LMFDB - Embedded newform 275.2.b.c.199.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,2,Mod(199,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.199"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{13})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 9 $ x^4 + 7*x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.3
Root			$1.30278i$ of defining polynomial
Character	$\chi$	$=$	275.199
Dual form			275.2.b.c.199.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.30278i q^{2} +2.30278i q^{3} +0.302776 q^{4} -3.00000 q^{6} -0.697224i q^{7} +3.00000i q^{8} -2.30278 q^{9} -1.00000 q^{11} +0.697224i q^{12} +5.00000i q^{13} +0.908327 q^{14} -3.30278 q^{16} -6.90833i q^{17} -3.00000i q^{18} +1.00000 q^{19} +1.60555 q^{21} -1.30278i q^{22} -7.30278i q^{23} -6.90833 q^{24} -6.51388 q^{26} +1.60555i q^{27} -0.211103i q^{28} -0.908327 q^{29} +10.2111 q^{31} +1.69722i q^{32} -2.30278i q^{33} +9.00000 q^{34} -0.697224 q^{36} -2.39445i q^{37} +1.30278i q^{38} -11.5139 q^{39} -5.60555 q^{41} +2.09167i q^{42} +7.21110i q^{43} -0.302776 q^{44} +9.51388 q^{46} +3.00000i q^{47} -7.60555i q^{48} +6.51388 q^{49} +15.9083 q^{51} +1.51388i q^{52} -1.30278i q^{53} -2.09167 q^{54} +2.09167 q^{56} +2.30278i q^{57} -1.18335i q^{58} +14.2111 q^{59} -7.90833 q^{61} +13.3028i q^{62} +1.60555i q^{63} -8.81665 q^{64} +3.00000 q^{66} +4.00000i q^{67} -2.09167i q^{68} +16.8167 q^{69} -2.60555 q^{71} -6.90833i q^{72} -7.90833i q^{73} +3.11943 q^{74} +0.302776 q^{76} +0.697224i q^{77} -15.0000i q^{78} +10.9083 q^{79} -10.6056 q^{81} -7.30278i q^{82} -3.51388i q^{83} +0.486122 q^{84} -9.39445 q^{86} -2.09167i q^{87} -3.00000i q^{88} -1.69722 q^{89} +3.48612 q^{91} -2.21110i q^{92} +23.5139i q^{93} -3.90833 q^{94} -3.90833 q^{96} -15.3028i q^{97} +8.48612i q^{98} +2.30278 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{4} - 12 q^{6} - 2 q^{9} - 4 q^{11} - 18 q^{14} - 6 q^{16} + 4 q^{19} - 8 q^{21} - 6 q^{24} + 10 q^{26} + 18 q^{29} + 12 q^{31} + 36 q^{34} - 10 q^{36} - 10 q^{39} - 8 q^{41} + 6 q^{44} + 2 q^{46}+ \cdots + 2 q^{99}+O(q^{100}) $ 4 * q - 6 * q^4 - 12 * q^6 - 2 * q^9 - 4 * q^11 - 18 * q^14 - 6 * q^16 + 4 * q^19 - 8 * q^21 - 6 * q^24 + 10 * q^26 + 18 * q^29 + 12 * q^31 + 36 * q^34 - 10 * q^36 - 10 * q^39 - 8 * q^41 + 6 * q^44 + 2 * q^46 - 10 * q^49 + 42 * q^51 - 30 * q^54 + 30 * q^56 + 28 * q^59 - 10 * q^61 + 8 * q^64 + 12 * q^66 + 24 * q^69 + 4 * q^71 - 38 * q^74 - 6 * q^76 + 22 * q^79 - 28 * q^81 + 38 * q^84 - 52 * q^86 - 14 * q^89 + 50 * q^91 + 6 * q^94 + 6 * q^96 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$1$	$-1$

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 $

$2$	1.30278i	0.921201i	0.887607	+	0.460601i	$0.152366\pi$
$2$	1.30278i	0.921201i	−0.887607	+	0.460601i	$0.847634\pi$
$3$	2.30278i	1.32951i	0.747062	+	0.664754i	$0.231464\pi$
$3$	2.30278i	1.32951i	−0.747062	+	0.664754i	$0.768536\pi$
$4$	0.302776	0.151388
$5$	0	0
$5$	0	0
$6$	−3.00000	−1.22474
$7$	− 0.697224i	− 0.263526i	−0.991281	−	0.131763i	$-0.957936\pi$
$7$	− 0.697224i	− 0.263526i	0.991281	−	0.131763i	$-0.0420638\pi$
$8$	3.00000i	1.06066i
$9$	−2.30278	−0.767592
$10$	0	0
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.697224i	0.201271i
$13$	5.00000i	1.38675i	0.720577	+	0.693375i	$0.243877\pi$
$13$	5.00000i	1.38675i	−0.720577	+	0.693375i	$0.756123\pi$
$14$	0.908327	0.242761
$15$	0	0
$16$	−3.30278	−0.825694
$17$	− 6.90833i	− 1.67552i	−0.546042	−	0.837758i	$-0.683866\pi$
$17$	− 6.90833i	− 1.67552i	0.546042	−	0.837758i	$-0.316134\pi$
$18$	− 3.00000i	− 0.707107i
$19$	1.00000	0.229416	0.114708	−	0.993399i	$-0.463407\pi$
$19$	1.00000	0.229416	0.114708	+	0.993399i	$0.463407\pi$
$20$	0	0
$21$	1.60555	0.350360
$22$	− 1.30278i	− 0.277753i
$23$	− 7.30278i	− 1.52273i	−0.648321	−	0.761367i	$-0.724529\pi$
$23$	− 7.30278i	− 1.52273i	0.648321	−	0.761367i	$-0.275471\pi$
$24$	−6.90833	−1.41016
$25$	0	0
$26$	−6.51388	−1.27748
$27$	1.60555i	0.308988i
$28$	− 0.211103i	− 0.0398946i
$29$	−0.908327	−0.168672	−0.0843360	−	0.996437i	$-0.526877\pi$
$29$	−0.908327	−0.168672	−0.0843360	+	0.996437i	$0.526877\pi$
$30$	0	0
$31$	10.2111	1.83397	0.916984	−	0.398924i	$-0.130616\pi$
$31$	10.2111	1.83397	0.916984	+	0.398924i	$0.130616\pi$
$32$	1.69722i	0.300030i
$33$	− 2.30278i	− 0.400862i
$34$	9.00000	1.54349
$35$	0	0
$36$	−0.697224	−0.116204
$37$	− 2.39445i	− 0.393645i	−0.980439	−	0.196822i	$-0.936938\pi$
$37$	− 2.39445i	− 0.393645i	0.980439	−	0.196822i	$-0.0630623\pi$
$38$	1.30278i	0.211338i
$39$	−11.5139	−1.84370
$40$	0	0
$41$	−5.60555	−0.875440	−0.437720	−	0.899111i	$-0.644214\pi$
$41$	−5.60555	−0.875440	−0.437720	+	0.899111i	$0.644214\pi$
$42$	2.09167i	0.322752i
$43$	7.21110i	1.09968i	0.835269	+	0.549841i	$0.185312\pi$
$43$	7.21110i	1.09968i	−0.835269	+	0.549841i	$0.814688\pi$
$44$	−0.302776	−0.0456451
$45$	0	0
$46$	9.51388	1.40274
$47$	3.00000i	0.437595i	0.975770	+	0.218797i	$0.0702134\pi$
$47$	3.00000i	0.437595i	−0.975770	+	0.218797i	$0.929787\pi$
$48$	− 7.60555i	− 1.09777i
$49$	6.51388	0.930554
$50$	0	0
$51$	15.9083	2.22761
$52$	1.51388i	0.209937i
$53$	− 1.30278i	− 0.178950i	−0.995989	−	0.0894750i	$-0.971481\pi$
$53$	− 1.30278i	− 0.178950i	0.995989	−	0.0894750i	$-0.0285189\pi$
$54$	−2.09167	−0.284641
$55$	0	0
$56$	2.09167	0.279512
$57$	2.30278i	0.305010i
$58$	− 1.18335i	− 0.155381i
$59$	14.2111	1.85013	0.925064	−	0.379811i	$-0.124011\pi$
$59$	14.2111	1.85013	0.925064	+	0.379811i	$0.124011\pi$
$60$	0	0
$61$	−7.90833	−1.01256	−0.506279	−	0.862370i	$-0.668979\pi$
$61$	−7.90833	−1.01256	−0.506279	+	0.862370i	$0.668979\pi$
$62$	13.3028i	1.68945i
$63$	1.60555i	0.202280i
$64$	−8.81665	−1.10208
$65$	0	0
$66$	3.00000	0.369274
$67$	4.00000i	0.488678i	0.969690	+	0.244339i	$0.0785709\pi$
$67$	4.00000i	0.488678i	−0.969690	+	0.244339i	$0.921429\pi$
$68$	− 2.09167i	− 0.253653i
$69$	16.8167	2.02449
$70$	0	0
$71$	−2.60555	−0.309222	−0.154611	−	0.987975i	$-0.549412\pi$
$71$	−2.60555	−0.309222	−0.154611	+	0.987975i	$0.549412\pi$
$72$	− 6.90833i	− 0.814154i
$73$	− 7.90833i	− 0.925600i	−0.886463	−	0.462800i	$-0.846845\pi$
$73$	− 7.90833i	− 0.925600i	0.886463	−	0.462800i	$-0.153155\pi$
$74$	3.11943	0.362626
$75$	0	0
$76$	0.302776	0.0347307
$77$	0.697224i	0.0794561i
$78$	− 15.0000i	− 1.69842i
$79$	10.9083	1.22728	0.613641	−	0.789585i	$-0.289704\pi$
$79$	10.9083	1.22728	0.613641	+	0.789585i	$0.289704\pi$
$80$	0	0
$81$	−10.6056	−1.17839
$82$	− 7.30278i	− 0.806457i
$83$	− 3.51388i	− 0.385698i	−0.981228	−	0.192849i	$-0.938227\pi$
$83$	− 3.51388i	− 0.385698i	0.981228	−	0.192849i	$-0.0617728\pi$
$84$	0.486122	0.0530402
$85$	0	0
$86$	−9.39445	−1.01303
$87$	− 2.09167i	− 0.224251i
$88$	− 3.00000i	− 0.319801i
$89$	−1.69722	−0.179905	−0.0899527	−	0.995946i	$-0.528672\pi$
$89$	−1.69722	−0.179905	−0.0899527	+	0.995946i	$0.528672\pi$
$90$	0	0
$91$	3.48612	0.365445
$92$	− 2.21110i	− 0.230523i
$93$	23.5139i	2.43828i
$94$	−3.90833	−0.403113
$95$	0	0
$96$	−3.90833	−0.398892
$97$	− 15.3028i	− 1.55376i	−0.629648	−	0.776881i	$-0.716801\pi$
$97$	− 15.3028i	− 1.55376i	0.629648	−	0.776881i	$-0.283199\pi$
$98$	8.48612i	0.857228i
$99$	2.30278	0.231438
$100$	0	0
$101$	−0.513878	−0.0511328	−0.0255664	−	0.999673i	$-0.508139\pi$
$101$	−0.513878	−0.0511328	−0.0255664	+	0.999673i	$0.508139\pi$
$102$	20.7250i	2.05208i
$103$	2.90833i	0.286566i	0.989682	+	0.143283i	$0.0457659\pi$
$103$	2.90833i	0.286566i	−0.989682	+	0.143283i	$0.954234\pi$
$104$	−15.0000	−1.47087
$105$	0	0
$106$	1.69722	0.164849
$107$	3.00000i	0.290021i	0.989430	+	0.145010i	$0.0463216\pi$
$107$	3.00000i	0.290021i	−0.989430	+	0.145010i	$0.953678\pi$
$108$	0.486122i	0.0467771i
$109$	−11.5139	−1.10283	−0.551415	−	0.834231i	$-0.685912\pi$
$109$	−11.5139	−1.10283	−0.551415	+	0.834231i	$0.685912\pi$
$110$	0	0
$111$	5.51388	0.523354
$112$	2.30278i	0.217592i
$113$	− 10.8167i	− 1.01755i	−0.860901	−	0.508773i	$-0.830099\pi$
$113$	− 10.8167i	− 1.01755i	0.860901	−	0.508773i	$-0.169901\pi$
$114$	−3.00000	−0.280976
$115$	0	0
$116$	−0.275019	−0.0255349
$117$	− 11.5139i	− 1.06446i
$118$	18.5139i	1.70434i
$119$	−4.81665	−0.441542
$120$	0	0
$121$	1.00000	0.0909091
$122$	− 10.3028i	− 0.932769i
$123$	− 12.9083i	− 1.16390i
$124$	3.09167	0.277640
$125$	0	0
$126$	−2.09167	−0.186341
$127$	− 8.11943i	− 0.720483i	−0.932859	−	0.360241i	$-0.882694\pi$
$127$	− 8.11943i	− 0.720483i	0.932859	−	0.360241i	$-0.117306\pi$
$128$	− 8.09167i	− 0.715210i
$129$	−16.6056	−1.46204
$130$	0	0
$131$	−9.90833	−0.865695	−0.432847	−	0.901467i	$-0.642491\pi$
$131$	−9.90833	−0.865695	−0.432847	+	0.901467i	$0.642491\pi$
$132$	− 0.697224i	− 0.0606856i
$133$	− 0.697224i	− 0.0604570i
$134$	−5.21110	−0.450171
$135$	0	0
$136$	20.7250	1.77715
$137$	12.9083i	1.10283i	0.834230	+	0.551416i	$0.185912\pi$
$137$	12.9083i	1.10283i	−0.834230	+	0.551416i	$0.814088\pi$
$138$	21.9083i	1.86496i
$139$	6.21110	0.526819	0.263409	−	0.964684i	$-0.415153\pi$
$139$	6.21110	0.526819	0.263409	+	0.964684i	$0.415153\pi$
$140$	0	0
$141$	−6.90833	−0.581786
$142$	− 3.39445i	− 0.284856i
$143$	− 5.00000i	− 0.418121i
$144$	7.60555	0.633796
$145$	0	0
$146$	10.3028	0.852664
$147$	15.0000i	1.23718i
$148$	− 0.724981i	− 0.0595930i
$149$	−17.2111	−1.40999	−0.704994	−	0.709213i	$-0.749050\pi$
$149$	−17.2111	−1.40999	−0.704994	+	0.709213i	$0.749050\pi$
$150$	0	0
$151$	0.816654	0.0664583	0.0332292	−	0.999448i	$-0.489421\pi$
$151$	0.816654	0.0664583	0.0332292	+	0.999448i	$0.489421\pi$
$152$	3.00000i	0.243332i
$153$	15.9083i	1.28611i
$154$	−0.908327	−0.0731951
$155$	0	0
$156$	−3.48612	−0.279113
$157$	− 19.2111i	− 1.53321i	−0.642117	−	0.766606i	$-0.721944\pi$
$157$	− 19.2111i	− 1.53321i	0.642117	−	0.766606i	$-0.278056\pi$
$158$	14.2111i	1.13057i
$159$	3.00000	0.237915
$160$	0	0
$161$	−5.09167	−0.401280
$162$	− 13.8167i	− 1.08554i
$163$	9.30278i	0.728650i	0.931272	+	0.364325i	$0.118700\pi$
$163$	9.30278i	0.728650i	−0.931272	+	0.364325i	$0.881300\pi$
$164$	−1.69722	−0.132531
$165$	0	0
$166$	4.57779	0.355306
$167$	− 13.4222i	− 1.03864i	−0.854579	−	0.519321i	$-0.826185\pi$
$167$	− 13.4222i	− 1.03864i	0.854579	−	0.519321i	$-0.173815\pi$
$168$	4.81665i	0.371613i
$169$	−12.0000	−0.923077
$170$	0	0
$171$	−2.30278	−0.176098
$172$	2.18335i	0.166479i
$173$	− 4.81665i	− 0.366203i	−0.983094	−	0.183102i	$-0.941386\pi$
$173$	− 4.81665i	− 0.366203i	0.983094	−	0.183102i	$-0.0586138\pi$
$174$	2.72498	0.206580
$175$	0	0
$176$	3.30278	0.248956
$177$	32.7250i	2.45976i
$178$	− 2.21110i	− 0.165729i
$179$	−12.5139	−0.935331	−0.467666	−	0.883905i	$-0.654905\pi$
$179$	−12.5139	−0.935331	−0.467666	+	0.883905i	$0.654905\pi$
$180$	0	0
$181$	−19.9083	−1.47977	−0.739887	−	0.672731i	$-0.765121\pi$
$181$	−19.9083	−1.47977	−0.739887	+	0.672731i	$0.765121\pi$
$182$	4.54163i	0.336648i
$183$	− 18.2111i	− 1.34620i
$184$	21.9083	1.61510
$185$	0	0
$186$	−30.6333	−2.24614
$187$	6.90833i	0.505187i
$188$	0.908327i	0.0662465i
$189$	1.11943	0.0814265
$190$	0	0
$191$	10.3028	0.745483	0.372741	−	0.927935i	$-0.378418\pi$
$191$	10.3028	0.745483	0.372741	+	0.927935i	$0.378418\pi$
$192$	− 20.3028i	− 1.46523i
$193$	13.2111i	0.950956i	0.879728	+	0.475478i	$0.157725\pi$
$193$	13.2111i	0.950956i	−0.879728	+	0.475478i	$0.842275\pi$
$194$	19.9361	1.43133
$195$	0	0
$196$	1.97224	0.140875
$197$	− 13.3028i	− 0.947784i	−0.880583	−	0.473892i	$-0.842849\pi$
$197$	− 13.3028i	− 0.947784i	0.880583	−	0.473892i	$-0.157151\pi$
$198$	3.00000i	0.213201i
$199$	6.48612	0.459789	0.229894	−	0.973216i	$-0.426162\pi$
$199$	6.48612	0.459789	0.229894	+	0.973216i	$0.426162\pi$
$200$	0	0
$201$	−9.21110	−0.649701
$202$	− 0.669468i	− 0.0471036i
$203$	0.633308i	0.0444495i
$204$	4.81665	0.337233
$205$	0	0
$206$	−3.78890	−0.263985
$207$	16.8167i	1.16884i
$208$	− 16.5139i	− 1.14503i
$209$	−1.00000	−0.0691714
$210$	0	0
$211$	−25.2389	−1.73751	−0.868757	−	0.495238i	$-0.835081\pi$
$211$	−25.2389	−1.73751	−0.868757	+	0.495238i	$0.835081\pi$
$212$	− 0.394449i	− 0.0270908i
$213$	− 6.00000i	− 0.411113i
$214$	−3.90833	−0.267168
$215$	0	0
$216$	−4.81665	−0.327732
$217$	− 7.11943i	− 0.483298i
$218$	− 15.0000i	− 1.01593i
$219$	18.2111	1.23059
$220$	0	0
$221$	34.5416	2.32352
$222$	7.18335i	0.482115i
$223$	− 22.6333i	− 1.51564i	−0.652465	−	0.757819i	$-0.726265\pi$
$223$	− 22.6333i	− 1.51564i	0.652465	−	0.757819i	$-0.273735\pi$
$224$	1.18335	0.0790656
$225$	0	0
$226$	14.0917	0.937364
$227$	− 1.69722i	− 0.112649i	−0.998413	−	0.0563244i	$-0.982062\pi$
$227$	− 1.69722i	− 0.112649i	0.998413	−	0.0563244i	$-0.0179381\pi$
$228$	0.697224i	0.0461748i
$229$	18.7250	1.23738	0.618691	−	0.785635i	$-0.287663\pi$
$229$	18.7250	1.23738	0.618691	+	0.785635i	$0.287663\pi$
$230$	0	0
$231$	−1.60555	−0.105638
$232$	− 2.72498i	− 0.178904i
$233$	15.9083i	1.04219i	0.853499	+	0.521095i	$0.174476\pi$
$233$	15.9083i	1.04219i	−0.853499	+	0.521095i	$0.825524\pi$
$234$	15.0000	0.980581
$235$	0	0
$236$	4.30278	0.280087
$237$	25.1194i	1.63168i
$238$	− 6.27502i	− 0.406749i
$239$	−21.1194	−1.36610	−0.683051	−	0.730371i	$-0.739347\pi$
$239$	−21.1194	−1.36610	−0.683051	+	0.730371i	$0.739347\pi$
$240$	0	0
$241$	21.9361	1.41303	0.706514	−	0.707699i	$-0.250267\pi$
$241$	21.9361	1.41303	0.706514	+	0.707699i	$0.250267\pi$
$242$	1.30278i	0.0837456i
$243$	− 19.6056i	− 1.25770i
$244$	−2.39445	−0.153289
$245$	0	0
$246$	16.8167	1.07219
$247$	5.00000i	0.318142i
$248$	30.6333i	1.94522i
$249$	8.09167	0.512789
$250$	0	0
$251$	6.90833	0.436050	0.218025	−	0.975943i	$-0.430039\pi$
$251$	6.90833	0.436050	0.218025	+	0.975943i	$0.430039\pi$
$252$	0.486122i	0.0306228i
$253$	7.30278i	0.459122i
$254$	10.5778	0.663710
$255$	0	0
$256$	−7.09167	−0.443230
$257$	18.0000i	1.12281i	0.827541	+	0.561405i	$0.189739\pi$
$257$	18.0000i	1.12281i	−0.827541	+	0.561405i	$0.810261\pi$
$258$	− 21.6333i	− 1.34683i
$259$	−1.66947	−0.103736
$260$	0	0
$261$	2.09167	0.129471
$262$	− 12.9083i	− 0.797479i
$263$	− 22.8167i	− 1.40694i	−0.710727	−	0.703468i	$-0.751634\pi$
$263$	− 22.8167i	− 1.40694i	0.710727	−	0.703468i	$-0.248366\pi$
$264$	6.90833	0.425178
$265$	0	0
$266$	0.908327	0.0556931
$267$	− 3.90833i	− 0.239186i
$268$	1.21110i	0.0739799i
$269$	−8.72498	−0.531971	−0.265986	−	0.963977i	$-0.585697\pi$
$269$	−8.72498	−0.531971	−0.265986	+	0.963977i	$0.585697\pi$
$270$	0	0
$271$	−0.211103	−0.0128236	−0.00641178	−	0.999979i	$-0.502041\pi$
$271$	−0.211103	−0.0128236	−0.00641178	+	0.999979i	$0.502041\pi$
$272$	22.8167i	1.38346i
$273$	8.02776i	0.485862i
$274$	−16.8167	−1.01593
$275$	0	0
$276$	5.09167	0.306483
$277$	− 14.3944i	− 0.864879i	−0.901663	−	0.432439i	$-0.857653\pi$
$277$	− 14.3944i	− 0.864879i	0.901663	−	0.432439i	$-0.142347\pi$
$278$	8.09167i	0.485306i
$279$	−23.5139	−1.40774
$280$	0	0
$281$	−1.18335	−0.0705925	−0.0352963	−	0.999377i	$-0.511237\pi$
$281$	−1.18335	−0.0705925	−0.0352963	+	0.999377i	$0.511237\pi$
$282$	− 9.00000i	− 0.535942i
$283$	6.30278i	0.374661i	0.982297	+	0.187331i	$0.0599836\pi$
$283$	6.30278i	0.374661i	−0.982297	+	0.187331i	$0.940016\pi$
$284$	−0.788897	−0.0468125
$285$	0	0
$286$	6.51388	0.385174
$287$	3.90833i	0.230701i
$288$	− 3.90833i	− 0.230300i
$289$	−30.7250	−1.80735
$290$	0	0
$291$	35.2389	2.06574
$292$	− 2.39445i	− 0.140125i
$293$	0.788897i	0.0460879i	0.999734	+	0.0230439i	$0.00733576\pi$
$293$	0.788897i	0.0460879i	−0.999734	+	0.0230439i	$0.992664\pi$
$294$	−19.5416	−1.13969
$295$	0	0
$296$	7.18335	0.417524
$297$	− 1.60555i	− 0.0931635i
$298$	− 22.4222i	− 1.29888i
$299$	36.5139	2.11165
$300$	0	0
$301$	5.02776	0.289795
$302$	1.06392i	0.0612215i
$303$	− 1.18335i	− 0.0679815i
$304$	−3.30278	−0.189427
$305$	0	0
$306$	−20.7250	−1.18477
$307$	16.9083i	0.965009i	0.875893	+	0.482505i	$0.160273\pi$
$307$	16.9083i	0.965009i	−0.875893	+	0.482505i	$0.839727\pi$
$308$	0.211103i	0.0120287i
$309$	−6.69722	−0.380992
$310$	0	0
$311$	4.81665	0.273127	0.136564	−	0.990631i	$-0.456394\pi$
$311$	4.81665	0.273127	0.136564	+	0.990631i	$0.456394\pi$
$312$	− 34.5416i	− 1.95553i
$313$	0.183346i	0.0103633i	0.999987	+	0.00518167i	$0.00164938\pi$
$313$	0.183346i	0.0103633i	−0.999987	+	0.00518167i	$0.998351\pi$
$314$	25.0278	1.41240
$315$	0	0
$316$	3.30278	0.185796
$317$	0.908327i	0.0510167i	0.999675	+	0.0255084i	$0.00812044\pi$
$317$	0.908327i	0.0510167i	−0.999675	+	0.0255084i	$0.991880\pi$
$318$	3.90833i	0.219168i
$319$	0.908327	0.0508565
$320$	0	0
$321$	−6.90833	−0.385585
$322$	− 6.63331i	− 0.369660i
$323$	− 6.90833i	− 0.384390i
$324$	−3.21110	−0.178395
$325$	0	0
$326$	−12.1194	−0.671233
$327$	− 26.5139i	− 1.46622i
$328$	− 16.8167i	− 0.928544i
$329$	2.09167	0.115318
$330$	0	0
$331$	−21.6056	−1.18755	−0.593774	−	0.804632i	$-0.702363\pi$
$331$	−21.6056	−1.18755	−0.593774	+	0.804632i	$0.702363\pi$
$332$	− 1.06392i	− 0.0583900i
$333$	5.51388i	0.302159i
$334$	17.4861	0.956798
$335$	0	0
$336$	−5.30278	−0.289290
$337$	30.8444i	1.68020i	0.542430	+	0.840101i	$0.317504\pi$
$337$	30.8444i	1.68020i	−0.542430	+	0.840101i	$0.682496\pi$
$338$	− 15.6333i	− 0.850340i
$339$	24.9083	1.35283
$340$	0	0
$341$	−10.2111	−0.552962
$342$	− 3.00000i	− 0.162221i
$343$	− 9.42221i	− 0.508751i
$344$	−21.6333	−1.16639
$345$	0	0
$346$	6.27502	0.337347
$347$	12.5139i	0.671780i	0.941901	+	0.335890i	$0.109037\pi$
$347$	12.5139i	0.671780i	−0.941901	+	0.335890i	$0.890963\pi$
$348$	− 0.633308i	− 0.0339489i
$349$	5.18335	0.277458	0.138729	−	0.990330i	$-0.455698\pi$
$349$	5.18335	0.277458	0.138729	+	0.990330i	$0.455698\pi$
$350$	0	0
$351$	−8.02776	−0.428490
$352$	− 1.69722i	− 0.0904624i
$353$	18.6333i	0.991751i	0.868394	+	0.495875i	$0.165153\pi$
$353$	18.6333i	0.991751i	−0.868394	+	0.495875i	$0.834847\pi$
$354$	−42.6333	−2.26593
$355$	0	0
$356$	−0.513878	−0.0272355
$357$	− 11.0917i	− 0.587034i
$358$	− 16.3028i	− 0.861628i
$359$	−0.788897	−0.0416364	−0.0208182	−	0.999783i	$-0.506627\pi$
$359$	−0.788897	−0.0416364	−0.0208182	+	0.999783i	$0.506627\pi$
$360$	0	0
$361$	−18.0000	−0.947368
$362$	− 25.9361i	− 1.36317i
$363$	2.30278i	0.120864i
$364$	1.05551	0.0553239
$365$	0	0
$366$	23.7250	1.24012
$367$	20.6972i	1.08039i	0.841541	+	0.540193i	$0.181649\pi$
$367$	20.6972i	1.08039i	−0.841541	+	0.540193i	$0.818351\pi$
$368$	24.1194i	1.25731i
$369$	12.9083	0.671981
$370$	0	0
$371$	−0.908327	−0.0471580
$372$	7.11943i	0.369125i
$373$	27.4222i	1.41987i	0.704268	+	0.709934i	$0.251275\pi$
$373$	27.4222i	1.41987i	−0.704268	+	0.709934i	$0.748725\pi$
$374$	−9.00000	−0.465379
$375$	0	0
$376$	−9.00000	−0.464140
$377$	− 4.54163i	− 0.233906i
$378$	1.45837i	0.0750102i
$379$	−3.18335	−0.163518	−0.0817588	−	0.996652i	$-0.526054\pi$
$379$	−3.18335	−0.163518	−0.0817588	+	0.996652i	$0.526054\pi$
$380$	0	0
$381$	18.6972	0.957888
$382$	13.4222i	0.686740i
$383$	21.6333i	1.10541i	0.833377	+	0.552705i	$0.186404\pi$
$383$	21.6333i	1.10541i	−0.833377	+	0.552705i	$0.813596\pi$
$384$	18.6333	0.950877
$385$	0	0
$386$	−17.2111	−0.876022
$387$	− 16.6056i	− 0.844108i
$388$	− 4.63331i	− 0.235221i
$389$	−12.0000	−0.608424	−0.304212	−	0.952604i	$-0.598393\pi$
$389$	−12.0000	−0.608424	−0.304212	+	0.952604i	$0.598393\pi$
$390$	0	0
$391$	−50.4500	−2.55136
$392$	19.5416i	0.987002i
$393$	− 22.8167i	− 1.15095i
$394$	17.3305	0.873100
$395$	0	0
$396$	0.697224	0.0350368
$397$	− 21.6972i	− 1.08895i	−0.838776	−	0.544476i	$-0.816728\pi$
$397$	− 21.6972i	− 1.08895i	0.838776	−	0.544476i	$-0.183272\pi$
$398$	8.44996i	0.423558i
$399$	1.60555	0.0803781
$400$	0	0
$401$	−12.7889	−0.638647	−0.319324	−	0.947646i	$-0.603456\pi$
$401$	−12.7889	−0.638647	−0.319324	+	0.947646i	$0.603456\pi$
$402$	− 12.0000i	− 0.598506i
$403$	51.0555i	2.54326i
$404$	−0.155590	−0.00774088
$405$	0	0
$406$	−0.825058	−0.0409469
$407$	2.39445i	0.118688i
$408$	47.7250i	2.36274i
$409$	6.21110	0.307119	0.153560	−	0.988139i	$-0.450926\pi$
$409$	6.21110	0.307119	0.153560	+	0.988139i	$0.450926\pi$
$410$	0	0
$411$	−29.7250	−1.46623
$412$	0.880571i	0.0433826i
$413$	− 9.90833i	− 0.487557i
$414$	−21.9083	−1.07674
$415$	0	0
$416$	−8.48612	−0.416066
$417$	14.3028i	0.700410i
$418$	− 1.30278i	− 0.0637208i
$419$	−6.39445	−0.312389	−0.156195	−	0.987726i	$-0.549923\pi$
$419$	−6.39445	−0.312389	−0.156195	+	0.987726i	$0.549923\pi$
$420$	0	0
$421$	0.697224	0.0339806	0.0169903	−	0.999856i	$-0.494592\pi$
$421$	0.697224	0.0339806	0.0169903	+	0.999856i	$0.494592\pi$
$422$	− 32.8806i	− 1.60060i
$423$	− 6.90833i	− 0.335894i
$424$	3.90833	0.189805
$425$	0	0
$426$	7.81665	0.378718
$427$	5.51388i	0.266835i
$428$	0.908327i	0.0439056i
$429$	11.5139	0.555895
$430$	0	0
$431$	33.0000	1.58955	0.794777	−	0.606902i	$-0.207588\pi$
$431$	33.0000	1.58955	0.794777	+	0.606902i	$0.207588\pi$
$432$	− 5.30278i	− 0.255130i
$433$	5.00000i	0.240285i	0.992757	+	0.120142i	$0.0383351\pi$
$433$	5.00000i	0.240285i	−0.992757	+	0.120142i	$0.961665\pi$
$434$	9.27502	0.445215
$435$	0	0
$436$	−3.48612	−0.166955
$437$	− 7.30278i	− 0.349339i
$438$	23.7250i	1.13362i
$439$	−24.3028	−1.15991	−0.579954	−	0.814649i	$-0.696930\pi$
$439$	−24.3028	−1.15991	−0.579954	+	0.814649i	$0.696930\pi$
$440$	0	0
$441$	−15.0000	−0.714286
$442$	45.0000i	2.14043i
$443$	− 8.60555i	− 0.408862i	−0.978881	−	0.204431i	$-0.934466\pi$
$443$	− 8.60555i	− 0.408862i	0.978881	−	0.204431i	$-0.0655344\pi$
$444$	1.66947	0.0792294
$445$	0	0
$446$	29.4861	1.39621
$447$	− 39.6333i	− 1.87459i
$448$	6.14719i	0.290427i
$449$	−23.4861	−1.10838	−0.554189	−	0.832391i	$-0.686972\pi$
$449$	−23.4861	−1.10838	−0.554189	+	0.832391i	$0.686972\pi$
$450$	0	0
$451$	5.60555	0.263955
$452$	− 3.27502i	− 0.154044i
$453$	1.88057i	0.0883569i
$454$	2.21110	0.103772
$455$	0	0
$456$	−6.90833	−0.323512
$457$	20.6972i	0.968175i	0.875020	+	0.484088i	$0.160848\pi$
$457$	20.6972i	0.968175i	−0.875020	+	0.484088i	$0.839152\pi$
$458$	24.3944i	1.13988i
$459$	11.0917	0.517715
$460$	0	0
$461$	32.2111	1.50022	0.750110	−	0.661313i	$-0.230000\pi$
$461$	32.2111	1.50022	0.750110	+	0.661313i	$0.230000\pi$
$462$	− 2.09167i	− 0.0973134i
$463$	11.7889i	0.547877i	0.961747	+	0.273938i	$0.0883264\pi$
$463$	11.7889i	0.547877i	−0.961747	+	0.273938i	$0.911674\pi$
$464$	3.00000	0.139272
$465$	0	0
$466$	−20.7250	−0.960066
$467$	18.6333i	0.862247i	0.902293	+	0.431123i	$0.141883\pi$
$467$	18.6333i	0.862247i	−0.902293	+	0.431123i	$0.858117\pi$
$468$	− 3.48612i	− 0.161146i
$469$	2.78890	0.128779
$470$	0	0
$471$	44.2389	2.03842
$472$	42.6333i	1.96236i
$473$	− 7.21110i	− 0.331567i
$474$	−32.7250	−1.50311
$475$	0	0
$476$	−1.45837	−0.0668441
$477$	3.00000i	0.137361i
$478$	− 27.5139i	− 1.25846i
$479$	34.8167	1.59081	0.795407	−	0.606076i	$-0.207257\pi$
$479$	34.8167	1.59081	0.795407	+	0.606076i	$0.207257\pi$
$480$	0	0
$481$	11.9722	0.545887
$482$	28.5778i	1.30168i
$483$	− 11.7250i	− 0.533505i
$484$	0.302776	0.0137625
$485$	0	0
$486$	25.5416	1.15859
$487$	− 4.21110i	− 0.190823i	−0.995438	−	0.0954116i	$-0.969583\pi$
$487$	− 4.21110i	− 0.190823i	0.995438	−	0.0954116i	$-0.0304167\pi$
$488$	− 23.7250i	− 1.07398i
$489$	−21.4222	−0.968746
$490$	0	0
$491$	−9.78890	−0.441767	−0.220883	−	0.975300i	$-0.570894\pi$
$491$	−9.78890	−0.441767	−0.220883	+	0.975300i	$0.570894\pi$
$492$	− 3.90833i	− 0.176201i
$493$	6.27502i	0.282613i
$494$	−6.51388	−0.293073
$495$	0	0
$496$	−33.7250	−1.51430
$497$	1.81665i	0.0814881i
$498$	10.5416i	0.472382i
$499$	3.48612	0.156060	0.0780301	−	0.996951i	$-0.475137\pi$
$499$	3.48612	0.156060	0.0780301	+	0.996951i	$0.475137\pi$
$500$	0	0
$501$	30.9083	1.38088
$502$	9.00000i	0.401690i
$503$	9.39445i	0.418878i	0.977822	+	0.209439i	$0.0671637\pi$
$503$	9.39445i	0.418878i	−0.977822	+	0.209439i	$0.932836\pi$
$504$	−4.81665	−0.214551
$505$	0	0
$506$	−9.51388	−0.422943
$507$	− 27.6333i	− 1.22724i
$508$	− 2.45837i	− 0.109072i
$509$	22.6972	1.00604	0.503018	−	0.864276i	$-0.332223\pi$
$509$	22.6972	1.00604	0.503018	+	0.864276i	$0.332223\pi$
$510$	0	0
$511$	−5.51388	−0.243920
$512$	− 25.4222i	− 1.12351i
$513$	1.60555i	0.0708868i
$514$	−23.4500	−1.03433
$515$	0	0
$516$	−5.02776	−0.221335
$517$	− 3.00000i	− 0.131940i
$518$	− 2.17494i	− 0.0955615i
$519$	11.0917	0.486870
$520$	0	0
$521$	−41.4500	−1.81596	−0.907978	−	0.419018i	$-0.862374\pi$
$521$	−41.4500	−1.81596	−0.907978	+	0.419018i	$0.862374\pi$
$522$	2.72498i	0.119269i
$523$	− 32.4222i	− 1.41772i	−0.705347	−	0.708862i	$-0.749209\pi$
$523$	− 32.4222i	− 1.41772i	0.705347	−	0.708862i	$-0.250791\pi$
$524$	−3.00000	−0.131056
$525$	0	0
$526$	29.7250	1.29607
$527$	− 70.5416i	− 3.07284i
$528$	7.60555i	0.330989i
$529$	−30.3305	−1.31872
$530$	0	0
$531$	−32.7250	−1.42014
$532$	− 0.211103i	− 0.00915246i
$533$	− 28.0278i	− 1.21402i
$534$	5.09167	0.220338
$535$	0	0
$536$	−12.0000	−0.518321
$537$	− 28.8167i	− 1.24353i
$538$	− 11.3667i	− 0.490053i
$539$	−6.51388	−0.280573
$540$	0	0
$541$	25.7250	1.10600	0.553002	−	0.833180i	$-0.313482\pi$
$541$	25.7250	1.10600	0.553002	+	0.833180i	$0.313482\pi$
$542$	− 0.275019i	− 0.0118131i
$543$	− 45.8444i	− 1.96737i
$544$	11.7250	0.502704
$545$	0	0
$546$	−10.4584	−0.447577
$547$	7.11943i	0.304405i	0.988349	+	0.152202i	$0.0486366\pi$
$547$	7.11943i	0.304405i	−0.988349	+	0.152202i	$0.951363\pi$
$548$	3.90833i	0.166955i
$549$	18.2111	0.777231
$550$	0	0
$551$	−0.908327	−0.0386960
$552$	50.4500i	2.14729i
$553$	− 7.60555i	− 0.323421i
$554$	18.7527	0.796727
$555$	0	0
$556$	1.88057	0.0797540
$557$	− 19.4222i	− 0.822945i	−0.911422	−	0.411473i	$-0.865015\pi$
$557$	− 19.4222i	− 0.822945i	0.911422	−	0.411473i	$-0.134985\pi$
$558$	− 30.6333i	− 1.29681i
$559$	−36.0555	−1.52499
$560$	0	0
$561$	−15.9083	−0.671650
$562$	− 1.54163i	− 0.0650299i
$563$	8.09167i	0.341023i	0.985356	+	0.170512i	$0.0545421\pi$
$563$	8.09167i	0.341023i	−0.985356	+	0.170512i	$0.945458\pi$
$564$	−2.09167	−0.0880753
$565$	0	0
$566$	−8.21110	−0.345138
$567$	7.39445i	0.310538i
$568$	− 7.81665i	− 0.327980i
$569$	46.1472	1.93459	0.967295	−	0.253653i	$-0.0816321\pi$
$569$	46.1472	1.93459	0.967295	+	0.253653i	$0.0816321\pi$
$570$	0	0
$571$	22.3305	0.934504	0.467252	−	0.884124i	$-0.345244\pi$
$571$	22.3305	0.934504	0.467252	+	0.884124i	$0.345244\pi$
$572$	− 1.51388i	− 0.0632984i
$573$	23.7250i	0.991125i
$574$	−5.09167	−0.212522
$575$	0	0
$576$	20.3028	0.845949
$577$	− 44.3583i	− 1.84666i	−0.384008	−	0.923330i	$-0.625456\pi$
$577$	− 44.3583i	− 1.84666i	0.384008	−	0.923330i	$-0.374544\pi$
$578$	− 40.0278i	− 1.66494i
$579$	−30.4222	−1.26430
$580$	0	0
$581$	−2.44996	−0.101642
$582$	45.9083i	1.90296i
$583$	1.30278i	0.0539555i
$584$	23.7250	0.981747
$585$	0	0
$586$	−1.02776	−0.0424562
$587$	− 16.5416i	− 0.682746i	−0.939928	−	0.341373i	$-0.889108\pi$
$587$	− 16.5416i	− 0.682746i	0.939928	−	0.341373i	$-0.110892\pi$
$588$	4.54163i	0.187294i
$589$	10.2111	0.420741
$590$	0	0
$591$	30.6333	1.26009
$592$	7.90833i	0.325030i
$593$	− 6.39445i	− 0.262589i	−0.991343	−	0.131294i	$-0.958087\pi$
$593$	− 6.39445i	− 0.262589i	0.991343	−	0.131294i	$-0.0419133\pi$
$594$	2.09167	0.0858224
$595$	0	0
$596$	−5.21110	−0.213455
$597$	14.9361i	0.611293i
$598$	47.5694i	1.94526i
$599$	24.9083	1.01773	0.508863	−	0.860847i	$-0.330066\pi$
$599$	24.9083	1.01773	0.508863	+	0.860847i	$0.330066\pi$
$600$	0	0
$601$	−1.90833	−0.0778423	−0.0389211	−	0.999242i	$-0.512392\pi$
$601$	−1.90833	−0.0778423	−0.0389211	+	0.999242i	$0.512392\pi$
$602$	6.55004i	0.266960i
$603$	− 9.21110i	− 0.375105i
$604$	0.247263	0.0100610
$605$	0	0
$606$	1.54163	0.0626246
$607$	− 7.21110i	− 0.292690i	−0.989234	−	0.146345i	$-0.953249\pi$
$607$	− 7.21110i	− 0.292690i	0.989234	−	0.146345i	$-0.0467509\pi$
$608$	1.69722i	0.0688315i
$609$	−1.45837	−0.0590959
$610$	0	0
$611$	−15.0000	−0.606835
$612$	4.81665i	0.194702i
$613$	− 15.8806i	− 0.641410i	−0.947179	−	0.320705i	$-0.896080\pi$
$613$	− 15.8806i	− 0.641410i	0.947179	−	0.320705i	$-0.103920\pi$
$614$	−22.0278	−0.888968
$615$	0	0
$616$	−2.09167	−0.0842759
$617$	− 3.39445i	− 0.136655i	−0.997663	−	0.0683277i	$-0.978234\pi$
$617$	− 3.39445i	− 0.136655i	0.997663	−	0.0683277i	$-0.0217663\pi$
$618$	− 8.72498i	− 0.350970i
$619$	11.4222	0.459097	0.229549	−	0.973297i	$-0.426275\pi$
$619$	11.4222	0.459097	0.229549	+	0.973297i	$0.426275\pi$
$620$	0	0
$621$	11.7250	0.470507
$622$	6.27502i	0.251605i
$623$	1.18335i	0.0474098i
$624$	38.0278	1.52233
$625$	0	0
$626$	−0.238859	−0.00954672
$627$	− 2.30278i	− 0.0919640i
$628$	− 5.81665i	− 0.232110i
$629$	−16.5416	−0.659558
$630$	0	0
$631$	6.93608	0.276121	0.138061	−	0.990424i	$-0.455913\pi$
$631$	6.93608	0.276121	0.138061	+	0.990424i	$0.455913\pi$
$632$	32.7250i	1.30173i
$633$	− 58.1194i	− 2.31004i
$634$	−1.18335	−0.0469967
$635$	0	0
$636$	0.908327	0.0360175
$637$	32.5694i	1.29045i
$638$	1.18335i	0.0468491i
$639$	6.00000	0.237356
$640$	0	0
$641$	27.7889	1.09760	0.548798	−	0.835955i	$-0.315086\pi$
$641$	27.7889	1.09760	0.548798	+	0.835955i	$0.315086\pi$
$642$	− 9.00000i	− 0.355202i
$643$	− 22.0000i	− 0.867595i	−0.901010	−	0.433798i	$-0.857173\pi$
$643$	− 22.0000i	− 0.867595i	0.901010	−	0.433798i	$-0.142827\pi$
$644$	−1.54163	−0.0607489
$645$	0	0
$646$	9.00000	0.354100
$647$	33.2389i	1.30675i	0.757033	+	0.653377i	$0.226648\pi$
$647$	33.2389i	1.30675i	−0.757033	+	0.653377i	$0.773352\pi$
$648$	− 31.8167i	− 1.24988i
$649$	−14.2111	−0.557835
$650$	0	0
$651$	16.3944	0.642549
$652$	2.81665i	0.110309i
$653$	6.11943i	0.239472i	0.992806	+	0.119736i	$0.0382048\pi$
$653$	6.11943i	0.239472i	−0.992806	+	0.119736i	$0.961795\pi$
$654$	34.5416	1.35068
$655$	0	0
$656$	18.5139	0.722846
$657$	18.2111i	0.710483i
$658$	2.72498i	0.106231i
$659$	30.9083	1.20402	0.602009	−	0.798489i	$-0.294367\pi$
$659$	30.9083	1.20402	0.602009	+	0.798489i	$0.294367\pi$
$660$	0	0
$661$	−8.81665	−0.342928	−0.171464	−	0.985190i	$-0.554850\pi$
$661$	−8.81665	−0.342928	−0.171464	+	0.985190i	$0.554850\pi$
$662$	− 28.1472i	− 1.09397i
$663$	79.5416i	3.08914i
$664$	10.5416	0.409095
$665$	0	0
$666$	−7.18335	−0.278349
$667$	6.63331i	0.256843i
$668$	− 4.06392i	− 0.157238i
$669$	52.1194	2.01505
$670$	0	0
$671$	7.90833	0.305298
$672$	2.72498i	0.105118i
$673$	30.0278i	1.15748i	0.815510	+	0.578742i	$0.196456\pi$
$673$	30.0278i	1.15748i	−0.815510	+	0.578742i	$0.803544\pi$
$674$	−40.1833	−1.54780
$675$	0	0
$676$	−3.63331	−0.139743
$677$	− 24.2389i	− 0.931575i	−0.884897	−	0.465788i	$-0.845771\pi$
$677$	− 24.2389i	− 0.931575i	0.884897	−	0.465788i	$-0.154229\pi$
$678$	32.4500i	1.24623i
$679$	−10.6695	−0.409457
$680$	0	0
$681$	3.90833	0.149767
$682$	− 13.3028i	− 0.509390i
$683$	47.8444i	1.83072i	0.402642	+	0.915358i	$0.368092\pi$
$683$	47.8444i	1.83072i	−0.402642	+	0.915358i	$0.631908\pi$
$684$	−0.697224	−0.0266590
$685$	0	0
$686$	12.2750	0.468662
$687$	43.1194i	1.64511i
$688$	− 23.8167i	− 0.908001i
$689$	6.51388	0.248159
$690$	0	0
$691$	27.5416	1.04773	0.523867	−	0.851800i	$-0.324489\pi$
$691$	27.5416	1.04773	0.523867	+	0.851800i	$0.324489\pi$
$692$	− 1.45837i	− 0.0554387i
$693$	− 1.60555i	− 0.0609898i
$694$	−16.3028	−0.618845
$695$	0	0
$696$	6.27502	0.237854
$697$	38.7250i	1.46681i
$698$	6.75274i	0.255595i
$699$	−36.6333	−1.38560
$700$	0	0
$701$	−41.2111	−1.55652	−0.778261	−	0.627941i	$-0.783898\pi$
$701$	−41.2111	−1.55652	−0.778261	+	0.627941i	$0.783898\pi$
$702$	− 10.4584i	− 0.394726i
$703$	− 2.39445i	− 0.0903083i
$704$	8.81665	0.332290
$705$	0	0
$706$	−24.2750	−0.913602
$707$	0.358288i	0.0134748i
$708$	9.90833i	0.372378i
$709$	31.6333	1.18801	0.594007	−	0.804460i	$-0.297545\pi$
$709$	31.6333	1.18801	0.594007	+	0.804460i	$0.297545\pi$
$710$	0	0
$711$	−25.1194	−0.942052
$712$	− 5.09167i	− 0.190819i
$713$	− 74.5694i	− 2.79265i
$714$	14.4500	0.540776
$715$	0	0
$716$	−3.78890	−0.141598
$717$	− 48.6333i	− 1.81624i
$718$	− 1.02776i	− 0.0383555i
$719$	−7.18335	−0.267894	−0.133947	−	0.990989i	$-0.542765\pi$
$719$	−7.18335	−0.267894	−0.133947	+	0.990989i	$0.542765\pi$
$720$	0	0
$721$	2.02776	0.0755176
$722$	− 23.4500i	− 0.872717i
$723$	50.5139i	1.87863i
$724$	−6.02776	−0.224020
$725$	0	0
$726$	−3.00000	−0.111340
$727$	39.3305i	1.45869i	0.684147	+	0.729344i	$0.260175\pi$
$727$	39.3305i	1.45869i	−0.684147	+	0.729344i	$0.739825\pi$
$728$	10.4584i	0.387613i
$729$	13.3305	0.493723
$730$	0	0
$731$	49.8167	1.84254
$732$	− 5.51388i	− 0.203799i
$733$	19.6056i	0.724148i	0.932149	+	0.362074i	$0.117931\pi$
$733$	19.6056i	0.724148i	−0.932149	+	0.362074i	$0.882069\pi$
$734$	−26.9638	−0.995253
$735$	0	0
$736$	12.3944	0.456865
$737$	− 4.00000i	− 0.147342i
$738$	16.8167i	0.619030i
$739$	−35.1194	−1.29189	−0.645945	−	0.763384i	$-0.723536\pi$
$739$	−35.1194	−1.29189	−0.645945	+	0.763384i	$0.723536\pi$
$740$	0	0
$741$	−11.5139	−0.422973
$742$	− 1.18335i	− 0.0434420i
$743$	40.6972i	1.49304i	0.665365	+	0.746518i	$0.268276\pi$
$743$	40.6972i	1.49304i	−0.665365	+	0.746518i	$0.731724\pi$
$744$	−70.5416	−2.58618
$745$	0	0
$746$	−35.7250	−1.30798
$747$	8.09167i	0.296059i
$748$	2.09167i	0.0764791i
$749$	2.09167	0.0764281
$750$	0	0
$751$	−45.3305	−1.65413	−0.827067	−	0.562103i	$-0.809992\pi$
$751$	−45.3305	−1.65413	−0.827067	+	0.562103i	$0.809992\pi$
$752$	− 9.90833i	− 0.361320i
$753$	15.9083i	0.579732i
$754$	5.91673	0.215475
$755$	0	0
$756$	0.338936	0.0123270
$757$	− 49.0555i	− 1.78295i	−0.453067	−	0.891476i	$-0.649670\pi$
$757$	− 49.0555i	− 1.78295i	0.453067	−	0.891476i	$-0.350330\pi$
$758$	− 4.14719i	− 0.150633i
$759$	−16.8167	−0.610406
$760$	0	0
$761$	−13.5778	−0.492195	−0.246097	−	0.969245i	$-0.579148\pi$
$761$	−13.5778	−0.492195	−0.246097	+	0.969245i	$0.579148\pi$
$762$	24.3583i	0.882408i
$763$	8.02776i	0.290624i
$764$	3.11943	0.112857
$765$	0	0
$766$	−28.1833	−1.01831
$767$	71.0555i	2.56567i
$768$	− 16.3305i	− 0.589277i
$769$	5.18335	0.186916	0.0934581	−	0.995623i	$-0.470208\pi$
$769$	5.18335	0.186916	0.0934581	+	0.995623i	$0.470208\pi$
$770$	0	0
$771$	−41.4500	−1.49278
$772$	4.00000i	0.143963i
$773$	3.11943i	0.112198i	0.998425	+	0.0560990i	$0.0178663\pi$
$773$	3.11943i	0.112198i	−0.998425	+	0.0560990i	$0.982134\pi$
$774$	21.6333	0.777593
$775$	0	0
$776$	45.9083	1.64801
$777$	− 3.84441i	− 0.137917i
$778$	− 15.6333i	− 0.560481i
$779$	−5.60555	−0.200840
$780$	0	0
$781$	2.60555	0.0932340
$782$	− 65.7250i	− 2.35032i
$783$	− 1.45837i	− 0.0521177i
$784$	−21.5139	−0.768353
$785$	0	0
$786$	29.7250	1.06025
$787$	− 10.2111i	− 0.363986i	−0.983300	−	0.181993i	$-0.941745\pi$
$787$	− 10.2111i	− 0.363986i	0.983300	−	0.181993i	$-0.0582549\pi$
$788$	− 4.02776i	− 0.143483i
$789$	52.5416	1.87053
$790$	0	0
$791$	−7.54163	−0.268150
$792$	6.90833i	0.245477i
$793$	− 39.5416i	− 1.40416i
$794$	28.2666	1.00314
$795$	0	0
$796$	1.96384	0.0696065
$797$	− 3.51388i	− 0.124468i	−0.998062	−	0.0622340i	$-0.980178\pi$
$797$	− 3.51388i	− 0.124468i	0.998062	−	0.0622340i	$-0.0198225\pi$
$798$	2.09167i	0.0740444i
$799$	20.7250	0.733197
$800$	0	0
$801$	3.90833	0.138094
$802$	− 16.6611i	− 0.588323i
$803$	7.90833i	0.279079i
$804$	−2.78890	−0.0983568
$805$	0	0
$806$	−66.5139	−2.34285
$807$	− 20.0917i	− 0.707260i
$808$	− 1.54163i	− 0.0542345i
$809$	−39.6333	−1.39343	−0.696716	−	0.717347i	$-0.745356\pi$
$809$	−39.6333	−1.39343	−0.696716	+	0.717347i	$0.745356\pi$
$810$	0	0
$811$	38.8722	1.36499	0.682493	−	0.730892i	$-0.260896\pi$
$811$	38.8722	1.36499	0.682493	+	0.730892i	$0.260896\pi$
$812$	0.191750i	0.00672911i
$813$	− 0.486122i	− 0.0170490i
$814$	−3.11943	−0.109336
$815$	0	0
$816$	−52.5416	−1.83933
$817$	7.21110i	0.252285i
$818$	8.09167i	0.282919i
$819$	−8.02776	−0.280513
$820$	0	0
$821$	12.0000	0.418803	0.209401	−	0.977830i	$-0.432848\pi$
$821$	12.0000	0.418803	0.209401	+	0.977830i	$0.432848\pi$
$822$	− 38.7250i	− 1.35069i
$823$	18.4222i	0.642158i	0.947052	+	0.321079i	$0.104045\pi$
$823$	18.4222i	0.642158i	−0.947052	+	0.321079i	$0.895955\pi$
$824$	−8.72498	−0.303949
$825$	0	0
$826$	12.9083	0.449138
$827$	− 13.8167i	− 0.480452i	−0.970717	−	0.240226i	$-0.922778\pi$
$827$	− 13.8167i	− 0.480452i	0.970717	−	0.240226i	$-0.0772216\pi$
$828$	5.09167i	0.176948i
$829$	−29.7527	−1.03336	−0.516678	−	0.856180i	$-0.672831\pi$
$829$	−29.7527	−1.03336	−0.516678	+	0.856180i	$0.672831\pi$
$830$	0	0
$831$	33.1472	1.14986
$832$	− 44.0833i	− 1.52831i
$833$	− 45.0000i	− 1.55916i
$834$	−18.6333	−0.645219
$835$	0	0
$836$	−0.302776	−0.0104717
$837$	16.3944i	0.566675i
$838$	− 8.33053i	− 0.287773i
$839$	9.11943	0.314838	0.157419	−	0.987532i	$-0.449683\pi$
$839$	9.11943	0.314838	0.157419	+	0.987532i	$0.449683\pi$
$840$	0	0
$841$	−28.1749	−0.971550
$842$	0.908327i	0.0313030i
$843$	− 2.72498i	− 0.0938533i
$844$	−7.64171	−0.263039
$845$	0	0
$846$	9.00000	0.309426
$847$	− 0.697224i	− 0.0239569i
$848$	4.30278i	0.147758i
$849$	−14.5139	−0.498115
$850$	0	0
$851$	−17.4861	−0.599417
$852$	− 1.81665i	− 0.0622375i
$853$	− 12.7250i	− 0.435695i	−0.975983	−	0.217848i	$-0.930096\pi$
$853$	− 12.7250i	− 0.435695i	0.975983	−	0.217848i	$-0.0699035\pi$
$854$	−7.18335	−0.245809
$855$	0	0
$856$	−9.00000	−0.307614
$857$	3.00000i	0.102478i	0.998686	+	0.0512390i	$0.0163170\pi$
$857$	3.00000i	0.102478i	−0.998686	+	0.0512390i	$0.983683\pi$
$858$	15.0000i	0.512092i
$859$	−41.3944	−1.41236	−0.706180	−	0.708032i	$-0.749583\pi$
$859$	−41.3944	−1.41236	−0.706180	+	0.708032i	$0.749583\pi$
$860$	0	0
$861$	−9.00000	−0.306719
$862$	42.9916i	1.46430i
$863$	− 12.3944i	− 0.421912i	−0.977496	−	0.210956i	$-0.932342\pi$
$863$	− 12.3944i	− 0.421912i	0.977496	−	0.210956i	$-0.0676577\pi$
$864$	−2.72498	−0.0927057
$865$	0	0
$866$	−6.51388	−0.221351
$867$	− 70.7527i	− 2.40289i
$868$	− 2.15559i	− 0.0731655i
$869$	−10.9083	−0.370040
$870$	0	0
$871$	−20.0000	−0.677674
$872$	− 34.5416i	− 1.16973i
$873$	35.2389i	1.19265i
$874$	9.51388	0.321812
$875$	0	0
$876$	5.51388	0.186297
$877$	− 20.0000i	− 0.675352i	−0.941262	−	0.337676i	$-0.890359\pi$
$877$	− 20.0000i	− 0.675352i	0.941262	−	0.337676i	$-0.109641\pi$
$878$	− 31.6611i	− 1.06851i
$879$	−1.81665	−0.0612742
$880$	0	0
$881$	19.5416	0.658374	0.329187	−	0.944265i	$-0.393225\pi$
$881$	19.5416	0.658374	0.329187	+	0.944265i	$0.393225\pi$
$882$	− 19.5416i	− 0.658001i
$883$	52.4500i	1.76508i	0.470236	+	0.882541i	$0.344169\pi$
$883$	52.4500i	1.76508i	−0.470236	+	0.882541i	$0.655831\pi$
$884$	10.4584	0.351753
$885$	0	0
$886$	11.2111	0.376644
$887$	3.23886i	0.108750i	0.998521	+	0.0543751i	$0.0173167\pi$
$887$	3.23886i	0.108750i	−0.998521	+	0.0543751i	$0.982683\pi$
$888$	16.5416i	0.555101i
$889$	−5.66106	−0.189866
$890$	0	0
$891$	10.6056	0.355299
$892$	− 6.85281i	− 0.229449i
$893$	3.00000i	0.100391i
$894$	51.6333	1.72688
$895$	0	0
$896$	−5.64171	−0.188476
$897$	84.0833i	2.80746i
$898$	− 30.5971i	− 1.02104i
$899$	−9.27502	−0.309339
$900$	0	0
$901$	−9.00000	−0.299833
$902$	7.30278i	0.243156i
$903$	11.5778i	0.385285i
$904$	32.4500	1.07927
$905$	0	0
$906$	−2.44996	−0.0813945
$907$	4.00000i	0.132818i	0.997792	+	0.0664089i	$0.0211542\pi$
$907$	4.00000i	0.132818i	−0.997792	+	0.0664089i	$0.978846\pi$
$908$	− 0.513878i	− 0.0170536i
$909$	1.18335	0.0392491
$910$	0	0
$911$	−24.7889	−0.821293	−0.410646	−	0.911795i	$-0.634697\pi$
$911$	−24.7889	−0.821293	−0.410646	+	0.911795i	$0.634697\pi$
$912$	− 7.60555i	− 0.251845i
$913$	3.51388i	0.116292i
$914$	−26.9638	−0.891885
$915$	0	0
$916$	5.66947	0.187324
$917$	6.90833i	0.228133i
$918$	14.4500i	0.476920i
$919$	−26.7889	−0.883684	−0.441842	−	0.897093i	$-0.645675\pi$
$919$	−26.7889	−0.883684	−0.441842	+	0.897093i	$0.645675\pi$
$920$	0	0
$921$	−38.9361	−1.28299
$922$	41.9638i	1.38201i
$923$	− 13.0278i	− 0.428814i
$924$	−0.486122	−0.0159922
$925$	0	0
$926$	−15.3583	−0.504705
$927$	− 6.69722i	− 0.219966i
$928$	− 1.54163i	− 0.0506066i
$929$	−53.6056	−1.75874	−0.879371	−	0.476138i	$-0.842036\pi$
$929$	−53.6056	−1.75874	−0.879371	+	0.476138i	$0.842036\pi$
$930$	0	0
$931$	6.51388	0.213484
$932$	4.81665i	0.157775i
$933$	11.0917i	0.363125i
$934$	−24.2750	−0.794303
$935$	0	0
$936$	34.5416	1.12903
$937$	9.21110i	0.300914i	0.988617	+	0.150457i	$0.0480744\pi$
$937$	9.21110i	0.300914i	−0.988617	+	0.150457i	$0.951926\pi$
$938$	3.63331i	0.118632i
$939$	−0.422205	−0.0137781
$940$	0	0
$941$	59.6056	1.94309	0.971543	−	0.236864i	$-0.0761197\pi$
$941$	59.6056	1.94309	0.971543	+	0.236864i	$0.0761197\pi$
$942$	57.6333i	1.87779i
$943$	40.9361i	1.33306i
$944$	−46.9361	−1.52764
$945$	0	0
$946$	9.39445	0.305440
$947$	− 6.63331i	− 0.215554i	−0.994175	−	0.107777i	$-0.965627\pi$
$947$	− 6.63331i	− 0.215554i	0.994175	−	0.107777i	$-0.0343732\pi$
$948$	7.60555i	0.247017i
$949$	39.5416	1.28358
$950$	0	0
$951$	−2.09167	−0.0678271
$952$	− 14.4500i	− 0.468326i
$953$	37.2666i	1.20718i	0.797293	+	0.603592i	$0.206264\pi$
$953$	37.2666i	1.20718i	−0.797293	+	0.603592i	$0.793736\pi$
$954$	−3.90833	−0.126537
$955$	0	0
$956$	−6.39445	−0.206811
$957$	2.09167i	0.0676142i
$958$	45.3583i	1.46546i
$959$	9.00000	0.290625
$960$	0	0
$961$	73.2666	2.36344
$962$	15.5971i	0.502872i
$963$	− 6.90833i	− 0.222618i
$964$	6.64171	0.213915
$965$	0	0
$966$	15.2750	0.491466
$967$	− 14.9083i	− 0.479419i	−0.970845	−	0.239710i	$-0.922948\pi$
$967$	− 14.9083i	− 0.479419i	0.970845	−	0.239710i	$-0.0770523\pi$
$968$	3.00000i	0.0964237i
$969$	15.9083	0.511049
$970$	0	0
$971$	45.3583	1.45562	0.727808	−	0.685781i	$-0.240539\pi$
$971$	45.3583	1.45562	0.727808	+	0.685781i	$0.240539\pi$
$972$	− 5.93608i	− 0.190400i
$973$	− 4.33053i	− 0.138830i
$974$	5.48612	0.175787
$975$	0	0
$976$	26.1194	0.836063
$977$	52.0278i	1.66452i	0.554389	+	0.832258i	$0.312952\pi$
$977$	52.0278i	1.66452i	−0.554389	+	0.832258i	$0.687048\pi$
$978$	− 27.9083i	− 0.892410i
$979$	1.69722	0.0542435
$980$	0	0
$981$	26.5139	0.846523
$982$	− 12.7527i	− 0.406956i
$983$	8.84441i	0.282093i	0.990003	+	0.141046i	$0.0450467\pi$
$983$	8.84441i	0.282093i	−0.990003	+	0.141046i	$0.954953\pi$
$984$	38.7250	1.23451
$985$	0	0
$986$	−8.17494	−0.260343
$987$	4.81665i	0.153316i
$988$	1.51388i	0.0481629i
$989$	52.6611	1.67452
$990$	0	0
$991$	−16.9083	−0.537111	−0.268555	−	0.963264i	$-0.586546\pi$
$991$	−16.9083	−0.537111	−0.268555	+	0.963264i	$0.586546\pi$
$992$	17.3305i	0.550245i
$993$	− 49.7527i	− 1.57886i
$994$	−2.36669	−0.0750669
$995$	0	0
$996$	2.44996	0.0776300
$997$	− 46.7250i	− 1.47979i	−0.672720	−	0.739897i	$-0.734874\pi$
$997$	− 46.7250i	− 1.47979i	0.672720	−	0.739897i	$-0.265126\pi$
$998$	4.54163i	0.143763i
$999$	3.84441	0.121632

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.b.c.199.3		4
3.2	odd	2		2475.2.c.k.199.2		4
4.3	odd	2		4400.2.b.y.4049.1		4
5.2	odd	4		275.2.a.f.1.1	yes	2
5.3	odd	4		275.2.a.e.1.2	✓	2
5.4	even	2	inner	275.2.b.c.199.2		4
15.2	even	4		2475.2.a.o.1.2		2
15.8	even	4		2475.2.a.t.1.1		2
15.14	odd	2		2475.2.c.k.199.3		4
20.3	even	4		4400.2.a.bs.1.2		2
20.7	even	4		4400.2.a.bh.1.1		2
20.19	odd	2		4400.2.b.y.4049.4		4
55.32	even	4		3025.2.a.h.1.2		2
55.43	even	4		3025.2.a.n.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.2.a.e.1.2	✓	2	5.3	odd	4
275.2.a.f.1.1	yes	2	5.2	odd	4
275.2.b.c.199.2		4	5.4	even	2	inner
275.2.b.c.199.3		4	1.1	even	1	trivial
2475.2.a.o.1.2		2	15.2	even	4
2475.2.a.t.1.1		2	15.8	even	4
2475.2.c.k.199.2		4	3.2	odd	2
2475.2.c.k.199.3		4	15.14	odd	2
3025.2.a.h.1.2		2	55.32	even	4
3025.2.a.n.1.1		2	55.43	even	4
4400.2.a.bh.1.1		2	20.7	even	4
4400.2.a.bs.1.2		2	20.3	even	4
4400.2.b.y.4049.1		4	4.3	odd	2
4400.2.b.y.4049.4		4	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.30278i q^{2} +2.30278i q^{3} +0.302776 q^{4} -3.00000 q^{6} -0.697224i q^{7} +3.00000i q^{8} -2.30278 q^{9} -1.00000 q^{11} +0.697224i q^{12} +5.00000i q^{13} +0.908327 q^{14} -3.30278 q^{16} -6.90833i q^{17} -3.00000i q^{18} +1.00000 q^{19} +1.60555 q^{21} -1.30278i q^{22} -7.30278i q^{23} -6.90833 q^{24} -6.51388 q^{26} +1.60555i q^{27} -0.211103i q^{28} -0.908327 q^{29} +10.2111 q^{31} +1.69722i q^{32} -2.30278i q^{33} +9.00000 q^{34} -0.697224 q^{36} -2.39445i q^{37} +1.30278i q^{38} -11.5139 q^{39} -5.60555 q^{41} +2.09167i q^{42} +7.21110i q^{43} -0.302776 q^{44} +9.51388 q^{46} +3.00000i q^{47} -7.60555i q^{48} +6.51388 q^{49} +15.9083 q^{51} +1.51388i q^{52} -1.30278i q^{53} -2.09167 q^{54} +2.09167 q^{56} +2.30278i q^{57} -1.18335i q^{58} +14.2111 q^{59} -7.90833 q^{61} +13.3028i q^{62} +1.60555i q^{63} -8.81665 q^{64} +3.00000 q^{66} +4.00000i q^{67} -2.09167i q^{68} +16.8167 q^{69} -2.60555 q^{71} -6.90833i q^{72} -7.90833i q^{73} +3.11943 q^{74} +0.302776 q^{76} +0.697224i q^{77} -15.0000i q^{78} +10.9083 q^{79} -10.6056 q^{81} -7.30278i q^{82} -3.51388i q^{83} +0.486122 q^{84} -9.39445 q^{86} -2.09167i q^{87} -3.00000i q^{88} -1.69722 q^{89} +3.48612 q^{91} -2.21110i q^{92} +23.5139i q^{93} -3.90833 q^{94} -3.90833 q^{96} -15.3028i q^{97} +8.48612i q^{98} +2.30278 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{4} - 12 q^{6} - 2 q^{9} - 4 q^{11} - 18 q^{14} - 6 q^{16} + 4 q^{19} - 8 q^{21} - 6 q^{24} + 10 q^{26} + 18 q^{29} + 12 q^{31} + 36 q^{34} - 10 q^{36} - 10 q^{39} - 8 q^{41} + 6 q^{44} + 2 q^{46}+ \cdots + 2 q^{99}+O(q^{100}) \) 4 * q - 6 * q^4 - 12 * q^6 - 2 * q^9 - 4 * q^11 - 18 * q^14 - 6 * q^16 + 4 * q^19 - 8 * q^21 - 6 * q^24 + 10 * q^26 + 18 * q^29 + 12 * q^31 + 36 * q^34 - 10 * q^36 - 10 * q^39 - 8 * q^41 + 6 * q^44 + 2 * q^46 - 10 * q^49 + 42 * q^51 - 30 * q^54 + 30 * q^56 + 28 * q^59 - 10 * q^61 + 8 * q^64 + 12 * q^66 + 24 * q^69 + 4 * q^71 - 38 * q^74 - 6 * q^76 + 22 * q^79 - 28 * q^81 + 38 * q^84 - 52 * q^86 - 14 * q^89 + 50 * q^91 + 6 * q^94 + 6 * q^96 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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