LMFDB - Embedded newform 27.10.c.a.19.5

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			19.5
Root			$0.500000 + 0.103648i$ of defining polynomial
Character	$\chi$	$=$	27.19
Dual form			27.10.c.a.10.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.839762 + 1.45451i) q^{2} +(254.590 + 440.962i) q^{4} +(-769.303 - 1332.47i) q^{5} +(-2828.47 + 4899.05i) q^{7} -1715.10 q^{8} +O(q^{10})$	\(q+(-0.839762 + 1.45451i) q^{2} +(254.590 + 440.962i) q^{4} +(-769.303 - 1332.47i) q^{5} +(-2828.47 + 4899.05i) q^{7} -1715.10 q^{8} +2584.13 q^{10} +(9908.00 - 17161.2i) q^{11} +(-49897.3 - 86424.6i) q^{13} +(-4750.48 - 8228.07i) q^{14} +(-128910. + 223278. i) q^{16} -503911. q^{17} -670691. q^{19} +(391713. - 678467. i) q^{20} +(16640.7 + 28822.6i) q^{22} +(-965127. - 1.67165e6i) q^{23} +(-207091. + 358693. i) q^{25} +167607. q^{26} -2.88039e6 q^{28} +(-2.16318e6 + 3.74674e6i) q^{29} +(-513125. - 888759. i) q^{31} +(-655571. - 1.13548e6i) q^{32} +(423165. - 732944. i) q^{34} +8.70380e6 q^{35} +1.81292e7 q^{37} +(563221. - 975527. i) q^{38} +(1.31943e6 + 2.28532e6i) q^{40} +(4.65192e6 + 8.05737e6i) q^{41} +(785991. - 1.36138e6i) q^{43} +1.00899e7 q^{44} +3.24191e6 q^{46} +(-1.91679e7 + 3.31997e7i) q^{47} +(4.17634e6 + 7.23363e6i) q^{49} +(-347815. - 602433. i) q^{50} +(2.54066e7 - 4.40056e7i) q^{52} +4.39042e7 q^{53} -3.04890e7 q^{55} +(4.85109e6 - 8.40234e6i) q^{56} +(-3.63312e6 - 6.29274e6i) q^{58} +(-8.09014e7 - 1.40125e8i) q^{59} +(-7.27905e7 + 1.26077e8i) q^{61} +1.72361e6 q^{62} -1.29801e8 q^{64} +(-7.67722e7 + 1.32973e8i) q^{65} +(4.07711e6 + 7.06176e6i) q^{67} +(-1.28290e8 - 2.22206e8i) q^{68} +(-7.30912e6 + 1.26598e7i) q^{70} +1.10960e8 q^{71} +1.42423e8 q^{73} +(-1.52242e7 + 2.63691e7i) q^{74} +(-1.70751e8 - 2.95749e8i) q^{76} +(5.60489e7 + 9.70796e7i) q^{77} +(1.00491e8 - 1.74056e8i) q^{79} +3.96682e8 q^{80} -1.56260e7 q^{82} +(-2.55985e8 + 4.43379e8i) q^{83} +(3.87660e8 + 6.71447e8i) q^{85} +(1.32009e6 + 2.28647e6i) q^{86} +(-1.69932e7 + 2.94330e7i) q^{88} -2.71324e8 q^{89} +5.64531e8 q^{91} +(4.91423e8 - 8.51169e8i) q^{92} +(-3.21929e7 - 5.57597e7i) q^{94} +(5.15965e8 + 8.93677e8i) q^{95} +(2.99491e8 - 5.18734e8i) q^{97} -1.40285e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.839762	+	1.45451i	−0.0371126	+	0.0642809i	−0.883985	−	0.467515i	$-0.845149\pi$
$2$	−0.839762	+	1.45451i	−0.0371126	+	0.0642809i	0.846872	+	0.531796i	$0.178483\pi$
$3$		0			0
$3$		0			0
$4$	254.590	+	440.962i	0.497245	+	0.861254i
$5$	−769.303	−	1332.47i	−0.550468	−	0.953439i	−0.998241	−	0.0592915i	$-0.981116\pi$
$5$	−769.303	−	1332.47i	−0.550468	−	0.953439i	0.447772	−	0.894148i	$-0.352217\pi$
$6$		0			0
$7$	−2828.47	+	4899.05i	−0.445256	+	0.771207i	−0.998070	−	0.0620982i	$-0.980221\pi$
$7$	−2828.47	+	4899.05i	−0.445256	+	0.771207i	0.552814	+	0.833305i	$0.313554\pi$
$8$	−1715.10			−0.148041
$9$		0			0
$10$	2584.13			0.0817172
$11$	9908.00	−	17161.2i	0.204042	−	0.353410i	−0.745785	−	0.666186i	$-0.767926\pi$
$11$	9908.00	−	17161.2i	0.204042	−	0.353410i	0.949827	+	0.312776i	$0.101259\pi$
$12$		0			0
$13$	−49897.3	−	86424.6i	−0.484542	−	0.839252i	0.515300	−	0.857010i	$-0.327680\pi$
$13$	−49897.3	−	86424.6i	−0.484542	−	0.839252i	−0.999842	+	0.0177581i	$0.994347\pi$
$14$	−4750.48	−	8228.07i	−0.0330492	−	0.0572430i
$15$		0			0
$16$	−128910.	+	223278.i	−0.491751	+	0.851738i
$17$	−503911.			−1.46330			−0.731650	−	0.681680i	$-0.761250\pi$
$17$	−503911.			−1.46330			−0.731650	+	0.681680i	$0.761250\pi$
$18$		0			0
$19$	−670691.			−1.18068			−0.590339	−	0.807156i	$-0.701006\pi$
$19$	−670691.			−1.18068			−0.590339	+	0.807156i	$0.701006\pi$
$20$	391713.	−	678467.i	0.547436	−	0.948186i
$21$		0			0
$22$	16640.7	+	28822.6i	0.0151450	+	0.0262320i
$23$	−965127.	−	1.67165e6i	−0.719133	−	1.24557i	−0.961344	−	0.275351i	$-0.911206\pi$
$23$	−965127.	−	1.67165e6i	−0.719133	−	1.24557i	0.242211	−	0.970224i	$-0.422127\pi$
$24$		0			0
$25$	−207091.	+	358693.i	−0.106031	+	0.183651i
$26$	167607.			0.0719305
$27$		0			0
$28$	−2.88039e6			−0.885607
$29$	−2.16318e6	+	3.74674e6i	−0.567939	+	0.983700i	0.428830	+	0.903385i	$0.358926\pi$
$29$	−2.16318e6	+	3.74674e6i	−0.567939	+	0.983700i	−0.996770	+	0.0803147i	$0.974407\pi$
$30$		0			0
$31$	−513125.	−	888759.i	−0.0997920	−	0.172845i	0.811806	−	0.583927i	$-0.198484\pi$
$31$	−513125.	−	888759.i	−0.0997920	−	0.172845i	−0.911598	+	0.411082i	$0.865151\pi$
$32$	−655571.	−	1.13548e6i	−0.110521	−	0.191428i
$33$		0			0
$34$	423165.	−	732944.i	0.0543069	−	0.0940623i
$35$	8.70380e6			0.980398
$36$		0			0
$37$	1.81292e7			1.59027			0.795133	−	0.606435i	$-0.207401\pi$
$37$	1.81292e7			1.59027			0.795133	+	0.606435i	$0.207401\pi$
$38$	563221.	−	975527.i	0.0438180	−	0.0758950i
$39$		0			0
$40$	1.31943e6	+	2.28532e6i	0.0814921	+	0.141148i
$41$	4.65192e6	+	8.05737e6i	0.257102	+	0.445313i	0.965464	−	0.260535i	$-0.0838991\pi$
$41$	4.65192e6	+	8.05737e6i	0.257102	+	0.445313i	−0.708362	+	0.705849i	$0.750566\pi$
$42$		0			0
$43$	785991.	−	1.36138e6i	0.0350598	−	0.0607254i	−0.847963	−	0.530055i	$-0.822171\pi$
$43$	785991.	−	1.36138e6i	0.0350598	−	0.0607254i	0.883023	+	0.469330i	$0.155504\pi$
$44$	1.00899e7			0.405835
$45$		0			0
$46$	3.24191e6			0.106756
$47$	−1.91679e7	+	3.31997e7i	−0.572972	+	0.992416i	0.423287	+	0.905996i	$0.360876\pi$
$47$	−1.91679e7	+	3.31997e7i	−0.572972	+	0.992416i	−0.996259	+	0.0864205i	$0.972457\pi$
$48$		0			0
$49$	4.17634e6	+	7.23363e6i	0.103494	+	0.179256i
$50$	−347815.	−	602433.i	−0.00787015	−	0.0136315i
$51$		0			0
$52$	2.54066e7	−	4.40056e7i	0.481873	−	0.834628i
$53$	4.39042e7			0.764301			0.382151	−	0.924100i	$-0.375184\pi$
$53$	4.39042e7			0.764301			0.382151	+	0.924100i	$0.375184\pi$
$54$		0			0
$55$	−3.04890e7			−0.449274
$56$	4.85109e6	−	8.40234e6i	0.0659164	−	0.114171i
$57$		0			0
$58$	−3.63312e6	−	6.29274e6i	−0.0421554	−	0.0730153i
$59$	−8.09014e7	−	1.40125e8i	−0.869204	−	1.50551i	−0.862811	−	0.505526i	$-0.831298\pi$
$59$	−8.09014e7	−	1.40125e8i	−0.869204	−	1.50551i	−0.00639284	−	0.999980i	$-0.502035\pi$
$60$		0			0
$61$	−7.27905e7	+	1.26077e8i	−0.673117	+	1.16587i	0.303899	+	0.952704i	$0.401712\pi$
$61$	−7.27905e7	+	1.26077e8i	−0.673117	+	1.16587i	−0.977015	+	0.213168i	$0.931622\pi$
$62$	1.72361e6			0.0148142
$63$		0			0
$64$	−1.29801e8			−0.967095
$65$	−7.67722e7	+	1.32973e8i	−0.533450	+	0.923963i
$66$		0			0
$67$	4.07711e6	+	7.06176e6i	0.0247181	+	0.0428131i	0.878120	−	0.478441i	$-0.158798\pi$
$67$	4.07711e6	+	7.06176e6i	0.0247181	+	0.0428131i	−0.853402	+	0.521254i	$0.825465\pi$
$68$	−1.28290e8	−	2.22206e8i	−0.727619	−	1.26027i
$69$		0			0
$70$	−7.30912e6	+	1.26598e7i	−0.0363851	+	0.0630209i
$71$	1.10960e8			0.518208			0.259104	−	0.965849i	$-0.416573\pi$
$71$	1.10960e8			0.518208			0.259104	+	0.965849i	$0.416573\pi$
$72$		0			0
$73$	1.42423e8			0.586986			0.293493	−	0.955961i	$-0.405182\pi$
$73$	1.42423e8			0.586986			0.293493	+	0.955961i	$0.405182\pi$
$74$	−1.52242e7	+	2.63691e7i	−0.0590189	+	0.102224i
$75$		0			0
$76$	−1.70751e8	−	2.95749e8i	−0.587086	−	1.01686i
$77$	5.60489e7	+	9.70796e7i	0.181702	+	0.314717i
$78$		0			0
$79$	1.00491e8	−	1.74056e8i	0.290273	−	0.502767i	−0.683602	−	0.729855i	$-0.739587\pi$
$79$	1.00491e8	−	1.74056e8i	0.290273	−	0.502767i	0.973874	+	0.227089i	$0.0729207\pi$
$80$	3.96682e8			1.08277
$81$		0			0
$82$	−1.56260e7			−0.0381669
$83$	−2.55985e8	+	4.43379e8i	−0.592056	+	1.02547i	0.401899	+	0.915684i	$0.368350\pi$
$83$	−2.55985e8	+	4.43379e8i	−0.592056	+	1.02547i	−0.993955	+	0.109788i	$0.964983\pi$
$84$		0			0
$85$	3.87660e8	+	6.71447e8i	0.805501	+	1.39517i
$86$	1.32009e6	+	2.28647e6i	0.00260232	+	0.00450735i
$87$		0			0
$88$	−1.69932e7	+	2.94330e7i	−0.0302066	+	0.0523194i
$89$	−2.71324e8			−0.458387			−0.229194	−	0.973381i	$-0.573609\pi$
$89$	−2.71324e8			−0.458387			−0.229194	+	0.973381i	$0.573609\pi$
$90$		0			0
$91$	5.64531e8			0.862982
$92$	4.91423e8	−	8.51169e8i	0.715171	−	1.23871i
$93$		0			0
$94$	−3.21929e7	−	5.57597e7i	−0.0425289	−	0.0736623i
$95$	5.15965e8	+	8.93677e8i	0.649926	+	1.12570i
$96$		0			0
$97$	2.99491e8	−	5.18734e8i	0.343488	−	0.594938i	−0.641590	−	0.767048i	$-0.721725\pi$
$97$	2.99491e8	−	5.18734e8i	0.343488	−	0.594938i	0.985078	+	0.172110i	$0.0550583\pi$
$98$	−1.40285e7			−0.0153637
$99$		0			0
$100$	−2.10893e8			−0.210893
$101$	−3.67526e8	+	6.36574e8i	−0.351433	+	0.608699i	−0.986501	−	0.163757i	$-0.947639\pi$
$101$	−3.67526e8	+	6.36574e8i	−0.351433	+	0.608699i	0.635068	+	0.772456i	$0.280972\pi$
$102$		0			0
$103$	−2.05884e8	−	3.56602e8i	−0.180242	−	0.312188i	0.761721	−	0.647905i	$-0.224355\pi$
$103$	−2.05884e8	−	3.56602e8i	−0.180242	−	0.312188i	−0.941963	+	0.335717i	$0.891021\pi$
$104$	8.55785e7	+	1.48226e8i	0.0717323	+	0.124244i
$105$		0			0
$106$	−3.68691e7	+	6.38591e7i	−0.0283652	+	0.0491300i
$107$	2.79607e8			0.206215			0.103108	−	0.994670i	$-0.467121\pi$
$107$	2.79607e8			0.206215			0.103108	+	0.994670i	$0.467121\pi$
$108$		0			0
$109$	−4.87814e8			−0.331006			−0.165503	−	0.986209i	$-0.552925\pi$
$109$	−4.87814e8			−0.331006			−0.165503	+	0.986209i	$0.552925\pi$
$110$	2.56035e7	−	4.43466e7i	0.0166737	−	0.0288797i
$111$		0			0
$112$	−7.29233e8	−	1.26307e9i	−0.437911	−	0.758483i
$113$	−1.14026e9	−	1.97498e9i	−0.657884	−	1.13949i	−0.981162	−	0.193185i	$-0.938118\pi$
$113$	−1.14026e9	−	1.97498e9i	−0.657884	−	1.13949i	0.323278	−	0.946304i	$-0.395215\pi$
$114$		0			0
$115$	−1.48495e9	+	2.57201e9i	−0.791720	+	1.37130i
$116$	−2.20289e9			−1.12962
$117$		0			0
$118$	2.71752e8			0.129034
$119$	1.42530e9	−	2.46868e9i	0.651544	−	1.12851i
$120$		0			0
$121$	9.82637e8	+	1.70198e9i	0.416734	+	0.721804i
$122$	−1.22253e8	−	2.11749e8i	−0.0499622	−	0.0865371i
$123$		0			0
$124$	2.61273e8	−	4.52538e8i	0.0992422	−	0.171893i
$125$	−2.36783e9			−0.867470
$126$		0			0
$127$	−3.67474e9			−1.25346			−0.626730	−	0.779237i	$-0.715607\pi$
$127$	−3.67474e9			−1.25346			−0.626730	+	0.779237i	$0.715607\pi$
$128$	4.44655e8	−	7.70164e8i	0.146412	−	0.253594i
$129$		0			0
$130$	−1.28941e8	−	2.23332e8i	−0.0395954	−	0.0685813i
$131$	2.53774e9	+	4.39550e9i	0.752882	+	1.30403i	0.946420	+	0.322937i	$0.104670\pi$
$131$	2.53774e9	+	4.39550e9i	0.752882	+	1.30403i	−0.193539	+	0.981093i	$0.561997\pi$
$132$		0			0
$133$	1.89703e9	−	3.28575e9i	0.525704	−	0.910547i
$134$	−1.36952e7			−0.00366942
$135$		0			0
$136$	8.64255e8			0.216629
$137$	1.00844e9	−	1.74667e9i	0.244573	−	0.423613i	−0.717439	−	0.696622i	$-0.754686\pi$
$137$	1.00844e9	−	1.74667e9i	0.244573	−	0.423613i	0.962011	+	0.273009i	$0.0880189\pi$
$138$		0			0
$139$	−1.32407e9	−	2.29335e9i	−0.300845	−	0.521079i	0.675483	−	0.737376i	$-0.263935\pi$
$139$	−1.32407e9	−	2.29335e9i	−0.300845	−	0.521079i	−0.976328	+	0.216297i	$0.930602\pi$
$140$	2.21590e9	+	3.83804e9i	0.487498	+	0.844372i
$141$		0			0
$142$	−9.31800e7	+	1.61393e8i	−0.0192320	+	0.0333109i
$143$	−1.97753e9			−0.395467
$144$		0			0
$145$	6.65657e9			1.25053
$146$	−1.19602e8	+	2.07156e8i	−0.0217846	+	0.0377320i
$147$		0			0
$148$	4.61550e9	+	7.99427e9i	0.790753	+	1.36962i
$149$	5.04632e8	+	8.74049e8i	0.0838758	+	0.145277i	0.904912	−	0.425599i	$-0.139937\pi$
$149$	5.04632e8	+	8.74049e8i	0.0838758	+	0.145277i	−0.821036	+	0.570877i	$0.806603\pi$
$150$		0			0
$151$	2.92210e8	−	5.06122e8i	0.0457402	−	0.0792244i	−0.842249	−	0.539089i	$-0.818769\pi$
$151$	2.92210e8	−	5.06122e8i	0.0457402	−	0.0792244i	0.887989	+	0.459864i	$0.152102\pi$
$152$	1.15030e9			0.174789
$153$		0			0
$154$	−1.88271e8			−0.0269737
$155$	−7.89498e8	+	1.36745e9i	−0.109865	+	0.190291i
$156$		0			0
$157$	−3.74231e9	−	6.48188e9i	−0.491577	−	0.851437i	0.508376	−	0.861135i	$-0.330246\pi$
$157$	−3.74231e9	−	6.48188e9i	−0.491577	−	0.851437i	−0.999953	+	0.00969862i	$0.996913\pi$
$158$	1.68777e8	+	2.92331e8i	0.0215455	+	0.0373180i
$159$		0			0
$160$	−1.00867e9	+	1.74706e9i	−0.121677	+	0.210750i
$161$	1.09193e10			1.28079
$162$		0			0
$163$	4.71277e9			0.522916			0.261458	−	0.965215i	$-0.415797\pi$
$163$	4.71277e9			0.522916			0.261458	+	0.965215i	$0.415797\pi$
$164$	−2.36866e9	+	4.10264e9i	−0.255685	+	0.442860i
$165$		0			0
$166$	−4.29933e8	−	7.44666e8i	−0.0439455	−	0.0761158i
$167$	−6.08835e9	−	1.05453e10i	−0.605725	−	1.04915i	−0.991936	−	0.126736i	$-0.959550\pi$
$167$	−6.08835e9	−	1.05453e10i	−0.605725	−	1.04915i	0.386212	−	0.922410i	$-0.373783\pi$
$168$		0			0
$169$	3.22776e8	−	5.59065e8i	0.0304377	−	0.0527196i
$170$	−1.30217e9			−0.119577
$171$		0			0
$172$	8.00421e8			0.0697333
$173$	−2.55251e9	+	4.42107e9i	−0.216650	+	0.375250i	−0.953782	−	0.300500i	$-0.902847\pi$
$173$	−2.55251e9	+	4.42107e9i	−0.216650	+	0.375250i	0.737131	+	0.675749i	$0.236180\pi$
$174$		0			0
$175$	−1.17150e9	−	2.02910e9i	−0.0944217	−	0.163543i
$176$	2.55447e9	+	4.42448e9i	0.200675	+	0.347580i
$177$		0			0
$178$	2.27847e8	−	3.94643e8i	0.0170119	−	0.0294655i
$179$	1.79471e9			0.130664			0.0653320	−	0.997864i	$-0.479189\pi$
$179$	1.79471e9			0.130664			0.0653320	+	0.997864i	$0.479189\pi$
$180$		0			0
$181$	−2.66921e10			−1.84854			−0.924271	−	0.381738i	$-0.875326\pi$
$181$	−2.66921e10			−1.84854			−0.924271	+	0.381738i	$0.875326\pi$
$182$	−4.74072e8	+	8.21117e8i	−0.0320275	+	0.0554733i
$183$		0			0
$184$	1.65528e9	+	2.86704e9i	0.106461	+	0.184397i
$185$	−1.39468e10	−	2.41566e10i	−0.875391	−	1.51622i
$186$		0			0
$187$	−4.99275e9	+	8.64769e9i	−0.298574	+	0.517146i
$188$	−1.95197e10			−1.13963
$189$		0			0
$190$	−1.73315e9			−0.0964817
$191$	−3.71413e8	+	6.43307e8i	−0.0201933	+	0.0349758i	−0.875945	−	0.482410i	$-0.839761\pi$
$191$	−3.71413e8	+	6.43307e8i	−0.0201933	+	0.0349758i	0.855752	+	0.517386i	$0.173095\pi$
$192$		0			0
$193$	1.01745e9	+	1.76227e9i	0.0527841	+	0.0914248i	0.891210	−	0.453591i	$-0.149857\pi$
$193$	1.01745e9	+	1.76227e9i	0.0527841	+	0.0914248i	−0.838426	+	0.545015i	$0.816524\pi$
$194$	5.03002e8	+	8.71226e8i	0.0254954	+	0.0441594i
$195$		0			0
$196$	−2.12650e9	+	3.68321e9i	−0.102923	+	0.178268i
$197$	3.40311e10			1.60982			0.804910	−	0.593396i	$-0.202213\pi$
$197$	3.40311e10			1.60982			0.804910	+	0.593396i	$0.202213\pi$
$198$		0			0
$199$	1.03084e9			0.0465963			0.0232982	−	0.999729i	$-0.492583\pi$
$199$	1.03084e9			0.0465963			0.0232982	+	0.999729i	$0.492583\pi$
$200$	3.55181e8	−	6.15192e8i	0.0156969	−	0.0271879i
$201$		0			0
$202$	−6.17269e8	−	1.06914e9i	−0.0260851	−	0.0451808i
$203$	−1.22370e10	−	2.11951e10i	−0.505757	−	0.875997i
$204$		0			0
$205$	7.15748e9	−	1.23971e10i	0.283053	−	0.490262i
$206$	6.91574e8			0.0267569
$207$		0			0
$208$	2.57289e10			0.953097
$209$	−6.64521e9	+	1.15098e10i	−0.240907	+	0.417264i
$210$		0			0
$211$	−7.42977e8	−	1.28687e9i	−0.0258050	−	0.0446956i	0.852835	−	0.522181i	$-0.174882\pi$
$211$	−7.42977e8	−	1.28687e9i	−0.0258050	−	0.0446956i	−0.878640	+	0.477486i	$0.841548\pi$
$212$	1.11776e10	+	1.93601e10i	0.380045	+	0.658258i
$213$		0			0
$214$	−2.34803e8	+	4.06691e8i	−0.00765319	+	0.0132557i
$215$	−2.41866e9			−0.0771973
$216$		0			0
$217$	5.80543e9			0.177732
$218$	4.09648e8	−	7.09531e8i	0.0122845	−	0.0212773i
$219$		0			0
$220$	−7.76218e9	−	1.34445e10i	−0.223399	−	0.386939i
$221$	2.51438e10	+	4.35503e10i	0.709031	+	1.22808i
$222$		0			0
$223$	9.28200e8	−	1.60769e9i	0.0251345	−	0.0435342i	−0.853185	−	0.521609i	$-0.825332\pi$
$223$	9.28200e8	−	1.60769e9i	0.0251345	−	0.0435342i	0.878319	+	0.478075i	$0.158665\pi$
$224$	7.41705e9			0.196841
$225$		0			0
$226$	3.83018e9			0.0976631
$227$	−3.48274e10	+	6.03228e10i	−0.870571	+	1.50787i	−0.00916491	+	0.999958i	$0.502917\pi$
$227$	−3.48274e10	+	6.03228e10i	−0.870571	+	1.50787i	−0.861407	+	0.507916i	$0.830416\pi$
$228$		0			0
$229$	1.01824e10	+	1.76365e10i	0.244676	+	0.423791i	0.962040	−	0.272907i	$-0.0879850\pi$
$229$	1.01824e10	+	1.76365e10i	0.244676	+	0.423791i	−0.717364	+	0.696698i	$0.754652\pi$
$230$	−2.49401e9	−	4.31975e9i	−0.0587655	−	0.101785i
$231$		0			0
$232$	3.71006e9	−	6.42602e9i	0.0840786	−	0.145628i
$233$	4.32644e10			0.961676			0.480838	−	0.876809i	$-0.340332\pi$
$233$	4.32644e10			0.961676			0.480838	+	0.876809i	$0.340332\pi$
$234$		0			0
$235$	5.89835e10			1.26161
$236$	4.11933e10	−	7.13489e10i	0.864415	−	1.49721i
$237$		0			0
$238$	2.39382e9	+	4.14622e9i	0.0483610	+	0.0837636i
$239$	−1.88376e10	−	3.26277e10i	−0.373452	−	0.646839i	0.616642	−	0.787244i	$-0.288493\pi$
$239$	−1.88376e10	−	3.26277e10i	−0.373452	−	0.646839i	−0.990094	+	0.140405i	$0.955159\pi$
$240$		0			0
$241$	1.67354e10	−	2.89865e10i	0.319565	−	0.553503i	−0.660832	−	0.750533i	$-0.729797\pi$
$241$	1.67354e10	−	2.89865e10i	0.319565	−	0.553503i	0.980397	+	0.197031i	$0.0631299\pi$
$242$	−3.30073e9			−0.0618643
$243$		0			0
$244$	−7.41268e10			−1.33882
$245$	6.42574e9	−	1.11297e10i	0.113940	−	0.197350i
$246$		0			0
$247$	3.34657e10	+	5.79642e10i	0.572088	+	0.990886i
$248$	8.80059e8	+	1.52431e9i	0.0147734	+	0.0255882i
$249$		0			0
$250$	1.98841e9	−	3.44403e9i	0.0321941	−	0.0557618i
$251$	−7.16769e10			−1.13985			−0.569925	−	0.821697i	$-0.693028\pi$
$251$	−7.16769e10			−1.13985			−0.569925	+	0.821697i	$0.693028\pi$
$252$		0			0
$253$	−3.82499e10			−0.586932
$254$	3.08591e9	−	5.34495e9i	0.0465191	−	0.0805735i
$255$		0			0
$256$	−3.24823e10	−	5.62611e10i	−0.472680	−	0.818706i
$257$	2.12935e10	+	3.68814e10i	0.304472	+	0.527361i	0.977144	−	0.212580i	$-0.0681866\pi$
$257$	2.12935e10	+	3.68814e10i	0.304472	+	0.527361i	−0.672671	+	0.739941i	$0.734853\pi$
$258$		0			0
$259$	−5.12778e10	+	8.88157e10i	−0.708076	+	1.22642i
$260$	−7.81816e10			−1.06102
$261$		0			0
$262$	−8.52440e9			−0.111766
$263$	−8.77911e9	+	1.52059e10i	−0.113149	+	0.195979i	−0.917038	−	0.398799i	$-0.869427\pi$
$263$	−8.77911e9	+	1.52059e10i	−0.113149	+	0.195979i	0.803889	+	0.594779i	$0.202760\pi$
$264$		0			0
$265$	−3.37756e10	−	5.85011e10i	−0.420724	−	0.728715i
$266$	3.18611e9	+	5.51850e9i	0.0390205	+	0.0675855i
$267$		0			0
$268$	−2.07598e9	+	3.59570e9i	−0.0245820	+	0.0425772i
$269$	−6.58769e10			−0.767093			−0.383546	−	0.923522i	$-0.625297\pi$
$269$	−6.58769e10			−0.767093			−0.383546	+	0.923522i	$0.625297\pi$
$270$		0			0
$271$	−2.84327e10			−0.320226			−0.160113	−	0.987099i	$-0.551186\pi$
$271$	−2.84327e10			−0.320226			−0.160113	+	0.987099i	$0.551186\pi$
$272$	6.49589e10	−	1.12512e11i	0.719580	−	1.24635i
$273$		0			0
$274$	1.69370e9	+	2.93358e9i	0.0181535	+	0.0314427i
$275$	4.10372e9	+	7.10785e9i	0.0432694	+	0.0749448i
$276$		0			0
$277$	3.36196e10	−	5.82308e10i	0.343110	−	0.594284i	−0.641899	−	0.766789i	$-0.721853\pi$
$277$	3.36196e10	−	5.82308e10i	0.343110	−	0.594284i	0.985009	+	0.172506i	$0.0551863\pi$
$278$	4.44760e9			0.0446605
$279$		0			0
$280$	−1.49278e10			−0.145140
$281$	6.55739e10	−	1.13577e11i	0.627412	−	1.08671i	−0.360657	−	0.932699i	$-0.617448\pi$
$281$	6.55739e10	−	1.13577e11i	0.627412	−	1.08671i	0.988069	−	0.154011i	$-0.0492192\pi$
$282$		0			0
$283$	−5.78539e9	−	1.00206e10i	−0.0536159	−	0.0928655i	0.837972	−	0.545714i	$-0.183741\pi$
$283$	−5.78539e9	−	1.00206e10i	−0.0536159	−	0.0928655i	−0.891588	+	0.452848i	$0.850408\pi$
$284$	2.82493e10	+	4.89292e10i	0.257676	+	0.446309i
$285$		0			0
$286$	1.66065e9	−	2.87634e9i	0.0146768	−	0.0254210i
$287$	−5.26313e10			−0.457905
$288$		0			0
$289$	1.35338e11			1.14125
$290$	−5.58993e9	+	9.68205e9i	−0.0464104	+	0.0803852i
$291$		0			0
$292$	3.62595e10	+	6.28032e10i	0.291876	+	0.505544i
$293$	7.90302e9	+	1.36884e10i	0.0626453	+	0.108505i	0.895647	−	0.444765i	$-0.146713\pi$
$293$	7.90302e9	+	1.36884e10i	0.0626453	+	0.108505i	−0.833002	+	0.553270i	$0.813380\pi$
$294$		0			0
$295$	−1.24475e11	+	2.15598e11i	−0.956939	+	1.65747i
$296$	−3.10932e10			−0.235425
$297$		0			0
$298$	−1.69508e9			−0.0124514
$299$	−9.63144e10	+	1.66821e11i	−0.696901	+	1.20707i
$300$		0			0
$301$	4.44630e9	+	7.70122e9i	0.0312212	+	0.0540767i
$302$	4.90773e8	+	8.50044e8i	0.00339508	+	0.00588045i
$303$		0			0
$304$	8.64585e10	−	1.49751e11i	0.580600	−	1.00563i
$305$	2.23992e11			1.48212
$306$		0			0
$307$	−4.10341e10			−0.263647			−0.131823	−	0.991273i	$-0.542083\pi$
$307$	−4.10341e10			−0.263647			−0.131823	+	0.991273i	$0.542083\pi$
$308$	−2.85389e10	+	4.94309e10i	−0.180701	+	0.312983i
$309$		0			0
$310$	−1.32598e9	−	2.29667e9i	−0.00815473	−	0.0141244i
$311$	−9.92341e9	−	1.71878e10i	−0.0601505	−	0.104184i	0.834382	−	0.551187i	$-0.185825\pi$
$311$	−9.92341e9	−	1.71878e10i	−0.0601505	−	0.104184i	−0.894533	+	0.447003i	$0.852491\pi$
$312$		0			0
$313$	1.51843e11	−	2.62999e11i	0.894219	−	1.54883i	0.0594516	−	0.998231i	$-0.481065\pi$
$313$	1.51843e11	−	2.62999e11i	0.894219	−	1.54883i	0.834768	−	0.550602i	$-0.185602\pi$
$314$	1.25706e10			0.0729748
$315$		0			0
$316$	1.02336e11			0.577347
$317$	−4.00681e10	+	6.94000e10i	−0.222860	+	0.386005i	−0.955675	−	0.294423i	$-0.904873\pi$
$317$	−4.00681e10	+	6.94000e10i	−0.222860	+	0.386005i	0.732815	+	0.680428i	$0.238206\pi$
$318$		0			0
$319$	4.28656e10	+	7.42454e10i	0.231767	+	0.401431i
$320$	9.98565e10	+	1.72957e11i	0.532355	+	0.922067i
$321$		0			0
$322$	−9.16963e9	+	1.58823e10i	−0.0475336	+	0.0823306i
$323$	3.37969e11			1.72769
$324$		0			0
$325$	4.13332e10			0.205506
$326$	−3.95761e9	+	6.85478e9i	−0.0194068	+	0.0336135i
$327$		0			0
$328$	−7.97849e9	−	1.38192e10i	−0.0380617	−	0.0659248i
$329$	−1.08431e11	−	1.87809e11i	−0.510239	−	0.883759i
$330$		0			0
$331$	7.05185e10	−	1.22142e11i	0.322907	−	0.559291i	−0.658180	−	0.752861i	$-0.728673\pi$
$331$	7.05185e10	−	1.22142e11i	0.322907	−	0.559291i	0.981086	+	0.193570i	$0.0620066\pi$
$332$	−2.60684e11			−1.17759
$333$		0			0
$334$	2.04511e10			0.0899201
$335$	6.27306e9	−	1.08653e10i	0.0272131	−	0.0471345i
$336$		0			0
$337$	−1.35877e10	−	2.35345e10i	−0.0573866	−	0.0993966i	0.835905	−	0.548874i	$-0.184943\pi$
$337$	−1.35877e10	−	2.35345e10i	−0.0573866	−	0.0993966i	−0.893292	+	0.449478i	$0.851610\pi$
$338$	5.42110e8	+	9.38963e8i	0.00225924	+	0.00391312i
$339$		0			0
$340$	−1.97388e11	+	3.41887e11i	−0.801063	+	1.38748i
$341$	−2.03362e10			−0.0814469
$342$		0			0
$343$	−2.75528e11			−1.07484
$344$	−1.34805e9	+	2.33489e9i	−0.00519031	+	0.00898987i
$345$		0			0
$346$	−4.28700e9	−	7.42530e9i	−0.0160809	−	0.0278530i
$347$	−1.36212e11	−	2.35926e11i	−0.504351	−	0.873562i	−0.999987	−	0.00503197i	$-0.998398\pi$
$347$	−1.36212e11	−	2.35926e11i	−0.504351	−	0.873562i	0.495636	−	0.868530i	$-0.334935\pi$
$348$		0			0
$349$	−1.41485e11	+	2.45060e11i	−0.510502	+	0.884215i	0.489424	+	0.872046i	$0.337207\pi$
$349$	−1.41485e11	+	2.45060e11i	−0.510502	+	0.884215i	−0.999926	+	0.0121691i	$0.996126\pi$
$350$	3.93513e9			0.0140169
$351$		0			0
$352$	−2.59816e10			−0.0902036
$353$	3.61560e10	−	6.26240e10i	0.123935	−	0.214662i	−0.797381	−	0.603476i	$-0.793782\pi$
$353$	3.61560e10	−	6.26240e10i	0.123935	−	0.214662i	0.921316	+	0.388814i	$0.127115\pi$
$354$		0			0
$355$	−8.53619e10	−	1.47851e11i	−0.285257	−	0.494080i
$356$	−6.90762e10	−	1.19643e11i	−0.227931	−	0.394788i
$357$		0			0
$358$	−1.50713e9	+	2.61043e9i	−0.00484928	+	0.00839920i
$359$	−3.88231e11			−1.23358			−0.616788	−	0.787130i	$-0.711566\pi$
$359$	−3.88231e11			−1.23358			−0.616788	+	0.787130i	$0.711566\pi$
$360$		0			0
$361$	1.27139e11			0.394000
$362$	2.24150e10	−	3.88239e10i	0.0686042	−	0.118826i
$363$		0			0
$364$	1.43724e11	+	2.48937e11i	0.429114	+	0.743247i
$365$	−1.09567e11	−	1.89775e11i	−0.323117	−	0.559655i
$366$		0			0
$367$	7.87077e10	−	1.36326e11i	0.226475	−	0.392266i	−0.730286	−	0.683141i	$-0.760613\pi$
$367$	7.87077e10	−	1.36326e11i	0.226475	−	0.392266i	0.956761	+	0.290876i	$0.0939466\pi$
$368$	4.97657e11			1.41454
$369$		0			0
$370$	4.68480e10			0.129952
$371$	−1.24182e11	+	2.15089e11i	−0.340310	+	0.589434i
$372$		0			0
$373$	−3.60084e11	−	6.23685e11i	−0.963196	−	1.66830i	−0.714386	−	0.699752i	$-0.753294\pi$
$373$	−3.60084e11	−	6.23685e11i	−0.963196	−	1.66830i	−0.248810	−	0.968552i	$-0.580039\pi$
$374$	−8.38544e9	−	1.45240e10i	−0.0221617	−	0.0383852i
$375$		0			0
$376$	3.28747e10	−	5.69406e10i	0.0848235	−	0.146919i
$377$	4.31747e11			1.10076
$378$		0			0
$379$	−7.20072e11			−1.79267			−0.896333	−	0.443381i	$-0.853779\pi$
$379$	−7.20072e11			−1.79267			−0.896333	+	0.443381i	$0.853779\pi$
$380$	−2.62718e11	+	4.55042e11i	−0.646345	+	1.11950i
$381$		0			0
$382$	−6.23798e8	−	1.08045e9i	−0.00149885	−	0.00259609i
$383$	−9.03420e10	−	1.56477e11i	−0.214533	−	0.371583i	0.738595	−	0.674150i	$-0.235490\pi$
$383$	−9.03420e10	−	1.56477e11i	−0.214533	−	0.371583i	−0.953128	+	0.302567i	$0.902156\pi$
$384$		0			0
$385$	8.62372e10	−	1.49367e11i	0.200042	−	0.346483i
$386$	−3.41765e9			−0.00783582
$387$		0			0
$388$	3.04989e11			0.683190
$389$	1.02355e11	−	1.77285e11i	0.226640	−	0.392553i	−0.730170	−	0.683266i	$-0.760559\pi$
$389$	1.02355e11	−	1.77285e11i	0.226640	−	0.392553i	0.956810	+	0.290713i	$0.0938924\pi$
$390$		0			0
$391$	4.86338e11	+	8.42362e11i	1.05231	+	1.82265i
$392$	−7.16282e9	−	1.24064e10i	−0.0153213	−	0.0265373i
$393$		0			0
$394$	−2.85780e10	+	4.94985e10i	−0.0597446	+	0.103481i
$395$	−3.09233e11			−0.639143
$396$		0			0
$397$	3.34553e11			0.675939			0.337970	−	0.941157i	$-0.390260\pi$
$397$	3.34553e11			0.675939			0.337970	+	0.941157i	$0.390260\pi$
$398$	−8.65658e8	+	1.49936e9i	−0.00172931	+	0.00299525i
$399$		0			0
$400$	−5.33921e10	−	9.24779e10i	−0.104281	−	0.180621i
$401$	2.20640e11	+	3.82159e11i	0.426122	+	0.738065i	0.996524	−	0.0833005i	$-0.0265461\pi$
$401$	2.20640e11	+	3.82159e11i	0.426122	+	0.738065i	−0.570403	+	0.821365i	$0.693213\pi$
$402$		0			0
$403$	−5.12071e10	+	8.86933e10i	−0.0967069	+	0.167501i
$404$	−3.74273e11			−0.698993
$405$		0			0
$406$	4.11046e10			0.0750798
$407$	1.79624e11	−	3.11117e11i	0.324481	−	0.562017i
$408$		0			0
$409$	9.64485e10	+	1.67054e11i	0.170428	+	0.295190i	0.938570	−	0.345090i	$-0.112152\pi$
$409$	9.64485e10	+	1.67054e11i	0.170428	+	0.295190i	−0.768142	+	0.640280i	$0.778818\pi$
$410$	1.20212e10	+	2.08213e10i	0.0210097	+	0.0363898i
$411$		0			0
$412$	1.04832e11	−	1.81574e11i	0.179249	−	0.310468i
$413$	9.15308e11			1.54807
$414$		0			0
$415$	7.87720e11			1.30363
$416$	−6.54224e10	+	1.13315e11i	−0.107104	+	0.185510i
$417$		0			0
$418$	−1.11608e10	−	1.93310e10i	−0.0178814	−	0.0309715i
$419$	2.96406e11	+	5.13391e11i	0.469812	+	0.813739i	0.999404	−	0.0345137i	$-0.0109882\pi$
$419$	2.96406e11	+	5.13391e11i	0.469812	+	0.813739i	−0.529592	+	0.848253i	$0.677655\pi$
$420$		0			0
$421$	2.60272e11	−	4.50804e11i	0.403792	−	0.699389i	−0.590388	−	0.807120i	$-0.701025\pi$
$421$	2.60272e11	−	4.50804e11i	0.403792	−	0.699389i	0.994180	+	0.107731i	$0.0343585\pi$
$422$	2.49569e9			0.00383076
$423$		0			0
$424$	−7.52999e10			−0.113148
$425$	1.04356e11	−	1.80749e11i	0.155155	−	0.268736i
$426$		0			0
$427$	−4.11771e11	−	7.13209e11i	−0.599419	−	1.03822i
$428$	7.11850e10	+	1.23296e11i	0.102540	+	0.177604i
$429$		0			0
$430$	2.03110e9	−	3.51797e9i	0.00286499	−	0.00496231i
$431$	−6.97508e11			−0.973647			−0.486824	−	0.873500i	$-0.661845\pi$
$431$	−6.97508e11			−0.973647			−0.486824	+	0.873500i	$0.661845\pi$
$432$		0			0
$433$	−1.30466e11			−0.178361			−0.0891806	−	0.996015i	$-0.528425\pi$
$433$	−1.30466e11			−0.178361			−0.0891806	+	0.996015i	$0.528425\pi$
$434$	−4.87518e9	+	8.44407e9i	−0.00659610	+	0.0114248i
$435$		0			0
$436$	−1.24192e11	−	2.15108e11i	−0.164591	−	0.285080i
$437$	6.47302e11	+	1.12116e12i	0.849064	+	1.47062i
$438$		0			0
$439$	−5.17724e11	+	8.96725e11i	−0.665286	+	1.15231i	0.313922	+	0.949449i	$0.398357\pi$
$439$	−5.17724e11	+	8.96725e11i	−0.665286	+	1.15231i	−0.979208	+	0.202860i	$0.934976\pi$
$440$	5.22915e10			0.0665111
$441$		0			0
$442$	−8.44591e10			−0.105256
$443$	−2.03377e10	+	3.52259e10i	−0.0250891	+	0.0434555i	−0.878297	−	0.478115i	$-0.841320\pi$
$443$	−2.03377e10	+	3.52259e10i	−0.0250891	+	0.0434555i	0.853208	+	0.521570i	$0.174654\pi$
$444$		0			0
$445$	2.08730e11	+	3.61531e11i	0.252328	+	0.437044i
$446$	1.55893e9	+	2.70015e9i	0.00186561	+	0.00323133i
$447$		0			0
$448$	3.67139e11	−	6.35903e11i	0.430605	−	0.745830i
$449$	−1.58095e12			−1.83574			−0.917869	−	0.396884i	$-0.870091\pi$
$449$	−1.58095e12			−1.83574			−0.917869	+	0.396884i	$0.870091\pi$
$450$		0			0
$451$	1.84365e11			0.209838
$452$	5.80595e11	−	1.00562e12i	0.654260	−	1.13321i
$453$		0			0
$454$	−5.84934e10	−	1.01314e11i	−0.0646183	−	0.111922i
$455$	−4.34296e11	−	7.52222e11i	−0.475044	−	0.822801i
$456$		0			0
$457$	−4.50612e11	+	7.80483e11i	−0.483259	+	0.837029i	−0.999815	−	0.0192243i	$-0.993880\pi$
$457$	−4.50612e11	+	7.80483e11i	−0.483259	+	0.837029i	0.516556	+	0.856253i	$0.327214\pi$
$458$	−3.42033e10			−0.0363223
$459$		0			0
$460$	−1.51221e12			−1.57472
$461$	5.57758e11	−	9.66065e11i	0.575164	−	0.996213i	−0.420860	−	0.907126i	$-0.638272\pi$
$461$	5.57758e11	−	9.66065e11i	0.575164	−	0.996213i	0.996024	−	0.0890874i	$-0.0283950\pi$
$462$		0			0
$463$	4.34497e11	+	7.52571e11i	0.439413	+	0.761085i	0.997644	−	0.0686000i	$-0.0218532\pi$
$463$	4.34497e11	+	7.52571e11i	0.439413	+	0.761085i	−0.558231	+	0.829685i	$0.688520\pi$
$464$	−5.57710e11	−	9.65982e11i	−0.558570	−	0.967471i
$465$		0			0
$466$	−3.63318e10	+	6.29285e10i	−0.0356903	+	0.0618174i
$467$	−1.02354e12			−0.995820			−0.497910	−	0.867229i	$-0.665899\pi$
$467$	−1.02354e12			−0.995820			−0.497910	+	0.867229i	$0.665899\pi$
$468$		0			0
$469$	−4.61279e10			−0.0440236
$470$	−4.95321e10	+	8.57922e10i	−0.0468217	+	0.0810975i
$471$		0			0
$472$	1.38754e11	+	2.40328e11i	0.128678	+	0.222877i
$473$	−1.55752e10	−	2.69770e10i	−0.0143073	−	0.0247810i
$474$		0			0
$475$	1.38894e11	−	2.40572e11i	0.125188	−	0.216832i
$476$	1.45146e12			1.29591
$477$		0			0
$478$	6.32765e10			0.0554392
$479$	−3.58035e11	+	6.20135e11i	−0.310753	+	0.538241i	−0.978526	−	0.206125i	$-0.933915\pi$
$479$	−3.58035e11	+	6.20135e11i	−0.310753	+	0.538241i	0.667772	+	0.744366i	$0.267248\pi$
$480$		0			0
$481$	−9.04595e11	−	1.56681e12i	−0.770551	−	1.33463i
$482$	2.81075e10	+	4.86836e10i	0.0237198	+	0.0410838i
$483$		0			0
$484$	−5.00338e11	+	8.66611e11i	−0.414438	+	0.717828i
$485$	−9.21597e11			−0.756316
$486$		0			0
$487$	−1.04858e12			−0.844739			−0.422369	−	0.906424i	$-0.638802\pi$
$487$	−1.04858e12			−0.844739			−0.422369	+	0.906424i	$0.638802\pi$
$488$	1.24843e11	−	2.16234e11i	0.0996492	−	0.172597i
$489$		0			0
$490$	1.07922e10	+	1.86926e10i	0.00845720	+	0.0146483i
$491$	9.12691e11	+	1.58083e12i	0.708691	+	1.22749i	0.965343	+	0.260985i	$0.0840474\pi$
$491$	9.12691e11	+	1.58083e12i	0.708691	+	1.22749i	−0.256652	+	0.966504i	$0.582619\pi$
$492$		0			0
$493$	1.09005e12	−	1.88802e12i	0.831066	−	1.43945i
$494$	−1.12413e11			−0.0849267
$495$		0			0
$496$	2.64587e11			0.196291
$497$	−3.13847e11	+	5.43599e11i	−0.230735	+	0.399645i
$498$		0			0
$499$	1.07718e12	+	1.86573e12i	0.777742	+	1.34709i	0.933240	+	0.359253i	$0.116968\pi$
$499$	1.07718e12	+	1.86573e12i	0.777742	+	1.34709i	−0.155498	+	0.987836i	$0.549698\pi$
$500$	−6.02824e11	−	1.04412e12i	−0.431346	−	0.747112i
$501$		0			0
$502$	6.01915e10	−	1.04255e11i	0.0423028	−	0.0732705i
$503$	9.53366e11			0.664055			0.332027	−	0.943270i	$-0.392267\pi$
$503$	9.53366e11			0.664055			0.332027	+	0.943270i	$0.392267\pi$
$504$		0			0
$505$	1.13096e12			0.773810
$506$	3.21208e10	−	5.56349e10i	0.0217826	−	0.0377285i
$507$		0			0
$508$	−9.35551e11	−	1.62042e12i	−0.623277	−	1.07955i
$509$	−8.49433e9	−	1.47126e10i	−0.00560918	−	0.00971538i	0.863207	−	0.504850i	$-0.168452\pi$
$509$	−8.49433e9	−	1.47126e10i	−0.00560918	−	0.00971538i	−0.868816	+	0.495134i	$0.835119\pi$
$510$		0			0
$511$	−4.02839e11	+	6.97738e11i	−0.261359	+	0.452688i
$512$	5.64436e11			0.362994
$513$		0			0
$514$	−7.15259e10			−0.0451990
$515$	−3.16774e11	+	5.48669e11i	−0.198435	+	0.343699i
$516$		0			0
$517$	3.79830e11	+	6.57885e11i	0.233820	+	0.404988i
$518$	−8.61222e10	−	1.49168e11i	−0.0525571	−	0.0910316i
$519$		0			0
$520$	1.31672e11	−	2.28062e11i	0.0789727	−	0.136785i
$521$	1.80540e12			1.07350			0.536751	−	0.843741i	$-0.319651\pi$
$521$	1.80540e12			1.07350			0.536751	+	0.843741i	$0.319651\pi$
$522$		0			0
$523$	2.69922e12			1.57754			0.788770	−	0.614688i	$-0.210718\pi$
$523$	2.69922e12			1.57754			0.788770	+	0.614688i	$0.210718\pi$
$524$	−1.29217e12	+	2.23810e12i	−0.748734	+	1.29685i
$525$		0			0
$526$	−1.47447e10	−	2.55386e10i	−0.00839848	−	0.0145466i
$527$	2.58569e11	+	4.47855e11i	0.146026	+	0.252924i
$528$		0			0
$529$	−9.62364e11	+	1.66686e12i	−0.534304	+	0.925442i
$530$	1.13454e11			0.0624566
$531$		0			0
$532$	1.93186e12			1.04562
$533$	4.64237e11	−	8.04081e11i	0.249153	−	0.431546i
$534$		0			0
$535$	−2.15102e11	−	3.72568e11i	−0.113515	−	0.196614i
$536$	−6.99263e9	−	1.21116e10i	−0.00365931	−	0.00633811i
$537$		0			0
$538$	5.53209e10	−	9.58186e10i	0.0284688	−	0.0493094i
$539$	1.65517e11			0.0844680
$540$		0			0
$541$	−2.63643e12			−1.32321			−0.661604	−	0.749854i	$-0.730124\pi$
$541$	−2.63643e12			−1.32321			−0.661604	+	0.749854i	$0.730124\pi$
$542$	2.38767e10	−	4.13556e10i	0.0118844	−	0.0205844i
$543$		0			0
$544$	3.30349e11	+	5.72182e11i	0.161725	+	0.280117i
$545$	3.75277e11	+	6.49999e11i	0.182208	+	0.315594i
$546$		0			0
$547$	1.76826e12	−	3.06272e12i	0.844507	−	1.46273i	−0.0415411	−	0.999137i	$-0.513227\pi$
$547$	1.76826e12	−	3.06272e12i	0.844507	−	1.46273i	0.886048	−	0.463593i	$-0.153440\pi$
$548$	1.02696e12			0.486451
$549$		0			0
$550$	−1.37846e10			−0.00642335
$551$	1.45083e12	−	2.51291e12i	0.670553	−	1.16143i
$552$		0			0
$553$	5.68472e11	+	9.84623e11i	0.258491	+	0.447720i
$554$	5.64649e10	+	9.78000e10i	0.0254674	+	0.0441108i
$555$		0			0
$556$	6.74186e11	−	1.16773e12i	0.299188	−	0.518208i
$557$	−1.41497e12			−0.622870			−0.311435	−	0.950267i	$-0.600810\pi$
$557$	−1.41497e12			−0.622870			−0.311435	+	0.950267i	$0.600810\pi$
$558$		0			0
$559$	−1.56875e11			−0.0679519
$560$	−1.12200e12	+	1.94337e12i	−0.482112	+	0.835042i
$561$		0			0
$562$	1.10133e11	+	1.90756e11i	0.0465698	+	0.0806612i
$563$	−8.98805e11	−	1.55678e12i	−0.377032	−	0.653038i	0.613597	−	0.789619i	$-0.289722\pi$
$563$	−8.98805e11	−	1.55678e12i	−0.377032	−	0.653038i	−0.990629	+	0.136581i	$0.956389\pi$
$564$		0			0
$565$	−1.75440e12	+	3.03872e12i	−0.724289	+	1.25451i
$566$	1.94334e10			0.00795930
$567$		0			0
$568$	−1.90307e11			−0.0767162
$569$	−1.26406e12	+	2.18942e12i	−0.505549	+	0.875637i	0.494430	+	0.869217i	$0.335377\pi$
$569$	−1.26406e12	+	2.18942e12i	−0.505549	+	0.875637i	−0.999979	+	0.00641942i	$0.997957\pi$
$570$		0			0
$571$	−2.35046e12	−	4.07112e12i	−0.925318	−	1.60270i	−0.791049	−	0.611753i	$-0.790464\pi$
$571$	−2.35046e12	−	4.07112e12i	−0.925318	−	1.60270i	−0.134270	−	0.990945i	$-0.542869\pi$
$572$	−5.03458e11	−	8.72015e11i	−0.196644	−	0.340598i
$573$		0			0
$574$	4.41977e10	−	7.65527e10i	0.0169940	−	0.0294345i
$575$	7.99478e11			0.305001
$576$		0			0
$577$	−2.61526e12			−0.982253			−0.491126	−	0.871088i	$-0.663415\pi$
$577$	−2.61526e12			−0.982253			−0.491126	+	0.871088i	$0.663415\pi$
$578$	−1.13652e11	+	1.96851e11i	−0.0423547	+	0.0733605i
$579$		0			0
$580$	1.69469e12	+	2.93529e12i	0.621820	+	1.07702i
$581$	−1.44809e12	−	2.50817e12i	−0.527234	−	0.913196i
$582$		0			0
$583$	4.35003e11	−	7.53447e11i	0.155949	−	0.270112i
$584$	−2.44269e11			−0.0868983
$585$		0			0
$586$	−2.65466e10			−0.00929972
$587$	−5.93246e11	+	1.02753e12i	−0.206236	+	0.357211i	−0.950526	−	0.310646i	$-0.899455\pi$
$587$	−5.93246e11	+	1.02753e12i	−0.206236	+	0.357211i	0.744290	+	0.667856i	$0.232788\pi$
$588$		0			0
$589$	3.44149e11	+	5.96083e11i	0.117822	+	0.204074i
$590$	−2.09059e11	−	3.62101e11i	−0.0710289	−	0.123026i
$591$		0			0
$592$	−2.33702e12	+	4.04784e12i	−0.782015	+	1.35449i
$593$	6.62653e11			0.220060			0.110030	−	0.993928i	$-0.464905\pi$
$593$	6.62653e11			0.220060			0.110030	+	0.993928i	$0.464905\pi$
$594$		0			0
$595$	−4.38594e12			−1.43462
$596$	−2.56948e11	+	4.45048e11i	−0.0834137	+	0.144477i
$597$		0			0
$598$	−1.61762e11	−	2.80181e11i	−0.0517276	−	0.0895948i
$599$	−2.85760e12	−	4.94951e12i	−0.906946	−	1.57088i	−0.818284	−	0.574814i	$-0.805074\pi$
$599$	−2.85760e12	−	4.94951e12i	−0.906946	−	1.57088i	−0.0886615	−	0.996062i	$-0.528259\pi$
$600$		0			0
$601$	1.97838e12	−	3.42666e12i	0.618551	−	1.07136i	−0.371200	−	0.928553i	$-0.621053\pi$
$601$	1.97838e12	−	3.42666e12i	0.618551	−	1.07136i	0.989750	−	0.142808i	$-0.0456132\pi$
$602$	−1.49353e10			−0.00463480
$603$		0			0
$604$	2.97574e11			0.0909765
$605$	1.51189e12	−	2.61867e12i	0.458798	−	0.794661i
$606$		0			0
$607$	−1.56657e12	−	2.71337e12i	−0.468381	−	0.811260i	0.530966	−	0.847393i	$-0.321829\pi$
$607$	−1.56657e12	−	2.71337e12i	−0.468381	−	0.811260i	−0.999347	+	0.0361333i	$0.988496\pi$
$608$	4.39686e11	+	7.61558e11i	0.130490	+	0.226015i
$609$		0			0
$610$	−1.88100e11	+	3.25798e11i	−0.0550052	+	0.0952719i
$611$	3.82569e12			1.11052
$612$		0			0
$613$	5.12506e12			1.46598			0.732988	−	0.680242i	$-0.238125\pi$
$613$	5.12506e12			1.46598			0.732988	+	0.680242i	$0.238125\pi$
$614$	3.44589e10	−	5.96845e10i	0.00978461	−	0.0169474i
$615$		0			0
$616$	−9.61292e10	−	1.66501e11i	−0.0268994	−	0.0465911i
$617$	1.16478e12	+	2.01746e12i	0.323565	+	0.560432i	0.981221	−	0.192887i	$-0.0617851\pi$
$617$	1.16478e12	+	2.01746e12i	0.323565	+	0.560432i	−0.657656	+	0.753319i	$0.728452\pi$
$618$		0			0
$619$	−2.89311e12	+	5.01102e12i	−0.792059	+	1.37189i	0.132631	+	0.991166i	$0.457658\pi$
$619$	−2.89311e12	+	5.01102e12i	−0.792059	+	1.37189i	−0.924690	+	0.380721i	$0.875676\pi$
$620$	−8.03991e11			−0.218519
$621$		0			0
$622$	3.33332e10			0.00892936
$623$	7.67430e11	−	1.32923e12i	0.204100	−	0.353511i
$624$		0			0
$625$	2.22605e12	+	3.85563e12i	0.583546	+	1.01073i
$626$	2.55023e11	+	4.41713e11i	0.0663736	+	0.114962i
$627$		0			0
$628$	1.90551e12	−	3.30044e12i	0.488869	−	0.846746i
$629$	−9.13548e12			−2.32704
$630$		0			0
$631$	3.68878e12			0.926297			0.463148	−	0.886281i	$-0.346720\pi$
$631$	3.68878e12			0.926297			0.463148	+	0.886281i	$0.346720\pi$
$632$	−1.72352e11	+	2.98522e11i	−0.0429724	+	0.0744303i
$633$		0			0
$634$	−6.72954e10	−	1.16559e11i	−0.0165418	−	0.0286513i
$635$	2.82699e12	+	4.89649e12i	0.689990	+	1.19510i
$636$		0			0
$637$	4.16776e11	−	7.21876e11i	0.100294	−	0.173714i
$638$	−1.43988e11			−0.0344058
$639$		0			0
$640$	−1.36830e12			−0.322382
$641$	−4.04098e11	+	6.99919e11i	−0.0945423	+	0.163752i	−0.909417	−	0.415884i	$-0.863472\pi$
$641$	−4.04098e11	+	6.99919e11i	−0.0945423	+	0.163752i	0.814875	+	0.579636i	$0.196805\pi$
$642$		0			0
$643$	−3.43977e12	−	5.95786e12i	−0.793561	−	1.37449i	−0.923749	−	0.382998i	$-0.874892\pi$
$643$	−3.43977e12	−	5.95786e12i	−0.793561	−	1.37449i	0.130188	−	0.991489i	$-0.458442\pi$
$644$	2.77995e12	+	4.81501e12i	0.636869	+	1.10309i
$645$		0			0
$646$	−2.83813e11	+	4.91579e11i	−0.0641189	+	0.111057i
$647$	6.68555e12			1.49992			0.749959	−	0.661484i	$-0.230073\pi$
$647$	6.68555e12			1.49992			0.749959	+	0.661484i	$0.230073\pi$
$648$		0			0
$649$	−3.20628e12			−0.709415
$650$	−3.47100e10	+	6.01195e10i	−0.00762684	+	0.0132101i
$651$		0			0
$652$	1.19982e12	+	2.07815e12i	0.260018	+	0.450364i
$653$	2.55043e12	+	4.41747e12i	0.548913	+	0.950746i	0.998349	+	0.0574332i	$0.0182916\pi$
$653$	2.55043e12	+	4.41747e12i	0.548913	+	0.950746i	−0.449436	+	0.893312i	$0.648375\pi$
$654$		0			0
$655$	3.90459e12	−	6.76294e12i	0.828875	−	1.43565i
$656$	−2.39871e12			−0.505721
$657$		0			0
$658$	3.64226e11			0.0757451
$659$	6.28162e11	−	1.08801e12i	0.129744	−	0.224723i	−0.793833	−	0.608135i	$-0.791918\pi$
$659$	6.28162e11	−	1.08801e12i	0.129744	−	0.224723i	0.923577	+	0.383412i	$0.125251\pi$
$660$		0			0
$661$	2.61889e12	+	4.53606e12i	0.533595	+	0.924213i	0.999230	+	0.0392363i	$0.0124925\pi$
$661$	2.61889e12	+	4.53606e12i	0.533595	+	0.924213i	−0.465635	+	0.884977i	$0.654174\pi$
$662$	1.18438e11	+	2.05140e11i	0.0239678	+	0.0415135i
$663$		0			0
$664$	4.39039e11	−	7.60437e11i	0.0876489	−	0.151812i
$665$	−5.83756e12			−1.15753
$666$		0			0
$667$	8.35098e12			1.63370
$668$	3.10006e12	−	5.36946e12i	0.602388	−	1.04337i
$669$		0			0
$670$	1.05358e10	+	1.82485e10i	0.00201990	+	0.00349857i
$671$	1.44242e12	+	2.49834e12i	0.274688	+	0.475773i
$672$		0			0
$673$	−1.20580e12	+	2.08851e12i	−0.226573	+	0.392436i	−0.956790	−	0.290779i	$-0.906086\pi$
$673$	−1.20580e12	+	2.08851e12i	−0.226573	+	0.392436i	0.730217	+	0.683215i	$0.239419\pi$
$674$	4.56417e10			0.00851907
$675$		0			0
$676$	3.28702e11			0.0605400
$677$	2.13731e12	−	3.70193e12i	0.391038	−	0.677297i	−0.601549	−	0.798836i	$-0.705449\pi$
$677$	2.13731e12	−	3.70193e12i	0.391038	−	0.677297i	0.992587	+	0.121539i	$0.0387828\pi$
$678$		0			0
$679$	1.69420e12	+	2.93444e12i	0.305880	+	0.529800i
$680$	−6.64874e11	−	1.15160e12i	−0.119247	−	0.206543i
$681$		0			0
$682$	1.70776e10	−	2.95792e10i	0.00302271	−	0.00523548i
$683$	6.17544e12			1.08586			0.542931	−	0.839777i	$-0.317315\pi$
$683$	6.17544e12			1.08586			0.542931	+	0.839777i	$0.317315\pi$
$684$		0			0
$685$	−3.10319e12			−0.538519
$686$	2.31378e11	−	4.00759e11i	0.0398900	−	0.0690915i
$687$		0			0
$688$	2.02644e11	+	3.50989e11i	0.0344814	+	0.0597236i
$689$	−2.19070e12	−	3.79440e12i	−0.370336	−	0.641441i
$690$		0			0
$691$	−7.07331e11	+	1.22513e12i	−0.118024	+	0.204424i	−0.918985	−	0.394293i	$-0.870989\pi$
$691$	−7.07331e11	+	1.22513e12i	−0.118024	+	0.204424i	0.800960	+	0.598717i	$0.204323\pi$
$692$	−2.59937e12			−0.430914
$693$		0			0
$694$	4.57543e11			0.0748712
$695$	−2.03721e12	+	3.52856e12i	−0.331211	+	0.573675i
$696$		0			0
$697$	−2.34415e12	−	4.06020e12i	−0.376217	−	0.651628i
$698$	−2.37628e11	−	4.11584e11i	−0.0378921	−	0.0656310i
$699$		0			0
$700$	5.96505e11	−	1.03318e12i	0.0939015	−	0.162642i
$701$	−7.79387e12			−1.21905			−0.609526	−	0.792766i	$-0.708640\pi$
$701$	−7.79387e12			−1.21905			−0.609526	+	0.792766i	$0.708640\pi$
$702$		0			0
$703$	−1.21591e13			−1.87759
$704$	−1.28607e12	+	2.22754e12i	−0.197328	+	0.341782i
$705$		0			0
$706$	6.07249e10	+	1.05179e11i	0.00919910	+	0.0159333i
$707$	−2.07907e12	−	3.60106e12i	−0.312955	−	0.542054i
$708$		0			0
$709$	−5.39708e12	+	9.34802e12i	−0.802142	+	1.38935i	0.116062	+	0.993242i	$0.462973\pi$
$709$	−5.39708e12	+	9.34802e12i	−0.802142	+	1.38935i	−0.918204	+	0.396108i	$0.870361\pi$
$710$	2.86735e11			0.0423465
$711$		0			0
$712$	4.65346e11			0.0678603
$713$	−9.90462e11	+	1.71553e12i	−0.143527	+	0.248597i
$714$		0			0
$715$	1.52132e12	+	2.63500e12i	0.217692	+	0.377054i
$716$	4.56915e11	+	7.91400e11i	0.0649721	+	0.112535i
$717$		0			0
$718$	3.26022e11	−	5.64687e11i	0.0457812	−	0.0792953i
$719$	1.54014e12			0.214921			0.107461	−	0.994209i	$-0.465728\pi$
$719$	1.54014e12			0.214921			0.107461	+	0.994209i	$0.465728\pi$
$720$		0			0
$721$	2.32935e12			0.321015
$722$	−1.06766e11	+	1.84925e11i	−0.0146224	+	0.0253267i
$723$		0			0
$724$	−6.79553e12	−	1.17702e13i	−0.919178	−	1.59206i
$725$	−8.95952e11	−	1.55183e12i	−0.120438	−	0.208605i
$726$		0			0
$727$	9.19987e11	−	1.59346e12i	0.122145	−	0.211562i	−0.798468	−	0.602037i	$-0.794356\pi$
$727$	9.19987e11	−	1.59346e12i	0.122145	−	0.211562i	0.920613	+	0.390475i	$0.127689\pi$
$728$	−9.68225e11			−0.127757
$729$		0			0
$730$	3.68039e11			0.0479669
$731$	−3.96070e11	+	6.86013e11i	−0.0513031	+	0.0888595i
$732$		0			0
$733$	−2.00213e12	−	3.46779e12i	−0.256168	−	0.443695i	0.709044	−	0.705164i	$-0.249127\pi$
$733$	−2.00213e12	−	3.46779e12i	−0.256168	−	0.443695i	−0.965212	+	0.261469i	$0.915793\pi$
$734$	1.32191e11	+	2.28962e11i	0.0168101	+	0.0291160i
$735$		0			0
$736$	−1.26542e12	+	2.19177e12i	−0.158959	+	0.275324i
$737$	1.61584e11			0.0201741
$738$		0			0
$739$	7.68031e12			0.947281			0.473641	−	0.880718i	$-0.342940\pi$
$739$	7.68031e12			0.947281			0.473641	+	0.880718i	$0.342940\pi$
$740$	7.10143e12	−	1.23000e13i	0.870569	−	1.50787i
$741$		0			0
$742$	−2.08566e11	−	3.61247e11i	−0.0252596	−	0.0437509i
$743$	2.01161e11	+	3.48421e11i	0.0242155	+	0.0419425i	0.877879	−	0.478882i	$-0.158958\pi$
$743$	2.01161e11	+	3.48421e11i	0.0242155	+	0.0419425i	−0.853664	+	0.520825i	$0.825625\pi$
$744$		0			0
$745$	7.76430e11	−	1.34482e12i	0.0923420	−	0.159941i
$746$	1.20954e12			0.142987
$747$		0			0
$748$	−5.08441e12			−0.593859
$749$	−7.90860e11	+	1.36981e12i	−0.0918187	+	0.159035i
$750$		0			0
$751$	4.29411e12	+	7.43762e12i	0.492599	+	0.853206i	0.999964	−	0.00852496i	$-0.00271361\pi$
$751$	4.29411e12	+	7.43762e12i	0.492599	+	0.853206i	−0.507365	+	0.861731i	$0.669380\pi$
$752$	−4.94184e12	−	8.55952e12i	−0.563519	−	0.976043i
$753$		0			0
$754$	−3.62565e11	+	6.27981e11i	−0.0408521	+	0.0707580i
$755$	−8.99191e11			−0.100714
$756$		0			0
$757$	−5.70537e12			−0.631470			−0.315735	−	0.948847i	$-0.602251\pi$
$757$	−5.70537e12			−0.631470			−0.315735	+	0.948847i	$0.602251\pi$
$758$	6.04689e11	−	1.04735e12i	0.0665305	−	0.115234i
$759$		0			0
$760$	−8.84928e11	−	1.53274e12i	−0.0962159	−	0.166651i
$761$	3.73302e11	+	6.46578e11i	0.0403487	+	0.0698860i	0.885495	−	0.464650i	$-0.153820\pi$
$761$	3.73302e11	+	6.46578e11i	0.0403487	+	0.0698860i	−0.845146	+	0.534536i	$0.820486\pi$
$762$		0			0
$763$	1.37977e12	−	2.38983e12i	0.147382	−	0.255274i
$764$	−3.78232e11			−0.0401641
$765$		0			0
$766$	3.03463e11			0.0318476
$767$	−8.07351e12	+	1.39837e13i	−0.842332	+	1.45896i
$768$		0			0
$769$	8.71089e12	+	1.50877e13i	0.898243	+	1.55580i	0.829739	+	0.558152i	$0.188489\pi$
$769$	8.71089e12	+	1.50877e13i	0.898243	+	1.55580i	0.0685041	+	0.997651i	$0.478177\pi$
$770$	1.44837e11	+	2.50866e11i	0.0148482	+	0.0257178i
$771$		0			0
$772$	−5.18062e11	+	8.97310e11i	−0.0524933	+	0.0909211i
$773$	8.20681e12			0.826736			0.413368	−	0.910564i	$-0.364352\pi$
$773$	8.20681e12			0.826736			0.413368	+	0.910564i	$0.364352\pi$
$774$		0			0
$775$	4.25055e11			0.0423241
$776$	−5.13656e11	+	8.89678e11i	−0.0508504	+	0.0880755i
$777$		0			0
$778$	1.71908e11	+	2.97754e11i	0.0168224	+	0.0291373i
$779$	−3.12000e12	−	5.40401e12i	−0.303554	−	0.525772i
$780$		0			0
$781$	1.09939e12	−	1.90420e12i	0.105736	−	0.183140i
$782$	−1.63363e12			−0.156215
$783$		0			0
$784$	−2.15348e12			−0.203572
$785$	−5.75795e12	+	9.97305e12i	−0.541195	+	0.937378i
$786$		0			0
$787$	−3.20680e11	−	5.55434e11i	−0.0297979	−	0.0516115i	0.850742	−	0.525584i	$-0.176153\pi$
$787$	−3.20680e11	−	5.55434e11i	−0.0297979	−	0.0516115i	−0.880540	+	0.473972i	$0.842820\pi$
$788$	8.66396e12	+	1.50064e13i	0.800476	+	1.38646i
$789$		0			0
$790$	2.59682e11	−	4.49782e11i	0.0237203	−	0.0410847i
$791$	1.29007e13			1.17171
$792$		0			0
$793$	1.45282e13			1.30461
$794$	−2.80945e11	+	4.86611e11i	−0.0250859	+	0.0434500i
$795$		0			0
$796$	2.62441e11	+	4.54560e11i	0.0231698	+	0.0401313i
$797$	1.70709e12	+	2.95676e12i	0.149863	+	0.259570i	0.931177	−	0.364569i	$-0.118784\pi$
$797$	1.70709e12	+	2.95676e12i	0.149863	+	0.259570i	−0.781314	+	0.624138i	$0.785450\pi$
$798$		0			0
$799$	9.65889e12	−	1.67297e13i	0.838430	−	1.45220i
$800$	5.43052e11			0.0468745
$801$		0			0
$802$	−7.41139e11			−0.0632579
$803$	1.41113e12	−	2.44415e12i	0.119770	−	0.207447i
$804$		0			0
$805$	−8.40027e12	−	1.45497e13i	−0.705037	−	1.22116i
$806$	−8.60036e10	−	1.48963e11i	−0.00717809	−	0.0124328i
$807$		0			0
$808$	6.30342e11	−	1.09178e12i	0.0520266	−	0.0901127i
$809$	1.64198e13			1.34772			0.673859	−	0.738860i	$-0.264636\pi$
$809$	1.64198e13			1.34772			0.673859	+	0.738860i	$0.264636\pi$
$810$		0			0
$811$	1.11691e13			0.906616			0.453308	−	0.891354i	$-0.350244\pi$
$811$	1.11691e13			0.906616			0.453308	+	0.891354i	$0.350244\pi$
$812$	6.23082e12	−	1.07921e13i	0.502971	−	0.871171i
$813$		0			0
$814$	3.01682e11	+	5.22529e11i	0.0240846	+	0.0417158i
$815$	−3.62555e12	−	6.27963e12i	−0.287849	−	0.498569i
$816$		0			0
$817$	−5.27157e11	+	9.13063e11i	−0.0413944	+	0.0716971i
$818$	−3.23975e11			−0.0253001
$819$		0			0
$820$	7.28888e12			0.562987
$821$	−1.12698e13	+	1.95199e13i	−0.865710	+	1.49945i	0.000629916		1.00000i	$0.499799\pi$
$821$	−1.12698e13	+	1.95199e13i	−0.865710	+	1.49945i	−0.866340	+	0.499454i	$0.833534\pi$
$822$		0			0
$823$	5.69466e11	+	9.86345e11i	0.0432682	+	0.0749427i	0.886848	−	0.462060i	$-0.152890\pi$
$823$	5.69466e11	+	9.86345e11i	0.0432682	+	0.0749427i	−0.843580	+	0.537003i	$0.819556\pi$
$824$	3.53111e11	+	6.11606e11i	0.0266832	+	0.0462167i
$825$		0			0
$826$	−7.68641e11	+	1.33132e12i	−0.0574531	+	0.0995116i
$827$	−3.06302e11			−0.0227706			−0.0113853	−	0.999935i	$-0.503624\pi$
$827$	−3.06302e11			−0.0227706			−0.0113853	+	0.999935i	$0.503624\pi$
$828$		0			0
$829$	−1.50391e13			−1.10593			−0.552964	−	0.833205i	$-0.686503\pi$
$829$	−1.50391e13			−1.10593			−0.552964	+	0.833205i	$0.686503\pi$
$830$	−6.61497e11	+	1.14575e12i	−0.0483812	+	0.0837987i
$831$		0			0
$832$	6.47673e12	+	1.12180e13i	0.468599	+	0.811636i
$833$	−2.10450e12	−	3.64510e12i	−0.151442	−	0.262305i
$834$		0			0
$835$	−9.36757e12	+	1.62251e13i	−0.666865	+	1.15504i
$836$	−6.76720e12			−0.479160
$837$		0			0
$838$	−9.95643e11			−0.0697438
$839$	−2.02104e12	+	3.50055e12i	−0.140814	+	0.243897i	−0.927803	−	0.373069i	$-0.878305\pi$
$839$	−2.02104e12	+	3.50055e12i	−0.140814	+	0.243897i	0.786989	+	0.616967i	$0.211639\pi$
$840$		0			0
$841$	−2.10514e12	−	3.64620e12i	−0.145110	−	0.251338i
$842$	4.37133e11	+	7.57137e11i	0.0299716	+	0.0519123i
$843$		0			0
$844$	3.78308e11	−	6.55249e11i	0.0256628	−	0.0444493i
$845$	−9.93251e11			−0.0670199
$846$		0			0
$847$	−1.11174e13			−0.742214
$848$	−5.65967e12	+	9.80284e12i	−0.375846	+	0.650984i
$849$		0			0
$850$	1.75268e11	+	3.03573e11i	0.0115164	+	0.0199470i
$851$	−1.74969e13	−	3.03056e13i	−1.14361	−	1.98080i
$852$		0			0
$853$	−9.97969e12	+	1.72853e13i	−0.645426	+	1.11791i	0.338777	+	0.940867i	$0.389987\pi$
$853$	−9.97969e12	+	1.72853e13i	−0.645426	+	1.11791i	−0.984203	+	0.177043i	$0.943347\pi$
$854$	1.38316e12			0.0889840
$855$		0			0
$856$	−4.79553e11			−0.0305284
$857$	1.42636e13	−	2.47053e13i	0.903266	−	1.56450i	0.0800373	−	0.996792i	$-0.474496\pi$
$857$	1.42636e13	−	2.47053e13i	0.903266	−	1.56450i	0.823228	−	0.567710i	$-0.192171\pi$
$858$		0			0
$859$	−5.23691e12	−	9.07060e12i	−0.328176	−	0.568417i	0.653974	−	0.756517i	$-0.273100\pi$
$859$	−5.23691e12	−	9.07060e12i	−0.328176	−	0.568417i	−0.982150	+	0.188100i	$0.939767\pi$
$860$	−6.15766e11	−	1.06654e12i	−0.0383860	−	0.0664865i
$861$		0			0
$862$	5.85741e11	−	1.01453e12i	0.0361346	−	0.0625869i
$863$	−1.55631e13			−0.955096			−0.477548	−	0.878606i	$-0.658474\pi$
$863$	−1.55631e13			−0.955096			−0.477548	+	0.878606i	$0.658474\pi$
$864$		0			0
$865$	7.85461e12			0.477037
$866$	1.09560e11	−	1.89764e11i	0.00661945	−	0.0114652i
$867$		0			0
$868$	1.47800e12	+	2.55998e12i	0.0883765	+	0.153073i
$869$	−1.99133e12	−	3.44909e12i	−0.118455	−	0.205171i
$870$		0			0
$871$	4.06873e11	−	7.04725e11i	0.0239540	−	0.0414895i
$872$	8.36648e11			0.0490025
$873$		0			0
$874$	−2.17432e12			−0.126044
$875$	6.69732e12	−	1.16001e13i	0.386247	−	0.668999i
$876$		0			0
$877$	−4.14167e12	−	7.17358e12i	−0.236416	−	0.409485i	0.723267	−	0.690568i	$-0.242640\pi$
$877$	−4.14167e12	−	7.17358e12i	−0.236416	−	0.409485i	−0.959683	+	0.281084i	$0.909306\pi$
$878$	−8.69530e11	−	1.50607e12i	−0.0493809	−	0.0855303i
$879$		0			0
$880$	3.93033e12	−	6.80752e12i	0.220931	−	0.382664i
$881$	3.05766e12			0.171001			0.0855004	−	0.996338i	$-0.472751\pi$
$881$	3.05766e12			0.171001			0.0855004	+	0.996338i	$0.472751\pi$
$882$		0			0
$883$	−1.81997e13			−1.00749			−0.503745	−	0.863852i	$-0.668045\pi$
$883$	−1.81997e13			−1.00749			−0.503745	+	0.863852i	$0.668045\pi$
$884$	−1.28027e13	+	2.21749e13i	−0.705125	+	1.22131i
$885$		0			0
$886$	−3.41576e10	−	5.91627e10i	−0.00186224	−	0.00322550i
$887$	8.95513e12	+	1.55107e13i	0.485753	+	0.841349i	0.999866	−	0.0163735i	$-0.00521207\pi$
$887$	8.95513e12	+	1.55107e13i	0.485753	+	0.841349i	−0.514113	+	0.857723i	$0.671879\pi$
$888$		0			0
$889$	1.03939e13	−	1.80028e13i	0.558111	−	0.966676i
$890$	−7.01134e11			−0.0374581
$891$		0			0
$892$	9.45241e11			0.0499920
$893$	1.28557e13	−	2.22667e13i	0.676495	−	1.17172i
$894$		0			0
$895$	−1.38068e12	−	2.39140e12i	−0.0719264	−	0.124580i
$896$	2.51538e12	+	4.35677e12i	0.130382	+	0.225828i
$897$		0			0
$898$	1.32762e12	−	2.29951e12i	0.0681290	−	0.118003i
$899$	4.43993e12			0.226703
$900$		0			0
$901$	−2.21238e13			−1.11840
$902$	−1.54823e11	+	2.68161e11i	−0.00778763	+	0.0134886i
$903$		0			0
$904$	1.95565e12	+	3.38728e12i	0.0973941	+	0.168692i
$905$	2.05343e13	+	3.55665e13i	1.01756	+	1.76247i
$906$		0			0
$907$	−4.58907e12	+	7.94851e12i	−0.225161	+	0.389989i	−0.956368	−	0.292166i	$-0.905624\pi$
$907$	−4.58907e12	+	7.94851e12i	−0.225161	+	0.389989i	0.731207	+	0.682156i	$0.238957\pi$
$908$	−3.54668e13			−1.73155
$909$		0			0
$910$	1.45882e12			0.0705205
$911$	1.07317e12	−	1.85879e12i	0.0516222	−	0.0894123i	−0.839060	−	0.544039i	$-0.816894\pi$
$911$	1.07317e12	−	1.85879e12i	0.0516222	−	0.0894123i	0.890682	+	0.454627i	$0.150227\pi$
$912$		0			0
$913$	5.07260e12	+	8.78600e12i	0.241608	+	0.418478i
$914$	−7.56814e11	−	1.31084e12i	−0.0358700	−	0.0621286i
$915$		0			0
$916$	−5.18468e12	+	8.98013e12i	−0.243328	+	0.421457i
$917$	−2.87117e13			−1.34090
$918$		0			0
$919$	1.70600e13			0.788967			0.394483	−	0.918903i	$-0.370924\pi$
$919$	1.70600e13			0.788967			0.394483	+	0.918903i	$0.370924\pi$
$920$	2.54683e12	−	4.41124e12i	0.117207	−	0.203009i
$921$		0			0
$922$	9.36768e11	+	1.62253e12i	0.0426916	+	0.0739441i
$923$	−5.53660e12	−	9.58968e12i	−0.251094	−	0.434907i
$924$		0			0
$925$	−3.75439e12	+	6.50280e12i	−0.168617	+	0.292053i
$926$	−1.45950e12			−0.0652310
$927$		0			0
$928$	5.67248e12			0.251077
$929$	2.08662e13	−	3.61414e13i	0.919123	−	1.59197i	0.118372	−	0.992969i	$-0.462232\pi$
$929$	2.08662e13	−	3.61414e13i	0.919123	−	1.59197i	0.800750	−	0.598998i	$-0.204434\pi$
$930$		0			0
$931$	−2.80103e12	−	4.85153e12i	−0.122193	−	0.211644i
$932$	1.10147e13	+	1.90780e13i	0.478189	+	0.828248i
$933$		0			0
$934$	8.59534e11	−	1.48876e12i	0.0369575	−	0.0640122i
$935$	1.53637e13			0.657423
$936$		0			0
$937$	3.48481e13			1.47690			0.738451	−	0.674308i	$-0.235558\pi$
$937$	3.48481e13			1.47690			0.738451	+	0.674308i	$0.235558\pi$
$938$	3.87365e10	−	6.70935e10i	0.00163383	−	0.00282988i
$939$		0			0
$940$	1.50166e13	+	2.60095e13i	0.627330	+	1.08657i
$941$	3.87082e12	+	6.70445e12i	0.160935	+	0.278747i	0.935204	−	0.354109i	$-0.115216\pi$
$941$	3.87082e12	+	6.70445e12i	0.160935	+	0.278747i	−0.774270	+	0.632856i	$0.781883\pi$
$942$		0			0
$943$	8.97939e12	−	1.55528e13i	0.369781	−	0.640479i
$944$	4.17158e13			1.70973
$945$		0			0
$946$	5.23179e10			0.00212393
$947$	−2.03097e13	+	3.51775e13i	−0.820596	+	1.42131i	0.0846427	+	0.996411i	$0.473025\pi$
$947$	−2.03097e13	+	3.51775e13i	−0.820596	+	1.42131i	−0.905239	+	0.424903i	$0.860308\pi$
$948$		0			0
$949$	−7.10653e12	−	1.23089e13i	−0.284420	−	0.492629i
$950$	2.33276e11	+	4.04046e11i	0.00929211	+	0.0160944i
$951$		0			0
$952$	−2.44452e12	+	4.23403e12i	−0.0964555	+	0.167066i
$953$	−3.21151e13			−1.26122			−0.630611	−	0.776099i	$-0.717196\pi$
$953$	−3.21151e13			−1.26122			−0.630611	+	0.776099i	$0.717196\pi$
$954$		0			0
$955$	1.14292e12			0.0444631
$956$	9.59172e12	−	1.66133e13i	0.371395	−	0.643275i
$957$		0			0
$958$	−6.01329e11	−	1.04153e12i	−0.0230657	−	0.0399510i
$959$	5.70469e12	+	9.88082e12i	0.217795	+	0.377233i
$960$		0			0
$961$	1.26932e13	−	2.19853e13i	0.480083	−	0.831528i
$962$	3.03858e12			0.114389
$963$		0			0
$964$	1.70426e13			0.635608
$965$	1.56545e12	−	2.71144e12i	0.0581120	−	0.100653i
$966$		0			0
$967$	1.09009e13	+	1.88808e13i	0.400905	+	0.694388i	0.993835	−	0.110866i	$-0.0353623\pi$
$967$	1.09009e13	+	1.88808e13i	0.400905	+	0.694388i	−0.592930	+	0.805254i	$0.702029\pi$
$968$	−1.68532e12	−	2.91905e12i	−0.0616939	−	0.106857i
$969$		0			0
$970$	7.73922e11	−	1.34047e12i	0.0280689	−	0.0486167i
$971$	2.45155e13			0.885024			0.442512	−	0.896763i	$-0.354087\pi$
$971$	2.45155e13			0.885024			0.442512	+	0.896763i	$0.354087\pi$
$972$		0			0
$973$	1.49803e13			0.535813
$974$	8.80560e11	−	1.52518e12i	0.0313505	−	0.0543006i
$975$		0			0
$976$	−1.87668e13	−	3.25050e13i	−0.662012	−	1.14664i
$977$	1.19050e13	+	2.06201e13i	0.418027	+	0.724044i	0.995741	−	0.0921955i	$-0.0293885\pi$
$977$	1.19050e13	+	2.06201e13i	0.418027	+	0.724044i	−0.577714	+	0.816239i	$0.696055\pi$
$978$		0			0
$979$	−2.68827e12	+	4.65623e12i	−0.0935301	+	0.161999i
$980$	6.54370e12			0.226624
$981$		0			0
$982$	−3.06577e12			−0.105205
$983$	−2.13368e13	+	3.69565e13i	−0.728852	+	1.26241i	0.228517	+	0.973540i	$0.426612\pi$
$983$	−2.13368e13	+	3.69565e13i	−0.728852	+	1.26241i	−0.957369	+	0.288869i	$0.906721\pi$
$984$		0			0
$985$	−2.61802e13	−	4.53454e13i	−0.886155	−	1.53487i
$986$	1.83077e12	+	3.17098e12i	0.0616860	+	0.106843i
$987$		0			0
$988$	−1.70400e13	+	2.95142e13i	−0.568936	+	0.985427i
$989$	−3.03433e12			−0.100851
$990$		0			0
$991$	−5.04883e13			−1.66287			−0.831437	−	0.555620i	$-0.812481\pi$
$991$	−5.04883e13			−1.66287			−0.831437	+	0.555620i	$0.812481\pi$
$992$	−6.72780e11	+	1.16529e12i	−0.0220582	+	0.0382060i
$993$		0			0
$994$	−5.27114e11	−	9.12987e11i	−0.0171264	−	0.0296637i
$995$	−7.93026e11	−	1.37356e12i	−0.0256498	−	0.0444267i
$996$		0			0
$997$	1.76670e13	−	3.06001e13i	0.566283	−	0.980831i	−0.430646	−	0.902521i	$-0.641714\pi$
$997$	1.76670e13	−	3.06001e13i	0.566283	−	0.980831i	0.996929	−	0.0783103i	$-0.0249525\pi$
$998$	−3.61830e12			−0.115456
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.10.c.a.19.5		16
3.2	odd	2		9.10.c.a.7.4	yes	16
9.2	odd	6		81.10.a.c.1.5		8
9.4	even	3	inner	27.10.c.a.10.5		16
9.5	odd	6		9.10.c.a.4.4	✓	16
9.7	even	3		81.10.a.d.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.10.c.a.4.4	✓	16	9.5	odd	6
9.10.c.a.7.4	yes	16	3.2	odd	2
27.10.c.a.10.5		16	9.4	even	3	inner
27.10.c.a.19.5		16	1.1	even	1	trivial
81.10.a.c.1.5		8	9.2	odd	6
81.10.a.d.1.4		8	9.7	even	3

Overview	Random
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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)

\(f(q)\)	\(=\)	\(q+(-0.839762 + 1.45451i) q^{2} +(254.590 + 440.962i) q^{4} +(-769.303 - 1332.47i) q^{5} +(-2828.47 + 4899.05i) q^{7} -1715.10 q^{8} +O(q^{10})\)	\(q+(-0.839762 + 1.45451i) q^{2} +(254.590 + 440.962i) q^{4} +(-769.303 - 1332.47i) q^{5} +(-2828.47 + 4899.05i) q^{7} -1715.10 q^{8} +2584.13 q^{10} +(9908.00 - 17161.2i) q^{11} +(-49897.3 - 86424.6i) q^{13} +(-4750.48 - 8228.07i) q^{14} +(-128910. + 223278. i) q^{16} -503911. q^{17} -670691. q^{19} +(391713. - 678467. i) q^{20} +(16640.7 + 28822.6i) q^{22} +(-965127. - 1.67165e6i) q^{23} +(-207091. + 358693. i) q^{25} +167607. q^{26} -2.88039e6 q^{28} +(-2.16318e6 + 3.74674e6i) q^{29} +(-513125. - 888759. i) q^{31} +(-655571. - 1.13548e6i) q^{32} +(423165. - 732944. i) q^{34} +8.70380e6 q^{35} +1.81292e7 q^{37} +(563221. - 975527. i) q^{38} +(1.31943e6 + 2.28532e6i) q^{40} +(4.65192e6 + 8.05737e6i) q^{41} +(785991. - 1.36138e6i) q^{43} +1.00899e7 q^{44} +3.24191e6 q^{46} +(-1.91679e7 + 3.31997e7i) q^{47} +(4.17634e6 + 7.23363e6i) q^{49} +(-347815. - 602433. i) q^{50} +(2.54066e7 - 4.40056e7i) q^{52} +4.39042e7 q^{53} -3.04890e7 q^{55} +(4.85109e6 - 8.40234e6i) q^{56} +(-3.63312e6 - 6.29274e6i) q^{58} +(-8.09014e7 - 1.40125e8i) q^{59} +(-7.27905e7 + 1.26077e8i) q^{61} +1.72361e6 q^{62} -1.29801e8 q^{64} +(-7.67722e7 + 1.32973e8i) q^{65} +(4.07711e6 + 7.06176e6i) q^{67} +(-1.28290e8 - 2.22206e8i) q^{68} +(-7.30912e6 + 1.26598e7i) q^{70} +1.10960e8 q^{71} +1.42423e8 q^{73} +(-1.52242e7 + 2.63691e7i) q^{74} +(-1.70751e8 - 2.95749e8i) q^{76} +(5.60489e7 + 9.70796e7i) q^{77} +(1.00491e8 - 1.74056e8i) q^{79} +3.96682e8 q^{80} -1.56260e7 q^{82} +(-2.55985e8 + 4.43379e8i) q^{83} +(3.87660e8 + 6.71447e8i) q^{85} +(1.32009e6 + 2.28647e6i) q^{86} +(-1.69932e7 + 2.94330e7i) q^{88} -2.71324e8 q^{89} +5.64531e8 q^{91} +(4.91423e8 - 8.51169e8i) q^{92} +(-3.21929e7 - 5.57597e7i) q^{94} +(5.15965e8 + 8.93677e8i) q^{95} +(2.99491e8 - 5.18734e8i) q^{97} -1.40285e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 15 q^{2} - 1793 q^{4} - 453 q^{5} - 343 q^{7} + 14478 q^{8}+O(q^{10}) \) 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

L-functions

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