LMFDB - Embedded newform 1925.2.a.bf.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1925,2,Mod(1,1925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1925, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1925.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1925 = 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1925.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:	$15.3712023891$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} - 7x^{6} + 30x^{5} + 24x^{4} - 66x^{3} - 42x^{2} + 34x + 14 $ x^8 - 4x^7 - 7x^6 + 30x^5 + 24x^4 - 66x^3 - 42x^2 + 34*x + 14
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 385)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-1.43000$ of defining polynomial
Character	$\chi$	$=$	1925.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.43000 q^{2} -2.50028 q^{3} +3.90488 q^{4} -6.07568 q^{6} +1.00000 q^{7} +4.62886 q^{8} +3.25142 q^{9} +O(q^{10})$	\(q+2.43000 q^{2} -2.50028 q^{3} +3.90488 q^{4} -6.07568 q^{6} +1.00000 q^{7} +4.62886 q^{8} +3.25142 q^{9} +1.00000 q^{11} -9.76332 q^{12} +2.18879 q^{13} +2.43000 q^{14} +3.43835 q^{16} +1.02233 q^{17} +7.90095 q^{18} -5.00442 q^{19} -2.50028 q^{21} +2.43000 q^{22} +7.86206 q^{23} -11.5735 q^{24} +5.31876 q^{26} -0.628633 q^{27} +3.90488 q^{28} -0.713907 q^{29} +6.58245 q^{31} -0.902538 q^{32} -2.50028 q^{33} +2.48427 q^{34} +12.6964 q^{36} +10.3830 q^{37} -12.1607 q^{38} -5.47261 q^{39} -3.45322 q^{41} -6.07568 q^{42} +10.8383 q^{43} +3.90488 q^{44} +19.1048 q^{46} -8.10803 q^{47} -8.59686 q^{48} +1.00000 q^{49} -2.55613 q^{51} +8.54699 q^{52} -4.48118 q^{53} -1.52757 q^{54} +4.62886 q^{56} +12.5125 q^{57} -1.73479 q^{58} +4.20757 q^{59} -6.44231 q^{61} +15.9953 q^{62} +3.25142 q^{63} -9.06987 q^{64} -6.07568 q^{66} +10.6283 q^{67} +3.99210 q^{68} -19.6574 q^{69} -5.41259 q^{71} +15.0504 q^{72} +7.84020 q^{73} +25.2307 q^{74} -19.5417 q^{76} +1.00000 q^{77} -13.2984 q^{78} +4.86426 q^{79} -8.18251 q^{81} -8.39130 q^{82} +8.48523 q^{83} -9.76332 q^{84} +26.3371 q^{86} +1.78497 q^{87} +4.62886 q^{88} +13.4233 q^{89} +2.18879 q^{91} +30.7004 q^{92} -16.4580 q^{93} -19.7025 q^{94} +2.25660 q^{96} -10.5599 q^{97} +2.43000 q^{98} +3.25142 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 6 q^{3} + 14 q^{4} - 6 q^{6} + 8 q^{7} + 12 q^{8} + 10 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 + 6 * q^3 + 14 * q^4 - 6 * q^6 + 8 * q^7 + 12 * q^8 + 10 * q^9	$ 8 q + 4 q^{2} + 6 q^{3} + 14 q^{4} - 6 q^{6} + 8 q^{7} + 12 q^{8} + 10 q^{9} + 8 q^{11} + 12 q^{12} + 6 q^{13} + 4 q^{14} + 18 q^{16} + 6 q^{17} + 6 q^{18} - 6 q^{19} + 6 q^{21} + 4 q^{22} + 4 q^{23} + 6 q^{24} - 4 q^{26} + 24 q^{27} + 14 q^{28} + 4 q^{29} - 14 q^{31} + 18 q^{32} + 6 q^{33} - 6 q^{34} + 18 q^{36} + 10 q^{37} - 30 q^{38} + 16 q^{39} - 4 q^{41} - 6 q^{42} + 34 q^{43} + 14 q^{44} - 24 q^{46} - 8 q^{47} + 12 q^{48} + 8 q^{49} + 16 q^{51} + 46 q^{52} + 18 q^{53} + 6 q^{54} + 12 q^{56} + 6 q^{57} - 6 q^{58} - 40 q^{59} + 26 q^{62} + 10 q^{63} + 10 q^{64} - 6 q^{66} + 42 q^{67} + 16 q^{68} - 50 q^{69} + 6 q^{71} + 28 q^{72} + 40 q^{73} - 44 q^{76} + 8 q^{77} - 76 q^{78} + 12 q^{79} + 40 q^{81} + 42 q^{82} + 2 q^{83} + 12 q^{84} + 44 q^{86} + 2 q^{87} + 12 q^{88} + 22 q^{89} + 6 q^{91} + 6 q^{92} - 32 q^{93} - 50 q^{94} - 16 q^{96} - 6 q^{97} + 4 q^{98} + 10 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 + 6 * q^3 + 14 * q^4 - 6 * q^6 + 8 * q^7 + 12 * q^8 + 10 * q^9 + 8 * q^11 + 12 * q^12 + 6 * q^13 + 4 * q^14 + 18 * q^16 + 6 * q^17 + 6 * q^18 - 6 * q^19 + 6 * q^21 + 4 * q^22 + 4 * q^23 + 6 * q^24 - 4 * q^26 + 24 * q^27 + 14 * q^28 + 4 * q^29 - 14 * q^31 + 18 * q^32 + 6 * q^33 - 6 * q^34 + 18 * q^36 + 10 * q^37 - 30 * q^38 + 16 * q^39 - 4 * q^41 - 6 * q^42 + 34 * q^43 + 14 * q^44 - 24 * q^46 - 8 * q^47 + 12 * q^48 + 8 * q^49 + 16 * q^51 + 46 * q^52 + 18 * q^53 + 6 * q^54 + 12 * q^56 + 6 * q^57 - 6 * q^58 - 40 * q^59 + 26 * q^62 + 10 * q^63 + 10 * q^64 - 6 * q^66 + 42 * q^67 + 16 * q^68 - 50 * q^69 + 6 * q^71 + 28 * q^72 + 40 * q^73 - 44 * q^76 + 8 * q^77 - 76 * q^78 + 12 * q^79 + 40 * q^81 + 42 * q^82 + 2 * q^83 + 12 * q^84 + 44 * q^86 + 2 * q^87 + 12 * q^88 + 22 * q^89 + 6 * q^91 + 6 * q^92 - 32 * q^93 - 50 * q^94 - 16 * q^96 - 6 * q^97 + 4 * q^98 + 10 * 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 $

$2$	2.43000	1.71827	0.859134	−	0.511751i	$-0.171003\pi$
$2$	2.43000	1.71827	0.859134	+	0.511751i	$0.171003\pi$
$3$	−2.50028	−1.44354	−0.721770	−	0.692133i	$-0.756671\pi$
$3$	−2.50028	−1.44354	−0.721770	+	0.692133i	$0.756671\pi$
$4$	3.90488	1.95244
$5$	0	0
$5$	0	0
$6$	−6.07568	−2.48039
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	4.62886	1.63655
$9$	3.25142	1.08381
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−9.76332	−2.81843
$13$	2.18879	0.607062	0.303531	−	0.952821i	$-0.401834\pi$
$13$	2.18879	0.607062	0.303531	+	0.952821i	$0.401834\pi$
$14$	2.43000	0.649444
$15$	0	0
$16$	3.43835	0.859588
$17$	1.02233	0.247953	0.123976	−	0.992285i	$-0.460435\pi$
$17$	1.02233	0.247953	0.123976	+	0.992285i	$0.460435\pi$
$18$	7.90095	1.86227
$19$	−5.00442	−1.14809	−0.574047	−	0.818823i	$-0.694627\pi$
$19$	−5.00442	−1.14809	−0.574047	+	0.818823i	$0.694627\pi$
$20$	0	0
$21$	−2.50028	−0.545607
$22$	2.43000	0.518077
$23$	7.86206	1.63935	0.819677	−	0.572827i	$-0.194153\pi$
$23$	7.86206	1.63935	0.819677	+	0.572827i	$0.194153\pi$
$24$	−11.5735	−2.36243
$25$	0	0
$26$	5.31876	1.04310
$27$	−0.628633	−0.120980
$28$	3.90488	0.737954
$29$	−0.713907	−0.132569	−0.0662846	−	0.997801i	$-0.521115\pi$
$29$	−0.713907	−0.132569	−0.0662846	+	0.997801i	$0.521115\pi$
$30$	0	0
$31$	6.58245	1.18224	0.591122	−	0.806582i	$-0.298685\pi$
$31$	6.58245	1.18224	0.591122	+	0.806582i	$0.298685\pi$
$32$	−0.902538	−0.159548
$33$	−2.50028	−0.435244
$34$	2.48427	0.426049
$35$	0	0
$36$	12.6964	2.11607
$37$	10.3830	1.70696	0.853480	−	0.521126i	$-0.174488\pi$
$37$	10.3830	1.70696	0.853480	+	0.521126i	$0.174488\pi$
$38$	−12.1607	−1.97273
$39$	−5.47261	−0.876319
$40$	0	0
$41$	−3.45322	−0.539302	−0.269651	−	0.962958i	$-0.586908\pi$
$41$	−3.45322	−0.539302	−0.269651	+	0.962958i	$0.586908\pi$
$42$	−6.07568	−0.937498
$43$	10.8383	1.65283	0.826414	−	0.563063i	$-0.190377\pi$
$43$	10.8383	1.65283	0.826414	+	0.563063i	$0.190377\pi$
$44$	3.90488	0.588683
$45$	0	0
$46$	19.1048	2.81685
$47$	−8.10803	−1.18268	−0.591339	−	0.806423i	$-0.701400\pi$
$47$	−8.10803	−1.18268	−0.591339	+	0.806423i	$0.701400\pi$
$48$	−8.59686	−1.24085
$49$	1.00000	0.142857
$50$	0	0
$51$	−2.55613	−0.357929
$52$	8.54699	1.18525
$53$	−4.48118	−0.615537	−0.307768	−	0.951461i	$-0.599582\pi$
$53$	−4.48118	−0.615537	−0.307768	+	0.951461i	$0.599582\pi$
$54$	−1.52757	−0.207877
$55$	0	0
$56$	4.62886	0.618558
$57$	12.5125	1.65732
$58$	−1.73479	−0.227789
$59$	4.20757	0.547779	0.273890	−	0.961761i	$-0.411690\pi$
$59$	4.20757	0.547779	0.273890	+	0.961761i	$0.411690\pi$
$60$	0	0
$61$	−6.44231	−0.824853	−0.412427	−	0.910991i	$-0.635319\pi$
$61$	−6.44231	−0.824853	−0.412427	+	0.910991i	$0.635319\pi$
$62$	15.9953	2.03141
$63$	3.25142	0.409641
$64$	−9.06987	−1.13373
$65$	0	0
$66$	−6.07568	−0.747865
$67$	10.6283	1.29846	0.649229	−	0.760593i	$-0.275092\pi$
$67$	10.6283	1.29846	0.649229	+	0.760593i	$0.275092\pi$
$68$	3.99210	0.484113
$69$	−19.6574	−2.36647
$70$	0	0
$71$	−5.41259	−0.642356	−0.321178	−	0.947019i	$-0.604079\pi$
$71$	−5.41259	−0.642356	−0.321178	+	0.947019i	$0.604079\pi$
$72$	15.0504	1.77371
$73$	7.84020	0.917626	0.458813	−	0.888533i	$-0.348275\pi$
$73$	7.84020	0.917626	0.458813	+	0.888533i	$0.348275\pi$
$74$	25.2307	2.93301
$75$	0	0
$76$	−19.5417	−2.24159
$77$	1.00000	0.113961
$78$	−13.2984	−1.50575
$79$	4.86426	0.547272	0.273636	−	0.961833i	$-0.411774\pi$
$79$	4.86426	0.547272	0.273636	+	0.961833i	$0.411774\pi$
$80$	0	0
$81$	−8.18251	−0.909168
$82$	−8.39130	−0.926664
$83$	8.48523	0.931375	0.465687	−	0.884949i	$-0.345807\pi$
$83$	8.48523	0.931375	0.465687	+	0.884949i	$0.345807\pi$
$84$	−9.76332	−1.06527
$85$	0	0
$86$	26.3371	2.84000
$87$	1.78497	0.191369
$88$	4.62886	0.493438
$89$	13.4233	1.42286	0.711431	−	0.702756i	$-0.248047\pi$
$89$	13.4233	1.42286	0.711431	+	0.702756i	$0.248047\pi$
$90$	0	0
$91$	2.18879	0.229448
$92$	30.7004	3.20074
$93$	−16.4580	−1.70662
$94$	−19.7025	−2.03216
$95$	0	0
$96$	2.25660	0.230314
$97$	−10.5599	−1.07219	−0.536097	−	0.844156i	$-0.680102\pi$
$97$	−10.5599	−1.07219	−0.536097	+	0.844156i	$0.680102\pi$
$98$	2.43000	0.245467
$99$	3.25142	0.326780
$100$	0	0
$101$	5.53381	0.550634	0.275317	−	0.961353i	$-0.411217\pi$
$101$	5.53381	0.550634	0.275317	+	0.961353i	$0.411217\pi$
$102$	−6.21138	−0.615018
$103$	−1.82365	−0.179690	−0.0898450	−	0.995956i	$-0.528637\pi$
$103$	−1.82365	−0.179690	−0.0898450	+	0.995956i	$0.528637\pi$
$104$	10.1316	0.993488
$105$	0	0
$106$	−10.8892	−1.05766
$107$	16.5536	1.60030	0.800151	−	0.599799i	$-0.204753\pi$
$107$	16.5536	1.60030	0.800151	+	0.599799i	$0.204753\pi$
$108$	−2.45474	−0.236207
$109$	−0.198212	−0.0189852	−0.00949262	−	0.999955i	$-0.503022\pi$
$109$	−0.198212	−0.0189852	−0.00949262	+	0.999955i	$0.503022\pi$
$110$	0	0
$111$	−25.9605	−2.46406
$112$	3.43835	0.324894
$113$	−15.5254	−1.46050	−0.730252	−	0.683178i	$-0.760597\pi$
$113$	−15.5254	−1.46050	−0.730252	+	0.683178i	$0.760597\pi$
$114$	30.4053	2.84772
$115$	0	0
$116$	−2.78773	−0.258834
$117$	7.11670	0.657939
$118$	10.2244	0.941231
$119$	1.02233	0.0937173
$120$	0	0
$121$	1.00000	0.0909091
$122$	−15.6548	−1.41732
$123$	8.63402	0.778504
$124$	25.7037	2.30826
$125$	0	0
$126$	7.90095	0.703873
$127$	−16.2033	−1.43781	−0.718906	−	0.695107i	$-0.755357\pi$
$127$	−16.2033	−1.43781	−0.718906	+	0.695107i	$0.755357\pi$
$128$	−20.2347	−1.78851
$129$	−27.0989	−2.38592
$130$	0	0
$131$	12.1451	1.06112	0.530560	−	0.847647i	$-0.321982\pi$
$131$	12.1451	1.06112	0.530560	+	0.847647i	$0.321982\pi$
$132$	−9.76332	−0.849788
$133$	−5.00442	−0.433939
$134$	25.8268	2.23110
$135$	0	0
$136$	4.73225	0.405787
$137$	2.96876	0.253639	0.126819	−	0.991926i	$-0.459523\pi$
$137$	2.96876	0.253639	0.126819	+	0.991926i	$0.459523\pi$
$138$	−47.7674	−4.06623
$139$	−13.7538	−1.16658	−0.583291	−	0.812263i	$-0.698235\pi$
$139$	−13.7538	−1.16658	−0.583291	+	0.812263i	$0.698235\pi$
$140$	0	0
$141$	20.2724	1.70724
$142$	−13.1526	−1.10374
$143$	2.18879	0.183036
$144$	11.1795	0.931629
$145$	0	0
$146$	19.0517	1.57673
$147$	−2.50028	−0.206220
$148$	40.5445	3.33274
$149$	−14.9667	−1.22612	−0.613058	−	0.790038i	$-0.710061\pi$
$149$	−14.9667	−1.22612	−0.613058	+	0.790038i	$0.710061\pi$
$150$	0	0
$151$	19.9665	1.62485	0.812426	−	0.583064i	$-0.198146\pi$
$151$	19.9665	1.62485	0.812426	+	0.583064i	$0.198146\pi$
$152$	−23.1648	−1.87891
$153$	3.32404	0.268733
$154$	2.43000	0.195815
$155$	0	0
$156$	−21.3699	−1.71096
$157$	0.104156	0.00831255	0.00415627	−	0.999991i	$-0.498677\pi$
$157$	0.104156	0.00831255	0.00415627	+	0.999991i	$0.498677\pi$
$158$	11.8201	0.940360
$159$	11.2042	0.888552
$160$	0	0
$161$	7.86206	0.619617
$162$	−19.8835	−1.56219
$163$	−2.55998	−0.200513	−0.100257	−	0.994962i	$-0.531966\pi$
$163$	−2.55998	−0.200513	−0.100257	+	0.994962i	$0.531966\pi$
$164$	−13.4844	−1.05296
$165$	0	0
$166$	20.6191	1.60035
$167$	−18.6016	−1.43943	−0.719716	−	0.694269i	$-0.755728\pi$
$167$	−18.6016	−1.43943	−0.719716	+	0.694269i	$0.755728\pi$
$168$	−11.5735	−0.892913
$169$	−8.20918	−0.631475
$170$	0	0
$171$	−16.2715	−1.24431
$172$	42.3224	3.22705
$173$	5.34756	0.406568	0.203284	−	0.979120i	$-0.434839\pi$
$173$	5.34756	0.406568	0.203284	+	0.979120i	$0.434839\pi$
$174$	4.33748	0.328823
$175$	0	0
$176$	3.43835	0.259176
$177$	−10.5201	−0.790741
$178$	32.6185	2.44486
$179$	−5.28594	−0.395090	−0.197545	−	0.980294i	$-0.563297\pi$
$179$	−5.28594	−0.395090	−0.197545	+	0.980294i	$0.563297\pi$
$180$	0	0
$181$	−11.1118	−0.825936	−0.412968	−	0.910746i	$-0.635508\pi$
$181$	−11.1118	−0.825936	−0.412968	+	0.910746i	$0.635508\pi$
$182$	5.31876	0.394253
$183$	16.1076	1.19071
$184$	36.3924	2.68288
$185$	0	0
$186$	−39.9929	−2.93242
$187$	1.02233	0.0747605
$188$	−31.6609	−2.30911
$189$	−0.628633	−0.0457263
$190$	0	0
$191$	−20.5819	−1.48925	−0.744625	−	0.667483i	$-0.767372\pi$
$191$	−20.5819	−1.48925	−0.744625	+	0.667483i	$0.767372\pi$
$192$	22.6773	1.63659
$193$	−14.1053	−1.01532	−0.507660	−	0.861558i	$-0.669489\pi$
$193$	−14.1053	−1.01532	−0.507660	+	0.861558i	$0.669489\pi$
$194$	−25.6605	−1.84232
$195$	0	0
$196$	3.90488	0.278920
$197$	−20.0564	−1.42896	−0.714479	−	0.699657i	$-0.753336\pi$
$197$	−20.0564	−1.42896	−0.714479	+	0.699657i	$0.753336\pi$
$198$	7.90095	0.561496
$199$	−18.0534	−1.27977	−0.639887	−	0.768469i	$-0.721019\pi$
$199$	−18.0534	−1.27977	−0.639887	+	0.768469i	$0.721019\pi$
$200$	0	0
$201$	−26.5739	−1.87438
$202$	13.4471	0.946137
$203$	−0.713907	−0.0501065
$204$	−9.98138	−0.698837
$205$	0	0
$206$	−4.43147	−0.308755
$207$	25.5629	1.77674
$208$	7.52585	0.521824
$209$	−5.00442	−0.346163
$210$	0	0
$211$	−16.7948	−1.15620	−0.578100	−	0.815966i	$-0.696206\pi$
$211$	−16.7948	−1.15620	−0.578100	+	0.815966i	$0.696206\pi$
$212$	−17.4985	−1.20180
$213$	13.5330	0.927266
$214$	40.2253	2.74974
$215$	0	0
$216$	−2.90985	−0.197990
$217$	6.58245	0.446846
$218$	−0.481654	−0.0326217
$219$	−19.6027	−1.32463
$220$	0	0
$221$	2.23768	0.150523
$222$	−63.0840	−4.23392
$223$	5.71317	0.382582	0.191291	−	0.981533i	$-0.438733\pi$
$223$	5.71317	0.382582	0.191291	+	0.981533i	$0.438733\pi$
$224$	−0.902538	−0.0603034
$225$	0	0
$226$	−37.7266	−2.50953
$227$	−6.94462	−0.460930	−0.230465	−	0.973081i	$-0.574025\pi$
$227$	−6.94462	−0.460930	−0.230465	+	0.973081i	$0.574025\pi$
$228$	48.8598	3.23582
$229$	−23.9008	−1.57941	−0.789704	−	0.613488i	$-0.789766\pi$
$229$	−23.9008	−1.57941	−0.789704	+	0.613488i	$0.789766\pi$
$230$	0	0
$231$	−2.50028	−0.164507
$232$	−3.30458	−0.216956
$233$	−8.70888	−0.570538	−0.285269	−	0.958448i	$-0.592083\pi$
$233$	−8.70888	−0.570538	−0.285269	+	0.958448i	$0.592083\pi$
$234$	17.2936	1.13052
$235$	0	0
$236$	16.4301	1.06951
$237$	−12.1620	−0.790010
$238$	2.48427	0.161031
$239$	10.6812	0.690911	0.345456	−	0.938435i	$-0.387724\pi$
$239$	10.6812	0.690911	0.345456	+	0.938435i	$0.387724\pi$
$240$	0	0
$241$	−16.2939	−1.04958	−0.524792	−	0.851230i	$-0.675857\pi$
$241$	−16.2939	−1.04958	−0.524792	+	0.851230i	$0.675857\pi$
$242$	2.43000	0.156206
$243$	22.3445	1.43340
$244$	−25.1565	−1.61048
$245$	0	0
$246$	20.9806	1.33768
$247$	−10.9537	−0.696964
$248$	30.4693	1.93480
$249$	−21.2155	−1.34448
$250$	0	0
$251$	−19.6904	−1.24284	−0.621422	−	0.783476i	$-0.713445\pi$
$251$	−19.6904	−1.24284	−0.621422	+	0.783476i	$0.713445\pi$
$252$	12.6964	0.799800
$253$	7.86206	0.494284
$254$	−39.3740	−2.47055
$255$	0	0
$256$	−31.0305	−1.93940
$257$	4.66987	0.291299	0.145649	−	0.989336i	$-0.453473\pi$
$257$	4.66987	0.291299	0.145649	+	0.989336i	$0.453473\pi$
$258$	−65.8502	−4.09966
$259$	10.3830	0.645170
$260$	0	0
$261$	−2.32122	−0.143680
$262$	29.5125	1.82329
$263$	−14.7116	−0.907154	−0.453577	−	0.891217i	$-0.649852\pi$
$263$	−14.7116	−0.907154	−0.453577	+	0.891217i	$0.649852\pi$
$264$	−11.5735	−0.712298
$265$	0	0
$266$	−12.1607	−0.745622
$267$	−33.5620	−2.05396
$268$	41.5024	2.53516
$269$	18.4161	1.12285	0.561423	−	0.827529i	$-0.310254\pi$
$269$	18.4161	1.12285	0.561423	+	0.827529i	$0.310254\pi$
$270$	0	0
$271$	20.3715	1.23748	0.618740	−	0.785596i	$-0.287643\pi$
$271$	20.3715	1.23748	0.618740	+	0.785596i	$0.287643\pi$
$272$	3.51515	0.213137
$273$	−5.47261	−0.331217
$274$	7.21409	0.435819
$275$	0	0
$276$	−76.7599	−4.62040
$277$	16.6359	0.999552	0.499776	−	0.866155i	$-0.333416\pi$
$277$	16.6359	0.999552	0.499776	+	0.866155i	$0.333416\pi$
$278$	−33.4217	−2.00450
$279$	21.4023	1.28132
$280$	0	0
$281$	−0.490443	−0.0292574	−0.0146287	−	0.999893i	$-0.504657\pi$
$281$	−0.490443	−0.0292574	−0.0146287	+	0.999893i	$0.504657\pi$
$282$	49.2618	2.93350
$283$	20.1541	1.19804	0.599018	−	0.800735i	$-0.295558\pi$
$283$	20.1541	1.19804	0.599018	+	0.800735i	$0.295558\pi$
$284$	−21.1355	−1.25416
$285$	0	0
$286$	5.31876	0.314505
$287$	−3.45322	−0.203837
$288$	−2.93453	−0.172919
$289$	−15.9548	−0.938520
$290$	0	0
$291$	26.4027	1.54776
$292$	30.6151	1.79161
$293$	17.0906	0.998442	0.499221	−	0.866475i	$-0.333620\pi$
$293$	17.0906	0.998442	0.499221	+	0.866475i	$0.333620\pi$
$294$	−6.07568	−0.354341
$295$	0	0
$296$	48.0616	2.79352
$297$	−0.628633	−0.0364770
$298$	−36.3689	−2.10680
$299$	17.2084	0.995190
$300$	0	0
$301$	10.8383	0.624710
$302$	48.5186	2.79193
$303$	−13.8361	−0.794863
$304$	−17.2070	−0.986888
$305$	0	0
$306$	8.07741	0.461755
$307$	20.5356	1.17203	0.586015	−	0.810300i	$-0.300696\pi$
$307$	20.5356	1.17203	0.586015	+	0.810300i	$0.300696\pi$
$308$	3.90488	0.222501
$309$	4.55965	0.259390
$310$	0	0
$311$	16.8438	0.955124	0.477562	−	0.878598i	$-0.341521\pi$
$311$	16.8438	0.955124	0.477562	+	0.878598i	$0.341521\pi$
$312$	−25.3320	−1.43414
$313$	−14.6119	−0.825915	−0.412958	−	0.910750i	$-0.635504\pi$
$313$	−14.6119	−0.825915	−0.412958	+	0.910750i	$0.635504\pi$
$314$	0.253099	0.0142832
$315$	0	0
$316$	18.9944	1.06852
$317$	−6.23266	−0.350061	−0.175031	−	0.984563i	$-0.556002\pi$
$317$	−6.23266	−0.350061	−0.175031	+	0.984563i	$0.556002\pi$
$318$	27.2262	1.52677
$319$	−0.713907	−0.0399711
$320$	0	0
$321$	−41.3888	−2.31010
$322$	19.1048	1.06467
$323$	−5.11619	−0.284673
$324$	−31.9518	−1.77510
$325$	0	0
$326$	−6.22075	−0.344535
$327$	0.495586	0.0274060
$328$	−15.9845	−0.882594
$329$	−8.10803	−0.447010
$330$	0	0
$331$	7.62313	0.419005	0.209502	−	0.977808i	$-0.432816\pi$
$331$	7.62313	0.419005	0.209502	+	0.977808i	$0.432816\pi$
$332$	33.1338	1.81846
$333$	33.7596	1.85002
$334$	−45.2017	−2.47333
$335$	0	0
$336$	−8.59686	−0.468997
$337$	−25.9050	−1.41113	−0.705567	−	0.708644i	$-0.749307\pi$
$337$	−25.9050	−1.41113	−0.705567	+	0.708644i	$0.749307\pi$
$338$	−19.9483	−1.08504
$339$	38.8178	2.10829
$340$	0	0
$341$	6.58245	0.356460
$342$	−39.5397	−2.13806
$343$	1.00000	0.0539949
$344$	50.1691	2.70494
$345$	0	0
$346$	12.9946	0.698592
$347$	13.1461	0.705722	0.352861	−	0.935676i	$-0.385209\pi$
$347$	13.1461	0.705722	0.352861	+	0.935676i	$0.385209\pi$
$348$	6.97011	0.373637
$349$	23.9659	1.28286	0.641431	−	0.767180i	$-0.278341\pi$
$349$	23.9659	1.28286	0.641431	+	0.767180i	$0.278341\pi$
$350$	0	0
$351$	−1.37595	−0.0734427
$352$	−0.902538	−0.0481055
$353$	13.4031	0.713375	0.356687	−	0.934224i	$-0.383906\pi$
$353$	13.4031	0.713375	0.356687	+	0.934224i	$0.383906\pi$
$354$	−25.5639	−1.35870
$355$	0	0
$356$	52.4163	2.77806
$357$	−2.55613	−0.135285
$358$	−12.8448	−0.678870
$359$	26.5377	1.40061	0.700303	−	0.713845i	$-0.253048\pi$
$359$	26.5377	1.40061	0.700303	+	0.713845i	$0.253048\pi$
$360$	0	0
$361$	6.04425	0.318118
$362$	−27.0017	−1.41918
$363$	−2.50028	−0.131231
$364$	8.54699	0.447984
$365$	0	0
$366$	39.1414	2.04596
$367$	30.2280	1.57789	0.788945	−	0.614464i	$-0.210628\pi$
$367$	30.2280	1.57789	0.788945	+	0.614464i	$0.210628\pi$
$368$	27.0325	1.40917
$369$	−11.2279	−0.584499
$370$	0	0
$371$	−4.48118	−0.232651
$372$	−64.2666	−3.33207
$373$	15.1447	0.784163	0.392081	−	0.919931i	$-0.371755\pi$
$373$	15.1447	0.784163	0.392081	+	0.919931i	$0.371755\pi$
$374$	2.48427	0.128459
$375$	0	0
$376$	−37.5310	−1.93551
$377$	−1.56260	−0.0804778
$378$	−1.52757	−0.0785700
$379$	−14.3909	−0.739212	−0.369606	−	0.929189i	$-0.620507\pi$
$379$	−14.3909	−0.739212	−0.369606	+	0.929189i	$0.620507\pi$
$380$	0	0
$381$	40.5129	2.07554
$382$	−50.0138	−2.55893
$383$	−4.49846	−0.229861	−0.114930	−	0.993374i	$-0.536664\pi$
$383$	−4.49846	−0.229861	−0.114930	+	0.993374i	$0.536664\pi$
$384$	50.5925	2.58179
$385$	0	0
$386$	−34.2758	−1.74459
$387$	35.2400	1.79135
$388$	−41.2352	−2.09340
$389$	−15.9080	−0.806568	−0.403284	−	0.915075i	$-0.632131\pi$
$389$	−15.9080	−0.806568	−0.403284	+	0.915075i	$0.632131\pi$
$390$	0	0
$391$	8.03766	0.406482
$392$	4.62886	0.233793
$393$	−30.3661	−1.53177
$394$	−48.7370	−2.45533
$395$	0	0
$396$	12.6964	0.638020
$397$	18.3076	0.918831	0.459415	−	0.888222i	$-0.348059\pi$
$397$	18.3076	0.918831	0.459415	+	0.888222i	$0.348059\pi$
$398$	−43.8698	−2.19899
$399$	12.5125	0.626408
$400$	0	0
$401$	−15.7942	−0.788726	−0.394363	−	0.918955i	$-0.629035\pi$
$401$	−15.7942	−0.788726	−0.394363	+	0.918955i	$0.629035\pi$
$402$	−64.5744	−3.22068
$403$	14.4076	0.717696
$404$	21.6089	1.07508
$405$	0	0
$406$	−1.73479	−0.0860963
$407$	10.3830	0.514668
$408$	−11.8320	−0.585770
$409$	−2.25224	−0.111366	−0.0556831	−	0.998448i	$-0.517734\pi$
$409$	−2.25224	−0.111366	−0.0556831	+	0.998448i	$0.517734\pi$
$410$	0	0
$411$	−7.42276	−0.366138
$412$	−7.12116	−0.350834
$413$	4.20757	0.207041
$414$	62.1178	3.05292
$415$	0	0
$416$	−1.97547	−0.0968554
$417$	34.3884	1.68401
$418$	−12.1607	−0.594801
$419$	−11.1791	−0.546137	−0.273069	−	0.961995i	$-0.588039\pi$
$419$	−11.1791	−0.546137	−0.273069	+	0.961995i	$0.588039\pi$
$420$	0	0
$421$	11.5373	0.562292	0.281146	−	0.959665i	$-0.409285\pi$
$421$	11.5373	0.562292	0.281146	+	0.959665i	$0.409285\pi$
$422$	−40.8112	−1.98666
$423$	−26.3627	−1.28180
$424$	−20.7428	−1.00736
$425$	0	0
$426$	32.8852	1.59329
$427$	−6.44231	−0.311765
$428$	64.6401	3.12450
$429$	−5.47261	−0.264220
$430$	0	0
$431$	−21.3197	−1.02693	−0.513467	−	0.858109i	$-0.671639\pi$
$431$	−21.3197	−1.02693	−0.513467	+	0.858109i	$0.671639\pi$
$432$	−2.16146	−0.103993
$433$	−11.4526	−0.550376	−0.275188	−	0.961390i	$-0.588740\pi$
$433$	−11.4526	−0.550376	−0.275188	+	0.961390i	$0.588740\pi$
$434$	15.9953	0.767801
$435$	0	0
$436$	−0.773994	−0.0370676
$437$	−39.3451	−1.88213
$438$	−47.6346	−2.27607
$439$	−5.88716	−0.280979	−0.140489	−	0.990082i	$-0.544868\pi$
$439$	−5.88716	−0.280979	−0.140489	+	0.990082i	$0.544868\pi$
$440$	0	0
$441$	3.25142	0.154830
$442$	5.43756	0.258638
$443$	25.0469	1.19001	0.595006	−	0.803721i	$-0.297150\pi$
$443$	25.0469	1.19001	0.595006	+	0.803721i	$0.297150\pi$
$444$	−101.373	−4.81094
$445$	0	0
$446$	13.8830	0.657379
$447$	37.4209	1.76995
$448$	−9.06987	−0.428511
$449$	0.578452	0.0272989	0.0136494	−	0.999907i	$-0.495655\pi$
$449$	0.578452	0.0272989	0.0136494	+	0.999907i	$0.495655\pi$
$450$	0	0
$451$	−3.45322	−0.162606
$452$	−60.6247	−2.85155
$453$	−49.9220	−2.34554
$454$	−16.8754	−0.792002
$455$	0	0
$456$	57.9186	2.71229
$457$	−17.6040	−0.823479	−0.411739	−	0.911302i	$-0.635079\pi$
$457$	−17.6040	−0.823479	−0.411739	+	0.911302i	$0.635079\pi$
$458$	−58.0788	−2.71384
$459$	−0.642673	−0.0299974
$460$	0	0
$461$	17.3358	0.807409	0.403705	−	0.914889i	$-0.367722\pi$
$461$	17.3358	0.807409	0.403705	+	0.914889i	$0.367722\pi$
$462$	−6.07568	−0.282666
$463$	16.9727	0.788786	0.394393	−	0.918942i	$-0.370955\pi$
$463$	16.9727	0.788786	0.394393	+	0.918942i	$0.370955\pi$
$464$	−2.45467	−0.113955
$465$	0	0
$466$	−21.1626	−0.980336
$467$	−41.7392	−1.93146	−0.965729	−	0.259552i	$-0.916425\pi$
$467$	−41.7392	−1.93146	−0.965729	+	0.259552i	$0.916425\pi$
$468$	27.7899	1.28459
$469$	10.6283	0.490771
$470$	0	0
$471$	−0.260419	−0.0119995
$472$	19.4763	0.896468
$473$	10.8383	0.498347
$474$	−29.5537	−1.35745
$475$	0	0
$476$	3.99210	0.182978
$477$	−14.5702	−0.667124
$478$	25.9554	1.18717
$479$	18.3940	0.840444	0.420222	−	0.907421i	$-0.361952\pi$
$479$	18.3940	0.840444	0.420222	+	0.907421i	$0.361952\pi$
$480$	0	0
$481$	22.7263	1.03623
$482$	−39.5942	−1.80347
$483$	−19.6574	−0.894442
$484$	3.90488	0.177495
$485$	0	0
$486$	54.2971	2.46297
$487$	−0.575587	−0.0260823	−0.0130412	−	0.999915i	$-0.504151\pi$
$487$	−0.575587	−0.0260823	−0.0130412	+	0.999915i	$0.504151\pi$
$488$	−29.8206	−1.34991
$489$	6.40068	0.289449
$490$	0	0
$491$	−28.2583	−1.27528	−0.637640	−	0.770334i	$-0.720089\pi$
$491$	−28.2583	−1.27528	−0.637640	+	0.770334i	$0.720089\pi$
$492$	33.7149	1.51998
$493$	−0.729852	−0.0328709
$494$	−26.6173	−1.19757
$495$	0	0
$496$	22.6328	1.01624
$497$	−5.41259	−0.242788
$498$	−51.5536	−2.31017
$499$	28.9995	1.29820	0.649098	−	0.760705i	$-0.275146\pi$
$499$	28.9995	1.29820	0.649098	+	0.760705i	$0.275146\pi$
$500$	0	0
$501$	46.5092	2.07788
$502$	−47.8475	−2.13554
$503$	−30.4022	−1.35557	−0.677783	−	0.735262i	$-0.737059\pi$
$503$	−30.4022	−1.35557	−0.677783	+	0.735262i	$0.737059\pi$
$504$	15.0504	0.670398
$505$	0	0
$506$	19.1048	0.849311
$507$	20.5253	0.911560
$508$	−63.2721	−2.80725
$509$	−4.00877	−0.177685	−0.0888427	−	0.996046i	$-0.528317\pi$
$509$	−4.00877	−0.177685	−0.0888427	+	0.996046i	$0.528317\pi$
$510$	0	0
$511$	7.84020	0.346830
$512$	−34.9346	−1.54390
$513$	3.14594	0.138897
$514$	11.3478	0.500529
$515$	0	0
$516$	−105.818	−4.65838
$517$	−8.10803	−0.356591
$518$	25.2307	1.10857
$519$	−13.3704	−0.586897
$520$	0	0
$521$	−44.3915	−1.94483	−0.972413	−	0.233267i	$-0.925058\pi$
$521$	−44.3915	−1.94483	−0.972413	+	0.233267i	$0.925058\pi$
$522$	−5.64055	−0.246880
$523$	−19.8255	−0.866907	−0.433454	−	0.901176i	$-0.642705\pi$
$523$	−19.8255	−0.866907	−0.433454	+	0.901176i	$0.642705\pi$
$524$	47.4251	2.07177
$525$	0	0
$526$	−35.7490	−1.55873
$527$	6.72947	0.293140
$528$	−8.59686	−0.374130
$529$	38.8120	1.68748
$530$	0	0
$531$	13.6806	0.593687
$532$	−19.5417	−0.847240
$533$	−7.55838	−0.327390
$534$	−81.5555	−3.52925
$535$	0	0
$536$	49.1971	2.12499
$537$	13.2164	0.570328
$538$	44.7510	1.92935
$539$	1.00000	0.0430730
$540$	0	0
$541$	−3.27130	−0.140644	−0.0703220	−	0.997524i	$-0.522403\pi$
$541$	−3.27130	−0.140644	−0.0703220	+	0.997524i	$0.522403\pi$
$542$	49.5027	2.12632
$543$	27.7828	1.19227
$544$	−0.922696	−0.0395603
$545$	0	0
$546$	−13.2984	−0.569120
$547$	−28.7381	−1.22875	−0.614376	−	0.789014i	$-0.710592\pi$
$547$	−28.7381	−1.22875	−0.614376	+	0.789014i	$0.710592\pi$
$548$	11.5927	0.495215
$549$	−20.9467	−0.893983
$550$	0	0
$551$	3.57269	0.152202
$552$	−90.9914	−3.87285
$553$	4.86426	0.206850
$554$	40.4251	1.71750
$555$	0	0
$556$	−53.7070	−2.27768
$557$	0.538809	0.0228301	0.0114150	−	0.999935i	$-0.496366\pi$
$557$	0.538809	0.0228301	0.0114150	+	0.999935i	$0.496366\pi$
$558$	52.0076	2.20166
$559$	23.7229	1.00337
$560$	0	0
$561$	−2.55613	−0.107920
$562$	−1.19177	−0.0502720
$563$	26.9355	1.13520	0.567599	−	0.823305i	$-0.307873\pi$
$563$	26.9355	1.13520	0.567599	+	0.823305i	$0.307873\pi$
$564$	79.1613	3.33329
$565$	0	0
$566$	48.9744	2.05855
$567$	−8.18251	−0.343633
$568$	−25.0541	−1.05125
$569$	16.1279	0.676115	0.338058	−	0.941125i	$-0.390230\pi$
$569$	16.1279	0.676115	0.338058	+	0.941125i	$0.390230\pi$
$570$	0	0
$571$	−13.6298	−0.570390	−0.285195	−	0.958469i	$-0.592058\pi$
$571$	−13.6298	−0.570390	−0.285195	+	0.958469i	$0.592058\pi$
$572$	8.54699	0.357368
$573$	51.4605	2.14979
$574$	−8.39130	−0.350246
$575$	0	0
$576$	−29.4900	−1.22875
$577$	−4.73286	−0.197032	−0.0985158	−	0.995135i	$-0.531410\pi$
$577$	−4.73286	−0.197032	−0.0985158	+	0.995135i	$0.531410\pi$
$578$	−38.7702	−1.61263
$579$	35.2672	1.46565
$580$	0	0
$581$	8.48523	0.352027
$582$	64.1586	2.65946
$583$	−4.48118	−0.185591
$584$	36.2912	1.50174
$585$	0	0
$586$	41.5300	1.71559
$587$	−10.5007	−0.433411	−0.216706	−	0.976237i	$-0.569531\pi$
$587$	−10.5007	−0.433411	−0.216706	+	0.976237i	$0.569531\pi$
$588$	−9.76332	−0.402633
$589$	−32.9414	−1.35733
$590$	0	0
$591$	50.1467	2.06276
$592$	35.7005	1.46728
$593$	10.8565	0.445821	0.222911	−	0.974839i	$-0.428444\pi$
$593$	10.8565	0.445821	0.222911	+	0.974839i	$0.428444\pi$
$594$	−1.52757	−0.0626772
$595$	0	0
$596$	−58.4431	−2.39392
$597$	45.1387	1.84740
$598$	41.8165	1.71000
$599$	18.5599	0.758337	0.379168	−	0.925328i	$-0.376210\pi$
$599$	18.5599	0.758337	0.379168	+	0.925328i	$0.376210\pi$
$600$	0	0
$601$	25.0213	1.02064	0.510319	−	0.859985i	$-0.329527\pi$
$601$	25.0213	1.02064	0.510319	+	0.859985i	$0.329527\pi$
$602$	26.3371	1.07342
$603$	34.5572	1.40728
$604$	77.9669	3.17243
$605$	0	0
$606$	−33.6217	−1.36579
$607$	−16.7628	−0.680381	−0.340191	−	0.940357i	$-0.610492\pi$
$607$	−16.7628	−0.680381	−0.340191	+	0.940357i	$0.610492\pi$
$608$	4.51668	0.183176
$609$	1.78497	0.0723307
$610$	0	0
$611$	−17.7468	−0.717959
$612$	12.9800	0.524686
$613$	−1.55822	−0.0629359	−0.0314680	−	0.999505i	$-0.510018\pi$
$613$	−1.55822	−0.0629359	−0.0314680	+	0.999505i	$0.510018\pi$
$614$	49.9015	2.01386
$615$	0	0
$616$	4.62886	0.186502
$617$	13.8150	0.556171	0.278086	−	0.960556i	$-0.410300\pi$
$617$	13.8150	0.556171	0.278086	+	0.960556i	$0.410300\pi$
$618$	11.0799	0.445701
$619$	32.7178	1.31504	0.657521	−	0.753437i	$-0.271605\pi$
$619$	32.7178	1.31504	0.657521	+	0.753437i	$0.271605\pi$
$620$	0	0
$621$	−4.94235	−0.198330
$622$	40.9304	1.64116
$623$	13.4233	0.537792
$624$	−18.8168	−0.753274
$625$	0	0
$626$	−35.5069	−1.41914
$627$	12.5125	0.499700
$628$	0.406717	0.0162298
$629$	10.6149	0.423245
$630$	0	0
$631$	50.0521	1.99254	0.996270	−	0.0862864i	$-0.0275000\pi$
$631$	50.0521	1.99254	0.996270	+	0.0862864i	$0.0275000\pi$
$632$	22.5160	0.895639
$633$	41.9917	1.66902
$634$	−15.1453	−0.601498
$635$	0	0
$636$	43.7512	1.73485
$637$	2.18879	0.0867232
$638$	−1.73479	−0.0686811
$639$	−17.5986	−0.696190
$640$	0	0
$641$	−26.8728	−1.06141	−0.530705	−	0.847556i	$-0.678073\pi$
$641$	−26.8728	−1.06141	−0.530705	+	0.847556i	$0.678073\pi$
$642$	−100.575	−3.96937
$643$	41.6315	1.64179	0.820893	−	0.571083i	$-0.193476\pi$
$643$	41.6315	1.64179	0.820893	+	0.571083i	$0.193476\pi$
$644$	30.7004	1.20977
$645$	0	0
$646$	−12.4323	−0.489144
$647$	−39.2826	−1.54436	−0.772179	−	0.635406i	$-0.780833\pi$
$647$	−39.2826	−1.54436	−0.772179	+	0.635406i	$0.780833\pi$
$648$	−37.8757	−1.48790
$649$	4.20757	0.165162
$650$	0	0
$651$	−16.4580	−0.645040
$652$	−9.99643	−0.391490
$653$	−39.7496	−1.55552	−0.777761	−	0.628560i	$-0.783645\pi$
$653$	−39.7496	−1.55552	−0.777761	+	0.628560i	$0.783645\pi$
$654$	1.20427	0.0470908
$655$	0	0
$656$	−11.8734	−0.463577
$657$	25.4918	0.994531
$658$	−19.7025	−0.768083
$659$	−17.9993	−0.701154	−0.350577	−	0.936534i	$-0.614015\pi$
$659$	−17.9993	−0.701154	−0.350577	+	0.936534i	$0.614015\pi$
$660$	0	0
$661$	49.8144	1.93755	0.968777	−	0.247934i	$-0.0797516\pi$
$661$	49.8144	1.93755	0.968777	+	0.247934i	$0.0797516\pi$
$662$	18.5242	0.719962
$663$	−5.59484	−0.217286
$664$	39.2770	1.52424
$665$	0	0
$666$	82.0358	3.17882
$667$	−5.61278	−0.217328
$668$	−72.6369	−2.81041
$669$	−14.2846	−0.552273
$670$	0	0
$671$	−6.44231	−0.248703
$672$	2.25660	0.0870503
$673$	−9.35471	−0.360598	−0.180299	−	0.983612i	$-0.557706\pi$
$673$	−9.35471	−0.360598	−0.180299	+	0.983612i	$0.557706\pi$
$674$	−62.9490	−2.42470
$675$	0	0
$676$	−32.0559	−1.23292
$677$	26.8099	1.03039	0.515195	−	0.857073i	$-0.327720\pi$
$677$	26.8099	1.03039	0.515195	+	0.857073i	$0.327720\pi$
$678$	94.3272	3.62261
$679$	−10.5599	−0.405251
$680$	0	0
$681$	17.3635	0.665371
$682$	15.9953	0.612493
$683$	−2.69604	−0.103161	−0.0515805	−	0.998669i	$-0.516426\pi$
$683$	−2.69604	−0.103161	−0.0515805	+	0.998669i	$0.516426\pi$
$684$	−63.5383	−2.42945
$685$	0	0
$686$	2.43000	0.0927777
$687$	59.7587	2.27994
$688$	37.2660	1.42075
$689$	−9.80838	−0.373669
$690$	0	0
$691$	4.42617	0.168379	0.0841897	−	0.996450i	$-0.473170\pi$
$691$	4.42617	0.168379	0.0841897	+	0.996450i	$0.473170\pi$
$692$	20.8816	0.793800
$693$	3.25142	0.123511
$694$	31.9451	1.21262
$695$	0	0
$696$	8.26239	0.313185
$697$	−3.53034	−0.133721
$698$	58.2370	2.20430
$699$	21.7747	0.823594
$700$	0	0
$701$	12.4835	0.471496	0.235748	−	0.971814i	$-0.424246\pi$
$701$	12.4835	0.471496	0.235748	+	0.971814i	$0.424246\pi$
$702$	−3.34355	−0.126194
$703$	−51.9611	−1.95975
$704$	−9.06987	−0.341834
$705$	0	0
$706$	32.5695	1.22577
$707$	5.53381	0.208120
$708$	−41.0799	−1.54388
$709$	−2.11209	−0.0793213	−0.0396607	−	0.999213i	$-0.512628\pi$
$709$	−2.11209	−0.0793213	−0.0396607	+	0.999213i	$0.512628\pi$
$710$	0	0
$711$	15.8158	0.593138
$712$	62.1344	2.32859
$713$	51.7516	1.93811
$714$	−6.21138	−0.232455
$715$	0	0
$716$	−20.6410	−0.771390
$717$	−26.7061	−0.997358
$718$	64.4866	2.40662
$719$	−25.9429	−0.967506	−0.483753	−	0.875205i	$-0.660727\pi$
$719$	−25.9429	−0.967506	−0.483753	+	0.875205i	$0.660727\pi$
$720$	0	0
$721$	−1.82365	−0.0679164
$722$	14.6875	0.546612
$723$	40.7395	1.51512
$724$	−43.3904	−1.61259
$725$	0	0
$726$	−6.07568	−0.225490
$727$	15.5245	0.575770	0.287885	−	0.957665i	$-0.407048\pi$
$727$	15.5245	0.575770	0.287885	+	0.957665i	$0.407048\pi$
$728$	10.1316	0.375503
$729$	−31.3201	−1.16000
$730$	0	0
$731$	11.0804	0.409823
$732$	62.8983	2.32479
$733$	26.3389	0.972848	0.486424	−	0.873723i	$-0.338301\pi$
$733$	26.3389	0.972848	0.486424	+	0.873723i	$0.338301\pi$
$734$	73.4540	2.71124
$735$	0	0
$736$	−7.09581	−0.261555
$737$	10.6283	0.391500
$738$	−27.2837	−1.00433
$739$	39.4086	1.44967	0.724834	−	0.688924i	$-0.241916\pi$
$739$	39.4086	1.44967	0.724834	+	0.688924i	$0.241916\pi$
$740$	0	0
$741$	27.3873	1.00610
$742$	−10.8892	−0.399757
$743$	−3.21448	−0.117928	−0.0589639	−	0.998260i	$-0.518780\pi$
$743$	−3.21448	−0.117928	−0.0589639	+	0.998260i	$0.518780\pi$
$744$	−76.1819	−2.79296
$745$	0	0
$746$	36.8016	1.34740
$747$	27.5891	1.00943
$748$	3.99210	0.145966
$749$	16.5536	0.604857
$750$	0	0
$751$	−23.8972	−0.872022	−0.436011	−	0.899941i	$-0.643609\pi$
$751$	−23.8972	−0.872022	−0.436011	+	0.899941i	$0.643609\pi$
$752$	−27.8783	−1.01662
$753$	49.2315	1.79410
$754$	−3.79711	−0.138282
$755$	0	0
$756$	−2.45474	−0.0892779
$757$	7.52029	0.273330	0.136665	−	0.990617i	$-0.456362\pi$
$757$	7.52029	0.273330	0.136665	+	0.990617i	$0.456362\pi$
$758$	−34.9699	−1.27016
$759$	−19.6574	−0.713518
$760$	0	0
$761$	−22.1308	−0.802241	−0.401121	−	0.916025i	$-0.631379\pi$
$761$	−22.1308	−0.802241	−0.401121	+	0.916025i	$0.631379\pi$
$762$	98.4463	3.56633
$763$	−0.198212	−0.00717575
$764$	−80.3698	−2.90768
$765$	0	0
$766$	−10.9312	−0.394962
$767$	9.20951	0.332536
$768$	77.5850	2.79961
$769$	−22.6729	−0.817607	−0.408803	−	0.912622i	$-0.634054\pi$
$769$	−22.6729	−0.817607	−0.408803	+	0.912622i	$0.634054\pi$
$770$	0	0
$771$	−11.6760	−0.420501
$772$	−55.0794	−1.98235
$773$	−12.6334	−0.454391	−0.227196	−	0.973849i	$-0.572956\pi$
$773$	−12.6334	−0.454391	−0.227196	+	0.973849i	$0.572956\pi$
$774$	85.6330	3.07802
$775$	0	0
$776$	−48.8803	−1.75470
$777$	−25.9605	−0.931329
$778$	−38.6564	−1.38590
$779$	17.2814	0.619169
$780$	0	0
$781$	−5.41259	−0.193678
$782$	19.5315	0.698444
$783$	0.448785	0.0160383
$784$	3.43835	0.122798
$785$	0	0
$786$	−73.7896	−2.63199
$787$	−11.2802	−0.402095	−0.201047	−	0.979581i	$-0.564435\pi$
$787$	−11.2802	−0.402095	−0.201047	+	0.979581i	$0.564435\pi$
$788$	−78.3179	−2.78996
$789$	36.7831	1.30951
$790$	0	0
$791$	−15.5254	−0.552018
$792$	15.0504	0.534793
$793$	−14.1009	−0.500737
$794$	44.4873	1.57880
$795$	0	0
$796$	−70.4965	−2.49868
$797$	−39.3280	−1.39307	−0.696535	−	0.717523i	$-0.745276\pi$
$797$	−39.3280	−1.39307	−0.696535	+	0.717523i	$0.745276\pi$
$798$	30.4053	1.07634
$799$	−8.28912	−0.293248
$800$	0	0
$801$	43.6447	1.54211
$802$	−38.3799	−1.35524
$803$	7.84020	0.276675
$804$	−103.768	−3.65961
$805$	0	0
$806$	35.0105	1.23319
$807$	−46.0454	−1.62087
$808$	25.6152	0.901141
$809$	1.89113	0.0664885	0.0332442	−	0.999447i	$-0.489416\pi$
$809$	1.89113	0.0664885	0.0332442	+	0.999447i	$0.489416\pi$
$810$	0	0
$811$	21.8957	0.768861	0.384431	−	0.923154i	$-0.374398\pi$
$811$	21.8957	0.768861	0.384431	+	0.923154i	$0.374398\pi$
$812$	−2.78773	−0.0978300
$813$	−50.9345	−1.78635
$814$	25.2307	0.884337
$815$	0	0
$816$	−8.78887	−0.307672
$817$	−54.2395	−1.89760
$818$	−5.47294	−0.191357
$819$	7.11670	0.248678
$820$	0	0
$821$	−32.2908	−1.12696	−0.563478	−	0.826131i	$-0.690537\pi$
$821$	−32.2908	−1.12696	−0.563478	+	0.826131i	$0.690537\pi$
$822$	−18.0373	−0.629122
$823$	5.92014	0.206363	0.103182	−	0.994663i	$-0.467098\pi$
$823$	5.92014	0.206363	0.103182	+	0.994663i	$0.467098\pi$
$824$	−8.44145	−0.294072
$825$	0	0
$826$	10.2244	0.355752
$827$	42.5713	1.48035	0.740175	−	0.672414i	$-0.234743\pi$
$827$	42.5713	1.48035	0.740175	+	0.672414i	$0.234743\pi$
$828$	99.8202	3.46899
$829$	1.76794	0.0614031	0.0307016	−	0.999529i	$-0.490226\pi$
$829$	1.76794	0.0614031	0.0307016	+	0.999529i	$0.490226\pi$
$830$	0	0
$831$	−41.5944	−1.44289
$832$	−19.8521	−0.688247
$833$	1.02233	0.0354218
$834$	83.5638	2.89358
$835$	0	0
$836$	−19.5417	−0.675864
$837$	−4.13794	−0.143028
$838$	−27.1653	−0.938409
$839$	−34.2706	−1.18315	−0.591576	−	0.806249i	$-0.701494\pi$
$839$	−34.2706	−1.18315	−0.591576	+	0.806249i	$0.701494\pi$
$840$	0	0
$841$	−28.4903	−0.982425
$842$	28.0355	0.966168
$843$	1.22625	0.0422342
$844$	−65.5816	−2.25741
$845$	0	0
$846$	−64.0612	−2.20247
$847$	1.00000	0.0343604
$848$	−15.4079	−0.529108
$849$	−50.3910	−1.72941
$850$	0	0
$851$	81.6320	2.79831
$852$	52.8448	1.81043
$853$	−23.1730	−0.793429	−0.396715	−	0.917942i	$-0.629850\pi$
$853$	−23.1730	−0.793429	−0.396715	+	0.917942i	$0.629850\pi$
$854$	−15.6548	−0.535696
$855$	0	0
$856$	76.6245	2.61897
$857$	15.0551	0.514274	0.257137	−	0.966375i	$-0.417221\pi$
$857$	15.0551	0.514274	0.257137	+	0.966375i	$0.417221\pi$
$858$	−13.2984	−0.454001
$859$	−25.8405	−0.881666	−0.440833	−	0.897589i	$-0.645317\pi$
$859$	−25.8405	−0.881666	−0.440833	+	0.897589i	$0.645317\pi$
$860$	0	0
$861$	8.63402	0.294247
$862$	−51.8068	−1.76455
$863$	−17.3654	−0.591126	−0.295563	−	0.955323i	$-0.595507\pi$
$863$	−17.3654	−0.591126	−0.295563	+	0.955323i	$0.595507\pi$
$864$	0.567365	0.0193021
$865$	0	0
$866$	−27.8297	−0.945692
$867$	39.8916	1.35479
$868$	25.7037	0.872441
$869$	4.86426	0.165009
$870$	0	0
$871$	23.2632	0.788245
$872$	−0.917495	−0.0310703
$873$	−34.3347	−1.16205
$874$	−95.6084	−3.23400
$875$	0	0
$876$	−76.5464	−2.58626
$877$	−25.0527	−0.845970	−0.422985	−	0.906137i	$-0.639018\pi$
$877$	−25.0527	−0.845970	−0.422985	+	0.906137i	$0.639018\pi$
$878$	−14.3058	−0.482797
$879$	−42.7313	−1.44129
$880$	0	0
$881$	24.0989	0.811911	0.405956	−	0.913893i	$-0.366939\pi$
$881$	24.0989	0.811911	0.405956	+	0.913893i	$0.366939\pi$
$882$	7.90095	0.266039
$883$	1.71538	0.0577271	0.0288635	−	0.999583i	$-0.490811\pi$
$883$	1.71538	0.0577271	0.0288635	+	0.999583i	$0.490811\pi$
$884$	8.73788	0.293887
$885$	0	0
$886$	60.8638	2.04476
$887$	37.6550	1.26433	0.632165	−	0.774833i	$-0.282166\pi$
$887$	37.6550	1.26433	0.632165	+	0.774833i	$0.282166\pi$
$888$	−120.168	−4.03257
$889$	−16.2033	−0.543442
$890$	0	0
$891$	−8.18251	−0.274124
$892$	22.3093	0.746970
$893$	40.5760	1.35782
$894$	90.9327	3.04124
$895$	0	0
$896$	−20.2347	−0.675993
$897$	−43.0260	−1.43660
$898$	1.40564	0.0469067
$899$	−4.69926	−0.156729
$900$	0	0
$901$	−4.58126	−0.152624
$902$	−8.39130	−0.279400
$903$	−27.0989	−0.901795
$904$	−71.8648	−2.39019
$905$	0	0
$906$	−121.310	−4.03026
$907$	48.0962	1.59701	0.798503	−	0.601990i	$-0.205625\pi$
$907$	48.0962	1.59701	0.798503	+	0.601990i	$0.205625\pi$
$908$	−27.1179	−0.899940
$909$	17.9927	0.596782
$910$	0	0
$911$	7.43333	0.246277	0.123139	−	0.992389i	$-0.460704\pi$
$911$	7.43333	0.246277	0.123139	+	0.992389i	$0.460704\pi$
$912$	43.0223	1.42461
$913$	8.48523	0.280820
$914$	−42.7776	−1.41496
$915$	0	0
$916$	−93.3298	−3.08370
$917$	12.1451	0.401066
$918$	−1.56169	−0.0515435
$919$	9.42157	0.310789	0.155395	−	0.987852i	$-0.450335\pi$
$919$	9.42157	0.310789	0.155395	+	0.987852i	$0.450335\pi$
$920$	0	0
$921$	−51.3449	−1.69187
$922$	42.1260	1.38735
$923$	−11.8470	−0.389950
$924$	−9.76332	−0.321190
$925$	0	0
$926$	41.2435	1.35535
$927$	−5.92947	−0.194749
$928$	0.644329	0.0211511
$929$	37.8034	1.24029	0.620145	−	0.784487i	$-0.287074\pi$
$929$	37.8034	1.24029	0.620145	+	0.784487i	$0.287074\pi$
$930$	0	0
$931$	−5.00442	−0.164013
$932$	−34.0072	−1.11394
$933$	−42.1143	−1.37876
$934$	−101.426	−3.31876
$935$	0	0
$936$	32.9422	1.07675
$937$	−14.6930	−0.479999	−0.240000	−	0.970773i	$-0.577147\pi$
$937$	−14.6930	−0.479999	−0.240000	+	0.970773i	$0.577147\pi$
$938$	25.8268	0.843275
$939$	36.5340	1.19224
$940$	0	0
$941$	−31.9751	−1.04236	−0.521179	−	0.853448i	$-0.674507\pi$
$941$	−31.9751	−1.04236	−0.521179	+	0.853448i	$0.674507\pi$
$942$	−0.632818	−0.0206183
$943$	−27.1494	−0.884106
$944$	14.4671	0.470864
$945$	0	0
$946$	26.3371	0.856293
$947$	−37.5943	−1.22165	−0.610825	−	0.791766i	$-0.709162\pi$
$947$	−37.5943	−1.22165	−0.610825	+	0.791766i	$0.709162\pi$
$948$	−47.4914	−1.54245
$949$	17.1606	0.557056
$950$	0	0
$951$	15.5834	0.505327
$952$	4.73225	0.153373
$953$	−1.43989	−0.0466425	−0.0233212	−	0.999728i	$-0.507424\pi$
$953$	−1.43989	−0.0466425	−0.0233212	+	0.999728i	$0.507424\pi$
$954$	−35.4056	−1.14630
$955$	0	0
$956$	41.7090	1.34896
$957$	1.78497	0.0576999
$958$	44.6974	1.44411
$959$	2.96876	0.0958664
$960$	0	0
$961$	12.3287	0.397699
$962$	55.2249	1.78052
$963$	53.8229	1.73442
$964$	−63.6259	−2.04925
$965$	0	0
$966$	−47.7674	−1.53689
$967$	4.70317	0.151244	0.0756219	−	0.997137i	$-0.475906\pi$
$967$	4.70317	0.151244	0.0756219	+	0.997137i	$0.475906\pi$
$968$	4.62886	0.148777
$969$	12.7919	0.410936
$970$	0	0
$971$	−18.1775	−0.583342	−0.291671	−	0.956519i	$-0.594211\pi$
$971$	−18.1775	−0.583342	−0.291671	+	0.956519i	$0.594211\pi$
$972$	87.2527	2.79863
$973$	−13.7538	−0.440927
$974$	−1.39867	−0.0448164
$975$	0	0
$976$	−22.1509	−0.709034
$977$	−20.4650	−0.654733	−0.327367	−	0.944897i	$-0.606161\pi$
$977$	−20.4650	−0.654733	−0.327367	+	0.944897i	$0.606161\pi$
$978$	15.5536	0.497350
$979$	13.4233	0.429009
$980$	0	0
$981$	−0.644470	−0.0205764
$982$	−68.6676	−2.19127
$983$	−54.7580	−1.74651	−0.873255	−	0.487263i	$-0.837995\pi$
$983$	−54.7580	−1.74651	−0.873255	+	0.487263i	$0.837995\pi$
$984$	39.9657	1.27406
$985$	0	0
$986$	−1.77354	−0.0564810
$987$	20.2724	0.645277
$988$	−42.7728	−1.36078
$989$	85.2116	2.70957
$990$	0	0
$991$	59.3711	1.88599	0.942993	−	0.332813i	$-0.107998\pi$
$991$	59.3711	1.88599	0.942993	+	0.332813i	$0.107998\pi$
$992$	−5.94092	−0.188624
$993$	−19.0600	−0.604850
$994$	−13.1526	−0.417174
$995$	0	0
$996$	−82.8440	−2.62501
$997$	−0.491550	−0.0155675	−0.00778377	−	0.999970i	$-0.502478\pi$
$997$	−0.491550	−0.0155675	−0.00778377	+	0.999970i	$0.502478\pi$
$998$	70.4687	2.23065
$999$	−6.52711	−0.206509

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1925.2.a.bf.1.7		8
5.2	odd	4		385.2.b.d.309.14	yes	16
5.3	odd	4		385.2.b.d.309.3	✓	16
5.4	even	2		1925.2.a.be.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.b.d.309.3	✓	16	5.3	odd	4
385.2.b.d.309.14	yes	16	5.2	odd	4
1925.2.a.be.1.2		8	5.4	even	2
1925.2.a.bf.1.7		8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1925 = 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1925.a (trivial)

\(f(q)\)	\(=\)	\(q+2.43000 q^{2} -2.50028 q^{3} +3.90488 q^{4} -6.07568 q^{6} +1.00000 q^{7} +4.62886 q^{8} +3.25142 q^{9} +O(q^{10})\)	\(q+2.43000 q^{2} -2.50028 q^{3} +3.90488 q^{4} -6.07568 q^{6} +1.00000 q^{7} +4.62886 q^{8} +3.25142 q^{9} +1.00000 q^{11} -9.76332 q^{12} +2.18879 q^{13} +2.43000 q^{14} +3.43835 q^{16} +1.02233 q^{17} +7.90095 q^{18} -5.00442 q^{19} -2.50028 q^{21} +2.43000 q^{22} +7.86206 q^{23} -11.5735 q^{24} +5.31876 q^{26} -0.628633 q^{27} +3.90488 q^{28} -0.713907 q^{29} +6.58245 q^{31} -0.902538 q^{32} -2.50028 q^{33} +2.48427 q^{34} +12.6964 q^{36} +10.3830 q^{37} -12.1607 q^{38} -5.47261 q^{39} -3.45322 q^{41} -6.07568 q^{42} +10.8383 q^{43} +3.90488 q^{44} +19.1048 q^{46} -8.10803 q^{47} -8.59686 q^{48} +1.00000 q^{49} -2.55613 q^{51} +8.54699 q^{52} -4.48118 q^{53} -1.52757 q^{54} +4.62886 q^{56} +12.5125 q^{57} -1.73479 q^{58} +4.20757 q^{59} -6.44231 q^{61} +15.9953 q^{62} +3.25142 q^{63} -9.06987 q^{64} -6.07568 q^{66} +10.6283 q^{67} +3.99210 q^{68} -19.6574 q^{69} -5.41259 q^{71} +15.0504 q^{72} +7.84020 q^{73} +25.2307 q^{74} -19.5417 q^{76} +1.00000 q^{77} -13.2984 q^{78} +4.86426 q^{79} -8.18251 q^{81} -8.39130 q^{82} +8.48523 q^{83} -9.76332 q^{84} +26.3371 q^{86} +1.78497 q^{87} +4.62886 q^{88} +13.4233 q^{89} +2.18879 q^{91} +30.7004 q^{92} -16.4580 q^{93} -19.7025 q^{94} +2.25660 q^{96} -10.5599 q^{97} +2.43000 q^{98} +3.25142 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 6 q^{3} + 14 q^{4} - 6 q^{6} + 8 q^{7} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 + 6 * q^3 + 14 * q^4 - 6 * q^6 + 8 * q^7 + 12 * q^8 + 10 * q^9	\( 8 q + 4 q^{2} + 6 q^{3} + 14 q^{4} - 6 q^{6} + 8 q^{7} + 12 q^{8} + 10 q^{9} + 8 q^{11} + 12 q^{12} + 6 q^{13} + 4 q^{14} + 18 q^{16} + 6 q^{17} + 6 q^{18} - 6 q^{19} + 6 q^{21} + 4 q^{22} + 4 q^{23} + 6 q^{24} - 4 q^{26} + 24 q^{27} + 14 q^{28} + 4 q^{29} - 14 q^{31} + 18 q^{32} + 6 q^{33} - 6 q^{34} + 18 q^{36} + 10 q^{37} - 30 q^{38} + 16 q^{39} - 4 q^{41} - 6 q^{42} + 34 q^{43} + 14 q^{44} - 24 q^{46} - 8 q^{47} + 12 q^{48} + 8 q^{49} + 16 q^{51} + 46 q^{52} + 18 q^{53} + 6 q^{54} + 12 q^{56} + 6 q^{57} - 6 q^{58} - 40 q^{59} + 26 q^{62} + 10 q^{63} + 10 q^{64} - 6 q^{66} + 42 q^{67} + 16 q^{68} - 50 q^{69} + 6 q^{71} + 28 q^{72} + 40 q^{73} - 44 q^{76} + 8 q^{77} - 76 q^{78} + 12 q^{79} + 40 q^{81} + 42 q^{82} + 2 q^{83} + 12 q^{84} + 44 q^{86} + 2 q^{87} + 12 q^{88} + 22 q^{89} + 6 q^{91} + 6 q^{92} - 32 q^{93} - 50 q^{94} - 16 q^{96} - 6 q^{97} + 4 q^{98} + 10 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 + 6 * q^3 + 14 * q^4 - 6 * q^6 + 8 * q^7 + 12 * q^8 + 10 * q^9 + 8 * q^11 + 12 * q^12 + 6 * q^13 + 4 * q^14 + 18 * q^16 + 6 * q^17 + 6 * q^18 - 6 * q^19 + 6 * q^21 + 4 * q^22 + 4 * q^23 + 6 * q^24 - 4 * q^26 + 24 * q^27 + 14 * q^28 + 4 * q^29 - 14 * q^31 + 18 * q^32 + 6 * q^33 - 6 * q^34 + 18 * q^36 + 10 * q^37 - 30 * q^38 + 16 * q^39 - 4 * q^41 - 6 * q^42 + 34 * q^43 + 14 * q^44 - 24 * q^46 - 8 * q^47 + 12 * q^48 + 8 * q^49 + 16 * q^51 + 46 * q^52 + 18 * q^53 + 6 * q^54 + 12 * q^56 + 6 * q^57 - 6 * q^58 - 40 * q^59 + 26 * q^62 + 10 * q^63 + 10 * q^64 - 6 * q^66 + 42 * q^67 + 16 * q^68 - 50 * q^69 + 6 * q^71 + 28 * q^72 + 40 * q^73 - 44 * q^76 + 8 * q^77 - 76 * q^78 + 12 * q^79 + 40 * q^81 + 42 * q^82 + 2 * q^83 + 12 * q^84 + 44 * q^86 + 2 * q^87 + 12 * q^88 + 22 * q^89 + 6 * q^91 + 6 * q^92 - 32 * q^93 - 50 * q^94 - 16 * q^96 - 6 * q^97 + 4 * q^98 + 10 * q^99

Introduction

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