LMFDB - Embedded newform 1859.2.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,2,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1859.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:	$14.8441897358$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 8x^{6} + 18x^{5} + 7x^{4} - 22x^{3} - 3x^{2} + 6x + 1 $ x^8 - 2x^7 - 8x^6 + 18x^5 + 7x^4 - 22x^3 - 3x^2 + 6*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.20621$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.20621 q^{2} +2.48500 q^{3} +2.86737 q^{4} -1.68345 q^{5} -5.48243 q^{6} +0.336274 q^{7} -1.91361 q^{8} +3.17521 q^{9} +O(q^{10})$	\(q-2.20621 q^{2} +2.48500 q^{3} +2.86737 q^{4} -1.68345 q^{5} -5.48243 q^{6} +0.336274 q^{7} -1.91361 q^{8} +3.17521 q^{9} +3.71405 q^{10} +1.00000 q^{11} +7.12541 q^{12} -0.741892 q^{14} -4.18337 q^{15} -1.51292 q^{16} +0.144194 q^{17} -7.00519 q^{18} -5.22231 q^{19} -4.82708 q^{20} +0.835641 q^{21} -2.20621 q^{22} -4.38689 q^{23} -4.75531 q^{24} -2.16599 q^{25} +0.435403 q^{27} +0.964223 q^{28} -2.44316 q^{29} +9.22941 q^{30} -10.1942 q^{31} +7.16504 q^{32} +2.48500 q^{33} -0.318122 q^{34} -0.566101 q^{35} +9.10452 q^{36} -4.55644 q^{37} +11.5215 q^{38} +3.22147 q^{40} +11.1758 q^{41} -1.84360 q^{42} +8.04583 q^{43} +2.86737 q^{44} -5.34532 q^{45} +9.67840 q^{46} -0.887789 q^{47} -3.75960 q^{48} -6.88692 q^{49} +4.77864 q^{50} +0.358321 q^{51} -5.33873 q^{53} -0.960592 q^{54} -1.68345 q^{55} -0.643497 q^{56} -12.9774 q^{57} +5.39013 q^{58} +11.8665 q^{59} -11.9953 q^{60} -2.40749 q^{61} +22.4906 q^{62} +1.06774 q^{63} -12.7818 q^{64} -5.48243 q^{66} -6.42376 q^{67} +0.413457 q^{68} -10.9014 q^{69} +1.24894 q^{70} +5.30052 q^{71} -6.07611 q^{72} -14.9244 q^{73} +10.0525 q^{74} -5.38249 q^{75} -14.9743 q^{76} +0.336274 q^{77} +5.95553 q^{79} +2.54693 q^{80} -8.44366 q^{81} -24.6562 q^{82} -11.5950 q^{83} +2.39609 q^{84} -0.242743 q^{85} -17.7508 q^{86} -6.07125 q^{87} -1.91361 q^{88} +7.37352 q^{89} +11.7929 q^{90} -12.5788 q^{92} -25.3326 q^{93} +1.95865 q^{94} +8.79150 q^{95} +17.8051 q^{96} +7.38121 q^{97} +15.1940 q^{98} +3.17521 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 4 q^{4} - 8 q^{5} - 4 q^{6} - 14 q^{7} + 6 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 4 * q^4 - 8 * q^5 - 4 * q^6 - 14 * q^7 + 6 * q^8 + 2 * q^9	$ 8 q - 2 q^{2} + 4 q^{4} - 8 q^{5} - 4 q^{6} - 14 q^{7} + 6 q^{8} + 2 q^{9} + 10 q^{10} + 8 q^{11} - 8 q^{12} - 6 q^{14} - 2 q^{15} + 12 q^{16} + 6 q^{17} - 6 q^{18} - 4 q^{19} - 16 q^{20} - 2 q^{21} - 2 q^{22} - 14 q^{23} - 26 q^{24} + 12 q^{25} + 24 q^{27} - 20 q^{28} - 10 q^{29} + 14 q^{30} - 32 q^{31} + 40 q^{32} - 14 q^{34} + 10 q^{35} - 24 q^{37} + 12 q^{38} - 14 q^{40} - 2 q^{41} - 2 q^{42} + 14 q^{43} + 4 q^{44} + 4 q^{45} - 14 q^{46} - 18 q^{47} - 6 q^{48} + 2 q^{49} - 38 q^{50} + 12 q^{51} - 8 q^{53} - 2 q^{54} - 8 q^{55} - 28 q^{56} - 24 q^{57} + 14 q^{58} - 18 q^{59} + 14 q^{60} - 4 q^{61} - 8 q^{63} + 6 q^{64} - 4 q^{66} + 14 q^{67} - 34 q^{68} - 10 q^{69} - 18 q^{70} + 12 q^{71} - 8 q^{72} - 26 q^{73} + 2 q^{74} - 18 q^{75} - 54 q^{76} - 14 q^{77} + 26 q^{79} - 24 q^{80} - 16 q^{81} - 64 q^{82} - 16 q^{83} + 74 q^{84} - 56 q^{85} - 32 q^{86} - 18 q^{87} + 6 q^{88} + 8 q^{89} - 20 q^{90} - 30 q^{92} - 48 q^{93} - 4 q^{94} + 22 q^{95} - 16 q^{96} - 20 q^{97} + 46 q^{98} + 2 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 + 4 * q^4 - 8 * q^5 - 4 * q^6 - 14 * q^7 + 6 * q^8 + 2 * q^9 + 10 * q^10 + 8 * q^11 - 8 * q^12 - 6 * q^14 - 2 * q^15 + 12 * q^16 + 6 * q^17 - 6 * q^18 - 4 * q^19 - 16 * q^20 - 2 * q^21 - 2 * q^22 - 14 * q^23 - 26 * q^24 + 12 * q^25 + 24 * q^27 - 20 * q^28 - 10 * q^29 + 14 * q^30 - 32 * q^31 + 40 * q^32 - 14 * q^34 + 10 * q^35 - 24 * q^37 + 12 * q^38 - 14 * q^40 - 2 * q^41 - 2 * q^42 + 14 * q^43 + 4 * q^44 + 4 * q^45 - 14 * q^46 - 18 * q^47 - 6 * q^48 + 2 * q^49 - 38 * q^50 + 12 * q^51 - 8 * q^53 - 2 * q^54 - 8 * q^55 - 28 * q^56 - 24 * q^57 + 14 * q^58 - 18 * q^59 + 14 * q^60 - 4 * q^61 - 8 * q^63 + 6 * q^64 - 4 * q^66 + 14 * q^67 - 34 * q^68 - 10 * q^69 - 18 * q^70 + 12 * q^71 - 8 * q^72 - 26 * q^73 + 2 * q^74 - 18 * q^75 - 54 * q^76 - 14 * q^77 + 26 * q^79 - 24 * q^80 - 16 * q^81 - 64 * q^82 - 16 * q^83 + 74 * q^84 - 56 * q^85 - 32 * q^86 - 18 * q^87 + 6 * q^88 + 8 * q^89 - 20 * q^90 - 30 * q^92 - 48 * q^93 - 4 * q^94 + 22 * q^95 - 16 * q^96 - 20 * q^97 + 46 * q^98 + 2 * 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 $

$2$	−2.20621	−1.56003	−0.780014	−	0.625762i	$-0.784788\pi$
$2$	−2.20621	−1.56003	−0.780014	+	0.625762i	$0.784788\pi$
$3$	2.48500	1.43471	0.717357	−	0.696706i	$-0.245352\pi$
$3$	2.48500	1.43471	0.717357	+	0.696706i	$0.245352\pi$
$4$	2.86737	1.43369
$5$	−1.68345	−0.752862	−0.376431	−	0.926445i	$-0.622849\pi$
$5$	−1.68345	−0.752862	−0.376431	+	0.926445i	$0.622849\pi$
$6$	−5.48243	−2.23819
$7$	0.336274	0.127100	0.0635499	−	0.997979i	$-0.479758\pi$
$7$	0.336274	0.127100	0.0635499	+	0.997979i	$0.479758\pi$
$8$	−1.91361	−0.676563
$9$	3.17521	1.05840
$10$	3.71405	1.17449
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	7.12541	2.05693
$13$	0	0
$13$	0	0
$14$	−0.741892	−0.198279
$15$	−4.18337	−1.08014
$16$	−1.51292	−0.378230
$17$	0.144194	0.0349721	0.0174861	−	0.999847i	$-0.494434\pi$
$17$	0.144194	0.0349721	0.0174861	+	0.999847i	$0.494434\pi$
$18$	−7.00519	−1.65114
$19$	−5.22231	−1.19808	−0.599040	−	0.800719i	$-0.704451\pi$
$19$	−5.22231	−1.19808	−0.599040	+	0.800719i	$0.704451\pi$
$20$	−4.82708	−1.07937
$21$	0.835641	0.182352
$22$	−2.20621	−0.470366
$23$	−4.38689	−0.914729	−0.457365	−	0.889279i	$-0.651207\pi$
$23$	−4.38689	−0.914729	−0.457365	+	0.889279i	$0.651207\pi$
$24$	−4.75531	−0.970674
$25$	−2.16599	−0.433199
$26$	0	0
$27$	0.435403	0.0837934
$28$	0.964223	0.182221
$29$	−2.44316	−0.453684	−0.226842	−	0.973932i	$-0.572840\pi$
$29$	−2.44316	−0.453684	−0.226842	+	0.973932i	$0.572840\pi$
$30$	9.22941	1.68505
$31$	−10.1942	−1.83093	−0.915467	−	0.402393i	$-0.868178\pi$
$31$	−10.1942	−1.83093	−0.915467	+	0.402393i	$0.868178\pi$
$32$	7.16504	1.26661
$33$	2.48500	0.432583
$34$	−0.318122	−0.0545575
$35$	−0.566101	−0.0956886
$36$	9.10452	1.51742
$37$	−4.55644	−0.749074	−0.374537	−	0.927212i	$-0.622198\pi$
$37$	−4.55644	−0.749074	−0.374537	+	0.927212i	$0.622198\pi$
$38$	11.5215	1.86904
$39$	0	0
$40$	3.22147	0.509358
$41$	11.1758	1.74537	0.872685	−	0.488283i	$-0.162377\pi$
$41$	11.1758	1.74537	0.872685	+	0.488283i	$0.162377\pi$
$42$	−1.84360	−0.284474
$43$	8.04583	1.22698	0.613489	−	0.789703i	$-0.289766\pi$
$43$	8.04583	1.22698	0.613489	+	0.789703i	$0.289766\pi$
$44$	2.86737	0.432273
$45$	−5.34532	−0.796833
$46$	9.67840	1.42700
$47$	−0.887789	−0.129497	−0.0647487	−	0.997902i	$-0.520625\pi$
$47$	−0.887789	−0.129497	−0.0647487	+	0.997902i	$0.520625\pi$
$48$	−3.75960	−0.542652
$49$	−6.88692	−0.983846
$50$	4.77864	0.675802
$51$	0.358321	0.0501750
$52$	0	0
$53$	−5.33873	−0.733331	−0.366666	−	0.930353i	$-0.619501\pi$
$53$	−5.33873	−0.733331	−0.366666	+	0.930353i	$0.619501\pi$
$54$	−0.960592	−0.130720
$55$	−1.68345	−0.226996
$56$	−0.643497	−0.0859909
$57$	−12.9774	−1.71890
$58$	5.39013	0.707759
$59$	11.8665	1.54488	0.772441	−	0.635086i	$-0.219036\pi$
$59$	11.8665	1.54488	0.772441	+	0.635086i	$0.219036\pi$
$60$	−11.9953	−1.54858
$61$	−2.40749	−0.308248	−0.154124	−	0.988052i	$-0.549255\pi$
$61$	−2.40749	−0.308248	−0.154124	+	0.988052i	$0.549255\pi$
$62$	22.4906	2.85631
$63$	1.06774	0.134523
$64$	−12.7818	−1.59772
$65$	0	0
$66$	−5.48243	−0.674841
$67$	−6.42376	−0.784788	−0.392394	−	0.919797i	$-0.628353\pi$
$67$	−6.42376	−0.784788	−0.392394	+	0.919797i	$0.628353\pi$
$68$	0.413457	0.0501390
$69$	−10.9014	−1.31237
$70$	1.24894	0.149277
$71$	5.30052	0.629056	0.314528	−	0.949248i	$-0.398154\pi$
$71$	5.30052	0.629056	0.314528	+	0.949248i	$0.398154\pi$
$72$	−6.07611	−0.716077
$73$	−14.9244	−1.74677	−0.873387	−	0.487027i	$-0.838081\pi$
$73$	−14.9244	−1.74677	−0.873387	+	0.487027i	$0.838081\pi$
$74$	10.0525	1.16858
$75$	−5.38249	−0.621516
$76$	−14.9743	−1.71767
$77$	0.336274	0.0383220
$78$	0	0
$79$	5.95553	0.670049	0.335025	−	0.942209i	$-0.391255\pi$
$79$	5.95553	0.670049	0.335025	+	0.942209i	$0.391255\pi$
$80$	2.54693	0.284755
$81$	−8.44366	−0.938185
$82$	−24.6562	−2.72283
$83$	−11.5950	−1.27271	−0.636357	−	0.771395i	$-0.719560\pi$
$83$	−11.5950	−1.27271	−0.636357	+	0.771395i	$0.719560\pi$
$84$	2.39609	0.261435
$85$	−0.242743	−0.0263292
$86$	−17.7508	−1.91412
$87$	−6.07125	−0.650906
$88$	−1.91361	−0.203991
$89$	7.37352	0.781591	0.390796	−	0.920477i	$-0.372200\pi$
$89$	7.37352	0.781591	0.390796	+	0.920477i	$0.372200\pi$
$90$	11.7929	1.24308
$91$	0	0
$92$	−12.5788	−1.31143
$93$	−25.3326	−2.62687
$94$	1.95865	0.202019
$95$	8.79150	0.901989
$96$	17.8051	1.81723
$97$	7.38121	0.749448	0.374724	−	0.927136i	$-0.377737\pi$
$97$	7.38121	0.749448	0.374724	+	0.927136i	$0.377737\pi$
$98$	15.1940	1.53483
$99$	3.17521	0.319121
$100$	−6.21071	−0.621071
$101$	−14.0876	−1.40177	−0.700886	−	0.713273i	$-0.747212\pi$
$101$	−14.0876	−1.40177	−0.700886	+	0.713273i	$0.747212\pi$
$102$	−0.790532	−0.0782744
$103$	−9.81986	−0.967579	−0.483790	−	0.875184i	$-0.660740\pi$
$103$	−9.81986	−0.967579	−0.483790	+	0.875184i	$0.660740\pi$
$104$	0	0
$105$	−1.40676	−0.137286
$106$	11.7784	1.14402
$107$	6.95718	0.672576	0.336288	−	0.941759i	$-0.390828\pi$
$107$	6.95718	0.672576	0.336288	+	0.941759i	$0.390828\pi$
$108$	1.24846	0.120133
$109$	6.92594	0.663385	0.331692	−	0.943388i	$-0.392380\pi$
$109$	6.92594	0.663385	0.331692	+	0.943388i	$0.392380\pi$
$110$	3.71405	0.354121
$111$	−11.3227	−1.07471
$112$	−0.508756	−0.0480729
$113$	4.06846	0.382728	0.191364	−	0.981519i	$-0.438709\pi$
$113$	4.06846	0.382728	0.191364	+	0.981519i	$0.438709\pi$
$114$	28.6309	2.68153
$115$	7.38511	0.688665
$116$	−7.00546	−0.650440
$117$	0	0
$118$	−26.1799	−2.41006
$119$	0.0484886	0.00444495
$120$	8.00533	0.730784
$121$	1.00000	0.0909091
$122$	5.31144	0.480875
$123$	27.7719	2.50411
$124$	−29.2306	−2.62498
$125$	12.0636	1.07900
$126$	−2.35567	−0.209859
$127$	3.76899	0.334444	0.167222	−	0.985919i	$-0.446520\pi$
$127$	3.76899	0.334444	0.167222	+	0.985919i	$0.446520\pi$
$128$	13.8692	1.22587
$129$	19.9939	1.76036
$130$	0	0
$131$	−13.7278	−1.19940	−0.599701	−	0.800224i	$-0.704714\pi$
$131$	−13.7278	−1.19940	−0.599701	+	0.800224i	$0.704714\pi$
$132$	7.12541	0.620188
$133$	−1.75613	−0.152276
$134$	14.1722	1.22429
$135$	−0.732980	−0.0630849
$136$	−0.275930	−0.0236608
$137$	−19.1145	−1.63306	−0.816530	−	0.577303i	$-0.804105\pi$
$137$	−19.1145	−1.63306	−0.816530	+	0.577303i	$0.804105\pi$
$138$	24.0508	2.04734
$139$	7.50407	0.636487	0.318243	−	0.948009i	$-0.396907\pi$
$139$	7.50407	0.636487	0.318243	+	0.948009i	$0.396907\pi$
$140$	−1.62322	−0.137187
$141$	−2.20615	−0.185792
$142$	−11.6941	−0.981344
$143$	0	0
$144$	−4.80384	−0.400320
$145$	4.11294	0.341561
$146$	32.9265	2.72502
$147$	−17.1140	−1.41154
$148$	−13.0650	−1.07394
$149$	−18.7218	−1.53375	−0.766876	−	0.641796i	$-0.778190\pi$
$149$	−18.7218	−1.53375	−0.766876	+	0.641796i	$0.778190\pi$
$150$	11.8749	0.969582
$151$	2.67555	0.217733	0.108866	−	0.994056i	$-0.465278\pi$
$151$	2.67555	0.217733	0.108866	+	0.994056i	$0.465278\pi$
$152$	9.99345	0.810576
$153$	0.457846	0.0370146
$154$	−0.741892	−0.0597834
$155$	17.1614	1.37844
$156$	0	0
$157$	17.2945	1.38025	0.690126	−	0.723689i	$-0.257555\pi$
$157$	17.2945	1.38025	0.690126	+	0.723689i	$0.257555\pi$
$158$	−13.1392	−1.04530
$159$	−13.2667	−1.05212
$160$	−12.0620	−0.953584
$161$	−1.47520	−0.116262
$162$	18.6285	1.46359
$163$	−3.68040	−0.288271	−0.144135	−	0.989558i	$-0.546040\pi$
$163$	−3.68040	−0.288271	−0.144135	+	0.989558i	$0.546040\pi$
$164$	32.0453	2.50231
$165$	−4.18337	−0.325675
$166$	25.5810	1.98547
$167$	6.70452	0.518811	0.259406	−	0.965768i	$-0.416473\pi$
$167$	6.70452	0.518811	0.259406	+	0.965768i	$0.416473\pi$
$168$	−1.59909	−0.123372
$169$	0	0
$170$	0.535543	0.0410743
$171$	−16.5819	−1.26805
$172$	23.0704	1.75910
$173$	9.98689	0.759289	0.379645	−	0.925132i	$-0.376046\pi$
$173$	9.98689	0.759289	0.379645	+	0.925132i	$0.376046\pi$
$174$	13.3945	1.01543
$175$	−0.728367	−0.0550594
$176$	−1.51292	−0.114041
$177$	29.4881	2.21646
$178$	−16.2675	−1.21930
$179$	−13.3089	−0.994758	−0.497379	−	0.867533i	$-0.665704\pi$
$179$	−13.3089	−0.994758	−0.497379	+	0.867533i	$0.665704\pi$
$180$	−15.3270	−1.14241
$181$	−12.5134	−0.930113	−0.465056	−	0.885281i	$-0.653966\pi$
$181$	−12.5134	−0.930113	−0.465056	+	0.885281i	$0.653966\pi$
$182$	0	0
$183$	−5.98261	−0.442247
$184$	8.39478	0.618871
$185$	7.67054	0.563949
$186$	55.8891	4.09798
$187$	0.144194	0.0105445
$188$	−2.54562	−0.185659
$189$	0.146415	0.0106501
$190$	−19.3959	−1.40713
$191$	−1.34878	−0.0975943	−0.0487971	−	0.998809i	$-0.515539\pi$
$191$	−1.34878	−0.0975943	−0.0487971	+	0.998809i	$0.515539\pi$
$192$	−31.7626	−2.29227
$193$	−4.74532	−0.341576	−0.170788	−	0.985308i	$-0.554631\pi$
$193$	−4.74532	−0.341576	−0.170788	+	0.985308i	$0.554631\pi$
$194$	−16.2845	−1.16916
$195$	0	0
$196$	−19.7474	−1.41053
$197$	4.17222	0.297259	0.148629	−	0.988893i	$-0.452514\pi$
$197$	4.17222	0.297259	0.148629	+	0.988893i	$0.452514\pi$
$198$	−7.00519	−0.497837
$199$	−21.3154	−1.51101	−0.755503	−	0.655145i	$-0.772608\pi$
$199$	−21.3154	−1.51101	−0.755503	+	0.655145i	$0.772608\pi$
$200$	4.14486	0.293086
$201$	−15.9630	−1.12595
$202$	31.0803	2.18680
$203$	−0.821572	−0.0576631
$204$	1.02744	0.0719352
$205$	−18.8140	−1.31402
$206$	21.6647	1.50945
$207$	−13.9293	−0.968153
$208$	0	0
$209$	−5.22231	−0.361235
$210$	3.10361	0.214170
$211$	20.5228	1.41284	0.706422	−	0.707791i	$-0.250308\pi$
$211$	20.5228	1.41284	0.706422	+	0.707791i	$0.250308\pi$
$212$	−15.3081	−1.05137
$213$	13.1718	0.902515
$214$	−15.3490	−1.04924
$215$	−13.5448	−0.923745
$216$	−0.833191	−0.0566915
$217$	−3.42805	−0.232711
$218$	−15.2801	−1.03490
$219$	−37.0872	−2.50612
$220$	−4.82708	−0.325442
$221$	0	0
$222$	24.9804	1.67657
$223$	−19.6456	−1.31557	−0.657783	−	0.753208i	$-0.728505\pi$
$223$	−19.6456	−1.31557	−0.657783	+	0.753208i	$0.728505\pi$
$224$	2.40942	0.160986
$225$	−6.87749	−0.458499
$226$	−8.97588	−0.597066
$227$	8.67982	0.576100	0.288050	−	0.957615i	$-0.406993\pi$
$227$	8.67982	0.576100	0.288050	+	0.957615i	$0.406993\pi$
$228$	−37.2111	−2.46437
$229$	−20.5716	−1.35941	−0.679705	−	0.733486i	$-0.737892\pi$
$229$	−20.5716	−1.35941	−0.679705	+	0.733486i	$0.737892\pi$
$230$	−16.2931	−1.07434
$231$	0.835641	0.0549811
$232$	4.67525	0.306945
$233$	14.1716	0.928414	0.464207	−	0.885727i	$-0.346339\pi$
$233$	14.1716	0.928414	0.464207	+	0.885727i	$0.346339\pi$
$234$	0	0
$235$	1.49455	0.0974936
$236$	34.0256	2.21488
$237$	14.7995	0.961329
$238$	−0.106976	−0.00693424
$239$	−5.16781	−0.334278	−0.167139	−	0.985933i	$-0.553453\pi$
$239$	−5.16781	−0.334278	−0.167139	+	0.985933i	$0.553453\pi$
$240$	6.32911	0.408542
$241$	−8.40947	−0.541701	−0.270851	−	0.962621i	$-0.587305\pi$
$241$	−8.40947	−0.541701	−0.270851	+	0.962621i	$0.587305\pi$
$242$	−2.20621	−0.141821
$243$	−22.2887	−1.42982
$244$	−6.90318	−0.441931
$245$	11.5938	0.740700
$246$	−61.2707	−3.90648
$247$	0	0
$248$	19.5077	1.23874
$249$	−28.8135	−1.82598
$250$	−26.6149	−1.68327
$251$	−7.17578	−0.452931	−0.226466	−	0.974019i	$-0.572717\pi$
$251$	−7.17578	−0.452931	−0.226466	+	0.974019i	$0.572717\pi$
$252$	3.06161	0.192864
$253$	−4.38689	−0.275801
$254$	−8.31520	−0.521742
$255$	−0.603216	−0.0377748
$256$	−5.03486	−0.314679
$257$	13.3333	0.831708	0.415854	−	0.909431i	$-0.363483\pi$
$257$	13.3333	0.831708	0.415854	+	0.909431i	$0.363483\pi$
$258$	−44.1107	−2.74621
$259$	−1.53221	−0.0952071
$260$	0	0
$261$	−7.75756	−0.480181
$262$	30.2864	1.87110
$263$	−4.02733	−0.248336	−0.124168	−	0.992261i	$-0.539626\pi$
$263$	−4.02733	−0.248336	−0.124168	+	0.992261i	$0.539626\pi$
$264$	−4.75531	−0.292669
$265$	8.98749	0.552097
$266$	3.87439	0.237554
$267$	18.3232	1.12136
$268$	−18.4193	−1.12514
$269$	24.7893	1.51143	0.755716	−	0.654899i	$-0.227289\pi$
$269$	24.7893	1.51143	0.755716	+	0.654899i	$0.227289\pi$
$270$	1.61711	0.0984141
$271$	−26.0809	−1.58430	−0.792151	−	0.610326i	$-0.791039\pi$
$271$	−26.0809	−1.58430	−0.792151	+	0.610326i	$0.791039\pi$
$272$	−0.218154	−0.0132275
$273$	0	0
$274$	42.1706	2.54762
$275$	−2.16599	−0.130614
$276$	−31.2584	−1.88153
$277$	0.904447	0.0543429	0.0271715	−	0.999631i	$-0.491350\pi$
$277$	0.904447	0.0543429	0.0271715	+	0.999631i	$0.491350\pi$
$278$	−16.5556	−0.992937
$279$	−32.3688	−1.93787
$280$	1.08330	0.0647393
$281$	4.92210	0.293628	0.146814	−	0.989164i	$-0.453098\pi$
$281$	4.92210	0.293628	0.146814	+	0.989164i	$0.453098\pi$
$282$	4.86724	0.289840
$283$	−29.9388	−1.77968	−0.889840	−	0.456273i	$-0.849184\pi$
$283$	−29.9388	−1.77968	−0.889840	+	0.456273i	$0.849184\pi$
$284$	15.1986	0.901868
$285$	21.8469	1.29410
$286$	0	0
$287$	3.75814	0.221836
$288$	22.7505	1.34059
$289$	−16.9792	−0.998777
$290$	−9.07403	−0.532845
$291$	18.3423	1.07524
$292$	−42.7939	−2.50433
$293$	−15.4613	−0.903257	−0.451629	−	0.892206i	$-0.649157\pi$
$293$	−15.4613	−0.903257	−0.451629	+	0.892206i	$0.649157\pi$
$294$	37.7571	2.20204
$295$	−19.9766	−1.16308
$296$	8.71924	0.506795
$297$	0.435403	0.0252647
$298$	41.3043	2.39269
$299$	0	0
$300$	−15.4336	−0.891059
$301$	2.70561	0.155949
$302$	−5.90282	−0.339669
$303$	−35.0077	−2.01114
$304$	7.90093	0.453150
$305$	4.05290	0.232068
$306$	−1.01010	−0.0577439
$307$	6.05444	0.345545	0.172773	−	0.984962i	$-0.444727\pi$
$307$	6.05444	0.345545	0.172773	+	0.984962i	$0.444727\pi$
$308$	0.964223	0.0549417
$309$	−24.4023	−1.38820
$310$	−37.8618	−2.15041
$311$	5.91438	0.335374	0.167687	−	0.985840i	$-0.446370\pi$
$311$	5.91438	0.335374	0.167687	+	0.985840i	$0.446370\pi$
$312$	0	0
$313$	16.7018	0.944043	0.472022	−	0.881587i	$-0.343524\pi$
$313$	16.7018	0.944043	0.472022	+	0.881587i	$0.343524\pi$
$314$	−38.1554	−2.15323
$315$	−1.79749	−0.101277
$316$	17.0767	0.960641
$317$	−10.8342	−0.608508	−0.304254	−	0.952591i	$-0.598407\pi$
$317$	−10.8342	−0.608508	−0.304254	+	0.952591i	$0.598407\pi$
$318$	29.2692	1.64134
$319$	−2.44316	−0.136791
$320$	21.5175	1.20286
$321$	17.2886	0.964955
$322$	3.25460	0.181372
$323$	−0.753024	−0.0418994
$324$	−24.2111	−1.34506
$325$	0	0
$326$	8.11974	0.449711
$327$	17.2109	0.951767
$328$	−21.3861	−1.18085
$329$	−0.298541	−0.0164591
$330$	9.22941	0.508062
$331$	28.8701	1.58684	0.793421	−	0.608673i	$-0.208298\pi$
$331$	28.8701	1.58684	0.793421	+	0.608673i	$0.208298\pi$
$332$	−33.2471	−1.82467
$333$	−14.4677	−0.792823
$334$	−14.7916	−0.809360
$335$	10.8141	0.590837
$336$	−1.26426	−0.0689709
$337$	22.2421	1.21160	0.605801	−	0.795616i	$-0.292853\pi$
$337$	22.2421	1.21160	0.605801	+	0.795616i	$0.292853\pi$
$338$	0	0
$339$	10.1101	0.549105
$340$	−0.696035	−0.0377478
$341$	−10.1942	−0.552047
$342$	36.5833	1.97820
$343$	−4.66981	−0.252146
$344$	−15.3966	−0.830127
$345$	18.3520	0.988037
$346$	−22.0332	−1.18451
$347$	2.29240	0.123062	0.0615312	−	0.998105i	$-0.480402\pi$
$347$	2.29240	0.123062	0.0615312	+	0.998105i	$0.480402\pi$
$348$	−17.4085	−0.933196
$349$	25.3366	1.35624	0.678118	−	0.734953i	$-0.262796\pi$
$349$	25.3366	1.35624	0.678118	+	0.734953i	$0.262796\pi$
$350$	1.60693	0.0858942
$351$	0	0
$352$	7.16504	0.381898
$353$	0.552385	0.0294005	0.0147002	−	0.999892i	$-0.495321\pi$
$353$	0.552385	0.0294005	0.0147002	+	0.999892i	$0.495321\pi$
$354$	−65.0571	−3.45775
$355$	−8.92316	−0.473592
$356$	21.1426	1.12056
$357$	0.120494	0.00637723
$358$	29.3624	1.55185
$359$	−18.2421	−0.962784	−0.481392	−	0.876506i	$-0.659869\pi$
$359$	−18.2421	−0.962784	−0.481392	+	0.876506i	$0.659869\pi$
$360$	10.2288	0.539107
$361$	8.27250	0.435395
$362$	27.6072	1.45100
$363$	2.48500	0.130429
$364$	0	0
$365$	25.1246	1.31508
$366$	13.1989	0.689918
$367$	28.8039	1.50355	0.751776	−	0.659418i	$-0.229197\pi$
$367$	28.8039	1.50355	0.751776	+	0.659418i	$0.229197\pi$
$368$	6.63701	0.345978
$369$	35.4856	1.84731
$370$	−16.9228	−0.879777
$371$	−1.79528	−0.0932062
$372$	−72.6379	−3.76610
$373$	3.76201	0.194789	0.0973946	−	0.995246i	$-0.468949\pi$
$373$	3.76201	0.194789	0.0973946	+	0.995246i	$0.468949\pi$
$374$	−0.318122	−0.0164497
$375$	29.9780	1.54806
$376$	1.69888	0.0876130
$377$	0	0
$378$	−0.323022	−0.0166145
$379$	21.3722	1.09781	0.548907	−	0.835883i	$-0.315044\pi$
$379$	21.3722	1.09781	0.548907	+	0.835883i	$0.315044\pi$
$380$	25.2085	1.29317
$381$	9.36594	0.479832
$382$	2.97569	0.152250
$383$	6.34011	0.323964	0.161982	−	0.986794i	$-0.448211\pi$
$383$	6.34011	0.323964	0.161982	+	0.986794i	$0.448211\pi$
$384$	34.4649	1.75878
$385$	−0.566101	−0.0288512
$386$	10.4692	0.532867
$387$	25.5472	1.29864
$388$	21.1647	1.07447
$389$	−7.02161	−0.356010	−0.178005	−	0.984030i	$-0.556964\pi$
$389$	−7.02161	−0.356010	−0.178005	+	0.984030i	$0.556964\pi$
$390$	0	0
$391$	−0.632561	−0.0319900
$392$	13.1789	0.665633
$393$	−34.1135	−1.72080
$394$	−9.20481	−0.463732
$395$	−10.0258	−0.504455
$396$	9.10452	0.457519
$397$	16.5239	0.829311	0.414656	−	0.909978i	$-0.363902\pi$
$397$	16.5239	0.829311	0.414656	+	0.909978i	$0.363902\pi$
$398$	47.0262	2.35721
$399$	−4.36397	−0.218472
$400$	3.27697	0.163849
$401$	13.8349	0.690880	0.345440	−	0.938441i	$-0.387730\pi$
$401$	13.8349	0.690880	0.345440	+	0.938441i	$0.387730\pi$
$402$	35.2178	1.75651
$403$	0	0
$404$	−40.3945	−2.00970
$405$	14.2145	0.706324
$406$	1.81256	0.0899560
$407$	−4.55644	−0.225854
$408$	−0.685686	−0.0339465
$409$	15.9129	0.786843	0.393421	−	0.919358i	$-0.371291\pi$
$409$	15.9129	0.786843	0.393421	+	0.919358i	$0.371291\pi$
$410$	41.5076	2.04991
$411$	−47.4994	−2.34297
$412$	−28.1572	−1.38720
$413$	3.99039	0.196354
$414$	30.7310	1.51035
$415$	19.5196	0.958179
$416$	0	0
$417$	18.6476	0.913177
$418$	11.5215	0.563536
$419$	11.8796	0.580358	0.290179	−	0.956972i	$-0.406285\pi$
$419$	11.8796	0.580358	0.290179	+	0.956972i	$0.406285\pi$
$420$	−4.03370	−0.196825
$421$	−12.3932	−0.604006	−0.302003	−	0.953307i	$-0.597655\pi$
$421$	−12.3932	−0.604006	−0.302003	+	0.953307i	$0.597655\pi$
$422$	−45.2775	−2.20408
$423$	−2.81892	−0.137061
$424$	10.2162	0.496145
$425$	−0.312323	−0.0151499
$426$	−29.0597	−1.40795
$427$	−0.809578	−0.0391782
$428$	19.9488	0.964264
$429$	0	0
$430$	29.8826	1.44107
$431$	16.1247	0.776702	0.388351	−	0.921512i	$-0.373045\pi$
$431$	16.1247	0.776702	0.388351	+	0.921512i	$0.373045\pi$
$432$	−0.658730	−0.0316932
$433$	−17.3833	−0.835386	−0.417693	−	0.908588i	$-0.637161\pi$
$433$	−17.3833	−0.835386	−0.417693	+	0.908588i	$0.637161\pi$
$434$	7.56300	0.363036
$435$	10.2207	0.490043
$436$	19.8592	0.951085
$437$	22.9097	1.09592
$438$	81.8222	3.90962
$439$	12.4698	0.595150	0.297575	−	0.954698i	$-0.403822\pi$
$439$	12.4698	0.595150	0.297575	+	0.954698i	$0.403822\pi$
$440$	3.22147	0.153577
$441$	−21.8674	−1.04131
$442$	0	0
$443$	−31.8864	−1.51497	−0.757485	−	0.652852i	$-0.773572\pi$
$443$	−31.8864	−1.51497	−0.757485	+	0.652852i	$0.773572\pi$
$444$	−32.4665	−1.54079
$445$	−12.4130	−0.588431
$446$	43.3423	2.05232
$447$	−46.5237	−2.20049
$448$	−4.29817	−0.203070
$449$	6.02668	0.284416	0.142208	−	0.989837i	$-0.454580\pi$
$449$	6.02668	0.284416	0.142208	+	0.989837i	$0.454580\pi$
$450$	15.1732	0.715271
$451$	11.1758	0.526249
$452$	11.6658	0.548712
$453$	6.64873	0.312384
$454$	−19.1495	−0.898732
$455$	0	0
$456$	24.8337	1.16294
$457$	−16.6738	−0.779968	−0.389984	−	0.920822i	$-0.627520\pi$
$457$	−16.6738	−0.779968	−0.389984	+	0.920822i	$0.627520\pi$
$458$	45.3853	2.12072
$459$	0.0627824	0.00293043
$460$	21.1759	0.987329
$461$	−36.6737	−1.70806	−0.854032	−	0.520220i	$-0.825850\pi$
$461$	−36.6737	−1.70806	−0.854032	+	0.520220i	$0.825850\pi$
$462$	−1.84360	−0.0857721
$463$	12.1287	0.563668	0.281834	−	0.959463i	$-0.409057\pi$
$463$	12.1287	0.563668	0.281834	+	0.959463i	$0.409057\pi$
$464$	3.69631	0.171597
$465$	42.6462	1.97767
$466$	−31.2656	−1.44835
$467$	−13.7912	−0.638179	−0.319089	−	0.947725i	$-0.603377\pi$
$467$	−13.7912	−0.638179	−0.319089	+	0.947725i	$0.603377\pi$
$468$	0	0
$469$	−2.16015	−0.0997463
$470$	−3.29729	−0.152093
$471$	42.9768	1.98027
$472$	−22.7078	−1.04521
$473$	8.04583	0.369948
$474$	−32.6508	−1.49970
$475$	11.3115	0.519006
$476$	0.139035	0.00637266
$477$	−16.9516	−0.776161
$478$	11.4013	0.521483
$479$	29.7342	1.35859	0.679295	−	0.733865i	$-0.262286\pi$
$479$	29.7342	1.35859	0.679295	+	0.733865i	$0.262286\pi$
$480$	−29.9740	−1.36812
$481$	0	0
$482$	18.5531	0.845069
$483$	−3.66586	−0.166802
$484$	2.86737	0.130335
$485$	−12.4259	−0.564231
$486$	49.1736	2.23056
$487$	−14.5106	−0.657537	−0.328769	−	0.944410i	$-0.606634\pi$
$487$	−14.5106	−0.657537	−0.328769	+	0.944410i	$0.606634\pi$
$488$	4.60700	0.208549
$489$	−9.14578	−0.413586
$490$	−25.5784	−1.15551
$491$	42.5048	1.91822	0.959108	−	0.283041i	$-0.0913431\pi$
$491$	42.5048	1.91822	0.959108	+	0.283041i	$0.0913431\pi$
$492$	79.6324	3.59010
$493$	−0.352289	−0.0158663
$494$	0	0
$495$	−5.34532	−0.240254
$496$	15.4230	0.692514
$497$	1.78243	0.0799528
$498$	63.5687	2.84858
$499$	−34.3952	−1.53974	−0.769869	−	0.638201i	$-0.779679\pi$
$499$	−34.3952	−1.53974	−0.769869	+	0.638201i	$0.779679\pi$
$500$	34.5908	1.54695
$501$	16.6607	0.744346
$502$	15.8313	0.706585
$503$	−3.66673	−0.163491	−0.0817456	−	0.996653i	$-0.526050\pi$
$503$	−3.66673	−0.163491	−0.0817456	+	0.996653i	$0.526050\pi$
$504$	−2.04324	−0.0910131
$505$	23.7159	1.05534
$506$	9.67840	0.430257
$507$	0	0
$508$	10.8071	0.479488
$509$	−34.8590	−1.54510	−0.772549	−	0.634955i	$-0.781018\pi$
$509$	−34.8590	−1.54510	−0.772549	+	0.634955i	$0.781018\pi$
$510$	1.33082	0.0589298
$511$	−5.01870	−0.222014
$512$	−16.6304	−0.734967
$513$	−2.27381	−0.100391
$514$	−29.4161	−1.29749
$515$	16.5312	0.728454
$516$	57.3299	2.52381
$517$	−0.887789	−0.0390449
$518$	3.38039	0.148526
$519$	24.8174	1.08936
$520$	0	0
$521$	28.8987	1.26607	0.633037	−	0.774121i	$-0.281808\pi$
$521$	28.8987	1.26607	0.633037	+	0.774121i	$0.281808\pi$
$522$	17.1148	0.749095
$523$	−35.5037	−1.55247	−0.776234	−	0.630444i	$-0.782873\pi$
$523$	−35.5037	−1.55247	−0.776234	+	0.630444i	$0.782873\pi$
$524$	−39.3627	−1.71957
$525$	−1.80999	−0.0789945
$526$	8.88515	0.387411
$527$	−1.46994	−0.0640316
$528$	−3.75960	−0.163616
$529$	−3.75523	−0.163271
$530$	−19.8283	−0.861287
$531$	37.6786	1.63511
$532$	−5.03547	−0.218315
$533$	0	0
$534$	−40.4248	−1.74935
$535$	−11.7121	−0.506357
$536$	12.2926	0.530958
$537$	−33.0727	−1.42719
$538$	−54.6905	−2.35788
$539$	−6.88692	−0.296641
$540$	−2.10173	−0.0904439
$541$	−10.6399	−0.457443	−0.228721	−	0.973492i	$-0.573455\pi$
$541$	−10.6399	−0.457443	−0.228721	+	0.973492i	$0.573455\pi$
$542$	57.5400	2.47155
$543$	−31.0957	−1.33445
$544$	1.03315	0.0442961
$545$	−11.6595	−0.499437
$546$	0	0
$547$	24.5162	1.04824	0.524119	−	0.851645i	$-0.324395\pi$
$547$	24.5162	1.04824	0.524119	+	0.851645i	$0.324395\pi$
$548$	−54.8083	−2.34129
$549$	−7.64430	−0.326251
$550$	4.77864	0.203762
$551$	12.7589	0.543549
$552$	20.8610	0.887904
$553$	2.00269	0.0851631
$554$	−1.99540	−0.0847765
$555$	19.0613	0.809106
$556$	21.5170	0.912523
$557$	4.63250	0.196285	0.0981426	−	0.995172i	$-0.468710\pi$
$557$	4.63250	0.196285	0.0981426	+	0.995172i	$0.468710\pi$
$558$	71.4124	3.02313
$559$	0	0
$560$	0.856466	0.0361923
$561$	0.358321	0.0151283
$562$	−10.8592	−0.458068
$563$	44.9000	1.89231	0.946156	−	0.323712i	$-0.104931\pi$
$563$	44.9000	1.89231	0.946156	+	0.323712i	$0.104931\pi$
$564$	−6.32586	−0.266367
$565$	−6.84905	−0.288141
$566$	66.0515	2.77635
$567$	−2.83939	−0.119243
$568$	−10.1431	−0.425595
$569$	3.18675	0.133596	0.0667978	−	0.997767i	$-0.478722\pi$
$569$	3.18675	0.133596	0.0667978	+	0.997767i	$0.478722\pi$
$570$	−48.1988	−2.01883
$571$	9.63072	0.403033	0.201517	−	0.979485i	$-0.435413\pi$
$571$	9.63072	0.403033	0.201517	+	0.979485i	$0.435413\pi$
$572$	0	0
$573$	−3.35171	−0.140020
$574$	−8.29126	−0.346070
$575$	9.50196	0.396259
$576$	−40.5848	−1.69103
$577$	27.6544	1.15127	0.575634	−	0.817708i	$-0.304755\pi$
$577$	27.6544	1.15127	0.575634	+	0.817708i	$0.304755\pi$
$578$	37.4597	1.55812
$579$	−11.7921	−0.490063
$580$	11.7933	0.489692
$581$	−3.89909	−0.161762
$582$	−40.4670	−1.67741
$583$	−5.33873	−0.221108
$584$	28.5595	1.18180
$585$	0	0
$586$	34.1108	1.40911
$587$	29.1153	1.20172	0.600858	−	0.799356i	$-0.294826\pi$
$587$	29.1153	1.20172	0.600858	+	0.799356i	$0.294826\pi$
$588$	−49.0722	−2.02370
$589$	53.2373	2.19360
$590$	44.0726	1.81444
$591$	10.3680	0.426481
$592$	6.89352	0.283322
$593$	−6.27876	−0.257838	−0.128919	−	0.991655i	$-0.541151\pi$
$593$	−6.27876	−0.257838	−0.128919	+	0.991655i	$0.541151\pi$
$594$	−0.960592	−0.0394136
$595$	−0.0816282	−0.00334643
$596$	−53.6824	−2.19892
$597$	−52.9686	−2.16786
$598$	0	0
$599$	−42.9316	−1.75414	−0.877068	−	0.480366i	$-0.840504\pi$
$599$	−42.9316	−1.75414	−0.877068	+	0.480366i	$0.840504\pi$
$600$	10.3000	0.420494
$601$	−21.3284	−0.870005	−0.435002	−	0.900429i	$-0.643252\pi$
$601$	−21.3284	−0.870005	−0.435002	+	0.900429i	$0.643252\pi$
$602$	−5.96914	−0.243284
$603$	−20.3968	−0.830623
$604$	7.67179	0.312161
$605$	−1.68345	−0.0684420
$606$	77.2345	3.13744
$607$	−13.4656	−0.546551	−0.273275	−	0.961936i	$-0.588107\pi$
$607$	−13.4656	−0.546551	−0.273275	+	0.961936i	$0.588107\pi$
$608$	−37.4180	−1.51750
$609$	−2.04161	−0.0827300
$610$	−8.94155	−0.362033
$611$	0	0
$612$	1.31281	0.0530674
$613$	26.3116	1.06272	0.531358	−	0.847147i	$-0.321682\pi$
$613$	26.3116	1.06272	0.531358	+	0.847147i	$0.321682\pi$
$614$	−13.3574	−0.539060
$615$	−46.7526	−1.88525
$616$	−0.643497	−0.0259272
$617$	31.8975	1.28415	0.642073	−	0.766643i	$-0.278074\pi$
$617$	31.8975	1.28415	0.642073	+	0.766643i	$0.278074\pi$
$618$	53.8367	2.16563
$619$	17.0725	0.686203	0.343101	−	0.939298i	$-0.388523\pi$
$619$	17.0725	0.686203	0.343101	+	0.939298i	$0.388523\pi$
$620$	49.2083	1.97625
$621$	−1.91006	−0.0766482
$622$	−13.0484	−0.523192
$623$	2.47952	0.0993400
$624$	0	0
$625$	−9.47851	−0.379141
$626$	−36.8478	−1.47273
$627$	−12.9774	−0.518268
$628$	49.5898	1.97885
$629$	−0.657010	−0.0261967
$630$	3.96565	0.157995
$631$	−30.5452	−1.21599	−0.607993	−	0.793942i	$-0.708025\pi$
$631$	−30.5452	−1.21599	−0.607993	+	0.793942i	$0.708025\pi$
$632$	−11.3965	−0.453330
$633$	50.9990	2.02703
$634$	23.9025	0.949289
$635$	−6.34492	−0.251790
$636$	−38.0407	−1.50841
$637$	0	0
$638$	5.39013	0.213397
$639$	16.8303	0.665795
$640$	−23.3481	−0.922915
$641$	13.0260	0.514498	0.257249	−	0.966345i	$-0.417184\pi$
$641$	13.0260	0.514498	0.257249	+	0.966345i	$0.417184\pi$
$642$	−38.1423	−1.50536
$643$	19.1962	0.757022	0.378511	−	0.925597i	$-0.376436\pi$
$643$	19.1962	0.757022	0.378511	+	0.925597i	$0.376436\pi$
$644$	−4.22994	−0.166683
$645$	−33.6587	−1.32531
$646$	1.66133	0.0653642
$647$	−17.7730	−0.698728	−0.349364	−	0.936987i	$-0.613602\pi$
$647$	−17.7730	−0.698728	−0.349364	+	0.936987i	$0.613602\pi$
$648$	16.1579	0.634741
$649$	11.8665	0.465800
$650$	0	0
$651$	−8.51869	−0.333874
$652$	−10.5531	−0.413290
$653$	0.735452	0.0287805	0.0143902	−	0.999896i	$-0.495419\pi$
$653$	0.735452	0.0287805	0.0143902	+	0.999896i	$0.495419\pi$
$654$	−37.9710	−1.48478
$655$	23.1101	0.902985
$656$	−16.9081	−0.660151
$657$	−47.3883	−1.84879
$658$	0.658644	0.0256766
$659$	−37.8565	−1.47468	−0.737339	−	0.675523i	$-0.763918\pi$
$659$	−37.8565	−1.47468	−0.737339	+	0.675523i	$0.763918\pi$
$660$	−11.9953	−0.466916
$661$	−30.5721	−1.18912	−0.594559	−	0.804052i	$-0.702673\pi$
$661$	−30.5721	−1.18912	−0.594559	+	0.804052i	$0.702673\pi$
$662$	−63.6935	−2.47552
$663$	0	0
$664$	22.1882	0.861071
$665$	2.95635	0.114643
$666$	31.9187	1.23683
$667$	10.7179	0.414998
$668$	19.2244	0.743812
$669$	−48.8192	−1.88746
$670$	−23.8582	−0.921722
$671$	−2.40749	−0.0929402
$672$	5.98740	0.230969
$673$	−35.0651	−1.35166	−0.675830	−	0.737057i	$-0.736215\pi$
$673$	−35.0651	−1.35166	−0.675830	+	0.737057i	$0.736215\pi$
$674$	−49.0707	−1.89013
$675$	−0.943080	−0.0362992
$676$	0	0
$677$	28.7474	1.10485	0.552426	−	0.833562i	$-0.313702\pi$
$677$	28.7474	1.10485	0.552426	+	0.833562i	$0.313702\pi$
$678$	−22.3050	−0.856619
$679$	2.48211	0.0952546
$680$	0.464515	0.0178133
$681$	21.5693	0.826539
$682$	22.4906	0.861209
$683$	1.37387	0.0525698	0.0262849	−	0.999654i	$-0.491632\pi$
$683$	1.37387	0.0525698	0.0262849	+	0.999654i	$0.491632\pi$
$684$	−47.5466	−1.81799
$685$	32.1783	1.22947
$686$	10.3026	0.393355
$687$	−51.1204	−1.95036
$688$	−12.1727	−0.464080
$689$	0	0
$690$	−40.4884	−1.54137
$691$	19.1956	0.730236	0.365118	−	0.930961i	$-0.381029\pi$
$691$	19.1956	0.730236	0.365118	+	0.930961i	$0.381029\pi$
$692$	28.6361	1.08858
$693$	1.06774	0.0405602
$694$	−5.05752	−0.191981
$695$	−12.6327	−0.479187
$696$	11.6180	0.440379
$697$	1.61148	0.0610393
$698$	−55.8979	−2.11577
$699$	35.2165	1.33201
$700$	−2.08850	−0.0789379
$701$	−8.21771	−0.310378	−0.155189	−	0.987885i	$-0.549599\pi$
$701$	−8.21771	−0.310378	−0.155189	+	0.987885i	$0.549599\pi$
$702$	0	0
$703$	23.7951	0.897450
$704$	−12.7818	−0.481731
$705$	3.71395	0.139875
$706$	−1.21868	−0.0458656
$707$	−4.73731	−0.178165
$708$	84.5535	3.17771
$709$	20.7010	0.777443	0.388722	−	0.921355i	$-0.372917\pi$
$709$	20.7010	0.777443	0.388722	+	0.921355i	$0.372917\pi$
$710$	19.6864	0.738817
$711$	18.9101	0.709183
$712$	−14.1100	−0.528796
$713$	44.7208	1.67481
$714$	−0.265836	−0.00994865
$715$	0	0
$716$	−38.1617	−1.42617
$717$	−12.8420	−0.479593
$718$	40.2460	1.50197
$719$	−10.8361	−0.404120	−0.202060	−	0.979373i	$-0.564764\pi$
$719$	−10.8361	−0.404120	−0.202060	+	0.979373i	$0.564764\pi$
$720$	8.08703	0.301386
$721$	−3.30216	−0.122979
$722$	−18.2509	−0.679228
$723$	−20.8975	−0.777186
$724$	−35.8805	−1.33349
$725$	5.29187	0.196535
$726$	−5.48243	−0.203472
$727$	30.6644	1.13728	0.568639	−	0.822587i	$-0.307470\pi$
$727$	30.6644	1.13728	0.568639	+	0.822587i	$0.307470\pi$
$728$	0	0
$729$	−30.0564	−1.11320
$730$	−55.4301	−2.05156
$731$	1.16016	0.0429100
$732$	−17.1544	−0.634044
$733$	38.5550	1.42406	0.712032	−	0.702147i	$-0.247775\pi$
$733$	38.5550	1.42406	0.712032	+	0.702147i	$0.247775\pi$
$734$	−63.5476	−2.34558
$735$	28.8105	1.06269
$736$	−31.4322	−1.15861
$737$	−6.42376	−0.236622
$738$	−78.2888	−2.88185
$739$	−40.4469	−1.48786	−0.743931	−	0.668256i	$-0.767041\pi$
$739$	−40.4469	−1.48786	−0.743931	+	0.668256i	$0.767041\pi$
$740$	21.9943	0.808526
$741$	0	0
$742$	3.96076	0.145404
$743$	49.6898	1.82294	0.911471	−	0.411364i	$-0.134947\pi$
$743$	49.6898	1.82294	0.911471	+	0.411364i	$0.134947\pi$
$744$	48.4766	1.77724
$745$	31.5173	1.15470
$746$	−8.29978	−0.303877
$747$	−36.8165	−1.34705
$748$	0.413457	0.0151175
$749$	2.33952	0.0854843
$750$	−66.1379	−2.41501
$751$	25.2579	0.921676	0.460838	−	0.887484i	$-0.347549\pi$
$751$	25.2579	0.921676	0.460838	+	0.887484i	$0.347549\pi$
$752$	1.34315	0.0489798
$753$	−17.8318	−0.649827
$754$	0	0
$755$	−4.50415	−0.163923
$756$	0.419826	0.0152689
$757$	5.77428	0.209870	0.104935	−	0.994479i	$-0.466537\pi$
$757$	5.77428	0.209870	0.104935	+	0.994479i	$0.466537\pi$
$758$	−47.1515	−1.71262
$759$	−10.9014	−0.395696
$760$	−16.8235	−0.610252
$761$	−9.00715	−0.326509	−0.163254	−	0.986584i	$-0.552199\pi$
$761$	−9.00715	−0.326509	−0.163254	+	0.986584i	$0.552199\pi$
$762$	−20.6633	−0.748551
$763$	2.32901	0.0843160
$764$	−3.86745	−0.139920
$765$	−0.770761	−0.0278669
$766$	−13.9876	−0.505393
$767$	0	0
$768$	−12.5116	−0.451474
$769$	2.37222	0.0855445	0.0427723	−	0.999085i	$-0.486381\pi$
$769$	2.37222	0.0855445	0.0427723	+	0.999085i	$0.486381\pi$
$770$	1.24894	0.0450086
$771$	33.1332	1.19326
$772$	−13.6066	−0.489712
$773$	9.63873	0.346681	0.173341	−	0.984862i	$-0.444544\pi$
$773$	9.63873	0.346681	0.173341	+	0.984862i	$0.444544\pi$
$774$	−56.3626	−2.02591
$775$	22.0806	0.793158
$776$	−14.1247	−0.507048
$777$	−3.80754	−0.136595
$778$	15.4912	0.555385
$779$	−58.3636	−2.09109
$780$	0	0
$781$	5.30052	0.189667
$782$	1.39556	0.0499053
$783$	−1.06376	−0.0380157
$784$	10.4194	0.372120
$785$	−29.1145	−1.03914
$786$	75.2617	2.68450
$787$	1.65984	0.0591671	0.0295835	−	0.999562i	$-0.490582\pi$
$787$	1.65984	0.0591671	0.0295835	+	0.999562i	$0.490582\pi$
$788$	11.9633	0.426176
$789$	−10.0079	−0.356291
$790$	22.1191	0.786964
$791$	1.36812	0.0486446
$792$	−6.07611	−0.215905
$793$	0	0
$794$	−36.4552	−1.29375
$795$	22.3339	0.792102
$796$	−61.1191	−2.16631
$797$	52.7702	1.86922	0.934608	−	0.355680i	$-0.115751\pi$
$797$	52.7702	1.86922	0.934608	+	0.355680i	$0.115751\pi$
$798$	9.62785	0.340822
$799$	−0.128014	−0.00452880
$800$	−15.5194	−0.548694
$801$	23.4125	0.827240
$802$	−30.5227	−1.07779
$803$	−14.9244	−0.526672
$804$	−45.7720	−1.61425
$805$	2.48342	0.0875291
$806$	0	0
$807$	61.6014	2.16847
$808$	26.9582	0.948387
$809$	10.5907	0.372349	0.186175	−	0.982517i	$-0.440391\pi$
$809$	10.5907	0.372349	0.186175	+	0.982517i	$0.440391\pi$
$810$	−31.3602	−1.10188
$811$	−14.7106	−0.516558	−0.258279	−	0.966070i	$-0.583155\pi$
$811$	−14.7106	−0.516558	−0.258279	+	0.966070i	$0.583155\pi$
$812$	−2.35575	−0.0826708
$813$	−64.8110	−2.27302
$814$	10.0525	0.352339
$815$	6.19577	0.217028
$816$	−0.542111	−0.0189777
$817$	−42.0178	−1.47002
$818$	−35.1073	−1.22750
$819$	0	0
$820$	−53.9466	−1.88390
$821$	−7.31975	−0.255461	−0.127731	−	0.991809i	$-0.540769\pi$
$821$	−7.31975	−0.255461	−0.127731	+	0.991809i	$0.540769\pi$
$822$	104.794	3.65510
$823$	2.08194	0.0725718	0.0362859	−	0.999341i	$-0.488447\pi$
$823$	2.08194	0.0725718	0.0362859	+	0.999341i	$0.488447\pi$
$824$	18.7914	0.654628
$825$	−5.38249	−0.187394
$826$	−8.80364	−0.306318
$827$	4.80456	0.167071	0.0835354	−	0.996505i	$-0.473379\pi$
$827$	4.80456	0.167071	0.0835354	+	0.996505i	$0.473379\pi$
$828$	−39.9405	−1.38803
$829$	−8.29610	−0.288135	−0.144068	−	0.989568i	$-0.546018\pi$
$829$	−8.29610	−0.288135	−0.144068	+	0.989568i	$0.546018\pi$
$830$	−43.0643	−1.49479
$831$	2.24755	0.0779666
$832$	0	0
$833$	−0.993051	−0.0344072
$834$	−41.1406	−1.42458
$835$	−11.2867	−0.390593
$836$	−14.9743	−0.517897
$837$	−4.43859	−0.153420
$838$	−26.2090	−0.905374
$839$	−21.8759	−0.755239	−0.377620	−	0.925961i	$-0.623257\pi$
$839$	−21.8759	−0.755239	−0.377620	+	0.925961i	$0.623257\pi$
$840$	2.69199	0.0928824
$841$	−23.0310	−0.794171
$842$	27.3420	0.942266
$843$	12.2314	0.421272
$844$	58.8464	2.02558
$845$	0	0
$846$	6.21913	0.213818
$847$	0.336274	0.0115545
$848$	8.07707	0.277368
$849$	−74.3980	−2.55333
$850$	0.689050	0.0236342
$851$	19.9886	0.685200
$852$	37.7684	1.29392
$853$	14.9307	0.511219	0.255610	−	0.966780i	$-0.417724\pi$
$853$	14.9307	0.511219	0.255610	+	0.966780i	$0.417724\pi$
$854$	1.78610	0.0611191
$855$	27.9149	0.954669
$856$	−13.3133	−0.455040
$857$	27.3522	0.934333	0.467167	−	0.884169i	$-0.345275\pi$
$857$	27.3522	0.934333	0.467167	+	0.884169i	$0.345275\pi$
$858$	0	0
$859$	−26.8367	−0.915656	−0.457828	−	0.889041i	$-0.651373\pi$
$859$	−26.8367	−0.915656	−0.457828	+	0.889041i	$0.651373\pi$
$860$	−38.8379	−1.32436
$861$	9.33897	0.318271
$862$	−35.5746	−1.21168
$863$	−22.5460	−0.767476	−0.383738	−	0.923442i	$-0.625363\pi$
$863$	−22.5460	−0.767476	−0.383738	+	0.923442i	$0.625363\pi$
$864$	3.11968	0.106134
$865$	−16.8124	−0.571640
$866$	38.3512	1.30323
$867$	−42.1933	−1.43296
$868$	−9.82949	−0.333635
$869$	5.95553	0.202028
$870$	−22.5489	−0.764480
$871$	0	0
$872$	−13.2535	−0.448821
$873$	23.4369	0.793219
$874$	−50.5436	−1.70966
$875$	4.05668	0.137141
$876$	−106.343	−3.59299
$877$	13.0668	0.441236	0.220618	−	0.975360i	$-0.429193\pi$
$877$	13.0668	0.441236	0.220618	+	0.975360i	$0.429193\pi$
$878$	−27.5110	−0.928450
$879$	−38.4212	−1.29592
$880$	2.54693	0.0858569
$881$	14.0067	0.471896	0.235948	−	0.971766i	$-0.424180\pi$
$881$	14.0067	0.471896	0.235948	+	0.971766i	$0.424180\pi$
$882$	48.2442	1.62447
$883$	−5.69200	−0.191551	−0.0957755	−	0.995403i	$-0.530533\pi$
$883$	−5.69200	−0.191551	−0.0957755	+	0.995403i	$0.530533\pi$
$884$	0	0
$885$	−49.6418	−1.66869
$886$	70.3483	2.36340
$887$	26.6418	0.894545	0.447273	−	0.894398i	$-0.352395\pi$
$887$	26.6418	0.894545	0.447273	+	0.894398i	$0.352395\pi$
$888$	21.6673	0.727106
$889$	1.26742	0.0425077
$890$	27.3856	0.917968
$891$	−8.44366	−0.282873
$892$	−56.3312	−1.88611
$893$	4.63631	0.155148
$894$	102.641	3.43283
$895$	22.4050	0.748915
$896$	4.66385	0.155808
$897$	0	0
$898$	−13.2961	−0.443698
$899$	24.9061	0.830665
$900$	−19.7203	−0.657344
$901$	−0.769812	−0.0256461
$902$	−24.6562	−0.820963
$903$	6.72342	0.223742
$904$	−7.78543	−0.258939
$905$	21.0657	0.700247
$906$	−14.6685	−0.487328
$907$	−35.3630	−1.17421	−0.587105	−	0.809511i	$-0.699733\pi$
$907$	−35.3630	−1.17421	−0.587105	+	0.809511i	$0.699733\pi$
$908$	24.8883	0.825947
$909$	−44.7312	−1.48364
$910$	0	0
$911$	11.4640	0.379819	0.189910	−	0.981802i	$-0.439180\pi$
$911$	11.4640	0.379819	0.189910	+	0.981802i	$0.439180\pi$
$912$	19.6338	0.650140
$913$	−11.5950	−0.383738
$914$	36.7860	1.21677
$915$	10.0714	0.332951
$916$	−58.9865	−1.94897
$917$	−4.61630	−0.152444
$918$	−0.138511	−0.00457155
$919$	36.7253	1.21145	0.605727	−	0.795672i	$-0.292882\pi$
$919$	36.7253	1.21145	0.605727	+	0.795672i	$0.292882\pi$
$920$	−14.1322	−0.465925
$921$	15.0453	0.495758
$922$	80.9100	2.66463
$923$	0	0
$924$	2.39609	0.0788257
$925$	9.86921	0.324498
$926$	−26.7584	−0.879337
$927$	−31.1801	−1.02409
$928$	−17.5053	−0.574641
$929$	2.34119	0.0768120	0.0384060	−	0.999262i	$-0.487772\pi$
$929$	2.34119	0.0768120	0.0384060	+	0.999262i	$0.487772\pi$
$930$	−94.0865	−3.08522
$931$	35.9656	1.17873
$932$	40.6353	1.33106
$933$	14.6972	0.481166
$934$	30.4262	0.995577
$935$	−0.242743	−0.00793855
$936$	0	0
$937$	−51.2193	−1.67326	−0.836631	−	0.547767i	$-0.815478\pi$
$937$	−51.2193	−1.67326	−0.836631	+	0.547767i	$0.815478\pi$
$938$	4.76574	0.155607
$939$	41.5040	1.35443
$940$	4.28543	0.139775
$941$	−20.6159	−0.672058	−0.336029	−	0.941852i	$-0.609084\pi$
$941$	−20.6159	−0.672058	−0.336029	+	0.941852i	$0.609084\pi$
$942$	−94.8160	−3.08927
$943$	−49.0271	−1.59654
$944$	−17.9530	−0.584321
$945$	−0.246482	−0.00801807
$946$	−17.7508	−0.577129
$947$	23.9223	0.777372	0.388686	−	0.921370i	$-0.372929\pi$
$947$	23.9223	0.777372	0.388686	+	0.921370i	$0.372929\pi$
$948$	42.4356	1.37824
$949$	0	0
$950$	−24.9555	−0.809664
$951$	−26.9229	−0.873034
$952$	−0.0927882	−0.00300728
$953$	39.5009	1.27956	0.639780	−	0.768558i	$-0.279026\pi$
$953$	39.5009	1.27956	0.639780	+	0.768558i	$0.279026\pi$
$954$	37.3989	1.21083
$955$	2.27060	0.0734750
$956$	−14.8180	−0.479250
$957$	−6.07125	−0.196256
$958$	−65.6000	−2.11944
$959$	−6.42770	−0.207561
$960$	53.4708	1.72576
$961$	72.9219	2.35232
$962$	0	0
$963$	22.0905	0.711858
$964$	−24.1131	−0.776630
$965$	7.98851	0.257159
$966$	8.08767	0.260216
$967$	23.9055	0.768750	0.384375	−	0.923177i	$-0.374417\pi$
$967$	23.9055	0.768750	0.384375	+	0.923177i	$0.374417\pi$
$968$	−1.91361	−0.0615057
$969$	−1.87126	−0.0601136
$970$	27.4142	0.880216
$971$	−43.8547	−1.40736	−0.703682	−	0.710515i	$-0.748462\pi$
$971$	−43.8547	−1.40736	−0.703682	+	0.710515i	$0.748462\pi$
$972$	−63.9100	−2.04991
$973$	2.52343	0.0808973
$974$	32.0134	1.02578
$975$	0	0
$976$	3.64234	0.116589
$977$	33.8398	1.08263	0.541316	−	0.840819i	$-0.317926\pi$
$977$	33.8398	1.08263	0.541316	+	0.840819i	$0.317926\pi$
$978$	20.1775	0.645206
$979$	7.37352	0.235659
$980$	33.2437	1.06193
$981$	21.9913	0.702129
$982$	−93.7747	−2.99247
$983$	−43.0887	−1.37432	−0.687158	−	0.726508i	$-0.741142\pi$
$983$	−43.0887	−1.37432	−0.687158	+	0.726508i	$0.741142\pi$
$984$	−53.1445	−1.69419
$985$	−7.02373	−0.223795
$986$	0.777223	0.0247518
$987$	−0.741872	−0.0236141
$988$	0	0
$989$	−35.2962	−1.12235
$990$	11.7929	0.374803
$991$	39.5491	1.25632	0.628160	−	0.778084i	$-0.283808\pi$
$991$	39.5491	1.25632	0.628160	+	0.778084i	$0.283808\pi$
$992$	−73.0419	−2.31908
$993$	71.7421	2.27667
$994$	−3.93241	−0.124729
$995$	35.8834	1.13758
$996$	−82.6190	−2.61788
$997$	5.76435	0.182559	0.0912794	−	0.995825i	$-0.470904\pi$
$997$	5.76435	0.182559	0.0912794	+	0.995825i	$0.470904\pi$
$998$	75.8830	2.40204
$999$	−1.98389	−0.0627674

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.o.1.1		8
13.6	odd	12		143.2.j.b.23.8	✓	16
13.11	odd	12		143.2.j.b.56.8	yes	16
13.12	even	2		1859.2.a.p.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.j.b.23.8	✓	16	13.6	odd	12
143.2.j.b.56.8	yes	16	13.11	odd	12
1859.2.a.o.1.1		8	1.1	even	1	trivial
1859.2.a.p.1.8		8	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-2.20621 q^{2} +2.48500 q^{3} +2.86737 q^{4} -1.68345 q^{5} -5.48243 q^{6} +0.336274 q^{7} -1.91361 q^{8} +3.17521 q^{9} +O(q^{10})\)	\(q-2.20621 q^{2} +2.48500 q^{3} +2.86737 q^{4} -1.68345 q^{5} -5.48243 q^{6} +0.336274 q^{7} -1.91361 q^{8} +3.17521 q^{9} +3.71405 q^{10} +1.00000 q^{11} +7.12541 q^{12} -0.741892 q^{14} -4.18337 q^{15} -1.51292 q^{16} +0.144194 q^{17} -7.00519 q^{18} -5.22231 q^{19} -4.82708 q^{20} +0.835641 q^{21} -2.20621 q^{22} -4.38689 q^{23} -4.75531 q^{24} -2.16599 q^{25} +0.435403 q^{27} +0.964223 q^{28} -2.44316 q^{29} +9.22941 q^{30} -10.1942 q^{31} +7.16504 q^{32} +2.48500 q^{33} -0.318122 q^{34} -0.566101 q^{35} +9.10452 q^{36} -4.55644 q^{37} +11.5215 q^{38} +3.22147 q^{40} +11.1758 q^{41} -1.84360 q^{42} +8.04583 q^{43} +2.86737 q^{44} -5.34532 q^{45} +9.67840 q^{46} -0.887789 q^{47} -3.75960 q^{48} -6.88692 q^{49} +4.77864 q^{50} +0.358321 q^{51} -5.33873 q^{53} -0.960592 q^{54} -1.68345 q^{55} -0.643497 q^{56} -12.9774 q^{57} +5.39013 q^{58} +11.8665 q^{59} -11.9953 q^{60} -2.40749 q^{61} +22.4906 q^{62} +1.06774 q^{63} -12.7818 q^{64} -5.48243 q^{66} -6.42376 q^{67} +0.413457 q^{68} -10.9014 q^{69} +1.24894 q^{70} +5.30052 q^{71} -6.07611 q^{72} -14.9244 q^{73} +10.0525 q^{74} -5.38249 q^{75} -14.9743 q^{76} +0.336274 q^{77} +5.95553 q^{79} +2.54693 q^{80} -8.44366 q^{81} -24.6562 q^{82} -11.5950 q^{83} +2.39609 q^{84} -0.242743 q^{85} -17.7508 q^{86} -6.07125 q^{87} -1.91361 q^{88} +7.37352 q^{89} +11.7929 q^{90} -12.5788 q^{92} -25.3326 q^{93} +1.95865 q^{94} +8.79150 q^{95} +17.8051 q^{96} +7.38121 q^{97} +15.1940 q^{98} +3.17521 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 4 q^{4} - 8 q^{5} - 4 q^{6} - 14 q^{7} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 4 * q^4 - 8 * q^5 - 4 * q^6 - 14 * q^7 + 6 * q^8 + 2 * q^9	\( 8 q - 2 q^{2} + 4 q^{4} - 8 q^{5} - 4 q^{6} - 14 q^{7} + 6 q^{8} + 2 q^{9} + 10 q^{10} + 8 q^{11} - 8 q^{12} - 6 q^{14} - 2 q^{15} + 12 q^{16} + 6 q^{17} - 6 q^{18} - 4 q^{19} - 16 q^{20} - 2 q^{21} - 2 q^{22} - 14 q^{23} - 26 q^{24} + 12 q^{25} + 24 q^{27} - 20 q^{28} - 10 q^{29} + 14 q^{30} - 32 q^{31} + 40 q^{32} - 14 q^{34} + 10 q^{35} - 24 q^{37} + 12 q^{38} - 14 q^{40} - 2 q^{41} - 2 q^{42} + 14 q^{43} + 4 q^{44} + 4 q^{45} - 14 q^{46} - 18 q^{47} - 6 q^{48} + 2 q^{49} - 38 q^{50} + 12 q^{51} - 8 q^{53} - 2 q^{54} - 8 q^{55} - 28 q^{56} - 24 q^{57} + 14 q^{58} - 18 q^{59} + 14 q^{60} - 4 q^{61} - 8 q^{63} + 6 q^{64} - 4 q^{66} + 14 q^{67} - 34 q^{68} - 10 q^{69} - 18 q^{70} + 12 q^{71} - 8 q^{72} - 26 q^{73} + 2 q^{74} - 18 q^{75} - 54 q^{76} - 14 q^{77} + 26 q^{79} - 24 q^{80} - 16 q^{81} - 64 q^{82} - 16 q^{83} + 74 q^{84} - 56 q^{85} - 32 q^{86} - 18 q^{87} + 6 q^{88} + 8 q^{89} - 20 q^{90} - 30 q^{92} - 48 q^{93} - 4 q^{94} + 22 q^{95} - 16 q^{96} - 20 q^{97} + 46 q^{98} + 2 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 4 * q^4 - 8 * q^5 - 4 * q^6 - 14 * q^7 + 6 * q^8 + 2 * q^9 + 10 * q^10 + 8 * q^11 - 8 * q^12 - 6 * q^14 - 2 * q^15 + 12 * q^16 + 6 * q^17 - 6 * q^18 - 4 * q^19 - 16 * q^20 - 2 * q^21 - 2 * q^22 - 14 * q^23 - 26 * q^24 + 12 * q^25 + 24 * q^27 - 20 * q^28 - 10 * q^29 + 14 * q^30 - 32 * q^31 + 40 * q^32 - 14 * q^34 + 10 * q^35 - 24 * q^37 + 12 * q^38 - 14 * q^40 - 2 * q^41 - 2 * q^42 + 14 * q^43 + 4 * q^44 + 4 * q^45 - 14 * q^46 - 18 * q^47 - 6 * q^48 + 2 * q^49 - 38 * q^50 + 12 * q^51 - 8 * q^53 - 2 * q^54 - 8 * q^55 - 28 * q^56 - 24 * q^57 + 14 * q^58 - 18 * q^59 + 14 * q^60 - 4 * q^61 - 8 * q^63 + 6 * q^64 - 4 * q^66 + 14 * q^67 - 34 * q^68 - 10 * q^69 - 18 * q^70 + 12 * q^71 - 8 * q^72 - 26 * q^73 + 2 * q^74 - 18 * q^75 - 54 * q^76 - 14 * q^77 + 26 * q^79 - 24 * q^80 - 16 * q^81 - 64 * q^82 - 16 * q^83 + 74 * q^84 - 56 * q^85 - 32 * q^86 - 18 * q^87 + 6 * q^88 + 8 * q^89 - 20 * q^90 - 30 * q^92 - 48 * q^93 - 4 * q^94 + 22 * q^95 - 16 * q^96 - 20 * q^97 + 46 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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