LMFDB - Embedded newform 8007.2.a.g.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.45801 q^{2} -1.00000 q^{3} +4.04182 q^{4} -3.57546 q^{5} +2.45801 q^{6} +3.37294 q^{7} -5.01881 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.45801 q^{2} -1.00000 q^{3} +4.04182 q^{4} -3.57546 q^{5} +2.45801 q^{6} +3.37294 q^{7} -5.01881 q^{8} +1.00000 q^{9} +8.78852 q^{10} -2.14222 q^{11} -4.04182 q^{12} +2.62627 q^{13} -8.29072 q^{14} +3.57546 q^{15} +4.25266 q^{16} -1.00000 q^{17} -2.45801 q^{18} -7.66808 q^{19} -14.4514 q^{20} -3.37294 q^{21} +5.26560 q^{22} -5.22005 q^{23} +5.01881 q^{24} +7.78391 q^{25} -6.45539 q^{26} -1.00000 q^{27} +13.6328 q^{28} +1.54538 q^{29} -8.78852 q^{30} -0.227539 q^{31} -0.415463 q^{32} +2.14222 q^{33} +2.45801 q^{34} -12.0598 q^{35} +4.04182 q^{36} -11.2449 q^{37} +18.8482 q^{38} -2.62627 q^{39} +17.9446 q^{40} -2.06113 q^{41} +8.29072 q^{42} -9.43862 q^{43} -8.65847 q^{44} -3.57546 q^{45} +12.8309 q^{46} -0.702326 q^{47} -4.25266 q^{48} +4.37672 q^{49} -19.1329 q^{50} +1.00000 q^{51} +10.6149 q^{52} -1.89733 q^{53} +2.45801 q^{54} +7.65942 q^{55} -16.9282 q^{56} +7.66808 q^{57} -3.79856 q^{58} +0.129353 q^{59} +14.4514 q^{60} +4.39664 q^{61} +0.559293 q^{62} +3.37294 q^{63} -7.48411 q^{64} -9.39011 q^{65} -5.26560 q^{66} +2.22734 q^{67} -4.04182 q^{68} +5.22005 q^{69} +29.6431 q^{70} -8.50510 q^{71} -5.01881 q^{72} +8.46689 q^{73} +27.6401 q^{74} -7.78391 q^{75} -30.9930 q^{76} -7.22558 q^{77} +6.45539 q^{78} -4.25177 q^{79} -15.2052 q^{80} +1.00000 q^{81} +5.06629 q^{82} -16.5110 q^{83} -13.6328 q^{84} +3.57546 q^{85} +23.2002 q^{86} -1.54538 q^{87} +10.7514 q^{88} +6.06029 q^{89} +8.78852 q^{90} +8.85823 q^{91} -21.0985 q^{92} +0.227539 q^{93} +1.72632 q^{94} +27.4169 q^{95} +0.415463 q^{96} +5.73822 q^{97} -10.7580 q^{98} -2.14222 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9}+O(q^{10}) $ 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9} + 8 q^{10} - 7 q^{11} - 61 q^{12} + 8 q^{13} - 8 q^{14} - q^{15} + 71 q^{16} - 56 q^{17} + q^{18} - 2 q^{19} - 4 q^{20} - 19 q^{21} + 47 q^{22} + 16 q^{23} + 85 q^{25} - 11 q^{26} - 56 q^{27} + 52 q^{28} + 17 q^{29} - 8 q^{30} + 23 q^{31} + 11 q^{32} + 7 q^{33} - q^{34} - 41 q^{35} + 61 q^{36} + 58 q^{37} - 22 q^{38} - 8 q^{39} + 38 q^{40} - q^{41} + 8 q^{42} + 27 q^{43} + 2 q^{44} + q^{45} + 46 q^{46} + 5 q^{47} - 71 q^{48} + 59 q^{49} - 4 q^{50} + 56 q^{51} + 25 q^{52} + 15 q^{53} - q^{54} + 9 q^{55} - 36 q^{56} + 2 q^{57} + 89 q^{58} - 61 q^{59} + 4 q^{60} + 47 q^{61} + 8 q^{62} + 19 q^{63} + 88 q^{64} + 39 q^{65} - 47 q^{66} + 20 q^{67} - 61 q^{68} - 16 q^{69} + 36 q^{70} - 2 q^{71} + 93 q^{73} + 48 q^{74} - 85 q^{75} + 38 q^{76} + 26 q^{77} + 11 q^{78} + 72 q^{79} + 42 q^{80} + 56 q^{81} + 33 q^{82} - 11 q^{83} - 52 q^{84} - q^{85} - 4 q^{86} - 17 q^{87} + 130 q^{88} - 6 q^{89} + 8 q^{90} + 37 q^{91} + 132 q^{92} - 23 q^{93} - 32 q^{94} + 12 q^{95} - 11 q^{96} + 100 q^{97} + 42 q^{98} - 7 q^{99}+O(q^{100}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9 + 8 * q^10 - 7 * q^11 - 61 * q^12 + 8 * q^13 - 8 * q^14 - q^15 + 71 * q^16 - 56 * q^17 + q^18 - 2 * q^19 - 4 * q^20 - 19 * q^21 + 47 * q^22 + 16 * q^23 + 85 * q^25 - 11 * q^26 - 56 * q^27 + 52 * q^28 + 17 * q^29 - 8 * q^30 + 23 * q^31 + 11 * q^32 + 7 * q^33 - q^34 - 41 * q^35 + 61 * q^36 + 58 * q^37 - 22 * q^38 - 8 * q^39 + 38 * q^40 - q^41 + 8 * q^42 + 27 * q^43 + 2 * q^44 + q^45 + 46 * q^46 + 5 * q^47 - 71 * q^48 + 59 * q^49 - 4 * q^50 + 56 * q^51 + 25 * q^52 + 15 * q^53 - q^54 + 9 * q^55 - 36 * q^56 + 2 * q^57 + 89 * q^58 - 61 * q^59 + 4 * q^60 + 47 * q^61 + 8 * q^62 + 19 * q^63 + 88 * q^64 + 39 * q^65 - 47 * q^66 + 20 * q^67 - 61 * q^68 - 16 * q^69 + 36 * q^70 - 2 * q^71 + 93 * q^73 + 48 * q^74 - 85 * q^75 + 38 * q^76 + 26 * q^77 + 11 * q^78 + 72 * q^79 + 42 * q^80 + 56 * q^81 + 33 * q^82 - 11 * q^83 - 52 * q^84 - q^85 - 4 * q^86 - 17 * q^87 + 130 * q^88 - 6 * q^89 + 8 * q^90 + 37 * q^91 + 132 * q^92 - 23 * q^93 - 32 * q^94 + 12 * q^95 - 11 * q^96 + 100 * q^97 + 42 * q^98 - 7 * 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 $

$2$	−2.45801	−1.73808	−0.869038	−	0.494745i	$-0.835261\pi$
$2$	−2.45801	−1.73808	−0.869038	+	0.494745i	$0.835261\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.04182	2.02091
$5$	−3.57546	−1.59899	−0.799497	−	0.600670i	$-0.794901\pi$
$5$	−3.57546	−1.59899	−0.799497	+	0.600670i	$0.794901\pi$
$6$	2.45801	1.00348
$7$	3.37294	1.27485	0.637426	−	0.770512i	$-0.279999\pi$
$7$	3.37294	1.27485	0.637426	+	0.770512i	$0.279999\pi$
$8$	−5.01881	−1.77442
$9$	1.00000	0.333333
$10$	8.78852	2.77917
$11$	−2.14222	−0.645904	−0.322952	−	0.946415i	$-0.604675\pi$
$11$	−2.14222	−0.645904	−0.322952	+	0.946415i	$0.604675\pi$
$12$	−4.04182	−1.16677
$13$	2.62627	0.728395	0.364197	−	0.931322i	$-0.381343\pi$
$13$	2.62627	0.728395	0.364197	+	0.931322i	$0.381343\pi$
$14$	−8.29072	−2.21579
$15$	3.57546	0.923180
$16$	4.25266	1.06317
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.45801	−0.579359
$19$	−7.66808	−1.75918	−0.879589	−	0.475735i	$-0.842182\pi$
$19$	−7.66808	−1.75918	−0.879589	+	0.475735i	$0.842182\pi$
$20$	−14.4514	−3.23142
$21$	−3.37294	−0.736036
$22$	5.26560	1.12263
$23$	−5.22005	−1.08846	−0.544228	−	0.838938i	$-0.683177\pi$
$23$	−5.22005	−1.08846	−0.544228	+	0.838938i	$0.683177\pi$
$24$	5.01881	1.02446
$25$	7.78391	1.55678
$26$	−6.45539	−1.26601
$27$	−1.00000	−0.192450
$28$	13.6328	2.57636
$29$	1.54538	0.286970	0.143485	−	0.989652i	$-0.454169\pi$
$29$	1.54538	0.286970	0.143485	+	0.989652i	$0.454169\pi$
$30$	−8.78852	−1.60456
$31$	−0.227539	−0.0408672	−0.0204336	−	0.999791i	$-0.506505\pi$
$31$	−0.227539	−0.0408672	−0.0204336	+	0.999791i	$0.506505\pi$
$32$	−0.415463	−0.0734442
$33$	2.14222	0.372913
$34$	2.45801	0.421545
$35$	−12.0598	−2.03848
$36$	4.04182	0.673636
$37$	−11.2449	−1.84865	−0.924327	−	0.381602i	$-0.875372\pi$
$37$	−11.2449	−1.84865	−0.924327	+	0.381602i	$0.875372\pi$
$38$	18.8482	3.05758
$39$	−2.62627	−0.420539
$40$	17.9446	2.83728
$41$	−2.06113	−0.321895	−0.160948	−	0.986963i	$-0.551455\pi$
$41$	−2.06113	−0.321895	−0.160948	+	0.986963i	$0.551455\pi$
$42$	8.29072	1.27929
$43$	−9.43862	−1.43938	−0.719688	−	0.694298i	$-0.755715\pi$
$43$	−9.43862	−1.43938	−0.719688	+	0.694298i	$0.755715\pi$
$44$	−8.65847	−1.30531
$45$	−3.57546	−0.532998
$46$	12.8309	1.89182
$47$	−0.702326	−0.102445	−0.0512224	−	0.998687i	$-0.516312\pi$
$47$	−0.702326	−0.102445	−0.0512224	+	0.998687i	$0.516312\pi$
$48$	−4.25266	−0.613819
$49$	4.37672	0.625245
$50$	−19.1329	−2.70581
$51$	1.00000	0.140028
$52$	10.6149	1.47202
$53$	−1.89733	−0.260619	−0.130309	−	0.991473i	$-0.541597\pi$
$53$	−1.89733	−0.260619	−0.130309	+	0.991473i	$0.541597\pi$
$54$	2.45801	0.334493
$55$	7.65942	1.03280
$56$	−16.9282	−2.26212
$57$	7.66808	1.01566
$58$	−3.79856	−0.498776
$59$	0.129353	0.0168403	0.00842015	−	0.999965i	$-0.497320\pi$
$59$	0.129353	0.0168403	0.00842015	+	0.999965i	$0.497320\pi$
$60$	14.4514	1.86566
$61$	4.39664	0.562932	0.281466	−	0.959571i	$-0.409179\pi$
$61$	4.39664	0.562932	0.281466	+	0.959571i	$0.409179\pi$
$62$	0.559293	0.0710303
$63$	3.37294	0.424950
$64$	−7.48411	−0.935514
$65$	−9.39011	−1.16470
$66$	−5.26560	−0.648151
$67$	2.22734	0.272113	0.136056	−	0.990701i	$-0.456557\pi$
$67$	2.22734	0.272113	0.136056	+	0.990701i	$0.456557\pi$
$68$	−4.04182	−0.490143
$69$	5.22005	0.628420
$70$	29.6431	3.54303
$71$	−8.50510	−1.00937	−0.504685	−	0.863304i	$-0.668391\pi$
$71$	−8.50510	−1.00937	−0.504685	+	0.863304i	$0.668391\pi$
$72$	−5.01881	−0.591473
$73$	8.46689	0.990975	0.495487	−	0.868615i	$-0.334989\pi$
$73$	8.46689	0.990975	0.495487	+	0.868615i	$0.334989\pi$
$74$	27.6401	3.21310
$75$	−7.78391	−0.898809
$76$	−30.9930	−3.55514
$77$	−7.22558	−0.823431
$78$	6.45539	0.730929
$79$	−4.25177	−0.478361	−0.239181	−	0.970975i	$-0.576879\pi$
$79$	−4.25177	−0.478361	−0.239181	+	0.970975i	$0.576879\pi$
$80$	−15.2052	−1.70000
$81$	1.00000	0.111111
$82$	5.06629	0.559478
$83$	−16.5110	−1.81231	−0.906156	−	0.422943i	$-0.860997\pi$
$83$	−16.5110	−1.81231	−0.906156	+	0.422943i	$0.860997\pi$
$84$	−13.6328	−1.48746
$85$	3.57546	0.387813
$86$	23.2002	2.50175
$87$	−1.54538	−0.165682
$88$	10.7514	1.14610
$89$	6.06029	0.642390	0.321195	−	0.947013i	$-0.395916\pi$
$89$	6.06029	0.642390	0.321195	+	0.947013i	$0.395916\pi$
$90$	8.78852	0.926391
$91$	8.85823	0.928595
$92$	−21.0985	−2.19967
$93$	0.227539	0.0235947
$94$	1.72632	0.178057
$95$	27.4169	2.81291
$96$	0.415463	0.0424030
$97$	5.73822	0.582628	0.291314	−	0.956627i	$-0.405907\pi$
$97$	5.73822	0.582628	0.291314	+	0.956627i	$0.405907\pi$
$98$	−10.7580	−1.08672
$99$	−2.14222	−0.215301
$100$	31.4612	3.14612
$101$	−2.14618	−0.213553	−0.106777	−	0.994283i	$-0.534053\pi$
$101$	−2.14618	−0.213553	−0.106777	+	0.994283i	$0.534053\pi$
$102$	−2.45801	−0.243379
$103$	−0.690572	−0.0680441	−0.0340221	−	0.999421i	$-0.510832\pi$
$103$	−0.690572	−0.0680441	−0.0340221	+	0.999421i	$0.510832\pi$
$104$	−13.1807	−1.29248
$105$	12.0598	1.17692
$106$	4.66366	0.452975
$107$	−15.1767	−1.46718	−0.733592	−	0.679590i	$-0.762158\pi$
$107$	−15.1767	−1.46718	−0.733592	+	0.679590i	$0.762158\pi$
$108$	−4.04182	−0.388924
$109$	17.8719	1.71182	0.855909	−	0.517126i	$-0.172998\pi$
$109$	17.8719	1.71182	0.855909	+	0.517126i	$0.172998\pi$
$110$	−18.8270	−1.79508
$111$	11.2449	1.06732
$112$	14.3440	1.35538
$113$	14.1168	1.32800	0.663999	−	0.747734i	$-0.268858\pi$
$113$	14.1168	1.32800	0.663999	+	0.747734i	$0.268858\pi$
$114$	−18.8482	−1.76530
$115$	18.6641	1.74043
$116$	6.24615	0.579940
$117$	2.62627	0.242798
$118$	−0.317951	−0.0292697
$119$	−3.37294	−0.309197
$120$	−17.9446	−1.63811
$121$	−6.41089	−0.582808
$122$	−10.8070	−0.978418
$123$	2.06113	0.185846
$124$	−0.919671	−0.0825889
$125$	−9.95376	−0.890291
$126$	−8.29072	−0.738596
$127$	13.7105	1.21661	0.608305	−	0.793703i	$-0.291850\pi$
$127$	13.7105	1.21661	0.608305	+	0.793703i	$0.291850\pi$
$128$	19.2270	1.69944
$129$	9.43862	0.831024
$130$	23.0810	2.02434
$131$	19.1725	1.67511	0.837555	−	0.546353i	$-0.183984\pi$
$131$	19.1725	1.67511	0.837555	+	0.546353i	$0.183984\pi$
$132$	8.65847	0.753623
$133$	−25.8640	−2.24269
$134$	−5.47482	−0.472953
$135$	3.57546	0.307727
$136$	5.01881	0.430360
$137$	−13.3473	−1.14033	−0.570167	−	0.821529i	$-0.693122\pi$
$137$	−13.3473	−1.14033	−0.570167	+	0.821529i	$0.693122\pi$
$138$	−12.8309	−1.09224
$139$	−5.68518	−0.482211	−0.241106	−	0.970499i	$-0.577510\pi$
$139$	−5.68518	−0.482211	−0.241106	+	0.970499i	$0.577510\pi$
$140$	−48.7436	−4.11958
$141$	0.702326	0.0591465
$142$	20.9056	1.75436
$143$	−5.62604	−0.470473
$144$	4.25266	0.354388
$145$	−5.52545	−0.458863
$146$	−20.8117	−1.72239
$147$	−4.37672	−0.360986
$148$	−45.4499	−3.73596
$149$	9.24995	0.757786	0.378893	−	0.925441i	$-0.376305\pi$
$149$	9.24995	0.757786	0.378893	+	0.925441i	$0.376305\pi$
$150$	19.1329	1.56220
$151$	4.18103	0.340248	0.170124	−	0.985423i	$-0.445583\pi$
$151$	4.18103	0.340248	0.170124	+	0.985423i	$0.445583\pi$
$152$	38.4846	3.12152
$153$	−1.00000	−0.0808452
$154$	17.7606	1.43119
$155$	0.813556	0.0653464
$156$	−10.6149	−0.849871
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	10.4509	0.831429
$159$	1.89733	0.150468
$160$	1.48547	0.117437
$161$	−17.6069	−1.38762
$162$	−2.45801	−0.193120
$163$	−3.09526	−0.242440	−0.121220	−	0.992626i	$-0.538681\pi$
$163$	−3.09526	−0.242440	−0.121220	+	0.992626i	$0.538681\pi$
$164$	−8.33073	−0.650521
$165$	−7.65942	−0.596285
$166$	40.5841	3.14994
$167$	−17.9547	−1.38938	−0.694690	−	0.719310i	$-0.744458\pi$
$167$	−17.9547	−1.38938	−0.694690	+	0.719310i	$0.744458\pi$
$168$	16.9282	1.30604
$169$	−6.10273	−0.469441
$170$	−8.78852	−0.674049
$171$	−7.66808	−0.586392
$172$	−38.1492	−2.90885
$173$	0.814367	0.0619151	0.0309576	−	0.999521i	$-0.490144\pi$
$173$	0.814367	0.0619151	0.0309576	+	0.999521i	$0.490144\pi$
$174$	3.79856	0.287968
$175$	26.2547	1.98467
$176$	−9.11014	−0.686703
$177$	−0.129353	−0.00972275
$178$	−14.8963	−1.11652
$179$	−22.4249	−1.67611	−0.838056	−	0.545584i	$-0.816308\pi$
$179$	−22.4249	−1.67611	−0.838056	+	0.545584i	$0.816308\pi$
$180$	−14.4514	−1.07714
$181$	−5.52877	−0.410951	−0.205475	−	0.978662i	$-0.565874\pi$
$181$	−5.52877	−0.410951	−0.205475	+	0.978662i	$0.565874\pi$
$182$	−21.7736	−1.61397
$183$	−4.39664	−0.325009
$184$	26.1984	1.93138
$185$	40.2058	2.95599
$186$	−0.559293	−0.0410094
$187$	2.14222	0.156655
$188$	−2.83867	−0.207032
$189$	−3.37294	−0.245345
$190$	−67.3910	−4.88906
$191$	0.841625	0.0608978	0.0304489	−	0.999536i	$-0.490306\pi$
$191$	0.841625	0.0608978	0.0304489	+	0.999536i	$0.490306\pi$
$192$	7.48411	0.540119
$193$	2.25506	0.162323	0.0811613	−	0.996701i	$-0.474137\pi$
$193$	2.25506	0.162323	0.0811613	+	0.996701i	$0.474137\pi$
$194$	−14.1046	−1.01265
$195$	9.39011	0.672439
$196$	17.6899	1.26356
$197$	1.86482	0.132863	0.0664316	−	0.997791i	$-0.478839\pi$
$197$	1.86482	0.132863	0.0664316	+	0.997791i	$0.478839\pi$
$198$	5.26560	0.374210
$199$	−22.6958	−1.60886	−0.804430	−	0.594047i	$-0.797529\pi$
$199$	−22.6958	−1.60886	−0.804430	+	0.594047i	$0.797529\pi$
$200$	−39.0660	−2.76238
$201$	−2.22734	−0.157104
$202$	5.27534	0.371171
$203$	5.21247	0.365844
$204$	4.04182	0.282984
$205$	7.36950	0.514708
$206$	1.69743	0.118266
$207$	−5.22005	−0.362818
$208$	11.1686	0.774404
$209$	16.4267	1.13626
$210$	−29.6431	−2.04557
$211$	−27.1362	−1.86814	−0.934068	−	0.357096i	$-0.883767\pi$
$211$	−27.1362	−1.86814	−0.934068	+	0.357096i	$0.883767\pi$
$212$	−7.66867	−0.526687
$213$	8.50510	0.582760
$214$	37.3044	2.55008
$215$	33.7474	2.30155
$216$	5.01881	0.341487
$217$	−0.767475	−0.0520996
$218$	−43.9293	−2.97527
$219$	−8.46689	−0.572140
$220$	30.9580	2.08719
$221$	−2.62627	−0.176662
$222$	−27.6401	−1.85508
$223$	−10.2296	−0.685025	−0.342513	−	0.939513i	$-0.611278\pi$
$223$	−10.2296	−0.685025	−0.342513	+	0.939513i	$0.611278\pi$
$224$	−1.40133	−0.0936304
$225$	7.78391	0.518927
$226$	−34.6993	−2.30816
$227$	13.4250	0.891046	0.445523	−	0.895270i	$-0.353018\pi$
$227$	13.4250	0.891046	0.445523	+	0.895270i	$0.353018\pi$
$228$	30.9930	2.05256
$229$	28.4840	1.88228	0.941139	−	0.338019i	$-0.109757\pi$
$229$	28.4840	1.88228	0.941139	+	0.338019i	$0.109757\pi$
$230$	−45.8765	−3.02501
$231$	7.22558	0.475408
$232$	−7.75598	−0.509205
$233$	6.43841	0.421794	0.210897	−	0.977508i	$-0.432362\pi$
$233$	6.43841	0.421794	0.210897	+	0.977508i	$0.432362\pi$
$234$	−6.45539	−0.422002
$235$	2.51114	0.163809
$236$	0.522820	0.0340327
$237$	4.25177	0.276182
$238$	8.29072	0.537408
$239$	−23.3098	−1.50778	−0.753891	−	0.656999i	$-0.771825\pi$
$239$	−23.3098	−1.50778	−0.753891	+	0.656999i	$0.771825\pi$
$240$	15.2052	0.981493
$241$	−7.66798	−0.493938	−0.246969	−	0.969023i	$-0.579435\pi$
$241$	−7.66798	−0.493938	−0.246969	+	0.969023i	$0.579435\pi$
$242$	15.7580	1.01296
$243$	−1.00000	−0.0641500
$244$	17.7704	1.13763
$245$	−15.6488	−0.999764
$246$	−5.06629	−0.323015
$247$	−20.1384	−1.28138
$248$	1.14198	0.0725155
$249$	16.5110	1.04634
$250$	24.4665	1.54739
$251$	10.7277	0.677127	0.338563	−	0.940944i	$-0.390059\pi$
$251$	10.7277	0.677127	0.338563	+	0.940944i	$0.390059\pi$
$252$	13.6328	0.858786
$253$	11.1825	0.703038
$254$	−33.7006	−2.11456
$255$	−3.57546	−0.223904
$256$	−32.2918	−2.01824
$257$	2.14935	0.134073	0.0670364	−	0.997751i	$-0.478646\pi$
$257$	2.14935	0.134073	0.0670364	+	0.997751i	$0.478646\pi$
$258$	−23.2002	−1.44438
$259$	−37.9284	−2.35676
$260$	−37.9531	−2.35375
$261$	1.54538	0.0956567
$262$	−47.1262	−2.91147
$263$	5.65226	0.348533	0.174267	−	0.984698i	$-0.444245\pi$
$263$	5.65226	0.348533	0.174267	+	0.984698i	$0.444245\pi$
$264$	−10.7514	−0.661703
$265$	6.78384	0.416728
$266$	63.5739	3.89796
$267$	−6.06029	−0.370884
$268$	9.00250	0.549915
$269$	3.74720	0.228471	0.114236	−	0.993454i	$-0.463558\pi$
$269$	3.74720	0.228471	0.114236	+	0.993454i	$0.463558\pi$
$270$	−8.78852	−0.534852
$271$	−4.93865	−0.300002	−0.150001	−	0.988686i	$-0.547928\pi$
$271$	−4.93865	−0.300002	−0.150001	+	0.988686i	$0.547928\pi$
$272$	−4.25266	−0.257855
$273$	−8.85823	−0.536125
$274$	32.8077	1.98199
$275$	−16.6749	−1.00553
$276$	21.0985	1.26998
$277$	14.9303	0.897077	0.448539	−	0.893764i	$-0.351945\pi$
$277$	14.9303	0.897077	0.448539	+	0.893764i	$0.351945\pi$
$278$	13.9742	0.838120
$279$	−0.227539	−0.0136224
$280$	60.5259	3.61712
$281$	1.15485	0.0688925	0.0344462	−	0.999407i	$-0.489033\pi$
$281$	1.15485	0.0688925	0.0344462	+	0.999407i	$0.489033\pi$
$282$	−1.72632	−0.102801
$283$	−13.0015	−0.772862	−0.386431	−	0.922318i	$-0.626292\pi$
$283$	−13.0015	−0.772862	−0.386431	+	0.922318i	$0.626292\pi$
$284$	−34.3761	−2.03985
$285$	−27.4169	−1.62404
$286$	13.8289	0.817718
$287$	−6.95208	−0.410368
$288$	−0.415463	−0.0244814
$289$	1.00000	0.0588235
$290$	13.5816	0.797539
$291$	−5.73822	−0.336381
$292$	34.2216	2.00267
$293$	−9.89707	−0.578193	−0.289097	−	0.957300i	$-0.593355\pi$
$293$	−9.89707	−0.578193	−0.289097	+	0.957300i	$0.593355\pi$
$294$	10.7580	0.627420
$295$	−0.462496	−0.0269275
$296$	56.4361	3.28028
$297$	2.14222	0.124304
$298$	−22.7365	−1.31709
$299$	−13.7092	−0.792825
$300$	−31.4612	−1.81641
$301$	−31.8359	−1.83499
$302$	−10.2770	−0.591376
$303$	2.14618	0.123295
$304$	−32.6097	−1.87030
$305$	−15.7200	−0.900125
$306$	2.45801	0.140515
$307$	−15.4228	−0.880227	−0.440114	−	0.897942i	$-0.645062\pi$
$307$	−15.4228	−0.880227	−0.440114	+	0.897942i	$0.645062\pi$
$308$	−29.2045	−1.66408
$309$	0.690572	0.0392853
$310$	−1.99973	−0.113577
$311$	−14.0158	−0.794761	−0.397381	−	0.917654i	$-0.630081\pi$
$311$	−14.0158	−0.794761	−0.397381	+	0.917654i	$0.630081\pi$
$312$	13.1807	0.746212
$313$	−3.09203	−0.174772	−0.0873860	−	0.996175i	$-0.527851\pi$
$313$	−3.09203	−0.174772	−0.0873860	+	0.996175i	$0.527851\pi$
$314$	−2.45801	−0.138714
$315$	−12.0598	−0.679493
$316$	−17.1849	−0.966725
$317$	22.3115	1.25314	0.626570	−	0.779365i	$-0.284458\pi$
$317$	22.3115	1.25314	0.626570	+	0.779365i	$0.284458\pi$
$318$	−4.66366	−0.261525
$319$	−3.31055	−0.185355
$320$	26.7591	1.49588
$321$	15.1767	0.847079
$322$	43.2780	2.41179
$323$	7.66808	0.426663
$324$	4.04182	0.224545
$325$	20.4426	1.13395
$326$	7.60819	0.421379
$327$	−17.8719	−0.988319
$328$	10.3445	0.571177
$329$	−2.36890	−0.130602
$330$	18.8270	1.03639
$331$	−1.78983	−0.0983781	−0.0491890	−	0.998789i	$-0.515664\pi$
$331$	−1.78983	−0.0983781	−0.0491890	+	0.998789i	$0.515664\pi$
$332$	−66.7343	−3.66252
$333$	−11.2449	−0.616218
$334$	44.1329	2.41485
$335$	−7.96376	−0.435107
$336$	−14.3440	−0.782528
$337$	9.66391	0.526427	0.263213	−	0.964738i	$-0.415218\pi$
$337$	9.66391	0.526427	0.263213	+	0.964738i	$0.415218\pi$
$338$	15.0006	0.815924
$339$	−14.1168	−0.766720
$340$	14.4514	0.783735
$341$	0.487438	0.0263963
$342$	18.8482	1.01919
$343$	−8.84817	−0.477756
$344$	47.3707	2.55406
$345$	−18.6641	−1.00484
$346$	−2.00172	−0.107613
$347$	−5.30424	−0.284747	−0.142373	−	0.989813i	$-0.545473\pi$
$347$	−5.30424	−0.284747	−0.142373	+	0.989813i	$0.545473\pi$
$348$	−6.24615	−0.334829
$349$	−30.9479	−1.65661	−0.828303	−	0.560281i	$-0.810693\pi$
$349$	−30.9479	−1.65661	−0.828303	+	0.560281i	$0.810693\pi$
$350$	−64.5342	−3.44950
$351$	−2.62627	−0.140180
$352$	0.890014	0.0474379
$353$	13.0587	0.695045	0.347523	−	0.937672i	$-0.387023\pi$
$353$	13.0587	0.695045	0.347523	+	0.937672i	$0.387023\pi$
$354$	0.317951	0.0168989
$355$	30.4096	1.61398
$356$	24.4946	1.29821
$357$	3.37294	0.178515
$358$	55.1205	2.91321
$359$	23.2706	1.22818	0.614088	−	0.789237i	$-0.289524\pi$
$359$	23.2706	1.22818	0.614088	+	0.789237i	$0.289524\pi$
$360$	17.9446	0.945762
$361$	39.7994	2.09470
$362$	13.5898	0.714263
$363$	6.41089	0.336484
$364$	35.8034	1.87661
$365$	−30.2730	−1.58456
$366$	10.8070	0.564890
$367$	18.1252	0.946127	0.473063	−	0.881028i	$-0.343148\pi$
$367$	18.1252	0.946127	0.473063	+	0.881028i	$0.343148\pi$
$368$	−22.1991	−1.15721
$369$	−2.06113	−0.107298
$370$	−98.8262	−5.13773
$371$	−6.39959	−0.332250
$372$	0.919671	0.0476827
$373$	32.5361	1.68466	0.842328	−	0.538966i	$-0.181185\pi$
$373$	32.5361	1.68466	0.842328	+	0.538966i	$0.181185\pi$
$374$	−5.26560	−0.272278
$375$	9.95376	0.514010
$376$	3.52484	0.181780
$377$	4.05858	0.209027
$378$	8.29072	0.426429
$379$	−20.2471	−1.04002	−0.520011	−	0.854159i	$-0.674072\pi$
$379$	−20.2471	−1.04002	−0.520011	+	0.854159i	$0.674072\pi$
$380$	110.814	5.68464
$381$	−13.7105	−0.702411
$382$	−2.06872	−0.105845
$383$	19.2315	0.982684	0.491342	−	0.870967i	$-0.336506\pi$
$383$	19.2315	0.982684	0.491342	+	0.870967i	$0.336506\pi$
$384$	−19.2270	−0.981171
$385$	25.8348	1.31666
$386$	−5.54296	−0.282129
$387$	−9.43862	−0.479792
$388$	23.1929	1.17744
$389$	−19.6622	−0.996914	−0.498457	−	0.866915i	$-0.666100\pi$
$389$	−19.6622	−0.996914	−0.498457	+	0.866915i	$0.666100\pi$
$390$	−23.0810	−1.16875
$391$	5.22005	0.263989
$392$	−21.9659	−1.10945
$393$	−19.1725	−0.967125
$394$	−4.58376	−0.230926
$395$	15.2020	0.764897
$396$	−8.65847	−0.435104
$397$	−33.6683	−1.68976	−0.844881	−	0.534954i	$-0.820329\pi$
$397$	−33.6683	−1.68976	−0.844881	+	0.534954i	$0.820329\pi$
$398$	55.7865	2.79632
$399$	25.8640	1.29482
$400$	33.1023	1.65512
$401$	27.2296	1.35978	0.679892	−	0.733313i	$-0.262027\pi$
$401$	27.2296	1.35978	0.679892	+	0.733313i	$0.262027\pi$
$402$	5.47482	0.273059
$403$	−0.597577	−0.0297675
$404$	−8.67448	−0.431571
$405$	−3.57546	−0.177666
$406$	−12.8123	−0.635865
$407$	24.0891	1.19405
$408$	−5.01881	−0.248468
$409$	−31.2534	−1.54538	−0.772691	−	0.634782i	$-0.781090\pi$
$409$	−31.2534	−1.54538	−0.772691	+	0.634782i	$0.781090\pi$
$410$	−18.1143	−0.894603
$411$	13.3473	0.658372
$412$	−2.79117	−0.137511
$413$	0.436299	0.0214689
$414$	12.8309	0.630606
$415$	59.0342	2.89788
$416$	−1.09112	−0.0534964
$417$	5.68518	0.278405
$418$	−40.3770	−1.97491
$419$	8.73519	0.426742	0.213371	−	0.976971i	$-0.431556\pi$
$419$	8.73519	0.426742	0.213371	+	0.976971i	$0.431556\pi$
$420$	48.7436	2.37844
$421$	−23.2047	−1.13093	−0.565463	−	0.824773i	$-0.691303\pi$
$421$	−23.2047	−1.13093	−0.565463	+	0.824773i	$0.691303\pi$
$422$	66.7012	3.24696
$423$	−0.702326	−0.0341483
$424$	9.52236	0.462447
$425$	−7.78391	−0.377575
$426$	−20.9056	−1.01288
$427$	14.8296	0.717654
$428$	−61.3413	−2.96505
$429$	5.62604	0.271628
$430$	−82.9515	−4.00028
$431$	22.5823	1.08775	0.543877	−	0.839165i	$-0.316956\pi$
$431$	22.5823	1.08775	0.543877	+	0.839165i	$0.316956\pi$
$432$	−4.25266	−0.204606
$433$	−25.1597	−1.20910	−0.604550	−	0.796567i	$-0.706647\pi$
$433$	−25.1597	−1.20910	−0.604550	+	0.796567i	$0.706647\pi$
$434$	1.88646	0.0905530
$435$	5.52545	0.264925
$436$	72.2350	3.45943
$437$	40.0277	1.91479
$438$	20.8117	0.994422
$439$	24.7641	1.18193	0.590963	−	0.806699i	$-0.298748\pi$
$439$	24.7641	1.18193	0.590963	+	0.806699i	$0.298748\pi$
$440$	−38.4412	−1.83261
$441$	4.37672	0.208415
$442$	6.45539	0.307052
$443$	−0.764546	−0.0363247	−0.0181623	−	0.999835i	$-0.505782\pi$
$443$	−0.764546	−0.0363247	−0.0181623	+	0.999835i	$0.505782\pi$
$444$	45.4499	2.15696
$445$	−21.6683	−1.02718
$446$	25.1445	1.19063
$447$	−9.24995	−0.437508
$448$	−25.2434	−1.19264
$449$	−15.0100	−0.708367	−0.354184	−	0.935176i	$-0.615241\pi$
$449$	−15.0100	−0.708367	−0.354184	+	0.935176i	$0.615241\pi$
$450$	−19.1329	−0.901935
$451$	4.41541	0.207913
$452$	57.0576	2.68376
$453$	−4.18103	−0.196442
$454$	−32.9987	−1.54871
$455$	−31.6723	−1.48482
$456$	−38.4846	−1.80221
$457$	−22.8423	−1.06852	−0.534259	−	0.845321i	$-0.679409\pi$
$457$	−22.8423	−1.06852	−0.534259	+	0.845321i	$0.679409\pi$
$458$	−70.0141	−3.27154
$459$	1.00000	0.0466760
$460$	75.4368	3.51726
$461$	4.27969	0.199325	0.0996626	−	0.995021i	$-0.468224\pi$
$461$	4.27969	0.199325	0.0996626	+	0.995021i	$0.468224\pi$
$462$	−17.7606	−0.826296
$463$	−11.4213	−0.530792	−0.265396	−	0.964139i	$-0.585503\pi$
$463$	−11.4213	−0.530792	−0.265396	+	0.964139i	$0.585503\pi$
$464$	6.57198	0.305097
$465$	−0.813556	−0.0377278
$466$	−15.8257	−0.733110
$467$	11.8483	0.548274	0.274137	−	0.961691i	$-0.411608\pi$
$467$	11.8483	0.548274	0.274137	+	0.961691i	$0.411608\pi$
$468$	10.6149	0.490673
$469$	7.51268	0.346903
$470$	−6.17240	−0.284712
$471$	−1.00000	−0.0460776
$472$	−0.649197	−0.0298817
$473$	20.2196	0.929699
$474$	−10.4509	−0.480026
$475$	−59.6876	−2.73866
$476$	−13.6328	−0.624859
$477$	−1.89733	−0.0868729
$478$	57.2956	2.62064
$479$	−13.3823	−0.611452	−0.305726	−	0.952120i	$-0.598899\pi$
$479$	−13.3823	−0.611452	−0.305726	+	0.952120i	$0.598899\pi$
$480$	−1.48547	−0.0678022
$481$	−29.5321	−1.34655
$482$	18.8480	0.858502
$483$	17.6069	0.801142
$484$	−25.9117	−1.17780
$485$	−20.5168	−0.931619
$486$	2.45801	0.111498
$487$	19.2066	0.870333	0.435166	−	0.900350i	$-0.356690\pi$
$487$	19.2066	0.870333	0.435166	+	0.900350i	$0.356690\pi$
$488$	−22.0659	−0.998876
$489$	3.09526	0.139973
$490$	38.4649	1.73767
$491$	17.1419	0.773605	0.386802	−	0.922163i	$-0.373580\pi$
$491$	17.1419	0.773605	0.386802	+	0.922163i	$0.373580\pi$
$492$	8.33073	0.375578
$493$	−1.54538	−0.0696004
$494$	49.5004	2.22713
$495$	7.65942	0.344266
$496$	−0.967646	−0.0434486
$497$	−28.6872	−1.28680
$498$	−40.5841	−1.81862
$499$	−10.0006	−0.447690	−0.223845	−	0.974625i	$-0.571861\pi$
$499$	−10.0006	−0.447690	−0.223845	+	0.974625i	$0.571861\pi$
$500$	−40.2313	−1.79920
$501$	17.9547	0.802158
$502$	−26.3688	−1.17690
$503$	21.6578	0.965675	0.482838	−	0.875710i	$-0.339606\pi$
$503$	21.6578	0.965675	0.482838	+	0.875710i	$0.339606\pi$
$504$	−16.9282	−0.754040
$505$	7.67358	0.341470
$506$	−27.4867	−1.22193
$507$	6.10273	0.271032
$508$	55.4154	2.45866
$509$	−32.9056	−1.45852	−0.729258	−	0.684239i	$-0.760135\pi$
$509$	−32.9056	−1.45852	−0.729258	+	0.684239i	$0.760135\pi$
$510$	8.78852	0.389162
$511$	28.5583	1.26335
$512$	40.9198	1.80842
$513$	7.66808	0.338554
$514$	−5.28313	−0.233029
$515$	2.46911	0.108802
$516$	38.1492	1.67942
$517$	1.50454	0.0661695
$518$	93.2285	4.09622
$519$	−0.814367	−0.0357467
$520$	47.1272	2.06666
$521$	11.9024	0.521455	0.260728	−	0.965412i	$-0.416038\pi$
$521$	11.9024	0.521455	0.260728	+	0.965412i	$0.416038\pi$
$522$	−3.79856	−0.166259
$523$	13.0262	0.569595	0.284797	−	0.958588i	$-0.408074\pi$
$523$	13.0262	0.569595	0.284797	+	0.958588i	$0.408074\pi$
$524$	77.4918	3.38524
$525$	−26.2547	−1.14585
$526$	−13.8933	−0.605778
$527$	0.227539	0.00991175
$528$	9.11014	0.396468
$529$	4.24891	0.184735
$530$	−16.6747	−0.724305
$531$	0.129353	0.00561343
$532$	−104.537	−4.53227
$533$	−5.41309	−0.234467
$534$	14.8963	0.644624
$535$	54.2636	2.34602
$536$	−11.1786	−0.482842
$537$	22.4249	0.967704
$538$	−9.21067	−0.397100
$539$	−9.37590	−0.403848
$540$	14.4514	0.621888
$541$	−24.5898	−1.05720	−0.528599	−	0.848872i	$-0.677282\pi$
$541$	−24.5898	−1.05720	−0.528599	+	0.848872i	$0.677282\pi$
$542$	12.1393	0.521426
$543$	5.52877	0.237262
$544$	0.415463	0.0178128
$545$	−63.9003	−2.73719
$546$	21.7736	0.931826
$547$	19.5757	0.836995	0.418497	−	0.908218i	$-0.362557\pi$
$547$	19.5757	0.836995	0.418497	+	0.908218i	$0.362557\pi$
$548$	−53.9472	−2.30451
$549$	4.39664	0.187644
$550$	40.9870	1.74769
$551$	−11.8501	−0.504831
$552$	−26.1984	−1.11508
$553$	−14.3410	−0.609840
$554$	−36.6989	−1.55919
$555$	−40.2058	−1.70664
$556$	−22.9785	−0.974505
$557$	5.12993	0.217362	0.108681	−	0.994077i	$-0.465337\pi$
$557$	5.12993	0.217362	0.108681	+	0.994077i	$0.465337\pi$
$558$	0.559293	0.0236768
$559$	−24.7883	−1.04843
$560$	−51.2863	−2.16724
$561$	−2.14222	−0.0904446
$562$	−2.83863	−0.119740
$563$	−20.1741	−0.850235	−0.425118	−	0.905138i	$-0.639767\pi$
$563$	−20.1741	−0.850235	−0.425118	+	0.905138i	$0.639767\pi$
$564$	2.83867	0.119530
$565$	−50.4741	−2.12346
$566$	31.9580	1.34329
$567$	3.37294	0.141650
$568$	42.6855	1.79104
$569$	37.7713	1.58346	0.791728	−	0.610874i	$-0.209182\pi$
$569$	37.7713	1.58346	0.791728	+	0.610874i	$0.209182\pi$
$570$	67.3910	2.82270
$571$	−4.12715	−0.172716	−0.0863579	−	0.996264i	$-0.527523\pi$
$571$	−4.12715	−0.172716	−0.0863579	+	0.996264i	$0.527523\pi$
$572$	−22.7394	−0.950784
$573$	−0.841625	−0.0351594
$574$	17.0883	0.713252
$575$	−40.6324	−1.69449
$576$	−7.48411	−0.311838
$577$	35.6769	1.48525	0.742625	−	0.669707i	$-0.233580\pi$
$577$	35.6769	1.48525	0.742625	+	0.669707i	$0.233580\pi$
$578$	−2.45801	−0.102240
$579$	−2.25506	−0.0937170
$580$	−22.3329	−0.927321
$581$	−55.6904	−2.31043
$582$	14.1046	0.584655
$583$	4.06451	0.168335
$584$	−42.4938	−1.75840
$585$	−9.39011	−0.388233
$586$	24.3271	1.00494
$587$	−4.36326	−0.180091	−0.0900456	−	0.995938i	$-0.528701\pi$
$587$	−4.36326	−0.180091	−0.0900456	+	0.995938i	$0.528701\pi$
$588$	−17.6899	−0.729519
$589$	1.74479	0.0718926
$590$	1.13682	0.0468021
$591$	−1.86482	−0.0767086
$592$	−47.8208	−1.96542
$593$	−1.05999	−0.0435286	−0.0217643	−	0.999763i	$-0.506928\pi$
$593$	−1.05999	−0.0435286	−0.0217643	+	0.999763i	$0.506928\pi$
$594$	−5.26560	−0.216050
$595$	12.0598	0.494404
$596$	37.3866	1.53142
$597$	22.6958	0.928876
$598$	33.6974	1.37799
$599$	3.47368	0.141931	0.0709653	−	0.997479i	$-0.477392\pi$
$599$	3.47368	0.141931	0.0709653	+	0.997479i	$0.477392\pi$
$600$	39.0660	1.59486
$601$	−5.64860	−0.230411	−0.115206	−	0.993342i	$-0.536753\pi$
$601$	−5.64860	−0.230411	−0.115206	+	0.993342i	$0.536753\pi$
$602$	78.2530	3.18935
$603$	2.22734	0.0907043
$604$	16.8990	0.687610
$605$	22.9219	0.931907
$606$	−5.27534	−0.214296
$607$	−10.3027	−0.418172	−0.209086	−	0.977897i	$-0.567049\pi$
$607$	−10.3027	−0.418172	−0.209086	+	0.977897i	$0.567049\pi$
$608$	3.18580	0.129201
$609$	−5.21247	−0.211220
$610$	38.6399	1.56449
$611$	−1.84449	−0.0746202
$612$	−4.04182	−0.163381
$613$	4.87325	0.196829	0.0984143	−	0.995146i	$-0.468623\pi$
$613$	4.87325	0.196829	0.0984143	+	0.995146i	$0.468623\pi$
$614$	37.9095	1.52990
$615$	−7.36950	−0.297167
$616$	36.2638	1.46111
$617$	−11.4536	−0.461105	−0.230553	−	0.973060i	$-0.574053\pi$
$617$	−11.4536	−0.461105	−0.230553	+	0.973060i	$0.574053\pi$
$618$	−1.69743	−0.0682808
$619$	−16.1328	−0.648434	−0.324217	−	0.945983i	$-0.605101\pi$
$619$	−16.1328	−0.648434	−0.324217	+	0.945983i	$0.605101\pi$
$620$	3.28825	0.132059
$621$	5.22005	0.209473
$622$	34.4509	1.38136
$623$	20.4410	0.818951
$624$	−11.1686	−0.447103
$625$	−3.33029	−0.133211
$626$	7.60025	0.303767
$627$	−16.4267	−0.656020
$628$	4.04182	0.161286
$629$	11.2449	0.448364
$630$	29.6431	1.18101
$631$	35.0006	1.39335	0.696676	−	0.717386i	$-0.254662\pi$
$631$	35.0006	1.39335	0.696676	+	0.717386i	$0.254662\pi$
$632$	21.3388	0.848813
$633$	27.1362	1.07857
$634$	−54.8420	−2.17805
$635$	−49.0214	−1.94535
$636$	7.66867	0.304083
$637$	11.4944	0.455426
$638$	8.13736	0.322161
$639$	−8.50510	−0.336457
$640$	−68.7452	−2.71739
$641$	−10.3602	−0.409205	−0.204603	−	0.978845i	$-0.565590\pi$
$641$	−10.3602	−0.409205	−0.204603	+	0.978845i	$0.565590\pi$
$642$	−37.3044	−1.47229
$643$	48.6390	1.91813	0.959067	−	0.283178i	$-0.0913888\pi$
$643$	48.6390	1.91813	0.959067	+	0.283178i	$0.0913888\pi$
$644$	−71.1639	−2.80425
$645$	−33.7474	−1.32880
$646$	−18.8482	−0.741573
$647$	13.3079	0.523188	0.261594	−	0.965178i	$-0.415752\pi$
$647$	13.3079	0.523188	0.261594	+	0.965178i	$0.415752\pi$
$648$	−5.01881	−0.197158
$649$	−0.277102	−0.0108772
$650$	−50.2482	−1.97090
$651$	0.767475	0.0300797
$652$	−12.5105	−0.489949
$653$	17.6645	0.691265	0.345632	−	0.938370i	$-0.387664\pi$
$653$	17.6645	0.691265	0.345632	+	0.938370i	$0.387664\pi$
$654$	43.9293	1.71777
$655$	−68.5505	−2.67849
$656$	−8.76531	−0.342228
$657$	8.46689	0.330325
$658$	5.82279	0.226996
$659$	−7.51802	−0.292861	−0.146430	−	0.989221i	$-0.546778\pi$
$659$	−7.51802	−0.292861	−0.146430	+	0.989221i	$0.546778\pi$
$660$	−30.9580	−1.20504
$661$	28.4259	1.10564	0.552820	−	0.833301i	$-0.313552\pi$
$661$	28.4259	1.10564	0.552820	+	0.833301i	$0.313552\pi$
$662$	4.39943	0.170989
$663$	2.62627	0.101996
$664$	82.8654	3.21580
$665$	92.4755	3.58605
$666$	27.6401	1.07103
$667$	−8.06696	−0.312354
$668$	−72.5698	−2.80781
$669$	10.2296	0.395500
$670$	19.5750	0.756249
$671$	−9.41857	−0.363600
$672$	1.40133	0.0540576
$673$	30.6747	1.18242	0.591212	−	0.806516i	$-0.298650\pi$
$673$	30.6747	1.18242	0.591212	+	0.806516i	$0.298650\pi$
$674$	−23.7540	−0.914970
$675$	−7.78391	−0.299603
$676$	−24.6661	−0.948697
$677$	26.9713	1.03659	0.518297	−	0.855201i	$-0.326566\pi$
$677$	26.9713	1.03659	0.518297	+	0.855201i	$0.326566\pi$
$678$	34.6993	1.33262
$679$	19.3547	0.742765
$680$	−17.9446	−0.688143
$681$	−13.4250	−0.514446
$682$	−1.19813	−0.0458787
$683$	−37.9914	−1.45370	−0.726851	−	0.686795i	$-0.759017\pi$
$683$	−37.9914	−1.45370	−0.726851	+	0.686795i	$0.759017\pi$
$684$	−30.9930	−1.18505
$685$	47.7226	1.82339
$686$	21.7489	0.830377
$687$	−28.4840	−1.08673
$688$	−40.1393	−1.53029
$689$	−4.98290	−0.189833
$690$	45.8765	1.74649
$691$	−21.5333	−0.819166	−0.409583	−	0.912273i	$-0.634326\pi$
$691$	−21.5333	−0.819166	−0.409583	+	0.912273i	$0.634326\pi$
$692$	3.29152	0.125125
$693$	−7.22558	−0.274477
$694$	13.0379	0.494912
$695$	20.3271	0.771053
$696$	7.75598	0.293990
$697$	2.06113	0.0780710
$698$	76.0704	2.87931
$699$	−6.43841	−0.243523
$700$	106.117	4.01083
$701$	12.2286	0.461867	0.230934	−	0.972970i	$-0.425822\pi$
$701$	12.2286	0.461867	0.230934	+	0.972970i	$0.425822\pi$
$702$	6.45539	0.243643
$703$	86.2269	3.25211
$704$	16.0326	0.604252
$705$	−2.51114	−0.0945749
$706$	−32.0985	−1.20804
$707$	−7.23894	−0.272248
$708$	−0.522820	−0.0196488
$709$	−35.1236	−1.31909	−0.659547	−	0.751663i	$-0.729252\pi$
$709$	−35.1236	−1.31909	−0.659547	+	0.751663i	$0.729252\pi$
$710$	−74.7472	−2.80521
$711$	−4.25177	−0.159454
$712$	−30.4155	−1.13987
$713$	1.18776	0.0444821
$714$	−8.29072	−0.310272
$715$	20.1157	0.752284
$716$	−90.6372	−3.38727
$717$	23.3098	0.870519
$718$	−57.1994	−2.13466
$719$	17.1913	0.641128	0.320564	−	0.947227i	$-0.396128\pi$
$719$	17.1913	0.641128	0.320564	+	0.947227i	$0.396128\pi$
$720$	−15.2052	−0.566665
$721$	−2.32926	−0.0867461
$722$	−97.8274	−3.64076
$723$	7.66798	0.285175
$724$	−22.3463	−0.830494
$725$	12.0291	0.446750
$726$	−15.7580	−0.584836
$727$	−6.57024	−0.243677	−0.121838	−	0.992550i	$-0.538879\pi$
$727$	−6.57024	−0.243677	−0.121838	+	0.992550i	$0.538879\pi$
$728$	−44.4578	−1.64772
$729$	1.00000	0.0370370
$730$	74.4114	2.75409
$731$	9.43862	0.349100
$732$	−17.7704	−0.656813
$733$	−44.5856	−1.64681	−0.823404	−	0.567455i	$-0.807928\pi$
$733$	−44.5856	−1.64681	−0.823404	+	0.567455i	$0.807928\pi$
$734$	−44.5519	−1.64444
$735$	15.6488	0.577214
$736$	2.16874	0.0799408
$737$	−4.77145	−0.175759
$738$	5.06629	0.186493
$739$	2.62280	0.0964812	0.0482406	−	0.998836i	$-0.484639\pi$
$739$	2.62280	0.0964812	0.0482406	+	0.998836i	$0.484639\pi$
$740$	162.504	5.97378
$741$	20.1384	0.739803
$742$	15.7303	0.577476
$743$	38.8170	1.42406	0.712028	−	0.702151i	$-0.247777\pi$
$743$	38.8170	1.42406	0.712028	+	0.702151i	$0.247777\pi$
$744$	−1.14198	−0.0418668
$745$	−33.0728	−1.21169
$746$	−79.9741	−2.92806
$747$	−16.5110	−0.604104
$748$	8.65847	0.316585
$749$	−51.1900	−1.87044
$750$	−24.4665	−0.893389
$751$	11.2189	0.409382	0.204691	−	0.978827i	$-0.434381\pi$
$751$	11.2189	0.409382	0.204691	+	0.978827i	$0.434381\pi$
$752$	−2.98675	−0.108916
$753$	−10.7277	−0.390939
$754$	−9.97603	−0.363306
$755$	−14.9491	−0.544054
$756$	−13.6328	−0.495820
$757$	−2.99004	−0.108675	−0.0543374	−	0.998523i	$-0.517305\pi$
$757$	−2.99004	−0.108675	−0.0543374	+	0.998523i	$0.517305\pi$
$758$	49.7675	1.80764
$759$	−11.1825	−0.405899
$760$	−137.600	−4.99129
$761$	−46.3277	−1.67938	−0.839688	−	0.543068i	$-0.817262\pi$
$761$	−46.3277	−1.67938	−0.839688	+	0.543068i	$0.817262\pi$
$762$	33.7006	1.22084
$763$	60.2809	2.18231
$764$	3.40169	0.123069
$765$	3.57546	0.129271
$766$	−47.2713	−1.70798
$767$	0.339715	0.0122664
$768$	32.2918	1.16523
$769$	39.2330	1.41478	0.707389	−	0.706824i	$-0.249873\pi$
$769$	39.2330	1.41478	0.707389	+	0.706824i	$0.249873\pi$
$770$	−63.5022	−2.28846
$771$	−2.14935	−0.0774070
$772$	9.11454	0.328039
$773$	−6.23494	−0.224255	−0.112128	−	0.993694i	$-0.535767\pi$
$773$	−6.23494	−0.224255	−0.112128	+	0.993694i	$0.535767\pi$
$774$	23.2002	0.833915
$775$	−1.77114	−0.0636213
$776$	−28.7991	−1.03383
$777$	37.9284	1.36067
$778$	48.3299	1.73271
$779$	15.8049	0.566271
$780$	37.9531	1.35894
$781$	18.2198	0.651956
$782$	−12.8309	−0.458833
$783$	−1.54538	−0.0552274
$784$	18.6127	0.664739
$785$	−3.57546	−0.127614
$786$	47.1262	1.68094
$787$	52.1136	1.85765	0.928824	−	0.370520i	$-0.120821\pi$
$787$	52.1136	1.85765	0.928824	+	0.370520i	$0.120821\pi$
$788$	7.53728	0.268504
$789$	−5.65226	−0.201226
$790$	−37.3668	−1.32945
$791$	47.6151	1.69300
$792$	10.7514	0.382035
$793$	11.5467	0.410037
$794$	82.7570	2.93694
$795$	−6.78384	−0.240598
$796$	−91.7322	−3.25136
$797$	−15.8827	−0.562593	−0.281296	−	0.959621i	$-0.590764\pi$
$797$	−15.8827	−0.562593	−0.281296	+	0.959621i	$0.590764\pi$
$798$	−63.5739	−2.25049
$799$	0.702326	0.0248465
$800$	−3.23393	−0.114337
$801$	6.06029	0.214130
$802$	−66.9308	−2.36341
$803$	−18.1380	−0.640074
$804$	−9.00250	−0.317494
$805$	62.9528	2.21879
$806$	1.46885	0.0517381
$807$	−3.74720	−0.131908
$808$	10.7713	0.378932
$809$	41.3953	1.45538	0.727690	−	0.685906i	$-0.240594\pi$
$809$	41.3953	1.45538	0.727690	+	0.685906i	$0.240594\pi$
$810$	8.78852	0.308797
$811$	−11.9987	−0.421332	−0.210666	−	0.977558i	$-0.567563\pi$
$811$	−11.9987	−0.421332	−0.210666	+	0.977558i	$0.567563\pi$
$812$	21.0679	0.739338
$813$	4.93865	0.173206
$814$	−59.2113	−2.07535
$815$	11.0670	0.387660
$816$	4.25266	0.148873
$817$	72.3761	2.53212
$818$	76.8213	2.68599
$819$	8.85823	0.309532
$820$	29.7862	1.04018
$821$	−13.9271	−0.486058	−0.243029	−	0.970019i	$-0.578141\pi$
$821$	−13.9271	−0.486058	−0.243029	+	0.970019i	$0.578141\pi$
$822$	−32.8077	−1.14430
$823$	−5.76373	−0.200911	−0.100455	−	0.994942i	$-0.532030\pi$
$823$	−5.76373	−0.200911	−0.100455	+	0.994942i	$0.532030\pi$
$824$	3.46585	0.120739
$825$	16.6749	0.580544
$826$	−1.07243	−0.0373145
$827$	26.5401	0.922889	0.461445	−	0.887169i	$-0.347331\pi$
$827$	26.5401	0.922889	0.461445	+	0.887169i	$0.347331\pi$
$828$	−21.0985	−0.733223
$829$	−55.3935	−1.92390	−0.961948	−	0.273233i	$-0.911907\pi$
$829$	−55.3935	−1.92390	−0.961948	+	0.273233i	$0.911907\pi$
$830$	−145.107	−5.03673
$831$	−14.9303	−0.517928
$832$	−19.6553	−0.681424
$833$	−4.37672	−0.151644
$834$	−13.9742	−0.483889
$835$	64.1964	2.22161
$836$	66.3938	2.29628
$837$	0.227539	0.00786489
$838$	−21.4712	−0.741710
$839$	31.0295	1.07126	0.535628	−	0.844454i	$-0.320075\pi$
$839$	31.0295	1.07126	0.535628	+	0.844454i	$0.320075\pi$
$840$	−60.5259	−2.08834
$841$	−26.6118	−0.917648
$842$	57.0373	1.96564
$843$	−1.15485	−0.0397751
$844$	−109.680	−3.77533
$845$	21.8201	0.750633
$846$	1.72632	0.0593523
$847$	−21.6235	−0.742994
$848$	−8.06871	−0.277081
$849$	13.0015	0.446212
$850$	19.1329	0.656254
$851$	58.6990	2.01218
$852$	34.3761	1.17771
$853$	1.64881	0.0564543	0.0282271	−	0.999602i	$-0.491014\pi$
$853$	1.64881	0.0564543	0.0282271	+	0.999602i	$0.491014\pi$
$854$	−36.4513	−1.24734
$855$	27.4169	0.937638
$856$	76.1689	2.60340
$857$	36.4157	1.24394	0.621968	−	0.783043i	$-0.286333\pi$
$857$	36.4157	1.24394	0.621968	+	0.783043i	$0.286333\pi$
$858$	−13.8289	−0.472110
$859$	33.2288	1.13375	0.566876	−	0.823803i	$-0.308152\pi$
$859$	33.2288	1.13375	0.566876	+	0.823803i	$0.308152\pi$
$860$	136.401	4.65123
$861$	6.95208	0.236926
$862$	−55.5077	−1.89060
$863$	49.2853	1.67769	0.838845	−	0.544370i	$-0.183231\pi$
$863$	49.2853	1.67769	0.838845	+	0.544370i	$0.183231\pi$
$864$	0.415463	0.0141343
$865$	−2.91173	−0.0990019
$866$	61.8429	2.10151
$867$	−1.00000	−0.0339618
$868$	−3.10199	−0.105289
$869$	9.10823	0.308976
$870$	−13.5816	−0.460460
$871$	5.84958	0.198206
$872$	−89.6958	−3.03748
$873$	5.73822	0.194209
$874$	−98.3886	−3.32804
$875$	−33.5734	−1.13499
$876$	−34.2216	−1.15624
$877$	24.4692	0.826265	0.413132	−	0.910671i	$-0.364435\pi$
$877$	24.4692	0.826265	0.413132	+	0.910671i	$0.364435\pi$
$878$	−60.8705	−2.05428
$879$	9.89707	0.333820
$880$	32.5729	1.09803
$881$	45.4955	1.53278	0.766391	−	0.642374i	$-0.222051\pi$
$881$	45.4955	1.53278	0.766391	+	0.642374i	$0.222051\pi$
$882$	−10.7580	−0.362241
$883$	32.6820	1.09984	0.549919	−	0.835218i	$-0.314659\pi$
$883$	32.6820	1.09984	0.549919	+	0.835218i	$0.314659\pi$
$884$	−10.6149	−0.357017
$885$	0.462496	0.0155466
$886$	1.87926	0.0631350
$887$	−26.5848	−0.892631	−0.446315	−	0.894876i	$-0.647264\pi$
$887$	−26.5848	−0.892631	−0.446315	+	0.894876i	$0.647264\pi$
$888$	−56.4361	−1.89387
$889$	46.2447	1.55100
$890$	53.2610	1.78531
$891$	−2.14222	−0.0717671
$892$	−41.3462	−1.38437
$893$	5.38549	0.180218
$894$	22.7365	0.760422
$895$	80.1792	2.68009
$896$	64.8513	2.16653
$897$	13.7092	0.457738
$898$	36.8948	1.23120
$899$	−0.351634	−0.0117277
$900$	31.4612	1.04871
$901$	1.89733	0.0632093
$902$	−10.8531	−0.361369
$903$	31.8359	1.05943
$904$	−70.8496	−2.35642
$905$	19.7679	0.657108
$906$	10.2770	0.341431
$907$	10.7373	0.356526	0.178263	−	0.983983i	$-0.442952\pi$
$907$	10.7373	0.356526	0.178263	+	0.983983i	$0.442952\pi$
$908$	54.2613	1.80072
$909$	−2.14618	−0.0711843
$910$	77.8507	2.58073
$911$	32.6521	1.08181	0.540906	−	0.841083i	$-0.318081\pi$
$911$	32.6521	1.08181	0.540906	+	0.841083i	$0.318081\pi$
$912$	32.6097	1.07982
$913$	35.3701	1.17058
$914$	56.1467	1.85717
$915$	15.7200	0.519687
$916$	115.127	3.80391
$917$	64.6677	2.13552
$918$	−2.45801	−0.0811265
$919$	−5.75478	−0.189833	−0.0949164	−	0.995485i	$-0.530258\pi$
$919$	−5.75478	−0.189833	−0.0949164	+	0.995485i	$0.530258\pi$
$920$	−93.6715	−3.08826
$921$	15.4228	0.508199
$922$	−10.5195	−0.346443
$923$	−22.3367	−0.735220
$924$	29.2045	0.960757
$925$	−87.5294	−2.87795
$926$	28.0737	0.922558
$927$	−0.690572	−0.0226814
$928$	−0.642049	−0.0210763
$929$	29.0186	0.952069	0.476034	−	0.879427i	$-0.342074\pi$
$929$	29.0186	0.952069	0.476034	+	0.879427i	$0.342074\pi$
$930$	1.99973	0.0655737
$931$	−33.5610	−1.09992
$932$	26.0229	0.852408
$933$	14.0158	0.458856
$934$	−29.1233	−0.952942
$935$	−7.65942	−0.250490
$936$	−13.1807	−0.430826
$937$	23.2713	0.760240	0.380120	−	0.924937i	$-0.375883\pi$
$937$	23.2713	0.760240	0.380120	+	0.924937i	$0.375883\pi$
$938$	−18.4662	−0.602944
$939$	3.09203	0.100905
$940$	10.1496	0.331042
$941$	32.3790	1.05553	0.527763	−	0.849392i	$-0.323031\pi$
$941$	32.3790	1.05553	0.527763	+	0.849392i	$0.323031\pi$
$942$	2.45801	0.0800863
$943$	10.7592	0.350369
$944$	0.550094	0.0179040
$945$	12.0598	0.392306
$946$	−49.7000	−1.61589
$947$	−17.9230	−0.582419	−0.291210	−	0.956659i	$-0.594058\pi$
$947$	−17.9230	−0.582419	−0.291210	+	0.956659i	$0.594058\pi$
$948$	17.1849	0.558139
$949$	22.2363	0.721821
$950$	146.713	4.75999
$951$	−22.3115	−0.723501
$952$	16.9282	0.548645
$953$	25.3470	0.821070	0.410535	−	0.911845i	$-0.365342\pi$
$953$	25.3470	0.821070	0.410535	+	0.911845i	$0.365342\pi$
$954$	4.66366	0.150992
$955$	−3.00919	−0.0973753
$956$	−94.2138	−3.04709
$957$	3.31055	0.107015
$958$	32.8938	1.06275
$959$	−45.0195	−1.45376
$960$	−26.7591	−0.863647
$961$	−30.9482	−0.998330
$962$	72.5903	2.34041
$963$	−15.1767	−0.489061
$964$	−30.9926	−0.998204
$965$	−8.06287	−0.259553
$966$	−43.2780	−1.39245
$967$	−11.3470	−0.364894	−0.182447	−	0.983216i	$-0.558402\pi$
$967$	−11.3470	−0.364894	−0.182447	+	0.983216i	$0.558402\pi$
$968$	32.1751	1.03415
$969$	−7.66808	−0.246334
$970$	50.4305	1.61923
$971$	−31.5171	−1.01143	−0.505716	−	0.862700i	$-0.668772\pi$
$971$	−31.5171	−1.01143	−0.505716	+	0.862700i	$0.668772\pi$
$972$	−4.04182	−0.129641
$973$	−19.1758	−0.614747
$974$	−47.2100	−1.51270
$975$	−20.4426	−0.654688
$976$	18.6974	0.598490
$977$	−40.4608	−1.29446	−0.647228	−	0.762297i	$-0.724072\pi$
$977$	−40.4608	−1.29446	−0.647228	+	0.762297i	$0.724072\pi$
$978$	−7.60819	−0.243283
$979$	−12.9825	−0.414922
$980$	−63.2495	−2.02043
$981$	17.8719	0.570606
$982$	−42.1351	−1.34458
$983$	58.6797	1.87159	0.935795	−	0.352543i	$-0.114683\pi$
$983$	58.6797	1.87159	0.935795	+	0.352543i	$0.114683\pi$
$984$	−10.3445	−0.329769
$985$	−6.66760	−0.212447
$986$	3.79856	0.120971
$987$	2.36890	0.0754030
$988$	−81.3958	−2.58954
$989$	49.2701	1.56670
$990$	−18.8270	−0.598360
$991$	35.9611	1.14234	0.571171	−	0.820831i	$-0.306490\pi$
$991$	35.9611	1.14234	0.571171	+	0.820831i	$0.306490\pi$
$992$	0.0945340	0.00300146
$993$	1.78983	0.0567986
$994$	70.5134	2.23655
$995$	81.1478	2.57256
$996$	66.7343	2.11456
$997$	35.7280	1.13152	0.565758	−	0.824571i	$-0.308584\pi$
$997$	35.7280	1.13152	0.565758	+	0.824571i	$0.308584\pi$
$998$	24.5817	0.778120
$999$	11.2449	0.355773

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.g.1.6	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.g.1.6	✓	56	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.45801 q^{2} -1.00000 q^{3} +4.04182 q^{4} -3.57546 q^{5} +2.45801 q^{6} +3.37294 q^{7} -5.01881 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.45801 q^{2} -1.00000 q^{3} +4.04182 q^{4} -3.57546 q^{5} +2.45801 q^{6} +3.37294 q^{7} -5.01881 q^{8} +1.00000 q^{9} +8.78852 q^{10} -2.14222 q^{11} -4.04182 q^{12} +2.62627 q^{13} -8.29072 q^{14} +3.57546 q^{15} +4.25266 q^{16} -1.00000 q^{17} -2.45801 q^{18} -7.66808 q^{19} -14.4514 q^{20} -3.37294 q^{21} +5.26560 q^{22} -5.22005 q^{23} +5.01881 q^{24} +7.78391 q^{25} -6.45539 q^{26} -1.00000 q^{27} +13.6328 q^{28} +1.54538 q^{29} -8.78852 q^{30} -0.227539 q^{31} -0.415463 q^{32} +2.14222 q^{33} +2.45801 q^{34} -12.0598 q^{35} +4.04182 q^{36} -11.2449 q^{37} +18.8482 q^{38} -2.62627 q^{39} +17.9446 q^{40} -2.06113 q^{41} +8.29072 q^{42} -9.43862 q^{43} -8.65847 q^{44} -3.57546 q^{45} +12.8309 q^{46} -0.702326 q^{47} -4.25266 q^{48} +4.37672 q^{49} -19.1329 q^{50} +1.00000 q^{51} +10.6149 q^{52} -1.89733 q^{53} +2.45801 q^{54} +7.65942 q^{55} -16.9282 q^{56} +7.66808 q^{57} -3.79856 q^{58} +0.129353 q^{59} +14.4514 q^{60} +4.39664 q^{61} +0.559293 q^{62} +3.37294 q^{63} -7.48411 q^{64} -9.39011 q^{65} -5.26560 q^{66} +2.22734 q^{67} -4.04182 q^{68} +5.22005 q^{69} +29.6431 q^{70} -8.50510 q^{71} -5.01881 q^{72} +8.46689 q^{73} +27.6401 q^{74} -7.78391 q^{75} -30.9930 q^{76} -7.22558 q^{77} +6.45539 q^{78} -4.25177 q^{79} -15.2052 q^{80} +1.00000 q^{81} +5.06629 q^{82} -16.5110 q^{83} -13.6328 q^{84} +3.57546 q^{85} +23.2002 q^{86} -1.54538 q^{87} +10.7514 q^{88} +6.06029 q^{89} +8.78852 q^{90} +8.85823 q^{91} -21.0985 q^{92} +0.227539 q^{93} +1.72632 q^{94} +27.4169 q^{95} +0.415463 q^{96} +5.73822 q^{97} -10.7580 q^{98} -2.14222 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9}+O(q^{10}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9} + 8 q^{10} - 7 q^{11} - 61 q^{12} + 8 q^{13} - 8 q^{14} - q^{15} + 71 q^{16} - 56 q^{17} + q^{18} - 2 q^{19} - 4 q^{20} - 19 q^{21} + 47 q^{22} + 16 q^{23} + 85 q^{25} - 11 q^{26} - 56 q^{27} + 52 q^{28} + 17 q^{29} - 8 q^{30} + 23 q^{31} + 11 q^{32} + 7 q^{33} - q^{34} - 41 q^{35} + 61 q^{36} + 58 q^{37} - 22 q^{38} - 8 q^{39} + 38 q^{40} - q^{41} + 8 q^{42} + 27 q^{43} + 2 q^{44} + q^{45} + 46 q^{46} + 5 q^{47} - 71 q^{48} + 59 q^{49} - 4 q^{50} + 56 q^{51} + 25 q^{52} + 15 q^{53} - q^{54} + 9 q^{55} - 36 q^{56} + 2 q^{57} + 89 q^{58} - 61 q^{59} + 4 q^{60} + 47 q^{61} + 8 q^{62} + 19 q^{63} + 88 q^{64} + 39 q^{65} - 47 q^{66} + 20 q^{67} - 61 q^{68} - 16 q^{69} + 36 q^{70} - 2 q^{71} + 93 q^{73} + 48 q^{74} - 85 q^{75} + 38 q^{76} + 26 q^{77} + 11 q^{78} + 72 q^{79} + 42 q^{80} + 56 q^{81} + 33 q^{82} - 11 q^{83} - 52 q^{84} - q^{85} - 4 q^{86} - 17 q^{87} + 130 q^{88} - 6 q^{89} + 8 q^{90} + 37 q^{91} + 132 q^{92} - 23 q^{93} - 32 q^{94} + 12 q^{95} - 11 q^{96} + 100 q^{97} + 42 q^{98} - 7 q^{99}+O(q^{100}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9 + 8 * q^10 - 7 * q^11 - 61 * q^12 + 8 * q^13 - 8 * q^14 - q^15 + 71 * q^16 - 56 * q^17 + q^18 - 2 * q^19 - 4 * q^20 - 19 * q^21 + 47 * q^22 + 16 * q^23 + 85 * q^25 - 11 * q^26 - 56 * q^27 + 52 * q^28 + 17 * q^29 - 8 * q^30 + 23 * q^31 + 11 * q^32 + 7 * q^33 - q^34 - 41 * q^35 + 61 * q^36 + 58 * q^37 - 22 * q^38 - 8 * q^39 + 38 * q^40 - q^41 + 8 * q^42 + 27 * q^43 + 2 * q^44 + q^45 + 46 * q^46 + 5 * q^47 - 71 * q^48 + 59 * q^49 - 4 * q^50 + 56 * q^51 + 25 * q^52 + 15 * q^53 - q^54 + 9 * q^55 - 36 * q^56 + 2 * q^57 + 89 * q^58 - 61 * q^59 + 4 * q^60 + 47 * q^61 + 8 * q^62 + 19 * q^63 + 88 * q^64 + 39 * q^65 - 47 * q^66 + 20 * q^67 - 61 * q^68 - 16 * q^69 + 36 * q^70 - 2 * q^71 + 93 * q^73 + 48 * q^74 - 85 * q^75 + 38 * q^76 + 26 * q^77 + 11 * q^78 + 72 * q^79 + 42 * q^80 + 56 * q^81 + 33 * q^82 - 11 * q^83 - 52 * q^84 - q^85 - 4 * q^86 - 17 * q^87 + 130 * q^88 - 6 * q^89 + 8 * q^90 + 37 * q^91 + 132 * q^92 - 23 * q^93 - 32 * q^94 + 12 * q^95 - 11 * q^96 + 100 * q^97 + 42 * q^98 - 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more