LMFDB - Embedded newform 2057.4.a.u.1.19

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			1.19
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)

$f(q)$	$=$	$q-2.16938 q^{2} -6.51073 q^{3} -3.29381 q^{4} -10.9160 q^{5} +14.1242 q^{6} -25.2888 q^{7} +24.5005 q^{8} +15.3896 q^{9} +O(q^{10})$	\(q-2.16938 q^{2} -6.51073 q^{3} -3.29381 q^{4} -10.9160 q^{5} +14.1242 q^{6} -25.2888 q^{7} +24.5005 q^{8} +15.3896 q^{9} +23.6809 q^{10} +21.4451 q^{12} +30.9841 q^{13} +54.8610 q^{14} +71.0710 q^{15} -26.8004 q^{16} +17.0000 q^{17} -33.3858 q^{18} +145.576 q^{19} +35.9551 q^{20} +164.649 q^{21} +94.4647 q^{23} -159.516 q^{24} -5.84125 q^{25} -67.2161 q^{26} +75.5923 q^{27} +83.2965 q^{28} +24.6187 q^{29} -154.180 q^{30} -43.1436 q^{31} -137.864 q^{32} -36.8794 q^{34} +276.052 q^{35} -50.6903 q^{36} +83.8351 q^{37} -315.810 q^{38} -201.729 q^{39} -267.447 q^{40} +446.576 q^{41} -357.185 q^{42} +489.756 q^{43} -167.992 q^{45} -204.929 q^{46} -249.632 q^{47} +174.490 q^{48} +296.525 q^{49} +12.6719 q^{50} -110.682 q^{51} -102.056 q^{52} -478.301 q^{53} -163.988 q^{54} -619.589 q^{56} -947.809 q^{57} -53.4073 q^{58} -630.255 q^{59} -234.094 q^{60} +492.718 q^{61} +93.5947 q^{62} -389.184 q^{63} +513.482 q^{64} -338.222 q^{65} +139.959 q^{67} -55.9947 q^{68} -615.034 q^{69} -598.862 q^{70} +626.037 q^{71} +377.053 q^{72} -74.2120 q^{73} -181.870 q^{74} +38.0308 q^{75} -479.501 q^{76} +437.626 q^{78} -103.795 q^{79} +292.553 q^{80} -907.679 q^{81} -968.792 q^{82} +407.483 q^{83} -542.321 q^{84} -185.572 q^{85} -1062.47 q^{86} -160.286 q^{87} -497.441 q^{89} +364.439 q^{90} -783.551 q^{91} -311.148 q^{92} +280.896 q^{93} +541.546 q^{94} -1589.11 q^{95} +897.595 q^{96} +1029.51 q^{97} -643.273 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.16938	−0.766990	−0.383495	−	0.923543i	$-0.625280\pi$
$2$	−2.16938	−0.766990	−0.383495	+	0.923543i	$0.625280\pi$
$3$	−6.51073	−1.25299	−0.626495	−	0.779425i	$-0.715511\pi$
$3$	−6.51073	−1.25299	−0.626495	+	0.779425i	$0.715511\pi$
$4$	−3.29381	−0.411726
$5$	−10.9160	−0.976355	−0.488178	−	0.872744i	$-0.662338\pi$
$5$	−10.9160	−0.976355	−0.488178	+	0.872744i	$0.662338\pi$
$6$	14.1242	0.961031
$7$	−25.2888	−1.36547	−0.682734	−	0.730667i	$-0.739209\pi$
$7$	−25.2888	−1.36547	−0.682734	+	0.730667i	$0.739209\pi$
$8$	24.5005	1.08278
$9$	15.3896	0.569985
$10$	23.6809	0.748855
$11$	0	0
$11$	0	0
$12$	21.4451	0.515888
$13$	30.9841	0.661033	0.330517	−	0.943800i	$-0.392777\pi$
$13$	30.9841	0.661033	0.330517	+	0.943800i	$0.392777\pi$
$14$	54.8610	1.04730
$15$	71.0710	1.22336
$16$	−26.8004	−0.418756
$17$	17.0000	0.242536
$17$	17.0000	0.242536
$18$	−33.3858	−0.437173
$19$	145.576	1.75776	0.878882	−	0.477039i	$-0.158290\pi$
$19$	145.576	1.75776	0.878882	+	0.477039i	$0.158290\pi$
$20$	35.9551	0.401991
$21$	164.649	1.71092
$22$	0	0
$23$	94.4647	0.856402	0.428201	−	0.903683i	$-0.359148\pi$
$23$	94.4647	0.856402	0.428201	+	0.903683i	$0.359148\pi$
$24$	−159.516	−1.35671
$25$	−5.84125	−0.0467300
$26$	−67.2161	−0.507006
$27$	75.5923	0.538805
$28$	83.2965	0.562198
$29$	24.6187	0.157641	0.0788204	−	0.996889i	$-0.474885\pi$
$29$	24.6187	0.157641	0.0788204	+	0.996889i	$0.474885\pi$
$30$	−154.180	−0.938308
$31$	−43.1436	−0.249962	−0.124981	−	0.992159i	$-0.539887\pi$
$31$	−43.1436	−0.249962	−0.124981	+	0.992159i	$0.539887\pi$
$32$	−137.864	−0.761598
$33$	0	0
$34$	−36.8794	−0.186022
$35$	276.052	1.33318
$36$	−50.6903	−0.234677
$37$	83.8351	0.372497	0.186249	−	0.982503i	$-0.440367\pi$
$37$	83.8351	0.372497	0.186249	+	0.982503i	$0.440367\pi$
$38$	−315.810	−1.34819
$39$	−201.729	−0.828268
$40$	−267.447	−1.05718
$41$	446.576	1.70106	0.850530	−	0.525926i	$-0.176281\pi$
$41$	446.576	1.70106	0.850530	+	0.525926i	$0.176281\pi$
$42$	−357.185	−1.31226
$43$	489.756	1.73691	0.868455	−	0.495768i	$-0.165113\pi$
$43$	489.756	1.73691	0.868455	+	0.495768i	$0.165113\pi$
$44$	0	0
$45$	−167.992	−0.556508
$46$	−204.929	−0.656852
$47$	−249.632	−0.774736	−0.387368	−	0.921925i	$-0.626616\pi$
$47$	−249.632	−0.774736	−0.387368	+	0.921925i	$0.626616\pi$
$48$	174.490	0.524697
$49$	296.525	0.864503
$50$	12.6719	0.0358414
$51$	−110.682	−0.303895
$52$	−102.056	−0.272165
$53$	−478.301	−1.23962	−0.619809	−	0.784753i	$-0.712790\pi$
$53$	−478.301	−1.23962	−0.619809	+	0.784753i	$0.712790\pi$
$54$	−163.988	−0.413258
$55$	0	0
$56$	−619.589	−1.47850
$57$	−947.809	−2.20246
$58$	−53.4073	−0.120909
$59$	−630.255	−1.39072	−0.695358	−	0.718663i	$-0.744754\pi$
$59$	−630.255	−1.39072	−0.695358	+	0.718663i	$0.744754\pi$
$60$	−234.094	−0.503690
$61$	492.718	1.03420	0.517099	−	0.855925i	$-0.327012\pi$
$61$	492.718	1.03420	0.517099	+	0.855925i	$0.327012\pi$
$62$	93.5947	0.191718
$63$	−389.184	−0.778296
$64$	513.482	1.00289
$65$	−338.222	−0.645404
$66$	0	0
$67$	139.959	0.255205	0.127602	−	0.991825i	$-0.459272\pi$
$67$	139.959	0.255205	0.127602	+	0.991825i	$0.459272\pi$
$68$	−55.9947	−0.0998582
$69$	−615.034	−1.07306
$70$	−598.862	−1.02254
$71$	626.037	1.04644	0.523218	−	0.852199i	$-0.324731\pi$
$71$	626.037	1.04644	0.523218	+	0.852199i	$0.324731\pi$
$72$	377.053	0.617168
$73$	−74.2120	−0.118984	−0.0594921	−	0.998229i	$-0.518948\pi$
$73$	−74.2120	−0.118984	−0.0594921	+	0.998229i	$0.518948\pi$
$74$	−181.870	−0.285702
$75$	38.0308	0.0585522
$76$	−479.501	−0.723717
$77$	0	0
$78$	437.626	0.635274
$79$	−103.795	−0.147820	−0.0739102	−	0.997265i	$-0.523548\pi$
$79$	−103.795	−0.147820	−0.0739102	+	0.997265i	$0.523548\pi$
$80$	292.553	0.408855
$81$	−907.679	−1.24510
$82$	−968.792	−1.30470
$83$	407.483	0.538880	0.269440	−	0.963017i	$-0.413161\pi$
$83$	407.483	0.538880	0.269440	+	0.963017i	$0.413161\pi$
$84$	−542.321	−0.704429
$85$	−185.572	−0.236801
$86$	−1062.47	−1.33219
$87$	−160.286	−0.197522
$88$	0	0
$89$	−497.441	−0.592456	−0.296228	−	0.955117i	$-0.595729\pi$
$89$	−497.441	−0.592456	−0.296228	+	0.955117i	$0.595729\pi$
$90$	364.439	0.426836
$91$	−783.551	−0.902620
$92$	−311.148	−0.352603
$93$	280.896	0.313200
$94$	541.546	0.594215
$95$	−1589.11	−1.71620
$96$	897.595	0.954275
$97$	1029.51	1.07763	0.538817	−	0.842423i	$-0.318871\pi$
$97$	1029.51	1.07763	0.538817	+	0.842423i	$0.318871\pi$
$98$	−643.273	−0.663066
$99$	0	0
$100$	19.2399	0.0192399
$101$	1875.75	1.84796	0.923981	−	0.382439i	$-0.124916\pi$
$101$	1875.75	1.84796	0.923981	+	0.382439i	$0.124916\pi$
$102$	240.112	0.233084
$103$	−1345.48	−1.28713	−0.643565	−	0.765391i	$-0.722545\pi$
$103$	−1345.48	−1.28713	−0.643565	+	0.765391i	$0.722545\pi$
$104$	759.126	0.715754
$105$	−1797.30	−1.67046
$106$	1037.62	0.950775
$107$	1283.86	1.15995	0.579977	−	0.814633i	$-0.303062\pi$
$107$	1283.86	1.15995	0.579977	+	0.814633i	$0.303062\pi$
$108$	−248.986	−0.221840
$109$	−1113.58	−0.978549	−0.489274	−	0.872130i	$-0.662738\pi$
$109$	−1113.58	−0.978549	−0.489274	+	0.872130i	$0.662738\pi$
$110$	0	0
$111$	−545.828	−0.466736
$112$	677.750	0.571798
$113$	1305.17	1.08655	0.543276	−	0.839554i	$-0.317184\pi$
$113$	1305.17	1.08655	0.543276	+	0.839554i	$0.317184\pi$
$114$	2056.15	1.68927
$115$	−1031.18	−0.836153
$116$	−81.0893	−0.0649048
$117$	476.832	0.376779
$118$	1367.26	1.06667
$119$	−429.910	−0.331175
$120$	1741.28	1.32463
$121$	0	0
$122$	−1068.89	−0.793220
$123$	−2907.54	−2.13141
$124$	142.107	0.102916
$125$	1428.26	1.02198
$126$	844.288	0.596945
$127$	123.382	0.0862079	0.0431039	−	0.999071i	$-0.486275\pi$
$127$	123.382	0.0862079	0.0431039	+	0.999071i	$0.486275\pi$
$128$	−11.0238	−0.00761231
$129$	−3188.67	−2.17633
$130$	733.730	0.495018
$131$	−1829.55	−1.22022	−0.610109	−	0.792317i	$-0.708874\pi$
$131$	−1829.55	−1.22022	−0.610109	+	0.792317i	$0.708874\pi$
$132$	0	0
$133$	−3681.46	−2.40017
$134$	−303.624	−0.195740
$135$	−825.164	−0.526065
$136$	416.509	0.262613
$137$	1123.13	0.700402	0.350201	−	0.936675i	$-0.386113\pi$
$137$	1123.13	0.700402	0.350201	+	0.936675i	$0.386113\pi$
$138$	1334.24	0.823029
$139$	−1421.54	−0.867434	−0.433717	−	0.901049i	$-0.642798\pi$
$139$	−1421.54	−0.867434	−0.433717	+	0.901049i	$0.642798\pi$
$140$	−909.263	−0.548906
$141$	1625.29	0.970737
$142$	−1358.11	−0.802606
$143$	0	0
$144$	−412.447	−0.238685
$145$	−268.738	−0.153913
$146$	160.994	0.0912598
$147$	−1930.59	−1.08321
$148$	−276.137	−0.153367
$149$	−633.135	−0.348110	−0.174055	−	0.984736i	$-0.555687\pi$
$149$	−633.135	−0.348110	−0.174055	+	0.984736i	$0.555687\pi$
$150$	−82.5031	−0.0449090
$151$	−2815.45	−1.51734	−0.758670	−	0.651475i	$-0.774151\pi$
$151$	−2815.45	−1.51734	−0.758670	+	0.651475i	$0.774151\pi$
$152$	3566.70	1.90327
$153$	261.623	0.138242
$154$	0	0
$155$	470.955	0.244052
$156$	664.456	0.341019
$157$	1898.43	0.965039	0.482520	−	0.875885i	$-0.339722\pi$
$157$	1898.43	0.965039	0.482520	+	0.875885i	$0.339722\pi$
$158$	225.170	0.113377
$159$	3114.09	1.55323
$160$	1504.92	0.743591
$161$	−2388.90	−1.16939
$162$	1969.10	0.954981
$163$	−2025.81	−0.973459	−0.486730	−	0.873553i	$-0.661810\pi$
$163$	−2025.81	−0.973459	−0.486730	+	0.873553i	$0.661810\pi$
$164$	−1470.94	−0.700370
$165$	0	0
$166$	−883.984	−0.413316
$167$	2053.69	0.951612	0.475806	−	0.879550i	$-0.342156\pi$
$167$	2053.69	0.951612	0.475806	+	0.879550i	$0.342156\pi$
$168$	4033.98	1.85255
$169$	−1236.99	−0.563035
$170$	402.575	0.181624
$171$	2240.36	1.00190
$172$	−1613.16	−0.715130
$173$	−2805.45	−1.23292	−0.616458	−	0.787388i	$-0.711433\pi$
$173$	−2805.45	−1.23292	−0.616458	+	0.787388i	$0.711433\pi$
$174$	347.720	0.151498
$175$	147.718	0.0638083
$176$	0	0
$177$	4103.42	1.74255
$178$	1079.14	0.454408
$179$	762.370	0.318336	0.159168	−	0.987251i	$-0.449119\pi$
$179$	762.370	0.318336	0.159168	+	0.987251i	$0.449119\pi$
$180$	553.335	0.229129
$181$	919.147	0.377457	0.188728	−	0.982029i	$-0.439563\pi$
$181$	919.147	0.377457	0.188728	+	0.982029i	$0.439563\pi$
$182$	1699.82	0.692301
$183$	−3207.96	−1.29584
$184$	2314.43	0.927295
$185$	−915.143	−0.363690
$186$	−609.370	−0.240221
$187$	0	0
$188$	822.240	0.318979
$189$	−1911.64	−0.735721
$190$	3447.38	1.31631
$191$	2968.26	1.12448	0.562239	−	0.826975i	$-0.309940\pi$
$191$	2968.26	1.12448	0.562239	+	0.826975i	$0.309940\pi$
$192$	−3343.14	−1.25662
$193$	4202.99	1.56755	0.783777	−	0.621042i	$-0.213291\pi$
$193$	4202.99	1.56755	0.783777	+	0.621042i	$0.213291\pi$
$194$	−2233.39	−0.826535
$195$	2202.07	0.808684
$196$	−976.695	−0.355938
$197$	3049.33	1.10282	0.551411	−	0.834234i	$-0.314090\pi$
$197$	3049.33	1.10282	0.551411	+	0.834234i	$0.314090\pi$
$198$	0	0
$199$	1504.00	0.535759	0.267879	−	0.963452i	$-0.413677\pi$
$199$	1504.00	0.535759	0.267879	+	0.963452i	$0.413677\pi$
$200$	−143.114	−0.0505983
$201$	−911.236	−0.319769
$202$	−4069.21	−1.41737
$203$	−622.579	−0.215253
$204$	364.566	0.125121
$205$	−4874.82	−1.66084
$206$	2918.86	0.987216
$207$	1453.77	0.488136
$208$	−830.385	−0.276812
$209$	0	0
$210$	3899.03	1.28123
$211$	3945.79	1.28739	0.643695	−	0.765282i	$-0.277401\pi$
$211$	3945.79	1.28739	0.643695	+	0.765282i	$0.277401\pi$
$212$	1575.43	0.510383
$213$	−4075.96	−1.31117
$214$	−2785.17	−0.889673
$215$	−5346.17	−1.69584
$216$	1852.05	0.583407
$217$	1091.05	0.341315
$218$	2415.78	0.750537
$219$	483.174	0.149086
$220$	0	0
$221$	526.729	0.160324
$222$	1184.11	0.357982
$223$	−489.831	−0.147092	−0.0735460	−	0.997292i	$-0.523432\pi$
$223$	−489.831	−0.147092	−0.0735460	+	0.997292i	$0.523432\pi$
$224$	3486.42	1.03994
$225$	−89.8944	−0.0266354
$226$	−2831.41	−0.833375
$227$	468.087	0.136864	0.0684318	−	0.997656i	$-0.478200\pi$
$227$	468.087	0.136864	0.0684318	+	0.997656i	$0.478200\pi$
$228$	3121.90	0.906810
$229$	2023.98	0.584054	0.292027	−	0.956410i	$-0.405670\pi$
$229$	2023.98	0.584054	0.292027	+	0.956410i	$0.405670\pi$
$230$	2237.01	0.641321
$231$	0	0
$232$	603.172	0.170690
$233$	−6957.74	−1.95630	−0.978148	−	0.207912i	$-0.933333\pi$
$233$	−6957.74	−1.95630	−0.978148	+	0.207912i	$0.933333\pi$
$234$	−1034.43	−0.288986
$235$	2724.98	0.756418
$236$	2075.94	0.572594
$237$	675.779	0.185218
$238$	932.637	0.254008
$239$	−1209.29	−0.327292	−0.163646	−	0.986519i	$-0.552325\pi$
$239$	−1209.29	−0.327292	−0.163646	+	0.986519i	$0.552325\pi$
$240$	−1904.73	−0.512291
$241$	1009.13	0.269725	0.134863	−	0.990864i	$-0.456941\pi$
$241$	1009.13	0.269725	0.134863	+	0.990864i	$0.456941\pi$
$242$	0	0
$243$	3868.66	1.02130
$244$	−1622.92	−0.425806
$245$	−3236.86	−0.844062
$246$	6307.54	1.63477
$247$	4510.55	1.16194
$248$	−1057.04	−0.270654
$249$	−2653.01	−0.675212
$250$	−3098.44	−0.783849
$251$	−932.752	−0.234561	−0.117280	−	0.993099i	$-0.537418\pi$
$251$	−932.752	−0.234561	−0.117280	+	0.993099i	$0.537418\pi$
$252$	1281.90	0.320444
$253$	0	0
$254$	−267.662	−0.0661206
$255$	1208.21	0.296709
$256$	−4083.94	−0.997056
$257$	−2212.13	−0.536921	−0.268460	−	0.963291i	$-0.586515\pi$
$257$	−2212.13	−0.536921	−0.268460	+	0.963291i	$0.586515\pi$
$258$	6917.42	1.66922
$259$	−2120.09	−0.508633
$260$	1114.04	0.265729
$261$	378.872	0.0898528
$262$	3968.98	0.935895
$263$	−403.163	−0.0945251	−0.0472625	−	0.998883i	$-0.515050\pi$
$263$	−403.163	−0.0945251	−0.0472625	+	0.998883i	$0.515050\pi$
$264$	0	0
$265$	5221.13	1.21031
$266$	7986.47	1.84091
$267$	3238.70	0.742342
$268$	−460.998	−0.105074
$269$	4697.53	1.06473	0.532367	−	0.846514i	$-0.321303\pi$
$269$	4697.53	1.06473	0.532367	+	0.846514i	$0.321303\pi$
$270$	1790.09	0.403487
$271$	1843.96	0.413331	0.206666	−	0.978412i	$-0.433739\pi$
$271$	1843.96	0.413331	0.206666	+	0.978412i	$0.433739\pi$
$272$	−455.607	−0.101563
$273$	5101.49	1.13097
$274$	−2436.48	−0.537202
$275$	0	0
$276$	2025.80	0.441808
$277$	−7212.51	−1.56447	−0.782234	−	0.622985i	$-0.785920\pi$
$277$	−7212.51	−1.56447	−0.782234	+	0.622985i	$0.785920\pi$
$278$	3083.85	0.665313
$279$	−663.962	−0.142474
$280$	6763.43	1.44354
$281$	−9056.20	−1.92259	−0.961295	−	0.275522i	$-0.911149\pi$
$281$	−9056.20	−1.92259	−0.961295	+	0.275522i	$0.911149\pi$
$282$	−3525.86	−0.744546
$283$	503.497	0.105759	0.0528795	−	0.998601i	$-0.483160\pi$
$283$	503.497	0.105759	0.0528795	+	0.998601i	$0.483160\pi$
$284$	−2062.05	−0.430845
$285$	10346.3	2.15039
$286$	0	0
$287$	−11293.4	−2.32274
$288$	−2121.67	−0.434099
$289$	289.000	0.0588235
$290$	582.993	0.118050
$291$	−6702.84	−1.35027
$292$	244.440	0.0489889
$293$	4057.71	0.809058	0.404529	−	0.914525i	$-0.367435\pi$
$293$	4057.71	0.809058	0.404529	+	0.914525i	$0.367435\pi$
$294$	4188.18	0.830815
$295$	6879.86	1.35783
$296$	2054.00	0.403333
$297$	0	0
$298$	1373.51	0.266997
$299$	2926.90	0.566110
$300$	−125.266	−0.0241075
$301$	−12385.4	−2.37169
$302$	6107.78	1.16379
$303$	−12212.5	−2.31548
$304$	−3901.51	−0.736075
$305$	−5378.51	−1.00975
$306$	−567.559	−0.106030
$307$	5176.63	0.962365	0.481182	−	0.876621i	$-0.340208\pi$
$307$	5176.63	0.962365	0.481182	+	0.876621i	$0.340208\pi$
$308$	0	0
$309$	8760.08	1.61276
$310$	−1021.68	−0.187185
$311$	−1800.53	−0.328292	−0.164146	−	0.986436i	$-0.552487\pi$
$311$	−1800.53	−0.328292	−0.164146	+	0.986436i	$0.552487\pi$
$312$	−4942.46	−0.896833
$313$	1028.28	0.185692	0.0928461	−	0.995680i	$-0.470404\pi$
$313$	1028.28	0.185692	0.0928461	+	0.995680i	$0.470404\pi$
$314$	−4118.41	−0.740176
$315$	4248.33	0.759893
$316$	341.880	0.0608615
$317$	7890.76	1.39807	0.699037	−	0.715086i	$-0.253612\pi$
$317$	7890.76	1.39807	0.699037	+	0.715086i	$0.253612\pi$
$318$	−6755.63	−1.19131
$319$	0	0
$320$	−5605.16	−0.979182
$321$	−8358.84	−1.45341
$322$	5182.42	0.896911
$323$	2474.80	0.426321
$324$	2989.72	0.512641
$325$	−180.986	−0.0308901
$326$	4394.75	0.746634
$327$	7250.23	1.22611
$328$	10941.3	1.84187
$329$	6312.90	1.05788
$330$	0	0
$331$	4570.45	0.758956	0.379478	−	0.925201i	$-0.376104\pi$
$331$	4570.45	0.758956	0.379478	+	0.925201i	$0.376104\pi$
$332$	−1342.17	−0.221871
$333$	1290.19	0.212318
$334$	−4455.23	−0.729877
$335$	−1527.79	−0.249171
$336$	−4412.65	−0.716457
$337$	−11037.0	−1.78405	−0.892025	−	0.451986i	$-0.850716\pi$
$337$	−11037.0	−1.78405	−0.892025	+	0.451986i	$0.850716\pi$
$338$	2683.49	0.431842
$339$	−8497.63	−1.36144
$340$	611.237	0.0974971
$341$	0	0
$342$	−4860.19	−0.768447
$343$	1175.31	0.185017
$344$	11999.3	1.88069
$345$	6713.70	1.04769
$346$	6086.08	0.945634
$347$	8393.57	1.29853	0.649266	−	0.760562i	$-0.275076\pi$
$347$	8393.57	1.29853	0.649266	+	0.760562i	$0.275076\pi$
$348$	527.951	0.0813251
$349$	9694.42	1.48691	0.743453	−	0.668788i	$-0.233187\pi$
$349$	9694.42	1.48691	0.743453	+	0.668788i	$0.233187\pi$
$350$	−320.457	−0.0489403
$351$	2342.16	0.356168
$352$	0	0
$353$	−11062.1	−1.66791	−0.833957	−	0.551829i	$-0.813930\pi$
$353$	−11062.1	−1.66791	−0.833957	+	0.551829i	$0.813930\pi$
$354$	−8901.87	−1.33652
$355$	−6833.82	−1.02169
$356$	1638.47	0.243930
$357$	2799.03	0.414959
$358$	−1653.87	−0.244161
$359$	−21.8247	−0.00320853	−0.00160426	−	0.999999i	$-0.500511\pi$
$359$	−21.8247	−0.00320853	−0.00160426	+	0.999999i	$0.500511\pi$
$360$	−4115.90	−0.602575
$361$	14333.5	2.08974
$362$	−1993.98	−0.289506
$363$	0	0
$364$	2580.86	0.371632
$365$	810.097	0.116171
$366$	6959.26	0.993897
$367$	4916.82	0.699335	0.349668	−	0.936874i	$-0.386295\pi$
$367$	4916.82	0.699335	0.349668	+	0.936874i	$0.386295\pi$
$368$	−2531.69	−0.358624
$369$	6872.62	0.969578
$370$	1985.29	0.278947
$371$	12095.7	1.69266
$372$	−925.218	−0.128952
$373$	12579.5	1.74623	0.873114	−	0.487516i	$-0.162097\pi$
$373$	12579.5	1.74623	0.873114	+	0.487516i	$0.162097\pi$
$374$	0	0
$375$	−9299.02	−1.28053
$376$	−6116.12	−0.838869
$377$	762.788	0.104206
$378$	4147.07	0.564291
$379$	4006.18	0.542965	0.271482	−	0.962443i	$-0.412486\pi$
$379$	4006.18	0.542965	0.271482	+	0.962443i	$0.412486\pi$
$380$	5234.22	0.706605
$381$	−803.308	−0.108018
$382$	−6439.26	−0.862464
$383$	−3230.24	−0.430959	−0.215480	−	0.976508i	$-0.569132\pi$
$383$	−3230.24	−0.430959	−0.215480	+	0.976508i	$0.569132\pi$
$384$	71.7730	0.00953815
$385$	0	0
$386$	−9117.87	−1.20230
$387$	7537.14	0.990012
$388$	−3390.99	−0.443690
$389$	−264.126	−0.0344260	−0.0172130	−	0.999852i	$-0.505479\pi$
$389$	−264.126	−0.0344260	−0.0172130	+	0.999852i	$0.505479\pi$
$390$	−4777.12	−0.620253
$391$	1605.90	0.207708
$392$	7265.01	0.936067
$393$	11911.7	1.52892
$394$	−6615.14	−0.845853
$395$	1133.02	0.144325
$396$	0	0
$397$	4.79655	0.000606377 0	0.000303189	−	1.00000i	$-0.499903\pi$
$397$	4.79655	0.000606377 0	0.000303189		1.00000i	$0.499903\pi$
$398$	−3262.75	−0.410922
$399$	23969.0	3.00739
$400$	156.548	0.0195685
$401$	−8241.81	−1.02638	−0.513188	−	0.858276i	$-0.671536\pi$
$401$	−8241.81	−1.02638	−0.513188	+	0.858276i	$0.671536\pi$
$402$	1976.81	0.245260
$403$	−1336.76	−0.165233
$404$	−6178.36	−0.760853
$405$	9908.22	1.21566
$406$	1350.61	0.165097
$407$	0	0
$408$	−2711.78	−0.329051
$409$	−11417.0	−1.38027	−0.690137	−	0.723678i	$-0.742450\pi$
$409$	−11417.0	−1.38027	−0.690137	+	0.723678i	$0.742450\pi$
$410$	10575.3	1.27385
$411$	−7312.36	−0.877597
$412$	4431.76	0.529945
$413$	15938.4	1.89898
$414$	−3153.78	−0.374396
$415$	−4448.08	−0.526139
$416$	−4271.59	−0.503442
$417$	9255.25	1.08689
$418$	0	0
$419$	−408.658	−0.0476474	−0.0238237	−	0.999716i	$-0.507584\pi$
$419$	−408.658	−0.0476474	−0.0238237	+	0.999716i	$0.507584\pi$
$420$	5919.97	0.687773
$421$	−3456.24	−0.400111	−0.200056	−	0.979785i	$-0.564112\pi$
$421$	−3456.24	−0.400111	−0.200056	+	0.979785i	$0.564112\pi$
$422$	−8559.90	−0.987415
$423$	−3841.74	−0.441588
$424$	−11718.6	−1.34223
$425$	−99.3012	−0.0113337
$426$	8842.29	1.00566
$427$	−12460.3	−1.41217
$428$	−4228.77	−0.477583
$429$	0	0
$430$	11597.9	1.30069
$431$	11305.7	1.26351	0.631757	−	0.775166i	$-0.282334\pi$
$431$	11305.7	1.26351	0.631757	+	0.775166i	$0.282334\pi$
$432$	−2025.90	−0.225628
$433$	−8649.55	−0.959978	−0.479989	−	0.877274i	$-0.659359\pi$
$433$	−8649.55	−0.959978	−0.479989	+	0.877274i	$0.659359\pi$
$434$	−2366.90	−0.261785
$435$	1749.68	0.192852
$436$	3667.92	0.402894
$437$	13751.8	1.50535
$438$	−1048.19	−0.114348
$439$	8598.38	0.934802	0.467401	−	0.884045i	$-0.345190\pi$
$439$	8598.38	0.934802	0.467401	+	0.884045i	$0.345190\pi$
$440$	0	0
$441$	4563.39	0.492753
$442$	−1142.67	−0.122967
$443$	−13262.1	−1.42236	−0.711178	−	0.703012i	$-0.751838\pi$
$443$	−13262.1	−1.42236	−0.711178	+	0.703012i	$0.751838\pi$
$444$	1797.85	0.192167
$445$	5430.06	0.578448
$446$	1062.63	0.112818
$447$	4122.17	0.436179
$448$	−12985.4	−1.36942
$449$	−5556.03	−0.583976	−0.291988	−	0.956422i	$-0.594317\pi$
$449$	−5556.03	−0.583976	−0.291988	+	0.956422i	$0.594317\pi$
$450$	195.015	0.0204291
$451$	0	0
$452$	−4298.99	−0.447361
$453$	18330.7	1.90121
$454$	−1015.46	−0.104973
$455$	8553.23	0.881278
$456$	−23221.8	−2.38478
$457$	−9298.47	−0.951782	−0.475891	−	0.879504i	$-0.657874\pi$
$457$	−9298.47	−0.951782	−0.475891	+	0.879504i	$0.657874\pi$
$458$	−4390.78	−0.447964
$459$	1285.07	0.130679
$460$	3396.49	0.344266
$461$	−8818.50	−0.890929	−0.445465	−	0.895300i	$-0.646961\pi$
$461$	−8818.50	−0.890929	−0.445465	+	0.895300i	$0.646961\pi$
$462$	0	0
$463$	−6827.20	−0.685285	−0.342643	−	0.939466i	$-0.611322\pi$
$463$	−6827.20	−0.685285	−0.342643	+	0.939466i	$0.611322\pi$
$464$	−659.792	−0.0660130
$465$	−3066.26	−0.305794
$466$	15094.0	1.50046
$467$	14825.6	1.46906	0.734528	−	0.678578i	$-0.237404\pi$
$467$	14825.6	1.46906	0.734528	+	0.678578i	$0.237404\pi$
$468$	−1570.59	−0.155130
$469$	−3539.40	−0.348474
$470$	−5911.51	−0.580165
$471$	−12360.2	−1.20918
$472$	−15441.6	−1.50584
$473$	0	0
$474$	−1466.02	−0.142060
$475$	−850.348	−0.0821403
$476$	1416.04	0.136353
$477$	−7360.86	−0.706563
$478$	2623.41	0.251030
$479$	−8066.00	−0.769405	−0.384703	−	0.923041i	$-0.625696\pi$
$479$	−8066.00	−0.769405	−0.384703	+	0.923041i	$0.625696\pi$
$480$	−9798.13	−0.931712
$481$	2597.55	0.246233
$482$	−2189.18	−0.206877
$483$	15553.5	1.46523
$484$	0	0
$485$	−11238.1	−1.05215
$486$	−8392.59	−0.783324
$487$	10488.7	0.975948	0.487974	−	0.872858i	$-0.337736\pi$
$487$	10488.7	0.975948	0.487974	+	0.872858i	$0.337736\pi$
$488$	12071.9	1.11981
$489$	13189.5	1.21973
$490$	7021.96	0.647388
$491$	15944.3	1.46549	0.732747	−	0.680502i	$-0.238238\pi$
$491$	15944.3	1.46549	0.732747	+	0.680502i	$0.238238\pi$
$492$	9576.86	0.877557
$493$	418.518	0.0382335
$494$	−9785.08	−0.891198
$495$	0	0
$496$	1156.27	0.104673
$497$	−15831.7	−1.42888
$498$	5755.38	0.517881
$499$	−9959.59	−0.893492	−0.446746	−	0.894661i	$-0.647417\pi$
$499$	−9959.59	−0.893492	−0.446746	+	0.894661i	$0.647417\pi$
$500$	−4704.42	−0.420776
$501$	−13371.0	−1.19236
$502$	2023.49	0.179906
$503$	4276.94	0.379124	0.189562	−	0.981869i	$-0.439293\pi$
$503$	4276.94	0.379124	0.189562	+	0.981869i	$0.439293\pi$
$504$	−9535.22	−0.842723
$505$	−20475.7	−1.80427
$506$	0	0
$507$	8053.69	0.705477
$508$	−406.397	−0.0354940
$509$	8219.52	0.715764	0.357882	−	0.933767i	$-0.383499\pi$
$509$	8219.52	0.715764	0.357882	+	0.933767i	$0.383499\pi$
$510$	−2621.06	−0.227573
$511$	1876.73	0.162469
$512$	8947.80	0.772345
$513$	11004.5	0.947093
$514$	4798.93	0.411813
$515$	14687.3	1.25670
$516$	10502.9	0.896052
$517$	0	0
$518$	4599.28	0.390117
$519$	18265.5	1.54483
$520$	−8286.61	−0.698830
$521$	18038.9	1.51689	0.758445	−	0.651737i	$-0.225959\pi$
$521$	18038.9	1.51689	0.758445	+	0.651737i	$0.225959\pi$
$522$	−821.916	−0.0689163
$523$	−4470.11	−0.373737	−0.186869	−	0.982385i	$-0.559834\pi$
$523$	−4470.11	−0.373737	−0.186869	+	0.982385i	$0.559834\pi$
$524$	6026.18	0.502395
$525$	−961.754	−0.0799512
$526$	874.612	0.0724998
$527$	−733.441	−0.0606247
$528$	0	0
$529$	−3243.42	−0.266575
$530$	−11326.6	−0.928294
$531$	−9699.37	−0.792687
$532$	12126.0	0.988213
$533$	13836.7	1.12446
$534$	−7025.96	−0.569369
$535$	−14014.6	−1.13253
$536$	3429.07	0.276331
$537$	−4963.58	−0.398872
$538$	−10190.7	−0.816641
$539$	0	0
$540$	2717.93	0.216595
$541$	5712.83	0.454000	0.227000	−	0.973895i	$-0.427108\pi$
$541$	5712.83	0.454000	0.227000	+	0.973895i	$0.427108\pi$
$542$	−4000.25	−0.317021
$543$	−5984.31	−0.472949
$544$	−2343.69	−0.184715
$545$	12155.8	0.955411
$546$	−11067.0	−0.867446
$547$	−7013.08	−0.548186	−0.274093	−	0.961703i	$-0.588378\pi$
$547$	−7013.08	−0.548186	−0.274093	+	0.961703i	$0.588378\pi$
$548$	−3699.36	−0.288374
$549$	7582.73	0.589477
$550$	0	0
$551$	3583.91	0.277095
$552$	−15068.6	−1.16189
$553$	2624.85	0.201844
$554$	15646.6	1.19993
$555$	5958.25	0.455700
$556$	4682.27	0.357145
$557$	4393.28	0.334199	0.167100	−	0.985940i	$-0.446560\pi$
$557$	4393.28	0.334199	0.167100	+	0.985940i	$0.446560\pi$
$558$	1440.38	0.109277
$559$	15174.6	1.14816
$560$	−7398.31	−0.558278
$561$	0	0
$562$	19646.3	1.47461
$563$	3607.76	0.270069	0.135035	−	0.990841i	$-0.456885\pi$
$563$	3607.76	0.270069	0.135035	+	0.990841i	$0.456885\pi$
$564$	−5353.38	−0.399677
$565$	−14247.3	−1.06086
$566$	−1092.27	−0.0811161
$567$	22954.1	1.70015
$568$	15338.2	1.13306
$569$	−3688.53	−0.271760	−0.135880	−	0.990725i	$-0.543386\pi$
$569$	−3688.53	−0.271760	−0.135880	+	0.990725i	$0.543386\pi$
$570$	−22444.9	−1.64933
$571$	−20522.7	−1.50412	−0.752058	−	0.659097i	$-0.770939\pi$
$571$	−20522.7	−1.50412	−0.752058	+	0.659097i	$0.770939\pi$
$572$	0	0
$573$	−19325.5	−1.40896
$574$	24499.6	1.78152
$575$	−551.792	−0.0400197
$576$	7902.27	0.571634
$577$	−20103.0	−1.45043	−0.725216	−	0.688522i	$-0.758260\pi$
$577$	−20103.0	−1.45043	−0.725216	+	0.688522i	$0.758260\pi$
$578$	−626.950	−0.0451171
$579$	−27364.5	−1.96413
$580$	885.170	0.0633701
$581$	−10304.8	−0.735824
$582$	14541.0	1.03564
$583$	0	0
$584$	−1818.23	−0.128834
$585$	−5205.09	−0.367870
$586$	−8802.71	−0.620540
$587$	−16181.8	−1.13781	−0.568905	−	0.822403i	$-0.692633\pi$
$587$	−16181.8	−1.13781	−0.568905	+	0.822403i	$0.692633\pi$
$588$	6358.99	0.445987
$589$	−6280.69	−0.439374
$590$	−14925.0	−1.04145
$591$	−19853.4	−1.38182
$592$	−2246.81	−0.155986
$593$	−17581.7	−1.21753	−0.608763	−	0.793352i	$-0.708334\pi$
$593$	−17581.7	−1.21753	−0.608763	+	0.793352i	$0.708334\pi$
$594$	0	0
$595$	4692.89	0.323344
$596$	2085.42	0.143326
$597$	−9792.16	−0.671301
$598$	−6349.55	−0.434201
$599$	−8038.45	−0.548317	−0.274159	−	0.961684i	$-0.588399\pi$
$599$	−8038.45	−0.548317	−0.274159	+	0.961684i	$0.588399\pi$
$600$	931.774	0.0633992
$601$	−4862.71	−0.330040	−0.165020	−	0.986290i	$-0.552769\pi$
$601$	−4862.71	−0.330040	−0.165020	+	0.986290i	$0.552769\pi$
$602$	26868.5	1.81907
$603$	2153.91	0.145463
$604$	9273.56	0.624728
$605$	0	0
$606$	26493.5	1.77595
$607$	20181.6	1.34950	0.674750	−	0.738046i	$-0.264251\pi$
$607$	20181.6	1.34950	0.674750	+	0.738046i	$0.264251\pi$
$608$	−20069.8	−1.33871
$609$	4053.44	0.269711
$610$	11668.0	0.774465
$611$	−7734.62	−0.512127
$612$	−861.735	−0.0569176
$613$	27726.1	1.82683	0.913415	−	0.407028i	$-0.133435\pi$
$613$	27726.1	1.82683	0.913415	+	0.407028i	$0.133435\pi$
$614$	−11230.1	−0.738124
$615$	31738.6	2.08102
$616$	0	0
$617$	8524.43	0.556209	0.278104	−	0.960551i	$-0.410294\pi$
$617$	8524.43	0.556209	0.278104	+	0.960551i	$0.410294\pi$
$618$	−19003.9	−1.23697
$619$	20038.2	1.30114	0.650568	−	0.759448i	$-0.274531\pi$
$619$	20038.2	1.30114	0.650568	+	0.759448i	$0.274531\pi$
$620$	−1551.23	−0.100482
$621$	7140.80	0.461434
$622$	3906.03	0.251797
$623$	12579.7	0.808980
$624$	5406.41	0.346842
$625$	−14860.7	−0.951086
$626$	−2230.72	−0.142424
$627$	0	0
$628$	−6253.06	−0.397332
$629$	1425.20	0.0903439
$630$	−9216.23	−0.582831
$631$	29726.2	1.87541	0.937703	−	0.347439i	$-0.112948\pi$
$631$	29726.2	1.87541	0.937703	+	0.347439i	$0.112948\pi$
$632$	−2543.02	−0.160057
$633$	−25689.9	−1.61309
$634$	−17118.0	−1.07231
$635$	−1346.84	−0.0841695
$636$	−10257.2	−0.639504
$637$	9187.54	0.571466
$638$	0	0
$639$	9634.46	0.596453
$640$	120.336	0.00743232
$641$	−28974.4	−1.78537	−0.892683	−	0.450685i	$-0.851180\pi$
$641$	−28974.4	−1.78537	−0.892683	+	0.450685i	$0.851180\pi$
$642$	18133.5	1.11475
$643$	25165.6	1.54344	0.771722	−	0.635960i	$-0.219396\pi$
$643$	25165.6	1.54344	0.771722	+	0.635960i	$0.219396\pi$
$644$	7868.58	0.481468
$645$	34807.5	2.12487
$646$	−5368.77	−0.326984
$647$	−12348.4	−0.750332	−0.375166	−	0.926958i	$-0.622414\pi$
$647$	−12348.4	−0.750332	−0.375166	+	0.926958i	$0.622414\pi$
$648$	−22238.6	−1.34817
$649$	0	0
$650$	392.626	0.0236924
$651$	−7103.54	−0.427665
$652$	6672.63	0.400798
$653$	−14152.1	−0.848107	−0.424053	−	0.905637i	$-0.639393\pi$
$653$	−14152.1	−0.848107	−0.424053	+	0.905637i	$0.639393\pi$
$654$	−15728.5	−0.940416
$655$	19971.3	1.19137
$656$	−11968.4	−0.712329
$657$	−1142.09	−0.0678192
$658$	−13695.1	−0.811382
$659$	−4143.11	−0.244905	−0.122453	−	0.992474i	$-0.539076\pi$
$659$	−4143.11	−0.244905	−0.122453	+	0.992474i	$0.539076\pi$
$660$	0	0
$661$	−8733.48	−0.513907	−0.256954	−	0.966424i	$-0.582719\pi$
$661$	−8733.48	−0.513907	−0.256954	+	0.966424i	$0.582719\pi$
$662$	−9915.02	−0.582112
$663$	−3429.39	−0.200885
$664$	9983.54	0.583489
$665$	40186.7	2.34342
$666$	−2798.90	−0.162846
$667$	2325.60	0.135004
$668$	−6764.45	−0.391803
$669$	3189.16	0.184305
$670$	3314.35	0.191111
$671$	0	0
$672$	−22699.1	−1.30303
$673$	−4915.27	−0.281530	−0.140765	−	0.990043i	$-0.544956\pi$
$673$	−4915.27	−0.281530	−0.140765	+	0.990043i	$0.544956\pi$
$674$	23943.5	1.36835
$675$	−441.553	−0.0251784
$676$	4074.40	0.231816
$677$	−3395.99	−0.192790	−0.0963948	−	0.995343i	$-0.530731\pi$
$677$	−3395.99	−0.192790	−0.0963948	+	0.995343i	$0.530731\pi$
$678$	18434.6	1.04421
$679$	−26035.0	−1.47148
$680$	−4546.60	−0.256403
$681$	−3047.59	−0.171489
$682$	0	0
$683$	7957.99	0.445833	0.222917	−	0.974837i	$-0.428442\pi$
$683$	7957.99	0.445833	0.222917	+	0.974837i	$0.428442\pi$
$684$	−7379.32	−0.412508
$685$	−12260.0	−0.683841
$686$	−2549.69	−0.141906
$687$	−13177.6	−0.731815
$688$	−13125.7	−0.727342
$689$	−14819.7	−0.819429
$690$	−14564.5	−0.803569
$691$	−7798.41	−0.429328	−0.214664	−	0.976688i	$-0.568866\pi$
$691$	−7798.41	−0.429328	−0.214664	+	0.976688i	$0.568866\pi$
$692$	9240.61	0.507623
$693$	0	0
$694$	−18208.8	−0.995961
$695$	15517.5	0.846924
$696$	−3927.09	−0.213873
$697$	7591.79	0.412568
$698$	−21030.8	−1.14044
$699$	45300.0	2.45122
$700$	−486.555	−0.0262715
$701$	−18195.2	−0.980349	−0.490175	−	0.871624i	$-0.663067\pi$
$701$	−18195.2	−0.980349	−0.490175	+	0.871624i	$0.663067\pi$
$702$	−5081.02	−0.273178
$703$	12204.4	0.654763
$704$	0	0
$705$	−17741.6	−0.947784
$706$	23997.8	1.27927
$707$	−47435.5	−2.52333
$708$	−13515.9	−0.717454
$709$	−28913.5	−1.53155	−0.765775	−	0.643109i	$-0.777644\pi$
$709$	−28913.5	−1.53155	−0.765775	+	0.643109i	$0.777644\pi$
$710$	14825.1	0.783629
$711$	−1597.36	−0.0842554
$712$	−12187.6	−0.641500
$713$	−4075.55	−0.214068
$714$	−6072.14	−0.318269
$715$	0	0
$716$	−2511.10	−0.131067
$717$	7873.39	0.410093
$718$	47.3459	0.00246091
$719$	−3319.70	−0.172189	−0.0860946	−	0.996287i	$-0.527439\pi$
$719$	−3319.70	−0.172189	−0.0860946	+	0.996287i	$0.527439\pi$
$720$	4502.26	0.233041
$721$	34025.7	1.75754
$722$	−31094.8	−1.60281
$723$	−6570.17	−0.337963
$724$	−3027.49	−0.155409
$725$	−143.804	−0.00736655
$726$	0	0
$727$	32239.8	1.64472	0.822358	−	0.568970i	$-0.192658\pi$
$727$	32239.8	1.64472	0.822358	+	0.568970i	$0.192658\pi$
$728$	−19197.4	−0.977339
$729$	−680.471	−0.0345715
$730$	−1757.40	−0.0891020
$731$	8325.86	0.421262
$732$	10566.4	0.533531
$733$	−30253.9	−1.52449	−0.762247	−	0.647287i	$-0.775904\pi$
$733$	−30253.9	−1.52449	−0.762247	+	0.647287i	$0.775904\pi$
$734$	−10666.4	−0.536383
$735$	21074.3	1.05760
$736$	−13023.3	−0.652234
$737$	0	0
$738$	−14909.3	−0.743657
$739$	−8786.71	−0.437381	−0.218690	−	0.975794i	$-0.570179\pi$
$739$	−8786.71	−0.437381	−0.218690	+	0.975794i	$0.570179\pi$
$740$	3014.30	0.149741
$741$	−29367.0	−1.45590
$742$	−26240.1	−1.29825
$743$	−25295.9	−1.24901	−0.624507	−	0.781019i	$-0.714700\pi$
$743$	−25295.9	−1.24901	−0.624507	+	0.781019i	$0.714700\pi$
$744$	6882.11	0.339127
$745$	6911.29	0.339879
$746$	−27289.7	−1.33934
$747$	6270.99	0.307153
$748$	0	0
$749$	−32467.2	−1.58388
$750$	20173.1	0.982155
$751$	−3759.52	−0.182672	−0.0913361	−	0.995820i	$-0.529114\pi$
$751$	−3759.52	−0.182672	−0.0913361	+	0.995820i	$0.529114\pi$
$752$	6690.24	0.324425
$753$	6072.89	0.293903
$754$	−1654.78	−0.0799249
$755$	30733.5	1.48146
$756$	6296.57	0.302915
$757$	31241.0	1.49996	0.749982	−	0.661458i	$-0.230062\pi$
$757$	31241.0	1.49996	0.749982	+	0.661458i	$0.230062\pi$
$758$	−8690.91	−0.416449
$759$	0	0
$760$	−38934.0	−1.85827
$761$	−36366.4	−1.73230	−0.866151	−	0.499782i	$-0.833413\pi$
$761$	−36366.4	−1.73230	−0.866151	+	0.499782i	$0.833413\pi$
$762$	1742.68	0.0828485
$763$	28161.2	1.33618
$764$	−9776.86	−0.462977
$765$	−2855.87	−0.134973
$766$	7007.60	0.330542
$767$	−19527.9	−0.919310
$768$	26589.4	1.24930
$769$	−17672.8	−0.828734	−0.414367	−	0.910110i	$-0.635997\pi$
$769$	−17672.8	−0.828734	−0.414367	+	0.910110i	$0.635997\pi$
$770$	0	0
$771$	14402.5	0.672756
$772$	−13843.8	−0.645402
$773$	2415.26	0.112381	0.0561907	−	0.998420i	$-0.482105\pi$
$773$	2415.26	0.112381	0.0561907	+	0.998420i	$0.482105\pi$
$774$	−16350.9	−0.759330
$775$	252.013	0.0116807
$776$	25223.4	1.16684
$777$	13803.3	0.637313
$778$	572.989	0.0264044
$779$	65011.0	2.99006
$780$	−7253.19	−0.332956
$781$	0	0
$782$	−3483.80	−0.159310
$783$	1860.99	0.0849377
$784$	−7946.97	−0.362016
$785$	−20723.2	−0.942221
$786$	−25841.0	−1.17267
$787$	−13036.9	−0.590487	−0.295244	−	0.955422i	$-0.595401\pi$
$787$	−13036.9	−0.590487	−0.295244	+	0.955422i	$0.595401\pi$
$788$	−10043.9	−0.454060
$789$	2624.89	0.118439
$790$	−2457.95	−0.110696
$791$	−33006.3	−1.48365
$792$	0	0
$793$	15266.4	0.683640
$794$	−10.4055	−0.000465086 0
$795$	−33993.4	−1.51650
$796$	−4953.90	−0.220586
$797$	−11372.2	−0.505425	−0.252713	−	0.967541i	$-0.581323\pi$
$797$	−11372.2	−0.505425	−0.252713	+	0.967541i	$0.581323\pi$
$798$	−51997.7	−2.30664
$799$	−4243.75	−0.187901
$800$	805.298	0.0355895
$801$	−7655.41	−0.337691
$802$	17879.6	0.787220
$803$	0	0
$804$	3001.43	0.131657
$805$	26077.2	1.14174
$806$	2899.95	0.126732
$807$	−30584.3	−1.33410
$808$	45956.8	2.00094
$809$	−10931.4	−0.475067	−0.237533	−	0.971379i	$-0.576339\pi$
$809$	−10931.4	−0.475067	−0.237533	+	0.971379i	$0.576339\pi$
$810$	−21494.7	−0.932401
$811$	−17626.1	−0.763175	−0.381588	−	0.924333i	$-0.624623\pi$
$811$	−17626.1	−0.763175	−0.381588	+	0.924333i	$0.624623\pi$
$812$	2050.65	0.0886254
$813$	−12005.5	−0.517900
$814$	0	0
$815$	22113.7	0.950442
$816$	2966.33	0.127258
$817$	71297.0	3.05308
$818$	24767.7	1.05866
$819$	−12058.5	−0.514480
$820$	16056.7	0.683810
$821$	14091.1	0.599005	0.299503	−	0.954095i	$-0.403179\pi$
$821$	14091.1	0.599005	0.299503	+	0.954095i	$0.403179\pi$
$822$	15863.3	0.673108
$823$	22606.9	0.957507	0.478753	−	0.877949i	$-0.341089\pi$
$823$	22606.9	0.957507	0.478753	+	0.877949i	$0.341089\pi$
$824$	−32965.0	−1.39368
$825$	0	0
$826$	−34576.4	−1.45650
$827$	21574.5	0.907156	0.453578	−	0.891217i	$-0.350147\pi$
$827$	21574.5	0.907156	0.453578	+	0.891217i	$0.350147\pi$
$828$	−4788.44	−0.200978
$829$	19547.0	0.818934	0.409467	−	0.912325i	$-0.365715\pi$
$829$	19547.0	0.818934	0.409467	+	0.912325i	$0.365715\pi$
$830$	9649.55	0.403543
$831$	46958.7	1.96026
$832$	15909.8	0.662947
$833$	5040.92	0.209673
$834$	−20078.1	−0.833631
$835$	−22418.0	−0.929112
$836$	0	0
$837$	−3261.32	−0.134681
$838$	886.534	0.0365451
$839$	−17095.2	−0.703447	−0.351723	−	0.936104i	$-0.614404\pi$
$839$	−17095.2	−0.703447	−0.351723	+	0.936104i	$0.614404\pi$
$840$	−44034.8	−1.80875
$841$	−23782.9	−0.975149
$842$	7497.88	0.306881
$843$	58962.5	2.40899
$844$	−12996.7	−0.530051
$845$	13502.9	0.549722
$846$	8334.17	0.338693
$847$	0	0
$848$	12818.7	0.519098
$849$	−3278.13	−0.132515
$850$	215.422	0.00869283
$851$	7919.46	0.319008
$852$	13425.4	0.539844
$853$	−20502.0	−0.822949	−0.411475	−	0.911421i	$-0.634986\pi$
$853$	−20502.0	−0.822949	−0.411475	+	0.911421i	$0.634986\pi$
$854$	27031.0	1.08312
$855$	−24455.8	−0.978209
$856$	31455.1	1.25597
$857$	28198.9	1.12398	0.561992	−	0.827142i	$-0.310035\pi$
$857$	28198.9	1.12398	0.561992	+	0.827142i	$0.310035\pi$
$858$	0	0
$859$	−21056.9	−0.836383	−0.418192	−	0.908359i	$-0.637336\pi$
$859$	−21056.9	−0.836383	−0.418192	+	0.908359i	$0.637336\pi$
$860$	17609.3	0.698222
$861$	73528.2	2.91037
$862$	−24526.2	−0.969103
$863$	−26619.9	−1.05000	−0.525001	−	0.851101i	$-0.675935\pi$
$863$	−26619.9	−1.05000	−0.525001	+	0.851101i	$0.675935\pi$
$864$	−10421.5	−0.410353
$865$	30624.3	1.20376
$866$	18764.1	0.736294
$867$	−1881.60	−0.0737053
$868$	−3593.71	−0.140528
$869$	0	0
$870$	−3795.71	−0.147916
$871$	4336.50	0.168699
$872$	−27283.3	−1.05955
$873$	15843.7	0.614235
$874$	−29832.9	−1.15459
$875$	−36119.0	−1.39548
$876$	−1591.48	−0.0613826
$877$	−7919.35	−0.304923	−0.152462	−	0.988309i	$-0.548720\pi$
$877$	−7919.35	−0.304923	−0.152462	+	0.988309i	$0.548720\pi$
$878$	−18653.1	−0.716984
$879$	−26418.7	−1.01374
$880$	0	0
$881$	9873.80	0.377590	0.188795	−	0.982017i	$-0.439542\pi$
$881$	9873.80	0.377590	0.188795	+	0.982017i	$0.439542\pi$
$882$	−9899.71	−0.377937
$883$	5745.93	0.218988	0.109494	−	0.993987i	$-0.465077\pi$
$883$	5745.93	0.218988	0.109494	+	0.993987i	$0.465077\pi$
$884$	−1734.94	−0.0660096
$885$	−44792.9	−1.70135
$886$	28770.6	1.09093
$887$	28679.8	1.08565	0.542825	−	0.839846i	$-0.317355\pi$
$887$	28679.8	1.08565	0.542825	+	0.839846i	$0.317355\pi$
$888$	−13373.1	−0.505372
$889$	−3120.19	−0.117714
$890$	−11779.8	−0.443664
$891$	0	0
$892$	1613.41	0.0605616
$893$	−36340.6	−1.36180
$894$	−8942.54	−0.334545
$895$	−8322.02	−0.310809
$896$	278.779	0.0103944
$897$	−19056.3	−0.709331
$898$	12053.1	0.447904
$899$	−1062.14	−0.0394042
$900$	296.095	0.0109665
$901$	−8131.12	−0.300652
$902$	0	0
$903$	80637.7	2.97171
$904$	31977.4	1.17650
$905$	−10033.4	−0.368532
$906$	−39766.1	−1.45821
$907$	−1499.32	−0.0548889	−0.0274444	−	0.999623i	$-0.508737\pi$
$907$	−1499.32	−0.0548889	−0.0274444	+	0.999623i	$0.508737\pi$
$908$	−1541.79	−0.0563503
$909$	28867.0	1.05331
$910$	−18555.2	−0.675932
$911$	−17362.9	−0.631458	−0.315729	−	0.948849i	$-0.602249\pi$
$911$	−17362.9	−0.631458	−0.315729	+	0.948849i	$0.602249\pi$
$912$	25401.6	0.922294
$913$	0	0
$914$	20171.9	0.730007
$915$	35018.0	1.26520
$916$	−6666.60	−0.240470
$917$	46267.2	1.66617
$918$	−2787.80	−0.100230
$919$	−20882.8	−0.749576	−0.374788	−	0.927111i	$-0.622284\pi$
$919$	−20882.8	−0.749576	−0.374788	+	0.927111i	$0.622284\pi$
$920$	−25264.3	−0.905370
$921$	−33703.6	−1.20583
$922$	19130.6	0.683334
$923$	19397.2	0.691729
$924$	0	0
$925$	−489.702	−0.0174068
$926$	14810.8	0.525607
$927$	−20706.4	−0.733644
$928$	−3394.04	−0.120059
$929$	−29059.7	−1.02628	−0.513141	−	0.858304i	$-0.671518\pi$
$929$	−29059.7	−1.02628	−0.513141	+	0.858304i	$0.671518\pi$
$930$	6651.87	0.234541
$931$	43167.0	1.51959
$932$	22917.5	0.805457
$933$	11722.8	0.411346
$934$	−32162.4	−1.12675
$935$	0	0
$936$	11682.6	0.407969
$937$	49980.8	1.74259	0.871293	−	0.490763i	$-0.163282\pi$
$937$	49980.8	1.74259	0.871293	+	0.490763i	$0.163282\pi$
$938$	7678.29	0.267276
$939$	−6694.83	−0.232670
$940$	−8975.56	−0.311437
$941$	−21410.6	−0.741728	−0.370864	−	0.928687i	$-0.620938\pi$
$941$	−21410.6	−0.741728	−0.370864	+	0.928687i	$0.620938\pi$
$942$	26813.8	0.927433
$943$	42185.7	1.45679
$944$	16891.1	0.582371
$945$	20867.4	0.718325
$946$	0	0
$947$	39348.1	1.35020	0.675101	−	0.737725i	$-0.264100\pi$
$947$	39348.1	1.35020	0.675101	+	0.737725i	$0.264100\pi$
$948$	−2225.89	−0.0762588
$949$	−2299.39	−0.0786526
$950$	1844.73	0.0630008
$951$	−51374.6	−1.75177
$952$	−10533.0	−0.358589
$953$	−25252.6	−0.858355	−0.429178	−	0.903220i	$-0.641197\pi$
$953$	−25252.6	−0.858355	−0.429178	+	0.903220i	$0.641197\pi$
$954$	15968.5	0.541927
$955$	−32401.4	−1.09789
$956$	3983.18	0.134754
$957$	0	0
$958$	17498.2	0.590126
$959$	−28402.5	−0.956377
$960$	36493.7	1.22691
$961$	−27929.6	−0.937519
$962$	−5635.07	−0.188859
$963$	19758.0	0.661156
$964$	−3323.88	−0.111053
$965$	−45879.8	−1.53049
$966$	−33741.4	−1.12382
$967$	34276.7	1.13988	0.569940	−	0.821686i	$-0.306966\pi$
$967$	34276.7	1.13988	0.569940	+	0.821686i	$0.306966\pi$
$968$	0	0
$969$	−16112.7	−0.534176
$970$	24379.6	0.806992
$971$	−11166.2	−0.369044	−0.184522	−	0.982828i	$-0.559074\pi$
$971$	−11166.2	−0.369044	−0.184522	+	0.982828i	$0.559074\pi$
$972$	−12742.6	−0.420494
$973$	35949.0	1.18445
$974$	−22753.8	−0.748542
$975$	1178.35	0.0387050
$976$	−13205.0	−0.433077
$977$	29420.2	0.963395	0.481697	−	0.876338i	$-0.340020\pi$
$977$	29420.2	0.963395	0.481697	+	0.876338i	$0.340020\pi$
$978$	−28613.0	−0.935525
$979$	0	0
$980$	10661.6	0.347522
$981$	−17137.6	−0.557758
$982$	−34589.2	−1.12402
$983$	56336.7	1.82794	0.913968	−	0.405786i	$-0.133002\pi$
$983$	56336.7	1.82794	0.913968	+	0.405786i	$0.133002\pi$
$984$	−71236.1	−2.30785
$985$	−33286.4	−1.07675
$986$	−907.924	−0.0293247
$987$	−41101.6	−1.32551
$988$	−14856.9	−0.478401
$989$	46264.7	1.48749
$990$	0	0
$991$	5570.22	0.178551	0.0892755	−	0.996007i	$-0.471545\pi$
$991$	5570.22	0.178551	0.0892755	+	0.996007i	$0.471545\pi$
$992$	5947.95	0.190371
$993$	−29756.9	−0.950965
$994$	34345.0	1.09593
$995$	−16417.7	−0.523091
$996$	8738.50	0.278002
$997$	−10978.7	−0.348746	−0.174373	−	0.984680i	$-0.555790\pi$
$997$	−10978.7	−0.348746	−0.174373	+	0.984680i	$0.555790\pi$
$998$	21606.1	0.685299
$999$	6337.29	0.200704

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2057.4.a.u.1.19		52
11.7	odd	10		187.4.g.b.137.17	yes	104
11.8	odd	10		187.4.g.b.86.17	✓	104
11.10	odd	2		2057.4.a.v.1.34		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.4.g.b.86.17	✓	104	11.8	odd	10
187.4.g.b.137.17	yes	104	11.7	odd	10
2057.4.a.u.1.19		52	1.1	even	1	trivial
2057.4.a.v.1.34		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)

\(f(q)\)	\(=\)	\(q-2.16938 q^{2} -6.51073 q^{3} -3.29381 q^{4} -10.9160 q^{5} +14.1242 q^{6} -25.2888 q^{7} +24.5005 q^{8} +15.3896 q^{9} +O(q^{10})\)	\(q-2.16938 q^{2} -6.51073 q^{3} -3.29381 q^{4} -10.9160 q^{5} +14.1242 q^{6} -25.2888 q^{7} +24.5005 q^{8} +15.3896 q^{9} +23.6809 q^{10} +21.4451 q^{12} +30.9841 q^{13} +54.8610 q^{14} +71.0710 q^{15} -26.8004 q^{16} +17.0000 q^{17} -33.3858 q^{18} +145.576 q^{19} +35.9551 q^{20} +164.649 q^{21} +94.4647 q^{23} -159.516 q^{24} -5.84125 q^{25} -67.2161 q^{26} +75.5923 q^{27} +83.2965 q^{28} +24.6187 q^{29} -154.180 q^{30} -43.1436 q^{31} -137.864 q^{32} -36.8794 q^{34} +276.052 q^{35} -50.6903 q^{36} +83.8351 q^{37} -315.810 q^{38} -201.729 q^{39} -267.447 q^{40} +446.576 q^{41} -357.185 q^{42} +489.756 q^{43} -167.992 q^{45} -204.929 q^{46} -249.632 q^{47} +174.490 q^{48} +296.525 q^{49} +12.6719 q^{50} -110.682 q^{51} -102.056 q^{52} -478.301 q^{53} -163.988 q^{54} -619.589 q^{56} -947.809 q^{57} -53.4073 q^{58} -630.255 q^{59} -234.094 q^{60} +492.718 q^{61} +93.5947 q^{62} -389.184 q^{63} +513.482 q^{64} -338.222 q^{65} +139.959 q^{67} -55.9947 q^{68} -615.034 q^{69} -598.862 q^{70} +626.037 q^{71} +377.053 q^{72} -74.2120 q^{73} -181.870 q^{74} +38.0308 q^{75} -479.501 q^{76} +437.626 q^{78} -103.795 q^{79} +292.553 q^{80} -907.679 q^{81} -968.792 q^{82} +407.483 q^{83} -542.321 q^{84} -185.572 q^{85} -1062.47 q^{86} -160.286 q^{87} -497.441 q^{89} +364.439 q^{90} -783.551 q^{91} -311.148 q^{92} +280.896 q^{93} +541.546 q^{94} -1589.11 q^{95} +897.595 q^{96} +1029.51 q^{97} -643.273 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - q^{2} + 20 q^{3} + 235 q^{4} + 40 q^{5} + 24 q^{6} + 42 q^{7} - 45 q^{8} + 572 q^{9}+O(q^{10}) \) 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

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more