LMFDB - Embedded newform 2057.4.a.u.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2057,4,Mod(1,2057)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2057, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("2057.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2057 = 11^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2057.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:	$121.366928882$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	no (minimal twist has level 187)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	2057.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.78655 q^{2} +5.72685 q^{3} +14.9110 q^{4} +0.431714 q^{5} -27.4118 q^{6} -26.0630 q^{7} -33.0800 q^{8} +5.79678 q^{9} +O(q^{10})$	\(q-4.78655 q^{2} +5.72685 q^{3} +14.9110 q^{4} +0.431714 q^{5} -27.4118 q^{6} -26.0630 q^{7} -33.0800 q^{8} +5.79678 q^{9} -2.06642 q^{10} +85.3932 q^{12} -64.5081 q^{13} +124.752 q^{14} +2.47236 q^{15} +39.0506 q^{16} +17.0000 q^{17} -27.7465 q^{18} -87.1729 q^{19} +6.43729 q^{20} -149.259 q^{21} +197.571 q^{23} -189.444 q^{24} -124.814 q^{25} +308.771 q^{26} -121.428 q^{27} -388.626 q^{28} +154.126 q^{29} -11.8341 q^{30} +119.027 q^{31} +77.7224 q^{32} -81.3713 q^{34} -11.2518 q^{35} +86.4359 q^{36} -348.669 q^{37} +417.257 q^{38} -369.428 q^{39} -14.2811 q^{40} +265.786 q^{41} +714.435 q^{42} -295.791 q^{43} +2.50255 q^{45} -945.683 q^{46} +130.616 q^{47} +223.637 q^{48} +336.280 q^{49} +597.426 q^{50} +97.3564 q^{51} -961.882 q^{52} -490.232 q^{53} +581.219 q^{54} +862.163 q^{56} -499.226 q^{57} -737.730 q^{58} -567.337 q^{59} +36.8654 q^{60} -216.261 q^{61} -569.727 q^{62} -151.081 q^{63} -684.426 q^{64} -27.8490 q^{65} +443.190 q^{67} +253.487 q^{68} +1131.46 q^{69} +53.8570 q^{70} -814.737 q^{71} -191.757 q^{72} -490.120 q^{73} +1668.92 q^{74} -714.789 q^{75} -1299.84 q^{76} +1768.28 q^{78} -1125.31 q^{79} +16.8587 q^{80} -851.910 q^{81} -1272.20 q^{82} +285.100 q^{83} -2225.60 q^{84} +7.33913 q^{85} +1415.82 q^{86} +882.655 q^{87} +404.506 q^{89} -11.9786 q^{90} +1681.28 q^{91} +2945.99 q^{92} +681.647 q^{93} -625.200 q^{94} -37.6337 q^{95} +445.104 q^{96} +414.146 q^{97} -1609.62 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - q^{2} + 20 q^{3} + 235 q^{4} + 40 q^{5} + 24 q^{6} + 42 q^{7} - 45 q^{8} + 572 q^{9}+O(q^{10}) $ 52 * q - q^2 + 20 * q^3 + 235 * q^4 + 40 * q^5 + 24 * q^6 + 42 * q^7 - 45 * q^8 + 572 * q^9	\( 52 q - q^{2} + 20 q^{3} + 235 q^{4} + 40 q^{5} + 24 q^{6} + 42 q^{7} - 45 q^{8} + 572 q^{9} - 33 q^{10} + 233 q^{12} - 12 q^{13} + 73 q^{14} + 400 q^{15} + 1223 q^{16} + 884 q^{17} - 201 q^{18} + 44 q^{19} + 655 q^{20} - 260 q^{21} + 572 q^{23} + 104 q^{24} + 1858 q^{25} + 465 q^{26} + 1070 q^{27} + 577 q^{28} - 322 q^{29} + 320 q^{30} + 1110 q^{31} - 481 q^{32} - 17 q^{34} - 102 q^{35} + 2507 q^{36} + 1678 q^{37} - 360 q^{38} + 1282 q^{39} - 1791 q^{40} + 826 q^{41} + 2133 q^{42} - 270 q^{43} + 710 q^{45} - 2158 q^{46} + 2464 q^{47} + 2201 q^{48} + 3224 q^{49} - 2379 q^{50} + 340 q^{51} + 3664 q^{52} + 992 q^{53} - 1202 q^{54} + 1731 q^{56} - 1016 q^{57} + 1358 q^{58} + 1442 q^{59} + 1444 q^{60} + 140 q^{61} - 464 q^{62} + 766 q^{63} + 8427 q^{64} + 1268 q^{65} + 5766 q^{67} + 3995 q^{68} + 2460 q^{69} + 2422 q^{70} + 2704 q^{71} - 5455 q^{72} - 4 q^{73} + 4008 q^{74} + 5204 q^{75} + 1935 q^{76} + 4092 q^{78} + 2180 q^{79} + 5040 q^{80} + 7192 q^{81} + 3197 q^{82} - 4200 q^{83} - 7951 q^{84} + 680 q^{85} + 3091 q^{86} + 752 q^{87} - 240 q^{89} + 4495 q^{90} + 5494 q^{91} + 6902 q^{92} + 6266 q^{93} - 5990 q^{94} - 3168 q^{95} + 9467 q^{96} + 5322 q^{97} + 4610 q^{98}+O(q^{100}) \) 52 * q - q^2 + 20 * q^3 + 235 * q^4 + 40 * q^5 + 24 * q^6 + 42 * q^7 - 45 * q^8 + 572 * q^9 - 33 * q^10 + 233 * q^12 - 12 * q^13 + 73 * q^14 + 400 * q^15 + 1223 * q^16 + 884 * q^17 - 201 * q^18 + 44 * q^19 + 655 * q^20 - 260 * q^21 + 572 * q^23 + 104 * q^24 + 1858 * q^25 + 465 * q^26 + 1070 * q^27 + 577 * q^28 - 322 * q^29 + 320 * q^30 + 1110 * q^31 - 481 * q^32 - 17 * q^34 - 102 * q^35 + 2507 * q^36 + 1678 * q^37 - 360 * q^38 + 1282 * q^39 - 1791 * q^40 + 826 * q^41 + 2133 * q^42 - 270 * q^43 + 710 * q^45 - 2158 * q^46 + 2464 * q^47 + 2201 * q^48 + 3224 * q^49 - 2379 * q^50 + 340 * q^51 + 3664 * q^52 + 992 * q^53 - 1202 * q^54 + 1731 * q^56 - 1016 * q^57 + 1358 * q^58 + 1442 * q^59 + 1444 * q^60 + 140 * q^61 - 464 * q^62 + 766 * q^63 + 8427 * q^64 + 1268 * q^65 + 5766 * q^67 + 3995 * q^68 + 2460 * q^69 + 2422 * q^70 + 2704 * q^71 - 5455 * q^72 - 4 * q^73 + 4008 * q^74 + 5204 * q^75 + 1935 * q^76 + 4092 * q^78 + 2180 * q^79 + 5040 * q^80 + 7192 * q^81 + 3197 * q^82 - 4200 * q^83 - 7951 * q^84 + 680 * q^85 + 3091 * q^86 + 752 * q^87 - 240 * q^89 + 4495 * q^90 + 5494 * q^91 + 6902 * q^92 + 6266 * q^93 - 5990 * q^94 - 3168 * q^95 + 9467 * q^96 + 5322 * q^97 + 4610 * 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 $

$2$	−4.78655	−1.69230	−0.846150	−	0.532945i	$-0.821085\pi$
$2$	−4.78655	−1.69230	−0.846150	+	0.532945i	$0.821085\pi$
$3$	5.72685	1.10213	0.551066	−	0.834462i	$-0.314221\pi$
$3$	5.72685	1.10213	0.551066	+	0.834462i	$0.314221\pi$
$4$	14.9110	1.86388
$5$	0.431714	0.0386136	0.0193068	−	0.999814i	$-0.493854\pi$
$5$	0.431714	0.0386136	0.0193068	+	0.999814i	$0.493854\pi$
$6$	−27.4118	−1.86514
$7$	−26.0630	−1.40727	−0.703635	−	0.710561i	$-0.748441\pi$
$7$	−26.0630	−1.40727	−0.703635	+	0.710561i	$0.748441\pi$
$8$	−33.0800	−1.46194
$9$	5.79678	0.214695
$10$	−2.06642	−0.0653458
$11$	0	0
$11$	0	0
$12$	85.3932	2.05424
$13$	−64.5081	−1.37626	−0.688128	−	0.725589i	$-0.741567\pi$
$13$	−64.5081	−1.37626	−0.688128	+	0.725589i	$0.741567\pi$
$14$	124.752	2.38152
$15$	2.47236	0.0425573
$16$	39.0506	0.610165
$17$	17.0000	0.242536
$17$	17.0000	0.242536
$18$	−27.7465	−0.363329
$19$	−87.1729	−1.05257	−0.526285	−	0.850308i	$-0.676415\pi$
$19$	−87.1729	−1.05257	−0.526285	+	0.850308i	$0.676415\pi$
$20$	6.43729	0.0719711
$21$	−149.259	−1.55100
$22$	0	0
$23$	197.571	1.79115	0.895574	−	0.444912i	$-0.146765\pi$
$23$	197.571	1.79115	0.895574	+	0.444912i	$0.146765\pi$
$24$	−189.444	−1.61125
$25$	−124.814	−0.998509
$26$	308.771	2.32904
$27$	−121.428	−0.865509
$28$	−388.626	−2.62298
$29$	154.126	0.986912	0.493456	−	0.869771i	$-0.335733\pi$
$29$	154.126	0.986912	0.493456	+	0.869771i	$0.335733\pi$
$30$	−11.8341	−0.0720198
$31$	119.027	0.689607	0.344803	−	0.938675i	$-0.387946\pi$
$31$	119.027	0.689607	0.344803	+	0.938675i	$0.387946\pi$
$32$	77.7224	0.429360
$33$	0	0
$34$	−81.3713	−0.410443
$35$	−11.2518	−0.0543398
$36$	86.4359	0.400166
$37$	−348.669	−1.54921	−0.774607	−	0.632443i	$-0.782052\pi$
$37$	−348.669	−1.54921	−0.774607	+	0.632443i	$0.782052\pi$
$38$	417.257	1.78126
$39$	−369.428	−1.51682
$40$	−14.2811	−0.0564509
$41$	265.786	1.01241	0.506204	−	0.862414i	$-0.331048\pi$
$41$	265.786	1.01241	0.506204	+	0.862414i	$0.331048\pi$
$42$	714.435	2.62475
$43$	−295.791	−1.04901	−0.524507	−	0.851406i	$-0.675750\pi$
$43$	−295.791	−1.04901	−0.524507	+	0.851406i	$0.675750\pi$
$44$	0	0
$45$	2.50255	0.00829017
$46$	−945.683	−3.03116
$47$	130.616	0.405368	0.202684	−	0.979244i	$-0.435034\pi$
$47$	130.616	0.405368	0.202684	+	0.979244i	$0.435034\pi$
$48$	223.637	0.672482
$49$	336.280	0.980409
$50$	597.426	1.68978
$51$	97.3564	0.267306
$52$	−961.882	−2.56517
$53$	−490.232	−1.27054	−0.635269	−	0.772291i	$-0.719111\pi$
$53$	−490.232	−1.27054	−0.635269	+	0.772291i	$0.719111\pi$
$54$	581.219	1.46470
$55$	0	0
$56$	862.163	2.05735
$57$	−499.226	−1.16007
$58$	−737.730	−1.67015
$59$	−567.337	−1.25188	−0.625941	−	0.779870i	$-0.715285\pi$
$59$	−567.337	−1.25188	−0.625941	+	0.779870i	$0.715285\pi$
$60$	36.8654	0.0793217
$61$	−216.261	−0.453924	−0.226962	−	0.973904i	$-0.572879\pi$
$61$	−216.261	−0.453924	−0.226962	+	0.973904i	$0.572879\pi$
$62$	−569.727	−1.16702
$63$	−151.081	−0.302134
$64$	−684.426	−1.33677
$65$	−27.8490	−0.0531422
$66$	0	0
$67$	443.190	0.808124	0.404062	−	0.914732i	$-0.367598\pi$
$67$	443.190	0.808124	0.404062	+	0.914732i	$0.367598\pi$
$68$	253.487	0.452057
$69$	1131.46	1.97408
$70$	53.8570	0.0919593
$71$	−814.737	−1.36185	−0.680926	−	0.732352i	$-0.738422\pi$
$71$	−814.737	−1.36185	−0.680926	+	0.732352i	$0.738422\pi$
$72$	−191.757	−0.313872
$73$	−490.120	−0.785811	−0.392906	−	0.919579i	$-0.628530\pi$
$73$	−490.120	−0.785811	−0.392906	+	0.919579i	$0.628530\pi$
$74$	1668.92	2.62173
$75$	−714.789	−1.10049
$76$	−1299.84	−1.96186
$77$	0	0
$78$	1768.28	2.56691
$79$	−1125.31	−1.60263	−0.801315	−	0.598242i	$-0.795866\pi$
$79$	−1125.31	−1.60263	−0.801315	+	0.598242i	$0.795866\pi$
$80$	16.8587	0.0235607
$81$	−851.910	−1.16860
$82$	−1272.20	−1.71330
$83$	285.100	0.377034	0.188517	−	0.982070i	$-0.439632\pi$
$83$	285.100	0.377034	0.188517	+	0.982070i	$0.439632\pi$
$84$	−2225.60	−2.89087
$85$	7.33913	0.00936518
$86$	1415.82	1.77525
$87$	882.655	1.08771
$88$	0	0
$89$	404.506	0.481770	0.240885	−	0.970554i	$-0.422562\pi$
$89$	404.506	0.481770	0.240885	+	0.970554i	$0.422562\pi$
$90$	−11.9786	−0.0140295
$91$	1681.28	1.93676
$92$	2945.99	3.33848
$93$	681.647	0.760038
$94$	−625.200	−0.686005
$95$	−37.6337	−0.0406435
$96$	445.104	0.473211
$97$	414.146	0.433507	0.216753	−	0.976226i	$-0.430453\pi$
$97$	414.146	0.433507	0.216753	+	0.976226i	$0.430453\pi$
$98$	−1609.62	−1.65915
$99$	0	0
$100$	−1861.10	−1.86110
$101$	−1152.00	−1.13493	−0.567467	−	0.823396i	$-0.692077\pi$
$101$	−1152.00	−1.13493	−0.567467	+	0.823396i	$0.692077\pi$
$102$	−466.001	−0.452362
$103$	1471.88	1.40805	0.704024	−	0.710176i	$-0.251385\pi$
$103$	1471.88	1.40805	0.704024	+	0.710176i	$0.251385\pi$
$104$	2133.93	2.01201
$105$	−64.4371	−0.0598897
$106$	2346.52	2.15013
$107$	1377.01	1.24412	0.622058	−	0.782971i	$-0.286297\pi$
$107$	1377.01	1.24412	0.622058	+	0.782971i	$0.286297\pi$
$108$	−1810.61	−1.61320
$109$	−12.6352	−0.0111030	−0.00555152	−	0.999985i	$-0.501767\pi$
$109$	−12.6352	−0.0111030	−0.00555152	+	0.999985i	$0.501767\pi$
$110$	0	0
$111$	−1996.78	−1.70744
$112$	−1017.78	−0.858667
$113$	1556.60	1.29587	0.647933	−	0.761697i	$-0.275634\pi$
$113$	1556.60	1.29587	0.647933	+	0.761697i	$0.275634\pi$
$114$	2389.57	1.96319
$115$	85.2941	0.0691628
$116$	2298.17	1.83948
$117$	−373.939	−0.295476
$118$	2715.59	2.11856
$119$	−443.071	−0.341313
$120$	−81.7855	−0.0622163
$121$	0	0
$122$	1035.14	0.768175
$123$	1522.11	1.11581
$124$	1774.81	1.28534
$125$	−107.848	−0.0771697
$126$	723.158	0.511302
$127$	−474.286	−0.331387	−0.165693	−	0.986177i	$-0.552986\pi$
$127$	−474.286	−0.331387	−0.165693	+	0.986177i	$0.552986\pi$
$128$	2654.26	1.83286
$129$	−1693.95	−1.15615
$130$	133.301	0.0899326
$131$	123.779	0.0825547	0.0412773	−	0.999148i	$-0.486857\pi$
$131$	123.779	0.0825547	0.0412773	+	0.999148i	$0.486857\pi$
$132$	0	0
$133$	2271.99	1.48125
$134$	−2121.35	−1.36759
$135$	−52.4219	−0.0334205
$136$	−562.359	−0.354573
$137$	−595.132	−0.371136	−0.185568	−	0.982631i	$-0.559412\pi$
$137$	−595.132	−0.371136	−0.185568	+	0.982631i	$0.559412\pi$
$138$	−5415.78	−3.34074
$139$	1082.42	0.660504	0.330252	−	0.943893i	$-0.392866\pi$
$139$	1082.42	0.660504	0.330252	+	0.943893i	$0.392866\pi$
$140$	−167.775	−0.101283
$141$	748.018	0.446770
$142$	3899.78	2.30466
$143$	0	0
$144$	226.367	0.131000
$145$	66.5382	0.0381082
$146$	2345.98	1.32983
$147$	1925.83	1.08054
$148$	−5199.02	−2.88755
$149$	2378.07	1.30751	0.653755	−	0.756706i	$-0.273193\pi$
$149$	2378.07	1.30751	0.653755	+	0.756706i	$0.273193\pi$
$150$	3421.37	1.86236
$151$	1206.36	0.650145	0.325072	−	0.945689i	$-0.394611\pi$
$151$	1206.36	0.650145	0.325072	+	0.945689i	$0.394611\pi$
$152$	2883.68	1.53880
$153$	98.5452	0.0520713
$154$	0	0
$155$	51.3854	0.0266282
$156$	−5508.55	−2.82716
$157$	1221.50	0.620933	0.310466	−	0.950584i	$-0.399515\pi$
$157$	1221.50	0.620933	0.310466	+	0.950584i	$0.399515\pi$
$158$	5386.37	2.71213
$159$	−2807.48	−1.40030
$160$	33.5538	0.0165791
$161$	−5149.30	−2.52063
$162$	4077.71	1.97762
$163$	−735.357	−0.353359	−0.176680	−	0.984268i	$-0.556536\pi$
$163$	−735.357	−0.353359	−0.176680	+	0.984268i	$0.556536\pi$
$164$	3963.14	1.88701
$165$	0	0
$166$	−1364.64	−0.638054
$167$	36.9380	0.0171158	0.00855792	−	0.999963i	$-0.497276\pi$
$167$	36.9380	0.0171158	0.00855792	+	0.999963i	$0.497276\pi$
$168$	4937.48	2.26747
$169$	1964.30	0.894081
$170$	−35.1291	−0.0158487
$171$	−505.322	−0.225982
$172$	−4410.54	−1.95524
$173$	1187.37	0.521816	0.260908	−	0.965364i	$-0.415978\pi$
$173$	1187.37	0.521816	0.260908	+	0.965364i	$0.415978\pi$
$174$	−4224.87	−1.84073
$175$	3253.02	1.40517
$176$	0	0
$177$	−3249.05	−1.37974
$178$	−1936.19	−0.815299
$179$	−2251.74	−0.940240	−0.470120	−	0.882603i	$-0.655789\pi$
$179$	−2251.74	−0.940240	−0.470120	+	0.882603i	$0.655789\pi$
$180$	37.3155	0.0154519
$181$	4332.54	1.77920	0.889600	−	0.456740i	$-0.150983\pi$
$181$	4332.54	1.77920	0.889600	+	0.456740i	$0.150983\pi$
$182$	−8047.50	−3.27759
$183$	−1238.49	−0.500284
$184$	−6535.65	−2.61856
$185$	−150.525	−0.0598208
$186$	−3262.74	−1.28621
$187$	0	0
$188$	1947.62	0.755558
$189$	3164.77	1.21801
$190$	180.135	0.0687811
$191$	2863.52	1.08480	0.542401	−	0.840120i	$-0.317516\pi$
$191$	2863.52	1.08480	0.542401	+	0.840120i	$0.317516\pi$
$192$	−3919.60	−1.47330
$193$	3531.80	1.31723	0.658613	−	0.752482i	$-0.271144\pi$
$193$	3531.80	1.31723	0.658613	+	0.752482i	$0.271144\pi$
$194$	−1982.33	−0.733624
$195$	−159.487	−0.0585698
$196$	5014.29	1.82736
$197$	−422.185	−0.152688	−0.0763438	−	0.997082i	$-0.524325\pi$
$197$	−422.185	−0.152688	−0.0763438	+	0.997082i	$0.524325\pi$
$198$	0	0
$199$	−3802.36	−1.35448	−0.677241	−	0.735761i	$-0.736825\pi$
$199$	−3802.36	−1.35448	−0.677241	+	0.735761i	$0.736825\pi$
$200$	4128.83	1.45976
$201$	2538.08	0.890660
$202$	5514.11	1.92065
$203$	−4016.98	−1.38885
$204$	1451.68	0.498227
$205$	114.743	0.0390928
$206$	−7045.24	−2.38284
$207$	1145.28	0.384551
$208$	−2519.08	−0.839743
$209$	0	0
$210$	308.431	0.101351
$211$	620.976	0.202605	0.101303	−	0.994856i	$-0.467699\pi$
$211$	620.976	0.202605	0.101303	+	0.994856i	$0.467699\pi$
$212$	−7309.86	−2.36813
$213$	−4665.87	−1.50094
$214$	−6591.12	−2.10542
$215$	−127.697	−0.0405063
$216$	4016.82	1.26532
$217$	−3102.19	−0.970463
$218$	60.4789	0.0187897
$219$	−2806.84	−0.866068
$220$	0	0
$221$	−1096.64	−0.333791
$222$	9557.66	2.88950
$223$	−4263.98	−1.28044	−0.640218	−	0.768194i	$-0.721156\pi$
$223$	−4263.98	−1.28044	−0.640218	+	0.768194i	$0.721156\pi$
$224$	−2025.68	−0.604225
$225$	−723.517	−0.214375
$226$	−7450.76	−2.19300
$227$	−2469.56	−0.722072	−0.361036	−	0.932552i	$-0.617577\pi$
$227$	−2469.56	−0.722072	−0.361036	+	0.932552i	$0.617577\pi$
$228$	−7443.97	−2.16223
$229$	−3390.03	−0.978251	−0.489125	−	0.872213i	$-0.662684\pi$
$229$	−3390.03	−0.978251	−0.489125	+	0.872213i	$0.662684\pi$
$230$	−408.264	−0.117044
$231$	0	0
$232$	−5098.47	−1.44281
$233$	5839.33	1.64183	0.820916	−	0.571048i	$-0.193463\pi$
$233$	5839.33	1.64183	0.820916	+	0.571048i	$0.193463\pi$
$234$	1789.88	0.500034
$235$	56.3887	0.0156527
$236$	−8459.59	−2.33336
$237$	−6444.51	−1.76631
$238$	2120.78	0.577604
$239$	4220.32	1.14222	0.571108	−	0.820875i	$-0.306514\pi$
$239$	4220.32	1.14222	0.571108	+	0.820875i	$0.306514\pi$
$240$	96.5469	0.0259670
$241$	−1025.73	−0.274162	−0.137081	−	0.990560i	$-0.543772\pi$
$241$	−1025.73	−0.274162	−0.137081	+	0.990560i	$0.543772\pi$
$242$	0	0
$243$	−1600.21	−0.422444
$244$	−3224.67	−0.846059
$245$	145.177	0.0378572
$246$	−7285.67	−1.88828
$247$	5623.36	1.44861
$248$	−3937.40	−1.00817
$249$	1632.72	0.415541
$250$	516.219	0.130594
$251$	−328.427	−0.0825901	−0.0412950	−	0.999147i	$-0.513148\pi$
$251$	−328.427	−0.0825901	−0.0412950	+	0.999147i	$0.513148\pi$
$252$	−2252.78	−0.563142
$253$	0	0
$254$	2270.19	0.560806
$255$	42.0301	0.0103217
$256$	−7229.33	−1.76497
$257$	−1407.21	−0.341555	−0.170777	−	0.985310i	$-0.554628\pi$
$257$	−1407.21	−0.341555	−0.170777	+	0.985310i	$0.554628\pi$
$258$	8108.16	1.95656
$259$	9087.37	2.18016
$260$	−415.258	−0.0990507
$261$	893.432	0.211885
$262$	−592.476	−0.139707
$263$	−1640.74	−0.384686	−0.192343	−	0.981328i	$-0.561609\pi$
$263$	−1640.74	−0.384686	−0.192343	+	0.981328i	$0.561609\pi$
$264$	0	0
$265$	−211.640	−0.0490601
$266$	−10875.0	−2.50672
$267$	2316.54	0.530974
$268$	6608.42	1.50625
$269$	1971.85	0.446936	0.223468	−	0.974711i	$-0.428262\pi$
$269$	1971.85	0.446936	0.223468	+	0.974711i	$0.428262\pi$
$270$	250.920	0.0565574
$271$	−2536.37	−0.568537	−0.284268	−	0.958745i	$-0.591751\pi$
$271$	−2536.37	−0.568537	−0.284268	+	0.958745i	$0.591751\pi$
$272$	663.859	0.147987
$273$	9628.41	2.13457
$274$	2848.63	0.628073
$275$	0	0
$276$	16871.2	3.67945
$277$	3503.47	0.759939	0.379970	−	0.924999i	$-0.375934\pi$
$277$	3503.47	0.759939	0.379970	+	0.924999i	$0.375934\pi$
$278$	−5181.07	−1.11777
$279$	689.971	0.148055
$280$	372.208	0.0794416
$281$	−1363.24	−0.289410	−0.144705	−	0.989475i	$-0.546223\pi$
$281$	−1363.24	−0.289410	−0.144705	+	0.989475i	$0.546223\pi$
$282$	−3580.43	−0.756068
$283$	−3279.62	−0.688881	−0.344441	−	0.938808i	$-0.611931\pi$
$283$	−3279.62	−0.688881	−0.344441	+	0.938808i	$0.611931\pi$
$284$	−12148.6	−2.53833
$285$	−215.522	−0.0447946
$286$	0	0
$287$	−6927.18	−1.42473
$288$	450.539	0.0921815
$289$	289.000	0.0588235
$290$	−318.488	−0.0644906
$291$	2371.75	0.477782
$292$	−7308.20	−1.46466
$293$	4452.18	0.887710	0.443855	−	0.896099i	$-0.353610\pi$
$293$	4452.18	0.887710	0.443855	+	0.896099i	$0.353610\pi$
$294$	−9218.06	−1.82860
$295$	−244.927	−0.0483397
$296$	11534.0	2.26486
$297$	0	0
$298$	−11382.7	−2.21270
$299$	−12744.9	−2.46508
$300$	−10658.2	−2.05118
$301$	7709.19	1.47625
$302$	−5774.28	−1.10024
$303$	−6597.33	−1.25085
$304$	−3404.15	−0.642241
$305$	−93.3627	−0.0175276
$306$	−471.691	−0.0881202
$307$	4356.29	0.809858	0.404929	−	0.914348i	$-0.367296\pi$
$307$	4356.29	0.809858	0.404929	+	0.914348i	$0.367296\pi$
$308$	0	0
$309$	8429.25	1.55186
$310$	−245.959	−0.0450629
$311$	4071.67	0.742389	0.371195	−	0.928555i	$-0.378948\pi$
$311$	4071.67	0.742389	0.371195	+	0.928555i	$0.378948\pi$
$312$	12220.7	2.21750
$313$	10865.3	1.96212	0.981058	−	0.193713i	$-0.0620529\pi$
$313$	10865.3	1.96212	0.981058	+	0.193713i	$0.0620529\pi$
$314$	−5846.77	−1.05080
$315$	−65.2239	−0.0116665
$316$	−16779.6	−2.98711
$317$	−1861.82	−0.329875	−0.164937	−	0.986304i	$-0.552742\pi$
$317$	−1861.82	−0.329875	−0.164937	+	0.986304i	$0.552742\pi$
$318$	13438.2	2.36973
$319$	0	0
$320$	−295.476	−0.0516176
$321$	7885.92	1.37118
$322$	24647.4	4.26566
$323$	−1481.94	−0.255286
$324$	−12702.9	−2.17813
$325$	8051.49	1.37420
$326$	3519.82	0.597990
$327$	−72.3598	−0.0122370
$328$	−8792.18	−1.48008
$329$	−3404.25	−0.570463
$330$	0	0
$331$	841.650	0.139762	0.0698811	−	0.997555i	$-0.477738\pi$
$331$	841.650	0.139762	0.0698811	+	0.997555i	$0.477738\pi$
$332$	4251.14	0.702745
$333$	−2021.16	−0.332609
$334$	−176.805	−0.0289651
$335$	191.331	0.0312046
$336$	−5828.64	−0.946365
$337$	−6920.04	−1.11857	−0.559286	−	0.828975i	$-0.688924\pi$
$337$	−6920.04	−1.11857	−0.559286	+	0.828975i	$0.688924\pi$
$338$	−9402.19	−1.51305
$339$	8914.43	1.42822
$340$	109.434	0.0174556
$341$	0	0
$342$	2418.75	0.382429
$343$	175.132	0.0275692
$344$	9784.74	1.53360
$345$	488.466	0.0762265
$346$	−5683.41	−0.883069
$347$	3979.80	0.615697	0.307849	−	0.951435i	$-0.400391\pi$
$347$	3979.80	0.615697	0.307849	+	0.951435i	$0.400391\pi$
$348$	13161.3	2.02735
$349$	10871.7	1.66747	0.833737	−	0.552162i	$-0.186197\pi$
$349$	10871.7	1.66747	0.833737	+	0.552162i	$0.186197\pi$
$350$	−15570.7	−2.37797
$351$	7833.07	1.19116
$352$	0	0
$353$	10094.0	1.52196	0.760980	−	0.648775i	$-0.224718\pi$
$353$	10094.0	1.52196	0.760980	+	0.648775i	$0.224718\pi$
$354$	15551.8	2.33493
$355$	−351.733	−0.0525860
$356$	6031.60	0.897961
$357$	−2537.40	−0.376172
$358$	10778.1	1.59117
$359$	10587.7	1.55654	0.778270	−	0.627929i	$-0.216097\pi$
$359$	10587.7	1.55654	0.778270	+	0.627929i	$0.216097\pi$
$360$	−82.7841	−0.0121197
$361$	740.108	0.107903
$362$	−20737.9	−3.01094
$363$	0	0
$364$	25069.5	3.60989
$365$	−211.591	−0.0303430
$366$	5928.10	0.846630
$367$	13030.9	1.85343	0.926713	−	0.375770i	$-0.122622\pi$
$367$	13030.9	1.85343	0.926713	+	0.375770i	$0.122622\pi$
$368$	7715.26	1.09290
$369$	1540.70	0.217359
$370$	720.496	0.101235
$371$	12776.9	1.78799
$372$	10164.1	1.41662
$373$	5132.56	0.712477	0.356239	−	0.934395i	$-0.384059\pi$
$373$	5132.56	0.712477	0.356239	+	0.934395i	$0.384059\pi$
$374$	0	0
$375$	−617.629	−0.0850512
$376$	−4320.78	−0.592625
$377$	−9942.36	−1.35824
$378$	−15148.3	−2.06123
$379$	−12143.9	−1.64588	−0.822941	−	0.568127i	$-0.807668\pi$
$379$	−12143.9	−1.64588	−0.822941	+	0.568127i	$0.807668\pi$
$380$	−561.157	−0.0757546
$381$	−2716.16	−0.365232
$382$	−13706.4	−1.83581
$383$	8580.56	1.14477	0.572384	−	0.819986i	$-0.306019\pi$
$383$	8580.56	1.14477	0.572384	+	0.819986i	$0.306019\pi$
$384$	15200.5	2.02005
$385$	0	0
$386$	−16905.1	−2.22914
$387$	−1714.63	−0.225219
$388$	6175.35	0.808004
$389$	−4635.87	−0.604236	−0.302118	−	0.953271i	$-0.597694\pi$
$389$	−4635.87	−0.604236	−0.302118	+	0.953271i	$0.597694\pi$
$390$	763.392	0.0991176
$391$	3358.71	0.434417
$392$	−11124.1	−1.43330
$393$	708.866	0.0909862
$394$	2020.81	0.258393
$395$	−485.814	−0.0618834
$396$	0	0
$397$	−13641.4	−1.72454	−0.862272	−	0.506446i	$-0.830959\pi$
$397$	−13641.4	−1.72454	−0.862272	+	0.506446i	$0.830959\pi$
$398$	18200.2	2.29219
$399$	13011.3	1.63253
$400$	−4874.04	−0.609255
$401$	−8114.95	−1.01058	−0.505289	−	0.862950i	$-0.668614\pi$
$401$	−8114.95	−1.01058	−0.505289	+	0.862950i	$0.668614\pi$
$402$	−12148.7	−1.50726
$403$	−7678.18	−0.949076
$404$	−17177.5	−2.11538
$405$	−367.781	−0.0451239
$406$	19227.5	2.35035
$407$	0	0
$408$	−3220.55	−0.390786
$409$	4826.19	0.583471	0.291736	−	0.956499i	$-0.405767\pi$
$409$	4826.19	0.583471	0.291736	+	0.956499i	$0.405767\pi$
$410$	−549.224	−0.0661567
$411$	−3408.23	−0.409041
$412$	21947.3	2.62443
$413$	14786.5	1.76174
$414$	−5481.91	−0.650776
$415$	123.082	0.0145586
$416$	−5013.72	−0.590909
$417$	6198.88	0.727962
$418$	0	0
$419$	5981.25	0.697382	0.348691	−	0.937238i	$-0.386626\pi$
$419$	5981.25	0.697382	0.348691	+	0.937238i	$0.386626\pi$
$420$	−960.823	−0.111627
$421$	−9865.62	−1.14209	−0.571046	−	0.820918i	$-0.693462\pi$
$421$	−9865.62	−1.14209	−0.571046	+	0.820918i	$0.693462\pi$
$422$	−2972.33	−0.342869
$423$	757.152	0.0870307
$424$	16216.9	1.85745
$425$	−2121.83	−0.242174
$426$	22333.4	2.54004
$427$	5636.41	0.638793
$428$	20532.6	2.31888
$429$	0	0
$430$	611.227	0.0685487
$431$	−13041.7	−1.45753	−0.728764	−	0.684765i	$-0.759905\pi$
$431$	−13041.7	−1.45753	−0.728764	+	0.684765i	$0.759905\pi$
$432$	−4741.82	−0.528104
$433$	4269.03	0.473802	0.236901	−	0.971534i	$-0.423868\pi$
$433$	4269.03	0.473802	0.236901	+	0.971534i	$0.423868\pi$
$434$	14848.8	1.64231
$435$	381.054	0.0420003
$436$	−188.404	−0.0206947
$437$	−17222.8	−1.88531
$438$	13435.1	1.46565
$439$	326.848	0.0355344	0.0177672	−	0.999842i	$-0.494344\pi$
$439$	326.848	0.0355344	0.0177672	+	0.999842i	$0.494344\pi$
$440$	0	0
$441$	1949.34	0.210489
$442$	5249.11	0.564875
$443$	−5434.66	−0.582863	−0.291431	−	0.956592i	$-0.594132\pi$
$443$	−5434.66	−0.582863	−0.291431	+	0.956592i	$0.594132\pi$
$444$	−29774.0	−3.18246
$445$	174.631	0.0186029
$446$	20409.7	2.16688
$447$	13618.8	1.44105
$448$	17838.2	1.88120
$449$	5184.50	0.544926	0.272463	−	0.962166i	$-0.412162\pi$
$449$	5184.50	0.544926	0.272463	+	0.962166i	$0.412162\pi$
$450$	3463.15	0.362787
$451$	0	0
$452$	23210.6	2.41534
$453$	6908.62	0.716546
$454$	11820.7	1.22196
$455$	725.829	0.0747855
$456$	16514.4	1.69596
$457$	−13379.9	−1.36956	−0.684778	−	0.728751i	$-0.740101\pi$
$457$	−13379.9	−1.36956	−0.684778	+	0.728751i	$0.740101\pi$
$458$	16226.5	1.65549
$459$	−2064.27	−0.209917
$460$	1271.82	0.128911
$461$	−415.191	−0.0419466	−0.0209733	−	0.999780i	$-0.506676\pi$
$461$	−415.191	−0.0419466	−0.0209733	+	0.999780i	$0.506676\pi$
$462$	0	0
$463$	−1874.52	−0.188156	−0.0940781	−	0.995565i	$-0.529990\pi$
$463$	−1874.52	−0.188156	−0.0940781	+	0.995565i	$0.529990\pi$
$464$	6018.70	0.602179
$465$	294.276	0.0293478
$466$	−27950.2	−2.77847
$467$	12979.7	1.28614	0.643070	−	0.765807i	$-0.277660\pi$
$467$	12979.7	1.28614	0.643070	+	0.765807i	$0.277660\pi$
$468$	−5575.82	−0.550731
$469$	−11550.9	−1.13725
$470$	−269.907	−0.0264891
$471$	6995.35	0.684350
$472$	18767.5	1.83018
$473$	0	0
$474$	30846.9	2.98913
$475$	10880.4	1.05100
$476$	−6606.65	−0.636166
$477$	−2841.77	−0.272779
$478$	−20200.7	−1.93297
$479$	10224.9	0.975336	0.487668	−	0.873029i	$-0.337848\pi$
$479$	10224.9	0.975336	0.487668	+	0.873029i	$0.337848\pi$
$480$	192.158	0.0182724
$481$	22492.0	2.13211
$482$	4909.71	0.463965
$483$	−29489.2	−2.77807
$484$	0	0
$485$	178.793	0.0167393
$486$	7659.50	0.714901
$487$	−3589.79	−0.334023	−0.167011	−	0.985955i	$-0.553412\pi$
$487$	−3589.79	−0.334023	−0.167011	+	0.985955i	$0.553412\pi$
$488$	7153.90	0.663610
$489$	−4211.28	−0.389449
$490$	−694.896	−0.0640657
$491$	6258.65	0.575252	0.287626	−	0.957743i	$-0.407134\pi$
$491$	6258.65	0.575252	0.287626	+	0.957743i	$0.407134\pi$
$492$	22696.3	2.07973
$493$	2620.14	0.239361
$494$	−26916.5	−2.45147
$495$	0	0
$496$	4648.06	0.420774
$497$	21234.5	1.91649
$498$	−7815.11	−0.703220
$499$	−13769.2	−1.23526	−0.617630	−	0.786469i	$-0.711907\pi$
$499$	−13769.2	−1.23526	−0.617630	+	0.786469i	$0.711907\pi$
$500$	−1608.12	−0.143835
$501$	211.538	0.0188639
$502$	1572.03	0.139767
$503$	6975.52	0.618336	0.309168	−	0.951007i	$-0.399949\pi$
$503$	6975.52	0.618336	0.309168	+	0.951007i	$0.399949\pi$
$504$	4997.77	0.441703
$505$	−497.334	−0.0438239
$506$	0	0
$507$	11249.2	0.985395
$508$	−7072.10	−0.617664
$509$	−1078.00	−0.0938736	−0.0469368	−	0.998898i	$-0.514946\pi$
$509$	−1078.00	−0.0938736	−0.0469368	+	0.998898i	$0.514946\pi$
$510$	−201.179	−0.0174674
$511$	12774.0	1.10585
$512$	13369.4	1.15401
$513$	10585.2	0.911009
$514$	6735.69	0.578013
$515$	635.432	0.0543699
$516$	−25258.5	−2.15493
$517$	0	0
$518$	−43497.1	−3.68949
$519$	6799.90	0.575110
$520$	921.245	0.0776909
$521$	15907.9	1.33769	0.668847	−	0.743400i	$-0.266788\pi$
$521$	15907.9	1.33769	0.668847	+	0.743400i	$0.266788\pi$
$522$	−4276.46	−0.358574
$523$	−1123.90	−0.0939672	−0.0469836	−	0.998896i	$-0.514961\pi$
$523$	−1123.90	−0.0939672	−0.0469836	+	0.998896i	$0.514961\pi$
$524$	1845.68	0.153872
$525$	18629.5	1.54869
$526$	7853.49	0.651005
$527$	2023.45	0.167254
$528$	0	0
$529$	26867.3	2.20821
$530$	1013.02	0.0830244
$531$	−3288.73	−0.268773
$532$	33877.7	2.76087
$533$	−17145.3	−1.39333
$534$	−11088.2	−0.898567
$535$	594.473	0.0480399
$536$	−14660.7	−1.18143
$537$	−12895.4	−1.03627
$538$	−9438.36	−0.756351
$539$	0	0
$540$	−781.665	−0.0622917
$541$	−8752.40	−0.695554	−0.347777	−	0.937577i	$-0.613063\pi$
$541$	−8752.40	−0.695554	−0.347777	+	0.937577i	$0.613063\pi$
$542$	12140.4	0.962134
$543$	24811.8	1.96091
$544$	1321.28	0.104135
$545$	−5.45478	−0.000428729 0
$546$	−46086.8	−3.61233
$547$	−9332.08	−0.729453	−0.364727	−	0.931115i	$-0.618838\pi$
$547$	−9332.08	−0.729453	−0.364727	+	0.931115i	$0.618838\pi$
$548$	−8874.03	−0.691752
$549$	−1253.61	−0.0974553
$550$	0	0
$551$	−13435.6	−1.03879
$552$	−37428.6	−2.88599
$553$	29329.1	2.25533
$554$	−16769.5	−1.28605
$555$	−862.035	−0.0659304
$556$	16140.1	1.23110
$557$	10960.6	0.833779	0.416890	−	0.908957i	$-0.363120\pi$
$557$	10960.6	0.833779	0.416890	+	0.908957i	$0.363120\pi$
$558$	−3302.58	−0.250554
$559$	19080.9	1.44371
$560$	−439.387	−0.0331563
$561$	0	0
$562$	6525.23	0.489769
$563$	−9622.56	−0.720324	−0.360162	−	0.932890i	$-0.617279\pi$
$563$	−9622.56	−0.720324	−0.360162	+	0.932890i	$0.617279\pi$
$564$	11153.7	0.832724
$565$	672.007	0.0500381
$566$	15698.1	1.16579
$567$	22203.3	1.64454
$568$	26951.5	1.99095
$569$	14225.0	1.04806	0.524028	−	0.851701i	$-0.324429\pi$
$569$	14225.0	1.04806	0.524028	+	0.851701i	$0.324429\pi$
$570$	1031.61	0.0758058
$571$	−6056.91	−0.443912	−0.221956	−	0.975057i	$-0.571244\pi$
$571$	−6056.91	−0.443912	−0.221956	+	0.975057i	$0.571244\pi$
$572$	0	0
$573$	16398.9	1.19559
$574$	33157.3	2.41107
$575$	−24659.6	−1.78848
$576$	−3967.47	−0.286998
$577$	−399.123	−0.0287967	−0.0143983	−	0.999896i	$-0.504583\pi$
$577$	−399.123	−0.0287967	−0.0143983	+	0.999896i	$0.504583\pi$
$578$	−1383.31	−0.0995470
$579$	20226.1	1.45176
$580$	992.153	0.0710291
$581$	−7430.57	−0.530588
$582$	−11352.5	−0.808550
$583$	0	0
$584$	16213.2	1.14881
$585$	−161.435	−0.0114094
$586$	−21310.6	−1.50227
$587$	2308.53	0.162323	0.0811613	−	0.996701i	$-0.474137\pi$
$587$	2308.53	0.162323	0.0811613	+	0.996701i	$0.474137\pi$
$588$	28716.1	2.01400
$589$	−10375.9	−0.725859
$590$	1172.36	0.0818053
$591$	−2417.79	−0.168282
$592$	−13615.7	−0.945276
$593$	−12753.2	−0.883154	−0.441577	−	0.897223i	$-0.645581\pi$
$593$	−12753.2	−0.883154	−0.441577	+	0.897223i	$0.645581\pi$
$594$	0	0
$595$	−191.280	−0.0131793
$596$	35459.5	2.43704
$597$	−21775.5	−1.49282
$598$	61004.2	4.17165
$599$	16629.0	1.13429	0.567147	−	0.823617i	$-0.308047\pi$
$599$	16629.0	1.13429	0.567147	+	0.823617i	$0.308047\pi$
$600$	23645.2	1.60885
$601$	−11146.4	−0.756525	−0.378262	−	0.925698i	$-0.623478\pi$
$601$	−11146.4	−0.756525	−0.378262	+	0.925698i	$0.623478\pi$
$602$	−36900.4	−2.49825
$603$	2569.08	0.173501
$604$	17988.0	1.21179
$605$	0	0
$606$	31578.4	2.11681
$607$	18510.4	1.23775	0.618873	−	0.785491i	$-0.287589\pi$
$607$	18510.4	1.23775	0.618873	+	0.785491i	$0.287589\pi$
$608$	−6775.28	−0.451931
$609$	−23004.6	−1.53070
$610$	446.885	0.0296620
$611$	−8425.80	−0.557891
$612$	1469.41	0.0970546
$613$	−16762.3	−1.10444	−0.552221	−	0.833698i	$-0.686220\pi$
$613$	−16762.3	−1.10444	−0.552221	+	0.833698i	$0.686220\pi$
$614$	−20851.6	−1.37052
$615$	657.117	0.0430854
$616$	0	0
$617$	−19193.4	−1.25235	−0.626173	−	0.779684i	$-0.715380\pi$
$617$	−19193.4	−1.25235	−0.626173	+	0.779684i	$0.715380\pi$
$618$	−40347.0	−2.62621
$619$	−30560.4	−1.98437	−0.992185	−	0.124777i	$-0.960179\pi$
$619$	−30560.4	−1.98437	−0.992185	+	0.124777i	$0.960179\pi$
$620$	766.209	0.0496318
$621$	−23990.6	−1.55026
$622$	−19489.2	−1.25635
$623$	−10542.6	−0.677980
$624$	−14426.4	−0.925508
$625$	15555.1	0.995529
$626$	−52007.2	−3.32049
$627$	0	0
$628$	18213.8	1.15734
$629$	−5927.38	−0.375739
$630$	312.197	0.0197432
$631$	−5455.48	−0.344183	−0.172091	−	0.985081i	$-0.555052\pi$
$631$	−5455.48	−0.344183	−0.172091	+	0.985081i	$0.555052\pi$
$632$	37225.4	2.34295
$633$	3556.23	0.223298
$634$	8911.69	0.558247
$635$	−204.756	−0.0127960
$636$	−41862.5	−2.60999
$637$	−21692.8	−1.34929
$638$	0	0
$639$	−4722.85	−0.292383
$640$	1145.88	0.0707732
$641$	29402.5	1.81174	0.905871	−	0.423553i	$-0.139217\pi$
$641$	29402.5	1.81174	0.905871	+	0.423553i	$0.139217\pi$
$642$	−37746.3	−2.32045
$643$	4853.31	0.297661	0.148830	−	0.988863i	$-0.452449\pi$
$643$	4853.31	0.297661	0.148830	+	0.988863i	$0.452449\pi$
$644$	−76781.3	−4.69815
$645$	−731.300	−0.0446433
$646$	7093.37	0.432020
$647$	15205.2	0.923926	0.461963	−	0.886899i	$-0.347145\pi$
$647$	15205.2	0.923926	0.461963	+	0.886899i	$0.347145\pi$
$648$	28181.2	1.70843
$649$	0	0
$650$	−38538.8	−2.32557
$651$	−17765.8	−1.06958
$652$	−10964.9	−0.658619
$653$	−3446.12	−0.206519	−0.103260	−	0.994654i	$-0.532927\pi$
$653$	−3446.12	−0.206519	−0.103260	+	0.994654i	$0.532927\pi$
$654$	346.353	0.0207087
$655$	53.4373	0.00318774
$656$	10379.1	0.617736
$657$	−2841.12	−0.168710
$658$	16294.6	0.965394
$659$	25007.3	1.47822	0.739108	−	0.673587i	$-0.235247\pi$
$659$	25007.3	1.47822	0.739108	+	0.673587i	$0.235247\pi$
$660$	0	0
$661$	−1273.77	−0.0749531	−0.0374765	−	0.999298i	$-0.511932\pi$
$661$	−1273.77	−0.0749531	−0.0374765	+	0.999298i	$0.511932\pi$
$662$	−4028.60	−0.236519
$663$	−6280.28	−0.367882
$664$	−9431.10	−0.551201
$665$	980.848	0.0571964
$666$	9674.37	0.562874
$667$	30450.8	1.76771
$668$	550.783	0.0319019
$669$	−24419.2	−1.41121
$670$	−915.816	−0.0528076
$671$	0	0
$672$	−11600.8	−0.665936
$673$	−11822.7	−0.677163	−0.338582	−	0.940937i	$-0.609947\pi$
$673$	−11822.7	−0.677163	−0.338582	+	0.940937i	$0.609947\pi$
$674$	33123.1	1.89296
$675$	15155.8	0.864219
$676$	29289.7	1.66646
$677$	−523.109	−0.0296967	−0.0148484	−	0.999890i	$-0.504727\pi$
$677$	−523.109	−0.0296967	−0.0148484	+	0.999890i	$0.504727\pi$
$678$	−42669.3	−2.41697
$679$	−10793.9	−0.610061
$680$	−242.778	−0.0136913
$681$	−14142.8	−0.795819
$682$	0	0
$683$	−215.567	−0.0120768	−0.00603838	−	0.999982i	$-0.501922\pi$
$683$	−215.567	−0.0120768	−0.00603838	+	0.999982i	$0.501922\pi$
$684$	−7534.86	−0.421203
$685$	−256.927	−0.0143309
$686$	−838.276	−0.0466553
$687$	−19414.2	−1.07816
$688$	−11550.8	−0.640072
$689$	31623.9	1.74859
$690$	−2338.07	−0.128998
$691$	−2339.73	−0.128810	−0.0644049	−	0.997924i	$-0.520515\pi$
$691$	−2339.73	−0.128810	−0.0644049	+	0.997924i	$0.520515\pi$
$692$	17704.9	0.972602
$693$	0	0
$694$	−19049.5	−1.04194
$695$	467.297	0.0255044
$696$	−29198.2	−1.59016
$697$	4518.36	0.245545
$698$	−52037.9	−2.82187
$699$	33440.9	1.80952
$700$	48505.9	2.61907
$701$	−52.2232	−0.00281376	−0.00140688	−	0.999999i	$-0.500448\pi$
$701$	−52.2232	−0.00281376	−0.00140688	+	0.999999i	$0.500448\pi$
$702$	−37493.3	−2.01580
$703$	30394.5	1.63066
$704$	0	0
$705$	322.930	0.0172514
$706$	−48315.6	−2.57561
$707$	30024.6	1.59716
$708$	−48446.7	−2.57167
$709$	9556.87	0.506228	0.253114	−	0.967436i	$-0.418545\pi$
$709$	9556.87	0.506228	0.253114	+	0.967436i	$0.418545\pi$
$710$	1683.59	0.0889914
$711$	−6523.20	−0.344077
$712$	−13381.0	−0.704319
$713$	23516.2	1.23519
$714$	12145.4	0.636596
$715$	0	0
$716$	−33575.8	−1.75249
$717$	24169.1	1.25887
$718$	−50678.6	−2.63413
$719$	23218.9	1.20434	0.602169	−	0.798368i	$-0.294303\pi$
$719$	23218.9	1.20434	0.602169	+	0.798368i	$0.294303\pi$
$720$	97.7258	0.00505837
$721$	−38361.7	−1.98151
$722$	−3542.56	−0.182604
$723$	−5874.20	−0.302163
$724$	64602.7	3.31621
$725$	−19237.0	−0.985440
$726$	0	0
$727$	−18386.3	−0.937978	−0.468989	−	0.883204i	$-0.655382\pi$
$727$	−18386.3	−0.937978	−0.468989	+	0.883204i	$0.655382\pi$
$728$	−55616.5	−2.83144
$729$	13837.4	0.703013
$730$	1012.79	0.0513495
$731$	−5028.44	−0.254423
$732$	−18467.2	−0.932469
$733$	−10467.3	−0.527447	−0.263723	−	0.964598i	$-0.584951\pi$
$733$	−10467.3	−0.527447	−0.263723	+	0.964598i	$0.584951\pi$
$734$	−62373.0	−3.13655
$735$	831.405	0.0417236
$736$	15355.7	0.769047
$737$	0	0
$738$	−7374.63	−0.367837
$739$	4659.64	0.231945	0.115973	−	0.993252i	$-0.463002\pi$
$739$	4659.64	0.231945	0.115973	+	0.993252i	$0.463002\pi$
$740$	−2244.49	−0.111499
$741$	32204.1	1.59655
$742$	−61157.3	−3.02582
$743$	24453.6	1.20743	0.603713	−	0.797202i	$-0.293687\pi$
$743$	24453.6	1.20743	0.603713	+	0.797202i	$0.293687\pi$
$744$	−22548.9	−1.11113
$745$	1026.65	0.0504877
$746$	−24567.3	−1.20573
$747$	1652.66	0.0809474
$748$	0	0
$749$	−35889.0	−1.75081
$750$	2956.31	0.143932
$751$	−31385.9	−1.52502	−0.762509	−	0.646977i	$-0.776033\pi$
$751$	−31385.9	−1.52502	−0.762509	+	0.646977i	$0.776033\pi$
$752$	5100.63	0.247342
$753$	−1880.85	−0.0910252
$754$	47589.6	2.29855
$755$	520.800	0.0251045
$756$	47190.0	2.27021
$757$	22764.8	1.09300	0.546499	−	0.837459i	$-0.315960\pi$
$757$	22764.8	1.09300	0.546499	+	0.837459i	$0.315960\pi$
$758$	58127.2	2.78532
$759$	0	0
$760$	1244.92	0.0594185
$761$	−14538.5	−0.692537	−0.346269	−	0.938135i	$-0.612551\pi$
$761$	−14538.5	−0.692537	−0.346269	+	0.938135i	$0.612551\pi$
$762$	13001.0	0.618082
$763$	329.311	0.0156250
$764$	42698.0	2.02194
$765$	42.5433	0.00201066
$766$	−41071.3	−1.93729
$767$	36597.9	1.72291
$768$	−41401.2	−1.94523
$769$	−31854.1	−1.49374	−0.746870	−	0.664970i	$-0.768445\pi$
$769$	−31854.1	−1.49374	−0.746870	+	0.664970i	$0.768445\pi$
$770$	0	0
$771$	−8058.90	−0.376439
$772$	52662.8	2.45515
$773$	−13879.4	−0.645806	−0.322903	−	0.946432i	$-0.604659\pi$
$773$	−13879.4	−0.645806	−0.322903	+	0.946432i	$0.604659\pi$
$774$	8207.16	0.381137
$775$	−14856.1	−0.688579
$776$	−13699.9	−0.633762
$777$	52042.0	2.40283
$778$	22189.8	1.02255
$779$	−23169.3	−1.06563
$780$	−2378.12	−0.109167
$781$	0	0
$782$	−16076.6	−0.735165
$783$	−18715.1	−0.854181
$784$	13131.9	0.598212
$785$	527.339	0.0239765
$786$	−3393.02	−0.153976
$787$	16561.4	0.750129	0.375065	−	0.926999i	$-0.377621\pi$
$787$	16561.4	0.750129	0.375065	+	0.926999i	$0.377621\pi$
$788$	−6295.22	−0.284591
$789$	−9396.28	−0.423975
$790$	2325.37	0.104725
$791$	−40569.8	−1.82363
$792$	0	0
$793$	13950.6	0.624715
$794$	65295.3	2.91844
$795$	−1212.03	−0.0540707
$796$	−56697.1	−2.52459
$797$	26220.1	1.16532	0.582661	−	0.812715i	$-0.302011\pi$
$797$	26220.1	1.16532	0.582661	+	0.812715i	$0.302011\pi$
$798$	−62279.3	−2.76274
$799$	2220.47	0.0983163
$800$	−9700.81	−0.428719
$801$	2344.83	0.103434
$802$	38842.6	1.71020
$803$	0	0
$804$	37845.4	1.66008
$805$	−2223.02	−0.0973307
$806$	36752.0	1.60612
$807$	11292.5	0.492583
$808$	38108.2	1.65921
$809$	22335.9	0.970689	0.485345	−	0.874323i	$-0.338694\pi$
$809$	22335.9	0.970689	0.485345	+	0.874323i	$0.338694\pi$
$810$	1760.40	0.0763632
$811$	−40153.0	−1.73855	−0.869274	−	0.494331i	$-0.835413\pi$
$811$	−40153.0	−1.73855	−0.869274	+	0.494331i	$0.835413\pi$
$812$	−59897.3	−2.58865
$813$	−14525.4	−0.626603
$814$	0	0
$815$	−317.464	−0.0136445
$816$	3801.82	0.163101
$817$	25784.9	1.10416
$818$	−23100.8	−0.987409
$819$	9745.98	0.415814
$820$	1710.94	0.0728642
$821$	−13825.2	−0.587700	−0.293850	−	0.955852i	$-0.594937\pi$
$821$	−13825.2	−0.587700	−0.293850	+	0.955852i	$0.594937\pi$
$822$	16313.7	0.692219
$823$	14242.5	0.603236	0.301618	−	0.953429i	$-0.402473\pi$
$823$	14242.5	0.603236	0.301618	+	0.953429i	$0.402473\pi$
$824$	−48689.9	−2.05849
$825$	0	0
$826$	−70776.4	−2.98139
$827$	24472.0	1.02899	0.514495	−	0.857493i	$-0.327979\pi$
$827$	24472.0	1.02899	0.514495	+	0.857493i	$0.327979\pi$
$828$	17077.2	0.716757
$829$	28875.8	1.20977	0.604884	−	0.796314i	$-0.293220\pi$
$829$	28875.8	1.20977	0.604884	+	0.796314i	$0.293220\pi$
$830$	−589.136	−0.0246376
$831$	20063.8	0.837554
$832$	44151.0	1.83974
$833$	5716.77	0.237784
$834$	−29671.2	−1.23193
$835$	15.9466	0.000660905 0
$836$	0	0
$837$	−14453.1	−0.596861
$838$	−28629.5	−1.18018
$839$	−5789.89	−0.238247	−0.119123	−	0.992879i	$-0.538008\pi$
$839$	−5789.89	−0.238247	−0.119123	+	0.992879i	$0.538008\pi$
$840$	2131.58	0.0875552
$841$	−634.248	−0.0260055
$842$	47222.2	1.93276
$843$	−7807.08	−0.318968
$844$	9259.39	0.377632
$845$	848.013	0.0345237
$846$	−3624.14	−0.147282
$847$	0	0
$848$	−19143.8	−0.775238
$849$	−18781.9	−0.759238
$850$	10156.2	0.409831
$851$	−68887.0	−2.77487
$852$	−69573.0	−2.79757
$853$	14877.2	0.597168	0.298584	−	0.954383i	$-0.403486\pi$
$853$	14877.2	0.597168	0.298584	+	0.954383i	$0.403486\pi$
$854$	−26978.9	−1.08103
$855$	−218.154	−0.00872598
$856$	−45551.4	−1.81883
$857$	−32618.4	−1.30014	−0.650072	−	0.759872i	$-0.725261\pi$
$857$	−32618.4	−1.30014	−0.650072	+	0.759872i	$0.725261\pi$
$858$	0	0
$859$	−13553.7	−0.538354	−0.269177	−	0.963091i	$-0.586752\pi$
$859$	−13553.7	−0.538354	−0.269177	+	0.963091i	$0.586752\pi$
$860$	−1904.09	−0.0754988
$861$	−39670.9	−1.57024
$862$	62424.5	2.46657
$863$	−5763.91	−0.227353	−0.113677	−	0.993518i	$-0.536263\pi$
$863$	−5763.91	−0.227353	−0.113677	+	0.993518i	$0.536263\pi$
$864$	−9437.64	−0.371615
$865$	512.604	0.0201492
$866$	−20433.9	−0.801816
$867$	1655.06	0.0648313
$868$	−46256.9	−1.80883
$869$	0	0
$870$	−1823.93	−0.0710771
$871$	−28589.4	−1.11219
$872$	417.972	0.0162320
$873$	2400.71	0.0930720
$874$	82437.9	3.19051
$875$	2810.84	0.108599
$876$	−41852.9	−1.61425
$877$	12680.3	0.488238	0.244119	−	0.969745i	$-0.421501\pi$
$877$	12680.3	0.488238	0.244119	+	0.969745i	$0.421501\pi$
$878$	−1564.47	−0.0601348
$879$	25497.0	0.978374
$880$	0	0
$881$	−17080.9	−0.653200	−0.326600	−	0.945163i	$-0.605903\pi$
$881$	−17080.9	−0.653200	−0.326600	+	0.945163i	$0.605903\pi$
$882$	−9330.62	−0.356211
$883$	34460.3	1.31334	0.656671	−	0.754177i	$-0.271964\pi$
$883$	34460.3	1.31334	0.656671	+	0.754177i	$0.271964\pi$
$884$	−16352.0	−0.622146
$885$	−1402.66	−0.0532768
$886$	26013.2	0.986379
$887$	−31863.5	−1.20617	−0.603084	−	0.797678i	$-0.706061\pi$
$887$	−31863.5	−1.20617	−0.603084	+	0.797678i	$0.706061\pi$
$888$	66053.3	2.49618
$889$	12361.3	0.466351
$890$	−835.877	−0.0314817
$891$	0	0
$892$	−63580.3	−2.38658
$893$	−11386.2	−0.426679
$894$	−65187.2	−2.43869
$895$	−972.106	−0.0363061
$896$	−69178.0	−2.57932
$897$	−72988.3	−2.71684
$898$	−24815.8	−0.922178
$899$	18345.1	0.680581
$900$	−10788.4	−0.399570
$901$	−8333.94	−0.308151
$902$	0	0
$903$	44149.4	1.62702
$904$	−51492.4	−1.89448
$905$	1870.42	0.0687014
$906$	−33068.4	−1.21261
$907$	37512.2	1.37329	0.686645	−	0.726993i	$-0.259083\pi$
$907$	37512.2	1.37329	0.686645	+	0.726993i	$0.259083\pi$
$908$	−36823.7	−1.34586
$909$	−6677.89	−0.243665
$910$	−3474.22	−0.126559
$911$	−50154.2	−1.82402	−0.912010	−	0.410167i	$-0.865470\pi$
$911$	−50154.2	−1.82402	−0.912010	+	0.410167i	$0.865470\pi$
$912$	−19495.0	−0.707835
$913$	0	0
$914$	64043.7	2.31770
$915$	−534.674	−0.0193178
$916$	−50548.8	−1.82334
$917$	−3226.07	−0.116177
$918$	9880.72	0.355242
$919$	−38039.5	−1.36541	−0.682703	−	0.730696i	$-0.739196\pi$
$919$	−38039.5	−1.36541	−0.682703	+	0.730696i	$0.739196\pi$
$920$	−2821.53	−0.101112
$921$	24947.8	0.892571
$922$	1987.33	0.0709862
$923$	52557.1	1.87426
$924$	0	0
$925$	43518.7	1.54690
$926$	8972.47	0.318417
$927$	8532.18	0.302302
$928$	11979.0	0.423740
$929$	9240.29	0.326334	0.163167	−	0.986598i	$-0.447829\pi$
$929$	9240.29	0.326334	0.163167	+	0.986598i	$0.447829\pi$
$930$	−1408.57	−0.0496653
$931$	−29314.5	−1.03195
$932$	87070.4	3.06018
$933$	23317.8	0.818211
$934$	−62127.8	−2.17653
$935$	0	0
$936$	12369.9	0.431968
$937$	3596.09	0.125378	0.0626889	−	0.998033i	$-0.480032\pi$
$937$	3596.09	0.125378	0.0626889	+	0.998033i	$0.480032\pi$
$938$	55288.8	1.92457
$939$	62223.9	2.16251
$940$	840.814	0.0291748
$941$	−16301.9	−0.564746	−0.282373	−	0.959305i	$-0.591122\pi$
$941$	−16301.9	−0.564746	−0.282373	+	0.959305i	$0.591122\pi$
$942$	−33483.6	−1.15813
$943$	52511.6	1.81337
$944$	−22154.8	−0.763855
$945$	1366.27	0.0470316
$946$	0	0
$947$	−30934.1	−1.06148	−0.530741	−	0.847534i	$-0.678086\pi$
$947$	−30934.1	−1.06148	−0.530741	+	0.847534i	$0.678086\pi$
$948$	−96094.2	−3.29219
$949$	31616.7	1.08148
$950$	−52079.4	−1.77861
$951$	−10662.4	−0.363566
$952$	14656.8	0.498980
$953$	−47714.5	−1.62185	−0.810926	−	0.585148i	$-0.801036\pi$
$953$	−47714.5	−1.62185	−0.810926	+	0.585148i	$0.801036\pi$
$954$	13602.2	0.461624
$955$	1236.22	0.0418881
$956$	62929.3	2.12895
$957$	0	0
$958$	−48941.8	−1.65056
$959$	15510.9	0.522288
$960$	−1692.15	−0.0568894
$961$	−15623.7	−0.524442
$962$	−107659.	−3.60818
$963$	7982.21	0.267106
$964$	−15294.7	−0.511005
$965$	1524.73	0.0508629
$966$	141152.	4.70132
$967$	16213.5	0.539184	0.269592	−	0.962975i	$-0.413111\pi$
$967$	16213.5	0.539184	0.269592	+	0.962975i	$0.413111\pi$
$968$	0	0
$969$	−8486.84	−0.281359
$970$	−855.799	−0.0283279
$971$	22830.8	0.754557	0.377278	−	0.926100i	$-0.376860\pi$
$971$	22830.8	0.754557	0.377278	+	0.926100i	$0.376860\pi$
$972$	−23860.8	−0.787384
$973$	−28211.2	−0.929507
$974$	17182.7	0.565266
$975$	46109.7	1.51455
$976$	−8445.10	−0.276968
$977$	26004.4	0.851539	0.425769	−	0.904832i	$-0.360003\pi$
$977$	26004.4	0.851539	0.425769	+	0.904832i	$0.360003\pi$
$978$	20157.5	0.659064
$979$	0	0
$980$	2164.74	0.0705612
$981$	−73.2433	−0.00238377
$982$	−29957.3	−0.973499
$983$	21359.4	0.693041	0.346521	−	0.938042i	$-0.387363\pi$
$983$	21359.4	0.693041	0.346521	+	0.938042i	$0.387363\pi$
$984$	−50351.5	−1.63125
$985$	−182.263	−0.00589582
$986$	−12541.4	−0.405071
$987$	−19495.6	−0.628726
$988$	83850.0	2.70002
$989$	−58439.7	−1.87894
$990$	0	0
$991$	40254.5	1.29034	0.645169	−	0.764040i	$-0.276787\pi$
$991$	40254.5	1.29034	0.645169	+	0.764040i	$0.276787\pi$
$992$	9251.03	0.296089
$993$	4820.00	0.154036
$994$	−101640.	−3.24328
$995$	−1641.53	−0.0523015
$996$	24345.6	0.774518
$997$	−24332.6	−0.772938	−0.386469	−	0.922302i	$-0.626305\pi$
$997$	−24332.6	−0.772938	−0.386469	+	0.922302i	$0.626305\pi$
$998$	65906.9	2.09043
$999$	42338.1	1.34086

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2057.4.a.u.1.5		52
11.2	odd	10		187.4.g.b.103.2	yes	104
11.6	odd	10		187.4.g.b.69.2	✓	104
11.10	odd	2		2057.4.a.v.1.48		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.4.g.b.69.2	✓	104	11.6	odd	10
187.4.g.b.103.2	yes	104	11.2	odd	10
2057.4.a.u.1.5		52	1.1	even	1	trivial
2057.4.a.v.1.48		52	11.10	odd	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:	\( N \)	\(=\)	\( 2057 = 11^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2057.a (trivial)

\(f(q)\)	\(=\)	\(q-4.78655 q^{2} +5.72685 q^{3} +14.9110 q^{4} +0.431714 q^{5} -27.4118 q^{6} -26.0630 q^{7} -33.0800 q^{8} +5.79678 q^{9} +O(q^{10})\)	\(q-4.78655 q^{2} +5.72685 q^{3} +14.9110 q^{4} +0.431714 q^{5} -27.4118 q^{6} -26.0630 q^{7} -33.0800 q^{8} +5.79678 q^{9} -2.06642 q^{10} +85.3932 q^{12} -64.5081 q^{13} +124.752 q^{14} +2.47236 q^{15} +39.0506 q^{16} +17.0000 q^{17} -27.7465 q^{18} -87.1729 q^{19} +6.43729 q^{20} -149.259 q^{21} +197.571 q^{23} -189.444 q^{24} -124.814 q^{25} +308.771 q^{26} -121.428 q^{27} -388.626 q^{28} +154.126 q^{29} -11.8341 q^{30} +119.027 q^{31} +77.7224 q^{32} -81.3713 q^{34} -11.2518 q^{35} +86.4359 q^{36} -348.669 q^{37} +417.257 q^{38} -369.428 q^{39} -14.2811 q^{40} +265.786 q^{41} +714.435 q^{42} -295.791 q^{43} +2.50255 q^{45} -945.683 q^{46} +130.616 q^{47} +223.637 q^{48} +336.280 q^{49} +597.426 q^{50} +97.3564 q^{51} -961.882 q^{52} -490.232 q^{53} +581.219 q^{54} +862.163 q^{56} -499.226 q^{57} -737.730 q^{58} -567.337 q^{59} +36.8654 q^{60} -216.261 q^{61} -569.727 q^{62} -151.081 q^{63} -684.426 q^{64} -27.8490 q^{65} +443.190 q^{67} +253.487 q^{68} +1131.46 q^{69} +53.8570 q^{70} -814.737 q^{71} -191.757 q^{72} -490.120 q^{73} +1668.92 q^{74} -714.789 q^{75} -1299.84 q^{76} +1768.28 q^{78} -1125.31 q^{79} +16.8587 q^{80} -851.910 q^{81} -1272.20 q^{82} +285.100 q^{83} -2225.60 q^{84} +7.33913 q^{85} +1415.82 q^{86} +882.655 q^{87} +404.506 q^{89} -11.9786 q^{90} +1681.28 q^{91} +2945.99 q^{92} +681.647 q^{93} -625.200 q^{94} -37.6337 q^{95} +445.104 q^{96} +414.146 q^{97} -1609.62 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - q^{2} + 20 q^{3} + 235 q^{4} + 40 q^{5} + 24 q^{6} + 42 q^{7} - 45 q^{8} + 572 q^{9}+O(q^{10}) \) 52 * q - q^2 + 20 * q^3 + 235 * q^4 + 40 * q^5 + 24 * q^6 + 42 * q^7 - 45 * q^8 + 572 * q^9	\( 52 q - q^{2} + 20 q^{3} + 235 q^{4} + 40 q^{5} + 24 q^{6} + 42 q^{7} - 45 q^{8} + 572 q^{9} - 33 q^{10} + 233 q^{12} - 12 q^{13} + 73 q^{14} + 400 q^{15} + 1223 q^{16} + 884 q^{17} - 201 q^{18} + 44 q^{19} + 655 q^{20} - 260 q^{21} + 572 q^{23} + 104 q^{24} + 1858 q^{25} + 465 q^{26} + 1070 q^{27} + 577 q^{28} - 322 q^{29} + 320 q^{30} + 1110 q^{31} - 481 q^{32} - 17 q^{34} - 102 q^{35} + 2507 q^{36} + 1678 q^{37} - 360 q^{38} + 1282 q^{39} - 1791 q^{40} + 826 q^{41} + 2133 q^{42} - 270 q^{43} + 710 q^{45} - 2158 q^{46} + 2464 q^{47} + 2201 q^{48} + 3224 q^{49} - 2379 q^{50} + 340 q^{51} + 3664 q^{52} + 992 q^{53} - 1202 q^{54} + 1731 q^{56} - 1016 q^{57} + 1358 q^{58} + 1442 q^{59} + 1444 q^{60} + 140 q^{61} - 464 q^{62} + 766 q^{63} + 8427 q^{64} + 1268 q^{65} + 5766 q^{67} + 3995 q^{68} + 2460 q^{69} + 2422 q^{70} + 2704 q^{71} - 5455 q^{72} - 4 q^{73} + 4008 q^{74} + 5204 q^{75} + 1935 q^{76} + 4092 q^{78} + 2180 q^{79} + 5040 q^{80} + 7192 q^{81} + 3197 q^{82} - 4200 q^{83} - 7951 q^{84} + 680 q^{85} + 3091 q^{86} + 752 q^{87} - 240 q^{89} + 4495 q^{90} + 5494 q^{91} + 6902 q^{92} + 6266 q^{93} - 5990 q^{94} - 3168 q^{95} + 9467 q^{96} + 5322 q^{97} + 4610 q^{98}+O(q^{100}) \) 52 * q - q^2 + 20 * q^3 + 235 * q^4 + 40 * q^5 + 24 * q^6 + 42 * q^7 - 45 * q^8 + 572 * q^9 - 33 * q^10 + 233 * q^12 - 12 * q^13 + 73 * q^14 + 400 * q^15 + 1223 * q^16 + 884 * q^17 - 201 * q^18 + 44 * q^19 + 655 * q^20 - 260 * q^21 + 572 * q^23 + 104 * q^24 + 1858 * q^25 + 465 * q^26 + 1070 * q^27 + 577 * q^28 - 322 * q^29 + 320 * q^30 + 1110 * q^31 - 481 * q^32 - 17 * q^34 - 102 * q^35 + 2507 * q^36 + 1678 * q^37 - 360 * q^38 + 1282 * q^39 - 1791 * q^40 + 826 * q^41 + 2133 * q^42 - 270 * q^43 + 710 * q^45 - 2158 * q^46 + 2464 * q^47 + 2201 * q^48 + 3224 * q^49 - 2379 * q^50 + 340 * q^51 + 3664 * q^52 + 992 * q^53 - 1202 * q^54 + 1731 * q^56 - 1016 * q^57 + 1358 * q^58 + 1442 * q^59 + 1444 * q^60 + 140 * q^61 - 464 * q^62 + 766 * q^63 + 8427 * q^64 + 1268 * q^65 + 5766 * q^67 + 3995 * q^68 + 2460 * q^69 + 2422 * q^70 + 2704 * q^71 - 5455 * q^72 - 4 * q^73 + 4008 * q^74 + 5204 * q^75 + 1935 * q^76 + 4092 * q^78 + 2180 * q^79 + 5040 * q^80 + 7192 * q^81 + 3197 * q^82 - 4200 * q^83 - 7951 * q^84 + 680 * q^85 + 3091 * q^86 + 752 * q^87 - 240 * q^89 + 4495 * q^90 + 5494 * q^91 + 6902 * q^92 + 6266 * q^93 - 5990 * q^94 - 3168 * q^95 + 9467 * q^96 + 5322 * q^97 + 4610 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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