LMFDB - Embedded newform 5775.2.a.bq.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5775,2,Mod(1,5775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5775, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("5775.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5775 = 3 \cdot 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5775.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:	$46.1136071673$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1155)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.81361$ of defining polynomial
Character	$\chi$	$=$	5775.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.81361 q^{2} -1.00000 q^{3} +1.28917 q^{4} -1.81361 q^{6} +1.00000 q^{7} -1.28917 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.81361 q^{2} -1.00000 q^{3} +1.28917 q^{4} -1.81361 q^{6} +1.00000 q^{7} -1.28917 q^{8} +1.00000 q^{9} +1.00000 q^{11} -1.28917 q^{12} -5.10278 q^{13} +1.81361 q^{14} -4.91638 q^{16} +1.91638 q^{17} +1.81361 q^{18} +3.33804 q^{19} -1.00000 q^{21} +1.81361 q^{22} +2.28917 q^{23} +1.28917 q^{24} -9.25443 q^{26} -1.00000 q^{27} +1.28917 q^{28} +1.18639 q^{29} -2.52444 q^{31} -6.33804 q^{32} -1.00000 q^{33} +3.47556 q^{34} +1.28917 q^{36} -3.94610 q^{37} +6.05390 q^{38} +5.10278 q^{39} -1.68111 q^{41} -1.81361 q^{42} -7.01916 q^{43} +1.28917 q^{44} +4.15165 q^{46} -2.52444 q^{47} +4.91638 q^{48} +1.00000 q^{49} -1.91638 q^{51} -6.57834 q^{52} -0.289169 q^{53} -1.81361 q^{54} -1.28917 q^{56} -3.33804 q^{57} +2.15165 q^{58} -10.4408 q^{59} +6.49472 q^{61} -4.57834 q^{62} +1.00000 q^{63} -1.66196 q^{64} -1.81361 q^{66} +0.578337 q^{67} +2.47054 q^{68} -2.28917 q^{69} -13.3083 q^{71} -1.28917 q^{72} -0.372787 q^{73} -7.15667 q^{74} +4.30330 q^{76} +1.00000 q^{77} +9.25443 q^{78} +15.4061 q^{79} +1.00000 q^{81} -3.04888 q^{82} -15.7491 q^{83} -1.28917 q^{84} -12.7300 q^{86} -1.18639 q^{87} -1.28917 q^{88} -0.0297193 q^{89} -5.10278 q^{91} +2.95112 q^{92} +2.52444 q^{93} -4.57834 q^{94} +6.33804 q^{96} -15.8030 q^{97} +1.81361 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} - 3 q^{3} + 3 q^{4} + q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - q^2 - 3 * q^3 + 3 * q^4 + q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	$ 3 q - q^{2} - 3 q^{3} + 3 q^{4} + q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} + 3 q^{11} - 3 q^{12} - 8 q^{13} - q^{14} - q^{16} - 8 q^{17} - q^{18} - 2 q^{19} - 3 q^{21} - q^{22} + 6 q^{23} + 3 q^{24} - 2 q^{26} - 3 q^{27} + 3 q^{28} + 10 q^{29} - 2 q^{31} - 7 q^{32} - 3 q^{33} + 16 q^{34} + 3 q^{36} - 8 q^{37} + 22 q^{38} + 8 q^{39} + 4 q^{41} + q^{42} + 3 q^{44} - 6 q^{46} - 2 q^{47} + q^{48} + 3 q^{49} + 8 q^{51} - 18 q^{52} + q^{54} - 3 q^{56} + 2 q^{57} - 12 q^{58} - 12 q^{59} + 4 q^{61} - 12 q^{62} + 3 q^{63} - 17 q^{64} + q^{66} - 2 q^{68} - 6 q^{69} - 18 q^{71} - 3 q^{72} - 14 q^{73} - 18 q^{74} - 24 q^{76} + 3 q^{77} + 2 q^{78} + 2 q^{79} + 3 q^{81} + 2 q^{82} - 6 q^{83} - 3 q^{84} - 18 q^{86} - 10 q^{87} - 3 q^{88} - 10 q^{89} - 8 q^{91} + 20 q^{92} + 2 q^{93} - 12 q^{94} + 7 q^{96} - 10 q^{97} - q^{98} + 3 q^{99}+O(q^{100}) $ 3 * q - q^2 - 3 * q^3 + 3 * q^4 + q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 + 3 * q^11 - 3 * q^12 - 8 * q^13 - q^14 - q^16 - 8 * q^17 - q^18 - 2 * q^19 - 3 * q^21 - q^22 + 6 * q^23 + 3 * q^24 - 2 * q^26 - 3 * q^27 + 3 * q^28 + 10 * q^29 - 2 * q^31 - 7 * q^32 - 3 * q^33 + 16 * q^34 + 3 * q^36 - 8 * q^37 + 22 * q^38 + 8 * q^39 + 4 * q^41 + q^42 + 3 * q^44 - 6 * q^46 - 2 * q^47 + q^48 + 3 * q^49 + 8 * q^51 - 18 * q^52 + q^54 - 3 * q^56 + 2 * q^57 - 12 * q^58 - 12 * q^59 + 4 * q^61 - 12 * q^62 + 3 * q^63 - 17 * q^64 + q^66 - 2 * q^68 - 6 * q^69 - 18 * q^71 - 3 * q^72 - 14 * q^73 - 18 * q^74 - 24 * q^76 + 3 * q^77 + 2 * q^78 + 2 * q^79 + 3 * q^81 + 2 * q^82 - 6 * q^83 - 3 * q^84 - 18 * q^86 - 10 * q^87 - 3 * q^88 - 10 * q^89 - 8 * q^91 + 20 * q^92 + 2 * q^93 - 12 * q^94 + 7 * q^96 - 10 * q^97 - q^98 + 3 * 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 $

$2$	1.81361	1.28241	0.641207	−	0.767368i	$-0.278434\pi$
$2$	1.81361	1.28241	0.641207	+	0.767368i	$0.278434\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.28917	0.644584
$5$	0	0
$5$	0	0
$6$	−1.81361	−0.740402
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.28917	−0.455790
$9$	1.00000	0.333333
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.28917	−0.372151
$13$	−5.10278	−1.41526	−0.707628	−	0.706586i	$-0.750235\pi$
$13$	−5.10278	−1.41526	−0.707628	+	0.706586i	$0.750235\pi$
$14$	1.81361	0.484707
$15$	0	0
$16$	−4.91638	−1.22910
$17$	1.91638	0.464791	0.232395	−	0.972621i	$-0.425344\pi$
$17$	1.91638	0.464791	0.232395	+	0.972621i	$0.425344\pi$
$18$	1.81361	0.427471
$19$	3.33804	0.765800	0.382900	−	0.923790i	$-0.374925\pi$
$19$	3.33804	0.765800	0.382900	+	0.923790i	$0.374925\pi$
$20$	0	0
$21$	−1.00000	−0.218218
$22$	1.81361	0.386662
$23$	2.28917	0.477325	0.238662	−	0.971103i	$-0.423291\pi$
$23$	2.28917	0.477325	0.238662	+	0.971103i	$0.423291\pi$
$24$	1.28917	0.263150
$25$	0	0
$26$	−9.25443	−1.81494
$27$	−1.00000	−0.192450
$28$	1.28917	0.243630
$29$	1.18639	0.220308	0.110154	−	0.993915i	$-0.464866\pi$
$29$	1.18639	0.220308	0.110154	+	0.993915i	$0.464866\pi$
$30$	0	0
$31$	−2.52444	−0.453402	−0.226701	−	0.973964i	$-0.572794\pi$
$31$	−2.52444	−0.453402	−0.226701	+	0.973964i	$0.572794\pi$
$32$	−6.33804	−1.12042
$33$	−1.00000	−0.174078
$34$	3.47556	0.596054
$35$	0	0
$36$	1.28917	0.214861
$37$	−3.94610	−0.648735	−0.324367	−	0.945931i	$-0.605151\pi$
$37$	−3.94610	−0.648735	−0.324367	+	0.945931i	$0.605151\pi$
$38$	6.05390	0.982072
$39$	5.10278	0.817098
$40$	0	0
$41$	−1.68111	−0.262546	−0.131273	−	0.991346i	$-0.541906\pi$
$41$	−1.68111	−0.262546	−0.131273	+	0.991346i	$0.541906\pi$
$42$	−1.81361	−0.279846
$43$	−7.01916	−1.07041	−0.535206	−	0.844722i	$-0.679766\pi$
$43$	−7.01916	−1.07041	−0.535206	+	0.844722i	$0.679766\pi$
$44$	1.28917	0.194349
$45$	0	0
$46$	4.15165	0.612128
$47$	−2.52444	−0.368227	−0.184114	−	0.982905i	$-0.558941\pi$
$47$	−2.52444	−0.368227	−0.184114	+	0.982905i	$0.558941\pi$
$48$	4.91638	0.709619
$49$	1.00000	0.142857
$50$	0	0
$51$	−1.91638	−0.268347
$52$	−6.57834	−0.912251
$53$	−0.289169	−0.0397204	−0.0198602	−	0.999803i	$-0.506322\pi$
$53$	−0.289169	−0.0397204	−0.0198602	+	0.999803i	$0.506322\pi$
$54$	−1.81361	−0.246801
$55$	0	0
$56$	−1.28917	−0.172272
$57$	−3.33804	−0.442135
$58$	2.15165	0.282526
$59$	−10.4408	−1.35928	−0.679639	−	0.733546i	$-0.737864\pi$
$59$	−10.4408	−1.35928	−0.679639	+	0.733546i	$0.737864\pi$
$60$	0	0
$61$	6.49472	0.831564	0.415782	−	0.909464i	$-0.363508\pi$
$61$	6.49472	0.831564	0.415782	+	0.909464i	$0.363508\pi$
$62$	−4.57834	−0.581449
$63$	1.00000	0.125988
$64$	−1.66196	−0.207744
$65$	0	0
$66$	−1.81361	−0.223240
$67$	0.578337	0.0706551	0.0353276	−	0.999376i	$-0.488753\pi$
$67$	0.578337	0.0706551	0.0353276	+	0.999376i	$0.488753\pi$
$68$	2.47054	0.299597
$69$	−2.28917	−0.275584
$70$	0	0
$71$	−13.3083	−1.57941	−0.789704	−	0.613488i	$-0.789766\pi$
$71$	−13.3083	−1.57941	−0.789704	+	0.613488i	$0.789766\pi$
$72$	−1.28917	−0.151930
$73$	−0.372787	−0.0436314	−0.0218157	−	0.999762i	$-0.506945\pi$
$73$	−0.372787	−0.0436314	−0.0218157	+	0.999762i	$0.506945\pi$
$74$	−7.15667	−0.831946
$75$	0	0
$76$	4.30330	0.493623
$77$	1.00000	0.113961
$78$	9.25443	1.04786
$79$	15.4061	1.73332	0.866660	−	0.498900i	$-0.166263\pi$
$79$	15.4061	1.73332	0.866660	+	0.498900i	$0.166263\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−3.04888	−0.336692
$83$	−15.7491	−1.72869	−0.864347	−	0.502897i	$-0.832268\pi$
$83$	−15.7491	−1.72869	−0.864347	+	0.502897i	$0.832268\pi$
$84$	−1.28917	−0.140660
$85$	0	0
$86$	−12.7300	−1.37271
$87$	−1.18639	−0.127195
$88$	−1.28917	−0.137426
$89$	−0.0297193	−0.00315024	−0.00157512	−	0.999999i	$-0.500501\pi$
$89$	−0.0297193	−0.00315024	−0.00157512	+	0.999999i	$0.500501\pi$
$90$	0	0
$91$	−5.10278	−0.534916
$92$	2.95112	0.307676
$93$	2.52444	0.261772
$94$	−4.57834	−0.472219
$95$	0	0
$96$	6.33804	0.646874
$97$	−15.8030	−1.60456	−0.802278	−	0.596951i	$-0.796379\pi$
$97$	−15.8030	−1.60456	−0.802278	+	0.596951i	$0.796379\pi$
$98$	1.81361	0.183202
$99$	1.00000	0.100504
$100$	0	0
$101$	−6.41110	−0.637928	−0.318964	−	0.947767i	$-0.603335\pi$
$101$	−6.41110	−0.637928	−0.318964	+	0.947767i	$0.603335\pi$
$102$	−3.47556	−0.344132
$103$	−4.81361	−0.474299	−0.237149	−	0.971473i	$-0.576213\pi$
$103$	−4.81361	−0.474299	−0.237149	+	0.971473i	$0.576213\pi$
$104$	6.57834	0.645059
$105$	0	0
$106$	−0.524438	−0.0509379
$107$	13.8867	1.34247	0.671237	−	0.741243i	$-0.265763\pi$
$107$	13.8867	1.34247	0.671237	+	0.741243i	$0.265763\pi$
$108$	−1.28917	−0.124050
$109$	−2.25945	−0.216416	−0.108208	−	0.994128i	$-0.534511\pi$
$109$	−2.25945	−0.216416	−0.108208	+	0.994128i	$0.534511\pi$
$110$	0	0
$111$	3.94610	0.374547
$112$	−4.91638	−0.464554
$113$	−9.17081	−0.862717	−0.431359	−	0.902181i	$-0.641966\pi$
$113$	−9.17081	−0.862717	−0.431359	+	0.902181i	$0.641966\pi$
$114$	−6.05390	−0.567000
$115$	0	0
$116$	1.52946	0.142007
$117$	−5.10278	−0.471752
$118$	−18.9355	−1.74316
$119$	1.91638	0.175674
$120$	0	0
$121$	1.00000	0.0909091
$122$	11.7789	1.06641
$123$	1.68111	0.151581
$124$	−3.25443	−0.292256
$125$	0	0
$126$	1.81361	0.161569
$127$	−15.5975	−1.38405	−0.692027	−	0.721872i	$-0.743282\pi$
$127$	−15.5975	−1.38405	−0.692027	+	0.721872i	$0.743282\pi$
$128$	9.66196	0.854004
$129$	7.01916	0.618002
$130$	0	0
$131$	−5.36776	−0.468984	−0.234492	−	0.972118i	$-0.575343\pi$
$131$	−5.36776	−0.468984	−0.234492	+	0.972118i	$0.575343\pi$
$132$	−1.28917	−0.112208
$133$	3.33804	0.289445
$134$	1.04888	0.0906091
$135$	0	0
$136$	−2.47054	−0.211847
$137$	−19.2927	−1.64829	−0.824145	−	0.566379i	$-0.808344\pi$
$137$	−19.2927	−1.64829	−0.824145	+	0.566379i	$0.808344\pi$
$138$	−4.15165	−0.353412
$139$	−3.52946	−0.299365	−0.149682	−	0.988734i	$-0.547825\pi$
$139$	−3.52946	−0.299365	−0.149682	+	0.988734i	$0.547825\pi$
$140$	0	0
$141$	2.52444	0.212596
$142$	−24.1361	−2.02545
$143$	−5.10278	−0.426715
$144$	−4.91638	−0.409698
$145$	0	0
$146$	−0.676089	−0.0559535
$147$	−1.00000	−0.0824786
$148$	−5.08719	−0.418164
$149$	13.3622	1.09468	0.547338	−	0.836912i	$-0.315641\pi$
$149$	13.3622	1.09468	0.547338	+	0.836912i	$0.315641\pi$
$150$	0	0
$151$	12.5783	1.02361	0.511805	−	0.859101i	$-0.328977\pi$
$151$	12.5783	1.02361	0.511805	+	0.859101i	$0.328977\pi$
$152$	−4.30330	−0.349044
$153$	1.91638	0.154930
$154$	1.81361	0.146145
$155$	0	0
$156$	6.57834	0.526688
$157$	1.59749	0.127494	0.0637469	−	0.997966i	$-0.479695\pi$
$157$	1.59749	0.127494	0.0637469	+	0.997966i	$0.479695\pi$
$158$	27.9406	2.22283
$159$	0.289169	0.0229326
$160$	0	0
$161$	2.28917	0.180412
$162$	1.81361	0.142490
$163$	8.62219	0.675342	0.337671	−	0.941264i	$-0.390361\pi$
$163$	8.62219	0.675342	0.337671	+	0.941264i	$0.390361\pi$
$164$	−2.16724	−0.169233
$165$	0	0
$166$	−28.5628	−2.21690
$167$	−17.6272	−1.36403	−0.682017	−	0.731336i	$-0.738897\pi$
$167$	−17.6272	−1.36403	−0.682017	+	0.731336i	$0.738897\pi$
$168$	1.28917	0.0994615
$169$	13.0383	1.00295
$170$	0	0
$171$	3.33804	0.255267
$172$	−9.04888	−0.689970
$173$	−20.0383	−1.52348	−0.761742	−	0.647880i	$-0.775656\pi$
$173$	−20.0383	−1.52348	−0.761742	+	0.647880i	$0.775656\pi$
$174$	−2.15165	−0.163116
$175$	0	0
$176$	−4.91638	−0.370586
$177$	10.4408	0.784780
$178$	−0.0538991	−0.00403991
$179$	−4.89722	−0.366036	−0.183018	−	0.983110i	$-0.558587\pi$
$179$	−4.89722	−0.366036	−0.183018	+	0.983110i	$0.558587\pi$
$180$	0	0
$181$	−6.41110	−0.476533	−0.238267	−	0.971200i	$-0.576579\pi$
$181$	−6.41110	−0.476533	−0.238267	+	0.971200i	$0.576579\pi$
$182$	−9.25443	−0.685984
$183$	−6.49472	−0.480103
$184$	−2.95112	−0.217560
$185$	0	0
$186$	4.57834	0.335700
$187$	1.91638	0.140140
$188$	−3.25443	−0.237353
$189$	−1.00000	−0.0727393
$190$	0	0
$191$	−10.0978	−0.730648	−0.365324	−	0.930880i	$-0.619042\pi$
$191$	−10.0978	−0.730648	−0.365324	+	0.930880i	$0.619042\pi$
$192$	1.66196	0.119941
$193$	−7.04888	−0.507389	−0.253695	−	0.967284i	$-0.581646\pi$
$193$	−7.04888	−0.507389	−0.253695	+	0.967284i	$0.581646\pi$
$194$	−28.6605	−2.05770
$195$	0	0
$196$	1.28917	0.0920835
$197$	0.372787	0.0265600	0.0132800	−	0.999912i	$-0.495773\pi$
$197$	0.372787	0.0265600	0.0132800	+	0.999912i	$0.495773\pi$
$198$	1.81361	0.128887
$199$	−23.6655	−1.67760	−0.838802	−	0.544436i	$-0.816744\pi$
$199$	−23.6655	−1.67760	−0.838802	+	0.544436i	$0.816744\pi$
$200$	0	0
$201$	−0.578337	−0.0407928
$202$	−11.6272	−0.818088
$203$	1.18639	0.0832685
$204$	−2.47054	−0.172972
$205$	0	0
$206$	−8.72999	−0.608247
$207$	2.28917	0.159108
$208$	25.0872	1.73948
$209$	3.33804	0.230897
$210$	0	0
$211$	3.52946	0.242978	0.121489	−	0.992593i	$-0.461233\pi$
$211$	3.52946	0.242978	0.121489	+	0.992593i	$0.461233\pi$
$212$	−0.372787	−0.0256031
$213$	13.3083	0.911871
$214$	25.1849	1.72161
$215$	0	0
$216$	1.28917	0.0877168
$217$	−2.52444	−0.171370
$218$	−4.09775	−0.277535
$219$	0.372787	0.0251906
$220$	0	0
$221$	−9.77886	−0.657798
$222$	7.15667	0.480325
$223$	26.6847	1.78694	0.893469	−	0.449124i	$-0.148264\pi$
$223$	26.6847	1.78694	0.893469	+	0.449124i	$0.148264\pi$
$224$	−6.33804	−0.423478
$225$	0	0
$226$	−16.6322	−1.10636
$227$	24.6902	1.63875	0.819374	−	0.573260i	$-0.194321\pi$
$227$	24.6902	1.63875	0.819374	+	0.573260i	$0.194321\pi$
$228$	−4.30330	−0.284993
$229$	−18.8972	−1.24876	−0.624382	−	0.781119i	$-0.714649\pi$
$229$	−18.8972	−1.24876	−0.624382	+	0.781119i	$0.714649\pi$
$230$	0	0
$231$	−1.00000	−0.0657952
$232$	−1.52946	−0.100414
$233$	15.0333	0.984864	0.492432	−	0.870351i	$-0.336108\pi$
$233$	15.0333	0.984864	0.492432	+	0.870351i	$0.336108\pi$
$234$	−9.25443	−0.604981
$235$	0	0
$236$	−13.4600	−0.876170
$237$	−15.4061	−1.00073
$238$	3.47556	0.225287
$239$	0.0680325	0.00440066	0.00220033	−	0.999998i	$-0.499300\pi$
$239$	0.0680325	0.00440066	0.00220033	+	0.999998i	$0.499300\pi$
$240$	0	0
$241$	−15.9305	−1.02617	−0.513087	−	0.858336i	$-0.671498\pi$
$241$	−15.9305	−1.02617	−0.513087	+	0.858336i	$0.671498\pi$
$242$	1.81361	0.116583
$243$	−1.00000	−0.0641500
$244$	8.37279	0.536013
$245$	0	0
$246$	3.04888	0.194389
$247$	−17.0333	−1.08380
$248$	3.25443	0.206656
$249$	15.7491	0.998061
$250$	0	0
$251$	8.41110	0.530904	0.265452	−	0.964124i	$-0.414479\pi$
$251$	8.41110	0.530904	0.265452	+	0.964124i	$0.414479\pi$
$252$	1.28917	0.0812100
$253$	2.28917	0.143919
$254$	−28.2877	−1.77493
$255$	0	0
$256$	20.8469	1.30293
$257$	−2.72999	−0.170292	−0.0851460	−	0.996368i	$-0.527136\pi$
$257$	−2.72999	−0.170292	−0.0851460	+	0.996368i	$0.527136\pi$
$258$	12.7300	0.792534
$259$	−3.94610	−0.245199
$260$	0	0
$261$	1.18639	0.0734359
$262$	−9.73501	−0.601431
$263$	−12.7144	−0.784004	−0.392002	−	0.919964i	$-0.628217\pi$
$263$	−12.7144	−0.784004	−0.392002	+	0.919964i	$0.628217\pi$
$264$	1.28917	0.0793428
$265$	0	0
$266$	6.05390	0.371188
$267$	0.0297193	0.00181879
$268$	0.745574	0.0455432
$269$	25.1552	1.53374	0.766870	−	0.641802i	$-0.221813\pi$
$269$	25.1552	1.53374	0.766870	+	0.641802i	$0.221813\pi$
$270$	0	0
$271$	−15.8086	−0.960303	−0.480152	−	0.877186i	$-0.659418\pi$
$271$	−15.8086	−0.960303	−0.480152	+	0.877186i	$0.659418\pi$
$272$	−9.42166	−0.571272
$273$	5.10278	0.308834
$274$	−34.9894	−2.11379
$275$	0	0
$276$	−2.95112	−0.177637
$277$	14.2439	0.855831	0.427915	−	0.903819i	$-0.359248\pi$
$277$	14.2439	0.855831	0.427915	+	0.903819i	$0.359248\pi$
$278$	−6.40105	−0.383910
$279$	−2.52444	−0.151134
$280$	0	0
$281$	11.9305	0.711715	0.355857	−	0.934540i	$-0.384189\pi$
$281$	11.9305	0.711715	0.355857	+	0.934540i	$0.384189\pi$
$282$	4.57834	0.272636
$283$	7.98441	0.474624	0.237312	−	0.971433i	$-0.423734\pi$
$283$	7.98441	0.474624	0.237312	+	0.971433i	$0.423734\pi$
$284$	−17.1567	−1.01806
$285$	0	0
$286$	−9.25443	−0.547226
$287$	−1.68111	−0.0992329
$288$	−6.33804	−0.373473
$289$	−13.3275	−0.783970
$290$	0	0
$291$	15.8030	0.926391
$292$	−0.480585	−0.0281241
$293$	33.3069	1.94581	0.972904	−	0.231209i	$-0.0742681\pi$
$293$	33.3069	1.94581	0.972904	+	0.231209i	$0.0742681\pi$
$294$	−1.81361	−0.105772
$295$	0	0
$296$	5.08719	0.295687
$297$	−1.00000	−0.0580259
$298$	24.2338	1.40383
$299$	−11.6811	−0.675536
$300$	0	0
$301$	−7.01916	−0.404577
$302$	22.8122	1.31269
$303$	6.41110	0.368308
$304$	−16.4111	−0.941241
$305$	0	0
$306$	3.47556	0.198685
$307$	−20.4705	−1.16832	−0.584158	−	0.811640i	$-0.698575\pi$
$307$	−20.4705	−1.16832	−0.584158	+	0.811640i	$0.698575\pi$
$308$	1.28917	0.0734572
$309$	4.81361	0.273837
$310$	0	0
$311$	3.89220	0.220707	0.110353	−	0.993892i	$-0.464802\pi$
$311$	3.89220	0.220707	0.110353	+	0.993892i	$0.464802\pi$
$312$	−6.57834	−0.372425
$313$	13.4303	0.759123	0.379561	−	0.925167i	$-0.376075\pi$
$313$	13.4303	0.759123	0.379561	+	0.925167i	$0.376075\pi$
$314$	2.89722	0.163500
$315$	0	0
$316$	19.8610	1.11727
$317$	29.0872	1.63370	0.816850	−	0.576851i	$-0.195719\pi$
$317$	29.0872	1.63370	0.816850	+	0.576851i	$0.195719\pi$
$318$	0.524438	0.0294090
$319$	1.18639	0.0664253
$320$	0	0
$321$	−13.8867	−0.775078
$322$	4.15165	0.231362
$323$	6.39697	0.355937
$324$	1.28917	0.0716205
$325$	0	0
$326$	15.6373	0.866068
$327$	2.25945	0.124948
$328$	2.16724	0.119666
$329$	−2.52444	−0.139177
$330$	0	0
$331$	−19.8086	−1.08878	−0.544389	−	0.838833i	$-0.683238\pi$
$331$	−19.8086	−1.08878	−0.544389	+	0.838833i	$0.683238\pi$
$332$	−20.3033	−1.11429
$333$	−3.94610	−0.216245
$334$	−31.9688	−1.74926
$335$	0	0
$336$	4.91638	0.268211
$337$	21.4303	1.16738	0.583690	−	0.811976i	$-0.301608\pi$
$337$	21.4303	1.16738	0.583690	+	0.811976i	$0.301608\pi$
$338$	23.6464	1.28619
$339$	9.17081	0.498090
$340$	0	0
$341$	−2.52444	−0.136706
$342$	6.05390	0.327357
$343$	1.00000	0.0539949
$344$	9.04888	0.487883
$345$	0	0
$346$	−36.3416	−1.95374
$347$	30.6167	1.64359	0.821794	−	0.569785i	$-0.192973\pi$
$347$	30.6167	1.64359	0.821794	+	0.569785i	$0.192973\pi$
$348$	−1.52946	−0.0819877
$349$	−6.38692	−0.341884	−0.170942	−	0.985281i	$-0.554681\pi$
$349$	−6.38692	−0.341884	−0.170942	+	0.985281i	$0.554681\pi$
$350$	0	0
$351$	5.10278	0.272366
$352$	−6.33804	−0.337819
$353$	−10.6378	−0.566192	−0.283096	−	0.959092i	$-0.591361\pi$
$353$	−10.6378	−0.566192	−0.283096	+	0.959092i	$0.591361\pi$
$354$	18.9355	1.00641
$355$	0	0
$356$	−0.0383132	−0.00203060
$357$	−1.91638	−0.101426
$358$	−8.88164	−0.469409
$359$	−32.3713	−1.70849	−0.854247	−	0.519868i	$-0.825981\pi$
$359$	−32.3713	−1.70849	−0.854247	+	0.519868i	$0.825981\pi$
$360$	0	0
$361$	−7.85746	−0.413550
$362$	−11.6272	−0.611113
$363$	−1.00000	−0.0524864
$364$	−6.57834	−0.344799
$365$	0	0
$366$	−11.7789	−0.615691
$367$	−19.7053	−1.02861	−0.514304	−	0.857608i	$-0.671950\pi$
$367$	−19.7053	−1.02861	−0.514304	+	0.857608i	$0.671950\pi$
$368$	−11.2544	−0.586678
$369$	−1.68111	−0.0875152
$370$	0	0
$371$	−0.289169	−0.0150129
$372$	3.25443	0.168734
$373$	−5.12695	−0.265464	−0.132732	−	0.991152i	$-0.542375\pi$
$373$	−5.12695	−0.265464	−0.132732	+	0.991152i	$0.542375\pi$
$374$	3.47556	0.179717
$375$	0	0
$376$	3.25443	0.167834
$377$	−6.05390	−0.311792
$378$	−1.81361	−0.0932819
$379$	9.07306	0.466052	0.233026	−	0.972471i	$-0.425137\pi$
$379$	9.07306	0.466052	0.233026	+	0.972471i	$0.425137\pi$
$380$	0	0
$381$	15.5975	0.799084
$382$	−18.3133	−0.936992
$383$	6.16170	0.314848	0.157424	−	0.987531i	$-0.449681\pi$
$383$	6.16170	0.314848	0.157424	+	0.987531i	$0.449681\pi$
$384$	−9.66196	−0.493060
$385$	0	0
$386$	−12.7839	−0.650683
$387$	−7.01916	−0.356804
$388$	−20.3728	−1.03427
$389$	10.9739	0.556396	0.278198	−	0.960524i	$-0.410263\pi$
$389$	10.9739	0.556396	0.278198	+	0.960524i	$0.410263\pi$
$390$	0	0
$391$	4.38692	0.221856
$392$	−1.28917	−0.0651128
$393$	5.36776	0.270768
$394$	0.676089	0.0340609
$395$	0	0
$396$	1.28917	0.0647832
$397$	−31.9305	−1.60255	−0.801273	−	0.598298i	$-0.795844\pi$
$397$	−31.9305	−1.60255	−0.801273	+	0.598298i	$0.795844\pi$
$398$	−42.9200	−2.15138
$399$	−3.33804	−0.167111
$400$	0	0
$401$	−14.7300	−0.735581	−0.367790	−	0.929909i	$-0.619886\pi$
$401$	−14.7300	−0.735581	−0.367790	+	0.929909i	$0.619886\pi$
$402$	−1.04888	−0.0523132
$403$	12.8816	0.641680
$404$	−8.26499	−0.411199
$405$	0	0
$406$	2.15165	0.106785
$407$	−3.94610	−0.195601
$408$	2.47054	0.122310
$409$	−2.36274	−0.116830	−0.0584150	−	0.998292i	$-0.518605\pi$
$409$	−2.36274	−0.116830	−0.0584150	+	0.998292i	$0.518605\pi$
$410$	0	0
$411$	19.2927	0.951641
$412$	−6.20555	−0.305726
$413$	−10.4408	−0.513759
$414$	4.15165	0.204043
$415$	0	0
$416$	32.3416	1.58568
$417$	3.52946	0.172838
$418$	6.05390	0.296106
$419$	−11.5975	−0.566575	−0.283287	−	0.959035i	$-0.591425\pi$
$419$	−11.5975	−0.566575	−0.283287	+	0.959035i	$0.591425\pi$
$420$	0	0
$421$	15.4842	0.754652	0.377326	−	0.926081i	$-0.376844\pi$
$421$	15.4842	0.754652	0.377326	+	0.926081i	$0.376844\pi$
$422$	6.40105	0.311598
$423$	−2.52444	−0.122742
$424$	0.372787	0.0181041
$425$	0	0
$426$	24.1361	1.16940
$427$	6.49472	0.314301
$428$	17.9022	0.865338
$429$	5.10278	0.246364
$430$	0	0
$431$	−23.9688	−1.15454	−0.577269	−	0.816554i	$-0.695882\pi$
$431$	−23.9688	−1.15454	−0.577269	+	0.816554i	$0.695882\pi$
$432$	4.91638	0.236540
$433$	−4.73553	−0.227575	−0.113787	−	0.993505i	$-0.536298\pi$
$433$	−4.73553	−0.227575	−0.113787	+	0.993505i	$0.536298\pi$
$434$	−4.57834	−0.219767
$435$	0	0
$436$	−2.91281	−0.139498
$437$	7.64135	0.365535
$438$	0.676089	0.0323048
$439$	−13.3764	−0.638419	−0.319209	−	0.947684i	$-0.603417\pi$
$439$	−13.3764	−0.638419	−0.319209	+	0.947684i	$0.603417\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	−17.7350	−0.843568
$443$	−11.1950	−0.531890	−0.265945	−	0.963988i	$-0.585684\pi$
$443$	−11.1950	−0.531890	−0.265945	+	0.963988i	$0.585684\pi$
$444$	5.08719	0.241427
$445$	0	0
$446$	48.3955	2.29159
$447$	−13.3622	−0.632012
$448$	−1.66196	−0.0785200
$449$	9.23884	0.436008	0.218004	−	0.975948i	$-0.430045\pi$
$449$	9.23884	0.436008	0.218004	+	0.975948i	$0.430045\pi$
$450$	0	0
$451$	−1.68111	−0.0791605
$452$	−11.8227	−0.556094
$453$	−12.5783	−0.590982
$454$	44.7783	2.10155
$455$	0	0
$456$	4.30330	0.201521
$457$	−13.7053	−0.641107	−0.320553	−	0.947230i	$-0.603869\pi$
$457$	−13.7053	−0.641107	−0.320553	+	0.947230i	$0.603869\pi$
$458$	−34.2721	−1.60143
$459$	−1.91638	−0.0894490
$460$	0	0
$461$	−12.6167	−0.587616	−0.293808	−	0.955864i	$-0.594923\pi$
$461$	−12.6167	−0.587616	−0.293808	+	0.955864i	$0.594923\pi$
$462$	−1.81361	−0.0843766
$463$	−21.0972	−0.980472	−0.490236	−	0.871590i	$-0.663089\pi$
$463$	−21.0972	−0.980472	−0.490236	+	0.871590i	$0.663089\pi$
$464$	−5.83276	−0.270779
$465$	0	0
$466$	27.2645	1.26300
$467$	29.7944	1.37872	0.689361	−	0.724418i	$-0.257891\pi$
$467$	29.7944	1.37872	0.689361	+	0.724418i	$0.257891\pi$
$468$	−6.57834	−0.304084
$469$	0.578337	0.0267051
$470$	0	0
$471$	−1.59749	−0.0736086
$472$	13.4600	0.619546
$473$	−7.01916	−0.322741
$474$	−27.9406	−1.28335
$475$	0	0
$476$	2.47054	0.113237
$477$	−0.289169	−0.0132401
$478$	0.123384	0.00564346
$479$	30.0822	1.37449	0.687245	−	0.726426i	$-0.258820\pi$
$479$	30.0822	1.37449	0.687245	+	0.726426i	$0.258820\pi$
$480$	0	0
$481$	20.1361	0.918126
$482$	−28.8917	−1.31598
$483$	−2.28917	−0.104161
$484$	1.28917	0.0585986
$485$	0	0
$486$	−1.81361	−0.0822669
$487$	23.8016	1.07855	0.539277	−	0.842129i	$-0.318698\pi$
$487$	23.8016	1.07855	0.539277	+	0.842129i	$0.318698\pi$
$488$	−8.37279	−0.379018
$489$	−8.62219	−0.389909
$490$	0	0
$491$	−32.9980	−1.48918	−0.744590	−	0.667522i	$-0.767355\pi$
$491$	−32.9980	−1.48918	−0.744590	+	0.667522i	$0.767355\pi$
$492$	2.16724	0.0977066
$493$	2.27358	0.102397
$494$	−30.8917	−1.38988
$495$	0	0
$496$	12.4111	0.557275
$497$	−13.3083	−0.596960
$498$	28.5628	1.27993
$499$	7.44584	0.333322	0.166661	−	0.986014i	$-0.446701\pi$
$499$	7.44584	0.333322	0.166661	+	0.986014i	$0.446701\pi$
$500$	0	0
$501$	17.6272	0.787526
$502$	15.2544	0.680838
$503$	−13.7592	−0.613492	−0.306746	−	0.951791i	$-0.599240\pi$
$503$	−13.7592	−0.613492	−0.306746	+	0.951791i	$0.599240\pi$
$504$	−1.28917	−0.0574241
$505$	0	0
$506$	4.15165	0.184563
$507$	−13.0383	−0.579052
$508$	−20.1078	−0.892139
$509$	−9.43026	−0.417989	−0.208994	−	0.977917i	$-0.567019\pi$
$509$	−9.43026	−0.417989	−0.208994	+	0.977917i	$0.567019\pi$
$510$	0	0
$511$	−0.372787	−0.0164911
$512$	18.4842	0.816892
$513$	−3.33804	−0.147378
$514$	−4.95112	−0.218385
$515$	0	0
$516$	9.04888	0.398355
$517$	−2.52444	−0.111025
$518$	−7.15667	−0.314446
$519$	20.0383	0.879584
$520$	0	0
$521$	15.9703	0.699671	0.349835	−	0.936811i	$-0.386238\pi$
$521$	15.9703	0.699671	0.349835	+	0.936811i	$0.386238\pi$
$522$	2.15165	0.0941752
$523$	13.6756	0.597991	0.298996	−	0.954255i	$-0.403348\pi$
$523$	13.6756	0.597991	0.298996	+	0.954255i	$0.403348\pi$
$524$	−6.91995	−0.302300
$525$	0	0
$526$	−23.0589	−1.00542
$527$	−4.83779	−0.210737
$528$	4.91638	0.213958
$529$	−17.7597	−0.772161
$530$	0	0
$531$	−10.4408	−0.453093
$532$	4.30330	0.186572
$533$	8.57834	0.371569
$534$	0.0538991	0.00233244
$535$	0	0
$536$	−0.745574	−0.0322039
$537$	4.89722	0.211331
$538$	45.6217	1.96689
$539$	1.00000	0.0430730
$540$	0	0
$541$	13.7406	0.590752	0.295376	−	0.955381i	$-0.404555\pi$
$541$	13.7406	0.590752	0.295376	+	0.955381i	$0.404555\pi$
$542$	−28.6705	−1.23151
$543$	6.41110	0.275127
$544$	−12.1461	−0.520760
$545$	0	0
$546$	9.25443	0.396053
$547$	37.8797	1.61962	0.809809	−	0.586694i	$-0.199571\pi$
$547$	37.8797	1.61962	0.809809	+	0.586694i	$0.199571\pi$
$548$	−24.8716	−1.06246
$549$	6.49472	0.277188
$550$	0	0
$551$	3.96023	0.168712
$552$	2.95112	0.125608
$553$	15.4061	0.655133
$554$	25.8328	1.09753
$555$	0	0
$556$	−4.55007	−0.192966
$557$	22.3799	0.948268	0.474134	−	0.880453i	$-0.342761\pi$
$557$	22.3799	0.948268	0.474134	+	0.880453i	$0.342761\pi$
$558$	−4.57834	−0.193816
$559$	35.8172	1.51491
$560$	0	0
$561$	−1.91638	−0.0809097
$562$	21.6373	0.912713
$563$	−24.5783	−1.03585	−0.517927	−	0.855425i	$-0.673296\pi$
$563$	−24.5783	−1.03585	−0.517927	+	0.855425i	$0.673296\pi$
$564$	3.25443	0.137036
$565$	0	0
$566$	14.4806	0.608664
$567$	1.00000	0.0419961
$568$	17.1567	0.719878
$569$	14.5980	0.611980	0.305990	−	0.952035i	$-0.401013\pi$
$569$	14.5980	0.611980	0.305990	+	0.952035i	$0.401013\pi$
$570$	0	0
$571$	−18.7995	−0.786733	−0.393367	−	0.919382i	$-0.628690\pi$
$571$	−18.7995	−0.786733	−0.393367	+	0.919382i	$0.628690\pi$
$572$	−6.57834	−0.275054
$573$	10.0978	0.421840
$574$	−3.04888	−0.127258
$575$	0	0
$576$	−1.66196	−0.0692481
$577$	−2.00000	−0.0832611	−0.0416305	−	0.999133i	$-0.513255\pi$
$577$	−2.00000	−0.0832611	−0.0416305	+	0.999133i	$0.513255\pi$
$578$	−24.1708	−1.00537
$579$	7.04888	0.292941
$580$	0	0
$581$	−15.7491	−0.653385
$582$	28.6605	1.18802
$583$	−0.289169	−0.0119761
$584$	0.480585	0.0198868
$585$	0	0
$586$	60.4056	2.49533
$587$	2.79947	0.115547	0.0577733	−	0.998330i	$-0.481600\pi$
$587$	2.79947	0.115547	0.0577733	+	0.998330i	$0.481600\pi$
$588$	−1.28917	−0.0531644
$589$	−8.42669	−0.347216
$590$	0	0
$591$	−0.372787	−0.0153344
$592$	19.4005	0.797357
$593$	−25.4983	−1.04709	−0.523545	−	0.851998i	$-0.675391\pi$
$593$	−25.4983	−1.04709	−0.523545	+	0.851998i	$0.675391\pi$
$594$	−1.81361	−0.0744132
$595$	0	0
$596$	17.2262	0.705611
$597$	23.6655	0.968566
$598$	−21.1849	−0.866317
$599$	23.1950	0.947721	0.473861	−	0.880600i	$-0.342860\pi$
$599$	23.1950	0.947721	0.473861	+	0.880600i	$0.342860\pi$
$600$	0	0
$601$	2.63078	0.107312	0.0536560	−	0.998559i	$-0.482913\pi$
$601$	2.63078	0.107312	0.0536560	+	0.998559i	$0.482913\pi$
$602$	−12.7300	−0.518836
$603$	0.578337	0.0235517
$604$	16.2156	0.659803
$605$	0	0
$606$	11.6272	0.472323
$607$	−45.4882	−1.84631	−0.923155	−	0.384427i	$-0.874399\pi$
$607$	−45.4882	−1.84631	−0.923155	+	0.384427i	$0.874399\pi$
$608$	−21.1567	−0.858016
$609$	−1.18639	−0.0480751
$610$	0	0
$611$	12.8816	0.521135
$612$	2.47054	0.0998656
$613$	−34.4111	−1.38985	−0.694926	−	0.719082i	$-0.744563\pi$
$613$	−34.4111	−1.38985	−0.694926	+	0.719082i	$0.744563\pi$
$614$	−37.1255	−1.49826
$615$	0	0
$616$	−1.28917	−0.0519421
$617$	42.8505	1.72509	0.862547	−	0.505976i	$-0.168868\pi$
$617$	42.8505	1.72509	0.862547	+	0.505976i	$0.168868\pi$
$618$	8.72999	0.351172
$619$	26.6761	1.07220	0.536101	−	0.844154i	$-0.319897\pi$
$619$	26.6761	1.07220	0.536101	+	0.844154i	$0.319897\pi$
$620$	0	0
$621$	−2.28917	−0.0918612
$622$	7.05892	0.283037
$623$	−0.0297193	−0.00119068
$624$	−25.0872	−1.00429
$625$	0	0
$626$	24.3572	0.973510
$627$	−3.33804	−0.133309
$628$	2.05944	0.0821805
$629$	−7.56223	−0.301526
$630$	0	0
$631$	15.1708	0.603940	0.301970	−	0.953317i	$-0.402356\pi$
$631$	15.1708	0.603940	0.301970	+	0.953317i	$0.402356\pi$
$632$	−19.8610	−0.790029
$633$	−3.52946	−0.140283
$634$	52.7527	2.09508
$635$	0	0
$636$	0.372787	0.0147820
$637$	−5.10278	−0.202179
$638$	2.15165	0.0851847
$639$	−13.3083	−0.526469
$640$	0	0
$641$	17.6655	0.697746	0.348873	−	0.937170i	$-0.386564\pi$
$641$	17.6655	0.697746	0.348873	+	0.937170i	$0.386564\pi$
$642$	−25.1849	−0.993970
$643$	−21.9108	−0.864079	−0.432040	−	0.901855i	$-0.642206\pi$
$643$	−21.9108	−0.864079	−0.432040	+	0.901855i	$0.642206\pi$
$644$	2.95112	0.116291
$645$	0	0
$646$	11.6016	0.456458
$647$	44.0455	1.73161	0.865803	−	0.500385i	$-0.166808\pi$
$647$	44.0455	1.73161	0.865803	+	0.500385i	$0.166808\pi$
$648$	−1.28917	−0.0506433
$649$	−10.4408	−0.409838
$650$	0	0
$651$	2.52444	0.0989405
$652$	11.1155	0.435315
$653$	24.7003	0.966596	0.483298	−	0.875456i	$-0.339439\pi$
$653$	24.7003	0.966596	0.483298	+	0.875456i	$0.339439\pi$
$654$	4.09775	0.160235
$655$	0	0
$656$	8.26499	0.322694
$657$	−0.372787	−0.0145438
$658$	−4.57834	−0.178482
$659$	31.6741	1.23385	0.616924	−	0.787023i	$-0.288378\pi$
$659$	31.6741	1.23385	0.616924	+	0.787023i	$0.288378\pi$
$660$	0	0
$661$	1.63275	0.0635067	0.0317534	−	0.999496i	$-0.489891\pi$
$661$	1.63275	0.0635067	0.0317534	+	0.999496i	$0.489891\pi$
$662$	−35.9250	−1.39626
$663$	9.77886	0.379780
$664$	20.3033	0.787921
$665$	0	0
$666$	−7.15667	−0.277315
$667$	2.71585	0.105158
$668$	−22.7244	−0.879235
$669$	−26.6847	−1.03169
$670$	0	0
$671$	6.49472	0.250726
$672$	6.33804	0.244495
$673$	15.5280	0.598561	0.299280	−	0.954165i	$-0.403253\pi$
$673$	15.5280	0.598561	0.299280	+	0.954165i	$0.403253\pi$
$674$	38.8661	1.49706
$675$	0	0
$676$	16.8086	0.646484
$677$	−5.33804	−0.205158	−0.102579	−	0.994725i	$-0.532709\pi$
$677$	−5.33804	−0.205158	−0.102579	+	0.994725i	$0.532709\pi$
$678$	16.6322	0.638757
$679$	−15.8030	−0.606465
$680$	0	0
$681$	−24.6902	−0.946131
$682$	−4.57834	−0.175314
$683$	32.4111	1.24018	0.620088	−	0.784532i	$-0.287097\pi$
$683$	32.4111	1.24018	0.620088	+	0.784532i	$0.287097\pi$
$684$	4.30330	0.164541
$685$	0	0
$686$	1.81361	0.0692438
$687$	18.8972	0.720974
$688$	34.5089	1.31564
$689$	1.47556	0.0562144
$690$	0	0
$691$	1.73501	0.0660029	0.0330015	−	0.999455i	$-0.489493\pi$
$691$	1.73501	0.0660029	0.0330015	+	0.999455i	$0.489493\pi$
$692$	−25.8328	−0.982014
$693$	1.00000	0.0379869
$694$	55.5266	2.10776
$695$	0	0
$696$	1.52946	0.0579741
$697$	−3.22165	−0.122029
$698$	−11.5834	−0.438437
$699$	−15.0333	−0.568611
$700$	0	0
$701$	−1.59749	−0.0603365	−0.0301683	−	0.999545i	$-0.509604\pi$
$701$	−1.59749	−0.0603365	−0.0301683	+	0.999545i	$0.509604\pi$
$702$	9.25443	0.349286
$703$	−13.1723	−0.496801
$704$	−1.66196	−0.0626373
$705$	0	0
$706$	−19.2927	−0.726092
$707$	−6.41110	−0.241114
$708$	13.4600	0.505857
$709$	27.3280	1.02632	0.513162	−	0.858292i	$-0.328474\pi$
$709$	27.3280	1.02632	0.513162	+	0.858292i	$0.328474\pi$
$710$	0	0
$711$	15.4061	0.577773
$712$	0.0383132	0.00143585
$713$	−5.77886	−0.216420
$714$	−3.47556	−0.130070
$715$	0	0
$716$	−6.31335	−0.235941
$717$	−0.0680325	−0.00254072
$718$	−58.7089	−2.19100
$719$	3.32246	0.123907	0.0619534	−	0.998079i	$-0.480267\pi$
$719$	3.32246	0.123907	0.0619534	+	0.998079i	$0.480267\pi$
$720$	0	0
$721$	−4.81361	−0.179268
$722$	−14.2503	−0.530343
$723$	15.9305	0.592462
$724$	−8.26499	−0.307166
$725$	0	0
$726$	−1.81361	−0.0673093
$727$	35.4897	1.31624	0.658120	−	0.752913i	$-0.271352\pi$
$727$	35.4897	1.31624	0.658120	+	0.752913i	$0.271352\pi$
$728$	6.57834	0.243809
$729$	1.00000	0.0370370
$730$	0	0
$731$	−13.4514	−0.497517
$732$	−8.37279	−0.309467
$733$	41.6344	1.53780	0.768900	−	0.639369i	$-0.220804\pi$
$733$	41.6344	1.53780	0.768900	+	0.639369i	$0.220804\pi$
$734$	−35.7376	−1.31910
$735$	0	0
$736$	−14.5089	−0.534803
$737$	0.578337	0.0213033
$738$	−3.04888	−0.112231
$739$	−33.7038	−1.23982	−0.619908	−	0.784675i	$-0.712830\pi$
$739$	−33.7038	−1.23982	−0.619908	+	0.784675i	$0.712830\pi$
$740$	0	0
$741$	17.0333	0.625734
$742$	−0.524438	−0.0192527
$743$	6.15719	0.225885	0.112943	−	0.993602i	$-0.463972\pi$
$743$	6.15719	0.225885	0.112943	+	0.993602i	$0.463972\pi$
$744$	−3.25443	−0.119313
$745$	0	0
$746$	−9.29828	−0.340434
$747$	−15.7491	−0.576231
$748$	2.47054	0.0903318
$749$	13.8867	0.507408
$750$	0	0
$751$	9.95469	0.363252	0.181626	−	0.983368i	$-0.441864\pi$
$751$	9.95469	0.363252	0.181626	+	0.983368i	$0.441864\pi$
$752$	12.4111	0.452586
$753$	−8.41110	−0.306518
$754$	−10.9794	−0.399846
$755$	0	0
$756$	−1.28917	−0.0468866
$757$	25.1466	0.913970	0.456985	−	0.889474i	$-0.348929\pi$
$757$	25.1466	0.913970	0.456985	+	0.889474i	$0.348929\pi$
$758$	16.4550	0.597671
$759$	−2.28917	−0.0830916
$760$	0	0
$761$	−9.25443	−0.335473	−0.167736	−	0.985832i	$-0.553646\pi$
$761$	−9.25443	−0.335473	−0.167736	+	0.985832i	$0.553646\pi$
$762$	28.2877	1.02476
$763$	−2.25945	−0.0817976
$764$	−13.0177	−0.470964
$765$	0	0
$766$	11.1749	0.403765
$767$	53.2772	1.92373
$768$	−20.8469	−0.752248
$769$	−18.0524	−0.650988	−0.325494	−	0.945544i	$-0.605531\pi$
$769$	−18.0524	−0.650988	−0.325494	+	0.945544i	$0.605531\pi$
$770$	0	0
$771$	2.72999	0.0983181
$772$	−9.08719	−0.327055
$773$	−33.8922	−1.21902	−0.609509	−	0.792779i	$-0.708633\pi$
$773$	−33.8922	−1.21902	−0.609509	+	0.792779i	$0.708633\pi$
$774$	−12.7300	−0.457570
$775$	0	0
$776$	20.3728	0.731340
$777$	3.94610	0.141566
$778$	19.9022	0.713530
$779$	−5.61163	−0.201057
$780$	0	0
$781$	−13.3083	−0.476209
$782$	7.95615	0.284511
$783$	−1.18639	−0.0423982
$784$	−4.91638	−0.175585
$785$	0	0
$786$	9.73501	0.347236
$787$	37.1567	1.32449	0.662246	−	0.749286i	$-0.269603\pi$
$787$	37.1567	1.32449	0.662246	+	0.749286i	$0.269603\pi$
$788$	0.480585	0.0171201
$789$	12.7144	0.452645
$790$	0	0
$791$	−9.17081	−0.326076
$792$	−1.28917	−0.0458086
$793$	−33.1411	−1.17687
$794$	−57.9094	−2.05513
$795$	0	0
$796$	−30.5089	−1.08136
$797$	−18.7144	−0.662898	−0.331449	−	0.943473i	$-0.607538\pi$
$797$	−18.7144	−0.662898	−0.331449	+	0.943473i	$0.607538\pi$
$798$	−6.05390	−0.214306
$799$	−4.83779	−0.171149
$800$	0	0
$801$	−0.0297193	−0.00105008
$802$	−26.7144	−0.943318
$803$	−0.372787	−0.0131554
$804$	−0.745574	−0.0262944
$805$	0	0
$806$	23.3622	0.822899
$807$	−25.1552	−0.885506
$808$	8.26499	0.290761
$809$	−34.5955	−1.21631	−0.608157	−	0.793817i	$-0.708091\pi$
$809$	−34.5955	−1.21631	−0.608157	+	0.793817i	$0.708091\pi$
$810$	0	0
$811$	25.0177	0.878490	0.439245	−	0.898367i	$-0.355246\pi$
$811$	25.0177	0.878490	0.439245	+	0.898367i	$0.355246\pi$
$812$	1.52946	0.0536736
$813$	15.8086	0.554431
$814$	−7.15667	−0.250841
$815$	0	0
$816$	9.42166	0.329824
$817$	−23.4303	−0.819721
$818$	−4.28508	−0.149824
$819$	−5.10278	−0.178305
$820$	0	0
$821$	32.7330	1.14239	0.571196	−	0.820814i	$-0.306480\pi$
$821$	32.7330	1.14239	0.571196	+	0.820814i	$0.306480\pi$
$822$	34.9894	1.22040
$823$	41.3366	1.44090	0.720452	−	0.693505i	$-0.243935\pi$
$823$	41.3366	1.44090	0.720452	+	0.693505i	$0.243935\pi$
$824$	6.20555	0.216181
$825$	0	0
$826$	−18.9355	−0.658852
$827$	−4.30330	−0.149640	−0.0748202	−	0.997197i	$-0.523838\pi$
$827$	−4.30330	−0.149640	−0.0748202	+	0.997197i	$0.523838\pi$
$828$	2.95112	0.102559
$829$	−10.6378	−0.369465	−0.184733	−	0.982789i	$-0.559142\pi$
$829$	−10.6378	−0.369465	−0.184733	+	0.982789i	$0.559142\pi$
$830$	0	0
$831$	−14.2439	−0.494114
$832$	8.48059	0.294011
$833$	1.91638	0.0663987
$834$	6.40105	0.221650
$835$	0	0
$836$	4.30330	0.148833
$837$	2.52444	0.0872573
$838$	−21.0333	−0.726583
$839$	−13.9703	−0.482308	−0.241154	−	0.970487i	$-0.577526\pi$
$839$	−13.9703	−0.482308	−0.241154	+	0.970487i	$0.577526\pi$
$840$	0	0
$841$	−27.5925	−0.951464
$842$	28.0822	0.967775
$843$	−11.9305	−0.410909
$844$	4.55007	0.156620
$845$	0	0
$846$	−4.57834	−0.157406
$847$	1.00000	0.0343604
$848$	1.42166	0.0488201
$849$	−7.98441	−0.274024
$850$	0	0
$851$	−9.03329	−0.309657
$852$	17.1567	0.587778
$853$	−2.62219	−0.0897821	−0.0448910	−	0.998992i	$-0.514294\pi$
$853$	−2.62219	−0.0897821	−0.0448910	+	0.998992i	$0.514294\pi$
$854$	11.7789	0.403064
$855$	0	0
$856$	−17.9022	−0.611886
$857$	−45.8610	−1.56658	−0.783291	−	0.621655i	$-0.786461\pi$
$857$	−45.8610	−1.56658	−0.783291	+	0.621655i	$0.786461\pi$
$858$	9.25443	0.315941
$859$	12.3078	0.419937	0.209969	−	0.977708i	$-0.432664\pi$
$859$	12.3078	0.419937	0.209969	+	0.977708i	$0.432664\pi$
$860$	0	0
$861$	1.68111	0.0572921
$862$	−43.4700	−1.48059
$863$	15.8086	0.538130	0.269065	−	0.963122i	$-0.413285\pi$
$863$	15.8086	0.538130	0.269065	+	0.963122i	$0.413285\pi$
$864$	6.33804	0.215625
$865$	0	0
$866$	−8.58838	−0.291845
$867$	13.3275	0.452625
$868$	−3.25443	−0.110462
$869$	15.4061	0.522615
$870$	0	0
$871$	−2.95112	−0.0999950
$872$	2.91281	0.0986402
$873$	−15.8030	−0.534852
$874$	13.8584	0.468767
$875$	0	0
$876$	0.480585	0.0162375
$877$	−20.4892	−0.691870	−0.345935	−	0.938258i	$-0.612438\pi$
$877$	−20.4892	−0.691870	−0.345935	+	0.938258i	$0.612438\pi$
$878$	−24.2594	−0.818717
$879$	−33.3069	−1.12341
$880$	0	0
$881$	−2.03977	−0.0687215	−0.0343607	−	0.999409i	$-0.510940\pi$
$881$	−2.03977	−0.0687215	−0.0343607	+	0.999409i	$0.510940\pi$
$882$	1.81361	0.0610673
$883$	49.7522	1.67429	0.837147	−	0.546977i	$-0.184222\pi$
$883$	49.7522	1.67429	0.837147	+	0.546977i	$0.184222\pi$
$884$	−12.6066	−0.424006
$885$	0	0
$886$	−20.3033	−0.682103
$887$	55.9446	1.87844	0.939219	−	0.343319i	$-0.111551\pi$
$887$	55.9446	1.87844	0.939219	+	0.343319i	$0.111551\pi$
$888$	−5.08719	−0.170715
$889$	−15.5975	−0.523123
$890$	0	0
$891$	1.00000	0.0335013
$892$	34.4011	1.15183
$893$	−8.42669	−0.281988
$894$	−24.2338	−0.810500
$895$	0	0
$896$	9.66196	0.322783
$897$	11.6811	0.390021
$898$	16.7556	0.559142
$899$	−2.99498	−0.0998881
$900$	0	0
$901$	−0.554157	−0.0184617
$902$	−3.04888	−0.101516
$903$	7.01916	0.233583
$904$	11.8227	0.393218
$905$	0	0
$906$	−22.8122	−0.757883
$907$	41.7789	1.38724	0.693622	−	0.720339i	$-0.256014\pi$
$907$	41.7789	1.38724	0.693622	+	0.720339i	$0.256014\pi$
$908$	31.8299	1.05631
$909$	−6.41110	−0.212643
$910$	0	0
$911$	26.6167	0.881849	0.440924	−	0.897544i	$-0.354651\pi$
$911$	26.6167	0.881849	0.440924	+	0.897544i	$0.354651\pi$
$912$	16.4111	0.543426
$913$	−15.7491	−0.521221
$914$	−24.8560	−0.822164
$915$	0	0
$916$	−24.3617	−0.804933
$917$	−5.36776	−0.177259
$918$	−3.47556	−0.114711
$919$	32.7738	1.08111	0.540555	−	0.841309i	$-0.318214\pi$
$919$	32.7738	1.08111	0.540555	+	0.841309i	$0.318214\pi$
$920$	0	0
$921$	20.4705	0.674527
$922$	−22.8816	−0.753567
$923$	67.9094	2.23526
$924$	−1.28917	−0.0424105
$925$	0	0
$926$	−38.2621	−1.25737
$927$	−4.81361	−0.158100
$928$	−7.51941	−0.246837
$929$	−0.264989	−0.00869400	−0.00434700	−	0.999991i	$-0.501384\pi$
$929$	−0.264989	−0.00869400	−0.00434700	+	0.999991i	$0.501384\pi$
$930$	0	0
$931$	3.33804	0.109400
$932$	19.3804	0.634828
$933$	−3.89220	−0.127425
$934$	54.0354	1.76809
$935$	0	0
$936$	6.57834	0.215020
$937$	−26.0610	−0.851377	−0.425689	−	0.904870i	$-0.639968\pi$
$937$	−26.0610	−0.851377	−0.425689	+	0.904870i	$0.639968\pi$
$938$	1.04888	0.0342470
$939$	−13.4303	−0.438280
$940$	0	0
$941$	30.3472	0.989289	0.494644	−	0.869095i	$-0.335298\pi$
$941$	30.3472	0.989289	0.494644	+	0.869095i	$0.335298\pi$
$942$	−2.89722	−0.0943967
$943$	−3.84835	−0.125319
$944$	51.3311	1.67068
$945$	0	0
$946$	−12.7300	−0.413888
$947$	43.3380	1.40830	0.704149	−	0.710053i	$-0.251329\pi$
$947$	43.3380	1.40830	0.704149	+	0.710053i	$0.251329\pi$
$948$	−19.8610	−0.645056
$949$	1.90225	0.0617496
$950$	0	0
$951$	−29.0872	−0.943217
$952$	−2.47054	−0.0800706
$953$	−15.9022	−0.515124	−0.257562	−	0.966262i	$-0.582919\pi$
$953$	−15.9022	−0.515124	−0.257562	+	0.966262i	$0.582919\pi$
$954$	−0.524438	−0.0169793
$955$	0	0
$956$	0.0877054	0.00283659
$957$	−1.18639	−0.0383507
$958$	54.5572	1.76266
$959$	−19.2927	−0.622995
$960$	0	0
$961$	−24.6272	−0.794426
$962$	36.5189	1.17742
$963$	13.8867	0.447491
$964$	−20.5371	−0.661456
$965$	0	0
$966$	−4.15165	−0.133577
$967$	23.6852	0.761665	0.380832	−	0.924644i	$-0.375638\pi$
$967$	23.6852	0.761665	0.380832	+	0.924644i	$0.375638\pi$
$968$	−1.28917	−0.0414354
$969$	−6.39697	−0.205500
$970$	0	0
$971$	18.9597	0.608446	0.304223	−	0.952601i	$-0.401603\pi$
$971$	18.9597	0.608446	0.304223	+	0.952601i	$0.401603\pi$
$972$	−1.28917	−0.0413501
$973$	−3.52946	−0.113149
$974$	43.1667	1.38315
$975$	0	0
$976$	−31.9305	−1.02207
$977$	23.9063	0.764831	0.382416	−	0.923990i	$-0.375092\pi$
$977$	23.9063	0.764831	0.382416	+	0.923990i	$0.375092\pi$
$978$	−15.6373	−0.500024
$979$	−0.0297193	−0.000949833 0
$980$	0	0
$981$	−2.25945	−0.0721387
$982$	−59.8454	−1.90974
$983$	1.62721	0.0519000	0.0259500	−	0.999663i	$-0.491739\pi$
$983$	1.62721	0.0519000	0.0259500	+	0.999663i	$0.491739\pi$
$984$	−2.16724	−0.0690890
$985$	0	0
$986$	4.12338	0.131315
$987$	2.52444	0.0803537
$988$	−21.9588	−0.698602
$989$	−16.0680	−0.510934
$990$	0	0
$991$	−20.9058	−0.664095	−0.332048	−	0.943263i	$-0.607739\pi$
$991$	−20.9058	−0.664095	−0.332048	+	0.943263i	$0.607739\pi$
$992$	16.0000	0.508001
$993$	19.8086	0.628606
$994$	−24.1361	−0.765549
$995$	0	0
$996$	20.3033	0.643335
$997$	−0.0977518	−0.00309583	−0.00154792	−	0.999999i	$-0.500493\pi$
$997$	−0.0977518	−0.00309583	−0.00154792	+	0.999999i	$0.500493\pi$
$998$	13.5038	0.427456
$999$	3.94610	0.124849

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5775.2.a.bq.1.3		3
5.4	even	2		1155.2.a.t.1.1	✓	3
15.14	odd	2		3465.2.a.bb.1.3		3
35.34	odd	2		8085.2.a.bl.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.a.t.1.1	✓	3	5.4	even	2
3465.2.a.bb.1.3		3	15.14	odd	2
5775.2.a.bq.1.3		3	1.1	even	1	trivial
8085.2.a.bl.1.1		3	35.34	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:	\( N \)	\(=\)	\( 5775 = 3 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5775.a (trivial)

\(f(q)\)	\(=\)	\(q+1.81361 q^{2} -1.00000 q^{3} +1.28917 q^{4} -1.81361 q^{6} +1.00000 q^{7} -1.28917 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.81361 q^{2} -1.00000 q^{3} +1.28917 q^{4} -1.81361 q^{6} +1.00000 q^{7} -1.28917 q^{8} +1.00000 q^{9} +1.00000 q^{11} -1.28917 q^{12} -5.10278 q^{13} +1.81361 q^{14} -4.91638 q^{16} +1.91638 q^{17} +1.81361 q^{18} +3.33804 q^{19} -1.00000 q^{21} +1.81361 q^{22} +2.28917 q^{23} +1.28917 q^{24} -9.25443 q^{26} -1.00000 q^{27} +1.28917 q^{28} +1.18639 q^{29} -2.52444 q^{31} -6.33804 q^{32} -1.00000 q^{33} +3.47556 q^{34} +1.28917 q^{36} -3.94610 q^{37} +6.05390 q^{38} +5.10278 q^{39} -1.68111 q^{41} -1.81361 q^{42} -7.01916 q^{43} +1.28917 q^{44} +4.15165 q^{46} -2.52444 q^{47} +4.91638 q^{48} +1.00000 q^{49} -1.91638 q^{51} -6.57834 q^{52} -0.289169 q^{53} -1.81361 q^{54} -1.28917 q^{56} -3.33804 q^{57} +2.15165 q^{58} -10.4408 q^{59} +6.49472 q^{61} -4.57834 q^{62} +1.00000 q^{63} -1.66196 q^{64} -1.81361 q^{66} +0.578337 q^{67} +2.47054 q^{68} -2.28917 q^{69} -13.3083 q^{71} -1.28917 q^{72} -0.372787 q^{73} -7.15667 q^{74} +4.30330 q^{76} +1.00000 q^{77} +9.25443 q^{78} +15.4061 q^{79} +1.00000 q^{81} -3.04888 q^{82} -15.7491 q^{83} -1.28917 q^{84} -12.7300 q^{86} -1.18639 q^{87} -1.28917 q^{88} -0.0297193 q^{89} -5.10278 q^{91} +2.95112 q^{92} +2.52444 q^{93} -4.57834 q^{94} +6.33804 q^{96} -15.8030 q^{97} +1.81361 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} - 3 q^{3} + 3 q^{4} + q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - q^2 - 3 * q^3 + 3 * q^4 + q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - q^{2} - 3 q^{3} + 3 q^{4} + q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} + 3 q^{11} - 3 q^{12} - 8 q^{13} - q^{14} - q^{16} - 8 q^{17} - q^{18} - 2 q^{19} - 3 q^{21} - q^{22} + 6 q^{23} + 3 q^{24} - 2 q^{26} - 3 q^{27} + 3 q^{28} + 10 q^{29} - 2 q^{31} - 7 q^{32} - 3 q^{33} + 16 q^{34} + 3 q^{36} - 8 q^{37} + 22 q^{38} + 8 q^{39} + 4 q^{41} + q^{42} + 3 q^{44} - 6 q^{46} - 2 q^{47} + q^{48} + 3 q^{49} + 8 q^{51} - 18 q^{52} + q^{54} - 3 q^{56} + 2 q^{57} - 12 q^{58} - 12 q^{59} + 4 q^{61} - 12 q^{62} + 3 q^{63} - 17 q^{64} + q^{66} - 2 q^{68} - 6 q^{69} - 18 q^{71} - 3 q^{72} - 14 q^{73} - 18 q^{74} - 24 q^{76} + 3 q^{77} + 2 q^{78} + 2 q^{79} + 3 q^{81} + 2 q^{82} - 6 q^{83} - 3 q^{84} - 18 q^{86} - 10 q^{87} - 3 q^{88} - 10 q^{89} - 8 q^{91} + 20 q^{92} + 2 q^{93} - 12 q^{94} + 7 q^{96} - 10 q^{97} - q^{98} + 3 q^{99}+O(q^{100}) \) 3 * q - q^2 - 3 * q^3 + 3 * q^4 + q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 + 3 * q^11 - 3 * q^12 - 8 * q^13 - q^14 - q^16 - 8 * q^17 - q^18 - 2 * q^19 - 3 * q^21 - q^22 + 6 * q^23 + 3 * q^24 - 2 * q^26 - 3 * q^27 + 3 * q^28 + 10 * q^29 - 2 * q^31 - 7 * q^32 - 3 * q^33 + 16 * q^34 + 3 * q^36 - 8 * q^37 + 22 * q^38 + 8 * q^39 + 4 * q^41 + q^42 + 3 * q^44 - 6 * q^46 - 2 * q^47 + q^48 + 3 * q^49 + 8 * q^51 - 18 * q^52 + q^54 - 3 * q^56 + 2 * q^57 - 12 * q^58 - 12 * q^59 + 4 * q^61 - 12 * q^62 + 3 * q^63 - 17 * q^64 + q^66 - 2 * q^68 - 6 * q^69 - 18 * q^71 - 3 * q^72 - 14 * q^73 - 18 * q^74 - 24 * q^76 + 3 * q^77 + 2 * q^78 + 2 * q^79 + 3 * q^81 + 2 * q^82 - 6 * q^83 - 3 * q^84 - 18 * q^86 - 10 * q^87 - 3 * q^88 - 10 * q^89 - 8 * q^91 + 20 * q^92 + 2 * q^93 - 12 * q^94 + 7 * q^96 - 10 * q^97 - q^98 + 3 * q^99

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