LMFDB - Embedded newform 3.23.b.a.2.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,23,Mod(2,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 23, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 23);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 23 $
Character orbit:	$[\chi]$	$=$	3.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:	$9.20122304526$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 126474x^{4} + 3861674040x^{2} + 9831214131200 $ x^6 + 126474x^4 + 3861674040x^2 + 9831214131200
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{21}\cdot 3^{22} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.4
Root			$52.8797i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.23.b.a.2.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+634.557i q^{2} +(48229.8 + 170455. i) q^{3} +3.79164e6 q^{4} +2.56634e6i q^{5} +(-1.08163e8 + 3.06045e7i) q^{6} +8.97619e8 q^{7} +5.06753e9i q^{8} +(-2.67288e10 + 1.64420e10i) q^{9} +O(q^{10})$	\(q+634.557i q^{2} +(48229.8 + 170455. i) q^{3} +3.79164e6 q^{4} +2.56634e6i q^{5} +(-1.08163e8 + 3.06045e7i) q^{6} +8.97619e8 q^{7} +5.06753e9i q^{8} +(-2.67288e10 + 1.64420e10i) q^{9} -1.62849e9 q^{10} +4.54805e11i q^{11} +(1.82870e11 + 6.46305e11i) q^{12} -1.52981e12 q^{13} +5.69590e11i q^{14} +(-4.37446e11 + 1.23774e11i) q^{15} +1.26877e13 q^{16} -5.06681e13i q^{17} +(-1.04334e13 - 1.69610e13i) q^{18} +2.10259e13 q^{19} +9.73064e12i q^{20} +(4.32920e13 + 1.53004e14i) q^{21} -2.88599e14 q^{22} +1.03543e15i q^{23} +(-8.63787e14 + 2.44406e14i) q^{24} +2.37760e15 q^{25} -9.70754e14i q^{26} +(-4.09175e15 - 3.76307e15i) q^{27} +3.40345e15 q^{28} -1.09681e16i q^{29} +(-7.85416e13 - 2.77584e14i) q^{30} +2.32177e16 q^{31} +2.93058e16i q^{32} +(-7.75238e16 + 2.19351e16i) q^{33} +3.21518e16 q^{34} +2.30359e15i q^{35} +(-1.01346e17 + 6.23423e16i) q^{36} +2.29827e17 q^{37} +1.33421e16i q^{38} +(-7.37826e16 - 2.60765e17i) q^{39} -1.30050e16 q^{40} -7.03825e17i q^{41} +(-9.70895e16 + 2.74712e16i) q^{42} +3.20294e17 q^{43} +1.72446e18i q^{44} +(-4.21958e16 - 6.85952e16i) q^{45} -6.57037e17 q^{46} -3.71198e17i q^{47} +(6.11923e17 + 2.16268e18i) q^{48} -3.10410e18 q^{49} +1.50872e18i q^{50} +(8.63664e18 - 2.44371e18i) q^{51} -5.80051e18 q^{52} -1.31183e19i q^{53} +(2.38788e18 - 2.59645e18i) q^{54} -1.16718e18 q^{55} +4.54871e18i q^{56} +(1.01408e18 + 3.58398e18i) q^{57} +6.95989e18 q^{58} +2.62199e19i q^{59} +(-1.65864e18 + 4.69307e17i) q^{60} -3.33360e19 q^{61} +1.47330e19i q^{62} +(-2.39923e19 + 1.47587e19i) q^{63} +3.46197e19 q^{64} -3.92602e18i q^{65} +(-1.39191e19 - 4.91933e19i) q^{66} +1.84254e20 q^{67} -1.92115e20i q^{68} +(-1.76494e20 + 4.99384e19i) q^{69} -1.46176e18 q^{70} +6.16084e19i q^{71} +(-8.33206e19 - 1.35449e20i) q^{72} +5.98508e19 q^{73} +1.45838e20i q^{74} +(1.14671e20 + 4.05274e20i) q^{75} +7.97228e19 q^{76} +4.08241e20i q^{77} +(1.65470e20 - 4.68193e19i) q^{78} -1.05786e21 q^{79} +3.25608e19i q^{80} +(4.44090e20 - 8.78953e20i) q^{81} +4.46617e20 q^{82} -1.35231e21i q^{83} +(1.64148e20 + 5.80135e20i) q^{84} +1.30032e20 q^{85} +2.03245e20i q^{86} +(1.86957e21 - 5.28990e20i) q^{87} -2.30474e21 q^{88} -7.46198e20i q^{89} +(4.35276e19 - 2.67756e19i) q^{90} -1.37319e21 q^{91} +3.92597e21i q^{92} +(1.11979e21 + 3.95758e21i) q^{93} +2.35546e20 q^{94} +5.39597e19i q^{95} +(-4.99533e21 + 1.41341e21i) q^{96} +5.46728e21 q^{97} -1.96973e21i q^{98} +(-7.47792e21 - 1.21564e22i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 86670 q^{3} - 11258688 q^{4} + 293575104 q^{6} - 3447063060 q^{7} + 57339715158 q^{9}+O(q^{10}) $ 6 * q + 86670 * q^3 - 11258688 * q^4 + 293575104 * q^6 - 3447063060 * q^7 + 57339715158 * q^9	$ 6 q + 86670 q^{3} - 11258688 q^{4} + 293575104 q^{6} - 3447063060 q^{7} + 57339715158 q^{9} - 186869600640 q^{10} - 1325972980800 q^{12} + 2025132496860 q^{13} + 2628031314240 q^{15} - 9703467227136 q^{16} + 42127150135680 q^{18} + 100485688668636 q^{19} - 789079193287812 q^{21} + 10\!\cdots\!00 q^{22}+ \cdots - 60\!\cdots\!60 q^{99}+O(q^{100}) $ 6 * q + 86670 * q^3 - 11258688 * q^4 + 293575104 * q^6 - 3447063060 * q^7 + 57339715158 * q^9 - 186869600640 * q^10 - 1325972980800 * q^12 + 2025132496860 * q^13 + 2628031314240 * q^15 - 9703467227136 * q^16 + 42127150135680 * q^18 + 100485688668636 * q^19 - 789079193287812 * q^21 + 1045890315676800 * q^22 - 2472467233277952 * q^24 + 1396569263732790 * q^25 - 10731657558901410 * q^27 + 44570708098492800 * q^28 - 116169123436801920 * q^30 + 114109662401153292 * q^31 - 174850022773609920 * q^33 + 319017868488396288 * q^34 - 707589966262651200 * q^36 + 683782874080661820 * q^37 - 1038045209126993748 * q^39 + 1781949720499015680 * q^40 - 1108714403505421440 * q^42 + 273273330169769340 * q^43 + 3228622736179443840 * q^45 - 8349686917048426752 * q^46 + 10392767955626526720 * q^48 - 8294807529216677070 * q^49 + 14237699192275302144 * q^51 - 22636595958302682240 * q^52 + 48383805955937626944 * q^54 - 40874587160137441920 * q^55 + 43721391850797114540 * q^57 - 67285958146132360320 * q^58 - 44311576503733309440 * q^60 + 121649250388145492892 * q^61 - 184494903535705683060 * q^63 + 285203601894474055680 * q^64 - 374640791614422030720 * q^66 + 75701571086175260700 * q^67 - 233446021721582921856 * q^69 + 1113607014897000234240 * q^70 - 639860863731149721600 * q^72 - 57178481309533986900 * q^73 - 333973626119358339330 * q^75 - 731229802672243966080 * q^76 + 735750453969076417920 * q^78 + 384537395891327736396 * q^79 + 3109769787236091157926 * q^81 - 5166859472437001068800 * q^82 + 6698665889827068753792 * q^84 - 6772579853411844011520 * q^85 + 4995406256507248236480 * q^87 - 404168025320661381120 * q^88 - 3858783621100493362560 * q^90 - 2806742501496183911304 * q^91 + 2087220280517252053020 * q^93 + 8135725180445469439488 * q^94 - 15069021592890694238208 * q^96 + 1565231688506989945740 * q^97 - 6095367699696122981760 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$			634.557i			0.309842i	0.987927	+	0.154921i	$0.0495123\pi$
$2$			634.557i			0.309842i	−0.987927	+	0.154921i	$0.950488\pi$
$3$	48229.8	+	170455.i	0.272259	+	0.962224i
$3$	48229.8	+	170455.i	0.272259	+	0.962224i
$4$	3.79164e6			0.903998
$5$			2.56634e6i			0.0525586i	0.999655	+	0.0262793i	$0.00836593\pi$
$5$			2.56634e6i			0.0525586i	−0.999655	+	0.0262793i	$0.991634\pi$
$6$	−1.08163e8	+	3.06045e7i	−0.298138	+	0.0843572i
$7$	8.97619e8			0.453956			0.226978	−	0.973900i	$-0.427115\pi$
$7$	8.97619e8			0.453956			0.226978	+	0.973900i	$0.427115\pi$
$8$			5.06753e9i			0.589939i
$9$	−2.67288e10	+	1.64420e10i	−0.851750	+	0.523948i
$10$	−1.62849e9			−0.0162849
$11$			4.54805e11i			1.59406i	0.603937	+	0.797032i	$0.293598\pi$
$11$			4.54805e11i			1.59406i	−0.603937	+	0.797032i	$0.706402\pi$
$12$	1.82870e11	+	6.46305e11i	0.246121	+	0.869849i
$13$	−1.52981e12			−0.853615			−0.426807	−	0.904343i	$-0.640362\pi$
$13$	−1.52981e12			−0.853615			−0.426807	+	0.904343i	$0.640362\pi$
$14$			5.69590e11i			0.140655i
$15$	−4.37446e11	+	1.23774e11i	−0.0505732	+	0.0143095i
$16$	1.26877e13			0.721210
$17$		−	5.06681e13i		−	1.47842i	−0.673477	−	0.739208i	$-0.735200\pi$
$17$		−	5.06681e13i		−	1.47842i	0.673477	−	0.739208i	$-0.264800\pi$
$18$	−1.04334e13	−	1.69610e13i	−0.162341	−	0.263908i
$19$	2.10259e13			0.180495			0.0902476	−	0.995919i	$-0.471234\pi$
$19$	2.10259e13			0.180495			0.0902476	+	0.995919i	$0.471234\pi$
$20$			9.73064e12i			0.0475129i
$21$	4.32920e13	+	1.53004e14i	0.123593	+	0.436807i
$22$	−2.88599e14			−0.493908
$23$			1.03543e15i			1.08671i	0.839503	+	0.543354i	$0.182846\pi$
$23$			1.03543e15i			1.08671i	−0.839503	+	0.543354i	$0.817154\pi$
$24$	−8.63787e14	+	2.44406e14i	−0.567653	+	0.160616i
$25$	2.37760e15			0.997238
$26$		−	9.70754e14i		−	0.264486i
$27$	−4.09175e15	−	3.76307e15i	−0.736051	−	0.676926i
$28$	3.40345e15			0.410375
$29$		−	1.09681e16i		−	0.898989i	−0.893283	−	0.449494i	$-0.851604\pi$
$29$		−	1.09681e16i		−	0.898989i	0.893283	−	0.449494i	$-0.148396\pi$
$30$	−7.85416e13	−	2.77584e14i	−0.00443370	−	0.0156697i
$31$	2.32177e16			0.913779			0.456889	−	0.889523i	$-0.348963\pi$
$31$	2.32177e16			0.913779			0.456889	+	0.889523i	$0.348963\pi$
$32$			2.93058e16i			0.813400i
$33$	−7.75238e16	+	2.19351e16i	−1.53385	+	0.433998i
$34$	3.21518e16			0.458075
$35$			2.30359e15i			0.0238593i
$36$	−1.01346e17	+	6.23423e16i	−0.769981	+	0.473648i
$37$	2.29827e17			1.29176			0.645880	−	0.763439i	$-0.276490\pi$
$37$	2.29827e17			1.29176			0.645880	+	0.763439i	$0.276490\pi$
$38$			1.33421e16i			0.0559250i
$39$	−7.37826e16	−	2.60765e17i	−0.232404	−	0.821369i
$40$	−1.30050e16			−0.0310064
$41$		−	7.03825e17i		−	1.27892i	−0.768825	−	0.639459i	$-0.779159\pi$
$41$		−	7.03825e17i		−	1.27892i	0.768825	−	0.639459i	$-0.220841\pi$
$42$	−9.70895e16	+	2.74712e16i	−0.135341	+	0.0382944i
$43$	3.20294e17			0.344664			0.172332	−	0.985039i	$-0.444870\pi$
$43$	3.20294e17			0.344664			0.172332	+	0.985039i	$0.444870\pi$
$44$			1.72446e18i			1.44103i
$45$	−4.21958e16	−	6.85952e16i	−0.0275380	−	0.0447668i
$46$	−6.57037e17			−0.336708
$47$		−	3.71198e17i		−	0.150151i	−0.997178	−	0.0750756i	$-0.976080\pi$
$47$		−	3.71198e17i		−	0.150151i	0.997178	−	0.0750756i	$-0.0239198\pi$
$48$	6.11923e17	+	2.16268e18i	0.196356	+	0.693966i
$49$	−3.10410e18			−0.793924
$50$			1.50872e18i			0.308986i
$51$	8.63664e18	−	2.44371e18i	1.42257	−	0.402511i
$52$	−5.80051e18			−0.771666
$53$		−	1.31183e19i		−	1.41528i	−0.706574	−	0.707639i	$-0.749760\pi$
$53$		−	1.31183e19i		−	1.41528i	0.706574	−	0.707639i	$-0.250240\pi$
$54$	2.38788e18	−	2.59645e18i	0.209740	−	0.228060i
$55$	−1.16718e18			−0.0837818
$56$			4.54871e18i			0.267806i
$57$	1.01408e18	+	3.58398e18i	0.0491414	+	0.173677i
$58$	6.95989e18			0.278545
$59$			2.62199e19i			0.869480i	0.900556	+	0.434740i	$0.143160\pi$
$59$			2.62199e19i			0.869480i	−0.900556	+	0.434740i	$0.856840\pi$
$60$	−1.65864e18	+	4.69307e17i	−0.0457180	+	0.0129358i
$61$	−3.33360e19			−0.766099			−0.383050	−	0.923728i	$-0.625126\pi$
$61$	−3.33360e19			−0.766099			−0.383050	+	0.923728i	$0.625126\pi$
$62$			1.47330e19i			0.283127i
$63$	−2.39923e19	+	1.47587e19i	−0.386657	+	0.237849i
$64$	3.46197e19			0.469185
$65$		−	3.92602e18i		−	0.0448648i
$66$	−1.39191e19	−	4.91933e19i	−0.134471	−	0.475250i
$67$	1.84254e20			1.50867			0.754333	−	0.656492i	$-0.227960\pi$
$67$	1.84254e20			1.50867			0.754333	+	0.656492i	$0.227960\pi$
$68$		−	1.92115e20i		−	1.33648i
$69$	−1.76494e20	+	4.99384e19i	−1.04566	+	0.295866i
$70$	−1.46176e18			−0.00739261
$71$			6.16084e19i			0.266562i	0.991078	+	0.133281i	$0.0425513\pi$
$71$			6.16084e19i			0.266562i	−0.991078	+	0.133281i	$0.957449\pi$
$72$	−8.33206e19	−	1.35449e20i	−0.309097	−	0.502481i
$73$	5.98508e19			0.190774			0.0953869	−	0.995440i	$-0.469591\pi$
$73$	5.98508e19			0.190774			0.0953869	+	0.995440i	$0.469591\pi$
$74$			1.45838e20i			0.400242i
$75$	1.14671e20	+	4.05274e20i	0.271507	+	0.959566i
$76$	7.97228e19			0.163167
$77$			4.08241e20i			0.723634i
$78$	1.65470e20	−	4.68193e19i	0.254495	−	0.0720085i
$79$	−1.05786e21			−1.41426			−0.707132	−	0.707081i	$-0.750011\pi$
$79$	−1.05786e21			−1.41426			−0.707132	+	0.707081i	$0.750011\pi$
$80$			3.25608e19i			0.0379058i
$81$	4.44090e20	−	8.78953e20i	0.450958	−	0.892545i
$82$	4.46617e20			0.396262
$83$		−	1.35231e21i		−	1.05007i	−0.851081	−	0.525035i	$-0.824052\pi$
$83$		−	1.35231e21i		−	1.05007i	0.851081	−	0.525035i	$-0.175948\pi$
$84$	1.64148e20	+	5.80135e20i	0.111728	+	0.394873i
$85$	1.30032e20			0.0777035
$86$			2.03245e20i			0.106791i
$87$	1.86957e21	−	5.28990e20i	0.865029	−	0.244757i
$88$	−2.30474e21			−0.940400
$89$		−	7.46198e20i		−	0.268883i	−0.990922	−	0.134442i	$-0.957076\pi$
$89$		−	7.46198e20i		−	0.268883i	0.990922	−	0.134442i	$-0.0429241\pi$
$90$	4.35276e19	−	2.67756e19i	0.0138706	−	0.00853242i
$91$	−1.37319e21			−0.387503
$92$			3.92597e21i			0.982383i
$93$	1.11979e21	+	3.95758e21i	0.248784	+	0.879260i
$94$	2.35546e20			0.0465231
$95$			5.39597e19i			0.00948658i
$96$	−4.99533e21	+	1.41341e21i	−0.782673	+	0.221455i
$97$	5.46728e21			0.764332			0.382166	−	0.924094i	$-0.375178\pi$
$97$	5.46728e21			0.764332			0.382166	+	0.924094i	$0.375178\pi$
$98$		−	1.96973e21i		−	0.245991i
$99$	−7.47792e21	−	1.21564e22i	−0.835206	−	1.35774i
$100$	9.01501e21			0.901501
$101$		−	3.76219e21i		−	0.337214i	−0.985683	−	0.168607i	$-0.946073\pi$
$101$		−	3.76219e21i		−	0.337214i	0.985683	−	0.168607i	$-0.0539269\pi$
$102$	1.55067e21	+	5.48044e21i	0.124715	+	0.440771i
$103$	1.62984e21			0.117743			0.0588716	−	0.998266i	$-0.481250\pi$
$103$	1.62984e21			0.117743			0.0588716	+	0.998266i	$0.481250\pi$
$104$		−	7.75239e21i		−	0.503580i
$105$	−3.92659e20	+	1.11102e20i	−0.0229580	+	0.00649590i
$106$	8.32428e21			0.438513
$107$			1.32901e22i			0.631403i	0.948859	+	0.315701i	$0.102240\pi$
$107$			1.32901e22i			0.631403i	−0.948859	+	0.315701i	$0.897760\pi$
$108$	−1.55145e22	−	1.42682e22i	−0.665389	−	0.611939i
$109$	−2.06868e22			−0.801680			−0.400840	−	0.916148i	$-0.631282\pi$
$109$	−2.06868e22			−0.801680			−0.400840	+	0.916148i	$0.631282\pi$
$110$		−	7.40644e20i		−	0.0259591i
$111$	1.10845e22	+	3.91752e22i	0.351693	+	1.24296i
$112$	1.13887e22			0.327397
$113$			4.20738e22i			1.09685i	0.836198	+	0.548427i	$0.184773\pi$
$113$			4.20738e22i			1.09685i	−0.836198	+	0.548427i	$0.815227\pi$
$114$	−2.27424e21	+	6.43489e20i	−0.0538124	+	0.0152261i
$115$	−2.65726e21			−0.0571159
$116$		−	4.15872e22i		−	0.812684i
$117$	4.08902e22	−	2.51533e22i	0.727067	−	0.447249i
$118$	−1.66380e22			−0.269402
$119$		−	4.54807e22i		−	0.671135i
$120$	−6.27229e20	−	2.21677e21i	−0.00844175	−	0.0298351i
$121$	−1.25445e23			−1.54104
$122$		−	2.11536e22i		−	0.237370i
$123$	1.19971e23	−	3.39454e22i	1.23061	−	0.348196i
$124$	8.80333e22			0.826054
$125$			1.22204e22i			0.104972i
$126$	−9.36522e21	−	1.52245e22i	−0.0736956	−	0.119803i
$127$	−6.06941e22			−0.437830			−0.218915	−	0.975744i	$-0.570252\pi$
$127$	−6.06941e22			−0.437830			−0.218915	+	0.975744i	$0.570252\pi$
$128$			1.44886e23i			0.958773i
$129$	1.54477e22	+	5.45958e22i	0.0938378	+	0.331644i
$130$	2.49128e21			0.0139010
$131$		−	4.49359e21i		−	0.0230467i	−0.999934	−	0.0115234i	$-0.996332\pi$
$131$		−	4.49359e21i		−	0.0230467i	0.999934	−	0.0115234i	$-0.00366808\pi$
$132$	−2.93943e23	+	8.31702e22i	−1.38659	+	0.392333i
$133$	1.88733e22			0.0819368
$134$			1.16919e23i			0.467448i
$135$	9.65731e21	−	1.05008e22i	0.0355783	−	0.0386859i
$136$	2.56762e23			0.872175
$137$		−	2.17085e23i		−	0.680305i	−0.940370	−	0.340152i	$-0.889521\pi$
$137$		−	2.17085e23i		−	0.680305i	0.940370	−	0.340152i	$-0.110479\pi$
$138$	−3.16888e22	−	1.11995e23i	−0.0916717	−	0.323989i
$139$	1.65363e23			0.441849			0.220925	−	0.975291i	$-0.429092\pi$
$139$	1.65363e23			0.441849			0.220925	+	0.975291i	$0.429092\pi$
$140$			8.73440e21i			0.0215687i
$141$	6.32725e22	−	1.79028e22i	0.144479	−	0.0408799i
$142$	−3.90940e22			−0.0825922
$143$		−	6.95767e23i		−	1.36072i
$144$	−3.39126e23	+	2.08611e23i	−0.614291	+	0.377876i
$145$	2.81479e22			0.0472496
$146$			3.79787e22i			0.0591097i
$147$	−1.49710e23	−	5.29110e23i	−0.216153	−	0.763933i
$148$	8.71422e23			1.16775
$149$			1.29054e24i			1.60592i	0.596033	+	0.802960i	$0.296743\pi$
$149$			1.29054e24i			1.60592i	−0.596033	+	0.802960i	$0.703257\pi$
$150$	−2.57169e23	+	7.27653e22i	−0.297314	+	0.0841242i
$151$	−1.02305e24			−1.09938			−0.549691	−	0.835368i	$-0.685254\pi$
$151$	−1.02305e24			−1.09938			−0.549691	+	0.835368i	$0.685254\pi$
$152$			1.06550e23i			0.106481i
$153$	8.33087e23	+	1.35430e24i	0.774613	+	1.25924i
$154$	−2.59052e23			−0.224212
$155$			5.95846e22i			0.0480270i
$156$	−2.79757e23	−	9.88726e23i	−0.210093	−	0.742516i
$157$	−1.15645e24			−0.809526			−0.404763	−	0.914422i	$-0.632646\pi$
$157$	−1.15645e24			−0.809526			−0.404763	+	0.914422i	$0.632646\pi$
$158$		−	6.71273e23i		−	0.438199i
$159$	2.23607e24	−	6.32691e23i	1.36181	−	0.385322i
$160$	−7.52087e22			−0.0427512
$161$			9.29419e23i			0.493318i
$162$	5.57745e23	+	2.81800e23i	0.276548	+	0.139726i
$163$	−9.36187e23			−0.433810			−0.216905	−	0.976193i	$-0.569596\pi$
$163$	−9.36187e23			−0.433810			−0.216905	+	0.976193i	$0.569596\pi$
$164$		−	2.66865e24i		−	1.15614i
$165$	−5.62930e22	−	1.98952e23i	−0.0228103	−	0.0806168i
$166$	8.58120e23			0.325356
$167$		−	1.70989e24i		−	0.606859i	−0.952854	−	0.303429i	$-0.901868\pi$
$167$		−	1.70989e24i		−	0.606859i	0.952854	−	0.303429i	$-0.0981316\pi$
$168$	−7.75352e23	+	2.19384e23i	−0.257689	+	0.0729125i
$169$	−8.71507e23			−0.271342
$170$			8.25124e22i			0.0240758i
$171$	−5.61999e23	+	3.45709e23i	−0.153737	+	0.0945700i
$172$	1.21444e24			0.311576
$173$			5.24499e24i			1.26252i	0.775572	+	0.631260i	$0.217462\pi$
$173$			5.24499e24i			1.26252i	−0.775572	+	0.631260i	$0.782538\pi$
$174$	3.35674e23	+	1.18635e24i	0.0758362	+	0.268022i
$175$	2.13418e24			0.452702
$176$			5.77041e24i			1.14965i
$177$	−4.46932e24	+	1.26458e24i	−0.836635	+	0.236724i
$178$	4.73505e23			0.0833114
$179$		−	6.85545e24i		−	1.13410i	−0.823682	−	0.567052i	$-0.808084\pi$
$179$		−	6.85545e24i		−	1.13410i	0.823682	−	0.567052i	$-0.191916\pi$
$180$	−1.59991e23	−	2.60089e23i	−0.0248943	−	0.0404691i
$181$	2.46571e23			0.0360976			0.0180488	−	0.999837i	$-0.494255\pi$
$181$	2.46571e23			0.0360976			0.0180488	+	0.999837i	$0.494255\pi$
$182$		−	8.71367e23i		−	0.120065i
$183$	−1.60779e24	−	5.68229e24i	−0.208577	−	0.737159i
$184$	−5.24706e24			−0.641092
$185$			5.89814e23i			0.0678932i
$186$	−2.51131e24	+	7.10568e23i	−0.272432	+	0.0770838i
$187$	2.30441e25			2.35669
$188$		−	1.40745e24i		−	0.135736i
$189$	−3.67284e24	−	3.37780e24i	−0.334135	−	0.307294i
$190$	−3.42405e22			−0.00293934
$191$		−	1.19517e25i		−	0.968414i	−0.874954	−	0.484207i	$-0.839108\pi$
$191$		−	1.19517e25i		−	0.968414i	0.874954	−	0.484207i	$-0.160892\pi$
$192$	1.66970e24	+	5.90111e24i	0.127740	+	0.451461i
$193$	−6.43828e24			−0.465200			−0.232600	−	0.972572i	$-0.574723\pi$
$193$	−6.43828e24			−0.465200			−0.232600	+	0.972572i	$0.574723\pi$
$194$			3.46930e24i			0.236822i
$195$	6.69211e23	−	1.89351e23i	0.0431700	−	0.0122148i
$196$	−1.17696e25			−0.717706
$197$			1.37996e25i			0.795678i	0.917455	+	0.397839i	$0.130240\pi$
$197$			1.37996e25i			0.795678i	−0.917455	+	0.397839i	$0.869760\pi$
$198$	7.71393e24	−	4.74516e24i	0.420686	−	0.258782i
$199$	−2.34558e25			−1.21023			−0.605114	−	0.796139i	$-0.706872\pi$
$199$	−2.34558e25			−1.21023			−0.605114	+	0.796139i	$0.706872\pi$
$200$			1.20486e25i			0.588309i
$201$	8.88652e24	+	3.14070e25i	0.410747	+	1.45168i
$202$	2.38732e24			0.104483
$203$		−	9.84519e24i		−	0.408101i
$204$	3.27470e25	−	9.26568e24i	1.28600	−	0.363870i
$205$	1.80625e24			0.0672181
$206$			1.03423e24i			0.0364818i
$207$	−1.70245e25	−	2.76758e25i	−0.569379	−	0.925605i
$208$	−1.94098e25			−0.615636
$209$			9.56270e24i			0.287721i
$210$	−7.05004e22	−	2.49165e23i	−0.00201270	−	0.00711335i
$211$	2.12594e25			0.576028			0.288014	−	0.957626i	$-0.407005\pi$
$211$	2.12594e25			0.576028			0.288014	+	0.957626i	$0.407005\pi$
$212$		−	4.97397e25i		−	1.27941i
$213$	−1.05015e25	+	2.97136e24i	−0.256492	+	0.0725738i
$214$	−8.43332e24			−0.195635
$215$			8.21984e23i			0.0181151i
$216$	1.90695e25	−	2.07351e25i	0.399345	−	0.434225i
$217$	2.08407e25			0.414815
$218$		−	1.31269e25i		−	0.248394i
$219$	2.88659e24	+	1.02019e25i	0.0519398	+	0.183567i
$220$	−4.42554e24			−0.0757386
$221$			7.75128e25i			1.26200i
$222$	−2.48589e25	+	7.03375e24i	−0.385122	+	0.108969i
$223$	1.45332e25			0.214293			0.107147	−	0.994243i	$-0.465829\pi$
$223$	1.45332e25			0.214293			0.107147	+	0.994243i	$0.465829\pi$
$224$			2.63055e25i			0.369248i
$225$	−6.35505e25	+	3.90926e25i	−0.849398	+	0.522500i
$226$	−2.66982e25			−0.339852
$227$		−	2.76745e25i		−	0.335579i	−0.985823	−	0.167790i	$-0.946337\pi$
$227$		−	2.76745e25i		−	0.335579i	0.985823	−	0.167790i	$-0.0536629\pi$
$228$	3.84501e24	+	1.35892e25i	0.0444237	+	0.157003i
$229$	8.87110e25			0.976759			0.488379	−	0.872631i	$-0.337588\pi$
$229$	8.87110e25			0.976759			0.488379	+	0.872631i	$0.337588\pi$
$230$		−	1.68618e24i		−	0.0176969i
$231$	−6.95868e25	+	1.96894e25i	−0.696298	+	0.197016i
$232$	5.55813e25			0.530348
$233$		−	6.39561e25i		−	0.582059i	−0.956714	−	0.291029i	$-0.906002\pi$
$233$		−	6.39561e25i		−	0.582059i	0.956714	−	0.291029i	$-0.0939978\pi$
$234$	1.59612e25	+	2.59471e25i	0.138577	+	0.225276i
$235$	9.52619e23			0.00789174
$236$			9.94167e25i			0.786008i
$237$	−5.10204e25	−	1.80318e26i	−0.385046	−	1.36084i
$238$	2.88600e25			0.207946
$239$		−	1.54833e26i		−	1.06534i	−0.846324	−	0.532669i	$-0.821189\pi$
$239$		−	1.54833e26i		−	1.06534i	0.846324	−	0.532669i	$-0.178811\pi$
$240$	−5.55016e24	+	1.57040e24i	−0.0364739	+	0.0103202i
$241$	−1.59574e25			−0.100178			−0.0500892	−	0.998745i	$-0.515951\pi$
$241$	−1.59574e25			−0.100178			−0.0500892	+	0.998745i	$0.515951\pi$
$242$		−	7.96018e25i		−	0.477478i
$243$	1.71240e26	+	3.33057e25i	0.981606	+	0.190919i
$244$	−1.26398e26			−0.692552
$245$		−	7.96618e24i		−	0.0417276i
$246$	2.15403e25	+	7.61282e25i	0.107886	+	0.381293i
$247$	−3.21658e25			−0.154073
$248$			1.17657e26i			0.539074i
$249$	2.30509e26	−	6.52218e25i	1.01040	−	0.285891i
$250$	−7.75451e24			−0.0325248
$251$			4.68439e26i			1.88036i	0.340674	+	0.940182i	$0.389345\pi$
$251$			4.68439e26i			1.88036i	−0.340674	+	0.940182i	$0.610655\pi$
$252$	−9.09702e25	+	5.59596e25i	−0.349537	+	0.215015i
$253$	−4.70917e26			−1.73228
$254$		−	3.85138e25i		−	0.135658i
$255$	6.27140e24	+	2.21645e25i	0.0211555	+	0.0747682i
$256$	5.32674e25			0.172116
$257$		−	4.03799e26i		−	1.24997i	−0.780635	−	0.624987i	$-0.785104\pi$
$257$		−	4.03799e26i		−	1.24997i	0.780635	−	0.624987i	$-0.214896\pi$
$258$	−3.46441e25	+	9.80246e24i	−0.102757	+	0.0290749i
$259$	2.06297e26			0.586402
$260$		−	1.48861e25i		−	0.0405577i
$261$	1.80338e26	+	2.93165e26i	0.471023	+	0.765714i
$262$	2.85144e24			0.00714085
$263$			1.08512e26i			0.260593i	0.991475	+	0.130296i	$0.0415929\pi$
$263$			1.08512e26i			0.260593i	−0.991475	+	0.130296i	$0.958407\pi$
$264$	−1.11157e26	−	3.92855e26i	−0.256032	−	0.904875i
$265$	3.36659e25			0.0743850
$266$			1.19762e25i			0.0253875i
$267$	1.27193e26	−	3.59890e25i	0.258726	−	0.0732058i
$268$	6.98624e26			1.36383
$269$		−	5.82469e26i		−	1.09143i	−0.837970	−	0.545717i	$-0.816257\pi$
$269$		−	5.82469e26i		−	1.09143i	0.837970	−	0.545717i	$-0.183743\pi$
$270$	6.66337e24	+	6.12811e24i	0.0119865	+	0.0110236i
$271$	−1.12902e27			−1.95003			−0.975014	−	0.222144i	$-0.928695\pi$
$271$	−1.12902e27			−1.95003			−0.975014	+	0.222144i	$0.928695\pi$
$272$		−	6.42860e26i		−	1.06625i
$273$	−6.62287e25	−	2.34067e26i	−0.105501	−	0.372865i
$274$	1.37753e26			0.210787
$275$			1.08134e27i			1.58966i
$276$	−6.69201e26	+	1.89349e26i	−0.945272	+	0.267462i
$277$	1.27014e27			1.72415			0.862073	−	0.506784i	$-0.169166\pi$
$277$	1.27014e27			1.72415			0.862073	+	0.506784i	$0.169166\pi$
$278$			1.04932e26i			0.136904i
$279$	−6.20583e26	+	3.81747e26i	−0.778312	+	0.478772i
$280$	−1.16735e25			−0.0140755
$281$			9.81868e26i			1.13837i	0.822209	+	0.569185i	$0.192741\pi$
$281$			9.81868e26i			1.13837i	−0.822209	+	0.569185i	$0.807259\pi$
$282$	1.13603e25	+	4.01500e25i	0.0126663	+	0.0447657i
$283$	4.86330e26			0.521531			0.260765	−	0.965402i	$-0.416025\pi$
$283$	4.86330e26			0.521531			0.260765	+	0.965402i	$0.416025\pi$
$284$			2.33597e26i			0.240972i
$285$	−9.19770e24	+	2.60246e24i	−0.00912822	+	0.00258280i
$286$	4.41504e26			0.421607
$287$		−	6.31767e26i		−	0.580572i
$288$	−4.81847e26	−	7.83310e26i	−0.426179	−	0.692814i
$289$	−1.39270e27			−1.18571
$290$			1.78614e25i			0.0146399i
$291$	2.63686e26	+	9.31926e26i	0.208096	+	0.735459i
$292$	2.26933e26			0.172459
$293$		−	1.66808e27i		−	1.22088i	−0.792063	−	0.610440i	$-0.790993\pi$
$293$		−	1.66808e27i		−	1.22088i	0.792063	−	0.610440i	$-0.209007\pi$
$294$	3.35750e26	−	9.49996e25i	0.236699	−	0.0669732i
$295$	−6.72893e25			−0.0456987
$296$			1.16466e27i			0.762060i
$297$	1.71146e27	−	1.86095e27i	1.07906	−	1.17331i
$298$	−8.18923e26			−0.497582
$299$		−	1.58401e27i		−	0.927631i
$300$	4.34792e26	+	1.53665e27i	0.245441	+	0.867446i
$301$	2.87502e26			0.156462
$302$		−	6.49180e26i		−	0.340635i
$303$	6.41285e26	−	1.81450e26i	0.324475	−	0.0918094i
$304$	2.66770e26			0.130175
$305$		−	8.55514e25i		−	0.0402651i
$306$	−8.59380e26	+	5.28641e26i	−0.390166	+	0.240008i
$307$	−3.02980e27			−1.32706			−0.663532	−	0.748148i	$-0.730943\pi$
$307$	−3.02980e27			−1.32706			−0.663532	+	0.748148i	$0.730943\pi$
$308$			1.54791e27i			0.654164i
$309$	7.86069e25	+	2.77815e26i	0.0320566	+	0.113295i
$310$	−3.78098e25			−0.0148808
$311$			4.31241e27i			1.63816i	0.573681	+	0.819079i	$0.305515\pi$
$311$			4.31241e27i			1.63816i	−0.573681	+	0.819079i	$0.694485\pi$
$312$	1.32143e27	−	3.73896e26i	0.484557	−	0.137104i
$313$	1.34419e27			0.475855			0.237927	−	0.971283i	$-0.423532\pi$
$313$	1.34419e27			0.475855			0.237927	+	0.971283i	$0.423532\pi$
$314$		−	7.33833e26i		−	0.250825i
$315$	−3.78758e25	−	6.15724e25i	−0.0125010	−	0.0203222i
$316$	−4.01103e27			−1.27849
$317$		−	1.59985e27i		−	0.492523i	−0.969203	−	0.246261i	$-0.920798\pi$
$317$		−	1.59985e27i		−	0.492523i	0.969203	−	0.246261i	$-0.0792022\pi$
$318$	4.01478e26	+	1.41892e27i	0.119389	+	0.421947i
$319$	4.98836e27			1.43305
$320$			8.88459e25i			0.0246597i
$321$	−2.26536e27	+	6.40979e26i	−0.607551	+	0.171905i
$322$	−5.89769e26			−0.152851
$323$		−	1.06534e27i		−	0.266847i
$324$	1.68383e27	−	3.33267e27i	0.407665	−	0.806859i
$325$	−3.63729e27			−0.851257
$326$		−	5.94064e26i		−	0.134412i
$327$	−9.97718e26	−	3.52616e27i	−0.218264	−	0.771396i
$328$	3.56666e27			0.754483
$329$		−	3.33194e26i		−	0.0681620i
$330$	1.26247e26	−	3.57211e25i	0.0249785	−	0.00706760i
$331$	7.64020e27			1.46217			0.731083	−	0.682289i	$-0.239015\pi$
$331$	7.64020e27			1.46217			0.731083	+	0.682289i	$0.239015\pi$
$332$		−	5.12749e27i		−	0.949261i
$333$	−6.14301e27	+	3.77882e27i	−1.10026	+	0.676815i
$334$	1.08502e27			0.188030
$335$			4.72857e26i			0.0792934i
$336$	5.49274e26	+	1.94126e27i	0.0891368	+	0.315030i
$337$	1.98642e27			0.311990			0.155995	−	0.987758i	$-0.450142\pi$
$337$	1.98642e27			0.311990			0.155995	+	0.987758i	$0.450142\pi$
$338$		−	5.53020e26i		−	0.0840731i
$339$	−7.17170e27	+	2.02921e27i	−1.05542	+	0.298628i
$340$	4.93033e26			0.0702438
$341$			1.05595e28i			1.45662i
$342$	−2.19372e26	−	3.56620e26i	−0.0293018	−	0.0476342i
$343$	−6.29583e27			−0.814362
$344$			1.62310e27i			0.203331i
$345$	−1.28159e26	−	4.52943e26i	−0.0155503	−	0.0549583i
$346$	−3.32825e27			−0.391182
$347$		−	3.72382e27i		−	0.423998i	−0.977270	−	0.211999i	$-0.932003\pi$
$347$		−	3.72382e27i		−	0.423998i	0.977270	−	0.211999i	$-0.0679974\pi$
$348$	7.08875e27	−	2.00574e27i	0.781984	−	0.221260i
$349$	1.03630e28			1.10765			0.553827	−	0.832632i	$-0.313167\pi$
$349$	1.03630e28			1.10765			0.553827	+	0.832632i	$0.313167\pi$
$350$			1.35426e27i			0.140266i
$351$	6.25963e27	+	5.75680e27i	0.628304	+	0.577834i
$352$	−1.33284e28			−1.29661
$353$			4.70352e27i			0.443508i	0.975103	+	0.221754i	$0.0711782\pi$
$353$			4.70352e27i			0.443508i	−0.975103	+	0.221754i	$0.928822\pi$
$354$	−8.02449e26	−	2.83604e27i	−0.0733469	−	0.259225i
$355$	−1.58108e26			−0.0140101
$356$		−	2.82931e27i		−	0.243070i
$357$	7.75241e27	−	2.19352e27i	0.645783	−	0.182722i
$358$	4.35017e27			0.351393
$359$		−	1.78774e28i		−	1.40045i	−0.713924	−	0.700223i	$-0.753084\pi$
$359$		−	1.78774e28i		−	1.40045i	0.713924	−	0.700223i	$-0.246916\pi$
$360$	3.47609e26	−	2.13829e26i	0.0264097	−	0.0162457i
$361$	−1.31279e28			−0.967421
$362$			1.56463e26i			0.0111845i
$363$	−6.05017e27	−	2.13827e28i	−0.419561	−	1.48282i
$364$	−5.20665e27			−0.350302
$365$			1.53597e26i			0.0100268i
$366$	3.60573e27	−	1.02023e27i	0.228403	−	0.0646260i
$367$	1.37751e28			0.846777			0.423388	−	0.905948i	$-0.360841\pi$
$367$	1.37751e28			0.846777			0.423388	+	0.905948i	$0.360841\pi$
$368$			1.31371e28i			0.783745i
$369$	1.15723e28	+	1.88124e28i	0.670086	+	1.08932i
$370$	−3.74270e26			−0.0210362
$371$		−	1.17752e28i		−	0.642473i
$372$	4.24583e27	+	1.50057e28i	0.224900	+	0.794849i
$373$	−1.54597e28			−0.795065			−0.397532	−	0.917588i	$-0.630133\pi$
$373$	−1.54597e28			−0.795065			−0.397532	+	0.917588i	$0.630133\pi$
$374$			1.46228e28i			0.730201i
$375$	−2.08302e27	+	5.89385e26i	−0.101007	+	0.0285796i
$376$	1.88106e27			0.0885800
$377$			1.67792e28i			0.767390i
$378$	2.14341e27	−	2.33062e27i	0.0952127	−	0.103529i
$379$	−1.43985e28			−0.621277			−0.310639	−	0.950528i	$-0.600543\pi$
$379$	−1.43985e28			−0.621277			−0.310639	+	0.950528i	$0.600543\pi$
$380$			2.04596e26i			0.00857585i
$381$	−2.92726e27	−	1.03456e28i	−0.119203	−	0.421291i
$382$	7.58400e27			0.300055
$383$		−	1.66071e28i		−	0.638423i	−0.947684	−	0.319211i	$-0.896582\pi$
$383$		−	1.66071e28i		−	0.638423i	0.947684	−	0.319211i	$-0.103418\pi$
$384$	−2.46965e28	+	6.98781e27i	−0.922555	+	0.261034i
$385$	−1.04769e27			−0.0380332
$386$		−	4.08546e27i		−	0.144139i
$387$	−8.56109e27	+	5.26629e27i	−0.293568	+	0.180586i
$388$	2.07300e28			0.690955
$389$			3.87537e27i			0.125565i	0.998027	+	0.0627823i	$0.0199974\pi$
$389$			3.87537e27i			0.125565i	−0.998027	+	0.0627823i	$0.980003\pi$
$390$	1.20154e26	+	4.24652e26i	0.00378467	+	0.0133759i
$391$	5.24631e28			1.60661
$392$		−	1.57301e28i		−	0.468367i
$393$	7.65956e26	−	2.16725e26i	0.0221761	−	0.00627467i
$394$	−8.75662e27			−0.246535
$395$		−	2.71483e27i		−	0.0743318i
$396$	−2.83536e28	−	4.60927e28i	−0.755024	−	1.22740i
$397$	1.40537e28			0.363994			0.181997	−	0.983299i	$-0.441744\pi$
$397$	1.40537e28			0.363994			0.181997	+	0.983299i	$0.441744\pi$
$398$		−	1.48841e28i		−	0.374979i
$399$	9.10254e26	+	3.21705e27i	0.0223080	+	0.0788416i
$400$	3.01662e28			0.719218
$401$		−	1.32647e28i		−	0.307687i	−0.988095	−	0.153844i	$-0.950835\pi$
$401$		−	1.32647e28i		−	0.307687i	0.988095	−	0.153844i	$-0.0491652\pi$
$402$	−1.99295e28	+	5.63900e27i	−0.449790	+	0.127267i
$403$	−3.55188e28			−0.780015
$404$		−	1.42649e28i		−	0.304841i
$405$	2.25569e27	+	1.13969e27i	0.0469110	+	0.0237017i
$406$	6.24733e27			0.126447
$407$			1.04526e29i			2.05915i
$408$	1.23836e28	+	4.37665e28i	0.237457	+	0.839228i
$409$	−6.25768e28			−1.16804			−0.584019	−	0.811740i	$-0.698520\pi$
$409$	−6.25768e28			−1.16804			−0.584019	+	0.811740i	$0.698520\pi$
$410$			1.14617e27i			0.0208270i
$411$	3.70032e28	−	1.04700e28i	0.654606	−	0.185219i
$412$	6.17977e27			0.106440
$413$			2.35355e28i			0.394706i
$414$	1.75618e28	−	1.08030e28i	0.286791	−	0.176417i
$415$	3.47050e27			0.0551903
$416$		−	4.48325e28i		−	0.694330i
$417$	7.97540e27	+	2.81869e28i	0.120297	+	0.425158i
$418$	−6.06807e27			−0.0891480
$419$			8.86074e27i			0.126799i	0.997988	+	0.0633995i	$0.0201942\pi$
$419$			8.86074e27i			0.126799i	−0.997988	+	0.0633995i	$0.979806\pi$
$420$	−1.48882e27	+	4.21259e26i	−0.0207540	+	0.00587228i
$421$	−9.59743e28			−1.30332			−0.651661	−	0.758510i	$-0.725928\pi$
$421$	−9.59743e28			−1.30332			−0.651661	+	0.758510i	$0.725928\pi$
$422$			1.34903e28i			0.178478i
$423$	6.10324e27	+	9.92168e27i	0.0786713	+	0.127891i
$424$	6.64772e28			0.834927
$425$		−	1.20468e29i		−	1.47433i
$426$	−1.88550e27	−	6.66378e27i	−0.0224864	−	0.0794722i
$427$	−2.99230e28			−0.347775
$428$			5.03913e28i			0.570787i
$429$	1.18597e29	−	3.35567e28i	1.30931	−	0.370467i
$430$	−5.21595e26			−0.00561281
$431$		−	8.10825e28i		−	0.850505i	−0.905075	−	0.425253i	$-0.860185\pi$
$431$		−	8.10825e28i		−	0.850505i	0.905075	−	0.425253i	$-0.139815\pi$
$432$	−5.19148e28	−	4.77446e28i	−0.530848	−	0.488206i
$433$	8.99261e28			0.896435			0.448217	−	0.893925i	$-0.352059\pi$
$433$	8.99261e28			0.896435			0.448217	+	0.893925i	$0.352059\pi$
$434$			1.32246e28i			0.128527i
$435$	1.35757e27	+	4.79796e27i	0.0128641	+	0.0454647i
$436$	−7.84368e28			−0.724717
$437$			2.17708e28i			0.196146i
$438$	−6.47367e27	+	1.83171e27i	−0.0568768	+	0.0160931i
$439$	−8.56774e28			−0.734102			−0.367051	−	0.930201i	$-0.619633\pi$
$439$	−8.56774e28			−0.734102			−0.367051	+	0.930201i	$0.619633\pi$
$440$		−	5.91474e27i		−	0.0494261i
$441$	8.29690e28	−	5.10377e28i	0.676225	−	0.415975i
$442$	−4.91863e28			−0.391020
$443$			8.02193e28i			0.622068i	0.950399	+	0.311034i	$0.100675\pi$
$443$			8.02193e28i			0.622068i	−0.950399	+	0.311034i	$0.899325\pi$
$444$	4.20285e28	+	1.48538e29i	0.317930	+	1.12364i
$445$	1.91500e27			0.0141321
$446$			9.22215e27i			0.0663970i
$447$	−2.19980e29	+	6.22427e28i	−1.54526	+	0.437226i
$448$	3.10753e28			0.212989
$449$			6.61838e28i			0.442631i	0.975202	+	0.221316i	$0.0710351\pi$
$449$			6.61838e28i			0.442631i	−0.975202	+	0.221316i	$0.928965\pi$
$450$	−2.48064e28	−	4.03264e28i	−0.161893	−	0.263179i
$451$	3.20103e29			2.03868
$452$			1.59529e29i			0.991555i
$453$	−4.93413e28	−	1.74383e29i	−0.299316	−	1.05785i
$454$	1.75610e28			0.103977
$455$		−	3.52407e27i		−	0.0203666i
$456$	−1.81619e28	+	5.13887e27i	−0.102459	+	0.0289904i
$457$	1.17663e28			0.0647981			0.0323991	−	0.999475i	$-0.489685\pi$
$457$	1.17663e28			0.0647981			0.0323991	+	0.999475i	$0.489685\pi$
$458$			5.62922e28i			0.302641i
$459$	−1.90668e29	+	2.07322e29i	−1.00078	+	1.08819i
$460$	−1.00754e28			−0.0516327
$461$		−	3.81875e29i		−	1.91078i	−0.295346	−	0.955390i	$-0.595435\pi$
$461$		−	3.81875e29i		−	1.91078i	0.295346	−	0.955390i	$-0.404565\pi$
$462$	−1.24940e28	−	4.41568e28i	−0.0610437	−	0.215743i
$463$	−3.90433e28			−0.186276			−0.0931378	−	0.995653i	$-0.529690\pi$
$463$	−3.90433e28			−0.186276			−0.0931378	+	0.995653i	$0.529690\pi$
$464$		−	1.39160e29i		−	0.648360i
$465$	−1.01565e28	+	2.87375e27i	−0.0462127	+	0.0130758i
$466$	4.05838e28			0.180346
$467$		−	4.96399e28i		−	0.215449i	−0.994181	−	0.107725i	$-0.965643\pi$
$467$		−	4.96399e28i		−	0.215449i	0.994181	−	0.107725i	$-0.0343565\pi$
$468$	1.55041e29	−	9.53722e28i	0.657267	−	0.404313i
$469$	1.65390e29			0.684868
$470$			6.04491e26i			0.00244519i
$471$	−5.57754e28	−	1.97123e29i	−0.220401	−	0.778946i
$472$	−1.32871e29			−0.512940
$473$			1.45671e29i			0.549417i
$474$	1.14422e29	−	3.23753e28i	0.421645	−	0.119303i
$475$	4.99912e28			0.179997
$476$		−	1.72446e29i		−	0.606705i
$477$	2.15691e29	+	3.50636e29i	0.741531	+	1.20546i
$478$	9.82504e28			0.330086
$479$			3.94959e29i			1.29677i	0.761314	+	0.648383i	$0.224555\pi$
$479$			3.94959e29i			1.29677i	−0.761314	+	0.648383i	$0.775445\pi$
$480$	−3.62730e27	−	1.28197e28i	−0.0116394	−	0.0411362i
$481$	−3.51593e29			−1.10267
$482$		−	1.01259e28i		−	0.0310395i
$483$	−1.58424e29	+	4.48257e28i	−0.474682	+	0.134310i
$484$	−4.75642e29			−1.39310
$485$			1.40309e28i			0.0401723i
$486$	−2.11344e28	+	1.08662e29i	−0.0591548	+	0.304143i
$487$	2.85794e29			0.782051			0.391026	−	0.920380i	$-0.372120\pi$
$487$	2.85794e29			0.782051			0.391026	+	0.920380i	$0.372120\pi$
$488$		−	1.68931e29i		−	0.451952i
$489$	−4.51521e28	−	1.59578e29i	−0.118108	−	0.417422i
$490$	5.05499e27			0.0129290
$491$			5.21641e29i			1.30459i	0.757963	+	0.652297i	$0.226195\pi$
$491$			5.21641e29i			1.30459i	−0.757963	+	0.652297i	$0.773805\pi$
$492$	4.54886e29	−	1.28709e29i	1.11246	−	0.314769i
$493$	−5.55734e29			−1.32908
$494$		−	2.04110e28i		−	0.0477384i
$495$	3.11975e28	−	1.91909e28i	0.0713612	−	0.0438973i
$496$	2.94579e29			0.659027
$497$			5.53009e28i			0.121007i
$498$	4.13869e28	+	1.46271e29i	0.0885810	+	0.313065i
$499$	3.17671e29			0.665076			0.332538	−	0.943090i	$-0.392095\pi$
$499$	3.17671e29			0.665076			0.332538	+	0.943090i	$0.392095\pi$
$500$			4.63352e28i			0.0948945i
$501$	2.91460e29	−	8.24678e28i	0.583934	−	0.165223i
$502$	−2.97251e29			−0.582616
$503$		−	6.15651e29i		−	1.18056i	−0.807200	−	0.590278i	$-0.799018\pi$
$503$		−	6.15651e29i		−	1.18056i	0.807200	−	0.590278i	$-0.200982\pi$
$504$	−7.47901e28	−	1.21582e29i	−0.140316	−	0.228104i
$505$	9.65506e27			0.0177235
$506$		−	2.98824e29i		−	0.536734i
$507$	−4.20326e28	−	1.48553e29i	−0.0738752	−	0.261092i
$508$	−2.30130e29			−0.395797
$509$		−	8.72791e29i		−	1.46898i	−0.678622	−	0.734488i	$-0.737423\pi$
$509$		−	8.72791e29i		−	1.46898i	0.678622	−	0.734488i	$-0.262577\pi$
$510$	−1.40647e28	+	3.97956e27i	−0.0231663	+	0.00655485i
$511$	5.37232e28			0.0866028
$512$			6.41496e29i			1.01210i
$513$	−8.60330e28	−	7.91221e28i	−0.132854	−	0.122182i
$514$	2.56233e29			0.387295
$515$			4.18272e27i			0.00618842i
$516$	5.85723e28	+	2.07008e29i	0.0848292	+	0.299806i
$517$	1.68822e29			0.239350
$518$			1.30907e29i			0.181692i
$519$	−8.94036e29	+	2.52965e29i	−1.21483	+	0.343732i
$520$	1.98953e28			0.0264675
$521$			1.40880e30i			1.83500i	0.397741	+	0.917498i	$0.369794\pi$
$521$			1.40880e30i			1.83500i	−0.397741	+	0.917498i	$0.630206\pi$
$522$	−1.86030e29	+	1.14435e29i	−0.237250	+	0.145943i
$523$	1.27849e30			1.59654			0.798271	−	0.602299i	$-0.205748\pi$
$523$	1.27849e30			1.59654			0.798271	+	0.602299i	$0.205748\pi$
$524$		−	1.70381e28i		−	0.0208342i
$525$	1.02931e29	+	3.63782e29i	0.123252	+	0.435600i
$526$	−6.88567e28			−0.0807427
$527$		−	1.17640e30i		−	1.35095i
$528$	−9.83596e29	+	2.78306e29i	−1.10623	+	0.313003i
$529$	−1.64262e29			−0.180936
$530$			2.13629e28i			0.0230476i
$531$	−4.31109e29	−	7.00829e29i	−0.455562	−	0.740580i
$532$	7.15607e28			0.0740707
$533$			1.07672e30i			1.09170i
$534$	2.28370e28	+	8.07113e28i	0.0226822	+	0.0801642i
$535$	−3.41069e28			−0.0331857
$536$			9.33712e29i			0.890021i
$537$	1.16855e30	−	3.30637e29i	1.09126	−	0.308770i
$538$	3.69609e29			0.338172
$539$		−	1.41176e30i		−	1.26557i
$540$	3.66171e28	−	3.98154e28i	0.0321627	−	0.0349719i
$541$	−1.57318e30			−1.35396			−0.676982	−	0.735999i	$-0.736713\pi$
$541$	−1.57318e30			−1.35396			−0.676982	+	0.735999i	$0.736713\pi$
$542$		−	7.16429e29i		−	0.604201i
$543$	1.18921e28	+	4.20293e28i	0.00982787	+	0.0347339i
$544$	1.48487e30			1.20254
$545$		−	5.30892e28i		−	0.0421352i
$546$	1.48529e29	−	4.20259e28i	0.115529	−	0.0326887i
$547$	−9.42184e28			−0.0718249			−0.0359125	−	0.999355i	$-0.511434\pi$
$547$	−9.42184e28			−0.0718249			−0.0359125	+	0.999355i	$0.511434\pi$
$548$		−	8.23109e29i		−	0.614994i
$549$	8.91032e29	−	5.48111e29i	0.652525	−	0.401396i
$550$	−6.86174e29			−0.492544
$551$		−	2.30615e29i		−	0.162263i
$552$	−2.53065e29	−	8.94389e29i	−0.174543	−	0.616874i
$553$	−9.49556e29			−0.642013
$554$			8.05976e29i			0.534213i
$555$	−1.00537e29	+	2.84466e28i	−0.0653284	+	0.0184845i
$556$	6.26995e29			0.399431
$557$			1.89002e29i			0.118048i	0.998257	+	0.0590242i	$0.0187989\pi$
$557$			1.89002e29i			0.118048i	−0.998257	+	0.0590242i	$0.981201\pi$
$558$	−2.42240e29	−	3.93795e29i	−0.148344	−	0.241154i
$559$	−4.89991e29			−0.294210
$560$			2.92272e28i			0.0172076i
$561$	1.11141e30	+	3.92799e30i	0.641629	+	2.26766i
$562$	−6.23051e29			−0.352715
$563$			9.85747e29i			0.547234i	0.961839	+	0.273617i	$0.0882201\pi$
$563$			9.85747e29i			0.547234i	−0.961839	+	0.273617i	$0.911780\pi$
$564$	2.39907e29	−	6.78809e28i	0.130609	−	0.0369554i
$565$	−1.07976e29			−0.0576492
$566$			3.08604e29i			0.161592i
$567$	3.98624e29	−	7.88964e29i	0.204715	−	0.405176i
$568$	−3.12203e29			−0.157255
$569$			1.47077e30i			0.726623i	0.931668	+	0.363311i	$0.118354\pi$
$569$			1.47077e30i			0.726623i	−0.931668	+	0.363311i	$0.881646\pi$
$570$	−1.65141e27	−	5.83646e27i	−0.000800261	−	0.00282831i
$571$	−1.14696e30			−0.545194			−0.272597	−	0.962128i	$-0.587883\pi$
$571$	−1.14696e30			−0.545194			−0.272597	+	0.962128i	$0.587883\pi$
$572$		−	2.63810e30i		−	1.23008i
$573$	2.03722e30	−	5.76426e29i	0.931831	−	0.263659i
$574$	4.00892e29			0.179886
$575$			2.46183e30i			1.08371i
$576$	−9.25344e29	+	5.69218e29i	−0.399628	+	0.245828i
$577$	−4.46369e30			−1.89130			−0.945650	−	0.325187i	$-0.894573\pi$
$577$	−4.46369e30			−1.89130			−0.945650	+	0.325187i	$0.894573\pi$
$578$		−	8.83744e29i		−	0.367384i
$579$	−3.10517e29	−	1.09744e30i	−0.126655	−	0.447627i
$580$	1.06727e29			0.0427136
$581$		−	1.21386e30i		−	0.476685i
$582$	−5.91360e29	+	1.67324e29i	−0.227876	+	0.0644769i
$583$	5.96625e30			2.25604
$584$			3.03296e29i			0.112545i
$585$	6.45518e28	+	1.04938e29i	0.0235068	+	0.0382136i
$586$	1.05849e30			0.378280
$587$		−	3.37868e30i		−	1.18503i	−0.805560	−	0.592514i	$-0.798136\pi$
$587$		−	3.37868e30i		−	1.18503i	0.805560	−	0.592514i	$-0.201864\pi$
$588$	−5.67647e29	−	2.00620e30i	−0.195402	−	0.690594i
$589$	4.88174e29			0.164933
$590$		−	4.26989e28i		−	0.0141594i
$591$	−2.35221e30	+	6.65551e29i	−0.765621	+	0.216630i
$592$	2.91597e30			0.931631
$593$		−	2.00698e30i		−	0.629420i	−0.949188	−	0.314710i	$-0.898093\pi$
$593$		−	2.00698e30i		−	0.629420i	0.949188	−	0.314710i	$-0.101907\pi$
$594$	1.18088e30	+	1.08602e30i	0.363542	+	0.334339i
$595$	1.16719e29			0.0352740
$596$			4.89328e30i			1.45175i
$597$	−1.13127e30	−	3.99817e30i	−0.329495	−	1.16451i
$598$	1.00514e30			0.287419
$599$			1.49421e30i			0.419485i	0.977757	+	0.209743i	$0.0672626\pi$
$599$			1.49421e30i			0.419485i	−0.977757	+	0.209743i	$0.932737\pi$
$600$	−2.05374e30	+	5.81100e29i	−0.566085	+	0.160172i
$601$	−2.18938e30			−0.592518			−0.296259	−	0.955108i	$-0.595739\pi$
$601$	−2.18938e30			−0.592518			−0.296259	+	0.955108i	$0.595739\pi$
$602$			1.82436e29i			0.0484786i
$603$	−4.92488e30	+	3.02950e30i	−1.28501	+	0.790462i
$604$	−3.87902e30			−0.993839
$605$		−	3.21934e29i		−	0.0809948i
$606$	1.15140e29	+	4.06931e29i	0.0284464	+	0.100536i
$607$	6.64897e30			1.61316			0.806582	−	0.591122i	$-0.201315\pi$
$607$	6.64897e30			1.61316			0.806582	+	0.591122i	$0.201315\pi$
$608$			6.16182e29i			0.146815i
$609$	1.67816e30	−	4.74832e29i	0.392685	−	0.111109i
$610$	5.42872e28			0.0124758
$611$			5.67863e29i			0.128171i
$612$	3.15877e30	+	5.13502e30i	0.700248	+	1.13835i
$613$	−1.47531e30			−0.321231			−0.160615	−	0.987017i	$-0.551348\pi$
$613$	−1.47531e30			−0.321231			−0.160615	+	0.987017i	$0.551348\pi$
$614$		−	1.92258e30i		−	0.411180i
$615$	8.71153e28	+	3.07885e29i	0.0183007	+	0.0646789i
$616$	−2.06878e30			−0.426900
$617$			3.74802e30i			0.759740i	0.925040	+	0.379870i	$0.124031\pi$
$617$			3.74802e30i			0.759740i	−0.925040	+	0.379870i	$0.875969\pi$
$618$	−1.76289e29	+	4.98805e28i	−0.0351036	+	0.00993248i
$619$	1.70965e29			0.0334433			0.0167217	−	0.999860i	$-0.494677\pi$
$619$	1.70965e29			0.0334433			0.0167217	+	0.999860i	$0.494677\pi$
$620$			2.25923e29i			0.0434163i
$621$	3.89638e30	−	4.23671e30i	0.735621	−	0.799874i
$622$	−2.73647e30			−0.507570
$623$		−	6.69801e29i		−	0.122061i
$624$	−9.36129e29	−	3.30849e30i	−0.167612	−	0.592379i
$625$	5.63728e30			0.991720
$626$			8.52967e29i			0.147440i
$627$	−1.63001e30	+	4.61207e29i	−0.276852	+	0.0783345i
$628$	−4.38485e30			−0.731810
$629$		−	1.16449e31i		−	1.90976i
$630$	3.90712e28	−	2.40343e28i	0.00629666	−	0.00387334i
$631$	−6.59210e30			−1.04400			−0.522000	−	0.852945i	$-0.674814\pi$
$631$	−6.59210e30			−1.04400			−0.522000	+	0.852945i	$0.674814\pi$
$632$		−	5.36075e30i		−	0.834329i
$633$	1.02534e30	+	3.62377e30i	0.156829	+	0.554268i
$634$	1.01519e30			0.152604
$635$		−	1.55762e29i		−	0.0230117i
$636$	8.47839e30	−	2.39894e30i	1.23108	−	0.348330i
$637$	4.74870e30			0.677705
$638$			3.16539e30i			0.444018i
$639$	−1.01297e30	−	1.64672e30i	−0.139665	−	0.227044i
$640$	−3.71826e29			−0.0503918
$641$			6.27180e30i			0.835514i	0.908559	+	0.417757i	$0.137184\pi$
$641$			6.27180e30i			0.835514i	−0.908559	+	0.417757i	$0.862816\pi$
$642$	−4.06737e29	−	1.43750e30i	−0.0532634	−	0.188245i
$643$	−2.53701e30			−0.326589			−0.163295	−	0.986577i	$-0.552212\pi$
$643$	−2.53701e30			−0.326589			−0.163295	+	0.986577i	$0.552212\pi$
$644$			3.52402e30i			0.445958i
$645$	−1.40111e29	+	3.96441e28i	−0.0174308	+	0.00493199i
$646$	6.76021e29			0.0826804
$647$			1.29877e31i			1.56165i	0.624750	+	0.780825i	$0.285201\pi$
$647$			1.29877e31i			1.56165i	−0.624750	+	0.780825i	$0.714799\pi$
$648$	4.45412e30	+	2.25044e30i	0.526547	+	0.266037i
$649$	−1.19250e31			−1.38601
$650$		−	2.30806e30i		−	0.263755i
$651$	1.00514e30	+	3.55240e30i	0.112937	+	0.399145i
$652$	−3.54969e30			−0.392163
$653$		−	6.47158e30i		−	0.703016i	−0.936185	−	0.351508i	$-0.885669\pi$
$653$		−	6.47158e30i		−	0.703016i	0.936185	−	0.351508i	$-0.114331\pi$
$654$	2.23755e30	−	6.33109e29i	0.239011	−	0.0676274i
$655$	1.15321e28			0.00121130
$656$		−	8.92990e30i		−	0.922368i
$657$	−1.59974e30	+	9.84069e29i	−0.162492	+	0.0999554i
$658$	2.11430e29			0.0211194
$659$			1.28556e31i			1.26285i	0.775437	+	0.631426i	$0.217530\pi$
$659$			1.28556e31i			1.26285i	−0.775437	+	0.631426i	$0.782470\pi$
$660$	−2.13443e29	−	7.54356e29i	−0.0206205	−	0.0728775i
$661$	5.17697e30			0.491880			0.245940	−	0.969285i	$-0.420903\pi$
$661$	5.17697e30			0.491880			0.245940	+	0.969285i	$0.420903\pi$
$662$			4.84814e30i			0.453041i
$663$	−1.32125e31	+	3.73843e30i	−1.21432	+	0.343590i
$664$	6.85290e30			0.619477
$665$			4.84352e28i			0.00430649i
$666$	−2.39788e30	−	3.89809e30i	−0.209706	−	0.340906i
$667$	1.13567e31			0.976939
$668$		−	6.48330e30i		−	0.548599i
$669$	7.00934e29	+	2.47726e30i	0.0583432	+	0.206198i
$670$	−3.00055e29			−0.0245684
$671$		−	1.51614e31i		−	1.22121i
$672$	−4.48390e30	+	1.26871e30i	−0.355299	+	0.100531i
$673$	1.47973e31			1.15350			0.576749	−	0.816921i	$-0.304321\pi$
$673$	1.47973e31			1.15350			0.576749	+	0.816921i	$0.304321\pi$
$674$			1.26049e30i			0.0966677i
$675$	−9.72855e30	−	8.94707e30i	−0.734018	−	0.675056i
$676$	−3.30444e30			−0.245293
$677$		−	1.40668e31i		−	1.02735i	−0.857984	−	0.513677i	$-0.828283\pi$
$677$		−	1.40668e31i		−	1.02735i	0.857984	−	0.513677i	$-0.171717\pi$
$678$	−1.28765e30	−	4.55085e30i	−0.0925276	−	0.327014i
$679$	4.90753e30			0.346973
$680$			6.58939e29i			0.0458403i
$681$	4.71726e30	−	1.33473e30i	0.322902	−	0.0913644i
$682$	−6.70062e30			−0.451323
$683$			7.69466e29i			0.0509990i	0.999675	+	0.0254995i	$0.00811762\pi$
$683$			7.69466e29i			0.0509990i	−0.999675	+	0.0254995i	$0.991882\pi$
$684$	−2.13090e30	+	1.31080e30i	−0.138978	+	0.0854911i
$685$	5.57114e29			0.0357559
$686$		−	3.99506e30i		−	0.252324i
$687$	4.27851e30	+	1.51212e31i	0.265931	+	0.939861i
$688$	4.06379e30			0.248575
$689$			2.00685e31i			1.20810i
$690$	2.87418e29	−	8.13241e28i	0.0170284	−	0.00481814i
$691$	4.11565e30			0.239982			0.119991	−	0.992775i	$-0.461713\pi$
$691$	4.11565e30			0.239982			0.119991	+	0.992775i	$0.461713\pi$
$692$			1.98871e31i			1.14131i
$693$	−6.71232e30	−	1.09118e31i	−0.379146	−	0.616356i
$694$	2.36297e30			0.131372
$695$			4.24376e29i			0.0232230i
$696$	2.68068e30	+	9.47412e30i	0.144392	+	0.510314i
$697$	−3.56615e31			−1.89077
$698$			6.57588e30i			0.343198i
$699$	1.09016e31	−	3.08459e30i	0.560071	−	0.158471i
$700$	8.09204e30			0.409241
$701$		−	2.27239e31i		−	1.13132i	−0.824640	−	0.565658i	$-0.808622\pi$
$701$		−	2.27239e31i		−	1.13132i	0.824640	−	0.565658i	$-0.191378\pi$
$702$	−3.65302e30	+	3.97209e30i	−0.179037	+	0.194675i
$703$	4.83233e30			0.233157
$704$			1.57452e31i			0.747910i
$705$	4.59446e28	+	1.62379e29i	0.00214859	+	0.00759362i
$706$	−2.98465e30			−0.137417
$707$		−	3.37701e30i		−	0.153080i
$708$	−1.69461e31	+	4.79485e30i	−0.756316	+	0.213998i
$709$	−1.72067e31			−0.756117			−0.378058	−	0.925782i	$-0.623408\pi$
$709$	−1.72067e31			−0.756117			−0.378058	+	0.925782i	$0.623408\pi$
$710$		−	1.00329e29i		−	0.00434093i
$711$	2.82754e31	−	1.73934e31i	1.20460	−	0.741000i
$712$	3.78138e30			0.158625
$713$			2.40403e31i			0.993012i
$714$	1.39191e30	+	4.91934e30i	0.0566151	+	0.200091i
$715$	1.78557e30			0.0715174
$716$		−	2.59934e31i		−	1.02523i
$717$	2.63921e31	−	7.46757e30i	1.02509	−	0.290047i
$718$	1.13442e31			0.433917
$719$		−	1.67074e31i		−	0.629350i	−0.949199	−	0.314675i	$-0.898104\pi$
$719$		−	1.67074e31i		−	0.629350i	0.949199	−	0.314675i	$-0.101896\pi$
$720$	−5.35366e29	−	8.70313e29i	−0.0198607	−	0.0322863i
$721$	1.46298e30			0.0534502
$722$		−	8.33039e30i		−	0.299748i
$723$	−7.69621e29	−	2.72002e30i	−0.0272744	−	0.0963940i
$724$	9.34909e29			0.0326321
$725$		−	2.60778e31i		−	0.896505i
$726$	1.35685e31	−	3.83918e30i	0.459441	−	0.129998i
$727$	−5.89636e31			−1.96655			−0.983276	−	0.182121i	$-0.941704\pi$
$727$	−5.89636e31			−1.96655			−0.983276	+	0.182121i	$0.941704\pi$
$728$		−	6.95869e30i		−	0.228603i
$729$	2.58176e30	+	3.07951e31i	0.0835435	+	0.996504i
$730$	−9.74663e28			−0.00310673
$731$		−	1.62287e31i		−	0.509557i
$732$	−6.09615e30	−	2.15452e31i	−0.188553	−	0.666390i
$733$	2.16750e31			0.660411			0.330206	−	0.943909i	$-0.392882\pi$
$733$	2.16750e31			0.660411			0.330206	+	0.943909i	$0.392882\pi$
$734$			8.74110e30i			0.262367i
$735$	1.35788e30	−	3.84207e29i	0.0401513	−	0.0113607i
$736$	−3.03440e31			−0.883929
$737$			8.37995e31i			2.40491i
$738$	−1.19376e31	+	7.34329e30i	−0.337517	+	0.207621i
$739$	2.38405e31			0.664090			0.332045	−	0.943263i	$-0.392261\pi$
$739$	2.38405e31			0.664090			0.332045	+	0.943263i	$0.392261\pi$
$740$			2.23636e30i			0.0613753i
$741$	−1.55135e30	−	5.48282e30i	−0.0419478	−	0.148253i
$742$	7.47203e30			0.199065
$743$		−	3.19425e30i		−	0.0838479i	−0.999121	−	0.0419239i	$-0.986651\pi$
$743$		−	3.19425e30i		−	0.0838479i	0.999121	−	0.0419239i	$-0.0133487\pi$
$744$	−2.00552e31	+	5.67456e30i	−0.518710	+	0.146767i
$745$	−3.31197e30			−0.0844050
$746$		−	9.81002e30i		−	0.246345i
$747$	2.22348e31	+	3.61458e31i	0.550182	+	0.894398i
$748$	8.73750e31			2.13044
$749$			1.19294e31i			0.286629i
$750$	−3.73998e29	−	1.32180e30i	−0.00885515	−	0.0312961i
$751$	−3.25961e31			−0.760548			−0.380274	−	0.924874i	$-0.624170\pi$
$751$	−3.25961e31			−0.760548			−0.380274	+	0.924874i	$0.624170\pi$
$752$		−	4.70963e30i		−	0.108291i
$753$	−7.98477e31	+	2.25927e31i	−1.80933	+	0.511945i
$754$	−1.06473e31			−0.237770
$755$		−	2.62548e30i		−	0.0577820i
$756$	−1.39261e31	−	1.28074e31i	−0.302057	−	0.277793i
$757$	4.87520e31			1.04217			0.521084	−	0.853506i	$-0.325528\pi$
$757$	4.87520e31			1.04217			0.521084	+	0.853506i	$0.325528\pi$
$758$		−	9.13665e30i		−	0.192498i
$759$	−2.27122e31	−	8.02702e31i	−0.471629	−	1.66684i
$760$	−2.73443e29			−0.00559650
$761$			4.94746e31i			0.998048i	0.866588	+	0.499024i	$0.166308\pi$
$761$			4.94746e31i			0.998048i	−0.866588	+	0.499024i	$0.833692\pi$
$762$	6.56488e30	−	1.85751e30i	0.130534	−	0.0369341i
$763$	−1.85688e31			−0.363927
$764$		−	4.53164e31i		−	0.875444i
$765$	−3.47559e30	+	2.13798e30i	−0.0661840	+	0.0407126i
$766$	1.05382e31			0.197810
$767$		−	4.01117e31i		−	0.742201i
$768$	2.56908e30	+	9.07970e30i	0.0468601	+	0.165614i
$769$	2.18341e31			0.392596			0.196298	−	0.980544i	$-0.437108\pi$
$769$	2.18341e31			0.392596			0.196298	+	0.980544i	$0.437108\pi$
$770$		−	6.64816e29i		−	0.0117843i
$771$	6.88296e31	−	1.94752e31i	1.20276	−	0.340316i
$772$	−2.44117e31			−0.420540
$773$		−	5.73569e31i		−	0.974117i	−0.873369	−	0.487059i	$-0.838070\pi$
$773$		−	5.73569e31i		−	0.974117i	0.873369	−	0.487059i	$-0.161930\pi$
$774$	−3.34176e30	−	5.43250e30i	−0.0559531	−	0.0909597i
$775$	5.52025e31			0.911255
$776$			2.77056e31i			0.450909i
$777$	9.94966e30	+	3.51644e31i	0.159653	+	0.564250i
$778$	−2.45914e30			−0.0389052
$779$		−	1.47986e31i		−	0.230838i
$780$	2.53741e30	−	7.17952e29i	0.0390256	−	0.0110422i
$781$	−2.80198e31			−0.424917
$782$			3.32908e31i			0.497795i
$783$	−4.12738e31	+	4.48789e31i	−0.608548	+	0.661702i
$784$	−3.93838e31			−0.572586
$785$		−	2.96784e30i		−	0.0425476i
$786$	1.37524e29	+	4.86042e29i	0.00194416	+	0.00687110i
$787$	−5.02293e31			−0.700221			−0.350111	−	0.936708i	$-0.613856\pi$
$787$	−5.02293e31			−0.700221			−0.350111	+	0.936708i	$0.613856\pi$
$788$			5.23231e31i			0.719291i
$789$	−1.84963e31	+	5.23349e30i	−0.250749	+	0.0709487i
$790$	1.72271e30			0.0230311
$791$			3.77663e31i			0.497924i
$792$	6.16030e31	−	3.78946e31i	0.800986	−	0.492720i
$793$	5.09979e31			0.653954
$794$			8.91785e30i			0.112781i
$795$	1.62370e30	+	5.73852e30i	0.0202520	+	0.0715751i
$796$	−8.89361e31			−1.09404
$797$		−	6.01654e31i		−	0.729971i	−0.931013	−	0.364985i	$-0.881074\pi$
$797$		−	6.01654e31i		−	0.729971i	0.931013	−	0.364985i	$-0.118926\pi$
$798$	−2.04140e30	+	5.77608e29i	−0.0244284	+	0.00691196i
$799$	−1.88079e31			−0.221986
$800$			6.96775e31i			0.811153i
$801$	1.22690e31	+	1.99450e31i	0.140881	+	0.229021i
$802$	8.41720e30			0.0953344
$803$			2.72204e31i			0.304105i
$804$	3.36945e31	+	1.19084e32i	0.371315	+	1.31231i
$805$	−2.38520e30			−0.0259281
$806$		−	2.25387e31i		−	0.241682i
$807$	9.92848e31	−	2.80923e31i	1.05020	−	0.297152i
$808$	1.90650e31			0.198936
$809$		−	7.06646e31i		−	0.727391i	−0.931518	−	0.363696i	$-0.881515\pi$
$809$		−	7.06646e31i		−	0.727391i	0.931518	−	0.363696i	$-0.118485\pi$
$810$	−7.23195e29	+	1.43136e30i	−0.00734379	+	0.0145350i
$811$	−9.20570e31			−0.922205			−0.461102	−	0.887347i	$-0.652546\pi$
$811$	−9.20570e31			−0.922205			−0.461102	+	0.887347i	$0.652546\pi$
$812$		−	3.73294e31i		−	0.368923i
$813$	−5.44526e31	−	1.92448e32i	−0.530912	−	1.87636i
$814$	−6.63279e31			−0.638011
$815$		−	2.40257e30i		−	0.0228004i
$816$	1.09579e32	−	3.10050e31i	1.02597	−	0.290295i
$817$	6.73449e30			0.0622102
$818$		−	3.97085e31i		−	0.361907i
$819$	3.67038e31	−	2.25780e31i	0.330056	−	0.203031i
$820$	6.84867e30			0.0607651
$821$			5.43653e30i			0.0475934i	0.999717	+	0.0237967i	$0.00757544\pi$
$821$			5.43653e30i			0.0475934i	−0.999717	+	0.0237967i	$0.992425\pi$
$822$	6.64379e30	+	2.34807e31i	0.0573886	+	0.202824i
$823$	1.44520e32			1.23177			0.615885	−	0.787836i	$-0.288799\pi$
$823$	1.44520e32			1.23177			0.615885	+	0.787836i	$0.288799\pi$
$824$			8.25927e30i			0.0694612i
$825$	−1.84321e32	+	5.21530e31i	−1.52961	+	0.432799i
$826$	−1.49346e31			−0.122296
$827$		−	8.76228e31i		−	0.708038i	−0.935238	−	0.354019i	$-0.884815\pi$
$827$		−	8.76228e31i		−	0.708038i	0.935238	−	0.354019i	$-0.115185\pi$
$828$	−6.45509e31	−	1.04937e32i	−0.514717	−	0.836745i
$829$	1.45217e32			1.14266			0.571330	−	0.820720i	$-0.306427\pi$
$829$	1.45217e32			1.14266			0.571330	+	0.820720i	$0.306427\pi$
$830$			2.20223e30i			0.0171003i
$831$	6.12586e31	+	2.16502e32i	0.469414	+	1.65902i
$832$	−5.29617e31			−0.400503
$833$			1.57279e32i			1.17375i
$834$	−1.78862e31	+	5.06084e30i	−0.131732	+	0.0372732i
$835$	4.38816e30			0.0318957
$836$			3.62583e31i			0.260099i
$837$	−9.50013e31	−	8.73700e31i	−0.672588	−	0.618560i
$838$	−5.62264e30			−0.0392877
$839$			1.19979e32i			0.827413i	0.910410	+	0.413706i	$0.135766\pi$
$839$			1.19979e32i			0.827413i	−0.910410	+	0.413706i	$0.864234\pi$
$840$	−5.63013e29	−	1.98982e30i	−0.00383218	−	0.0135438i
$841$	2.85528e31			0.191819
$842$		−	6.09011e31i		−	0.403824i
$843$	−1.67364e32	+	4.73553e31i	−1.09537	+	0.309931i
$844$	8.06080e31			0.520729
$845$		−	2.23658e30i		−	0.0142614i
$846$	−6.29587e30	+	3.87285e30i	−0.0396261	+	0.0243757i
$847$	−1.12602e32			−0.699563
$848$		−	1.66440e32i		−	1.02071i
$849$	2.34556e31	+	8.28974e31i	0.141991	+	0.501829i
$850$	7.64441e31			0.456810
$851$			2.37969e32i			1.40377i
$852$	−3.98178e31	+	1.12663e31i	−0.231869	+	0.0656066i
$853$	2.32758e32			1.33803			0.669013	−	0.743250i	$-0.266717\pi$
$853$	2.32758e32			1.33803			0.669013	+	0.743250i	$0.266717\pi$
$854$		−	1.89878e31i		−	0.107755i
$855$	−8.87207e29	−	1.44228e30i	−0.00497047	−	0.00808020i
$856$	−6.73480e31			−0.372489
$857$		−	1.63518e32i		−	0.892844i	−0.894823	−	0.446422i	$-0.852698\pi$
$857$		−	1.63518e32i		−	0.892844i	0.894823	−	0.446422i	$-0.147302\pi$
$858$	2.12936e31	+	7.52565e31i	0.114786	+	0.405680i
$859$	−1.18107e32			−0.628565			−0.314283	−	0.949329i	$-0.601764\pi$
$859$	−1.18107e32			−0.628565			−0.314283	+	0.949329i	$0.601764\pi$
$860$			3.11667e30i			0.0163760i
$861$	1.07688e32	−	3.04700e31i	0.558640	−	0.158066i
$862$	5.14514e31			0.263522
$863$			1.18236e32i			0.597904i	0.954268	+	0.298952i	$0.0966371\pi$
$863$			1.18236e32i			0.597904i	−0.954268	+	0.298952i	$0.903363\pi$
$864$	1.10280e32	−	1.19912e32i	0.550611	−	0.598704i
$865$	−1.34604e31			−0.0663563
$866$			5.70632e31i			0.277753i
$867$	−6.71694e31	−	2.37392e32i	−0.322821	−	1.14092i
$868$	7.90204e31			0.374992
$869$		−	4.81120e32i		−	2.25443i
$870$	−3.04458e30	+	8.61454e29i	−0.0140869	+	0.00398584i
$871$	−2.81874e32			−1.28782
$872$		−	1.04831e32i		−	0.472942i
$873$	−1.46134e32	+	8.98932e31i	−0.651020	+	0.400470i
$874$	−1.38148e31			−0.0607742
$875$			1.09692e31i			0.0476527i
$876$	1.09449e31	+	3.86819e31i	0.0469535	+	0.165944i
$877$	2.05585e32			0.870955			0.435477	−	0.900200i	$-0.356580\pi$
$877$	2.05585e32			0.870955			0.435477	+	0.900200i	$0.356580\pi$
$878$		−	5.43671e31i		−	0.227456i
$879$	2.84333e32	−	8.04511e31i	1.17476	−	0.332395i
$880$	−1.48088e31			−0.0604243
$881$			3.13678e32i			1.26401i	0.774966	+	0.632003i	$0.217767\pi$
$881$			3.13678e32i			1.26401i	−0.774966	+	0.632003i	$0.782233\pi$
$882$	3.23863e31	+	5.26485e31i	0.128886	+	0.209523i
$883$	−1.81247e32			−0.712365			−0.356182	−	0.934416i	$-0.615922\pi$
$883$	−1.81247e32			−0.712365			−0.356182	+	0.934416i	$0.615922\pi$
$884$			2.93901e32i			1.14084i
$885$	−3.24535e30	−	1.14698e31i	−0.0124419	−	0.0439724i
$886$	−5.09037e31			−0.192743
$887$			1.06780e32i			0.399327i	0.979865	+	0.199664i	$0.0639849\pi$
$887$			1.06780e32i			0.399327i	−0.979865	+	0.199664i	$0.936015\pi$
$888$	−1.98522e32	+	5.61711e31i	−0.733272	+	0.207477i
$889$	−5.44802e31			−0.198755
$890$			1.21517e30i			0.00437873i
$891$	3.99752e32	+	2.01974e32i	1.42277	+	0.718855i
$892$	5.51048e31			0.193721
$893$		−	7.80477e30i		−	0.0271016i
$894$	−3.94965e31	−	1.39590e32i	−0.135471	−	0.478785i
$895$	1.75934e31			0.0596070
$896$			1.30052e32i			0.435240i
$897$	2.70003e32	−	7.63965e31i	0.892589	−	0.252555i
$898$	−4.19974e31			−0.137146
$899$		−	2.54655e32i		−	0.821477i
$900$	−2.40961e32	+	1.48225e32i	−0.767854	+	0.472339i
$901$	−6.64677e32			−2.09237
$902$			2.03124e32i			0.631667i
$903$	1.38662e31	+	4.90062e31i	0.0425982	+	0.150552i
$904$	−2.13211e32			−0.647077
$905$			6.32785e29i			0.00189724i
$906$	1.10656e32	−	3.13098e31i	0.327767	−	0.0927408i
$907$	2.64776e31			0.0774815			0.0387407	−	0.999249i	$-0.487665\pi$
$907$	2.64776e31			0.0774815			0.0387407	+	0.999249i	$0.487665\pi$
$908$		−	1.04932e32i		−	0.303363i
$909$	6.18580e31	+	1.00559e32i	0.176682	+	0.287222i
$910$	2.23622e30			0.00631044
$911$		−	4.05859e32i		−	1.13155i	−0.824560	−	0.565774i	$-0.808577\pi$
$911$		−	4.05859e32i		−	1.13155i	0.824560	−	0.565774i	$-0.191423\pi$
$912$	1.28663e31	+	4.54723e31i	0.0354413	+	0.125257i
$913$	6.15039e32			1.67388
$914$			7.46640e30i			0.0200772i
$915$	1.45827e31	−	4.12613e30i	0.0387441	−	0.0109625i
$916$	3.36360e32			0.882988
$917$		−	4.03353e30i		−	0.0104622i
$918$	−1.31557e32	−	1.20989e32i	−0.337167	−	0.310083i
$919$	−2.56221e32			−0.648851			−0.324425	−	0.945911i	$-0.605171\pi$
$919$	−2.56221e32			−0.648851			−0.324425	+	0.945911i	$0.605171\pi$
$920$		−	1.34657e31i		−	0.0336949i
$921$	−1.46127e32	−	5.16445e32i	−0.361304	−	1.27693i
$922$	2.42321e32			0.592040
$923$		−	9.42495e31i		−	0.227541i
$924$	−2.63848e32	+	7.46552e31i	−0.629452	+	0.178102i
$925$	5.46437e32			1.28819
$926$		−	2.47752e31i		−	0.0577160i
$927$	−4.35637e31	+	2.67979e31i	−0.100288	+	0.0616912i
$928$	3.21430e32			0.731237
$929$		−	7.36318e31i		−	0.165536i	−0.996569	−	0.0827680i	$-0.973624\pi$
$929$		−	7.36318e31i		−	0.165536i	0.996569	−	0.0827680i	$-0.0263760\pi$
$930$	−1.82356e30	−	6.44487e30i	−0.00405142	−	0.0143186i
$931$	−6.52666e31			−0.143300
$932$		−	2.42499e32i		−	0.526180i
$933$	−7.35072e32	+	2.07987e32i	−1.57628	+	0.446003i
$934$	3.14993e31			0.0667553
$935$			5.91390e31i			0.123864i
$936$	1.27465e32	+	2.07212e32i	0.263850	+	0.428925i
$937$	−9.63908e32			−1.97197			−0.985984	−	0.166838i	$-0.946644\pi$
$937$	−9.63908e32			−1.97197			−0.985984	+	0.166838i	$0.946644\pi$
$938$			1.04949e32i			0.212201i
$939$	6.48302e31	+	2.29125e32i	0.129556	+	0.457879i
$940$	3.61199e30			0.00713411
$941$			3.17400e32i			0.619614i	0.950800	+	0.309807i	$0.100264\pi$
$941$			3.17400e32i			0.619614i	−0.950800	+	0.309807i	$0.899736\pi$
$942$	1.25086e32	−	3.53926e31i	0.241350	−	0.0682894i
$943$	7.28760e32			1.38981
$944$			3.32670e32i			0.627078i
$945$	8.66859e30	−	9.42574e30i	0.0161510	−	0.0175617i
$946$	−9.24368e31			−0.170232
$947$			5.32754e32i			0.969788i	0.874573	+	0.484894i	$0.161142\pi$
$947$			5.32754e32i			0.969788i	−0.874573	+	0.484894i	$0.838858\pi$
$948$	−1.93451e32	−	6.83701e32i	−0.348080	−	1.23020i
$949$	−9.15606e31			−0.162847
$950$			3.17223e31i			0.0557705i
$951$	2.72702e32	−	7.71603e31i	0.473917	−	0.134094i
$952$	2.30475e32			0.395929
$953$			6.69580e32i			1.13705i	0.822665	+	0.568526i	$0.192486\pi$
$953$			6.69580e32i			1.13705i	−0.822665	+	0.568526i	$0.807514\pi$
$954$	−2.22498e32	+	1.36868e32i	−0.373503	+	0.229758i
$955$	3.06720e31			0.0508985
$956$		−	5.87072e32i		−	0.963062i
$957$	2.40587e32	+	8.50291e32i	0.390159	+	1.37891i
$958$	−2.50624e32			−0.401793
$959$		−	1.94860e32i		−	0.308828i
$960$	−1.51442e31	+	4.28502e30i	−0.0237282	+	0.00671381i
$961$	−1.06528e32			−0.165008
$962$		−	2.23105e32i		−	0.341652i
$963$	−2.18516e32	−	3.55229e32i	−0.330822	−	0.537798i
$964$	−6.05047e31			−0.0905610
$965$		−	1.65228e31i		−	0.0244503i
$966$	−2.84444e31	−	1.00529e32i	−0.0416149	−	0.147077i
$967$	−6.62071e31			−0.0957664			−0.0478832	−	0.998853i	$-0.515248\pi$
$967$	−6.62071e31			−0.0957664			−0.0478832	+	0.998853i	$0.515248\pi$
$968$		−	6.35696e32i		−	0.909118i
$969$	1.81593e32	−	5.13813e31i	0.256767	−	0.0726514i
$970$	−8.90340e30			−0.0124471
$971$		−	8.07920e32i		−	1.11675i	−0.829588	−	0.558376i	$-0.811425\pi$
$971$		−	8.07920e32i		−	1.11675i	0.829588	−	0.558376i	$-0.188575\pi$
$972$	6.49282e32	+	1.26283e32i	0.887370	+	0.172591i
$973$	1.48433e32			0.200580
$974$			1.81353e32i			0.242312i
$975$	−1.75426e32	−	6.19994e32i	−0.231762	−	0.819100i
$976$	−4.22956e32			−0.552518
$977$			2.37096e32i			0.306255i	0.988206	+	0.153128i	$0.0489345\pi$
$977$			2.37096e32i			0.306255i	−0.988206	+	0.153128i	$0.951065\pi$
$978$	1.01261e32	−	2.86516e31i	0.129335	−	0.0365950i
$979$	3.39374e32			0.428617
$980$		−	3.02049e31i		−	0.0377216i
$981$	5.52933e32	−	3.40132e32i	0.682831	−	0.420038i
$982$	−3.31011e32			−0.404218
$983$		−	4.35578e31i		−	0.0525990i	−0.999654	−	0.0262995i	$-0.991628\pi$
$983$		−	4.35578e31i		−	0.0525990i	0.999654	−	0.0262995i	$-0.00837235\pi$
$984$	1.72019e32	+	6.07955e32i	0.205414	+	0.725982i
$985$	−3.54144e31			−0.0418197
$986$		−	3.52645e32i		−	0.411805i
$987$	5.67946e31	−	1.60699e31i	0.0655871	−	0.0185577i
$988$	−1.21961e32			−0.139282
$989$			3.31641e32i			0.374550i
$990$	1.21777e31	+	1.97966e31i	0.0136012	+	0.0221107i
$991$	−1.04870e33			−1.15836			−0.579178	−	0.815201i	$-0.696626\pi$
$991$	−1.04870e33			−1.15836			−0.579178	+	0.815201i	$0.696626\pi$
$992$			6.80415e32i			0.743268i
$993$	3.68485e32	+	1.30231e33i	0.398087	+	1.40693i
$994$	−3.50915e31			−0.0374932
$995$		−	6.01956e31i		−	0.0636079i
$996$	8.74007e32	−	2.47298e32i	0.913402	−	0.258445i
$997$	−1.34722e33			−1.39249			−0.696243	−	0.717807i	$-0.745146\pi$
$997$	−1.34722e33			−1.39249			−0.696243	+	0.717807i	$0.745146\pi$
$998$			2.01580e32i			0.206069i
$999$	−9.40396e32	−	8.64855e32i	−0.950802	−	0.874426i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.23.b.a.2.4	yes	6
3.2	odd	2	inner	3.23.b.a.2.3	✓	6
4.3	odd	2		48.23.e.b.17.3		6
12.11	even	2		48.23.e.b.17.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.23.b.a.2.3	✓	6	3.2	odd	2	inner
3.23.b.a.2.4	yes	6	1.1	even	1	trivial
48.23.e.b.17.3		6	4.3	odd	2
48.23.e.b.17.4		6	12.11	even	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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 23 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+634.557i q^{2} +(48229.8 + 170455. i) q^{3} +3.79164e6 q^{4} +2.56634e6i q^{5} +(-1.08163e8 + 3.06045e7i) q^{6} +8.97619e8 q^{7} +5.06753e9i q^{8} +(-2.67288e10 + 1.64420e10i) q^{9} +O(q^{10})\)	\(q+634.557i q^{2} +(48229.8 + 170455. i) q^{3} +3.79164e6 q^{4} +2.56634e6i q^{5} +(-1.08163e8 + 3.06045e7i) q^{6} +8.97619e8 q^{7} +5.06753e9i q^{8} +(-2.67288e10 + 1.64420e10i) q^{9} -1.62849e9 q^{10} +4.54805e11i q^{11} +(1.82870e11 + 6.46305e11i) q^{12} -1.52981e12 q^{13} +5.69590e11i q^{14} +(-4.37446e11 + 1.23774e11i) q^{15} +1.26877e13 q^{16} -5.06681e13i q^{17} +(-1.04334e13 - 1.69610e13i) q^{18} +2.10259e13 q^{19} +9.73064e12i q^{20} +(4.32920e13 + 1.53004e14i) q^{21} -2.88599e14 q^{22} +1.03543e15i q^{23} +(-8.63787e14 + 2.44406e14i) q^{24} +2.37760e15 q^{25} -9.70754e14i q^{26} +(-4.09175e15 - 3.76307e15i) q^{27} +3.40345e15 q^{28} -1.09681e16i q^{29} +(-7.85416e13 - 2.77584e14i) q^{30} +2.32177e16 q^{31} +2.93058e16i q^{32} +(-7.75238e16 + 2.19351e16i) q^{33} +3.21518e16 q^{34} +2.30359e15i q^{35} +(-1.01346e17 + 6.23423e16i) q^{36} +2.29827e17 q^{37} +1.33421e16i q^{38} +(-7.37826e16 - 2.60765e17i) q^{39} -1.30050e16 q^{40} -7.03825e17i q^{41} +(-9.70895e16 + 2.74712e16i) q^{42} +3.20294e17 q^{43} +1.72446e18i q^{44} +(-4.21958e16 - 6.85952e16i) q^{45} -6.57037e17 q^{46} -3.71198e17i q^{47} +(6.11923e17 + 2.16268e18i) q^{48} -3.10410e18 q^{49} +1.50872e18i q^{50} +(8.63664e18 - 2.44371e18i) q^{51} -5.80051e18 q^{52} -1.31183e19i q^{53} +(2.38788e18 - 2.59645e18i) q^{54} -1.16718e18 q^{55} +4.54871e18i q^{56} +(1.01408e18 + 3.58398e18i) q^{57} +6.95989e18 q^{58} +2.62199e19i q^{59} +(-1.65864e18 + 4.69307e17i) q^{60} -3.33360e19 q^{61} +1.47330e19i q^{62} +(-2.39923e19 + 1.47587e19i) q^{63} +3.46197e19 q^{64} -3.92602e18i q^{65} +(-1.39191e19 - 4.91933e19i) q^{66} +1.84254e20 q^{67} -1.92115e20i q^{68} +(-1.76494e20 + 4.99384e19i) q^{69} -1.46176e18 q^{70} +6.16084e19i q^{71} +(-8.33206e19 - 1.35449e20i) q^{72} +5.98508e19 q^{73} +1.45838e20i q^{74} +(1.14671e20 + 4.05274e20i) q^{75} +7.97228e19 q^{76} +4.08241e20i q^{77} +(1.65470e20 - 4.68193e19i) q^{78} -1.05786e21 q^{79} +3.25608e19i q^{80} +(4.44090e20 - 8.78953e20i) q^{81} +4.46617e20 q^{82} -1.35231e21i q^{83} +(1.64148e20 + 5.80135e20i) q^{84} +1.30032e20 q^{85} +2.03245e20i q^{86} +(1.86957e21 - 5.28990e20i) q^{87} -2.30474e21 q^{88} -7.46198e20i q^{89} +(4.35276e19 - 2.67756e19i) q^{90} -1.37319e21 q^{91} +3.92597e21i q^{92} +(1.11979e21 + 3.95758e21i) q^{93} +2.35546e20 q^{94} +5.39597e19i q^{95} +(-4.99533e21 + 1.41341e21i) q^{96} +5.46728e21 q^{97} -1.96973e21i q^{98} +(-7.47792e21 - 1.21564e22i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 86670 q^{3} - 11258688 q^{4} + 293575104 q^{6} - 3447063060 q^{7} + 57339715158 q^{9}+O(q^{10}) \) 6 * q + 86670 * q^3 - 11258688 * q^4 + 293575104 * q^6 - 3447063060 * q^7 + 57339715158 * q^9	\( 6 q + 86670 q^{3} - 11258688 q^{4} + 293575104 q^{6} - 3447063060 q^{7} + 57339715158 q^{9} - 186869600640 q^{10} - 1325972980800 q^{12} + 2025132496860 q^{13} + 2628031314240 q^{15} - 9703467227136 q^{16} + 42127150135680 q^{18} + 100485688668636 q^{19} - 789079193287812 q^{21} + 10\!\cdots\!00 q^{22}+ \cdots - 60\!\cdots\!60 q^{99}+O(q^{100}) \) 6 * q + 86670 * q^3 - 11258688 * q^4 + 293575104 * q^6 - 3447063060 * q^7 + 57339715158 * q^9 - 186869600640 * q^10 - 1325972980800 * q^12 + 2025132496860 * q^13 + 2628031314240 * q^15 - 9703467227136 * q^16 + 42127150135680 * q^18 + 100485688668636 * q^19 - 789079193287812 * q^21 + 1045890315676800 * q^22 - 2472467233277952 * q^24 + 1396569263732790 * q^25 - 10731657558901410 * q^27 + 44570708098492800 * q^28 - 116169123436801920 * q^30 + 114109662401153292 * q^31 - 174850022773609920 * q^33 + 319017868488396288 * q^34 - 707589966262651200 * q^36 + 683782874080661820 * q^37 - 1038045209126993748 * q^39 + 1781949720499015680 * q^40 - 1108714403505421440 * q^42 + 273273330169769340 * q^43 + 3228622736179443840 * q^45 - 8349686917048426752 * q^46 + 10392767955626526720 * q^48 - 8294807529216677070 * q^49 + 14237699192275302144 * q^51 - 22636595958302682240 * q^52 + 48383805955937626944 * q^54 - 40874587160137441920 * q^55 + 43721391850797114540 * q^57 - 67285958146132360320 * q^58 - 44311576503733309440 * q^60 + 121649250388145492892 * q^61 - 184494903535705683060 * q^63 + 285203601894474055680 * q^64 - 374640791614422030720 * q^66 + 75701571086175260700 * q^67 - 233446021721582921856 * q^69 + 1113607014897000234240 * q^70 - 639860863731149721600 * q^72 - 57178481309533986900 * q^73 - 333973626119358339330 * q^75 - 731229802672243966080 * q^76 + 735750453969076417920 * q^78 + 384537395891327736396 * q^79 + 3109769787236091157926 * q^81 - 5166859472437001068800 * q^82 + 6698665889827068753792 * q^84 - 6772579853411844011520 * q^85 + 4995406256507248236480 * q^87 - 404168025320661381120 * q^88 - 3858783621100493362560 * q^90 - 2806742501496183911304 * q^91 + 2087220280517252053020 * q^93 + 8135725180445469439488 * q^94 - 15069021592890694238208 * q^96 + 1565231688506989945740 * q^97 - 6095367699696122981760 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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