LMFDB - Embedded newform 6025.2.a.g.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$48.1098672178$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2x^{10} - 11x^{9} + 15x^{8} + 43x^{7} - 28x^{6} - 62x^{5} + 14x^{4} + 31x^{3} + x^{2} - 5x - 1 $ x^11 - 2x^10 - 11x^9 + 15x^8 + 43x^7 - 28x^6 - 62x^5 + 14x^4 + 31x^3 + x^2 - 5*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1205)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.514683$ of defining polynomial
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.428259 q^{2} -2.33128 q^{3} -1.81659 q^{4} +0.998390 q^{6} +3.85771 q^{7} +1.63449 q^{8} +2.43486 q^{9} +O(q^{10})$	\(q-0.428259 q^{2} -2.33128 q^{3} -1.81659 q^{4} +0.998390 q^{6} +3.85771 q^{7} +1.63449 q^{8} +2.43486 q^{9} -0.897246 q^{11} +4.23499 q^{12} +4.05733 q^{13} -1.65210 q^{14} +2.93320 q^{16} +3.01844 q^{17} -1.04275 q^{18} -5.78422 q^{19} -8.99339 q^{21} +0.384253 q^{22} +7.46083 q^{23} -3.81045 q^{24} -1.73759 q^{26} +1.31751 q^{27} -7.00789 q^{28} +9.45012 q^{29} +8.89095 q^{31} -4.52515 q^{32} +2.09173 q^{33} -1.29267 q^{34} -4.42315 q^{36} +9.60614 q^{37} +2.47714 q^{38} -9.45876 q^{39} +5.69346 q^{41} +3.85150 q^{42} -3.09108 q^{43} +1.62993 q^{44} -3.19516 q^{46} +9.19000 q^{47} -6.83812 q^{48} +7.88192 q^{49} -7.03682 q^{51} -7.37052 q^{52} -3.93333 q^{53} -0.564233 q^{54} +6.30539 q^{56} +13.4846 q^{57} -4.04710 q^{58} -6.77334 q^{59} -1.83657 q^{61} -3.80762 q^{62} +9.39297 q^{63} -3.92848 q^{64} -0.895801 q^{66} +8.14775 q^{67} -5.48328 q^{68} -17.3933 q^{69} +6.27670 q^{71} +3.97975 q^{72} -11.6000 q^{73} -4.11391 q^{74} +10.5076 q^{76} -3.46131 q^{77} +4.05080 q^{78} +14.4227 q^{79} -10.3760 q^{81} -2.43828 q^{82} +4.57440 q^{83} +16.3373 q^{84} +1.32378 q^{86} -22.0309 q^{87} -1.46654 q^{88} -12.1532 q^{89} +15.6520 q^{91} -13.5533 q^{92} -20.7273 q^{93} -3.93570 q^{94} +10.5494 q^{96} +6.63653 q^{97} -3.37550 q^{98} -2.18466 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 4 q^{2} + 8 q^{3} + 6 q^{4} + 7 q^{6} + 9 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) $ 11 * q + 4 * q^2 + 8 * q^3 + 6 * q^4 + 7 * q^6 + 9 * q^7 + 12 * q^8 + 9 * q^9	$ 11 q + 4 q^{2} + 8 q^{3} + 6 q^{4} + 7 q^{6} + 9 q^{7} + 12 q^{8} + 9 q^{9} - 3 q^{11} + 28 q^{12} + 9 q^{13} + 2 q^{14} - 16 q^{16} + 4 q^{17} + 6 q^{18} - 33 q^{19} + 2 q^{21} - 6 q^{22} + 31 q^{23} + 32 q^{24} - 20 q^{26} + 32 q^{27} + q^{28} + q^{29} + 6 q^{31} - 7 q^{32} + 35 q^{33} + 9 q^{34} + 33 q^{36} + 23 q^{37} - 20 q^{38} + 14 q^{39} + 8 q^{41} + 26 q^{42} + 19 q^{43} + 6 q^{46} + 35 q^{47} - 16 q^{48} + 4 q^{49} - 3 q^{51} + 3 q^{52} - 14 q^{53} + 9 q^{54} + 33 q^{56} - q^{57} + 11 q^{58} - 6 q^{59} + 9 q^{61} + 23 q^{62} + 31 q^{63} + 18 q^{64} - 36 q^{66} + 54 q^{67} - q^{68} + 17 q^{69} - 5 q^{71} + 64 q^{72} - 17 q^{73} + 8 q^{74} - 31 q^{76} + 18 q^{77} - 15 q^{78} - 16 q^{79} + 43 q^{81} + 61 q^{82} + 29 q^{83} + 69 q^{84} + 5 q^{86} - 5 q^{87} + 14 q^{88} - 5 q^{89} - 54 q^{91} + 6 q^{92} + 25 q^{93} - 19 q^{94} + 9 q^{96} - 6 q^{97} + 29 q^{98} + 60 q^{99}+O(q^{100}) $ 11 * q + 4 * q^2 + 8 * q^3 + 6 * q^4 + 7 * q^6 + 9 * q^7 + 12 * q^8 + 9 * q^9 - 3 * q^11 + 28 * q^12 + 9 * q^13 + 2 * q^14 - 16 * q^16 + 4 * q^17 + 6 * q^18 - 33 * q^19 + 2 * q^21 - 6 * q^22 + 31 * q^23 + 32 * q^24 - 20 * q^26 + 32 * q^27 + q^28 + q^29 + 6 * q^31 - 7 * q^32 + 35 * q^33 + 9 * q^34 + 33 * q^36 + 23 * q^37 - 20 * q^38 + 14 * q^39 + 8 * q^41 + 26 * q^42 + 19 * q^43 + 6 * q^46 + 35 * q^47 - 16 * q^48 + 4 * q^49 - 3 * q^51 + 3 * q^52 - 14 * q^53 + 9 * q^54 + 33 * q^56 - q^57 + 11 * q^58 - 6 * q^59 + 9 * q^61 + 23 * q^62 + 31 * q^63 + 18 * q^64 - 36 * q^66 + 54 * q^67 - q^68 + 17 * q^69 - 5 * q^71 + 64 * q^72 - 17 * q^73 + 8 * q^74 - 31 * q^76 + 18 * q^77 - 15 * q^78 - 16 * q^79 + 43 * q^81 + 61 * q^82 + 29 * q^83 + 69 * q^84 + 5 * q^86 - 5 * q^87 + 14 * q^88 - 5 * q^89 - 54 * q^91 + 6 * q^92 + 25 * q^93 - 19 * q^94 + 9 * q^96 - 6 * q^97 + 29 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.428259	−0.302825	−0.151412	−	0.988471i	$-0.548382\pi$
$2$	−0.428259	−0.302825	−0.151412	+	0.988471i	$0.548382\pi$
$3$	−2.33128	−1.34596	−0.672982	−	0.739659i	$-0.734987\pi$
$3$	−2.33128	−1.34596	−0.672982	+	0.739659i	$0.734987\pi$
$4$	−1.81659	−0.908297
$5$	0	0
$5$	0	0
$6$	0.998390	0.407591
$7$	3.85771	1.45808	0.729039	−	0.684473i	$-0.239968\pi$
$7$	3.85771	1.45808	0.729039	+	0.684473i	$0.239968\pi$
$8$	1.63449	0.577879
$9$	2.43486	0.811619
$10$	0	0
$11$	−0.897246	−0.270530	−0.135265	−	0.990809i	$-0.543189\pi$
$11$	−0.897246	−0.270530	−0.135265	+	0.990809i	$0.543189\pi$
$12$	4.23499	1.22254
$13$	4.05733	1.12530	0.562650	−	0.826695i	$-0.309782\pi$
$13$	4.05733	1.12530	0.562650	+	0.826695i	$0.309782\pi$
$14$	−1.65210	−0.441542
$15$	0	0
$16$	2.93320	0.733301
$17$	3.01844	0.732079	0.366039	−	0.930599i	$-0.380714\pi$
$17$	3.01844	0.732079	0.366039	+	0.930599i	$0.380714\pi$
$18$	−1.04275	−0.245778
$19$	−5.78422	−1.32699	−0.663495	−	0.748180i	$-0.730928\pi$
$19$	−5.78422	−1.32699	−0.663495	+	0.748180i	$0.730928\pi$
$20$	0	0
$21$	−8.99339	−1.96252
$22$	0.384253	0.0819231
$23$	7.46083	1.55569	0.777845	−	0.628456i	$-0.216313\pi$
$23$	7.46083	1.55569	0.777845	+	0.628456i	$0.216313\pi$
$24$	−3.81045	−0.777805
$25$	0	0
$26$	−1.73759	−0.340769
$27$	1.31751	0.253554
$28$	−7.00789	−1.32437
$29$	9.45012	1.75484	0.877422	−	0.479720i	$-0.159262\pi$
$29$	9.45012	1.75484	0.877422	+	0.479720i	$0.159262\pi$
$30$	0	0
$31$	8.89095	1.59686	0.798430	−	0.602087i	$-0.205664\pi$
$31$	8.89095	1.59686	0.798430	+	0.602087i	$0.205664\pi$
$32$	−4.52515	−0.799941
$33$	2.09173	0.364123
$34$	−1.29267	−0.221691
$35$	0	0
$36$	−4.42315	−0.737191
$37$	9.60614	1.57924	0.789620	−	0.613597i	$-0.210278\pi$
$37$	9.60614	1.57924	0.789620	+	0.613597i	$0.210278\pi$
$38$	2.47714	0.401845
$39$	−9.45876	−1.51461
$40$	0	0
$41$	5.69346	0.889170	0.444585	−	0.895737i	$-0.353351\pi$
$41$	5.69346	0.889170	0.444585	+	0.895737i	$0.353351\pi$
$42$	3.85150	0.594299
$43$	−3.09108	−0.471385	−0.235692	−	0.971828i	$-0.575736\pi$
$43$	−3.09108	−0.471385	−0.235692	+	0.971828i	$0.575736\pi$
$44$	1.62993	0.245721
$45$	0	0
$46$	−3.19516	−0.471101
$47$	9.19000	1.34050	0.670250	−	0.742136i	$-0.266187\pi$
$47$	9.19000	1.34050	0.670250	+	0.742136i	$0.266187\pi$
$48$	−6.83812	−0.986997
$49$	7.88192	1.12599
$50$	0	0
$51$	−7.03682	−0.985351
$52$	−7.37052	−1.02211
$53$	−3.93333	−0.540284	−0.270142	−	0.962821i	$-0.587071\pi$
$53$	−3.93333	−0.540284	−0.270142	+	0.962821i	$0.587071\pi$
$54$	−0.564233	−0.0767824
$55$	0	0
$56$	6.30539	0.842593
$57$	13.4846	1.78608
$58$	−4.04710	−0.531410
$59$	−6.77334	−0.881814	−0.440907	−	0.897553i	$-0.645343\pi$
$59$	−6.77334	−0.881814	−0.440907	+	0.897553i	$0.645343\pi$
$60$	0	0
$61$	−1.83657	−0.235149	−0.117575	−	0.993064i	$-0.537512\pi$
$61$	−1.83657	−0.235149	−0.117575	+	0.993064i	$0.537512\pi$
$62$	−3.80762	−0.483569
$63$	9.39297	1.18340
$64$	−3.92848	−0.491059
$65$	0	0
$66$	−0.895801	−0.110265
$67$	8.14775	0.995406	0.497703	−	0.867348i	$-0.334177\pi$
$67$	8.14775	0.995406	0.497703	+	0.867348i	$0.334177\pi$
$68$	−5.48328	−0.664945
$69$	−17.3933	−2.09390
$70$	0	0
$71$	6.27670	0.744907	0.372454	−	0.928051i	$-0.378517\pi$
$71$	6.27670	0.744907	0.372454	+	0.928051i	$0.378517\pi$
$72$	3.97975	0.469018
$73$	−11.6000	−1.35767	−0.678837	−	0.734289i	$-0.737516\pi$
$73$	−11.6000	−1.35767	−0.678837	+	0.734289i	$0.737516\pi$
$74$	−4.11391	−0.478232
$75$	0	0
$76$	10.5076	1.20530
$77$	−3.46131	−0.394453
$78$	4.05080	0.458662
$79$	14.4227	1.62268	0.811340	−	0.584575i	$-0.198739\pi$
$79$	14.4227	1.62268	0.811340	+	0.584575i	$0.198739\pi$
$80$	0	0
$81$	−10.3760	−1.15289
$82$	−2.43828	−0.269262
$83$	4.57440	0.502106	0.251053	−	0.967973i	$-0.419223\pi$
$83$	4.57440	0.502106	0.251053	+	0.967973i	$0.419223\pi$
$84$	16.3373	1.78255
$85$	0	0
$86$	1.32378	0.142747
$87$	−22.0309	−2.36196
$88$	−1.46654	−0.156334
$89$	−12.1532	−1.28824	−0.644121	−	0.764924i	$-0.722777\pi$
$89$	−12.1532	−1.28824	−0.644121	+	0.764924i	$0.722777\pi$
$90$	0	0
$91$	15.6520	1.64078
$92$	−13.5533	−1.41303
$93$	−20.7273	−2.14932
$94$	−3.93570	−0.405936
$95$	0	0
$96$	10.5494	1.07669
$97$	6.63653	0.673838	0.336919	−	0.941534i	$-0.390615\pi$
$97$	6.63653	0.673838	0.336919	+	0.941534i	$0.390615\pi$
$98$	−3.37550	−0.340977
$99$	−2.18466	−0.219567
$100$	0	0
$101$	−8.73239	−0.868905	−0.434453	−	0.900695i	$-0.643058\pi$
$101$	−8.73239	−0.868905	−0.434453	+	0.900695i	$0.643058\pi$
$102$	3.01358	0.298389
$103$	−1.10886	−0.109259	−0.0546294	−	0.998507i	$-0.517398\pi$
$103$	−1.10886	−0.109259	−0.0546294	+	0.998507i	$0.517398\pi$
$104$	6.63166	0.650288
$105$	0	0
$106$	1.68448	0.163611
$107$	11.5779	1.11928	0.559638	−	0.828737i	$-0.310940\pi$
$107$	11.5779	1.11928	0.559638	+	0.828737i	$0.310940\pi$
$108$	−2.39337	−0.230303
$109$	20.0859	1.92388	0.961942	−	0.273254i	$-0.0881000\pi$
$109$	20.0859	1.92388	0.961942	+	0.273254i	$0.0881000\pi$
$110$	0	0
$111$	−22.3946	−2.12560
$112$	11.3155	1.06921
$113$	−3.90857	−0.367687	−0.183844	−	0.982956i	$-0.558854\pi$
$113$	−3.90857	−0.367687	−0.183844	+	0.982956i	$0.558854\pi$
$114$	−5.77491	−0.540869
$115$	0	0
$116$	−17.1670	−1.59392
$117$	9.87902	0.913315
$118$	2.90074	0.267035
$119$	11.6443	1.06743
$120$	0	0
$121$	−10.1950	−0.926814
$122$	0.786529	0.0712090
$123$	−13.2730	−1.19679
$124$	−16.1512	−1.45042
$125$	0	0
$126$	−4.02262	−0.358364
$127$	−8.47069	−0.751652	−0.375826	−	0.926690i	$-0.622641\pi$
$127$	−8.47069	−0.751652	−0.375826	+	0.926690i	$0.622641\pi$
$128$	10.7327	0.948646
$129$	7.20616	0.634467
$130$	0	0
$131$	−14.3726	−1.25574	−0.627870	−	0.778318i	$-0.716073\pi$
$131$	−14.3726	−1.25574	−0.627870	+	0.778318i	$0.716073\pi$
$132$	−3.79982	−0.330732
$133$	−22.3138	−1.93485
$134$	−3.48934	−0.301433
$135$	0	0
$136$	4.93360	0.423053
$137$	−12.1101	−1.03463	−0.517316	−	0.855794i	$-0.673069\pi$
$137$	−12.1101	−1.03463	−0.517316	+	0.855794i	$0.673069\pi$
$138$	7.44881	0.634085
$139$	−17.0064	−1.44246	−0.721232	−	0.692694i	$-0.756424\pi$
$139$	−17.0064	−1.44246	−0.721232	+	0.692694i	$0.756424\pi$
$140$	0	0
$141$	−21.4244	−1.80426
$142$	−2.68805	−0.225576
$143$	−3.64042	−0.304427
$144$	7.14193	0.595161
$145$	0	0
$146$	4.96779	0.411137
$147$	−18.3749	−1.51554
$148$	−17.4505	−1.43442
$149$	−8.62117	−0.706273	−0.353137	−	0.935572i	$-0.614885\pi$
$149$	−8.62117	−0.706273	−0.353137	+	0.935572i	$0.614885\pi$
$150$	0	0
$151$	21.0527	1.71324	0.856622	−	0.515944i	$-0.172559\pi$
$151$	21.0527	1.71324	0.856622	+	0.515944i	$0.172559\pi$
$152$	−9.45425	−0.766841
$153$	7.34946	0.594169
$154$	1.48234	0.119450
$155$	0	0
$156$	17.1827	1.37572
$157$	−2.11927	−0.169136	−0.0845679	−	0.996418i	$-0.526951\pi$
$157$	−2.11927	−0.169136	−0.0845679	+	0.996418i	$0.526951\pi$
$158$	−6.17664	−0.491387
$159$	9.16968	0.727203
$160$	0	0
$161$	28.7817	2.26832
$162$	4.44363	0.349125
$163$	−4.07781	−0.319399	−0.159699	−	0.987166i	$-0.551052\pi$
$163$	−4.07781	−0.319399	−0.159699	+	0.987166i	$0.551052\pi$
$164$	−10.3427	−0.807631
$165$	0	0
$166$	−1.95903	−0.152050
$167$	7.96965	0.616710	0.308355	−	0.951271i	$-0.400221\pi$
$167$	7.96965	0.616710	0.308355	+	0.951271i	$0.400221\pi$
$168$	−14.6996	−1.13410
$169$	3.46192	0.266302
$170$	0	0
$171$	−14.0837	−1.07701
$172$	5.61523	0.428157
$173$	7.42394	0.564432	0.282216	−	0.959351i	$-0.408931\pi$
$173$	7.42394	0.564432	0.282216	+	0.959351i	$0.408931\pi$
$174$	9.43491	0.715258
$175$	0	0
$176$	−2.63181	−0.198380
$177$	15.7905	1.18689
$178$	5.20473	0.390111
$179$	−4.84011	−0.361767	−0.180884	−	0.983505i	$-0.557896\pi$
$179$	−4.84011	−0.361767	−0.180884	+	0.983505i	$0.557896\pi$
$180$	0	0
$181$	−13.5267	−1.00543	−0.502717	−	0.864451i	$-0.667666\pi$
$181$	−13.5267	−1.00543	−0.502717	+	0.864451i	$0.667666\pi$
$182$	−6.70310	−0.496867
$183$	4.28157	0.316502
$184$	12.1946	0.899001
$185$	0	0
$186$	8.87663	0.650866
$187$	−2.70828	−0.198049
$188$	−16.6945	−1.21757
$189$	5.08255	0.369701
$190$	0	0
$191$	−4.66153	−0.337296	−0.168648	−	0.985676i	$-0.553940\pi$
$191$	−4.66153	−0.337296	−0.168648	+	0.985676i	$0.553940\pi$
$192$	9.15837	0.660948
$193$	−13.9870	−1.00680	−0.503402	−	0.864053i	$-0.667918\pi$
$193$	−13.9870	−1.00680	−0.503402	+	0.864053i	$0.667918\pi$
$194$	−2.84215	−0.204055
$195$	0	0
$196$	−14.3183	−1.02273
$197$	−22.2611	−1.58604	−0.793020	−	0.609196i	$-0.791492\pi$
$197$	−22.2611	−1.58604	−0.793020	+	0.609196i	$0.791492\pi$
$198$	0.935602	0.0664903
$199$	−22.3437	−1.58391	−0.791953	−	0.610582i	$-0.790935\pi$
$199$	−22.3437	−1.58391	−0.791953	+	0.610582i	$0.790935\pi$
$200$	0	0
$201$	−18.9947	−1.33978
$202$	3.73972	0.263126
$203$	36.4558	2.55870
$204$	12.7830	0.894992
$205$	0	0
$206$	0.474877	0.0330863
$207$	18.1660	1.26263
$208$	11.9010	0.825184
$209$	5.18987	0.358990
$210$	0	0
$211$	−21.9959	−1.51426	−0.757129	−	0.653265i	$-0.773399\pi$
$211$	−21.9959	−1.51426	−0.757129	+	0.653265i	$0.773399\pi$
$212$	7.14526	0.490738
$213$	−14.6327	−1.00262
$214$	−4.95832	−0.338944
$215$	0	0
$216$	2.15345	0.146524
$217$	34.2987	2.32835
$218$	−8.60198	−0.582599
$219$	27.0428	1.82738
$220$	0	0
$221$	12.2468	0.823808
$222$	9.59067	0.643684
$223$	8.21473	0.550099	0.275050	−	0.961430i	$-0.411306\pi$
$223$	8.21473	0.550099	0.275050	+	0.961430i	$0.411306\pi$
$224$	−17.4567	−1.16638
$225$	0	0
$226$	1.67388	0.111345
$227$	−6.24680	−0.414614	−0.207307	−	0.978276i	$-0.566470\pi$
$227$	−6.24680	−0.414614	−0.207307	+	0.978276i	$0.566470\pi$
$228$	−24.4961	−1.62229
$229$	3.87268	0.255914	0.127957	−	0.991780i	$-0.459158\pi$
$229$	3.87268	0.255914	0.127957	+	0.991780i	$0.459158\pi$
$230$	0	0
$231$	8.06928	0.530920
$232$	15.4461	1.01409
$233$	11.4350	0.749131	0.374565	−	0.927201i	$-0.377792\pi$
$233$	11.4350	0.749131	0.374565	+	0.927201i	$0.377792\pi$
$234$	−4.23077	−0.276574
$235$	0	0
$236$	12.3044	0.800950
$237$	−33.6233	−2.18407
$238$	−4.98675	−0.323243
$239$	25.2167	1.63113	0.815565	−	0.578665i	$-0.196426\pi$
$239$	25.2167	1.63113	0.815565	+	0.578665i	$0.196426\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	4.36608	0.280662
$243$	20.2369	1.29820
$244$	3.33631	0.213585
$245$	0	0
$246$	5.68430	0.362418
$247$	−23.4685	−1.49326
$248$	14.5322	0.922793
$249$	−10.6642	−0.675816
$250$	0	0
$251$	−11.6887	−0.737787	−0.368894	−	0.929472i	$-0.620263\pi$
$251$	−11.6887	−0.737787	−0.368894	+	0.929472i	$0.620263\pi$
$252$	−17.0632	−1.07488
$253$	−6.69419	−0.420860
$254$	3.62764	0.227619
$255$	0	0
$256$	3.26058	0.203786
$257$	−11.5434	−0.720060	−0.360030	−	0.932941i	$-0.617234\pi$
$257$	−11.5434	−0.720060	−0.360030	+	0.932941i	$0.617234\pi$
$258$	−3.08610	−0.192132
$259$	37.0577	2.30265
$260$	0	0
$261$	23.0097	1.42426
$262$	6.15519	0.380269
$263$	20.1253	1.24098	0.620488	−	0.784216i	$-0.286935\pi$
$263$	20.1253	1.24098	0.620488	+	0.784216i	$0.286935\pi$
$264$	3.41891	0.210419
$265$	0	0
$266$	9.55609	0.585922
$267$	28.3326	1.73393
$268$	−14.8012	−0.904124
$269$	18.0966	1.10337	0.551684	−	0.834053i	$-0.313985\pi$
$269$	18.0966	1.10337	0.551684	+	0.834053i	$0.313985\pi$
$270$	0	0
$271$	7.96928	0.484099	0.242050	−	0.970264i	$-0.422180\pi$
$271$	7.96928	0.484099	0.242050	+	0.970264i	$0.422180\pi$
$272$	8.85369	0.536834
$273$	−36.4892	−2.20842
$274$	5.18624	0.313312
$275$	0	0
$276$	31.5965	1.90189
$277$	27.3064	1.64068	0.820342	−	0.571873i	$-0.193783\pi$
$277$	27.3064	1.64068	0.820342	+	0.571873i	$0.193783\pi$
$278$	7.28313	0.436813
$279$	21.6482	1.29604
$280$	0	0
$281$	19.1167	1.14041	0.570203	−	0.821504i	$-0.306864\pi$
$281$	19.1167	1.14041	0.570203	+	0.821504i	$0.306864\pi$
$282$	9.17520	0.546375
$283$	18.9251	1.12498	0.562490	−	0.826804i	$-0.309844\pi$
$283$	18.9251	1.12498	0.562490	+	0.826804i	$0.309844\pi$
$284$	−11.4022	−0.676597
$285$	0	0
$286$	1.55904	0.0921881
$287$	21.9637	1.29648
$288$	−11.0181	−0.649247
$289$	−7.88904	−0.464061
$290$	0	0
$291$	−15.4716	−0.906962
$292$	21.0725	1.23317
$293$	7.61714	0.444998	0.222499	−	0.974933i	$-0.428579\pi$
$293$	7.61714	0.444998	0.222499	+	0.974933i	$0.428579\pi$
$294$	7.86923	0.458943
$295$	0	0
$296$	15.7011	0.912610
$297$	−1.18213	−0.0685939
$298$	3.69209	0.213877
$299$	30.2710	1.75062
$300$	0	0
$301$	−11.9245	−0.687315
$302$	−9.01600	−0.518812
$303$	20.3576	1.16951
$304$	−16.9663	−0.973084
$305$	0	0
$306$	−3.14747	−0.179929
$307$	−13.3140	−0.759870	−0.379935	−	0.925013i	$-0.624054\pi$
$307$	−13.3140	−0.759870	−0.379935	+	0.925013i	$0.624054\pi$
$308$	6.28780	0.358281
$309$	2.58505	0.147058
$310$	0	0
$311$	25.5153	1.44684	0.723421	−	0.690407i	$-0.242569\pi$
$311$	25.5153	1.44684	0.723421	+	0.690407i	$0.242569\pi$
$312$	−15.4602	−0.875264
$313$	9.16216	0.517876	0.258938	−	0.965894i	$-0.416627\pi$
$313$	9.16216	0.517876	0.258938	+	0.965894i	$0.416627\pi$
$314$	0.907594	0.0512185
$315$	0	0
$316$	−26.2002	−1.47388
$317$	16.0963	0.904057	0.452028	−	0.892004i	$-0.350701\pi$
$317$	16.0963	0.904057	0.452028	+	0.892004i	$0.350701\pi$
$318$	−3.92699	−0.220215
$319$	−8.47908	−0.474737
$320$	0	0
$321$	−26.9912	−1.50650
$322$	−12.3260	−0.686902
$323$	−17.4593	−0.971461
$324$	18.8491	1.04717
$325$	0	0
$326$	1.74636	0.0967217
$327$	−46.8259	−2.58948
$328$	9.30591	0.513833
$329$	35.4523	1.95455
$330$	0	0
$331$	23.8674	1.31187	0.655936	−	0.754817i	$-0.272274\pi$
$331$	23.8674	1.31187	0.655936	+	0.754817i	$0.272274\pi$
$332$	−8.30983	−0.456061
$333$	23.3896	1.28174
$334$	−3.41307	−0.186755
$335$	0	0
$336$	−26.3795	−1.43912
$337$	−13.8152	−0.752560	−0.376280	−	0.926506i	$-0.622797\pi$
$337$	−13.8152	−0.752560	−0.376280	+	0.926506i	$0.622797\pi$
$338$	−1.48260	−0.0806427
$339$	9.11196	0.494894
$340$	0	0
$341$	−7.97736	−0.431998
$342$	6.03149	0.326145
$343$	3.40219	0.183701
$344$	−5.05233	−0.272403
$345$	0	0
$346$	−3.17937	−0.170924
$347$	−8.61730	−0.462601	−0.231301	−	0.972882i	$-0.574298\pi$
$347$	−8.61730	−0.462601	−0.231301	+	0.972882i	$0.574298\pi$
$348$	40.0211	2.14536
$349$	−9.11159	−0.487732	−0.243866	−	0.969809i	$-0.578416\pi$
$349$	−9.11159	−0.487732	−0.243866	+	0.969809i	$0.578416\pi$
$350$	0	0
$351$	5.34556	0.285325
$352$	4.06017	0.216408
$353$	−6.60170	−0.351373	−0.175686	−	0.984446i	$-0.556214\pi$
$353$	−6.60170	−0.351373	−0.175686	+	0.984446i	$0.556214\pi$
$354$	−6.76244	−0.359420
$355$	0	0
$356$	22.0775	1.17011
$357$	−27.1460	−1.43672
$358$	2.07282	0.109552
$359$	20.7318	1.09418	0.547092	−	0.837072i	$-0.315735\pi$
$359$	20.7318	1.09418	0.547092	+	0.837072i	$0.315735\pi$
$360$	0	0
$361$	14.4572	0.760905
$362$	5.79294	0.304470
$363$	23.7673	1.24746
$364$	−28.4333	−1.49031
$365$	0	0
$366$	−1.83362	−0.0958447
$367$	−19.7703	−1.03200	−0.516001	−	0.856588i	$-0.672580\pi$
$367$	−19.7703	−1.03200	−0.516001	+	0.856588i	$0.672580\pi$
$368$	21.8841	1.14079
$369$	13.8628	0.721667
$370$	0	0
$371$	−15.1736	−0.787776
$372$	37.6530	1.95222
$373$	7.46683	0.386618	0.193309	−	0.981138i	$-0.438078\pi$
$373$	7.46683	0.386618	0.193309	+	0.981138i	$0.438078\pi$
$374$	1.15984	0.0599741
$375$	0	0
$376$	15.0210	0.774647
$377$	38.3423	1.97473
$378$	−2.17665	−0.111955
$379$	−24.4326	−1.25502	−0.627509	−	0.778609i	$-0.715925\pi$
$379$	−24.4326	−1.25502	−0.627509	+	0.778609i	$0.715925\pi$
$380$	0	0
$381$	19.7475	1.01170
$382$	1.99634	0.102142
$383$	5.36054	0.273911	0.136955	−	0.990577i	$-0.456268\pi$
$383$	5.36054	0.273911	0.136955	+	0.990577i	$0.456268\pi$
$384$	−25.0209	−1.27684
$385$	0	0
$386$	5.99004	0.304885
$387$	−7.52633	−0.382585
$388$	−12.0559	−0.612045
$389$	−19.1806	−0.972494	−0.486247	−	0.873821i	$-0.661634\pi$
$389$	−19.1806	−0.972494	−0.486247	+	0.873821i	$0.661634\pi$
$390$	0	0
$391$	22.5200	1.13889
$392$	12.8829	0.650686
$393$	33.5065	1.69018
$394$	9.53352	0.480292
$395$	0	0
$396$	3.96865	0.199432
$397$	−13.9485	−0.700055	−0.350027	−	0.936739i	$-0.613828\pi$
$397$	−13.9485	−0.700055	−0.350027	+	0.936739i	$0.613828\pi$
$398$	9.56890	0.479646
$399$	52.0198	2.60424
$400$	0	0
$401$	36.6699	1.83121	0.915604	−	0.402082i	$-0.131713\pi$
$401$	36.6699	1.83121	0.915604	+	0.402082i	$0.131713\pi$
$402$	8.13463	0.405718
$403$	36.0735	1.79695
$404$	15.8632	0.789224
$405$	0	0
$406$	−15.6125	−0.774836
$407$	−8.61906	−0.427231
$408$	−11.5016	−0.569414
$409$	−31.5171	−1.55842	−0.779210	−	0.626763i	$-0.784379\pi$
$409$	−31.5171	−1.55842	−0.779210	+	0.626763i	$0.784379\pi$
$410$	0	0
$411$	28.2319	1.39258
$412$	2.01434	0.0992395
$413$	−26.1296	−1.28575
$414$	−7.77977	−0.382355
$415$	0	0
$416$	−18.3600	−0.900174
$417$	39.6466	1.94150
$418$	−2.22260	−0.108711
$419$	11.4209	0.557946	0.278973	−	0.960299i	$-0.410006\pi$
$419$	11.4209	0.557946	0.278973	+	0.960299i	$0.410006\pi$
$420$	0	0
$421$	−31.5109	−1.53575	−0.767873	−	0.640602i	$-0.778685\pi$
$421$	−31.5109	−1.53575	−0.767873	+	0.640602i	$0.778685\pi$
$422$	9.41992	0.458555
$423$	22.3763	1.08797
$424$	−6.42898	−0.312219
$425$	0	0
$426$	6.26659	0.303617
$427$	−7.08497	−0.342866
$428$	−21.0323	−1.01663
$429$	8.48683	0.409748
$430$	0	0
$431$	−34.3331	−1.65377	−0.826885	−	0.562371i	$-0.809889\pi$
$431$	−34.3331	−1.65377	−0.826885	+	0.562371i	$0.809889\pi$
$432$	3.86451	0.185932
$433$	7.24847	0.348339	0.174170	−	0.984716i	$-0.444276\pi$
$433$	7.24847	0.348339	0.174170	+	0.984716i	$0.444276\pi$
$434$	−14.6887	−0.705080
$435$	0	0
$436$	−36.4880	−1.74746
$437$	−43.1551	−2.06439
$438$	−11.5813	−0.553376
$439$	24.4858	1.16864	0.584322	−	0.811522i	$-0.301360\pi$
$439$	24.4858	1.16864	0.584322	+	0.811522i	$0.301360\pi$
$440$	0	0
$441$	19.1913	0.913874
$442$	−5.24480	−0.249469
$443$	−22.6110	−1.07428	−0.537140	−	0.843493i	$-0.680495\pi$
$443$	−22.6110	−1.07428	−0.537140	+	0.843493i	$0.680495\pi$
$444$	40.6819	1.93068
$445$	0	0
$446$	−3.51803	−0.166584
$447$	20.0983	0.950618
$448$	−15.1549	−0.716002
$449$	−33.3317	−1.57302	−0.786510	−	0.617577i	$-0.788114\pi$
$449$	−33.3317	−1.57302	−0.786510	+	0.617577i	$0.788114\pi$
$450$	0	0
$451$	−5.10844	−0.240547
$452$	7.10028	0.333969
$453$	−49.0797	−2.30596
$454$	2.67524	0.125555
$455$	0	0
$456$	22.0405	1.03214
$457$	−6.30025	−0.294713	−0.147357	−	0.989083i	$-0.547077\pi$
$457$	−6.30025	−0.294713	−0.147357	+	0.989083i	$0.547077\pi$
$458$	−1.65851	−0.0774971
$459$	3.97681	0.185622
$460$	0	0
$461$	2.08658	0.0971819	0.0485910	−	0.998819i	$-0.484527\pi$
$461$	2.08658	0.0971819	0.0485910	+	0.998819i	$0.484527\pi$
$462$	−3.45574	−0.160776
$463$	−7.26250	−0.337517	−0.168758	−	0.985657i	$-0.553976\pi$
$463$	−7.26250	−0.337517	−0.168758	+	0.985657i	$0.553976\pi$
$464$	27.7191	1.28683
$465$	0	0
$466$	−4.89713	−0.226855
$467$	33.1005	1.53171	0.765854	−	0.643014i	$-0.222316\pi$
$467$	33.1005	1.53171	0.765854	+	0.643014i	$0.222316\pi$
$468$	−17.9462	−0.829562
$469$	31.4316	1.45138
$470$	0	0
$471$	4.94060	0.227651
$472$	−11.0710	−0.509582
$473$	2.77345	0.127524
$474$	14.3995	0.661389
$475$	0	0
$476$	−21.1529	−0.969541
$477$	−9.57709	−0.438505
$478$	−10.7993	−0.493946
$479$	−25.2185	−1.15226	−0.576131	−	0.817357i	$-0.695438\pi$
$479$	−25.2185	−1.15226	−0.576131	+	0.817357i	$0.695438\pi$
$480$	0	0
$481$	38.9753	1.77712
$482$	−0.428259	−0.0195066
$483$	−67.0981	−3.05307
$484$	18.5201	0.841822
$485$	0	0
$486$	−8.66664	−0.393127
$487$	23.0207	1.04317	0.521584	−	0.853200i	$-0.325341\pi$
$487$	23.0207	1.04317	0.521584	+	0.853200i	$0.325341\pi$
$488$	−3.00186	−0.135888
$489$	9.50650	0.429899
$490$	0	0
$491$	32.6537	1.47364	0.736819	−	0.676090i	$-0.236327\pi$
$491$	32.6537	1.47364	0.736819	+	0.676090i	$0.236327\pi$
$492$	24.1117	1.08704
$493$	28.5246	1.28468
$494$	10.0506	0.452197
$495$	0	0
$496$	26.0790	1.17098
$497$	24.2137	1.08613
$498$	4.56703	0.204654
$499$	−29.2397	−1.30895	−0.654474	−	0.756085i	$-0.727110\pi$
$499$	−29.2397	−1.30895	−0.654474	+	0.756085i	$0.727110\pi$
$500$	0	0
$501$	−18.5795	−0.830070
$502$	5.00581	0.223420
$503$	19.7160	0.879091	0.439546	−	0.898220i	$-0.355139\pi$
$503$	19.7160	0.879091	0.439546	+	0.898220i	$0.355139\pi$
$504$	15.3527	0.683864
$505$	0	0
$506$	2.86685	0.127447
$507$	−8.07070	−0.358432
$508$	15.3878	0.682723
$509$	8.71025	0.386075	0.193037	−	0.981191i	$-0.438166\pi$
$509$	8.71025	0.386075	0.193037	+	0.981191i	$0.438166\pi$
$510$	0	0
$511$	−44.7493	−1.97959
$512$	−22.8618	−1.01036
$513$	−7.62074	−0.336464
$514$	4.94358	0.218052
$515$	0	0
$516$	−13.0907	−0.576284
$517$	−8.24569	−0.362645
$518$	−15.8703	−0.697300
$519$	−17.3073	−0.759705
$520$	0	0
$521$	−12.0949	−0.529885	−0.264943	−	0.964264i	$-0.585353\pi$
$521$	−12.0949	−0.529885	−0.264943	+	0.964264i	$0.585353\pi$
$522$	−9.85410	−0.431302
$523$	−5.42540	−0.237236	−0.118618	−	0.992940i	$-0.537846\pi$
$523$	−5.42540	−0.237236	−0.118618	+	0.992940i	$0.537846\pi$
$524$	26.1092	1.14059
$525$	0	0
$526$	−8.61881	−0.375798
$527$	26.8368	1.16903
$528$	6.13547	0.267012
$529$	32.6639	1.42017
$530$	0	0
$531$	−16.4921	−0.715697
$532$	40.5352	1.75742
$533$	23.1003	1.00058
$534$	−12.1337	−0.525075
$535$	0	0
$536$	13.3174	0.575224
$537$	11.2837	0.486926
$538$	−7.75002	−0.334127
$539$	−7.07202	−0.304613
$540$	0	0
$541$	12.1893	0.524061	0.262030	−	0.965060i	$-0.415608\pi$
$541$	12.1893	0.524061	0.262030	+	0.965060i	$0.415608\pi$
$542$	−3.41291	−0.146597
$543$	31.5346	1.35328
$544$	−13.6589	−0.585620
$545$	0	0
$546$	15.6268	0.668765
$547$	0.0992296	0.00424275	0.00212138	−	0.999998i	$-0.499325\pi$
$547$	0.0992296	0.00424275	0.00212138	+	0.999998i	$0.499325\pi$
$548$	21.9991	0.939754
$549$	−4.47180	−0.190852
$550$	0	0
$551$	−54.6616	−2.32866
$552$	−28.4291	−1.21002
$553$	55.6385	2.36599
$554$	−11.6942	−0.496840
$555$	0	0
$556$	30.8937	1.31019
$557$	−4.31269	−0.182735	−0.0913674	−	0.995817i	$-0.529124\pi$
$557$	−4.31269	−0.182735	−0.0913674	+	0.995817i	$0.529124\pi$
$558$	−9.27102	−0.392474
$559$	−12.5415	−0.530450
$560$	0	0
$561$	6.31375	0.266567
$562$	−8.18689	−0.345343
$563$	−43.4321	−1.83044	−0.915222	−	0.402950i	$-0.867985\pi$
$563$	−43.4321	−1.83044	−0.915222	+	0.402950i	$0.867985\pi$
$564$	38.9195	1.63881
$565$	0	0
$566$	−8.10483	−0.340671
$567$	−40.0278	−1.68101
$568$	10.2592	0.430466
$569$	11.7227	0.491442	0.245721	−	0.969341i	$-0.420975\pi$
$569$	11.7227	0.491442	0.245721	+	0.969341i	$0.420975\pi$
$570$	0	0
$571$	−41.4995	−1.73670	−0.868351	−	0.495951i	$-0.834820\pi$
$571$	−41.4995	−1.73670	−0.868351	+	0.495951i	$0.834820\pi$
$572$	6.61317	0.276511
$573$	10.8673	0.453989
$574$	−9.40616	−0.392605
$575$	0	0
$576$	−9.56527	−0.398553
$577$	19.9489	0.830485	0.415242	−	0.909711i	$-0.363697\pi$
$577$	19.9489	0.830485	0.415242	+	0.909711i	$0.363697\pi$
$578$	3.37855	0.140529
$579$	32.6075	1.35512
$580$	0	0
$581$	17.6467	0.732109
$582$	6.62585	0.274650
$583$	3.52916	0.146163
$584$	−18.9600	−0.784572
$585$	0	0
$586$	−3.26210	−0.134756
$587$	35.0891	1.44828	0.724142	−	0.689651i	$-0.242236\pi$
$587$	35.0891	1.44828	0.724142	+	0.689651i	$0.242236\pi$
$588$	33.3798	1.37656
$589$	−51.4272	−2.11902
$590$	0	0
$591$	51.8969	2.13475
$592$	28.1768	1.15806
$593$	−15.2108	−0.624634	−0.312317	−	0.949978i	$-0.601105\pi$
$593$	−15.2108	−0.624634	−0.312317	+	0.949978i	$0.601105\pi$
$594$	0.506256	0.0207719
$595$	0	0
$596$	15.6612	0.641506
$597$	52.0895	2.13188
$598$	−12.9638	−0.530130
$599$	12.8871	0.526553	0.263277	−	0.964720i	$-0.415197\pi$
$599$	12.8871	0.526553	0.263277	+	0.964720i	$0.415197\pi$
$600$	0	0
$601$	13.8983	0.566923	0.283461	−	0.958984i	$-0.408517\pi$
$601$	13.8983	0.566923	0.283461	+	0.958984i	$0.408517\pi$
$602$	5.10676	0.208136
$603$	19.8386	0.807890
$604$	−38.2442	−1.55614
$605$	0	0
$606$	−8.71833	−0.354158
$607$	44.0751	1.78895	0.894476	−	0.447115i	$-0.147549\pi$
$607$	44.0751	1.78895	0.894476	+	0.447115i	$0.147549\pi$
$608$	26.1745	1.06151
$609$	−84.9886	−3.44391
$610$	0	0
$611$	37.2869	1.50846
$612$	−13.3510	−0.539682
$613$	−5.27684	−0.213130	−0.106565	−	0.994306i	$-0.533985\pi$
$613$	−5.27684	−0.213130	−0.106565	+	0.994306i	$0.533985\pi$
$614$	5.70184	0.230107
$615$	0	0
$616$	−5.65748	−0.227946
$617$	−8.18380	−0.329467	−0.164734	−	0.986338i	$-0.552676\pi$
$617$	−8.18380	−0.329467	−0.164734	+	0.986338i	$0.552676\pi$
$618$	−1.10707	−0.0445329
$619$	−0.876684	−0.0352369	−0.0176185	−	0.999845i	$-0.505608\pi$
$619$	−0.876684	−0.0352369	−0.0176185	+	0.999845i	$0.505608\pi$
$620$	0	0
$621$	9.82968	0.394452
$622$	−10.9272	−0.438139
$623$	−46.8837	−1.87835
$624$	−27.7445	−1.11067
$625$	0	0
$626$	−3.92378	−0.156826
$627$	−12.0990	−0.483188
$628$	3.84985	0.153626
$629$	28.9955	1.15613
$630$	0	0
$631$	−24.3741	−0.970319	−0.485159	−	0.874426i	$-0.661238\pi$
$631$	−24.3741	−0.970319	−0.485159	+	0.874426i	$0.661238\pi$
$632$	23.5737	0.937713
$633$	51.2785	2.03814
$634$	−6.89337	−0.273771
$635$	0	0
$636$	−16.6576	−0.660516
$637$	31.9795	1.26708
$638$	3.63124	0.143762
$639$	15.2829	0.604581
$640$	0	0
$641$	−43.6968	−1.72592	−0.862960	−	0.505272i	$-0.831392\pi$
$641$	−43.6968	−1.72592	−0.862960	+	0.505272i	$0.831392\pi$
$642$	11.5592	0.456206
$643$	−10.4095	−0.410511	−0.205255	−	0.978708i	$-0.565803\pi$
$643$	−10.4095	−0.410511	−0.205255	+	0.978708i	$0.565803\pi$
$644$	−52.2847	−2.06030
$645$	0	0
$646$	7.47710	0.294182
$647$	−30.9867	−1.21821	−0.609106	−	0.793089i	$-0.708471\pi$
$647$	−30.9867	−1.21821	−0.609106	+	0.793089i	$0.708471\pi$
$648$	−16.9595	−0.666233
$649$	6.07735	0.238557
$650$	0	0
$651$	−79.9598	−3.13387
$652$	7.40772	0.290109
$653$	2.74665	0.107485	0.0537424	−	0.998555i	$-0.482885\pi$
$653$	2.74665	0.107485	0.0537424	+	0.998555i	$0.482885\pi$
$654$	20.0536	0.784158
$655$	0	0
$656$	16.7001	0.652029
$657$	−28.2443	−1.10191
$658$	−15.1828	−0.591886
$659$	8.45972	0.329544	0.164772	−	0.986332i	$-0.447311\pi$
$659$	8.45972	0.329544	0.164772	+	0.986332i	$0.447311\pi$
$660$	0	0
$661$	9.42387	0.366546	0.183273	−	0.983062i	$-0.441331\pi$
$661$	9.42387	0.366546	0.183273	+	0.983062i	$0.441331\pi$
$662$	−10.2214	−0.397267
$663$	−28.5507	−1.10882
$664$	7.47681	0.290156
$665$	0	0
$666$	−10.0168	−0.388143
$667$	70.5057	2.72999
$668$	−14.4776	−0.560156
$669$	−19.1508	−0.740413
$670$	0	0
$671$	1.64786	0.0636149
$672$	40.6964	1.56990
$673$	24.6824	0.951438	0.475719	−	0.879597i	$-0.342188\pi$
$673$	24.6824	0.951438	0.475719	+	0.879597i	$0.342188\pi$
$674$	5.91646	0.227894
$675$	0	0
$676$	−6.28891	−0.241881
$677$	30.8489	1.18562	0.592810	−	0.805343i	$-0.298019\pi$
$677$	30.8489	1.18562	0.592810	+	0.805343i	$0.298019\pi$
$678$	−3.90228	−0.149866
$679$	25.6018	0.982508
$680$	0	0
$681$	14.5630	0.558056
$682$	3.41637	0.130820
$683$	3.14294	0.120261	0.0601307	−	0.998191i	$-0.480848\pi$
$683$	3.14294	0.120261	0.0601307	+	0.998191i	$0.480848\pi$
$684$	25.5845	0.978246
$685$	0	0
$686$	−1.45702	−0.0556292
$687$	−9.02830	−0.344451
$688$	−9.06676	−0.345667
$689$	−15.9588	−0.607982
$690$	0	0
$691$	−46.6737	−1.77555	−0.887775	−	0.460278i	$-0.847750\pi$
$691$	−46.6737	−1.77555	−0.887775	+	0.460278i	$0.847750\pi$
$692$	−13.4863	−0.512672
$693$	−8.42780	−0.320146
$694$	3.69043	0.140087
$695$	0	0
$696$	−36.0092	−1.36493
$697$	17.1854	0.650942
$698$	3.90212	0.147697
$699$	−26.6581	−1.00830
$700$	0	0
$701$	−14.9555	−0.564860	−0.282430	−	0.959288i	$-0.591141\pi$
$701$	−14.9555	−0.564860	−0.282430	+	0.959288i	$0.591141\pi$
$702$	−2.28928	−0.0864033
$703$	−55.5640	−2.09564
$704$	3.52481	0.132846
$705$	0	0
$706$	2.82723	0.106404
$707$	−33.6870	−1.26693
$708$	−28.6850	−1.07805
$709$	−5.08709	−0.191050	−0.0955249	−	0.995427i	$-0.530453\pi$
$709$	−5.08709	−0.191050	−0.0955249	+	0.995427i	$0.530453\pi$
$710$	0	0
$711$	35.1172	1.31700
$712$	−19.8643	−0.744448
$713$	66.3338	2.48422
$714$	11.6255	0.435074
$715$	0	0
$716$	8.79253	0.328592
$717$	−58.7870	−2.19544
$718$	−8.87858	−0.331346
$719$	−15.6606	−0.584042	−0.292021	−	0.956412i	$-0.594328\pi$
$719$	−15.6606	−0.584042	−0.292021	+	0.956412i	$0.594328\pi$
$720$	0	0
$721$	−4.27764	−0.159308
$722$	−6.19142	−0.230421
$723$	−2.33128	−0.0867012
$724$	24.5726	0.913233
$725$	0	0
$726$	−10.1785	−0.377761
$727$	30.0268	1.11363	0.556816	−	0.830636i	$-0.312023\pi$
$727$	30.0268	1.11363	0.556816	+	0.830636i	$0.312023\pi$
$728$	25.5830	0.948170
$729$	−16.0498	−0.594436
$730$	0	0
$731$	−9.33022	−0.345091
$732$	−7.77787	−0.287478
$733$	−36.0556	−1.33174	−0.665872	−	0.746066i	$-0.731940\pi$
$733$	−36.0556	−1.33174	−0.665872	+	0.746066i	$0.731940\pi$
$734$	8.46681	0.312516
$735$	0	0
$736$	−33.7614	−1.24446
$737$	−7.31053	−0.269287
$738$	−5.93685	−0.218539
$739$	−43.1274	−1.58647	−0.793234	−	0.608917i	$-0.791604\pi$
$739$	−43.1274	−1.58647	−0.793234	+	0.608917i	$0.791604\pi$
$740$	0	0
$741$	54.7116	2.00988
$742$	6.49824	0.238558
$743$	−10.6988	−0.392501	−0.196251	−	0.980554i	$-0.562877\pi$
$743$	−10.6988	−0.392501	−0.196251	+	0.980554i	$0.562877\pi$
$744$	−33.8785	−1.24205
$745$	0	0
$746$	−3.19773	−0.117077
$747$	11.1380	0.407518
$748$	4.91985	0.179887
$749$	44.6641	1.63199
$750$	0	0
$751$	−0.854171	−0.0311691	−0.0155846	−	0.999879i	$-0.504961\pi$
$751$	−0.854171	−0.0311691	−0.0155846	+	0.999879i	$0.504961\pi$
$752$	26.9561	0.982990
$753$	27.2497	0.993035
$754$	−16.4204	−0.597996
$755$	0	0
$756$	−9.23294	−0.335799
$757$	−12.9294	−0.469926	−0.234963	−	0.972004i	$-0.575497\pi$
$757$	−12.9294	−0.469926	−0.234963	+	0.972004i	$0.575497\pi$
$758$	10.4635	0.380050
$759$	15.6060	0.566463
$760$	0	0
$761$	−6.26520	−0.227113	−0.113557	−	0.993532i	$-0.536224\pi$
$761$	−6.26520	−0.227113	−0.113557	+	0.993532i	$0.536224\pi$
$762$	−8.45705	−0.306367
$763$	77.4857	2.80517
$764$	8.46810	0.306365
$765$	0	0
$766$	−2.29570	−0.0829469
$767$	−27.4817	−0.992306
$768$	−7.60131	−0.274289
$769$	−13.7255	−0.494956	−0.247478	−	0.968894i	$-0.579602\pi$
$769$	−13.7255	−0.494956	−0.247478	+	0.968894i	$0.579602\pi$
$770$	0	0
$771$	26.9110	0.969175
$772$	25.4086	0.914477
$773$	−6.06244	−0.218051	−0.109025	−	0.994039i	$-0.534773\pi$
$773$	−6.06244	−0.218051	−0.109025	+	0.994039i	$0.534773\pi$
$774$	3.22321	0.115856
$775$	0	0
$776$	10.8473	0.389397
$777$	−86.3918	−3.09929
$778$	8.21425	0.294495
$779$	−32.9322	−1.17992
$780$	0	0
$781$	−5.63174	−0.201520
$782$	−9.64440	−0.344883
$783$	12.4506	0.444948
$784$	23.1193	0.825689
$785$	0	0
$786$	−14.3495	−0.511829
$787$	−3.35462	−0.119579	−0.0597897	−	0.998211i	$-0.519043\pi$
$787$	−3.35462	−0.119579	−0.0597897	+	0.998211i	$0.519043\pi$
$788$	40.4394	1.44059
$789$	−46.9176	−1.67031
$790$	0	0
$791$	−15.0781	−0.536116
$792$	−3.57081	−0.126883
$793$	−7.45159	−0.264614
$794$	5.97356	0.211994
$795$	0	0
$796$	40.5895	1.43866
$797$	−10.7289	−0.380036	−0.190018	−	0.981781i	$-0.560855\pi$
$797$	−10.7289	−0.380036	−0.190018	+	0.981781i	$0.560855\pi$
$798$	−22.2779	−0.788629
$799$	27.7394	0.981351
$800$	0	0
$801$	−29.5914	−1.04556
$802$	−15.7042	−0.554535
$803$	10.4080	0.367291
$804$	34.5056	1.21692
$805$	0	0
$806$	−15.4488	−0.544160
$807$	−42.1882	−1.48509
$808$	−14.2730	−0.502122
$809$	−23.3937	−0.822478	−0.411239	−	0.911528i	$-0.634904\pi$
$809$	−23.3937	−0.822478	−0.411239	+	0.911528i	$0.634904\pi$
$810$	0	0
$811$	−9.30684	−0.326807	−0.163404	−	0.986559i	$-0.552247\pi$
$811$	−9.30684	−0.326807	−0.163404	+	0.986559i	$0.552247\pi$
$812$	−66.2254	−2.32406
$813$	−18.5786	−0.651580
$814$	3.69119	0.129376
$815$	0	0
$816$	−20.6404	−0.722559
$817$	17.8795	0.625523
$818$	13.4975	0.471928
$819$	38.1104	1.33168
$820$	0	0
$821$	14.6070	0.509787	0.254893	−	0.966969i	$-0.417960\pi$
$821$	14.6070	0.509787	0.254893	+	0.966969i	$0.417960\pi$
$822$	−12.0906	−0.421707
$823$	−32.4360	−1.13065	−0.565324	−	0.824869i	$-0.691249\pi$
$823$	−32.4360	−1.13065	−0.565324	+	0.824869i	$0.691249\pi$
$824$	−1.81241	−0.0631384
$825$	0	0
$826$	11.1902	0.389358
$827$	39.1147	1.36015	0.680076	−	0.733141i	$-0.261947\pi$
$827$	39.1147	1.36015	0.680076	+	0.733141i	$0.261947\pi$
$828$	−33.0003	−1.14684
$829$	−42.0846	−1.46166	−0.730830	−	0.682560i	$-0.760867\pi$
$829$	−42.0846	−1.46166	−0.730830	+	0.682560i	$0.760867\pi$
$830$	0	0
$831$	−63.6589	−2.20830
$832$	−15.9391	−0.552590
$833$	23.7911	0.824312
$834$	−16.9790	−0.587935
$835$	0	0
$836$	−9.42788	−0.326070
$837$	11.7139	0.404891
$838$	−4.89109	−0.168960
$839$	8.17805	0.282338	0.141169	−	0.989986i	$-0.454914\pi$
$839$	8.17805	0.282338	0.141169	+	0.989986i	$0.454914\pi$
$840$	0	0
$841$	60.3048	2.07948
$842$	13.4948	0.465062
$843$	−44.5663	−1.53495
$844$	39.9576	1.37540
$845$	0	0
$846$	−9.58286	−0.329465
$847$	−39.3292	−1.35137
$848$	−11.5373	−0.396191
$849$	−44.1196	−1.51418
$850$	0	0
$851$	71.6697	2.45681
$852$	26.5817	0.910675
$853$	−56.2478	−1.92589	−0.962944	−	0.269700i	$-0.913075\pi$
$853$	−56.2478	−1.92589	−0.962944	+	0.269700i	$0.913075\pi$
$854$	3.03420	0.103828
$855$	0	0
$856$	18.9239	0.646806
$857$	13.6016	0.464621	0.232310	−	0.972642i	$-0.425371\pi$
$857$	13.6016	0.464621	0.232310	+	0.972642i	$0.425371\pi$
$858$	−3.63456	−0.124082
$859$	−34.2682	−1.16921	−0.584607	−	0.811316i	$-0.698751\pi$
$859$	−34.2682	−1.16921	−0.584607	+	0.811316i	$0.698751\pi$
$860$	0	0
$861$	−51.2036	−1.74501
$862$	14.7035	0.500802
$863$	5.12475	0.174449	0.0872243	−	0.996189i	$-0.472200\pi$
$863$	5.12475	0.174449	0.0872243	+	0.996189i	$0.472200\pi$
$864$	−5.96191	−0.202828
$865$	0	0
$866$	−3.10422	−0.105486
$867$	18.3915	0.624609
$868$	−62.3068	−2.11483
$869$	−12.9407	−0.438983
$870$	0	0
$871$	33.0581	1.12013
$872$	32.8303	1.11177
$873$	16.1590	0.546900
$874$	18.4815	0.625147
$875$	0	0
$876$	−49.1258	−1.65981
$877$	−37.2511	−1.25788	−0.628940	−	0.777454i	$-0.716511\pi$
$877$	−37.2511	−1.25788	−0.628940	+	0.777454i	$0.716511\pi$
$878$	−10.4863	−0.353894
$879$	−17.7577	−0.598951
$880$	0	0
$881$	−28.3213	−0.954168	−0.477084	−	0.878858i	$-0.658306\pi$
$881$	−28.3213	−0.954168	−0.477084	+	0.878858i	$0.658306\pi$
$882$	−8.21886	−0.276743
$883$	4.79555	0.161383	0.0806915	−	0.996739i	$-0.474287\pi$
$883$	4.79555	0.161383	0.0806915	+	0.996739i	$0.474287\pi$
$884$	−22.2475	−0.748263
$885$	0	0
$886$	9.68334	0.325318
$887$	−48.8631	−1.64066	−0.820331	−	0.571890i	$-0.806211\pi$
$887$	−48.8631	−1.64066	−0.820331	+	0.571890i	$0.806211\pi$
$888$	−36.6037	−1.22834
$889$	−32.6774	−1.09597
$890$	0	0
$891$	9.30986	0.311892
$892$	−14.9228	−0.499653
$893$	−53.1570	−1.77883
$894$	−8.60728	−0.287871
$895$	0	0
$896$	41.4036	1.38320
$897$	−70.5702	−2.35627
$898$	14.2746	0.476349
$899$	84.0205	2.80224
$900$	0	0
$901$	−11.8725	−0.395530
$902$	2.18773	0.0728435
$903$	27.7993	0.925101
$904$	−6.38851	−0.212479
$905$	0	0
$906$	21.0188	0.698303
$907$	−31.3959	−1.04248	−0.521241	−	0.853409i	$-0.674531\pi$
$907$	−31.3959	−1.04248	−0.521241	+	0.853409i	$0.674531\pi$
$908$	11.3479	0.376593
$909$	−21.2621	−0.705220
$910$	0	0
$911$	−38.4230	−1.27301	−0.636506	−	0.771272i	$-0.719621\pi$
$911$	−38.4230	−1.27301	−0.636506	+	0.771272i	$0.719621\pi$
$912$	39.5532	1.30974
$913$	−4.10436	−0.135835
$914$	2.69814	0.0892465
$915$	0	0
$916$	−7.03509	−0.232446
$917$	−55.4453	−1.83097
$918$	−1.70310	−0.0562108
$919$	16.3980	0.540920	0.270460	−	0.962731i	$-0.412824\pi$
$919$	16.3980	0.540920	0.270460	+	0.962731i	$0.412824\pi$
$920$	0	0
$921$	31.0386	1.02276
$922$	−0.893598	−0.0294291
$923$	25.4666	0.838245
$924$	−14.6586	−0.482233
$925$	0	0
$926$	3.11023	0.102208
$927$	−2.69991	−0.0886765
$928$	−42.7632	−1.40377
$929$	−2.98102	−0.0978042	−0.0489021	−	0.998804i	$-0.515572\pi$
$929$	−2.98102	−0.0978042	−0.0489021	+	0.998804i	$0.515572\pi$
$930$	0	0
$931$	−45.5908	−1.49418
$932$	−20.7727	−0.680433
$933$	−59.4834	−1.94740
$934$	−14.1756	−0.463839
$935$	0	0
$936$	16.1471	0.527786
$937$	−43.4968	−1.42098	−0.710489	−	0.703708i	$-0.751526\pi$
$937$	−43.4968	−1.42098	−0.710489	+	0.703708i	$0.751526\pi$
$938$	−13.4609	−0.439513
$939$	−21.3595	−0.697042
$940$	0	0
$941$	12.1046	0.394599	0.197299	−	0.980343i	$-0.436783\pi$
$941$	12.1046	0.394599	0.197299	+	0.980343i	$0.436783\pi$
$942$	−2.11585	−0.0689382
$943$	42.4780	1.38327
$944$	−19.8676	−0.646635
$945$	0	0
$946$	−1.18776	−0.0386173
$947$	6.10171	0.198279	0.0991395	−	0.995074i	$-0.468391\pi$
$947$	6.10171	0.198279	0.0991395	+	0.995074i	$0.468391\pi$
$948$	61.0799	1.98378
$949$	−47.0649	−1.52779
$950$	0	0
$951$	−37.5249	−1.21683
$952$	19.0324	0.616844
$953$	36.1488	1.17097	0.585487	−	0.810682i	$-0.300903\pi$
$953$	36.1488	1.17097	0.585487	+	0.810682i	$0.300903\pi$
$954$	4.10147	0.132790
$955$	0	0
$956$	−45.8085	−1.48155
$957$	19.7671	0.638979
$958$	10.8000	0.348933
$959$	−46.7171	−1.50857
$960$	0	0
$961$	48.0489	1.54996
$962$	−16.6915	−0.538155
$963$	28.1905	0.908425
$964$	−1.81659	−0.0585086
$965$	0	0
$966$	28.7354	0.924545
$967$	14.6234	0.470256	0.235128	−	0.971964i	$-0.424449\pi$
$967$	14.6234	0.470256	0.235128	+	0.971964i	$0.424449\pi$
$968$	−16.6635	−0.535586
$969$	40.7025	1.30755
$970$	0	0
$971$	30.6893	0.984865	0.492432	−	0.870351i	$-0.336108\pi$
$971$	30.6893	0.984865	0.492432	+	0.870351i	$0.336108\pi$
$972$	−36.7623	−1.17915
$973$	−65.6057	−2.10322
$974$	−9.85883	−0.315897
$975$	0	0
$976$	−5.38705	−0.172435
$977$	−20.3359	−0.650602	−0.325301	−	0.945611i	$-0.605466\pi$
$977$	−20.3359	−0.650602	−0.325301	+	0.945611i	$0.605466\pi$
$978$	−4.07124	−0.130184
$979$	10.9044	0.348508
$980$	0	0
$981$	48.9064	1.56146
$982$	−13.9842	−0.446254
$983$	46.7245	1.49028	0.745140	−	0.666908i	$-0.232383\pi$
$983$	46.7245	1.49028	0.745140	+	0.666908i	$0.232383\pi$
$984$	−21.6947	−0.691601
$985$	0	0
$986$	−12.2159	−0.389034
$987$	−82.6493	−2.63076
$988$	42.6327	1.35633
$989$	−23.0620	−0.733328
$990$	0	0
$991$	−6.29224	−0.199880	−0.0999398	−	0.994993i	$-0.531865\pi$
$991$	−6.29224	−0.199880	−0.0999398	+	0.994993i	$0.531865\pi$
$992$	−40.2329	−1.27739
$993$	−55.6416	−1.76573
$994$	−10.3697	−0.328907
$995$	0	0
$996$	19.3725	0.613842
$997$	−25.5620	−0.809556	−0.404778	−	0.914415i	$-0.632651\pi$
$997$	−25.5620	−0.809556	−0.404778	+	0.914415i	$0.632651\pi$
$998$	12.5221	0.396381
$999$	12.6561	0.400423

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.g.1.5		11
5.4	even	2		1205.2.a.b.1.7	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.b.1.7	✓	11	5.4	even	2
6025.2.a.g.1.5		11	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q-0.428259 q^{2} -2.33128 q^{3} -1.81659 q^{4} +0.998390 q^{6} +3.85771 q^{7} +1.63449 q^{8} +2.43486 q^{9} +O(q^{10})\)	\(q-0.428259 q^{2} -2.33128 q^{3} -1.81659 q^{4} +0.998390 q^{6} +3.85771 q^{7} +1.63449 q^{8} +2.43486 q^{9} -0.897246 q^{11} +4.23499 q^{12} +4.05733 q^{13} -1.65210 q^{14} +2.93320 q^{16} +3.01844 q^{17} -1.04275 q^{18} -5.78422 q^{19} -8.99339 q^{21} +0.384253 q^{22} +7.46083 q^{23} -3.81045 q^{24} -1.73759 q^{26} +1.31751 q^{27} -7.00789 q^{28} +9.45012 q^{29} +8.89095 q^{31} -4.52515 q^{32} +2.09173 q^{33} -1.29267 q^{34} -4.42315 q^{36} +9.60614 q^{37} +2.47714 q^{38} -9.45876 q^{39} +5.69346 q^{41} +3.85150 q^{42} -3.09108 q^{43} +1.62993 q^{44} -3.19516 q^{46} +9.19000 q^{47} -6.83812 q^{48} +7.88192 q^{49} -7.03682 q^{51} -7.37052 q^{52} -3.93333 q^{53} -0.564233 q^{54} +6.30539 q^{56} +13.4846 q^{57} -4.04710 q^{58} -6.77334 q^{59} -1.83657 q^{61} -3.80762 q^{62} +9.39297 q^{63} -3.92848 q^{64} -0.895801 q^{66} +8.14775 q^{67} -5.48328 q^{68} -17.3933 q^{69} +6.27670 q^{71} +3.97975 q^{72} -11.6000 q^{73} -4.11391 q^{74} +10.5076 q^{76} -3.46131 q^{77} +4.05080 q^{78} +14.4227 q^{79} -10.3760 q^{81} -2.43828 q^{82} +4.57440 q^{83} +16.3373 q^{84} +1.32378 q^{86} -22.0309 q^{87} -1.46654 q^{88} -12.1532 q^{89} +15.6520 q^{91} -13.5533 q^{92} -20.7273 q^{93} -3.93570 q^{94} +10.5494 q^{96} +6.63653 q^{97} -3.37550 q^{98} -2.18466 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 4 q^{2} + 8 q^{3} + 6 q^{4} + 7 q^{6} + 9 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) \) 11 * q + 4 * q^2 + 8 * q^3 + 6 * q^4 + 7 * q^6 + 9 * q^7 + 12 * q^8 + 9 * q^9	\( 11 q + 4 q^{2} + 8 q^{3} + 6 q^{4} + 7 q^{6} + 9 q^{7} + 12 q^{8} + 9 q^{9} - 3 q^{11} + 28 q^{12} + 9 q^{13} + 2 q^{14} - 16 q^{16} + 4 q^{17} + 6 q^{18} - 33 q^{19} + 2 q^{21} - 6 q^{22} + 31 q^{23} + 32 q^{24} - 20 q^{26} + 32 q^{27} + q^{28} + q^{29} + 6 q^{31} - 7 q^{32} + 35 q^{33} + 9 q^{34} + 33 q^{36} + 23 q^{37} - 20 q^{38} + 14 q^{39} + 8 q^{41} + 26 q^{42} + 19 q^{43} + 6 q^{46} + 35 q^{47} - 16 q^{48} + 4 q^{49} - 3 q^{51} + 3 q^{52} - 14 q^{53} + 9 q^{54} + 33 q^{56} - q^{57} + 11 q^{58} - 6 q^{59} + 9 q^{61} + 23 q^{62} + 31 q^{63} + 18 q^{64} - 36 q^{66} + 54 q^{67} - q^{68} + 17 q^{69} - 5 q^{71} + 64 q^{72} - 17 q^{73} + 8 q^{74} - 31 q^{76} + 18 q^{77} - 15 q^{78} - 16 q^{79} + 43 q^{81} + 61 q^{82} + 29 q^{83} + 69 q^{84} + 5 q^{86} - 5 q^{87} + 14 q^{88} - 5 q^{89} - 54 q^{91} + 6 q^{92} + 25 q^{93} - 19 q^{94} + 9 q^{96} - 6 q^{97} + 29 q^{98} + 60 q^{99}+O(q^{100}) \) 11 * q + 4 * q^2 + 8 * q^3 + 6 * q^4 + 7 * q^6 + 9 * q^7 + 12 * q^8 + 9 * q^9 - 3 * q^11 + 28 * q^12 + 9 * q^13 + 2 * q^14 - 16 * q^16 + 4 * q^17 + 6 * q^18 - 33 * q^19 + 2 * q^21 - 6 * q^22 + 31 * q^23 + 32 * q^24 - 20 * q^26 + 32 * q^27 + q^28 + q^29 + 6 * q^31 - 7 * q^32 + 35 * q^33 + 9 * q^34 + 33 * q^36 + 23 * q^37 - 20 * q^38 + 14 * q^39 + 8 * q^41 + 26 * q^42 + 19 * q^43 + 6 * q^46 + 35 * q^47 - 16 * q^48 + 4 * q^49 - 3 * q^51 + 3 * q^52 - 14 * q^53 + 9 * q^54 + 33 * q^56 - q^57 + 11 * q^58 - 6 * q^59 + 9 * q^61 + 23 * q^62 + 31 * q^63 + 18 * q^64 - 36 * q^66 + 54 * q^67 - q^68 + 17 * q^69 - 5 * q^71 + 64 * q^72 - 17 * q^73 + 8 * q^74 - 31 * q^76 + 18 * q^77 - 15 * q^78 - 16 * q^79 + 43 * q^81 + 61 * q^82 + 29 * q^83 + 69 * q^84 + 5 * q^86 - 5 * q^87 + 14 * q^88 - 5 * q^89 - 54 * q^91 + 6 * q^92 + 25 * q^93 - 19 * q^94 + 9 * q^96 - 6 * q^97 + 29 * q^98 + 60 * q^99

Introduction

L-functions

Modular forms

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Database

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