LMFDB - Embedded newform 1922.2.a.m.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1922,2,Mod(1,1922)] 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("1922.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1922, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1922 = 2 \cdot 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1922.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,-4,6,4,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$15.3472472685$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{15})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} + 4x + 1 $ x^4 - x^3 - 4x^2 + 4x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 62)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.82709$ of defining polynomial
Character	$\chi$	$=$	1922.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +2.61803 q^{3} +1.00000 q^{4} -0.338261 q^{5} -2.61803 q^{6} +3.37441 q^{7} -1.00000 q^{8} +3.85410 q^{9} +0.338261 q^{10} -3.95630 q^{11} +2.61803 q^{12} +5.65418 q^{13} -3.37441 q^{14} -0.885579 q^{15} +1.00000 q^{16} +6.25085 q^{17} -3.85410 q^{18} +0.963852 q^{19} -0.338261 q^{20} +8.83432 q^{21} +3.95630 q^{22} +0.812307 q^{23} -2.61803 q^{24} -4.88558 q^{25} -5.65418 q^{26} +2.23607 q^{27} +3.37441 q^{28} -4.65983 q^{29} +0.885579 q^{30} -1.00000 q^{32} -10.3577 q^{33} -6.25085 q^{34} -1.14143 q^{35} +3.85410 q^{36} -1.98331 q^{37} -0.963852 q^{38} +14.8028 q^{39} +0.338261 q^{40} +6.92015 q^{41} -8.83432 q^{42} +8.12920 q^{43} -3.95630 q^{44} -1.30369 q^{45} -0.812307 q^{46} -1.49797 q^{47} +2.61803 q^{48} +4.38664 q^{49} +4.88558 q^{50} +16.3649 q^{51} +5.65418 q^{52} -8.89183 q^{53} -2.23607 q^{54} +1.33826 q^{55} -3.37441 q^{56} +2.52340 q^{57} +4.65983 q^{58} -7.81604 q^{59} -0.885579 q^{60} -7.56231 q^{61} +13.0053 q^{63} +1.00000 q^{64} -1.91259 q^{65} +10.3577 q^{66} +0.576239 q^{67} +6.25085 q^{68} +2.12665 q^{69} +1.14143 q^{70} +7.49159 q^{71} -3.85410 q^{72} +11.0342 q^{73} +1.98331 q^{74} -12.7906 q^{75} +0.963852 q^{76} -13.3502 q^{77} -14.8028 q^{78} +14.5363 q^{79} -0.338261 q^{80} -5.70820 q^{81} -6.92015 q^{82} -1.59102 q^{83} +8.83432 q^{84} -2.11442 q^{85} -8.12920 q^{86} -12.1996 q^{87} +3.95630 q^{88} +7.44224 q^{89} +1.30369 q^{90} +19.0795 q^{91} +0.812307 q^{92} +1.49797 q^{94} -0.326034 q^{95} -2.61803 q^{96} +0.0742058 q^{97} -4.38664 q^{98} -15.2480 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 6 q^{3} + 4 q^{4} + 3 q^{5} - 6 q^{6} + q^{7} - 4 q^{8} + 2 q^{9} - 3 q^{10} - 7 q^{11} + 6 q^{12} + 10 q^{13} - q^{14} + 7 q^{15} + 4 q^{16} + 3 q^{17} - 2 q^{18} + 12 q^{19} + 3 q^{20}+ \cdots - 11 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 6 * q^3 + 4 * q^4 + 3 * q^5 - 6 * q^6 + q^7 - 4 * q^8 + 2 * q^9 - 3 * q^10 - 7 * q^11 + 6 * q^12 + 10 * q^13 - q^14 + 7 * q^15 + 4 * q^16 + 3 * q^17 - 2 * q^18 + 12 * q^19 + 3 * q^20 - q^21 + 7 * q^22 + 10 * q^23 - 6 * q^24 - 9 * q^25 - 10 * q^26 + q^28 + 6 * q^29 - 7 * q^30 - 4 * q^32 - 13 * q^33 - 3 * q^34 - 8 * q^35 + 2 * q^36 + 8 * q^37 - 12 * q^38 + 20 * q^39 - 3 * q^40 + 27 * q^41 + q^42 + 30 * q^43 - 7 * q^44 + 9 * q^45 - 10 * q^46 - 3 * q^47 + 6 * q^48 + 11 * q^49 + 9 * q^50 + 7 * q^51 + 10 * q^52 + 4 * q^53 + q^55 - q^56 + 18 * q^57 - 6 * q^58 + 3 * q^59 + 7 * q^60 + 10 * q^61 - 7 * q^63 + 4 * q^64 + 10 * q^65 + 13 * q^66 + 18 * q^67 + 3 * q^68 + 25 * q^69 + 8 * q^70 - 12 * q^71 - 2 * q^72 + 7 * q^73 - 8 * q^74 - 6 * q^75 + 12 * q^76 - 8 * q^77 - 20 * q^78 + 24 * q^79 + 3 * q^80 + 4 * q^81 - 27 * q^82 - 9 * q^83 - q^84 - 19 * q^85 - 30 * q^86 - q^87 + 7 * q^88 - 9 * q^89 - 9 * q^90 + 30 * q^91 + 10 * q^92 + 3 * q^94 + 9 * q^95 - 6 * q^96 + 13 * q^97 - 11 * q^98 - 11 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.61803	1.51152	0.755761	−	0.654847i	$-0.227267\pi$
$3$	2.61803	1.51152	0.755761	+	0.654847i	$0.227267\pi$
$4$	1.00000	0.500000
$5$	−0.338261	−0.151275	−0.0756375	−	0.997135i	$-0.524099\pi$
$5$	−0.338261	−0.151275	−0.0756375	+	0.997135i	$0.524099\pi$
$6$	−2.61803	−1.06881
$7$	3.37441	1.27541	0.637703	−	0.770282i	$-0.279885\pi$
$7$	3.37441	1.27541	0.637703	+	0.770282i	$0.279885\pi$
$8$	−1.00000	−0.353553
$9$	3.85410	1.28470
$10$	0.338261	0.106968
$11$	−3.95630	−1.19287	−0.596434	−	0.802662i	$-0.703416\pi$
$11$	−3.95630	−1.19287	−0.596434	+	0.802662i	$0.703416\pi$
$12$	2.61803	0.755761
$13$	5.65418	1.56819	0.784094	−	0.620642i	$-0.213128\pi$
$13$	5.65418	1.56819	0.784094	+	0.620642i	$0.213128\pi$
$14$	−3.37441	−0.901849
$15$	−0.885579	−0.228656
$16$	1.00000	0.250000
$17$	6.25085	1.51605	0.758027	−	0.652223i	$-0.226163\pi$
$17$	6.25085	1.51605	0.758027	+	0.652223i	$0.226163\pi$
$18$	−3.85410	−0.908421
$19$	0.963852	0.221123	0.110561	−	0.993869i	$-0.464735\pi$
$19$	0.963852	0.221123	0.110561	+	0.993869i	$0.464735\pi$
$20$	−0.338261	−0.0756375
$21$	8.83432	1.92781
$22$	3.95630	0.843485
$23$	0.812307	0.169378	0.0846889	−	0.996407i	$-0.473010\pi$
$23$	0.812307	0.169378	0.0846889	+	0.996407i	$0.473010\pi$
$24$	−2.61803	−0.534404
$25$	−4.88558	−0.977116
$26$	−5.65418	−1.10888
$27$	2.23607	0.430331
$28$	3.37441	0.637703
$29$	−4.65983	−0.865308	−0.432654	−	0.901560i	$-0.642423\pi$
$29$	−4.65983	−0.865308	−0.432654	+	0.901560i	$0.642423\pi$
$30$	0.885579	0.161684
$31$	0	0
$31$	0	0
$32$	−1.00000	−0.176777
$33$	−10.3577	−1.80305
$34$	−6.25085	−1.07201
$35$	−1.14143	−0.192937
$36$	3.85410	0.642350
$37$	−1.98331	−0.326054	−0.163027	−	0.986622i	$-0.552126\pi$
$37$	−1.98331	−0.326054	−0.163027	+	0.986622i	$0.552126\pi$
$38$	−0.963852	−0.156357
$39$	14.8028	2.37035
$40$	0.338261	0.0534838
$41$	6.92015	1.08075	0.540373	−	0.841426i	$-0.318283\pi$
$41$	6.92015	1.08075	0.540373	+	0.841426i	$0.318283\pi$
$42$	−8.83432	−1.36316
$43$	8.12920	1.23969	0.619846	−	0.784723i	$-0.287195\pi$
$43$	8.12920	1.23969	0.619846	+	0.784723i	$0.287195\pi$
$44$	−3.95630	−0.596434
$45$	−1.30369	−0.194343
$46$	−0.812307	−0.119768
$47$	−1.49797	−0.218501	−0.109250	−	0.994014i	$-0.534845\pi$
$47$	−1.49797	−0.218501	−0.109250	+	0.994014i	$0.534845\pi$
$48$	2.61803	0.377881
$49$	4.38664	0.626662
$50$	4.88558	0.690925
$51$	16.3649	2.29155
$52$	5.65418	0.784094
$53$	−8.89183	−1.22139	−0.610693	−	0.791867i	$-0.709109\pi$
$53$	−8.89183	−1.22139	−0.610693	+	0.791867i	$0.709109\pi$
$54$	−2.23607	−0.304290
$55$	1.33826	0.180451
$56$	−3.37441	−0.450924
$57$	2.52340	0.334232
$58$	4.65983	0.611865
$59$	−7.81604	−1.01756	−0.508781	−	0.860896i	$-0.669904\pi$
$59$	−7.81604	−1.01756	−0.508781	+	0.860896i	$0.669904\pi$
$60$	−0.885579	−0.114328
$61$	−7.56231	−0.968254	−0.484127	−	0.874998i	$-0.660863\pi$
$61$	−7.56231	−0.968254	−0.484127	+	0.874998i	$0.660863\pi$
$62$	0	0
$63$	13.0053	1.63852
$64$	1.00000	0.125000
$65$	−1.91259	−0.237228
$66$	10.3577	1.27495
$67$	0.576239	0.0703988	0.0351994	−	0.999380i	$-0.488793\pi$
$67$	0.576239	0.0703988	0.0351994	+	0.999380i	$0.488793\pi$
$68$	6.25085	0.758027
$69$	2.12665	0.256018
$70$	1.14143	0.136427
$71$	7.49159	0.889088	0.444544	−	0.895757i	$-0.353366\pi$
$71$	7.49159	0.889088	0.444544	+	0.895757i	$0.353366\pi$
$72$	−3.85410	−0.454210
$73$	11.0342	1.29146	0.645730	−	0.763566i	$-0.276553\pi$
$73$	11.0342	1.29146	0.645730	+	0.763566i	$0.276553\pi$
$74$	1.98331	0.230555
$75$	−12.7906	−1.47693
$76$	0.963852	0.110561
$77$	−13.3502	−1.52139
$78$	−14.8028	−1.67609
$79$	14.5363	1.63546	0.817729	−	0.575603i	$-0.195233\pi$
$79$	14.5363	1.63546	0.817729	+	0.575603i	$0.195233\pi$
$80$	−0.338261	−0.0378188
$81$	−5.70820	−0.634245
$82$	−6.92015	−0.764202
$83$	−1.59102	−0.174637	−0.0873187	−	0.996180i	$-0.527830\pi$
$83$	−1.59102	−0.174637	−0.0873187	+	0.996180i	$0.527830\pi$
$84$	8.83432	0.963903
$85$	−2.11442	−0.229341
$86$	−8.12920	−0.876595
$87$	−12.1996	−1.30793
$88$	3.95630	0.421742
$89$	7.44224	0.788876	0.394438	−	0.918923i	$-0.370939\pi$
$89$	7.44224	0.788876	0.394438	+	0.918923i	$0.370939\pi$
$90$	1.30369	0.137421
$91$	19.0795	2.00008
$92$	0.812307	0.0846889
$93$	0	0
$94$	1.49797	0.154503
$95$	−0.326034	−0.0334504
$96$	−2.61803	−0.267202
$97$	0.0742058	0.00753446	0.00376723	−	0.999993i	$-0.498801\pi$
$97$	0.0742058	0.00753446	0.00376723	+	0.999993i	$0.498801\pi$
$98$	−4.38664	−0.443117
$99$	−15.2480	−1.53248
$100$	−4.88558	−0.488558
$101$	5.15780	0.513220	0.256610	−	0.966515i	$-0.417394\pi$
$101$	5.15780	0.513220	0.256610	+	0.966515i	$0.417394\pi$
$102$	−16.3649	−1.62037
$103$	−3.92831	−0.387068	−0.193534	−	0.981094i	$-0.561995\pi$
$103$	−3.92831	−0.387068	−0.193534	+	0.981094i	$0.561995\pi$
$104$	−5.65418	−0.554438
$105$	−2.98831	−0.291629
$106$	8.89183	0.863651
$107$	0.583466	0.0564058	0.0282029	−	0.999602i	$-0.491022\pi$
$107$	0.583466	0.0564058	0.0282029	+	0.999602i	$0.491022\pi$
$108$	2.23607	0.215166
$109$	−3.86068	−0.369786	−0.184893	−	0.982759i	$-0.559194\pi$
$109$	−3.86068	−0.369786	−0.184893	+	0.982759i	$0.559194\pi$
$110$	−1.33826	−0.127598
$111$	−5.19236	−0.492837
$112$	3.37441	0.318852
$113$	−16.7051	−1.57148	−0.785742	−	0.618554i	$-0.787719\pi$
$113$	−16.7051	−1.57148	−0.785742	+	0.618554i	$0.787719\pi$
$114$	−2.52340	−0.236338
$115$	−0.274772	−0.0256226
$116$	−4.65983	−0.432654
$117$	21.7918	2.01465
$118$	7.81604	0.719525
$119$	21.0929	1.93359
$120$	0.885579	0.0808420
$121$	4.65227	0.422934
$122$	7.56231	0.684659
$123$	18.1172	1.63357
$124$	0	0
$125$	3.34391	0.299088
$126$	−13.0053	−1.15861
$127$	−6.72766	−0.596983	−0.298492	−	0.954412i	$-0.596483\pi$
$127$	−6.72766	−0.596983	−0.298492	+	0.954412i	$0.596483\pi$
$128$	−1.00000	−0.0883883
$129$	21.2825	1.87382
$130$	1.91259	0.167745
$131$	−7.25394	−0.633780	−0.316890	−	0.948462i	$-0.602639\pi$
$131$	−7.25394	−0.633780	−0.316890	+	0.948462i	$0.602639\pi$
$132$	−10.3577	−0.901523
$133$	3.25243	0.282022
$134$	−0.576239	−0.0497795
$135$	−0.756375	−0.0650984
$136$	−6.25085	−0.536006
$137$	−1.24074	−0.106003	−0.0530017	−	0.998594i	$-0.516879\pi$
$137$	−1.24074	−0.106003	−0.0530017	+	0.998594i	$0.516879\pi$
$138$	−2.12665	−0.181032
$139$	18.6492	1.58180	0.790901	−	0.611944i	$-0.209612\pi$
$139$	18.6492	1.58180	0.790901	+	0.611944i	$0.209612\pi$
$140$	−1.14143	−0.0964686
$141$	−3.92173	−0.330269
$142$	−7.49159	−0.628680
$143$	−22.3696	−1.87064
$144$	3.85410	0.321175
$145$	1.57624	0.130900
$146$	−11.0342	−0.913200
$147$	11.4844	0.947214
$148$	−1.98331	−0.163027
$149$	−6.82730	−0.559314	−0.279657	−	0.960100i	$-0.590221\pi$
$149$	−6.82730	−0.559314	−0.279657	+	0.960100i	$0.590221\pi$
$150$	12.7906	1.04435
$151$	−0.465555	−0.0378864	−0.0189432	−	0.999821i	$-0.506030\pi$
$151$	−0.465555	−0.0378864	−0.0189432	+	0.999821i	$0.506030\pi$
$152$	−0.963852	−0.0781787
$153$	24.0914	1.94768
$154$	13.3502	1.07579
$155$	0	0
$156$	14.8028	1.18518
$157$	−2.93237	−0.234029	−0.117014	−	0.993130i	$-0.537332\pi$
$157$	−2.93237	−0.234029	−0.117014	+	0.993130i	$0.537332\pi$
$158$	−14.5363	−1.15644
$159$	−23.2791	−1.84615
$160$	0.338261	0.0267419
$161$	2.74106	0.216026
$162$	5.70820	0.448479
$163$	−3.11600	−0.244064	−0.122032	−	0.992526i	$-0.538941\pi$
$163$	−3.11600	−0.244064	−0.122032	+	0.992526i	$0.538941\pi$
$164$	6.92015	0.540373
$165$	3.50361	0.272756
$166$	1.59102	0.123487
$167$	−6.41523	−0.496425	−0.248213	−	0.968706i	$-0.579843\pi$
$167$	−6.41523	−0.496425	−0.248213	+	0.968706i	$0.579843\pi$
$168$	−8.83432	−0.681582
$169$	18.9698	1.45921
$170$	2.11442	0.162169
$171$	3.71478	0.284077
$172$	8.12920	0.619846
$173$	14.3426	1.09045	0.545224	−	0.838290i	$-0.316445\pi$
$173$	14.3426	1.09045	0.545224	+	0.838290i	$0.316445\pi$
$174$	12.1996	0.924849
$175$	−16.4859	−1.24622
$176$	−3.95630	−0.298217
$177$	−20.4627	−1.53807
$178$	−7.44224	−0.557819
$179$	−19.1215	−1.42921	−0.714605	−	0.699528i	$-0.753393\pi$
$179$	−19.1215	−1.42921	−0.714605	+	0.699528i	$0.753393\pi$
$180$	−1.30369	−0.0971716
$181$	−6.20557	−0.461256	−0.230628	−	0.973042i	$-0.574078\pi$
$181$	−6.20557	−0.461256	−0.230628	+	0.973042i	$0.574078\pi$
$182$	−19.0795	−1.41427
$183$	−19.7984	−1.46354
$184$	−0.812307	−0.0598841
$185$	0.670876	0.0493238
$186$	0	0
$187$	−24.7302	−1.80845
$188$	−1.49797	−0.109250
$189$	7.54541	0.548848
$190$	0.326034	0.0236530
$191$	−13.7173	−0.992552	−0.496276	−	0.868165i	$-0.665300\pi$
$191$	−13.7173	−0.992552	−0.496276	+	0.868165i	$0.665300\pi$
$192$	2.61803	0.188940
$193$	−15.0823	−1.08565	−0.542823	−	0.839847i	$-0.682645\pi$
$193$	−15.0823	−1.08565	−0.542823	+	0.839847i	$0.682645\pi$
$194$	−0.0742058	−0.00532767
$195$	−5.00723	−0.358575
$196$	4.38664	0.313331
$197$	6.69440	0.476956	0.238478	−	0.971148i	$-0.423352\pi$
$197$	6.69440	0.476956	0.238478	+	0.971148i	$0.423352\pi$
$198$	15.2480	1.08363
$199$	21.3309	1.51211	0.756054	−	0.654509i	$-0.227125\pi$
$199$	21.3309	1.51211	0.756054	+	0.654509i	$0.227125\pi$
$200$	4.88558	0.345463
$201$	1.50861	0.106409
$202$	−5.15780	−0.362901
$203$	−15.7242	−1.10362
$204$	16.3649	1.14578
$205$	−2.34082	−0.163490
$206$	3.92831	0.273698
$207$	3.13072	0.217600
$208$	5.65418	0.392047
$209$	−3.81328	−0.263770
$210$	2.98831	0.206213
$211$	−17.5708	−1.20963	−0.604813	−	0.796367i	$-0.706752\pi$
$211$	−17.5708	−1.20963	−0.604813	+	0.796367i	$0.706752\pi$
$212$	−8.89183	−0.610693
$213$	19.6132	1.34388
$214$	−0.583466	−0.0398849
$215$	−2.74979	−0.187534
$216$	−2.23607	−0.152145
$217$	0	0
$218$	3.86068	0.261478
$219$	28.8880	1.95207
$220$	1.33826	0.0902256
$221$	35.3435	2.37746
$222$	5.19236	0.348489
$223$	7.27819	0.487384	0.243692	−	0.969853i	$-0.421641\pi$
$223$	7.27819	0.487384	0.243692	+	0.969853i	$0.421641\pi$
$224$	−3.37441	−0.225462
$225$	−18.8295	−1.25530
$226$	16.7051	1.11121
$227$	−0.167305	−0.0111044	−0.00555221	−	0.999985i	$-0.501767\pi$
$227$	−0.167305	−0.0111044	−0.00555221	+	0.999985i	$0.501767\pi$
$228$	2.52340	0.167116
$229$	0.754795	0.0498783	0.0249391	−	0.999689i	$-0.492061\pi$
$229$	0.754795	0.0498783	0.0249391	+	0.999689i	$0.492061\pi$
$230$	0.274772	0.0181179
$231$	−34.9512	−2.29962
$232$	4.65983	0.305933
$233$	6.96352	0.456195	0.228098	−	0.973638i	$-0.426749\pi$
$233$	6.96352	0.456195	0.228098	+	0.973638i	$0.426749\pi$
$234$	−21.7918	−1.42457
$235$	0.506704	0.0330537
$236$	−7.81604	−0.508781
$237$	38.0565	2.47203
$238$	−21.0929	−1.36725
$239$	18.3076	1.18422	0.592111	−	0.805856i	$-0.298295\pi$
$239$	18.3076	1.18422	0.592111	+	0.805856i	$0.298295\pi$
$240$	−0.885579	−0.0571639
$241$	9.86133	0.635224	0.317612	−	0.948221i	$-0.397119\pi$
$241$	9.86133	0.635224	0.317612	+	0.948221i	$0.397119\pi$
$242$	−4.65227	−0.299059
$243$	−21.6525	−1.38901
$244$	−7.56231	−0.484127
$245$	−1.48383	−0.0947984
$246$	−18.1172	−1.15511
$247$	5.44980	0.346762
$248$	0	0
$249$	−4.16535	−0.263968
$250$	−3.34391	−0.211487
$251$	8.55861	0.540215	0.270107	−	0.962830i	$-0.412941\pi$
$251$	8.55861	0.540215	0.270107	+	0.962830i	$0.412941\pi$
$252$	13.0053	0.819258
$253$	−3.21373	−0.202045
$254$	6.72766	0.422131
$255$	−5.53563	−0.346654
$256$	1.00000	0.0625000
$257$	−25.9439	−1.61834	−0.809169	−	0.587576i	$-0.800082\pi$
$257$	−25.9439	−1.61834	−0.809169	+	0.587576i	$0.800082\pi$
$258$	−21.2825	−1.32499
$259$	−6.69249	−0.415851
$260$	−1.91259	−0.118614
$261$	−17.9595	−1.11166
$262$	7.25394	0.448150
$263$	−0.742168	−0.0457641	−0.0228820	−	0.999738i	$-0.507284\pi$
$263$	−0.742168	−0.0457641	−0.0228820	+	0.999738i	$0.507284\pi$
$264$	10.3577	0.637473
$265$	3.00776	0.184765
$266$	−3.25243	−0.199419
$267$	19.4840	1.19240
$268$	0.576239	0.0351994
$269$	18.3092	1.11633	0.558166	−	0.829729i	$-0.311505\pi$
$269$	18.3092	1.11633	0.558166	+	0.829729i	$0.311505\pi$
$270$	0.756375	0.0460315
$271$	12.0610	0.732656	0.366328	−	0.930486i	$-0.380615\pi$
$271$	12.0610	0.732656	0.366328	+	0.930486i	$0.380615\pi$
$272$	6.25085	0.379014
$273$	49.9508	3.02316
$274$	1.24074	0.0749557
$275$	19.3288	1.16557
$276$	2.12665	0.128009
$277$	−19.7054	−1.18398	−0.591991	−	0.805945i	$-0.701658\pi$
$277$	−19.7054	−1.18398	−0.591991	+	0.805945i	$0.701658\pi$
$278$	−18.6492	−1.11850
$279$	0	0
$280$	1.14143	0.0682136
$281$	26.5451	1.58355	0.791773	−	0.610815i	$-0.209158\pi$
$281$	26.5451	1.58355	0.791773	+	0.610815i	$0.209158\pi$
$282$	3.92173	0.233535
$283$	−28.0603	−1.66801	−0.834005	−	0.551757i	$-0.813958\pi$
$283$	−28.0603	−1.66801	−0.834005	+	0.551757i	$0.813958\pi$
$284$	7.49159	0.444544
$285$	−0.853568	−0.0505610
$286$	22.3696	1.32274
$287$	23.3514	1.37839
$288$	−3.85410	−0.227105
$289$	22.0731	1.29842
$290$	−1.57624	−0.0925600
$291$	0.194273	0.0113885
$292$	11.0342	0.645730
$293$	−19.2933	−1.12713	−0.563563	−	0.826073i	$-0.690570\pi$
$293$	−19.2933	−1.12713	−0.563563	+	0.826073i	$0.690570\pi$
$294$	−11.4844	−0.669782
$295$	2.64386	0.153932
$296$	1.98331	0.115277
$297$	−8.84655	−0.513329
$298$	6.82730	0.395495
$299$	4.59293	0.265616
$300$	−12.7906	−0.738466
$301$	27.4313	1.58111
$302$	0.465555	0.0267897
$303$	13.5033	0.775743
$304$	0.963852	0.0552807
$305$	2.55803	0.146473
$306$	−24.0914	−1.37721
$307$	13.2244	0.754757	0.377379	−	0.926059i	$-0.376826\pi$
$307$	13.2244	0.754757	0.377379	+	0.926059i	$0.376826\pi$
$308$	−13.3502	−0.760696
$309$	−10.2844	−0.585062
$310$	0	0
$311$	−33.7062	−1.91130	−0.955651	−	0.294502i	$-0.904846\pi$
$311$	−33.7062	−1.91130	−0.955651	+	0.294502i	$0.904846\pi$
$312$	−14.8028	−0.838046
$313$	21.9907	1.24299	0.621495	−	0.783418i	$-0.286526\pi$
$313$	21.9907	1.24299	0.621495	+	0.783418i	$0.286526\pi$
$314$	2.93237	0.165483
$315$	−4.39919	−0.247867
$316$	14.5363	0.817729
$317$	25.0361	1.40617	0.703083	−	0.711108i	$-0.251806\pi$
$317$	25.0361	1.40617	0.703083	+	0.711108i	$0.251806\pi$
$318$	23.2791	1.30543
$319$	18.4357	1.03220
$320$	−0.338261	−0.0189094
$321$	1.52753	0.0852586
$322$	−2.74106	−0.152753
$323$	6.02490	0.335234
$324$	−5.70820	−0.317122
$325$	−27.6240	−1.53230
$326$	3.11600	0.172579
$327$	−10.1074	−0.558940
$328$	−6.92015	−0.382101
$329$	−5.05475	−0.278677
$330$	−3.50361	−0.192868
$331$	−6.88992	−0.378704	−0.189352	−	0.981909i	$-0.560639\pi$
$331$	−6.88992	−0.378704	−0.189352	+	0.981909i	$0.560639\pi$
$332$	−1.59102	−0.0873187
$333$	−7.64386	−0.418881
$334$	6.41523	0.351026
$335$	−0.194919	−0.0106496
$336$	8.83432	0.481952
$337$	−29.2082	−1.59107	−0.795536	−	0.605906i	$-0.792811\pi$
$337$	−29.2082	−1.59107	−0.795536	+	0.605906i	$0.792811\pi$
$338$	−18.9698	−1.03182
$339$	−43.7346	−2.37533
$340$	−2.11442	−0.114671
$341$	0	0
$342$	−3.71478	−0.200873
$343$	−8.81856	−0.476157
$344$	−8.12920	−0.438297
$345$	−0.719363	−0.0387292
$346$	−14.3426	−0.771063
$347$	13.7867	0.740112	0.370056	−	0.929010i	$-0.379339\pi$
$347$	13.7867	0.740112	0.370056	+	0.929010i	$0.379339\pi$
$348$	−12.1996	−0.653967
$349$	−33.9615	−1.81792	−0.908958	−	0.416887i	$-0.863121\pi$
$349$	−33.9615	−1.81792	−0.908958	+	0.416887i	$0.863121\pi$
$350$	16.4859	0.881211
$351$	12.6431	0.674841
$352$	3.95630	0.210871
$353$	−1.41784	−0.0754640	−0.0377320	−	0.999288i	$-0.512013\pi$
$353$	−1.41784	−0.0754640	−0.0377320	+	0.999288i	$0.512013\pi$
$354$	20.4627	1.08758
$355$	−2.53411	−0.134497
$356$	7.44224	0.394438
$357$	55.2220	2.92266
$358$	19.1215	1.01060
$359$	2.54534	0.134338	0.0671689	−	0.997742i	$-0.478603\pi$
$359$	2.54534	0.134338	0.0671689	+	0.997742i	$0.478603\pi$
$360$	1.30369	0.0687107
$361$	−18.0710	−0.951105
$362$	6.20557	0.326157
$363$	12.1798	0.639274
$364$	19.0795	1.00004
$365$	−3.73245	−0.195366
$366$	19.7984	1.03488
$367$	9.53372	0.497656	0.248828	−	0.968548i	$-0.419955\pi$
$367$	9.53372	0.497656	0.248828	+	0.968548i	$0.419955\pi$
$368$	0.812307	0.0423444
$369$	26.6710	1.38843
$370$	−0.670876	−0.0348772
$371$	−30.0047	−1.55776
$372$	0	0
$373$	−22.2606	−1.15261	−0.576306	−	0.817234i	$-0.695506\pi$
$373$	−22.2606	−1.15261	−0.576306	+	0.817234i	$0.695506\pi$
$374$	24.7302	1.27877
$375$	8.75446	0.452079
$376$	1.49797	0.0772517
$377$	−26.3475	−1.35697
$378$	−7.54541	−0.388094
$379$	3.78318	0.194329	0.0971645	−	0.995268i	$-0.469023\pi$
$379$	3.78318	0.194329	0.0971645	+	0.995268i	$0.469023\pi$
$380$	−0.326034	−0.0167252
$381$	−17.6132	−0.902353
$382$	13.7173	0.701840
$383$	−17.1405	−0.875839	−0.437919	−	0.899014i	$-0.644284\pi$
$383$	−17.1405	−0.875839	−0.437919	+	0.899014i	$0.644284\pi$
$384$	−2.61803	−0.133601
$385$	4.51584	0.230149
$386$	15.0823	0.767668
$387$	31.3308	1.59263
$388$	0.0742058	0.00376723
$389$	−7.20536	−0.365326	−0.182663	−	0.983176i	$-0.558472\pi$
$389$	−7.20536	−0.365326	−0.182663	+	0.983176i	$0.558472\pi$
$390$	5.00723	0.253551
$391$	5.07761	0.256786
$392$	−4.38664	−0.221559
$393$	−18.9911	−0.957973
$394$	−6.69440	−0.337259
$395$	−4.91706	−0.247404
$396$	−15.2480	−0.766239
$397$	14.6418	0.734852	0.367426	−	0.930053i	$-0.380239\pi$
$397$	14.6418	0.734852	0.367426	+	0.930053i	$0.380239\pi$
$398$	−21.3309	−1.06922
$399$	8.51498	0.426282
$400$	−4.88558	−0.244279
$401$	24.9065	1.24377	0.621886	−	0.783107i	$-0.286367\pi$
$401$	24.9065	1.24377	0.621886	+	0.783107i	$0.286367\pi$
$402$	−1.50861	−0.0752428
$403$	0	0
$404$	5.15780	0.256610
$405$	1.93086	0.0959454
$406$	15.7242	0.780377
$407$	7.84655	0.388939
$408$	−16.3649	−0.810185
$409$	−34.2296	−1.69254	−0.846271	−	0.532752i	$-0.821158\pi$
$409$	−34.2296	−1.69254	−0.846271	+	0.532752i	$0.821158\pi$
$410$	2.34082	0.115605
$411$	−3.24830	−0.160227
$412$	−3.92831	−0.193534
$413$	−26.3745	−1.29781
$414$	−3.13072	−0.153866
$415$	0.538181	0.0264183
$416$	−5.65418	−0.277219
$417$	48.8242	2.39093
$418$	3.81328	0.186514
$419$	−19.2606	−0.940944	−0.470472	−	0.882415i	$-0.655916\pi$
$419$	−19.2606	−0.940944	−0.470472	+	0.882415i	$0.655916\pi$
$420$	−2.98831	−0.145814
$421$	−25.1864	−1.22751	−0.613756	−	0.789496i	$-0.710342\pi$
$421$	−25.1864	−1.22751	−0.613756	+	0.789496i	$0.710342\pi$
$422$	17.5708	0.855335
$423$	−5.77332	−0.280708
$424$	8.89183	0.431825
$425$	−30.5390	−1.48136
$426$	−19.6132	−0.950264
$427$	−25.5183	−1.23492
$428$	0.583466	0.0282029
$429$	−58.5644	−2.82752
$430$	2.74979	0.132607
$431$	26.0521	1.25489	0.627443	−	0.778662i	$-0.284102\pi$
$431$	26.0521	1.25489	0.627443	+	0.778662i	$0.284102\pi$
$432$	2.23607	0.107583
$433$	7.86224	0.377835	0.188917	−	0.981993i	$-0.439502\pi$
$433$	7.86224	0.377835	0.188917	+	0.981993i	$0.439502\pi$
$434$	0	0
$435$	4.12665	0.197858
$436$	−3.86068	−0.184893
$437$	0.782944	0.0374533
$438$	−28.8880	−1.38032
$439$	29.0718	1.38752	0.693762	−	0.720205i	$-0.255952\pi$
$439$	29.0718	1.38752	0.693762	+	0.720205i	$0.255952\pi$
$440$	−1.33826	−0.0637991
$441$	16.9065	0.805074
$442$	−35.3435	−1.68112
$443$	25.0906	1.19209	0.596045	−	0.802951i	$-0.296738\pi$
$443$	25.0906	1.19209	0.596045	+	0.802951i	$0.296738\pi$
$444$	−5.19236	−0.246419
$445$	−2.51742	−0.119337
$446$	−7.27819	−0.344632
$447$	−17.8741	−0.845415
$448$	3.37441	0.159426
$449$	−26.5947	−1.25508	−0.627541	−	0.778583i	$-0.715939\pi$
$449$	−26.5947	−1.25508	−0.627541	+	0.778583i	$0.715939\pi$
$450$	18.8295	0.887632
$451$	−27.3781	−1.28919
$452$	−16.7051	−0.785742
$453$	−1.21884	−0.0572661
$454$	0.167305	0.00785201
$455$	−6.45386	−0.302562
$456$	−2.52340	−0.118169
$457$	−7.07421	−0.330917	−0.165459	−	0.986217i	$-0.552910\pi$
$457$	−7.07421	−0.330917	−0.165459	+	0.986217i	$0.552910\pi$
$458$	−0.754795	−0.0352693
$459$	13.9773	0.652406
$460$	−0.274772	−0.0128113
$461$	−19.6259	−0.914068	−0.457034	−	0.889449i	$-0.651088\pi$
$461$	−19.6259	−0.914068	−0.457034	+	0.889449i	$0.651088\pi$
$462$	34.9512	1.62608
$463$	−3.78773	−0.176031	−0.0880153	−	0.996119i	$-0.528052\pi$
$463$	−3.78773	−0.176031	−0.0880153	+	0.996119i	$0.528052\pi$
$464$	−4.65983	−0.216327
$465$	0	0
$466$	−6.96352	−0.322579
$467$	3.44631	0.159476	0.0797380	−	0.996816i	$-0.474592\pi$
$467$	3.44631	0.159476	0.0797380	+	0.996816i	$0.474592\pi$
$468$	21.7918	1.00733
$469$	1.94447	0.0897871
$470$	−0.506704	−0.0233725
$471$	−7.67706	−0.353740
$472$	7.81604	0.359763
$473$	−32.1615	−1.47879
$474$	−38.0565	−1.74799
$475$	−4.70898	−0.216063
$476$	21.0929	0.966793
$477$	−34.2700	−1.56912
$478$	−18.3076	−0.837372
$479$	−0.287330	−0.0131284	−0.00656422	−	0.999978i	$-0.502089\pi$
$479$	−0.287330	−0.0131284	−0.00656422	+	0.999978i	$0.502089\pi$
$480$	0.885579	0.0404210
$481$	−11.2140	−0.511313
$482$	−9.86133	−0.449171
$483$	7.17618	0.326528
$484$	4.65227	0.211467
$485$	−0.0251009	−0.00113978
$486$	21.6525	0.982176
$487$	13.1774	0.597124	0.298562	−	0.954390i	$-0.403493\pi$
$487$	13.1774	0.597124	0.298562	+	0.954390i	$0.403493\pi$
$488$	7.56231	0.342330
$489$	−8.15780	−0.368908
$490$	1.48383	0.0670326
$491$	−24.2416	−1.09401	−0.547004	−	0.837130i	$-0.684232\pi$
$491$	−24.2416	−1.09401	−0.547004	+	0.837130i	$0.684232\pi$
$492$	18.1172	0.816786
$493$	−29.1279	−1.31185
$494$	−5.44980	−0.245198
$495$	5.15780	0.231826
$496$	0	0
$497$	25.2797	1.13395
$498$	4.16535	0.186654
$499$	15.0653	0.674414	0.337207	−	0.941431i	$-0.390518\pi$
$499$	15.0653	0.674414	0.337207	+	0.941431i	$0.390518\pi$
$500$	3.34391	0.149544
$501$	−16.7953	−0.750358
$502$	−8.55861	−0.381990
$503$	−17.1496	−0.764664	−0.382332	−	0.924025i	$-0.624879\pi$
$503$	−17.1496	−0.764664	−0.382332	+	0.924025i	$0.624879\pi$
$504$	−13.0053	−0.579303
$505$	−1.74468	−0.0776373
$506$	3.21373	0.142868
$507$	49.6635	2.20563
$508$	−6.72766	−0.298492
$509$	−0.591422	−0.0262143	−0.0131072	−	0.999914i	$-0.504172\pi$
$509$	−0.591422	−0.0262143	−0.0131072	+	0.999914i	$0.504172\pi$
$510$	5.53563	0.245122
$511$	37.2340	1.64714
$512$	−1.00000	−0.0441942
$513$	2.15524	0.0951561
$514$	25.9439	1.14434
$515$	1.32879	0.0585537
$516$	21.2825	0.936911
$517$	5.92640	0.260643
$518$	6.69249	0.294051
$519$	37.5494	1.64824
$520$	1.91259	0.0838726
$521$	−31.1139	−1.36313	−0.681563	−	0.731760i	$-0.738699\pi$
$521$	−31.1139	−1.36313	−0.681563	+	0.731760i	$0.738699\pi$
$522$	17.9595	0.786064
$523$	−42.2837	−1.84894	−0.924468	−	0.381261i	$-0.875490\pi$
$523$	−42.2837	−1.84894	−0.924468	+	0.381261i	$0.875490\pi$
$524$	−7.25394	−0.316890
$525$	−43.1608	−1.88369
$526$	0.742168	0.0323601
$527$	0	0
$528$	−10.3577	−0.450762
$529$	−22.3402	−0.971311
$530$	−3.00776	−0.130649
$531$	−30.1238	−1.30726
$532$	3.25243	0.141011
$533$	39.1278	1.69481
$534$	−19.4840	−0.843157
$535$	−0.197364	−0.00853279
$536$	−0.576239	−0.0248897
$537$	−50.0608	−2.16028
$538$	−18.3092	−0.789366
$539$	−17.3548	−0.747525
$540$	−0.756375	−0.0325492
$541$	23.7211	1.01985	0.509924	−	0.860219i	$-0.329673\pi$
$541$	23.7211	1.01985	0.509924	+	0.860219i	$0.329673\pi$
$542$	−12.0610	−0.518066
$543$	−16.2464	−0.697199
$544$	−6.25085	−0.268003
$545$	1.30592	0.0559394
$546$	−49.9508	−2.13770
$547$	−31.7143	−1.35601	−0.678003	−	0.735059i	$-0.737155\pi$
$547$	−31.7143	−1.35601	−0.678003	+	0.735059i	$0.737155\pi$
$548$	−1.24074	−0.0530017
$549$	−29.1459	−1.24392
$550$	−19.3288	−0.824183
$551$	−4.49139	−0.191339
$552$	−2.12665	−0.0905162
$553$	49.0513	2.08587
$554$	19.7054	0.837202
$555$	1.75638	0.0745540
$556$	18.6492	0.790901
$557$	−22.9754	−0.973500	−0.486750	−	0.873541i	$-0.661818\pi$
$557$	−22.9754	−0.973500	−0.486750	+	0.873541i	$0.661818\pi$
$558$	0	0
$559$	45.9640	1.94407
$560$	−1.14143	−0.0482343
$561$	−64.7445	−2.73352
$562$	−26.5451	−1.11974
$563$	−33.3755	−1.40661	−0.703304	−	0.710889i	$-0.748293\pi$
$563$	−33.3755	−1.40661	−0.703304	+	0.710889i	$0.748293\pi$
$564$	−3.92173	−0.165135
$565$	5.65069	0.237726
$566$	28.0603	1.17946
$567$	−19.2618	−0.808920
$568$	−7.49159	−0.314340
$569$	25.3450	1.06252	0.531259	−	0.847209i	$-0.321719\pi$
$569$	25.3450	1.06252	0.531259	+	0.847209i	$0.321719\pi$
$570$	0.853568	0.0357520
$571$	15.4290	0.645685	0.322843	−	0.946453i	$-0.395362\pi$
$571$	15.4290	0.645685	0.322843	+	0.946453i	$0.395362\pi$
$572$	−22.3696	−0.935320
$573$	−35.9125	−1.50026
$574$	−23.3514	−0.974669
$575$	−3.96859	−0.165502
$576$	3.85410	0.160588
$577$	−26.9408	−1.12156	−0.560780	−	0.827965i	$-0.689499\pi$
$577$	−26.9408	−1.12156	−0.560780	+	0.827965i	$0.689499\pi$
$578$	−22.0731	−0.918122
$579$	−39.4859	−1.64098
$580$	1.57624	0.0654498
$581$	−5.36876	−0.222734
$582$	−0.194273	−0.00805289
$583$	35.1787	1.45695
$584$	−11.0342	−0.456600
$585$	−7.37132	−0.304767
$586$	19.2933	0.796999
$587$	−18.5271	−0.764695	−0.382347	−	0.924019i	$-0.624884\pi$
$587$	−18.5271	−0.764695	−0.382347	+	0.924019i	$0.624884\pi$
$588$	11.4844	0.473607
$589$	0	0
$590$	−2.64386	−0.108846
$591$	17.5262	0.720930
$592$	−1.98331	−0.0815134
$593$	−25.2480	−1.03681	−0.518405	−	0.855135i	$-0.673474\pi$
$593$	−25.2480	−1.03681	−0.518405	+	0.855135i	$0.673474\pi$
$594$	8.84655	0.362978
$595$	−7.13492	−0.292503
$596$	−6.82730	−0.279657
$597$	55.8450	2.28559
$598$	−4.59293	−0.187819
$599$	−8.20183	−0.335118	−0.167559	−	0.985862i	$-0.553588\pi$
$599$	−8.20183	−0.335118	−0.167559	+	0.985862i	$0.553588\pi$
$600$	12.7906	0.522175
$601$	−45.1625	−1.84221	−0.921107	−	0.389309i	$-0.872714\pi$
$601$	−45.1625	−1.84221	−0.921107	+	0.389309i	$0.872714\pi$
$602$	−27.4313	−1.11801
$603$	2.22089	0.0904414
$604$	−0.465555	−0.0189432
$605$	−1.57368	−0.0639793
$606$	−13.5033	−0.548533
$607$	−8.01815	−0.325447	−0.162723	−	0.986672i	$-0.552028\pi$
$607$	−8.01815	−0.325447	−0.162723	+	0.986672i	$0.552028\pi$
$608$	−0.963852	−0.0390894
$609$	−41.1664	−1.66815
$610$	−2.55803	−0.103572
$611$	−8.46977	−0.342650
$612$	24.0914	0.973838
$613$	−4.29415	−0.173439	−0.0867195	−	0.996233i	$-0.527638\pi$
$613$	−4.29415	−0.173439	−0.0867195	+	0.996233i	$0.527638\pi$
$614$	−13.2244	−0.533694
$615$	−6.12834	−0.247119
$616$	13.3502	0.537893
$617$	3.84154	0.154655	0.0773274	−	0.997006i	$-0.475361\pi$
$617$	3.84154	0.154655	0.0773274	+	0.997006i	$0.475361\pi$
$618$	10.2844	0.413701
$619$	−20.6266	−0.829055	−0.414527	−	0.910037i	$-0.636053\pi$
$619$	−20.6266	−0.829055	−0.414527	+	0.910037i	$0.636053\pi$
$620$	0	0
$621$	1.81637	0.0728886
$622$	33.7062	1.35149
$623$	25.1132	1.00614
$624$	14.8028	0.592588
$625$	23.2968	0.931871
$626$	−21.9907	−0.878927
$627$	−9.98331	−0.398695
$628$	−2.93237	−0.117014
$629$	−12.3974	−0.494315
$630$	4.39919	0.175268
$631$	13.7117	0.545856	0.272928	−	0.962035i	$-0.412008\pi$
$631$	13.7117	0.545856	0.272928	+	0.962035i	$0.412008\pi$
$632$	−14.5363	−0.578222
$633$	−46.0011	−1.82838
$634$	−25.0361	−0.994309
$635$	2.27571	0.0903086
$636$	−23.2791	−0.923077
$637$	24.8028	0.982724
$638$	−18.4357	−0.729875
$639$	28.8734	1.14221
$640$	0.338261	0.0133709
$641$	−23.2940	−0.920059	−0.460029	−	0.887904i	$-0.652161\pi$
$641$	−23.2940	−0.920059	−0.460029	+	0.887904i	$0.652161\pi$
$642$	−1.52753	−0.0602869
$643$	−15.2632	−0.601920	−0.300960	−	0.953637i	$-0.597307\pi$
$643$	−15.2632	−0.601920	−0.300960	+	0.953637i	$0.597307\pi$
$644$	2.74106	0.108013
$645$	−7.19906	−0.283463
$646$	−6.02490	−0.237046
$647$	27.8967	1.09673	0.548366	−	0.836239i	$-0.315250\pi$
$647$	27.8967	1.09673	0.548366	+	0.836239i	$0.315250\pi$
$648$	5.70820	0.224239
$649$	30.9226	1.21382
$650$	27.6240	1.08350
$651$	0	0
$652$	−3.11600	−0.122032
$653$	−7.44224	−0.291237	−0.145619	−	0.989341i	$-0.546517\pi$
$653$	−7.44224	−0.291237	−0.145619	+	0.989341i	$0.546517\pi$
$654$	10.1074	0.395231
$655$	2.45373	0.0958751
$656$	6.92015	0.270186
$657$	42.5271	1.65914
$658$	5.05475	0.197055
$659$	18.3455	0.714639	0.357319	−	0.933982i	$-0.383691\pi$
$659$	18.3455	0.714639	0.357319	+	0.933982i	$0.383691\pi$
$660$	3.50361	0.136378
$661$	1.91857	0.0746236	0.0373118	−	0.999304i	$-0.488121\pi$
$661$	1.91857	0.0746236	0.0373118	+	0.999304i	$0.488121\pi$
$662$	6.88992	0.267784
$663$	92.5304	3.59358
$664$	1.59102	0.0617437
$665$	−1.10017	−0.0426628
$666$	7.64386	0.296194
$667$	−3.78521	−0.146564
$668$	−6.41523	−0.248213
$669$	19.0546	0.736692
$670$	0.194919	0.00753039
$671$	29.9187	1.15500
$672$	−8.83432	−0.340791
$673$	17.3855	0.670160	0.335080	−	0.942190i	$-0.391237\pi$
$673$	17.3855	0.670160	0.335080	+	0.942190i	$0.391237\pi$
$674$	29.2082	1.12506
$675$	−10.9245	−0.420484
$676$	18.9698	0.729607
$677$	48.1653	1.85114	0.925572	−	0.378571i	$-0.123585\pi$
$677$	48.1653	1.85114	0.925572	+	0.378571i	$0.123585\pi$
$678$	43.7346	1.67962
$679$	0.250401	0.00960950
$680$	2.11442	0.0810843
$681$	−0.438010	−0.0167846
$682$	0	0
$683$	30.1537	1.15380	0.576900	−	0.816815i	$-0.304262\pi$
$683$	30.1537	1.15380	0.576900	+	0.816815i	$0.304262\pi$
$684$	3.71478	0.142038
$685$	0.419694	0.0160357
$686$	8.81856	0.336694
$687$	1.97608	0.0753921
$688$	8.12920	0.309923
$689$	−50.2760	−1.91536
$690$	0.719363	0.0273857
$691$	−19.3143	−0.734752	−0.367376	−	0.930073i	$-0.619744\pi$
$691$	−19.3143	−0.734752	−0.367376	+	0.930073i	$0.619744\pi$
$692$	14.3426	0.545224
$693$	−51.4529	−1.95453
$694$	−13.7867	−0.523338
$695$	−6.30829	−0.239287
$696$	12.1996	0.462424
$697$	43.2568	1.63847
$698$	33.9615	1.28546
$699$	18.2307	0.689550
$700$	−16.4859	−0.623110
$701$	30.0446	1.13477	0.567385	−	0.823453i	$-0.307955\pi$
$701$	30.0446	1.13477	0.567385	+	0.823453i	$0.307955\pi$
$702$	−12.6431	−0.477184
$703$	−1.91161	−0.0720979
$704$	−3.95630	−0.149108
$705$	1.32657	0.0499614
$706$	1.41784	0.0533611
$707$	17.4045	0.654564
$708$	−20.4627	−0.769034
$709$	−12.5737	−0.472216	−0.236108	−	0.971727i	$-0.575872\pi$
$709$	−12.5737	−0.472216	−0.236108	+	0.971727i	$0.575872\pi$
$710$	2.53411	0.0951036
$711$	56.0243	2.10107
$712$	−7.44224	−0.278910
$713$	0	0
$714$	−55.2220	−2.06663
$715$	7.56677	0.282981
$716$	−19.1215	−0.714605
$717$	47.9300	1.78998
$718$	−2.54534	−0.0949912
$719$	−19.1018	−0.712378	−0.356189	−	0.934414i	$-0.615924\pi$
$719$	−19.1018	−0.712378	−0.356189	+	0.934414i	$0.615924\pi$
$720$	−1.30369	−0.0485858
$721$	−13.2557	−0.493669
$722$	18.0710	0.672533
$723$	25.8173	0.960155
$724$	−6.20557	−0.230628
$725$	22.7660	0.845507
$726$	−12.1798	−0.452035
$727$	2.32129	0.0860920	0.0430460	−	0.999073i	$-0.486294\pi$
$727$	2.32129	0.0860920	0.0430460	+	0.999073i	$0.486294\pi$
$728$	−19.0795	−0.707134
$729$	−39.5623	−1.46527
$730$	3.73245	0.138144
$731$	50.8144	1.87944
$732$	−19.7984	−0.731769
$733$	25.3211	0.935257	0.467628	−	0.883925i	$-0.345109\pi$
$733$	25.3211	0.935257	0.467628	+	0.883925i	$0.345109\pi$
$734$	−9.53372	−0.351896
$735$	−3.88471	−0.143290
$736$	−0.812307	−0.0299420
$737$	−2.27977	−0.0839765
$738$	−26.6710	−0.981771
$739$	14.9935	0.551545	0.275772	−	0.961223i	$-0.411066\pi$
$739$	14.9935	0.551545	0.275772	+	0.961223i	$0.411066\pi$
$740$	0.670876	0.0246619
$741$	14.2677	0.524139
$742$	30.0047	1.10151
$743$	45.0197	1.65161	0.825807	−	0.563953i	$-0.190720\pi$
$743$	45.0197	1.65161	0.825807	+	0.563953i	$0.190720\pi$
$744$	0	0
$745$	2.30941	0.0846102
$746$	22.2606	0.815020
$747$	−6.13196	−0.224357
$748$	−24.7302	−0.904226
$749$	1.96885	0.0719403
$750$	−8.75446	−0.319668
$751$	29.4708	1.07540	0.537702	−	0.843135i	$-0.319292\pi$
$751$	29.4708	1.07540	0.537702	+	0.843135i	$0.319292\pi$
$752$	−1.49797	−0.0546252
$753$	22.4067	0.816547
$754$	26.3475	0.959520
$755$	0.157479	0.00573126
$756$	7.54541	0.274424
$757$	36.7324	1.33506	0.667531	−	0.744582i	$-0.267351\pi$
$757$	36.7324	1.33506	0.667531	+	0.744582i	$0.267351\pi$
$758$	−3.78318	−0.137411
$759$	−8.41365	−0.305396
$760$	0.326034	0.0118265
$761$	−16.9870	−0.615780	−0.307890	−	0.951422i	$-0.599623\pi$
$761$	−16.9870	−0.615780	−0.307890	+	0.951422i	$0.599623\pi$
$762$	17.6132	0.638060
$763$	−13.0275	−0.471628
$764$	−13.7173	−0.496276
$765$	−8.14919	−0.294635
$766$	17.1405	0.619311
$767$	−44.1933	−1.59573
$768$	2.61803	0.0944702
$769$	−0.979639	−0.0353267	−0.0176633	−	0.999844i	$-0.505623\pi$
$769$	−0.979639	−0.0353267	−0.0176633	+	0.999844i	$0.505623\pi$
$770$	−4.51584	−0.162740
$771$	−67.9221	−2.44616
$772$	−15.0823	−0.542823
$773$	−35.6725	−1.28305	−0.641525	−	0.767102i	$-0.721698\pi$
$773$	−35.6725	−1.28305	−0.641525	+	0.767102i	$0.721698\pi$
$774$	−31.3308	−1.12616
$775$	0	0
$776$	−0.0742058	−0.00266383
$777$	−17.5212	−0.628568
$778$	7.20536	0.258325
$779$	6.67000	0.238978
$780$	−5.00723	−0.179287
$781$	−29.6389	−1.06056
$782$	−5.07761	−0.181575
$783$	−10.4197	−0.372369
$784$	4.38664	0.156666
$785$	0.991909	0.0354027
$786$	18.9911	0.677389
$787$	21.2980	0.759190	0.379595	−	0.925153i	$-0.376063\pi$
$787$	21.2980	0.759190	0.379595	+	0.925153i	$0.376063\pi$
$788$	6.69440	0.238478
$789$	−1.94302	−0.0691734
$790$	4.91706	0.174941
$791$	−56.3699	−2.00428
$792$	15.2480	0.541813
$793$	−42.7587	−1.51840
$794$	−14.6418	−0.519619
$795$	7.87442	0.279277
$796$	21.3309	0.756054
$797$	−4.80923	−0.170352	−0.0851758	−	0.996366i	$-0.527145\pi$
$797$	−4.80923	−0.170352	−0.0851758	+	0.996366i	$0.527145\pi$
$798$	−8.51498	−0.301427
$799$	−9.36357	−0.331259
$800$	4.88558	0.172731
$801$	28.6831	1.01347
$802$	−24.9065	−0.879480
$803$	−43.6547	−1.54054
$804$	1.50861	0.0532047
$805$	−0.927193	−0.0326793
$806$	0	0
$807$	47.9341	1.68736
$808$	−5.15780	−0.181451
$809$	−4.13827	−0.145494	−0.0727469	−	0.997350i	$-0.523177\pi$
$809$	−4.13827	−0.145494	−0.0727469	+	0.997350i	$0.523177\pi$
$810$	−1.93086	−0.0678436
$811$	34.9018	1.22557	0.612784	−	0.790250i	$-0.290049\pi$
$811$	34.9018	1.22557	0.612784	+	0.790250i	$0.290049\pi$
$812$	−15.7242	−0.551810
$813$	31.5762	1.10743
$814$	−7.84655	−0.275021
$815$	1.05402	0.0369208
$816$	16.3649	0.572888
$817$	7.83535	0.274124
$818$	34.2296	1.19681
$819$	73.5344	2.56950
$820$	−2.34082	−0.0817449
$821$	5.31434	0.185472	0.0927359	−	0.995691i	$-0.470439\pi$
$821$	5.31434	0.185472	0.0927359	+	0.995691i	$0.470439\pi$
$822$	3.24830	0.113297
$823$	15.4139	0.537294	0.268647	−	0.963239i	$-0.413423\pi$
$823$	15.4139	0.537294	0.268647	+	0.963239i	$0.413423\pi$
$824$	3.92831	0.136849
$825$	50.6034	1.76179
$826$	26.3745	0.917687
$827$	40.0029	1.39104	0.695518	−	0.718509i	$-0.255175\pi$
$827$	40.0029	1.39104	0.695518	+	0.718509i	$0.255175\pi$
$828$	3.13072	0.108800
$829$	−21.8402	−0.758540	−0.379270	−	0.925286i	$-0.623825\pi$
$829$	−21.8402	−0.758540	−0.379270	+	0.925286i	$0.623825\pi$
$830$	−0.538181	−0.0186805
$831$	−51.5894	−1.78962
$832$	5.65418	0.196023
$833$	27.4202	0.950054
$834$	−48.8242	−1.69064
$835$	2.17002	0.0750967
$836$	−3.81328	−0.131885
$837$	0	0
$838$	19.2606	0.665348
$839$	−54.6421	−1.88646	−0.943228	−	0.332147i	$-0.892227\pi$
$839$	−54.6421	−1.88646	−0.943228	+	0.332147i	$0.892227\pi$
$840$	2.98831	0.103106
$841$	−7.28600	−0.251241
$842$	25.1864	0.867982
$843$	69.4959	2.39357
$844$	−17.5708	−0.604813
$845$	−6.41674	−0.220743
$846$	5.77332	0.198491
$847$	15.6987	0.539413
$848$	−8.89183	−0.305347
$849$	−73.4627	−2.52123
$850$	30.5390	1.04748
$851$	−1.61105	−0.0552262
$852$	19.6132	0.671938
$853$	47.6586	1.63180	0.815899	−	0.578194i	$-0.196242\pi$
$853$	47.6586	1.63180	0.815899	+	0.578194i	$0.196242\pi$
$854$	25.5183	0.873219
$855$	−1.25657	−0.0429737
$856$	−0.583466	−0.0199425
$857$	38.7020	1.32203	0.661017	−	0.750371i	$-0.270125\pi$
$857$	38.7020	1.32203	0.661017	+	0.750371i	$0.270125\pi$
$858$	58.5644	1.99936
$859$	4.97675	0.169805	0.0849023	−	0.996389i	$-0.472942\pi$
$859$	4.97675	0.169805	0.0849023	+	0.996389i	$0.472942\pi$
$860$	−2.74979	−0.0937672
$861$	61.1348	2.08347
$862$	−26.0521	−0.887338
$863$	−51.4200	−1.75036	−0.875179	−	0.483799i	$-0.839257\pi$
$863$	−51.4200	−1.75036	−0.875179	+	0.483799i	$0.839257\pi$
$864$	−2.23607	−0.0760726
$865$	−4.85155	−0.164958
$866$	−7.86224	−0.267170
$867$	57.7882	1.96259
$868$	0	0
$869$	−57.5098	−1.95089
$870$	−4.12665	−0.139906
$871$	3.25816	0.110399
$872$	3.86068	0.130739
$873$	0.285997	0.00967952
$874$	−0.782944	−0.0264835
$875$	11.2837	0.381459
$876$	28.8880	0.976035
$877$	54.2465	1.83178	0.915888	−	0.401435i	$-0.131488\pi$
$877$	54.2465	1.83178	0.915888	+	0.401435i	$0.131488\pi$
$878$	−29.0718	−0.981127
$879$	−50.5105	−1.70368
$880$	1.33826	0.0451128
$881$	−10.5683	−0.356054	−0.178027	−	0.984026i	$-0.556971\pi$
$881$	−10.5683	−0.356054	−0.178027	+	0.984026i	$0.556971\pi$
$882$	−16.9065	−0.569273
$883$	−14.4225	−0.485356	−0.242678	−	0.970107i	$-0.578026\pi$
$883$	−14.4225	−0.485356	−0.242678	+	0.970107i	$0.578026\pi$
$884$	35.3435	1.18873
$885$	6.92173	0.232671
$886$	−25.0906	−0.842936
$887$	−19.8400	−0.666163	−0.333082	−	0.942898i	$-0.608089\pi$
$887$	−19.8400	−0.666163	−0.333082	+	0.942898i	$0.608089\pi$
$888$	5.19236	0.174244
$889$	−22.7019	−0.761396
$890$	2.51742	0.0843841
$891$	22.5833	0.756570
$892$	7.27819	0.243692
$893$	−1.44382	−0.0483155
$894$	17.8741	0.597799
$895$	6.46807	0.216204
$896$	−3.37441	−0.112731
$897$	12.0245	0.401485
$898$	26.5947	0.887477
$899$	0	0
$900$	−18.8295	−0.627651
$901$	−55.5815	−1.85169
$902$	27.3781	0.911593
$903$	71.8160	2.38989
$904$	16.7051	0.555604
$905$	2.09910	0.0697765
$906$	1.21884	0.0404932
$907$	−27.7160	−0.920296	−0.460148	−	0.887842i	$-0.652204\pi$
$907$	−27.7160	−0.920296	−0.460148	+	0.887842i	$0.652204\pi$
$908$	−0.167305	−0.00555221
$909$	19.8787	0.659334
$910$	6.45386	0.213943
$911$	35.5990	1.17945	0.589724	−	0.807605i	$-0.299236\pi$
$911$	35.5990	1.17945	0.589724	+	0.807605i	$0.299236\pi$
$912$	2.52340	0.0835580
$913$	6.29456	0.208319
$914$	7.07421	0.233994
$915$	6.69702	0.221397
$916$	0.754795	0.0249391
$917$	−24.4778	−0.808327
$918$	−13.9773	−0.461321
$919$	32.6081	1.07564	0.537821	−	0.843059i	$-0.319248\pi$
$919$	32.6081	1.07564	0.537821	+	0.843059i	$0.319248\pi$
$920$	0.274772	0.00905897
$921$	34.6220	1.14083
$922$	19.6259	0.646343
$923$	42.3588	1.39426
$924$	−34.9512	−1.14981
$925$	9.68960	0.318592
$926$	3.78773	0.124472
$927$	−15.1401	−0.497266
$928$	4.65983	0.152966
$929$	−1.46885	−0.0481914	−0.0240957	−	0.999710i	$-0.507671\pi$
$929$	−1.46885	−0.0481914	−0.0240957	+	0.999710i	$0.507671\pi$
$930$	0	0
$931$	4.22807	0.138569
$932$	6.96352	0.228098
$933$	−88.2439	−2.88898
$934$	−3.44631	−0.112767
$935$	8.36527	0.273574
$936$	−21.7918	−0.712287
$937$	5.24232	0.171259	0.0856295	−	0.996327i	$-0.472710\pi$
$937$	5.24232	0.171259	0.0856295	+	0.996327i	$0.472710\pi$
$938$	−1.94447	−0.0634891
$939$	57.5725	1.87881
$940$	0.506704	0.0165269
$941$	−53.7672	−1.75276	−0.876380	−	0.481621i	$-0.840048\pi$
$941$	−53.7672	−1.75276	−0.876380	+	0.481621i	$0.840048\pi$
$942$	7.67706	0.250132
$943$	5.62129	0.183054
$944$	−7.81604	−0.254391
$945$	−2.55232	−0.0830269
$946$	32.1615	1.04566
$947$	−37.9099	−1.23191	−0.615953	−	0.787783i	$-0.711229\pi$
$947$	−37.9099	−1.23191	−0.615953	+	0.787783i	$0.711229\pi$
$948$	38.0565	1.23602
$949$	62.3896	2.02525
$950$	4.70898	0.152779
$951$	65.5453	2.12545
$952$	−21.0929	−0.683626
$953$	−31.3287	−1.01484	−0.507419	−	0.861700i	$-0.669400\pi$
$953$	−31.3287	−1.01484	−0.507419	+	0.861700i	$0.669400\pi$
$954$	34.2700	1.10953
$955$	4.64004	0.150148
$956$	18.3076	0.592111
$957$	48.2652	1.56019
$958$	0.287330	0.00928320
$959$	−4.18676	−0.135197
$960$	−0.885579	−0.0285820
$961$	0	0
$962$	11.2140	0.361553
$963$	2.24874	0.0724645
$964$	9.86133	0.317612
$965$	5.10175	0.164231
$966$	−7.17618	−0.230890
$967$	−7.19508	−0.231378	−0.115689	−	0.993285i	$-0.536908\pi$
$967$	−7.19508	−0.231378	−0.115689	+	0.993285i	$0.536908\pi$
$968$	−4.65227	−0.149530
$969$	15.7734	0.506714
$970$	0.0251009	0.000805943 0
$971$	−15.6695	−0.502858	−0.251429	−	0.967876i	$-0.580901\pi$
$971$	−15.6695	−0.502858	−0.251429	+	0.967876i	$0.580901\pi$
$972$	−21.6525	−0.694503
$973$	62.9300	2.01744
$974$	−13.1774	−0.422230
$975$	−72.3205	−2.31611
$976$	−7.56231	−0.242064
$977$	11.0877	0.354726	0.177363	−	0.984146i	$-0.443243\pi$
$977$	11.0877	0.354726	0.177363	+	0.984146i	$0.443243\pi$
$978$	8.15780	0.260858
$979$	−29.4437	−0.941024
$980$	−1.48383	−0.0473992
$981$	−14.8795	−0.475065
$982$	24.2416	0.773580
$983$	11.9959	0.382610	0.191305	−	0.981531i	$-0.438728\pi$
$983$	11.9959	0.382610	0.191305	+	0.981531i	$0.438728\pi$
$984$	−18.1172	−0.577555
$985$	−2.26445	−0.0721515
$986$	29.1279	0.927621
$987$	−13.2335	−0.421227
$988$	5.44980	0.173381
$989$	6.60341	0.209976
$990$	−5.15780	−0.163925
$991$	35.5304	1.12866	0.564330	−	0.825550i	$-0.309135\pi$
$991$	35.5304	1.12866	0.564330	+	0.825550i	$0.309135\pi$
$992$	0	0
$993$	−18.0380	−0.572420
$994$	−25.2797	−0.801823
$995$	−7.21542	−0.228744
$996$	−4.16535	−0.131984
$997$	−23.0958	−0.731450	−0.365725	−	0.930723i	$-0.619179\pi$
$997$	−23.0958	−0.731450	−0.365725	+	0.930723i	$0.619179\pi$
$998$	−15.0653	−0.476882
$999$	−4.43481	−0.140311

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1922.2.a.m.1.3		4
31.12	odd	30		62.2.g.b.51.1	yes	8
31.13	odd	30		62.2.g.b.45.1	✓	8
31.30	odd	2		1922.2.a.h.1.1		4
93.44	even	30		558.2.ba.c.541.1		8
93.74	even	30		558.2.ba.c.361.1		8
124.43	even	30		496.2.bg.b.113.1		8
124.75	even	30		496.2.bg.b.417.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.2.g.b.45.1	✓	8	31.13	odd	30
62.2.g.b.51.1	yes	8	31.12	odd	30
496.2.bg.b.113.1		8	124.43	even	30
496.2.bg.b.417.1		8	124.75	even	30
558.2.ba.c.361.1		8	93.74	even	30
558.2.ba.c.541.1		8	93.44	even	30
1922.2.a.h.1.1		4	31.30	odd	2
1922.2.a.m.1.3		4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1922 = 2 \cdot 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1922.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.61803 q^{3} +1.00000 q^{4} -0.338261 q^{5} -2.61803 q^{6} +3.37441 q^{7} -1.00000 q^{8} +3.85410 q^{9} +0.338261 q^{10} -3.95630 q^{11} +2.61803 q^{12} +5.65418 q^{13} -3.37441 q^{14} -0.885579 q^{15} +1.00000 q^{16} +6.25085 q^{17} -3.85410 q^{18} +0.963852 q^{19} -0.338261 q^{20} +8.83432 q^{21} +3.95630 q^{22} +0.812307 q^{23} -2.61803 q^{24} -4.88558 q^{25} -5.65418 q^{26} +2.23607 q^{27} +3.37441 q^{28} -4.65983 q^{29} +0.885579 q^{30} -1.00000 q^{32} -10.3577 q^{33} -6.25085 q^{34} -1.14143 q^{35} +3.85410 q^{36} -1.98331 q^{37} -0.963852 q^{38} +14.8028 q^{39} +0.338261 q^{40} +6.92015 q^{41} -8.83432 q^{42} +8.12920 q^{43} -3.95630 q^{44} -1.30369 q^{45} -0.812307 q^{46} -1.49797 q^{47} +2.61803 q^{48} +4.38664 q^{49} +4.88558 q^{50} +16.3649 q^{51} +5.65418 q^{52} -8.89183 q^{53} -2.23607 q^{54} +1.33826 q^{55} -3.37441 q^{56} +2.52340 q^{57} +4.65983 q^{58} -7.81604 q^{59} -0.885579 q^{60} -7.56231 q^{61} +13.0053 q^{63} +1.00000 q^{64} -1.91259 q^{65} +10.3577 q^{66} +0.576239 q^{67} +6.25085 q^{68} +2.12665 q^{69} +1.14143 q^{70} +7.49159 q^{71} -3.85410 q^{72} +11.0342 q^{73} +1.98331 q^{74} -12.7906 q^{75} +0.963852 q^{76} -13.3502 q^{77} -14.8028 q^{78} +14.5363 q^{79} -0.338261 q^{80} -5.70820 q^{81} -6.92015 q^{82} -1.59102 q^{83} +8.83432 q^{84} -2.11442 q^{85} -8.12920 q^{86} -12.1996 q^{87} +3.95630 q^{88} +7.44224 q^{89} +1.30369 q^{90} +19.0795 q^{91} +0.812307 q^{92} +1.49797 q^{94} -0.326034 q^{95} -2.61803 q^{96} +0.0742058 q^{97} -4.38664 q^{98} -15.2480 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 6 q^{3} + 4 q^{4} + 3 q^{5} - 6 q^{6} + q^{7} - 4 q^{8} + 2 q^{9} - 3 q^{10} - 7 q^{11} + 6 q^{12} + 10 q^{13} - q^{14} + 7 q^{15} + 4 q^{16} + 3 q^{17} - 2 q^{18} + 12 q^{19} + 3 q^{20}+ \cdots - 11 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 6 * q^3 + 4 * q^4 + 3 * q^5 - 6 * q^6 + q^7 - 4 * q^8 + 2 * q^9 - 3 * q^10 - 7 * q^11 + 6 * q^12 + 10 * q^13 - q^14 + 7 * q^15 + 4 * q^16 + 3 * q^17 - 2 * q^18 + 12 * q^19 + 3 * q^20 - q^21 + 7 * q^22 + 10 * q^23 - 6 * q^24 - 9 * q^25 - 10 * q^26 + q^28 + 6 * q^29 - 7 * q^30 - 4 * q^32 - 13 * q^33 - 3 * q^34 - 8 * q^35 + 2 * q^36 + 8 * q^37 - 12 * q^38 + 20 * q^39 - 3 * q^40 + 27 * q^41 + q^42 + 30 * q^43 - 7 * q^44 + 9 * q^45 - 10 * q^46 - 3 * q^47 + 6 * q^48 + 11 * q^49 + 9 * q^50 + 7 * q^51 + 10 * q^52 + 4 * q^53 + q^55 - q^56 + 18 * q^57 - 6 * q^58 + 3 * q^59 + 7 * q^60 + 10 * q^61 - 7 * q^63 + 4 * q^64 + 10 * q^65 + 13 * q^66 + 18 * q^67 + 3 * q^68 + 25 * q^69 + 8 * q^70 - 12 * q^71 - 2 * q^72 + 7 * q^73 - 8 * q^74 - 6 * q^75 + 12 * q^76 - 8 * q^77 - 20 * q^78 + 24 * q^79 + 3 * q^80 + 4 * q^81 - 27 * q^82 - 9 * q^83 - q^84 - 19 * q^85 - 30 * q^86 - q^87 + 7 * q^88 - 9 * q^89 - 9 * q^90 + 30 * q^91 + 10 * q^92 + 3 * q^94 + 9 * q^95 - 6 * q^96 + 13 * q^97 - 11 * q^98 - 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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