LMFDB - Embedded newform 7935.2.a.bh.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7935,2,Mod(1,7935)] 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("7935.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7935, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.a (trivial)

Newform invariants

comment:select newform

sage:traces = [8,0,8,8,-8,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$63.3612940039$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 12x^{6} - 2x^{5} + 44x^{4} + 12x^{3} - 50x^{2} - 8x + 16 $ x^8 - 12x^6 - 2x^5 + 44x^4 + 12x^3 - 50x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.37125$ of defining polynomial
Character	$\chi$	$=$	7935.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.37125 q^{2} +1.00000 q^{3} -0.119679 q^{4} -1.00000 q^{5} -1.37125 q^{6} +3.47202 q^{7} +2.90661 q^{8} +1.00000 q^{9} +1.37125 q^{10} -2.80654 q^{11} -0.119679 q^{12} +3.04207 q^{13} -4.76100 q^{14} -1.00000 q^{15} -3.74632 q^{16} -5.76511 q^{17} -1.37125 q^{18} +0.670825 q^{19} +0.119679 q^{20} +3.47202 q^{21} +3.84846 q^{22} +2.90661 q^{24} +1.00000 q^{25} -4.17144 q^{26} +1.00000 q^{27} -0.415527 q^{28} -5.26414 q^{29} +1.37125 q^{30} +7.53104 q^{31} -0.676078 q^{32} -2.80654 q^{33} +7.90539 q^{34} -3.47202 q^{35} -0.119679 q^{36} -6.45981 q^{37} -0.919868 q^{38} +3.04207 q^{39} -2.90661 q^{40} +2.07761 q^{41} -4.76100 q^{42} +2.75944 q^{43} +0.335883 q^{44} -1.00000 q^{45} +5.29345 q^{47} -3.74632 q^{48} +5.05492 q^{49} -1.37125 q^{50} -5.76511 q^{51} -0.364072 q^{52} -0.442976 q^{53} -1.37125 q^{54} +2.80654 q^{55} +10.0918 q^{56} +0.670825 q^{57} +7.21844 q^{58} -14.0444 q^{59} +0.119679 q^{60} -11.1325 q^{61} -10.3269 q^{62} +3.47202 q^{63} +8.41971 q^{64} -3.04207 q^{65} +3.84846 q^{66} -1.42906 q^{67} +0.689962 q^{68} +4.76100 q^{70} -13.1413 q^{71} +2.90661 q^{72} +8.08313 q^{73} +8.85800 q^{74} +1.00000 q^{75} -0.0802836 q^{76} -9.74436 q^{77} -4.17144 q^{78} -5.53536 q^{79} +3.74632 q^{80} +1.00000 q^{81} -2.84891 q^{82} -2.35317 q^{83} -0.415527 q^{84} +5.76511 q^{85} -3.78388 q^{86} -5.26414 q^{87} -8.15750 q^{88} -15.0404 q^{89} +1.37125 q^{90} +10.5621 q^{91} +7.53104 q^{93} -7.25864 q^{94} -0.670825 q^{95} -0.676078 q^{96} -10.0065 q^{97} -6.93155 q^{98} -2.80654 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{3} + 8 q^{4} - 8 q^{5} - 6 q^{7} + 6 q^{8} + 8 q^{9} - 12 q^{11} + 8 q^{12} + 4 q^{13} - 8 q^{15} - 20 q^{17} - 4 q^{19} - 8 q^{20} - 6 q^{21} - 14 q^{22} + 6 q^{24} + 8 q^{25} - 22 q^{26} + 8 q^{27}+ \cdots - 12 q^{99}+O(q^{100}) $ 8 * q + 8 * q^3 + 8 * q^4 - 8 * q^5 - 6 * q^7 + 6 * q^8 + 8 * q^9 - 12 * q^11 + 8 * q^12 + 4 * q^13 - 8 * q^15 - 20 * q^17 - 4 * q^19 - 8 * q^20 - 6 * q^21 - 14 * q^22 + 6 * q^24 + 8 * q^25 - 22 * q^26 + 8 * q^27 + 8 * q^28 + 2 * q^31 + 12 * q^32 - 12 * q^33 - 8 * q^34 + 6 * q^35 + 8 * q^36 - 2 * q^37 + 2 * q^38 + 4 * q^39 - 6 * q^40 + 28 * q^41 - 4 * q^43 - 54 * q^44 - 8 * q^45 - 12 * q^47 + 14 * q^49 - 20 * q^51 - 22 * q^52 - 6 * q^53 + 12 * q^55 + 24 * q^56 - 4 * q^57 + 32 * q^58 + 2 * q^59 - 8 * q^60 - 32 * q^61 - 24 * q^62 - 6 * q^63 - 8 * q^64 - 4 * q^65 - 14 * q^66 - 32 * q^67 - 34 * q^68 + 2 * q^71 + 6 * q^72 - 2 * q^73 - 6 * q^74 + 8 * q^75 - 24 * q^76 - 30 * q^77 - 22 * q^78 + 36 * q^79 + 8 * q^81 + 16 * q^82 - 10 * q^83 + 8 * q^84 + 20 * q^85 - 50 * q^86 - 6 * q^88 - 42 * q^89 - 4 * q^91 + 2 * q^93 - 40 * q^94 + 4 * q^95 + 12 * q^96 - 16 * q^97 - 12 * 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 $

$2$	−1.37125	−0.969619	−0.484809	−	0.874620i	$-0.661111\pi$
$2$	−1.37125	−0.969619	−0.484809	+	0.874620i	$0.661111\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.119679	−0.0598394
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.37125	−0.559810
$7$	3.47202	1.31230	0.656150	−	0.754630i	$-0.272184\pi$
$7$	3.47202	1.31230	0.656150	+	0.754630i	$0.272184\pi$
$8$	2.90661	1.02764
$9$	1.00000	0.333333
$10$	1.37125	0.433627
$11$	−2.80654	−0.846203	−0.423102	−	0.906082i	$-0.639059\pi$
$11$	−2.80654	−0.846203	−0.423102	+	0.906082i	$0.639059\pi$
$12$	−0.119679	−0.0345483
$13$	3.04207	0.843719	0.421860	−	0.906661i	$-0.361377\pi$
$13$	3.04207	0.843719	0.421860	+	0.906661i	$0.361377\pi$
$14$	−4.76100	−1.27243
$15$	−1.00000	−0.258199
$16$	−3.74632	−0.936580
$17$	−5.76511	−1.39824	−0.699122	−	0.715002i	$-0.746426\pi$
$17$	−5.76511	−1.39824	−0.699122	+	0.715002i	$0.746426\pi$
$18$	−1.37125	−0.323206
$19$	0.670825	0.153898	0.0769489	−	0.997035i	$-0.475482\pi$
$19$	0.670825	0.153898	0.0769489	+	0.997035i	$0.475482\pi$
$20$	0.119679	0.0267610
$21$	3.47202	0.757657
$22$	3.84846	0.820495
$23$	0	0
$23$	0	0
$24$	2.90661	0.593308
$25$	1.00000	0.200000
$26$	−4.17144	−0.818086
$27$	1.00000	0.192450
$28$	−0.415527	−0.0785273
$29$	−5.26414	−0.977526	−0.488763	−	0.872417i	$-0.662552\pi$
$29$	−5.26414	−0.977526	−0.488763	+	0.872417i	$0.662552\pi$
$30$	1.37125	0.250354
$31$	7.53104	1.35261	0.676307	−	0.736620i	$-0.263579\pi$
$31$	7.53104	1.35261	0.676307	+	0.736620i	$0.263579\pi$
$32$	−0.676078	−0.119515
$33$	−2.80654	−0.488556
$34$	7.90539	1.35576
$35$	−3.47202	−0.586879
$36$	−0.119679	−0.0199465
$37$	−6.45981	−1.06199	−0.530993	−	0.847376i	$-0.678181\pi$
$37$	−6.45981	−1.06199	−0.530993	+	0.847376i	$0.678181\pi$
$38$	−0.919868	−0.149222
$39$	3.04207	0.487122
$40$	−2.90661	−0.459575
$41$	2.07761	0.324467	0.162234	−	0.986752i	$-0.448130\pi$
$41$	2.07761	0.324467	0.162234	+	0.986752i	$0.448130\pi$
$42$	−4.76100	−0.734638
$43$	2.75944	0.420811	0.210406	−	0.977614i	$-0.432522\pi$
$43$	2.75944	0.420811	0.210406	+	0.977614i	$0.432522\pi$
$44$	0.335883	0.0506363
$45$	−1.00000	−0.149071
$46$	0	0
$47$	5.29345	0.772129	0.386065	−	0.922472i	$-0.373834\pi$
$47$	5.29345	0.772129	0.386065	+	0.922472i	$0.373834\pi$
$48$	−3.74632	−0.540735
$49$	5.05492	0.722132
$50$	−1.37125	−0.193924
$51$	−5.76511	−0.807277
$52$	−0.364072	−0.0504877
$53$	−0.442976	−0.0608474	−0.0304237	−	0.999537i	$-0.509686\pi$
$53$	−0.442976	−0.0608474	−0.0304237	+	0.999537i	$0.509686\pi$
$54$	−1.37125	−0.186603
$55$	2.80654	0.378434
$56$	10.0918	1.34857
$57$	0.670825	0.0888530
$58$	7.21844	0.947828
$59$	−14.0444	−1.82842	−0.914212	−	0.405237i	$-0.867189\pi$
$59$	−14.0444	−1.82842	−0.914212	+	0.405237i	$0.867189\pi$
$60$	0.119679	0.0154505
$61$	−11.1325	−1.42537	−0.712684	−	0.701485i	$-0.752521\pi$
$61$	−11.1325	−1.42537	−0.712684	+	0.701485i	$0.752521\pi$
$62$	−10.3269	−1.31152
$63$	3.47202	0.437433
$64$	8.41971	1.05246
$65$	−3.04207	−0.377323
$66$	3.84846	0.473713
$67$	−1.42906	−0.174587	−0.0872936	−	0.996183i	$-0.527822\pi$
$67$	−1.42906	−0.174587	−0.0872936	+	0.996183i	$0.527822\pi$
$68$	0.689962	0.0836701
$69$	0	0
$70$	4.76100	0.569048
$71$	−13.1413	−1.55958	−0.779790	−	0.626041i	$-0.784674\pi$
$71$	−13.1413	−1.55958	−0.779790	+	0.626041i	$0.784674\pi$
$72$	2.90661	0.342547
$73$	8.08313	0.946059	0.473030	−	0.881047i	$-0.343160\pi$
$73$	8.08313	0.946059	0.473030	+	0.881047i	$0.343160\pi$
$74$	8.85800	1.02972
$75$	1.00000	0.115470
$76$	−0.0802836	−0.00920916
$77$	−9.74436	−1.11047
$78$	−4.17144	−0.472322
$79$	−5.53536	−0.622776	−0.311388	−	0.950283i	$-0.600794\pi$
$79$	−5.53536	−0.622776	−0.311388	+	0.950283i	$0.600794\pi$
$80$	3.74632	0.418851
$81$	1.00000	0.111111
$82$	−2.84891	−0.314610
$83$	−2.35317	−0.258294	−0.129147	−	0.991625i	$-0.541224\pi$
$83$	−2.35317	−0.258294	−0.129147	+	0.991625i	$0.541224\pi$
$84$	−0.415527	−0.0453378
$85$	5.76511	0.625314
$86$	−3.78388	−0.408026
$87$	−5.26414	−0.564375
$88$	−8.15750	−0.869592
$89$	−15.0404	−1.59428	−0.797139	−	0.603795i	$-0.793654\pi$
$89$	−15.0404	−1.59428	−0.797139	+	0.603795i	$0.793654\pi$
$90$	1.37125	0.144542
$91$	10.5621	1.10721
$92$	0	0
$93$	7.53104	0.780932
$94$	−7.25864	−0.748671
$95$	−0.670825	−0.0688252
$96$	−0.676078	−0.0690019
$97$	−10.0065	−1.01600	−0.508001	−	0.861356i	$-0.669615\pi$
$97$	−10.0065	−1.01600	−0.508001	+	0.861356i	$0.669615\pi$
$98$	−6.93155	−0.700193
$99$	−2.80654	−0.282068
$100$	−0.119679	−0.0119679
$101$	11.5918	1.15343	0.576715	−	0.816946i	$-0.304334\pi$
$101$	11.5918	1.15343	0.576715	+	0.816946i	$0.304334\pi$
$102$	7.90539	0.782751
$103$	11.0664	1.09040	0.545201	−	0.838305i	$-0.316453\pi$
$103$	11.0664	1.09040	0.545201	+	0.838305i	$0.316453\pi$
$104$	8.84211	0.867040
$105$	−3.47202	−0.338834
$106$	0.607429	0.0589987
$107$	9.52021	0.920354	0.460177	−	0.887827i	$-0.347786\pi$
$107$	9.52021	0.920354	0.460177	+	0.887827i	$0.347786\pi$
$108$	−0.119679	−0.0115161
$109$	−3.85799	−0.369529	−0.184764	−	0.982783i	$-0.559152\pi$
$109$	−3.85799	−0.369529	−0.184764	+	0.982783i	$0.559152\pi$
$110$	−3.84846	−0.366936
$111$	−6.45981	−0.613138
$112$	−13.0073	−1.22907
$113$	−9.57568	−0.900804	−0.450402	−	0.892826i	$-0.648719\pi$
$113$	−9.57568	−0.900804	−0.450402	+	0.892826i	$0.648719\pi$
$114$	−0.919868	−0.0861535
$115$	0	0
$116$	0.630006	0.0584946
$117$	3.04207	0.281240
$118$	19.2583	1.77287
$119$	−20.0166	−1.83492
$120$	−2.90661	−0.265336
$121$	−3.12334	−0.283940
$122$	15.2654	1.38206
$123$	2.07761	0.187331
$124$	−0.901306	−0.0809397
$125$	−1.00000	−0.0894427
$126$	−4.76100	−0.424144
$127$	−8.48093	−0.752561	−0.376281	−	0.926506i	$-0.622797\pi$
$127$	−8.48093	−0.752561	−0.376281	+	0.926506i	$0.622797\pi$
$128$	−10.1934	−0.900974
$129$	2.75944	0.242955
$130$	4.17144	0.365859
$131$	3.17550	0.277445	0.138723	−	0.990331i	$-0.455700\pi$
$131$	3.17550	0.277445	0.138723	+	0.990331i	$0.455700\pi$
$132$	0.335883	0.0292349
$133$	2.32912	0.201960
$134$	1.95959	0.169283
$135$	−1.00000	−0.0860663
$136$	−16.7569	−1.43689
$137$	15.6431	1.33648	0.668240	−	0.743945i	$-0.267048\pi$
$137$	15.6431	1.33648	0.668240	+	0.743945i	$0.267048\pi$
$138$	0	0
$139$	−21.5530	−1.82810	−0.914049	−	0.405603i	$-0.867061\pi$
$139$	−21.5530	−1.82810	−0.914049	+	0.405603i	$0.867061\pi$
$140$	0.415527	0.0351185
$141$	5.29345	0.445789
$142$	18.0199	1.51220
$143$	−8.53770	−0.713958
$144$	−3.74632	−0.312193
$145$	5.26414	0.437163
$146$	−11.0840	−0.917317
$147$	5.05492	0.416923
$148$	0.773102	0.0635486
$149$	−4.73586	−0.387977	−0.193988	−	0.981004i	$-0.562142\pi$
$149$	−4.73586	−0.387977	−0.193988	+	0.981004i	$0.562142\pi$
$150$	−1.37125	−0.111962
$151$	−21.1299	−1.71953	−0.859765	−	0.510690i	$-0.829390\pi$
$151$	−21.1299	−1.71953	−0.859765	+	0.510690i	$0.829390\pi$
$152$	1.94982	0.158152
$153$	−5.76511	−0.466081
$154$	13.3619	1.07674
$155$	−7.53104	−0.604908
$156$	−0.364072	−0.0291491
$157$	20.1000	1.60416	0.802079	−	0.597218i	$-0.203727\pi$
$157$	20.1000	1.60416	0.802079	+	0.597218i	$0.203727\pi$
$158$	7.59035	0.603856
$159$	−0.442976	−0.0351302
$160$	0.676078	0.0534487
$161$	0	0
$162$	−1.37125	−0.107735
$163$	−9.35235	−0.732533	−0.366266	−	0.930510i	$-0.619364\pi$
$163$	−9.35235	−0.732533	−0.366266	+	0.930510i	$0.619364\pi$
$164$	−0.248645	−0.0194159
$165$	2.80654	0.218489
$166$	3.22678	0.250447
$167$	−10.2986	−0.796927	−0.398464	−	0.917184i	$-0.630457\pi$
$167$	−10.2986	−0.796927	−0.398464	+	0.917184i	$0.630457\pi$
$168$	10.0918	0.778599
$169$	−3.74579	−0.288138
$170$	−7.90539	−0.606316
$171$	0.670825	0.0512993
$172$	−0.330247	−0.0251811
$173$	3.96885	0.301746	0.150873	−	0.988553i	$-0.451792\pi$
$173$	3.96885	0.301746	0.150873	+	0.988553i	$0.451792\pi$
$174$	7.21844	0.547229
$175$	3.47202	0.262460
$176$	10.5142	0.792537
$177$	−14.0444	−1.05564
$178$	20.6241	1.54584
$179$	18.9645	1.41747	0.708735	−	0.705475i	$-0.249266\pi$
$179$	18.9645	1.41747	0.708735	+	0.705475i	$0.249266\pi$
$180$	0.119679	0.00892033
$181$	22.0972	1.64247	0.821235	−	0.570590i	$-0.193286\pi$
$181$	22.0972	1.64247	0.821235	+	0.570590i	$0.193286\pi$
$182$	−14.4833	−1.07357
$183$	−11.1325	−0.822937
$184$	0	0
$185$	6.45981	0.474935
$186$	−10.3269	−0.757207
$187$	16.1800	1.18320
$188$	−0.633514	−0.0462038
$189$	3.47202	0.252552
$190$	0.919868	0.0667342
$191$	−15.1417	−1.09562	−0.547808	−	0.836604i	$-0.684538\pi$
$191$	−15.1417	−1.09562	−0.547808	+	0.836604i	$0.684538\pi$
$192$	8.41971	0.607640
$193$	22.2054	1.59838	0.799191	−	0.601077i	$-0.205261\pi$
$193$	22.2054	1.59838	0.799191	+	0.601077i	$0.205261\pi$
$194$	13.7213	0.985135
$195$	−3.04207	−0.217847
$196$	−0.604967	−0.0432120
$197$	−15.4762	−1.10263	−0.551317	−	0.834296i	$-0.685875\pi$
$197$	−15.4762	−1.10263	−0.551317	+	0.834296i	$0.685875\pi$
$198$	3.84846	0.273498
$199$	−17.1307	−1.21436	−0.607180	−	0.794564i	$-0.707699\pi$
$199$	−17.1307	−1.21436	−0.607180	+	0.794564i	$0.707699\pi$
$200$	2.90661	0.205528
$201$	−1.42906	−0.100798
$202$	−15.8953	−1.11839
$203$	−18.2772	−1.28281
$204$	0.689962	0.0483070
$205$	−2.07761	−0.145106
$206$	−15.1747	−1.05727
$207$	0	0
$208$	−11.3966	−0.790210
$209$	−1.88270	−0.130229
$210$	4.76100	0.328540
$211$	1.27592	0.0878377	0.0439189	−	0.999035i	$-0.486016\pi$
$211$	1.27592	0.0878377	0.0439189	+	0.999035i	$0.486016\pi$
$212$	0.0530148	0.00364107
$213$	−13.1413	−0.900424
$214$	−13.0546	−0.892392
$215$	−2.75944	−0.188192
$216$	2.90661	0.197769
$217$	26.1479	1.77504
$218$	5.29026	0.358302
$219$	8.08313	0.546208
$220$	−0.335883	−0.0226452
$221$	−17.5379	−1.17973
$222$	8.85800	0.594510
$223$	17.3376	1.16101	0.580504	−	0.814257i	$-0.302855\pi$
$223$	17.3376	1.16101	0.580504	+	0.814257i	$0.302855\pi$
$224$	−2.34736	−0.156839
$225$	1.00000	0.0666667
$226$	13.1306	0.873436
$227$	23.7748	1.57799	0.788993	−	0.614402i	$-0.210603\pi$
$227$	23.7748	1.57799	0.788993	+	0.614402i	$0.210603\pi$
$228$	−0.0802836	−0.00531691
$229$	5.27824	0.348796	0.174398	−	0.984675i	$-0.444202\pi$
$229$	5.27824	0.348796	0.174398	+	0.984675i	$0.444202\pi$
$230$	0	0
$231$	−9.74436	−0.641132
$232$	−15.3008	−1.00455
$233$	27.7882	1.82047	0.910233	−	0.414097i	$-0.135903\pi$
$233$	27.7882	1.82047	0.910233	+	0.414097i	$0.135903\pi$
$234$	−4.17144	−0.272695
$235$	−5.29345	−0.345307
$236$	1.68082	0.109412
$237$	−5.53536	−0.359560
$238$	27.4477	1.77917
$239$	13.4464	0.869776	0.434888	−	0.900485i	$-0.356788\pi$
$239$	13.4464	0.869776	0.434888	+	0.900485i	$0.356788\pi$
$240$	3.74632	0.241824
$241$	−17.7246	−1.14174	−0.570869	−	0.821041i	$-0.693394\pi$
$241$	−17.7246	−1.14174	−0.570869	+	0.821041i	$0.693394\pi$
$242$	4.28287	0.275314
$243$	1.00000	0.0641500
$244$	1.33232	0.0852932
$245$	−5.05492	−0.322947
$246$	−2.84891	−0.181640
$247$	2.04070	0.129847
$248$	21.8898	1.39000
$249$	−2.35317	−0.149126
$250$	1.37125	0.0867253
$251$	−12.5848	−0.794343	−0.397172	−	0.917744i	$-0.630008\pi$
$251$	−12.5848	−0.794343	−0.397172	+	0.917744i	$0.630008\pi$
$252$	−0.415527	−0.0261758
$253$	0	0
$254$	11.6295	0.729697
$255$	5.76511	0.361025
$256$	−2.86180	−0.178863
$257$	−16.1913	−1.00999	−0.504994	−	0.863123i	$-0.668505\pi$
$257$	−16.1913	−1.00999	−0.504994	+	0.863123i	$0.668505\pi$
$258$	−3.78388	−0.235574
$259$	−22.4286	−1.39364
$260$	0.364072	0.0225788
$261$	−5.26414	−0.325842
$262$	−4.35440	−0.269016
$263$	−7.31656	−0.451158	−0.225579	−	0.974225i	$-0.572427\pi$
$263$	−7.31656	−0.451158	−0.225579	+	0.974225i	$0.572427\pi$
$264$	−8.15750	−0.502059
$265$	0.442976	0.0272118
$266$	−3.19380	−0.195824
$267$	−15.0404	−0.920457
$268$	0.171028	0.0104472
$269$	27.0700	1.65048	0.825242	−	0.564779i	$-0.191039\pi$
$269$	27.0700	1.65048	0.825242	+	0.564779i	$0.191039\pi$
$270$	1.37125	0.0834515
$271$	27.8541	1.69202	0.846009	−	0.533169i	$-0.178999\pi$
$271$	27.8541	1.69202	0.846009	+	0.533169i	$0.178999\pi$
$272$	21.5979	1.30957
$273$	10.5621	0.639250
$274$	−21.4506	−1.29588
$275$	−2.80654	−0.169241
$276$	0	0
$277$	−5.77947	−0.347255	−0.173627	−	0.984811i	$-0.555549\pi$
$277$	−5.77947	−0.347255	−0.173627	+	0.984811i	$0.555549\pi$
$278$	29.5545	1.77256
$279$	7.53104	0.450872
$280$	−10.0918	−0.603100
$281$	9.91216	0.591310	0.295655	−	0.955295i	$-0.404462\pi$
$281$	9.91216	0.591310	0.295655	+	0.955295i	$0.404462\pi$
$282$	−7.25864	−0.432246
$283$	−7.41805	−0.440957	−0.220479	−	0.975392i	$-0.570762\pi$
$283$	−7.41805	−0.440957	−0.220479	+	0.975392i	$0.570762\pi$
$284$	1.57273	0.0933244
$285$	−0.670825	−0.0397363
$286$	11.7073	0.692267
$287$	7.21349	0.425799
$288$	−0.676078	−0.0398383
$289$	16.2365	0.955087
$290$	−7.21844	−0.423881
$291$	−10.0065	−0.586589
$292$	−0.967380	−0.0566116
$293$	−1.68483	−0.0984291	−0.0492145	−	0.998788i	$-0.515672\pi$
$293$	−1.68483	−0.0984291	−0.0492145	+	0.998788i	$0.515672\pi$
$294$	−6.93155	−0.404256
$295$	14.0444	0.817696
$296$	−18.7761	−1.09134
$297$	−2.80654	−0.162852
$298$	6.49404	0.376190
$299$	0	0
$300$	−0.119679	−0.00690966
$301$	9.58084	0.552230
$302$	28.9744	1.66729
$303$	11.5918	0.665933
$304$	−2.51313	−0.144138
$305$	11.1325	0.637444
$306$	7.90539	0.451921
$307$	−8.68397	−0.495620	−0.247810	−	0.968809i	$-0.579711\pi$
$307$	−8.68397	−0.495620	−0.247810	+	0.968809i	$0.579711\pi$
$308$	1.16619	0.0664500
$309$	11.0664	0.629544
$310$	10.3269	0.586530
$311$	10.8008	0.612459	0.306229	−	0.951958i	$-0.400933\pi$
$311$	10.8008	0.612459	0.306229	+	0.951958i	$0.400933\pi$
$312$	8.84211	0.500586
$313$	−4.41578	−0.249595	−0.124797	−	0.992182i	$-0.539828\pi$
$313$	−4.41578	−0.249595	−0.124797	+	0.992182i	$0.539828\pi$
$314$	−27.5621	−1.55542
$315$	−3.47202	−0.195626
$316$	0.662465	0.0372666
$317$	−25.0524	−1.40708	−0.703541	−	0.710655i	$-0.748399\pi$
$317$	−25.0524	−1.40708	−0.703541	+	0.710655i	$0.748399\pi$
$318$	0.607429	0.0340629
$319$	14.7740	0.827186
$320$	−8.41971	−0.470676
$321$	9.52021	0.531366
$322$	0	0
$323$	−3.86738	−0.215187
$324$	−0.119679	−0.00664882
$325$	3.04207	0.168744
$326$	12.8244	0.710278
$327$	−3.85799	−0.213347
$328$	6.03878	0.333436
$329$	18.3790	1.01327
$330$	−3.84846	−0.211851
$331$	7.19813	0.395645	0.197823	−	0.980238i	$-0.436613\pi$
$331$	7.19813	0.395645	0.197823	+	0.980238i	$0.436613\pi$
$332$	0.281625	0.0154562
$333$	−6.45981	−0.353995
$334$	14.1219	0.772716
$335$	1.42906	0.0780778
$336$	−13.0073	−0.709606
$337$	−34.7407	−1.89245	−0.946223	−	0.323516i	$-0.895135\pi$
$337$	−34.7407	−1.89245	−0.946223	+	0.323516i	$0.895135\pi$
$338$	5.13641	0.279384
$339$	−9.57568	−0.520079
$340$	−0.689962	−0.0374184
$341$	−21.1362	−1.14459
$342$	−0.919868	−0.0497407
$343$	−6.75334	−0.364646
$344$	8.02061	0.432442
$345$	0	0
$346$	−5.44228	−0.292579
$347$	4.63077	0.248593	0.124296	−	0.992245i	$-0.460333\pi$
$347$	4.63077	0.248593	0.124296	+	0.992245i	$0.460333\pi$
$348$	0.630006	0.0337719
$349$	−18.3425	−0.981853	−0.490926	−	0.871201i	$-0.663342\pi$
$349$	−18.3425	−0.981853	−0.490926	+	0.871201i	$0.663342\pi$
$350$	−4.76100	−0.254486
$351$	3.04207	0.162374
$352$	1.89744	0.101134
$353$	−18.6381	−0.992007	−0.496004	−	0.868320i	$-0.665200\pi$
$353$	−18.6381	−0.992007	−0.496004	+	0.868320i	$0.665200\pi$
$354$	19.2583	1.02357
$355$	13.1413	0.697465
$356$	1.80002	0.0954007
$357$	−20.0166	−1.05939
$358$	−26.0050	−1.37441
$359$	−15.3875	−0.812120	−0.406060	−	0.913846i	$-0.633098\pi$
$359$	−15.3875	−0.812120	−0.406060	+	0.913846i	$0.633098\pi$
$360$	−2.90661	−0.153192
$361$	−18.5500	−0.976315
$362$	−30.3007	−1.59257
$363$	−3.12334	−0.163933
$364$	−1.26406	−0.0662550
$365$	−8.08313	−0.423091
$366$	15.2654	0.797935
$367$	−26.9544	−1.40701	−0.703505	−	0.710691i	$-0.748383\pi$
$367$	−26.9544	−1.40701	−0.703505	+	0.710691i	$0.748383\pi$
$368$	0	0
$369$	2.07761	0.108156
$370$	−8.85800	−0.460505
$371$	−1.53802	−0.0798500
$372$	−0.901306	−0.0467305
$373$	14.9334	0.773224	0.386612	−	0.922243i	$-0.373645\pi$
$373$	14.9334	0.773224	0.386612	+	0.922243i	$0.373645\pi$
$374$	−22.1868	−1.14725
$375$	−1.00000	−0.0516398
$376$	15.3860	0.793471
$377$	−16.0139	−0.824758
$378$	−4.76100	−0.244879
$379$	−32.1952	−1.65376	−0.826878	−	0.562381i	$-0.809885\pi$
$379$	−32.1952	−1.65376	−0.826878	+	0.562381i	$0.809885\pi$
$380$	0.0802836	0.00411846
$381$	−8.48093	−0.434491
$382$	20.7630	1.06233
$383$	30.3742	1.55205	0.776023	−	0.630704i	$-0.217234\pi$
$383$	30.3742	1.55205	0.776023	+	0.630704i	$0.217234\pi$
$384$	−10.1934	−0.520177
$385$	9.74436	0.496619
$386$	−30.4492	−1.54982
$387$	2.75944	0.140270
$388$	1.19756	0.0607970
$389$	21.1940	1.07458	0.537290	−	0.843398i	$-0.319448\pi$
$389$	21.1940	1.07458	0.537290	+	0.843398i	$0.319448\pi$
$390$	4.17144	0.211229
$391$	0	0
$392$	14.6927	0.742092
$393$	3.17550	0.160183
$394$	21.2217	1.06913
$395$	5.53536	0.278514
$396$	0.335883	0.0168788
$397$	36.7191	1.84288	0.921439	−	0.388524i	$-0.127015\pi$
$397$	36.7191	1.84288	0.921439	+	0.388524i	$0.127015\pi$
$398$	23.4904	1.17747
$399$	2.32912	0.116602
$400$	−3.74632	−0.187316
$401$	−17.9254	−0.895153	−0.447577	−	0.894246i	$-0.647713\pi$
$401$	−17.9254	−0.895153	−0.447577	+	0.894246i	$0.647713\pi$
$402$	1.95959	0.0977356
$403$	22.9100	1.14123
$404$	−1.38730	−0.0690206
$405$	−1.00000	−0.0496904
$406$	25.0626	1.24383
$407$	18.1297	0.898656
$408$	−16.7569	−0.829590
$409$	3.72064	0.183974	0.0919868	−	0.995760i	$-0.470678\pi$
$409$	3.72064	0.183974	0.0919868	+	0.995760i	$0.470678\pi$
$410$	2.84891	0.140698
$411$	15.6431	0.771618
$412$	−1.32441	−0.0652490
$413$	−48.7624	−2.39944
$414$	0	0
$415$	2.35317	0.115513
$416$	−2.05668	−0.100837
$417$	−21.5530	−1.05545
$418$	2.58164	0.126272
$419$	−21.9694	−1.07327	−0.536637	−	0.843813i	$-0.680305\pi$
$419$	−21.9694	−1.07327	−0.536637	+	0.843813i	$0.680305\pi$
$420$	0.415527	0.0202757
$421$	5.01874	0.244598	0.122299	−	0.992493i	$-0.460973\pi$
$421$	5.01874	0.244598	0.122299	+	0.992493i	$0.460973\pi$
$422$	−1.74960	−0.0851691
$423$	5.29345	0.257376
$424$	−1.28756	−0.0625292
$425$	−5.76511	−0.279649
$426$	18.0199	0.873068
$427$	−38.6522	−1.87051
$428$	−1.13937	−0.0550734
$429$	−8.53770	−0.412204
$430$	3.78388	0.182475
$431$	−25.6688	−1.23642	−0.618212	−	0.786011i	$-0.712143\pi$
$431$	−25.6688	−1.23642	−0.618212	+	0.786011i	$0.712143\pi$
$432$	−3.74632	−0.180245
$433$	−39.1736	−1.88256	−0.941281	−	0.337625i	$-0.890376\pi$
$433$	−39.1736	−1.88256	−0.941281	+	0.337625i	$0.890376\pi$
$434$	−35.8553	−1.72111
$435$	5.26414	0.252396
$436$	0.461720	0.0221124
$437$	0	0
$438$	−11.0840	−0.529613
$439$	−27.1017	−1.29349	−0.646746	−	0.762705i	$-0.723871\pi$
$439$	−27.1017	−1.29349	−0.646746	+	0.762705i	$0.723871\pi$
$440$	8.15750	0.388894
$441$	5.05492	0.240711
$442$	24.0488	1.14388
$443$	−2.91033	−0.138274	−0.0691369	−	0.997607i	$-0.522025\pi$
$443$	−2.91033	−0.138274	−0.0691369	+	0.997607i	$0.522025\pi$
$444$	0.773102	0.0366898
$445$	15.0404	0.712983
$446$	−23.7741	−1.12574
$447$	−4.73586	−0.223999
$448$	29.2334	1.38115
$449$	28.4901	1.34453	0.672266	−	0.740310i	$-0.265321\pi$
$449$	28.4901	1.34453	0.672266	+	0.740310i	$0.265321\pi$
$450$	−1.37125	−0.0646413
$451$	−5.83088	−0.274565
$452$	1.14601	0.0539036
$453$	−21.1299	−0.992771
$454$	−32.6011	−1.53005
$455$	−10.5621	−0.495161
$456$	1.94982	0.0913089
$457$	19.1164	0.894226	0.447113	−	0.894477i	$-0.352452\pi$
$457$	19.1164	0.894226	0.447113	+	0.894477i	$0.352452\pi$
$458$	−7.23777	−0.338199
$459$	−5.76511	−0.269092
$460$	0	0
$461$	−27.1735	−1.26560	−0.632798	−	0.774317i	$-0.718094\pi$
$461$	−27.1735	−1.26560	−0.632798	+	0.774317i	$0.718094\pi$
$462$	13.3619	0.621653
$463$	−27.1271	−1.26070	−0.630352	−	0.776310i	$-0.717089\pi$
$463$	−27.1271	−1.26070	−0.630352	+	0.776310i	$0.717089\pi$
$464$	19.7211	0.915531
$465$	−7.53104	−0.349244
$466$	−38.1045	−1.76516
$467$	0.770602	0.0356592	0.0178296	−	0.999841i	$-0.494324\pi$
$467$	0.770602	0.0356592	0.0178296	+	0.999841i	$0.494324\pi$
$468$	−0.364072	−0.0168292
$469$	−4.96172	−0.229111
$470$	7.25864	0.334816
$471$	20.1000	0.926161
$472$	−40.8215	−1.87896
$473$	−7.74448	−0.356092
$474$	7.59035	0.348636
$475$	0.670825	0.0307796
$476$	2.39556	0.109800
$477$	−0.442976	−0.0202825
$478$	−18.4384	−0.843351
$479$	−22.9715	−1.04959	−0.524797	−	0.851228i	$-0.675859\pi$
$479$	−22.9715	−1.04959	−0.524797	+	0.851228i	$0.675859\pi$
$480$	0.676078	0.0308586
$481$	−19.6512	−0.896018
$482$	24.3048	1.10705
$483$	0	0
$484$	0.373798	0.0169908
$485$	10.0065	0.454370
$486$	−1.37125	−0.0622011
$487$	−3.07813	−0.139484	−0.0697418	−	0.997565i	$-0.522218\pi$
$487$	−3.07813	−0.139484	−0.0697418	+	0.997565i	$0.522218\pi$
$488$	−32.3577	−1.46477
$489$	−9.35235	−0.422928
$490$	6.93155	0.313136
$491$	−18.4761	−0.833813	−0.416906	−	0.908949i	$-0.636886\pi$
$491$	−18.4761	−0.833813	−0.416906	+	0.908949i	$0.636886\pi$
$492$	−0.248645	−0.0112098
$493$	30.3483	1.36682
$494$	−2.79830	−0.125902
$495$	2.80654	0.126145
$496$	−28.2137	−1.26683
$497$	−45.6267	−2.04664
$498$	3.22678	0.144596
$499$	34.5390	1.54618	0.773088	−	0.634299i	$-0.218711\pi$
$499$	34.5390	1.54618	0.773088	+	0.634299i	$0.218711\pi$
$500$	0.119679	0.00535220
$501$	−10.2986	−0.460106
$502$	17.2568	0.770210
$503$	−37.1739	−1.65750	−0.828752	−	0.559617i	$-0.810948\pi$
$503$	−37.1739	−1.65750	−0.828752	+	0.559617i	$0.810948\pi$
$504$	10.0918	0.449524
$505$	−11.5918	−0.515829
$506$	0	0
$507$	−3.74579	−0.166356
$508$	1.01499	0.0450328
$509$	−26.0697	−1.15552	−0.577760	−	0.816207i	$-0.696073\pi$
$509$	−26.0697	−1.15552	−0.577760	+	0.816207i	$0.696073\pi$
$510$	−7.90539	−0.350057
$511$	28.0648	1.24151
$512$	24.3109	1.07440
$513$	0.670825	0.0296177
$514$	22.2024	0.979304
$515$	−11.0664	−0.487643
$516$	−0.330247	−0.0145383
$517$	−14.8563	−0.653378
$518$	30.7552	1.35130
$519$	3.96885	0.174213
$520$	−8.84211	−0.387752
$521$	2.30920	0.101168	0.0505839	−	0.998720i	$-0.483892\pi$
$521$	2.30920	0.101168	0.0505839	+	0.998720i	$0.483892\pi$
$522$	7.21844	0.315943
$523$	19.7119	0.861941	0.430970	−	0.902366i	$-0.358171\pi$
$523$	19.7119	0.861941	0.430970	+	0.902366i	$0.358171\pi$
$524$	−0.380041	−0.0166022
$525$	3.47202	0.151531
$526$	10.0328	0.437452
$527$	−43.4173	−1.89129
$528$	10.5142	0.457571
$529$	0	0
$530$	−0.607429	−0.0263850
$531$	−14.0444	−0.609475
$532$	−0.278746	−0.0120852
$533$	6.32023	0.273759
$534$	20.6241	0.892493
$535$	−9.52021	−0.411595
$536$	−4.15371	−0.179413
$537$	18.9645	0.818377
$538$	−37.1196	−1.60034
$539$	−14.1868	−0.611070
$540$	0.119679	0.00515016
$541$	−2.06261	−0.0886786	−0.0443393	−	0.999017i	$-0.514118\pi$
$541$	−2.06261	−0.0886786	−0.0443393	+	0.999017i	$0.514118\pi$
$542$	−38.1949	−1.64061
$543$	22.0972	0.948280
$544$	3.89766	0.167111
$545$	3.85799	0.165258
$546$	−14.4833	−0.619829
$547$	−11.2357	−0.480404	−0.240202	−	0.970723i	$-0.577214\pi$
$547$	−11.2357	−0.480404	−0.240202	+	0.970723i	$0.577214\pi$
$548$	−1.87215	−0.0799743
$549$	−11.1325	−0.475123
$550$	3.84846	0.164099
$551$	−3.53132	−0.150439
$552$	0	0
$553$	−19.2189	−0.817270
$554$	7.92509	0.336705
$555$	6.45981	0.274204
$556$	2.57943	0.109392
$557$	−35.8299	−1.51816	−0.759081	−	0.650996i	$-0.774352\pi$
$557$	−35.8299	−1.51816	−0.759081	+	0.650996i	$0.774352\pi$
$558$	−10.3269	−0.437174
$559$	8.39443	0.355046
$560$	13.0073	0.549659
$561$	16.1800	0.683120
$562$	−13.5920	−0.573345
$563$	−19.2385	−0.810806	−0.405403	−	0.914138i	$-0.632869\pi$
$563$	−19.2385	−0.810806	−0.405403	+	0.914138i	$0.632869\pi$
$564$	−0.633514	−0.0266758
$565$	9.57568	0.402852
$566$	10.1720	0.427560
$567$	3.47202	0.145811
$568$	−38.1964	−1.60269
$569$	−8.42493	−0.353192	−0.176596	−	0.984283i	$-0.556509\pi$
$569$	−8.42493	−0.353192	−0.176596	+	0.984283i	$0.556509\pi$
$570$	0.919868	0.0385290
$571$	4.53814	0.189915	0.0949576	−	0.995481i	$-0.469728\pi$
$571$	4.53814	0.189915	0.0949576	+	0.995481i	$0.469728\pi$
$572$	1.02178	0.0427228
$573$	−15.1417	−0.632554
$574$	−9.89148	−0.412863
$575$	0	0
$576$	8.41971	0.350821
$577$	−17.1015	−0.711945	−0.355973	−	0.934496i	$-0.615850\pi$
$577$	−17.1015	−0.711945	−0.355973	+	0.934496i	$0.615850\pi$
$578$	−22.2642	−0.926070
$579$	22.2054	0.922827
$580$	−0.630006	−0.0261596
$581$	−8.17026	−0.338959
$582$	13.7213	0.568768
$583$	1.24323	0.0514892
$584$	23.4945	0.972209
$585$	−3.04207	−0.125774
$586$	2.31033	0.0954387
$587$	17.1876	0.709410	0.354705	−	0.934978i	$-0.384581\pi$
$587$	17.1876	0.709410	0.354705	+	0.934978i	$0.384581\pi$
$588$	−0.604967	−0.0249484
$589$	5.05201	0.208164
$590$	−19.2583	−0.792853
$591$	−15.4762	−0.636606
$592$	24.2005	0.994635
$593$	−3.94806	−0.162127	−0.0810637	−	0.996709i	$-0.525832\pi$
$593$	−3.94806	−0.162127	−0.0810637	+	0.996709i	$0.525832\pi$
$594$	3.84846	0.157904
$595$	20.0166	0.820599
$596$	0.566782	0.0232163
$597$	−17.1307	−0.701111
$598$	0	0
$599$	0.565506	0.0231059	0.0115530	−	0.999933i	$-0.496322\pi$
$599$	0.565506	0.0231059	0.0115530	+	0.999933i	$0.496322\pi$
$600$	2.90661	0.118662
$601$	42.3726	1.72841	0.864207	−	0.503136i	$-0.167820\pi$
$601$	42.3726	1.72841	0.864207	+	0.503136i	$0.167820\pi$
$602$	−13.1377	−0.535453
$603$	−1.42906	−0.0581958
$604$	2.52881	0.102896
$605$	3.12334	0.126982
$606$	−15.8953	−0.645701
$607$	−28.8537	−1.17114	−0.585568	−	0.810623i	$-0.699128\pi$
$607$	−28.8537	−1.17114	−0.585568	+	0.810623i	$0.699128\pi$
$608$	−0.453530	−0.0183931
$609$	−18.2772	−0.740629
$610$	−15.2654	−0.618078
$611$	16.1031	0.651460
$612$	0.689962	0.0278900
$613$	−0.225157	−0.00909401	−0.00454700	−	0.999990i	$-0.501447\pi$
$613$	−0.225157	−0.00909401	−0.00454700	+	0.999990i	$0.501447\pi$
$614$	11.9079	0.480563
$615$	−2.07761	−0.0837771
$616$	−28.3230	−1.14117
$617$	−18.0884	−0.728213	−0.364106	−	0.931357i	$-0.618626\pi$
$617$	−18.0884	−0.728213	−0.364106	+	0.931357i	$0.618626\pi$
$618$	−15.1747	−0.610418
$619$	45.9641	1.84745	0.923726	−	0.383053i	$-0.125127\pi$
$619$	45.9641	1.84745	0.923726	+	0.383053i	$0.125127\pi$
$620$	0.901306	0.0361973
$621$	0	0
$622$	−14.8106	−0.593851
$623$	−52.2206	−2.09217
$624$	−11.3966	−0.456228
$625$	1.00000	0.0400000
$626$	6.05513	0.242012
$627$	−1.88270	−0.0751877
$628$	−2.40555	−0.0959919
$629$	37.2415	1.48492
$630$	4.76100	0.189683
$631$	−30.8156	−1.22675	−0.613374	−	0.789792i	$-0.710188\pi$
$631$	−30.8156	−1.22675	−0.613374	+	0.789792i	$0.710188\pi$
$632$	−16.0891	−0.639990
$633$	1.27592	0.0507131
$634$	34.3530	1.36433
$635$	8.48093	0.336556
$636$	0.0530148	0.00210217
$637$	15.3774	0.609277
$638$	−20.2588	−0.802055
$639$	−13.1413	−0.519860
$640$	10.1934	0.402928
$641$	−26.0052	−1.02714	−0.513571	−	0.858047i	$-0.671678\pi$
$641$	−26.0052	−1.02714	−0.513571	+	0.858047i	$0.671678\pi$
$642$	−13.0546	−0.515223
$643$	13.3526	0.526576	0.263288	−	0.964717i	$-0.415193\pi$
$643$	13.3526	0.526576	0.263288	+	0.964717i	$0.415193\pi$
$644$	0	0
$645$	−2.75944	−0.108653
$646$	5.30314	0.208649
$647$	−41.5075	−1.63183	−0.815914	−	0.578173i	$-0.803766\pi$
$647$	−41.5075	−1.63183	−0.815914	+	0.578173i	$0.803766\pi$
$648$	2.90661	0.114182
$649$	39.4161	1.54722
$650$	−4.17144	−0.163617
$651$	26.1479	1.02482
$652$	1.11928	0.0438343
$653$	0.611199	0.0239181	0.0119590	−	0.999928i	$-0.496193\pi$
$653$	0.611199	0.0239181	0.0119590	+	0.999928i	$0.496193\pi$
$654$	5.29026	0.206866
$655$	−3.17550	−0.124077
$656$	−7.78337	−0.303890
$657$	8.08313	0.315353
$658$	−25.2021	−0.982481
$659$	30.7554	1.19806	0.599031	−	0.800726i	$-0.295553\pi$
$659$	30.7554	1.19806	0.599031	+	0.800726i	$0.295553\pi$
$660$	−0.335883	−0.0130742
$661$	30.9944	1.20554	0.602772	−	0.797913i	$-0.294063\pi$
$661$	30.9944	1.20554	0.602772	+	0.797913i	$0.294063\pi$
$662$	−9.87043	−0.383625
$663$	−17.5379	−0.681115
$664$	−6.83974	−0.265433
$665$	−2.32912	−0.0903193
$666$	8.85800	0.343241
$667$	0	0
$668$	1.23252	0.0476877
$669$	17.3376	0.670309
$670$	−1.95959	−0.0757057
$671$	31.2437	1.20615
$672$	−2.34736	−0.0905512
$673$	20.5577	0.792442	0.396221	−	0.918155i	$-0.370321\pi$
$673$	20.5577	0.792442	0.396221	+	0.918155i	$0.370321\pi$
$674$	47.6381	1.83495
$675$	1.00000	0.0384900
$676$	0.448292	0.0172420
$677$	30.7164	1.18053	0.590264	−	0.807210i	$-0.299024\pi$
$677$	30.7164	1.18053	0.590264	+	0.807210i	$0.299024\pi$
$678$	13.1306	0.504279
$679$	−34.7426	−1.33330
$680$	16.7569	0.642598
$681$	23.7748	0.911051
$682$	28.9829	1.10981
$683$	−4.93111	−0.188683	−0.0943417	−	0.995540i	$-0.530075\pi$
$683$	−4.93111	−0.188683	−0.0943417	+	0.995540i	$0.530075\pi$
$684$	−0.0802836	−0.00306972
$685$	−15.6431	−0.597692
$686$	9.26051	0.353568
$687$	5.27824	0.201377
$688$	−10.3378	−0.394123
$689$	−1.34756	−0.0513381
$690$	0	0
$691$	19.6070	0.745884	0.372942	−	0.927855i	$-0.378349\pi$
$691$	19.6070	0.745884	0.372942	+	0.927855i	$0.378349\pi$
$692$	−0.474987	−0.0180563
$693$	−9.74436	−0.370158
$694$	−6.34993	−0.241040
$695$	21.5530	0.817550
$696$	−15.3008	−0.579974
$697$	−11.9776	−0.453685
$698$	25.1521	0.952023
$699$	27.7882	1.05105
$700$	−0.415527	−0.0157055
$701$	−5.90139	−0.222892	−0.111446	−	0.993770i	$-0.535548\pi$
$701$	−5.90139	−0.222892	−0.111446	+	0.993770i	$0.535548\pi$
$702$	−4.17144	−0.157441
$703$	−4.33340	−0.163437
$704$	−23.6302	−0.890598
$705$	−5.29345	−0.199363
$706$	25.5575	0.961869
$707$	40.2471	1.51365
$708$	1.68082	0.0631689
$709$	−12.1381	−0.455855	−0.227928	−	0.973678i	$-0.573195\pi$
$709$	−12.1381	−0.455855	−0.227928	+	0.973678i	$0.573195\pi$
$710$	−18.0199	−0.676276
$711$	−5.53536	−0.207592
$712$	−43.7165	−1.63834
$713$	0	0
$714$	27.4477	1.02720
$715$	8.53770	0.319292
$716$	−2.26964	−0.0848206
$717$	13.4464	0.502165
$718$	21.1001	0.787447
$719$	5.26194	0.196237	0.0981186	−	0.995175i	$-0.468718\pi$
$719$	5.26194	0.196237	0.0981186	+	0.995175i	$0.468718\pi$
$720$	3.74632	0.139617
$721$	38.4227	1.43094
$722$	25.4366	0.946654
$723$	−17.7246	−0.659183
$724$	−2.64456	−0.0982844
$725$	−5.26414	−0.195505
$726$	4.28287	0.158952
$727$	2.53017	0.0938388	0.0469194	−	0.998899i	$-0.485060\pi$
$727$	2.53017	0.0938388	0.0469194	+	0.998899i	$0.485060\pi$
$728$	30.7000	1.13782
$729$	1.00000	0.0370370
$730$	11.0840	0.410237
$731$	−15.9085	−0.588397
$732$	1.33232	0.0492441
$733$	−32.0597	−1.18415	−0.592075	−	0.805883i	$-0.701691\pi$
$733$	−32.0597	−1.18415	−0.592075	+	0.805883i	$0.701691\pi$
$734$	36.9612	1.36426
$735$	−5.05492	−0.186454
$736$	0	0
$737$	4.01071	0.147736
$738$	−2.84891	−0.104870
$739$	18.1504	0.667673	0.333836	−	0.942631i	$-0.391657\pi$
$739$	18.1504	0.667673	0.333836	+	0.942631i	$0.391657\pi$
$740$	−0.773102	−0.0284198
$741$	2.04070	0.0749670
$742$	2.10901	0.0774241
$743$	−19.6818	−0.722054	−0.361027	−	0.932555i	$-0.617574\pi$
$743$	−19.6818	−0.722054	−0.361027	+	0.932555i	$0.617574\pi$
$744$	21.8898	0.802518
$745$	4.73586	0.173509
$746$	−20.4774	−0.749732
$747$	−2.35317	−0.0860980
$748$	−1.93640	−0.0708019
$749$	33.0544	1.20778
$750$	1.37125	0.0500709
$751$	−20.1462	−0.735144	−0.367572	−	0.929995i	$-0.619811\pi$
$751$	−20.1462	−0.735144	−0.367572	+	0.929995i	$0.619811\pi$
$752$	−19.8310	−0.723161
$753$	−12.5848	−0.458614
$754$	21.9590	0.799700
$755$	21.1299	0.768997
$756$	−0.415527	−0.0151126
$757$	−31.5113	−1.14530	−0.572648	−	0.819801i	$-0.694084\pi$
$757$	−31.5113	−1.14530	−0.572648	+	0.819801i	$0.694084\pi$
$758$	44.1476	1.60351
$759$	0	0
$760$	−1.94982	−0.0707275
$761$	28.7809	1.04331	0.521653	−	0.853158i	$-0.325316\pi$
$761$	28.7809	1.04331	0.521653	+	0.853158i	$0.325316\pi$
$762$	11.6295	0.421291
$763$	−13.3950	−0.484932
$764$	1.81214	0.0655610
$765$	5.76511	0.208438
$766$	−41.6505	−1.50489
$767$	−42.7241	−1.54268
$768$	−2.86180	−0.103266
$769$	4.35790	0.157150	0.0785750	−	0.996908i	$-0.474963\pi$
$769$	4.35790	0.157150	0.0785750	+	0.996908i	$0.474963\pi$
$770$	−13.3619	−0.481531
$771$	−16.1913	−0.583117
$772$	−2.65752	−0.0956463
$773$	46.4278	1.66989	0.834947	−	0.550331i	$-0.185498\pi$
$773$	46.4278	1.66989	0.834947	+	0.550331i	$0.185498\pi$
$774$	−3.78388	−0.136009
$775$	7.53104	0.270523
$776$	−29.0848	−1.04408
$777$	−22.4286	−0.804621
$778$	−29.0623	−1.04193
$779$	1.39371	0.0499348
$780$	0.364072	0.0130359
$781$	36.8814	1.31972
$782$	0	0
$783$	−5.26414	−0.188125
$784$	−18.9374	−0.676334
$785$	−20.1000	−0.717401
$786$	−4.35440	−0.155316
$787$	22.9768	0.819034	0.409517	−	0.912302i	$-0.365697\pi$
$787$	22.9768	0.819034	0.409517	+	0.912302i	$0.365697\pi$
$788$	1.85217	0.0659810
$789$	−7.31656	−0.260476
$790$	−7.59035	−0.270053
$791$	−33.2469	−1.18213
$792$	−8.15750	−0.289864
$793$	−33.8658	−1.20261
$794$	−50.3510	−1.78689
$795$	0.442976	0.0157107
$796$	2.05018	0.0726666
$797$	−51.8980	−1.83832	−0.919161	−	0.393882i	$-0.871132\pi$
$797$	−51.8980	−1.83832	−0.919161	+	0.393882i	$0.871132\pi$
$798$	−3.19380	−0.113059
$799$	−30.5173	−1.07963
$800$	−0.676078	−0.0239030
$801$	−15.0404	−0.531426
$802$	24.5802	0.867957
$803$	−22.6856	−0.800558
$804$	0.171028	0.00603169
$805$	0	0
$806$	−31.4153	−1.10656
$807$	27.0700	0.952908
$808$	33.6929	1.18531
$809$	−21.2426	−0.746851	−0.373425	−	0.927660i	$-0.621817\pi$
$809$	−21.2426	−0.746851	−0.373425	+	0.927660i	$0.621817\pi$
$810$	1.37125	0.0481807
$811$	4.03607	0.141726	0.0708629	−	0.997486i	$-0.477425\pi$
$811$	4.03607	0.141726	0.0708629	+	0.997486i	$0.477425\pi$
$812$	2.18739	0.0767625
$813$	27.8541	0.976887
$814$	−24.8603	−0.871354
$815$	9.35235	0.327599
$816$	21.5979	0.756079
$817$	1.85110	0.0647619
$818$	−5.10192	−0.178384
$819$	10.5621	0.369071
$820$	0.248645	0.00868308
$821$	12.1581	0.424321	0.212160	−	0.977235i	$-0.431950\pi$
$821$	12.1581	0.424321	0.212160	+	0.977235i	$0.431950\pi$
$822$	−21.4506	−0.748175
$823$	17.1088	0.596376	0.298188	−	0.954507i	$-0.403618\pi$
$823$	17.1088	0.596376	0.298188	+	0.954507i	$0.403618\pi$
$824$	32.1656	1.12054
$825$	−2.80654	−0.0977111
$826$	66.8653	2.32654
$827$	27.7573	0.965216	0.482608	−	0.875836i	$-0.339690\pi$
$827$	27.7573	0.965216	0.482608	+	0.875836i	$0.339690\pi$
$828$	0	0
$829$	−14.5103	−0.503964	−0.251982	−	0.967732i	$-0.581082\pi$
$829$	−14.5103	−0.503964	−0.251982	+	0.967732i	$0.581082\pi$
$830$	−3.22678	−0.112003
$831$	−5.77947	−0.200488
$832$	25.6134	0.887984
$833$	−29.1422	−1.00972
$834$	29.5545	1.02339
$835$	10.2986	0.356397
$836$	0.225319	0.00779282
$837$	7.53104	0.260311
$838$	30.1254	1.04067
$839$	−28.4461	−0.982070	−0.491035	−	0.871140i	$-0.663381\pi$
$839$	−28.4461	−0.982070	−0.491035	+	0.871140i	$0.663381\pi$
$840$	−10.0918	−0.348200
$841$	−1.28884	−0.0444427
$842$	−6.88193	−0.237167
$843$	9.91216	0.341393
$844$	−0.152700	−0.00525616
$845$	3.74579	0.128859
$846$	−7.25864	−0.249557
$847$	−10.8443	−0.372615
$848$	1.65953	0.0569884
$849$	−7.41805	−0.254587
$850$	7.90539	0.271153
$851$	0	0
$852$	1.57273	0.0538809
$853$	19.9093	0.681681	0.340841	−	0.940121i	$-0.389288\pi$
$853$	19.9093	0.681681	0.340841	+	0.940121i	$0.389288\pi$
$854$	53.0018	1.81368
$855$	−0.670825	−0.0229417
$856$	27.6715	0.945792
$857$	11.9881	0.409505	0.204752	−	0.978814i	$-0.434361\pi$
$857$	11.9881	0.409505	0.204752	+	0.978814i	$0.434361\pi$
$858$	11.7073	0.399681
$859$	49.4277	1.68645	0.843226	−	0.537559i	$-0.180653\pi$
$859$	49.4277	1.68645	0.843226	+	0.537559i	$0.180653\pi$
$860$	0.330247	0.0112613
$861$	7.21349	0.245835
$862$	35.1983	1.19886
$863$	56.2795	1.91578	0.957889	−	0.287139i	$-0.0927042\pi$
$863$	56.2795	1.91578	0.957889	+	0.287139i	$0.0927042\pi$
$864$	−0.676078	−0.0230006
$865$	−3.96885	−0.134945
$866$	53.7167	1.82537
$867$	16.2365	0.551420
$868$	−3.12935	−0.106217
$869$	15.5352	0.526995
$870$	−7.21844	−0.244728
$871$	−4.34730	−0.147303
$872$	−11.2137	−0.379742
$873$	−10.0065	−0.338667
$874$	0	0
$875$	−3.47202	−0.117376
$876$	−0.967380	−0.0326847
$877$	−15.2399	−0.514615	−0.257308	−	0.966330i	$-0.582835\pi$
$877$	−15.2399	−0.514615	−0.257308	+	0.966330i	$0.582835\pi$
$878$	37.1631	1.25419
$879$	−1.68483	−0.0568281
$880$	−10.5142	−0.354433
$881$	−13.4652	−0.453654	−0.226827	−	0.973935i	$-0.572835\pi$
$881$	−13.4652	−0.453654	−0.226827	+	0.973935i	$0.572835\pi$
$882$	−6.93155	−0.233398
$883$	−36.6299	−1.23269	−0.616347	−	0.787475i	$-0.711388\pi$
$883$	−36.6299	−1.23269	−0.616347	+	0.787475i	$0.711388\pi$
$884$	2.09891	0.0705941
$885$	14.0444	0.472097
$886$	3.99078	0.134073
$887$	35.2368	1.18314	0.591568	−	0.806255i	$-0.298509\pi$
$887$	35.2368	1.18314	0.591568	+	0.806255i	$0.298509\pi$
$888$	−18.7761	−0.630085
$889$	−29.4460	−0.987586
$890$	−20.6241	−0.691322
$891$	−2.80654	−0.0940226
$892$	−2.07494	−0.0694741
$893$	3.55098	0.118829
$894$	6.49404	0.217193
$895$	−18.9645	−0.633912
$896$	−35.3915	−1.18235
$897$	0	0
$898$	−39.0670	−1.30368
$899$	−39.6444	−1.32222
$900$	−0.119679	−0.00398929
$901$	2.55380	0.0850795
$902$	7.99558	0.266224
$903$	9.58084	0.318830
$904$	−27.8327	−0.925702
$905$	−22.0972	−0.734535
$906$	28.9744	0.962609
$907$	3.75149	0.124566	0.0622831	−	0.998059i	$-0.480162\pi$
$907$	3.75149	0.124566	0.0622831	+	0.998059i	$0.480162\pi$
$908$	−2.84534	−0.0944258
$909$	11.5918	0.384477
$910$	14.4833	0.480117
$911$	−30.5307	−1.01153	−0.505763	−	0.862672i	$-0.668789\pi$
$911$	−30.5307	−1.01153	−0.505763	+	0.862672i	$0.668789\pi$
$912$	−2.51313	−0.0832179
$913$	6.60427	0.218569
$914$	−26.2133	−0.867059
$915$	11.1325	0.368029
$916$	−0.631693	−0.0208717
$917$	11.0254	0.364091
$918$	7.90539	0.260917
$919$	−29.6084	−0.976692	−0.488346	−	0.872650i	$-0.662400\pi$
$919$	−29.6084	−0.976692	−0.488346	+	0.872650i	$0.662400\pi$
$920$	0	0
$921$	−8.68397	−0.286146
$922$	37.2616	1.22715
$923$	−39.9767	−1.31585
$924$	1.16619	0.0383650
$925$	−6.45981	−0.212397
$926$	37.1980	1.22240
$927$	11.0664	0.363467
$928$	3.55897	0.116829
$929$	29.8571	0.979579	0.489789	−	0.871841i	$-0.337074\pi$
$929$	29.8571	0.979579	0.489789	+	0.871841i	$0.337074\pi$
$930$	10.3269	0.338633
$931$	3.39097	0.111135
$932$	−3.32566	−0.108936
$933$	10.8008	0.353603
$934$	−1.05669	−0.0345759
$935$	−16.1800	−0.529143
$936$	8.84211	0.289013
$937$	8.56968	0.279959	0.139980	−	0.990154i	$-0.455296\pi$
$937$	8.56968	0.279959	0.139980	+	0.990154i	$0.455296\pi$
$938$	6.80375	0.222150
$939$	−4.41578	−0.144104
$940$	0.633514	0.0206630
$941$	−8.81651	−0.287410	−0.143705	−	0.989621i	$-0.545902\pi$
$941$	−8.81651	−0.287410	−0.143705	+	0.989621i	$0.545902\pi$
$942$	−27.5621	−0.898023
$943$	0	0
$944$	52.6148	1.71246
$945$	−3.47202	−0.112945
$946$	10.6196	0.345273
$947$	13.1947	0.428771	0.214385	−	0.976749i	$-0.431225\pi$
$947$	13.1947	0.428771	0.214385	+	0.976749i	$0.431225\pi$
$948$	0.662465	0.0215159
$949$	24.5895	0.798208
$950$	−0.919868	−0.0298444
$951$	−25.0524	−0.812379
$952$	−58.1803	−1.88563
$953$	−14.6848	−0.475688	−0.237844	−	0.971303i	$-0.576441\pi$
$953$	−14.6848	−0.475688	−0.237844	+	0.971303i	$0.576441\pi$
$954$	0.607429	0.0196662
$955$	15.1417	0.489974
$956$	−1.60925	−0.0520469
$957$	14.7740	0.477576
$958$	31.4996	1.01771
$959$	54.3132	1.75386
$960$	−8.41971	−0.271745
$961$	25.7166	0.829566
$962$	26.9467	0.868796
$963$	9.52021	0.306785
$964$	2.12125	0.0683210
$965$	−22.2054	−0.714818
$966$	0	0
$967$	−37.9550	−1.22055	−0.610275	−	0.792189i	$-0.708941\pi$
$967$	−37.9550	−1.22055	−0.610275	+	0.792189i	$0.708941\pi$
$968$	−9.07832	−0.291788
$969$	−3.86738	−0.124238
$970$	−13.7213	−0.440566
$971$	2.62391	0.0842054	0.0421027	−	0.999113i	$-0.486594\pi$
$971$	2.62391	0.0842054	0.0421027	+	0.999113i	$0.486594\pi$
$972$	−0.119679	−0.00383870
$973$	−74.8323	−2.39901
$974$	4.22089	0.135246
$975$	3.04207	0.0974243
$976$	41.7058	1.33497
$977$	−11.9010	−0.380747	−0.190374	−	0.981712i	$-0.560970\pi$
$977$	−11.9010	−0.380747	−0.190374	+	0.981712i	$0.560970\pi$
$978$	12.8244	0.410079
$979$	42.2115	1.34908
$980$	0.604967	0.0193250
$981$	−3.85799	−0.123176
$982$	25.3352	0.808480
$983$	8.92531	0.284673	0.142337	−	0.989818i	$-0.454538\pi$
$983$	8.92531	0.284673	0.142337	+	0.989818i	$0.454538\pi$
$984$	6.03878	0.192509
$985$	15.4762	0.493113
$986$	−41.6151	−1.32529
$987$	18.3790	0.585009
$988$	−0.244229	−0.00776994
$989$	0	0
$990$	−3.84846	−0.122312
$991$	−13.6460	−0.433479	−0.216739	−	0.976229i	$-0.569542\pi$
$991$	−13.6460	−0.433479	−0.216739	+	0.976229i	$0.569542\pi$
$992$	−5.09157	−0.161658
$993$	7.19813	0.228426
$994$	62.5655	1.98446
$995$	17.1307	0.543078
$996$	0.281625	0.00892362
$997$	−11.5027	−0.364293	−0.182147	−	0.983271i	$-0.558305\pi$
$997$	−11.5027	−0.364293	−0.182147	+	0.983271i	$0.558305\pi$
$998$	−47.3615	−1.49920
$999$	−6.45981	−0.204379

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bh.1.3	✓	8
23.22	odd	2		7935.2.a.bi.1.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7935.2.a.bh.1.3	✓	8	1.1	even	1	trivial
7935.2.a.bi.1.3	yes	8	23.22	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:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q-1.37125 q^{2} +1.00000 q^{3} -0.119679 q^{4} -1.00000 q^{5} -1.37125 q^{6} +3.47202 q^{7} +2.90661 q^{8} +1.00000 q^{9} +1.37125 q^{10} -2.80654 q^{11} -0.119679 q^{12} +3.04207 q^{13} -4.76100 q^{14} -1.00000 q^{15} -3.74632 q^{16} -5.76511 q^{17} -1.37125 q^{18} +0.670825 q^{19} +0.119679 q^{20} +3.47202 q^{21} +3.84846 q^{22} +2.90661 q^{24} +1.00000 q^{25} -4.17144 q^{26} +1.00000 q^{27} -0.415527 q^{28} -5.26414 q^{29} +1.37125 q^{30} +7.53104 q^{31} -0.676078 q^{32} -2.80654 q^{33} +7.90539 q^{34} -3.47202 q^{35} -0.119679 q^{36} -6.45981 q^{37} -0.919868 q^{38} +3.04207 q^{39} -2.90661 q^{40} +2.07761 q^{41} -4.76100 q^{42} +2.75944 q^{43} +0.335883 q^{44} -1.00000 q^{45} +5.29345 q^{47} -3.74632 q^{48} +5.05492 q^{49} -1.37125 q^{50} -5.76511 q^{51} -0.364072 q^{52} -0.442976 q^{53} -1.37125 q^{54} +2.80654 q^{55} +10.0918 q^{56} +0.670825 q^{57} +7.21844 q^{58} -14.0444 q^{59} +0.119679 q^{60} -11.1325 q^{61} -10.3269 q^{62} +3.47202 q^{63} +8.41971 q^{64} -3.04207 q^{65} +3.84846 q^{66} -1.42906 q^{67} +0.689962 q^{68} +4.76100 q^{70} -13.1413 q^{71} +2.90661 q^{72} +8.08313 q^{73} +8.85800 q^{74} +1.00000 q^{75} -0.0802836 q^{76} -9.74436 q^{77} -4.17144 q^{78} -5.53536 q^{79} +3.74632 q^{80} +1.00000 q^{81} -2.84891 q^{82} -2.35317 q^{83} -0.415527 q^{84} +5.76511 q^{85} -3.78388 q^{86} -5.26414 q^{87} -8.15750 q^{88} -15.0404 q^{89} +1.37125 q^{90} +10.5621 q^{91} +7.53104 q^{93} -7.25864 q^{94} -0.670825 q^{95} -0.676078 q^{96} -10.0065 q^{97} -6.93155 q^{98} -2.80654 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} + 8 q^{4} - 8 q^{5} - 6 q^{7} + 6 q^{8} + 8 q^{9} - 12 q^{11} + 8 q^{12} + 4 q^{13} - 8 q^{15} - 20 q^{17} - 4 q^{19} - 8 q^{20} - 6 q^{21} - 14 q^{22} + 6 q^{24} + 8 q^{25} - 22 q^{26} + 8 q^{27}+ \cdots - 12 q^{99}+O(q^{100}) \) 8 * q + 8 * q^3 + 8 * q^4 - 8 * q^5 - 6 * q^7 + 6 * q^8 + 8 * q^9 - 12 * q^11 + 8 * q^12 + 4 * q^13 - 8 * q^15 - 20 * q^17 - 4 * q^19 - 8 * q^20 - 6 * q^21 - 14 * q^22 + 6 * q^24 + 8 * q^25 - 22 * q^26 + 8 * q^27 + 8 * q^28 + 2 * q^31 + 12 * q^32 - 12 * q^33 - 8 * q^34 + 6 * q^35 + 8 * q^36 - 2 * q^37 + 2 * q^38 + 4 * q^39 - 6 * q^40 + 28 * q^41 - 4 * q^43 - 54 * q^44 - 8 * q^45 - 12 * q^47 + 14 * q^49 - 20 * q^51 - 22 * q^52 - 6 * q^53 + 12 * q^55 + 24 * q^56 - 4 * q^57 + 32 * q^58 + 2 * q^59 - 8 * q^60 - 32 * q^61 - 24 * q^62 - 6 * q^63 - 8 * q^64 - 4 * q^65 - 14 * q^66 - 32 * q^67 - 34 * q^68 + 2 * q^71 + 6 * q^72 - 2 * q^73 - 6 * q^74 + 8 * q^75 - 24 * q^76 - 30 * q^77 - 22 * q^78 + 36 * q^79 + 8 * q^81 + 16 * q^82 - 10 * q^83 + 8 * q^84 + 20 * q^85 - 50 * q^86 - 6 * q^88 - 42 * q^89 - 4 * q^91 + 2 * q^93 - 40 * q^94 + 4 * q^95 + 12 * q^96 - 16 * q^97 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more