LMFDB - Embedded newform 162.12.c.j.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,12,Mod(55,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("162.55");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	162.c (of order $3$, degree $2$, not 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:	$124.471595251$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 6)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			55.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	162.55
Dual form			162.12.c.j.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(16.0000 - 27.7128i) q^{2} +(-512.000 - 886.810i) q^{4} +(5865.00 + 10158.5i) q^{5} +(25004.0 - 43308.2i) q^{7} -32768.0 q^{8} +O(q^{10})$	\(q+(16.0000 - 27.7128i) q^{2} +(-512.000 - 886.810i) q^{4} +(5865.00 + 10158.5i) q^{5} +(25004.0 - 43308.2i) q^{7} -32768.0 q^{8} +375360. q^{10} +(265710. - 460223. i) q^{11} +(-666283. - 1.15404e6i) q^{13} +(-800128. - 1.38586e6i) q^{14} +(-524288. + 908093. i) q^{16} -5.10968e6 q^{17} +2.90140e6 q^{19} +(6.00576e6 - 1.04023e7i) q^{20} +(-8.50272e6 - 1.47271e7i) q^{22} +(-1.52985e7 - 2.64978e7i) q^{23} +(-4.43824e7 + 7.68726e7i) q^{25} -4.26421e7 q^{26} -5.12082e7 q^{28} +(3.85033e7 - 6.66897e7i) q^{29} +(1.19709e8 + 2.07342e8i) q^{31} +(1.67772e7 + 2.90590e7i) q^{32} +(-8.17548e7 + 1.41604e8i) q^{34} +5.86594e8 q^{35} -7.85042e8 q^{37} +(4.64225e7 - 8.04061e7i) q^{38} +(-1.92184e8 - 3.32873e8i) q^{40} +(-2.05626e8 - 3.56156e8i) q^{41} +(-1.75617e8 + 3.04177e8i) q^{43} -5.44174e8 q^{44} -9.79104e8 q^{46} +(-4.79108e7 + 8.29840e7i) q^{47} +(-2.61737e8 - 4.53341e8i) q^{49} +(1.42024e9 + 2.45992e9i) q^{50} +(-6.82274e8 + 1.18173e9i) q^{52} -1.46586e9 q^{53} +6.23356e9 q^{55} +(-8.19331e8 + 1.41912e9i) q^{56} +(-1.23211e9 - 2.13407e9i) q^{58} +(-2.81058e9 - 4.86806e9i) q^{59} +(5.23679e9 - 9.07039e9i) q^{61} +7.66139e9 q^{62} +1.07374e9 q^{64} +(7.81550e9 - 1.35368e10i) q^{65} +(-2.25765e9 - 3.91037e9i) q^{67} +(2.61616e9 + 4.53131e9i) q^{68} +(9.38550e9 - 1.62562e10i) q^{70} -8.50958e9 q^{71} +2.01250e9 q^{73} +(-1.25607e10 + 2.17557e10i) q^{74} +(-1.48552e9 - 2.57299e9i) q^{76} +(-1.32876e10 - 2.30148e10i) q^{77} +(1.11192e10 - 1.92590e10i) q^{79} -1.22998e10 q^{80} -1.31601e10 q^{82} +(-3.16432e9 + 5.48077e9i) q^{83} +(-2.99683e10 - 5.19066e10i) q^{85} +(5.61973e9 + 9.73366e9i) q^{86} +(-8.70679e9 + 1.50806e10i) q^{88} -5.01237e10 q^{89} -6.66390e10 q^{91} +(-1.56657e10 + 2.71337e10i) q^{92} +(1.53315e9 + 2.65549e9i) q^{94} +(1.70167e10 + 2.94738e10i) q^{95} +(-4.74030e10 + 8.21044e10i) q^{97} -1.67511e10 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 32 q^{2} - 1024 q^{4} + 11730 q^{5} + 50008 q^{7} - 65536 q^{8}+O(q^{10}) $ 2 * q + 32 * q^2 - 1024 * q^4 + 11730 * q^5 + 50008 * q^7 - 65536 * q^8	\( 2 q + 32 q^{2} - 1024 q^{4} + 11730 q^{5} + 50008 q^{7} - 65536 q^{8} + 750720 q^{10} + 531420 q^{11} - 1332566 q^{13} - 1600256 q^{14} - 1048576 q^{16} - 10219356 q^{17} + 5802808 q^{19} + 12011520 q^{20} - 17005440 q^{22} - 30597000 q^{23} - 88764775 q^{25} - 85284224 q^{26} - 102416384 q^{28} + 77006634 q^{29} + 239418352 q^{31} + 33554432 q^{32} - 163509696 q^{34} + 1173187680 q^{35} - 1570083332 q^{37} + 92844928 q^{38} - 384368640 q^{40} - 411252954 q^{41} - 351233348 q^{43} - 1088348160 q^{44} - 1958208000 q^{46} - 95821680 q^{47} - 523473321 q^{49} + 2840472800 q^{50} - 1364547584 q^{52} - 2931714756 q^{53} + 12467113200 q^{55} - 1638662144 q^{56} - 2464212288 q^{58} - 5621152020 q^{59} + 10473587770 q^{61} + 15322774528 q^{62} + 2147483648 q^{64} + 15630999180 q^{65} - 4515307532 q^{67} + 5232310272 q^{68} + 18771002880 q^{70} - 17019159120 q^{71} + 4024993972 q^{73} - 25121333312 q^{74} - 2971037696 q^{76} - 26575251360 q^{77} + 22238409568 q^{79} - 24599592960 q^{80} - 26320189056 q^{82} - 6328647516 q^{83} - 59936522940 q^{85} + 11239467136 q^{86} - 17413570560 q^{88} - 100247413356 q^{89} - 133277921056 q^{91} - 31331328000 q^{92} + 3066293760 q^{94} + 34033468920 q^{95} - 94805961314 q^{97} - 33502292544 q^{98}+O(q^{100}) \) 2 * q + 32 * q^2 - 1024 * q^4 + 11730 * q^5 + 50008 * q^7 - 65536 * q^8 + 750720 * q^10 + 531420 * q^11 - 1332566 * q^13 - 1600256 * q^14 - 1048576 * q^16 - 10219356 * q^17 + 5802808 * q^19 + 12011520 * q^20 - 17005440 * q^22 - 30597000 * q^23 - 88764775 * q^25 - 85284224 * q^26 - 102416384 * q^28 + 77006634 * q^29 + 239418352 * q^31 + 33554432 * q^32 - 163509696 * q^34 + 1173187680 * q^35 - 1570083332 * q^37 + 92844928 * q^38 - 384368640 * q^40 - 411252954 * q^41 - 351233348 * q^43 - 1088348160 * q^44 - 1958208000 * q^46 - 95821680 * q^47 - 523473321 * q^49 + 2840472800 * q^50 - 1364547584 * q^52 - 2931714756 * q^53 + 12467113200 * q^55 - 1638662144 * q^56 - 2464212288 * q^58 - 5621152020 * q^59 + 10473587770 * q^61 + 15322774528 * q^62 + 2147483648 * q^64 + 15630999180 * q^65 - 4515307532 * q^67 + 5232310272 * q^68 + 18771002880 * q^70 - 17019159120 * q^71 + 4024993972 * q^73 - 25121333312 * q^74 - 2971037696 * q^76 - 26575251360 * q^77 + 22238409568 * q^79 - 24599592960 * q^80 - 26320189056 * q^82 - 6328647516 * q^83 - 59936522940 * q^85 + 11239467136 * q^86 - 17413570560 * q^88 - 100247413356 * q^89 - 133277921056 * q^91 - 31331328000 * q^92 + 3066293760 * q^94 + 34033468920 * q^95 - 94805961314 * q^97 - 33502292544 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	16.0000	−	27.7128i	0.353553	−	0.612372i
$2$	16.0000	−	27.7128i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−512.000	−	886.810i	−0.250000	−	0.433013i
$5$	5865.00	+	10158.5i	0.839330	+	1.45376i	0.890455	+	0.455071i	$0.150386\pi$
$5$	5865.00	+	10158.5i	0.839330	+	1.45376i	−0.0511248	+	0.998692i	$0.516281\pi$
$6$		0			0
$7$	25004.0	−	43308.2i	0.562303	−	0.973937i	−0.434992	−	0.900434i	$-0.643249\pi$
$7$	25004.0	−	43308.2i	0.562303	−	0.973937i	0.997295	−	0.0735028i	$-0.0234178\pi$
$8$	−32768.0			−0.353553
$9$		0			0
$10$	375360.			1.18699
$11$	265710.	−	460223.i	0.497449	−	0.861606i	−0.502547	−	0.864550i	$-0.667604\pi$
$11$	265710.	−	460223.i	0.497449	−	0.861606i	0.999996	+	0.00294371i	$0.000937013\pi$
$12$		0			0
$13$	−666283.	−	1.15404e6i	−0.497703	−	0.862047i	0.502293	−	0.864697i	$-0.332490\pi$
$13$	−666283.	−	1.15404e6i	−0.497703	−	0.862047i	−0.999996	+	0.00265027i	$0.999156\pi$
$14$	−800128.	−	1.38586e6i	−0.397608	−	0.688678i
$15$		0			0
$16$	−524288.	+	908093.i	−0.125000	+	0.216506i
$17$	−5.10968e6			−0.872820			−0.436410	−	0.899748i	$-0.643750\pi$
$17$	−5.10968e6			−0.872820			−0.436410	+	0.899748i	$0.643750\pi$
$18$		0			0
$19$	2.90140e6			0.268821			0.134411	−	0.990926i	$-0.457086\pi$
$19$	2.90140e6			0.268821			0.134411	+	0.990926i	$0.457086\pi$
$20$	6.00576e6	−	1.04023e7i	0.419665	−	0.726882i
$21$		0			0
$22$	−8.50272e6	−	1.47271e7i	−0.351749	−	0.609248i
$23$	−1.52985e7	−	2.64978e7i	−0.495616	−	0.858433i	0.504371	−	0.863487i	$-0.331725\pi$
$23$	−1.52985e7	−	2.64978e7i	−0.495616	−	0.858433i	−0.999987	+	0.00505426i	$0.998391\pi$
$24$		0			0
$25$	−4.43824e7	+	7.68726e7i	−0.908951	+	1.57435i
$26$	−4.26421e7			−0.703858
$27$		0			0
$28$	−5.12082e7			−0.562303
$29$	3.85033e7	−	6.66897e7i	0.348585	−	0.603768i	−0.637413	−	0.770522i	$-0.719995\pi$
$29$	3.85033e7	−	6.66897e7i	0.348585	−	0.603768i	0.985998	+	0.166755i	$0.0533288\pi$
$30$		0			0
$31$	1.19709e8	+	2.07342e8i	0.750997	+	1.30076i	0.947340	+	0.320229i	$0.103760\pi$
$31$	1.19709e8	+	2.07342e8i	0.750997	+	1.30076i	−0.196343	+	0.980535i	$0.562907\pi$
$32$	1.67772e7	+	2.90590e7i	0.0883883	+	0.153093i
$33$		0			0
$34$	−8.17548e7	+	1.41604e8i	−0.308588	+	0.534491i
$35$	5.86594e8			1.88783
$36$		0			0
$37$	−7.85042e8			−1.86116			−0.930579	−	0.366091i	$-0.880696\pi$
$37$	−7.85042e8			−1.86116			−0.930579	+	0.366091i	$0.880696\pi$
$38$	4.64225e7	−	8.04061e7i	0.0950426	−	0.164619i
$39$		0			0
$40$	−1.92184e8	−	3.32873e8i	−0.296748	−	0.513983i
$41$	−2.05626e8	−	3.56156e8i	−0.277184	−	0.480096i	0.693500	−	0.720457i	$-0.256068\pi$
$41$	−2.05626e8	−	3.56156e8i	−0.277184	−	0.480096i	−0.970684	+	0.240360i	$0.922734\pi$
$42$		0			0
$43$	−1.75617e8	+	3.04177e8i	−0.182175	+	0.315537i	−0.942621	−	0.333865i	$-0.891647\pi$
$43$	−1.75617e8	+	3.04177e8i	−0.182175	+	0.315537i	0.760446	+	0.649401i	$0.224980\pi$
$44$	−5.44174e8			−0.497449
$45$		0			0
$46$	−9.79104e8			−0.700908
$47$	−4.79108e7	+	8.29840e7i	−0.0304716	+	0.0527784i	−0.880859	−	0.473379i	$-0.843034\pi$
$47$	−4.79108e7	+	8.29840e7i	−0.0304716	+	0.0527784i	0.850387	+	0.526157i	$0.176368\pi$
$48$		0			0
$49$	−2.61737e8	−	4.53341e8i	−0.132369	−	0.229270i
$50$	1.42024e9	+	2.45992e9i	0.642726	+	1.11323i
$51$		0			0
$52$	−6.82274e8	+	1.18173e9i	−0.248852	+	0.431023i
$53$	−1.46586e9			−0.481476			−0.240738	−	0.970590i	$-0.577389\pi$
$53$	−1.46586e9			−0.481476			−0.240738	+	0.970590i	$0.577389\pi$
$54$		0			0
$55$	6.23356e9			1.67009
$56$	−8.19331e8	+	1.41912e9i	−0.198804	+	0.344339i
$57$		0			0
$58$	−1.23211e9	−	2.13407e9i	−0.246487	−	0.426928i
$59$	−2.81058e9	−	4.86806e9i	−0.511811	−	0.886482i	−0.999906	−	0.0136918i	$-0.995642\pi$
$59$	−2.81058e9	−	4.86806e9i	−0.511811	−	0.886482i	0.488096	−	0.872790i	$-0.337692\pi$
$60$		0			0
$61$	5.23679e9	−	9.07039e9i	0.793874	−	1.37503i	−0.129678	−	0.991556i	$-0.541394\pi$
$61$	5.23679e9	−	9.07039e9i	0.793874	−	1.37503i	0.923552	−	0.383473i	$-0.125272\pi$
$62$	7.66139e9			1.06207
$63$		0			0
$64$	1.07374e9			0.125000
$65$	7.81550e9	−	1.35368e10i	0.835475	−	1.44708i
$66$		0			0
$67$	−2.25765e9	−	3.91037e9i	−0.204289	−	0.353840i	0.745617	−	0.666375i	$-0.232155\pi$
$67$	−2.25765e9	−	3.91037e9i	−0.204289	−	0.353840i	−0.949906	+	0.312535i	$0.898822\pi$
$68$	2.61616e9	+	4.53131e9i	0.218205	+	0.377942i
$69$		0			0
$70$	9.38550e9	−	1.62562e10i	0.667449	−	1.15606i
$71$	−8.50958e9			−0.559741			−0.279871	−	0.960038i	$-0.590292\pi$
$71$	−8.50958e9			−0.559741			−0.279871	+	0.960038i	$0.590292\pi$
$72$		0			0
$73$	2.01250e9			0.113621			0.0568106	−	0.998385i	$-0.481907\pi$
$73$	2.01250e9			0.113621			0.0568106	+	0.998385i	$0.481907\pi$
$74$	−1.25607e10	+	2.17557e10i	−0.658019	+	1.13972i
$75$		0			0
$76$	−1.48552e9	−	2.57299e9i	−0.0672053	−	0.116403i
$77$	−1.32876e10	−	2.30148e10i	−0.559433	−	0.968967i
$78$		0			0
$79$	1.11192e10	−	1.92590e10i	0.406560	−	0.704183i	−0.587942	−	0.808903i	$-0.700062\pi$
$79$	1.11192e10	−	1.92590e10i	0.406560	−	0.704183i	0.994502	+	0.104721i	$0.0333949\pi$
$80$	−1.22998e10			−0.419665
$81$		0			0
$82$	−1.31601e10			−0.391997
$83$	−3.16432e9	+	5.48077e9i	−0.0881762	+	0.152726i	−0.906740	−	0.421690i	$-0.861437\pi$
$83$	−3.16432e9	+	5.48077e9i	−0.0881762	+	0.152726i	0.818564	+	0.574415i	$0.194771\pi$
$84$		0			0
$85$	−2.99683e10	−	5.19066e10i	−0.732584	−	1.26887i
$86$	5.61973e9	+	9.73366e9i	0.128817	+	0.223118i
$87$		0			0
$88$	−8.70679e9	+	1.50806e10i	−0.175875	+	0.304624i
$89$	−5.01237e10			−0.951477			−0.475738	−	0.879587i	$-0.657819\pi$
$89$	−5.01237e10			−0.951477			−0.475738	+	0.879587i	$0.657819\pi$
$90$		0			0
$91$	−6.66390e10			−1.11944
$92$	−1.56657e10	+	2.71337e10i	−0.247808	+	0.429216i
$93$		0			0
$94$	1.53315e9	+	2.65549e9i	0.0215467	+	0.0373200i
$95$	1.70167e10	+	2.94738e10i	0.225630	+	0.390802i
$96$		0			0
$97$	−4.74030e10	+	8.21044e10i	−0.560481	+	0.970782i	0.436973	+	0.899475i	$0.356050\pi$
$97$	−4.74030e10	+	8.21044e10i	−0.560481	+	0.970782i	−0.997454	+	0.0713075i	$0.977283\pi$
$98$	−1.67511e10			−0.187198
$99$		0			0
$100$	9.08951e10			0.908951
$101$	−6.89760e9	+	1.19470e10i	−0.0653026	+	0.113107i	−0.896828	−	0.442379i	$-0.854135\pi$
$101$	−6.89760e9	+	1.19470e10i	−0.0653026	+	0.113107i	0.831526	+	0.555486i	$0.187468\pi$
$102$		0			0
$103$	−3.25918e10	−	5.64507e10i	−0.277015	−	0.479805i	0.693626	−	0.720335i	$-0.256012\pi$
$103$	−3.25918e10	−	5.64507e10i	−0.277015	−	0.479805i	−0.970642	+	0.240530i	$0.922679\pi$
$104$	2.18328e10	+	3.78155e10i	0.175965	+	0.304780i
$105$		0			0
$106$	−2.34537e10	+	4.06230e10i	−0.170227	+	0.294842i
$107$	9.33399e10			0.643363			0.321682	−	0.946848i	$-0.395752\pi$
$107$	9.33399e10			0.643363			0.321682	+	0.946848i	$0.395752\pi$
$108$		0			0
$109$	−1.51369e11			−0.942307			−0.471154	−	0.882051i	$-0.656162\pi$
$109$	−1.51369e11			−0.942307			−0.471154	+	0.882051i	$0.656162\pi$
$110$	9.97369e10	−	1.72749e11i	0.590468	−	1.02272i
$111$		0			0
$112$	2.62186e10	+	4.54119e10i	0.140576	+	0.243484i
$113$	−1.18674e11	−	2.05550e11i	−0.605935	−	1.04951i	−0.991903	−	0.126998i	$-0.959466\pi$
$113$	−1.18674e11	−	2.05550e11i	−0.605935	−	1.04951i	0.385968	−	0.922512i	$-0.373867\pi$
$114$		0			0
$115$	1.79451e11	−	3.10819e11i	0.831972	−	1.44102i
$116$	−7.88548e10			−0.348585
$117$		0			0
$118$	−1.79877e11			−0.723809
$119$	−1.27762e11	+	2.21291e11i	−0.490789	+	0.850071i
$120$		0			0
$121$	1.45223e9	+	2.51533e9i	0.00508997	+	0.00881608i
$122$	−1.67577e11	−	2.90253e11i	−0.561353	−	0.972293i
$123$		0			0
$124$	1.22582e11	−	2.12319e11i	0.375498	−	0.650382i
$125$	−4.68457e11			−1.37298
$126$		0			0
$127$	5.14414e11			1.38163			0.690816	−	0.723031i	$-0.257251\pi$
$127$	5.14414e11			1.38163			0.690816	+	0.723031i	$0.257251\pi$
$128$	1.71799e10	−	2.97564e10i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−2.50096e11	−	4.33179e11i	−0.590770	−	1.02324i
$131$	−1.49286e11	−	2.58571e11i	−0.338086	−	0.585581i	0.645987	−	0.763348i	$-0.276446\pi$
$131$	−1.49286e11	−	2.58571e11i	−0.338086	−	0.585581i	−0.984073	+	0.177767i	$0.943113\pi$
$132$		0			0
$133$	7.25467e10	−	1.25655e11i	0.151159	−	0.261815i
$134$	−1.44490e11			−0.288909
$135$		0			0
$136$	1.67434e11			0.308588
$137$	3.08058e11	−	5.33572e11i	0.545343	−	0.944561i	−0.453243	−	0.891387i	$-0.649733\pi$
$137$	3.08058e11	−	5.33572e11i	0.545343	−	0.944561i	0.998585	−	0.0531740i	$-0.0169338\pi$
$138$		0			0
$139$	2.61407e11	+	4.52770e11i	0.427303	+	0.740110i	0.996632	−	0.0819992i	$-0.0261305\pi$
$139$	2.61407e11	+	4.52770e11i	0.427303	+	0.740110i	−0.569330	+	0.822109i	$0.692797\pi$
$140$	−3.00336e11	−	5.20197e11i	−0.471958	−	0.817455i
$141$		0			0
$142$	−1.36153e11	+	2.35824e11i	−0.197898	+	0.342770i
$143$	−7.08152e11			−0.990327
$144$		0			0
$145$	9.03288e11			1.17031
$146$	3.22000e10	−	5.57720e10i	0.0401712	−	0.0695785i
$147$		0			0
$148$	4.01941e11	+	6.96183e11i	0.465289	+	0.805905i
$149$	6.35073e11	+	1.09998e12i	0.708434	+	1.22704i	0.965438	+	0.260633i	$0.0839313\pi$
$149$	6.35073e11	+	1.09998e12i	0.708434	+	1.22704i	−0.257004	+	0.966410i	$0.582735\pi$
$150$		0			0
$151$	−6.26856e11	+	1.08575e12i	−0.649822	+	1.12552i	0.333343	+	0.942806i	$0.391823\pi$
$151$	−6.26856e11	+	1.08575e12i	−0.649822	+	1.12552i	−0.983165	+	0.182719i	$0.941510\pi$
$152$	−9.50732e10			−0.0950426
$153$		0			0
$154$	−8.50408e11			−0.791158
$155$	−1.40419e12	+	2.43213e12i	−1.26067	+	2.18354i
$156$		0			0
$157$	−3.03354e11	−	5.25424e11i	−0.253806	−	0.439604i	0.710765	−	0.703430i	$-0.248349\pi$
$157$	−3.03354e11	−	5.25424e11i	−0.253806	−	0.439604i	−0.964570	+	0.263825i	$0.915016\pi$
$158$	−3.55815e11	−	6.16289e11i	−0.287481	−	0.497932i
$159$		0			0
$160$	−1.96797e11	+	3.40862e11i	−0.148374	+	0.256991i
$161$	−1.53009e12			−1.11475
$162$		0			0
$163$	−1.58401e12			−1.07827			−0.539133	−	0.842221i	$-0.681248\pi$
$163$	−1.58401e12			−1.07827			−0.539133	+	0.842221i	$0.681248\pi$
$164$	−2.10562e11	+	3.64703e11i	−0.138592	+	0.240048i
$165$		0			0
$166$	1.01258e11	+	1.75385e11i	0.0623500	+	0.107993i
$167$	−1.47636e12	−	2.55713e12i	−0.879533	−	1.52340i	−0.851854	−	0.523780i	$-0.824522\pi$
$167$	−1.47636e12	−	2.55713e12i	−0.879533	−	1.52340i	−0.0276794	−	0.999617i	$-0.508812\pi$
$168$		0			0
$169$	8.21412e9	−	1.42273e10i	0.00458336	−	0.00793862i
$170$	−1.91797e12			−1.03603
$171$		0			0
$172$	3.59663e11			0.182175
$173$	1.32705e12	−	2.29852e12i	0.651079	−	1.12770i	−0.331782	−	0.943356i	$-0.607650\pi$
$173$	1.32705e12	−	2.29852e12i	0.651079	−	1.12770i	0.982861	−	0.184347i	$-0.0590169\pi$
$174$		0			0
$175$	2.21947e12	+	3.84424e12i	1.02221	+	1.77052i
$176$	2.78617e11	+	4.82579e11i	0.124362	+	0.215402i
$177$		0			0
$178$	−8.01979e11	+	1.38907e12i	−0.336398	+	0.582658i
$179$	−4.06450e12			−1.65316			−0.826580	−	0.562819i	$-0.809717\pi$
$179$	−4.06450e12			−1.65316			−0.826580	+	0.562819i	$0.809717\pi$
$180$		0			0
$181$	−1.68073e12			−0.643082			−0.321541	−	0.946896i	$-0.604201\pi$
$181$	−1.68073e12			−0.643082			−0.321541	+	0.946896i	$0.604201\pi$
$182$	−1.06622e12	+	1.84675e12i	−0.395782	+	0.685514i
$183$		0			0
$184$	5.01301e11	+	8.68279e11i	0.175227	+	0.303502i
$185$	−4.60427e12	−	7.97483e12i	−1.56213	−	2.70568i
$186$		0			0
$187$	−1.35769e12	+	2.35159e12i	−0.434183	+	0.752027i
$188$	9.81214e10			0.0304716
$189$		0			0
$190$	1.08907e12			0.319089
$191$	−2.04568e11	+	3.54321e11i	−0.0582309	+	0.100859i	−0.893671	−	0.448722i	$-0.851879\pi$
$191$	−2.04568e11	+	3.54321e11i	−0.0582309	+	0.100859i	0.835440	+	0.549581i	$0.185213\pi$
$192$		0			0
$193$	−2.35953e12	−	4.08682e12i	−0.634249	−	1.09855i	−0.986674	−	0.162712i	$-0.947976\pi$
$193$	−2.35953e12	−	4.08682e12i	−0.634249	−	1.09855i	0.352424	−	0.935840i	$-0.385357\pi$
$194$	1.51690e12	+	2.62734e12i	0.396320	+	0.686447i
$195$		0			0
$196$	−2.68018e11	+	4.64221e11i	−0.0661845	+	0.114635i
$197$	−3.60899e12			−0.866605			−0.433303	−	0.901249i	$-0.642652\pi$
$197$	−3.60899e12			−0.866605			−0.433303	+	0.901249i	$0.642652\pi$
$198$		0			0
$199$	1.72140e12			0.391012			0.195506	−	0.980703i	$-0.437365\pi$
$199$	1.72140e12			0.391012			0.195506	+	0.980703i	$0.437365\pi$
$200$	1.45432e12	−	2.51896e12i	0.321363	−	0.556617i
$201$		0			0
$202$	2.20723e11	+	3.82304e11i	0.0461759	+	0.0799790i
$203$	−1.92547e12	−	3.33502e12i	−0.392021	−	0.679000i
$204$		0			0
$205$	2.41200e12	−	4.17770e12i	0.465298	−	0.805919i
$206$	−2.08588e12			−0.391759
$207$		0			0
$208$	1.39730e12			0.248852
$209$	7.70932e11	−	1.33529e12i	0.133725	−	0.231618i
$210$		0			0
$211$	−8.51723e11	−	1.47523e12i	−0.140199	−	0.242832i	0.787372	−	0.616478i	$-0.211441\pi$
$211$	−8.51723e11	−	1.47523e12i	−0.140199	−	0.242832i	−0.927571	+	0.373646i	$0.878108\pi$
$212$	7.50519e11	+	1.29994e12i	0.120369	+	0.208485i
$213$		0			0
$214$	1.49344e12	−	2.58671e12i	0.227463	−	0.393978i
$215$	−4.11997e12			−0.611621
$216$		0			0
$217$	1.19728e13			1.68915
$218$	−2.42191e12	+	4.19487e12i	−0.333156	+	0.577043i
$219$		0			0
$220$	−3.19158e12	−	5.52798e12i	−0.417524	−	0.723172i
$221$	3.40449e12	+	5.89675e12i	0.434405	+	0.752411i
$222$		0			0
$223$	7.31264e12	−	1.26659e13i	0.887969	−	1.53801i	0.0456958	−	0.998955i	$-0.485450\pi$
$223$	7.31264e12	−	1.26659e13i	0.887969	−	1.53801i	0.842273	−	0.539051i	$-0.181217\pi$
$224$	1.67799e12			0.198804
$225$		0			0
$226$	−7.59517e12			−0.856921
$227$	−1.68228e12	+	2.91380e12i	−0.185249	+	0.320861i	−0.943661	−	0.330915i	$-0.892643\pi$
$227$	−1.68228e12	+	2.91380e12i	−0.185249	+	0.320861i	0.758411	+	0.651776i	$0.225976\pi$
$228$		0			0
$229$	−9.49602e11	−	1.64476e12i	−0.0996429	−	0.172587i	0.811894	−	0.583805i	$-0.198437\pi$
$229$	−9.49602e11	−	1.64476e12i	−0.0996429	−	0.172587i	−0.911537	+	0.411218i	$0.865103\pi$
$230$	−5.74244e12	−	9.94621e12i	−0.588293	−	1.01895i
$231$		0			0
$232$	−1.26168e12	+	2.18529e12i	−0.123244	+	0.213464i
$233$	1.51901e12			0.144912			0.0724560	−	0.997372i	$-0.476916\pi$
$233$	1.51901e12			0.144912			0.0724560	+	0.997372i	$0.476916\pi$
$234$		0			0
$235$	−1.12399e12			−0.102303
$236$	−2.87803e12	+	4.98489e12i	−0.255905	+	0.443241i
$237$		0			0
$238$	4.08840e12	+	7.08131e12i	0.347040	+	0.601091i
$239$	−4.15748e12	−	7.20097e12i	−0.344859	−	0.597314i	0.640469	−	0.767984i	$-0.278740\pi$
$239$	−4.15748e12	−	7.20097e12i	−0.344859	−	0.597314i	−0.985328	+	0.170670i	$0.945407\pi$
$240$		0			0
$241$	6.50631e12	−	1.12693e13i	0.515515	−	0.892898i	−0.484323	−	0.874889i	$-0.660934\pi$
$241$	6.50631e12	−	1.12693e13i	0.515515	−	0.892898i	0.999838	−	0.0180085i	$-0.00573260\pi$
$242$	9.29425e10			0.00719830
$243$		0			0
$244$	−1.07250e13			−0.793874
$245$	3.07017e12	−	5.31769e12i	0.222203	−	0.384866i
$246$		0			0
$247$	−1.93316e12	−	3.34832e12i	−0.133793	−	0.231736i
$248$	−3.92263e12	−	6.79419e12i	−0.265517	−	0.459890i
$249$		0			0
$250$	−7.49531e12	+	1.29823e13i	−0.485422	+	0.840776i
$251$	−1.87138e13			−1.18565			−0.592825	−	0.805331i	$-0.701987\pi$
$251$	−1.87138e13			−1.18565			−0.592825	+	0.805331i	$0.701987\pi$
$252$		0			0
$253$	−1.62599e13			−0.986175
$254$	8.23063e12	−	1.42559e13i	0.488481	−	0.846073i
$255$		0			0
$256$	−5.49756e11	−	9.52205e11i	−0.0312500	−	0.0541266i
$257$	2.74213e12	+	4.74952e12i	0.152566	+	0.264251i	0.932170	−	0.362021i	$-0.117913\pi$
$257$	2.74213e12	+	4.74952e12i	0.152566	+	0.264251i	−0.779604	+	0.626272i	$0.784580\pi$
$258$		0			0
$259$	−1.96292e13	+	3.39987e13i	−1.04653	+	1.81265i
$260$	−1.60061e13			−0.835475
$261$		0			0
$262$	−9.55430e12			−0.478125
$263$	−9.79707e12	+	1.69690e13i	−0.480109	+	0.831573i	−0.999740	−	0.0228179i	$-0.992736\pi$
$263$	−9.79707e12	+	1.69690e13i	−0.480109	+	0.831573i	0.519631	+	0.854391i	$0.326070\pi$
$264$		0			0
$265$	−8.59725e12	−	1.48909e13i	−0.404117	−	0.699952i
$266$	−2.32149e12	−	4.02095e12i	−0.106885	−	0.185131i
$267$		0			0
$268$	−2.31184e12	+	4.00422e12i	−0.102145	+	0.176920i
$269$	3.57029e13			1.54549			0.772745	−	0.634717i	$-0.218883\pi$
$269$	3.57029e13			1.54549			0.772745	+	0.634717i	$0.218883\pi$
$270$		0			0
$271$	3.60387e13			1.49774			0.748872	−	0.662714i	$-0.230596\pi$
$271$	3.60387e13			1.49774			0.748872	+	0.662714i	$0.230596\pi$
$272$	2.67894e12	−	4.64007e12i	0.109102	−	0.188971i
$273$		0			0
$274$	−9.85786e12	−	1.70743e13i	−0.385616	−	0.667906i
$275$	2.35857e13	+	4.08516e13i	0.904313	+	1.56632i
$276$		0			0
$277$	2.03652e13	−	3.52736e13i	0.750326	−	1.29960i	−0.197339	−	0.980335i	$-0.563230\pi$
$277$	2.03652e13	−	3.52736e13i	0.750326	−	1.29960i	0.947665	−	0.319267i	$-0.103437\pi$
$278$	1.67300e13			0.604297
$279$		0			0
$280$	−1.92215e13			−0.667449
$281$	−2.04413e12	+	3.54054e12i	−0.0696023	+	0.120555i	−0.898726	−	0.438510i	$-0.855506\pi$
$281$	−2.04413e12	+	3.54054e12i	−0.0696023	+	0.120555i	0.829124	+	0.559065i	$0.188840\pi$
$282$		0			0
$283$	6.67775e12	+	1.15662e13i	0.218678	+	0.378761i	0.954404	−	0.298518i	$-0.0964923\pi$
$283$	6.67775e12	+	1.15662e13i	0.218678	+	0.378761i	−0.735726	+	0.677279i	$0.763159\pi$
$284$	4.35690e12	+	7.54638e12i	0.139935	+	0.242375i
$285$		0			0
$286$	−1.13304e13	+	1.96249e13i	−0.350133	+	0.606449i
$287$	−2.05659e13			−0.623445
$288$		0			0
$289$	−8.16309e12			−0.238186
$290$	1.44526e13	−	2.50326e13i	0.413768	−	0.716668i
$291$		0			0
$292$	−1.03040e12	−	1.78470e12i	−0.0284053	−	0.0491994i
$293$	−1.09717e13	−	1.90035e13i	−0.296825	−	0.514116i	0.678583	−	0.734524i	$-0.262595\pi$
$293$	−1.09717e13	−	1.90035e13i	−0.296825	−	0.514116i	−0.975408	+	0.220408i	$0.929261\pi$
$294$		0			0
$295$	3.29681e13	−	5.71023e13i	0.859156	−	1.48810i
$296$	2.57242e13			0.658019
$297$		0			0
$298$	4.06447e13			1.00188
$299$	−2.03863e13	+	3.53100e13i	−0.493340	+	0.854489i
$300$		0			0
$301$	8.78224e12	+	1.52113e13i	0.204875	+	0.354854i
$302$	2.00594e13	+	3.47439e13i	0.459494	+	0.795866i
$303$		0			0
$304$	−1.52117e12	+	2.63475e12i	−0.0336026	+	0.0582015i
$305$	1.22855e14			2.66529
$306$		0			0
$307$	2.52177e11			0.00527770			0.00263885	−	0.999997i	$-0.499160\pi$
$307$	2.52177e11			0.00527770			0.00263885	+	0.999997i	$0.499160\pi$
$308$	−1.36065e13	+	2.35672e13i	−0.279717	+	0.484484i
$309$		0			0
$310$	4.49340e13	+	7.78280e13i	0.891428	+	1.54400i
$311$	2.47876e13	+	4.29334e13i	0.483117	+	0.836783i	0.999812	−	0.0193862i	$-0.00617121\pi$
$311$	2.47876e13	+	4.29334e13i	0.483117	+	0.836783i	−0.516695	+	0.856170i	$0.672838\pi$
$312$		0			0
$313$	−1.62159e13	+	2.80868e13i	−0.305104	+	0.528455i	−0.977284	−	0.211932i	$-0.932024\pi$
$313$	−1.62159e13	+	2.80868e13i	−0.305104	+	0.528455i	0.672181	+	0.740387i	$0.265358\pi$
$314$	−1.94146e13			−0.358935
$315$		0			0
$316$	−2.27721e13			−0.406560
$317$	4.78211e13	−	8.28286e13i	0.839061	−	1.45330i	−0.0516198	−	0.998667i	$-0.516438\pi$
$317$	4.78211e13	−	8.28286e13i	0.839061	−	1.45330i	0.890681	−	0.454629i	$-0.150228\pi$
$318$		0			0
$319$	−2.04614e13	−	3.54402e13i	−0.346807	−	0.600687i
$320$	6.29750e12	+	1.09076e13i	0.104916	+	0.181720i
$321$		0			0
$322$	−2.44815e13	+	4.24032e13i	−0.394122	+	0.682640i
$323$	−1.48252e13			−0.234632
$324$		0			0
$325$	1.18285e14			1.80955
$326$	−2.53441e13	+	4.38973e13i	−0.381224	+	0.660300i
$327$		0			0
$328$	6.73797e12	+	1.16705e13i	0.0979993	+	0.169740i
$329$	2.39593e12	+	4.14986e12i	0.0342686	+	0.0593549i
$330$		0			0
$331$	6.07895e13	−	1.05291e14i	0.840959	−	1.45658i	−0.0481260	−	0.998841i	$-0.515325\pi$
$331$	6.07895e13	−	1.05291e14i	0.840959	−	1.45658i	0.889085	−	0.457742i	$-0.151342\pi$
$332$	6.48054e12			0.0881762
$333$		0			0
$334$	−9.44872e13			−1.24385
$335$	2.64823e13	−	4.58687e13i	0.342933	−	0.593977i
$336$		0			0
$337$	4.19048e13	+	7.25813e13i	0.525169	+	0.909620i	0.999570	+	0.0293112i	$0.00933138\pi$
$337$	4.19048e13	+	7.25813e13i	0.525169	+	0.909620i	−0.474401	+	0.880309i	$0.657335\pi$
$338$	−2.62852e11	−	4.55273e11i	−0.00324093	−	0.00561345i
$339$		0			0
$340$	−3.06875e13	+	5.31523e13i	−0.366292	+	0.634436i
$341$	1.27232e14			1.49433
$342$		0			0
$343$	7.27043e13			0.826880
$344$	5.75461e12	−	9.96727e12i	0.0644087	−	0.111559i
$345$		0			0
$346$	−4.24656e13	−	7.35526e13i	−0.460383	−	0.797406i
$347$	3.89728e13	+	6.75029e13i	0.415863	+	0.720295i	0.995519	−	0.0945661i	$-0.0301464\pi$
$347$	3.89728e13	+	6.75029e13i	0.415863	+	0.720295i	−0.579656	+	0.814861i	$0.696813\pi$
$348$		0			0
$349$	−5.60894e13	+	9.71498e13i	−0.579884	+	1.00439i	0.415608	+	0.909544i	$0.363569\pi$
$349$	−5.60894e13	+	9.71498e13i	−0.579884	+	1.00439i	−0.995492	+	0.0948449i	$0.969764\pi$
$350$	1.42046e14			1.44563
$351$		0			0
$352$	1.78315e13			0.175875
$353$	7.98604e13	−	1.38322e14i	0.775480	−	1.34317i	−0.159045	−	0.987271i	$-0.550841\pi$
$353$	7.98604e13	−	1.38322e14i	0.775480	−	1.34317i	0.934524	−	0.355899i	$-0.115825\pi$
$354$		0			0
$355$	−4.99087e13	−	8.64444e13i	−0.469808	−	0.813731i
$356$	2.56633e13	+	4.44502e13i	0.237869	+	0.412001i
$357$		0			0
$358$	−6.50319e13	+	1.12639e14i	−0.584480	+	1.01235i
$359$	−2.46378e12			−0.0218063			−0.0109032	−	0.999941i	$-0.503471\pi$
$359$	−2.46378e12			−0.0218063			−0.0109032	+	0.999941i	$0.503471\pi$
$360$		0			0
$361$	−1.08072e14			−0.927735
$362$	−2.68917e13	+	4.65778e13i	−0.227364	+	0.393806i
$363$		0			0
$364$	3.41191e13	+	5.90961e13i	0.279860	+	0.484731i
$365$	1.18033e13	+	2.04439e13i	0.0953658	+	0.165178i
$366$		0			0
$367$	−6.70402e13	+	1.16117e14i	−0.525620	+	0.910400i	0.473935	+	0.880560i	$0.342833\pi$
$367$	−6.70402e13	+	1.16117e14i	−0.525620	+	0.910400i	−0.999555	+	0.0298402i	$0.990500\pi$
$368$	3.20833e13			0.247808
$369$		0			0
$370$	−2.94673e14			−2.20918
$371$	−3.66523e13	+	6.34836e13i	−0.270735	+	0.468927i
$372$		0			0
$373$	6.28422e13	+	1.08846e14i	0.450664	+	0.780573i	0.998427	−	0.0560606i	$-0.0178540\pi$
$373$	6.28422e13	+	1.08846e14i	0.450664	+	0.780573i	−0.547764	+	0.836633i	$0.684521\pi$
$374$	4.34462e13	+	7.52510e13i	0.307014	+	0.531763i
$375$		0			0
$376$	1.56994e12	−	2.71922e12i	0.0107733	−	0.0186600i
$377$	−1.02616e14			−0.693968
$378$		0			0
$379$	5.62301e13			0.369363			0.184681	−	0.982798i	$-0.440875\pi$
$379$	5.62301e13			0.369363			0.184681	+	0.982798i	$0.440875\pi$
$380$	1.74251e13	−	3.01812e13i	0.112815	−	0.195401i
$381$		0			0
$382$	6.54616e12	+	1.13383e13i	0.0411754	+	0.0713180i
$383$	−5.39129e13	−	9.33799e13i	−0.334272	−	0.578976i	0.649073	−	0.760726i	$-0.275157\pi$
$383$	−5.39129e13	−	9.33799e13i	−0.334272	−	0.578976i	−0.983345	+	0.181751i	$0.941824\pi$
$384$		0			0
$385$	1.55864e14	−	2.69964e14i	0.939099	−	1.62657i
$386$	−1.51010e14			−0.896964
$387$		0			0
$388$	9.70813e13			0.560481
$389$	−1.18814e14	+	2.05793e14i	−0.676311	+	1.17141i	0.299773	+	0.954011i	$0.403089\pi$
$389$	−1.18814e14	+	2.05793e14i	−0.676311	+	1.17141i	−0.976084	+	0.217395i	$0.930244\pi$
$390$		0			0
$391$	7.81704e13	+	1.35395e14i	0.432584	+	0.749257i
$392$	8.57659e12	+	1.48551e13i	0.0467995	+	0.0810591i
$393$		0			0
$394$	−5.77438e13	+	1.00015e14i	−0.306391	+	0.530685i
$395$	2.60857e14			1.36495
$396$		0			0
$397$	2.85970e14			1.45537			0.727683	−	0.685914i	$-0.240597\pi$
$397$	2.85970e14			1.45537			0.727683	+	0.685914i	$0.240597\pi$
$398$	2.75424e13	−	4.77048e13i	0.138244	−	0.239445i
$399$		0			0
$400$	−4.65383e13	−	8.06067e13i	−0.227238	−	0.393587i
$401$	4.65853e13	+	8.06882e13i	0.224365	+	0.388612i	0.956129	−	0.292947i	$-0.0946359\pi$
$401$	4.65853e13	+	8.06882e13i	0.224365	+	0.388612i	−0.731764	+	0.681558i	$0.761303\pi$
$402$		0			0
$403$	1.59520e14	−	2.76297e14i	0.747547	−	1.29479i
$404$	1.41263e13			0.0653026
$405$		0			0
$406$	−1.23230e14			−0.554402
$407$	−2.08593e14	+	3.61294e14i	−0.925830	+	1.60358i
$408$		0			0
$409$	−1.28475e14	−	2.22525e14i	−0.555061	−	0.961393i	−0.997899	−	0.0647915i	$-0.979362\pi$
$409$	−1.28475e14	−	2.22525e14i	−0.555061	−	0.961393i	0.442838	−	0.896601i	$-0.353972\pi$
$410$	−7.71840e13	−	1.33687e14i	−0.329015	−	0.569871i
$411$		0			0
$412$	−3.33740e13	+	5.78055e13i	−0.138508	+	0.239902i
$413$	−2.81103e14			−1.15117
$414$		0			0
$415$	−7.42350e13			−0.296036
$416$	2.23567e13	−	3.87230e13i	0.0879823	−	0.152390i
$417$		0			0
$418$	−2.46698e13	−	4.27294e13i	−0.0945576	−	0.163779i
$419$	1.48046e14	+	2.56423e14i	0.560039	+	0.970017i	0.997492	+	0.0707754i	$0.0225474\pi$
$419$	1.48046e14	+	2.56423e14i	0.560039	+	0.970017i	−0.437453	+	0.899241i	$0.644119\pi$
$420$		0			0
$421$	1.70243e14	−	2.94869e14i	0.627360	−	1.08662i	−0.360720	−	0.932674i	$-0.617469\pi$
$421$	1.70243e14	−	2.94869e14i	0.627360	−	1.08662i	0.988079	−	0.153944i	$-0.0491977\pi$
$422$	−5.45103e13			−0.198271
$423$		0			0
$424$	4.80332e13			0.170227
$425$	2.26780e14	−	3.92794e14i	0.793350	−	1.37412i
$426$		0			0
$427$	−2.61882e14	−	4.53592e14i	−0.892795	−	1.54637i
$428$	−4.77900e13	−	8.27747e13i	−0.160841	−	0.278585i
$429$		0			0
$430$	−6.59195e13	+	1.14176e14i	−0.216241	+	0.374540i
$431$	1.37789e14			0.446261			0.223130	−	0.974789i	$-0.428372\pi$
$431$	1.37789e14			0.446261			0.223130	+	0.974789i	$0.428372\pi$
$432$		0			0
$433$	3.52377e14			1.11256			0.556280	−	0.830995i	$-0.312228\pi$
$433$	3.52377e14			1.11256			0.556280	+	0.830995i	$0.312228\pi$
$434$	1.91565e14	−	3.31801e14i	0.597205	−	1.03439i
$435$		0			0
$436$	7.75012e13	+	1.34236e14i	0.235577	+	0.408031i
$437$	−4.43871e13	−	7.68808e13i	−0.133232	−	0.230765i
$438$		0			0
$439$	2.14592e14	−	3.71685e14i	0.628145	−	1.08798i	−0.359779	−	0.933038i	$-0.617148\pi$
$439$	2.14592e14	−	3.71685e14i	0.628145	−	1.08798i	0.987924	−	0.154941i	$-0.0495187\pi$
$440$	−2.04261e14			−0.590468
$441$		0			0
$442$	2.17887e14			0.614341
$443$	1.80541e14	−	3.12705e14i	0.502753	−	0.870793i	−0.497242	−	0.867612i	$-0.665654\pi$
$443$	1.80541e14	−	3.12705e14i	0.502753	−	0.870793i	0.999995	−	0.00318140i	$-0.00101267\pi$
$444$		0			0
$445$	−2.93976e14	−	5.09181e14i	−0.798603	−	1.38322i
$446$	−2.34005e14	−	4.05308e14i	−0.627889	−	1.08754i
$447$		0			0
$448$	2.68478e13	−	4.65018e13i	0.0702879	−	0.121742i
$449$	−6.27688e12			−0.0162326			−0.00811632	−	0.999967i	$-0.502584\pi$
$449$	−6.27688e12			−0.0162326			−0.00811632	+	0.999967i	$0.502584\pi$
$450$		0			0
$451$	−2.18548e14			−0.551539
$452$	−1.21523e14	+	2.10483e14i	−0.302967	+	0.524755i
$453$		0			0
$454$	5.38331e13	+	9.32416e13i	0.130991	+	0.226883i
$455$	−3.90838e14	−	6.76950e14i	−0.939580	−	1.62740i
$456$		0			0
$457$	−2.30453e14	+	3.99157e14i	−0.540809	+	0.936708i	0.458049	+	0.888927i	$0.348548\pi$
$457$	−2.30453e14	+	3.99157e14i	−0.540809	+	0.936708i	−0.998858	+	0.0477814i	$0.984785\pi$
$458$	−6.07745e13			−0.140916
$459$		0			0
$460$	−3.67516e14			−0.831972
$461$	−3.98699e14	+	6.90567e14i	−0.891847	+	1.54472i	−0.0541881	+	0.998531i	$0.517257\pi$
$461$	−3.98699e14	+	6.90567e14i	−0.891847	+	1.54472i	−0.837659	+	0.546194i	$0.816076\pi$
$462$		0			0
$463$	2.90449e14	+	5.03072e14i	0.634416	+	1.09884i	0.986639	+	0.162924i	$0.0520925\pi$
$463$	2.90449e14	+	5.03072e14i	0.634416	+	1.09884i	−0.352223	+	0.935916i	$0.614574\pi$
$464$	4.03737e13	+	6.99292e13i	0.0871463	+	0.150942i
$465$		0			0
$466$	2.43042e13	−	4.20962e13i	0.0512341	−	0.0887401i
$467$	−8.22532e14			−1.71360			−0.856801	−	0.515647i	$-0.827552\pi$
$467$	−8.22532e14			−1.71360			−0.856801	+	0.515647i	$0.827552\pi$
$468$		0			0
$469$	−2.25801e14			−0.459490
$470$	−1.79838e13	+	3.11489e13i	−0.0361696	+	0.0626476i
$471$		0			0
$472$	9.20970e13	+	1.59517e14i	0.180952	+	0.313419i
$473$	9.33262e13	+	1.61646e14i	0.181246	+	0.313927i
$474$		0			0
$475$	−1.28771e14	+	2.23038e14i	−0.244345	+	0.423218i
$476$	2.61657e14			0.490789
$477$		0			0
$478$	−2.66079e14			−0.487705
$479$	2.44117e14	−	4.22824e14i	0.442337	−	0.766151i	−0.555525	−	0.831500i	$-0.687483\pi$
$479$	2.44117e14	−	4.22824e14i	0.442337	−	0.766151i	0.997862	+	0.0653491i	$0.0208161\pi$
$480$		0			0
$481$	5.23060e14	+	9.05966e14i	0.926304	+	1.60441i
$482$	−2.08202e14	−	3.60616e14i	−0.364524	−	0.631374i
$483$		0			0
$484$	1.48708e12	−	2.57570e12i	0.00254498	−	0.00440804i
$485$	−1.11207e15			−1.88172
$486$		0			0
$487$	−2.97281e13			−0.0491766			−0.0245883	−	0.999698i	$-0.507827\pi$
$487$	−2.97281e13			−0.0491766			−0.0245883	+	0.999698i	$0.507827\pi$
$488$	−1.71599e14	+	2.97219e14i	−0.280677	+	0.486146i
$489$		0			0
$490$	−9.82455e13	−	1.70166e14i	−0.157121	−	0.272141i
$491$	−4.08068e14	−	7.06794e14i	−0.645333	−	1.11775i	−0.984225	−	0.176924i	$-0.943385\pi$
$491$	−4.08068e14	−	7.06794e14i	−0.645333	−	1.11775i	0.338892	−	0.940825i	$-0.389948\pi$
$492$		0			0
$493$	−1.96740e14	+	3.40763e14i	−0.304252	+	0.526980i
$494$	−1.23722e14			−0.189212
$495$		0			0
$496$	−2.51048e14			−0.375498
$497$	−2.12774e14	+	3.68535e14i	−0.314744	+	0.545153i
$498$		0			0
$499$	−3.04958e14	−	5.28203e14i	−0.441253	−	0.764272i	0.556530	−	0.830828i	$-0.312132\pi$
$499$	−3.04958e14	−	5.28203e14i	−0.441253	−	0.764272i	−0.997783	+	0.0665553i	$0.978799\pi$
$500$	2.39850e14	+	4.15432e14i	0.343245	+	0.594518i
$501$		0			0
$502$	−2.99421e14	+	5.18612e14i	−0.419191	+	0.726060i
$503$	2.40472e14			0.332998			0.166499	−	0.986042i	$-0.446754\pi$
$503$	2.40472e14			0.332998			0.166499	+	0.986042i	$0.446754\pi$
$504$		0			0
$505$	−1.61818e14			−0.219242
$506$	−2.60158e14	+	4.50606e14i	−0.348665	+	0.603906i
$507$		0			0
$508$	−2.63380e14	−	4.56188e14i	−0.345408	−	0.598264i
$509$	7.83599e13	+	1.35723e14i	0.101659	+	0.176079i	0.912368	−	0.409370i	$-0.134252\pi$
$509$	7.83599e13	+	1.35723e14i	0.101659	+	0.176079i	−0.810709	+	0.585449i	$0.800918\pi$
$510$		0			0
$511$	5.03205e13	−	8.71576e13i	0.0638895	−	0.110660i
$512$	−3.51844e13			−0.0441942
$513$		0			0
$514$	1.75497e14			0.215760
$515$	3.82302e14	−	6.62167e14i	0.465015	−	0.805430i
$516$		0			0
$517$	2.54608e13	+	4.40994e13i	0.0303161	+	0.0525091i
$518$	6.28134e14	+	1.08796e15i	0.740012	+	1.28174i
$519$		0			0
$520$	−2.56098e14	+	4.43575e14i	−0.295385	+	0.511622i
$521$	−1.00579e14			−0.114788			−0.0573942	−	0.998352i	$-0.518279\pi$
$521$	−1.00579e14			−0.114788			−0.0573942	+	0.998352i	$0.518279\pi$
$522$		0			0
$523$	1.22443e15			1.36827			0.684137	−	0.729354i	$-0.260179\pi$
$523$	1.22443e15			1.36827			0.684137	+	0.729354i	$0.260179\pi$
$524$	−1.52869e14	+	2.64776e14i	−0.169043	+	0.292791i
$525$		0			0
$526$	3.13506e14	+	5.43009e14i	0.339488	+	0.588011i
$527$	−6.11675e14	−	1.05945e15i	−0.655485	−	1.13533i
$528$		0			0
$529$	8.31667e12	−	1.44049e13i	0.00872858	−	0.0151183i
$530$	−5.50224e14			−0.571508
$531$		0			0
$532$	−1.48576e14			−0.151159
$533$	−2.74011e14	+	4.74601e14i	−0.275910	+	0.477891i
$534$		0			0
$535$	5.47438e14	+	9.48191e14i	0.539995	+	0.935298i
$536$	7.39788e13	+	1.28135e14i	0.0722272	+	0.125101i
$537$		0			0
$538$	5.71246e14	−	9.89428e14i	0.546413	−	0.946415i
$539$	−2.78184e14			−0.263387
$540$		0			0
$541$	−3.62345e14			−0.336154			−0.168077	−	0.985774i	$-0.553756\pi$
$541$	−3.62345e14			−0.336154			−0.168077	+	0.985774i	$0.553756\pi$
$542$	5.76619e14	−	9.98733e14i	0.529533	−	0.917177i
$543$		0			0
$544$	−8.57262e13	−	1.48482e14i	−0.0771471	−	0.133623i
$545$	−8.87782e14	−	1.53768e15i	−0.790907	−	1.36989i
$546$		0			0
$547$	−6.63152e14	+	1.14861e15i	−0.579006	+	1.00287i	0.416588	+	0.909095i	$0.363226\pi$
$547$	−6.63152e14	+	1.14861e15i	−0.579006	+	1.00287i	−0.995594	+	0.0937719i	$0.970108\pi$
$548$	−6.30903e14			−0.545343
$549$		0			0
$550$	1.50948e15			1.27889
$551$	1.11714e14	−	1.93494e14i	0.0937071	−	0.162305i
$552$		0			0
$553$	−5.56049e14	−	9.63105e14i	−0.457220	−	0.791928i
$554$	−6.51686e14	−	1.12875e15i	−0.530560	−	0.918958i
$555$		0			0
$556$	2.67681e14	−	4.63637e14i	0.213651	−	0.370055i
$557$	−2.24474e15			−1.77404			−0.887018	−	0.461735i	$-0.847227\pi$
$557$	−2.24474e15			−1.77404			−0.887018	+	0.461735i	$0.847227\pi$
$558$		0			0
$559$	4.68042e14			0.362677
$560$	−3.07544e14	+	5.32682e14i	−0.235979	+	0.408728i
$561$		0			0
$562$	6.54122e13	+	1.13297e14i	0.0492163	+	0.0852451i
$563$	5.50889e14	+	9.54168e14i	0.410457	+	0.710933i	0.994940	−	0.100473i	$-0.0320357\pi$
$563$	5.50889e14	+	9.54168e14i	0.410457	+	0.710933i	−0.584482	+	0.811406i	$0.698702\pi$
$564$		0			0
$565$	1.39205e15	−	2.41110e15i	1.01716	−	1.76177i
$566$	4.27376e14			0.309257
$567$		0			0
$568$	2.78842e14			0.197898
$569$	−8.45537e14	+	1.46451e15i	−0.594313	+	1.02938i	0.399330	+	0.916807i	$0.369243\pi$
$569$	−8.45537e14	+	1.46451e15i	−0.594313	+	1.02938i	−0.993643	+	0.112573i	$0.964091\pi$
$570$		0			0
$571$	1.18287e15	+	2.04880e15i	0.815529	+	1.41254i	0.908947	+	0.416911i	$0.136887\pi$
$571$	1.18287e15	+	2.04880e15i	0.815529	+	1.41254i	−0.0934177	+	0.995627i	$0.529779\pi$
$572$	3.62574e14	+	6.27996e14i	0.247582	+	0.428824i
$573$		0			0
$574$	−3.29055e14	+	5.69940e14i	−0.220421	+	0.381780i
$575$	2.71594e15			1.80197
$576$		0			0
$577$	−3.25902e14			−0.212139			−0.106069	−	0.994359i	$-0.533827\pi$
$577$	−3.25902e14			−0.212139			−0.106069	+	0.994359i	$0.533827\pi$
$578$	−1.30609e14	+	2.26222e14i	−0.0842115	+	0.145859i
$579$		0			0
$580$	−4.62483e14	−	8.01045e14i	−0.292578	−	0.506761i
$581$	1.58242e14	+	2.74082e14i	0.0991635	+	0.171756i
$582$		0			0
$583$	−3.89493e14	+	6.74622e14i	−0.239509	+	0.414842i
$584$	−6.59455e13			−0.0401712
$585$		0			0
$586$	−7.02187e14			−0.419774
$587$	1.38342e15	−	2.39615e15i	0.819303	−	1.41907i	−0.0868939	−	0.996218i	$-0.527694\pi$
$587$	1.38342e15	−	2.39615e15i	0.819303	−	1.41907i	0.906197	−	0.422856i	$-0.138973\pi$
$588$		0			0
$589$	3.47325e14	+	6.01584e14i	0.201884	+	0.349673i
$590$	−1.05498e15	−	1.82728e15i	−0.607515	−	1.05225i
$591$		0			0
$592$	4.11588e14	−	7.12891e14i	0.232645	−	0.402953i
$593$	1.95966e15			1.09744			0.548719	−	0.836007i	$-0.315116\pi$
$593$	1.95966e15			1.09744			0.548719	+	0.836007i	$0.315116\pi$
$594$		0			0
$595$	−2.99731e15			−1.64774
$596$	6.50315e14	−	1.12638e15i	0.354217	−	0.613522i
$597$		0			0
$598$	6.52360e14	+	1.12992e15i	0.348844	+	0.604215i
$599$	1.68696e15	+	2.92191e15i	0.893837	+	1.54817i	0.835238	+	0.549889i	$0.185330\pi$
$599$	1.68696e15	+	2.92191e15i	0.893837	+	1.54817i	0.0585987	+	0.998282i	$0.481337\pi$
$600$		0			0
$601$	−1.56793e15	+	2.71573e15i	−0.815673	+	1.41279i	0.0931699	+	0.995650i	$0.470300\pi$
$601$	−1.56793e15	+	2.71573e15i	−0.815673	+	1.41279i	−0.908843	+	0.417138i	$0.863033\pi$
$602$	5.62063e14			0.289737
$603$		0			0
$604$	1.28380e15			0.649822
$605$	−1.70346e13	+	2.95048e13i	−0.00854433	+	0.0147992i
$606$		0			0
$607$	−1.83784e15	−	3.18323e15i	−0.905253	−	1.56794i	−0.820577	−	0.571536i	$-0.806348\pi$
$607$	−1.83784e15	−	3.18323e15i	−0.905253	−	1.56794i	−0.0846760	−	0.996409i	$-0.526986\pi$
$608$	4.86775e13	+	8.43119e13i	0.0237607	+	0.0411547i
$609$		0			0
$610$	1.96568e15	−	3.40466e15i	0.942322	−	1.63215i
$611$	1.27689e14			0.0606633
$612$		0			0
$613$	−9.78886e14			−0.456772			−0.228386	−	0.973571i	$-0.573345\pi$
$613$	−9.78886e14			−0.456772			−0.228386	+	0.973571i	$0.573345\pi$
$614$	4.03483e12	−	6.98853e12i	0.00186595	−	0.00323191i
$615$		0			0
$616$	4.35409e14	+	7.54150e14i	0.197790	+	0.342582i
$617$	7.31277e14	+	1.26661e15i	0.329241	+	0.570261i	0.982361	−	0.186992i	$-0.0598739\pi$
$617$	7.31277e14	+	1.26661e15i	0.329241	+	0.570261i	−0.653121	+	0.757254i	$0.726541\pi$
$618$		0			0
$619$	−2.15051e15	+	3.72479e15i	−0.951135	+	1.64741i	−0.208159	+	0.978095i	$0.566747\pi$
$619$	−2.15051e15	+	3.72479e15i	−0.951135	+	1.64741i	−0.742975	+	0.669319i	$0.766586\pi$
$620$	2.87578e15			1.26067
$621$		0			0
$622$	1.58641e15			0.683231
$623$	−1.25329e15	+	2.17077e15i	−0.535018	+	0.926678i
$624$		0			0
$625$	−5.80391e14	−	1.00527e15i	−0.243434	−	0.421639i
$626$	5.18909e14	+	8.98777e14i	0.215741	+	0.373674i
$627$		0			0
$628$	−3.10634e14	+	5.38034e14i	−0.126903	+	0.219802i
$629$	4.01131e15			1.62446
$630$		0			0
$631$	−5.95346e14			−0.236924			−0.118462	−	0.992959i	$-0.537796\pi$
$631$	−5.95346e14			−0.236924			−0.118462	+	0.992959i	$0.537796\pi$
$632$	−3.64354e14	+	6.31080e14i	−0.143741	+	0.248966i
$633$		0			0
$634$	−1.53027e15	−	2.65051e15i	−0.593306	−	1.02764i
$635$	3.01704e15	+	5.22566e15i	1.15965	+	2.00857i
$636$		0			0
$637$	−3.48781e14	+	6.04107e14i	−0.131761	+	0.228216i
$638$	−1.30953e15			−0.490459
$639$		0			0
$640$	4.03040e14			0.148374
$641$	3.75631e14	−	6.50612e14i	0.137101	−	0.237467i	−0.789297	−	0.614012i	$-0.789555\pi$
$641$	3.75631e14	−	6.50612e14i	0.137101	−	0.237467i	0.926398	+	0.376545i	$0.122888\pi$
$642$		0			0
$643$	−7.30722e14	−	1.26565e15i	−0.262175	−	0.454101i	0.704644	−	0.709561i	$-0.251107\pi$
$643$	−7.30722e14	−	1.26565e15i	−0.262175	−	0.454101i	−0.966820	+	0.255460i	$0.917773\pi$
$644$	7.83409e14	+	1.35690e15i	0.278687	+	0.482699i
$645$		0			0
$646$	−2.37204e14	+	4.10849e14i	−0.0829551	+	0.143682i
$647$	−3.57862e15			−1.24091			−0.620457	−	0.784241i	$-0.713053\pi$
$647$	−3.57862e15			−1.24091			−0.620457	+	0.784241i	$0.713053\pi$
$648$		0			0
$649$	−2.98719e15			−1.01840
$650$	1.89256e15	−	3.27801e15i	0.639773	−	1.10812i
$651$		0			0
$652$	8.11012e14	+	1.40471e15i	0.269566	+	0.466903i
$653$	−3.65698e14	−	6.33407e14i	−0.120531	−	0.208766i	0.799446	−	0.600738i	$-0.205126\pi$
$653$	−3.65698e14	−	6.33407e14i	−0.120531	−	0.208766i	−0.919977	+	0.391972i	$0.871793\pi$
$654$		0			0
$655$	1.75112e15	−	3.03303e15i	0.567531	−	0.982993i
$656$	4.31230e14			0.138592
$657$		0			0
$658$	1.53339e14			0.0484631
$659$	8.49935e14	−	1.47213e15i	0.266389	−	0.461399i	−0.701538	−	0.712632i	$-0.747503\pi$
$659$	8.49935e14	−	1.47213e15i	0.266389	−	0.461399i	0.967927	+	0.251233i	$0.0808361\pi$
$660$		0			0
$661$	8.93022e13	+	1.54676e14i	0.0275267	+	0.0476776i	0.879461	−	0.475972i	$-0.157904\pi$
$661$	8.93022e13	+	1.54676e14i	0.0275267	+	0.0476776i	−0.851934	+	0.523649i	$0.824570\pi$
$662$	−1.94526e15	−	3.36930e15i	−0.594648	−	1.02996i
$663$		0			0
$664$	1.03689e14	−	1.79594e14i	0.0311750	−	0.0539967i
$665$	1.70195e15			0.507489
$666$		0			0
$667$	−2.35617e15			−0.691059
$668$	−1.51179e15	+	2.61851e15i	−0.439767	+	0.761698i
$669$		0			0
$670$	−8.47433e14	−	1.46780e15i	−0.242490	−	0.420005i
$671$	−2.78294e15	−	4.82019e15i	−0.789823	−	1.36801i
$672$		0			0
$673$	4.63338e14	−	8.02525e14i	0.129364	−	0.224066i	−0.794066	−	0.607831i	$-0.792040\pi$
$673$	4.63338e14	−	8.02525e14i	0.129364	−	0.224066i	0.923431	+	0.383766i	$0.125373\pi$
$674$	2.68191e15			0.742702
$675$		0			0
$676$	−1.68225e13			−0.00458336
$677$	7.48322e13	−	1.29613e14i	0.0202232	−	0.0350277i	−0.855737	−	0.517412i	$-0.826896\pi$
$677$	7.48322e13	−	1.29613e14i	0.0202232	−	0.0350277i	0.875960	+	0.482384i	$0.160229\pi$
$678$		0			0
$679$	2.37053e15	+	4.10588e15i	0.630320	+	1.09175i
$680$	9.82000e14	+	1.70087e15i	0.259008	+	0.448614i
$681$		0			0
$682$	2.03571e15	−	3.52595e15i	0.528325	−	0.915086i
$683$	6.74856e15			1.73739			0.868694	−	0.495348i	$-0.164960\pi$
$683$	6.74856e15			1.73739			0.868694	+	0.495348i	$0.164960\pi$
$684$		0			0
$685$	7.22704e15			1.83089
$686$	1.16327e15	−	2.01484e15i	0.292346	−	0.506358i
$687$		0			0
$688$	−1.84147e14	−	3.18953e14i	−0.0455438	−	0.0788842i
$689$	9.76676e14	+	1.69165e15i	0.239632	+	0.415055i
$690$		0			0
$691$	8.06359e14	−	1.39665e15i	0.194715	−	0.337256i	−0.752092	−	0.659058i	$-0.770955\pi$
$691$	8.06359e14	−	1.39665e15i	0.194715	−	0.337256i	0.946807	+	0.321802i	$0.104289\pi$
$692$	−2.71780e15			−0.651079
$693$		0			0
$694$	2.49426e15			0.588119
$695$	−3.06630e15	+	5.31099e15i	−0.717297	+	1.24239i
$696$		0			0
$697$	1.05069e15	+	1.81984e15i	0.241931	+	0.419038i
$698$	1.79486e15	+	3.10879e15i	0.410040	+	0.710210i
$699$		0			0
$700$	2.27274e15	−	3.93650e15i	0.511106	−	0.885261i
$701$	4.16261e14			0.0928789			0.0464394	−	0.998921i	$-0.485213\pi$
$701$	4.16261e14			0.0928789			0.0464394	+	0.998921i	$0.485213\pi$
$702$		0			0
$703$	−2.27772e15			−0.500319
$704$	2.85304e14	−	4.94161e14i	0.0621811	−	0.107701i
$705$		0			0
$706$	−2.55553e15	−	4.42631e15i	−0.548347	−	0.949765i
$707$	3.44935e14	+	5.97445e14i	0.0734397	+	0.127201i
$708$		0			0
$709$	1.41486e15	−	2.45061e15i	0.296592	−	0.513713i	−0.678762	−	0.734358i	$-0.737483\pi$
$709$	1.41486e15	−	2.45061e15i	0.296592	−	0.513713i	0.975354	+	0.220646i	$0.0708165\pi$
$710$	−3.19416e15			−0.664408
$711$		0			0
$712$	1.64245e15			0.336398
$713$	3.66274e15	−	6.34405e15i	0.744413	−	1.28936i
$714$		0			0
$715$	−4.15331e15	−	7.19375e15i	−0.831211	−	1.43970i
$716$	2.08102e15	+	3.60444e15i	0.413290	+	0.715839i
$717$		0			0
$718$	−3.94205e13	+	6.82783e13i	−0.00770970	+	0.0133536i
$719$	6.81122e15			1.32195			0.660977	−	0.750406i	$-0.270142\pi$
$719$	6.81122e15			1.32195			0.660977	+	0.750406i	$0.270142\pi$
$720$		0			0
$721$	−3.25970e15			−0.623066
$722$	−1.72915e15	+	2.99498e15i	−0.328004	+	0.568119i
$723$		0			0
$724$	8.60535e14	+	1.49049e15i	0.160771	+	0.278463i
$725$	3.41774e15	+	5.91970e15i	0.633694	+	1.09759i
$726$		0			0
$727$	−1.36596e15	+	2.36590e15i	−0.249458	+	0.432074i	−0.963376	−	0.268156i	$-0.913586\pi$
$727$	−1.36596e15	+	2.36590e15i	−0.249458	+	0.432074i	0.713918	+	0.700230i	$0.246919\pi$
$728$	2.18363e15			0.395782
$729$		0			0
$730$	7.55411e14			0.134868
$731$	8.97345e14	−	1.55425e15i	0.159006	−	0.275407i
$732$		0			0
$733$	3.29184e15	+	5.70163e15i	0.574602	+	0.995239i	0.996085	+	0.0884030i	$0.0281763\pi$
$733$	3.29184e15	+	5.70163e15i	0.574602	+	0.995239i	−0.421483	+	0.906836i	$0.638490\pi$
$734$	2.14528e15	+	3.71574e15i	0.371669	+	0.643750i
$735$		0			0
$736$	5.13332e14	−	8.89118e14i	0.0876134	−	0.151751i
$737$	−2.39952e15			−0.406494
$738$		0			0
$739$	4.37564e15			0.730294			0.365147	−	0.930950i	$-0.381019\pi$
$739$	4.37564e15			0.730294			0.365147	+	0.930950i	$0.381019\pi$
$740$	−4.71477e15	+	8.16622e15i	−0.781063	+	1.35284i
$741$		0			0
$742$	1.17287e15	+	2.03148e15i	0.191439	+	0.331582i
$743$	−2.45030e15	−	4.24404e15i	−0.396990	−	0.687608i	0.596363	−	0.802715i	$-0.296612\pi$
$743$	−2.45030e15	−	4.24404e15i	−0.396990	−	0.687608i	−0.993353	+	0.115108i	$0.963279\pi$
$744$		0			0
$745$	−7.44941e15	+	1.29028e16i	−1.18922	+	2.05979i
$746$	4.02190e15			0.637335
$747$		0			0
$748$	2.78055e15			0.434183
$749$	2.33387e15	−	4.04238e15i	0.361765	−	0.626596i
$750$		0			0
$751$	3.52468e14	+	6.10492e14i	0.0538394	+	0.0932525i	0.891689	−	0.452649i	$-0.149521\pi$
$751$	3.52468e14	+	6.10492e14i	0.0538394	+	0.0932525i	−0.837850	+	0.545901i	$0.816187\pi$
$752$	−5.02382e13	−	8.70150e13i	−0.00761791	−	0.0131946i
$753$		0			0
$754$	−1.64186e15	+	2.84379e15i	−0.245355	+	0.424967i
$755$	−1.47060e16			−2.18166
$756$		0			0
$757$	5.25516e15			0.768348			0.384174	−	0.923261i	$-0.374486\pi$
$757$	5.25516e15			0.768348			0.384174	+	0.923261i	$0.374486\pi$
$758$	8.99682e14	−	1.55829e15i	0.130589	−	0.226188i
$759$		0			0
$760$	−5.57604e14	−	9.65799e14i	−0.0797722	−	0.138169i
$761$	−1.90668e15	−	3.30247e15i	−0.270808	−	0.469054i	0.698261	−	0.715844i	$-0.253958\pi$
$761$	−1.90668e15	−	3.30247e15i	−0.270808	−	0.469054i	−0.969069	+	0.246790i	$0.920624\pi$
$762$		0			0
$763$	−3.78484e15	+	6.55554e15i	−0.529862	+	0.917748i
$764$	4.18954e14			0.0582309
$765$		0			0
$766$	−3.45043e15			−0.472732
$767$	−3.74528e15	+	6.48701e15i	−0.509459	+	0.882410i
$768$		0			0
$769$	4.90621e15	+	8.49780e15i	0.657886	+	1.13949i	0.981162	+	0.193188i	$0.0618827\pi$
$769$	4.90621e15	+	8.49780e15i	0.657886	+	1.13949i	−0.323275	+	0.946305i	$0.604784\pi$
$770$	−4.98764e15	−	8.63885e15i	−0.664043	−	1.15016i
$771$		0			0
$772$	−2.41616e15	+	4.18491e15i	−0.317125	+	0.549276i
$773$	7.09136e15			0.924149			0.462075	−	0.886841i	$-0.347105\pi$
$773$	7.09136e15			0.924149			0.462075	+	0.886841i	$0.347105\pi$
$774$		0			0
$775$	−2.12519e16			−2.73048
$776$	1.55330e15	−	2.69040e15i	0.198160	−	0.343223i
$777$		0			0
$778$	3.80206e15	+	6.58537e15i	0.478224	+	0.828309i
$779$	−5.96605e14	−	1.03335e15i	−0.0745129	−	0.129060i
$780$		0			0
$781$	−2.26108e15	+	3.91631e15i	−0.278442	+	0.482276i
$782$	5.00291e15			0.611766
$783$		0			0
$784$	5.48902e14			0.0661845
$785$	3.55834e15	−	6.16323e15i	0.426054	−	0.737947i
$786$		0			0
$787$	1.23200e15	+	2.13388e15i	0.145462	+	0.251947i	0.929545	−	0.368708i	$-0.120200\pi$
$787$	1.23200e15	+	2.13388e15i	0.145462	+	0.251947i	−0.784083	+	0.620656i	$0.786867\pi$
$788$	1.84780e15	+	3.20049e15i	0.216651	+	0.375251i
$789$		0			0
$790$	4.17370e15	−	7.22907e15i	0.482584	−	0.835860i
$791$	−1.18693e16			−1.36288
$792$		0			0
$793$	−1.39567e16			−1.58045
$794$	4.57551e15	−	7.92502e15i	0.514549	−	0.891226i
$795$		0			0
$796$	−8.81357e14	−	1.52655e15i	−0.0977529	−	0.169313i
$797$	−1.52468e15	−	2.64082e15i	−0.167941	−	0.290883i	0.769754	−	0.638340i	$-0.220379\pi$
$797$	−1.52468e15	−	2.64082e15i	−0.167941	−	0.290883i	−0.937696	+	0.347457i	$0.887045\pi$
$798$		0			0
$799$	2.44809e14	−	4.24022e14i	0.0265962	−	0.0460660i
$800$	−2.97845e15			−0.321363
$801$		0			0
$802$	2.98146e15			0.317300
$803$	5.34741e14	−	9.26198e14i	0.0565207	−	0.0978967i
$804$		0			0
$805$	−8.97401e15	−	1.55434e16i	−0.935640	−	1.62058i
$806$	−5.10465e15	−	8.84152e15i	−0.528595	−	0.915554i
$807$		0			0
$808$	2.26021e14	−	3.91479e14i	0.0230880	−	0.0399895i
$809$	−3.92265e15			−0.397982			−0.198991	−	0.980001i	$-0.563766\pi$
$809$	−3.92265e15			−0.397982			−0.198991	+	0.980001i	$0.563766\pi$
$810$		0			0
$811$	1.75012e16			1.75168			0.875838	−	0.482606i	$-0.160310\pi$
$811$	1.75012e16			1.75168			0.875838	+	0.482606i	$0.160310\pi$
$812$	−1.97169e15	+	3.41506e15i	−0.196011	+	0.339500i
$813$		0			0
$814$	6.67499e15	+	1.15614e16i	0.654661	+	1.13391i
$815$	−9.29021e15	−	1.60911e16i	−0.905021	−	1.56754i
$816$		0			0
$817$	−5.09535e14	+	8.82540e14i	−0.0489725	+	0.0848229i
$818$	−8.22240e15			−0.784974
$819$		0			0
$820$	−4.93977e15			−0.465298
$821$	−2.24074e15	+	3.88108e15i	−0.209655	+	0.363133i	−0.951606	−	0.307321i	$-0.900567\pi$
$821$	−2.24074e15	+	3.88108e15i	−0.209655	+	0.363133i	0.741951	+	0.670454i	$0.233901\pi$
$822$		0			0
$823$	1.19410e15	+	2.06823e15i	0.110240	+	0.190942i	0.915867	−	0.401482i	$-0.131505\pi$
$823$	1.19410e15	+	2.06823e15i	0.110240	+	0.190942i	−0.805627	+	0.592423i	$0.798171\pi$
$824$	1.06797e15	+	1.84978e15i	0.0979397	+	0.169637i
$825$		0			0
$826$	−4.49764e15	+	7.79014e15i	−0.407000	+	0.704945i
$827$	3.42245e15			0.307650			0.153825	−	0.988098i	$-0.450841\pi$
$827$	3.42245e15			0.307650			0.153825	+	0.988098i	$0.450841\pi$
$828$		0			0
$829$	7.18881e15			0.637686			0.318843	−	0.947808i	$-0.396706\pi$
$829$	7.18881e15			0.637686			0.318843	+	0.947808i	$0.396706\pi$
$830$	−1.18776e15	+	2.05726e15i	−0.104664	+	0.181284i
$831$		0			0
$832$	−7.15416e14	−	1.23914e15i	−0.0622129	−	0.107756i
$833$	1.33739e15	+	2.31643e15i	0.115534	+	0.200111i
$834$		0			0
$835$	1.73177e16	−	2.99952e16i	1.47644	−	2.55727i
$836$	−1.57887e15			−0.133725
$837$		0			0
$838$	9.47492e15			0.792015
$839$	−6.25504e15	+	1.08340e16i	−0.519444	+	0.899704i	0.480300	+	0.877104i	$0.340528\pi$
$839$	−6.25504e15	+	1.08340e16i	−0.519444	+	0.899704i	−0.999745	+	0.0226000i	$0.992806\pi$
$840$		0			0
$841$	3.13524e15	+	5.43040e15i	0.256976	+	0.445096i
$842$	−5.44776e15	−	9.43580e15i	−0.443610	−	0.768355i
$843$		0			0
$844$	−8.72164e14	+	1.51063e15i	−0.0700995	+	0.121416i
$845$	1.92703e14			0.0153878
$846$		0			0
$847$	1.45246e14			0.0114484
$848$	7.68531e14	−	1.33114e15i	0.0601845	−	0.104243i
$849$		0			0
$850$	−7.25695e15	−	1.25694e16i	−0.560983	−	0.971652i
$851$	1.20100e16	+	2.08019e16i	0.922421	+	1.59768i
$852$		0			0
$853$	−2.94258e15	+	5.09670e15i	−0.223105	+	0.386429i	−0.955749	−	0.294183i	$-0.904953\pi$
$853$	−2.94258e15	+	5.09670e15i	−0.223105	+	0.386429i	0.732644	+	0.680612i	$0.238286\pi$
$854$	−1.67604e16			−1.26260
$855$		0			0
$856$	−3.05856e15			−0.227463
$857$	−1.28998e15	+	2.23430e15i	−0.0953207	+	0.165100i	−0.909742	−	0.415173i	$-0.863721\pi$
$857$	−1.28998e15	+	2.23430e15i	−0.0953207	+	0.165100i	0.814422	+	0.580273i	$0.197054\pi$
$858$		0			0
$859$	1.57437e15	+	2.72689e15i	0.114854	+	0.198932i	0.917721	−	0.397225i	$-0.130027\pi$
$859$	1.57437e15	+	2.72689e15i	0.114854	+	0.198932i	−0.802868	+	0.596157i	$0.796693\pi$
$860$	2.10942e15	+	3.65363e15i	0.152905	+	0.264840i
$861$		0			0
$862$	2.20462e15	−	3.81851e15i	0.157777	−	0.273278i
$863$	−2.28539e16			−1.62518			−0.812589	−	0.582837i	$-0.801942\pi$
$863$	−2.28539e16			−1.62518			−0.812589	+	0.582837i	$0.801942\pi$
$864$		0			0
$865$	3.11326e16			2.18588
$866$	5.63803e15	−	9.76535e15i	0.393350	−	0.681302i
$867$		0			0
$868$	−6.13009e15	−	1.06176e16i	−0.422288	−	0.731424i
$869$	−5.90897e15	−	1.02346e16i	−0.404485	−	0.700589i
$870$		0			0
$871$	−3.00847e15	+	5.21083e15i	−0.203351	+	0.352214i
$872$	4.96007e15			0.333156
$873$		0			0
$874$	−2.84078e15			−0.188419
$875$	−1.17133e16	+	2.02880e16i	−0.772031	+	1.33720i
$876$		0			0
$877$	9.18477e15	+	1.59085e16i	0.597820	+	1.03545i	0.993142	+	0.116912i	$0.0372996\pi$
$877$	9.18477e15	+	1.59085e16i	0.597820	+	1.03545i	−0.395322	+	0.918543i	$0.629367\pi$
$878$	−6.86696e15	−	1.18939e16i	−0.444165	−	0.769317i
$879$		0			0
$880$	−3.26818e15	+	5.66065e15i	−0.208762	+	0.361586i
$881$	−1.17507e16			−0.745925			−0.372963	−	0.927846i	$-0.621658\pi$
$881$	−1.17507e16			−0.745925			−0.372963	+	0.927846i	$0.621658\pi$
$882$		0			0
$883$	−7.76791e15			−0.486990			−0.243495	−	0.969902i	$-0.578294\pi$
$883$	−7.76791e15			−0.486990			−0.243495	+	0.969902i	$0.578294\pi$
$884$	3.48620e15	−	6.03827e15i	0.217202	−	0.376206i
$885$		0			0
$886$	−5.77730e15	−	1.00066e16i	−0.355500	−	0.615744i
$887$	−2.31375e15	−	4.00753e15i	−0.141493	−	0.245074i	0.786566	−	0.617506i	$-0.211857\pi$
$887$	−2.31375e15	−	4.00753e15i	−0.141493	−	0.245074i	−0.928059	+	0.372433i	$0.878524\pi$
$888$		0			0
$889$	1.28624e16	−	2.22783e16i	0.776896	−	1.34562i
$890$	−1.88144e16			−1.12940
$891$		0			0
$892$	−1.49763e16			−0.887969
$893$	−1.39009e14	+	2.40770e14i	−0.00819142	+	0.0141879i
$894$		0			0
$895$	−2.38383e16	−	4.12891e16i	−1.38755	−	2.40330i
$896$	−8.59131e14	−	1.48806e15i	−0.0497010	−	0.0860847i
$897$		0			0
$898$	−1.00430e14	+	1.73950e14i	−0.00573910	+	0.00994042i
$899$	1.84368e16			1.04715
$900$		0			0
$901$	7.49006e15			0.420241
$902$	−3.49677e15	+	6.05658e15i	−0.194998	+	0.337747i
$903$		0			0
$904$	3.88873e15	+	6.73547e15i	0.214230	+	0.371058i
$905$	−9.85749e15	−	1.70737e16i	−0.539758	−	0.934889i
$906$		0			0
$907$	−9.62556e15	+	1.66720e16i	−0.520698	+	0.901875i	0.479012	+	0.877808i	$0.340995\pi$
$907$	−9.62556e15	+	1.66720e16i	−0.520698	+	0.901875i	−0.999710	+	0.0240671i	$0.992338\pi$
$908$	3.44532e15			0.185249
$909$		0			0
$910$	−2.50136e16			−1.32877
$911$	9.00491e15	−	1.55970e16i	0.475476	−	0.823548i	−0.524129	−	0.851639i	$-0.675609\pi$
$911$	9.00491e15	−	1.55970e16i	0.475476	−	0.823548i	0.999605	+	0.0280901i	$0.00894255\pi$
$912$		0			0
$913$	1.68158e15	+	2.91259e15i	0.0877262	+	0.151946i
$914$	7.37450e15	+	1.27730e16i	0.382410	+	0.662353i
$915$		0			0
$916$	−9.72392e14	+	1.68423e15i	−0.0498215	+	0.0862933i
$917$	−1.49310e16			−0.760426
$918$		0			0
$919$	−5.42882e15			−0.273193			−0.136597	−	0.990627i	$-0.543616\pi$
$919$	−5.42882e15			−0.273193			−0.136597	+	0.990627i	$0.543616\pi$
$920$	−5.88026e15	+	1.01849e16i	−0.294147	+	0.509477i
$921$		0			0
$922$	1.27584e16	+	2.20982e16i	0.630631	+	1.09229i
$923$	5.66979e15	+	9.82036e15i	0.278585	+	0.482523i
$924$		0			0
$925$	3.48420e16	−	6.03482e16i	1.69170	−	2.93011i
$926$	1.85887e16			0.897199
$927$		0			0
$928$	2.58391e15			0.123244
$929$	−1.38155e16	+	2.39292e16i	−0.655059	+	1.13460i	0.326820	+	0.945087i	$0.394023\pi$
$929$	−1.38155e16	+	2.39292e16i	−0.655059	+	1.13460i	−0.981879	+	0.189509i	$0.939310\pi$
$930$		0			0
$931$	−7.59404e14	−	1.31533e15i	−0.0355836	−	0.0616326i
$932$	−7.77735e14	−	1.34708e15i	−0.0362280	−	0.0627487i
$933$		0			0
$934$	−1.31605e16	+	2.27947e16i	−0.605850	+	1.04936i
$935$	−3.18515e16			−1.45769
$936$		0			0
$937$	−2.46060e16			−1.11294			−0.556472	−	0.830867i	$-0.687845\pi$
$937$	−2.46060e16			−1.11294			−0.556472	+	0.830867i	$0.687845\pi$
$938$	−3.61282e15	+	6.25759e15i	−0.162454	+	0.281379i
$939$		0			0
$940$	5.75482e14	+	9.96764e14i	0.0255758	+	0.0442985i
$941$	−1.55946e16	−	2.70106e16i	−0.689019	−	1.19342i	−0.972156	−	0.234337i	$-0.924708\pi$
$941$	−1.55946e16	−	2.70106e16i	−0.689019	−	1.19342i	0.283136	−	0.959080i	$-0.408625\pi$
$942$		0			0
$943$	−6.29155e15	+	1.08973e16i	−0.274754	+	0.475887i
$944$	5.89421e15			0.255905
$945$		0			0
$946$	5.97288e15			0.256320
$947$	1.58595e16	−	2.74694e16i	0.676649	−	1.17199i	−0.299334	−	0.954148i	$-0.596765\pi$
$947$	1.58595e16	−	2.74694e16i	0.676649	−	1.17199i	0.975984	−	0.217843i	$-0.0699020\pi$
$948$		0			0
$949$	−1.34089e15	−	2.32249e15i	−0.0565496	−	0.0979468i
$950$	4.12068e15	+	7.13723e15i	0.172778	+	0.299261i
$951$		0			0
$952$	4.18652e15	−	7.25126e15i	0.173520	−	0.300546i
$953$	9.40992e15			0.387771			0.193885	−	0.981024i	$-0.437891\pi$
$953$	9.40992e15			0.387771			0.193885	+	0.981024i	$0.437891\pi$
$954$		0			0
$955$	−4.79916e15			−0.195500
$956$	−4.25726e15	+	7.37379e15i	−0.172430	+	0.298657i
$957$		0			0
$958$	−7.81176e15	−	1.35304e16i	−0.312780	−	0.541750i
$959$	−1.54054e16	−	2.66829e16i	−0.613295	−	1.06226i
$960$		0			0
$961$	−1.59563e16	+	2.76372e16i	−0.627993	+	1.08772i
$962$	3.34758e16			1.30999
$963$		0			0
$964$	−1.33249e16			−0.515515
$965$	2.76773e16	−	4.79384e16i	1.06469	−	1.84410i
$966$		0			0
$967$	6.38654e15	+	1.10618e16i	0.242896	+	0.420708i	0.961538	−	0.274672i	$-0.0885693\pi$
$967$	6.38654e15	+	1.10618e16i	0.242896	+	0.420708i	−0.718642	+	0.695380i	$0.755236\pi$
$968$	−4.75866e13	−	8.24224e13i	−0.00179958	−	0.00311696i
$969$		0			0
$970$	−1.77932e16	+	3.08187e16i	−0.665287	+	1.15231i
$971$	3.51105e16			1.30536			0.652681	−	0.757632i	$-0.273644\pi$
$971$	3.51105e16			1.30536			0.652681	+	0.757632i	$0.273644\pi$
$972$		0			0
$973$	2.61449e16			0.961094
$974$	−4.75650e14	+	8.23850e14i	−0.0173865	+	0.0301144i
$975$		0			0
$976$	5.49118e15	+	9.51100e15i	0.198468	+	0.343757i
$977$	2.54334e16	+	4.40520e16i	0.914081	+	1.58323i	0.808241	+	0.588851i	$0.200420\pi$
$977$	2.54334e16	+	4.40520e16i	0.914081	+	1.58323i	0.105839	+	0.994383i	$0.466247\pi$
$978$		0			0
$979$	−1.33184e16	+	2.30681e16i	−0.473311	+	0.819798i
$980$	−6.28771e15			−0.222203
$981$		0			0
$982$	−2.61163e16			−0.912639
$983$	2.12838e16	−	3.68646e16i	0.739614	−	1.28105i	−0.213055	−	0.977040i	$-0.568342\pi$
$983$	2.12838e16	−	3.68646e16i	0.739614	−	1.28105i	0.952669	−	0.304009i	$-0.0983252\pi$
$984$		0			0
$985$	−2.11667e16	−	3.66618e16i	−0.727368	−	1.25984i
$986$	6.29567e15	+	1.09044e16i	0.215139	+	0.372631i
$987$		0			0
$988$	−1.97955e15	+	3.42868e15i	−0.0668965	+	0.115868i
$989$	1.07467e16			0.361156
$990$		0			0
$991$	2.24124e16			0.744873			0.372437	−	0.928058i	$-0.378522\pi$
$991$	2.24124e16			0.744873			0.372437	+	0.928058i	$0.378522\pi$
$992$	−4.01677e15	+	6.95726e15i	−0.132759	+	0.229945i
$993$		0			0
$994$	6.80875e15	+	1.17931e16i	0.222558	+	0.385481i
$995$	1.00960e16	+	1.74868e16i	0.328188	+	0.568438i
$996$		0			0
$997$	1.01634e16	−	1.76035e16i	0.326750	−	0.565947i	−0.655115	−	0.755529i	$-0.727380\pi$
$997$	1.01634e16	−	1.76035e16i	0.326750	−	0.565947i	0.981865	+	0.189582i	$0.0607133\pi$
$998$	−1.95173e16			−0.624026
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.12.c.j.55.1		2
3.2	odd	2		162.12.c.a.55.1		2
9.2	odd	6		18.12.a.e.1.1		1
9.4	even	3	inner	162.12.c.j.109.1		2
9.5	odd	6		162.12.c.a.109.1		2
9.7	even	3		6.12.a.b.1.1	✓	1
36.7	odd	6		48.12.a.a.1.1		1
36.11	even	6		144.12.a.o.1.1		1
45.7	odd	12		150.12.c.b.49.1		2
45.34	even	6		150.12.a.f.1.1		1
45.43	odd	12		150.12.c.b.49.2		2
72.43	odd	6		192.12.a.t.1.1		1
72.61	even	6		192.12.a.j.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.12.a.b.1.1	✓	1	9.7	even	3
18.12.a.e.1.1		1	9.2	odd	6
48.12.a.a.1.1		1	36.7	odd	6
144.12.a.o.1.1		1	36.11	even	6
150.12.a.f.1.1		1	45.34	even	6
150.12.c.b.49.1		2	45.7	odd	12
150.12.c.b.49.2		2	45.43	odd	12
162.12.c.a.55.1		2	3.2	odd	2
162.12.c.a.109.1		2	9.5	odd	6
162.12.c.j.55.1		2	1.1	even	1	trivial
162.12.c.j.109.1		2	9.4	even	3	inner
192.12.a.j.1.1		1	72.61	even	6
192.12.a.t.1.1		1	72.43	odd	6

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	162.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(16.0000 - 27.7128i) q^{2} +(-512.000 - 886.810i) q^{4} +(5865.00 + 10158.5i) q^{5} +(25004.0 - 43308.2i) q^{7} -32768.0 q^{8} +O(q^{10})\)	\(q+(16.0000 - 27.7128i) q^{2} +(-512.000 - 886.810i) q^{4} +(5865.00 + 10158.5i) q^{5} +(25004.0 - 43308.2i) q^{7} -32768.0 q^{8} +375360. q^{10} +(265710. - 460223. i) q^{11} +(-666283. - 1.15404e6i) q^{13} +(-800128. - 1.38586e6i) q^{14} +(-524288. + 908093. i) q^{16} -5.10968e6 q^{17} +2.90140e6 q^{19} +(6.00576e6 - 1.04023e7i) q^{20} +(-8.50272e6 - 1.47271e7i) q^{22} +(-1.52985e7 - 2.64978e7i) q^{23} +(-4.43824e7 + 7.68726e7i) q^{25} -4.26421e7 q^{26} -5.12082e7 q^{28} +(3.85033e7 - 6.66897e7i) q^{29} +(1.19709e8 + 2.07342e8i) q^{31} +(1.67772e7 + 2.90590e7i) q^{32} +(-8.17548e7 + 1.41604e8i) q^{34} +5.86594e8 q^{35} -7.85042e8 q^{37} +(4.64225e7 - 8.04061e7i) q^{38} +(-1.92184e8 - 3.32873e8i) q^{40} +(-2.05626e8 - 3.56156e8i) q^{41} +(-1.75617e8 + 3.04177e8i) q^{43} -5.44174e8 q^{44} -9.79104e8 q^{46} +(-4.79108e7 + 8.29840e7i) q^{47} +(-2.61737e8 - 4.53341e8i) q^{49} +(1.42024e9 + 2.45992e9i) q^{50} +(-6.82274e8 + 1.18173e9i) q^{52} -1.46586e9 q^{53} +6.23356e9 q^{55} +(-8.19331e8 + 1.41912e9i) q^{56} +(-1.23211e9 - 2.13407e9i) q^{58} +(-2.81058e9 - 4.86806e9i) q^{59} +(5.23679e9 - 9.07039e9i) q^{61} +7.66139e9 q^{62} +1.07374e9 q^{64} +(7.81550e9 - 1.35368e10i) q^{65} +(-2.25765e9 - 3.91037e9i) q^{67} +(2.61616e9 + 4.53131e9i) q^{68} +(9.38550e9 - 1.62562e10i) q^{70} -8.50958e9 q^{71} +2.01250e9 q^{73} +(-1.25607e10 + 2.17557e10i) q^{74} +(-1.48552e9 - 2.57299e9i) q^{76} +(-1.32876e10 - 2.30148e10i) q^{77} +(1.11192e10 - 1.92590e10i) q^{79} -1.22998e10 q^{80} -1.31601e10 q^{82} +(-3.16432e9 + 5.48077e9i) q^{83} +(-2.99683e10 - 5.19066e10i) q^{85} +(5.61973e9 + 9.73366e9i) q^{86} +(-8.70679e9 + 1.50806e10i) q^{88} -5.01237e10 q^{89} -6.66390e10 q^{91} +(-1.56657e10 + 2.71337e10i) q^{92} +(1.53315e9 + 2.65549e9i) q^{94} +(1.70167e10 + 2.94738e10i) q^{95} +(-4.74030e10 + 8.21044e10i) q^{97} -1.67511e10 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 32 q^{2} - 1024 q^{4} + 11730 q^{5} + 50008 q^{7} - 65536 q^{8}+O(q^{10}) \) 2 * q + 32 * q^2 - 1024 * q^4 + 11730 * q^5 + 50008 * q^7 - 65536 * q^8	\( 2 q + 32 q^{2} - 1024 q^{4} + 11730 q^{5} + 50008 q^{7} - 65536 q^{8} + 750720 q^{10} + 531420 q^{11} - 1332566 q^{13} - 1600256 q^{14} - 1048576 q^{16} - 10219356 q^{17} + 5802808 q^{19} + 12011520 q^{20} - 17005440 q^{22} - 30597000 q^{23} - 88764775 q^{25} - 85284224 q^{26} - 102416384 q^{28} + 77006634 q^{29} + 239418352 q^{31} + 33554432 q^{32} - 163509696 q^{34} + 1173187680 q^{35} - 1570083332 q^{37} + 92844928 q^{38} - 384368640 q^{40} - 411252954 q^{41} - 351233348 q^{43} - 1088348160 q^{44} - 1958208000 q^{46} - 95821680 q^{47} - 523473321 q^{49} + 2840472800 q^{50} - 1364547584 q^{52} - 2931714756 q^{53} + 12467113200 q^{55} - 1638662144 q^{56} - 2464212288 q^{58} - 5621152020 q^{59} + 10473587770 q^{61} + 15322774528 q^{62} + 2147483648 q^{64} + 15630999180 q^{65} - 4515307532 q^{67} + 5232310272 q^{68} + 18771002880 q^{70} - 17019159120 q^{71} + 4024993972 q^{73} - 25121333312 q^{74} - 2971037696 q^{76} - 26575251360 q^{77} + 22238409568 q^{79} - 24599592960 q^{80} - 26320189056 q^{82} - 6328647516 q^{83} - 59936522940 q^{85} + 11239467136 q^{86} - 17413570560 q^{88} - 100247413356 q^{89} - 133277921056 q^{91} - 31331328000 q^{92} + 3066293760 q^{94} + 34033468920 q^{95} - 94805961314 q^{97} - 33502292544 q^{98}+O(q^{100}) \) 2 * q + 32 * q^2 - 1024 * q^4 + 11730 * q^5 + 50008 * q^7 - 65536 * q^8 + 750720 * q^10 + 531420 * q^11 - 1332566 * q^13 - 1600256 * q^14 - 1048576 * q^16 - 10219356 * q^17 + 5802808 * q^19 + 12011520 * q^20 - 17005440 * q^22 - 30597000 * q^23 - 88764775 * q^25 - 85284224 * q^26 - 102416384 * q^28 + 77006634 * q^29 + 239418352 * q^31 + 33554432 * q^32 - 163509696 * q^34 + 1173187680 * q^35 - 1570083332 * q^37 + 92844928 * q^38 - 384368640 * q^40 - 411252954 * q^41 - 351233348 * q^43 - 1088348160 * q^44 - 1958208000 * q^46 - 95821680 * q^47 - 523473321 * q^49 + 2840472800 * q^50 - 1364547584 * q^52 - 2931714756 * q^53 + 12467113200 * q^55 - 1638662144 * q^56 - 2464212288 * q^58 - 5621152020 * q^59 + 10473587770 * q^61 + 15322774528 * q^62 + 2147483648 * q^64 + 15630999180 * q^65 - 4515307532 * q^67 + 5232310272 * q^68 + 18771002880 * q^70 - 17019159120 * q^71 + 4024993972 * q^73 - 25121333312 * q^74 - 2971037696 * q^76 - 26575251360 * q^77 + 22238409568 * q^79 - 24599592960 * q^80 - 26320189056 * q^82 - 6328647516 * q^83 - 59936522940 * q^85 + 11239467136 * q^86 - 17413570560 * q^88 - 100247413356 * q^89 - 133277921056 * q^91 - 31331328000 * q^92 + 3066293760 * q^94 + 34033468920 * q^95 - 94805961314 * q^97 - 33502292544 * q^98

Introduction

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