LMFDB - Embedded newform 6.27.b.a.5.7

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			5.7
Root			$530.624 - 1.41421i$ of defining polynomial
Character	$\chi$	$=$	6.5
Dual form			6.27.b.a.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5792.62i q^{2} +(793293. - 1.38295e6i) q^{3} -3.35544e7 q^{4} +1.58663e9i q^{5} +(8.01091e9 + 4.59524e9i) q^{6} +2.87923e10 q^{7} -1.94368e11i q^{8} +(-1.28324e12 - 2.19417e12i) q^{9} +O(q^{10})$	\(q+5792.62i q^{2} +(793293. - 1.38295e6i) q^{3} -3.35544e7 q^{4} +1.58663e9i q^{5} +(8.01091e9 + 4.59524e9i) q^{6} +2.87923e10 q^{7} -1.94368e11i q^{8} +(-1.28324e12 - 2.19417e12i) q^{9} -9.19074e12 q^{10} +3.05361e12i q^{11} +(-2.66185e13 + 4.64041e13i) q^{12} +9.27639e13 q^{13} +1.66783e14i q^{14} +(2.19423e15 + 1.25866e15i) q^{15} +1.12590e15 q^{16} +1.38935e16i q^{17} +(1.27100e16 - 7.43331e15i) q^{18} -7.11477e16 q^{19} -5.32385e16i q^{20} +(2.28407e16 - 3.98183e16i) q^{21} -1.76884e16 q^{22} +3.71709e17i q^{23} +(-2.68801e17 - 1.54191e17i) q^{24} -1.02728e18 q^{25} +5.37346e17i q^{26} +(-4.05241e18 + 3.40358e16i) q^{27} -9.66109e17 q^{28} +1.20948e19i q^{29} +(-7.29095e18 + 1.27103e19i) q^{30} -2.98206e19 q^{31} +6.52191e18i q^{32} +(4.22300e18 + 2.42241e18i) q^{33} -8.04797e19 q^{34} +4.56827e19i q^{35} +(4.30583e19 + 7.36241e19i) q^{36} -4.00682e20 q^{37} -4.12132e20i q^{38} +(7.35890e19 - 1.28288e20i) q^{39} +3.08390e20 q^{40} +1.14484e21i q^{41} +(2.30652e20 + 1.32308e20i) q^{42} +3.02689e21 q^{43} -1.02462e20i q^{44} +(3.48134e21 - 2.03602e21i) q^{45} -2.15317e21 q^{46} -6.86906e21i q^{47} +(8.93168e20 - 1.55706e21i) q^{48} -8.55848e21 q^{49} -5.95064e21i q^{50} +(1.92140e22 + 1.10216e22i) q^{51} -3.11264e21 q^{52} +2.16396e22i q^{53} +(-1.97156e20 - 2.34741e22i) q^{54} -4.84496e21 q^{55} -5.59630e21i q^{56} +(-5.64410e22 + 9.83938e22i) q^{57} -7.00608e22 q^{58} +8.99826e22i q^{59} +(-7.36262e22 - 4.22337e22i) q^{60} +4.94708e21 q^{61} -1.72739e23i q^{62} +(-3.69474e22 - 6.31752e22i) q^{63} -3.77789e22 q^{64} +1.47182e23i q^{65} +(-1.40321e22 + 2.44622e22i) q^{66} +7.08276e23 q^{67} -4.66188e23i q^{68} +(5.14055e23 + 2.94874e23i) q^{69} -2.64623e23 q^{70} -4.06775e23i q^{71} +(-4.26476e23 + 2.49421e23i) q^{72} +1.88343e24 q^{73} -2.32100e24i q^{74} +(-8.14934e23 + 1.42068e24i) q^{75} +2.38732e24 q^{76} +8.79206e22i q^{77} +(7.43123e23 + 4.26273e23i) q^{78} -2.41553e24 q^{79} +1.78639e24i q^{80} +(-3.16768e24 + 5.63129e24i) q^{81} -6.63161e24 q^{82} -1.68124e25i q^{83} +(-7.66408e23 + 1.33608e24i) q^{84} -2.20438e25 q^{85} +1.75336e25i q^{86} +(1.67266e25 + 9.59475e24i) q^{87} +5.93525e23 q^{88} -8.57062e24i q^{89} +(1.17939e25 + 2.01661e25i) q^{90} +2.67089e24 q^{91} -1.24725e25i q^{92} +(-2.36564e25 + 4.12404e25i) q^{93} +3.97899e25 q^{94} -1.12885e26i q^{95} +(9.01948e24 + 5.17378e24i) q^{96} +2.54469e25 q^{97} -4.95760e25i q^{98} +(6.70015e24 - 3.91851e24i) 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
$3$	793293.	−	1.38295e6i	0.497574	−	0.867422i
$3$	793293.	−	1.38295e6i	0.497574	−	0.867422i
$4$	−3.35544e7			−0.500000
$5$			1.58663e9i			1.29977i	0.760034	+	0.649884i	$0.225182\pi$
$5$			1.58663e9i			1.29977i	−0.760034	+	0.649884i	$0.774818\pi$
$6$	8.01091e9	+	4.59524e9i	0.613360	+	0.351838i
$7$	2.87923e10			0.297168			0.148584	−	0.988900i	$-0.452528\pi$
$7$	2.87923e10			0.297168			0.148584	+	0.988900i	$0.452528\pi$
$8$		−	1.94368e11i		−	0.353553i
$9$	−1.28324e12	−	2.19417e12i	−0.504841	−	0.863212i
$10$	−9.19074e12			−0.919074
$11$			3.05361e12i			0.0884523i	0.999022	+	0.0442262i	$0.0140822\pi$
$11$			3.05361e12i			0.0884523i	−0.999022	+	0.0442262i	$0.985918\pi$
$12$	−2.66185e13	+	4.64041e13i	−0.248787	+	0.433711i
$13$	9.27639e13			0.306278			0.153139	−	0.988205i	$-0.451062\pi$
$13$	9.27639e13			0.306278			0.153139	+	0.988205i	$0.451062\pi$
$14$			1.66783e14i			0.210129i
$15$	2.19423e15	+	1.25866e15i	1.12745	+	0.646730i
$16$	1.12590e15			0.250000
$17$			1.38935e16i			1.40273i	0.712801	+	0.701367i	$0.247426\pi$
$17$			1.38935e16i			1.40273i	−0.712801	+	0.701367i	$0.752574\pi$
$18$	1.27100e16	−	7.43331e15i	0.610383	−	0.356977i
$19$	−7.11477e16			−1.69186			−0.845930	−	0.533295i	$-0.820954\pi$
$19$	−7.11477e16			−1.69186			−0.845930	+	0.533295i	$0.820954\pi$
$20$		−	5.32385e16i		−	0.649884i
$21$	2.28407e16	−	3.98183e16i	0.147863	−	0.257770i
$22$	−1.76884e16			−0.0625452
$23$			3.71709e17i			0.737465i	0.929536	+	0.368732i	$0.120208\pi$
$23$			3.71709e17i			0.737465i	−0.929536	+	0.368732i	$0.879792\pi$
$24$	−2.68801e17	−	1.54191e17i	−0.306680	−	0.175919i
$25$	−1.02728e18			−0.689396
$26$			5.37346e17i			0.216571i
$27$	−4.05241e18	+	3.40358e16i	−0.999965	+	0.00839861i
$28$	−9.66109e17			−0.148584
$29$			1.20948e19i			1.17876i	0.807855	+	0.589381i	$0.200628\pi$
$29$			1.20948e19i			1.17876i	−0.807855	+	0.589381i	$0.799372\pi$
$30$	−7.29095e18	+	1.27103e19i	−0.457307	+	0.797225i
$31$	−2.98206e19			−1.22128			−0.610638	−	0.791910i	$-0.709087\pi$
$31$	−2.98206e19			−1.22128			−0.610638	+	0.791910i	$0.709087\pi$
$32$			6.52191e18i			0.176777i
$33$	4.22300e18	+	2.42241e18i	0.0767255	+	0.0440115i
$34$	−8.04797e19			−0.991882
$35$			4.56827e19i			0.386249i
$36$	4.30583e19	+	7.36241e19i	0.252421	+	0.431606i
$37$	−4.00682e20			−1.64504			−0.822522	−	0.568734i	$-0.807433\pi$
$37$	−4.00682e20			−1.64504			−0.822522	+	0.568734i	$0.807433\pi$
$38$		−	4.12132e20i		−	1.19633i
$39$	7.35890e19	−	1.28288e20i	0.152396	−	0.265672i
$40$	3.08390e20			0.459537
$41$			1.14484e21i			1.23752i	0.785579	+	0.618762i	$0.212365\pi$
$41$			1.14484e21i			1.23752i	−0.785579	+	0.618762i	$0.787635\pi$
$42$	2.30652e20	+	1.32308e20i	0.182271	+	0.104555i
$43$	3.02689e21			1.76160			0.880798	−	0.473493i	$-0.157007\pi$
$43$	3.02689e21			1.76160			0.880798	+	0.473493i	$0.157007\pi$
$44$		−	1.02462e20i		−	0.0442262i
$45$	3.48134e21	−	2.03602e21i	1.12198	−	0.656176i
$46$	−2.15317e21			−0.521466
$47$		−	6.86906e21i		−	1.25784i	−0.777470	−	0.628920i	$-0.783497\pi$
$47$		−	6.86906e21i		−	1.25784i	0.777470	−	0.628920i	$-0.216503\pi$
$48$	8.93168e20	−	1.55706e21i	0.124393	−	0.216855i
$49$	−8.55848e21			−0.911691
$50$		−	5.95064e21i		−	0.487476i
$51$	1.92140e22	+	1.10216e22i	1.21676	+	0.697963i
$52$	−3.11264e21			−0.153139
$53$			2.16396e22i			0.831117i	0.909567	+	0.415558i	$0.136414\pi$
$53$			2.16396e22i			0.831117i	−0.909567	+	0.415558i	$0.863586\pi$
$54$	−1.97156e20	−	2.34741e22i	−0.00593871	−	0.707082i
$55$	−4.84496e21			−0.114967
$56$		−	5.59630e21i		−	0.105065i
$57$	−5.64410e22	+	9.83938e22i	−0.841824	+	1.46756i
$58$	−7.00608e22			−0.833511
$59$			8.99826e22i			0.857201i	0.903494	+	0.428600i	$0.140993\pi$
$59$			8.99826e22i			0.857201i	−0.903494	+	0.428600i	$0.859007\pi$
$60$	−7.36262e22	−	4.22337e22i	−0.563723	−	0.323365i
$61$	4.94708e21			0.0305535			0.0152768	−	0.999883i	$-0.495137\pi$
$61$	4.94708e21			0.0305535			0.0152768	+	0.999883i	$0.495137\pi$
$62$		−	1.72739e23i		−	0.863572i
$63$	−3.69474e22	−	6.31752e22i	−0.150023	−	0.256519i
$64$	−3.77789e22			−0.125000
$65$			1.47182e23i			0.398090i
$66$	−1.40321e22	+	2.44622e22i	−0.0311209	+	0.0542531i
$67$	7.08276e23			1.29190			0.645952	−	0.763378i	$-0.276461\pi$
$67$	7.08276e23			1.29190			0.645952	+	0.763378i	$0.276461\pi$
$68$		−	4.66188e23i		−	0.701367i
$69$	5.14055e23	+	2.94874e23i	0.639693	+	0.366943i
$70$	−2.64623e23			−0.273119
$71$		−	4.06775e23i		−	0.349137i	−0.984645	−	0.174568i	$-0.944147\pi$
$71$		−	4.06775e23i		−	0.349137i	0.984645	−	0.174568i	$-0.0558530\pi$
$72$	−4.26476e23	+	2.49421e23i	−0.305192	+	0.178488i
$73$	1.88343e24			1.12655			0.563276	−	0.826269i	$-0.309541\pi$
$73$	1.88343e24			1.12655			0.563276	+	0.826269i	$0.309541\pi$
$74$		−	2.32100e24i		−	1.16322i
$75$	−8.14934e23	+	1.42068e24i	−0.343025	+	0.597997i
$76$	2.38732e24			0.845930
$77$			8.79206e22i			0.0262852i
$78$	7.43123e23	+	4.26273e23i	0.187858	+	0.107760i
$79$	−2.41553e24			−0.517441			−0.258721	−	0.965952i	$-0.583301\pi$
$79$	−2.41553e24			−0.517441			−0.258721	+	0.965952i	$0.583301\pi$
$80$			1.78639e24i			0.324942i
$81$	−3.16768e24	+	5.63129e24i	−0.490271	+	0.871570i
$82$	−6.63161e24			−0.875062
$83$		−	1.68124e25i		−	1.89502i	−0.319730	−	0.947509i	$-0.603592\pi$
$83$		−	1.68124e25i		−	1.89502i	0.319730	−	0.947509i	$-0.396408\pi$
$84$	−7.66408e23	+	1.33608e24i	−0.0739314	+	0.128885i
$85$	−2.20438e25			−1.82323
$86$			1.75336e25i			1.24564i
$87$	1.67266e25	+	9.59475e24i	1.02248	+	0.586521i
$88$	5.93525e23			0.0312726
$89$		−	8.57062e24i		−	0.389890i	−0.980814	−	0.194945i	$-0.937547\pi$
$89$		−	8.57062e24i		−	0.389890i	0.980814	−	0.194945i	$-0.0624528\pi$
$90$	1.17939e25	+	2.01661e25i	0.463987	+	0.793356i
$91$	2.67089e24			0.0910159
$92$		−	1.24725e25i		−	0.368732i
$93$	−2.36564e25	+	4.12404e25i	−0.607675	+	1.05936i
$94$	3.97899e25			0.889427
$95$		−	1.12885e26i		−	2.19902i
$96$	9.01948e24	+	5.17378e24i	0.153340	+	0.0879594i
$97$	2.54469e25			0.378096			0.189048	−	0.981968i	$-0.439460\pi$
$97$	2.54469e25			0.378096			0.189048	+	0.981968i	$0.439460\pi$
$98$		−	4.95760e25i		−	0.644663i
$99$	6.70015e24	−	3.91851e24i	0.0763531	−	0.0446544i
$100$	3.44698e25			0.344698
$101$		−	8.23839e25i		−	0.723876i	−0.932202	−	0.361938i	$-0.882115\pi$
$101$		−	8.23839e25i		−	0.723876i	0.932202	−	0.361938i	$-0.117885\pi$
$102$	−6.38439e25	+	1.11299e26i	−0.493534	+	0.860380i
$103$	8.17404e25			0.556612			0.278306	−	0.960492i	$-0.410227\pi$
$103$	8.17404e25			0.556612			0.278306	+	0.960492i	$0.410227\pi$
$104$		−	1.80303e25i		−	0.108286i
$105$	6.31769e25	+	3.62398e25i	0.335041	+	0.192187i
$106$	−1.25350e26			−0.587688
$107$			1.33762e26i			0.555064i	0.960716	+	0.277532i	$0.0895165\pi$
$107$			1.33762e26i			0.555064i	−0.960716	+	0.277532i	$0.910483\pi$
$108$	1.35976e26	−	1.14205e24i	0.499982	−	0.00419930i
$109$	3.14189e25			0.102482			0.0512409	−	0.998686i	$-0.483682\pi$
$109$	3.14189e25			0.102482			0.0512409	+	0.998686i	$0.483682\pi$
$110$		−	2.80650e25i		−	0.0812943i
$111$	−3.17858e26	+	5.54123e26i	−0.818530	+	1.42695i
$112$	3.24172e25			0.0742919
$113$			2.57516e25i			0.0525756i	0.999654	+	0.0262878i	$0.00836863\pi$
$113$			2.57516e25i			0.0525756i	−0.999654	+	0.0262878i	$0.991631\pi$
$114$	−5.69958e26	−	3.26941e26i	−1.03772	−	0.595260i
$115$	−5.89765e26			−0.958533
$116$		−	4.05836e26i		−	0.589381i
$117$	−1.19038e26	−	2.03540e26i	−0.154622	−	0.264383i
$118$	−5.21235e26			−0.606133
$119$			4.00025e26i			0.416847i
$120$	2.44644e26	−	4.26488e26i	0.228654	−	0.398613i
$121$	1.18249e27			0.992176
$122$			2.86566e25i			0.0216046i
$123$	1.58325e27	+	9.08191e26i	1.07346	+	0.615759i
$124$	1.00061e27			0.610638
$125$			7.34351e26i			0.403714i
$126$	3.65950e26	−	2.14022e26i	0.181386	−	0.106082i
$127$	−7.18494e26			−0.321347			−0.160674	−	0.987008i	$-0.551367\pi$
$127$	−7.18494e26			−0.321347			−0.160674	+	0.987008i	$0.551367\pi$
$128$		−	2.18839e26i		−	0.0883883i
$129$	2.40121e27	−	4.18603e27i	0.876523	−	1.52805i
$130$	−8.52569e26			−0.281492
$131$			9.23282e25i			0.0275935i	0.999905	+	0.0137968i	$0.00439179\pi$
$131$			9.23282e25i			0.0275935i	−0.999905	+	0.0137968i	$0.995608\pi$
$132$	−1.41700e26	−	8.12826e25i	−0.0383627	−	0.0220058i
$133$	−2.04851e27			−0.502766
$134$			4.10277e27i			0.913513i
$135$	−5.40023e25	−	6.42968e27i	−0.0109162	−	1.29972i
$136$	2.70045e27			0.495941
$137$			6.40147e27i			1.06884i	0.845219	+	0.534420i	$0.179470\pi$
$137$			6.40147e27i			1.06884i	−0.845219	+	0.534420i	$0.820530\pi$
$138$	−1.70809e27	+	2.97773e27i	−0.259468	+	0.452331i
$139$	2.40123e27			0.332079			0.166040	−	0.986119i	$-0.446902\pi$
$139$	2.40123e27			0.332079			0.166040	+	0.986119i	$0.446902\pi$
$140$		−	1.53286e27i		−	0.193125i
$141$	−9.49957e27	−	5.44918e27i	−1.09108	−	0.625868i
$142$	2.35629e27			0.246877
$143$			2.83265e26i			0.0270910i
$144$	−1.44480e27	−	2.47042e27i	−0.126210	−	0.215803i
$145$	−1.91900e28			−1.53212
$146$			1.09100e28i			0.796592i
$147$	−6.78939e27	+	1.18360e28i	−0.453633	+	0.790821i
$148$	1.34447e28			0.822522
$149$			1.21396e28i			0.680432i	0.940347	+	0.340216i	$0.110500\pi$
$149$			1.21396e28i			0.680432i	−0.940347	+	0.340216i	$0.889500\pi$
$150$	−8.22944e27	−	4.72060e27i	−0.422848	−	0.242555i
$151$	−3.52925e27			−0.166334			−0.0831672	−	0.996536i	$-0.526504\pi$
$151$	−3.52925e27			−0.166334			−0.0831672	+	0.996536i	$0.526504\pi$
$152$			1.38288e28i			0.598163i
$153$	3.04847e28	−	1.78287e28i	1.21086	−	0.708158i
$154$	−5.09290e26			−0.0185864
$155$		−	4.73142e28i		−	1.58737i
$156$	−2.46924e27	+	4.30463e27i	−0.0761979	+	0.132836i
$157$	3.57601e28			1.01556			0.507778	−	0.861488i	$-0.330467\pi$
$157$	3.57601e28			1.01556			0.507778	+	0.861488i	$0.330467\pi$
$158$		−	1.39923e28i		−	0.365886i
$159$	2.99264e28	+	1.71665e28i	0.720929	+	0.413542i
$160$	−1.03479e28			−0.229769
$161$			1.07024e28i			0.219151i
$162$	−3.26199e28	−	1.83492e28i	−0.616293	−	0.346674i
$163$	−9.61442e27			−0.167681			−0.0838406	−	0.996479i	$-0.526719\pi$
$163$	−9.61442e27			−0.167681			−0.0838406	+	0.996479i	$0.526719\pi$
$164$		−	3.84144e28i		−	0.618762i
$165$	−3.84347e27	+	6.70034e27i	−0.0572048	+	0.0997253i
$166$	9.73875e28			1.33998
$167$		−	1.73923e27i		−	0.0221331i	−0.999939	−	0.0110666i	$-0.996477\pi$
$167$		−	1.73923e27i		−	0.0221331i	0.999939	−	0.0110666i	$-0.00352267\pi$
$168$	−7.73941e27	−	4.43951e27i	−0.0911354	−	0.0522774i
$169$	−8.31282e28			−0.906194
$170$		−	1.27691e29i		−	1.28922i
$171$	9.12995e28	+	1.56110e29i	0.854120	+	1.46043i
$172$	−1.01565e29			−0.880798
$173$			8.03836e28i			0.646500i	0.946314	+	0.323250i	$0.104775\pi$
$173$			8.03836e28i			0.646500i	−0.946314	+	0.323250i	$0.895225\pi$
$174$	−5.55787e28	+	9.68906e28i	−0.414733	+	0.723005i
$175$	−2.95777e28			−0.204866
$176$			3.43806e27i			0.0221131i
$177$	1.24442e29	+	7.13826e28i	0.743555	+	0.426520i
$178$	4.96463e28			0.275694
$179$		−	1.45253e28i		−	0.0749954i	−0.999297	−	0.0374977i	$-0.988061\pi$
$179$		−	1.45253e28i		−	0.0749954i	0.999297	−	0.0374977i	$-0.0119387\pi$
$180$	−1.16814e29	+	6.83177e28i	−0.560988	+	0.328088i
$181$	−4.01580e29			−1.79453			−0.897265	−	0.441492i	$-0.854449\pi$
$181$	−4.01580e29			−1.79453			−0.897265	+	0.441492i	$0.854449\pi$
$182$			1.54714e28i			0.0643580i
$183$	3.92449e27	−	6.84157e27i	0.0152026	−	0.0265028i
$184$	7.22484e28			0.260733
$185$		−	6.35734e29i		−	2.13817i
$186$	−2.38890e29	−	1.37033e29i	−0.749082	−	0.429691i
$187$	−4.24253e28			−0.124075
$188$			2.30488e29i			0.628920i
$189$	−1.16678e29	+	9.79969e26i	−0.297157	+	0.00249580i
$190$	6.53901e29			1.55494
$191$			3.14860e29i			0.699333i	0.936874	+	0.349667i	$0.113705\pi$
$191$			3.14860e29i			0.699333i	−0.936874	+	0.349667i	$0.886295\pi$
$192$	−2.99698e28	+	5.22464e28i	−0.0621967	+	0.108428i
$193$	8.53011e29			1.65466			0.827332	−	0.561713i	$-0.189858\pi$
$193$	8.53011e29			1.65466			0.827332	+	0.561713i	$0.189858\pi$
$194$			1.47404e29i			0.267354i
$195$	2.03545e29	+	1.16758e29i	0.345312	+	0.198079i
$196$	2.87175e29			0.455846
$197$		−	4.14591e29i		−	0.615970i	−0.951391	−	0.307985i	$-0.900345\pi$
$197$		−	4.14591e29i		−	0.615970i	0.951391	−	0.307985i	$-0.0996546\pi$
$198$	2.26985e28	+	3.88114e28i	0.0315754	+	0.0539898i
$199$	−4.22740e29			−0.550787			−0.275394	−	0.961332i	$-0.588808\pi$
$199$	−4.22740e29			−0.550787			−0.275394	+	0.961332i	$0.588808\pi$
$200$			1.99670e29i			0.243738i
$201$	5.61870e29	−	9.79510e29i	0.642817	−	1.12062i
$202$	4.77218e29			0.511858
$203$			3.48238e29i			0.350290i
$204$	−6.44715e29	−	3.69824e29i	−0.608381	−	0.348982i
$205$	−1.81643e30			−1.60849
$206$			4.73491e29i			0.393584i
$207$	8.15593e29	−	4.76991e29i	0.636589	−	0.372303i
$208$	1.04443e29			0.0765694
$209$		−	2.17258e29i		−	0.149649i
$210$	−2.09923e29	+	3.65960e29i	−0.135897	+	0.236910i
$211$	−1.37050e30			−0.834080			−0.417040	−	0.908888i	$-0.636932\pi$
$211$	−1.37050e30			−0.834080			−0.417040	+	0.908888i	$0.636932\pi$
$212$		−	7.26103e29i		−	0.415558i
$213$	−5.62549e29	−	3.22692e29i	−0.302849	−	0.173721i
$214$	−7.74832e29			−0.392490
$215$			4.80255e30i			2.28966i
$216$	6.61547e27	+	7.87659e29i	0.00296936	+	0.353541i
$217$	−8.58602e29			−0.362924
$218$			1.81998e29i			0.0724656i
$219$	1.49411e30	−	2.60468e30i	0.560542	−	0.977196i
$220$	1.62570e29			0.0574837
$221$			1.28881e30i			0.429626i
$222$	−3.20982e30	−	1.84123e30i	−1.00900	−	0.578788i
$223$	4.46398e30			1.32361			0.661803	−	0.749678i	$-0.269792\pi$
$223$	4.46398e30			1.32361			0.661803	+	0.749678i	$0.269792\pi$
$224$			1.87781e29i			0.0525323i
$225$	1.31824e30	+	2.25403e30i	0.348035	+	0.595095i
$226$	−1.49169e29			−0.0371765
$227$			3.57077e30i			0.840283i	0.907459	+	0.420141i	$0.138020\pi$
$227$			3.57077e30i			0.840283i	−0.907459	+	0.420141i	$0.861980\pi$
$228$	1.89385e30	−	3.30155e30i	0.420912	−	0.733778i
$229$	−6.54977e30			−1.37520			−0.687599	−	0.726091i	$-0.741335\pi$
$229$	−6.54977e30			−1.37520			−0.687599	+	0.726091i	$0.741335\pi$
$230$		−	3.41628e30i		−	0.677785i
$231$	1.21590e29	+	6.97468e28i	0.0228003	+	0.0130788i
$232$	2.35085e30			0.416755
$233$		−	8.50163e30i		−	1.42520i	−0.701572	−	0.712599i	$-0.747518\pi$
$233$		−	8.50163e30i		−	1.42520i	0.701572	−	0.712599i	$-0.252482\pi$
$234$	1.17903e30	−	6.89543e29i	0.186947	−	0.109334i
$235$	1.08987e31			1.63490
$236$		−	3.01932e30i		−	0.428600i
$237$	−1.91623e30	+	3.34056e30i	−0.257465	+	0.448840i
$238$	−2.31719e30			−0.294756
$239$		−	3.46739e30i		−	0.417667i	−0.977951	−	0.208834i	$-0.933033\pi$
$239$		−	3.46739e30i		−	0.417667i	0.977951	−	0.208834i	$-0.0669667\pi$
$240$	2.47048e30	+	1.41713e30i	0.281862	+	0.161682i
$241$	6.85124e30			0.740539			0.370269	−	0.928924i	$-0.379265\pi$
$241$	6.85124e30			0.740539			0.370269	+	0.928924i	$0.379265\pi$
$242$			6.84973e30i			0.701575i
$243$	5.27489e30	+	8.84800e30i	0.512073	+	0.858942i
$244$	−1.65997e29			−0.0152768
$245$		−	1.35792e31i		−	1.18499i
$246$	−5.26081e30	+	9.17118e30i	−0.435407	+	0.759047i
$247$	−6.59994e30			−0.518179
$248$			5.79616e30i			0.431786i
$249$	−2.32506e31	−	1.33371e31i	−1.64378	−	0.942911i
$250$	−4.25381e30			−0.285469
$251$			9.30021e30i			0.592563i	0.955101	+	0.296282i	$0.0957467\pi$
$251$			9.30021e30i			0.592563i	−0.955101	+	0.296282i	$0.904253\pi$
$252$	1.23975e30	+	2.11981e30i	0.0750113	+	0.128259i
$253$	−1.13506e30			−0.0652305
$254$		−	4.16196e30i		−	0.227227i
$255$	−1.74872e31	+	3.04855e31i	−0.907190	+	1.58151i
$256$	1.26765e30			0.0625000
$257$		−	1.84248e31i		−	0.863518i	−0.901989	−	0.431759i	$-0.857893\pi$
$257$		−	1.84248e31i		−	0.863518i	0.901989	−	0.431759i	$-0.142107\pi$
$258$	2.42481e31	+	1.39093e31i	1.08049	+	0.619795i
$259$	−1.15366e31			−0.488854
$260$		−	4.93861e30i		−	0.199045i
$261$	2.65381e31	−	1.55206e31i	1.01752	−	0.595088i
$262$	−5.34822e29			−0.0195116
$263$			2.69702e31i			0.936395i	0.883624	+	0.468198i	$0.155096\pi$
$263$			2.69702e31i			0.936395i	−0.883624	+	0.468198i	$0.844904\pi$
$264$	4.70839e29	−	8.20816e29i	0.0155604	−	0.0271266i
$265$	−3.43340e31			−1.08026
$266$		−	1.18662e31i		−	0.355509i
$267$	−1.18527e31	−	6.79901e30i	−0.338199	−	0.193999i
$268$	−2.37658e31			−0.645952
$269$		−	6.69567e31i		−	1.73386i	−0.498428	−	0.866931i	$-0.666089\pi$
$269$		−	6.69567e31i		−	1.73386i	0.498428	−	0.866931i	$-0.333911\pi$
$270$	3.72447e31	−	3.12814e29i	0.919042	−	0.00771894i
$271$	5.49436e31			1.29216			0.646080	−	0.763270i	$-0.276407\pi$
$271$	5.49436e31			1.29216			0.646080	+	0.763270i	$0.276407\pi$
$272$			1.56427e31i			0.350683i
$273$	2.11879e30	−	3.69370e30i	0.0452871	−	0.0789492i
$274$	−3.70813e31			−0.755783
$275$		−	3.13692e30i		−	0.0609786i
$276$	−1.72488e31	−	9.89433e30i	−0.319846	−	0.183471i
$277$	7.50906e31			1.32846			0.664230	−	0.747528i	$-0.268760\pi$
$277$	7.50906e31			1.32846			0.664230	+	0.747528i	$0.268760\pi$
$278$			1.39094e31i			0.234815i
$279$	3.82669e31	+	6.54314e31i	0.616550	+	1.05422i
$280$	8.87926e30			0.136560
$281$			5.97895e31i			0.877896i	0.898512	+	0.438948i	$0.144649\pi$
$281$			5.97895e31i			0.877896i	−0.898512	+	0.438948i	$0.855351\pi$
$282$	3.15650e31	−	5.50274e31i	0.442555	−	0.771508i
$283$	1.36015e32			1.82123			0.910613	−	0.413260i	$-0.135610\pi$
$283$	1.36015e32			1.82123			0.910613	+	0.413260i	$0.135610\pi$
$284$			1.36491e31i			0.174568i
$285$	−1.56115e32	−	8.95510e31i	−1.90748	−	1.09418i
$286$	−1.64085e30			−0.0191562
$287$			3.29625e31i			0.367752i
$288$	1.43102e31	−	8.36916e30i	0.152596	−	0.0892441i
$289$	−9.49282e31			−0.967662
$290$		−	1.11161e32i		−	1.08337i
$291$	2.01868e31	−	3.51918e31i	0.188131	−	0.327969i
$292$	−6.31973e31			−0.563276
$293$			2.23842e32i			1.90837i	0.299213	+	0.954186i	$0.403276\pi$
$293$			2.23842e32i			1.90837i	−0.299213	+	0.954186i	$0.596724\pi$
$294$	−6.85612e31	−	3.93283e31i	−0.559195	−	0.320767i
$295$	−1.42769e32			−1.11416
$296$			7.78798e31i			0.581611i
$297$	−1.03932e29	−	1.23745e31i	−0.000742876	−	0.0884492i
$298$	−7.03203e31			−0.481138
$299$			3.44812e31i			0.225869i
$300$	2.73446e31	−	4.76700e31i	0.171513	−	0.298998i
$301$	8.71510e31			0.523489
$302$		−	2.04436e31i		−	0.117616i
$303$	−1.13933e32	−	6.53545e31i	−0.627906	−	0.360182i
$304$	−8.01052e31			−0.422965
$305$			7.84919e30i			0.0397125i
$306$	1.03275e32	+	1.76586e32i	0.500743	+	0.856205i
$307$	1.08211e32			0.502888			0.251444	−	0.967872i	$-0.419095\pi$
$307$	1.08211e32			0.502888			0.251444	+	0.967872i	$0.419095\pi$
$308$		−	2.95012e30i		−	0.0131426i
$309$	6.48441e31	−	1.13043e32i	0.276956	−	0.482818i
$310$	2.74073e32			1.12244
$311$			2.09678e32i			0.823508i	0.911295	+	0.411754i	$0.135084\pi$
$311$			2.09678e32i			0.823508i	−0.911295	+	0.411754i	$0.864916\pi$
$312$	−2.49351e31	−	1.43033e31i	−0.0939292	−	0.0538800i
$313$	−2.59132e31			−0.0936365			−0.0468182	−	0.998903i	$-0.514908\pi$
$313$	−2.59132e31			−0.0936365			−0.0468182	+	0.998903i	$0.514908\pi$
$314$			2.07145e32i			0.718106i
$315$	1.00236e32	−	5.86218e31i	0.333415	−	0.194994i
$316$	8.10519e31			0.258721
$317$		−	4.68404e32i		−	1.43499i	−0.696562	−	0.717497i	$-0.745288\pi$
$317$		−	4.68404e32i		−	1.43499i	0.696562	−	0.717497i	$-0.254712\pi$
$318$	−9.94390e31	+	1.73352e32i	−0.292418	+	0.509774i
$319$	−3.69330e31			−0.104264
$320$		−	5.99412e31i		−	0.162471i
$321$	1.84986e32	+	1.06112e32i	0.481475	+	0.276185i
$322$	−6.19947e31			−0.154963
$323$		−	9.88490e32i		−	2.37323i
$324$	1.06290e32	−	1.88955e32i	0.245135	−	0.435785i
$325$	−9.52945e31			−0.211147
$326$		−	5.56927e31i		−	0.118569i
$327$	2.49244e31	−	4.34508e31i	0.0509922	−	0.0888949i
$328$	2.22520e32			0.437531
$329$		−	1.97776e32i		−	0.373790i
$330$	−3.88125e31	−	2.22638e31i	−0.0705164	−	0.0404499i
$331$	−5.57205e32			−0.973310			−0.486655	−	0.873594i	$-0.661783\pi$
$331$	−5.57205e32			−0.973310			−0.486655	+	0.873594i	$0.661783\pi$
$332$			5.64129e32i			0.947509i
$333$	5.14170e32	+	8.79164e32i	0.830486	+	1.42002i
$334$	1.00747e31			0.0156505
$335$			1.12377e33i			1.67917i
$336$	2.57164e31	−	4.48314e31i	0.0369657	−	0.0644425i
$337$	−4.04141e32			−0.558913			−0.279456	−	0.960158i	$-0.590154\pi$
$337$	−4.04141e32			−0.558913			−0.279456	+	0.960158i	$0.590154\pi$
$338$		−	4.81530e32i		−	0.640776i
$339$	3.56131e31	+	2.04285e31i	0.0456052	+	0.0261602i
$340$	7.39668e32			0.911614
$341$		−	9.10605e31i		−	0.108025i
$342$	−9.04287e32	+	5.28863e32i	−1.03268	+	0.603954i
$343$	−5.16705e32			−0.568093
$344$		−	5.88330e32i		−	0.622818i
$345$	−4.67856e32	+	8.15616e32i	−0.476941	+	0.831452i
$346$	−4.65632e32			−0.457144
$347$		−	1.00744e33i		−	0.952656i	−0.879268	−	0.476328i	$-0.841967\pi$
$347$		−	1.00744e33i		−	0.952656i	0.879268	−	0.476328i	$-0.158033\pi$
$348$	−5.61251e32	−	3.21947e32i	−0.511242	−	0.293260i
$349$	2.11077e32			0.185229			0.0926146	−	0.995702i	$-0.470478\pi$
$349$	2.11077e32			0.185229			0.0926146	+	0.995702i	$0.470478\pi$
$350$		−	1.71333e32i		−	0.144862i
$351$	−3.75918e32	+	3.15730e30i	−0.306267	+	0.00257231i
$352$	−1.99154e31			−0.0156363
$353$			3.98867e32i			0.301826i	0.988547	+	0.150913i	$0.0482214\pi$
$353$			3.98867e32i			0.301826i	−0.988547	+	0.150913i	$0.951779\pi$
$354$	−4.13492e32	+	7.20842e32i	−0.301596	+	0.525773i
$355$	6.45401e32			0.453796
$356$			2.87582e32i			0.194945i
$357$	5.53215e32	+	3.17337e32i	0.361582	+	0.207412i
$358$	8.41393e31			0.0530298
$359$		−	6.10392e32i		−	0.371006i	−0.982644	−	0.185503i	$-0.940609\pi$
$359$		−	6.10392e32i		−	0.371006i	0.982644	−	0.185503i	$-0.0593914\pi$
$360$	−3.95738e32	−	6.76660e32i	−0.231993	−	0.396678i
$361$	3.29355e33			1.86239
$362$		−	2.32620e33i		−	1.26892i
$363$	9.38063e32	−	1.63533e33i	0.493681	−	0.860635i
$364$	−8.96201e31			−0.0455079
$365$			2.98830e33i			1.46426i
$366$	3.96306e31	+	2.27331e31i	0.0187403	+	0.0107499i
$367$	−2.96372e33			−1.35263			−0.676313	−	0.736614i	$-0.736423\pi$
$367$	−2.96372e33			−1.35263			−0.676313	+	0.736614i	$0.736423\pi$
$368$			4.18507e32i			0.184366i
$369$	2.51197e33	−	1.46910e33i	1.06825	−	0.624753i
$370$	3.68257e33			1.51192
$371$			6.23052e32i			0.246981i
$372$	7.93778e32	−	1.38380e33i	0.303837	−	0.529681i
$373$	−3.52576e33			−1.30328			−0.651641	−	0.758528i	$-0.725919\pi$
$373$	−3.52576e33			−1.30328			−0.651641	+	0.758528i	$0.725919\pi$
$374$		−	2.45754e32i		−	0.0877343i
$375$	1.01557e33	+	5.82555e32i	0.350190	+	0.200877i
$376$	−1.33513e33			−0.444714
$377$			1.12196e33i			0.361029i
$378$	−5.67659e30	−	6.75873e32i	−0.00176479	−	0.210122i
$379$	1.88881e33			0.567385			0.283693	−	0.958915i	$-0.408440\pi$
$379$	1.88881e33			0.567385			0.283693	+	0.958915i	$0.408440\pi$
$380$			3.78780e33i			1.09951i
$381$	−5.69976e32	+	9.93642e32i	−0.159894	+	0.278744i
$382$	−1.82387e33			−0.494503
$383$		−	3.99775e33i		−	1.04769i	−0.851815	−	0.523843i	$-0.824498\pi$
$383$		−	3.99775e33i		−	1.04769i	0.851815	−	0.523843i	$-0.175502\pi$
$384$	−3.02643e32	−	1.73603e32i	−0.0766700	−	0.0439797i
$385$	−1.39497e32			−0.0341646
$386$			4.94117e33i			1.17002i
$387$	−3.88422e33	−	6.64150e33i	−0.889326	−	1.52063i
$388$	−8.53856e32			−0.189048
$389$			3.42601e33i			0.733574i	0.930305	+	0.366787i	$0.119542\pi$
$389$			3.42601e33i			0.733574i	−0.930305	+	0.366787i	$0.880458\pi$
$390$	−6.76337e32	+	1.17906e33i	−0.140063	+	0.244172i
$391$	−5.16433e33			−1.03447
$392$			1.66350e33i			0.322332i
$393$	1.27685e32	+	7.32433e31i	0.0239352	+	0.0137298i
$394$	2.40157e33			0.435556
$395$		−	3.83256e33i		−	0.672553i
$396$	−2.24820e32	+	1.31484e32i	−0.0381766	+	0.0223272i
$397$	2.17513e33			0.357444			0.178722	−	0.983900i	$-0.442804\pi$
$397$	2.17513e33			0.357444			0.178722	+	0.983900i	$0.442804\pi$
$398$		−	2.44877e33i		−	0.389465i
$399$	−1.62507e33	+	2.83298e33i	−0.250163	+	0.436110i
$400$	−1.15661e33			−0.172349
$401$			5.43513e33i			0.784031i	0.919959	+	0.392015i	$0.128222\pi$
$401$			5.43513e33i			0.784031i	−0.919959	+	0.392015i	$0.871778\pi$
$402$	5.67393e33	+	3.25470e33i	0.792401	+	0.454540i
$403$	−2.76627e33			−0.374050
$404$			2.76434e33i			0.361938i
$405$	−8.93477e33	−	5.02594e33i	−1.13284	−	0.637238i
$406$	−2.01721e33			−0.247693
$407$		−	1.22353e33i		−	0.145508i
$408$	2.14225e33	−	3.73459e33i	0.246767	−	0.430190i
$409$	−1.07193e32			−0.0119609			−0.00598047	−	0.999982i	$-0.501904\pi$
$409$	−1.07193e32			−0.0119609			−0.00598047	+	0.999982i	$0.501904\pi$
$410$		−	1.05219e34i		−	1.13738i
$411$	8.85292e33	+	5.07824e33i	0.927134	+	0.531826i
$412$	−2.74275e33			−0.278306
$413$			2.59081e33i			0.254732i
$414$	2.76303e33	+	4.72442e33i	0.263258	+	0.450136i
$415$	2.66750e34			2.46308
$416$			6.04998e32i			0.0541428i
$417$	1.90488e33	−	3.32078e33i	0.165234	−	0.288053i
$418$	1.25849e33			0.105818
$419$		−	9.21284e32i		−	0.0750951i	−0.999295	−	0.0375475i	$-0.988045\pi$
$419$		−	9.21284e32i		−	0.0750951i	0.999295	−	0.0375475i	$-0.0119546\pi$
$420$	−2.11987e33	−	1.21601e33i	−0.167520	−	0.0960937i
$421$	1.41486e34			1.08404			0.542021	−	0.840365i	$-0.317659\pi$
$421$	1.41486e34			1.08404			0.542021	+	0.840365i	$0.317659\pi$
$422$		−	7.93879e33i		−	0.589783i
$423$	−1.50719e34	+	8.81465e33i	−1.08578	+	0.635009i
$424$	4.20604e33			0.293844
$425$		−	1.42725e34i		−	0.967038i
$426$	1.86923e33	−	3.25863e33i	0.122839	−	0.214146i
$427$	1.42438e32			0.00907953
$428$		−	4.48830e33i		−	0.277532i
$429$	3.91742e32	+	2.24712e32i	0.0234993	+	0.0134798i
$430$	−2.78193e34			−1.61904
$431$		−	3.79718e32i		−	0.0214416i	−0.999943	−	0.0107208i	$-0.996587\pi$
$431$		−	3.79718e32i		−	0.0214416i	0.999943	−	0.0107208i	$-0.00341260\pi$
$432$	−4.56261e33	+	3.83209e31i	−0.249991	+	0.00209965i
$433$	−8.02965e33			−0.426928			−0.213464	−	0.976951i	$-0.568475\pi$
$433$	−8.02965e33			−0.426928			−0.213464	+	0.976951i	$0.568475\pi$
$434$		−	4.97356e33i		−	0.256626i
$435$	−1.52233e34	+	2.65389e34i	−0.762341	+	1.32899i
$436$	−1.05424e33			−0.0512409
$437$		−	2.64463e34i		−	1.24769i
$438$	1.50879e34	+	8.65480e33i	0.690982	+	0.396363i
$439$	−2.04784e34			−0.910452			−0.455226	−	0.890376i	$-0.650442\pi$
$439$	−2.04784e34			−0.910452			−0.455226	+	0.890376i	$0.650442\pi$
$440$			9.41705e32i			0.0406471i
$441$	1.09826e34	+	1.87788e34i	0.460259	+	0.786983i
$442$	−7.46561e33			−0.303792
$443$			3.68110e34i			1.45455i	0.686346	+	0.727275i	$0.259214\pi$
$443$			3.68110e34i			1.45455i	−0.686346	+	0.727275i	$0.740786\pi$
$444$	1.06655e34	−	1.85933e34i	0.409265	−	0.713473i
$445$	1.35984e34			0.506766
$446$			2.58581e34i			0.935931i
$447$	1.67885e34	+	9.63030e33i	0.590221	+	0.338565i
$448$	−1.08774e33			−0.0371460
$449$		−	3.40391e33i		−	0.112921i	−0.998405	−	0.0564606i	$-0.982018\pi$
$449$		−	3.40391e33i		−	0.112921i	0.998405	−	0.0564606i	$-0.0179815\pi$
$450$	−1.30567e34	+	7.63609e33i	−0.420796	+	0.246098i
$451$	−3.49589e33			−0.109462
$452$		−	8.64079e32i		−	0.0262878i
$453$	−2.79973e33	+	4.88078e33i	−0.0827636	+	0.144282i
$454$	−2.06841e34			−0.594170
$455$			4.23771e33i			0.118300i
$456$	1.91246e34	+	1.09703e34i	0.518859	+	0.297630i
$457$	−6.50335e34			−1.71485			−0.857426	−	0.514607i	$-0.827938\pi$
$457$	−6.50335e34			−1.71485			−0.857426	+	0.514607i	$0.827938\pi$
$458$		−	3.79403e34i		−	0.972411i
$459$	−4.72876e32	−	5.63021e34i	−0.0117810	−	1.40268i
$460$	1.97892e34			0.479266
$461$		−	5.07071e34i		−	1.19387i	−0.802290	−	0.596935i	$-0.796385\pi$
$461$		−	5.07071e34i		−	1.19387i	0.802290	−	0.596935i	$-0.203615\pi$
$462$	−4.04016e32	+	7.04323e32i	−0.00924812	+	0.0161223i
$463$	5.68380e34			1.26499			0.632493	−	0.774566i	$-0.282032\pi$
$463$	5.68380e34			1.26499			0.632493	+	0.774566i	$0.282032\pi$
$464$			1.36176e34i			0.294691i
$465$	−6.54332e34	−	3.75340e34i	−1.37692	−	0.789836i
$466$	4.92467e34			1.00777
$467$			4.30050e34i			0.855854i	0.903813	+	0.427927i	$0.140756\pi$
$467$			4.30050e34i			0.855854i	−0.903813	+	0.427927i	$0.859244\pi$
$468$	3.99426e33	+	6.82966e33i	0.0773108	+	0.132191i
$469$	2.03929e34			0.383912
$470$			6.31318e34i			1.15605i
$471$	2.83683e34	−	4.94545e34i	0.505313	−	0.880915i
$472$	1.74897e34			0.303066
$473$			9.24294e33i			0.155817i
$474$	−1.93506e34	−	1.11000e34i	−0.317378	−	0.182055i
$475$	7.30886e34			1.16636
$476$		−	1.34226e34i		−	0.208424i
$477$	4.74808e34	−	2.77687e34i	0.717430	−	0.419582i
$478$	2.00853e34			0.295335
$479$		−	3.75919e34i		−	0.537938i	−0.963149	−	0.268969i	$-0.913317\pi$
$479$		−	3.75919e34i		−	0.537938i	0.963149	−	0.268969i	$-0.0866829\pi$
$480$	−8.20888e33	+	1.43106e34i	−0.114327	+	0.199306i
$481$	−3.71688e34			−0.503840
$482$			3.96866e34i			0.523640i
$483$	1.48008e34	+	8.49010e33i	0.190096	+	0.109044i
$484$	−3.96779e34			−0.496088
$485$			4.03748e34i			0.491437i
$486$	−5.12531e34	+	3.05554e34i	−0.607364	+	0.362090i
$487$	3.99382e33			0.0460799			0.0230400	−	0.999735i	$-0.492665\pi$
$487$	3.99382e33			0.0460799			0.0230400	+	0.999735i	$0.492665\pi$
$488$		−	9.61555e32i		−	0.0108023i
$489$	−7.62705e33	+	1.32963e34i	−0.0834337	+	0.145450i
$490$	7.86588e34			0.837912
$491$			1.29437e35i			1.34276i	0.741114	+	0.671379i	$0.234298\pi$
$491$			1.29437e35i			1.34276i	−0.741114	+	0.671379i	$0.765702\pi$
$492$	−5.31252e34	−	3.04738e34i	−0.536728	−	0.307880i
$493$	−1.68040e35			−1.65349
$494$		−	3.82309e34i		−	0.366408i
$495$	6.21723e33	+	1.06307e34i	0.0580403	+	0.0992413i
$496$	−3.35750e34			−0.305319
$497$		−	1.17120e34i		−	0.103752i
$498$	7.72568e34	−	1.34682e35i	0.666738	−	1.16233i
$499$	−1.97727e35			−1.66249			−0.831243	−	0.555909i	$-0.812370\pi$
$499$	−1.97727e35			−1.66249			−0.831243	+	0.555909i	$0.812370\pi$
$500$		−	2.46407e34i		−	0.201857i
$501$	−2.40527e33	−	1.37972e33i	−0.0191988	−	0.0110129i
$502$	−5.38726e34			−0.419005
$503$			4.04800e34i			0.306801i	0.988164	+	0.153400i	$0.0490224\pi$
$503$			4.04800e34i			0.306801i	−0.988164	+	0.153400i	$0.950978\pi$
$504$	−1.22792e34	+	7.18139e33i	−0.0906931	+	0.0530410i
$505$	1.30713e35			0.940871
$506$		−	6.57495e33i		−	0.0461249i
$507$	−6.59450e34	+	1.14962e35i	−0.450898	+	0.786052i
$508$	2.41087e34			0.160674
$509$		−	2.25455e34i		−	0.146463i	−0.997315	−	0.0732315i	$-0.976669\pi$
$509$		−	2.25455e34i		−	0.146463i	0.997315	−	0.0732315i	$-0.0233312\pi$
$510$	−1.76591e35	−	1.01297e35i	−1.11829	−	0.641480i
$511$	5.42281e34			0.334775
$512$			7.34302e33i			0.0441942i
$513$	2.88320e35	−	2.42157e33i	1.69180	−	0.0142093i
$514$	1.06728e35			0.610599
$515$			1.29692e35i			0.723467i
$516$	−8.05711e34	+	1.40460e35i	−0.438262	+	0.764023i
$517$	2.09755e34			0.111259
$518$		−	6.68268e34i		−	0.345672i
$519$	1.11167e35	+	6.37678e34i	0.560788	+	0.321681i
$520$	2.86075e34			0.140746
$521$		−	1.91445e35i		−	0.918656i	−0.888267	−	0.459328i	$-0.848090\pi$
$521$		−	1.91445e35i		−	0.918656i	0.888267	−	0.459328i	$-0.151910\pi$
$522$	8.99047e34	+	1.53725e35i	0.420791	+	0.719497i
$523$	2.52805e34			0.115416			0.0577078	−	0.998334i	$-0.481621\pi$
$523$	2.52805e34			0.115416			0.0577078	+	0.998334i	$0.481621\pi$
$524$		−	3.09802e33i		−	0.0137968i
$525$	−2.34638e34	+	4.09045e34i	−0.101936	+	0.177705i
$526$	−1.56228e35			−0.662131
$527$		−	4.14312e35i		−	1.71312i
$528$	4.75467e33	+	2.72739e33i	0.0191814	+	0.0110029i
$529$	1.15885e35			0.456146
$530$		−	1.98884e35i		−	0.763858i
$531$	1.97437e35	−	1.15469e35i	0.739946	−	0.432750i
$532$	6.87365e34			0.251383
$533$			1.06200e35i			0.379026i
$534$	3.93841e34	−	6.86584e34i	0.137178	−	0.239143i
$535$	−2.12231e35			−0.721455
$536$		−	1.37666e35i		−	0.456757i
$537$	−2.00877e34	−	1.15228e34i	−0.0650527	−	0.0373157i
$538$	3.87855e35			1.22603
$539$		−	2.61343e34i		−	0.0806412i
$540$	1.81201e33	+	2.15744e35i	0.00545812	+	0.649861i
$541$	−2.78129e35			−0.817867			−0.408933	−	0.912564i	$-0.634099\pi$
$541$	−2.78129e35			−0.817867			−0.408933	+	0.912564i	$0.634099\pi$
$542$			3.18267e35i			0.913695i
$543$	−3.18571e35	+	5.55366e35i	−0.892911	+	1.55662i
$544$	−9.06120e34			−0.247971
$545$			4.98502e34i			0.133203i
$546$	2.13962e34	+	1.22734e34i	0.0558255	+	0.0320228i
$547$	1.86368e35			0.474827			0.237413	−	0.971409i	$-0.423700\pi$
$547$	1.86368e35			0.474827			0.237413	+	0.971409i	$0.423700\pi$
$548$		−	2.14798e35i		−	0.534420i
$549$	−6.34829e33	−	1.08547e34i	−0.0154247	−	0.0263742i
$550$	1.81710e34			0.0431184
$551$		−	8.60521e35i		−	1.99430i
$552$	5.73141e34	−	9.99159e34i	0.129734	−	0.226166i
$553$	−6.95488e34			−0.153767
$554$			4.34971e35i			0.939363i
$555$	−8.79189e35	−	5.04323e35i	−1.85470	−	1.06390i
$556$	−8.05719e34			−0.166040
$557$			7.84909e35i			1.58016i	0.613002	+	0.790081i	$0.289962\pi$
$557$			7.84909e35i			1.58016i	−0.613002	+	0.790081i	$0.710038\pi$
$558$	−3.79019e35	+	2.21666e35i	−0.745446	+	0.435967i
$559$	2.80786e35			0.539537
$560$			5.14342e34i			0.0965623i
$561$	−3.36557e34	+	5.86721e34i	−0.0617365	+	0.107625i
$562$	−3.46338e35			−0.620766
$563$		−	3.48401e35i		−	0.610197i	−0.952321	−	0.305099i	$-0.901311\pi$
$563$		−	3.48401e35i		−	0.610197i	0.952321	−	0.305099i	$-0.0986894\pi$
$564$	3.18753e35	+	1.82844e35i	0.545539	+	0.312934i
$565$	−4.08582e34			−0.0683360
$566$			7.87884e35i			1.28780i
$567$	−9.12048e34	+	1.62138e35i	−0.145693	+	0.259003i
$568$	−7.90640e34			−0.123438
$569$			8.42514e35i			1.28564i	0.766019	+	0.642818i	$0.222235\pi$
$569$			8.42514e35i			1.28564i	−0.766019	+	0.642818i	$0.777765\pi$
$570$	5.18735e35	−	9.04312e35i	0.773699	−	1.34879i
$571$	3.46097e35			0.504578			0.252289	−	0.967652i	$-0.418817\pi$
$571$	3.46097e35			0.504578			0.252289	+	0.967652i	$0.418817\pi$
$572$		−	9.50480e33i		−	0.0135455i
$573$	4.35436e35	+	2.49776e35i	0.606617	+	0.347970i
$574$	−1.90939e35			−0.260040
$575$		−	3.81849e35i		−	0.508405i
$576$	4.84794e34	+	8.28934e34i	0.0631051	+	0.107902i
$577$	−4.58018e35			−0.582904			−0.291452	−	0.956585i	$-0.594138\pi$
$577$	−4.58018e35			−0.582904			−0.291452	+	0.956585i	$0.594138\pi$
$578$		−	5.49883e35i		−	0.684240i
$579$	6.76688e35	−	1.17967e36i	0.823317	−	1.43529i
$580$	6.43911e35			0.766058
$581$		−	4.84066e35i		−	0.563138i
$582$	2.03853e35	+	1.16935e35i	0.231909	+	0.133028i
$583$	−6.60788e34			−0.0735142
$584$		−	3.66078e35i		−	0.398296i
$585$	3.22942e35	−	1.88870e35i	0.343636	−	0.200972i
$586$	−1.29663e36			−1.34942
$587$			1.27657e36i			1.29941i	0.760184	+	0.649707i	$0.225109\pi$
$587$			1.27657e36i			1.29941i	−0.760184	+	0.649707i	$0.774891\pi$
$588$	2.27814e35	−	3.97149e35i	0.226817	−	0.395410i
$589$	2.12167e36			2.06623
$590$		−	8.27007e35i		−	0.787831i
$591$	−5.73359e35	−	3.28892e35i	−0.534305	−	0.306490i
$592$	−4.51128e35			−0.411261
$593$			1.13168e34i			0.0100929i	0.999987	+	0.00504643i	$0.00160633\pi$
$593$			1.13168e34i			0.0100929i	−0.999987	+	0.00504643i	$0.998394\pi$
$594$	7.16808e34	−	6.02040e32i	0.0625430	−	0.000525293i
$595$	−6.34692e35			−0.541805
$596$		−	4.07339e35i		−	0.340216i
$597$	−3.35357e35	+	5.84629e35i	−0.274057	+	0.477765i
$598$	−1.99736e35			−0.159714
$599$			1.64099e36i			1.28398i	0.766714	+	0.641989i	$0.221890\pi$
$599$			1.64099e36i			1.28398i	−0.766714	+	0.641989i	$0.778110\pi$
$600$	2.76134e35	+	1.58397e35i	0.211424	+	0.121278i
$601$	7.24380e35			0.542748			0.271374	−	0.962474i	$-0.412522\pi$
$601$	7.24380e35			0.542748			0.271374	+	0.962474i	$0.412522\pi$
$602$			5.04832e35i			0.370163i
$603$	−9.08887e35	−	1.55408e36i	−0.652206	−	1.11519i
$604$	1.18422e35			0.0831672
$605$			1.87618e36i			1.28960i
$606$	3.78574e35	−	6.59969e35i	0.254687	−	0.443997i
$607$	7.15781e35			0.471332			0.235666	−	0.971834i	$-0.424273\pi$
$607$	7.15781e35			0.471332			0.235666	+	0.971834i	$0.424273\pi$
$608$		−	4.64019e35i		−	0.299081i
$609$	4.81596e35	+	2.76255e35i	0.303849	+	0.174295i
$610$	−4.54674e34			−0.0280810
$611$		−	6.37201e35i		−	0.385248i
$612$	−1.02290e36	+	5.98230e35i	−0.605428	+	0.354079i
$613$	−1.91216e36			−1.10800			−0.553998	−	0.832518i	$-0.686898\pi$
$613$	−1.91216e36			−1.10800			−0.553998	+	0.832518i	$0.686898\pi$
$614$			6.26823e35i			0.355595i
$615$	−1.44096e36	+	2.51204e36i	−0.800344	+	1.39524i
$616$	1.70889e34			0.00929322
$617$		−	5.56714e35i		−	0.296432i	−0.988955	−	0.148216i	$-0.952647\pi$
$617$		−	5.56714e35i		−	0.296432i	0.988955	−	0.148216i	$-0.0473531\pi$
$618$	6.54814e35	+	3.75617e35i	0.341404	+	0.195837i
$619$	1.85822e36			0.948677			0.474339	−	0.880342i	$-0.342687\pi$
$619$	1.85822e36			0.948677			0.474339	+	0.880342i	$0.342687\pi$
$620$			1.58760e36i			0.793687i
$621$	−1.26514e34	−	1.50632e36i	−0.00619368	−	0.737439i
$622$	−1.21459e36			−0.582308
$623$		−	2.46768e35i		−	0.115863i
$624$	8.28538e34	−	1.44439e35i	0.0380989	−	0.0664180i
$625$	−2.69591e36			−1.21413
$626$		−	1.50105e35i		−	0.0662110i
$627$	−3.00457e35	−	1.72349e35i	−0.129809	−	0.0744613i
$628$	−1.19991e36			−0.507778
$629$		−	5.56687e36i		−	2.30756i
$630$	3.39574e35	+	5.80627e35i	0.137882	+	0.235760i
$631$	−5.66913e35			−0.225494			−0.112747	−	0.993624i	$-0.535965\pi$
$631$	−5.66913e35			−0.225494			−0.112747	+	0.993624i	$0.535965\pi$
$632$			4.69503e35i			0.182943i
$633$	−1.08721e36	+	1.89534e36i	−0.415016	+	0.723499i
$634$	2.71328e36			1.01469
$635$		−	1.13998e36i		−	0.417677i
$636$	−1.00416e36	−	5.76012e35i	−0.360464	−	0.206771i
$637$	−7.93918e35			−0.279231
$638$		−	2.13939e35i		−	0.0737260i
$639$	−8.92533e35	+	5.21989e35i	−0.301379	+	0.176259i
$640$	3.47217e35			0.114884
$641$		−	1.26457e36i		−	0.410005i	−0.978761	−	0.205003i	$-0.934280\pi$
$641$		−	1.26457e36i		−	0.410005i	0.978761	−	0.205003i	$-0.0657203\pi$
$642$	−6.14669e35	+	1.07155e36i	−0.195293	+	0.340454i
$643$	4.97215e36			1.54811			0.774054	−	0.633120i	$-0.218226\pi$
$643$	4.97215e36			1.54811			0.774054	+	0.633120i	$0.218226\pi$
$644$		−	3.59111e35i		−	0.109575i
$645$	6.64169e36	+	3.80983e36i	1.98610	+	1.13928i
$646$	5.72594e36			1.67813
$647$		−	7.08464e35i		−	0.203499i	−0.994810	−	0.101749i	$-0.967556\pi$
$647$		−	7.08464e35i		−	0.203499i	0.994810	−	0.101749i	$-0.0324440\pi$
$648$	1.09454e36	+	6.15696e35i	0.308147	+	0.173337i
$649$	−2.74772e35			−0.0758214
$650$		−	5.52005e35i		−	0.149303i
$651$	−6.81123e35	+	1.18740e36i	−0.180581	+	0.314808i
$652$	3.22606e35			0.0838406
$653$		−	2.78764e36i		−	0.710174i	−0.934833	−	0.355087i	$-0.884451\pi$
$653$		−	2.78764e36i		−	0.710174i	0.934833	−	0.355087i	$-0.115549\pi$
$654$	2.51694e35	+	1.44378e35i	0.0628582	+	0.0360569i
$655$	−1.46491e35			−0.0358652
$656$			1.28897e36i			0.309381i
$657$	−2.41688e36	−	4.13255e36i	−0.568730	−	0.972453i
$658$	1.14564e36			0.264309
$659$			4.14809e36i			0.938291i	0.883121	+	0.469146i	$0.155438\pi$
$659$			4.14809e36i			0.938291i	−0.883121	+	0.469146i	$0.844562\pi$
$660$	1.28965e35	−	2.24826e35i	0.0286024	−	0.0498626i
$661$	−4.55858e36			−0.991312			−0.495656	−	0.868519i	$-0.665072\pi$
$661$	−4.55858e36			−0.991312			−0.495656	+	0.868519i	$0.665072\pi$
$662$		−	3.22768e36i		−	0.688234i
$663$	1.78237e36	+	1.02241e36i	0.372667	+	0.213771i
$664$	−3.26778e36			−0.669990
$665$		−	3.25022e36i		−	0.653479i
$666$	−5.09266e36	+	2.97839e36i	−1.00411	+	0.587242i
$667$	−4.49576e36			−0.869296
$668$			5.83589e34i			0.0110666i
$669$	3.54124e36	−	6.17346e36i	0.658591	−	1.14812i
$670$	−6.50958e36			−1.18736
$671$			1.51065e34i			0.00270253i
$672$	2.59691e35	+	1.48965e35i	0.0455677	+	0.0261387i
$673$	−1.83201e36			−0.315306			−0.157653	−	0.987495i	$-0.550393\pi$
$673$	−1.83201e36			−0.315306			−0.157653	+	0.987495i	$0.550393\pi$
$674$		−	2.34103e36i		−	0.395211i
$675$	4.16296e36	−	3.49643e34i	0.689371	−	0.00578996i
$676$	2.78932e36			0.453097
$677$			1.01747e37i			1.62132i	0.585517	+	0.810660i	$0.300892\pi$
$677$			1.01747e37i			1.62132i	−0.585517	+	0.810660i	$0.699108\pi$
$678$	−1.18335e35	+	2.06293e35i	−0.0184981	+	0.0322477i
$679$	7.32674e35			0.112358
$680$			4.28461e36i			0.644608i
$681$	4.93819e36	+	2.83266e36i	0.728880	+	0.418102i
$682$	5.27479e35			0.0763850
$683$			3.71841e36i			0.528309i	0.964480	+	0.264155i	$0.0850929\pi$
$683$			3.71841e36i			0.528309i	−0.964480	+	0.264155i	$0.914907\pi$
$684$	−3.06350e36	−	5.23819e36i	−0.427060	−	0.730217i
$685$	−1.01568e37			−1.38924
$686$		−	2.99308e36i		−	0.401702i
$687$	−5.19589e36	+	9.05801e36i	−0.684262	+	1.19288i
$688$	3.40797e36			0.440399
$689$			2.00737e36i			0.254553i
$690$	−4.72455e36	−	2.71011e36i	−0.587925	−	0.337248i
$691$	9.87788e36			1.20628			0.603141	−	0.797634i	$-0.293915\pi$
$691$	9.87788e36			1.20628			0.603141	+	0.797634i	$0.293915\pi$
$692$		−	2.69723e36i		−	0.323250i
$693$	1.92913e35	−	1.12823e35i	0.0226897	−	0.0132698i
$694$	5.83572e36			0.673630
$695$			3.80987e36i			0.431626i
$696$	1.86491e36	−	3.25111e36i	0.207366	−	0.361503i
$697$	−1.59058e37			−1.73592
$698$			1.22269e36i			0.130977i
$699$	−1.17573e37	−	6.74428e36i	−1.23625	−	0.709141i
$700$	9.92464e35			0.102433
$701$			1.12853e37i			1.14335i	0.820482	+	0.571673i	$0.193705\pi$
$701$			1.12853e37i			1.14335i	−0.820482	+	0.571673i	$0.806295\pi$
$702$	−1.82890e34	−	2.17755e36i	−0.00181890	−	0.216563i
$703$	2.85076e37			2.78318
$704$		−	1.15362e35i		−	0.0110565i
$705$	8.64583e36	−	1.50723e37i	0.813483	−	1.41815i
$706$	−2.31048e36			−0.213423
$707$		−	2.37202e36i		−	0.215113i
$708$	−4.17557e36	−	2.39520e36i	−0.371777	−	0.213260i
$709$	7.15383e36			0.625370			0.312685	−	0.949857i	$-0.398771\pi$
$709$	7.15383e36			0.625370			0.312685	+	0.949857i	$0.398771\pi$
$710$			3.73856e36i			0.320883i
$711$	3.09971e36	+	5.30009e36i	0.261226	+	0.446662i
$712$	−1.66585e36			−0.137847
$713$		−	1.10846e37i		−	0.900648i
$714$	−1.83821e36	+	3.20456e36i	−0.146663	+	0.255677i
$715$	−4.49437e35			−0.0352120
$716$			4.87387e35i			0.0374977i
$717$	−4.79523e36	−	2.75066e36i	−0.362294	−	0.207820i
$718$	3.53577e36			0.262341
$719$		−	2.02421e37i		−	1.47496i	−0.675371	−	0.737478i	$-0.736017\pi$
$719$		−	2.02421e37i		−	1.47496i	0.675371	−	0.737478i	$-0.263983\pi$
$720$	3.91964e36	−	2.29236e36i	0.280494	−	0.164044i
$721$	2.35349e36			0.165407
$722$			1.90783e37i			1.31691i
$723$	5.43504e36	−	9.47493e36i	0.368473	−	0.642360i
$724$	1.34748e37			0.897265
$725$		−	1.24248e37i		−	0.812634i
$726$	9.47284e36	+	5.43384e36i	0.608561	+	0.349085i
$727$	−2.60217e37			−1.64205			−0.821027	−	0.570889i	$-0.806599\pi$
$727$	−2.60217e37			−1.64205			−0.821027	+	0.570889i	$0.806599\pi$
$728$		−	5.19135e35i		−	0.0321790i
$729$	1.64209e37	−	2.75854e35i	0.999859	−	0.0167966i
$730$	−1.73101e37			−1.03538
$731$			4.20540e37i			2.47105i
$732$	−1.31684e35	+	2.29565e35i	−0.00760131	+	0.0132514i
$733$	−4.00712e35			−0.0227238			−0.0113619	−	0.999935i	$-0.503617\pi$
$733$	−4.00712e35			−0.0227238			−0.0113619	+	0.999935i	$0.503617\pi$
$734$		−	1.71677e37i		−	0.956451i
$735$	−1.87793e37	−	1.07722e37i	−1.02788	−	0.589618i
$736$	−2.42425e36			−0.130367
$737$			2.16280e36i			0.114272i
$738$	8.50993e36	+	1.45509e37i	0.441767	+	0.755364i
$739$	2.66498e36			0.135930			0.0679650	−	0.997688i	$-0.478349\pi$
$739$	2.66498e36			0.135930			0.0679650	+	0.997688i	$0.478349\pi$
$740$			2.13317e37i			1.06909i
$741$	−5.23569e36	+	9.12739e36i	−0.257832	+	0.449480i
$742$	−3.60910e36			−0.174642
$743$		−	1.87280e37i		−	0.890505i	−0.895405	−	0.445252i	$-0.853114\pi$
$743$		−	1.87280e37i		−	0.890505i	0.895405	−	0.445252i	$-0.146886\pi$
$744$	8.01581e36	+	4.59806e36i	0.374541	+	0.214845i
$745$	−1.92611e37			−0.884403
$746$		−	2.04234e37i		−	0.921559i
$747$	−3.68892e37	+	2.15743e37i	−1.63580	+	0.956683i
$748$	1.42356e36			0.0620375
$749$			3.85131e36i			0.164947i
$750$	−3.37452e36	+	5.88281e36i	−0.142042	+	0.247622i
$751$	1.70059e37			0.703526			0.351763	−	0.936089i	$-0.385582\pi$
$751$	1.70059e37			0.703526			0.351763	+	0.936089i	$0.385582\pi$
$752$		−	7.73388e36i		−	0.314460i
$753$	1.28617e37	+	7.37779e36i	0.514002	+	0.294844i
$754$	−6.49912e36			−0.255286
$755$		−	5.59961e36i		−	0.216196i
$756$	3.91507e36	−	3.28823e34i	0.148579	−	0.00124790i
$757$	−9.08079e36			−0.338748			−0.169374	−	0.985552i	$-0.554175\pi$
$757$	−9.08079e36			−0.338748			−0.169374	+	0.985552i	$0.554175\pi$
$758$			1.09411e37i			0.401202i
$759$	−9.00432e35	+	1.56973e36i	−0.0324570	+	0.0565823i
$760$	−2.19413e37			−0.777472
$761$		−	4.37798e37i		−	1.52501i	−0.646982	−	0.762505i	$-0.723969\pi$
$761$		−	4.37798e37i		−	1.52501i	0.646982	−	0.762505i	$-0.276031\pi$
$762$	−5.75579e36	−	3.30165e36i	−0.197102	−	0.113062i
$763$	9.04623e35			0.0304543
$764$		−	1.05650e37i		−	0.349667i
$765$	2.82875e37	+	4.83679e37i	0.920440	+	1.57383i
$766$	2.31574e37			0.740827
$767$			8.34714e36i			0.262542i
$768$	1.00562e36	−	1.75310e36i	0.0310983	−	0.0542139i
$769$	3.32261e37			1.01027			0.505134	−	0.863041i	$-0.331443\pi$
$769$	3.32261e37			1.01027			0.505134	+	0.863041i	$0.331443\pi$
$770$		−	8.08055e35i		−	0.0241580i
$771$	−2.54805e37	−	1.46162e37i	−0.749034	−	0.429664i
$772$	−2.86223e37			−0.827332
$773$			1.42411e37i			0.404772i	0.979306	+	0.202386i	$0.0648695\pi$
$773$			1.42411e37i			0.404772i	−0.979306	+	0.202386i	$0.935130\pi$
$774$	3.84717e37	−	2.24998e37i	1.07525	−	0.628848i
$775$	3.06341e37			0.841942
$776$		−	4.94606e36i		−	0.133677i
$777$	−9.15187e36	+	1.59545e37i	−0.243241	+	0.424043i
$778$	−1.98456e37			−0.518715
$779$		−	8.14526e37i		−	2.09372i
$780$	−6.82985e36	−	3.91776e36i	−0.172656	−	0.0990395i
$781$	1.24213e36			0.0308819
$782$		−	2.99150e37i		−	0.731478i
$783$	−4.11658e35	−	4.90133e37i	−0.00989996	−	1.17872i
$784$	−9.63600e36			−0.227923
$785$			5.67381e37i			1.31999i
$786$	−4.24270e35	+	7.39632e35i	−0.00970844	+	0.0169248i
$787$	4.32824e37			0.974182			0.487091	−	0.873351i	$-0.338058\pi$
$787$	4.32824e37			0.974182			0.487091	+	0.873351i	$0.338058\pi$
$788$			1.39114e37i			0.307985i
$789$	3.72984e37	+	2.13953e37i	0.812250	+	0.465926i
$790$	2.22006e37			0.475567
$791$			7.41447e35i			0.0156238i
$792$	−7.61634e35	−	1.30229e36i	−0.0157877	−	0.0269949i
$793$	4.58911e35			0.00935787
$794$			1.25997e37i			0.252751i
$795$	−2.72369e37	+	4.74822e37i	−0.537508	+	0.937040i
$796$	1.41848e37			0.275394
$797$			6.67652e37i			1.27524i	0.770351	+	0.637620i	$0.220081\pi$
$797$			6.67652e37i			1.27524i	−0.770351	+	0.637620i	$0.779919\pi$
$798$	−1.64104e37	−	9.41339e36i	−0.308377	−	0.176892i
$799$	9.54352e37			1.76441
$800$		−	6.69982e36i		−	0.121869i
$801$	−1.88054e37	+	1.09981e37i	−0.336558	+	0.196833i
$802$	−3.14836e37			−0.554393
$803$			5.75125e36i			0.0996461i
$804$	−1.88532e37	+	3.28669e37i	−0.321408	+	0.560312i
$805$	−1.69807e37			−0.284845
$806$		−	1.60240e37i		−	0.264493i
$807$	−9.25979e37	−	5.31163e37i	−1.50399	−	0.862724i
$808$	−1.60128e37			−0.255929
$809$		−	2.40528e36i		−	0.0378299i	−0.999821	−	0.0189149i	$-0.993979\pi$
$809$		−	2.40528e36i		−	0.0378299i	0.999821	−	0.0189149i	$-0.00602117\pi$
$810$	2.91133e37	−	5.17557e37i	0.450595	−	0.801038i
$811$	−2.83237e37			−0.431399			−0.215699	−	0.976460i	$-0.569203\pi$
$811$	−2.83237e37			−0.431399			−0.215699	+	0.976460i	$0.569203\pi$
$812$		−	1.16849e37i		−	0.175145i
$813$	4.35863e37	−	7.59842e37i	0.642944	−	1.12085i
$814$	7.08743e36			0.102890
$815$		−	1.52545e37i		−	0.217947i
$816$	2.16330e37	+	1.24092e37i	0.304190	+	0.174491i
$817$	−2.15356e38			−2.98037
$818$		−	6.20931e35i		−	0.00845766i
$819$	−3.42738e36	−	5.86038e36i	−0.0459486	−	0.0785660i
$820$	6.09494e37			0.804247
$821$			1.12590e38i			1.46231i	0.682213	+	0.731154i	$0.261018\pi$
$821$			1.12590e38i			1.46231i	−0.682213	+	0.731154i	$0.738982\pi$
$822$	−2.94163e37	+	5.12816e37i	−0.376058	+	0.655583i
$823$	−1.20533e38			−1.51673			−0.758366	−	0.651829i	$-0.774002\pi$
$823$	−1.20533e38			−1.51673			−0.758366	+	0.651829i	$0.774002\pi$
$824$		−	1.58877e37i		−	0.196792i
$825$	−4.33820e36	−	2.48849e36i	−0.0528942	−	0.0303414i
$826$	−1.50076e37			−0.180123
$827$			2.94411e37i			0.347843i	0.984760	+	0.173921i	$0.0556439\pi$
$827$			2.94411e37i			0.347843i	−0.984760	+	0.173921i	$0.944356\pi$
$828$	−2.73668e37	+	1.60052e37i	−0.318294	+	0.186151i
$829$	1.17109e38			1.34085			0.670427	−	0.741976i	$-0.266111\pi$
$829$	1.17109e38			1.34085			0.670427	+	0.741976i	$0.266111\pi$
$830$			1.54518e38i			1.74166i
$831$	5.95688e37	−	1.03847e38i	0.661006	−	1.15233i
$832$	−3.50452e36			−0.0382847
$833$		−	1.18907e38i		−	1.27886i
$834$	1.92360e37	+	1.10342e37i	0.203684	+	0.116838i
$835$	2.75952e36			0.0287679
$836$			7.28996e36i			0.0748244i
$837$	1.20845e38	−	1.01497e36i	1.22123	−	0.0102570i
$838$	5.33665e36			0.0531002
$839$			1.39033e38i			1.36211i	0.732232	+	0.681055i	$0.238479\pi$
$839$			1.39033e38i			1.36211i	−0.732232	+	0.681055i	$0.761521\pi$
$840$	7.04386e36	−	1.22796e37i	0.0679485	−	0.118455i
$841$	−4.10047e37			−0.389481
$842$			8.19574e37i			0.766533i
$843$	8.26860e37	+	4.74306e37i	0.761506	+	0.436818i
$844$	4.59864e37			0.417040
$845$		−	1.31894e38i		−	1.17784i
$846$	−5.10599e37	−	8.73057e37i	−0.449019	−	0.767764i
$847$	3.40467e37			0.294843
$848$			2.43640e37i			0.207779i
$849$	1.07900e38	−	1.88102e38i	0.906194	−	1.57977i
$850$	8.26751e37			0.683799
$851$		−	1.48937e38i		−	1.21316i
$852$	1.88760e37	+	1.08277e37i	0.151424	+	0.0868606i
$853$	9.59119e37			0.757766			0.378883	−	0.925445i	$-0.376308\pi$
$853$	9.59119e37			0.757766			0.378883	+	0.925445i	$0.376308\pi$
$854$			8.25088e35i			0.00642019i
$855$	−2.47689e38	+	1.44859e38i	−1.89822	+	1.11016i
$856$	2.59990e37			0.196245
$857$			1.15578e38i			0.859259i	0.903005	+	0.429629i	$0.141356\pi$
$857$			1.15578e38i			0.859259i	−0.903005	+	0.429629i	$0.858644\pi$
$858$	−1.30167e36	+	2.26921e36i	−0.00953163	+	0.0166165i
$859$	7.94057e36			0.0572718			0.0286359	−	0.999590i	$-0.490884\pi$
$859$	7.94057e36			0.0572718			0.0286359	+	0.999590i	$0.490884\pi$
$860$		−	1.61147e38i		−	1.14483i
$861$	4.55855e37	+	2.61489e37i	0.318996	+	0.182984i
$862$	2.19956e36			0.0151615
$863$		−	6.18942e37i		−	0.420252i	−0.977674	−	0.210126i	$-0.932613\pi$
$863$		−	6.18942e37i		−	0.420252i	0.977674	−	0.210126i	$-0.0673873\pi$
$864$	−2.21978e35	−	2.64295e37i	−0.00148468	−	0.176770i
$865$	−1.27539e38			−0.840299
$866$		−	4.65127e37i		−	0.301883i
$867$	−7.53059e37	+	1.31281e38i	−0.481483	+	0.839371i
$868$	2.88099e37			0.181462
$869$		−	7.37611e36i		−	0.0457689i
$870$	−1.53730e38	−	8.81829e37i	−0.939739	−	0.539056i
$871$	6.57024e37			0.395681
$872$		−	6.10683e36i		−	0.0362328i
$873$	−3.26544e37	−	5.58348e37i	−0.190878	−	0.326377i
$874$	1.53193e38			0.882248
$875$			2.11436e37i			0.119971i
$876$	−5.01339e37	+	8.73987e37i	−0.280271	+	0.488598i
$877$	−2.21429e38			−1.21966			−0.609830	−	0.792532i	$-0.708762\pi$
$877$	−2.21429e38			−1.21966			−0.609830	+	0.792532i	$0.708762\pi$
$878$		−	1.18624e38i		−	0.643787i
$879$	3.09563e38	+	1.77573e38i	1.65536	+	0.949556i
$880$	−5.45494e36			−0.0287419
$881$		−	2.62402e38i		−	1.36232i	−0.732133	−	0.681162i	$-0.761475\pi$
$881$		−	2.62402e38i		−	1.36232i	0.732133	−	0.681162i	$-0.238525\pi$
$882$	−1.08778e38	+	6.36179e37i	−0.556481	+	0.325452i
$883$	2.23889e38			1.12861			0.564304	−	0.825567i	$-0.309144\pi$
$883$	2.23889e38			1.12861			0.564304	+	0.825567i	$0.309144\pi$
$884$		−	4.32454e37i		−	0.214813i
$885$	−1.13258e38	+	1.97443e38i	−0.554377	+	0.966448i
$886$	−2.13232e38			−1.02852
$887$			3.46337e38i			1.64623i	0.567871	+	0.823117i	$0.307767\pi$
$887$			3.46337e38i			1.64623i	−0.567871	+	0.823117i	$0.692233\pi$
$888$	1.07704e38	+	6.17815e37i	0.504502	+	0.289394i
$889$	−2.06871e37			−0.0954941
$890$			7.87704e37i			0.358338i
$891$	−1.71958e37	−	9.67287e36i	−0.0770924	−	0.0433656i
$892$	−1.49786e38			−0.661803
$893$			4.88718e38i			2.12809i
$894$	−5.57846e37	+	9.72496e37i	−0.239402	+	0.417350i
$895$	2.30462e37			0.0974766
$896$		−	6.30088e36i		−	0.0262662i
$897$	4.76858e37	+	2.73537e37i	0.195924	+	0.112386i
$898$	1.97175e37			0.0798473
$899$		−	3.60675e38i		−	1.43959i
$900$	−4.42329e37	−	7.56326e37i	−0.174018	−	0.297547i
$901$	−3.00649e38			−1.16584
$902$		−	2.02504e37i		−	0.0774012i
$903$	6.91363e37	−	1.20525e38i	0.260474	−	0.454086i
$904$	5.00528e36			0.0185883
$905$		−	6.37159e38i		−	2.33247i
$906$	−2.82725e37	−	1.62178e37i	−0.102023	−	0.0585227i
$907$	−2.64377e37			−0.0940435			−0.0470217	−	0.998894i	$-0.514973\pi$
$907$	−2.64377e37			−0.0940435			−0.0470217	+	0.998894i	$0.514973\pi$
$908$		−	1.19815e38i		−	0.420141i
$909$	−1.80764e38	+	1.05718e38i	−0.624859	+	0.365442i
$910$	−2.45474e37			−0.0836504
$911$			3.84631e38i			1.29213i	0.763283	+	0.646064i	$0.223586\pi$
$911$			3.84631e38i			1.29213i	−0.763283	+	0.646064i	$0.776414\pi$
$912$	−6.35469e37	+	1.10782e38i	−0.210456	+	0.366889i
$913$	5.13384e37			0.167619
$914$		−	3.76715e38i		−	1.21258i
$915$	1.08550e37	+	6.22671e36i	0.0344475	+	0.0197599i
$916$	2.19774e38			0.687599
$917$			2.65834e36i			0.00819991i
$918$	3.26137e38	−	2.73919e36i	0.991847	−	0.00833043i
$919$	3.44098e36			0.0103176			0.00515882	−	0.999987i	$-0.498358\pi$
$919$	3.44098e36			0.0103176			0.00515882	+	0.999987i	$0.498358\pi$
$920$			1.14631e38i			0.338892i
$921$	8.58427e37	−	1.49650e38i	0.250224	−	0.436216i
$922$	2.93727e38			0.844193
$923$		−	3.77340e37i		−	0.106933i
$924$	−4.07988e36	−	2.34031e36i	−0.0114002	−	0.00653941i
$925$	4.11612e38			1.13409
$926$			3.29241e38i			0.894480i
$927$	−1.04892e38	−	1.79352e38i	−0.281001	−	0.480475i
$928$	−7.88815e37			−0.208378
$929$		−	2.18355e38i		−	0.568798i	−0.958706	−	0.284399i	$-0.908206\pi$
$929$		−	2.18355e38i		−	0.568798i	0.958706	−	0.284399i	$-0.0917940\pi$
$930$	2.17420e38	−	3.79030e38i	0.558498	−	0.973632i
$931$	6.08917e38			1.54245
$932$			2.85267e38i			0.712599i
$933$	2.89974e38	+	1.66336e38i	0.714329	+	0.409756i
$934$	−2.49112e38			−0.605180
$935$		−	6.73133e37i		−	0.161269i
$936$	−3.95616e37	+	2.31372e37i	−0.0934734	+	0.0546670i
$937$	−4.94253e38			−1.15169			−0.575844	−	0.817560i	$-0.695326\pi$
$937$	−4.94253e38			−1.15169			−0.575844	+	0.817560i	$0.695326\pi$
$938$			1.18128e38i			0.271467i
$939$	−2.05568e37	+	3.58367e37i	−0.0465910	+	0.0812223i
$940$	−3.65698e38			−0.817450
$941$		−	3.82370e38i		−	0.842982i	−0.906833	−	0.421491i	$-0.861507\pi$
$941$		−	3.82370e38i		−	0.842982i	0.906833	−	0.421491i	$-0.138493\pi$
$942$	2.86471e38	+	1.64327e38i	0.622901	+	0.357311i
$943$	−4.25546e38			−0.912630
$944$			1.01311e38i			0.214300i
$945$	−1.55485e36	−	1.85125e38i	−0.00324395	−	0.386235i
$946$	−5.35408e37			−0.110179
$947$			3.54589e38i			0.719740i	0.933002	+	0.359870i	$0.117179\pi$
$947$			3.54589e38i			0.719740i	−0.933002	+	0.359870i	$0.882821\pi$
$948$	6.42979e37	−	1.12091e38i	0.128733	−	0.224420i
$949$	1.74714e38			0.345038
$950$			4.23374e38i			0.824741i
$951$	−6.47779e38	−	3.71581e38i	−1.24474	−	0.714015i
$952$	7.77521e37			0.147378
$953$		−	1.36946e38i		−	0.256060i	−0.991770	−	0.128030i	$-0.959135\pi$
$953$		−	1.36946e38i		−	0.256060i	0.991770	−	0.128030i	$-0.0408654\pi$
$954$	1.60854e38	+	2.75038e38i	0.296689	+	0.507300i
$955$	−4.99567e38			−0.908971
$956$			1.16346e38i			0.208834i
$957$	−2.92987e37	+	5.10765e37i	−0.0518791	+	0.0904411i
$958$	2.17755e38			0.380380
$959$			1.84313e38i			0.317625i
$960$	−8.28957e37	−	4.75509e37i	−0.140931	−	0.0808412i
$961$	2.93049e38			0.491515
$962$		−	2.15305e38i		−	0.356269i
$963$	2.93496e38	−	1.71648e38i	0.479138	−	0.280219i
$964$	−2.29890e38			−0.370269
$965$			1.35341e39i			2.15068i
$966$	−4.91799e37	+	8.57356e37i	−0.0771055	+	0.134418i
$967$	5.51139e38			0.852544			0.426272	−	0.904595i	$-0.359827\pi$
$967$	5.51139e38			0.852544			0.426272	+	0.904595i	$0.359827\pi$
$968$		−	2.29839e38i		−	0.350787i
$969$	−1.36703e39	−	7.84162e38i	−2.05859	−	1.18086i
$970$	−2.33876e38			−0.347498
$971$			4.19479e38i			0.614978i	0.951552	+	0.307489i	$0.0994888\pi$
$971$			4.19479e38i			0.614978i	−0.951552	+	0.307489i	$0.900511\pi$
$972$	−1.76996e38	−	2.96890e38i	−0.256037	−	0.429471i
$973$	6.91369e37			0.0986832
$974$			2.31347e37i			0.0325834i
$975$	−7.55964e37	+	1.31788e38i	−0.105061	+	0.183153i
$976$	5.56992e36			0.00763838
$977$		−	7.69988e38i		−	1.04197i	−0.853566	−	0.520985i	$-0.825565\pi$
$977$		−	7.69988e38i		−	1.04197i	0.853566	−	0.520985i	$-0.174435\pi$
$978$	−7.70202e37	−	4.41806e37i	−0.102849	−	0.0589966i
$979$	2.61714e37			0.0344867
$980$			4.55641e38i			0.592493i
$981$	−4.03180e37	−	6.89384e37i	−0.0517370	−	0.0884635i
$982$	−7.49777e38			−0.949473
$983$			5.21324e38i			0.651497i	0.945457	+	0.325748i	$0.105616\pi$
$983$			5.21324e38i			0.651497i	−0.945457	+	0.325748i	$0.894384\pi$
$984$	1.76523e38	−	3.07734e38i	0.217704	−	0.379524i
$985$	6.57803e38			0.800617
$986$		−	9.73389e38i		−	1.16919i
$987$	−2.73515e38	−	1.56894e38i	−0.324233	−	0.185988i
$988$	2.21457e38			0.259089
$989$			1.12512e39i			1.29911i
$990$	−6.15793e37	+	3.60141e37i	−0.0701742	+	0.0410407i
$991$	1.47434e38			0.165821			0.0829104	−	0.996557i	$-0.473578\pi$
$991$	1.47434e38			0.165821			0.0829104	+	0.996557i	$0.473578\pi$
$992$		−	1.94487e38i		−	0.215893i
$993$	−4.42027e38	+	7.70587e38i	−0.484293	+	0.844271i
$994$	6.78430e37			0.0733639
$995$		−	6.70733e38i		−	0.715895i
$996$	7.80162e38	+	4.47519e38i	0.821890	+	0.471455i
$997$	1.60385e39			1.66773			0.833867	−	0.551965i	$-0.186122\pi$
$997$	1.60385e39			1.66773			0.833867	+	0.551965i	$0.186122\pi$
$998$		−	1.14536e39i		−	1.17556i
$999$	1.62373e39	−	1.36375e37i	1.64499	−	0.0138161i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.27.b.a.5.7	yes	8
3.2	odd	2	inner	6.27.b.a.5.3	✓	8
4.3	odd	2		48.27.e.b.17.4		8
12.11	even	2		48.27.e.b.17.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.27.b.a.5.3	✓	8	3.2	odd	2	inner
6.27.b.a.5.7	yes	8	1.1	even	1	trivial
48.27.e.b.17.3		8	12.11	even	2
48.27.e.b.17.4		8	4.3	odd	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)

\(f(q)\)	\(=\)	\(q+5792.62i q^{2} +(793293. - 1.38295e6i) q^{3} -3.35544e7 q^{4} +1.58663e9i q^{5} +(8.01091e9 + 4.59524e9i) q^{6} +2.87923e10 q^{7} -1.94368e11i q^{8} +(-1.28324e12 - 2.19417e12i) q^{9} +O(q^{10})\)	\(q+5792.62i q^{2} +(793293. - 1.38295e6i) q^{3} -3.35544e7 q^{4} +1.58663e9i q^{5} +(8.01091e9 + 4.59524e9i) q^{6} +2.87923e10 q^{7} -1.94368e11i q^{8} +(-1.28324e12 - 2.19417e12i) q^{9} -9.19074e12 q^{10} +3.05361e12i q^{11} +(-2.66185e13 + 4.64041e13i) q^{12} +9.27639e13 q^{13} +1.66783e14i q^{14} +(2.19423e15 + 1.25866e15i) q^{15} +1.12590e15 q^{16} +1.38935e16i q^{17} +(1.27100e16 - 7.43331e15i) q^{18} -7.11477e16 q^{19} -5.32385e16i q^{20} +(2.28407e16 - 3.98183e16i) q^{21} -1.76884e16 q^{22} +3.71709e17i q^{23} +(-2.68801e17 - 1.54191e17i) q^{24} -1.02728e18 q^{25} +5.37346e17i q^{26} +(-4.05241e18 + 3.40358e16i) q^{27} -9.66109e17 q^{28} +1.20948e19i q^{29} +(-7.29095e18 + 1.27103e19i) q^{30} -2.98206e19 q^{31} +6.52191e18i q^{32} +(4.22300e18 + 2.42241e18i) q^{33} -8.04797e19 q^{34} +4.56827e19i q^{35} +(4.30583e19 + 7.36241e19i) q^{36} -4.00682e20 q^{37} -4.12132e20i q^{38} +(7.35890e19 - 1.28288e20i) q^{39} +3.08390e20 q^{40} +1.14484e21i q^{41} +(2.30652e20 + 1.32308e20i) q^{42} +3.02689e21 q^{43} -1.02462e20i q^{44} +(3.48134e21 - 2.03602e21i) q^{45} -2.15317e21 q^{46} -6.86906e21i q^{47} +(8.93168e20 - 1.55706e21i) q^{48} -8.55848e21 q^{49} -5.95064e21i q^{50} +(1.92140e22 + 1.10216e22i) q^{51} -3.11264e21 q^{52} +2.16396e22i q^{53} +(-1.97156e20 - 2.34741e22i) q^{54} -4.84496e21 q^{55} -5.59630e21i q^{56} +(-5.64410e22 + 9.83938e22i) q^{57} -7.00608e22 q^{58} +8.99826e22i q^{59} +(-7.36262e22 - 4.22337e22i) q^{60} +4.94708e21 q^{61} -1.72739e23i q^{62} +(-3.69474e22 - 6.31752e22i) q^{63} -3.77789e22 q^{64} +1.47182e23i q^{65} +(-1.40321e22 + 2.44622e22i) q^{66} +7.08276e23 q^{67} -4.66188e23i q^{68} +(5.14055e23 + 2.94874e23i) q^{69} -2.64623e23 q^{70} -4.06775e23i q^{71} +(-4.26476e23 + 2.49421e23i) q^{72} +1.88343e24 q^{73} -2.32100e24i q^{74} +(-8.14934e23 + 1.42068e24i) q^{75} +2.38732e24 q^{76} +8.79206e22i q^{77} +(7.43123e23 + 4.26273e23i) q^{78} -2.41553e24 q^{79} +1.78639e24i q^{80} +(-3.16768e24 + 5.63129e24i) q^{81} -6.63161e24 q^{82} -1.68124e25i q^{83} +(-7.66408e23 + 1.33608e24i) q^{84} -2.20438e25 q^{85} +1.75336e25i q^{86} +(1.67266e25 + 9.59475e24i) q^{87} +5.93525e23 q^{88} -8.57062e24i q^{89} +(1.17939e25 + 2.01661e25i) q^{90} +2.67089e24 q^{91} -1.24725e25i q^{92} +(-2.36564e25 + 4.12404e25i) q^{93} +3.97899e25 q^{94} -1.12885e26i q^{95} +(9.01948e24 + 5.17378e24i) q^{96} +2.54469e25 q^{97} -4.95760e25i q^{98} +(6.70015e24 - 3.91851e24i) 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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Groups

Database

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