LMFDB - Embedded newform 1573.4.a.p.1.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1573,4,Mod(1,1573)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1573, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1573.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1573 = 11^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1573.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$92.8100044390$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.34
Character	$\chi$	$=$	1573.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.46923 q^{2} -6.64067 q^{3} +21.9125 q^{4} -12.5247 q^{5} -36.3193 q^{6} +3.24336 q^{7} +76.0904 q^{8} +17.0984 q^{9} +O(q^{10})$	\(q+5.46923 q^{2} -6.64067 q^{3} +21.9125 q^{4} -12.5247 q^{5} -36.3193 q^{6} +3.24336 q^{7} +76.0904 q^{8} +17.0984 q^{9} -68.5006 q^{10} -145.513 q^{12} -13.0000 q^{13} +17.7387 q^{14} +83.1725 q^{15} +240.856 q^{16} +117.219 q^{17} +93.5152 q^{18} -79.4522 q^{19} -274.448 q^{20} -21.5381 q^{21} -178.384 q^{23} -505.291 q^{24} +31.8689 q^{25} -71.1000 q^{26} +65.7530 q^{27} +71.0700 q^{28} -115.557 q^{29} +454.890 q^{30} +11.8626 q^{31} +708.573 q^{32} +641.098 q^{34} -40.6222 q^{35} +374.669 q^{36} -38.3825 q^{37} -434.542 q^{38} +86.3286 q^{39} -953.012 q^{40} +360.758 q^{41} -117.797 q^{42} -270.693 q^{43} -214.153 q^{45} -975.622 q^{46} +142.891 q^{47} -1599.44 q^{48} -332.481 q^{49} +174.298 q^{50} -778.413 q^{51} -284.862 q^{52} -259.379 q^{53} +359.618 q^{54} +246.789 q^{56} +527.615 q^{57} -632.010 q^{58} +117.262 q^{59} +1822.51 q^{60} -41.7814 q^{61} +64.8791 q^{62} +55.4564 q^{63} +1948.50 q^{64} +162.821 q^{65} -829.330 q^{67} +2568.56 q^{68} +1184.59 q^{69} -222.172 q^{70} -127.208 q^{71} +1301.03 q^{72} +430.920 q^{73} -209.923 q^{74} -211.631 q^{75} -1740.99 q^{76} +472.151 q^{78} -849.306 q^{79} -3016.66 q^{80} -898.301 q^{81} +1973.07 q^{82} -1364.22 q^{83} -471.952 q^{84} -1468.14 q^{85} -1480.48 q^{86} +767.378 q^{87} -136.417 q^{89} -1171.25 q^{90} -42.1637 q^{91} -3908.83 q^{92} -78.7754 q^{93} +781.504 q^{94} +995.117 q^{95} -4705.40 q^{96} -1020.70 q^{97} -1818.41 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} - 36 q^{6} + 36 q^{7} + 57 q^{8} + 265 q^{9}+O(q^{10}) $ 34 * q + 3 * q^2 - 29 * q^3 + 97 * q^4 - 28 * q^5 - 36 * q^6 + 36 * q^7 + 57 * q^8 + 265 * q^9	\( 34 q + 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} - 36 q^{6} + 36 q^{7} + 57 q^{8} + 265 q^{9} + 18 q^{10} - 262 q^{12} - 442 q^{13} - 231 q^{14} - 196 q^{15} + 225 q^{16} + 209 q^{17} + 190 q^{18} + 107 q^{19} - 211 q^{20} + 68 q^{21} - 632 q^{23} - 152 q^{24} + 296 q^{25} - 39 q^{26} - 920 q^{27} + 931 q^{28} + 32 q^{29} + 300 q^{30} - 290 q^{31} - 876 q^{32} - 602 q^{34} - 104 q^{35} - 611 q^{36} - 656 q^{37} - 1361 q^{38} + 377 q^{39} - 1159 q^{40} + 1121 q^{41} + 79 q^{42} - 349 q^{43} - 1024 q^{45} - 490 q^{46} - 1608 q^{47} - 1827 q^{48} + 808 q^{49} + 1322 q^{50} - 1414 q^{51} - 1261 q^{52} - 2608 q^{53} - 3131 q^{54} - 1675 q^{56} + 2150 q^{57} - 1673 q^{58} - 2011 q^{59} - 201 q^{60} + 236 q^{61} - 1396 q^{62} - 1206 q^{63} + 1331 q^{64} + 364 q^{65} - 3213 q^{67} + 1321 q^{68} - 162 q^{69} + 174 q^{70} - 3756 q^{71} + 5074 q^{72} - 823 q^{73} - 2550 q^{74} - 3063 q^{75} - 2004 q^{76} + 468 q^{78} + 2120 q^{79} - 5005 q^{80} + 710 q^{81} - 2534 q^{82} + 3843 q^{83} - 7191 q^{84} - 1582 q^{85} - 3542 q^{86} - 962 q^{87} - 3633 q^{89} + 995 q^{90} - 468 q^{91} - 2072 q^{92} - 508 q^{93} + 6309 q^{94} - 1916 q^{95} + 2150 q^{96} + 1195 q^{97} + 1487 q^{98}+O(q^{100}) \) 34 * q + 3 * q^2 - 29 * q^3 + 97 * q^4 - 28 * q^5 - 36 * q^6 + 36 * q^7 + 57 * q^8 + 265 * q^9 + 18 * q^10 - 262 * q^12 - 442 * q^13 - 231 * q^14 - 196 * q^15 + 225 * q^16 + 209 * q^17 + 190 * q^18 + 107 * q^19 - 211 * q^20 + 68 * q^21 - 632 * q^23 - 152 * q^24 + 296 * q^25 - 39 * q^26 - 920 * q^27 + 931 * q^28 + 32 * q^29 + 300 * q^30 - 290 * q^31 - 876 * q^32 - 602 * q^34 - 104 * q^35 - 611 * q^36 - 656 * q^37 - 1361 * q^38 + 377 * q^39 - 1159 * q^40 + 1121 * q^41 + 79 * q^42 - 349 * q^43 - 1024 * q^45 - 490 * q^46 - 1608 * q^47 - 1827 * q^48 + 808 * q^49 + 1322 * q^50 - 1414 * q^51 - 1261 * q^52 - 2608 * q^53 - 3131 * q^54 - 1675 * q^56 + 2150 * q^57 - 1673 * q^58 - 2011 * q^59 - 201 * q^60 + 236 * q^61 - 1396 * q^62 - 1206 * q^63 + 1331 * q^64 + 364 * q^65 - 3213 * q^67 + 1321 * q^68 - 162 * q^69 + 174 * q^70 - 3756 * q^71 + 5074 * q^72 - 823 * q^73 - 2550 * q^74 - 3063 * q^75 - 2004 * q^76 + 468 * q^78 + 2120 * q^79 - 5005 * q^80 + 710 * q^81 - 2534 * q^82 + 3843 * q^83 - 7191 * q^84 - 1582 * q^85 - 3542 * q^86 - 962 * q^87 - 3633 * q^89 + 995 * q^90 - 468 * q^91 - 2072 * q^92 - 508 * q^93 + 6309 * q^94 - 1916 * q^95 + 2150 * q^96 + 1195 * q^97 + 1487 * 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 $

$2$	5.46923	1.93366	0.966832	−	0.255413i	$-0.0822114\pi$
$2$	5.46923	1.93366	0.966832	+	0.255413i	$0.0822114\pi$
$3$	−6.64067	−1.27800	−0.638998	−	0.769208i	$-0.720651\pi$
$3$	−6.64067	−1.27800	−0.638998	+	0.769208i	$0.720651\pi$
$4$	21.9125	2.73906
$5$	−12.5247	−1.12025	−0.560123	−	0.828409i	$-0.689246\pi$
$5$	−12.5247	−1.12025	−0.560123	+	0.828409i	$0.689246\pi$
$6$	−36.3193	−2.47122
$7$	3.24336	0.175125	0.0875625	−	0.996159i	$-0.472092\pi$
$7$	3.24336	0.175125	0.0875625	+	0.996159i	$0.472092\pi$
$8$	76.0904	3.36275
$9$	17.0984	0.633275
$10$	−68.5006	−2.16618
$11$	0	0
$11$	0	0
$12$	−145.513	−3.50051
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	17.7387	0.338633
$15$	83.1725	1.43167
$16$	240.856	3.76338
$17$	117.219	1.67234	0.836171	−	0.548469i	$-0.184789\pi$
$17$	117.219	1.67234	0.836171	+	0.548469i	$0.184789\pi$
$18$	93.5152	1.22454
$19$	−79.4522	−0.959346	−0.479673	−	0.877447i	$-0.659245\pi$
$19$	−79.4522	−0.959346	−0.479673	+	0.877447i	$0.659245\pi$
$20$	−274.448	−3.06842
$21$	−21.5381	−0.223809
$22$	0	0
$23$	−178.384	−1.61720	−0.808600	−	0.588358i	$-0.799774\pi$
$23$	−178.384	−1.61720	−0.808600	+	0.588358i	$0.799774\pi$
$24$	−505.291	−4.29759
$25$	31.8689	0.254951
$26$	−71.1000	−0.536302
$27$	65.7530	0.468673
$28$	71.0700	0.479678
$29$	−115.557	−0.739947	−0.369974	−	0.929042i	$-0.620633\pi$
$29$	−115.557	−0.739947	−0.369974	+	0.929042i	$0.620633\pi$
$30$	454.890	2.76837
$31$	11.8626	0.0687284	0.0343642	−	0.999409i	$-0.489059\pi$
$31$	11.8626	0.0687284	0.0343642	+	0.999409i	$0.489059\pi$
$32$	708.573	3.91435
$33$	0	0
$34$	641.098	3.23375
$35$	−40.6222	−0.196183
$36$	374.669	1.73458
$37$	−38.3825	−0.170542	−0.0852708	−	0.996358i	$-0.527176\pi$
$37$	−38.3825	−0.170542	−0.0852708	+	0.996358i	$0.527176\pi$
$38$	−434.542	−1.85505
$39$	86.3286	0.354452
$40$	−953.012	−3.76711
$41$	360.758	1.37417	0.687085	−	0.726577i	$-0.258890\pi$
$41$	360.758	1.37417	0.687085	+	0.726577i	$0.258890\pi$
$42$	−117.797	−0.432772
$43$	−270.693	−0.960005	−0.480003	−	0.877267i	$-0.659364\pi$
$43$	−270.693	−0.960005	−0.480003	+	0.877267i	$0.659364\pi$
$44$	0	0
$45$	−214.153	−0.709424
$46$	−975.622	−3.12712
$47$	142.891	0.443464	0.221732	−	0.975108i	$-0.428829\pi$
$47$	142.891	0.443464	0.221732	+	0.975108i	$0.428829\pi$
$48$	−1599.44	−4.80958
$49$	−332.481	−0.969331
$50$	174.298	0.492990
$51$	−778.413	−2.13725
$52$	−284.862	−0.759678
$53$	−259.379	−0.672235	−0.336117	−	0.941820i	$-0.609114\pi$
$53$	−259.379	−0.672235	−0.336117	+	0.941820i	$0.609114\pi$
$54$	359.618	0.906256
$55$	0	0
$56$	246.789	0.588902
$57$	527.615	1.22604
$58$	−632.010	−1.43081
$59$	117.262	0.258749	0.129375	−	0.991596i	$-0.458703\pi$
$59$	117.262	0.258749	0.129375	+	0.991596i	$0.458703\pi$
$60$	1822.51	3.92143
$61$	−41.7814	−0.0876977	−0.0438489	−	0.999038i	$-0.513962\pi$
$61$	−41.7814	−0.0876977	−0.0438489	+	0.999038i	$0.513962\pi$
$62$	64.8791	0.132898
$63$	55.4564	0.110902
$64$	1948.50	3.80567
$65$	162.821	0.310700
$66$	0	0
$67$	−829.330	−1.51222	−0.756110	−	0.654445i	$-0.772902\pi$
$67$	−829.330	−1.51222	−0.756110	+	0.654445i	$0.772902\pi$
$68$	2568.56	4.58064
$69$	1184.59	2.06678
$70$	−222.172	−0.379352
$71$	−127.208	−0.212632	−0.106316	−	0.994332i	$-0.533905\pi$
$71$	−127.208	−0.212632	−0.106316	+	0.994332i	$0.533905\pi$
$72$	1301.03	2.12955
$73$	430.920	0.690895	0.345447	−	0.938438i	$-0.387727\pi$
$73$	430.920	0.690895	0.345447	+	0.938438i	$0.387727\pi$
$74$	−209.923	−0.329770
$75$	−211.631	−0.325826
$76$	−1740.99	−2.62770
$77$	0	0
$78$	472.151	0.685392
$79$	−849.306	−1.20955	−0.604775	−	0.796396i	$-0.706737\pi$
$79$	−849.306	−1.20955	−0.604775	+	0.796396i	$0.706737\pi$
$80$	−3016.66	−4.21591
$81$	−898.301	−1.23224
$82$	1973.07	2.65718
$83$	−1364.22	−1.80413	−0.902066	−	0.431599i	$-0.857950\pi$
$83$	−1364.22	−1.80413	−0.902066	+	0.431599i	$0.857950\pi$
$84$	−471.952	−0.613026
$85$	−1468.14	−1.87343
$86$	−1480.48	−1.85633
$87$	767.378	0.945650
$88$	0	0
$89$	−136.417	−0.162474	−0.0812370	−	0.996695i	$-0.525887\pi$
$89$	−136.417	−0.162474	−0.0812370	+	0.996695i	$0.525887\pi$
$90$	−1171.25	−1.37179
$91$	−42.1637	−0.0485710
$92$	−3908.83	−4.42960
$93$	−78.7754	−0.0878347
$94$	781.504	0.857511
$95$	995.117	1.07470
$96$	−4705.40	−5.00253
$97$	−1020.70	−1.06841	−0.534207	−	0.845354i	$-0.679390\pi$
$97$	−1020.70	−1.06841	−0.534207	+	0.845354i	$0.679390\pi$
$98$	−1818.41	−1.87436
$99$	0	0
$100$	698.325	0.698325
$101$	−353.711	−0.348471	−0.174236	−	0.984704i	$-0.555745\pi$
$101$	−353.711	−0.348471	−0.174236	+	0.984704i	$0.555745\pi$
$102$	−4257.32	−4.13272
$103$	−636.564	−0.608956	−0.304478	−	0.952519i	$-0.598482\pi$
$103$	−636.564	−0.608956	−0.304478	+	0.952519i	$0.598482\pi$
$104$	−989.175	−0.932659
$105$	269.759	0.250721
$106$	−1418.60	−1.29988
$107$	−1654.41	−1.49475	−0.747373	−	0.664405i	$-0.768685\pi$
$107$	−1654.41	−1.49475	−0.747373	+	0.664405i	$0.768685\pi$
$108$	1440.81	1.28372
$109$	−1537.68	−1.35122	−0.675608	−	0.737261i	$-0.736119\pi$
$109$	−1537.68	−1.35122	−0.675608	+	0.737261i	$0.736119\pi$
$110$	0	0
$111$	254.885	0.217952
$112$	781.183	0.659061
$113$	1797.25	1.49620	0.748101	−	0.663585i	$-0.230966\pi$
$113$	1797.25	1.49620	0.748101	+	0.663585i	$0.230966\pi$
$114$	2885.65	2.37075
$115$	2234.21	1.81166
$116$	−2532.15	−2.02676
$117$	−222.280	−0.175639
$118$	641.332	0.500334
$119$	380.184	0.292869
$120$	6328.63	4.81435
$121$	0	0
$122$	−228.512	−0.169578
$123$	−2395.67	−1.75618
$124$	259.938	0.188251
$125$	1166.44	0.834638
$126$	303.304	0.214448
$127$	−600.650	−0.419678	−0.209839	−	0.977736i	$-0.567294\pi$
$127$	−600.650	−0.419678	−0.209839	+	0.977736i	$0.567294\pi$
$128$	4988.21	3.44453
$129$	1797.58	1.22688
$130$	890.508	0.600790
$131$	−922.875	−0.615511	−0.307756	−	0.951465i	$-0.599578\pi$
$131$	−922.875	−0.615511	−0.307756	+	0.951465i	$0.599578\pi$
$132$	0	0
$133$	−257.692	−0.168006
$134$	−4535.79	−2.92413
$135$	−823.539	−0.525029
$136$	8919.25	5.62367
$137$	−589.227	−0.367453	−0.183727	−	0.982977i	$-0.558816\pi$
$137$	−589.227	−0.367453	−0.183727	+	0.982977i	$0.558816\pi$
$138$	6478.78	3.99645
$139$	−1632.71	−0.996291	−0.498145	−	0.867093i	$-0.665985\pi$
$139$	−1632.71	−0.996291	−0.498145	+	0.867093i	$0.665985\pi$
$140$	−890.133	−0.537357
$141$	−948.892	−0.566746
$142$	−695.732	−0.411159
$143$	0	0
$144$	4118.26	2.38325
$145$	1447.33	0.828923
$146$	2356.80	1.33596
$147$	2207.89	1.23880
$148$	−841.055	−0.467123
$149$	−3204.49	−1.76189	−0.880946	−	0.473217i	$-0.843093\pi$
$149$	−3204.49	−1.76189	−0.880946	+	0.473217i	$0.843093\pi$
$150$	−1157.46	−0.630039
$151$	1414.67	0.762412	0.381206	−	0.924490i	$-0.375509\pi$
$151$	1414.67	0.762412	0.381206	+	0.924490i	$0.375509\pi$
$152$	−6045.55	−3.22604
$153$	2004.26	1.05905
$154$	0	0
$155$	−148.575	−0.0769927
$156$	1891.67	0.970865
$157$	2462.19	1.25162	0.625810	−	0.779975i	$-0.284768\pi$
$157$	2462.19	1.25162	0.625810	+	0.779975i	$0.284768\pi$
$158$	−4645.05	−2.33886
$159$	1722.45	0.859114
$160$	−8874.69	−4.38504
$161$	−578.564	−0.283212
$162$	−4913.01	−2.38273
$163$	2594.86	1.24690	0.623452	−	0.781862i	$-0.285730\pi$
$163$	2594.86	1.24690	0.623452	+	0.781862i	$0.285730\pi$
$164$	7905.10	3.76393
$165$	0	0
$166$	−7461.25	−3.48858
$167$	926.263	0.429200	0.214600	−	0.976702i	$-0.431155\pi$
$167$	926.263	0.429200	0.214600	+	0.976702i	$0.431155\pi$
$168$	−1638.84	−0.752615
$169$	169.000	0.0769231
$170$	−8029.58	−3.62259
$171$	−1358.51	−0.607530
$172$	−5931.54	−2.62951
$173$	−1192.47	−0.524055	−0.262027	−	0.965060i	$-0.584391\pi$
$173$	−1192.47	−0.524055	−0.262027	+	0.965060i	$0.584391\pi$
$174$	4196.97	1.82857
$175$	103.362	0.0446483
$176$	0	0
$177$	−778.698	−0.330681
$178$	−746.097	−0.314170
$179$	2134.38	0.891234	0.445617	−	0.895224i	$-0.352984\pi$
$179$	2134.38	0.891234	0.445617	+	0.895224i	$0.352984\pi$
$180$	−4692.62	−1.94315
$181$	2360.23	0.969250	0.484625	−	0.874722i	$-0.338956\pi$
$181$	2360.23	0.969250	0.484625	+	0.874722i	$0.338956\pi$
$182$	−230.603	−0.0939199
$183$	277.456	0.112077
$184$	−13573.3	−5.43824
$185$	480.730	0.191049
$186$	−430.840	−0.169843
$187$	0	0
$188$	3131.10	1.21467
$189$	213.261	0.0820764
$190$	5442.52	2.07812
$191$	839.405	0.317996	0.158998	−	0.987279i	$-0.449174\pi$
$191$	839.405	0.317996	0.158998	+	0.987279i	$0.449174\pi$
$192$	−12939.3	−4.86363
$193$	−250.854	−0.0935588	−0.0467794	−	0.998905i	$-0.514896\pi$
$193$	−250.854	−0.0935588	−0.0467794	+	0.998905i	$0.514896\pi$
$194$	−5582.43	−2.06595
$195$	−1081.24	−0.397074
$196$	−7285.47	−2.65505
$197$	2872.37	1.03882	0.519410	−	0.854525i	$-0.326152\pi$
$197$	2872.37	1.03882	0.519410	+	0.854525i	$0.326152\pi$
$198$	0	0
$199$	2507.49	0.893221	0.446610	−	0.894729i	$-0.352631\pi$
$199$	2507.49	0.893221	0.446610	+	0.894729i	$0.352631\pi$
$200$	2424.91	0.857337
$201$	5507.30	1.93261
$202$	−1934.53	−0.673826
$203$	−374.795	−0.129583
$204$	−17056.9	−5.85404
$205$	−4518.40	−1.53941
$206$	−3481.51	−1.17752
$207$	−3050.09	−1.02413
$208$	−3131.13	−1.04377
$209$	0	0
$210$	1475.37	0.484811
$211$	5422.96	1.76935	0.884674	−	0.466211i	$-0.154381\pi$
$211$	5422.96	1.76935	0.884674	+	0.466211i	$0.154381\pi$
$212$	−5683.63	−1.84129
$213$	844.748	0.271743
$214$	−9048.34	−2.89034
$215$	3390.35	1.07544
$216$	5003.17	1.57603
$217$	38.4746	0.0120361
$218$	−8409.90	−2.61280
$219$	−2861.59	−0.882961
$220$	0	0
$221$	−1523.85	−0.463824
$222$	1394.03	0.421445
$223$	−5674.73	−1.70407	−0.852036	−	0.523483i	$-0.824632\pi$
$223$	−5674.73	−1.70407	−0.852036	+	0.523483i	$0.824632\pi$
$224$	2298.16	0.685501
$225$	544.908	0.161454
$226$	9829.56	2.89315
$227$	−903.384	−0.264140	−0.132070	−	0.991240i	$-0.542162\pi$
$227$	−903.384	−0.264140	−0.132070	+	0.991240i	$0.542162\pi$
$228$	11561.3	3.35820
$229$	−5621.37	−1.62214	−0.811071	−	0.584947i	$-0.801115\pi$
$229$	−5621.37	−1.62214	−0.811071	+	0.584947i	$0.801115\pi$
$230$	12219.4	3.50315
$231$	0	0
$232$	−8792.81	−2.48826
$233$	−1854.42	−0.521404	−0.260702	−	0.965419i	$-0.583954\pi$
$233$	−1854.42	−0.521404	−0.260702	+	0.965419i	$0.583954\pi$
$234$	−1215.70	−0.339627
$235$	−1789.67	−0.496789
$236$	2569.50	0.708729
$237$	5639.96	1.54580
$238$	2079.31	0.566310
$239$	4386.24	1.18712	0.593562	−	0.804789i	$-0.297721\pi$
$239$	4386.24	1.18712	0.593562	+	0.804789i	$0.297721\pi$
$240$	20032.6	5.38791
$241$	−352.900	−0.0943249	−0.0471625	−	0.998887i	$-0.515018\pi$
$241$	−352.900	−0.0943249	−0.0471625	+	0.998887i	$0.515018\pi$
$242$	0	0
$243$	4189.99	1.10612
$244$	−915.533	−0.240209
$245$	4164.23	1.08589
$246$	−13102.5	−3.39587
$247$	1032.88	0.266075
$248$	902.627	0.231117
$249$	9059.35	2.30567
$250$	6379.54	1.61391
$251$	2452.60	0.616760	0.308380	−	0.951263i	$-0.400213\pi$
$251$	2452.60	0.616760	0.308380	+	0.951263i	$0.400213\pi$
$252$	1215.19	0.303768
$253$	0	0
$254$	−3285.09	−0.811516
$255$	9749.41	2.39424
$256$	11693.6	2.85489
$257$	4773.42	1.15859	0.579295	−	0.815118i	$-0.303328\pi$
$257$	4773.42	1.15859	0.579295	+	0.815118i	$0.303328\pi$
$258$	9831.37	2.37238
$259$	−124.488	−0.0298661
$260$	3567.82	0.851026
$261$	−1975.85	−0.468590
$262$	−5047.41	−1.19019
$263$	1594.08	0.373746	0.186873	−	0.982384i	$-0.440165\pi$
$263$	1594.08	0.373746	0.186873	+	0.982384i	$0.440165\pi$
$264$	0	0
$265$	3248.65	0.753068
$266$	−1409.38	−0.324866
$267$	905.901	0.207641
$268$	−18172.6	−4.14206
$269$	−1957.62	−0.443711	−0.221855	−	0.975080i	$-0.571211\pi$
$269$	−1957.62	−0.443711	−0.221855	+	0.975080i	$0.571211\pi$
$270$	−4504.12	−1.01523
$271$	−2391.43	−0.536048	−0.268024	−	0.963412i	$-0.586371\pi$
$271$	−2391.43	−0.536048	−0.268024	+	0.963412i	$0.586371\pi$
$272$	28232.9	6.29365
$273$	279.995	0.0620735
$274$	−3222.62	−0.710531
$275$	0	0
$276$	25957.2	5.66102
$277$	793.632	0.172147	0.0860736	−	0.996289i	$-0.472568\pi$
$277$	793.632	0.172147	0.0860736	+	0.996289i	$0.472568\pi$
$278$	−8929.65	−1.92649
$279$	202.831	0.0435240
$280$	−3090.96	−0.659715
$281$	−3722.19	−0.790203	−0.395102	−	0.918637i	$-0.629291\pi$
$281$	−3722.19	−0.790203	−0.395102	+	0.918637i	$0.629291\pi$
$282$	−5189.71	−1.09590
$283$	−4600.80	−0.966392	−0.483196	−	0.875512i	$-0.660524\pi$
$283$	−4600.80	−0.966392	−0.483196	+	0.875512i	$0.660524\pi$
$284$	−2787.45	−0.582411
$285$	−6608.24	−1.37347
$286$	0	0
$287$	1170.07	0.240652
$288$	12115.5	2.47886
$289$	8827.33	1.79673
$290$	7915.75	1.60286
$291$	6778.11	1.36543
$292$	9442.50	1.89240
$293$	3676.70	0.733089	0.366545	−	0.930400i	$-0.380541\pi$
$293$	3676.70	0.733089	0.366545	+	0.930400i	$0.380541\pi$
$294$	12075.5	2.39543
$295$	−1468.67	−0.289863
$296$	−2920.54	−0.573489
$297$	0	0
$298$	−17526.1	−3.40691
$299$	2318.99	0.448531
$300$	−4637.34	−0.892457
$301$	−877.954	−0.168121
$302$	7737.15	1.47425
$303$	2348.88	0.445345
$304$	−19136.5	−3.61038
$305$	523.301	0.0982430
$306$	10961.8	2.04785
$307$	1442.62	0.268192	0.134096	−	0.990968i	$-0.457187\pi$
$307$	1442.62	0.268192	0.134096	+	0.990968i	$0.457187\pi$
$308$	0	0
$309$	4227.21	0.778244
$310$	−812.593	−0.148878
$311$	−26.0142	−0.00474319	−0.00237160	−	0.999997i	$-0.500755\pi$
$311$	−26.0142	−0.00474319	−0.00237160	+	0.999997i	$0.500755\pi$
$312$	6568.78	1.19194
$313$	6491.21	1.17222	0.586110	−	0.810231i	$-0.300659\pi$
$313$	6491.21	1.17222	0.586110	+	0.810231i	$0.300659\pi$
$314$	13466.3	2.42021
$315$	−694.576	−0.124238
$316$	−18610.4	−3.31303
$317$	−2305.12	−0.408419	−0.204209	−	0.978927i	$-0.565462\pi$
$317$	−2305.12	−0.408419	−0.204209	+	0.978927i	$0.565462\pi$
$318$	9420.47	1.66124
$319$	0	0
$320$	−24404.5	−4.26328
$321$	10986.4	1.91028
$322$	−3164.30	−0.547638
$323$	−9313.31	−1.60436
$324$	−19684.0	−3.37517
$325$	−414.295	−0.0707107
$326$	14191.9	2.41109
$327$	10211.2	1.72685
$328$	27450.2	4.62099
$329$	463.448	0.0776617
$330$	0	0
$331$	−5062.59	−0.840680	−0.420340	−	0.907367i	$-0.638089\pi$
$331$	−5062.59	−0.840680	−0.420340	+	0.907367i	$0.638089\pi$
$332$	−29893.5	−4.94162
$333$	−656.280	−0.108000
$334$	5065.94	0.829928
$335$	10387.1	1.69406
$336$	−5187.58	−0.842278
$337$	947.132	0.153097	0.0765483	−	0.997066i	$-0.475610\pi$
$337$	947.132	0.153097	0.0765483	+	0.997066i	$0.475610\pi$
$338$	924.300	0.148743
$339$	−11934.9	−1.91214
$340$	−32170.5	−5.13144
$341$	0	0
$342$	−7429.99	−1.17476
$343$	−2190.83	−0.344879
$344$	−20597.1	−3.22826
$345$	−14836.6	−2.31530
$346$	−6521.86	−1.01335
$347$	3170.84	0.490547	0.245274	−	0.969454i	$-0.421122\pi$
$347$	3170.84	0.490547	0.245274	+	0.969454i	$0.421122\pi$
$348$	16815.1	2.59019
$349$	2735.95	0.419633	0.209816	−	0.977741i	$-0.432713\pi$
$349$	2735.95	0.419633	0.209816	+	0.977741i	$0.432713\pi$
$350$	565.312	0.0863348
$351$	−854.789	−0.129986
$352$	0	0
$353$	−4547.64	−0.685684	−0.342842	−	0.939393i	$-0.611390\pi$
$353$	−4547.64	−0.685684	−0.342842	+	0.939393i	$0.611390\pi$
$354$	−4258.87	−0.639425
$355$	1593.25	0.238200
$356$	−2989.24	−0.445026
$357$	−2524.67	−0.374286
$358$	11673.4	1.72335
$359$	−7436.80	−1.09331	−0.546656	−	0.837357i	$-0.684100\pi$
$359$	−7436.80	−1.09331	−0.546656	+	0.837357i	$0.684100\pi$
$360$	−16295.0	−2.38562
$361$	−546.353	−0.0796548
$362$	12908.6	1.87420
$363$	0	0
$364$	−923.910	−0.133039
$365$	−5397.15	−0.773972
$366$	1517.47	0.216720
$367$	9322.36	1.32595	0.662975	−	0.748642i	$-0.269294\pi$
$367$	9322.36	1.32595	0.662975	+	0.748642i	$0.269294\pi$
$368$	−42964.8	−6.08613
$369$	6168.40	0.870228
$370$	2629.22	0.369424
$371$	−841.260	−0.117725
$372$	−1726.16	−0.240584
$373$	9437.02	1.31000	0.655001	−	0.755628i	$-0.272668\pi$
$373$	9437.02	1.31000	0.655001	+	0.755628i	$0.272668\pi$
$374$	0	0
$375$	−7745.95	−1.06666
$376$	10872.6	1.49126
$377$	1502.25	0.205224
$378$	1166.37	0.158708
$379$	−9409.31	−1.27526	−0.637630	−	0.770343i	$-0.720085\pi$
$379$	−9409.31	−1.27526	−0.637630	+	0.770343i	$0.720085\pi$
$380$	21805.5	2.94367
$381$	3988.72	0.536347
$382$	4590.90	0.614898
$383$	6797.25	0.906849	0.453424	−	0.891295i	$-0.350202\pi$
$383$	6797.25	0.906849	0.453424	+	0.891295i	$0.350202\pi$
$384$	−33125.0	−4.40210
$385$	0	0
$386$	−1371.98	−0.180911
$387$	−4628.42	−0.607948
$388$	−22366.0	−2.92645
$389$	−8989.76	−1.17172	−0.585860	−	0.810412i	$-0.699243\pi$
$389$	−8989.76	−1.17172	−0.585860	+	0.810412i	$0.699243\pi$
$390$	−5913.56	−0.767808
$391$	−20910.0	−2.70451
$392$	−25298.6	−3.25962
$393$	6128.50	0.786621
$394$	15709.6	2.00873
$395$	10637.3	1.35499
$396$	0	0
$397$	−404.316	−0.0511134	−0.0255567	−	0.999673i	$-0.508136\pi$
$397$	−404.316	−0.0511134	−0.0255567	+	0.999673i	$0.508136\pi$
$398$	13714.0	1.72719
$399$	1711.25	0.214711
$400$	7675.81	0.959476
$401$	−11256.7	−1.40183	−0.700913	−	0.713247i	$-0.747224\pi$
$401$	−11256.7	−1.40183	−0.700913	+	0.713247i	$0.747224\pi$
$402$	30120.7	3.73702
$403$	−154.213	−0.0190618
$404$	−7750.68	−0.954482
$405$	11251.0	1.38041
$406$	−2049.84	−0.250571
$407$	0	0
$408$	−59229.7	−7.18703
$409$	11156.5	1.34879	0.674394	−	0.738371i	$-0.264405\pi$
$409$	11156.5	1.34879	0.674394	+	0.738371i	$0.264405\pi$
$410$	−24712.2	−2.97670
$411$	3912.86	0.469604
$412$	−13948.7	−1.66797
$413$	380.323	0.0453135
$414$	−16681.6	−1.98033
$415$	17086.5	2.02107
$416$	−9211.45	−1.08565
$417$	10842.3	1.27326
$418$	0	0
$419$	−4932.60	−0.575115	−0.287557	−	0.957763i	$-0.592843\pi$
$419$	−4932.60	−0.575115	−0.287557	+	0.957763i	$0.592843\pi$
$420$	5911.07	0.686740
$421$	6826.66	0.790288	0.395144	−	0.918619i	$-0.370695\pi$
$421$	6826.66	0.790288	0.395144	+	0.918619i	$0.370695\pi$
$422$	29659.4	3.42132
$423$	2443.21	0.280835
$424$	−19736.3	−2.26056
$425$	3735.64	0.426365
$426$	4620.12	0.525459
$427$	−135.512	−0.0153581
$428$	−36252.2	−4.09419
$429$	0	0
$430$	18542.6	2.07954
$431$	931.211	0.104072	0.0520358	−	0.998645i	$-0.483429\pi$
$431$	931.211	0.104072	0.0520358	+	0.998645i	$0.483429\pi$
$432$	15837.0	1.76379
$433$	−7540.35	−0.836873	−0.418437	−	0.908246i	$-0.637422\pi$
$433$	−7540.35	−0.836873	−0.418437	+	0.908246i	$0.637422\pi$
$434$	210.426	0.0232737
$435$	−9611.20	−1.05936
$436$	−33694.2	−3.70106
$437$	14173.0	1.55146
$438$	−15650.7	−1.70735
$439$	−13513.0	−1.46911	−0.734553	−	0.678551i	$-0.762608\pi$
$439$	−13513.0	−1.46911	−0.734553	+	0.678551i	$0.762608\pi$
$440$	0	0
$441$	−5684.90	−0.613853
$442$	−8334.28	−0.896880
$443$	4185.05	0.448843	0.224422	−	0.974492i	$-0.427951\pi$
$443$	4185.05	0.448843	0.224422	+	0.974492i	$0.427951\pi$
$444$	5585.16	0.596982
$445$	1708.59	0.182011
$446$	−31036.4	−3.29510
$447$	21279.9	2.25169
$448$	6319.69	0.666468
$449$	7340.91	0.771579	0.385790	−	0.922587i	$-0.373929\pi$
$449$	7340.91	0.771579	0.385790	+	0.922587i	$0.373929\pi$
$450$	2980.22	0.312198
$451$	0	0
$452$	39382.1	4.09818
$453$	−9394.35	−0.974360
$454$	−4940.81	−0.510757
$455$	528.089	0.0544114
$456$	40146.4	4.12287
$457$	−13041.5	−1.33491	−0.667455	−	0.744650i	$-0.732616\pi$
$457$	−13041.5	−1.33491	−0.667455	+	0.744650i	$0.732616\pi$
$458$	−30744.6	−3.13668
$459$	7707.51	0.783781
$460$	48957.0	4.96225
$461$	17459.8	1.76395	0.881976	−	0.471294i	$-0.156213\pi$
$461$	17459.8	1.76395	0.881976	+	0.471294i	$0.156213\pi$
$462$	0	0
$463$	7599.88	0.762843	0.381421	−	0.924401i	$-0.375435\pi$
$463$	7599.88	0.762843	0.381421	+	0.924401i	$0.375435\pi$
$464$	−27832.7	−2.78470
$465$	986.640	0.0983964
$466$	−10142.2	−1.00822
$467$	6158.03	0.610192	0.305096	−	0.952322i	$-0.401312\pi$
$467$	6158.03	0.610192	0.305096	+	0.952322i	$0.401312\pi$
$468$	−4870.69	−0.481085
$469$	−2689.82	−0.264828
$470$	−9788.13	−0.960623
$471$	−16350.6	−1.59957
$472$	8922.51	0.870110
$473$	0	0
$474$	30846.2	2.98906
$475$	−2532.05	−0.244586
$476$	8330.77	0.802185
$477$	−4434.98	−0.425710
$478$	23989.4	2.29550
$479$	9924.77	0.946710	0.473355	−	0.880872i	$-0.343043\pi$
$479$	9924.77	0.946710	0.473355	+	0.880872i	$0.343043\pi$
$480$	58933.8	5.60406
$481$	498.972	0.0472998
$482$	−1930.09	−0.182393
$483$	3842.05	0.361944
$484$	0	0
$485$	12784.0	1.19689
$486$	22916.0	2.13887
$487$	7933.09	0.738158	0.369079	−	0.929398i	$-0.379673\pi$
$487$	7933.09	0.738158	0.369079	+	0.929398i	$0.379673\pi$
$488$	−3179.16	−0.294906
$489$	−17231.6	−1.59354
$490$	22775.1	2.09975
$491$	9480.12	0.871348	0.435674	−	0.900104i	$-0.356510\pi$
$491$	9480.12	0.871348	0.435674	+	0.900104i	$0.356510\pi$
$492$	−52495.1	−4.81029
$493$	−13545.5	−1.23745
$494$	5649.05	0.514499
$495$	0	0
$496$	2857.17	0.258651
$497$	−412.583	−0.0372372
$498$	49547.6	4.45840
$499$	5696.50	0.511043	0.255521	−	0.966803i	$-0.417753\pi$
$499$	5696.50	0.511043	0.255521	+	0.966803i	$0.417753\pi$
$500$	25559.6	2.28612
$501$	−6151.00	−0.548516
$502$	13413.8	1.19261
$503$	5555.17	0.492431	0.246215	−	0.969215i	$-0.420813\pi$
$503$	5555.17	0.492431	0.246215	+	0.969215i	$0.420813\pi$
$504$	4219.70	0.372937
$505$	4430.14	0.390373
$506$	0	0
$507$	−1122.27	−0.0983074
$508$	−13161.7	−1.14952
$509$	1694.93	0.147596	0.0737980	−	0.997273i	$-0.476488\pi$
$509$	1694.93	0.147596	0.0737980	+	0.997273i	$0.476488\pi$
$510$	53321.8	4.62966
$511$	1397.63	0.120993
$512$	24049.5	2.07588
$513$	−5224.22	−0.449620
$514$	26106.9	2.24033
$515$	7972.79	0.682181
$516$	39389.4	3.36050
$517$	0	0
$518$	−680.855	−0.0577511
$519$	7918.76	0.669740
$520$	12389.1	1.04481
$521$	9797.92	0.823905	0.411952	−	0.911205i	$-0.364847\pi$
$521$	9797.92	0.823905	0.411952	+	0.911205i	$0.364847\pi$
$522$	−10806.4	−0.906096
$523$	−16170.6	−1.35199	−0.675996	−	0.736905i	$-0.736286\pi$
$523$	−16170.6	−1.35199	−0.675996	+	0.736905i	$0.736286\pi$
$524$	−20222.5	−1.68592
$525$	−686.394	−0.0570604
$526$	8718.38	0.722698
$527$	1390.52	0.114937
$528$	0	0
$529$	19653.8	1.61534
$530$	17767.6	1.45618
$531$	2005.00	0.163860
$532$	−5646.67	−0.460177
$533$	−4689.86	−0.381126
$534$	4954.58	0.401509
$535$	20721.0	1.67448
$536$	−63104.0	−5.08522
$537$	−14173.7	−1.13899
$538$	−10706.7	−0.857987
$539$	0	0
$540$	−18045.7	−1.43808
$541$	2056.00	0.163391	0.0816954	−	0.996657i	$-0.473967\pi$
$541$	2056.00	0.163391	0.0816954	+	0.996657i	$0.473967\pi$
$542$	−13079.3	−1.03654
$543$	−15673.5	−1.23870
$544$	83058.4	6.54614
$545$	19259.0	1.51369
$546$	1531.36	0.120029
$547$	14696.9	1.14880	0.574399	−	0.818575i	$-0.305236\pi$
$547$	14696.9	1.14880	0.574399	+	0.818575i	$0.305236\pi$
$548$	−12911.4	−1.00647
$549$	−714.397	−0.0555368
$550$	0	0
$551$	9181.29	0.709866
$552$	90135.7	6.95006
$553$	−2754.61	−0.211823
$554$	4340.56	0.332875
$555$	−3192.37	−0.244159
$556$	−35776.6	−2.72890
$557$	−4950.75	−0.376607	−0.188303	−	0.982111i	$-0.560299\pi$
$557$	−4950.75	−0.376607	−0.188303	+	0.982111i	$0.560299\pi$
$558$	1109.33	0.0841608
$559$	3519.00	0.266258
$560$	−9784.11	−0.738311
$561$	0	0
$562$	−20357.5	−1.52799
$563$	−17416.8	−1.30378	−0.651892	−	0.758312i	$-0.726024\pi$
$563$	−17416.8	−1.30378	−0.651892	+	0.758312i	$0.726024\pi$
$564$	−20792.6	−1.55235
$565$	−22510.1	−1.67611
$566$	−25162.8	−1.86868
$567$	−2913.52	−0.215796
$568$	−9679.34	−0.715028
$569$	−19715.5	−1.45257	−0.726287	−	0.687391i	$-0.758756\pi$
$569$	−19715.5	−1.45257	−0.726287	+	0.687391i	$0.758756\pi$
$570$	−36142.0	−2.65583
$571$	7272.08	0.532972	0.266486	−	0.963839i	$-0.414137\pi$
$571$	7272.08	0.532972	0.266486	+	0.963839i	$0.414137\pi$
$572$	0	0
$573$	−5574.21	−0.406398
$574$	6399.38	0.465339
$575$	−5684.89	−0.412307
$576$	33316.3	2.41003
$577$	−10297.9	−0.742993	−0.371497	−	0.928434i	$-0.621155\pi$
$577$	−10297.9	−0.742993	−0.371497	+	0.928434i	$0.621155\pi$
$578$	48278.7	3.47427
$579$	1665.84	0.119568
$580$	31714.5	2.27047
$581$	−4424.67	−0.315949
$582$	37071.0	2.64028
$583$	0	0
$584$	32788.8	2.32331
$585$	2783.99	0.196759
$586$	20108.7	1.41755
$587$	−21375.9	−1.50303	−0.751513	−	0.659719i	$-0.770676\pi$
$587$	−21375.9	−1.50303	−0.751513	+	0.659719i	$0.770676\pi$
$588$	48380.3	3.39315
$589$	−942.507	−0.0659343
$590$	−8032.52	−0.560497
$591$	−19074.4	−1.32761
$592$	−9244.65	−0.641812
$593$	−20461.9	−1.41698	−0.708490	−	0.705721i	$-0.750623\pi$
$593$	−20461.9	−1.41698	−0.708490	+	0.705721i	$0.750623\pi$
$594$	0	0
$595$	−4761.70	−0.328085
$596$	−70218.2	−4.82592
$597$	−16651.4	−1.14153
$598$	12683.1	0.867308
$599$	5309.39	0.362163	0.181082	−	0.983468i	$-0.442040\pi$
$599$	5309.39	0.362163	0.181082	+	0.983468i	$0.442040\pi$
$600$	−16103.0	−1.09567
$601$	1174.26	0.0796990	0.0398495	−	0.999206i	$-0.487312\pi$
$601$	1174.26	0.0796990	0.0398495	+	0.999206i	$0.487312\pi$
$602$	−4801.73	−0.325090
$603$	−14180.2	−0.957651
$604$	30998.9	2.08829
$605$	0	0
$606$	12846.5	0.861147
$607$	20894.7	1.39718	0.698591	−	0.715521i	$-0.253811\pi$
$607$	20894.7	1.39718	0.698591	+	0.715521i	$0.253811\pi$
$608$	−56297.7	−3.75522
$609$	2488.88	0.165607
$610$	2862.05	0.189969
$611$	−1857.58	−0.122995
$612$	43918.3	2.90081
$613$	894.843	0.0589598	0.0294799	−	0.999565i	$-0.490615\pi$
$613$	894.843	0.0589598	0.0294799	+	0.999565i	$0.490615\pi$
$614$	7890.04	0.518593
$615$	30005.2	1.96736
$616$	0	0
$617$	−19232.1	−1.25487	−0.627435	−	0.778669i	$-0.715895\pi$
$617$	−19232.1	−1.25487	−0.627435	+	0.778669i	$0.715895\pi$
$618$	23119.6	1.50486
$619$	7264.45	0.471701	0.235851	−	0.971789i	$-0.424212\pi$
$619$	7264.45	0.471701	0.235851	+	0.971789i	$0.424212\pi$
$620$	−3255.65	−0.210887
$621$	−11729.3	−0.757938
$622$	−142.278	−0.00917174
$623$	−442.450	−0.0284533
$624$	20792.8	1.33394
$625$	−18593.0	−1.18995
$626$	35501.9	2.26668
$627$	0	0
$628$	53952.7	3.42826
$629$	−4499.16	−0.285204
$630$	−3798.80	−0.240234
$631$	14035.0	0.885459	0.442729	−	0.896655i	$-0.354010\pi$
$631$	14035.0	0.885459	0.442729	+	0.896655i	$0.354010\pi$
$632$	−64624.1	−4.06742
$633$	−36012.1	−2.26122
$634$	−12607.3	−0.789744
$635$	7522.98	0.470142
$636$	37743.1	2.35316
$637$	4322.25	0.268844
$638$	0	0
$639$	−2175.06	−0.134654
$640$	−62476.0	−3.85872
$641$	7389.29	0.455319	0.227660	−	0.973741i	$-0.426893\pi$
$641$	7389.29	0.455319	0.227660	+	0.973741i	$0.426893\pi$
$642$	60087.0	3.69384
$643$	−521.927	−0.0320106	−0.0160053	−	0.999872i	$-0.505095\pi$
$643$	−521.927	−0.0320106	−0.0160053	+	0.999872i	$0.505095\pi$
$644$	−12677.7	−0.775735
$645$	−22514.2	−1.37441
$646$	−50936.6	−3.10228
$647$	−30333.5	−1.84317	−0.921587	−	0.388171i	$-0.873107\pi$
$647$	−30333.5	−1.84317	−0.921587	+	0.388171i	$0.873107\pi$
$648$	−68352.1	−4.14371
$649$	0	0
$650$	−2265.88	−0.136731
$651$	−255.497	−0.0153821
$652$	56859.8	3.41534
$653$	−10097.5	−0.605125	−0.302563	−	0.953130i	$-0.597842\pi$
$653$	−10097.5	−0.605125	−0.302563	+	0.953130i	$0.597842\pi$
$654$	55847.3	3.33915
$655$	11558.8	0.689524
$656$	86890.8	5.17152
$657$	7368.05	0.437527
$658$	2534.70	0.150172
$659$	−14902.7	−0.880923	−0.440461	−	0.897772i	$-0.645185\pi$
$659$	−14902.7	−0.880923	−0.440461	+	0.897772i	$0.645185\pi$
$660$	0	0
$661$	21896.1	1.28844	0.644221	−	0.764840i	$-0.277182\pi$
$661$	21896.1	1.28844	0.644221	+	0.764840i	$0.277182\pi$
$662$	−27688.4	−1.62559
$663$	10119.4	0.592766
$664$	−103804.	−6.06685
$665$	3227.52	0.188208
$666$	−3589.35	−0.208835
$667$	20613.6	1.19664
$668$	20296.7	1.17560
$669$	37684.0	2.17780
$670$	56809.6	3.27574
$671$	0	0
$672$	−15261.3	−0.876068
$673$	14350.5	0.821947	0.410974	−	0.911647i	$-0.365189\pi$
$673$	14350.5	0.821947	0.410974	+	0.911647i	$0.365189\pi$
$674$	5180.08	0.296037
$675$	2095.47	0.119489
$676$	3703.20	0.210697
$677$	19138.7	1.08650	0.543250	−	0.839571i	$-0.317193\pi$
$677$	19138.7	1.08650	0.543250	+	0.839571i	$0.317193\pi$
$678$	−65274.8	−3.69744
$679$	−3310.49	−0.187106
$680$	−111711.	−6.29989
$681$	5999.07	0.337570
$682$	0	0
$683$	−26209.4	−1.46834	−0.734168	−	0.678967i	$-0.762428\pi$
$683$	−26209.4	−1.46834	−0.734168	+	0.678967i	$0.762428\pi$
$684$	−29768.2	−1.66406
$685$	7379.91	0.411638
$686$	−11982.1	−0.666881
$687$	37329.6	2.07309
$688$	−65197.9	−3.61286
$689$	3371.93	0.186444
$690$	−81145.0	−4.47701
$691$	−19215.1	−1.05785	−0.528927	−	0.848667i	$-0.677405\pi$
$691$	−19215.1	−1.05785	−0.528927	+	0.848667i	$0.677405\pi$
$692$	−26129.8	−1.43542
$693$	0	0
$694$	17342.1	0.948553
$695$	20449.2	1.11609
$696$	58390.1	3.17999
$697$	42287.8	2.29808
$698$	14963.5	0.811429
$699$	12314.6	0.666352
$700$	2264.92	0.122294
$701$	20973.2	1.13002	0.565012	−	0.825083i	$-0.308872\pi$
$701$	20973.2	1.13002	0.565012	+	0.825083i	$0.308872\pi$
$702$	−4675.04	−0.251350
$703$	3049.57	0.163609
$704$	0	0
$705$	11884.6	0.634895
$706$	−24872.1	−1.32588
$707$	−1147.21	−0.0610260
$708$	−17063.2	−0.905753
$709$	7895.98	0.418250	0.209125	−	0.977889i	$-0.432938\pi$
$709$	7895.98	0.418250	0.209125	+	0.977889i	$0.432938\pi$
$710$	8713.85	0.460599
$711$	−14521.8	−0.765978
$712$	−10380.0	−0.546360
$713$	−2116.09	−0.111148
$714$	−13808.0	−0.723743
$715$	0	0
$716$	46769.5	2.44114
$717$	−29127.6	−1.51714
$718$	−40673.6	−2.11410
$719$	−14864.8	−0.771021	−0.385510	−	0.922703i	$-0.625975\pi$
$719$	−14864.8	−0.771021	−0.385510	+	0.922703i	$0.625975\pi$
$720$	−51580.1	−2.66983
$721$	−2064.61	−0.106644
$722$	−2988.13	−0.154026
$723$	2343.49	0.120547
$724$	51718.4	2.65483
$725$	−3682.68	−0.188650
$726$	0	0
$727$	1570.98	0.0801435	0.0400718	−	0.999197i	$-0.487241\pi$
$727$	1570.98	0.0801435	0.0400718	+	0.999197i	$0.487241\pi$
$728$	−3208.25	−0.163332
$729$	−3570.17	−0.181383
$730$	−29518.2	−1.49660
$731$	−31730.3	−1.60546
$732$	6079.75	0.306986
$733$	−36898.0	−1.85929	−0.929644	−	0.368459i	$-0.879886\pi$
$733$	−36898.0	−1.85929	−0.929644	+	0.368459i	$0.879886\pi$
$734$	50986.1	2.56394
$735$	−27653.3	−1.38776
$736$	−126398.	−6.33029
$737$	0	0
$738$	33736.4	1.68273
$739$	−19744.5	−0.982833	−0.491417	−	0.870925i	$-0.663521\pi$
$739$	−19744.5	−0.982833	−0.491417	+	0.870925i	$0.663521\pi$
$740$	10534.0	0.523293
$741$	−6859.00	−0.340043
$742$	−4601.04	−0.227641
$743$	18196.6	0.898479	0.449240	−	0.893411i	$-0.351695\pi$
$743$	18196.6	0.898479	0.449240	+	0.893411i	$0.351695\pi$
$744$	−5994.05	−0.295366
$745$	40135.4	1.97375
$746$	51613.2	2.53310
$747$	−23326.1	−1.14251
$748$	0	0
$749$	−5365.85	−0.261767
$750$	−42364.4	−2.06257
$751$	−29660.6	−1.44119	−0.720593	−	0.693358i	$-0.756130\pi$
$751$	−29660.6	−1.44119	−0.720593	+	0.693358i	$0.756130\pi$
$752$	34416.2	1.66892
$753$	−16286.9	−0.788217
$754$	8216.13	0.396835
$755$	−17718.4	−0.854089
$756$	4673.07	0.224812
$757$	27382.3	1.31470	0.657349	−	0.753586i	$-0.271678\pi$
$757$	27382.3	1.31470	0.657349	+	0.753586i	$0.271678\pi$
$758$	−51461.6	−2.46592
$759$	0	0
$760$	75718.8	3.61396
$761$	−8060.70	−0.383969	−0.191984	−	0.981398i	$-0.561492\pi$
$761$	−8060.70	−0.383969	−0.191984	+	0.981398i	$0.561492\pi$
$762$	21815.2	1.03711
$763$	−4987.24	−0.236632
$764$	18393.4	0.871009
$765$	−25102.9	−1.18640
$766$	37175.7	1.75354
$767$	−1524.41	−0.0717641
$768$	−77653.6	−3.64855
$769$	16281.5	0.763493	0.381747	−	0.924267i	$-0.375323\pi$
$769$	16281.5	0.763493	0.381747	+	0.924267i	$0.375323\pi$
$770$	0	0
$771$	−31698.7	−1.48067
$772$	−5496.82	−0.256263
$773$	34161.1	1.58951	0.794753	−	0.606933i	$-0.207600\pi$
$773$	34161.1	1.58951	0.794753	+	0.606933i	$0.207600\pi$
$774$	−25313.9	−1.17557
$775$	378.047	0.0175224
$776$	−77665.3	−3.59281
$777$	826.685	0.0381688
$778$	−49167.0	−2.26571
$779$	−28663.0	−1.31830
$780$	−23692.7	−1.08761
$781$	0	0
$782$	−114362.	−5.22962
$783$	−7598.25	−0.346793
$784$	−80080.0	−3.64796
$785$	−30838.3	−1.40212
$786$	33518.2	1.52106
$787$	11325.7	0.512985	0.256493	−	0.966546i	$-0.417433\pi$
$787$	11325.7	0.512985	0.256493	+	0.966546i	$0.417433\pi$
$788$	62940.6	2.84539
$789$	−10585.7	−0.477645
$790$	58178.0	2.62010
$791$	5829.13	0.262023
$792$	0	0
$793$	543.158	0.0243230
$794$	−2211.29	−0.0988361
$795$	−21573.2	−0.962419
$796$	54945.2	2.44658
$797$	8889.78	0.395097	0.197548	−	0.980293i	$-0.436702\pi$
$797$	8889.78	0.395097	0.197548	+	0.980293i	$0.436702\pi$
$798$	9359.20	0.415178
$799$	16749.6	0.741624
$800$	22581.4	0.997968
$801$	−2332.52	−0.102891
$802$	−61565.4	−2.71066
$803$	0	0
$804$	120678.	5.29353
$805$	7246.35	0.317268
$806$	−843.428	−0.0368592
$807$	12999.9	0.567061
$808$	−26914.0	−1.17182
$809$	1898.09	0.0824888	0.0412444	−	0.999149i	$-0.486868\pi$
$809$	1898.09	0.0824888	0.0412444	+	0.999149i	$0.486868\pi$
$810$	61534.2	2.66925
$811$	−14268.6	−0.617801	−0.308900	−	0.951094i	$-0.599961\pi$
$811$	−14268.6	−0.617801	−0.308900	+	0.951094i	$0.599961\pi$
$812$	−8212.67	−0.354936
$813$	15880.7	0.685067
$814$	0	0
$815$	−32500.0	−1.39684
$816$	−187485.	−8.04326
$817$	21507.1	0.920977
$818$	61017.6	2.60810
$819$	−720.933	−0.0307588
$820$	−99009.2	−4.21653
$821$	−41021.5	−1.74380	−0.871900	−	0.489684i	$-0.837112\pi$
$821$	−41021.5	−1.74380	−0.871900	+	0.489684i	$0.837112\pi$
$822$	21400.3	0.908056
$823$	31709.8	1.34306	0.671528	−	0.740979i	$-0.265638\pi$
$823$	31709.8	1.34306	0.671528	+	0.740979i	$0.265638\pi$
$824$	−48436.4	−2.04777
$825$	0	0
$826$	2080.07	0.0876211
$827$	−5639.93	−0.237146	−0.118573	−	0.992945i	$-0.537832\pi$
$827$	−5639.93	−0.237146	−0.118573	+	0.992945i	$0.537832\pi$
$828$	−66834.9	−2.80516
$829$	−4938.42	−0.206898	−0.103449	−	0.994635i	$-0.532988\pi$
$829$	−4938.42	−0.206898	−0.103449	+	0.994635i	$0.532988\pi$
$830$	93450.1	3.90807
$831$	−5270.25	−0.220003
$832$	−25330.5	−1.05550
$833$	−38973.1	−1.62105
$834$	59298.8	2.46205
$835$	−11601.2	−0.480809
$836$	0	0
$837$	779.999	0.0322111
$838$	−26977.5	−1.11208
$839$	9717.93	0.399881	0.199941	−	0.979808i	$-0.435925\pi$
$839$	9717.93	0.399881	0.199941	+	0.979808i	$0.435925\pi$
$840$	20526.0	0.843114
$841$	−11035.5	−0.452478
$842$	37336.6	1.52815
$843$	24717.8	1.00988
$844$	118830.	4.84634
$845$	−2116.68	−0.0861728
$846$	13362.5	0.543040
$847$	0	0
$848$	−62473.0	−2.52987
$849$	30552.4	1.23505
$850$	20431.1	0.824447
$851$	6846.82	0.275800
$852$	18510.5	0.744319
$853$	30235.8	1.21366	0.606831	−	0.794831i	$-0.292441\pi$
$853$	30235.8	1.21366	0.606831	+	0.794831i	$0.292441\pi$
$854$	−741.147	−0.0296973
$855$	17014.9	0.680583
$856$	−125885.	−5.02646
$857$	−21265.6	−0.847631	−0.423816	−	0.905748i	$-0.639310\pi$
$857$	−21265.6	−0.847631	−0.423816	+	0.905748i	$0.639310\pi$
$858$	0	0
$859$	−5590.03	−0.222037	−0.111018	−	0.993818i	$-0.535411\pi$
$859$	−5590.03	−0.222037	−0.111018	+	0.993818i	$0.535411\pi$
$860$	74290.9	2.94570
$861$	−7770.04	−0.307552
$862$	5093.00	0.201239
$863$	−39075.2	−1.54129	−0.770646	−	0.637264i	$-0.780066\pi$
$863$	−39075.2	−1.54129	−0.770646	+	0.637264i	$0.780066\pi$
$864$	46590.8	1.83455
$865$	14935.3	0.587070
$866$	−41239.9	−1.61823
$867$	−58619.3	−2.29621
$868$	843.073	0.0329675
$869$	0	0
$870$	−52565.9	−2.04845
$871$	10781.3	0.419414
$872$	−117002.	−4.54381
$873$	−17452.3	−0.676600
$874$	77515.3	2.99999
$875$	3783.19	0.146166
$876$	−62704.5	−2.41848
$877$	16902.3	0.650798	0.325399	−	0.945577i	$-0.394501\pi$
$877$	16902.3	0.650798	0.325399	+	0.945577i	$0.394501\pi$
$878$	−73905.4	−2.84076
$879$	−24415.7	−0.936886
$880$	0	0
$881$	−27870.9	−1.06583	−0.532914	−	0.846170i	$-0.678903\pi$
$881$	−27870.9	−1.06583	−0.532914	+	0.846170i	$0.678903\pi$
$882$	−31092.0	−1.18699
$883$	−20312.0	−0.774125	−0.387062	−	0.922054i	$-0.626510\pi$
$883$	−20312.0	−0.774125	−0.387062	+	0.922054i	$0.626510\pi$
$884$	−33391.3	−1.27044
$885$	9752.98	0.370444
$886$	22889.0	0.867912
$887$	4039.59	0.152916	0.0764578	−	0.997073i	$-0.475639\pi$
$887$	4039.59	0.152916	0.0764578	+	0.997073i	$0.475639\pi$
$888$	19394.3	0.732917
$889$	−1948.13	−0.0734961
$890$	9344.66	0.351948
$891$	0	0
$892$	−124347.	−4.66755
$893$	−11353.0	−0.425436
$894$	116385.	4.35402
$895$	−26732.5	−0.998402
$896$	16178.6	0.603223
$897$	−15399.6	−0.573221
$898$	40149.1	1.49197
$899$	−1370.81	−0.0508554
$900$	11940.3	0.442232
$901$	−30404.2	−1.12421
$902$	0	0
$903$	5830.20	0.214858
$904$	136753.	5.03136
$905$	−29561.2	−1.08580
$906$	−51379.8	−1.88408
$907$	10174.4	0.372474	0.186237	−	0.982505i	$-0.440371\pi$
$907$	10174.4	0.372474	0.186237	+	0.982505i	$0.440371\pi$
$908$	−19795.4	−0.723493
$909$	−6047.91	−0.220678
$910$	2888.24	0.105213
$911$	−33833.5	−1.23046	−0.615232	−	0.788346i	$-0.710938\pi$
$911$	−33833.5	−1.23046	−0.615232	+	0.788346i	$0.710938\pi$
$912$	127079.	4.61405
$913$	0	0
$914$	−71326.8	−2.58127
$915$	−3475.07	−0.125554
$916$	−123178.	−4.44314
$917$	−2993.22	−0.107791
$918$	42154.1	1.51557
$919$	−1539.24	−0.0552501	−0.0276250	−	0.999618i	$-0.508794\pi$
$919$	−1539.24	−0.0552501	−0.0276250	+	0.999618i	$0.508794\pi$
$920$	170002.	6.09217
$921$	−9579.98	−0.342748
$922$	95491.4	3.41089
$923$	1653.71	0.0589735
$924$	0	0
$925$	−1223.21	−0.0434798
$926$	41565.5	1.47508
$927$	−10884.2	−0.385637
$928$	−81880.9	−2.89641
$929$	15087.6	0.532840	0.266420	−	0.963857i	$-0.414159\pi$
$929$	15087.6	0.532840	0.266420	+	0.963857i	$0.414159\pi$
$930$	5396.16	0.190266
$931$	26416.3	0.929924
$932$	−40634.9	−1.42815
$933$	172.752	0.00606178
$934$	33679.6	1.17991
$935$	0	0
$936$	−16913.3	−0.590630
$937$	31496.5	1.09813	0.549065	−	0.835780i	$-0.314984\pi$
$937$	31496.5	1.09813	0.549065	+	0.835780i	$0.314984\pi$
$938$	−14711.2	−0.512088
$939$	−43106.0	−1.49809
$940$	−39216.1	−1.36073
$941$	12096.9	0.419072	0.209536	−	0.977801i	$-0.432805\pi$
$941$	12096.9	0.419072	0.209536	+	0.977801i	$0.432805\pi$
$942$	−89425.2	−3.09302
$943$	−64353.5	−2.22231
$944$	28243.3	0.973771
$945$	−2671.03	−0.0919457
$946$	0	0
$947$	41425.7	1.42149	0.710747	−	0.703448i	$-0.248357\pi$
$947$	41425.7	1.42149	0.710747	+	0.703448i	$0.248357\pi$
$948$	123585.	4.23404
$949$	−5601.95	−0.191620
$950$	−13848.4	−0.472948
$951$	15307.6	0.521958
$952$	28928.3	0.984846
$953$	−43623.4	−1.48279	−0.741395	−	0.671069i	$-0.765836\pi$
$953$	−43623.4	−1.48279	−0.741395	+	0.671069i	$0.765836\pi$
$954$	−24255.9	−0.823180
$955$	−10513.3	−0.356234
$956$	96113.3	3.25160
$957$	0	0
$958$	54280.8	1.83062
$959$	−1911.08	−0.0643502
$960$	162062.	5.44846
$961$	−29650.3	−0.995276
$962$	2728.99	0.0914618
$963$	−28287.8	−0.946585
$964$	−7732.91	−0.258361
$965$	3141.88	0.104809
$966$	21013.0	0.699879
$967$	52971.3	1.76157	0.880787	−	0.473513i	$-0.157014\pi$
$967$	52971.3	1.76157	0.880787	+	0.473513i	$0.157014\pi$
$968$	0	0
$969$	61846.6	2.05036
$970$	69918.4	2.31438
$971$	34144.0	1.12846	0.564229	−	0.825618i	$-0.309174\pi$
$971$	34144.0	1.12846	0.564229	+	0.825618i	$0.309174\pi$
$972$	91812.9	3.02973
$973$	−5295.46	−0.174476
$974$	43387.9	1.42735
$975$	2751.20	0.0903680
$976$	−10063.3	−0.330039
$977$	−1506.33	−0.0493263	−0.0246632	−	0.999696i	$-0.507851\pi$
$977$	−1506.33	−0.0493263	−0.0246632	+	0.999696i	$0.507851\pi$
$978$	−94243.6	−3.08137
$979$	0	0
$980$	91248.5	2.97431
$981$	−26291.8	−0.855692
$982$	51849.0	1.68489
$983$	19294.9	0.626056	0.313028	−	0.949744i	$-0.398657\pi$
$983$	19294.9	0.626056	0.313028	+	0.949744i	$0.398657\pi$
$984$	−182288.	−5.90561
$985$	−35975.6	−1.16373
$986$	−74083.6	−2.39280
$987$	−3077.60	−0.0992514
$988$	22632.9	0.728794
$989$	48287.2	1.55252
$990$	0	0
$991$	2676.87	0.0858059	0.0429030	−	0.999079i	$-0.486339\pi$
$991$	2676.87	0.0858059	0.0429030	+	0.999079i	$0.486339\pi$
$992$	8405.50	0.269027
$993$	33618.9	1.07439
$994$	−2256.51	−0.0720042
$995$	−31405.6	−1.00063
$996$	198513.	6.31537
$997$	−11362.4	−0.360934	−0.180467	−	0.983581i	$-0.557761\pi$
$997$	−11362.4	−0.360934	−0.180467	+	0.983581i	$0.557761\pi$
$998$	31155.4	0.988185
$999$	−2523.76	−0.0799283

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.4.a.p.1.34		34
11.2	odd	10		143.4.h.a.92.17	yes	68
11.6	odd	10		143.4.h.a.14.17	✓	68
11.10	odd	2		1573.4.a.o.1.1		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.a.14.17	✓	68	11.6	odd	10
143.4.h.a.92.17	yes	68	11.2	odd	10
1573.4.a.o.1.1		34	11.10	odd	2
1573.4.a.p.1.34		34	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1573 = 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1573.a (trivial)

\(f(q)\)	\(=\)	\(q+5.46923 q^{2} -6.64067 q^{3} +21.9125 q^{4} -12.5247 q^{5} -36.3193 q^{6} +3.24336 q^{7} +76.0904 q^{8} +17.0984 q^{9} +O(q^{10})\)	\(q+5.46923 q^{2} -6.64067 q^{3} +21.9125 q^{4} -12.5247 q^{5} -36.3193 q^{6} +3.24336 q^{7} +76.0904 q^{8} +17.0984 q^{9} -68.5006 q^{10} -145.513 q^{12} -13.0000 q^{13} +17.7387 q^{14} +83.1725 q^{15} +240.856 q^{16} +117.219 q^{17} +93.5152 q^{18} -79.4522 q^{19} -274.448 q^{20} -21.5381 q^{21} -178.384 q^{23} -505.291 q^{24} +31.8689 q^{25} -71.1000 q^{26} +65.7530 q^{27} +71.0700 q^{28} -115.557 q^{29} +454.890 q^{30} +11.8626 q^{31} +708.573 q^{32} +641.098 q^{34} -40.6222 q^{35} +374.669 q^{36} -38.3825 q^{37} -434.542 q^{38} +86.3286 q^{39} -953.012 q^{40} +360.758 q^{41} -117.797 q^{42} -270.693 q^{43} -214.153 q^{45} -975.622 q^{46} +142.891 q^{47} -1599.44 q^{48} -332.481 q^{49} +174.298 q^{50} -778.413 q^{51} -284.862 q^{52} -259.379 q^{53} +359.618 q^{54} +246.789 q^{56} +527.615 q^{57} -632.010 q^{58} +117.262 q^{59} +1822.51 q^{60} -41.7814 q^{61} +64.8791 q^{62} +55.4564 q^{63} +1948.50 q^{64} +162.821 q^{65} -829.330 q^{67} +2568.56 q^{68} +1184.59 q^{69} -222.172 q^{70} -127.208 q^{71} +1301.03 q^{72} +430.920 q^{73} -209.923 q^{74} -211.631 q^{75} -1740.99 q^{76} +472.151 q^{78} -849.306 q^{79} -3016.66 q^{80} -898.301 q^{81} +1973.07 q^{82} -1364.22 q^{83} -471.952 q^{84} -1468.14 q^{85} -1480.48 q^{86} +767.378 q^{87} -136.417 q^{89} -1171.25 q^{90} -42.1637 q^{91} -3908.83 q^{92} -78.7754 q^{93} +781.504 q^{94} +995.117 q^{95} -4705.40 q^{96} -1020.70 q^{97} -1818.41 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} - 36 q^{6} + 36 q^{7} + 57 q^{8} + 265 q^{9}+O(q^{10}) \) 34 * q + 3 * q^2 - 29 * q^3 + 97 * q^4 - 28 * q^5 - 36 * q^6 + 36 * q^7 + 57 * q^8 + 265 * q^9	\( 34 q + 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} - 36 q^{6} + 36 q^{7} + 57 q^{8} + 265 q^{9} + 18 q^{10} - 262 q^{12} - 442 q^{13} - 231 q^{14} - 196 q^{15} + 225 q^{16} + 209 q^{17} + 190 q^{18} + 107 q^{19} - 211 q^{20} + 68 q^{21} - 632 q^{23} - 152 q^{24} + 296 q^{25} - 39 q^{26} - 920 q^{27} + 931 q^{28} + 32 q^{29} + 300 q^{30} - 290 q^{31} - 876 q^{32} - 602 q^{34} - 104 q^{35} - 611 q^{36} - 656 q^{37} - 1361 q^{38} + 377 q^{39} - 1159 q^{40} + 1121 q^{41} + 79 q^{42} - 349 q^{43} - 1024 q^{45} - 490 q^{46} - 1608 q^{47} - 1827 q^{48} + 808 q^{49} + 1322 q^{50} - 1414 q^{51} - 1261 q^{52} - 2608 q^{53} - 3131 q^{54} - 1675 q^{56} + 2150 q^{57} - 1673 q^{58} - 2011 q^{59} - 201 q^{60} + 236 q^{61} - 1396 q^{62} - 1206 q^{63} + 1331 q^{64} + 364 q^{65} - 3213 q^{67} + 1321 q^{68} - 162 q^{69} + 174 q^{70} - 3756 q^{71} + 5074 q^{72} - 823 q^{73} - 2550 q^{74} - 3063 q^{75} - 2004 q^{76} + 468 q^{78} + 2120 q^{79} - 5005 q^{80} + 710 q^{81} - 2534 q^{82} + 3843 q^{83} - 7191 q^{84} - 1582 q^{85} - 3542 q^{86} - 962 q^{87} - 3633 q^{89} + 995 q^{90} - 468 q^{91} - 2072 q^{92} - 508 q^{93} + 6309 q^{94} - 1916 q^{95} + 2150 q^{96} + 1195 q^{97} + 1487 q^{98}+O(q^{100}) \) 34 * q + 3 * q^2 - 29 * q^3 + 97 * q^4 - 28 * q^5 - 36 * q^6 + 36 * q^7 + 57 * q^8 + 265 * q^9 + 18 * q^10 - 262 * q^12 - 442 * q^13 - 231 * q^14 - 196 * q^15 + 225 * q^16 + 209 * q^17 + 190 * q^18 + 107 * q^19 - 211 * q^20 + 68 * q^21 - 632 * q^23 - 152 * q^24 + 296 * q^25 - 39 * q^26 - 920 * q^27 + 931 * q^28 + 32 * q^29 + 300 * q^30 - 290 * q^31 - 876 * q^32 - 602 * q^34 - 104 * q^35 - 611 * q^36 - 656 * q^37 - 1361 * q^38 + 377 * q^39 - 1159 * q^40 + 1121 * q^41 + 79 * q^42 - 349 * q^43 - 1024 * q^45 - 490 * q^46 - 1608 * q^47 - 1827 * q^48 + 808 * q^49 + 1322 * q^50 - 1414 * q^51 - 1261 * q^52 - 2608 * q^53 - 3131 * q^54 - 1675 * q^56 + 2150 * q^57 - 1673 * q^58 - 2011 * q^59 - 201 * q^60 + 236 * q^61 - 1396 * q^62 - 1206 * q^63 + 1331 * q^64 + 364 * q^65 - 3213 * q^67 + 1321 * q^68 - 162 * q^69 + 174 * q^70 - 3756 * q^71 + 5074 * q^72 - 823 * q^73 - 2550 * q^74 - 3063 * q^75 - 2004 * q^76 + 468 * q^78 + 2120 * q^79 - 5005 * q^80 + 710 * q^81 - 2534 * q^82 + 3843 * q^83 - 7191 * q^84 - 1582 * q^85 - 3542 * q^86 - 962 * q^87 - 3633 * q^89 + 995 * q^90 - 468 * q^91 - 2072 * q^92 - 508 * q^93 + 6309 * q^94 - 1916 * q^95 + 2150 * q^96 + 1195 * q^97 + 1487 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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