LMFDB - Embedded newform 10.10.b.a.9.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

chi := DirichletCharacter("10.9");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 10 $
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:	$5.15035836164$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{319})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 159x^{2} + 6400 $ x^4 - 159*x^2 + 6400
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			9.4
Root			$8.93029 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	10.9
Dual form			10.10.b.a.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+16.0000i q^{2} +254.606i q^{3} -256.000 q^{4} +(69.4228 - 1395.82i) q^{5} -4073.69 q^{6} +4788.05i q^{7} -4096.00i q^{8} -45141.1 q^{9} +O(q^{10})$	\(q+16.0000i q^{2} +254.606i q^{3} -256.000 q^{4} +(69.4228 - 1395.82i) q^{5} -4073.69 q^{6} +4788.05i q^{7} -4096.00i q^{8} -45141.1 q^{9} +(22333.1 + 1110.77i) q^{10} +22672.8 q^{11} -65179.1i q^{12} +131546. i q^{13} -76608.7 q^{14} +(355383. + 17675.5i) q^{15} +65536.0 q^{16} +16522.2i q^{17} -722257. i q^{18} +173684. q^{19} +(-17772.2 + 357329. i) q^{20} -1.21906e6 q^{21} +362764. i q^{22} +2.08964e6i q^{23} +1.04286e6 q^{24} +(-1.94349e6 - 193803. i) q^{25} -2.10474e6 q^{26} -6.48177e6i q^{27} -1.22574e6i q^{28} +4.08468e6 q^{29} +(-282807. + 5.68613e6i) q^{30} +2.73719e6 q^{31} +1.04858e6i q^{32} +5.77261e6i q^{33} -264356. q^{34} +(6.68324e6 + 332400. i) q^{35} +1.15561e7 q^{36} -1.32992e7i q^{37} +2.77894e6i q^{38} -3.34925e7 q^{39} +(-5.71727e6 - 284356. i) q^{40} +1.49196e7 q^{41} -1.95050e7i q^{42} -2.38880e6i q^{43} -5.80422e6 q^{44} +(-3.13382e6 + 6.30087e7i) q^{45} -3.34343e7 q^{46} -2.41417e7i q^{47} +1.66858e7i q^{48} +1.74282e7 q^{49} +(3.10085e6 - 3.10958e7i) q^{50} -4.20666e6 q^{51} -3.36759e7i q^{52} +1.58870e7i q^{53} +1.03708e8 q^{54} +(1.57401e6 - 3.16470e7i) q^{55} +1.96118e7 q^{56} +4.42209e7i q^{57} +6.53548e7i q^{58} +9.17479e7 q^{59} +(-9.09781e7 - 4.52492e6i) q^{60} -9.24480e7 q^{61} +4.37950e7i q^{62} -2.16137e8i q^{63} -1.67772e7 q^{64} +(1.83615e8 + 9.13233e6i) q^{65} -9.23618e7 q^{66} +5.16583e7i q^{67} -4.22969e6i q^{68} -5.32035e8 q^{69} +(-5.31840e6 + 1.06932e8i) q^{70} +1.36557e8 q^{71} +1.84898e8i q^{72} +2.97223e8i q^{73} +2.12787e8 q^{74} +(4.93434e7 - 4.94823e8i) q^{75} -4.44631e7 q^{76} +1.08558e8i q^{77} -5.35880e8i q^{78} -3.08136e8 q^{79} +(4.54970e6 - 9.14763e7i) q^{80} +7.61784e8 q^{81} +2.38714e8i q^{82} -6.97423e7i q^{83} +3.12080e8 q^{84} +(2.30620e7 + 1.14702e6i) q^{85} +3.82208e7 q^{86} +1.03998e9i q^{87} -9.28676e7i q^{88} +7.43324e8 q^{89} +(-1.00814e9 - 5.01411e7i) q^{90} -6.29850e8 q^{91} -5.34949e8i q^{92} +6.96904e8i q^{93} +3.86266e8 q^{94} +(1.20576e7 - 2.42431e8i) q^{95} -2.66973e8 q^{96} -1.60553e9i q^{97} +2.78852e8i q^{98} -1.02347e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 1024 q^{4} - 2580 q^{5} - 4864 q^{6} - 71972 q^{9}+O(q^{10}) $ 4 * q - 1024 * q^4 - 2580 * q^5 - 4864 * q^6 - 71972 * q^9	\( 4 q - 1024 q^{4} - 2580 q^{5} - 4864 q^{6} - 71972 q^{9} + 55040 q^{10} - 103632 q^{11} + 185088 q^{14} + 644240 q^{15} + 262144 q^{16} + 317520 q^{19} + 660480 q^{20} - 4607632 q^{21} + 1245184 q^{24} - 401100 q^{25} - 5881344 q^{26} + 6668280 q^{29} - 5029120 q^{30} + 19247488 q^{31} - 2977792 q^{34} + 6511920 q^{35} + 18424832 q^{36} - 56263584 q^{39} - 14090240 q^{40} + 22774248 q^{41} + 26529792 q^{44} - 31158860 q^{45} - 31649024 q^{46} - 107972628 q^{49} - 22003200 q^{50} + 7292288 q^{51} + 302103040 q^{54} + 205671440 q^{55} - 47382528 q^{56} + 254661360 q^{59} - 164925440 q^{60} - 286581832 q^{61} - 67108864 q^{64} + 401103840 q^{65} - 429298688 q^{66} - 1289928464 q^{69} - 470536960 q^{70} + 802871328 q^{71} + 1078414848 q^{74} + 279560800 q^{75} - 81285120 q^{76} - 1033168320 q^{79} - 169082880 q^{80} + 1276755764 q^{81} + 1179553792 q^{84} + 95745920 q^{85} + 337295616 q^{86} - 276356760 q^{89} - 1921304320 q^{90} - 155016672 q^{91} + 1457997568 q^{94} + 64690800 q^{95} - 318767104 q^{96} - 3410843824 q^{99}+O(q^{100}) \) 4 * q - 1024 * q^4 - 2580 * q^5 - 4864 * q^6 - 71972 * q^9 + 55040 * q^10 - 103632 * q^11 + 185088 * q^14 + 644240 * q^15 + 262144 * q^16 + 317520 * q^19 + 660480 * q^20 - 4607632 * q^21 + 1245184 * q^24 - 401100 * q^25 - 5881344 * q^26 + 6668280 * q^29 - 5029120 * q^30 + 19247488 * q^31 - 2977792 * q^34 + 6511920 * q^35 + 18424832 * q^36 - 56263584 * q^39 - 14090240 * q^40 + 22774248 * q^41 + 26529792 * q^44 - 31158860 * q^45 - 31649024 * q^46 - 107972628 * q^49 - 22003200 * q^50 + 7292288 * q^51 + 302103040 * q^54 + 205671440 * q^55 - 47382528 * q^56 + 254661360 * q^59 - 164925440 * q^60 - 286581832 * q^61 - 67108864 * q^64 + 401103840 * q^65 - 429298688 * q^66 - 1289928464 * q^69 - 470536960 * q^70 + 802871328 * q^71 + 1078414848 * q^74 + 279560800 * q^75 - 81285120 * q^76 - 1033168320 * q^79 - 169082880 * q^80 + 1276755764 * q^81 + 1179553792 * q^84 + 95745920 * q^85 + 337295616 * q^86 - 276356760 * q^89 - 1921304320 * q^90 - 155016672 * q^91 + 1457997568 * q^94 + 64690800 * q^95 - 318767104 * q^96 - 3410843824 * 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 $

$2$			16.0000i			0.707107i
$2$			16.0000i			0.707107i
$3$			254.606i			1.81477i	0.420296	+	0.907387i	$0.361926\pi$
$3$			254.606i			1.81477i	−0.420296	+	0.907387i	$0.638074\pi$
$4$	−256.000			−0.500000
$5$	69.4228	−	1395.82i	0.0496749	−	0.998765i
$5$	69.4228	−	1395.82i	0.0496749	−	0.998765i
$6$	−4073.69			−1.28324
$7$			4788.05i			0.753732i	0.926268	+	0.376866i	$0.122998\pi$
$7$			4788.05i			0.753732i	−0.926268	+	0.376866i	$0.877002\pi$
$8$		−	4096.00i		−	0.353553i
$9$	−45141.1			−2.29340
$10$	22333.1	+	1110.77i	0.706234	+	0.0351255i
$11$	22672.8			0.466914			0.233457	−	0.972367i	$-0.424996\pi$
$11$	22672.8			0.466914			0.233457	+	0.972367i	$0.424996\pi$
$12$		−	65179.1i		−	0.907387i
$13$			131546.i			1.27742i	0.769447	+	0.638711i	$0.220532\pi$
$13$			131546.i			1.27742i	−0.769447	+	0.638711i	$0.779468\pi$
$14$	−76608.7			−0.532969
$15$	355383.	+	17675.5i	1.81253	+	0.0901488i
$16$	65536.0			0.250000
$17$			16522.2i			0.0479787i	0.999712	+	0.0239894i	$0.00763679\pi$
$17$			16522.2i			0.0479787i	−0.999712	+	0.0239894i	$0.992363\pi$
$18$		−	722257.i		−	1.62168i
$19$	173684.			0.305751			0.152876	−	0.988245i	$-0.451147\pi$
$19$	173684.			0.305751			0.152876	+	0.988245i	$0.451147\pi$
$20$	−17772.2	+	357329.i	−0.0248375	+	0.499383i
$21$	−1.21906e6			−1.36785
$22$			362764.i			0.330158i
$23$			2.08964e6i			1.55703i	0.627626	+	0.778515i	$0.284027\pi$
$23$			2.08964e6i			1.55703i	−0.627626	+	0.778515i	$0.715973\pi$
$24$	1.04286e6			0.641619
$25$	−1.94349e6	−	193803.i	−0.995065	−	0.0992272i
$26$	−2.10474e6			−0.903273
$27$		−	6.48177e6i		−	2.34724i
$28$		−	1.22574e6i		−	0.376866i
$29$	4.08468e6			1.07242			0.536212	−	0.844083i	$-0.319855\pi$
$29$	4.08468e6			1.07242			0.536212	+	0.844083i	$0.319855\pi$
$30$	−282807.	+	5.68613e6i	−0.0637448	+	1.28165i
$31$	2.73719e6			0.532325			0.266163	−	0.963928i	$-0.414244\pi$
$31$	2.73719e6			0.532325			0.266163	+	0.963928i	$0.414244\pi$
$32$			1.04858e6i			0.176777i
$33$			5.77261e6i			0.847344i
$34$	−264356.			−0.0339261
$35$	6.68324e6	+	332400.i	0.752802	+	0.0374416i
$36$	1.15561e7			1.14670
$37$		−	1.32992e7i		−	1.16659i	−0.812261	−	0.583294i	$-0.801764\pi$
$37$		−	1.32992e7i		−	1.16659i	0.812261	−	0.583294i	$-0.198236\pi$
$38$			2.77894e6i			0.216199i
$39$	−3.34925e7			−2.31823
$40$	−5.71727e6	−	284356.i	−0.353117	−	0.0175627i
$41$	1.49196e7			0.824575			0.412288	−	0.911054i	$-0.364730\pi$
$41$	1.49196e7			0.824575			0.412288	+	0.911054i	$0.364730\pi$
$42$		−	1.95050e7i		−	0.967218i
$43$		−	2.38880e6i		−	0.106554i	−0.998580	−	0.0532772i	$-0.983033\pi$
$43$		−	2.38880e6i		−	0.106554i	0.998580	−	0.0532772i	$-0.0169667\pi$
$44$	−5.80422e6			−0.233457
$45$	−3.13382e6	+	6.30087e7i	−0.113925	+	2.29057i
$46$	−3.34343e7			−1.10099
$47$		−	2.41417e7i		−	0.721650i	−0.932634	−	0.360825i	$-0.882495\pi$
$47$		−	2.41417e7i		−	0.721650i	0.932634	−	0.360825i	$-0.117505\pi$
$48$			1.66858e7i			0.453693i
$49$	1.74282e7			0.431888
$50$	3.10085e6	−	3.10958e7i	0.0701642	−	0.703617i
$51$	−4.20666e6			−0.0870706
$52$		−	3.36759e7i		−	0.638711i
$53$			1.58870e7i			0.276568i	0.990393	+	0.138284i	$0.0441586\pi$
$53$			1.58870e7i			0.276568i	−0.990393	+	0.138284i	$0.955841\pi$
$54$	1.03708e8			1.65975
$55$	1.57401e6	−	3.16470e7i	0.0231939	−	0.466338i
$56$	1.96118e7			0.266485
$57$			4.42209e7i			0.554869i
$58$			6.53548e7i			0.758319i
$59$	9.17479e7			0.985739			0.492870	−	0.870103i	$-0.335948\pi$
$59$	9.17479e7			0.985739			0.492870	+	0.870103i	$0.335948\pi$
$60$	−9.09781e7	−	4.52492e6i	−0.906267	−	0.0450744i
$61$	−9.24480e7			−0.854896			−0.427448	−	0.904040i	$-0.640587\pi$
$61$	−9.24480e7			−0.854896			−0.427448	+	0.904040i	$0.640587\pi$
$62$			4.37950e7i			0.376411i
$63$		−	2.16137e8i		−	1.72861i
$64$	−1.67772e7			−0.125000
$65$	1.83615e8	+	9.13233e6i	1.27584	+	0.0634558i
$66$	−9.23618e7			−0.599163
$67$			5.16583e7i			0.313187i	0.987663	+	0.156593i	$0.0500512\pi$
$67$			5.16583e7i			0.313187i	−0.987663	+	0.156593i	$0.949949\pi$
$68$		−	4.22969e6i		−	0.0239894i
$69$	−5.32035e8			−2.82566
$70$	−5.31840e6	+	1.06932e8i	−0.0264752	+	0.532311i
$71$	1.36557e8			0.637751			0.318876	−	0.947797i	$-0.396695\pi$
$71$	1.36557e8			0.637751			0.318876	+	0.947797i	$0.396695\pi$
$72$			1.84898e8i			0.810841i
$73$			2.97223e8i			1.22498i	0.790478	+	0.612491i	$0.209832\pi$
$73$			2.97223e8i			1.22498i	−0.790478	+	0.612491i	$0.790168\pi$
$74$	2.12787e8			0.824902
$75$	4.93434e7	−	4.94823e8i	0.180075	−	1.80582i
$76$	−4.44631e7			−0.152876
$77$			1.08558e8i			0.351928i
$78$		−	5.35880e8i		−	1.63924i
$79$	−3.08136e8			−0.890062			−0.445031	−	0.895515i	$-0.646807\pi$
$79$	−3.08136e8			−0.890062			−0.445031	+	0.895515i	$0.646807\pi$
$80$	4.54970e6	−	9.14763e7i	0.0124187	−	0.249691i
$81$	7.61784e8			1.96630
$82$			2.38714e8i			0.583063i
$83$		−	6.97423e7i		−	0.161304i	−0.996742	−	0.0806519i	$-0.974300\pi$
$83$		−	6.97423e7i		−	0.161304i	0.996742	−	0.0806519i	$-0.0257002\pi$
$84$	3.12080e8			0.683927
$85$	2.30620e7	+	1.14702e6i	0.0479195	+	0.00238334i
$86$	3.82208e7			0.0753453
$87$			1.03998e9i			1.94621i
$88$		−	9.28676e7i		−	0.165079i
$89$	7.43324e8			1.25581			0.627904	−	0.778291i	$-0.283913\pi$
$89$	7.43324e8			1.25581			0.627904	+	0.778291i	$0.283913\pi$
$90$	−1.00814e9	−	5.01411e7i	−1.61968	−	0.0805569i
$91$	−6.29850e8			−0.962834
$92$		−	5.34949e8i		−	0.778515i
$93$			6.96904e8i			0.966050i
$94$	3.86266e8			0.510284
$95$	1.20576e7	−	2.42431e8i	0.0151882	−	0.305374i
$96$	−2.66973e8			−0.320810
$97$		−	1.60553e9i		−	1.84139i	−0.390284	−	0.920694i	$-0.627623\pi$
$97$		−	1.60553e9i		−	1.84139i	0.390284	−	0.920694i	$-0.372377\pi$
$98$			2.78852e8i			0.305391i
$99$	−1.02347e9			−1.07082
$100$	4.97532e8	+	4.96136e7i	0.497532	+	0.0496136i
$101$	−1.27833e9			−1.22236			−0.611178	−	0.791494i	$-0.709304\pi$
$101$	−1.27833e9			−1.22236			−0.611178	+	0.791494i	$0.709304\pi$
$102$		−	6.73065e7i		−	0.0615682i
$103$		−	1.66282e9i		−	1.45572i	−0.685725	−	0.727861i	$-0.740515\pi$
$103$		−	1.66282e9i		−	1.45572i	0.685725	−	0.727861i	$-0.259485\pi$
$104$	5.38814e8			0.451637
$105$	−8.46309e7	+	1.70159e9i	−0.0679480	+	1.36616i
$106$	−2.54193e8			−0.195563
$107$			1.90635e9i			1.40597i	0.711207	+	0.702983i	$0.248149\pi$
$107$			1.90635e9i			1.40597i	−0.711207	+	0.702983i	$0.751851\pi$
$108$			1.65933e9i			1.17362i
$109$	−6.12845e8			−0.415845			−0.207922	−	0.978145i	$-0.566670\pi$
$109$	−6.12845e8			−0.415845			−0.207922	+	0.978145i	$0.566670\pi$
$110$	5.06352e8	+	2.51841e7i	0.329751	+	0.0164006i
$111$	3.38605e9			2.11709
$112$			3.13789e8i			0.188433i
$113$		−	1.52122e9i		−	0.877687i	−0.898564	−	0.438843i	$-0.855388\pi$
$113$		−	1.52122e9i		−	0.877687i	0.898564	−	0.438843i	$-0.144612\pi$
$114$	−7.07534e8			−0.392352
$115$	2.91676e9	+	1.45069e8i	1.55511	+	0.0773454i
$116$	−1.04568e9			−0.536212
$117$		−	5.93815e9i		−	2.92964i
$118$			1.46797e9i			0.697023i
$119$	−7.91092e7			−0.0361631
$120$	7.23987e7	−	1.45565e9i	0.0318724	−	0.640827i
$121$	−1.84389e9			−0.781991
$122$		−	1.47917e9i		−	0.604503i
$123$			3.79862e9i			1.49642i
$124$	−7.00720e8			−0.266163
$125$	−4.05436e8	+	2.69930e9i	−0.148535	+	0.988907i
$126$	3.45820e9			1.22231
$127$			4.88293e8i			0.166557i	0.996526	+	0.0832787i	$0.0265392\pi$
$127$			4.88293e8i			0.166557i	−0.996526	+	0.0832787i	$0.973461\pi$
$128$		−	2.68435e8i		−	0.0883883i
$129$	6.08202e8			0.193372
$130$	−1.46117e8	+	2.93784e9i	−0.0448700	+	0.902158i
$131$	−4.98938e9			−1.48022			−0.740110	−	0.672486i	$-0.765226\pi$
$131$	−4.98938e9			−1.48022			−0.740110	+	0.672486i	$0.765226\pi$
$132$		−	1.47779e9i		−	0.423672i
$133$			8.31606e8i			0.230455i
$134$	−8.26533e8			−0.221457
$135$	−9.04736e9	−	4.49983e8i	−2.34434	−	0.116599i
$136$	6.76751e7			0.0169630
$137$			1.31314e9i			0.318470i	0.987241	+	0.159235i	$0.0509028\pi$
$137$			1.31314e9i			0.318470i	−0.987241	+	0.159235i	$0.949097\pi$
$138$		−	8.51256e9i		−	1.99804i
$139$	6.81739e9			1.54900			0.774500	−	0.632574i	$-0.218002\pi$
$139$	6.81739e9			1.54900			0.774500	+	0.632574i	$0.218002\pi$
$140$	−1.71091e9	−	8.50943e7i	−0.376401	−	0.0187208i
$141$	6.14660e9			1.30963
$142$			2.18491e9i			0.450958i
$143$			2.98252e9i			0.596446i
$144$	−2.95837e9			−0.573351
$145$	2.83570e8	−	5.70146e9i	0.0532726	−	1.07110i
$146$	−4.75557e9			−0.866193
$147$			4.43733e9i			0.783778i
$148$			3.40459e9i			0.583294i
$149$	3.84585e9			0.639226			0.319613	−	0.947548i	$-0.396447\pi$
$149$	3.84585e9			0.639226			0.319613	+	0.947548i	$0.396447\pi$
$150$	7.91716e9	+	7.89494e8i	1.27691	+	0.127332i
$151$	4.08263e9			0.639063			0.319532	−	0.947576i	$-0.396474\pi$
$151$	4.08263e9			0.639063			0.319532	+	0.947576i	$0.396474\pi$
$152$		−	7.11409e8i		−	0.108099i
$153$		−	7.45832e8i		−	0.110035i
$154$	−1.73693e9			−0.248851
$155$	1.90023e8	−	3.82061e9i	0.0264432	−	0.531668i
$156$	8.57408e9			1.15912
$157$			4.74150e8i			0.0622826i	0.999515	+	0.0311413i	$0.00991419\pi$
$157$			4.74150e8i			0.0622826i	−0.999515	+	0.0311413i	$0.990086\pi$
$158$		−	4.93017e9i		−	0.629369i
$159$	−4.04493e9			−0.501908
$160$	1.46362e9	+	7.27951e7i	0.176558	+	0.00878137i
$161$	−1.00053e10			−1.17358
$162$			1.21885e10i			1.39038i
$163$		−	5.77882e9i		−	0.641203i	−0.947214	−	0.320601i	$-0.896115\pi$
$163$		−	5.77882e9i		−	0.641203i	0.947214	−	0.320601i	$-0.103885\pi$
$164$	−3.81942e9			−0.412288
$165$	8.05751e9	+	4.00751e8i	0.846298	+	0.0420918i
$166$	1.11588e9			0.114059
$167$		−	3.79221e9i		−	0.377284i	−0.982046	−	0.188642i	$-0.939591\pi$
$167$		−	3.79221e9i		−	0.377284i	0.982046	−	0.188642i	$-0.0604085\pi$
$168$			4.99329e9i			0.483609i
$169$	−6.69997e9			−0.631805
$170$	−1.83523e7	+	3.68992e8i	−0.00168528	+	0.0338842i
$171$	−7.84027e9			−0.701211
$172$			6.11532e8i			0.0532772i
$173$		−	1.42923e9i		−	0.121310i	−0.998159	−	0.0606548i	$-0.980681\pi$
$173$		−	1.42923e9i		−	0.121310i	0.998159	−	0.0606548i	$-0.0193189\pi$
$174$	−1.66397e10			−1.37618
$175$	9.27939e8	−	9.30550e9i	0.0747908	−	0.750012i
$176$	1.48588e9			0.116729
$177$			2.33595e10i			1.78889i
$178$			1.18932e10i			0.887990i
$179$	1.24763e10			0.908340			0.454170	−	0.890915i	$-0.349936\pi$
$179$	1.24763e10			0.908340			0.454170	+	0.890915i	$0.349936\pi$
$180$	8.02258e8	−	1.61302e10i	0.0569624	−	1.14529i
$181$	−1.08573e10			−0.751913			−0.375956	−	0.926637i	$-0.622686\pi$
$181$	−1.08573e10			−0.751913			−0.375956	+	0.926637i	$0.622686\pi$
$182$		−	1.00776e10i		−	0.680826i
$183$		−	2.35378e10i		−	1.55144i
$184$	8.55918e9			0.550493
$185$	−1.85632e10	−	9.23268e8i	−1.16515	−	0.0579502i
$186$	−1.11505e10			−0.683100
$187$			3.74605e8i			0.0224020i
$188$			6.18026e9i			0.360825i
$189$	3.10350e10			1.76919
$190$	3.87889e9	+	1.92922e8i	0.215932	+	0.0107397i
$191$	2.91949e10			1.58729			0.793646	−	0.608379i	$-0.208180\pi$
$191$	2.91949e10			1.58729			0.793646	+	0.608379i	$0.208180\pi$
$192$		−	4.27158e9i		−	0.226847i
$193$			5.33710e8i			0.0276883i	0.999904	+	0.0138442i	$0.00440688\pi$
$193$			5.33710e8i			0.0276883i	−0.999904	+	0.0138442i	$0.995593\pi$
$194$	2.56885e10			1.30206
$195$	−2.32514e9	+	4.67494e10i	−0.115158	+	2.31537i
$196$	−4.46163e9			−0.215944
$197$			2.85727e10i			1.35162i	0.737077	+	0.675809i	$0.236205\pi$
$197$			2.85727e10i			1.35162i	−0.737077	+	0.675809i	$0.763795\pi$
$198$		−	1.63756e10i		−	0.757186i
$199$	−2.44466e10			−1.10504			−0.552522	−	0.833498i	$-0.686334\pi$
$199$	−2.44466e10			−1.10504			−0.552522	+	0.833498i	$0.686334\pi$
$200$	−7.93818e8	+	7.96052e9i	−0.0350821	+	0.351809i
$201$	−1.31525e10			−0.568363
$202$		−	2.04533e10i		−	0.864336i
$203$			1.95576e10i			0.808321i
$204$	1.07690e9			0.0435353
$205$	1.03576e9	−	2.08251e10i	0.0409607	−	0.823557i
$206$	2.66051e10			1.02935
$207$		−	9.43287e10i		−	3.57090i
$208$			8.62103e9i			0.319355i
$209$	3.93789e9			0.142760
$210$	−2.72254e10	−	1.35409e9i	−0.966024	−	0.0480465i
$211$	2.94476e10			1.02277			0.511385	−	0.859351i	$-0.329132\pi$
$211$	2.94476e10			1.02277			0.511385	+	0.859351i	$0.329132\pi$
$212$		−	4.06708e9i		−	0.138284i
$213$			3.47682e10i			1.15737i
$214$	−3.05015e10			−0.994168
$215$	−3.33433e9	−	1.65837e8i	−0.106423	−	0.00529308i
$216$	−2.65493e10			−0.829873
$217$			1.31058e10i			0.401231i
$218$		−	9.80551e9i		−	0.294047i
$219$	−7.56747e10			−2.22307
$220$	−4.02946e8	+	8.10164e9i	−0.0115970	+	0.233169i
$221$	−2.17344e9			−0.0612891
$222$			5.41768e10i			1.49701i
$223$			3.39795e10i			0.920123i	0.887887	+	0.460061i	$0.152173\pi$
$223$			3.39795e10i			0.920123i	−0.887887	+	0.460061i	$0.847827\pi$
$224$	−5.02063e9			−0.133242
$225$	8.77310e10	+	8.74848e9i	2.28209	+	0.227568i
$226$	2.43395e10			0.620618
$227$		−	1.56120e10i		−	0.390250i	−0.980778	−	0.195125i	$-0.937489\pi$
$227$		−	1.56120e10i		−	0.390250i	0.980778	−	0.195125i	$-0.0625112\pi$
$228$		−	1.13205e10i		−	0.277435i
$229$	−5.39130e10			−1.29549			−0.647744	−	0.761858i	$-0.724287\pi$
$229$	−5.39130e10			−1.29549			−0.647744	+	0.761858i	$0.724287\pi$
$230$	−2.32110e9	+	4.66682e10i	−0.0546914	+	1.09963i
$231$	−2.76395e10			−0.638670
$232$		−	1.67308e10i		−	0.379159i
$233$		−	7.59413e10i		−	1.68802i	−0.536330	−	0.844008i	$-0.680190\pi$
$233$		−	7.59413e10i		−	1.68802i	0.536330	−	0.844008i	$-0.319810\pi$
$234$	9.50104e10			2.07157
$235$	−3.36973e10	−	1.67598e9i	−0.720759	−	0.0358479i
$236$	−2.34875e10			−0.492870
$237$		−	7.84532e10i		−	1.61526i
$238$		−	1.26575e9i		−	0.0255712i
$239$	6.70401e10			1.32906			0.664529	−	0.747262i	$-0.268632\pi$
$239$	6.70401e10			1.32906			0.664529	+	0.747262i	$0.268632\pi$
$240$	2.32904e10	+	1.15838e9i	0.453133	+	0.0225372i
$241$	3.19687e10			0.610447			0.305223	−	0.952281i	$-0.401269\pi$
$241$	3.19687e10			0.610447			0.305223	+	0.952281i	$0.401269\pi$
$242$		−	2.95023e10i		−	0.552951i
$243$			6.63739e10i			1.22115i
$244$	2.36667e10			0.427448
$245$	1.20992e9	−	2.43266e10i	0.0214540	−	0.431355i
$246$	−6.07779e10			−1.05813
$247$			2.28475e10i			0.390573i
$248$		−	1.12115e10i		−	0.188205i
$249$	1.77568e10			0.292730
$250$	−4.31887e10	−	6.48698e9i	−0.699263	−	0.105030i
$251$	7.52832e10			1.19720			0.598600	−	0.801048i	$-0.295724\pi$
$251$	7.52832e10			1.19720			0.598600	+	0.801048i	$0.295724\pi$
$252$			5.53312e10i			0.864306i
$253$			4.73780e10i			0.727000i
$254$	−7.81269e9			−0.117774
$255$	−2.92038e8	+	5.87172e9i	−0.00432522	+	0.0869631i
$256$	4.29497e9			0.0625000
$257$			8.40723e10i			1.20214i	0.799197	+	0.601069i	$0.205258\pi$
$257$			8.40723e10i			1.20214i	−0.799197	+	0.601069i	$0.794742\pi$
$258$			9.73123e9i			0.136735i
$259$	6.36771e10			0.879295
$260$	−4.70054e10	−	2.33788e9i	−0.637922	−	0.0317279i
$261$	−1.84387e11			−2.45950
$262$		−	7.98301e10i		−	1.04667i
$263$		−	1.14528e11i		−	1.47608i	−0.674758	−	0.738039i	$-0.735752\pi$
$263$		−	1.14528e11i		−	1.47608i	0.674758	−	0.738039i	$-0.264248\pi$
$264$	2.36446e10			0.299581
$265$	2.21754e10	+	1.10292e9i	0.276226	+	0.0137385i
$266$	−1.33057e10			−0.162956
$267$			1.89255e11i			2.27901i
$268$		−	1.32245e10i		−	0.156593i
$269$	−9.83288e10			−1.14497			−0.572487	−	0.819914i	$-0.694021\pi$
$269$	−9.83288e10			−1.14497			−0.572487	+	0.819914i	$0.694021\pi$
$270$	7.19973e9	−	1.44758e11i	0.0824478	−	1.65770i
$271$	−2.22694e9			−0.0250811			−0.0125406	−	0.999921i	$-0.503992\pi$
$271$	−2.22694e9			−0.0250811			−0.0125406	+	0.999921i	$0.503992\pi$
$272$			1.08280e9i			0.0119947i
$273$		−	1.60364e11i		−	1.74733i
$274$	−2.10103e10			−0.225193
$275$	−4.40642e10	−	4.39405e9i	−0.464610	−	0.0463306i
$276$	1.36201e11			1.41283
$277$		−	2.36816e10i		−	0.241686i	−0.992672	−	0.120843i	$-0.961440\pi$
$277$		−	2.36816e10i		−	0.241686i	0.992672	−	0.120843i	$-0.0385598\pi$
$278$			1.09078e11i			1.09531i
$279$	−1.23560e11			−1.22084
$280$	1.36151e9	−	2.73745e10i	0.0132376	−	0.266156i
$281$	1.30111e9			0.0124490			0.00622451	−	0.999981i	$-0.498019\pi$
$281$	1.30111e9			0.0124490			0.00622451	+	0.999981i	$0.498019\pi$
$282$			9.83456e10i			0.926049i
$283$			1.62403e11i			1.50507i	0.658553	+	0.752534i	$0.271169\pi$
$283$			1.62403e11i			1.50507i	−0.658553	+	0.752534i	$0.728831\pi$
$284$	−3.49586e10			−0.318876
$285$	6.17243e10	+	3.06994e9i	0.554184	+	0.0275631i
$286$	−4.77203e10			−0.421751
$287$			7.14358e10i			0.621509i
$288$		−	4.73338e10i		−	0.405420i
$289$	1.18315e11			0.997698
$290$	9.12234e10	+	4.53712e9i	0.757382	+	0.0376694i
$291$	4.08777e11			3.34170
$292$		−	7.60891e10i		−	0.612491i
$293$		−	2.01290e10i		−	0.159557i	−0.996813	−	0.0797787i	$-0.974579\pi$
$293$		−	2.01290e10i		−	0.159557i	0.996813	−	0.0797787i	$-0.0254214\pi$
$294$	−7.09972e10			−0.554215
$295$	6.36940e9	−	1.28063e11i	0.0489665	−	0.984522i
$296$	−5.44735e10			−0.412451
$297$		−	1.46960e11i		−	1.09596i
$298$			6.15336e10i			0.452001i
$299$	−2.74885e11			−1.98898
$300$	−1.26319e10	+	1.26675e11i	−0.0900375	+	0.902909i
$301$	1.14377e10			0.0803135
$302$			6.53221e10i			0.451886i
$303$		−	3.25471e11i		−	2.21830i
$304$	1.13825e10			0.0764378
$305$	−6.41800e9	+	1.29041e11i	−0.0424669	+	0.853841i
$306$	1.19333e10			0.0778062
$307$			1.28834e11i			0.827766i	0.910330	+	0.413883i	$0.135828\pi$
$307$			1.28834e11i			0.827766i	−0.910330	+	0.413883i	$0.864172\pi$
$308$		−	2.77909e10i		−	0.175964i
$309$	4.23364e11			2.64180
$310$	6.11298e10	+	3.04037e9i	0.375946	+	0.0186982i
$311$	−2.16554e11			−1.31264			−0.656320	−	0.754483i	$-0.727888\pi$
$311$	−2.16554e11			−1.31264			−0.656320	+	0.754483i	$0.727888\pi$
$312$			1.37185e11i			0.819618i
$313$			2.10212e11i			1.23796i	0.785405	+	0.618982i	$0.212455\pi$
$313$			2.10212e11i			1.23796i	−0.785405	+	0.618982i	$0.787545\pi$
$314$	−7.58640e9			−0.0440405
$315$	−3.01688e11	−	1.50049e10i	−1.72648	−	0.0858687i
$316$	7.88828e10			0.445031
$317$		−	8.70887e10i		−	0.484390i	−0.970228	−	0.242195i	$-0.922133\pi$
$317$		−	8.70887e10i		−	0.484390i	0.970228	−	0.242195i	$-0.0778674\pi$
$318$		−	6.47189e10i		−	0.354902i
$319$	9.26109e10			0.500730
$320$	−1.16472e9	+	2.34179e10i	−0.00620937	+	0.124846i
$321$	−4.85367e11			−2.55151
$322$		−	1.60085e11i		−	0.829849i
$323$			2.86965e9i			0.0146696i
$324$	−1.95017e11			−0.983149
$325$	2.54941e10	−	2.55659e11i	0.126755	−	1.27112i
$326$	9.24612e10			0.453399
$327$		−	1.56034e11i		−	0.754664i
$328$		−	6.11108e10i		−	0.291531i
$329$	1.15591e11			0.543931
$330$	−6.41202e9	+	1.28920e11i	−0.0297634	+	0.598423i
$331$	−1.94118e11			−0.888873			−0.444436	−	0.895810i	$-0.646596\pi$
$331$	−1.94118e11			−0.888873			−0.444436	+	0.895810i	$0.646596\pi$
$332$			1.78540e10i			0.0806519i
$333$			6.00340e11i			2.67546i
$334$	6.06753e10			0.266780
$335$	7.21056e10	+	3.58627e9i	0.312800	+	0.0155575i
$336$	−7.98926e10			−0.341963
$337$		−	3.33772e11i		−	1.40966i	−0.709375	−	0.704831i	$-0.751023\pi$
$337$		−	3.33772e11i		−	1.40966i	0.709375	−	0.704831i	$-0.248977\pi$
$338$		−	1.07200e11i		−	0.446753i
$339$	3.87312e11			1.59280
$340$	−5.90388e9	−	2.93637e8i	−0.0239598	−	0.00119167i
$341$	6.20596e10			0.248550
$342$		−	1.25444e11i		−	0.495831i
$343$			2.76662e11i			1.07926i
$344$	−9.78452e9			−0.0376727
$345$	−3.69354e10	+	7.42624e11i	−0.140364	+	2.82217i
$346$	2.28677e10			0.0857788
$347$		−	1.31507e11i		−	0.486930i	−0.969910	−	0.243465i	$-0.921716\pi$
$347$		−	1.31507e11i		−	0.486930i	0.969910	−	0.243465i	$-0.0782842\pi$
$348$		−	2.66235e11i		−	0.973104i
$349$	−1.83355e11			−0.661573			−0.330786	−	0.943706i	$-0.607314\pi$
$349$	−1.83355e11			−0.661573			−0.330786	+	0.943706i	$0.607314\pi$
$350$	1.48888e11	+	1.48470e10i	0.530339	+	0.0528851i
$351$	8.52654e11			2.99841
$352$			2.37741e10i			0.0825396i
$353$		−	2.99531e11i		−	1.02673i	−0.858171	−	0.513365i	$-0.828399\pi$
$353$		−	2.99531e11i		−	1.02673i	0.858171	−	0.513365i	$-0.171601\pi$
$354$	−3.73753e11			−1.26494
$355$	9.48017e9	−	1.90609e11i	0.0316803	−	0.636964i
$356$	−1.90291e11			−0.627904
$357$		−	2.01417e10i		−	0.0656279i
$358$			1.99621e11i			0.642294i
$359$	−6.25349e10			−0.198700			−0.0993500	−	0.995053i	$-0.531676\pi$
$359$	−6.25349e10			−0.198700			−0.0993500	+	0.995053i	$0.531676\pi$
$360$	2.58084e11	+	1.28361e10i	0.809840	+	0.0402785i
$361$	−2.92522e11			−0.906516
$362$		−	1.73716e11i		−	0.531683i
$363$		−	4.69466e11i		−	1.41914i
$364$	1.61242e11			0.481417
$365$	4.14869e11	+	2.06341e10i	1.22347	+	0.0608509i
$366$	3.76605e11			1.09704
$367$			4.06657e10i			0.117012i	0.998287	+	0.0585061i	$0.0186337\pi$
$367$			4.06657e10i			0.117012i	−0.998287	+	0.0585061i	$0.981366\pi$
$368$			1.36947e11i			0.389257i
$369$	−6.73488e11			−1.89108
$370$	1.47723e10	−	2.97012e11i	0.0409770	−	0.823884i
$371$	−7.60679e10			−0.208458
$372$		−	1.78407e11i		−	0.483025i
$373$			3.44510e11i			0.921537i	0.887520	+	0.460768i	$0.152426\pi$
$373$			3.44510e11i			0.921537i	−0.887520	+	0.460768i	$0.847574\pi$
$374$	−5.99367e9			−0.0158406
$375$	−6.87256e11	−	1.03226e11i	−1.79464	−	0.269557i
$376$	−9.88842e10			−0.255142
$377$			5.37325e11i			1.36994i
$378$			4.96560e11i			1.25100i
$379$	−4.30309e10			−0.107128			−0.0535642	−	0.998564i	$-0.517058\pi$
$379$	−4.30309e10			−0.107128			−0.0535642	+	0.998564i	$0.517058\pi$
$380$	−3.08675e9	+	6.20623e10i	−0.00759409	+	0.152687i
$381$	−1.24322e11			−0.302264
$382$			4.67119e11i			1.12239i
$383$		−	2.89909e11i		−	0.688441i	−0.938889	−	0.344220i	$-0.888143\pi$
$383$		−	2.89909e11i		−	0.688441i	0.938889	−	0.344220i	$-0.111857\pi$
$384$	6.83452e10			0.160405
$385$	1.51527e11	+	7.53642e9i	0.351494	+	0.0174820i
$386$	−8.53935e9			−0.0195786
$387$			1.07833e11i			0.244372i
$388$			4.11016e11i			0.920694i
$389$	5.10079e11			1.12944			0.564722	−	0.825282i	$-0.308984\pi$
$389$	5.10079e11			1.12944			0.564722	+	0.825282i	$0.308984\pi$
$390$	−7.47990e11	−	3.72023e10i	−1.63721	−	0.0814290i
$391$	−3.45256e10			−0.0747043
$392$		−	7.13860e10i		−	0.152695i
$393$		−	1.27033e12i		−	2.68626i
$394$	−4.57164e11			−0.955738
$395$	−2.13917e10	+	4.30101e11i	−0.0442138	+	0.888964i
$396$	2.62009e11			0.535412
$397$		−	2.54945e11i		−	0.515097i	−0.966265	−	0.257549i	$-0.917085\pi$
$397$		−	2.54945e11i		−	0.515097i	0.966265	−	0.257549i	$-0.0829148\pi$
$398$		−	3.91145e11i		−	0.781384i
$399$	−2.11732e11			−0.418223
$400$	−1.27368e11	−	1.27011e10i	−0.248766	−	0.0248068i
$401$	5.09680e11			0.984347			0.492173	−	0.870497i	$-0.336203\pi$
$401$	5.09680e11			0.984347			0.492173	+	0.870497i	$0.336203\pi$
$402$		−	2.10440e11i		−	0.401894i
$403$			3.60067e11i			0.680003i
$404$	3.27253e11			0.611178
$405$	5.28852e10	−	1.06331e12i	0.0976757	−	1.96387i
$406$	−3.12922e11			−0.571569
$407$		−	3.01529e11i		−	0.544697i
$408$			1.72305e10i			0.0307841i
$409$	1.06695e12			1.88533			0.942666	−	0.333737i	$-0.108310\pi$
$409$	1.06695e12			1.88533			0.942666	+	0.333737i	$0.108310\pi$
$410$	3.33201e11	+	1.65722e10i	0.582343	+	0.0289636i
$411$	−3.34333e11			−0.577952
$412$			4.25682e11i			0.727861i
$413$			4.39293e11i			0.742983i
$414$	1.50926e12			2.52501
$415$	−9.73474e10	−	4.84171e9i	−0.161105	−	0.00801276i
$416$	−1.37936e11			−0.225818
$417$			1.73575e12i			2.81108i
$418$			6.30062e10i			0.100946i
$419$	−4.72157e11			−0.748383			−0.374191	−	0.927352i	$-0.622080\pi$
$419$	−4.72157e11			−0.748383			−0.374191	+	0.927352i	$0.622080\pi$
$420$	2.16655e10	−	4.35607e11i	0.0339740	−	0.683082i
$421$	−4.82741e11			−0.748936			−0.374468	−	0.927240i	$-0.622175\pi$
$421$	−4.82741e11			−0.748936			−0.374468	+	0.927240i	$0.622175\pi$
$422$			4.71161e11i			0.723208i
$423$			1.08978e12i			1.65503i
$424$	6.50733e10			0.0977815
$425$	3.20206e9	−	3.21107e10i	0.00476080	−	0.0477420i
$426$	−5.56291e11			−0.818387
$427$		−	4.42645e11i		−	0.644363i
$428$		−	4.88025e11i		−	0.702983i
$429$	−7.59367e11			−1.08241
$430$	2.65339e9	−	5.33492e10i	0.00374278	−	0.0752523i
$431$	1.22570e12			1.71095			0.855476	−	0.517843i	$-0.173265\pi$
$431$	1.22570e12			1.71095			0.855476	+	0.517843i	$0.173265\pi$
$432$		−	4.24789e11i		−	0.586809i
$433$		−	1.24088e12i		−	1.69642i	−0.529661	−	0.848210i	$-0.677681\pi$
$433$		−	1.24088e12i		−	1.69642i	0.529661	−	0.848210i	$-0.322319\pi$
$434$	−2.09692e11			−0.283713
$435$	1.45162e12	+	7.21985e10i	1.94381	+	0.0966778i
$436$	1.56888e11			0.207922
$437$			3.62937e11i			0.476064i
$438$		−	1.21080e12i		−	1.57194i
$439$	−1.20939e12			−1.55409			−0.777047	−	0.629442i	$-0.783283\pi$
$439$	−1.20939e12			−1.55409			−0.777047	+	0.629442i	$0.783283\pi$
$440$	−1.29626e11	−	6.44713e9i	−0.164875	−	0.00820030i
$441$	−7.86729e11			−0.990493
$442$		−	3.47751e10i		−	0.0433379i
$443$		−	4.45765e10i		−	0.0549907i	−0.999622	−	0.0274954i	$-0.991247\pi$
$443$		−	4.45765e10i		−	0.0549907i	0.999622	−	0.0274954i	$-0.00875315\pi$
$444$	−8.66829e11			−1.05855
$445$	5.16037e10	−	1.03754e12i	0.0623822	−	1.25426i
$446$	−5.43673e11			−0.650625
$447$			9.79176e11i			1.16005i
$448$		−	8.03301e10i		−	0.0942165i
$449$	−7.28323e11			−0.845698			−0.422849	−	0.906200i	$-0.638970\pi$
$449$	−7.28323e11			−0.845698			−0.422849	+	0.906200i	$0.638970\pi$
$450$	−1.39976e11	+	1.40370e12i	−0.160915	+	1.61368i
$451$	3.38269e11			0.385006
$452$			3.89433e11i			0.438843i
$453$			1.03946e12i			1.15975i
$454$	2.49792e11			0.275948
$455$	−4.37260e10	+	8.79156e11i	−0.0478287	+	0.961645i
$456$	1.81129e11			0.196176
$457$		−	1.61869e12i		−	1.73596i	−0.496598	−	0.867981i	$-0.665418\pi$
$457$		−	1.61869e12i		−	1.73596i	0.496598	−	0.867981i	$-0.334582\pi$
$458$		−	8.62607e11i		−	0.916049i
$459$	1.07093e11			0.112617
$460$	−7.46691e11	−	3.71377e10i	−0.777554	−	0.0386727i
$461$	−5.26233e11			−0.542655			−0.271328	−	0.962487i	$-0.587463\pi$
$461$	−5.26233e11			−0.542655			−0.271328	+	0.962487i	$0.587463\pi$
$462$		−	4.42233e11i		−	0.451608i
$463$			1.71642e12i			1.73583i	0.496709	+	0.867917i	$0.334542\pi$
$463$			1.71642e12i			1.73583i	−0.496709	+	0.867917i	$0.665458\pi$
$464$	2.67693e11			0.268106
$465$	9.72750e11	+	4.83810e10i	0.964857	+	0.0479885i
$466$	1.21506e12			1.19361
$467$		−	1.36109e12i		−	1.32422i	−0.749405	−	0.662112i	$-0.769661\pi$
$467$		−	1.36109e12i		−	1.32422i	0.749405	−	0.662112i	$-0.230339\pi$
$468$			1.52017e12i			1.46482i
$469$	−2.47342e11			−0.236059
$470$	2.68157e10	−	5.39157e11i	0.0253483	−	0.509654i
$471$	−1.20721e11			−0.113029
$472$		−	3.75799e11i		−	0.348511i
$473$		−	5.41606e10i		−	0.0497518i
$474$	1.25525e12			1.14216
$475$	−3.37552e11	−	3.36605e10i	−0.304242	−	0.0303388i
$476$	2.02520e10			0.0180816
$477$		−	7.17158e11i		−	0.634282i
$478$			1.07264e12i			0.939786i
$479$	7.71338e11			0.669476			0.334738	−	0.942311i	$-0.391352\pi$
$479$	7.71338e11			0.669476			0.334738	+	0.942311i	$0.391352\pi$
$480$	−1.85341e10	+	3.72646e11i	−0.0159362	+	0.320414i
$481$	1.74946e12			1.49022
$482$			5.11499e11i			0.431651i
$483$		−	2.54741e12i		−	2.12979i
$484$	4.72037e11			0.390996
$485$	−2.24103e12	−	1.11460e11i	−1.83912	−	0.0914709i
$486$	−1.06198e12			−0.863483
$487$		−	7.00790e10i		−	0.0564557i	−0.999602	−	0.0282278i	$-0.991014\pi$
$487$		−	7.00790e10i		−	0.0564557i	0.999602	−	0.0282278i	$-0.00898639\pi$
$488$			3.78667e11i			0.302251i
$489$	1.47132e12			1.16364
$490$	3.89226e11	+	1.93587e10i	0.305014	+	0.0151703i
$491$	−3.27391e11			−0.254214			−0.127107	−	0.991889i	$-0.540569\pi$
$491$	−3.27391e11			−0.254214			−0.127107	+	0.991889i	$0.540569\pi$
$492$		−	9.72447e11i		−	0.748209i
$493$			6.74880e10i			0.0514536i
$494$	−3.65560e11			−0.276177
$495$	−7.10524e10	+	1.42858e12i	−0.0531931	+	1.06950i
$496$	1.79384e11			0.133081
$497$			6.53841e11i			0.480694i
$498$			2.84108e11i			0.206991i
$499$	1.55301e12			1.12130			0.560649	−	0.828054i	$-0.310552\pi$
$499$	1.55301e12			1.12130			0.560649	+	0.828054i	$0.310552\pi$
$500$	1.03792e11	−	6.91020e11i	0.0742673	−	0.494454i
$501$	9.65518e11			0.684685
$502$			1.20453e12i			0.846548i
$503$		−	3.75654e11i		−	0.261657i	−0.991405	−	0.130828i	$-0.958236\pi$
$503$		−	3.75654e11i		−	0.261657i	0.991405	−	0.130828i	$-0.0417637\pi$
$504$	−8.85299e11			−0.611157
$505$	−8.87454e10	+	1.78432e12i	−0.0607204	+	1.22085i
$506$	−7.58048e11			−0.514066
$507$		−	1.70585e12i		−	1.14658i
$508$		−	1.25003e11i		−	0.0832787i
$509$	−1.82659e12			−1.20618			−0.603090	−	0.797673i	$-0.706064\pi$
$509$	−1.82659e12			−1.20618			−0.603090	+	0.797673i	$0.706064\pi$
$510$	−9.39476e10	−	4.67261e9i	−0.0614922	−	0.00305840i
$511$	−1.42312e12			−0.923308
$512$			6.87195e10i			0.0441942i
$513$		−	1.12578e12i		−	0.717670i
$514$	−1.34516e12			−0.850039
$515$	−2.32100e12	−	1.15438e11i	−1.45392	−	0.0723129i
$516$	−1.55700e11			−0.0966861
$517$		−	5.47358e11i		−	0.336949i
$518$			1.01883e12i			0.621756i
$519$	3.63890e11			0.220149
$520$	3.74060e10	−	7.52086e11i	0.0224350	−	0.451079i
$521$	1.09737e12			0.652506			0.326253	−	0.945283i	$-0.394214\pi$
$521$	1.09737e12			0.652506			0.326253	+	0.945283i	$0.394214\pi$
$522$		−	2.95019e12i		−	1.73913i
$523$			2.23460e12i			1.30600i	0.757359	+	0.652999i	$0.226490\pi$
$523$			2.23460e12i			1.30600i	−0.757359	+	0.652999i	$0.773510\pi$
$524$	1.27728e12			0.740110
$525$	2.36923e12	+	2.36258e11i	1.36110	+	0.135728i
$526$	1.83244e12			1.04375
$527$			4.52245e10i			0.0255403i
$528$			3.78314e11i			0.211836i
$529$	−2.56546e12			−1.42434
$530$	−1.76468e10	+	3.54806e11i	−0.00971458	+	0.195321i
$531$	−4.14160e12			−2.26070
$532$		−	2.12891e11i		−	0.115227i
$533$			1.96262e12i			1.05333i
$534$	−3.02807e12			−1.61150
$535$	2.66091e12	+	1.32344e11i	1.40423	+	0.0698413i
$536$	2.11592e11			0.110728
$537$			3.17655e12i			1.64843i
$538$		−	1.57326e12i		−	0.809619i
$539$	3.95146e11			0.201655
$540$	2.31613e12	+	1.15196e11i	1.17217	+	0.0582994i
$541$	−1.87101e11			−0.0939049			−0.0469525	−	0.998897i	$-0.514951\pi$
$541$	−1.87101e11			−0.0939049			−0.0469525	+	0.998897i	$0.514951\pi$
$542$		−	3.56310e10i		−	0.0177350i
$543$		−	2.76433e12i		−	1.36455i
$544$	−1.73248e10			−0.00848152
$545$	−4.25454e10	+	8.55419e11i	−0.0206571	+	0.415331i
$546$	2.56582e12			1.23555
$547$			1.68930e12i			0.806796i	0.915025	+	0.403398i	$0.132171\pi$
$547$			1.68930e12i			0.806796i	−0.915025	+	0.403398i	$0.867829\pi$
$548$		−	3.36164e11i		−	0.159235i
$549$	4.17320e12			1.96062
$550$	7.03048e10	−	7.05027e11i	0.0327607	−	0.328529i
$551$	7.09442e11			0.327895
$552$			2.17922e12i			0.999021i
$553$		−	1.47537e12i		−	0.670869i
$554$	3.78906e11			0.170898
$555$	2.35069e11	−	4.72631e12i	0.105166	−	2.11448i
$556$	−1.74525e12			−0.774500
$557$		−	1.21557e12i		−	0.535094i	−0.963545	−	0.267547i	$-0.913787\pi$
$557$		−	1.21557e12i		−	0.535094i	0.963545	−	0.267547i	$-0.0862130\pi$
$558$		−	1.97695e12i		−	0.863262i
$559$	3.14238e11			0.136115
$560$	4.37993e11	+	2.17841e10i	0.188200	+	0.00936040i
$561$	−9.53765e10			−0.0406545
$562$			2.08177e10i			0.00880279i
$563$		−	1.35075e12i		−	0.566615i	−0.959029	−	0.283308i	$-0.908568\pi$
$563$		−	1.35075e12i		−	0.566615i	0.959029	−	0.283308i	$-0.0914318\pi$
$564$	−1.57353e12			−0.654816
$565$	−2.12335e12	−	1.05608e11i	−0.876603	−	0.0435990i
$566$	−2.59845e12			−1.06424
$567$			3.64746e12i			1.48206i
$568$		−	5.59337e11i		−	0.225479i
$569$	1.96503e12			0.785894			0.392947	−	0.919561i	$-0.371456\pi$
$569$	1.96503e12			0.785894			0.392947	+	0.919561i	$0.371456\pi$
$570$	−4.91190e10	+	9.87588e11i	−0.0194901	+	0.391867i
$571$	4.44321e12			1.74918			0.874590	−	0.484863i	$-0.161131\pi$
$571$	4.44321e12			1.74918			0.874590	+	0.484863i	$0.161131\pi$
$572$		−	7.63525e11i		−	0.298223i
$573$			7.43319e12i			2.88058i
$574$	−1.14297e12			−0.439473
$575$	4.04980e11	−	4.06119e12i	0.154500	−	1.54935i
$576$	7.57341e11			0.286675
$577$		−	7.74499e11i		−	0.290891i	−0.989366	−	0.145445i	$-0.953538\pi$
$577$		−	7.74499e11i		−	0.290891i	0.989366	−	0.145445i	$-0.0464615\pi$
$578$			1.89304e12i			0.705479i
$579$	−1.35885e11			−0.0502481
$580$	−7.25939e10	+	1.45957e12i	−0.0266363	+	0.535550i
$581$	3.33929e11			0.121580
$582$			6.54043e12i			2.36294i
$583$			3.60203e11i			0.129133i
$584$	1.21743e12			0.433097
$585$	−8.28857e12	−	4.12243e11i	−2.92603	−	0.145530i
$586$	3.22063e11			0.112824
$587$		−	5.79614e11i		−	0.201496i	−0.994912	−	0.100748i	$-0.967876\pi$
$587$		−	5.79614e11i		−	0.201496i	0.994912	−	0.100748i	$-0.0321237\pi$
$588$		−	1.13596e12i		−	0.391889i
$589$	4.75405e11			0.162759
$590$	2.04901e12	+	1.01910e11i	0.696162	+	0.0346246i
$591$	−7.27478e12			−2.45288
$592$		−	8.71576e11i		−	0.291647i
$593$		−	3.11892e12i		−	1.03576i	−0.855454	−	0.517879i	$-0.826722\pi$
$593$		−	3.11892e12i		−	1.03576i	0.855454	−	0.517879i	$-0.173278\pi$
$594$	2.35135e12			0.774959
$595$	−5.49199e9	+	1.10422e11i	−0.00179640	+	0.0361185i
$596$	−9.84538e11			−0.319613
$597$		−	6.22424e12i		−	2.00540i
$598$		−	4.39816e12i		−	1.40642i
$599$	3.65634e12			1.16045			0.580225	−	0.814456i	$-0.302965\pi$
$599$	3.65634e12			1.16045			0.580225	+	0.814456i	$0.302965\pi$
$600$	−2.02679e12	−	2.02111e11i	−0.638453	−	0.0636661i
$601$	−5.00312e12			−1.56425			−0.782124	−	0.623123i	$-0.785864\pi$
$601$	−5.00312e12			−1.56425			−0.782124	+	0.623123i	$0.785864\pi$
$602$			1.83003e11i			0.0567902i
$603$		−	2.33191e12i		−	0.718264i
$604$	−1.04515e12			−0.319532
$605$	−1.28008e11	+	2.57374e12i	−0.0388454	+	0.781026i
$606$	5.20753e12			1.56857
$607$			4.66337e12i			1.39428i	0.716934	+	0.697141i	$0.245545\pi$
$607$			4.66337e12i			1.39428i	−0.716934	+	0.697141i	$0.754455\pi$
$608$			1.82121e11i			0.0540497i
$609$	−4.97948e12			−1.46692
$610$	−2.06465e12	−	1.02688e11i	−0.603757	−	0.0300286i
$611$	3.17575e12			0.921851
$612$			1.90933e11i			0.0550173i
$613$		−	6.42000e12i		−	1.83638i	−0.396139	−	0.918190i	$-0.629650\pi$
$613$		−	6.42000e12i		−	1.83638i	0.396139	−	0.918190i	$-0.370350\pi$
$614$	−2.06134e12			−0.585319
$615$	5.30218e12	+	2.63711e11i	1.49457	+	0.0743345i
$616$	4.44654e11			0.124425
$617$			2.91245e12i			0.809050i	0.914527	+	0.404525i	$0.132563\pi$
$617$			2.91245e12i			0.809050i	−0.914527	+	0.404525i	$0.867437\pi$
$618$			6.77382e12i			1.86804i
$619$	−9.63523e10			−0.0263787			−0.0131894	−	0.999913i	$-0.504198\pi$
$619$	−9.63523e10			−0.0263787			−0.0131894	+	0.999913i	$0.504198\pi$
$620$	−4.86460e10	+	9.78077e11i	−0.0132216	+	0.265834i
$621$	1.35446e13			3.65472
$622$		−	3.46487e12i		−	0.928176i
$623$			3.55907e12i			0.946543i
$624$	−2.19496e12			−0.579558
$625$	3.73958e12	+	7.53308e11i	0.980308	+	0.197475i
$626$	−3.36339e12			−0.875373
$627$			1.00261e12i			0.259076i
$628$		−	1.21382e11i		−	0.0311413i
$629$	2.19732e11			0.0559714
$630$	2.40078e11	−	4.82701e12i	0.0607184	−	1.22080i
$631$	−5.22061e12			−1.31096			−0.655480	−	0.755213i	$-0.727534\pi$
$631$	−5.22061e12			−1.31096			−0.655480	+	0.755213i	$0.727534\pi$
$632$			1.26212e12i			0.314685i
$633$			7.49752e12i			1.85610i
$634$	1.39342e12			0.342515
$635$	6.81568e11	+	3.38987e10i	0.166352	+	0.00827373i
$636$	1.03550e12			0.250954
$637$			2.29262e12i			0.551702i
$638$			1.48177e12i			0.354070i
$639$	−6.16433e12			−1.46262
$640$	−3.74687e11	−	1.86356e10i	−0.0882792	−	0.00439069i
$641$	5.72517e12			1.33945			0.669726	−	0.742608i	$-0.266412\pi$
$641$	5.72517e12			1.33945			0.669726	+	0.742608i	$0.266412\pi$
$642$		−	7.76587e12i		−	1.80419i
$643$		−	1.79153e12i		−	0.413309i	−0.978414	−	0.206654i	$-0.933742\pi$
$643$		−	1.79153e12i		−	0.413309i	0.978414	−	0.206654i	$-0.0662575\pi$
$644$	2.56136e12			0.586792
$645$	4.22231e10	−	8.48938e11i	0.00960575	−	0.193133i
$646$	−4.59143e10			−0.0103729
$647$		−	3.37135e12i		−	0.756370i	−0.925730	−	0.378185i	$-0.876548\pi$
$647$		−	3.37135e12i		−	0.756370i	0.925730	−	0.378185i	$-0.123452\pi$
$648$		−	3.12027e12i		−	0.695191i
$649$	2.08018e12			0.460256
$650$	4.09054e12	+	4.07906e11i	0.898815	+	0.0896293i
$651$	−3.33681e12			−0.728143
$652$			1.47938e12i			0.320601i
$653$		−	2.66457e12i		−	0.573479i	−0.958009	−	0.286739i	$-0.907429\pi$
$653$		−	2.66457e12i		−	0.573479i	0.958009	−	0.286739i	$-0.0925714\pi$
$654$	2.49654e12			0.533628
$655$	−3.46377e11	+	6.96427e12i	−0.0735298	+	1.47839i
$656$	9.77772e11			0.206144
$657$		−	1.34170e13i		−	2.80938i
$658$			1.84946e12i			0.384617i
$659$	−3.70933e12			−0.766146			−0.383073	−	0.923718i	$-0.625134\pi$
$659$	−3.70933e12			−0.766146			−0.383073	+	0.923718i	$0.625134\pi$
$660$	−2.06272e12	−	1.02592e11i	−0.423149	−	0.0210459i
$661$	−5.60206e12			−1.14141			−0.570705	−	0.821156i	$-0.693330\pi$
$661$	−5.60206e12			−1.14141			−0.570705	+	0.821156i	$0.693330\pi$
$662$		−	3.10589e12i		−	0.628528i
$663$		−	5.53371e11i		−	0.111226i
$664$	−2.85664e11			−0.0570295
$665$	1.16077e12	+	5.77325e10i	0.230170	+	0.0114478i
$666$	−9.60544e12			−1.89183
$667$			8.53552e12i			1.66980i
$668$			9.70805e11i			0.188642i
$669$	−8.65139e12			−1.66981
$670$	−5.73803e10	+	1.15369e12i	−0.0110008	+	0.221183i
$671$	−2.09605e12			−0.399163
$672$		−	1.27828e12i		−	0.241805i
$673$		−	1.97705e12i		−	0.371493i	−0.982598	−	0.185746i	$-0.940530\pi$
$673$		−	1.97705e12i		−	0.371493i	0.982598	−	0.185746i	$-0.0594703\pi$
$674$	5.34035e12			0.996782
$675$	−1.25619e12	+	1.25972e13i	−0.232910	+	2.33565i
$676$	1.71519e12			0.315902
$677$			1.55123e12i			0.283810i	0.989880	+	0.141905i	$0.0453228\pi$
$677$			1.55123e12i			0.283810i	−0.989880	+	0.141905i	$0.954677\pi$
$678$			6.19699e12i			1.12628i
$679$	7.68735e12			1.38791
$680$	4.69820e9	−	9.44621e10i	0.000842638	−	0.0169421i
$681$	3.97491e12			0.708215
$682$			9.92953e11i			0.175752i
$683$			6.96146e12i			1.22407i	0.790830	+	0.612036i	$0.209649\pi$
$683$			6.96146e12i			1.22407i	−0.790830	+	0.612036i	$0.790351\pi$
$684$	2.00711e12			0.350605
$685$	1.83291e12	+	9.11620e10i	0.318077	+	0.0158200i
$686$	−4.42659e12			−0.763152
$687$		−	1.37265e13i		−	2.35102i
$688$		−	1.56552e11i		−	0.0266386i
$689$	−2.08988e12			−0.353293
$690$	−1.18820e13	−	5.90966e11i	−1.99557	−	0.0992526i
$691$	−8.36212e12			−1.39529			−0.697646	−	0.716443i	$-0.745769\pi$
$691$	−8.36212e12			−1.39529			−0.697646	+	0.716443i	$0.745769\pi$
$692$			3.65883e11i			0.0606548i
$693$		−	4.90043e12i		−	0.807114i
$694$	2.10412e12			0.344312
$695$	4.73283e11	−	9.51583e12i	0.0769465	−	1.54709i
$696$	4.25977e12			0.688088
$697$			2.46506e11i			0.0395621i
$698$		−	2.93367e12i		−	0.467802i
$699$	1.93351e13			3.06337
$700$	−2.37552e11	+	2.38221e12i	−0.0373954	+	0.375006i
$701$	−4.13171e12			−0.646247			−0.323123	−	0.946357i	$-0.604733\pi$
$701$	−4.13171e12			−0.646247			−0.323123	+	0.946357i	$0.604733\pi$
$702$			1.36425e13i			2.12019i
$703$		−	2.30985e12i		−	0.356686i
$704$	−3.80386e11			−0.0583643
$705$	4.26715e11	−	8.57953e12i	0.0650559	−	1.30801i
$706$	4.79250e12			0.726007
$707$		−	6.12071e12i		−	0.921328i
$708$		−	5.98004e12i		−	0.894447i
$709$	−4.22719e12			−0.628266			−0.314133	−	0.949379i	$-0.601714\pi$
$709$	−4.22719e12			−0.628266			−0.314133	+	0.949379i	$0.601714\pi$
$710$	3.04974e12	+	1.51683e11i	0.450401	+	0.0224013i
$711$	1.39096e13			2.04127
$712$		−	3.04465e12i		−	0.443995i
$713$			5.71975e12i			0.828846i
$714$	3.22267e11			0.0464059
$715$	4.16305e12	+	2.07055e11i	0.595710	+	0.0296284i
$716$	−3.19394e12			−0.454170
$717$			1.70688e13i			2.41194i
$718$		−	1.00056e12i		−	0.140502i
$719$	−1.34429e13			−1.87591			−0.937954	−	0.346760i	$-0.887282\pi$
$719$	−1.34429e13			−1.87591			−0.937954	+	0.346760i	$0.887282\pi$
$720$	−2.05378e11	+	4.12934e12i	−0.0284812	+	0.572643i
$721$	7.96167e12			1.09722
$722$		−	4.68035e12i		−	0.641004i
$723$			8.13941e12i			1.10782i
$724$	2.77946e12			0.375956
$725$	−7.93851e12	−	7.91623e11i	−1.06713	−	0.106414i
$726$	7.51145e12			1.00348
$727$		−	6.20467e12i		−	0.823785i	−0.911233	−	0.411892i	$-0.864868\pi$
$727$		−	6.20467e12i		−	0.823785i	0.911233	−	0.411892i	$-0.135132\pi$
$728$			2.57987e12i			0.340413i
$729$	−1.90497e12			−0.249813
$730$	−3.30145e11	+	6.63791e12i	−0.0430281	+	0.865124i
$731$	3.94683e10			0.00511235
$732$			6.02568e12i			0.775722i
$733$		−	1.45106e13i		−	1.85660i	−0.371831	−	0.928300i	$-0.621270\pi$
$733$		−	1.45106e13i		−	1.85660i	0.371831	−	0.928300i	$-0.378730\pi$
$734$	−6.50652e11			−0.0827401
$735$	6.19370e12	+	3.08052e11i	0.782811	+	0.0389342i
$736$	−2.19115e12			−0.275247
$737$			1.17124e12i			0.146231i
$738$		−	1.07758e13i		−	1.33720i
$739$	−8.77240e12			−1.08198			−0.540989	−	0.841030i	$-0.681950\pi$
$739$	−8.77240e12			−1.08198			−0.540989	+	0.841030i	$0.681950\pi$
$740$	4.75219e12	+	2.36357e11i	0.582574	+	0.0289751i
$741$	−5.81710e12			−0.708802
$742$		−	1.21709e12i		−	0.147402i
$743$			5.03647e12i			0.606285i	0.952945	+	0.303142i	$0.0980358\pi$
$743$			5.03647e12i			0.606285i	−0.952945	+	0.303142i	$0.901964\pi$
$744$	2.85452e12			0.341550
$745$	2.66990e11	−	5.36810e12i	0.0317535	−	0.638437i
$746$	−5.51217e12			−0.651625
$747$			3.14824e12i			0.369935i
$748$		−	9.58988e10i		−	0.0112010i
$749$	−9.12767e12			−1.05972
$750$	1.65162e12	−	1.09961e13i	0.190605	−	1.26900i
$751$	8.65348e12			0.992685			0.496342	−	0.868127i	$-0.334676\pi$
$751$	8.65348e12			0.992685			0.496342	+	0.868127i	$0.334676\pi$
$752$		−	1.58215e12i		−	0.180413i
$753$			1.91675e13i			2.17265i
$754$	−8.59720e12			−0.968692
$755$	2.83428e11	−	5.69860e12i	0.0317454	−	0.638274i
$756$	−7.94496e12			−0.884594
$757$			4.54387e12i			0.502915i	0.967868	+	0.251457i	$0.0809099\pi$
$757$			4.54387e12i			0.502915i	−0.967868	+	0.251457i	$0.919090\pi$
$758$		−	6.88495e11i		−	0.0757512i
$759$	−1.20627e13			−1.31934
$760$	−9.92997e11	−	4.93880e10i	−0.107966	−	0.00536983i
$761$	1.14418e13			1.23670			0.618351	−	0.785902i	$-0.287801\pi$
$761$	1.14418e13			1.23670			0.618351	+	0.785902i	$0.287801\pi$
$762$		−	1.98916e12i		−	0.213733i
$763$		−	2.93433e12i		−	0.313435i
$764$	−7.47390e12			−0.793646
$765$	−1.04104e12	−	5.17777e10i	−0.109899	−	0.00546596i
$766$	4.63854e12			0.486801
$767$			1.20691e13i			1.25920i
$768$			1.09352e12i			0.113423i
$769$	1.80380e13			1.86003			0.930016	−	0.367518i	$-0.119793\pi$
$769$	1.80380e13			1.86003			0.930016	+	0.367518i	$0.119793\pi$
$770$	−1.20583e11	+	2.42444e12i	−0.0123617	+	0.248544i
$771$	−2.14053e13			−2.18161
$772$		−	1.36630e11i		−	0.0138442i
$773$		−	3.13678e12i		−	0.315992i	−0.987440	−	0.157996i	$-0.949497\pi$
$773$		−	3.13678e12i		−	0.315992i	0.987440	−	0.157996i	$-0.0505033\pi$
$774$	−1.72533e12			−0.172797
$775$	−5.31969e12	−	5.30476e11i	−0.529698	−	0.0528212i
$776$	−6.57625e12			−0.651029
$777$			1.62126e13i			1.59572i
$778$			8.16127e12i			0.798637i
$779$	2.59130e12			0.252115
$780$	5.95237e11	−	1.19678e13i	0.0575790	−	1.15768i
$781$	3.09612e12			0.297775
$782$		−	5.52410e11i		−	0.0528239i
$783$		−	2.64759e13i		−	2.51723i
$784$	1.14218e12			0.107972
$785$	6.61826e11	+	3.29168e10i	0.0622058	+	0.00309389i
$786$	2.03252e13			1.89948
$787$		−	5.28159e12i		−	0.490770i	−0.969426	−	0.245385i	$-0.921086\pi$
$787$		−	5.28159e12i		−	0.490770i	0.969426	−	0.245385i	$-0.0789144\pi$
$788$		−	7.31462e12i		−	0.675809i
$789$	2.91594e13			2.67875
$790$	−6.88162e12	−	3.42267e11i	−0.628592	−	0.0312639i
$791$	7.28368e12			0.661541
$792$			4.19214e12i			0.378593i
$793$		−	1.21612e13i		−	1.09206i
$794$	4.07912e12			0.364229
$795$	−2.80811e11	+	5.64598e12i	−0.0249322	+	0.501288i
$796$	6.25833e12			0.552522
$797$			1.49680e13i			1.31402i	0.753881	+	0.657011i	$0.228179\pi$
$797$			1.49680e13i			1.31402i	−0.753881	+	0.657011i	$0.771821\pi$
$798$		−	3.38771e12i		−	0.295728i
$799$	3.98874e11			0.0346239
$800$	2.03217e11	−	2.03789e12i	0.0175411	−	0.175904i
$801$	−3.35544e13			−2.88007
$802$			8.15488e12i			0.696038i
$803$			6.73887e12i			0.571962i
$804$	3.36704e12			0.284182
$805$	−6.94597e11	+	1.39656e13i	−0.0582977	+	1.17213i
$806$	−5.76108e12			−0.480835
$807$		−	2.50351e13i		−	2.07787i
$808$			5.23605e12i			0.432168i
$809$	7.67334e12			0.629819			0.314910	−	0.949122i	$-0.398026\pi$
$809$	7.67334e12			0.629819			0.314910	+	0.949122i	$0.398026\pi$
$810$	1.70130e13	+	8.46163e11i	1.38867	+	0.0690672i
$811$	−1.09542e13			−0.889175			−0.444587	−	0.895736i	$-0.646650\pi$
$811$	−1.09542e13			−0.889175			−0.444587	+	0.895736i	$0.646650\pi$
$812$		−	5.00675e12i		−	0.404160i
$813$		−	5.66992e11i		−	0.0455165i
$814$	4.82447e12			0.385159
$815$	−8.06618e12	−	4.01182e11i	−0.640411	−	0.0318517i
$816$	−2.75687e11			−0.0217676
$817$		−	4.14896e11i		−	0.0325791i
$818$			1.70712e13i			1.33313i
$819$	2.84321e13			2.20817
$820$	−2.65155e11	+	5.33122e12i	−0.0204804	+	0.411779i
$821$	9.17326e12			0.704660			0.352330	−	0.935876i	$-0.385389\pi$
$821$	9.17326e12			0.704660			0.352330	+	0.935876i	$0.385389\pi$
$822$		−	5.34933e12i		−	0.408673i
$823$			9.50868e12i			0.722472i	0.932475	+	0.361236i	$0.117645\pi$
$823$			9.50868e12i			0.722472i	−0.932475	+	0.361236i	$0.882355\pi$
$824$	−6.81092e12			−0.514675
$825$	1.11875e12	−	1.12190e13i	0.0840796	−	0.843162i
$826$	−7.02869e12			−0.525369
$827$		−	9.88575e11i		−	0.0734911i	−0.999325	−	0.0367456i	$-0.988301\pi$
$827$		−	9.88575e11i		−	0.0734911i	0.999325	−	0.0367456i	$-0.0116991\pi$
$828$			2.41482e13i			1.78545i
$829$	−6.00947e12			−0.441917			−0.220959	−	0.975283i	$-0.570919\pi$
$829$	−6.00947e12			−0.441917			−0.220959	+	0.975283i	$0.570919\pi$
$830$	7.74673e10	−	1.55756e12i	0.00566587	−	0.113918i
$831$	6.02947e12			0.438606
$832$		−	2.20698e12i		−	0.159678i
$833$			2.87953e11i			0.0207214i
$834$	−2.77719e13			−1.98774
$835$	−5.29323e12	−	2.63266e11i	−0.376818	−	0.0187415i
$836$	−1.00810e12			−0.0713798
$837$		−	1.77418e13i		−	1.24949i
$838$		−	7.55452e12i		−	0.529186i
$839$	−1.12593e13			−0.784484			−0.392242	−	0.919862i	$-0.628300\pi$
$839$	−1.12593e13			−0.784484			−0.392242	+	0.919862i	$0.628300\pi$
$840$	6.96971e12	+	3.46648e11i	0.483012	+	0.0240233i
$841$	2.17744e12			0.150094
$842$		−	7.72386e12i		−	0.529578i
$843$			3.31270e11i			0.0225922i
$844$	−7.53858e12			−0.511385
$845$	−4.65131e11	+	9.35194e12i	−0.0313849	+	0.631025i
$846$	−1.74365e13			−1.17029
$847$		−	8.82865e12i		−	0.589412i
$848$			1.04117e12i			0.0691419i
$849$	−4.13488e13			−2.73136
$850$	5.13772e11	+	5.12330e10i	0.0337587	+	0.00336639i
$851$	2.77906e13			1.81641
$852$		−	8.90065e12i		−	0.578687i
$853$		−	1.60111e13i		−	1.03550i	−0.855532	−	0.517751i	$-0.826769\pi$
$853$		−	1.60111e13i		−	1.03550i	0.855532	−	0.517751i	$-0.173231\pi$
$854$	7.08233e12			0.455633
$855$	−5.44294e11	+	1.09436e13i	−0.0348326	+	0.700345i
$856$	7.80839e12			0.497084
$857$		−	2.37698e13i		−	1.50526i	−0.658442	−	0.752631i	$-0.728784\pi$
$857$		−	2.37698e13i		−	1.50526i	0.658442	−	0.752631i	$-0.271216\pi$
$858$		−	1.21499e13i		−	0.765383i
$859$	9.00506e12			0.564309			0.282155	−	0.959369i	$-0.408951\pi$
$859$	9.00506e12			0.564309			0.282155	+	0.959369i	$0.408951\pi$
$860$	8.53587e11	+	4.24543e10i	0.0532114	+	0.00264654i
$861$	−1.81880e13			−1.12790
$862$			1.96113e13i			1.20983i
$863$		−	2.23368e13i		−	1.37080i	−0.728169	−	0.685398i	$-0.759628\pi$
$863$		−	2.23368e13i		−	1.37080i	0.728169	−	0.685398i	$-0.240372\pi$
$864$	6.79663e12			0.414937
$865$	−1.99495e12	−	9.92213e10i	−0.121160	−	0.00602605i
$866$	1.98540e13			1.19955
$867$			3.01236e13i			1.81060i
$868$		−	3.35508e12i		−	0.200615i
$869$	−6.98629e12			−0.415583
$870$	−1.15518e12	+	2.32260e13i	−0.0683615	+	1.37448i
$871$	−6.79547e12			−0.400072
$872$			2.51021e12i			0.147023i
$873$			7.24753e13i			4.22305i
$874$	−5.80700e12			−0.336628
$875$	−1.29244e13	−	1.94125e12i	−0.745371	−	0.111955i
$876$	1.93727e13			1.11153
$877$			5.15128e12i			0.294047i	0.989133	+	0.147023i	$0.0469693\pi$
$877$			5.15128e12i			0.294047i	−0.989133	+	0.147023i	$0.953031\pi$
$878$		−	1.93503e13i		−	1.09891i
$879$	5.12495e12			0.289561
$880$	1.03154e11	−	2.07402e12i	0.00579849	−	0.116584i
$881$	7.13386e12			0.398963			0.199482	−	0.979902i	$-0.436074\pi$
$881$	7.13386e12			0.398963			0.199482	+	0.979902i	$0.436074\pi$
$882$		−	1.25877e13i		−	0.700384i
$883$			1.68937e13i			0.935192i	0.883942	+	0.467596i	$0.154880\pi$
$883$			1.68937e13i			0.935192i	−0.883942	+	0.467596i	$0.845120\pi$
$884$	5.56401e11			0.0306445
$885$	3.26056e13	+	1.62169e12i	1.78668	+	0.0888632i
$886$	7.13225e11			0.0388843
$887$			1.25560e13i			0.681073i	0.940231	+	0.340537i	$0.110609\pi$
$887$			1.25560e13i			0.681073i	−0.940231	+	0.340537i	$0.889391\pi$
$888$		−	1.38693e13i		−	0.748506i
$889$	−2.33797e12			−0.125540
$890$	1.66007e13	+	8.25659e11i	0.886894	+	0.0441109i
$891$	1.72717e13			0.918092
$892$		−	8.69876e12i		−	0.460061i
$893$		−	4.19301e12i		−	0.220645i
$894$	−1.56668e13			−0.820279
$895$	8.66143e11	−	1.74147e13i	0.0451218	−	0.907219i
$896$	1.28528e12			0.0666211
$897$		−	6.99874e13i		−	3.60955i
$898$		−	1.16532e13i		−	0.597999i
$899$	1.11805e13			0.570879
$900$	−2.24591e13	−	2.23961e12i	−1.14104	−	0.113784i
$901$	−2.62489e11			−0.0132694
$902$			5.41230e12i			0.272240i
$903$			2.91210e12i			0.145751i
$904$	−6.23092e12			−0.310309
$905$	−7.53743e11	+	1.51548e13i	−0.0373512	+	0.750984i
$906$	−1.66314e13			−0.820071
$907$		−	9.91682e11i		−	0.0486564i	−0.999704	−	0.0243282i	$-0.992255\pi$
$907$		−	9.91682e11i		−	0.0486564i	0.999704	−	0.0243282i	$-0.00774466\pi$
$908$			3.99668e12i			0.195125i
$909$	5.77053e13			2.80335
$910$	−1.40665e13	−	6.99616e11i	−0.679986	−	0.0338200i
$911$	4.26457e12			0.205136			0.102568	−	0.994726i	$-0.467294\pi$
$911$	4.26457e12			0.205136			0.102568	+	0.994726i	$0.467294\pi$
$912$			2.89806e12i			0.138717i
$913$		−	1.58125e12i		−	0.0753150i
$914$	2.58990e13			1.22751
$915$	−3.28545e13	−	1.63406e12i	−1.54953	−	0.0770679i
$916$	1.38017e13			0.647744
$917$		−	2.38894e13i		−	1.11569i
$918$			1.71349e12i			0.0796325i
$919$	−1.87200e13			−0.865736			−0.432868	−	0.901457i	$-0.642498\pi$
$919$	−1.87200e13			−0.865736			−0.432868	+	0.901457i	$0.642498\pi$
$920$	5.94203e11	−	1.19471e13i	0.0273457	−	0.549814i
$921$	−3.28019e13			−1.50221
$922$		−	8.41973e12i		−	0.383715i
$923$			1.79636e13i			0.814677i
$924$	7.07572e12			0.319335
$925$	−2.57743e12	+	2.58468e13i	−0.115757	+	1.16083i
$926$	−2.74627e13			−1.22742
$927$			7.50616e13i			3.33856i
$928$			4.28309e12i			0.189580i
$929$	2.63022e13			1.15857			0.579284	−	0.815126i	$-0.303332\pi$
$929$	2.63022e13			1.15857			0.579284	+	0.815126i	$0.303332\pi$
$930$	−7.74097e11	+	1.55640e13i	−0.0339330	+	0.682257i
$931$	3.02700e12			0.132050
$932$			1.94410e13i			0.844008i
$933$		−	5.51360e13i		−	2.38214i
$934$	2.17775e13			0.936367
$935$	5.22880e11	+	2.60061e10i	0.0223743	+	0.00111282i
$936$	−2.43227e13			−1.03579
$937$			2.42588e13i			1.02811i	0.857757	+	0.514056i	$0.171858\pi$
$937$			2.42588e13i			1.02811i	−0.857757	+	0.514056i	$0.828142\pi$
$938$		−	3.95748e12i		−	0.166919i
$939$	−5.35212e13			−2.24662
$940$	8.62652e12	+	4.29051e11i	0.360380	+	0.0179240i
$941$	−6.41319e12			−0.266637			−0.133319	−	0.991073i	$-0.542563\pi$
$941$	−6.41319e12			−0.266637			−0.133319	+	0.991073i	$0.542563\pi$
$942$		−	1.93154e12i		−	0.0799235i
$943$			3.11767e13i			1.28389i
$944$	6.01279e12			0.246435
$945$	2.15454e12	−	4.33192e13i	0.0878843	−	1.76700i
$946$	8.66570e11			0.0351798
$947$		−	1.66444e13i		−	0.672500i	−0.941773	−	0.336250i	$-0.890841\pi$
$947$		−	1.66444e13i		−	0.672500i	0.941773	−	0.336250i	$-0.109159\pi$
$948$			2.00840e13i			0.807631i
$949$	−3.90986e13			−1.56482
$950$	5.38568e11	−	5.40083e12i	0.0214528	−	0.215132i
$951$	2.21733e13			0.879058
$952$			3.24031e11i			0.0127856i
$953$		−	8.34836e12i		−	0.327856i	−0.986472	−	0.163928i	$-0.947584\pi$
$953$		−	8.34836e12i		−	0.327856i	0.986472	−	0.163928i	$-0.0524164\pi$
$954$	1.14745e13			0.448505
$955$	2.02679e12	−	4.07508e13i	0.0788487	−	1.58533i
$956$	−1.71623e13			−0.664529
$957$			2.35793e13i			0.908712i
$958$			1.23414e13i			0.473391i
$959$	−6.28738e12			−0.240041
$960$	−5.96234e12	−	2.96545e11i	−0.226567	−	0.0112686i
$961$	−1.89474e13			−0.716630
$962$			2.79914e13i			1.05375i
$963$		−	8.60545e13i		−	3.22445i
$964$	−8.18398e12			−0.305223
$965$	7.44961e11	+	3.70516e10i	0.0276542	+	0.00137542i
$966$	4.07585e13			1.50599
$967$		−	7.78660e12i		−	0.286371i	−0.989696	−	0.143185i	$-0.954265\pi$
$967$		−	7.78660e12i		−	0.286371i	0.989696	−	0.143185i	$-0.0457345\pi$
$968$			7.55259e12i			0.276476i
$969$	−7.30628e11			−0.0266219
$970$	1.78337e12	−	3.58564e13i	0.0646797	−	1.30045i
$971$	−2.49047e13			−0.899071			−0.449536	−	0.893262i	$-0.648410\pi$
$971$	−2.49047e13			−0.899071			−0.449536	+	0.893262i	$0.648410\pi$
$972$		−	1.69917e13i		−	0.610575i
$973$			3.26420e13i			1.16753i
$974$	1.12126e12			0.0399202
$975$	6.50922e13	+	6.49095e12i	2.30679	+	0.230032i
$976$	−6.05867e12			−0.213724
$977$			1.85806e13i			0.652429i	0.945296	+	0.326215i	$0.105773\pi$
$977$			1.85806e13i			0.652429i	−0.945296	+	0.326215i	$0.894227\pi$
$978$			2.35411e13i			0.822816i
$979$	1.68532e13			0.586354
$980$	−3.09739e11	+	6.22761e12i	−0.0107270	+	0.215677i
$981$	2.76645e13			0.953700
$982$		−	5.23825e12i		−	0.179757i
$983$			7.22251e12i			0.246716i	0.992362	+	0.123358i	$0.0393663\pi$
$983$			7.22251e12i			0.246716i	−0.992362	+	0.123358i	$0.960634\pi$
$984$	1.55591e13			0.529064
$985$	3.98823e13	+	1.98360e12i	1.34995	+	0.0671415i
$986$	−1.07981e12			−0.0363832
$987$			2.94302e13i			0.987111i
$988$		−	5.84896e12i		−	0.195287i
$989$	4.99174e12			0.165908
$990$	−2.28573e13	−	1.13684e12i	−0.756251	−	0.0376132i
$991$	2.71238e13			0.893344			0.446672	−	0.894698i	$-0.352609\pi$
$991$	2.71238e13			0.893344			0.446672	+	0.894698i	$0.352609\pi$
$992$			2.87015e12i			0.0941027i
$993$		−	4.94235e13i		−	1.61310i
$994$	−1.04615e13			−0.339902
$995$	−1.69715e12	+	3.41230e13i	−0.0548930	+	1.10368i
$996$	−4.54573e12			−0.146365
$997$		−	2.34124e13i		−	0.750442i	−0.926935	−	0.375221i	$-0.877567\pi$
$997$		−	2.34124e13i		−	0.750442i	0.926935	−	0.375221i	$-0.122433\pi$
$998$			2.48481e13i			0.792877i
$999$	−8.62023e13			−2.73826

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.10.b.a.9.4	yes	4
3.2	odd	2		90.10.c.b.19.1		4
4.3	odd	2		80.10.c.a.49.1		4
5.2	odd	4		50.10.a.h.1.2		2
5.3	odd	4		50.10.a.i.1.1		2
5.4	even	2	inner	10.10.b.a.9.1	✓	4
15.14	odd	2		90.10.c.b.19.3		4
20.3	even	4		400.10.a.s.1.2		2
20.7	even	4		400.10.a.m.1.1		2
20.19	odd	2		80.10.c.a.49.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.10.b.a.9.1	✓	4	5.4	even	2	inner
10.10.b.a.9.4	yes	4	1.1	even	1	trivial
50.10.a.h.1.2		2	5.2	odd	4
50.10.a.i.1.1		2	5.3	odd	4
80.10.c.a.49.1		4	4.3	odd	2
80.10.c.a.49.4		4	20.19	odd	2
90.10.c.b.19.1		4	3.2	odd	2
90.10.c.b.19.3		4	15.14	odd	2
400.10.a.m.1.1		2	20.7	even	4
400.10.a.s.1.2		2	20.3	even	4

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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	10.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+16.0000i q^{2} +254.606i q^{3} -256.000 q^{4} +(69.4228 - 1395.82i) q^{5} -4073.69 q^{6} +4788.05i q^{7} -4096.00i q^{8} -45141.1 q^{9} +O(q^{10})\)	\(q+16.0000i q^{2} +254.606i q^{3} -256.000 q^{4} +(69.4228 - 1395.82i) q^{5} -4073.69 q^{6} +4788.05i q^{7} -4096.00i q^{8} -45141.1 q^{9} +(22333.1 + 1110.77i) q^{10} +22672.8 q^{11} -65179.1i q^{12} +131546. i q^{13} -76608.7 q^{14} +(355383. + 17675.5i) q^{15} +65536.0 q^{16} +16522.2i q^{17} -722257. i q^{18} +173684. q^{19} +(-17772.2 + 357329. i) q^{20} -1.21906e6 q^{21} +362764. i q^{22} +2.08964e6i q^{23} +1.04286e6 q^{24} +(-1.94349e6 - 193803. i) q^{25} -2.10474e6 q^{26} -6.48177e6i q^{27} -1.22574e6i q^{28} +4.08468e6 q^{29} +(-282807. + 5.68613e6i) q^{30} +2.73719e6 q^{31} +1.04858e6i q^{32} +5.77261e6i q^{33} -264356. q^{34} +(6.68324e6 + 332400. i) q^{35} +1.15561e7 q^{36} -1.32992e7i q^{37} +2.77894e6i q^{38} -3.34925e7 q^{39} +(-5.71727e6 - 284356. i) q^{40} +1.49196e7 q^{41} -1.95050e7i q^{42} -2.38880e6i q^{43} -5.80422e6 q^{44} +(-3.13382e6 + 6.30087e7i) q^{45} -3.34343e7 q^{46} -2.41417e7i q^{47} +1.66858e7i q^{48} +1.74282e7 q^{49} +(3.10085e6 - 3.10958e7i) q^{50} -4.20666e6 q^{51} -3.36759e7i q^{52} +1.58870e7i q^{53} +1.03708e8 q^{54} +(1.57401e6 - 3.16470e7i) q^{55} +1.96118e7 q^{56} +4.42209e7i q^{57} +6.53548e7i q^{58} +9.17479e7 q^{59} +(-9.09781e7 - 4.52492e6i) q^{60} -9.24480e7 q^{61} +4.37950e7i q^{62} -2.16137e8i q^{63} -1.67772e7 q^{64} +(1.83615e8 + 9.13233e6i) q^{65} -9.23618e7 q^{66} +5.16583e7i q^{67} -4.22969e6i q^{68} -5.32035e8 q^{69} +(-5.31840e6 + 1.06932e8i) q^{70} +1.36557e8 q^{71} +1.84898e8i q^{72} +2.97223e8i q^{73} +2.12787e8 q^{74} +(4.93434e7 - 4.94823e8i) q^{75} -4.44631e7 q^{76} +1.08558e8i q^{77} -5.35880e8i q^{78} -3.08136e8 q^{79} +(4.54970e6 - 9.14763e7i) q^{80} +7.61784e8 q^{81} +2.38714e8i q^{82} -6.97423e7i q^{83} +3.12080e8 q^{84} +(2.30620e7 + 1.14702e6i) q^{85} +3.82208e7 q^{86} +1.03998e9i q^{87} -9.28676e7i q^{88} +7.43324e8 q^{89} +(-1.00814e9 - 5.01411e7i) q^{90} -6.29850e8 q^{91} -5.34949e8i q^{92} +6.96904e8i q^{93} +3.86266e8 q^{94} +(1.20576e7 - 2.42431e8i) q^{95} -2.66973e8 q^{96} -1.60553e9i q^{97} +2.78852e8i q^{98} -1.02347e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 1024 q^{4} - 2580 q^{5} - 4864 q^{6} - 71972 q^{9}+O(q^{10}) \) 4 * q - 1024 * q^4 - 2580 * q^5 - 4864 * q^6 - 71972 * q^9	\( 4 q - 1024 q^{4} - 2580 q^{5} - 4864 q^{6} - 71972 q^{9} + 55040 q^{10} - 103632 q^{11} + 185088 q^{14} + 644240 q^{15} + 262144 q^{16} + 317520 q^{19} + 660480 q^{20} - 4607632 q^{21} + 1245184 q^{24} - 401100 q^{25} - 5881344 q^{26} + 6668280 q^{29} - 5029120 q^{30} + 19247488 q^{31} - 2977792 q^{34} + 6511920 q^{35} + 18424832 q^{36} - 56263584 q^{39} - 14090240 q^{40} + 22774248 q^{41} + 26529792 q^{44} - 31158860 q^{45} - 31649024 q^{46} - 107972628 q^{49} - 22003200 q^{50} + 7292288 q^{51} + 302103040 q^{54} + 205671440 q^{55} - 47382528 q^{56} + 254661360 q^{59} - 164925440 q^{60} - 286581832 q^{61} - 67108864 q^{64} + 401103840 q^{65} - 429298688 q^{66} - 1289928464 q^{69} - 470536960 q^{70} + 802871328 q^{71} + 1078414848 q^{74} + 279560800 q^{75} - 81285120 q^{76} - 1033168320 q^{79} - 169082880 q^{80} + 1276755764 q^{81} + 1179553792 q^{84} + 95745920 q^{85} + 337295616 q^{86} - 276356760 q^{89} - 1921304320 q^{90} - 155016672 q^{91} + 1457997568 q^{94} + 64690800 q^{95} - 318767104 q^{96} - 3410843824 q^{99}+O(q^{100}) \) 4 * q - 1024 * q^4 - 2580 * q^5 - 4864 * q^6 - 71972 * q^9 + 55040 * q^10 - 103632 * q^11 + 185088 * q^14 + 644240 * q^15 + 262144 * q^16 + 317520 * q^19 + 660480 * q^20 - 4607632 * q^21 + 1245184 * q^24 - 401100 * q^25 - 5881344 * q^26 + 6668280 * q^29 - 5029120 * q^30 + 19247488 * q^31 - 2977792 * q^34 + 6511920 * q^35 + 18424832 * q^36 - 56263584 * q^39 - 14090240 * q^40 + 22774248 * q^41 + 26529792 * q^44 - 31158860 * q^45 - 31649024 * q^46 - 107972628 * q^49 - 22003200 * q^50 + 7292288 * q^51 + 302103040 * q^54 + 205671440 * q^55 - 47382528 * q^56 + 254661360 * q^59 - 164925440 * q^60 - 286581832 * q^61 - 67108864 * q^64 + 401103840 * q^65 - 429298688 * q^66 - 1289928464 * q^69 - 470536960 * q^70 + 802871328 * q^71 + 1078414848 * q^74 + 279560800 * q^75 - 81285120 * q^76 - 1033168320 * q^79 - 169082880 * q^80 + 1276755764 * q^81 + 1179553792 * q^84 + 95745920 * q^85 + 337295616 * q^86 - 276356760 * q^89 - 1921304320 * q^90 - 155016672 * q^91 + 1457997568 * q^94 + 64690800 * q^95 - 318767104 * q^96 - 3410843824 * q^99

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