LMFDB - Embedded newform 575.2.a.j.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,2,Mod(1,575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(575, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("575.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	575.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:	$4.59139811622$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.5744.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} - 2x + 1 $ x^4 - 5x^2 - 2x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 115)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.37988$ of defining polynomial
Character	$\chi$	$=$	575.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.37988 q^{2} -1.95969 q^{3} +3.66382 q^{4} -4.66382 q^{6} +2.28394 q^{7} +3.95969 q^{8} +0.840379 q^{9} +O(q^{10})$	\(q+2.37988 q^{2} -1.95969 q^{3} +3.66382 q^{4} -4.66382 q^{6} +2.28394 q^{7} +3.95969 q^{8} +0.840379 q^{9} +1.12432 q^{11} -7.17995 q^{12} +5.95969 q^{13} +5.43550 q^{14} +2.09594 q^{16} +5.80007 q^{17} +2.00000 q^{18} -4.08401 q^{19} -4.47581 q^{21} +2.67575 q^{22} -1.00000 q^{23} -7.75976 q^{24} +14.1833 q^{26} +4.23218 q^{27} +8.36795 q^{28} -0.408263 q^{29} -3.19187 q^{31} -2.93130 q^{32} -2.20332 q^{33} +13.8035 q^{34} +3.07900 q^{36} -9.80345 q^{37} -9.71944 q^{38} -11.6791 q^{39} +6.27087 q^{41} -10.6519 q^{42} +7.75474 q^{43} +4.11931 q^{44} -2.37988 q^{46} -6.40020 q^{47} -4.10738 q^{48} -1.78361 q^{49} -11.3663 q^{51} +21.8352 q^{52} -6.73590 q^{53} +10.0721 q^{54} +9.04370 q^{56} +8.00339 q^{57} -0.971615 q^{58} -4.75976 q^{59} -6.33265 q^{61} -7.59627 q^{62} +1.91938 q^{63} -11.1680 q^{64} -5.24363 q^{66} +0.283942 q^{67} +21.2504 q^{68} +1.95969 q^{69} -13.9516 q^{71} +3.32764 q^{72} +9.61659 q^{73} -23.3310 q^{74} -14.9631 q^{76} +2.56788 q^{77} -27.7949 q^{78} +4.48387 q^{79} -10.8149 q^{81} +14.9239 q^{82} -10.8223 q^{83} -16.3986 q^{84} +18.4553 q^{86} +0.800068 q^{87} +4.45196 q^{88} +5.68414 q^{89} +13.6116 q^{91} -3.66382 q^{92} +6.25508 q^{93} -15.2317 q^{94} +5.74444 q^{96} +11.0676 q^{97} -4.24477 q^{98} +0.944856 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{4} - 6 q^{6} + 6 q^{7} + 6 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 2 * q^4 - 6 * q^6 + 6 * q^7 + 6 * q^8 + 4 * q^9	$ 4 q + 2 q^{3} + 2 q^{4} - 6 q^{6} + 6 q^{7} + 6 q^{8} + 4 q^{9} + 2 q^{11} - 10 q^{12} + 14 q^{13} - 4 q^{14} + 2 q^{16} + 14 q^{17} + 8 q^{18} - 4 q^{19} - 2 q^{21} + 4 q^{22} - 4 q^{23} - 12 q^{24} + 6 q^{26} + 14 q^{27} + 18 q^{28} + 4 q^{29} + 2 q^{32} + 14 q^{33} + 14 q^{34} - 8 q^{36} + 2 q^{37} - 10 q^{38} - 8 q^{39} - 8 q^{41} - 24 q^{42} + 4 q^{43} + 6 q^{44} + 2 q^{47} + 10 q^{51} + 18 q^{52} + 4 q^{53} + 22 q^{54} + 14 q^{56} - 8 q^{61} - 28 q^{62} - 12 q^{63} - 20 q^{64} - 8 q^{66} - 2 q^{67} + 8 q^{68} - 2 q^{69} - 24 q^{71} - 12 q^{72} + 18 q^{73} - 36 q^{74} - 18 q^{76} + 4 q^{77} - 32 q^{78} + 24 q^{79} + 8 q^{81} + 32 q^{82} - 6 q^{83} + 2 q^{84} + 14 q^{86} - 6 q^{87} - 10 q^{88} - 8 q^{89} + 26 q^{91} - 2 q^{92} + 2 q^{93} - 42 q^{94} + 30 q^{96} + 34 q^{97} - 28 q^{98} + 36 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^4 - 6 * q^6 + 6 * q^7 + 6 * q^8 + 4 * q^9 + 2 * q^11 - 10 * q^12 + 14 * q^13 - 4 * q^14 + 2 * q^16 + 14 * q^17 + 8 * q^18 - 4 * q^19 - 2 * q^21 + 4 * q^22 - 4 * q^23 - 12 * q^24 + 6 * q^26 + 14 * q^27 + 18 * q^28 + 4 * q^29 + 2 * q^32 + 14 * q^33 + 14 * q^34 - 8 * q^36 + 2 * q^37 - 10 * q^38 - 8 * q^39 - 8 * q^41 - 24 * q^42 + 4 * q^43 + 6 * q^44 + 2 * q^47 + 10 * q^51 + 18 * q^52 + 4 * q^53 + 22 * q^54 + 14 * q^56 - 8 * q^61 - 28 * q^62 - 12 * q^63 - 20 * q^64 - 8 * q^66 - 2 * q^67 + 8 * q^68 - 2 * q^69 - 24 * q^71 - 12 * q^72 + 18 * q^73 - 36 * q^74 - 18 * q^76 + 4 * q^77 - 32 * q^78 + 24 * q^79 + 8 * q^81 + 32 * q^82 - 6 * q^83 + 2 * q^84 + 14 * q^86 - 6 * q^87 - 10 * q^88 - 8 * q^89 + 26 * q^91 - 2 * q^92 + 2 * q^93 - 42 * q^94 + 30 * q^96 + 34 * q^97 - 28 * q^98 + 36 * q^99

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 $

$2$	2.37988	1.68283	0.841414	−	0.540391i	$-0.181724\pi$
$2$	2.37988	1.68283	0.841414	+	0.540391i	$0.181724\pi$
$3$	−1.95969	−1.13143	−0.565713	−	0.824602i	$-0.691399\pi$
$3$	−1.95969	−1.13143	−0.565713	+	0.824602i	$0.691399\pi$
$4$	3.66382	1.83191
$5$	0	0
$5$	0	0
$6$	−4.66382	−1.90400
$7$	2.28394	0.863249	0.431624	−	0.902053i	$-0.357941\pi$
$7$	2.28394	0.863249	0.431624	+	0.902053i	$0.357941\pi$
$8$	3.95969	1.39996
$9$	0.840379	0.280126
$10$	0	0
$11$	1.12432	0.338996	0.169498	−	0.985531i	$-0.445785\pi$
$11$	1.12432	0.338996	0.169498	+	0.985531i	$0.445785\pi$
$12$	−7.17995	−2.07267
$13$	5.95969	1.65292	0.826460	−	0.562995i	$-0.190351\pi$
$13$	5.95969	1.65292	0.826460	+	0.562995i	$0.190351\pi$
$14$	5.43550	1.45270
$15$	0	0
$16$	2.09594	0.523984
$17$	5.80007	1.40672	0.703362	−	0.710832i	$-0.251682\pi$
$17$	5.80007	1.40672	0.703362	+	0.710832i	$0.251682\pi$
$18$	2.00000	0.471405
$19$	−4.08401	−0.936936	−0.468468	−	0.883480i	$-0.655194\pi$
$19$	−4.08401	−0.936936	−0.468468	+	0.883480i	$0.655194\pi$
$20$	0	0
$21$	−4.47581	−0.976703
$22$	2.67575	0.570471
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−7.75976	−1.58395
$25$	0	0
$26$	14.1833	2.78158
$27$	4.23218	0.814484
$28$	8.36795	1.58139
$29$	−0.408263	−0.0758125	−0.0379062	−	0.999281i	$-0.512069\pi$
$29$	−0.408263	−0.0758125	−0.0379062	+	0.999281i	$0.512069\pi$
$30$	0	0
$31$	−3.19187	−0.573277	−0.286639	−	0.958039i	$-0.592538\pi$
$31$	−3.19187	−0.573277	−0.286639	+	0.958039i	$0.592538\pi$
$32$	−2.93130	−0.518186
$33$	−2.20332	−0.383549
$34$	13.8035	2.36727
$35$	0	0
$36$	3.07900	0.513166
$37$	−9.80345	−1.61168	−0.805839	−	0.592135i	$-0.798285\pi$
$37$	−9.80345	−1.61168	−0.805839	+	0.592135i	$0.798285\pi$
$38$	−9.71944	−1.57670
$39$	−11.6791	−1.87016
$40$	0	0
$41$	6.27087	0.979345	0.489673	−	0.871906i	$-0.337116\pi$
$41$	6.27087	0.979345	0.489673	+	0.871906i	$0.337116\pi$
$42$	−10.6519	−1.64362
$43$	7.75474	1.18259	0.591294	−	0.806456i	$-0.298617\pi$
$43$	7.75474	1.18259	0.591294	+	0.806456i	$0.298617\pi$
$44$	4.11931	0.621009
$45$	0	0
$46$	−2.37988	−0.350894
$47$	−6.40020	−0.933566	−0.466783	−	0.884372i	$-0.654587\pi$
$47$	−6.40020	−0.933566	−0.466783	+	0.884372i	$0.654587\pi$
$48$	−4.10738	−0.592850
$49$	−1.78361	−0.254801
$50$	0	0
$51$	−11.3663	−1.59160
$52$	21.8352	3.02800
$53$	−6.73590	−0.925247	−0.462624	−	0.886555i	$-0.653092\pi$
$53$	−6.73590	−0.925247	−0.462624	+	0.886555i	$0.653092\pi$
$54$	10.0721	1.37064
$55$	0	0
$56$	9.04370	1.20851
$57$	8.00339	1.06007
$58$	−0.971615	−0.127579
$59$	−4.75976	−0.619667	−0.309834	−	0.950791i	$-0.600273\pi$
$59$	−4.75976	−0.619667	−0.309834	+	0.950791i	$0.600273\pi$
$60$	0	0
$61$	−6.33265	−0.810813	−0.405406	−	0.914137i	$-0.632870\pi$
$61$	−6.33265	−0.810813	−0.405406	+	0.914137i	$0.632870\pi$
$62$	−7.59627	−0.964727
$63$	1.91938	0.241819
$64$	−11.1680	−1.39600
$65$	0	0
$66$	−5.24363	−0.645446
$67$	0.283942	0.0346890	0.0173445	−	0.999850i	$-0.494479\pi$
$67$	0.283942	0.0346890	0.0173445	+	0.999850i	$0.494479\pi$
$68$	21.2504	2.57699
$69$	1.95969	0.235919
$70$	0	0
$71$	−13.9516	−1.65575	−0.827877	−	0.560910i	$-0.810451\pi$
$71$	−13.9516	−1.65575	−0.827877	+	0.560910i	$0.810451\pi$
$72$	3.32764	0.392166
$73$	9.61659	1.12554	0.562769	−	0.826615i	$-0.309736\pi$
$73$	9.61659	1.12554	0.562769	+	0.826615i	$0.309736\pi$
$74$	−23.3310	−2.71218
$75$	0	0
$76$	−14.9631	−1.71638
$77$	2.56788	0.292637
$78$	−27.7949	−3.14715
$79$	4.48387	0.504475	0.252238	−	0.967665i	$-0.418834\pi$
$79$	4.48387	0.504475	0.252238	+	0.967665i	$0.418834\pi$
$80$	0	0
$81$	−10.8149	−1.20166
$82$	14.9239	1.64807
$83$	−10.8223	−1.18790	−0.593951	−	0.804501i	$-0.702433\pi$
$83$	−10.8223	−1.18790	−0.593951	+	0.804501i	$0.702433\pi$
$84$	−16.3986	−1.78923
$85$	0	0
$86$	18.4553	1.99009
$87$	0.800068	0.0857763
$88$	4.45196	0.474581
$89$	5.68414	0.602518	0.301259	−	0.953542i	$-0.402593\pi$
$89$	5.68414	0.602518	0.301259	+	0.953542i	$0.402593\pi$
$90$	0	0
$91$	13.6116	1.42688
$92$	−3.66382	−0.381980
$93$	6.25508	0.648621
$94$	−15.2317	−1.57103
$95$	0	0
$96$	5.74444	0.586290
$97$	11.0676	1.12374	0.561870	−	0.827226i	$-0.310082\pi$
$97$	11.0676	1.12374	0.561870	+	0.827226i	$0.310082\pi$
$98$	−4.24477	−0.428787
$99$	0.944856	0.0949616
$100$	0	0
$101$	1.60014	0.159219	0.0796097	−	0.996826i	$-0.474633\pi$
$101$	1.60014	0.159219	0.0796097	+	0.996826i	$0.474633\pi$
$102$	−27.0505	−2.67840
$103$	1.23218	0.121411	0.0607054	−	0.998156i	$-0.480665\pi$
$103$	1.23218	0.121411	0.0607054	+	0.998156i	$0.480665\pi$
$104$	23.5985	2.31402
$105$	0	0
$106$	−16.0306	−1.55703
$107$	−0.235232	−0.0227408	−0.0113704	−	0.999935i	$-0.503619\pi$
$107$	−0.235232	−0.0227408	−0.0113704	+	0.999935i	$0.503619\pi$
$108$	15.5060	1.49206
$109$	7.43550	0.712192	0.356096	−	0.934449i	$-0.384108\pi$
$109$	7.43550	0.712192	0.356096	+	0.934449i	$0.384108\pi$
$110$	0	0
$111$	19.2117	1.82350
$112$	4.78700	0.452329
$113$	−2.28394	−0.214855	−0.107428	−	0.994213i	$-0.534261\pi$
$113$	−2.28394	−0.214855	−0.107428	+	0.994213i	$0.534261\pi$
$114$	19.0471	1.78392
$115$	0	0
$116$	−1.49580	−0.138882
$117$	5.00840	0.463027
$118$	−11.3276	−1.04279
$119$	13.2470	1.21435
$120$	0	0
$121$	−9.73590	−0.885082
$122$	−15.0709	−1.36446
$123$	−12.2890	−1.10806
$124$	−11.6944	−1.05019
$125$	0	0
$126$	4.56788	0.406939
$127$	−10.2151	−0.906444	−0.453222	−	0.891398i	$-0.649725\pi$
$127$	−10.2151	−0.906444	−0.453222	+	0.891398i	$0.649725\pi$
$128$	−20.7159	−1.83105
$129$	−15.1969	−1.33801
$130$	0	0
$131$	−16.2232	−1.41742	−0.708712	−	0.705498i	$-0.750724\pi$
$131$	−16.2232	−1.41742	−0.708712	+	0.705498i	$0.750724\pi$
$132$	−8.07256	−0.702626
$133$	−9.32764	−0.808809
$134$	0.675747	0.0583756
$135$	0	0
$136$	22.9665	1.96936
$137$	−4.89715	−0.418392	−0.209196	−	0.977874i	$-0.567085\pi$
$137$	−4.89715	−0.418392	−0.209196	+	0.977874i	$0.567085\pi$
$138$	4.66382	0.397011
$139$	4.43889	0.376502	0.188251	−	0.982121i	$-0.439718\pi$
$139$	4.43889	0.376502	0.188251	+	0.982121i	$0.439718\pi$
$140$	0	0
$141$	12.5424	1.05626
$142$	−33.2032	−2.78635
$143$	6.70060	0.560333
$144$	1.76138	0.146782
$145$	0	0
$146$	22.8863	1.89409
$147$	3.49532	0.288289
$148$	−35.9181	−2.95245
$149$	−2.78361	−0.228042	−0.114021	−	0.993478i	$-0.536373\pi$
$149$	−2.78361	−0.228042	−0.114021	+	0.993478i	$0.536373\pi$
$150$	0	0
$151$	11.9278	0.970669	0.485334	−	0.874329i	$-0.338698\pi$
$151$	11.9278	0.970669	0.485334	+	0.874329i	$0.338698\pi$
$152$	−16.1714	−1.31167
$153$	4.87426	0.394060
$154$	6.11125	0.492459
$155$	0	0
$156$	−42.7902	−3.42596
$157$	22.9550	1.83201	0.916005	−	0.401167i	$-0.131395\pi$
$157$	22.9550	1.83201	0.916005	+	0.401167i	$0.131395\pi$
$158$	10.6711	0.848945
$159$	13.2003	1.04685
$160$	0	0
$161$	−2.28394	−0.180000
$162$	−25.7381	−2.02218
$163$	−10.2083	−0.799578	−0.399789	−	0.916607i	$-0.630917\pi$
$163$	−10.2083	−0.799578	−0.399789	+	0.916607i	$0.630917\pi$
$164$	22.9753	1.79407
$165$	0	0
$166$	−25.7557	−1.99903
$167$	6.84715	0.529849	0.264924	−	0.964269i	$-0.414653\pi$
$167$	6.84715	0.529849	0.264924	+	0.964269i	$0.414653\pi$
$168$	−17.7228	−1.36735
$169$	22.5179	1.73215
$170$	0	0
$171$	−3.43212	−0.262461
$172$	28.4120	2.16639
$173$	4.29539	0.326572	0.163286	−	0.986579i	$-0.447791\pi$
$173$	4.29539	0.326572	0.163286	+	0.986579i	$0.447791\pi$
$174$	1.90406	0.144347
$175$	0	0
$176$	2.35651	0.177628
$177$	9.32764	0.701108
$178$	13.5276	1.01393
$179$	−14.8626	−1.11088	−0.555442	−	0.831555i	$-0.687451\pi$
$179$	−14.8626	−1.11088	−0.555442	+	0.831555i	$0.687451\pi$
$180$	0	0
$181$	13.1311	0.976027	0.488013	−	0.872836i	$-0.337722\pi$
$181$	13.1311	0.976027	0.488013	+	0.872836i	$0.337722\pi$
$182$	32.3939	2.40120
$183$	12.4100	0.917375
$184$	−3.95969	−0.291912
$185$	0	0
$186$	14.8863	1.09152
$187$	6.52114	0.476873
$188$	−23.4492	−1.71021
$189$	9.66606	0.703103
$190$	0	0
$191$	13.9819	1.01170	0.505848	−	0.862623i	$-0.331180\pi$
$191$	13.9819	1.01170	0.505848	+	0.862623i	$0.331180\pi$
$192$	21.8858	1.57947
$193$	8.71267	0.627152	0.313576	−	0.949563i	$-0.398473\pi$
$193$	8.71267	0.627152	0.313576	+	0.949563i	$0.398473\pi$
$194$	26.3394	1.89106
$195$	0	0
$196$	−6.53483	−0.466773
$197$	−22.4876	−1.60218	−0.801088	−	0.598547i	$-0.795745\pi$
$197$	−22.4876	−1.60218	−0.801088	+	0.598547i	$0.795745\pi$
$198$	2.24864	0.159804
$199$	9.01078	0.638757	0.319379	−	0.947627i	$-0.396526\pi$
$199$	9.01078	0.638757	0.319379	+	0.947627i	$0.396526\pi$
$200$	0	0
$201$	−0.556437	−0.0392481
$202$	3.80813	0.267939
$203$	−0.932448	−0.0654450
$204$	−41.6442	−2.91568
$205$	0	0
$206$	2.93245	0.204313
$207$	−0.840379	−0.0584104
$208$	12.4911	0.866104
$209$	−4.59174	−0.317617
$210$	0	0
$211$	5.60014	0.385529	0.192765	−	0.981245i	$-0.438255\pi$
$211$	5.60014	0.385529	0.192765	+	0.981245i	$0.438255\pi$
$212$	−24.6791	−1.69497
$213$	27.3408	1.87336
$214$	−0.559824	−0.0382688
$215$	0	0
$216$	16.7581	1.14025
$217$	−7.29005	−0.494881
$218$	17.6956	1.19850
$219$	−18.8455	−1.27346
$220$	0	0
$221$	34.5666	2.32520
$222$	45.7215	3.06863
$223$	−7.06517	−0.473119	−0.236559	−	0.971617i	$-0.576020\pi$
$223$	−7.06517	−0.473119	−0.236559	+	0.971617i	$0.576020\pi$
$224$	−6.69493	−0.447324
$225$	0	0
$226$	−5.43550	−0.361564
$227$	25.1072	1.66643	0.833213	−	0.552952i	$-0.186499\pi$
$227$	25.1072	1.66643	0.833213	+	0.552952i	$0.186499\pi$
$228$	29.3230	1.94196
$229$	−3.20366	−0.211704	−0.105852	−	0.994382i	$-0.533757\pi$
$229$	−3.20366	−0.211704	−0.105852	+	0.994382i	$0.533757\pi$
$230$	0	0
$231$	−5.03225	−0.331098
$232$	−1.61659	−0.106135
$233$	18.6388	1.22107	0.610535	−	0.791989i	$-0.290954\pi$
$233$	18.6388	1.22107	0.610535	+	0.791989i	$0.290954\pi$
$234$	11.9194	0.779194
$235$	0	0
$236$	−17.4389	−1.13518
$237$	−8.78700	−0.570777
$238$	31.5263	2.04355
$239$	3.18185	0.205817	0.102908	−	0.994691i	$-0.467185\pi$
$239$	3.18185	0.205817	0.102908	+	0.994691i	$0.467185\pi$
$240$	0	0
$241$	4.79844	0.309095	0.154547	−	0.987985i	$-0.450608\pi$
$241$	4.79844	0.309095	0.154547	+	0.987985i	$0.450608\pi$
$242$	−23.1703	−1.48944
$243$	8.49728	0.545101
$244$	−23.2017	−1.48534
$245$	0	0
$246$	−29.2462	−1.86467
$247$	−24.3394	−1.54868
$248$	−12.6388	−0.802566
$249$	21.2083	1.34402
$250$	0	0
$251$	−2.24668	−0.141809	−0.0709045	−	0.997483i	$-0.522589\pi$
$251$	−2.24668	−0.141809	−0.0709045	+	0.997483i	$0.522589\pi$
$252$	7.03225	0.442990
$253$	−1.12432	−0.0706855
$254$	−24.3107	−1.52539
$255$	0	0
$256$	−26.9653	−1.68533
$257$	11.0148	0.687086	0.343543	−	0.939137i	$-0.388373\pi$
$257$	11.0148	0.687086	0.343543	+	0.939137i	$0.388373\pi$
$258$	−36.1667	−2.25164
$259$	−22.3905	−1.39128
$260$	0	0
$261$	−0.343095	−0.0212371
$262$	−38.6092	−2.38528
$263$	−11.0585	−0.681898	−0.340949	−	0.940082i	$-0.610748\pi$
$263$	−11.0585	−0.681898	−0.340949	+	0.940082i	$0.610748\pi$
$264$	−8.72446	−0.536953
$265$	0	0
$266$	−22.1986	−1.36109
$267$	−11.1392	−0.681705
$268$	1.04031	0.0635471
$269$	−9.90392	−0.603853	−0.301926	−	0.953331i	$-0.597630\pi$
$269$	−9.90392	−0.603853	−0.301926	+	0.953331i	$0.597630\pi$
$270$	0	0
$271$	4.82655	0.293192	0.146596	−	0.989196i	$-0.453168\pi$
$271$	4.82655	0.293192	0.146596	+	0.989196i	$0.453168\pi$
$272$	12.1566	0.737100
$273$	−26.6745	−1.61441
$274$	−11.6546	−0.704081
$275$	0	0
$276$	7.17995	0.432182
$277$	7.54303	0.453217	0.226608	−	0.973986i	$-0.427236\pi$
$277$	7.54303	0.453217	0.226608	+	0.973986i	$0.427236\pi$
$278$	10.5640	0.633588
$279$	−2.68238	−0.160590
$280$	0	0
$281$	6.01145	0.358613	0.179306	−	0.983793i	$-0.442615\pi$
$281$	6.01145	0.358613	0.179306	+	0.983793i	$0.442615\pi$
$282$	29.8494	1.77751
$283$	−15.6388	−0.929631	−0.464816	−	0.885407i	$-0.653879\pi$
$283$	−15.6388	−0.929631	−0.464816	+	0.885407i	$0.653879\pi$
$284$	−51.1163	−3.03319
$285$	0	0
$286$	15.9466	0.942943
$287$	14.3223	0.845419
$288$	−2.46341	−0.145158
$289$	16.6408	0.978870
$290$	0	0
$291$	−21.6890	−1.27143
$292$	35.2335	2.06188
$293$	−3.21639	−0.187904	−0.0939518	−	0.995577i	$-0.529950\pi$
$293$	−3.21639	−0.187904	−0.0939518	+	0.995577i	$0.529950\pi$
$294$	8.31844	0.485141
$295$	0	0
$296$	−38.8186	−2.25629
$297$	4.75833	0.276106
$298$	−6.62465	−0.383756
$299$	−5.95969	−0.344658
$300$	0	0
$301$	17.7114	1.02087
$302$	28.3867	1.63347
$303$	−3.13577	−0.180145
$304$	−8.55982	−0.490940
$305$	0	0
$306$	11.6001	0.663136
$307$	−34.4702	−1.96732	−0.983659	−	0.180044i	$-0.942376\pi$
$307$	−34.4702	−1.96732	−0.983659	+	0.180044i	$0.942376\pi$
$308$	9.40826	0.536086
$309$	−2.41470	−0.137367
$310$	0	0
$311$	−18.7443	−1.06289	−0.531446	−	0.847092i	$-0.678351\pi$
$311$	−18.7443	−1.06289	−0.531446	+	0.847092i	$0.678351\pi$
$312$	−46.2457	−2.61815
$313$	9.91260	0.560294	0.280147	−	0.959957i	$-0.409617\pi$
$313$	9.91260	0.560294	0.280147	+	0.959957i	$0.409617\pi$
$314$	54.6301	3.08296
$315$	0	0
$316$	16.4281	0.924153
$317$	−9.24024	−0.518984	−0.259492	−	0.965745i	$-0.583555\pi$
$317$	−9.24024	−0.518984	−0.259492	+	0.965745i	$0.583555\pi$
$318$	31.4150	1.76167
$319$	−0.459018	−0.0257001
$320$	0	0
$321$	0.460982	0.0257295
$322$	−5.43550	−0.302909
$323$	−23.6875	−1.31801
$324$	−39.6238	−2.20132
$325$	0	0
$326$	−24.2946	−1.34555
$327$	−14.5713	−0.805793
$328$	24.8307	1.37105
$329$	−14.6177	−0.805899
$330$	0	0
$331$	−23.9684	−1.31742	−0.658712	−	0.752395i	$-0.728898\pi$
$331$	−23.9684	−1.31742	−0.658712	+	0.752395i	$0.728898\pi$
$332$	−39.6509	−2.17613
$333$	−8.23862	−0.451474
$334$	16.2954	0.891644
$335$	0	0
$336$	−9.38102	−0.511777
$337$	9.76477	0.531921	0.265960	−	0.963984i	$-0.414311\pi$
$337$	9.76477	0.531921	0.265960	+	0.963984i	$0.414311\pi$
$338$	53.5898	2.91490
$339$	4.47581	0.243093
$340$	0	0
$341$	−3.58869	−0.194338
$342$	−8.16802	−0.441676
$343$	−20.0613	−1.08321
$344$	30.7064	1.65558
$345$	0	0
$346$	10.2225	0.549565
$347$	1.38441	0.0743190	0.0371595	−	0.999309i	$-0.488169\pi$
$347$	1.38441	0.0743190	0.0371595	+	0.999309i	$0.488169\pi$
$348$	2.93130	0.157134
$349$	−32.3106	−1.72954	−0.864772	−	0.502164i	$-0.832537\pi$
$349$	−32.3106	−1.72954	−0.864772	+	0.502164i	$0.832537\pi$
$350$	0	0
$351$	25.2225	1.34628
$352$	−3.29573	−0.175663
$353$	11.4386	0.608813	0.304406	−	0.952542i	$-0.401542\pi$
$353$	11.4386	0.608813	0.304406	+	0.952542i	$0.401542\pi$
$354$	22.1986	1.17984
$355$	0	0
$356$	20.8257	1.10376
$357$	−25.9600	−1.37395
$358$	−35.3712	−1.86943
$359$	9.95568	0.525441	0.262720	−	0.964872i	$-0.415380\pi$
$359$	9.95568	0.525441	0.262720	+	0.964872i	$0.415380\pi$
$360$	0	0
$361$	−2.32087	−0.122151
$362$	31.2504	1.64248
$363$	19.0793	1.00141
$364$	49.8704	2.61392
$365$	0	0
$366$	29.5343	1.54378
$367$	27.6785	1.44481	0.722403	−	0.691472i	$-0.243037\pi$
$367$	27.6785	1.44481	0.722403	+	0.691472i	$0.243037\pi$
$368$	−2.09594	−0.109258
$369$	5.26991	0.274341
$370$	0	0
$371$	−15.3844	−0.798719
$372$	22.9175	1.18822
$373$	28.7356	1.48787	0.743936	−	0.668251i	$-0.232957\pi$
$373$	28.7356	1.48787	0.743936	+	0.668251i	$0.232957\pi$
$374$	15.5195	0.802495
$375$	0	0
$376$	−25.3428	−1.30696
$377$	−2.43312	−0.125312
$378$	23.0040	1.18320
$379$	−18.2715	−0.938546	−0.469273	−	0.883053i	$-0.655484\pi$
$379$	−18.2715	−0.938546	−0.469273	+	0.883053i	$0.655484\pi$
$380$	0	0
$381$	20.0184	1.02557
$382$	33.2753	1.70251
$383$	−29.0356	−1.48365	−0.741826	−	0.670593i	$-0.766040\pi$
$383$	−29.0356	−1.48365	−0.741826	+	0.670593i	$0.766040\pi$
$384$	40.5967	2.07169
$385$	0	0
$386$	20.7351	1.05539
$387$	6.51693	0.331274
$388$	40.5495	2.05859
$389$	2.86423	0.145222	0.0726112	−	0.997360i	$-0.476867\pi$
$389$	2.86423	0.145222	0.0726112	+	0.997360i	$0.476867\pi$
$390$	0	0
$391$	−5.80007	−0.293322
$392$	−7.06254	−0.356712
$393$	31.7923	1.60371
$394$	−53.5177	−2.69619
$395$	0	0
$396$	3.46178	0.173961
$397$	16.5592	0.831080	0.415540	−	0.909575i	$-0.363593\pi$
$397$	16.5592	0.831080	0.415540	+	0.909575i	$0.363593\pi$
$398$	21.4446	1.07492
$399$	18.2793	0.915108
$400$	0	0
$401$	−3.09479	−0.154547	−0.0772733	−	0.997010i	$-0.524621\pi$
$401$	−3.09479	−0.154547	−0.0772733	+	0.997010i	$0.524621\pi$
$402$	−1.32425	−0.0660477
$403$	−19.0226	−0.947582
$404$	5.86261	0.291676
$405$	0	0
$406$	−2.21911	−0.110133
$407$	−11.0222	−0.546352
$408$	−45.0071	−2.22818
$409$	8.93617	0.441865	0.220933	−	0.975289i	$-0.429090\pi$
$409$	8.93617	0.441865	0.220933	+	0.975289i	$0.429090\pi$
$410$	0	0
$411$	9.59689	0.473379
$412$	4.51450	0.222413
$413$	−10.8710	−0.534927
$414$	−2.00000	−0.0982946
$415$	0	0
$416$	−17.4697	−0.856520
$417$	−8.69884	−0.425984
$418$	−10.9278	−0.534495
$419$	24.1237	1.17852	0.589260	−	0.807944i	$-0.299419\pi$
$419$	24.1237	1.17852	0.589260	+	0.807944i	$0.299419\pi$
$420$	0	0
$421$	23.8602	1.16288	0.581438	−	0.813591i	$-0.302490\pi$
$421$	23.8602	1.16288	0.581438	+	0.813591i	$0.302490\pi$
$422$	13.3276	0.648779
$423$	−5.37860	−0.261516
$424$	−26.6721	−1.29531
$425$	0	0
$426$	65.0679	3.15255
$427$	−14.4634	−0.699933
$428$	−0.861848	−0.0416590
$429$	−13.1311	−0.633975
$430$	0	0
$431$	4.45096	0.214395	0.107198	−	0.994238i	$-0.465812\pi$
$431$	4.45096	0.214395	0.107198	+	0.994238i	$0.465812\pi$
$432$	8.87039	0.426777
$433$	8.10929	0.389707	0.194854	−	0.980832i	$-0.437577\pi$
$433$	8.10929	0.389707	0.194854	+	0.980832i	$0.437577\pi$
$434$	−17.3494	−0.832799
$435$	0	0
$436$	27.2423	1.30467
$437$	4.08401	0.195365
$438$	−44.8501	−2.14302
$439$	4.47180	0.213428	0.106714	−	0.994290i	$-0.465967\pi$
$439$	4.47180	0.213428	0.106714	+	0.994290i	$0.465967\pi$
$440$	0	0
$441$	−1.49891	−0.0713766
$442$	82.2643	3.91291
$443$	9.60047	0.456132	0.228066	−	0.973646i	$-0.426760\pi$
$443$	9.60047	0.456132	0.228066	+	0.973646i	$0.426760\pi$
$444$	70.3883	3.34048
$445$	0	0
$446$	−16.8142	−0.796177
$447$	5.45501	0.258013
$448$	−25.5071	−1.20510
$449$	−6.79944	−0.320886	−0.160443	−	0.987045i	$-0.551292\pi$
$449$	−6.79944	−0.320886	−0.160443	+	0.987045i	$0.551292\pi$
$450$	0	0
$451$	7.05047	0.331994
$452$	−8.36795	−0.393595
$453$	−23.3747	−1.09824
$454$	59.7522	2.80431
$455$	0	0
$456$	31.6909	1.48406
$457$	−19.5582	−0.914894	−0.457447	−	0.889237i	$-0.651236\pi$
$457$	−19.5582	−0.914894	−0.457447	+	0.889237i	$0.651236\pi$
$458$	−7.62431	−0.356261
$459$	24.5470	1.14575
$460$	0	0
$461$	−42.7081	−1.98912	−0.994558	−	0.104184i	$-0.966777\pi$
$461$	−42.7081	−1.98912	−0.994558	+	0.104184i	$0.966777\pi$
$462$	−11.9761	−0.557181
$463$	−7.42209	−0.344934	−0.172467	−	0.985015i	$-0.555174\pi$
$463$	−7.42209	−0.344934	−0.172467	+	0.985015i	$0.555174\pi$
$464$	−0.855693	−0.0397245
$465$	0	0
$466$	44.3581	2.05485
$467$	−22.5041	−1.04136	−0.520682	−	0.853751i	$-0.674322\pi$
$467$	−22.5041	−1.04136	−0.520682	+	0.853751i	$0.674322\pi$
$468$	18.3499	0.848223
$469$	0.648506	0.0299452
$470$	0	0
$471$	−44.9847	−2.07278
$472$	−18.8472	−0.867510
$473$	8.71882	0.400892
$474$	−20.9120	−0.960519
$475$	0	0
$476$	48.5347	2.22458
$477$	−5.66071	−0.259186
$478$	7.57241	0.346354
$479$	−10.1667	−0.464530	−0.232265	−	0.972653i	$-0.574614\pi$
$479$	−10.1667	−0.464530	−0.232265	+	0.972653i	$0.574614\pi$
$480$	0	0
$481$	−58.4255	−2.66398
$482$	11.4197	0.520153
$483$	4.47581	0.203657
$484$	−35.6706	−1.62139
$485$	0	0
$486$	20.2225	0.917311
$487$	34.9917	1.58562	0.792812	−	0.609467i	$-0.208616\pi$
$487$	34.9917	1.58562	0.792812	+	0.609467i	$0.208616\pi$
$488$	−25.0753	−1.13511
$489$	20.0051	0.904664
$490$	0	0
$491$	−2.27087	−0.102483	−0.0512415	−	0.998686i	$-0.516318\pi$
$491$	−2.27087	−0.102483	−0.0512415	+	0.998686i	$0.516318\pi$
$492$	−45.0245	−2.02986
$493$	−2.36795	−0.106647
$494$	−57.9249	−2.60616
$495$	0	0
$496$	−6.68996	−0.300388
$497$	−31.8647	−1.42933
$498$	50.4732	2.26176
$499$	20.9929	0.939773	0.469887	−	0.882727i	$-0.344295\pi$
$499$	20.9929	0.939773	0.469887	+	0.882727i	$0.344295\pi$
$500$	0	0
$501$	−13.4183	−0.599485
$502$	−5.34682	−0.238640
$503$	−18.5041	−0.825055	−0.412528	−	0.910945i	$-0.635354\pi$
$503$	−18.5041	−0.825055	−0.412528	+	0.910945i	$0.635354\pi$
$504$	7.60014	0.338537
$505$	0	0
$506$	−2.67575	−0.118951
$507$	−44.1280	−1.95980
$508$	−37.4263	−1.66052
$509$	−41.8472	−1.85484	−0.927421	−	0.374019i	$-0.877980\pi$
$509$	−41.8472	−1.85484	−0.927421	+	0.374019i	$0.877980\pi$
$510$	0	0
$511$	21.9637	0.971619
$512$	−22.7423	−1.00508
$513$	−17.2843	−0.763120
$514$	26.2140	1.15625
$515$	0	0
$516$	−55.6786	−2.45112
$517$	−7.19588	−0.316475
$518$	−53.2867	−2.34128
$519$	−8.41762	−0.369493
$520$	0	0
$521$	34.1103	1.49440	0.747199	−	0.664600i	$-0.231398\pi$
$521$	34.1103	1.49440	0.747199	+	0.664600i	$0.231398\pi$
$522$	−0.816525	−0.0357383
$523$	36.4755	1.59496	0.797482	−	0.603343i	$-0.206165\pi$
$523$	36.4755	1.59496	0.797482	+	0.603343i	$0.206165\pi$
$524$	−59.4387	−2.59659
$525$	0	0
$526$	−26.3180	−1.14752
$527$	−18.5131	−0.806442
$528$	−4.61802	−0.200973
$529$	1.00000	0.0434783
$530$	0	0
$531$	−4.00000	−0.173585
$532$	−34.1748	−1.48167
$533$	37.3724	1.61878
$534$	−26.5098	−1.14719
$535$	0	0
$536$	1.12432	0.0485633
$537$	29.1261	1.25688
$538$	−23.5701	−1.01618
$539$	−2.00535	−0.0863765
$540$	0	0
$541$	28.2171	1.21315	0.606573	−	0.795028i	$-0.292544\pi$
$541$	28.2171	1.21315	0.606573	+	0.795028i	$0.292544\pi$
$542$	11.4866	0.493392
$543$	−25.7329	−1.10430
$544$	−17.0018	−0.728945
$545$	0	0
$546$	−63.4820	−2.71678
$547$	15.1638	0.648356	0.324178	−	0.945996i	$-0.394912\pi$
$547$	15.1638	0.648356	0.324178	+	0.945996i	$0.394912\pi$
$548$	−17.9423	−0.766456
$549$	−5.32183	−0.227130
$550$	0	0
$551$	1.66735	0.0710314
$552$	7.75976	0.330277
$553$	10.2409	0.435488
$554$	17.9515	0.762686
$555$	0	0
$556$	16.2633	0.689717
$557$	−9.52222	−0.403469	−0.201735	−	0.979440i	$-0.564658\pi$
$557$	−9.52222	−0.403469	−0.201735	+	0.979440i	$0.564658\pi$
$558$	−6.38375	−0.270245
$559$	46.2159	1.95472
$560$	0	0
$561$	−12.7794	−0.539547
$562$	14.3065	0.603484
$563$	32.7494	1.38022	0.690112	−	0.723702i	$-0.257561\pi$
$563$	32.7494	1.38022	0.690112	+	0.723702i	$0.257561\pi$
$564$	45.9531	1.93498
$565$	0	0
$566$	−37.2185	−1.56441
$567$	−24.7006	−1.03733
$568$	−55.2441	−2.31799
$569$	−26.8926	−1.12740	−0.563698	−	0.825981i	$-0.690622\pi$
$569$	−26.8926	−1.12740	−0.563698	+	0.825981i	$0.690622\pi$
$570$	0	0
$571$	0.920000	0.0385008	0.0192504	−	0.999815i	$-0.493872\pi$
$571$	0.920000	0.0385008	0.0192504	+	0.999815i	$0.493872\pi$
$572$	24.5498	1.02648
$573$	−27.4002	−1.14466
$574$	34.0853	1.42269
$575$	0	0
$576$	−9.38537	−0.391057
$577$	42.5888	1.77300	0.886498	−	0.462732i	$-0.153131\pi$
$577$	42.5888	1.77300	0.886498	+	0.462732i	$0.153131\pi$
$578$	39.6030	1.64727
$579$	−17.0741	−0.709576
$580$	0	0
$581$	−24.7175	−1.02545
$582$	−51.6171	−2.13960
$583$	−7.57332	−0.313655
$584$	38.0787	1.57571
$585$	0	0
$586$	−7.65462	−0.316209
$587$	9.51212	0.392607	0.196304	−	0.980543i	$-0.437106\pi$
$587$	9.51212	0.392607	0.196304	+	0.980543i	$0.437106\pi$
$588$	12.8062	0.528120
$589$	13.0356	0.537124
$590$	0	0
$591$	44.0687	1.81274
$592$	−20.5474	−0.844494
$593$	−31.0719	−1.27597	−0.637986	−	0.770048i	$-0.720232\pi$
$593$	−31.0719	−1.27597	−0.637986	+	0.770048i	$0.720232\pi$
$594$	11.3243	0.464640
$595$	0	0
$596$	−10.1986	−0.417753
$597$	−17.6583	−0.722707
$598$	−14.1833	−0.580000
$599$	2.04065	0.0833787	0.0416893	−	0.999131i	$-0.486726\pi$
$599$	2.04065	0.0833787	0.0416893	+	0.999131i	$0.486726\pi$
$600$	0	0
$601$	−25.2377	−1.02947	−0.514733	−	0.857351i	$-0.672109\pi$
$601$	−25.2377	−1.02947	−0.514733	+	0.857351i	$0.672109\pi$
$602$	42.1509	1.71794
$603$	0.238619	0.00971731
$604$	43.7012	1.77818
$605$	0	0
$606$	−7.46274	−0.303153
$607$	10.4305	0.423361	0.211680	−	0.977339i	$-0.432106\pi$
$607$	10.4305	0.423361	0.211680	+	0.977339i	$0.432106\pi$
$608$	11.9715	0.485507
$609$	1.82731	0.0740463
$610$	0	0
$611$	−38.1432	−1.54311
$612$	17.8584	0.721883
$613$	−4.97745	−0.201037	−0.100519	−	0.994935i	$-0.532050\pi$
$613$	−4.97745	−0.201037	−0.100519	+	0.994935i	$0.532050\pi$
$614$	−82.0348	−3.31066
$615$	0	0
$616$	10.1680	0.409681
$617$	30.5881	1.23143	0.615715	−	0.787969i	$-0.288867\pi$
$617$	30.5881	1.23143	0.615715	+	0.787969i	$0.288867\pi$
$618$	−5.74669	−0.231166
$619$	−48.0404	−1.93091	−0.965453	−	0.260579i	$-0.916087\pi$
$619$	−48.0404	−1.93091	−0.965453	+	0.260579i	$0.916087\pi$
$620$	0	0
$621$	−4.23218	−0.169832
$622$	−44.6092	−1.78866
$623$	12.9823	0.520123
$624$	−24.4787	−0.979933
$625$	0	0
$626$	23.5908	0.942878
$627$	8.99837	0.359360
$628$	84.1030	3.35608
$629$	−56.8607	−2.26718
$630$	0	0
$631$	10.6157	0.422605	0.211303	−	0.977421i	$-0.432229\pi$
$631$	10.6157	0.422605	0.211303	+	0.977421i	$0.432229\pi$
$632$	17.7547	0.706246
$633$	−10.9745	−0.436198
$634$	−21.9907	−0.873360
$635$	0	0
$636$	48.3634	1.91773
$637$	−10.6298	−0.421166
$638$	−1.09241	−0.0432488
$639$	−11.7247	−0.463820
$640$	0	0
$641$	3.47844	0.137390	0.0686951	−	0.997638i	$-0.478116\pi$
$641$	3.47844	0.137390	0.0686951	+	0.997638i	$0.478116\pi$
$642$	1.09708	0.0432983
$643$	2.05348	0.0809813	0.0404906	−	0.999180i	$-0.487108\pi$
$643$	2.05348	0.0809813	0.0404906	+	0.999180i	$0.487108\pi$
$644$	−8.36795	−0.329743
$645$	0	0
$646$	−56.3734	−2.21798
$647$	−19.3408	−0.760367	−0.380184	−	0.924911i	$-0.624139\pi$
$647$	−19.3408	−0.760367	−0.380184	+	0.924911i	$0.624139\pi$
$648$	−42.8236	−1.68227
$649$	−5.35149	−0.210064
$650$	0	0
$651$	14.2862	0.559922
$652$	−37.4015	−1.46476
$653$	21.9288	0.858139	0.429070	−	0.903271i	$-0.358841\pi$
$653$	21.9288	0.858139	0.429070	+	0.903271i	$0.358841\pi$
$654$	−34.6778	−1.35601
$655$	0	0
$656$	13.1433	0.513161
$657$	8.08158	0.315293
$658$	−34.7883	−1.35619
$659$	38.1351	1.48553	0.742767	−	0.669550i	$-0.233513\pi$
$659$	38.1351	1.48553	0.742767	+	0.669550i	$0.233513\pi$
$660$	0	0
$661$	−28.9007	−1.12411	−0.562053	−	0.827101i	$-0.689988\pi$
$661$	−28.9007	−1.12411	−0.562053	+	0.827101i	$0.689988\pi$
$662$	−57.0419	−2.21700
$663$	−67.7398	−2.63079
$664$	−42.8529	−1.66302
$665$	0	0
$666$	−19.6069	−0.759752
$667$	0.408263	0.0158080
$668$	25.0867	0.970635
$669$	13.8455	0.535299
$670$	0	0
$671$	−7.11993	−0.274862
$672$	13.1200	0.506114
$673$	49.5051	1.90828	0.954140	−	0.299361i	$-0.0967735\pi$
$673$	49.5051	1.90828	0.954140	+	0.299361i	$0.0967735\pi$
$674$	23.2390	0.895131
$675$	0	0
$676$	82.5015	3.17313
$677$	6.87426	0.264199	0.132100	−	0.991236i	$-0.457828\pi$
$677$	6.87426	0.264199	0.132100	+	0.991236i	$0.457828\pi$
$678$	10.6519	0.409083
$679$	25.2776	0.970067
$680$	0	0
$681$	−49.2024	−1.88544
$682$	−8.54064	−0.327038
$683$	−36.9887	−1.41533	−0.707666	−	0.706547i	$-0.750252\pi$
$683$	−36.9887	−1.41533	−0.707666	+	0.706547i	$0.750252\pi$
$684$	−12.5747	−0.480804
$685$	0	0
$686$	−47.7433	−1.82285
$687$	6.27817	0.239527
$688$	16.2535	0.619657
$689$	−40.1439	−1.52936
$690$	0	0
$691$	38.5485	1.46645	0.733227	−	0.679984i	$-0.238013\pi$
$691$	38.5485	1.46645	0.733227	+	0.679984i	$0.238013\pi$
$692$	15.7375	0.598251
$693$	2.15800	0.0819755
$694$	3.29472	0.125066
$695$	0	0
$696$	3.16802	0.120083
$697$	36.3715	1.37767
$698$	−76.8952	−2.91053
$699$	−36.5263	−1.38155
$700$	0	0
$701$	−36.3146	−1.37158	−0.685791	−	0.727798i	$-0.740544\pi$
$701$	−36.3146	−1.37158	−0.685791	+	0.727798i	$0.740544\pi$
$702$	60.0265	2.26555
$703$	40.0374	1.51004
$704$	−12.5564	−0.473239
$705$	0	0
$706$	27.2224	1.02453
$707$	3.65462	0.137446
$708$	34.1748	1.28437
$709$	−3.24463	−0.121855	−0.0609274	−	0.998142i	$-0.519406\pi$
$709$	−3.24463	−0.121855	−0.0609274	+	0.998142i	$0.519406\pi$
$710$	0	0
$711$	3.76815	0.141317
$712$	22.5074	0.843502
$713$	3.19187	0.119537
$714$	−61.7817	−2.31212
$715$	0	0
$716$	−54.4539	−2.03504
$717$	−6.23543	−0.232867
$718$	23.6933	0.884226
$719$	10.4214	0.388654	0.194327	−	0.980937i	$-0.437748\pi$
$719$	10.4214	0.388654	0.194327	+	0.980937i	$0.437748\pi$
$720$	0	0
$721$	2.81424	0.104808
$722$	−5.52338	−0.205559
$723$	−9.40345	−0.349718
$724$	48.1100	1.78799
$725$	0	0
$726$	45.4065	1.68519
$727$	−9.67651	−0.358882	−0.179441	−	0.983769i	$-0.557429\pi$
$727$	−9.67651	−0.358882	−0.179441	+	0.983769i	$0.557429\pi$
$728$	53.8976	1.99758
$729$	15.7927	0.584914
$730$	0	0
$731$	44.9780	1.66357
$732$	45.4681	1.68055
$733$	15.5782	0.575396	0.287698	−	0.957721i	$-0.407110\pi$
$733$	15.5782	0.575396	0.287698	+	0.957721i	$0.407110\pi$
$734$	65.8715	2.43136
$735$	0	0
$736$	2.93130	0.108049
$737$	0.319242	0.0117594
$738$	12.5417	0.461668
$739$	14.4328	0.530919	0.265459	−	0.964122i	$-0.414476\pi$
$739$	14.4328	0.530919	0.265459	+	0.964122i	$0.414476\pi$
$740$	0	0
$741$	47.6977	1.75222
$742$	−36.6130	−1.34411
$743$	−4.50305	−0.165201	−0.0826005	−	0.996583i	$-0.526323\pi$
$743$	−4.50305	−0.165201	−0.0826005	+	0.996583i	$0.526323\pi$
$744$	24.7682	0.908045
$745$	0	0
$746$	68.3872	2.50383
$747$	−9.09483	−0.332763
$748$	23.8923	0.873588
$749$	−0.537257	−0.0196309
$750$	0	0
$751$	18.5451	0.676721	0.338361	−	0.941017i	$-0.390128\pi$
$751$	18.5451	0.676721	0.338361	+	0.941017i	$0.390128\pi$
$752$	−13.4144	−0.489174
$753$	4.40279	0.160447
$754$	−5.79053	−0.210878
$755$	0	0
$756$	35.4147	1.28802
$757$	−27.0366	−0.982663	−0.491332	−	0.870973i	$-0.663490\pi$
$757$	−27.0366	−0.982663	−0.491332	+	0.870973i	$0.663490\pi$
$758$	−43.4840	−1.57941
$759$	2.20332	0.0799754
$760$	0	0
$761$	15.4066	0.558490	0.279245	−	0.960220i	$-0.409916\pi$
$761$	15.4066	0.558490	0.279245	+	0.960220i	$0.409916\pi$
$762$	47.6414	1.72587
$763$	16.9823	0.614799
$764$	51.2272	1.85334
$765$	0	0
$766$	−69.1013	−2.49673
$767$	−28.3667	−1.02426
$768$	52.8436	1.90683
$769$	15.1216	0.545299	0.272650	−	0.962113i	$-0.412100\pi$
$769$	15.1216	0.545299	0.272650	+	0.962113i	$0.412100\pi$
$770$	0	0
$771$	−21.5856	−0.777388
$772$	31.9217	1.14889
$773$	−28.7131	−1.03274	−0.516370	−	0.856366i	$-0.672717\pi$
$773$	−28.7131	−1.03274	−0.516370	+	0.856366i	$0.672717\pi$
$774$	15.5095	0.557477
$775$	0	0
$776$	43.8241	1.57319
$777$	43.8784	1.57413
$778$	6.81653	0.244384
$779$	−25.6103	−0.917584
$780$	0	0
$781$	−15.6861	−0.561293
$782$	−13.8035	−0.493611
$783$	−1.72784	−0.0617481
$784$	−3.73833	−0.133512
$785$	0	0
$786$	75.6619	2.69877
$787$	−16.3131	−0.581501	−0.290750	−	0.956799i	$-0.593905\pi$
$787$	−16.3131	−0.581501	−0.290750	+	0.956799i	$0.593905\pi$
$788$	−82.3905	−2.93504
$789$	21.6713	0.771518
$790$	0	0
$791$	−5.21639	−0.185473
$792$	3.74134	0.132943
$793$	−37.7406	−1.34021
$794$	39.4088	1.39857
$795$	0	0
$796$	33.0139	1.17015
$797$	2.88374	0.102147	0.0510736	−	0.998695i	$-0.483736\pi$
$797$	2.88374	0.102147	0.0510736	+	0.998695i	$0.483736\pi$
$798$	43.5024	1.53997
$799$	−37.1216	−1.31327
$800$	0	0
$801$	4.77684	0.168781
$802$	−7.36523	−0.260075
$803$	10.8121	0.381552
$804$	−2.03869	−0.0718989
$805$	0	0
$806$	−45.2714	−1.59462
$807$	19.4086	0.683215
$808$	6.33604	0.222901
$809$	39.7878	1.39886	0.699432	−	0.714699i	$-0.253436\pi$
$809$	39.7878	1.39886	0.699432	+	0.714699i	$0.253436\pi$
$810$	0	0
$811$	38.5454	1.35351	0.676756	−	0.736208i	$-0.263385\pi$
$811$	38.5454	1.35351	0.676756	+	0.736208i	$0.263385\pi$
$812$	−3.41632	−0.119889
$813$	−9.45853	−0.331725
$814$	−26.2316	−0.919416
$815$	0	0
$816$	−23.8231	−0.833975
$817$	−31.6705	−1.10801
$818$	21.2670	0.743583
$819$	11.4389	0.399707
$820$	0	0
$821$	−16.3428	−0.570368	−0.285184	−	0.958473i	$-0.592055\pi$
$821$	−16.3428	−0.570368	−0.285184	+	0.958473i	$0.592055\pi$
$822$	22.8394	0.796616
$823$	38.6446	1.34707	0.673534	−	0.739157i	$-0.264776\pi$
$823$	38.6446	1.34707	0.673534	+	0.739157i	$0.264776\pi$
$824$	4.87907	0.169970
$825$	0	0
$826$	−25.8717	−0.900191
$827$	21.6969	0.754474	0.377237	−	0.926117i	$-0.376874\pi$
$827$	21.6969	0.754474	0.377237	+	0.926117i	$0.376874\pi$
$828$	−3.07900	−0.107003
$829$	13.9429	0.484259	0.242129	−	0.970244i	$-0.422154\pi$
$829$	13.9429	0.484259	0.242129	+	0.970244i	$0.422154\pi$
$830$	0	0
$831$	−14.7820	−0.512781
$832$	−66.5579	−2.30748
$833$	−10.3451	−0.358435
$834$	−20.7022	−0.716858
$835$	0	0
$836$	−16.8233	−0.581846
$837$	−13.5086	−0.466925
$838$	57.4115	1.98325
$839$	52.4484	1.81072	0.905360	−	0.424644i	$-0.139601\pi$
$839$	52.4484	1.81072	0.905360	+	0.424644i	$0.139601\pi$
$840$	0	0
$841$	−28.8333	−0.994252
$842$	56.7844	1.95692
$843$	−11.7806	−0.405744
$844$	20.5179	0.706255
$845$	0	0
$846$	−12.8004	−0.440087
$847$	−22.2362	−0.764046
$848$	−14.1180	−0.484815
$849$	30.6472	1.05181
$850$	0	0
$851$	9.80345	0.336058
$852$	100.172	3.43183
$853$	30.4634	1.04305	0.521524	−	0.853237i	$-0.325364\pi$
$853$	30.4634	1.04305	0.521524	+	0.853237i	$0.325364\pi$
$854$	−34.4211	−1.17787
$855$	0	0
$856$	−0.931446	−0.0318362
$857$	−42.4911	−1.45147	−0.725735	−	0.687975i	$-0.758500\pi$
$857$	−42.4911	−1.45147	−0.725735	+	0.687975i	$0.758500\pi$
$858$	−31.2504	−1.06687
$859$	−15.5856	−0.531775	−0.265888	−	0.964004i	$-0.585665\pi$
$859$	−15.5856	−0.531775	−0.265888	+	0.964004i	$0.585665\pi$
$860$	0	0
$861$	−28.0673	−0.956529
$862$	10.5927	0.360790
$863$	50.8852	1.73215	0.866076	−	0.499913i	$-0.166635\pi$
$863$	50.8852	1.73215	0.866076	+	0.499913i	$0.166635\pi$
$864$	−12.4058	−0.422055
$865$	0	0
$866$	19.2991	0.655811
$867$	−32.6108	−1.10752
$868$	−26.7094	−0.906577
$869$	5.04131	0.171015
$870$	0	0
$871$	1.69220	0.0573382
$872$	29.4423	0.997041
$873$	9.30094	0.314789
$874$	9.71944	0.328765
$875$	0	0
$876$	−69.0466	−2.33287
$877$	−30.1080	−1.01667	−0.508337	−	0.861158i	$-0.669740\pi$
$877$	−30.1080	−1.01667	−0.508337	+	0.861158i	$0.669740\pi$
$878$	10.6424	0.359162
$879$	6.30312	0.212599
$880$	0	0
$881$	20.2245	0.681379	0.340690	−	0.940176i	$-0.389339\pi$
$881$	20.2245	0.681379	0.340690	+	0.940176i	$0.389339\pi$
$882$	−3.56722	−0.120115
$883$	−30.6482	−1.03139	−0.515697	−	0.856771i	$-0.672467\pi$
$883$	−30.6482	−1.03139	−0.515697	+	0.856771i	$0.672467\pi$
$884$	126.646	4.25956
$885$	0	0
$886$	22.8480	0.767592
$887$	14.0064	0.470290	0.235145	−	0.971960i	$-0.424443\pi$
$887$	14.0064	0.470290	0.235145	+	0.971960i	$0.424443\pi$
$888$	76.0724	2.55282
$889$	−23.3307	−0.782487
$890$	0	0
$891$	−12.1594	−0.407356
$892$	−25.8855	−0.866711
$893$	26.1385	0.874691
$894$	12.9823	0.434192
$895$	0	0
$896$	−47.3139	−1.58065
$897$	11.6791	0.389955
$898$	−16.1818	−0.539995
$899$	1.30312	0.0434616
$900$	0	0
$901$	−39.0687	−1.30157
$902$	16.7793	0.558688
$903$	−34.7088	−1.15504
$904$	−9.04370	−0.300789
$905$	0	0
$906$	−55.6290	−1.84815
$907$	−36.4739	−1.21109	−0.605547	−	0.795809i	$-0.707046\pi$
$907$	−36.4739	−1.21109	−0.605547	+	0.795809i	$0.707046\pi$
$908$	91.9884	3.05274
$909$	1.34472	0.0446016
$910$	0	0
$911$	−14.2327	−0.471549	−0.235775	−	0.971808i	$-0.575763\pi$
$911$	−14.2327	−0.471549	−0.235775	+	0.971808i	$0.575763\pi$
$912$	16.7746	0.555462
$913$	−12.1677	−0.402693
$914$	−46.5461	−1.53961
$915$	0	0
$916$	−11.7376	−0.387822
$917$	−37.0528	−1.22359
$918$	58.4188	1.92811
$919$	34.3246	1.13226	0.566132	−	0.824315i	$-0.308439\pi$
$919$	34.3246	1.13226	0.566132	+	0.824315i	$0.308439\pi$
$920$	0	0
$921$	67.5508	2.22588
$922$	−101.640	−3.34734
$923$	−83.1474	−2.73683
$924$	−18.4373	−0.606541
$925$	0	0
$926$	−17.6637	−0.580464
$927$	1.03550	0.0340103
$928$	1.19674	0.0392850
$929$	6.14579	0.201637	0.100818	−	0.994905i	$-0.467854\pi$
$929$	6.14579	0.201637	0.100818	+	0.994905i	$0.467854\pi$
$930$	0	0
$931$	7.28428	0.238733
$932$	68.2893	2.23689
$933$	36.7330	1.20258
$934$	−53.5569	−1.75244
$935$	0	0
$936$	19.8317	0.648219
$937$	18.4581	0.602998	0.301499	−	0.953466i	$-0.402513\pi$
$937$	18.4581	0.602998	0.301499	+	0.953466i	$0.402513\pi$
$938$	1.54337	0.0503927
$939$	−19.4256	−0.633931
$940$	0	0
$941$	30.7623	1.00282	0.501411	−	0.865209i	$-0.332815\pi$
$941$	30.7623	1.00282	0.501411	+	0.865209i	$0.332815\pi$
$942$	−107.058	−3.48814
$943$	−6.27087	−0.204208
$944$	−9.97615	−0.324696
$945$	0	0
$946$	20.7497	0.674632
$947$	11.4692	0.372698	0.186349	−	0.982484i	$-0.440334\pi$
$947$	11.4692	0.372698	0.186349	+	0.982484i	$0.440334\pi$
$948$	−32.1940	−1.04561
$949$	57.3119	1.86042
$950$	0	0
$951$	18.1080	0.587192
$952$	52.4541	1.70005
$953$	2.40664	0.0779586	0.0389793	−	0.999240i	$-0.487589\pi$
$953$	2.40664	0.0779586	0.0389793	+	0.999240i	$0.487589\pi$
$954$	−13.4718	−0.436166
$955$	0	0
$956$	11.6577	0.377038
$957$	0.899533	0.0290778
$958$	−24.1956	−0.781724
$959$	−11.1848	−0.361176
$960$	0	0
$961$	−20.8119	−0.671353
$962$	−139.046	−4.48301
$963$	−0.197684	−0.00637029
$964$	17.5806	0.566234
$965$	0	0
$966$	10.6519	0.342719
$967$	57.4766	1.84832	0.924162	−	0.382001i	$-0.124765\pi$
$967$	57.4766	1.84832	0.924162	+	0.382001i	$0.124765\pi$
$968$	−38.5511	−1.23908
$969$	46.4202	1.49123
$970$	0	0
$971$	53.1909	1.70698	0.853489	−	0.521111i	$-0.174482\pi$
$971$	53.1909	1.70698	0.853489	+	0.521111i	$0.174482\pi$
$972$	31.1325	0.998576
$973$	10.1382	0.325015
$974$	83.2759	2.66833
$975$	0	0
$976$	−13.2728	−0.424853
$977$	54.4716	1.74270	0.871350	−	0.490661i	$-0.163245\pi$
$977$	54.4716	1.74270	0.871350	+	0.490661i	$0.163245\pi$
$978$	47.6098	1.52239
$979$	6.39080	0.204251
$980$	0	0
$981$	6.24864	0.199504
$982$	−5.40440	−0.172461
$983$	37.5908	1.19896	0.599480	−	0.800390i	$-0.295374\pi$
$983$	37.5908	1.19896	0.599480	+	0.800390i	$0.295374\pi$
$984$	−48.6604	−1.55124
$985$	0	0
$986$	−5.63544	−0.179469
$987$	28.6461	0.911816
$988$	−89.1753	−2.83704
$989$	−7.75474	−0.246587
$990$	0	0
$991$	14.0545	0.446455	0.223228	−	0.974766i	$-0.428341\pi$
$991$	14.0545	0.446455	0.223228	+	0.974766i	$0.428341\pi$
$992$	9.35635	0.297064
$993$	46.9706	1.49057
$994$	−75.8341	−2.40531
$995$	0	0
$996$	77.7035	2.46213
$997$	10.9378	0.346404	0.173202	−	0.984886i	$-0.444589\pi$
$997$	10.9378	0.346404	0.173202	+	0.984886i	$0.444589\pi$
$998$	49.9606	1.58148
$999$	−41.4900	−1.31269

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.2.a.j.1.4		4
3.2	odd	2		5175.2.a.bw.1.1		4
4.3	odd	2		9200.2.a.ck.1.4		4
5.2	odd	4		115.2.b.b.24.8	yes	8
5.3	odd	4		115.2.b.b.24.1	✓	8
5.4	even	2		575.2.a.i.1.1		4
15.2	even	4		1035.2.b.e.829.1		8
15.8	even	4		1035.2.b.e.829.8		8
15.14	odd	2		5175.2.a.bv.1.4		4
20.3	even	4		1840.2.e.d.369.7		8
20.7	even	4		1840.2.e.d.369.2		8
20.19	odd	2		9200.2.a.cq.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.b.b.24.1	✓	8	5.3	odd	4
115.2.b.b.24.8	yes	8	5.2	odd	4
575.2.a.i.1.1		4	5.4	even	2
575.2.a.j.1.4		4	1.1	even	1	trivial
1035.2.b.e.829.1		8	15.2	even	4
1035.2.b.e.829.8		8	15.8	even	4
1840.2.e.d.369.2		8	20.7	even	4
1840.2.e.d.369.7		8	20.3	even	4
5175.2.a.bv.1.4		4	15.14	odd	2
5175.2.a.bw.1.1		4	3.2	odd	2
9200.2.a.ck.1.4		4	4.3	odd	2
9200.2.a.cq.1.1		4	20.19	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:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.a (trivial)

\(f(q)\)	\(=\)	\(q+2.37988 q^{2} -1.95969 q^{3} +3.66382 q^{4} -4.66382 q^{6} +2.28394 q^{7} +3.95969 q^{8} +0.840379 q^{9} +O(q^{10})\)	\(q+2.37988 q^{2} -1.95969 q^{3} +3.66382 q^{4} -4.66382 q^{6} +2.28394 q^{7} +3.95969 q^{8} +0.840379 q^{9} +1.12432 q^{11} -7.17995 q^{12} +5.95969 q^{13} +5.43550 q^{14} +2.09594 q^{16} +5.80007 q^{17} +2.00000 q^{18} -4.08401 q^{19} -4.47581 q^{21} +2.67575 q^{22} -1.00000 q^{23} -7.75976 q^{24} +14.1833 q^{26} +4.23218 q^{27} +8.36795 q^{28} -0.408263 q^{29} -3.19187 q^{31} -2.93130 q^{32} -2.20332 q^{33} +13.8035 q^{34} +3.07900 q^{36} -9.80345 q^{37} -9.71944 q^{38} -11.6791 q^{39} +6.27087 q^{41} -10.6519 q^{42} +7.75474 q^{43} +4.11931 q^{44} -2.37988 q^{46} -6.40020 q^{47} -4.10738 q^{48} -1.78361 q^{49} -11.3663 q^{51} +21.8352 q^{52} -6.73590 q^{53} +10.0721 q^{54} +9.04370 q^{56} +8.00339 q^{57} -0.971615 q^{58} -4.75976 q^{59} -6.33265 q^{61} -7.59627 q^{62} +1.91938 q^{63} -11.1680 q^{64} -5.24363 q^{66} +0.283942 q^{67} +21.2504 q^{68} +1.95969 q^{69} -13.9516 q^{71} +3.32764 q^{72} +9.61659 q^{73} -23.3310 q^{74} -14.9631 q^{76} +2.56788 q^{77} -27.7949 q^{78} +4.48387 q^{79} -10.8149 q^{81} +14.9239 q^{82} -10.8223 q^{83} -16.3986 q^{84} +18.4553 q^{86} +0.800068 q^{87} +4.45196 q^{88} +5.68414 q^{89} +13.6116 q^{91} -3.66382 q^{92} +6.25508 q^{93} -15.2317 q^{94} +5.74444 q^{96} +11.0676 q^{97} -4.24477 q^{98} +0.944856 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{4} - 6 q^{6} + 6 q^{7} + 6 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 2 * q^4 - 6 * q^6 + 6 * q^7 + 6 * q^8 + 4 * q^9	\( 4 q + 2 q^{3} + 2 q^{4} - 6 q^{6} + 6 q^{7} + 6 q^{8} + 4 q^{9} + 2 q^{11} - 10 q^{12} + 14 q^{13} - 4 q^{14} + 2 q^{16} + 14 q^{17} + 8 q^{18} - 4 q^{19} - 2 q^{21} + 4 q^{22} - 4 q^{23} - 12 q^{24} + 6 q^{26} + 14 q^{27} + 18 q^{28} + 4 q^{29} + 2 q^{32} + 14 q^{33} + 14 q^{34} - 8 q^{36} + 2 q^{37} - 10 q^{38} - 8 q^{39} - 8 q^{41} - 24 q^{42} + 4 q^{43} + 6 q^{44} + 2 q^{47} + 10 q^{51} + 18 q^{52} + 4 q^{53} + 22 q^{54} + 14 q^{56} - 8 q^{61} - 28 q^{62} - 12 q^{63} - 20 q^{64} - 8 q^{66} - 2 q^{67} + 8 q^{68} - 2 q^{69} - 24 q^{71} - 12 q^{72} + 18 q^{73} - 36 q^{74} - 18 q^{76} + 4 q^{77} - 32 q^{78} + 24 q^{79} + 8 q^{81} + 32 q^{82} - 6 q^{83} + 2 q^{84} + 14 q^{86} - 6 q^{87} - 10 q^{88} - 8 q^{89} + 26 q^{91} - 2 q^{92} + 2 q^{93} - 42 q^{94} + 30 q^{96} + 34 q^{97} - 28 q^{98} + 36 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^4 - 6 * q^6 + 6 * q^7 + 6 * q^8 + 4 * q^9 + 2 * q^11 - 10 * q^12 + 14 * q^13 - 4 * q^14 + 2 * q^16 + 14 * q^17 + 8 * q^18 - 4 * q^19 - 2 * q^21 + 4 * q^22 - 4 * q^23 - 12 * q^24 + 6 * q^26 + 14 * q^27 + 18 * q^28 + 4 * q^29 + 2 * q^32 + 14 * q^33 + 14 * q^34 - 8 * q^36 + 2 * q^37 - 10 * q^38 - 8 * q^39 - 8 * q^41 - 24 * q^42 + 4 * q^43 + 6 * q^44 + 2 * q^47 + 10 * q^51 + 18 * q^52 + 4 * q^53 + 22 * q^54 + 14 * q^56 - 8 * q^61 - 28 * q^62 - 12 * q^63 - 20 * q^64 - 8 * q^66 - 2 * q^67 + 8 * q^68 - 2 * q^69 - 24 * q^71 - 12 * q^72 + 18 * q^73 - 36 * q^74 - 18 * q^76 + 4 * q^77 - 32 * q^78 + 24 * q^79 + 8 * q^81 + 32 * q^82 - 6 * q^83 + 2 * q^84 + 14 * q^86 - 6 * q^87 - 10 * q^88 - 8 * q^89 + 26 * q^91 - 2 * q^92 + 2 * q^93 - 42 * q^94 + 30 * q^96 + 34 * q^97 - 28 * q^98 + 36 * q^99

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