LMFDB - Embedded newform 153.10.a.f.1.7

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			1.7
Root			$42.3973$ 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)

$f(q)$	$=$	$q+42.3973 q^{2} +1285.53 q^{4} +2498.37 q^{5} +2872.61 q^{7} +32795.8 q^{8} +O(q^{10})$	\(q+42.3973 q^{2} +1285.53 q^{4} +2498.37 q^{5} +2872.61 q^{7} +32795.8 q^{8} +105924. q^{10} -36573.4 q^{11} +69902.2 q^{13} +121791. q^{14} +732260. q^{16} -83521.0 q^{17} +640587. q^{19} +3.21175e6 q^{20} -1.55061e6 q^{22} -2.09284e6 q^{23} +4.28875e6 q^{25} +2.96367e6 q^{26} +3.69283e6 q^{28} -4.99200e6 q^{29} -5.61791e6 q^{31} +1.42544e7 q^{32} -3.54107e6 q^{34} +7.17685e6 q^{35} +3.47843e6 q^{37} +2.71592e7 q^{38} +8.19361e7 q^{40} -469632. q^{41} +3.50525e6 q^{43} -4.70163e7 q^{44} -8.87310e7 q^{46} -1.55290e6 q^{47} -3.21017e7 q^{49} +1.81832e8 q^{50} +8.98617e7 q^{52} -1.03903e8 q^{53} -9.13740e7 q^{55} +9.42094e7 q^{56} -2.11648e8 q^{58} +7.79169e7 q^{59} +1.79259e7 q^{61} -2.38185e8 q^{62} +2.29433e8 q^{64} +1.74642e8 q^{65} +8.26939e7 q^{67} -1.07369e8 q^{68} +3.04279e8 q^{70} +1.03521e8 q^{71} +1.43348e7 q^{73} +1.47476e8 q^{74} +8.23496e8 q^{76} -1.05061e8 q^{77} +3.90455e8 q^{79} +1.82946e9 q^{80} -1.99111e7 q^{82} +3.47368e8 q^{83} -2.08667e8 q^{85} +1.48613e8 q^{86} -1.19945e9 q^{88} +4.95430e7 q^{89} +2.00802e8 q^{91} -2.69042e9 q^{92} -6.58387e7 q^{94} +1.60043e9 q^{95} +6.49870e8 q^{97} -1.36103e9 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	42.3973	1.87372	0.936858	−	0.349711i	$-0.113720\pi$
$2$	42.3973	1.87372	0.936858	+	0.349711i	$0.113720\pi$
$3$	0	0
$3$	0	0
$4$	1285.53	2.51081
$5$	2498.37	1.78769	0.893846	−	0.448375i	$-0.147997\pi$
$5$	2498.37	1.78769	0.893846	+	0.448375i	$0.147997\pi$
$6$	0	0
$7$	2872.61	0.452205	0.226102	−	0.974104i	$-0.427402\pi$
$7$	2872.61	0.452205	0.226102	+	0.974104i	$0.427402\pi$
$8$	32795.8	2.83082
$9$	0	0
$10$	105924.	3.34962
$11$	−36573.4	−0.753178	−0.376589	−	0.926380i	$-0.622903\pi$
$11$	−36573.4	−0.753178	−0.376589	+	0.926380i	$0.622903\pi$
$12$	0	0
$13$	69902.2	0.678806	0.339403	−	0.940641i	$-0.389775\pi$
$13$	69902.2	0.678806	0.339403	+	0.940641i	$0.389775\pi$
$14$	121791.	0.847303
$15$	0	0
$16$	732260.	2.79335
$17$	−83521.0	−0.242536
$17$	−83521.0	−0.242536
$18$	0	0
$19$	640587.	1.12768	0.563841	−	0.825883i	$-0.309323\pi$
$19$	640587.	1.12768	0.563841	+	0.825883i	$0.309323\pi$
$20$	3.21175e6	4.48855
$21$	0	0
$22$	−1.55061e6	−1.41124
$23$	−2.09284e6	−1.55941	−0.779707	−	0.626144i	$-0.784632\pi$
$23$	−2.09284e6	−1.55941	−0.779707	+	0.626144i	$0.784632\pi$
$24$	0	0
$25$	4.28875e6	2.19584
$26$	2.96367e6	1.27189
$27$	0	0
$28$	3.69283e6	1.13540
$29$	−4.99200e6	−1.31064	−0.655321	−	0.755351i	$-0.727466\pi$
$29$	−4.99200e6	−1.31064	−0.655321	+	0.755351i	$0.727466\pi$
$30$	0	0
$31$	−5.61791e6	−1.09257	−0.546283	−	0.837601i	$-0.683958\pi$
$31$	−5.61791e6	−1.09257	−0.546283	+	0.837601i	$0.683958\pi$
$32$	1.42544e7	2.40312
$33$	0	0
$34$	−3.54107e6	−0.454443
$35$	7.17685e6	0.808402
$36$	0	0
$37$	3.47843e6	0.305123	0.152562	−	0.988294i	$-0.451248\pi$
$37$	3.47843e6	0.305123	0.152562	+	0.988294i	$0.451248\pi$
$38$	2.71592e7	2.11296
$39$	0	0
$40$	8.19361e7	5.06064
$41$	−469632.	−0.0259555	−0.0129778	−	0.999916i	$-0.504131\pi$
$41$	−469632.	−0.0259555	−0.0129778	+	0.999916i	$0.504131\pi$
$42$	0	0
$43$	3.50525e6	0.156355	0.0781773	−	0.996939i	$-0.475090\pi$
$43$	3.50525e6	0.156355	0.0781773	+	0.996939i	$0.475090\pi$
$44$	−4.70163e7	−1.89109
$45$	0	0
$46$	−8.87310e7	−2.92190
$47$	−1.55290e6	−0.0464197	−0.0232098	−	0.999731i	$-0.507389\pi$
$47$	−1.55290e6	−0.0464197	−0.0232098	+	0.999731i	$0.507389\pi$
$48$	0	0
$49$	−3.21017e7	−0.795511
$50$	1.81832e8	4.11438
$51$	0	0
$52$	8.98617e7	1.70435
$53$	−1.03903e8	−1.80878	−0.904390	−	0.426706i	$-0.859674\pi$
$53$	−1.03903e8	−1.80878	−0.904390	+	0.426706i	$0.859674\pi$
$54$	0	0
$55$	−9.13740e7	−1.34645
$56$	9.42094e7	1.28011
$57$	0	0
$58$	−2.11648e8	−2.45577
$59$	7.79169e7	0.837139	0.418569	−	0.908185i	$-0.362532\pi$
$59$	7.79169e7	0.837139	0.418569	+	0.908185i	$0.362532\pi$
$60$	0	0
$61$	1.79259e7	0.165766	0.0828831	−	0.996559i	$-0.473587\pi$
$61$	1.79259e7	0.165766	0.0828831	+	0.996559i	$0.473587\pi$
$62$	−2.38185e8	−2.04716
$63$	0	0
$64$	2.29433e8	1.70941
$65$	1.74642e8	1.21350
$66$	0	0
$67$	8.26939e7	0.501345	0.250673	−	0.968072i	$-0.419348\pi$
$67$	8.26939e7	0.501345	0.250673	+	0.968072i	$0.419348\pi$
$68$	−1.07369e8	−0.608960
$69$	0	0
$70$	3.04279e8	1.51472
$71$	1.03521e8	0.483465	0.241732	−	0.970343i	$-0.422284\pi$
$71$	1.03521e8	0.483465	0.241732	+	0.970343i	$0.422284\pi$
$72$	0	0
$73$	1.43348e7	0.0590797	0.0295399	−	0.999564i	$-0.490596\pi$
$73$	1.43348e7	0.0590797	0.0295399	+	0.999564i	$0.490596\pi$
$74$	1.47476e8	0.571714
$75$	0	0
$76$	8.23496e8	2.83140
$77$	−1.05061e8	−0.340591
$78$	0	0
$79$	3.90455e8	1.12784	0.563922	−	0.825828i	$-0.309292\pi$
$79$	3.90455e8	1.12784	0.563922	+	0.825828i	$0.309292\pi$
$80$	1.82946e9	4.99365
$81$	0	0
$82$	−1.99111e7	−0.0486333
$83$	3.47368e8	0.803411	0.401706	−	0.915769i	$-0.368418\pi$
$83$	3.47368e8	0.803411	0.401706	+	0.915769i	$0.368418\pi$
$84$	0	0
$85$	−2.08667e8	−0.433579
$86$	1.48613e8	0.292964
$87$	0	0
$88$	−1.19945e9	−2.13212
$89$	4.95430e7	0.0837004	0.0418502	−	0.999124i	$-0.486675\pi$
$89$	4.95430e7	0.0837004	0.0418502	+	0.999124i	$0.486675\pi$
$90$	0	0
$91$	2.00802e8	0.306959
$92$	−2.69042e9	−3.91539
$93$	0	0
$94$	−6.58387e7	−0.0869772
$95$	1.60043e9	2.01595
$96$	0	0
$97$	6.49870e8	0.745338	0.372669	−	0.927964i	$-0.378443\pi$
$97$	6.49870e8	0.745338	0.372669	+	0.927964i	$0.378443\pi$
$98$	−1.36103e9	−1.49056
$99$	0	0
$100$	5.51334e9	5.51334
$101$	5.41669e8	0.517950	0.258975	−	0.965884i	$-0.416615\pi$
$101$	5.41669e8	0.517950	0.258975	+	0.965884i	$0.416615\pi$
$102$	0	0
$103$	1.38535e9	1.21281	0.606403	−	0.795157i	$-0.292612\pi$
$103$	1.38535e9	1.21281	0.606403	+	0.795157i	$0.292612\pi$
$104$	2.29250e9	1.92158
$105$	0	0
$106$	−4.40520e9	−3.38914
$107$	−3.51366e8	−0.259139	−0.129569	−	0.991570i	$-0.541359\pi$
$107$	−3.51366e8	−0.259139	−0.129569	+	0.991570i	$0.541359\pi$
$108$	0	0
$109$	−8.82255e8	−0.598652	−0.299326	−	0.954151i	$-0.596762\pi$
$109$	−8.82255e8	−0.598652	−0.299326	+	0.954151i	$0.596762\pi$
$110$	−3.87401e9	−2.52286
$111$	0	0
$112$	2.10349e9	1.26317
$113$	−1.98816e9	−1.14709	−0.573545	−	0.819174i	$-0.694432\pi$
$113$	−1.98816e9	−1.14709	−0.573545	+	0.819174i	$0.694432\pi$
$114$	0	0
$115$	−5.22871e9	−2.78775
$116$	−6.41739e9	−3.29077
$117$	0	0
$118$	3.30347e9	1.56856
$119$	−2.39923e8	−0.109676
$120$	0	0
$121$	−1.02034e9	−0.432723
$122$	7.60009e8	0.310598
$123$	0	0
$124$	−7.22202e9	−2.74322
$125$	5.83527e9	2.13780
$126$	0	0
$127$	−3.59412e8	−0.122596	−0.0612980	−	0.998120i	$-0.519524\pi$
$127$	−3.59412e8	−0.122596	−0.0612980	+	0.998120i	$0.519524\pi$
$128$	2.42907e9	0.799826
$129$	0	0
$130$	7.40435e9	2.27375
$131$	−2.17687e8	−0.0645820	−0.0322910	−	0.999479i	$-0.510280\pi$
$131$	−2.17687e8	−0.0645820	−0.0322910	+	0.999479i	$0.510280\pi$
$132$	0	0
$133$	1.84015e9	0.509943
$134$	3.50600e9	0.939378
$135$	0	0
$136$	−2.73914e9	−0.686576
$137$	−3.81268e9	−0.924671	−0.462336	−	0.886705i	$-0.652989\pi$
$137$	−3.81268e9	−0.924671	−0.462336	+	0.886705i	$0.652989\pi$
$138$	0	0
$139$	1.05651e9	0.240054	0.120027	−	0.992771i	$-0.461702\pi$
$139$	1.05651e9	0.240054	0.120027	+	0.992771i	$0.461702\pi$
$140$	9.22608e9	2.02974
$141$	0	0
$142$	4.38900e9	0.905875
$143$	−2.55656e9	−0.511262
$144$	0	0
$145$	−1.24719e10	−2.34302
$146$	6.07757e8	0.110699
$147$	0	0
$148$	4.47164e9	0.766106
$149$	−1.11231e10	−1.84879	−0.924394	−	0.381439i	$-0.875429\pi$
$149$	−1.11231e10	−1.84879	−0.924394	+	0.381439i	$0.875429\pi$
$150$	0	0
$151$	−4.54386e8	−0.0711261	−0.0355630	−	0.999367i	$-0.511322\pi$
$151$	−4.54386e8	−0.0711261	−0.0355630	+	0.999367i	$0.511322\pi$
$152$	2.10085e10	3.19227
$153$	0	0
$154$	−4.45430e9	−0.638170
$155$	−1.40357e10	−1.95317
$156$	0	0
$157$	1.18078e10	1.55102	0.775512	−	0.631332i	$-0.217492\pi$
$157$	1.18078e10	1.55102	0.775512	+	0.631332i	$0.217492\pi$
$158$	1.65542e10	2.11326
$159$	0	0
$160$	3.56129e10	4.29603
$161$	−6.01192e9	−0.705175
$162$	0	0
$163$	9.05833e8	0.100509	0.0502544	−	0.998736i	$-0.483997\pi$
$163$	9.05833e8	0.100509	0.0502544	+	0.998736i	$0.483997\pi$
$164$	−6.03728e8	−0.0651694
$165$	0	0
$166$	1.47275e10	1.50536
$167$	−1.08715e10	−1.08159	−0.540797	−	0.841153i	$-0.681877\pi$
$167$	−1.08715e10	−1.08159	−0.540797	+	0.841153i	$0.681877\pi$
$168$	0	0
$169$	−5.71818e9	−0.539222
$170$	−8.84691e9	−0.812403
$171$	0	0
$172$	4.50611e9	0.392576
$173$	2.10914e10	1.79019	0.895093	−	0.445880i	$-0.147109\pi$
$173$	2.10914e10	1.79019	0.895093	+	0.445880i	$0.147109\pi$
$174$	0	0
$175$	1.23199e10	0.992970
$176$	−2.67812e10	−2.10389
$177$	0	0
$178$	2.10049e9	0.156831
$179$	2.13633e10	1.55535	0.777676	−	0.628665i	$-0.216398\pi$
$179$	2.13633e10	1.55535	0.777676	+	0.628665i	$0.216398\pi$
$180$	0	0
$181$	−1.23594e10	−0.855937	−0.427969	−	0.903794i	$-0.640771\pi$
$181$	−1.23594e10	−0.855937	−0.427969	+	0.903794i	$0.640771\pi$
$182$	8.51345e9	0.575154
$183$	0	0
$184$	−6.86364e10	−4.41443
$185$	8.69042e9	0.545466
$186$	0	0
$187$	3.05464e9	0.182673
$188$	−1.99630e9	−0.116551
$189$	0	0
$190$	6.78538e10	3.77731
$191$	−2.02521e10	−1.10108	−0.550540	−	0.834809i	$-0.685578\pi$
$191$	−2.02521e10	−1.10108	−0.550540	+	0.834809i	$0.685578\pi$
$192$	0	0
$193$	−2.75114e10	−1.42727	−0.713633	−	0.700520i	$-0.752952\pi$
$193$	−2.75114e10	−1.42727	−0.713633	+	0.700520i	$0.752952\pi$
$194$	2.75527e10	1.39655
$195$	0	0
$196$	−4.12679e10	−1.99738
$197$	−1.58792e10	−0.751156	−0.375578	−	0.926791i	$-0.622556\pi$
$197$	−1.58792e10	−0.751156	−0.375578	+	0.926791i	$0.622556\pi$
$198$	0	0
$199$	3.50786e10	1.58563	0.792817	−	0.609460i	$-0.208614\pi$
$199$	3.50786e10	1.58563	0.792817	+	0.609460i	$0.208614\pi$
$200$	1.40653e11	6.21604
$201$	0	0
$202$	2.29653e10	0.970491
$203$	−1.43401e10	−0.592678
$204$	0	0
$205$	−1.17332e9	−0.0464005
$206$	5.87351e10	2.27245
$207$	0	0
$208$	5.11866e10	1.89614
$209$	−2.34284e10	−0.849346
$210$	0	0
$211$	−2.22358e10	−0.772293	−0.386146	−	0.922438i	$-0.626194\pi$
$211$	−2.22358e10	−0.772293	−0.386146	+	0.922438i	$0.626194\pi$
$212$	−1.33571e11	−4.54150
$213$	0	0
$214$	−1.48970e10	−0.485552
$215$	8.75742e9	0.279514
$216$	0	0
$217$	−1.61381e10	−0.494063
$218$	−3.74052e10	−1.12170
$219$	0	0
$220$	−1.17464e11	−3.38068
$221$	−5.83830e9	−0.164635
$222$	0	0
$223$	4.29725e9	0.116364	0.0581821	−	0.998306i	$-0.481470\pi$
$223$	4.29725e9	0.116364	0.0581821	+	0.998306i	$0.481470\pi$
$224$	4.09474e10	1.08670
$225$	0	0
$226$	−8.42925e10	−2.14932
$227$	−2.64486e10	−0.661129	−0.330565	−	0.943783i	$-0.607239\pi$
$227$	−2.64486e10	−0.661129	−0.330565	+	0.943783i	$0.607239\pi$
$228$	0	0
$229$	−1.98494e10	−0.476966	−0.238483	−	0.971147i	$-0.576650\pi$
$229$	−1.98494e10	−0.476966	−0.238483	+	0.971147i	$0.576650\pi$
$230$	−2.21683e11	−5.22345
$231$	0	0
$232$	−1.63717e11	−3.71019
$233$	2.09016e10	0.464598	0.232299	−	0.972644i	$-0.425375\pi$
$233$	2.09016e10	0.464598	0.232299	+	0.972644i	$0.425375\pi$
$234$	0	0
$235$	−3.87972e9	−0.0829841
$236$	1.00165e11	2.10190
$237$	0	0
$238$	−1.01721e10	−0.205501
$239$	3.88402e10	0.769999	0.385000	−	0.922917i	$-0.374202\pi$
$239$	3.88402e10	0.769999	0.385000	+	0.922917i	$0.374202\pi$
$240$	0	0
$241$	−1.37408e10	−0.262383	−0.131192	−	0.991357i	$-0.541880\pi$
$241$	−1.37408e10	−0.262383	−0.131192	+	0.991357i	$0.541880\pi$
$242$	−4.32596e10	−0.810799
$243$	0	0
$244$	2.30443e10	0.416207
$245$	−8.02022e10	−1.42213
$246$	0	0
$247$	4.47785e10	0.765478
$248$	−1.84244e11	−3.09286
$249$	0	0
$250$	2.47400e11	4.00562
$251$	7.04853e10	1.12090	0.560450	−	0.828188i	$-0.310628\pi$
$251$	7.04853e10	1.12090	0.560450	+	0.828188i	$0.310628\pi$
$252$	0	0
$253$	7.65423e10	1.17452
$254$	−1.52381e10	−0.229710
$255$	0	0
$256$	−1.44835e10	−0.210762
$257$	−6.32271e10	−0.904075	−0.452038	−	0.891999i	$-0.649303\pi$
$257$	−6.32271e10	−0.904075	−0.452038	+	0.891999i	$0.649303\pi$
$258$	0	0
$259$	9.99216e9	0.137978
$260$	2.24508e11	3.04686
$261$	0	0
$262$	−9.22934e9	−0.121008
$263$	7.65063e9	0.0986044	0.0493022	−	0.998784i	$-0.484300\pi$
$263$	7.65063e9	0.0986044	0.0493022	+	0.998784i	$0.484300\pi$
$264$	0	0
$265$	−2.59588e11	−3.23354
$266$	7.80177e10	0.955489
$267$	0	0
$268$	1.06306e11	1.25878
$269$	−5.99383e10	−0.697942	−0.348971	−	0.937134i	$-0.613469\pi$
$269$	−5.99383e10	−0.697942	−0.348971	+	0.937134i	$0.613469\pi$
$270$	0	0
$271$	−4.61140e10	−0.519363	−0.259681	−	0.965694i	$-0.583618\pi$
$271$	−4.61140e10	−0.519363	−0.259681	+	0.965694i	$0.583618\pi$
$272$	−6.11591e10	−0.677487
$273$	0	0
$274$	−1.61647e11	−1.73257
$275$	−1.56854e11	−1.65386
$276$	0	0
$277$	3.74719e9	0.0382426	0.0191213	−	0.999817i	$-0.493913\pi$
$277$	3.74719e9	0.0382426	0.0191213	+	0.999817i	$0.493913\pi$
$278$	4.47934e10	0.449792
$279$	0	0
$280$	2.35370e11	2.28845
$281$	1.09177e10	0.104461	0.0522305	−	0.998635i	$-0.483367\pi$
$281$	1.09177e10	0.104461	0.0522305	+	0.998635i	$0.483367\pi$
$282$	0	0
$283$	2.09684e10	0.194324	0.0971620	−	0.995269i	$-0.469024\pi$
$283$	2.09684e10	0.194324	0.0971620	+	0.995269i	$0.469024\pi$
$284$	1.33079e11	1.21389
$285$	0	0
$286$	−1.08391e11	−0.957960
$287$	−1.34907e9	−0.0117372
$288$	0	0
$289$	6.97576e9	0.0588235
$290$	−5.28775e11	−4.39016
$291$	0	0
$292$	1.84279e10	0.148338
$293$	2.40168e11	1.90375	0.951875	−	0.306485i	$-0.0991531\pi$
$293$	2.40168e11	1.90375	0.951875	+	0.306485i	$0.0991531\pi$
$294$	0	0
$295$	1.94666e11	1.49655
$296$	1.14078e11	0.863750
$297$	0	0
$298$	−4.71589e11	−3.46410
$299$	−1.46294e11	−1.05854
$300$	0	0
$301$	1.00692e10	0.0707042
$302$	−1.92648e10	−0.133270
$303$	0	0
$304$	4.69076e11	3.15001
$305$	4.47855e10	0.296339
$306$	0	0
$307$	−2.30483e11	−1.48087	−0.740435	−	0.672128i	$-0.765380\pi$
$307$	−2.30483e11	−1.48087	−0.740435	+	0.672128i	$0.765380\pi$
$308$	−1.35059e11	−0.855158
$309$	0	0
$310$	−5.95074e11	−3.65968
$311$	−1.47492e11	−0.894016	−0.447008	−	0.894530i	$-0.647510\pi$
$311$	−1.47492e11	−0.894016	−0.447008	+	0.894530i	$0.647510\pi$
$312$	0	0
$313$	1.79761e11	1.05863	0.529317	−	0.848424i	$-0.322448\pi$
$313$	1.79761e11	1.05863	0.529317	+	0.848424i	$0.322448\pi$
$314$	5.00617e11	2.90618
$315$	0	0
$316$	5.01943e11	2.83180
$317$	−4.91432e10	−0.273336	−0.136668	−	0.990617i	$-0.543639\pi$
$317$	−4.91432e10	−0.273336	−0.136668	+	0.990617i	$0.543639\pi$
$318$	0	0
$319$	1.82574e11	0.987146
$320$	5.73209e11	3.05589
$321$	0	0
$322$	−2.54889e11	−1.32130
$323$	−5.35025e10	−0.273503
$324$	0	0
$325$	2.99793e11	1.49055
$326$	3.84049e10	0.188325
$327$	0	0
$328$	−1.54019e10	−0.0734756
$329$	−4.46086e9	−0.0209912
$330$	0	0
$331$	2.45275e11	1.12312	0.561562	−	0.827434i	$-0.310200\pi$
$331$	2.45275e11	1.12312	0.561562	+	0.827434i	$0.310200\pi$
$332$	4.46553e11	2.01721
$333$	0	0
$334$	−4.60922e11	−2.02660
$335$	2.06600e11	0.896251
$336$	0	0
$337$	6.51138e10	0.275004	0.137502	−	0.990502i	$-0.456093\pi$
$337$	6.51138e10	0.275004	0.137502	+	0.990502i	$0.456093\pi$
$338$	−2.42435e11	−1.01035
$339$	0	0
$340$	−2.68248e11	−1.08863
$341$	2.05466e11	0.822896
$342$	0	0
$343$	−2.08136e11	−0.811938
$344$	1.14957e11	0.442612
$345$	0	0
$346$	8.94219e11	3.35430
$347$	7.31021e10	0.270675	0.135337	−	0.990800i	$-0.456788\pi$
$347$	7.31021e10	0.270675	0.135337	+	0.990800i	$0.456788\pi$
$348$	0	0
$349$	1.43103e11	0.516337	0.258169	−	0.966100i	$-0.416881\pi$
$349$	1.43103e11	0.516337	0.258169	+	0.966100i	$0.416881\pi$
$350$	5.22331e11	1.86054
$351$	0	0
$352$	−5.21332e11	−1.80998
$353$	−3.76830e11	−1.29169	−0.645846	−	0.763467i	$-0.723495\pi$
$353$	−3.76830e11	−1.29169	−0.645846	+	0.763467i	$0.723495\pi$
$354$	0	0
$355$	2.58634e11	0.864286
$356$	6.36892e10	0.210156
$357$	0	0
$358$	9.05745e11	2.91429
$359$	3.51198e11	1.11590	0.557952	−	0.829873i	$-0.311587\pi$
$359$	3.51198e11	1.11590	0.557952	+	0.829873i	$0.311587\pi$
$360$	0	0
$361$	8.76640e10	0.271668
$362$	−5.24003e11	−1.60378
$363$	0	0
$364$	2.58137e11	0.770716
$365$	3.58137e10	0.105616
$366$	0	0
$367$	−4.78044e11	−1.37553	−0.687766	−	0.725933i	$-0.741408\pi$
$367$	−4.78044e11	−1.37553	−0.687766	+	0.725933i	$0.741408\pi$
$368$	−1.53251e12	−4.35599
$369$	0	0
$370$	3.68451e11	1.02205
$371$	−2.98472e11	−0.817939
$372$	0	0
$373$	6.76181e11	1.80873	0.904364	−	0.426762i	$-0.140346\pi$
$373$	6.76181e11	1.80873	0.904364	+	0.426762i	$0.140346\pi$
$374$	1.29509e11	0.342276
$375$	0	0
$376$	−5.09284e10	−0.131406
$377$	−3.48952e11	−0.889672
$378$	0	0
$379$	−5.13122e11	−1.27745	−0.638725	−	0.769435i	$-0.720538\pi$
$379$	−5.13122e11	−1.27745	−0.638725	+	0.769435i	$0.720538\pi$
$380$	2.05740e12	5.06166
$381$	0	0
$382$	−8.58633e11	−2.06311
$383$	7.63819e11	1.81383	0.906914	−	0.421316i	$-0.138432\pi$
$383$	7.63819e11	1.81383	0.906914	+	0.421316i	$0.138432\pi$
$384$	0	0
$385$	−2.62481e11	−0.608871
$386$	−1.16641e12	−2.67429
$387$	0	0
$388$	8.35429e11	1.87140
$389$	−3.33397e11	−0.738224	−0.369112	−	0.929385i	$-0.620338\pi$
$389$	−3.33397e11	−0.738224	−0.369112	+	0.929385i	$0.620338\pi$
$390$	0	0
$391$	1.74796e11	0.378214
$392$	−1.05280e12	−2.25195
$393$	0	0
$394$	−6.73235e11	−1.40745
$395$	9.75503e11	2.01624
$396$	0	0
$397$	−6.95415e11	−1.40503	−0.702517	−	0.711667i	$-0.747941\pi$
$397$	−6.95415e11	−1.40503	−0.702517	+	0.711667i	$0.747941\pi$
$398$	1.48724e12	2.97103
$399$	0	0
$400$	3.14048e12	6.13375
$401$	−5.82880e11	−1.12572	−0.562859	−	0.826553i	$-0.690299\pi$
$401$	−5.82880e11	−1.12572	−0.562859	+	0.826553i	$0.690299\pi$
$402$	0	0
$403$	−3.92705e11	−0.741640
$404$	6.96334e11	1.30047
$405$	0	0
$406$	−6.07980e11	−1.11051
$407$	−1.27218e11	−0.229812
$408$	0	0
$409$	2.34282e11	0.413985	0.206993	−	0.978343i	$-0.433632\pi$
$409$	2.34282e11	0.413985	0.206993	+	0.978343i	$0.433632\pi$
$410$	−4.97455e10	−0.0869413
$411$	0	0
$412$	1.78091e12	3.04512
$413$	2.23825e11	0.378558
$414$	0	0
$415$	8.67854e11	1.43625
$416$	9.96417e11	1.63125
$417$	0	0
$418$	−9.93302e11	−1.59143
$419$	6.51621e11	1.03284	0.516419	−	0.856336i	$-0.327265\pi$
$419$	6.51621e11	1.03284	0.516419	+	0.856336i	$0.327265\pi$
$420$	0	0
$421$	−5.97500e11	−0.926976	−0.463488	−	0.886103i	$-0.653402\pi$
$421$	−5.97500e11	−0.926976	−0.463488	+	0.886103i	$0.653402\pi$
$422$	−9.42739e11	−1.44706
$423$	0	0
$424$	−3.40757e12	−5.12034
$425$	−3.58201e11	−0.532570
$426$	0	0
$427$	5.14939e10	0.0749602
$428$	−4.51692e11	−0.650648
$429$	0	0
$430$	3.71291e11	0.523729
$431$	1.45053e11	0.202478	0.101239	−	0.994862i	$-0.467719\pi$
$431$	1.45053e11	0.202478	0.101239	+	0.994862i	$0.467719\pi$
$432$	0	0
$433$	−2.07018e11	−0.283017	−0.141509	−	0.989937i	$-0.545195\pi$
$433$	−2.07018e11	−0.283017	−0.141509	+	0.989937i	$0.545195\pi$
$434$	−6.84211e11	−0.925734
$435$	0	0
$436$	−1.13417e12	−1.50310
$437$	−1.34065e12	−1.75853
$438$	0	0
$439$	1.27742e12	1.64151	0.820757	−	0.571278i	$-0.193552\pi$
$439$	1.27742e12	1.64151	0.820757	+	0.571278i	$0.193552\pi$
$440$	−2.99668e12	−3.81156
$441$	0	0
$442$	−2.47529e11	−0.308479
$443$	−2.56214e10	−0.0316072	−0.0158036	−	0.999875i	$-0.505031\pi$
$443$	−2.56214e10	−0.0316072	−0.0158036	+	0.999875i	$0.505031\pi$
$444$	0	0
$445$	1.23777e11	0.149630
$446$	1.82192e11	0.218033
$447$	0	0
$448$	6.59070e11	0.773002
$449$	6.93244e11	0.804967	0.402483	−	0.915427i	$-0.368147\pi$
$449$	6.93244e11	0.804967	0.402483	+	0.915427i	$0.368147\pi$
$450$	0	0
$451$	1.71760e10	0.0195491
$452$	−2.55584e12	−2.88012
$453$	0	0
$454$	−1.12135e12	−1.23877
$455$	5.01678e11	0.548749
$456$	0	0
$457$	−1.01211e12	−1.08544	−0.542721	−	0.839913i	$-0.682606\pi$
$457$	−1.01211e12	−1.08544	−0.542721	+	0.839913i	$0.682606\pi$
$458$	−8.41560e11	−0.893698
$459$	0	0
$460$	−6.72168e12	−6.99951
$461$	−4.59728e11	−0.474075	−0.237037	−	0.971501i	$-0.576176\pi$
$461$	−4.59728e11	−0.474075	−0.237037	+	0.971501i	$0.576176\pi$
$462$	0	0
$463$	−7.53078e11	−0.761598	−0.380799	−	0.924658i	$-0.624351\pi$
$463$	−7.53078e11	−0.761598	−0.380799	+	0.924658i	$0.624351\pi$
$464$	−3.65544e12	−3.66108
$465$	0	0
$466$	8.86170e11	0.870523
$467$	1.22063e12	1.18757	0.593783	−	0.804625i	$-0.297634\pi$
$467$	1.22063e12	1.18757	0.593783	+	0.804625i	$0.297634\pi$
$468$	0	0
$469$	2.37547e11	0.226711
$470$	−1.64490e11	−0.155488
$471$	0	0
$472$	2.55534e12	2.36979
$473$	−1.28199e11	−0.117763
$474$	0	0
$475$	2.74732e12	2.47621
$476$	−3.08429e11	−0.275375
$477$	0	0
$478$	1.64672e12	1.44276
$479$	−1.22689e12	−1.06487	−0.532436	−	0.846470i	$-0.678723\pi$
$479$	−1.22689e12	−1.06487	−0.532436	+	0.846470i	$0.678723\pi$
$480$	0	0
$481$	2.43150e11	0.207120
$482$	−5.82574e11	−0.491631
$483$	0	0
$484$	−1.31168e12	−1.08648
$485$	1.62362e12	1.33243
$486$	0	0
$487$	1.96428e12	1.58242	0.791211	−	0.611543i	$-0.209451\pi$
$487$	1.96428e12	1.58242	0.791211	+	0.611543i	$0.209451\pi$
$488$	5.87892e11	0.469255
$489$	0	0
$490$	−3.40036e12	−2.66466
$491$	2.27273e12	1.76474	0.882371	−	0.470554i	$-0.155946\pi$
$491$	2.27273e12	1.76474	0.882371	+	0.470554i	$0.155946\pi$
$492$	0	0
$493$	4.16937e11	0.317877
$494$	1.89849e12	1.43429
$495$	0	0
$496$	−4.11377e12	−3.05192
$497$	2.97374e11	0.218625
$498$	0	0
$499$	2.31148e12	1.66893	0.834464	−	0.551063i	$-0.185778\pi$
$499$	2.31148e12	1.66893	0.834464	+	0.551063i	$0.185778\pi$
$500$	7.50144e12	5.36759
$501$	0	0
$502$	2.98839e12	2.10025
$503$	2.10646e12	1.46723	0.733615	−	0.679565i	$-0.237832\pi$
$503$	2.10646e12	1.46723	0.733615	+	0.679565i	$0.237832\pi$
$504$	0	0
$505$	1.35329e12	0.925935
$506$	3.24519e12	2.20071
$507$	0	0
$508$	−4.62037e11	−0.307815
$509$	1.57634e12	1.04093	0.520464	−	0.853884i	$-0.325759\pi$
$509$	1.57634e12	1.04093	0.520464	+	0.853884i	$0.325759\pi$
$510$	0	0
$511$	4.11782e10	0.0267161
$512$	−1.85774e12	−1.19473
$513$	0	0
$514$	−2.68066e12	−1.69398
$515$	3.46112e12	2.16812
$516$	0	0
$517$	5.67946e10	0.0349623
$518$	4.23641e11	0.258532
$519$	0	0
$520$	5.72752e12	3.43520
$521$	3.90823e11	0.232386	0.116193	−	0.993227i	$-0.462931\pi$
$521$	3.90823e11	0.232386	0.116193	+	0.993227i	$0.462931\pi$
$522$	0	0
$523$	−2.52838e12	−1.47770	−0.738849	−	0.673871i	$-0.764630\pi$
$523$	−2.52838e12	−1.47770	−0.738849	+	0.673871i	$0.764630\pi$
$524$	−2.79844e11	−0.162153
$525$	0	0
$526$	3.24366e11	0.184757
$527$	4.69214e11	0.264986
$528$	0	0
$529$	2.57884e12	1.43177
$530$	−1.10058e13	−6.05874
$531$	0	0
$532$	2.36558e12	1.28037
$533$	−3.28283e10	−0.0176188
$534$	0	0
$535$	−8.77843e11	−0.463260
$536$	2.71201e12	1.41922
$537$	0	0
$538$	−2.54123e12	−1.30774
$539$	1.17407e12	0.599161
$540$	0	0
$541$	1.45109e12	0.728296	0.364148	−	0.931341i	$-0.381360\pi$
$541$	1.45109e12	0.728296	0.364148	+	0.931341i	$0.381360\pi$
$542$	−1.95511e12	−0.973138
$543$	0	0
$544$	−1.19054e12	−0.582842
$545$	−2.20420e12	−1.07021
$546$	0	0
$547$	−2.60966e10	−0.0124635	−0.00623177	−	0.999981i	$-0.501984\pi$
$547$	−2.60966e10	−0.0124635	−0.00623177	+	0.999981i	$0.501984\pi$
$548$	−4.90133e12	−2.32167
$549$	0	0
$550$	−6.65019e12	−3.09886
$551$	−3.19781e12	−1.47799
$552$	0	0
$553$	1.12162e12	0.510016
$554$	1.58871e11	0.0716557
$555$	0	0
$556$	1.35818e12	0.602729
$557$	2.42622e12	1.06803	0.534013	−	0.845477i	$-0.320683\pi$
$557$	2.42622e12	1.06803	0.534013	+	0.845477i	$0.320683\pi$
$558$	0	0
$559$	2.45025e11	0.106134
$560$	5.25532e12	2.25815
$561$	0	0
$562$	4.62883e11	0.195730
$563$	3.14392e12	1.31881	0.659406	−	0.751787i	$-0.270808\pi$
$563$	3.14392e12	1.31881	0.659406	+	0.751787i	$0.270808\pi$
$564$	0	0
$565$	−4.96716e12	−2.05064
$566$	8.89004e11	0.364108
$567$	0	0
$568$	3.39504e12	1.36860
$569$	4.68855e12	1.87514	0.937570	−	0.347798i	$-0.113070\pi$
$569$	4.68855e12	1.87514	0.937570	+	0.347798i	$0.113070\pi$
$570$	0	0
$571$	2.51532e12	0.990216	0.495108	−	0.868831i	$-0.335128\pi$
$571$	2.51532e12	0.990216	0.495108	+	0.868831i	$0.335128\pi$
$572$	−3.28654e12	−1.28368
$573$	0	0
$574$	−5.71969e10	−0.0219922
$575$	−8.97569e12	−3.42423
$576$	0	0
$577$	1.66387e12	0.624924	0.312462	−	0.949930i	$-0.398846\pi$
$577$	1.66387e12	0.624924	0.312462	+	0.949930i	$0.398846\pi$
$578$	2.95754e11	0.110219
$579$	0	0
$580$	−1.60330e13	−5.88288
$581$	9.97850e11	0.363306
$582$	0	0
$583$	3.80007e12	1.36233
$584$	4.70121e11	0.167244
$585$	0	0
$586$	1.01825e13	3.56709
$587$	−1.10214e12	−0.383147	−0.191573	−	0.981478i	$-0.561359\pi$
$587$	−1.10214e12	−0.383147	−0.191573	+	0.981478i	$0.561359\pi$
$588$	0	0
$589$	−3.59876e12	−1.23207
$590$	8.25330e12	2.80410
$591$	0	0
$592$	2.54711e12	0.852316
$593$	1.47081e12	0.488438	0.244219	−	0.969720i	$-0.421468\pi$
$593$	1.47081e12	0.488438	0.244219	+	0.969720i	$0.421468\pi$
$594$	0	0
$595$	−5.99418e11	−0.196066
$596$	−1.42991e13	−4.64195
$597$	0	0
$598$	−6.20250e12	−1.98340
$599$	−3.93181e12	−1.24788	−0.623938	−	0.781473i	$-0.714468\pi$
$599$	−3.93181e12	−1.24788	−0.623938	+	0.781473i	$0.714468\pi$
$600$	0	0
$601$	8.77198e11	0.274260	0.137130	−	0.990553i	$-0.456212\pi$
$601$	8.77198e11	0.274260	0.137130	+	0.990553i	$0.456212\pi$
$602$	4.26907e11	0.132480
$603$	0	0
$604$	−5.84129e11	−0.178584
$605$	−2.54919e12	−0.773575
$606$	0	0
$607$	−1.09458e12	−0.327265	−0.163632	−	0.986521i	$-0.552321\pi$
$607$	−1.09458e12	−0.327265	−0.163632	+	0.986521i	$0.552321\pi$
$608$	9.13121e12	2.70995
$609$	0	0
$610$	1.89879e12	0.555254
$611$	−1.08551e11	−0.0315100
$612$	0	0
$613$	−4.47212e12	−1.27921	−0.639605	−	0.768704i	$-0.720902\pi$
$613$	−4.47212e12	−1.27921	−0.639605	+	0.768704i	$0.720902\pi$
$614$	−9.77188e12	−2.77473
$615$	0	0
$616$	−3.44555e12	−0.964152
$617$	2.92442e12	0.812376	0.406188	−	0.913790i	$-0.366858\pi$
$617$	2.92442e12	0.812376	0.406188	+	0.913790i	$0.366858\pi$
$618$	0	0
$619$	1.52167e12	0.416593	0.208296	−	0.978066i	$-0.433208\pi$
$619$	1.52167e12	0.416593	0.208296	+	0.978066i	$0.433208\pi$
$620$	−1.80433e13	−4.90404
$621$	0	0
$622$	−6.25325e12	−1.67513
$623$	1.42318e11	0.0378497
$624$	0	0
$625$	6.20223e12	1.62588
$626$	7.62139e12	1.98358
$627$	0	0
$628$	1.51793e13	3.89433
$629$	−2.90522e11	−0.0740033
$630$	0	0
$631$	−6.61053e12	−1.65998	−0.829992	−	0.557775i	$-0.811655\pi$
$631$	−6.61053e12	−1.65998	−0.829992	+	0.557775i	$0.811655\pi$
$632$	1.28053e13	3.19273
$633$	0	0
$634$	−2.08354e12	−0.512154
$635$	−8.97946e11	−0.219164
$636$	0	0
$637$	−2.24398e12	−0.539998
$638$	7.74066e12	1.84963
$639$	0	0
$640$	6.06873e12	1.42984
$641$	−3.36551e12	−0.787389	−0.393694	−	0.919241i	$-0.628803\pi$
$641$	−3.36551e12	−0.787389	−0.393694	+	0.919241i	$0.628803\pi$
$642$	0	0
$643$	−1.05715e12	−0.243887	−0.121943	−	0.992537i	$-0.538913\pi$
$643$	−1.05715e12	−0.243887	−0.121943	+	0.992537i	$0.538913\pi$
$644$	−7.72852e12	−1.77056
$645$	0	0
$646$	−2.26836e12	−0.512467
$647$	−3.32786e12	−0.746613	−0.373307	−	0.927708i	$-0.621776\pi$
$647$	−3.32786e12	−0.746613	−0.373307	+	0.927708i	$0.621776\pi$
$648$	0	0
$649$	−2.84968e12	−0.630515
$650$	1.27104e13	2.79287
$651$	0	0
$652$	1.16448e12	0.252358
$653$	6.30246e12	1.35644	0.678220	−	0.734859i	$-0.262751\pi$
$653$	6.30246e12	1.35644	0.678220	+	0.734859i	$0.262751\pi$
$654$	0	0
$655$	−5.43863e11	−0.115453
$656$	−3.43893e11	−0.0725029
$657$	0	0
$658$	−1.89129e11	−0.0393315
$659$	−2.83854e12	−0.586287	−0.293143	−	0.956069i	$-0.594701\pi$
$659$	−2.83854e12	−0.586287	−0.293143	+	0.956069i	$0.594701\pi$
$660$	0	0
$661$	6.58551e12	1.34178	0.670892	−	0.741555i	$-0.265911\pi$
$661$	6.58551e12	1.34178	0.670892	+	0.741555i	$0.265911\pi$
$662$	1.03990e13	2.10442
$663$	0	0
$664$	1.13922e13	2.27432
$665$	4.59740e12	0.911621
$666$	0	0
$667$	1.04475e13	2.04383
$668$	−1.39757e13	−2.71568
$669$	0	0
$670$	8.75931e12	1.67932
$671$	−6.55609e11	−0.124851
$672$	0	0
$673$	−2.50086e12	−0.469918	−0.234959	−	0.972005i	$-0.575496\pi$
$673$	−2.50086e12	−0.469918	−0.234959	+	0.972005i	$0.575496\pi$
$674$	2.76065e12	0.515279
$675$	0	0
$676$	−7.35091e12	−1.35388
$677$	−1.03159e13	−1.88737	−0.943687	−	0.330839i	$-0.892668\pi$
$677$	−1.03159e13	−1.88737	−0.943687	+	0.330839i	$0.892668\pi$
$678$	0	0
$679$	1.86682e12	0.337045
$680$	−6.84339e12	−1.22739
$681$	0	0
$682$	8.71121e12	1.54187
$683$	−9.27753e12	−1.63132	−0.815660	−	0.578531i	$-0.803626\pi$
$683$	−9.27753e12	−1.63132	−0.815660	+	0.578531i	$0.803626\pi$
$684$	0	0
$685$	−9.52550e12	−1.65303
$686$	−8.82440e12	−1.52134
$687$	0	0
$688$	2.56675e12	0.436753
$689$	−7.26304e12	−1.22781
$690$	0	0
$691$	1.58767e12	0.264917	0.132458	−	0.991189i	$-0.457713\pi$
$691$	1.58767e12	0.264917	0.132458	+	0.991189i	$0.457713\pi$
$692$	2.71137e13	4.49481
$693$	0	0
$694$	3.09934e12	0.507167
$695$	2.63957e12	0.429142
$696$	0	0
$697$	3.92241e10	0.00629514
$698$	6.06717e12	0.967469
$699$	0	0
$700$	1.58376e13	2.49316
$701$	1.15310e13	1.80358	0.901791	−	0.432172i	$-0.142253\pi$
$701$	1.15310e13	1.80358	0.901791	+	0.432172i	$0.142253\pi$
$702$	0	0
$703$	2.22824e12	0.344082
$704$	−8.39113e12	−1.28749
$705$	0	0
$706$	−1.59766e13	−2.42026
$707$	1.55600e12	0.234220
$708$	0	0
$709$	−1.03429e12	−0.153722	−0.0768609	−	0.997042i	$-0.524490\pi$
$709$	−1.03429e12	−0.153722	−0.0768609	+	0.997042i	$0.524490\pi$
$710$	1.09654e13	1.61943
$711$	0	0
$712$	1.62480e12	0.236941
$713$	1.17574e13	1.70376
$714$	0	0
$715$	−6.38724e12	−0.913979
$716$	2.74632e13	3.90519
$717$	0	0
$718$	1.48899e13	2.09089
$719$	−8.27525e12	−1.15478	−0.577392	−	0.816467i	$-0.695930\pi$
$719$	−8.27525e12	−1.15478	−0.577392	+	0.816467i	$0.695930\pi$
$720$	0	0
$721$	3.97956e12	0.548437
$722$	3.71672e12	0.509029
$723$	0	0
$724$	−1.58884e13	−2.14909
$725$	−2.14095e13	−2.87796
$726$	0	0
$727$	5.25612e12	0.697848	0.348924	−	0.937151i	$-0.386547\pi$
$727$	5.25612e12	0.697848	0.348924	+	0.937151i	$0.386547\pi$
$728$	6.58544e12	0.868948
$729$	0	0
$730$	1.51841e12	0.197895
$731$	−2.92762e11	−0.0379215
$732$	0	0
$733$	7.86667e12	1.00652	0.503261	−	0.864134i	$-0.332133\pi$
$733$	7.86667e12	1.00652	0.503261	+	0.864134i	$0.332133\pi$
$734$	−2.02678e13	−2.57735
$735$	0	0
$736$	−2.98323e13	−3.74746
$737$	−3.02439e12	−0.377602
$738$	0	0
$739$	−8.65193e12	−1.06712	−0.533560	−	0.845762i	$-0.679146\pi$
$739$	−8.65193e12	−1.06712	−0.533560	+	0.845762i	$0.679146\pi$
$740$	1.11718e13	1.36956
$741$	0	0
$742$	−1.26544e13	−1.53258
$743$	−9.67486e12	−1.16465	−0.582325	−	0.812956i	$-0.697857\pi$
$743$	−9.67486e12	−1.16465	−0.582325	+	0.812956i	$0.697857\pi$
$744$	0	0
$745$	−2.77896e13	−3.30506
$746$	2.86683e13	3.38904
$747$	0	0
$748$	3.92685e12	0.458656
$749$	−1.00934e12	−0.117184
$750$	0	0
$751$	5.48720e12	0.629464	0.314732	−	0.949181i	$-0.398085\pi$
$751$	5.48720e12	0.629464	0.314732	+	0.949181i	$0.398085\pi$
$752$	−1.13712e12	−0.129666
$753$	0	0
$754$	−1.47946e13	−1.66699
$755$	−1.13523e12	−0.127151
$756$	0	0
$757$	1.33117e13	1.47333	0.736667	−	0.676255i	$-0.236398\pi$
$757$	1.33117e13	1.47333	0.736667	+	0.676255i	$0.236398\pi$
$758$	−2.17550e13	−2.39358
$759$	0	0
$760$	5.24872e13	5.70680
$761$	−9.94914e12	−1.07536	−0.537681	−	0.843148i	$-0.680699\pi$
$761$	−9.94914e12	−1.07536	−0.537681	+	0.843148i	$0.680699\pi$
$762$	0	0
$763$	−2.53437e12	−0.270713
$764$	−2.60347e13	−2.76460
$765$	0	0
$766$	3.23839e13	3.39860
$767$	5.44656e12	0.568255
$768$	0	0
$769$	5.14283e12	0.530315	0.265157	−	0.964205i	$-0.414576\pi$
$769$	5.14283e12	0.530315	0.265157	+	0.964205i	$0.414576\pi$
$770$	−1.11285e13	−1.14085
$771$	0	0
$772$	−3.53668e13	−3.58359
$773$	3.51233e12	0.353824	0.176912	−	0.984227i	$-0.443389\pi$
$773$	3.51233e12	0.353824	0.176912	+	0.984227i	$0.443389\pi$
$774$	0	0
$775$	−2.40938e13	−2.39910
$776$	2.13130e13	2.10992
$777$	0	0
$778$	−1.41351e13	−1.38322
$779$	−3.00840e11	−0.0292696
$780$	0	0
$781$	−3.78610e12	−0.364135
$782$	7.41090e12	0.708665
$783$	0	0
$784$	−2.35068e13	−2.22214
$785$	2.95002e13	2.77275
$786$	0	0
$787$	6.67867e12	0.620589	0.310294	−	0.950641i	$-0.399572\pi$
$787$	6.67867e12	0.620589	0.310294	+	0.950641i	$0.399572\pi$
$788$	−2.04132e13	−1.88601
$789$	0	0
$790$	4.13587e13	3.77785
$791$	−5.71119e12	−0.518719
$792$	0	0
$793$	1.25306e12	0.112523
$794$	−2.94838e13	−2.63263
$795$	0	0
$796$	4.50947e13	3.98122
$797$	4.54726e12	0.399197	0.199599	−	0.979878i	$-0.436036\pi$
$797$	4.54726e12	0.399197	0.199599	+	0.979878i	$0.436036\pi$
$798$	0	0
$799$	1.29699e11	0.0112584
$800$	6.11337e13	5.27687
$801$	0	0
$802$	−2.47126e13	−2.10927
$803$	−5.24272e11	−0.0444976
$804$	0	0
$805$	−1.50200e13	−1.26063
$806$	−1.66496e13	−1.38962
$807$	0	0
$808$	1.77645e13	1.46623
$809$	−6.56062e12	−0.538488	−0.269244	−	0.963072i	$-0.586774\pi$
$809$	−6.56062e12	−0.538488	−0.269244	+	0.963072i	$0.586774\pi$
$810$	0	0
$811$	1.03164e13	0.837403	0.418702	−	0.908124i	$-0.362485\pi$
$811$	1.03164e13	0.837403	0.418702	+	0.908124i	$0.362485\pi$
$812$	−1.84346e13	−1.48810
$813$	0	0
$814$	−5.39370e12	−0.430603
$815$	2.26311e12	0.179679
$816$	0	0
$817$	2.24542e12	0.176318
$818$	9.93295e12	0.775690
$819$	0	0
$820$	−1.50834e12	−0.116503
$821$	2.30549e13	1.77100	0.885500	−	0.464639i	$-0.153816\pi$
$821$	2.30549e13	1.77100	0.885500	+	0.464639i	$0.153816\pi$
$822$	0	0
$823$	−1.48191e12	−0.112596	−0.0562979	−	0.998414i	$-0.517930\pi$
$823$	−1.48191e12	−0.112596	−0.0562979	+	0.998414i	$0.517930\pi$
$824$	4.54336e13	3.43324
$825$	0	0
$826$	9.48956e12	0.709310
$827$	−1.73025e13	−1.28627	−0.643137	−	0.765751i	$-0.722368\pi$
$827$	−1.73025e13	−1.28627	−0.643137	+	0.765751i	$0.722368\pi$
$828$	0	0
$829$	−2.31346e13	−1.70124	−0.850622	−	0.525778i	$-0.823774\pi$
$829$	−2.31346e13	−1.70124	−0.850622	+	0.525778i	$0.823774\pi$
$830$	3.67947e13	2.69113
$831$	0	0
$832$	1.60379e13	1.16036
$833$	2.68117e12	0.192940
$834$	0	0
$835$	−2.71610e13	−1.93356
$836$	−3.01180e13	−2.13255
$837$	0	0
$838$	2.76270e13	1.93524
$839$	−4.17604e12	−0.290962	−0.145481	−	0.989361i	$-0.546473\pi$
$839$	−4.17604e12	−0.290962	−0.145481	+	0.989361i	$0.546473\pi$
$840$	0	0
$841$	1.04129e13	0.717780
$842$	−2.53324e13	−1.73689
$843$	0	0
$844$	−2.85849e13	−1.93908
$845$	−1.42862e13	−0.963962
$846$	0	0
$847$	−2.93103e12	−0.195679
$848$	−7.60839e13	−5.05256
$849$	0	0
$850$	−1.51868e13	−0.997884
$851$	−7.27981e12	−0.475814
$852$	0	0
$853$	6.57843e12	0.425453	0.212727	−	0.977112i	$-0.431766\pi$
$853$	6.57843e12	0.425453	0.212727	+	0.977112i	$0.431766\pi$
$854$	2.18321e12	0.140454
$855$	0	0
$856$	−1.15233e13	−0.733576
$857$	2.26445e13	1.43400	0.716999	−	0.697074i	$-0.245515\pi$
$857$	2.26445e13	1.43400	0.716999	+	0.697074i	$0.245515\pi$
$858$	0	0
$859$	−1.95924e13	−1.22777	−0.613886	−	0.789395i	$-0.710395\pi$
$859$	−1.95924e13	−1.22777	−0.613886	+	0.789395i	$0.710395\pi$
$860$	1.12580e13	0.701805
$861$	0	0
$862$	6.14986e12	0.379387
$863$	−8.76018e12	−0.537606	−0.268803	−	0.963195i	$-0.586628\pi$
$863$	−8.76018e12	−0.537606	−0.268803	+	0.963195i	$0.586628\pi$
$864$	0	0
$865$	5.26942e13	3.20030
$866$	−8.77703e12	−0.530294
$867$	0	0
$868$	−2.07460e13	−1.24050
$869$	−1.42802e13	−0.849467
$870$	0	0
$871$	5.78049e12	0.340316
$872$	−2.89342e13	−1.69468
$873$	0	0
$874$	−5.68399e13	−3.29497
$875$	1.67624e13	0.966721
$876$	0	0
$877$	1.76925e13	1.00993	0.504965	−	0.863140i	$-0.331505\pi$
$877$	1.76925e13	1.00993	0.504965	+	0.863140i	$0.331505\pi$
$878$	5.41593e13	3.07573
$879$	0	0
$880$	−6.69095e13	−3.76111
$881$	1.40172e13	0.783919	0.391959	−	0.919983i	$-0.371797\pi$
$881$	1.40172e13	0.783919	0.391959	+	0.919983i	$0.371797\pi$
$882$	0	0
$883$	−7.52196e12	−0.416397	−0.208199	−	0.978087i	$-0.566760\pi$
$883$	−7.52196e12	−0.416397	−0.208199	+	0.978087i	$0.566760\pi$
$884$	−7.50534e12	−0.413366
$885$	0	0
$886$	−1.08628e12	−0.0592229
$887$	4.64548e12	0.251985	0.125992	−	0.992031i	$-0.459789\pi$
$887$	4.64548e12	0.251985	0.125992	+	0.992031i	$0.459789\pi$
$888$	0	0
$889$	−1.03245e12	−0.0554384
$890$	5.24782e12	0.280365
$891$	0	0
$892$	5.52427e12	0.292168
$893$	−9.94765e11	−0.0523467
$894$	0	0
$895$	5.33734e13	2.78049
$896$	6.97777e12	0.361685
$897$	0	0
$898$	2.93917e13	1.50828
$899$	2.80446e13	1.43196
$900$	0	0
$901$	8.67807e12	0.438694
$902$	7.28217e11	0.0366295
$903$	0	0
$904$	−6.52031e13	−3.24721
$905$	−3.08783e13	−1.53015
$906$	0	0
$907$	−2.57831e13	−1.26503	−0.632517	−	0.774546i	$-0.717978\pi$
$907$	−2.57831e13	−1.26503	−0.632517	+	0.774546i	$0.717978\pi$
$908$	−3.40006e13	−1.65997
$909$	0	0
$910$	2.12698e13	1.02820
$911$	−3.74022e13	−1.79914	−0.899568	−	0.436781i	$-0.856118\pi$
$911$	−3.74022e13	−1.79914	−0.899568	+	0.436781i	$0.856118\pi$
$912$	0	0
$913$	−1.27044e13	−0.605112
$914$	−4.29110e13	−2.03381
$915$	0	0
$916$	−2.55170e13	−1.19757
$917$	−6.25329e11	−0.0292043
$918$	0	0
$919$	9.74612e12	0.450726	0.225363	−	0.974275i	$-0.427643\pi$
$919$	9.74612e12	0.450726	0.225363	+	0.974275i	$0.427643\pi$
$920$	−1.71480e14	−7.89164
$921$	0	0
$922$	−1.94912e13	−0.888281
$923$	7.23633e12	0.328179
$924$	0	0
$925$	1.49181e13	0.670002
$926$	−3.19285e13	−1.42702
$927$	0	0
$928$	−7.11582e13	−3.14963
$929$	−6.34542e12	−0.279505	−0.139752	−	0.990186i	$-0.544631\pi$
$929$	−6.34542e12	−0.279505	−0.139752	+	0.990186i	$0.544631\pi$
$930$	0	0
$931$	−2.05640e13	−0.897084
$932$	2.68697e13	1.16652
$933$	0	0
$934$	5.17514e13	2.22516
$935$	7.63164e12	0.326562
$936$	0	0
$937$	−2.80091e13	−1.18706	−0.593528	−	0.804813i	$-0.702265\pi$
$937$	−2.80091e13	−1.18706	−0.593528	+	0.804813i	$0.702265\pi$
$938$	1.00714e13	0.424791
$939$	0	0
$940$	−4.98751e12	−0.208357
$941$	−2.68353e13	−1.11571	−0.557857	−	0.829937i	$-0.688376\pi$
$941$	−2.68353e13	−1.11571	−0.557857	+	0.829937i	$0.688376\pi$
$942$	0	0
$943$	9.82866e11	0.0404755
$944$	5.70554e13	2.33842
$945$	0	0
$946$	−5.43528e12	−0.220654
$947$	1.27250e13	0.514140	0.257070	−	0.966393i	$-0.417243\pi$
$947$	1.27250e13	0.514140	0.257070	+	0.966393i	$0.417243\pi$
$948$	0	0
$949$	1.00203e12	0.0401037
$950$	1.16479e14	4.63972
$951$	0	0
$952$	−7.86846e12	−0.310473
$953$	2.88311e13	1.13225	0.566125	−	0.824319i	$-0.308442\pi$
$953$	2.88311e13	1.13225	0.566125	+	0.824319i	$0.308442\pi$
$954$	0	0
$955$	−5.05972e13	−1.96839
$956$	4.99303e13	1.93332
$957$	0	0
$958$	−5.20170e13	−1.99527
$959$	−1.09523e13	−0.418141
$960$	0	0
$961$	5.12133e12	0.193699
$962$	1.03089e13	0.388083
$963$	0	0
$964$	−1.76643e13	−0.658794
$965$	−6.87338e13	−2.55151
$966$	0	0
$967$	3.76299e13	1.38393	0.691964	−	0.721932i	$-0.256745\pi$
$967$	3.76299e13	1.38393	0.691964	+	0.721932i	$0.256745\pi$
$968$	−3.34628e13	−1.22496
$969$	0	0
$970$	6.88371e13	2.49660
$971$	5.14050e13	1.85575	0.927873	−	0.372895i	$-0.121635\pi$
$971$	5.14050e13	1.85575	0.927873	+	0.372895i	$0.121635\pi$
$972$	0	0
$973$	3.03495e12	0.108553
$974$	8.32801e13	2.96501
$975$	0	0
$976$	1.31264e13	0.463043
$977$	2.18727e13	0.768027	0.384013	−	0.923328i	$-0.374542\pi$
$977$	2.18727e13	0.768027	0.384013	+	0.923328i	$0.374542\pi$
$978$	0	0
$979$	−1.81195e12	−0.0630413
$980$	−1.03103e14	−3.57069
$981$	0	0
$982$	9.63577e13	3.30663
$983$	1.94063e13	0.662906	0.331453	−	0.943472i	$-0.392461\pi$
$983$	1.94063e13	0.662906	0.331453	+	0.943472i	$0.392461\pi$
$984$	0	0
$985$	−3.96722e13	−1.34284
$986$	1.76770e13	0.595611
$987$	0	0
$988$	5.75642e13	1.92197
$989$	−7.33593e12	−0.243822
$990$	0	0
$991$	3.18629e12	0.104943	0.0524716	−	0.998622i	$-0.483290\pi$
$991$	3.18629e12	0.104943	0.0524716	+	0.998622i	$0.483290\pi$
$992$	−8.00802e13	−2.62556
$993$	0	0
$994$	1.26079e13	0.409641
$995$	8.76394e13	2.83462
$996$	0	0
$997$	−2.11989e13	−0.679492	−0.339746	−	0.940517i	$-0.610341\pi$
$997$	−2.11989e13	−0.679492	−0.339746	+	0.940517i	$0.610341\pi$
$998$	9.80005e13	3.12709
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.10.a.f.1.7		7
3.2	odd	2		17.10.a.b.1.1	✓	7
12.11	even	2		272.10.a.g.1.3		7
51.50	odd	2		289.10.a.b.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.a.b.1.1	✓	7	3.2	odd	2
153.10.a.f.1.7		7	1.1	even	1	trivial
272.10.a.g.1.3		7	12.11	even	2
289.10.a.b.1.1		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)

\(f(q)\)	\(=\)	\(q+42.3973 q^{2} +1285.53 q^{4} +2498.37 q^{5} +2872.61 q^{7} +32795.8 q^{8} +O(q^{10})\)	\(q+42.3973 q^{2} +1285.53 q^{4} +2498.37 q^{5} +2872.61 q^{7} +32795.8 q^{8} +105924. q^{10} -36573.4 q^{11} +69902.2 q^{13} +121791. q^{14} +732260. q^{16} -83521.0 q^{17} +640587. q^{19} +3.21175e6 q^{20} -1.55061e6 q^{22} -2.09284e6 q^{23} +4.28875e6 q^{25} +2.96367e6 q^{26} +3.69283e6 q^{28} -4.99200e6 q^{29} -5.61791e6 q^{31} +1.42544e7 q^{32} -3.54107e6 q^{34} +7.17685e6 q^{35} +3.47843e6 q^{37} +2.71592e7 q^{38} +8.19361e7 q^{40} -469632. q^{41} +3.50525e6 q^{43} -4.70163e7 q^{44} -8.87310e7 q^{46} -1.55290e6 q^{47} -3.21017e7 q^{49} +1.81832e8 q^{50} +8.98617e7 q^{52} -1.03903e8 q^{53} -9.13740e7 q^{55} +9.42094e7 q^{56} -2.11648e8 q^{58} +7.79169e7 q^{59} +1.79259e7 q^{61} -2.38185e8 q^{62} +2.29433e8 q^{64} +1.74642e8 q^{65} +8.26939e7 q^{67} -1.07369e8 q^{68} +3.04279e8 q^{70} +1.03521e8 q^{71} +1.43348e7 q^{73} +1.47476e8 q^{74} +8.23496e8 q^{76} -1.05061e8 q^{77} +3.90455e8 q^{79} +1.82946e9 q^{80} -1.99111e7 q^{82} +3.47368e8 q^{83} -2.08667e8 q^{85} +1.48613e8 q^{86} -1.19945e9 q^{88} +4.95430e7 q^{89} +2.00802e8 q^{91} -2.69042e9 q^{92} -6.58387e7 q^{94} +1.60043e9 q^{95} +6.49870e8 q^{97} -1.36103e9 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + q^{2} + 2389 q^{4} - 1362 q^{5} + 9388 q^{7} - 16821 q^{8}+O(q^{10}) \) 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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