LMFDB - Embedded newform 10.14.b.a.9.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,14,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, 14, names="a")

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

chi := DirichletCharacter("10.9");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 14 $
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:	$10.7230928952$
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} - 2x^{5} + 2x^{4} + 160950x^{3} + 43599609x^{2} + 975553632x + 10914144768 $ x^6 - 2x^5 + 2x^4 + 160950x^3 + 43599609x^2 + 975553632*x + 10914144768
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{21}\cdot 5^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			9.2
Root			$-11.7164 - 11.7164i$ of defining polynomial
Character	$\chi$	$=$	10.9
Dual form			10.14.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)

$f(q)$	$=$	$q-64.0000i q^{2} +180.328i q^{3} -4096.00 q^{4} +(33325.2 + 10494.5i) q^{5} +11541.0 q^{6} -386506. i q^{7} +262144. i q^{8} +1.56180e6 q^{9} +O(q^{10})$	\(q-64.0000i q^{2} +180.328i q^{3} -4096.00 q^{4} +(33325.2 + 10494.5i) q^{5} +11541.0 q^{6} -386506. i q^{7} +262144. i q^{8} +1.56180e6 q^{9} +(671650. - 2.13281e6i) q^{10} -8.76708e6 q^{11} -738622. i q^{12} -3.09578e7i q^{13} -2.47364e7 q^{14} +(-1.89245e6 + 6.00945e6i) q^{15} +1.67772e7 q^{16} -1.18462e8i q^{17} -9.99555e7i q^{18} +9.77316e7 q^{19} +(-1.36500e8 - 4.29856e7i) q^{20} +6.96977e7 q^{21} +5.61093e8i q^{22} +2.65105e8i q^{23} -4.72718e7 q^{24} +(1.00043e9 + 6.99464e8i) q^{25} -1.98130e9 q^{26} +5.69137e8i q^{27} +1.58313e9i q^{28} +3.94902e9 q^{29} +(3.84605e8 + 1.21117e8i) q^{30} +4.11359e8 q^{31} -1.07374e9i q^{32} -1.58095e9i q^{33} -7.58156e9 q^{34} +(4.05620e9 - 1.28804e10i) q^{35} -6.39715e9 q^{36} -4.34418e9i q^{37} -6.25482e9i q^{38} +5.58255e9 q^{39} +(-2.75108e9 + 8.73600e9i) q^{40} -4.06741e10 q^{41} -4.46065e9i q^{42} -2.14022e10i q^{43} +3.59100e10 q^{44} +(5.20474e10 + 1.63904e10i) q^{45} +1.69667e10 q^{46} +1.15435e11i q^{47} +3.02539e9i q^{48} -5.24978e10 q^{49} +(4.47657e10 - 6.40277e10i) q^{50} +2.13620e10 q^{51} +1.26803e11i q^{52} +1.13298e11i q^{53} +3.64248e10 q^{54} +(-2.92165e11 - 9.20064e10i) q^{55} +1.01320e11 q^{56} +1.76237e10i q^{57} -2.52737e11i q^{58} -7.68729e10 q^{59} +(7.75148e9 - 2.46147e10i) q^{60} +1.14756e11 q^{61} -2.63270e10i q^{62} -6.03647e11i q^{63} -6.87195e10 q^{64} +(3.24888e11 - 1.03168e12i) q^{65} -1.01181e11 q^{66} +1.23899e12i q^{67} +4.85220e11i q^{68} -4.78057e10 q^{69} +(-8.24344e11 - 2.59597e11i) q^{70} +6.95554e11 q^{71} +4.09418e11i q^{72} -3.96904e11i q^{73} -2.78027e11 q^{74} +(-1.26133e11 + 1.80406e11i) q^{75} -4.00309e11 q^{76} +3.38853e12i q^{77} -3.57283e11i q^{78} +5.70369e11 q^{79} +(5.59104e11 + 1.76069e11i) q^{80} +2.38739e12 q^{81} +2.60314e12i q^{82} -1.89284e12i q^{83} -2.85482e11 q^{84} +(1.24320e12 - 3.94777e12i) q^{85} -1.36974e12 q^{86} +7.12117e11i q^{87} -2.29824e12i q^{88} -4.80874e11 q^{89} +(1.04899e12 - 3.33104e12i) q^{90} -1.19654e13 q^{91} -1.08587e12i q^{92} +7.41794e10i q^{93} +7.38785e12 q^{94} +(3.25692e12 + 1.02565e12i) q^{95} +1.93625e11 q^{96} -3.52771e12i q^{97} +3.35986e12i q^{98} -1.36925e13 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 24576 q^{4} - 2470 q^{5} - 23296 q^{6} + 4260922 q^{9}+O(q^{10}) $ 6 * q - 24576 * q^4 - 2470 * q^5 - 23296 * q^6 + 4260922 * q^9	\( 6 q - 24576 q^{4} - 2470 q^{5} - 23296 q^{6} + 4260922 q^{9} - 2269440 q^{10} + 673672 q^{11} - 1211648 q^{14} + 80128760 q^{15} + 100663296 q^{16} + 142606200 q^{19} + 10117120 q^{20} - 926360008 q^{21} + 95420416 q^{24} + 1820907150 q^{25} - 3369156096 q^{26} + 1402368660 q^{29} + 6491083520 q^{30} - 22270466688 q^{31} + 10743816192 q^{34} + 40910703880 q^{35} - 17452736512 q^{36} + 80990077584 q^{39} + 9295626240 q^{40} - 159550828628 q^{41} - 2759360512 q^{44} + 112298555110 q^{45} - 48346742016 q^{46} - 142584010062 q^{49} + 33045516800 q^{50} + 47596879232 q^{51} + 104187005440 q^{54} - 465712133640 q^{55} + 4962910208 q^{56} - 129517581080 q^{59} - 328207400960 q^{60} + 2208324934212 q^{61} - 412316860416 q^{64} - 475107396240 q^{65} + 1429010971648 q^{66} - 2470574584136 q^{69} - 1324581354240 q^{70} + 1016718596592 q^{71} + 1548283182592 q^{74} - 1495698537200 q^{75} - 584114995200 q^{76} - 23303633760 q^{79} - 41439723520 q^{80} - 2585393406754 q^{81} + 3794370592768 q^{84} + 9460560132480 q^{85} - 10908216246016 q^{86} - 1102941191140 q^{89} - 1112244801280 q^{90} - 9640398296208 q^{91} + 20956004804352 q^{94} + 26900168949000 q^{95} - 390842023936 q^{96} - 11776973376136 q^{99}+O(q^{100}) \) 6 * q - 24576 * q^4 - 2470 * q^5 - 23296 * q^6 + 4260922 * q^9 - 2269440 * q^10 + 673672 * q^11 - 1211648 * q^14 + 80128760 * q^15 + 100663296 * q^16 + 142606200 * q^19 + 10117120 * q^20 - 926360008 * q^21 + 95420416 * q^24 + 1820907150 * q^25 - 3369156096 * q^26 + 1402368660 * q^29 + 6491083520 * q^30 - 22270466688 * q^31 + 10743816192 * q^34 + 40910703880 * q^35 - 17452736512 * q^36 + 80990077584 * q^39 + 9295626240 * q^40 - 159550828628 * q^41 - 2759360512 * q^44 + 112298555110 * q^45 - 48346742016 * q^46 - 142584010062 * q^49 + 33045516800 * q^50 + 47596879232 * q^51 + 104187005440 * q^54 - 465712133640 * q^55 + 4962910208 * q^56 - 129517581080 * q^59 - 328207400960 * q^60 + 2208324934212 * q^61 - 412316860416 * q^64 - 475107396240 * q^65 + 1429010971648 * q^66 - 2470574584136 * q^69 - 1324581354240 * q^70 + 1016718596592 * q^71 + 1548283182592 * q^74 - 1495698537200 * q^75 - 584114995200 * q^76 - 23303633760 * q^79 - 41439723520 * q^80 - 2585393406754 * q^81 + 3794370592768 * q^84 + 9460560132480 * q^85 - 10908216246016 * q^86 - 1102941191140 * q^89 - 1112244801280 * q^90 - 9640398296208 * q^91 + 20956004804352 * q^94 + 26900168949000 * q^95 - 390842023936 * q^96 - 11776973376136 * 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 $

$2$		−	64.0000i		−	0.707107i
$2$		−	64.0000i		−	0.707107i
$3$			180.328i			0.142815i	0.997447	+	0.0714075i	$0.0227491\pi$
$3$			180.328i			0.142815i	−0.997447	+	0.0714075i	$0.977251\pi$
$4$	−4096.00			−0.500000
$5$	33325.2	+	10494.5i	0.953822	+	0.300371i
$5$	33325.2	+	10494.5i	0.953822	+	0.300371i
$6$	11541.0			0.100985
$7$		−	386506.i		−	1.24171i	−0.783927	−	0.620853i	$-0.786786\pi$
$7$		−	386506.i		−	1.24171i	0.783927	−	0.620853i	$-0.213214\pi$
$8$			262144.i			0.353553i
$9$	1.56180e6			0.979604
$10$	671650.	−	2.13281e6i	0.212394	−	0.674454i
$11$	−8.76708e6			−1.49212			−0.746058	−	0.665881i	$-0.768056\pi$
$11$	−8.76708e6			−1.49212			−0.746058	+	0.665881i	$0.768056\pi$
$12$		−	738622.i		−	0.0714075i
$13$		−	3.09578e7i		−	1.77885i	−0.457084	−	0.889423i	$-0.651106\pi$
$13$		−	3.09578e7i		−	1.77885i	0.457084	−	0.889423i	$-0.348894\pi$
$14$	−2.47364e7			−0.878019
$15$	−1.89245e6	+	6.00945e6i	−0.0428975	+	0.136220i
$16$	1.67772e7			0.250000
$17$		−	1.18462e8i		−	1.19031i	−0.803610	−	0.595156i	$-0.797090\pi$
$17$		−	1.18462e8i		−	1.19031i	0.803610	−	0.595156i	$-0.202910\pi$
$18$		−	9.99555e7i		−	0.692685i
$19$	9.77316e7			0.476581			0.238290	−	0.971194i	$-0.423413\pi$
$19$	9.77316e7			0.476581			0.238290	+	0.971194i	$0.423413\pi$
$20$	−1.36500e8	−	4.29856e7i	−0.476911	−	0.150185i
$21$	6.96977e7			0.177334
$22$			5.61093e8i			1.05509i
$23$			2.65105e8i			0.373411i	0.982416	+	0.186705i	$0.0597809\pi$
$23$			2.65105e8i			0.373411i	−0.982416	+	0.186705i	$0.940219\pi$
$24$	−4.72718e7			−0.0504927
$25$	1.00043e9	+	6.99464e8i	0.819555	+	0.573001i
$26$	−1.98130e9			−1.25783
$27$			5.69137e8i			0.282717i
$28$			1.58313e9i			0.620853i
$29$	3.94902e9			1.23283			0.616414	−	0.787422i	$-0.288585\pi$
$29$	3.94902e9			1.23283			0.616414	+	0.787422i	$0.288585\pi$
$30$	3.84605e8	+	1.21117e8i	0.0963222	+	0.0303331i
$31$	4.11359e8			0.0832473			0.0416236	−	0.999133i	$-0.486747\pi$
$31$	4.11359e8			0.0832473			0.0416236	+	0.999133i	$0.486747\pi$
$32$		−	1.07374e9i		−	0.176777i
$33$		−	1.58095e9i		−	0.213097i
$34$	−7.58156e9			−0.841678
$35$	4.05620e9	−	1.28804e10i	0.372972	−	1.18437i
$36$	−6.39715e9			−0.489802
$37$		−	4.34418e9i		−	0.278353i	−0.990268	−	0.139177i	$-0.955554\pi$
$37$		−	4.34418e9i		−	0.278353i	0.990268	−	0.139177i	$-0.0444456\pi$
$38$		−	6.25482e9i		−	0.336994i
$39$	5.58255e9			0.254046
$40$	−2.75108e9	+	8.73600e9i	−0.106197	+	0.337227i
$41$	−4.06741e10			−1.33728			−0.668640	−	0.743586i	$-0.733123\pi$
$41$	−4.06741e10			−1.33728			−0.668640	+	0.743586i	$0.733123\pi$
$42$		−	4.46065e9i		−	0.125394i
$43$		−	2.14022e10i		−	0.516314i	−0.966103	−	0.258157i	$-0.916885\pi$
$43$		−	2.14022e10i		−	0.516314i	0.966103	−	0.258157i	$-0.0831152\pi$
$44$	3.59100e10			0.746058
$45$	5.20474e10	+	1.63904e10i	0.934368	+	0.294244i
$46$	1.69667e10			0.264041
$47$			1.15435e11i			1.56207i	0.624484	+	0.781037i	$0.285309\pi$
$47$			1.15435e11i			1.56207i	−0.624484	+	0.781037i	$0.714691\pi$
$48$			3.02539e9i			0.0357038i
$49$	−5.24978e10			−0.541834
$50$	4.47657e10	−	6.40277e10i	0.405173	−	0.579513i
$51$	2.13620e10			0.169994
$52$			1.26803e11i			0.889423i
$53$			1.13298e11i			0.702151i	0.936347	+	0.351076i	$0.114184\pi$
$53$			1.13298e11i			0.702151i	−0.936347	+	0.351076i	$0.885816\pi$
$54$	3.64248e10			0.199911
$55$	−2.92165e11	−	9.20064e10i	−1.42321	−	0.448188i
$56$	1.01320e11			0.439009
$57$			1.76237e10i			0.0680629i
$58$		−	2.52737e11i		−	0.871741i
$59$	−7.68729e10			−0.237266			−0.118633	−	0.992938i	$-0.537851\pi$
$59$	−7.68729e10			−0.237266			−0.118633	+	0.992938i	$0.537851\pi$
$60$	7.75148e9	−	2.46147e10i	0.0214487	−	0.0681101i
$61$	1.14756e11			0.285189			0.142594	−	0.989781i	$-0.454456\pi$
$61$	1.14756e11			0.285189			0.142594	+	0.989781i	$0.454456\pi$
$62$		−	2.63270e10i		−	0.0588647i
$63$		−	6.03647e11i		−	1.21638i
$64$	−6.87195e10			−0.125000
$65$	3.24888e11	−	1.03168e12i	0.534314	−	1.69670i
$66$	−1.01181e11			−0.150682
$67$			1.23899e12i			1.67332i	0.547720	+	0.836662i	$0.315496\pi$
$67$			1.23899e12i			1.67332i	−0.547720	+	0.836662i	$0.684504\pi$
$68$			4.85220e11i			0.595156i
$69$	−4.78057e10			−0.0533286
$70$	−8.24344e11	−	2.59597e11i	−0.837474	−	0.263731i
$71$	6.95554e11			0.644394			0.322197	−	0.946673i	$-0.395579\pi$
$71$	6.95554e11			0.644394			0.322197	+	0.946673i	$0.395579\pi$
$72$			4.09418e11i			0.346342i
$73$		−	3.96904e11i		−	0.306964i	−0.988151	−	0.153482i	$-0.950951\pi$
$73$		−	3.96904e11i		−	0.306964i	0.988151	−	0.153482i	$-0.0490487\pi$
$74$	−2.78027e11			−0.196825
$75$	−1.26133e11	+	1.80406e11i	−0.0818332	+	0.117045i
$76$	−4.00309e11			−0.238290
$77$			3.38853e12i			1.85277i
$78$		−	3.57283e11i		−	0.179638i
$79$	5.70369e11			0.263986			0.131993	−	0.991251i	$-0.457862\pi$
$79$	5.70369e11			0.263986			0.131993	+	0.991251i	$0.457862\pi$
$80$	5.59104e11	+	1.76069e11i	0.238456	+	0.0750927i
$81$	2.38739e12			0.939228
$82$			2.60314e12i			0.945600i
$83$		−	1.89284e12i		−	0.635487i	−0.948177	−	0.317744i	$-0.897075\pi$
$83$		−	1.89284e12i		−	0.635487i	0.948177	−	0.317744i	$-0.102925\pi$
$84$	−2.85482e11			−0.0886672
$85$	1.24320e12	−	3.94777e12i	0.357535	−	1.13535i
$86$	−1.36974e12			−0.365089
$87$			7.12117e11i			0.176066i
$88$		−	2.29824e12i		−	0.527543i
$89$	−4.80874e11			−0.102564			−0.0512822	−	0.998684i	$-0.516331\pi$
$89$	−4.80874e11			−0.102564			−0.0512822	+	0.998684i	$0.516331\pi$
$90$	1.04899e12	−	3.33104e12i	0.208062	−	0.660698i
$91$	−1.19654e13			−2.20881
$92$		−	1.08587e12i		−	0.186705i
$93$			7.41794e10i			0.0118890i
$94$	7.38785e12			1.10455
$95$	3.25692e12	+	1.02565e12i	0.454574	+	0.143151i
$96$	1.93625e11			0.0252464
$97$		−	3.52771e12i		−	0.430008i	−0.976613	−	0.215004i	$-0.931024\pi$
$97$		−	3.52771e12i		−	0.430008i	0.976613	−	0.215004i	$-0.0689765\pi$
$98$			3.35986e12i			0.383135i
$99$	−1.36925e13			−1.46168
$100$	−4.09777e12	−	2.86500e12i	−0.409777	−	0.286500i
$101$	7.33647e12			0.687699			0.343849	−	0.939025i	$-0.388269\pi$
$101$	7.33647e12			0.687699			0.343849	+	0.939025i	$0.388269\pi$
$102$		−	1.36717e12i		−	0.120204i
$103$		−	1.09675e12i		−	0.0905035i	−0.998976	−	0.0452518i	$-0.985591\pi$
$103$		−	1.09675e12i		−	0.0905035i	0.998976	−	0.0452518i	$-0.0144090\pi$
$104$	8.11541e12			0.628917
$105$	2.32269e12	+	7.31444e11i	0.169145	+	0.0532661i
$106$	7.25110e12			0.496496
$107$			2.29476e13i			1.47823i	0.673578	+	0.739116i	$0.264757\pi$
$107$			2.29476e13i			1.47823i	−0.673578	+	0.739116i	$0.735243\pi$
$108$		−	2.33118e12i		−	0.141359i
$109$	1.53048e13			0.874090			0.437045	−	0.899440i	$-0.356025\pi$
$109$	1.53048e13			0.874090			0.437045	+	0.899440i	$0.356025\pi$
$110$	−5.88841e12	+	1.86985e13i	−0.316917	+	1.00636i
$111$	7.83375e11			0.0397530
$112$		−	6.48449e12i		−	0.310427i
$113$			1.84344e13i			0.832950i	0.909147	+	0.416475i	$0.136735\pi$
$113$			1.84344e13i			0.832950i	−0.909147	+	0.416475i	$0.863265\pi$
$114$	1.12792e12			0.0481278
$115$	−2.78215e12	+	8.83467e12i	−0.112162	+	0.356167i
$116$	−1.61752e13			−0.616414
$117$		−	4.83501e13i		−	1.74257i
$118$			4.91986e12i			0.167772i
$119$	−4.57862e13			−1.47802
$120$	−1.57534e12	−	4.96095e11i	−0.0481611	−	0.0151665i
$121$	4.23390e13			1.22641
$122$		−	7.34440e12i		−	0.201659i
$123$		−	7.33466e12i		−	0.190984i
$124$	−1.68493e12			−0.0416236
$125$	2.59991e13	+	3.38088e13i	0.609597	+	0.792712i
$126$	−3.86334e13			−0.860111
$127$		−	8.20985e13i		−	1.73625i	−0.496349	−	0.868123i	$-0.665326\pi$
$127$		−	8.20985e13i		−	1.73625i	0.496349	−	0.868123i	$-0.334674\pi$
$128$			4.39805e12i			0.0883883i
$129$	3.85941e12			0.0737374
$130$	−6.60272e13	−	2.07928e13i	−1.19975	−	0.377817i
$131$	5.56886e13			0.962726			0.481363	−	0.876521i	$-0.340142\pi$
$131$	5.56886e13			0.962726			0.481363	+	0.876521i	$0.340142\pi$
$132$			6.47556e12i			0.106548i
$133$		−	3.77738e13i		−	0.591773i
$134$	7.92950e13			1.18322
$135$	−5.97282e12	+	1.89666e13i	−0.0849200	+	0.269662i
$136$	3.10541e13			0.420839
$137$		−	4.02804e13i		−	0.520487i	−0.965543	−	0.260244i	$-0.916197\pi$
$137$		−	4.02804e13i		−	0.520487i	0.965543	−	0.260244i	$-0.0838029\pi$
$138$			3.05956e12i			0.0377090i
$139$	−1.26300e14			−1.48528			−0.742640	−	0.669691i	$-0.766427\pi$
$139$	−1.26300e14			−1.48528			−0.742640	+	0.669691i	$0.766427\pi$
$140$	−1.66142e13	+	5.27580e13i	−0.186486	+	0.592184i
$141$	−2.08161e13			−0.223088
$142$		−	4.45155e13i		−	0.455656i
$143$			2.71410e14i			2.65425i
$144$	2.62027e13			0.244901
$145$	1.31602e14	+	4.14431e13i	1.17590	+	0.370306i
$146$	−2.54019e13			−0.217056
$147$		−	9.46680e12i		−	0.0773821i
$148$			1.77937e13i			0.139177i
$149$	1.16410e13			0.0871523			0.0435762	−	0.999050i	$-0.486125\pi$
$149$	1.16410e13			0.0871523			0.0435762	+	0.999050i	$0.486125\pi$
$150$	1.15460e13	+	8.07249e12i	0.0827631	+	0.0578648i
$151$	−2.01909e14			−1.38613			−0.693067	−	0.720873i	$-0.743741\pi$
$151$	−2.01909e14			−1.38613			−0.693067	+	0.720873i	$0.743741\pi$
$152$			2.56198e13i			0.168497i
$153$		−	1.85014e14i		−	1.16603i
$154$	2.16866e14			1.31011
$155$	1.37086e13	+	4.31702e12i	0.0794031	+	0.0250051i
$156$	−2.28661e13			−0.127023
$157$			2.26013e14i			1.20444i	0.798329	+	0.602222i	$0.205718\pi$
$157$			2.26013e14i			1.20444i	−0.798329	+	0.602222i	$0.794282\pi$
$158$		−	3.65036e13i		−	0.186666i
$159$	−2.04308e13			−0.100278
$160$	1.12684e13	−	3.57826e13i	0.0530986	−	0.168614i
$161$	1.02465e14			0.463666
$162$		−	1.52793e14i		−	0.664134i
$163$		−	3.38983e14i		−	1.41566i	−0.706384	−	0.707829i	$-0.749675\pi$
$163$		−	3.38983e14i		−	1.41566i	0.706384	−	0.707829i	$-0.250325\pi$
$164$	1.66601e14			0.668640
$165$	1.65913e13	−	5.26853e13i	0.0640080	−	0.203256i
$166$	−1.21142e14			−0.449357
$167$		−	2.58310e13i		−	0.0921476i	−0.998938	−	0.0460738i	$-0.985329\pi$
$167$		−	2.58310e13i		−	0.0921476i	0.998938	−	0.0460738i	$-0.0146709\pi$
$168$			1.82708e13i			0.0626972i
$169$	−6.55511e14			−2.16430
$170$	−2.52657e14	−	7.95649e13i	−0.802811	−	0.252816i
$171$	1.52638e14			0.466860
$172$			8.76635e13i			0.258157i
$173$			1.83600e14i			0.520681i	0.965517	+	0.260341i	$0.0838348\pi$
$173$			1.83600e14i			0.520681i	−0.965517	+	0.260341i	$0.916165\pi$
$174$	4.55755e13			0.124498
$175$	2.70347e14	−	3.86673e14i	0.711499	−	1.01765i
$176$	−1.47087e14			−0.373029
$177$		−	1.38623e13i		−	0.0338851i
$178$			3.07759e13i			0.0725239i
$179$	3.65553e14			0.830626			0.415313	−	0.909678i	$-0.363672\pi$
$179$	3.65553e14			0.830626			0.415313	+	0.909678i	$0.363672\pi$
$180$	−2.13186e14	−	6.71351e13i	−0.467184	−	0.147122i
$181$	2.38594e14			0.504370			0.252185	−	0.967679i	$-0.418851\pi$
$181$	2.38594e14			0.504370			0.252185	+	0.967679i	$0.418851\pi$
$182$			7.65784e14i			1.56186i
$183$			2.06937e13i			0.0407293i
$184$	−6.94956e13			−0.132021
$185$	4.55901e13	−	1.44770e14i	0.0836092	−	0.265500i
$186$	4.74748e12			0.00840677
$187$			1.03857e15i			1.77608i
$188$		−	4.72822e14i		−	0.781037i
$189$	2.19975e14			0.351052
$190$	6.56414e13	−	2.08443e14i	0.101223	−	0.321432i
$191$	4.97339e14			0.741201			0.370600	−	0.928792i	$-0.379152\pi$
$191$	4.97339e14			0.741201			0.370600	+	0.928792i	$0.379152\pi$
$192$		−	1.23920e13i		−	0.0178519i
$193$			2.99351e14i			0.416925i	0.978030	+	0.208463i	$0.0668460\pi$
$193$			2.99351e14i			0.416925i	−0.978030	+	0.208463i	$0.933154\pi$
$194$	−2.25773e14			−0.304062
$195$	1.86039e14	+	5.85862e13i	0.242315	+	0.0763080i
$196$	2.15031e14			0.270917
$197$			8.69796e13i			0.106020i	0.998594	+	0.0530099i	$0.0168815\pi$
$197$			8.69796e13i			0.106020i	−0.998594	+	0.0530099i	$0.983119\pi$
$198$			8.76318e14i			1.03357i
$199$	−2.97381e14			−0.339444			−0.169722	−	0.985492i	$-0.554287\pi$
$199$	−2.97381e14			−0.339444			−0.169722	+	0.985492i	$0.554287\pi$
$200$	−1.83360e14	+	2.62257e14i	−0.202586	+	0.289756i
$201$	−2.23423e14			−0.238976
$202$		−	4.69534e14i		−	0.486277i
$203$		−	1.52632e15i		−	1.53081i
$204$	−8.74986e13			−0.0849972
$205$	−1.35547e15	−	4.26855e14i	−1.27553	−	0.401680i
$206$	−7.01920e13			−0.0639957
$207$			4.14042e14i			0.365794i
$208$		−	5.19386e14i		−	0.444712i
$209$	−8.56821e14			−0.711114
$210$	4.68124e13	−	1.48652e14i	0.0376648	−	0.119604i
$211$	1.01507e15			0.791879			0.395940	−	0.918277i	$-0.370419\pi$
$211$	1.01507e15			0.791879			0.395940	+	0.918277i	$0.370419\pi$
$212$		−	4.64070e14i		−	0.351076i
$213$			1.25428e14i			0.0920292i
$214$	1.46865e15			1.04527
$215$	2.24606e14	−	7.13233e14i	0.155086	−	0.492472i
$216$	−1.49196e14			−0.0999556
$217$		−	1.58993e14i		−	0.103369i
$218$		−	9.79509e14i		−	0.618075i
$219$	7.15728e13			0.0438390
$220$	1.19671e15	+	3.76858e14i	0.711607	+	0.224094i
$221$	−3.66732e15			−2.11738
$222$		−	5.01360e13i		−	0.0281096i
$223$			1.07195e15i			0.583704i	0.956463	+	0.291852i	$0.0942715\pi$
$223$			1.07195e15i			0.583704i	−0.956463	+	0.291852i	$0.905729\pi$
$224$	−4.15008e14			−0.219505
$225$	1.56248e15	+	1.09243e15i	0.802839	+	0.561314i
$226$	1.17980e15			0.588985
$227$		−	2.84453e15i		−	1.37988i	−0.723865	−	0.689942i	$-0.757636\pi$
$227$		−	2.84453e15i		−	1.37988i	0.723865	−	0.689942i	$-0.242364\pi$
$228$		−	7.21867e13i		−	0.0340315i
$229$	1.89338e15			0.867577			0.433788	−	0.901015i	$-0.357177\pi$
$229$	1.89338e15			0.867577			0.433788	+	0.901015i	$0.357177\pi$
$230$	5.65419e14	+	1.78058e14i	0.251848	+	0.0793103i
$231$	−6.11045e14			−0.264603
$232$			1.03521e15i			0.435871i
$233$			2.59627e15i			1.06301i	0.847056	+	0.531504i	$0.178373\pi$
$233$			2.59627e15i			1.06301i	−0.847056	+	0.531504i	$0.821627\pi$
$234$	−3.09440e15			−1.23218
$235$	−1.21144e15	+	3.84690e15i	−0.469202	+	1.48994i
$236$	3.14871e14			0.118633
$237$			1.02853e14i			0.0377011i
$238$			2.93032e15i			1.04512i
$239$	4.03953e15			1.40199			0.700994	−	0.713167i	$-0.252740\pi$
$239$	4.03953e15			1.40199			0.700994	+	0.713167i	$0.252740\pi$
$240$	−3.17501e13	+	1.00822e14i	−0.0107244	+	0.0340550i
$241$	−1.36189e15			−0.447747			−0.223873	−	0.974618i	$-0.571870\pi$
$241$	−1.36189e15			−0.447747			−0.223873	+	0.974618i	$0.571870\pi$
$242$		−	2.70970e15i		−	0.867203i
$243$			1.33790e15i			0.416853i
$244$	−4.70042e14			−0.142594
$245$	−1.74950e15	−	5.50939e14i	−0.516814	−	0.162751i
$246$	−4.69418e14			−0.135046
$247$		−	3.02556e15i		−	0.847764i
$248$			1.07835e14i			0.0294324i
$249$	3.41332e14			0.0907572
$250$	2.16377e15	−	1.66394e15i	0.560532	−	0.431050i
$251$	3.48984e15			0.880900			0.440450	−	0.897777i	$-0.354819\pi$
$251$	3.48984e15			0.880900			0.440450	+	0.897777i	$0.354819\pi$
$252$			2.47254e15i			0.608190i
$253$		−	2.32419e15i		−	0.557172i
$254$	−5.25431e15			−1.22771
$255$	7.11891e14	+	2.24184e14i	0.162145	+	0.0510614i
$256$	2.81475e14			0.0625000
$257$		−	6.33886e15i		−	1.37229i	−0.727465	−	0.686144i	$-0.759302\pi$
$257$		−	6.33886e15i		−	1.37229i	0.727465	−	0.686144i	$-0.240698\pi$
$258$		−	2.47002e14i		−	0.0521402i
$259$	−1.67905e15			−0.345633
$260$	−1.33074e15	+	4.22574e15i	−0.267157	+	0.848352i
$261$	6.16760e15			1.20768
$262$		−	3.56407e15i		−	0.680750i
$263$		−	3.10756e15i		−	0.579039i	−0.957172	−	0.289519i	$-0.906505\pi$
$263$		−	3.10756e15i		−	0.579039i	0.957172	−	0.289519i	$-0.0934955\pi$
$264$	4.14436e14			0.0753410
$265$	−1.18901e15	+	3.77569e15i	−0.210906	+	0.669728i
$266$	−2.41753e15			−0.418447
$267$		−	8.67148e13i		−	0.0146477i
$268$		−	5.07488e15i		−	0.836662i
$269$	7.16967e15			1.15374			0.576872	−	0.816834i	$-0.304273\pi$
$269$	7.16967e15			1.15374			0.576872	+	0.816834i	$0.304273\pi$
$270$	1.21386e15	+	3.82261e14i	0.190680	+	0.0600475i
$271$	−1.21980e16			−1.87063			−0.935314	−	0.353819i	$-0.884883\pi$
$271$	−1.21980e16			−1.87063			−0.935314	+	0.353819i	$0.884883\pi$
$272$		−	1.98746e15i		−	0.297578i
$273$		−	2.15769e15i		−	0.315451i
$274$	−2.57795e15			−0.368040
$275$	−8.77088e15	−	6.13226e15i	−1.22287	−	0.854984i
$276$	1.95812e14			0.0266643
$277$			5.77964e15i			0.768745i	0.923178	+	0.384373i	$0.125582\pi$
$277$			5.77964e15i			0.768745i	−0.923178	+	0.384373i	$0.874418\pi$
$278$			8.08322e15i			1.05025i
$279$	6.42462e14			0.0815493
$280$	3.37651e15	+	1.06331e15i	0.418737	+	0.131866i
$281$	7.62781e15			0.924291			0.462146	−	0.886804i	$-0.347080\pi$
$281$	7.62781e15			0.924291			0.462146	+	0.886804i	$0.347080\pi$
$282$			1.33223e15i			0.157747i
$283$			1.14798e16i			1.32838i	0.747563	+	0.664190i	$0.231224\pi$
$283$			1.14798e16i			1.32838i	−0.747563	+	0.664190i	$0.768776\pi$
$284$	−2.84899e15			−0.322197
$285$	−1.84952e14	+	5.87313e14i	−0.0204441	+	0.0649199i
$286$	1.73702e16			1.87684
$287$			1.57208e16i			1.66051i
$288$		−	1.67698e15i		−	0.173171i
$289$	−4.12866e15			−0.416843
$290$	2.65236e15	−	8.42252e15i	0.261846	−	0.831486i
$291$	6.36143e14			0.0614116
$292$			1.62572e15i			0.153482i
$293$		−	5.12736e15i		−	0.473428i	−0.971579	−	0.236714i	$-0.923930\pi$
$293$		−	5.12736e15i		−	0.473428i	0.971579	−	0.236714i	$-0.0760705\pi$
$294$	−6.05875e14			−0.0547174
$295$	−2.56180e15	−	8.06744e14i	−0.226309	−	0.0712677i
$296$	1.13880e15			0.0984127
$297$		−	4.98967e15i		−	0.421847i
$298$		−	7.45023e14i		−	0.0616260i
$299$	8.20706e15			0.664240
$300$	5.16639e14	−	7.38941e14i	0.0409166	−	0.0585224i
$301$	−8.27209e15			−0.641111
$302$			1.29222e16i			0.980145i
$303$			1.32297e15i			0.0982138i
$304$	1.63966e15			0.119145
$305$	3.82427e15	+	1.20431e15i	0.272020	+	0.0856624i
$306$	−1.18409e16			−0.824511
$307$		−	4.29777e15i		−	0.292984i	−0.989212	−	0.146492i	$-0.953202\pi$
$307$		−	4.29777e15i		−	0.292984i	0.989212	−	0.146492i	$-0.0467982\pi$
$308$		−	1.38794e16i		−	0.926385i
$309$	1.97774e14			0.0129253
$310$	2.76289e14	−	8.77351e14i	0.0176812	−	0.0561465i
$311$	−1.63784e16			−1.02643			−0.513213	−	0.858261i	$-0.671545\pi$
$311$	−1.63784e16			−1.02643			−0.513213	+	0.858261i	$0.671545\pi$
$312$			1.46343e15i			0.0898189i
$313$		−	1.00766e16i		−	0.605726i	−0.953034	−	0.302863i	$-0.902058\pi$
$313$		−	1.00766e16i		−	0.605726i	0.953034	−	0.302863i	$-0.0979424\pi$
$314$	1.44649e16			0.851670
$315$	6.33499e15	−	2.01166e16i	0.365365	−	1.16021i
$316$	−2.33623e15			−0.131993
$317$			2.53657e16i			1.40398i	0.712186	+	0.701991i	$0.247705\pi$
$317$			2.53657e16i			1.40398i	−0.712186	+	0.701991i	$0.752295\pi$
$318$			1.30757e15i			0.0709071i
$319$	−3.46214e16			−1.83952
$320$	−2.29009e15	−	7.21178e14i	−0.119228	−	0.0375464i
$321$	−4.13808e15			−0.211114
$322$		−	6.55773e15i		−	0.327862i
$323$		−	1.15775e16i		−	0.567280i
$324$	−9.77875e15			−0.469614
$325$	2.16539e16	−	3.09712e16i	1.01928	−	1.45786i
$326$	−2.16949e16			−1.00102
$327$			2.75988e15i			0.124833i
$328$		−	1.06625e16i		−	0.472800i
$329$	4.46164e16			1.93964
$330$	−3.37186e15	−	1.06184e15i	−0.143724	−	0.0452605i
$331$	4.02658e16			1.68289			0.841443	−	0.540345i	$-0.181706\pi$
$331$	4.02658e16			1.68289			0.841443	+	0.540345i	$0.181706\pi$
$332$			7.75308e15i			0.317744i
$333$		−	6.78476e15i		−	0.272676i
$334$	−1.65318e15			−0.0651582
$335$	−1.30026e16	+	4.12894e16i	−0.502618	+	1.59605i
$336$	1.16933e15			0.0443336
$337$			8.96775e15i			0.333495i	0.986000	+	0.166747i	$0.0533265\pi$
$337$			8.96775e15i			0.333495i	−0.986000	+	0.166747i	$0.946674\pi$
$338$			4.19527e16i			1.53039i
$339$	−3.32423e15			−0.118958
$340$	−5.09216e15	+	1.61701e16i	−0.178768	+	0.567673i
$341$	−3.60642e15			−0.124215
$342$		−	9.76881e15i		−	0.330120i
$343$		−	1.71575e16i		−	0.568907i
$344$	5.61047e15			0.182545
$345$	−1.59313e15	−	5.01698e14i	−0.0508661	−	0.0160184i
$346$	1.17504e16			0.368177
$347$			8.65607e15i			0.266182i	0.991104	+	0.133091i	$0.0424903\pi$
$347$			8.65607e15i			0.266182i	−0.991104	+	0.133091i	$0.957510\pi$
$348$		−	2.91683e15i		−	0.0880332i
$349$	−2.38116e16			−0.705380			−0.352690	−	0.935740i	$-0.614733\pi$
$349$	−2.38116e16			−0.705380			−0.352690	+	0.935740i	$0.614733\pi$
$350$	−2.47471e16	−	1.73022e16i	−0.719584	−	0.503106i
$351$	1.76192e16			0.502911
$352$			9.41358e15i			0.263771i
$353$			6.03856e16i			1.66111i	0.556938	+	0.830554i	$0.311976\pi$
$353$			6.03856e16i			1.66111i	−0.556938	+	0.830554i	$0.688024\pi$
$354$	−8.87187e14			−0.0239604
$355$	2.31795e16	+	7.29951e15i	0.614638	+	0.193557i
$356$	1.96966e15			0.0512822
$357$		−	8.25652e15i		−	0.211083i
$358$		−	2.33954e16i		−	0.587342i
$359$	−2.03452e16			−0.501589			−0.250795	−	0.968040i	$-0.580692\pi$
$359$	−2.03452e16			−0.501589			−0.250795	+	0.968040i	$0.580692\pi$
$360$	−4.29665e15	+	1.36439e16i	−0.104031	+	0.330349i
$361$	−3.25015e16			−0.772871
$362$		−	1.52700e16i		−	0.356643i
$363$			7.63489e15i			0.175150i
$364$	4.90102e16			1.10440
$365$	4.16532e15	−	1.32269e16i	0.0922030	−	0.292789i
$366$	1.32440e15			0.0287999
$367$		−	4.76835e16i		−	1.01868i	−0.860565	−	0.509341i	$-0.829889\pi$
$367$		−	4.76835e16i		−	1.01868i	0.860565	−	0.509341i	$-0.170111\pi$
$368$			4.44772e15i			0.0933526i
$369$	−6.35250e16			−1.31001
$370$	−9.26531e15	−	2.91776e15i	−0.187737	−	0.0591206i
$371$	4.37905e16			0.871866
$372$		−	3.03839e14i		−	0.00594448i
$373$		−	1.06022e15i		−	0.0203839i	−0.999948	−	0.0101920i	$-0.996756\pi$
$373$		−	1.06022e15i		−	0.0203839i	0.999948	−	0.0101920i	$-0.00324426\pi$
$374$	6.64682e16			1.25588
$375$	−6.09667e15	+	4.68835e15i	−0.113211	+	0.0870596i
$376$	−3.02606e16			−0.552277
$377$		−	1.22253e17i		−	2.19301i
$378$		−	1.40784e16i		−	0.248231i
$379$	1.83582e15			0.0318181			0.0159091	−	0.999873i	$-0.494936\pi$
$379$	1.83582e15			0.0318181			0.0159091	+	0.999873i	$0.494936\pi$
$380$	−1.33404e16	−	4.20105e15i	−0.227287	−	0.0715755i
$381$	1.48046e16			0.247962
$382$		−	3.18297e16i		−	0.524108i
$383$		−	1.35715e16i		−	0.219703i	−0.993948	−	0.109851i	$-0.964963\pi$
$383$		−	1.35715e16i		−	0.219703i	0.993948	−	0.109851i	$-0.0350375\pi$
$384$	−7.93089e14			−0.0126232
$385$	−3.55610e16	+	1.12923e17i	−0.556518	+	1.76721i
$386$	1.91585e16			0.294811
$387$		−	3.34261e16i		−	0.505783i
$388$			1.44495e16i			0.215004i
$389$	−1.06008e17			−1.55120			−0.775598	−	0.631227i	$-0.782552\pi$
$389$	−1.06008e17			−1.55120			−0.775598	+	0.631227i	$0.782552\pi$
$390$	3.74952e15	−	1.19065e16i	0.0539579	−	0.171342i
$391$	3.14048e16			0.444475
$392$		−	1.37620e16i		−	0.191567i
$393$			1.00422e16i			0.137492i
$394$	5.56670e15			0.0749673
$395$	1.90077e16	+	5.98576e15i	0.251795	+	0.0792936i
$396$	5.60844e16			0.730841
$397$			8.58871e16i			1.10101i	0.834833	+	0.550503i	$0.185564\pi$
$397$			8.58871e16i			1.10101i	−0.834833	+	0.550503i	$0.814436\pi$
$398$			1.90324e16i			0.240023i
$399$	6.81166e15			0.0845142
$400$	1.67845e16	+	1.17351e16i	0.204889	+	0.143250i
$401$	−7.04529e16			−0.846175			−0.423088	−	0.906089i	$-0.639054\pi$
$401$	−7.04529e16			−0.846175			−0.423088	+	0.906089i	$0.639054\pi$
$402$			1.42991e16i			0.168981i
$403$		−	1.27348e16i		−	0.148084i
$404$	−3.00502e16			−0.343849
$405$	7.95602e16	+	2.50545e16i	0.895856	+	0.282117i
$406$	−9.76845e16			−1.08245
$407$			3.80857e16i			0.415335i
$408$			5.59991e15i			0.0601021i
$409$	8.68888e16			0.917830			0.458915	−	0.888480i	$-0.348238\pi$
$409$	8.68888e16			0.917830			0.458915	+	0.888480i	$0.348238\pi$
$410$	−2.73187e16	+	8.67502e16i	−0.284031	+	0.901935i
$411$	7.26367e15			0.0743334
$412$			4.49229e15i			0.0452518i
$413$			2.97118e16i			0.294614i
$414$	2.64987e16			0.258656
$415$	1.98645e16	−	6.30793e16i	0.190882	−	0.606142i
$416$	−3.32407e16			−0.314459
$417$		−	2.27754e16i		−	0.212120i
$418$			5.48365e16i			0.502834i
$419$	1.84886e17			1.66922			0.834608	−	0.550844i	$-0.185694\pi$
$419$	1.84886e17			1.66922			0.834608	+	0.550844i	$0.185694\pi$
$420$	−9.51373e15	−	2.99599e15i	−0.0845727	−	0.0266330i
$421$	−3.13509e16			−0.274421			−0.137210	−	0.990542i	$-0.543814\pi$
$421$	−3.13509e16			−0.274421			−0.137210	+	0.990542i	$0.543814\pi$
$422$		−	6.49643e16i		−	0.559943i
$423$			1.80287e17i			1.53021i
$424$	−2.97005e16			−0.248248
$425$	8.28599e16	−	1.18513e17i	0.682050	−	0.975526i
$426$	8.02736e15			0.0650745
$427$		−	4.43540e16i		−	0.354121i
$428$		−	9.39934e16i		−	0.739116i
$429$	−4.89426e16			−0.379066
$430$	−4.56469e16	−	1.43748e16i	−0.348230	−	0.109662i
$431$	−2.37837e16			−0.178722			−0.0893609	−	0.995999i	$-0.528482\pi$
$431$	−2.37837e16			−0.178722			−0.0893609	+	0.995999i	$0.528482\pi$
$432$			9.54853e15i			0.0706793i
$433$		−	1.78323e17i		−	1.30027i	−0.759817	−	0.650137i	$-0.774711\pi$
$433$		−	1.78323e17i		−	1.30027i	0.759817	−	0.650137i	$-0.225289\pi$
$434$	−1.01755e16			−0.0730927
$435$	−7.47333e15	+	2.37314e16i	−0.0528852	+	0.167936i
$436$	−6.26886e16			−0.437045
$437$			2.59091e16i			0.177960i
$438$		−	4.58066e15i		−	0.0309989i
$439$	−2.00316e17			−1.33566			−0.667831	−	0.744313i	$-0.732777\pi$
$439$	−2.00316e17			−1.33566			−0.667831	+	0.744313i	$0.732777\pi$
$440$	2.41189e16	−	7.65892e16i	0.158458	−	0.503182i
$441$	−8.19913e16			−0.530783
$442$			2.34709e17i			1.49722i
$443$		−	2.03004e17i		−	1.27609i	−0.770001	−	0.638043i	$-0.779744\pi$
$443$		−	2.03004e17i		−	1.27609i	0.770001	−	0.638043i	$-0.220256\pi$
$444$	−3.20870e15			−0.0198765
$445$	−1.60252e16	−	5.04654e15i	−0.0978281	−	0.0308073i
$446$	6.86048e16			0.412741
$447$			2.09919e15i			0.0124467i
$448$			2.65605e16i			0.155213i
$449$	6.75297e16			0.388950			0.194475	−	0.980907i	$-0.437700\pi$
$449$	6.75297e16			0.388950			0.194475	+	0.980907i	$0.437700\pi$
$450$	6.99153e16	−	9.99988e16i	0.396909	−	0.567693i
$451$	3.56593e17			1.99538
$452$		−	7.55073e16i		−	0.416475i
$453$		−	3.64097e16i		−	0.197961i
$454$	−1.82050e17			−0.975725
$455$	−3.98748e17	−	1.25571e17i	−2.10681	−	0.663461i
$456$	−4.61995e15			−0.0240639
$457$			2.86962e17i			1.47356i	0.676130	+	0.736782i	$0.263656\pi$
$457$			2.86962e17i			1.47356i	−0.676130	+	0.736782i	$0.736344\pi$
$458$		−	1.21177e17i		−	0.613470i
$459$	6.74211e16			0.336522
$460$	1.13957e16	−	3.61868e16i	0.0560808	−	0.178084i
$461$	−2.29767e17			−1.11489			−0.557443	−	0.830215i	$-0.688218\pi$
$461$	−2.29767e17			−1.11489			−0.557443	+	0.830215i	$0.688218\pi$
$462$			3.91069e16i			0.187103i
$463$			8.12971e16i			0.383529i	0.981441	+	0.191765i	$0.0614210\pi$
$463$			8.12971e16i			0.383529i	−0.981441	+	0.191765i	$0.938579\pi$
$464$	6.62536e16			0.308207
$465$	−7.78477e14	+	2.47204e15i	−0.00357110	+	0.0113400i
$466$	1.66161e17			0.751660
$467$			5.34782e16i			0.238571i	0.992860	+	0.119285i	$0.0380604\pi$
$467$			5.34782e16i			0.238571i	−0.992860	+	0.119285i	$0.961940\pi$
$468$			1.98042e17i			0.871283i
$469$	4.78875e17			2.07778
$470$	2.46201e17	+	7.75320e16i	1.05355	+	0.331776i
$471$	−4.07564e16			−0.172013
$472$		−	2.01518e16i		−	0.0838861i
$473$			1.87635e17i			0.770401i
$474$	6.58261e15			0.0266587
$475$	9.77739e16	+	6.83597e16i	0.390584	+	0.273081i
$476$	1.87540e17			0.739009
$477$			1.76950e17i			0.687830i
$478$		−	2.58530e17i		−	0.991355i
$479$	−5.08284e17			−1.92276			−0.961382	−	0.275219i	$-0.911250\pi$
$479$	−5.08284e17			−1.92276			−0.961382	+	0.275219i	$0.911250\pi$
$480$	6.45260e15	+	2.03201e15i	0.0240806	+	0.00758327i
$481$	−1.34486e17			−0.495148
$482$			8.71612e16i			0.316605i
$483$			1.84772e16i			0.0662185i
$484$	−1.73421e17			−0.613205
$485$	3.70216e16	−	1.17562e17i	0.129162	−	0.410151i
$486$	8.56256e16			0.294760
$487$			4.73289e17i			1.60764i	0.594875	+	0.803818i	$0.297202\pi$
$487$			4.73289e17i			1.60764i	−0.594875	+	0.803818i	$0.702798\pi$
$488$			3.00827e16i			0.100829i
$489$	6.11280e16			0.202177
$490$	−3.52601e16	+	1.11968e17i	−0.115083	+	0.365443i
$491$	1.08502e17			0.349469			0.174734	−	0.984616i	$-0.444093\pi$
$491$	1.08502e17			0.349469			0.174734	+	0.984616i	$0.444093\pi$
$492$			3.00428e16i			0.0954919i
$493$		−	4.67809e17i		−	1.46745i
$494$	−1.93636e17			−0.599460
$495$	−4.56304e17	−	1.43696e17i	−1.39419	−	0.439047i
$496$	6.90146e15			0.0208118
$497$		−	2.68836e17i		−	0.800148i
$498$		−	2.18452e16i		−	0.0641750i
$499$	1.57760e17			0.457451			0.228725	−	0.973491i	$-0.426544\pi$
$499$	1.57760e17			0.457451			0.228725	+	0.973491i	$0.426544\pi$
$500$	−1.06492e17	−	1.38481e17i	−0.304798	−	0.396356i
$501$	4.65804e15			0.0131601
$502$		−	2.23350e17i		−	0.622890i
$503$			1.83636e17i			0.505551i	0.967525	+	0.252776i	$0.0813435\pi$
$503$			1.83636e17i			0.505551i	−0.967525	+	0.252776i	$0.918657\pi$
$504$	1.58242e17			0.430055
$505$	2.44489e17	+	7.69928e16i	0.655943	+	0.206565i
$506$	−1.48748e17			−0.393980
$507$		−	1.18207e17i		−	0.309094i
$508$			3.36276e17i			0.868123i
$509$	4.08498e17			1.04118			0.520588	−	0.853808i	$-0.325713\pi$
$509$	4.08498e17			1.04118			0.520588	+	0.853808i	$0.325713\pi$
$510$	1.43478e16	−	4.55610e16i	0.0361059	−	0.114654i
$511$	−1.53406e17			−0.381159
$512$		−	1.80144e16i		−	0.0441942i
$513$			5.56227e16i			0.134738i
$514$	−4.05687e17			−0.970355
$515$	1.15099e16	−	3.65494e16i	0.0271846	−	0.0863243i
$516$	−1.58082e16			−0.0368687
$517$		−	1.01203e18i		−	2.33080i
$518$			1.07459e17i			0.244399i
$519$	−3.31081e16			−0.0743611
$520$	2.70447e17	+	8.51673e16i	0.599875	+	0.188908i
$521$	1.78419e17			0.390837			0.195419	−	0.980720i	$-0.437393\pi$
$521$	1.78419e17			0.390837			0.195419	+	0.980720i	$0.437393\pi$
$522$		−	3.94726e17i		−	0.853961i
$523$		−	5.75398e17i		−	1.22944i	−0.788745	−	0.614720i	$-0.789269\pi$
$523$		−	5.75398e17i		−	1.22944i	0.788745	−	0.614720i	$-0.210731\pi$
$524$	−2.28101e17			−0.481363
$525$	6.97278e16	+	4.87510e16i	0.145335	+	0.101613i
$526$	−1.98884e17			−0.409442
$527$		−	4.87304e16i		−	0.0990902i
$528$		−	2.65239e16i		−	0.0532742i
$529$	4.33756e17			0.860565
$530$	2.41644e17	+	7.60968e16i	0.473569	+	0.149133i
$531$	−1.20060e17			−0.232426
$532$			1.54722e17i			0.295887i
$533$			1.25918e18i			2.37882i
$534$	−5.54975e15			−0.0103575
$535$	−2.40824e17	+	7.64733e17i	−0.444018	+	1.40997i
$536$	−3.24792e17			−0.591609
$537$			6.59193e16i			0.118626i
$538$		−	4.58859e17i		−	0.815820i
$539$	4.60252e17			0.808480
$540$	2.44647e16	−	7.76872e16i	0.0424600	−	0.134831i
$541$	−8.16715e17			−1.40052			−0.700258	−	0.713890i	$-0.746932\pi$
$541$	−8.16715e17			−1.40052			−0.700258	+	0.713890i	$0.746932\pi$
$542$			7.80670e17i			1.32273i
$543$			4.30251e16i			0.0720316i
$544$	−1.27198e17			−0.210419
$545$	5.10036e17	+	1.60617e17i	0.833727	+	0.262551i
$546$	−1.38092e17			−0.223057
$547$		−	2.53194e17i		−	0.404144i	−0.979371	−	0.202072i	$-0.935233\pi$
$547$		−	2.53194e17i		−	0.404144i	0.979371	−	0.202072i	$-0.0647675\pi$
$548$			1.64989e17i			0.260244i
$549$	1.79227e17			0.279372
$550$	−3.92465e17	+	5.61336e17i	−0.604565	+	0.864700i
$551$	3.85944e17			0.587542
$552$		−	1.25320e16i		−	0.0188545i
$553$		−	2.20451e17i		−	0.327792i
$554$	3.69897e17			0.543585
$555$	2.61061e16	+	8.22115e15i	0.0379173	+	0.0119407i
$556$	5.17326e17			0.742640
$557$		−	1.83246e17i		−	0.260001i	−0.991514	−	0.130001i	$-0.958502\pi$
$557$		−	1.83246e17i		−	0.260001i	0.991514	−	0.130001i	$-0.0414980\pi$
$558$		−	4.11176e16i		−	0.0576641i
$559$	−6.62566e17			−0.918444
$560$	6.80517e16	−	2.16097e17i	0.0932431	−	0.296092i
$561$	−1.87282e17			−0.253651
$562$		−	4.88180e17i		−	0.653572i
$563$			5.12235e17i			0.677899i	0.940805	+	0.338949i	$0.110072\pi$
$563$			5.12235e17i			0.677899i	−0.940805	+	0.338949i	$0.889928\pi$
$564$	8.52629e16			0.111544
$565$	−1.93460e17	+	6.14330e17i	−0.250194	+	0.794486i
$566$	7.34707e17			0.939307
$567$		−	9.22741e17i		−	1.16624i
$568$			1.82335e17i			0.227828i
$569$	−1.59192e18			−1.96649			−0.983245	−	0.182291i	$-0.941649\pi$
$569$	−1.59192e18			−1.96649			−0.983245	+	0.182291i	$0.941649\pi$
$570$	3.75880e16	+	1.18370e16i	0.0459053	+	0.0144562i
$571$	1.54322e18			1.86335			0.931674	−	0.363294i	$-0.118348\pi$
$571$	1.54322e18			1.86335			0.931674	+	0.363294i	$0.118348\pi$
$572$		−	1.11169e18i		−	1.32712i
$573$			8.96840e16i			0.105855i
$574$	1.00613e18			1.17416
$575$	−1.85431e17	+	2.65220e17i	−0.213965	+	0.306030i
$576$	−1.07326e17			−0.122450
$577$			8.30550e17i			0.936964i	0.883473	+	0.468482i	$0.155199\pi$
$577$			8.30550e17i			0.936964i	−0.883473	+	0.468482i	$0.844801\pi$
$578$			2.64234e17i			0.294753i
$579$	−5.39813e16			−0.0595432
$580$	−5.39041e17	−	1.69751e17i	−0.587950	−	0.185153i
$581$	−7.31595e17			−0.789089
$582$		−	4.07132e16i		−	0.0434246i
$583$		−	9.93296e17i		−	1.04769i
$584$	1.04046e17			0.108528
$585$	5.07411e17	−	1.61128e18i	0.523416	−	1.66210i
$586$	−3.28151e17			−0.334764
$587$			1.35873e17i			0.137083i	0.997648	+	0.0685416i	$0.0218346\pi$
$587$			1.35873e17i			0.137083i	−0.997648	+	0.0685416i	$0.978165\pi$
$588$			3.87760e16i			0.0386910i
$589$	4.02028e16			0.0396741
$590$	−5.16316e16	+	1.63955e17i	−0.0503939	+	0.160025i
$591$	−1.56848e16			−0.0151412
$592$		−	7.28832e16i		−	0.0695883i
$593$		−	9.65712e17i		−	0.911994i	−0.889981	−	0.455997i	$-0.849283\pi$
$593$		−	9.65712e17i		−	0.911994i	0.889981	−	0.455997i	$-0.150717\pi$
$594$	−3.19339e17			−0.298291
$595$	−1.52584e18	−	4.80505e17i	−1.40977	−	0.443954i
$596$	−4.76815e16			−0.0435762
$597$		−	5.36259e16i		−	0.0484777i
$598$		−	5.25252e17i		−	0.469689i
$599$	−6.60993e17			−0.584686			−0.292343	−	0.956314i	$-0.594435\pi$
$599$	−6.60993e17			−0.584686			−0.292343	+	0.956314i	$0.594435\pi$
$600$	−4.72923e16	−	3.30649e16i	−0.0413816	−	0.0289324i
$601$	−1.78533e18			−1.54538			−0.772689	−	0.634785i	$-0.781089\pi$
$601$	−1.78533e18			−1.54538			−0.772689	+	0.634785i	$0.781089\pi$
$602$			5.29414e17i			0.453334i
$603$			1.93505e18i			1.63919i
$604$	8.27019e17			0.693067
$605$	1.41096e18	+	4.44328e17i	1.16978	+	0.368378i
$606$	8.46700e16			0.0694476
$607$			2.51863e17i			0.204379i	0.994765	+	0.102190i	$0.0325849\pi$
$607$			2.51863e17i			0.204379i	−0.994765	+	0.102190i	$0.967415\pi$
$608$		−	1.04939e17i		−	0.0842484i
$609$	2.75238e17			0.218623
$610$	7.70760e16	−	2.44754e17i	0.0605725	−	0.192347i
$611$	3.57362e18			2.77869
$612$			7.57819e17i			0.583017i
$613$		−	6.63538e17i		−	0.505095i	−0.967585	−	0.252547i	$-0.918732\pi$
$613$		−	6.63538e17i		−	0.505095i	0.967585	−	0.252547i	$-0.0812684\pi$
$614$	−2.75057e17			−0.207171
$615$	7.69738e16	−	2.44429e17i	0.0573660	−	0.182165i
$616$	−8.88282e17			−0.655053
$617$			1.50494e18i			1.09816i	0.835770	+	0.549080i	$0.185022\pi$
$617$			1.50494e18i			1.09816i	−0.835770	+	0.549080i	$0.814978\pi$
$618$		−	1.26575e16i		−	0.00913954i
$619$	−5.34277e17			−0.381748			−0.190874	−	0.981615i	$-0.561132\pi$
$619$	−5.34277e17			−0.381748			−0.190874	+	0.981615i	$0.561132\pi$
$620$	−5.61505e16	−	1.76825e16i	−0.0397016	−	0.0125025i
$621$	−1.50881e17			−0.105570
$622$			1.04821e18i			0.725793i
$623$			1.85861e17i			0.127355i
$624$	9.36596e16			0.0635115
$625$	5.11616e17	+	1.39953e18i	0.343340	+	0.939211i
$626$	−6.44903e17			−0.428313
$627$		−	1.54508e17i		−	0.101558i
$628$		−	9.25751e17i		−	0.602222i
$629$	−5.14620e17			−0.331327
$630$	−1.28747e18	−	4.05439e17i	−0.820393	−	0.258352i
$631$	1.89366e18			1.19429			0.597147	−	0.802132i	$-0.296301\pi$
$631$	1.89366e18			1.19429			0.597147	+	0.802132i	$0.296301\pi$
$632$			1.49519e17i			0.0933330i
$633$			1.83045e17i			0.113092i
$634$	1.62340e18			0.992765
$635$	8.61585e17	−	2.73595e18i	0.521518	−	1.65607i
$636$	8.36847e16			0.0501389
$637$			1.62522e18i			0.963840i
$638$			2.21577e18i			1.30074i
$639$	1.08632e18			0.631251
$640$	−4.61554e16	+	1.46566e17i	−0.0265493	+	0.0843068i
$641$	−1.96495e18			−1.11886			−0.559428	−	0.828879i	$-0.688979\pi$
$641$	−1.96495e18			−1.11886			−0.559428	+	0.828879i	$0.688979\pi$
$642$			2.64837e17i			0.149280i
$643$		−	2.19336e18i		−	1.22388i	−0.790905	−	0.611939i	$-0.790390\pi$
$643$		−	2.19336e18i		−	1.22388i	0.790905	−	0.611939i	$-0.209610\pi$
$644$	−4.19695e17			−0.231833
$645$	1.28616e17	+	4.05027e16i	0.0703324	+	0.0221486i
$646$	−7.40959e17			−0.401128
$647$			1.81344e18i			0.971908i	0.873984	+	0.485954i	$0.161528\pi$
$647$			1.81344e18i			0.971908i	−0.873984	+	0.485954i	$0.838472\pi$
$648$			6.25840e17i			0.332067i
$649$	6.73951e17			0.354028
$650$	−1.98216e18	−	1.38585e18i	−1.03086	−	0.720740i
$651$	2.86708e16			0.0147626
$652$			1.38847e18i			0.707829i
$653$		−	1.24664e18i		−	0.629225i	−0.949220	−	0.314613i	$-0.898125\pi$
$653$		−	1.24664e18i		−	0.629225i	0.949220	−	0.314613i	$-0.101875\pi$
$654$	1.76632e17			0.0882704
$655$	1.85583e18	+	5.84426e17i	0.918270	+	0.289175i
$656$	−6.82398e17			−0.334320
$657$		−	6.19887e17i		−	0.300703i
$658$		−	2.85545e18i		−	1.37153i
$659$	−2.48978e18			−1.18415			−0.592075	−	0.805883i	$-0.701691\pi$
$659$	−2.48978e18			−1.18415			−0.592075	+	0.805883i	$0.701691\pi$
$660$	−6.79579e16	+	2.15799e17i	−0.0320040	+	0.101628i
$661$	−2.94318e18			−1.37248			−0.686242	−	0.727373i	$-0.740741\pi$
$661$	−2.94318e18			−1.37248			−0.686242	+	0.727373i	$0.740741\pi$
$662$		−	2.57701e18i		−	1.18998i
$663$		−	6.61319e17i		−	0.302394i
$664$	4.96197e17			0.224679
$665$	3.96419e17	−	1.25882e18i	0.177752	−	0.564447i
$666$	−4.34224e17			−0.192811
$667$			1.04690e18i			0.460351i
$668$			1.05804e17i			0.0460738i
$669$	−1.93302e17			−0.0833617
$670$	2.64252e18	+	8.32164e17i	1.12858	+	0.355404i
$671$	−1.00608e18			−0.425535
$672$		−	7.48373e16i		−	0.0313486i
$673$		−	3.20709e17i		−	0.133049i	−0.997785	−	0.0665247i	$-0.978809\pi$
$673$		−	3.20709e17i		−	0.133049i	0.997785	−	0.0665247i	$-0.0211911\pi$
$674$	5.73936e17			0.235817
$675$	−3.98091e17	+	5.69383e17i	−0.161997	+	0.231702i
$676$	2.68497e18			1.08215
$677$		−	4.55008e18i		−	1.81632i	−0.418620	−	0.908162i	$-0.637486\pi$
$677$		−	4.55008e18i		−	1.81632i	0.418620	−	0.908162i	$-0.362514\pi$
$678$			2.12751e17i			0.0841159i
$679$	−1.36348e18			−0.533944
$680$	1.03488e18	+	3.25898e17i	0.401406	+	0.126408i
$681$	5.12947e17			0.197068
$682$			2.30811e17i			0.0878330i
$683$			1.56224e18i			0.588860i	0.955673	+	0.294430i	$0.0951299\pi$
$683$			1.56224e18i			0.588860i	−0.955673	+	0.294430i	$0.904870\pi$
$684$	−6.25204e17			−0.233430
$685$	4.22724e17	−	1.34235e18i	0.156339	−	0.496453i
$686$	−1.09808e18			−0.402278
$687$			3.41429e17i			0.123903i
$688$		−	3.59070e17i		−	0.129079i
$689$	3.50747e18			1.24902
$690$	−3.21087e16	+	1.01961e17i	−0.0113267	+	0.0359677i
$691$	6.01430e17			0.210173			0.105087	−	0.994463i	$-0.466488\pi$
$691$	6.01430e17			0.210173			0.105087	+	0.994463i	$0.466488\pi$
$692$		−	7.52024e17i		−	0.260341i
$693$			5.29222e18i			1.81498i
$694$	5.53989e17			0.188219
$695$	−4.20898e18	−	1.32546e18i	−1.41669	−	0.446135i
$696$	−1.86677e17			−0.0622489
$697$			4.81833e18i			1.59178i
$698$			1.52394e18i			0.498779i
$699$	−4.68179e17			−0.151813
$700$	−1.10734e18	+	1.58381e18i	−0.355749	+	0.508823i
$701$	3.37174e18			1.07322			0.536608	−	0.843831i	$-0.319705\pi$
$701$	3.37174e18			1.07322			0.536608	+	0.843831i	$0.319705\pi$
$702$		−	1.12763e18i		−	0.355611i
$703$		−	4.24563e17i		−	0.132658i
$704$	6.02469e17			0.186514
$705$	−6.93702e17	−	2.18455e17i	−0.212786	−	0.0670091i
$706$	3.86468e18			1.17458
$707$		−	2.83559e18i		−	0.853920i
$708$			5.67800e16i			0.0169426i
$709$	−4.31797e18			−1.27667			−0.638335	−	0.769758i	$-0.720377\pi$
$709$	−4.31797e18			−1.27667			−0.638335	+	0.769758i	$0.720377\pi$
$710$	4.67169e17	−	1.48349e18i	0.136866	−	0.434614i
$711$	8.90806e17			0.258601
$712$		−	1.26058e17i		−	0.0362620i
$713$			1.09053e17i			0.0310854i
$714$	−5.28417e17			−0.149258
$715$	−2.84832e18	+	9.04478e18i	−0.797258	+	2.53168i
$716$	−1.49731e18			−0.415313
$717$			7.28438e17i			0.200225i
$718$			1.30209e18i			0.354677i
$719$	−2.06718e17			−0.0558007			−0.0279004	−	0.999611i	$-0.508882\pi$
$719$	−2.06718e17			−0.0558007			−0.0279004	+	0.999611i	$0.508882\pi$
$720$	8.73211e17	+	2.74985e17i	0.233592	+	0.0735611i
$721$	−4.23900e17			−0.112379
$722$			2.08010e18i			0.546502i
$723$		−	2.45587e17i		−	0.0639450i
$724$	−9.77282e17			−0.252185
$725$	3.95073e18	+	2.76220e18i	1.01037	+	0.706412i
$726$	4.88633e17			0.123850
$727$		−	4.18391e18i		−	1.05101i	−0.850789	−	0.525507i	$-0.823876\pi$
$727$		−	4.18391e18i		−	1.05101i	0.850789	−	0.525507i	$-0.176124\pi$
$728$		−	3.13665e18i		−	0.780931i
$729$	3.56501e18			0.879695
$730$	−8.46522e17	−	2.66581e17i	−0.207033	−	0.0651973i
$731$	−2.53535e18			−0.614575
$732$		−	8.47615e16i		−	0.0203646i
$733$		−	4.24077e18i		−	1.00988i	−0.863155	−	0.504938i	$-0.831515\pi$
$733$		−	4.24077e18i		−	1.00988i	0.863155	−	0.504938i	$-0.168485\pi$
$734$	−3.05174e18			−0.720317
$735$	9.93496e16	−	3.15483e17i	0.0232433	−	0.0738088i
$736$	2.84654e17			0.0660103
$737$		−	1.08623e19i		−	2.49679i
$738$			4.06560e18i			0.926314i
$739$	2.21027e18			0.499179			0.249590	−	0.968352i	$-0.419704\pi$
$739$	2.21027e18			0.499179			0.249590	+	0.968352i	$0.419704\pi$
$740$	−1.86737e17	+	5.92980e17i	−0.0418046	+	0.132750i
$741$	5.45591e17			0.121074
$742$		−	2.80259e18i		−	0.616502i
$743$			5.02624e18i			1.09601i	0.836474	+	0.548007i	$0.184613\pi$
$743$			5.02624e18i			1.09601i	−0.836474	+	0.548007i	$0.815387\pi$
$744$	−1.94457e16			−0.00420338
$745$	3.87938e17	+	1.22167e17i	0.0831278	+	0.0261780i
$746$	−6.78540e16			−0.0144136
$747$		−	2.95625e18i		−	0.622526i
$748$		−	4.25396e18i		−	0.888042i
$749$	8.86938e18			1.83553
$750$	3.00054e17	+	3.90187e17i	0.0615604	+	0.0800524i
$751$	2.24950e18			0.457538			0.228769	−	0.973481i	$-0.426530\pi$
$751$	2.24950e18			0.457538			0.228769	+	0.973481i	$0.426530\pi$
$752$			1.93668e18i			0.390519i
$753$			6.29315e17i			0.125806i
$754$	−7.82420e18			−1.55069
$755$	−6.72865e18	−	2.11894e18i	−1.32213	−	0.416354i
$756$	−9.01017e17			−0.175526
$757$			1.59423e18i			0.307912i	0.988078	+	0.153956i	$0.0492015\pi$
$757$			1.59423e18i			0.307912i	−0.988078	+	0.153956i	$0.950799\pi$
$758$		−	1.17492e17i		−	0.0224988i
$759$	4.19116e17			0.0795725
$760$	−2.68867e17	+	8.53783e17i	−0.0506115	+	0.160716i
$761$	−3.88789e18			−0.725628			−0.362814	−	0.931862i	$-0.618184\pi$
$761$	−3.88789e18			−0.725628			−0.362814	+	0.931862i	$0.618184\pi$
$762$		−	9.47496e17i		−	0.175336i
$763$		−	5.91541e18i		−	1.08536i
$764$	−2.03710e18			−0.370600
$765$	1.94164e18	−	6.16564e18i	0.350243	−	1.11219i
$766$	−8.68575e17			−0.155353
$767$			2.37982e18i			0.422059i
$768$			5.07577e16i			0.00892594i
$769$	3.62896e17			0.0632791			0.0316396	−	0.999499i	$-0.489927\pi$
$769$	3.62896e17			0.0632791			0.0316396	+	0.999499i	$0.489927\pi$
$770$	7.22709e18	+	2.27590e18i	1.24961	+	0.393518i
$771$	1.14307e18			0.195983
$772$		−	1.22614e18i		−	0.208463i
$773$			4.71689e18i			0.795224i	0.917554	+	0.397612i	$0.130161\pi$
$773$			4.71689e18i			0.795224i	−0.917554	+	0.397612i	$0.869839\pi$
$774$	−2.13927e18			−0.357643
$775$	4.11537e17	+	2.87731e17i	0.0682257	+	0.0477008i
$776$	9.24768e17			0.152031
$777$		−	3.02779e17i		−	0.0493616i
$778$			6.78452e18i			1.09686i
$779$	−3.97514e18			−0.637323
$780$	−7.62018e17	−	2.39969e17i	−0.121157	−	0.0381540i
$781$	−6.09798e18			−0.961511
$782$		−	2.00991e18i		−	0.314291i
$783$			2.24753e18i			0.348542i
$784$	−8.80767e17			−0.135459
$785$	−2.37190e18	+	7.53194e18i	−0.361780	+	1.14882i
$786$	6.42700e17			0.0972214
$787$			8.51700e18i			1.27776i	0.769305	+	0.638882i	$0.220603\pi$
$787$			8.51700e18i			1.27776i	−0.769305	+	0.638882i	$0.779397\pi$
$788$		−	3.56269e17i		−	0.0530099i
$789$	5.60379e17			0.0826955
$790$	3.83088e17	−	1.21649e18i	0.0560690	−	0.178046i
$791$	7.12500e18			1.03428
$792$		−	3.58940e18i		−	0.516783i
$793$		−	3.55260e18i		−	0.507307i
$794$	5.49677e18			0.778529
$795$	−6.80861e17	−	2.14412e17i	−0.0956472	−	0.0301205i
$796$	1.21807e18			0.169722
$797$			6.15351e18i			0.850440i	0.905090	+	0.425220i	$0.139803\pi$
$797$			6.15351e18i			0.850440i	−0.905090	+	0.425220i	$0.860197\pi$
$798$		−	4.35947e17i		−	0.0597605i
$799$	1.36747e19			1.85936
$800$	7.51044e17	−	1.07421e18i	0.101293	−	0.144878i
$801$	−7.51031e17			−0.100472
$802$			4.50898e18i			0.598336i
$803$			3.47969e18i			0.458025i
$804$	9.15141e17			0.119488
$805$	3.41465e18	+	1.07532e18i	0.442255	+	0.139272i
$806$	−8.15026e17			−0.104711
$807$			1.29289e18i			0.164772i
$808$			1.92321e18i			0.243138i
$809$	2.68248e18			0.336412			0.168206	−	0.985752i	$-0.446203\pi$
$809$	2.68248e18			0.336412			0.168206	+	0.985752i	$0.446203\pi$
$810$	1.60349e18	−	5.09185e18i	0.199487	−	0.633466i
$811$	−1.61487e19			−1.99298			−0.996488	−	0.0837371i	$-0.973314\pi$
$811$	−1.61487e19			−1.99298			−0.996488	+	0.0837371i	$0.973314\pi$
$812$			6.25181e18i			0.765405i
$813$		−	2.19963e18i		−	0.267154i
$814$	2.43749e18			0.293686
$815$	3.55747e18	−	1.12967e19i	0.425223	−	1.35029i
$816$	3.58394e17			0.0424986
$817$		−	2.09167e18i		−	0.246065i
$818$		−	5.56088e18i		−	0.649004i
$819$	−1.86876e19			−2.16375
$820$	5.55201e18	+	1.74840e18i	0.637764	+	0.200840i
$821$	−5.61523e17			−0.0639936			−0.0319968	−	0.999488i	$-0.510187\pi$
$821$	−5.61523e17			−0.0639936			−0.0319968	+	0.999488i	$0.510187\pi$
$822$		−	4.64875e17i		−	0.0525617i
$823$		−	1.06048e19i		−	1.18960i	−0.803872	−	0.594802i	$-0.797230\pi$
$823$		−	1.06048e19i		−	1.18960i	0.803872	−	0.594802i	$-0.202770\pi$
$824$	2.87506e17			0.0319978
$825$	1.10582e18	−	1.58163e18i	0.122105	−	0.174644i
$826$	1.90156e18			0.208324
$827$			1.45953e19i			1.58645i	0.608929	+	0.793225i	$0.291599\pi$
$827$			1.45953e19i			1.58645i	−0.608929	+	0.793225i	$0.708401\pi$
$828$		−	1.69592e18i		−	0.182897i
$829$	−4.18260e18			−0.447550			−0.223775	−	0.974641i	$-0.571838\pi$
$829$	−4.18260e18			−0.447550			−0.223775	+	0.974641i	$0.571838\pi$
$830$	−4.03708e18	−	1.27133e18i	−0.428607	−	0.134974i
$831$	−1.04223e18			−0.109788
$832$			2.12740e18i			0.222356i
$833$			6.21899e18i			0.644952i
$834$	−1.45763e18			−0.149992
$835$	2.71084e17	−	8.60823e17i	0.0276785	−	0.0878924i
$836$	3.50954e18			0.355557
$837$			2.34120e17i			0.0235354i
$838$		−	1.18327e19i		−	1.18031i
$839$	5.08061e18			0.502878			0.251439	−	0.967873i	$-0.419096\pi$
$839$	5.08061e18			0.502878			0.251439	+	0.967873i	$0.419096\pi$
$840$	−1.91744e17	+	6.08879e17i	−0.0188324	+	0.0598020i
$841$	5.33414e18			0.519865
$842$			2.00646e18i			0.194045i
$843$			1.37550e18i			0.132003i
$844$	−4.15772e18			−0.395940
$845$	−2.18450e19	−	6.87928e18i	−2.06435	−	0.650091i
$846$	1.15384e19			1.08203
$847$		−	1.63643e19i		−	1.52284i
$848$			1.90083e18i			0.175538i
$849$	−2.07012e18			−0.189713
$850$	−7.58485e18	−	5.30303e18i	−0.689801	−	0.482282i
$851$	1.15166e18			0.103940
$852$		−	5.13751e17i		−	0.0460146i
$853$		−	1.71151e19i		−	1.52128i	−0.649171	−	0.760642i	$-0.724884\pi$
$853$		−	1.71151e19i		−	1.52128i	0.649171	−	0.760642i	$-0.275116\pi$
$854$	−2.83865e18			−0.250401
$855$	5.08668e18	+	1.60186e18i	0.445302	+	0.140231i
$856$	−6.01557e18			−0.522634
$857$			8.84586e18i			0.762719i	0.924427	+	0.381360i	$0.124544\pi$
$857$			8.84586e18i			0.762719i	−0.924427	+	0.381360i	$0.875456\pi$
$858$			3.13233e18i			0.268040i
$859$	1.44469e19			1.22693			0.613465	−	0.789722i	$-0.289775\pi$
$859$	1.44469e19			1.22693			0.613465	+	0.789722i	$0.289775\pi$
$860$	−9.19987e17	+	2.92140e18i	−0.0775429	+	0.246236i
$861$	−2.83489e18			−0.237146
$862$			1.52216e18i			0.126375i
$863$			3.94338e18i			0.324936i	0.986714	+	0.162468i	$0.0519455\pi$
$863$			3.94338e18i			0.324936i	−0.986714	+	0.162468i	$0.948055\pi$
$864$	6.11106e17			0.0499778
$865$	−1.92679e18	+	6.11849e18i	−0.156397	+	0.496637i
$866$	−1.14127e19			−0.919433
$867$		−	7.44510e17i		−	0.0595315i
$868$			6.51234e17i			0.0516843i
$869$	−5.00047e18			−0.393897
$870$	1.51881e18	+	4.78293e17i	0.118749	+	0.0373955i
$871$	3.83563e19			2.97659
$872$			4.01207e18i			0.309038i
$873$		−	5.50960e18i		−	0.421238i
$874$	1.65818e18			0.125837
$875$	1.30673e19	−	1.00488e19i	0.984315	−	0.756940i
$876$	−2.93162e17			−0.0219195
$877$			2.05628e19i			1.52611i	0.646336	+	0.763053i	$0.276300\pi$
$877$			2.05628e19i			1.52611i	−0.646336	+	0.763053i	$0.723700\pi$
$878$			1.28202e19i			0.944456i
$879$	9.24604e17			0.0676127
$880$	−4.90171e18	−	1.54361e18i	−0.355803	−	0.112047i
$881$	9.26266e18			0.667409			0.333705	−	0.942678i	$-0.391701\pi$
$881$	9.26266e18			0.667409			0.333705	+	0.942678i	$0.391701\pi$
$882$			5.24744e18i			0.375320i
$883$			1.39004e19i			0.986924i	0.869767	+	0.493462i	$0.164269\pi$
$883$			1.39004e19i			0.986924i	−0.869767	+	0.493462i	$0.835731\pi$
$884$	1.50214e19			1.05869
$885$	1.45478e17	−	4.61964e17i	0.0101781	−	0.0323204i
$886$	−1.29922e19			−0.902329
$887$			2.65692e18i			0.183179i	0.995797	+	0.0915894i	$0.0291947\pi$
$887$			2.65692e18i			0.183179i	−0.995797	+	0.0915894i	$0.970805\pi$
$888$			2.05357e17i			0.0140548i
$889$	−3.17316e19			−2.15591
$890$	−3.22979e17	+	1.02561e18i	−0.0217841	+	0.0691749i
$891$	−2.09304e19			−1.40144
$892$		−	4.39070e18i		−	0.291852i
$893$			1.12817e19i			0.744455i
$894$	1.34348e17			0.00880112
$895$	1.21821e19	+	3.83631e18i	0.792270	+	0.249496i
$896$	1.69987e18			0.109752
$897$			1.47996e18i			0.0948635i
$898$		−	4.32190e18i		−	0.275029i
$899$	1.62447e18			0.102630
$900$	−6.39992e18	−	4.47458e18i	−0.401419	−	0.280657i
$901$	1.34216e19			0.835779
$902$		−	2.28219e19i		−	1.41095i
$903$		−	1.49169e18i		−	0.0915602i
$904$	−4.83247e18			−0.294492
$905$	7.95119e18	+	2.50393e18i	0.481079	+	0.151498i
$906$	−2.33022e18			−0.139979
$907$		−	1.91381e19i		−	1.14143i	−0.821147	−	0.570717i	$-0.806665\pi$
$907$		−	1.91381e19i		−	1.14143i	0.821147	−	0.570717i	$-0.193335\pi$
$908$			1.16512e19i			0.689942i
$909$	1.14581e19			0.673673
$910$	−8.03654e18	+	2.55199e19i	−0.469138	+	1.48974i
$911$	−1.78849e19			−1.03661			−0.518306	−	0.855195i	$-0.673437\pi$
$911$	−1.78849e19			−1.03661			−0.518306	+	0.855195i	$0.673437\pi$
$912$			2.95677e17i			0.0170157i
$913$			1.65947e19i			0.948221i
$914$	1.83656e19			1.04197
$915$	−2.17171e17	+	6.89622e17i	−0.0122339	+	0.0388485i
$916$	−7.75530e18			−0.433788
$917$		−	2.15240e19i		−	1.19542i
$918$		−	4.31495e18i		−	0.237957i
$919$	−3.81500e18			−0.208903			−0.104451	−	0.994530i	$-0.533309\pi$
$919$	−3.81500e18			−0.208903			−0.104451	+	0.994530i	$0.533309\pi$
$920$	−2.31595e18	−	7.29324e17i	−0.125924	−	0.0396551i
$921$	7.75006e17			0.0418425
$922$			1.47051e19i			0.788344i
$923$		−	2.15328e19i		−	1.14628i
$924$	2.50284e18			0.132302
$925$	3.03860e18	−	4.34606e18i	0.159497	−	0.228126i
$926$	5.20301e18			0.271196
$927$		−	1.71291e18i		−	0.0886576i
$928$		−	4.24023e18i		−	0.217935i
$929$	−1.36131e19			−0.694793			−0.347397	−	0.937718i	$-0.612934\pi$
$929$	−1.36131e19			−0.694793			−0.347397	+	0.937718i	$0.612934\pi$
$930$	1.58211e17	+	4.98225e16i	0.00801856	+	0.00252515i
$931$	−5.13069e18			−0.258228
$932$		−	1.06343e19i		−	0.531504i
$933$		−	2.95347e18i		−	0.146589i
$934$	3.42261e18			0.168695
$935$	−1.08993e19	+	3.46104e19i	−0.533484	+	1.69407i
$936$	1.26747e19			0.616090
$937$		−	3.00740e19i		−	1.45172i	−0.687841	−	0.725861i	$-0.741441\pi$
$937$		−	3.00740e19i		−	1.45172i	0.687841	−	0.725861i	$-0.258559\pi$
$938$		−	3.06480e19i		−	1.46921i
$939$	1.81709e18			0.0865067
$940$	4.96205e18	−	1.57569e19i	0.234601	−	0.744971i
$941$	−1.57143e18			−0.0737842			−0.0368921	−	0.999319i	$-0.511746\pi$
$941$	−1.57143e18			−0.0737842			−0.0368921	+	0.999319i	$0.511746\pi$
$942$			2.60841e18i			0.121631i
$943$		−	1.07829e19i		−	0.499355i
$944$	−1.28971e18			−0.0593164
$945$	7.33070e18	+	2.30853e18i	0.334841	+	0.105446i
$946$	1.20086e19			0.544756
$947$		−	7.18352e18i		−	0.323640i	−0.986820	−	0.161820i	$-0.948264\pi$
$947$		−	7.18352e18i		−	0.323640i	0.986820	−	0.161820i	$-0.0517364\pi$
$948$		−	4.21287e17i		−	0.0188506i
$949$	−1.22873e19			−0.546041
$950$	4.37502e18	−	6.25753e18i	0.193098	−	0.276185i
$951$	−4.57413e18			−0.200510
$952$		−	1.20026e19i		−	0.522558i
$953$		−	9.37433e18i		−	0.405356i	−0.979245	−	0.202678i	$-0.935036\pi$
$953$		−	9.37433e18i		−	0.405356i	0.979245	−	0.202678i	$-0.0649645\pi$
$954$	1.13248e19			0.486369
$955$	1.65739e19	+	5.21934e18i	0.706974	+	0.222635i
$956$	−1.65459e19			−0.700994
$957$		−	6.24319e18i		−	0.262711i
$958$			3.25302e19i			1.35960i
$959$	−1.55686e19			−0.646292
$960$	1.30048e17	−	4.12966e17i	0.00536218	−	0.0170275i
$961$	−2.42483e19			−0.993070
$962$			8.60712e18i			0.350122i
$963$			3.58397e19i			1.44808i
$964$	5.57832e18			0.223873
$965$	−3.14155e18	+	9.97593e18i	−0.125232	+	0.397673i
$966$	1.18254e18			0.0468236
$967$			2.08048e19i			0.818258i	0.912476	+	0.409129i	$0.134167\pi$
$967$			2.08048e19i			0.818258i	−0.912476	+	0.409129i	$0.865833\pi$
$968$			1.10989e19i			0.433601i
$969$	2.08774e18			0.0810161
$970$	−7.52394e18	−	2.36939e18i	−0.290021	−	0.0913313i
$971$	−1.41973e19			−0.543602			−0.271801	−	0.962353i	$-0.587619\pi$
$971$	−1.41973e19			−0.543602			−0.271801	+	0.962353i	$0.587619\pi$
$972$		−	5.48004e18i		−	0.208427i
$973$			4.88158e19i			1.84428i
$974$	3.02905e19			1.13677
$975$	5.58496e18	+	3.90479e18i	0.208205	+	0.145569i
$976$	1.92529e18			0.0712972
$977$		−	2.91063e19i		−	1.07071i	−0.844627	−	0.535355i	$-0.820178\pi$
$977$		−	2.91063e19i		−	1.07071i	0.844627	−	0.535355i	$-0.179822\pi$
$978$		−	3.91219e18i		−	0.142961i
$979$	4.21586e18			0.153038
$980$	7.16595e18	+	2.25665e18i	0.258407	+	0.0813756i
$981$	2.39032e19			0.856262
$982$		−	6.94413e18i		−	0.247112i
$983$		−	3.73810e19i		−	1.32146i	−0.750625	−	0.660728i	$-0.770247\pi$
$983$		−	3.73810e19i		−	1.32146i	0.750625	−	0.660728i	$-0.229753\pi$
$984$	1.92274e18			0.0675230
$985$	−9.12810e17	+	2.89861e18i	−0.0318453	+	0.101124i
$986$	−2.99398e19			−1.03764
$987$			8.04556e18i			0.277010i
$988$			1.23927e19i			0.423882i
$989$	5.67383e18			0.192797
$990$	−9.19654e18	+	2.92035e19i	−0.310453	+	0.985838i
$991$	−2.16079e19			−0.724658			−0.362329	−	0.932050i	$-0.618018\pi$
$991$	−2.16079e19			−0.724658			−0.362329	+	0.932050i	$0.618018\pi$
$992$		−	4.41693e17i		−	0.0147162i
$993$			7.26104e18i			0.240342i
$994$	−1.72055e19			−0.565790
$995$	−9.91026e18	−	3.12087e18i	−0.323769	−	0.101959i
$996$	−1.39809e18			−0.0453786
$997$			2.44979e19i			0.789969i	0.918688	+	0.394984i	$0.129250\pi$
$997$			2.44979e19i			0.789969i	−0.918688	+	0.394984i	$0.870750\pi$
$998$		−	1.00967e19i		−	0.323466i
$999$	2.47243e18			0.0786952

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.14.b.a.9.2	✓	6
3.2	odd	2		90.14.c.b.19.4		6
4.3	odd	2		80.14.c.b.49.3		6
5.2	odd	4		50.14.a.j.1.2		3
5.3	odd	4		50.14.a.i.1.2		3
5.4	even	2	inner	10.14.b.a.9.5	yes	6
15.14	odd	2		90.14.c.b.19.1		6
20.19	odd	2		80.14.c.b.49.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.14.b.a.9.2	✓	6	1.1	even	1	trivial
10.14.b.a.9.5	yes	6	5.4	even	2	inner
50.14.a.i.1.2		3	5.3	odd	4
50.14.a.j.1.2		3	5.2	odd	4
80.14.c.b.49.3		6	4.3	odd	2
80.14.c.b.49.4		6	20.19	odd	2
90.14.c.b.19.1		6	15.14	odd	2
90.14.c.b.19.4		6	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:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	10.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-64.0000i q^{2} +180.328i q^{3} -4096.00 q^{4} +(33325.2 + 10494.5i) q^{5} +11541.0 q^{6} -386506. i q^{7} +262144. i q^{8} +1.56180e6 q^{9} +O(q^{10})\)	\(q-64.0000i q^{2} +180.328i q^{3} -4096.00 q^{4} +(33325.2 + 10494.5i) q^{5} +11541.0 q^{6} -386506. i q^{7} +262144. i q^{8} +1.56180e6 q^{9} +(671650. - 2.13281e6i) q^{10} -8.76708e6 q^{11} -738622. i q^{12} -3.09578e7i q^{13} -2.47364e7 q^{14} +(-1.89245e6 + 6.00945e6i) q^{15} +1.67772e7 q^{16} -1.18462e8i q^{17} -9.99555e7i q^{18} +9.77316e7 q^{19} +(-1.36500e8 - 4.29856e7i) q^{20} +6.96977e7 q^{21} +5.61093e8i q^{22} +2.65105e8i q^{23} -4.72718e7 q^{24} +(1.00043e9 + 6.99464e8i) q^{25} -1.98130e9 q^{26} +5.69137e8i q^{27} +1.58313e9i q^{28} +3.94902e9 q^{29} +(3.84605e8 + 1.21117e8i) q^{30} +4.11359e8 q^{31} -1.07374e9i q^{32} -1.58095e9i q^{33} -7.58156e9 q^{34} +(4.05620e9 - 1.28804e10i) q^{35} -6.39715e9 q^{36} -4.34418e9i q^{37} -6.25482e9i q^{38} +5.58255e9 q^{39} +(-2.75108e9 + 8.73600e9i) q^{40} -4.06741e10 q^{41} -4.46065e9i q^{42} -2.14022e10i q^{43} +3.59100e10 q^{44} +(5.20474e10 + 1.63904e10i) q^{45} +1.69667e10 q^{46} +1.15435e11i q^{47} +3.02539e9i q^{48} -5.24978e10 q^{49} +(4.47657e10 - 6.40277e10i) q^{50} +2.13620e10 q^{51} +1.26803e11i q^{52} +1.13298e11i q^{53} +3.64248e10 q^{54} +(-2.92165e11 - 9.20064e10i) q^{55} +1.01320e11 q^{56} +1.76237e10i q^{57} -2.52737e11i q^{58} -7.68729e10 q^{59} +(7.75148e9 - 2.46147e10i) q^{60} +1.14756e11 q^{61} -2.63270e10i q^{62} -6.03647e11i q^{63} -6.87195e10 q^{64} +(3.24888e11 - 1.03168e12i) q^{65} -1.01181e11 q^{66} +1.23899e12i q^{67} +4.85220e11i q^{68} -4.78057e10 q^{69} +(-8.24344e11 - 2.59597e11i) q^{70} +6.95554e11 q^{71} +4.09418e11i q^{72} -3.96904e11i q^{73} -2.78027e11 q^{74} +(-1.26133e11 + 1.80406e11i) q^{75} -4.00309e11 q^{76} +3.38853e12i q^{77} -3.57283e11i q^{78} +5.70369e11 q^{79} +(5.59104e11 + 1.76069e11i) q^{80} +2.38739e12 q^{81} +2.60314e12i q^{82} -1.89284e12i q^{83} -2.85482e11 q^{84} +(1.24320e12 - 3.94777e12i) q^{85} -1.36974e12 q^{86} +7.12117e11i q^{87} -2.29824e12i q^{88} -4.80874e11 q^{89} +(1.04899e12 - 3.33104e12i) q^{90} -1.19654e13 q^{91} -1.08587e12i q^{92} +7.41794e10i q^{93} +7.38785e12 q^{94} +(3.25692e12 + 1.02565e12i) q^{95} +1.93625e11 q^{96} -3.52771e12i q^{97} +3.35986e12i q^{98} -1.36925e13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 24576 q^{4} - 2470 q^{5} - 23296 q^{6} + 4260922 q^{9}+O(q^{10}) \) 6 * q - 24576 * q^4 - 2470 * q^5 - 23296 * q^6 + 4260922 * q^9	\( 6 q - 24576 q^{4} - 2470 q^{5} - 23296 q^{6} + 4260922 q^{9} - 2269440 q^{10} + 673672 q^{11} - 1211648 q^{14} + 80128760 q^{15} + 100663296 q^{16} + 142606200 q^{19} + 10117120 q^{20} - 926360008 q^{21} + 95420416 q^{24} + 1820907150 q^{25} - 3369156096 q^{26} + 1402368660 q^{29} + 6491083520 q^{30} - 22270466688 q^{31} + 10743816192 q^{34} + 40910703880 q^{35} - 17452736512 q^{36} + 80990077584 q^{39} + 9295626240 q^{40} - 159550828628 q^{41} - 2759360512 q^{44} + 112298555110 q^{45} - 48346742016 q^{46} - 142584010062 q^{49} + 33045516800 q^{50} + 47596879232 q^{51} + 104187005440 q^{54} - 465712133640 q^{55} + 4962910208 q^{56} - 129517581080 q^{59} - 328207400960 q^{60} + 2208324934212 q^{61} - 412316860416 q^{64} - 475107396240 q^{65} + 1429010971648 q^{66} - 2470574584136 q^{69} - 1324581354240 q^{70} + 1016718596592 q^{71} + 1548283182592 q^{74} - 1495698537200 q^{75} - 584114995200 q^{76} - 23303633760 q^{79} - 41439723520 q^{80} - 2585393406754 q^{81} + 3794370592768 q^{84} + 9460560132480 q^{85} - 10908216246016 q^{86} - 1102941191140 q^{89} - 1112244801280 q^{90} - 9640398296208 q^{91} + 20956004804352 q^{94} + 26900168949000 q^{95} - 390842023936 q^{96} - 11776973376136 q^{99}+O(q^{100}) \) 6 * q - 24576 * q^4 - 2470 * q^5 - 23296 * q^6 + 4260922 * q^9 - 2269440 * q^10 + 673672 * q^11 - 1211648 * q^14 + 80128760 * q^15 + 100663296 * q^16 + 142606200 * q^19 + 10117120 * q^20 - 926360008 * q^21 + 95420416 * q^24 + 1820907150 * q^25 - 3369156096 * q^26 + 1402368660 * q^29 + 6491083520 * q^30 - 22270466688 * q^31 + 10743816192 * q^34 + 40910703880 * q^35 - 17452736512 * q^36 + 80990077584 * q^39 + 9295626240 * q^40 - 159550828628 * q^41 - 2759360512 * q^44 + 112298555110 * q^45 - 48346742016 * q^46 - 142584010062 * q^49 + 33045516800 * q^50 + 47596879232 * q^51 + 104187005440 * q^54 - 465712133640 * q^55 + 4962910208 * q^56 - 129517581080 * q^59 - 328207400960 * q^60 + 2208324934212 * q^61 - 412316860416 * q^64 - 475107396240 * q^65 + 1429010971648 * q^66 - 2470574584136 * q^69 - 1324581354240 * q^70 + 1016718596592 * q^71 + 1548283182592 * q^74 - 1495698537200 * q^75 - 584114995200 * q^76 - 23303633760 * q^79 - 41439723520 * q^80 - 2585393406754 * q^81 + 3794370592768 * q^84 + 9460560132480 * q^85 - 10908216246016 * q^86 - 1102941191140 * q^89 - 1112244801280 * q^90 - 9640398296208 * q^91 + 20956004804352 * q^94 + 26900168949000 * q^95 - 390842023936 * q^96 - 11776973376136 * q^99

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