LMFDB - Embedded newform 126.16.g.c.37.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,16,Mod(37,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("126.37");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	126.g (of order $3$, degree $2$, 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:	$179.793816426$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7979102 x^{8} - 3342530557 x^{7} + 48610066963550 x^{6} + \cdots + 51\!\cdots\!56 $ x^10 - x^9 + 7979102x^8 - 3342530557x^7 + 48610066963550x^6 - 20531463882664153x^5 + 122945882607722292337x^4 - 89586690298994071428648x^3 + 238785864099387585455090736x^2 - 108333121326673799746890760320x + 51761574501460447109413728819456
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{18}\cdot 3^{7}\cdot 5^{4}\cdot 7^{6} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.5
Root			$-942.293 + 1632.10i$ of defining polynomial
Character	$\chi$	$=$	126.37
Dual form			126.16.g.c.109.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-64.0000 + 110.851i) q^{2} +(-8192.00 - 14189.0i) q^{4} +(99492.8 - 172327. i) q^{5} +(2.03263e6 - 784833. i) q^{7} +2.09715e6 q^{8} +O(q^{10})$	\(q+(-64.0000 + 110.851i) q^{2} +(-8192.00 - 14189.0i) q^{4} +(99492.8 - 172327. i) q^{5} +(2.03263e6 - 784833. i) q^{7} +2.09715e6 q^{8} +(1.27351e7 + 2.20578e7i) q^{10} +(-2.41555e7 - 4.18386e7i) q^{11} -2.49387e8 q^{13} +(-4.30888e7 + 2.75549e8i) q^{14} +(-1.34218e8 + 2.32472e8i) q^{16} +(9.16603e8 + 1.58760e9i) q^{17} +(-1.64208e9 + 2.84417e9i) q^{19} -3.26018e9 q^{20} +6.18381e9 q^{22} +(1.55962e10 - 2.70135e10i) q^{23} +(-4.53885e9 - 7.86151e9i) q^{25} +(1.59608e10 - 2.76449e10i) q^{26} +(-2.77873e10 - 2.24116e10i) q^{28} -1.10574e11 q^{29} +(1.78686e10 + 3.09493e10i) q^{31} +(-1.71799e10 - 2.97564e10i) q^{32} -2.34650e11 q^{34} +(6.69848e10 - 4.28362e11i) q^{35} +(4.58620e11 - 7.94354e11i) q^{37} +(-2.10186e11 - 3.64053e11i) q^{38} +(2.08652e11 - 3.61395e11i) q^{40} +2.82110e11 q^{41} +1.12963e12 q^{43} +(-3.95764e11 + 6.85483e11i) q^{44} +(1.99632e12 + 3.45773e12i) q^{46} +(1.96516e12 - 3.40375e12i) q^{47} +(3.51564e12 - 3.19055e12i) q^{49} +1.16194e12 q^{50} +(2.04298e12 + 3.53854e12i) q^{52} +(-3.03333e12 - 5.25388e12i) q^{53} -9.61320e12 q^{55} +(4.26274e12 - 1.64591e12i) q^{56} +(7.07674e12 - 1.22573e13i) q^{58} +(3.30595e12 + 5.72607e12i) q^{59} +(8.03169e12 - 1.39113e13i) q^{61} -4.57435e12 q^{62} +4.39805e12 q^{64} +(-2.48122e13 + 4.29760e13i) q^{65} +(4.53733e13 + 7.85889e13i) q^{67} +(1.50176e13 - 2.60113e13i) q^{68} +(4.31974e13 + 3.48405e13i) q^{70} -7.43060e13 q^{71} +(-7.21893e13 - 1.25036e14i) q^{73} +(5.87034e13 + 1.01677e14i) q^{74} +5.38077e13 q^{76} +(-8.19356e13 - 6.60845e13i) q^{77} +(4.61192e13 - 7.98807e13i) q^{79} +(2.67074e13 + 4.62586e13i) q^{80} +(-1.80551e13 + 3.12723e13i) q^{82} -3.24677e14 q^{83} +3.64782e14 q^{85} +(-7.22965e13 + 1.25221e14i) q^{86} +(-5.06578e13 - 8.77419e13i) q^{88} +(-1.41340e14 + 2.44808e14i) q^{89} +(-5.06912e14 + 1.95727e14i) q^{91} -5.11058e14 q^{92} +(2.51540e14 + 4.35680e14i) q^{94} +(3.26750e14 + 5.65948e14i) q^{95} -5.07472e13 q^{97} +(1.28676e14 + 5.93908e14i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 640 q^{2} - 81920 q^{4} - 10969 q^{5} + 2375276 q^{7} + 20971520 q^{8}+O(q^{10}) $ 10 * q - 640 * q^2 - 81920 * q^4 - 10969 * q^5 + 2375276 * q^7 + 20971520 * q^8	\( 10 q - 640 q^{2} - 81920 q^{4} - 10969 q^{5} + 2375276 q^{7} + 20971520 q^{8} - 1404032 q^{10} + 3405409 q^{11} + 369408276 q^{13} - 411547520 q^{14} - 1342177280 q^{16} + 3201713287 q^{17} - 1063446451 q^{19} + 359432192 q^{20} - 871784704 q^{22} + 31680429991 q^{23} + 39012502244 q^{25} - 23642129664 q^{26} + 13761560576 q^{28} - 294935242276 q^{29} + 30201804075 q^{31} - 171798691840 q^{32} - 819638601472 q^{34} + 1540311474205 q^{35} + 1369689837461 q^{37} - 136121145728 q^{38} - 23003660288 q^{40} - 3634838274156 q^{41} + 415602663752 q^{43} + 55794221056 q^{44} + 4055095038848 q^{46} + 12606978599835 q^{47} - 8067928630838 q^{49} - 9987200574464 q^{50} - 3026192596992 q^{52} - 10616682242361 q^{53} - 40851384759514 q^{55} + 4981314813952 q^{56} + 18875855505664 q^{58} - 39993786962755 q^{59} + 5148862074165 q^{61} - 7731661843200 q^{62} + 43980465111040 q^{64} - 91302240851010 q^{65} - 29267240444285 q^{67} + 52456870494208 q^{68} + 18327124839296 q^{70} + 37767657205600 q^{71} + 243869659370917 q^{73} + 175320299195008 q^{74} + 34847013306368 q^{76} - 35960055270559 q^{77} + 137356615917609 q^{79} - 2944468516864 q^{80} + 232629649545984 q^{82} + 914604166510648 q^{83} + 264981492485402 q^{85} - 26598570480128 q^{86} + 7141660295168 q^{88} - 315332760149685 q^{89} - 26\!\cdots\!20 q^{91}+ \cdots + 12\!\cdots\!56 q^{98}+O(q^{100}) \) 10 * q - 640 * q^2 - 81920 * q^4 - 10969 * q^5 + 2375276 * q^7 + 20971520 * q^8 - 1404032 * q^10 + 3405409 * q^11 + 369408276 * q^13 - 411547520 * q^14 - 1342177280 * q^16 + 3201713287 * q^17 - 1063446451 * q^19 + 359432192 * q^20 - 871784704 * q^22 + 31680429991 * q^23 + 39012502244 * q^25 - 23642129664 * q^26 + 13761560576 * q^28 - 294935242276 * q^29 + 30201804075 * q^31 - 171798691840 * q^32 - 819638601472 * q^34 + 1540311474205 * q^35 + 1369689837461 * q^37 - 136121145728 * q^38 - 23003660288 * q^40 - 3634838274156 * q^41 + 415602663752 * q^43 + 55794221056 * q^44 + 4055095038848 * q^46 + 12606978599835 * q^47 - 8067928630838 * q^49 - 9987200574464 * q^50 - 3026192596992 * q^52 - 10616682242361 * q^53 - 40851384759514 * q^55 + 4981314813952 * q^56 + 18875855505664 * q^58 - 39993786962755 * q^59 + 5148862074165 * q^61 - 7731661843200 * q^62 + 43980465111040 * q^64 - 91302240851010 * q^65 - 29267240444285 * q^67 + 52456870494208 * q^68 + 18327124839296 * q^70 + 37767657205600 * q^71 + 243869659370917 * q^73 + 175320299195008 * q^74 + 34847013306368 * q^76 - 35960055270559 * q^77 + 137356615917609 * q^79 - 2944468516864 * q^80 + 232629649545984 * q^82 + 914604166510648 * q^83 + 264981492485402 * q^85 - 26598570480128 * q^86 + 7141660295168 * q^88 - 315332760149685 * q^89 - 2638730194011720 * q^91 - 1038104329945088 * q^92 + 1613693260778880 * q^94 + 1346257729549705 * q^95 + 58320039716044 * q^97 + 1279096378461056 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−64.0000	+	110.851i	−0.353553	+	0.612372i
$2$	−64.0000	+	110.851i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−8192.00	−	14189.0i	−0.250000	−	0.433013i
$5$	99492.8	−	172327.i	0.569530	−	0.986455i	−0.427082	−	0.904213i	$-0.640459\pi$
$5$	99492.8	−	172327.i	0.569530	−	0.986455i	0.996612	−	0.0822422i	$-0.0262081\pi$
$6$		0			0
$7$	2.03263e6	−	784833.i	0.932876	−	0.360198i
$7$	2.03263e6	−	784833.i	0.932876	−	0.360198i
$8$	2.09715e6			0.353553
$9$		0			0
$10$	1.27351e7	+	2.20578e7i	0.402719	+	0.697529i
$11$	−2.41555e7	−	4.18386e7i	−0.373741	−	0.647339i	0.616396	−	0.787436i	$-0.288592\pi$
$11$	−2.41555e7	−	4.18386e7i	−0.373741	−	0.647339i	−0.990138	+	0.140097i	$0.955259\pi$
$12$		0			0
$13$	−2.49387e8			−1.10230			−0.551149	−	0.834407i	$-0.685810\pi$
$13$	−2.49387e8			−1.10230			−0.551149	+	0.834407i	$0.685810\pi$
$14$	−4.30888e7	+	2.75549e8i	−0.109246	+	0.698617i
$15$		0			0
$16$	−1.34218e8	+	2.32472e8i	−0.125000	+	0.216506i
$17$	9.16603e8	+	1.58760e9i	0.541769	+	0.938372i	0.998803	+	0.0489224i	$0.0155787\pi$
$17$	9.16603e8	+	1.58760e9i	0.541769	+	0.938372i	−0.457033	+	0.889450i	$0.651088\pi$
$18$		0			0
$19$	−1.64208e9	+	2.84417e9i	−0.421446	+	0.729967i	−0.996081	−	0.0884433i	$-0.971811\pi$
$19$	−1.64208e9	+	2.84417e9i	−0.421446	+	0.729967i	0.574635	+	0.818410i	$0.305144\pi$
$20$	−3.26018e9			−0.569530
$21$		0			0
$22$	6.18381e9			0.528550
$23$	1.55962e10	−	2.70135e10i	0.955127	−	1.65433i	0.221050	−	0.975262i	$-0.429051\pi$
$23$	1.55962e10	−	2.70135e10i	0.955127	−	1.65433i	0.734077	−	0.679067i	$-0.237615\pi$
$24$		0			0
$25$	−4.53885e9	−	7.86151e9i	−0.148729	−	0.257606i
$26$	1.59608e10	−	2.76449e10i	0.389721	−	0.675016i
$27$		0			0
$28$	−2.77873e10	−	2.24116e10i	−0.389189	−	0.313897i
$29$	−1.10574e11			−1.19033			−0.595166	−	0.803603i	$-0.702914\pi$
$29$	−1.10574e11			−1.19033			−0.595166	+	0.803603i	$0.702914\pi$
$30$		0			0
$31$	1.78686e10	+	3.09493e10i	0.116648	+	0.202040i	0.918437	−	0.395567i	$-0.129452\pi$
$31$	1.78686e10	+	3.09493e10i	0.116648	+	0.202040i	−0.801789	+	0.597607i	$0.796118\pi$
$32$	−1.71799e10	−	2.97564e10i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−2.34650e11			−0.766178
$35$	6.69848e10	−	4.28362e11i	0.175981	−	1.12538i
$36$		0			0
$37$	4.58620e11	−	7.94354e11i	0.794219	−	1.37563i	−0.129115	−	0.991630i	$-0.541214\pi$
$37$	4.58620e11	−	7.94354e11i	0.794219	−	1.37563i	0.923334	−	0.383998i	$-0.125453\pi$
$38$	−2.10186e11	−	3.64053e11i	−0.298008	−	0.516164i
$39$		0			0
$40$	2.08652e11	−	3.61395e11i	0.201359	−	0.348764i
$41$	2.82110e11			0.226225			0.113112	−	0.993582i	$-0.463918\pi$
$41$	2.82110e11			0.226225			0.113112	+	0.993582i	$0.463918\pi$
$42$		0			0
$43$	1.12963e12			0.633758			0.316879	−	0.948466i	$-0.397365\pi$
$43$	1.12963e12			0.633758			0.316879	+	0.948466i	$0.397365\pi$
$44$	−3.95764e11	+	6.85483e11i	−0.186871	+	0.323669i
$45$		0			0
$46$	1.99632e12	+	3.45773e12i	0.675377	+	1.16979i
$47$	1.96516e12	−	3.40375e12i	0.565800	−	0.979995i	−0.431174	−	0.902269i	$-0.641901\pi$
$47$	1.96516e12	−	3.40375e12i	0.565800	−	0.979995i	0.996975	−	0.0777263i	$-0.0247660\pi$
$48$		0			0
$49$	3.51564e12	−	3.19055e12i	0.740514	−	0.672041i
$50$	1.16194e12			0.210334
$51$		0			0
$52$	2.04298e12	+	3.53854e12i	0.275574	+	0.477309i
$53$	−3.03333e12	−	5.25388e12i	−0.354691	−	0.614343i	0.632374	−	0.774663i	$-0.282081\pi$
$53$	−3.03333e12	−	5.25388e12i	−0.354691	−	0.614343i	−0.987065	+	0.160320i	$0.948747\pi$
$54$		0			0
$55$	−9.61320e12			−0.851428
$56$	4.26274e12	−	1.64591e12i	0.329821	−	0.127349i
$57$		0			0
$58$	7.07674e12	−	1.22573e13i	0.420846	−	0.728927i
$59$	3.30595e12	+	5.72607e12i	0.172944	+	0.299548i	0.939448	−	0.342692i	$-0.111339\pi$
$59$	3.30595e12	+	5.72607e12i	0.172944	+	0.299548i	−0.766504	+	0.642240i	$0.778005\pi$
$60$		0			0
$61$	8.03169e12	−	1.39113e13i	0.327215	−	0.566753i	−0.654743	−	0.755851i	$-0.727223\pi$
$61$	8.03169e12	−	1.39113e13i	0.327215	−	0.566753i	0.981958	+	0.189099i	$0.0605566\pi$
$62$	−4.57435e12			−0.164965
$63$		0			0
$64$	4.39805e12			0.125000
$65$	−2.48122e13	+	4.29760e13i	−0.627791	+	1.08737i
$66$		0			0
$67$	4.53733e13	+	7.85889e13i	0.914617	+	1.58416i	0.807461	+	0.589921i	$0.200841\pi$
$67$	4.53733e13	+	7.85889e13i	0.914617	+	1.58416i	0.107156	+	0.994242i	$0.465826\pi$
$68$	1.50176e13	−	2.60113e13i	0.270885	−	0.469186i
$69$		0			0
$70$	4.31974e13	+	3.48405e13i	0.626935	+	0.505649i
$71$	−7.43060e13			−0.969586			−0.484793	−	0.874629i	$-0.661105\pi$
$71$	−7.43060e13			−0.969586			−0.484793	+	0.874629i	$0.661105\pi$
$72$		0			0
$73$	−7.21893e13	−	1.25036e14i	−0.764806	−	1.32468i	−0.940349	−	0.340212i	$-0.889501\pi$
$73$	−7.21893e13	−	1.25036e14i	−0.764806	−	1.32468i	0.175543	−	0.984472i	$-0.443832\pi$
$74$	5.87034e13	+	1.01677e14i	0.561598	+	0.972716i
$75$		0			0
$76$	5.38077e13			0.421446
$77$	−8.19356e13	−	6.60845e13i	−0.581825	−	0.469266i
$78$		0			0
$79$	4.61192e13	−	7.98807e13i	0.270196	−	0.467993i	−0.698716	−	0.715399i	$-0.746245\pi$
$79$	4.61192e13	−	7.98807e13i	0.270196	−	0.467993i	0.968912	+	0.247406i	$0.0795783\pi$
$80$	2.67074e13	+	4.62586e13i	0.142383	+	0.246614i
$81$		0			0
$82$	−1.80551e13	+	3.12723e13i	−0.0799825	+	0.138534i
$83$	−3.24677e14			−1.31331			−0.656653	−	0.754193i	$-0.728028\pi$
$83$	−3.24677e14			−1.31331			−0.656653	+	0.754193i	$0.728028\pi$
$84$		0			0
$85$	3.64782e14			1.23422
$86$	−7.22965e13	+	1.25221e14i	−0.224067	+	0.388096i
$87$		0			0
$88$	−5.06578e13	−	8.77419e13i	−0.132138	−	0.228869i
$89$	−1.41340e14	+	2.44808e14i	−0.338720	+	0.586680i	−0.984192	−	0.177104i	$-0.943327\pi$
$89$	−1.41340e14	+	2.44808e14i	−0.338720	+	0.586680i	0.645472	+	0.763784i	$0.276661\pi$
$90$		0			0
$91$	−5.06912e14	+	1.95727e14i	−1.02831	+	0.397046i
$92$	−5.11058e14			−0.955127
$93$		0			0
$94$	2.51540e14	+	4.35680e14i	0.400081	+	0.692961i
$95$	3.26750e14	+	5.65948e14i	0.480053	+	0.831476i
$96$		0			0
$97$	−5.07472e13			−0.0637712			−0.0318856	−	0.999492i	$-0.510151\pi$
$97$	−5.07472e13			−0.0637712			−0.0318856	+	0.999492i	$0.510151\pi$
$98$	1.28676e14	+	5.93908e14i	0.149728	+	0.691073i
$99$		0			0
$100$	−7.43645e13	+	1.28803e14i	−0.0743645	+	0.128803i
$101$	−7.81654e14	−	1.35386e15i	−0.725444	−	1.25651i	−0.958791	−	0.284113i	$-0.908301\pi$
$101$	−7.81654e14	−	1.35386e15i	−0.725444	−	1.25651i	0.233346	−	0.972394i	$-0.425032\pi$
$102$		0			0
$103$	−4.29450e14	+	7.43828e14i	−0.344059	+	0.595928i	−0.985182	−	0.171510i	$-0.945135\pi$
$103$	−4.29450e14	+	7.43828e14i	−0.344059	+	0.595928i	0.641123	+	0.767438i	$0.278469\pi$
$104$	−5.23003e14			−0.389721
$105$		0			0
$106$	7.76532e14			0.501609
$107$	7.14251e13	−	1.23712e14i	0.0430004	−	0.0744789i	−0.843724	−	0.536777i	$-0.819642\pi$
$107$	7.14251e13	−	1.23712e14i	0.0430004	−	0.0744789i	0.886725	+	0.462298i	$0.152975\pi$
$108$		0			0
$109$	1.22012e15	+	2.11330e15i	0.639297	+	1.10729i	0.985587	+	0.169167i	$0.0541078\pi$
$109$	1.22012e15	+	2.11330e15i	0.639297	+	1.10729i	−0.346291	+	0.938127i	$0.612559\pi$
$110$	6.15245e14	−	1.06564e15i	0.301025	−	0.521391i
$111$		0			0
$112$	−9.03639e13	+	5.77869e14i	−0.0386242	+	0.246998i
$113$	−1.34454e15			−0.537632			−0.268816	−	0.963192i	$-0.586632\pi$
$113$	−1.34454e15			−0.537632			−0.268816	+	0.963192i	$0.586632\pi$
$114$		0			0
$115$	−3.10343e15	−	5.37529e15i	−1.08795	−	1.88438i
$116$	9.05823e14	+	1.56893e15i	0.297583	+	0.515429i
$117$		0			0
$118$	−8.46322e14			−0.244580
$119$	3.10912e15	+	2.50764e15i	0.843404	+	0.680240i
$120$		0			0
$121$	9.21646e14	−	1.59634e15i	0.220635	−	0.382151i
$122$	1.02806e15	+	1.78065e15i	0.231376	+	0.400755i
$123$		0			0
$124$	2.92758e14	−	5.07073e14i	0.0583239	−	0.101020i
$125$	4.26623e15			0.800238
$126$		0			0
$127$	−7.35409e15			−1.22462			−0.612310	−	0.790618i	$-0.709759\pi$
$127$	−7.35409e15			−1.22462			−0.612310	+	0.790618i	$0.709759\pi$
$128$	−2.81475e14	+	4.87529e14i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−3.17596e15	−	5.50093e15i	−0.443916	−	0.768884i
$131$	−3.35946e14	+	5.81875e14i	−0.0443337	+	0.0767883i	−0.887341	−	0.461114i	$-0.847450\pi$
$131$	−3.35946e14	+	5.81875e14i	−0.0443337	+	0.0767883i	0.843007	+	0.537903i	$0.180783\pi$
$132$		0			0
$133$	−1.10555e15	+	7.06991e15i	−0.130224	+	0.832773i
$134$	−1.16156e16			−1.29346
$135$		0			0
$136$	1.92226e15	+	3.32945e15i	0.191544	+	0.331765i
$137$	−8.69738e14	−	1.50643e15i	−0.0820321	−	0.142084i	0.822091	−	0.569357i	$-0.192808\pi$
$137$	−8.69738e14	−	1.50643e15i	−0.0820321	−	0.142084i	−0.904123	+	0.427273i	$0.859474\pi$
$138$		0			0
$139$	−5.39179e14			−0.0456165			−0.0228083	−	0.999740i	$-0.507261\pi$
$139$	−5.39179e14			−0.0456165			−0.0228083	+	0.999740i	$0.507261\pi$
$140$	−6.62675e15	+	2.55870e15i	−0.531301	+	0.205144i
$141$		0			0
$142$	4.75559e15	−	8.23692e15i	0.342801	−	0.593748i
$143$	6.02407e15	+	1.04340e16i	0.411974	+	0.713560i
$144$		0			0
$145$	−1.10013e16	+	1.90549e16i	−0.677930	+	1.17421i
$146$	1.84805e16			1.08160
$147$		0			0
$148$	−1.50281e16			−0.794219
$149$	−3.25376e15	+	5.63568e15i	−0.163489	+	0.283172i	−0.936118	−	0.351687i	$-0.885608\pi$
$149$	−3.25376e15	+	5.63568e15i	−0.163489	+	0.283172i	0.772629	+	0.634858i	$0.218942\pi$
$150$		0			0
$151$	1.65406e16	+	2.86491e16i	0.752009	+	1.30252i	0.946847	+	0.321683i	$0.104249\pi$
$151$	1.65406e16	+	2.86491e16i	0.752009	+	1.30252i	−0.194838	+	0.980835i	$0.562418\pi$
$152$	−3.44369e15	+	5.96465e15i	−0.149004	+	0.258082i
$153$		0			0
$154$	1.25694e16	−	4.85326e15i	0.493072	−	0.190383i
$155$	7.11117e15			0.265738
$156$		0			0
$157$	−1.88454e16	−	3.26412e16i	−0.639674	−	1.10795i	−0.985504	−	0.169650i	$-0.945736\pi$
$157$	−1.88454e16	−	3.26412e16i	−0.639674	−	1.10795i	0.345831	−	0.938297i	$-0.387597\pi$
$158$	5.90325e15	+	1.02247e16i	0.191057	+	0.330921i
$159$		0			0
$160$	−6.83709e15			−0.201359
$161$	1.05004e16	−	6.71490e16i	0.295128	−	1.88732i
$162$		0			0
$163$	−5.84623e15	+	1.01260e16i	−0.149785	+	0.259435i	−0.931148	−	0.364642i	$-0.881192\pi$
$163$	−5.84623e15	+	1.01260e16i	−0.149785	+	0.259435i	0.781363	+	0.624077i	$0.214525\pi$
$164$	−2.31105e15	−	4.00285e15i	−0.0565562	−	0.0979582i
$165$		0			0
$166$	2.07793e16	−	3.59908e16i	0.464323	−	0.804232i
$167$	−7.77600e16			−1.66105			−0.830525	−	0.556981i	$-0.811960\pi$
$167$	−7.77600e16			−1.66105			−0.830525	+	0.556981i	$0.811960\pi$
$168$		0			0
$169$	1.10080e16			0.215059
$170$	−2.33460e16	+	4.04365e16i	−0.436361	+	0.755800i
$171$		0			0
$172$	−9.25395e15	−	1.60283e16i	−0.158440	−	0.274425i
$173$	−3.43016e15	+	5.94122e15i	−0.0562301	+	0.0973934i	−0.892770	−	0.450512i	$-0.851241\pi$
$173$	−3.43016e15	+	5.94122e15i	−0.0562301	+	0.0973934i	0.836540	+	0.547906i	$0.184575\pi$
$174$		0			0
$175$	−1.53958e16	−	1.24173e16i	−0.231535	−	0.186742i
$176$	1.29684e16			0.186871
$177$		0			0
$178$	−1.80916e16	−	3.13355e16i	−0.239511	−	0.414846i
$179$	2.87992e16	+	4.98817e16i	0.365580	+	0.633204i	0.988869	−	0.148788i	$-0.0475372\pi$
$179$	2.87992e16	+	4.98817e16i	0.365580	+	0.633204i	−0.623289	+	0.781992i	$0.714204\pi$
$180$		0			0
$181$	6.62310e15			0.0773521			0.0386761	−	0.999252i	$-0.487686\pi$
$181$	6.62310e15			0.0773521			0.0386761	+	0.999252i	$0.487686\pi$
$182$	1.07458e16	−	6.87184e16i	0.120421	−	0.770083i
$183$		0			0
$184$	3.27077e16	−	5.66514e16i	0.337688	−	0.584894i
$185$	−9.12588e16	−	1.58065e17i	−0.904663	−	1.56692i
$186$		0			0
$187$	4.42820e16	−	7.66987e16i	0.404963	−	0.701417i
$188$	−6.43942e16			−0.565800
$189$		0			0
$190$	−8.36481e16			−0.678897
$191$	1.05152e17	−	1.82128e17i	0.820477	−	1.42111i	−0.0848499	−	0.996394i	$-0.527041\pi$
$191$	1.05152e17	−	1.82128e17i	0.820477	−	1.42111i	0.905327	−	0.424715i	$-0.139626\pi$
$192$		0			0
$193$	−9.72237e16	−	1.68396e17i	−0.701604	−	1.21521i	−0.967903	−	0.251323i	$-0.919134\pi$
$193$	−9.72237e16	−	1.68396e17i	−0.701604	−	1.21521i	0.266299	−	0.963890i	$-0.414199\pi$
$194$	3.24782e15	−	5.62540e15i	0.0225465	−	0.0390517i
$195$		0			0
$196$	−7.40707e16	−	2.37462e16i	−0.476131	−	0.152642i
$197$	9.62634e16			0.595613			0.297807	−	0.954626i	$-0.403745\pi$
$197$	9.62634e16			0.595613			0.297807	+	0.954626i	$0.403745\pi$
$198$		0			0
$199$	−7.00513e16	−	1.21332e17i	−0.401808	−	0.695952i	0.592136	−	0.805838i	$-0.298285\pi$
$199$	−7.00513e16	−	1.21332e17i	−0.401808	−	0.695952i	−0.993944	+	0.109886i	$0.964951\pi$
$200$	−9.51865e15	−	1.64868e16i	−0.0525836	−	0.0910775i
$201$		0			0
$202$	2.00103e17			1.02593
$203$	−2.24757e17	+	8.67822e16i	−1.11043	+	0.428756i
$204$		0			0
$205$	2.80679e16	−	4.86151e16i	0.128842	−	0.223160i
$206$	−5.49695e16	−	9.52100e16i	−0.243286	−	0.421385i
$207$		0			0
$208$	3.34722e16	−	5.79755e16i	0.137787	−	0.238654i
$209$	1.58661e17			0.630048
$210$		0			0
$211$	−8.90459e16			−0.329227			−0.164614	−	0.986358i	$-0.552638\pi$
$211$	−8.90459e16			−0.329227			−0.164614	+	0.986358i	$0.552638\pi$
$212$	−4.96981e16	+	8.60796e16i	−0.177346	+	0.307172i
$213$		0			0
$214$	9.14242e15	+	1.58351e16i	0.0304059	+	0.0526646i
$215$	1.12390e17	−	1.94666e17i	0.360944	−	0.625174i
$216$		0			0
$217$	6.06102e16	+	4.88847e16i	0.181592	+	0.146462i
$218$	−3.12350e17			−0.904102
$219$		0			0
$220$	7.87513e16	+	1.36401e17i	0.212857	+	0.368679i
$221$	−2.28589e17	−	3.95928e17i	−0.597191	−	1.03436i
$222$		0			0
$223$	−2.89017e17			−0.705727			−0.352864	−	0.935675i	$-0.614792\pi$
$223$	−2.89017e17			−0.705727			−0.352864	+	0.935675i	$0.614792\pi$
$224$	−5.82742e16	−	4.70005e16i	−0.137599	−	0.110979i
$225$		0			0
$226$	8.60505e16	−	1.49044e17i	0.190082	−	0.329231i
$227$	1.18295e17	+	2.04893e17i	0.252797	+	0.437858i	0.964295	−	0.264831i	$-0.0853161\pi$
$227$	1.18295e17	+	2.04893e17i	0.252797	+	0.437858i	−0.711498	+	0.702689i	$0.751983\pi$
$228$		0			0
$229$	3.33807e15	−	5.78170e15i	0.00667927	−	0.0115688i	−0.862666	−	0.505773i	$-0.831207\pi$
$229$	3.33807e15	−	5.78170e15i	0.00667927	−	0.0115688i	0.869346	+	0.494204i	$0.164541\pi$
$230$	7.94478e17			1.53859
$231$		0			0
$232$	−2.31891e17			−0.420846
$233$	−2.34392e17	+	4.05979e17i	−0.411883	+	0.713402i	−0.995096	−	0.0989176i	$-0.968462\pi$
$233$	−2.34392e17	+	4.05979e17i	−0.411883	+	0.713402i	0.583213	+	0.812319i	$0.301795\pi$
$234$		0			0
$235$	−3.91038e17	−	6.77297e17i	−0.644481	−	1.11627i
$236$	5.41646e16	−	9.38159e16i	0.0864720	−	0.149774i
$237$		0			0
$238$	−4.76958e17	+	1.84161e17i	−0.714748	+	0.275976i
$239$	−3.37324e17			−0.489850			−0.244925	−	0.969542i	$-0.578763\pi$
$239$	−3.37324e17			−0.489850			−0.244925	+	0.969542i	$0.578763\pi$
$240$		0			0
$241$	−5.35615e17	−	9.27712e17i	−0.730676	−	1.26557i	−0.956595	−	0.291421i	$-0.905872\pi$
$241$	−5.35615e17	−	9.27712e17i	−0.730676	−	1.26557i	0.225919	−	0.974146i	$-0.427462\pi$
$242$	1.17971e17	+	2.04331e17i	0.156012	+	0.270221i
$243$		0			0
$244$	−2.63182e17			−0.327215
$245$	−2.00037e17	−	9.23275e17i	−0.241193	−	1.11323i
$246$		0			0
$247$	4.09514e17	−	7.09298e17i	0.464559	−	0.804640i
$248$	3.74731e16	+	6.49053e16i	0.0412412	+	0.0714319i
$249$		0			0
$250$	−2.73039e17	+	4.72917e17i	−0.282927	+	0.490044i
$251$	−3.44616e17			−0.346563			−0.173282	−	0.984872i	$-0.555437\pi$
$251$	−3.44616e17			−0.346563			−0.173282	+	0.984872i	$0.555437\pi$
$252$		0			0
$253$	−1.50694e18			−1.42788
$254$	4.70662e17	−	8.15210e17i	0.432968	−	0.749923i
$255$		0			0
$256$	−3.60288e16	−	6.24037e16i	−0.0312500	−	0.0541266i
$257$	3.12841e17	−	5.41856e17i	0.263527	−	0.456442i	−0.703650	−	0.710547i	$-0.748448\pi$
$257$	3.12841e17	−	5.41856e17i	0.263527	−	0.456442i	0.967177	+	0.254105i	$0.0817809\pi$
$258$		0			0
$259$	3.08772e17	−	1.97457e18i	0.245409	−	1.56937i
$260$	8.13047e17			0.627791
$261$		0			0
$262$	−4.30010e16	−	7.44800e16i	−0.0313487	−	0.0542975i
$263$	−6.61618e17	−	1.14596e18i	−0.468748	−	0.811895i	0.530614	−	0.847613i	$-0.321961\pi$
$263$	−6.61618e17	−	1.14596e18i	−0.468748	−	0.811895i	−0.999362	+	0.0357187i	$0.988628\pi$
$264$		0			0
$265$	−1.20718e18			−0.808029
$266$	−7.12953e17	−	5.75026e17i	−0.463926	−	0.374175i
$267$		0			0
$268$	7.43396e17	−	1.28760e18i	0.457309	−	0.792082i
$269$	1.47717e18	+	2.55854e18i	0.883668	+	1.53056i	0.847233	+	0.531222i	$0.178267\pi$
$269$	1.47717e18	+	2.55854e18i	0.883668	+	1.53056i	0.0364352	+	0.999336i	$0.488400\pi$
$270$		0			0
$271$	−5.92516e17	+	1.02627e18i	−0.335298	+	0.580753i	−0.983542	−	0.180680i	$-0.942170\pi$
$271$	−5.92516e17	+	1.02627e18i	−0.335298	+	0.580753i	0.648244	+	0.761432i	$0.275504\pi$
$272$	−4.92098e17			−0.270885
$273$		0			0
$274$	2.22653e17			0.116011
$275$	−2.19276e17	+	3.79798e17i	−0.111172	+	0.192556i
$276$		0			0
$277$	4.23364e16	+	7.33287e16i	0.0203290	+	0.0352108i	0.876011	−	0.482291i	$-0.160195\pi$
$277$	4.23364e16	+	7.33287e16i	0.0203290	+	0.0352108i	−0.855682	+	0.517502i	$0.826862\pi$
$278$	3.45075e16	−	5.97687e16i	0.0161279	−	0.0279343i
$279$		0			0
$280$	1.40477e17	−	8.98340e17i	0.0622187	−	0.397883i
$281$	−2.22639e18			−0.960072			−0.480036	−	0.877249i	$-0.659376\pi$
$281$	−2.22639e18			−0.960072			−0.480036	+	0.877249i	$0.659376\pi$
$282$		0			0
$283$	−3.46646e17	−	6.00409e17i	−0.141739	−	0.245499i	0.786413	−	0.617701i	$-0.211936\pi$
$283$	−3.46646e17	−	6.00409e17i	−0.141739	−	0.245499i	−0.928151	+	0.372203i	$0.878603\pi$
$284$	6.08715e17	+	1.05433e18i	0.242397	+	0.419843i
$285$		0			0
$286$	−1.54216e18			−0.582619
$287$	5.73427e17	−	2.21409e17i	0.211039	−	0.0814858i
$288$		0			0
$289$	−2.49111e17	+	4.31473e17i	−0.0870280	+	0.150737i
$290$	−1.40817e18	−	2.43902e18i	−0.479369	−	0.830291i
$291$		0			0
$292$	−1.18275e18	+	2.04858e18i	−0.382403	+	0.662342i
$293$	−4.14016e18			−1.30470			−0.652349	−	0.757919i	$-0.726216\pi$
$293$	−4.14016e18			−1.30470			−0.652349	+	0.757919i	$0.726216\pi$
$294$		0			0
$295$	1.31567e18			0.393987
$296$	9.61796e17	−	1.66588e18i	0.280799	−	0.486358i
$297$		0			0
$298$	−4.16482e17	−	7.21368e17i	−0.115604	−	0.200233i
$299$	−3.88950e18	+	6.73681e18i	−1.05283	+	1.82356i
$300$		0			0
$301$	2.29613e18	−	8.86572e17i	0.591218	−	0.228279i
$302$	−4.23438e18			−1.06350
$303$		0			0
$304$	−4.40793e17	−	7.63475e17i	−0.105362	−	0.182492i
$305$	−1.59819e18	−	2.76815e18i	−0.372717	−	0.645566i
$306$		0			0
$307$	−1.65125e18			−0.366669			−0.183335	−	0.983051i	$-0.558689\pi$
$307$	−1.65125e18			−0.366669			−0.183335	+	0.983051i	$0.558689\pi$
$308$	−2.66453e17	+	1.70394e18i	−0.0577419	+	0.369254i
$309$		0			0
$310$	−4.55115e17	+	7.88282e17i	−0.0939525	+	0.162731i
$311$	1.44336e18	+	2.49998e18i	0.290852	+	0.503771i	0.974012	−	0.226498i	$-0.0727278\pi$
$311$	1.44336e18	+	2.49998e18i	0.290852	+	0.503771i	−0.683159	+	0.730270i	$0.739394\pi$
$312$		0			0
$313$	3.13305e17	−	5.42660e17i	0.0601706	−	0.104219i	−0.834371	−	0.551203i	$-0.814169\pi$
$313$	3.13305e17	−	5.42660e17i	0.0601706	−	0.104219i	0.894542	+	0.446985i	$0.147502\pi$
$314$	4.82443e18			0.904635
$315$		0			0
$316$	−1.51123e18			−0.270196
$317$	−1.04682e18	+	1.81314e18i	−0.182779	+	0.316582i	−0.942826	−	0.333286i	$-0.891843\pi$
$317$	−1.04682e18	+	1.81314e18i	−0.182779	+	0.316582i	0.760047	+	0.649868i	$0.225176\pi$
$318$		0			0
$319$	2.67097e18	+	4.62626e18i	0.444876	+	0.770549i
$320$	4.37574e17	−	7.57900e17i	0.0711913	−	0.123307i
$321$		0			0
$322$	6.77152e18	+	5.46151e18i	1.05140	+	0.847996i
$323$	−6.02054e18			−0.913307
$324$		0			0
$325$	1.13193e18	+	1.96056e18i	0.163943	+	0.283958i
$326$	−7.48317e17	−	1.29612e18i	−0.105914	−	0.183449i
$327$		0			0
$328$	5.91628e17			0.0799825
$329$	1.32307e18	−	8.46090e18i	0.174829	−	1.11801i
$330$		0			0
$331$	3.43842e18	−	5.95551e18i	0.434159	−	0.751985i	−0.563068	−	0.826411i	$-0.690379\pi$
$331$	3.43842e18	−	5.95551e18i	0.434159	−	0.751985i	0.997227	+	0.0744256i	$0.0237123\pi$
$332$	2.65975e18	+	4.60683e18i	0.328326	+	0.568678i
$333$		0			0
$334$	4.97664e18	−	8.61980e18i	0.587270	−	1.01718i
$335$	1.80573e19			2.08361
$336$		0			0
$337$	−3.93951e17			−0.0434729			−0.0217364	−	0.999764i	$-0.506919\pi$
$337$	−3.93951e17			−0.0434729			−0.0217364	+	0.999764i	$0.506919\pi$
$338$	−7.04512e17	+	1.22025e18i	−0.0760349	+	0.131696i
$339$		0			0
$340$	−2.98829e18	−	5.17587e18i	−0.308554	−	0.534431i
$341$	8.63248e17	−	1.49519e18i	0.0871923	−	0.151021i
$342$		0			0
$343$	4.64195e18	−	9.24442e18i	0.448740	−	0.893663i
$344$	2.36901e18			0.224067
$345$		0			0
$346$	−4.39061e17	−	7.60476e17i	−0.0397607	−	0.0688676i
$347$	1.51180e18	+	2.61851e18i	0.133975	+	0.232051i	0.925205	−	0.379467i	$-0.123893\pi$
$347$	1.51180e18	+	2.61851e18i	0.133975	+	0.232051i	−0.791231	+	0.611518i	$0.790559\pi$
$348$		0			0
$349$	−1.51974e19			−1.28996			−0.644981	−	0.764198i	$-0.723135\pi$
$349$	−1.51974e19			−1.28996			−0.644981	+	0.764198i	$0.723135\pi$
$350$	2.36181e18	−	9.11932e17i	0.196216	−	0.0757621i
$351$		0			0
$352$	−8.29977e17	+	1.43756e18i	−0.0660688	+	0.114434i
$353$	−2.81566e18	−	4.87687e18i	−0.219417	−	0.380041i	0.735213	−	0.677836i	$-0.237082\pi$
$353$	−2.81566e18	−	4.87687e18i	−0.219417	−	0.380041i	−0.954630	+	0.297795i	$0.903749\pi$
$354$		0			0
$355$	−7.39292e18	+	1.28049e19i	−0.552208	+	0.956453i
$356$	4.63144e18			0.338720
$357$		0			0
$358$	−7.37260e18			−0.517009
$359$	8.77950e18	−	1.52065e19i	0.602922	−	1.04429i	−0.389454	−	0.921046i	$-0.627336\pi$
$359$	8.77950e18	−	1.52065e19i	0.602922	−	1.04429i	0.992376	−	0.123246i	$-0.0393303\pi$
$360$		0			0
$361$	2.19771e18	+	3.80654e18i	0.144766	+	0.250742i
$362$	−4.23879e17	+	7.34179e17i	−0.0273481	+	0.0473683i
$363$		0			0
$364$	6.92979e18	+	5.58916e18i	0.429002	+	0.346008i
$365$	−2.87293e19			−1.74232
$366$		0			0
$367$	1.06542e18	+	1.84537e18i	0.0620192	+	0.107420i	0.895368	−	0.445327i	$-0.146913\pi$
$367$	1.06542e18	+	1.84537e18i	0.0620192	+	0.107420i	−0.833349	+	0.552748i	$0.813579\pi$
$368$	4.18658e18	+	7.25138e18i	0.238782	+	0.413582i
$369$		0			0
$370$	2.33623e19			1.27939
$371$	−1.02891e19	−	8.29856e18i	−0.552168	−	0.445347i
$372$		0			0
$373$	−6.58982e18	+	1.14139e19i	−0.339670	+	0.588326i	−0.984371	−	0.176110i	$-0.943649\pi$
$373$	−6.58982e18	+	1.14139e19i	−0.339670	+	0.588326i	0.644701	+	0.764435i	$0.276982\pi$
$374$	5.66810e18	+	9.81744e18i	0.286352	+	0.495977i
$375$		0			0
$376$	4.12123e18	−	7.13818e18i	0.200041	−	0.346480i
$377$	2.75757e19			1.31210
$378$		0			0
$379$	−1.46425e19			−0.669610			−0.334805	−	0.942287i	$-0.608670\pi$
$379$	−1.46425e19			−0.669610			−0.334805	+	0.942287i	$0.608670\pi$
$380$	5.35348e18	−	9.27250e18i	0.240026	−	0.415738i
$381$		0			0
$382$	1.34594e19	+	2.33124e19i	0.580165	+	1.00488i
$383$	1.56355e19	−	2.70815e19i	0.660878	−	1.14467i	−0.319507	−	0.947584i	$-0.603517\pi$
$383$	1.56355e19	−	2.70815e19i	0.660878	−	1.14467i	0.980385	−	0.197090i	$-0.0631493\pi$
$384$		0			0
$385$	−1.95401e19	+	7.54475e18i	−0.794276	+	0.306683i
$386$	2.48893e19			0.992218
$387$		0			0
$388$	4.15721e17	+	7.20051e17i	0.0159428	+	0.0276137i
$389$	2.26160e19	+	3.91720e19i	0.850732	+	1.47351i	0.880549	+	0.473956i	$0.157174\pi$
$389$	2.26160e19	+	3.91720e19i	0.850732	+	1.47351i	−0.0298165	+	0.999555i	$0.509492\pi$
$390$		0			0
$391$	5.71823e19			2.06983
$392$	7.37282e18	−	6.69108e18i	0.261811	−	0.237602i
$393$		0			0
$394$	−6.16086e18	+	1.06709e19i	−0.210581	+	0.364737i
$395$	−9.17705e18	−	1.58951e19i	−0.307769	−	0.533072i
$396$		0			0
$397$	−1.41591e19	+	2.45243e19i	−0.457202	+	0.791896i	−0.998812	−	0.0487333i	$-0.984482\pi$
$397$	−1.41591e19	+	2.45243e19i	−0.457202	+	0.791896i	0.541610	+	0.840630i	$0.317815\pi$
$398$	1.79331e19			0.568242
$399$		0			0
$400$	2.43677e18			0.0743645
$401$	−2.52789e19	+	4.37844e19i	−0.757139	+	1.31140i	0.187164	+	0.982329i	$0.440070\pi$
$401$	−2.52789e19	+	4.37844e19i	−0.757139	+	1.31140i	−0.944304	+	0.329075i	$0.893263\pi$
$402$		0			0
$403$	−4.45619e18	−	7.71834e18i	−0.128581	−	0.222708i
$404$	−1.28066e19	+	2.21817e19i	−0.362722	+	0.628253i
$405$		0			0
$406$	4.76451e18	−	3.04686e19i	0.130039	−	0.831586i
$407$	−4.43128e19			−1.18733
$408$		0			0
$409$	2.41397e19	+	4.18111e19i	0.623457	+	1.07986i	0.988837	+	0.149001i	$0.0476056\pi$
$409$	2.41397e19	+	4.18111e19i	0.623457	+	1.07986i	−0.365380	+	0.930858i	$0.619061\pi$
$410$	3.59270e18	+	6.22273e18i	0.0911049	+	0.157798i
$411$		0			0
$412$	1.40722e19			0.344059
$413$	1.12138e19	+	9.04438e18i	0.269232	+	0.217147i
$414$		0			0
$415$	−3.23030e19	+	5.59505e19i	−0.747967	+	1.29552i
$416$	4.28444e18	+	7.42086e18i	0.0974302	+	0.168754i
$417$		0			0
$418$	−1.01543e19	+	1.75878e19i	−0.222756	+	0.385824i
$419$	−7.80642e19			−1.68208			−0.841040	−	0.540973i	$-0.818056\pi$
$419$	−7.80642e19			−1.68208			−0.841040	+	0.540973i	$0.818056\pi$
$420$		0			0
$421$	1.71577e18			0.0356732			0.0178366	−	0.999841i	$-0.494322\pi$
$421$	1.71577e18			0.0356732			0.0178366	+	0.999841i	$0.494322\pi$
$422$	5.69894e18	−	9.87085e18i	0.116399	−	0.201610i
$423$		0			0
$424$	−6.36135e18	−	1.10182e19i	−0.125402	−	0.217203i
$425$	8.32064e18	−	1.44118e19i	0.161154	−	0.279126i
$426$		0			0
$427$	5.40744e18	−	3.45801e19i	0.101107	−	0.646572i
$428$	−2.34046e18			−0.0430004
$429$		0			0
$430$	1.43860e19	+	2.49172e19i	0.255226	+	0.442065i
$431$	1.73471e19	+	3.00460e19i	0.302445	+	0.523850i	0.976689	−	0.214658i	$-0.0688638\pi$
$431$	1.73471e19	+	3.00460e19i	0.302445	+	0.523850i	−0.674244	+	0.738509i	$0.735530\pi$
$432$		0			0
$433$	2.73135e19			0.459958			0.229979	−	0.973196i	$-0.426134\pi$
$433$	2.73135e19			0.459958			0.229979	+	0.973196i	$0.426134\pi$
$434$	−9.29798e18	+	3.59010e18i	−0.153892	+	0.0594201i
$435$		0			0
$436$	1.99904e19	−	3.46244e19i	0.319648	−	0.553647i
$437$	5.12206e19	+	8.87166e19i	0.805070	+	1.39442i
$438$		0			0
$439$	6.39414e18	−	1.10750e19i	0.0971176	−	0.168213i	−0.813373	−	0.581743i	$-0.802371\pi$
$439$	6.39414e18	−	1.10750e19i	0.0971176	−	0.168213i	0.910490	+	0.413530i	$0.135704\pi$
$440$	−2.01603e19			−0.301025
$441$		0			0
$442$	5.85188e19			0.844555
$443$	9.43133e18	−	1.63355e19i	0.133827	−	0.231796i	−0.791321	−	0.611400i	$-0.790607\pi$
$443$	9.43133e18	−	1.63355e19i	0.133827	−	0.231796i	0.925149	+	0.379604i	$0.123940\pi$
$444$		0			0
$445$	2.81247e19	+	4.87134e19i	0.385822	+	0.668264i
$446$	1.84971e19	−	3.20379e19i	0.249512	−	0.432168i
$447$		0			0
$448$	8.93962e18	−	3.45173e18i	0.116609	−	0.0450248i
$449$	−8.66206e19			−1.11115			−0.555576	−	0.831466i	$-0.687502\pi$
$449$	−8.66206e19			−1.11115			−0.555576	+	0.831466i	$0.687502\pi$
$450$		0			0
$451$	−6.81452e18	−	1.18031e19i	−0.0845495	−	0.146444i
$452$	1.10145e19	+	1.90776e19i	0.134408	+	0.232801i
$453$		0			0
$454$	−3.02835e19			−0.357510
$455$	−1.67052e19	+	1.06828e20i	−0.193984	+	1.24051i
$456$		0			0
$457$	7.11513e18	−	1.23238e19i	0.0799487	−	0.138475i	−0.823279	−	0.567637i	$-0.807858\pi$
$457$	7.11513e18	−	1.23238e19i	0.0799487	−	0.138475i	0.903228	+	0.429162i	$0.141191\pi$
$458$	4.27272e17	+	7.40058e17i	0.00472296	+	0.00818040i
$459$		0			0
$460$	−5.08466e19	+	8.80688e19i	−0.543974	+	0.942190i
$461$	4.06928e19			0.428312			0.214156	−	0.976799i	$-0.431300\pi$
$461$	4.06928e19			0.428312			0.214156	+	0.976799i	$0.431300\pi$
$462$		0			0
$463$	1.36927e20			1.39518			0.697592	−	0.716495i	$-0.254255\pi$
$463$	1.36927e20			1.39518			0.697592	+	0.716495i	$0.254255\pi$
$464$	1.48410e19	−	2.57054e19i	0.148792	−	0.257715i
$465$		0			0
$466$	−3.00022e19	−	5.19653e19i	−0.291245	−	0.504451i
$467$	−4.95750e19	+	8.58665e19i	−0.473572	+	0.820251i	−0.999542	−	0.0302517i	$-0.990369\pi$
$467$	−4.95750e19	+	8.58665e19i	−0.473572	+	0.820251i	0.525970	+	0.850503i	$0.323702\pi$
$468$		0			0
$469$	1.53906e20	+	1.24132e20i	1.42384	+	1.14838i
$470$	1.00106e20			0.911433
$471$		0			0
$472$	6.93307e18	+	1.20084e19i	0.0611450	+	0.105906i
$473$	−2.72868e19	−	4.72622e19i	−0.236862	−	0.410256i
$474$		0			0
$475$	2.98126e19			0.250725
$476$	1.01108e19	−	6.46577e19i	0.0837017	−	0.535264i
$477$		0			0
$478$	2.15887e19	−	3.73928e19i	0.173188	−	0.299971i
$479$	−1.09063e20	−	1.88903e20i	−0.861314	−	1.49184i	−0.870661	−	0.491884i	$-0.836308\pi$
$479$	−1.09063e20	−	1.88903e20i	−0.861314	−	1.49184i	0.00934648	−	0.999956i	$-0.497025\pi$
$480$		0			0
$481$	−1.14374e20	+	1.98101e20i	−0.875465	+	1.51635i
$482$	1.37117e20			1.03333
$483$		0			0
$484$	−3.02005e19			−0.220635
$485$	−5.04899e18	+	8.74510e18i	−0.0363196	+	0.0629074i
$486$		0			0
$487$	−1.20529e20	−	2.08763e20i	−0.840671	−	1.45609i	−0.889328	−	0.457270i	$-0.848827\pi$
$487$	−1.20529e20	−	2.08763e20i	−0.840671	−	1.45609i	0.0486570	−	0.998816i	$-0.484506\pi$
$488$	1.68437e19	−	2.91741e19i	0.115688	−	0.200377i
$489$		0			0
$490$	1.15149e20	+	3.69153e19i	0.766987	+	0.245887i
$491$	4.94688e19			0.324504			0.162252	−	0.986749i	$-0.448124\pi$
$491$	4.94688e19			0.324504			0.162252	+	0.986749i	$0.448124\pi$
$492$		0			0
$493$	−1.01353e20	−	1.75548e20i	−0.644886	−	1.11697i
$494$	5.24177e19	+	9.07902e19i	0.328493	+	0.568967i
$495$		0			0
$496$	−9.59311e18			−0.0583239
$497$	−1.51037e20	+	5.83178e19i	−0.904503	+	0.349243i
$498$		0			0
$499$	−7.70489e19	+	1.33453e20i	−0.447726	+	0.775484i	−0.998238	−	0.0593432i	$-0.981099\pi$
$499$	−7.70489e19	+	1.33453e20i	−0.447726	+	0.775484i	0.550512	+	0.834828i	$0.314433\pi$
$500$	−3.49489e19	−	6.05333e19i	−0.200059	−	0.346513i
$501$		0			0
$502$	2.20554e19	−	3.82011e19i	0.122529	−	0.212226i
$503$	−2.47074e20			−1.35228			−0.676141	−	0.736772i	$-0.736349\pi$
$503$	−2.47074e20			−1.35228			−0.676141	+	0.736772i	$0.736349\pi$
$504$		0			0
$505$	−3.11076e20			−1.65265
$506$	9.64442e19	−	1.67046e20i	0.504833	−	0.874396i
$507$		0			0
$508$	6.02447e19	+	1.04347e20i	0.306155	+	0.530276i
$509$	−5.45694e19	+	9.45170e19i	−0.273254	+	0.473289i	−0.969693	−	0.244327i	$-0.921433\pi$
$509$	−5.45694e19	+	9.45170e19i	−0.273254	+	0.473289i	0.696439	+	0.717616i	$0.254766\pi$
$510$		0			0
$511$	−2.44866e20	−	1.97495e20i	−1.19062	−	0.960283i
$512$	9.22337e18			0.0441942
$513$		0			0
$514$	4.00436e19	+	6.93576e19i	0.186342	+	0.322753i
$515$	8.54543e19	+	1.48011e20i	0.391904	+	0.678797i
$516$		0			0
$517$	−1.89877e20			−0.845852
$518$	1.99122e20	+	1.60600e20i	0.874272	+	0.705136i
$519$		0			0
$520$	−5.20350e19	+	9.01272e19i	−0.221958	+	0.384442i
$521$	−1.12175e20	−	1.94292e20i	−0.471641	−	0.816906i	0.527833	−	0.849348i	$-0.323005\pi$
$521$	−1.12175e20	−	1.94292e20i	−0.471641	−	0.816906i	−0.999474	+	0.0324425i	$0.989671\pi$
$522$		0			0
$523$	1.52260e20	−	2.63722e20i	0.622047	−	1.07742i	−0.367058	−	0.930198i	$-0.619635\pi$
$523$	1.52260e20	−	2.63722e20i	0.622047	−	1.07742i	0.989104	−	0.147218i	$-0.0470319\pi$
$524$	1.10083e19			0.0443337
$525$		0			0
$526$	1.69374e20			0.662909
$527$	−3.27568e19	+	5.67364e19i	−0.126392	+	0.218918i
$528$		0			0
$529$	−3.53168e20	−	6.11705e20i	−1.32454	−	2.29416i
$530$	7.72594e19	−	1.33817e20i	0.285681	−	0.494815i
$531$		0			0
$532$	1.09371e20	−	4.22300e19i	0.393157	−	0.151804i
$533$	−7.03546e19			−0.249367
$534$		0			0
$535$	−1.42126e19	−	2.46169e19i	−0.0489801	−	0.0848360i
$536$	9.51547e19	+	1.64813e20i	0.323366	+	0.560086i
$537$		0			0
$538$	−3.78156e20			−1.24970
$539$	−2.18410e20	−	7.00197e19i	−0.711799	−	0.228194i
$540$		0			0
$541$	−1.63589e20	+	2.83345e20i	−0.518531	+	0.898123i	0.481237	+	0.876591i	$0.340188\pi$
$541$	−1.63589e20	+	2.83345e20i	−0.518531	+	0.898123i	−0.999768	+	0.0215319i	$0.993146\pi$
$542$	−7.58421e19	−	1.31362e20i	−0.237091	−	0.410654i
$543$		0			0
$544$	3.14942e19	−	5.45496e19i	0.0957722	−	0.165882i
$545$	4.85571e20			1.45639
$546$		0			0
$547$	6.80917e20			1.98696			0.993480	−	0.114009i	$-0.0363694\pi$
$547$	6.80917e20			1.98696			0.993480	+	0.114009i	$0.0363694\pi$
$548$	−1.42498e19	+	2.46813e19i	−0.0410161	+	0.0710419i
$549$		0			0
$550$	−2.80674e19	−	4.86141e19i	−0.0786107	−	0.136158i
$551$	1.81572e20	−	3.14491e20i	0.501661	−	0.868903i
$552$		0			0
$553$	3.10503e19	−	1.98564e20i	0.0834887	−	0.533903i
$554$	−1.08381e19			−0.0287495
$555$		0			0
$556$	4.41696e18	+	7.65040e18i	0.0114041	+	0.0197525i
$557$	−1.10214e20	−	1.90895e20i	−0.280751	−	0.486275i	0.690819	−	0.723028i	$-0.257250\pi$
$557$	−1.10214e20	−	1.90895e20i	−0.280751	−	0.486275i	−0.971570	+	0.236753i	$0.923917\pi$
$558$		0			0
$559$	−2.81716e20			−0.698590
$560$	9.05916e19	+	7.30659e19i	0.221655	+	0.178774i
$561$		0			0
$562$	1.42489e20	−	2.46798e20i	0.339437	−	0.587922i
$563$	−1.80131e20	−	3.11996e20i	−0.423423	−	0.733391i	0.572848	−	0.819661i	$-0.305838\pi$
$563$	−1.80131e20	−	3.11996e20i	−0.423423	−	0.733391i	−0.996272	+	0.0862706i	$0.972505\pi$
$564$		0			0
$565$	−1.33772e20	+	2.31700e20i	−0.306198	+	0.530350i
$566$	8.87415e19			0.200449
$567$		0			0
$568$	−1.55831e20			−0.342801
$569$	1.36250e20	−	2.35992e20i	0.295797	−	0.512336i	−0.679373	−	0.733793i	$-0.737748\pi$
$569$	1.36250e20	−	2.35992e20i	0.295797	−	0.512336i	0.975170	+	0.221457i	$0.0710814\pi$
$570$		0			0
$571$	−1.03396e20	−	1.79087e20i	−0.218641	−	0.378697i	0.735752	−	0.677251i	$-0.236829\pi$
$571$	−1.03396e20	−	1.79087e20i	−0.218641	−	0.378697i	−0.954393	+	0.298554i	$0.903496\pi$
$572$	9.86984e19	−	1.70951e20i	0.205987	−	0.356780i
$573$		0			0
$574$	−1.21558e19	+	7.77353e19i	−0.0247141	+	0.158044i
$575$	−2.83156e20			−0.568220
$576$		0			0
$577$	−2.43346e20	−	4.21488e20i	−0.475780	−	0.824074i	0.523835	−	0.851819i	$-0.324501\pi$
$577$	−2.43346e20	−	4.21488e20i	−0.475780	−	0.824074i	−0.999615	+	0.0277451i	$0.991167\pi$
$578$	−3.18862e19	−	5.52286e19i	−0.0615381	−	0.106587i
$579$		0			0
$580$	3.60491e20			0.677930
$581$	−6.59949e20	+	2.54817e20i	−1.22515	+	0.473050i
$582$		0			0
$583$	−1.46543e20	+	2.53820e20i	−0.265126	+	0.459211i
$584$	−1.51392e20	−	2.62219e20i	−0.270400	−	0.468346i
$585$		0			0
$586$	2.64970e20	−	4.58942e20i	0.461280	−	0.798961i
$587$	−5.31834e19			−0.0914092			−0.0457046	−	0.998955i	$-0.514553\pi$
$587$	−5.31834e19			−0.0914092			−0.0457046	+	0.998955i	$0.514553\pi$
$588$		0			0
$589$	−1.17366e20			−0.196643
$590$	−8.42030e19	+	1.45844e20i	−0.139296	+	0.241267i
$591$		0			0
$592$	1.23110e20	+	2.13233e20i	0.198555	+	0.343907i
$593$	4.83480e20	−	8.37411e20i	0.769959	−	1.33361i	−0.167625	−	0.985851i	$-0.553610\pi$
$593$	4.83480e20	−	8.37411e20i	0.769959	−	1.33361i	0.937584	−	0.347758i	$-0.113057\pi$
$594$		0			0
$595$	7.41467e20	−	2.86293e20i	1.15137	−	0.444563i
$596$	1.06619e20			0.163489
$597$		0			0
$598$	−4.97856e20	−	8.62312e20i	−0.744466	−	1.28945i
$599$	−3.48232e20	−	6.03155e20i	−0.514241	−	0.890692i	−0.999863	−	0.0165234i	$-0.994740\pi$
$599$	−3.48232e20	−	6.03155e20i	−0.514241	−	0.890692i	0.485622	−	0.874169i	$-0.338593\pi$
$600$		0			0
$601$	8.50501e20			1.22494			0.612472	−	0.790492i	$-0.290175\pi$
$601$	8.50501e20			1.22494			0.612472	+	0.790492i	$0.290175\pi$
$602$	−4.86746e19	+	3.11269e20i	−0.0692354	+	0.442754i
$603$		0			0
$604$	2.71001e20	−	4.69387e20i	0.376005	−	0.651259i
$605$	−1.83394e20	−	3.17648e20i	−0.251316	−	0.435293i
$606$		0			0
$607$	−5.34194e20	+	9.25252e20i	−0.714141	+	1.23693i	0.249149	+	0.968465i	$0.419849\pi$
$607$	−5.34194e20	+	9.25252e20i	−0.714141	+	1.23693i	−0.963290	+	0.268463i	$0.913484\pi$
$608$	1.12843e20			0.149004
$609$		0			0
$610$	4.09137e20			0.527102
$611$	−4.90084e20	+	8.48851e20i	−0.623680	+	1.08025i
$612$		0			0
$613$	−5.16406e20	−	8.94442e20i	−0.641265	−	1.11070i	−0.985151	−	0.171693i	$-0.945076\pi$
$613$	−5.16406e20	−	8.94442e20i	−0.641265	−	1.11070i	0.343885	−	0.939012i	$-0.388257\pi$
$614$	1.05680e20	−	1.83043e20i	0.129637	−	0.224538i
$615$		0			0
$616$	−1.71831e20	−	1.38589e20i	−0.205706	−	0.165910i
$617$	−3.93036e20			−0.464829			−0.232415	−	0.972617i	$-0.574663\pi$
$617$	−3.93036e20			−0.464829			−0.232415	+	0.972617i	$0.574663\pi$
$618$		0			0
$619$	5.68813e20	+	9.85214e20i	0.656584	+	1.13724i	0.981494	+	0.191491i	$0.0613324\pi$
$619$	5.68813e20	+	9.85214e20i	0.656584	+	1.13724i	−0.324911	+	0.945745i	$0.605334\pi$
$620$	−5.82547e19	−	1.00900e20i	−0.0664345	−	0.115068i
$621$		0			0
$622$	−3.69501e20			−0.411327
$623$	−9.51592e19	+	6.08534e20i	−0.104662	+	0.669306i
$624$		0			0
$625$	5.62974e20	−	9.75099e20i	0.604488	−	1.04700i
$626$	4.01030e19	+	6.94604e19i	0.0425470	+	0.0736936i
$627$		0			0
$628$	−3.08763e20	+	5.34794e20i	−0.319837	+	0.553974i
$629$	1.68149e21			1.72113
$630$		0			0
$631$	−1.27156e20			−0.127092			−0.0635458	−	0.997979i	$-0.520241\pi$
$631$	−1.27156e20			−0.127092			−0.0635458	+	0.997979i	$0.520241\pi$
$632$	9.67189e19	−	1.67522e20i	0.0955286	−	0.165460i
$633$		0			0
$634$	−1.33992e20	−	2.32082e20i	−0.129244	−	0.223857i
$635$	−7.31679e20	+	1.26731e21i	−0.697458	+	1.20803i
$636$		0			0
$637$	−8.76754e20	+	7.95683e20i	−0.816267	+	0.740789i
$638$	−6.83769e20			−0.629150
$639$		0			0
$640$	5.60095e19	+	9.70112e19i	0.0503398	+	0.0871911i
$641$	−3.13507e20	−	5.43010e20i	−0.278492	−	0.482362i	0.692519	−	0.721400i	$-0.256501\pi$
$641$	−3.13507e20	−	5.43010e20i	−0.278492	−	0.482362i	−0.971010	+	0.239039i	$0.923168\pi$
$642$		0			0
$643$	−1.15089e21			−0.998737			−0.499369	−	0.866390i	$-0.666435\pi$
$643$	−1.15089e21			−0.998737			−0.499369	+	0.866390i	$0.666435\pi$
$644$	−1.03879e21	+	4.01095e20i	−0.891015	+	0.344035i
$645$		0			0
$646$	3.85315e20	−	6.67385e20i	0.322903	−	0.559284i
$647$	−2.45824e19	−	4.25780e19i	−0.0203630	−	0.0352698i	0.855664	−	0.517531i	$-0.173149\pi$
$647$	−2.45824e19	−	4.25780e19i	−0.0203630	−	0.0352698i	−0.876027	+	0.482261i	$0.839816\pi$
$648$		0			0
$649$	1.59714e20	−	2.76632e20i	0.129273	−	0.223907i
$650$	−2.89774e20			−0.231851
$651$		0			0
$652$	1.91569e20			0.149785
$653$	−2.42560e19	+	4.20125e19i	−0.0187486	+	0.0324736i	−0.875247	−	0.483675i	$-0.839302\pi$
$653$	−2.42560e19	+	4.20125e19i	−0.0187486	+	0.0324736i	0.856499	+	0.516149i	$0.172635\pi$
$654$		0			0
$655$	6.68483e19	+	1.15785e20i	0.0504988	+	0.0874664i
$656$	−3.78642e19	+	6.55827e19i	−0.0282781	+	0.0489791i
$657$		0			0
$658$	8.53225e20	+	6.88161e20i	0.622830	+	0.502338i
$659$	−2.95539e19			−0.0213292			−0.0106646	−	0.999943i	$-0.503395\pi$
$659$	−2.95539e19			−0.0213292			−0.0106646	+	0.999943i	$0.503395\pi$
$660$		0			0
$661$	1.68895e20	+	2.92535e20i	0.119153	+	0.206379i	0.919432	−	0.393248i	$-0.128649\pi$
$661$	1.68895e20	+	2.92535e20i	0.119153	+	0.206379i	−0.800279	+	0.599628i	$0.795315\pi$
$662$	4.40117e20	+	7.62306e20i	0.306997	+	0.531734i
$663$		0			0
$664$	−6.80897e20			−0.464323
$665$	1.10834e21	+	8.93921e20i	0.747326	+	0.602749i
$666$		0			0
$667$	−1.72454e21	+	2.98699e21i	−1.13692	+	1.96920i
$668$	6.37010e20	+	1.10333e21i	0.415263	+	0.719256i
$669$		0			0
$670$	−1.15567e21	+	2.00167e21i	−0.736667	+	1.27594i
$671$	−7.76038e20			−0.489175
$672$		0			0
$673$	−1.20273e20			−0.0741407			−0.0370703	−	0.999313i	$-0.511803\pi$
$673$	−1.20273e20			−0.0741407			−0.0370703	+	0.999313i	$0.511803\pi$
$674$	2.52129e19	−	4.36700e19i	0.0153700	−	0.0266216i
$675$		0			0
$676$	−9.01775e19	−	1.56192e20i	−0.0537648	−	0.0931234i
$677$	8.04944e19	−	1.39420e20i	0.0474625	−	0.0822075i	−0.841318	−	0.540540i	$-0.818220\pi$
$677$	8.04944e19	−	1.39420e20i	0.0474625	−	0.0822075i	0.888781	+	0.458333i	$0.151553\pi$
$678$		0			0
$679$	−1.03151e20	+	3.98281e19i	−0.0594906	+	0.0229703i
$680$	7.65003e20			0.436361
$681$		0			0
$682$	1.10496e20	+	1.91384e20i	0.0616542	+	0.106788i
$683$	1.16558e21	+	2.01884e21i	0.643259	+	1.11416i	0.984701	+	0.174254i	$0.0557515\pi$
$683$	1.16558e21	+	2.01884e21i	0.643259	+	1.11416i	−0.341442	+	0.939903i	$0.610915\pi$
$684$		0			0
$685$	−3.46131e20			−0.186879
$686$	7.27670e20	+	1.10621e21i	0.388601	+	0.590753i
$687$		0			0
$688$	−1.51617e20	+	2.62608e20i	−0.0792198	+	0.137213i
$689$	7.56473e20	+	1.31025e21i	0.390975	+	0.677189i
$690$		0			0
$691$	1.34056e21	−	2.32191e21i	0.677953	−	1.17425i	−0.297643	−	0.954677i	$-0.596201\pi$
$691$	1.34056e21	−	2.32191e21i	0.677953	−	1.17425i	0.975596	−	0.219572i	$-0.0704661\pi$
$692$	1.12400e20			0.0562301
$693$		0			0
$694$	−3.87021e20			−0.189469
$695$	−5.36445e19	+	9.29149e19i	−0.0259800	+	0.0449987i
$696$		0			0
$697$	2.58583e20	+	4.47879e20i	0.122562	+	0.212283i
$698$	9.72631e20	−	1.68465e21i	0.456071	−	0.789938i
$699$		0			0
$700$	−5.00669e19	+	3.20173e20i	−0.0229781	+	0.146943i
$701$	9.09411e20			0.412929			0.206464	−	0.978454i	$-0.433804\pi$
$701$	9.09411e20			0.412929			0.206464	+	0.978454i	$0.433804\pi$
$702$		0			0
$703$	1.50618e21	+	2.60879e21i	0.669442	+	1.15951i
$704$	−1.06237e20	−	1.84008e20i	−0.0467177	−	0.0809174i
$705$		0			0
$706$	7.20809e20			0.310302
$707$	−2.65137e21	−	2.13844e21i	−1.12934	−	0.910860i
$708$		0			0
$709$	1.17525e21	−	2.03559e21i	0.490098	−	0.848875i	−0.509837	−	0.860271i	$-0.670294\pi$
$709$	1.17525e21	−	2.03559e21i	0.490098	−	0.848875i	0.999935	+	0.0113958i	$0.00362747\pi$
$710$	−9.46293e20	−	1.63903e21i	−0.390470	−	0.676315i
$711$		0			0
$712$	−2.96412e20	+	5.13401e20i	−0.119756	+	0.207423i
$713$	1.11473e21			0.445654
$714$		0			0
$715$	2.39741e21			0.938526
$716$	4.71846e20	−	8.17262e20i	0.182790	−	0.316602i
$717$		0			0
$718$	1.12378e21	+	1.94644e21i	0.426330	+	0.738426i
$719$	8.56539e20	−	1.48357e21i	0.321574	−	0.556982i	−0.659239	−	0.751933i	$-0.729122\pi$
$719$	8.56539e20	−	1.48357e21i	0.321574	−	0.556982i	0.980813	+	0.194951i	$0.0624549\pi$
$720$		0			0
$721$	−2.89133e20	+	1.84898e21i	−0.106312	+	0.679856i
$722$	−5.62613e20			−0.204730
$723$		0			0
$724$	−5.42565e19	−	9.39750e19i	−0.0193380	−	0.0334945i
$725$	5.01879e20	+	8.69279e20i	0.177037	+	0.306637i
$726$		0			0
$727$	1.52922e21			0.528399			0.264200	−	0.964468i	$-0.414892\pi$
$727$	1.52922e21			0.528399			0.264200	+	0.964468i	$0.414892\pi$
$728$	−1.06307e21	+	4.10470e20i	−0.363561	+	0.140377i
$729$		0			0
$730$	1.83867e21	−	3.18468e21i	0.616003	−	1.06695i
$731$	1.03542e21	+	1.79341e21i	0.343351	+	0.594701i
$732$		0			0
$733$	−1.40330e21	+	2.43059e21i	−0.455902	+	0.789645i	−0.998740	−	0.0501924i	$-0.984017\pi$
$733$	−1.40330e21	+	2.43059e21i	−0.455902	+	0.789645i	0.542838	+	0.839838i	$0.317350\pi$
$734$	−2.72748e20			−0.0877084
$735$		0			0
$736$	−1.07177e21			−0.337688
$737$	2.19203e21	−	3.79671e21i	0.683660	−	1.18413i
$738$		0			0
$739$	−1.82599e21	−	3.16271e21i	−0.558040	−	0.966554i	−0.997660	−	0.0683700i	$-0.978220\pi$
$739$	−1.82599e21	−	3.16271e21i	−0.558040	−	0.966554i	0.439620	−	0.898184i	$-0.355113\pi$
$740$	−1.49518e21	+	2.58974e21i	−0.452332	+	0.783461i
$741$		0			0
$742$	1.57841e21	−	6.09448e20i	0.467939	−	0.180679i
$743$	8.25458e20			0.242258			0.121129	−	0.992637i	$-0.461348\pi$
$743$	8.25458e20			0.242258			0.121129	+	0.992637i	$0.461348\pi$
$744$		0			0
$745$	6.47452e20	+	1.12142e21i	0.186224	+	0.322549i
$746$	−8.43497e20	−	1.46098e21i	−0.240183	−	0.416009i
$747$		0			0
$748$	−1.45103e21			−0.404963
$749$	4.80879e19	−	3.07518e20i	0.0132869	−	0.0849683i
$750$		0			0
$751$	3.27731e21	−	5.67647e21i	0.887602	−	1.53737i	0.0449002	−	0.998991i	$-0.485703\pi$
$751$	3.27731e21	−	5.67647e21i	0.887602	−	1.53737i	0.842702	−	0.538380i	$-0.180964\pi$
$752$	5.27518e20	+	9.13687e20i	0.141450	+	0.244999i
$753$		0			0
$754$	−1.76485e21	+	3.05681e21i	−0.463898	+	0.803494i
$755$	6.58267e21			1.71317
$756$		0			0
$757$	1.59175e21			0.406122			0.203061	−	0.979166i	$-0.434911\pi$
$757$	1.59175e21			0.406122			0.203061	+	0.979166i	$0.434911\pi$
$758$	9.37122e20	−	1.62314e21i	0.236743	−	0.410051i
$759$		0			0
$760$	6.85245e20	+	1.18688e21i	0.169724	+	0.293971i
$761$	−1.35412e21	+	2.34541e21i	−0.332103	+	0.575219i	−0.982924	−	0.184012i	$-0.941091\pi$
$761$	−1.35412e21	+	2.34541e21i	−0.332103	+	0.575219i	0.650821	+	0.759231i	$0.274425\pi$
$762$		0			0
$763$	4.13864e21	+	3.33798e21i	0.995230	+	0.802694i
$764$	−3.44562e21			−0.820477
$765$		0			0
$766$	2.00135e21	+	3.46643e21i	0.467311	+	0.809407i
$767$	−8.24460e20	−	1.42801e21i	−0.190636	−	0.330191i
$768$		0			0
$769$	4.63957e21			1.05203			0.526017	−	0.850474i	$-0.323685\pi$
$769$	4.63957e21			1.05203			0.526017	+	0.850474i	$0.323685\pi$
$770$	4.14222e20	−	2.64891e21i	0.0930149	−	0.594822i
$771$		0			0
$772$	−1.59291e21	+	2.75901e21i	−0.350802	+	0.607607i
$773$	2.26636e21	+	3.92544e21i	0.494290	+	0.856135i	0.999978	−	0.00658085i	$-0.00209476\pi$
$773$	2.26636e21	+	3.92544e21i	0.494290	+	0.856135i	−0.505688	+	0.862716i	$0.668761\pi$
$774$		0			0
$775$	1.62205e20	−	2.80948e20i	0.0346978	−	0.0600984i
$776$	−1.06425e20			−0.0225465
$777$		0			0
$778$	−5.78968e21			−1.20312
$779$	−4.63248e20	+	8.02369e20i	−0.0953416	+	0.165136i
$780$		0			0
$781$	1.79490e21	+	3.10886e21i	0.362374	+	0.627651i
$782$	−3.65966e21	+	6.33873e21i	−0.731797	+	1.26751i
$783$		0			0
$784$	2.69854e20	+	1.24552e21i	0.0529368	+	0.244331i
$785$	−7.49994e21			−1.45725
$786$		0			0
$787$	1.29628e21	+	2.24522e21i	0.247109	+	0.428005i	0.962722	−	0.270491i	$-0.0871861\pi$
$787$	1.29628e21	+	2.24522e21i	0.247109	+	0.428005i	−0.715614	+	0.698496i	$0.753853\pi$
$788$	−7.88589e20	−	1.36588e21i	−0.148903	−	0.257908i
$789$		0			0
$790$	2.34933e21			0.435251
$791$	−2.73296e21	+	1.05524e21i	−0.501544	+	0.193654i
$792$		0			0
$793$	−2.00300e21	+	3.46930e21i	−0.360688	+	0.624730i
$794$	−1.81237e21	−	3.13911e21i	−0.323290	−	0.559955i
$795$		0			0
$796$	−1.14772e21	+	1.98791e21i	−0.200904	+	0.347976i
$797$	6.79185e21			1.17774			0.588872	−	0.808227i	$-0.299572\pi$
$797$	6.79185e21			1.17774			0.588872	+	0.808227i	$0.299572\pi$
$798$		0			0
$799$	7.20507e21			1.22613
$800$	−1.55954e20	+	2.70119e20i	−0.0262918	+	0.0455387i
$801$		0			0
$802$	−3.23570e21	−	5.60440e21i	−0.535378	−	0.927303i
$803$	−3.48754e21	+	6.04060e21i	−0.571679	+	0.990178i
$804$		0			0
$805$	−1.05268e22	−	8.49033e21i	−1.69367	−	1.36602i
$806$	1.14078e21			0.181840
$807$		0			0
$808$	−1.63925e21	−	2.83926e21i	−0.256483	−	0.444242i
$809$	2.18666e21	+	3.78741e21i	0.338975	+	0.587122i	0.984240	−	0.176837i	$-0.0565865\pi$
$809$	2.18666e21	+	3.78741e21i	0.338975	+	0.587122i	−0.645265	+	0.763959i	$0.723253\pi$
$810$		0			0
$811$	6.93567e21			1.05544			0.527718	−	0.849420i	$-0.323048\pi$
$811$	6.93567e21			1.05544			0.527718	+	0.849420i	$0.323048\pi$
$812$	3.07255e21	+	2.47814e21i	0.463265	+	0.373642i
$813$		0			0
$814$	2.83602e21	−	4.91213e21i	0.419785	−	0.727088i
$815$	1.16332e21	+	2.01492e21i	0.170614	+	0.295513i
$816$		0			0
$817$	−1.85495e21	+	3.21286e21i	−0.267095	+	0.462622i
$818$	−6.17975e21			−0.881701
$819$		0			0
$820$	−9.19730e20			−0.128842
$821$	6.05159e21	−	1.04817e22i	0.840032	−	1.45498i	−0.0498341	−	0.998758i	$-0.515869\pi$
$821$	6.05159e21	−	1.04817e22i	0.840032	−	1.45498i	0.889866	−	0.456221i	$-0.150797\pi$
$822$		0			0
$823$	−1.38673e21	−	2.40188e21i	−0.189013	−	0.327381i	0.755908	−	0.654678i	$-0.227196\pi$
$823$	−1.38673e21	−	2.40188e21i	−0.189013	−	0.327381i	−0.944922	+	0.327297i	$0.893862\pi$
$824$	−9.00621e20	+	1.55992e21i	−0.121643	+	0.210692i
$825$		0			0
$826$	−1.72026e21	+	6.64221e20i	−0.228163	+	0.0880973i
$827$	−1.13714e20			−0.0149459			−0.00747296	−	0.999972i	$-0.502379\pi$
$827$	−1.13714e20			−0.0149459			−0.00747296	+	0.999972i	$0.502379\pi$
$828$		0			0
$829$	−2.57439e21	−	4.45897e21i	−0.332288	−	0.575540i	0.650672	−	0.759359i	$-0.274487\pi$
$829$	−2.57439e21	−	4.45897e21i	−0.332288	−	0.575540i	−0.982960	+	0.183819i	$0.941154\pi$
$830$	−4.13479e21	−	7.16166e21i	−0.528892	−	0.916068i
$831$		0			0
$832$	−1.09682e21			−0.137787
$833$	8.28778e21	+	2.65696e21i	1.03181	+	0.330787i
$834$		0			0
$835$	−7.73656e21	+	1.34001e22i	−0.946018	+	1.63855i
$836$	−1.29975e21	−	2.25124e21i	−0.157512	−	0.272819i
$837$		0			0
$838$	4.99611e21	−	8.65351e21i	0.594705	−	1.03006i
$839$	7.99472e21			0.943167			0.471584	−	0.881821i	$-0.343683\pi$
$839$	7.99472e21			0.943167			0.471584	+	0.881821i	$0.343683\pi$
$840$		0			0
$841$	3.59744e21			0.416892
$842$	−1.09809e20	+	1.90195e20i	−0.0126124	+	0.0218453i
$843$		0			0
$844$	7.29464e20	+	1.26347e21i	0.0823068	+	0.142560i
$845$	1.09522e21	−	1.89697e21i	0.122483	−	0.212146i
$846$		0			0
$847$	6.20511e20	−	3.96811e21i	0.0681748	−	0.435971i
$848$	1.62851e21			0.177346
$849$		0			0
$850$	1.06504e21	+	1.84471e21i	0.113953	+	0.197372i
$851$	−1.43055e22	−	2.47779e22i	−1.51716	−	2.62780i
$852$		0			0
$853$	7.86585e21			0.819649			0.409825	−	0.912164i	$-0.365590\pi$
$853$	7.86585e21			0.819649			0.409825	+	0.912164i	$0.365590\pi$
$854$	3.48717e21	+	2.81255e21i	0.360196	+	0.290513i
$855$		0			0
$856$	1.49789e20	−	2.59443e20i	0.0152029	−	0.0263323i
$857$	−1.40423e21	−	2.43219e21i	−0.141280	−	0.244704i	0.786699	−	0.617337i	$-0.211789\pi$
$857$	−1.40423e21	−	2.43219e21i	−0.141280	−	0.244704i	−0.927979	+	0.372633i	$0.878455\pi$
$858$		0			0
$859$	−7.53790e20	+	1.30560e21i	−0.0745250	+	0.129081i	−0.900880	−	0.434069i	$-0.857077\pi$
$859$	−7.53790e20	+	1.30560e21i	−0.0745250	+	0.129081i	0.826355	+	0.563150i	$0.190411\pi$
$860$	−3.68280e21			−0.360944
$861$		0			0
$862$	−4.44085e21			−0.427722
$863$	2.40115e21	−	4.15892e21i	0.229265	−	0.397099i	−0.728325	−	0.685232i	$-0.759701\pi$
$863$	2.40115e21	−	4.15892e21i	0.229265	−	0.397099i	0.957591	+	0.288132i	$0.0930343\pi$
$864$		0			0
$865$	6.82553e20	+	1.18222e21i	0.0640495	+	0.110937i
$866$	−1.74806e21	+	3.02774e21i	−0.162620	+	0.281666i
$867$		0			0
$868$	1.97104e20	−	1.26046e21i	0.0180217	−	0.115247i
$869$	−4.45613e21			−0.403933
$870$		0			0
$871$	−1.13155e22	−	1.95990e22i	−1.00818	−	1.74622i
$872$	2.55877e21	+	4.43192e21i	0.226026	+	0.391488i
$873$		0			0
$874$	−1.31125e22			−1.13854
$875$	8.67168e21	−	3.34828e21i	0.746522	−	0.288244i
$876$		0			0
$877$	−4.70948e21	+	8.15705e21i	−0.398543	+	0.690298i	−0.993546	−	0.113426i	$-0.963818\pi$
$877$	−4.70948e21	+	8.15705e21i	−0.398543	+	0.690298i	0.595003	+	0.803724i	$0.297151\pi$
$878$	8.18450e20	+	1.41760e21i	0.0686725	+	0.118944i
$879$		0			0
$880$	1.29026e21	−	2.23480e21i	0.106428	−	0.184339i
$881$	−1.34200e21			−0.109757			−0.0548787	−	0.998493i	$-0.517477\pi$
$881$	−1.34200e21			−0.109757			−0.0548787	+	0.998493i	$0.517477\pi$
$882$		0			0
$883$	−1.87667e22			−1.50898			−0.754488	−	0.656314i	$-0.772115\pi$
$883$	−1.87667e22			−1.50898			−0.754488	+	0.656314i	$0.772115\pi$
$884$	−3.74520e21	+	6.48688e21i	−0.298595	+	0.517182i
$885$		0			0
$886$	1.20721e21	+	2.09095e21i	0.0946303	+	0.163904i
$887$	−3.25324e21	+	5.63478e21i	−0.252865	+	0.437975i	−0.964313	−	0.264763i	$-0.914706\pi$
$887$	−3.25324e21	+	5.63478e21i	−0.252865	+	0.437975i	0.711448	+	0.702738i	$0.248040\pi$
$888$		0			0
$889$	−1.49482e22	+	5.77173e21i	−1.14242	+	0.441106i
$890$	−7.19992e21			−0.545635
$891$		0			0
$892$	2.36763e21	+	4.10085e21i	0.176432	+	0.305589i
$893$	6.45389e21	+	1.11785e22i	0.476909	+	0.826031i
$894$		0			0
$895$	1.14613e22			0.832836
$896$	−1.89507e20	+	1.21188e21i	−0.0136557	+	0.0873271i
$897$		0			0
$898$	5.54372e21	−	9.60200e21i	0.392852	−	0.680439i
$899$	−1.97580e21	−	3.42218e21i	−0.138850	−	0.240495i
$900$		0			0
$901$	5.56072e21	−	9.63144e21i	0.384322	−	0.665665i
$902$	1.74452e21			0.119571
$903$		0			0
$904$	−2.81970e21			−0.190082
$905$	6.58951e20	−	1.14134e21i	0.0440544	−	0.0763044i
$906$		0			0
$907$	−4.05590e21	−	7.02502e21i	−0.266706	−	0.461948i	0.701303	−	0.712863i	$-0.252602\pi$
$907$	−4.05590e21	−	7.02502e21i	−0.266706	−	0.461948i	−0.968009	+	0.250915i	$0.919268\pi$
$908$	1.93815e21	−	3.35697e21i	0.126399	−	0.218929i
$909$		0			0
$910$	−1.07729e22	−	8.68877e21i	−0.691069	−	0.557376i
$911$	1.99116e22			1.26683			0.633414	−	0.773813i	$-0.281653\pi$
$911$	1.99116e22			1.26683			0.633414	+	0.773813i	$0.281653\pi$
$912$		0			0
$913$	7.84274e21	+	1.35840e22i	0.490836	+	0.850154i
$914$	9.10737e20	+	1.57744e21i	0.0565323	+	0.0979168i
$915$		0			0
$916$	−1.09382e20			−0.00667927
$917$	−2.26180e20	+	1.44640e21i	−0.0136988	+	0.0876028i
$918$		0			0
$919$	1.57127e22	−	2.72151e22i	0.936232	−	1.62160i	0.163809	−	0.986492i	$-0.447622\pi$
$919$	1.57127e22	−	2.72151e22i	0.936232	−	1.62160i	0.772423	−	0.635109i	$-0.219045\pi$
$920$	−6.50836e21	−	1.12728e22i	−0.384647	−	0.666229i
$921$		0			0
$922$	−2.60434e21	+	4.51085e21i	−0.151431	+	0.262287i
$923$	1.85310e22			1.06877
$924$		0			0
$925$	−8.32643e21			−0.472493
$926$	−8.76332e21	+	1.51785e22i	−0.493272	+	0.854372i
$927$		0			0
$928$	1.89965e21	+	3.29029e21i	0.105212	+	0.182232i
$929$	−1.13120e22	+	1.95930e22i	−0.621472	+	1.07642i	0.367740	+	0.929929i	$0.380132\pi$
$929$	−1.13120e22	+	1.95930e22i	−0.621472	+	1.07642i	−0.989212	+	0.146492i	$0.953202\pi$
$930$		0			0
$931$	3.30151e21	+	1.52382e22i	0.178480	+	0.823780i
$932$	7.68056e21			0.411883
$933$		0			0
$934$	−6.34560e21	−	1.09909e22i	−0.334866	−	0.580005i
$935$	−8.81149e21	−	1.52619e22i	−0.461277	−	0.798956i
$936$		0			0
$937$	−2.12173e22			−1.09306			−0.546530	−	0.837439i	$-0.684052\pi$
$937$	−2.12173e22			−1.09306			−0.546530	+	0.837439i	$0.684052\pi$
$938$	−2.36102e22	+	9.11628e21i	−1.20664	+	0.465904i
$939$		0			0
$940$	−6.40676e21	+	1.10968e22i	−0.322240	+	0.558136i
$941$	8.16253e21	+	1.41379e22i	0.407289	+	0.705445i	0.994585	−	0.103927i	$-0.0331408\pi$
$941$	8.16253e21	+	1.41379e22i	0.407289	+	0.705445i	−0.587296	+	0.809372i	$0.699807\pi$
$942$		0			0
$943$	4.39986e21	−	7.62078e21i	0.216073	−	0.374250i
$944$	−1.77487e21			−0.0864720
$945$		0			0
$946$	6.98543e21			0.334973
$947$	−5.18267e21	+	8.97665e21i	−0.246564	+	0.427061i	−0.962570	−	0.271033i	$-0.912635\pi$
$947$	−5.18267e21	+	8.97665e21i	−0.246564	+	0.427061i	0.716006	+	0.698094i	$0.245968\pi$
$948$		0			0
$949$	1.80031e22	+	3.11822e22i	0.843044	+	1.46019i
$950$	−1.90801e21	+	3.30476e21i	−0.0886447	+	0.153537i
$951$		0			0
$952$	6.52030e21	+	5.25889e21i	0.298188	+	0.240501i
$953$	−1.82955e22			−0.830132			−0.415066	−	0.909791i	$-0.636242\pi$
$953$	−1.82955e22			−0.830132			−0.415066	+	0.909791i	$0.636242\pi$
$954$		0			0
$955$	−2.09237e22	−	3.62409e22i	−0.934573	−	1.61873i
$956$	2.76336e21	+	4.78628e21i	0.122463	+	0.212111i
$957$		0			0
$958$	2.79202e22			1.21808
$959$	−2.95015e21	−	2.37942e21i	−0.127704	−	0.102999i
$960$		0			0
$961$	1.10941e22	−	1.92155e22i	0.472787	−	0.818890i
$962$	−1.46399e22	−	2.53570e22i	−0.619048	−	1.07222i
$963$		0			0
$964$	−8.77551e21	+	1.51996e22i	−0.365338	+	0.632784i
$965$	−3.86922e22			−1.59834
$966$		0			0
$967$	−3.42385e22			−1.39257			−0.696283	−	0.717767i	$-0.745164\pi$
$967$	−3.42385e22			−1.39257			−0.696283	+	0.717767i	$0.745164\pi$
$968$	1.93283e21	−	3.34776e21i	0.0780062	−	0.135111i
$969$		0			0
$970$	−6.46270e20	−	1.11937e21i	−0.0256818	−	0.0444822i
$971$	−5.48052e21	+	9.49253e21i	−0.216111	+	0.374316i	−0.953616	−	0.301027i	$-0.902671\pi$
$971$	−5.48052e21	+	9.49253e21i	−0.216111	+	0.374316i	0.737505	+	0.675342i	$0.236004\pi$
$972$		0			0
$973$	−1.09595e21	+	4.23166e20i	−0.0425546	+	0.0164310i
$974$	3.08556e22			1.18889
$975$		0			0
$976$	2.15599e21	+	3.73428e21i	0.0818037	+	0.141688i
$977$	−2.41490e22	−	4.18273e22i	−0.909264	−	1.57489i	−0.815089	−	0.579335i	$-0.803312\pi$
$977$	−2.41490e22	−	4.18273e22i	−0.909264	−	1.57489i	−0.0941747	−	0.995556i	$-0.530021\pi$
$978$		0			0
$979$	1.36566e22			0.506375
$980$	−1.14616e22	+	1.04018e22i	−0.421745	+	0.382747i
$981$		0			0
$982$	−3.16600e21	+	5.48368e21i	−0.114729	+	0.198717i
$983$	−1.21880e22	−	2.11103e22i	−0.438310	−	0.759176i	0.559249	−	0.829000i	$-0.311090\pi$
$983$	−1.21880e22	−	2.11103e22i	−0.438310	−	0.759176i	−0.997559	+	0.0698239i	$0.977756\pi$
$984$		0			0
$985$	9.57751e21	−	1.65887e22i	0.339220	−	0.587546i
$986$	2.59463e22			0.912006
$987$		0			0
$988$	−1.34189e22			−0.464559
$989$	1.76180e22	−	3.05153e22i	0.605320	−	1.04844i
$990$		0			0
$991$	−9.93627e21	−	1.72101e22i	−0.336257	−	0.582414i	0.647469	−	0.762092i	$-0.275828\pi$
$991$	−9.93627e21	−	1.72101e22i	−0.336257	−	0.582414i	−0.983725	+	0.179678i	$0.942494\pi$
$992$	6.13959e20	−	1.06341e21i	0.0206206	−	0.0357160i
$993$		0			0
$994$	3.20176e21	−	2.04750e22i	0.105923	−	0.677369i
$995$	−2.78784e22			−0.915366
$996$		0			0
$997$	−2.36370e22	−	4.09404e22i	−0.764501	−	1.32415i	−0.940510	−	0.339766i	$-0.889652\pi$
$997$	−2.36370e22	−	4.09404e22i	−0.764501	−	1.32415i	0.176009	−	0.984389i	$-0.443681\pi$
$998$	−9.86226e21	−	1.70819e22i	−0.316590	−	0.548350i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.16.g.c.37.5		10
3.2	odd	2		14.16.c.b.9.5	✓	10
7.4	even	3	inner	126.16.g.c.109.5		10
21.2	odd	6		98.16.a.h.1.1		5
21.5	even	6		98.16.a.i.1.5		5
21.11	odd	6		14.16.c.b.11.5	yes	10
21.17	even	6		98.16.c.n.67.1		10
21.20	even	2		98.16.c.n.79.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.16.c.b.9.5	✓	10	3.2	odd	2
14.16.c.b.11.5	yes	10	21.11	odd	6
98.16.a.h.1.1		5	21.2	odd	6
98.16.a.i.1.5		5	21.5	even	6
98.16.c.n.67.1		10	21.17	even	6
98.16.c.n.79.1		10	21.20	even	2
126.16.g.c.37.5		10	1.1	even	1	trivial
126.16.g.c.109.5		10	7.4	even	3	inner

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	126.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-64.0000 + 110.851i) q^{2} +(-8192.00 - 14189.0i) q^{4} +(99492.8 - 172327. i) q^{5} +(2.03263e6 - 784833. i) q^{7} +2.09715e6 q^{8} +O(q^{10})\)	\(q+(-64.0000 + 110.851i) q^{2} +(-8192.00 - 14189.0i) q^{4} +(99492.8 - 172327. i) q^{5} +(2.03263e6 - 784833. i) q^{7} +2.09715e6 q^{8} +(1.27351e7 + 2.20578e7i) q^{10} +(-2.41555e7 - 4.18386e7i) q^{11} -2.49387e8 q^{13} +(-4.30888e7 + 2.75549e8i) q^{14} +(-1.34218e8 + 2.32472e8i) q^{16} +(9.16603e8 + 1.58760e9i) q^{17} +(-1.64208e9 + 2.84417e9i) q^{19} -3.26018e9 q^{20} +6.18381e9 q^{22} +(1.55962e10 - 2.70135e10i) q^{23} +(-4.53885e9 - 7.86151e9i) q^{25} +(1.59608e10 - 2.76449e10i) q^{26} +(-2.77873e10 - 2.24116e10i) q^{28} -1.10574e11 q^{29} +(1.78686e10 + 3.09493e10i) q^{31} +(-1.71799e10 - 2.97564e10i) q^{32} -2.34650e11 q^{34} +(6.69848e10 - 4.28362e11i) q^{35} +(4.58620e11 - 7.94354e11i) q^{37} +(-2.10186e11 - 3.64053e11i) q^{38} +(2.08652e11 - 3.61395e11i) q^{40} +2.82110e11 q^{41} +1.12963e12 q^{43} +(-3.95764e11 + 6.85483e11i) q^{44} +(1.99632e12 + 3.45773e12i) q^{46} +(1.96516e12 - 3.40375e12i) q^{47} +(3.51564e12 - 3.19055e12i) q^{49} +1.16194e12 q^{50} +(2.04298e12 + 3.53854e12i) q^{52} +(-3.03333e12 - 5.25388e12i) q^{53} -9.61320e12 q^{55} +(4.26274e12 - 1.64591e12i) q^{56} +(7.07674e12 - 1.22573e13i) q^{58} +(3.30595e12 + 5.72607e12i) q^{59} +(8.03169e12 - 1.39113e13i) q^{61} -4.57435e12 q^{62} +4.39805e12 q^{64} +(-2.48122e13 + 4.29760e13i) q^{65} +(4.53733e13 + 7.85889e13i) q^{67} +(1.50176e13 - 2.60113e13i) q^{68} +(4.31974e13 + 3.48405e13i) q^{70} -7.43060e13 q^{71} +(-7.21893e13 - 1.25036e14i) q^{73} +(5.87034e13 + 1.01677e14i) q^{74} +5.38077e13 q^{76} +(-8.19356e13 - 6.60845e13i) q^{77} +(4.61192e13 - 7.98807e13i) q^{79} +(2.67074e13 + 4.62586e13i) q^{80} +(-1.80551e13 + 3.12723e13i) q^{82} -3.24677e14 q^{83} +3.64782e14 q^{85} +(-7.22965e13 + 1.25221e14i) q^{86} +(-5.06578e13 - 8.77419e13i) q^{88} +(-1.41340e14 + 2.44808e14i) q^{89} +(-5.06912e14 + 1.95727e14i) q^{91} -5.11058e14 q^{92} +(2.51540e14 + 4.35680e14i) q^{94} +(3.26750e14 + 5.65948e14i) q^{95} -5.07472e13 q^{97} +(1.28676e14 + 5.93908e14i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 640 q^{2} - 81920 q^{4} - 10969 q^{5} + 2375276 q^{7} + 20971520 q^{8}+O(q^{10}) \) 10 * q - 640 * q^2 - 81920 * q^4 - 10969 * q^5 + 2375276 * q^7 + 20971520 * q^8	\( 10 q - 640 q^{2} - 81920 q^{4} - 10969 q^{5} + 2375276 q^{7} + 20971520 q^{8} - 1404032 q^{10} + 3405409 q^{11} + 369408276 q^{13} - 411547520 q^{14} - 1342177280 q^{16} + 3201713287 q^{17} - 1063446451 q^{19} + 359432192 q^{20} - 871784704 q^{22} + 31680429991 q^{23} + 39012502244 q^{25} - 23642129664 q^{26} + 13761560576 q^{28} - 294935242276 q^{29} + 30201804075 q^{31} - 171798691840 q^{32} - 819638601472 q^{34} + 1540311474205 q^{35} + 1369689837461 q^{37} - 136121145728 q^{38} - 23003660288 q^{40} - 3634838274156 q^{41} + 415602663752 q^{43} + 55794221056 q^{44} + 4055095038848 q^{46} + 12606978599835 q^{47} - 8067928630838 q^{49} - 9987200574464 q^{50} - 3026192596992 q^{52} - 10616682242361 q^{53} - 40851384759514 q^{55} + 4981314813952 q^{56} + 18875855505664 q^{58} - 39993786962755 q^{59} + 5148862074165 q^{61} - 7731661843200 q^{62} + 43980465111040 q^{64} - 91302240851010 q^{65} - 29267240444285 q^{67} + 52456870494208 q^{68} + 18327124839296 q^{70} + 37767657205600 q^{71} + 243869659370917 q^{73} + 175320299195008 q^{74} + 34847013306368 q^{76} - 35960055270559 q^{77} + 137356615917609 q^{79} - 2944468516864 q^{80} + 232629649545984 q^{82} + 914604166510648 q^{83} + 264981492485402 q^{85} - 26598570480128 q^{86} + 7141660295168 q^{88} - 315332760149685 q^{89} - 26\!\cdots\!20 q^{91}+ \cdots + 12\!\cdots\!56 q^{98}+O(q^{100}) \) 10 * q - 640 * q^2 - 81920 * q^4 - 10969 * q^5 + 2375276 * q^7 + 20971520 * q^8 - 1404032 * q^10 + 3405409 * q^11 + 369408276 * q^13 - 411547520 * q^14 - 1342177280 * q^16 + 3201713287 * q^17 - 1063446451 * q^19 + 359432192 * q^20 - 871784704 * q^22 + 31680429991 * q^23 + 39012502244 * q^25 - 23642129664 * q^26 + 13761560576 * q^28 - 294935242276 * q^29 + 30201804075 * q^31 - 171798691840 * q^32 - 819638601472 * q^34 + 1540311474205 * q^35 + 1369689837461 * q^37 - 136121145728 * q^38 - 23003660288 * q^40 - 3634838274156 * q^41 + 415602663752 * q^43 + 55794221056 * q^44 + 4055095038848 * q^46 + 12606978599835 * q^47 - 8067928630838 * q^49 - 9987200574464 * q^50 - 3026192596992 * q^52 - 10616682242361 * q^53 - 40851384759514 * q^55 + 4981314813952 * q^56 + 18875855505664 * q^58 - 39993786962755 * q^59 + 5148862074165 * q^61 - 7731661843200 * q^62 + 43980465111040 * q^64 - 91302240851010 * q^65 - 29267240444285 * q^67 + 52456870494208 * q^68 + 18327124839296 * q^70 + 37767657205600 * q^71 + 243869659370917 * q^73 + 175320299195008 * q^74 + 34847013306368 * q^76 - 35960055270559 * q^77 + 137356615917609 * q^79 - 2944468516864 * q^80 + 232629649545984 * q^82 + 914604166510648 * q^83 + 264981492485402 * q^85 - 26598570480128 * q^86 + 7141660295168 * q^88 - 315332760149685 * q^89 - 2638730194011720 * q^91 - 1038104329945088 * q^92 + 1613693260778880 * q^94 + 1346257729549705 * q^95 + 58320039716044 * q^97 + 1279096378461056 * q^98

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