LMFDB - Embedded newform 27.8.c.a.10.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,8,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, 8, names="a")

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

chi := DirichletCharacter("27.10");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 8 $
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:	$8.43439568807$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 375 x^{10} - 1820 x^{9} + 50808 x^{8} - 192378 x^{7} + 3002887 x^{6} + \cdots + 754412211 $ x^12 - 6x^11 + 375x^10 - 1820x^9 + 50808x^8 - 192378x^7 + 3002887x^6 - 8342916x^5 + 72369348x^4 - 131054670x^3 + 513267363x^2 - 449098992*x + 754412211
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{21} $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			10.3
Root			$0.500000 + 1.48508i$ of defining polynomial
Character	$\chi$	$=$	27.10
Dual form			27.8.c.a.19.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.536120 - 0.928588i) q^{2} +(63.4251 - 109.856i) q^{4} +(-47.9866 + 83.1153i) q^{5} +(-189.000 - 327.358i) q^{7} -273.261 q^{8} +O(q^{10})$	\(q+(-0.536120 - 0.928588i) q^{2} +(63.4251 - 109.856i) q^{4} +(-47.9866 + 83.1153i) q^{5} +(-189.000 - 327.358i) q^{7} -273.261 q^{8} +102.906 q^{10} +(-3436.63 - 5952.41i) q^{11} +(4826.64 - 8359.99i) q^{13} +(-202.654 + 351.007i) q^{14} +(-7971.92 - 13807.8i) q^{16} -21431.3 q^{17} +5518.94 q^{19} +(6087.12 + 10543.2i) q^{20} +(-3684.89 + 6382.42i) q^{22} +(31486.4 - 54536.1i) q^{23} +(34457.1 + 59681.4i) q^{25} -10350.6 q^{26} -47949.5 q^{28} +(111113. + 192454. i) q^{29} +(-57729.1 + 99989.7i) q^{31} +(-26036.5 + 45096.6i) q^{32} +(11489.7 + 19900.8i) q^{34} +36277.9 q^{35} +81737.7 q^{37} +(-2958.82 - 5124.82i) q^{38} +(13112.9 - 22712.2i) q^{40} +(298773. - 517491. i) q^{41} +(-33874.2 - 58671.8i) q^{43} -871875. q^{44} -67522.1 q^{46} +(151740. + 262822. i) q^{47} +(340329. - 589468. i) q^{49} +(36946.3 - 63992.8i) q^{50} +(-612261. - 1.06047e6i) q^{52} -846755. q^{53} +659649. q^{55} +(51646.4 + 89454.2i) q^{56} +(119140. - 206357. i) q^{58} +(793119. - 1.37372e6i) q^{59} +(1.12706e6 + 1.95213e6i) q^{61} +123799. q^{62} -1.98498e6 q^{64} +(463228. + 802335. i) q^{65} +(-1.51172e6 + 2.61838e6i) q^{67} +(-1.35928e6 + 2.35434e6i) q^{68} +(-19449.3 - 33687.3i) q^{70} +4.41675e6 q^{71} +2.21484e6 q^{73} +(-43821.3 - 75900.6i) q^{74} +(350040. - 606287. i) q^{76} +(-1.29905e6 + 2.25002e6i) q^{77} +(-153821. - 266426. i) q^{79} +1.53018e6 q^{80} -640714. q^{82} +(-1.57735e6 - 2.73204e6i) q^{83} +(1.02841e6 - 1.78127e6i) q^{85} +(-36321.3 + 62910.3i) q^{86} +(939096. + 1.62656e6i) q^{88} -1.93441e6 q^{89} -3.64895e6 q^{91} +(-3.99406e6 - 6.91792e6i) q^{92} +(162702. - 281808. i) q^{94} +(-264836. + 458709. i) q^{95} +(-4.94528e6 - 8.56548e6i) q^{97} -729830. q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 9 q^{2} - 321 q^{4} + 180 q^{5} - 84 q^{7} - 5922 q^{8}+O(q^{10}) $ 12 * q + 9 * q^2 - 321 * q^4 + 180 * q^5 - 84 * q^7 - 5922 * q^8	\( 12 q + 9 q^{2} - 321 q^{4} + 180 q^{5} - 84 q^{7} - 5922 q^{8} + 252 q^{10} + 8460 q^{11} - 1848 q^{13} + 16272 q^{14} - 12417 q^{16} - 30564 q^{17} + 24432 q^{19} + 40788 q^{20} - 35001 q^{22} + 51588 q^{23} + 4746 q^{25} - 536472 q^{26} + 75516 q^{28} + 414648 q^{29} + 8196 q^{31} + 1048977 q^{32} - 106623 q^{34} - 2210616 q^{35} + 139344 q^{37} + 1952685 q^{38} + 305496 q^{40} + 1731582 q^{41} + 408372 q^{43} - 5169114 q^{44} - 1684008 q^{46} + 1631484 q^{47} - 179010 q^{49} + 1654461 q^{50} + 681594 q^{52} - 2835648 q^{53} - 16056 q^{55} + 1784466 q^{56} - 948384 q^{58} + 2055636 q^{59} - 2723196 q^{61} + 1026828 q^{62} + 7178178 q^{64} + 1387620 q^{65} + 3806556 q^{67} - 2142639 q^{68} + 953442 q^{70} - 2408400 q^{71} - 10670052 q^{73} - 9846504 q^{74} - 6727827 q^{76} - 3478824 q^{77} + 6020916 q^{79} + 38072448 q^{80} + 9403002 q^{82} - 9605052 q^{83} - 1698624 q^{85} - 34278561 q^{86} - 16459029 q^{88} + 24630264 q^{89} + 13570104 q^{91} - 39143394 q^{92} + 12602808 q^{94} - 10422072 q^{95} + 9977226 q^{97} + 95833314 q^{98}+O(q^{100}) \) 12 * q + 9 * q^2 - 321 * q^4 + 180 * q^5 - 84 * q^7 - 5922 * q^8 + 252 * q^10 + 8460 * q^11 - 1848 * q^13 + 16272 * q^14 - 12417 * q^16 - 30564 * q^17 + 24432 * q^19 + 40788 * q^20 - 35001 * q^22 + 51588 * q^23 + 4746 * q^25 - 536472 * q^26 + 75516 * q^28 + 414648 * q^29 + 8196 * q^31 + 1048977 * q^32 - 106623 * q^34 - 2210616 * q^35 + 139344 * q^37 + 1952685 * q^38 + 305496 * q^40 + 1731582 * q^41 + 408372 * q^43 - 5169114 * q^44 - 1684008 * q^46 + 1631484 * q^47 - 179010 * q^49 + 1654461 * q^50 + 681594 * q^52 - 2835648 * q^53 - 16056 * q^55 + 1784466 * q^56 - 948384 * q^58 + 2055636 * q^59 - 2723196 * q^61 + 1026828 * q^62 + 7178178 * q^64 + 1387620 * q^65 + 3806556 * q^67 - 2142639 * q^68 + 953442 * q^70 - 2408400 * q^71 - 10670052 * q^73 - 9846504 * q^74 - 6727827 * q^76 - 3478824 * q^77 + 6020916 * q^79 + 38072448 * q^80 + 9403002 * q^82 - 9605052 * q^83 - 1698624 * q^85 - 34278561 * q^86 - 16459029 * q^88 + 24630264 * q^89 + 13570104 * q^91 - 39143394 * q^92 + 12602808 * q^94 - 10422072 * q^95 + 9977226 * q^97 + 95833314 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.536120	−	0.928588i	−0.0473868	−	0.0820763i	0.841359	−	0.540476i	$-0.181756\pi$
$2$	−0.536120	−	0.928588i	−0.0473868	−	0.0820763i	−0.888746	+	0.458400i	$0.848423\pi$
$3$		0			0
$3$		0			0
$4$	63.4251	−	109.856i	0.495509	−	0.858247i
$5$	−47.9866	+	83.1153i	−0.171682	+	0.297362i	−0.939008	−	0.343895i	$-0.888254\pi$
$5$	−47.9866	+	83.1153i	−0.171682	+	0.297362i	0.767326	+	0.641257i	$0.221587\pi$
$6$		0			0
$7$	−189.000	−	327.358i	−0.208266	−	0.360728i	0.742902	−	0.669400i	$-0.233449\pi$
$7$	−189.000	−	327.358i	−0.208266	−	0.360728i	−0.951169	+	0.308672i	$0.900115\pi$
$8$	−273.261			−0.188696
$9$		0			0
$10$	102.906			0.0325419
$11$	−3436.63	−	5952.41i	−0.778499	−	1.34840i	−0.932807	−	0.360377i	$-0.882648\pi$
$11$	−3436.63	−	5952.41i	−0.778499	−	1.34840i	0.154308	−	0.988023i	$-0.450685\pi$
$12$		0			0
$13$	4826.64	−	8359.99i	0.609317	−	1.05537i	−0.382036	−	0.924147i	$-0.624777\pi$
$13$	4826.64	−	8359.99i	0.609317	−	1.05537i	0.991353	−	0.131220i	$-0.0418896\pi$
$14$	−202.654	+	351.007i	−0.0197382	+	0.0341875i
$15$		0			0
$16$	−7971.92	−	13807.8i	−0.486567	−	0.842759i
$17$	−21431.3			−1.05798			−0.528989	−	0.848629i	$-0.677429\pi$
$17$	−21431.3			−1.05798			−0.528989	+	0.848629i	$0.677429\pi$
$18$		0			0
$19$	5518.94			0.184594			0.0922972	−	0.995732i	$-0.470579\pi$
$19$	5518.94			0.184594			0.0922972	+	0.995732i	$0.470579\pi$
$20$	6087.12	+	10543.2i	0.170140	+	0.294691i
$21$		0			0
$22$	−3684.89	+	6382.42i	−0.0737812	+	0.127793i
$23$	31486.4	−	54536.1i	0.539605	−	0.934623i	−0.459320	−	0.888271i	$-0.651907\pi$
$23$	31486.4	−	54536.1i	0.539605	−	0.934623i	0.998925	−	0.0463526i	$-0.0147598\pi$
$24$		0			0
$25$	34457.1	+	59681.4i	0.441050	+	0.763922i
$26$	−10350.6			−0.115494
$27$		0			0
$28$	−47949.5			−0.412792
$29$	111113.	+	192454.i	0.846004	+	1.46532i	0.884747	+	0.466072i	$0.154331\pi$
$29$	111113.	+	192454.i	0.846004	+	1.46532i	−0.0387428	+	0.999249i	$0.512335\pi$
$30$		0			0
$31$	−57729.1	+	99989.7i	−0.348040	+	0.602822i	−0.985901	−	0.167329i	$-0.946486\pi$
$31$	−57729.1	+	99989.7i	−0.348040	+	0.602822i	0.637862	+	0.770151i	$0.279819\pi$
$32$	−26036.5	+	45096.6i	−0.140462	+	0.243287i
$33$		0			0
$34$	11489.7	+	19900.8i	0.0501342	+	0.0868350i
$35$	36277.9			0.143023
$36$		0			0
$37$	81737.7			0.265287			0.132644	−	0.991164i	$-0.457653\pi$
$37$	81737.7			0.265287			0.132644	+	0.991164i	$0.457653\pi$
$38$	−2958.82	−	5124.82i	−0.00874734	−	0.0151508i
$39$		0			0
$40$	13112.9	−	22712.2i	0.0323957	−	0.0561111i
$41$	298773.	−	517491.i	0.677015	−	1.17262i	−0.298860	−	0.954297i	$-0.596606\pi$
$41$	298773.	−	517491.i	0.677015	−	1.17262i	0.975875	−	0.218328i	$-0.0700602\pi$
$42$		0			0
$43$	−33874.2	−	58671.8i	−0.0649725	−	0.112536i	0.831709	−	0.555211i	$-0.187363\pi$
$43$	−33874.2	−	58671.8i	−0.0649725	−	0.112536i	−0.896682	+	0.442676i	$0.854029\pi$
$44$	−871875.			−1.54301
$45$		0			0
$46$	−67522.1			−0.102281
$47$	151740.	+	262822.i	0.213186	+	0.369249i	0.952710	−	0.303881i	$-0.0982827\pi$
$47$	151740.	+	262822.i	0.213186	+	0.369249i	−0.739524	+	0.673130i	$0.764949\pi$
$48$		0			0
$49$	340329.	−	589468.i	0.413250	−	0.715770i
$50$	36946.3	−	63992.8i	0.0417999	−	0.0723996i
$51$		0			0
$52$	−612261.	−	1.06047e6i	−0.603844	−	1.04589i
$53$	−846755.			−0.781254			−0.390627	−	0.920549i	$-0.627742\pi$
$53$	−846755.			−0.781254			−0.390627	+	0.920549i	$0.627742\pi$
$54$		0			0
$55$	659649.			0.534618
$56$	51646.4	+	89454.2i	0.0392990	+	0.0680679i
$57$		0			0
$58$	119140.	−	206357.i	0.0801788	−	0.138874i
$59$	793119.	−	1.37372e6i	0.502755	−	0.870797i	−0.497240	−	0.867613i	$-0.665653\pi$
$59$	793119.	−	1.37372e6i	0.502755	−	0.870797i	0.999995	−	0.00318395i	$-0.00101348\pi$
$60$		0			0
$61$	1.12706e6	+	1.95213e6i	0.635760	+	1.10117i	0.986353	+	0.164641i	$0.0526467\pi$
$61$	1.12706e6	+	1.95213e6i	0.635760	+	1.10117i	−0.350593	+	0.936528i	$0.614020\pi$
$62$	123799.			0.0659699
$63$		0			0
$64$	−1.98498e6			−0.946510
$65$	463228.	+	802335.i	0.209218	+	0.362376i
$66$		0			0
$67$	−1.51172e6	+	2.61838e6i	−0.614060	+	1.06358i	0.376489	+	0.926421i	$0.377131\pi$
$67$	−1.51172e6	+	2.61838e6i	−0.614060	+	1.06358i	−0.990549	+	0.137162i	$0.956202\pi$
$68$	−1.35928e6	+	2.35434e6i	−0.524238	+	0.908006i
$69$		0			0
$70$	−19449.3	−	33687.3i	−0.00677738	−	0.0117388i
$71$	4.41675e6			1.46453			0.732266	−	0.681018i	$-0.238463\pi$
$71$	4.41675e6			1.46453			0.732266	+	0.681018i	$0.238463\pi$
$72$		0			0
$73$	2.21484e6			0.666366			0.333183	−	0.942862i	$-0.391877\pi$
$73$	2.21484e6			0.666366			0.333183	+	0.942862i	$0.391877\pi$
$74$	−43821.3	−	75900.6i	−0.0125711	−	0.0217738i
$75$		0			0
$76$	350040.	−	606287.i	0.0914682	−	0.158428i
$77$	−1.29905e6	+	2.25002e6i	−0.324271	+	0.561653i
$78$		0			0
$79$	−153821.	−	266426.i	−0.0351011	−	0.0607969i	0.847941	−	0.530090i	$-0.177842\pi$
$79$	−153821.	−	266426.i	−0.0351011	−	0.0607969i	−0.883042	+	0.469293i	$0.844509\pi$
$80$	1.53018e6			0.334140
$81$		0			0
$82$	−640714.			−0.128326
$83$	−1.57735e6	−	2.73204e6i	−0.302798	−	0.524462i	0.673970	−	0.738758i	$-0.264588\pi$
$83$	−1.57735e6	−	2.73204e6i	−0.302798	−	0.524462i	−0.976769	+	0.214296i	$0.931254\pi$
$84$		0			0
$85$	1.02841e6	−	1.78127e6i	0.181636	−	0.314603i
$86$	−36321.3	+	62910.3i	−0.00615768	+	0.0106654i
$87$		0			0
$88$	939096.	+	1.62656e6i	0.146900	+	0.254438i
$89$	−1.93441e6			−0.290859			−0.145430	−	0.989369i	$-0.546456\pi$
$89$	−1.93441e6			−0.290859			−0.145430	+	0.989369i	$0.546456\pi$
$90$		0			0
$91$	−3.64895e6			−0.507601
$92$	−3.99406e6	−	6.91792e6i	−0.534758	−	0.926229i
$93$		0			0
$94$	162702.	−	281808.i	0.0202044	−	0.0349950i
$95$	−264836.	+	458709.i	−0.0316916	+	0.0548914i
$96$		0			0
$97$	−4.94528e6	−	8.56548e6i	−0.550161	−	0.952907i	−0.998262	−	0.0589243i	$-0.981233\pi$
$97$	−4.94528e6	−	8.56548e6i	−0.550161	−	0.952907i	0.448101	−	0.893983i	$-0.352100\pi$
$98$	−729830.			−0.0783304
$99$		0			0
$100$	8.74178e6			0.874178
$101$	−1.81183e6	−	3.13819e6i	−0.174982	−	0.303078i	0.765173	−	0.643825i	$-0.222653\pi$
$101$	−1.81183e6	−	3.13819e6i	−0.174982	−	0.303078i	−0.940155	+	0.340747i	$0.889320\pi$
$102$		0			0
$103$	5.27077e6	−	9.12924e6i	0.475274	−	0.823198i	−0.524325	−	0.851518i	$-0.675682\pi$
$103$	5.27077e6	−	9.12924e6i	0.475274	−	0.823198i	0.999599	+	0.0283201i	$0.00901577\pi$
$104$	−1.31893e6	+	2.28446e6i	−0.114976	+	0.199144i
$105$		0			0
$106$	453962.	+	786286.i	0.0370211	+	0.0641224i
$107$	−3.02433e6			−0.238663			−0.119332	−	0.992854i	$-0.538075\pi$
$107$	−3.02433e6			−0.238663			−0.119332	+	0.992854i	$0.538075\pi$
$108$		0			0
$109$	−4.94116e6			−0.365457			−0.182728	−	0.983163i	$-0.558493\pi$
$109$	−4.94116e6			−0.365457			−0.182728	+	0.983163i	$0.558493\pi$
$110$	−353651.	−	612542.i	−0.0253338	−	0.0438795i
$111$		0			0
$112$	−3.01339e6	+	5.21934e6i	−0.202671	+	0.351037i
$113$	−5.13984e6	+	8.90247e6i	−0.335101	+	0.580412i	−0.983504	−	0.180885i	$-0.942104\pi$
$113$	−5.13984e6	+	8.90247e6i	−0.335101	+	0.580412i	0.648403	+	0.761297i	$0.275437\pi$
$114$		0			0
$115$	3.02186e6	+	5.23401e6i	0.185281	+	0.320916i
$116$	2.81895e7			1.67681
$117$		0			0
$118$	−1.70083e6			−0.0952958
$119$	4.05052e6	+	7.01570e6i	0.220341	+	0.381642i
$120$		0			0
$121$	−1.38772e7	+	2.40361e7i	−0.712122	+	1.23343i
$122$	1.20848e6	−	2.09315e6i	0.0602533	−	0.104362i
$123$		0			0
$124$	7.32295e6	+	1.26837e7i	0.344913	+	0.597408i
$125$	−1.41118e7			−0.646246
$126$		0			0
$127$	170541.			0.00738780			0.00369390	−	0.999993i	$-0.498824\pi$
$127$	170541.			0.00738780			0.00369390	+	0.999993i	$0.498824\pi$
$128$	4.39686e6	+	7.61558e6i	0.185314	+	0.320973i
$129$		0			0
$130$	496692.	−	860296.i	0.0198283	−	0.0343436i
$131$	1.15434e7	−	1.99938e7i	0.448626	−	0.777043i	−0.549671	−	0.835381i	$-0.685247\pi$
$131$	1.15434e7	−	1.99938e7i	0.448626	−	0.777043i	0.998297	+	0.0583382i	$0.0185802\pi$
$132$		0			0
$133$	−1.04308e6	−	1.80667e6i	−0.0384448	−	0.0665884i
$134$	3.24186e6			0.116393
$135$		0			0
$136$	5.85633e6			0.199636
$137$	2.05760e7	+	3.56387e7i	0.683659	+	1.18413i	0.973856	+	0.227166i	$0.0729458\pi$
$137$	2.05760e7	+	3.56387e7i	0.683659	+	1.18413i	−0.290197	+	0.956967i	$0.593721\pi$
$138$		0			0
$139$	1.33148e7	−	2.30619e7i	0.420517	−	0.728357i	−0.575473	−	0.817821i	$-0.695182\pi$
$139$	1.33148e7	−	2.30619e7i	0.420517	−	0.728357i	0.995990	+	0.0894641i	$0.0285154\pi$
$140$	2.30093e6	−	3.98534e6i	0.0708690	−	0.122749i
$141$		0			0
$142$	−2.36791e6	−	4.10134e6i	−0.0693995	−	0.120203i
$143$	−6.63495e7			−1.89741
$144$		0			0
$145$	−2.13278e7			−0.580975
$146$	−1.18742e6	−	2.05668e6i	−0.0315770	−	0.0546929i
$147$		0			0
$148$	5.18423e6	−	8.97934e6i	0.131452	−	0.227682i
$149$	1.71742e7	−	2.97466e7i	0.425329	−	0.736691i	−0.571122	−	0.820865i	$-0.693492\pi$
$149$	1.71742e7	−	2.97466e7i	0.425329	−	0.736691i	0.996451	+	0.0841739i	$0.0268251\pi$
$150$		0			0
$151$	−9.30390e6	−	1.61148e7i	−0.219910	−	0.380896i	0.734870	−	0.678208i	$-0.237243\pi$
$151$	−9.30390e6	−	1.61148e7i	−0.219910	−	0.380896i	−0.954780	+	0.297312i	$0.903910\pi$
$152$	−1.50811e6			−0.0348322
$153$		0			0
$154$	2.78578e6			0.0614646
$155$	−5.54045e6	−	9.59634e6i	−0.119504	−	0.206988i
$156$		0			0
$157$	2.30168e6	−	3.98662e6i	0.0474674	−	0.0822159i	−0.841316	−	0.540544i	$-0.818218\pi$
$157$	2.30168e6	−	3.98662e6i	0.0474674	−	0.0822159i	0.888783	+	0.458328i	$0.151552\pi$
$158$	−164933.	+	285672.i	−0.00332666	+	0.00576194i
$159$		0			0
$160$	−2.49881e6	−	4.32806e6i	−0.0482295	−	0.0835360i
$161$	−2.38038e7			−0.449527
$162$		0			0
$163$	5.47085e7			0.989460			0.494730	−	0.869047i	$-0.335267\pi$
$163$	5.47085e7			0.989460			0.494730	+	0.869047i	$0.335267\pi$
$164$	−3.78995e7	−	6.56438e7i	−0.670934	−	1.16209i
$165$		0			0
$166$	−1.69129e6	+	2.92941e6i	−0.0286973	+	0.0497052i
$167$	2.50438e7	−	4.33771e7i	0.416094	−	0.720697i	−0.579448	−	0.815009i	$-0.696732\pi$
$167$	2.50438e7	−	4.33771e7i	0.416094	−	0.720697i	0.995543	+	0.0943125i	$0.0300653\pi$
$168$		0			0
$169$	−1.52186e7	−	2.63595e7i	−0.242534	−	0.420081i
$170$	−2.20542e6			−0.0344286
$171$		0			0
$172$	−8.59390e6			−0.128778
$173$	4.50180e7	+	7.79735e7i	0.661036	+	1.14495i	0.980344	+	0.197297i	$0.0632163\pi$
$173$	4.50180e7	+	7.79735e7i	0.661036	+	1.14495i	−0.319308	+	0.947651i	$0.603450\pi$
$174$		0			0
$175$	1.30248e7	−	2.25596e7i	0.183712	−	0.318199i
$176$	−5.47930e7	+	9.49043e7i	−0.757584	+	1.31217i
$177$		0			0
$178$	1.03708e6	+	1.79627e6i	0.0137829	+	0.0238727i
$179$	5.97762e7			0.779009			0.389505	−	0.921025i	$-0.372646\pi$
$179$	5.97762e7			0.779009			0.389505	+	0.921025i	$0.372646\pi$
$180$		0			0
$181$	−8.54935e7			−1.07166			−0.535831	−	0.844325i	$-0.680002\pi$
$181$	−8.54935e7			−1.07166			−0.535831	+	0.844325i	$0.680002\pi$
$182$	1.95627e6	+	3.38837e6i	0.0240536	+	0.0416620i
$183$		0			0
$184$	−8.60401e6	+	1.49026e7i	−0.101821	+	0.176360i
$185$	−3.92232e6	+	6.79365e6i	−0.0455451	+	0.0788864i
$186$		0			0
$187$	7.36513e7	+	1.27568e8i	0.823635	+	1.42658i
$188$	3.84966e7			0.422542
$189$		0			0
$190$	567935.			0.00600705
$191$	−2.09938e6	−	3.63623e6i	−0.0218009	−	0.0377602i	0.854919	−	0.518761i	$-0.173607\pi$
$191$	−2.09938e6	−	3.63623e6i	−0.0218009	−	0.0377602i	−0.876720	+	0.481001i	$0.840273\pi$
$192$		0			0
$193$	−7.67221e7	+	1.32887e8i	−0.768192	+	1.33055i	0.170350	+	0.985384i	$0.445510\pi$
$193$	−7.67221e7	+	1.32887e8i	−0.768192	+	1.33055i	−0.938542	+	0.345164i	$0.887823\pi$
$194$	−5.30253e6	+	9.18425e6i	−0.0521407	+	0.0903104i
$195$		0			0
$196$	−4.31709e7	−	7.47741e7i	−0.409538	−	0.709341i
$197$	8.45478e7			0.787899			0.393949	−	0.919132i	$-0.371108\pi$
$197$	8.45478e7			0.787899			0.393949	+	0.919132i	$0.371108\pi$
$198$		0			0
$199$	1.53751e8			1.38303			0.691516	−	0.722361i	$-0.256943\pi$
$199$	1.53751e8			1.38303			0.691516	+	0.722361i	$0.256943\pi$
$200$	−9.41577e6	−	1.63086e7i	−0.0832244	−	0.144149i
$201$		0			0
$202$	−1.94272e6	+	3.36489e6i	−0.0165837	+	0.0287238i
$203$	4.20008e7	−	7.27475e7i	0.352388	−	0.610355i
$204$		0			0
$205$	2.86743e7	+	4.96653e7i	0.232463	+	0.402638i
$206$	−1.13031e7			−0.0900868
$207$		0			0
$208$	−1.53910e8			−1.18589
$209$	−1.89666e7	−	3.28510e7i	−0.143707	−	0.248907i
$210$		0			0
$211$	5.67421e7	−	9.82802e7i	0.415831	−	0.720240i	−0.579684	−	0.814841i	$-0.696824\pi$
$211$	5.67421e7	−	9.82802e7i	0.415831	−	0.720240i	0.995515	+	0.0946009i	$0.0301575\pi$
$212$	−5.37055e7	+	9.30207e7i	−0.387118	+	0.670508i
$213$		0			0
$214$	1.62140e6	+	2.80835e6i	0.0113095	+	0.0195886i
$215$	6.50203e6			0.0446185
$216$		0			0
$217$	4.36432e7			0.289940
$218$	2.64906e6	+	4.58830e6i	0.0173178	+	0.0299954i
$219$		0			0
$220$	4.18383e7	−	7.24661e7i	0.264908	−	0.458834i
$221$	−1.03441e8	+	1.79165e8i	−0.644644	+	1.11656i
$222$		0			0
$223$	−9.54225e7	−	1.65277e8i	−0.576214	−	0.998032i	−0.995909	−	0.0903663i	$-0.971196\pi$
$223$	−9.54225e7	−	1.65277e8i	−0.576214	−	0.998032i	0.419695	−	0.907665i	$-0.362137\pi$
$224$	1.96836e7			0.117014
$225$		0			0
$226$	1.10223e7			0.0635174
$227$	−1.22286e8	−	2.11805e8i	−0.693882	−	1.20184i	−0.970556	−	0.240875i	$-0.922566\pi$
$227$	−1.22286e8	−	2.11805e8i	−0.693882	−	1.20184i	0.276675	−	0.960964i	$-0.410768\pi$
$228$		0			0
$229$	2.38117e7	−	4.12431e7i	0.131029	−	0.226948i	−0.793045	−	0.609164i	$-0.791505\pi$
$229$	2.38117e7	−	4.12431e7i	0.131029	−	0.226948i	0.924073	+	0.382215i	$0.124839\pi$
$230$	3.24016e6	−	5.61212e6i	0.0175598	−	0.0304144i
$231$		0			0
$232$	−3.03629e7	−	5.25900e7i	−0.159637	−	0.276500i
$233$	−6.05168e7			−0.313423			−0.156711	−	0.987644i	$-0.550089\pi$
$233$	−6.05168e7			−0.313423			−0.156711	+	0.987644i	$0.550089\pi$
$234$		0			0
$235$	−2.91260e7			−0.146401
$236$	−1.00607e8	−	1.74257e8i	−0.498239	−	0.862975i
$237$		0			0
$238$	4.34313e6	−	7.52252e6i	0.0208825	−	0.0361696i
$239$	1.06061e8	−	1.83702e8i	0.502529	−	0.870406i	−0.497466	−	0.867483i	$-0.665736\pi$
$239$	1.06061e8	−	1.83702e8i	0.502529	−	0.870406i	0.999996	−	0.00292308i	$-0.000930445\pi$
$240$		0			0
$241$	6.29484e7	+	1.09030e8i	0.289684	+	0.501748i	0.973734	−	0.227687i	$-0.0731164\pi$
$241$	6.29484e7	+	1.09030e8i	0.289684	+	0.501748i	−0.684050	+	0.729435i	$0.739783\pi$
$242$	2.97595e7			0.134981
$243$		0			0
$244$	2.85936e8			1.26010
$245$	3.26625e7	+	5.65731e7i	0.141895	+	0.245770i
$246$		0			0
$247$	2.66380e7	−	4.61383e7i	0.112476	−	0.194815i
$248$	1.57751e7	−	2.73233e7i	0.0656737	−	0.113750i
$249$		0			0
$250$	7.56564e6	+	1.31041e7i	0.0306235	+	0.0530415i
$251$	2.31606e7			0.0924469			0.0462235	−	0.998931i	$-0.485281\pi$
$251$	2.31606e7			0.0924469			0.0462235	+	0.998931i	$0.485281\pi$
$252$		0			0
$253$	−4.32829e8			−1.68033
$254$	−91430.4	−	158362.i	−0.000350084	−	0.000606364i
$255$		0			0
$256$	−1.22324e8	+	2.11871e8i	−0.455692	+	0.789282i
$257$	−1.40821e8	+	2.43910e8i	−0.517491	+	0.896320i	0.482303	+	0.876005i	$0.339801\pi$
$257$	−1.40821e8	+	2.43910e8i	−0.517491	+	0.896320i	−0.999794	+	0.0203158i	$0.993533\pi$
$258$		0			0
$259$	−1.54485e7	−	2.67575e7i	−0.0552504	−	0.0956966i
$260$	1.17521e8			0.414677
$261$		0			0
$262$	−2.47546e7			−0.0850358
$263$	2.51766e8	+	4.36072e8i	0.853399	+	1.47813i	0.878123	+	0.478436i	$0.158796\pi$
$263$	2.51766e8	+	4.36072e8i	0.853399	+	1.47813i	−0.0247240	+	0.999694i	$0.507871\pi$
$264$		0			0
$265$	4.06329e7	−	7.03783e7i	0.134127	−	0.232315i
$266$	−1.11844e6	+	1.93719e6i	−0.00364355	+	0.00631082i
$267$		0			0
$268$	1.91763e8	+	3.32143e8i	0.608544	+	1.05403i
$269$	−2.46817e8			−0.773110			−0.386555	−	0.922266i	$-0.626335\pi$
$269$	−2.46817e8			−0.773110			−0.386555	+	0.922266i	$0.626335\pi$
$270$		0			0
$271$	2.60029e8			0.793651			0.396825	−	0.917894i	$-0.370112\pi$
$271$	2.60029e8			0.793651			0.396825	+	0.917894i	$0.370112\pi$
$272$	1.70848e8	+	2.95918e8i	0.514778	+	0.891621i
$273$		0			0
$274$	2.20625e7	−	3.82133e7i	0.0647928	−	0.112224i
$275$	2.36832e8	−	4.10205e8i	0.686715	−	1.18942i
$276$		0			0
$277$	−1.42327e8	−	2.46517e8i	−0.402353	−	0.696895i	0.591657	−	0.806190i	$-0.298474\pi$
$277$	−1.42327e8	−	2.46517e8i	−0.402353	−	0.696895i	−0.994009	+	0.109295i	$0.965141\pi$
$278$	−2.85534e7			−0.0797078
$279$		0			0
$280$	−9.91334e6			−0.0269878
$281$	1.46270e8	+	2.53346e8i	0.393262	+	0.681149i	0.992878	−	0.119139i	$-0.0380133\pi$
$281$	1.46270e8	+	2.53346e8i	0.393262	+	0.681149i	−0.599616	+	0.800288i	$0.704680\pi$
$282$		0			0
$283$	−3.07846e8	+	5.33204e8i	−0.807385	+	1.39843i	0.107284	+	0.994228i	$0.465785\pi$
$283$	−3.07846e8	+	5.33204e8i	−0.807385	+	1.39843i	−0.914669	+	0.404203i	$0.867549\pi$
$284$	2.80133e8	−	4.85205e8i	0.725689	−	1.25693i
$285$		0			0
$286$	3.55713e7	+	6.16113e7i	0.0899122	+	0.155733i
$287$	−2.25873e8			−0.563998
$288$		0			0
$289$	4.89606e7			0.119318
$290$	1.14343e7	+	1.98047e7i	0.0275306	+	0.0476843i
$291$		0			0
$292$	1.40477e8	−	2.43313e8i	0.330191	−	0.571907i
$293$	−1.37477e8	+	2.38117e8i	−0.319296	+	0.553036i	−0.980341	−	0.197309i	$-0.936780\pi$
$293$	−1.37477e8	+	2.38117e8i	−0.319296	+	0.553036i	0.661046	+	0.750346i	$0.270113\pi$
$294$		0			0
$295$	7.61182e7	+	1.31841e8i	0.172628	+	0.299001i
$296$	−2.23357e7			−0.0500586
$297$		0			0
$298$	−3.68298e7			−0.0806199
$299$	−3.03947e8	−	5.26452e8i	−0.657581	−	1.13896i
$300$		0			0
$301$	−1.28045e7	+	2.21780e7i	−0.0270632	+	0.0468748i
$302$	−9.97602e6	+	1.72790e7i	−0.0208417	+	0.0360989i
$303$		0			0
$304$	−4.39966e7	−	7.62043e7i	−0.0898176	−	0.155569i
$305$	−2.16336e8			−0.436595
$306$		0			0
$307$	−2.66850e8			−0.526361			−0.263180	−	0.964747i	$-0.584771\pi$
$307$	−2.66850e8			−0.526361			−0.263180	+	0.964747i	$0.584771\pi$
$308$	1.64785e8	+	2.85415e8i	0.321358	+	0.556608i
$309$		0			0
$310$	−5.94069e6	+	1.02896e7i	−0.0113259	+	0.0196170i
$311$	−1.48397e8	+	2.57031e8i	−0.279746	+	0.484535i	−0.971322	−	0.237770i	$-0.923584\pi$
$311$	−1.48397e8	+	2.57031e8i	−0.279746	+	0.484535i	0.691575	+	0.722304i	$0.256917\pi$
$312$		0			0
$313$	−2.91474e8	−	5.04847e8i	−0.537272	−	0.930582i	−0.999050	−	0.0435864i	$-0.986122\pi$
$313$	−2.91474e8	−	5.04847e8i	−0.537272	−	0.930582i	0.461778	−	0.886996i	$-0.347212\pi$
$314$	−4.93590e6			−0.00899731
$315$		0			0
$316$	−3.90245e7			−0.0695716
$317$	−2.38836e8	−	4.13677e8i	−0.421108	−	0.729380i	0.574940	−	0.818195i	$-0.305025\pi$
$317$	−2.38836e8	−	4.13677e8i	−0.421108	−	0.729380i	−0.996048	+	0.0888155i	$0.971692\pi$
$318$		0			0
$319$	7.63709e8	−	1.32278e9i	1.31723	−	2.28150i
$320$	9.52523e7	−	1.64982e8i	0.162499	−	0.281457i
$321$		0			0
$322$	1.27617e7	+	2.21039e7i	0.0213016	+	0.0368955i
$323$	−1.18278e8			−0.195297
$324$		0			0
$325$	6.65247e8			1.07496
$326$	−2.93303e7	−	5.08017e7i	−0.0468873	−	0.0812113i
$327$		0			0
$328$	−8.16431e7	+	1.41410e8i	−0.127750	+	0.221269i
$329$	5.73579e7	−	9.93468e7i	0.0887989	−	0.153804i
$330$		0			0
$331$	−2.57440e7	−	4.45899e7i	−0.0390192	−	0.0675832i	0.845856	−	0.533411i	$-0.179090\pi$
$331$	−2.57440e7	−	4.45899e7i	−0.0390192	−	0.0675832i	−0.884875	+	0.465828i	$0.845757\pi$
$332$	−4.00174e8			−0.600157
$333$		0			0
$334$	−5.37059e7			−0.0788695
$335$	−1.45085e8	−	2.51295e8i	−0.210846	−	0.365196i
$336$		0			0
$337$	−5.32165e8	+	9.21737e8i	−0.757428	+	1.31190i	0.186730	+	0.982411i	$0.440211\pi$
$337$	−5.32165e8	+	9.21737e8i	−0.757428	+	1.31190i	−0.944158	+	0.329493i	$0.893122\pi$
$338$	−1.63181e7	+	2.82637e7i	−0.0229858	+	0.0398126i
$339$		0			0
$340$	−1.30455e8	−	2.25954e8i	−0.180005	−	0.311777i
$341$	7.93573e8			1.08379
$342$		0			0
$343$	−5.68589e8			−0.760797
$344$	9.25649e6	+	1.60327e7i	0.0122600	+	0.0212350i
$345$		0			0
$346$	4.82702e7	−	8.36064e7i	0.0626488	−	0.108511i
$347$	−1.06766e8	+	1.84925e8i	−0.137177	+	0.237598i	−0.926427	−	0.376474i	$-0.877136\pi$
$347$	−1.06766e8	+	1.84925e8i	−0.137177	+	0.237598i	0.789250	+	0.614072i	$0.210470\pi$
$348$		0			0
$349$	6.11768e8	+	1.05961e9i	0.770367	+	1.33432i	0.937362	+	0.348357i	$0.113260\pi$
$349$	6.11768e8	+	1.05961e9i	0.770367	+	1.33432i	−0.166995	+	0.985958i	$0.553406\pi$
$350$	−2.79314e7			−0.0348221
$351$		0			0
$352$	3.57911e8			0.437397
$353$	2.42364e8	+	4.19787e8i	0.293263	+	0.507946i	0.974579	−	0.224043i	$-0.0719255\pi$
$353$	2.42364e8	+	4.19787e8i	0.293263	+	0.507946i	−0.681316	+	0.731989i	$0.738592\pi$
$354$		0			0
$355$	−2.11945e8	+	3.67100e8i	−0.251434	+	0.435497i
$356$	−1.22690e8	+	2.12506e8i	−0.144123	+	0.249629i
$357$		0			0
$358$	−3.20472e7	−	5.55074e7i	−0.0369147	−	0.0639382i
$359$	1.03710e9			1.18302			0.591510	−	0.806298i	$-0.298532\pi$
$359$	1.03710e9			1.18302			0.591510	+	0.806298i	$0.298532\pi$
$360$		0			0
$361$	−8.63413e8			−0.965925
$362$	4.58348e7	+	7.93882e7i	0.0507827	+	0.0879581i
$363$		0			0
$364$	−2.31435e8	+	4.00857e8i	−0.251521	+	0.435647i
$365$	−1.06283e8	+	1.84087e8i	−0.114403	+	0.198152i
$366$		0			0
$367$	2.17164e7	+	3.76140e7i	0.0229328	+	0.0397208i	0.877264	−	0.480008i	$-0.159366\pi$
$367$	2.17164e7	+	3.76140e7i	0.0229328	+	0.0397208i	−0.854331	+	0.519729i	$0.826033\pi$
$368$	−1.00403e9			−1.05022
$369$		0			0
$370$	8.41134e6			0.00863295
$371$	1.60037e8	+	2.77192e8i	0.162709	+	0.281820i
$372$		0			0
$373$	3.07699e8	−	5.32951e8i	0.307005	−	0.531749i	−0.670701	−	0.741728i	$-0.734006\pi$
$373$	3.07699e8	−	5.32951e8i	0.307005	−	0.531749i	0.977706	+	0.209980i	$0.0673398\pi$
$374$	7.89719e7	−	1.36783e8i	0.0780588	−	0.135202i
$375$		0			0
$376$	−4.14647e7	−	7.18190e7i	−0.0402273	−	0.0696757i
$377$	2.14521e9			2.06194
$378$		0			0
$379$	2.02795e9			1.91346			0.956732	−	0.290972i	$-0.0939785\pi$
$379$	2.02795e9			1.91346			0.956732	+	0.290972i	$0.0939785\pi$
$380$	3.35945e7	+	5.81873e7i	0.0314069	+	0.0543984i
$381$		0			0
$382$	−2.25104e6	+	3.89891e6i	−0.00206615	+	0.00357867i
$383$	−8.76819e8	+	1.51870e9i	−0.797470	+	1.38126i	0.123789	+	0.992309i	$0.460496\pi$
$383$	−8.76819e8	+	1.51870e9i	−0.797470	+	1.38126i	−0.921259	+	0.388950i	$0.872838\pi$
$384$		0			0
$385$	−1.24674e8	−	2.15941e8i	−0.111343	−	0.192852i
$386$	1.64529e8			0.145609
$387$		0			0
$388$	−1.25462e9			−1.09044
$389$	−9.95771e8	−	1.72473e9i	−0.857701	−	1.48558i	−0.874116	−	0.485716i	$-0.838559\pi$
$389$	−9.95771e8	−	1.72473e9i	−0.857701	−	1.48558i	0.0164155	−	0.999865i	$-0.494775\pi$
$390$		0			0
$391$	−6.74794e8	+	1.16878e9i	−0.570890	+	0.988811i
$392$	−9.29987e7	+	1.61078e8i	−0.0779786	+	0.135063i
$393$		0			0
$394$	−4.53278e7	−	7.85101e7i	−0.0373360	−	0.0646679i
$395$	2.95254e7			0.0241049
$396$		0			0
$397$	−6.38185e8			−0.511894			−0.255947	−	0.966691i	$-0.582387\pi$
$397$	−6.38185e8			−0.511894			−0.255947	+	0.966691i	$0.582387\pi$
$398$	−8.24290e7	−	1.42771e8i	−0.0655375	−	0.113514i
$399$		0			0
$400$	5.49378e8	−	9.51550e8i	0.429201	−	0.743399i
$401$	1.48115e8	−	2.56543e8i	0.114708	−	0.198681i	−0.802955	−	0.596040i	$-0.796740\pi$
$401$	1.48115e8	−	2.56543e8i	0.114708	−	0.198681i	0.917663	+	0.397359i	$0.130073\pi$
$402$		0			0
$403$	5.57275e8	+	9.65228e8i	0.424133	+	0.734619i
$404$	−4.59663e8			−0.346821
$405$		0			0
$406$	−9.00700e7			−0.0667942
$407$	−2.80902e8	−	4.86537e8i	−0.206526	−	0.357713i
$408$		0			0
$409$	6.35656e8	−	1.10099e9i	0.459399	−	0.795703i	−0.539530	−	0.841966i	$-0.681398\pi$
$409$	6.35656e8	−	1.10099e9i	0.459399	−	0.795703i	0.998929	+	0.0462633i	$0.0147313\pi$
$410$	3.07457e7	−	5.32531e7i	0.0220313	−	0.0381594i
$411$		0			0
$412$	−6.68599e8	−	1.15805e9i	−0.471005	−	0.815804i
$413$	−5.99599e8			−0.418828
$414$		0			0
$415$	3.02766e8			0.207940
$416$	2.51338e8	+	4.35330e8i	0.171171	+	0.296477i
$417$		0			0
$418$	−2.03367e7	+	3.52242e7i	−0.0136196	+	0.0235898i
$419$	7.61372e8	−	1.31874e9i	0.505648	−	0.875808i	−0.494331	−	0.869274i	$-0.664587\pi$
$419$	7.61372e8	−	1.31874e9i	0.505648	−	0.875808i	0.999979	−	0.00653376i	$-0.00207978\pi$
$420$		0			0
$421$	−3.38969e8	−	5.87112e8i	−0.221398	−	0.383472i	0.733835	−	0.679328i	$-0.237729\pi$
$421$	−3.38969e8	−	5.87112e8i	−0.221398	−	0.383472i	−0.955233	+	0.295856i	$0.904395\pi$
$422$	−1.21682e8			−0.0788196
$423$		0			0
$424$	2.31385e8			0.147419
$425$	−7.38459e8	−	1.27905e9i	−0.466622	−	0.808212i
$426$		0			0
$427$	4.26030e8	−	7.37906e8i	0.264815	−	0.458673i
$428$	−1.91818e8	+	3.32239e8i	−0.118260	+	0.204832i
$429$		0			0
$430$	−3.48587e6	−	6.03771e6i	−0.00211433	−	0.00366212i
$431$	−2.16495e9			−1.30250			−0.651249	−	0.758864i	$-0.725755\pi$
$431$	−2.16495e9			−1.30250			−0.651249	+	0.758864i	$0.725755\pi$
$432$		0			0
$433$	2.16892e9			1.28392			0.641958	−	0.766740i	$-0.278122\pi$
$433$	2.16892e9			1.28392			0.641958	+	0.766740i	$0.278122\pi$
$434$	−2.33980e7	−	4.05266e7i	−0.0137393	−	0.0237972i
$435$		0			0
$436$	−3.13394e8	+	5.42814e8i	−0.181087	+	0.313652i
$437$	1.73772e8	−	3.00982e8i	0.0996081	−	0.172526i
$438$		0			0
$439$	−1.15576e9	−	2.00183e9i	−0.651990	−	1.12928i	−0.982639	−	0.185526i	$-0.940601\pi$
$439$	−1.15576e9	−	2.00183e9i	−0.651990	−	1.12928i	0.330650	−	0.943754i	$-0.392732\pi$
$440$	−1.80256e8			−0.100880
$441$		0			0
$442$	2.21827e8			0.122190
$443$	1.62369e9	+	2.81231e9i	0.887340	+	1.53692i	0.843008	+	0.537901i	$0.180783\pi$
$443$	1.62369e9	+	2.81231e9i	0.887340	+	1.53692i	0.0443318	+	0.999017i	$0.485884\pi$
$444$		0			0
$445$	9.28257e7	−	1.60779e8i	0.0499354	−	0.0864906i
$446$	−1.02316e8	+	1.77216e8i	−0.0546099	+	0.0945870i
$447$		0			0
$448$	3.75161e8	+	6.49798e8i	0.197126	+	0.341433i
$449$	3.03696e8			0.158335			0.0791674	−	0.996861i	$-0.474774\pi$
$449$	3.03696e8			0.158335			0.0791674	+	0.996861i	$0.474774\pi$
$450$		0			0
$451$	−4.10709e9			−2.10822
$452$	6.51991e8	+	1.12928e9i	0.332091	+	0.575198i
$453$		0			0
$454$	−1.31120e8	+	2.27106e8i	−0.0657617	+	0.113903i
$455$	1.75101e8	−	3.03283e8i	0.0871461	−	0.150941i
$456$		0			0
$457$	1.78119e9	+	3.08512e9i	0.872981	+	1.51205i	0.858898	+	0.512146i	$0.171149\pi$
$457$	1.78119e9	+	3.08512e9i	0.872981	+	1.51205i	0.0140826	+	0.999901i	$0.495517\pi$
$458$	−5.10638e7			−0.0248361
$459$		0			0
$460$	7.66647e8			0.367234
$461$	2.75342e8	+	4.76906e8i	0.130894	+	0.226715i	0.924021	−	0.382341i	$-0.124882\pi$
$461$	2.75342e8	+	4.76906e8i	0.130894	+	0.226715i	−0.793128	+	0.609056i	$0.791549\pi$
$462$		0			0
$463$	−1.30055e9	+	2.25262e9i	−0.608966	+	1.05476i	0.382445	+	0.923978i	$0.375082\pi$
$463$	−1.30055e9	+	2.25262e9i	−0.608966	+	1.05476i	−0.991411	+	0.130782i	$0.958251\pi$
$464$	1.77157e9	−	3.06845e9i	0.823276	−	1.42596i
$465$		0			0
$466$	3.24443e7	+	5.61952e7i	0.0148521	+	0.0257246i
$467$	−1.05366e9			−0.478732			−0.239366	−	0.970929i	$-0.576940\pi$
$467$	−1.05366e9			−0.478732			−0.239366	+	0.970929i	$0.576940\pi$
$468$		0			0
$469$	1.14287e9			0.511552
$470$	1.56151e7	+	2.70461e7i	0.00693747	+	0.0120160i
$471$		0			0
$472$	−2.16728e8	+	3.75385e8i	−0.0948678	+	0.164316i
$473$	−2.32826e8	+	4.03267e8i	−0.101162	+	0.175218i
$474$		0			0
$475$	1.90167e8	+	3.29378e8i	0.0814154	+	0.141016i
$476$	1.02762e9			0.436724
$477$		0			0
$478$	−2.27445e8			−0.0952530
$479$	1.72916e9	+	2.99499e9i	0.718886	+	1.24515i	0.961442	+	0.275009i	$0.0886809\pi$
$479$	1.72916e9	+	2.99499e9i	0.718886	+	1.24515i	−0.242556	+	0.970137i	$0.577986\pi$
$480$		0			0
$481$	3.94519e8	−	6.83326e8i	0.161644	−	0.279976i
$482$	6.74958e7	−	1.16906e8i	0.0274544	−	0.0475524i
$483$		0			0
$484$	1.76033e9	+	3.04898e9i	0.705726	+	1.22235i
$485$	9.49230e8			0.377811
$486$		0			0
$487$	−1.34523e9			−0.527769			−0.263884	−	0.964554i	$-0.585004\pi$
$487$	−1.34523e9			−0.527769			−0.263884	+	0.964554i	$0.585004\pi$
$488$	−3.07982e8	−	5.33440e8i	−0.119965	−	0.207786i
$489$		0			0
$490$	3.50221e7	−	6.06600e7i	0.0134479	−	0.0232925i
$491$	−1.95921e8	+	3.39344e8i	−0.0746955	+	0.129376i	−0.900954	−	0.433915i	$-0.857132\pi$
$491$	−1.95921e8	+	3.39344e8i	−0.0746955	+	0.129376i	0.826258	+	0.563291i	$0.190465\pi$
$492$		0			0
$493$	−2.38129e9	−	4.12452e9i	−0.895053	−	1.55028i
$494$	−5.71246e7			−0.0213196
$495$		0			0
$496$	1.84085e9			0.677379
$497$	−8.34768e8	−	1.44586e9i	−0.305013	−	0.528298i
$498$		0			0
$499$	−5.33695e7	+	9.24386e7i	−0.0192283	+	0.0333044i	−0.875479	−	0.483255i	$-0.839454\pi$
$499$	−5.33695e7	+	9.24386e7i	−0.0192283	+	0.0333044i	0.856251	+	0.516560i	$0.172788\pi$
$500$	−8.95045e8	+	1.55026e9i	−0.320221	+	0.554639i
$501$		0			0
$502$	−1.24169e7	−	2.15067e7i	−0.00438076	−	0.00758771i
$503$	−1.35896e9			−0.476121			−0.238061	−	0.971250i	$-0.576512\pi$
$503$	−1.35896e9			−0.476121			−0.238061	+	0.971250i	$0.576512\pi$
$504$		0			0
$505$	3.47775e8			0.120165
$506$	2.32048e8	+	4.01919e8i	0.0796254	+	0.137915i
$507$		0			0
$508$	1.08166e7	−	1.87349e7i	0.00366072	−	0.00634056i
$509$	−5.33570e8	+	9.24170e8i	−0.179341	+	0.310627i	−0.941655	−	0.336580i	$-0.890730\pi$
$509$	−5.33570e8	+	9.24170e8i	−0.179341	+	0.310627i	0.762314	+	0.647207i	$0.224063\pi$
$510$		0			0
$511$	−4.18606e8	−	7.25047e8i	−0.138782	−	0.240377i
$512$	1.38792e9			0.457003
$513$		0			0
$514$	3.01989e8			0.0980889
$515$	5.05853e8	+	8.76163e8i	0.163192	+	0.282657i
$516$		0			0
$517$	1.04295e9	−	1.80644e9i	0.331930	−	0.574920i
$518$	−1.65645e7	+	2.86905e7i	−0.00523628	+	0.00906951i
$519$		0			0
$520$	−1.26582e8	−	2.19247e8i	−0.0394785	−	0.0683788i
$521$	−2.11037e9			−0.653774			−0.326887	−	0.945063i	$-0.606000\pi$
$521$	−2.11037e9			−0.653774			−0.326887	+	0.945063i	$0.606000\pi$
$522$		0			0
$523$	−3.37759e9			−1.03241			−0.516203	−	0.856466i	$-0.672655\pi$
$523$	−3.37759e9			−1.03241			−0.516203	+	0.856466i	$0.672655\pi$
$524$	−1.46428e9	−	2.53622e9i	−0.444597	−	0.770064i
$525$		0			0
$526$	2.69954e8	−	4.67574e8i	0.0808797	−	0.140088i
$527$	1.23721e9	−	2.14291e9i	0.368218	−	0.637773i
$528$		0			0
$529$	−2.80378e8	−	4.85629e8i	−0.0823473	−	0.142630i
$530$	−8.71365e7			−0.0254235
$531$		0			0
$532$	−2.64631e8			−0.0761990
$533$	−2.88414e9	−	4.99548e9i	−0.825033	−	1.42900i
$534$		0			0
$535$	1.45127e8	−	2.51368e8i	0.0409742	−	0.0709695i
$536$	4.13095e8	−	7.15502e8i	0.115871	−	0.200694i
$537$		0			0
$538$	1.32323e8	+	2.29191e8i	0.0366352	+	0.0634540i
$539$	−4.67834e9			−1.28686
$540$		0			0
$541$	5.69866e9			1.54733			0.773665	−	0.633595i	$-0.218422\pi$
$541$	5.69866e9			1.54733			0.773665	+	0.633595i	$0.218422\pi$
$542$	−1.39407e8	−	2.41460e8i	−0.0376086	−	0.0651400i
$543$		0			0
$544$	5.57995e8	−	9.66477e8i	0.148605	−	0.257392i
$545$	2.37110e8	−	4.10686e8i	0.0627424	−	0.108673i
$546$		0			0
$547$	3.90063e8	+	6.75609e8i	0.101901	+	0.176498i	0.912468	−	0.409148i	$-0.134174\pi$
$547$	3.90063e8	+	6.75609e8i	0.101901	+	0.176498i	−0.810567	+	0.585646i	$0.800841\pi$
$548$	5.22015e9			1.35504
$549$		0			0
$550$	−5.07882e8			−0.130165
$551$	6.13227e8	+	1.06214e9i	0.156168	+	0.270490i
$552$		0			0
$553$	−5.81444e7	+	1.00709e8i	−0.0146208	+	0.0253239i
$554$	−1.52608e8	+	2.64325e8i	−0.0381324	+	0.0660473i
$555$		0			0
$556$	−1.68899e9	−	2.92541e9i	−0.416740	−	0.721814i
$557$	−2.67894e8			−0.0656855			−0.0328428	−	0.999461i	$-0.510456\pi$
$557$	−2.67894e8			−0.0656855			−0.0328428	+	0.999461i	$0.510456\pi$
$558$		0			0
$559$	−6.53994e8			−0.158355
$560$	−2.89205e8	−	5.00917e8i	−0.0695901	−	0.120534i
$561$		0			0
$562$	1.56836e8	−	2.71648e8i	0.0372708	−	0.0645550i
$563$	−7.47380e8	+	1.29450e9i	−0.176507	+	0.305719i	−0.940682	−	0.339290i	$-0.889813\pi$
$563$	−7.47380e8	+	1.29450e9i	−0.176507	+	0.305719i	0.764175	+	0.645009i	$0.223146\pi$
$564$		0			0
$565$	−4.93288e8	−	8.54399e8i	−0.115062	−	0.199293i
$566$	6.60170e8			0.153038
$567$		0			0
$568$	−1.20693e9			−0.276351
$569$	1.46960e9	+	2.54543e9i	0.334431	+	0.579252i	0.983375	−	0.181584i	$-0.0581224\pi$
$569$	1.46960e9	+	2.54543e9i	0.334431	+	0.579252i	−0.648944	+	0.760836i	$0.724789\pi$
$570$		0			0
$571$	−5.10469e8	+	8.84159e8i	−0.114748	+	0.198749i	−0.917679	−	0.397323i	$-0.869939\pi$
$571$	−5.10469e8	+	8.84159e8i	−0.114748	+	0.198749i	0.802931	+	0.596072i	$0.203273\pi$
$572$	−4.20822e9	+	7.28886e9i	−0.940184	+	1.62845i
$573$		0			0
$574$	1.21095e8	+	2.09743e8i	0.0267261	+	0.0462909i
$575$	4.33972e9			0.951972
$576$		0			0
$577$	−1.38209e9			−0.299517			−0.149759	−	0.988723i	$-0.547850\pi$
$577$	−1.38209e9			−0.299517			−0.149759	+	0.988723i	$0.547850\pi$
$578$	−2.62488e7	−	4.54642e7i	−0.00565407	−	0.00979314i
$579$		0			0
$580$	−1.35272e9	+	2.34298e9i	−0.287878	+	0.498620i
$581$	−5.96238e8	+	1.03271e9i	−0.126126	+	0.218456i
$582$		0			0
$583$	2.90998e9	+	5.04023e9i	0.608205	+	1.05344i
$584$	−6.05230e8			−0.125741
$585$		0			0
$586$	2.94817e8			0.0605216
$587$	4.84184e8	+	8.38631e8i	0.0988045	+	0.171134i	0.911190	−	0.411986i	$-0.135165\pi$
$587$	4.84184e8	+	8.38631e8i	0.0988045	+	0.171134i	−0.812386	+	0.583121i	$0.801831\pi$
$588$		0			0
$589$	−3.18604e8	+	5.51838e8i	−0.0642461	+	0.111278i
$590$	8.16171e7	−	1.41365e8i	0.0163606	−	0.0283374i
$591$		0			0
$592$	−6.51606e8	−	1.12862e9i	−0.129080	−	0.223573i
$593$	9.04128e9			1.78049			0.890243	−	0.455487i	$-0.150535\pi$
$593$	9.04128e9			1.78049			0.890243	+	0.455487i	$0.150535\pi$
$594$		0			0
$595$	−7.77482e8			−0.151315
$596$	−2.17855e9	−	3.77337e9i	−0.421508	−	0.730074i
$597$		0			0
$598$	−3.25905e8	+	5.64484e8i	−0.0623213	+	0.107944i
$599$	1.01533e9	−	1.75860e9i	0.193025	−	0.334329i	−0.753226	−	0.657761i	$-0.771504\pi$
$599$	1.01533e9	−	1.75860e9i	0.193025	−	0.334329i	0.946251	+	0.323433i	$0.104837\pi$
$600$		0			0
$601$	4.82712e9	+	8.36082e9i	0.907043	+	1.57104i	0.818152	+	0.575003i	$0.194999\pi$
$601$	4.82712e9	+	8.36082e9i	0.907043	+	1.57104i	0.0888912	+	0.996041i	$0.471668\pi$
$602$	2.74589e7			0.00512975
$603$		0			0
$604$	−2.36040e9			−0.435870
$605$	−1.33184e9	−	2.30682e9i	−0.244517	−	0.423516i
$606$		0			0
$607$	−1.31611e9	+	2.27957e9i	−0.238854	+	0.413707i	−0.960386	−	0.278674i	$-0.910105\pi$
$607$	−1.31611e9	+	2.27957e9i	−0.238854	+	0.413707i	0.721532	+	0.692381i	$0.243438\pi$
$608$	−1.43694e8	+	2.48885e8i	−0.0259284	+	0.0449094i
$609$		0			0
$610$	1.15982e8	+	2.00887e8i	0.0206888	+	0.0358341i
$611$	2.92958e9			0.519591
$612$		0			0
$613$	2.08477e9			0.365549			0.182775	−	0.983155i	$-0.441492\pi$
$613$	2.08477e9			0.365549			0.182775	+	0.983155i	$0.441492\pi$
$614$	1.43064e8	+	2.47794e8i	0.0249425	+	0.0432018i
$615$		0			0
$616$	3.54979e8	−	6.14841e8i	0.0611885	−	0.105982i
$617$	−6.10199e8	+	1.05690e9i	−0.104586	+	0.181148i	−0.913569	−	0.406684i	$-0.866685\pi$
$617$	−6.10199e8	+	1.05690e9i	−0.104586	+	0.181148i	0.808983	+	0.587832i	$0.200018\pi$
$618$		0			0
$619$	−3.67056e9	−	6.35760e9i	−0.622036	−	1.07740i	−0.989106	−	0.147205i	$-0.952972\pi$
$619$	−3.67056e9	−	6.35760e9i	−0.622036	−	1.07740i	0.367070	−	0.930193i	$-0.380361\pi$
$620$	−1.40561e9			−0.236862
$621$		0			0
$622$	3.18235e8			0.0530251
$623$	3.65604e8	+	6.33244e8i	0.0605763	+	0.104921i
$624$		0			0
$625$	−2.01478e9	+	3.48970e9i	−0.330101	+	0.571752i
$626$	−3.12530e8	+	5.41318e8i	−0.0509192	+	0.0881946i
$627$		0			0
$628$	−2.91968e8	−	5.05704e8i	−0.0470410	−	0.0814774i
$629$	−1.75174e9			−0.280668
$630$		0			0
$631$	6.34065e9			1.00469			0.502344	−	0.864668i	$-0.332471\pi$
$631$	6.34065e9			1.00469			0.502344	+	0.864668i	$0.332471\pi$
$632$	4.20332e7	+	7.28037e7i	0.00662343	+	0.0114721i
$633$		0			0
$634$	−2.56090e8	+	4.43561e8i	−0.0399099	+	0.0691259i
$635$	−8.18368e6	+	1.41746e7i	−0.00126835	+	0.00219685i
$636$		0			0
$637$	−3.28529e9	−	5.69030e9i	−0.503601	−	0.872262i
$638$	−1.63776e9			−0.249677
$639$		0			0
$640$	−8.43962e8			−0.127260
$641$	2.49342e9	+	4.31873e9i	0.373932	+	0.647669i	0.990167	−	0.139894i	$-0.0446760\pi$
$641$	2.49342e9	+	4.31873e9i	0.373932	+	0.647669i	−0.616235	+	0.787563i	$0.711343\pi$
$642$		0			0
$643$	3.63643e9	−	6.29848e9i	0.539432	−	0.934324i	−0.459502	−	0.888176i	$-0.651972\pi$
$643$	3.63643e9	−	6.29848e9i	0.539432	−	0.934324i	0.998935	−	0.0461474i	$-0.0146944\pi$
$644$	−1.50976e9	+	2.61498e9i	−0.222744	+	0.385805i
$645$		0			0
$646$	6.34112e7	+	1.09831e8i	0.00925449	+	0.0160292i
$647$	−1.00709e10			−1.46185			−0.730927	−	0.682456i	$-0.760912\pi$
$647$	−1.00709e10			−1.46185			−0.730927	+	0.682456i	$0.760912\pi$
$648$		0			0
$649$	−1.09026e10			−1.56558
$650$	−3.56653e8	−	6.17741e8i	−0.0509388	−	0.0882286i
$651$		0			0
$652$	3.46990e9	−	6.01004e9i	0.490286	−	0.849201i
$653$	5.46146e9	−	9.45953e9i	0.767561	−	1.32945i	−0.171321	−	0.985215i	$-0.554804\pi$
$653$	5.46146e9	−	9.45953e9i	0.767561	−	1.32945i	0.938882	−	0.344239i	$-0.111863\pi$
$654$		0			0
$655$	1.10786e9	+	1.91887e9i	0.154042	+	0.266809i
$656$	−9.52719e9			−1.31765
$657$		0			0
$658$	−1.23003e8			−0.0168316
$659$	4.48446e9	+	7.76731e9i	0.610395	+	1.05724i	0.991174	+	0.132569i	$0.0423226\pi$
$659$	4.48446e9	+	7.76731e9i	0.610395	+	1.05724i	−0.380779	+	0.924666i	$0.624344\pi$
$660$		0			0
$661$	3.63575e9	−	6.29731e9i	0.489654	−	0.848106i	−0.510275	−	0.860011i	$-0.670456\pi$
$661$	3.63575e9	−	6.29731e9i	0.489654	−	0.848106i	0.999929	+	0.0119055i	$0.00378974\pi$
$662$	−2.76038e7	+	4.78111e7i	−0.00369799	+	0.00640510i
$663$		0			0
$664$	4.31027e8	+	7.46561e8i	0.0571368	+	0.0989639i
$665$	2.00216e8			0.0264012
$666$		0			0
$667$	1.39942e10			1.82603
$668$	−3.17681e9	−	5.50239e9i	−0.412357	−	0.714223i
$669$		0			0
$670$	−1.55566e8	+	2.69448e8i	−0.0199827	+	0.0346110i
$671$	7.74659e9	−	1.34175e10i	0.989878	−	1.71452i
$672$		0			0
$673$	−8.24962e8	−	1.42888e9i	−0.104323	−	0.180693i	0.809138	−	0.587618i	$-0.199934\pi$
$673$	−8.24962e8	−	1.42888e9i	−0.104323	−	0.180693i	−0.913462	+	0.406925i	$0.866601\pi$
$674$	1.14122e9			0.143568
$675$		0			0
$676$	−3.86098e9			−0.480711
$677$	−4.51758e9	−	7.82468e9i	−0.559559	−	0.969184i	−0.997533	−	0.0701969i	$-0.977637\pi$
$677$	−4.51758e9	−	7.82468e9i	−0.559559	−	0.969184i	0.437974	−	0.898988i	$-0.355696\pi$
$678$		0			0
$679$	−1.86932e9	+	3.23776e9i	−0.229160	+	0.396917i
$680$	−2.81025e8	+	4.86750e8i	−0.0342740	+	0.0593643i
$681$		0			0
$682$	−4.25451e8	−	7.36903e8i	−0.0513575	−	0.0889539i
$683$	−1.01503e10			−1.21901			−0.609507	−	0.792781i	$-0.708632\pi$
$683$	−1.01503e10			−1.21901			−0.609507	+	0.792781i	$0.708632\pi$
$684$		0			0
$685$	−3.94950e9			−0.469488
$686$	3.04832e8	+	5.27985e8i	0.0360518	+	0.0624435i
$687$		0			0
$688$	−5.40085e8	+	9.35454e8i	−0.0632270	+	0.109512i
$689$	−4.08698e9	+	7.07886e9i	−0.476031	+	0.824510i
$690$		0			0
$691$	−3.87489e8	−	6.71151e8i	−0.0446773	−	0.0773833i	0.842822	−	0.538192i	$-0.180893\pi$
$691$	−3.87489e8	−	6.71151e8i	−0.0446773	−	0.0773833i	−0.887499	+	0.460809i	$0.847559\pi$
$692$	1.14211e10			1.31020
$693$		0			0
$694$	2.28959e8			0.0260015
$695$	1.27787e9	+	2.21333e9i	0.144391	+	0.250092i
$696$		0			0
$697$	−6.40309e9	+	1.10905e10i	−0.716267	+	1.24061i
$698$	6.55963e8	−	1.13616e9i	0.0730105	−	0.126458i
$699$		0			0
$700$	−1.65220e9	−	2.86169e9i	−0.182062	−	0.315340i
$701$	8.19680e8			0.0898735			0.0449367	−	0.998990i	$-0.485691\pi$
$701$	8.19680e8			0.0898735			0.0449367	+	0.998990i	$0.485691\pi$
$702$		0			0
$703$	4.51106e8			0.0489705
$704$	6.82163e9	+	1.18154e10i	0.736858	+	1.27627i
$705$		0			0
$706$	2.59873e8	−	4.50113e8i	0.0277936	−	0.0481399i
$707$	−6.84874e8	+	1.18624e9i	−0.0728858	+	0.126242i
$708$		0			0
$709$	5.66193e9	+	9.80675e9i	0.596627	+	1.03339i	0.993315	+	0.115434i	$0.0368260\pi$
$709$	5.66193e9	+	9.80675e9i	0.596627	+	1.03339i	−0.396689	+	0.917953i	$0.629841\pi$
$710$	4.54512e8			0.0476586
$711$		0			0
$712$	5.28598e8			0.0548840
$713$	3.63537e9	+	6.29664e9i	0.375608	+	0.650572i
$714$		0			0
$715$	3.18389e9	−	5.51465e9i	0.325752	−	0.564218i
$716$	3.79131e9	−	6.56675e9i	0.386006	−	0.668582i
$717$		0			0
$718$	−5.56013e8	−	9.63042e8i	−0.0560595	−	0.0970979i
$719$	−9.90135e9			−0.993443			−0.496722	−	0.867910i	$-0.665463\pi$
$719$	−9.90135e9			−0.993443			−0.496722	+	0.867910i	$0.665463\pi$
$720$		0			0
$721$	−3.98471e9			−0.395934
$722$	4.62893e8	+	8.01755e8i	0.0457721	+	0.0792796i
$723$		0			0
$724$	−5.42244e9	+	9.39194e9i	−0.531018	+	0.919751i
$725$	−7.65726e9	+	1.32628e10i	−0.746261	+	1.29256i
$726$		0			0
$727$	−1.10550e9	−	1.91478e9i	−0.106706	−	0.184820i	0.807728	−	0.589555i	$-0.200697\pi$
$727$	−1.10550e9	−	1.91478e9i	−0.106706	−	0.184820i	−0.914434	+	0.404736i	$0.867364\pi$
$728$	9.97114e8			0.0957822
$729$		0			0
$730$	2.27922e8			0.0216848
$731$	7.25967e8	+	1.25741e9i	0.0687395	+	0.119060i
$732$		0			0
$733$	3.22097e9	−	5.57889e9i	0.302081	−	0.523219i	−0.674526	−	0.738251i	$-0.735652\pi$
$733$	3.22097e9	−	5.57889e9i	0.302081	−	0.523219i	0.976607	+	0.215032i	$0.0689854\pi$
$734$	2.32852e7	−	4.03312e7i	0.00217342	−	0.00376448i
$735$		0			0
$736$	1.63959e9	+	2.83986e9i	0.151588	+	0.262558i
$737$	2.07809e10			1.91218
$738$		0			0
$739$	−9.98230e8			−0.0909861			−0.0454931	−	0.998965i	$-0.514486\pi$
$739$	−9.98230e8			−0.0909861			−0.0454931	+	0.998965i	$0.514486\pi$
$740$	4.97547e8	+	8.61777e8i	0.0451360	+	0.0781779i
$741$		0			0
$742$	1.71598e8	−	2.97217e8i	0.0154205	−	0.0267091i
$743$	6.80423e9	−	1.17853e10i	0.608580	−	1.05409i	−0.382894	−	0.923792i	$-0.625073\pi$
$743$	6.80423e9	−	1.17853e10i	0.608580	−	1.05409i	0.991475	−	0.130300i	$-0.0415940\pi$
$744$		0			0
$745$	1.64826e9	+	2.85488e9i	0.146043	+	0.252953i
$746$	−6.59856e8			−0.0581920
$747$		0			0
$748$	1.86854e10			1.63247
$749$	5.71599e8	+	9.90038e8i	0.0497056	+	0.0860926i
$750$		0			0
$751$	−4.45214e9	+	7.71134e9i	−0.383556	+	0.664339i	−0.991568	−	0.129589i	$-0.958634\pi$
$751$	−4.45214e9	+	7.71134e9i	−0.383556	+	0.664339i	0.608011	+	0.793928i	$0.291967\pi$
$752$	2.41932e9	−	4.19039e9i	0.207459	−	0.359329i
$753$		0			0
$754$	−1.15009e9	−	1.99202e9i	−0.0977086	−	0.169236i
$755$	1.78585e9			0.151019
$756$		0			0
$757$	−1.43586e10			−1.20303			−0.601515	−	0.798862i	$-0.705436\pi$
$757$	−1.43586e10			−1.20303			−0.601515	+	0.798862i	$0.705436\pi$
$758$	−1.08723e9	−	1.88313e9i	−0.0906729	−	0.157050i
$759$		0			0
$760$	7.23692e7	−	1.25347e8i	0.00598007	−	0.0103578i
$761$	−7.73625e9	+	1.33996e10i	−0.636332	+	1.10216i	0.349899	+	0.936787i	$0.386216\pi$
$761$	−7.73625e9	+	1.33996e10i	−0.636332	+	1.10216i	−0.986231	+	0.165372i	$0.947117\pi$
$762$		0			0
$763$	9.33881e8	+	1.61753e9i	0.0761124	+	0.131831i
$764$	−5.32613e8			−0.0432101
$765$		0			0
$766$	1.88032e9			0.151158
$767$	−7.65620e9	−	1.32609e10i	−0.612674	−	1.06118i
$768$		0			0
$769$	−1.94877e9	+	3.37536e9i	−0.154532	+	0.267657i	−0.932888	−	0.360166i	$-0.882720\pi$
$769$	−1.94877e9	+	3.37536e9i	−0.154532	+	0.267657i	0.778357	+	0.627822i	$0.216054\pi$
$770$	−1.33680e8	+	2.31541e8i	−0.0105524	+	0.0182772i
$771$		0			0
$772$	9.73222e9	+	1.68567e10i	0.761292	+	1.31860i
$773$	−1.64518e10			−1.28110			−0.640552	−	0.767915i	$-0.721295\pi$
$773$	−1.64518e10			−1.28110			−0.640552	+	0.767915i	$0.721295\pi$
$774$		0			0
$775$	−7.95670e9			−0.614012
$776$	1.35135e9	+	2.34061e9i	0.103813	+	0.179810i
$777$		0			0
$778$	−1.06771e9	+	1.84932e9i	−0.0812874	+	0.140794i
$779$	1.64891e9	−	2.85600e9i	0.124973	−	0.216460i
$780$		0			0
$781$	−1.51787e10	−	2.62904e10i	−1.14014	−	1.97478i
$782$	1.44708e9			0.108211
$783$		0			0
$784$	−1.08523e10			−0.804296
$785$	2.20899e8	+	3.82609e8i	0.0162986	+	0.0282300i
$786$		0			0
$787$	6.77595e9	−	1.17363e10i	0.495517	−	0.858261i	−0.504469	−	0.863430i	$-0.668312\pi$
$787$	6.77595e9	−	1.17363e10i	0.495517	−	0.858261i	0.999987	+	0.00516849i	$0.00164519\pi$
$788$	5.36246e9	−	9.28805e9i	0.390411	−	0.676212i
$789$		0			0
$790$	−1.58292e7	−	2.74169e7i	−0.00114226	−	0.00197844i
$791$	3.88573e9			0.279161
$792$		0			0
$793$	2.17597e10			1.54952
$794$	3.42144e8	+	5.92611e8i	0.0242570	+	0.0420144i
$795$		0			0
$796$	9.75168e9	−	1.68904e10i	0.685305	−	1.18698i
$797$	−1.02025e10	+	1.76712e10i	−0.713841	+	1.23641i	0.249564	+	0.968358i	$0.419713\pi$
$797$	−1.02025e10	+	1.76712e10i	−0.713841	+	1.23641i	−0.963405	+	0.268051i	$0.913621\pi$
$798$		0			0
$799$	−3.25199e9	−	5.63261e9i	−0.225546	−	0.390657i
$800$	−3.58857e9			−0.247803
$801$		0			0
$802$	−3.17631e8			−0.0217426
$803$	−7.61160e9	−	1.31837e10i	−0.518766	−	0.898529i
$804$		0			0
$805$	1.14226e9	−	1.97846e9i	0.0771757	−	0.133672i
$806$	5.97533e8	−	1.03496e9i	0.0401966	−	0.0696225i
$807$		0			0
$808$	4.95103e8	+	8.57544e8i	0.0330184	+	0.0571895i
$809$	1.26810e9			0.0842039			0.0421020	−	0.999113i	$-0.486595\pi$
$809$	1.26810e9			0.0842039			0.0421020	+	0.999113i	$0.486595\pi$
$810$		0			0
$811$	−5.53400e9			−0.364306			−0.182153	−	0.983270i	$-0.558307\pi$
$811$	−5.53400e9			−0.364306			−0.182153	+	0.983270i	$0.558307\pi$
$812$	−5.32782e9	−	9.22805e9i	−0.349223	−	0.604872i
$813$		0			0
$814$	−3.01195e8	+	5.21685e8i	−0.0195732	+	0.0339018i
$815$	−2.62528e9	+	4.54711e9i	−0.169873	+	0.294228i
$816$		0			0
$817$	−1.86950e8	−	3.23807e8i	−0.0119936	−	0.0207734i
$818$	−1.36315e9			−0.0870779
$819$		0			0
$820$	7.27468e9			0.460750
$821$	−1.23545e10	−	2.13986e10i	−0.779156	−	1.34954i	−0.932429	−	0.361354i	$-0.882315\pi$
$821$	−1.23545e10	−	2.13986e10i	−0.779156	−	1.34954i	0.153273	−	0.988184i	$-0.451019\pi$
$822$		0			0
$823$	1.43656e10	−	2.48820e10i	0.898307	−	1.55591i	0.0686504	−	0.997641i	$-0.478131\pi$
$823$	1.43656e10	−	2.48820e10i	0.898307	−	1.55591i	0.829657	−	0.558273i	$-0.188536\pi$
$824$	−1.44029e9	+	2.49466e9i	−0.0896822	+	0.155334i
$825$		0			0
$826$	3.21457e8	+	5.56780e8i	0.0198469	+	0.0343759i
$827$	2.73341e10			1.68049			0.840244	−	0.542208i	$-0.182411\pi$
$827$	2.73341e10			1.68049			0.840244	+	0.542208i	$0.182411\pi$
$828$		0			0
$829$	−9.08667e9			−0.553942			−0.276971	−	0.960878i	$-0.589331\pi$
$829$	−9.08667e9			−0.553942			−0.276971	+	0.960878i	$0.589331\pi$
$830$	−1.62319e8	−	2.81145e8i	−0.00985363	−	0.0170670i
$831$		0			0
$832$	−9.58077e9	+	1.65944e10i	−0.576725	+	0.998917i
$833$	−7.29369e9	+	1.26330e10i	−0.437210	+	0.757269i
$834$		0			0
$835$	2.40353e9	+	4.16304e9i	0.142872	+	0.247462i
$836$	−4.81183e9			−0.284832
$837$		0			0
$838$	−1.63275e9			−0.0958441
$839$	5.28596e9	+	9.15555e9i	0.308999	+	0.535202i	0.978144	−	0.207930i	$-0.0666727\pi$
$839$	5.28596e9	+	9.15555e9i	0.308999	+	0.535202i	−0.669145	+	0.743132i	$0.733339\pi$
$840$		0			0
$841$	−1.60673e10	+	2.78294e10i	−0.931445	+	1.61331i
$842$	−3.63457e8	+	6.29526e8i	−0.0209827	+	0.0363430i
$843$		0			0
$844$	−7.19775e9	−	1.24669e10i	−0.412096	−	0.713771i
$845$	2.92117e9			0.166555
$846$		0			0
$847$	1.04912e10			0.593244
$848$	6.75026e9	+	1.16918e10i	0.380132	+	0.658409i
$849$		0			0
$850$	−7.91805e8	+	1.37145e9i	−0.0442234	+	0.0765972i
$851$	2.57363e9	−	4.45766e9i	0.143150	−	0.247944i
$852$		0			0
$853$	6.77091e9	+	1.17276e10i	0.373530	+	0.646973i	0.990106	−	0.140322i	$-0.0448139\pi$
$853$	6.77091e9	+	1.17276e10i	0.373530	+	0.646973i	−0.616576	+	0.787296i	$0.711481\pi$
$854$	−9.13614e8			−0.0501950
$855$		0			0
$856$	8.26431e8			0.0450348
$857$	−3.88750e9	−	6.73335e9i	−0.210978	−	0.365425i	0.741043	−	0.671458i	$-0.234332\pi$
$857$	−3.88750e9	−	6.73335e9i	−0.210978	−	0.365425i	−0.952021	+	0.306033i	$0.900998\pi$
$858$		0			0
$859$	−1.34575e10	+	2.33091e10i	−0.724418	+	1.25473i	0.234796	+	0.972045i	$0.424558\pi$
$859$	−1.34575e10	+	2.33091e10i	−0.724418	+	1.25473i	−0.959213	+	0.282683i	$0.908775\pi$
$860$	4.12393e8	−	7.14285e8i	0.0221089	−	0.0382937i
$861$		0			0
$862$	1.16067e9	+	2.01034e9i	0.0617212	+	0.106904i
$863$	1.15462e10			0.611509			0.305754	−	0.952110i	$-0.401091\pi$
$863$	1.15462e10			0.611509			0.305754	+	0.952110i	$0.401091\pi$
$864$		0			0
$865$	−8.64106e9			−0.453952
$866$	−1.16280e9	−	2.01404e9i	−0.0608407	−	0.105379i
$867$		0			0
$868$	2.76808e9	−	4.79445e9i	0.143668	−	0.248840i
$869$	−1.05725e9	+	1.83121e9i	−0.0546523	+	0.0946606i
$870$		0			0
$871$	1.45931e10	+	2.52760e10i	0.748314	+	1.29612i
$872$	1.35023e9			0.0689602
$873$		0			0
$874$	−3.72651e8			−0.0188804
$875$	2.66714e9	+	4.61962e9i	0.134591	+	0.233119i
$876$		0			0
$877$	1.33604e10	−	2.31409e10i	0.668839	−	1.15846i	−0.309390	−	0.950935i	$-0.600125\pi$
$877$	1.33604e10	−	2.31409e10i	0.668839	−	1.15846i	0.978229	−	0.207528i	$-0.0665418\pi$
$878$	−1.23925e9	+	2.14644e9i	−0.0617914	+	0.107026i
$879$		0			0
$880$	−5.25867e9	−	9.10828e9i	−0.260128	−	0.450554i
$881$	2.97092e10			1.46378			0.731890	−	0.681423i	$-0.238639\pi$
$881$	2.97092e10			1.46378			0.731890	+	0.681423i	$0.238639\pi$
$882$		0			0
$883$	7.34350e9			0.358956			0.179478	−	0.983762i	$-0.442559\pi$
$883$	7.34350e9			0.358956			0.179478	+	0.983762i	$0.442559\pi$
$884$	1.31215e10	+	2.27271e10i	0.638854	+	1.10653i
$885$		0			0
$886$	1.74099e9	−	3.01548e9i	0.0840964	−	0.145659i
$887$	−2.72475e9	+	4.71940e9i	−0.131097	+	0.227067i	−0.924100	−	0.382151i	$-0.875183\pi$
$887$	−2.72475e9	+	4.71940e9i	−0.131097	+	0.227067i	0.793003	+	0.609218i	$0.208517\pi$
$888$		0			0
$889$	−3.22323e7	−	5.58279e7i	−0.00153863	−	0.00266499i
$890$	−1.99063e8			−0.00946511
$891$		0			0
$892$	−2.42087e10			−1.14208
$893$	8.37446e8	+	1.45050e9i	0.0393529	+	0.0681613i
$894$		0			0
$895$	−2.86846e9	+	4.96831e9i	−0.133742	+	0.231648i
$896$	1.66202e9	−	2.87870e9i	0.0771893	−	0.133696i
$897$		0			0
$898$	−1.62817e8	−	2.82008e8i	−0.00750298	−	0.0129955i
$899$	−2.56578e10			−1.17777
$900$		0			0
$901$	1.81470e10			0.826549
$902$	2.20190e9	+	3.81380e9i	0.0999019	+	0.173035i
$903$		0			0
$904$	1.40452e9	−	2.43270e9i	0.0632321	−	0.109521i
$905$	4.10255e9	−	7.10582e9i	0.183985	−	0.318672i
$906$		0			0
$907$	−6.64670e8	−	1.15124e9i	−0.0295788	−	0.0512320i	0.850857	−	0.525397i	$-0.176083\pi$
$907$	−6.64670e8	−	1.15124e9i	−0.0295788	−	0.0512320i	−0.880436	+	0.474165i	$0.842750\pi$
$908$	−3.10240e10			−1.37530
$909$		0			0
$910$	−3.75500e8			−0.0165183
$911$	6.94966e9	+	1.20372e10i	0.304543	+	0.527484i	0.977160	−	0.212507i	$-0.0681628\pi$
$911$	6.94966e9	+	1.20372e10i	0.304543	+	0.527484i	−0.672616	+	0.739991i	$0.734830\pi$
$912$		0			0
$913$	−1.08415e10	+	1.87780e10i	−0.471457	+	0.816587i
$914$	1.90987e9	−	3.30799e9i	0.0827355	−	0.143302i
$915$		0			0
$916$	−3.02052e9	−	5.23170e9i	−0.129852	−	0.224910i
$917$	−8.72683e9			−0.373735
$918$		0			0
$919$	5.44634e9			0.231473			0.115737	−	0.993280i	$-0.463077\pi$
$919$	5.44634e9			0.231473			0.115737	+	0.993280i	$0.463077\pi$
$920$	−8.25755e8	−	1.43025e9i	−0.0349618	−	0.0605556i
$921$		0			0
$922$	2.95233e8	−	5.11358e8i	0.0124053	−	0.0214866i
$923$	2.13181e10	−	3.69240e10i	0.892364	−	1.54562i
$924$		0			0
$925$	2.81644e9	+	4.87822e9i	0.117005	+	0.202659i
$926$	2.78900e9			0.115428
$927$		0			0
$928$	−1.15720e10			−0.475324
$929$	1.13507e10	+	1.96600e10i	0.464481	+	0.804505i	0.999178	−	0.0405392i	$-0.0129076\pi$
$929$	1.13507e10	+	1.96600e10i	0.464481	+	0.804505i	−0.534697	+	0.845044i	$0.679574\pi$
$930$		0			0
$931$	1.87826e9	−	3.25324e9i	0.0762837	−	0.132127i
$932$	−3.83829e9	+	6.64811e9i	−0.155304	+	0.268994i
$933$		0			0
$934$	5.64889e8	+	9.78417e8i	0.0226856	+	0.0392925i
$935$	−1.41371e10			−0.565614
$936$		0			0
$937$	5.57763e9			0.221494			0.110747	−	0.993849i	$-0.464676\pi$
$937$	5.57763e9			0.221494			0.110747	+	0.993849i	$0.464676\pi$
$938$	−6.12713e8	−	1.06125e9i	−0.0242408	−	0.0419863i
$939$		0			0
$940$	−1.84732e9	+	3.19966e9i	−0.0725430	+	0.125648i
$941$	6.72015e9	−	1.16396e10i	0.262915	−	0.455382i	−0.704100	−	0.710100i	$-0.748650\pi$
$941$	6.72015e9	−	1.16396e10i	0.262915	−	0.455382i	0.967015	+	0.254719i	$0.0819828\pi$
$942$		0			0
$943$	−1.88146e10	−	3.25879e10i	−0.730642	−	1.26551i
$944$	−2.52907e10			−0.978496
$945$		0			0
$946$	4.99291e8			0.0191750
$947$	−1.11328e10	−	1.92826e10i	−0.425971	−	0.737804i	0.570539	−	0.821270i	$-0.306734\pi$
$947$	−1.11328e10	−	1.92826e10i	−0.425971	−	0.737804i	−0.996511	+	0.0834662i	$0.973401\pi$
$948$		0			0
$949$	1.06903e10	−	1.85161e10i	0.406028	−	0.703262i
$950$	2.03904e8	−	3.53173e8i	0.00771603	−	0.0133646i
$951$		0			0
$952$	−1.10685e9	−	1.91712e9i	−0.0415775	−	0.0720144i
$953$	1.10753e9			0.0414506			0.0207253	−	0.999785i	$-0.493402\pi$
$953$	1.10753e9			0.0414506			0.0207253	+	0.999785i	$0.493402\pi$
$954$		0			0
$955$	4.02968e8			0.0149713
$956$	−1.34538e10	−	2.33027e10i	−0.498016	−	0.862588i
$957$		0			0
$958$	1.85407e9	−	3.21135e9i	0.0681314	−	0.118007i
$959$	7.77775e9	−	1.34715e10i	0.284767	−	0.493230i
$960$		0			0
$961$	7.09102e9	+	1.22820e10i	0.257737	+	0.446413i
$962$	−8.46038e8			−0.0306392
$963$		0			0
$964$	1.59700e10			0.574165
$965$	−7.36327e9	−	1.27536e10i	−0.263770	−	0.456863i
$966$		0			0
$967$	1.23923e10	−	2.14641e10i	0.440717	−	0.763344i	−0.557026	−	0.830495i	$-0.688058\pi$
$967$	1.23923e10	−	2.14641e10i	0.440717	−	0.763344i	0.997743	+	0.0671509i	$0.0213909\pi$
$968$	3.79211e9	−	6.56812e9i	0.134374	−	0.232743i
$969$		0			0
$970$	−5.08901e8	−	8.81443e8i	−0.0179033	−	0.0310094i
$971$	−4.78327e9			−0.167671			−0.0838354	−	0.996480i	$-0.526717\pi$
$971$	−4.78327e9			−0.167671			−0.0838354	+	0.996480i	$0.526717\pi$
$972$		0			0
$973$	−1.00660e10			−0.350318
$974$	7.21203e8	+	1.24916e9i	0.0250093	+	0.0433173i
$975$		0			0
$976$	1.79697e10	−	3.11244e10i	0.618680	−	1.07159i
$977$	−1.70856e10	+	2.95931e10i	−0.586136	+	1.01522i	0.408596	+	0.912715i	$0.366018\pi$
$977$	−1.70856e10	+	2.95931e10i	−0.586136	+	1.01522i	−0.994733	+	0.102503i	$0.967315\pi$
$978$		0			0
$979$	6.64784e9	+	1.15144e10i	0.226434	+	0.392195i
$980$	8.28650e9			0.281242
$981$		0			0
$982$	4.20148e8			0.0141583
$983$	1.45430e10	+	2.51892e10i	0.488334	+	0.845820i	0.999910	−	0.0134184i	$-0.00427135\pi$
$983$	1.45430e10	+	2.51892e10i	0.488334	+	0.845820i	−0.511576	+	0.859238i	$0.670938\pi$
$984$		0			0
$985$	−4.05716e9	+	7.02721e9i	−0.135268	+	0.234291i
$986$	−2.55332e9	+	4.42248e9i	−0.0848274	+	0.146925i
$987$		0			0
$988$	−3.37903e9	−	5.85266e9i	−0.111466	−	0.193065i
$989$	−4.26631e9			−0.140238
$990$		0			0
$991$	4.02625e9			0.131415			0.0657073	−	0.997839i	$-0.479070\pi$
$991$	4.02625e9			0.131415			0.0657073	+	0.997839i	$0.479070\pi$
$992$	−3.00613e9	−	5.20677e9i	−0.0977725	−	0.169347i
$993$		0			0
$994$	−8.95072e8	+	1.55031e9i	−0.0289072	+	0.0500687i
$995$	−7.37799e9	+	1.27791e10i	−0.237442	+	0.411262i
$996$		0			0
$997$	−1.99806e10	−	3.46074e10i	−0.638522	−	1.10595i	−0.985757	−	0.168174i	$-0.946213\pi$
$997$	−1.99806e10	−	3.46074e10i	−0.638522	−	1.10595i	0.347235	−	0.937778i	$-0.387120\pi$
$998$	1.14450e8			0.00364467
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.8.c.a.10.3		12
3.2	odd	2		9.8.c.a.4.4	✓	12
4.3	odd	2		432.8.i.c.145.3		12
9.2	odd	6		9.8.c.a.7.4	yes	12
9.4	even	3		81.8.a.c.1.4		6
9.5	odd	6		81.8.a.e.1.3		6
9.7	even	3	inner	27.8.c.a.19.3		12
12.11	even	2		144.8.i.c.49.4		12
36.7	odd	6		432.8.i.c.289.3		12
36.11	even	6		144.8.i.c.97.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.8.c.a.4.4	✓	12	3.2	odd	2
9.8.c.a.7.4	yes	12	9.2	odd	6
27.8.c.a.10.3		12	1.1	even	1	trivial
27.8.c.a.19.3		12	9.7	even	3	inner
81.8.a.c.1.4		6	9.4	even	3
81.8.a.e.1.3		6	9.5	odd	6
144.8.i.c.49.4		12	12.11	even	2
144.8.i.c.97.4		12	36.11	even	6
432.8.i.c.145.3		12	4.3	odd	2
432.8.i.c.289.3		12	36.7	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	27.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.536120 - 0.928588i) q^{2} +(63.4251 - 109.856i) q^{4} +(-47.9866 + 83.1153i) q^{5} +(-189.000 - 327.358i) q^{7} -273.261 q^{8} +O(q^{10})\)	\(q+(-0.536120 - 0.928588i) q^{2} +(63.4251 - 109.856i) q^{4} +(-47.9866 + 83.1153i) q^{5} +(-189.000 - 327.358i) q^{7} -273.261 q^{8} +102.906 q^{10} +(-3436.63 - 5952.41i) q^{11} +(4826.64 - 8359.99i) q^{13} +(-202.654 + 351.007i) q^{14} +(-7971.92 - 13807.8i) q^{16} -21431.3 q^{17} +5518.94 q^{19} +(6087.12 + 10543.2i) q^{20} +(-3684.89 + 6382.42i) q^{22} +(31486.4 - 54536.1i) q^{23} +(34457.1 + 59681.4i) q^{25} -10350.6 q^{26} -47949.5 q^{28} +(111113. + 192454. i) q^{29} +(-57729.1 + 99989.7i) q^{31} +(-26036.5 + 45096.6i) q^{32} +(11489.7 + 19900.8i) q^{34} +36277.9 q^{35} +81737.7 q^{37} +(-2958.82 - 5124.82i) q^{38} +(13112.9 - 22712.2i) q^{40} +(298773. - 517491. i) q^{41} +(-33874.2 - 58671.8i) q^{43} -871875. q^{44} -67522.1 q^{46} +(151740. + 262822. i) q^{47} +(340329. - 589468. i) q^{49} +(36946.3 - 63992.8i) q^{50} +(-612261. - 1.06047e6i) q^{52} -846755. q^{53} +659649. q^{55} +(51646.4 + 89454.2i) q^{56} +(119140. - 206357. i) q^{58} +(793119. - 1.37372e6i) q^{59} +(1.12706e6 + 1.95213e6i) q^{61} +123799. q^{62} -1.98498e6 q^{64} +(463228. + 802335. i) q^{65} +(-1.51172e6 + 2.61838e6i) q^{67} +(-1.35928e6 + 2.35434e6i) q^{68} +(-19449.3 - 33687.3i) q^{70} +4.41675e6 q^{71} +2.21484e6 q^{73} +(-43821.3 - 75900.6i) q^{74} +(350040. - 606287. i) q^{76} +(-1.29905e6 + 2.25002e6i) q^{77} +(-153821. - 266426. i) q^{79} +1.53018e6 q^{80} -640714. q^{82} +(-1.57735e6 - 2.73204e6i) q^{83} +(1.02841e6 - 1.78127e6i) q^{85} +(-36321.3 + 62910.3i) q^{86} +(939096. + 1.62656e6i) q^{88} -1.93441e6 q^{89} -3.64895e6 q^{91} +(-3.99406e6 - 6.91792e6i) q^{92} +(162702. - 281808. i) q^{94} +(-264836. + 458709. i) q^{95} +(-4.94528e6 - 8.56548e6i) q^{97} -729830. q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 9 q^{2} - 321 q^{4} + 180 q^{5} - 84 q^{7} - 5922 q^{8}+O(q^{10}) \) 12 * q + 9 * q^2 - 321 * q^4 + 180 * q^5 - 84 * q^7 - 5922 * q^8	\( 12 q + 9 q^{2} - 321 q^{4} + 180 q^{5} - 84 q^{7} - 5922 q^{8} + 252 q^{10} + 8460 q^{11} - 1848 q^{13} + 16272 q^{14} - 12417 q^{16} - 30564 q^{17} + 24432 q^{19} + 40788 q^{20} - 35001 q^{22} + 51588 q^{23} + 4746 q^{25} - 536472 q^{26} + 75516 q^{28} + 414648 q^{29} + 8196 q^{31} + 1048977 q^{32} - 106623 q^{34} - 2210616 q^{35} + 139344 q^{37} + 1952685 q^{38} + 305496 q^{40} + 1731582 q^{41} + 408372 q^{43} - 5169114 q^{44} - 1684008 q^{46} + 1631484 q^{47} - 179010 q^{49} + 1654461 q^{50} + 681594 q^{52} - 2835648 q^{53} - 16056 q^{55} + 1784466 q^{56} - 948384 q^{58} + 2055636 q^{59} - 2723196 q^{61} + 1026828 q^{62} + 7178178 q^{64} + 1387620 q^{65} + 3806556 q^{67} - 2142639 q^{68} + 953442 q^{70} - 2408400 q^{71} - 10670052 q^{73} - 9846504 q^{74} - 6727827 q^{76} - 3478824 q^{77} + 6020916 q^{79} + 38072448 q^{80} + 9403002 q^{82} - 9605052 q^{83} - 1698624 q^{85} - 34278561 q^{86} - 16459029 q^{88} + 24630264 q^{89} + 13570104 q^{91} - 39143394 q^{92} + 12602808 q^{94} - 10422072 q^{95} + 9977226 q^{97} + 95833314 q^{98}+O(q^{100}) \) 12 * q + 9 * q^2 - 321 * q^4 + 180 * q^5 - 84 * q^7 - 5922 * q^8 + 252 * q^10 + 8460 * q^11 - 1848 * q^13 + 16272 * q^14 - 12417 * q^16 - 30564 * q^17 + 24432 * q^19 + 40788 * q^20 - 35001 * q^22 + 51588 * q^23 + 4746 * q^25 - 536472 * q^26 + 75516 * q^28 + 414648 * q^29 + 8196 * q^31 + 1048977 * q^32 - 106623 * q^34 - 2210616 * q^35 + 139344 * q^37 + 1952685 * q^38 + 305496 * q^40 + 1731582 * q^41 + 408372 * q^43 - 5169114 * q^44 - 1684008 * q^46 + 1631484 * q^47 - 179010 * q^49 + 1654461 * q^50 + 681594 * q^52 - 2835648 * q^53 - 16056 * q^55 + 1784466 * q^56 - 948384 * q^58 + 2055636 * q^59 - 2723196 * q^61 + 1026828 * q^62 + 7178178 * q^64 + 1387620 * q^65 + 3806556 * q^67 - 2142639 * q^68 + 953442 * q^70 - 2408400 * q^71 - 10670052 * q^73 - 9846504 * q^74 - 6727827 * q^76 - 3478824 * q^77 + 6020916 * q^79 + 38072448 * q^80 + 9403002 * q^82 - 9605052 * q^83 - 1698624 * q^85 - 34278561 * q^86 - 16459029 * q^88 + 24630264 * q^89 + 13570104 * q^91 - 39143394 * q^92 + 12602808 * q^94 - 10422072 * q^95 + 9977226 * q^97 + 95833314 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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