LMFDB - Embedded newform 6.13.b.a.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,13,Mod(5,6)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 13, names="a")

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

chi := DirichletCharacter("6.5");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	6.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:	$5.48396290366$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{1009})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 499x^{2} + 500x + 64518 $ x^4 - 2x^3 - 499x^2 + 500*x + 64518
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{9}\cdot 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.2
Root			$-15.3824 + 1.41421i$ of defining polynomial
Character	$\chi$	$=$	6.5
Dual form			6.13.b.a.5.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-45.2548i q^{2} +(385.589 + 618.678i) q^{3} -2048.00 q^{4} +16348.2i q^{5} +(27998.2 - 17449.7i) q^{6} +213230. q^{7} +92681.9i q^{8} +(-234084. + 477110. i) q^{9} +O(q^{10})$	\(q-45.2548i q^{2} +(385.589 + 618.678i) q^{3} -2048.00 q^{4} +16348.2i q^{5} +(27998.2 - 17449.7i) q^{6} +213230. q^{7} +92681.9i q^{8} +(-234084. + 477110. i) q^{9} +739833. q^{10} +852.534i q^{11} +(-789685. - 1.26705e6i) q^{12} -3.33264e6 q^{13} -9.64970e6i q^{14} +(-1.01142e7 + 6.30366e6i) q^{15} +4.19430e6 q^{16} +4.86457e6i q^{17} +(2.15915e7 + 1.05934e7i) q^{18} +139363. q^{19} -3.34810e7i q^{20} +(8.22192e7 + 1.31921e8i) q^{21} +38581.3 q^{22} -2.14185e8i q^{23} +(-5.73403e7 + 3.57371e7i) q^{24} -2.31215e7 q^{25} +1.50818e8i q^{26} +(-3.85438e8 + 3.91457e7i) q^{27} -4.36696e8 q^{28} -8.70204e8i q^{29} +(2.85271e8 + 4.57718e8i) q^{30} +1.12677e9 q^{31} -1.89813e8i q^{32} +(-527444. + 328727. i) q^{33} +2.20145e8 q^{34} +3.48592e9i q^{35} +(4.79404e8 - 9.77122e8i) q^{36} +1.03091e8 q^{37} -6.30686e6i q^{38} +(-1.28503e9 - 2.06183e9i) q^{39} -1.51518e9 q^{40} -6.26279e8i q^{41} +(5.97006e9 - 3.72081e9i) q^{42} -5.27511e9 q^{43} -1.74599e6i q^{44} +(-7.79987e9 - 3.82684e9i) q^{45} -9.69290e9 q^{46} +1.16315e10i q^{47} +(1.61728e9 + 2.59492e9i) q^{48} +3.16259e10 q^{49} +1.04636e9i q^{50} +(-3.00960e9 + 1.87572e9i) q^{51} +6.82525e9 q^{52} -2.31027e10i q^{53} +(1.77153e9 + 1.74429e10i) q^{54} -1.39374e7 q^{55} +1.97626e10i q^{56} +(5.37369e7 + 8.62209e7i) q^{57} -3.93810e10 q^{58} -3.43476e10i q^{59} +(2.07140e10 - 1.29099e10i) q^{60} -1.42406e10 q^{61} -5.09916e10i q^{62} +(-4.99138e10 + 1.01734e11i) q^{63} -8.58993e9 q^{64} -5.44825e10i q^{65} +(1.48765e7 + 2.38694e7i) q^{66} -4.78304e10 q^{67} -9.96263e9i q^{68} +(1.32511e11 - 8.25872e10i) q^{69} +1.57755e11 q^{70} +2.46340e11i q^{71} +(-4.42195e10 - 2.16953e10i) q^{72} +5.45866e9 q^{73} -4.66537e9i q^{74} +(-8.91540e9 - 1.43048e10i) q^{75} -2.85416e8 q^{76} +1.81786e8i q^{77} +(-9.33079e10 + 5.81537e10i) q^{78} -3.27325e9 q^{79} +6.85691e10i q^{80} +(-1.72839e11 - 2.23368e11i) q^{81} -2.83421e10 q^{82} -1.55235e11i q^{83} +(-1.68385e11 - 2.70174e11i) q^{84} -7.95267e10 q^{85} +2.38724e11i q^{86} +(5.38376e11 - 3.35541e11i) q^{87} -7.90144e7 q^{88} +2.37864e10i q^{89} +(-1.73183e11 + 3.52982e11i) q^{90} -7.10620e11 q^{91} +4.38651e11i q^{92} +(4.34468e11 + 6.97105e11i) q^{93} +5.26383e11 q^{94} +2.27833e9i q^{95} +(1.17433e11 - 7.31895e10i) q^{96} +7.71674e11 q^{97} -1.43122e12i q^{98} +(-4.06753e8 - 1.99564e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 780 q^{3} - 8192 q^{4} - 9984 q^{6} + 153080 q^{7} - 1530972 q^{9}+O(q^{10}) $ 4 * q + 780 * q^3 - 8192 * q^4 - 9984 * q^6 + 153080 * q^7 - 1530972 * q^9	\( 4 q + 780 q^{3} - 8192 q^{4} - 9984 q^{6} + 153080 q^{7} - 1530972 q^{9} + 1641984 q^{10} - 1597440 q^{12} + 7253000 q^{13} - 17613792 q^{15} + 16777216 q^{16} + 42600960 q^{18} - 120268072 q^{19} + 163232328 q^{21} - 159244800 q^{22} + 20447232 q^{24} + 435605764 q^{25} - 784941300 q^{27} - 313507840 q^{28} + 571258368 q^{30} + 2731727672 q^{31} - 2567489760 q^{33} - 3097810944 q^{34} + 3135430656 q^{36} - 15280120 q^{37} - 2508657000 q^{39} - 3362783232 q^{40} + 20958988800 q^{42} + 1629119960 q^{43} - 15576677568 q^{45} - 29905849344 q^{46} + 3271557120 q^{48} + 72937649100 q^{49} - 63012636288 q^{51} - 14854144000 q^{52} + 38602586880 q^{54} + 6285799872 q^{55} - 424311000 q^{57} - 62351992320 q^{58} + 36073046016 q^{60} + 45477065096 q^{61} + 45447449400 q^{63} - 34359738368 q^{64} - 673085952 q^{66} - 213433609960 q^{67} + 95560926912 q^{69} + 293322353664 q^{70} - 87246766080 q^{72} - 254383625080 q^{73} - 15705158772 q^{75} + 246309011456 q^{76} - 645782208000 q^{78} + 308580159032 q^{79} + 219015659268 q^{81} + 234603709440 q^{82} - 334299807744 q^{84} - 18844054272 q^{85} + 1341091294560 q^{87} + 326133350400 q^{88} - 432622121472 q^{90} - 3323734346000 q^{91} + 871044956040 q^{93} + 775668172800 q^{94} - 41875931136 q^{96} + 1276228475720 q^{97} - 23456841408 q^{99}+O(q^{100}) \) 4 * q + 780 * q^3 - 8192 * q^4 - 9984 * q^6 + 153080 * q^7 - 1530972 * q^9 + 1641984 * q^10 - 1597440 * q^12 + 7253000 * q^13 - 17613792 * q^15 + 16777216 * q^16 + 42600960 * q^18 - 120268072 * q^19 + 163232328 * q^21 - 159244800 * q^22 + 20447232 * q^24 + 435605764 * q^25 - 784941300 * q^27 - 313507840 * q^28 + 571258368 * q^30 + 2731727672 * q^31 - 2567489760 * q^33 - 3097810944 * q^34 + 3135430656 * q^36 - 15280120 * q^37 - 2508657000 * q^39 - 3362783232 * q^40 + 20958988800 * q^42 + 1629119960 * q^43 - 15576677568 * q^45 - 29905849344 * q^46 + 3271557120 * q^48 + 72937649100 * q^49 - 63012636288 * q^51 - 14854144000 * q^52 + 38602586880 * q^54 + 6285799872 * q^55 - 424311000 * q^57 - 62351992320 * q^58 + 36073046016 * q^60 + 45477065096 * q^61 + 45447449400 * q^63 - 34359738368 * q^64 - 673085952 * q^66 - 213433609960 * q^67 + 95560926912 * q^69 + 293322353664 * q^70 - 87246766080 * q^72 - 254383625080 * q^73 - 15705158772 * q^75 + 246309011456 * q^76 - 645782208000 * q^78 + 308580159032 * q^79 + 219015659268 * q^81 + 234603709440 * q^82 - 334299807744 * q^84 - 18844054272 * q^85 + 1341091294560 * q^87 + 326133350400 * q^88 - 432622121472 * q^90 - 3323734346000 * q^91 + 871044956040 * q^93 + 775668172800 * q^94 - 41875931136 * q^96 + 1276228475720 * q^97 - 23456841408 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/6\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$-1$

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 $

$2$		−	45.2548i		−	0.707107i
$2$		−	45.2548i		−	0.707107i
$3$	385.589	+	618.678i	0.528928	+	0.848667i
$3$	385.589	+	618.678i	0.528928	+	0.848667i
$4$	−2048.00			−0.500000
$5$			16348.2i			1.04628i	0.852246	+	0.523141i	$0.175240\pi$
$5$			16348.2i			1.04628i	−0.852246	+	0.523141i	$0.824760\pi$
$6$	27998.2	−	17449.7i	0.600098	−	0.374009i
$7$	213230.			1.81243			0.906214	−	0.422820i	$-0.138960\pi$
$7$	213230.			1.81243			0.906214	+	0.422820i	$0.138960\pi$
$8$			92681.9i			0.353553i
$9$	−234084.	+	477110.i	−0.440470	+	0.897767i
$10$	739833.			0.739833
$11$			852.534i			0.000481233i	1.00000		0.000240617i	$7.65906e-5\pi$
$11$			852.534i			0.000481233i	−1.00000		0.000240617i	$0.999923\pi$
$12$	−789685.	−	1.26705e6i	−0.264464	−	0.424333i
$13$	−3.33264e6			−0.690444			−0.345222	−	0.938521i	$-0.612196\pi$
$13$	−3.33264e6			−0.690444			−0.345222	+	0.938521i	$0.612196\pi$
$14$		−	9.64970e6i		−	1.28158i
$15$	−1.01142e7	+	6.30366e6i	−0.887945	+	0.553408i
$16$	4.19430e6			0.250000
$17$			4.86457e6i			0.201535i	0.994910	+	0.100768i	$0.0321298\pi$
$17$			4.86457e6i			0.201535i	−0.994910	+	0.100768i	$0.967870\pi$
$18$	2.15915e7	+	1.05934e7i	0.634817	+	0.311459i
$19$	139363.			0.00296228			0.00148114	−	0.999999i	$-0.499529\pi$
$19$	139363.			0.00296228			0.00148114	+	0.999999i	$0.499529\pi$
$20$		−	3.34810e7i		−	0.523141i
$21$	8.22192e7	+	1.31921e8i	0.958644	+	1.53815i
$22$	38581.3			0.000340283
$23$		−	2.14185e8i		−	1.44684i	−0.690406	−	0.723422i	$-0.742568\pi$
$23$		−	2.14185e8i		−	1.44684i	0.690406	−	0.723422i	$-0.257432\pi$
$24$	−5.73403e7	+	3.57371e7i	−0.300049	+	0.187004i
$25$	−2.31215e7			−0.0947058
$26$			1.50818e8i			0.488218i
$27$	−3.85438e8	+	3.91457e7i	−0.994882	+	0.101042i
$28$	−4.36696e8			−0.906214
$29$		−	8.70204e8i		−	1.46296i	−0.681861	−	0.731481i	$-0.738829\pi$
$29$		−	8.70204e8i		−	1.46296i	0.681861	−	0.731481i	$-0.261171\pi$
$30$	2.85271e8	+	4.57718e8i	0.391318	+	0.627872i
$31$	1.12677e9			1.26959			0.634795	−	0.772681i	$-0.281085\pi$
$31$	1.12677e9			1.26959			0.634795	+	0.772681i	$0.281085\pi$
$32$		−	1.89813e8i		−	0.176777i
$33$	−527444.	+	328727.i	−0.000408406	+	0.000254538i
$34$	2.20145e8			0.142507
$35$			3.48592e9i			1.89631i
$36$	4.79404e8	−	9.77122e8i	0.220235	−	0.448884i
$37$	1.03091e8			0.0401800			0.0200900	−	0.999798i	$-0.493605\pi$
$37$	1.03091e8			0.0401800			0.0200900	+	0.999798i	$0.493605\pi$
$38$		−	6.30686e6i		−	0.00209465i
$39$	−1.28503e9	−	2.06183e9i	−0.365195	−	0.585957i
$40$	−1.51518e9			−0.369917
$41$		−	6.26279e8i		−	0.131845i	−0.997825	−	0.0659226i	$-0.979001\pi$
$41$		−	6.26279e8i		−	0.131845i	0.997825	−	0.0659226i	$-0.0209990\pi$
$42$	5.97006e9	−	3.72081e9i	1.08763	−	0.677864i
$43$	−5.27511e9			−0.834490			−0.417245	−	0.908794i	$-0.637004\pi$
$43$	−5.27511e9			−0.834490			−0.417245	+	0.908794i	$0.637004\pi$
$44$		−	1.74599e6i		−	0.000240617i
$45$	−7.79987e9	−	3.82684e9i	−0.939318	−	0.460856i
$46$	−9.69290e9			−1.02307
$47$			1.16315e10i			1.07907i	0.841963	+	0.539535i	$0.181400\pi$
$47$			1.16315e10i			1.07907i	−0.841963	+	0.539535i	$0.818600\pi$
$48$	1.61728e9	+	2.59492e9i	0.132232	+	0.212167i
$49$	3.16259e10			2.28489
$50$			1.04636e9i			0.0669671i
$51$	−3.00960e9	+	1.87572e9i	−0.171036	+	0.106598i
$52$	6.82525e9			0.345222
$53$		−	2.31027e10i		−	1.04233i	−0.853454	−	0.521167i	$-0.825497\pi$
$53$		−	2.31027e10i		−	1.04233i	0.853454	−	0.521167i	$-0.174503\pi$
$54$	1.77153e9	+	1.74429e10i	0.0714474	+	0.703488i
$55$	−1.39374e7			−0.000503505
$56$			1.97626e10i			0.640790i
$57$	5.37369e7	+	8.62209e7i	0.00156683	+	0.00251399i
$58$	−3.93810e10			−1.03447
$59$		−	3.43476e10i		−	0.814299i	−0.913362	−	0.407150i	$-0.866523\pi$
$59$		−	3.43476e10i		−	0.814299i	0.913362	−	0.407150i	$-0.133477\pi$
$60$	2.07140e10	−	1.29099e10i	0.443972	−	0.276704i
$61$	−1.42406e10			−0.276407			−0.138204	−	0.990404i	$-0.544133\pi$
$61$	−1.42406e10			−0.276407			−0.138204	+	0.990404i	$0.544133\pi$
$62$		−	5.09916e10i		−	0.897735i
$63$	−4.99138e10	+	1.01734e11i	−0.798320	+	1.62714i
$64$	−8.58993e9			−0.125000
$65$		−	5.44825e10i		−	0.722399i
$66$	1.48765e7	+	2.38694e7i	0.000179985	+	0.000288787i
$67$	−4.78304e10			−0.528756			−0.264378	−	0.964419i	$-0.585167\pi$
$67$	−4.78304e10			−0.528756			−0.264378	+	0.964419i	$0.585167\pi$
$68$		−	9.96263e9i		−	0.100768i
$69$	1.32511e11	−	8.25872e10i	1.22789	−	0.765277i
$70$	1.57755e11			1.34089
$71$			2.46340e11i			1.92302i	0.274762	+	0.961512i	$0.411401\pi$
$71$			2.46340e11i			1.92302i	−0.274762	+	0.961512i	$0.588599\pi$
$72$	−4.42195e10	−	2.16953e10i	−0.317409	−	0.155730i
$73$	5.45866e9			0.0360702			0.0180351	−	0.999837i	$-0.494259\pi$
$73$	5.45866e9			0.0360702			0.0180351	+	0.999837i	$0.494259\pi$
$74$		−	4.66537e9i		−	0.0284116i
$75$	−8.91540e9	−	1.43048e10i	−0.0500926	−	0.0803737i
$76$	−2.85416e8			−0.00148114
$77$			1.81786e8i			0.000872200i
$78$	−9.33079e10	+	5.81537e10i	−0.414334	+	0.258232i
$79$	−3.27325e9			−0.0134653			−0.00673266	−	0.999977i	$-0.502143\pi$
$79$	−3.27325e9			−0.0134653			−0.00673266	+	0.999977i	$0.502143\pi$
$80$			6.85691e10i			0.261570i
$81$	−1.72839e11	−	2.23368e11i	−0.611972	−	0.790879i
$82$	−2.83421e10			−0.0932287
$83$		−	1.55235e11i		−	0.474812i	−0.971411	−	0.237406i	$-0.923703\pi$
$83$		−	1.55235e11i		−	0.474812i	0.971411	−	0.237406i	$-0.0762971\pi$
$84$	−1.68385e11	−	2.70174e11i	−0.479322	−	0.769073i
$85$	−7.95267e10			−0.210862
$86$			2.38724e11i			0.590073i
$87$	5.38376e11	−	3.35541e11i	1.24157	−	0.773802i
$88$	−7.90144e7			−0.000170142
$89$			2.37864e10i			0.0478618i	0.999714	+	0.0239309i	$0.00761817\pi$
$89$			2.37864e10i			0.0478618i	−0.999714	+	0.0239309i	$0.992382\pi$
$90$	−1.73183e11	+	3.52982e11i	−0.325874	+	0.664198i
$91$	−7.10620e11			−1.25138
$92$			4.38651e11i			0.723422i
$93$	4.34468e11	+	6.97105e11i	0.671521	+	1.07746i
$94$	5.26383e11			0.763018
$95$			2.27833e9i			0.00309938i
$96$	1.17433e11	−	7.31895e10i	0.150024	−	0.0935022i
$97$	7.71674e11			0.926410			0.463205	−	0.886251i	$-0.346699\pi$
$97$	7.71674e11			0.926410			0.463205	+	0.886251i	$0.346699\pi$
$98$		−	1.43122e12i		−	1.61566i
$99$	−4.06753e8	−	1.99564e8i	−0.000432035	−	0.000211969i
$100$	4.73529e10			0.0473529
$101$			3.92747e11i			0.369986i	0.982740	+	0.184993i	$0.0592262\pi$
$101$			3.92747e11i			0.369986i	−0.982740	+	0.184993i	$0.940774\pi$
$102$	8.48854e10	+	1.36199e11i	0.0753758	+	0.120941i
$103$	4.24634e11			0.355624			0.177812	−	0.984064i	$-0.443098\pi$
$103$	4.24634e11			0.355624			0.177812	+	0.984064i	$0.443098\pi$
$104$		−	3.08876e11i		−	0.244109i
$105$	−2.15666e12	+	1.34413e12i	−1.60934	+	1.00301i
$106$	−1.04551e12			−0.737042
$107$		−	1.74326e12i		−	1.16161i	−0.814043	−	0.580805i	$-0.802738\pi$
$107$		−	1.74326e12i		−	1.16161i	0.814043	−	0.580805i	$-0.197262\pi$
$108$	7.89376e11	−	8.01704e10i	0.497441	−	0.0505210i
$109$	−2.44553e12			−1.45819			−0.729094	−	0.684414i	$-0.760058\pi$
$109$	−2.44553e12			−1.45819			−0.729094	+	0.684414i	$0.760058\pi$
$110$			6.30733e8i			0.000356032i
$111$	3.97507e10	+	6.37801e10i	0.0212524	+	0.0340995i
$112$	8.94353e11			0.453107
$113$		−	2.15570e11i		−	0.103542i	−0.998659	−	0.0517710i	$-0.983513\pi$
$113$		−	2.15570e11i		−	0.103542i	0.998659	−	0.0517710i	$-0.0164866\pi$
$114$	3.90191e9	−	2.43185e9i	0.00177766	−	0.00110792i
$115$	3.50153e12			1.51381
$116$			1.78218e12i			0.731481i
$117$	7.80118e11	−	1.59004e12i	0.304120	−	0.619858i
$118$	−1.55439e12			−0.575796
$119$			1.03727e12i			0.365268i
$120$	−5.84235e11	−	9.37407e11i	−0.195659	−	0.313936i
$121$	3.13843e12			1.00000
$122$			6.44456e11i			0.195449i
$123$	3.87465e11	−	2.41486e11i	0.111893	−	0.0697366i
$124$	−2.30761e12			−0.634795
$125$			3.61325e12i			0.947193i
$126$	4.60397e12	+	2.25884e12i	1.15056	+	0.564498i
$127$	−1.47297e12			−0.351052			−0.175526	−	0.984475i	$-0.556163\pi$
$127$	−1.47297e12			−0.351052			−0.175526	+	0.984475i	$0.556163\pi$
$128$			3.88736e11i			0.0883883i
$129$	−2.03402e12	−	3.26360e12i	−0.441385	−	0.708203i
$130$	−2.46560e12			−0.510813
$131$		−	3.60486e12i		−	0.713281i	−0.934242	−	0.356641i	$-0.883922\pi$
$131$		−	3.60486e12i		−	0.713281i	0.934242	−	0.356641i	$-0.116078\pi$
$132$	1.08020e9	−	6.73233e8i	0.000204203	−	0.000127269i
$133$	2.97165e10			0.00536892
$134$			2.16456e12i			0.373887i
$135$	−6.39960e11	−	6.30120e12i	−0.105718	−	1.04093i
$136$	−4.50857e11			−0.0712534
$137$			6.26064e12i			0.946881i	0.880826	+	0.473441i	$0.156988\pi$
$137$			6.26064e12i			0.946881i	−0.880826	+	0.473441i	$0.843012\pi$
$138$	−3.73747e12	−	5.99678e12i	−0.541132	−	0.868248i
$139$	−8.13201e12			−1.12748			−0.563740	−	0.825952i	$-0.690638\pi$
$139$	−8.13201e12			−1.12748			−0.563740	+	0.825952i	$0.690638\pi$
$140$		−	7.13917e12i		−	0.948155i
$141$	−7.19617e12	+	4.48498e12i	−0.915771	+	0.570750i
$142$	1.11481e13			1.35978
$143$		−	2.84119e9i		−	0.000332264i
$144$	−9.81819e11	+	2.00115e12i	−0.110118	+	0.224442i
$145$	1.42262e13			1.53067
$146$		−	2.47031e11i		−	0.0255055i
$147$	1.21946e13	+	1.95662e13i	1.20854	+	1.93911i
$148$	−2.11130e11			−0.0200900
$149$		−	1.13143e13i		−	1.03398i	−0.855992	−	0.516989i	$-0.827053\pi$
$149$		−	1.13143e13i		−	1.03398i	0.855992	−	0.516989i	$-0.172947\pi$
$150$	−6.47361e11	+	4.03465e11i	−0.0568328	+	0.0354208i
$151$	−1.38841e13			−1.17126			−0.585632	−	0.810577i	$-0.699154\pi$
$151$	−1.38841e13			−1.17126			−0.585632	+	0.810577i	$0.699154\pi$
$152$			1.29164e10i			0.00104733i
$153$	−2.32093e12	−	1.13872e12i	−0.180932	−	0.0887702i
$154$	8.22670e9			0.000616739
$155$			1.84205e13i			1.32835i
$156$	2.63174e12	+	4.22263e12i	0.182598	+	0.292978i
$157$	5.93112e12			0.396040			0.198020	−	0.980198i	$-0.436549\pi$
$157$	5.93112e12			0.396040			0.198020	+	0.980198i	$0.436549\pi$
$158$			1.48130e11i			0.00952142i
$159$	1.42931e13	−	8.90813e12i	0.884595	−	0.551320i
$160$	3.10308e12			0.184958
$161$		−	4.56707e13i		−	2.62230i
$162$	−1.01085e13	+	7.82180e12i	−0.559236	+	0.432730i
$163$	−1.74928e13			−0.932684			−0.466342	−	0.884605i	$-0.654428\pi$
$163$	−1.74928e13			−0.932684			−0.466342	+	0.884605i	$0.654428\pi$
$164$			1.28262e12i			0.0659226i
$165$	−5.37408e9	−	8.62273e9i	−0.000266318	−	0.000427308i
$166$	−7.02514e12			−0.335743
$167$			3.60095e12i			0.166004i	0.996549	+	0.0830020i	$0.0264508\pi$
$167$			3.60095e12i			0.166004i	−0.996549	+	0.0830020i	$0.973549\pi$
$168$	−1.22267e13	+	7.62023e12i	−0.543817	+	0.338932i
$169$	−1.21916e13			−0.523287
$170$			3.59897e12i			0.149102i
$171$	−3.26227e10	+	6.64916e10i	−0.00130480	+	0.00265944i
$172$	1.08034e13			0.417245
$173$			3.24459e13i			1.21027i	0.796122	+	0.605136i	$0.206881\pi$
$173$			3.24459e13i			1.21027i	−0.796122	+	0.605136i	$0.793119\pi$
$174$	−1.51848e13	−	2.43641e13i	−0.547161	−	0.877921i
$175$	−4.93021e12			−0.171647
$176$			3.57579e9i			0.000120308i
$177$	2.12501e13	−	1.32440e13i	0.691068	−	0.430706i
$178$	1.07645e12			0.0338434
$179$			2.20723e11i			0.00671011i	0.999994	+	0.00335506i	$0.00106795\pi$
$179$			2.20723e11i			0.00671011i	−0.999994	+	0.00335506i	$0.998932\pi$
$180$	1.59741e13	+	7.83737e12i	0.469659	+	0.230428i
$181$	5.43002e13			1.54429			0.772147	−	0.635444i	$-0.219183\pi$
$181$	5.43002e13			1.54429			0.772147	+	0.635444i	$0.219183\pi$
$182$			3.21590e13i			0.884859i
$183$	−5.49101e12	−	8.81035e12i	−0.146199	−	0.234578i
$184$	1.98511e13			0.511537
$185$			1.68535e12i			0.0420397i
$186$	3.15474e13	−	1.96618e13i	0.761878	−	0.474837i
$187$	−4.14721e9			−9.69853e−5
$188$		−	2.38214e13i		−	0.539535i
$189$	−8.21870e13	+	8.34705e12i	−1.80315	+	0.183131i
$190$	1.03106e11			0.00219159
$191$			6.56069e13i			1.35129i	0.737226	+	0.675646i	$0.236135\pi$
$191$			6.56069e13i			1.35129i	−0.737226	+	0.675646i	$0.763865\pi$
$192$	−3.31218e12	−	5.31440e12i	−0.0661160	−	0.106083i
$193$	−4.70043e12			−0.0909480			−0.0454740	−	0.998966i	$-0.514480\pi$
$193$	−4.70043e12			−0.0909480			−0.0454740	+	0.998966i	$0.514480\pi$
$194$		−	3.49220e13i		−	0.655071i
$195$	3.37071e13	−	2.10078e13i	0.613076	−	0.382097i
$196$	−6.47698e13			−1.14245
$197$			7.41144e13i			1.26796i	0.773350	+	0.633979i	$0.218579\pi$
$197$			7.41144e13i			1.26796i	−0.773350	+	0.633979i	$0.781421\pi$
$198$	−9.03126e9	+	1.84075e10i	−0.000149885	+	0.000305495i
$199$	−6.50316e13			−1.04714			−0.523572	−	0.851982i	$-0.675401\pi$
$199$	−6.50316e13			−1.04714			−0.523572	+	0.851982i	$0.675401\pi$
$200$		−	2.14295e12i		−	0.0334836i
$201$	−1.84429e13	−	2.95916e13i	−0.279674	−	0.448738i
$202$	1.77737e13			0.261619
$203$		−	1.85554e14i		−	2.65151i
$204$	6.16366e12	−	3.84148e12i	0.0855180	−	0.0532988i
$205$	1.02385e13			0.137947
$206$		−	1.92168e13i		−	0.251464i
$207$	1.02190e14	+	5.01372e13i	1.29893	+	0.637292i
$208$	−1.39781e13			−0.172611
$209$			1.18812e8i			1.42555e-6i
$210$	6.08285e13	+	9.75994e13i	0.709236	+	1.13797i
$211$	2.09872e12			0.0237826			0.0118913	−	0.999929i	$-0.496215\pi$
$211$	2.09872e12			0.0237826			0.0118913	+	0.999929i	$0.496215\pi$
$212$			4.73143e13i			0.521167i
$213$	−1.52405e14	+	9.49859e13i	−1.63201	+	1.01714i
$214$	−7.88911e13			−0.821383
$215$		−	8.62383e13i		−	0.873111i
$216$	−3.62810e12	−	3.57231e13i	−0.0357237	−	0.351744i
$217$	2.40260e14			2.30104
$218$			1.10672e14i			1.03109i
$219$	2.10480e12	+	3.37715e12i	0.0190786	+	0.0306116i
$220$	2.85437e10			0.000251753
$221$		−	1.62119e13i		−	0.139149i
$222$	2.88636e12	−	1.79891e12i	0.0241120	−	0.0150277i
$223$	1.35273e14			1.09997			0.549985	−	0.835175i	$-0.314634\pi$
$223$	1.35273e14			1.09997			0.549985	+	0.835175i	$0.314634\pi$
$224$		−	4.04738e13i		−	0.320395i
$225$	5.41238e12	−	1.10315e13i	0.0417151	−	0.0850238i
$226$	−9.75556e12			−0.0732153
$227$			1.47283e14i			1.07646i	0.842799	+	0.538228i	$0.180906\pi$
$227$			1.47283e14i			1.07646i	−0.842799	+	0.538228i	$0.819094\pi$
$228$	−1.10053e11	−	1.76581e11i	−0.000783417	−	0.00125700i
$229$	−2.38967e14			−1.65701			−0.828506	−	0.559980i	$-0.810809\pi$
$229$	−2.38967e14			−1.65701			−0.828506	+	0.559980i	$0.810809\pi$
$230$		−	1.58461e14i		−	1.07042i
$231$	−1.12467e11	+	7.00946e10i	−0.000740207	+	0.000461331i
$232$	8.06522e13			0.517235
$233$		−	1.61488e14i		−	1.00927i	−0.863334	−	0.504633i	$-0.831628\pi$
$233$		−	1.61488e14i		−	1.00927i	0.863334	−	0.504633i	$-0.168372\pi$
$234$	−7.19569e13	−	3.53041e13i	−0.438306	−	0.215045i
$235$	−1.90154e14			−1.12901
$236$			7.03438e13i			0.407150i
$237$	−1.26213e12	−	2.02509e12i	−0.00712218	−	0.0114276i
$238$	4.69416e13			0.258283
$239$		−	5.62519e13i		−	0.301821i	−0.988547	−	0.150911i	$-0.951779\pi$
$239$		−	5.62519e13i		−	0.301821i	0.988547	−	0.150911i	$-0.0482206\pi$
$240$	−4.24222e13	+	2.64395e13i	−0.221986	+	0.138352i
$241$	−8.88716e13			−0.453587			−0.226794	−	0.973943i	$-0.572824\pi$
$241$	−8.88716e13			−0.453587			−0.226794	+	0.973943i	$0.572824\pi$
$242$		−	1.42029e14i		−	0.707107i
$243$	7.15480e13	−	1.93060e14i	0.347504	−	0.937679i
$244$	2.91647e13			0.138204
$245$			5.17025e14i			2.39064i
$246$	−1.09284e13	−	1.75347e13i	−0.0493113	−	0.0791201i
$247$	−4.64448e11			−0.00204529
$248$			1.04431e14i			0.448868i
$249$	9.60405e13	−	5.98569e13i	0.402957	−	0.251141i
$250$	1.63517e14			0.669767
$251$			2.67084e14i			1.06808i	0.845458	+	0.534041i	$0.179327\pi$
$251$			2.67084e14i			1.06808i	−0.845458	+	0.534041i	$0.820673\pi$
$252$	1.02223e14	−	2.08352e14i	0.399160	−	0.813569i
$253$	1.82600e11			0.000696269
$254$			6.66590e13i			0.248231i
$255$	−3.06646e13	−	4.92014e13i	−0.111531	−	0.178952i
$256$	1.75922e13			0.0625000
$257$		−	3.21863e14i		−	1.11705i	−0.829488	−	0.558524i	$-0.811368\pi$
$257$		−	3.21863e14i		−	1.11705i	0.829488	−	0.558524i	$-0.188632\pi$
$258$	−1.47693e14	+	9.20494e13i	−0.500775	+	0.312106i
$259$	2.19821e13			0.0728234
$260$			1.11580e14i			0.361200i
$261$	4.15183e14	+	2.03701e14i	1.31340	+	0.644391i
$262$	−1.63137e14			−0.504366
$263$			1.73324e13i			0.0523750i	0.999657	+	0.0261875i	$0.00833669\pi$
$263$			1.73324e13i			0.0523750i	−0.999657	+	0.0261875i	$0.991663\pi$
$264$	−3.04671e10	−	4.88845e10i	−8.99927e−5	−	0.000144393i
$265$	3.77686e14			1.09058
$266$		−	1.34481e12i		−	0.00379640i
$267$	−1.47161e13	+	9.17178e12i	−0.0406187	+	0.0253155i
$268$	9.79568e13			0.264378
$269$		−	3.54423e14i		−	0.935424i	−0.883881	−	0.467712i	$-0.845079\pi$
$269$		−	3.54423e14i		−	0.935424i	0.883881	−	0.467712i	$-0.154921\pi$
$270$	−2.85160e14	+	2.89613e13i	−0.736047	+	0.0747541i
$271$	−5.34635e14			−1.34971			−0.674857	−	0.737948i	$-0.735795\pi$
$271$	−5.34635e14			−1.34971			−0.674857	+	0.737948i	$0.735795\pi$
$272$			2.04035e13i			0.0503838i
$273$	−2.74007e14	−	4.39645e14i	−0.661890	−	1.06200i
$274$	2.83324e14			0.669546
$275$		−	1.97119e10i		−	4.55756e-5i
$276$	−2.71383e14	+	1.69139e14i	−0.613944	+	0.382638i
$277$	−2.82862e14			−0.626174			−0.313087	−	0.949724i	$-0.601363\pi$
$277$	−2.82862e14			−0.626174			−0.313087	+	0.949724i	$0.601363\pi$
$278$			3.68013e14i			0.797249i
$279$	−2.63758e14	+	5.37591e14i	−0.559216	+	1.13980i
$280$	−3.23082e14			−0.670447
$281$		−	7.49040e14i		−	1.52148i	−0.649056	−	0.760741i	$-0.724836\pi$
$281$		−	7.49040e14i		−	1.52148i	0.649056	−	0.760741i	$-0.275164\pi$
$282$	2.02967e14	+	3.25661e14i	0.403581	+	0.647548i
$283$	2.80787e14			0.546586			0.273293	−	0.961931i	$-0.411887\pi$
$283$	2.80787e14			0.546586			0.273293	+	0.961931i	$0.411887\pi$
$284$		−	5.04504e14i		−	0.961512i
$285$	−1.40955e12	+	8.78498e11i	−0.00263034	+	0.00163935i
$286$	−1.28578e11			−0.000234946
$287$		−	1.33542e14i		−	0.238960i
$288$	9.05615e13	+	4.44321e13i	0.158704	+	0.0778649i
$289$	5.58958e14			0.959384
$290$		−	6.43806e14i		−	1.08235i
$291$	2.97549e14	+	4.77418e14i	0.490004	+	0.786213i
$292$	−1.11793e13			−0.0180351
$293$			8.61814e14i			1.36210i	0.732238	+	0.681048i	$0.238476\pi$
$293$			8.61814e14i			1.36210i	−0.732238	+	0.681048i	$0.761524\pi$
$294$	8.85467e14	−	5.51863e14i	1.37116	−	0.854570i
$295$	5.61519e14			0.851986
$296$			9.55467e12i			0.0142058i
$297$	−3.33730e10	−	3.28599e11i	−4.86247e−5	−	0.000478770i
$298$	−5.12028e14			−0.731132
$299$			7.13801e14i			0.998965i
$300$	1.82587e13	+	2.92962e13i	0.0250463	+	0.0401868i
$301$	−1.12481e15			−1.51245
$302$			6.28321e14i			0.828209i
$303$	−2.42984e14	+	1.51439e14i	−0.313995	+	0.195696i
$304$	5.84532e11			0.000740571
$305$		−	2.32808e14i		−	0.289200i
$306$	−5.15324e13	+	1.05034e14i	−0.0627700	+	0.127938i
$307$	1.26432e14			0.151018			0.0755089	−	0.997145i	$-0.475942\pi$
$307$	1.26432e14			0.151018			0.0755089	+	0.997145i	$0.475942\pi$
$308$		−	3.72298e11i		−	0.000436100i
$309$	1.63734e14	+	2.62712e14i	0.188100	+	0.301807i
$310$	8.33618e14			0.939284
$311$		−	8.13557e14i		−	0.899137i	−0.893246	−	0.449568i	$-0.851578\pi$
$311$		−	8.13557e14i		−	0.899137i	0.893246	−	0.449568i	$-0.148422\pi$
$312$	1.91094e14	−	1.19099e14i	0.207167	−	0.129116i
$313$	3.32819e14			0.353950			0.176975	−	0.984215i	$-0.443369\pi$
$313$	3.32819e14			0.353950			0.176975	+	0.984215i	$0.443369\pi$
$314$		−	2.68412e14i		−	0.280042i
$315$	−1.66317e15	−	8.15998e14i	−1.70245	−	0.835268i
$316$	6.70361e12			0.00673266
$317$			1.24336e14i			0.122529i	0.998122	+	0.0612646i	$0.0195134\pi$
$317$			1.24336e14i			0.122529i	−0.998122	+	0.0612646i	$0.980487\pi$
$318$	−4.03136e14	−	6.46833e14i	−0.389842	−	0.625503i
$319$	7.41879e11			0.000704026
$320$		−	1.40430e14i		−	0.130785i
$321$	1.07852e15	−	6.72183e14i	0.985820	−	0.614408i
$322$	−2.06682e15			−1.85425
$323$			6.77941e11i			0.000597004i
$324$	3.53974e14	+	4.57457e14i	0.305986	+	0.395440i
$325$	7.70558e13			0.0653891
$326$			7.91635e14i			0.659507i
$327$	−9.42967e14	−	1.51299e15i	−0.771277	−	1.23752i
$328$	5.80447e13			0.0466143
$329$			2.48019e15i			1.95574i
$330$	−3.90220e11	+	2.43203e11i	−0.000302153	+	0.000188315i
$331$	2.28684e15			1.73887			0.869436	−	0.494046i	$-0.164483\pi$
$331$	2.28684e15			1.73887			0.869436	+	0.494046i	$0.164483\pi$
$332$			3.17922e14i			0.237406i
$333$	−2.41319e13	+	4.91858e13i	−0.0176981	+	0.0360723i
$334$	1.62961e14			0.117383
$335$		−	7.81940e14i		−	0.553228i
$336$	3.44852e14	+	5.53316e14i	0.239661	+	0.384537i
$337$	−2.39633e15			−1.63594			−0.817971	−	0.575259i	$-0.804901\pi$
$337$	−2.39633e15			−1.63594			−0.817971	+	0.575259i	$0.804901\pi$
$338$			5.51728e14i			0.370020i
$339$	1.33368e14	−	8.31211e13i	0.0878727	−	0.0547663i
$340$	1.62871e14			0.105431
$341$			9.60605e11i			0.000610968i
$342$	3.00907e12	+	1.47633e12i	0.00188051	+	0.000922631i
$343$	3.79221e15			2.32878
$344$		−	4.88907e14i		−	0.295037i
$345$	1.35015e15	+	2.16632e15i	0.800695	+	1.28472i
$346$	1.46833e15			0.855792
$347$		−	1.31976e15i		−	0.755992i	−0.925807	−	0.377996i	$-0.876613\pi$
$347$		−	1.31976e15i		−	0.755992i	0.925807	−	0.377996i	$-0.123387\pi$
$348$	−1.10259e15	+	6.87188e14i	−0.620784	+	0.386901i
$349$	−1.28865e15			−0.713153			−0.356577	−	0.934266i	$-0.616056\pi$
$349$	−1.28865e15			−0.713153			−0.356577	+	0.934266i	$0.616056\pi$
$350$			2.23116e14i			0.121373i
$351$	1.28453e15	−	1.30459e14i	0.686910	−	0.0697638i
$352$	1.61822e11			8.50708e−5
$353$		−	3.58069e15i		−	1.85062i	−0.379206	−	0.925312i	$-0.623803\pi$
$353$		−	3.58069e15i		−	1.85062i	0.379206	−	0.925312i	$-0.376197\pi$
$354$	−5.99356e14	−	9.61669e14i	−0.304555	−	0.488659i
$355$	−4.02720e15			−2.01203
$356$		−	4.87146e13i		−	0.0239309i
$357$	−6.41738e14	+	3.99961e14i	−0.309990	+	0.193200i
$358$	9.98879e12			0.00474476
$359$			4.18957e15i			1.95705i	0.206119	+	0.978527i	$0.433916\pi$
$359$			4.18957e15i			1.95705i	−0.206119	+	0.978527i	$0.566084\pi$
$360$	3.54679e14	−	7.22907e14i	0.162937	−	0.332099i
$361$	−2.21330e15			−0.999991
$362$		−	2.45735e15i		−	1.09198i
$363$	1.21014e15	+	1.94168e15i	0.528928	+	0.848666i
$364$	1.45535e15			0.625690
$365$			8.92390e13i			0.0377396i
$366$	−3.98711e14	+	2.48495e14i	−0.165871	+	0.103379i
$367$	−2.83408e15			−1.15989			−0.579944	−	0.814656i	$-0.696926\pi$
$367$	−2.83408e15			−1.15989			−0.579944	+	0.814656i	$0.696926\pi$
$368$		−	8.98356e14i		−	0.361711i
$369$	2.98804e14	+	1.46602e14i	0.118366	+	0.0580739i
$370$	7.62701e13			0.0297265
$371$		−	4.92619e15i		−	1.88916i
$372$	−8.89790e14	−	1.42767e15i	−0.335761	−	0.538729i
$373$	2.91810e15			1.08355			0.541773	−	0.840525i	$-0.317753\pi$
$373$	2.91810e15			1.08355			0.541773	+	0.840525i	$0.317753\pi$
$374$			1.87681e11i			6.85790e-5i
$375$	−2.23544e15	+	1.39323e15i	−0.803851	+	0.500997i
$376$	−1.07803e15			−0.381509
$377$			2.90008e15i			1.01009i
$378$	3.77744e14	+	3.71936e15i	0.129493	+	1.27502i
$379$	3.26035e15			1.10009			0.550045	−	0.835135i	$-0.314610\pi$
$379$	3.26035e15			1.10009			0.550045	+	0.835135i	$0.314610\pi$
$380$		−	4.66602e12i		−	0.00154969i
$381$	−5.67960e14	−	9.11294e14i	−0.185681	−	0.297926i
$382$	2.96903e15			0.955507
$383$			1.73473e15i			0.549589i	0.961503	+	0.274795i	$0.0886099\pi$
$383$			1.73473e15i			0.549589i	−0.961503	+	0.274795i	$0.911390\pi$
$384$	−2.40502e14	+	1.49892e14i	−0.0750122	+	0.0467511i
$385$	−2.97187e12			−0.000912567
$386$			2.12717e14i			0.0643100i
$387$	1.23482e15	−	2.51681e15i	0.367568	−	0.749177i
$388$	−1.58039e15			−0.463205
$389$		−	1.33357e15i		−	0.384872i	−0.981309	−	0.192436i	$-0.938361\pi$
$389$		−	1.33357e15i		−	0.384872i	0.981309	−	0.192436i	$-0.0616388\pi$
$390$	−9.50706e14	−	1.52541e15i	−0.270183	−	0.433510i
$391$	1.04192e15			0.291590
$392$			2.93115e15i			0.807832i
$393$	2.23025e15	−	1.38999e15i	0.605338	−	0.377275i
$394$	3.35403e15			0.896582
$395$		−	5.35116e13i		−	0.0140885i
$396$	8.33029e11	+	4.08708e11i	0.000216018	+	0.000105984i
$397$	2.26697e15			0.579032			0.289516	−	0.957173i	$-0.406506\pi$
$397$	2.26697e15			0.579032			0.289516	+	0.957173i	$0.406506\pi$
$398$			2.94299e15i			0.740442i
$399$	1.14583e13	+	1.83849e13i	0.00283977	+	0.00455643i
$400$	−9.69788e13			−0.0236765
$401$			3.99606e15i			0.961094i	0.876969	+	0.480547i	$0.159562\pi$
$401$			3.99606e15i			0.961094i	−0.876969	+	0.480547i	$0.840438\pi$
$402$	−1.33917e15	+	8.34629e14i	−0.317306	+	0.197759i
$403$	−3.75510e15			−0.876580
$404$		−	8.04346e14i		−	0.184993i
$405$	3.65165e15	−	2.82560e15i	0.827483	−	0.640295i
$406$	−8.39721e15			−1.87490
$407$			8.78886e10i			1.93360e-5i
$408$	−1.73845e14	−	2.78935e14i	−0.0376879	−	0.0604704i
$409$	−5.79463e15			−1.23790			−0.618950	−	0.785430i	$-0.712442\pi$
$409$	−5.79463e15			−1.23790			−0.618950	+	0.785430i	$0.712442\pi$
$410$		−	4.63342e14i		−	0.0975435i
$411$	−3.87332e15	+	2.41403e15i	−0.803587	+	0.500832i
$412$	−8.69651e14			−0.177812
$413$		−	7.32394e15i		−	1.47586i
$414$	2.26895e15	−	4.62458e15i	0.450633	−	0.918482i
$415$	2.53781e15			0.496787
$416$			6.32577e14i			0.122054i
$417$	−3.13561e15	−	5.03110e15i	−0.596356	−	0.956855i
$418$	5.37681e9			1.00801e−6
$419$			6.90384e15i			1.27587i	0.770090	+	0.637935i	$0.220211\pi$
$419$			6.90384e15i			1.27587i	−0.770090	+	0.637935i	$0.779789\pi$
$420$	4.41685e15	−	2.75278e15i	0.804668	−	0.501506i
$421$	7.83870e15			1.40783			0.703917	−	0.710282i	$-0.251433\pi$
$421$	7.83870e15			1.40783			0.703917	+	0.710282i	$0.251433\pi$
$422$		−	9.49771e13i		−	0.0168168i
$423$	−5.54952e15	−	2.72275e15i	−0.968754	−	0.475298i
$424$	2.14120e15			0.368521
$425$		−	1.12476e14i		−	0.0190865i
$426$	4.29857e15	+	6.89707e15i	0.719228	+	1.15400i
$427$	−3.03653e15			−0.500968
$428$			3.57020e15i			0.580805i
$429$	1.75778e12	−	1.09553e12i	0.000281982	−	0.000175744i
$430$	−3.90270e15			−0.617383
$431$			6.94879e14i			0.108404i	0.998530	+	0.0542021i	$0.0172615\pi$
$431$			6.94879e14i			0.108404i	−0.998530	+	0.0542021i	$0.982738\pi$
$432$	−1.61664e15	+	1.64189e14i	−0.248721	+	0.0252605i
$433$	2.62269e15			0.397942			0.198971	−	0.980005i	$-0.436240\pi$
$433$	2.62269e15			0.397942			0.198971	+	0.980005i	$0.436240\pi$
$434$		−	1.08729e16i		−	1.62708i
$435$	5.48547e15	+	8.80146e15i	0.809615	+	1.29903i
$436$	5.00844e15			0.729094
$437$		−	2.98495e13i		−	0.00428596i
$438$	1.52832e14	−	9.52522e13i	0.0216457	−	0.0134906i
$439$	1.67437e15			0.233918			0.116959	−	0.993137i	$-0.462685\pi$
$439$	1.67437e15			0.233918			0.116959	+	0.993137i	$0.462685\pi$
$440$		−	1.29174e12i		−	0.000178016i
$441$	−7.40311e15	+	1.50890e16i	−1.00643	+	2.05130i
$442$	−7.33665e14			−0.0983930
$443$			5.35024e15i			0.707866i	0.935271	+	0.353933i	$0.115156\pi$
$443$			5.35024e15i			0.707866i	−0.935271	+	0.353933i	$0.884844\pi$
$444$	−8.14095e13	−	1.30622e14i	−0.0106262	−	0.0170497i
$445$	−3.88864e14			−0.0500770
$446$		−	6.12174e15i		−	0.777796i
$447$	6.99992e15	−	4.36267e15i	0.877502	−	0.546900i
$448$	−1.83163e15			−0.226553
$449$			1.97158e15i			0.240622i	0.992736	+	0.120311i	$0.0383892\pi$
$449$			1.97158e15i			0.240622i	−0.992736	+	0.120311i	$0.961611\pi$
$450$	−4.99230e14	−	2.44936e14i	−0.0601209	−	0.0294970i
$451$	5.33924e11			6.34483e−5
$452$			4.41486e14i			0.0517710i
$453$	−5.35354e15	−	8.58976e15i	−0.619515	−	0.994013i
$454$	6.66525e15			0.761169
$455$		−	1.16173e16i		−	1.30930i
$456$	−7.99112e12	+	4.98043e12i	−0.000888830	+	0.000553960i
$457$	1.63785e16			1.79794			0.898972	−	0.438005i	$-0.144315\pi$
$457$	1.63785e16			1.79794			0.898972	+	0.438005i	$0.144315\pi$
$458$			1.08144e16i			1.17168i
$459$	−1.90427e14	−	1.87499e15i	−0.0203635	−	0.200504i
$460$	−7.17113e15			−0.756903
$461$		−	1.61711e16i		−	1.68475i	−0.538895	−	0.842373i	$-0.681158\pi$
$461$		−	1.61711e16i		−	1.68475i	0.538895	−	0.842373i	$-0.318842\pi$
$462$	3.17212e12	+	5.08968e12i	0.000326210	+	0.000523405i
$463$	−1.56118e16			−1.58477			−0.792385	−	0.610022i	$-0.791161\pi$
$463$	−1.56118e16			−1.58477			−0.792385	+	0.610022i	$0.791161\pi$
$464$		−	3.64990e15i		−	0.365741i
$465$	−1.13964e16	+	7.10275e15i	−1.12732	+	0.702601i
$466$	−7.30813e15			−0.713659
$467$		−	2.62791e15i		−	0.253343i	−0.991945	−	0.126671i	$-0.959571\pi$
$467$		−	2.62791e15i		−	0.253343i	0.991945	−	0.126671i	$-0.0404294\pi$
$468$	−1.59768e15	+	3.25640e15i	−0.152060	+	0.309929i
$469$	−1.01989e16			−0.958333
$470$			8.60539e15i			0.798332i
$471$	2.28697e15	+	3.66945e15i	0.209477	+	0.336106i
$472$	3.18340e15			0.287898
$473$		−	4.49721e12i		−	0.000401584i
$474$	−9.16450e13	+	5.71174e13i	−0.00808051	+	0.00503614i
$475$	−3.22229e12			−0.000280545
$476$		−	2.12433e15i		−	0.182634i
$477$	1.10225e16	+	5.40797e15i	0.935774	+	0.459117i
$478$	−2.54567e15			−0.213420
$479$			2.69109e15i			0.222800i	0.993776	+	0.111400i	$0.0355335\pi$
$479$			2.69109e15i			0.222800i	−0.993776	+	0.111400i	$0.964467\pi$
$480$	1.19651e15	+	1.91981e15i	0.0978296	+	0.156968i
$481$	−3.43565e14			−0.0277421
$482$			4.02187e15i			0.320735i
$483$	2.82555e16	−	1.76101e16i	2.22546	−	1.38701i
$484$	−6.42750e15			−0.500000
$485$			1.26154e16i			0.969286i
$486$	−8.73688e15	−	3.23789e15i	−0.663039	−	0.245722i
$487$	8.07683e15			0.605434			0.302717	−	0.953080i	$-0.402106\pi$
$487$	8.07683e15			0.605434			0.302717	+	0.953080i	$0.402106\pi$
$488$		−	1.31985e15i		−	0.0977247i
$489$	−6.74504e15	−	1.08224e16i	−0.493323	−	0.791538i
$490$	2.33979e16			1.69044
$491$		−	7.92699e15i		−	0.565743i	−0.959158	−	0.282872i	$-0.908713\pi$
$491$		−	7.92699e15i		−	0.565743i	0.959158	−	0.282872i	$-0.0912871\pi$
$492$	−7.93528e14	+	4.94563e14i	−0.0559463	+	0.0348683i
$493$	4.23317e15			0.294838
$494$			2.10185e13i			0.00144624i
$495$	3.26251e12	−	6.64965e12i	0.000221779	−	0.000452031i
$496$	4.72600e15			0.317397
$497$			5.25272e16i			3.48534i
$498$	−2.70881e15	−	4.34630e15i	−0.177584	−	0.284934i
$499$	−1.32012e16			−0.855086			−0.427543	−	0.903995i	$-0.640621\pi$
$499$	−1.32012e16			−0.855086			−0.427543	+	0.903995i	$0.640621\pi$
$500$		−	7.39994e15i		−	0.473596i
$501$	−2.22783e15	+	1.38849e15i	−0.140882	+	0.0878042i
$502$	1.20868e16			0.755249
$503$		−	1.23673e16i		−	0.763603i	−0.924244	−	0.381801i	$-0.875304\pi$
$503$		−	1.23673e16i		−	0.763603i	0.924244	−	0.381801i	$-0.124696\pi$
$504$	−9.42894e15	−	4.62610e15i	−0.575280	−	0.282249i
$505$	−6.42069e15			−0.387109
$506$		−	8.26352e12i		−	0.000492337i
$507$	−4.70094e15	−	7.54267e15i	−0.276781	−	0.444096i
$508$	3.01664e15			0.175526
$509$		−	4.42398e15i		−	0.254394i	−0.991877	−	0.127197i	$-0.959402\pi$
$509$		−	4.42398e15i		−	0.254394i	0.991877	−	0.127197i	$-0.0405980\pi$
$510$	−2.22660e15	+	1.38772e15i	−0.126538	+	0.0788644i
$511$	1.16395e15			0.0653747
$512$		−	7.96131e14i		−	0.0441942i
$513$	−5.37158e13	+	5.45547e12i	−0.00294712	+	0.000299315i
$514$	−1.45658e16			−0.789873
$515$			6.94199e15i			0.372083i
$516$	4.16568e15	+	6.68384e15i	0.220692	+	0.354102i
$517$	−9.91627e12			−0.000519284
$518$		−	9.94797e14i		−	0.0514939i
$519$	−2.00736e16	+	1.25108e16i	−1.02712	+	0.640147i
$520$	5.04954e15			0.255407
$521$		−	3.06402e16i		−	1.53202i	−0.642827	−	0.766012i	$-0.722238\pi$
$521$		−	3.06402e16i		−	1.53202i	0.642827	−	0.766012i	$-0.277762\pi$
$522$	9.21845e15	−	1.87891e16i	0.455654	−	0.928714i
$523$	−1.47007e16			−0.718339			−0.359169	−	0.933272i	$-0.616940\pi$
$523$	−1.47007e16			−0.718339			−0.359169	+	0.933272i	$0.616940\pi$
$524$			7.38276e15i			0.356641i
$525$	−1.90103e15	−	3.05021e15i	−0.0907892	−	0.145671i
$526$	7.84375e14			0.0370347
$527$			5.48122e15i			0.255867i
$528$	−2.21226e12	+	1.37878e12i	−0.000102102	+	6.36344e-5i
$529$	−2.39605e16			−1.09336
$530$		−	1.70921e16i		−	0.771154i
$531$	1.63876e16	+	8.04021e15i	0.731051	+	0.358674i
$532$	−6.08593e13			−0.00268446
$533$			2.08716e15i			0.0910317i
$534$	4.15067e14	+	6.65977e14i	0.0179007	+	0.0287218i
$535$	2.84991e16			1.21537
$536$		−	4.43302e15i		−	0.186944i
$537$	−1.36557e14	+	8.51083e13i	−0.00569465	+	0.00354917i
$538$	−1.60394e16			−0.661444
$539$			2.69621e13i			0.00109957i
$540$	1.31064e15	+	1.29048e16i	0.0528592	+	0.520464i
$541$	3.68694e16			1.47056			0.735279	−	0.677764i	$-0.237051\pi$
$541$	3.68694e16			1.47056			0.735279	+	0.677764i	$0.237051\pi$
$542$			2.41948e16i			0.954392i
$543$	2.09375e16	+	3.35943e16i	0.816821	+	1.31059i
$544$	9.23356e14			0.0356267
$545$		−	3.99799e16i		−	1.52568i
$546$	−1.98961e16	+	1.24001e16i	−0.750950	+	0.468027i
$547$	−1.01158e16			−0.377638			−0.188819	−	0.982012i	$-0.560466\pi$
$547$	−1.01158e16			−0.377638			−0.188819	+	0.982012i	$0.560466\pi$
$548$		−	1.28218e16i		−	0.473441i
$549$	3.33350e15	−	6.79434e15i	0.121749	−	0.248149i
$550$	−8.92059e11			−3.22268e−5
$551$		−	1.21274e14i		−	0.00433371i
$552$	7.65434e15	+	1.22814e16i	0.270566	+	0.434124i
$553$	−6.97956e14			−0.0244049
$554$			1.28009e16i			0.442772i
$555$	−1.04269e15	+	6.49851e14i	−0.0356777	+	0.0222360i
$556$	1.66544e16			0.563740
$557$			1.61921e16i			0.542216i	0.962549	+	0.271108i	$0.0873901\pi$
$557$			1.61921e16i			0.542216i	−0.962549	+	0.271108i	$0.912610\pi$
$558$	2.43286e16	+	1.19363e16i	0.805957	+	0.395426i
$559$	1.75801e16			0.576168
$560$			1.46210e16i			0.474078i
$561$	−1.59912e12	−	2.56579e12i	−5.12983e−5	−	8.23082e-5i
$562$	−3.38977e16			−1.07585
$563$		−	3.83169e15i		−	0.120321i	−0.998189	−	0.0601603i	$-0.980839\pi$
$563$		−	3.83169e15i		−	0.120321i	0.998189	−	0.0601603i	$-0.0191612\pi$
$564$	1.47378e16	−	9.18525e15i	0.457885	−	0.285375i
$565$	3.52416e15			0.108334
$566$		−	1.27070e16i		−	0.386495i
$567$	−3.68545e16	−	4.76288e16i	−1.10915	−	1.43341i
$568$	−2.28313e16			−0.679892
$569$		−	2.04968e16i		−	0.603966i	−0.953313	−	0.301983i	$-0.902351\pi$
$569$		−	2.04968e16i		−	0.603966i	0.953313	−	0.301983i	$-0.0976486\pi$
$570$	3.97563e13	+	6.37891e13i	0.00115920	+	0.00185993i
$571$	−5.05437e16			−1.45831			−0.729156	−	0.684347i	$-0.760087\pi$
$571$	−5.05437e16			−1.45831			−0.729156	+	0.684347i	$0.760087\pi$
$572$			5.81875e12i			0.000166132i
$573$	−4.05895e16	+	2.52973e16i	−1.14680	+	0.714736i
$574$	−6.04340e15			−0.168970
$575$			4.95228e15i			0.137025i
$576$	2.01077e15	−	4.09835e15i	0.0550588	−	0.112221i
$577$	7.29450e16			1.97670			0.988350	−	0.152201i	$-0.0486361\pi$
$577$	7.29450e16			1.97670			0.988350	+	0.152201i	$0.0486361\pi$
$578$		−	2.52956e16i		−	0.678387i
$579$	−1.81243e15	−	2.90805e15i	−0.0481050	−	0.0771846i
$580$	−2.91353e16			−0.765336
$581$		−	3.31008e16i		−	0.860562i
$582$	2.16055e16	−	1.34655e16i	0.555937	−	0.346485i
$583$	1.96958e13			0.000501606
$584$			5.05919e14i			0.0127528i
$585$	2.59942e16	+	1.27535e16i	0.648546	+	0.318195i
$586$	3.90013e16			0.963148
$587$			4.66769e16i			1.14097i	0.821309	+	0.570484i	$0.193244\pi$
$587$			4.66769e16i			1.14097i	−0.821309	+	0.570484i	$0.806756\pi$
$588$	−2.49745e16	−	4.00716e16i	−0.604272	−	0.969557i
$589$	1.57030e14			0.00376088
$590$		−	2.54115e16i		−	0.602445i
$591$	−4.58529e16	+	2.85776e16i	−1.07607	+	0.670659i
$592$	4.32395e14			0.0100450
$593$			4.10162e16i			0.943250i	0.881799	+	0.471625i	$0.156332\pi$
$593$			4.10162e16i			0.943250i	−0.881799	+	0.471625i	$0.843668\pi$
$594$	−1.48707e13	+	1.51029e12i	−0.000338542	+	3.43829e-5i
$595$	−1.69575e16			−0.382173
$596$			2.31717e16i			0.516989i
$597$	−2.50754e16	−	4.02336e16i	−0.553863	−	0.888675i
$598$	3.23030e16			0.706375
$599$			6.56038e16i			1.42026i	0.704070	+	0.710131i	$0.251364\pi$
$599$			6.56038e16i			1.42026i	−0.704070	+	0.710131i	$0.748636\pi$
$600$	1.32580e15	−	8.26296e14i	0.0284164	−	0.0177104i
$601$	−3.64543e16			−0.773574			−0.386787	−	0.922169i	$-0.626415\pi$
$601$	−3.64543e16			−0.773574			−0.386787	+	0.922169i	$0.626415\pi$
$602$			5.09033e16i			1.06947i
$603$	1.11963e16	−	2.28204e16i	0.232901	−	0.474700i
$604$	2.84346e16			0.585632
$605$			5.13075e16i			1.04628i
$606$	6.85334e15	+	1.09962e16i	0.138378	+	0.222028i
$607$	4.33490e16			0.866657			0.433328	−	0.901236i	$-0.357339\pi$
$607$	4.33490e16			0.866657			0.433328	+	0.901236i	$0.357339\pi$
$608$		−	2.64529e13i		−	0.000523663i
$609$	1.14798e17	−	7.15475e16i	2.25025	−	1.40246i
$610$	−1.05357e16			−0.204495
$611$		−	3.87637e16i		−	0.745037i
$612$	4.75327e15	+	2.33209e15i	0.0904658	+	0.0443851i
$613$	−6.00389e16			−1.13154			−0.565770	−	0.824563i	$-0.691421\pi$
$613$	−6.00389e16			−1.13154			−0.565770	+	0.824563i	$0.691421\pi$
$614$		−	5.72168e15i		−	0.106786i
$615$	3.94785e15	+	6.33433e15i	0.0729642	+	0.117071i
$616$	−1.68483e13			−0.000308369
$617$		−	5.58533e16i		−	1.01237i	−0.862426	−	0.506184i	$-0.831056\pi$
$617$		−	5.58533e16i		−	1.01237i	0.862426	−	0.506184i	$-0.168944\pi$
$618$	1.18890e16	−	7.40976e15i	0.213410	−	0.133007i
$619$	9.05726e16			1.61010			0.805050	−	0.593207i	$-0.202138\pi$
$619$	9.05726e16			1.61010			0.805050	+	0.593207i	$0.202138\pi$
$620$		−	3.77252e16i		−	0.664174i
$621$	8.38442e15	+	8.25549e16i	0.146192	+	1.43944i
$622$	−3.68174e16			−0.635786
$623$			5.07199e15i			0.0867461i
$624$	−5.38980e15	−	8.64795e15i	−0.0912988	−	0.146489i
$625$	−6.47149e16			−1.08574
$626$		−	1.50617e16i		−	0.250281i
$627$	−7.35063e10	+	4.58125e10i	−1.20982e−6	+	7.54013e-7i
$628$	−1.21469e16			−0.198020
$629$			5.01493e14i			0.00809769i
$630$	−3.69279e16	+	7.52665e16i	−0.590624	+	1.20381i
$631$	1.84537e15			0.0292353			0.0146176	−	0.999893i	$-0.495347\pi$
$631$	1.84537e15			0.0292353			0.0146176	+	0.999893i	$0.495347\pi$
$632$		−	3.03371e14i		−	0.00476071i
$633$	8.09241e14	+	1.29843e15i	0.0125793	+	0.0201835i
$634$	5.62679e15			0.0866413
$635$		−	2.40803e16i		−	0.367299i
$636$	−2.92723e16	+	1.82439e16i	−0.442297	+	0.275660i
$637$	−1.05398e17			−1.57759
$638$		−	3.35736e13i		−	0.000497822i
$639$	−1.17531e17	−	5.76642e16i	−1.72643	−	0.847035i
$640$	−6.35512e15			−0.0924791
$641$		−	5.16756e16i		−	0.744967i	−0.928039	−	0.372484i	$-0.878506\pi$
$641$		−	5.16756e16i		−	0.744967i	0.928039	−	0.372484i	$-0.121494\pi$
$642$	−3.04195e16	−	4.88082e16i	−0.434452	−	0.697080i
$643$	4.40389e16			0.623119			0.311560	−	0.950227i	$-0.399149\pi$
$643$	4.40389e16			0.623119			0.311560	+	0.950227i	$0.399149\pi$
$644$			9.35336e16i			1.31115i
$645$	5.33538e16	−	3.32525e16i	0.740980	−	0.461813i
$646$	3.06801e13			0.000422145
$647$		−	1.08919e17i		−	1.48483i	−0.669938	−	0.742417i	$-0.733679\pi$
$647$		−	1.08919e17i		−	1.48483i	0.669938	−	0.742417i	$-0.266321\pi$
$648$	2.07021e16	−	1.60190e16i	0.279618	−	0.216365i
$649$	2.92825e13			0.000391868
$650$		−	3.48715e15i		−	0.0462371i
$651$	9.26417e16	+	1.48644e17i	1.21708	+	1.95281i
$652$	3.58253e16			0.466342
$653$			7.87031e16i			1.01511i	0.861620	+	0.507555i	$0.169450\pi$
$653$			7.87031e16i			1.01511i	−0.861620	+	0.507555i	$0.830550\pi$
$654$	−6.84703e16	+	4.26738e16i	−0.875056	+	0.545375i
$655$	5.89328e16			0.746293
$656$		−	2.62680e15i		−	0.0329613i
$657$	−1.27778e15	+	2.60438e15i	−0.0158879	+	0.0323827i
$658$	1.12241e17			1.38291
$659$		−	1.09352e17i		−	1.33510i	−0.744563	−	0.667552i	$-0.767342\pi$
$659$		−	1.09352e17i		−	1.33510i	0.744563	−	0.667552i	$-0.232658\pi$
$660$	1.10061e13	+	1.76594e13i	0.000133159	+	0.000213654i
$661$	3.34365e16			0.400877			0.200439	−	0.979706i	$-0.435763\pi$
$661$	3.34365e16			0.400877			0.200439	+	0.979706i	$0.435763\pi$
$662$		−	1.03490e17i		−	1.22957i
$663$	1.00299e16	−	6.25110e15i	0.118091	−	0.0735996i
$664$	1.43875e16			0.167871
$665$			4.85809e14i			0.00561741i
$666$	2.22589e15	+	1.09209e15i	0.0255070	+	0.0125145i
$667$	−1.86385e17			−2.11668
$668$		−	7.37475e15i		−	0.0830020i
$669$	5.21596e16	+	8.36902e16i	0.581805	+	0.933507i
$670$	−3.53865e16			−0.391191
$671$		−	1.21406e13i		−	0.000133016i
$672$	2.50402e16	−	1.56062e16i	0.271909	−	0.169466i
$673$	6.72254e16			0.723507			0.361754	−	0.932274i	$-0.382178\pi$
$673$	6.72254e16			0.723507			0.361754	+	0.932274i	$0.382178\pi$
$674$			1.08446e17i			1.15679i
$675$	8.91192e15	−	9.05109e14i	0.0942212	−	0.00956926i
$676$	2.49684e16			0.261644
$677$			1.55113e17i			1.61108i	0.592541	+	0.805540i	$0.298125\pi$
$677$			1.55113e17i			1.61108i	−0.592541	+	0.805540i	$0.701875\pi$
$678$	−3.76163e15	−	6.03555e15i	−0.0387256	−	0.0621354i
$679$	1.64544e17			1.67905
$680$		−	7.37068e15i		−	0.0745511i
$681$	−9.11205e16	+	5.67905e16i	−0.913552	+	0.569368i
$682$	4.34720e13			0.000432020
$683$			1.18185e17i			1.16422i	0.813108	+	0.582112i	$0.197774\pi$
$683$			1.18185e17i			1.16422i	−0.813108	+	0.582112i	$0.802226\pi$
$684$	6.68113e13	−	1.36175e14i	0.000652399	−	0.00132972i
$685$	−1.02350e17			−0.990705
$686$		−	1.71616e17i		−	1.64669i
$687$	−9.21431e16	−	1.47844e17i	−0.876441	−	1.40625i
$688$	−2.21254e16			−0.208622
$689$			7.69930e16i			0.719674i
$690$	9.80364e16	−	6.11008e16i	0.908432	−	0.566177i
$691$	−5.12178e16			−0.470493			−0.235246	−	0.971936i	$-0.575590\pi$
$691$	−5.12178e16			−0.470493			−0.235246	+	0.971936i	$0.575590\pi$
$692$		−	6.64492e16i		−	0.605136i
$693$	−8.67320e13	−	4.25532e13i	−0.000783033	−	0.000384178i
$694$	−5.97254e16			−0.534567
$695$		−	1.32943e17i		−	1.17966i
$696$	3.10986e16	+	4.98977e16i	0.273580	+	0.438960i
$697$	3.04657e15			0.0265714
$698$			5.83177e16i			0.504275i
$699$	9.99092e16	−	6.22680e16i	0.856530	−	0.533829i
$700$	1.00971e16			0.0858237
$701$		−	1.12571e15i		−	0.00948680i	−0.999989	−	0.00474340i	$-0.998490\pi$
$701$		−	1.12571e15i		−	0.00948680i	0.999989	−	0.00474340i	$-0.00150988\pi$
$702$	−5.90388e15	−	5.81310e16i	−0.0493304	−	0.485719i
$703$	1.43671e13			0.000119025
$704$		−	7.32321e12i		−	6.01541e-5i
$705$	−7.33212e16	−	1.17644e17i	−0.597166	−	0.958154i
$706$	−1.62043e17			−1.30859
$707$			8.37456e16i			0.670572i
$708$	−4.35202e16	+	2.71238e16i	−0.345534	+	0.215353i
$709$	−1.43351e17			−1.12855			−0.564277	−	0.825585i	$-0.690845\pi$
$709$	−1.43351e17			−1.12855			−0.564277	+	0.825585i	$0.690845\pi$
$710$			1.82250e17i			1.42272i
$711$	7.66215e14	−	1.56170e15i	0.00593107	−	0.0120887i
$712$	−2.20457e15			−0.0169217
$713$		−	2.41336e17i		−	1.83690i
$714$	1.81001e16	+	2.90417e16i	0.136613	+	0.219196i
$715$	4.64482e13			0.000347642
$716$		−	4.52041e14i		−	0.00335506i
$717$	3.48018e16	−	2.16901e16i	0.256146	−	0.159642i
$718$	1.89598e17			1.38385
$719$			2.30075e17i			1.66531i	0.553790	+	0.832657i	$0.313181\pi$
$719$			2.30075e17i			1.66531i	−0.553790	+	0.832657i	$0.686819\pi$
$720$	−3.27150e16	−	1.60509e16i	−0.234829	−	0.115214i
$721$	9.05449e16			0.644544
$722$			1.00162e17i			0.707101i
$723$	−3.42679e16	−	5.49829e16i	−0.239915	−	0.384944i
$724$	−1.11207e17			−0.772147
$725$			2.01205e16i			0.138551i
$726$	8.78702e16	−	5.47648e16i	0.600098	−	0.374009i
$727$	1.72351e17			1.16736			0.583682	−	0.811982i	$-0.301611\pi$
$727$	1.72351e17			1.16736			0.583682	+	0.811982i	$0.301611\pi$
$728$		−	6.58616e16i		−	0.442430i
$729$	1.47030e17	−	3.01765e16i	0.979581	−	0.201050i
$730$	4.03850e15			0.0266859
$731$		−	2.56611e16i		−	0.168179i
$732$	1.12456e16	+	1.80436e16i	0.0730997	+	0.117289i
$733$	2.34182e17			1.50983			0.754917	−	0.655821i	$-0.227677\pi$
$733$	2.34182e17			1.50983			0.754917	+	0.655821i	$0.227677\pi$
$734$			1.28256e17i			0.820165i
$735$	−3.19872e17	+	1.99359e17i	−2.02886	+	1.26448i
$736$	−4.06550e16			−0.255768
$737$		−	4.07771e13i		−	0.000254455i
$738$	6.63444e15	−	1.35223e16i	0.0410644	−	0.0836976i
$739$	9.00848e16			0.553076			0.276538	−	0.961003i	$-0.410813\pi$
$739$	9.00848e16			0.553076			0.276538	+	0.961003i	$0.410813\pi$
$740$		−	3.45159e15i		−	0.0210198i
$741$	−1.79086e14	−	2.87343e14i	−0.00108181	−	0.00173577i
$742$	−2.22934e17			−1.33584
$743$			1.50861e17i			0.896695i	0.893859	+	0.448347i	$0.147987\pi$
$743$			1.50861e17i			0.896695i	−0.893859	+	0.448347i	$0.852013\pi$
$744$	−6.46090e16	+	4.02673e16i	−0.380939	+	0.237419i
$745$	1.84968e17			1.08183
$746$		−	1.32058e17i		−	0.766183i
$747$	7.40643e16	+	3.63380e16i	0.426270	+	0.209140i
$748$	8.49348e12			4.84927e−5
$749$		−	3.71717e17i		−	2.10533i
$750$	6.30504e16	+	1.01165e17i	0.354258	+	0.568409i
$751$	4.79730e16			0.267397			0.133699	−	0.991022i	$-0.457315\pi$
$751$	4.79730e16			0.267397			0.133699	+	0.991022i	$0.457315\pi$
$752$			4.87862e16i			0.269767i
$753$	−1.65239e17	+	1.02984e17i	−0.906446	+	0.564939i
$754$	1.31243e17			0.714244
$755$		−	2.26979e17i		−	1.22547i
$756$	1.68319e17	−	1.70948e16i	0.901576	−	0.0915656i
$757$	−1.64543e17			−0.874387			−0.437193	−	0.899368i	$-0.644027\pi$
$757$	−1.64543e17			−0.874387			−0.437193	+	0.899368i	$0.644027\pi$
$758$		−	1.47546e17i		−	0.777881i
$759$	7.04084e13	+	1.12970e14i	0.000368276	+	0.000590900i
$760$	−2.11160e14			−0.00109580
$761$			1.00600e17i			0.517952i	0.965884	+	0.258976i	$0.0833851\pi$
$761$			1.00600e17i			0.517952i	−0.965884	+	0.258976i	$0.916615\pi$
$762$	−4.12405e16	+	2.57029e16i	−0.210666	+	0.131296i
$763$	−5.21461e17			−2.64286
$764$		−	1.34363e17i		−	0.675646i
$765$	1.86159e16	−	3.79430e16i	0.0928786	−	0.189305i
$766$	7.85048e16			0.388618
$767$			1.14468e17i			0.562228i
$768$	6.78335e15	+	1.08839e16i	0.0330580	+	0.0530417i
$769$	−1.40719e17			−0.680448			−0.340224	−	0.940344i	$-0.610503\pi$
$769$	−1.40719e17			−0.680448			−0.340224	+	0.940344i	$0.610503\pi$
$770$			1.34491e14i			0.000645282i
$771$	1.99129e17	−	1.24107e17i	0.948002	−	0.590838i
$772$	9.62647e15			0.0454740
$773$			3.75325e16i			0.175926i	0.996124	+	0.0879630i	$0.0280357\pi$
$773$			3.75325e16i			0.175926i	−0.996124	+	0.0879630i	$0.971964\pi$
$774$	−1.13898e17	−	5.58815e16i	−0.529748	−	0.259910i
$775$	−2.60525e16			−0.120238
$776$			7.15202e16i			0.327535i
$777$	8.47606e15	+	1.35999e16i	0.0385184	+	0.0618028i
$778$	−6.03503e16			−0.272146
$779$		−	8.72802e13i		−	0.000390563i
$780$	−6.90322e16	+	4.30241e16i	−0.306538	+	0.191049i
$781$	−2.10013e14			−0.000925423
$782$		−	4.71518e16i		−	0.206185i
$783$	3.40648e16	+	3.35410e17i	0.147821	+	1.45548i
$784$	1.32649e17			0.571223
$785$			9.69629e16i			0.414369i
$786$	−6.29039e16	−	1.00930e17i	−0.266773	−	0.428039i
$787$	−4.58335e16			−0.192901			−0.0964505	−	0.995338i	$-0.530749\pi$
$787$	−4.58335e16			−0.192901			−0.0964505	+	0.995338i	$0.530749\pi$
$788$		−	1.51786e17i		−	0.633979i
$789$	−1.07232e16	+	6.68317e15i	−0.0444489	+	0.0277026i
$790$	−2.42166e15			−0.00996209
$791$		−	4.59660e16i		−	0.187662i
$792$	1.84960e13	−	3.76986e13i	7.49423e−5	−	0.000152748i
$793$	4.74588e16			0.190844
$794$		−	1.02591e17i		−	0.409437i
$795$	1.45632e17	+	2.33666e17i	0.576836	+	0.925536i
$796$	1.33185e17			0.523572
$797$		−	1.29546e17i		−	0.505445i	−0.967539	−	0.252722i	$-0.918674\pi$
$797$		−	1.29546e17i		−	0.505445i	0.967539	−	0.252722i	$-0.0813259\pi$
$798$	8.32006e14	−	5.18545e14i	0.00322188	−	0.00200802i
$799$	−5.65823e16			−0.217470
$800$			4.38876e15i			0.0167418i
$801$	−1.13488e16	−	5.56802e15i	−0.0429688	−	0.0210817i
$802$	1.80841e17			0.679596
$803$			4.65369e12i			1.73582e-5i
$804$	3.77710e16	+	6.06037e16i	0.139837	+	0.224369i
$805$	7.46632e17			2.74367
$806$			1.69937e17i			0.619836i
$807$	2.19274e17	−	1.36661e17i	0.793863	−	0.494772i
$808$	−3.64006e16			−0.130810
$809$			2.60549e17i			0.929390i	0.885471	+	0.464695i	$0.153836\pi$
$809$			2.60549e17i			0.929390i	−0.885471	+	0.464695i	$0.846164\pi$
$810$	−1.27872e17	−	1.65255e17i	−0.452757	−	0.585119i
$811$	−3.19955e17			−1.12451			−0.562255	−	0.826964i	$-0.690066\pi$
$811$	−3.19955e17			−1.12451			−0.562255	+	0.826964i	$0.690066\pi$
$812$			3.80014e17i			1.32576i
$813$	−2.06149e17	−	3.30767e17i	−0.713902	−	1.14546i
$814$	3.97738e12			1.36726e−5
$815$		−	2.85976e17i		−	0.975850i
$816$	−1.26232e16	+	7.86734e15i	−0.0427590	+	0.0266494i
$817$	−7.35156e14			−0.00247199
$818$			2.62235e17i			0.875327i
$819$	1.66345e17	−	3.39044e17i	0.551195	−	1.12345i
$820$	−2.09684e16			−0.0689736
$821$			1.13668e17i			0.371176i	0.982628	+	0.185588i	$0.0594190\pi$
$821$			1.13668e17i			0.371176i	−0.982628	+	0.185588i	$0.940581\pi$
$822$	1.09247e17	+	1.75287e17i	0.354142	+	0.568222i
$823$	−1.72768e17			−0.555987			−0.277993	−	0.960583i	$-0.589669\pi$
$823$	−1.72768e17			−0.555987			−0.277993	+	0.960583i	$0.589669\pi$
$824$			3.93559e16i			0.125732i
$825$	1.21953e13	−	7.60068e12i	3.86785e−5	−	2.41062e-5i
$826$	−3.31444e17			−1.04359
$827$			4.52728e17i			1.41516i	0.706635	+	0.707579i	$0.250212\pi$
$827$			4.52728e17i			1.41516i	−0.706635	+	0.707579i	$0.749788\pi$
$828$	−2.09285e17	−	1.02681e17i	−0.649465	−	0.318646i
$829$	−1.77589e17			−0.547129			−0.273565	−	0.961854i	$-0.588203\pi$
$829$	−1.77589e17			−0.547129			−0.273565	+	0.961854i	$0.588203\pi$
$830$		−	1.14848e17i		−	0.351281i
$831$	−1.09068e17	−	1.75000e17i	−0.331201	−	0.531413i
$832$	2.86272e16			0.0863055
$833$			1.53846e17i			0.460486i
$834$	−2.27681e17	+	1.41902e17i	−0.676599	+	0.421688i
$835$	−5.88689e16			−0.173687
$836$		−	2.43327e11i		−	7.12774e-7i
$837$	−4.34298e17	+	4.41080e16i	−1.26309	+	0.128282i
$838$	3.12432e17			0.902176
$839$		−	5.04507e17i		−	1.44642i	−0.690626	−	0.723212i	$-0.742665\pi$
$839$		−	5.04507e17i		−	1.44642i	0.690626	−	0.723212i	$-0.257335\pi$
$840$	−1.24577e17	−	1.99884e17i	−0.354618	−	0.568986i
$841$	−4.03441e17			−1.14026
$842$		−	3.54739e17i		−	0.995489i
$843$	4.63414e17	−	2.88821e17i	1.29123	−	0.804755i
$844$	−4.29817e15			−0.0118913
$845$		−	1.99310e17i		−	0.547506i
$846$	−1.23218e17	+	2.51143e17i	−0.336087	+	0.685012i
$847$	6.69208e17			1.81243
$848$		−	9.68997e16i		−	0.260584i
$849$	1.08268e17	+	1.73717e17i	0.289105	+	0.463870i
$850$	−5.09009e15			−0.0134962
$851$		−	2.20805e16i		−	0.0581343i
$852$	3.12126e17	−	1.94531e17i	0.816004	−	0.508571i
$853$	2.11142e17			0.548125			0.274062	−	0.961712i	$-0.411633\pi$
$853$	2.11142e17			0.548125			0.274062	+	0.961712i	$0.411633\pi$
$854$			1.37418e17i			0.354238i
$855$	−1.08702e15	−	5.33321e14i	−0.00278252	−	0.00136519i
$856$	1.61569e17			0.410691
$857$			3.30745e17i			0.834850i	0.908711	+	0.417425i	$0.137067\pi$
$857$			3.30745e17i			0.834850i	−0.908711	+	0.417425i	$0.862933\pi$
$858$	−4.95780e13	−	7.95481e13i	−0.000124270	−	0.000199391i
$859$	−5.19425e17			−1.29290			−0.646448	−	0.762958i	$-0.723746\pi$
$859$	−5.19425e17			−1.29290			−0.646448	+	0.762958i	$0.723746\pi$
$860$			1.76616e17i			0.436556i
$861$	8.26192e16	−	5.14921e16i	0.202797	−	0.126393i
$862$	3.14467e16			0.0766533
$863$			1.99479e17i			0.482872i	0.970417	+	0.241436i	$0.0776185\pi$
$863$			1.99479e17i			0.482872i	−0.970417	+	0.241436i	$0.922382\pi$
$864$	7.43035e15	+	7.31609e16i	0.0178619	+	0.175872i
$865$	−5.30430e17			−1.26629
$866$		−	1.18689e17i		−	0.281388i
$867$	2.15528e17	+	3.45815e17i	0.507445	+	0.814197i
$868$	−4.92053e17			−1.15052
$869$		−	2.79056e12i		−	6.47995e-6i
$870$	3.98309e17	−	2.48244e17i	0.918553	−	0.572484i
$871$	1.59402e17			0.365077
$872$		−	2.26656e17i		−	0.515547i
$873$	−1.80636e17	+	3.68173e17i	−0.408056	+	0.831701i
$874$	−1.35083e15			−0.00303063
$875$			7.70455e17i			1.71672i
$876$	−4.31062e15	−	6.91641e15i	−0.00953928	−	0.0153058i
$877$	6.49409e17			1.42732			0.713659	−	0.700493i	$-0.247036\pi$
$877$	6.49409e17			1.42732			0.713659	+	0.700493i	$0.247036\pi$
$878$		−	7.57733e16i		−	0.165405i
$879$	−5.33186e17	+	3.32306e17i	−1.15597	+	0.720451i
$880$	−5.84575e13			−0.000125876
$881$		−	6.36797e17i		−	1.36190i	−0.732330	−	0.680950i	$-0.761567\pi$
$881$		−	6.36797e17i		−	1.36190i	0.732330	−	0.680950i	$-0.238433\pi$
$882$	6.82852e17	+	3.35026e17i	1.45049	+	0.711652i
$883$	5.49439e17			1.15919			0.579596	−	0.814904i	$-0.303210\pi$
$883$	5.49439e17			1.15919			0.579596	+	0.814904i	$0.303210\pi$
$884$			3.32019e16i			0.0695743i
$885$	2.16515e17	+	3.47400e17i	0.450639	+	0.723052i
$886$	2.42124e17			0.500537
$887$		−	8.29101e17i		−	1.70242i	−0.524828	−	0.851208i	$-0.675871\pi$
$887$		−	8.29101e17i		−	1.70242i	0.524828	−	0.851208i	$-0.324129\pi$
$888$	−5.91126e15	+	3.68417e15i	−0.0120560	+	0.00751384i
$889$	−3.14082e17			−0.636256
$890$			1.75980e16i			0.0354098i
$891$	1.90428e14	−	1.47351e14i	0.000380597	−	0.000294501i
$892$	−2.77038e17			−0.549985
$893$			1.62101e15i			0.00319651i
$894$	−1.97432e17	−	3.16780e17i	−0.386716	−	0.620488i
$895$	−3.60842e15			−0.00702067
$896$			8.28903e16i			0.160197i
$897$	−4.41613e17	+	2.75234e17i	−0.847788	+	0.528381i
$898$	8.92234e16			0.170146
$899$		−	9.80516e17i		−	1.85736i
$900$	−1.10846e16	+	2.25926e16i	−0.0208576	+	0.0425119i
$901$	1.12385e17			0.210067
$902$		−	2.41626e13i		−	4.48647e-5i
$903$	−4.33715e17	−	6.95897e17i	−0.799978	−	1.28357i
$904$	1.99794e16			0.0366076
$905$			8.87708e17i			1.61577i
$906$	−3.88728e17	+	2.42273e17i	−0.702873	+	0.438063i
$907$	3.36656e16			0.0604704			0.0302352	−	0.999543i	$-0.490374\pi$
$907$	3.36656e16			0.0604704			0.0302352	+	0.999543i	$0.490374\pi$
$908$		−	3.01635e17i		−	0.538228i
$909$	−1.87384e17	−	9.19358e16i	−0.332161	−	0.162968i
$910$	−5.25740e17			−0.925812
$911$			8.60034e17i			1.50455i	0.658852	+	0.752273i	$0.271042\pi$
$911$			8.60034e17i			1.50455i	−0.658852	+	0.752273i	$0.728958\pi$
$912$	2.25389e14	+	3.61637e14i	0.000391709	+	0.000628498i
$913$	1.32343e14			0.000228495
$914$		−	7.41205e17i		−	1.27134i
$915$	1.44033e17	−	8.97679e16i	0.245434	−	0.152966i
$916$	4.89405e17			0.828506
$917$		−	7.68666e17i		−	1.29277i
$918$	−8.48522e16	+	8.61774e15i	−0.141777	+	0.0143992i
$919$	−2.02825e17			−0.336689			−0.168344	−	0.985728i	$-0.553842\pi$
$919$	−2.02825e17			−0.336689			−0.168344	+	0.985728i	$0.553842\pi$
$920$			3.24528e17i			0.535212i
$921$	4.87509e16	+	7.82210e16i	0.0798776	+	0.128164i
$922$	−7.31821e17			−1.19130
$923$		−	8.20963e17i		−	1.32774i
$924$	2.30332e14	−	1.43554e14i	0.000370104	−	0.000230666i
$925$	−2.38362e15			−0.00380529
$926$			7.06508e17i			1.12060i
$927$	−9.94000e16	+	2.02597e17i	−0.156642	+	0.319268i
$928$	−1.65176e17			−0.258618
$929$			6.11878e17i			0.951855i	0.879485	+	0.475927i	$0.157887\pi$
$929$			6.11878e17i			0.951855i	−0.879485	+	0.475927i	$0.842113\pi$
$930$	3.21434e17	+	5.15741e17i	0.496814	+	0.797139i
$931$	4.40748e15			0.00676850
$932$			3.30728e17i			0.504633i
$933$	5.03330e17	−	3.13698e17i	0.763067	−	0.475579i
$934$	−1.18926e17			−0.179141
$935$		−	6.77992e13i		−	0.000101474i
$936$	1.47368e17	+	7.23028e16i	0.219153	+	0.107523i
$937$	1.33073e18			1.96632			0.983159	−	0.182750i	$-0.0584998\pi$
$937$	1.33073e18			1.96632			0.983159	+	0.182750i	$0.0584998\pi$
$938$			4.61550e17i			0.677644i
$939$	1.28331e17	+	2.05908e17i	0.187214	+	0.300386i
$940$	3.89435e17			0.564506
$941$		−	2.77081e17i		−	0.399088i	−0.979889	−	0.199544i	$-0.936054\pi$
$941$		−	2.77081e17i		−	0.399088i	0.979889	−	0.199544i	$-0.0639461\pi$
$942$	1.66061e17	−	1.03497e17i	0.237663	−	0.148122i
$943$	−1.34139e17			−0.190760
$944$		−	1.44064e17i		−	0.203575i
$945$	−1.36459e17	−	1.34361e18i	−0.191607	−	1.88661i
$946$	−2.03521e14			−0.000283963
$947$			6.35509e17i			0.881093i	0.897730	+	0.440546i	$0.145215\pi$
$947$			6.35509e17i			0.881093i	−0.897730	+	0.440546i	$0.854785\pi$
$948$	2.58484e15	+	4.14738e15i	0.00356109	+	0.00571378i
$949$	−1.81918e16			−0.0249045
$950$			1.45824e14i			0.000198376i
$951$	−7.69237e16	+	4.79424e16i	−0.103987	+	0.0648092i
$952$	−9.61364e16			−0.129142
$953$		−	1.30060e15i		−	0.00173615i	−1.00000		0.000868073i	$-0.999724\pi$
$953$		−	1.30060e15i		−	0.00173615i	1.00000		0.000868073i	$-0.000276316\pi$
$954$	2.44737e17	−	4.98823e17i	0.324645	−	0.661692i
$955$	−1.07255e18			−1.41383
$956$			1.15204e17i			0.150911i
$957$	2.86060e14	+	4.58984e14i	0.000372379	+	0.000597483i
$958$	1.21785e17			0.157543
$959$			1.33496e18i			1.71615i
$960$	8.68807e16	−	5.41480e16i	0.110993	−	0.0691760i
$961$	4.81937e17			0.611857
$962$			1.55480e16i			0.0196166i
$963$	8.31729e17	+	4.08070e17i	1.04286	+	0.511655i
$964$	1.82009e17			0.226794
$965$		−	7.68433e16i		−	0.0951573i
$966$	−7.96942e17	−	1.27870e18i	−0.980763	−	1.57364i
$967$	9.51560e17			1.16380			0.581898	−	0.813261i	$-0.302310\pi$
$967$	9.51560e17			1.16380			0.581898	+	0.813261i	$0.302310\pi$
$968$			2.90875e17i			0.353553i
$969$	−4.19427e14	+	2.61406e14i	−0.000506657	+	0.000315772i
$970$	5.70910e17			0.685389
$971$			1.36651e18i			1.63041i	0.579170	+	0.815207i	$0.303377\pi$
$971$			1.36651e18i			1.63041i	−0.579170	+	0.815207i	$0.696623\pi$
$972$	−1.46530e17	+	3.95386e17i	−0.173752	+	0.468839i
$973$	−1.73399e18			−2.04348
$974$		−	3.65515e17i		−	0.428107i
$975$	2.97118e16	+	4.76727e16i	0.0345861	+	0.0554935i
$976$	−5.97294e16			−0.0691018
$977$		−	1.55405e18i		−	1.78689i	−0.449172	−	0.893445i	$-0.648281\pi$
$977$		−	1.55405e18i		−	1.78689i	0.449172	−	0.893445i	$-0.351719\pi$
$978$	−4.89767e17	+	3.05245e17i	−0.559702	+	0.348832i
$979$	−2.02787e13			−2.30327e−5
$980$		−	1.05887e18i		−	1.19532i
$981$	5.72459e17	−	1.16679e18i	0.642288	−	1.30911i
$982$	−3.58735e17			−0.400041
$983$		−	6.30549e17i		−	0.698873i	−0.936960	−	0.349436i	$-0.886373\pi$
$983$		−	6.30549e17i		−	0.698873i	0.936960	−	0.349436i	$-0.113627\pi$
$984$	2.23814e16	+	3.59110e16i	0.0246556	+	0.0395600i
$985$	−1.21163e18			−1.32664
$986$		−	1.91571e17i		−	0.208482i
$987$	−1.53444e18	+	9.56334e17i	−1.65977	+	1.03444i
$988$	9.51189e14			0.00102265
$989$			1.12985e18i			1.20738i
$990$	−3.00929e14	−	1.47644e14i	−0.000319634	−	0.000156822i
$991$	−8.66851e17			−0.915171			−0.457586	−	0.889166i	$-0.651286\pi$
$991$	−8.66851e17			−0.915171			−0.457586	+	0.889166i	$0.651286\pi$
$992$		−	2.13874e17i		−	0.224434i
$993$	8.81779e17	+	1.41482e18i	0.919738	+	1.47572i
$994$	2.37711e18			2.46451
$995$		−	1.06315e18i		−	1.09561i
$996$	−1.96691e17	+	1.22587e17i	−0.201478	+	0.125571i
$997$	−1.45262e18			−1.47905			−0.739524	−	0.673131i	$-0.764949\pi$
$997$	−1.45262e18			−1.47905			−0.739524	+	0.673131i	$0.764949\pi$
$998$			5.97417e17i			0.604637i
$999$	−3.97352e16	+	4.03557e15i	−0.0399744	+	0.00405987i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.13.b.a.5.2	✓	4
3.2	odd	2	inner	6.13.b.a.5.4	yes	4
4.3	odd	2		48.13.e.c.17.1		4
5.2	odd	4		150.13.b.a.149.7		8
5.3	odd	4		150.13.b.a.149.2		8
5.4	even	2		150.13.d.a.101.3		4
8.3	odd	2		192.13.e.h.65.4		4
8.5	even	2		192.13.e.e.65.1		4
9.2	odd	6		162.13.d.d.53.4		8
9.4	even	3		162.13.d.d.107.4		8
9.5	odd	6		162.13.d.d.107.1		8
9.7	even	3		162.13.d.d.53.1		8
12.11	even	2		48.13.e.c.17.2		4
15.2	even	4		150.13.b.a.149.1		8
15.8	even	4		150.13.b.a.149.8		8
15.14	odd	2		150.13.d.a.101.1		4
24.5	odd	2		192.13.e.e.65.2		4
24.11	even	2		192.13.e.h.65.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.13.b.a.5.2	✓	4	1.1	even	1	trivial
6.13.b.a.5.4	yes	4	3.2	odd	2	inner
48.13.e.c.17.1		4	4.3	odd	2
48.13.e.c.17.2		4	12.11	even	2
150.13.b.a.149.1		8	15.2	even	4
150.13.b.a.149.2		8	5.3	odd	4
150.13.b.a.149.7		8	5.2	odd	4
150.13.b.a.149.8		8	15.8	even	4
150.13.d.a.101.1		4	15.14	odd	2
150.13.d.a.101.3		4	5.4	even	2
162.13.d.d.53.1		8	9.7	even	3
162.13.d.d.53.4		8	9.2	odd	6
162.13.d.d.107.1		8	9.5	odd	6
162.13.d.d.107.4		8	9.4	even	3
192.13.e.e.65.1		4	8.5	even	2
192.13.e.e.65.2		4	24.5	odd	2
192.13.e.h.65.3		4	24.11	even	2
192.13.e.h.65.4		4	8.3	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:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	6.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-45.2548i q^{2} +(385.589 + 618.678i) q^{3} -2048.00 q^{4} +16348.2i q^{5} +(27998.2 - 17449.7i) q^{6} +213230. q^{7} +92681.9i q^{8} +(-234084. + 477110. i) q^{9} +O(q^{10})\)	\(q-45.2548i q^{2} +(385.589 + 618.678i) q^{3} -2048.00 q^{4} +16348.2i q^{5} +(27998.2 - 17449.7i) q^{6} +213230. q^{7} +92681.9i q^{8} +(-234084. + 477110. i) q^{9} +739833. q^{10} +852.534i q^{11} +(-789685. - 1.26705e6i) q^{12} -3.33264e6 q^{13} -9.64970e6i q^{14} +(-1.01142e7 + 6.30366e6i) q^{15} +4.19430e6 q^{16} +4.86457e6i q^{17} +(2.15915e7 + 1.05934e7i) q^{18} +139363. q^{19} -3.34810e7i q^{20} +(8.22192e7 + 1.31921e8i) q^{21} +38581.3 q^{22} -2.14185e8i q^{23} +(-5.73403e7 + 3.57371e7i) q^{24} -2.31215e7 q^{25} +1.50818e8i q^{26} +(-3.85438e8 + 3.91457e7i) q^{27} -4.36696e8 q^{28} -8.70204e8i q^{29} +(2.85271e8 + 4.57718e8i) q^{30} +1.12677e9 q^{31} -1.89813e8i q^{32} +(-527444. + 328727. i) q^{33} +2.20145e8 q^{34} +3.48592e9i q^{35} +(4.79404e8 - 9.77122e8i) q^{36} +1.03091e8 q^{37} -6.30686e6i q^{38} +(-1.28503e9 - 2.06183e9i) q^{39} -1.51518e9 q^{40} -6.26279e8i q^{41} +(5.97006e9 - 3.72081e9i) q^{42} -5.27511e9 q^{43} -1.74599e6i q^{44} +(-7.79987e9 - 3.82684e9i) q^{45} -9.69290e9 q^{46} +1.16315e10i q^{47} +(1.61728e9 + 2.59492e9i) q^{48} +3.16259e10 q^{49} +1.04636e9i q^{50} +(-3.00960e9 + 1.87572e9i) q^{51} +6.82525e9 q^{52} -2.31027e10i q^{53} +(1.77153e9 + 1.74429e10i) q^{54} -1.39374e7 q^{55} +1.97626e10i q^{56} +(5.37369e7 + 8.62209e7i) q^{57} -3.93810e10 q^{58} -3.43476e10i q^{59} +(2.07140e10 - 1.29099e10i) q^{60} -1.42406e10 q^{61} -5.09916e10i q^{62} +(-4.99138e10 + 1.01734e11i) q^{63} -8.58993e9 q^{64} -5.44825e10i q^{65} +(1.48765e7 + 2.38694e7i) q^{66} -4.78304e10 q^{67} -9.96263e9i q^{68} +(1.32511e11 - 8.25872e10i) q^{69} +1.57755e11 q^{70} +2.46340e11i q^{71} +(-4.42195e10 - 2.16953e10i) q^{72} +5.45866e9 q^{73} -4.66537e9i q^{74} +(-8.91540e9 - 1.43048e10i) q^{75} -2.85416e8 q^{76} +1.81786e8i q^{77} +(-9.33079e10 + 5.81537e10i) q^{78} -3.27325e9 q^{79} +6.85691e10i q^{80} +(-1.72839e11 - 2.23368e11i) q^{81} -2.83421e10 q^{82} -1.55235e11i q^{83} +(-1.68385e11 - 2.70174e11i) q^{84} -7.95267e10 q^{85} +2.38724e11i q^{86} +(5.38376e11 - 3.35541e11i) q^{87} -7.90144e7 q^{88} +2.37864e10i q^{89} +(-1.73183e11 + 3.52982e11i) q^{90} -7.10620e11 q^{91} +4.38651e11i q^{92} +(4.34468e11 + 6.97105e11i) q^{93} +5.26383e11 q^{94} +2.27833e9i q^{95} +(1.17433e11 - 7.31895e10i) q^{96} +7.71674e11 q^{97} -1.43122e12i q^{98} +(-4.06753e8 - 1.99564e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 780 q^{3} - 8192 q^{4} - 9984 q^{6} + 153080 q^{7} - 1530972 q^{9}+O(q^{10}) \) 4 * q + 780 * q^3 - 8192 * q^4 - 9984 * q^6 + 153080 * q^7 - 1530972 * q^9	\( 4 q + 780 q^{3} - 8192 q^{4} - 9984 q^{6} + 153080 q^{7} - 1530972 q^{9} + 1641984 q^{10} - 1597440 q^{12} + 7253000 q^{13} - 17613792 q^{15} + 16777216 q^{16} + 42600960 q^{18} - 120268072 q^{19} + 163232328 q^{21} - 159244800 q^{22} + 20447232 q^{24} + 435605764 q^{25} - 784941300 q^{27} - 313507840 q^{28} + 571258368 q^{30} + 2731727672 q^{31} - 2567489760 q^{33} - 3097810944 q^{34} + 3135430656 q^{36} - 15280120 q^{37} - 2508657000 q^{39} - 3362783232 q^{40} + 20958988800 q^{42} + 1629119960 q^{43} - 15576677568 q^{45} - 29905849344 q^{46} + 3271557120 q^{48} + 72937649100 q^{49} - 63012636288 q^{51} - 14854144000 q^{52} + 38602586880 q^{54} + 6285799872 q^{55} - 424311000 q^{57} - 62351992320 q^{58} + 36073046016 q^{60} + 45477065096 q^{61} + 45447449400 q^{63} - 34359738368 q^{64} - 673085952 q^{66} - 213433609960 q^{67} + 95560926912 q^{69} + 293322353664 q^{70} - 87246766080 q^{72} - 254383625080 q^{73} - 15705158772 q^{75} + 246309011456 q^{76} - 645782208000 q^{78} + 308580159032 q^{79} + 219015659268 q^{81} + 234603709440 q^{82} - 334299807744 q^{84} - 18844054272 q^{85} + 1341091294560 q^{87} + 326133350400 q^{88} - 432622121472 q^{90} - 3323734346000 q^{91} + 871044956040 q^{93} + 775668172800 q^{94} - 41875931136 q^{96} + 1276228475720 q^{97} - 23456841408 q^{99}+O(q^{100}) \) 4 * q + 780 * q^3 - 8192 * q^4 - 9984 * q^6 + 153080 * q^7 - 1530972 * q^9 + 1641984 * q^10 - 1597440 * q^12 + 7253000 * q^13 - 17613792 * q^15 + 16777216 * q^16 + 42600960 * q^18 - 120268072 * q^19 + 163232328 * q^21 - 159244800 * q^22 + 20447232 * q^24 + 435605764 * q^25 - 784941300 * q^27 - 313507840 * q^28 + 571258368 * q^30 + 2731727672 * q^31 - 2567489760 * q^33 - 3097810944 * q^34 + 3135430656 * q^36 - 15280120 * q^37 - 2508657000 * q^39 - 3362783232 * q^40 + 20958988800 * q^42 + 1629119960 * q^43 - 15576677568 * q^45 - 29905849344 * q^46 + 3271557120 * q^48 + 72937649100 * q^49 - 63012636288 * q^51 - 14854144000 * q^52 + 38602586880 * q^54 + 6285799872 * q^55 - 424311000 * q^57 - 62351992320 * q^58 + 36073046016 * q^60 + 45477065096 * q^61 + 45447449400 * q^63 - 34359738368 * q^64 - 673085952 * q^66 - 213433609960 * q^67 + 95560926912 * q^69 + 293322353664 * q^70 - 87246766080 * q^72 - 254383625080 * q^73 - 15705158772 * q^75 + 246309011456 * q^76 - 645782208000 * q^78 + 308580159032 * q^79 + 219015659268 * q^81 + 234603709440 * q^82 - 334299807744 * q^84 - 18844054272 * q^85 + 1341091294560 * q^87 + 326133350400 * q^88 - 432622121472 * q^90 - 3323734346000 * q^91 + 871044956040 * q^93 + 775668172800 * q^94 - 41875931136 * q^96 + 1276228475720 * q^97 - 23456841408 * q^99

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