LMFDB - Embedded newform 1295.2.a.h.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1295,2,Mod(1,1295)] 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("1295.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1295, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1295 = 5 \cdot 7 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1295.a (trivial)

Newform invariants

comment:select newform

sage:traces = [12,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$10.3406270618$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5 x^{11} - 7 x^{10} + 63 x^{9} - 11 x^{8} - 279 x^{7} + 171 x^{6} + 503 x^{5} - 367 x^{4} + \cdots - 26 $ x^12 - 5x^11 - 7x^10 + 63x^9 - 11x^8 - 279x^7 + 171x^6 + 503x^5 - 367x^4 - 310x^3 + 216x^2 + 42*x - 26
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.876141$ of defining polynomial
Character	$\chi$	$=$	1295.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.876141 q^{2} +0.718988 q^{3} -1.23238 q^{4} +1.00000 q^{5} -0.629935 q^{6} -1.00000 q^{7} +2.83202 q^{8} -2.48306 q^{9} -0.876141 q^{10} +0.114427 q^{11} -0.886064 q^{12} -5.71328 q^{13} +0.876141 q^{14} +0.718988 q^{15} -0.0164961 q^{16} +3.29191 q^{17} +2.17551 q^{18} -0.312598 q^{19} -1.23238 q^{20} -0.718988 q^{21} -0.100254 q^{22} +9.00051 q^{23} +2.03619 q^{24} +1.00000 q^{25} +5.00564 q^{26} -3.94225 q^{27} +1.23238 q^{28} +9.18065 q^{29} -0.629935 q^{30} +2.16041 q^{31} -5.64958 q^{32} +0.0822717 q^{33} -2.88418 q^{34} -1.00000 q^{35} +3.06006 q^{36} -1.00000 q^{37} +0.273880 q^{38} -4.10778 q^{39} +2.83202 q^{40} +6.64159 q^{41} +0.629935 q^{42} -0.971397 q^{43} -0.141017 q^{44} -2.48306 q^{45} -7.88572 q^{46} -0.611192 q^{47} -0.0118605 q^{48} +1.00000 q^{49} -0.876141 q^{50} +2.36685 q^{51} +7.04091 q^{52} +6.82366 q^{53} +3.45397 q^{54} +0.114427 q^{55} -2.83202 q^{56} -0.224754 q^{57} -8.04355 q^{58} -7.75992 q^{59} -0.886064 q^{60} -12.7740 q^{61} -1.89283 q^{62} +2.48306 q^{63} +4.98283 q^{64} -5.71328 q^{65} -0.0720816 q^{66} +0.659857 q^{67} -4.05688 q^{68} +6.47126 q^{69} +0.876141 q^{70} +15.1600 q^{71} -7.03206 q^{72} +10.1944 q^{73} +0.876141 q^{74} +0.718988 q^{75} +0.385238 q^{76} -0.114427 q^{77} +3.59899 q^{78} +11.3613 q^{79} -0.0164961 q^{80} +4.61473 q^{81} -5.81897 q^{82} +13.1089 q^{83} +0.886064 q^{84} +3.29191 q^{85} +0.851081 q^{86} +6.60078 q^{87} +0.324059 q^{88} -9.92316 q^{89} +2.17551 q^{90} +5.71328 q^{91} -11.0920 q^{92} +1.55331 q^{93} +0.535490 q^{94} -0.312598 q^{95} -4.06199 q^{96} +5.10646 q^{97} -0.876141 q^{98} -0.284129 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 5 q^{2} + 4 q^{3} + 15 q^{4} + 12 q^{5} + 6 q^{6} - 12 q^{7} + 21 q^{8} + 18 q^{9} + 5 q^{10} - 4 q^{11} + 8 q^{12} + 6 q^{13} - 5 q^{14} + 4 q^{15} + 21 q^{16} + 20 q^{17} + 14 q^{18} - 4 q^{19}+ \cdots - 24 q^{99}+O(q^{100}) $ 12 * q + 5 * q^2 + 4 * q^3 + 15 * q^4 + 12 * q^5 + 6 * q^6 - 12 * q^7 + 21 * q^8 + 18 * q^9 + 5 * q^10 - 4 * q^11 + 8 * q^12 + 6 * q^13 - 5 * q^14 + 4 * q^15 + 21 * q^16 + 20 * q^17 + 14 * q^18 - 4 * q^19 + 15 * q^20 - 4 * q^21 + 2 * q^22 + 20 * q^23 + 4 * q^24 + 12 * q^25 + 6 * q^26 + 10 * q^27 - 15 * q^28 - 12 * q^29 + 6 * q^30 + 47 * q^32 + 20 * q^33 - 28 * q^34 - 12 * q^35 + 39 * q^36 - 12 * q^37 + 8 * q^38 + 21 * q^40 + 24 * q^41 - 6 * q^42 + 14 * q^43 - 16 * q^44 + 18 * q^45 + 20 * q^46 + 18 * q^47 - 19 * q^48 + 12 * q^49 + 5 * q^50 - 20 * q^51 + 22 * q^52 + 36 * q^53 - 46 * q^54 - 4 * q^55 - 21 * q^56 + 36 * q^57 + 28 * q^58 + 4 * q^59 + 8 * q^60 - 39 * q^62 - 18 * q^63 + 9 * q^64 + 6 * q^65 - 21 * q^66 + 6 * q^67 - 6 * q^68 - 6 * q^69 - 5 * q^70 - 12 * q^71 + 17 * q^72 + 32 * q^73 - 5 * q^74 + 4 * q^75 - 13 * q^76 + 4 * q^77 + 74 * q^78 + 14 * q^79 + 21 * q^80 - 16 * q^81 - 26 * q^82 - 18 * q^83 - 8 * q^84 + 20 * q^85 - 36 * q^86 - 18 * q^87 + 27 * q^88 + 14 * q^90 - 6 * q^91 + 39 * q^92 + 52 * q^93 + 38 * q^94 - 4 * q^95 - 53 * q^96 + 38 * q^97 + 5 * q^98 - 24 * q^99

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 $

$2$	−0.876141	−0.619526	−0.309763	−	0.950814i	$-0.600250\pi$
$2$	−0.876141	−0.619526	−0.309763	+	0.950814i	$0.600250\pi$
$3$	0.718988	0.415108	0.207554	−	0.978224i	$-0.433450\pi$
$3$	0.718988	0.415108	0.207554	+	0.978224i	$0.433450\pi$
$4$	−1.23238	−0.616188
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.629935	−0.257170
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.83202	1.00127
$9$	−2.48306	−0.827685
$10$	−0.876141	−0.277060
$11$	0.114427	0.0345010	0.0172505	−	0.999851i	$-0.494509\pi$
$11$	0.114427	0.0345010	0.0172505	+	0.999851i	$0.494509\pi$
$12$	−0.886064	−0.255785
$13$	−5.71328	−1.58458	−0.792289	−	0.610146i	$-0.791111\pi$
$13$	−5.71328	−1.58458	−0.792289	+	0.610146i	$0.791111\pi$
$14$	0.876141	0.234159
$15$	0.718988	0.185642
$16$	−0.0164961	−0.00412403
$17$	3.29191	0.798406	0.399203	−	0.916862i	$-0.369287\pi$
$17$	3.29191	0.798406	0.399203	+	0.916862i	$0.369287\pi$
$18$	2.17551	0.512772
$19$	−0.312598	−0.0717149	−0.0358574	−	0.999357i	$-0.511416\pi$
$19$	−0.312598	−0.0717149	−0.0358574	+	0.999357i	$0.511416\pi$
$20$	−1.23238	−0.275568
$21$	−0.718988	−0.156896
$22$	−0.100254	−0.0213743
$23$	9.00051	1.87674	0.938368	−	0.345638i	$-0.112337\pi$
$23$	9.00051	1.87674	0.938368	+	0.345638i	$0.112337\pi$
$24$	2.03619	0.415635
$25$	1.00000	0.200000
$26$	5.00564	0.981686
$27$	−3.94225	−0.758687
$28$	1.23238	0.232897
$29$	9.18065	1.70480	0.852402	−	0.522887i	$-0.175145\pi$
$29$	9.18065	1.70480	0.852402	+	0.522887i	$0.175145\pi$
$30$	−0.629935	−0.115010
$31$	2.16041	0.388022	0.194011	−	0.980999i	$-0.437850\pi$
$31$	2.16041	0.388022	0.194011	+	0.980999i	$0.437850\pi$
$32$	−5.64958	−0.998715
$33$	0.0822717	0.0143217
$34$	−2.88418	−0.494633
$35$	−1.00000	−0.169031
$36$	3.06006	0.510010
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	0.273880	0.0444292
$39$	−4.10778	−0.657771
$40$	2.83202	0.447781
$41$	6.64159	1.03724	0.518621	−	0.855004i	$-0.326446\pi$
$41$	6.64159	1.03724	0.518621	+	0.855004i	$0.326446\pi$
$42$	0.629935	0.0972012
$43$	−0.971397	−0.148137	−0.0740683	−	0.997253i	$-0.523598\pi$
$43$	−0.971397	−0.148137	−0.0740683	+	0.997253i	$0.523598\pi$
$44$	−0.141017	−0.0212591
$45$	−2.48306	−0.370152
$46$	−7.88572	−1.16269
$47$	−0.611192	−0.0891515	−0.0445757	−	0.999006i	$-0.514194\pi$
$47$	−0.611192	−0.0891515	−0.0445757	+	0.999006i	$0.514194\pi$
$48$	−0.0118605	−0.00171192
$49$	1.00000	0.142857
$50$	−0.876141	−0.123905
$51$	2.36685	0.331425
$52$	7.04091	0.976398
$53$	6.82366	0.937301	0.468651	−	0.883384i	$-0.344740\pi$
$53$	6.82366	0.937301	0.468651	+	0.883384i	$0.344740\pi$
$54$	3.45397	0.470026
$55$	0.114427	0.0154293
$56$	−2.83202	−0.378444
$57$	−0.224754	−0.0297694
$58$	−8.04355	−1.05617
$59$	−7.75992	−1.01026	−0.505128	−	0.863045i	$-0.668555\pi$
$59$	−7.75992	−1.01026	−0.505128	+	0.863045i	$0.668555\pi$
$60$	−0.886064	−0.114390
$61$	−12.7740	−1.63554	−0.817771	−	0.575544i	$-0.804790\pi$
$61$	−12.7740	−1.63554	−0.817771	+	0.575544i	$0.804790\pi$
$62$	−1.89283	−0.240390
$63$	2.48306	0.312836
$64$	4.98283	0.622853
$65$	−5.71328	−0.708645
$66$	−0.0720816	−0.00887263
$67$	0.659857	0.0806144	0.0403072	−	0.999187i	$-0.487166\pi$
$67$	0.659857	0.0806144	0.0403072	+	0.999187i	$0.487166\pi$
$68$	−4.05688	−0.491969
$69$	6.47126	0.779048
$70$	0.876141	0.104719
$71$	15.1600	1.79917	0.899583	−	0.436750i	$-0.143870\pi$
$71$	15.1600	1.79917	0.899583	+	0.436750i	$0.143870\pi$
$72$	−7.03206	−0.828736
$73$	10.1944	1.19316	0.596579	−	0.802554i	$-0.296526\pi$
$73$	10.1944	1.19316	0.596579	+	0.802554i	$0.296526\pi$
$74$	0.876141	0.101849
$75$	0.718988	0.0830216
$76$	0.385238	0.0441899
$77$	−0.114427	−0.0130402
$78$	3.59899	0.407506
$79$	11.3613	1.27825	0.639125	−	0.769102i	$-0.279296\pi$
$79$	11.3613	1.27825	0.639125	+	0.769102i	$0.279296\pi$
$80$	−0.0164961	−0.00184432
$81$	4.61473	0.512748
$82$	−5.81897	−0.642598
$83$	13.1089	1.43889	0.719443	−	0.694552i	$-0.244397\pi$
$83$	13.1089	1.43889	0.719443	+	0.694552i	$0.244397\pi$
$84$	0.886064	0.0966775
$85$	3.29191	0.357058
$86$	0.851081	0.0917744
$87$	6.60078	0.707678
$88$	0.324059	0.0345448
$89$	−9.92316	−1.05185	−0.525926	−	0.850530i	$-0.676281\pi$
$89$	−9.92316	−1.05185	−0.525926	+	0.850530i	$0.676281\pi$
$90$	2.17551	0.229319
$91$	5.71328	0.598914
$92$	−11.0920	−1.15642
$93$	1.55331	0.161071
$94$	0.535490	0.0552316
$95$	−0.312598	−0.0320719
$96$	−4.06199	−0.414575
$97$	5.10646	0.518482	0.259241	−	0.965813i	$-0.416528\pi$
$97$	5.10646	0.518482	0.259241	+	0.965813i	$0.416528\pi$
$98$	−0.876141	−0.0885036
$99$	−0.284129	−0.0285560
$100$	−1.23238	−0.123238
$101$	17.4258	1.73393	0.866964	−	0.498370i	$-0.166068\pi$
$101$	17.4258	1.73393	0.866964	+	0.498370i	$0.166068\pi$
$102$	−2.07369	−0.205326
$103$	15.4685	1.52416	0.762080	−	0.647483i	$-0.224178\pi$
$103$	15.4685	1.52416	0.762080	+	0.647483i	$0.224178\pi$
$104$	−16.1801	−1.58659
$105$	−0.718988	−0.0701661
$106$	−5.97849	−0.580682
$107$	−14.2478	−1.37739	−0.688695	−	0.725051i	$-0.741816\pi$
$107$	−14.2478	−1.37739	−0.688695	+	0.725051i	$0.741816\pi$
$108$	4.85834	0.467494
$109$	−11.9739	−1.14689	−0.573445	−	0.819244i	$-0.694393\pi$
$109$	−11.9739	−1.14689	−0.573445	+	0.819244i	$0.694393\pi$
$110$	−0.100254	−0.00955886
$111$	−0.718988	−0.0682434
$112$	0.0164961	0.00155874
$113$	9.80238	0.922130	0.461065	−	0.887366i	$-0.347467\pi$
$113$	9.80238	0.922130	0.461065	+	0.887366i	$0.347467\pi$
$114$	0.196917	0.0184429
$115$	9.00051	0.839302
$116$	−11.3140	−1.05048
$117$	14.1864	1.31153
$118$	6.79879	0.625879
$119$	−3.29191	−0.301769
$120$	2.03619	0.185878
$121$	−10.9869	−0.998810
$122$	11.1918	1.01326
$123$	4.77523	0.430568
$124$	−2.66244	−0.239095
$125$	1.00000	0.0894427
$126$	−2.17551	−0.193810
$127$	−8.49956	−0.754214	−0.377107	−	0.926170i	$-0.623081\pi$
$127$	−8.49956	−0.754214	−0.377107	+	0.926170i	$0.623081\pi$
$128$	6.93351	0.612841
$129$	−0.698423	−0.0614927
$130$	5.00564	0.439023
$131$	6.06293	0.529721	0.264860	−	0.964287i	$-0.414674\pi$
$131$	6.06293	0.529721	0.264860	+	0.964287i	$0.414674\pi$
$132$	−0.101390	−0.00882484
$133$	0.312598	0.0271057
$134$	−0.578128	−0.0499427
$135$	−3.94225	−0.339295
$136$	9.32276	0.799420
$137$	11.6680	0.996868	0.498434	−	0.866928i	$-0.333909\pi$
$137$	11.6680	0.996868	0.498434	+	0.866928i	$0.333909\pi$
$138$	−5.66974	−0.482640
$139$	−7.16747	−0.607937	−0.303968	−	0.952682i	$-0.598312\pi$
$139$	−7.16747	−0.607937	−0.303968	+	0.952682i	$0.598312\pi$
$140$	1.23238	0.104155
$141$	−0.439440	−0.0370075
$142$	−13.2823	−1.11463
$143$	−0.653753	−0.0546696
$144$	0.0409608	0.00341340
$145$	9.18065	0.762412
$146$	−8.93169	−0.739192
$147$	0.718988	0.0593012
$148$	1.23238	0.101301
$149$	−16.0189	−1.31232	−0.656159	−	0.754622i	$-0.727820\pi$
$149$	−16.0189	−1.31232	−0.656159	+	0.754622i	$0.727820\pi$
$150$	−0.629935	−0.0514340
$151$	18.1940	1.48061	0.740303	−	0.672273i	$-0.234682\pi$
$151$	18.1940	1.48061	0.740303	+	0.672273i	$0.234682\pi$
$152$	−0.885283	−0.0718060
$153$	−8.17401	−0.660829
$154$	0.100254	0.00807871
$155$	2.16041	0.173529
$156$	5.06233	0.405311
$157$	−13.2990	−1.06138	−0.530689	−	0.847567i	$-0.678067\pi$
$157$	−13.2990	−1.06138	−0.530689	+	0.847567i	$0.678067\pi$
$158$	−9.95414	−0.791909
$159$	4.90613	0.389081
$160$	−5.64958	−0.446639
$161$	−9.00051	−0.709340
$162$	−4.04316	−0.317661
$163$	4.21116	0.329844	0.164922	−	0.986307i	$-0.447263\pi$
$163$	4.21116	0.329844	0.164922	+	0.986307i	$0.447263\pi$
$164$	−8.18494	−0.639136
$165$	0.0822717	0.00640484
$166$	−11.4852	−0.891427
$167$	23.3506	1.80692	0.903461	−	0.428670i	$-0.141018\pi$
$167$	23.3506	1.80692	0.903461	+	0.428670i	$0.141018\pi$
$168$	−2.03619	−0.157095
$169$	19.6415	1.51089
$170$	−2.88418	−0.221207
$171$	0.776198	0.0593574
$172$	1.19713	0.0912800
$173$	−19.6976	−1.49758	−0.748791	−	0.662806i	$-0.769365\pi$
$173$	−19.6976	−1.49758	−0.748791	+	0.662806i	$0.769365\pi$
$174$	−5.78322	−0.438425
$175$	−1.00000	−0.0755929
$176$	−0.00188760	−0.000142283 0
$177$	−5.57929	−0.419365
$178$	8.69409	0.651650
$179$	−1.22265	−0.0913848	−0.0456924	−	0.998956i	$-0.514549\pi$
$179$	−1.22265	−0.0913848	−0.0456924	+	0.998956i	$0.514549\pi$
$180$	3.06006	0.228083
$181$	2.81754	0.209426	0.104713	−	0.994502i	$-0.466608\pi$
$181$	2.81754	0.209426	0.104713	+	0.994502i	$0.466608\pi$
$182$	−5.00564	−0.371043
$183$	−9.18435	−0.678927
$184$	25.4896	1.87912
$185$	−1.00000	−0.0735215
$186$	−1.36092	−0.0997876
$187$	0.376684	0.0275458
$188$	0.753218	0.0549341
$189$	3.94225	0.286757
$190$	0.273880	0.0198693
$191$	−20.6219	−1.49215	−0.746074	−	0.665863i	$-0.768064\pi$
$191$	−20.6219	−1.49215	−0.746074	+	0.665863i	$0.768064\pi$
$192$	3.58259	0.258551
$193$	5.96948	0.429693	0.214846	−	0.976648i	$-0.431075\pi$
$193$	5.96948	0.429693	0.214846	+	0.976648i	$0.431075\pi$
$194$	−4.47398	−0.321213
$195$	−4.10778	−0.294164
$196$	−1.23238	−0.0880269
$197$	19.5027	1.38951	0.694756	−	0.719245i	$-0.255512\pi$
$197$	19.5027	1.38951	0.694756	+	0.719245i	$0.255512\pi$
$198$	0.248937	0.0176912
$199$	−5.87440	−0.416425	−0.208213	−	0.978084i	$-0.566765\pi$
$199$	−5.87440	−0.416425	−0.208213	+	0.978084i	$0.566765\pi$
$200$	2.83202	0.200254
$201$	0.474430	0.0334637
$202$	−15.2674	−1.07421
$203$	−9.18065	−0.644355
$204$	−2.91685	−0.204220
$205$	6.64159	0.463869
$206$	−13.5526	−0.944256
$207$	−22.3488	−1.55335
$208$	0.0942468	0.00653484
$209$	−0.0357696	−0.00247424
$210$	0.629935	0.0434697
$211$	0.0805448	0.00554493	0.00277247	−	0.999996i	$-0.499117\pi$
$211$	0.0805448	0.00554493	0.00277247	+	0.999996i	$0.499117\pi$
$212$	−8.40931	−0.577554
$213$	10.8999	0.746849
$214$	12.4831	0.853328
$215$	−0.971397	−0.0662487
$216$	−11.1645	−0.759650
$217$	−2.16041	−0.146659
$218$	10.4908	0.710527
$219$	7.32962	0.495290
$220$	−0.141017	−0.00950737
$221$	−18.8076	−1.26514
$222$	0.629935	0.0422785
$223$	5.44656	0.364729	0.182364	−	0.983231i	$-0.441625\pi$
$223$	5.44656	0.364729	0.182364	+	0.983231i	$0.441625\pi$
$224$	5.64958	0.377479
$225$	−2.48306	−0.165537
$226$	−8.58827	−0.571283
$227$	−6.41573	−0.425827	−0.212913	−	0.977071i	$-0.568295\pi$
$227$	−6.41573	−0.425827	−0.212913	+	0.977071i	$0.568295\pi$
$228$	0.276982	0.0183436
$229$	−8.32658	−0.550236	−0.275118	−	0.961410i	$-0.588717\pi$
$229$	−8.32658	−0.550236	−0.275118	+	0.961410i	$0.588717\pi$
$230$	−7.88572	−0.519969
$231$	−0.0822717	−0.00541308
$232$	25.9998	1.70697
$233$	17.5713	1.15114	0.575568	−	0.817754i	$-0.304781\pi$
$233$	17.5713	1.15114	0.575568	+	0.817754i	$0.304781\pi$
$234$	−12.4293	−0.812527
$235$	−0.611192	−0.0398697
$236$	9.56314	0.622507
$237$	8.16867	0.530612
$238$	2.88418	0.186954
$239$	−23.0891	−1.49351	−0.746754	−	0.665100i	$-0.768389\pi$
$239$	−23.0891	−1.49351	−0.746754	+	0.665100i	$0.768389\pi$
$240$	−0.0118605	−0.000765593 0
$241$	−0.970127	−0.0624914	−0.0312457	−	0.999512i	$-0.509947\pi$
$241$	−0.970127	−0.0624914	−0.0312457	+	0.999512i	$0.509947\pi$
$242$	9.62608	0.618788
$243$	15.1447	0.971533
$244$	15.7424	1.00780
$245$	1.00000	0.0638877
$246$	−4.18377	−0.266748
$247$	1.78596	0.113638
$248$	6.11834	0.388515
$249$	9.42513	0.597293
$250$	−0.876141	−0.0554120
$251$	2.18434	0.137874	0.0689371	−	0.997621i	$-0.478039\pi$
$251$	2.18434	0.137874	0.0689371	+	0.997621i	$0.478039\pi$
$252$	−3.06006	−0.192766
$253$	1.02990	0.0647493
$254$	7.44682	0.467255
$255$	2.36685	0.148218
$256$	−16.0404	−1.00252
$257$	15.3430	0.957073	0.478536	−	0.878068i	$-0.341167\pi$
$257$	15.3430	0.957073	0.478536	+	0.878068i	$0.341167\pi$
$258$	0.611917	0.0380963
$259$	1.00000	0.0621370
$260$	7.04091	0.436658
$261$	−22.7961	−1.41104
$262$	−5.31198	−0.328175
$263$	−16.8229	−1.03734	−0.518672	−	0.854973i	$-0.673574\pi$
$263$	−16.8229	−1.03734	−0.518672	+	0.854973i	$0.673574\pi$
$264$	0.232995	0.0143398
$265$	6.82366	0.419174
$266$	−0.273880	−0.0167927
$267$	−7.13464	−0.436633
$268$	−0.813192	−0.0496736
$269$	11.5361	0.703370	0.351685	−	0.936118i	$-0.385609\pi$
$269$	11.5361	0.703370	0.351685	+	0.936118i	$0.385609\pi$
$270$	3.45397	0.210202
$271$	−8.15653	−0.495474	−0.247737	−	0.968827i	$-0.579687\pi$
$271$	−8.15653	−0.495474	−0.247737	+	0.968827i	$0.579687\pi$
$272$	−0.0543038	−0.00329265
$273$	4.10778	0.248614
$274$	−10.2229	−0.617585
$275$	0.114427	0.00690021
$276$	−7.97503	−0.480040
$277$	17.8545	1.07277	0.536387	−	0.843972i	$-0.319789\pi$
$277$	17.8545	1.07277	0.536387	+	0.843972i	$0.319789\pi$
$278$	6.27972	0.376632
$279$	−5.36443	−0.321160
$280$	−2.83202	−0.169245
$281$	−14.9418	−0.891351	−0.445675	−	0.895195i	$-0.647036\pi$
$281$	−14.9418	−0.891351	−0.445675	+	0.895195i	$0.647036\pi$
$282$	0.385011	0.0229271
$283$	−21.7390	−1.29225	−0.646124	−	0.763232i	$-0.723611\pi$
$283$	−21.7390	−1.29225	−0.646124	+	0.763232i	$0.723611\pi$
$284$	−18.6829	−1.10862
$285$	−0.224754	−0.0133133
$286$	0.572780	0.0338692
$287$	−6.64159	−0.392041
$288$	14.0282	0.826622
$289$	−6.16330	−0.362547
$290$	−8.04355	−0.472333
$291$	3.67148	0.215226
$292$	−12.5633	−0.735210
$293$	−13.5247	−0.790120	−0.395060	−	0.918655i	$-0.629276\pi$
$293$	−13.5247	−0.790120	−0.395060	+	0.918655i	$0.629276\pi$
$294$	−0.629935	−0.0367386
$295$	−7.75992	−0.451800
$296$	−2.83202	−0.164608
$297$	−0.451100	−0.0261755
$298$	14.0348	0.813015
$299$	−51.4224	−2.97383
$300$	−0.886064	−0.0511569
$301$	0.971397	0.0559904
$302$	−15.9405	−0.917273
$303$	12.5289	0.719768
$304$	0.00515665	0.000295754 0
$305$	−12.7740	−0.731436
$306$	7.16158	0.409401
$307$	−16.5649	−0.945410	−0.472705	−	0.881221i	$-0.656722\pi$
$307$	−16.5649	−0.945410	−0.472705	+	0.881221i	$0.656722\pi$
$308$	0.141017	0.00803519
$309$	11.1217	0.632691
$310$	−1.89283	−0.107505
$311$	−25.0292	−1.41927	−0.709637	−	0.704567i	$-0.751141\pi$
$311$	−25.0292	−1.41927	−0.709637	+	0.704567i	$0.751141\pi$
$312$	−11.6333	−0.658606
$313$	19.5353	1.10420	0.552101	−	0.833777i	$-0.313826\pi$
$313$	19.5353	1.10420	0.552101	+	0.833777i	$0.313826\pi$
$314$	11.6518	0.657551
$315$	2.48306	0.139904
$316$	−14.0015	−0.787643
$317$	18.3922	1.03301	0.516503	−	0.856285i	$-0.327233\pi$
$317$	18.3922	1.03301	0.516503	+	0.856285i	$0.327233\pi$
$318$	−4.29846	−0.241046
$319$	1.05051	0.0588175
$320$	4.98283	0.278548
$321$	−10.2440	−0.571766
$322$	7.88572	0.439454
$323$	−1.02905	−0.0572576
$324$	−5.68709	−0.315949
$325$	−5.71328	−0.316916
$326$	−3.68957	−0.204347
$327$	−8.60908	−0.476083
$328$	18.8091	1.03856
$329$	0.611192	0.0336961
$330$	−0.0720816	−0.00396796
$331$	−18.7753	−1.03198	−0.515992	−	0.856593i	$-0.672577\pi$
$331$	−18.7753	−1.03198	−0.515992	+	0.856593i	$0.672577\pi$
$332$	−16.1551	−0.886624
$333$	2.48306	0.136071
$334$	−20.4584	−1.11943
$335$	0.659857	0.0360518
$336$	0.0118605	0.000647044 0
$337$	34.3589	1.87165	0.935824	−	0.352468i	$-0.114658\pi$
$337$	34.3589	1.87165	0.935824	+	0.352468i	$0.114658\pi$
$338$	−17.2087	−0.936032
$339$	7.04779	0.382784
$340$	−4.05688	−0.220015
$341$	0.247210	0.0133872
$342$	−0.680059	−0.0367734
$343$	−1.00000	−0.0539949
$344$	−2.75101	−0.148325
$345$	6.47126	0.348401
$346$	17.2579	0.927790
$347$	9.88104	0.530442	0.265221	−	0.964188i	$-0.414555\pi$
$347$	9.88104	0.530442	0.265221	+	0.964188i	$0.414555\pi$
$348$	−8.13465	−0.436063
$349$	5.57413	0.298376	0.149188	−	0.988809i	$-0.452334\pi$
$349$	5.57413	0.298376	0.149188	+	0.988809i	$0.452334\pi$
$350$	0.876141	0.0468317
$351$	22.5232	1.20220
$352$	−0.646465	−0.0344567
$353$	35.3560	1.88181	0.940904	−	0.338672i	$-0.109978\pi$
$353$	35.3560	1.88181	0.940904	+	0.338672i	$0.109978\pi$
$354$	4.88825	0.259807
$355$	15.1600	0.804612
$356$	12.2291	0.648139
$357$	−2.36685	−0.125267
$358$	1.07121	0.0566152
$359$	−16.9427	−0.894201	−0.447101	−	0.894484i	$-0.647543\pi$
$359$	−16.9427	−0.894201	−0.447101	+	0.894484i	$0.647543\pi$
$360$	−7.03206	−0.370622
$361$	−18.9023	−0.994857
$362$	−2.46856	−0.129745
$363$	−7.89946	−0.414614
$364$	−7.04091	−0.369044
$365$	10.1944	0.533597
$366$	8.04679	0.420612
$367$	7.53502	0.393325	0.196662	−	0.980471i	$-0.436990\pi$
$367$	7.53502	0.393325	0.196662	+	0.980471i	$0.436990\pi$
$368$	−0.148473	−0.00773971
$369$	−16.4914	−0.858510
$370$	0.876141	0.0455484
$371$	−6.82366	−0.354267
$372$	−1.91427	−0.0992501
$373$	−22.7257	−1.17669	−0.588347	−	0.808609i	$-0.700221\pi$
$373$	−22.7257	−1.17669	−0.588347	+	0.808609i	$0.700221\pi$
$374$	−0.330028	−0.0170654
$375$	0.718988	0.0371284
$376$	−1.73091	−0.0892647
$377$	−52.4516	−2.70139
$378$	−3.45397	−0.177653
$379$	22.4081	1.15102	0.575512	−	0.817793i	$-0.304803\pi$
$379$	22.4081	1.15102	0.575512	+	0.817793i	$0.304803\pi$
$380$	0.385238	0.0197623
$381$	−6.11109	−0.313080
$382$	18.0677	0.924424
$383$	−24.0313	−1.22794	−0.613971	−	0.789329i	$-0.710429\pi$
$383$	−24.0313	−1.22794	−0.613971	+	0.789329i	$0.710429\pi$
$384$	4.98511	0.254395
$385$	−0.114427	−0.00583174
$386$	−5.23011	−0.266206
$387$	2.41203	0.122611
$388$	−6.29308	−0.319483
$389$	−17.1547	−0.869776	−0.434888	−	0.900485i	$-0.643212\pi$
$389$	−17.1547	−0.869776	−0.434888	+	0.900485i	$0.643212\pi$
$390$	3.59899	0.182242
$391$	29.6289	1.49840
$392$	2.83202	0.143039
$393$	4.35918	0.219891
$394$	−17.0872	−0.860839
$395$	11.3613	0.571651
$396$	0.350153	0.0175959
$397$	−23.6825	−1.18859	−0.594294	−	0.804248i	$-0.702568\pi$
$397$	−23.6825	−1.18859	−0.594294	+	0.804248i	$0.702568\pi$
$398$	5.14681	0.257986
$399$	0.224754	0.0112518
$400$	−0.0164961	−0.000824806 0
$401$	−30.8739	−1.54177	−0.770885	−	0.636974i	$-0.780186\pi$
$401$	−30.8739	−1.54177	−0.770885	+	0.636974i	$0.780186\pi$
$402$	−0.415667	−0.0207316
$403$	−12.3430	−0.614851
$404$	−21.4751	−1.06843
$405$	4.61473	0.229308
$406$	8.04355	0.399195
$407$	−0.114427	−0.00567193
$408$	6.70296	0.331846
$409$	19.4230	0.960403	0.480202	−	0.877158i	$-0.340563\pi$
$409$	19.4230	0.960403	0.480202	+	0.877158i	$0.340563\pi$
$410$	−5.81897	−0.287378
$411$	8.38919	0.413808
$412$	−19.0631	−0.939170
$413$	7.75992	0.381841
$414$	19.5807	0.962338
$415$	13.1089	0.643489
$416$	32.2776	1.58254
$417$	−5.15333	−0.252360
$418$	0.0313393	0.00153285
$419$	−26.8830	−1.31332	−0.656659	−	0.754187i	$-0.728031\pi$
$419$	−26.8830	−1.31332	−0.656659	+	0.754187i	$0.728031\pi$
$420$	0.886064	0.0432355
$421$	22.0634	1.07530	0.537652	−	0.843167i	$-0.319311\pi$
$421$	22.0634	1.07530	0.537652	+	0.843167i	$0.319311\pi$
$422$	−0.0705687	−0.00343523
$423$	1.51762	0.0737894
$424$	19.3247	0.938491
$425$	3.29191	0.159681
$426$	−9.54985	−0.462692
$427$	12.7740	0.618177
$428$	17.5587	0.848731
$429$	−0.470041	−0.0226938
$430$	0.851081	0.0410428
$431$	19.0831	0.919200	0.459600	−	0.888126i	$-0.347993\pi$
$431$	19.0831	0.919200	0.459600	+	0.888126i	$0.347993\pi$
$432$	0.0650319	0.00312885
$433$	−5.29735	−0.254574	−0.127287	−	0.991866i	$-0.540627\pi$
$433$	−5.29735	−0.254574	−0.127287	+	0.991866i	$0.540627\pi$
$434$	1.89283	0.0908587
$435$	6.60078	0.316483
$436$	14.7563	0.706699
$437$	−2.81354	−0.134590
$438$	−6.42178	−0.306845
$439$	−29.4245	−1.40435	−0.702177	−	0.712002i	$-0.747789\pi$
$439$	−29.4245	−1.40435	−0.702177	+	0.712002i	$0.747789\pi$
$440$	0.324059	0.0154489
$441$	−2.48306	−0.118241
$442$	16.4781	0.783785
$443$	22.0475	1.04751	0.523754	−	0.851869i	$-0.324531\pi$
$443$	22.0475	1.04751	0.523754	+	0.851869i	$0.324531\pi$
$444$	0.886064	0.0420507
$445$	−9.92316	−0.470403
$446$	−4.77196	−0.225959
$447$	−11.5174	−0.544754
$448$	−4.98283	−0.235416
$449$	31.8846	1.50473	0.752363	−	0.658748i	$-0.228914\pi$
$449$	31.8846	1.50473	0.752363	+	0.658748i	$0.228914\pi$
$450$	2.17551	0.102554
$451$	0.759977	0.0357859
$452$	−12.0802	−0.568206
$453$	13.0813	0.614612
$454$	5.62108	0.263811
$455$	5.71328	0.267842
$456$	−0.636508	−0.0298072
$457$	0.803601	0.0375909	0.0187954	−	0.999823i	$-0.494017\pi$
$457$	0.803601	0.0375909	0.0187954	+	0.999823i	$0.494017\pi$
$458$	7.29526	0.340885
$459$	−12.9776	−0.605741
$460$	−11.0920	−0.517168
$461$	0.311372	0.0145021	0.00725103	−	0.999974i	$-0.497692\pi$
$461$	0.311372	0.0145021	0.00725103	+	0.999974i	$0.497692\pi$
$462$	0.0720816	0.00335354
$463$	3.53814	0.164431	0.0822156	−	0.996615i	$-0.473800\pi$
$463$	3.53814	0.164431	0.0822156	+	0.996615i	$0.473800\pi$
$464$	−0.151445	−0.00703066
$465$	1.55331	0.0720332
$466$	−15.3950	−0.713159
$467$	−16.1538	−0.747510	−0.373755	−	0.927528i	$-0.621930\pi$
$467$	−16.1538	−0.747510	−0.373755	+	0.927528i	$0.621930\pi$
$468$	−17.4830	−0.808150
$469$	−0.659857	−0.0304694
$470$	0.535490	0.0247003
$471$	−9.56185	−0.440587
$472$	−21.9762	−1.01154
$473$	−0.111154	−0.00511087
$474$	−7.15691	−0.328728
$475$	−0.312598	−0.0143430
$476$	4.05688	0.185947
$477$	−16.9435	−0.775790
$478$	20.2293	0.925266
$479$	−15.8324	−0.723400	−0.361700	−	0.932294i	$-0.617804\pi$
$479$	−15.8324	−0.723400	−0.361700	+	0.932294i	$0.617804\pi$
$480$	−4.06199	−0.185403
$481$	5.71328	0.260503
$482$	0.849969	0.0387150
$483$	−6.47126	−0.294453
$484$	13.5400	0.615455
$485$	5.10646	0.231872
$486$	−13.2689	−0.601889
$487$	−31.7753	−1.43988	−0.719938	−	0.694038i	$-0.755830\pi$
$487$	−31.7753	−1.43988	−0.719938	+	0.694038i	$0.755830\pi$
$488$	−36.1762	−1.63762
$489$	3.02778	0.136921
$490$	−0.876141	−0.0395800
$491$	−24.0367	−1.08476	−0.542380	−	0.840133i	$-0.682477\pi$
$491$	−24.0367	−1.08476	−0.542380	+	0.840133i	$0.682477\pi$
$492$	−5.88487	−0.265311
$493$	30.2219	1.36113
$494$	−1.56475	−0.0704015
$495$	−0.284129	−0.0127706
$496$	−0.0356384	−0.00160021
$497$	−15.1600	−0.680021
$498$	−8.25774	−0.370038
$499$	20.4281	0.914486	0.457243	−	0.889342i	$-0.348837\pi$
$499$	20.4281	0.914486	0.457243	+	0.889342i	$0.348837\pi$
$500$	−1.23238	−0.0551135
$501$	16.7888	0.750068
$502$	−1.91379	−0.0854165
$503$	18.4272	0.821629	0.410814	−	0.911719i	$-0.365244\pi$
$503$	18.4272	0.821629	0.410814	+	0.911719i	$0.365244\pi$
$504$	7.03206	0.313233
$505$	17.4258	0.775436
$506$	−0.902339	−0.0401139
$507$	14.1220	0.627181
$508$	10.4747	0.464738
$509$	40.8471	1.81052	0.905258	−	0.424862i	$-0.139677\pi$
$509$	40.8471	1.81052	0.905258	+	0.424862i	$0.139677\pi$
$510$	−2.07369	−0.0918247
$511$	−10.1944	−0.450972
$512$	0.186631	0.00824799
$513$	1.23234	0.0544092
$514$	−13.4427	−0.592931
$515$	15.4685	0.681625
$516$	0.860720	0.0378911
$517$	−0.0699368	−0.00307582
$518$	−0.876141	−0.0384954
$519$	−14.1624	−0.621658
$520$	−16.1801	−0.709544
$521$	−39.1440	−1.71493	−0.857465	−	0.514543i	$-0.827962\pi$
$521$	−39.1440	−1.71493	−0.857465	+	0.514543i	$0.827962\pi$
$522$	19.9726	0.874176
$523$	−14.5951	−0.638200	−0.319100	−	0.947721i	$-0.603381\pi$
$523$	−14.5951	−0.638200	−0.319100	+	0.947721i	$0.603381\pi$
$524$	−7.47181	−0.326408
$525$	−0.718988	−0.0313792
$526$	14.7392	0.642662
$527$	7.11190	0.309799
$528$	−0.00135716	−5.90629e−5 0
$529$	58.0092	2.52214
$530$	−5.97849	−0.259689
$531$	19.2683	0.836174
$532$	−0.385238	−0.0167022
$533$	−37.9452	−1.64359
$534$	6.25095	0.270505
$535$	−14.2478	−0.615988
$536$	1.86873	0.0807167
$537$	−0.879068	−0.0379346
$538$	−10.1073	−0.435756
$539$	0.114427	0.00492872
$540$	4.85834	0.209070
$541$	22.4283	0.964269	0.482134	−	0.876097i	$-0.339862\pi$
$541$	22.4283	0.964269	0.482134	+	0.876097i	$0.339862\pi$
$542$	7.14627	0.306959
$543$	2.02578	0.0869344
$544$	−18.5979	−0.797380
$545$	−11.9739	−0.512904
$546$	−3.59899	−0.154023
$547$	23.6670	1.01193	0.505963	−	0.862555i	$-0.331137\pi$
$547$	23.6670	1.01193	0.505963	+	0.862555i	$0.331137\pi$
$548$	−14.3794	−0.614259
$549$	31.7185	1.35371
$550$	−0.100254	−0.00427485
$551$	−2.86985	−0.122260
$552$	18.3267	0.780038
$553$	−11.3613	−0.483133
$554$	−15.6431	−0.664611
$555$	−0.718988	−0.0305194
$556$	8.83302	0.374604
$557$	22.7481	0.963866	0.481933	−	0.876208i	$-0.339935\pi$
$557$	22.7481	0.963866	0.481933	+	0.876208i	$0.339935\pi$
$558$	4.70000	0.198967
$559$	5.54986	0.234734
$560$	0.0164961	0.000697088 0
$561$	0.270831	0.0114345
$562$	13.0911	0.552215
$563$	−23.2077	−0.978087	−0.489044	−	0.872259i	$-0.662654\pi$
$563$	−23.2077	−0.978087	−0.489044	+	0.872259i	$0.662654\pi$
$564$	0.541555	0.0228036
$565$	9.80238	0.412389
$566$	19.0464	0.800581
$567$	−4.61473	−0.193801
$568$	42.9335	1.80145
$569$	16.2779	0.682406	0.341203	−	0.939990i	$-0.389166\pi$
$569$	16.2779	0.682406	0.341203	+	0.939990i	$0.389166\pi$
$570$	0.196917	0.00824793
$571$	31.5538	1.32048	0.660242	−	0.751053i	$-0.270454\pi$
$571$	31.5538	1.32048	0.660242	+	0.751053i	$0.270454\pi$
$572$	0.805670	0.0336867
$573$	−14.8269	−0.619403
$574$	5.81897	0.242879
$575$	9.00051	0.375347
$576$	−12.3726	−0.515527
$577$	21.3388	0.888347	0.444174	−	0.895941i	$-0.353497\pi$
$577$	21.3388	0.888347	0.444174	+	0.895941i	$0.353497\pi$
$578$	5.39993	0.224607
$579$	4.29199	0.178369
$580$	−11.3140	−0.469789
$581$	−13.1089	−0.543848
$582$	−3.21674	−0.133338
$583$	0.780810	0.0323379
$584$	28.8706	1.19467
$585$	14.1864	0.586535
$586$	11.8495	0.489499
$587$	3.57151	0.147412	0.0737059	−	0.997280i	$-0.476517\pi$
$587$	3.57151	0.147412	0.0737059	+	0.997280i	$0.476517\pi$
$588$	−0.886064	−0.0365407
$589$	−0.675341	−0.0278270
$590$	6.79879	0.279902
$591$	14.0222	0.576798
$592$	0.0164961	0.000677986 0
$593$	26.3711	1.08293	0.541467	−	0.840722i	$-0.317869\pi$
$593$	26.3711	1.08293	0.541467	+	0.840722i	$0.317869\pi$
$594$	0.395227	0.0162164
$595$	−3.29191	−0.134955
$596$	19.7413	0.808635
$597$	−4.22363	−0.172861
$598$	45.0533	1.84237
$599$	26.1845	1.06987	0.534934	−	0.844894i	$-0.320336\pi$
$599$	26.1845	1.06987	0.534934	+	0.844894i	$0.320336\pi$
$600$	2.03619	0.0831270
$601$	−16.1387	−0.658309	−0.329155	−	0.944276i	$-0.606764\pi$
$601$	−16.1387	−0.658309	−0.329155	+	0.944276i	$0.606764\pi$
$602$	−0.851081	−0.0346875
$603$	−1.63846	−0.0667233
$604$	−22.4218	−0.912332
$605$	−10.9869	−0.446681
$606$	−10.9771	−0.445914
$607$	−30.1568	−1.22403	−0.612014	−	0.790847i	$-0.709640\pi$
$607$	−30.1568	−1.22403	−0.612014	+	0.790847i	$0.709640\pi$
$608$	1.76605	0.0716227
$609$	−6.60078	−0.267477
$610$	11.1918	0.453143
$611$	3.49191	0.141267
$612$	10.0735	0.407195
$613$	−38.4084	−1.55130	−0.775651	−	0.631163i	$-0.782578\pi$
$613$	−38.4084	−1.55130	−0.775651	+	0.631163i	$0.782578\pi$
$614$	14.5132	0.585705
$615$	4.77523	0.192556
$616$	−0.324059	−0.0130567
$617$	−23.1570	−0.932264	−0.466132	−	0.884715i	$-0.654353\pi$
$617$	−23.1570	−0.932264	−0.466132	+	0.884715i	$0.654353\pi$
$618$	−9.74418	−0.391969
$619$	24.4919	0.984411	0.492205	−	0.870479i	$-0.336191\pi$
$619$	24.4919	0.984411	0.492205	+	0.870479i	$0.336191\pi$
$620$	−2.66244	−0.106926
$621$	−35.4823	−1.42386
$622$	21.9291	0.879277
$623$	9.92316	0.397563
$624$	0.0677624	0.00271267
$625$	1.00000	0.0400000
$626$	−17.1157	−0.684081
$627$	−0.0257180	−0.00102708
$628$	16.3894	0.654009
$629$	−3.29191	−0.131257
$630$	−2.17551	−0.0866743
$631$	−9.15512	−0.364459	−0.182230	−	0.983256i	$-0.558331\pi$
$631$	−9.15512	−0.364459	−0.182230	+	0.983256i	$0.558331\pi$
$632$	32.1755	1.27987
$633$	0.0579108	0.00230175
$634$	−16.1141	−0.639974
$635$	−8.49956	−0.337295
$636$	−6.04620	−0.239747
$637$	−5.71328	−0.226368
$638$	−0.920399	−0.0364389
$639$	−37.6432	−1.48914
$640$	6.93351	0.274071
$641$	15.0890	0.595979	0.297989	−	0.954569i	$-0.403684\pi$
$641$	15.0890	0.595979	0.297989	+	0.954569i	$0.403684\pi$
$642$	8.97522	0.354223
$643$	−16.2653	−0.641441	−0.320720	−	0.947174i	$-0.603925\pi$
$643$	−16.2653	−0.641441	−0.320720	+	0.947174i	$0.603925\pi$
$644$	11.0920	0.437087
$645$	−0.698423	−0.0275004
$646$	0.901589	0.0354726
$647$	33.2026	1.30533	0.652663	−	0.757648i	$-0.273652\pi$
$647$	33.2026	1.30533	0.652663	+	0.757648i	$0.273652\pi$
$648$	13.0690	0.513399
$649$	−0.887944	−0.0348549
$650$	5.00564	0.196337
$651$	−1.55331	−0.0608791
$652$	−5.18974	−0.203246
$653$	16.0514	0.628140	0.314070	−	0.949400i	$-0.398307\pi$
$653$	16.0514	0.628140	0.314070	+	0.949400i	$0.398307\pi$
$654$	7.54277	0.294946
$655$	6.06293	0.236898
$656$	−0.109560	−0.00427761
$657$	−25.3131	−0.987560
$658$	−0.535490	−0.0208756
$659$	−17.9712	−0.700060	−0.350030	−	0.936738i	$-0.613829\pi$
$659$	−17.9712	−0.700060	−0.350030	+	0.936738i	$0.613829\pi$
$660$	−0.101390	−0.00394659
$661$	−2.12294	−0.0825727	−0.0412863	−	0.999147i	$-0.513146\pi$
$661$	−2.12294	−0.0825727	−0.0412863	+	0.999147i	$0.513146\pi$
$662$	16.4498	0.639341
$663$	−13.5225	−0.525169
$664$	37.1246	1.44071
$665$	0.312598	0.0121220
$666$	−2.17551	−0.0842992
$667$	82.6305	3.19947
$668$	−28.7767	−1.11340
$669$	3.91601	0.151402
$670$	−0.578128	−0.0223350
$671$	−1.46169	−0.0564279
$672$	4.06199	0.156694
$673$	38.6333	1.48920	0.744601	−	0.667509i	$-0.232640\pi$
$673$	38.6333	1.48920	0.744601	+	0.667509i	$0.232640\pi$
$674$	−30.1032	−1.15953
$675$	−3.94225	−0.151737
$676$	−24.2057	−0.930990
$677$	35.6725	1.37101	0.685503	−	0.728070i	$-0.259583\pi$
$677$	35.6725	1.37101	0.685503	+	0.728070i	$0.259583\pi$
$678$	−6.17486	−0.237144
$679$	−5.10646	−0.195968
$680$	9.32276	0.357512
$681$	−4.61283	−0.176764
$682$	−0.216591	−0.00829369
$683$	6.22776	0.238299	0.119149	−	0.992876i	$-0.461983\pi$
$683$	6.22776	0.238299	0.119149	+	0.992876i	$0.461983\pi$
$684$	−0.956568	−0.0365753
$685$	11.6680	0.445813
$686$	0.876141	0.0334512
$687$	−5.98672	−0.228408
$688$	0.0160243	0.000610920 0
$689$	−38.9854	−1.48523
$690$	−5.66974	−0.215843
$691$	−15.9806	−0.607932	−0.303966	−	0.952683i	$-0.598311\pi$
$691$	−15.9806	−0.607932	−0.303966	+	0.952683i	$0.598311\pi$
$692$	24.2749	0.922792
$693$	0.284129	0.0107932
$694$	−8.65719	−0.328622
$695$	−7.16747	−0.271878
$696$	18.6935	0.708577
$697$	21.8635	0.828141
$698$	−4.88373	−0.184852
$699$	12.6336	0.477846
$700$	1.23238	0.0465794
$701$	22.0812	0.833996	0.416998	−	0.908907i	$-0.363082\pi$
$701$	22.0812	0.833996	0.416998	+	0.908907i	$0.363082\pi$
$702$	−19.7335	−0.744793
$703$	0.312598	0.0117899
$704$	0.570170	0.0214891
$705$	−0.439440	−0.0165503
$706$	−30.9768	−1.16583
$707$	−17.4258	−0.655363
$708$	6.87579	0.258408
$709$	7.57960	0.284658	0.142329	−	0.989819i	$-0.454541\pi$
$709$	7.57960	0.284658	0.142329	+	0.989819i	$0.454541\pi$
$710$	−13.2823	−0.498477
$711$	−28.2108	−1.05799
$712$	−28.1026	−1.05319
$713$	19.4448	0.728215
$714$	2.07369	0.0776060
$715$	−0.653753	−0.0244490
$716$	1.50676	0.0563102
$717$	−16.6008	−0.619967
$718$	14.8442	0.553981
$719$	35.4884	1.32349	0.661747	−	0.749727i	$-0.269815\pi$
$719$	35.4884	1.32349	0.661747	+	0.749727i	$0.269815\pi$
$720$	0.0409608	0.00152652
$721$	−15.4685	−0.576079
$722$	16.5611	0.616339
$723$	−0.697510	−0.0259407
$724$	−3.47227	−0.129046
$725$	9.18065	0.340961
$726$	6.92104	0.256864
$727$	45.6137	1.69172	0.845858	−	0.533408i	$-0.179089\pi$
$727$	45.6137	1.69172	0.845858	+	0.533408i	$0.179089\pi$
$728$	16.1801	0.599675
$729$	−2.95534	−0.109457
$730$	−8.93169	−0.330577
$731$	−3.19775	−0.118273
$732$	11.3186	0.418346
$733$	−48.7585	−1.80094	−0.900469	−	0.434921i	$-0.856776\pi$
$733$	−48.7585	−1.80094	−0.900469	+	0.434921i	$0.856776\pi$
$734$	−6.60174	−0.243675
$735$	0.718988	0.0265203
$736$	−50.8491	−1.87432
$737$	0.0755055	0.00278128
$738$	14.4488	0.531869
$739$	29.7412	1.09405	0.547023	−	0.837118i	$-0.315761\pi$
$739$	29.7412	1.09405	0.547023	+	0.837118i	$0.315761\pi$
$740$	1.23238	0.0453031
$741$	1.28408	0.0471720
$742$	5.97849	0.219477
$743$	−17.4951	−0.641835	−0.320917	−	0.947107i	$-0.603991\pi$
$743$	−17.4951	−0.641835	−0.320917	+	0.947107i	$0.603991\pi$
$744$	4.39901	0.161276
$745$	−16.0189	−0.586887
$746$	19.9110	0.728992
$747$	−32.5501	−1.19094
$748$	−0.464216	−0.0169734
$749$	14.2478	0.520604
$750$	−0.629935	−0.0230020
$751$	−7.80252	−0.284718	−0.142359	−	0.989815i	$-0.545469\pi$
$751$	−7.80252	−0.284718	−0.142359	+	0.989815i	$0.545469\pi$
$752$	0.0100823	0.000367663 0
$753$	1.57051	0.0572327
$754$	45.9550	1.67358
$755$	18.1940	0.662147
$756$	−4.85834	−0.176696
$757$	18.2138	0.661993	0.330996	−	0.943632i	$-0.392615\pi$
$757$	18.2138	0.661993	0.330996	+	0.943632i	$0.392615\pi$
$758$	−19.6326	−0.713089
$759$	0.740487	0.0268780
$760$	−0.885283	−0.0321126
$761$	40.3367	1.46220	0.731102	−	0.682268i	$-0.239006\pi$
$761$	40.3367	1.46220	0.731102	+	0.682268i	$0.239006\pi$
$762$	5.35417	0.193961
$763$	11.9739	0.433483
$764$	25.4140	0.919444
$765$	−8.17401	−0.295532
$766$	21.0548	0.760741
$767$	44.3346	1.60083
$768$	−11.5329	−0.416156
$769$	20.4279	0.736648	0.368324	−	0.929697i	$-0.379932\pi$
$769$	20.4279	0.736648	0.368324	+	0.929697i	$0.379932\pi$
$770$	0.100254	0.00361291
$771$	11.0315	0.397289
$772$	−7.35665	−0.264771
$773$	−18.8969	−0.679676	−0.339838	−	0.940484i	$-0.610372\pi$
$773$	−18.8969	−0.679676	−0.339838	+	0.940484i	$0.610372\pi$
$774$	−2.11328	−0.0759603
$775$	2.16041	0.0776044
$776$	14.4616	0.519141
$777$	0.718988	0.0257936
$778$	15.0299	0.538849
$779$	−2.07615	−0.0743857
$780$	5.06233	0.181260
$781$	1.73472	0.0620731
$782$	−25.9591	−0.928296
$783$	−36.1925	−1.29341
$784$	−0.0164961	−0.000589147 0
$785$	−13.2990	−0.474663
$786$	−3.81925	−0.136228
$787$	−3.39723	−0.121098	−0.0605490	−	0.998165i	$-0.519285\pi$
$787$	−3.39723	−0.121098	−0.0605490	+	0.998165i	$0.519285\pi$
$788$	−24.0347	−0.856201
$789$	−12.0955	−0.430610
$790$	−9.95414	−0.354153
$791$	−9.80238	−0.348532
$792$	−0.804657	−0.0285923
$793$	72.9813	2.59164
$794$	20.7492	0.736361
$795$	4.90613	0.174002
$796$	7.23947	0.256596
$797$	29.7760	1.05472	0.527360	−	0.849642i	$-0.323182\pi$
$797$	29.7760	1.05472	0.527360	+	0.849642i	$0.323182\pi$
$798$	−0.196917	−0.00697077
$799$	−2.01199	−0.0711791
$800$	−5.64958	−0.199743
$801$	24.6398	0.870603
$802$	27.0499	0.955166
$803$	1.16651	0.0411652
$804$	−0.584676	−0.0206199
$805$	−9.00051	−0.317226
$806$	10.8143	0.380916
$807$	8.29434	0.291975
$808$	49.3501	1.73613
$809$	17.0974	0.601111	0.300556	−	0.953764i	$-0.402828\pi$
$809$	17.0974	0.601111	0.300556	+	0.953764i	$0.402828\pi$
$810$	−4.04316	−0.142062
$811$	−24.0341	−0.843951	−0.421975	−	0.906607i	$-0.638663\pi$
$811$	−24.0341	−0.843951	−0.421975	+	0.906607i	$0.638663\pi$
$812$	11.3140	0.397044
$813$	−5.86445	−0.205675
$814$	0.100254	0.00351391
$815$	4.21116	0.147511
$816$	−0.0390438	−0.00136681
$817$	0.303657	0.0106236
$818$	−17.0173	−0.594994
$819$	−14.1864	−0.495712
$820$	−8.18494	−0.285830
$821$	26.8560	0.937282	0.468641	−	0.883389i	$-0.344744\pi$
$821$	26.8560	0.937282	0.468641	+	0.883389i	$0.344744\pi$
$822$	−7.35012	−0.256365
$823$	−29.2431	−1.01935	−0.509675	−	0.860367i	$-0.670234\pi$
$823$	−29.2431	−1.01935	−0.509675	+	0.860367i	$0.670234\pi$
$824$	43.8072	1.52610
$825$	0.0822717	0.00286433
$826$	−6.79879	−0.236560
$827$	−1.40966	−0.0490185	−0.0245093	−	0.999700i	$-0.507802\pi$
$827$	−1.40966	−0.0490185	−0.0245093	+	0.999700i	$0.507802\pi$
$828$	27.5421	0.957154
$829$	−19.8577	−0.689685	−0.344843	−	0.938661i	$-0.612068\pi$
$829$	−19.8577	−0.689685	−0.344843	+	0.938661i	$0.612068\pi$
$830$	−11.4852	−0.398658
$831$	12.8372	0.445317
$832$	−28.4683	−0.986959
$833$	3.29191	0.114058
$834$	4.51504	0.156343
$835$	23.3506	0.808080
$836$	0.0440817	0.00152460
$837$	−8.51690	−0.294387
$838$	23.5533	0.813635
$839$	−22.8133	−0.787604	−0.393802	−	0.919195i	$-0.628840\pi$
$839$	−22.8133	−0.787604	−0.393802	+	0.919195i	$0.628840\pi$
$840$	−2.03619	−0.0702552
$841$	55.2843	1.90636
$842$	−19.3307	−0.666178
$843$	−10.7430	−0.370007
$844$	−0.0992615	−0.00341672
$845$	19.6415	0.675689
$846$	−1.32965	−0.0457144
$847$	10.9869	0.377515
$848$	−0.112564	−0.00386546
$849$	−15.6301	−0.536423
$850$	−2.88418	−0.0989266
$851$	−9.00051	−0.308534
$852$	−13.4328	−0.460199
$853$	−6.33523	−0.216914	−0.108457	−	0.994101i	$-0.534591\pi$
$853$	−6.33523	−0.216914	−0.108457	+	0.994101i	$0.534591\pi$
$854$	−11.1918	−0.382976
$855$	0.776198	0.0265454
$856$	−40.3501	−1.37914
$857$	−50.4396	−1.72299	−0.861493	−	0.507770i	$-0.830470\pi$
$857$	−50.4396	−1.72299	−0.861493	+	0.507770i	$0.830470\pi$
$858$	0.411822	0.0140594
$859$	7.08800	0.241840	0.120920	−	0.992662i	$-0.461416\pi$
$859$	7.08800	0.241840	0.120920	+	0.992662i	$0.461416\pi$
$860$	1.19713	0.0408217
$861$	−4.77523	−0.162739
$862$	−16.7195	−0.569468
$863$	−17.6572	−0.601058	−0.300529	−	0.953773i	$-0.597163\pi$
$863$	−17.6572	−0.601058	−0.300529	+	0.953773i	$0.597163\pi$
$864$	22.2721	0.757712
$865$	−19.6976	−0.669739
$866$	4.64122	0.157715
$867$	−4.43134	−0.150496
$868$	2.66244	0.0903692
$869$	1.30004	0.0441010
$870$	−5.78322	−0.196069
$871$	−3.76995	−0.127740
$872$	−33.9102	−1.14835
$873$	−12.6796	−0.429140
$874$	2.46506	0.0833819
$875$	−1.00000	−0.0338062
$876$	−9.03285	−0.305192
$877$	10.9493	0.369732	0.184866	−	0.982764i	$-0.440815\pi$
$877$	10.9493	0.369732	0.184866	+	0.982764i	$0.440815\pi$
$878$	25.7800	0.870033
$879$	−9.72408	−0.327985
$880$	−0.00188760	−6.36310e−5 0
$881$	−6.77764	−0.228345	−0.114172	−	0.993461i	$-0.536422\pi$
$881$	−6.77764	−0.228345	−0.114172	+	0.993461i	$0.536422\pi$
$882$	2.17551	0.0732532
$883$	6.79285	0.228598	0.114299	−	0.993446i	$-0.463538\pi$
$883$	6.79285	0.228598	0.114299	+	0.993446i	$0.463538\pi$
$884$	23.1781	0.779562
$885$	−5.57929	−0.187546
$886$	−19.3167	−0.648958
$887$	−30.1072	−1.01090	−0.505451	−	0.862856i	$-0.668674\pi$
$887$	−30.1072	−1.01090	−0.505451	+	0.862856i	$0.668674\pi$
$888$	−2.03619	−0.0683300
$889$	8.49956	0.285066
$890$	8.69409	0.291427
$891$	0.528050	0.0176903
$892$	−6.71221	−0.224741
$893$	0.191057	0.00639349
$894$	10.0909	0.337489
$895$	−1.22265	−0.0408685
$896$	−6.93351	−0.231632
$897$	−36.9721	−1.23446
$898$	−27.9354	−0.932217
$899$	19.8340	0.661501
$900$	3.06006	0.102002
$901$	22.4629	0.748347
$902$	−0.665847	−0.0221703
$903$	0.698423	0.0232421
$904$	27.7605	0.923301
$905$	2.81754	0.0936581
$906$	−11.4610	−0.380768
$907$	21.2242	0.704736	0.352368	−	0.935861i	$-0.385376\pi$
$907$	21.2242	0.704736	0.352368	+	0.935861i	$0.385376\pi$
$908$	7.90659	0.262389
$909$	−43.2691	−1.43515
$910$	−5.00564	−0.165935
$911$	−23.6039	−0.782031	−0.391016	−	0.920384i	$-0.627876\pi$
$911$	−23.6039	−0.782031	−0.391016	+	0.920384i	$0.627876\pi$
$912$	0.00370757	0.000122770 0
$913$	1.50001	0.0496430
$914$	−0.704068	−0.0232885
$915$	−9.18435	−0.303625
$916$	10.2615	0.339049
$917$	−6.06293	−0.200216
$918$	11.3702	0.375272
$919$	−5.34575	−0.176340	−0.0881700	−	0.996105i	$-0.528102\pi$
$919$	−5.34575	−0.176340	−0.0881700	+	0.996105i	$0.528102\pi$
$920$	25.4896	0.840368
$921$	−11.9100	−0.392447
$922$	−0.272806	−0.00898440
$923$	−86.6135	−2.85092
$924$	0.101390	0.00333547
$925$	−1.00000	−0.0328798
$926$	−3.09991	−0.101869
$927$	−38.4092	−1.26153
$928$	−51.8669	−1.70261
$929$	−49.8629	−1.63595	−0.817975	−	0.575254i	$-0.804903\pi$
$929$	−49.8629	−1.63595	−0.817975	+	0.575254i	$0.804903\pi$
$930$	−1.36092	−0.0446264
$931$	−0.312598	−0.0102450
$932$	−21.6545	−0.709317
$933$	−17.9957	−0.589152
$934$	14.1530	0.463101
$935$	0.376684	0.0123189
$936$	40.1761	1.31320
$937$	−25.2218	−0.823962	−0.411981	−	0.911193i	$-0.635163\pi$
$937$	−25.2218	−0.823962	−0.411981	+	0.911193i	$0.635163\pi$
$938$	0.578128	0.0188766
$939$	14.0457	0.458363
$940$	0.753218	0.0245673
$941$	−11.4341	−0.372740	−0.186370	−	0.982480i	$-0.559672\pi$
$941$	−11.4341	−0.372740	−0.186370	+	0.982480i	$0.559672\pi$
$942$	8.37753	0.272955
$943$	59.7777	1.94663
$944$	0.128009	0.00416632
$945$	3.94225	0.128242
$946$	0.0973866	0.00316631
$947$	43.4845	1.41306	0.706529	−	0.707684i	$-0.250260\pi$
$947$	43.4845	1.41306	0.706529	+	0.707684i	$0.250260\pi$
$948$	−10.0669	−0.326957
$949$	−58.2431	−1.89065
$950$	0.273880	0.00888584
$951$	13.2237	0.428809
$952$	−9.32276	−0.302152
$953$	−18.4119	−0.596418	−0.298209	−	0.954501i	$-0.596389\pi$
$953$	−18.4119	−0.596418	−0.298209	+	0.954501i	$0.596389\pi$
$954$	14.8449	0.480622
$955$	−20.6219	−0.667309
$956$	28.4544	0.920282
$957$	0.755307	0.0244156
$958$	13.8714	0.448165
$959$	−11.6680	−0.376781
$960$	3.58259	0.115628
$961$	−26.3326	−0.849439
$962$	−5.00564	−0.161388
$963$	35.3782	1.14005
$964$	1.19556	0.0385065
$965$	5.96948	0.192164
$966$	5.66974	0.182421
$967$	−52.2987	−1.68181	−0.840906	−	0.541182i	$-0.817977\pi$
$967$	−52.2987	−1.68181	−0.840906	+	0.541182i	$0.817977\pi$
$968$	−31.1151	−1.00008
$969$	−0.739872	−0.0237681
$970$	−4.47398	−0.143651
$971$	42.2725	1.35659	0.678295	−	0.734790i	$-0.262719\pi$
$971$	42.2725	1.35659	0.678295	+	0.734790i	$0.262719\pi$
$972$	−18.6640	−0.598647
$973$	7.16747	0.229779
$974$	27.8397	0.892040
$975$	−4.10778	−0.131554
$976$	0.210721	0.00674502
$977$	61.4953	1.96741	0.983704	−	0.179795i	$-0.0575434\pi$
$977$	61.4953	1.96741	0.983704	+	0.179795i	$0.0575434\pi$
$978$	−2.65276	−0.0848260
$979$	−1.13548	−0.0362900
$980$	−1.23238	−0.0393668
$981$	29.7318	0.949263
$982$	21.0595	0.672037
$983$	−19.0773	−0.608471	−0.304235	−	0.952597i	$-0.598401\pi$
$983$	−19.0773	−0.608471	−0.304235	+	0.952597i	$0.598401\pi$
$984$	13.5235	0.431114
$985$	19.5027	0.621409
$986$	−26.4787	−0.843253
$987$	0.439440	0.0139875
$988$	−2.20097	−0.0700223
$989$	−8.74307	−0.278013
$990$	0.248937	0.00791173
$991$	−12.9195	−0.410403	−0.205201	−	0.978720i	$-0.565785\pi$
$991$	−12.9195	−0.410403	−0.205201	+	0.978720i	$0.565785\pi$
$992$	−12.2054	−0.387523
$993$	−13.4992	−0.428385
$994$	13.2823	0.421290
$995$	−5.87440	−0.186231
$996$	−11.6153	−0.368045
$997$	14.8034	0.468829	0.234415	−	0.972137i	$-0.424683\pi$
$997$	14.8034	0.468829	0.234415	+	0.972137i	$0.424683\pi$
$998$	−17.8979	−0.566547
$999$	3.94225	0.124727

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1295.2.a.h.1.4	✓	12
5.4	even	2		6475.2.a.r.1.9		12
7.6	odd	2		9065.2.a.m.1.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1295.2.a.h.1.4	✓	12	1.1	even	1	trivial
6475.2.a.r.1.9		12	5.4	even	2
9065.2.a.m.1.4		12	7.6	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:	\( N \)	\(=\)	\( 1295 = 5 \cdot 7 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1295.a (trivial)

\(f(q)\)	\(=\)	\(q-0.876141 q^{2} +0.718988 q^{3} -1.23238 q^{4} +1.00000 q^{5} -0.629935 q^{6} -1.00000 q^{7} +2.83202 q^{8} -2.48306 q^{9} -0.876141 q^{10} +0.114427 q^{11} -0.886064 q^{12} -5.71328 q^{13} +0.876141 q^{14} +0.718988 q^{15} -0.0164961 q^{16} +3.29191 q^{17} +2.17551 q^{18} -0.312598 q^{19} -1.23238 q^{20} -0.718988 q^{21} -0.100254 q^{22} +9.00051 q^{23} +2.03619 q^{24} +1.00000 q^{25} +5.00564 q^{26} -3.94225 q^{27} +1.23238 q^{28} +9.18065 q^{29} -0.629935 q^{30} +2.16041 q^{31} -5.64958 q^{32} +0.0822717 q^{33} -2.88418 q^{34} -1.00000 q^{35} +3.06006 q^{36} -1.00000 q^{37} +0.273880 q^{38} -4.10778 q^{39} +2.83202 q^{40} +6.64159 q^{41} +0.629935 q^{42} -0.971397 q^{43} -0.141017 q^{44} -2.48306 q^{45} -7.88572 q^{46} -0.611192 q^{47} -0.0118605 q^{48} +1.00000 q^{49} -0.876141 q^{50} +2.36685 q^{51} +7.04091 q^{52} +6.82366 q^{53} +3.45397 q^{54} +0.114427 q^{55} -2.83202 q^{56} -0.224754 q^{57} -8.04355 q^{58} -7.75992 q^{59} -0.886064 q^{60} -12.7740 q^{61} -1.89283 q^{62} +2.48306 q^{63} +4.98283 q^{64} -5.71328 q^{65} -0.0720816 q^{66} +0.659857 q^{67} -4.05688 q^{68} +6.47126 q^{69} +0.876141 q^{70} +15.1600 q^{71} -7.03206 q^{72} +10.1944 q^{73} +0.876141 q^{74} +0.718988 q^{75} +0.385238 q^{76} -0.114427 q^{77} +3.59899 q^{78} +11.3613 q^{79} -0.0164961 q^{80} +4.61473 q^{81} -5.81897 q^{82} +13.1089 q^{83} +0.886064 q^{84} +3.29191 q^{85} +0.851081 q^{86} +6.60078 q^{87} +0.324059 q^{88} -9.92316 q^{89} +2.17551 q^{90} +5.71328 q^{91} -11.0920 q^{92} +1.55331 q^{93} +0.535490 q^{94} -0.312598 q^{95} -4.06199 q^{96} +5.10646 q^{97} -0.876141 q^{98} -0.284129 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 5 q^{2} + 4 q^{3} + 15 q^{4} + 12 q^{5} + 6 q^{6} - 12 q^{7} + 21 q^{8} + 18 q^{9} + 5 q^{10} - 4 q^{11} + 8 q^{12} + 6 q^{13} - 5 q^{14} + 4 q^{15} + 21 q^{16} + 20 q^{17} + 14 q^{18} - 4 q^{19}+ \cdots - 24 q^{99}+O(q^{100}) \) 12 * q + 5 * q^2 + 4 * q^3 + 15 * q^4 + 12 * q^5 + 6 * q^6 - 12 * q^7 + 21 * q^8 + 18 * q^9 + 5 * q^10 - 4 * q^11 + 8 * q^12 + 6 * q^13 - 5 * q^14 + 4 * q^15 + 21 * q^16 + 20 * q^17 + 14 * q^18 - 4 * q^19 + 15 * q^20 - 4 * q^21 + 2 * q^22 + 20 * q^23 + 4 * q^24 + 12 * q^25 + 6 * q^26 + 10 * q^27 - 15 * q^28 - 12 * q^29 + 6 * q^30 + 47 * q^32 + 20 * q^33 - 28 * q^34 - 12 * q^35 + 39 * q^36 - 12 * q^37 + 8 * q^38 + 21 * q^40 + 24 * q^41 - 6 * q^42 + 14 * q^43 - 16 * q^44 + 18 * q^45 + 20 * q^46 + 18 * q^47 - 19 * q^48 + 12 * q^49 + 5 * q^50 - 20 * q^51 + 22 * q^52 + 36 * q^53 - 46 * q^54 - 4 * q^55 - 21 * q^56 + 36 * q^57 + 28 * q^58 + 4 * q^59 + 8 * q^60 - 39 * q^62 - 18 * q^63 + 9 * q^64 + 6 * q^65 - 21 * q^66 + 6 * q^67 - 6 * q^68 - 6 * q^69 - 5 * q^70 - 12 * q^71 + 17 * q^72 + 32 * q^73 - 5 * q^74 + 4 * q^75 - 13 * q^76 + 4 * q^77 + 74 * q^78 + 14 * q^79 + 21 * q^80 - 16 * q^81 - 26 * q^82 - 18 * q^83 - 8 * q^84 + 20 * q^85 - 36 * q^86 - 18 * q^87 + 27 * q^88 + 14 * q^90 - 6 * q^91 + 39 * q^92 + 52 * q^93 + 38 * q^94 - 4 * q^95 - 53 * q^96 + 38 * q^97 + 5 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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