.221759\pi$
$347$			1.35715e33i			1.28335i	−0.766978	+	0.641673i	$0.778241\pi$
$348$	8.80176e31	+	5.52227e31i	0.0801751	+	0.0503023i
$349$	−1.11648e33			−0.979762			−0.489881	−	0.871789i	$-0.662960\pi$
$349$	−1.11648e33			−0.979762			−0.489881	+	0.871789i	$0.662960\pi$
$350$			2.45307e33i			2.07408i
$351$	−4.48420e32	−	4.96103e31i	−0.365336	−	0.0404184i
$352$	3.00039e32			0.235572
$353$			8.58483e32i			0.649622i	0.945779	+	0.324811i	$0.105301\pi$
$353$			8.58483e32i			0.649622i	−0.945779	+	0.324811i	$0.894699\pi$
$354$	−1.15262e32	+	1.83712e32i	−0.0840707	+	0.133997i
$355$	1.10503e33			0.776973
$356$		−	1.06809e33i		−	0.724030i
$357$	1.52764e31	+	9.58452e30i	0.00998471	+	0.00626446i
$358$	1.21522e33			0.765904
$359$		−	2.36186e32i		−	0.143558i	−0.997421	−	0.0717788i	$-0.977132\pi$
$359$		−	2.36186e32i		−	0.143558i	0.997421	−	0.0717788i	$-0.0228676\pi$
$360$	4.65809e32	+	9.63949e32i	0.273071	+	0.565095i
$361$	−6.52248e32			−0.368824
$362$		−	1.69868e33i		−	0.926617i
$363$	7.83454e32	−	1.24872e33i	0.412314	−	0.657172i
$364$	4.93493e32			0.250590
$365$		−	2.24373e33i		−	1.09942i
$366$	−6.38543e32	−	4.00625e32i	−0.301951	−	0.189445i
$367$	−1.98346e31			−0.00905243			−0.00452622	−	0.999990i	$-0.501441\pi$
$367$	−1.98346e31			−0.00905243			−0.00452622	+	0.999990i	$0.501441\pi$
$368$			5.50932e32i			0.242704i
$369$	−1.82373e33	+	8.81279e32i	−0.775562	+	0.374775i
$370$	5.76096e32			0.236523
$371$		−	3.51641e33i		−	1.39392i
$372$	−1.22090e33	+	1.94596e33i	−0.467330	+	0.744861i
$373$	3.37726e33			1.24839			0.624194	−	0.781269i	$-0.285427\pi$
$373$	3.37726e33			1.24839			0.624194	+	0.781269i	$0.285427\pi$
$374$		−	2.28173e31i		−	0.00814580i
$375$	5.02020e33	+	3.14970e33i	1.73107	+	1.08608i
$376$	5.14923e32			0.171514
$377$		−	2.16230e32i		−	0.0695790i
$378$	3.41023e32	−	3.08245e33i	0.106021	−	0.958303i
$379$	1.20521e32			0.0362037			0.0181019	−	0.999836i	$-0.494238\pi$
$379$	1.20521e32			0.0362037			0.0181019	+	0.999836i	$0.494238\pi$
$380$		−	2.42924e33i		−	0.705153i
$381$	−1.37528e33	+	2.19201e33i	−0.385804	+	0.614920i
$382$	−7.95990e32			−0.215816
$383$			3.46216e33i			0.907326i	0.891173	+	0.453663i	$0.149883\pi$
$383$			3.46216e33i			0.907326i	−0.891173	+	0.453663i	$0.850117\pi$
$384$	−2.95547e32	−	1.85428e32i	−0.0748721	−	0.0469752i
$385$	−1.31700e34			−3.22549
$386$			1.63129e33i			0.386274i
$387$	1.66992e33	+	3.45575e33i	0.382343	+	0.791224i
$388$	−2.23831e33			−0.495573
$389$		−	2.25390e33i		−	0.482603i	−0.970450	−	0.241302i	$-0.922426\pi$
$389$		−	2.25390e33i		−	0.482603i	0.970450	−	0.241302i	$-0.0775743\pi$
$390$	1.18405e33	−	1.88722e33i	0.245205	−	0.390825i
$391$	4.18972e31			0.00839242
$392$			1.56766e33i			0.303763i
$393$	2.38488e33	+	1.49629e33i	0.447057	+	0.280486i
$394$	−4.18065e33			−0.758217
$395$		−	2.15732e33i		−	0.378575i
$396$	−3.53292e33	+	1.70721e33i	−0.599924	+	0.289901i
$397$	1.20298e34			1.97689			0.988446	−	0.151572i	$-0.0484336\pi$
$397$	1.20298e34			1.97689			0.988446	+	0.151572i	$0.0484336\pi$
$398$		−	4.78845e32i		−	0.0761579i
$399$	−3.73986e33	+	5.96084e33i	−0.575716	+	0.917614i
$400$	−3.60912e33			−0.537800
$401$			4.68076e33i			0.675211i	0.941288	+	0.337606i	$0.109617\pi$
$401$			4.68076e33i			0.675211i	−0.941288	+	0.337606i	$0.890383\pi$
$402$	7.10524e33	+	4.45787e33i	0.992293	+	0.622570i
$403$	4.78057e33			0.646418
$404$		−	5.35443e33i		−	0.701060i
$405$	−1.09697e34	−	8.69994e33i	−1.39085	−	1.10306i
$406$	1.48637e33			0.182511
$407$			2.11142e33i			0.251100i
$408$	−1.41014e31	+	2.24757e31i	−0.00162435	+	0.00258899i
$409$	7.12255e33			0.794753			0.397377	−	0.917656i	$-0.369921\pi$
$409$	7.12255e33			0.794753			0.397377	+	0.917656i	$0.369921\pi$
$410$		−	1.00023e34i		−	1.08121i
$411$	−8.62338e33	−	5.41035e33i	−0.903095	−	0.566607i
$412$	−8.23787e32			−0.0835894
$413$			3.10239e33i			0.305032i
$414$	−3.13479e33	−	6.48715e33i	−0.298678	−	0.618087i
$415$	9.21078e32			0.0850494
$416$			7.26059e32i			0.0649769i
$417$	9.48746e33	−	1.51217e34i	0.822965	−	1.31169i
$418$	8.90328e33			0.748615
$419$			1.17801e33i			0.0960214i	0.998847	+	0.0480107i	$0.0152882\pi$
$419$			1.17801e33i			0.0960214i	−0.998847	+	0.0480107i	$0.984712\pi$
$420$	1.29728e34	+	8.13920e33i	1.02516	+	0.643193i
$421$	6.92833e33			0.530837			0.265419	−	0.964133i	$-0.414490\pi$
$421$	6.92833e33			0.530837			0.265419	+	0.964133i	$0.414490\pi$
$422$			1.51149e34i			1.12291i
$423$	−6.06316e33	+	2.92990e33i	−0.436791	+	0.211071i
$424$	5.17357e33			0.361438
$425$			2.74465e32i			0.0185965i
$426$	2.50294e33	−	3.98936e33i	0.164485	−	0.262167i
$427$	−1.07832e34			−0.687362
$428$			7.29769e33i			0.451249i
$429$	6.91674e33	+	4.33960e33i	0.414913	+	0.260319i
$430$	−1.89533e34			−1.10305
$431$		−	2.65110e34i		−	1.49700i	−0.663137	−	0.748498i	$-0.730775\pi$
$431$		−	2.65110e34i		−	1.49700i	0.663137	−	0.748498i	$-0.269225\pi$
$432$	4.53510e33	+	5.01735e32i	0.248484	+	0.0274907i
$433$	2.96791e33			0.157800			0.0789002	−	0.996883i	$-0.474859\pi$
$433$	2.96791e33			0.157800			0.0789002	+	0.996883i	$0.474859\pi$
$434$			3.28618e34i			1.69560i
$435$	3.56629e33	−	5.68418e33i	0.178589	−	0.284648i
$436$	−6.87663e33			−0.334235
$437$			1.63482e34i			0.771279i
$438$	−8.10025e33	−	5.08214e33i	−0.370967	−	0.232746i
$439$	1.15642e34			0.514136			0.257068	−	0.966393i	$-0.417244\pi$
$439$	1.15642e34			0.514136			0.257068	+	0.966393i	$0.417244\pi$
$440$		−	1.93765e34i		−	0.836356i
$441$	−8.91996e33	−	1.84590e34i	−0.373819	−	0.773584i
$442$	5.52152e31			0.00224683
$443$			2.89237e34i			1.14289i	0.820639	+	0.571447i	$0.193618\pi$
$443$			2.89237e34i			1.14289i	−0.820639	+	0.571447i	$0.806382\pi$
$444$	1.30488e33	−	2.07981e33i	0.0500718	−	0.0798077i
$445$	−6.89771e34			−2.57054
$446$			1.77346e34i			0.641901i
$447$	−3.34518e34	−	2.09878e34i	−1.17604	−	0.737854i
$448$	−4.99096e33			−0.170439
$449$			2.46792e34i			0.818707i	0.912376	+	0.409354i	$0.134246\pi$
$449$			2.46792e34i			0.818707i	−0.912376	+	0.409354i	$0.865754\pi$
$450$	4.24969e34	−	2.05358e34i	1.36960	−	0.661833i
$451$	3.66591e34			1.14785
$452$		−	8.14393e33i		−	0.247762i
$453$	−2.86072e34	+	4.55960e34i	−0.845665	+	1.34788i
$454$	−2.58408e34			−0.742302
$455$		−	3.18698e34i		−	0.889675i
$456$	−8.76997e33	−	5.50233e33i	−0.237933	−	0.149281i
$457$	4.16231e34			1.09755			0.548775	−	0.835970i	$-0.315094\pi$
$457$	4.16231e34			1.09755			0.548775	+	0.835970i	$0.315094\pi$
$458$		−	5.22582e34i		−	1.33938i
$459$	3.81558e31	−	3.44885e32i	0.000950596	−	0.00859229i
$460$	3.55792e34			0.861677
$461$		−	1.78667e34i		−	0.420660i	−0.977630	−	0.210330i	$-0.932546\pi$
$461$		−	1.78667e34i		−	0.420660i	0.977630	−	0.210330i	$-0.0674539\pi$
$462$	−2.98306e34	+	4.75459e34i	−0.682835	+	1.08835i
$463$	−2.35519e34			−0.524171			−0.262086	−	0.965045i	$-0.584410\pi$
$463$	−2.35519e34			−0.524171			−0.262086	+	0.965045i	$0.584410\pi$
$464$			2.18685e33i			0.0473243i
$465$	1.25670e35	+	7.88460e34i	2.64450	+	1.65917i
$466$	−2.86134e34			−0.585534
$467$			6.36041e34i			1.26580i	0.774233	+	0.632901i	$0.218136\pi$
$467$			6.36041e34i			1.26580i	−0.774233	+	0.632901i	$0.781864\pi$
$468$	−4.13126e33	−	8.54925e33i	−0.0799624	−	0.165475i
$469$	1.19988e35			2.25886
$470$		−	3.32538e34i		−	0.608932i
$471$	4.89164e34	−	7.79661e34i	0.871329	−	1.38878i
$472$	−4.56444e33			−0.0790936
$473$		−	6.94646e34i		−	1.17103i
$474$	−7.78830e33	−	4.88642e33i	−0.127739	−	0.0801443i
$475$	−1.07096e35			−1.70906
$476$			3.79551e32i			0.00589359i
$477$	−6.09182e34	+	2.94375e34i	−0.920466	+	0.444797i
$478$	2.87492e34			0.422731
$479$		−	1.26659e35i		−	1.81248i	−0.422766	−	0.906239i	$-0.638941\pi$
$479$		−	1.26659e35i		−	1.81248i	0.422766	−	0.906239i	$-0.361059\pi$
$480$	−1.19749e34	+	1.90864e34i	−0.166777	+	0.265820i
$481$	−5.10939e33			−0.0692601
$482$		−	3.82936e34i		−	0.505260i
$483$	−8.73039e34	−	5.47750e34i	−1.12130	−	0.703509i
$484$	3.10252e34			0.387904
$485$			1.44550e35i			1.75945i
$486$	−5.62551e34	+	1.98967e34i	−0.666639	+	0.235782i
$487$	3.02361e34			0.348859			0.174429	−	0.984670i	$-0.444192\pi$
$487$	3.02361e34			0.348859			0.174429	+	0.984670i	$0.444192\pi$
$488$		−	1.58649e34i		−	0.178230i
$489$	−3.55666e34	+	5.66883e34i	−0.389069	+	0.620124i
$490$	1.01240e35			1.07846
$491$		−	1.31865e33i		−	0.0136795i	−0.999977	−	0.00683975i	$-0.997823\pi$
$491$		−	1.31865e33i		−	0.0136795i	0.999977	−	0.00683975i	$-0.00217718\pi$
$492$	−3.61102e34	−	2.26557e34i	−0.364824	−	0.228893i
$493$	1.66305e32			0.00163642
$494$			2.15449e34i			0.206488i
$495$	1.10252e35	+	2.28156e35i	1.02924	+	2.12993i
$496$	−4.83484e34			−0.439663
$497$		−	6.73691e34i		−	0.596798i
$498$	2.08628e33	−	3.32525e33i	0.0180049	−	0.0286974i
$499$	−1.09699e34			−0.0922346			−0.0461173	−	0.998936i	$-0.514685\pi$
$499$	−1.09699e34			−0.0922346			−0.0461173	+	0.998936i	$0.514685\pi$
$500$			1.24730e35i			1.02178i
$501$	−3.55005e34	−	2.22732e34i	−0.283363	−	0.177784i
$502$	−2.49447e34			−0.194012
$503$		−	8.46002e34i		−	0.641192i	−0.947216	−	0.320596i	$-0.896117\pi$
$503$		−	8.46002e34i		−	0.641192i	0.947216	−	0.320596i	$-0.103883\pi$
$504$	5.87679e34	−	2.83984e34i	0.434053	−	0.209748i
$505$	−3.45789e35			−2.48899
$506$			1.30400e35i			0.914786i
$507$	6.72266e34	−	1.07150e35i	0.459661	−	0.732637i
$508$	−5.44617e34			−0.362964
$509$		−	1.24095e35i		−	0.806161i	−0.915164	−	0.403081i	$-0.867939\pi$
$509$		−	1.24095e35i		−	0.806161i	0.915164	−	0.403081i	$-0.132061\pi$
$510$	1.45148e33	+	9.10667e32i	0.00919176	+	0.00576696i
$511$	−1.36791e35			−0.844470
$512$		−	7.34302e33i		−	0.0441942i
$513$	1.34573e35	+	1.48883e34i	0.789648	+	0.0873616i
$514$	2.15767e35			1.23443
$515$			5.32002e34i			0.296770i
$516$	−4.29299e34	+	6.84245e34i	−0.233515	+	0.372191i
$517$	1.21877e35			0.646463
$518$		−	3.51221e34i		−	0.181675i
$519$	−7.40437e34	−	4.64554e34i	−0.373519	−	0.234348i
$520$	4.68889e34			0.230689
$521$			1.52918e35i			0.733784i	0.930264	+	0.366892i	$0.119578\pi$
$521$			1.52918e35i			0.733784i	−0.930264	+	0.366892i	$0.880422\pi$
$522$	−1.24431e34	−	2.57498e34i	−0.0582387	−	0.120520i
$523$	−4.59618e33			−0.0209834			−0.0104917	−	0.999945i	$-0.503340\pi$
$523$	−4.59618e33			−0.0209834			−0.0104917	+	0.999945i	$0.503340\pi$
$524$			5.92536e34i			0.263881i
$525$	3.58827e35	−	5.71922e35i	1.55888	−	2.48465i
$526$	1.10277e35			0.467380
$527$			3.67679e33i			0.0152030i
$528$	−6.99526e34	−	4.38887e34i	−0.282204	−	0.177056i
$529$	1.46128e34			0.0575187
$530$		−	3.34109e35i		−	1.28322i
$531$	5.37457e34	−	2.59715e34i	0.201426	−	0.0973348i
$532$	−1.48100e35			−0.541633
$533$			8.87106e34i			0.316608i
$534$	−1.56236e35	+	2.49019e35i	−0.544183	+	0.867355i
$535$	4.71285e35			1.60208
$536$			1.76534e35i			0.585713i
$537$	−2.83322e35	−	1.77758e35i	−0.917518	−	0.575656i
$538$	2.89434e35			0.914913
$539$			3.71049e35i			1.14493i
$540$	3.24020e34	−	2.92877e35i	0.0976008	−	0.882199i
$541$	−5.46093e34			−0.160584			−0.0802919	−	0.996771i	$-0.525585\pi$
$541$	−5.46093e34			−0.160584			−0.0802919	+	0.996771i	$0.525585\pi$
$542$			8.84284e34i			0.253864i
$543$	−2.48477e35	+	3.96039e35i	−0.696448	+	1.11004i
$544$	−5.58420e32			−0.00152818
$545$			4.44093e35i			1.18664i
$546$	−1.15056e35	−	7.21865e34i	−0.300195	−	0.188344i
$547$	−1.49218e35			−0.380176			−0.190088	−	0.981767i	$-0.560877\pi$
$547$	−1.49218e35			−0.380176			−0.190088	+	0.981767i	$0.560877\pi$
$548$		−	2.14252e35i		−	0.533063i
$549$	9.02710e34	+	1.86808e35i	0.219335	+	0.453894i
$550$	−8.54238e35			−2.02705
$551$			6.48919e34i			0.150390i
$552$	8.05884e34	−	1.28447e35i	0.182417	−	0.290748i
$553$	−1.31523e35			−0.290786
$554$		−	3.91245e35i		−	0.844933i
$555$	−1.34314e35	−	8.42694e34i	−0.283343	−	0.177771i
$556$	3.75708e35			0.774244
$557$		−	3.60677e35i		−	0.726108i	−0.931768	−	0.363054i	$-0.881734\pi$
$557$		−	3.60677e35i		−	0.726108i	0.931768	−	0.363054i	$-0.118266\pi$
$558$	5.69296e35	−	2.75101e35i	1.11968	−	0.541062i
$559$	1.68096e35			0.323001
$560$			3.22316e35i			0.605115i
$561$	−3.33764e33	+	5.31975e33i	−0.00612240	+	0.00975829i
$562$	−4.62501e35			−0.828974
$563$			8.38376e35i			1.46835i	0.678960	+	0.734175i	$0.262431\pi$
$563$			8.38376e35i			1.46835i	−0.678960	+	0.734175i	$0.737569\pi$
$564$	−1.20052e35	−	7.53212e34i	−0.205466	−	0.128911i
$565$	−5.25935e35			−0.879635
$566$			4.61931e35i			0.755029i
$567$	−5.30398e35	+	6.68775e35i	−0.847271	+	1.06832i
$568$	9.91177e34			0.154747
$569$		−	1.18063e36i		−	1.80158i	−0.434252	−	0.900792i	$-0.642987\pi$
$569$		−	1.18063e36i		−	1.80158i	0.434252	−	0.900792i	$-0.357013\pi$
$570$	−3.55341e35	+	5.66365e35i	−0.529995	+	0.844741i
$571$	1.17559e36			1.71391			0.856955	−	0.515391i	$-0.172353\pi$
$571$	1.17559e36			1.71391			0.856955	+	0.515391i	$0.172353\pi$
$572$			1.71850e35i			0.244907i
$573$	1.85581e35	+	1.16435e35i	0.258538	+	0.162208i
$574$	−6.09800e35			−0.830487
$575$		−	1.56855e36i		−	2.08842i
$576$	4.17816e34	+	8.64631e34i	0.0543866	+	0.112548i
$577$	−5.74190e34			−0.0730752			−0.0365376	−	0.999332i	$-0.511633\pi$
$577$	−5.74190e34			−0.0730752			−0.0365376	+	0.999332i	$0.511633\pi$
$578$		−	5.68217e35i		−	0.707054i
$579$	2.38619e35	−	3.80327e35i	0.290325	−	0.462739i
$580$	1.41227e35			0.168017
$581$		−	5.61542e34i		−	0.0653270i
$582$	5.21851e35	+	3.27412e35i	0.593674	+	0.372474i
$583$	1.22453e36			1.36231
$584$		−	2.01255e35i		−	0.218968i
$585$	−5.52111e35	+	2.66797e35i	−0.587490	+	0.283893i
$586$	1.19803e36			1.24681
$587$			3.53080e35i			0.359400i	0.983721	+	0.179700i	$0.0575127\pi$
$587$			3.53080e35i			0.359400i	−0.983721	+	0.179700i	$0.942487\pi$
$588$	2.29313e35	−	3.65493e35i	0.228309	−	0.363893i
$589$	−1.43468e36			−1.39719
$590$			2.94771e35i			0.280808i
$591$	9.74699e35	+	6.11532e35i	0.908309	+	0.569878i
$592$	5.16740e34			0.0471074
$593$			7.13936e35i			0.636720i	0.947970	+	0.318360i	$0.103132\pi$
$593$			7.13936e35i			0.636720i	−0.947970	+	0.318360i	$0.896868\pi$
$594$	1.07341e36	+	1.18755e35i	0.936572	+	0.103616i
$595$	2.45114e34			0.0209242
$596$		−	8.31128e35i		−	0.694171i
$597$	−7.00438e34	+	1.11640e35i	−0.0572405	+	0.0912336i
$598$	−3.15552e35			−0.252322
$599$		−	4.48157e35i		−	0.350656i	−0.984510	−	0.175328i	$-0.943901\pi$
$599$		−	4.48157e35i		−	0.350656i	0.984510	−	0.175328i	$-0.0560986\pi$
$600$	8.41448e35	+	5.27929e35i	0.644260	+	0.404212i
$601$	9.13293e35			0.684293			0.342147	−	0.939647i	$-0.388846\pi$
$601$	9.13293e35			0.684293			0.342147	+	0.939647i	$0.388846\pi$
$602$			1.15550e36i			0.847257i
$603$	−1.00447e36	−	2.07866e36i	−0.720796	−	1.49162i
$604$	−1.13286e36			−0.795600
$605$		−	2.00361e36i		−	1.37718i
$606$	−7.83227e35	+	1.24836e36i	−0.526919	+	0.839837i
$607$	−2.61813e36			−1.72401			−0.862003	−	0.506904i	$-0.830790\pi$
$607$	−2.61813e36			−1.72401			−0.862003	+	0.506904i	$0.830790\pi$
$608$		−	2.17895e35i		−	0.140443i
$609$	−3.46540e35	−	2.17421e35i	−0.218640	−	0.137176i
$610$	−1.02456e36			−0.632774
$611$			2.94927e35i			0.178311i
$612$	6.57533e33	−	3.17740e33i	0.00389179	−	0.00188063i
$613$	−4.52076e35			−0.261954			−0.130977	−	0.991385i	$-0.541811\pi$
$613$	−4.52076e35			−0.261954			−0.130977	+	0.991385i	$0.541811\pi$
$614$		−	2.08203e36i		−	1.18113i
$615$	−1.46311e36	+	2.33200e36i	−0.812643	+	1.29524i
$616$	−1.18130e36			−0.642410
$617$		−	9.78916e35i		−	0.521241i	−0.965441	−	0.260620i	$-0.916073\pi$
$617$		−	9.78916e35i		−	0.521241i	0.965441	−	0.260620i	$-0.0839271\pi$
$618$	1.92062e35	+	1.20501e35i	0.100136	+	0.0628261i
$619$	3.25227e36			1.66038			0.830190	−	0.557480i	$-0.188232\pi$
$619$	3.25227e36			1.66038			0.830190	+	0.557480i	$0.188232\pi$
$620$			3.12234e36i			1.56095i
$621$	−2.18058e35	+	1.97099e36i	−0.106753	+	0.964927i
$622$	2.14182e35			0.102685
$623$			4.20524e36i			1.97445i
$624$	1.06205e35	−	1.69277e35i	0.0488368	−	0.0778393i
$625$	3.27841e36			1.47646
$626$			3.61597e35i			0.159499i
$627$	−2.07576e36	−	1.30234e36i	−0.896806	−	0.562661i
$628$	1.93711e36			0.819745
$629$		−	3.92969e33i		−	0.00162892i
$630$	−1.83397e36	−	3.79523e36i	−0.744672	−	1.54103i
$631$	−1.82437e36			−0.725656			−0.362828	−	0.931856i	$-0.618189\pi$
$631$	−1.82437e36			−0.725656			−0.362828	+	0.931856i	$0.618189\pi$
$632$		−	1.93505e35i		−	0.0753996i
$633$	2.21096e36	−	3.52397e36i	0.843980	−	1.34519i
$634$	1.78313e36			0.666841
$635$			3.51714e36i			1.28864i
$636$	−1.20619e36	−	7.56772e35i	−0.432987	−	0.271658i
$637$	−8.97895e35			−0.315801
$638$			5.17602e35i			0.178372i
$639$	−1.16710e36	+	5.63977e35i	−0.394091	+	0.190436i
$640$	−4.74212e35			−0.156904
$641$			2.99981e35i			0.0972612i	0.998817	+	0.0486306i	$0.0154857\pi$
$641$			2.99981e35i			0.0972612i	−0.998817	+	0.0486306i	$0.984514\pi$
$642$	1.06748e36	−	1.70142e36i	0.339160	−	0.540575i
$643$	−1.47812e35			−0.0460220			−0.0230110	−	0.999735i	$-0.507325\pi$
$643$	−1.47812e35			−0.0460220			−0.0230110	+	0.999735i	$0.507325\pi$
$644$		−	2.16911e36i		−	0.661860i
$645$	4.41886e36	+	2.77242e36i	1.32140	+	0.829053i
$646$	−1.65704e34			−0.00485636
$647$		−	2.89285e36i		−	0.830941i	−0.909607	−	0.415470i	$-0.863617\pi$
$647$		−	2.89285e36i		−	0.830941i	0.909607	−	0.415470i	$-0.136383\pi$
$648$	−9.83945e35	−	7.80356e35i	−0.277010	−	0.219694i
$649$	−1.08035e36			−0.298115
$650$		−	2.06716e36i		−	0.559113i
$651$	4.80691e36	−	7.66156e36i	1.27442	−	2.03126i
$652$	−1.40845e36			−0.366036
$653$			2.51343e36i			0.640317i	0.947364	+	0.320159i	$0.103736\pi$
$653$			2.51343e36i			0.640317i	−0.947364	+	0.320159i	$0.896264\pi$
$654$	1.60325e36	+	1.00589e36i	0.400398	+	0.251212i
$655$	3.82660e36			0.936864
$656$		−	8.97177e35i		−	0.215342i
$657$	1.14514e36	+	2.36975e36i	0.269468	+	0.557639i
$658$	−2.02734e36			−0.467724
$659$		−	3.79601e36i		−	0.858652i	−0.903150	−	0.429326i	$-0.858751\pi$
$659$		−	3.79601e36i		−	0.858652i	0.903150	−	0.429326i	$-0.141249\pi$
$660$	−2.83433e36	+	4.51754e36i	−0.628607	+	1.00192i
$661$	−6.57193e36			−1.42914			−0.714569	−	0.699565i	$-0.753377\pi$
$661$	−6.57193e36			−1.42914			−0.714569	+	0.699565i	$0.753377\pi$
$662$			1.58909e36i			0.338841i
$663$	−1.28732e34	−	8.07669e33i	−0.00269159	−	0.00168872i
$664$	8.26177e34			0.0169390
$665$			9.56432e36i			1.92297i
$666$	−6.08454e35	+	2.94023e35i	−0.119967	+	0.0579718i
$667$	−9.50422e35			−0.183773
$668$		−	8.82029e35i		−	0.167259i
$669$	2.59416e36	−	4.13473e36i	0.482455	−	0.768968i
$670$	1.14005e37			2.07947
$671$		−	3.75506e36i		−	0.671775i
$672$	1.16362e36	+	7.30060e35i	0.204178	+	0.128103i
$673$	−3.80792e36			−0.655379			−0.327689	−	0.944786i	$-0.606270\pi$
$673$	−3.80792e36			−0.655379			−0.327689	+	0.944786i	$0.606270\pi$
$674$			5.45474e36i			0.920864i
$675$	−1.29118e37	−	1.42848e36i	−2.13816	−	0.236552i
$676$	2.66220e36			0.432448
$677$			6.46878e36i			1.03079i	0.856953	+	0.515394i	$0.172355\pi$
$677$			6.46878e36i			1.03079i	−0.856953	+	0.515394i	$0.827645\pi$
$678$	−1.19127e36	+	1.89872e36i	−0.186219	+	0.296807i
$679$	8.81261e36			1.35144
$680$			3.60628e34i			0.00542555i
$681$	6.02467e36	+	3.77991e36i	0.889243	+	0.557916i
$682$	−1.14435e37			−1.65715
$683$		−	1.24929e37i		−	1.77498i	−0.460827	−	0.887490i	$-0.652447\pi$
$683$		−	1.24929e37i		−	1.77498i	0.460827	−	0.887490i	$-0.347553\pi$
$684$	1.23981e36	+	2.56568e36i	0.172833	+	0.357663i
$685$	−1.38364e37			−1.89255
$686$			1.01170e36i			0.135781i
$687$	−7.64415e36	+	1.21837e37i	−1.00668	+	1.60451i
$688$	−1.70005e36			−0.219690
$689$			2.96321e36i			0.375762i
$690$	−8.29512e36	−	5.20440e36i	−1.03225	−	0.647639i
$691$	−1.18543e37			−1.44765			−0.723824	−	0.689984i	$-0.757617\pi$
$691$	−1.18543e37			−1.44765			−0.723824	+	0.689984i	$0.757617\pi$
$692$		−	1.83966e36i		−	0.220474i
$693$	1.39097e37	−	6.72159e36i	1.63601	−	0.790569i
$694$	7.86144e36			0.907463
$695$		−	2.42632e37i		−	2.74882i
$696$	3.19884e35	−	5.09852e35i	0.0355691	−	0.0566923i
$697$	−6.82284e34			−0.00744627
$698$			6.46735e36i			0.692797i
$699$	6.67107e36	+	4.18547e36i	0.701443	+	0.440089i
$700$	1.42097e37			1.46660
$701$		−	2.05242e36i		−	0.207937i	−0.994581	−	0.103969i	$-0.966846\pi$
$701$		−	2.05242e36i		−	0.207937i	0.994581	−	0.103969i	$-0.0331541\pi$
$702$	−2.87373e35	+	2.59752e36i	−0.0285801	+	0.258331i
$703$	1.53336e36			0.149701
$704$		−	1.73801e36i		−	0.166574i
$705$	−4.86425e36	+	7.75295e36i	−0.457675	+	0.729472i
$706$	4.97286e36			0.459352
$707$			2.10813e37i			1.91181i
$708$	1.06418e36	+	6.67670e35i	0.0947504	+	0.0594469i
$709$	1.78947e37			1.56431			0.782156	−	0.623083i	$-0.214120\pi$
$709$	1.78947e37			1.56431			0.782156	+	0.623083i	$0.214120\pi$
$710$		−	6.40102e36i		−	0.549403i
$711$	1.10104e36	+	2.27849e36i	0.0927890	+	0.192018i
$712$	−6.18702e36			−0.511967
$713$		−	2.10126e37i		−	1.70733i
$714$	5.55195e34	−	8.84906e34i	0.00442964	−	0.00706025i
$715$	1.10981e37			0.869500
$716$		−	7.03929e36i		−	0.541576i
$717$	−6.70275e36	−	4.20534e36i	−0.506412	−	0.317726i
$718$	−1.36813e36			−0.101510
$719$			1.10339e35i			0.00803998i	0.999992	+	0.00401999i	$0.00127961\pi$
$719$			1.10339e35i			0.00803998i	−0.999992	+	0.00401999i	$0.998720\pi$
$720$	5.58379e36	−	2.69825e36i	0.399583	−	0.193090i
$721$	3.24339e36			0.227951
$722$			3.77822e36i			0.260798i
$723$	−5.60146e36	+	8.92798e36i	−0.379755	+	0.605278i
$724$	−9.83981e36			−0.655217
$725$		−	6.22615e36i		−	0.407216i
$726$	−7.23336e36	−	4.53825e36i	−0.464691	−	0.291550i
$727$	−5.25196e36			−0.331416			−0.165708	−	0.986175i	$-0.552991\pi$
$727$	−5.25196e36			−0.331416			−0.165708	+	0.986175i	$0.552991\pi$
$728$		−	2.85862e36i		−	0.177194i
$729$	1.60260e37	+	3.58998e36i	0.975816	+	0.218592i
$730$	−1.29971e37			−0.777406
$731$			1.29285e35i			0.00759664i
$732$	−2.32067e36	+	3.69883e36i	−0.133958	+	0.213511i
$733$	1.30630e37			0.740786			0.370393	−	0.928875i	$-0.379223\pi$
$733$	1.30630e37			0.740786			0.370393	+	0.928875i	$0.379223\pi$
$734$			1.14894e35i			0.00640104i
$735$	−2.36036e37	−	1.48090e37i	−1.29194	−	0.810570i
$736$	3.19134e36			0.171617
$737$			4.17836e37i			2.20764i
$738$	5.10491e36	+	1.05641e37i	0.265006	+	0.548406i
$739$	3.25764e37			1.66160			0.830799	−	0.556573i	$-0.187884\pi$
$739$	3.25764e37			1.66160			0.830799	+	0.556573i	$0.187884\pi$
$740$		−	3.33711e36i		−	0.167247i
$741$	3.15151e36	−	5.02309e36i	0.155197	−	0.247363i
$742$	−2.03692e37			−0.985653
$743$			1.37784e37i			0.655156i	0.944824	+	0.327578i	$0.106232\pi$
$743$			1.37784e37i			0.655156i	−0.944824	+	0.327578i	$0.893768\pi$
$744$	1.12722e37	+	7.07223e36i	0.526696	+	0.330452i
$745$	−5.36743e37			−2.46453
$746$		−	1.95632e37i		−	0.882744i
$747$	−9.72813e35	+	4.70092e35i	−0.0431381	+	0.0208456i
$748$	−1.32172e35			−0.00575995
$749$		−	2.87322e37i		−	1.23057i
$750$	1.82450e37	−	2.90801e37i	0.767976	−	1.22405i
$751$	−2.54645e37			−1.05346			−0.526728	−	0.850034i	$-0.676581\pi$
$751$	−2.54645e37			−1.05346			−0.526728	+	0.850034i	$0.676581\pi$
$752$		−	2.98275e36i		−	0.121279i
$753$	5.81573e36	+	3.64882e36i	0.232418	+	0.145820i
$754$	−1.25254e36			−0.0491998
$755$			7.31599e37i			2.82464i
$756$	−1.78555e37	−	1.97542e36i	−0.677623	−	0.0749679i
$757$	−3.62029e37			−1.35051			−0.675254	−	0.737585i	$-0.735966\pi$
$757$	−3.62029e37			−1.35051			−0.675254	+	0.737585i	$0.735966\pi$
$758$		−	6.98133e35i		−	0.0255999i
$759$	1.90744e37	−	3.04020e37i	0.687556	−	1.09587i
$760$	−1.40716e37			−0.498618
$761$			1.73601e37i			0.604715i	0.953195	+	0.302357i	$0.0977736\pi$
$761$			1.73601e37i			0.604715i	−0.953195	+	0.302357i	$0.902226\pi$
$762$	1.26975e37	+	7.96648e36i	0.434814	+	0.272805i
$763$	2.70745e37			0.911467
$764$			4.61087e36i			0.152605i
$765$	−2.05196e35	−	4.24635e35i	−0.00667684	−	0.0138171i
$766$	2.00550e37			0.641576
$767$		−	2.61432e36i		−	0.0822280i
$768$	−1.07411e36	+	1.71199e36i	−0.0332165	+	0.0529426i
$769$	3.78894e36			0.115206			0.0576030	−	0.998340i	$-0.481654\pi$
$769$	3.78894e36			0.115206			0.0576030	+	0.998340i	$0.481654\pi$
$770$			7.62887e37i			2.28077i
$771$	−5.03051e37	−	3.15617e37i	−1.47879	−	0.927798i
$772$	9.44943e36			0.273137
$773$		−	5.59686e37i		−	1.59078i	−0.606095	−	0.795392i	$-0.707265\pi$
$773$		−	5.59686e37i		−	1.59078i	0.606095	−	0.795392i	$-0.292735\pi$
$774$	2.00178e37	−	9.67321e36i	0.559480	−	0.270357i
$775$	1.37652e38			3.78321
$776$			1.29657e37i			0.350423i
$777$	−5.13755e36	+	8.18856e36i	−0.136547	+	0.217638i
$778$	−1.30560e37			−0.341252
$779$		−	2.66226e37i		−	0.684327i
$780$	−1.09319e37	−	6.85875e36i	−0.276355	−	0.173386i
$781$	2.34601e37			0.583265
$782$		−	2.42694e35i		−	0.00593433i
$783$	−8.65551e35	+	7.82358e36i	−0.0208156	+	0.188149i
$784$	9.08088e36			0.214793
$785$		−	1.25099e38i		−	2.91036i
$786$	8.66742e36	−	1.38147e37i	0.198334	−	0.316117i
$787$	−4.61854e37			−1.03952			−0.519761	−	0.854312i	$-0.673979\pi$
$787$	−4.61854e37			−1.03952			−0.519761	+	0.854312i	$0.673979\pi$
$788$			2.42169e37i			0.536140i
$789$	−2.57105e37	−	1.61309e37i	−0.559900	−	0.351284i
$790$	−1.24965e37			−0.267693
$791$			3.20641e37i			0.675654i
$792$	9.88923e36	+	2.04649e37i	0.204991	+	0.424211i
$793$	9.08680e36			0.185293
$794$		−	6.96842e37i		−	1.39787i
$795$	−4.88724e37	+	7.78960e37i	−0.964475	+	1.53724i
$796$	−2.77377e36			−0.0538518
$797$			8.50956e37i			1.62536i	0.582711	+	0.812679i	$0.301992\pi$
$797$			8.50956e37i			1.62536i	−0.582711	+	0.812679i	$0.698008\pi$
$798$	3.45289e37	+	2.16636e37i	0.648851	+	0.407093i
$799$	−2.26832e35			−0.00419369
$800$			2.09062e37i			0.380282i
$801$	7.28514e37	−	3.52040e37i	1.30381	−	0.630041i
$802$	2.71139e37			0.477446
$803$		−	4.76348e37i		−	0.825321i
$804$	2.58227e37	−	4.11580e37i	0.440224	−	0.701657i
$805$	−1.40081e38			−2.34982
$806$		−	2.76920e37i		−	0.457087i
$807$	−6.74801e37	−	4.23374e37i	−1.09602	−	0.687651i
$808$	−3.10161e37			−0.495724
$809$			8.78081e37i			1.38103i	0.723317	+	0.690516i	$0.242617\pi$
$809$			8.78081e37i			1.38103i	−0.723317	+	0.690516i	$0.757383\pi$
$810$	−5.03954e37	+	6.35432e37i	−0.779984	+	0.983476i
$811$	6.32372e37			0.963167			0.481584	−	0.876400i	$-0.340062\pi$
$811$	6.32372e37			0.963167			0.481584	+	0.876400i	$0.340062\pi$
$812$		−	8.60998e36i		−	0.129055i
$813$	1.29350e37	−	2.06166e37i	0.190805	−	0.304117i
$814$	1.22307e37			0.177555
$815$			9.09579e37i			1.29955i
$816$	1.30193e35	+	8.16838e34i	0.00183069	+	0.00114859i
$817$	−5.04467e37			−0.698146
$818$		−	4.12582e37i		−	0.561975i
$819$	1.62655e37	+	3.36599e37i	0.218060	+	0.451255i
$820$	−5.79397e37			−0.764533
$821$		−	3.77145e37i		−	0.489832i	−0.969544	−	0.244916i	$-0.921240\pi$
$821$		−	3.77145e37i		−	0.489832i	0.969544	−	0.244916i	$-0.0787604\pi$
$822$	−3.13401e37	+	4.99519e37i	−0.400652	+	0.638585i
$823$	1.01324e38			1.27501			0.637503	−	0.770448i	$-0.279967\pi$
$823$	1.01324e38			1.27501			0.637503	+	0.770448i	$0.279967\pi$
$824$			4.77189e36i			0.0591067i
$825$	1.99161e38	+	1.24955e38i	2.42831	+	1.52353i
$826$	1.79710e37			0.215690
$827$		−	7.58580e37i		−	0.896252i	−0.893970	−	0.448126i	$-0.852092\pi$
$827$		−	7.58580e37i		−	0.896252i	0.893970	−	0.448126i	$-0.147908\pi$
$828$	−3.75776e37	+	1.81586e37i	−0.437054	+	0.211197i
$829$	−8.50538e37			−0.973833			−0.486917	−	0.873448i	$-0.661878\pi$
$829$	−8.50538e37			−0.973833			−0.486917	+	0.873448i	$0.661878\pi$
$830$		−	5.33545e36i		−	0.0601390i
$831$	−5.72300e37	+	9.12169e37i	−0.635054	+	1.01219i
$832$	4.20578e36			0.0459456
$833$		−	6.90581e35i		−	0.00742728i
$834$	−8.75944e37	−	5.49572e37i	−0.927508	−	0.581924i
$835$	−5.69614e37			−0.593823
$836$		−	5.15733e37i		−	0.529350i
$837$	−1.72969e38	−	1.91362e37i	−1.74799	−	0.193386i
$838$	6.82379e36			0.0678974
$839$		−	1.19209e38i		−	1.16789i	−0.811793	−	0.583946i	$-0.801508\pi$
$839$		−	1.19209e38i		−	1.16789i	0.811793	−	0.583946i	$-0.198492\pi$
$840$	4.71473e37	−	7.51464e37i	0.454806	−	0.724899i
$841$	1.01508e38			0.964167
$842$		−	4.01332e37i		−	0.375359i
$843$	1.07830e38	+	6.76531e37i	0.993072	+	0.623059i
$844$	8.75550e37			0.794015
$845$		−	1.71925e38i		−	1.53533i
$846$	1.69718e37	+	3.51216e37i	0.149249	+	0.308858i
$847$	−1.22151e38			−1.05782
$848$		−	2.99685e37i		−	0.255576i
$849$	6.75697e37	−	1.07697e38i	0.567482	−	0.904490i
$850$	1.58987e36			0.0131497
$851$			2.24580e37i			0.182930i
$852$	−2.31088e37	−	1.44986e37i	−0.185380	−	0.116308i
$853$	2.73284e37			0.215912			0.107956	−	0.994156i	$-0.465569\pi$
$853$	2.73284e37			0.215912			0.107956	+	0.994156i	$0.465569\pi$
$854$			6.24630e37i			0.486038i
$855$	1.65692e38	−	8.00673e37i	1.26982	−	0.613614i
$856$	4.22727e37			0.319081
$857$			1.65481e38i			1.23026i	0.788425	+	0.615130i	$0.210897\pi$
$857$			1.65481e38i			1.23026i	−0.788425	+	0.615130i	$0.789103\pi$
$858$	2.51377e37	−	4.00660e37i	0.184073	−	0.293388i
$859$	2.33457e38			1.68382			0.841911	−	0.539616i	$-0.181430\pi$
$859$	2.33457e38			1.68382			0.841911	+	0.539616i	$0.181430\pi$
$860$			1.09789e38i			0.779972i
$861$	1.42172e38	+	8.91995e37i	0.994885	+	0.624197i
$862$	−1.53568e38			−1.05854
$863$			2.52228e38i			1.71259i	0.516488	+	0.856294i	$0.327239\pi$
$863$			2.52228e38i			1.71259i	−0.516488	+	0.856294i	$0.672761\pi$
$864$	2.90636e36	−	2.62701e37i	0.0194388	−	0.175705i
$865$	−1.18805e38			−0.782754
$866$		−	1.71920e37i		−	0.111582i
$867$	−8.31169e37	+	1.32477e38i	−0.531424	+	0.847018i
$868$	1.90356e38			1.19897
$869$		−	4.58004e37i		−	0.284192i
$870$	−3.29263e37	−	2.06581e37i	−0.201276	−	0.126282i
$871$	−1.01111e38			−0.608925
$872$			3.98337e37i			0.236340i
$873$	−7.37743e37	−	1.52669e38i	−0.431241	−	0.892414i
$874$	9.46990e37			0.545377
$875$		−	4.91081e38i		−	2.78643i
$876$	−2.94389e37	+	4.69216e37i	−0.164577	+	0.262313i
$877$	−2.75592e37			−0.151800			−0.0759002	−	0.997115i	$-0.524183\pi$
$877$	−2.75592e37			−0.151800			−0.0759002	+	0.997115i	$0.524183\pi$
$878$		−	6.69871e37i		−	0.363549i
$879$	−2.79315e38	−	1.75244e38i	−1.49362	−	0.937103i
$880$	−1.12241e38			−0.591393
$881$			3.40974e38i			1.77025i	0.465352	+	0.885126i	$0.345928\pi$
$881$			3.40974e38i			1.77025i	−0.465352	+	0.885126i	$0.654072\pi$
$882$	−1.06926e38	+	5.16700e37i	−0.547007	+	0.264330i
$883$	−2.10383e38			−1.06053			−0.530264	−	0.847832i	$-0.677907\pi$
$883$	−2.10383e38			−1.06053			−0.530264	+	0.847832i	$0.677907\pi$
$884$		−	3.19841e35i		−	0.00158875i
$885$	4.31181e37	−	6.87245e37i	0.211056	−	0.336395i
$886$	1.67544e38			0.808148
$887$			2.47550e38i			1.17667i	0.808616	+	0.588336i	$0.200217\pi$
$887$			2.47550e38i			1.17667i	−0.808616	+	0.588336i	$0.799783\pi$
$888$	−1.20475e37	−	7.55869e36i	−0.0564325	−	0.0354061i
$889$	2.14425e38			0.989812
$890$			3.99558e38i			1.81765i
$891$	−2.32889e38	−	1.84702e38i	−1.04409	−	0.828058i
$892$	1.02730e38			0.453892
$893$		−	8.85095e37i		−	0.385408i
$894$	−1.21575e38	+	1.93774e38i	−0.521741	+	0.831585i
$895$	−4.54598e38			−1.92277
$896$			2.89107e37i			0.120519i
$897$	7.35693e37	+	4.61578e37i	0.302270	+	0.189646i
$898$	1.42957e38			0.578913
$899$		−	8.34066e37i		−	0.332908i
$900$	−1.18956e38	−	2.46168e38i	−0.467986	−	0.968455i
$901$	−2.27904e36			−0.00883751
$902$		−	2.12352e38i		−	0.811655i
$903$	1.69022e38	−	2.69399e38i	0.636801	−	1.01498i
$904$	−4.71747e37			−0.175194
$905$			6.35455e38i			2.32623i
$906$	2.64120e38	+	1.65710e38i	0.953092	+	0.597975i
$907$	9.99317e37			0.355475			0.177737	−	0.984078i	$-0.443122\pi$
$907$	9.99317e37			0.355475			0.177737	+	0.984078i	$0.443122\pi$
$908$			1.49686e38i			0.524887i
$909$	3.65211e38	−	1.76481e38i	1.26245	−	0.610053i
$910$	−1.84610e38			−0.629095
$911$		−	2.95129e38i		−	0.991454i	−0.868478	−	0.495727i	$-0.834902\pi$
$911$		−	2.95129e38i		−	0.991454i	0.868478	−	0.495727i	$-0.165098\pi$
$912$	−3.18729e37	+	5.08011e37i	−0.105557	+	0.168244i
$913$	1.95547e37			0.0638456
$914$		−	2.41107e38i		−	0.776085i
$915$	2.38871e38	+	1.49869e38i	0.758034	+	0.475595i
$916$	−3.02712e38			−0.947083
$917$		−	2.33292e38i		−	0.719611i
$918$	−1.99779e36	−	2.21022e35i	−0.00607567	−	0.000672173i
$919$	4.66479e38			1.39872			0.699360	−	0.714770i	$-0.253469\pi$
$919$	4.66479e38			1.39872			0.699360	+	0.714770i	$0.253469\pi$
$920$		−	2.06097e38i		−	0.609298i
$921$	−3.04552e38	+	4.85414e38i	−0.887740	+	1.41494i
$922$	−1.03495e38			−0.297452
$923$			5.67706e37i			0.160880i
$924$	2.75415e38	+	1.72797e38i	0.769578	+	0.482837i
$925$	−1.47120e38			−0.405350
$926$			1.36427e38i			0.370645i
$927$	−2.71519e37	−	5.61884e37i	−0.0727384	−	0.150525i
$928$	1.26676e37			0.0334633
$929$		−	3.89862e36i		−	0.0101556i	−0.999987	−	0.00507782i	$-0.998384\pi$
$929$		−	3.89862e36i		−	0.0101556i	0.999987	−	0.00507782i	$-0.00161633\pi$
$930$	4.56725e38	−	7.27958e38i	1.17321	−	1.86994i
$931$	2.69464e38			0.682581
$932$			1.65746e38i			0.414035i
$933$	−4.99356e37	−	3.13299e37i	−0.123012	−	0.0771787i
$934$	3.68434e38			0.895057
$935$			8.53567e36i			0.0204497i
$936$	−4.95226e37	+	2.39308e37i	−0.117008	+	0.0565420i
$937$	−3.03490e38			−0.707180			−0.353590	−	0.935400i	$-0.615039\pi$
$937$	−3.03490e38			−0.707180			−0.353590	+	0.935400i	$0.615039\pi$
$938$		−	6.95043e38i		−	1.59726i
$939$	5.28932e37	−	8.43047e37i	0.119880	−	0.191073i
$940$	−1.92626e38			−0.430580
$941$		−	2.87865e38i		−	0.634635i	−0.948319	−	0.317318i	$-0.897218\pi$
$941$		−	2.87865e38i		−	0.634635i	0.948319	−	0.317318i	$-0.102782\pi$
$942$	−4.51628e38	−	2.83354e38i	−0.982017	−	0.616123i
$943$	3.89921e38			0.836228
$944$			2.64400e37i			0.0559276i
$945$	−1.27572e38	+	1.15311e39i	−0.266160	+	2.40578i
$946$	−4.02382e38			−0.828045
$947$		−	3.24312e38i		−	0.658284i	−0.944280	−	0.329142i	$-0.893240\pi$
$947$		−	3.24312e38i		−	0.658284i	0.944280	−	0.329142i	$-0.106760\pi$
$948$	−2.83052e37	+	4.51147e37i	−0.0566706	+	0.0903253i
$949$	1.15271e38			0.227645
$950$			6.20366e38i			1.20848i
$951$	−4.15728e38	−	2.60830e38i	−0.798845	−	0.501200i
$952$	2.19860e36			0.00416740
$953$		−	1.90900e38i		−	0.356943i	−0.983945	−	0.178472i	$-0.942885\pi$
$953$		−	1.90900e38i		−	0.356943i	0.983945	−	0.178472i	$-0.0571153\pi$
$954$	1.70520e38	+	3.52876e38i	0.314519	+	0.650868i
$955$	2.97770e38			0.541797
$956$		−	1.66533e38i		−	0.298916i
$957$	7.57131e37	−	1.20676e38i	0.134065	−	0.213682i
$958$	−7.33685e38			−1.28162
$959$			8.43548e38i			1.45368i
$960$	1.10560e38	+	6.93661e37i	0.187963	+	0.117929i
$961$	1.24780e39			2.09286
$962$			2.95968e37i			0.0489743i
$963$	−4.97756e38	+	2.40531e38i	−0.812596	+	0.392671i
$964$	−2.21820e38			−0.357273
$965$		−	6.10245e38i		−	0.969726i
$966$	−3.17290e38	+	5.05718e38i	−0.497456	+	0.792877i
$967$	−7.02378e38			−1.08649			−0.543246	−	0.839574i	$-0.682805\pi$
$967$	−7.02378e38			−1.08649			−0.543246	+	0.839574i	$0.682805\pi$
$968$		−	1.79717e38i		−	0.274290i
$969$	3.86331e36	+	2.42386e36i	0.00581769	+	0.00365005i
$970$	8.37324e38			1.24412
$971$		−	1.06597e38i		−	0.156278i	−0.996942	−	0.0781388i	$-0.975102\pi$
$971$		−	1.06597e38i		−	0.156278i	0.996942	−	0.0781388i	$-0.0248977\pi$
$972$	1.15254e38	+	3.25864e38i	0.166723	+	0.471385i
$973$	−1.47922e39			−2.11138
$974$		−	1.75146e38i		−	0.246680i
$975$	−3.02377e38	+	4.81948e38i	−0.420231	+	0.669792i
$976$	−9.18996e37			−0.126028
$977$		−	4.99578e37i		−	0.0676042i	−0.999429	−	0.0338021i	$-0.989238\pi$
$977$		−	4.99578e37i		−	0.0676042i	0.999429	−	0.0338021i	$-0.0107616\pi$
$978$	3.28374e38	+	2.06024e38i	0.438494	+	0.275113i
$979$	−1.46440e39			−1.92968
$980$		−	5.86444e38i		−	0.762583i
$981$	−2.26653e38	−	4.69037e38i	−0.290846	−	0.601880i
$982$	−7.63844e36			−0.00967287
$983$			8.31675e38i			1.03934i	0.854367	+	0.519670i	$0.173945\pi$
$983$			8.31675e38i			1.03934i	−0.854367	+	0.519670i	$0.826055\pi$
$984$	−1.31236e38	+	2.09173e38i	−0.161852	+	0.257970i
$985$	1.56393e39			1.90347
$986$		−	9.63341e35i		−	0.00115712i
$987$	4.72665e38	+	2.96552e38i	0.560312	+	0.351543i
$988$	1.24801e38			0.146009
$989$		−	7.38854e38i		−	0.853114i
$990$	1.32162e39	−	6.38647e38i	1.50609	−	0.727785i
$991$	1.38401e39			1.55662			0.778310	−	0.627880i	$-0.216077\pi$
$991$	1.38401e39			1.55662			0.778310	+	0.627880i	$0.216077\pi$
$992$			2.80064e38i			0.310889i
$993$	2.32447e38	−	3.70489e38i	0.254674	−	0.405915i
$994$	−3.90243e38			−0.422000
$995$			1.79130e38i			0.191191i
$996$	−1.92619e37	−	1.20850e37i	−0.0202921	−	0.0127314i
$997$	4.52636e38			0.470665			0.235332	−	0.971915i	$-0.424382\pi$
$997$	4.52636e38			0.470665			0.235332	+	0.971915i	$0.424382\pi$
$998$			6.35442e37i			0.0652197i
$999$	1.84867e38	+	2.04525e37i	0.187287	+	0.0207203i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.27.b.a.5.1	✓	8
3.2	odd	2	inner	6.27.b.a.5.5	yes	8
4.3	odd	2		48.27.e.b.17.7		8
12.11	even	2		48.27.e.b.17.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.27.b.a.5.1	✓	8	1.1	even	1	trivial
6.27.b.a.5.5	yes	8	3.2	odd	2	inner
48.27.e.b.17.7		8	4.3	odd	2
48.27.e.b.17.8		8	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:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 27 \)
Character orbit:	\([\chi]\)	\(=\)	6.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5792.62i q^{2} +(-847324. + 1.35052e6i) q^{3} -3.35544e7 q^{4} +2.16695e9i q^{5} +(7.82305e9 + 4.90823e9i) q^{6} +1.32110e11 q^{7} +1.94368e11i q^{8} +(-1.10595e12 - 2.28866e12i) q^{9} +O(q^{10})\)	\(q-5792.62i q^{2} +(-847324. + 1.35052e6i) q^{3} -3.35544e7 q^{4} +2.16695e9i q^{5} +(7.82305e9 + 4.90823e9i) q^{6} +1.32110e11 q^{7} +1.94368e11i q^{8} +(-1.10595e12 - 2.28866e12i) q^{9} +1.25523e13 q^{10} +4.60048e13i q^{11} +(2.84315e13 - 4.53160e13i) q^{12} -1.11326e14 q^{13} -7.65260e14i q^{14} +(-2.92651e15 - 1.83611e15i) q^{15} +1.12590e15 q^{16} -8.56222e13i q^{17} +(-1.32573e16 + 6.40634e15i) q^{18} +3.34097e16 q^{19} -7.27106e16i q^{20} +(-1.11940e17 + 1.78417e17i) q^{21} +2.66488e17 q^{22} +4.89326e17i q^{23} +(-2.62498e17 - 1.64693e17i) q^{24} -3.20554e18 q^{25} +6.44870e17i q^{26} +(4.02798e18 + 4.45630e17i) q^{27} -4.43286e18 q^{28} +1.94231e18i q^{29} +(-1.06359e19 + 1.69521e19i) q^{30} -4.29420e19 q^{31} -6.52191e18i q^{32} +(-6.21304e19 - 3.89810e19i) q^{33} -4.95977e17 q^{34} +2.86274e20i q^{35} +(3.71095e19 + 7.67947e19i) q^{36} +4.58957e19 q^{37} -1.93529e20i q^{38} +(9.43294e19 - 1.50348e20i) q^{39} -4.21185e20 q^{40} -7.96853e20i q^{41} +(1.03350e21 + 6.48424e20i) q^{42} -1.50994e21 q^{43} -1.54366e21i q^{44} +(4.95940e21 - 2.39653e21i) q^{45} +2.83448e21 q^{46} -2.64922e21i q^{47} +(-9.54003e20 + 1.52055e21i) q^{48} +8.06544e21 q^{49} +1.85685e22i q^{50} +(1.15635e20 + 7.25498e19i) q^{51} +3.73549e21 q^{52} -2.66174e22i q^{53} +(2.58136e21 - 2.33325e22i) q^{54} -9.96899e22 q^{55} +2.56779e22i q^{56} +(-2.83088e22 + 4.51205e22i) q^{57} +1.12511e22 q^{58} +2.34835e22i q^{59} +(9.81973e22 + 6.16095e22i) q^{60} -8.16232e22 q^{61} +2.48746e23i q^{62} +(-1.46106e23 - 3.02354e23i) q^{63} -3.77789e22 q^{64} -2.41238e23i q^{65} +(-2.25802e23 + 3.59898e23i) q^{66} +9.08244e23 q^{67} +2.87301e21i q^{68} +(-6.60845e23 - 4.14618e23i) q^{69} +1.65828e24 q^{70} -5.09949e23i q^{71} +(4.44842e23 - 2.14961e23i) q^{72} -1.03543e24 q^{73} -2.65856e23i q^{74} +(2.71613e24 - 4.32915e24i) q^{75} -1.12104e24 q^{76} +6.07767e24i q^{77} +(-8.70911e23 - 5.46414e23i) q^{78} -9.95558e23 q^{79} +2.43976e24i q^{80} +(-4.01484e24 + 5.06228e24i) q^{81} -4.61587e24 q^{82} -4.25058e23i q^{83} +(3.75607e24 - 5.98667e24i) q^{84} +1.85539e23 q^{85} +8.74653e24i q^{86} +(-2.62313e24 - 1.64577e24i) q^{87} -8.94186e24 q^{88} +3.18315e25i q^{89} +(-1.38822e25 - 2.87279e25i) q^{90} -1.47072e25 q^{91} -1.64191e25i q^{92} +(3.63858e25 - 5.79940e25i) q^{93} -1.53459e25 q^{94} +7.23969e25i q^{95} +(8.80798e24 + 5.52617e24i) q^{96} +6.67068e25 q^{97} -4.67200e25i q^{98} +(1.05289e26 - 5.08789e25i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2194920 q^{3} - 268435456 q^{4} + 8978890752 q^{6} + 183211263760 q^{7} - 4853931303096 q^{9}+O(q^{10}) \) 8 * q + 2194920 * q^3 - 268435456 * q^4 + 8978890752 * q^6 + 183211263760 * q^7 - 4853931303096 * q^9	\( 8 q + 2194920 q^{3} - 268435456 q^{4} + 8978890752 q^{6} + 183211263760 q^{7} - 4853931303096 q^{9} + 18696278507520 q^{10} - 73649293885440 q^{12} + 512429022548560 q^{13} - 10\!\cdots\!40 q^{15}+ \cdots + 49\!\cdots\!36 q^{99}+O(q^{100}) \) 8 * q + 2194920 * q^3 - 268435456 * q^4 + 8978890752 * q^6 + 183211263760 * q^7 - 4853931303096 * q^9 + 18696278507520 * q^10 - 73649293885440 * q^12 + 512429022548560 * q^13 - 1064426665559040 * q^15 + 9007199254740992 * q^16 - 1881283573186560 * q^18 + 13250502825732304 * q^19 - 376087240418977584 * q^21 + 428662713355468800 * q^22 - 301281579173412864 * q^24 - 5623831579932691000 * q^25 + 11144542948278241320 * q^27 - 6147549891468984320 * q^28 - 12961438025281044480 * q^30 - 31284409294003569776 * q^31 - 27135100230528798720 * q^33 - 98764413849435635712 * q^34 + 162870907842406121472 * q^36 - 884494012218278308400 * q^37 + 1550610890749922311440 * q^39 - 627343005833641328640 * q^40 + 2912220856097001308160 * q^42 - 5161357724259210085040 * q^43 + 20490779480380306513920 * q^45 - 10789778429003593678848 * q^46 + 2471260223527012270080 * q^48 - 29984991896355791854440 * q^49 + 55593505357359326429184 * q^51 - 17194264791932123217920 * q^52 + 6309825934293776793600 * q^54 - 76225105088113564293120 * q^55 + 66535314651975639764880 * q^57 - 142582792844514288599040 * q^58 + 35716232168487549665280 * q^60 + 235221054408754640644432 * q^61 - 635461358798759743298160 * q^63 - 302231454903657293676544 * q^64 - 1507842687345202066489344 * q^66 + 4218736573110688595120080 * q^67 - 2608639506957020943089664 * q^69 + 1864568339879729269309440 * q^70 + 63125401729205450833920 * q^72 + 1648536069669962768198800 * q^73 + 2584159434345978668025000 * q^75 - 444613096031842444771328 * q^76 - 313072373593422745436160 * q^78 - 9378866636279258011040624 * q^79 - 746539638785265647226744 * q^81 - 6997685112389596533227520 * q^82 + 12619393734706234851852288 * q^84 - 41457721476781794937282560 * q^85 + 55271553720839002987729920 * q^87 - 14383533866221569677721600 * q^88 + 32441993904208401898536960 * q^90 - 71633324581325574226388320 * q^91 + 18549099857564620426167120 * q^93 + 67962530415252490428088320 * q^94 + 10109332261226898153013248 * q^96 - 92292347027073928712964080 * q^97 + 4908019641378975318951936 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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