LMFDB - Embedded newform 153.10.a.f.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,10,Mod(1,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, 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("153.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	153.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:	$78.8004829331$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 2986x^{5} + 8252x^{4} + 2252056x^{3} - 10388768x^{2} - 243559296x - 675998208 $ x^7 - x^6 - 2986x^5 + 8252x^4 + 2252056x^3 - 10388768x^2 - 243559296*x - 675998208
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$16.8116$ of defining polynomial
Character	$\chi$	$=$	153.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+16.8116 q^{2} -229.369 q^{4} +1103.40 q^{5} -5164.29 q^{7} -12463.6 q^{8} +O(q^{10})$	\(q+16.8116 q^{2} -229.369 q^{4} +1103.40 q^{5} -5164.29 q^{7} -12463.6 q^{8} +18549.9 q^{10} -44537.1 q^{11} +69656.8 q^{13} -86820.2 q^{14} -92097.3 q^{16} -83521.0 q^{17} -170217. q^{19} -253085. q^{20} -748741. q^{22} +2.00737e6 q^{23} -735637. q^{25} +1.17105e6 q^{26} +1.18453e6 q^{28} -155688. q^{29} +4.27490e6 q^{31} +4.83307e6 q^{32} -1.40413e6 q^{34} -5.69827e6 q^{35} +1.51022e7 q^{37} -2.86163e6 q^{38} -1.37523e7 q^{40} -1.59320e7 q^{41} +1.49261e7 q^{43} +1.02154e7 q^{44} +3.37471e7 q^{46} -3.36137e7 q^{47} -1.36837e7 q^{49} -1.23673e7 q^{50} -1.59771e7 q^{52} +5.50379e7 q^{53} -4.91421e7 q^{55} +6.43658e7 q^{56} -2.61737e6 q^{58} +7.94611e7 q^{59} +1.27852e7 q^{61} +7.18682e7 q^{62} +1.28406e8 q^{64} +7.68593e7 q^{65} +2.73169e8 q^{67} +1.91571e7 q^{68} -9.57973e7 q^{70} -3.88392e6 q^{71} +2.32369e8 q^{73} +2.53892e8 q^{74} +3.90425e7 q^{76} +2.30002e8 q^{77} +3.38948e8 q^{79} -1.01620e8 q^{80} -2.67843e8 q^{82} -5.74624e8 q^{83} -9.21569e7 q^{85} +2.50932e8 q^{86} +5.55093e8 q^{88} +9.82429e8 q^{89} -3.59728e8 q^{91} -4.60427e8 q^{92} -5.65102e8 q^{94} -1.87817e8 q^{95} -1.03147e9 q^{97} -2.30046e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + q^{2} + 2389 q^{4} - 1362 q^{5} + 9388 q^{7} - 16821 q^{8}+O(q^{10}) $ 7 * q + q^2 + 2389 * q^4 - 1362 * q^5 + 9388 * q^7 - 16821 * q^8	\( 7 q + q^{2} + 2389 q^{4} - 1362 q^{5} + 9388 q^{7} - 16821 q^{8} + 154226 q^{10} - 135536 q^{11} + 166122 q^{13} - 447252 q^{14} + 1463585 q^{16} - 584647 q^{17} + 777172 q^{19} + 917162 q^{20} - 1222520 q^{22} - 1357764 q^{23} + 1065785 q^{25} + 14379966 q^{26} - 3328892 q^{28} - 967002 q^{29} + 3546740 q^{31} - 4825461 q^{32} - 83521 q^{34} + 530736 q^{35} + 18296498 q^{37} + 49363020 q^{38} + 127155062 q^{40} - 10285686 q^{41} + 21913204 q^{43} - 96696624 q^{44} - 151509484 q^{46} - 56639800 q^{47} + 27010351 q^{49} + 261150303 q^{50} - 156226378 q^{52} - 121813562 q^{53} + 40793128 q^{55} + 196175436 q^{56} - 236833910 q^{58} - 29222388 q^{59} - 49915846 q^{61} + 73506556 q^{62} + 317922057 q^{64} + 122633668 q^{65} + 301863420 q^{67} - 199531669 q^{68} + 966315960 q^{70} - 652473940 q^{71} + 306656342 q^{73} - 249173874 q^{74} + 128694700 q^{76} + 102442536 q^{77} + 959147884 q^{79} + 692173602 q^{80} + 1046441254 q^{82} + 1512945268 q^{83} + 113755602 q^{85} + 164953236 q^{86} + 1132038848 q^{88} + 1971327114 q^{89} - 1061062864 q^{91} - 901186756 q^{92} + 2534831232 q^{94} + 3249631512 q^{95} + 2006526254 q^{97} + 2170640009 q^{98}+O(q^{100}) \) 7 * q + q^2 + 2389 * q^4 - 1362 * q^5 + 9388 * q^7 - 16821 * q^8 + 154226 * q^10 - 135536 * q^11 + 166122 * q^13 - 447252 * q^14 + 1463585 * q^16 - 584647 * q^17 + 777172 * q^19 + 917162 * q^20 - 1222520 * q^22 - 1357764 * q^23 + 1065785 * q^25 + 14379966 * q^26 - 3328892 * q^28 - 967002 * q^29 + 3546740 * q^31 - 4825461 * q^32 - 83521 * q^34 + 530736 * q^35 + 18296498 * q^37 + 49363020 * q^38 + 127155062 * q^40 - 10285686 * q^41 + 21913204 * q^43 - 96696624 * q^44 - 151509484 * q^46 - 56639800 * q^47 + 27010351 * q^49 + 261150303 * q^50 - 156226378 * q^52 - 121813562 * q^53 + 40793128 * q^55 + 196175436 * q^56 - 236833910 * q^58 - 29222388 * q^59 - 49915846 * q^61 + 73506556 * q^62 + 317922057 * q^64 + 122633668 * q^65 + 301863420 * q^67 - 199531669 * q^68 + 966315960 * q^70 - 652473940 * q^71 + 306656342 * q^73 - 249173874 * q^74 + 128694700 * q^76 + 102442536 * q^77 + 959147884 * q^79 + 692173602 * q^80 + 1046441254 * q^82 + 1512945268 * q^83 + 113755602 * q^85 + 164953236 * q^86 + 1132038848 * q^88 + 1971327114 * q^89 - 1061062864 * q^91 - 901186756 * q^92 + 2534831232 * q^94 + 3249631512 * q^95 + 2006526254 * q^97 + 2170640009 * 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 $

$2$	16.8116	0.742977	0.371488	−	0.928438i	$-0.378848\pi$
$2$	16.8116	0.742977	0.371488	+	0.928438i	$0.378848\pi$
$3$	0	0
$3$	0	0
$4$	−229.369	−0.447986
$5$	1103.40	0.789528	0.394764	−	0.918783i	$-0.370826\pi$
$5$	1103.40	0.789528	0.394764	+	0.918783i	$0.370826\pi$
$6$	0	0
$7$	−5164.29	−0.812961	−0.406480	−	0.913660i	$-0.633244\pi$
$7$	−5164.29	−0.812961	−0.406480	+	0.913660i	$0.633244\pi$
$8$	−12463.6	−1.07582
$9$	0	0
$10$	18549.9	0.586601
$11$	−44537.1	−0.917180	−0.458590	−	0.888648i	$-0.651645\pi$
$11$	−44537.1	−0.917180	−0.458590	+	0.888648i	$0.651645\pi$
$12$	0	0
$13$	69656.8	0.676424	0.338212	−	0.941070i	$-0.390178\pi$
$13$	69656.8	0.676424	0.338212	+	0.941070i	$0.390178\pi$
$14$	−86820.2	−0.604011
$15$	0	0
$16$	−92097.3	−0.351323
$17$	−83521.0	−0.242536
$17$	−83521.0	−0.242536
$18$	0	0
$19$	−170217.	−0.299648	−0.149824	−	0.988713i	$-0.547871\pi$
$19$	−170217.	−0.299648	−0.149824	+	0.988713i	$0.547871\pi$
$20$	−253085.	−0.353697
$21$	0	0
$22$	−748741.	−0.681443
$23$	2.00737e6	1.49572	0.747861	−	0.663855i	$-0.231081\pi$
$23$	2.00737e6	1.49572	0.747861	+	0.663855i	$0.231081\pi$
$24$	0	0
$25$	−735637.	−0.376646
$26$	1.17105e6	0.502567
$27$	0	0
$28$	1.18453e6	0.364195
$29$	−155688.	−0.0408755	−0.0204378	−	0.999791i	$-0.506506\pi$
$29$	−155688.	−0.0408755	−0.0204378	+	0.999791i	$0.506506\pi$
$30$	0	0
$31$	4.27490e6	0.831379	0.415689	−	0.909507i	$-0.363540\pi$
$31$	4.27490e6	0.831379	0.415689	+	0.909507i	$0.363540\pi$
$32$	4.83307e6	0.814795
$33$	0	0
$34$	−1.40413e6	−0.180198
$35$	−5.69827e6	−0.641855
$36$	0	0
$37$	1.51022e7	1.32474	0.662371	−	0.749176i	$-0.269550\pi$
$37$	1.51022e7	1.32474	0.662371	+	0.749176i	$0.269550\pi$
$38$	−2.86163e6	−0.222632
$39$	0	0
$40$	−1.37523e7	−0.849389
$41$	−1.59320e7	−0.880526	−0.440263	−	0.897869i	$-0.645115\pi$
$41$	−1.59320e7	−0.880526	−0.440263	+	0.897869i	$0.645115\pi$
$42$	0	0
$43$	1.49261e7	0.665790	0.332895	−	0.942964i	$-0.391975\pi$
$43$	1.49261e7	0.665790	0.332895	+	0.942964i	$0.391975\pi$
$44$	1.02154e7	0.410883
$45$	0	0
$46$	3.37471e7	1.11129
$47$	−3.36137e7	−1.00479	−0.502396	−	0.864638i	$-0.667548\pi$
$47$	−3.36137e7	−1.00479	−0.502396	+	0.864638i	$0.667548\pi$
$48$	0	0
$49$	−1.36837e7	−0.339095
$50$	−1.23673e7	−0.279839
$51$	0	0
$52$	−1.59771e7	−0.303028
$53$	5.50379e7	0.958121	0.479060	−	0.877782i	$-0.340977\pi$
$53$	5.50379e7	0.958121	0.479060	+	0.877782i	$0.340977\pi$
$54$	0	0
$55$	−4.91421e7	−0.724139
$56$	6.43658e7	0.874599
$57$	0	0
$58$	−2.61737e6	−0.0303696
$59$	7.94611e7	0.853730	0.426865	−	0.904315i	$-0.359618\pi$
$59$	7.94611e7	0.853730	0.426865	+	0.904315i	$0.359618\pi$
$60$	0	0
$61$	1.27852e7	0.118229	0.0591146	−	0.998251i	$-0.481172\pi$
$61$	1.27852e7	0.118229	0.0591146	+	0.998251i	$0.481172\pi$
$62$	7.18682e7	0.617695
$63$	0	0
$64$	1.28406e8	0.956697
$65$	7.68593e7	0.534055
$66$	0	0
$67$	2.73169e8	1.65613	0.828066	−	0.560631i	$-0.189441\pi$
$67$	2.73169e8	1.65613	0.828066	+	0.560631i	$0.189441\pi$
$68$	1.91571e7	0.108652
$69$	0	0
$70$	−9.57973e7	−0.476883
$71$	−3.88392e6	−0.0181388	−0.00906938	−	0.999959i	$-0.502887\pi$
$71$	−3.88392e6	−0.0181388	−0.00906938	+	0.999959i	$0.502887\pi$
$72$	0	0
$73$	2.32369e8	0.957690	0.478845	−	0.877900i	$-0.341056\pi$
$73$	2.32369e8	0.957690	0.478845	+	0.877900i	$0.341056\pi$
$74$	2.53892e8	0.984253
$75$	0	0
$76$	3.90425e7	0.134238
$77$	2.30002e8	0.745631
$78$	0	0
$79$	3.38948e8	0.979064	0.489532	−	0.871985i	$-0.337168\pi$
$79$	3.38948e8	0.979064	0.489532	+	0.871985i	$0.337168\pi$
$80$	−1.01620e8	−0.277379
$81$	0	0
$82$	−2.67843e8	−0.654210
$83$	−5.74624e8	−1.32902	−0.664511	−	0.747278i	$-0.731360\pi$
$83$	−5.74624e8	−1.32902	−0.664511	+	0.747278i	$0.731360\pi$
$84$	0	0
$85$	−9.21569e7	−0.191489
$86$	2.50932e8	0.494666
$87$	0	0
$88$	5.55093e8	0.986720
$89$	9.82429e8	1.65976	0.829882	−	0.557940i	$-0.188408\pi$
$89$	9.82429e8	1.65976	0.829882	+	0.557940i	$0.188408\pi$
$90$	0	0
$91$	−3.59728e8	−0.549906
$92$	−4.60427e8	−0.670062
$93$	0	0
$94$	−5.65102e8	−0.746537
$95$	−1.87817e8	−0.236581
$96$	0	0
$97$	−1.03147e9	−1.18300	−0.591500	−	0.806305i	$-0.701464\pi$
$97$	−1.03147e9	−1.18300	−0.591500	+	0.806305i	$0.701464\pi$
$98$	−2.30046e8	−0.251940
$99$	0	0
$100$	1.68732e8	0.168732
$101$	5.23482e7	0.0500559	0.0250280	−	0.999687i	$-0.492033\pi$
$101$	5.23482e7	0.0500559	0.0250280	+	0.999687i	$0.492033\pi$
$102$	0	0
$103$	4.65791e8	0.407778	0.203889	−	0.978994i	$-0.434642\pi$
$103$	4.65791e8	0.407778	0.203889	+	0.978994i	$0.434642\pi$
$104$	−8.68177e8	−0.727710
$105$	0	0
$106$	9.25277e8	0.711861
$107$	1.44228e9	1.06371	0.531854	−	0.846836i	$-0.321496\pi$
$107$	1.44228e9	1.06371	0.531854	+	0.846836i	$0.321496\pi$
$108$	0	0
$109$	2.37882e9	1.61414	0.807072	−	0.590453i	$-0.201051\pi$
$109$	2.37882e9	1.61414	0.807072	+	0.590453i	$0.201051\pi$
$110$	−8.26160e8	−0.538018
$111$	0	0
$112$	4.75617e8	0.285612
$113$	5.54552e8	0.319955	0.159978	−	0.987121i	$-0.448858\pi$
$113$	5.54552e8	0.319955	0.159978	+	0.987121i	$0.448858\pi$
$114$	0	0
$115$	2.21492e9	1.18091
$116$	3.57099e7	0.0183117
$117$	0	0
$118$	1.33587e9	0.634302
$119$	4.31327e8	0.197172
$120$	0	0
$121$	−3.74397e8	−0.158781
$122$	2.14941e8	0.0878415
$123$	0	0
$124$	−9.80529e8	−0.372446
$125$	−2.96678e9	−1.08690
$126$	0	0
$127$	3.25473e9	1.11019	0.555097	−	0.831786i	$-0.312681\pi$
$127$	3.25473e9	1.11019	0.555097	+	0.831786i	$0.312681\pi$
$128$	−3.15822e8	−0.103991
$129$	0	0
$130$	1.29213e9	0.396791
$131$	2.29117e9	0.679731	0.339865	−	0.940474i	$-0.389618\pi$
$131$	2.29117e9	0.679731	0.339865	+	0.940474i	$0.389618\pi$
$132$	0	0
$133$	8.79051e8	0.243602
$134$	4.59242e9	1.23047
$135$	0	0
$136$	1.04097e9	0.260925
$137$	−7.07071e9	−1.71483	−0.857413	−	0.514628i	$-0.827930\pi$
$137$	−7.07071e9	−1.71483	−0.857413	+	0.514628i	$0.827930\pi$
$138$	0	0
$139$	−2.13323e9	−0.484697	−0.242349	−	0.970189i	$-0.577918\pi$
$139$	−2.13323e9	−0.484697	−0.242349	+	0.970189i	$0.577918\pi$
$140$	1.30700e9	0.287542
$141$	0	0
$142$	−6.52951e7	−0.0134767
$143$	−3.10231e9	−0.620402
$144$	0	0
$145$	−1.71786e8	−0.0322724
$146$	3.90650e9	0.711541
$147$	0	0
$148$	−3.46396e9	−0.593465
$149$	8.98904e9	1.49408	0.747042	−	0.664777i	$-0.231473\pi$
$149$	8.98904e9	1.49408	0.747042	+	0.664777i	$0.231473\pi$
$150$	0	0
$151$	4.53054e9	0.709175	0.354588	−	0.935023i	$-0.384621\pi$
$151$	4.53054e9	0.709175	0.354588	+	0.935023i	$0.384621\pi$
$152$	2.12152e9	0.322368
$153$	0	0
$154$	3.86672e9	0.553987
$155$	4.71692e9	0.656396
$156$	0	0
$157$	−3.69961e9	−0.485967	−0.242984	−	0.970030i	$-0.578126\pi$
$157$	−3.69961e9	−0.485967	−0.242984	+	0.970030i	$0.578126\pi$
$158$	5.69827e9	0.727422
$159$	0	0
$160$	5.33280e9	0.643303
$161$	−1.03666e10	−1.21596
$162$	0	0
$163$	1.71522e10	1.90317	0.951583	−	0.307393i	$-0.0994565\pi$
$163$	1.71522e10	1.90317	0.951583	+	0.307393i	$0.0994565\pi$
$164$	3.65430e9	0.394463
$165$	0	0
$166$	−9.66037e9	−0.987433
$167$	−1.39036e10	−1.38326	−0.691628	−	0.722254i	$-0.743106\pi$
$167$	−1.39036e10	−1.38326	−0.691628	+	0.722254i	$0.743106\pi$
$168$	0	0
$169$	−5.75242e9	−0.542451
$170$	−1.54931e9	−0.142272
$171$	0	0
$172$	−3.42357e9	−0.298264
$173$	−1.51288e9	−0.128409	−0.0642047	−	0.997937i	$-0.520451\pi$
$173$	−1.51288e9	−0.128409	−0.0642047	+	0.997937i	$0.520451\pi$
$174$	0	0
$175$	3.79904e9	0.306198
$176$	4.10174e9	0.322227
$177$	0	0
$178$	1.65162e10	1.23317
$179$	2.09830e10	1.52767	0.763835	−	0.645411i	$-0.223314\pi$
$179$	2.09830e10	1.52767	0.763835	+	0.645411i	$0.223314\pi$
$180$	0	0
$181$	−1.75141e10	−1.21293	−0.606464	−	0.795111i	$-0.707413\pi$
$181$	−1.75141e10	−1.21293	−0.606464	+	0.795111i	$0.707413\pi$
$182$	−6.04762e9	−0.408567
$183$	0	0
$184$	−2.50190e10	−1.60913
$185$	1.66637e10	1.04592
$186$	0	0
$187$	3.71978e9	0.222449
$188$	7.70993e9	0.450132
$189$	0	0
$190$	−3.15752e9	−0.175774
$191$	−1.64385e10	−0.893741	−0.446871	−	0.894599i	$-0.647462\pi$
$191$	−1.64385e10	−0.893741	−0.446871	+	0.894599i	$0.647462\pi$
$192$	0	0
$193$	−9.12709e9	−0.473505	−0.236753	−	0.971570i	$-0.576083\pi$
$193$	−9.12709e9	−0.473505	−0.236753	+	0.971570i	$0.576083\pi$
$194$	−1.73407e10	−0.878942
$195$	0	0
$196$	3.13861e9	0.151910
$197$	−1.53151e9	−0.0724472	−0.0362236	−	0.999344i	$-0.511533\pi$
$197$	−1.53151e9	−0.0724472	−0.0362236	+	0.999344i	$0.511533\pi$
$198$	0	0
$199$	1.77679e10	0.803152	0.401576	−	0.915826i	$-0.368463\pi$
$199$	1.77679e10	0.803152	0.401576	+	0.915826i	$0.368463\pi$
$200$	9.16870e9	0.405203
$201$	0	0
$202$	8.80059e8	0.0371904
$203$	8.04017e8	0.0332302
$204$	0	0
$205$	−1.75793e10	−0.695200
$206$	7.83072e9	0.302970
$207$	0	0
$208$	−6.41521e9	−0.237643
$209$	7.58097e9	0.274832
$210$	0	0
$211$	5.19005e10	1.80260	0.901302	−	0.433192i	$-0.142613\pi$
$211$	5.19005e10	1.80260	0.901302	+	0.433192i	$0.142613\pi$
$212$	−1.26240e10	−0.429224
$213$	0	0
$214$	2.42471e10	0.790310
$215$	1.64694e10	0.525660
$216$	0	0
$217$	−2.20769e10	−0.675878
$218$	3.99919e10	1.19927
$219$	0	0
$220$	1.12717e10	0.324404
$221$	−5.81781e9	−0.164057
$222$	0	0
$223$	−6.09533e10	−1.65054	−0.825269	−	0.564740i	$-0.808976\pi$
$223$	−6.09533e10	−1.65054	−0.825269	+	0.564740i	$0.808976\pi$
$224$	−2.49594e10	−0.662396
$225$	0	0
$226$	9.32293e9	0.237719
$227$	−6.35858e10	−1.58944	−0.794720	−	0.606977i	$-0.792382\pi$
$227$	−6.35858e10	−1.58944	−0.794720	+	0.606977i	$0.792382\pi$
$228$	0	0
$229$	−6.22903e10	−1.49679	−0.748395	−	0.663254i	$-0.769175\pi$
$229$	−6.22903e10	−1.49679	−0.748395	+	0.663254i	$0.769175\pi$
$230$	3.72365e10	0.877392
$231$	0	0
$232$	1.94043e9	0.0439747
$233$	−8.69026e10	−1.93166	−0.965831	−	0.259172i	$-0.916550\pi$
$233$	−8.69026e10	−1.93166	−0.965831	+	0.259172i	$0.916550\pi$
$234$	0	0
$235$	−3.70893e10	−0.793311
$236$	−1.82259e10	−0.382459
$237$	0	0
$238$	7.25131e9	0.146494
$239$	−7.04686e10	−1.39703	−0.698514	−	0.715597i	$-0.746155\pi$
$239$	−7.04686e10	−1.39703	−0.698514	+	0.715597i	$0.746155\pi$
$240$	0	0
$241$	6.25058e10	1.19356	0.596779	−	0.802405i	$-0.296447\pi$
$241$	6.25058e10	1.19356	0.596779	+	0.802405i	$0.296447\pi$
$242$	−6.29423e9	−0.117971
$243$	0	0
$244$	−2.93253e9	−0.0529649
$245$	−1.50986e10	−0.267725
$246$	0	0
$247$	−1.18568e10	−0.202689
$248$	−5.32808e10	−0.894413
$249$	0	0
$250$	−4.98764e10	−0.807541
$251$	7.26518e9	0.115535	0.0577676	−	0.998330i	$-0.481602\pi$
$251$	7.26518e9	0.115535	0.0577676	+	0.998330i	$0.481602\pi$
$252$	0	0
$253$	−8.94022e10	−1.37185
$254$	5.47174e10	0.824848
$255$	0	0
$256$	−7.10532e10	−1.03396
$257$	8.23779e10	1.17791	0.588955	−	0.808166i	$-0.299540\pi$
$257$	8.23779e10	1.17791	0.588955	+	0.808166i	$0.299540\pi$
$258$	0	0
$259$	−7.79920e10	−1.07696
$260$	−1.76291e10	−0.239249
$261$	0	0
$262$	3.85184e10	0.505024
$263$	−8.05229e10	−1.03781	−0.518906	−	0.854831i	$-0.673660\pi$
$263$	−8.05229e10	−1.03781	−0.518906	+	0.854831i	$0.673660\pi$
$264$	0	0
$265$	6.07287e10	0.756463
$266$	1.47783e10	0.180991
$267$	0	0
$268$	−6.26564e10	−0.741923
$269$	−3.37804e10	−0.393350	−0.196675	−	0.980469i	$-0.563014\pi$
$269$	−3.37804e10	−0.393350	−0.196675	+	0.980469i	$0.563014\pi$
$270$	0	0
$271$	5.31396e10	0.598489	0.299245	−	0.954176i	$-0.403265\pi$
$271$	5.31396e10	0.598489	0.299245	+	0.954176i	$0.403265\pi$
$272$	7.69206e9	0.0852084
$273$	0	0
$274$	−1.18870e11	−1.27408
$275$	3.27631e10	0.345452
$276$	0	0
$277$	−1.33887e11	−1.36640	−0.683201	−	0.730231i	$-0.739413\pi$
$277$	−1.33887e11	−1.36640	−0.683201	+	0.730231i	$0.739413\pi$
$278$	−3.58631e10	−0.360119
$279$	0	0
$280$	7.10211e10	0.690520
$281$	6.71427e10	0.642422	0.321211	−	0.947008i	$-0.395910\pi$
$281$	6.71427e10	0.642422	0.321211	+	0.947008i	$0.395910\pi$
$282$	0	0
$283$	1.11880e11	1.03684	0.518420	−	0.855126i	$-0.326520\pi$
$283$	1.11880e11	1.03684	0.518420	+	0.855126i	$0.326520\pi$
$284$	8.90850e8	0.00812591
$285$	0	0
$286$	−5.21550e10	−0.460944
$287$	8.22774e10	0.715833
$288$	0	0
$289$	6.97576e9	0.0588235
$290$	−2.88800e9	−0.0239776
$291$	0	0
$292$	−5.32981e10	−0.429031
$293$	−1.51192e11	−1.19846	−0.599230	−	0.800577i	$-0.704526\pi$
$293$	−1.51192e11	−1.19846	−0.599230	+	0.800577i	$0.704526\pi$
$294$	0	0
$295$	8.76773e10	0.674044
$296$	−1.88228e11	−1.42518
$297$	0	0
$298$	1.51121e11	1.11007
$299$	1.39827e11	1.01174
$300$	0	0
$301$	−7.70825e10	−0.541261
$302$	7.61658e10	0.526901
$303$	0	0
$304$	1.56765e10	0.105273
$305$	1.41072e10	0.0933452
$306$	0	0
$307$	6.62355e10	0.425567	0.212784	−	0.977099i	$-0.431747\pi$
$307$	6.62355e10	0.425567	0.212784	+	0.977099i	$0.431747\pi$
$308$	−5.27553e10	−0.334032
$309$	0	0
$310$	7.92992e10	0.487687
$311$	9.27102e10	0.561960	0.280980	−	0.959714i	$-0.409340\pi$
$311$	9.27102e10	0.561960	0.280980	+	0.959714i	$0.409340\pi$
$312$	0	0
$313$	2.58675e11	1.52337	0.761684	−	0.647949i	$-0.224373\pi$
$313$	2.58675e11	1.52337	0.761684	+	0.647949i	$0.224373\pi$
$314$	−6.21965e10	−0.361062
$315$	0	0
$316$	−7.77440e10	−0.438607
$317$	4.47169e10	0.248717	0.124358	−	0.992237i	$-0.460313\pi$
$317$	4.47169e10	0.248717	0.124358	+	0.992237i	$0.460313\pi$
$318$	0	0
$319$	6.93388e9	0.0374902
$320$	1.41683e11	0.755338
$321$	0	0
$322$	−1.74280e11	−0.903433
$323$	1.42167e10	0.0726754
$324$	0	0
$325$	−5.12421e10	−0.254772
$326$	2.88357e11	1.41401
$327$	0	0
$328$	1.98570e11	0.947287
$329$	1.73591e11	0.816856
$330$	0	0
$331$	4.78159e10	0.218951	0.109475	−	0.993990i	$-0.465083\pi$
$331$	4.78159e10	0.218951	0.109475	+	0.993990i	$0.465083\pi$
$332$	1.31801e11	0.595383
$333$	0	0
$334$	−2.33742e11	−1.02773
$335$	3.01414e11	1.30756
$336$	0	0
$337$	3.76342e11	1.58945	0.794727	−	0.606968i	$-0.207614\pi$
$337$	3.76342e11	1.58945	0.794727	+	0.606968i	$0.207614\pi$
$338$	−9.67077e10	−0.403029
$339$	0	0
$340$	2.11379e10	0.0857841
$341$	−1.90392e11	−0.762524
$342$	0	0
$343$	2.79064e11	1.08863
$344$	−1.86033e11	−0.716270
$345$	0	0
$346$	−2.54340e10	−0.0954052
$347$	1.77078e11	0.655665	0.327833	−	0.944736i	$-0.393682\pi$
$347$	1.77078e11	0.655665	0.327833	+	0.944736i	$0.393682\pi$
$348$	0	0
$349$	2.43883e11	0.879967	0.439984	−	0.898006i	$-0.354984\pi$
$349$	2.43883e11	0.879967	0.439984	+	0.898006i	$0.354984\pi$
$350$	6.38681e10	0.227498
$351$	0	0
$352$	−2.15251e11	−0.747313
$353$	−1.91758e11	−0.657304	−0.328652	−	0.944451i	$-0.606594\pi$
$353$	−1.91758e11	−0.657304	−0.328652	+	0.944451i	$0.606594\pi$
$354$	0	0
$355$	−4.28551e9	−0.0143211
$356$	−2.25338e11	−0.743550
$357$	0	0
$358$	3.52759e11	1.13502
$359$	6.43139e10	0.204352	0.102176	−	0.994766i	$-0.467419\pi$
$359$	6.43139e10	0.204352	0.102176	+	0.994766i	$0.467419\pi$
$360$	0	0
$361$	−2.93714e11	−0.910211
$362$	−2.94441e11	−0.901177
$363$	0	0
$364$	8.25104e10	0.246350
$365$	2.56395e11	0.756123
$366$	0	0
$367$	7.24947e10	0.208597	0.104299	−	0.994546i	$-0.466740\pi$
$367$	7.24947e10	0.208597	0.104299	+	0.994546i	$0.466740\pi$
$368$	−1.84873e11	−0.525482
$369$	0	0
$370$	2.80144e11	0.777095
$371$	−2.84232e11	−0.778914
$372$	0	0
$373$	−5.44526e10	−0.145656	−0.0728281	−	0.997345i	$-0.523202\pi$
$373$	−5.44526e10	−0.145656	−0.0728281	+	0.997345i	$0.523202\pi$
$374$	6.25356e10	0.165274
$375$	0	0
$376$	4.18949e11	1.08097
$377$	−1.08447e10	−0.0276492
$378$	0	0
$379$	−2.15005e11	−0.535270	−0.267635	−	0.963520i	$-0.586242\pi$
$379$	−2.15005e11	−0.535270	−0.267635	+	0.963520i	$0.586242\pi$
$380$	4.30794e10	0.105985
$381$	0	0
$382$	−2.76358e11	−0.664029
$383$	4.29189e11	1.01919	0.509594	−	0.860415i	$-0.329796\pi$
$383$	4.29189e11	1.01919	0.509594	+	0.860415i	$0.329796\pi$
$384$	0	0
$385$	2.53784e11	0.588696
$386$	−1.53441e11	−0.351803
$387$	0	0
$388$	2.36587e11	0.529967
$389$	2.02217e11	0.447760	0.223880	−	0.974617i	$-0.428128\pi$
$389$	2.02217e11	0.447760	0.223880	+	0.974617i	$0.428128\pi$
$390$	0	0
$391$	−1.67657e11	−0.362766
$392$	1.70549e11	0.364805
$393$	0	0
$394$	−2.57472e10	−0.0538266
$395$	3.73995e11	0.772998
$396$	0	0
$397$	1.81106e11	0.365911	0.182955	−	0.983121i	$-0.441434\pi$
$397$	1.81106e11	0.365911	0.182955	+	0.983121i	$0.441434\pi$
$398$	2.98708e11	0.596723
$399$	0	0
$400$	6.77501e10	0.132324
$401$	1.40602e11	0.271545	0.135772	−	0.990740i	$-0.456648\pi$
$401$	1.40602e11	0.271545	0.135772	+	0.990740i	$0.456648\pi$
$402$	0	0
$403$	2.97776e11	0.562364
$404$	−1.20070e10	−0.0224243
$405$	0	0
$406$	1.35168e10	0.0246893
$407$	−6.72606e11	−1.21503
$408$	0	0
$409$	−6.11843e11	−1.08115	−0.540574	−	0.841297i	$-0.681793\pi$
$409$	−6.11843e11	−1.08115	−0.540574	+	0.841297i	$0.681793\pi$
$410$	−2.95537e11	−0.516517
$411$	0	0
$412$	−1.06838e11	−0.182679
$413$	−4.10360e11	−0.694049
$414$	0	0
$415$	−6.34039e11	−1.04930
$416$	3.36656e11	0.551146
$417$	0	0
$418$	1.27449e11	0.204193
$419$	−2.89071e10	−0.0458186	−0.0229093	−	0.999738i	$-0.507293\pi$
$419$	−2.89071e10	−0.0458186	−0.0229093	+	0.999738i	$0.507293\pi$
$420$	0	0
$421$	1.06260e12	1.64854	0.824272	−	0.566193i	$-0.191584\pi$
$421$	1.06260e12	1.64854	0.824272	+	0.566193i	$0.191584\pi$
$422$	8.72532e11	1.33929
$423$	0	0
$424$	−6.85971e11	−1.03077
$425$	6.14411e10	0.0913501
$426$	0	0
$427$	−6.60267e10	−0.0961156
$428$	−3.30814e11	−0.476526
$429$	0	0
$430$	2.76878e11	0.390553
$431$	5.09485e10	0.0711187	0.0355594	−	0.999368i	$-0.488679\pi$
$431$	5.09485e10	0.0711187	0.0355594	+	0.999368i	$0.488679\pi$
$432$	0	0
$433$	−1.02428e12	−1.40030	−0.700152	−	0.713994i	$-0.746885\pi$
$433$	−1.02428e12	−1.40030	−0.700152	+	0.713994i	$0.746885\pi$
$434$	−3.71148e11	−0.502162
$435$	0	0
$436$	−5.45627e11	−0.723113
$437$	−3.41688e11	−0.448191
$438$	0	0
$439$	3.70271e11	0.475805	0.237903	−	0.971289i	$-0.423540\pi$
$439$	3.70271e11	0.475805	0.237903	+	0.971289i	$0.423540\pi$
$440$	6.12489e11	0.779043
$441$	0	0
$442$	−9.78069e10	−0.121890
$443$	1.17113e12	1.44473	0.722366	−	0.691511i	$-0.243054\pi$
$443$	1.17113e12	1.44473	0.722366	+	0.691511i	$0.243054\pi$
$444$	0	0
$445$	1.08401e12	1.31043
$446$	−1.02473e12	−1.22631
$447$	0	0
$448$	−6.63124e11	−0.777757
$449$	−6.79800e10	−0.0789355	−0.0394678	−	0.999221i	$-0.512566\pi$
$449$	−6.79800e10	−0.0789355	−0.0394678	+	0.999221i	$0.512566\pi$
$450$	0	0
$451$	7.09563e11	0.807601
$452$	−1.27197e11	−0.143335
$453$	0	0
$454$	−1.06898e12	−1.18092
$455$	−3.96924e11	−0.434166
$456$	0	0
$457$	1.72167e12	1.84640	0.923202	−	0.384315i	$-0.125562\pi$
$457$	1.72167e12	1.84640	0.923202	+	0.384315i	$0.125562\pi$
$458$	−1.04720e12	−1.11208
$459$	0	0
$460$	−5.08034e11	−0.529033
$461$	−1.42332e12	−1.46774	−0.733868	−	0.679292i	$-0.762287\pi$
$461$	−1.42332e12	−1.46774	−0.733868	+	0.679292i	$0.762287\pi$
$462$	0	0
$463$	1.62089e12	1.63922	0.819611	−	0.572920i	$-0.194189\pi$
$463$	1.62089e12	1.63922	0.819611	+	0.572920i	$0.194189\pi$
$464$	1.43384e10	0.0143605
$465$	0	0
$466$	−1.46098e12	−1.43518
$467$	1.13569e12	1.10493	0.552465	−	0.833536i	$-0.313687\pi$
$467$	1.13569e12	1.10493	0.552465	+	0.833536i	$0.313687\pi$
$468$	0	0
$469$	−1.41072e12	−1.34637
$470$	−6.23533e11	−0.589412
$471$	0	0
$472$	−9.90374e11	−0.918460
$473$	−6.64763e11	−0.610649
$474$	0	0
$475$	1.25218e11	0.112861
$476$	−9.89328e10	−0.0883302
$477$	0	0
$478$	−1.18469e12	−1.03796
$479$	−1.54480e11	−0.134080	−0.0670398	−	0.997750i	$-0.521355\pi$
$479$	−1.54480e11	−0.134080	−0.0670398	+	0.997750i	$0.521355\pi$
$480$	0	0
$481$	1.05197e12	0.896087
$482$	1.05083e12	0.886786
$483$	0	0
$484$	8.58750e10	0.0711316
$485$	−1.13813e12	−0.934011
$486$	0	0
$487$	−9.40063e11	−0.757315	−0.378657	−	0.925537i	$-0.623614\pi$
$487$	−9.40063e11	−0.757315	−0.378657	+	0.925537i	$0.623614\pi$
$488$	−1.59350e11	−0.127193
$489$	0	0
$490$	−2.53832e11	−0.198913
$491$	5.38393e11	0.418055	0.209027	−	0.977910i	$-0.432970\pi$
$491$	5.38393e11	0.418055	0.209027	+	0.977910i	$0.432970\pi$
$492$	0	0
$493$	1.30032e10	0.00991377
$494$	−1.99332e11	−0.150593
$495$	0	0
$496$	−3.93707e11	−0.292083
$497$	2.00577e10	0.0147461
$498$	0	0
$499$	−6.12934e11	−0.442549	−0.221274	−	0.975212i	$-0.571022\pi$
$499$	−6.12934e11	−0.442549	−0.221274	+	0.975212i	$0.571022\pi$
$500$	6.80485e11	0.486916
$501$	0	0
$502$	1.22140e11	0.0858400
$503$	2.31510e12	1.61255	0.806277	−	0.591538i	$-0.201479\pi$
$503$	2.31510e12	1.61255	0.806277	+	0.591538i	$0.201479\pi$
$504$	0	0
$505$	5.77609e10	0.0395205
$506$	−1.50300e12	−1.01925
$507$	0	0
$508$	−7.46534e11	−0.497351
$509$	1.48597e12	0.981249	0.490625	−	0.871371i	$-0.336769\pi$
$509$	1.48597e12	0.981249	0.490625	+	0.871371i	$0.336769\pi$
$510$	0	0
$511$	−1.20002e12	−0.778564
$512$	−1.03282e12	−0.664217
$513$	0	0
$514$	1.38491e12	0.875159
$515$	5.13954e11	0.321952
$516$	0	0
$517$	1.49706e12	0.921575
$518$	−1.31117e12	−0.800159
$519$	0	0
$520$	−9.57945e11	−0.574547
$521$	2.26648e11	0.134766	0.0673832	−	0.997727i	$-0.478535\pi$
$521$	2.26648e11	0.134766	0.0673832	+	0.997727i	$0.478535\pi$
$522$	0	0
$523$	−1.52624e12	−0.891998	−0.445999	−	0.895033i	$-0.647152\pi$
$523$	−1.52624e12	−0.891998	−0.445999	+	0.895033i	$0.647152\pi$
$524$	−5.25523e11	−0.304510
$525$	0	0
$526$	−1.35372e12	−0.771070
$527$	−3.57044e11	−0.201639
$528$	0	0
$529$	2.22836e12	1.23719
$530$	1.02095e12	0.562034
$531$	0	0
$532$	−2.01627e11	−0.109130
$533$	−1.10977e12	−0.595609
$534$	0	0
$535$	1.59141e12	0.839827
$536$	−3.40468e12	−1.78170
$537$	0	0
$538$	−5.67903e11	−0.292250
$539$	6.09432e11	0.311011
$540$	0	0
$541$	8.24488e11	0.413806	0.206903	−	0.978361i	$-0.433662\pi$
$541$	8.24488e11	0.413806	0.206903	+	0.978361i	$0.433662\pi$
$542$	8.93364e11	0.444663
$543$	0	0
$544$	−4.03663e11	−0.197617
$545$	2.62479e12	1.27441
$546$	0	0
$547$	−3.27510e11	−0.156416	−0.0782082	−	0.996937i	$-0.524920\pi$
$547$	−3.27510e11	−0.156416	−0.0782082	+	0.996937i	$0.524920\pi$
$548$	1.62180e12	0.768218
$549$	0	0
$550$	5.50802e11	0.256663
$551$	2.65007e10	0.0122483
$552$	0	0
$553$	−1.75043e12	−0.795941
$554$	−2.25085e12	−1.01520
$555$	0	0
$556$	4.89296e11	0.217137
$557$	−6.54333e11	−0.288038	−0.144019	−	0.989575i	$-0.546003\pi$
$557$	−6.54333e11	−0.288038	−0.144019	+	0.989575i	$0.546003\pi$
$558$	0	0
$559$	1.03970e12	0.450356
$560$	5.24795e11	0.225499
$561$	0	0
$562$	1.12878e12	0.477304
$563$	2.05130e12	0.860483	0.430242	−	0.902714i	$-0.358428\pi$
$563$	2.05130e12	0.860483	0.430242	+	0.902714i	$0.358428\pi$
$564$	0	0
$565$	6.11892e11	0.252614
$566$	1.88088e12	0.770348
$567$	0	0
$568$	4.84077e10	0.0195140
$569$	−9.21470e11	−0.368533	−0.184266	−	0.982876i	$-0.558991\pi$
$569$	−9.21470e11	−0.368533	−0.184266	+	0.982876i	$0.558991\pi$
$570$	0	0
$571$	−1.70877e12	−0.672701	−0.336351	−	0.941737i	$-0.609193\pi$
$571$	−1.70877e12	−0.672701	−0.336351	+	0.941737i	$0.609193\pi$
$572$	7.11573e11	0.277931
$573$	0	0
$574$	1.38322e12	0.531847
$575$	−1.47669e12	−0.563358
$576$	0	0
$577$	−1.50384e12	−0.564820	−0.282410	−	0.959294i	$-0.591134\pi$
$577$	−1.50384e12	−0.564820	−0.282410	+	0.959294i	$0.591134\pi$
$578$	1.17274e11	0.0437045
$579$	0	0
$580$	3.94022e10	0.0144576
$581$	2.96753e12	1.08044
$582$	0	0
$583$	−2.45123e12	−0.878769
$584$	−2.89616e12	−1.03030
$585$	0	0
$586$	−2.54178e12	−0.890428
$587$	3.06312e12	1.06486	0.532430	−	0.846474i	$-0.321279\pi$
$587$	3.06312e12	1.06486	0.532430	+	0.846474i	$0.321279\pi$
$588$	0	0
$589$	−7.27662e11	−0.249121
$590$	1.47400e12	0.500799
$591$	0	0
$592$	−1.39087e12	−0.465413
$593$	7.03492e11	0.233622	0.116811	−	0.993154i	$-0.462733\pi$
$593$	7.03492e11	0.233622	0.116811	+	0.993154i	$0.462733\pi$
$594$	0	0
$595$	4.75925e11	0.155673
$596$	−2.06180e12	−0.669328
$597$	0	0
$598$	2.35072e12	0.751701
$599$	−2.22780e12	−0.707060	−0.353530	−	0.935423i	$-0.615019\pi$
$599$	−2.22780e12	−0.707060	−0.353530	+	0.935423i	$0.615019\pi$
$600$	0	0
$601$	−3.12659e12	−0.977541	−0.488771	−	0.872412i	$-0.662555\pi$
$601$	−3.12659e12	−0.977541	−0.488771	+	0.872412i	$0.662555\pi$
$602$	−1.29588e12	−0.402144
$603$	0	0
$604$	−1.03916e12	−0.317700
$605$	−4.13109e11	−0.125362
$606$	0	0
$607$	8.02028e11	0.239795	0.119898	−	0.992786i	$-0.461743\pi$
$607$	8.02028e11	0.239795	0.119898	+	0.992786i	$0.461743\pi$
$608$	−8.22671e11	−0.244152
$609$	0	0
$610$	2.37165e11	0.0693533
$611$	−2.34143e12	−0.679665
$612$	0	0
$613$	4.27823e12	1.22375	0.611874	−	0.790955i	$-0.290416\pi$
$613$	4.27823e12	1.22375	0.611874	+	0.790955i	$0.290416\pi$
$614$	1.11353e12	0.316186
$615$	0	0
$616$	−2.86666e12	−0.802165
$617$	2.33959e12	0.649914	0.324957	−	0.945729i	$-0.394650\pi$
$617$	2.33959e12	0.649914	0.324957	+	0.945729i	$0.394650\pi$
$618$	0	0
$619$	7.17485e12	1.96429	0.982144	−	0.188131i	$-0.0602429\pi$
$619$	7.17485e12	1.96429	0.982144	+	0.188131i	$0.0602429\pi$
$620$	−1.08191e12	−0.294056
$621$	0	0
$622$	1.55861e12	0.417523
$623$	−5.07355e12	−1.34932
$624$	0	0
$625$	−1.83675e12	−0.481492
$626$	4.34875e12	1.13183
$627$	0	0
$628$	8.48574e11	0.217706
$629$	−1.26135e12	−0.321297
$630$	0	0
$631$	2.21641e12	0.556567	0.278283	−	0.960499i	$-0.410235\pi$
$631$	2.21641e12	0.556567	0.278283	+	0.960499i	$0.410235\pi$
$632$	−4.22452e12	−1.05330
$633$	0	0
$634$	7.51764e11	0.184791
$635$	3.59127e12	0.876528
$636$	0	0
$637$	−9.53164e11	−0.229372
$638$	1.16570e11	0.0278544
$639$	0	0
$640$	−3.48477e11	−0.0821040
$641$	−5.69709e10	−0.0133288	−0.00666442	−	0.999978i	$-0.502121\pi$
$641$	−5.69709e10	−0.0133288	−0.00666442	+	0.999978i	$0.502121\pi$
$642$	0	0
$643$	−3.26271e12	−0.752713	−0.376356	−	0.926475i	$-0.622823\pi$
$643$	−3.26271e12	−0.752713	−0.376356	+	0.926475i	$0.622823\pi$
$644$	2.37778e12	0.544734
$645$	0	0
$646$	2.39006e11	0.0539962
$647$	−4.42290e12	−0.992289	−0.496144	−	0.868240i	$-0.665251\pi$
$647$	−4.42290e12	−0.992289	−0.496144	+	0.868240i	$0.665251\pi$
$648$	0	0
$649$	−3.53897e12	−0.783024
$650$	−8.61464e11	−0.189290
$651$	0	0
$652$	−3.93419e12	−0.852591
$653$	−4.99365e12	−1.07475	−0.537376	−	0.843343i	$-0.680584\pi$
$653$	−4.99365e12	−1.07475	−0.537376	+	0.843343i	$0.680584\pi$
$654$	0	0
$655$	2.52808e12	0.536666
$656$	1.46729e12	0.309349
$657$	0	0
$658$	2.91835e12	0.606905
$659$	−1.68196e12	−0.347401	−0.173701	−	0.984799i	$-0.555572\pi$
$659$	−1.68196e12	−0.347401	−0.173701	+	0.984799i	$0.555572\pi$
$660$	0	0
$661$	8.83788e12	1.80070	0.900351	−	0.435165i	$-0.143310\pi$
$661$	8.83788e12	1.80070	0.900351	+	0.435165i	$0.143310\pi$
$662$	8.03864e11	0.162675
$663$	0	0
$664$	7.16190e12	1.42979
$665$	9.69943e11	0.192331
$666$	0	0
$667$	−3.12522e11	−0.0611385
$668$	3.18904e12	0.619678
$669$	0	0
$670$	5.06727e12	0.971488
$671$	−5.69417e11	−0.108437
$672$	0	0
$673$	4.41749e12	0.830057	0.415029	−	0.909808i	$-0.363772\pi$
$673$	4.41749e12	0.830057	0.415029	+	0.909808i	$0.363772\pi$
$674$	6.32692e12	1.18093
$675$	0	0
$676$	1.31943e12	0.243010
$677$	8.50941e12	1.55686	0.778431	−	0.627730i	$-0.216016\pi$
$677$	8.50941e12	1.55686	0.778431	+	0.627730i	$0.216016\pi$
$678$	0	0
$679$	5.32682e12	0.961733
$680$	1.14861e12	0.206007
$681$	0	0
$682$	−3.20080e12	−0.566537
$683$	−3.49030e12	−0.613719	−0.306859	−	0.951755i	$-0.599278\pi$
$683$	−3.49030e12	−0.613719	−0.306859	+	0.951755i	$0.599278\pi$
$684$	0	0
$685$	−7.80181e12	−1.35390
$686$	4.69153e12	0.808828
$687$	0	0
$688$	−1.37465e12	−0.233907
$689$	3.83376e12	0.648095
$690$	0	0
$691$	3.30831e12	0.552019	0.276010	−	0.961155i	$-0.410988\pi$
$691$	3.30831e12	0.552019	0.276010	+	0.961155i	$0.410988\pi$
$692$	3.47007e11	0.0575256
$693$	0	0
$694$	2.97697e12	0.487144
$695$	−2.35380e12	−0.382682
$696$	0	0
$697$	1.33065e12	0.213559
$698$	4.10007e12	0.653795
$699$	0	0
$700$	−8.71381e11	−0.137172
$701$	−1.72300e12	−0.269497	−0.134749	−	0.990880i	$-0.543023\pi$
$701$	−1.72300e12	−0.269497	−0.134749	+	0.990880i	$0.543023\pi$
$702$	0	0
$703$	−2.57065e12	−0.396957
$704$	−5.71881e12	−0.877463
$705$	0	0
$706$	−3.22376e12	−0.488362
$707$	−2.70341e11	−0.0406935
$708$	0	0
$709$	8.11666e12	1.20634	0.603169	−	0.797613i	$-0.293904\pi$
$709$	8.11666e12	1.20634	0.603169	+	0.797613i	$0.293904\pi$
$710$	−7.20465e10	−0.0106402
$711$	0	0
$712$	−1.22446e13	−1.78561
$713$	8.58130e12	1.24351
$714$	0	0
$715$	−3.42309e12	−0.489825
$716$	−4.81285e12	−0.684374
$717$	0	0
$718$	1.08122e12	0.151829
$719$	3.41170e12	0.476092	0.238046	−	0.971254i	$-0.423493\pi$
$719$	3.41170e12	0.476092	0.238046	+	0.971254i	$0.423493\pi$
$720$	0	0
$721$	−2.40548e12	−0.331508
$722$	−4.93781e12	−0.676265
$723$	0	0
$724$	4.01719e12	0.543374
$725$	1.14530e11	0.0153956
$726$	0	0
$727$	−6.77588e12	−0.899624	−0.449812	−	0.893123i	$-0.648509\pi$
$727$	−6.77588e12	−0.899624	−0.449812	+	0.893123i	$0.648509\pi$
$728$	4.48352e12	0.591599
$729$	0	0
$730$	4.31043e12	0.561781
$731$	−1.24664e12	−0.161478
$732$	0	0
$733$	−1.34191e13	−1.71694	−0.858469	−	0.512866i	$-0.828584\pi$
$733$	−1.34191e13	−1.71694	−0.858469	+	0.512866i	$0.828584\pi$
$734$	1.21875e12	0.154983
$735$	0	0
$736$	9.70174e12	1.21871
$737$	−1.21661e13	−1.51897
$738$	0	0
$739$	9.85851e12	1.21594	0.607969	−	0.793961i	$-0.291984\pi$
$739$	9.85851e12	1.21594	0.607969	+	0.793961i	$0.291984\pi$
$740$	−3.82213e12	−0.468557
$741$	0	0
$742$	−4.77840e12	−0.578715
$743$	−6.66107e12	−0.801853	−0.400926	−	0.916110i	$-0.631312\pi$
$743$	−6.66107e12	−0.801853	−0.400926	+	0.916110i	$0.631312\pi$
$744$	0	0
$745$	9.91849e12	1.17962
$746$	−9.15437e11	−0.108219
$747$	0	0
$748$	−8.53201e11	−0.0996539
$749$	−7.44835e12	−0.864752
$750$	0	0
$751$	2.09306e12	0.240106	0.120053	−	0.992767i	$-0.461694\pi$
$751$	2.09306e12	0.240106	0.120053	+	0.992767i	$0.461694\pi$
$752$	3.09573e12	0.353007
$753$	0	0
$754$	−1.82318e11	−0.0205427
$755$	4.99899e12	0.559913
$756$	0	0
$757$	1.26189e13	1.39666	0.698330	−	0.715776i	$-0.253927\pi$
$757$	1.26189e13	1.39666	0.698330	+	0.715776i	$0.253927\pi$
$758$	−3.61459e12	−0.397693
$759$	0	0
$760$	2.34088e12	0.254518
$761$	6.62893e12	0.716494	0.358247	−	0.933627i	$-0.383375\pi$
$761$	6.62893e12	0.716494	0.358247	+	0.933627i	$0.383375\pi$
$762$	0	0
$763$	−1.22849e13	−1.31224
$764$	3.77047e12	0.400383
$765$	0	0
$766$	7.21538e12	0.757233
$767$	5.53501e12	0.577483
$768$	0	0
$769$	3.47382e12	0.358210	0.179105	−	0.983830i	$-0.442680\pi$
$769$	3.47382e12	0.358210	0.179105	+	0.983830i	$0.442680\pi$
$770$	4.26653e12	0.437388
$771$	0	0
$772$	2.09347e12	0.212123
$773$	1.16131e13	1.16988	0.584941	−	0.811076i	$-0.301118\pi$
$773$	1.16131e13	1.16988	0.584941	+	0.811076i	$0.301118\pi$
$774$	0	0
$775$	−3.14478e12	−0.313135
$776$	1.28559e13	1.27269
$777$	0	0
$778$	3.39961e12	0.332675
$779$	2.71190e12	0.263848
$780$	0	0
$781$	1.72978e11	0.0166365
$782$	−2.81859e12	−0.269527
$783$	0	0
$784$	1.26023e12	0.119132
$785$	−4.08214e12	−0.383685
$786$	0	0
$787$	−1.50665e13	−1.39999	−0.699997	−	0.714146i	$-0.746815\pi$
$787$	−1.50665e13	−1.39999	−0.699997	+	0.714146i	$0.746815\pi$
$788$	3.51280e11	0.0324553
$789$	0	0
$790$	6.28747e12	0.574320
$791$	−2.86387e12	−0.260111
$792$	0	0
$793$	8.90579e11	0.0799730
$794$	3.04469e12	0.271863
$795$	0	0
$796$	−4.07540e12	−0.359800
$797$	7.67142e12	0.673463	0.336731	−	0.941601i	$-0.390679\pi$
$797$	7.67142e12	0.673463	0.336731	+	0.941601i	$0.390679\pi$
$798$	0	0
$799$	2.80745e12	0.243698
$800$	−3.55538e12	−0.306889
$801$	0	0
$802$	2.36375e12	0.201751
$803$	−1.03490e13	−0.878374
$804$	0	0
$805$	−1.14385e13	−0.960037
$806$	5.00611e12	0.417823
$807$	0	0
$808$	−6.52448e11	−0.0538512
$809$	6.00907e12	0.493218	0.246609	−	0.969115i	$-0.420684\pi$
$809$	6.00907e12	0.493218	0.246609	+	0.969115i	$0.420684\pi$
$810$	0	0
$811$	−1.51786e13	−1.23208	−0.616038	−	0.787717i	$-0.711263\pi$
$811$	−1.51786e13	−1.23208	−0.616038	+	0.787717i	$0.711263\pi$
$812$	−1.84416e11	−0.0148867
$813$	0	0
$814$	−1.13076e13	−0.902737
$815$	1.89258e13	1.50260
$816$	0	0
$817$	−2.54067e12	−0.199503
$818$	−1.02861e13	−0.803267
$819$	0	0
$820$	4.03214e12	0.311440
$821$	−1.51618e13	−1.16468	−0.582339	−	0.812946i	$-0.697862\pi$
$821$	−1.51618e13	−1.16468	−0.582339	+	0.812946i	$0.697862\pi$
$822$	0	0
$823$	−8.88314e12	−0.674943	−0.337472	−	0.941336i	$-0.609572\pi$
$823$	−8.88314e12	−0.674943	−0.337472	+	0.941336i	$0.609572\pi$
$824$	−5.80545e12	−0.438696
$825$	0	0
$826$	−6.89883e12	−0.515662
$827$	−9.71703e9	−0.000722368 0	−0.000361184	−	1.00000i	$-0.500115\pi$
$827$	−9.71703e9	−0.000722368 0	−0.000361184		1.00000i	$0.500115\pi$
$828$	0	0
$829$	−6.15249e12	−0.452434	−0.226217	−	0.974077i	$-0.572636\pi$
$829$	−6.15249e12	−0.452434	−0.226217	+	0.974077i	$0.572636\pi$
$830$	−1.06592e13	−0.779606
$831$	0	0
$832$	8.94433e12	0.647132
$833$	1.14288e12	0.0822426
$834$	0	0
$835$	−1.53412e13	−1.09212
$836$	−1.73884e12	−0.123121
$837$	0	0
$838$	−4.85976e11	−0.0340421
$839$	−2.01899e13	−1.40671	−0.703355	−	0.710839i	$-0.748316\pi$
$839$	−2.01899e13	−1.40671	−0.703355	+	0.710839i	$0.748316\pi$
$840$	0	0
$841$	−1.44829e13	−0.998329
$842$	1.78641e13	1.22483
$843$	0	0
$844$	−1.19043e13	−0.807540
$845$	−6.34722e12	−0.428280
$846$	0	0
$847$	1.93350e12	0.129083
$848$	−5.06884e12	−0.336610
$849$	0	0
$850$	1.03293e12	0.0678710
$851$	3.03156e13	1.98145
$852$	0	0
$853$	−2.71140e13	−1.75357	−0.876784	−	0.480885i	$-0.840315\pi$
$853$	−2.71140e13	−1.75357	−0.876784	+	0.480885i	$0.840315\pi$
$854$	−1.11002e12	−0.0714117
$855$	0	0
$856$	−1.79760e13	−1.14436
$857$	−2.66987e13	−1.69074	−0.845371	−	0.534180i	$-0.820620\pi$
$857$	−2.66987e13	−1.69074	−0.845371	+	0.534180i	$0.820620\pi$
$858$	0	0
$859$	2.62702e13	1.64624	0.823122	−	0.567864i	$-0.192230\pi$
$859$	2.62702e13	1.64624	0.823122	+	0.567864i	$0.192230\pi$
$860$	−3.77756e12	−0.235488
$861$	0	0
$862$	8.56529e11	0.0528396
$863$	−2.34256e13	−1.43761	−0.718806	−	0.695211i	$-0.755311\pi$
$863$	−2.34256e13	−1.43761	−0.718806	+	0.695211i	$0.755311\pi$
$864$	0	0
$865$	−1.66931e12	−0.101383
$866$	−1.72198e13	−1.04039
$867$	0	0
$868$	5.06374e12	0.302784
$869$	−1.50958e13	−0.897978
$870$	0	0
$871$	1.90281e13	1.12025
$872$	−2.96487e13	−1.73653
$873$	0	0
$874$	−5.74434e12	−0.332996
$875$	1.53213e13	0.883607
$876$	0	0
$877$	−4.84217e12	−0.276402	−0.138201	−	0.990404i	$-0.544132\pi$
$877$	−4.84217e12	−0.276402	−0.138201	+	0.990404i	$0.544132\pi$
$878$	6.22486e12	0.353512
$879$	0	0
$880$	4.52586e12	0.254407
$881$	−1.59269e13	−0.890718	−0.445359	−	0.895352i	$-0.646924\pi$
$881$	−1.59269e13	−0.890718	−0.445359	+	0.895352i	$0.646924\pi$
$882$	0	0
$883$	4.71830e12	0.261194	0.130597	−	0.991436i	$-0.458311\pi$
$883$	4.71830e12	0.261194	0.130597	+	0.991436i	$0.458311\pi$
$884$	1.33442e12	0.0734951
$885$	0	0
$886$	1.96886e13	1.07340
$887$	−1.26007e13	−0.683502	−0.341751	−	0.939790i	$-0.611020\pi$
$887$	−1.26007e13	−0.683502	−0.341751	+	0.939790i	$0.611020\pi$
$888$	0	0
$889$	−1.68084e13	−0.902544
$890$	1.82240e13	0.973618
$891$	0	0
$892$	1.39808e13	0.739417
$893$	5.72163e12	0.301084
$894$	0	0
$895$	2.31527e13	1.20614
$896$	1.63100e12	0.0845408
$897$	0	0
$898$	−1.14286e12	−0.0586473
$899$	−6.65550e11	−0.0339830
$900$	0	0
$901$	−4.59682e12	−0.232378
$902$	1.19289e13	0.600029
$903$	0	0
$904$	−6.91173e12	−0.344214
$905$	−1.93251e13	−0.957640
$906$	0	0
$907$	−2.04459e13	−1.00317	−0.501584	−	0.865109i	$-0.667249\pi$
$907$	−2.04459e13	−1.00317	−0.501584	+	0.865109i	$0.667249\pi$
$908$	1.45846e13	0.712046
$909$	0	0
$910$	−6.67294e12	−0.322575
$911$	−6.21126e12	−0.298777	−0.149388	−	0.988779i	$-0.547730\pi$
$911$	−6.21126e12	−0.298777	−0.149388	+	0.988779i	$0.547730\pi$
$912$	0	0
$913$	2.55921e13	1.21895
$914$	2.89441e13	1.37183
$915$	0	0
$916$	1.42874e13	0.670540
$917$	−1.18323e13	−0.552594
$918$	0	0
$919$	−9.32576e12	−0.431285	−0.215642	−	0.976472i	$-0.569185\pi$
$919$	−9.32576e12	−0.431285	−0.215642	+	0.976472i	$0.569185\pi$
$920$	−2.76060e13	−1.27045
$921$	0	0
$922$	−2.39283e13	−1.09049
$923$	−2.70542e11	−0.0122695
$924$	0	0
$925$	−1.11097e13	−0.498959
$926$	2.72498e13	1.21790
$927$	0	0
$928$	−7.52450e11	−0.0333052
$929$	−2.57119e13	−1.13256	−0.566282	−	0.824211i	$-0.691619\pi$
$929$	−2.57119e13	−1.13256	−0.566282	+	0.824211i	$0.691619\pi$
$930$	0	0
$931$	2.32920e12	0.101609
$932$	1.99327e13	0.865357
$933$	0	0
$934$	1.90928e13	0.820937
$935$	4.10440e12	0.175629
$936$	0	0
$937$	7.29891e12	0.309336	0.154668	−	0.987967i	$-0.450569\pi$
$937$	7.29891e12	0.309336	0.154668	+	0.987967i	$0.450569\pi$
$938$	−2.37166e13	−1.00032
$939$	0	0
$940$	8.50713e12	0.355392
$941$	1.10493e13	0.459389	0.229695	−	0.973263i	$-0.426227\pi$
$941$	1.10493e13	0.459389	0.229695	+	0.973263i	$0.426227\pi$
$942$	0	0
$943$	−3.19813e13	−1.31702
$944$	−7.31815e12	−0.299935
$945$	0	0
$946$	−1.11758e13	−0.453698
$947$	9.10292e12	0.367795	0.183898	−	0.982945i	$-0.441129\pi$
$947$	9.10292e12	0.367795	0.183898	+	0.982945i	$0.441129\pi$
$948$	0	0
$949$	1.61861e13	0.647804
$950$	2.10512e12	0.0838534
$951$	0	0
$952$	−5.37589e12	−0.212121
$953$	−4.09267e13	−1.60727	−0.803635	−	0.595123i	$-0.797104\pi$
$953$	−4.09267e13	−1.60727	−0.803635	+	0.595123i	$0.797104\pi$
$954$	0	0
$955$	−1.81382e13	−0.705633
$956$	1.61633e13	0.625848
$957$	0	0
$958$	−2.59707e12	−0.0996181
$959$	3.65152e13	1.39409
$960$	0	0
$961$	−8.16481e12	−0.308810
$962$	1.76853e13	0.665772
$963$	0	0
$964$	−1.43369e13	−0.534697
$965$	−1.00708e13	−0.373845
$966$	0	0
$967$	5.16443e13	1.89934	0.949671	−	0.313248i	$-0.101417\pi$
$967$	5.16443e13	1.89934	0.949671	+	0.313248i	$0.101417\pi$
$968$	4.66635e12	0.170820
$969$	0	0
$970$	−1.91338e13	−0.693949
$971$	4.69234e13	1.69396	0.846979	−	0.531627i	$-0.178419\pi$
$971$	4.69234e13	1.69396	0.846979	+	0.531627i	$0.178419\pi$
$972$	0	0
$973$	1.10166e13	0.394040
$974$	−1.58040e13	−0.562667
$975$	0	0
$976$	−1.17749e12	−0.0415366
$977$	4.71530e13	1.65571	0.827854	−	0.560944i	$-0.189562\pi$
$977$	4.71530e13	1.65571	0.827854	+	0.560944i	$0.189562\pi$
$978$	0	0
$979$	−4.37545e13	−1.52230
$980$	3.46314e12	0.119937
$981$	0	0
$982$	9.05128e12	0.310605
$983$	−4.10494e13	−1.40222	−0.701110	−	0.713053i	$-0.747312\pi$
$983$	−4.10494e13	−1.40222	−0.701110	+	0.713053i	$0.747312\pi$
$984$	0	0
$985$	−1.68986e12	−0.0571990
$986$	2.18605e11	0.00736570
$987$	0	0
$988$	2.71958e12	0.0908019
$989$	2.99621e13	0.995837
$990$	0	0
$991$	8.40949e12	0.276973	0.138487	−	0.990364i	$-0.455776\pi$
$991$	8.40949e12	0.276973	0.138487	+	0.990364i	$0.455776\pi$
$992$	2.06609e13	0.677403
$993$	0	0
$994$	3.37203e11	0.0109560
$995$	1.96051e13	0.634110
$996$	0	0
$997$	2.54531e13	0.815854	0.407927	−	0.913015i	$-0.366252\pi$
$997$	2.54531e13	0.815854	0.407927	+	0.913015i	$0.366252\pi$
$998$	−1.03044e13	−0.328803
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.10.a.f.1.5		7
3.2	odd	2		17.10.a.b.1.3	✓	7
12.11	even	2		272.10.a.g.1.5		7
51.50	odd	2		289.10.a.b.1.3		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.a.b.1.3	✓	7	3.2	odd	2
153.10.a.f.1.5		7	1.1	even	1	trivial
272.10.a.g.1.5		7	12.11	even	2
289.10.a.b.1.3		7	51.50	odd	2

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	153.a (trivial)

\(f(q)\)	\(=\)	\(q+16.8116 q^{2} -229.369 q^{4} +1103.40 q^{5} -5164.29 q^{7} -12463.6 q^{8} +O(q^{10})\)	\(q+16.8116 q^{2} -229.369 q^{4} +1103.40 q^{5} -5164.29 q^{7} -12463.6 q^{8} +18549.9 q^{10} -44537.1 q^{11} +69656.8 q^{13} -86820.2 q^{14} -92097.3 q^{16} -83521.0 q^{17} -170217. q^{19} -253085. q^{20} -748741. q^{22} +2.00737e6 q^{23} -735637. q^{25} +1.17105e6 q^{26} +1.18453e6 q^{28} -155688. q^{29} +4.27490e6 q^{31} +4.83307e6 q^{32} -1.40413e6 q^{34} -5.69827e6 q^{35} +1.51022e7 q^{37} -2.86163e6 q^{38} -1.37523e7 q^{40} -1.59320e7 q^{41} +1.49261e7 q^{43} +1.02154e7 q^{44} +3.37471e7 q^{46} -3.36137e7 q^{47} -1.36837e7 q^{49} -1.23673e7 q^{50} -1.59771e7 q^{52} +5.50379e7 q^{53} -4.91421e7 q^{55} +6.43658e7 q^{56} -2.61737e6 q^{58} +7.94611e7 q^{59} +1.27852e7 q^{61} +7.18682e7 q^{62} +1.28406e8 q^{64} +7.68593e7 q^{65} +2.73169e8 q^{67} +1.91571e7 q^{68} -9.57973e7 q^{70} -3.88392e6 q^{71} +2.32369e8 q^{73} +2.53892e8 q^{74} +3.90425e7 q^{76} +2.30002e8 q^{77} +3.38948e8 q^{79} -1.01620e8 q^{80} -2.67843e8 q^{82} -5.74624e8 q^{83} -9.21569e7 q^{85} +2.50932e8 q^{86} +5.55093e8 q^{88} +9.82429e8 q^{89} -3.59728e8 q^{91} -4.60427e8 q^{92} -5.65102e8 q^{94} -1.87817e8 q^{95} -1.03147e9 q^{97} -2.30046e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + q^{2} + 2389 q^{4} - 1362 q^{5} + 9388 q^{7} - 16821 q^{8}+O(q^{10}) \) 7 * q + q^2 + 2389 * q^4 - 1362 * q^5 + 9388 * q^7 - 16821 * q^8	\( 7 q + q^{2} + 2389 q^{4} - 1362 q^{5} + 9388 q^{7} - 16821 q^{8} + 154226 q^{10} - 135536 q^{11} + 166122 q^{13} - 447252 q^{14} + 1463585 q^{16} - 584647 q^{17} + 777172 q^{19} + 917162 q^{20} - 1222520 q^{22} - 1357764 q^{23} + 1065785 q^{25} + 14379966 q^{26} - 3328892 q^{28} - 967002 q^{29} + 3546740 q^{31} - 4825461 q^{32} - 83521 q^{34} + 530736 q^{35} + 18296498 q^{37} + 49363020 q^{38} + 127155062 q^{40} - 10285686 q^{41} + 21913204 q^{43} - 96696624 q^{44} - 151509484 q^{46} - 56639800 q^{47} + 27010351 q^{49} + 261150303 q^{50} - 156226378 q^{52} - 121813562 q^{53} + 40793128 q^{55} + 196175436 q^{56} - 236833910 q^{58} - 29222388 q^{59} - 49915846 q^{61} + 73506556 q^{62} + 317922057 q^{64} + 122633668 q^{65} + 301863420 q^{67} - 199531669 q^{68} + 966315960 q^{70} - 652473940 q^{71} + 306656342 q^{73} - 249173874 q^{74} + 128694700 q^{76} + 102442536 q^{77} + 959147884 q^{79} + 692173602 q^{80} + 1046441254 q^{82} + 1512945268 q^{83} + 113755602 q^{85} + 164953236 q^{86} + 1132038848 q^{88} + 1971327114 q^{89} - 1061062864 q^{91} - 901186756 q^{92} + 2534831232 q^{94} + 3249631512 q^{95} + 2006526254 q^{97} + 2170640009 q^{98}+O(q^{100}) \) 7 * q + q^2 + 2389 * q^4 - 1362 * q^5 + 9388 * q^7 - 16821 * q^8 + 154226 * q^10 - 135536 * q^11 + 166122 * q^13 - 447252 * q^14 + 1463585 * q^16 - 584647 * q^17 + 777172 * q^19 + 917162 * q^20 - 1222520 * q^22 - 1357764 * q^23 + 1065785 * q^25 + 14379966 * q^26 - 3328892 * q^28 - 967002 * q^29 + 3546740 * q^31 - 4825461 * q^32 - 83521 * q^34 + 530736 * q^35 + 18296498 * q^37 + 49363020 * q^38 + 127155062 * q^40 - 10285686 * q^41 + 21913204 * q^43 - 96696624 * q^44 - 151509484 * q^46 - 56639800 * q^47 + 27010351 * q^49 + 261150303 * q^50 - 156226378 * q^52 - 121813562 * q^53 + 40793128 * q^55 + 196175436 * q^56 - 236833910 * q^58 - 29222388 * q^59 - 49915846 * q^61 + 73506556 * q^62 + 317922057 * q^64 + 122633668 * q^65 + 301863420 * q^67 - 199531669 * q^68 + 966315960 * q^70 - 652473940 * q^71 + 306656342 * q^73 - 249173874 * q^74 + 128694700 * q^76 + 102442536 * q^77 + 959147884 * q^79 + 692173602 * q^80 + 1046441254 * q^82 + 1512945268 * q^83 + 113755602 * q^85 + 164953236 * q^86 + 1132038848 * q^88 + 1971327114 * q^89 - 1061062864 * q^91 - 901186756 * q^92 + 2534831232 * q^94 + 3249631512 * q^95 + 2006526254 * q^97 + 2170640009 * q^98

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