LMFDB - Embedded newform 342.10.a.l.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,10,Mod(1,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

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

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

chi := DirichletCharacter("342.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	342.a (trivial)

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:	yes
Analytic conductor:	$176.142255968$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 34433x^{2} - 2723303x - 48270488 $ x^4 - x^3 - 34433x^2 - 2723303x - 48270488
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 38)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-67.1081$ of defining polynomial
Character	$\chi$	$=$	342.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+16.0000 q^{2} +256.000 q^{4} +2367.11 q^{5} +5859.40 q^{7} +4096.00 q^{8} +O(q^{10})$	\(q+16.0000 q^{2} +256.000 q^{4} +2367.11 q^{5} +5859.40 q^{7} +4096.00 q^{8} +37873.7 q^{10} +38743.9 q^{11} +179439. q^{13} +93750.4 q^{14} +65536.0 q^{16} -184492. q^{17} +130321. q^{19} +605979. q^{20} +619902. q^{22} +115333. q^{23} +3.65006e6 q^{25} +2.87102e6 q^{26} +1.50001e6 q^{28} -569755. q^{29} +5.80788e6 q^{31} +1.04858e6 q^{32} -2.95187e6 q^{34} +1.38698e7 q^{35} +3.15312e6 q^{37} +2.08514e6 q^{38} +9.69566e6 q^{40} -54772.2 q^{41} -1.63249e7 q^{43} +9.91844e6 q^{44} +1.84533e6 q^{46} -2.84428e7 q^{47} -6.02101e6 q^{49} +5.84010e7 q^{50} +4.59363e7 q^{52} -7.33201e7 q^{53} +9.17109e7 q^{55} +2.40001e7 q^{56} -9.11608e6 q^{58} +1.45518e7 q^{59} +9.96035e7 q^{61} +9.29260e7 q^{62} +1.67772e7 q^{64} +4.24751e8 q^{65} -2.49050e8 q^{67} -4.72299e7 q^{68} +2.21917e8 q^{70} +1.33230e8 q^{71} -2.28114e8 q^{73} +5.04499e7 q^{74} +3.33622e7 q^{76} +2.27016e8 q^{77} -6.65788e8 q^{79} +1.55131e8 q^{80} -876356. q^{82} +3.48852e8 q^{83} -4.36712e8 q^{85} -2.61199e8 q^{86} +1.58695e8 q^{88} -2.61939e8 q^{89} +1.05140e9 q^{91} +2.95252e7 q^{92} -4.55084e8 q^{94} +3.08484e8 q^{95} -1.10091e9 q^{97} -9.63361e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 64 q^{2} + 1024 q^{4} + 1395 q^{5} + 12307 q^{7} + 16384 q^{8}+O(q^{10}) $ 4 * q + 64 * q^2 + 1024 * q^4 + 1395 * q^5 + 12307 * q^7 + 16384 * q^8	\( 4 q + 64 q^{2} + 1024 q^{4} + 1395 q^{5} + 12307 q^{7} + 16384 q^{8} + 22320 q^{10} + 104249 q^{11} + 120486 q^{13} + 196912 q^{14} + 262144 q^{16} + 412139 q^{17} + 521284 q^{19} + 357120 q^{20} + 1667984 q^{22} - 3010300 q^{23} + 9760585 q^{25} + 1927776 q^{26} + 3150592 q^{28} - 6153240 q^{29} + 12774024 q^{31} + 4194304 q^{32} + 6594224 q^{34} - 9823425 q^{35} + 20506048 q^{37} + 8340544 q^{38} + 5713920 q^{40} - 11620300 q^{41} + 7698327 q^{43} + 26687744 q^{44} - 48164800 q^{46} + 31581083 q^{47} + 18970383 q^{49} + 156169360 q^{50} + 30844416 q^{52} - 72549422 q^{53} + 21332505 q^{55} + 50409472 q^{56} - 98451840 q^{58} + 149234120 q^{59} + 129004373 q^{61} + 204384384 q^{62} + 67108864 q^{64} - 124691700 q^{65} + 132595266 q^{67} + 105507584 q^{68} - 157174800 q^{70} + 47138482 q^{71} - 39332795 q^{73} + 328096768 q^{74} + 133448704 q^{76} + 165933719 q^{77} - 307010840 q^{79} + 91422720 q^{80} - 185924800 q^{82} + 746568232 q^{83} - 105005985 q^{85} + 123173232 q^{86} + 427003904 q^{88} - 286943482 q^{89} + 3155781114 q^{91} - 770636800 q^{92} + 505297328 q^{94} + 181797795 q^{95} + 793519958 q^{97} + 303526128 q^{98}+O(q^{100}) \) 4 * q + 64 * q^2 + 1024 * q^4 + 1395 * q^5 + 12307 * q^7 + 16384 * q^8 + 22320 * q^10 + 104249 * q^11 + 120486 * q^13 + 196912 * q^14 + 262144 * q^16 + 412139 * q^17 + 521284 * q^19 + 357120 * q^20 + 1667984 * q^22 - 3010300 * q^23 + 9760585 * q^25 + 1927776 * q^26 + 3150592 * q^28 - 6153240 * q^29 + 12774024 * q^31 + 4194304 * q^32 + 6594224 * q^34 - 9823425 * q^35 + 20506048 * q^37 + 8340544 * q^38 + 5713920 * q^40 - 11620300 * q^41 + 7698327 * q^43 + 26687744 * q^44 - 48164800 * q^46 + 31581083 * q^47 + 18970383 * q^49 + 156169360 * q^50 + 30844416 * q^52 - 72549422 * q^53 + 21332505 * q^55 + 50409472 * q^56 - 98451840 * q^58 + 149234120 * q^59 + 129004373 * q^61 + 204384384 * q^62 + 67108864 * q^64 - 124691700 * q^65 + 132595266 * q^67 + 105507584 * q^68 - 157174800 * q^70 + 47138482 * q^71 - 39332795 * q^73 + 328096768 * q^74 + 133448704 * q^76 + 165933719 * q^77 - 307010840 * q^79 + 91422720 * q^80 - 185924800 * q^82 + 746568232 * q^83 - 105005985 * q^85 + 123173232 * q^86 + 427003904 * q^88 - 286943482 * q^89 + 3155781114 * q^91 - 770636800 * q^92 + 505297328 * q^94 + 181797795 * q^95 + 793519958 * q^97 + 303526128 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	16.0000	0.707107
$2$	16.0000	0.707107
$3$	0	0
$3$	0	0
$4$	256.000	0.500000
$5$	2367.11	1.69376	0.846881	−	0.531782i	$-0.178477\pi$
$5$	2367.11	1.69376	0.846881	+	0.531782i	$0.178477\pi$
$6$	0	0
$7$	5859.40	0.922385	0.461192	−	0.887300i	$-0.347422\pi$
$7$	5859.40	0.922385	0.461192	+	0.887300i	$0.347422\pi$
$8$	4096.00	0.353553
$9$	0	0
$10$	37873.7	1.19767
$11$	38743.9	0.797878	0.398939	−	0.916978i	$-0.369379\pi$
$11$	38743.9	0.797878	0.398939	+	0.916978i	$0.369379\pi$
$12$	0	0
$13$	179439.	1.74249	0.871247	−	0.490845i	$-0.163312\pi$
$13$	179439.	1.74249	0.871247	+	0.490845i	$0.163312\pi$
$14$	93750.4	0.652225
$15$	0	0
$16$	65536.0	0.250000
$17$	−184492.	−0.535744	−0.267872	−	0.963455i	$-0.586320\pi$
$17$	−184492.	−0.535744	−0.267872	+	0.963455i	$0.586320\pi$
$18$	0	0
$19$	130321.	0.229416
$19$	130321.	0.229416
$20$	605979.	0.846881
$21$	0	0
$22$	619902.	0.564185
$23$	115333.	0.0859366	0.0429683	−	0.999076i	$-0.486319\pi$
$23$	115333.	0.0859366	0.0429683	+	0.999076i	$0.486319\pi$
$24$	0	0
$25$	3.65006e6	1.86883
$26$	2.87102e6	1.23213
$27$	0	0
$28$	1.50001e6	0.461192
$29$	−569755.	−0.149588	−0.0747941	−	0.997199i	$-0.523830\pi$
$29$	−569755.	−0.149588	−0.0747941	+	0.997199i	$0.523830\pi$
$30$	0	0
$31$	5.80788e6	1.12951	0.564755	−	0.825259i	$-0.308971\pi$
$31$	5.80788e6	1.12951	0.564755	+	0.825259i	$0.308971\pi$
$32$	1.04858e6	0.176777
$33$	0	0
$34$	−2.95187e6	−0.378828
$35$	1.38698e7	1.56230
$36$	0	0
$37$	3.15312e6	0.276587	0.138294	−	0.990391i	$-0.455838\pi$
$37$	3.15312e6	0.276587	0.138294	+	0.990391i	$0.455838\pi$
$38$	2.08514e6	0.162221
$39$	0	0
$40$	9.69566e6	0.598836
$41$	−54772.2	−0.00302714	−0.00151357	−	0.999999i	$-0.500482\pi$
$41$	−54772.2	−0.00302714	−0.00151357	+	0.999999i	$0.500482\pi$
$42$	0	0
$43$	−1.63249e7	−0.728187	−0.364094	−	0.931362i	$-0.618621\pi$
$43$	−1.63249e7	−0.728187	−0.364094	+	0.931362i	$0.618621\pi$
$44$	9.91844e6	0.398939
$45$	0	0
$46$	1.84533e6	0.0607663
$47$	−2.84428e7	−0.850220	−0.425110	−	0.905142i	$-0.639765\pi$
$47$	−2.84428e7	−0.850220	−0.425110	+	0.905142i	$0.639765\pi$
$48$	0	0
$49$	−6.02101e6	−0.149206
$50$	5.84010e7	1.32146
$51$	0	0
$52$	4.59363e7	0.871247
$53$	−7.33201e7	−1.27639	−0.638193	−	0.769877i	$-0.720318\pi$
$53$	−7.33201e7	−1.27639	−0.638193	+	0.769877i	$0.720318\pi$
$54$	0	0
$55$	9.17109e7	1.35142
$56$	2.40001e7	0.326112
$57$	0	0
$58$	−9.11608e6	−0.105775
$59$	1.45518e7	0.156345	0.0781725	−	0.996940i	$-0.475091\pi$
$59$	1.45518e7	0.156345	0.0781725	+	0.996940i	$0.475091\pi$
$60$	0	0
$61$	9.96035e7	0.921065	0.460533	−	0.887643i	$-0.347658\pi$
$61$	9.96035e7	0.921065	0.460533	+	0.887643i	$0.347658\pi$
$62$	9.29260e7	0.798684
$63$	0	0
$64$	1.67772e7	0.125000
$65$	4.24751e8	2.95137
$66$	0	0
$67$	−2.49050e8	−1.50991	−0.754954	−	0.655778i	$-0.772341\pi$
$67$	−2.49050e8	−1.50991	−0.754954	+	0.655778i	$0.772341\pi$
$68$	−4.72299e7	−0.267872
$69$	0	0
$70$	2.21917e8	1.10471
$71$	1.33230e8	0.622215	0.311108	−	0.950375i	$-0.399300\pi$
$71$	1.33230e8	0.622215	0.311108	+	0.950375i	$0.399300\pi$
$72$	0	0
$73$	−2.28114e8	−0.940153	−0.470077	−	0.882626i	$-0.655774\pi$
$73$	−2.28114e8	−0.940153	−0.470077	+	0.882626i	$0.655774\pi$
$74$	5.04499e7	0.195577
$75$	0	0
$76$	3.33622e7	0.114708
$77$	2.27016e8	0.735950
$78$	0	0
$79$	−6.65788e8	−1.92315	−0.961577	−	0.274534i	$-0.911476\pi$
$79$	−6.65788e8	−1.92315	−0.961577	+	0.274534i	$0.911476\pi$
$80$	1.55131e8	0.423441
$81$	0	0
$82$	−876356.	−0.00214051
$83$	3.48852e8	0.806844	0.403422	−	0.915014i	$-0.367821\pi$
$83$	3.48852e8	0.806844	0.403422	+	0.915014i	$0.367821\pi$
$84$	0	0
$85$	−4.36712e8	−0.907422
$86$	−2.61199e8	−0.514906
$87$	0	0
$88$	1.58695e8	0.282092
$89$	−2.61939e8	−0.442533	−0.221267	−	0.975213i	$-0.571019\pi$
$89$	−2.61939e8	−0.442533	−0.221267	+	0.975213i	$0.571019\pi$
$90$	0	0
$91$	1.05140e9	1.60725
$92$	2.95252e7	0.0429683
$93$	0	0
$94$	−4.55084e8	−0.601197
$95$	3.08484e8	0.388576
$96$	0	0
$97$	−1.10091e9	−1.26264	−0.631321	−	0.775521i	$-0.717487\pi$
$97$	−1.10091e9	−1.26264	−0.631321	+	0.775521i	$0.717487\pi$
$98$	−9.63361e7	−0.105505
$99$	0	0
$100$	9.34416e8	0.934416
$101$	−1.22467e9	−1.17104	−0.585521	−	0.810658i	$-0.699110\pi$
$101$	−1.22467e9	−1.17104	−0.585521	+	0.810658i	$0.699110\pi$
$102$	0	0
$103$	1.37095e9	1.20020	0.600100	−	0.799925i	$-0.295128\pi$
$103$	1.37095e9	1.20020	0.600100	+	0.799925i	$0.295128\pi$
$104$	7.34981e8	0.616065
$105$	0	0
$106$	−1.17312e9	−0.902541
$107$	−1.42672e9	−1.05223	−0.526115	−	0.850413i	$-0.676352\pi$
$107$	−1.42672e9	−1.05223	−0.526115	+	0.850413i	$0.676352\pi$
$108$	0	0
$109$	−2.50340e9	−1.69868	−0.849340	−	0.527846i	$-0.823000\pi$
$109$	−2.50340e9	−1.69868	−0.849340	+	0.527846i	$0.823000\pi$
$110$	1.46737e9	0.955595
$111$	0	0
$112$	3.84002e8	0.230596
$113$	3.27341e9	1.88863	0.944317	−	0.329036i	$-0.106724\pi$
$113$	3.27341e9	1.88863	0.944317	+	0.329036i	$0.106724\pi$
$114$	0	0
$115$	2.73005e8	0.145556
$116$	−1.45857e8	−0.0747941
$117$	0	0
$118$	2.32830e8	0.110553
$119$	−1.08101e9	−0.494162
$120$	0	0
$121$	−8.56858e8	−0.363391
$122$	1.59366e9	0.651291
$123$	0	0
$124$	1.48682e9	0.564755
$125$	4.01683e9	1.47160
$126$	0	0
$127$	−4.27729e9	−1.45899	−0.729494	−	0.683987i	$-0.760244\pi$
$127$	−4.27729e9	−1.45899	−0.729494	+	0.683987i	$0.760244\pi$
$128$	2.68435e8	0.0883883
$129$	0	0
$130$	6.79601e9	2.08693
$131$	−3.80463e9	−1.12873	−0.564367	−	0.825524i	$-0.690880\pi$
$131$	−3.80463e9	−1.12873	−0.564367	+	0.825524i	$0.690880\pi$
$132$	0	0
$133$	7.63603e8	0.211610
$134$	−3.98481e9	−1.06767
$135$	0	0
$136$	−7.55678e8	−0.189414
$137$	−1.42380e8	−0.0345308	−0.0172654	−	0.999851i	$-0.505496\pi$
$137$	−1.42380e8	−0.0345308	−0.0172654	+	0.999851i	$0.505496\pi$
$138$	0	0
$139$	2.12706e9	0.483295	0.241648	−	0.970364i	$-0.422312\pi$
$139$	2.12706e9	0.483295	0.241648	+	0.970364i	$0.422312\pi$
$140$	3.55067e9	0.781151
$141$	0	0
$142$	2.13169e9	0.439972
$143$	6.95216e9	1.39030
$144$	0	0
$145$	−1.34867e9	−0.253367
$146$	−3.64982e9	−0.664789
$147$	0	0
$148$	8.07198e8	0.138294
$149$	−5.74897e9	−0.955547	−0.477773	−	0.878483i	$-0.658556\pi$
$149$	−5.74897e9	−0.955547	−0.477773	+	0.878483i	$0.658556\pi$
$150$	0	0
$151$	3.66097e9	0.573059	0.286530	−	0.958071i	$-0.407498\pi$
$151$	3.66097e9	0.573059	0.286530	+	0.958071i	$0.407498\pi$
$152$	5.33795e8	0.0811107
$153$	0	0
$154$	3.63226e9	0.520395
$155$	1.37479e10	1.91312
$156$	0	0
$157$	−1.22861e9	−0.161386	−0.0806930	−	0.996739i	$-0.525713\pi$
$157$	−1.22861e9	−0.161386	−0.0806930	+	0.996739i	$0.525713\pi$
$158$	−1.06526e10	−1.35988
$159$	0	0
$160$	2.48209e9	0.299418
$161$	6.75782e8	0.0792666
$162$	0	0
$163$	−6.60342e8	−0.0732697	−0.0366349	−	0.999329i	$-0.511664\pi$
$163$	−6.60342e8	−0.0732697	−0.0366349	+	0.999329i	$0.511664\pi$
$164$	−1.40217e7	−0.00151357
$165$	0	0
$166$	5.58163e9	0.570525
$167$	1.05713e10	1.05173	0.525865	−	0.850568i	$-0.323742\pi$
$167$	1.05713e10	1.05173	0.525865	+	0.850568i	$0.323742\pi$
$168$	0	0
$169$	2.15938e10	2.03629
$170$	−6.98738e9	−0.641645
$171$	0	0
$172$	−4.17918e9	−0.364094
$173$	1.23439e10	1.04772	0.523861	−	0.851804i	$-0.324491\pi$
$173$	1.23439e10	1.04772	0.523861	+	0.851804i	$0.324491\pi$
$174$	0	0
$175$	2.13872e10	1.72378
$176$	2.53912e9	0.199469
$177$	0	0
$178$	−4.19103e9	−0.312918
$179$	−3.15457e9	−0.229669	−0.114834	−	0.993385i	$-0.536634\pi$
$179$	−3.15457e9	−0.229669	−0.114834	+	0.993385i	$0.536634\pi$
$180$	0	0
$181$	1.16218e10	0.804857	0.402429	−	0.915451i	$-0.368166\pi$
$181$	1.16218e10	0.804857	0.402429	+	0.915451i	$0.368166\pi$
$182$	1.68225e10	1.13650
$183$	0	0
$184$	4.72404e8	0.0303832
$185$	7.46376e9	0.468474
$186$	0	0
$187$	−7.14793e9	−0.427458
$188$	−7.28135e9	−0.425110
$189$	0	0
$190$	4.93574e9	0.274765
$191$	3.25043e9	0.176722	0.0883610	−	0.996089i	$-0.471837\pi$
$191$	3.25043e9	0.176722	0.0883610	+	0.996089i	$0.471837\pi$
$192$	0	0
$193$	2.45765e9	0.127501	0.0637503	−	0.997966i	$-0.479694\pi$
$193$	2.45765e9	0.127501	0.0637503	+	0.997966i	$0.479694\pi$
$194$	−1.76146e10	−0.892823
$195$	0	0
$196$	−1.54138e9	−0.0746031
$197$	1.10866e10	0.524445	0.262223	−	0.965007i	$-0.415545\pi$
$197$	1.10866e10	0.524445	0.262223	+	0.965007i	$0.415545\pi$
$198$	0	0
$199$	−1.66765e10	−0.753817	−0.376908	−	0.926251i	$-0.623013\pi$
$199$	−1.66765e10	−0.753817	−0.376908	+	0.926251i	$0.623013\pi$
$200$	1.49507e10	0.660732
$201$	0	0
$202$	−1.95947e10	−0.828051
$203$	−3.33842e9	−0.137978
$204$	0	0
$205$	−1.29652e8	−0.00512726
$206$	2.19352e10	0.848669
$207$	0	0
$208$	1.17597e10	0.435624
$209$	5.04914e9	0.183046
$210$	0	0
$211$	2.51893e10	0.874872	0.437436	−	0.899249i	$-0.355887\pi$
$211$	2.51893e10	0.874872	0.437436	+	0.899249i	$0.355887\pi$
$212$	−1.87699e10	−0.638193
$213$	0	0
$214$	−2.28275e10	−0.744039
$215$	−3.86428e10	−1.23338
$216$	0	0
$217$	3.40307e10	1.04184
$218$	−4.00545e10	−1.20115
$219$	0	0
$220$	2.34780e10	0.675708
$221$	−3.31050e10	−0.933530
$222$	0	0
$223$	4.72569e10	1.27966	0.639829	−	0.768518i	$-0.279005\pi$
$223$	4.72569e10	1.27966	0.639829	+	0.768518i	$0.279005\pi$
$224$	6.14403e9	0.163056
$225$	0	0
$226$	5.23746e10	1.33547
$227$	3.66710e10	0.916657	0.458328	−	0.888783i	$-0.348448\pi$
$227$	3.66710e10	0.916657	0.458328	+	0.888783i	$0.348448\pi$
$228$	0	0
$229$	1.94037e10	0.466258	0.233129	−	0.972446i	$-0.425104\pi$
$229$	1.94037e10	0.466258	0.233129	+	0.972446i	$0.425104\pi$
$230$	4.36808e9	0.102924
$231$	0	0
$232$	−2.33372e9	−0.0528874
$233$	3.57852e10	0.795430	0.397715	−	0.917509i	$-0.369803\pi$
$233$	3.57852e10	0.795430	0.397715	+	0.917509i	$0.369803\pi$
$234$	0	0
$235$	−6.73270e10	−1.44007
$236$	3.72527e9	0.0781725
$237$	0	0
$238$	−1.72962e10	−0.349425
$239$	−5.18718e9	−0.102835	−0.0514174	−	0.998677i	$-0.516374\pi$
$239$	−5.18718e9	−0.102835	−0.0514174	+	0.998677i	$0.516374\pi$
$240$	0	0
$241$	1.46244e10	0.279254	0.139627	−	0.990204i	$-0.455410\pi$
$241$	1.46244e10	0.279254	0.139627	+	0.990204i	$0.455410\pi$
$242$	−1.37097e10	−0.256957
$243$	0	0
$244$	2.54985e10	0.460533
$245$	−1.42524e10	−0.252720
$246$	0	0
$247$	2.33846e10	0.399756
$248$	2.37891e10	0.399342
$249$	0	0
$250$	6.42693e10	1.04057
$251$	−1.36902e8	−0.00217710	−0.00108855	−	0.999999i	$-0.500346\pi$
$251$	−1.36902e8	−0.00217710	−0.00108855	+	0.999999i	$0.500346\pi$
$252$	0	0
$253$	4.46845e9	0.0685669
$254$	−6.84366e10	−1.03166
$255$	0	0
$256$	4.29497e9	0.0625000
$257$	−5.04580e10	−0.721491	−0.360745	−	0.932664i	$-0.617478\pi$
$257$	−5.04580e10	−0.721491	−0.360745	+	0.932664i	$0.617478\pi$
$258$	0	0
$259$	1.84754e10	0.255120
$260$	1.08736e11	1.47569
$261$	0	0
$262$	−6.08741e10	−0.798135
$263$	−2.49089e10	−0.321036	−0.160518	−	0.987033i	$-0.551316\pi$
$263$	−2.49089e10	−0.321036	−0.160518	+	0.987033i	$0.551316\pi$
$264$	0	0
$265$	−1.73556e11	−2.16189
$266$	1.22177e10	0.149631
$267$	0	0
$268$	−6.37569e10	−0.754954
$269$	−1.21965e11	−1.42020	−0.710101	−	0.704100i	$-0.751351\pi$
$269$	−1.21965e11	−1.42020	−0.710101	+	0.704100i	$0.751351\pi$
$270$	0	0
$271$	−1.00248e10	−0.112905	−0.0564524	−	0.998405i	$-0.517979\pi$
$271$	−1.00248e10	−0.112905	−0.0564524	+	0.998405i	$0.517979\pi$
$272$	−1.20909e10	−0.133936
$273$	0	0
$274$	−2.27808e9	−0.0244170
$275$	1.41418e11	1.49110
$276$	0	0
$277$	4.21205e10	0.429868	0.214934	−	0.976629i	$-0.431046\pi$
$277$	4.21205e10	0.429868	0.214934	+	0.976629i	$0.431046\pi$
$278$	3.40329e10	0.341741
$279$	0	0
$280$	5.68108e10	0.552357
$281$	1.07825e11	1.03167	0.515836	−	0.856687i	$-0.327481\pi$
$281$	1.07825e11	1.03167	0.515836	+	0.856687i	$0.327481\pi$
$282$	0	0
$283$	4.94720e10	0.458480	0.229240	−	0.973370i	$-0.426376\pi$
$283$	4.94720e10	0.458480	0.229240	+	0.973370i	$0.426376\pi$
$284$	3.41070e10	0.311108
$285$	0	0
$286$	1.11235e11	0.983088
$287$	−3.20933e8	−0.00279219
$288$	0	0
$289$	−8.45506e10	−0.712979
$290$	−2.15787e10	−0.179157
$291$	0	0
$292$	−5.83971e10	−0.470077
$293$	3.72945e9	0.0295624	0.0147812	−	0.999891i	$-0.495295\pi$
$293$	3.72945e9	0.0295624	0.0147812	+	0.999891i	$0.495295\pi$
$294$	0	0
$295$	3.44458e10	0.264811
$296$	1.29152e10	0.0977884
$297$	0	0
$298$	−9.19835e10	−0.675674
$299$	2.06952e10	0.149744
$300$	0	0
$301$	−9.56543e10	−0.671669
$302$	5.85755e10	0.405214
$303$	0	0
$304$	8.54072e9	0.0573539
$305$	2.35772e11	1.56007
$306$	0	0
$307$	1.97134e11	1.26660	0.633300	−	0.773907i	$-0.281700\pi$
$307$	1.97134e11	1.26660	0.633300	+	0.773907i	$0.281700\pi$
$308$	5.81161e10	0.367975
$309$	0	0
$310$	2.19966e11	1.35278
$311$	2.55635e11	1.54953	0.774763	−	0.632252i	$-0.217869\pi$
$311$	2.55635e11	1.54953	0.774763	+	0.632252i	$0.217869\pi$
$312$	0	0
$313$	5.67565e10	0.334246	0.167123	−	0.985936i	$-0.446552\pi$
$313$	5.67565e10	0.334246	0.167123	+	0.985936i	$0.446552\pi$
$314$	−1.96578e10	−0.114117
$315$	0	0
$316$	−1.70442e11	−0.961577
$317$	−1.17647e11	−0.654354	−0.327177	−	0.944963i	$-0.606097\pi$
$317$	−1.17647e11	−0.654354	−0.327177	+	0.944963i	$0.606097\pi$
$318$	0	0
$319$	−2.20745e10	−0.119353
$320$	3.97134e10	0.211720
$321$	0	0
$322$	1.08125e10	0.0560500
$323$	−2.40432e10	−0.122908
$324$	0	0
$325$	6.54963e11	3.25643
$326$	−1.05655e10	−0.0518095
$327$	0	0
$328$	−2.24347e8	−0.00107026
$329$	−1.66658e11	−0.784230
$330$	0	0
$331$	−2.89438e11	−1.32535	−0.662673	−	0.748909i	$-0.730578\pi$
$331$	−2.89438e11	−1.32535	−0.662673	+	0.748909i	$0.730578\pi$
$332$	8.93061e10	0.403422
$333$	0	0
$334$	1.69141e11	0.743685
$335$	−5.89528e11	−2.55743
$336$	0	0
$337$	9.82619e10	0.415002	0.207501	−	0.978235i	$-0.433467\pi$
$337$	9.82619e10	0.415002	0.207501	+	0.978235i	$0.433467\pi$
$338$	3.45501e11	1.43987
$339$	0	0
$340$	−1.11798e11	−0.453711
$341$	2.25020e11	0.901210
$342$	0	0
$343$	−2.71728e11	−1.06001
$344$	−6.68669e10	−0.257453
$345$	0	0
$346$	1.97503e11	0.740852
$347$	2.54903e11	0.943827	0.471914	−	0.881645i	$-0.343563\pi$
$347$	2.54903e11	0.943827	0.471914	+	0.881645i	$0.343563\pi$
$348$	0	0
$349$	4.14692e11	1.49628	0.748138	−	0.663543i	$-0.230948\pi$
$349$	4.14692e11	1.49628	0.748138	+	0.663543i	$0.230948\pi$
$350$	3.42195e11	1.21890
$351$	0	0
$352$	4.06259e10	0.141046
$353$	1.12437e11	0.385410	0.192705	−	0.981257i	$-0.438274\pi$
$353$	1.12437e11	0.385410	0.192705	+	0.981257i	$0.438274\pi$
$354$	0	0
$355$	3.15370e11	1.05388
$356$	−6.70565e10	−0.221267
$357$	0	0
$358$	−5.04732e10	−0.162400
$359$	−1.53457e11	−0.487596	−0.243798	−	0.969826i	$-0.578393\pi$
$359$	−1.53457e11	−0.487596	−0.243798	+	0.969826i	$0.578393\pi$
$360$	0	0
$361$	1.69836e10	0.0526316
$362$	1.85948e11	0.569120
$363$	0	0
$364$	2.69160e11	0.803625
$365$	−5.39969e11	−1.59240
$366$	0	0
$367$	3.10410e11	0.893180	0.446590	−	0.894739i	$-0.352638\pi$
$367$	3.10410e11	0.893180	0.446590	+	0.894739i	$0.352638\pi$
$368$	7.55846e9	0.0214841
$369$	0	0
$370$	1.19420e11	0.331261
$371$	−4.29612e11	−1.17732
$372$	0	0
$373$	−4.01840e11	−1.07489	−0.537444	−	0.843300i	$-0.680610\pi$
$373$	−4.01840e11	−1.07489	−0.537444	+	0.843300i	$0.680610\pi$
$374$	−1.14367e11	−0.302258
$375$	0	0
$376$	−1.16502e11	−0.300598
$377$	−1.02236e11	−0.260656
$378$	0	0
$379$	−4.14457e11	−1.03182	−0.515909	−	0.856644i	$-0.672546\pi$
$379$	−4.14457e11	−1.03182	−0.515909	+	0.856644i	$0.672546\pi$
$380$	7.89718e10	0.194288
$381$	0	0
$382$	5.20069e10	0.124961
$383$	−2.40472e11	−0.571044	−0.285522	−	0.958372i	$-0.592167\pi$
$383$	−2.40472e11	−0.571044	−0.285522	+	0.958372i	$0.592167\pi$
$384$	0	0
$385$	5.37371e11	1.24652
$386$	3.93224e10	0.0901565
$387$	0	0
$388$	−2.81834e11	−0.631321
$389$	2.15388e11	0.476923	0.238461	−	0.971152i	$-0.423357\pi$
$389$	2.15388e11	0.476923	0.238461	+	0.971152i	$0.423357\pi$
$390$	0	0
$391$	−2.12780e10	−0.0460400
$392$	−2.46621e10	−0.0527524
$393$	0	0
$394$	1.77385e11	0.370839
$395$	−1.57599e12	−3.25737
$396$	0	0
$397$	−9.46770e11	−1.91288	−0.956439	−	0.291932i	$-0.905702\pi$
$397$	−9.46770e11	−1.91288	−0.956439	+	0.291932i	$0.905702\pi$
$398$	−2.66824e11	−0.533029
$399$	0	0
$400$	2.39210e11	0.467208
$401$	−2.94360e10	−0.0568498	−0.0284249	−	0.999596i	$-0.509049\pi$
$401$	−2.94360e10	−0.0568498	−0.0284249	+	0.999596i	$0.509049\pi$
$402$	0	0
$403$	1.04216e12	1.96816
$404$	−3.13515e11	−0.585521
$405$	0	0
$406$	−5.34148e10	−0.0975650
$407$	1.22164e11	0.220683
$408$	0	0
$409$	−9.56914e11	−1.69090	−0.845450	−	0.534054i	$-0.820668\pi$
$409$	−9.56914e11	−1.69090	−0.845450	+	0.534054i	$0.820668\pi$
$410$	−2.07443e9	−0.00362552
$411$	0	0
$412$	3.50963e11	0.600100
$413$	8.52651e10	0.144210
$414$	0	0
$415$	8.25769e11	1.36660
$416$	1.88155e11	0.308032
$417$	0	0
$418$	8.07863e10	0.129433
$419$	8.06056e11	1.27762	0.638811	−	0.769364i	$-0.279427\pi$
$419$	8.06056e11	1.27762	0.638811	+	0.769364i	$0.279427\pi$
$420$	0	0
$421$	−1.29752e11	−0.201300	−0.100650	−	0.994922i	$-0.532092\pi$
$421$	−1.29752e11	−0.201300	−0.100650	+	0.994922i	$0.532092\pi$
$422$	4.03028e11	0.618628
$423$	0	0
$424$	−3.00319e11	−0.451270
$425$	−6.73407e11	−1.00121
$426$	0	0
$427$	5.83617e11	0.849577
$428$	−3.65239e11	−0.526115
$429$	0	0
$430$	−6.18285e11	−0.872129
$431$	1.30045e12	1.81530	0.907648	−	0.419732i	$-0.137876\pi$
$431$	1.30045e12	1.81530	0.907648	+	0.419732i	$0.137876\pi$
$432$	0	0
$433$	−7.31189e11	−0.999618	−0.499809	−	0.866136i	$-0.666596\pi$
$433$	−7.31189e11	−0.999618	−0.499809	+	0.866136i	$0.666596\pi$
$434$	5.44491e11	0.736694
$435$	0	0
$436$	−6.40871e11	−0.849340
$437$	1.50303e10	0.0197152
$438$	0	0
$439$	1.03899e12	1.33513	0.667563	−	0.744553i	$-0.267337\pi$
$439$	1.03899e12	1.33513	0.667563	+	0.744553i	$0.267337\pi$
$440$	3.75648e11	0.477797
$441$	0	0
$442$	−5.29680e11	−0.660105
$443$	4.22964e10	0.0521779	0.0260889	−	0.999660i	$-0.491695\pi$
$443$	4.22964e10	0.0521779	0.0260889	+	0.999660i	$0.491695\pi$
$444$	0	0
$445$	−6.20038e11	−0.749546
$446$	7.56111e11	0.904854
$447$	0	0
$448$	9.83045e10	0.115298
$449$	1.99335e11	0.231459	0.115730	−	0.993281i	$-0.463079\pi$
$449$	1.99335e11	0.231459	0.115730	+	0.993281i	$0.463079\pi$
$450$	0	0
$451$	−2.12209e9	−0.00241529
$452$	8.37994e11	0.944317
$453$	0	0
$454$	5.86736e11	0.648174
$455$	2.48878e12	2.72230
$456$	0	0
$457$	6.57751e11	0.705405	0.352702	−	0.935736i	$-0.385263\pi$
$457$	6.57751e11	0.705405	0.352702	+	0.935736i	$0.385263\pi$
$458$	3.10460e11	0.329694
$459$	0	0
$460$	6.98893e10	0.0727781
$461$	−8.30559e11	−0.856478	−0.428239	−	0.903665i	$-0.640866\pi$
$461$	−8.30559e11	−0.856478	−0.428239	+	0.903665i	$0.640866\pi$
$462$	0	0
$463$	−1.09774e12	−1.11016	−0.555080	−	0.831797i	$-0.687312\pi$
$463$	−1.09774e12	−1.11016	−0.555080	+	0.831797i	$0.687312\pi$
$464$	−3.73395e10	−0.0373970
$465$	0	0
$466$	5.72564e11	0.562454
$467$	−6.31199e11	−0.614102	−0.307051	−	0.951693i	$-0.599342\pi$
$467$	−6.31199e11	−0.614102	−0.307051	+	0.951693i	$0.599342\pi$
$468$	0	0
$469$	−1.45929e12	−1.39272
$470$	−1.07723e12	−1.01828
$471$	0	0
$472$	5.96044e10	0.0552763
$473$	−6.32491e11	−0.581004
$474$	0	0
$475$	4.75680e11	0.428739
$476$	−2.76739e11	−0.247081
$477$	0	0
$478$	−8.29948e10	−0.0727152
$479$	1.03045e12	0.894370	0.447185	−	0.894442i	$-0.352427\pi$
$479$	1.03045e12	0.894370	0.447185	+	0.894442i	$0.352427\pi$
$480$	0	0
$481$	5.65792e11	0.481952
$482$	2.33990e11	0.197463
$483$	0	0
$484$	−2.19356e11	−0.181696
$485$	−2.60598e12	−2.13862
$486$	0	0
$487$	−6.97434e11	−0.561853	−0.280927	−	0.959729i	$-0.590642\pi$
$487$	−6.97434e11	−0.561853	−0.280927	+	0.959729i	$0.590642\pi$
$488$	4.07976e11	0.325646
$489$	0	0
$490$	−2.28038e11	−0.178700
$491$	−1.25643e12	−0.975600	−0.487800	−	0.872955i	$-0.662201\pi$
$491$	−1.25643e12	−0.975600	−0.487800	+	0.872955i	$0.662201\pi$
$492$	0	0
$493$	1.05115e11	0.0801409
$494$	3.74154e11	0.282670
$495$	0	0
$496$	3.80625e11	0.282377
$497$	7.80650e11	0.573922
$498$	0	0
$499$	−7.26198e11	−0.524327	−0.262164	−	0.965023i	$-0.584436\pi$
$499$	−7.26198e11	−0.524327	−0.262164	+	0.965023i	$0.584436\pi$
$500$	1.02831e12	0.735798
$501$	0	0
$502$	−2.19044e9	−0.00153944
$503$	−1.01445e12	−0.706602	−0.353301	−	0.935510i	$-0.614941\pi$
$503$	−1.01445e12	−0.706602	−0.353301	+	0.935510i	$0.614941\pi$
$504$	0	0
$505$	−2.89892e12	−1.98347
$506$	7.14952e10	0.0484841
$507$	0	0
$508$	−1.09499e12	−0.729494
$509$	1.88479e12	1.24461	0.622306	−	0.782774i	$-0.286196\pi$
$509$	1.88479e12	1.24461	0.622306	+	0.782774i	$0.286196\pi$
$510$	0	0
$511$	−1.33661e12	−0.867183
$512$	6.87195e10	0.0441942
$513$	0	0
$514$	−8.07328e11	−0.510171
$515$	3.24518e12	2.03285
$516$	0	0
$517$	−1.10198e12	−0.678372
$518$	2.95606e11	0.180397
$519$	0	0
$520$	1.73978e12	1.04347
$521$	−1.02179e12	−0.607562	−0.303781	−	0.952742i	$-0.598249\pi$
$521$	−1.02179e12	−0.607562	−0.303781	+	0.952742i	$0.598249\pi$
$522$	0	0
$523$	−1.23513e12	−0.721862	−0.360931	−	0.932593i	$-0.617541\pi$
$523$	−1.23513e12	−0.721862	−0.360931	+	0.932593i	$0.617541\pi$
$524$	−9.73985e11	−0.564367
$525$	0	0
$526$	−3.98542e11	−0.227007
$527$	−1.07151e12	−0.605127
$528$	0	0
$529$	−1.78785e12	−0.992615
$530$	−2.77690e12	−1.52869
$531$	0	0
$532$	1.95482e11	0.105805
$533$	−9.82827e9	−0.00527478
$534$	0	0
$535$	−3.37719e12	−1.78223
$536$	−1.02011e12	−0.533833
$537$	0	0
$538$	−1.95144e12	−1.00423
$539$	−2.33277e11	−0.119048
$540$	0	0
$541$	−8.75167e11	−0.439241	−0.219621	−	0.975585i	$-0.570482\pi$
$541$	−8.75167e11	−0.439241	−0.219621	+	0.975585i	$0.570482\pi$
$542$	−1.60396e11	−0.0798358
$543$	0	0
$544$	−1.93454e11	−0.0947070
$545$	−5.92582e12	−2.87716
$546$	0	0
$547$	1.97687e12	0.944138	0.472069	−	0.881562i	$-0.343507\pi$
$547$	1.97687e12	0.944138	0.472069	+	0.881562i	$0.343507\pi$
$548$	−3.64493e10	−0.0172654
$549$	0	0
$550$	2.26268e12	1.05437
$551$	−7.42510e10	−0.0343179
$552$	0	0
$553$	−3.90112e12	−1.77389
$554$	6.73929e11	0.303962
$555$	0	0
$556$	5.44526e11	0.241648
$557$	−2.44569e12	−1.07660	−0.538298	−	0.842755i	$-0.680932\pi$
$557$	−2.44569e12	−1.07660	−0.538298	+	0.842755i	$0.680932\pi$
$558$	0	0
$559$	−2.92933e12	−1.26886
$560$	9.08973e11	0.390575
$561$	0	0
$562$	1.72520e12	0.729503
$563$	4.54810e11	0.190784	0.0953920	−	0.995440i	$-0.469590\pi$
$563$	4.54810e11	0.190784	0.0953920	+	0.995440i	$0.469590\pi$
$564$	0	0
$565$	7.74852e12	3.19890
$566$	7.91552e11	0.324195
$567$	0	0
$568$	5.45711e11	0.219986
$569$	−4.19643e12	−1.67832	−0.839160	−	0.543885i	$-0.816953\pi$
$569$	−4.19643e12	−1.67832	−0.839160	+	0.543885i	$0.816953\pi$
$570$	0	0
$571$	3.03648e12	1.19539	0.597694	−	0.801725i	$-0.296084\pi$
$571$	3.03648e12	1.19539	0.597694	+	0.801725i	$0.296084\pi$
$572$	1.77975e12	0.695149
$573$	0	0
$574$	−5.13492e9	−0.00197438
$575$	4.20972e11	0.160601
$576$	0	0
$577$	−5.21026e12	−1.95690	−0.978449	−	0.206487i	$-0.933797\pi$
$577$	−5.21026e12	−1.95690	−0.978449	+	0.206487i	$0.933797\pi$
$578$	−1.35281e12	−0.504152
$579$	0	0
$580$	−3.45260e11	−0.126683
$581$	2.04406e12	0.744221
$582$	0	0
$583$	−2.84071e12	−1.01840
$584$	−9.34354e11	−0.332394
$585$	0	0
$586$	5.96712e10	0.0209038
$587$	2.61266e12	0.908264	0.454132	−	0.890935i	$-0.349950\pi$
$587$	2.61266e12	0.908264	0.454132	+	0.890935i	$0.349950\pi$
$588$	0	0
$589$	7.56888e11	0.259127
$590$	5.51132e11	0.187250
$591$	0	0
$592$	2.06643e11	0.0691469
$593$	−3.90508e12	−1.29683	−0.648417	−	0.761286i	$-0.724569\pi$
$593$	−3.90508e12	−1.29683	−0.648417	+	0.761286i	$0.724569\pi$
$594$	0	0
$595$	−2.55887e12	−0.836993
$596$	−1.47174e12	−0.477773
$597$	0	0
$598$	3.31123e11	0.105885
$599$	−1.12506e12	−0.357070	−0.178535	−	0.983934i	$-0.557136\pi$
$599$	−1.12506e12	−0.357070	−0.178535	+	0.983934i	$0.557136\pi$
$600$	0	0
$601$	−7.83252e11	−0.244887	−0.122444	−	0.992475i	$-0.539073\pi$
$601$	−7.83252e11	−0.244887	−0.122444	+	0.992475i	$0.539073\pi$
$602$	−1.53047e12	−0.474942
$603$	0	0
$604$	9.37207e11	0.286530
$605$	−2.02827e12	−0.615499
$606$	0	0
$607$	2.19285e12	0.655633	0.327816	−	0.944741i	$-0.393687\pi$
$607$	2.19285e12	0.655633	0.327816	+	0.944741i	$0.393687\pi$
$608$	1.36651e11	0.0405554
$609$	0	0
$610$	3.77235e12	1.10313
$611$	−5.10374e12	−1.48150
$612$	0	0
$613$	−6.85830e11	−0.196175	−0.0980877	−	0.995178i	$-0.531273\pi$
$613$	−6.85830e11	−0.196175	−0.0980877	+	0.995178i	$0.531273\pi$
$614$	3.15415e12	0.895621
$615$	0	0
$616$	9.29858e11	0.260198
$617$	−4.20809e12	−1.16897	−0.584483	−	0.811406i	$-0.698703\pi$
$617$	−4.20809e12	−1.16897	−0.584483	+	0.811406i	$0.698703\pi$
$618$	0	0
$619$	−5.42304e12	−1.48469	−0.742344	−	0.670019i	$-0.766286\pi$
$619$	−5.42304e12	−1.48469	−0.742344	+	0.670019i	$0.766286\pi$
$620$	3.51945e12	0.956560
$621$	0	0
$622$	4.09016e12	1.09568
$623$	−1.53481e12	−0.408186
$624$	0	0
$625$	2.37923e12	0.623701
$626$	9.08105e11	0.236348
$627$	0	0
$628$	−3.14524e11	−0.0806930
$629$	−5.81725e11	−0.148180
$630$	0	0
$631$	−4.74716e12	−1.19207	−0.596035	−	0.802959i	$-0.703258\pi$
$631$	−4.74716e12	−1.19207	−0.596035	+	0.802959i	$0.703258\pi$
$632$	−2.72707e12	−0.679938
$633$	0	0
$634$	−1.88234e12	−0.462698
$635$	−1.01248e13	−2.47118
$636$	0	0
$637$	−1.08040e12	−0.259991
$638$	−3.53192e11	−0.0843953
$639$	0	0
$640$	6.35415e11	0.149709
$641$	5.71232e12	1.33645	0.668223	−	0.743961i	$-0.267055\pi$
$641$	5.71232e12	1.33645	0.668223	+	0.743961i	$0.267055\pi$
$642$	0	0
$643$	8.29997e12	1.91482	0.957409	−	0.288736i	$-0.0932350\pi$
$643$	8.29997e12	1.91482	0.957409	+	0.288736i	$0.0932350\pi$
$644$	1.73000e11	0.0396333
$645$	0	0
$646$	−3.84691e11	−0.0869091
$647$	1.16040e12	0.260339	0.130169	−	0.991492i	$-0.458448\pi$
$647$	1.16040e12	0.260339	0.130169	+	0.991492i	$0.458448\pi$
$648$	0	0
$649$	5.63795e11	0.124744
$650$	1.04794e13	2.30264
$651$	0	0
$652$	−1.69047e11	−0.0366349
$653$	1.07293e12	0.230921	0.115461	−	0.993312i	$-0.463166\pi$
$653$	1.07293e12	0.230921	0.115461	+	0.993312i	$0.463166\pi$
$654$	0	0
$655$	−9.00596e12	−1.91181
$656$	−3.58955e9	−0.000756786 0
$657$	0	0
$658$	−2.66652e12	−0.554535
$659$	9.14394e12	1.88864	0.944319	−	0.329031i	$-0.106722\pi$
$659$	9.14394e12	1.88864	0.944319	+	0.329031i	$0.106722\pi$
$660$	0	0
$661$	8.78371e12	1.78966	0.894832	−	0.446403i	$-0.147295\pi$
$661$	8.78371e12	1.78966	0.894832	+	0.446403i	$0.147295\pi$
$662$	−4.63101e12	−0.937161
$663$	0	0
$664$	1.42890e12	0.285262
$665$	1.80753e12	0.358416
$666$	0	0
$667$	−6.57115e10	−0.0128551
$668$	2.70625e12	0.525865
$669$	0	0
$670$	−9.43246e12	−1.80837
$671$	3.85903e12	0.734897
$672$	0	0
$673$	7.23901e12	1.36023	0.680114	−	0.733106i	$-0.261930\pi$
$673$	7.23901e12	1.36023	0.680114	+	0.733106i	$0.261930\pi$
$674$	1.57219e12	0.293451
$675$	0	0
$676$	5.52801e12	1.01814
$677$	5.18390e12	0.948435	0.474218	−	0.880408i	$-0.342731\pi$
$677$	5.18390e12	0.948435	0.474218	+	0.880408i	$0.342731\pi$
$678$	0	0
$679$	−6.45070e12	−1.16464
$680$	−1.78877e12	−0.320822
$681$	0	0
$682$	3.60032e12	0.637252
$683$	−2.31773e12	−0.407539	−0.203769	−	0.979019i	$-0.565319\pi$
$683$	−2.31773e12	−0.407539	−0.203769	+	0.979019i	$0.565319\pi$
$684$	0	0
$685$	−3.37029e11	−0.0584871
$686$	−4.34764e12	−0.749541
$687$	0	0
$688$	−1.06987e12	−0.182047
$689$	−1.31565e13	−2.22409
$690$	0	0
$691$	−2.82266e12	−0.470985	−0.235492	−	0.971876i	$-0.575670\pi$
$691$	−2.82266e12	−0.470985	−0.235492	+	0.971876i	$0.575670\pi$
$692$	3.16005e12	0.523861
$693$	0	0
$694$	4.07845e12	0.667387
$695$	5.03497e12	0.818587
$696$	0	0
$697$	1.01050e10	0.00162177
$698$	6.63508e12	1.05803
$699$	0	0
$700$	5.47512e12	0.861891
$701$	9.84845e12	1.54041	0.770206	−	0.637795i	$-0.220153\pi$
$701$	9.84845e12	1.54041	0.770206	+	0.637795i	$0.220153\pi$
$702$	0	0
$703$	4.10918e11	0.0634535
$704$	6.50015e11	0.0997347
$705$	0	0
$706$	1.79899e12	0.272526
$707$	−7.17582e12	−1.08015
$708$	0	0
$709$	4.56333e12	0.678225	0.339112	−	0.940746i	$-0.389873\pi$
$709$	4.56333e12	0.678225	0.339112	+	0.940746i	$0.389873\pi$
$710$	5.04592e12	0.745209
$711$	0	0
$712$	−1.07290e12	−0.156459
$713$	6.69840e11	0.0970662
$714$	0	0
$715$	1.64565e13	2.35483
$716$	−8.07571e11	−0.114834
$717$	0	0
$718$	−2.45530e12	−0.344783
$719$	9.06278e12	1.26468	0.632341	−	0.774690i	$-0.282094\pi$
$719$	9.06278e12	1.26468	0.632341	+	0.774690i	$0.282094\pi$
$720$	0	0
$721$	8.03293e12	1.10705
$722$	2.71737e11	0.0372161
$723$	0	0
$724$	2.97517e12	0.402429
$725$	−2.07964e12	−0.279555
$726$	0	0
$727$	−1.15554e11	−0.0153420	−0.00767100	−	0.999971i	$-0.502442\pi$
$727$	−1.15554e11	−0.0153420	−0.00767100	+	0.999971i	$0.502442\pi$
$728$	4.30655e12	0.568249
$729$	0	0
$730$	−8.63951e12	−1.12599
$731$	3.01182e12	0.390122
$732$	0	0
$733$	1.08986e13	1.39444	0.697222	−	0.716855i	$-0.254419\pi$
$733$	1.08986e13	1.39444	0.697222	+	0.716855i	$0.254419\pi$
$734$	4.96657e12	0.631574
$735$	0	0
$736$	1.20935e11	0.0151916
$737$	−9.64918e12	−1.20472
$738$	0	0
$739$	−8.91416e12	−1.09946	−0.549731	−	0.835341i	$-0.685270\pi$
$739$	−8.91416e12	−1.09946	−0.549731	+	0.835341i	$0.685270\pi$
$740$	1.91072e12	0.234237
$741$	0	0
$742$	−6.87379e12	−0.832490
$743$	−6.16929e12	−0.742652	−0.371326	−	0.928503i	$-0.621097\pi$
$743$	−6.16929e12	−0.742652	−0.371326	+	0.928503i	$0.621097\pi$
$744$	0	0
$745$	−1.36084e13	−1.61847
$746$	−6.42943e12	−0.760060
$747$	0	0
$748$	−1.82987e12	−0.213729
$749$	−8.35971e12	−0.970561
$750$	0	0
$751$	6.30977e12	0.723826	0.361913	−	0.932212i	$-0.382124\pi$
$751$	6.30977e12	0.723826	0.361913	+	0.932212i	$0.382124\pi$
$752$	−1.86403e12	−0.212555
$753$	0	0
$754$	−1.63578e12	−0.184312
$755$	8.66589e12	0.970626
$756$	0	0
$757$	−9.13291e12	−1.01083	−0.505414	−	0.862877i	$-0.668660\pi$
$757$	−9.13291e12	−1.01083	−0.505414	+	0.862877i	$0.668660\pi$
$758$	−6.63131e12	−0.729605
$759$	0	0
$760$	1.26355e12	0.137382
$761$	−5.56499e12	−0.601497	−0.300748	−	0.953704i	$-0.597236\pi$
$761$	−5.56499e12	−0.601497	−0.300748	+	0.953704i	$0.597236\pi$
$762$	0	0
$763$	−1.46684e13	−1.56684
$764$	8.32110e11	0.0883610
$765$	0	0
$766$	−3.84755e12	−0.403789
$767$	2.61117e12	0.272430
$768$	0	0
$769$	1.09213e13	1.12618	0.563089	−	0.826396i	$-0.309613\pi$
$769$	1.09213e13	1.12618	0.563089	+	0.826396i	$0.309613\pi$
$770$	8.59794e12	0.881426
$771$	0	0
$772$	6.29158e11	0.0637503
$773$	1.06326e13	1.07111	0.535553	−	0.844502i	$-0.320103\pi$
$773$	1.06326e13	1.07111	0.535553	+	0.844502i	$0.320103\pi$
$774$	0	0
$775$	2.11991e13	2.11086
$776$	−4.50934e12	−0.446412
$777$	0	0
$778$	3.44621e12	0.337235
$779$	−7.13797e9	−0.000694475 0
$780$	0	0
$781$	5.16186e12	0.496451
$782$	−3.40448e11	−0.0325552
$783$	0	0
$784$	−3.94593e11	−0.0373016
$785$	−2.90825e12	−0.273349
$786$	0	0
$787$	−2.50979e12	−0.233212	−0.116606	−	0.993178i	$-0.537202\pi$
$787$	−2.50979e12	−0.233212	−0.116606	+	0.993178i	$0.537202\pi$
$788$	2.83817e12	0.262223
$789$	0	0
$790$	−2.52159e13	−2.30331
$791$	1.91803e13	1.74205
$792$	0	0
$793$	1.78727e13	1.60495
$794$	−1.51483e13	−1.35261
$795$	0	0
$796$	−4.26918e12	−0.376908
$797$	1.17969e13	1.03563	0.517815	−	0.855493i	$-0.326746\pi$
$797$	1.17969e13	1.03563	0.517815	+	0.855493i	$0.326746\pi$
$798$	0	0
$799$	5.24746e12	0.455500
$800$	3.82737e12	0.330366
$801$	0	0
$802$	−4.70976e11	−0.0401989
$803$	−8.83802e12	−0.750127
$804$	0	0
$805$	1.59965e12	0.134259
$806$	1.66745e13	1.39170
$807$	0	0
$808$	−5.01624e12	−0.414026
$809$	6.47962e12	0.531840	0.265920	−	0.963995i	$-0.414324\pi$
$809$	6.47962e12	0.531840	0.265920	+	0.963995i	$0.414324\pi$
$810$	0	0
$811$	−5.08224e12	−0.412536	−0.206268	−	0.978496i	$-0.566132\pi$
$811$	−5.08224e12	−0.412536	−0.206268	+	0.978496i	$0.566132\pi$
$812$	−8.54636e11	−0.0689889
$813$	0	0
$814$	1.95463e12	0.156046
$815$	−1.56310e12	−0.124102
$816$	0	0
$817$	−2.12748e12	−0.167058
$818$	−1.53106e13	−1.19565
$819$	0	0
$820$	−3.31908e10	−0.00256363
$821$	−8.99329e11	−0.0690835	−0.0345418	−	0.999403i	$-0.510997\pi$
$821$	−8.99329e11	−0.0690835	−0.0345418	+	0.999403i	$0.510997\pi$
$822$	0	0
$823$	−7.62233e12	−0.579147	−0.289573	−	0.957156i	$-0.593513\pi$
$823$	−7.62233e12	−0.579147	−0.289573	+	0.957156i	$0.593513\pi$
$824$	5.61540e12	0.424334
$825$	0	0
$826$	1.36424e12	0.101972
$827$	−2.54111e12	−0.188907	−0.0944537	−	0.995529i	$-0.530110\pi$
$827$	−2.54111e12	−0.188907	−0.0944537	+	0.995529i	$0.530110\pi$
$828$	0	0
$829$	2.04803e13	1.50605	0.753027	−	0.657990i	$-0.228593\pi$
$829$	2.04803e13	1.50605	0.753027	+	0.657990i	$0.228593\pi$
$830$	1.32123e13	0.966334
$831$	0	0
$832$	3.01048e12	0.217812
$833$	1.11083e12	0.0799363
$834$	0	0
$835$	2.50234e13	1.78138
$836$	1.29258e12	0.0915228
$837$	0	0
$838$	1.28969e13	0.903415
$839$	−1.60416e13	−1.11769	−0.558843	−	0.829273i	$-0.688755\pi$
$839$	−1.60416e13	−1.11769	−0.558843	+	0.829273i	$0.688755\pi$
$840$	0	0
$841$	−1.41825e13	−0.977623
$842$	−2.07603e12	−0.142340
$843$	0	0
$844$	6.44846e12	0.437436
$845$	5.11148e13	3.44899
$846$	0	0
$847$	−5.02068e12	−0.335187
$848$	−4.80511e12	−0.319096
$849$	0	0
$850$	−1.07745e13	−0.707966
$851$	3.63658e11	0.0237690
$852$	0	0
$853$	1.69954e13	1.09916	0.549581	−	0.835440i	$-0.314787\pi$
$853$	1.69954e13	1.09916	0.549581	+	0.835440i	$0.314787\pi$
$854$	9.33787e12	0.600741
$855$	0	0
$856$	−5.84383e12	−0.372019
$857$	4.81872e12	0.305153	0.152577	−	0.988292i	$-0.451243\pi$
$857$	4.81872e12	0.305153	0.152577	+	0.988292i	$0.451243\pi$
$858$	0	0
$859$	1.43473e13	0.899084	0.449542	−	0.893259i	$-0.351587\pi$
$859$	1.43473e13	0.899084	0.449542	+	0.893259i	$0.351587\pi$
$860$	−9.89256e12	−0.616688
$861$	0	0
$862$	2.08073e13	1.28361
$863$	−1.16081e13	−0.712380	−0.356190	−	0.934414i	$-0.615924\pi$
$863$	−1.16081e13	−0.712380	−0.356190	+	0.934414i	$0.615924\pi$
$864$	0	0
$865$	2.92194e13	1.77459
$866$	−1.16990e13	−0.706837
$867$	0	0
$868$	8.71186e12	0.520921
$869$	−2.57952e13	−1.53444
$870$	0	0
$871$	−4.46893e13	−2.63101
$872$	−1.02539e13	−0.600574
$873$	0	0
$874$	2.40485e11	0.0139408
$875$	2.35362e13	1.35738
$876$	0	0
$877$	6.32859e11	0.0361251	0.0180625	−	0.999837i	$-0.494250\pi$
$877$	6.32859e11	0.0361251	0.0180625	+	0.999837i	$0.494250\pi$
$878$	1.66239e13	0.944077
$879$	0	0
$880$	6.01036e12	0.337854
$881$	−1.78534e13	−0.998457	−0.499229	−	0.866470i	$-0.666383\pi$
$881$	−1.78534e13	−0.998457	−0.499229	+	0.866470i	$0.666383\pi$
$882$	0	0
$883$	−3.78633e12	−0.209602	−0.104801	−	0.994493i	$-0.533421\pi$
$883$	−3.78633e12	−0.209602	−0.104801	+	0.994493i	$0.533421\pi$
$884$	−8.47488e12	−0.466765
$885$	0	0
$886$	6.76742e11	0.0368953
$887$	1.59149e13	0.863274	0.431637	−	0.902048i	$-0.357936\pi$
$887$	1.59149e13	0.863274	0.431637	+	0.902048i	$0.357936\pi$
$888$	0	0
$889$	−2.50624e13	−1.34575
$890$	−9.92061e12	−0.530009
$891$	0	0
$892$	1.20978e13	0.639829
$893$	−3.70669e12	−0.195054
$894$	0	0
$895$	−7.46721e12	−0.389004
$896$	1.57287e12	0.0815281
$897$	0	0
$898$	3.18936e12	0.163666
$899$	−3.30907e12	−0.168961
$900$	0	0
$901$	1.35270e13	0.683815
$902$	−3.39534e10	−0.00170787
$903$	0	0
$904$	1.34079e13	0.667733
$905$	2.75100e13	1.36324
$906$	0	0
$907$	−8.91543e12	−0.437431	−0.218715	−	0.975789i	$-0.570187\pi$
$907$	−8.91543e12	−0.437431	−0.218715	+	0.975789i	$0.570187\pi$
$908$	9.38778e12	0.458328
$909$	0	0
$910$	3.98206e13	1.92496
$911$	2.65789e13	1.27851	0.639256	−	0.768994i	$-0.279243\pi$
$911$	2.65789e13	1.27851	0.639256	+	0.768994i	$0.279243\pi$
$912$	0	0
$913$	1.35159e13	0.643763
$914$	1.05240e13	0.498796
$915$	0	0
$916$	4.96736e12	0.233129
$917$	−2.22928e13	−1.04113
$918$	0	0
$919$	1.52684e13	0.706110	0.353055	−	0.935603i	$-0.385143\pi$
$919$	1.52684e13	0.706110	0.353055	+	0.935603i	$0.385143\pi$
$920$	1.11823e12	0.0514619
$921$	0	0
$922$	−1.32889e13	−0.605621
$923$	2.39067e13	1.08421
$924$	0	0
$925$	1.15091e13	0.516896
$926$	−1.75639e13	−0.785001
$927$	0	0
$928$	−5.97431e11	−0.0264437
$929$	3.74604e13	1.65007	0.825033	−	0.565084i	$-0.191156\pi$
$929$	3.74604e13	1.65007	0.825033	+	0.565084i	$0.191156\pi$
$930$	0	0
$931$	−7.84664e11	−0.0342303
$932$	9.16102e12	0.397715
$933$	0	0
$934$	−1.00992e13	−0.434235
$935$	−1.69199e13	−0.724012
$936$	0	0
$937$	−2.62942e13	−1.11438	−0.557188	−	0.830386i	$-0.688120\pi$
$937$	−2.62942e13	−1.11438	−0.557188	+	0.830386i	$0.688120\pi$
$938$	−2.33486e13	−0.984799
$939$	0	0
$940$	−1.72357e13	−0.720036
$941$	−3.58875e13	−1.49207	−0.746036	−	0.665906i	$-0.768045\pi$
$941$	−3.58875e13	−1.49207	−0.746036	+	0.665906i	$0.768045\pi$
$942$	0	0
$943$	−6.31704e9	−0.000260143 0
$944$	9.53670e11	0.0390863
$945$	0	0
$946$	−1.01199e13	−0.410832
$947$	−3.11985e13	−1.26054	−0.630272	−	0.776374i	$-0.717057\pi$
$947$	−3.11985e13	−1.26054	−0.630272	+	0.776374i	$0.717057\pi$
$948$	0	0
$949$	−4.09325e13	−1.63821
$950$	7.61088e12	0.303165
$951$	0	0
$952$	−4.42782e12	−0.174713
$953$	−3.83515e13	−1.50614	−0.753068	−	0.657942i	$-0.771427\pi$
$953$	−3.83515e13	−1.50614	−0.753068	+	0.657942i	$0.771427\pi$
$954$	0	0
$955$	7.69411e12	0.299325
$956$	−1.32792e12	−0.0514174
$957$	0	0
$958$	1.64872e13	0.632415
$959$	−8.34263e11	−0.0318507
$960$	0	0
$961$	7.29182e12	0.275791
$962$	9.05267e12	0.340792
$963$	0	0
$964$	3.74383e12	0.139627
$965$	5.81751e12	0.215956
$966$	0	0
$967$	2.52076e13	0.927071	0.463536	−	0.886078i	$-0.346581\pi$
$967$	2.52076e13	0.927071	0.463536	+	0.886078i	$0.346581\pi$
$968$	−3.50969e12	−0.128478
$969$	0	0
$970$	−4.16957e13	−1.51223
$971$	9.11601e12	0.329093	0.164546	−	0.986369i	$-0.447384\pi$
$971$	9.11601e12	0.329093	0.164546	+	0.986369i	$0.447384\pi$
$972$	0	0
$973$	1.24633e13	0.445784
$974$	−1.11589e13	−0.397290
$975$	0	0
$976$	6.52762e12	0.230266
$977$	−4.10489e13	−1.44137	−0.720685	−	0.693262i	$-0.756173\pi$
$977$	−4.10489e13	−1.44137	−0.720685	+	0.693262i	$0.756173\pi$
$978$	0	0
$979$	−1.01486e13	−0.353087
$980$	−3.64860e12	−0.126360
$981$	0	0
$982$	−2.01029e13	−0.689854
$983$	−3.76886e12	−0.128742	−0.0643708	−	0.997926i	$-0.520504\pi$
$983$	−3.76886e12	−0.128742	−0.0643708	+	0.997926i	$0.520504\pi$
$984$	0	0
$985$	2.62431e13	0.888286
$986$	1.68184e12	0.0566682
$987$	0	0
$988$	5.98647e12	0.199878
$989$	−1.88280e12	−0.0625779
$990$	0	0
$991$	−3.54987e13	−1.16918	−0.584590	−	0.811329i	$-0.698745\pi$
$991$	−3.54987e13	−1.16918	−0.584590	+	0.811329i	$0.698745\pi$
$992$	6.09000e12	0.199671
$993$	0	0
$994$	1.24904e13	0.405824
$995$	−3.94750e13	−1.27679
$996$	0	0
$997$	−3.48328e13	−1.11650	−0.558252	−	0.829672i	$-0.688528\pi$
$997$	−3.48328e13	−1.11650	−0.558252	+	0.829672i	$0.688528\pi$
$998$	−1.16192e13	−0.370755
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.10.a.l.1.3		4
3.2	odd	2		38.10.a.d.1.4	✓	4
12.11	even	2		304.10.a.e.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.a.d.1.4	✓	4	3.2	odd	2
304.10.a.e.1.1		4	12.11	even	2
342.10.a.l.1.3		4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	342.a (trivial)

\(f(q)\)	\(=\)	\(q+16.0000 q^{2} +256.000 q^{4} +2367.11 q^{5} +5859.40 q^{7} +4096.00 q^{8} +O(q^{10})\)	\(q+16.0000 q^{2} +256.000 q^{4} +2367.11 q^{5} +5859.40 q^{7} +4096.00 q^{8} +37873.7 q^{10} +38743.9 q^{11} +179439. q^{13} +93750.4 q^{14} +65536.0 q^{16} -184492. q^{17} +130321. q^{19} +605979. q^{20} +619902. q^{22} +115333. q^{23} +3.65006e6 q^{25} +2.87102e6 q^{26} +1.50001e6 q^{28} -569755. q^{29} +5.80788e6 q^{31} +1.04858e6 q^{32} -2.95187e6 q^{34} +1.38698e7 q^{35} +3.15312e6 q^{37} +2.08514e6 q^{38} +9.69566e6 q^{40} -54772.2 q^{41} -1.63249e7 q^{43} +9.91844e6 q^{44} +1.84533e6 q^{46} -2.84428e7 q^{47} -6.02101e6 q^{49} +5.84010e7 q^{50} +4.59363e7 q^{52} -7.33201e7 q^{53} +9.17109e7 q^{55} +2.40001e7 q^{56} -9.11608e6 q^{58} +1.45518e7 q^{59} +9.96035e7 q^{61} +9.29260e7 q^{62} +1.67772e7 q^{64} +4.24751e8 q^{65} -2.49050e8 q^{67} -4.72299e7 q^{68} +2.21917e8 q^{70} +1.33230e8 q^{71} -2.28114e8 q^{73} +5.04499e7 q^{74} +3.33622e7 q^{76} +2.27016e8 q^{77} -6.65788e8 q^{79} +1.55131e8 q^{80} -876356. q^{82} +3.48852e8 q^{83} -4.36712e8 q^{85} -2.61199e8 q^{86} +1.58695e8 q^{88} -2.61939e8 q^{89} +1.05140e9 q^{91} +2.95252e7 q^{92} -4.55084e8 q^{94} +3.08484e8 q^{95} -1.10091e9 q^{97} -9.63361e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 64 q^{2} + 1024 q^{4} + 1395 q^{5} + 12307 q^{7} + 16384 q^{8}+O(q^{10}) \) 4 * q + 64 * q^2 + 1024 * q^4 + 1395 * q^5 + 12307 * q^7 + 16384 * q^8	\( 4 q + 64 q^{2} + 1024 q^{4} + 1395 q^{5} + 12307 q^{7} + 16384 q^{8} + 22320 q^{10} + 104249 q^{11} + 120486 q^{13} + 196912 q^{14} + 262144 q^{16} + 412139 q^{17} + 521284 q^{19} + 357120 q^{20} + 1667984 q^{22} - 3010300 q^{23} + 9760585 q^{25} + 1927776 q^{26} + 3150592 q^{28} - 6153240 q^{29} + 12774024 q^{31} + 4194304 q^{32} + 6594224 q^{34} - 9823425 q^{35} + 20506048 q^{37} + 8340544 q^{38} + 5713920 q^{40} - 11620300 q^{41} + 7698327 q^{43} + 26687744 q^{44} - 48164800 q^{46} + 31581083 q^{47} + 18970383 q^{49} + 156169360 q^{50} + 30844416 q^{52} - 72549422 q^{53} + 21332505 q^{55} + 50409472 q^{56} - 98451840 q^{58} + 149234120 q^{59} + 129004373 q^{61} + 204384384 q^{62} + 67108864 q^{64} - 124691700 q^{65} + 132595266 q^{67} + 105507584 q^{68} - 157174800 q^{70} + 47138482 q^{71} - 39332795 q^{73} + 328096768 q^{74} + 133448704 q^{76} + 165933719 q^{77} - 307010840 q^{79} + 91422720 q^{80} - 185924800 q^{82} + 746568232 q^{83} - 105005985 q^{85} + 123173232 q^{86} + 427003904 q^{88} - 286943482 q^{89} + 3155781114 q^{91} - 770636800 q^{92} + 505297328 q^{94} + 181797795 q^{95} + 793519958 q^{97} + 303526128 q^{98}+O(q^{100}) \) 4 * q + 64 * q^2 + 1024 * q^4 + 1395 * q^5 + 12307 * q^7 + 16384 * q^8 + 22320 * q^10 + 104249 * q^11 + 120486 * q^13 + 196912 * q^14 + 262144 * q^16 + 412139 * q^17 + 521284 * q^19 + 357120 * q^20 + 1667984 * q^22 - 3010300 * q^23 + 9760585 * q^25 + 1927776 * q^26 + 3150592 * q^28 - 6153240 * q^29 + 12774024 * q^31 + 4194304 * q^32 + 6594224 * q^34 - 9823425 * q^35 + 20506048 * q^37 + 8340544 * q^38 + 5713920 * q^40 - 11620300 * q^41 + 7698327 * q^43 + 26687744 * q^44 - 48164800 * q^46 + 31581083 * q^47 + 18970383 * q^49 + 156169360 * q^50 + 30844416 * q^52 - 72549422 * q^53 + 21332505 * q^55 + 50409472 * q^56 - 98451840 * q^58 + 149234120 * q^59 + 129004373 * q^61 + 204384384 * q^62 + 67108864 * q^64 - 124691700 * q^65 + 132595266 * q^67 + 105507584 * q^68 - 157174800 * q^70 + 47138482 * q^71 - 39332795 * q^73 + 328096768 * q^74 + 133448704 * q^76 + 165933719 * q^77 - 307010840 * q^79 + 91422720 * q^80 - 185924800 * q^82 + 746568232 * q^83 - 105005985 * q^85 + 123173232 * q^86 + 427003904 * q^88 - 286943482 * q^89 + 3155781114 * q^91 - 770636800 * q^92 + 505297328 * q^94 + 181797795 * q^95 + 793519958 * q^97 + 303526128 * q^98

Introduction

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