LMFDB - Embedded newform 2541.2.a.bj.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2541,2,Mod(1,2541)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2541, 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("2541.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2541 = 3 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2541.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:	$20.2899871536$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.34292$ of defining polynomial
Character	$\chi$	$=$	2541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.34292 q^{2} +1.00000 q^{3} +3.48929 q^{4} -0.146365 q^{5} +2.34292 q^{6} +1.00000 q^{7} +3.48929 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.34292 q^{2} +1.00000 q^{3} +3.48929 q^{4} -0.146365 q^{5} +2.34292 q^{6} +1.00000 q^{7} +3.48929 q^{8} +1.00000 q^{9} -0.342923 q^{10} +3.48929 q^{12} +4.34292 q^{13} +2.34292 q^{14} -0.146365 q^{15} +1.19656 q^{16} -0.146365 q^{17} +2.34292 q^{18} -1.83221 q^{19} -0.510711 q^{20} +1.00000 q^{21} +8.81079 q^{23} +3.48929 q^{24} -4.97858 q^{25} +10.1751 q^{26} +1.00000 q^{27} +3.48929 q^{28} +4.34292 q^{29} -0.342923 q^{30} +0.292731 q^{31} -4.17513 q^{32} -0.342923 q^{34} -0.146365 q^{35} +3.48929 q^{36} -3.48929 q^{37} -4.29273 q^{38} +4.34292 q^{39} -0.510711 q^{40} +2.80344 q^{41} +2.34292 q^{42} -7.86098 q^{43} -0.146365 q^{45} +20.6430 q^{46} -0.949808 q^{47} +1.19656 q^{48} +1.00000 q^{49} -11.6644 q^{50} -0.146365 q^{51} +15.1537 q^{52} -4.51071 q^{53} +2.34292 q^{54} +3.48929 q^{56} -1.83221 q^{57} +10.1751 q^{58} +8.02877 q^{59} -0.510711 q^{60} +5.43910 q^{61} +0.685846 q^{62} +1.00000 q^{63} -12.1751 q^{64} -0.635654 q^{65} -7.76060 q^{67} -0.510711 q^{68} +8.81079 q^{69} -0.342923 q^{70} -3.53948 q^{71} +3.48929 q^{72} +16.1825 q^{73} -8.17513 q^{74} -4.97858 q^{75} -6.39312 q^{76} +10.1751 q^{78} +13.0790 q^{79} -0.175135 q^{80} +1.00000 q^{81} +6.56825 q^{82} -12.9070 q^{83} +3.48929 q^{84} +0.0214229 q^{85} -18.4177 q^{86} +4.34292 q^{87} -9.81079 q^{89} -0.342923 q^{90} +4.34292 q^{91} +30.7434 q^{92} +0.292731 q^{93} -2.22533 q^{94} +0.268173 q^{95} -4.17513 q^{96} -17.4219 q^{97} +2.34292 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} + 3 q^{3} + 3 q^{4} + q^{5} + q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + q^2 + 3 * q^3 + 3 * q^4 + q^5 + q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + q^{2} + 3 q^{3} + 3 q^{4} + q^{5} + q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9} + 5 q^{10} + 3 q^{12} + 7 q^{13} + q^{14} + q^{15} - q^{16} + q^{17} + q^{18} + 8 q^{19} - 9 q^{20} + 3 q^{21} - 2 q^{23} + 3 q^{24} + 11 q^{26} + 3 q^{27} + 3 q^{28} + 7 q^{29} + 5 q^{30} - 2 q^{31} + 7 q^{32} + 5 q^{34} + q^{35} + 3 q^{36} - 3 q^{37} - 10 q^{38} + 7 q^{39} - 9 q^{40} + 13 q^{41} + q^{42} + 8 q^{43} + q^{45} + 20 q^{46} - 6 q^{47} - q^{48} + 3 q^{49} - 8 q^{50} + q^{51} + 11 q^{52} - 21 q^{53} + q^{54} + 3 q^{56} + 8 q^{57} + 11 q^{58} + 6 q^{59} - 9 q^{60} + 12 q^{61} - 10 q^{62} + 3 q^{63} - 17 q^{64} + 7 q^{65} + 2 q^{67} - 9 q^{68} - 2 q^{69} + 5 q^{70} + 3 q^{72} - 4 q^{73} - 5 q^{74} - 10 q^{76} + 11 q^{78} + 18 q^{79} + 19 q^{80} + 3 q^{81} - 9 q^{82} - 12 q^{83} + 3 q^{84} + 15 q^{85} - 36 q^{86} + 7 q^{87} - q^{89} + 5 q^{90} + 7 q^{91} + 44 q^{92} - 2 q^{93} + 16 q^{94} + 8 q^{95} + 7 q^{96} - 25 q^{97} + q^{98}+O(q^{100}) $ 3 * q + q^2 + 3 * q^3 + 3 * q^4 + q^5 + q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9 + 5 * q^10 + 3 * q^12 + 7 * q^13 + q^14 + q^15 - q^16 + q^17 + q^18 + 8 * q^19 - 9 * q^20 + 3 * q^21 - 2 * q^23 + 3 * q^24 + 11 * q^26 + 3 * q^27 + 3 * q^28 + 7 * q^29 + 5 * q^30 - 2 * q^31 + 7 * q^32 + 5 * q^34 + q^35 + 3 * q^36 - 3 * q^37 - 10 * q^38 + 7 * q^39 - 9 * q^40 + 13 * q^41 + q^42 + 8 * q^43 + q^45 + 20 * q^46 - 6 * q^47 - q^48 + 3 * q^49 - 8 * q^50 + q^51 + 11 * q^52 - 21 * q^53 + q^54 + 3 * q^56 + 8 * q^57 + 11 * q^58 + 6 * q^59 - 9 * q^60 + 12 * q^61 - 10 * q^62 + 3 * q^63 - 17 * q^64 + 7 * q^65 + 2 * q^67 - 9 * q^68 - 2 * q^69 + 5 * q^70 + 3 * q^72 - 4 * q^73 - 5 * q^74 - 10 * q^76 + 11 * q^78 + 18 * q^79 + 19 * q^80 + 3 * q^81 - 9 * q^82 - 12 * q^83 + 3 * q^84 + 15 * q^85 - 36 * q^86 + 7 * q^87 - q^89 + 5 * q^90 + 7 * q^91 + 44 * q^92 - 2 * q^93 + 16 * q^94 + 8 * q^95 + 7 * q^96 - 25 * q^97 + q^98

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 $

$2$	2.34292	1.65670	0.828348	−	0.560213i	$-0.189281\pi$
$2$	2.34292	1.65670	0.828348	+	0.560213i	$0.189281\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.48929	1.74464
$5$	−0.146365	−0.0654566	−0.0327283	−	0.999464i	$-0.510420\pi$
$5$	−0.146365	−0.0654566	−0.0327283	+	0.999464i	$0.510420\pi$
$6$	2.34292	0.956494
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	3.48929	1.23365
$9$	1.00000	0.333333
$10$	−0.342923	−0.108442
$11$	0	0
$11$	0	0
$12$	3.48929	1.00727
$13$	4.34292	1.20451	0.602255	−	0.798304i	$-0.294269\pi$
$13$	4.34292	1.20451	0.602255	+	0.798304i	$0.294269\pi$
$14$	2.34292	0.626173
$15$	−0.146365	−0.0377914
$16$	1.19656	0.299139
$17$	−0.146365	−0.0354988	−0.0177494	−	0.999842i	$-0.505650\pi$
$17$	−0.146365	−0.0354988	−0.0177494	+	0.999842i	$0.505650\pi$
$18$	2.34292	0.552232
$19$	−1.83221	−0.420338	−0.210169	−	0.977665i	$-0.567401\pi$
$19$	−1.83221	−0.420338	−0.210169	+	0.977665i	$0.567401\pi$
$20$	−0.510711	−0.114199
$21$	1.00000	0.218218
$22$	0	0
$23$	8.81079	1.83718	0.918588	−	0.395216i	$-0.129330\pi$
$23$	8.81079	1.83718	0.918588	+	0.395216i	$0.129330\pi$
$24$	3.48929	0.712248
$25$	−4.97858	−0.995715
$26$	10.1751	1.99551
$27$	1.00000	0.192450
$28$	3.48929	0.659414
$29$	4.34292	0.806461	0.403230	−	0.915099i	$-0.367887\pi$
$29$	4.34292	0.806461	0.403230	+	0.915099i	$0.367887\pi$
$30$	−0.342923	−0.0626089
$31$	0.292731	0.0525760	0.0262880	−	0.999654i	$-0.491631\pi$
$31$	0.292731	0.0525760	0.0262880	+	0.999654i	$0.491631\pi$
$32$	−4.17513	−0.738067
$33$	0	0
$34$	−0.342923	−0.0588108
$35$	−0.146365	−0.0247403
$36$	3.48929	0.581548
$37$	−3.48929	−0.573636	−0.286818	−	0.957985i	$-0.592597\pi$
$37$	−3.48929	−0.573636	−0.286818	+	0.957985i	$0.592597\pi$
$38$	−4.29273	−0.696373
$39$	4.34292	0.695424
$40$	−0.510711	−0.0807506
$41$	2.80344	0.437824	0.218912	−	0.975745i	$-0.429749\pi$
$41$	2.80344	0.437824	0.218912	+	0.975745i	$0.429749\pi$
$42$	2.34292	0.361521
$43$	−7.86098	−1.19879	−0.599394	−	0.800454i	$-0.704592\pi$
$43$	−7.86098	−1.19879	−0.599394	+	0.800454i	$0.704592\pi$
$44$	0	0
$45$	−0.146365	−0.0218189
$46$	20.6430	3.04364
$47$	−0.949808	−0.138544	−0.0692719	−	0.997598i	$-0.522068\pi$
$47$	−0.949808	−0.138544	−0.0692719	+	0.997598i	$0.522068\pi$
$48$	1.19656	0.172708
$49$	1.00000	0.142857
$50$	−11.6644	−1.64960
$51$	−0.146365	−0.0204953
$52$	15.1537	2.10144
$53$	−4.51071	−0.619594	−0.309797	−	0.950803i	$-0.600261\pi$
$53$	−4.51071	−0.619594	−0.309797	+	0.950803i	$0.600261\pi$
$54$	2.34292	0.318831
$55$	0	0
$56$	3.48929	0.466276
$57$	−1.83221	−0.242682
$58$	10.1751	1.33606
$59$	8.02877	1.04526	0.522628	−	0.852561i	$-0.324952\pi$
$59$	8.02877	1.04526	0.522628	+	0.852561i	$0.324952\pi$
$60$	−0.510711	−0.0659326
$61$	5.43910	0.696405	0.348202	−	0.937419i	$-0.386792\pi$
$61$	5.43910	0.696405	0.348202	+	0.937419i	$0.386792\pi$
$62$	0.685846	0.0871026
$63$	1.00000	0.125988
$64$	−12.1751	−1.52189
$65$	−0.635654	−0.0788432
$66$	0	0
$67$	−7.76060	−0.948108	−0.474054	−	0.880496i	$-0.657210\pi$
$67$	−7.76060	−0.948108	−0.474054	+	0.880496i	$0.657210\pi$
$68$	−0.510711	−0.0619329
$69$	8.81079	1.06069
$70$	−0.342923	−0.0409871
$71$	−3.53948	−0.420059	−0.210030	−	0.977695i	$-0.567356\pi$
$71$	−3.53948	−0.420059	−0.210030	+	0.977695i	$0.567356\pi$
$72$	3.48929	0.411217
$73$	16.1825	1.89402	0.947008	−	0.321210i	$-0.104089\pi$
$73$	16.1825	1.89402	0.947008	+	0.321210i	$0.104089\pi$
$74$	−8.17513	−0.950340
$75$	−4.97858	−0.574877
$76$	−6.39312	−0.733341
$77$	0	0
$78$	10.1751	1.15211
$79$	13.0790	1.47150	0.735749	−	0.677254i	$-0.236830\pi$
$79$	13.0790	1.47150	0.735749	+	0.677254i	$0.236830\pi$
$80$	−0.175135	−0.0195807
$81$	1.00000	0.111111
$82$	6.56825	0.725342
$83$	−12.9070	−1.41672	−0.708362	−	0.705850i	$-0.750565\pi$
$83$	−12.9070	−1.41672	−0.708362	+	0.705850i	$0.750565\pi$
$84$	3.48929	0.380713
$85$	0.0214229	0.00232364
$86$	−18.4177	−1.98603
$87$	4.34292	0.465610
$88$	0	0
$89$	−9.81079	−1.03994	−0.519971	−	0.854184i	$-0.674057\pi$
$89$	−9.81079	−1.03994	−0.519971	+	0.854184i	$0.674057\pi$
$90$	−0.342923	−0.0361473
$91$	4.34292	0.455262
$92$	30.7434	3.20522
$93$	0.292731	0.0303548
$94$	−2.22533	−0.229525
$95$	0.268173	0.0275139
$96$	−4.17513	−0.426123
$97$	−17.4219	−1.76892	−0.884462	−	0.466612i	$-0.845474\pi$
$97$	−17.4219	−1.76892	−0.884462	+	0.466612i	$0.845474\pi$
$98$	2.34292	0.236671
$99$	0	0
$100$	−17.3717	−1.73717
$101$	−15.6357	−1.55581	−0.777903	−	0.628385i	$-0.783716\pi$
$101$	−15.6357	−1.55581	−0.777903	+	0.628385i	$0.783716\pi$
$102$	−0.342923	−0.0339544
$103$	4.16779	0.410664	0.205332	−	0.978692i	$-0.434173\pi$
$103$	4.16779	0.410664	0.205332	+	0.978692i	$0.434173\pi$
$104$	15.1537	1.48594
$105$	−0.146365	−0.0142838
$106$	−10.5682	−1.02648
$107$	−5.49663	−0.531380	−0.265690	−	0.964059i	$-0.585600\pi$
$107$	−5.49663	−0.531380	−0.265690	+	0.964059i	$0.585600\pi$
$108$	3.48929	0.335757
$109$	5.87819	0.563029	0.281514	−	0.959557i	$-0.409163\pi$
$109$	5.87819	0.563029	0.281514	+	0.959557i	$0.409163\pi$
$110$	0	0
$111$	−3.48929	−0.331189
$112$	1.19656	0.113064
$113$	−3.88240	−0.365226	−0.182613	−	0.983185i	$-0.558456\pi$
$113$	−3.88240	−0.365226	−0.182613	+	0.983185i	$0.558456\pi$
$114$	−4.29273	−0.402051
$115$	−1.28960	−0.120255
$116$	15.1537	1.40699
$117$	4.34292	0.401503
$118$	18.8108	1.73167
$119$	−0.146365	−0.0134173
$120$	−0.510711	−0.0466214
$121$	0	0
$122$	12.7434	1.15373
$123$	2.80344	0.252778
$124$	1.02142	0.0917265
$125$	1.46052	0.130633
$126$	2.34292	0.208724
$127$	−17.6686	−1.56784	−0.783919	−	0.620863i	$-0.786782\pi$
$127$	−17.6686	−1.56784	−0.783919	+	0.620863i	$0.786782\pi$
$128$	−20.1751	−1.78325
$129$	−7.86098	−0.692121
$130$	−1.48929	−0.130619
$131$	18.0288	1.57518	0.787590	−	0.616199i	$-0.211328\pi$
$131$	18.0288	1.57518	0.787590	+	0.616199i	$0.211328\pi$
$132$	0	0
$133$	−1.83221	−0.158873
$134$	−18.1825	−1.57073
$135$	−0.146365	−0.0125971
$136$	−0.510711	−0.0437931
$137$	−21.5542	−1.84150	−0.920749	−	0.390156i	$-0.872421\pi$
$137$	−21.5542	−1.84150	−0.920749	+	0.390156i	$0.872421\pi$
$138$	20.6430	1.75725
$139$	13.5395	1.14840	0.574202	−	0.818714i	$-0.305312\pi$
$139$	13.5395	1.14840	0.574202	+	0.818714i	$0.305312\pi$
$140$	−0.510711	−0.0431630
$141$	−0.949808	−0.0799883
$142$	−8.29273	−0.695911
$143$	0	0
$144$	1.19656	0.0997131
$145$	−0.635654	−0.0527882
$146$	37.9143	3.13781
$147$	1.00000	0.0824786
$148$	−12.1751	−1.00079
$149$	10.3001	0.843815	0.421908	−	0.906639i	$-0.361361\pi$
$149$	10.3001	0.843815	0.421908	+	0.906639i	$0.361361\pi$
$150$	−11.6644	−0.952396
$151$	1.31836	0.107287	0.0536435	−	0.998560i	$-0.482917\pi$
$151$	1.31836	0.107287	0.0536435	+	0.998560i	$0.482917\pi$
$152$	−6.39312	−0.518550
$153$	−0.146365	−0.0118329
$154$	0	0
$155$	−0.0428457	−0.00344145
$156$	15.1537	1.21327
$157$	9.85677	0.786656	0.393328	−	0.919398i	$-0.371324\pi$
$157$	9.85677	0.786656	0.393328	+	0.919398i	$0.371324\pi$
$158$	30.6430	2.43783
$159$	−4.51071	−0.357723
$160$	0.611096	0.0483114
$161$	8.81079	0.694387
$162$	2.34292	0.184077
$163$	−0.292731	−0.0229285	−0.0114642	−	0.999934i	$-0.503649\pi$
$163$	−0.292731	−0.0229285	−0.0114642	+	0.999934i	$0.503649\pi$
$164$	9.78202	0.763847
$165$	0	0
$166$	−30.2400	−2.34708
$167$	−15.7360	−1.21769	−0.608846	−	0.793289i	$-0.708367\pi$
$167$	−15.7360	−1.21769	−0.608846	+	0.793289i	$0.708367\pi$
$168$	3.48929	0.269204
$169$	5.86098	0.450845
$170$	0.0501921	0.00384956
$171$	−1.83221	−0.140113
$172$	−27.4292	−2.09146
$173$	−17.7360	−1.34845	−0.674223	−	0.738528i	$-0.735521\pi$
$173$	−17.7360	−1.34845	−0.674223	+	0.738528i	$0.735521\pi$
$174$	10.1751	0.771375
$175$	−4.97858	−0.376345
$176$	0	0
$177$	8.02877	0.603479
$178$	−22.9859	−1.72287
$179$	−23.2285	−1.73618	−0.868088	−	0.496410i	$-0.834651\pi$
$179$	−23.2285	−1.73618	−0.868088	+	0.496410i	$0.834651\pi$
$180$	−0.510711	−0.0380662
$181$	25.1109	1.86648	0.933238	−	0.359259i	$-0.116970\pi$
$181$	25.1109	1.86648	0.933238	+	0.359259i	$0.116970\pi$
$182$	10.1751	0.754231
$183$	5.43910	0.402070
$184$	30.7434	2.26643
$185$	0.510711	0.0375483
$186$	0.685846	0.0502887
$187$	0	0
$188$	−3.31415	−0.241710
$189$	1.00000	0.0727393
$190$	0.628308	0.0455822
$191$	−17.8898	−1.29446	−0.647228	−	0.762296i	$-0.724072\pi$
$191$	−17.8898	−1.29446	−0.647228	+	0.762296i	$0.724072\pi$
$192$	−12.1751	−0.878665
$193$	−10.3288	−0.743487	−0.371743	−	0.928336i	$-0.621240\pi$
$193$	−10.3288	−0.743487	−0.371743	+	0.928336i	$0.621240\pi$
$194$	−40.8181	−2.93057
$195$	−0.635654	−0.0455201
$196$	3.48929	0.249235
$197$	14.8610	1.05880	0.529401	−	0.848372i	$-0.322417\pi$
$197$	14.8610	1.05880	0.529401	+	0.848372i	$0.322417\pi$
$198$	0	0
$199$	0.0674041	0.00477815	0.00238908	−	0.999997i	$-0.499240\pi$
$199$	0.0674041	0.00477815	0.00238908	+	0.999997i	$0.499240\pi$
$200$	−17.3717	−1.22836
$201$	−7.76060	−0.547390
$202$	−36.6331	−2.57750
$203$	4.34292	0.304813
$204$	−0.510711	−0.0357570
$205$	−0.410327	−0.0286585
$206$	9.76481	0.680346
$207$	8.81079	0.612392
$208$	5.19656	0.360316
$209$	0	0
$210$	−0.342923	−0.0236639
$211$	−13.1323	−0.904064	−0.452032	−	0.892002i	$-0.649301\pi$
$211$	−13.1323	−0.904064	−0.452032	+	0.892002i	$0.649301\pi$
$212$	−15.7392	−1.08097
$213$	−3.53948	−0.242521
$214$	−12.8782	−0.880335
$215$	1.15058	0.0784687
$216$	3.48929	0.237416
$217$	0.292731	0.0198719
$218$	13.7722	0.932768
$219$	16.1825	1.09351
$220$	0	0
$221$	−0.635654	−0.0427587
$222$	−8.17513	−0.548679
$223$	5.37169	0.359715	0.179858	−	0.983693i	$-0.442436\pi$
$223$	5.37169	0.359715	0.179858	+	0.983693i	$0.442436\pi$
$224$	−4.17513	−0.278963
$225$	−4.97858	−0.331905
$226$	−9.09617	−0.605068
$227$	−6.85785	−0.455171	−0.227586	−	0.973758i	$-0.573083\pi$
$227$	−6.85785	−0.455171	−0.227586	+	0.973758i	$0.573083\pi$
$228$	−6.39312	−0.423394
$229$	−8.76060	−0.578917	−0.289458	−	0.957191i	$-0.593475\pi$
$229$	−8.76060	−0.578917	−0.289458	+	0.957191i	$0.593475\pi$
$230$	−3.02142	−0.199227
$231$	0	0
$232$	15.1537	0.994890
$233$	1.36435	0.0893813	0.0446906	−	0.999001i	$-0.485770\pi$
$233$	1.36435	0.0893813	0.0446906	+	0.999001i	$0.485770\pi$
$234$	10.1751	0.665169
$235$	0.139019	0.00906861
$236$	28.0147	1.82360
$237$	13.0790	0.849570
$238$	−0.342923	−0.0222284
$239$	4.97858	0.322037	0.161019	−	0.986951i	$-0.448522\pi$
$239$	4.97858	0.322037	0.161019	+	0.986951i	$0.448522\pi$
$240$	−0.175135	−0.0113049
$241$	14.1678	0.912627	0.456314	−	0.889819i	$-0.349169\pi$
$241$	14.1678	0.912627	0.456314	+	0.889819i	$0.349169\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	18.9786	1.21498
$245$	−0.146365	−0.00935095
$246$	6.56825	0.418776
$247$	−7.95715	−0.506302
$248$	1.02142	0.0648604
$249$	−12.9070	−0.817945
$250$	3.42188	0.216419
$251$	−2.82908	−0.178570	−0.0892848	−	0.996006i	$-0.528458\pi$
$251$	−2.82908	−0.178570	−0.0892848	+	0.996006i	$0.528458\pi$
$252$	3.48929	0.219805
$253$	0	0
$254$	−41.3963	−2.59743
$255$	0.0214229	0.00134155
$256$	−22.9185	−1.43241
$257$	−22.9901	−1.43409	−0.717043	−	0.697029i	$-0.754505\pi$
$257$	−22.9901	−1.43409	−0.717043	+	0.697029i	$0.754505\pi$
$258$	−18.4177	−1.14663
$259$	−3.48929	−0.216814
$260$	−2.21798	−0.137553
$261$	4.34292	0.268820
$262$	42.2400	2.60960
$263$	3.63986	0.224444	0.112222	−	0.993683i	$-0.464203\pi$
$263$	3.63986	0.224444	0.112222	+	0.993683i	$0.464203\pi$
$264$	0	0
$265$	0.660212	0.0405565
$266$	−4.29273	−0.263204
$267$	−9.81079	−0.600411
$268$	−27.0790	−1.65411
$269$	−7.54683	−0.460138	−0.230069	−	0.973174i	$-0.573895\pi$
$269$	−7.54683	−0.460138	−0.230069	+	0.973174i	$0.573895\pi$
$270$	−0.342923	−0.0208696
$271$	23.6644	1.43751	0.718756	−	0.695263i	$-0.244712\pi$
$271$	23.6644	1.43751	0.718756	+	0.695263i	$0.244712\pi$
$272$	−0.175135	−0.0106191
$273$	4.34292	0.262846
$274$	−50.4998	−3.05080
$275$	0	0
$276$	30.7434	1.85053
$277$	31.8929	1.91626	0.958129	−	0.286337i	$-0.0924378\pi$
$277$	31.8929	1.91626	0.958129	+	0.286337i	$0.0924378\pi$
$278$	31.7220	1.90256
$279$	0.292731	0.0175253
$280$	−0.510711	−0.0305208
$281$	−30.5082	−1.81997	−0.909983	−	0.414645i	$-0.863906\pi$
$281$	−30.5082	−1.81997	−0.909983	+	0.414645i	$0.863906\pi$
$282$	−2.22533	−0.132516
$283$	22.6430	1.34599	0.672993	−	0.739649i	$-0.265008\pi$
$283$	22.6430	1.34599	0.672993	+	0.739649i	$0.265008\pi$
$284$	−12.3503	−0.732854
$285$	0.268173	0.0158852
$286$	0	0
$287$	2.80344	0.165482
$288$	−4.17513	−0.246022
$289$	−16.9786	−0.998740
$290$	−1.48929	−0.0874540
$291$	−17.4219	−1.02129
$292$	56.4653	3.30438
$293$	−1.81079	−0.105787	−0.0528937	−	0.998600i	$-0.516844\pi$
$293$	−1.81079	−0.105787	−0.0528937	+	0.998600i	$0.516844\pi$
$294$	2.34292	0.136642
$295$	−1.17513	−0.0684190
$296$	−12.1751	−0.707665
$297$	0	0
$298$	24.1323	1.39795
$299$	38.2646	2.21290
$300$	−17.3717	−1.00296
$301$	−7.86098	−0.453099
$302$	3.08883	0.177742
$303$	−15.6357	−0.898245
$304$	−2.19235	−0.125740
$305$	−0.796096	−0.0455843
$306$	−0.342923	−0.0196036
$307$	29.8469	1.70345	0.851726	−	0.523987i	$-0.175556\pi$
$307$	29.8469	1.70345	0.851726	+	0.523987i	$0.175556\pi$
$308$	0	0
$309$	4.16779	0.237097
$310$	−0.100384	−0.00570144
$311$	−5.09304	−0.288800	−0.144400	−	0.989519i	$-0.546125\pi$
$311$	−5.09304	−0.288800	−0.144400	+	0.989519i	$0.546125\pi$
$312$	15.1537	0.857910
$313$	−22.0319	−1.24532	−0.622658	−	0.782494i	$-0.713947\pi$
$313$	−22.0319	−1.24532	−0.622658	+	0.782494i	$0.713947\pi$
$314$	23.0937	1.30325
$315$	−0.146365	−0.00824676
$316$	45.6363	2.56724
$317$	−7.08883	−0.398148	−0.199074	−	0.979984i	$-0.563793\pi$
$317$	−7.08883	−0.398148	−0.199074	+	0.979984i	$0.563793\pi$
$318$	−10.5682	−0.592638
$319$	0	0
$320$	1.78202	0.0996179
$321$	−5.49663	−0.306792
$322$	20.6430	1.15039
$323$	0.268173	0.0149215
$324$	3.48929	0.193849
$325$	−21.6216	−1.19935
$326$	−0.685846	−0.0379855
$327$	5.87819	0.325065
$328$	9.78202	0.540122
$329$	−0.949808	−0.0523646
$330$	0	0
$331$	−34.6044	−1.90203	−0.951014	−	0.309148i	$-0.899956\pi$
$331$	−34.6044	−1.90203	−0.951014	+	0.309148i	$0.899956\pi$
$332$	−45.0361	−2.47168
$333$	−3.48929	−0.191212
$334$	−36.8683	−2.01735
$335$	1.13588	0.0620599
$336$	1.19656	0.0652776
$337$	−12.5254	−0.682302	−0.341151	−	0.940008i	$-0.610817\pi$
$337$	−12.5254	−0.682302	−0.341151	+	0.940008i	$0.610817\pi$
$338$	13.7318	0.746913
$339$	−3.88240	−0.210863
$340$	0.0747505	0.00405392
$341$	0	0
$342$	−4.29273	−0.232124
$343$	1.00000	0.0539949
$344$	−27.4292	−1.47889
$345$	−1.28960	−0.0694295
$346$	−41.5542	−2.23397
$347$	27.6461	1.48412	0.742061	−	0.670332i	$-0.233848\pi$
$347$	27.6461	1.48412	0.742061	+	0.670332i	$0.233848\pi$
$348$	15.1537	0.812324
$349$	−11.2969	−0.604711	−0.302356	−	0.953195i	$-0.597773\pi$
$349$	−11.2969	−0.604711	−0.302356	+	0.953195i	$0.597773\pi$
$350$	−11.6644	−0.623490
$351$	4.34292	0.231808
$352$	0	0
$353$	16.8034	0.894357	0.447178	−	0.894445i	$-0.352429\pi$
$353$	16.8034	0.894357	0.447178	+	0.894445i	$0.352429\pi$
$354$	18.8108	0.999782
$355$	0.518058	0.0274957
$356$	−34.2327	−1.81433
$357$	−0.146365	−0.00774648
$358$	−54.4225	−2.87632
$359$	29.0607	1.53376	0.766882	−	0.641788i	$-0.221807\pi$
$359$	29.0607	1.53376	0.766882	+	0.641788i	$0.221807\pi$
$360$	−0.510711	−0.0269169
$361$	−15.6430	−0.823316
$362$	58.8328	3.09218
$363$	0	0
$364$	15.1537	0.794270
$365$	−2.36856	−0.123976
$366$	12.7434	0.666107
$367$	17.6974	0.923797	0.461898	−	0.886933i	$-0.347168\pi$
$367$	17.6974	0.923797	0.461898	+	0.886933i	$0.347168\pi$
$368$	10.5426	0.549572
$369$	2.80344	0.145941
$370$	1.19656	0.0622061
$371$	−4.51071	−0.234184
$372$	1.02142	0.0529583
$373$	−12.7820	−0.661828	−0.330914	−	0.943661i	$-0.607357\pi$
$373$	−12.7820	−0.661828	−0.330914	+	0.943661i	$0.607357\pi$
$374$	0	0
$375$	1.46052	0.0754209
$376$	−3.31415	−0.170914
$377$	18.8610	0.971390
$378$	2.34292	0.120507
$379$	−19.6258	−1.00811	−0.504055	−	0.863672i	$-0.668159\pi$
$379$	−19.6258	−1.00811	−0.504055	+	0.863672i	$0.668159\pi$
$380$	0.935731	0.0480020
$381$	−17.6686	−0.905192
$382$	−41.9143	−2.14452
$383$	29.5500	1.50993	0.754966	−	0.655764i	$-0.227653\pi$
$383$	29.5500	1.50993	0.754966	+	0.655764i	$0.227653\pi$
$384$	−20.1751	−1.02956
$385$	0	0
$386$	−24.1997	−1.23173
$387$	−7.86098	−0.399596
$388$	−60.7900	−3.08614
$389$	−13.0962	−0.664002	−0.332001	−	0.943279i	$-0.607724\pi$
$389$	−13.0962	−0.664002	−0.332001	+	0.943279i	$0.607724\pi$
$390$	−1.48929	−0.0754131
$391$	−1.28960	−0.0652176
$392$	3.48929	0.176236
$393$	18.0288	0.909431
$394$	34.8181	1.75411
$395$	−1.91431	−0.0963193
$396$	0	0
$397$	24.4679	1.22801	0.614003	−	0.789303i	$-0.289558\pi$
$397$	24.4679	1.22801	0.614003	+	0.789303i	$0.289558\pi$
$398$	0.157923	0.00791595
$399$	−1.83221	−0.0917253
$400$	−5.95715	−0.297858
$401$	24.1751	1.20725	0.603624	−	0.797269i	$-0.293723\pi$
$401$	24.1751	1.20725	0.603624	+	0.797269i	$0.293723\pi$
$402$	−18.1825	−0.906860
$403$	1.27131	0.0633284
$404$	−54.5573	−2.71433
$405$	−0.146365	−0.00727296
$406$	10.1751	0.504983
$407$	0	0
$408$	−0.510711	−0.0252840
$409$	5.22112	0.258168	0.129084	−	0.991634i	$-0.458796\pi$
$409$	5.22112	0.258168	0.129084	+	0.991634i	$0.458796\pi$
$410$	−0.961365	−0.0474784
$411$	−21.5542	−1.06319
$412$	14.5426	0.716463
$413$	8.02877	0.395070
$414$	20.6430	1.01455
$415$	1.88913	0.0927339
$416$	−18.1323	−0.889009
$417$	13.5395	0.663031
$418$	0	0
$419$	−22.6718	−1.10759	−0.553794	−	0.832654i	$-0.686821\pi$
$419$	−22.6718	−1.10759	−0.553794	+	0.832654i	$0.686821\pi$
$420$	−0.510711	−0.0249202
$421$	−2.41454	−0.117677	−0.0588387	−	0.998268i	$-0.518740\pi$
$421$	−2.41454	−0.117677	−0.0588387	+	0.998268i	$0.518740\pi$
$422$	−30.7679	−1.49776
$423$	−0.949808	−0.0461812
$424$	−15.7392	−0.764362
$425$	0.728692	0.0353467
$426$	−8.29273	−0.401784
$427$	5.43910	0.263216
$428$	−19.1793	−0.927069
$429$	0	0
$430$	2.69571	0.129999
$431$	−1.35700	−0.0653644	−0.0326822	−	0.999466i	$-0.510405\pi$
$431$	−1.35700	−0.0653644	−0.0326822	+	0.999466i	$0.510405\pi$
$432$	1.19656	0.0575694
$433$	20.6503	0.992392	0.496196	−	0.868210i	$-0.334730\pi$
$433$	20.6503	0.992392	0.496196	+	0.868210i	$0.334730\pi$
$434$	0.685846	0.0329217
$435$	−0.635654	−0.0304773
$436$	20.5107	0.982285
$437$	−16.1432	−0.772235
$438$	37.9143	1.81162
$439$	−20.3074	−0.969220	−0.484610	−	0.874730i	$-0.661039\pi$
$439$	−20.3074	−0.969220	−0.484610	+	0.874730i	$0.661039\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	−1.48929	−0.0708382
$443$	−9.81752	−0.466444	−0.233222	−	0.972423i	$-0.574927\pi$
$443$	−9.81752	−0.466444	−0.233222	+	0.972423i	$0.574927\pi$
$444$	−12.1751	−0.577806
$445$	1.43596	0.0680711
$446$	12.5855	0.595939
$447$	10.3001	0.487177
$448$	−12.1751	−0.575221
$449$	10.0748	0.475457	0.237728	−	0.971332i	$-0.423597\pi$
$449$	10.0748	0.475457	0.237728	+	0.971332i	$0.423597\pi$
$450$	−11.6644	−0.549866
$451$	0	0
$452$	−13.5468	−0.637189
$453$	1.31836	0.0619422
$454$	−16.0674	−0.754081
$455$	−0.635654	−0.0297999
$456$	−6.39312	−0.299385
$457$	14.6791	0.686660	0.343330	−	0.939215i	$-0.388445\pi$
$457$	14.6791	0.686660	0.343330	+	0.939215i	$0.388445\pi$
$458$	−20.5254	−0.959089
$459$	−0.146365	−0.00683176
$460$	−4.49977	−0.209803
$461$	27.1396	1.26402	0.632009	−	0.774961i	$-0.282230\pi$
$461$	27.1396	1.26402	0.632009	+	0.774961i	$0.282230\pi$
$462$	0	0
$463$	23.2369	1.07991	0.539955	−	0.841694i	$-0.318441\pi$
$463$	23.2369	1.07991	0.539955	+	0.841694i	$0.318441\pi$
$464$	5.19656	0.241244
$465$	−0.0428457	−0.00198692
$466$	3.19656	0.148078
$467$	23.8568	1.10396	0.551980	−	0.833857i	$-0.313873\pi$
$467$	23.8568	1.10396	0.551980	+	0.833857i	$0.313873\pi$
$468$	15.1537	0.700481
$469$	−7.76060	−0.358351
$470$	0.325711	0.0150239
$471$	9.85677	0.454176
$472$	28.0147	1.28948
$473$	0	0
$474$	30.6430	1.40748
$475$	9.12181	0.418537
$476$	−0.510711	−0.0234084
$477$	−4.51071	−0.206531
$478$	11.6644	0.533518
$479$	−17.2081	−0.786259	−0.393129	−	0.919483i	$-0.628608\pi$
$479$	−17.2081	−0.786259	−0.393129	+	0.919483i	$0.628608\pi$
$480$	0.611096	0.0278926
$481$	−15.1537	−0.690950
$482$	33.1940	1.51195
$483$	8.81079	0.400905
$484$	0	0
$485$	2.54996	0.115788
$486$	2.34292	0.106277
$487$	−3.16044	−0.143213	−0.0716066	−	0.997433i	$-0.522813\pi$
$487$	−3.16044	−0.143213	−0.0716066	+	0.997433i	$0.522813\pi$
$488$	18.9786	0.859120
$489$	−0.292731	−0.0132378
$490$	−0.342923	−0.0154917
$491$	4.22533	0.190686	0.0953432	−	0.995444i	$-0.469605\pi$
$491$	4.22533	0.190686	0.0953432	+	0.995444i	$0.469605\pi$
$492$	9.78202	0.441007
$493$	−0.635654	−0.0286284
$494$	−18.6430	−0.838788
$495$	0	0
$496$	0.350269	0.0157276
$497$	−3.53948	−0.158767
$498$	−30.2400	−1.35509
$499$	30.5615	1.36812	0.684061	−	0.729425i	$-0.260212\pi$
$499$	30.5615	1.36812	0.684061	+	0.729425i	$0.260212\pi$
$500$	5.09617	0.227908
$501$	−15.7360	−0.703034
$502$	−6.62831	−0.295836
$503$	−0.513847	−0.0229113	−0.0114557	−	0.999934i	$-0.503647\pi$
$503$	−0.513847	−0.0229113	−0.0114557	+	0.999934i	$0.503647\pi$
$504$	3.48929	0.155425
$505$	2.28852	0.101838
$506$	0	0
$507$	5.86098	0.260295
$508$	−61.6510	−2.73532
$509$	24.9217	1.10463	0.552316	−	0.833635i	$-0.313744\pi$
$509$	24.9217	1.10463	0.552316	+	0.833635i	$0.313744\pi$
$510$	0.0501921	0.00222254
$511$	16.1825	0.715871
$512$	−13.3461	−0.589818
$513$	−1.83221	−0.0808941
$514$	−53.8641	−2.37584
$515$	−0.610020	−0.0268807
$516$	−27.4292	−1.20750
$517$	0	0
$518$	−8.17513	−0.359195
$519$	−17.7360	−0.778526
$520$	−2.21798	−0.0972649
$521$	−31.8855	−1.39693	−0.698465	−	0.715644i	$-0.746133\pi$
$521$	−31.8855	−1.39693	−0.698465	+	0.715644i	$0.746133\pi$
$522$	10.1751	0.445354
$523$	5.34713	0.233814	0.116907	−	0.993143i	$-0.462702\pi$
$523$	5.34713	0.233814	0.116907	+	0.993143i	$0.462702\pi$
$524$	62.9076	2.74813
$525$	−4.97858	−0.217283
$526$	8.52792	0.371835
$527$	−0.0428457	−0.00186639
$528$	0	0
$529$	54.6300	2.37522
$530$	1.54683	0.0671899
$531$	8.02877	0.348419
$532$	−6.39312	−0.277177
$533$	12.1751	0.527364
$534$	−22.9859	−0.994698
$535$	0.804518	0.0347823
$536$	−27.0790	−1.16963
$537$	−23.2285	−1.00238
$538$	−17.6816	−0.762309
$539$	0	0
$540$	−0.510711	−0.0219775
$541$	27.8610	1.19784	0.598919	−	0.800810i	$-0.295597\pi$
$541$	27.8610	1.19784	0.598919	+	0.800810i	$0.295597\pi$
$542$	55.4439	2.38152
$543$	25.1109	1.07761
$544$	0.611096	0.0262005
$545$	−0.860365	−0.0368540
$546$	10.1751	0.435456
$547$	−30.7005	−1.31266	−0.656330	−	0.754474i	$-0.727892\pi$
$547$	−30.7005	−1.31266	−0.656330	+	0.754474i	$0.727892\pi$
$548$	−75.2087	−3.21276
$549$	5.43910	0.232135
$550$	0	0
$551$	−7.95715	−0.338986
$552$	30.7434	1.30853
$553$	13.0790	0.556174
$554$	74.7226	3.17466
$555$	0.510711	0.0216785
$556$	47.2432	2.00356
$557$	16.7434	0.709440	0.354720	−	0.934973i	$-0.384576\pi$
$557$	16.7434	0.709440	0.354720	+	0.934973i	$0.384576\pi$
$558$	0.685846	0.0290342
$559$	−34.1396	−1.44395
$560$	−0.175135	−0.00740079
$561$	0	0
$562$	−71.4783	−3.01513
$563$	−27.6932	−1.16713	−0.583564	−	0.812067i	$-0.698342\pi$
$563$	−27.6932	−1.16713	−0.583564	+	0.812067i	$0.698342\pi$
$564$	−3.31415	−0.139551
$565$	0.568250	0.0239065
$566$	53.0508	2.22989
$567$	1.00000	0.0419961
$568$	−12.3503	−0.518206
$569$	−11.6827	−0.489765	−0.244882	−	0.969553i	$-0.578749\pi$
$569$	−11.6827	−0.489765	−0.244882	+	0.969553i	$0.578749\pi$
$570$	0.628308	0.0263169
$571$	−24.1151	−1.00918	−0.504592	−	0.863358i	$-0.668357\pi$
$571$	−24.1151	−1.00918	−0.504592	+	0.863358i	$0.668357\pi$
$572$	0	0
$573$	−17.8898	−0.747355
$574$	6.56825	0.274153
$575$	−43.8652	−1.82930
$576$	−12.1751	−0.507297
$577$	44.2572	1.84245	0.921226	−	0.389027i	$-0.127189\pi$
$577$	44.2572	1.84245	0.921226	+	0.389027i	$0.127189\pi$
$578$	−39.7795	−1.65461
$579$	−10.3288	−0.429252
$580$	−2.21798	−0.0920966
$581$	−12.9070	−0.535471
$582$	−40.8181	−1.69197
$583$	0	0
$584$	56.4653	2.33655
$585$	−0.635654	−0.0262811
$586$	−4.24254	−0.175258
$587$	8.42188	0.347608	0.173804	−	0.984780i	$-0.444394\pi$
$587$	8.42188	0.347608	0.173804	+	0.984780i	$0.444394\pi$
$588$	3.48929	0.143896
$589$	−0.536345	−0.0220997
$590$	−2.75325	−0.113350
$591$	14.8610	0.611299
$592$	−4.17513	−0.171597
$593$	1.94560	0.0798961	0.0399480	−	0.999202i	$-0.487281\pi$
$593$	1.94560	0.0798961	0.0399480	+	0.999202i	$0.487281\pi$
$594$	0	0
$595$	0.0214229	0.000878251 0
$596$	35.9399	1.47216
$597$	0.0674041	0.00275867
$598$	89.6510	3.66610
$599$	31.0361	1.26810	0.634051	−	0.773292i	$-0.281391\pi$
$599$	31.0361	1.26810	0.634051	+	0.773292i	$0.281391\pi$
$600$	−17.3717	−0.709196
$601$	−5.80031	−0.236599	−0.118300	−	0.992978i	$-0.537744\pi$
$601$	−5.80031	−0.236599	−0.118300	+	0.992978i	$0.537744\pi$
$602$	−18.4177	−0.750648
$603$	−7.76060	−0.316036
$604$	4.60015	0.187178
$605$	0	0
$606$	−36.6331	−1.48812
$607$	2.57560	0.104540	0.0522701	−	0.998633i	$-0.483354\pi$
$607$	2.57560	0.104540	0.0522701	+	0.998633i	$0.483354\pi$
$608$	7.64973	0.310238
$609$	4.34292	0.175984
$610$	−1.86519	−0.0755194
$611$	−4.12494	−0.166877
$612$	−0.510711	−0.0206443
$613$	15.8353	0.639584	0.319792	−	0.947488i	$-0.396387\pi$
$613$	15.8353	0.639584	0.319792	+	0.947488i	$0.396387\pi$
$614$	69.9290	2.82210
$615$	−0.410327	−0.0165460
$616$	0	0
$617$	−1.72448	−0.0694250	−0.0347125	−	0.999397i	$-0.511052\pi$
$617$	−1.72448	−0.0694250	−0.0347125	+	0.999397i	$0.511052\pi$
$618$	9.76481	0.392798
$619$	−17.3288	−0.696505	−0.348253	−	0.937401i	$-0.613225\pi$
$619$	−17.3288	−0.696505	−0.348253	+	0.937401i	$0.613225\pi$
$620$	−0.149501	−0.00600411
$621$	8.81079	0.353565
$622$	−11.9326	−0.478454
$623$	−9.81079	−0.393061
$624$	5.19656	0.208029
$625$	24.6791	0.987165
$626$	−51.6191	−2.06311
$627$	0	0
$628$	34.3931	1.37243
$629$	0.510711	0.0203634
$630$	−0.342923	−0.0136624
$631$	6.54683	0.260625	0.130313	−	0.991473i	$-0.458402\pi$
$631$	6.54683	0.260625	0.130313	+	0.991473i	$0.458402\pi$
$632$	45.6363	1.81531
$633$	−13.1323	−0.521962
$634$	−16.6086	−0.659611
$635$	2.58608	0.102625
$636$	−15.7392	−0.624099
$637$	4.34292	0.172073
$638$	0	0
$639$	−3.53948	−0.140020
$640$	2.95294	0.116725
$641$	16.0930	0.635637	0.317818	−	0.948152i	$-0.397050\pi$
$641$	16.0930	0.635637	0.317818	+	0.948152i	$0.397050\pi$
$642$	−12.8782	−0.508262
$643$	−3.21377	−0.126739	−0.0633694	−	0.997990i	$-0.520185\pi$
$643$	−3.21377	−0.126739	−0.0633694	+	0.997990i	$0.520185\pi$
$644$	30.7434	1.21146
$645$	1.15058	0.0453039
$646$	0.628308	0.0247204
$647$	−37.8083	−1.48640	−0.743198	−	0.669071i	$-0.766692\pi$
$647$	−37.8083	−1.48640	−0.743198	+	0.669071i	$0.766692\pi$
$648$	3.48929	0.137072
$649$	0	0
$650$	−50.6577	−1.98696
$651$	0.292731	0.0114730
$652$	−1.02142	−0.0400020
$653$	−13.9754	−0.546901	−0.273451	−	0.961886i	$-0.588165\pi$
$653$	−13.9754	−0.546901	−0.273451	+	0.961886i	$0.588165\pi$
$654$	13.7722	0.538534
$655$	−2.63879	−0.103106
$656$	3.35448	0.130970
$657$	16.1825	0.631339
$658$	−2.22533	−0.0867523
$659$	8.31729	0.323996	0.161998	−	0.986791i	$-0.448206\pi$
$659$	8.31729	0.323996	0.161998	+	0.986791i	$0.448206\pi$
$660$	0	0
$661$	−38.2474	−1.48765	−0.743825	−	0.668374i	$-0.766990\pi$
$661$	−38.2474	−1.48765	−0.743825	+	0.668374i	$0.766990\pi$
$662$	−81.0754	−3.15108
$663$	−0.635654	−0.0246868
$664$	−45.0361	−1.74774
$665$	0.268173	0.0103993
$666$	−8.17513	−0.316780
$667$	38.2646	1.48161
$668$	−54.9076	−2.12444
$669$	5.37169	0.207682
$670$	2.66129	0.102815
$671$	0	0
$672$	−4.17513	−0.161059
$673$	−7.86098	−0.303019	−0.151509	−	0.988456i	$-0.548413\pi$
$673$	−7.86098	−0.303019	−0.151509	+	0.988456i	$0.548413\pi$
$674$	−29.3461	−1.13037
$675$	−4.97858	−0.191626
$676$	20.4507	0.786564
$677$	−31.9603	−1.22833	−0.614167	−	0.789176i	$-0.710508\pi$
$677$	−31.9603	−1.22833	−0.614167	+	0.789176i	$0.710508\pi$
$678$	−9.09617	−0.349336
$679$	−17.4219	−0.668591
$680$	0.0747505	0.00286655
$681$	−6.85785	−0.262793
$682$	0	0
$683$	35.1856	1.34634	0.673170	−	0.739488i	$-0.264932\pi$
$683$	35.1856	1.34634	0.673170	+	0.739488i	$0.264932\pi$
$684$	−6.39312	−0.244447
$685$	3.15479	0.120538
$686$	2.34292	0.0894532
$687$	−8.76060	−0.334238
$688$	−9.40612	−0.358605
$689$	−19.5897	−0.746307
$690$	−3.02142	−0.115024
$691$	2.05754	0.0782725	0.0391362	−	0.999234i	$-0.487539\pi$
$691$	2.05754	0.0782725	0.0391362	+	0.999234i	$0.487539\pi$
$692$	−61.8862	−2.35256
$693$	0	0
$694$	64.7728	2.45874
$695$	−1.98171	−0.0751706
$696$	15.1537	0.574400
$697$	−0.410327	−0.0155423
$698$	−26.4679	−1.00182
$699$	1.36435	0.0516043
$700$	−17.3717	−0.656588
$701$	−11.1207	−0.420024	−0.210012	−	0.977699i	$-0.567350\pi$
$701$	−11.1207	−0.420024	−0.210012	+	0.977699i	$0.567350\pi$
$702$	10.1751	0.384036
$703$	6.39312	0.241121
$704$	0	0
$705$	0.139019	0.00523576
$706$	39.3692	1.48168
$707$	−15.6357	−0.588039
$708$	28.0147	1.05286
$709$	26.6901	1.00237	0.501183	−	0.865341i	$-0.332898\pi$
$709$	26.6901	1.00237	0.501183	+	0.865341i	$0.332898\pi$
$710$	1.21377	0.0455520
$711$	13.0790	0.490499
$712$	−34.2327	−1.28292
$713$	2.57919	0.0965915
$714$	−0.342923	−0.0128336
$715$	0	0
$716$	−81.0508	−3.02901
$717$	4.97858	0.185928
$718$	68.0869	2.54098
$719$	19.8996	0.742130	0.371065	−	0.928607i	$-0.378993\pi$
$719$	19.8996	0.742130	0.371065	+	0.928607i	$0.378993\pi$
$720$	−0.175135	−0.00652689
$721$	4.16779	0.155217
$722$	−36.6503	−1.36398
$723$	14.1678	0.526906
$724$	87.6191	3.25634
$725$	−21.6216	−0.803005
$726$	0	0
$727$	17.3618	0.643915	0.321957	−	0.946754i	$-0.395659\pi$
$727$	17.3618	0.643915	0.321957	+	0.946754i	$0.395659\pi$
$728$	15.1537	0.561634
$729$	1.00000	0.0370370
$730$	−5.54935	−0.205391
$731$	1.15058	0.0425556
$732$	18.9786	0.701468
$733$	33.3790	1.23288	0.616441	−	0.787401i	$-0.288574\pi$
$733$	33.3790	1.23288	0.616441	+	0.787401i	$0.288574\pi$
$734$	41.4637	1.53045
$735$	−0.146365	−0.00539877
$736$	−36.7862	−1.35596
$737$	0	0
$738$	6.56825	0.241781
$739$	15.2369	0.560498	0.280249	−	0.959927i	$-0.409583\pi$
$739$	15.2369	0.560498	0.280249	+	0.959927i	$0.409583\pi$
$740$	1.78202	0.0655083
$741$	−7.95715	−0.292313
$742$	−10.5682	−0.387973
$743$	−23.3387	−0.856214	−0.428107	−	0.903728i	$-0.640819\pi$
$743$	−23.3387	−0.856214	−0.428107	+	0.903728i	$0.640819\pi$
$744$	1.02142	0.0374472
$745$	−1.50758	−0.0552333
$746$	−29.9473	−1.09645
$747$	−12.9070	−0.472241
$748$	0	0
$749$	−5.49663	−0.200843
$750$	3.42188	0.124950
$751$	29.6174	1.08075	0.540377	−	0.841423i	$-0.318282\pi$
$751$	29.6174	1.08075	0.540377	+	0.841423i	$0.318282\pi$
$752$	−1.13650	−0.0414439
$753$	−2.82908	−0.103097
$754$	44.1898	1.60930
$755$	−0.192963	−0.00702265
$756$	3.48929	0.126904
$757$	−25.4360	−0.924486	−0.462243	−	0.886753i	$-0.652955\pi$
$757$	−25.4360	−0.924486	−0.462243	+	0.886753i	$0.652955\pi$
$758$	−45.9817	−1.67013
$759$	0	0
$760$	0.935731	0.0339425
$761$	44.9473	1.62934	0.814669	−	0.579926i	$-0.196919\pi$
$761$	44.9473	1.62934	0.814669	+	0.579926i	$0.196919\pi$
$762$	−41.3963	−1.49963
$763$	5.87819	0.212805
$764$	−62.4225	−2.25837
$765$	0.0214229	0.000774545 0
$766$	69.2333	2.50150
$767$	34.8683	1.25902
$768$	−22.9185	−0.827001
$769$	−32.6749	−1.17829	−0.589144	−	0.808028i	$-0.700535\pi$
$769$	−32.6749	−1.17829	−0.589144	+	0.808028i	$0.700535\pi$
$770$	0	0
$771$	−22.9901	−0.827969
$772$	−36.0403	−1.29712
$773$	−49.6222	−1.78479	−0.892393	−	0.451259i	$-0.850975\pi$
$773$	−49.6222	−1.78479	−0.892393	+	0.451259i	$0.850975\pi$
$774$	−18.4177	−0.662010
$775$	−1.45738	−0.0523508
$776$	−60.7900	−2.18223
$777$	−3.48929	−0.125178
$778$	−30.6833	−1.10005
$779$	−5.13650	−0.184034
$780$	−2.21798	−0.0794164
$781$	0	0
$782$	−3.02142	−0.108046
$783$	4.34292	0.155203
$784$	1.19656	0.0427342
$785$	−1.44269	−0.0514918
$786$	42.2400	1.50665
$787$	40.2583	1.43505	0.717527	−	0.696531i	$-0.245274\pi$
$787$	40.2583	1.43505	0.717527	+	0.696531i	$0.245274\pi$
$788$	51.8543	1.84723
$789$	3.63986	0.129583
$790$	−4.48508	−0.159572
$791$	−3.88240	−0.138042
$792$	0	0
$793$	23.6216	0.838827
$794$	57.3263	2.03444
$795$	0.660212	0.0234153
$796$	0.235192	0.00833618
$797$	17.4862	0.619391	0.309696	−	0.950836i	$-0.399773\pi$
$797$	17.4862	0.619391	0.309696	+	0.950836i	$0.399773\pi$
$798$	−4.29273	−0.151961
$799$	0.139019	0.00491814
$800$	20.7862	0.734904
$801$	−9.81079	−0.346647
$802$	56.6405	2.00004
$803$	0	0
$804$	−27.0790	−0.955001
$805$	−1.28960	−0.0454523
$806$	2.97858	0.104916
$807$	−7.54683	−0.265661
$808$	−54.5573	−1.91932
$809$	25.9473	0.912258	0.456129	−	0.889914i	$-0.349236\pi$
$809$	25.9473	0.912258	0.456129	+	0.889914i	$0.349236\pi$
$810$	−0.342923	−0.0120491
$811$	−18.2829	−0.641998	−0.320999	−	0.947079i	$-0.604019\pi$
$811$	−18.2829	−0.641998	−0.320999	+	0.947079i	$0.604019\pi$
$812$	15.1537	0.531791
$813$	23.6644	0.829948
$814$	0	0
$815$	0.0428457	0.00150082
$816$	−0.175135	−0.00613094
$817$	14.4030	0.503897
$818$	12.2327	0.427705
$819$	4.34292	0.151754
$820$	−1.43175	−0.0499989
$821$	−25.3288	−0.883983	−0.441991	−	0.897019i	$-0.645728\pi$
$821$	−25.3288	−0.883983	−0.441991	+	0.897019i	$0.645728\pi$
$822$	−50.4998	−1.76138
$823$	39.2713	1.36891	0.684456	−	0.729054i	$-0.260040\pi$
$823$	39.2713	1.36891	0.684456	+	0.729054i	$0.260040\pi$
$824$	14.5426	0.506616
$825$	0	0
$826$	18.8108	0.654511
$827$	−27.4047	−0.952954	−0.476477	−	0.879187i	$-0.658086\pi$
$827$	−27.4047	−0.952954	−0.476477	+	0.879187i	$0.658086\pi$
$828$	30.7434	1.06841
$829$	38.5155	1.33770	0.668850	−	0.743397i	$-0.266787\pi$
$829$	38.5155	1.33770	0.668850	+	0.743397i	$0.266787\pi$
$830$	4.42610	0.153632
$831$	31.8929	1.10635
$832$	−52.8757	−1.83313
$833$	−0.146365	−0.00507126
$834$	31.7220	1.09844
$835$	2.30321	0.0797060
$836$	0	0
$837$	0.292731	0.0101183
$838$	−53.1182	−1.83494
$839$	−17.7276	−0.612025	−0.306013	−	0.952027i	$-0.598995\pi$
$839$	−17.7276	−0.612025	−0.306013	+	0.952027i	$0.598995\pi$
$840$	−0.510711	−0.0176212
$841$	−10.1390	−0.349621
$842$	−5.65708	−0.194956
$843$	−30.5082	−1.05076
$844$	−45.8223	−1.57727
$845$	−0.857845	−0.0295108
$846$	−2.22533	−0.0765083
$847$	0	0
$848$	−5.39733	−0.185345
$849$	22.6430	0.777106
$850$	1.70727	0.0585588
$851$	−30.7434	−1.05387
$852$	−12.3503	−0.423113
$853$	15.3032	0.523972	0.261986	−	0.965072i	$-0.415623\pi$
$853$	15.3032	0.523972	0.261986	+	0.965072i	$0.415623\pi$
$854$	12.7434	0.436070
$855$	0.268173	0.00917131
$856$	−19.1793	−0.655537
$857$	10.7722	0.367970	0.183985	−	0.982929i	$-0.441100\pi$
$857$	10.7722	0.367970	0.183985	+	0.982929i	$0.441100\pi$
$858$	0	0
$859$	47.2516	1.61220	0.806101	−	0.591777i	$-0.201574\pi$
$859$	47.2516	1.61220	0.806101	+	0.591777i	$0.201574\pi$
$860$	4.01469	0.136900
$861$	2.80344	0.0955411
$862$	−3.17935	−0.108289
$863$	−34.0294	−1.15837	−0.579187	−	0.815195i	$-0.696630\pi$
$863$	−34.0294	−1.15837	−0.579187	+	0.815195i	$0.696630\pi$
$864$	−4.17513	−0.142041
$865$	2.59594	0.0882647
$866$	48.3822	1.64409
$867$	−16.9786	−0.576623
$868$	1.02142	0.0346694
$869$	0	0
$870$	−1.48929	−0.0504916
$871$	−33.7037	−1.14201
$872$	20.5107	0.694580
$873$	−17.4219	−0.589641
$874$	−37.8223	−1.27936
$875$	1.46052	0.0493746
$876$	56.4653	1.90779
$877$	−3.25410	−0.109883	−0.0549415	−	0.998490i	$-0.517497\pi$
$877$	−3.25410	−0.109883	−0.0549415	+	0.998490i	$0.517497\pi$
$878$	−47.5787	−1.60570
$879$	−1.81079	−0.0610764
$880$	0	0
$881$	−13.3545	−0.449924	−0.224962	−	0.974368i	$-0.572226\pi$
$881$	−13.3545	−0.449924	−0.224962	+	0.974368i	$0.572226\pi$
$882$	2.34292	0.0788903
$883$	−25.4741	−0.857273	−0.428636	−	0.903477i	$-0.641006\pi$
$883$	−25.4741	−0.857273	−0.428636	+	0.903477i	$0.641006\pi$
$884$	−2.21798	−0.0745988
$885$	−1.17513	−0.0395017
$886$	−23.0017	−0.772757
$887$	21.6932	0.728386	0.364193	−	0.931323i	$-0.381345\pi$
$887$	21.6932	0.728386	0.364193	+	0.931323i	$0.381345\pi$
$888$	−12.1751	−0.408571
$889$	−17.6686	−0.592587
$890$	3.36435	0.112773
$891$	0	0
$892$	18.7434	0.627575
$893$	1.74025	0.0582352
$894$	24.1323	0.807104
$895$	3.39985	0.113644
$896$	−20.1751	−0.674004
$897$	38.2646	1.27762
$898$	23.6044	0.787688
$899$	1.27131	0.0424005
$900$	−17.3717	−0.579056
$901$	0.660212	0.0219949
$902$	0	0
$903$	−7.86098	−0.261597
$904$	−13.5468	−0.450561
$905$	−3.67536	−0.122173
$906$	3.08883	0.102619
$907$	1.21377	0.0403026	0.0201513	−	0.999797i	$-0.493585\pi$
$907$	1.21377	0.0403026	0.0201513	+	0.999797i	$0.493585\pi$
$908$	−23.9290	−0.794112
$909$	−15.6357	−0.518602
$910$	−1.48929	−0.0493694
$911$	57.0080	1.88876	0.944379	−	0.328859i	$-0.106664\pi$
$911$	57.0080	1.88876	0.944379	+	0.328859i	$0.106664\pi$
$912$	−2.19235	−0.0725959
$913$	0	0
$914$	34.3920	1.13759
$915$	−0.796096	−0.0263181
$916$	−30.5682	−1.01000
$917$	18.0288	0.595362
$918$	−0.342923	−0.0113181
$919$	6.45065	0.212787	0.106394	−	0.994324i	$-0.466070\pi$
$919$	6.45065	0.212787	0.106394	+	0.994324i	$0.466070\pi$
$920$	−4.49977	−0.148353
$921$	29.8469	0.983489
$922$	63.5861	2.09410
$923$	−15.3717	−0.505965
$924$	0	0
$925$	17.3717	0.571178
$926$	54.4422	1.78908
$927$	4.16779	0.136888
$928$	−18.1323	−0.595222
$929$	2.74652	0.0901104	0.0450552	−	0.998984i	$-0.485654\pi$
$929$	2.74652	0.0901104	0.0450552	+	0.998984i	$0.485654\pi$
$930$	−0.100384	−0.00329173
$931$	−1.83221	−0.0600483
$932$	4.76060	0.155939
$933$	−5.09304	−0.166739
$934$	55.8946	1.82893
$935$	0	0
$936$	15.1537	0.495315
$937$	25.8923	0.845864	0.422932	−	0.906162i	$-0.361001\pi$
$937$	25.8923	0.845864	0.422932	+	0.906162i	$0.361001\pi$
$938$	−18.1825	−0.593679
$939$	−22.0319	−0.718984
$940$	0.485078	0.0158215
$941$	−9.01890	−0.294008	−0.147004	−	0.989136i	$-0.546963\pi$
$941$	−9.01890	−0.294008	−0.147004	+	0.989136i	$0.546963\pi$
$942$	23.0937	0.752432
$943$	24.7005	0.804360
$944$	9.60688	0.312677
$945$	−0.146365	−0.00476127
$946$	0	0
$947$	39.2003	1.27384	0.636919	−	0.770930i	$-0.280208\pi$
$947$	39.2003	1.27384	0.636919	+	0.770930i	$0.280208\pi$
$948$	45.6363	1.48220
$949$	70.2793	2.28136
$950$	21.3717	0.693389
$951$	−7.08883	−0.229871
$952$	−0.510711	−0.0165523
$953$	−55.4464	−1.79609	−0.898043	−	0.439907i	$-0.855011\pi$
$953$	−55.4464	−1.79609	−0.898043	+	0.439907i	$0.855011\pi$
$954$	−10.5682	−0.342160
$955$	2.61844	0.0847308
$956$	17.3717	0.561841
$957$	0	0
$958$	−40.3173	−1.30259
$959$	−21.5542	−0.696021
$960$	1.78202	0.0575144
$961$	−30.9143	−0.997236
$962$	−35.5040	−1.14469
$963$	−5.49663	−0.177127
$964$	49.4355	1.59221
$965$	1.51179	0.0486661
$966$	20.6430	0.664178
$967$	23.9467	0.770073	0.385037	−	0.922901i	$-0.374189\pi$
$967$	23.9467	0.770073	0.385037	+	0.922901i	$0.374189\pi$
$968$	0	0
$969$	0.268173	0.00861494
$970$	5.97437	0.191825
$971$	−6.42188	−0.206088	−0.103044	−	0.994677i	$-0.532858\pi$
$971$	−6.42188	−0.206088	−0.103044	+	0.994677i	$0.532858\pi$
$972$	3.48929	0.111919
$973$	13.5395	0.434056
$974$	−7.40467	−0.237261
$975$	−21.6216	−0.692445
$976$	6.50819	0.208322
$977$	38.5584	1.23359	0.616796	−	0.787123i	$-0.288430\pi$
$977$	38.5584	1.23359	0.616796	+	0.787123i	$0.288430\pi$
$978$	−0.685846	−0.0219309
$979$	0	0
$980$	−0.510711	−0.0163141
$981$	5.87819	0.187676
$982$	9.89962	0.315909
$983$	21.6069	0.689153	0.344576	−	0.938758i	$-0.388023\pi$
$983$	21.6069	0.689153	0.344576	+	0.938758i	$0.388023\pi$
$984$	9.78202	0.311839
$985$	−2.17513	−0.0693056
$986$	−1.48929	−0.0474286
$987$	−0.949808	−0.0302327
$988$	−27.7648	−0.883316
$989$	−69.2614	−2.20239
$990$	0	0
$991$	34.4507	1.09436	0.547181	−	0.837015i	$-0.315701\pi$
$991$	34.4507	1.09436	0.547181	+	0.837015i	$0.315701\pi$
$992$	−1.22219	−0.0388046
$993$	−34.6044	−1.09814
$994$	−8.29273	−0.263029
$995$	−0.00986564	−0.000312762 0
$996$	−45.0361	−1.42702
$997$	−7.76733	−0.245994	−0.122997	−	0.992407i	$-0.539251\pi$
$997$	−7.76733	−0.245994	−0.122997	+	0.992407i	$0.539251\pi$
$998$	71.6033	2.26656
$999$	−3.48929	−0.110396

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2541.2.a.bj.1.3	yes	3
3.2	odd	2		7623.2.a.ca.1.1		3
11.10	odd	2		2541.2.a.bh.1.1	✓	3
33.32	even	2		7623.2.a.cc.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2541.2.a.bh.1.1	✓	3	11.10	odd	2
2541.2.a.bj.1.3	yes	3	1.1	even	1	trivial
7623.2.a.ca.1.1		3	3.2	odd	2
7623.2.a.cc.1.3		3	33.32	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:	\( N \)	\(=\)	\( 2541 = 3 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2541.a (trivial)

\(f(q)\)	\(=\)	\(q+2.34292 q^{2} +1.00000 q^{3} +3.48929 q^{4} -0.146365 q^{5} +2.34292 q^{6} +1.00000 q^{7} +3.48929 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.34292 q^{2} +1.00000 q^{3} +3.48929 q^{4} -0.146365 q^{5} +2.34292 q^{6} +1.00000 q^{7} +3.48929 q^{8} +1.00000 q^{9} -0.342923 q^{10} +3.48929 q^{12} +4.34292 q^{13} +2.34292 q^{14} -0.146365 q^{15} +1.19656 q^{16} -0.146365 q^{17} +2.34292 q^{18} -1.83221 q^{19} -0.510711 q^{20} +1.00000 q^{21} +8.81079 q^{23} +3.48929 q^{24} -4.97858 q^{25} +10.1751 q^{26} +1.00000 q^{27} +3.48929 q^{28} +4.34292 q^{29} -0.342923 q^{30} +0.292731 q^{31} -4.17513 q^{32} -0.342923 q^{34} -0.146365 q^{35} +3.48929 q^{36} -3.48929 q^{37} -4.29273 q^{38} +4.34292 q^{39} -0.510711 q^{40} +2.80344 q^{41} +2.34292 q^{42} -7.86098 q^{43} -0.146365 q^{45} +20.6430 q^{46} -0.949808 q^{47} +1.19656 q^{48} +1.00000 q^{49} -11.6644 q^{50} -0.146365 q^{51} +15.1537 q^{52} -4.51071 q^{53} +2.34292 q^{54} +3.48929 q^{56} -1.83221 q^{57} +10.1751 q^{58} +8.02877 q^{59} -0.510711 q^{60} +5.43910 q^{61} +0.685846 q^{62} +1.00000 q^{63} -12.1751 q^{64} -0.635654 q^{65} -7.76060 q^{67} -0.510711 q^{68} +8.81079 q^{69} -0.342923 q^{70} -3.53948 q^{71} +3.48929 q^{72} +16.1825 q^{73} -8.17513 q^{74} -4.97858 q^{75} -6.39312 q^{76} +10.1751 q^{78} +13.0790 q^{79} -0.175135 q^{80} +1.00000 q^{81} +6.56825 q^{82} -12.9070 q^{83} +3.48929 q^{84} +0.0214229 q^{85} -18.4177 q^{86} +4.34292 q^{87} -9.81079 q^{89} -0.342923 q^{90} +4.34292 q^{91} +30.7434 q^{92} +0.292731 q^{93} -2.22533 q^{94} +0.268173 q^{95} -4.17513 q^{96} -17.4219 q^{97} +2.34292 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + 3 q^{3} + 3 q^{4} + q^{5} + q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + q^2 + 3 * q^3 + 3 * q^4 + q^5 + q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + q^{2} + 3 q^{3} + 3 q^{4} + q^{5} + q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9} + 5 q^{10} + 3 q^{12} + 7 q^{13} + q^{14} + q^{15} - q^{16} + q^{17} + q^{18} + 8 q^{19} - 9 q^{20} + 3 q^{21} - 2 q^{23} + 3 q^{24} + 11 q^{26} + 3 q^{27} + 3 q^{28} + 7 q^{29} + 5 q^{30} - 2 q^{31} + 7 q^{32} + 5 q^{34} + q^{35} + 3 q^{36} - 3 q^{37} - 10 q^{38} + 7 q^{39} - 9 q^{40} + 13 q^{41} + q^{42} + 8 q^{43} + q^{45} + 20 q^{46} - 6 q^{47} - q^{48} + 3 q^{49} - 8 q^{50} + q^{51} + 11 q^{52} - 21 q^{53} + q^{54} + 3 q^{56} + 8 q^{57} + 11 q^{58} + 6 q^{59} - 9 q^{60} + 12 q^{61} - 10 q^{62} + 3 q^{63} - 17 q^{64} + 7 q^{65} + 2 q^{67} - 9 q^{68} - 2 q^{69} + 5 q^{70} + 3 q^{72} - 4 q^{73} - 5 q^{74} - 10 q^{76} + 11 q^{78} + 18 q^{79} + 19 q^{80} + 3 q^{81} - 9 q^{82} - 12 q^{83} + 3 q^{84} + 15 q^{85} - 36 q^{86} + 7 q^{87} - q^{89} + 5 q^{90} + 7 q^{91} + 44 q^{92} - 2 q^{93} + 16 q^{94} + 8 q^{95} + 7 q^{96} - 25 q^{97} + q^{98}+O(q^{100}) \) 3 * q + q^2 + 3 * q^3 + 3 * q^4 + q^5 + q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9 + 5 * q^10 + 3 * q^12 + 7 * q^13 + q^14 + q^15 - q^16 + q^17 + q^18 + 8 * q^19 - 9 * q^20 + 3 * q^21 - 2 * q^23 + 3 * q^24 + 11 * q^26 + 3 * q^27 + 3 * q^28 + 7 * q^29 + 5 * q^30 - 2 * q^31 + 7 * q^32 + 5 * q^34 + q^35 + 3 * q^36 - 3 * q^37 - 10 * q^38 + 7 * q^39 - 9 * q^40 + 13 * q^41 + q^42 + 8 * q^43 + q^45 + 20 * q^46 - 6 * q^47 - q^48 + 3 * q^49 - 8 * q^50 + q^51 + 11 * q^52 - 21 * q^53 + q^54 + 3 * q^56 + 8 * q^57 + 11 * q^58 + 6 * q^59 - 9 * q^60 + 12 * q^61 - 10 * q^62 + 3 * q^63 - 17 * q^64 + 7 * q^65 + 2 * q^67 - 9 * q^68 - 2 * q^69 + 5 * q^70 + 3 * q^72 - 4 * q^73 - 5 * q^74 - 10 * q^76 + 11 * q^78 + 18 * q^79 + 19 * q^80 + 3 * q^81 - 9 * q^82 - 12 * q^83 + 3 * q^84 + 15 * q^85 - 36 * q^86 + 7 * q^87 - q^89 + 5 * q^90 + 7 * q^91 + 44 * q^92 - 2 * q^93 + 16 * q^94 + 8 * q^95 + 7 * q^96 - 25 * q^97 + q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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