LMFDB - Embedded newform 1573.2.a.s.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1573,2,Mod(1,1573)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1573, 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("1573.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1573 = 11^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1573.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:	$12.5604682379$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 21 x^{12} + 19 x^{11} + 169 x^{10} - 136 x^{9} - 649 x^{8} + 455 x^{7} + 1207 x^{6} + \cdots - 29 $ x^14 - x^13 - 21x^12 + 19x^11 + 169x^10 - 136x^9 - 649x^8 + 455x^7 + 1207x^6 - 708x^5 - 1001x^4 + 414x^3 + 343x^2 - 67x - 29
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
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			1.2
Root			$-2.36242$ of defining polynomial
Character	$\chi$	$=$	1573.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.36242 q^{2} +1.82138 q^{3} +3.58104 q^{4} +2.13488 q^{5} -4.30288 q^{6} -1.07801 q^{7} -3.73509 q^{8} +0.317434 q^{9} +O(q^{10})$	\(q-2.36242 q^{2} +1.82138 q^{3} +3.58104 q^{4} +2.13488 q^{5} -4.30288 q^{6} -1.07801 q^{7} -3.73509 q^{8} +0.317434 q^{9} -5.04348 q^{10} +6.52245 q^{12} +1.00000 q^{13} +2.54672 q^{14} +3.88842 q^{15} +1.66178 q^{16} +1.18355 q^{17} -0.749914 q^{18} +1.02803 q^{19} +7.64508 q^{20} -1.96347 q^{21} -5.23055 q^{23} -6.80303 q^{24} -0.442306 q^{25} -2.36242 q^{26} -4.88598 q^{27} -3.86041 q^{28} +7.07299 q^{29} -9.18611 q^{30} +5.18072 q^{31} +3.54435 q^{32} -2.79605 q^{34} -2.30142 q^{35} +1.13675 q^{36} +9.88524 q^{37} -2.42865 q^{38} +1.82138 q^{39} -7.97396 q^{40} +1.44558 q^{41} +4.63856 q^{42} +12.3409 q^{43} +0.677682 q^{45} +12.3568 q^{46} +7.73579 q^{47} +3.02674 q^{48} -5.83789 q^{49} +1.04491 q^{50} +2.15570 q^{51} +3.58104 q^{52} +7.65138 q^{53} +11.5427 q^{54} +4.02648 q^{56} +1.87244 q^{57} -16.7094 q^{58} +12.5485 q^{59} +13.9246 q^{60} -5.13676 q^{61} -12.2390 q^{62} -0.342198 q^{63} -11.6968 q^{64} +2.13488 q^{65} -4.78456 q^{67} +4.23834 q^{68} -9.52682 q^{69} +5.43694 q^{70} +15.2168 q^{71} -1.18565 q^{72} -5.03654 q^{73} -23.3531 q^{74} -0.805609 q^{75} +3.68143 q^{76} -4.30288 q^{78} -0.646065 q^{79} +3.54770 q^{80} -9.85154 q^{81} -3.41507 q^{82} -0.455255 q^{83} -7.03128 q^{84} +2.52673 q^{85} -29.1545 q^{86} +12.8826 q^{87} -13.3715 q^{89} -1.60097 q^{90} -1.07801 q^{91} -18.7308 q^{92} +9.43607 q^{93} -18.2752 q^{94} +2.19472 q^{95} +6.45562 q^{96} +11.7912 q^{97} +13.7916 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + q^{2} + 9 q^{3} + 15 q^{4} + 9 q^{5} + 13 q^{6} - q^{7} + 3 q^{8} + 17 q^{9}+O(q^{10}) $ 14 * q + q^2 + 9 * q^3 + 15 * q^4 + 9 * q^5 + 13 * q^6 - q^7 + 3 * q^8 + 17 * q^9	\( 14 q + q^{2} + 9 q^{3} + 15 q^{4} + 9 q^{5} + 13 q^{6} - q^{7} + 3 q^{8} + 17 q^{9} - 12 q^{10} + 19 q^{12} + 14 q^{13} + 9 q^{14} + 19 q^{15} + 13 q^{16} - 4 q^{17} - 15 q^{18} + 5 q^{19} + 17 q^{20} + 25 q^{23} + 29 q^{24} + 13 q^{25} + q^{26} + 33 q^{27} + 15 q^{28} - 16 q^{29} - 8 q^{30} + 6 q^{31} + 12 q^{32} + 13 q^{34} + 8 q^{35} + 24 q^{36} + 11 q^{37} + 22 q^{38} + 9 q^{39} - 43 q^{40} + q^{41} - 5 q^{42} - 16 q^{43} + 39 q^{45} + 22 q^{46} + 38 q^{47} + 6 q^{48} + 9 q^{49} + 8 q^{50} - 24 q^{51} + 15 q^{52} + 52 q^{53} - 21 q^{54} + 17 q^{56} + 9 q^{57} - 19 q^{58} + 27 q^{59} + 13 q^{60} - 19 q^{61} - 56 q^{62} + 11 q^{63} - 29 q^{64} + 9 q^{65} + 29 q^{67} - 14 q^{68} + 21 q^{69} - 68 q^{70} + 34 q^{71} + 65 q^{72} - 18 q^{73} - 18 q^{74} + 11 q^{75} + 3 q^{76} + 13 q^{78} - 17 q^{79} - q^{80} + 18 q^{81} + 9 q^{82} + 16 q^{83} - 21 q^{84} + 2 q^{85} + 9 q^{86} - 6 q^{87} + 19 q^{89} + 13 q^{90} - q^{91} + 22 q^{92} + 2 q^{93} + 75 q^{94} - 29 q^{95} - 13 q^{96} - 20 q^{97} + 81 q^{98}+O(q^{100}) \) 14 * q + q^2 + 9 * q^3 + 15 * q^4 + 9 * q^5 + 13 * q^6 - q^7 + 3 * q^8 + 17 * q^9 - 12 * q^10 + 19 * q^12 + 14 * q^13 + 9 * q^14 + 19 * q^15 + 13 * q^16 - 4 * q^17 - 15 * q^18 + 5 * q^19 + 17 * q^20 + 25 * q^23 + 29 * q^24 + 13 * q^25 + q^26 + 33 * q^27 + 15 * q^28 - 16 * q^29 - 8 * q^30 + 6 * q^31 + 12 * q^32 + 13 * q^34 + 8 * q^35 + 24 * q^36 + 11 * q^37 + 22 * q^38 + 9 * q^39 - 43 * q^40 + q^41 - 5 * q^42 - 16 * q^43 + 39 * q^45 + 22 * q^46 + 38 * q^47 + 6 * q^48 + 9 * q^49 + 8 * q^50 - 24 * q^51 + 15 * q^52 + 52 * q^53 - 21 * q^54 + 17 * q^56 + 9 * q^57 - 19 * q^58 + 27 * q^59 + 13 * q^60 - 19 * q^61 - 56 * q^62 + 11 * q^63 - 29 * q^64 + 9 * q^65 + 29 * q^67 - 14 * q^68 + 21 * q^69 - 68 * q^70 + 34 * q^71 + 65 * q^72 - 18 * q^73 - 18 * q^74 + 11 * q^75 + 3 * q^76 + 13 * q^78 - 17 * q^79 - q^80 + 18 * q^81 + 9 * q^82 + 16 * q^83 - 21 * q^84 + 2 * q^85 + 9 * q^86 - 6 * q^87 + 19 * q^89 + 13 * q^90 - q^91 + 22 * q^92 + 2 * q^93 + 75 * q^94 - 29 * q^95 - 13 * q^96 - 20 * q^97 + 81 * 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 $

$2$	−2.36242	−1.67049	−0.835243	−	0.549881i	$-0.814673\pi$
$2$	−2.36242	−1.67049	−0.835243	+	0.549881i	$0.814673\pi$
$3$	1.82138	1.05158	0.525788	−	0.850616i	$-0.323771\pi$
$3$	1.82138	1.05158	0.525788	+	0.850616i	$0.323771\pi$
$4$	3.58104	1.79052
$5$	2.13488	0.954745	0.477373	−	0.878701i	$-0.341589\pi$
$5$	2.13488	0.954745	0.477373	+	0.878701i	$0.341589\pi$
$6$	−4.30288	−1.75664
$7$	−1.07801	−0.407451	−0.203725	−	0.979028i	$-0.565305\pi$
$7$	−1.07801	−0.407451	−0.203725	+	0.979028i	$0.565305\pi$
$8$	−3.73509	−1.32055
$9$	0.317434	0.105811
$10$	−5.04348	−1.59489
$11$	0	0
$11$	0	0
$12$	6.52245	1.88287
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	2.54672	0.680640
$15$	3.88842	1.00399
$16$	1.66178	0.415446
$17$	1.18355	0.287053	0.143526	−	0.989646i	$-0.454156\pi$
$17$	1.18355	0.287053	0.143526	+	0.989646i	$0.454156\pi$
$18$	−0.749914	−0.176756
$19$	1.02803	0.235847	0.117923	−	0.993023i	$-0.462376\pi$
$19$	1.02803	0.235847	0.117923	+	0.993023i	$0.462376\pi$
$20$	7.64508	1.70949
$21$	−1.96347	−0.428465
$22$	0	0
$23$	−5.23055	−1.09064	−0.545322	−	0.838227i	$-0.683593\pi$
$23$	−5.23055	−1.09064	−0.545322	+	0.838227i	$0.683593\pi$
$24$	−6.80303	−1.38866
$25$	−0.442306	−0.0884612
$26$	−2.36242	−0.463309
$27$	−4.88598	−0.940307
$28$	−3.86041	−0.729549
$29$	7.07299	1.31342	0.656711	−	0.754143i	$-0.271947\pi$
$29$	7.07299	1.31342	0.656711	+	0.754143i	$0.271947\pi$
$30$	−9.18611	−1.67715
$31$	5.18072	0.930484	0.465242	−	0.885184i	$-0.345967\pi$
$31$	5.18072	0.930484	0.465242	+	0.885184i	$0.345967\pi$
$32$	3.54435	0.626559
$33$	0	0
$34$	−2.79605	−0.479518
$35$	−2.30142	−0.389012
$36$	1.13675	0.189458
$37$	9.88524	1.62512	0.812561	−	0.582875i	$-0.198072\pi$
$37$	9.88524	1.62512	0.812561	+	0.582875i	$0.198072\pi$
$38$	−2.42865	−0.393979
$39$	1.82138	0.291655
$40$	−7.97396	−1.26079
$41$	1.44558	0.225762	0.112881	−	0.993609i	$-0.463992\pi$
$41$	1.44558	0.225762	0.112881	+	0.993609i	$0.463992\pi$
$42$	4.63856	0.715745
$43$	12.3409	1.88197	0.940987	−	0.338444i	$-0.109900\pi$
$43$	12.3409	1.88197	0.940987	+	0.338444i	$0.109900\pi$
$44$	0	0
$45$	0.677682	0.101023
$46$	12.3568	1.82191
$47$	7.73579	1.12838	0.564191	−	0.825645i	$-0.309188\pi$
$47$	7.73579	1.12838	0.564191	+	0.825645i	$0.309188\pi$
$48$	3.02674	0.436873
$49$	−5.83789	−0.833984
$50$	1.04491	0.147773
$51$	2.15570	0.301858
$52$	3.58104	0.496601
$53$	7.65138	1.05100	0.525499	−	0.850794i	$-0.323879\pi$
$53$	7.65138	1.05100	0.525499	+	0.850794i	$0.323879\pi$
$54$	11.5427	1.57077
$55$	0	0
$56$	4.02648	0.538061
$57$	1.87244	0.248011
$58$	−16.7094	−2.19405
$59$	12.5485	1.63367	0.816835	−	0.576871i	$-0.195726\pi$
$59$	12.5485	1.63367	0.816835	+	0.576871i	$0.195726\pi$
$60$	13.9246	1.79766
$61$	−5.13676	−0.657695	−0.328847	−	0.944383i	$-0.606660\pi$
$61$	−5.13676	−0.657695	−0.328847	+	0.944383i	$0.606660\pi$
$62$	−12.2390	−1.55436
$63$	−0.342198	−0.0431129
$64$	−11.6968	−1.46210
$65$	2.13488	0.264799
$66$	0	0
$67$	−4.78456	−0.584527	−0.292263	−	0.956338i	$-0.594408\pi$
$67$	−4.78456	−0.584527	−0.292263	+	0.956338i	$0.594408\pi$
$68$	4.23834	0.513975
$69$	−9.52682	−1.14689
$70$	5.43694	0.649838
$71$	15.2168	1.80590	0.902952	−	0.429741i	$-0.141395\pi$
$71$	15.2168	1.80590	0.902952	+	0.429741i	$0.141395\pi$
$72$	−1.18565	−0.139730
$73$	−5.03654	−0.589482	−0.294741	−	0.955577i	$-0.595233\pi$
$73$	−5.03654	−0.589482	−0.294741	+	0.955577i	$0.595233\pi$
$74$	−23.3531	−2.71474
$75$	−0.805609	−0.0930237
$76$	3.68143	0.422289
$77$	0	0
$78$	−4.30288	−0.487205
$79$	−0.646065	−0.0726880	−0.0363440	−	0.999339i	$-0.511571\pi$
$79$	−0.646065	−0.0726880	−0.0363440	+	0.999339i	$0.511571\pi$
$80$	3.54770	0.396645
$81$	−9.85154	−1.09462
$82$	−3.41507	−0.377131
$83$	−0.455255	−0.0499708	−0.0249854	−	0.999688i	$-0.507954\pi$
$83$	−0.455255	−0.0499708	−0.0249854	+	0.999688i	$0.507954\pi$
$84$	−7.03128	−0.767176
$85$	2.52673	0.274062
$86$	−29.1545	−3.14381
$87$	12.8826	1.38116
$88$	0	0
$89$	−13.3715	−1.41738	−0.708688	−	0.705522i	$-0.750713\pi$
$89$	−13.3715	−1.41738	−0.708688	+	0.705522i	$0.750713\pi$
$90$	−1.60097	−0.168757
$91$	−1.07801	−0.113006
$92$	−18.7308	−1.95282
$93$	9.43607	0.978474
$94$	−18.2752	−1.88494
$95$	2.19472	0.225174
$96$	6.45562	0.658874
$97$	11.7912	1.19722	0.598610	−	0.801041i	$-0.295720\pi$
$97$	11.7912	1.19722	0.598610	+	0.801041i	$0.295720\pi$
$98$	13.7916	1.39316
$99$	0	0
$100$	−1.58392	−0.158392
$101$	−6.33172	−0.630030	−0.315015	−	0.949087i	$-0.602010\pi$
$101$	−6.33172	−0.630030	−0.315015	+	0.949087i	$0.602010\pi$
$102$	−5.09267	−0.504249
$103$	−3.84453	−0.378813	−0.189406	−	0.981899i	$-0.560656\pi$
$103$	−3.84453	−0.378813	−0.189406	+	0.981899i	$0.560656\pi$
$104$	−3.73509	−0.366256
$105$	−4.19177	−0.409075
$106$	−18.0758	−1.75568
$107$	3.79641	0.367012	0.183506	−	0.983019i	$-0.441255\pi$
$107$	3.79641	0.367012	0.183506	+	0.983019i	$0.441255\pi$
$108$	−17.4969	−1.68364
$109$	−10.8273	−1.03707	−0.518534	−	0.855057i	$-0.673522\pi$
$109$	−10.8273	−1.03707	−0.518534	+	0.855057i	$0.673522\pi$
$110$	0	0
$111$	18.0048	1.70894
$112$	−1.79142	−0.169274
$113$	6.07919	0.571882	0.285941	−	0.958247i	$-0.407694\pi$
$113$	6.07919	0.571882	0.285941	+	0.958247i	$0.407694\pi$
$114$	−4.42350	−0.414299
$115$	−11.1666	−1.04129
$116$	25.3287	2.35171
$117$	0.317434	0.0293468
$118$	−29.6448	−2.72902
$119$	−1.27588	−0.116960
$120$	−14.5236	−1.32582
$121$	0	0
$122$	12.1352	1.09867
$123$	2.63295	0.237405
$124$	18.5524	1.66605
$125$	−11.6186	−1.03920
$126$	0.808417	0.0720195
$127$	1.41631	0.125677	0.0628384	−	0.998024i	$-0.479985\pi$
$127$	1.41631	0.125677	0.0628384	+	0.998024i	$0.479985\pi$
$128$	20.5441	1.81586
$129$	22.4775	1.97904
$130$	−5.04348	−0.442342
$131$	5.34497	0.466992	0.233496	−	0.972358i	$-0.424983\pi$
$131$	5.34497	0.466992	0.233496	+	0.972358i	$0.424983\pi$
$132$	0	0
$133$	−1.10823	−0.0960959
$134$	11.3031	0.976443
$135$	−10.4310	−0.897754
$136$	−4.42067	−0.379069
$137$	0.640661	0.0547354	0.0273677	−	0.999625i	$-0.491288\pi$
$137$	0.640661	0.0547354	0.0273677	+	0.999625i	$0.491288\pi$
$138$	22.5064	1.91587
$139$	−17.8431	−1.51343	−0.756717	−	0.653743i	$-0.773198\pi$
$139$	−17.8431	−1.51343	−0.756717	+	0.653743i	$0.773198\pi$
$140$	−8.24150	−0.696533
$141$	14.0898	1.18658
$142$	−35.9486	−3.01674
$143$	0	0
$144$	0.527507	0.0439589
$145$	15.1000	1.25398
$146$	11.8984	0.984722
$147$	−10.6330	−0.876997
$148$	35.3995	2.90982
$149$	7.22802	0.592142	0.296071	−	0.955166i	$-0.404323\pi$
$149$	7.22802	0.592142	0.296071	+	0.955166i	$0.404323\pi$
$150$	1.90319	0.155395
$151$	16.4121	1.33560	0.667799	−	0.744342i	$-0.267237\pi$
$151$	16.4121	1.33560	0.667799	+	0.744342i	$0.267237\pi$
$152$	−3.83980	−0.311449
$153$	0.375699	0.0303735
$154$	0	0
$155$	11.0602	0.888375
$156$	6.52245	0.522214
$157$	0.154224	0.0123084	0.00615421	−	0.999981i	$-0.498041\pi$
$157$	0.154224	0.0123084	0.00615421	+	0.999981i	$0.498041\pi$
$158$	1.52628	0.121424
$159$	13.9361	1.10520
$160$	7.56675	0.598204
$161$	5.63859	0.444384
$162$	23.2735	1.82854
$163$	−5.76554	−0.451592	−0.225796	−	0.974175i	$-0.572498\pi$
$163$	−5.76554	−0.451592	−0.225796	+	0.974175i	$0.572498\pi$
$164$	5.17668	0.404231
$165$	0	0
$166$	1.07551	0.0834755
$167$	−19.9529	−1.54400	−0.772001	−	0.635621i	$-0.780744\pi$
$167$	−19.9529	−1.54400	−0.772001	+	0.635621i	$0.780744\pi$
$168$	7.33376	0.565812
$169$	1.00000	0.0769231
$170$	−5.96921	−0.457817
$171$	0.326333	0.0249553
$172$	44.1934	3.36971
$173$	−11.9428	−0.907994	−0.453997	−	0.891003i	$-0.650002\pi$
$173$	−11.9428	−0.907994	−0.453997	+	0.891003i	$0.650002\pi$
$174$	−30.4342	−2.30721
$175$	0.476812	0.0360436
$176$	0	0
$177$	22.8555	1.71793
$178$	31.5891	2.36771
$179$	3.36066	0.251187	0.125594	−	0.992082i	$-0.459916\pi$
$179$	3.36066	0.251187	0.125594	+	0.992082i	$0.459916\pi$
$180$	2.42681	0.180884
$181$	−4.88480	−0.363084	−0.181542	−	0.983383i	$-0.558109\pi$
$181$	−4.88480	−0.363084	−0.181542	+	0.983383i	$0.558109\pi$
$182$	2.54672	0.188776
$183$	−9.35601	−0.691616
$184$	19.5366	1.44026
$185$	21.1038	1.55158
$186$	−22.2920	−1.63453
$187$	0	0
$188$	27.7022	2.02039
$189$	5.26715	0.383129
$190$	−5.18486	−0.376149
$191$	23.8139	1.72312	0.861558	−	0.507660i	$-0.169489\pi$
$191$	23.8139	1.72312	0.861558	+	0.507660i	$0.169489\pi$
$192$	−21.3044	−1.53751
$193$	−20.5458	−1.47892	−0.739461	−	0.673199i	$-0.764920\pi$
$193$	−20.5458	−1.47892	−0.739461	+	0.673199i	$0.764920\pi$
$194$	−27.8559	−1.99994
$195$	3.88842	0.278456
$196$	−20.9057	−1.49327
$197$	15.4653	1.10185	0.550927	−	0.834553i	$-0.314274\pi$
$197$	15.4653	1.10185	0.550927	+	0.834553i	$0.314274\pi$
$198$	0	0
$199$	−21.3373	−1.51256	−0.756280	−	0.654248i	$-0.772985\pi$
$199$	−21.3373	−1.51256	−0.756280	+	0.654248i	$0.772985\pi$
$200$	1.65205	0.116818
$201$	−8.71451	−0.614674
$202$	14.9582	1.05246
$203$	−7.62477	−0.535154
$204$	7.71964	0.540483
$205$	3.08613	0.215545
$206$	9.08241	0.632801
$207$	−1.66035	−0.115403
$208$	1.66178	0.115224
$209$	0	0
$210$	9.90274	0.683354
$211$	3.66130	0.252054	0.126027	−	0.992027i	$-0.459777\pi$
$211$	3.66130	0.252054	0.126027	+	0.992027i	$0.459777\pi$
$212$	27.3999	1.88183
$213$	27.7157	1.89905
$214$	−8.96872	−0.613089
$215$	26.3463	1.79681
$216$	18.2496	1.24173
$217$	−5.58488	−0.379126
$218$	25.5787	1.73241
$219$	−9.17346	−0.619885
$220$	0	0
$221$	1.18355	0.0796142
$222$	−42.5350	−2.85476
$223$	−2.06269	−0.138128	−0.0690638	−	0.997612i	$-0.522001\pi$
$223$	−2.06269	−0.138128	−0.0690638	+	0.997612i	$0.522001\pi$
$224$	−3.82086	−0.255292
$225$	−0.140403	−0.00936020
$226$	−14.3616	−0.955320
$227$	5.71198	0.379117	0.189559	−	0.981869i	$-0.439294\pi$
$227$	5.71198	0.379117	0.189559	+	0.981869i	$0.439294\pi$
$228$	6.70529	0.444069
$229$	−11.7859	−0.778835	−0.389417	−	0.921061i	$-0.627324\pi$
$229$	−11.7859	−0.778835	−0.389417	+	0.921061i	$0.627324\pi$
$230$	26.3801	1.73946
$231$	0	0
$232$	−26.4183	−1.73444
$233$	26.7518	1.75257	0.876284	−	0.481794i	$-0.160015\pi$
$233$	26.7518	1.75257	0.876284	+	0.481794i	$0.160015\pi$
$234$	−0.749914	−0.0490234
$235$	16.5150	1.07732
$236$	44.9366	2.92512
$237$	−1.17673	−0.0764369
$238$	3.01417	0.195380
$239$	22.8275	1.47659	0.738295	−	0.674478i	$-0.235631\pi$
$239$	22.8275	1.47659	0.738295	+	0.674478i	$0.235631\pi$
$240$	6.46172	0.417102
$241$	−18.4323	−1.18733	−0.593664	−	0.804713i	$-0.702319\pi$
$241$	−18.4323	−1.18733	−0.593664	+	0.804713i	$0.702319\pi$
$242$	0	0
$243$	−3.28548	−0.210764
$244$	−18.3950	−1.17762
$245$	−12.4632	−0.796242
$246$	−6.22015	−0.396582
$247$	1.02803	0.0654122
$248$	−19.3505	−1.22876
$249$	−0.829194	−0.0525481
$250$	27.4482	1.73597
$251$	11.9892	0.756751	0.378376	−	0.925652i	$-0.376483\pi$
$251$	11.9892	0.756751	0.378376	+	0.925652i	$0.376483\pi$
$252$	−1.22543	−0.0771946
$253$	0	0
$254$	−3.34591	−0.209941
$255$	4.60214	0.288197
$256$	−25.1403	−1.57127
$257$	−6.02852	−0.376049	−0.188024	−	0.982164i	$-0.560208\pi$
$257$	−6.02852	−0.376049	−0.188024	+	0.982164i	$0.560208\pi$
$258$	−53.1015	−3.30595
$259$	−10.6564	−0.662157
$260$	7.64508	0.474128
$261$	2.24521	0.138975
$262$	−12.6271	−0.780103
$263$	−9.26488	−0.571297	−0.285648	−	0.958334i	$-0.592209\pi$
$263$	−9.26488	−0.571297	−0.285648	+	0.958334i	$0.592209\pi$
$264$	0	0
$265$	16.3347	1.00344
$266$	2.61811	0.160527
$267$	−24.3546	−1.49048
$268$	−17.1337	−1.04661
$269$	9.20464	0.561217	0.280608	−	0.959822i	$-0.409464\pi$
$269$	9.20464	0.561217	0.280608	+	0.959822i	$0.409464\pi$
$270$	24.6423	1.49968
$271$	8.79483	0.534248	0.267124	−	0.963662i	$-0.413927\pi$
$271$	8.79483	0.534248	0.267124	+	0.963662i	$0.413927\pi$
$272$	1.96680	0.119255
$273$	−1.96347	−0.118835
$274$	−1.51351	−0.0914346
$275$	0	0
$276$	−34.1160	−2.05354
$277$	−18.9032	−1.13579	−0.567893	−	0.823102i	$-0.692241\pi$
$277$	−18.9032	−1.13579	−0.567893	+	0.823102i	$0.692241\pi$
$278$	42.1530	2.52817
$279$	1.64454	0.0984558
$280$	8.59603	0.513711
$281$	5.24690	0.313004	0.156502	−	0.987678i	$-0.449978\pi$
$281$	5.24690	0.313004	0.156502	+	0.987678i	$0.449978\pi$
$282$	−33.2862	−1.98216
$283$	−8.82012	−0.524302	−0.262151	−	0.965027i	$-0.584432\pi$
$283$	−8.82012	−0.524302	−0.262151	+	0.965027i	$0.584432\pi$
$284$	54.4921	3.23351
$285$	3.99743	0.236787
$286$	0	0
$287$	−1.55835	−0.0919867
$288$	1.12510	0.0662970
$289$	−15.5992	−0.917601
$290$	−35.6725	−2.09476
$291$	21.4764	1.25897
$292$	−18.0361	−1.05548
$293$	9.67691	0.565331	0.282666	−	0.959218i	$-0.408781\pi$
$293$	9.67691	0.565331	0.282666	+	0.959218i	$0.408781\pi$
$294$	25.1197	1.46501
$295$	26.7894	1.55974
$296$	−36.9223	−2.14606
$297$	0	0
$298$	−17.0756	−0.989165
$299$	−5.23055	−0.302490
$300$	−2.88492	−0.166561
$301$	−13.3037	−0.766811
$302$	−38.7723	−2.23110
$303$	−11.5325	−0.662524
$304$	1.70837	0.0979816
$305$	−10.9663	−0.627931
$306$	−0.887560	−0.0507384
$307$	25.1565	1.43576	0.717879	−	0.696168i	$-0.245113\pi$
$307$	25.1565	1.43576	0.717879	+	0.696168i	$0.245113\pi$
$308$	0	0
$309$	−7.00236	−0.398350
$310$	−26.1288	−1.48402
$311$	−29.1282	−1.65171	−0.825853	−	0.563885i	$-0.809306\pi$
$311$	−29.1282	−1.65171	−0.825853	+	0.563885i	$0.809306\pi$
$312$	−6.80303	−0.385146
$313$	−22.6607	−1.28086	−0.640429	−	0.768017i	$-0.721244\pi$
$313$	−22.6607	−1.28086	−0.640429	+	0.768017i	$0.721244\pi$
$314$	−0.364342	−0.0205610
$315$	−0.730550	−0.0411618
$316$	−2.31359	−0.130149
$317$	6.85548	0.385042	0.192521	−	0.981293i	$-0.438334\pi$
$317$	6.85548	0.385042	0.192521	+	0.981293i	$0.438334\pi$
$318$	−32.9229	−1.84623
$319$	0	0
$320$	−24.9713	−1.39594
$321$	6.91471	0.385941
$322$	−13.3207	−0.742336
$323$	1.21673	0.0677005
$324$	−35.2788	−1.95993
$325$	−0.442306	−0.0245347
$326$	13.6206	0.754378
$327$	−19.7207	−1.09056
$328$	−5.39937	−0.298131
$329$	−8.33928	−0.459760
$330$	0	0
$331$	−1.87735	−0.103189	−0.0515944	−	0.998668i	$-0.516430\pi$
$331$	−1.87735	−0.103189	−0.0515944	+	0.998668i	$0.516430\pi$
$332$	−1.63029	−0.0894738
$333$	3.13791	0.171956
$334$	47.1372	2.57923
$335$	−10.2144	−0.558074
$336$	−3.26287	−0.178004
$337$	33.7657	1.83933	0.919667	−	0.392700i	$-0.128459\pi$
$337$	33.7657	1.83933	0.919667	+	0.392700i	$0.128459\pi$
$338$	−2.36242	−0.128499
$339$	11.0725	0.601377
$340$	9.04833	0.490715
$341$	0	0
$342$	−0.770936	−0.0416874
$343$	13.8394	0.747258
$344$	−46.0945	−2.48525
$345$	−20.3386	−1.09499
$346$	28.2139	1.51679
$347$	−21.6087	−1.16001	−0.580007	−	0.814612i	$-0.696950\pi$
$347$	−21.6087	−1.16001	−0.580007	+	0.814612i	$0.696950\pi$
$348$	46.1332	2.47300
$349$	−25.6955	−1.37545	−0.687724	−	0.725972i	$-0.741390\pi$
$349$	−25.6955	−1.37545	−0.687724	+	0.725972i	$0.741390\pi$
$350$	−1.12643	−0.0602103
$351$	−4.88598	−0.260794
$352$	0	0
$353$	12.8401	0.683410	0.341705	−	0.939807i	$-0.388996\pi$
$353$	12.8401	0.683410	0.341705	+	0.939807i	$0.388996\pi$
$354$	−53.9945	−2.86977
$355$	32.4860	1.72418
$356$	−47.8839	−2.53784
$357$	−2.32387	−0.122992
$358$	−7.93930	−0.419605
$359$	−16.2548	−0.857893	−0.428947	−	0.903330i	$-0.641115\pi$
$359$	−16.2548	−0.857893	−0.428947	+	0.903330i	$0.641115\pi$
$360$	−2.53121	−0.133406
$361$	−17.9431	−0.944376
$362$	11.5400	0.606527
$363$	0	0
$364$	−3.86041	−0.202340
$365$	−10.7524	−0.562805
$366$	22.1028	1.15533
$367$	1.88486	0.0983891	0.0491945	−	0.998789i	$-0.484335\pi$
$367$	1.88486	0.0983891	0.0491945	+	0.998789i	$0.484335\pi$
$368$	−8.69203	−0.453103
$369$	0.458876	0.0238881
$370$	−49.8560	−2.59189
$371$	−8.24829	−0.428230
$372$	33.7910	1.75198
$373$	20.2429	1.04814	0.524070	−	0.851675i	$-0.324413\pi$
$373$	20.2429	1.04814	0.524070	+	0.851675i	$0.324413\pi$
$374$	0	0
$375$	−21.1620	−1.09280
$376$	−28.8939	−1.49009
$377$	7.07299	0.364278
$378$	−12.4432	−0.640011
$379$	26.5544	1.36401	0.682005	−	0.731347i	$-0.261108\pi$
$379$	26.5544	1.36401	0.682005	+	0.731347i	$0.261108\pi$
$380$	7.85939	0.403178
$381$	2.57964	0.132159
$382$	−56.2586	−2.87844
$383$	2.30196	0.117625	0.0588123	−	0.998269i	$-0.481269\pi$
$383$	2.30196	0.117625	0.0588123	+	0.998269i	$0.481269\pi$
$384$	37.4187	1.90952
$385$	0	0
$386$	48.5380	2.47052
$387$	3.91743	0.199134
$388$	42.2249	2.14365
$389$	−32.2965	−1.63750	−0.818749	−	0.574151i	$-0.805332\pi$
$389$	−32.2965	−1.63750	−0.818749	+	0.574151i	$0.805332\pi$
$390$	−9.18611	−0.465157
$391$	−6.19061	−0.313073
$392$	21.8051	1.10132
$393$	9.73523	0.491077
$394$	−36.5355	−1.84063
$395$	−1.37927	−0.0693985
$396$	0	0
$397$	−19.5159	−0.979474	−0.489737	−	0.871870i	$-0.662907\pi$
$397$	−19.5159	−0.979474	−0.489737	+	0.871870i	$0.662907\pi$
$398$	50.4077	2.52671
$399$	−2.01852	−0.101052
$400$	−0.735017	−0.0367508
$401$	−16.3606	−0.817007	−0.408504	−	0.912757i	$-0.633949\pi$
$401$	−16.3606	−0.817007	−0.408504	+	0.912757i	$0.633949\pi$
$402$	20.5874	1.02680
$403$	5.18072	0.258070
$404$	−22.6742	−1.12808
$405$	−21.0318	−1.04508
$406$	18.0129	0.893967
$407$	0	0
$408$	−8.05173	−0.398620
$409$	−3.83393	−0.189576	−0.0947879	−	0.995497i	$-0.530217\pi$
$409$	−3.83393	−0.189576	−0.0947879	+	0.995497i	$0.530217\pi$
$410$	−7.29075	−0.360065
$411$	1.16689	0.0575584
$412$	−13.7674	−0.678273
$413$	−13.5274	−0.665640
$414$	3.92246	0.192778
$415$	−0.971914	−0.0477094
$416$	3.54435	0.173776
$417$	−32.4991	−1.59149
$418$	0	0
$419$	−31.1596	−1.52225	−0.761124	−	0.648606i	$-0.775352\pi$
$419$	−31.1596	−1.52225	−0.761124	+	0.648606i	$0.775352\pi$
$420$	−15.0109	−0.732458
$421$	−3.47262	−0.169245	−0.0846226	−	0.996413i	$-0.526968\pi$
$421$	−3.47262	−0.169245	−0.0846226	+	0.996413i	$0.526968\pi$
$422$	−8.64954	−0.421053
$423$	2.45560	0.119396
$424$	−28.5786	−1.38790
$425$	−0.523491	−0.0253931
$426$	−65.4761	−3.17233
$427$	5.53749	0.267978
$428$	13.5951	0.657144
$429$	0	0
$430$	−62.2412	−3.00154
$431$	−7.33722	−0.353421	−0.176711	−	0.984263i	$-0.556546\pi$
$431$	−7.33722	−0.353421	−0.176711	+	0.984263i	$0.556546\pi$
$432$	−8.11944	−0.390647
$433$	35.3375	1.69821	0.849106	−	0.528222i	$-0.177141\pi$
$433$	35.3375	1.69821	0.849106	+	0.528222i	$0.177141\pi$
$434$	13.1938	0.633325
$435$	27.5028	1.31866
$436$	−38.7731	−1.85689
$437$	−5.37717	−0.257225
$438$	21.6716	1.03551
$439$	−22.2003	−1.05956	−0.529782	−	0.848134i	$-0.677726\pi$
$439$	−22.2003	−1.05956	−0.529782	+	0.848134i	$0.677726\pi$
$440$	0	0
$441$	−1.85314	−0.0882450
$442$	−2.79605	−0.132994
$443$	7.42472	0.352759	0.176380	−	0.984322i	$-0.443561\pi$
$443$	7.42472	0.352759	0.176380	+	0.984322i	$0.443561\pi$
$444$	64.4760	3.05989
$445$	−28.5465	−1.35323
$446$	4.87294	0.230740
$447$	13.1650	0.622683
$448$	12.6093	0.595735
$449$	−15.9685	−0.753601	−0.376800	−	0.926295i	$-0.622976\pi$
$449$	−15.9685	−0.753601	−0.376800	+	0.926295i	$0.622976\pi$
$450$	0.331691	0.0156361
$451$	0	0
$452$	21.7698	1.02397
$453$	29.8927	1.40448
$454$	−13.4941	−0.633310
$455$	−2.30142	−0.107892
$456$	−6.99374	−0.327512
$457$	−23.7945	−1.11306	−0.556529	−	0.830828i	$-0.687867\pi$
$457$	−23.7945	−1.11306	−0.556529	+	0.830828i	$0.687867\pi$
$458$	27.8433	1.30103
$459$	−5.78280	−0.269918
$460$	−39.9879	−1.86445
$461$	−0.0626903	−0.00291978	−0.00145989	−	0.999999i	$-0.500465\pi$
$461$	−0.0626903	−0.00291978	−0.00145989	+	0.999999i	$0.500465\pi$
$462$	0	0
$463$	−10.0284	−0.466061	−0.233031	−	0.972469i	$-0.574864\pi$
$463$	−10.0284	−0.466061	−0.233031	+	0.972469i	$0.574864\pi$
$464$	11.7538	0.545655
$465$	20.1448	0.934194
$466$	−63.1991	−2.92764
$467$	−13.4311	−0.621518	−0.310759	−	0.950489i	$-0.600583\pi$
$467$	−13.4311	−0.621518	−0.310759	+	0.950489i	$0.600583\pi$
$468$	1.13675	0.0525461
$469$	5.15781	0.238166
$470$	−39.0153	−1.79964
$471$	0.280901	0.0129432
$472$	−46.8697	−2.15735
$473$	0	0
$474$	2.77994	0.127687
$475$	−0.454705	−0.0208633
$476$	−4.56899	−0.209419
$477$	2.42881	0.111208
$478$	−53.9283	−2.46662
$479$	−38.8479	−1.77500	−0.887502	−	0.460803i	$-0.847561\pi$
$479$	−38.8479	−1.77500	−0.887502	+	0.460803i	$0.847561\pi$
$480$	13.7819	0.629057
$481$	9.88524	0.450728
$482$	43.5449	1.98342
$483$	10.2700	0.467303
$484$	0	0
$485$	25.1728	1.14304
$486$	7.76170	0.352078
$487$	35.5713	1.61189	0.805945	−	0.591990i	$-0.201658\pi$
$487$	35.5713	1.61189	0.805945	+	0.591990i	$0.201658\pi$
$488$	19.1863	0.868522
$489$	−10.5013	−0.474883
$490$	29.4433	1.33011
$491$	−5.34701	−0.241307	−0.120654	−	0.992695i	$-0.538499\pi$
$491$	−5.34701	−0.241307	−0.120654	+	0.992695i	$0.538499\pi$
$492$	9.42872	0.425079
$493$	8.37124	0.377022
$494$	−2.42865	−0.109270
$495$	0	0
$496$	8.60923	0.386566
$497$	−16.4039	−0.735817
$498$	1.95891	0.0877808
$499$	−2.13466	−0.0955605	−0.0477802	−	0.998858i	$-0.515215\pi$
$499$	−2.13466	−0.0955605	−0.0477802	+	0.998858i	$0.515215\pi$
$500$	−41.6069	−1.86072
$501$	−36.3419	−1.62364
$502$	−28.3235	−1.26414
$503$	15.9955	0.713206	0.356603	−	0.934256i	$-0.383935\pi$
$503$	15.9955	0.713206	0.356603	+	0.934256i	$0.383935\pi$
$504$	1.27814	0.0569329
$505$	−13.5174	−0.601518
$506$	0	0
$507$	1.82138	0.0808904
$508$	5.07185	0.225027
$509$	−2.71848	−0.120494	−0.0602471	−	0.998183i	$-0.519189\pi$
$509$	−2.71848	−0.120494	−0.0602471	+	0.998183i	$0.519189\pi$
$510$	−10.8722	−0.481430
$511$	5.42945	0.240185
$512$	18.3038	0.808920
$513$	−5.02295	−0.221768
$514$	14.2419	0.628184
$515$	−8.20760	−0.361670
$516$	80.4930	3.54351
$517$	0	0
$518$	25.1750	1.10612
$519$	−21.7524	−0.954825
$520$	−7.97396	−0.349681
$521$	7.02377	0.307717	0.153858	−	0.988093i	$-0.450830\pi$
$521$	7.02377	0.307717	0.153858	+	0.988093i	$0.450830\pi$
$522$	−5.30413	−0.232156
$523$	40.2088	1.75821	0.879104	−	0.476630i	$-0.158142\pi$
$523$	40.2088	1.75821	0.879104	+	0.476630i	$0.158142\pi$
$524$	19.1406	0.836159
$525$	0.868457	0.0379026
$526$	21.8876	0.954343
$527$	6.13164	0.267098
$528$	0	0
$529$	4.35861	0.189505
$530$	−38.5896	−1.67622
$531$	3.98331	0.172861
$532$	−3.96863	−0.172062
$533$	1.44558	0.0626150
$534$	57.5359	2.48982
$535$	8.10486	0.350403
$536$	17.8708	0.771899
$537$	6.12104	0.264143
$538$	−21.7452	−0.937504
$539$	0	0
$540$	−37.3537	−1.60745
$541$	−18.4408	−0.792832	−0.396416	−	0.918071i	$-0.629746\pi$
$541$	−18.4408	−0.792832	−0.396416	+	0.918071i	$0.629746\pi$
$542$	−20.7771	−0.892453
$543$	−8.89708	−0.381810
$544$	4.19492	0.179855
$545$	−23.1150	−0.990136
$546$	4.63856	0.198512
$547$	13.9331	0.595735	0.297867	−	0.954607i	$-0.403725\pi$
$547$	13.9331	0.595735	0.297867	+	0.954607i	$0.403725\pi$
$548$	2.29423	0.0980048
$549$	−1.63058	−0.0695916
$550$	0	0
$551$	7.27127	0.309766
$552$	35.5836	1.51454
$553$	0.696466	0.0296168
$554$	44.6575	1.89731
$555$	38.4380	1.63160
$556$	−63.8970	−2.70983
$557$	23.2610	0.985599	0.492799	−	0.870143i	$-0.335974\pi$
$557$	23.2610	0.985599	0.492799	+	0.870143i	$0.335974\pi$
$558$	−3.88509	−0.164469
$559$	12.3409	0.521965
$560$	−3.82447	−0.161613
$561$	0	0
$562$	−12.3954	−0.522868
$563$	−8.40233	−0.354116	−0.177058	−	0.984200i	$-0.556658\pi$
$563$	−8.40233	−0.354116	−0.177058	+	0.984200i	$0.556658\pi$
$564$	50.4563	2.12459
$565$	12.9783	0.546001
$566$	20.8369	0.875838
$567$	10.6201	0.446002
$568$	−56.8362	−2.38480
$569$	23.3850	0.980352	0.490176	−	0.871624i	$-0.336933\pi$
$569$	23.3850	0.980352	0.490176	+	0.871624i	$0.336933\pi$
$570$	−9.44362	−0.395550
$571$	−11.1741	−0.467623	−0.233812	−	0.972282i	$-0.575120\pi$
$571$	−11.1741	−0.467623	−0.233812	+	0.972282i	$0.575120\pi$
$572$	0	0
$573$	43.3743	1.81199
$574$	3.68149	0.153662
$575$	2.31350	0.0964797
$576$	−3.71297	−0.154707
$577$	31.5321	1.31270	0.656349	−	0.754458i	$-0.272100\pi$
$577$	31.5321	1.31270	0.656349	+	0.754458i	$0.272100\pi$
$578$	36.8519	1.53284
$579$	−37.4218	−1.55520
$580$	54.0736	2.24528
$581$	0.490771	0.0203606
$582$	−50.7363	−2.10309
$583$	0	0
$584$	18.8119	0.778444
$585$	0.677682	0.0280187
$586$	−22.8610	−0.944378
$587$	−9.45635	−0.390305	−0.195153	−	0.980773i	$-0.562520\pi$
$587$	−9.45635	−0.390305	−0.195153	+	0.980773i	$0.562520\pi$
$588$	−38.0773	−1.57028
$589$	5.32595	0.219452
$590$	−63.2879	−2.60552
$591$	28.1682	1.15868
$592$	16.4271	0.675150
$593$	−29.0535	−1.19308	−0.596541	−	0.802582i	$-0.703459\pi$
$593$	−29.0535	−1.19308	−0.596541	+	0.802582i	$0.703459\pi$
$594$	0	0
$595$	−2.72385	−0.111667
$596$	25.8838	1.06024
$597$	−38.8634	−1.59057
$598$	12.3568	0.505306
$599$	30.1763	1.23297	0.616484	−	0.787367i	$-0.288556\pi$
$599$	30.1763	1.23297	0.616484	+	0.787367i	$0.288556\pi$
$600$	3.00902	0.122843
$601$	10.1735	0.414984	0.207492	−	0.978237i	$-0.433470\pi$
$601$	10.1735	0.414984	0.207492	+	0.978237i	$0.433470\pi$
$602$	31.4289	1.28095
$603$	−1.51878	−0.0618496
$604$	58.7725	2.39142
$605$	0	0
$606$	27.2446	1.10674
$607$	−11.5102	−0.467185	−0.233592	−	0.972335i	$-0.575048\pi$
$607$	−11.5102	−0.467185	−0.233592	+	0.972335i	$0.575048\pi$
$608$	3.64371	0.147772
$609$	−13.8876	−0.562755
$610$	25.9072	1.04895
$611$	7.73579	0.312957
$612$	1.34539	0.0543843
$613$	−0.176543	−0.00713050	−0.00356525	−	0.999994i	$-0.501135\pi$
$613$	−0.176543	−0.00713050	−0.00356525	+	0.999994i	$0.501135\pi$
$614$	−59.4303	−2.39841
$615$	5.62103	0.226662
$616$	0	0
$617$	14.4909	0.583380	0.291690	−	0.956513i	$-0.405782\pi$
$617$	14.4909	0.583380	0.291690	+	0.956513i	$0.405782\pi$
$618$	16.5425	0.665439
$619$	16.5284	0.664333	0.332167	−	0.943221i	$-0.392220\pi$
$619$	16.5284	0.664333	0.332167	+	0.943221i	$0.392220\pi$
$620$	39.6070	1.59066
$621$	25.5563	1.02554
$622$	68.8130	2.75915
$623$	14.4146	0.577511
$624$	3.02674	0.121167
$625$	−22.5928	−0.903713
$626$	53.5342	2.13966
$627$	0	0
$628$	0.552283	0.0220385
$629$	11.6997	0.466496
$630$	1.72587	0.0687603
$631$	2.46444	0.0981080	0.0490540	−	0.998796i	$-0.484379\pi$
$631$	2.46444	0.0981080	0.0490540	+	0.998796i	$0.484379\pi$
$632$	2.41311	0.0959885
$633$	6.66863	0.265054
$634$	−16.1955	−0.643207
$635$	3.02364	0.119989
$636$	49.9057	1.97889
$637$	−5.83789	−0.231306
$638$	0	0
$639$	4.83034	0.191085
$640$	43.8592	1.73369
$641$	4.25164	0.167930	0.0839649	−	0.996469i	$-0.473242\pi$
$641$	4.25164	0.167930	0.0839649	+	0.996469i	$0.473242\pi$
$642$	−16.3355	−0.644709
$643$	−2.08213	−0.0821111	−0.0410556	−	0.999157i	$-0.513072\pi$
$643$	−2.08213	−0.0821111	−0.0410556	+	0.999157i	$0.513072\pi$
$644$	20.1921	0.795678
$645$	47.9868	1.88948
$646$	−2.87443	−0.113093
$647$	−24.4909	−0.962838	−0.481419	−	0.876490i	$-0.659879\pi$
$647$	−24.4909	−0.962838	−0.481419	+	0.876490i	$0.659879\pi$
$648$	36.7964	1.44550
$649$	0	0
$650$	1.04491	0.0409849
$651$	−10.1722	−0.398680
$652$	−20.6466	−0.808585
$653$	6.80654	0.266360	0.133180	−	0.991092i	$-0.457481\pi$
$653$	6.80654	0.266360	0.133180	+	0.991092i	$0.457481\pi$
$654$	46.5886	1.82176
$655$	11.4108	0.445858
$656$	2.40224	0.0937917
$657$	−1.59877	−0.0623739
$658$	19.7009	0.768022
$659$	−43.2019	−1.68291	−0.841453	−	0.540331i	$-0.818299\pi$
$659$	−43.2019	−1.68291	−0.841453	+	0.540331i	$0.818299\pi$
$660$	0	0
$661$	−24.8882	−0.968040	−0.484020	−	0.875057i	$-0.660824\pi$
$661$	−24.8882	−0.968040	−0.484020	+	0.875057i	$0.660824\pi$
$662$	4.43511	0.172375
$663$	2.15570	0.0837203
$664$	1.70042	0.0659891
$665$	−2.36594	−0.0917472
$666$	−7.41307	−0.287251
$667$	−36.9956	−1.43248
$668$	−71.4522	−2.76457
$669$	−3.75694	−0.145252
$670$	24.1308	0.932255
$671$	0	0
$672$	−6.95924	−0.268458
$673$	6.30068	0.242873	0.121437	−	0.992599i	$-0.461250\pi$
$673$	6.30068	0.242873	0.121437	+	0.992599i	$0.461250\pi$
$674$	−79.7688	−3.07258
$675$	2.16110	0.0831807
$676$	3.58104	0.137732
$677$	−48.4748	−1.86304	−0.931518	−	0.363694i	$-0.881515\pi$
$677$	−48.4748	−1.86304	−0.931518	+	0.363694i	$0.881515\pi$
$678$	−26.1580	−1.00459
$679$	−12.7111	−0.487808
$680$	−9.43758	−0.361914
$681$	10.4037	0.398670
$682$	0	0
$683$	27.0779	1.03611	0.518054	−	0.855348i	$-0.326657\pi$
$683$	27.0779	1.03611	0.518054	+	0.855348i	$0.326657\pi$
$684$	1.16861	0.0446830
$685$	1.36773	0.0522583
$686$	−32.6945	−1.24828
$687$	−21.4667	−0.819004
$688$	20.5079	0.781858
$689$	7.65138	0.291494
$690$	48.0483	1.82917
$691$	−31.7460	−1.20768	−0.603838	−	0.797107i	$-0.706362\pi$
$691$	−31.7460	−1.20768	−0.603838	+	0.797107i	$0.706362\pi$
$692$	−42.7677	−1.62578
$693$	0	0
$694$	51.0488	1.93779
$695$	−38.0928	−1.44494
$696$	−48.1178	−1.82390
$697$	1.71092	0.0648055
$698$	60.7036	2.29767
$699$	48.7253	1.84296
$700$	1.70748	0.0645368
$701$	−5.85607	−0.221181	−0.110590	−	0.993866i	$-0.535274\pi$
$701$	−5.85607	−0.221181	−0.110590	+	0.993866i	$0.535274\pi$
$702$	11.5427	0.435653
$703$	10.1623	0.383280
$704$	0	0
$705$	30.0801	1.13288
$706$	−30.3337	−1.14163
$707$	6.82568	0.256706
$708$	81.8467	3.07599
$709$	−45.8036	−1.72019	−0.860094	−	0.510135i	$-0.829595\pi$
$709$	−45.8036	−1.72019	−0.860094	+	0.510135i	$0.829595\pi$
$710$	−76.7457	−2.88022
$711$	−0.205083	−0.00769122
$712$	49.9438	1.87172
$713$	−27.0980	−1.01483
$714$	5.48996	0.205457
$715$	0	0
$716$	12.0347	0.449756
$717$	41.5776	1.55275
$718$	38.4006	1.43310
$719$	−18.8579	−0.703280	−0.351640	−	0.936135i	$-0.614376\pi$
$719$	−18.8579	−0.703280	−0.351640	+	0.936135i	$0.614376\pi$
$720$	1.12616	0.0419695
$721$	4.14445	0.154348
$722$	42.3893	1.57757
$723$	−33.5723	−1.24857
$724$	−17.4927	−0.650110
$725$	−3.12843	−0.116187
$726$	0	0
$727$	−18.7319	−0.694727	−0.347363	−	0.937731i	$-0.612923\pi$
$727$	−18.7319	−0.694727	−0.347363	+	0.937731i	$0.612923\pi$
$728$	4.02648	0.149231
$729$	23.5705	0.872981
$730$	25.4017	0.940158
$731$	14.6061	0.540226
$732$	−33.5043	−1.23835
$733$	−2.78779	−0.102969	−0.0514846	−	0.998674i	$-0.516395\pi$
$733$	−2.78779	−0.102969	−0.0514846	+	0.998674i	$0.516395\pi$
$734$	−4.45285	−0.164358
$735$	−22.7002	−0.837309
$736$	−18.5389	−0.683352
$737$	0	0
$738$	−1.08406	−0.0399048
$739$	11.0941	0.408102	0.204051	−	0.978960i	$-0.434589\pi$
$739$	11.0941	0.408102	0.204051	+	0.978960i	$0.434589\pi$
$740$	75.5734	2.77813
$741$	1.87244	0.0687858
$742$	19.4859	0.715351
$743$	22.8191	0.837153	0.418577	−	0.908181i	$-0.362529\pi$
$743$	22.8191	0.837153	0.418577	+	0.908181i	$0.362529\pi$
$744$	−35.2446	−1.29213
$745$	15.4309	0.565345
$746$	−47.8224	−1.75090
$747$	−0.144514	−0.00528748
$748$	0	0
$749$	−4.09257	−0.149539
$750$	49.9936	1.82551
$751$	12.3826	0.451846	0.225923	−	0.974145i	$-0.427460\pi$
$751$	12.3826	0.451846	0.225923	+	0.974145i	$0.427460\pi$
$752$	12.8552	0.468781
$753$	21.8369	0.795781
$754$	−16.7094	−0.608520
$755$	35.0378	1.27516
$756$	18.8619	0.686000
$757$	−12.4395	−0.452120	−0.226060	−	0.974113i	$-0.572585\pi$
$757$	−12.4395	−0.452120	−0.226060	+	0.974113i	$0.572585\pi$
$758$	−62.7328	−2.27856
$759$	0	0
$760$	−8.19749	−0.297354
$761$	42.7827	1.55087	0.775437	−	0.631425i	$-0.217530\pi$
$761$	42.7827	1.55087	0.775437	+	0.631425i	$0.217530\pi$
$762$	−6.09419	−0.220769
$763$	11.6720	0.422554
$764$	85.2787	3.08527
$765$	0.802071	0.0289989
$766$	−5.43820	−0.196490
$767$	12.5485	0.453099
$768$	−45.7901	−1.65231
$769$	3.24436	0.116994	0.0584972	−	0.998288i	$-0.481369\pi$
$769$	3.24436	0.116994	0.0584972	+	0.998288i	$0.481369\pi$
$770$	0	0
$771$	−10.9802	−0.395444
$772$	−73.5755	−2.64804
$773$	−8.31443	−0.299049	−0.149525	−	0.988758i	$-0.547774\pi$
$773$	−8.31443	−0.299049	−0.149525	+	0.988758i	$0.547774\pi$
$774$	−9.25463	−0.332651
$775$	−2.29146	−0.0823118
$776$	−44.0414	−1.58099
$777$	−19.4094	−0.696308
$778$	76.2981	2.73542
$779$	1.48610	0.0532452
$780$	13.9246	0.498581
$781$	0	0
$782$	14.6248	0.522983
$783$	−34.5585	−1.23502
$784$	−9.70130	−0.346475
$785$	0.329249	0.0117514
$786$	−22.9987	−0.820338
$787$	−12.2857	−0.437938	−0.218969	−	0.975732i	$-0.570269\pi$
$787$	−12.2857	−0.437938	−0.218969	+	0.975732i	$0.570269\pi$
$788$	55.3818	1.97289
$789$	−16.8749	−0.600762
$790$	3.25842	0.115929
$791$	−6.55344	−0.233013
$792$	0	0
$793$	−5.13676	−0.182412
$794$	46.1048	1.63620
$795$	29.7518	1.05519
$796$	−76.4097	−2.70827
$797$	−9.90121	−0.350719	−0.175360	−	0.984504i	$-0.556109\pi$
$797$	−9.90121	−0.350719	−0.175360	+	0.984504i	$0.556109\pi$
$798$	4.76859	0.168806
$799$	9.15570	0.323905
$800$	−1.56769	−0.0554262
$801$	−4.24457	−0.149974
$802$	38.6505	1.36480
$803$	0	0
$804$	−31.2070	−1.10059
$805$	12.0377	0.424273
$806$	−12.2390	−0.431102
$807$	16.7652	0.590162
$808$	23.6496	0.831989
$809$	27.1590	0.954860	0.477430	−	0.878670i	$-0.341568\pi$
$809$	27.1590	0.954860	0.477430	+	0.878670i	$0.341568\pi$
$810$	49.6860	1.74579
$811$	−46.7602	−1.64197	−0.820987	−	0.570947i	$-0.806576\pi$
$811$	−46.7602	−1.64197	−0.820987	+	0.570947i	$0.806576\pi$
$812$	−27.3046	−0.958205
$813$	16.0187	0.561802
$814$	0	0
$815$	−12.3087	−0.431155
$816$	3.58230	0.125406
$817$	12.6869	0.443858
$818$	9.05737	0.316683
$819$	−0.342198	−0.0119574
$820$	11.0516	0.385938
$821$	−36.9147	−1.28833	−0.644166	−	0.764886i	$-0.722795\pi$
$821$	−36.9147	−1.28833	−0.644166	+	0.764886i	$0.722795\pi$
$822$	−2.75668	−0.0961504
$823$	52.6237	1.83435	0.917174	−	0.398487i	$-0.130464\pi$
$823$	52.6237	1.83435	0.917174	+	0.398487i	$0.130464\pi$
$824$	14.3597	0.500243
$825$	0	0
$826$	31.9574	1.11194
$827$	−18.8272	−0.654684	−0.327342	−	0.944906i	$-0.606153\pi$
$827$	−18.8272	−0.654684	−0.327342	+	0.944906i	$0.606153\pi$
$828$	−5.94580	−0.206631
$829$	−28.0041	−0.972623	−0.486311	−	0.873786i	$-0.661658\pi$
$829$	−28.0041	−0.972623	−0.486311	+	0.873786i	$0.661658\pi$
$830$	2.29607	0.0796978
$831$	−34.4300	−1.19436
$832$	−11.6968	−0.405514
$833$	−6.90943	−0.239398
$834$	76.7767	2.65856
$835$	−42.5970	−1.47413
$836$	0	0
$837$	−25.3129	−0.874941
$838$	73.6123	2.54289
$839$	−14.0562	−0.485273	−0.242637	−	0.970117i	$-0.578012\pi$
$839$	−14.0562	−0.485273	−0.242637	+	0.970117i	$0.578012\pi$
$840$	15.6567	0.540206
$841$	21.0272	0.725076
$842$	8.20380	0.282722
$843$	9.55661	0.329147
$844$	13.1113	0.451309
$845$	2.13488	0.0734420
$846$	−5.80118	−0.199449
$847$	0	0
$848$	12.7149	0.436633
$849$	−16.0648	−0.551343
$850$	1.23671	0.0424187
$851$	−51.7052	−1.77243
$852$	99.2510	3.40028
$853$	49.8628	1.70727	0.853634	−	0.520873i	$-0.174394\pi$
$853$	49.8628	1.70727	0.853634	+	0.520873i	$0.174394\pi$
$854$	−13.0819	−0.447654
$855$	0.696680	0.0238259
$856$	−14.1799	−0.484660
$857$	−43.3736	−1.48161	−0.740807	−	0.671718i	$-0.765557\pi$
$857$	−43.3736	−1.48161	−0.740807	+	0.671718i	$0.765557\pi$
$858$	0	0
$859$	−7.89562	−0.269395	−0.134698	−	0.990887i	$-0.543006\pi$
$859$	−7.89562	−0.269395	−0.134698	+	0.990887i	$0.543006\pi$
$860$	94.3474	3.21722
$861$	−2.83836	−0.0967310
$862$	17.3336	0.590385
$863$	−13.4001	−0.456145	−0.228072	−	0.973644i	$-0.573242\pi$
$863$	−13.4001	−0.456145	−0.228072	+	0.973644i	$0.573242\pi$
$864$	−17.3176	−0.589157
$865$	−25.4964	−0.866903
$866$	−83.4822	−2.83684
$867$	−28.4121	−0.964926
$868$	−19.9997	−0.678834
$869$	0	0
$870$	−64.9732	−2.20280
$871$	−4.78456	−0.162119
$872$	40.4410	1.36951
$873$	3.74294	0.126679
$874$	12.7032	0.429691
$875$	12.5250	0.423424
$876$	−32.8506	−1.10992
$877$	−39.9806	−1.35005	−0.675025	−	0.737795i	$-0.735867\pi$
$877$	−39.9806	−1.35005	−0.675025	+	0.737795i	$0.735867\pi$
$878$	52.4465	1.76998
$879$	17.6254	0.594489
$880$	0	0
$881$	21.3954	0.720828	0.360414	−	0.932792i	$-0.382635\pi$
$881$	21.3954	0.720828	0.360414	+	0.932792i	$0.382635\pi$
$882$	4.37791	0.147412
$883$	−22.3631	−0.752578	−0.376289	−	0.926502i	$-0.622800\pi$
$883$	−22.3631	−0.752578	−0.376289	+	0.926502i	$0.622800\pi$
$884$	4.23834	0.142551
$885$	48.7938	1.64018
$886$	−17.5403	−0.589279
$887$	−44.3426	−1.48888	−0.744439	−	0.667690i	$-0.767283\pi$
$887$	−44.3426	−1.48888	−0.744439	+	0.667690i	$0.767283\pi$
$888$	−67.2496	−2.25675
$889$	−1.52680	−0.0512071
$890$	67.4389	2.26056
$891$	0	0
$892$	−7.38657	−0.247321
$893$	7.95265	0.266125
$894$	−31.1013	−1.04018
$895$	7.17459	0.239820
$896$	−22.1468	−0.739874
$897$	−9.52682	−0.318091
$898$	37.7244	1.25888
$899$	36.6432	1.22212
$900$	−0.502789	−0.0167596
$901$	9.05579	0.301692
$902$	0	0
$903$	−24.2311	−0.806360
$904$	−22.7063	−0.755201
$905$	−10.4284	−0.346653
$906$	−70.6193	−2.34617
$907$	−7.77880	−0.258291	−0.129145	−	0.991626i	$-0.541223\pi$
$907$	−7.77880	−0.258291	−0.129145	+	0.991626i	$0.541223\pi$
$908$	20.4548	0.678818
$909$	−2.00990	−0.0666643
$910$	5.43694	0.180233
$911$	26.5426	0.879395	0.439697	−	0.898146i	$-0.355086\pi$
$911$	26.5426	0.879395	0.439697	+	0.898146i	$0.355086\pi$
$912$	3.11159	0.103035
$913$	0	0
$914$	56.2126	1.85935
$915$	−19.9739	−0.660317
$916$	−42.2059	−1.39452
$917$	−5.76194	−0.190276
$918$	13.6614	0.450894
$919$	20.6094	0.679843	0.339921	−	0.940454i	$-0.389600\pi$
$919$	20.6094	0.679843	0.339921	+	0.940454i	$0.389600\pi$
$920$	41.7081	1.37508
$921$	45.8196	1.50981
$922$	0.148101	0.00487745
$923$	15.2168	0.500868
$924$	0	0
$925$	−4.37230	−0.143760
$926$	23.6914	0.778548
$927$	−1.22039	−0.0400827
$928$	25.0692	0.822936
$929$	−39.3557	−1.29122	−0.645609	−	0.763668i	$-0.723397\pi$
$929$	−39.3557	−1.29122	−0.645609	+	0.763668i	$0.723397\pi$
$930$	−47.5906	−1.56056
$931$	−6.00154	−0.196693
$932$	95.7993	3.13801
$933$	−53.0535	−1.73689
$934$	31.7300	1.03824
$935$	0	0
$936$	−1.18565	−0.0387540
$937$	30.6091	0.999955	0.499977	−	0.866039i	$-0.333342\pi$
$937$	30.6091	0.999955	0.499977	+	0.866039i	$0.333342\pi$
$938$	−12.1849	−0.397852
$939$	−41.2738	−1.34692
$940$	59.1408	1.92896
$941$	−50.6480	−1.65108	−0.825539	−	0.564345i	$-0.809129\pi$
$941$	−50.6480	−1.65108	−0.825539	+	0.564345i	$0.809129\pi$
$942$	−0.663607	−0.0216215
$943$	−7.56117	−0.246226
$944$	20.8528	0.678701
$945$	11.2447	0.365790
$946$	0	0
$947$	33.0294	1.07331	0.536655	−	0.843802i	$-0.319688\pi$
$947$	33.0294	1.07331	0.536655	+	0.843802i	$0.319688\pi$
$948$	−4.21393	−0.136862
$949$	−5.03654	−0.163493
$950$	1.07421	0.0348519
$951$	12.4864	0.404901
$952$	4.76554	0.154452
$953$	13.2576	0.429457	0.214728	−	0.976674i	$-0.431113\pi$
$953$	13.2576	0.429457	0.214728	+	0.976674i	$0.431113\pi$
$954$	−5.73787	−0.185771
$955$	50.8398	1.64514
$956$	81.7463	2.64386
$957$	0	0
$958$	91.7751	2.96512
$959$	−0.690641	−0.0223020
$960$	−45.4822	−1.46793
$961$	−4.16018	−0.134199
$962$	−23.3531	−0.752935
$963$	1.20511	0.0388341
$964$	−66.0068	−2.12594
$965$	−43.8628	−1.41199
$966$	−24.2622	−0.780623
$967$	12.3240	0.396314	0.198157	−	0.980170i	$-0.436504\pi$
$967$	12.3240	0.396314	0.198157	+	0.980170i	$0.436504\pi$
$968$	0	0
$969$	2.21613	0.0711922
$970$	−59.4689	−1.90943
$971$	46.6986	1.49863	0.749315	−	0.662214i	$-0.230383\pi$
$971$	46.6986	1.49863	0.749315	+	0.662214i	$0.230383\pi$
$972$	−11.7655	−0.377377
$973$	19.2351	0.616649
$974$	−84.0345	−2.69264
$975$	−0.805609	−0.0258001
$976$	−8.53618	−0.273237
$977$	27.9965	0.895686	0.447843	−	0.894112i	$-0.352192\pi$
$977$	27.9965	0.895686	0.447843	+	0.894112i	$0.352192\pi$
$978$	24.8084	0.793285
$979$	0	0
$980$	−44.6311	−1.42569
$981$	−3.43696	−0.109734
$982$	12.6319	0.403100
$983$	7.93937	0.253227	0.126613	−	0.991952i	$-0.459589\pi$
$983$	7.93937	0.253227	0.126613	+	0.991952i	$0.459589\pi$
$984$	−9.83432	−0.313507
$985$	33.0164	1.05199
$986$	−19.7764	−0.629809
$987$	−15.1890	−0.483472
$988$	3.68143	0.117122
$989$	−64.5498	−2.05256
$990$	0	0
$991$	30.0106	0.953317	0.476659	−	0.879089i	$-0.341848\pi$
$991$	30.0106	0.953317	0.476659	+	0.879089i	$0.341848\pi$
$992$	18.3623	0.583003
$993$	−3.41938	−0.108511
$994$	38.7530	1.22917
$995$	−45.5524	−1.44411
$996$	−2.96938	−0.0940884
$997$	20.7135	0.656003	0.328002	−	0.944677i	$-0.393625\pi$
$997$	20.7135	0.656003	0.328002	+	0.944677i	$0.393625\pi$
$998$	5.04297	0.159632
$999$	−48.2991	−1.52811

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.2.a.s.1.2		14
11.5	even	5		143.2.h.c.14.7	✓	28
11.9	even	5		143.2.h.c.92.7	yes	28
11.10	odd	2		1573.2.a.r.1.13		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.h.c.14.7	✓	28	11.5	even	5
143.2.h.c.92.7	yes	28	11.9	even	5
1573.2.a.r.1.13		14	11.10	odd	2
1573.2.a.s.1.2		14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1573 = 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1573.a (trivial)

\(f(q)\)	\(=\)	\(q-2.36242 q^{2} +1.82138 q^{3} +3.58104 q^{4} +2.13488 q^{5} -4.30288 q^{6} -1.07801 q^{7} -3.73509 q^{8} +0.317434 q^{9} +O(q^{10})\)	\(q-2.36242 q^{2} +1.82138 q^{3} +3.58104 q^{4} +2.13488 q^{5} -4.30288 q^{6} -1.07801 q^{7} -3.73509 q^{8} +0.317434 q^{9} -5.04348 q^{10} +6.52245 q^{12} +1.00000 q^{13} +2.54672 q^{14} +3.88842 q^{15} +1.66178 q^{16} +1.18355 q^{17} -0.749914 q^{18} +1.02803 q^{19} +7.64508 q^{20} -1.96347 q^{21} -5.23055 q^{23} -6.80303 q^{24} -0.442306 q^{25} -2.36242 q^{26} -4.88598 q^{27} -3.86041 q^{28} +7.07299 q^{29} -9.18611 q^{30} +5.18072 q^{31} +3.54435 q^{32} -2.79605 q^{34} -2.30142 q^{35} +1.13675 q^{36} +9.88524 q^{37} -2.42865 q^{38} +1.82138 q^{39} -7.97396 q^{40} +1.44558 q^{41} +4.63856 q^{42} +12.3409 q^{43} +0.677682 q^{45} +12.3568 q^{46} +7.73579 q^{47} +3.02674 q^{48} -5.83789 q^{49} +1.04491 q^{50} +2.15570 q^{51} +3.58104 q^{52} +7.65138 q^{53} +11.5427 q^{54} +4.02648 q^{56} +1.87244 q^{57} -16.7094 q^{58} +12.5485 q^{59} +13.9246 q^{60} -5.13676 q^{61} -12.2390 q^{62} -0.342198 q^{63} -11.6968 q^{64} +2.13488 q^{65} -4.78456 q^{67} +4.23834 q^{68} -9.52682 q^{69} +5.43694 q^{70} +15.2168 q^{71} -1.18565 q^{72} -5.03654 q^{73} -23.3531 q^{74} -0.805609 q^{75} +3.68143 q^{76} -4.30288 q^{78} -0.646065 q^{79} +3.54770 q^{80} -9.85154 q^{81} -3.41507 q^{82} -0.455255 q^{83} -7.03128 q^{84} +2.52673 q^{85} -29.1545 q^{86} +12.8826 q^{87} -13.3715 q^{89} -1.60097 q^{90} -1.07801 q^{91} -18.7308 q^{92} +9.43607 q^{93} -18.2752 q^{94} +2.19472 q^{95} +6.45562 q^{96} +11.7912 q^{97} +13.7916 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + q^{2} + 9 q^{3} + 15 q^{4} + 9 q^{5} + 13 q^{6} - q^{7} + 3 q^{8} + 17 q^{9}+O(q^{10}) \) 14 * q + q^2 + 9 * q^3 + 15 * q^4 + 9 * q^5 + 13 * q^6 - q^7 + 3 * q^8 + 17 * q^9	\( 14 q + q^{2} + 9 q^{3} + 15 q^{4} + 9 q^{5} + 13 q^{6} - q^{7} + 3 q^{8} + 17 q^{9} - 12 q^{10} + 19 q^{12} + 14 q^{13} + 9 q^{14} + 19 q^{15} + 13 q^{16} - 4 q^{17} - 15 q^{18} + 5 q^{19} + 17 q^{20} + 25 q^{23} + 29 q^{24} + 13 q^{25} + q^{26} + 33 q^{27} + 15 q^{28} - 16 q^{29} - 8 q^{30} + 6 q^{31} + 12 q^{32} + 13 q^{34} + 8 q^{35} + 24 q^{36} + 11 q^{37} + 22 q^{38} + 9 q^{39} - 43 q^{40} + q^{41} - 5 q^{42} - 16 q^{43} + 39 q^{45} + 22 q^{46} + 38 q^{47} + 6 q^{48} + 9 q^{49} + 8 q^{50} - 24 q^{51} + 15 q^{52} + 52 q^{53} - 21 q^{54} + 17 q^{56} + 9 q^{57} - 19 q^{58} + 27 q^{59} + 13 q^{60} - 19 q^{61} - 56 q^{62} + 11 q^{63} - 29 q^{64} + 9 q^{65} + 29 q^{67} - 14 q^{68} + 21 q^{69} - 68 q^{70} + 34 q^{71} + 65 q^{72} - 18 q^{73} - 18 q^{74} + 11 q^{75} + 3 q^{76} + 13 q^{78} - 17 q^{79} - q^{80} + 18 q^{81} + 9 q^{82} + 16 q^{83} - 21 q^{84} + 2 q^{85} + 9 q^{86} - 6 q^{87} + 19 q^{89} + 13 q^{90} - q^{91} + 22 q^{92} + 2 q^{93} + 75 q^{94} - 29 q^{95} - 13 q^{96} - 20 q^{97} + 81 q^{98}+O(q^{100}) \) 14 * q + q^2 + 9 * q^3 + 15 * q^4 + 9 * q^5 + 13 * q^6 - q^7 + 3 * q^8 + 17 * q^9 - 12 * q^10 + 19 * q^12 + 14 * q^13 + 9 * q^14 + 19 * q^15 + 13 * q^16 - 4 * q^17 - 15 * q^18 + 5 * q^19 + 17 * q^20 + 25 * q^23 + 29 * q^24 + 13 * q^25 + q^26 + 33 * q^27 + 15 * q^28 - 16 * q^29 - 8 * q^30 + 6 * q^31 + 12 * q^32 + 13 * q^34 + 8 * q^35 + 24 * q^36 + 11 * q^37 + 22 * q^38 + 9 * q^39 - 43 * q^40 + q^41 - 5 * q^42 - 16 * q^43 + 39 * q^45 + 22 * q^46 + 38 * q^47 + 6 * q^48 + 9 * q^49 + 8 * q^50 - 24 * q^51 + 15 * q^52 + 52 * q^53 - 21 * q^54 + 17 * q^56 + 9 * q^57 - 19 * q^58 + 27 * q^59 + 13 * q^60 - 19 * q^61 - 56 * q^62 + 11 * q^63 - 29 * q^64 + 9 * q^65 + 29 * q^67 - 14 * q^68 + 21 * q^69 - 68 * q^70 + 34 * q^71 + 65 * q^72 - 18 * q^73 - 18 * q^74 + 11 * q^75 + 3 * q^76 + 13 * q^78 - 17 * q^79 - q^80 + 18 * q^81 + 9 * q^82 + 16 * q^83 - 21 * q^84 + 2 * q^85 + 9 * q^86 - 6 * q^87 + 19 * q^89 + 13 * q^90 - q^91 + 22 * q^92 + 2 * q^93 + 75 * q^94 - 29 * q^95 - 13 * q^96 - 20 * q^97 + 81 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more