LMFDB - Embedded newform 378.10.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,10,Mod(1,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, 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("378.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	378.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:	$194.683546070$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 4538x^{2} - 16x + 4333377 $ x^4 - 4538x^2 - 16x + 4333377
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{6}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-36.9671$ of defining polynomial
Character	$\chi$	$=$	378.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-16.0000 q^{2} +256.000 q^{4} -199.866 q^{5} +2401.00 q^{7} -4096.00 q^{8} +O(q^{10})$	\(q-16.0000 q^{2} +256.000 q^{4} -199.866 q^{5} +2401.00 q^{7} -4096.00 q^{8} +3197.85 q^{10} -50613.1 q^{11} +122939. q^{13} -38416.0 q^{14} +65536.0 q^{16} +589003. q^{17} -642178. q^{19} -51165.7 q^{20} +809810. q^{22} +1.63211e6 q^{23} -1.91318e6 q^{25} -1.96703e6 q^{26} +614656. q^{28} +3.67579e6 q^{29} -6.80335e6 q^{31} -1.04858e6 q^{32} -9.42405e6 q^{34} -479878. q^{35} -3.03208e6 q^{37} +1.02748e7 q^{38} +818650. q^{40} +1.01880e7 q^{41} +4.00519e7 q^{43} -1.29570e7 q^{44} -2.61137e7 q^{46} -3.58706e7 q^{47} +5.76480e6 q^{49} +3.06109e7 q^{50} +3.14725e7 q^{52} -6.11668e7 q^{53} +1.01158e7 q^{55} -9.83450e6 q^{56} -5.88126e7 q^{58} +1.52338e8 q^{59} +1.21633e8 q^{61} +1.08854e8 q^{62} +1.67772e7 q^{64} -2.45714e7 q^{65} -1.84459e8 q^{67} +1.50785e8 q^{68} +7.67805e6 q^{70} +8.11102e6 q^{71} -6.98449e7 q^{73} +4.85133e7 q^{74} -1.64397e8 q^{76} -1.21522e8 q^{77} -1.70782e8 q^{79} -1.30984e7 q^{80} -1.63007e8 q^{82} +3.01006e8 q^{83} -1.17722e8 q^{85} -6.40830e8 q^{86} +2.07311e8 q^{88} +2.40684e7 q^{89} +2.95177e8 q^{91} +4.17820e8 q^{92} +5.73930e8 q^{94} +1.28349e8 q^{95} -1.49659e9 q^{97} -9.22368e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 64 q^{2} + 1024 q^{4} + 2208 q^{5} + 9604 q^{7} - 16384 q^{8}+O(q^{10}) $ 4 * q - 64 * q^2 + 1024 * q^4 + 2208 * q^5 + 9604 * q^7 - 16384 * q^8	\( 4 q - 64 q^{2} + 1024 q^{4} + 2208 q^{5} + 9604 q^{7} - 16384 q^{8} - 35328 q^{10} + 14784 q^{11} + 21464 q^{13} - 153664 q^{14} + 262144 q^{16} + 485568 q^{17} - 46828 q^{19} + 565248 q^{20} - 236544 q^{22} - 430944 q^{23} - 2143688 q^{25} - 343424 q^{26} + 2458624 q^{28} + 2580000 q^{29} - 6228604 q^{31} - 4194304 q^{32} - 7769088 q^{34} + 5301408 q^{35} + 8995220 q^{37} + 749248 q^{38} - 9043968 q^{40} + 22028736 q^{41} + 21954176 q^{43} + 3784704 q^{44} + 6895104 q^{46} + 33437472 q^{47} + 23059204 q^{49} + 34299008 q^{50} + 5494784 q^{52} + 111929472 q^{53} + 77520996 q^{55} - 39337984 q^{56} - 41280000 q^{58} + 285328416 q^{59} + 36406592 q^{61} + 99657664 q^{62} + 67108864 q^{64} - 30754848 q^{65} + 40399496 q^{67} + 124305408 q^{68} - 84822528 q^{70} + 99955872 q^{71} + 10196576 q^{73} - 143923520 q^{74} - 11987968 q^{76} + 35496384 q^{77} + 54438704 q^{79} + 144703488 q^{80} - 352459776 q^{82} - 54880032 q^{83} + 736315344 q^{85} - 351266816 q^{86} - 60555264 q^{88} + 100706112 q^{89} + 51535064 q^{91} - 110321664 q^{92} - 534999552 q^{94} + 1873022496 q^{95} - 1861020208 q^{97} - 368947264 q^{98}+O(q^{100}) \) 4 * q - 64 * q^2 + 1024 * q^4 + 2208 * q^5 + 9604 * q^7 - 16384 * q^8 - 35328 * q^10 + 14784 * q^11 + 21464 * q^13 - 153664 * q^14 + 262144 * q^16 + 485568 * q^17 - 46828 * q^19 + 565248 * q^20 - 236544 * q^22 - 430944 * q^23 - 2143688 * q^25 - 343424 * q^26 + 2458624 * q^28 + 2580000 * q^29 - 6228604 * q^31 - 4194304 * q^32 - 7769088 * q^34 + 5301408 * q^35 + 8995220 * q^37 + 749248 * q^38 - 9043968 * q^40 + 22028736 * q^41 + 21954176 * q^43 + 3784704 * q^44 + 6895104 * q^46 + 33437472 * q^47 + 23059204 * q^49 + 34299008 * q^50 + 5494784 * q^52 + 111929472 * q^53 + 77520996 * q^55 - 39337984 * q^56 - 41280000 * q^58 + 285328416 * q^59 + 36406592 * q^61 + 99657664 * q^62 + 67108864 * q^64 - 30754848 * q^65 + 40399496 * q^67 + 124305408 * q^68 - 84822528 * q^70 + 99955872 * q^71 + 10196576 * q^73 - 143923520 * q^74 - 11987968 * q^76 + 35496384 * q^77 + 54438704 * q^79 + 144703488 * q^80 - 352459776 * q^82 - 54880032 * q^83 + 736315344 * q^85 - 351266816 * q^86 - 60555264 * q^88 + 100706112 * q^89 + 51535064 * q^91 - 110321664 * q^92 - 534999552 * q^94 + 1873022496 * q^95 - 1861020208 * q^97 - 368947264 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−16.0000	−0.707107
$2$	−16.0000	−0.707107
$3$	0	0
$3$	0	0
$4$	256.000	0.500000
$5$	−199.866	−0.143012	−0.0715062	−	0.997440i	$-0.522781\pi$
$5$	−199.866	−0.143012	−0.0715062	+	0.997440i	$0.522781\pi$
$6$	0	0
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	−4096.00	−0.353553
$9$	0	0
$10$	3197.85	0.101125
$11$	−50613.1	−1.04231	−0.521154	−	0.853463i	$-0.674498\pi$
$11$	−50613.1	−1.04231	−0.521154	+	0.853463i	$0.674498\pi$
$12$	0	0
$13$	122939.	1.19384	0.596920	−	0.802301i	$-0.296391\pi$
$13$	122939.	1.19384	0.596920	+	0.802301i	$0.296391\pi$
$14$	−38416.0	−0.267261
$15$	0	0
$16$	65536.0	0.250000
$17$	589003.	1.71040	0.855200	−	0.518299i	$-0.173434\pi$
$17$	589003.	1.71040	0.855200	+	0.518299i	$0.173434\pi$
$18$	0	0
$19$	−642178.	−1.13048	−0.565241	−	0.824926i	$-0.691217\pi$
$19$	−642178.	−1.13048	−0.565241	+	0.824926i	$0.691217\pi$
$20$	−51165.7	−0.0715062
$21$	0	0
$22$	809810.	0.737023
$23$	1.63211e6	1.21611	0.608056	−	0.793894i	$-0.291949\pi$
$23$	1.63211e6	1.21611	0.608056	+	0.793894i	$0.291949\pi$
$24$	0	0
$25$	−1.91318e6	−0.979547
$26$	−1.96703e6	−0.844172
$27$	0	0
$28$	614656.	0.188982
$29$	3.67579e6	0.965071	0.482536	−	0.875876i	$-0.339716\pi$
$29$	3.67579e6	0.965071	0.482536	+	0.875876i	$0.339716\pi$
$30$	0	0
$31$	−6.80335e6	−1.32311	−0.661554	−	0.749897i	$-0.730103\pi$
$31$	−6.80335e6	−1.32311	−0.661554	+	0.749897i	$0.730103\pi$
$32$	−1.04858e6	−0.176777
$33$	0	0
$34$	−9.42405e6	−1.20944
$35$	−479878.	−0.0540536
$36$	0	0
$37$	−3.03208e6	−0.265970	−0.132985	−	0.991118i	$-0.542456\pi$
$37$	−3.03208e6	−0.265970	−0.132985	+	0.991118i	$0.542456\pi$
$38$	1.02748e7	0.799372
$39$	0	0
$40$	818650.	0.0505625
$41$	1.01880e7	0.563067	0.281533	−	0.959551i	$-0.409157\pi$
$41$	1.01880e7	0.563067	0.281533	+	0.959551i	$0.409157\pi$
$42$	0	0
$43$	4.00519e7	1.78655	0.893274	−	0.449512i	$-0.148402\pi$
$43$	4.00519e7	1.78655	0.893274	+	0.449512i	$0.148402\pi$
$44$	−1.29570e7	−0.521154
$45$	0	0
$46$	−2.61137e7	−0.859922
$47$	−3.58706e7	−1.07226	−0.536128	−	0.844136i	$-0.680114\pi$
$47$	−3.58706e7	−1.07226	−0.536128	+	0.844136i	$0.680114\pi$
$48$	0	0
$49$	5.76480e6	0.142857
$50$	3.06109e7	0.692645
$51$	0	0
$52$	3.14725e7	0.596920
$53$	−6.11668e7	−1.06482	−0.532408	−	0.846488i	$-0.678713\pi$
$53$	−6.11668e7	−1.06482	−0.532408	+	0.846488i	$0.678713\pi$
$54$	0	0
$55$	1.01158e7	0.149063
$56$	−9.83450e6	−0.133631
$57$	0	0
$58$	−5.88126e7	−0.682408
$59$	1.52338e8	1.63672	0.818358	−	0.574708i	$-0.194885\pi$
$59$	1.52338e8	1.63672	0.818358	+	0.574708i	$0.194885\pi$
$60$	0	0
$61$	1.21633e8	1.12478	0.562391	−	0.826871i	$-0.309881\pi$
$61$	1.21633e8	1.12478	0.562391	+	0.826871i	$0.309881\pi$
$62$	1.08854e8	0.935579
$63$	0	0
$64$	1.67772e7	0.125000
$65$	−2.45714e7	−0.170734
$66$	0	0
$67$	−1.84459e8	−1.11831	−0.559156	−	0.829062i	$-0.688875\pi$
$67$	−1.84459e8	−1.11831	−0.559156	+	0.829062i	$0.688875\pi$
$68$	1.50785e8	0.855200
$69$	0	0
$70$	7.67805e6	0.0382217
$71$	8.11102e6	0.0378803	0.0189401	−	0.999821i	$-0.493971\pi$
$71$	8.11102e6	0.0378803	0.0189401	+	0.999821i	$0.493971\pi$
$72$	0	0
$73$	−6.98449e7	−0.287860	−0.143930	−	0.989588i	$-0.545974\pi$
$73$	−6.98449e7	−0.287860	−0.143930	+	0.989588i	$0.545974\pi$
$74$	4.85133e7	0.188069
$75$	0	0
$76$	−1.64397e8	−0.565241
$77$	−1.21522e8	−0.393955
$78$	0	0
$79$	−1.70782e8	−0.493311	−0.246655	−	0.969103i	$-0.579332\pi$
$79$	−1.70782e8	−0.493311	−0.246655	+	0.969103i	$0.579332\pi$
$80$	−1.30984e7	−0.0357531
$81$	0	0
$82$	−1.63007e8	−0.398148
$83$	3.01006e8	0.696183	0.348092	−	0.937461i	$-0.386830\pi$
$83$	3.01006e8	0.696183	0.348092	+	0.937461i	$0.386830\pi$
$84$	0	0
$85$	−1.17722e8	−0.244608
$86$	−6.40830e8	−1.26328
$87$	0	0
$88$	2.07311e8	0.368512
$89$	2.40684e7	0.0406623	0.0203312	−	0.999793i	$-0.493528\pi$
$89$	2.40684e7	0.0406623	0.0203312	+	0.999793i	$0.493528\pi$
$90$	0	0
$91$	2.95177e8	0.451229
$92$	4.17820e8	0.608056
$93$	0	0
$94$	5.73930e8	0.758200
$95$	1.28349e8	0.161673
$96$	0	0
$97$	−1.49659e9	−1.71645	−0.858224	−	0.513275i	$-0.828432\pi$
$97$	−1.49659e9	−1.71645	−0.858224	+	0.513275i	$0.828432\pi$
$98$	−9.22368e7	−0.101015
$99$	0	0
$100$	−4.89774e8	−0.489774
$101$	−6.20121e8	−0.592967	−0.296483	−	0.955038i	$-0.595814\pi$
$101$	−6.20121e8	−0.592967	−0.296483	+	0.955038i	$0.595814\pi$
$102$	0	0
$103$	1.44717e9	1.26693	0.633466	−	0.773770i	$-0.281632\pi$
$103$	1.44717e9	1.26693	0.633466	+	0.773770i	$0.281632\pi$
$104$	−5.03560e8	−0.422086
$105$	0	0
$106$	9.78669e8	0.752938
$107$	−3.15250e8	−0.232503	−0.116251	−	0.993220i	$-0.537088\pi$
$107$	−3.15250e8	−0.232503	−0.116251	+	0.993220i	$0.537088\pi$
$108$	0	0
$109$	−1.53540e9	−1.04185	−0.520923	−	0.853604i	$-0.674412\pi$
$109$	−1.53540e9	−1.04185	−0.520923	+	0.853604i	$0.674412\pi$
$110$	−1.61853e8	−0.105403
$111$	0	0
$112$	1.57352e8	0.0944911
$113$	2.66257e9	1.53620	0.768100	−	0.640330i	$-0.221202\pi$
$113$	2.66257e9	1.53620	0.768100	+	0.640330i	$0.221202\pi$
$114$	0	0
$115$	−3.26203e8	−0.173919
$116$	9.41001e8	0.482536
$117$	0	0
$118$	−2.43740e9	−1.15733
$119$	1.41420e9	0.646470
$120$	0	0
$121$	2.03741e8	0.0864061
$122$	−1.94613e9	−0.795342
$123$	0	0
$124$	−1.74166e9	−0.661554
$125$	7.72742e8	0.283100
$126$	0	0
$127$	2.47154e9	0.843046	0.421523	−	0.906818i	$-0.361496\pi$
$127$	2.47154e9	0.843046	0.421523	+	0.906818i	$0.361496\pi$
$128$	−2.68435e8	−0.0883883
$129$	0	0
$130$	3.93142e8	0.120727
$131$	4.08578e9	1.21214	0.606072	−	0.795410i	$-0.292744\pi$
$131$	4.08578e9	1.21214	0.606072	+	0.795410i	$0.292744\pi$
$132$	0	0
$133$	−1.54187e9	−0.427282
$134$	2.95134e9	0.790766
$135$	0	0
$136$	−2.41256e9	−0.604718
$137$	−5.30813e9	−1.28736	−0.643679	−	0.765296i	$-0.722593\pi$
$137$	−5.30813e9	−1.28736	−0.643679	+	0.765296i	$0.722593\pi$
$138$	0	0
$139$	−6.28807e9	−1.42873	−0.714365	−	0.699773i	$-0.753285\pi$
$139$	−6.28807e9	−1.42873	−0.714365	+	0.699773i	$0.753285\pi$
$140$	−1.22849e8	−0.0270268
$141$	0	0
$142$	−1.29776e8	−0.0267854
$143$	−6.22235e9	−1.24435
$144$	0	0
$145$	−7.34664e8	−0.138017
$146$	1.11752e9	0.203548
$147$	0	0
$148$	−7.76212e8	−0.132985
$149$	−6.92791e9	−1.15150	−0.575750	−	0.817626i	$-0.695290\pi$
$149$	−6.92791e9	−1.15150	−0.575750	+	0.817626i	$0.695290\pi$
$150$	0	0
$151$	−2.36750e9	−0.370591	−0.185295	−	0.982683i	$-0.559324\pi$
$151$	−2.36750e9	−0.370591	−0.185295	+	0.982683i	$0.559324\pi$
$152$	2.63036e9	0.399686
$153$	0	0
$154$	1.94435e9	0.278569
$155$	1.35976e9	0.189221
$156$	0	0
$157$	−5.66572e9	−0.744229	−0.372114	−	0.928187i	$-0.621367\pi$
$157$	−5.66572e9	−0.744229	−0.372114	+	0.928187i	$0.621367\pi$
$158$	2.73252e9	0.348823
$159$	0	0
$160$	2.09575e8	0.0252812
$161$	3.91869e9	0.459648
$162$	0	0
$163$	1.14184e10	1.26696	0.633479	−	0.773760i	$-0.281626\pi$
$163$	1.14184e10	1.26696	0.633479	+	0.773760i	$0.281626\pi$
$164$	2.60812e9	0.281533
$165$	0	0
$166$	−4.81609e9	−0.492276
$167$	7.48161e9	0.744340	0.372170	−	0.928165i	$-0.378614\pi$
$167$	7.48161e9	0.744340	0.372170	+	0.928165i	$0.378614\pi$
$168$	0	0
$169$	4.50959e9	0.425253
$170$	1.88355e9	0.172964
$171$	0	0
$172$	1.02533e10	0.893274
$173$	−1.55522e10	−1.32003	−0.660014	−	0.751254i	$-0.729450\pi$
$173$	−1.55522e10	−1.32003	−0.660014	+	0.751254i	$0.729450\pi$
$174$	0	0
$175$	−4.59354e9	−0.370234
$176$	−3.31698e9	−0.260577
$177$	0	0
$178$	−3.85095e8	−0.0287526
$179$	2.15624e10	1.56985	0.784927	−	0.619588i	$-0.212701\pi$
$179$	2.15624e10	1.56985	0.784927	+	0.619588i	$0.212701\pi$
$180$	0	0
$181$	−2.56055e10	−1.77329	−0.886644	−	0.462452i	$-0.846970\pi$
$181$	−2.56055e10	−1.77329	−0.886644	+	0.462452i	$0.846970\pi$
$182$	−4.72284e9	−0.319067
$183$	0	0
$184$	−6.68512e9	−0.429961
$185$	6.06009e8	0.0380370
$186$	0	0
$187$	−2.98113e10	−1.78276
$188$	−9.18288e9	−0.536128
$189$	0	0
$190$	−2.05359e9	−0.114320
$191$	3.23740e10	1.76013	0.880067	−	0.474849i	$-0.157497\pi$
$191$	3.23740e10	1.76013	0.880067	+	0.474849i	$0.157497\pi$
$192$	0	0
$193$	−8.10073e9	−0.420258	−0.210129	−	0.977674i	$-0.567388\pi$
$193$	−8.10073e9	−0.420258	−0.210129	+	0.977674i	$0.567388\pi$
$194$	2.39455e10	1.21371
$195$	0	0
$196$	1.47579e9	0.0714286
$197$	−2.76627e10	−1.30857	−0.654285	−	0.756248i	$-0.727030\pi$
$197$	−2.76627e10	−1.30857	−0.654285	+	0.756248i	$0.727030\pi$
$198$	0	0
$199$	4.90059e9	0.221518	0.110759	−	0.993847i	$-0.464672\pi$
$199$	4.90059e9	0.221518	0.110759	+	0.993847i	$0.464672\pi$
$200$	7.83638e9	0.346322
$201$	0	0
$202$	9.92194e9	0.419291
$203$	8.82556e9	0.364763
$204$	0	0
$205$	−2.03623e9	−0.0805255
$206$	−2.31548e10	−0.895857
$207$	0	0
$208$	8.05696e9	0.298460
$209$	3.25026e10	1.17831
$210$	0	0
$211$	4.77457e10	1.65830	0.829150	−	0.559026i	$-0.188825\pi$
$211$	4.77457e10	1.65830	0.829150	+	0.559026i	$0.188825\pi$
$212$	−1.56587e10	−0.532408
$213$	0	0
$214$	5.04400e9	0.164404
$215$	−8.00500e9	−0.255498
$216$	0	0
$217$	−1.63349e10	−0.500088
$218$	2.45665e10	0.736696
$219$	0	0
$220$	2.58965e9	0.0745315
$221$	7.24117e10	2.04194
$222$	0	0
$223$	4.81785e10	1.30461	0.652306	−	0.757955i	$-0.273802\pi$
$223$	4.81785e10	1.30461	0.652306	+	0.757955i	$0.273802\pi$
$224$	−2.51763e9	−0.0668153
$225$	0	0
$226$	−4.26011e10	−1.08626
$227$	3.49542e10	0.873743	0.436871	−	0.899524i	$-0.356087\pi$
$227$	3.49542e10	0.873743	0.436871	+	0.899524i	$0.356087\pi$
$228$	0	0
$229$	−4.55630e9	−0.109484	−0.0547422	−	0.998501i	$-0.517434\pi$
$229$	−4.55630e9	−0.109484	−0.0547422	+	0.998501i	$0.517434\pi$
$230$	5.21925e9	0.122979
$231$	0	0
$232$	−1.50560e10	−0.341204
$233$	4.97031e10	1.10480	0.552398	−	0.833580i	$-0.313713\pi$
$233$	4.97031e10	1.10480	0.552398	+	0.833580i	$0.313713\pi$
$234$	0	0
$235$	7.16932e9	0.153346
$236$	3.89985e10	0.818358
$237$	0	0
$238$	−2.26272e10	−0.457124
$239$	8.80428e10	1.74543	0.872717	−	0.488227i	$-0.162356\pi$
$239$	8.80428e10	1.74543	0.872717	+	0.488227i	$0.162356\pi$
$240$	0	0
$241$	8.74081e10	1.66907	0.834536	−	0.550954i	$-0.185736\pi$
$241$	8.74081e10	1.66907	0.834536	+	0.550954i	$0.185736\pi$
$242$	−3.25986e9	−0.0610984
$243$	0	0
$244$	3.11382e10	0.562391
$245$	−1.15219e9	−0.0204303
$246$	0	0
$247$	−7.89489e10	−1.34961
$248$	2.78665e10	0.467790
$249$	0	0
$250$	−1.23639e10	−0.200182
$251$	−6.98903e9	−0.111144	−0.0555719	−	0.998455i	$-0.517698\pi$
$251$	−6.98903e9	−0.111144	−0.0555719	+	0.998455i	$0.517698\pi$
$252$	0	0
$253$	−8.26062e10	−1.26756
$254$	−3.95447e10	−0.596124
$255$	0	0
$256$	4.29497e9	0.0625000
$257$	−1.21302e11	−1.73448	−0.867240	−	0.497890i	$-0.834108\pi$
$257$	−1.21302e11	−1.73448	−0.867240	+	0.497890i	$0.834108\pi$
$258$	0	0
$259$	−7.28002e9	−0.100527
$260$	−6.29027e9	−0.0853669
$261$	0	0
$262$	−6.53725e10	−0.857116
$263$	−8.38237e10	−1.08035	−0.540177	−	0.841552i	$-0.681643\pi$
$263$	−8.38237e10	−1.08035	−0.540177	+	0.841552i	$0.681643\pi$
$264$	0	0
$265$	1.22252e10	0.152282
$266$	2.46699e10	0.302134
$267$	0	0
$268$	−4.72215e10	−0.559156
$269$	1.30983e11	1.52521	0.762603	−	0.646867i	$-0.223921\pi$
$269$	1.30983e11	1.52521	0.762603	+	0.646867i	$0.223921\pi$
$270$	0	0
$271$	1.37963e11	1.55382	0.776912	−	0.629610i	$-0.216785\pi$
$271$	1.37963e11	1.55382	0.776912	+	0.629610i	$0.216785\pi$
$272$	3.86009e10	0.427600
$273$	0	0
$274$	8.49302e10	0.910300
$275$	9.68320e10	1.02099
$276$	0	0
$277$	1.88523e11	1.92400	0.962000	−	0.273050i	$-0.0880324\pi$
$277$	1.88523e11	1.92400	0.962000	+	0.273050i	$0.0880324\pi$
$278$	1.00609e11	1.01027
$279$	0	0
$280$	1.96558e9	0.0191108
$281$	1.20149e11	1.14958	0.574791	−	0.818300i	$-0.305083\pi$
$281$	1.20149e11	1.14958	0.574791	+	0.818300i	$0.305083\pi$
$282$	0	0
$283$	2.95054e10	0.273440	0.136720	−	0.990610i	$-0.456344\pi$
$283$	2.95054e10	0.273440	0.136720	+	0.990610i	$0.456344\pi$
$284$	2.07642e9	0.0189401
$285$	0	0
$286$	9.95576e10	0.879887
$287$	2.44613e10	0.212819
$288$	0	0
$289$	2.28337e11	1.92547
$290$	1.17546e10	0.0975928
$291$	0	0
$292$	−1.78803e10	−0.143930
$293$	2.32454e10	0.184261	0.0921303	−	0.995747i	$-0.470632\pi$
$293$	2.32454e10	0.184261	0.0921303	+	0.995747i	$0.470632\pi$
$294$	0	0
$295$	−3.04471e10	−0.234071
$296$	1.24194e10	0.0940346
$297$	0	0
$298$	1.10847e11	0.814234
$299$	2.00650e11	1.45184
$300$	0	0
$301$	9.61646e10	0.675252
$302$	3.78801e10	0.262047
$303$	0	0
$304$	−4.20857e10	−0.282621
$305$	−2.43104e10	−0.160858
$306$	0	0
$307$	−2.77209e11	−1.78108	−0.890542	−	0.454902i	$-0.849674\pi$
$307$	−2.77209e11	−1.78108	−0.890542	+	0.454902i	$0.849674\pi$
$308$	−3.11097e10	−0.196978
$309$	0	0
$310$	−2.17561e10	−0.133799
$311$	4.91875e9	0.0298149	0.0149074	−	0.999889i	$-0.495255\pi$
$311$	4.91875e9	0.0298149	0.0149074	+	0.999889i	$0.495255\pi$
$312$	0	0
$313$	1.74244e11	1.02615	0.513073	−	0.858345i	$-0.328507\pi$
$313$	1.74244e11	1.02615	0.513073	+	0.858345i	$0.328507\pi$
$314$	9.06515e10	0.526249
$315$	0	0
$316$	−4.37202e10	−0.246655
$317$	3.04789e11	1.69524	0.847622	−	0.530601i	$-0.178034\pi$
$317$	3.04789e11	1.69524	0.847622	+	0.530601i	$0.178034\pi$
$318$	0	0
$319$	−1.86043e11	−1.00590
$320$	−3.35319e9	−0.0178765
$321$	0	0
$322$	−6.26991e10	−0.325020
$323$	−3.78245e11	−1.93358
$324$	0	0
$325$	−2.35205e11	−1.16942
$326$	−1.82695e11	−0.895875
$327$	0	0
$328$	−4.17299e10	−0.199074
$329$	−8.61254e10	−0.405275
$330$	0	0
$331$	1.03012e11	0.471694	0.235847	−	0.971790i	$-0.424214\pi$
$331$	1.03012e11	0.471694	0.235847	+	0.971790i	$0.424214\pi$
$332$	7.70575e10	0.348092
$333$	0	0
$334$	−1.19706e11	−0.526328
$335$	3.68670e10	0.159932
$336$	0	0
$337$	1.01745e11	0.429713	0.214857	−	0.976646i	$-0.431072\pi$
$337$	1.01745e11	0.429713	0.214857	+	0.976646i	$0.431072\pi$
$338$	−7.21535e10	−0.300699
$339$	0	0
$340$	−3.01367e10	−0.122304
$341$	3.44339e11	1.37909
$342$	0	0
$343$	1.38413e10	0.0539949
$344$	−1.64052e11	−0.631640
$345$	0	0
$346$	2.48834e11	0.933400
$347$	9.32686e10	0.345345	0.172672	−	0.984979i	$-0.444760\pi$
$347$	9.32686e10	0.345345	0.172672	+	0.984979i	$0.444760\pi$
$348$	0	0
$349$	−1.61420e11	−0.582427	−0.291214	−	0.956658i	$-0.594059\pi$
$349$	−1.61420e11	−0.582427	−0.291214	+	0.956658i	$0.594059\pi$
$350$	7.34967e10	0.261795
$351$	0	0
$352$	5.30717e10	0.184256
$353$	8.25018e9	0.0282799	0.0141399	−	0.999900i	$-0.495499\pi$
$353$	8.25018e9	0.0282799	0.0141399	+	0.999900i	$0.495499\pi$
$354$	0	0
$355$	−1.62112e9	−0.00541735
$356$	6.16151e9	0.0203312
$357$	0	0
$358$	−3.44999e11	−1.11005
$359$	1.07865e11	0.342732	0.171366	−	0.985207i	$-0.445182\pi$
$359$	1.07865e11	0.342732	0.171366	+	0.985207i	$0.445182\pi$
$360$	0	0
$361$	8.97043e10	0.277991
$362$	4.09688e11	1.25390
$363$	0	0
$364$	7.55654e10	0.225614
$365$	1.39596e10	0.0411676
$366$	0	0
$367$	1.70471e11	0.490517	0.245259	−	0.969458i	$-0.421127\pi$
$367$	1.70471e11	0.490517	0.245259	+	0.969458i	$0.421127\pi$
$368$	1.06962e11	0.304028
$369$	0	0
$370$	−9.69614e9	−0.0268962
$371$	−1.46861e11	−0.402462
$372$	0	0
$373$	3.25371e11	0.870341	0.435170	−	0.900348i	$-0.356688\pi$
$373$	3.25371e11	0.870341	0.435170	+	0.900348i	$0.356688\pi$
$374$	4.76981e11	1.26060
$375$	0	0
$376$	1.46926e11	0.379100
$377$	4.51899e11	1.15214
$378$	0	0
$379$	9.92389e10	0.247062	0.123531	−	0.992341i	$-0.460578\pi$
$379$	9.92389e10	0.247062	0.123531	+	0.992341i	$0.460578\pi$
$380$	3.28574e10	0.0808365
$381$	0	0
$382$	−5.17984e11	−1.24460
$383$	3.93114e11	0.933521	0.466761	−	0.884384i	$-0.345421\pi$
$383$	3.93114e11	0.933521	0.466761	+	0.884384i	$0.345421\pi$
$384$	0	0
$385$	2.42881e10	0.0563405
$386$	1.29612e11	0.297168
$387$	0	0
$388$	−3.83128e11	−0.858224
$389$	5.44740e11	1.20619	0.603096	−	0.797669i	$-0.293934\pi$
$389$	5.44740e11	1.20619	0.603096	+	0.797669i	$0.293934\pi$
$390$	0	0
$391$	9.61318e11	2.08004
$392$	−2.36126e10	−0.0505076
$393$	0	0
$394$	4.42604e11	0.925299
$395$	3.41335e10	0.0705495
$396$	0	0
$397$	3.31643e11	0.670059	0.335030	−	0.942208i	$-0.391254\pi$
$397$	3.31643e11	0.670059	0.335030	+	0.942208i	$0.391254\pi$
$398$	−7.84094e10	−0.156637
$399$	0	0
$400$	−1.25382e11	−0.244887
$401$	−1.94667e10	−0.0375962	−0.0187981	−	0.999823i	$-0.505984\pi$
$401$	−1.94667e10	−0.0375962	−0.0187981	+	0.999823i	$0.505984\pi$
$402$	0	0
$403$	−8.36400e11	−1.57958
$404$	−1.58751e11	−0.296483
$405$	0	0
$406$	−1.41209e11	−0.257926
$407$	1.53463e11	0.277223
$408$	0	0
$409$	−9.73906e11	−1.72093	−0.860463	−	0.509513i	$-0.829826\pi$
$409$	−9.73906e11	−1.72093	−0.860463	+	0.509513i	$0.829826\pi$
$410$	3.25796e10	0.0569401
$411$	0	0
$412$	3.70477e11	0.633466
$413$	3.65763e11	0.618621
$414$	0	0
$415$	−6.01608e10	−0.0995628
$416$	−1.28911e11	−0.211043
$417$	0	0
$418$	−5.20042e11	−0.833192
$419$	4.71751e11	0.747739	0.373870	−	0.927481i	$-0.378031\pi$
$419$	4.71751e11	0.747739	0.373870	+	0.927481i	$0.378031\pi$
$420$	0	0
$421$	1.13941e12	1.76771	0.883857	−	0.467757i	$-0.154938\pi$
$421$	1.13941e12	1.76771	0.883857	+	0.467757i	$0.154938\pi$
$422$	−7.63931e11	−1.17260
$423$	0	0
$424$	2.50539e11	0.376469
$425$	−1.12687e12	−1.67542
$426$	0	0
$427$	2.92042e11	0.425128
$428$	−8.07040e10	−0.116251
$429$	0	0
$430$	1.28080e11	0.180665
$431$	1.67223e11	0.233425	0.116713	−	0.993166i	$-0.462764\pi$
$431$	1.67223e11	0.233425	0.116713	+	0.993166i	$0.462764\pi$
$432$	0	0
$433$	−1.29409e12	−1.76917	−0.884585	−	0.466379i	$-0.845558\pi$
$433$	−1.29409e12	−1.76917	−0.884585	+	0.466379i	$0.845558\pi$
$434$	2.61358e11	0.353616
$435$	0	0
$436$	−3.93063e11	−0.520923
$437$	−1.04810e12	−1.37479
$438$	0	0
$439$	6.00173e11	0.771233	0.385617	−	0.922659i	$-0.373989\pi$
$439$	6.00173e11	0.771233	0.385617	+	0.922659i	$0.373989\pi$
$440$	−4.14345e10	−0.0527017
$441$	0	0
$442$	−1.15859e12	−1.44387
$443$	7.52406e11	0.928187	0.464093	−	0.885786i	$-0.346380\pi$
$443$	7.52406e11	0.928187	0.464093	+	0.885786i	$0.346380\pi$
$444$	0	0
$445$	−4.81045e9	−0.00581522
$446$	−7.70856e11	−0.922501
$447$	0	0
$448$	4.02821e10	0.0472456
$449$	6.87305e10	0.0798070	0.0399035	−	0.999204i	$-0.487295\pi$
$449$	6.87305e10	0.0798070	0.0399035	+	0.999204i	$0.487295\pi$
$450$	0	0
$451$	−5.15645e11	−0.586889
$452$	6.81617e11	0.768100
$453$	0	0
$454$	−5.59268e11	−0.617829
$455$	−5.89959e10	−0.0645313
$456$	0	0
$457$	1.02161e11	0.109562	0.0547810	−	0.998498i	$-0.482554\pi$
$457$	1.02161e11	0.109562	0.0547810	+	0.998498i	$0.482554\pi$
$458$	7.29007e10	0.0774171
$459$	0	0
$460$	−8.35079e10	−0.0869596
$461$	4.43821e11	0.457672	0.228836	−	0.973465i	$-0.426508\pi$
$461$	4.43821e11	0.457672	0.228836	+	0.973465i	$0.426508\pi$
$462$	0	0
$463$	−6.15085e11	−0.622044	−0.311022	−	0.950403i	$-0.600671\pi$
$463$	−6.15085e11	−0.622044	−0.311022	+	0.950403i	$0.600671\pi$
$464$	2.40896e11	0.241268
$465$	0	0
$466$	−7.95250e11	−0.781209
$467$	9.74928e11	0.948520	0.474260	−	0.880385i	$-0.342716\pi$
$467$	9.74928e11	0.948520	0.474260	+	0.880385i	$0.342716\pi$
$468$	0	0
$469$	−4.42886e11	−0.422682
$470$	−1.14709e11	−0.108432
$471$	0	0
$472$	−6.23975e11	−0.578667
$473$	−2.02715e12	−1.86213
$474$	0	0
$475$	1.22860e12	1.10736
$476$	3.62034e11	0.323235
$477$	0	0
$478$	−1.40869e12	−1.23421
$479$	−1.44114e12	−1.25083	−0.625414	−	0.780293i	$-0.715070\pi$
$479$	−1.44114e12	−1.25083	−0.625414	+	0.780293i	$0.715070\pi$
$480$	0	0
$481$	−3.72762e11	−0.317526
$482$	−1.39853e12	−1.18021
$483$	0	0
$484$	5.21577e10	0.0432031
$485$	2.99118e11	0.245473
$486$	0	0
$487$	8.59942e11	0.692770	0.346385	−	0.938092i	$-0.387409\pi$
$487$	8.59942e11	0.692770	0.346385	+	0.938092i	$0.387409\pi$
$488$	−4.98211e11	−0.397671
$489$	0	0
$490$	1.84350e10	0.0144464
$491$	−1.02636e12	−0.796952	−0.398476	−	0.917179i	$-0.630461\pi$
$491$	−1.02636e12	−0.796952	−0.398476	+	0.917179i	$0.630461\pi$
$492$	0	0
$493$	2.16505e12	1.65066
$494$	1.26318e12	0.954322
$495$	0	0
$496$	−4.45865e11	−0.330777
$497$	1.94746e10	0.0143174
$498$	0	0
$499$	−1.47345e12	−1.06386	−0.531929	−	0.846789i	$-0.678533\pi$
$499$	−1.47345e12	−1.06386	−0.531929	+	0.846789i	$0.678533\pi$
$500$	1.97822e11	0.141550
$501$	0	0
$502$	1.11825e11	0.0785906
$503$	−9.96005e11	−0.693754	−0.346877	−	0.937911i	$-0.612758\pi$
$503$	−9.96005e11	−0.693754	−0.346877	+	0.937911i	$0.612758\pi$
$504$	0	0
$505$	1.23941e11	0.0848016
$506$	1.32170e12	0.896303
$507$	0	0
$508$	6.32715e11	0.421523
$509$	8.84343e11	0.583970	0.291985	−	0.956423i	$-0.405684\pi$
$509$	8.84343e11	0.583970	0.291985	+	0.956423i	$0.405684\pi$
$510$	0	0
$511$	−1.67698e11	−0.108801
$512$	−6.87195e10	−0.0441942
$513$	0	0
$514$	1.94083e12	1.22646
$515$	−2.89241e11	−0.181187
$516$	0	0
$517$	1.81553e12	1.11762
$518$	1.16480e11	0.0710835
$519$	0	0
$520$	1.00644e11	0.0603635
$521$	−7.20145e11	−0.428204	−0.214102	−	0.976811i	$-0.568682\pi$
$521$	−7.20145e11	−0.428204	−0.214102	+	0.976811i	$0.568682\pi$
$522$	0	0
$523$	−2.01760e12	−1.17917	−0.589585	−	0.807706i	$-0.700709\pi$
$523$	−2.01760e12	−1.17917	−0.589585	+	0.807706i	$0.700709\pi$
$524$	1.04596e12	0.606072
$525$	0	0
$526$	1.34118e12	0.763925
$527$	−4.00720e12	−2.26304
$528$	0	0
$529$	8.62628e11	0.478931
$530$	−1.95602e11	−0.107679
$531$	0	0
$532$	−3.94718e11	−0.213641
$533$	1.25250e12	0.672211
$534$	0	0
$535$	6.30077e10	0.0332508
$536$	7.55544e11	0.395383
$537$	0	0
$538$	−2.09572e12	−1.07848
$539$	−2.91775e11	−0.148901
$540$	0	0
$541$	8.51866e11	0.427547	0.213773	−	0.976883i	$-0.431425\pi$
$541$	8.51866e11	0.427547	0.213773	+	0.976883i	$0.431425\pi$
$542$	−2.20741e12	−1.09872
$543$	0	0
$544$	−6.17615e11	−0.302359
$545$	3.06875e11	0.148997
$546$	0	0
$547$	−1.39264e12	−0.665112	−0.332556	−	0.943084i	$-0.607911\pi$
$547$	−1.39264e12	−0.665112	−0.332556	+	0.943084i	$0.607911\pi$
$548$	−1.35888e12	−0.643679
$549$	0	0
$550$	−1.54931e12	−0.721949
$551$	−2.36051e12	−1.09100
$552$	0	0
$553$	−4.10048e11	−0.186454
$554$	−3.01637e12	−1.36047
$555$	0	0
$556$	−1.60974e12	−0.714365
$557$	−3.44521e12	−1.51659	−0.758294	−	0.651913i	$-0.773967\pi$
$557$	−3.44521e12	−1.51659	−0.758294	+	0.651913i	$0.773967\pi$
$558$	0	0
$559$	4.92395e12	2.13285
$560$	−3.14493e10	−0.0135134
$561$	0	0
$562$	−1.92238e12	−0.812877
$563$	6.69368e11	0.280787	0.140394	−	0.990096i	$-0.455163\pi$
$563$	6.69368e11	0.280787	0.140394	+	0.990096i	$0.455163\pi$
$564$	0	0
$565$	−5.32156e11	−0.219695
$566$	−4.72086e11	−0.193351
$567$	0	0
$568$	−3.32228e10	−0.0133927
$569$	2.68445e12	1.07362	0.536810	−	0.843703i	$-0.319629\pi$
$569$	2.68445e12	1.07362	0.536810	+	0.843703i	$0.319629\pi$
$570$	0	0
$571$	2.73085e12	1.07507	0.537533	−	0.843243i	$-0.319356\pi$
$571$	2.73085e12	1.07507	0.537533	+	0.843243i	$0.319356\pi$
$572$	−1.59292e12	−0.622174
$573$	0	0
$574$	−3.91381e11	−0.150486
$575$	−3.12252e12	−1.19124
$576$	0	0
$577$	6.41104e11	0.240789	0.120395	−	0.992726i	$-0.461584\pi$
$577$	6.41104e11	0.240789	0.120395	+	0.992726i	$0.461584\pi$
$578$	−3.65339e12	−1.36151
$579$	0	0
$580$	−1.88074e11	−0.0690085
$581$	7.22715e11	0.263132
$582$	0	0
$583$	3.09584e12	1.10987
$584$	2.86085e11	0.101774
$585$	0	0
$586$	−3.71926e11	−0.130292
$587$	3.45704e12	1.20180	0.600902	−	0.799323i	$-0.294808\pi$
$587$	3.45704e12	1.20180	0.600902	+	0.799323i	$0.294808\pi$
$588$	0	0
$589$	4.36896e12	1.49575
$590$	4.87154e11	0.165513
$591$	0	0
$592$	−1.98710e11	−0.0664925
$593$	1.79190e12	0.595068	0.297534	−	0.954711i	$-0.403836\pi$
$593$	1.79190e12	0.595068	0.297534	+	0.954711i	$0.403836\pi$
$594$	0	0
$595$	−2.82650e11	−0.0924532
$596$	−1.77355e12	−0.575750
$597$	0	0
$598$	−3.21041e12	−1.02661
$599$	−9.99187e11	−0.317122	−0.158561	−	0.987349i	$-0.550685\pi$
$599$	−9.99187e11	−0.317122	−0.158561	+	0.987349i	$0.550685\pi$
$600$	0	0
$601$	−1.95773e12	−0.612095	−0.306047	−	0.952016i	$-0.599007\pi$
$601$	−1.95773e12	−0.612095	−0.306047	+	0.952016i	$0.599007\pi$
$602$	−1.53863e12	−0.477475
$603$	0	0
$604$	−6.06081e11	−0.185295
$605$	−4.07209e10	−0.0123571
$606$	0	0
$607$	1.51708e12	0.453584	0.226792	−	0.973943i	$-0.427176\pi$
$607$	1.51708e12	0.453584	0.226792	+	0.973943i	$0.427176\pi$
$608$	6.73372e11	0.199843
$609$	0	0
$610$	3.88966e11	0.113744
$611$	−4.40991e12	−1.28010
$612$	0	0
$613$	−1.93197e12	−0.552622	−0.276311	−	0.961068i	$-0.589112\pi$
$613$	−1.93197e12	−0.552622	−0.276311	+	0.961068i	$0.589112\pi$
$614$	4.43534e12	1.25942
$615$	0	0
$616$	4.97755e11	0.139284
$617$	−4.05385e12	−1.12612	−0.563060	−	0.826416i	$-0.690376\pi$
$617$	−4.05385e12	−1.12612	−0.563060	+	0.826416i	$0.690376\pi$
$618$	0	0
$619$	5.47177e12	1.49803	0.749014	−	0.662555i	$-0.230528\pi$
$619$	5.47177e12	1.49803	0.749014	+	0.662555i	$0.230528\pi$
$620$	3.48098e11	0.0946104
$621$	0	0
$622$	−7.87000e10	−0.0210823
$623$	5.77883e10	0.0153689
$624$	0	0
$625$	3.58223e12	0.939061
$626$	−2.78791e12	−0.725595
$627$	0	0
$628$	−1.45042e12	−0.372114
$629$	−1.78590e12	−0.454915
$630$	0	0
$631$	3.52966e12	0.886340	0.443170	−	0.896438i	$-0.353854\pi$
$631$	3.52966e12	0.886340	0.443170	+	0.896438i	$0.353854\pi$
$632$	6.99524e11	0.174412
$633$	0	0
$634$	−4.87662e12	−1.19872
$635$	−4.93977e11	−0.120566
$636$	0	0
$637$	7.08721e11	0.170549
$638$	2.97669e12	0.711280
$639$	0	0
$640$	5.36511e10	0.0126406
$641$	−3.99993e12	−0.935818	−0.467909	−	0.883777i	$-0.654993\pi$
$641$	−3.99993e12	−0.935818	−0.467909	+	0.883777i	$0.654993\pi$
$642$	0	0
$643$	−8.43828e11	−0.194672	−0.0973362	−	0.995252i	$-0.531032\pi$
$643$	−8.43828e11	−0.194672	−0.0973362	+	0.995252i	$0.531032\pi$
$644$	1.00319e12	0.229824
$645$	0	0
$646$	6.05191e12	1.36725
$647$	−1.15655e12	−0.259475	−0.129737	−	0.991548i	$-0.541413\pi$
$647$	−1.15655e12	−0.259475	−0.129737	+	0.991548i	$0.541413\pi$
$648$	0	0
$649$	−7.71029e12	−1.70596
$650$	3.76328e12	0.826907
$651$	0	0
$652$	2.92312e12	0.633479
$653$	6.41327e11	0.138029	0.0690145	−	0.997616i	$-0.478015\pi$
$653$	6.41327e11	0.138029	0.0690145	+	0.997616i	$0.478015\pi$
$654$	0	0
$655$	−8.16608e11	−0.173352
$656$	6.67678e11	0.140767
$657$	0	0
$658$	1.37801e12	0.286573
$659$	1.69261e9	0.000349600 0	0.000174800	−	1.00000i	$-0.499944\pi$
$659$	1.69261e9	0.000349600 0	0.000174800		1.00000i	$0.499944\pi$
$660$	0	0
$661$	−2.92324e12	−0.595604	−0.297802	−	0.954628i	$-0.596253\pi$
$661$	−2.92324e12	−0.595604	−0.297802	+	0.954628i	$0.596253\pi$
$662$	−1.64819e12	−0.333538
$663$	0	0
$664$	−1.23292e12	−0.246138
$665$	3.08167e11	0.0611066
$666$	0	0
$667$	5.99929e12	1.17364
$668$	1.91529e12	0.372170
$669$	0	0
$670$	−5.89873e11	−0.113089
$671$	−6.15625e12	−1.17237
$672$	0	0
$673$	2.69340e12	0.506096	0.253048	−	0.967454i	$-0.418567\pi$
$673$	2.69340e12	0.506096	0.253048	+	0.967454i	$0.418567\pi$
$674$	−1.62792e12	−0.303853
$675$	0	0
$676$	1.15446e12	0.212626
$677$	9.32131e11	0.170541	0.0852703	−	0.996358i	$-0.472825\pi$
$677$	9.32131e11	0.170541	0.0852703	+	0.996358i	$0.472825\pi$
$678$	0	0
$679$	−3.59332e12	−0.648756
$680$	4.82188e11	0.0864821
$681$	0	0
$682$	−5.50943e12	−0.975162
$683$	8.68281e12	1.52675	0.763373	−	0.645957i	$-0.223542\pi$
$683$	8.68281e12	1.52675	0.763373	+	0.645957i	$0.223542\pi$
$684$	0	0
$685$	1.06091e12	0.184108
$686$	−2.21461e11	−0.0381802
$687$	0	0
$688$	2.62484e12	0.446637
$689$	−7.51981e12	−1.27122
$690$	0	0
$691$	1.06795e13	1.78197	0.890986	−	0.454031i	$-0.150015\pi$
$691$	1.06795e13	1.78197	0.890986	+	0.454031i	$0.150015\pi$
$692$	−3.98135e12	−0.660014
$693$	0	0
$694$	−1.49230e12	−0.244196
$695$	1.25677e12	0.204326
$696$	0	0
$697$	6.00074e12	0.963069
$698$	2.58271e12	0.411838
$699$	0	0
$700$	−1.17595e12	−0.185117
$701$	−7.49234e11	−0.117189	−0.0585944	−	0.998282i	$-0.518662\pi$
$701$	−7.49234e11	−0.117189	−0.0585944	+	0.998282i	$0.518662\pi$
$702$	0	0
$703$	1.94713e12	0.300675
$704$	−8.49147e11	−0.130289
$705$	0	0
$706$	−1.32003e11	−0.0199969
$707$	−1.48891e12	−0.224120
$708$	0	0
$709$	−2.59276e12	−0.385350	−0.192675	−	0.981263i	$-0.561716\pi$
$709$	−2.59276e12	−0.385350	−0.192675	+	0.981263i	$0.561716\pi$
$710$	2.59379e10	0.00383064
$711$	0	0
$712$	−9.85842e10	−0.0143763
$713$	−1.11038e13	−1.60905
$714$	0	0
$715$	1.24363e12	0.177957
$716$	5.51998e12	0.784927
$717$	0	0
$718$	−1.72583e12	−0.242348
$719$	−6.26178e11	−0.0873811	−0.0436906	−	0.999045i	$-0.513912\pi$
$719$	−6.26178e11	−0.0873811	−0.0436906	+	0.999045i	$0.513912\pi$
$720$	0	0
$721$	3.47467e12	0.478855
$722$	−1.43527e12	−0.196569
$723$	0	0
$724$	−6.55500e12	−0.886644
$725$	−7.03244e12	−0.945333
$726$	0	0
$727$	1.60398e12	0.212958	0.106479	−	0.994315i	$-0.466042\pi$
$727$	1.60398e12	0.212958	0.106479	+	0.994315i	$0.466042\pi$
$728$	−1.20905e12	−0.159534
$729$	0	0
$730$	−2.23354e11	−0.0291099
$731$	2.35907e13	3.05571
$732$	0	0
$733$	8.01480e12	1.02547	0.512737	−	0.858545i	$-0.328631\pi$
$733$	8.01480e12	1.02547	0.512737	+	0.858545i	$0.328631\pi$
$734$	−2.72754e12	−0.346848
$735$	0	0
$736$	−1.71139e12	−0.214980
$737$	9.33604e12	1.16563
$738$	0	0
$739$	−1.14131e13	−1.40767	−0.703836	−	0.710362i	$-0.748531\pi$
$739$	−1.14131e13	−1.40767	−0.703836	+	0.710362i	$0.748531\pi$
$740$	1.55138e11	0.0190185
$741$	0	0
$742$	2.34978e12	0.284584
$743$	−1.14320e13	−1.37618	−0.688088	−	0.725627i	$-0.741550\pi$
$743$	−1.14320e13	−1.37618	−0.688088	+	0.725627i	$0.741550\pi$
$744$	0	0
$745$	1.38465e12	0.164679
$746$	−5.20594e12	−0.615424
$747$	0	0
$748$	−7.63169e12	−0.891382
$749$	−7.56915e11	−0.0878778
$750$	0	0
$751$	1.78346e12	0.204590	0.102295	−	0.994754i	$-0.467381\pi$
$751$	1.78346e12	0.204590	0.102295	+	0.994754i	$0.467381\pi$
$752$	−2.35082e12	−0.268064
$753$	0	0
$754$	−7.23038e12	−0.814686
$755$	4.73183e11	0.0529991
$756$	0	0
$757$	−3.66387e12	−0.405516	−0.202758	−	0.979229i	$-0.564991\pi$
$757$	−3.66387e12	−0.405516	−0.202758	+	0.979229i	$0.564991\pi$
$758$	−1.58782e12	−0.174699
$759$	0	0
$760$	−5.25719e11	−0.0571600
$761$	−6.33939e12	−0.685199	−0.342599	−	0.939482i	$-0.611307\pi$
$761$	−6.33939e12	−0.685199	−0.342599	+	0.939482i	$0.611307\pi$
$762$	0	0
$763$	−3.68650e12	−0.393781
$764$	8.28774e12	0.880067
$765$	0	0
$766$	−6.28982e12	−0.660099
$767$	1.87283e13	1.95398
$768$	0	0
$769$	−5.65834e11	−0.0583473	−0.0291736	−	0.999574i	$-0.509288\pi$
$769$	−5.65834e11	−0.0583473	−0.0291736	+	0.999574i	$0.509288\pi$
$770$	−3.88610e11	−0.0398387
$771$	0	0
$772$	−2.07379e12	−0.210129
$773$	8.39882e12	0.846078	0.423039	−	0.906111i	$-0.360963\pi$
$773$	8.39882e12	0.846078	0.423039	+	0.906111i	$0.360963\pi$
$774$	0	0
$775$	1.30160e13	1.29605
$776$	6.13004e12	0.606856
$777$	0	0
$778$	−8.71584e12	−0.852906
$779$	−6.54248e12	−0.636537
$780$	0	0
$781$	−4.10524e11	−0.0394829
$782$	−1.53811e13	−1.47081
$783$	0	0
$784$	3.77802e11	0.0357143
$785$	1.13238e12	0.106434
$786$	0	0
$787$	−1.76158e13	−1.63688	−0.818438	−	0.574594i	$-0.805160\pi$
$787$	−1.76158e13	−1.63688	−0.818438	+	0.574594i	$0.805160\pi$
$788$	−7.08166e12	−0.654285
$789$	0	0
$790$	−5.46136e11	−0.0498861
$791$	6.39282e12	0.580629
$792$	0	0
$793$	1.49535e13	1.34281
$794$	−5.30628e12	−0.473803
$795$	0	0
$796$	1.25455e12	0.110759
$797$	1.13741e13	0.998519	0.499259	−	0.866453i	$-0.333606\pi$
$797$	1.13741e13	0.998519	0.499259	+	0.866453i	$0.333606\pi$
$798$	0	0
$799$	−2.11279e13	−1.83399
$800$	2.00611e12	0.173161
$801$	0	0
$802$	3.11468e11	0.0265845
$803$	3.53507e12	0.300039
$804$	0	0
$805$	−7.83213e11	−0.0657353
$806$	1.33824e13	1.11693
$807$	0	0
$808$	2.54002e12	0.209645
$809$	−6.34760e12	−0.521004	−0.260502	−	0.965473i	$-0.583888\pi$
$809$	−6.34760e12	−0.521004	−0.260502	+	0.965473i	$0.583888\pi$
$810$	0	0
$811$	8.22506e12	0.667645	0.333822	−	0.942636i	$-0.391661\pi$
$811$	8.22506e12	0.667645	0.333822	+	0.942636i	$0.391661\pi$
$812$	2.25934e12	0.182381
$813$	0	0
$814$	−2.45541e12	−0.196026
$815$	−2.28215e12	−0.181191
$816$	0	0
$817$	−2.57204e13	−2.01966
$818$	1.55825e13	1.21688
$819$	0	0
$820$	−5.21274e11	−0.0402627
$821$	−2.29542e12	−0.176327	−0.0881634	−	0.996106i	$-0.528100\pi$
$821$	−2.29542e12	−0.176327	−0.0881634	+	0.996106i	$0.528100\pi$
$822$	0	0
$823$	1.98447e13	1.50781	0.753903	−	0.656986i	$-0.228169\pi$
$823$	1.98447e13	1.50781	0.753903	+	0.656986i	$0.228169\pi$
$824$	−5.92763e12	−0.447928
$825$	0	0
$826$	−5.85221e12	−0.437431
$827$	−1.16461e12	−0.0865773	−0.0432887	−	0.999063i	$-0.513784\pi$
$827$	−1.16461e12	−0.0865773	−0.0432887	+	0.999063i	$0.513784\pi$
$828$	0	0
$829$	3.99395e12	0.293702	0.146851	−	0.989159i	$-0.453086\pi$
$829$	3.99395e12	0.293702	0.146851	+	0.989159i	$0.453086\pi$
$830$	9.62572e11	0.0704015
$831$	0	0
$832$	2.06258e12	0.149230
$833$	3.39549e12	0.244343
$834$	0	0
$835$	−1.49532e12	−0.106450
$836$	8.32067e12	0.589156
$837$	0	0
$838$	−7.54802e12	−0.528731
$839$	1.14941e13	0.800840	0.400420	−	0.916332i	$-0.368864\pi$
$839$	1.14941e13	0.800840	0.400420	+	0.916332i	$0.368864\pi$
$840$	0	0
$841$	−9.95737e11	−0.0686377
$842$	−1.82306e13	−1.24996
$843$	0	0
$844$	1.22229e13	0.829150
$845$	−9.01313e11	−0.0608164
$846$	0	0
$847$	4.89183e11	0.0326585
$848$	−4.00863e12	−0.266204
$849$	0	0
$850$	1.80299e13	1.18470
$851$	−4.94868e12	−0.323450
$852$	0	0
$853$	2.54044e13	1.64300	0.821501	−	0.570207i	$-0.193137\pi$
$853$	2.54044e13	1.64300	0.821501	+	0.570207i	$0.193137\pi$
$854$	−4.67267e12	−0.300611
$855$	0	0
$856$	1.29126e12	0.0822021
$857$	7.69898e12	0.487550	0.243775	−	0.969832i	$-0.421614\pi$
$857$	7.69898e12	0.487550	0.243775	+	0.969832i	$0.421614\pi$
$858$	0	0
$859$	−1.34485e13	−0.842763	−0.421382	−	0.906883i	$-0.638455\pi$
$859$	−1.34485e13	−0.842763	−0.421382	+	0.906883i	$0.638455\pi$
$860$	−2.04928e12	−0.127749
$861$	0	0
$862$	−2.67557e12	−0.165057
$863$	−2.45542e12	−0.150687	−0.0753437	−	0.997158i	$-0.524005\pi$
$863$	−2.45542e12	−0.150687	−0.0753437	+	0.997158i	$0.524005\pi$
$864$	0	0
$865$	3.10834e12	0.188780
$866$	2.07055e13	1.25099
$867$	0	0
$868$	−4.18172e12	−0.250044
$869$	8.64382e12	0.514182
$870$	0	0
$871$	−2.26773e13	−1.33509
$872$	6.28901e12	0.368348
$873$	0	0
$874$	1.67697e13	0.972127
$875$	1.85535e12	0.107002
$876$	0	0
$877$	5.09940e12	0.291086	0.145543	−	0.989352i	$-0.453507\pi$
$877$	5.09940e12	0.291086	0.145543	+	0.989352i	$0.453507\pi$
$878$	−9.60276e12	−0.545344
$879$	0	0
$880$	6.62951e11	0.0372657
$881$	1.49642e13	0.836876	0.418438	−	0.908245i	$-0.362578\pi$
$881$	1.49642e13	0.836876	0.418438	+	0.908245i	$0.362578\pi$
$882$	0	0
$883$	−2.29453e12	−0.127020	−0.0635098	−	0.997981i	$-0.520229\pi$
$883$	−2.29453e12	−0.127020	−0.0635098	+	0.997981i	$0.520229\pi$
$884$	1.85374e13	1.02097
$885$	0	0
$886$	−1.20385e13	−0.656327
$887$	−1.29897e13	−0.704599	−0.352299	−	0.935887i	$-0.614600\pi$
$887$	−1.29897e13	−0.704599	−0.352299	+	0.935887i	$0.614600\pi$
$888$	0	0
$889$	5.93418e12	0.318642
$890$	7.69672e10	0.00411198
$891$	0	0
$892$	1.23337e13	0.652306
$893$	2.30353e13	1.21217
$894$	0	0
$895$	−4.30959e12	−0.224508
$896$	−6.44514e11	−0.0334077
$897$	0	0
$898$	−1.09969e12	−0.0564321
$899$	−2.50077e13	−1.27689
$900$	0	0
$901$	−3.60274e13	−1.82126
$902$	8.25031e12	0.414993
$903$	0	0
$904$	−1.09059e13	−0.543129
$905$	5.11766e12	0.253602
$906$	0	0
$907$	−3.30861e13	−1.62335	−0.811677	−	0.584106i	$-0.801445\pi$
$907$	−3.30861e13	−1.62335	−0.811677	+	0.584106i	$0.801445\pi$
$908$	8.94829e12	0.436871
$909$	0	0
$910$	9.43934e11	0.0456305
$911$	4.12333e13	1.98343	0.991713	−	0.128477i	$-0.0410087\pi$
$911$	4.12333e13	1.98343	0.991713	+	0.128477i	$0.0410087\pi$
$912$	0	0
$913$	−1.52348e13	−0.725637
$914$	−1.63457e12	−0.0774721
$915$	0	0
$916$	−1.16641e12	−0.0547422
$917$	9.80997e12	0.458148
$918$	0	0
$919$	1.17114e13	0.541614	0.270807	−	0.962634i	$-0.412709\pi$
$919$	1.17114e13	0.541614	0.270807	+	0.962634i	$0.412709\pi$
$920$	1.33613e12	0.0614897
$921$	0	0
$922$	−7.10114e12	−0.323623
$923$	9.97164e11	0.0452230
$924$	0	0
$925$	5.80091e12	0.260530
$926$	9.84137e12	0.439851
$927$	0	0
$928$	−3.85434e12	−0.170602
$929$	3.66791e13	1.61565	0.807827	−	0.589419i	$-0.200643\pi$
$929$	3.66791e13	1.61565	0.807827	+	0.589419i	$0.200643\pi$
$930$	0	0
$931$	−3.70203e12	−0.161498
$932$	1.27240e13	0.552398
$933$	0	0
$934$	−1.55989e13	−0.670705
$935$	5.95826e12	0.254957
$936$	0	0
$937$	3.49134e12	0.147967	0.0739833	−	0.997259i	$-0.476429\pi$
$937$	3.49134e12	0.147967	0.0739833	+	0.997259i	$0.476429\pi$
$938$	7.08617e12	0.298881
$939$	0	0
$940$	1.83534e12	0.0766730
$941$	−6.56499e12	−0.272948	−0.136474	−	0.990644i	$-0.543577\pi$
$941$	−6.56499e12	−0.272948	−0.136474	+	0.990644i	$0.543577\pi$
$942$	0	0
$943$	1.66279e13	0.684753
$944$	9.98361e12	0.409179
$945$	0	0
$946$	3.24344e13	1.31673
$947$	−2.47176e13	−0.998693	−0.499346	−	0.866402i	$-0.666426\pi$
$947$	−2.47176e13	−0.998693	−0.499346	+	0.866402i	$0.666426\pi$
$948$	0	0
$949$	−8.58669e12	−0.343659
$950$	−1.96576e13	−0.783023
$951$	0	0
$952$	−5.79255e12	−0.228562
$953$	3.46073e13	1.35909	0.679546	−	0.733632i	$-0.262177\pi$
$953$	3.46073e13	1.35909	0.679546	+	0.733632i	$0.262177\pi$
$954$	0	0
$955$	−6.47045e12	−0.251721
$956$	2.25390e13	0.872717
$957$	0	0
$958$	2.30583e13	0.884469
$959$	−1.27448e13	−0.486576
$960$	0	0
$961$	1.98460e13	0.750616
$962$	5.96419e12	0.224524
$963$	0	0
$964$	2.23765e13	0.834536
$965$	1.61906e12	0.0601021
$966$	0	0
$967$	3.17837e13	1.16892	0.584460	−	0.811422i	$-0.301306\pi$
$967$	3.17837e13	1.16892	0.584460	+	0.811422i	$0.301306\pi$
$968$	−8.34524e11	−0.0305492
$969$	0	0
$970$	−4.78588e12	−0.173576
$971$	1.92546e13	0.695101	0.347551	−	0.937661i	$-0.387013\pi$
$971$	1.92546e13	0.695101	0.347551	+	0.937661i	$0.387013\pi$
$972$	0	0
$973$	−1.50976e13	−0.540010
$974$	−1.37591e13	−0.489862
$975$	0	0
$976$	7.97137e12	0.281196
$977$	−1.74023e12	−0.0611057	−0.0305528	−	0.999533i	$-0.509727\pi$
$977$	−1.74023e12	−0.0611057	−0.0305528	+	0.999533i	$0.509727\pi$
$978$	0	0
$979$	−1.21818e12	−0.0423827
$980$	−2.94960e11	−0.0102152
$981$	0	0
$982$	1.64217e13	0.563530
$983$	3.97740e13	1.35865	0.679326	−	0.733837i	$-0.262272\pi$
$983$	3.97740e13	1.35865	0.679326	+	0.733837i	$0.262272\pi$
$984$	0	0
$985$	5.52884e12	0.187142
$986$	−3.46408e13	−1.16719
$987$	0	0
$988$	−2.02109e13	−0.674807
$989$	6.53690e13	2.17264
$990$	0	0
$991$	−4.32234e12	−0.142360	−0.0711799	−	0.997463i	$-0.522676\pi$
$991$	−4.32234e12	−0.142360	−0.0711799	+	0.997463i	$0.522676\pi$
$992$	7.13383e12	0.233895
$993$	0	0
$994$	−3.11593e11	−0.0101239
$995$	−9.79460e11	−0.0316798
$996$	0	0
$997$	−3.09849e13	−0.993166	−0.496583	−	0.867989i	$-0.665412\pi$
$997$	−3.09849e13	−0.993166	−0.496583	+	0.867989i	$0.665412\pi$
$998$	2.35752e13	0.752261
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.10.a.d.1.2	✓	4
3.2	odd	2		378.10.a.e.1.3	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.10.a.d.1.2	✓	4	1.1	even	1	trivial
378.10.a.e.1.3	yes	4	3.2	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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	378.a (trivial)

\(f(q)\)	\(=\)	\(q-16.0000 q^{2} +256.000 q^{4} -199.866 q^{5} +2401.00 q^{7} -4096.00 q^{8} +O(q^{10})\)	\(q-16.0000 q^{2} +256.000 q^{4} -199.866 q^{5} +2401.00 q^{7} -4096.00 q^{8} +3197.85 q^{10} -50613.1 q^{11} +122939. q^{13} -38416.0 q^{14} +65536.0 q^{16} +589003. q^{17} -642178. q^{19} -51165.7 q^{20} +809810. q^{22} +1.63211e6 q^{23} -1.91318e6 q^{25} -1.96703e6 q^{26} +614656. q^{28} +3.67579e6 q^{29} -6.80335e6 q^{31} -1.04858e6 q^{32} -9.42405e6 q^{34} -479878. q^{35} -3.03208e6 q^{37} +1.02748e7 q^{38} +818650. q^{40} +1.01880e7 q^{41} +4.00519e7 q^{43} -1.29570e7 q^{44} -2.61137e7 q^{46} -3.58706e7 q^{47} +5.76480e6 q^{49} +3.06109e7 q^{50} +3.14725e7 q^{52} -6.11668e7 q^{53} +1.01158e7 q^{55} -9.83450e6 q^{56} -5.88126e7 q^{58} +1.52338e8 q^{59} +1.21633e8 q^{61} +1.08854e8 q^{62} +1.67772e7 q^{64} -2.45714e7 q^{65} -1.84459e8 q^{67} +1.50785e8 q^{68} +7.67805e6 q^{70} +8.11102e6 q^{71} -6.98449e7 q^{73} +4.85133e7 q^{74} -1.64397e8 q^{76} -1.21522e8 q^{77} -1.70782e8 q^{79} -1.30984e7 q^{80} -1.63007e8 q^{82} +3.01006e8 q^{83} -1.17722e8 q^{85} -6.40830e8 q^{86} +2.07311e8 q^{88} +2.40684e7 q^{89} +2.95177e8 q^{91} +4.17820e8 q^{92} +5.73930e8 q^{94} +1.28349e8 q^{95} -1.49659e9 q^{97} -9.22368e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 64 q^{2} + 1024 q^{4} + 2208 q^{5} + 9604 q^{7} - 16384 q^{8}+O(q^{10}) \) 4 * q - 64 * q^2 + 1024 * q^4 + 2208 * q^5 + 9604 * q^7 - 16384 * q^8	\( 4 q - 64 q^{2} + 1024 q^{4} + 2208 q^{5} + 9604 q^{7} - 16384 q^{8} - 35328 q^{10} + 14784 q^{11} + 21464 q^{13} - 153664 q^{14} + 262144 q^{16} + 485568 q^{17} - 46828 q^{19} + 565248 q^{20} - 236544 q^{22} - 430944 q^{23} - 2143688 q^{25} - 343424 q^{26} + 2458624 q^{28} + 2580000 q^{29} - 6228604 q^{31} - 4194304 q^{32} - 7769088 q^{34} + 5301408 q^{35} + 8995220 q^{37} + 749248 q^{38} - 9043968 q^{40} + 22028736 q^{41} + 21954176 q^{43} + 3784704 q^{44} + 6895104 q^{46} + 33437472 q^{47} + 23059204 q^{49} + 34299008 q^{50} + 5494784 q^{52} + 111929472 q^{53} + 77520996 q^{55} - 39337984 q^{56} - 41280000 q^{58} + 285328416 q^{59} + 36406592 q^{61} + 99657664 q^{62} + 67108864 q^{64} - 30754848 q^{65} + 40399496 q^{67} + 124305408 q^{68} - 84822528 q^{70} + 99955872 q^{71} + 10196576 q^{73} - 143923520 q^{74} - 11987968 q^{76} + 35496384 q^{77} + 54438704 q^{79} + 144703488 q^{80} - 352459776 q^{82} - 54880032 q^{83} + 736315344 q^{85} - 351266816 q^{86} - 60555264 q^{88} + 100706112 q^{89} + 51535064 q^{91} - 110321664 q^{92} - 534999552 q^{94} + 1873022496 q^{95} - 1861020208 q^{97} - 368947264 q^{98}+O(q^{100}) \) 4 * q - 64 * q^2 + 1024 * q^4 + 2208 * q^5 + 9604 * q^7 - 16384 * q^8 - 35328 * q^10 + 14784 * q^11 + 21464 * q^13 - 153664 * q^14 + 262144 * q^16 + 485568 * q^17 - 46828 * q^19 + 565248 * q^20 - 236544 * q^22 - 430944 * q^23 - 2143688 * q^25 - 343424 * q^26 + 2458624 * q^28 + 2580000 * q^29 - 6228604 * q^31 - 4194304 * q^32 - 7769088 * q^34 + 5301408 * q^35 + 8995220 * q^37 + 749248 * q^38 - 9043968 * q^40 + 22028736 * q^41 + 21954176 * q^43 + 3784704 * q^44 + 6895104 * q^46 + 33437472 * q^47 + 23059204 * q^49 + 34299008 * q^50 + 5494784 * q^52 + 111929472 * q^53 + 77520996 * q^55 - 39337984 * q^56 - 41280000 * q^58 + 285328416 * q^59 + 36406592 * q^61 + 99657664 * q^62 + 67108864 * q^64 - 30754848 * q^65 + 40399496 * q^67 + 124305408 * q^68 - 84822528 * q^70 + 99955872 * q^71 + 10196576 * q^73 - 143923520 * q^74 - 11987968 * q^76 + 35496384 * q^77 + 54438704 * q^79 + 144703488 * q^80 - 352459776 * q^82 - 54880032 * q^83 + 736315344 * q^85 - 351266816 * q^86 - 60555264 * q^88 + 100706112 * q^89 + 51535064 * q^91 - 110321664 * q^92 - 534999552 * q^94 + 1873022496 * q^95 - 1861020208 * q^97 - 368947264 * q^98

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