LMFDB - Embedded newform 27.10.c.a.19.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,10,Mod(10,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("27.10");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	27.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:	$13.9059675764$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 1984 x^{14} - 13748 x^{13} + 1552498 x^{12} - 9136628 x^{11} + 609566956 x^{10} + \cdots + 13\!\cdots\!25 $ x^16 - 8x^15 + 1984x^14 - 13748x^13 + 1552498x^12 - 9136628x^11 + 609566956x^10 - 2964409064x^9 + 126210674407x^8 - 487156186164x^7 + 13162328064828x^6 - 37794288146040x^5 + 578928267028062x^4 - 1095428523832956x^3 + 5807598664427172x^2 - 5266103139591300*x + 1336504689748125
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{40}\cdot 17^{2} $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			19.7
Root			$0.500000 - 15.6774i$ of defining polynomial
Character	$\chi$	$=$	27.19
Dual form			27.10.c.a.10.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(12.8270 - 22.2170i) q^{2} +(-73.0637 - 126.550i) q^{4} +(353.226 + 611.805i) q^{5} +(2284.21 - 3956.36i) q^{7} +9386.09 q^{8} +O(q^{10})$	\(q+(12.8270 - 22.2170i) q^{2} +(-73.0637 - 126.550i) q^{4} +(353.226 + 611.805i) q^{5} +(2284.21 - 3956.36i) q^{7} +9386.09 q^{8} +18123.3 q^{10} +(35716.7 - 61863.1i) q^{11} +(13201.0 + 22864.9i) q^{13} +(-58599.1 - 101497. i) q^{14} +(157804. - 273325. i) q^{16} +314759. q^{17} -904019. q^{19} +(51616.0 - 89401.5i) q^{20} +(-916276. - 1.58704e6i) q^{22} +(-55921.2 - 96858.3i) q^{23} +(727026. - 1.25925e6i) q^{25} +677318. q^{26} -667571. q^{28} +(2.19402e6 - 3.80015e6i) q^{29} +(4.94392e6 + 8.56313e6i) q^{31} +(-1.64546e6 - 2.85003e6i) q^{32} +(4.03742e6 - 6.99301e6i) q^{34} +3.22736e6 q^{35} -6.32122e6 q^{37} +(-1.15959e7 + 2.00846e7i) q^{38} +(3.31541e6 + 5.74246e6i) q^{40} +(2.68019e6 + 4.64223e6i) q^{41} +(-1.12275e7 + 1.94466e7i) q^{43} -1.04384e7 q^{44} -2.86920e6 q^{46} +(-2.23644e7 + 3.87363e7i) q^{47} +(9.74159e6 + 1.68729e7i) q^{49} +(-1.86511e7 - 3.23047e7i) q^{50} +(1.92903e6 - 3.34118e6i) q^{52} +4.00972e7 q^{53} +5.04642e7 q^{55} +(2.14398e7 - 3.71348e7i) q^{56} +(-5.62853e7 - 9.74890e7i) q^{58} +(-4.79118e7 - 8.29857e7i) q^{59} +(-1.01113e7 + 1.75132e7i) q^{61} +2.53663e8 q^{62} +7.71659e7 q^{64} +(-9.32588e6 + 1.61529e7i) q^{65} +(-9.12489e7 - 1.58048e8i) q^{67} +(-2.29975e7 - 3.98328e7i) q^{68} +(4.13974e7 - 7.17024e7i) q^{70} -1.38543e8 q^{71} -2.17970e8 q^{73} +(-8.10823e7 + 1.40439e8i) q^{74} +(6.60510e7 + 1.14404e8i) q^{76} +(-1.63169e8 - 2.82617e8i) q^{77} +(-1.97294e8 + 3.41722e8i) q^{79} +2.22962e8 q^{80} +1.37515e8 q^{82} +(-2.36638e8 + 4.09870e8i) q^{83} +(1.11181e8 + 1.92571e8i) q^{85} +(2.88030e8 + 4.98883e8i) q^{86} +(3.35240e8 - 5.80653e8i) q^{88} -2.60507e8 q^{89} +1.20616e8 q^{91} +(-8.17161e6 + 1.41537e7i) q^{92} +(5.73736e8 + 9.93741e8i) q^{94} +(-3.19323e8 - 5.53083e8i) q^{95} +(-2.87421e8 + 4.97828e8i) q^{97} +4.99822e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 15 q^{2} - 1793 q^{4} - 453 q^{5} - 343 q^{7} + 14478 q^{8}+O(q^{10}) $ 16 * q - 15 * q^2 - 1793 * q^4 - 453 * q^5 - 343 * q^7 + 14478 * q^8	\( 16 q - 15 q^{2} - 1793 q^{4} - 453 q^{5} - 343 q^{7} + 14478 q^{8} + 1020 q^{10} - 99150 q^{11} + 32435 q^{13} - 394824 q^{14} - 328193 q^{16} + 831078 q^{17} - 170554 q^{19} - 1855164 q^{20} + 529359 q^{22} - 1064559 q^{23} - 2293229 q^{25} - 2436312 q^{26} + 1225724 q^{28} + 1309053 q^{29} - 2359819 q^{31} - 5760063 q^{32} + 981801 q^{34} + 31066554 q^{35} + 16391516 q^{37} - 39490203 q^{38} - 16760496 q^{40} - 54747318 q^{41} + 15249608 q^{43} + 332509926 q^{44} + 2390520 q^{46} - 156295545 q^{47} + 15239583 q^{49} - 315590163 q^{50} - 19773358 q^{52} + 525516228 q^{53} - 7579770 q^{55} - 470339790 q^{56} + 55408560 q^{58} - 307774074 q^{59} + 69192125 q^{61} + 914436924 q^{62} - 403588478 q^{64} - 482470359 q^{65} + 14328044 q^{67} - 915409575 q^{68} - 229271934 q^{70} + 1239601392 q^{71} + 598613198 q^{73} - 1022736000 q^{74} + 119954093 q^{76} - 717995541 q^{77} + 30257531 q^{79} + 2927826528 q^{80} - 202376022 q^{82} - 1176168291 q^{83} + 4818366 q^{85} - 1426944009 q^{86} + 911312427 q^{88} + 3317041296 q^{89} - 739230122 q^{91} + 76813998 q^{92} - 1954316784 q^{94} + 391400652 q^{95} - 267311278 q^{97} - 4827300318 q^{98}+O(q^{100}) \) 16 * q - 15 * q^2 - 1793 * q^4 - 453 * q^5 - 343 * q^7 + 14478 * q^8 + 1020 * q^10 - 99150 * q^11 + 32435 * q^13 - 394824 * q^14 - 328193 * q^16 + 831078 * q^17 - 170554 * q^19 - 1855164 * q^20 + 529359 * q^22 - 1064559 * q^23 - 2293229 * q^25 - 2436312 * q^26 + 1225724 * q^28 + 1309053 * q^29 - 2359819 * q^31 - 5760063 * q^32 + 981801 * q^34 + 31066554 * q^35 + 16391516 * q^37 - 39490203 * q^38 - 16760496 * q^40 - 54747318 * q^41 + 15249608 * q^43 + 332509926 * q^44 + 2390520 * q^46 - 156295545 * q^47 + 15239583 * q^49 - 315590163 * q^50 - 19773358 * q^52 + 525516228 * q^53 - 7579770 * q^55 - 470339790 * q^56 + 55408560 * q^58 - 307774074 * q^59 + 69192125 * q^61 + 914436924 * q^62 - 403588478 * q^64 - 482470359 * q^65 + 14328044 * q^67 - 915409575 * q^68 - 229271934 * q^70 + 1239601392 * q^71 + 598613198 * q^73 - 1022736000 * q^74 + 119954093 * q^76 - 717995541 * q^77 + 30257531 * q^79 + 2927826528 * q^80 - 202376022 * q^82 - 1176168291 * q^83 + 4818366 * q^85 - 1426944009 * q^86 + 911312427 * q^88 + 3317041296 * q^89 - 739230122 * q^91 + 76813998 * q^92 - 1954316784 * q^94 + 391400652 * q^95 - 267311278 * q^97 - 4827300318 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

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

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 $

$2$	12.8270	−	22.2170i	0.566879	−	0.981862i	−0.429994	−	0.902832i	$-0.641484\pi$
$2$	12.8270	−	22.2170i	0.566879	−	0.981862i	0.996872	−	0.0790305i	$-0.0251825\pi$
$3$		0			0
$3$		0			0
$4$	−73.0637	−	126.550i	−0.142703	−	0.247168i
$5$	353.226	+	611.805i	0.252748	+	0.437772i	0.964281	−	0.264880i	$-0.0853324\pi$
$5$	353.226	+	611.805i	0.252748	+	0.437772i	−0.711534	+	0.702652i	$0.751999\pi$
$6$		0			0
$7$	2284.21	−	3956.36i	0.359579	−	0.622809i	−0.628311	−	0.777962i	$-0.716254\pi$
$7$	2284.21	−	3956.36i	0.359579	−	0.622809i	0.987891	+	0.155153i	$0.0495870\pi$
$8$	9386.09			0.810177
$9$		0			0
$10$	18123.3			0.573109
$11$	35716.7	−	61863.1i	0.735537	−	1.27399i	−0.218951	−	0.975736i	$-0.570263\pi$
$11$	35716.7	−	61863.1i	0.735537	−	1.27399i	0.954487	−	0.298251i	$-0.0964032\pi$
$12$		0			0
$13$	13201.0	+	22864.9i	0.128193	+	0.222036i	0.922976	−	0.384857i	$-0.125749\pi$
$13$	13201.0	+	22864.9i	0.128193	+	0.222036i	−0.794784	+	0.606893i	$0.792416\pi$
$14$	−58599.1	−	101497.i	−0.407675	−	0.706114i
$15$		0			0
$16$	157804.	−	273325.i	0.601975	−	1.04265i
$17$	314759.			0.914026			0.457013	−	0.889460i	$-0.348919\pi$
$17$	314759.			0.914026			0.457013	+	0.889460i	$0.348919\pi$
$18$		0			0
$19$	−904019.			−1.59143			−0.795713	−	0.605674i	$-0.792904\pi$
$19$	−904019.			−1.59143			−0.795713	+	0.605674i	$0.792904\pi$
$20$	51616.0	−	89401.5i	0.0721355	−	0.124942i
$21$		0			0
$22$	−916276.	−	1.58704e6i	−0.833920	−	1.44439i
$23$	−55921.2	−	96858.3i	−0.0416678	−	0.0721708i	0.844439	−	0.535651i	$-0.179934\pi$
$23$	−55921.2	−	96858.3i	−0.0416678	−	0.0721708i	−0.886107	+	0.463480i	$0.846600\pi$
$24$		0			0
$25$	727026.	−	1.25925e6i	0.372237	−	0.644734i
$26$	677318.			0.290678
$27$		0			0
$28$	−667571.			−0.205251
$29$	2.19402e6	−	3.80015e6i	0.576035	−	0.997722i	−0.419893	−	0.907573i	$-0.637933\pi$
$29$	2.19402e6	−	3.80015e6i	0.576035	−	0.997722i	0.995928	−	0.0901485i	$-0.0287342\pi$
$30$		0			0
$31$	4.94392e6	+	8.56313e6i	0.961488	+	1.66535i	0.718767	+	0.695251i	$0.244707\pi$
$31$	4.94392e6	+	8.56313e6i	0.961488	+	1.66535i	0.242721	+	0.970096i	$0.421960\pi$
$32$	−1.64546e6	−	2.85003e6i	−0.277404	−	0.480478i
$33$		0			0
$34$	4.03742e6	−	6.99301e6i	0.518142	−	0.897448i
$35$	3.22736e6			0.363531
$36$		0			0
$37$	−6.32122e6			−0.554489			−0.277245	−	0.960799i	$-0.589421\pi$
$37$	−6.32122e6			−0.554489			−0.277245	+	0.960799i	$0.589421\pi$
$38$	−1.15959e7	+	2.00846e7i	−0.902145	+	1.56256i
$39$		0			0
$40$	3.31541e6	+	5.74246e6i	0.204770	+	0.354673i
$41$	2.68019e6	+	4.64223e6i	0.148128	+	0.256566i	0.930536	−	0.366201i	$-0.119342\pi$
$41$	2.68019e6	+	4.64223e6i	0.148128	+	0.256566i	−0.782407	+	0.622767i	$0.786008\pi$
$42$		0			0
$43$	−1.12275e7	+	1.94466e7i	−0.500812	+	0.867432i	0.499187	+	0.866494i	$0.333632\pi$
$43$	−1.12275e7	+	1.94466e7i	−0.500812	+	0.867432i	−1.00000		0.000938191i	$0.999701\pi$
$44$	−1.04384e7			−0.419852
$45$		0			0
$46$	−2.86920e6			−0.0944824
$47$	−2.23644e7	+	3.87363e7i	−0.668524	+	1.15792i	0.309793	+	0.950804i	$0.399740\pi$
$47$	−2.23644e7	+	3.87363e7i	−0.668524	+	1.15792i	−0.978317	+	0.207114i	$0.933593\pi$
$48$		0			0
$49$	9.74159e6	+	1.68729e7i	0.241406	+	0.418127i
$50$	−1.86511e7	−	3.23047e7i	−0.422027	−	0.730971i
$51$		0			0
$52$	1.92903e6	−	3.34118e6i	0.0365868	−	0.0633702i
$53$	4.00972e7			0.698027			0.349013	−	0.937118i	$-0.386517\pi$
$53$	4.00972e7			0.698027			0.349013	+	0.937118i	$0.386517\pi$
$54$		0			0
$55$	5.04642e7			0.743621
$56$	2.14398e7	−	3.71348e7i	0.291323	−	0.504586i
$57$		0			0
$58$	−5.62853e7	−	9.74890e7i	−0.653084	−	1.13117i
$59$	−4.79118e7	−	8.29857e7i	−0.514764	−	0.891598i	−0.999853	−	0.0171331i	$-0.994546\pi$
$59$	−4.79118e7	−	8.29857e7i	−0.514764	−	0.891598i	0.485089	−	0.874465i	$-0.338787\pi$
$60$		0			0
$61$	−1.01113e7	+	1.75132e7i	−0.0935020	+	0.161950i	−0.908982	−	0.416834i	$-0.863139\pi$
$61$	−1.01113e7	+	1.75132e7i	−0.0935020	+	0.161950i	0.815480	+	0.578785i	$0.196473\pi$
$62$	2.53663e8			2.18019
$63$		0			0
$64$	7.71659e7			0.574931
$65$	−9.32588e6	+	1.61529e7i	−0.0648007	+	0.112238i
$66$		0			0
$67$	−9.12489e7	−	1.58048e8i	−0.553211	−	0.958190i	−0.998040	−	0.0625744i	$-0.980069\pi$
$67$	−9.12489e7	−	1.58048e8i	−0.553211	−	0.958190i	0.444829	−	0.895615i	$-0.353264\pi$
$68$	−2.29975e7	−	3.98328e7i	−0.130434	−	0.225918i
$69$		0			0
$70$	4.13974e7	−	7.17024e7i	0.206078	−	0.356938i
$71$	−1.38543e8			−0.647025			−0.323512	−	0.946224i	$-0.604864\pi$
$71$	−1.38543e8			−0.647025			−0.323512	+	0.946224i	$0.604864\pi$
$72$		0			0
$73$	−2.17970e8			−0.898347			−0.449173	−	0.893445i	$-0.648281\pi$
$73$	−2.17970e8			−0.898347			−0.449173	+	0.893445i	$0.648281\pi$
$74$	−8.10823e7	+	1.40439e8i	−0.314328	+	0.544432i
$75$		0			0
$76$	6.60510e7	+	1.14404e8i	0.227101	+	0.393350i
$77$	−1.63169e8	−	2.82617e8i	−0.528967	−	0.916198i
$78$		0			0
$79$	−1.97294e8	+	3.41722e8i	−0.569890	+	0.987078i	0.426686	+	0.904400i	$0.359681\pi$
$79$	−1.97294e8	+	3.41722e8i	−0.569890	+	0.987078i	−0.996576	+	0.0826785i	$0.973653\pi$
$80$	2.22962e8			0.608591
$81$		0			0
$82$	1.37515e8			0.335883
$83$	−2.36638e8	+	4.09870e8i	−0.547310	+	0.947969i	0.451147	+	0.892450i	$0.351015\pi$
$83$	−2.36638e8	+	4.09870e8i	−0.547310	+	0.947969i	−0.998458	+	0.0555197i	$0.982318\pi$
$84$		0			0
$85$	1.11181e8	+	1.92571e8i	0.231018	+	0.400135i
$86$	2.88030e8	+	4.98883e8i	0.567799	+	0.983458i
$87$		0			0
$88$	3.35240e8	−	5.80653e8i	0.595915	−	1.03215i
$89$	−2.60507e8			−0.440113			−0.220057	−	0.975487i	$-0.570624\pi$
$89$	−2.60507e8			−0.440113			−0.220057	+	0.975487i	$0.570624\pi$
$90$		0			0
$91$	1.20616e8			0.184381
$92$	−8.17161e6	+	1.41537e7i	−0.0118922	+	0.0205979i
$93$		0			0
$94$	5.73736e8	+	9.93741e8i	0.757944	+	1.31280i
$95$	−3.19323e8	−	5.53083e8i	−0.402229	−	0.696682i
$96$		0			0
$97$	−2.87421e8	+	4.97828e8i	−0.329644	+	0.570961i	−0.982441	−	0.186572i	$-0.940262\pi$
$97$	−2.87421e8	+	4.97828e8i	−0.329644	+	0.570961i	0.652797	+	0.757533i	$0.273595\pi$
$98$	4.99822e8			0.547391
$99$		0			0
$100$	−2.12477e8			−0.212477
$101$	7.03860e7	−	1.21912e8i	0.0673039	−	0.116574i	−0.830410	−	0.557153i	$-0.811894\pi$
$101$	7.03860e7	−	1.21912e8i	0.0673039	−	0.116574i	0.897714	+	0.440579i	$0.145227\pi$
$102$		0			0
$103$	1.70819e7	+	2.95867e7i	0.0149544	+	0.0259017i	0.873406	−	0.486993i	$-0.161906\pi$
$103$	1.70819e7	+	2.95867e7i	0.0149544	+	0.0259017i	−0.858451	+	0.512895i	$0.828573\pi$
$104$	1.23906e8	+	2.14612e8i	0.103859	+	0.179888i
$105$		0			0
$106$	5.14326e8	−	8.90839e8i	0.395696	−	0.685366i
$107$	−1.61837e9			−1.19358			−0.596790	−	0.802397i	$-0.703557\pi$
$107$	−1.61837e9			−1.19358			−0.596790	+	0.802397i	$0.703557\pi$
$108$		0			0
$109$	−8.56262e8			−0.581015			−0.290508	−	0.956873i	$-0.593824\pi$
$109$	−8.56262e8			−0.581015			−0.290508	+	0.956873i	$0.593824\pi$
$110$	6.47305e8	−	1.12116e9i	0.421543	−	0.730133i
$111$		0			0
$112$	−7.20914e8	−	1.24866e9i	−0.432915	−	0.749831i
$113$	9.66311e8	+	1.67370e9i	0.557524	+	0.965661i	0.997702	+	0.0677501i	$0.0215821\pi$
$113$	9.66311e8	+	1.67370e9i	0.557524	+	0.965661i	−0.440178	+	0.897911i	$0.645085\pi$
$114$		0			0
$115$	3.95056e7	−	6.84257e7i	0.0210629	−	0.0364820i
$116$	−6.41212e8			−0.328807
$117$		0			0
$118$	−2.45826e9			−1.16724
$119$	7.18976e8	−	1.24530e9i	0.328665	−	0.569264i
$120$		0			0
$121$	−1.37239e9	−	2.37705e9i	−0.582028	−	1.00810i
$122$	2.59394e8	+	4.49284e8i	0.106009	+	0.183612i
$123$		0			0
$124$	7.22443e8	−	1.25131e9i	0.274414	−	0.475298i
$125$	2.40700e9			0.881824
$126$		0			0
$127$	4.98705e9			1.70109			0.850545	−	0.525903i	$-0.176272\pi$
$127$	4.98705e9			1.70109			0.850545	+	0.525903i	$0.176272\pi$
$128$	1.83228e9	−	3.17361e9i	0.603320	−	1.04498i
$129$		0			0
$130$	2.39246e8	+	4.14387e8i	0.0734683	+	0.127251i
$131$	−9.58360e7	−	1.65993e8i	−0.0284320	−	0.0492457i	0.851459	−	0.524421i	$-0.175718\pi$
$131$	−9.58360e7	−	1.65993e8i	−0.0284320	−	0.0492457i	−0.879891	+	0.475175i	$0.842385\pi$
$132$		0			0
$133$	−2.06497e9	+	3.57663e9i	−0.572243	+	0.991155i
$134$	−4.68180e9			−1.25441
$135$		0			0
$136$	2.95436e9			0.740523
$137$	5.00385e8	−	8.66692e8i	0.121356	−	0.210195i	−0.798947	−	0.601402i	$-0.794609\pi$
$137$	5.00385e8	−	8.66692e8i	0.121356	−	0.210195i	0.920303	+	0.391207i	$0.127942\pi$
$138$		0			0
$139$	6.75119e8	+	1.16934e9i	0.153396	+	0.265689i	0.932474	−	0.361238i	$-0.117646\pi$
$139$	6.75119e8	+	1.16934e9i	0.153396	+	0.265689i	−0.779078	+	0.626927i	$0.784312\pi$
$140$	−2.35803e8	−	4.08423e8i	−0.0518768	−	0.0898533i
$141$		0			0
$142$	−1.77709e9	+	3.07800e9i	−0.366785	+	0.635290i
$143$	1.88599e9			0.377161
$144$		0			0
$145$	3.09993e9			0.582366
$146$	−2.79590e9	+	4.84264e9i	−0.509253	+	0.882053i
$147$		0			0
$148$	4.61852e8	+	7.99951e8i	0.0791270	+	0.137052i
$149$	1.76496e9	+	3.05700e9i	0.293357	+	0.508110i	0.974601	−	0.223947i	$-0.0718941\pi$
$149$	1.76496e9	+	3.05700e9i	0.293357	+	0.508110i	−0.681244	+	0.732056i	$0.738561\pi$
$150$		0			0
$151$	−2.86323e8	+	4.95926e8i	−0.0448188	+	0.0776284i	−0.887565	−	0.460683i	$-0.847604\pi$
$151$	−2.86323e8	+	4.95926e8i	−0.0448188	+	0.0776284i	0.842746	+	0.538312i	$0.180938\pi$
$152$	−8.48521e9			−1.28934
$153$		0			0
$154$	−8.37186e9			−1.19944
$155$	−3.49264e9	+	6.04943e9i	−0.486028	+	0.841825i
$156$		0			0
$157$	−4.20086e8	−	7.27610e8i	−0.0551810	−	0.0955763i	0.837115	−	0.547026i	$-0.184240\pi$
$157$	−4.20086e8	−	7.27610e8i	−0.0551810	−	0.0955763i	−0.892296	+	0.451450i	$0.850907\pi$
$158$	5.06137e9	+	8.76654e9i	0.646117	+	1.11911i
$159$		0			0
$160$	1.16244e9	−	2.01340e9i	0.140227	−	0.242880i
$161$	−5.10942e8			−0.0599315
$162$		0			0
$163$	−7.00425e9			−0.777173			−0.388586	−	0.921412i	$-0.627037\pi$
$163$	−7.00425e9			−0.777173			−0.388586	+	0.921412i	$0.627037\pi$
$164$	3.91650e8	−	6.78357e8i	0.0422766	−	0.0732253i
$165$		0			0
$166$	6.07072e9	+	1.05148e10i	0.620517	+	1.07477i
$167$	−4.63508e9	−	8.02820e9i	−0.461141	−	0.798719i	0.537877	−	0.843023i	$-0.319226\pi$
$167$	−4.63508e9	−	8.02820e9i	−0.461141	−	0.798719i	−0.999018	+	0.0443040i	$0.985893\pi$
$168$		0			0
$169$	4.95372e9	−	8.58009e9i	0.467133	−	0.809099i
$170$	5.70448e9			0.523836
$171$		0			0
$172$	3.28129e9			0.285869
$173$	4.13667e9	−	7.16492e9i	0.351110	−	0.608141i	−0.635334	−	0.772237i	$-0.719138\pi$
$173$	4.13667e9	−	7.16492e9i	0.351110	−	0.608141i	0.986444	+	0.164097i	$0.0524709\pi$
$174$		0			0
$175$	−3.32136e9	−	5.75276e9i	−0.267697	−	0.463665i
$176$	−1.12725e10	−	1.95245e10i	−0.885549	−	1.53382i
$177$		0			0
$178$	−3.34152e9	+	5.78769e9i	−0.249491	+	0.432131i
$179$	2.36310e10			1.72046			0.860229	−	0.509907i	$-0.170320\pi$
$179$	2.36310e10			1.72046			0.860229	+	0.509907i	$0.170320\pi$
$180$		0			0
$181$	1.40618e10			0.973841			0.486921	−	0.873446i	$-0.338120\pi$
$181$	1.40618e10			0.973841			0.486921	+	0.873446i	$0.338120\pi$
$182$	1.54714e9	−	2.67972e9i	0.104522	−	0.181037i
$183$		0			0
$184$	−5.24881e8	−	9.09121e8i	−0.0337583	−	0.0584711i
$185$	−2.23282e9	−	3.86735e9i	−0.140146	−	0.242740i
$186$		0			0
$187$	1.12422e10	−	1.94720e10i	0.672299	−	1.16446i
$188$	6.53611e9			0.381600
$189$		0			0
$190$	−1.63838e10			−0.912061
$191$	−4.87596e9	+	8.44541e9i	−0.265100	+	0.459167i	−0.967590	−	0.252527i	$-0.918738\pi$
$191$	−4.87596e9	+	8.44541e9i	−0.265100	+	0.459167i	0.702490	+	0.711694i	$0.252072\pi$
$192$		0			0
$193$	−4.97588e9	−	8.61847e9i	−0.258144	−	0.447118i	0.707601	−	0.706612i	$-0.249778\pi$
$193$	−4.97588e9	−	8.61847e9i	−0.258144	−	0.447118i	−0.965745	+	0.259494i	$0.916444\pi$
$194$	7.37349e9	+	1.27713e10i	0.373737	+	0.647331i
$195$		0			0
$196$	1.42351e9	−	2.46560e9i	0.0688984	−	0.119336i
$197$	3.23117e9			0.152849			0.0764244	−	0.997075i	$-0.475650\pi$
$197$	3.23117e9			0.152849			0.0764244	+	0.997075i	$0.475650\pi$
$198$		0			0
$199$	−2.90155e10			−1.31157			−0.655785	−	0.754947i	$-0.727662\pi$
$199$	−2.90155e10			−1.31157			−0.655785	+	0.754947i	$0.727662\pi$
$200$	6.82393e9	−	1.18194e10i	0.301578	−	0.522348i
$201$		0			0
$202$	−1.80568e9	−	3.12754e9i	−0.0763063	−	0.132166i
$203$	−1.00232e10	−	1.73607e10i	−0.414260	−	0.717520i
$204$		0			0
$205$	−1.89343e9	+	3.27951e9i	−0.0748783	+	0.129693i
$206$	8.76437e8			0.0339092
$207$		0			0
$208$	8.33270e9			0.308675
$209$	−3.22886e10	+	5.59255e10i	−1.17055	+	2.02746i
$210$		0			0
$211$	2.12768e9	+	3.68525e9i	0.0738985	+	0.127996i	0.900607	−	0.434635i	$-0.143123\pi$
$211$	2.12768e9	+	3.68525e9i	0.0738985	+	0.127996i	−0.826708	+	0.562631i	$0.809789\pi$
$212$	−2.92965e9	−	5.07430e9i	−0.0996102	−	0.172530i
$213$		0			0
$214$	−2.07589e10	+	3.59554e10i	−0.676615	+	1.17193i
$215$	−1.58634e10			−0.506317
$216$		0			0
$217$	4.51718e10			1.38292
$218$	−1.09833e10	+	1.90236e10i	−0.329365	+	0.570477i
$219$		0			0
$220$	−3.68710e9	−	6.38625e9i	−0.106117	−	0.183799i
$221$	4.15515e9	+	7.19692e9i	0.117171	+	0.202947i
$222$		0			0
$223$	−2.11759e10	+	3.66777e10i	−0.573416	+	0.993185i	0.422796	+	0.906225i	$0.361049\pi$
$223$	−2.11759e10	+	3.66777e10i	−0.573416	+	0.993185i	−0.996212	+	0.0869601i	$0.972285\pi$
$224$	−1.50343e10			−0.398995
$225$		0			0
$226$	4.95795e10			1.26419
$227$	2.96301e10	−	5.13208e10i	0.740656	−	1.28285i	−0.211541	−	0.977369i	$-0.567848\pi$
$227$	2.96301e10	−	5.13208e10i	0.740656	−	1.28285i	0.952197	−	0.305485i	$-0.0988186\pi$
$228$		0			0
$229$	3.07523e10	+	5.32645e10i	0.738954	+	1.27991i	0.952967	+	0.303075i	$0.0980133\pi$
$229$	3.07523e10	+	5.32645e10i	0.738954	+	1.27991i	−0.214013	+	0.976831i	$0.568653\pi$
$230$	−1.01348e9	−	1.75539e9i	−0.0238802	−	0.0413617i
$231$		0			0
$232$	2.05932e10	−	3.56685e10i	0.466690	−	0.808331i
$233$	4.69389e10			1.04335			0.521677	−	0.853143i	$-0.325307\pi$
$233$	4.69389e10			1.04335			0.521677	+	0.853143i	$0.325307\pi$
$234$		0			0
$235$	−3.15987e10			−0.675872
$236$	−7.00123e9	+	1.21265e10i	−0.146916	+	0.254467i
$237$		0			0
$238$	−1.84446e10	−	3.19470e10i	−0.372626	−	0.645407i
$239$	5.22440e9	+	9.04892e9i	0.103573	+	0.179393i	0.913154	−	0.407614i	$-0.133639\pi$
$239$	5.22440e9	+	9.04892e9i	0.103573	+	0.179393i	−0.809581	+	0.587008i	$0.800306\pi$
$240$		0			0
$241$	−1.49700e10	+	2.59288e10i	−0.285854	+	0.495114i	−0.972816	−	0.231580i	$-0.925611\pi$
$241$	−1.49700e10	+	2.59288e10i	−0.285854	+	0.495114i	0.686962	+	0.726693i	$0.258944\pi$
$242$	−7.04147e10			−1.31976
$243$		0			0
$244$	2.95507e9			0.0533719
$245$	−6.88196e9	+	1.19199e10i	−0.122030	+	0.211361i
$246$		0			0
$247$	−1.19340e10	−	2.06703e10i	−0.204009	−	0.353354i
$248$	4.64041e10	+	8.03743e10i	0.778976	+	1.34923i
$249$		0			0
$250$	3.08746e10	−	5.34764e10i	0.499887	−	0.865830i
$251$	1.50652e9			0.0239576			0.0119788	−	0.999928i	$-0.496187\pi$
$251$	1.50652e9			0.0239576			0.0119788	+	0.999928i	$0.496187\pi$
$252$		0			0
$253$	−7.98928e9			−0.122593
$254$	6.39689e10	−	1.10797e11i	0.964311	−	1.67024i
$255$		0			0
$256$	−2.72509e10	−	4.72000e10i	−0.396553	−	0.686850i
$257$	−4.35790e10	−	7.54811e10i	−0.623130	−	1.07929i	−0.988899	−	0.148587i	$-0.952528\pi$
$257$	−4.35790e10	−	7.54811e10i	−0.623130	−	1.07929i	0.365770	−	0.930705i	$-0.380806\pi$
$258$		0			0
$259$	−1.44390e10	+	2.50090e10i	−0.199383	+	0.345341i
$260$	2.72553e9			0.0369889
$261$		0			0
$262$	−4.91715e9			−0.0644700
$263$	−2.10643e10	+	3.64844e10i	−0.271485	+	0.470226i	−0.969242	−	0.246108i	$-0.920848\pi$
$263$	−2.10643e10	+	3.64844e10i	−0.271485	+	0.470226i	0.697757	+	0.716334i	$0.254181\pi$
$264$		0			0
$265$	1.41633e10	+	2.45316e10i	0.176425	+	0.305577i
$266$	5.29747e10	+	9.17548e10i	0.648785	+	1.12373i
$267$		0			0
$268$	−1.33340e10	+	2.30951e10i	−0.157889	+	0.273472i
$269$	−6.32241e10			−0.736202			−0.368101	−	0.929786i	$-0.619992\pi$
$269$	−6.32241e10			−0.736202			−0.368101	+	0.929786i	$0.619992\pi$
$270$		0			0
$271$	−1.63811e11			−1.84493			−0.922467	−	0.386075i	$-0.873831\pi$
$271$	−1.63811e11			−1.84493			−0.922467	+	0.386075i	$0.873831\pi$
$272$	4.96703e10	−	8.60314e10i	0.550220	−	0.953009i
$273$		0			0
$274$	−1.28369e10	−	2.22341e10i	−0.137588	−	0.238310i
$275$	−5.19339e10	−	8.99522e10i	−0.547588	−	0.948451i
$276$		0			0
$277$	8.63022e10	−	1.49480e11i	0.880771	−	1.52554i	0.0302857	−	0.999541i	$-0.490358\pi$
$277$	8.63022e10	−	1.49480e11i	0.880771	−	1.52554i	0.850485	−	0.525999i	$-0.176308\pi$
$278$	3.46390e10			0.347827
$279$		0			0
$280$	3.02923e10			0.294525
$281$	−1.27714e10	+	2.21208e10i	−0.122197	+	0.211652i	−0.920634	−	0.390427i	$-0.872327\pi$
$281$	−1.27714e10	+	2.21208e10i	−0.122197	+	0.211652i	0.798437	+	0.602079i	$0.205661\pi$
$282$		0			0
$283$	3.69467e10	+	6.39936e10i	0.342402	+	0.593058i	0.984878	−	0.173248i	$-0.0554261\pi$
$283$	3.69467e10	+	6.39936e10i	0.342402	+	0.593058i	−0.642476	+	0.766306i	$0.722093\pi$
$284$	1.01224e10	+	1.75326e10i	0.0923321	+	0.159924i
$285$		0			0
$286$	2.41916e10	−	4.19010e10i	0.213805	−	0.370320i
$287$	2.44885e10			0.213056
$288$		0			0
$289$	−1.95145e10			−0.164557
$290$	3.97628e10	−	6.88712e10i	0.330131	−	0.571803i
$291$		0			0
$292$	1.59257e10	+	2.75841e10i	0.128196	+	0.222043i
$293$	1.01768e11	+	1.76267e11i	0.806687	+	1.39722i	0.915146	+	0.403122i	$0.132075\pi$
$293$	1.01768e11	+	1.76267e11i	0.806687	+	1.39722i	−0.108459	+	0.994101i	$0.534592\pi$
$294$		0			0
$295$	3.38474e10	−	5.86253e10i	0.260211	−	0.450699i
$296$	−5.93316e10			−0.449234
$297$		0			0
$298$	9.05566e10			0.665192
$299$	1.47643e9	−	2.55726e9i	0.0106830	−	0.0185035i
$300$		0			0
$301$	5.12919e10	+	8.88401e10i	0.360163	+	0.623821i
$302$	7.34533e9	+	1.27225e10i	0.0508136	+	0.0880118i
$303$		0			0
$304$	−1.42658e11	+	2.47091e11i	−0.957998	+	1.65930i
$305$	−1.42862e10			−0.0945297
$306$		0			0
$307$	8.22523e10			0.528476			0.264238	−	0.964457i	$-0.414880\pi$
$307$	8.22523e10			0.528476			0.264238	+	0.964457i	$0.414880\pi$
$308$	−2.38434e10	+	4.12980e10i	−0.150970	+	0.261488i
$309$		0			0
$310$	8.96002e10	+	1.55192e11i	0.551038	+	0.954425i
$311$	−1.16047e11	−	2.00999e11i	−0.703415	−	1.21835i	−0.967261	−	0.253785i	$-0.918324\pi$
$311$	−1.16047e11	−	2.00999e11i	−0.703415	−	1.21835i	0.263846	−	0.964565i	$-0.415009\pi$
$312$		0			0
$313$	−3.15040e10	+	5.45665e10i	−0.185531	+	0.321349i	−0.943755	−	0.330645i	$-0.892734\pi$
$313$	−3.15040e10	+	5.45665e10i	−0.185531	+	0.321349i	0.758224	+	0.651994i	$0.226067\pi$
$314$	−2.15537e10			−0.125124
$315$		0			0
$316$	5.76600e10			0.325299
$317$	−1.15735e11	+	2.00459e11i	−0.643722	+	1.11496i	0.340873	+	0.940109i	$0.389277\pi$
$317$	−1.15735e11	+	2.00459e11i	−0.643722	+	1.11496i	−0.984595	+	0.174850i	$0.944056\pi$
$318$		0			0
$319$	−1.56726e11	−	2.71458e11i	−0.847390	−	1.46772i
$320$	2.72570e10	+	4.72105e10i	0.145312	+	0.251689i
$321$		0			0
$322$	−6.55385e9	+	1.13516e10i	−0.0339739	+	0.0588445i
$323$	−2.84548e11			−1.45460
$324$		0			0
$325$	3.83899e10			0.190872
$326$	−8.98436e10	+	1.55614e11i	−0.440563	+	0.763077i
$327$		0			0
$328$	2.51565e10	+	4.35724e10i	0.120010	+	0.207864i
$329$	1.02170e11	+	1.76963e11i	0.480775	+	0.832726i
$330$		0			0
$331$	−7.72274e10	+	1.33762e11i	−0.353627	+	0.612500i	−0.986882	−	0.161443i	$-0.948385\pi$
$331$	−7.72274e10	+	1.33762e11i	−0.353627	+	0.612500i	0.633255	+	0.773943i	$0.281718\pi$
$332$	6.91587e10			0.312410
$333$		0			0
$334$	−2.37817e11			−1.04564
$335$	6.44629e10	−	1.11653e11i	0.279646	−	0.484361i
$336$		0			0
$337$	−6.76249e10	−	1.17130e11i	−0.285609	−	0.494690i	0.687148	−	0.726518i	$-0.258863\pi$
$337$	−6.76249e10	−	1.17130e11i	−0.285609	−	0.494690i	−0.972757	+	0.231828i	$0.925529\pi$
$338$	−1.27083e11	−	2.20113e11i	−0.529616	−	0.917321i
$339$		0			0
$340$	1.62466e10	−	2.81399e10i	0.0659337	−	0.114201i
$341$	7.06323e11			2.82884
$342$		0			0
$343$	2.73359e11			1.06638
$344$	−1.05382e11	+	1.82528e11i	−0.405747	+	0.702774i
$345$		0			0
$346$	−1.06122e11	−	1.83809e11i	−0.398074	−	0.689484i
$347$	−1.41753e11	−	2.45523e11i	−0.524867	−	0.909096i	−0.999581	−	0.0289556i	$-0.990782\pi$
$347$	−1.41753e11	−	2.45523e11i	−0.524867	−	0.909096i	0.474714	−	0.880140i	$-0.342551\pi$
$348$		0			0
$349$	−4.86799e10	+	8.43160e10i	−0.175645	+	0.304225i	−0.940384	−	0.340114i	$-0.889534\pi$
$349$	−4.86799e10	+	8.43160e10i	−0.175645	+	0.304225i	0.764740	+	0.644340i	$0.222868\pi$
$350$	−1.70412e11			−0.607008
$351$		0			0
$352$	−2.35082e11			−0.816164
$353$	1.91861e10	−	3.32314e10i	0.0657660	−	0.113910i	−0.831268	−	0.555873i	$-0.812384\pi$
$353$	1.91861e10	−	3.32314e10i	0.0657660	−	0.113910i	0.897034	+	0.441962i	$0.145718\pi$
$354$		0			0
$355$	−4.89368e10	−	8.47611e10i	−0.163534	−	0.283249i
$356$	1.90336e10	+	3.29672e10i	0.0628053	+	0.108782i
$357$		0			0
$358$	3.03115e11	−	5.25011e11i	0.975291	−	1.68925i
$359$	4.48036e11			1.42360			0.711800	−	0.702383i	$-0.247880\pi$
$359$	4.48036e11			1.42360			0.711800	+	0.702383i	$0.247880\pi$
$360$		0			0
$361$	4.94563e11			1.53264
$362$	1.80371e11	−	3.12412e11i	0.552050	−	0.956178i
$363$		0			0
$364$	−8.81262e9	−	1.52639e10i	−0.0263117	−	0.0455732i
$365$	−7.69926e10	−	1.33355e11i	−0.227055	−	0.393271i
$366$		0			0
$367$	3.74037e10	−	6.47850e10i	0.107626	−	0.186414i	−0.807182	−	0.590302i	$-0.799008\pi$
$367$	3.74037e10	−	6.47850e10i	0.107626	−	0.186414i	0.914808	+	0.403889i	$0.132342\pi$
$368$	−3.52983e10			−0.100332
$369$		0			0
$370$	−1.14561e11			−0.317783
$371$	9.15902e10	−	1.58639e11i	0.250996	−	0.434738i
$372$		0			0
$373$	1.39696e11	+	2.41961e11i	0.373675	+	0.647225i	0.990128	−	0.140167i	$-0.0447641\pi$
$373$	1.39696e11	+	2.41961e11i	0.373675	+	0.647225i	−0.616452	+	0.787392i	$0.711431\pi$
$374$	−2.88406e11	−	4.99535e11i	−0.762224	−	1.32021i
$375$		0			0
$376$	−2.09914e11	+	3.63582e11i	−0.541623	+	0.938118i
$377$	1.15853e11			0.295374
$378$		0			0
$379$	−6.40616e11			−1.59485			−0.797427	−	0.603415i	$-0.793806\pi$
$379$	−6.40616e11			−1.59485			−0.797427	+	0.603415i	$0.793806\pi$
$380$	−4.66618e10	+	8.08206e10i	−0.114798	+	0.198836i
$381$		0			0
$382$	1.25088e11	+	2.16659e11i	0.300559	+	0.520584i
$383$	1.66528e11	+	2.88435e11i	0.395451	+	0.684942i	0.993159	−	0.116772i	$-0.0372548\pi$
$383$	1.66528e11	+	2.88435e11i	0.395451	+	0.684942i	−0.597707	+	0.801714i	$0.703921\pi$
$384$		0			0
$385$	1.15271e11	−	1.99655e11i	0.267390	−	0.463134i
$386$	−2.55302e11			−0.585345
$387$		0			0
$388$	8.40002e10			0.188164
$389$	−8.15796e10	+	1.41300e11i	−0.180638	+	0.312873i	−0.942098	−	0.335338i	$-0.891149\pi$
$389$	−8.15796e10	+	1.41300e11i	−0.180638	+	0.312873i	0.761460	+	0.648212i	$0.224483\pi$
$390$		0			0
$391$	−1.76017e10	−	3.04870e10i	−0.0380855	−	0.0659660i
$392$	9.14355e10	+	1.58371e11i	0.195581	+	0.338757i
$393$		0			0
$394$	4.14462e10	−	7.17870e10i	0.0866467	−	0.150076i
$395$	−2.78757e11			−0.576153
$396$		0			0
$397$	2.79119e11			0.563939			0.281969	−	0.959423i	$-0.409012\pi$
$397$	2.79119e11			0.563939			0.281969	+	0.959423i	$0.409012\pi$
$398$	−3.72182e11	+	6.44638e11i	−0.743501	+	1.28778i
$399$		0			0
$400$	−2.29455e11	−	3.97428e11i	−0.448155	−	0.776227i
$401$	3.79966e11	+	6.58121e11i	0.733830	+	1.27103i	0.955235	+	0.295848i	$0.0956024\pi$
$401$	3.79966e11	+	6.58121e11i	0.733830	+	1.27103i	−0.221405	+	0.975182i	$0.571064\pi$
$402$		0			0
$403$	−1.30530e11	+	2.26084e11i	−0.246511	+	0.426970i
$404$	−2.05707e10			−0.0384178
$405$		0			0
$406$	−5.14269e11			−0.939341
$407$	−2.25773e11	+	3.91051e11i	−0.407847	+	0.706412i
$408$		0			0
$409$	1.89971e10	+	3.29039e10i	0.0335685	+	0.0581423i	0.882322	−	0.470647i	$-0.155979\pi$
$409$	1.89971e10	+	3.29039e10i	0.0335685	+	0.0581423i	−0.848753	+	0.528789i	$0.822646\pi$
$410$	4.85739e10	+	8.41325e10i	0.0848938	+	0.147040i
$411$		0			0
$412$	2.49613e9	−	4.32342e9i	0.00426805	−	0.00739248i
$413$	−4.37762e11			−0.740394
$414$		0			0
$415$	−3.34347e11			−0.553326
$416$	4.34436e10	−	7.52465e10i	0.0711223	−	0.123187i
$417$		0			0
$418$	8.28331e11	+	1.43471e12i	1.32712	+	2.29864i
$419$	−3.66823e11	−	6.35355e11i	−0.581424	−	1.00706i	−0.995311	−	0.0967277i	$-0.969162\pi$
$419$	−3.66823e11	−	6.35355e11i	−0.581424	−	1.00706i	0.413887	−	0.910328i	$-0.364171\pi$
$420$		0			0
$421$	1.60716e11	−	2.78368e11i	0.249339	−	0.431867i	−0.714004	−	0.700142i	$-0.753120\pi$
$421$	1.60716e11	−	2.78368e11i	0.249339	−	0.431867i	0.963342	+	0.268275i	$0.0864535\pi$
$422$	1.09167e11			0.167566
$423$		0			0
$424$	3.76356e11			0.565525
$425$	2.28838e11	−	3.96359e11i	0.340234	−	0.589303i
$426$		0			0
$427$	4.61924e10	+	8.00077e10i	0.0672428	+	0.116468i
$428$	1.18244e11	+	2.04805e11i	0.170327	+	0.295015i
$429$		0			0
$430$	−2.03479e11	+	3.52437e11i	−0.287020	+	0.497133i
$431$	−3.86098e11			−0.538952			−0.269476	−	0.963007i	$-0.586850\pi$
$431$	−3.86098e11			−0.538952			−0.269476	+	0.963007i	$0.586850\pi$
$432$		0			0
$433$	5.48808e11			0.750282			0.375141	−	0.926968i	$-0.377594\pi$
$433$	5.48808e11			0.750282			0.375141	+	0.926968i	$0.377594\pi$
$434$	5.79418e11	−	1.00358e12i	0.783950	−	1.35784i
$435$		0			0
$436$	6.25617e10	+	1.08360e11i	0.0829123	+	0.143608i
$437$	5.05538e10	+	8.75617e10i	0.0663113	+	0.114854i
$438$		0			0
$439$	1.50050e11	−	2.59895e11i	0.192817	−	0.333969i	−0.753365	−	0.657602i	$-0.771571\pi$
$439$	1.50050e11	−	2.59895e11i	0.192817	−	0.333969i	0.946183	+	0.323633i	$0.104904\pi$
$440$	4.73662e11			0.602465
$441$		0			0
$442$	2.13192e11			0.265687
$443$	2.11330e11	−	3.66034e11i	0.260702	−	0.451549i	−0.705727	−	0.708484i	$-0.749379\pi$
$443$	2.11330e11	−	3.66034e11i	0.260702	−	0.451549i	0.966429	+	0.256935i	$0.0827127\pi$
$444$		0			0
$445$	−9.20178e10	−	1.59379e11i	−0.111238	−	0.192669i
$446$	5.43246e11	+	9.40929e11i	0.650114	+	1.12603i
$447$		0			0
$448$	1.76263e11	−	3.05296e11i	0.206733	−	0.358072i
$449$	−1.63406e12			−1.89741			−0.948704	−	0.316165i	$-0.897605\pi$
$449$	−1.63406e12			−1.89741			−0.948704	+	0.316165i	$0.897605\pi$
$450$		0			0
$451$	3.82911e11			0.435816
$452$	1.41205e11	−	2.44573e11i	0.159120	−	0.275605i
$453$		0			0
$454$	−7.60130e11	−	1.31658e12i	−0.839724	−	1.45445i
$455$	4.26045e10	+	7.37932e10i	0.0466020	+	0.0807170i
$456$		0			0
$457$	−6.23184e11	+	1.07939e12i	−0.668334	+	1.15759i	0.310036	+	0.950725i	$0.399659\pi$
$457$	−6.23184e11	+	1.07939e12i	−0.668334	+	1.15759i	−0.978370	+	0.206863i	$0.933675\pi$
$458$	1.57784e12			1.67559
$459$		0			0
$460$	−1.15457e10			−0.0120229
$461$	1.44026e11	−	2.49459e11i	0.148520	−	0.257244i	−0.782161	−	0.623077i	$-0.785882\pi$
$461$	1.44026e11	−	2.49459e11i	0.148520	−	0.257244i	0.930681	+	0.365833i	$0.119216\pi$
$462$		0			0
$463$	−7.86329e11	−	1.36196e12i	−0.795225	−	1.37737i	−0.922696	−	0.385527i	$-0.874020\pi$
$463$	−7.86329e11	−	1.36196e12i	−0.795225	−	1.37737i	0.127472	−	0.991842i	$-0.459314\pi$
$464$	−6.92449e11	−	1.19936e12i	−0.693517	−	1.20121i
$465$		0			0
$466$	6.02085e11	−	1.04284e12i	0.591454	−	1.02443i
$467$	−2.12882e11			−0.207116			−0.103558	−	0.994623i	$-0.533023\pi$
$467$	−2.12882e11			−0.207116			−0.103558	+	0.994623i	$0.533023\pi$
$468$		0			0
$469$	−8.33726e11			−0.795693
$470$	−4.05317e11	+	7.02029e11i	−0.383137	+	0.663613i
$471$		0			0
$472$	−4.49705e11	−	7.78911e11i	−0.417050	−	0.722352i
$473$	8.02019e11	+	1.38914e12i	0.736732	+	1.27606i
$474$		0			0
$475$	−6.57245e11	+	1.13838e12i	−0.592388	+	1.02605i
$476$	−2.10124e11			−0.187605
$477$		0			0
$478$	2.68053e11			0.234853
$479$	7.62418e11	−	1.32055e12i	0.661733	−	1.14616i	−0.318426	−	0.947948i	$-0.603154\pi$
$479$	7.62418e11	−	1.32055e12i	0.661733	−	1.14616i	0.980160	−	0.198208i	$-0.0635123\pi$
$480$		0			0
$481$	−8.34466e10	−	1.44534e11i	−0.0710814	−	0.123117i
$482$	3.84040e11	+	6.65176e11i	0.324089	+	0.561339i
$483$		0			0
$484$	−2.00544e11	+	3.47353e11i	−0.166114	+	0.287718i
$485$	−4.06098e11			−0.333267
$486$		0			0
$487$	−1.81008e12			−1.45820			−0.729101	−	0.684406i	$-0.760062\pi$
$487$	−1.81008e12			−1.45820			−0.729101	+	0.684406i	$0.760062\pi$
$488$	−9.49052e10	+	1.64381e11i	−0.0757532	+	0.131208i
$489$		0			0
$490$	1.76550e11	+	3.05793e11i	0.138352	+	0.239632i
$491$	−5.76915e11	−	9.99245e11i	−0.447966	−	0.775899i	0.550288	−	0.834975i	$-0.314518\pi$
$491$	−5.76915e11	−	9.99245e11i	−0.447966	−	0.775899i	−0.998254	+	0.0590757i	$0.981185\pi$
$492$		0			0
$493$	6.90587e11	−	1.19613e12i	0.526511	−	0.911944i
$494$	−6.12309e11			−0.462593
$495$		0			0
$496$	3.12068e12			2.31517
$497$	−3.16460e11	+	5.48125e11i	−0.232657	+	0.402973i
$498$		0			0
$499$	1.00972e12	+	1.74888e12i	0.729032	+	1.26272i	0.957293	+	0.289121i	$0.0933629\pi$
$499$	1.00972e12	+	1.74888e12i	0.729032	+	1.26272i	−0.228260	+	0.973600i	$0.573304\pi$
$500$	−1.75865e11	−	3.04607e11i	−0.125839	−	0.217959i
$501$		0			0
$502$	1.93241e10	−	3.34703e10i	0.0135810	−	0.0235230i
$503$	7.16624e11			0.499155			0.249578	−	0.968355i	$-0.419708\pi$
$503$	7.16624e11			0.499155			0.249578	+	0.968355i	$0.419708\pi$
$504$		0			0
$505$	9.94486e10			0.0680437
$506$	−1.02478e11	+	1.77498e11i	−0.0694953	+	0.120369i
$507$		0			0
$508$	−3.64372e11	−	6.31112e11i	−0.242750	−	0.420455i
$509$	−7.90670e11	−	1.36948e12i	−0.522114	−	0.904327i	−0.999669	−	0.0257257i	$-0.991810\pi$
$509$	−7.90670e11	−	1.36948e12i	−0.522114	−	0.904327i	0.477555	−	0.878602i	$-0.341523\pi$
$510$		0			0
$511$	−4.97889e11	+	8.62369e11i	−0.323027	+	0.559499i
$512$	4.78068e11			0.307450
$513$		0			0
$514$	−2.23595e12			−1.41296
$515$	−1.20675e10	+	2.09015e10i	−0.00755936	+	0.0130932i
$516$		0			0
$517$	1.59757e12	+	2.76707e12i	0.983448	+	1.70338i
$518$	3.70417e11	+	6.41582e11i	0.226052	+	0.391533i
$519$		0			0
$520$	−8.75336e10	+	1.51613e11i	−0.0525001	+	0.0909328i
$521$	−1.03065e12			−0.612834			−0.306417	−	0.951897i	$-0.599130\pi$
$521$	−1.03065e12			−0.612834			−0.306417	+	0.951897i	$0.599130\pi$
$522$		0			0
$523$	2.03811e12			1.19116			0.595579	−	0.803297i	$-0.296923\pi$
$523$	2.03811e12			1.19116			0.595579	+	0.803297i	$0.296923\pi$
$524$	−1.40043e10	+	2.42561e10i	−0.00811465	+	0.0140550i
$525$		0			0
$526$	5.40383e11	+	9.35971e11i	0.307798	+	0.533122i
$527$	1.55615e12	+	2.69532e12i	0.878825	+	1.52217i
$528$		0			0
$529$	8.94322e11	−	1.54901e12i	0.496528	−	0.860011i
$530$	7.26693e11			0.400046
$531$		0			0
$532$	6.03497e11			0.326642
$533$	−7.07626e10	+	1.22564e11i	−0.0379779	+	0.0657797i
$534$		0			0
$535$	−5.71651e11	−	9.90128e11i	−0.301675	−	0.522516i
$536$	−8.56471e11	−	1.48345e12i	−0.448199	−	0.776303i
$537$		0			0
$538$	−8.10975e11	+	1.40465e12i	−0.417337	+	0.722849i
$539$	1.39175e12			0.710251
$540$		0			0
$541$	−1.53998e12			−0.772905			−0.386453	−	0.922309i	$-0.626300\pi$
$541$	−1.53998e12			−0.772905			−0.386453	+	0.922309i	$0.626300\pi$
$542$	−2.10120e12	+	3.63939e12i	−1.04585	+	1.81147i
$543$		0			0
$544$	−5.17925e11	−	8.97072e11i	−0.253555	−	0.439170i
$545$	−3.02454e11	−	5.23865e11i	−0.146850	−	0.254352i
$546$		0			0
$547$	9.59604e11	−	1.66208e12i	0.458299	−	0.793797i	−0.540572	−	0.841298i	$-0.681792\pi$
$547$	9.59604e11	−	1.66208e12i	0.458299	−	0.793797i	0.998871	+	0.0475005i	$0.0151256\pi$
$548$	−1.46240e11			−0.0692713
$549$		0			0
$550$	−2.66463e12			−1.24166
$551$	−1.98343e12	+	3.43541e12i	−0.916717	+	1.58780i
$552$		0			0
$553$	9.01319e11	+	1.56113e12i	0.409841	+	0.709865i
$554$	−2.21400e12	−	3.83475e12i	−0.998580	−	1.72959i
$555$		0			0
$556$	9.86533e10	−	1.70873e11i	0.0437799	−	0.0758291i
$557$	2.71058e11			0.119320			0.0596601	−	0.998219i	$-0.480998\pi$
$557$	2.71058e11			0.119320			0.0596601	+	0.998219i	$0.480998\pi$
$558$		0			0
$559$	−5.92858e11			−0.256802
$560$	5.09291e11	−	8.82118e11i	0.218836	−	0.379036i
$561$		0			0
$562$	3.27638e11	+	5.67486e11i	0.138542	+	0.239962i
$563$	1.54117e11	+	2.66939e11i	0.0646492	+	0.111976i	0.896538	−	0.442966i	$-0.146074\pi$
$563$	1.54117e11	+	2.66939e11i	0.0646492	+	0.111976i	−0.831889	+	0.554942i	$0.812740\pi$
$564$		0			0
$565$	−6.82652e11	+	1.18239e12i	−0.281826	+	0.488137i
$566$	1.89566e12			0.776402
$567$		0			0
$568$	−1.30037e12			−0.524205
$569$	1.79082e12	−	3.10180e12i	0.716222	−	1.24053i	−0.246264	−	0.969203i	$-0.579203\pi$
$569$	1.79082e12	−	3.10180e12i	0.716222	−	1.24053i	0.962486	−	0.271330i	$-0.0874636\pi$
$570$		0			0
$571$	4.45411e10	+	7.71475e10i	0.0175347	+	0.0303710i	0.874660	−	0.484738i	$-0.161085\pi$
$571$	4.45411e10	+	7.71475e10i	0.0175347	+	0.0303710i	−0.857125	+	0.515109i	$0.827752\pi$
$572$	−1.37797e11	−	2.38672e11i	−0.0538219	−	0.0932222i
$573$		0			0
$574$	3.14113e11	−	5.44060e11i	0.120777	−	0.209191i
$575$	−1.62624e11			−0.0620413
$576$		0			0
$577$	−4.29975e11			−0.161492			−0.0807462	−	0.996735i	$-0.525730\pi$
$577$	−4.29975e11			−0.161492			−0.0807462	+	0.996735i	$0.525730\pi$
$578$	−2.50312e11	+	4.33553e11i	−0.0932838	+	0.161572i
$579$		0			0
$580$	−2.26493e11	−	3.92297e11i	−0.0831051	−	0.143942i
$581$	1.08106e12	+	1.87245e12i	0.393603	+	0.681740i
$582$		0			0
$583$	1.43214e12	−	2.48054e12i	0.513424	−	0.889277i
$584$	−2.04589e12			−0.727820
$585$		0			0
$586$	5.22149e12			1.82917
$587$	1.13503e12	−	1.96594e12i	0.394582	−	0.683436i	−0.598466	−	0.801148i	$-0.704223\pi$
$587$	1.13503e12	−	1.96594e12i	0.394582	−	0.683436i	0.993048	+	0.117712i	$0.0375561\pi$
$588$		0			0
$589$	−4.46940e12	−	7.74123e12i	−1.53014	−	2.65028i
$590$	−8.68320e11	−	1.50397e12i	−0.295016	−	0.510983i
$591$		0			0
$592$	−9.97514e11	+	1.72774e12i	−0.333788	+	0.578138i
$593$	4.09944e12			1.36138			0.680688	−	0.732573i	$-0.261681\pi$
$593$	4.09944e12			1.36138			0.680688	+	0.732573i	$0.261681\pi$
$594$		0			0
$595$	1.01584e12			0.332277
$596$	2.57909e11	−	4.46712e11i	0.0837256	−	0.145017i
$597$		0			0
$598$	−3.78764e10	−	6.56039e10i	−0.0121119	−	0.0209785i
$599$	−8.09154e11	−	1.40150e12i	−0.256809	−	0.444806i	0.708576	−	0.705634i	$-0.249338\pi$
$599$	−8.09154e11	−	1.40150e12i	−0.256809	−	0.444806i	−0.965385	+	0.260828i	$0.916005\pi$
$600$		0			0
$601$	−8.60804e11	+	1.49096e12i	−0.269134	+	0.466155i	−0.968639	−	0.248474i	$-0.920071\pi$
$601$	−8.60804e11	+	1.49096e12i	−0.269134	+	0.466155i	0.699504	+	0.714629i	$0.253404\pi$
$602$	2.63168e12			0.816675
$603$		0			0
$604$	8.36793e10			0.0255830
$605$	9.69528e11	−	1.67927e12i	0.294213	−	0.509591i
$606$		0			0
$607$	2.07028e12	+	3.58583e12i	0.618985	+	1.07211i	0.989671	+	0.143356i	$0.0457894\pi$
$607$	2.07028e12	+	3.58583e12i	0.618985	+	1.07211i	−0.370686	+	0.928758i	$0.620877\pi$
$608$	1.48753e12	+	2.57648e12i	0.441468	+	0.764646i
$609$		0			0
$610$	−1.83249e11	+	3.17397e11i	−0.0535869	+	0.0928152i
$611$	−1.18093e12			−0.342799
$612$		0			0
$613$	1.88290e12			0.538585			0.269292	−	0.963058i	$-0.413210\pi$
$613$	1.88290e12			0.538585			0.269292	+	0.963058i	$0.413210\pi$
$614$	1.05505e12	−	1.82740e12i	0.299582	−	0.518891i
$615$		0			0
$616$	−1.53152e12	−	2.65267e12i	−0.428557	−	0.742283i
$617$	−1.45653e12	−	2.52278e12i	−0.404609	−	0.700803i	0.589667	−	0.807646i	$-0.299259\pi$
$617$	−1.45653e12	−	2.52278e12i	−0.404609	−	0.700803i	−0.994276	+	0.106844i	$0.965926\pi$
$618$		0			0
$619$	1.23748e12	−	2.14337e12i	0.338789	−	0.586799i	−0.645417	−	0.763831i	$-0.723316\pi$
$619$	1.23748e12	−	2.14337e12i	0.338789	−	0.586799i	0.984205	+	0.177032i	$0.0566495\pi$
$620$	1.02074e12			0.277430
$621$		0			0
$622$	−5.95413e12			−1.59500
$623$	−5.95052e11	+	1.03066e12i	−0.158255	+	0.274107i
$624$		0			0
$625$	−5.69756e11	−	9.86847e11i	−0.149358	−	0.258696i
$626$	8.08203e11	+	1.39985e12i	0.210347	+	0.364331i
$627$		0			0
$628$	−6.13860e10	+	1.06324e11i	−0.0157489	+	0.0272780i
$629$	−1.98966e12			−0.506817
$630$		0			0
$631$	5.10645e12			1.28229			0.641146	−	0.767419i	$-0.278459\pi$
$631$	5.10645e12			1.28229			0.641146	+	0.767419i	$0.278459\pi$
$632$	−1.85182e12	+	3.20744e12i	−0.461712	+	0.799708i
$633$		0			0
$634$	2.96907e12	+	5.14257e12i	0.729824	+	1.26409i
$635$	1.76155e12	+	3.05110e12i	0.429946	+	0.744689i
$636$		0			0
$637$	−2.57198e11	+	4.45480e11i	−0.0618928	+	0.107202i
$638$	−8.04130e12			−1.92147
$639$		0			0
$640$	2.58884e12			0.609951
$641$	−3.03247e11	+	5.25239e11i	−0.0709472	+	0.122884i	−0.899317	−	0.437298i	$-0.855936\pi$
$641$	−3.03247e11	+	5.25239e11i	−0.0709472	+	0.122884i	0.828370	+	0.560182i	$0.189269\pi$
$642$		0			0
$643$	1.25492e12	+	2.17359e12i	0.289512	+	0.501450i	0.973693	−	0.227862i	$-0.0731736\pi$
$643$	1.25492e12	+	2.17359e12i	0.289512	+	0.501450i	−0.684181	+	0.729312i	$0.739840\pi$
$644$	3.73313e10	+	6.46598e10i	0.00855238	+	0.0148132i
$645$		0			0
$646$	−3.64990e12	+	6.32182e12i	−0.824584	+	1.42822i
$647$	−2.81592e12			−0.631758			−0.315879	−	0.948799i	$-0.602299\pi$
$647$	−2.81592e12			−0.631758			−0.315879	+	0.948799i	$0.602299\pi$
$648$		0			0
$649$	−6.84501e12			−1.51451
$650$	4.92428e11	−	8.52910e11i	0.108201	−	0.187410i
$651$		0			0
$652$	5.11757e11	+	8.86389e11i	0.110905	+	0.192092i
$653$	5.41859e10	+	9.38527e10i	0.0116621	+	0.0201994i	0.871798	−	0.489866i	$-0.162954\pi$
$653$	5.41859e10	+	9.38527e10i	0.0116621	+	0.0201994i	−0.860135	+	0.510066i	$0.829621\pi$
$654$		0			0
$655$	6.77035e10	−	1.17266e11i	0.0143723	−	0.0248935i
$656$	1.69178e12			0.356678
$657$		0			0
$658$	5.24213e12			1.09016
$659$	−3.26356e12	+	5.65265e12i	−0.674073	+	1.16753i	0.302666	+	0.953097i	$0.402123\pi$
$659$	−3.26356e12	+	5.65265e12i	−0.674073	+	1.16753i	−0.976739	+	0.214432i	$0.931210\pi$
$660$		0			0
$661$	−2.14242e12	−	3.71079e12i	−0.436515	−	0.756066i	0.560903	−	0.827881i	$-0.310454\pi$
$661$	−2.14242e12	−	3.71079e12i	−0.436515	−	0.756066i	−0.997418	+	0.0718158i	$0.977121\pi$
$662$	1.98119e12	+	3.43153e12i	0.400927	+	0.694426i
$663$		0			0
$664$	−2.22111e12	+	3.84707e12i	−0.443418	+	0.768023i
$665$	−2.91760e12			−0.578533
$666$		0			0
$667$	−4.90768e11			−0.0960085
$668$	−6.77313e11	+	1.17314e12i	−0.131612	+	0.227959i
$669$		0			0
$670$	−1.65373e12	−	2.86435e12i	−0.317050	−	0.549147i
$671$	7.22282e11	+	1.25103e12i	0.137548	+	0.238241i
$672$		0			0
$673$	−2.48556e12	+	4.30512e12i	−0.467043	+	0.808942i	−0.999291	−	0.0376463i	$-0.988014\pi$
$673$	−2.48556e12	+	4.30512e12i	−0.467043	+	0.808942i	0.532248	+	0.846588i	$0.321347\pi$
$674$	−3.46970e12			−0.647623
$675$		0			0
$676$	−1.44775e12			−0.266644
$677$	3.82144e12	−	6.61893e12i	0.699163	−	1.21099i	−0.269595	−	0.962974i	$-0.586890\pi$
$677$	3.82144e12	−	6.61893e12i	0.699163	−	1.21099i	0.968757	−	0.248011i	$-0.0797770\pi$
$678$		0			0
$679$	1.31306e12	+	2.27428e12i	0.237066	+	0.410611i
$680$	1.04356e12	+	1.80749e12i	0.187165	+	0.324180i
$681$		0			0
$682$	9.06000e12	−	1.56924e13i	1.60361	−	2.77753i
$683$	4.20646e12			0.739646			0.369823	−	0.929102i	$-0.379418\pi$
$683$	4.20646e12			0.739646			0.369823	+	0.929102i	$0.379418\pi$
$684$		0			0
$685$	7.06995e11			0.122690
$686$	3.50638e12	−	6.07323e12i	0.604506	−	1.04703i
$687$		0			0
$688$	3.54349e12	+	6.13750e12i	0.602952	+	1.04434i
$689$	5.29324e11	+	9.16816e11i	0.0894818	+	0.154987i
$690$		0			0
$691$	1.16845e12	−	2.02381e12i	0.194966	−	0.337690i	−0.751924	−	0.659250i	$-0.770874\pi$
$691$	1.16845e12	−	2.02381e12i	0.194966	−	0.337690i	0.946889	+	0.321560i	$0.104207\pi$
$692$	−1.20896e12			−0.200417
$693$		0			0
$694$	−7.27305e12			−1.19014
$695$	−4.76938e11	+	8.26082e11i	−0.0775409	+	0.134305i
$696$		0			0
$697$	8.43615e11	+	1.46118e12i	0.135393	+	0.234508i
$698$	1.24883e12	+	2.16304e12i	0.199138	+	0.344918i
$699$		0			0
$700$	−4.85341e11	+	8.40635e11i	−0.0764022	+	0.132333i
$701$	−1.10126e12			−0.172250			−0.0861251	−	0.996284i	$-0.527448\pi$
$701$	−1.10126e12			−0.172250			−0.0861251	+	0.996284i	$0.527448\pi$
$702$		0			0
$703$	5.71450e12			0.882429
$704$	2.75611e12	−	4.77373e12i	0.422883	−	0.732454i
$705$		0			0
$706$	−4.92201e11	−	8.52518e11i	−0.0745627	−	0.129146i
$707$	−3.21553e11	−	5.56946e11i	−0.0484022	−	0.0838350i
$708$		0			0
$709$	−6.57748e11	+	1.13925e12i	−0.0977578	+	0.169322i	−0.910756	−	0.412944i	$-0.864500\pi$
$709$	−6.57748e11	+	1.13925e12i	−0.0977578	+	0.169322i	0.812998	+	0.582266i	$0.197834\pi$
$710$	−2.51085e12			−0.370816
$711$		0			0
$712$	−2.44514e12			−0.356570
$713$	5.52940e11	−	9.57720e11i	0.0801263	−	0.138783i
$714$		0			0
$715$	6.66180e11	+	1.15386e12i	0.0953266	+	0.165111i
$716$	−1.72657e12	−	2.99051e12i	−0.245514	−	0.425243i
$717$		0			0
$718$	5.74695e12	−	9.95402e12i	0.807008	−	1.39778i
$719$	1.32450e13			1.84830			0.924151	−	0.382027i	$-0.124774\pi$
$719$	1.32450e13			1.84830			0.924151	+	0.382027i	$0.124774\pi$
$720$		0			0
$721$	1.56074e11			0.0215091
$722$	6.34376e12	−	1.09877e13i	0.868819	−	1.50484i
$723$		0			0
$724$	−1.02741e12	−	1.77952e12i	−0.138970	−	0.240702i
$725$	−3.19021e12	−	5.52561e12i	−0.428843	−	0.742778i
$726$		0			0
$727$	−2.35848e12	+	4.08501e12i	−0.313132	+	0.542360i	−0.979039	−	0.203675i	$-0.934712\pi$
$727$	−2.35848e12	+	4.08501e12i	−0.313132	+	0.542360i	0.665907	+	0.746035i	$0.268045\pi$
$728$	1.13211e12			0.149382
$729$		0			0
$730$	−3.95034e12			−0.514851
$731$	−3.53396e12	+	6.12100e12i	−0.457755	+	0.792855i
$732$		0			0
$733$	−8.29559e11	−	1.43684e12i	−0.106140	−	0.183840i	0.808063	−	0.589096i	$-0.200516\pi$
$733$	−8.29559e11	−	1.43684e12i	−0.106140	−	0.183840i	−0.914203	+	0.405256i	$0.867183\pi$
$734$	−9.59553e11	−	1.66199e12i	−0.122022	−	0.211348i
$735$		0			0
$736$	−1.84032e11	+	3.18753e11i	−0.0231177	+	0.0400410i
$737$	−1.30364e13			−1.62763
$738$		0			0
$739$	−5.72028e12			−0.705533			−0.352767	−	0.935711i	$-0.614759\pi$
$739$	−5.72028e12			−0.705533			−0.352767	+	0.935711i	$0.614759\pi$
$740$	−3.26276e11	+	5.65126e11i	−0.0399984	+	0.0692792i
$741$		0			0
$742$	−2.34966e12	−	4.06972e12i	−0.284568	−	0.492887i
$743$	−3.35872e12	−	5.81747e12i	−0.404318	−	0.700300i	0.589923	−	0.807459i	$-0.299158\pi$
$743$	−3.35872e12	−	5.81747e12i	−0.404318	−	0.700300i	−0.994242	+	0.107159i	$0.965825\pi$
$744$		0			0
$745$	−1.24686e12	+	2.15962e12i	−0.148291	+	0.256847i
$746$	7.16752e12			0.847314
$747$		0			0
$748$	−3.28558e12			−0.383755
$749$	−3.69670e12	+	6.40287e12i	−0.429186	+	0.743373i
$750$		0			0
$751$	−4.55508e12	−	7.88962e12i	−0.522536	−	0.905058i	−0.999656	−	0.0262203i	$-0.991653\pi$
$751$	−4.55508e12	−	7.88962e12i	−0.522536	−	0.905058i	0.477121	−	0.878838i	$-0.341680\pi$
$752$	7.05839e12	+	1.22255e13i	0.804869	+	1.39407i
$753$		0			0
$754$	1.48605e12	−	2.57391e12i	0.167441	−	0.290016i
$755$	−4.04547e11			−0.0453114
$756$		0			0
$757$	−4.86606e12			−0.538575			−0.269288	−	0.963060i	$-0.586788\pi$
$757$	−4.86606e12			−0.538575			−0.269288	+	0.963060i	$0.586788\pi$
$758$	−8.21717e12	+	1.42326e13i	−0.904089	+	1.56593i
$759$		0			0
$760$	−2.99719e12	−	5.19129e12i	−0.325877	−	0.564435i
$761$	1.85589e12	+	3.21450e12i	0.200596	+	0.347442i	0.948720	−	0.316116i	$-0.102379\pi$
$761$	1.85589e12	+	3.21450e12i	0.200596	+	0.347442i	−0.748125	+	0.663558i	$0.769046\pi$
$762$		0			0
$763$	−1.95588e12	+	3.38768e12i	−0.208921	+	0.361862i
$764$	1.42502e12			0.151322
$765$		0			0
$766$	8.54423e12			0.896692
$767$	1.26497e12	−	2.19099e12i	0.131978	−	0.228592i
$768$		0			0
$769$	3.31651e12	+	5.74436e12i	0.341989	+	0.592343i	0.984802	−	0.173681i	$-0.0555660\pi$
$769$	3.31651e12	+	5.74436e12i	0.341989	+	0.592343i	−0.642813	+	0.766023i	$0.722233\pi$
$770$	−2.95716e12	−	5.12194e12i	−0.303156	−	0.525081i
$771$		0			0
$772$	−7.27112e11	+	1.25940e12i	−0.0736756	+	0.127610i
$773$	7.34772e12			0.740193			0.370096	−	0.928993i	$-0.379325\pi$
$773$	7.34772e12			0.740193			0.370096	+	0.928993i	$0.379325\pi$
$774$		0			0
$775$	1.43774e13			1.43161
$776$	−2.69776e12	+	4.67266e12i	−0.267070	+	0.462579i
$777$		0			0
$778$	2.09284e12	+	3.62491e12i	0.204799	+	0.354723i
$779$	−2.42295e12	−	4.19666e12i	−0.235736	−	0.408306i
$780$		0			0
$781$	−4.94829e12	+	8.57069e12i	−0.475911	+	0.824301i
$782$	−9.03108e11			−0.0863593
$783$		0			0
$784$	6.14905e12			0.581281
$785$	2.96770e11	−	5.14021e11i	0.0278937	−	0.0483134i
$786$		0			0
$787$	1.90682e12	+	3.30271e12i	0.177184	+	0.306891i	0.940915	−	0.338643i	$-0.109968\pi$
$787$	1.90682e12	+	3.30271e12i	0.177184	+	0.306891i	−0.763731	+	0.645535i	$0.776635\pi$
$788$	−2.36081e11	−	4.08905e11i	−0.0218119	−	0.0377793i
$789$		0			0
$790$	−3.57561e12	+	6.19314e12i	−0.326609	+	0.565703i
$791$	8.82902e12			0.801897
$792$		0			0
$793$	−5.33916e11			−0.0479451
$794$	3.58026e12	−	6.20119e12i	0.319685	−	0.553710i
$795$		0			0
$796$	2.11998e12	+	3.67192e12i	0.187164	+	0.324178i
$797$	−8.93658e12	−	1.54786e13i	−0.784529	−	1.35884i	−0.929280	−	0.369376i	$-0.879572\pi$
$797$	−8.93658e12	−	1.54786e13i	−0.784529	−	1.35884i	0.144751	−	0.989468i	$-0.453762\pi$
$798$		0			0
$799$	−7.03941e12	+	1.21926e13i	−0.611048	+	1.05837i
$800$	−4.78518e12			−0.413041
$801$		0			0
$802$	1.94953e13			1.66397
$803$	−7.78517e12	+	1.34843e13i	−0.660767	+	1.14448i
$804$		0			0
$805$	−1.80478e11	−	3.12597e11i	−0.0151476	−	0.0262363i
$806$	3.34861e12	+	5.79996e12i	0.279484	+	0.484080i
$807$		0			0
$808$	6.60650e11	−	1.14428e12i	0.0545281	−	0.0944454i
$809$	−1.16949e13			−0.959908			−0.479954	−	0.877294i	$-0.659347\pi$
$809$	−1.16949e13			−0.959908			−0.479954	+	0.877294i	$0.659347\pi$
$810$		0			0
$811$	−3.78089e12			−0.306902			−0.153451	−	0.988156i	$-0.549039\pi$
$811$	−3.78089e12			−0.306902			−0.153451	+	0.988156i	$0.549039\pi$
$812$	−1.46466e12	+	2.53687e12i	−0.118232	+	0.204784i
$813$		0			0
$814$	5.79198e12	+	1.00320e13i	0.462400	+	0.800900i
$815$	−2.47408e12	−	4.28524e12i	−0.196429	−	0.340224i
$816$		0			0
$817$	1.01499e13	−	1.75801e13i	0.797006	−	1.38045i
$818$	9.74701e11			0.0761170
$819$		0			0
$820$	5.53363e11			0.0427413
$821$	3.66299e12	−	6.34448e12i	0.281379	−	0.487362i	−0.690346	−	0.723480i	$-0.742542\pi$
$821$	3.66299e12	−	6.34448e12i	0.281379	−	0.487362i	0.971725	+	0.236117i	$0.0758750\pi$
$822$		0			0
$823$	−3.23057e12	−	5.59552e12i	−0.245460	−	0.425149i	0.716801	−	0.697278i	$-0.245606\pi$
$823$	−3.23057e12	−	5.59552e12i	−0.245460	−	0.425149i	−0.962261	+	0.272129i	$0.912272\pi$
$824$	1.60332e11	+	2.77703e11i	0.0121157	+	0.0209850i
$825$		0			0
$826$	−5.61517e12	+	9.72576e12i	−0.419713	+	0.726965i
$827$	1.17187e13			0.871176			0.435588	−	0.900146i	$-0.356540\pi$
$827$	1.17187e13			0.871176			0.435588	+	0.900146i	$0.356540\pi$
$828$		0			0
$829$	−2.81041e12			−0.206669			−0.103334	−	0.994647i	$-0.532951\pi$
$829$	−2.81041e12			−0.206669			−0.103334	+	0.994647i	$0.532951\pi$
$830$	−4.28867e12	+	7.42819e12i	−0.313668	+	0.543290i
$831$		0			0
$832$	1.01867e12	+	1.76439e12i	0.0737018	+	0.127655i
$833$	3.06626e12	+	5.31091e12i	0.220651	+	0.382179i
$834$		0			0
$835$	3.27446e12	−	5.67153e12i	0.233105	−	0.403749i
$836$	9.43650e12			0.668163
$837$		0			0
$838$	−1.88209e13			−1.31839
$839$	−8.01390e12	+	1.38805e13i	−0.558361	+	0.967109i	0.439273	+	0.898354i	$0.355236\pi$
$839$	−8.01390e12	+	1.38805e13i	−0.558361	+	0.967109i	−0.997634	+	0.0687556i	$0.978097\pi$
$840$		0			0
$841$	−2.37384e12	−	4.11162e12i	−0.163633	−	0.283420i
$842$	−4.12300e12	−	7.14125e12i	−0.282689	−	0.489632i
$843$		0			0
$844$	3.10913e11	−	5.38517e11i	0.0210910	−	0.0365307i
$845$	6.99912e12			0.472268
$846$		0			0
$847$	−1.25393e13			−0.837141
$848$	6.32749e12	−	1.09595e13i	0.420194	−	0.727798i
$849$		0			0
$850$	−5.87061e12	−	1.01682e13i	−0.385743	−	0.668127i
$851$	3.53490e11	+	6.12263e11i	0.0231044	+	0.0400179i
$852$		0			0
$853$	8.96613e12	−	1.55298e13i	0.579875	−	1.00437i	−0.415618	−	0.909539i	$-0.636435\pi$
$853$	8.96613e12	−	1.55298e13i	0.579875	−	1.00437i	0.995493	−	0.0948337i	$-0.0302319\pi$
$854$	2.37004e12			0.152474
$855$		0			0
$856$	−1.51902e13			−0.967011
$857$	−2.18082e12	+	3.77729e12i	−0.138104	+	0.239203i	−0.926779	−	0.375607i	$-0.877434\pi$
$857$	−2.18082e12	+	3.77729e12i	−0.138104	+	0.239203i	0.788675	+	0.614810i	$0.210767\pi$
$858$		0			0
$859$	−3.67580e12	−	6.36667e12i	−0.230347	−	0.398973i	0.727563	−	0.686041i	$-0.240653\pi$
$859$	−3.67580e12	−	6.36667e12i	−0.230347	−	0.398973i	−0.957910	+	0.287068i	$0.907319\pi$
$860$	1.15904e12	+	2.00751e12i	0.0722527	+	0.125145i
$861$		0			0
$862$	−4.95248e12	+	8.57795e12i	−0.305520	+	0.529177i
$863$	−1.41639e13			−0.869231			−0.434615	−	0.900616i	$-0.643116\pi$
$863$	−1.41639e13			−0.869231			−0.434615	+	0.900616i	$0.643116\pi$
$864$		0			0
$865$	5.84471e12			0.354969
$866$	7.03956e12	−	1.21929e13i	0.425319	−	0.736674i
$867$		0			0
$868$	−3.30042e12	−	5.71649e12i	−0.197347	−	0.341815i
$869$	1.40933e13	+	2.44104e13i	0.838350	+	1.45206i
$870$		0			0
$871$	2.40916e12	−	4.17278e12i	0.141835	−	0.245666i
$872$	−8.03695e12			−0.470725
$873$		0			0
$874$	2.59381e12			0.150362
$875$	5.49810e12	−	9.52299e12i	0.317085	−	0.549208i
$876$		0			0
$877$	2.34330e12	+	4.05872e12i	0.133761	+	0.231681i	0.925124	−	0.379666i	$-0.123961\pi$
$877$	2.34330e12	+	4.05872e12i	0.133761	+	0.231681i	−0.791362	+	0.611347i	$0.790628\pi$
$878$	−3.84939e12	−	6.66733e12i	−0.218608	−	0.378640i
$879$		0			0
$880$	7.96346e12	−	1.37931e13i	0.447641	−	0.775337i
$881$	−1.22598e13			−0.685635			−0.342817	−	0.939402i	$-0.611381\pi$
$881$	−1.22598e13			−0.685635			−0.342817	+	0.939402i	$0.611381\pi$
$882$		0			0
$883$	−6.77194e12			−0.374878			−0.187439	−	0.982276i	$-0.560019\pi$
$883$	−6.77194e12			−0.374878			−0.187439	+	0.982276i	$0.560019\pi$
$884$	6.07181e11	−	1.05167e12i	0.0334413	−	0.0579220i
$885$		0			0
$886$	−5.42145e12	−	9.39023e12i	−0.295573	−	0.511947i
$887$	−1.08701e13	−	1.88276e13i	−0.589627	−	1.02126i	−0.994281	−	0.106795i	$-0.965941\pi$
$887$	−1.08701e13	−	1.88276e13i	−0.589627	−	1.02126i	0.404654	−	0.914470i	$-0.367392\pi$
$888$		0			0
$889$	1.13915e13	−	1.97306e13i	0.611676	−	1.05945i
$890$	−4.72125e12			−0.252233
$891$		0			0
$892$	6.18875e12			0.327311
$893$	2.02179e13	−	3.50183e13i	1.06391	−	1.84274i
$894$		0			0
$895$	8.34709e12	+	1.44576e13i	0.434842	+	0.753169i
$896$	−8.37063e12	−	1.44984e13i	−0.433883	−	0.751507i
$897$		0			0
$898$	−2.09601e13	+	3.63040e13i	−1.07560	+	1.86299i
$899$	4.33882e13			2.21540
$900$		0			0
$901$	1.26210e13			0.638015
$902$	4.91159e12	−	8.50713e12i	0.247055	−	0.427911i
$903$		0			0
$904$	9.06989e12	+	1.57095e13i	0.451694	+	0.782356i
$905$	4.96700e12	+	8.60309e12i	0.246136	+	0.426320i
$906$		0			0
$907$	1.13948e13	−	1.97364e13i	0.559079	−	0.968354i	−0.438494	−	0.898734i	$-0.644488\pi$
$907$	1.13948e13	−	1.97364e13i	0.559079	−	0.968354i	0.997574	−	0.0696198i	$-0.0221786\pi$
$908$	−8.65954e12			−0.422774
$909$		0			0
$910$	2.18595e12			0.105671
$911$	−5.63882e12	+	9.76672e12i	−0.271241	+	0.469803i	−0.969180	−	0.246354i	$-0.920767\pi$
$911$	−5.63882e12	+	9.76672e12i	−0.271241	+	0.469803i	0.697939	+	0.716157i	$0.254101\pi$
$912$		0			0
$913$	1.69039e13	+	2.92784e13i	0.805134	+	1.39453i
$914$	1.59872e13	+	2.76906e13i	0.757728	+	1.31242i
$915$		0			0
$916$	4.49375e12	−	7.78340e12i	0.210901	−	0.365292i
$917$	−8.75637e11			−0.0408942
$918$		0			0
$919$	−2.27954e12			−0.105421			−0.0527105	−	0.998610i	$-0.516786\pi$
$919$	−2.27954e12			−0.105421			−0.0527105	+	0.998610i	$0.516786\pi$
$920$	3.70803e11	−	6.42250e11i	0.0170647	−	0.0295569i
$921$		0			0
$922$	−3.69483e12	−	6.39963e12i	−0.168386	−	0.291653i
$923$	−1.82891e12	−	3.16776e12i	−0.0829438	−	0.143663i
$924$		0			0
$925$	−4.59569e12	+	7.95997e12i	−0.206402	+	0.357498i
$926$	−4.03450e13			−1.80318
$927$		0			0
$928$	−1.44407e13			−0.639179
$929$	−9.43673e12	+	1.63449e13i	−0.415672	+	0.719965i	−0.995499	−	0.0947745i	$-0.969787\pi$
$929$	−9.43673e12	+	1.63449e13i	−0.415672	+	0.719965i	0.579827	+	0.814740i	$0.303120\pi$
$930$		0			0
$931$	−8.80659e12	−	1.52535e13i	−0.384179	−	0.665418i
$932$	−3.42953e12	−	5.94012e12i	−0.148889	−	0.257884i
$933$		0			0
$934$	−2.73064e12	+	4.72961e12i	−0.117410	+	0.203359i
$935$	1.58841e13			0.679689
$936$		0			0
$937$	−1.08798e13			−0.461096			−0.230548	−	0.973061i	$-0.574052\pi$
$937$	−1.08798e13			−0.461096			−0.230548	+	0.973061i	$0.574052\pi$
$938$	−1.06942e13	+	1.85229e13i	−0.451061	+	0.781261i
$939$		0			0
$940$	2.30872e12	+	3.99882e12i	0.0964486	+	0.167054i
$941$	1.41900e13	+	2.45778e13i	0.589970	+	1.02186i	0.994236	+	0.107216i	$0.0341936\pi$
$941$	1.41900e13	+	2.45778e13i	0.589970	+	1.02186i	−0.404266	+	0.914641i	$0.632473\pi$
$942$		0			0
$943$	2.99759e11	−	5.19198e11i	0.0123444	−	0.0213811i
$944$	−3.02427e13			−1.23950
$945$		0			0
$946$	4.11500e13			1.67055
$947$	1.79187e12	−	3.10361e12i	0.0723988	−	0.125398i	−0.827553	−	0.561387i	$-0.810268\pi$
$947$	1.79187e12	−	3.10361e12i	0.0723988	−	0.125398i	0.899952	+	0.435989i	$0.143601\pi$
$948$		0			0
$949$	−2.87743e12	−	4.98385e12i	−0.115161	−	0.199465i
$950$	1.68610e13	+	2.92040e13i	0.671624	+	1.16329i
$951$		0			0
$952$	6.74837e12	−	1.16885e13i	0.266276	−	0.461204i
$953$	−2.91182e12			−0.114353			−0.0571763	−	0.998364i	$-0.518210\pi$
$953$	−2.91182e12			−0.114353			−0.0571763	+	0.998364i	$0.518210\pi$
$954$		0			0
$955$	−6.88926e12			−0.268014
$956$	7.63428e11	−	1.32230e12i	0.0295602	−	0.0511998i
$957$		0			0
$958$	−1.95591e13	−	3.38773e13i	−0.750245	−	1.29946i
$959$	−2.28597e12	−	3.95941e12i	−0.0872743	−	0.151163i
$960$		0			0
$961$	−3.56649e13	+	6.17735e13i	−1.34892	+	2.33640i
$962$	−4.28148e12			−0.161178
$963$		0			0
$964$	4.37505e12			0.163168
$965$	3.51522e12	−	6.08853e12i	0.130491	−	0.226016i
$966$		0			0
$967$	1.34163e13	+	2.32377e13i	0.493417	+	0.854623i	0.999971	−	0.00758529i	$-0.00241450\pi$
$967$	1.34163e13	+	2.32377e13i	0.493417	+	0.854623i	−0.506555	+	0.862208i	$0.669081\pi$
$968$	−1.28814e13	−	2.23112e13i	−0.471546	−	0.816742i
$969$		0			0
$970$	−5.20902e12	+	9.02228e12i	−0.188922	+	0.327223i
$971$	−5.18797e13			−1.87288			−0.936442	−	0.350824i	$-0.885902\pi$
$971$	−5.18797e13			−1.87288			−0.936442	+	0.350824i	$0.885902\pi$
$972$		0			0
$973$	6.16844e12			0.220632
$974$	−2.32179e13	+	4.02146e13i	−0.826624	+	1.43175i
$975$		0			0
$976$	3.19120e12	+	5.52731e12i	0.112572	+	0.194980i
$977$	2.77975e13	+	4.81466e13i	0.976067	+	1.69060i	0.676367	+	0.736565i	$0.263553\pi$
$977$	2.77975e13	+	4.81466e13i	0.976067	+	1.69060i	0.299700	+	0.954034i	$0.403113\pi$
$978$		0			0
$979$	−9.30445e12	+	1.61158e13i	−0.323719	+	0.560698i
$980$	2.01129e12			0.0696557
$981$		0			0
$982$	−2.96003e13			−1.01577
$983$	2.01121e13	−	3.48351e13i	0.687015	−	1.18994i	−0.285785	−	0.958294i	$-0.592254\pi$
$983$	2.01121e13	−	3.48351e13i	0.687015	−	1.18994i	0.972799	−	0.231650i	$-0.0744125\pi$
$984$		0			0
$985$	1.14133e12	+	1.97685e12i	0.0386322	+	0.0669129i
$986$	−1.77163e13	−	3.06856e13i	−0.596935	−	1.03392i
$987$		0			0
$988$	−1.74388e12	+	3.02049e12i	−0.0582252	+	0.100849i
$989$	2.51142e12			0.0834710
$990$		0			0
$991$	1.34682e13			0.443588			0.221794	−	0.975094i	$-0.428809\pi$
$991$	1.34682e13			0.443588			0.221794	+	0.975094i	$0.428809\pi$
$992$	1.62701e13	−	2.81806e13i	0.533442	−	0.923949i
$993$		0			0
$994$	8.11847e12	+	1.40616e13i	0.263776	+	0.456874i
$995$	−1.02490e13	−	1.77518e13i	−0.331496	−	0.574169i
$996$		0			0
$997$	1.87292e13	−	3.24399e13i	0.600331	−	1.03980i	−0.392440	−	0.919778i	$-0.628369\pi$
$997$	1.87292e13	−	3.24399e13i	0.600331	−	1.03980i	0.992771	−	0.120026i	$-0.0382977\pi$
$998$	5.18065e13			1.65309
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.10.c.a.19.7		16
3.2	odd	2		9.10.c.a.7.2	yes	16
9.2	odd	6		81.10.a.c.1.7		8
9.4	even	3	inner	27.10.c.a.10.7		16
9.5	odd	6		9.10.c.a.4.2	✓	16
9.7	even	3		81.10.a.d.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.10.c.a.4.2	✓	16	9.5	odd	6
9.10.c.a.7.2	yes	16	3.2	odd	2
27.10.c.a.10.7		16	9.4	even	3	inner
27.10.c.a.19.7		16	1.1	even	1	trivial
81.10.a.c.1.7		8	9.2	odd	6
81.10.a.d.1.2		8	9.7	even	3

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	27.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(12.8270 - 22.2170i) q^{2} +(-73.0637 - 126.550i) q^{4} +(353.226 + 611.805i) q^{5} +(2284.21 - 3956.36i) q^{7} +9386.09 q^{8} +O(q^{10})\)	\(q+(12.8270 - 22.2170i) q^{2} +(-73.0637 - 126.550i) q^{4} +(353.226 + 611.805i) q^{5} +(2284.21 - 3956.36i) q^{7} +9386.09 q^{8} +18123.3 q^{10} +(35716.7 - 61863.1i) q^{11} +(13201.0 + 22864.9i) q^{13} +(-58599.1 - 101497. i) q^{14} +(157804. - 273325. i) q^{16} +314759. q^{17} -904019. q^{19} +(51616.0 - 89401.5i) q^{20} +(-916276. - 1.58704e6i) q^{22} +(-55921.2 - 96858.3i) q^{23} +(727026. - 1.25925e6i) q^{25} +677318. q^{26} -667571. q^{28} +(2.19402e6 - 3.80015e6i) q^{29} +(4.94392e6 + 8.56313e6i) q^{31} +(-1.64546e6 - 2.85003e6i) q^{32} +(4.03742e6 - 6.99301e6i) q^{34} +3.22736e6 q^{35} -6.32122e6 q^{37} +(-1.15959e7 + 2.00846e7i) q^{38} +(3.31541e6 + 5.74246e6i) q^{40} +(2.68019e6 + 4.64223e6i) q^{41} +(-1.12275e7 + 1.94466e7i) q^{43} -1.04384e7 q^{44} -2.86920e6 q^{46} +(-2.23644e7 + 3.87363e7i) q^{47} +(9.74159e6 + 1.68729e7i) q^{49} +(-1.86511e7 - 3.23047e7i) q^{50} +(1.92903e6 - 3.34118e6i) q^{52} +4.00972e7 q^{53} +5.04642e7 q^{55} +(2.14398e7 - 3.71348e7i) q^{56} +(-5.62853e7 - 9.74890e7i) q^{58} +(-4.79118e7 - 8.29857e7i) q^{59} +(-1.01113e7 + 1.75132e7i) q^{61} +2.53663e8 q^{62} +7.71659e7 q^{64} +(-9.32588e6 + 1.61529e7i) q^{65} +(-9.12489e7 - 1.58048e8i) q^{67} +(-2.29975e7 - 3.98328e7i) q^{68} +(4.13974e7 - 7.17024e7i) q^{70} -1.38543e8 q^{71} -2.17970e8 q^{73} +(-8.10823e7 + 1.40439e8i) q^{74} +(6.60510e7 + 1.14404e8i) q^{76} +(-1.63169e8 - 2.82617e8i) q^{77} +(-1.97294e8 + 3.41722e8i) q^{79} +2.22962e8 q^{80} +1.37515e8 q^{82} +(-2.36638e8 + 4.09870e8i) q^{83} +(1.11181e8 + 1.92571e8i) q^{85} +(2.88030e8 + 4.98883e8i) q^{86} +(3.35240e8 - 5.80653e8i) q^{88} -2.60507e8 q^{89} +1.20616e8 q^{91} +(-8.17161e6 + 1.41537e7i) q^{92} +(5.73736e8 + 9.93741e8i) q^{94} +(-3.19323e8 - 5.53083e8i) q^{95} +(-2.87421e8 + 4.97828e8i) q^{97} +4.99822e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 15 q^{2} - 1793 q^{4} - 453 q^{5} - 343 q^{7} + 14478 q^{8}+O(q^{10}) \) 16 * q - 15 * q^2 - 1793 * q^4 - 453 * q^5 - 343 * q^7 + 14478 * q^8	\( 16 q - 15 q^{2} - 1793 q^{4} - 453 q^{5} - 343 q^{7} + 14478 q^{8} + 1020 q^{10} - 99150 q^{11} + 32435 q^{13} - 394824 q^{14} - 328193 q^{16} + 831078 q^{17} - 170554 q^{19} - 1855164 q^{20} + 529359 q^{22} - 1064559 q^{23} - 2293229 q^{25} - 2436312 q^{26} + 1225724 q^{28} + 1309053 q^{29} - 2359819 q^{31} - 5760063 q^{32} + 981801 q^{34} + 31066554 q^{35} + 16391516 q^{37} - 39490203 q^{38} - 16760496 q^{40} - 54747318 q^{41} + 15249608 q^{43} + 332509926 q^{44} + 2390520 q^{46} - 156295545 q^{47} + 15239583 q^{49} - 315590163 q^{50} - 19773358 q^{52} + 525516228 q^{53} - 7579770 q^{55} - 470339790 q^{56} + 55408560 q^{58} - 307774074 q^{59} + 69192125 q^{61} + 914436924 q^{62} - 403588478 q^{64} - 482470359 q^{65} + 14328044 q^{67} - 915409575 q^{68} - 229271934 q^{70} + 1239601392 q^{71} + 598613198 q^{73} - 1022736000 q^{74} + 119954093 q^{76} - 717995541 q^{77} + 30257531 q^{79} + 2927826528 q^{80} - 202376022 q^{82} - 1176168291 q^{83} + 4818366 q^{85} - 1426944009 q^{86} + 911312427 q^{88} + 3317041296 q^{89} - 739230122 q^{91} + 76813998 q^{92} - 1954316784 q^{94} + 391400652 q^{95} - 267311278 q^{97} - 4827300318 q^{98}+O(q^{100}) \) 16 * q - 15 * q^2 - 1793 * q^4 - 453 * q^5 - 343 * q^7 + 14478 * q^8 + 1020 * q^10 - 99150 * q^11 + 32435 * q^13 - 394824 * q^14 - 328193 * q^16 + 831078 * q^17 - 170554 * q^19 - 1855164 * q^20 + 529359 * q^22 - 1064559 * q^23 - 2293229 * q^25 - 2436312 * q^26 + 1225724 * q^28 + 1309053 * q^29 - 2359819 * q^31 - 5760063 * q^32 + 981801 * q^34 + 31066554 * q^35 + 16391516 * q^37 - 39490203 * q^38 - 16760496 * q^40 - 54747318 * q^41 + 15249608 * q^43 + 332509926 * q^44 + 2390520 * q^46 - 156295545 * q^47 + 15239583 * q^49 - 315590163 * q^50 - 19773358 * q^52 + 525516228 * q^53 - 7579770 * q^55 - 470339790 * q^56 + 55408560 * q^58 - 307774074 * q^59 + 69192125 * q^61 + 914436924 * q^62 - 403588478 * q^64 - 482470359 * q^65 + 14328044 * q^67 - 915409575 * q^68 - 229271934 * q^70 + 1239601392 * q^71 + 598613198 * q^73 - 1022736000 * q^74 + 119954093 * q^76 - 717995541 * q^77 + 30257531 * q^79 + 2927826528 * q^80 - 202376022 * q^82 - 1176168291 * q^83 + 4818366 * q^85 - 1426944009 * q^86 + 911312427 * q^88 + 3317041296 * q^89 - 739230122 * q^91 + 76813998 * q^92 - 1954316784 * q^94 + 391400652 * q^95 - 267311278 * q^97 - 4827300318 * q^98

Introduction

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