LMFDB - Embedded newform 10.16.b.a.9.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,16,Mod(9,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("10.9");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	10.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:	$14.2693505100$
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} - 4 x^{7} + 8 x^{6} + 6172534 x^{5} + 23752924445 x^{4} + 1095295465934 x^{3} + \cdots + 59\!\cdots\!64 $ x^8 - 4x^7 + 8x^6 + 6172534x^5 + 23752924445x^4 + 1095295465934x^3 + 14478882731282x^2 - 41384481648202964*x + 59143904715457383364
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{38}\cdot 3^{2}\cdot 5^{11} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			9.4
Root			$283.331 - 283.331i$ of defining polynomial
Character	$\chi$	$=$	10.9
Dual form			10.16.b.a.9.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-128.000i q^{2} +5604.61i q^{3} -16384.0 q^{4} +(162285. - 64661.7i) q^{5} +717390. q^{6} +750784. i q^{7} +2.09715e6i q^{8} -1.70628e7 q^{9} +O(q^{10})$	\(q-128.000i q^{2} +5604.61i q^{3} -16384.0 q^{4} +(162285. - 64661.7i) q^{5} +717390. q^{6} +750784. i q^{7} +2.09715e6i q^{8} -1.70628e7 q^{9} +(-8.27669e6 - 2.07725e7i) q^{10} -6.42490e7 q^{11} -9.18260e7i q^{12} +3.28952e8i q^{13} +9.61003e7 q^{14} +(3.62404e8 + 9.09545e8i) q^{15} +2.68435e8 q^{16} +6.22608e8i q^{17} +2.18403e9i q^{18} -4.73142e9 q^{19} +(-2.65888e9 + 1.05942e9i) q^{20} -4.20785e9 q^{21} +8.22387e9i q^{22} +1.90311e10i q^{23} -1.17537e10 q^{24} +(2.21553e10 - 2.09872e10i) q^{25} +4.21058e10 q^{26} -1.52101e10i q^{27} -1.23008e10i q^{28} -1.83680e11 q^{29} +(1.16422e11 - 4.63877e10i) q^{30} +1.39047e11 q^{31} -3.43597e10i q^{32} -3.60091e11i q^{33} +7.96938e10 q^{34} +(4.85469e10 + 1.21841e11i) q^{35} +2.79556e11 q^{36} -5.52467e11i q^{37} +6.05622e11i q^{38} -1.84365e12 q^{39} +(1.35605e11 + 3.40336e11i) q^{40} +6.85825e11 q^{41} +5.38605e11i q^{42} +1.71935e11i q^{43} +1.05266e12 q^{44} +(-2.76903e12 + 1.10331e12i) q^{45} +2.43598e12 q^{46} +5.47086e12i q^{47} +1.50448e12i q^{48} +4.18389e12 q^{49} +(-2.68637e12 - 2.83588e12i) q^{50} -3.48947e12 q^{51} -5.38954e12i q^{52} -8.40382e12i q^{53} -1.94690e12 q^{54} +(-1.04267e13 + 4.15445e12i) q^{55} -1.57451e12 q^{56} -2.65178e13i q^{57} +2.35110e13i q^{58} +2.89419e13 q^{59} +(-5.93762e12 - 1.49020e13i) q^{60} +4.32242e13 q^{61} -1.77980e13i q^{62} -1.28104e13i q^{63} -4.39805e12 q^{64} +(2.12706e13 + 5.33839e13i) q^{65} -4.60916e13 q^{66} +3.51746e13i q^{67} -1.02008e13i q^{68} -1.06662e14 q^{69} +(1.55957e13 - 6.21401e12i) q^{70} -5.12379e13 q^{71} -3.57832e13i q^{72} +1.73922e13i q^{73} -7.07158e13 q^{74} +(1.17625e14 + 1.24172e14i) q^{75} +7.75196e13 q^{76} -4.82371e13i q^{77} +2.35987e14i q^{78} +1.09277e14 q^{79} +(4.35631e13 - 1.73575e13i) q^{80} -1.59585e14 q^{81} -8.77856e13i q^{82} -1.44003e14i q^{83} +6.89415e13 q^{84} +(4.02589e13 + 1.01040e14i) q^{85} +2.20076e13 q^{86} -1.02946e15i q^{87} -1.34740e14i q^{88} -1.30531e14 q^{89} +(1.41223e14 + 3.54436e14i) q^{90} -2.46972e14 q^{91} -3.11805e14i q^{92} +7.79304e14i q^{93} +7.00270e14 q^{94} +(-7.67839e14 + 3.05942e14i) q^{95} +1.92573e14 q^{96} -6.80028e14i q^{97} -5.35537e14i q^{98} +1.09627e15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 131072 q^{4} + 251400 q^{5} - 53248 q^{6} - 43491176 q^{9}+O(q^{10}) $ 8 * q - 131072 * q^4 + 251400 * q^5 - 53248 * q^6 - 43491176 * q^9	\( 8 q - 131072 q^{4} + 251400 q^{5} - 53248 q^{6} - 43491176 q^{9} + 4403200 q^{10} + 95435616 q^{11} - 499347456 q^{14} + 5448800 q^{15} + 2147483648 q^{16} + 6479216160 q^{19} - 4118937600 q^{20} - 14760325504 q^{21} + 872415232 q^{24} - 2241855000 q^{25} + 66288525312 q^{26} - 244549636560 q^{29} - 32701542400 q^{30} + 522311705216 q^{31} + 322563211264 q^{34} - 1829607146400 q^{35} + 712559427584 q^{36} - 2307595824192 q^{39} - 72142028800 q^{40} + 6699117519216 q^{41} - 1563617132544 q^{44} - 9090807477800 q^{45} + 12178733699072 q^{46} - 15809163185544 q^{49} - 13485542400000 q^{50} + 40555579650176 q^{51} - 7241111674880 q^{54} - 39746288199200 q^{55} + 8181308719104 q^{56} + 3791808509280 q^{59} - 89273139200 q^{60} + 57800629300816 q^{61} - 35184372088832 q^{64} + 58028394892800 q^{65} - 82398766186496 q^{66} + 59060996328448 q^{69} + 60817223987200 q^{70} - 245426235422784 q^{71} + 53331092987904 q^{74} + 226448486200000 q^{75} - 106155477565440 q^{76} + 624094605411840 q^{79} + 67484673638400 q^{80} - 13\!\cdots\!52 q^{81}+ \cdots + 16\!\cdots\!48 q^{99}+O(q^{100}) \) 8 * q - 131072 * q^4 + 251400 * q^5 - 53248 * q^6 - 43491176 * q^9 + 4403200 * q^10 + 95435616 * q^11 - 499347456 * q^14 + 5448800 * q^15 + 2147483648 * q^16 + 6479216160 * q^19 - 4118937600 * q^20 - 14760325504 * q^21 + 872415232 * q^24 - 2241855000 * q^25 + 66288525312 * q^26 - 244549636560 * q^29 - 32701542400 * q^30 + 522311705216 * q^31 + 322563211264 * q^34 - 1829607146400 * q^35 + 712559427584 * q^36 - 2307595824192 * q^39 - 72142028800 * q^40 + 6699117519216 * q^41 - 1563617132544 * q^44 - 9090807477800 * q^45 + 12178733699072 * q^46 - 15809163185544 * q^49 - 13485542400000 * q^50 + 40555579650176 * q^51 - 7241111674880 * q^54 - 39746288199200 * q^55 + 8181308719104 * q^56 + 3791808509280 * q^59 - 89273139200 * q^60 + 57800629300816 * q^61 - 35184372088832 * q^64 + 58028394892800 * q^65 - 82398766186496 * q^66 + 59060996328448 * q^69 + 60817223987200 * q^70 - 245426235422784 * q^71 + 53331092987904 * q^74 + 226448486200000 * q^75 - 106155477565440 * q^76 + 624094605411840 * q^79 + 67484673638400 * q^80 - 1376711600108152 * q^81 + 241833173057536 * q^84 + 1092463762441600 * q^85 - 8937574699008 * q^86 - 635249793637680 * q^89 + 851824438169600 * q^90 - 976491706492224 * q^91 - 537030386200576 * q^94 - 1859590136604000 * q^95 - 14293651161088 * q^96 + 1626246829353248 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$-1$

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 $

$2$		−	128.000i		−	0.707107i
$2$		−	128.000i		−	0.707107i
$3$			5604.61i			1.47957i	0.672842	+	0.739786i	$0.265073\pi$
$3$			5604.61i			1.47957i	−0.672842	+	0.739786i	$0.734927\pi$
$4$	−16384.0			−0.500000
$5$	162285.	−	64661.7i	0.928974	−	0.370145i
$5$	162285.	−	64661.7i	0.928974	−	0.370145i
$6$	717390.			1.04622
$7$			750784.i			0.344572i	0.985047	+	0.172286i	$0.0551153\pi$
$7$			750784.i			0.344572i	−0.985047	+	0.172286i	$0.944885\pi$
$8$			2.09715e6i			0.353553i
$9$	−1.70628e7			−1.18913
$10$	−8.27669e6	−	2.07725e7i	−0.261732	−	0.656884i
$11$	−6.42490e7			−0.994080			−0.497040	−	0.867728i	$-0.665580\pi$
$11$	−6.42490e7			−0.994080			−0.497040	+	0.867728i	$0.665580\pi$
$12$		−	9.18260e7i		−	0.739786i
$13$			3.28952e8i			1.45397i	0.686651	+	0.726987i	$0.259080\pi$
$13$			3.28952e8i			1.45397i	−0.686651	+	0.726987i	$0.740920\pi$
$14$	9.61003e7			0.243649
$15$	3.62404e8	+	9.09545e8i	0.547656	+	1.37448i
$16$	2.68435e8			0.250000
$17$			6.22608e8i			0.368000i	0.982926	+	0.184000i	$0.0589046\pi$
$17$			6.22608e8i			0.368000i	−0.982926	+	0.184000i	$0.941095\pi$
$18$			2.18403e9i			0.840844i
$19$	−4.73142e9			−1.21434			−0.607169	−	0.794573i	$-0.707695\pi$
$19$	−4.73142e9			−1.21434			−0.607169	+	0.794573i	$0.707695\pi$
$20$	−2.65888e9	+	1.05942e9i	−0.464487	+	0.185073i
$21$	−4.20785e9			−0.509819
$22$			8.22387e9i			0.702921i
$23$			1.90311e10i			1.16548i	0.812659	+	0.582739i	$0.198019\pi$
$23$			1.90311e10i			1.16548i	−0.812659	+	0.582739i	$0.801981\pi$
$24$	−1.17537e10			−0.523108
$25$	2.21553e10	−	2.09872e10i	0.725985	−	0.687710i
$26$	4.21058e10			1.02812
$27$		−	1.52101e10i		−	0.279837i
$28$		−	1.23008e10i		−	0.172286i
$29$	−1.83680e11			−1.97732			−0.988660	−	0.150170i	$-0.952018\pi$
$29$	−1.83680e11			−1.97732			−0.988660	+	0.150170i	$0.952018\pi$
$30$	1.16422e11	−	4.63877e10i	0.971907	−	0.387251i
$31$	1.39047e11			0.907713			0.453857	−	0.891075i	$-0.350048\pi$
$31$	1.39047e11			0.907713			0.453857	+	0.891075i	$0.350048\pi$
$32$		−	3.43597e10i		−	0.176777i
$33$		−	3.60091e11i		−	1.47081i
$34$	7.96938e10			0.260215
$35$	4.85469e10	+	1.21841e11i	0.127542	+	0.320098i
$36$	2.79556e11			0.594567
$37$		−	5.52467e11i		−	0.956740i	−0.878158	−	0.478370i	$-0.841228\pi$
$37$		−	5.52467e11i		−	0.956740i	0.878158	−	0.478370i	$-0.158772\pi$
$38$			6.05622e11i			0.858667i
$39$	−1.84365e12			−2.15126
$40$	1.35605e11	+	3.40336e11i	0.130866	+	0.328442i
$41$	6.85825e11			0.549964			0.274982	−	0.961449i	$-0.411328\pi$
$41$	6.85825e11			0.549964			0.274982	+	0.961449i	$0.411328\pi$
$42$			5.38605e11i			0.360496i
$43$			1.71935e11i			0.0964606i	0.998836	+	0.0482303i	$0.0153581\pi$
$43$			1.71935e11i			0.0964606i	−0.998836	+	0.0482303i	$0.984642\pi$
$44$	1.05266e12			0.497040
$45$	−2.76903e12	+	1.10331e12i	−1.10467	+	0.440152i
$46$	2.43598e12			0.824118
$47$			5.47086e12i			1.57515i	0.616219	+	0.787575i	$0.288664\pi$
$47$			5.47086e12i			1.57515i	−0.616219	+	0.787575i	$0.711336\pi$
$48$			1.50448e12i			0.369893i
$49$	4.18389e12			0.881270
$50$	−2.68637e12	−	2.83588e12i	−0.486285	−	0.513349i
$51$	−3.48947e12			−0.544482
$52$		−	5.38954e12i		−	0.726987i
$53$		−	8.40382e12i		−	0.982670i	−0.870971	−	0.491335i	$-0.836509\pi$
$53$		−	8.40382e12i		−	0.982670i	0.870971	−	0.491335i	$-0.163491\pi$
$54$	−1.94690e12			−0.197874
$55$	−1.04267e13	+	4.15445e12i	−0.923474	+	0.367954i
$56$	−1.57451e12			−0.121825
$57$		−	2.65178e13i		−	1.79670i
$58$			2.35110e13i			1.39818i
$59$	2.89419e13			1.51404			0.757019	−	0.653393i	$-0.226655\pi$
$59$	2.89419e13			1.51404			0.757019	+	0.653393i	$0.226655\pi$
$60$	−5.93762e12	−	1.49020e13i	−0.273828	−	0.687242i
$61$	4.32242e13			1.76098			0.880488	−	0.474068i	$-0.157215\pi$
$61$	4.32242e13			1.76098			0.880488	+	0.474068i	$0.157215\pi$
$62$		−	1.77980e13i		−	0.641850i
$63$		−	1.28104e13i		−	0.409742i
$64$	−4.39805e12			−0.125000
$65$	2.12706e13	+	5.33839e13i	0.538181	+	1.35070i
$66$	−4.60916e13			−1.04002
$67$			3.51746e13i			0.709035i	0.935049	+	0.354518i	$0.115355\pi$
$67$			3.51746e13i			0.709035i	−0.935049	+	0.354518i	$0.884645\pi$
$68$		−	1.02008e13i		−	0.184000i
$69$	−1.06662e14			−1.72441
$70$	1.55957e13	−	6.21401e12i	0.226344	−	0.0901855i
$71$	−5.12379e13			−0.668581			−0.334290	−	0.942470i	$-0.608497\pi$
$71$	−5.12379e13			−0.668581			−0.334290	+	0.942470i	$0.608497\pi$
$72$		−	3.57832e13i		−	0.420422i
$73$			1.73922e13i			0.184261i	0.995747	+	0.0921304i	$0.0293677\pi$
$73$			1.73922e13i			0.184261i	−0.995747	+	0.0921304i	$0.970632\pi$
$74$	−7.07158e13			−0.676517
$75$	1.17625e14	+	1.24172e14i	1.01752	+	1.07415i
$76$	7.75196e13			0.607169
$77$		−	4.82371e13i		−	0.342532i
$78$			2.35987e14i			1.52117i
$79$	1.09277e14			0.640212			0.320106	−	0.947382i	$-0.396281\pi$
$79$	1.09277e14			0.640212			0.320106	+	0.947382i	$0.396281\pi$
$80$	4.35631e13	−	1.73575e13i	0.232243	−	0.0925363i
$81$	−1.59585e14			−0.775095
$82$		−	8.77856e13i		−	0.388883i
$83$		−	1.44003e14i		−	0.582485i	−0.956649	−	0.291242i	$-0.905931\pi$
$83$		−	1.44003e14i		−	0.582485i	0.956649	−	0.291242i	$-0.0940686\pi$
$84$	6.89415e13			0.254909
$85$	4.02589e13	+	1.01040e14i	0.136213	+	0.341862i
$86$	2.20076e13			0.0682079
$87$		−	1.02946e15i		−	2.92559i
$88$		−	1.34740e14i		−	0.351460i
$89$	−1.30531e14			−0.312816			−0.156408	−	0.987693i	$-0.549991\pi$
$89$	−1.30531e14			−0.312816			−0.156408	+	0.987693i	$0.549991\pi$
$90$	1.41223e14	+	3.54436e14i	0.311234	+	0.781122i
$91$	−2.46972e14			−0.500999
$92$		−	3.11805e14i		−	0.582739i
$93$			7.79304e14i			1.34303i
$94$	7.00270e14			1.11380
$95$	−7.67839e14	+	3.05942e14i	−1.12809	+	0.449481i
$96$	1.92573e14			0.261554
$97$		−	6.80028e14i		−	0.854553i	−0.904121	−	0.427276i	$-0.859473\pi$
$97$		−	6.80028e14i		−	0.854553i	0.904121	−	0.427276i	$-0.140527\pi$
$98$		−	5.35537e14i		−	0.623152i
$99$	1.09627e15			1.18209
$100$	−3.62993e14	+	3.43855e14i	−0.362993	+	0.343855i
$101$	−2.05175e14			−0.190421			−0.0952103	−	0.995457i	$-0.530352\pi$
$101$	−2.05175e14			−0.190421			−0.0952103	+	0.995457i	$0.530352\pi$
$102$			4.46653e14i			0.385007i
$103$			1.95096e15i			1.56304i	0.623883	+	0.781518i	$0.285554\pi$
$103$			1.95096e15i			1.56304i	−0.623883	+	0.781518i	$0.714446\pi$
$104$	−6.89861e14			−0.514058
$105$	−6.82872e14	+	2.72087e14i	−0.473608	+	0.188707i
$106$	−1.07569e15			−0.694852
$107$		−	5.56074e14i		−	0.334776i	−0.985891	−	0.167388i	$-0.946467\pi$
$107$		−	5.56074e14i		−	0.334776i	0.985891	−	0.167388i	$-0.0535333\pi$
$108$			2.49203e14i			0.139918i
$109$	−7.26916e14			−0.380878			−0.190439	−	0.981699i	$-0.560991\pi$
$109$	−7.26916e14			−0.380878			−0.190439	+	0.981699i	$0.560991\pi$
$110$	5.31769e14	+	1.33461e15i	0.260183	+	0.652995i
$111$	3.09637e15			1.41557
$112$			2.01537e14i			0.0861429i
$113$		−	2.73996e14i		−	0.109561i	−0.998498	−	0.0547805i	$-0.982554\pi$
$113$		−	2.73996e14i		−	0.109561i	0.998498	−	0.0547805i	$-0.0174459\pi$
$114$	−3.39428e15			−1.27046
$115$	1.23058e15	+	3.08846e15i	0.431396	+	1.08270i
$116$	3.00941e15			0.988660
$117$		−	5.61282e15i		−	1.72897i
$118$		−	3.70456e15i		−	1.07059i
$119$	−4.67444e14			−0.126802
$120$	−1.90745e15	+	7.60015e14i	−0.485953	+	0.193626i
$121$	−4.93127e13			−0.0118051
$122$		−	5.53270e15i		−	1.24520i
$123$			3.84378e15i			0.813711i
$124$	−2.27815e15			−0.453857
$125$	2.23841e15	−	4.83852e15i	0.419869	−	0.907585i
$126$	−1.63974e15			−0.289731
$127$			2.58397e15i			0.430288i	0.976582	+	0.215144i	$0.0690221\pi$
$127$			2.58397e15i			0.430288i	−0.976582	+	0.215144i	$0.930978\pi$
$128$			5.62950e14i			0.0883883i
$129$	−9.63627e14			−0.142720
$130$	6.83314e15	−	2.72263e15i	0.955092	−	0.380552i
$131$	5.04151e15			0.665312			0.332656	−	0.943048i	$-0.392055\pi$
$131$	5.04151e15			0.665312			0.332656	+	0.943048i	$0.392055\pi$
$132$			5.89973e15i			0.735406i
$133$		−	3.55228e15i		−	0.418427i
$134$	4.50235e15			0.501364
$135$	−9.83512e14	−	2.46838e15i	−0.103580	−	0.259961i
$136$	−1.30570e15			−0.130108
$137$			8.36791e15i			0.789247i	0.918843	+	0.394623i	$0.129125\pi$
$137$			8.36791e15i			0.789247i	−0.918843	+	0.394623i	$0.870875\pi$
$138$			1.36527e16i			1.21934i
$139$	1.00021e16			0.846210			0.423105	−	0.906081i	$-0.360940\pi$
$139$	1.00021e16			0.846210			0.423105	+	0.906081i	$0.360940\pi$
$140$	−7.95393e14	−	1.99624e15i	−0.0637708	−	0.160049i
$141$	−3.06621e16			−2.33055
$142$			6.55845e15i			0.472758i
$143$		−	2.11348e16i		−	1.44537i
$144$	−4.58025e15			−0.297283
$145$	−2.98085e16	+	1.18771e16i	−1.83688	+	0.731895i
$146$	2.22620e15			0.130292
$147$			2.34491e16i			1.30390i
$148$			9.05163e15i			0.478370i
$149$	1.91906e16			0.964255			0.482127	−	0.876101i	$-0.339864\pi$
$149$	1.91906e16			0.964255			0.482127	+	0.876101i	$0.339864\pi$
$150$	1.58940e16	−	1.50560e16i	0.759537	−	0.719493i
$151$	−1.28498e16			−0.584210			−0.292105	−	0.956386i	$-0.594356\pi$
$151$	−1.28498e16			−0.584210			−0.292105	+	0.956386i	$0.594356\pi$
$152$		−	9.92251e15i		−	0.429333i
$153$		−	1.06234e16i		−	0.437601i
$154$	−6.17435e15			−0.242207
$155$	2.25652e16	−	8.99101e15i	0.843242	−	0.335986i
$156$	3.02063e16			1.07563
$157$			2.18265e16i			0.740861i	0.928860	+	0.370431i	$0.120790\pi$
$157$			2.18265e16i			0.740861i	−0.928860	+	0.370431i	$0.879210\pi$
$158$		−	1.39874e16i		−	0.452698i
$159$	4.71001e16			1.45393
$160$	−2.22176e15	−	5.57607e15i	−0.0654330	−	0.164221i
$161$	−1.42882e16			−0.401591
$162$			2.04269e16i			0.548075i
$163$		−	1.03504e16i		−	0.265185i	−0.991171	−	0.132592i	$-0.957670\pi$
$163$		−	1.03504e16i		−	0.265185i	0.991171	−	0.132592i	$-0.0423301\pi$
$164$	−1.12366e16			−0.274982
$165$	−2.32841e16	−	5.84374e16i	−0.544414	−	1.36635i
$166$	−1.84323e16			−0.411879
$167$		−	1.43702e16i		−	0.306964i	−0.988151	−	0.153482i	$-0.950951\pi$
$167$		−	1.43702e16i		−	0.306964i	0.988151	−	0.153482i	$-0.0490488\pi$
$168$		−	8.82451e15i		−	0.180248i
$169$	−5.70232e16			−1.11404
$170$	1.29331e16	−	5.15313e15i	0.241733	−	0.0963174i
$171$	8.07311e16			1.44401
$172$		−	2.81698e15i		−	0.0482303i
$173$		−	9.96258e16i		−	1.63315i	−0.577240	−	0.816575i	$-0.695870\pi$
$173$		−	9.96258e16i		−	1.63315i	0.577240	−	0.816575i	$-0.304130\pi$
$174$	−1.31770e17			−2.06870
$175$	1.57569e16	+	1.66339e16i	0.236966	+	0.250154i
$176$	−1.72467e16			−0.248520
$177$			1.62208e17i			2.24013i
$178$			1.67080e16i			0.221194i
$179$	4.87802e16			0.619221			0.309611	−	0.950863i	$-0.399801\pi$
$179$	4.87802e16			0.619221			0.309611	+	0.950863i	$0.399801\pi$
$180$	4.53678e16	−	1.80766e16i	0.552337	−	0.220076i
$181$	5.99244e16			0.699866			0.349933	−	0.936775i	$-0.386204\pi$
$181$	5.99244e16			0.699866			0.349933	+	0.936775i	$0.386204\pi$
$182$			3.16124e16i			0.354259i
$183$			2.42255e17i			2.60549i
$184$	−3.99110e16			−0.412059
$185$	−3.57235e16	−	8.96572e16i	−0.354132	−	0.888786i
$186$	9.97509e16			0.949664
$187$		−	4.00019e16i		−	0.365821i
$188$		−	8.96346e16i		−	0.787575i
$189$	1.14195e16			0.0964238
$190$	3.91605e16	+	9.82834e16i	0.317831	+	0.797679i
$191$	−5.97882e16			−0.466514			−0.233257	−	0.972415i	$-0.574938\pi$
$191$	−5.97882e16			−0.466514			−0.233257	+	0.972415i	$0.574938\pi$
$192$		−	2.46493e16i		−	0.184947i
$193$			1.14841e17i			0.828734i	0.910110	+	0.414367i	$0.135997\pi$
$193$			1.14841e17i			0.828734i	−0.910110	+	0.414367i	$0.864003\pi$
$194$	−8.70436e16			−0.604260
$195$	−2.99196e17	+	1.19213e17i	−1.99846	+	0.796278i
$196$	−6.85488e16			−0.440635
$197$		−	2.39868e17i		−	1.48415i	−0.670320	−	0.742073i	$-0.733843\pi$
$197$		−	2.39868e17i		−	1.48415i	0.670320	−	0.742073i	$-0.266157\pi$
$198$		−	1.40322e17i		−	0.835866i
$199$	3.00933e17			1.72612			0.863062	−	0.505097i	$-0.168543\pi$
$199$	3.00933e17			1.72612			0.863062	+	0.505097i	$0.168543\pi$
$200$	4.40135e16	+	4.64631e16i	0.243142	+	0.256675i
$201$	−1.97140e17			−1.04907
$202$			2.62624e16i			0.134648i
$203$		−	1.37904e17i		−	0.681329i
$204$	5.71716e16			0.272241
$205$	1.11299e17	−	4.43466e16i	0.510902	−	0.203566i
$206$	2.49723e17			1.10523
$207$		−	3.24723e17i		−	1.38591i
$208$			8.83023e16i			0.363494i
$209$	3.03989e17			1.20715
$210$	3.48271e16	+	8.74076e16i	0.133436	+	0.334892i
$211$	−2.88668e17			−1.06728			−0.533642	−	0.845711i	$-0.679177\pi$
$211$	−2.88668e17			−1.06728			−0.533642	+	0.845711i	$0.679177\pi$
$212$			1.37688e17i			0.491335i
$213$		−	2.87169e17i		−	0.989213i
$214$	−7.11775e16			−0.236722
$215$	1.11176e16	+	2.79024e16i	0.0357044	+	0.0896094i
$216$	3.18979e16			0.0989372
$217$			1.04394e17i			0.312772i
$218$			9.30452e16i			0.269321i
$219$	−9.74765e16			−0.272627
$220$	1.70830e17	−	6.80665e16i	0.461737	−	0.183977i
$221$	−2.04808e17			−0.535062
$222$		−	3.96335e17i		−	1.00096i
$223$			4.42828e17i			1.08131i	0.841246	+	0.540653i	$0.181823\pi$
$223$			4.42828e17i			1.08131i	−0.841246	+	0.540653i	$0.818177\pi$
$224$	2.57967e16			0.0609123
$225$	−3.78031e17	+	3.58101e17i	−0.863293	+	0.817779i
$226$	−3.50715e16			−0.0774713
$227$		−	5.69523e17i		−	1.21707i	−0.793525	−	0.608537i	$-0.791757\pi$
$227$		−	5.69523e17i		−	1.21707i	0.793525	−	0.608537i	$-0.208243\pi$
$228$			4.34467e17i			0.898351i
$229$	1.19767e17			0.239647			0.119823	−	0.992795i	$-0.461767\pi$
$229$	1.19767e17			0.239647			0.119823	+	0.992795i	$0.461767\pi$
$230$	3.95323e17	−	1.57514e17i	0.765584	−	0.305043i
$231$	2.70350e17			0.506801
$232$		−	3.85205e17i		−	0.699088i
$233$			8.54125e17i			1.50090i	0.660927	+	0.750450i	$0.270163\pi$
$233$			8.54125e17i			1.50090i	−0.660927	+	0.750450i	$0.729837\pi$
$234$	−7.18441e17			−1.22257
$235$	3.53755e17	+	8.87839e17i	0.583034	+	1.46327i
$236$	−4.74184e17			−0.757019
$237$			6.12453e17i			0.947240i
$238$			5.98328e16i			0.0896628i
$239$	−6.74888e17			−0.980048			−0.490024	−	0.871709i	$-0.663012\pi$
$239$	−6.74888e17			−0.980048			−0.490024	+	0.871709i	$0.663012\pi$
$240$	9.72820e16	+	2.44154e17i	0.136914	+	0.343621i
$241$	2.59048e17			0.353389			0.176695	−	0.984266i	$-0.443460\pi$
$241$	2.59048e17			0.353389			0.176695	+	0.984266i	$0.443460\pi$
$242$			6.31203e15i			0.00834745i
$243$		−	1.11266e18i		−	1.42665i
$244$	−7.08186e17			−0.880488
$245$	6.78982e17	−	2.70537e17i	0.818677	−	0.326198i
$246$	4.92004e17			0.575381
$247$		−	1.55641e18i		−	1.76562i
$248$			2.91603e17i			0.320925i
$249$	8.07079e17			0.861828
$250$	−6.19330e17	−	2.86516e17i	−0.641759	−	0.296892i
$251$	−3.10940e17			−0.312697			−0.156348	−	0.987702i	$-0.549972\pi$
$251$	−3.10940e17			−0.312697			−0.156348	+	0.987702i	$0.549972\pi$
$252$			2.09886e17i			0.204871i
$253$		−	1.22273e18i		−	1.15858i
$254$	3.30748e17			0.304260
$255$	−5.66290e17	+	2.25635e17i	−0.505810	+	0.201537i
$256$	7.20576e16			0.0625000
$257$			2.21827e18i			1.86860i	0.356489	+	0.934300i	$0.383974\pi$
$257$			2.21827e18i			1.86860i	−0.356489	+	0.934300i	$0.616026\pi$
$258$			1.23344e17i			0.100919i
$259$	4.14784e17			0.329665
$260$	−3.48497e17	−	8.74642e17i	−0.269091	−	0.675352i
$261$	3.13409e18			2.35130
$262$		−	6.45313e17i		−	0.470447i
$263$			5.94995e17i			0.421546i	0.977535	+	0.210773i	$0.0675981\pi$
$263$			5.94995e17i			0.421546i	−0.977535	+	0.210773i	$0.932402\pi$
$264$	7.55165e17			0.520011
$265$	−5.43405e17	−	1.36381e18i	−0.363730	−	0.912874i
$266$	−4.54691e17			−0.295872
$267$		−	7.31575e17i		−	0.462833i
$268$		−	5.76300e17i		−	0.354518i
$269$	3.12429e17			0.186900			0.0934499	−	0.995624i	$-0.470211\pi$
$269$	3.12429e17			0.186900			0.0934499	+	0.995624i	$0.470211\pi$
$270$	−3.15952e17	+	1.25890e17i	−0.183820	+	0.0732422i
$271$	−2.94759e18			−1.66800			−0.834002	−	0.551761i	$-0.813956\pi$
$271$	−2.94759e18			−1.66800			−0.834002	+	0.551761i	$0.813956\pi$
$272$			1.67130e17i			0.0920000i
$273$		−	1.38418e18i		−	0.741263i
$274$	1.07109e18			0.558082
$275$	−1.42346e18	+	1.34841e18i	−0.721687	+	0.683639i
$276$	1.74755e18			0.862205
$277$			2.49111e18i			1.19618i	0.801430	+	0.598088i	$0.204073\pi$
$277$			2.49111e18i			1.19618i	−0.801430	+	0.598088i	$0.795927\pi$
$278$		−	1.28026e18i		−	0.598361i
$279$	−2.37253e18			−1.07939
$280$	−2.55519e17	+	1.01810e17i	−0.113172	+	0.0450927i
$281$	−2.25219e18			−0.971198			−0.485599	−	0.874182i	$-0.661398\pi$
$281$	−2.25219e18			−0.971198			−0.485599	+	0.874182i	$0.661398\pi$
$282$			3.92474e18i			1.64795i
$283$			2.94583e18i			1.20451i	0.798305	+	0.602254i	$0.205730\pi$
$283$			2.94583e18i			1.20451i	−0.798305	+	0.602254i	$0.794270\pi$
$284$	8.39482e17			0.334290
$285$	−1.71468e18	−	4.30344e18i	−0.665040	−	1.66909i
$286$	−2.70526e18			−1.02203
$287$			5.14906e17i			0.189502i
$288$			5.86272e17i			0.210211i
$289$	2.47478e18			0.864576
$290$	1.52026e18	+	3.81549e18i	0.517528	+	1.29887i
$291$	3.81129e18			1.26437
$292$		−	2.84954e17i		−	0.0921304i
$293$			2.02736e18i			0.638885i	0.947606	+	0.319443i	$0.103496\pi$
$293$			2.02736e18i			0.638885i	−0.947606	+	0.319443i	$0.896504\pi$
$294$	3.00148e18			0.921999
$295$	4.69684e18	−	1.87143e18i	1.40650	−	0.560414i
$296$	1.15861e18			0.338259
$297$			9.77235e17i			0.278180i
$298$		−	2.45640e18i		−	0.681831i
$299$	−6.26030e18			−1.69458
$300$	−1.92717e18	−	2.03443e18i	−0.508758	−	0.537074i
$301$	−1.29086e17			−0.0332376
$302$			1.64477e18i			0.413099i
$303$		−	1.14993e18i		−	0.281741i
$304$	−1.27008e18			−0.303585
$305$	7.01465e18	−	2.79495e18i	1.63590	−	0.651817i
$306$	−1.35980e18			−0.309431
$307$			4.98190e17i			0.110626i	0.998469	+	0.0553130i	$0.0176157\pi$
$307$			4.98190e17i			0.110626i	−0.998469	+	0.0553130i	$0.982384\pi$
$308$			7.90317e17i			0.171266i
$309$	−1.09344e19			−2.31262
$310$	−1.15085e18	−	2.88835e18i	−0.237578	−	0.596262i
$311$	−3.32674e18			−0.670372			−0.335186	−	0.942152i	$-0.608799\pi$
$311$	−3.32674e18			−0.670372			−0.335186	+	0.942152i	$0.608799\pi$
$312$		−	3.86641e18i		−	0.760585i
$313$		−	5.87386e18i		−	1.12808i	−0.825746	−	0.564042i	$-0.809246\pi$
$313$		−	5.87386e18i		−	1.12808i	0.825746	−	0.564042i	$-0.190754\pi$
$314$	2.79379e18			0.523868
$315$	−8.28345e17	−	2.07894e18i	−0.151664	−	0.380639i
$316$	−1.79039e18			−0.320106
$317$			6.17308e18i			1.07785i	0.842354	+	0.538924i	$0.181169\pi$
$317$			6.17308e18i			1.07785i	−0.842354	+	0.538924i	$0.818831\pi$
$318$		−	6.02882e18i		−	1.02808i
$319$	1.18013e19			1.96561
$320$	−7.13737e17	+	2.84385e17i	−0.116122	+	0.0462681i
$321$	3.11658e18			0.495325
$322$			1.82889e18i			0.283968i
$323$		−	2.94582e18i		−	0.446876i
$324$	2.61464e18			0.387548
$325$	6.90379e18	+	7.28802e18i	0.999913	+	1.05556i
$326$	−1.32485e18			−0.187514
$327$		−	4.07408e18i		−	0.563536i
$328$			1.43828e18i			0.194442i
$329$	−4.10743e18			−0.542752
$330$	−7.47998e18	+	2.98036e18i	−0.966153	+	0.384959i
$331$	9.77672e18			1.23448			0.617239	−	0.786776i	$-0.288251\pi$
$331$	9.77672e18			1.23448			0.617239	+	0.786776i	$0.288251\pi$
$332$			2.35934e18i			0.291242i
$333$			9.42662e18i			1.13769i
$334$	−1.83938e18			−0.217057
$335$	2.27445e18	+	5.70831e18i	0.262446	+	0.658675i
$336$	−1.12954e18			−0.127455
$337$		−	6.39590e18i		−	0.705793i	−0.935662	−	0.352896i	$-0.885197\pi$
$337$		−	6.39590e18i		−	0.705793i	0.935662	−	0.352896i	$-0.114803\pi$
$338$			7.29897e18i			0.787747i
$339$	1.53564e18			0.162103
$340$	−6.59601e17	−	1.65544e18i	−0.0681067	−	0.170931i
$341$	−8.93363e18			−0.902340
$342$		−	1.03336e19i		−	1.02107i
$343$			6.70559e18i			0.648233i
$344$	−3.60573e17			−0.0341040
$345$	−1.73096e19	+	6.89692e18i	−1.60193	+	0.638282i
$346$	−1.27521e19			−1.15481
$347$		−	7.24939e18i		−	0.642437i	−0.947005	−	0.321218i	$-0.895908\pi$
$347$		−	7.24939e18i		−	0.642437i	0.947005	−	0.321218i	$-0.104092\pi$
$348$			1.68666e19i			1.46279i
$349$	−2.75878e18			−0.234168			−0.117084	−	0.993122i	$-0.537355\pi$
$349$	−2.75878e18			−0.234168			−0.117084	+	0.993122i	$0.537355\pi$
$350$	2.12913e18	−	2.01688e18i	0.176886	−	0.167560i
$351$	5.00339e18			0.406875
$352$			2.20758e18i			0.175730i
$353$		−	1.14599e19i		−	0.893037i	−0.894774	−	0.446518i	$-0.852664\pi$
$353$		−	1.14599e19i		−	0.893037i	0.894774	−	0.446518i	$-0.147336\pi$
$354$	2.07626e19			1.58401
$355$	−8.31515e18	+	3.31313e18i	−0.621094	+	0.247472i
$356$	2.13862e18			0.156408
$357$		−	2.61984e18i		−	0.187613i
$358$		−	6.24386e18i		−	0.437855i
$359$	−1.51795e18			−0.104243			−0.0521216	−	0.998641i	$-0.516598\pi$
$359$	−1.51795e18			−0.104243			−0.0521216	+	0.998641i	$0.516598\pi$
$360$	−2.31380e18	−	5.80708e18i	−0.155617	−	0.390561i
$361$	7.20523e18			0.474618
$362$		−	7.67033e18i		−	0.494880i
$363$		−	2.76379e17i		−	0.0174665i
$364$	4.04638e18			0.250499
$365$	1.12461e18	+	2.82249e18i	0.0682032	+	0.171174i
$366$	3.10086e19			1.84236
$367$			1.52340e19i			0.886784i	0.896328	+	0.443392i	$0.146225\pi$
$367$			1.52340e19i			0.886784i	−0.896328	+	0.443392i	$0.853775\pi$
$368$			5.10861e18i			0.291370i
$369$	−1.17021e19			−0.653980
$370$	−1.14761e19	+	4.57260e18i	−0.628467	+	0.250409i
$371$	6.30945e18			0.338600
$372$		−	1.27681e19i		−	0.671514i
$373$		−	1.35173e19i		−	0.696747i	−0.937356	−	0.348374i	$-0.886734\pi$
$373$		−	1.35173e19i		−	0.696747i	0.937356	−	0.348374i	$-0.113266\pi$
$374$	−5.12025e18			−0.258675
$375$	2.71180e19	+	1.25454e19i	1.34284	+	0.621226i
$376$	−1.14732e19			−0.556899
$377$		−	6.04218e19i		−	2.87497i
$378$		−	1.46170e18i		−	0.0681819i
$379$	−1.52188e19			−0.695962			−0.347981	−	0.937502i	$-0.613133\pi$
$379$	−1.52188e19			−0.695962			−0.347981	+	0.937502i	$0.613133\pi$
$380$	1.25803e19	−	5.01255e18i	0.564044	−	0.224741i
$381$	−1.44821e19			−0.636642
$382$			7.65289e18i			0.329876i
$383$		−	1.68289e18i		−	0.0711319i	−0.999367	−	0.0355660i	$-0.988677\pi$
$383$		−	1.68289e18i		−	0.0711319i	0.999367	−	0.0355660i	$-0.0113234\pi$
$384$	−3.15512e18			−0.130777
$385$	−3.11909e18	−	7.82817e18i	−0.126786	−	0.318203i
$386$	1.46996e19			0.586004
$387$		−	2.93368e18i		−	0.114704i
$388$			1.11416e19i			0.427276i
$389$	−1.26842e19			−0.477135			−0.238567	−	0.971126i	$-0.576678\pi$
$389$	−1.26842e19			−0.477135			−0.238567	+	0.971126i	$0.576678\pi$
$390$	1.52593e19	+	3.82971e19i	0.563054	+	1.41313i
$391$	−1.18489e19			−0.428896
$392$			8.77424e18i			0.311576i
$393$			2.82557e19i			0.984378i
$394$	−3.07032e19			−1.04945
$395$	1.77340e19	−	7.06601e18i	0.594740	−	0.236971i
$396$	−1.79612e19			−0.591047
$397$			4.97579e18i			0.160669i	0.996768	+	0.0803347i	$0.0255989\pi$
$397$			4.97579e18i			0.160669i	−0.996768	+	0.0803347i	$0.974401\pi$
$398$		−	3.85195e19i		−	1.22055i
$399$	1.99091e19			0.619092
$400$	5.94727e18	−	5.63372e18i	0.181496	−	0.171928i
$401$	1.84208e19			0.551728			0.275864	−	0.961197i	$-0.411036\pi$
$401$	1.84208e19			0.551728			0.275864	+	0.961197i	$0.411036\pi$
$402$			2.52339e19i			0.741804i
$403$			4.57397e19i			1.31979i
$404$	3.36159e18			0.0952103
$405$	−2.58983e19	+	1.03190e19i	−0.720043	+	0.286898i
$406$	−1.76517e19			−0.481772
$407$			3.54955e19i			0.951076i
$408$		−	7.31796e18i		−	0.192504i
$409$	4.88294e19			1.26112			0.630560	−	0.776141i	$-0.282825\pi$
$409$	4.88294e19			1.26112			0.630560	+	0.776141i	$0.282825\pi$
$410$	−5.67636e18	−	1.42463e19i	−0.143943	−	0.361262i
$411$	−4.68989e19			−1.16775
$412$		−	3.19645e19i		−	0.781518i
$413$			2.17291e19i			0.521695i
$414$	−4.15645e19			−0.979986
$415$	−9.31145e18	−	2.33695e19i	−0.215604	−	0.541113i
$416$	1.13027e19			0.257029
$417$			5.60576e19i			1.25203i
$418$		−	3.89106e19i		−	0.853584i
$419$	−6.57564e18			−0.141688			−0.0708440	−	0.997487i	$-0.522569\pi$
$419$	−6.57564e18			−0.141688			−0.0708440	+	0.997487i	$0.522569\pi$
$420$	1.11882e19	−	4.45787e18i	0.236804	−	0.0943534i
$421$	7.89697e18			0.164189			0.0820946	−	0.996625i	$-0.473839\pi$
$421$	7.89697e18			0.164189			0.0820946	+	0.996625i	$0.473839\pi$
$422$			3.69495e19i			0.754683i
$423$		−	9.33480e19i		−	1.87306i
$424$	1.76241e19			0.347426
$425$	1.30668e19	+	1.37941e19i	0.253077	+	0.267162i
$426$	−3.67576e19			−0.699479
$427$			3.24521e19i			0.606783i
$428$			9.11072e18i			0.167388i
$429$	1.18452e20			2.13852
$430$	3.57151e18	−	1.42305e18i	0.0633634	−	0.0252468i
$431$	3.95542e19			0.689626			0.344813	−	0.938671i	$-0.387942\pi$
$431$	3.95542e19			0.689626			0.344813	+	0.938671i	$0.387942\pi$
$432$		−	4.08294e18i		−	0.0699591i
$433$			8.53099e19i			1.43661i	0.695726	+	0.718307i	$0.255083\pi$
$433$			8.53099e19i			1.43661i	−0.695726	+	0.718307i	$0.744917\pi$
$434$	1.33625e19			0.221163
$435$	−6.65663e19	−	1.67065e20i	−1.08289	−	2.71780i
$436$	1.19098e19			0.190439
$437$		−	9.00440e19i		−	1.41529i
$438$			1.24770e19i			0.192777i
$439$	9.44015e19			1.43382			0.716911	−	0.697165i	$-0.245555\pi$
$439$	9.44015e19			1.43382			0.716911	+	0.697165i	$0.245555\pi$
$440$	−8.71251e18	−	2.18663e19i	−0.130091	−	0.326498i
$441$	−7.13886e19			−1.04795
$442$			2.62154e19i			0.378346i
$443$		−	8.71116e19i		−	1.23608i	−0.786145	−	0.618042i	$-0.787926\pi$
$443$		−	8.71116e19i		−	1.23608i	0.786145	−	0.618042i	$-0.212074\pi$
$444$	−5.07309e19			−0.707783
$445$	−2.11832e19	+	8.44035e18i	−0.290598	+	0.115787i
$446$	5.66819e19			0.764598
$447$			1.07556e20i			1.42668i
$448$		−	3.30198e18i		−	0.0430715i
$449$	−1.16838e20			−1.49877			−0.749385	−	0.662134i	$-0.769651\pi$
$449$	−1.16838e20			−1.49877			−0.749385	+	0.662134i	$0.769651\pi$
$450$	4.58369e19	+	4.83880e19i	0.578257	+	0.610441i
$451$	−4.40636e19			−0.546708
$452$			4.48915e18i			0.0547805i
$453$		−	7.20181e19i		−	0.864381i
$454$	−7.28989e19			−0.860602
$455$	−4.00798e19	+	1.59696e19i	−0.465415	+	0.185442i
$456$	5.56118e19			0.635230
$457$		−	3.05114e19i		−	0.342839i	−0.985198	−	0.171420i	$-0.945165\pi$
$457$		−	3.05114e19i		−	0.342839i	0.985198	−	0.171420i	$-0.0548354\pi$
$458$		−	1.53302e19i		−	0.169456i
$459$	9.46994e18			0.102980
$460$	−2.01618e19	−	5.06013e19i	−0.215698	−	0.541350i
$461$	1.18278e20			1.24493			0.622466	−	0.782647i	$-0.286131\pi$
$461$	1.18278e20			1.24493			0.622466	+	0.782647i	$0.286131\pi$
$462$		−	3.46048e19i		−	0.358362i
$463$			1.82647e18i			0.0186104i	0.999957	+	0.00930520i	$0.00296198\pi$
$463$			1.82647e18i			0.0186104i	−0.999957	+	0.00930520i	$0.997038\pi$
$464$	−4.93062e19			−0.494330
$465$	5.03911e19	+	1.26469e20i	0.497115	+	1.24764i
$466$	1.09328e20			1.06130
$467$			1.63148e20i			1.55849i	0.626719	+	0.779245i	$0.284397\pi$
$467$			1.63148e20i			1.55849i	−0.626719	+	0.779245i	$0.715603\pi$
$468$			9.19605e19i			0.864485i
$469$	−2.64085e19			−0.244313
$470$	1.13643e20	−	4.52806e19i	1.03469	−	0.412267i
$471$	−1.22329e20			−1.09616
$472$			6.06955e19i			0.535293i
$473$		−	1.10466e19i		−	0.0958895i
$474$	7.83940e19			0.669800
$475$	−1.04826e20	+	9.92995e19i	−0.881592	+	0.835113i
$476$	7.65860e18			0.0634012
$477$			1.43392e20i			1.16853i
$478$			8.63856e19i			0.692998i
$479$	−1.85416e20			−1.46431			−0.732153	−	0.681140i	$-0.761484\pi$
$479$	−1.85416e20			−1.46431			−0.732153	+	0.681140i	$0.761484\pi$
$480$	3.12517e19	−	1.24521e19i	0.242977	−	0.0968129i
$481$	1.81735e20			1.39108
$482$		−	3.31582e19i		−	0.249884i
$483$		−	8.00799e19i		−	0.594183i
$484$	8.07939e17			0.00590254
$485$	−4.39718e19	−	1.10358e20i	−0.316308	−	0.793857i
$486$	−1.42421e20			−1.00879
$487$		−	1.86622e20i		−	1.30165i	−0.759226	−	0.650827i	$-0.774422\pi$
$487$		−	1.86622e20i		−	1.30165i	0.759226	−	0.650827i	$-0.225578\pi$
$488$			9.06478e19i			0.622599i
$489$	5.80097e19			0.392360
$490$	−3.46287e19	−	8.69097e19i	−0.230657	−	0.578892i
$491$	−1.02791e20			−0.674289			−0.337144	−	0.941453i	$-0.609461\pi$
$491$	−1.02791e20			−0.674289			−0.337144	+	0.941453i	$0.609461\pi$
$492$		−	6.29765e19i		−	0.406856i
$493$		−	1.14361e20i		−	0.727654i
$494$	−1.99220e20			−1.24848
$495$	1.77908e20	−	7.08864e19i	1.09813	−	0.437546i
$496$	3.73251e19			0.226928
$497$		−	3.84686e19i		−	0.230374i
$498$		−	1.03306e20i		−	0.609405i
$499$	−5.39171e19			−0.313309			−0.156654	−	0.987653i	$-0.550071\pi$
$499$	−5.39171e19			−0.313309			−0.156654	+	0.987653i	$0.550071\pi$
$500$	−3.66740e19	+	7.92743e19i	−0.209934	+	0.453792i
$501$	8.05391e19			0.454176
$502$			3.98003e19i			0.221110i
$503$			2.48897e20i			1.36226i	0.732163	+	0.681129i	$0.238511\pi$
$503$			2.48897e20i			1.36226i	−0.732163	+	0.681129i	$0.761489\pi$
$504$	2.68655e19			0.144866
$505$	−3.32968e19	+	1.32670e19i	−0.176896	+	0.0704833i
$506$	−1.56509e20			−0.819239
$507$		−	3.19593e20i		−	1.64831i
$508$		−	4.23357e19i		−	0.215144i
$509$	3.29526e20			1.65008			0.825042	−	0.565072i	$-0.191151\pi$
$509$	3.29526e20			1.65008			0.825042	+	0.565072i	$0.191151\pi$
$510$	2.88813e19	+	7.24851e19i	0.142508	+	0.357662i
$511$	−1.30578e19			−0.0634911
$512$		−	9.22337e18i		−	0.0441942i
$513$			7.19655e19i			0.339816i
$514$	2.83939e20			1.32130
$515$	1.26152e20	+	3.16611e20i	0.578550	+	1.45202i
$516$	1.57881e19			0.0713602
$517$		−	3.51497e20i		−	1.56582i
$518$		−	5.30923e19i		−	0.233109i
$519$	5.58364e20			2.41636
$520$	−1.11954e20	+	4.46076e19i	−0.477546	+	0.190276i
$521$	−1.11713e20			−0.469701			−0.234850	−	0.972032i	$-0.575460\pi$
$521$	−1.11713e20			−0.469701			−0.234850	+	0.972032i	$0.575460\pi$
$522$		−	4.01163e20i		−	1.66262i
$523$			5.45166e19i			0.222724i	0.993780	+	0.111362i	$0.0355212\pi$
$523$			5.45166e19i			0.222724i	−0.993780	+	0.111362i	$0.964479\pi$
$524$	−8.26000e19			−0.332656
$525$	−9.32263e19	+	8.83112e19i	−0.370121	+	0.350608i
$526$	7.61594e19			0.298078
$527$			8.65717e19i			0.334038i
$528$		−	9.66611e19i		−	0.367703i
$529$	−9.55461e19			−0.358340
$530$	−1.74568e20	+	6.95558e19i	−0.645500	+	0.257196i
$531$	−4.93829e20			−1.80039
$532$			5.82005e19i			0.209213i
$533$			2.25603e20i			0.799633i
$534$	−9.36416e19			−0.327273
$535$	−3.59567e19	−	9.02425e19i	−0.123916	−	0.310998i
$536$	−7.37664e19			−0.250682
$537$			2.73394e20i			0.916182i
$538$		−	3.99909e19i		−	0.132158i
$539$	−2.68810e20			−0.876053
$540$	1.61139e19	+	4.04419e19i	0.0517901	+	0.129980i
$541$	−3.30314e19			−0.104700			−0.0523501	−	0.998629i	$-0.516671\pi$
$541$	−3.30314e19			−0.104700			−0.0523501	+	0.998629i	$0.516671\pi$
$542$			3.77291e20i			1.17946i
$543$			3.35853e20i			1.03550i
$544$	2.13926e19			0.0650538
$545$	−1.17968e20	+	4.70036e19i	−0.353825	+	0.140980i
$546$	−1.77175e20			−0.524152
$547$		−	3.11541e20i		−	0.909096i	−0.890722	−	0.454548i	$-0.849801\pi$
$547$		−	3.11541e20i		−	0.909096i	0.890722	−	0.454548i	$-0.150199\pi$
$548$		−	1.37100e20i		−	0.394623i
$549$	−7.37525e20			−2.09404
$550$	1.72596e20	+	1.82202e20i	0.483406	+	0.510310i
$551$	8.69068e20			2.40114
$552$		−	2.23686e20i		−	0.609671i
$553$			8.20431e19i			0.220599i
$554$	3.18863e20			0.845825
$555$	5.02494e20	−	2.00216e20i	1.31502	−	0.523964i
$556$	−1.63874e20			−0.423105
$557$			8.43383e19i			0.214838i	0.994214	+	0.107419i	$0.0342586\pi$
$557$			8.43383e19i			0.214838i	−0.994214	+	0.107419i	$0.965741\pi$
$558$			3.03683e20i			0.763246i
$559$	−5.65581e19			−0.140251
$560$	1.30317e19	+	3.27065e19i	0.0318854	+	0.0800245i
$561$	2.24195e20			0.541259
$562$			2.88280e20i			0.686741i
$563$		−	4.37638e20i		−	1.02873i	−0.857571	−	0.514365i	$-0.828027\pi$
$563$		−	4.37638e20i		−	1.02873i	0.857571	−	0.514365i	$-0.171973\pi$
$564$	5.02367e20			1.16527
$565$	−1.77170e19	−	4.44655e19i	−0.0405534	−	0.101779i
$566$	3.77066e20			0.851715
$567$		−	1.19814e20i		−	0.267076i
$568$		−	1.07454e20i		−	0.236379i
$569$	−4.68812e20			−1.01779			−0.508894	−	0.860829i	$-0.669945\pi$
$569$	−4.68812e20			−1.01779			−0.508894	+	0.860829i	$0.669945\pi$
$570$	−5.50840e20	+	2.19480e20i	−1.18022	+	0.470254i
$571$	−5.13667e20			−1.08620			−0.543102	−	0.839667i	$-0.682750\pi$
$571$	−5.13667e20			−1.08620			−0.543102	+	0.839667i	$0.682750\pi$
$572$			3.46273e20i			0.722683i
$573$		−	3.35090e20i		−	0.690242i
$574$	6.59080e19			0.133998
$575$	3.99410e20	+	4.21639e20i	0.801511	+	0.846120i
$576$	7.50428e19			0.148642
$577$		−	4.05010e20i		−	0.791857i	−0.918281	−	0.395929i	$-0.870423\pi$
$577$		−	4.05010e20i		−	0.791857i	0.918281	−	0.395929i	$-0.129577\pi$
$578$		−	3.16772e20i		−	0.611348i
$579$	−6.43637e20			−1.22617
$580$	4.88383e20	−	1.94594e20i	0.918440	−	0.365948i
$581$	1.08115e20			0.200708
$582$		−	4.87846e20i		−	0.894046i
$583$			5.39937e20i			0.976852i
$584$	−3.64741e19			−0.0651461
$585$	−3.62935e20	−	9.10877e20i	−0.639970	−	1.60617i
$586$	2.59502e20			0.451760
$587$		−	5.40996e20i		−	0.929840i	−0.885353	−	0.464920i	$-0.846083\pi$
$587$		−	5.40996e20i		−	0.929840i	0.885353	−	0.464920i	$-0.153917\pi$
$588$		−	3.84189e20i		−	0.651951i
$589$	−6.57890e20			−1.10227
$590$	−2.39543e20	−	6.01195e20i	−0.396272	−	0.994547i
$591$	1.34437e21			2.19590
$592$		−	1.48302e20i		−	0.239185i
$593$		−	1.54553e20i		−	0.246131i	−0.992399	−	0.123065i	$-0.960728\pi$
$593$		−	1.54553e20i		−	0.246131i	0.992399	−	0.123065i	$-0.0392725\pi$
$594$	1.25086e20			0.196703
$595$	−7.58592e19	+	3.02257e19i	−0.117796	+	0.0469353i
$596$	−3.14419e20			−0.482127
$597$			1.68661e21i			2.55393i
$598$			8.01318e20i			1.19825i
$599$	6.17238e20			0.911489			0.455745	−	0.890111i	$-0.349373\pi$
$599$	6.17238e20			0.911489			0.455745	+	0.890111i	$0.349373\pi$
$600$	−2.60407e20	+	2.46678e20i	−0.379769	+	0.359747i
$601$	1.18917e20			0.171271			0.0856356	−	0.996327i	$-0.472708\pi$
$601$	1.18917e20			0.171271			0.0856356	+	0.996327i	$0.472708\pi$
$602$			1.65230e19i			0.0235025i
$603$		−	6.00175e20i		−	0.843137i
$604$	2.10531e20			0.292105
$605$	−8.00272e18	+	3.18864e18i	−0.0109666	+	0.00436959i
$606$	−1.47191e20			−0.199221
$607$			7.93441e20i			1.06072i	0.847773	+	0.530359i	$0.177943\pi$
$607$			7.93441e20i			1.06072i	−0.847773	+	0.530359i	$0.822057\pi$
$608$			1.62570e20i			0.214667i
$609$	7.72899e20			1.00807
$610$	−3.57754e20	−	8.97875e20i	−0.460904	−	1.15676i
$611$	−1.79965e21			−2.29023
$612$			1.74054e20i			0.218800i
$613$		−	6.26963e20i		−	0.778554i	−0.921121	−	0.389277i	$-0.872725\pi$
$613$		−	6.26963e20i		−	0.778554i	0.921121	−	0.389277i	$-0.127275\pi$
$614$	6.37683e19			0.0782244
$615$	2.48545e20	+	6.23788e20i	0.301191	+	0.755917i
$616$	1.01161e20			0.121103
$617$			1.14148e20i			0.134999i	0.997719	+	0.0674994i	$0.0215021\pi$
$617$			1.14148e20i			0.134999i	−0.997719	+	0.0674994i	$0.978498\pi$
$618$			1.39960e21i			1.63527i
$619$	4.25748e20			0.491443			0.245721	−	0.969341i	$-0.420975\pi$
$619$	4.25748e20			0.491443			0.245721	+	0.969341i	$0.420975\pi$
$620$	−3.69709e20	+	1.47309e20i	−0.421621	+	0.167993i
$621$	2.89465e20			0.326143
$622$			4.25823e20i			0.474025i
$623$		−	9.80005e19i		−	0.107787i
$624$	−4.94900e20			−0.537815
$625$	5.03933e19	−	9.29958e20i	0.0541094	−	0.998535i
$626$	−7.51855e20			−0.797676
$627$			1.70374e21i			1.78606i
$628$		−	3.57606e20i		−	0.370431i
$629$	3.43971e20			0.352080
$630$	−2.66105e20	+	1.06028e20i	−0.269153	+	0.107243i
$631$	−3.77220e20			−0.377029			−0.188515	−	0.982070i	$-0.560367\pi$
$631$	−3.77220e20			−0.377029			−0.188515	+	0.982070i	$0.560367\pi$
$632$			2.29170e20i			0.226349i
$633$		−	1.61787e21i		−	1.57912i
$634$	7.90155e20			0.762154
$635$	1.67084e20	+	4.19339e20i	0.159269	+	0.399726i
$636$	−7.71688e20			−0.726965
$637$			1.37630e21i			1.28134i
$638$		−	1.51056e21i		−	1.38990i
$639$	8.74260e20			0.795032
$640$	3.64013e19	+	9.13584e19i	0.0327165	+	0.0821105i
$641$	1.29617e21			1.15141			0.575703	−	0.817659i	$-0.304729\pi$
$641$	1.29617e21			1.15141			0.575703	+	0.817659i	$0.304729\pi$
$642$		−	3.98922e20i		−	0.350248i
$643$			1.68831e21i			1.46511i	0.680707	+	0.732556i	$0.261673\pi$
$643$			1.68831e21i			1.46511i	−0.680707	+	0.732556i	$0.738327\pi$
$644$	2.34098e20			0.200795
$645$	−1.56382e20	+	6.23097e19i	−0.132584	+	0.0528272i
$646$	−3.77065e20			−0.315989
$647$		−	1.32846e21i		−	1.10044i	−0.835020	−	0.550220i	$-0.814544\pi$
$647$		−	1.32846e21i		−	1.10044i	0.835020	−	0.550220i	$-0.185456\pi$
$648$		−	3.34674e20i		−	0.274038i
$649$	−1.85949e21			−1.50507
$650$	9.32867e20	−	8.83685e20i	0.746397	−	0.707045i
$651$	−5.85089e20			−0.462769
$652$			1.69580e20i			0.132592i
$653$			6.95323e18i			0.00537449i	0.999996	+	0.00268725i	$0.000855378\pi$
$653$			6.95323e18i			0.00537449i	−0.999996	+	0.00268725i	$0.999145\pi$
$654$	−5.21482e20			−0.398480
$655$	8.18161e20	−	3.25992e20i	0.618058	−	0.246262i
$656$	1.84100e20			0.137491
$657$		−	2.96759e20i		−	0.219111i
$658$			5.25752e20i			0.383784i
$659$	1.12023e21			0.808478			0.404239	−	0.914653i	$-0.367536\pi$
$659$	1.12023e21			0.808478			0.404239	+	0.914653i	$0.367536\pi$
$660$	3.81486e20	+	9.57438e20i	0.272207	+	0.683173i
$661$	2.70300e20			0.190693			0.0953464	−	0.995444i	$-0.469604\pi$
$661$	2.70300e20			0.190693			0.0953464	+	0.995444i	$0.469604\pi$
$662$		−	1.25142e21i		−	0.872908i
$663$		−	1.14787e21i		−	0.791663i
$664$	3.01995e20			0.205939
$665$	−2.29696e20	−	5.76481e20i	−0.154879	−	0.388708i
$666$	1.20661e21			0.804469
$667$		−	3.49563e21i		−	2.30452i
$668$			2.35441e20i			0.153482i
$669$	−2.48188e21			−1.59987
$670$	7.30663e20	−	2.91129e20i	0.465754	−	0.185577i
$671$	−2.77711e21			−1.75055
$672$			1.44581e20i			0.0901241i
$673$			2.82519e21i			1.74154i	0.491686	+	0.870772i	$0.336381\pi$
$673$			2.82519e21i			1.74154i	−0.491686	+	0.870772i	$0.663619\pi$
$674$	−8.18675e20			−0.499071
$675$	−3.19219e20	−	3.36985e20i	−0.192446	−	0.203157i
$676$	9.34268e20			0.557021
$677$		−	8.23638e20i		−	0.485648i	−0.970070	−	0.242824i	$-0.921926\pi$
$677$		−	8.23638e20i		−	0.485648i	0.970070	−	0.242824i	$-0.0780737\pi$
$678$		−	1.96562e20i		−	0.114624i
$679$	5.10554e20			0.294455
$680$	−2.11896e20	+	8.44290e19i	−0.120867	+	0.0481587i
$681$	3.19195e21			1.80075
$682$			1.14350e21i			0.638051i
$683$		−	1.62704e21i		−	0.897930i	−0.893549	−	0.448965i	$-0.851793\pi$
$683$		−	1.62704e21i		−	0.897930i	0.893549	−	0.448965i	$-0.148207\pi$
$684$	−1.32270e21			−0.722005
$685$	5.41083e20	+	1.35799e21i	0.292136	+	0.733190i
$686$	8.58315e20			0.458370
$687$			6.71248e20i			0.354574i
$688$			4.61533e19i			0.0241151i
$689$	2.76445e21			1.42878
$690$	8.82806e20	+	2.21563e21i	0.451333	+	1.13274i
$691$	−2.05132e21			−1.03741			−0.518703	−	0.854955i	$-0.673585\pi$
$691$	−2.05132e21			−1.03741			−0.518703	+	0.854955i	$0.673585\pi$
$692$			1.63227e21i			0.816575i
$693$			8.23059e20i			0.407316i
$694$	−9.27922e20			−0.454271
$695$	1.62318e21	−	6.46750e20i	0.786107	−	0.313221i
$696$	2.15892e21			1.03435
$697$			4.27000e20i			0.202387i
$698$			3.53124e20i			0.165581i
$699$	−4.78704e21			−2.22069
$700$	−2.58161e20	−	2.72529e20i	−0.118483	−	0.125077i
$701$	1.24371e21			0.564723			0.282361	−	0.959308i	$-0.408882\pi$
$701$	1.24371e21			0.564723			0.282361	+	0.959308i	$0.408882\pi$
$702$		−	6.40434e20i		−	0.287704i
$703$			2.61396e21i			1.16181i
$704$	2.82570e20			0.124260
$705$	−4.97599e21	+	1.98266e21i	−2.16502	+	0.862640i
$706$	−1.46686e21			−0.631472
$707$		−	1.54042e20i		−	0.0656136i
$708$		−	2.65762e21i		−	1.12006i
$709$	3.39327e21			1.41505			0.707526	−	0.706688i	$-0.249811\pi$
$709$	3.39327e21			1.41505			0.707526	+	0.706688i	$0.249811\pi$
$710$	4.24081e20	+	1.06434e21i	0.174989	+	0.439180i
$711$	−1.86456e21			−0.761298
$712$		−	2.73743e20i		−	0.110597i
$713$			2.64621e21i			1.05792i
$714$	−3.35340e20			−0.132663
$715$	−1.36661e21	−	3.42986e21i	−0.534995	−	1.34271i
$716$	−7.99215e20			−0.309611
$717$		−	3.78248e21i		−	1.45005i
$718$			1.94297e20i			0.0737111i
$719$	1.72253e21			0.646695			0.323348	−	0.946280i	$-0.395192\pi$
$719$	1.72253e21			0.646695			0.323348	+	0.946280i	$0.395192\pi$
$720$	−7.43306e20	+	2.96167e20i	−0.276169	+	0.110038i
$721$	−1.46475e21			−0.538578
$722$		−	9.22269e20i		−	0.335605i
$723$			1.45187e21i			0.522865i
$724$	−9.81802e20			−0.349933
$725$	−4.06949e21	+	3.85494e21i	−1.43551	+	1.35982i
$726$	−3.53765e19			−0.0123506
$727$		−	6.25379e20i		−	0.216090i	−0.994146	−	0.108045i	$-0.965541\pi$
$727$		−	6.25379e20i		−	0.216090i	0.994146	−	0.108045i	$-0.0344591\pi$
$728$		−	5.17937e20i		−	0.177130i
$729$	3.94616e21			1.33573
$730$	3.61279e20	−	1.43950e20i	0.121038	−	0.0482270i
$731$	−1.07048e20			−0.0354975
$732$		−	3.96911e21i		−	1.30275i
$733$		−	1.77444e20i		−	0.0576478i	−0.999585	−	0.0288239i	$-0.990824\pi$
$733$		−	1.77444e20i		−	0.0576478i	0.999585	−	0.0288239i	$-0.00917620\pi$
$734$	1.94995e21			0.627051
$735$	1.51625e21	+	3.80543e21i	0.482633	+	1.21129i
$736$	6.53902e20			0.206029
$737$		−	2.25993e21i		−	0.704838i
$738$			1.49786e21i			0.462434i
$739$	2.45610e21			0.750606			0.375303	−	0.926902i	$-0.377539\pi$
$739$	2.45610e21			0.750606			0.375303	+	0.926902i	$0.377539\pi$
$740$	5.85293e20	+	1.46894e21i	0.177066	+	0.444393i
$741$	8.72307e21			2.61236
$742$		−	8.07610e20i		−	0.239426i
$743$		−	5.42139e21i		−	1.59109i	−0.605894	−	0.795545i	$-0.707185\pi$
$743$		−	5.42139e21i		−	1.59109i	0.605894	−	0.795545i	$-0.292815\pi$
$744$	−1.63432e21			−0.474832
$745$	3.11435e21	−	1.24090e21i	0.895767	−	0.356914i
$746$	−1.73022e21			−0.492675
$747$			2.45708e21i			0.692652i
$748$			6.55392e20i			0.182911i
$749$	4.17492e20			0.115354
$750$	1.60581e21	−	3.47111e21i	0.439273	−	0.949529i
$751$	1.03866e21			0.281302			0.140651	−	0.990059i	$-0.455080\pi$
$751$	1.03866e21			0.281302			0.140651	+	0.990059i	$0.455080\pi$
$752$			1.46857e21i			0.393787i
$753$		−	1.74270e21i		−	0.462657i
$754$	−7.73400e21			−2.03291
$755$	−2.08533e21	+	8.30889e20i	−0.542716	+	0.216242i
$756$	−1.87097e20			−0.0482119
$757$		−	6.88817e21i		−	1.75746i	−0.477322	−	0.878728i	$-0.658393\pi$
$757$		−	6.88817e21i		−	1.75746i	0.477322	−	0.878728i	$-0.341607\pi$
$758$			1.94800e21i			0.492120i
$759$	6.85291e21			1.71420
$760$	−6.41606e20	−	1.61028e21i	−0.158916	−	0.398840i
$761$	−4.49406e21			−1.10218			−0.551091	−	0.834445i	$-0.685788\pi$
$761$	−4.49406e21			−1.10218			−0.551091	+	0.834445i	$0.685788\pi$
$762$			1.85371e21i			0.450174i
$763$		−	5.45757e20i		−	0.131240i
$764$	9.79570e20			0.233257
$765$	−6.86928e20	−	1.72402e21i	−0.161976	−	0.406520i
$766$	−2.15410e20			−0.0502979
$767$			9.52048e21i			2.20137i
$768$			4.03855e20i			0.0924733i
$769$	−4.75150e21			−1.07741			−0.538707	−	0.842493i	$-0.681087\pi$
$769$	−4.75150e21			−1.07741			−0.538707	+	0.842493i	$0.681087\pi$
$770$	−1.00201e21	+	3.99244e20i	−0.225004	+	0.0896516i
$771$	−1.24325e22			−2.76473
$772$		−	1.88155e21i		−	0.414367i
$773$		−	7.06050e21i		−	1.53989i	−0.638111	−	0.769944i	$-0.720284\pi$
$773$		−	7.06050e21i		−	1.53989i	0.638111	−	0.769944i	$-0.279716\pi$
$774$	−3.75511e20			−0.0811083
$775$	3.08063e21	−	2.91821e21i	0.658987	−	0.624244i
$776$	1.42612e21			0.302130
$777$			2.32470e21i			0.487764i
$778$			1.62358e21i			0.337385i
$779$	−3.24493e21			−0.667842
$780$	4.90203e21	−	1.95319e21i	0.999232	−	0.398139i
$781$	3.29198e21			0.664623
$782$			1.51666e21i			0.303275i
$783$			2.79380e21i			0.553327i
$784$	1.12310e21			0.220318
$785$	1.41134e21	+	3.54212e21i	0.274226	+	0.688241i
$786$	3.61673e21			0.696060
$787$			1.34454e21i			0.256308i	0.991754	+	0.128154i	$0.0409052\pi$
$787$			1.34454e21i			0.256308i	−0.991754	+	0.128154i	$0.959095\pi$
$788$			3.93000e21i			0.742073i
$789$	−3.33472e21			−0.623708
$790$	−9.04449e20	−	2.26995e21i	−0.167564	−	0.420545i
$791$	2.05712e20			0.0377516
$792$			2.29904e21i			0.417933i
$793$			1.42187e22i			2.56041i
$794$	6.36901e20			0.113610
$795$	7.64365e21	−	3.04557e21i	1.35066	−	0.538165i
$796$	−4.93049e21			−0.863062
$797$			8.52034e21i			1.47747i	0.673994	+	0.738737i	$0.264577\pi$
$797$			8.52034e21i			1.47747i	−0.673994	+	0.738737i	$0.735423\pi$
$798$		−	2.54837e21i		−	0.437764i
$799$	−3.40620e21			−0.579655
$800$	−7.21116e20	−	7.61251e20i	−0.121571	−	0.128337i
$801$	2.22722e21			0.371980
$802$		−	2.35786e21i		−	0.390131i
$803$		−	1.11743e21i		−	0.183170i
$804$	3.22994e21			0.524534
$805$	−2.31876e21	+	9.23900e20i	−0.373068	+	0.148647i
$806$	5.85468e21			0.933234
$807$			1.75104e21i			0.276532i
$808$		−	4.30283e20i		−	0.0673239i
$809$	−9.23911e21			−1.43224			−0.716120	−	0.697977i	$-0.754084\pi$
$809$	−9.23911e21			−1.43224			−0.716120	+	0.697977i	$0.754084\pi$
$810$	1.32084e21	+	3.31498e21i	0.202867	+	0.509147i
$811$	4.95567e21			0.754130			0.377065	−	0.926187i	$-0.376933\pi$
$811$	4.95567e21			0.754130			0.377065	+	0.926187i	$0.376933\pi$
$812$			2.25942e21i			0.340664i
$813$		−	1.65201e22i		−	2.46793i
$814$	4.54342e21			0.672512
$815$	−6.69271e20	−	1.67971e21i	−0.0981567	−	0.246350i
$816$	−9.36699e20			−0.136121
$817$		−	8.13495e20i		−	0.117136i
$818$		−	6.25016e21i		−	0.891746i
$819$	4.21402e21			0.595754
$820$	−1.82352e21	+	7.26574e20i	−0.255451	+	0.101783i
$821$	−6.59812e21			−0.915896			−0.457948	−	0.888979i	$-0.651415\pi$
$821$	−6.59812e21			−0.915896			−0.457948	+	0.888979i	$0.651415\pi$
$822$			6.00306e21i			0.825722i
$823$		−	7.50862e21i		−	1.02344i	−0.859153	−	0.511719i	$-0.829009\pi$
$823$		−	7.50862e21i		−	1.02344i	0.859153	−	0.511719i	$-0.170991\pi$
$824$	−4.09146e21			−0.552616
$825$	−7.55731e21	−	7.97792e21i	−1.01149	−	1.06779i
$826$	2.78132e21			0.368894
$827$		−	4.41426e20i		−	0.0580186i	−0.999579	−	0.0290093i	$-0.990765\pi$
$827$		−	4.41426e20i		−	0.0580186i	0.999579	−	0.0290093i	$-0.00923524\pi$
$828$			5.32025e21i			0.692955i
$829$	1.86495e21			0.240717			0.120359	−	0.992730i	$-0.461596\pi$
$829$	1.86495e21			0.240717			0.120359	+	0.992730i	$0.461596\pi$
$830$	−2.99129e21	+	1.19187e21i	−0.382625	+	0.152455i
$831$	−1.39617e22			−1.76983
$832$		−	1.44674e21i		−	0.181747i
$833$			2.60492e21i			0.324307i
$834$	7.17538e21			0.885318
$835$	−9.29198e20	−	2.33206e21i	−0.113621	−	0.285162i
$836$	−4.98056e21			−0.603575
$837$		−	2.11492e21i		−	0.254011i
$838$			8.41682e20i			0.100189i
$839$	1.66094e22			1.95948			0.979738	−	0.200284i	$-0.0641865\pi$
$839$	1.66094e22			1.95948			0.979738	+	0.200284i	$0.0641865\pi$
$840$	−5.70607e20	−	1.43209e21i	−0.0667180	−	0.167446i
$841$	2.51092e22			2.90980
$842$		−	1.01081e21i		−	0.116099i
$843$		−	1.26227e22i		−	1.43696i
$844$	4.72953e21			0.533642
$845$	−9.25402e21	+	3.68722e21i	−1.03492	+	0.412357i
$846$	−1.19485e22			−1.32446
$847$		−	3.70232e19i		−	0.00406769i
$848$		−	2.25588e21i		−	0.245667i
$849$	−1.65102e22			−1.78216
$850$	1.76564e21	−	1.67255e21i	0.188912	−	0.178953i
$851$	1.05140e22			1.11506
$852$			4.70497e21i			0.494607i
$853$			1.50225e22i			1.56540i	0.622399	+	0.782700i	$0.286158\pi$
$853$			1.50225e22i			1.56540i	−0.622399	+	0.782700i	$0.713842\pi$
$854$	4.15386e21			0.429060
$855$	1.31015e22	−	5.22021e21i	1.34145	−	0.534493i
$856$	1.16617e21			0.118361
$857$		−	1.56603e21i		−	0.157559i	−0.996892	−	0.0787796i	$-0.974898\pi$
$857$		−	1.56603e21i		−	0.157559i	0.996892	−	0.0787796i	$-0.0251023\pi$
$858$		−	1.51619e22i		−	1.51217i
$859$	1.39501e22			1.37920			0.689602	−	0.724189i	$-0.257786\pi$
$859$	1.39501e22			1.37920			0.689602	+	0.724189i	$0.257786\pi$
$860$	−1.82150e20	−	4.57153e20i	−0.0178522	−	0.0448047i
$861$	−2.88585e21			−0.280382
$862$		−	5.06294e21i		−	0.487639i
$863$			1.80173e22i			1.72032i	0.510027	+	0.860159i	$0.329635\pi$
$863$			1.80173e22i			1.72032i	−0.510027	+	0.860159i	$0.670365\pi$
$864$	−5.22616e20			−0.0494686
$865$	−6.44197e21	−	1.61678e22i	−0.604502	−	1.51715i
$866$	1.09197e22			1.01584
$867$			1.38702e22i			1.27920i
$868$		−	1.71039e21i		−	0.156386i
$869$	−7.02091e21			−0.636422
$870$	−2.13844e22	+	8.52049e21i	−1.92177	+	0.765720i
$871$	−1.15707e22			−1.03092
$872$		−	1.52445e21i		−	0.134661i
$873$			1.16032e22i			1.01618i
$874$	−1.15256e22			−1.00076
$875$	3.63268e21	+	1.68056e21i	0.312728	+	0.144675i
$876$	1.59706e21			0.136314
$877$			4.89491e21i			0.414236i	0.978316	+	0.207118i	$0.0664084\pi$
$877$			4.89491e21i			0.414236i	−0.978316	+	0.207118i	$0.933592\pi$
$878$		−	1.20834e22i		−	1.01386i
$879$	−1.13625e22			−0.945277
$880$	−2.79888e21	+	1.11520e21i	−0.230869	+	0.0919884i
$881$	3.98219e21			0.325689			0.162844	−	0.986652i	$-0.447933\pi$
$881$	3.98219e21			0.325689			0.162844	+	0.986652i	$0.447933\pi$
$882$			9.13775e21i			0.741011i
$883$			2.06182e22i			1.65785i	0.559358	+	0.828926i	$0.311048\pi$
$883$			2.06182e22i			1.65785i	−0.559358	+	0.828926i	$0.688952\pi$
$884$	3.35557e21			0.267531
$885$	1.04886e22	+	2.63239e22i	0.829172	+	2.08102i
$886$	−1.11503e22			−0.874044
$887$		−	4.04614e21i		−	0.314495i	−0.987559	−	0.157248i	$-0.949738\pi$
$887$		−	4.04614e21i		−	0.314495i	0.987559	−	0.157248i	$-0.0502621\pi$
$888$			6.49355e21i			0.500478i
$889$	−1.94000e21			−0.148265
$890$	1.08036e21	+	2.71145e21i	0.0818739	+	0.205484i
$891$	1.02532e22			0.770506
$892$		−	7.25529e21i		−	0.540653i
$893$		−	2.58850e22i		−	1.91276i
$894$	1.37672e22			1.00882
$895$	7.91630e21	−	3.15421e21i	0.575240	−	0.229202i
$896$	−4.22654e20			−0.0304561
$897$		−	3.50865e22i		−	2.50725i
$898$			1.49552e22i			1.05979i
$899$	−2.55402e22			−1.79484
$900$	6.19366e21	−	5.86712e21i	0.431647	−	0.408890i
$901$	5.23228e21			0.361622
$902$			5.64014e21i			0.386581i
$903$		−	7.23475e20i		−	0.0491774i
$904$	5.74611e20			0.0387356
$905$	9.72484e21	−	3.87481e21i	0.650157	−	0.259052i
$906$	−9.21832e21			−0.611210
$907$		−	7.20594e21i		−	0.473844i	−0.971529	−	0.236922i	$-0.923861\pi$
$907$		−	7.20594e21i		−	0.473844i	0.971529	−	0.236922i	$-0.0761387\pi$
$908$			9.33106e21i			0.608537i
$909$	3.50085e21			0.226436
$910$	2.04411e21	+	5.13021e21i	0.131127	+	0.329098i
$911$	5.00099e21			0.318177			0.159088	−	0.987264i	$-0.449145\pi$
$911$	5.00099e21			0.318177			0.159088	+	0.987264i	$0.449145\pi$
$912$		−	7.11831e21i		−	0.449175i
$913$			9.25202e21i			0.579036i
$914$	−3.90546e21			−0.242424
$915$	1.56646e22	+	3.93144e22i	0.964410	+	2.42043i
$916$	−1.96226e21			−0.119823
$917$			3.78508e21i			0.229248i
$918$		−	1.21215e21i		−	0.0728177i
$919$	−2.86248e22			−1.70560			−0.852798	−	0.522240i	$-0.825096\pi$
$919$	−2.86248e22			−1.70560			−0.852798	+	0.522240i	$0.825096\pi$
$920$	−6.47696e21	+	2.58071e21i	−0.382792	+	0.152522i
$921$	−2.79216e21			−0.163679
$922$		−	1.51395e22i		−	0.880300i
$923$		−	1.68548e22i		−	0.972099i
$924$	−4.42942e21			−0.253400
$925$	−1.15948e22	−	1.22401e22i	−0.657960	−	0.694579i
$926$	2.33788e20			0.0131595
$927$		−	3.32887e22i		−	1.85866i
$928$			6.31120e21i			0.349544i
$929$	1.10822e22			0.608848			0.304424	−	0.952537i	$-0.401536\pi$
$929$	1.10822e22			0.608848			0.304424	+	0.952537i	$0.401536\pi$
$930$	1.61881e22	−	6.45006e21i	0.882213	−	0.351513i
$931$	−1.97957e22			−1.07016
$932$		−	1.39940e22i		−	0.750450i
$933$		−	1.86451e22i		−	0.991864i
$934$	2.08829e22			1.10202
$935$	−2.58659e21	−	6.49172e21i	−0.135407	−	0.339838i
$936$	1.17709e22			0.611283
$937$			1.43905e22i			0.741361i	0.928760	+	0.370681i	$0.120876\pi$
$937$			1.43905e22i			0.741361i	−0.928760	+	0.370681i	$0.879124\pi$
$938$			3.38029e21i			0.172756i
$939$	3.29207e22			1.66908
$940$	−5.79592e21	−	1.45464e22i	−0.291517	−	0.731636i
$941$	1.25183e22			0.624629			0.312314	−	0.949979i	$-0.398896\pi$
$941$	1.25183e22			0.624629			0.312314	+	0.949979i	$0.398896\pi$
$942$			1.56581e22i			0.775101i
$943$			1.30520e22i			0.640971i
$944$	7.76903e21			0.378509
$945$	1.85322e21	−	7.38405e20i	0.0895752	−	0.0356908i
$946$	−1.41397e21			−0.0678041
$947$		−	1.64165e22i		−	0.781010i	−0.920601	−	0.390505i	$-0.872300\pi$
$947$		−	1.64165e22i		−	0.781010i	0.920601	−	0.390505i	$-0.127700\pi$
$948$		−	1.00344e22i		−	0.473620i
$949$	−5.72119e21			−0.267911
$950$	1.27103e22	+	1.34177e22i	0.590514	+	0.623380i
$951$	−3.45977e22			−1.59475
$952$		−	9.80301e20i		−	0.0448314i
$953$		−	2.57492e22i		−	1.16833i	−0.811633	−	0.584167i	$-0.801421\pi$
$953$		−	2.57492e22i		−	1.16833i	0.811633	−	0.584167i	$-0.198579\pi$
$954$	1.83542e22			0.826272
$955$	−9.70273e21	+	3.86600e21i	−0.433380	+	0.172678i
$956$	1.10574e22			0.490024
$957$			6.61415e22i			2.90827i
$958$			2.37333e22i			1.03542i
$959$	−6.28249e21			−0.271952
$960$	−1.59387e21	−	4.00022e21i	−0.0684570	−	0.171810i
$961$	−4.13121e21			−0.176056
$962$		−	2.32621e22i		−	0.983639i
$963$			9.48816e21i			0.398093i
$964$	−4.24425e21			−0.176695
$965$	7.42578e21	+	1.86369e22i	0.306752	+	0.769873i
$966$	−1.02502e22			−0.420151
$967$		−	4.00899e22i		−	1.63056i	−0.579067	−	0.815280i	$-0.696583\pi$
$967$		−	4.00899e22i		−	1.63056i	0.579067	−	0.815280i	$-0.303417\pi$
$968$		−	1.03416e20i		−	0.00417372i
$969$	1.65102e22			0.661186
$970$	−1.41259e22	+	5.62838e21i	−0.561342	+	0.223664i
$971$	−1.38608e22			−0.546566			−0.273283	−	0.961934i	$-0.588110\pi$
$971$	−1.38608e22			−0.546566			−0.273283	+	0.961934i	$0.588110\pi$
$972$			1.82298e22i			0.713323i
$973$			7.50938e21i			0.291580i
$974$	−2.38876e22			−0.920408
$975$	−4.08465e22	+	3.86931e22i	−1.56178	+	1.47944i
$976$	1.16029e22			0.440244
$977$			4.91986e20i			0.0185244i	0.999957	+	0.00926219i	$0.00294829\pi$
$977$			4.91986e20i			0.0185244i	−0.999957	+	0.00926219i	$0.997052\pi$
$978$		−	7.42524e21i		−	0.277440i
$979$	8.38648e21			0.310964
$980$	−1.11244e22	+	4.43248e21i	−0.409339	+	0.163099i
$981$	1.24032e22			0.452914
$982$			1.31573e22i			0.476794i
$983$		−	1.63436e22i		−	0.587754i	−0.955843	−	0.293877i	$-0.905054\pi$
$983$		−	1.63436e22i		−	0.587754i	0.955843	−	0.293877i	$-0.0949456\pi$
$984$	−8.06099e21			−0.287690
$985$	−1.55103e22	−	3.89271e22i	−0.549349	−	1.37873i
$986$	−1.46382e22			−0.514529
$987$		−	2.30206e22i		−	0.803041i
$988$			2.55002e22i			0.882808i
$989$	−3.27210e21			−0.112423
$990$	−9.07346e21	−	2.27722e22i	−0.309392	−	0.776498i
$991$	6.79151e21			0.229834			0.114917	−	0.993375i	$-0.463340\pi$
$991$	6.79151e21			0.229834			0.114917	+	0.993375i	$0.463340\pi$
$992$		−	4.77762e21i		−	0.160463i
$993$			5.47947e22i			1.82650i
$994$	−4.92398e21			−0.162899
$995$	4.88370e22	−	1.94589e22i	1.60352	−	0.638916i
$996$	−1.32232e22			−0.430914
$997$			1.28125e22i			0.414400i	0.978299	+	0.207200i	$0.0664350\pi$
$997$			1.28125e22i			0.414400i	−0.978299	+	0.207200i	$0.933565\pi$
$998$			6.90139e21i			0.221543i
$999$	−8.40310e21			−0.267731

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.16.b.a.9.4	✓	8
3.2	odd	2		90.16.c.c.19.5		8
4.3	odd	2		80.16.c.c.49.1		8
5.2	odd	4		50.16.a.k.1.4		4
5.3	odd	4		50.16.a.j.1.1		4
5.4	even	2	inner	10.16.b.a.9.5	yes	8
15.14	odd	2		90.16.c.c.19.1		8
20.19	odd	2		80.16.c.c.49.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.16.b.a.9.4	✓	8	1.1	even	1	trivial
10.16.b.a.9.5	yes	8	5.4	even	2	inner
50.16.a.j.1.1		4	5.3	odd	4
50.16.a.k.1.4		4	5.2	odd	4
80.16.c.c.49.1		8	4.3	odd	2
80.16.c.c.49.8		8	20.19	odd	2
90.16.c.c.19.1		8	15.14	odd	2
90.16.c.c.19.5		8	3.2	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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	10.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-128.000i q^{2} +5604.61i q^{3} -16384.0 q^{4} +(162285. - 64661.7i) q^{5} +717390. q^{6} +750784. i q^{7} +2.09715e6i q^{8} -1.70628e7 q^{9} +O(q^{10})\)	\(q-128.000i q^{2} +5604.61i q^{3} -16384.0 q^{4} +(162285. - 64661.7i) q^{5} +717390. q^{6} +750784. i q^{7} +2.09715e6i q^{8} -1.70628e7 q^{9} +(-8.27669e6 - 2.07725e7i) q^{10} -6.42490e7 q^{11} -9.18260e7i q^{12} +3.28952e8i q^{13} +9.61003e7 q^{14} +(3.62404e8 + 9.09545e8i) q^{15} +2.68435e8 q^{16} +6.22608e8i q^{17} +2.18403e9i q^{18} -4.73142e9 q^{19} +(-2.65888e9 + 1.05942e9i) q^{20} -4.20785e9 q^{21} +8.22387e9i q^{22} +1.90311e10i q^{23} -1.17537e10 q^{24} +(2.21553e10 - 2.09872e10i) q^{25} +4.21058e10 q^{26} -1.52101e10i q^{27} -1.23008e10i q^{28} -1.83680e11 q^{29} +(1.16422e11 - 4.63877e10i) q^{30} +1.39047e11 q^{31} -3.43597e10i q^{32} -3.60091e11i q^{33} +7.96938e10 q^{34} +(4.85469e10 + 1.21841e11i) q^{35} +2.79556e11 q^{36} -5.52467e11i q^{37} +6.05622e11i q^{38} -1.84365e12 q^{39} +(1.35605e11 + 3.40336e11i) q^{40} +6.85825e11 q^{41} +5.38605e11i q^{42} +1.71935e11i q^{43} +1.05266e12 q^{44} +(-2.76903e12 + 1.10331e12i) q^{45} +2.43598e12 q^{46} +5.47086e12i q^{47} +1.50448e12i q^{48} +4.18389e12 q^{49} +(-2.68637e12 - 2.83588e12i) q^{50} -3.48947e12 q^{51} -5.38954e12i q^{52} -8.40382e12i q^{53} -1.94690e12 q^{54} +(-1.04267e13 + 4.15445e12i) q^{55} -1.57451e12 q^{56} -2.65178e13i q^{57} +2.35110e13i q^{58} +2.89419e13 q^{59} +(-5.93762e12 - 1.49020e13i) q^{60} +4.32242e13 q^{61} -1.77980e13i q^{62} -1.28104e13i q^{63} -4.39805e12 q^{64} +(2.12706e13 + 5.33839e13i) q^{65} -4.60916e13 q^{66} +3.51746e13i q^{67} -1.02008e13i q^{68} -1.06662e14 q^{69} +(1.55957e13 - 6.21401e12i) q^{70} -5.12379e13 q^{71} -3.57832e13i q^{72} +1.73922e13i q^{73} -7.07158e13 q^{74} +(1.17625e14 + 1.24172e14i) q^{75} +7.75196e13 q^{76} -4.82371e13i q^{77} +2.35987e14i q^{78} +1.09277e14 q^{79} +(4.35631e13 - 1.73575e13i) q^{80} -1.59585e14 q^{81} -8.77856e13i q^{82} -1.44003e14i q^{83} +6.89415e13 q^{84} +(4.02589e13 + 1.01040e14i) q^{85} +2.20076e13 q^{86} -1.02946e15i q^{87} -1.34740e14i q^{88} -1.30531e14 q^{89} +(1.41223e14 + 3.54436e14i) q^{90} -2.46972e14 q^{91} -3.11805e14i q^{92} +7.79304e14i q^{93} +7.00270e14 q^{94} +(-7.67839e14 + 3.05942e14i) q^{95} +1.92573e14 q^{96} -6.80028e14i q^{97} -5.35537e14i q^{98} +1.09627e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 131072 q^{4} + 251400 q^{5} - 53248 q^{6} - 43491176 q^{9}+O(q^{10}) \) 8 * q - 131072 * q^4 + 251400 * q^5 - 53248 * q^6 - 43491176 * q^9	\( 8 q - 131072 q^{4} + 251400 q^{5} - 53248 q^{6} - 43491176 q^{9} + 4403200 q^{10} + 95435616 q^{11} - 499347456 q^{14} + 5448800 q^{15} + 2147483648 q^{16} + 6479216160 q^{19} - 4118937600 q^{20} - 14760325504 q^{21} + 872415232 q^{24} - 2241855000 q^{25} + 66288525312 q^{26} - 244549636560 q^{29} - 32701542400 q^{30} + 522311705216 q^{31} + 322563211264 q^{34} - 1829607146400 q^{35} + 712559427584 q^{36} - 2307595824192 q^{39} - 72142028800 q^{40} + 6699117519216 q^{41} - 1563617132544 q^{44} - 9090807477800 q^{45} + 12178733699072 q^{46} - 15809163185544 q^{49} - 13485542400000 q^{50} + 40555579650176 q^{51} - 7241111674880 q^{54} - 39746288199200 q^{55} + 8181308719104 q^{56} + 3791808509280 q^{59} - 89273139200 q^{60} + 57800629300816 q^{61} - 35184372088832 q^{64} + 58028394892800 q^{65} - 82398766186496 q^{66} + 59060996328448 q^{69} + 60817223987200 q^{70} - 245426235422784 q^{71} + 53331092987904 q^{74} + 226448486200000 q^{75} - 106155477565440 q^{76} + 624094605411840 q^{79} + 67484673638400 q^{80} - 13\!\cdots\!52 q^{81}+ \cdots + 16\!\cdots\!48 q^{99}+O(q^{100}) \) 8 * q - 131072 * q^4 + 251400 * q^5 - 53248 * q^6 - 43491176 * q^9 + 4403200 * q^10 + 95435616 * q^11 - 499347456 * q^14 + 5448800 * q^15 + 2147483648 * q^16 + 6479216160 * q^19 - 4118937600 * q^20 - 14760325504 * q^21 + 872415232 * q^24 - 2241855000 * q^25 + 66288525312 * q^26 - 244549636560 * q^29 - 32701542400 * q^30 + 522311705216 * q^31 + 322563211264 * q^34 - 1829607146400 * q^35 + 712559427584 * q^36 - 2307595824192 * q^39 - 72142028800 * q^40 + 6699117519216 * q^41 - 1563617132544 * q^44 - 9090807477800 * q^45 + 12178733699072 * q^46 - 15809163185544 * q^49 - 13485542400000 * q^50 + 40555579650176 * q^51 - 7241111674880 * q^54 - 39746288199200 * q^55 + 8181308719104 * q^56 + 3791808509280 * q^59 - 89273139200 * q^60 + 57800629300816 * q^61 - 35184372088832 * q^64 + 58028394892800 * q^65 - 82398766186496 * q^66 + 59060996328448 * q^69 + 60817223987200 * q^70 - 245426235422784 * q^71 + 53331092987904 * q^74 + 226448486200000 * q^75 - 106155477565440 * q^76 + 624094605411840 * q^79 + 67484673638400 * q^80 - 1376711600108152 * q^81 + 241833173057536 * q^84 + 1092463762441600 * q^85 - 8937574699008 * q^86 - 635249793637680 * q^89 + 851824438169600 * q^90 - 976491706492224 * q^91 - 537030386200576 * q^94 - 1859590136604000 * q^95 - 14293651161088 * q^96 + 1626246829353248 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more