LMFDB - Embedded newform 10.14.b.a.9.1

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			9.1
Root			$62.8643 + 62.8643i$ of defining polynomial
Character	$\chi$	$=$	10.9
Dual form			10.14.b.a.9.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-64.0000i q^{2} -1311.29i q^{3} -4096.00 q^{4} +(-34287.6 + 6712.97i) q^{5} -83922.3 q^{6} -77461.9i q^{7} +262144. i q^{8} -125146. q^{9} +O(q^{10})$	\(q-64.0000i q^{2} -1311.29i q^{3} -4096.00 q^{4} +(-34287.6 + 6712.97i) q^{5} -83922.3 q^{6} -77461.9i q^{7} +262144. i q^{8} -125146. q^{9} +(429630. + 2.19441e6i) q^{10} -1.81656e6 q^{11} +5.37102e6i q^{12} +1.73929e7i q^{13} -4.95756e6 q^{14} +(8.80262e6 + 4.49608e7i) q^{15} +1.67772e7 q^{16} +8.60543e7i q^{17} +8.00935e6i q^{18} -2.99455e8 q^{19} +(1.40442e8 - 2.74963e7i) q^{20} -1.01575e8 q^{21} +1.16260e8i q^{22} -7.95262e8i q^{23} +3.43746e8 q^{24} +(1.13058e9 - 4.60343e8i) q^{25} +1.11314e9 q^{26} -1.92651e9i q^{27} +3.17284e8i q^{28} -4.13720e9 q^{29} +(2.87749e9 - 5.63368e8i) q^{30} -6.75807e9 q^{31} -1.07374e9i q^{32} +2.38203e9i q^{33} +5.50748e9 q^{34} +(5.20000e8 + 2.65598e9i) q^{35} +5.12599e8 q^{36} +2.16919e10i q^{37} +1.91651e10i q^{38} +2.28070e10 q^{39} +(-1.75977e9 - 8.98829e9i) q^{40} -3.63965e10 q^{41} +6.50078e9i q^{42} -5.57791e10i q^{43} +7.44062e9 q^{44} +(4.29096e9 - 8.40103e8i) q^{45} -5.08967e10 q^{46} +1.47029e10i q^{47} -2.19997e10i q^{48} +9.08887e10 q^{49} +(-2.94620e10 - 7.23568e10i) q^{50} +1.12842e11 q^{51} -7.12412e10i q^{52} -1.46143e11i q^{53} -1.23297e11 q^{54} +(6.22854e10 - 1.21945e10i) q^{55} +2.03062e10 q^{56} +3.92671e11i q^{57} +2.64781e11i q^{58} -3.00889e11 q^{59} +(-3.60555e10 - 1.84160e11i) q^{60} +2.74029e11 q^{61} +4.32516e11i q^{62} +9.69406e9i q^{63} -6.87195e10 q^{64} +(-1.16758e11 - 5.96360e11i) q^{65} +1.52450e11 q^{66} +1.30838e12i q^{67} -3.52478e11i q^{68} -1.04281e12 q^{69} +(1.69983e11 - 3.32800e10i) q^{70} +3.01298e11 q^{71} -3.28063e10i q^{72} -1.13949e12i q^{73} +1.38828e12 q^{74} +(-6.03641e11 - 1.48251e12i) q^{75} +1.22657e12 q^{76} +1.40714e11i q^{77} -1.45965e12i q^{78} +2.12461e12 q^{79} +(-5.75250e11 + 1.12625e11i) q^{80} -2.72573e12 q^{81} +2.32938e12i q^{82} -1.37413e12i q^{83} +4.16050e11 q^{84} +(-5.77680e11 - 2.95060e12i) q^{85} -3.56986e12 q^{86} +5.42505e12i q^{87} -4.76200e11i q^{88} -8.59655e11 q^{89} +(-5.37666e10 - 2.74621e11i) q^{90} +1.34729e12 q^{91} +3.25739e12i q^{92} +8.86176e12i q^{93} +9.40983e11 q^{94} +(1.02676e13 - 2.01023e12i) q^{95} -1.40798e12 q^{96} +5.78046e12i q^{97} -5.81687e12i q^{98} +2.27335e11 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
$3$		−	1311.29i		−	1.03851i	−0.854621	−	0.519253i	$-0.826210\pi$
$3$		−	1311.29i		−	1.03851i	0.854621	−	0.519253i	$-0.173790\pi$
$4$	−4096.00			−0.500000
$5$	−34287.6	+	6712.97i	−0.981368	+	0.192136i
$5$	−34287.6	+	6712.97i	−0.981368	+	0.192136i
$6$	−83922.3			−0.734335
$7$		−	77461.9i		−	0.248858i	−0.992229	−	0.124429i	$-0.960290\pi$
$7$		−	77461.9i		−	0.248858i	0.992229	−	0.124429i	$-0.0397098\pi$
$8$			262144.i			0.353553i
$9$	−125146.			−0.0784949
$10$	429630.	+	2.19441e6i	0.135861	+	0.693932i
$11$	−1.81656e6			−0.309170			−0.154585	−	0.987980i	$-0.549404\pi$
$11$	−1.81656e6			−0.309170			−0.154585	+	0.987980i	$0.549404\pi$
$12$			5.37102e6i			0.519253i
$13$			1.73929e7i			0.999401i	0.866198	+	0.499700i	$0.166557\pi$
$13$			1.73929e7i			0.999401i	−0.866198	+	0.499700i	$0.833443\pi$
$14$	−4.95756e6			−0.175969
$15$	8.80262e6	+	4.49608e7i	0.199535	+	1.01916i
$16$	1.67772e7			0.250000
$17$			8.60543e7i			0.864678i	0.901711	+	0.432339i	$0.142312\pi$
$17$			8.60543e7i			0.864678i	−0.901711	+	0.432339i	$0.857688\pi$
$18$			8.00935e6i			0.0555042i
$19$	−2.99455e8			−1.46027			−0.730135	−	0.683303i	$-0.760543\pi$
$19$	−2.99455e8			−1.46027			−0.730135	+	0.683303i	$0.760543\pi$
$20$	1.40442e8	−	2.74963e7i	0.490684	−	0.0960682i
$21$	−1.01575e8			−0.258440
$22$			1.16260e8i			0.218616i
$23$		−	7.95262e8i		−	1.12016i	−0.828439	−	0.560079i	$-0.810771\pi$
$23$		−	7.95262e8i		−	1.12016i	0.828439	−	0.560079i	$-0.189229\pi$
$24$	3.43746e8			0.367167
$25$	1.13058e9	−	4.60343e8i	0.926167	−	0.377113i
$26$	1.11314e9			0.706683
$27$		−	1.92651e9i		−	0.956989i
$28$			3.17284e8i			0.124429i
$29$	−4.13720e9			−1.29157			−0.645787	−	0.763517i	$-0.723471\pi$
$29$	−4.13720e9			−1.29157			−0.645787	+	0.763517i	$0.723471\pi$
$30$	2.87749e9	−	5.63368e8i	0.720653	−	0.141092i
$31$	−6.75807e9			−1.36764			−0.683820	−	0.729651i	$-0.739683\pi$
$31$	−6.75807e9			−1.36764			−0.683820	+	0.729651i	$0.739683\pi$
$32$		−	1.07374e9i		−	0.176777i
$33$			2.38203e9i			0.321074i
$34$	5.50748e9			0.611420
$35$	5.20000e8	+	2.65598e9i	0.0478146	+	0.244221i
$36$	5.12599e8			0.0392474
$37$			2.16919e10i			1.38991i	0.719055	+	0.694953i	$0.244575\pi$
$37$			2.16919e10i			1.38991i	−0.719055	+	0.694953i	$0.755425\pi$
$38$			1.91651e10i			1.03257i
$39$	2.28070e10			1.03788
$40$	−1.75977e9	−	8.98829e9i	−0.0679305	−	0.346966i
$41$	−3.63965e10			−1.19664			−0.598321	−	0.801256i	$-0.704165\pi$
$41$	−3.63965e10			−1.19664			−0.598321	+	0.801256i	$0.704165\pi$
$42$			6.50078e9i			0.182745i
$43$		−	5.57791e10i		−	1.34563i	−0.739810	−	0.672816i	$-0.765084\pi$
$43$		−	5.57791e10i		−	1.34563i	0.739810	−	0.672816i	$-0.234916\pi$
$44$	7.44062e9			0.154585
$45$	4.29096e9	−	8.40103e8i	0.0770324	−	0.0150817i
$46$	−5.08967e10			−0.792071
$47$			1.47029e10i			0.198960i	0.995040	+	0.0994800i	$0.0317179\pi$
$47$			1.47029e10i			0.198960i	−0.995040	+	0.0994800i	$0.968282\pi$
$48$		−	2.19997e10i		−	0.259627i
$49$	9.08887e10			0.938070
$50$	−2.94620e10	−	7.23568e10i	−0.266659	−	0.654899i
$51$	1.12842e11			0.897974
$52$		−	7.12412e10i		−	0.499700i
$53$		−	1.46143e11i		−	0.905700i	−0.891587	−	0.452850i	$-0.850407\pi$
$53$		−	1.46143e11i		−	0.905700i	0.891587	−	0.452850i	$-0.149593\pi$
$54$	−1.23297e11			−0.676693
$55$	6.22854e10	−	1.21945e10i	0.303409	−	0.0594027i
$56$	2.03062e10			0.0879845
$57$			3.92671e11i			1.51650i
$58$			2.64781e11i			0.913281i
$59$	−3.00889e11			−0.928685			−0.464342	−	0.885656i	$-0.653709\pi$
$59$	−3.00889e11			−0.928685			−0.464342	+	0.885656i	$0.653709\pi$
$60$	−3.60555e10	−	1.84160e11i	−0.0997675	−	0.509578i
$61$	2.74029e11			0.681009			0.340505	−	0.940243i	$-0.389402\pi$
$61$	2.74029e11			0.681009			0.340505	+	0.940243i	$0.389402\pi$
$62$			4.32516e11i			0.967067i
$63$			9.69406e9i			0.0195340i
$64$	−6.87195e10			−0.125000
$65$	−1.16758e11	−	5.96360e11i	−0.192021	−	0.980780i
$66$	1.52450e11			0.227034
$67$			1.30838e12i			1.76704i	0.468391	+	0.883521i	$0.344834\pi$
$67$			1.30838e12i			1.76704i	−0.468391	+	0.883521i	$0.655166\pi$
$68$		−	3.52478e11i		−	0.432339i
$69$	−1.04281e12			−1.16329
$70$	1.69983e11	−	3.32800e10i	0.172690	−	0.0338100i
$71$	3.01298e11			0.279136			0.139568	−	0.990212i	$-0.455429\pi$
$71$	3.01298e11			0.279136			0.139568	+	0.990212i	$0.455429\pi$
$72$		−	3.28063e10i		−	0.0277521i
$73$		−	1.13949e12i		−	0.881278i	−0.897684	−	0.440639i	$-0.854752\pi$
$73$		−	1.13949e12i		−	0.881278i	0.897684	−	0.440639i	$-0.145248\pi$
$74$	1.38828e12			0.982812
$75$	−6.03641e11	−	1.48251e12i	−0.391634	−	0.961830i
$76$	1.22657e12			0.730135
$77$			1.40714e11i			0.0769392i
$78$		−	1.45965e12i		−	0.733895i
$79$	2.12461e12			0.983337			0.491669	−	0.870782i	$-0.336387\pi$
$79$	2.12461e12			0.983337			0.491669	+	0.870782i	$0.336387\pi$
$80$	−5.75250e11	+	1.12625e11i	−0.245342	+	0.0480341i
$81$	−2.72573e12			−1.07233
$82$			2.32938e12i			0.846154i
$83$		−	1.37413e12i		−	0.461340i	−0.973032	−	0.230670i	$-0.925908\pi$
$83$		−	1.37413e12i		−	0.461340i	0.973032	−	0.230670i	$-0.0740918\pi$
$84$	4.16050e11			0.129220
$85$	−5.77680e11	−	2.95060e12i	−0.166136	−	0.848568i
$86$	−3.56986e12			−0.951506
$87$			5.42505e12i			1.34131i
$88$		−	4.76200e11i		−	0.109308i
$89$	−8.59655e11			−0.183354			−0.0916768	−	0.995789i	$-0.529223\pi$
$89$	−8.59655e11			−0.183354			−0.0916768	+	0.995789i	$0.529223\pi$
$90$	−5.37666e10	−	2.74621e11i	−0.0106644	−	0.0544701i
$91$	1.34729e12			0.248708
$92$			3.25739e12i			0.560079i
$93$			8.86176e12i			1.42030i
$94$	9.40983e11			0.140686
$95$	1.02676e13	−	2.01023e12i	1.43306	−	0.280571i
$96$	−1.40798e12			−0.183584
$97$			5.78046e12i			0.704606i	0.935886	+	0.352303i	$0.114601\pi$
$97$			5.78046e12i			0.704606i	−0.935886	+	0.352303i	$0.885399\pi$
$98$		−	5.81687e12i		−	0.663316i
$99$	2.27335e11			0.0242682
$100$	−4.63084e12	+	1.88557e12i	−0.463084	+	0.188557i
$101$	−3.86978e11			−0.0362741			−0.0181371	−	0.999836i	$-0.505774\pi$
$101$	−3.86978e11			−0.0362741			−0.0181371	+	0.999836i	$0.505774\pi$
$102$		−	7.22187e12i		−	0.634963i
$103$		−	1.29238e12i		−	0.106647i	−0.998577	−	0.0533236i	$-0.983019\pi$
$103$		−	1.29238e12i		−	0.106647i	0.998577	−	0.0533236i	$-0.0169815\pi$
$104$	−4.55944e12			−0.353341
$105$	3.48275e12	−	6.81868e11i	0.253625	−	0.0496558i
$106$	−9.35314e12			−0.640427
$107$		−	2.52548e13i		−	1.62686i	−0.581665	−	0.813429i	$-0.697598\pi$
$107$		−	2.52548e13i		−	1.62686i	0.581665	−	0.813429i	$-0.302402\pi$
$108$			7.89098e12i			0.478494i
$109$	−2.71264e13			−1.54925			−0.774623	−	0.632423i	$-0.782060\pi$
$109$	−2.71264e13			−1.54925			−0.774623	+	0.632423i	$0.782060\pi$
$110$	−7.80448e11	−	3.98626e12i	−0.0420041	−	0.214543i
$111$	2.84442e13			1.44343
$112$		−	1.29960e12i		−	0.0622144i
$113$		−	3.50156e13i		−	1.58216i	−0.611711	−	0.791081i	$-0.709518\pi$
$113$		−	3.50156e13i		−	1.58216i	0.611711	−	0.791081i	$-0.290482\pi$
$114$	2.51309e13			1.07233
$115$	5.33857e12	+	2.72676e13i	0.215223	+	1.09929i
$116$	1.69460e13			0.645787
$117$		−	2.17665e12i		−	0.0784478i
$118$			1.92569e13i			0.656679i
$119$	6.66593e12			0.215182
$120$	−1.17862e13	+	2.30755e12i	−0.360326	+	0.0705462i
$121$	−3.12228e13			−0.904414
$122$		−	1.75379e13i		−	0.481546i
$123$			4.77262e13i			1.24272i
$124$	2.76811e13			0.683820
$125$	−3.56744e13	+	2.33736e13i	−0.836454	+	0.548037i
$126$	6.20420e11			0.0138127
$127$		−	3.62259e12i		−	0.0766116i	−0.999266	−	0.0383058i	$-0.987804\pi$
$127$		−	3.62259e12i		−	0.0766116i	0.999266	−	0.0383058i	$-0.0121961\pi$
$128$			4.39805e12i			0.0883883i
$129$	−7.31423e13			−1.39745
$130$	−3.81670e13	+	7.47251e12i	−0.693516	+	0.135780i
$131$	3.69284e13			0.638406			0.319203	−	0.947686i	$-0.396585\pi$
$131$	3.69284e13			0.638406			0.319203	+	0.947686i	$0.396585\pi$
$132$		−	9.75678e12i		−	0.160537i
$133$			2.31963e13i			0.363399i
$134$	8.37362e13			1.24949
$135$	1.29326e13	+	6.60554e13i	0.183872	+	0.939158i
$136$	−2.25586e13			−0.305710
$137$		−	1.38277e14i		−	1.78676i	−0.449301	−	0.893381i	$-0.648327\pi$
$137$		−	1.38277e14i		−	1.78676i	0.449301	−	0.893381i	$-0.351673\pi$
$138$			6.67402e13i			0.822571i
$139$	8.68530e12			0.102138			0.0510691	−	0.998695i	$-0.483737\pi$
$139$	8.68530e12			0.102138			0.0510691	+	0.998695i	$0.483737\pi$
$140$	−2.12992e12	−	1.08789e13i	−0.0239073	−	0.122110i
$141$	1.92796e13			0.206621
$142$		−	1.92830e13i		−	0.197379i
$143$		−	3.15952e13i		−	0.308984i
$144$	−2.09960e12			−0.0196237
$145$	1.41855e14	−	2.77729e13i	1.26751	−	0.248159i
$146$	−7.29275e13			−0.623157
$147$		−	1.19181e14i		−	0.974191i
$148$		−	8.88498e13i		−	0.694953i
$149$	−8.75155e13			−0.655201			−0.327600	−	0.944816i	$-0.606240\pi$
$149$	−8.75155e13			−0.655201			−0.327600	+	0.944816i	$0.606240\pi$
$150$	−9.48804e13	+	3.86331e13i	−0.680117	+	0.276927i
$151$	7.11335e13			0.488342			0.244171	−	0.969732i	$-0.421484\pi$
$151$	7.11335e13			0.488342			0.244171	+	0.969732i	$0.421484\pi$
$152$		−	7.85003e13i		−	0.516283i
$153$		−	1.07694e13i		−	0.0678728i
$154$	9.00570e12			0.0544042
$155$	2.31718e14	−	4.53667e13i	1.34216	−	0.262773i
$156$	−9.34176e13			−0.518942
$157$			3.51899e14i			1.87530i	0.347583	+	0.937649i	$0.387003\pi$
$157$			3.51899e14i			1.87530i	−0.347583	+	0.937649i	$0.612997\pi$
$158$		−	1.35975e14i		−	0.695324i
$159$	−1.91635e14			−0.940575
$160$	7.20800e12	+	3.68160e13i	0.0339653	+	0.173483i
$161$	−6.16025e13			−0.278760
$162$			1.74447e14i			0.758254i
$163$			2.27151e14i			0.948626i	0.880356	+	0.474313i	$0.157304\pi$
$163$			2.27151e14i			0.948626i	−0.880356	+	0.474313i	$0.842696\pi$
$164$	1.49080e14			0.598321
$165$	−1.59905e13	−	8.16739e13i	−0.0616901	−	0.315092i
$166$	−8.79445e13			−0.326217
$167$		−	7.16344e13i		−	0.255543i	−0.991804	−	0.127772i	$-0.959218\pi$
$167$		−	7.16344e13i		−	0.255543i	0.991804	−	0.127772i	$-0.0407825\pi$
$168$		−	2.66272e13i		−	0.0913724i
$169$	3.62931e11			0.00119829
$170$	−1.88838e14	+	3.69715e13i	−0.600028	+	0.117476i
$171$	3.74756e13			0.114624
$172$			2.28471e14i			0.672816i
$173$			1.63643e12i			0.00464085i	0.999997	+	0.00232042i	$0.000738615\pi$
$173$			1.63643e12i			0.00464085i	−0.999997	+	0.00232042i	$0.999261\pi$
$174$	3.47203e14			0.948448
$175$	−3.56591e13	−	8.75765e13i	−0.0938475	−	0.230484i
$176$	−3.04768e13			−0.0772924
$177$			3.94551e14i			0.964445i
$178$			5.50179e13i			0.129651i
$179$	−1.64540e14			−0.373876			−0.186938	−	0.982372i	$-0.559856\pi$
$179$	−1.64540e14			−0.373876			−0.186938	+	0.982372i	$0.559856\pi$
$180$	−1.75758e13	+	3.44106e12i	−0.0385162	+	0.00754086i
$181$	1.61247e14			0.340865			0.170432	−	0.985369i	$-0.445484\pi$
$181$	1.61247e14			0.340865			0.170432	+	0.985369i	$0.445484\pi$
$182$		−	8.62263e13i		−	0.175863i
$183$		−	3.59330e14i		−	0.707232i
$184$	2.08473e14			0.396035
$185$	−1.45617e14	−	7.43761e14i	−0.267052	−	1.36401i
$186$	5.67152e14			1.00431
$187$		−	1.56323e14i		−	0.267332i
$188$		−	6.02229e13i		−	0.0994800i
$189$	−1.49231e14			−0.238154
$190$	−1.28655e14	−	6.57125e14i	−0.198394	−	1.01333i
$191$	−6.02389e14			−0.897760			−0.448880	−	0.893592i	$-0.648177\pi$
$191$	−6.02389e14			−0.897760			−0.448880	+	0.893592i	$0.648177\pi$
$192$			9.01108e13i			0.129813i
$193$		−	8.04612e14i		−	1.12063i	−0.828278	−	0.560317i	$-0.810679\pi$
$193$		−	8.04612e14i		−	1.12063i	0.828278	−	0.560317i	$-0.189321\pi$
$194$	3.69950e14			0.498232
$195$	−7.81998e14	+	1.53103e14i	−1.01855	+	0.199415i
$196$	−3.72280e14			−0.469035
$197$			1.31981e15i			1.60872i	0.594141	+	0.804361i	$0.297492\pi$
$197$			1.31981e15i			1.60872i	−0.594141	+	0.804361i	$0.702508\pi$
$198$		−	1.45495e13i		−	0.0171602i
$199$	−4.58439e14			−0.523283			−0.261641	−	0.965165i	$-0.584264\pi$
$199$	−4.58439e14			−0.523283			−0.261641	+	0.965165i	$0.584264\pi$
$200$	1.20676e14	+	2.96373e14i	0.133330	+	0.327450i
$201$	1.71566e15			1.83508
$202$			2.47666e13i			0.0256497i
$203$			3.20475e14i			0.321418i
$204$	−4.62200e14			−0.448987
$205$	1.24795e15	−	2.44329e14i	1.17435	−	0.229919i
$206$	−8.27125e13			−0.0754110
$207$			9.95239e13i			0.0879266i
$208$			2.91804e14i			0.249850i
$209$	5.43977e14			0.451471
$210$	−4.36395e13	−	2.22896e14i	−0.0351119	−	0.179340i
$211$	−2.24561e14			−0.175186			−0.0875929	−	0.996156i	$-0.527917\pi$
$211$	−2.24561e14			−0.175186			−0.0875929	+	0.996156i	$0.527917\pi$
$212$			5.98601e14i			0.452850i
$213$		−	3.95087e14i		−	0.289885i
$214$	−1.61631e15			−1.15036
$215$	3.74443e14	+	1.91253e15i	0.258545	+	1.32056i
$216$	5.05023e14			0.338347
$217$			5.23493e14i			0.340347i
$218$			1.73609e15i			1.09548i
$219$	−1.49420e15			−0.915212
$220$	−2.55121e14	+	4.99487e13i	−0.151705	+	0.0297014i
$221$	−1.49673e15			−0.864160
$222$		−	1.82043e15i		−	1.02066i
$223$		−	2.44107e14i		−	0.132922i	−0.997789	−	0.0664612i	$-0.978829\pi$
$223$		−	2.44107e14i		−	0.132922i	0.997789	−	0.0664612i	$-0.0211709\pi$
$224$	−8.31741e13			−0.0439922
$225$	−1.41487e14	+	5.76102e13i	−0.0726994	+	0.0296015i
$226$	−2.24100e15			−1.11876
$227$		−	2.37433e15i		−	1.15179i	−0.817523	−	0.575895i	$-0.804654\pi$
$227$		−	2.37433e15i		−	1.15179i	0.817523	−	0.575895i	$-0.195346\pi$
$228$		−	1.60838e15i		−	0.758249i
$229$	4.19562e15			1.92250			0.961248	−	0.275686i	$-0.0889051\pi$
$229$	4.19562e15			1.92250			0.961248	+	0.275686i	$0.0889051\pi$
$230$	1.74513e15	−	3.41668e14i	0.777313	−	0.152186i
$231$	1.84516e14			0.0799018
$232$		−	1.08454e15i		−	0.456641i
$233$			2.16868e15i			0.887935i	0.896043	+	0.443967i	$0.146429\pi$
$233$			2.16868e15i			0.887935i	−0.896043	+	0.443967i	$0.853571\pi$
$234$	−1.39306e14			−0.0554710
$235$	−9.86999e13	−	5.04126e14i	−0.0382275	−	0.195253i
$236$	1.23244e15			0.464342
$237$		−	2.78597e15i		−	1.02120i
$238$		−	4.26620e14i		−	0.152157i
$239$	3.78432e15			1.31341			0.656707	−	0.754146i	$-0.271949\pi$
$239$	3.78432e15			1.31341			0.656707	+	0.754146i	$0.271949\pi$
$240$	1.47683e14	+	7.54317e14i	0.0498837	+	0.254789i
$241$	−1.46077e15			−0.480254			−0.240127	−	0.970742i	$-0.577189\pi$
$241$	−1.46077e15			−0.480254			−0.240127	+	0.970742i	$0.577189\pi$
$242$			1.99826e15i			0.639517i
$243$			5.02727e14i			0.156636i
$244$	−1.12242e15			−0.340505
$245$	−3.11635e15	+	6.10133e14i	−0.920592	+	0.180237i
$246$	3.05448e15			0.878736
$247$		−	5.20838e15i		−	1.45939i
$248$		−	1.77159e15i		−	0.483534i
$249$	−1.80188e15			−0.479104
$250$	1.49591e15	+	2.28316e15i	0.387521	+	0.591462i
$251$	−5.27310e15			−1.33103			−0.665513	−	0.746386i	$-0.731787\pi$
$251$	−5.27310e15			−1.33103			−0.665513	+	0.746386i	$0.731787\pi$
$252$		−	3.97069e13i		−	0.00976702i
$253$			1.44464e15i			0.346319i
$254$	−2.31846e14			−0.0541726
$255$	−3.86907e15	+	7.57504e14i	−0.881243	+	0.172534i
$256$	2.81475e14			0.0625000
$257$			1.09851e15i			0.237815i	0.992905	+	0.118907i	$0.0379392\pi$
$257$			1.09851e15i			0.237815i	−0.992905	+	0.118907i	$0.962061\pi$
$258$			4.68111e15i			0.988145i
$259$	1.68029e15			0.345889
$260$	4.78240e14	+	2.44269e15i	0.0960107	+	0.490390i
$261$	5.17755e14			0.101382
$262$		−	2.36342e15i		−	0.451421i
$263$			5.38405e15i			1.00322i	0.865093	+	0.501611i	$0.167259\pi$
$263$			5.38405e15i			1.00322i	−0.865093	+	0.501611i	$0.832741\pi$
$264$	−6.24434e14			−0.113517
$265$	9.81053e14	+	5.01089e15i	0.174018	+	0.888826i
$266$	1.48457e15			0.256962
$267$			1.12725e15i			0.190414i
$268$		−	5.35912e15i		−	0.883521i
$269$	−2.25501e15			−0.362876			−0.181438	−	0.983402i	$-0.558075\pi$
$269$	−2.25501e15			−0.362876			−0.181438	+	0.983402i	$0.558075\pi$
$270$	4.22755e15	−	8.27687e14i	0.664085	−	0.130017i
$271$	9.56523e15			1.46688			0.733440	−	0.679754i	$-0.237913\pi$
$271$	9.56523e15			1.46688			0.733440	+	0.679754i	$0.237913\pi$
$272$			1.44375e15i			0.216170i
$273$		−	1.76668e15i		−	0.258285i
$274$	−8.84973e15			−1.26343
$275$	−2.05375e15	+	8.36240e14i	−0.286343	+	0.116592i
$276$	4.27137e15			0.581645
$277$		−	1.11206e15i		−	0.147914i	−0.997261	−	0.0739569i	$-0.976437\pi$
$277$		−	1.11206e15i		−	0.147914i	0.997261	−	0.0739569i	$-0.0235627\pi$
$278$		−	5.55859e14i		−	0.0722226i
$279$	8.45746e14			0.107353
$280$	−6.96250e14	+	1.36315e14i	−0.0863451	+	0.0169050i
$281$	−3.70112e15			−0.448479			−0.224240	−	0.974534i	$-0.571990\pi$
$281$	−3.70112e15			−0.448479			−0.224240	+	0.974534i	$0.571990\pi$
$282$		−	1.23390e15i		−	0.146103i
$283$		−	2.38218e15i		−	0.275653i	−0.990456	−	0.137827i	$-0.955988\pi$
$283$		−	2.38218e15i		−	0.275653i	0.990456	−	0.137827i	$-0.0440117\pi$
$284$	−1.23411e15			−0.139568
$285$	−2.63599e15	−	1.34637e16i	−0.291375	−	1.48824i
$286$	−2.02209e15			−0.218485
$287$			2.81934e15i			0.297794i
$288$			1.34375e14i			0.0138761i
$289$	2.49923e15			0.252331
$290$	−1.77747e15	−	9.07870e15i	−0.175475	−	0.896265i
$291$	7.57984e15			0.731738
$292$			4.66736e15i			0.440639i
$293$		−	1.41389e16i		−	1.30549i	−0.757576	−	0.652747i	$-0.773617\pi$
$293$		−	1.41389e16i		−	1.30549i	0.757576	−	0.652747i	$-0.226383\pi$
$294$	−7.62758e15			−0.688857
$295$	1.03168e16	−	2.01986e15i	0.911382	−	0.178434i
$296$	−5.68639e15			−0.491406
$297$			3.49962e15i			0.295872i
$298$			5.60099e15i			0.463297i
$299$	1.38319e16			1.11949
$300$	2.47252e15	+	6.07235e15i	0.195817	+	0.480915i
$301$	−4.32075e15			−0.334871
$302$		−	4.55254e15i		−	0.345310i
$303$			5.07438e14i			0.0376709i
$304$	−5.02402e15			−0.365067
$305$	−9.39580e15	+	1.83955e15i	−0.668321	+	0.130847i
$306$	−6.89239e14			−0.0479933
$307$			2.42316e16i			1.65189i	0.563749	+	0.825946i	$0.309359\pi$
$307$			2.42316e16i			1.65189i	−0.563749	+	0.825946i	$0.690641\pi$
$308$		−	5.76365e14i		−	0.0384696i
$309$	−1.69468e15			−0.110754
$310$	−2.90347e15	−	1.48299e16i	−0.185809	−	0.949049i
$311$	−3.03804e15			−0.190393			−0.0951966	−	0.995458i	$-0.530348\pi$
$311$	−3.03804e15			−0.190393			−0.0951966	+	0.995458i	$0.530348\pi$
$312$			5.97872e15i			0.366947i
$313$			1.11181e16i			0.668333i	0.942514	+	0.334167i	$0.108455\pi$
$313$			1.11181e16i			0.668333i	−0.942514	+	0.334167i	$0.891545\pi$
$314$	2.25215e16			1.32604
$315$	−6.50760e13	−	3.32386e14i	−0.00375320	−	0.0191701i
$316$	−8.70239e15			−0.491669
$317$			4.32419e15i			0.239342i	0.992814	+	0.119671i	$0.0381840\pi$
$317$			4.32419e15i			0.239342i	−0.992814	+	0.119671i	$0.961816\pi$
$318$			1.22646e16i			0.665087i
$319$	7.51546e15			0.399316
$320$	2.35623e15	−	4.61312e14i	0.122671	−	0.0240171i
$321$	−3.31162e16			−1.68950
$322$			3.94256e15i			0.197113i
$323$		−	2.57694e16i		−	1.26266i
$324$	1.11646e16			0.536167
$325$	8.00670e15	+	1.96640e16i	0.376887	+	0.925612i
$326$	1.45377e16			0.670780
$327$			3.55705e16i			1.60890i
$328$		−	9.54112e15i		−	0.423077i
$329$	1.13891e15			0.0495127
$330$	−5.22713e15	+	1.02339e15i	−0.222804	+	0.0436215i
$331$	1.52621e15			0.0637872			0.0318936	−	0.999491i	$-0.489846\pi$
$331$	1.52621e15			0.0637872			0.0318936	+	0.999491i	$0.489846\pi$
$332$			5.62845e15i			0.230670i
$333$		−	2.71465e15i		−	0.109100i
$334$	−4.58460e15			−0.180697
$335$	−8.78310e15	−	4.48611e16i	−0.339513	−	1.73412i
$336$	−1.70414e15			−0.0646100
$337$		−	2.49741e16i		−	0.928744i	−0.885640	−	0.464372i	$-0.846280\pi$
$337$		−	2.49741e16i		−	0.928744i	0.885640	−	0.464372i	$-0.153720\pi$
$338$		−	2.32276e13i		−	0.000847315i
$339$	−4.59154e16			−1.64309
$340$	2.36618e15	+	1.20856e16i	0.0830681	+	0.424284i
$341$	1.22764e16			0.422832
$342$		−	2.39844e15i		−	0.0810511i
$343$		−	1.45456e16i		−	0.482303i
$344$	1.46222e16			0.475753
$345$	3.57556e16	−	7.00039e15i	1.14162	−	0.223511i
$346$	1.04731e14			0.00328158
$347$		−	3.54595e16i		−	1.09041i	−0.838302	−	0.545207i	$-0.816451\pi$
$347$		−	3.54595e16i		−	1.09041i	0.838302	−	0.545207i	$-0.183549\pi$
$348$		−	2.22210e16i		−	0.670654i
$349$	−4.25252e16			−1.25974			−0.629871	−	0.776700i	$-0.716892\pi$
$349$	−4.25252e16			−1.25974			−0.629871	+	0.776700i	$0.716892\pi$
$350$	−5.60490e15	+	2.28218e15i	−0.162977	+	0.0663602i
$351$	3.35076e16			0.956415
$352$			1.95051e15i			0.0546540i
$353$			2.60676e16i			0.717078i	0.933515	+	0.358539i	$0.116725\pi$
$353$			2.60676e16i			0.717078i	−0.933515	+	0.358539i	$0.883275\pi$
$354$	2.52513e16			0.681965
$355$	−1.03308e16	+	2.02260e15i	−0.273935	+	0.0536323i
$356$	3.52115e15			0.0916768
$357$		−	8.74094e15i		−	0.223468i
$358$			1.05306e16i			0.264370i
$359$	5.52328e15			0.136170			0.0680852	−	0.997680i	$-0.478311\pi$
$359$	5.52328e15			0.136170			0.0680852	+	0.997680i	$0.478311\pi$
$360$	2.20228e14	+	1.12485e15i	0.00533220	+	0.0272351i
$361$	4.76202e16			1.13239
$362$		−	1.03198e16i		−	0.241028i
$363$			4.09420e16i			0.939240i
$364$	−5.51848e15			−0.124354
$365$	7.64938e15	+	3.90704e16i	0.169326	+	0.864858i
$366$	−2.29971e16			−0.500089
$367$		−	5.13840e15i		−	0.109774i	−0.998493	−	0.0548869i	$-0.982520\pi$
$367$		−	5.13840e15i		−	0.109774i	0.998493	−	0.0548869i	$-0.0174798\pi$
$368$		−	1.33423e16i		−	0.280039i
$369$	4.55488e15			0.0939303
$370$	−4.76007e16	+	9.31948e15i	−0.964500	+	0.188834i
$371$	−1.13205e16			−0.225390
$372$		−	3.62978e16i		−	0.710151i
$373$			5.41155e16i			1.04043i	0.854034	+	0.520217i	$0.174149\pi$
$373$			5.41155e16i			1.04043i	−0.854034	+	0.520217i	$0.825851\pi$
$374$	−1.00046e16			−0.189032
$375$	3.06494e16	+	4.67794e16i	0.569140	+	0.868662i
$376$	−3.85427e15			−0.0703430
$377$		−	7.19578e16i		−	1.29080i
$378$			9.55079e15i			0.168400i
$379$	−9.08168e16			−1.57402			−0.787012	−	0.616938i	$-0.788373\pi$
$379$	−9.08168e16			−1.57402			−0.787012	+	0.616938i	$0.788373\pi$
$380$	−4.20560e16	+	8.23391e15i	−0.716531	+	0.140285i
$381$	−4.75024e15			−0.0795616
$382$			3.85529e16i			0.634812i
$383$			4.76314e16i			0.771083i	0.922691	+	0.385541i	$0.125985\pi$
$383$			4.76314e16i			0.771083i	−0.922691	+	0.385541i	$0.874015\pi$
$384$	5.76709e15			0.0917918
$385$	−9.44609e14	−	4.82475e15i	−0.0147828	−	0.0755057i
$386$	−5.14951e16			−0.792408
$387$			6.98054e15i			0.105625i
$388$		−	2.36768e16i		−	0.352303i
$389$	1.00191e17			1.46607			0.733037	−	0.680189i	$-0.238102\pi$
$389$	1.00191e17			1.46607			0.733037	+	0.680189i	$0.238102\pi$
$390$	9.79859e15	+	5.00479e16i	0.141008	+	0.720221i
$391$	6.84357e16			0.968576
$392$			2.38259e16i			0.331658i
$393$		−	4.84237e16i		−	0.662989i
$394$	8.44678e16			1.13754
$395$	−7.28476e16	+	1.42624e16i	−0.965016	+	0.188935i
$396$	−9.31165e14			−0.0121341
$397$		−	2.83869e16i		−	0.363898i	−0.983308	−	0.181949i	$-0.941759\pi$
$397$		−	2.83869e16i		−	0.363898i	0.983308	−	0.181949i	$-0.0582405\pi$
$398$			2.93401e16i			0.370017i
$399$	3.04170e16			0.377392
$400$	1.89679e16	−	7.72328e15i	0.231542	−	0.0942783i
$401$	1.16518e16			0.139945			0.0699723	−	0.997549i	$-0.477709\pi$
$401$	1.16518e16			0.139945			0.0699723	+	0.997549i	$0.477709\pi$
$402$		−	1.09802e17i		−	1.29760i
$403$		−	1.17542e17i		−	1.36682i
$404$	1.58506e15			0.0181371
$405$	9.34586e16	−	1.82977e16i	1.05235	−	0.206034i
$406$	2.05104e16			0.227277
$407$		−	3.94045e16i		−	0.429717i
$408$			2.95808e16i			0.317482i
$409$	2.95537e16			0.312184			0.156092	−	0.987743i	$-0.450110\pi$
$409$	2.95537e16			0.312184			0.156092	+	0.987743i	$0.450110\pi$
$410$	−1.56370e16	−	7.98687e16i	−0.162577	−	0.830389i
$411$	−1.81321e17			−1.85556
$412$			5.29360e15i			0.0533236i
$413$			2.33074e16i			0.231110i
$414$	6.36953e15			0.0621735
$415$	9.22452e15	+	4.71157e16i	0.0886403	+	0.452744i
$416$	1.86755e16			0.176671
$417$		−	1.13889e16i		−	0.106071i
$418$		−	3.48145e16i		−	0.319238i
$419$	−1.73573e17			−1.56708			−0.783539	−	0.621342i	$-0.786588\pi$
$419$	−1.73573e17			−1.56708			−0.783539	+	0.621342i	$0.786588\pi$
$420$	−1.42653e16	+	2.79293e15i	−0.126812	+	0.0248279i
$421$	−1.22285e17			−1.07038			−0.535190	−	0.844732i	$-0.679760\pi$
$421$	−1.22285e17			−1.07038			−0.535190	+	0.844732i	$0.679760\pi$
$422$			1.43719e16i			0.123875i
$423$		−	1.84001e15i		−	0.0156173i
$424$	3.83105e16			0.320213
$425$	3.96145e16	+	9.72909e16i	0.326082	+	0.800837i
$426$	−2.52856e16			−0.204979
$427$		−	2.12268e16i		−	0.169474i
$428$			1.03444e17i			0.813429i
$429$	−4.14303e16			−0.320882
$430$	1.22402e17	−	2.39644e16i	0.933778	−	0.182819i
$431$	1.57439e17			1.18307			0.591536	−	0.806278i	$-0.298522\pi$
$431$	1.57439e17			1.18307			0.591536	+	0.806278i	$0.298522\pi$
$432$		−	3.23215e16i		−	0.239247i
$433$		−	6.72143e16i		−	0.490106i	−0.969510	−	0.245053i	$-0.921195\pi$
$433$		−	6.72143e16i		−	0.490106i	0.969510	−	0.245053i	$-0.0788054\pi$
$434$	3.35035e16			0.240662
$435$	−3.64182e16	−	1.86012e17i	−0.257714	−	1.31632i
$436$	1.11110e17			0.774623
$437$			2.38145e17i			1.63573i
$438$			9.56288e16i			0.647153i
$439$	1.77239e16			0.118179			0.0590895	−	0.998253i	$-0.481180\pi$
$439$	1.77239e16			0.118179			0.0590895	+	0.998253i	$0.481180\pi$
$440$	3.19672e15	+	1.63277e16i	0.0210020	+	0.107271i
$441$	−1.13744e16			−0.0736337
$442$			9.57908e16i			0.611054i
$443$			1.47385e17i			0.926462i	0.886237	+	0.463231i	$0.153310\pi$
$443$			1.47385e17i			0.926462i	−0.886237	+	0.463231i	$0.846690\pi$
$444$	−1.16507e17			−0.721713
$445$	2.94755e16	−	5.77084e15i	0.179937	−	0.0352289i
$446$	−1.56228e16			−0.0939903
$447$			1.14758e17i			0.680430i
$448$			5.32314e15i			0.0311072i
$449$	−2.11034e16			−0.121549			−0.0607746	−	0.998152i	$-0.519357\pi$
$449$	−2.11034e16			−0.121549			−0.0607746	+	0.998152i	$0.519357\pi$
$450$	3.68705e15	+	9.05518e15i	0.0209314	+	0.0514062i
$451$	6.61163e16			0.369966
$452$			1.43424e17i			0.791081i
$453$		−	9.32763e16i		−	0.507146i
$454$	−1.51957e17			−0.814439
$455$	−4.61952e16	+	9.04429e15i	−0.244075	+	0.0477860i
$456$	−1.02936e17			−0.536163
$457$			1.92373e17i			0.987843i	0.869507	+	0.493921i	$0.164437\pi$
$457$			1.92373e17i			0.987843i	−0.869507	+	0.493921i	$0.835563\pi$
$458$		−	2.68520e17i		−	1.35941i
$459$	1.65784e17			0.827487
$460$	−2.18668e16	−	1.11688e17i	−0.107612	−	0.549643i
$461$	−1.62978e17			−0.790809			−0.395405	−	0.918507i	$-0.629396\pi$
$461$	−1.62978e17			−0.790809			−0.395405	+	0.918507i	$0.629396\pi$
$462$		−	1.18090e16i		−	0.0564991i
$463$		−	2.42342e17i		−	1.14328i	−0.820505	−	0.571640i	$-0.806307\pi$
$463$		−	2.42342e17i		−	1.14328i	0.820505	−	0.571640i	$-0.193693\pi$
$464$	−6.94107e16			−0.322894
$465$	−5.94887e16	−	3.03848e17i	−0.272892	−	1.39384i
$466$	1.38795e17			0.627865
$467$		−	5.12065e16i		−	0.228436i	−0.993456	−	0.114218i	$-0.963564\pi$
$467$		−	5.12065e16i		−	0.228436i	0.993456	−	0.114218i	$-0.0364363\pi$
$468$			8.91557e15i			0.0392239i
$469$	1.01349e17			0.439742
$470$	−3.22640e16	+	6.31679e15i	−0.138065	+	0.0270309i
$471$	4.61440e17			1.94751
$472$		−	7.88762e16i		−	0.328340i
$473$			1.01326e17i			0.416029i
$474$	−1.78302e17			−0.722098
$475$	−3.38556e17	+	1.37852e17i	−1.35245	+	0.550687i
$476$	−2.73037e16			−0.107591
$477$			1.82892e16i			0.0710928i
$478$		−	2.42196e17i		−	0.928724i
$479$	4.75502e17			1.79875			0.899376	−	0.437176i	$-0.144021\pi$
$479$	4.75502e17			1.79875			0.899376	+	0.437176i	$0.144021\pi$
$480$	4.82763e16	−	9.45174e15i	0.180163	−	0.0352731i
$481$	−3.77284e17			−1.38907
$482$			9.34892e16i			0.339591i
$483$			8.07784e16i			0.289494i
$484$	1.27889e17			0.452207
$485$	−3.88041e16	−	1.98198e17i	−0.135381	−	0.691478i
$486$	3.21746e16			0.110758
$487$		−	6.70409e14i		−	0.00227720i	−0.999999	−	0.00113860i	$-0.999638\pi$
$487$		−	6.70409e14i		−	0.00227720i	0.999999	−	0.00113860i	$-0.000362428\pi$
$488$			7.18351e16i			0.240773i
$489$	2.97860e17			0.985154
$490$	3.90485e16	+	1.99447e17i	0.127447	+	0.650957i
$491$	2.37313e17			0.764350			0.382175	−	0.924090i	$-0.375175\pi$
$491$	2.37313e17			0.764350			0.382175	+	0.924090i	$0.375175\pi$
$492$		−	1.95486e17i		−	0.621360i
$493$		−	3.56024e17i		−	1.11680i
$494$	−3.33336e17			−1.03195
$495$	−7.79478e15	+	1.52609e15i	−0.0238161	+	0.00466281i
$496$	−1.13382e17			−0.341910
$497$		−	2.33391e16i		−	0.0694652i
$498$			1.15320e17i			0.338778i
$499$	−3.98058e17			−1.15423			−0.577115	−	0.816663i	$-0.695822\pi$
$499$	−3.98058e17			−1.15423			−0.577115	+	0.816663i	$0.695822\pi$
$500$	1.46122e17	−	9.57382e16i	0.418227	−	0.274019i
$501$	−9.39332e16			−0.265383
$502$			3.37478e17i			0.941178i
$503$			5.67147e17i			1.56136i	0.624929	+	0.780681i	$0.285128\pi$
$503$			5.67147e17i			1.56136i	−0.624929	+	0.780681i	$0.714872\pi$
$504$	−2.54124e15			−0.00690633
$505$	1.32685e16	−	2.59777e15i	0.0355983	−	0.00696959i
$506$	9.24569e16			0.244884
$507$		−	4.75906e14i		−	0.00124443i
$508$			1.48381e16i			0.0383058i
$509$	1.41581e15			0.00360861			0.00180431	−	0.999998i	$-0.499426\pi$
$509$	1.41581e15			0.00360861			0.00180431	+	0.999998i	$0.499426\pi$
$510$	4.84802e16	+	2.47621e17i	0.122000	+	0.623133i
$511$	−8.82672e16			−0.219313
$512$		−	1.80144e16i		−	0.0441942i
$513$			5.76903e17i			1.39746i
$514$	7.03047e16			0.168161
$515$	8.67574e15	+	4.43127e16i	0.0204908	+	0.104660i
$516$	2.99591e17			0.698724
$517$		−	2.67086e16i		−	0.0615123i
$518$		−	1.07539e17i		−	0.244580i
$519$	2.14583e15			0.00481955
$520$	1.56332e17	−	3.06074e16i	0.346758	−	0.0678898i
$521$	−8.73597e17			−1.91367			−0.956833	−	0.290638i	$-0.906132\pi$
$521$	−8.73597e17			−1.91367			−0.956833	+	0.290638i	$0.906132\pi$
$522$		−	3.31363e16i		−	0.0716879i
$523$			1.46635e15i			0.00313312i	0.999999	+	0.00156656i	$0.000498652\pi$
$523$			1.46635e15i			0.00313312i	−0.999999	+	0.00156656i	$0.999501\pi$
$524$	−1.51259e17			−0.319203
$525$	−1.14838e17	+	4.67592e16i	−0.239359	+	0.0974612i
$526$	3.44579e17			0.709385
$527$		−	5.81561e17i		−	1.18257i
$528$			3.99638e16i			0.0802686i
$529$	−1.28405e17			−0.254753
$530$	3.20697e17	−	6.27874e16i	0.628495	−	0.123049i
$531$	3.76551e16			0.0728970
$532$		−	9.50122e16i		−	0.181700i
$533$		−	6.33040e17i		−	1.19593i
$534$	7.21442e16			0.134643
$535$	1.69535e17	+	8.65926e17i	0.312579	+	1.59655i
$536$	−3.42983e17			−0.624744
$537$			2.15759e17i			0.388272i
$538$			1.44320e17i			0.256592i
$539$	−1.65104e17			−0.290023
$540$	−5.29720e16	−	2.70563e17i	−0.0919362	−	0.469579i
$541$	−3.23779e17			−0.555222			−0.277611	−	0.960694i	$-0.589543\pi$
$541$	−3.23779e17			−0.555222			−0.277611	+	0.960694i	$0.589543\pi$
$542$		−	6.12174e17i		−	1.03724i
$543$		−	2.11441e17i		−	0.353990i
$544$	9.24001e16			0.152855
$545$	9.30100e17	−	1.82099e17i	1.52038	−	0.297667i
$546$	−1.13067e17			−0.182635
$547$		−	9.06120e17i		−	1.44633i	−0.690674	−	0.723166i	$-0.742686\pi$
$547$		−	9.06120e17i		−	1.44633i	0.690674	−	0.723166i	$-0.257314\pi$
$548$			5.66383e17i			0.893381i
$549$	−3.42937e16			−0.0534557
$550$	5.35194e16	+	1.31440e17i	0.0824430	+	0.202475i
$551$	1.23890e18			1.88605
$552$		−	2.73368e17i		−	0.411285i
$553$		−	1.64576e17i		−	0.244711i
$554$	−7.11717e16			−0.104591
$555$	−9.75283e17	+	1.90945e17i	−1.41653	+	0.277335i
$556$	−3.55750e16			−0.0510691
$557$		−	9.13949e17i		−	1.29677i	−0.761312	−	0.648385i	$-0.775445\pi$
$557$		−	9.13949e17i		−	1.29677i	0.761312	−	0.648385i	$-0.224555\pi$
$558$		−	5.41278e16i		−	0.0759098i
$559$	9.70159e17			1.34483
$560$	8.72415e15	+	4.45600e16i	0.0119537	+	0.0610552i
$561$	−2.04984e17			−0.277626
$562$			2.36872e17i			0.317123i
$563$		−	4.66678e17i		−	0.617608i	−0.951126	−	0.308804i	$-0.900071\pi$
$563$		−	4.66678e17i		−	0.617608i	0.951126	−	0.308804i	$-0.0999288\pi$
$564$	−7.89694e16			−0.103311
$565$	2.35058e17	+	1.20060e18i	0.303991	+	1.55268i
$566$	−1.52460e17			−0.194916
$567$			2.11140e17i			0.266858i
$568$			7.89833e16i			0.0986896i
$569$	−1.63436e17			−0.201891			−0.100946	−	0.994892i	$-0.532187\pi$
$569$	−1.63436e17			−0.201891			−0.100946	+	0.994892i	$0.532187\pi$
$570$	−8.61679e17	+	1.68703e17i	−1.05235	+	0.206033i
$571$	−3.48487e17			−0.420777			−0.210389	−	0.977618i	$-0.567473\pi$
$571$	−3.48487e17			−0.420777			−0.210389	+	0.977618i	$0.567473\pi$
$572$			1.29414e17i			0.154492i
$573$			7.89904e17i			0.932329i
$574$	1.80438e17			0.210572
$575$	−3.66093e17	−	8.99103e17i	−0.422426	−	1.03745i
$576$	8.59998e15			0.00981186
$577$			5.26092e17i			0.593497i	0.954956	+	0.296749i	$0.0959023\pi$
$577$			5.26092e17i			0.593497i	−0.954956	+	0.296749i	$0.904098\pi$
$578$		−	1.59951e17i		−	0.178425i
$579$	−1.05508e18			−1.16379
$580$	−5.81037e17	+	1.13758e17i	−0.633755	+	0.124079i
$581$	−1.06443e17			−0.114808
$582$		−	4.85110e17i		−	0.517417i
$583$			2.65477e17i			0.280015i
$584$	2.98711e17			0.311579
$585$	1.46118e16	+	7.46322e16i	0.0150727	+	0.0769862i
$586$	−9.04887e17			−0.923123
$587$			8.95281e17i			0.903257i	0.892206	+	0.451629i	$0.149157\pi$
$587$			8.95281e17i			0.903257i	−0.892206	+	0.451629i	$0.850843\pi$
$588$			4.88165e17i			0.487096i
$589$	2.02374e18			1.99712
$590$	−1.29271e17	−	6.60273e17i	−0.126172	−	0.644444i
$591$	1.73065e18			1.67067
$592$			3.63929e17i			0.347477i
$593$			1.30072e18i			1.22836i	0.789164	+	0.614182i	$0.210514\pi$
$593$			1.30072e18i			1.22836i	−0.789164	+	0.614182i	$0.789486\pi$
$594$	2.23975e17			0.209213
$595$	−2.28559e17	+	4.47482e16i	−0.211173	+	0.0413443i
$596$	3.58464e17			0.327600
$597$			6.01144e17i			0.543432i
$598$		−	8.85241e17i		−	0.791596i
$599$	−2.15974e18			−1.91042			−0.955208	−	0.295936i	$-0.904368\pi$
$599$	−2.15974e18			−1.91042			−0.955208	+	0.295936i	$0.904368\pi$
$600$	3.88630e17	−	1.58241e17i	0.340058	−	0.138464i
$601$	8.73803e17			0.756361			0.378181	−	0.925732i	$-0.376550\pi$
$601$	8.73803e17			0.756361			0.378181	+	0.925732i	$0.376550\pi$
$602$			2.76528e17i			0.236789i
$603$		−	1.63738e17i		−	0.138704i
$604$	−2.91363e17			−0.244171
$605$	1.07056e18	−	2.09598e17i	0.887563	−	0.173771i
$606$	3.24761e16			0.0266374
$607$			1.26745e18i			1.02850i	0.857641	+	0.514249i	$0.171929\pi$
$607$			1.26745e18i			1.02850i	−0.857641	+	0.514249i	$0.828071\pi$
$608$			3.21537e17i			0.258142i
$609$	4.20235e17			0.333795
$610$	1.17731e17	+	6.01331e17i	0.0925226	+	0.472574i
$611$	−2.55725e17			−0.198841
$612$			4.41113e16i			0.0339364i
$613$		−	2.25430e18i		−	1.71601i	−0.513645	−	0.858003i	$-0.671705\pi$
$613$		−	2.25430e18i		−	1.71601i	0.513645	−	0.858003i	$-0.328295\pi$
$614$	1.55082e18			1.16806
$615$	−3.20385e17	−	1.63642e18i	−0.238772	−	1.21957i
$616$	−3.68873e16			−0.0272021
$617$		−	2.21840e18i		−	1.61877i	−0.587275	−	0.809387i	$-0.699799\pi$
$617$		−	2.21840e18i		−	1.61877i	0.587275	−	0.809387i	$-0.300201\pi$
$618$			1.08460e17i			0.0783147i
$619$	−2.68448e18			−1.91810			−0.959049	−	0.283241i	$-0.908590\pi$
$619$	−2.68448e18			−1.91810			−0.959049	+	0.283241i	$0.908590\pi$
$620$	−9.49117e17	+	1.85822e17i	−0.671079	+	0.131387i
$621$	−1.53208e18			−1.07198
$622$			1.94435e17i			0.134628i
$623$			6.65905e16i			0.0456289i
$624$	3.82638e17			0.259471
$625$	1.06628e18	−	1.04091e18i	0.715571	−	0.698540i
$626$	7.11559e17			0.472583
$627$		−	7.13309e17i		−	0.468855i
$628$		−	1.44138e18i		−	0.937649i
$629$	−1.86668e18			−1.20182
$630$	−2.12727e16	+	4.16486e15i	−0.0135553	+	0.00265391i
$631$	4.00810e17			0.252783			0.126391	−	0.991980i	$-0.459661\pi$
$631$	4.00810e17			0.252783			0.126391	+	0.991980i	$0.459661\pi$
$632$			5.56953e17i			0.347662i
$633$			2.94464e17i			0.181931i
$634$	2.76748e17			0.169241
$635$	2.43183e16	+	1.24210e17i	0.0147199	+	0.0751842i
$636$	7.84937e17			0.470288
$637$			1.58082e18i			0.937508i
$638$		−	4.80990e17i		−	0.282359i
$639$	−3.77062e16			−0.0219108
$640$	−2.95240e16	−	1.50798e17i	−0.0169826	−	0.0867415i
$641$	−1.26616e17			−0.0720960			−0.0360480	−	0.999350i	$-0.511477\pi$
$641$	−1.26616e17			−0.0720960			−0.0360480	+	0.999350i	$0.511477\pi$
$642$			2.11944e18i			1.19466i
$643$		−	1.66181e18i		−	0.927279i	−0.886024	−	0.463640i	$-0.846543\pi$
$643$		−	1.66181e18i		−	0.927279i	0.886024	−	0.463640i	$-0.153457\pi$
$644$	2.52324e17			0.139380
$645$	2.50787e18	−	4.91002e17i	1.37141	−	0.268501i
$646$	−1.64924e18			−0.892838
$647$			2.43109e18i			1.30294i	0.758675	+	0.651469i	$0.225847\pi$
$647$			2.43109e18i			1.30294i	−0.758675	+	0.651469i	$0.774153\pi$
$648$		−	7.14533e17i		−	0.379127i
$649$	5.46582e17			0.287121
$650$	1.25849e18	−	5.12429e17i	0.654507	−	0.266500i
$651$	6.86449e17			0.353453
$652$		−	9.30410e17i		−	0.474313i
$653$			1.97732e18i			0.998024i	0.866595	+	0.499012i	$0.166304\pi$
$653$			1.97732e18i			0.998024i	−0.866595	+	0.499012i	$0.833696\pi$
$654$	2.27651e18			1.13767
$655$	−1.26619e18	+	2.47899e17i	−0.626512	+	0.122661i
$656$	−6.10632e17			−0.299161
$657$			1.42603e17i			0.0691758i
$658$		−	7.28903e16i		−	0.0350108i
$659$	1.10258e18			0.524390			0.262195	−	0.965015i	$-0.415554\pi$
$659$	1.10258e18			0.524390			0.262195	+	0.965015i	$0.415554\pi$
$660$	6.54970e16	+	3.34536e17i	0.0308451	+	0.157546i
$661$	−1.89932e18			−0.885706			−0.442853	−	0.896594i	$-0.646034\pi$
$661$	−1.89932e18			−0.885706			−0.442853	+	0.896594i	$0.646034\pi$
$662$		−	9.76777e16i		−	0.0451043i
$663$			1.96264e18i			0.897436i
$664$	3.60221e17			0.163108
$665$	−1.55716e17	−	7.95347e17i	−0.0698222	−	0.356628i
$666$	−1.73738e17			−0.0771457
$667$			3.29016e18i			1.44677i
$668$			2.93415e17i			0.127772i
$669$	−3.20094e17			−0.138041
$670$	−2.87111e18	+	5.62119e17i	−1.22621	+	0.240072i
$671$	−4.97790e17			−0.210547
$672$			1.09065e17i			0.0456862i
$673$		−	2.39990e18i		−	0.995625i	−0.867285	−	0.497812i	$-0.834137\pi$
$673$		−	2.39990e18i		−	0.995625i	0.867285	−	0.497812i	$-0.165863\pi$
$674$	−1.59834e18			−0.656721
$675$	−8.86856e17	−	2.17806e18i	−0.360893	−	0.886331i
$676$	−1.48656e15			−0.000599143
$677$			1.81960e18i			0.726358i	0.931719	+	0.363179i	$0.118309\pi$
$677$			1.81960e18i			0.726358i	−0.931719	+	0.363179i	$0.881691\pi$
$678$			2.93858e18i			1.16184i
$679$	4.47766e17			0.175347
$680$	7.73481e17	−	1.51435e17i	0.300014	−	0.0587380i
$681$	−3.11343e18			−1.19614
$682$		−	7.85691e17i		−	0.298988i
$683$			1.12411e18i			0.423716i	0.977300	+	0.211858i	$0.0679515\pi$
$683$			1.12411e18i			0.423716i	−0.977300	+	0.211858i	$0.932049\pi$
$684$	−1.53500e17			−0.0573118
$685$	9.28250e17	+	4.74119e18i	0.343302	+	1.75347i
$686$	−9.30919e17			−0.341040
$687$		−	5.50165e18i		−	1.99652i
$688$		−	9.35818e17i		−	0.336408i
$689$	2.54185e18			0.905158
$690$	−4.48025e17	−	2.28836e18i	−0.158046	−	0.807245i
$691$	5.62706e18			1.96641			0.983205	−	0.182505i	$-0.0584207\pi$
$691$	5.62706e18			1.96641			0.983205	+	0.182505i	$0.0584207\pi$
$692$		−	6.70281e15i		−	0.00232042i
$693$		−	1.76098e16i		−	0.00603933i
$694$	−2.26941e18			−0.771039
$695$	−2.97798e17	+	5.83042e16i	−0.100235	+	0.0196245i
$696$	−1.42214e18			−0.474224
$697$		−	3.13208e18i		−	1.03471i
$698$			2.72161e18i			0.890772i
$699$	2.84375e18			0.922126
$700$	1.46060e17	+	3.58713e17i	0.0469238	+	0.115242i
$701$	1.84373e18			0.586853			0.293427	−	0.955982i	$-0.405204\pi$
$701$	1.84373e18			0.586853			0.293427	+	0.955982i	$0.405204\pi$
$702$		−	2.14448e18i		−	0.676288i
$703$		−	6.49573e18i		−	2.02964i
$704$	1.24833e17			0.0386462
$705$	−6.61052e17	+	1.29424e17i	−0.202771	+	0.0396994i
$706$	1.66833e18			0.507050
$707$			2.99760e16i			0.00902710i
$708$		−	1.61608e18i		−	0.482222i
$709$	1.49341e18			0.441547			0.220774	−	0.975325i	$-0.429142\pi$
$709$	1.49341e18			0.441547			0.220774	+	0.975325i	$0.429142\pi$
$710$	1.29447e17	+	6.61169e17i	0.0379237	+	0.193702i
$711$	−2.65886e17			−0.0771869
$712$		−	2.25353e17i		−	0.0648253i
$713$			5.37443e18i			1.53197i
$714$	−5.59420e17			−0.158015
$715$	2.12097e17	+	1.08332e18i	0.0593671	+	0.303227i
$716$	6.73957e17			0.186938
$717$		−	4.96232e18i		−	1.36399i
$718$		−	3.53490e17i		−	0.0962871i
$719$	−4.68340e18			−1.26422			−0.632111	−	0.774878i	$-0.717811\pi$
$719$	−4.68340e18			−1.26422			−0.632111	+	0.774878i	$0.717811\pi$
$720$	7.19904e16	−	1.40946e16i	0.0192581	−	0.00377043i
$721$	−1.00110e17			−0.0265400
$722$		−	3.04769e18i		−	0.800718i
$723$			1.91548e18i			0.498746i
$724$	−6.60469e17			−0.170432
$725$	−4.67742e18	+	1.90453e18i	−1.19621	+	0.487070i
$726$	2.62029e18			0.664143
$727$			3.00825e18i			0.755684i	0.925870	+	0.377842i	$0.123334\pi$
$727$			3.00825e18i			0.755684i	−0.925870	+	0.377842i	$0.876666\pi$
$728$			3.53183e17i			0.0879317i
$729$	−3.68647e18			−0.909666
$730$	2.50051e18	−	4.89560e17i	0.611547	−	0.119731i
$731$	4.80003e18			1.16354
$732$			1.47182e18i			0.353616i
$733$		−	4.85585e18i		−	1.15635i	−0.815913	−	0.578175i	$-0.803765\pi$
$733$		−	4.85585e18i		−	1.15635i	0.815913	−	0.578175i	$-0.196235\pi$
$734$	−3.28858e17			−0.0776218
$735$	8.00059e17	+	4.08643e18i	0.187178	+	0.956040i
$736$	−8.53906e17			−0.198018
$737$		−	2.37674e18i		−	0.546316i
$738$		−	2.91512e17i		−	0.0664188i
$739$	1.75403e18			0.396140			0.198070	−	0.980188i	$-0.436533\pi$
$739$	1.75403e18			0.396140			0.198070	+	0.980188i	$0.436533\pi$
$740$	5.96446e17	+	3.04645e18i	0.133526	+	0.682005i
$741$	−6.82967e18			−1.51559
$742$			7.24512e17i			0.159375i
$743$			1.49117e18i			0.325162i	0.986695	+	0.162581i	$0.0519819\pi$
$743$			1.49117e18i			0.325162i	−0.986695	+	0.162581i	$0.948018\pi$
$744$	−2.32306e18			−0.502153
$745$	3.00070e18	−	5.87489e17i	0.642993	−	0.125888i
$746$	3.46339e18			0.735698
$747$			1.71967e17i			0.0362128i
$748$			6.40297e17i			0.133666i
$749$	−1.95629e18			−0.404856
$750$	2.99388e18	−	1.96156e18i	0.614237	−	0.402443i
$751$	1.41983e18			0.288787			0.144394	−	0.989520i	$-0.453877\pi$
$751$	1.41983e18			0.288787			0.144394	+	0.989520i	$0.453877\pi$
$752$			2.46673e17i			0.0497400i
$753$			6.91453e18i			1.38228i
$754$	−4.60530e18			−0.912734
$755$	−2.43900e18	+	4.77517e17i	−0.479243	+	0.0938283i
$756$	6.11251e17			0.119077
$757$			1.71556e18i			0.331347i	0.986181	+	0.165674i	$0.0529798\pi$
$757$			1.71556e18i			0.331347i	−0.986181	+	0.165674i	$0.947020\pi$
$758$			5.81228e18i			1.11300i
$759$	1.89433e18			0.359654
$760$	5.26970e17	+	2.69159e18i	0.0991968	+	0.506664i
$761$	−8.31616e18			−1.55211			−0.776055	−	0.630666i	$-0.782782\pi$
$761$	−8.31616e18			−1.55211			−0.776055	+	0.630666i	$0.782782\pi$
$762$			3.04016e17i			0.0562586i
$763$			2.10127e18i			0.385542i
$764$	2.46739e18			0.448880
$765$	7.22945e16	+	3.69256e17i	0.0130408	+	0.0666082i
$766$	3.04841e18			0.545238
$767$		−	5.23333e18i		−	0.928128i
$768$		−	3.69094e17i		−	0.0649066i
$769$	1.49585e18			0.260836			0.130418	−	0.991459i	$-0.458368\pi$
$769$	1.49585e18			0.260836			0.130418	+	0.991459i	$0.458368\pi$
$770$	−3.08784e17	+	6.04550e16i	−0.0533906	+	0.0104530i
$771$	1.44046e18			0.246972
$772$			3.29569e18i			0.560317i
$773$		−	8.71998e18i		−	1.47011i	−0.678009	−	0.735053i	$-0.737157\pi$
$773$		−	8.71998e18i		−	1.47011i	0.678009	−	0.735053i	$-0.262843\pi$
$774$	4.46754e17			0.0746883
$775$	−7.64050e18	+	3.11103e18i	−1.26666	+	0.515755i
$776$	−1.51531e18			−0.249116
$777$		−	2.20334e18i		−	0.359208i
$778$		−	6.41221e18i		−	1.03667i
$779$	1.08991e19			1.74742
$780$	3.20306e18	−	6.27110e17i	0.509273	−	0.0997077i
$781$	−5.47324e17			−0.0863004
$782$		−	4.37988e18i		−	0.684887i
$783$			7.97036e18i			1.23602i
$784$	1.52486e18			0.234517
$785$	−2.36229e18	−	1.20658e19i	−0.360313	−	1.84036i
$786$	−3.09912e18			−0.468804
$787$		−	5.40920e18i		−	0.811516i	−0.913981	−	0.405758i	$-0.867008\pi$
$787$		−	5.40920e18i		−	0.811516i	0.913981	−	0.405758i	$-0.132992\pi$
$788$		−	5.40594e18i		−	0.804361i
$789$	7.06003e18			1.04185
$790$	9.12795e17	+	4.66225e18i	0.133597	+	0.682369i
$791$	−2.71237e18			−0.393733
$792$			5.95946e16i			0.00858011i
$793$			4.76616e18i			0.680601i
$794$	−1.81676e18			−0.257314
$795$	6.57070e18	−	1.28644e18i	0.923051	−	0.180719i
$796$	1.87777e18			0.261641
$797$			4.72808e18i			0.653439i	0.945121	+	0.326720i	$0.105943\pi$
$797$			4.72808e18i			0.653439i	−0.945121	+	0.326720i	$0.894057\pi$
$798$		−	1.94669e18i		−	0.266857i
$799$	−1.26524e18			−0.172036
$800$	−4.94290e17	−	1.21395e18i	−0.0666648	−	0.163725i
$801$	1.07583e17			0.0143923
$802$		−	7.45718e17i		−	0.0989557i
$803$			2.06995e18i			0.272464i
$804$	−7.02733e18			−0.917542
$805$	2.11220e18	−	4.13536e17i	0.273566	−	0.0535599i
$806$	−7.52271e18			−0.966488
$807$			2.95696e18i			0.376849i
$808$		−	1.01444e17i		−	0.0128248i
$809$	6.71362e18			0.841960			0.420980	−	0.907070i	$-0.361686\pi$
$809$	6.71362e18			0.841960			0.420980	+	0.907070i	$0.361686\pi$
$810$	−1.17106e18	−	5.98135e18i	−0.145688	−	0.744127i
$811$	−1.00466e19			−1.23989			−0.619945	−	0.784645i	$-0.712845\pi$
$811$	−1.00466e19			−1.23989			−0.619945	+	0.784645i	$0.712845\pi$
$812$		−	1.31267e18i		−	0.160709i
$813$		−	1.25427e19i		−	1.52336i
$814$	−2.52189e18			−0.303856
$815$	−1.52486e18	−	7.78846e18i	−0.182266	−	0.930952i
$816$	1.89317e18			0.224493
$817$			1.67033e19i			1.96499i
$818$		−	1.89144e18i		−	0.220747i
$819$	−1.68608e17			−0.0195223
$820$	−5.11160e18	+	1.00077e18i	−0.587174	+	0.114959i
$821$	1.05179e19			1.19866			0.599332	−	0.800501i	$-0.295433\pi$
$821$	1.05179e19			1.19866			0.599332	+	0.800501i	$0.295433\pi$
$822$			1.16045e19i			1.31208i
$823$		−	1.15767e19i		−	1.29863i	−0.760518	−	0.649317i	$-0.775055\pi$
$823$		−	1.15767e19i		−	1.29863i	0.760518	−	0.649317i	$-0.224945\pi$
$824$	3.38791e17			0.0377055
$825$	1.09655e18	+	2.69306e18i	0.121081	+	0.297369i
$826$	1.49168e18			0.163420
$827$		−	2.90388e17i		−	0.0315640i	−0.999875	−	0.0157820i	$-0.994976\pi$
$827$		−	2.90388e17i		−	0.0315640i	0.999875	−	0.0157820i	$-0.00502378\pi$
$828$		−	4.07650e17i		−	0.0439633i
$829$	−3.39030e18			−0.362771			−0.181386	−	0.983412i	$-0.558058\pi$
$829$	−3.39030e18			−0.362771			−0.181386	+	0.983412i	$0.558058\pi$
$830$	3.01541e18	−	5.90369e17i	0.320139	−	0.0626781i
$831$	−1.45822e18			−0.153609
$832$		−	1.19523e18i		−	0.124925i
$833$			7.82136e18i			0.811129i
$834$	−7.28890e17			−0.0750037
$835$	4.80880e17	+	2.45617e18i	0.0490992	+	0.250782i
$836$	−2.22813e18			−0.225735
$837$			1.30195e19i			1.30882i
$838$			1.11087e19i			1.10809i
$839$	−2.12691e18			−0.210522			−0.105261	−	0.994445i	$-0.533568\pi$
$839$	−2.12691e18			−0.210522			−0.105261	+	0.994445i	$0.533568\pi$
$840$	1.78748e17	+	9.12982e17i	0.0175560	+	0.0896700i
$841$	6.85580e18			0.668166
$842$			7.82621e18i			0.756873i
$843$			4.85323e18i			0.465749i
$844$	9.19803e17			0.0875929
$845$	−1.24440e16	+	2.43634e15i	−0.00117596	+	0.000230234i
$846$	−1.17760e17			−0.0110431
$847$			2.41858e18i			0.225070i
$848$		−	2.45187e18i		−	0.226425i
$849$	−3.12372e18			−0.286267
$850$	6.22662e18	−	2.53533e18i	0.566277	−	0.230575i
$851$	1.72507e19			1.55691
$852$			1.61828e18i			0.144942i
$853$		−	3.62847e18i		−	0.322518i	−0.986912	−	0.161259i	$-0.948445\pi$
$853$		−	3.62847e18i		−	0.322518i	0.986912	−	0.161259i	$-0.0515555\pi$
$854$	−1.35852e18			−0.119836
$855$	−1.28495e18	+	2.51573e17i	−0.112488	+	0.0220234i
$856$	6.62039e18			0.575181
$857$			1.55052e18i			0.133691i	0.997763	+	0.0668456i	$0.0212935\pi$
$857$			1.55052e18i			0.133691i	−0.997763	+	0.0668456i	$0.978707\pi$
$858$			2.65154e18i			0.226898i
$859$	−1.87024e19			−1.58834			−0.794168	−	0.607698i	$-0.792093\pi$
$859$	−1.87024e19			−1.58834			−0.794168	+	0.607698i	$0.792093\pi$
$860$	−1.53372e18	−	7.83373e18i	−0.129273	−	0.660280i
$861$	3.69696e18			0.309261
$862$		−	1.00761e19i		−	0.836559i
$863$		−	6.30662e18i		−	0.519669i	−0.965653	−	0.259834i	$-0.916332\pi$
$863$		−	6.30662e18i		−	0.519669i	0.965653	−	0.259834i	$-0.0836680\pi$
$864$	−2.06857e18			−0.169173
$865$	−1.09853e16	−	5.61092e16i	−0.000891677	−	0.00455438i
$866$	−4.30172e18			−0.346558
$867$		−	3.27721e18i		−	0.262047i
$868$		−	2.14423e18i		−	0.170174i
$869$	−3.85947e18			−0.304018
$870$	−1.19048e19	+	2.33077e18i	−0.930777	+	0.182232i
$871$	−2.27565e19			−1.76598
$872$		−	7.11103e18i		−	0.547741i
$873$		−	7.23403e17i		−	0.0553080i
$874$	1.52413e19			1.15664
$875$	1.81056e18	+	2.76341e18i	0.136383	+	0.208158i
$876$	6.12024e18			0.457606
$877$			3.53133e18i			0.262084i	0.991377	+	0.131042i	$0.0418323\pi$
$877$			3.53133e18i			0.262084i	−0.991377	+	0.131042i	$0.958168\pi$
$878$		−	1.13433e18i		−	0.0835651i
$879$	−1.85401e19			−1.35576
$880$	1.04498e18	−	2.04590e17i	0.0758523	−	0.0148507i
$881$	1.42642e18			0.102779			0.0513896	−	0.998679i	$-0.483635\pi$
$881$	1.42642e18			0.102779			0.0513896	+	0.998679i	$0.483635\pi$
$882$			7.27960e17i			0.0520669i
$883$		−	1.06719e19i		−	0.757699i	−0.925458	−	0.378849i	$-0.876320\pi$
$883$		−	1.06719e19i		−	0.757699i	0.925458	−	0.378849i	$-0.123680\pi$
$884$	6.13061e18			0.432080
$885$	−2.64861e18	−	1.35282e19i	−0.185305	−	0.946475i
$886$	9.43261e18			0.655108
$887$		−	4.47688e18i		−	0.308654i	−0.988020	−	0.154327i	$-0.950679\pi$
$887$		−	4.47688e18i		−	0.308654i	0.988020	−	0.154327i	$-0.0493209\pi$
$888$			7.45648e18i			0.510328i
$889$	−2.80612e17			−0.0190654
$890$	−3.69334e17	−	1.88643e18i	−0.0249106	−	0.127235i
$891$	4.95144e18			0.331533
$892$			9.99861e17i			0.0664612i
$893$		−	4.40284e18i		−	0.290535i
$894$	7.34450e18			0.481137
$895$	5.64169e18	−	1.10455e18i	0.366910	−	0.0718352i
$896$	3.40681e17			0.0219961
$897$		−	1.81376e19i		−	1.16259i
$898$			1.35062e18i			0.0859482i
$899$	2.79595e19			1.76641
$900$	5.79531e17	−	2.35971e17i	0.0363497	−	0.0148007i
$901$	1.25762e19			0.783140
$902$		−	4.23145e18i		−	0.261605i
$903$			5.66574e18i			0.347765i
$904$	9.17912e18			0.559379
$905$	−5.52879e18	+	1.08245e18i	−0.334514	+	0.0654925i
$906$	−5.96968e18			−0.358606
$907$		−	8.54426e17i		−	0.0509597i	−0.999675	−	0.0254799i	$-0.991889\pi$
$907$		−	8.54426e17i		−	0.0509597i	0.999675	−	0.0254799i	$-0.00811137\pi$
$908$			9.72527e18i			0.575895i
$909$	4.84288e16			0.00284733
$910$	5.78835e17	+	2.95649e18i	0.0337898	+	0.172587i
$911$	−2.14955e19			−1.24589			−0.622944	−	0.782267i	$-0.714063\pi$
$911$	−2.14955e19			−1.24589			−0.622944	+	0.782267i	$0.714063\pi$
$912$			6.58792e18i			0.379125i
$913$			2.49619e18i			0.142632i
$914$	1.23118e19			0.698510
$915$	2.41218e18	+	1.23206e19i	0.135885	+	0.694055i
$916$	−1.71853e19			−0.961248
$917$		−	2.86054e18i		−	0.158872i
$918$		−	1.06102e19i		−	0.585122i
$919$	−1.69194e19			−0.926475			−0.463238	−	0.886234i	$-0.653312\pi$
$919$	−1.69194e19			−0.926475			−0.463238	+	0.886234i	$0.653312\pi$
$920$	−7.14804e18	+	1.39947e18i	−0.388657	+	0.0760929i
$921$	3.17745e19			1.71550
$922$			1.04306e19i			0.559186i
$923$			5.24043e18i			0.278969i
$924$	−7.55778e17			−0.0399509
$925$	9.98570e18	+	2.45243e19i	0.524152	+	1.28729i
$926$	−1.55099e19			−0.808421
$927$			1.61737e17i			0.00837126i
$928$			4.44229e18i			0.228320i
$929$	−1.18385e19			−0.604221			−0.302111	−	0.953273i	$-0.597691\pi$
$929$	−1.18385e19			−0.604221			−0.302111	+	0.953273i	$0.597691\pi$
$930$	−1.94463e19	+	3.80728e18i	−0.985593	+	0.192964i
$931$	−2.72170e19			−1.36983
$932$		−	8.88289e18i		−	0.443967i
$933$			3.98374e18i			0.197725i
$934$	−3.27722e18			−0.161529
$935$	1.04939e18	+	5.35993e18i	0.0513643	+	0.262351i
$936$	5.70596e17			0.0277355
$937$		−	1.75991e19i		−	0.849540i	−0.905301	−	0.424770i	$-0.860355\pi$
$937$		−	1.75991e19i		−	0.849540i	0.905301	−	0.424770i	$-0.139645\pi$
$938$		−	6.48636e18i		−	0.310944i
$939$	1.45790e19			0.694068
$940$	4.04275e17	+	2.06490e18i	0.0191137	+	0.0976265i
$941$	−2.49075e19			−1.16949			−0.584747	−	0.811216i	$-0.698806\pi$
$941$	−2.49075e19			−1.16949			−0.584747	+	0.811216i	$0.698806\pi$
$942$		−	2.95322e19i		−	1.37710i
$943$			2.89447e19i			1.34043i
$944$	−5.04808e18			−0.232171
$945$	5.11678e18	−	1.00178e18i	0.233717	−	0.0457581i
$946$	6.48486e18			0.294177
$947$			1.42977e19i			0.644157i	0.946713	+	0.322079i	$0.104382\pi$
$947$			1.42977e19i			0.644157i	−0.946713	+	0.322079i	$0.895618\pi$
$948$			1.14113e19i			0.510601i
$949$	1.98190e19			0.880749
$950$	8.82253e18	+	2.16676e19i	0.389394	+	0.956329i
$951$	5.67025e18			0.248558
$952$			1.74743e18i			0.0760783i
$953$			2.07380e19i			0.896734i	0.893850	+	0.448367i	$0.147994\pi$
$953$			2.07380e19i			0.896734i	−0.893850	+	0.448367i	$0.852006\pi$
$954$	1.17051e18			0.0502702
$955$	2.06545e19	−	4.04382e18i	0.881033	−	0.172492i
$956$	−1.55006e19			−0.656707
$957$		−	9.85492e18i		−	0.414692i
$958$		−	3.04321e19i		−	1.27191i
$959$	−1.07112e19			−0.444649
$960$	−6.04912e17	−	3.08968e18i	−0.0249419	−	0.127395i
$961$	2.12540e19			0.870438
$962$			2.41462e19i			0.982223i
$963$			3.16054e18i			0.127700i
$964$	5.98331e18			0.240127
$965$	5.40134e18	+	2.75882e19i	0.215315	+	1.09975i
$966$	5.16982e18			0.204703
$967$		−	4.90254e19i		−	1.92819i	−0.265562	−	0.964094i	$-0.585557\pi$
$967$		−	4.90254e19i		−	1.92819i	0.265562	−	0.964094i	$-0.414443\pi$
$968$		−	8.18488e18i		−	0.319759i
$969$	−3.37910e19			−1.31128
$970$	−1.26847e19	+	2.48346e18i	−0.488949	+	0.0957285i
$971$	4.18342e19			1.60179			0.800896	−	0.598803i	$-0.204357\pi$
$971$	4.18342e19			1.60179			0.800896	+	0.598803i	$0.204357\pi$
$972$		−	2.05917e18i		−	0.0783180i
$973$		−	6.72780e17i		−	0.0254179i
$974$	−4.29062e16			−0.00161022
$975$	2.57851e19	−	1.04991e19i	0.961254	−	0.391400i
$976$	4.59745e18			0.170252
$977$		−	1.93811e19i		−	0.712958i	−0.934303	−	0.356479i	$-0.883977\pi$
$977$		−	1.93811e19i		−	0.712958i	0.934303	−	0.356479i	$-0.116023\pi$
$978$		−	1.90630e19i		−	0.696609i
$979$	1.56161e18			0.0566873
$980$	1.27646e19	−	2.49911e18i	0.460296	−	0.0901187i
$981$	3.39477e18			0.121608
$982$		−	1.51881e19i		−	0.540477i
$983$		−	1.38462e19i		−	0.489478i	−0.969589	−	0.244739i	$-0.921298\pi$
$983$		−	1.38462e19i		−	0.489478i	0.969589	−	0.244739i	$-0.0787024\pi$
$984$	−1.25111e19			−0.439368
$985$	−8.85985e18	−	4.52531e19i	−0.309094	−	1.57875i
$986$	−2.27855e19			−0.789695
$987$		−	1.49344e18i		−	0.0514192i
$988$			2.13335e19i			0.729697i
$989$	−4.43590e19			−1.50732
$990$	9.76701e16	+	4.98866e17i	0.00329710	+	0.0168405i
$991$	−2.06428e19			−0.692294			−0.346147	−	0.938180i	$-0.612510\pi$
$991$	−2.06428e19			−0.692294			−0.346147	+	0.938180i	$0.612510\pi$
$992$			7.25642e18i			0.241767i
$993$		−	2.00130e18i		−	0.0662434i
$994$	−1.49370e18			−0.0491193
$995$	1.57188e19	−	3.07749e18i	0.513533	−	0.100542i
$996$	7.38050e18			0.239552
$997$			4.48913e18i			0.144758i	0.997377	+	0.0723792i	$0.0230592\pi$
$997$			4.48913e18i			0.144758i	−0.997377	+	0.0723792i	$0.976941\pi$
$998$			2.54757e19i			0.816164i
$999$	4.17896e19			1.33012

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.14.b.a.9.1	✓	6
3.2	odd	2		90.14.c.b.19.6		6
4.3	odd	2		80.14.c.b.49.6		6
5.2	odd	4		50.14.a.j.1.1		3
5.3	odd	4		50.14.a.i.1.3		3
5.4	even	2	inner	10.14.b.a.9.6	yes	6
15.14	odd	2		90.14.c.b.19.3		6
20.19	odd	2		80.14.c.b.49.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.14.b.a.9.1	✓	6	1.1	even	1	trivial
10.14.b.a.9.6	yes	6	5.4	even	2	inner
50.14.a.i.1.3		3	5.3	odd	4
50.14.a.j.1.1		3	5.2	odd	4
80.14.c.b.49.1		6	20.19	odd	2
80.14.c.b.49.6		6	4.3	odd	2
90.14.c.b.19.3		6	15.14	odd	2
90.14.c.b.19.6		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)

\(f(q)\)	\(=\)	\(q-64.0000i q^{2} -1311.29i q^{3} -4096.00 q^{4} +(-34287.6 + 6712.97i) q^{5} -83922.3 q^{6} -77461.9i q^{7} +262144. i q^{8} -125146. q^{9} +O(q^{10})\)	\(q-64.0000i q^{2} -1311.29i q^{3} -4096.00 q^{4} +(-34287.6 + 6712.97i) q^{5} -83922.3 q^{6} -77461.9i q^{7} +262144. i q^{8} -125146. q^{9} +(429630. + 2.19441e6i) q^{10} -1.81656e6 q^{11} +5.37102e6i q^{12} +1.73929e7i q^{13} -4.95756e6 q^{14} +(8.80262e6 + 4.49608e7i) q^{15} +1.67772e7 q^{16} +8.60543e7i q^{17} +8.00935e6i q^{18} -2.99455e8 q^{19} +(1.40442e8 - 2.74963e7i) q^{20} -1.01575e8 q^{21} +1.16260e8i q^{22} -7.95262e8i q^{23} +3.43746e8 q^{24} +(1.13058e9 - 4.60343e8i) q^{25} +1.11314e9 q^{26} -1.92651e9i q^{27} +3.17284e8i q^{28} -4.13720e9 q^{29} +(2.87749e9 - 5.63368e8i) q^{30} -6.75807e9 q^{31} -1.07374e9i q^{32} +2.38203e9i q^{33} +5.50748e9 q^{34} +(5.20000e8 + 2.65598e9i) q^{35} +5.12599e8 q^{36} +2.16919e10i q^{37} +1.91651e10i q^{38} +2.28070e10 q^{39} +(-1.75977e9 - 8.98829e9i) q^{40} -3.63965e10 q^{41} +6.50078e9i q^{42} -5.57791e10i q^{43} +7.44062e9 q^{44} +(4.29096e9 - 8.40103e8i) q^{45} -5.08967e10 q^{46} +1.47029e10i q^{47} -2.19997e10i q^{48} +9.08887e10 q^{49} +(-2.94620e10 - 7.23568e10i) q^{50} +1.12842e11 q^{51} -7.12412e10i q^{52} -1.46143e11i q^{53} -1.23297e11 q^{54} +(6.22854e10 - 1.21945e10i) q^{55} +2.03062e10 q^{56} +3.92671e11i q^{57} +2.64781e11i q^{58} -3.00889e11 q^{59} +(-3.60555e10 - 1.84160e11i) q^{60} +2.74029e11 q^{61} +4.32516e11i q^{62} +9.69406e9i q^{63} -6.87195e10 q^{64} +(-1.16758e11 - 5.96360e11i) q^{65} +1.52450e11 q^{66} +1.30838e12i q^{67} -3.52478e11i q^{68} -1.04281e12 q^{69} +(1.69983e11 - 3.32800e10i) q^{70} +3.01298e11 q^{71} -3.28063e10i q^{72} -1.13949e12i q^{73} +1.38828e12 q^{74} +(-6.03641e11 - 1.48251e12i) q^{75} +1.22657e12 q^{76} +1.40714e11i q^{77} -1.45965e12i q^{78} +2.12461e12 q^{79} +(-5.75250e11 + 1.12625e11i) q^{80} -2.72573e12 q^{81} +2.32938e12i q^{82} -1.37413e12i q^{83} +4.16050e11 q^{84} +(-5.77680e11 - 2.95060e12i) q^{85} -3.56986e12 q^{86} +5.42505e12i q^{87} -4.76200e11i q^{88} -8.59655e11 q^{89} +(-5.37666e10 - 2.74621e11i) q^{90} +1.34729e12 q^{91} +3.25739e12i q^{92} +8.86176e12i q^{93} +9.40983e11 q^{94} +(1.02676e13 - 2.01023e12i) q^{95} -1.40798e12 q^{96} +5.78046e12i q^{97} -5.81687e12i q^{98} +2.27335e11 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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