LMFDB - Embedded newform 775.2.b.e.249.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(249,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("775.249");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.b (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$6.18840615665$
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} - 2x^{5} + 28x^{4} - 12x^{3} + 2x^{2} + 8x + 16 $ x^8 - 2x^5 + 28x^4 - 12x^3 + 2x^2 + 8*x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 155)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			249.7
Root			$-1.71822 + 1.71822i$ of defining polynomial
Character	$\chi$	$=$	775.249
Dual form			775.2.b.e.249.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.27244i q^{2} +0.632112i q^{3} -3.16400 q^{4} -1.43644 q^{6} +3.43644i q^{7} -2.64511i q^{8} +2.60043 q^{9} +O(q^{10})$	\(q+2.27244i q^{2} +0.632112i q^{3} -3.16400 q^{4} -1.43644 q^{6} +3.43644i q^{7} -2.64511i q^{8} +2.60043 q^{9} -3.10845 q^{11} -2.00000i q^{12} -0.563561i q^{13} -7.80911 q^{14} -0.317122 q^{16} -1.74056i q^{17} +5.90934i q^{18} -4.53667 q^{19} -2.17221 q^{21} -7.06377i q^{22} +9.24555i q^{23} +1.67201 q^{24} +1.28066 q^{26} +3.54010i q^{27} -10.8729i q^{28} -4.17221 q^{29} +1.00000 q^{31} -6.01087i q^{32} -1.96489i q^{33} +3.95532 q^{34} -8.22776 q^{36} -0.804326i q^{37} -10.3093i q^{38} +0.356234 q^{39} +9.97311 q^{41} -4.93623i q^{42} -3.74056i q^{43} +9.83511 q^{44} -21.0100 q^{46} -2.73578i q^{47} -0.200457i q^{48} -4.80911 q^{49} +1.10023 q^{51} +1.78311i q^{52} -10.7692i q^{53} -8.04468 q^{54} +9.08977 q^{56} -2.86768i q^{57} -9.48112i q^{58} -8.90934 q^{59} +4.73578 q^{61} +2.27244i q^{62} +8.93623i q^{63} +13.0251 q^{64} +4.46509 q^{66} -0.891553i q^{67} +5.50712i q^{68} -5.84422 q^{69} -3.60043 q^{71} -6.87844i q^{72} +8.98611i q^{73} +1.82779 q^{74} +14.3540 q^{76} -10.6820i q^{77} +0.809521i q^{78} +14.3093 q^{79} +5.56356 q^{81} +22.6633i q^{82} +14.9414i q^{83} +6.87288 q^{84} +8.50021 q^{86} -2.63731i q^{87} +8.22220i q^{88} -10.5262 q^{89} +1.93664 q^{91} -29.2529i q^{92} +0.632112i q^{93} +6.21689 q^{94} +3.79954 q^{96} +9.80911i q^{97} -10.9284i q^{98} -8.08331 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 18 q^{4} + 16 q^{6} - 14 q^{9}+O(q^{10}) $ 8 * q - 18 * q^4 + 16 * q^6 - 14 * q^9	$ 8 q - 18 q^{4} + 16 q^{6} - 14 q^{9} - 12 q^{11} - 16 q^{14} + 22 q^{16} - 10 q^{19} + 4 q^{21} + 28 q^{24} - 24 q^{26} - 12 q^{29} + 8 q^{31} + 36 q^{34} - 50 q^{36} + 12 q^{39} + 26 q^{41} - 40 q^{44} - 52 q^{46} + 8 q^{49} + 10 q^{51} - 60 q^{54} - 8 q^{56} - 26 q^{59} + 44 q^{61} - 94 q^{64} - 40 q^{66} - 40 q^{69} + 6 q^{71} + 36 q^{74} + 28 q^{76} + 32 q^{79} + 72 q^{81} + 32 q^{86} + 24 q^{89} - 48 q^{91} + 24 q^{94} + 28 q^{96} + 104 q^{99}+O(q^{100}) $ 8 * q - 18 * q^4 + 16 * q^6 - 14 * q^9 - 12 * q^11 - 16 * q^14 + 22 * q^16 - 10 * q^19 + 4 * q^21 + 28 * q^24 - 24 * q^26 - 12 * q^29 + 8 * q^31 + 36 * q^34 - 50 * q^36 + 12 * q^39 + 26 * q^41 - 40 * q^44 - 52 * q^46 + 8 * q^49 + 10 * q^51 - 60 * q^54 - 8 * q^56 - 26 * q^59 + 44 * q^61 - 94 * q^64 - 40 * q^66 - 40 * q^69 + 6 * q^71 + 36 * q^74 + 28 * q^76 + 32 * q^79 + 72 * q^81 + 32 * q^86 + 24 * q^89 - 48 * q^91 + 24 * q^94 + 28 * q^96 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$1$	$-1$

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 $

$2$	2.27244i	1.60686i	0.595399	+	0.803430i	$0.296994\pi$
$2$	2.27244i	1.60686i	−0.595399	+	0.803430i	$0.703006\pi$
$3$	0.632112i	0.364950i	0.983210	+	0.182475i	$0.0584109\pi$
$3$	0.632112i	0.364950i	−0.983210	+	0.182475i	$0.941589\pi$
$4$	−3.16400	−1.58200
$5$	0	0
$5$	0	0
$6$	−1.43644	−0.586424
$7$	3.43644i	1.29885i	0.760425	+	0.649426i	$0.224991\pi$
$7$	3.43644i	1.29885i	−0.760425	+	0.649426i	$0.775009\pi$
$8$	− 2.64511i	− 0.935189i
$9$	2.60043	0.866811
$10$	0	0
$11$	−3.10845	−0.937232	−0.468616	−	0.883402i	$-0.655247\pi$
$11$	−3.10845	−0.937232	−0.468616	+	0.883402i	$0.655247\pi$
$12$	− 2.00000i	− 0.577350i
$13$	− 0.563561i	− 0.156304i	−0.996941	−	0.0781519i	$-0.975098\pi$
$13$	− 0.563561i	− 0.156304i	0.996941	−	0.0781519i	$-0.0249019\pi$
$14$	−7.80911	−2.08707
$15$	0	0
$16$	−0.317122	−0.0792805
$17$	− 1.74056i	− 0.422148i	−0.977470	−	0.211074i	$-0.932304\pi$
$17$	− 1.74056i	− 0.422148i	0.977470	−	0.211074i	$-0.0676960\pi$
$18$	5.90934i	1.39284i
$19$	−4.53667	−1.04078	−0.520391	−	0.853928i	$-0.674214\pi$
$19$	−4.53667	−1.04078	−0.520391	+	0.853928i	$0.674214\pi$
$20$	0	0
$21$	−2.17221	−0.474016
$22$	− 7.06377i	− 1.50600i
$23$	9.24555i	1.92783i	0.266210	+	0.963915i	$0.414228\pi$
$23$	9.24555i	1.92783i	−0.266210	+	0.963915i	$0.585772\pi$
$24$	1.67201	0.341297
$25$	0	0
$26$	1.28066	0.251158
$27$	3.54010i	0.681293i
$28$	− 10.8729i	− 2.05478i
$29$	−4.17221	−0.774761	−0.387380	−	0.921920i	$-0.626620\pi$
$29$	−4.17221	−0.774761	−0.387380	+	0.921920i	$0.626620\pi$
$30$	0	0
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	− 6.01087i	− 1.06258i
$33$	− 1.96489i	− 0.342043i
$34$	3.95532	0.678332
$35$	0	0
$36$	−8.22776	−1.37129
$37$	− 0.804326i	− 0.132230i	−0.997812	−	0.0661152i	$-0.978940\pi$
$37$	− 0.804326i	− 0.132230i	0.997812	−	0.0661152i	$-0.0210605\pi$
$38$	− 10.3093i	− 1.67239i
$39$	0.356234	0.0570431
$40$	0	0
$41$	9.97311	1.55754	0.778769	−	0.627311i	$-0.215845\pi$
$41$	9.97311	1.55754	0.778769	+	0.627311i	$0.215845\pi$
$42$	− 4.93623i	− 0.761677i
$43$	− 3.74056i	− 0.570430i	−0.958464	−	0.285215i	$-0.907935\pi$
$43$	− 3.74056i	− 0.570430i	0.958464	−	0.285215i	$-0.0920650\pi$
$44$	9.83511	1.48270
$45$	0	0
$46$	−21.0100	−3.09775
$47$	− 2.73578i	− 0.399054i	−0.979892	−	0.199527i	$-0.936059\pi$
$47$	− 2.73578i	− 0.399054i	0.979892	−	0.199527i	$-0.0639405\pi$
$48$	− 0.200457i	− 0.0289334i
$49$	−4.80911	−0.687016
$50$	0	0
$51$	1.10023	0.154063
$52$	1.78311i	0.247272i
$53$	− 10.7692i	− 1.47927i	−0.673011	−	0.739633i	$-0.734999\pi$
$53$	− 10.7692i	− 1.47927i	0.673011	−	0.739633i	$-0.265001\pi$
$54$	−8.04468	−1.09474
$55$	0	0
$56$	9.08977	1.21467
$57$	− 2.86768i	− 0.379834i
$58$	− 9.48112i	− 1.24493i
$59$	−8.90934	−1.15990	−0.579949	−	0.814653i	$-0.696927\pi$
$59$	−8.90934	−1.15990	−0.579949	+	0.814653i	$0.696927\pi$
$60$	0	0
$61$	4.73578	0.606354	0.303177	−	0.952934i	$-0.401953\pi$
$61$	4.73578	0.606354	0.303177	+	0.952934i	$0.401953\pi$
$62$	2.27244i	0.288601i
$63$	8.93623i	1.12586i
$64$	13.0251	1.62814
$65$	0	0
$66$	4.46509	0.549615
$67$	− 0.891553i	− 0.108921i	−0.998516	−	0.0544603i	$-0.982656\pi$
$67$	− 0.891553i	− 0.108921i	0.998516	−	0.0544603i	$-0.0173438\pi$
$68$	5.50712i	0.667837i
$69$	−5.84422	−0.703562
$70$	0	0
$71$	−3.60043	−0.427293	−0.213646	−	0.976911i	$-0.568534\pi$
$71$	−3.60043	−0.427293	−0.213646	+	0.976911i	$0.568534\pi$
$72$	− 6.87844i	− 0.810632i
$73$	8.98611i	1.05174i	0.850564	+	0.525872i	$0.176261\pi$
$73$	8.98611i	1.05174i	−0.850564	+	0.525872i	$0.823739\pi$
$74$	1.82779	0.212476
$75$	0	0
$76$	14.3540	1.64652
$77$	− 10.6820i	− 1.21733i
$78$	0.809521i	0.0916603i
$79$	14.3093	1.60992	0.804962	−	0.593327i	$-0.202186\pi$
$79$	14.3093	1.60992	0.804962	+	0.593327i	$0.202186\pi$
$80$	0	0
$81$	5.56356	0.618173
$82$	22.6633i	2.50274i
$83$	14.9414i	1.64003i	0.572339	+	0.820017i	$0.306036\pi$
$83$	14.9414i	1.64003i	−0.572339	+	0.820017i	$0.693964\pi$
$84$	6.87288	0.749892
$85$	0	0
$86$	8.50021	0.916601
$87$	− 2.63731i	− 0.282749i
$88$	8.22220i	0.876489i
$89$	−10.5262	−1.11578	−0.557888	−	0.829916i	$-0.688388\pi$
$89$	−10.5262	−1.11578	−0.557888	+	0.829916i	$0.688388\pi$
$90$	0	0
$91$	1.93664	0.203015
$92$	− 29.2529i	− 3.04982i
$93$	0.632112i	0.0655470i
$94$	6.21689	0.641224
$95$	0	0
$96$	3.79954	0.387789
$97$	9.80911i	0.995964i	0.867187	+	0.497982i	$0.165925\pi$
$97$	9.80911i	0.995964i	−0.867187	+	0.497982i	$0.834075\pi$
$98$	− 10.9284i	− 1.10394i
$99$	−8.08331	−0.812403
$100$	0	0
$101$	7.47290	0.743581	0.371791	−	0.928317i	$-0.378744\pi$
$101$	7.47290	0.743581	0.371791	+	0.928317i	$0.378744\pi$
$102$	2.50021i	0.247557i
$103$	11.0638i	1.09015i	0.838389	+	0.545073i	$0.183498\pi$
$103$	11.0638i	1.09015i	−0.838389	+	0.545073i	$0.816502\pi$
$104$	−1.49068	−0.146174
$105$	0	0
$106$	24.4724	2.37697
$107$	15.0100i	1.45107i	0.688186	+	0.725535i	$0.258407\pi$
$107$	15.0100i	1.45107i	−0.688186	+	0.725535i	$0.741593\pi$
$108$	− 11.2009i	− 1.07780i
$109$	−8.33621	−0.798464	−0.399232	−	0.916850i	$-0.630723\pi$
$109$	−8.33621	−0.798464	−0.399232	+	0.916850i	$0.630723\pi$
$110$	0	0
$111$	0.508424	0.0482575
$112$	− 1.08977i	− 0.102974i
$113$	19.7904i	1.86173i	0.365367	+	0.930864i	$0.380944\pi$
$113$	19.7904i	1.86173i	−0.365367	+	0.930864i	$0.619056\pi$
$114$	6.51664	0.610340
$115$	0	0
$116$	13.2009	1.22567
$117$	− 1.46550i	− 0.135486i
$118$	− 20.2460i	− 1.86379i
$119$	5.98132	0.548307
$120$	0	0
$121$	−1.33756	−0.121596
$122$	10.7618i	0.974326i
$123$	6.30412i	0.568423i
$124$	−3.16400	−0.284135
$125$	0	0
$126$	−20.3071	−1.80910
$127$	− 6.18178i	− 0.548544i	−0.961652	−	0.274272i	$-0.911563\pi$
$127$	− 6.18178i	− 0.548544i	0.961652	−	0.274272i	$-0.0884369\pi$
$128$	17.5771i	1.55361i
$129$	2.36445	0.208178
$130$	0	0
$131$	−20.6364	−1.80301	−0.901506	−	0.432767i	$-0.857537\pi$
$131$	−20.6364	−1.80301	−0.901506	+	0.432767i	$0.857537\pi$
$132$	6.21689i	0.541111i
$133$	− 15.5900i	− 1.35182i
$134$	2.02600	0.175020
$135$	0	0
$136$	−4.60398	−0.394788
$137$	− 5.55878i	− 0.474918i	−0.971398	−	0.237459i	$-0.923685\pi$
$137$	− 5.55878i	− 0.474918i	0.971398	−	0.237459i	$-0.0763146\pi$
$138$	− 13.2807i	− 1.13052i
$139$	11.8702	1.00682	0.503410	−	0.864048i	$-0.332079\pi$
$139$	11.8702	1.00682	0.503410	+	0.864048i	$0.332079\pi$
$140$	0	0
$141$	1.72932	0.145635
$142$	− 8.18178i	− 0.686600i
$143$	1.75180i	0.146493i
$144$	−0.824655	−0.0687213
$145$	0	0
$146$	−20.4204	−1.69001
$147$	− 3.03990i	− 0.250726i
$148$	2.54489i	0.209188i
$149$	−1.41865	−0.116221	−0.0581103	−	0.998310i	$-0.518508\pi$
$149$	−1.41865	−0.116221	−0.0581103	+	0.998310i	$0.518508\pi$
$150$	0	0
$151$	13.8069	1.12359	0.561794	−	0.827277i	$-0.310112\pi$
$151$	13.8069	1.12359	0.561794	+	0.827277i	$0.310112\pi$
$152$	12.0000i	0.973329i
$153$	− 4.52621i	− 0.365922i
$154$	24.2742	1.95607
$155$	0	0
$156$	−1.12712	−0.0902421
$157$	3.82779i	0.305491i	0.988266	+	0.152745i	$0.0488114\pi$
$157$	3.82779i	0.305491i	−0.988266	+	0.152745i	$0.951189\pi$
$158$	32.5171i	2.58692i
$159$	6.80735	0.539858
$160$	0	0
$161$	−31.7718	−2.50397
$162$	12.6429i	0.993318i
$163$	− 10.0260i	− 0.785297i	−0.919689	−	0.392649i	$-0.871559\pi$
$163$	− 10.0260i	− 0.785297i	0.919689	−	0.392649i	$-0.128441\pi$
$164$	−31.5549	−2.46402
$165$	0	0
$166$	−33.9535	−2.63531
$167$	7.26942i	0.562525i	0.959631	+	0.281262i	$0.0907531\pi$
$167$	7.26942i	0.562525i	−0.959631	+	0.281262i	$0.909247\pi$
$168$	5.74575i	0.443295i
$169$	12.6824	0.975569
$170$	0	0
$171$	−11.7973	−0.902162
$172$	11.8351i	0.902419i
$173$	16.1349i	1.22671i	0.789807	+	0.613355i	$0.210181\pi$
$173$	16.1349i	1.22671i	−0.789807	+	0.613355i	$0.789819\pi$
$174$	5.99313	0.454338
$175$	0	0
$176$	0.985757	0.0743043
$177$	− 5.63170i	− 0.423305i
$178$	− 23.9202i	− 1.79290i
$179$	7.29934	0.545578	0.272789	−	0.962074i	$-0.412054\pi$
$179$	7.29934	0.545578	0.272789	+	0.962074i	$0.412054\pi$
$180$	0	0
$181$	19.2104	1.42790	0.713950	−	0.700196i	$-0.246904\pi$
$181$	19.2104	1.42790	0.713950	+	0.700196i	$0.246904\pi$
$182$	4.40091i	0.326217i
$183$	2.99354i	0.221289i
$184$	24.4555	1.80289
$185$	0	0
$186$	−1.43644	−0.105325
$187$	5.41044i	0.395650i
$188$	8.65598i	0.631302i
$189$	−12.1653	−0.884899
$190$	0	0
$191$	−4.46509	−0.323083	−0.161541	−	0.986866i	$-0.551647\pi$
$191$	−4.46509	−0.323083	−0.161541	+	0.986866i	$0.551647\pi$
$192$	8.23333i	0.594189i
$193$	6.34443i	0.456682i	0.973581	+	0.228341i	$0.0733301\pi$
$193$	6.34443i	0.456682i	−0.973581	+	0.228341i	$0.926670\pi$
$194$	−22.2906	−1.60037
$195$	0	0
$196$	15.2160	1.08686
$197$	− 7.43644i	− 0.529824i	−0.964273	−	0.264912i	$-0.914657\pi$
$197$	− 7.43644i	− 0.529824i	0.964273	−	0.264912i	$-0.0853430\pi$
$198$	− 18.3689i	− 1.30542i
$199$	4.29975	0.304801	0.152401	−	0.988319i	$-0.451300\pi$
$199$	4.29975	0.304801	0.152401	+	0.988319i	$0.451300\pi$
$200$	0	0
$201$	0.563561	0.0397506
$202$	16.9817i	1.19483i
$203$	− 14.3376i	− 1.00630i
$204$	−3.48112	−0.243727
$205$	0	0
$206$	−25.1418	−1.75171
$207$	24.0424i	1.67107i
$208$	0.178718i	0.0123919i
$209$	14.1020	0.975455
$210$	0	0
$211$	−4.53532	−0.312224	−0.156112	−	0.987739i	$-0.549896\pi$
$211$	−4.53532	−0.312224	−0.156112	+	0.987739i	$0.549896\pi$
$212$	34.0737i	2.34019i
$213$	− 2.27588i	− 0.155941i
$214$	−34.1093	−2.33166
$215$	0	0
$216$	9.36397	0.637138
$217$	3.43644i	0.233281i
$218$	− 18.9436i	− 1.28302i
$219$	−5.68023	−0.383834
$220$	0	0
$221$	−0.980912	−0.0659833
$222$	1.15537i	0.0775431i
$223$	− 19.5214i	− 1.30725i	−0.756818	−	0.653626i	$-0.773247\pi$
$223$	− 19.5214i	− 1.30725i	0.756818	−	0.653626i	$-0.226753\pi$
$224$	20.6560	1.38014
$225$	0	0
$226$	−44.9726	−2.99153
$227$	− 25.3193i	− 1.68050i	−0.542199	−	0.840250i	$-0.682408\pi$
$227$	− 25.3193i	− 1.68050i	0.542199	−	0.840250i	$-0.317592\pi$
$228$	9.07333i	0.600896i
$229$	19.0642	1.25980	0.629900	−	0.776676i	$-0.283096\pi$
$229$	19.0642	1.25980	0.629900	+	0.776676i	$0.283096\pi$
$230$	0	0
$231$	6.75221	0.444263
$232$	11.0360i	0.724548i
$233$	8.36310i	0.547885i	0.961746	+	0.273943i	$0.0883278\pi$
$233$	8.36310i	0.547885i	−0.961746	+	0.273943i	$0.911672\pi$
$234$	3.33028	0.217707
$235$	0	0
$236$	28.1891	1.83495
$237$	9.04509i	0.587542i
$238$	13.5922i	0.881052i
$239$	−26.9084	−1.74056	−0.870281	−	0.492555i	$-0.836063\pi$
$239$	−26.9084	−1.74056	−0.870281	+	0.492555i	$0.836063\pi$
$240$	0	0
$241$	18.5262	1.19338	0.596689	−	0.802473i	$-0.296483\pi$
$241$	18.5262	1.19338	0.596689	+	0.802473i	$0.296483\pi$
$242$	− 3.03952i	− 0.195388i
$243$	14.1371i	0.906895i
$244$	−14.9840	−0.959251
$245$	0	0
$246$	−14.3258	−0.913377
$247$	2.55669i	0.162678i
$248$	− 2.64511i	− 0.167965i
$249$	−9.44466	−0.598531
$250$	0	0
$251$	17.0733	1.07766	0.538830	−	0.842415i	$-0.318867\pi$
$251$	17.0733	1.07766	0.538830	+	0.842415i	$0.318867\pi$
$252$	− 28.2742i	− 1.78111i
$253$	− 28.7393i	− 1.80682i
$254$	14.0477	0.881434
$255$	0	0
$256$	−13.8927	−0.868293
$257$	21.6793i	1.35232i	0.736755	+	0.676160i	$0.236357\pi$
$257$	21.6793i	1.35232i	−0.736755	+	0.676160i	$0.763643\pi$
$258$	5.37308i	0.334514i
$259$	2.76402	0.171748
$260$	0	0
$261$	−10.8496	−0.671571
$262$	− 46.8951i	− 2.89719i
$263$	− 14.7059i	− 0.906802i	−0.891307	−	0.453401i	$-0.850211\pi$
$263$	− 14.7059i	− 0.906802i	0.891307	−	0.453401i	$-0.149789\pi$
$264$	−5.19735	−0.319875
$265$	0	0
$266$	35.4273	2.17219
$267$	− 6.65374i	− 0.407203i
$268$	2.82087i	0.172312i
$269$	−14.4204	−0.879228	−0.439614	−	0.898187i	$-0.644885\pi$
$269$	−14.4204	−0.879228	−0.439614	+	0.898187i	$0.644885\pi$
$270$	0	0
$271$	8.37267	0.508604	0.254302	−	0.967125i	$-0.418154\pi$
$271$	8.37267	0.508604	0.254302	+	0.967125i	$0.418154\pi$
$272$	0.551970i	0.0334681i
$273$	1.22418i	0.0740905i
$274$	12.6320	0.763127
$275$	0	0
$276$	18.4911	1.11303
$277$	7.73832i	0.464951i	0.972602	+	0.232475i	$0.0746825\pi$
$277$	7.73832i	0.464951i	−0.972602	+	0.232475i	$0.925318\pi$
$278$	26.9744i	1.61782i
$279$	2.60043	0.155684
$280$	0	0
$281$	30.5158	1.82042	0.910209	−	0.414150i	$-0.135921\pi$
$281$	30.5158	1.82042	0.910209	+	0.414150i	$0.135921\pi$
$282$	3.92977i	0.234015i
$283$	28.8824i	1.71688i	0.512911	+	0.858442i	$0.328567\pi$
$283$	28.8824i	1.71688i	−0.512911	+	0.858442i	$0.671433\pi$
$284$	11.3918	0.675977
$285$	0	0
$286$	−3.98087	−0.235394
$287$	34.2720i	2.02301i
$288$	− 15.6309i	− 0.921058i
$289$	13.9705	0.821791
$290$	0	0
$291$	−6.20046	−0.363477
$292$	− 28.4320i	− 1.66386i
$293$	− 6.06112i	− 0.354094i	−0.984202	−	0.177047i	$-0.943346\pi$
$293$	− 6.06112i	− 0.354094i	0.984202	−	0.177047i	$-0.0566545\pi$
$294$	6.90799	0.402882
$295$	0	0
$296$	−2.12753	−0.123660
$297$	− 11.0042i	− 0.638530i
$298$	− 3.22381i	− 0.186750i
$299$	5.21043	0.301327
$300$	0	0
$301$	12.8542	0.740904
$302$	31.3753i	1.80545i
$303$	4.72371i	0.271370i
$304$	1.43868	0.0825138
$305$	0	0
$306$	10.2856	0.587986
$307$	2.69110i	0.153589i	0.997047	+	0.0767945i	$0.0244685\pi$
$307$	2.69110i	0.153589i	−0.997047	+	0.0767945i	$0.975531\pi$
$308$	33.7978i	1.92581i
$309$	−6.99354	−0.397849
$310$	0	0
$311$	−12.3175	−0.698463	−0.349232	−	0.937036i	$-0.613557\pi$
$311$	−12.3175	−0.698463	−0.349232	+	0.937036i	$0.613557\pi$
$312$	− 0.942280i	− 0.0533461i
$313$	− 21.0190i	− 1.18806i	−0.804442	−	0.594032i	$-0.797535\pi$
$313$	− 21.0190i	− 1.18806i	0.804442	−	0.594032i	$-0.202465\pi$
$314$	−8.69842	−0.490880
$315$	0	0
$316$	−45.2746	−2.54690
$317$	21.7553i	1.22190i	0.791669	+	0.610950i	$0.209212\pi$
$317$	21.7553i	1.22190i	−0.791669	+	0.610950i	$0.790788\pi$
$318$	15.4693i	0.867476i
$319$	12.9691	0.726131
$320$	0	0
$321$	−9.48799	−0.529568
$322$	− 72.1995i	− 4.02352i
$323$	7.89634i	0.439364i
$324$	−17.6031	−0.977949
$325$	0	0
$326$	22.7835	1.26186
$327$	− 5.26942i	− 0.291400i
$328$	− 26.3800i	− 1.45659i
$329$	9.40133	0.518312
$330$	0	0
$331$	15.7718	0.866894	0.433447	−	0.901179i	$-0.357297\pi$
$331$	15.7718	0.866894	0.433447	+	0.901179i	$0.357297\pi$
$332$	− 47.2746i	− 2.59453i
$333$	− 2.09160i	− 0.114619i
$334$	−16.5193	−0.903898
$335$	0	0
$336$	0.688857	0.0375802
$337$	− 28.4225i	− 1.54827i	−0.633018	−	0.774137i	$-0.718184\pi$
$337$	− 28.4225i	− 1.54827i	0.633018	−	0.774137i	$-0.281816\pi$
$338$	28.8200i	1.56760i
$339$	−12.5098	−0.679438
$340$	0	0
$341$	−3.10845	−0.168332
$342$	− 26.8087i	− 1.44965i
$343$	7.52886i	0.406520i
$344$	−9.89420	−0.533460
$345$	0	0
$346$	−36.6655	−1.97115
$347$	− 11.3731i	− 0.610539i	−0.952266	−	0.305270i	$-0.901253\pi$
$347$	− 11.3731i	− 0.610539i	0.952266	−	0.305270i	$-0.0987466\pi$
$348$	8.34443i	0.447308i
$349$	−26.0789	−1.39597	−0.697986	−	0.716112i	$-0.745920\pi$
$349$	−26.0789	−1.39597	−0.697986	+	0.716112i	$0.745920\pi$
$350$	0	0
$351$	1.99507	0.106489
$352$	18.6845i	0.995886i
$353$	1.21954i	0.0649098i	0.999473	+	0.0324549i	$0.0103325\pi$
$353$	1.21954i	0.0649098i	−0.999473	+	0.0324549i	$0.989667\pi$
$354$	12.7977	0.680191
$355$	0	0
$356$	33.3049	1.76516
$357$	3.78087i	0.200105i
$358$	16.5873i	0.876667i
$359$	33.0524	1.74444	0.872220	−	0.489114i	$-0.162680\pi$
$359$	33.0524	1.74444	0.872220	+	0.489114i	$0.162680\pi$
$360$	0	0
$361$	1.58135	0.0832288
$362$	43.6546i	2.29444i
$363$	− 0.845487i	− 0.0443765i
$364$	−6.12753	−0.321170
$365$	0	0
$366$	−6.80265	−0.355580
$367$	− 12.8468i	− 0.670596i	−0.942112	−	0.335298i	$-0.891163\pi$
$367$	− 12.8468i	− 0.670596i	0.942112	−	0.335298i	$-0.108837\pi$
$368$	− 2.93197i	− 0.152839i
$369$	25.9344	1.35009
$370$	0	0
$371$	37.0077	1.92135
$372$	− 2.00000i	− 0.103695i
$373$	0.933993i	0.0483603i	0.999708	+	0.0241802i	$0.00769754\pi$
$373$	0.933993i	0.0483603i	−0.999708	+	0.0241802i	$0.992302\pi$
$374$	−12.2949	−0.635754
$375$	0	0
$376$	−7.23644	−0.373191
$377$	2.35130i	0.121098i
$378$	− 27.6450i	− 1.42191i
$379$	−7.57219	−0.388957	−0.194479	−	0.980907i	$-0.562302\pi$
$379$	−7.57219	−0.388957	−0.194479	+	0.980907i	$0.562302\pi$
$380$	0	0
$381$	3.90758	0.200191
$382$	− 10.1467i	− 0.519149i
$383$	− 20.3145i	− 1.03802i	−0.854767	−	0.519011i	$-0.826300\pi$
$383$	− 20.3145i	− 1.03802i	0.854767	−	0.519011i	$-0.173700\pi$
$384$	−11.1107	−0.566990
$385$	0	0
$386$	−14.4174	−0.733824
$387$	− 9.72708i	− 0.494455i
$388$	− 31.0360i	− 1.57561i
$389$	21.0455	1.06705	0.533526	−	0.845784i	$-0.320867\pi$
$389$	21.0455	1.06705	0.533526	+	0.845784i	$0.320867\pi$
$390$	0	0
$391$	16.0924	0.813829
$392$	12.7206i	0.642489i
$393$	− 13.0445i	− 0.658009i
$394$	16.8989	0.851353
$395$	0	0
$396$	25.5756	1.28522
$397$	− 16.6507i	− 0.835674i	−0.908522	−	0.417837i	$-0.862788\pi$
$397$	− 16.6507i	− 0.835674i	0.908522	−	0.417837i	$-0.137212\pi$
$398$	9.77093i	0.489773i
$399$	9.85461	0.493348
$400$	0	0
$401$	−34.5904	−1.72736	−0.863681	−	0.504039i	$-0.831847\pi$
$401$	−34.5904	−1.72736	−0.863681	+	0.504039i	$0.831847\pi$
$402$	1.28066i	0.0638736i
$403$	− 0.563561i	− 0.0280730i
$404$	−23.6442	−1.17634
$405$	0	0
$406$	32.5813	1.61698
$407$	2.50021i	0.123931i
$408$	− 2.91023i	− 0.144078i
$409$	−21.5735	−1.06674	−0.533371	−	0.845881i	$-0.679075\pi$
$409$	−21.5735	−1.06674	−0.533371	+	0.845881i	$0.679075\pi$
$410$	0	0
$411$	3.51377	0.173322
$412$	− 35.0057i	− 1.72461i
$413$	− 30.6164i	− 1.50653i
$414$	−54.6351	−2.68517
$415$	0	0
$416$	−3.38749	−0.166086
$417$	7.50331i	0.367439i
$418$	32.0460i	1.56742i
$419$	−4.80511	−0.234745	−0.117373	−	0.993088i	$-0.537447\pi$
$419$	−4.80511	−0.234745	−0.117373	+	0.993088i	$0.537447\pi$
$420$	0	0
$421$	−1.16358	−0.0567096	−0.0283548	−	0.999598i	$-0.509027\pi$
$421$	−1.16358	−0.0567096	−0.0283548	+	0.999598i	$0.509027\pi$
$422$	− 10.3063i	− 0.501701i
$423$	− 7.11421i	− 0.345904i
$424$	−28.4858	−1.38339
$425$	0	0
$426$	5.17180	0.250575
$427$	16.2742i	0.787564i
$428$	− 47.4915i	− 2.29559i
$429$	−1.10733	−0.0534626
$430$	0	0
$431$	−5.86507	−0.282510	−0.141255	−	0.989973i	$-0.545114\pi$
$431$	−5.86507	−0.282510	−0.141255	+	0.989973i	$0.545114\pi$
$432$	− 1.12264i	− 0.0540133i
$433$	12.1444i	0.583624i	0.956476	+	0.291812i	$0.0942582\pi$
$433$	12.1444i	0.583624i	−0.956476	+	0.291812i	$0.905742\pi$
$434$	−7.80911	−0.374849
$435$	0	0
$436$	26.3757	1.26317
$437$	− 41.9440i	− 2.00645i
$438$	− 12.9080i	− 0.616768i
$439$	17.1002	0.816149	0.408075	−	0.912949i	$-0.366200\pi$
$439$	17.1002	0.816149	0.408075	+	0.912949i	$0.366200\pi$
$440$	0	0
$441$	−12.5058	−0.595513
$442$	− 2.22907i	− 0.106026i
$443$	− 21.9722i	− 1.04393i	−0.852966	−	0.521966i	$-0.825199\pi$
$443$	− 21.9722i	− 1.04393i	0.852966	−	0.521966i	$-0.174801\pi$
$444$	−1.60865	−0.0763433
$445$	0	0
$446$	44.3613	2.10057
$447$	− 0.896748i	− 0.0424147i
$448$	44.7600i	2.11471i
$449$	−24.2169	−1.14287	−0.571433	−	0.820649i	$-0.693612\pi$
$449$	−24.2169	−1.14287	−0.571433	+	0.820649i	$0.693612\pi$
$450$	0	0
$451$	−31.0009	−1.45977
$452$	− 62.6168i	− 2.94525i
$453$	8.72749i	0.410053i
$454$	57.5366	2.70033
$455$	0	0
$456$	−7.58535	−0.355216
$457$	− 30.9844i	− 1.44939i	−0.689069	−	0.724695i	$-0.741981\pi$
$457$	− 30.9844i	− 1.44939i	0.689069	−	0.724695i	$-0.258019\pi$
$458$	43.3224i	2.02432i
$459$	6.16176	0.287606
$460$	0	0
$461$	−20.0291	−0.932847	−0.466423	−	0.884562i	$-0.654458\pi$
$461$	−20.0291	−0.932847	−0.466423	+	0.884562i	$0.654458\pi$
$462$	15.3440i	0.713868i
$463$	− 21.3349i	− 0.991517i	−0.868460	−	0.495759i	$-0.834890\pi$
$463$	− 21.3349i	− 0.991517i	0.868460	−	0.495759i	$-0.165110\pi$
$464$	1.32310	0.0614234
$465$	0	0
$466$	−19.0047	−0.880375
$467$	5.90534i	0.273267i	0.990622	+	0.136633i	$0.0436282\pi$
$467$	5.90534i	0.273267i	−0.990622	+	0.136633i	$0.956372\pi$
$468$	4.63685i	0.214338i
$469$	3.06377	0.141472
$470$	0	0
$471$	−2.41959	−0.111489
$472$	23.5662i	1.08472i
$473$	11.6273i	0.534625i
$474$	−20.5545	−0.944097
$475$	0	0
$476$	−18.9249	−0.867421
$477$	− 28.0046i	− 1.28224i
$478$	− 61.1479i	− 2.79684i
$479$	13.2433	0.605102	0.302551	−	0.953133i	$-0.402162\pi$
$479$	13.2433	0.605102	0.302551	+	0.953133i	$0.402162\pi$
$480$	0	0
$481$	−0.453287	−0.0206681
$482$	42.0997i	1.91759i
$483$	− 20.0833i	− 0.913822i
$484$	4.23203	0.192365
$485$	0	0
$486$	−32.1258	−1.45725
$487$	10.8803i	0.493034i	0.969138	+	0.246517i	$0.0792861\pi$
$487$	10.8803i	0.493034i	−0.969138	+	0.246517i	$0.920714\pi$
$488$	− 12.5267i	− 0.567056i
$489$	6.33756	0.286594
$490$	0	0
$491$	17.9053	0.808057	0.404028	−	0.914746i	$-0.367610\pi$
$491$	17.9053	0.808057	0.404028	+	0.914746i	$0.367610\pi$
$492$	− 19.9462i	− 0.899245i
$493$	7.26199i	0.327063i
$494$	−5.80993	−0.261401
$495$	0	0
$496$	−0.317122	−0.0142392
$497$	− 12.3727i	− 0.554990i
$498$	− 21.4624i	− 0.961755i
$499$	33.5458	1.50171	0.750857	−	0.660465i	$-0.229641\pi$
$499$	33.5458	1.50171	0.750857	+	0.660465i	$0.229641\pi$
$500$	0	0
$501$	−4.59509	−0.205293
$502$	38.7982i	1.73165i
$503$	− 8.89155i	− 0.396455i	−0.980156	−	0.198227i	$-0.936482\pi$
$503$	− 8.89155i	− 0.396455i	0.980156	−	0.198227i	$-0.0635184\pi$
$504$	23.6374	1.05289
$505$	0	0
$506$	65.3084	2.90331
$507$	8.01670i	0.356034i
$508$	19.5591i	0.867796i
$509$	−37.5600	−1.66482	−0.832408	−	0.554164i	$-0.813038\pi$
$509$	−37.5600	−1.66482	−0.832408	+	0.554164i	$0.813038\pi$
$510$	0	0
$511$	−30.8802	−1.36606
$512$	3.58383i	0.158384i
$513$	− 16.0603i	− 0.709078i
$514$	−49.2650	−2.17299
$515$	0	0
$516$	−7.48112	−0.329338
$517$	8.50401i	0.374006i
$518$	6.28107i	0.275975i
$519$	−10.1990	−0.447688
$520$	0	0
$521$	−0.568717	−0.0249160	−0.0124580	−	0.999922i	$-0.503966\pi$
$521$	−0.568717	−0.0249160	−0.0124580	+	0.999922i	$0.503966\pi$
$522$	− 24.6550i	− 1.07912i
$523$	17.2763i	0.755439i	0.925920	+	0.377720i	$0.123292\pi$
$523$	17.2763i	0.755439i	−0.925920	+	0.377720i	$0.876708\pi$
$524$	65.2935	2.85236
$525$	0	0
$526$	33.4182	1.45710
$527$	− 1.74056i	− 0.0758199i
$528$	0.623109i	0.0271173i
$529$	−62.4802	−2.71653
$530$	0	0
$531$	−23.1681	−1.00541
$532$	49.3266i	2.13858i
$533$	− 5.62046i	− 0.243449i
$534$	15.1203	0.654317
$535$	0	0
$536$	−2.35826	−0.101861
$537$	4.61400i	0.199109i
$538$	− 32.7696i	− 1.41280i
$539$	14.9489	0.643893
$540$	0	0
$541$	−13.1471	−0.565237	−0.282619	−	0.959232i	$-0.591203\pi$
$541$	−13.1471	−0.565237	−0.282619	+	0.959232i	$0.591203\pi$
$542$	19.0264i	0.817255i
$543$	12.1431i	0.521112i
$544$	−10.4623	−0.448566
$545$	0	0
$546$	−2.78187	−0.119053
$547$	28.6156i	1.22351i	0.791046	+	0.611757i	$0.209537\pi$
$547$	28.6156i	1.22351i	−0.791046	+	0.611757i	$0.790463\pi$
$548$	17.5880i	0.751320i
$549$	12.3151	0.525595
$550$	0	0
$551$	18.9279	0.806358
$552$	15.4586i	0.657963i
$553$	49.1731i	2.09105i
$554$	−17.5849	−0.747110
$555$	0	0
$556$	−37.5573	−1.59279
$557$	14.9340i	0.632774i	0.948630	+	0.316387i	$0.102470\pi$
$557$	14.9340i	0.632774i	−0.948630	+	0.316387i	$0.897530\pi$
$558$	5.90934i	0.250162i
$559$	−2.10804	−0.0891604
$560$	0	0
$561$	−3.42000	−0.144393
$562$	69.3453i	2.92515i
$563$	14.8473i	0.625740i	0.949796	+	0.312870i	$0.101290\pi$
$563$	14.8473i	0.625740i	−0.949796	+	0.312870i	$0.898710\pi$
$564$	−5.47155	−0.230394
$565$	0	0
$566$	−65.6337	−2.75879
$567$	19.1188i	0.802916i
$568$	9.52356i	0.399600i
$569$	31.9157	1.33798	0.668988	−	0.743273i	$-0.266728\pi$
$569$	31.9157	1.33798	0.668988	+	0.743273i	$0.266728\pi$
$570$	0	0
$571$	25.8573	1.08209	0.541047	−	0.840992i	$-0.318028\pi$
$571$	25.8573	1.08209	0.541047	+	0.840992i	$0.318028\pi$
$572$	− 5.54269i	− 0.231752i
$573$	− 2.82244i	− 0.117909i
$574$	−77.8811	−3.25069
$575$	0	0
$576$	33.8709	1.41129
$577$	− 12.3987i	− 0.516164i	−0.966123	−	0.258082i	$-0.916910\pi$
$577$	− 12.3987i	− 0.516164i	0.966123	−	0.258082i	$-0.0830904\pi$
$578$	31.7471i	1.32050i
$579$	−4.01039	−0.166666
$580$	0	0
$581$	−51.3453	−2.13016
$582$	− 14.0902i	− 0.584057i
$583$	33.4755i	1.38641i
$584$	23.7693	0.983580
$585$	0	0
$586$	13.7735	0.568980
$587$	16.8446i	0.695252i	0.937633	+	0.347626i	$0.113012\pi$
$587$	16.8446i	0.695252i	−0.937633	+	0.347626i	$0.886988\pi$
$588$	9.61822i	0.396649i
$589$	−4.53667	−0.186930
$590$	0	0
$591$	4.70066	0.193359
$592$	0.255070i	0.0104833i
$593$	16.8564i	0.692211i	0.938196	+	0.346106i	$0.112496\pi$
$593$	16.8564i	0.692211i	−0.938196	+	0.346106i	$0.887504\pi$
$594$	25.0065	1.02603
$595$	0	0
$596$	4.48861	0.183861
$597$	2.71792i	0.111237i
$598$	11.8404i	0.484191i
$599$	−2.02600	−0.0827803	−0.0413901	−	0.999143i	$-0.513179\pi$
$599$	−2.02600	−0.0827803	−0.0413901	+	0.999143i	$0.513179\pi$
$600$	0	0
$601$	36.9800	1.50844	0.754222	−	0.656620i	$-0.228014\pi$
$601$	36.9800	1.50844	0.754222	+	0.656620i	$0.228014\pi$
$602$	29.2104i	1.19053i
$603$	− 2.31843i	− 0.0944136i
$604$	−43.6849	−1.77751
$605$	0	0
$606$	−10.7344	−0.436054
$607$	5.10158i	0.207067i	0.994626	+	0.103533i	$0.0330148\pi$
$607$	5.10158i	0.207067i	−0.994626	+	0.103533i	$0.966985\pi$
$608$	27.2693i	1.10592i
$609$	9.06294	0.367249
$610$	0	0
$611$	−1.54178	−0.0623737
$612$	14.3209i	0.578888i
$613$	− 22.3263i	− 0.901751i	−0.892587	−	0.450876i	$-0.851112\pi$
$613$	− 22.3263i	− 0.901751i	0.892587	−	0.450876i	$-0.148888\pi$
$614$	−6.11536	−0.246796
$615$	0	0
$616$	−28.2551	−1.13843
$617$	− 35.2360i	− 1.41855i	−0.704933	−	0.709274i	$-0.749023\pi$
$617$	− 35.2360i	− 1.41855i	0.704933	−	0.709274i	$-0.250977\pi$
$618$	− 15.8924i	− 0.639287i
$619$	4.21002	0.169215	0.0846076	−	0.996414i	$-0.473036\pi$
$619$	4.21002	0.169215	0.0846076	+	0.996414i	$0.473036\pi$
$620$	0	0
$621$	−32.7302	−1.31342
$622$	− 27.9909i	− 1.12233i
$623$	− 36.1727i	− 1.44923i
$624$	−0.112970	−0.00452241
$625$	0	0
$626$	47.7644	1.90905
$627$	8.91404i	0.355992i
$628$	− 12.1111i	− 0.483285i
$629$	−1.39998	−0.0558208
$630$	0	0
$631$	−27.5289	−1.09591	−0.547953	−	0.836509i	$-0.684593\pi$
$631$	−27.5289	−1.09591	−0.547953	+	0.836509i	$0.684593\pi$
$632$	− 37.8498i	− 1.50558i
$633$	− 2.86683i	− 0.113946i
$634$	−49.4377	−1.96342
$635$	0	0
$636$	−21.5384	−0.854054
$637$	2.71023i	0.107383i
$638$	29.4716i	1.16679i
$639$	−9.36269	−0.370382
$640$	0	0
$641$	7.72932	0.305290	0.152645	−	0.988281i	$-0.451221\pi$
$641$	7.72932	0.305290	0.152645	+	0.988281i	$0.451221\pi$
$642$	− 21.5609i	− 0.850941i
$643$	3.55572i	0.140224i	0.997539	+	0.0701119i	$0.0223356\pi$
$643$	3.55572i	0.140224i	−0.997539	+	0.0701119i	$0.977664\pi$
$644$	100.526	3.96127
$645$	0	0
$646$	−17.9440	−0.705996
$647$	12.3428i	0.485244i	0.970121	+	0.242622i	$0.0780074\pi$
$647$	12.3428i	0.485244i	−0.970121	+	0.242622i	$0.921993\pi$
$648$	− 14.7163i	− 0.578109i
$649$	27.6942	1.08709
$650$	0	0
$651$	−2.17221	−0.0851358
$652$	31.7222i	1.24234i
$653$	− 8.83731i	− 0.345831i	−0.984937	−	0.172915i	$-0.944681\pi$
$653$	− 8.83731i	− 0.345831i	0.984937	−	0.172915i	$-0.0553187\pi$
$654$	11.9745	0.468238
$655$	0	0
$656$	−3.16269	−0.123482
$657$	23.3678i	0.911664i
$658$	21.3640i	0.832854i
$659$	20.9853	0.817472	0.408736	−	0.912653i	$-0.365970\pi$
$659$	20.9853	0.817472	0.408736	+	0.912653i	$0.365970\pi$
$660$	0	0
$661$	27.1613	1.05645	0.528227	−	0.849103i	$-0.322857\pi$
$661$	27.1613	1.05645	0.528227	+	0.849103i	$0.322857\pi$
$662$	35.8404i	1.39298i
$663$	− 0.620046i	− 0.0240806i
$664$	39.5218	1.53374
$665$	0	0
$666$	4.75304	0.184176
$667$	− 38.5744i	− 1.49361i
$668$	− 23.0004i	− 0.889913i
$669$	12.3397	0.477082
$670$	0	0
$671$	−14.7209	−0.568294
$672$	13.0569i	0.503681i
$673$	− 16.0079i	− 0.617059i	−0.951215	−	0.308529i	$-0.900163\pi$
$673$	− 16.0079i	− 0.617059i	0.951215	−	0.308529i	$-0.0998368\pi$
$674$	64.5886	2.48786
$675$	0	0
$676$	−40.1271	−1.54335
$677$	− 5.16362i	− 0.198454i	−0.995065	−	0.0992271i	$-0.968363\pi$
$677$	− 5.16362i	− 0.198454i	0.995065	−	0.0992271i	$-0.0316370\pi$
$678$	− 28.4277i	− 1.09176i
$679$	−33.7084	−1.29361
$680$	0	0
$681$	16.0046	0.613299
$682$	− 7.06377i	− 0.270486i
$683$	28.6989i	1.09813i	0.835779	+	0.549066i	$0.185016\pi$
$683$	28.6989i	1.09813i	−0.835779	+	0.549066i	$0.814984\pi$
$684$	37.3266	1.42722
$685$	0	0
$686$	−17.1089	−0.653221
$687$	12.0507i	0.459764i
$688$	1.18621i	0.0452240i
$689$	−6.06911	−0.231215
$690$	0	0
$691$	4.87199	0.185339	0.0926695	−	0.995697i	$-0.470460\pi$
$691$	4.87199	0.185339	0.0926695	+	0.995697i	$0.470460\pi$
$692$	− 51.0506i	− 1.94065i
$693$	− 27.7778i	− 1.05519i
$694$	25.8447	0.981051
$695$	0	0
$696$	−6.97598	−0.264424
$697$	− 17.3588i	− 0.657511i
$698$	− 59.2628i	− 2.24313i
$699$	−5.28642	−0.199951
$700$	0	0
$701$	23.1089	0.872811	0.436406	−	0.899750i	$-0.356251\pi$
$701$	23.1089	0.872811	0.436406	+	0.899750i	$0.356251\pi$
$702$	4.53367i	0.171112i
$703$	3.64896i	0.137623i
$704$	−40.4879	−1.52594
$705$	0	0
$706$	−2.77135	−0.104301
$707$	25.6802i	0.965802i
$708$	17.8187i	0.669667i
$709$	20.9935	0.788429	0.394214	−	0.919018i	$-0.371017\pi$
$709$	20.9935	0.788429	0.394214	+	0.919018i	$0.371017\pi$
$710$	0	0
$711$	37.2104	1.39550
$712$	27.8430i	1.04346i
$713$	9.24555i	0.346248i
$714$	−8.59180	−0.321540
$715$	0	0
$716$	−23.0951	−0.863103
$717$	− 17.0092i	− 0.635219i
$718$	75.1097i	2.80307i
$719$	−10.2482	−0.382193	−0.191097	−	0.981571i	$-0.561204\pi$
$719$	−10.2482	−0.382193	−0.191097	+	0.981571i	$0.561204\pi$
$720$	0	0
$721$	−38.0200	−1.41594
$722$	3.59352i	0.133737i
$723$	11.7106i	0.435523i
$724$	−60.7817	−2.25894
$725$	0	0
$726$	1.92132	0.0713069
$727$	− 13.5877i	− 0.503941i	−0.967735	−	0.251971i	$-0.918921\pi$
$727$	− 13.5877i	− 0.503941i	0.967735	−	0.251971i	$-0.0810786\pi$
$728$	− 5.12264i	− 0.189858i
$729$	7.75445	0.287202
$730$	0	0
$731$	−6.51066	−0.240806
$732$	− 9.47155i	− 0.350079i
$733$	− 20.1440i	− 0.744035i	−0.928226	−	0.372017i	$-0.878666\pi$
$733$	− 20.1440i	− 0.744035i	0.928226	−	0.372017i	$-0.121334\pi$
$734$	29.1935	1.07755
$735$	0	0
$736$	55.5738	2.04848
$737$	2.77135i	0.102084i
$738$	58.9345i	2.16941i
$739$	32.6022	1.19929	0.599646	−	0.800266i	$-0.295308\pi$
$739$	32.6022	1.19929	0.599646	+	0.800266i	$0.295308\pi$
$740$	0	0
$741$	−1.61612	−0.0593695
$742$	84.0980i	3.08733i
$743$	− 29.0404i	− 1.06539i	−0.846308	−	0.532694i	$-0.821180\pi$
$743$	− 29.0404i	− 1.06539i	0.846308	−	0.532694i	$-0.178820\pi$
$744$	1.67201	0.0612988
$745$	0	0
$746$	−2.12245	−0.0777083
$747$	38.8542i	1.42160i
$748$	− 17.1186i	− 0.625918i
$749$	−51.5809	−1.88472
$750$	0	0
$751$	−6.59867	−0.240789	−0.120395	−	0.992726i	$-0.538416\pi$
$751$	−6.59867	−0.240789	−0.120395	+	0.992726i	$0.538416\pi$
$752$	0.867575i	0.0316372i
$753$	10.7923i	0.393292i
$754$	−5.34319	−0.194588
$755$	0	0
$756$	38.4911	1.39991
$757$	− 31.1970i	− 1.13387i	−0.823762	−	0.566936i	$-0.808129\pi$
$757$	− 31.1970i	− 1.13387i	0.823762	−	0.566936i	$-0.191871\pi$
$758$	− 17.2074i	− 0.625000i
$759$	18.1665	0.659401
$760$	0	0
$761$	5.04285	0.182803	0.0914016	−	0.995814i	$-0.470865\pi$
$761$	5.04285	0.182803	0.0914016	+	0.995814i	$0.470865\pi$
$762$	8.87975i	0.321679i
$763$	− 28.6469i	− 1.03709i
$764$	14.1275	0.511116
$765$	0	0
$766$	46.1636	1.66796
$767$	5.02096i	0.181296i
$768$	− 8.78174i	− 0.316884i
$769$	−12.3271	−0.444527	−0.222263	−	0.974987i	$-0.571344\pi$
$769$	−12.3271	−0.444527	−0.222263	+	0.974987i	$0.571344\pi$
$770$	0	0
$771$	−13.7038	−0.493529
$772$	− 20.0737i	− 0.722470i
$773$	− 4.19395i	− 0.150846i	−0.997152	−	0.0754230i	$-0.975969\pi$
$773$	− 4.19395i	− 0.150846i	0.997152	−	0.0754230i	$-0.0240307\pi$
$774$	22.1042	0.794520
$775$	0	0
$776$	25.9462	0.931415
$777$	1.74717i	0.0626794i
$778$	47.8248i	1.71460i
$779$	−45.2447	−1.62106
$780$	0	0
$781$	11.1918	0.400473
$782$	36.5691i	1.30771i
$783$	− 14.7701i	− 0.527839i
$784$	1.52508	0.0544670
$785$	0	0
$786$	29.6429	1.05733
$787$	− 23.8260i	− 0.849305i	−0.905356	−	0.424653i	$-0.860396\pi$
$787$	− 23.8260i	− 0.849305i	0.905356	−	0.424653i	$-0.139604\pi$
$788$	23.5289i	0.838181i
$789$	9.29575	0.330937
$790$	0	0
$791$	−68.0086	−2.41811
$792$	21.3813i	0.759751i
$793$	− 2.66890i	− 0.0947755i
$794$	37.8377	1.34281
$795$	0	0
$796$	−13.6044	−0.482195
$797$	− 28.9019i	− 1.02376i	−0.859057	−	0.511880i	$-0.828949\pi$
$797$	− 28.9019i	− 1.02376i	0.859057	−	0.511880i	$-0.171051\pi$
$798$	22.3940i	0.792741i
$799$	−4.76178	−0.168460
$800$	0	0
$801$	−27.3727	−0.967167
$802$	− 78.6047i	− 2.77563i
$803$	− 27.9328i	− 0.985728i
$804$	−1.78311	−0.0628853
$805$	0	0
$806$	1.28066	0.0451094
$807$	− 9.11532i	− 0.320874i
$808$	− 19.7667i	− 0.695389i
$809$	−18.0760	−0.635518	−0.317759	−	0.948172i	$-0.602930\pi$
$809$	−18.0760	−0.635518	−0.317759	+	0.948172i	$0.602930\pi$
$810$	0	0
$811$	12.4729	0.437981	0.218991	−	0.975727i	$-0.429724\pi$
$811$	12.4729	0.437981	0.218991	+	0.975727i	$0.429724\pi$
$812$	45.3640i	1.59196i
$813$	5.29247i	0.185615i
$814$	−5.68157	−0.199139
$815$	0	0
$816$	−0.348907	−0.0122142
$817$	16.9697i	0.593694i
$818$	− 49.0246i	− 1.71411i
$819$	5.03612	0.175976
$820$	0	0
$821$	35.4373	1.23677	0.618384	−	0.785876i	$-0.287787\pi$
$821$	35.4373	1.23677	0.618384	+	0.785876i	$0.287787\pi$
$822$	7.98484i	0.278503i
$823$	42.9296i	1.49643i	0.663455	+	0.748216i	$0.269089\pi$
$823$	42.9296i	1.49643i	−0.663455	+	0.748216i	$0.730911\pi$
$824$	29.2649	1.01949
$825$	0	0
$826$	69.5740	2.42079
$827$	− 18.5210i	− 0.644039i	−0.946733	−	0.322019i	$-0.895638\pi$
$827$	− 18.5210i	− 0.644039i	0.946733	−	0.322019i	$-0.104362\pi$
$828$	− 76.0702i	− 2.64362i
$829$	−26.5858	−0.923362	−0.461681	−	0.887046i	$-0.652753\pi$
$829$	−26.5858	−0.923362	−0.461681	+	0.887046i	$0.652753\pi$
$830$	0	0
$831$	−4.89149	−0.169684
$832$	− 7.34045i	− 0.254484i
$833$	8.37054i	0.290022i
$834$	−17.0508	−0.590423
$835$	0	0
$836$	−44.6186	−1.54317
$837$	3.54010i	0.122364i
$838$	− 10.9193i	− 0.377202i
$839$	−24.0446	−0.830112	−0.415056	−	0.909796i	$-0.636238\pi$
$839$	−24.0446	−0.830112	−0.415056	+	0.909796i	$0.636238\pi$
$840$	0	0
$841$	−11.5926	−0.399746
$842$	− 2.64418i	− 0.0911244i
$843$	19.2894i	0.664361i
$844$	14.3497	0.493938
$845$	0	0
$846$	16.1666	0.555820
$847$	− 4.59644i	− 0.157935i
$848$	3.41516i	0.117277i
$849$	−18.2569	−0.626577
$850$	0	0
$851$	7.43644	0.254918
$852$	7.20087i	0.246698i
$853$	5.32310i	0.182260i	0.995839	+	0.0911298i	$0.0290478\pi$
$853$	5.32310i	0.182260i	−0.995839	+	0.0911298i	$0.970952\pi$
$854$	−36.9822	−1.26550
$855$	0	0
$856$	39.7031	1.35702
$857$	− 14.9184i	− 0.509602i	−0.966993	−	0.254801i	$-0.917990\pi$
$857$	− 14.9184i	− 0.509602i	0.966993	−	0.254801i	$-0.0820100\pi$
$858$	− 2.51635i	− 0.0859069i
$859$	−31.3782	−1.07061	−0.535305	−	0.844659i	$-0.679803\pi$
$859$	−31.3782	−1.07061	−0.535305	+	0.844659i	$0.679803\pi$
$860$	0	0
$861$	−21.6637	−0.738298
$862$	− 13.3280i	− 0.453955i
$863$	− 38.4329i	− 1.30827i	−0.756377	−	0.654136i	$-0.773032\pi$
$863$	− 38.4329i	− 1.30827i	0.756377	−	0.654136i	$-0.226968\pi$
$864$	21.2791	0.723929
$865$	0	0
$866$	−27.5975	−0.937802
$867$	8.83089i	0.299913i
$868$	− 10.8729i	− 0.369049i
$869$	−44.4797	−1.50887
$870$	0	0
$871$	−0.502445	−0.0170247
$872$	22.0502i	0.746715i
$873$	25.5079i	0.863313i
$874$	95.3153	3.22409
$875$	0	0
$876$	17.9722	0.607225
$877$	2.29975i	0.0776570i	0.999246	+	0.0388285i	$0.0123626\pi$
$877$	2.29975i	0.0776570i	−0.999246	+	0.0388285i	$0.987637\pi$
$878$	38.8593i	1.31144i
$879$	3.83131	0.129227
$880$	0	0
$881$	25.2993	0.852356	0.426178	−	0.904639i	$-0.359860\pi$
$881$	25.2993	0.852356	0.426178	+	0.904639i	$0.359860\pi$
$882$	− 28.4187i	− 0.956906i
$883$	2.93567i	0.0987931i	0.998779	+	0.0493966i	$0.0157298\pi$
$883$	2.93567i	0.0987931i	−0.998779	+	0.0493966i	$0.984270\pi$
$884$	3.10360	0.104385
$885$	0	0
$886$	49.9306	1.67745
$887$	− 2.26157i	− 0.0759362i	−0.999279	−	0.0379681i	$-0.987911\pi$
$887$	− 2.26157i	− 0.0759362i	0.999279	−	0.0379681i	$-0.0120885\pi$
$888$	− 1.34484i	− 0.0451299i
$889$	21.2433	0.712478
$890$	0	0
$891$	−17.2940	−0.579372
$892$	61.7657i	2.06807i
$893$	12.4113i	0.415328i
$894$	2.03781	0.0681545
$895$	0	0
$896$	−60.4026	−2.01791
$897$	3.29358i	0.109969i
$898$	− 55.0315i	− 1.83643i
$899$	−4.17221	−0.139151
$900$	0	0
$901$	−18.7445	−0.624468
$902$	− 70.4477i	− 2.34565i
$903$	8.12530i	0.270393i
$904$	52.3479	1.74107
$905$	0	0
$906$	−19.8327	−0.658898
$907$	24.3904i	0.809870i	0.914346	+	0.404935i	$0.132706\pi$
$907$	24.3904i	0.809870i	−0.914346	+	0.404935i	$0.867294\pi$
$908$	80.1101i	2.65855i
$909$	19.4328	0.644545
$910$	0	0
$911$	32.3326	1.07123	0.535614	−	0.844463i	$-0.320080\pi$
$911$	32.3326	1.07123	0.535614	+	0.844463i	$0.320080\pi$
$912$	0.909405i	0.0301134i
$913$	− 46.4446i	− 1.53709i
$914$	70.4103	2.32897
$915$	0	0
$916$	−60.3191	−1.99300
$917$	− 70.9158i	− 2.34185i
$918$	14.0022i	0.462143i
$919$	−13.1553	−0.433953	−0.216977	−	0.976177i	$-0.569620\pi$
$919$	−13.1553	−0.433953	−0.216977	+	0.976177i	$0.569620\pi$
$920$	0	0
$921$	−1.70107	−0.0560523
$922$	− 45.5149i	− 1.49895i
$923$	2.02907i	0.0667875i
$924$	−21.3640	−0.702823
$925$	0	0
$926$	48.4824	1.59323
$927$	28.7706i	0.944950i
$928$	25.0786i	0.823247i
$929$	−37.1635	−1.21930	−0.609648	−	0.792672i	$-0.708689\pi$
$929$	−37.1635	−1.21930	−0.609648	+	0.792672i	$0.708689\pi$
$930$	0	0
$931$	21.8173	0.715034
$932$	− 26.4608i	− 0.866753i
$933$	− 7.78606i	− 0.254904i
$934$	−13.4195	−0.439101
$935$	0	0
$936$	−3.87643	−0.126705
$937$	− 49.5180i	− 1.61768i	−0.588028	−	0.808841i	$-0.700095\pi$
$937$	− 49.5180i	− 1.61768i	0.588028	−	0.808841i	$-0.299905\pi$
$938$	6.96224i	0.227325i
$939$	13.2864	0.433584
$940$	0	0
$941$	−3.31354	−0.108018	−0.0540091	−	0.998540i	$-0.517200\pi$
$941$	−3.31354	−0.108018	−0.0540091	+	0.998540i	$0.517200\pi$
$942$	− 5.49838i	− 0.179147i
$943$	92.2068i	3.00267i
$944$	2.82535	0.0919573
$945$	0	0
$946$	−26.4224	−0.859068
$947$	22.7250i	0.738463i	0.929337	+	0.369231i	$0.120379\pi$
$947$	22.7250i	0.738463i	−0.929337	+	0.369231i	$0.879621\pi$
$948$	− 28.6186i	− 0.929490i
$949$	5.06422	0.164392
$950$	0	0
$951$	−13.7518	−0.445933
$952$	− 15.8213i	− 0.512771i
$953$	38.8212i	1.25754i	0.777590	+	0.628771i	$0.216442\pi$
$953$	38.8212i	1.25754i	−0.777590	+	0.628771i	$0.783558\pi$
$954$	63.6389	2.06039
$955$	0	0
$956$	85.1382	2.75357
$957$	8.19793i	0.265001i
$958$	30.0947i	0.972314i
$959$	19.1024	0.616849
$960$	0	0
$961$	1.00000	0.0322581
$962$	− 1.03007i	− 0.0332108i
$963$	39.0325i	1.25780i
$964$	−58.6168	−1.88792
$965$	0	0
$966$	45.6382	1.46838
$967$	− 18.3414i	− 0.589819i	−0.955525	−	0.294909i	$-0.904711\pi$
$967$	− 18.3414i	− 0.589819i	0.955525	−	0.294909i	$-0.0952894\pi$
$968$	3.53799i	0.113715i
$969$	−4.99137	−0.160346
$970$	0	0
$971$	43.6911	1.40211	0.701057	−	0.713106i	$-0.252712\pi$
$971$	43.6911	1.40211	0.701057	+	0.713106i	$0.252712\pi$
$972$	− 44.7297i	− 1.43471i
$973$	40.7913i	1.30771i
$974$	−24.7249	−0.792236
$975$	0	0
$976$	−1.50182	−0.0480721
$977$	− 20.3120i	− 0.649839i	−0.945742	−	0.324919i	$-0.894663\pi$
$977$	− 20.3120i	− 0.649839i	0.945742	−	0.324919i	$-0.105337\pi$
$978$	14.4017i	0.460517i
$979$	32.7202	1.04574
$980$	0	0
$981$	−21.6778	−0.692118
$982$	40.6889i	1.29843i
$983$	9.48240i	0.302442i	0.988500	+	0.151221i	$0.0483204\pi$
$983$	9.48240i	0.302442i	−0.988500	+	0.151221i	$0.951680\pi$
$984$	16.6751	0.531583
$985$	0	0
$986$	−16.5024	−0.525545
$987$	5.94269i	0.189158i
$988$	− 8.08936i	− 0.257357i
$989$	34.5835	1.09969
$990$	0	0
$991$	−35.9493	−1.14197	−0.570983	−	0.820962i	$-0.693438\pi$
$991$	−35.9493	−1.14197	−0.570983	+	0.820962i	$0.693438\pi$
$992$	− 6.01087i	− 0.190845i
$993$	9.96952i	0.316373i
$994$	28.1162	0.891791
$995$	0	0
$996$	29.8829	0.946875
$997$	38.9329i	1.23302i	0.787348	+	0.616508i	$0.211453\pi$
$997$	38.9329i	1.23302i	−0.787348	+	0.616508i	$0.788547\pi$
$998$	76.2308i	2.41304i
$999$	2.84740	0.0900877

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.b.e.249.7		8
5.2	odd	4		775.2.a.g.1.1		4
5.3	odd	4		155.2.a.d.1.4	✓	4
5.4	even	2	inner	775.2.b.e.249.2		8
15.2	even	4		6975.2.a.bj.1.4		4
15.8	even	4		1395.2.a.m.1.1		4
20.3	even	4		2480.2.a.z.1.3		4
35.13	even	4		7595.2.a.q.1.4		4
40.3	even	4		9920.2.a.cd.1.2		4
40.13	odd	4		9920.2.a.ch.1.3		4
155.123	even	4		4805.2.a.j.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.a.d.1.4	✓	4	5.3	odd	4
775.2.a.g.1.1		4	5.2	odd	4
775.2.b.e.249.2		8	5.4	even	2	inner
775.2.b.e.249.7		8	1.1	even	1	trivial
1395.2.a.m.1.1		4	15.8	even	4
2480.2.a.z.1.3		4	20.3	even	4
4805.2.a.j.1.4		4	155.123	even	4
6975.2.a.bj.1.4		4	15.2	even	4
7595.2.a.q.1.4		4	35.13	even	4
9920.2.a.cd.1.2		4	40.3	even	4
9920.2.a.ch.1.3		4	40.13	odd	4

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:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+2.27244i q^{2} +0.632112i q^{3} -3.16400 q^{4} -1.43644 q^{6} +3.43644i q^{7} -2.64511i q^{8} +2.60043 q^{9} +O(q^{10})\)	\(q+2.27244i q^{2} +0.632112i q^{3} -3.16400 q^{4} -1.43644 q^{6} +3.43644i q^{7} -2.64511i q^{8} +2.60043 q^{9} -3.10845 q^{11} -2.00000i q^{12} -0.563561i q^{13} -7.80911 q^{14} -0.317122 q^{16} -1.74056i q^{17} +5.90934i q^{18} -4.53667 q^{19} -2.17221 q^{21} -7.06377i q^{22} +9.24555i q^{23} +1.67201 q^{24} +1.28066 q^{26} +3.54010i q^{27} -10.8729i q^{28} -4.17221 q^{29} +1.00000 q^{31} -6.01087i q^{32} -1.96489i q^{33} +3.95532 q^{34} -8.22776 q^{36} -0.804326i q^{37} -10.3093i q^{38} +0.356234 q^{39} +9.97311 q^{41} -4.93623i q^{42} -3.74056i q^{43} +9.83511 q^{44} -21.0100 q^{46} -2.73578i q^{47} -0.200457i q^{48} -4.80911 q^{49} +1.10023 q^{51} +1.78311i q^{52} -10.7692i q^{53} -8.04468 q^{54} +9.08977 q^{56} -2.86768i q^{57} -9.48112i q^{58} -8.90934 q^{59} +4.73578 q^{61} +2.27244i q^{62} +8.93623i q^{63} +13.0251 q^{64} +4.46509 q^{66} -0.891553i q^{67} +5.50712i q^{68} -5.84422 q^{69} -3.60043 q^{71} -6.87844i q^{72} +8.98611i q^{73} +1.82779 q^{74} +14.3540 q^{76} -10.6820i q^{77} +0.809521i q^{78} +14.3093 q^{79} +5.56356 q^{81} +22.6633i q^{82} +14.9414i q^{83} +6.87288 q^{84} +8.50021 q^{86} -2.63731i q^{87} +8.22220i q^{88} -10.5262 q^{89} +1.93664 q^{91} -29.2529i q^{92} +0.632112i q^{93} +6.21689 q^{94} +3.79954 q^{96} +9.80911i q^{97} -10.9284i q^{98} -8.08331 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 18 q^{4} + 16 q^{6} - 14 q^{9}+O(q^{10}) \) 8 * q - 18 * q^4 + 16 * q^6 - 14 * q^9	\( 8 q - 18 q^{4} + 16 q^{6} - 14 q^{9} - 12 q^{11} - 16 q^{14} + 22 q^{16} - 10 q^{19} + 4 q^{21} + 28 q^{24} - 24 q^{26} - 12 q^{29} + 8 q^{31} + 36 q^{34} - 50 q^{36} + 12 q^{39} + 26 q^{41} - 40 q^{44} - 52 q^{46} + 8 q^{49} + 10 q^{51} - 60 q^{54} - 8 q^{56} - 26 q^{59} + 44 q^{61} - 94 q^{64} - 40 q^{66} - 40 q^{69} + 6 q^{71} + 36 q^{74} + 28 q^{76} + 32 q^{79} + 72 q^{81} + 32 q^{86} + 24 q^{89} - 48 q^{91} + 24 q^{94} + 28 q^{96} + 104 q^{99}+O(q^{100}) \) 8 * q - 18 * q^4 + 16 * q^6 - 14 * q^9 - 12 * q^11 - 16 * q^14 + 22 * q^16 - 10 * q^19 + 4 * q^21 + 28 * q^24 - 24 * q^26 - 12 * q^29 + 8 * q^31 + 36 * q^34 - 50 * q^36 + 12 * q^39 + 26 * q^41 - 40 * q^44 - 52 * q^46 + 8 * q^49 + 10 * q^51 - 60 * q^54 - 8 * q^56 - 26 * q^59 + 44 * q^61 - 94 * q^64 - 40 * q^66 - 40 * q^69 + 6 * q^71 + 36 * q^74 + 28 * q^76 + 32 * q^79 + 72 * q^81 + 32 * q^86 + 24 * q^89 - 48 * q^91 + 24 * q^94 + 28 * q^96 + 104 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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