LMFDB - Embedded newform 10.14.b.a.9.3

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			9.3
Root			$-50.1479 - 50.1479i$ of defining polynomial
Character	$\chi$	$=$	10.9
Dual form			10.14.b.a.9.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-64.0000i q^{2} +948.958i q^{3} -4096.00 q^{4} +(-272.592 - 34937.5i) q^{5} +60733.3 q^{6} +454502. i q^{7} +262144. i q^{8} +693802. q^{9} +O(q^{10})$	\(q-64.0000i q^{2} +948.958i q^{3} -4096.00 q^{4} +(-272.592 - 34937.5i) q^{5} +60733.3 q^{6} +454502. i q^{7} +262144. i q^{8} +693802. q^{9} +(-2.23600e6 + 17445.9i) q^{10} +1.09205e7 q^{11} -3.88693e6i q^{12} -1.27566e7i q^{13} +2.90881e7 q^{14} +(3.31542e7 - 258678. i) q^{15} +1.67772e7 q^{16} +1.16344e8i q^{17} -4.44033e7i q^{18} +2.73026e8 q^{19} +(1.11654e6 + 1.43104e8i) q^{20} -4.31303e8 q^{21} -6.98910e8i q^{22} +1.52448e8i q^{23} -2.48764e8 q^{24} +(-1.22055e9 + 1.90474e7i) q^{25} -8.16422e8 q^{26} +2.17133e9i q^{27} -1.86164e9i q^{28} +8.89364e8 q^{29} +(-1.65554e7 - 2.12187e9i) q^{30} -4.78852e9 q^{31} -1.07374e9i q^{32} +1.03631e10i q^{33} +7.44600e9 q^{34} +(1.58792e10 - 1.23894e8i) q^{35} -2.84181e9 q^{36} -5.25171e9i q^{37} -1.74737e10i q^{38} +1.21055e10 q^{39} +(9.15866e9 - 7.14583e7i) q^{40} -2.70484e9 q^{41} +2.76034e10i q^{42} -8.03912e9i q^{43} -4.47303e10 q^{44} +(-1.89125e8 - 2.42397e10i) q^{45} +9.75667e9 q^{46} +3.35808e10i q^{47} +1.59209e10i q^{48} -1.09683e11 q^{49} +(1.21903e9 + 7.81155e10i) q^{50} -1.10405e11 q^{51} +5.22510e10i q^{52} -1.38540e11i q^{53} +1.38965e11 q^{54} +(-2.97683e9 - 3.81534e11i) q^{55} -1.19145e11 q^{56} +2.59090e11i q^{57} -5.69193e10i q^{58} +3.13003e11 q^{59} +(-1.35800e11 + 1.05955e9i) q^{60} +7.15377e11 q^{61} +3.06465e11i q^{62} +3.15334e11i q^{63} -6.87195e10 q^{64} +(-4.45683e11 + 3.47734e9i) q^{65} +6.63236e11 q^{66} +4.70553e11i q^{67} -4.76544e11i q^{68} -1.44667e11 q^{69} +(-7.92919e9 - 1.01627e12i) q^{70} -4.88492e11 q^{71} +1.81876e11i q^{72} -1.10937e12i q^{73} -3.36110e11 q^{74} +(-1.80751e10 - 1.15825e12i) q^{75} -1.11832e12 q^{76} +4.96338e12i q^{77} -7.74750e11i q^{78} -2.70663e12 q^{79} +(-4.57333e9 - 5.86154e11i) q^{80} -9.54360e11 q^{81} +1.73110e11i q^{82} -1.70813e12i q^{83} +1.76662e12 q^{84} +(4.06476e12 - 3.17144e10i) q^{85} -5.14504e11 q^{86} +8.43969e11i q^{87} +2.86274e12i q^{88} +7.89059e11 q^{89} +(-1.55134e12 + 1.21040e10i) q^{90} +5.79789e12 q^{91} -6.24427e11i q^{92} -4.54411e12i q^{93} +2.14917e12 q^{94} +(-7.44248e10 - 9.53886e12i) q^{95} +1.01894e12 q^{96} +4.98929e12i q^{97} +7.01970e12i q^{98} +7.57665e12 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
$3$			948.958i			0.751551i	0.926711	+	0.375776i	$0.122624\pi$
$3$			948.958i			0.751551i	−0.926711	+	0.375776i	$0.877376\pi$
$4$	−4096.00			−0.500000
$5$	−272.592	−	34937.5i	−0.00780204	−	0.999970i
$5$	−272.592	−	34937.5i	−0.00780204	−	0.999970i
$6$	60733.3			0.531427
$7$			454502.i			1.46015i	0.683365	+	0.730076i	$0.260516\pi$
$7$			454502.i			1.46015i	−0.683365	+	0.730076i	$0.739484\pi$
$8$			262144.i			0.353553i
$9$	693802.			0.435170
$10$	−2.23600e6	+	17445.9i	−0.707085	+	0.00551687i
$11$	1.09205e7			1.85861			0.929307	−	0.369309i	$-0.120406\pi$
$11$	1.09205e7			1.85861			0.929307	+	0.369309i	$0.120406\pi$
$12$		−	3.88693e6i		−	0.375776i
$13$		−	1.27566e7i		−	0.732998i	−0.930418	−	0.366499i	$-0.880556\pi$
$13$		−	1.27566e7i		−	0.732998i	0.930418	−	0.366499i	$-0.119444\pi$
$14$	2.90881e7			1.03248
$15$	3.31542e7	−	258678.i	0.751529	−	0.00586363i
$16$	1.67772e7			0.250000
$17$			1.16344e8i			1.16903i	0.811384	+	0.584514i	$0.198715\pi$
$17$			1.16344e8i			1.16903i	−0.811384	+	0.584514i	$0.801285\pi$
$18$		−	4.44033e7i		−	0.307712i
$19$	2.73026e8			1.33139			0.665696	−	0.746223i	$-0.268135\pi$
$19$	2.73026e8			1.33139			0.665696	+	0.746223i	$0.268135\pi$
$20$	1.11654e6	+	1.43104e8i	0.00390102	+	0.499985i
$21$	−4.31303e8			−1.09738
$22$		−	6.98910e8i		−	1.31424i
$23$			1.52448e8i			0.214729i	0.994220	+	0.107365i	$0.0342412\pi$
$23$			1.52448e8i			0.214729i	−0.994220	+	0.107365i	$0.965759\pi$
$24$	−2.48764e8			−0.265714
$25$	−1.22055e9	+	1.90474e7i	−0.999878	+	0.0156036i
$26$	−8.16422e8			−0.518308
$27$			2.17133e9i			1.07860i
$28$		−	1.86164e9i		−	0.730076i
$29$	8.89364e8			0.277647			0.138823	−	0.990317i	$-0.455668\pi$
$29$	8.89364e8			0.277647			0.138823	+	0.990317i	$0.455668\pi$
$30$	−1.65554e7	−	2.12187e9i	−0.00414621	−	0.531411i
$31$	−4.78852e9			−0.969060			−0.484530	−	0.874775i	$-0.661009\pi$
$31$	−4.78852e9			−0.969060			−0.484530	+	0.874775i	$0.661009\pi$
$32$		−	1.07374e9i		−	0.176777i
$33$			1.03631e10i			1.39684i
$34$	7.44600e9			0.826628
$35$	1.58792e10	−	1.23894e8i	1.46011	−	0.0113922i
$36$	−2.84181e9			−0.217585
$37$		−	5.25171e9i		−	0.336504i	−0.985744	−	0.168252i	$-0.946188\pi$
$37$		−	5.25171e9i		−	0.336504i	0.985744	−	0.168252i	$-0.0538122\pi$
$38$		−	1.74737e10i		−	0.941437i
$39$	1.21055e10			0.550886
$40$	9.15866e9	−	7.14583e7i	0.353543	−	0.00275844i
$41$	−2.70484e9			−0.0889295			−0.0444648	−	0.999011i	$-0.514158\pi$
$41$	−2.70484e9			−0.0889295			−0.0444648	+	0.999011i	$0.514158\pi$
$42$			2.76034e10i			0.775965i
$43$		−	8.03912e9i		−	0.193938i	−0.995287	−	0.0969692i	$-0.969085\pi$
$43$		−	8.03912e9i		−	0.193938i	0.995287	−	0.0969692i	$-0.0309148\pi$
$44$	−4.47303e10			−0.929307
$45$	−1.89125e8	−	2.42397e10i	−0.00339522	−	0.435157i
$46$	9.75667e9			0.151836
$47$			3.35808e10i			0.454418i	0.973846	+	0.227209i	$0.0729600\pi$
$47$			3.35808e10i			0.454418i	−0.973846	+	0.227209i	$0.927040\pi$
$48$			1.59209e10i			0.187888i
$49$	−1.09683e11			−1.13205
$50$	1.21903e9	+	7.81155e10i	0.0110334	+	0.707021i
$51$	−1.10405e11			−0.878585
$52$			5.22510e10i			0.366499i
$53$		−	1.38540e11i		−	0.858580i	−0.903167	−	0.429290i	$-0.858764\pi$
$53$		−	1.38540e11i		−	0.858580i	0.903167	−	0.429290i	$-0.141236\pi$
$54$	1.38965e11			0.762688
$55$	−2.97683e9	−	3.81534e11i	−0.0145010	−	1.85856i
$56$	−1.19145e11			−0.516242
$57$			2.59090e11i			1.00061i
$58$		−	5.69193e10i		−	0.196326i
$59$	3.13003e11			0.966074			0.483037	−	0.875600i	$-0.339534\pi$
$59$	3.13003e11			0.966074			0.483037	+	0.875600i	$0.339534\pi$
$60$	−1.35800e11	+	1.05955e9i	−0.375764	+	0.00293182i
$61$	7.15377e11			1.77783			0.888917	−	0.458069i	$-0.151459\pi$
$61$	7.15377e11			1.77783			0.888917	+	0.458069i	$0.151459\pi$
$62$			3.06465e11i			0.685229i
$63$			3.15334e11i			0.635415i
$64$	−6.87195e10			−0.125000
$65$	−4.45683e11	+	3.47734e9i	−0.732976	+	0.00571888i
$66$	6.63236e11			0.987718
$67$			4.70553e11i			0.635510i	0.948173	+	0.317755i	$0.102929\pi$
$67$			4.70553e11i			0.635510i	−0.948173	+	0.317755i	$0.897071\pi$
$68$		−	4.76544e11i		−	0.584514i
$69$	−1.44667e11			−0.161380
$70$	−7.92919e9	−	1.01627e12i	−0.00805548	−	1.03245i
$71$	−4.88492e11			−0.452562			−0.226281	−	0.974062i	$-0.572657\pi$
$71$	−4.88492e11			−0.452562			−0.226281	+	0.974062i	$0.572657\pi$
$72$			1.81876e11i			0.153856i
$73$		−	1.10937e12i		−	0.857978i	−0.903310	−	0.428989i	$-0.858870\pi$
$73$		−	1.10937e12i		−	0.857978i	0.903310	−	0.428989i	$-0.141130\pi$
$74$	−3.36110e11			−0.237944
$75$	−1.80751e10	−	1.15825e12i	−0.0117269	−	0.751460i
$76$	−1.11832e12			−0.665696
$77$			4.96338e12i			2.71386i
$78$		−	7.74750e11i		−	0.389535i
$79$	−2.70663e12			−1.25272			−0.626358	−	0.779536i	$-0.715455\pi$
$79$	−2.70663e12			−1.25272			−0.626358	+	0.779536i	$0.715455\pi$
$80$	−4.57333e9	−	5.86154e11i	−0.00195051	−	0.249992i
$81$	−9.54360e11			−0.375456
$82$			1.73110e11i			0.0628827i
$83$		−	1.70813e12i		−	0.573474i	−0.958009	−	0.286737i	$-0.907429\pi$
$83$		−	1.70813e12i		−	0.573474i	0.958009	−	0.286737i	$-0.0925706\pi$
$84$	1.76662e12			0.548690
$85$	4.06476e12	−	3.17144e10i	1.16899	−	0.00912080i
$86$	−5.14504e11			−0.137135
$87$			8.43969e11i			0.208666i
$88$			2.86274e12i			0.657119i
$89$	7.89059e11			0.168296			0.0841481	−	0.996453i	$-0.473183\pi$
$89$	7.89059e11			0.168296			0.0841481	+	0.996453i	$0.473183\pi$
$90$	−1.55134e12	+	1.21040e10i	−0.307703	+	0.00240078i
$91$	5.79789e12			1.07029
$92$		−	6.24427e11i		−	0.107365i
$93$		−	4.54411e12i		−	0.728298i
$94$	2.14917e12			0.321322
$95$	−7.44248e10	−	9.53886e12i	−0.0103876	−	1.33135i
$96$	1.01894e12			0.132857
$97$			4.98929e12i			0.608167i	0.952645	+	0.304083i	$0.0983501\pi$
$97$			4.98929e12i			0.608167i	−0.952645	+	0.304083i	$0.901650\pi$
$98$			7.01970e12i			0.800478i
$99$	7.57665e12			0.808814
$100$	4.99939e12	−	7.80180e10i	0.499939	−	0.00780180i
$101$	−1.82670e13			−1.71229			−0.856146	−	0.516734i	$-0.827147\pi$
$101$	−1.82670e13			−1.71229			−0.856146	+	0.516734i	$0.827147\pi$
$102$			7.06594e12i			0.621253i
$103$		−	4.35513e12i		−	0.359385i	−0.983723	−	0.179692i	$-0.942490\pi$
$103$		−	4.35513e12i		−	0.359385i	0.983723	−	0.179692i	$-0.0575102\pi$
$104$	3.34406e12			0.259154
$105$	1.17570e11	+	1.50686e13i	0.00856180	+	1.09735i
$106$	−8.86653e12			−0.607108
$107$		−	2.32112e13i		−	1.49521i	−0.664142	−	0.747607i	$-0.731203\pi$
$107$		−	2.32112e13i		−	1.49521i	0.664142	−	0.747607i	$-0.268797\pi$
$108$		−	8.89378e12i		−	0.539302i
$109$	−1.51925e13			−0.867676			−0.433838	−	0.900991i	$-0.642841\pi$
$109$	−1.51925e13			−0.867676			−0.433838	+	0.900991i	$0.642841\pi$
$110$	−2.44182e13	+	1.90517e11i	−1.31420	+	0.0102537i
$111$	4.98365e12			0.252900
$112$			7.62527e12i			0.365038i
$113$			2.90883e13i			1.31434i	0.753741	+	0.657172i	$0.228247\pi$
$113$			2.90883e13i			1.31434i	−0.753741	+	0.657172i	$0.771753\pi$
$114$	1.65818e13			0.707538
$115$	5.32615e12	−	4.15561e10i	0.214722	−	0.00167532i
$116$	−3.64283e12			−0.138823
$117$		−	8.85055e12i		−	0.318979i
$118$		−	2.00322e13i		−	0.683118i
$119$	−5.28784e13			−1.70696
$120$	6.78110e10	+	8.69118e12i	0.00207311	+	0.265705i
$121$	8.47341e13			2.45444
$122$		−	4.57841e13i		−	1.25712i
$123$		−	2.56678e12i		−	0.0668351i
$124$	1.96138e13			0.484530
$125$	9.98181e11	+	4.26379e13i	0.0234042	+	0.999726i
$126$	2.01814e13			0.449307
$127$		−	2.92844e13i		−	0.619315i	−0.950848	−	0.309658i	$-0.899786\pi$
$127$		−	2.92844e13i		−	0.619315i	0.950848	−	0.309658i	$-0.100214\pi$
$128$			4.39805e12i			0.0883883i
$129$	7.62879e12			0.145755
$130$	2.22550e11	+	2.85237e13i	0.00404386	+	0.518292i
$131$	−2.29979e13			−0.397581			−0.198790	−	0.980042i	$-0.563701\pi$
$131$	−2.29979e13			−0.397581			−0.198790	+	0.980042i	$0.563701\pi$
$132$		−	4.24471e13i		−	0.698422i
$133$			1.24091e14i			1.94404i
$134$	3.01154e13			0.449374
$135$	7.58610e13	−	5.91888e11i	1.07857	−	0.00841531i
$136$	−3.04988e13			−0.413314
$137$		−	3.65959e13i		−	0.472877i	−0.971646	−	0.236439i	$-0.924020\pi$
$137$		−	3.65959e13i		−	0.472877i	0.971646	−	0.236439i	$-0.0759802\pi$
$138$			9.25867e12i			0.114113i
$139$	−3.84338e13			−0.451978			−0.225989	−	0.974130i	$-0.572561\pi$
$139$	−3.84338e13			−0.451978			−0.225989	+	0.974130i	$0.572561\pi$
$140$	−6.50410e13	+	5.07468e11i	−0.730054	+	0.00569608i
$141$	−3.18668e13			−0.341518
$142$			3.12635e13i			0.320010i
$143$		−	1.39308e14i		−	1.36236i
$144$	1.16401e13			0.108793
$145$	−2.42433e11	−	3.10721e13i	−0.00216621	−	0.277638i
$146$	−7.09994e13			−0.606682
$147$		−	1.04084e14i		−	0.850791i
$148$			2.15110e13i			0.168252i
$149$	−2.20268e14			−1.64907			−0.824537	−	0.565808i	$-0.808564\pi$
$149$	−2.20268e14			−1.64907			−0.824537	+	0.565808i	$0.808564\pi$
$150$	−7.41283e13	+	1.15681e12i	−0.531362	+	0.00829218i
$151$	3.34504e12			0.0229642			0.0114821	−	0.999934i	$-0.496345\pi$
$151$	3.34504e12			0.0229642			0.0114821	+	0.999934i	$0.496345\pi$
$152$			7.15722e13i			0.470718i
$153$			8.07195e13i			0.508726i
$154$	3.17656e14			1.91899
$155$	1.30531e12	+	1.67299e14i	0.00756064	+	0.969030i
$156$	−4.95840e13			−0.275443
$157$		−	1.34910e14i		−	0.718946i	−0.933155	−	0.359473i	$-0.882956\pi$
$157$		−	1.34910e14i		−	0.718946i	0.933155	−	0.359473i	$-0.117044\pi$
$158$			1.73224e14i			0.885804i
$159$	1.31468e14			0.645267
$160$	−3.75139e13	+	2.92693e11i	−0.176771	+	0.00137922i
$161$	−6.92879e13			−0.313537
$162$			6.10790e13i			0.265488i
$163$		−	3.24051e14i		−	1.35330i	−0.736304	−	0.676651i	$-0.763431\pi$
$163$		−	3.24051e14i		−	1.35330i	0.736304	−	0.676651i	$-0.236569\pi$
$164$	1.10790e13			0.0444648
$165$	3.62060e14	−	2.82489e12i	1.39680	−	0.0108982i
$166$	−1.09320e14			−0.405507
$167$			4.57413e14i			1.63174i	0.578234	+	0.815871i	$0.303742\pi$
$167$			4.57413e14i			1.63174i	−0.578234	+	0.815871i	$0.696258\pi$
$168$		−	1.13063e14i		−	0.387982i
$169$	1.40144e14			0.462714
$170$	−2.02972e12	−	2.60145e14i	−0.00644938	−	0.826602i
$171$	1.89426e14			0.579383
$172$			3.29283e13i			0.0969692i
$173$		−	1.61397e14i		−	0.457717i	−0.973460	−	0.228858i	$-0.926501\pi$
$173$		−	1.61397e14i		−	0.457717i	0.973460	−	0.228858i	$-0.0734993\pi$
$174$	5.40140e13			0.147549
$175$	−8.65706e12	−	5.54744e14i	−0.0227836	−	1.45998i
$176$	1.83215e14			0.464653
$177$			2.97027e14i			0.726055i
$178$		−	5.04998e13i		−	0.119003i
$179$	−6.37281e14			−1.44806			−0.724030	−	0.689768i	$-0.757712\pi$
$179$	−6.37281e14			−1.44806			−0.724030	+	0.689768i	$0.757712\pi$
$180$	7.74656e11	+	9.92859e13i	0.00169761	+	0.217579i
$181$	1.68242e14			0.355651			0.177826	−	0.984062i	$-0.443094\pi$
$181$	1.68242e14			0.355651			0.177826	+	0.984062i	$0.443094\pi$
$182$		−	3.71065e14i		−	0.756809i
$183$			6.78863e14i			1.33613i
$184$	−3.99633e13			−0.0759182
$185$	−1.83482e14	+	1.43157e12i	−0.336493	+	0.00262541i
$186$	−2.90823e14			−0.514985
$187$			1.27053e15i			2.17277i
$188$		−	1.37547e14i		−	0.227209i
$189$	−9.86875e14			−1.57493
$190$	−6.10487e14	+	4.76319e12i	−0.941408	+	0.00734512i
$191$	5.12678e14			0.764060			0.382030	−	0.924150i	$-0.375225\pi$
$191$	5.12678e14			0.764060			0.382030	+	0.924150i	$0.375225\pi$
$192$		−	6.52119e13i		−	0.0939439i
$193$		−	7.31821e14i		−	1.01925i	−0.860395	−	0.509627i	$-0.829783\pi$
$193$		−	7.31821e14i		−	1.01925i	0.860395	−	0.509627i	$-0.170217\pi$
$194$	3.19315e14			0.430039
$195$	−3.29985e12	−	4.22935e14i	−0.00429803	−	0.550869i
$196$	4.49261e14			0.566023
$197$		−	6.00125e14i		−	0.731495i	−0.930714	−	0.365748i	$-0.880813\pi$
$197$		−	6.00125e14i		−	0.731495i	0.930714	−	0.365748i	$-0.119187\pi$
$198$		−	4.84906e14i		−	0.571918i
$199$	−1.66629e14			−0.190197			−0.0950987	−	0.995468i	$-0.530317\pi$
$199$	−1.66629e14			−0.190197			−0.0950987	+	0.995468i	$0.530317\pi$
$200$	−4.99315e12	−	3.19961e14i	−0.00551671	−	0.353510i
$201$	−4.46535e14			−0.477619
$202$			1.16909e15i			1.21077i
$203$			4.04217e14i			0.405407i
$204$	4.52220e14			0.439292
$205$	7.37317e11	+	9.45002e13i	0.000693831	+	0.0889268i
$206$	−2.78728e14			−0.254123
$207$			1.05769e14i			0.0934437i
$208$		−	2.14020e14i		−	0.183250i
$209$	2.98158e15			2.47454
$210$	9.64393e14	−	7.52446e12i	0.775941	−	0.00605411i
$211$	−1.50601e14			−0.117488			−0.0587438	−	0.998273i	$-0.518709\pi$
$211$	−1.50601e14			−0.117488			−0.0587438	+	0.998273i	$0.518709\pi$
$212$			5.67458e14i			0.429290i
$213$		−	4.63559e14i		−	0.340124i
$214$	−1.48552e15			−1.05728
$215$	−2.80867e14	+	2.19140e12i	−0.193932	+	0.00151311i
$216$	−5.69202e14			−0.381344
$217$		−	2.17639e15i		−	1.41498i
$218$			9.72322e14i			0.613540i
$219$	1.05274e15			0.644815
$220$	1.21931e13	+	1.56276e15i	0.00725049	+	0.929278i
$221$	1.48415e15			0.856895
$222$		−	3.18954e14i		−	0.178827i
$223$			7.62572e14i			0.415240i	0.978210	+	0.207620i	$0.0665718\pi$
$223$			7.62572e14i			0.415240i	−0.978210	+	0.207620i	$0.933428\pi$
$224$	4.88018e14			0.258121
$225$	−8.46823e14	+	1.32151e13i	−0.435117	+	0.00679022i
$226$	1.86165e15			0.929381
$227$			8.39292e14i			0.407141i	0.979060	+	0.203570i	$0.0652546\pi$
$227$			8.39292e14i			0.407141i	−0.979060	+	0.203570i	$0.934745\pi$
$228$		−	1.06123e15i		−	0.500305i
$229$	−3.20496e15			−1.46856			−0.734280	−	0.678847i	$-0.762480\pi$
$229$	−3.20496e15			−1.46856			−0.734280	+	0.678847i	$0.762480\pi$
$230$	−2.65959e12	−	3.40874e14i	−0.00118463	−	0.151832i
$231$	−4.71003e15			−2.03961
$232$			2.33141e14i			0.0981629i
$233$		−	6.66372e14i		−	0.272837i	−0.990651	−	0.136419i	$-0.956441\pi$
$233$		−	6.66372e14i		−	0.272837i	0.990651	−	0.136419i	$-0.0435592\pi$
$234$	−5.66435e14			−0.225552
$235$	1.17323e15	−	9.15386e12i	0.454404	−	0.00354538i
$236$	−1.28206e15			−0.483037
$237$		−	2.56848e15i		−	0.941480i
$238$			3.38422e15i			1.20700i
$239$	1.81256e15			0.629081			0.314540	−	0.949244i	$-0.398150\pi$
$239$	1.81256e15			0.629081			0.314540	+	0.949244i	$0.398150\pi$
$240$	5.56235e14	−	4.33990e12i	0.187882	−	0.00146591i
$241$	−2.25908e15			−0.742713			−0.371357	−	0.928490i	$-0.621107\pi$
$241$	−2.25908e15			−0.742713			−0.371357	+	0.928490i	$0.621107\pi$
$242$		−	5.42298e15i		−	1.73555i
$243$			2.55616e15i			0.796430i
$244$	−2.93018e15			−0.888917
$245$	2.98987e13	+	3.83205e15i	0.00883227	+	1.13201i
$246$	−1.64274e14			−0.0472596
$247$		−	3.48289e15i		−	0.975908i
$248$		−	1.25528e15i		−	0.342614i
$249$	1.62094e15			0.430995
$250$	2.72883e15	−	6.38836e13i	0.706913	−	0.0165493i
$251$	4.09678e15			1.03410			0.517051	−	0.855955i	$-0.327030\pi$
$251$	4.09678e15			1.03410			0.517051	+	0.855955i	$0.327030\pi$
$252$		−	1.29161e15i		−	0.317708i
$253$			1.66480e15i			0.399098i
$254$	−1.87420e15			−0.437922
$255$	3.00956e13	+	3.85728e15i	0.00685475	+	0.878558i
$256$	2.81475e14			0.0625000
$257$			3.97811e15i			0.861214i	0.902540	+	0.430607i	$0.141701\pi$
$257$			3.97811e15i			0.861214i	−0.902540	+	0.430607i	$0.858299\pi$
$258$		−	4.88242e14i		−	0.103064i
$259$	2.38691e15			0.491347
$260$	1.82552e15	−	1.42432e13i	0.366488	−	0.00285944i
$261$	6.17042e14			0.120824
$262$			1.47187e15i			0.281132i
$263$		−	4.00498e15i		−	0.746257i	−0.927780	−	0.373128i	$-0.878285\pi$
$263$		−	4.00498e15i		−	0.746257i	0.927780	−	0.373128i	$-0.121715\pi$
$264$	−2.71662e15			−0.493859
$265$	−4.84023e15	+	3.77648e13i	−0.858554	+	0.00669867i
$266$	7.94182e15			1.37464
$267$			7.48783e14i			0.126483i
$268$		−	1.92739e15i		−	0.317755i
$269$	9.43541e15			1.51835			0.759174	−	0.650888i	$-0.225603\pi$
$269$	9.43541e15			1.51835			0.759174	+	0.650888i	$0.225603\pi$
$270$	−3.78808e13	−	4.85510e15i	−0.00595052	−	0.762665i
$271$	7.02518e15			1.07735			0.538675	−	0.842513i	$-0.318925\pi$
$271$	7.02518e15			1.07735			0.538675	+	0.842513i	$0.318925\pi$
$272$			1.95192e15i			0.292257i
$273$			5.50196e15i			0.804378i
$274$	−2.34214e15			−0.334375
$275$	−1.33290e16	+	2.08006e14i	−1.85839	+	0.0290011i
$276$	5.92555e14			0.0806900
$277$		−	1.03209e16i		−	1.37278i	−0.727234	−	0.686389i	$-0.759195\pi$
$277$		−	1.03209e16i		−	1.37278i	0.727234	−	0.686389i	$-0.240805\pi$
$278$			2.45977e15i			0.319597i
$279$	−3.32229e15			−0.421706
$280$	3.24779e13	+	4.16263e15i	0.00402774	+	0.516226i
$281$	−1.07766e16			−1.30584			−0.652922	−	0.757426i	$-0.726457\pi$
$281$	−1.07766e16			−1.30584			−0.652922	+	0.757426i	$0.726457\pi$
$282$			2.03947e15i			0.241490i
$283$		−	1.28451e16i		−	1.48637i	−0.669086	−	0.743185i	$-0.733314\pi$
$283$		−	1.28451e16i		−	1.48637i	0.669086	−	0.743185i	$-0.266686\pi$
$284$	2.00086e15			0.226281
$285$	9.05197e15	−	7.06260e13i	1.00058	−	0.00780680i
$286$	−8.91571e15			−0.963334
$287$		−	1.22935e15i		−	0.129851i
$288$		−	7.44964e14i		−	0.0769280i
$289$	−3.63128e15			−0.366626
$290$	−1.98862e15	+	1.55157e13i	−0.196320	+	0.00153174i
$291$	−4.73463e15			−0.457069
$292$			4.54396e15i			0.428989i
$293$			1.60607e16i			1.48294i	0.670983	+	0.741472i	$0.265872\pi$
$293$			1.60607e16i			1.48294i	−0.670983	+	0.741472i	$0.734128\pi$
$294$	−6.66140e15			−0.601600
$295$	−8.53221e13	−	1.09355e16i	−0.00753735	−	0.966045i
$296$	1.37671e15			0.118972
$297$			2.37120e16i			2.00471i
$298$			1.40971e16i			1.16607i
$299$	1.94472e15			0.157396
$300$	7.40358e13	+	4.74421e15i	0.00586345	+	0.375730i
$301$	3.65380e15			0.283180
$302$		−	2.14082e14i		−	0.0162381i
$303$		−	1.73346e16i		−	1.28688i
$304$	4.58062e15			0.332848
$305$	−1.95006e14	−	2.49935e16i	−0.0138707	−	1.77778i
$306$	5.16605e15			0.359724
$307$			3.69095e15i			0.251616i	0.992055	+	0.125808i	$0.0401524\pi$
$307$			3.69095e15i			0.251616i	−0.992055	+	0.125808i	$0.959848\pi$
$308$		−	2.03300e16i		−	1.35693i
$309$	4.13284e15			0.270096
$310$	1.07071e16	−	8.35400e13i	0.685208	−	0.00534618i
$311$	−7.43457e15			−0.465922			−0.232961	−	0.972486i	$-0.574841\pi$
$311$	−7.43457e15			−0.465922			−0.232961	+	0.972486i	$0.574841\pi$
$312$			3.17338e15i			0.194768i
$313$		−	1.39759e16i		−	0.840122i	−0.907496	−	0.420061i	$-0.862009\pi$
$313$		−	1.39759e16i		−	0.840122i	0.907496	−	0.420061i	$-0.137991\pi$
$314$	−8.63424e15			−0.508372
$315$	1.10170e16	−	8.59576e13i	0.635396	−	0.00495753i
$316$	1.10863e16			0.626358
$317$			1.71546e16i			0.949502i	0.880120	+	0.474751i	$0.157462\pi$
$317$			1.71546e16i			0.949502i	−0.880120	+	0.474751i	$0.842538\pi$
$318$		−	8.41396e15i		−	0.456273i
$319$	9.71227e15			0.516038
$320$	1.87324e13	+	2.40089e15i	0.000975255	+	0.124996i
$321$	2.20265e16			1.12373
$322$			4.43442e15i			0.221704i
$323$			3.17649e16i			1.55644i
$324$	3.90906e15			0.187728
$325$	2.42979e14	+	1.55701e16i	0.0114374	+	0.732909i
$326$	−2.07393e16			−0.956928
$327$		−	1.44171e16i		−	0.652103i
$328$		−	7.09057e14i		−	0.0314413i
$329$	−1.52625e16			−0.663519
$330$	−1.80793e14	−	2.31718e16i	−0.00770621	−	0.987688i
$331$	−1.30144e15			−0.0543928			−0.0271964	−	0.999630i	$-0.508658\pi$
$331$	−1.30144e15			−0.0543928			−0.0271964	+	0.999630i	$0.508658\pi$
$332$			6.99651e15i			0.286737i
$333$		−	3.64365e15i		−	0.146436i
$334$	2.92744e16			1.15382
$335$	1.64400e16	−	1.28269e14i	0.635491	−	0.00495827i
$336$	−7.23606e15			−0.274345
$337$			4.26730e16i			1.58694i	0.608612	+	0.793468i	$0.291726\pi$
$337$			4.26730e16i			1.58694i	−0.608612	+	0.793468i	$0.708274\pi$
$338$		−	8.96925e15i		−	0.327188i
$339$	−2.76036e16			−0.987797
$340$	−1.66492e16	+	1.29902e14i	−0.584496	+	0.00456040i
$341$	−5.22929e16			−1.80111
$342$		−	1.21233e16i		−	0.409685i
$343$		−	5.81483e15i		−	0.192808i
$344$	2.10741e15			0.0685676
$345$	3.94350e13	+	5.05429e15i	0.00125909	+	0.161375i
$346$	−1.03294e16			−0.323655
$347$		−	1.84259e16i		−	0.566613i	−0.959029	−	0.283306i	$-0.908569\pi$
$347$		−	1.84259e16i		−	0.566613i	0.959029	−	0.283306i	$-0.0914313\pi$
$348$		−	3.45690e15i		−	0.104333i
$349$	−6.19591e15			−0.183544			−0.0917720	−	0.995780i	$-0.529253\pi$
$349$	−6.19591e15			−0.183544			−0.0917720	+	0.995780i	$0.529253\pi$
$350$	−3.55036e16	+	5.54052e14i	−1.03236	+	0.0161105i
$351$	2.76988e16			0.790615
$352$		−	1.17258e16i		−	0.328560i
$353$		−	3.53266e16i		−	0.971775i	−0.874021	−	0.485888i	$-0.838496\pi$
$353$		−	3.53266e16i		−	0.971775i	0.874021	−	0.485888i	$-0.161504\pi$
$354$	1.90097e16			0.513398
$355$	1.33159e14	+	1.70667e16i	0.00353091	+	0.452549i
$356$	−3.23198e15			−0.0841481
$357$		−	5.01794e16i		−	1.28287i
$358$			4.07860e16i			1.02393i
$359$	−3.59772e15			−0.0886979			−0.0443490	−	0.999016i	$-0.514121\pi$
$359$	−3.59772e15			−0.0886979			−0.0443490	+	0.999016i	$0.514121\pi$
$360$	6.35430e15	−	4.95780e13i	0.153851	−	0.00120039i
$361$	3.24904e16			0.772606
$362$		−	1.07675e16i		−	0.251483i
$363$			8.04090e16i			1.84464i
$364$	−2.37482e16			−0.535145
$365$	−3.87585e16	+	3.02404e14i	−0.857952	+	0.00669398i
$366$	4.34472e16			0.944789
$367$		−	1.64558e16i		−	0.351551i	−0.984430	−	0.175776i	$-0.943757\pi$
$367$		−	1.64558e16i		−	0.351551i	0.984430	−	0.175776i	$-0.0562434\pi$
$368$			2.55765e15i			0.0536823i
$369$	−1.87662e15			−0.0386995
$370$	9.16208e13	+	1.17428e16i	0.00185645	+	0.237937i
$371$	6.29665e16			1.25366
$372$			1.86127e16i			0.364149i
$373$		−	4.96880e16i		−	0.955310i	−0.878548	−	0.477655i	$-0.841487\pi$
$373$		−	4.96880e16i		−	0.955310i	0.878548	−	0.477655i	$-0.158513\pi$
$374$	8.13138e16			1.53638
$375$	−4.04616e16	+	9.47231e14i	−0.751346	+	0.0175895i
$376$	−8.80301e15			−0.160661
$377$		−	1.13452e16i		−	0.203514i
$378$			6.31600e16i			1.11364i
$379$	−4.43290e16			−0.768304			−0.384152	−	0.923270i	$-0.625506\pi$
$379$	−4.43290e16			−0.768304			−0.384152	+	0.923270i	$0.625506\pi$
$380$	3.04844e14	+	3.90712e16i	0.00519379	+	0.665676i
$381$	2.77896e16			0.465447
$382$		−	3.28114e16i		−	0.540272i
$383$		−	3.51514e16i		−	0.569050i	−0.958669	−	0.284525i	$-0.908164\pi$
$383$		−	3.51514e16i		−	0.569050i	0.958669	−	0.284525i	$-0.0918358\pi$
$384$	−4.17356e15			−0.0664284
$385$	1.73408e17	−	1.35298e15i	2.71378	−	0.0211736i
$386$	−4.68366e16			−0.720722
$387$		−	5.57756e15i		−	0.0843962i
$388$		−	2.04361e16i		−	0.304083i
$389$	3.47937e16			0.509129			0.254565	−	0.967056i	$-0.418068\pi$
$389$	3.47937e16			0.509129			0.254565	+	0.967056i	$0.418068\pi$
$390$	−2.70678e16	+	2.11191e14i	−0.389523	+	0.00303917i
$391$	−1.77364e16			−0.251024
$392$		−	2.87527e16i		−	0.400239i
$393$		−	2.18241e16i		−	0.298802i
$394$	−3.84080e16			−0.517245
$395$	7.37805e14	+	9.45628e16i	0.00977373	+	1.25268i
$396$	−3.10340e16			−0.404407
$397$		−	1.15640e17i		−	1.48241i	−0.671279	−	0.741205i	$-0.734255\pi$
$397$		−	1.15640e17i		−	1.48241i	0.671279	−	0.741205i	$-0.265745\pi$
$398$			1.06642e16i			0.134490i
$399$	−1.17757e17			−1.46104
$400$	−2.04775e16	+	3.19562e14i	−0.249970	+	0.00390090i
$401$	−8.77040e16			−1.05337			−0.526685	−	0.850060i	$-0.676565\pi$
$401$	−8.77040e16			−1.05337			−0.526685	+	0.850060i	$0.676565\pi$
$402$			2.85782e16i			0.337727i
$403$			6.10852e16i			0.710319i
$404$	7.48215e16			0.856146
$405$	2.60151e14	+	3.33429e16i	0.00292932	+	0.375445i
$406$	2.58699e16			0.286666
$407$		−	5.73512e16i		−	0.625430i
$408$		−	2.89421e16i		−	0.310627i
$409$	−1.35424e17			−1.43053			−0.715263	−	0.698856i	$-0.753693\pi$
$409$	−1.35424e17			−1.43053			−0.715263	+	0.698856i	$0.753693\pi$
$410$	6.04801e15	−	4.71883e13i	0.0628807	−	0.000490613i
$411$	3.47279e16			0.355392
$412$			1.78386e16i			0.179692i
$413$			1.42260e17i			1.41062i
$414$	6.76920e15			0.0660747
$415$	−5.96778e16	+	4.65623e14i	−0.573457	+	0.00447427i
$416$	−1.36973e16			−0.129577
$417$		−	3.64721e16i		−	0.339685i
$418$		−	1.90821e17i		−	1.74977i
$419$	1.31145e17			1.18402			0.592012	−	0.805929i	$-0.298334\pi$
$419$	1.31145e17			1.18402			0.592012	+	0.805929i	$0.298334\pi$
$420$	−4.81566e14	−	6.17212e16i	−0.00428090	−	0.548673i
$421$	−1.44592e17			−1.26565			−0.632823	−	0.774297i	$-0.718104\pi$
$421$	−1.44592e17			−1.26565			−0.632823	+	0.774297i	$0.718104\pi$
$422$			9.63846e15i			0.0830762i
$423$			2.32984e16i			0.197749i
$424$	3.63173e16			0.303554
$425$	−2.21604e15	−	1.42004e17i	−0.0182410	−	1.16889i
$426$	−2.96677e16			−0.240504
$427$			3.25140e17i			2.59591i
$428$			9.50731e16i			0.747607i
$429$	1.32197e17			1.02388
$430$	1.40250e14	+	1.79755e16i	0.00106993	+	0.137131i
$431$	1.23829e17			0.930509			0.465255	−	0.885177i	$-0.345963\pi$
$431$	1.23829e17			0.930509			0.465255	+	0.885177i	$0.345963\pi$
$432$			3.64289e16i			0.269651i
$433$		−	4.74018e15i		−	0.0345639i	−0.999851	−	0.0172820i	$-0.994499\pi$
$433$		−	4.74018e15i		−	0.0345639i	0.999851	−	0.0172820i	$-0.00550129\pi$
$434$	−1.39289e17			−1.00054
$435$	2.94862e16	−	2.30059e14i	0.208659	−	0.00162802i
$436$	6.22286e16			0.433838
$437$			4.16223e16i			0.285889i
$438$		−	6.73754e16i		−	0.455953i
$439$	1.55602e17			1.03752			0.518761	−	0.854920i	$-0.326394\pi$
$439$	1.55602e17			1.03752			0.518761	+	0.854920i	$0.326394\pi$
$440$	1.00017e17	−	7.80359e14i	0.657099	−	0.00512687i
$441$	−7.60982e16			−0.492633
$442$		−	9.49856e16i		−	0.605917i
$443$		−	7.61390e16i		−	0.478611i	−0.970944	−	0.239306i	$-0.923080\pi$
$443$		−	7.61390e16i		−	0.478611i	0.970944	−	0.239306i	$-0.0769198\pi$
$444$	−2.04130e16			−0.126450
$445$	−2.15091e14	−	2.75677e16i	−0.00131305	−	0.168291i
$446$	4.88046e16			0.293619
$447$		−	2.09025e17i		−	1.23936i
$448$		−	3.12331e16i		−	0.182519i
$449$	2.17774e17			1.25431			0.627156	−	0.778894i	$-0.284219\pi$
$449$	2.17774e17			1.25431			0.627156	+	0.778894i	$0.284219\pi$
$450$	8.45767e14	+	5.41967e16i	0.00480141	+	0.307674i
$451$	−2.95381e16			−0.165286
$452$		−	1.19146e17i		−	0.657172i
$453$			3.17430e15i			0.0172588i
$454$	5.37147e16			0.287892
$455$	−1.58046e15	−	2.02564e17i	−0.00835044	−	1.07026i
$456$	−6.79190e16			−0.353769
$457$			3.26108e17i			1.67458i	0.546757	+	0.837291i	$0.315862\pi$
$457$			3.26108e17i			1.67458i	−0.546757	+	0.837291i	$0.684138\pi$
$458$			2.05117e17i			1.03843i
$459$	−2.52621e17			−1.26092
$460$	−2.18159e16	+	1.70214e14i	−0.107361	+	0.000837662i
$461$	1.33954e17			0.649980			0.324990	−	0.945717i	$-0.394639\pi$
$461$	1.33954e17			0.649980			0.324990	+	0.945717i	$0.394639\pi$
$462$			3.01442e17i			1.44222i
$463$		−	3.27858e17i		−	1.54671i	−0.633974	−	0.773355i	$-0.718577\pi$
$463$		−	3.27858e17i		−	1.54671i	0.633974	−	0.773355i	$-0.281423\pi$
$464$	1.49210e16			0.0694117
$465$	−1.58760e17	+	1.23869e15i	−0.728276	+	0.00568221i
$466$	−4.26478e16			−0.192925
$467$			3.01296e17i			1.34411i	0.740503	+	0.672053i	$0.234587\pi$
$467$			3.01296e17i			1.34411i	−0.740503	+	0.672053i	$0.765413\pi$
$468$			3.62519e16i			0.159490i
$469$	−2.13867e17			−0.927942
$470$	−5.85847e14	−	7.50867e16i	−0.00250696	−	0.321312i
$471$	1.28024e17			0.540325
$472$			8.20519e16i			0.341559i
$473$		−	8.77910e16i		−	0.360456i
$474$	−1.64382e17			−0.665727
$475$	−3.33243e17	+	5.20043e15i	−1.33123	+	0.0207745i
$476$	2.16590e17			0.853480
$477$		−	9.61190e16i		−	0.373628i
$478$		−	1.16004e17i		−	0.444827i
$479$	−2.30889e17			−0.873420			−0.436710	−	0.899602i	$-0.643856\pi$
$479$	−2.30889e17			−0.873420			−0.436710	+	0.899602i	$0.643856\pi$
$480$	−2.77754e14	−	3.55991e16i	−0.00103655	−	0.132853i
$481$	−6.69940e16			−0.246657
$482$			1.44581e17i			0.525178i
$483$		−	6.57513e16i		−	0.235639i
$484$	−3.47071e17			−1.22722
$485$	1.74313e17	−	1.36004e15i	0.608148	−	0.00474494i
$486$	1.63594e17			0.563161
$487$		−	1.33518e17i		−	0.453526i	−0.973950	−	0.226763i	$-0.927186\pi$
$487$		−	1.33518e17i		−	0.453526i	0.973950	−	0.226763i	$-0.0728142\pi$
$488$			1.87532e17i			0.628559i
$489$	3.07511e17			1.01708
$490$	2.45251e17	−	1.91351e15i	0.800453	−	0.00624536i
$491$	−4.64217e16			−0.149517			−0.0747586	−	0.997202i	$-0.523819\pi$
$491$	−4.64217e16			−0.149517			−0.0747586	+	0.997202i	$0.523819\pi$
$492$			1.05135e16i			0.0334176i
$493$			1.03472e17i			0.324577i
$494$	−2.22905e17			−0.690071
$495$	−2.06533e15	−	2.64709e17i	−0.00631039	−	0.808789i
$496$	−8.03381e16			−0.242265
$497$		−	2.22021e17i		−	0.660810i
$498$		−	1.03740e17i		−	0.304760i
$499$	6.34243e17			1.83909			0.919543	−	0.392988i	$-0.128559\pi$
$499$	6.34243e17			1.83909			0.919543	+	0.392988i	$0.128559\pi$
$500$	−4.08855e15	−	1.74645e17i	−0.0117021	−	0.499863i
$501$	−4.34066e17			−1.22634
$502$		−	2.62194e17i		−	0.731220i
$503$		−	3.40192e17i		−	0.936552i	−0.883582	−	0.468276i	$-0.844875\pi$
$503$		−	3.40192e17i		−	0.936552i	0.883582	−	0.468276i	$-0.155125\pi$
$504$	−8.26630e16			−0.224653
$505$	4.97943e15	+	6.38202e17i	0.0133594	+	1.71224i
$506$	1.06547e17			0.282205
$507$			1.32991e17i			0.347753i
$508$			1.19949e17i			0.309658i
$509$	1.87368e17			0.477562			0.238781	−	0.971073i	$-0.423252\pi$
$509$	1.87368e17			0.477562			0.238781	+	0.971073i	$0.423252\pi$
$510$	2.46866e17	−	1.92612e15i	0.621234	−	0.00484704i
$511$	5.04209e17			1.25278
$512$		−	1.80144e16i		−	0.0441942i
$513$			5.92831e17i			1.43605i
$514$	2.54599e17			0.608970
$515$	−1.52157e17	+	1.18717e15i	−0.359374	+	0.00280393i
$516$	−3.12475e16			−0.0728773
$517$			3.66718e17i			0.844587i
$518$		−	1.52762e17i		−	0.347435i
$519$	1.53159e17			0.343998
$520$	−9.11565e14	−	1.16833e17i	−0.00202193	−	0.259146i
$521$	−5.24891e17			−1.14980			−0.574902	−	0.818222i	$-0.694960\pi$
$521$	−5.24891e17			−1.14980			−0.574902	+	0.818222i	$0.694960\pi$
$522$		−	3.94907e16i		−	0.0854352i
$523$			5.12722e17i			1.09552i	0.836635	+	0.547761i	$0.184520\pi$
$523$			5.12722e17i			1.09552i	−0.836635	+	0.547761i	$0.815480\pi$
$524$	9.41995e16			0.198790
$525$	5.26429e17	−	8.21518e15i	1.09725	−	0.0171231i
$526$	−2.56319e17			−0.527683
$527$		−	5.57115e17i		−	1.13286i
$528$			1.73863e17i			0.349211i
$529$	4.80796e17			0.953891
$530$	2.41695e15	+	3.09774e17i	0.00473668	+	0.607089i
$531$	2.17162e17			0.420407
$532$		−	5.08277e17i		−	0.972018i
$533$			3.45045e16i			0.0651852i
$534$	4.79221e16			0.0894372
$535$	−8.10942e17	+	6.32719e15i	−1.49517	+	0.0116657i
$536$	−1.23353e17			−0.224687
$537$		−	6.04753e17i		−	1.08829i
$538$		−	6.03866e17i		−	1.07363i
$539$	−1.19779e18			−2.10404
$540$	−3.10727e17	+	2.42437e15i	−0.539286	+	0.00420766i
$541$	−6.25073e17			−1.07189			−0.535943	−	0.844254i	$-0.680044\pi$
$541$	−6.25073e17			−1.07189			−0.535943	+	0.844254i	$0.680044\pi$
$542$		−	4.49611e17i		−	0.761802i
$543$			1.59655e17i			0.267290i
$544$	1.24923e17			0.206657
$545$	4.14136e15	+	5.30789e17i	0.00676964	+	0.867650i
$546$	3.52125e17			0.568781
$547$		−	7.14088e16i		−	0.113981i	−0.998375	−	0.0569907i	$-0.981849\pi$
$547$		−	7.14088e16i		−	0.113981i	0.998375	−	0.0569907i	$-0.0181505\pi$
$548$			1.49897e17i			0.236439i
$549$	4.96330e17			0.773660
$550$	1.33124e16	+	8.53058e17i	0.0205068	+	1.31408i
$551$	2.42820e17			0.369657
$552$		−	3.79235e16i		−	0.0570564i
$553$		−	1.23017e18i		−	1.82916i
$554$	−6.60540e17			−0.970701
$555$	−1.35850e15	−	1.74116e17i	−0.00197313	−	0.252892i
$556$	1.57425e17			0.225989
$557$			3.05107e17i			0.432905i	0.976293	+	0.216453i	$0.0694487\pi$
$557$			3.05107e17i			0.432905i	−0.976293	+	0.216453i	$0.930551\pi$
$558$			2.12626e17i			0.298191i
$559$	−1.02552e17			−0.142156
$560$	2.66408e17	−	2.07859e15i	0.365027	−	0.00284804i
$561$	−1.20568e18			−1.63295
$562$			6.89703e17i			0.923370i
$563$			1.44683e18i			1.91476i	0.288831	+	0.957380i	$0.406733\pi$
$563$			1.44683e18i			1.91476i	−0.288831	+	0.957380i	$0.593267\pi$
$564$	1.30526e17			0.170759
$565$	1.01627e18	−	7.92925e15i	1.31430	−	0.0102546i
$566$	−8.22089e17			−1.05102
$567$		−	4.33758e17i		−	0.548224i
$568$		−	1.28055e17i		−	0.160005i
$569$	−4.28308e17			−0.529087			−0.264543	−	0.964374i	$-0.585221\pi$
$569$	−4.28308e17			−0.529087			−0.264543	+	0.964374i	$0.585221\pi$
$570$	−4.52006e15	−	5.79326e17i	−0.00552024	−	0.707517i
$571$	1.54978e18			1.87126			0.935632	−	0.352978i	$-0.114831\pi$
$571$	1.54978e18			1.87126			0.935632	+	0.352978i	$0.114831\pi$
$572$			5.70606e17i			0.681180i
$573$			4.86510e17i			0.574231i
$574$	−7.86786e16			−0.0918183
$575$	−2.90373e15	−	1.86071e17i	−0.00335055	−	0.214703i
$576$	−4.76777e16			−0.0543963
$577$		−	1.38103e18i		−	1.55797i	−0.627041	−	0.778986i	$-0.715734\pi$
$577$		−	1.38103e18i		−	1.55797i	0.627041	−	0.778986i	$-0.284266\pi$
$578$			2.32402e17i			0.259244i
$579$	6.94468e17			0.766022
$580$	9.93007e14	+	1.27271e17i	0.00108310	+	0.138819i
$581$	7.76349e17			0.837360
$582$			3.03016e17i			0.323196i
$583$		−	1.51292e18i		−	1.59577i
$584$	2.90814e17			0.303341
$585$	−3.09216e17	+	2.41259e15i	−0.318969	+	0.00248869i
$586$	1.02788e18			1.04860
$587$		−	6.66857e17i		−	0.672798i	−0.941720	−	0.336399i	$-0.890791\pi$
$587$		−	6.66857e17i		−	0.672798i	0.941720	−	0.336399i	$-0.109209\pi$
$588$			4.26330e17i			0.425396i
$589$	−1.30739e18			−1.29020
$590$	−6.99875e17	+	5.46062e15i	−0.683097	+	0.00532971i
$591$	5.69494e17			0.549756
$592$		−	8.81091e16i		−	0.0841259i
$593$			7.49253e17i			0.707576i	0.935326	+	0.353788i	$0.115107\pi$
$593$			7.49253e17i			0.707576i	−0.935326	+	0.353788i	$0.884893\pi$
$594$	1.51757e18			1.41754
$595$	1.44142e16	+	1.84744e18i	0.0133178	+	1.70691i
$596$	9.02217e17			0.824537
$597$		−	1.58124e17i		−	0.142943i
$598$		−	1.24462e17i		−	0.111296i
$599$	−7.63979e17			−0.675782			−0.337891	−	0.941185i	$-0.609714\pi$
$599$	−7.63979e17			−0.675782			−0.337891	+	0.941185i	$0.609714\pi$
$600$	3.03630e17	−	4.73829e15i	0.265681	−	0.00414609i
$601$	7.28383e17			0.630486			0.315243	−	0.949011i	$-0.397914\pi$
$601$	7.28383e17			0.630486			0.315243	+	0.949011i	$0.397914\pi$
$602$		−	2.33843e17i		−	0.200238i
$603$			3.26471e17i			0.276555i
$604$	−1.37013e16			−0.0114821
$605$	−2.30978e16	−	2.96040e18i	−0.0191497	−	2.45437i
$606$	−1.10941e18			−0.909958
$607$			1.97367e18i			1.60158i	0.598947	+	0.800789i	$0.295586\pi$
$607$			1.97367e18i			1.60158i	−0.598947	+	0.800789i	$0.704414\pi$
$608$		−	2.93160e17i		−	0.235359i
$609$	−3.83585e17			−0.304684
$610$	−1.59958e18	+	1.24804e16i	−1.25708	+	0.00980808i
$611$	4.28377e17			0.333087
$612$		−	3.30627e17i		−	0.254363i
$613$		−	1.55462e18i		−	1.18340i	−0.806158	−	0.591701i	$-0.798457\pi$
$613$		−	1.55462e18i		−	1.18340i	0.806158	−	0.591701i	$-0.201543\pi$
$614$	2.36221e17			0.177920
$615$	−8.96767e16	+	6.99682e14i	−0.0668331	+	0.000521450i
$616$	−1.30112e18			−0.959494
$617$			1.76969e18i			1.29135i	0.763612	+	0.645675i	$0.223424\pi$
$617$			1.76969e18i			1.29135i	−0.763612	+	0.645675i	$0.776576\pi$
$618$		−	2.64502e17i		−	0.190987i
$619$	−1.17872e18			−0.842213			−0.421106	−	0.907011i	$-0.638358\pi$
$619$	−1.17872e18			−0.842213			−0.421106	+	0.907011i	$0.638358\pi$
$620$	−5.34656e15	−	6.85257e17i	−0.00378032	−	0.484515i
$621$	−3.31015e17			−0.231608
$622$			4.75813e17i			0.329457i
$623$			3.58629e17i			0.245738i
$624$	2.03096e17			0.137721
$625$	1.48939e18	−	4.64967e16i	0.999513	−	0.0312034i
$626$	−8.94459e17			−0.594056
$627$			2.82939e18i			1.85975i
$628$			5.52591e17i			0.359473i
$629$	6.11004e17			0.393382
$630$	−5.50129e15	−	7.05088e17i	−0.00350551	−	0.449293i
$631$	−2.38732e18			−1.50564			−0.752818	−	0.658228i	$-0.771306\pi$
$631$	−2.38732e18			−1.50564			−0.752818	+	0.658228i	$0.771306\pi$
$632$		−	7.09526e17i		−	0.442902i
$633$		−	1.42914e17i		−	0.0882979i
$634$	1.09790e18			0.671399
$635$	−1.02312e18	+	7.98269e15i	−0.619296	+	0.00483192i
$636$	−5.38494e17			−0.322633
$637$			1.39918e18i			0.829788i
$638$		−	6.21586e17i		−	0.364894i
$639$	−3.38917e17			−0.196942
$640$	1.53657e17	−	1.19887e15i	0.0883857	−	0.000689609i
$641$	−1.87490e18			−1.06758			−0.533790	−	0.845617i	$-0.679233\pi$
$641$	−1.87490e18			−1.06758			−0.533790	+	0.845617i	$0.679233\pi$
$642$		−	1.40969e18i		−	0.794597i
$643$		−	2.53520e18i		−	1.41462i	−0.706902	−	0.707312i	$-0.749908\pi$
$643$		−	2.53520e18i		−	1.41462i	0.706902	−	0.707312i	$-0.250092\pi$
$644$	2.83803e17			0.156769
$645$	−2.07955e15	−	2.66531e17i	−0.00113718	−	0.145750i
$646$	2.03295e18			1.10057
$647$		−	3.57429e17i		−	0.191563i	−0.995402	−	0.0957815i	$-0.969465\pi$
$647$		−	3.57429e17i		−	0.191563i	0.995402	−	0.0957815i	$-0.0305350\pi$
$648$		−	2.50180e17i		−	0.132744i
$649$	3.41814e18			1.79556
$650$	9.96487e17	−	1.55507e16i	0.518245	−	0.00808747i
$651$	2.06530e18			1.06343
$652$			1.32731e18i			0.676651i
$653$			9.68553e17i			0.488864i	0.969666	+	0.244432i	$0.0786015\pi$
$653$			9.68553e17i			0.488864i	−0.969666	+	0.244432i	$0.921399\pi$
$654$	−9.22692e17			−0.461107
$655$	6.26905e15	+	8.03490e17i	0.00310194	+	0.397569i
$656$	−4.53796e16			−0.0222324
$657$		−	7.69681e17i		−	0.373367i
$658$			9.76803e17i			0.469179i
$659$	−1.95073e18			−0.927774			−0.463887	−	0.885894i	$-0.653546\pi$
$659$	−1.95073e18			−0.927774			−0.463887	+	0.885894i	$0.653546\pi$
$660$	−1.48300e18	+	1.15707e16i	−0.698401	+	0.00544911i
$661$	−3.27319e18			−1.52638			−0.763188	−	0.646177i	$-0.776367\pi$
$661$	−3.27319e18			−1.52638			−0.763188	+	0.646177i	$0.776367\pi$
$662$			8.32920e16i			0.0384615i
$663$			1.40839e18i			0.644001i
$664$	4.47776e17			0.202754
$665$	4.33543e18	−	3.38262e16i	1.94398	−	0.0151674i
$666$	−2.33194e17			−0.103546
$667$			1.35582e17i			0.0596188i
$668$		−	1.87356e18i		−	0.815871i
$669$	−7.23649e17			−0.312074
$670$	−8.20922e15	−	1.05216e18i	−0.00350603	−	0.449360i
$671$	7.81226e18			3.30430
$672$			4.63108e17i			0.193991i
$673$		−	3.71614e18i		−	1.54168i	−0.637028	−	0.770840i	$-0.719837\pi$
$673$		−	3.71614e18i		−	1.54168i	0.637028	−	0.770840i	$-0.280163\pi$
$674$	2.73107e18			1.12213
$675$	−4.13582e16	−	2.65023e18i	−0.0168301	−	1.07847i
$676$	−5.74032e17			−0.231357
$677$			2.14190e17i			0.0855015i	0.999086	+	0.0427507i	$0.0136121\pi$
$677$			2.14190e17i			0.0855015i	−0.999086	+	0.0427507i	$0.986388\pi$
$678$			1.76663e18i			0.698478i
$679$	−2.26764e18			−0.888017
$680$	8.31373e15	+	1.06555e18i	0.00322469	+	0.413301i
$681$	−7.96452e17			−0.305987
$682$			3.34675e18i			1.27358i
$683$			3.43179e18i			1.29356i	0.762677	+	0.646779i	$0.223884\pi$
$683$			3.43179e18i			1.29356i	−0.762677	+	0.646779i	$0.776116\pi$
$684$	−7.75890e17			−0.289691
$685$	−1.27857e18	+	9.97574e15i	−0.472863	+	0.00368941i
$686$	−3.72149e17			−0.136336
$687$		−	3.04137e18i		−	1.10370i
$688$		−	1.34874e17i		−	0.0484846i
$689$	−1.76729e18			−0.629337
$690$	3.23475e17	−	2.52384e15i	0.114109	−	0.000890313i
$691$	−2.29484e16			−0.00801945			−0.00400972	−	0.999992i	$-0.501276\pi$
$691$	−2.29484e16			−0.00801945			−0.00400972	+	0.999992i	$0.501276\pi$
$692$			6.61084e17i			0.228858i
$693$			3.44360e18i			1.18099i
$694$	−1.17926e18			−0.400656
$695$	1.04768e16	+	1.34278e18i	0.00352635	+	0.451964i
$696$	−2.21241e17			−0.0737745
$697$		−	3.14691e17i		−	0.103961i
$698$			3.96538e17i			0.129785i
$699$	6.32359e17			0.205051
$700$	3.54593e16	+	2.27223e18i	0.0113918	+	0.729988i
$701$	−4.54324e18			−1.44610			−0.723050	−	0.690796i	$-0.757260\pi$
$701$	−4.54324e18			−1.44610			−0.723050	+	0.690796i	$0.757260\pi$
$702$		−	1.77272e18i		−	0.559049i
$703$		−	1.43386e18i		−	0.448018i
$704$	−7.50449e17			−0.232327
$705$	8.68663e15	+	1.11335e18i	0.00266454	+	0.341508i
$706$	−2.26090e18			−0.687149
$707$		−	8.30237e18i		−	2.50021i
$708$		−	1.21662e18i		−	0.363027i
$709$	1.83457e18			0.542417			0.271209	−	0.962521i	$-0.412577\pi$
$709$	1.83457e18			0.542417			0.271209	+	0.962521i	$0.412577\pi$
$710$	1.09227e18	−	8.52218e15i	0.320000	−	0.00249673i
$711$	−1.87786e18			−0.545145
$712$			2.06847e17i			0.0595017i
$713$		−	7.30001e17i		−	0.208085i
$714$	−3.21148e18			−0.907125
$715$	−4.86707e18	+	3.79743e16i	−1.36232	+	0.0106292i
$716$	2.61030e18			0.724030
$717$			1.72004e18i			0.472787i
$718$			2.30254e17i			0.0627189i
$719$	4.11935e18			1.11196			0.555982	−	0.831195i	$-0.312343\pi$
$719$	4.11935e18			1.11196			0.555982	+	0.831195i	$0.312343\pi$
$720$	−3.17299e15	−	4.06675e17i	−0.000848804	−	0.108789i
$721$	1.97942e18			0.524756
$722$		−	2.07938e18i		−	0.546315i
$723$		−	2.14377e18i		−	0.558187i
$724$	−6.89120e17			−0.177826
$725$	−1.08552e18	+	1.69400e16i	−0.277613	+	0.00433229i
$726$	5.14618e18			1.30436
$727$			9.41236e17i			0.236442i	0.992987	+	0.118221i	$0.0377192\pi$
$727$			9.41236e17i			0.236442i	−0.992987	+	0.118221i	$0.962281\pi$
$728$			1.51988e18i			0.378404i
$729$	−3.94725e18			−0.974014
$730$	1.93539e16	+	2.48054e18i	0.00473336	+	0.606664i
$731$	9.35301e17			0.226719
$732$		−	2.78062e18i		−	0.668067i
$733$			3.76919e17i			0.0897577i	0.998992	+	0.0448789i	$0.0142902\pi$
$733$			3.76919e17i			0.0897577i	−0.998992	+	0.0448789i	$0.985710\pi$
$734$	−1.05317e18			−0.248584
$735$	−3.63645e18	+	2.83726e16i	−0.850765	+	0.00663791i
$736$	1.63690e17			0.0379591
$737$			5.13866e18i			1.18117i
$738$			1.20104e17i			0.0273647i
$739$	3.30244e18			0.745841			0.372921	−	0.927863i	$-0.378356\pi$
$739$	3.30244e18			0.745841			0.372921	+	0.927863i	$0.378356\pi$
$740$	7.51541e17	−	5.86373e15i	0.168247	−	0.00131271i
$741$	3.30511e18			0.733445
$742$		−	4.02985e18i		−	0.886470i
$743$			7.15981e18i			1.56126i	0.624995	+	0.780629i	$0.285101\pi$
$743$			7.15981e18i			1.56126i	−0.624995	+	0.780629i	$0.714899\pi$
$744$	1.19121e18			0.257492
$745$	6.00432e16	+	7.69560e18i	0.0128661	+	1.64902i
$746$	−3.18003e18			−0.675506
$747$		−	1.18511e18i		−	0.249559i
$748$		−	5.20408e18i		−	1.08639i
$749$	1.05495e19			2.18324
$750$	6.06228e16	+	2.58954e18i	0.0124376	+	0.531282i
$751$	2.67611e18			0.544307			0.272154	−	0.962254i	$-0.412264\pi$
$751$	2.67611e18			0.544307			0.272154	+	0.962254i	$0.412264\pi$
$752$			5.63393e17i			0.113604i
$753$			3.88767e18i			0.777181i
$754$	−7.26096e17			−0.143906
$755$	−9.11831e14	−	1.16867e17i	−0.000179167	−	0.0229635i
$756$	4.04224e18			0.787464
$757$		−	8.35791e18i		−	1.61426i	−0.590371	−	0.807132i	$-0.701019\pi$
$757$		−	8.35791e18i		−	1.61426i	0.590371	−	0.807132i	$-0.298981\pi$
$758$			2.83705e18i			0.543273i
$759$	−1.57983e18			−0.299943
$760$	2.50055e18	−	1.95100e16i	0.470704	−	0.00367256i
$761$	−1.33084e18			−0.248385			−0.124192	−	0.992258i	$-0.539634\pi$
$761$	−1.33084e18			−0.248385			−0.124192	+	0.992258i	$0.539634\pi$
$762$		−	1.77854e18i		−	0.329121i
$763$		−	6.90503e18i		−	1.26694i
$764$	−2.09993e18			−0.382030
$765$	2.82014e18	−	2.20035e16i	0.508711	−	0.00396910i
$766$	−2.24969e18			−0.402379
$767$		−	3.99285e18i		−	0.708131i
$768$			2.67108e17i			0.0469720i
$769$	−1.81901e18			−0.317186			−0.158593	−	0.987344i	$-0.550696\pi$
$769$	−1.81901e18			−0.317186			−0.158593	+	0.987344i	$0.550696\pi$
$770$	−8.65905e16	−	1.10981e19i	−0.0149720	−	1.91893i
$771$	−3.77506e18			−0.647247
$772$			2.99754e18i			0.509627i
$773$			5.26289e18i			0.887274i	0.896207	+	0.443637i	$0.146312\pi$
$773$			5.26289e18i			0.887274i	−0.896207	+	0.443637i	$0.853688\pi$
$774$	−3.56964e17			−0.0596772
$775$	5.84465e18	−	9.12087e16i	0.968942	−	0.0151208i
$776$	−1.30791e18			−0.215019
$777$			2.26508e18i			0.369272i
$778$		−	2.22680e18i		−	0.360009i
$779$	−7.38491e17			−0.118400
$780$	1.35162e16	+	1.73234e18i	0.00214902	+	0.275435i
$781$	−5.33457e18			−0.841139
$782$			1.13513e18i			0.177501i
$783$			1.93111e18i			0.299471i
$784$	−1.84017e18			−0.283012
$785$	−4.71342e18	+	3.67754e16i	−0.718924	+	0.00560924i
$786$	−1.39674e18			−0.211285
$787$			6.76678e18i			1.01519i	0.861596	+	0.507594i	$0.169465\pi$
$787$			6.76678e18i			1.01519i	−0.861596	+	0.507594i	$0.830535\pi$
$788$			2.45811e18i			0.365748i
$789$	3.80056e18			0.560850
$790$	6.05202e18	−	4.72195e16i	0.885777	−	0.00691107i
$791$	−1.32207e19			−1.91914
$792$			1.98617e18i			0.285959i
$793$		−	9.12577e18i		−	1.30315i
$794$	−7.40094e18			−1.04822
$795$	−3.58372e16	−	4.59317e18i	−0.00503440	−	0.645247i
$796$	6.82511e17			0.0950987
$797$			7.80908e17i			0.107925i	0.998543	+	0.0539623i	$0.0171851\pi$
$797$			7.80908e17i			0.107925i	−0.998543	+	0.0539623i	$0.982815\pi$
$798$			7.53645e18i			1.03311i
$799$	−3.90692e18			−0.531227
$800$	2.04520e16	+	1.31056e18i	0.00275835	+	0.176755i
$801$	5.47451e17			0.0732375
$802$			5.61306e18i			0.744845i
$803$		−	1.21148e19i		−	1.59465i
$804$	1.82901e18			0.238809
$805$	1.88873e16	+	2.42075e18i	0.00244623	+	0.313528i
$806$	3.90946e18			0.502271
$807$			8.95381e18i			1.14112i
$808$		−	4.78858e18i		−	0.605386i
$809$	−3.20569e18			−0.402028			−0.201014	−	0.979588i	$-0.564424\pi$
$809$	−3.20569e18			−0.402028			−0.201014	+	0.979588i	$0.564424\pi$
$810$	2.13395e18	−	1.66496e16i	0.265480	−	0.00207134i
$811$	7.89507e18			0.974362			0.487181	−	0.873301i	$-0.338025\pi$
$811$	7.89507e18			0.974362			0.487181	+	0.873301i	$0.338025\pi$
$812$		−	1.65567e18i		−	0.202703i
$813$			6.66660e18i			0.809684i
$814$	−3.67048e18			−0.442246
$815$	−1.13215e19	+	8.83338e16i	−1.35326	+	0.0105585i
$816$	−1.85229e18			−0.219646
$817$		−	2.19489e18i		−	0.258208i
$818$			8.66717e18i			1.01153i
$819$	4.02259e18			0.465758
$820$	−3.02005e15	−	3.87073e17i	−0.000346916	−	0.0444634i
$821$	3.93857e18			0.448857			0.224429	−	0.974491i	$-0.427948\pi$
$821$	3.93857e18			0.448857			0.224429	+	0.974491i	$0.427948\pi$
$822$		−	2.22259e18i		−	0.251300i
$823$			4.32313e18i			0.484953i	0.970157	+	0.242476i	$0.0779597\pi$
$823$			4.32313e18i			0.484953i	−0.970157	+	0.242476i	$0.922040\pi$
$824$	1.14167e18			0.127062
$825$	−1.97389e17	−	1.26487e19i	−0.0217958	−	1.39667i
$826$	9.10467e18			0.997456
$827$		−	4.71227e18i		−	0.512206i	−0.966650	−	0.256103i	$-0.917561\pi$
$827$		−	4.71227e18i		−	0.512206i	0.966650	−	0.256103i	$-0.0824386\pi$
$828$		−	4.33229e17i		−	0.0467219i
$829$	−2.15058e17			−0.0230118			−0.0115059	−	0.999934i	$-0.503663\pi$
$829$	−2.15058e17			−0.0230118			−0.0115059	+	0.999934i	$0.503663\pi$
$830$	2.97999e16	+	3.81938e18i	0.00316378	+	0.405495i
$831$	9.79413e18			1.03171
$832$			8.76626e17i			0.0916248i
$833$		−	1.27609e19i		−	1.32339i
$834$	−2.33421e18			−0.240193
$835$	1.59809e19	−	1.24687e17i	1.63169	−	0.0127309i
$836$	−1.22125e19			−1.23727
$837$		−	1.03975e19i		−	1.04523i
$838$		−	8.39328e18i		−	0.837231i
$839$	1.32950e19			1.31594			0.657971	−	0.753043i	$-0.271415\pi$
$839$	1.32950e19			1.31594			0.657971	+	0.753043i	$0.271415\pi$
$840$	−3.95016e18	+	3.08202e16i	−0.387971	+	0.00302705i
$841$	−9.46966e18			−0.922912
$842$			9.25392e18i			0.894946i
$843$		−	1.02265e19i		−	0.981408i
$844$	6.16861e17			0.0587438
$845$	−3.82023e16	−	4.89630e18i	−0.00361011	−	0.462700i
$846$	1.49110e18			0.139830
$847$			3.85118e19i			3.58386i
$848$		−	2.32431e18i		−	0.214645i
$849$	1.21895e19			1.11708
$850$	−9.08825e18	+	1.41827e17i	−0.826527	+	0.0128984i
$851$	8.00613e17			0.0722571
$852$			1.89874e18i			0.170062i
$853$			8.46944e18i			0.752811i	0.926455	+	0.376406i	$0.122840\pi$
$853$			8.46944e18i			0.752811i	−0.926455	+	0.376406i	$0.877160\pi$
$854$	2.08090e19			1.83558
$855$	−5.16361e16	−	6.61808e18i	−0.00452036	−	0.579365i
$856$	6.08468e18			0.528638
$857$			1.71134e19i			1.47557i	0.675033	+	0.737787i	$0.264129\pi$
$857$			1.71134e19i			1.47557i	−0.675033	+	0.737787i	$0.735871\pi$
$858$		−	8.46064e18i		−	0.723995i
$859$	−7.13031e18			−0.605554			−0.302777	−	0.953061i	$-0.597914\pi$
$859$	−7.13031e18			−0.605554			−0.302777	+	0.953061i	$0.597914\pi$
$860$	1.15043e18	−	8.97598e15i	0.0969662	−	0.000756557i
$861$	1.16660e18			0.0975895
$862$		−	7.92507e18i		−	0.657969i
$863$			2.60805e18i			0.214905i	0.994210	+	0.107452i	$0.0342693\pi$
$863$			2.60805e18i			0.214905i	−0.994210	+	0.107452i	$0.965731\pi$
$864$	2.33145e18			0.190672
$865$	−5.63882e18	+	4.39956e16i	−0.457703	+	0.00357112i
$866$	−3.03371e17			−0.0244404
$867$		−	3.44593e18i		−	0.275539i
$868$			8.91450e18i			0.707488i
$869$	−2.95577e19			−2.32831
$870$	−1.47238e16	−	1.88711e18i	−0.00115118	−	0.147544i
$871$	6.00266e18			0.465828
$872$		−	3.98263e18i		−	0.306770i
$873$			3.46158e18i			0.264656i
$874$	2.66383e18			0.202154
$875$	−1.93790e19	+	4.53675e17i	−1.45975	+	0.0341737i
$876$	−4.31203e18			−0.322407
$877$		−	2.51744e19i		−	1.86836i	−0.356796	−	0.934182i	$-0.616131\pi$
$877$		−	2.51744e19i		−	1.86836i	0.356796	−	0.934182i	$-0.383869\pi$
$878$		−	9.95855e18i		−	0.733638i
$879$	−1.52409e19			−1.11451
$880$	−4.99430e16	−	6.40108e18i	−0.00362524	−	0.464639i
$881$	9.05516e18			0.652458			0.326229	−	0.945291i	$-0.394222\pi$
$881$	9.05516e18			0.652458			0.326229	+	0.945291i	$0.394222\pi$
$882$			4.87029e18i			0.348344i
$883$			2.14294e19i			1.52148i	0.649057	+	0.760739i	$0.275164\pi$
$883$			2.14294e19i			1.52148i	−0.649057	+	0.760739i	$0.724836\pi$
$884$	−6.07908e18			−0.428448
$885$	1.03774e19	−	8.09671e16i	0.726032	−	0.00566470i
$886$	−4.87290e18			−0.338429
$887$		−	3.82856e18i		−	0.263956i	−0.991253	−	0.131978i	$-0.957867\pi$
$887$		−	3.82856e18i		−	0.263956i	0.991253	−	0.131978i	$-0.0421328\pi$
$888$			1.30644e18i			0.0894136i
$889$	1.33098e19			0.904295
$890$	−1.76434e18	+	1.37658e16i	−0.119000	+	0.000928469i
$891$	−1.04221e19			−0.697828
$892$		−	3.12350e18i		−	0.207620i
$893$			9.16845e18i			0.605008i
$894$	−1.33776e19			−0.876363
$895$	1.73718e17	+	2.22650e19i	0.0112978	+	1.44802i
$896$	−1.99892e18			−0.129061
$897$			1.84545e18i			0.118291i
$898$		−	1.39375e19i		−	0.886932i
$899$	−4.25874e18			−0.269056
$900$	3.46859e18	−	5.41291e16i	0.217559	−	0.00339511i
$901$	1.61182e19			1.00370
$902$			1.89044e18i			0.116875i
$903$			3.46730e18i			0.212824i
$904$	−7.62533e18			−0.464691
$905$	−4.58615e16	−	5.87796e18i	−0.00277480	−	0.355640i
$906$	2.03155e17			0.0122038
$907$		−	1.30005e19i		−	0.775374i	−0.921791	−	0.387687i	$-0.873274\pi$
$907$		−	1.30005e19i		−	0.775374i	0.921791	−	0.387687i	$-0.126726\pi$
$908$		−	3.43774e18i		−	0.203570i
$909$	−1.26737e19			−0.745139
$910$	−1.29641e19	+	1.01149e17i	−0.756786	+	0.00590465i
$911$	−1.73341e18			−0.100469			−0.0502345	−	0.998737i	$-0.515997\pi$
$911$	−1.73341e18			−0.100469			−0.0502345	+	0.998737i	$0.515997\pi$
$912$			4.34682e18i			0.250152i
$913$		−	1.86536e19i		−	1.06587i
$914$	2.08709e19			1.18411
$915$	2.37178e19	−	1.85052e17i	1.33609	−	0.0104246i
$916$	1.31275e19			0.734280
$917$		−	1.04526e19i		−	0.580529i
$918$			1.61677e19i			0.891604i
$919$	−8.77898e18			−0.480721			−0.240361	−	0.970684i	$-0.577266\pi$
$919$	−8.77898e18			−0.480721			−0.240361	+	0.970684i	$0.577266\pi$
$920$	1.08937e16	+	1.39622e18i	0.000592316	+	0.0759159i
$921$	−3.50256e18			−0.189103
$922$		−	8.57306e18i		−	0.459605i
$923$			6.23150e18i			0.331727i
$924$	1.92923e19			1.01980
$925$	1.00031e17	+	6.41000e18i	0.00525067	+	0.336463i
$926$	−2.09829e19			−1.09369
$927$		−	3.02160e18i		−	0.156394i
$928$		−	9.54947e17i		−	0.0490815i
$929$	1.99358e18			0.101749			0.0508746	−	0.998705i	$-0.483799\pi$
$929$	1.99358e18			0.101749			0.0508746	+	0.998705i	$0.483799\pi$
$930$	7.92760e16	+	1.01606e19i	0.00401793	+	0.514969i
$931$	−2.99463e19			−1.50720
$932$			2.72946e18i			0.136419i
$933$		−	7.05510e18i		−	0.350165i
$934$	1.92829e19			0.950426
$935$	4.43891e19	−	3.46336e17i	2.17271	−	0.0169520i
$936$	2.32012e18			0.112776
$937$		−	1.14570e18i		−	0.0553051i	−0.999618	−	0.0276525i	$-0.991197\pi$
$937$		−	1.14570e18i		−	0.0553051i	0.999618	−	0.0276525i	$-0.00880320\pi$
$938$			1.36875e19i			0.656154i
$939$	1.32626e19			0.631395
$940$	−4.80555e18	+	3.74942e16i	−0.227202	+	0.00177269i
$941$	3.92402e19			1.84246			0.921232	−	0.389014i	$-0.127184\pi$
$941$	3.92402e19			1.84246			0.921232	+	0.389014i	$0.127184\pi$
$942$		−	8.19353e18i		−	0.382067i
$943$		−	4.12347e17i		−	0.0190957i
$944$	5.25132e18			0.241519
$945$	2.69014e17	+	3.44790e19i	0.0122876	+	1.57488i
$946$	−5.61863e18			−0.254881
$947$		−	2.02669e19i		−	0.913087i	−0.889701	−	0.456543i	$-0.849087\pi$
$947$		−	2.02669e19i		−	0.913087i	0.889701	−	0.456543i	$-0.150913\pi$
$948$			1.05205e19i			0.470740i
$949$	−1.41517e19			−0.628896
$950$	3.32828e17	+	2.13276e19i	0.0146898	+	0.941322i
$951$	−1.62790e19			−0.713599
$952$		−	1.38618e19i		−	0.603501i
$953$		−	7.79187e18i		−	0.336929i	−0.985708	−	0.168464i	$-0.946119\pi$
$953$		−	7.79187e18i		−	0.336929i	0.985708	−	0.168464i	$-0.0538808\pi$
$954$	−6.15162e18			−0.264195
$955$	−1.39752e17	−	1.79117e19i	−0.00596123	−	0.764037i
$956$	−7.42425e18			−0.314540
$957$			9.21654e18i			0.387829i
$958$			1.47769e19i			0.617601i
$959$	1.66329e19			0.690473
$960$	−2.27834e18	+	1.77762e16i	−0.0939411	+	0.000732954i
$961$	−1.48759e18			−0.0609231
$962$			4.28761e18i			0.174413i
$963$		−	1.61040e19i		−	0.650673i
$964$	9.25320e18			0.371357
$965$	−2.55680e19	+	1.99489e17i	−1.01922	+	0.00795226i
$966$	−4.20808e18			−0.166622
$967$		−	1.54167e19i		−	0.606345i	−0.952936	−	0.303173i	$-0.901954\pi$
$967$		−	1.54167e19i		−	0.606345i	0.952936	−	0.303173i	$-0.0980458\pi$
$968$			2.22125e19i			0.867777i
$969$	−3.01435e19			−1.16974
$970$	−8.70426e16	−	1.11561e19i	−0.00335518	−	0.430026i
$971$	3.87568e17			0.0148396			0.00741982	−	0.999972i	$-0.497638\pi$
$971$	3.87568e17			0.0148396			0.00741982	+	0.999972i	$0.497638\pi$
$972$		−	1.04700e19i		−	0.398215i
$973$		−	1.74682e19i		−	0.659957i
$974$	−8.54516e18			−0.320691
$975$	−1.47754e19	+	2.30577e17i	−0.550819	+	0.00859580i
$976$	1.20020e19			0.444458
$977$		−	5.59657e18i		−	0.205877i	−0.994688	−	0.102938i	$-0.967176\pi$
$977$		−	5.59657e18i		−	0.205877i	0.994688	−	0.102938i	$-0.0328245\pi$
$978$		−	1.96807e19i		−	0.719181i
$979$	8.61690e18			0.312798
$980$	−1.22465e17	−	1.56961e19i	−0.00441613	−	0.566006i
$981$	−1.05406e19			−0.377587
$982$			2.97099e18i			0.105725i
$983$			2.41541e19i			0.853873i	0.904282	+	0.426937i	$0.140407\pi$
$983$			2.41541e19i			0.853873i	−0.904282	+	0.426937i	$0.859593\pi$
$984$	6.72865e17			0.0236298
$985$	−2.09669e19	+	1.63589e17i	−0.731473	+	0.00570715i
$986$	6.62220e18			0.229510
$987$		−	1.44835e19i		−	0.498669i
$988$			1.42659e19i			0.487954i
$989$	1.22555e18			0.0416442
$990$	−1.69414e19	+	1.32181e17i	−0.571900	+	0.00446212i
$991$	−2.43063e19			−0.815154			−0.407577	−	0.913171i	$-0.633626\pi$
$991$	−2.43063e19			−0.815154			−0.407577	+	0.913171i	$0.633626\pi$
$992$			5.14164e18i			0.171307i
$993$		−	1.23501e18i		−	0.0408790i
$994$	−1.42093e19			−0.467263
$995$	4.54216e16	+	5.82159e18i	0.00148393	+	0.190192i
$996$	−6.63939e18			−0.215498
$997$			2.66249e19i			0.858558i	0.903172	+	0.429279i	$0.141232\pi$
$997$			2.66249e19i			0.858558i	−0.903172	+	0.429279i	$0.858768\pi$
$998$		−	4.05916e19i		−	1.30043i
$999$	1.14032e19			0.362954

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.14.b.a.9.3	✓	6
3.2	odd	2		90.14.c.b.19.5		6
4.3	odd	2		80.14.c.b.49.2		6
5.2	odd	4		50.14.a.j.1.3		3
5.3	odd	4		50.14.a.i.1.1		3
5.4	even	2	inner	10.14.b.a.9.4	yes	6
15.14	odd	2		90.14.c.b.19.2		6
20.19	odd	2		80.14.c.b.49.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.14.b.a.9.3	✓	6	1.1	even	1	trivial
10.14.b.a.9.4	yes	6	5.4	even	2	inner
50.14.a.i.1.1		3	5.3	odd	4
50.14.a.j.1.3		3	5.2	odd	4
80.14.c.b.49.2		6	4.3	odd	2
80.14.c.b.49.5		6	20.19	odd	2
90.14.c.b.19.2		6	15.14	odd	2
90.14.c.b.19.5		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)

\(f(q)\)	\(=\)	\(q-64.0000i q^{2} +948.958i q^{3} -4096.00 q^{4} +(-272.592 - 34937.5i) q^{5} +60733.3 q^{6} +454502. i q^{7} +262144. i q^{8} +693802. q^{9} +O(q^{10})\)	\(q-64.0000i q^{2} +948.958i q^{3} -4096.00 q^{4} +(-272.592 - 34937.5i) q^{5} +60733.3 q^{6} +454502. i q^{7} +262144. i q^{8} +693802. q^{9} +(-2.23600e6 + 17445.9i) q^{10} +1.09205e7 q^{11} -3.88693e6i q^{12} -1.27566e7i q^{13} +2.90881e7 q^{14} +(3.31542e7 - 258678. i) q^{15} +1.67772e7 q^{16} +1.16344e8i q^{17} -4.44033e7i q^{18} +2.73026e8 q^{19} +(1.11654e6 + 1.43104e8i) q^{20} -4.31303e8 q^{21} -6.98910e8i q^{22} +1.52448e8i q^{23} -2.48764e8 q^{24} +(-1.22055e9 + 1.90474e7i) q^{25} -8.16422e8 q^{26} +2.17133e9i q^{27} -1.86164e9i q^{28} +8.89364e8 q^{29} +(-1.65554e7 - 2.12187e9i) q^{30} -4.78852e9 q^{31} -1.07374e9i q^{32} +1.03631e10i q^{33} +7.44600e9 q^{34} +(1.58792e10 - 1.23894e8i) q^{35} -2.84181e9 q^{36} -5.25171e9i q^{37} -1.74737e10i q^{38} +1.21055e10 q^{39} +(9.15866e9 - 7.14583e7i) q^{40} -2.70484e9 q^{41} +2.76034e10i q^{42} -8.03912e9i q^{43} -4.47303e10 q^{44} +(-1.89125e8 - 2.42397e10i) q^{45} +9.75667e9 q^{46} +3.35808e10i q^{47} +1.59209e10i q^{48} -1.09683e11 q^{49} +(1.21903e9 + 7.81155e10i) q^{50} -1.10405e11 q^{51} +5.22510e10i q^{52} -1.38540e11i q^{53} +1.38965e11 q^{54} +(-2.97683e9 - 3.81534e11i) q^{55} -1.19145e11 q^{56} +2.59090e11i q^{57} -5.69193e10i q^{58} +3.13003e11 q^{59} +(-1.35800e11 + 1.05955e9i) q^{60} +7.15377e11 q^{61} +3.06465e11i q^{62} +3.15334e11i q^{63} -6.87195e10 q^{64} +(-4.45683e11 + 3.47734e9i) q^{65} +6.63236e11 q^{66} +4.70553e11i q^{67} -4.76544e11i q^{68} -1.44667e11 q^{69} +(-7.92919e9 - 1.01627e12i) q^{70} -4.88492e11 q^{71} +1.81876e11i q^{72} -1.10937e12i q^{73} -3.36110e11 q^{74} +(-1.80751e10 - 1.15825e12i) q^{75} -1.11832e12 q^{76} +4.96338e12i q^{77} -7.74750e11i q^{78} -2.70663e12 q^{79} +(-4.57333e9 - 5.86154e11i) q^{80} -9.54360e11 q^{81} +1.73110e11i q^{82} -1.70813e12i q^{83} +1.76662e12 q^{84} +(4.06476e12 - 3.17144e10i) q^{85} -5.14504e11 q^{86} +8.43969e11i q^{87} +2.86274e12i q^{88} +7.89059e11 q^{89} +(-1.55134e12 + 1.21040e10i) q^{90} +5.79789e12 q^{91} -6.24427e11i q^{92} -4.54411e12i q^{93} +2.14917e12 q^{94} +(-7.44248e10 - 9.53886e12i) q^{95} +1.01894e12 q^{96} +4.98929e12i q^{97} +7.01970e12i q^{98} +7.57665e12 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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