LMFDB - Embedded newform 6.21.b.a.5.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,21,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, 21, names="a")

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

chi := DirichletCharacter("6.5");

S:= CuspForms(chi, 21);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 21 $
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:	$15.2108259062$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 3396x^{4} + 2813589x^{2} + 548136050 $ x^6 + 3396x^4 + 2813589x^2 + 548136050
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{31}\cdot 3^{17} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.6
Root			$16.8544i$ of defining polynomial
Character	$\chi$	$=$	6.5
Dual form			6.21.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)

$f(q)$	$=$	$q+724.077i q^{2} +(41792.5 + 41715.4i) q^{3} -524288. q^{4} -805527. i q^{5} +(-3.02052e7 + 3.02610e7i) q^{6} -3.63571e8 q^{7} -3.79625e8i q^{8} +(6.43531e6 + 3.48678e9i) q^{9} +O(q^{10})$	\(q+724.077i q^{2} +(41792.5 + 41715.4i) q^{3} -524288. q^{4} -805527. i q^{5} +(-3.02052e7 + 3.02610e7i) q^{6} -3.63571e8 q^{7} -3.79625e8i q^{8} +(6.43531e6 + 3.48678e9i) q^{9} +5.83264e8 q^{10} +7.52991e9i q^{11} +(-2.19113e10 - 2.18709e10i) q^{12} -1.09577e11 q^{13} -2.63254e11i q^{14} +(3.36029e10 - 3.36649e10i) q^{15} +2.74878e11 q^{16} -2.97597e12i q^{17} +(-2.52470e12 + 4.65966e9i) q^{18} -9.19319e12 q^{19} +4.22328e11i q^{20} +(-1.51945e13 - 1.51665e13i) q^{21} -5.45223e12 q^{22} -8.43375e12i q^{23} +(1.58362e13 - 1.58655e13i) q^{24} +9.47186e13 q^{25} -7.93420e13i q^{26} +(-1.45183e14 + 1.45990e14i) q^{27} +1.90616e14 q^{28} +6.14898e14i q^{29} +(2.43760e13 + 2.43311e13i) q^{30} +5.36607e14 q^{31} +1.99033e14i q^{32} +(-3.14113e14 + 3.14693e14i) q^{33} +2.15483e15 q^{34} +2.92866e14i q^{35} +(-3.37396e12 - 1.82808e15i) q^{36} -6.40512e15 q^{37} -6.65658e15i q^{38} +(-4.57948e15 - 4.57104e15i) q^{39} -3.05798e14 q^{40} +1.51532e16i q^{41} +(1.09817e16 - 1.10020e16i) q^{42} -2.28528e16 q^{43} -3.94784e15i q^{44} +(2.80869e15 - 5.18382e12i) q^{45} +6.10668e15 q^{46} +2.22157e16i q^{47} +(1.14878e16 + 1.14666e16i) q^{48} +5.23916e16 q^{49} +6.85836e16i q^{50} +(1.24144e17 - 1.24373e17i) q^{51} +5.74498e16 q^{52} +3.38516e17i q^{53} +(-1.05708e17 - 1.05124e17i) q^{54} +6.06554e15 q^{55} +1.38021e17i q^{56} +(-3.84206e17 - 3.83497e17i) q^{57} -4.45233e17 q^{58} -3.93698e17i q^{59} +(-1.76176e16 + 1.76501e16i) q^{60} +7.29236e17 q^{61} +3.88545e17i q^{62} +(-2.33969e15 - 1.26769e18i) q^{63} -1.44115e17 q^{64} +8.82670e16i q^{65} +(-2.27862e17 - 2.27442e17i) q^{66} -5.04483e17 q^{67} +1.56027e18i q^{68} +(3.51817e17 - 3.52467e17i) q^{69} -2.12058e17 q^{70} +6.11896e18i q^{71} +(1.32367e18 - 2.44301e15i) q^{72} +9.17001e17 q^{73} -4.63780e18i q^{74} +(3.95852e18 + 3.95122e18i) q^{75} +4.81988e18 q^{76} -2.73766e18i q^{77} +(3.30978e18 - 3.31590e18i) q^{78} -7.30923e18 q^{79} -2.21421e17i q^{80} +(-1.21576e19 + 4.48770e16i) q^{81} -1.09721e19 q^{82} -1.57590e19i q^{83} +(7.96631e18 + 7.95162e18i) q^{84} -2.39722e18 q^{85} -1.65472e19i q^{86} +(-2.56507e19 + 2.56981e19i) q^{87} +2.85854e18 q^{88} -2.49058e19i q^{89} +(3.75348e15 + 2.03371e18i) q^{90} +3.98389e19 q^{91} +4.42171e18i q^{92} +(2.24261e19 + 2.23848e19i) q^{93} -1.60859e19 q^{94} +7.40536e18i q^{95} +(-8.30274e18 + 8.31807e18i) q^{96} +8.81363e19 q^{97} +3.79356e19i q^{98} +(-2.62551e19 + 4.84573e16i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 18846 q^{3} - 3145728 q^{4} + 35057664 q^{6} - 566671812 q^{7} + 1944941382 q^{9}+O(q^{10}) $ 6 * q + 18846 * q^3 - 3145728 * q^4 + 35057664 * q^6 - 566671812 * q^7 + 1944941382 * q^9	$ 6 q + 18846 q^{3} - 3145728 q^{4} + 35057664 q^{6} - 566671812 q^{7} + 1944941382 q^{9} + 5360984064 q^{10} - 9880731648 q^{12} - 49898545620 q^{13} + 487708151328 q^{15} + 1649267441664 q^{16} - 3239129751552 q^{18} + 15927597287292 q^{19} - 20677554127188 q^{21} + 21184189636608 q^{22} - 18380312543232 q^{24} + 337510512308454 q^{25} - 10\!\cdots\!62 q^{27}+ \cdots - 22\!\cdots\!32 q^{99}+O(q^{100}) $ 6 * q + 18846 * q^3 - 3145728 * q^4 + 35057664 * q^6 - 566671812 * q^7 + 1944941382 * q^9 + 5360984064 * q^10 - 9880731648 * q^12 - 49898545620 * q^13 + 487708151328 * q^15 + 1649267441664 * q^16 - 3239129751552 * q^18 + 15927597287292 * q^19 - 20677554127188 * q^21 + 21184189636608 * q^22 - 18380312543232 * q^24 + 337510512308454 * q^25 - 1019514529044162 * q^27 + 297099230969856 * q^28 - 920809286295552 * q^30 + 1832545426397628 * q^31 - 3503562514347744 * q^33 + 2508713101983744 * q^34 - 1019709427286016 * q^36 + 424332326872812 * q^37 + 13854943345637340 * q^39 - 2810699612946432 * q^40 + 30169507188989952 * q^42 - 49488752333951556 * q^43 + 64297936569436992 * q^45 - 51218624034717696 * q^46 + 5180349034266624 * q^48 - 185965132589503470 * q^49 + 114461935953291648 * q^51 + 26161208686018560 * q^52 - 103567464750919680 * q^54 + 468503586680075712 * q^55 - 1250127589109383188 * q^57 + 330130684975472640 * q^58 - 255699531243454464 * q^60 + 3301830012872093484 * q^61 - 724019288731292484 * q^63 - 864691128455135232 * q^64 + 1110947414199017472 * q^66 - 2779226272508556228 * q^67 + 667934407322175168 * q^69 - 1866219302039371776 * q^70 + 1698236859181694976 * q^72 - 9149401536792501300 * q^73 + 9127347583517050878 * q^75 - 8350648126559748096 * q^76 + 19815256334884331520 * q^78 + 90056048403257148 * q^79 - 13310358127786728378 * q^81 - 19709381871486517248 * q^82 + 10840993498235142144 * q^84 + 78223886062534003968 * q^85 - 87334395308747540640 * q^87 - 11106616416197935104 * q^88 + 60406983770669457408 * q^90 + 132462766690215009720 * q^91 - 157075923546140581332 * q^93 - 106728395801434030080 * q^94 + 9636577302666018816 * q^96 + 92028905119987573836 * q^97 - 224342570810992842432 * 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 $

$2$			724.077i			0.707107i
$2$			724.077i			0.707107i
$3$	41792.5	+	41715.4i	0.707759	+	0.706454i
$3$	41792.5	+	41715.4i	0.707759	+	0.706454i
$4$	−524288.			−0.500000
$5$		−	805527.i		−	0.0824859i	−0.999149	−	0.0412430i	$-0.986868\pi$
$5$		−	805527.i		−	0.0824859i	0.999149	−	0.0412430i	$-0.0131318\pi$
$6$	−3.02052e7	+	3.02610e7i	−0.499538	+	0.500461i
$7$	−3.63571e8			−1.28709			−0.643545	−	0.765408i	$-0.722537\pi$
$7$	−3.63571e8			−1.28709			−0.643545	+	0.765408i	$0.722537\pi$
$8$		−	3.79625e8i		−	0.353553i
$9$	6.43531e6	+	3.48678e9i	0.00184563	+	0.999998i
$10$	5.83264e8			0.0583264
$11$			7.52991e9i			0.290310i	0.989409	+	0.145155i	$0.0463682\pi$
$11$			7.52991e9i			0.290310i	−0.989409	+	0.145155i	$0.953632\pi$
$12$	−2.19113e10	−	2.18709e10i	−0.353880	−	0.353227i
$13$	−1.09577e11			−0.794849			−0.397425	−	0.917635i	$-0.630096\pi$
$13$	−1.09577e11			−0.794849			−0.397425	+	0.917635i	$0.630096\pi$
$14$		−	2.63254e11i		−	0.910110i
$15$	3.36029e10	−	3.36649e10i	0.0582725	−	0.0583802i
$16$	2.74878e11			0.250000
$17$		−	2.97597e12i		−	1.47618i	−0.674702	−	0.738090i	$-0.735728\pi$
$17$		−	2.97597e12i		−	1.47618i	0.674702	−	0.738090i	$-0.264272\pi$
$18$	−2.52470e12	+	4.65966e9i	−0.707106	+	0.00130506i
$19$	−9.19319e12			−1.49944			−0.749722	−	0.661753i	$-0.769813\pi$
$19$	−9.19319e12			−1.49944			−0.749722	+	0.661753i	$0.769813\pi$
$20$			4.22328e11i			0.0412430i
$21$	−1.51945e13	−	1.51665e13i	−0.910949	−	0.909270i
$22$	−5.45223e12			−0.205281
$23$		−	8.43375e12i		−	0.203583i	−0.994806	−	0.101792i	$-0.967542\pi$
$23$		−	8.43375e12i		−	0.203583i	0.994806	−	0.101792i	$-0.0324575\pi$
$24$	1.58362e13	−	1.58655e13i	0.249769	−	0.250231i
$25$	9.47186e13			0.993196
$26$		−	7.93420e13i		−	0.562043i
$27$	−1.45183e14	+	1.45990e14i	−0.705146	+	0.709062i
$28$	1.90616e14			0.643545
$29$			6.14898e14i			1.46158i	0.682602	+	0.730790i	$0.260848\pi$
$29$			6.14898e14i			1.46158i	−0.682602	+	0.730790i	$0.739152\pi$
$30$	2.43760e13	+	2.43311e13i	0.0412810	+	0.0412049i
$31$	5.36607e14			0.654696			0.327348	−	0.944904i	$-0.393845\pi$
$31$	5.36607e14			0.654696			0.327348	+	0.944904i	$0.393845\pi$
$32$			1.99033e14i			0.176777i
$33$	−3.14113e14	+	3.14693e14i	−0.205091	+	0.205470i
$34$	2.15483e15			1.04382
$35$			2.92866e14i			0.106167i
$36$	−3.37396e12	−	1.82808e15i	−0.000922815	−	0.499999i
$37$	−6.40512e15			−1.33202			−0.666009	−	0.745943i	$-0.731999\pi$
$37$	−6.40512e15			−1.33202			−0.666009	+	0.745943i	$0.731999\pi$
$38$		−	6.65658e15i		−	1.06027i
$39$	−4.57948e15	−	4.57104e15i	−0.562562	−	0.561524i
$40$	−3.05798e14			−0.0291632
$41$			1.51532e16i			1.12893i	0.825457	+	0.564465i	$0.190917\pi$
$41$			1.51532e16i			1.12893i	−0.825457	+	0.564465i	$0.809083\pi$
$42$	1.09817e16	−	1.10020e16i	0.642951	−	0.644138i
$43$	−2.28528e16			−1.05744			−0.528719	−	0.848797i	$-0.677327\pi$
$43$	−2.28528e16			−1.05744			−0.528719	+	0.848797i	$0.677327\pi$
$44$		−	3.94784e15i		−	0.145155i
$45$	2.80869e15	−	5.18382e12i	0.0824858	−	0.000152238i
$46$	6.10668e15			0.143955
$47$			2.22157e16i			0.422359i	0.977447	+	0.211180i	$0.0677305\pi$
$47$			2.22157e16i			0.422359i	−0.977447	+	0.211180i	$0.932269\pi$
$48$	1.14878e16	+	1.14666e16i	0.176940	+	0.176613i
$49$	5.23916e16			0.656600
$50$			6.85836e16i			0.702296i
$51$	1.24144e17	−	1.24373e17i	1.04285	−	1.04478i
$52$	5.74498e16			0.397425
$53$			3.38516e17i			1.93562i	0.251679	+	0.967811i	$0.419017\pi$
$53$			3.38516e17i			1.93562i	−0.251679	+	0.967811i	$0.580983\pi$
$54$	−1.05708e17	−	1.05124e17i	−0.501382	−	0.498614i
$55$	6.06554e15			0.0239465
$56$			1.38021e17i			0.455055i
$57$	−3.84206e17	−	3.83497e17i	−1.06124	−	1.05929i
$58$	−4.45233e17			−1.03349
$59$		−	3.93698e17i		−	0.770270i	−0.922860	−	0.385135i	$-0.874155\pi$
$59$		−	3.93698e17i		−	0.770270i	0.922860	−	0.385135i	$-0.125845\pi$
$60$	−1.76176e16	+	1.76501e16i	−0.0291363	+	0.0291901i
$61$	7.29236e17			1.02228			0.511140	−	0.859498i	$-0.329223\pi$
$61$	7.29236e17			1.02228			0.511140	+	0.859498i	$0.329223\pi$
$62$			3.88545e17i			0.462940i
$63$	−2.33969e15	−	1.26769e18i	−0.00237549	−	1.28709i
$64$	−1.44115e17			−0.125000
$65$			8.82670e16i			0.0655639i
$66$	−2.27862e17	−	2.27442e17i	−0.145289	−	0.145021i
$67$	−5.04483e17			−0.276757			−0.138378	−	0.990379i	$-0.544189\pi$
$67$	−5.04483e17			−0.276757			−0.138378	+	0.990379i	$0.544189\pi$
$68$			1.56027e18i			0.738090i
$69$	3.51817e17	−	3.52467e17i	0.143822	−	0.144088i
$70$	−2.12058e17			−0.0750713
$71$			6.11896e18i			1.87973i	0.341553	+	0.939863i	$0.389047\pi$
$71$			6.11896e18i			1.87973i	−0.341553	+	0.939863i	$0.610953\pi$
$72$	1.32367e18	−	2.44301e15i	0.353553	−	0.000652529i
$73$	9.17001e17			0.213374			0.106687	−	0.994293i	$-0.465976\pi$
$73$	9.17001e17			0.213374			0.106687	+	0.994293i	$0.465976\pi$
$74$		−	4.63780e18i		−	0.941879i
$75$	3.95852e18	+	3.95122e18i	0.702943	+	0.701647i
$76$	4.81988e18			0.749722
$77$		−	2.73766e18i		−	0.373656i
$78$	3.30978e18	−	3.31590e18i	0.397058	−	0.397791i
$79$	−7.30923e18			−0.771970			−0.385985	−	0.922505i	$-0.626138\pi$
$79$	−7.30923e18			−0.771970			−0.385985	+	0.922505i	$0.626138\pi$
$80$		−	2.21421e17i		−	0.0206215i
$81$	−1.21576e19	+	4.48770e16i	−0.999993	+	0.00369125i
$82$	−1.09721e19			−0.798274
$83$		−	1.57590e19i		−	1.01566i	−0.861458	−	0.507829i	$-0.830448\pi$
$83$		−	1.57590e19i		−	1.01566i	0.861458	−	0.507829i	$-0.169552\pi$
$84$	7.96631e18	+	7.95162e18i	0.455475	+	0.454635i
$85$	−2.39722e18			−0.121764
$86$		−	1.65472e19i		−	0.747721i
$87$	−2.56507e19	+	2.56981e19i	−1.03254	+	1.03445i
$88$	2.85854e18			0.102640
$89$		−	2.49058e19i		−	0.798732i	−0.916792	−	0.399366i	$-0.869230\pi$
$89$		−	2.49058e19i		−	0.798732i	0.916792	−	0.399366i	$-0.130770\pi$
$90$	3.75348e15	+	2.03371e18i	0.000107649	+	0.0583263i
$91$	3.98389e19			1.02304
$92$			4.42171e18i			0.101792i
$93$	2.24261e19	+	2.23848e19i	0.463367	+	0.462513i
$94$	−1.60859e19			−0.298653
$95$			7.40536e18i			0.123683i
$96$	−8.30274e18	+	8.31807e18i	−0.124885	+	0.125115i
$97$	8.81363e19			1.19519			0.597596	−	0.801798i	$-0.296123\pi$
$97$	8.81363e19			1.19519			0.597596	+	0.801798i	$0.296123\pi$
$98$			3.79356e19i			0.464286i
$99$	−2.62551e19	+	4.84573e16i	−0.290310	+	0.000535806i
$100$	−4.96598e19			−0.496598
$101$		−	3.79360e19i		−	0.343430i	−0.985147	−	0.171715i	$-0.945069\pi$
$101$		−	3.79360e19i		−	0.343430i	0.985147	−	0.171715i	$-0.0549308\pi$
$102$	9.00557e19	+	8.98897e19i	0.738771	+	0.737409i
$103$	6.07442e19			0.451994			0.225997	−	0.974128i	$-0.427436\pi$
$103$	6.07442e19			0.451994			0.225997	+	0.974128i	$0.427436\pi$
$104$			4.15981e19i			0.281022i
$105$	−1.22170e19	+	1.22396e19i	−0.0750019	+	0.0751405i
$106$	−2.45112e20			−1.36869
$107$		−	1.68003e20i		−	0.854043i	−0.904241	−	0.427021i	$-0.859563\pi$
$107$		−	1.68003e20i		−	0.854043i	0.904241	−	0.427021i	$-0.140437\pi$
$108$	7.61179e19	−	7.65405e19i	0.352573	−	0.354531i
$109$	−1.05514e20			−0.445701			−0.222850	−	0.974853i	$-0.571536\pi$
$109$	−1.05514e20			−0.445701			−0.222850	+	0.974853i	$0.571536\pi$
$110$			4.39192e18i			0.0169328i
$111$	−2.67686e20	−	2.67192e20i	−0.942748	−	0.941010i
$112$	−9.99376e19			−0.321772
$113$			2.96849e20i			0.874481i	0.899345	+	0.437241i	$0.144044\pi$
$113$			2.96849e20i			0.874481i	−0.899345	+	0.437241i	$0.855956\pi$
$114$	2.77682e20	−	2.78195e20i	0.749030	−	0.750413i
$115$	−6.79361e18			−0.0167928
$116$		−	3.22383e20i		−	0.730790i
$117$	−7.05161e17	−	3.82070e20i	−0.00146700	−	0.794848i
$118$	2.85068e20			0.544663
$119$			1.08198e21i			1.89998i
$120$	−1.27801e19	−	1.27565e19i	−0.0206405	−	0.0206024i
$121$	6.16051e20			0.915720
$122$			5.28023e20i			0.722861i
$123$	−6.32123e20	+	6.33291e20i	−0.797537	+	0.799010i
$124$	−2.81337e20			−0.327348
$125$		−	1.53119e20i		−	0.164411i
$126$	9.17907e20	−	1.69412e18i	0.910108	−	0.00167973i
$127$	−2.54380e18			−0.00233048			−0.00116524	−	0.999999i	$-0.500371\pi$
$127$	−2.54380e18			−0.00233048			−0.00116524	+	0.999999i	$0.500371\pi$
$128$		−	1.04351e20i		−	0.0883883i
$129$	−9.55075e20	−	9.53314e20i	−0.748411	−	0.747031i
$130$	−6.39121e19			−0.0463607
$131$			1.41992e21i			0.954005i	0.878902	+	0.477003i	$0.158277\pi$
$131$			1.41992e21i			0.954005i	−0.878902	+	0.477003i	$0.841723\pi$
$132$	1.64686e20	−	1.64990e20i	0.102545	−	0.102735i
$133$	3.34238e21			1.92992
$134$		−	3.65285e20i		−	0.195697i
$135$	1.17598e20	+	1.16949e20i	0.0584876	+	0.0581647i
$136$	−1.12975e21			−0.521908
$137$		−	4.18638e21i		−	1.79735i	−0.438613	−	0.898676i	$-0.644530\pi$
$137$		−	4.18638e21i		−	1.79735i	0.438613	−	0.898676i	$-0.355470\pi$
$138$	2.55213e20	+	2.54743e20i	0.101886	+	0.101698i
$139$	−4.37665e21			−1.62552			−0.812762	−	0.582595i	$-0.802037\pi$
$139$	−4.37665e21			−1.62552			−0.812762	+	0.582595i	$0.802037\pi$
$140$		−	1.53546e20i		−	0.0530834i
$141$	−9.26738e20	+	9.28450e20i	−0.298377	+	0.298929i
$142$	−4.43060e21			−1.32917
$143$		−	8.25103e20i		−	0.230753i
$144$	1.76893e18	+	9.58438e20i	0.000461407	+	0.250000i
$145$	4.95316e20			0.120560
$146$			6.63980e20i			0.150878i
$147$	2.18957e21	+	2.18554e21i	0.464715	+	0.463858i
$148$	3.35813e21			0.666009
$149$		−	5.43464e21i		−	1.00765i	−0.863807	−	0.503823i	$-0.831927\pi$
$149$		−	5.43464e21i		−	1.00765i	0.863807	−	0.503823i	$-0.168073\pi$
$150$	−2.86099e21	+	2.86628e21i	−0.496140	+	0.497056i
$151$	2.46101e21			0.399342			0.199671	−	0.979863i	$-0.436013\pi$
$151$	2.46101e21			0.399342			0.199671	+	0.979863i	$0.436013\pi$
$152$			3.48996e21i			0.530133i
$153$	1.03765e22	−	1.91513e19i	1.47618	−	0.00272448i
$154$	1.98227e21			0.264214
$155$		−	4.32252e20i		−	0.0540032i
$156$	2.40097e21	+	2.39654e21i	0.281281	+	0.280762i
$157$	6.22259e21			0.683872			0.341936	−	0.939723i	$-0.388917\pi$
$157$	6.22259e21			0.683872			0.341936	+	0.939723i	$0.388917\pi$
$158$		−	5.29245e21i		−	0.545866i
$159$	−1.41213e22	+	1.41474e22i	−1.36743	+	1.36995i
$160$	1.60326e20			0.0145816
$161$			3.06627e21i			0.262030i
$162$	−3.24944e19	−	8.80303e21i	−0.00261011	−	0.707102i
$163$	−1.11796e22			−0.844407			−0.422203	−	0.906501i	$-0.638743\pi$
$163$	−1.11796e22			−0.844407			−0.422203	+	0.906501i	$0.638743\pi$
$164$		−	7.94466e21i		−	0.564465i
$165$	2.53494e20	+	2.53026e20i	0.0169484	+	0.0169171i
$166$	1.14107e22			0.718178
$167$			1.73774e22i			1.02996i	0.857203	+	0.514979i	$0.172200\pi$
$167$			1.73774e22i			1.02996i	−0.857203	+	0.514979i	$0.827800\pi$
$168$	−5.75759e21	+	5.76822e21i	−0.321475	+	0.322069i
$169$	−6.99790e21			−0.368215
$170$		−	1.73577e21i		−	0.0861002i
$171$	−5.91610e19	−	3.20546e22i	−0.00276742	−	1.49944i
$172$	1.19814e22			0.528719
$173$		−	7.77319e21i		−	0.323697i	−0.986816	−	0.161848i	$-0.948254\pi$
$173$		−	7.77319e21i		−	0.323697i	0.986816	−	0.161848i	$-0.0517455\pi$
$174$	−1.86074e22	−	1.85731e22i	−0.731465	−	0.730116i
$175$	−3.44369e22			−1.27833
$176$			2.06980e21i			0.0725776i
$177$	1.64233e22	−	1.64536e22i	0.544160	−	0.545165i
$178$	1.80338e22			0.564789
$179$			7.39680e21i			0.219035i	0.993985	+	0.109518i	$0.0349306\pi$
$179$			7.39680e21i			0.219035i	−0.993985	+	0.109518i	$0.965069\pi$
$180$	−1.47256e21	+	2.71781e18i	−0.0412429	+	7.61192e-5i
$181$	−1.29288e22			−0.342589			−0.171295	−	0.985220i	$-0.554795\pi$
$181$	−1.29288e22			−0.342589			−0.171295	+	0.985220i	$0.554795\pi$
$182$			2.88465e22i			0.723400i
$183$	3.04766e22	+	3.04204e22i	0.723528	+	0.722193i
$184$	−3.20166e21			−0.0719776
$185$			5.15950e21i			0.109873i
$186$	−1.62083e22	+	1.62383e22i	−0.327046	+	0.327650i
$187$	2.24088e22			0.428551
$188$		−	1.16474e22i		−	0.211180i
$189$	5.27845e22	−	5.30776e22i	0.907587	−	0.912626i
$190$	−5.36205e21			−0.0874571
$191$			1.13683e23i			1.75939i	0.475539	+	0.879695i	$0.342253\pi$
$191$			1.13683e23i			1.75939i	−0.475539	+	0.879695i	$0.657747\pi$
$192$	−6.02293e21	−	6.01182e21i	−0.0884699	−	0.0883067i
$193$	4.54944e22			0.634432			0.317216	−	0.948353i	$-0.397252\pi$
$193$	4.54944e22			0.634432			0.317216	+	0.948353i	$0.397252\pi$
$194$			6.38175e22i			0.845128i
$195$	−3.68209e21	+	3.68889e21i	−0.0463179	+	0.0464034i
$196$	−2.74683e22			−0.328300
$197$		−	4.92490e22i		−	0.559416i	−0.960085	−	0.279708i	$-0.909762\pi$
$197$		−	4.92490e22i		−	0.559416i	0.960085	−	0.279708i	$-0.0902377\pi$
$198$	−3.50868e19	−	1.90107e22i	−0.000378872	−	0.205280i
$199$	−5.74544e22			−0.589919			−0.294960	−	0.955510i	$-0.595306\pi$
$199$	−5.74544e22			−0.589919			−0.294960	+	0.955510i	$0.595306\pi$
$200$		−	3.59575e22i		−	0.351148i
$201$	−2.10836e22	−	2.10447e22i	−0.195877	−	0.195516i
$202$	2.74686e22			0.242842
$203$		−	2.23559e23i		−	1.88119i
$204$	−6.50871e22	+	6.52073e22i	−0.521427	+	0.522390i
$205$	1.22063e22			0.0931208
$206$			4.39835e22i			0.319608i
$207$	2.94066e22	−	5.42738e19i	0.203583	−	0.000375739i
$208$	−3.01202e22			−0.198712
$209$		−	6.92238e22i		−	0.435304i
$210$	−8.86241e21	−	8.84607e21i	−0.0531324	−	0.0530344i
$211$	1.23285e22			0.0704832			0.0352416	−	0.999379i	$-0.488780\pi$
$211$	1.23285e22			0.0704832			0.0352416	+	0.999379i	$0.488780\pi$
$212$		−	1.77480e23i		−	0.967811i
$213$	−2.55255e23	+	2.55727e23i	−1.32794	+	1.33039i
$214$	1.21647e23			0.603900
$215$			1.84085e22i			0.0872237i
$216$	5.54213e22	+	5.51153e22i	0.250691	+	0.249307i
$217$	−1.95095e23			−0.842653
$218$		−	7.64000e22i		−	0.315158i
$219$	3.83237e22	+	3.82531e22i	0.151017	+	0.150739i
$220$	−3.18009e21			−0.0119733
$221$			3.26097e23i			1.17334i
$222$	1.93468e23	−	1.93825e23i	0.665394	−	0.666624i
$223$	2.77290e23			0.911771			0.455885	−	0.890039i	$-0.349323\pi$
$223$	2.77290e23			0.911771			0.455885	+	0.890039i	$0.349323\pi$
$224$		−	7.23626e22i		−	0.227527i
$225$	6.09544e20	+	3.30263e23i	0.00183307	+	0.993194i
$226$	−2.14941e23			−0.618352
$227$		−	3.44678e23i		−	0.948758i	−0.880321	−	0.474379i	$-0.842673\pi$
$227$		−	3.44678e23i		−	0.948758i	0.880321	−	0.474379i	$-0.157327\pi$
$228$	2.01435e23	+	2.01063e23i	0.530622	+	0.529644i
$229$	3.61164e23			0.910647			0.455323	−	0.890326i	$-0.349524\pi$
$229$	3.61164e23			0.910647			0.455323	+	0.890326i	$0.349524\pi$
$230$		−	4.91910e21i		−	0.0118743i
$231$	1.14202e23	−	1.14413e23i	0.263971	−	0.264458i
$232$	2.33431e23			0.516747
$233$			3.43352e23i			0.728082i	0.931383	+	0.364041i	$0.118603\pi$
$233$			3.43352e23i			0.728082i	−0.931383	+	0.364041i	$0.881397\pi$
$234$	2.76648e23	−	5.10591e20i	0.562042	−	0.00103732i
$235$	1.78954e22			0.0348387
$236$			2.06411e23i			0.385135i
$237$	−3.05471e23	−	3.04907e23i	−0.546369	−	0.545362i
$238$	−7.83435e23			−1.34349
$239$		−	2.16021e23i		−	0.355236i	−0.984100	−	0.177618i	$-0.943161\pi$
$239$		−	2.16021e23i		−	0.355236i	0.984100	−	0.177618i	$-0.0568391\pi$
$240$	9.23669e21	−	9.25375e21i	0.0145681	−	0.0145950i
$241$	−9.22135e23			−1.39516			−0.697580	−	0.716506i	$-0.745740\pi$
$241$	−9.22135e23			−1.39516			−0.697580	+	0.716506i	$0.745740\pi$
$242$			4.46068e23i			0.647512i
$243$	−5.09967e23	−	5.05283e23i	−0.710362	−	0.703837i
$244$	−3.82330e23			−0.511140
$245$		−	4.22028e22i		−	0.0541603i
$246$	−4.58552e23	−	4.57706e23i	−0.564985	−	0.563944i
$247$	1.00736e24			1.19183
$248$		−	2.03710e23i		−	0.231470i
$249$	6.57392e23	−	6.58607e23i	0.717515	−	0.718841i
$250$	1.10870e23			0.116256
$251$		−	2.06405e23i		−	0.207962i	−0.994579	−	0.103981i	$-0.966842\pi$
$251$		−	2.06405e23i		−	0.207962i	0.994579	−	0.103981i	$-0.0331580\pi$
$252$	1.22667e21	+	6.64635e23i	0.00118775	+	0.643544i
$253$	6.35053e22			0.0591024
$254$		−	1.84191e21i		−	0.00164790i
$255$	−1.00186e23	−	1.00001e23i	−0.0861796	−	0.0860207i
$256$	7.55579e22			0.0625000
$257$			6.45642e23i			0.513642i	0.966459	+	0.256821i	$0.0826750\pi$
$257$			6.45642e23i			0.513642i	−0.966459	+	0.256821i	$0.917325\pi$
$258$	6.90273e23	−	6.91548e23i	0.528231	−	0.529207i
$259$	2.32872e24			1.71443
$260$		−	4.62773e22i		−	0.0327819i
$261$	−2.14401e24	+	3.95706e21i	−1.46158	+	0.00269754i
$262$	−1.02813e24			−0.674584
$263$			1.51145e24i			0.954631i	0.878732	+	0.477316i	$0.158390\pi$
$263$			1.51145e24i			0.954631i	−0.878732	+	0.477316i	$0.841610\pi$
$264$	1.19465e23	+	1.19245e23i	0.0726446	+	0.0725106i
$265$	2.72684e23			0.159662
$266$			2.42014e24i			1.36466i
$267$	1.03896e24	−	1.04088e24i	0.564268	−	0.565310i
$268$	2.64494e23			0.138378
$269$			3.30874e23i			0.166779i	0.996517	+	0.0833893i	$0.0265745\pi$
$269$			3.30874e23i			0.166779i	−0.996517	+	0.0833893i	$0.973425\pi$
$270$	−8.46802e22	+	8.51504e22i	−0.0411286	+	0.0413570i
$271$	−2.87491e24			−1.34565			−0.672824	−	0.739803i	$-0.734919\pi$
$271$	−2.87491e24			−1.34565			−0.672824	+	0.739803i	$0.734919\pi$
$272$		−	8.18028e23i		−	0.369045i
$273$	1.66497e24	+	1.66190e24i	0.724068	+	0.722732i
$274$	3.03126e24			1.27092
$275$			7.13222e23i			0.288335i
$276$	−1.84453e23	+	1.84794e23i	−0.0719111	+	0.0720440i
$277$	1.28399e24			0.482797			0.241398	−	0.970426i	$-0.422394\pi$
$277$	1.28399e24			0.482797			0.241398	+	0.970426i	$0.422394\pi$
$278$		−	3.16903e24i		−	1.14942i
$279$	3.45324e21	+	1.87103e24i	0.00120833	+	0.654695i
$280$	1.11179e23			0.0375356
$281$		−	2.56237e24i		−	0.834793i	−0.908724	−	0.417397i	$-0.862943\pi$
$281$		−	2.56237e24i		−	0.834793i	0.908724	−	0.417397i	$-0.137057\pi$
$282$	−6.72270e23	−	6.71030e23i	−0.211374	−	0.210985i
$283$	−5.83054e24			−1.76947			−0.884737	−	0.466090i	$-0.845662\pi$
$283$	−5.83054e24			−1.76947			−0.884737	+	0.466090i	$0.845662\pi$
$284$		−	3.20810e24i		−	0.939863i
$285$	−3.08917e23	+	3.09488e23i	−0.0873763	+	0.0875377i
$286$	5.97438e23			0.163167
$287$		−	5.50928e24i		−	1.45303i
$288$	−6.93984e23	+	1.28084e21i	−0.176776	+	0.000326264i
$289$	−4.79216e24			−1.17911
$290$			3.58647e23i			0.0852487i
$291$	3.68343e24	+	3.67664e24i	0.845907	+	0.844347i
$292$	−4.80773e23			−0.106687
$293$			1.20765e24i			0.258979i	0.991581	+	0.129489i	$0.0413338\pi$
$293$			1.20765e24i			0.258979i	−0.991581	+	0.129489i	$0.958666\pi$
$294$	−1.58250e24	+	1.58542e24i	−0.327997	+	0.328603i
$295$	−3.17134e23			−0.0635364
$296$			2.43155e24i			0.470940i
$297$	−1.09929e24	−	1.09322e24i	−0.205848	−	0.204711i
$298$	3.93510e24			0.712513
$299$			9.24142e23i			0.161818i
$300$	−2.07541e24	−	2.07158e24i	−0.351472	−	0.350824i
$301$	8.30862e24			1.36102
$302$			1.78196e24i			0.282377i
$303$	1.58252e24	−	1.58544e24i	0.242618	−	0.243066i
$304$	−2.52700e24			−0.374861
$305$		−	5.87419e23i		−	0.0843237i
$306$	1.38670e22	+	7.51342e24i	0.00192650	+	1.04382i
$307$	−1.19854e24			−0.161164			−0.0805822	−	0.996748i	$-0.525678\pi$
$307$	−1.19854e24			−0.161164			−0.0805822	+	0.996748i	$0.525678\pi$
$308$			1.43532e24i			0.186828i
$309$	2.53865e24	+	2.53397e24i	0.319903	+	0.319313i
$310$	3.12984e23			0.0381860
$311$		−	9.58705e23i		−	0.113261i	−0.998395	−	0.0566306i	$-0.981964\pi$
$311$		−	9.58705e23i		−	0.113261i	0.998395	−	0.0566306i	$-0.0180357\pi$
$312$	−1.73528e24	+	1.73849e24i	−0.198529	+	0.198896i
$313$	1.25498e25			1.39057			0.695284	−	0.718736i	$-0.255279\pi$
$313$	1.25498e25			1.39057			0.695284	+	0.718736i	$0.255279\pi$
$314$			4.50564e24i			0.483570i
$315$	−1.02116e24	+	1.88469e21i	−0.106167	+	0.000195945i
$316$	3.83214e24			0.385985
$317$		−	9.84338e24i		−	0.960620i	−0.877099	−	0.480310i	$-0.840524\pi$
$317$		−	9.84338e24i		−	0.960620i	0.877099	−	0.480310i	$-0.159476\pi$
$318$	−1.02438e25	−	1.02249e25i	−0.968703	−	0.966917i
$319$	−4.63012e24			−0.424312
$320$			1.16089e23i			0.0103107i
$321$	7.00832e24	−	7.02127e24i	0.603342	−	0.604457i
$322$	−2.22021e24			−0.185283
$323$			2.73586e25i			2.21345i
$324$	6.37407e24	−	2.35285e22i	0.499997	−	0.00184563i
$325$	−1.03790e25			−0.789441
$326$		−	8.09492e24i		−	0.597086i
$327$	−4.40967e24	−	4.40154e24i	−0.315449	−	0.314867i
$328$	5.75255e24			0.399137
$329$		−	8.07700e24i		−	0.543614i
$330$	−1.83211e23	+	1.83549e23i	−0.0119622	+	0.0119843i
$331$	−1.77602e25			−1.12504			−0.562520	−	0.826784i	$-0.690168\pi$
$331$	−1.77602e25			−1.12504			−0.562520	+	0.826784i	$0.690168\pi$
$332$			8.26225e24i			0.507829i
$333$	−4.12190e22	−	2.23332e25i	−0.00245841	−	1.33202i
$334$	−1.25826e25			−0.728290
$335$			4.06374e23i			0.0228285i
$336$	−4.17664e24	−	4.16894e24i	−0.227737	−	0.227317i
$337$	−4.77958e24			−0.252983			−0.126491	−	0.991968i	$-0.540372\pi$
$337$	−4.77958e24			−0.252983			−0.126491	+	0.991968i	$0.540372\pi$
$338$		−	5.06702e24i		−	0.260367i
$339$	−1.23832e25	+	1.24060e25i	−0.617781	+	0.618922i
$340$	1.25684e24			0.0608820
$341$			4.04060e24i			0.190065i
$342$	2.32100e25	−	4.28372e22i	1.06026	−	0.00195686i
$343$	9.96209e24			0.441987
$344$			8.67550e24i			0.373861i
$345$	−2.83922e23	−	2.83398e23i	−0.0118852	−	0.0118633i
$346$	5.62839e24			0.228888
$347$			1.74076e25i			0.687773i	0.939011	+	0.343887i	$0.111744\pi$
$347$			1.74076e25i			0.687773i	−0.939011	+	0.343887i	$0.888256\pi$
$348$	1.34484e25	−	1.34732e25i	0.516270	−	0.517224i
$349$	2.19322e25			0.818141			0.409071	−	0.912503i	$-0.365853\pi$
$349$	2.19322e25			0.818141			0.409071	+	0.912503i	$0.365853\pi$
$350$		−	2.49350e25i		−	0.903918i
$351$	1.59087e25	−	1.59971e25i	0.560485	−	0.563597i
$352$	−1.49870e24			−0.0513201
$353$			2.59460e25i			0.863621i	0.901964	+	0.431811i	$0.142125\pi$
$353$			2.59460e25i			0.863621i	−0.901964	+	0.431811i	$0.857875\pi$
$354$	1.19137e25	+	1.18917e25i	0.385490	+	0.384779i
$355$	4.92899e24			0.155051
$356$			1.30578e25i			0.399366i
$357$	−4.51351e25	+	4.52185e25i	−1.34225	+	1.34473i
$358$	−5.35586e24			−0.154881
$359$		−	4.81350e24i		−	0.135368i	−0.997707	−	0.0676841i	$-0.978439\pi$
$359$		−	4.81350e24i		−	0.135368i	0.997707	−	0.0676841i	$-0.0215610\pi$
$360$	−1.96791e21	−	1.06625e24i	−5.38244e−5	−	0.0291631i
$361$	4.69247e25			1.24833
$362$		−	9.36148e24i		−	0.242247i
$363$	2.57463e25	+	2.56988e25i	0.648109	+	0.646914i
$364$	−2.08871e25			−0.511521
$365$		−	7.38669e23i		−	0.0176003i
$366$	−2.20267e25	+	2.20674e25i	−0.510668	+	0.511611i
$367$	−4.68969e25			−1.05799			−0.528997	−	0.848624i	$-0.677432\pi$
$367$	−4.68969e25			−1.05799			−0.528997	+	0.848624i	$0.677432\pi$
$368$		−	2.31825e24i		−	0.0508958i
$369$	−5.28360e25	+	9.75158e22i	−1.12893	+	0.00208359i
$370$	−3.73588e24			−0.0776918
$371$		−	1.23075e26i		−	2.49132i
$372$	−1.17578e25	−	1.17361e25i	−0.231683	−	0.231256i
$373$	1.87545e25			0.359764			0.179882	−	0.983688i	$-0.442428\pi$
$373$	1.87545e25			0.359764			0.179882	+	0.983688i	$0.442428\pi$
$374$			1.62257e25i			0.303031i
$375$	6.38743e24	−	6.39923e24i	0.116149	−	0.116363i
$376$	8.43365e24			0.149327
$377$		−	6.73785e25i		−	1.16174i
$378$	3.84323e25	+	3.82200e25i	0.645324	+	0.641761i
$379$	7.50824e25			1.22785			0.613926	−	0.789363i	$-0.289589\pi$
$379$	7.50824e25			1.22785			0.613926	+	0.789363i	$0.289589\pi$
$380$		−	3.88254e24i		−	0.0618415i
$381$	−1.06312e23	−	1.06116e23i	−0.00164942	−	0.00164638i
$382$	−8.23153e25			−1.24408
$383$			4.04145e24i			0.0595044i	0.999557	+	0.0297522i	$0.00947182\pi$
$383$			4.04145e24i			0.0595044i	−0.999557	+	0.0297522i	$0.990528\pi$
$384$	4.35302e24	−	4.36107e24i	0.0624423	−	0.0625576i
$385$	−2.20525e24			−0.0308213
$386$			3.29415e25i			0.448611i
$387$	−1.47065e23	−	7.96826e25i	−0.00195164	−	1.05744i
$388$	−4.62088e25			−0.597596
$389$			4.28049e25i			0.539508i	0.962929	+	0.269754i	$0.0869424\pi$
$389$			4.28049e25i			0.539508i	−0.962929	+	0.269754i	$0.913058\pi$
$390$	−2.67104e24	−	2.66612e24i	−0.0328122	−	0.0327517i
$391$	−2.50986e25			−0.300526
$392$		−	1.98892e25i		−	0.232143i
$393$	−5.92325e25	+	5.93419e25i	−0.673961	+	0.675206i
$394$	3.56601e25			0.395567
$395$			5.88778e24i			0.0636767i
$396$	1.37652e25	−	2.54056e22i	0.145155	−	0.000267903i
$397$	−4.70070e25			−0.483346			−0.241673	−	0.970358i	$-0.577696\pi$
$397$	−4.70070e25			−0.483346			−0.241673	+	0.970358i	$0.577696\pi$
$398$		−	4.16014e25i		−	0.417136i
$399$	1.39686e26	+	1.39429e26i	1.36592	+	1.36340i
$400$	2.60360e25			0.248299
$401$			1.50490e26i			1.39979i	0.714246	+	0.699895i	$0.246770\pi$
$401$			1.50490e26i			1.39979i	−0.714246	+	0.699895i	$0.753230\pi$
$402$	1.52380e25	−	1.52661e25i	0.138251	−	0.138506i
$403$	−5.87997e25			−0.520385
$404$			1.98894e25i			0.171715i
$405$	3.61496e22	+	9.79326e24i	0.000304476	+	0.0824854i
$406$	1.61874e26			1.33020
$407$		−	4.82300e25i		−	0.386699i
$408$	−4.72151e25	−	4.71281e25i	−0.369385	−	0.368704i
$409$	9.99015e25			0.762674			0.381337	−	0.924436i	$-0.375464\pi$
$409$	9.99015e25			0.762674			0.381337	+	0.924436i	$0.375464\pi$
$410$			8.83833e24i			0.0658463i
$411$	1.74637e26	−	1.74959e26i	1.26975	−	1.27209i
$412$	−3.18475e25			−0.225997
$413$			1.43137e26i			0.991406i
$414$	3.92984e22	+	2.12927e25i	0.000265688	+	0.143955i
$415$	−1.26943e25			−0.0837774
$416$		−	2.18094e25i		−	0.140511i
$417$	−1.82911e26	−	1.82574e26i	−1.15048	−	1.14836i
$418$	5.01234e25			0.307807
$419$			1.68130e26i			1.00810i	0.863673	+	0.504052i	$0.168158\pi$
$419$			1.68130e26i			1.00810i	−0.863673	+	0.504052i	$0.831842\pi$
$420$	6.40524e24	−	6.41707e24i	0.0375010	−	0.0375703i
$421$	−2.69174e26			−1.53891			−0.769454	−	0.638702i	$-0.779471\pi$
$421$	−2.69174e26			−1.53891			−0.769454	+	0.638702i	$0.779471\pi$
$422$			8.92679e24i			0.0498392i
$423$	−7.74613e25	+	1.42965e23i	−0.422359	+	0.000779519i
$424$	1.28509e26			0.684345
$425$		−	2.81880e26i		−	1.46614i
$426$	−1.85166e26	−	1.84824e26i	−0.940730	−	0.938995i
$427$	−2.65129e26			−1.31577
$428$			8.80821e25i			0.427021i
$429$	3.44195e25	−	3.44831e25i	0.163016	−	0.163318i
$430$	−1.33292e25			−0.0616765
$431$			2.03349e26i			0.919325i	0.888094	+	0.459663i	$0.152030\pi$
$431$			2.03349e26i			0.919325i	−0.888094	+	0.459663i	$0.847970\pi$
$432$	−3.99077e25	+	4.01293e25i	−0.176287	+	0.177265i
$433$	2.77208e26			1.19654			0.598269	−	0.801296i	$-0.295856\pi$
$433$	2.77208e26			1.19654			0.598269	+	0.801296i	$0.295856\pi$
$434$		−	1.41264e26i		−	0.595845i
$435$	2.07005e25	+	2.06623e25i	0.0853273	+	0.0851700i
$436$	5.53195e25			0.222850
$437$			7.75330e25i			0.305262i
$438$	−2.76982e25	+	2.77493e25i	−0.106588	+	0.106785i
$439$	1.39900e26			0.526227			0.263113	−	0.964765i	$-0.415251\pi$
$439$	1.39900e26			0.526227			0.263113	+	0.964765i	$0.415251\pi$
$440$		−	2.30263e24i		−	0.00846638i
$441$	3.37156e23	+	1.82678e26i	0.00121184	+	0.656599i
$442$	−2.36119e26			−0.829677
$443$		−	3.90868e26i		−	1.34274i	−0.741121	−	0.671372i	$-0.765705\pi$
$443$		−	3.90868e26i		−	1.34274i	0.741121	−	0.671372i	$-0.234295\pi$
$444$	1.40344e26	+	1.40086e26i	0.471374	+	0.470505i
$445$	−2.00623e25			−0.0658842
$446$			2.00779e26i			0.644719i
$447$	2.26708e26	−	2.27127e26i	0.711855	−	0.713170i
$448$	5.23961e25			0.160886
$449$			1.44307e26i			0.433337i	0.976245	+	0.216668i	$0.0695190\pi$
$449$			1.44307e26i			0.433337i	−0.976245	+	0.216668i	$0.930481\pi$
$450$	−2.39136e26	+	4.41357e23i	−0.702294	+	0.00129618i
$451$	−1.14102e26			−0.327740
$452$		−	1.55634e26i		−	0.437241i
$453$	1.02852e26	+	1.02662e26i	0.282638	+	0.282116i
$454$	2.49574e26			0.670873
$455$		−	3.20913e25i		−	0.0843866i
$456$	−1.45585e26	+	1.45854e26i	−0.374515	+	0.375207i
$457$	4.81844e26			1.21267			0.606337	−	0.795208i	$-0.292638\pi$
$457$	4.81844e26			1.21267			0.606337	+	0.795208i	$0.292638\pi$
$458$			2.61511e26i			0.643925i
$459$	4.34460e26	+	4.32061e26i	1.04670	+	1.04092i
$460$	3.56181e24			0.00839638
$461$		−	2.75250e26i		−	0.634918i	−0.948272	−	0.317459i	$-0.897170\pi$
$461$		−	2.75250e26i		−	0.634918i	0.948272	−	0.317459i	$-0.102830\pi$
$462$	8.28441e25	+	8.26914e25i	0.187000	+	0.186655i
$463$	−4.81179e26			−1.06291			−0.531456	−	0.847086i	$-0.678355\pi$
$463$	−4.81179e26			−1.06291			−0.531456	+	0.847086i	$0.678355\pi$
$464$			1.69022e26i			0.365395i
$465$	1.80315e25	−	1.80649e25i	0.0381508	−	0.0382213i
$466$	−2.48613e26			−0.514832
$467$		−	3.81939e26i		−	0.774150i	−0.922048	−	0.387075i	$-0.873485\pi$
$467$		−	3.81939e26i		−	0.774150i	0.922048	−	0.387075i	$-0.126515\pi$
$468$	3.69707e23	+	2.00315e26i	0.000733499	+	0.397424i
$469$	1.83415e26			0.356211
$470$			1.29576e25i			0.0246347i
$471$	2.60057e26	+	2.59578e26i	0.484016	+	0.483124i
$472$	−1.49458e26			−0.272331
$473$		−	1.72079e26i		−	0.306985i
$474$	2.20777e26	−	2.21184e26i	0.385629	−	0.386341i
$475$	−8.70765e26			−1.48924
$476$		−	5.67267e26i		−	0.949988i
$477$	−1.18033e27	+	2.17846e24i	−1.93562	+	0.00357244i
$478$	1.56416e26			0.251190
$479$			3.81517e25i			0.0600011i	0.999550	+	0.0300005i	$0.00955090\pi$
$479$			3.81517e25i			0.0600011i	−0.999550	+	0.0300005i	$0.990449\pi$
$480$	6.70043e24	+	6.68807e24i	0.0103203	+	0.0103012i
$481$	7.01852e26			1.05875
$482$		−	6.67697e26i		−	0.986528i
$483$	−1.27910e26	+	1.28147e26i	−0.185112	+	0.185454i
$484$	−3.22988e26			−0.457860
$485$		−	7.09961e25i		−	0.0985864i
$486$	3.65864e26	−	3.69256e26i	0.497688	−	0.502302i
$487$	−1.00915e27			−1.34483			−0.672413	−	0.740176i	$-0.734742\pi$
$487$	−1.00915e27			−1.34483			−0.672413	+	0.740176i	$0.734742\pi$
$488$		−	2.76836e26i		−	0.361430i
$489$	−4.67225e26	−	4.66363e26i	−0.597637	−	0.596535i
$490$	3.05581e25			0.0382971
$491$			1.48221e27i			1.82009i	0.414505	+	0.910047i	$0.363955\pi$
$491$			1.48221e27i			1.82009i	−0.414505	+	0.910047i	$0.636045\pi$
$492$	3.31415e26	−	3.32027e26i	0.398768	−	0.399505i
$493$	1.82992e27			2.15756
$494$			7.29406e26i			0.842752i
$495$	3.90337e22	+	2.11492e25i	4.41964e−5	+	0.0239465i
$496$	1.47502e26			0.163674
$497$		−	2.22468e27i		−	2.41938i
$498$	4.76882e26	+	4.76003e26i	0.508297	+	0.507360i
$499$	3.86304e26			0.403575			0.201788	−	0.979429i	$-0.435325\pi$
$499$	3.86304e26			0.403575			0.201788	+	0.979429i	$0.435325\pi$
$500$			8.02786e25i			0.0822053i
$501$	−7.24904e26	+	7.26243e26i	−0.727618	+	0.728962i
$502$	1.49453e26			0.147051
$503$			1.39761e27i			1.34805i	0.738708	+	0.674026i	$0.235436\pi$
$503$			1.39761e27i			1.34805i	−0.738708	+	0.674026i	$0.764564\pi$
$504$	−4.81247e26	+	8.88206e23i	−0.455054	+	0.000839863i
$505$	−3.05585e25			−0.0283281
$506$			4.59828e25i			0.0417917i
$507$	−2.92460e26	−	2.91920e26i	−0.260607	−	0.260127i
$508$	1.33368e24			0.00116524
$509$			2.29175e27i			1.96331i	0.190665	+	0.981655i	$0.438936\pi$
$509$			2.29175e27i			1.96331i	−0.190665	+	0.981655i	$0.561064\pi$
$510$	7.24085e25	−	7.25423e25i	0.0608258	−	0.0609382i
$511$	−3.33395e26			−0.274631
$512$			5.47097e25i			0.0441942i
$513$	1.33470e27	−	1.34211e27i	1.05733	−	1.06320i
$514$	−4.67495e26			−0.363200
$515$		−	4.89311e25i		−	0.0372831i
$516$	5.00734e26	+	4.99811e26i	0.374206	+	0.373516i
$517$	−1.67282e26			−0.122615
$518$			1.68617e27i			1.21228i
$519$	3.24262e26	−	3.24861e26i	0.228677	−	0.229099i
$520$	3.35084e25			0.0231803
$521$			9.81031e26i			0.665741i	0.942973	+	0.332871i	$0.108017\pi$
$521$			9.81031e26i			0.665741i	−0.942973	+	0.332871i	$0.891983\pi$
$522$	−2.86522e24	−	1.55243e27i	−0.00190745	−	1.03349i
$523$	1.08594e27			0.709232			0.354616	−	0.935012i	$-0.384612\pi$
$523$	1.08594e27			0.709232			0.354616	+	0.935012i	$0.384612\pi$
$524$		−	7.44447e26i		−	0.477003i
$525$	−1.43920e27	−	1.43655e27i	−0.904751	−	0.903083i
$526$	−1.09440e27			−0.675026
$527$		−	1.59693e27i		−	0.966449i
$528$	−8.63427e25	+	8.65022e25i	−0.0512727	+	0.0513675i
$529$	1.64503e27			0.958554
$530$			1.97444e26i			0.112898i
$531$	1.37274e27	−	2.53357e24i	0.770268	−	0.00142163i
$532$	−1.75237e27			−0.964959
$533$		−	1.66044e27i		−	0.897329i
$534$	7.53675e26	+	7.52285e26i	0.399734	+	0.398997i
$535$	−1.35331e26			−0.0704465
$536$			1.91514e26i			0.0978483i
$537$	−3.08560e26	+	3.09131e26i	−0.154738	+	0.155024i
$538$	−2.39579e26			−0.117930
$539$			3.94504e26i			0.190618i
$540$	−6.16554e25	−	6.13150e25i	−0.0292438	−	0.0290823i
$541$	−3.41024e27			−1.58786			−0.793929	−	0.608010i	$-0.791968\pi$
$541$	−3.41024e27			−1.58786			−0.793929	+	0.608010i	$0.791968\pi$
$542$		−	2.08166e27i		−	0.951517i
$543$	−5.40328e26	−	5.39332e26i	−0.242471	−	0.242024i
$544$	5.92316e26			0.260954
$545$			8.49940e25i			0.0367640i
$546$	−1.20334e27	+	1.20556e27i	−0.511049	+	0.511993i
$547$	−2.62335e27			−1.09391			−0.546956	−	0.837161i	$-0.684214\pi$
$547$	−2.62335e27			−1.09391			−0.546956	+	0.837161i	$0.684214\pi$
$548$			2.19487e27i			0.898676i
$549$	4.69286e24	+	2.54268e27i	0.00188675	+	1.02228i
$550$	−5.16428e26			−0.203884
$551$		−	5.65287e27i		−	2.19156i
$552$	−1.33805e26	−	1.33559e26i	−0.0509428	−	0.0508488i
$553$	2.65742e27			0.993595
$554$			9.29709e26i			0.341389i
$555$	−2.15230e26	+	2.15628e26i	−0.0776201	+	0.0777634i
$556$	2.29462e27			0.812762
$557$			3.25407e27i			1.13208i	0.824379	+	0.566038i	$0.191524\pi$
$557$			3.25407e27i			1.13208i	−0.824379	+	0.566038i	$0.808476\pi$
$558$	−1.35477e27	+	2.50041e24i	−0.462939	+	0.000854416i
$559$	2.50414e27			0.840504
$560$			8.05024e25i			0.0265417i
$561$	9.36518e26	+	9.34791e26i	0.303310	+	0.302751i
$562$	1.85536e27			0.590288
$563$			3.38094e27i			1.05670i	0.849025	+	0.528352i	$0.177190\pi$
$563$			3.38094e27i			1.05670i	−0.849025	+	0.528352i	$0.822810\pi$
$564$	4.85878e26	−	4.86775e26i	0.149189	−	0.149464i
$565$	2.39119e26			0.0721324
$566$		−	4.22176e27i		−	1.25121i
$567$	4.42014e27	−	1.63160e25i	1.28708	−	0.00475097i
$568$	2.32291e27			0.664583
$569$		−	1.42049e27i		−	0.399316i	−0.979866	−	0.199658i	$-0.936017\pi$
$569$		−	1.42049e27i		−	0.399316i	0.979866	−	0.199658i	$-0.0639832\pi$
$570$	−2.24093e26	−	2.23680e26i	−0.0618985	−	0.0617844i
$571$	1.15178e25			0.00312614			0.00156307	−	0.999999i	$-0.499502\pi$
$571$	1.15178e25			0.00312614			0.00156307	+	0.999999i	$0.499502\pi$
$572$			4.32591e26i			0.115377i
$573$	−4.74233e27	+	4.75109e27i	−1.24293	+	1.24522i
$574$	3.98914e27			1.02745
$575$		−	7.98832e26i		−	0.202198i
$576$	−9.27426e23	−	5.02498e26i	−0.000230704	−	0.125000i
$577$	−4.17787e27			−1.02140			−0.510701	−	0.859759i	$-0.670614\pi$
$577$	−4.17787e27			−1.02140			−0.510701	+	0.859759i	$0.670614\pi$
$578$		−	3.46990e27i		−	0.833755i
$579$	1.90132e27	+	1.89782e27i	0.449025	+	0.448197i
$580$	−2.59688e26			−0.0602799
$581$			5.72951e27i			1.30724i
$582$	−2.66217e27	+	2.66709e27i	−0.597044	+	0.598147i
$583$	−2.54899e27			−0.561931
$584$		−	3.48117e26i		−	0.0754391i
$585$	−3.07767e26	+	5.68026e23i	−0.0655638	+	0.000121007i
$586$	−8.74431e26			−0.183126
$587$		−	6.55137e27i		−	1.34881i	−0.738361	−	0.674406i	$-0.764400\pi$
$587$		−	6.55137e27i		−	1.34881i	0.738361	−	0.674406i	$-0.235600\pi$
$588$	−1.14797e27	−	1.14585e27i	−0.232357	−	0.231929i
$589$	−4.93313e27			−0.981680
$590$		−	2.29630e26i		−	0.0449270i
$591$	2.05444e27	−	2.05824e27i	0.395202	−	0.395932i
$592$	−1.76063e27			−0.333005
$593$		−	7.48816e27i		−	1.39261i	−0.717748	−	0.696303i	$-0.754827\pi$
$593$		−	7.48816e27i		−	1.39261i	0.717748	−	0.696303i	$-0.245173\pi$
$594$	7.91574e26	−	7.95969e26i	0.144753	−	0.145557i
$595$	8.71561e26			0.156721
$596$			2.84931e27i			0.503823i
$597$	−2.40116e27	−	2.39673e27i	−0.417521	−	0.416751i
$598$	−6.69150e26			−0.114423
$599$			6.04562e27i			1.01665i	0.861165	+	0.508326i	$0.169736\pi$
$599$			6.04562e27i			1.01665i	−0.861165	+	0.508326i	$0.830264\pi$
$600$	1.49998e27	−	1.50275e27i	0.248070	−	0.248528i
$601$	3.88315e27			0.631596			0.315798	−	0.948827i	$-0.397728\pi$
$601$	3.88315e27			0.631596			0.315798	+	0.948827i	$0.397728\pi$
$602$			6.01608e27i			0.962385i
$603$	−3.24651e24	−	1.75902e27i	−0.000510791	−	0.276756i
$604$	−1.29028e27			−0.199671
$605$		−	4.96245e26i		−	0.0755340i
$606$	1.14798e27	+	1.14586e27i	0.171873	+	0.171556i
$607$	−4.08940e27			−0.602245			−0.301122	−	0.953586i	$-0.597361\pi$
$607$	−4.08940e27			−0.602245			−0.301122	+	0.953586i	$0.597361\pi$
$608$		−	1.82975e27i		−	0.265067i
$609$	9.32585e27	−	9.34308e27i	1.32897	−	1.33143i
$610$	4.25337e26			0.0596258
$611$		−	2.43433e27i		−	0.335712i
$612$	−5.44030e27	+	1.00408e25i	−0.738089	+	0.00136224i
$613$	−3.61790e27			−0.482895			−0.241447	−	0.970414i	$-0.577622\pi$
$613$	−3.61790e27			−0.482895			−0.241447	+	0.970414i	$0.577622\pi$
$614$		−	8.67837e26i		−	0.113960i
$615$	5.10133e26	+	5.09192e26i	0.0659071	+	0.0657855i
$616$	−1.03928e27			−0.132107
$617$			6.19841e26i			0.0775226i	0.999248	+	0.0387613i	$0.0123412\pi$
$617$			6.19841e26i			0.0775226i	−0.999248	+	0.0387613i	$0.987659\pi$
$618$	−1.83479e27	+	1.83818e27i	−0.225788	+	0.226205i
$619$	1.52572e27			0.184743			0.0923713	−	0.995725i	$-0.470555\pi$
$619$	1.52572e27			0.184743			0.0923713	+	0.995725i	$0.470555\pi$
$620$			2.26624e26i			0.0270016i
$621$	1.23124e27	+	1.22444e27i	0.144353	+	0.143556i
$622$	6.94176e26			0.0800877
$623$			9.05504e27i			1.02804i
$624$	−1.25880e27	−	1.25648e27i	−0.140640	−	0.140381i
$625$	8.90972e27			0.979635
$626$			9.08700e27i			0.983279i
$627$	2.88770e27	−	2.89303e27i	0.307522	−	0.308090i
$628$	−3.26243e27			−0.341936
$629$			1.90615e28i			1.96630i
$630$	−1.36466e24	−	7.39398e26i	−0.000138554	−	0.0750711i
$631$	1.61675e28			1.61566			0.807830	−	0.589416i	$-0.200642\pi$
$631$	1.61675e28			1.61566			0.807830	+	0.589416i	$0.200642\pi$
$632$			2.77477e27i			0.272933i
$633$	5.15238e26	+	5.14288e26i	0.0498851	+	0.0497931i
$634$	7.12737e27			0.679261
$635$			2.04910e24i			0.000192232i
$636$	7.40364e27	−	7.41732e27i	0.683714	−	0.684977i
$637$	−5.74090e27			−0.521898
$638$		−	3.35257e27i		−	0.300034i
$639$	−2.13355e28	+	3.93775e25i	−1.87972	+	0.00346928i
$640$	−8.40571e25			−0.00729079
$641$		−	1.31157e28i		−	1.11998i	−0.828499	−	0.559990i	$-0.810805\pi$
$641$		−	1.31157e28i		−	1.11998i	0.828499	−	0.559990i	$-0.189195\pi$
$642$	5.08394e27	+	5.07457e27i	0.427415	+	0.426627i
$643$	1.37768e27			0.114035			0.0570174	−	0.998373i	$-0.481841\pi$
$643$	1.37768e27			0.114035			0.0570174	+	0.998373i	$0.481841\pi$
$644$		−	1.60761e27i		−	0.131015i
$645$	−7.67920e26	+	7.69338e26i	−0.0616196	+	0.0617334i
$646$	−1.98098e28			−1.56514
$647$			6.44182e27i			0.501148i	0.968097	+	0.250574i	$0.0806193\pi$
$647$			6.44182e27i			0.501148i	−0.968097	+	0.250574i	$0.919381\pi$
$648$	1.70364e25	+	4.61532e27i	0.00130506	+	0.353551i
$649$	2.96451e27			0.223617
$650$		−	7.51516e27i		−	0.558219i
$651$	−8.15350e27	−	8.13846e27i	−0.596395	−	0.595295i
$652$	5.86135e27			0.422203
$653$		−	1.28868e28i		−	0.914142i	−0.889430	−	0.457071i	$-0.848898\pi$
$653$		−	1.28868e28i		−	0.914142i	0.889430	−	0.457071i	$-0.151102\pi$
$654$	3.18706e27	−	3.19294e27i	0.222645	−	0.223056i
$655$	1.14378e27			0.0786920
$656$			4.16529e27i			0.282232i
$657$	5.90119e24	+	3.19738e27i	0.000393809	+	0.213374i
$658$	5.84837e27			0.384393
$659$		−	1.94022e28i		−	1.25602i	−0.778206	−	0.628009i	$-0.783870\pi$
$659$		−	1.94022e28i		−	1.25602i	0.778206	−	0.628009i	$-0.216130\pi$
$660$	−1.32904e26	−	1.32659e26i	−0.00847419	−	0.00845856i
$661$	−2.25373e28			−1.41543			−0.707713	−	0.706500i	$-0.750273\pi$
$661$	−2.25373e28			−1.41543			−0.707713	+	0.706500i	$0.750273\pi$
$662$		−	1.28598e28i		−	0.795523i
$663$	−1.36033e28	+	1.36284e28i	−0.828911	+	0.830442i
$664$	−5.98251e27			−0.359089
$665$		−	2.69237e27i		−	0.159191i
$666$	1.61710e28	−	2.98457e25i	0.941878	−	0.00173836i
$667$	5.18589e27			0.297553
$668$		−	9.11075e27i		−	0.514979i
$669$	1.15886e28	+	1.15673e28i	0.645314	+	0.644124i
$670$	−2.94246e26			−0.0161422
$671$			5.49108e27i			0.296778i
$672$	3.01863e27	−	3.02421e27i	0.160738	−	0.161035i
$673$	2.20415e28			1.15635			0.578176	−	0.815912i	$-0.303765\pi$
$673$	2.20415e28			1.15635			0.578176	+	0.815912i	$0.303765\pi$
$674$		−	3.46079e27i		−	0.178886i
$675$	−1.37516e28	+	1.38279e28i	−0.700349	+	0.704237i
$676$	3.66892e27			0.184107
$677$			2.53010e28i			1.25098i	0.780232	+	0.625490i	$0.215101\pi$
$677$			2.53010e28i			1.25098i	−0.780232	+	0.625490i	$0.784899\pi$
$678$	−8.98293e27	−	8.96636e27i	−0.437644	−	0.436837i
$679$	−3.20438e28			−1.53832
$680$			9.10046e26i			0.0430501i
$681$	1.43784e28	−	1.44050e28i	0.670254	−	0.671492i
$682$	−2.92571e27			−0.134396
$683$			1.37371e28i			0.621855i	0.950434	+	0.310927i	$0.100640\pi$
$683$			1.37371e28i			0.621855i	−0.950434	+	0.310927i	$0.899360\pi$
$684$	3.10174e25	+	1.68058e28i	0.00138371	+	0.749720i
$685$	−3.37224e27			−0.148256
$686$			7.21332e27i			0.312532i
$687$	1.50939e28	+	1.50661e28i	0.644519	+	0.643330i
$688$	−6.28173e27			−0.264359
$689$		−	3.70935e28i		−	1.53853i
$690$	2.05202e26	−	2.05581e26i	0.00838863	−	0.00840412i
$691$	5.91223e27			0.238216			0.119108	−	0.992881i	$-0.461997\pi$
$691$	5.91223e27			0.238216			0.119108	+	0.992881i	$0.461997\pi$
$692$			4.07539e27i			0.161848i
$693$	9.54560e27	−	1.76177e25i	0.373655	−	0.000689630i
$694$	−1.26045e28			−0.486329
$695$			3.52551e27i			0.134083i
$696$	9.75564e27	+	9.73765e27i	0.365732	+	0.365058i
$697$	4.50956e28			1.66650
$698$			1.58806e28i			0.578513i
$699$	−1.43231e28	+	1.43495e28i	−0.514356	+	0.515307i
$700$	1.80549e28			0.639166
$701$		−	4.28515e28i		−	1.49550i	−0.663981	−	0.747750i	$-0.731134\pi$
$701$		−	4.28515e28i		−	1.49550i	0.663981	−	0.747750i	$-0.268866\pi$
$702$	1.15831e28	+	1.15191e28i	0.398523	+	0.396323i
$703$	5.88835e28			1.99729
$704$		−	1.08517e27i		−	0.0362888i
$705$	7.47891e26	+	7.46512e26i	0.0246574	+	0.0246119i
$706$	−1.87869e28			−0.610672
$707$			1.37924e28i			0.442025i
$708$	−8.61052e27	+	8.62642e27i	−0.272080	+	0.272583i
$709$	−5.69549e28			−1.77447			−0.887235	−	0.461318i	$-0.847377\pi$
$709$	−5.69549e28			−1.77447			−0.887235	+	0.461318i	$0.847377\pi$
$710$			3.56897e27i			0.109638i
$711$	−4.70372e25	−	2.54857e28i	−0.00142477	−	0.771969i
$712$	−9.45488e27			−0.282394
$713$		−	4.52561e27i		−	0.133285i
$714$	−3.27417e28	−	3.26813e28i	−0.950864	−	0.949111i
$715$	−6.64642e26			−0.0190339
$716$		−	3.87805e27i		−	0.109518i
$717$	9.01140e27	−	9.02805e27i	0.250958	−	0.251421i
$718$	3.48535e27			0.0957198
$719$		−	2.55879e28i		−	0.693019i	−0.938046	−	0.346510i	$-0.887367\pi$
$719$		−	2.55879e28i		−	0.693019i	0.938046	−	0.346510i	$-0.112633\pi$
$720$	7.72048e26	−	1.42492e24i	0.0206214	−	3.80596e-5i
$721$	−2.20848e28			−0.581757
$722$			3.39771e28i			0.882703i
$723$	−3.85383e28	−	3.84672e28i	−0.987438	−	0.985617i
$724$	6.77844e27			0.171295
$725$			5.82422e28i			1.45164i
$726$	−1.86079e28	+	1.86423e28i	−0.457437	+	0.458282i
$727$	−1.24111e28			−0.300930			−0.150465	−	0.988615i	$-0.548077\pi$
$727$	−1.24111e28			−0.300930			−0.150465	+	0.988615i	$0.548077\pi$
$728$		−	1.51239e28i		−	0.361700i
$729$	−2.34714e26	−	4.23905e28i	−0.00553686	−	0.999985i
$730$	5.34853e26			0.0124453
$731$			6.80092e28i			1.56097i
$732$	−1.59785e28	−	1.59490e28i	−0.361764	−	0.361097i
$733$	−2.22545e28			−0.497024			−0.248512	−	0.968629i	$-0.579942\pi$
$733$	−2.22545e28			−0.497024			−0.248512	+	0.968629i	$0.579942\pi$
$734$		−	3.39570e28i		−	0.748115i
$735$	1.76051e27	−	1.76376e27i	0.0382617	−	0.0383324i
$736$	1.67859e27			0.0359888
$737$		−	3.79871e27i		−	0.0803454i
$738$	−7.06090e25	−	3.82573e28i	−0.00147332	−	0.798272i
$739$	3.40139e27			0.0700183			0.0350091	−	0.999387i	$-0.488854\pi$
$739$	3.40139e27			0.0700183			0.0350091	+	0.999387i	$0.488854\pi$
$740$		−	2.70506e27i		−	0.0549364i
$741$	4.21000e28	+	4.20224e28i	0.843530	+	0.841974i
$742$	8.91155e28			1.76163
$743$		−	6.28612e28i		−	1.22601i	−0.790078	−	0.613006i	$-0.789960\pi$
$743$		−	6.28612e28i		−	1.22601i	0.790078	−	0.613006i	$-0.210040\pi$
$744$	8.49783e27	−	8.51353e27i	0.163523	−	0.163825i
$745$	−4.37774e27			−0.0831166
$746$			1.35797e28i			0.254392i
$747$	5.49481e28	−	1.01414e26i	1.01566	−	0.00187453i
$748$	−1.17487e28			−0.214275
$749$			6.10811e28i			1.09923i
$750$	4.63354e27	+	4.62500e27i	0.0822811	+	0.0821294i
$751$	−1.54822e28			−0.271291			−0.135645	−	0.990757i	$-0.543311\pi$
$751$	−1.54822e28			−0.271291			−0.135645	+	0.990757i	$0.543311\pi$
$752$			6.10661e27i			0.105590i
$753$	8.61027e27	−	8.62617e27i	0.146915	−	0.147187i
$754$	4.87872e28			0.821472
$755$		−	1.98241e27i		−	0.0329401i
$756$	−2.76743e28	+	2.78279e28i	−0.453793	+	0.456313i
$757$	−2.73490e28			−0.442571			−0.221285	−	0.975209i	$-0.571025\pi$
$757$	−2.73490e28			−0.442571			−0.221285	+	0.975209i	$0.571025\pi$
$758$			5.43655e28i			0.868223i
$759$	2.65404e27	+	2.64915e27i	0.0418302	+	0.0417531i
$760$	2.81126e27			0.0437285
$761$			5.31431e28i			0.815832i	0.913020	+	0.407916i	$0.133744\pi$
$761$			5.31431e28i			0.815832i	−0.913020	+	0.407916i	$0.866256\pi$
$762$	7.68358e25	−	7.69778e25i	0.00116416	−	0.00116631i
$763$	3.83617e28			0.573657
$764$		−	5.96027e28i		−	0.879695i
$765$	−1.54269e25	−	8.35858e27i	−0.000224731	−	0.121764i
$766$	−2.92632e27			−0.0420760
$767$			4.31401e28i			0.612248i
$768$	3.15775e27	+	3.15193e27i	0.0442349	+	0.0441534i
$769$	−1.39897e29			−1.93440			−0.967200	−	0.254018i	$-0.918248\pi$
$769$	−1.39897e29			−1.93440			−0.967200	+	0.254018i	$0.918248\pi$
$770$		−	1.59677e27i		−	0.0217940i
$771$	−2.69332e28	+	2.69830e28i	−0.362864	+	0.363535i
$772$	−2.38522e28			−0.317216
$773$			3.22372e28i			0.423216i	0.977355	+	0.211608i	$0.0678700\pi$
$773$			3.22372e28i			0.423216i	−0.977355	+	0.211608i	$0.932130\pi$
$774$	5.76964e28	−	1.06486e26i	0.747720	−	0.00138002i
$775$	5.08267e28			0.650241
$776$		−	3.34587e28i		−	0.422564i
$777$	9.73228e28	+	9.71434e28i	1.21340	+	1.21116i
$778$	−3.09941e28			−0.381490
$779$		−	1.39307e29i		−	1.69277i
$780$	1.93048e27	−	1.93404e27i	0.0231589	−	0.0232017i
$781$	−4.60752e28			−0.545704
$782$		−	1.81733e28i		−	0.212504i
$783$	−8.97686e28	−	8.92729e28i	−1.03635	−	1.03063i
$784$	1.44013e28			0.164150
$785$		−	5.01246e27i		−	0.0564098i
$786$	−4.29681e28	−	4.28889e28i	−0.477443	−	0.476562i
$787$	1.46996e29			1.61272			0.806360	−	0.591425i	$-0.201434\pi$
$787$	1.46996e29			1.61272			0.806360	+	0.591425i	$0.201434\pi$
$788$			2.58207e28i			0.279708i
$789$	−6.30506e28	+	6.31671e28i	−0.674403	+	0.675649i
$790$	−4.26321e27			−0.0450262
$791$		−	1.07926e29i		−	1.12554i
$792$	1.83956e25	+	9.96710e27i	0.000189436	+	0.102640i
$793$	−7.99073e28			−0.812558
$794$		−	3.40367e28i		−	0.341777i
$795$	1.13961e28	+	1.13751e28i	0.113002	+	0.112794i
$796$	3.01227e28			0.294960
$797$		−	1.69393e29i		−	1.63799i	−0.573801	−	0.818995i	$-0.694532\pi$
$797$		−	1.69393e29i		−	1.63799i	0.573801	−	0.818995i	$-0.305468\pi$
$798$	−1.00957e29	+	1.01144e29i	−0.964068	+	0.965849i
$799$	6.61133e28			0.623478
$800$			1.88521e28i			0.175574i
$801$	8.68412e28	−	1.60277e26i	0.798731	−	0.00147416i
$802$	−1.08966e29			−0.989801
$803$			6.90493e27i			0.0619447i
$804$	1.10539e28	+	1.10335e28i	0.0979386	+	0.0977580i
$805$	2.46996e27			0.0216138
$806$		−	4.25755e28i		−	0.367968i
$807$	−1.38026e28	+	1.38281e28i	−0.117821	+	0.118039i
$808$	−1.44015e28			−0.121421
$809$			1.09964e28i			0.0915727i	0.998951	+	0.0457864i	$0.0145793\pi$
$809$			1.09964e28i			0.0915727i	−0.998951	+	0.0457864i	$0.985421\pi$
$810$	−7.09108e27	+	2.61751e25i	−0.0583260	+	0.000215297i
$811$	−1.15750e29			−0.940396			−0.470198	−	0.882561i	$-0.655817\pi$
$811$	−1.15750e29			−0.940396			−0.470198	+	0.882561i	$0.655817\pi$
$812$			1.17209e29i			0.940593i
$813$	−1.20150e29	−	1.19928e29i	−0.952395	−	0.950638i
$814$	3.49222e28			0.273437
$815$			9.00550e27i			0.0696517i
$816$	3.41244e28	−	3.41874e28i	0.260713	−	0.261195i
$817$	2.10090e29			1.58557
$818$			7.23364e28i			0.539292i
$819$	2.56376e26	+	1.38909e29i	0.00188816	+	1.02304i
$820$	−6.39963e27			−0.0465604
$821$			6.50646e28i			0.467642i	0.972280	+	0.233821i	$0.0751230\pi$
$821$			6.50646e28i			0.467642i	−0.972280	+	0.233821i	$0.924877\pi$
$822$	1.26684e29	+	1.26450e29i	0.899505	+	0.897847i
$823$	9.49304e28			0.665897			0.332949	−	0.942945i	$-0.391956\pi$
$823$	9.49304e28			0.665897			0.332949	+	0.942945i	$0.391956\pi$
$824$		−	2.30600e28i		−	0.159804i
$825$	−2.97523e28	+	2.98073e28i	−0.203696	+	0.204072i
$826$	−1.03642e29			−0.701030
$827$			7.39489e28i			0.494170i	0.968994	+	0.247085i	$0.0794727\pi$
$827$			7.39489e28i			0.494170i	−0.968994	+	0.247085i	$0.920527\pi$
$828$	−1.54175e28	+	2.84551e25i	−0.101791	+	0.000187870i
$829$	2.50384e29			1.63328			0.816640	−	0.577147i	$-0.195834\pi$
$829$	2.50384e29			1.63328			0.816640	+	0.577147i	$0.195834\pi$
$830$		−	9.19164e27i		−	0.0592396i
$831$	5.36611e28	+	5.35622e28i	0.341704	+	0.341074i
$832$	1.57917e28			0.0993562
$833$		−	1.55916e29i		−	0.969260i
$834$	1.32197e29	−	1.32442e29i	0.812012	−	0.813512i
$835$	1.39979e28			0.0849570
$836$			3.62932e28i			0.217652i
$837$	−7.79065e28	+	7.83390e28i	−0.461657	+	0.464220i
$838$	−1.21739e29			−0.712838
$839$			2.79539e29i			1.61742i	0.588208	+	0.808710i	$0.299834\pi$
$839$			2.79539e29i			1.61742i	−0.588208	+	0.808710i	$0.700166\pi$
$840$	4.64646e27	+	4.63789e27i	0.0265662	+	0.0265172i
$841$	−2.01105e29			−1.13622
$842$		−	1.94903e29i		−	1.08817i
$843$	1.06890e29	−	1.07088e29i	0.589743	−	0.590833i
$844$	−6.46368e27			−0.0352416
$845$			5.63700e27i			0.0303725i
$846$	−1.03518e26	−	5.60880e28i	−0.000551203	−	0.298653i
$847$	−2.23978e29			−1.17861
$848$			9.30505e28i			0.483905i
$849$	−2.43673e29	−	2.43223e29i	−1.25236	−	1.25005i
$850$	2.04103e29			1.03671
$851$			5.40192e28i			0.271177i
$852$	1.33827e29	−	1.34074e29i	0.663970	−	0.665196i
$853$	2.04793e29			1.00421			0.502105	−	0.864807i	$-0.332559\pi$
$853$	2.04793e29			1.00421			0.502105	+	0.864807i	$0.332559\pi$
$854$		−	1.91974e29i		−	0.930387i
$855$	−2.58208e28	+	4.76558e25i	−0.123683	+	0.000228273i
$856$	−6.37782e28			−0.301950
$857$			4.15136e29i			1.94260i	0.237864	+	0.971298i	$0.423553\pi$
$857$			4.15136e29i			1.94260i	−0.237864	+	0.971298i	$0.576447\pi$
$858$	2.49684e28	+	2.49224e28i	0.115483	+	0.115270i
$859$	−3.68833e29			−1.68616			−0.843079	−	0.537790i	$-0.819259\pi$
$859$	−3.68833e29			−1.68616			−0.843079	+	0.537790i	$0.819259\pi$
$860$		−	9.65138e27i		−	0.0436119i
$861$	2.29822e29	−	2.30246e29i	1.02650	−	1.02840i
$862$	−1.47240e29			−0.650061
$863$		−	2.25722e29i		−	0.985065i	−0.870294	−	0.492533i	$-0.836071\pi$
$863$		−	2.25722e29i		−	0.985065i	0.870294	−	0.492533i	$-0.163929\pi$
$864$	−2.90567e28	−	2.88963e28i	−0.125346	−	0.124653i
$865$	−6.26151e27			−0.0267004
$866$			2.00720e29i			0.846079i
$867$	−2.00276e29	−	1.99907e29i	−0.834524	−	0.832985i
$868$	1.02286e29			0.421326
$869$		−	5.50378e28i		−	0.224111i
$870$	−1.49611e28	+	1.49888e28i	−0.0602243	+	0.0603355i
$871$	5.52796e28			0.219980
$872$			4.00556e28i			0.157579i
$873$	5.67185e26	+	3.07312e29i	0.00220588	+	1.19519i
$874$	−5.61399e28			−0.215853
$875$			5.56697e28i			0.211611i
$876$	−2.00927e28	−	2.00556e28i	−0.0755086	−	0.0753694i
$877$	−1.17025e29			−0.434793			−0.217396	−	0.976083i	$-0.569756\pi$
$877$	−1.17025e29			−0.434793			−0.217396	+	0.976083i	$0.569756\pi$
$878$			1.01299e29i			0.372099i
$879$	−5.03775e28	+	5.04706e28i	−0.182957	+	0.183295i
$880$	1.66728e27			0.00598663
$881$		−	2.06068e29i		−	0.731562i	−0.930701	−	0.365781i	$-0.880802\pi$
$881$		−	2.06068e29i		−	0.731562i	0.930701	−	0.365781i	$-0.119198\pi$
$882$	−1.32273e29	+	2.44127e26i	−0.464286	+	0.000856901i
$883$	1.64553e29			0.571082			0.285541	−	0.958367i	$-0.407827\pi$
$883$	1.64553e29			0.571082			0.285541	+	0.958367i	$0.407827\pi$
$884$		−	1.70969e29i		−	0.586670i
$885$	−1.32538e28	−	1.32294e28i	−0.0449685	−	0.0448855i
$886$	2.83019e29			0.949463
$887$			1.17405e29i			0.389449i	0.980858	+	0.194724i	$0.0623812\pi$
$887$			1.17405e29i			0.389449i	−0.980858	+	0.194724i	$0.937619\pi$
$888$	−1.01433e29	+	1.01620e29i	−0.332697	+	0.333312i
$889$	9.24851e26			0.00299954
$890$		−	1.45267e28i		−	0.0465871i
$891$	−3.37920e26	−	9.15455e28i	−0.00107161	−	0.290309i
$892$	−1.45380e29			−0.455885
$893$		−	2.04233e29i		−	0.633304i
$894$	1.64457e29	+	1.64154e29i	0.504287	+	0.503358i
$895$	5.95832e27			0.0180673
$896$			3.79388e28i			0.113764i
$897$	−3.85510e28	+	3.86222e28i	−0.114317	+	0.114528i
$898$	−1.04490e29			−0.306415
$899$			3.29959e29i			0.956891i
$900$	−3.19576e26	−	1.73153e29i	−0.000916536	−	0.496597i
$901$	1.00741e30			2.85733
$902$		−	8.26190e28i		−	0.231747i
$903$	3.47237e29	+	3.46597e29i	0.963272	+	0.961496i
$904$	1.12691e29			0.309176
$905$			1.04145e28i			0.0282588i
$906$	−7.43353e28	+	7.44727e28i	−0.199486	+	0.199855i
$907$	3.55363e28			0.0943190			0.0471595	−	0.998887i	$-0.484983\pi$
$907$	3.55363e28			0.0943190			0.0471595	+	0.998887i	$0.484983\pi$
$908$			1.80711e29i			0.474379i
$909$	1.32275e29	−	2.44130e26i	0.343429	−	0.000633845i
$910$	2.32366e28			0.0596703
$911$			1.10794e29i			0.281404i	0.990052	+	0.140702i	$0.0449360\pi$
$911$			1.10794e29i			0.281404i	−0.990052	+	0.140702i	$0.955064\pi$
$912$	−1.05610e29	−	1.05415e29i	−0.265311	−	0.264822i
$913$	1.18664e29			0.294856
$914$			3.48892e29i			0.857491i
$915$	2.45044e28	−	2.45497e28i	0.0595708	−	0.0596808i
$916$	−1.89354e29			−0.455323
$917$		−	5.16242e29i		−	1.22789i
$918$	−3.12846e29	+	3.14583e29i	−0.736044	+	0.740130i
$919$	−7.17188e29			−1.66908			−0.834541	−	0.550945i	$-0.814267\pi$
$919$	−7.17188e29			−1.66908			−0.834541	+	0.550945i	$0.814267\pi$
$920$			2.57902e27i			0.00593714i
$921$	−5.00900e28	−	4.99976e28i	−0.114066	−	0.113855i
$922$	1.99302e29			0.448955
$923$		−	6.70496e29i		−	1.49410i
$924$	−5.98749e28	+	5.99856e28i	−0.131985	+	0.132229i
$925$	−6.06684e29			−1.32296
$926$		−	3.48411e29i		−	0.751592i
$927$	3.90908e26	+	2.11802e29i	0.000834214	+	0.451993i
$928$	−1.22385e29			−0.258373
$929$			8.87877e28i			0.185437i	0.995692	+	0.0927184i	$0.0295556\pi$
$929$			8.87877e28i			0.185437i	−0.995692	+	0.0927184i	$0.970444\pi$
$930$	1.30804e28	+	1.30562e28i	0.0270265	+	0.0269767i
$931$	−4.81646e29			−0.984535
$932$		−	1.80015e29i		−	0.364041i
$933$	3.99928e28	−	4.00666e28i	0.0800138	−	0.0801616i
$934$	2.76553e29			0.547407
$935$		−	1.80509e28i		−	0.0353494i
$936$	−1.45043e29	+	2.67697e26i	−0.281021	+	0.000518662i
$937$	−2.44477e29			−0.468642			−0.234321	−	0.972159i	$-0.575287\pi$
$937$	−2.44477e29			−0.468642			−0.234321	+	0.972159i	$0.575287\pi$
$938$			1.32807e29i			0.251879i
$939$	5.24485e29	+	5.23518e29i	0.984186	+	0.982372i
$940$	−9.38232e27			−0.0174193
$941$		−	4.19504e29i		−	0.770619i	−0.922787	−	0.385310i	$-0.874095\pi$
$941$		−	4.19504e29i		−	0.770619i	0.922787	−	0.385310i	$-0.125905\pi$
$942$	−1.87954e29	+	1.88302e29i	−0.341620	+	0.342251i
$943$	1.27799e29			0.229831
$944$		−	1.08219e29i		−	0.192567i
$945$	−4.27554e28	−	4.25193e28i	−0.0752788	−	0.0748631i
$946$	1.24599e29			0.217071
$947$		−	1.10768e30i		−	1.90949i	−0.297433	−	0.954743i	$-0.596130\pi$
$947$		−	1.10768e30i		−	1.90949i	0.297433	−	0.954743i	$-0.403870\pi$
$948$	1.60155e29	+	1.59859e29i	0.273185	+	0.272681i
$949$	−1.00482e29			−0.169600
$950$		−	6.30502e29i		−	1.05305i
$951$	4.10621e29	−	4.11379e29i	0.678634	−	0.679888i
$952$	4.10745e29			0.671743
$953$			6.95375e29i			1.12536i	0.826676	+	0.562679i	$0.190229\pi$
$953$			6.95375e29i			1.12536i	−0.826676	+	0.562679i	$0.809771\pi$
$954$	−1.57737e27	−	8.54650e29i	−0.00252610	−	1.36869i
$955$	9.15747e28			0.145125
$956$			1.13257e29i			0.177618i
$957$	−1.93504e29	−	1.93147e29i	−0.300311	−	0.299757i
$958$	−2.76248e28			−0.0424272
$959$			1.52205e30i			2.31335i
$960$	−4.84268e27	+	4.85163e27i	−0.00728406	+	0.00729752i
$961$	−3.83843e29			−0.571373
$962$			5.08195e29i			0.748652i
$963$	5.85790e29	−	1.08115e27i	0.854042	−	0.00157625i
$964$	4.83465e29			0.697580
$965$		−	3.66470e28i		−	0.0523317i
$966$	−9.27882e28	−	9.26171e28i	−0.131136	−	0.130894i
$967$	−9.64276e29			−1.34877			−0.674383	−	0.738382i	$-0.735590\pi$
$967$	−9.64276e29			−1.34877			−0.674383	+	0.738382i	$0.735590\pi$
$968$		−	2.33868e29i		−	0.323756i
$969$	−1.14128e30	+	1.14339e30i	−1.56370	+	1.56659i
$970$	5.14067e28			0.0697111
$971$			8.85040e29i			1.18787i	0.804511	+	0.593937i	$0.202427\pi$
$971$			8.85040e29i			1.18787i	−0.804511	+	0.593937i	$0.797573\pi$
$972$	2.67370e29	+	2.64914e29i	0.355181	+	0.351918i
$973$	1.59122e30			2.09220
$974$		−	7.30703e29i		−	0.950936i
$975$	−4.33762e29	−	4.32962e29i	−0.558734	−	0.557704i
$976$	2.00451e29			0.255570
$977$			7.84234e29i			0.989692i	0.868981	+	0.494846i	$0.164776\pi$
$977$			7.84234e29i			0.989692i	−0.868981	+	0.494846i	$0.835224\pi$
$978$	3.37683e29	−	3.38307e29i	0.421814	−	0.422593i
$979$	1.87539e29			0.231880
$980$			2.21264e28i			0.0270801i
$981$	−6.79013e26	−	3.67903e29i	−0.000822599	−	0.445700i
$982$	−1.07323e30			−1.28700
$983$		−	2.58895e29i		−	0.307319i	−0.988124	−	0.153659i	$-0.950894\pi$
$983$		−	2.58895e29i		−	0.307319i	0.988124	−	0.153659i	$-0.0491058\pi$
$984$	2.40413e29	+	2.39970e29i	0.282493	+	0.281972i
$985$	−3.96714e28			−0.0461440
$986$			1.32500e30i			1.52562i
$987$	3.36935e29	−	3.37558e29i	0.384038	−	0.384748i
$988$	−5.28146e29			−0.595916
$989$			1.92735e29i			0.215277i
$990$	−1.53137e28	+	2.82634e25i	−0.0169327	+	3.12516e-5i
$991$	1.58655e30			1.73667			0.868337	−	0.495975i	$-0.165189\pi$
$991$	1.58655e30			1.73667			0.868337	+	0.495975i	$0.165189\pi$
$992$			1.06802e29i			0.115735i
$993$	−7.42243e29	−	7.40874e29i	−0.796257	−	0.794789i
$994$	1.61084e30			1.71076
$995$			4.62811e28i			0.0486600i
$996$	−3.44663e29	+	3.45300e29i	−0.358758	+	0.359420i
$997$	−3.38521e28			−0.0348846			−0.0174423	−	0.999848i	$-0.505552\pi$
$997$	−3.38521e28			−0.0348846			−0.0174423	+	0.999848i	$0.505552\pi$
$998$			2.79714e29i			0.285371i
$999$	9.29918e29	−	9.35081e29i	0.939268	−	0.944483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.21.b.a.5.6	yes	6
3.2	odd	2	inner	6.21.b.a.5.3	✓	6
4.3	odd	2		48.21.e.b.17.1		6
12.11	even	2		48.21.e.b.17.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.21.b.a.5.3	✓	6	3.2	odd	2	inner
6.21.b.a.5.6	yes	6	1.1	even	1	trivial
48.21.e.b.17.1		6	4.3	odd	2
48.21.e.b.17.2		6	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	6.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+724.077i q^{2} +(41792.5 + 41715.4i) q^{3} -524288. q^{4} -805527. i q^{5} +(-3.02052e7 + 3.02610e7i) q^{6} -3.63571e8 q^{7} -3.79625e8i q^{8} +(6.43531e6 + 3.48678e9i) q^{9} +O(q^{10})\)	\(q+724.077i q^{2} +(41792.5 + 41715.4i) q^{3} -524288. q^{4} -805527. i q^{5} +(-3.02052e7 + 3.02610e7i) q^{6} -3.63571e8 q^{7} -3.79625e8i q^{8} +(6.43531e6 + 3.48678e9i) q^{9} +5.83264e8 q^{10} +7.52991e9i q^{11} +(-2.19113e10 - 2.18709e10i) q^{12} -1.09577e11 q^{13} -2.63254e11i q^{14} +(3.36029e10 - 3.36649e10i) q^{15} +2.74878e11 q^{16} -2.97597e12i q^{17} +(-2.52470e12 + 4.65966e9i) q^{18} -9.19319e12 q^{19} +4.22328e11i q^{20} +(-1.51945e13 - 1.51665e13i) q^{21} -5.45223e12 q^{22} -8.43375e12i q^{23} +(1.58362e13 - 1.58655e13i) q^{24} +9.47186e13 q^{25} -7.93420e13i q^{26} +(-1.45183e14 + 1.45990e14i) q^{27} +1.90616e14 q^{28} +6.14898e14i q^{29} +(2.43760e13 + 2.43311e13i) q^{30} +5.36607e14 q^{31} +1.99033e14i q^{32} +(-3.14113e14 + 3.14693e14i) q^{33} +2.15483e15 q^{34} +2.92866e14i q^{35} +(-3.37396e12 - 1.82808e15i) q^{36} -6.40512e15 q^{37} -6.65658e15i q^{38} +(-4.57948e15 - 4.57104e15i) q^{39} -3.05798e14 q^{40} +1.51532e16i q^{41} +(1.09817e16 - 1.10020e16i) q^{42} -2.28528e16 q^{43} -3.94784e15i q^{44} +(2.80869e15 - 5.18382e12i) q^{45} +6.10668e15 q^{46} +2.22157e16i q^{47} +(1.14878e16 + 1.14666e16i) q^{48} +5.23916e16 q^{49} +6.85836e16i q^{50} +(1.24144e17 - 1.24373e17i) q^{51} +5.74498e16 q^{52} +3.38516e17i q^{53} +(-1.05708e17 - 1.05124e17i) q^{54} +6.06554e15 q^{55} +1.38021e17i q^{56} +(-3.84206e17 - 3.83497e17i) q^{57} -4.45233e17 q^{58} -3.93698e17i q^{59} +(-1.76176e16 + 1.76501e16i) q^{60} +7.29236e17 q^{61} +3.88545e17i q^{62} +(-2.33969e15 - 1.26769e18i) q^{63} -1.44115e17 q^{64} +8.82670e16i q^{65} +(-2.27862e17 - 2.27442e17i) q^{66} -5.04483e17 q^{67} +1.56027e18i q^{68} +(3.51817e17 - 3.52467e17i) q^{69} -2.12058e17 q^{70} +6.11896e18i q^{71} +(1.32367e18 - 2.44301e15i) q^{72} +9.17001e17 q^{73} -4.63780e18i q^{74} +(3.95852e18 + 3.95122e18i) q^{75} +4.81988e18 q^{76} -2.73766e18i q^{77} +(3.30978e18 - 3.31590e18i) q^{78} -7.30923e18 q^{79} -2.21421e17i q^{80} +(-1.21576e19 + 4.48770e16i) q^{81} -1.09721e19 q^{82} -1.57590e19i q^{83} +(7.96631e18 + 7.95162e18i) q^{84} -2.39722e18 q^{85} -1.65472e19i q^{86} +(-2.56507e19 + 2.56981e19i) q^{87} +2.85854e18 q^{88} -2.49058e19i q^{89} +(3.75348e15 + 2.03371e18i) q^{90} +3.98389e19 q^{91} +4.42171e18i q^{92} +(2.24261e19 + 2.23848e19i) q^{93} -1.60859e19 q^{94} +7.40536e18i q^{95} +(-8.30274e18 + 8.31807e18i) q^{96} +8.81363e19 q^{97} +3.79356e19i q^{98} +(-2.62551e19 + 4.84573e16i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 18846 q^{3} - 3145728 q^{4} + 35057664 q^{6} - 566671812 q^{7} + 1944941382 q^{9}+O(q^{10}) \) 6 * q + 18846 * q^3 - 3145728 * q^4 + 35057664 * q^6 - 566671812 * q^7 + 1944941382 * q^9	\( 6 q + 18846 q^{3} - 3145728 q^{4} + 35057664 q^{6} - 566671812 q^{7} + 1944941382 q^{9} + 5360984064 q^{10} - 9880731648 q^{12} - 49898545620 q^{13} + 487708151328 q^{15} + 1649267441664 q^{16} - 3239129751552 q^{18} + 15927597287292 q^{19} - 20677554127188 q^{21} + 21184189636608 q^{22} - 18380312543232 q^{24} + 337510512308454 q^{25} - 10\!\cdots\!62 q^{27}+ \cdots - 22\!\cdots\!32 q^{99}+O(q^{100}) \) 6 * q + 18846 * q^3 - 3145728 * q^4 + 35057664 * q^6 - 566671812 * q^7 + 1944941382 * q^9 + 5360984064 * q^10 - 9880731648 * q^12 - 49898545620 * q^13 + 487708151328 * q^15 + 1649267441664 * q^16 - 3239129751552 * q^18 + 15927597287292 * q^19 - 20677554127188 * q^21 + 21184189636608 * q^22 - 18380312543232 * q^24 + 337510512308454 * q^25 - 1019514529044162 * q^27 + 297099230969856 * q^28 - 920809286295552 * q^30 + 1832545426397628 * q^31 - 3503562514347744 * q^33 + 2508713101983744 * q^34 - 1019709427286016 * q^36 + 424332326872812 * q^37 + 13854943345637340 * q^39 - 2810699612946432 * q^40 + 30169507188989952 * q^42 - 49488752333951556 * q^43 + 64297936569436992 * q^45 - 51218624034717696 * q^46 + 5180349034266624 * q^48 - 185965132589503470 * q^49 + 114461935953291648 * q^51 + 26161208686018560 * q^52 - 103567464750919680 * q^54 + 468503586680075712 * q^55 - 1250127589109383188 * q^57 + 330130684975472640 * q^58 - 255699531243454464 * q^60 + 3301830012872093484 * q^61 - 724019288731292484 * q^63 - 864691128455135232 * q^64 + 1110947414199017472 * q^66 - 2779226272508556228 * q^67 + 667934407322175168 * q^69 - 1866219302039371776 * q^70 + 1698236859181694976 * q^72 - 9149401536792501300 * q^73 + 9127347583517050878 * q^75 - 8350648126559748096 * q^76 + 19815256334884331520 * q^78 + 90056048403257148 * q^79 - 13310358127786728378 * q^81 - 19709381871486517248 * q^82 + 10840993498235142144 * q^84 + 78223886062534003968 * q^85 - 87334395308747540640 * q^87 - 11106616416197935104 * q^88 + 60406983770669457408 * q^90 + 132462766690215009720 * q^91 - 157075923546140581332 * q^93 - 106728395801434030080 * q^94 + 9636577302666018816 * q^96 + 92028905119987573836 * q^97 - 224342570810992842432 * q^99

Introduction

L-functions

Modular forms

Varieties

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