LMFDB - Embedded newform 1573.4.a.q.1.20

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:	$0$
Dimension:	$38$
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q+0.453664 q^{2} +6.65479 q^{3} -7.79419 q^{4} -5.35620 q^{5} +3.01904 q^{6} -27.7636 q^{7} -7.16526 q^{8} +17.2862 q^{9} +O(q^{10})$	\(q+0.453664 q^{2} +6.65479 q^{3} -7.79419 q^{4} -5.35620 q^{5} +3.01904 q^{6} -27.7636 q^{7} -7.16526 q^{8} +17.2862 q^{9} -2.42992 q^{10} -51.8687 q^{12} -13.0000 q^{13} -12.5954 q^{14} -35.6444 q^{15} +59.1029 q^{16} -78.5360 q^{17} +7.84213 q^{18} -73.3278 q^{19} +41.7472 q^{20} -184.761 q^{21} +47.4408 q^{23} -47.6833 q^{24} -96.3111 q^{25} -5.89764 q^{26} -64.6434 q^{27} +216.395 q^{28} -69.5988 q^{29} -16.1706 q^{30} +273.316 q^{31} +84.1350 q^{32} -35.6290 q^{34} +148.708 q^{35} -134.732 q^{36} -234.731 q^{37} -33.2662 q^{38} -86.5122 q^{39} +38.3786 q^{40} +309.491 q^{41} -83.8195 q^{42} +375.060 q^{43} -92.5882 q^{45} +21.5222 q^{46} -502.720 q^{47} +393.317 q^{48} +427.819 q^{49} -43.6929 q^{50} -522.640 q^{51} +101.324 q^{52} +391.238 q^{53} -29.3264 q^{54} +198.934 q^{56} -487.981 q^{57} -31.5745 q^{58} +738.325 q^{59} +277.819 q^{60} -908.609 q^{61} +123.994 q^{62} -479.927 q^{63} -434.654 q^{64} +69.6306 q^{65} +235.932 q^{67} +612.124 q^{68} +315.708 q^{69} +67.4633 q^{70} +336.883 q^{71} -123.860 q^{72} +472.190 q^{73} -106.489 q^{74} -640.930 q^{75} +571.531 q^{76} -39.2475 q^{78} +145.435 q^{79} -316.567 q^{80} -896.915 q^{81} +140.405 q^{82} -1189.92 q^{83} +1440.06 q^{84} +420.654 q^{85} +170.151 q^{86} -463.165 q^{87} -354.291 q^{89} -42.0040 q^{90} +360.927 q^{91} -369.762 q^{92} +1818.86 q^{93} -228.066 q^{94} +392.758 q^{95} +559.900 q^{96} +705.353 q^{97} +194.086 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 3 q^{2} + 19 q^{3} + 181 q^{4} + 52 q^{5} - 104 q^{6} - 12 q^{7} - 57 q^{8} + 477 q^{9}+O(q^{10}) $ 38 * q - 3 * q^2 + 19 * q^3 + 181 * q^4 + 52 * q^5 - 104 * q^6 - 12 * q^7 - 57 * q^8 + 477 * q^9	\( 38 q - 3 q^{2} + 19 q^{3} + 181 q^{4} + 52 q^{5} - 104 q^{6} - 12 q^{7} - 57 q^{8} + 477 q^{9} + 30 q^{10} + 122 q^{12} - 494 q^{13} + 181 q^{14} + 264 q^{15} + 961 q^{16} + 33 q^{17} - 28 q^{18} - 107 q^{19} + 595 q^{20} - 148 q^{21} + 840 q^{23} - 968 q^{24} + 1428 q^{25} + 39 q^{26} + 1108 q^{27} + 353 q^{28} + 162 q^{29} + 48 q^{30} + 62 q^{31} - 1204 q^{32} - 58 q^{34} + 352 q^{35} + 3357 q^{36} + 304 q^{37} + 963 q^{38} - 247 q^{39} + 571 q^{40} - 361 q^{41} + 587 q^{42} - 483 q^{43} + 1136 q^{45} + 1860 q^{46} + 2892 q^{47} + 945 q^{48} + 2270 q^{49} + 782 q^{50} + 682 q^{51} - 2353 q^{52} + 1622 q^{53} - 3273 q^{54} + 3269 q^{56} - 62 q^{57} + 1683 q^{58} + 3417 q^{59} + 4279 q^{60} + 1714 q^{61} - 508 q^{62} - 3730 q^{63} + 4823 q^{64} - 676 q^{65} + 4939 q^{67} + 3699 q^{68} + 1818 q^{69} + 592 q^{70} + 1544 q^{71} + 5570 q^{72} - 617 q^{73} + 1398 q^{74} + 5457 q^{75} - 3316 q^{76} + 1352 q^{78} + 3176 q^{79} + 5091 q^{80} + 5994 q^{81} + 1238 q^{82} - 1659 q^{83} - 5157 q^{84} - 1074 q^{85} + 1144 q^{86} + 906 q^{87} + 3727 q^{89} + 6753 q^{90} + 156 q^{91} + 11004 q^{92} + 6956 q^{93} + 9255 q^{94} - 1768 q^{95} - 4812 q^{96} + 5723 q^{97} - 2043 q^{98}+O(q^{100}) \) 38 * q - 3 * q^2 + 19 * q^3 + 181 * q^4 + 52 * q^5 - 104 * q^6 - 12 * q^7 - 57 * q^8 + 477 * q^9 + 30 * q^10 + 122 * q^12 - 494 * q^13 + 181 * q^14 + 264 * q^15 + 961 * q^16 + 33 * q^17 - 28 * q^18 - 107 * q^19 + 595 * q^20 - 148 * q^21 + 840 * q^23 - 968 * q^24 + 1428 * q^25 + 39 * q^26 + 1108 * q^27 + 353 * q^28 + 162 * q^29 + 48 * q^30 + 62 * q^31 - 1204 * q^32 - 58 * q^34 + 352 * q^35 + 3357 * q^36 + 304 * q^37 + 963 * q^38 - 247 * q^39 + 571 * q^40 - 361 * q^41 + 587 * q^42 - 483 * q^43 + 1136 * q^45 + 1860 * q^46 + 2892 * q^47 + 945 * q^48 + 2270 * q^49 + 782 * q^50 + 682 * q^51 - 2353 * q^52 + 1622 * q^53 - 3273 * q^54 + 3269 * q^56 - 62 * q^57 + 1683 * q^58 + 3417 * q^59 + 4279 * q^60 + 1714 * q^61 - 508 * q^62 - 3730 * q^63 + 4823 * q^64 - 676 * q^65 + 4939 * q^67 + 3699 * q^68 + 1818 * q^69 + 592 * q^70 + 1544 * q^71 + 5570 * q^72 - 617 * q^73 + 1398 * q^74 + 5457 * q^75 - 3316 * q^76 + 1352 * q^78 + 3176 * q^79 + 5091 * q^80 + 5994 * q^81 + 1238 * q^82 - 1659 * q^83 - 5157 * q^84 - 1074 * q^85 + 1144 * q^86 + 906 * q^87 + 3727 * q^89 + 6753 * q^90 + 156 * q^91 + 11004 * q^92 + 6956 * q^93 + 9255 * q^94 - 1768 * q^95 - 4812 * q^96 + 5723 * q^97 - 2043 * 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 $

$2$	0.453664	0.160395	0.0801973	−	0.996779i	$-0.474445\pi$
$2$	0.453664	0.160395	0.0801973	+	0.996779i	$0.474445\pi$
$3$	6.65479	1.28071	0.640357	−	0.768077i	$-0.278786\pi$
$3$	6.65479	1.28071	0.640357	+	0.768077i	$0.278786\pi$
$4$	−7.79419	−0.974274
$5$	−5.35620	−0.479073	−0.239536	−	0.970887i	$-0.576995\pi$
$5$	−5.35620	−0.479073	−0.239536	+	0.970887i	$0.576995\pi$
$6$	3.01904	0.205420
$7$	−27.7636	−1.49910	−0.749548	−	0.661950i	$-0.769729\pi$
$7$	−27.7636	−1.49910	−0.749548	+	0.661950i	$0.769729\pi$
$8$	−7.16526	−0.316663
$9$	17.2862	0.640229
$10$	−2.42992	−0.0768407
$11$	0	0
$11$	0	0
$12$	−51.8687	−1.24777
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	−12.5954	−0.240447
$15$	−35.6444	−0.613556
$16$	59.1029	0.923483
$17$	−78.5360	−1.12046	−0.560229	−	0.828338i	$-0.689287\pi$
$17$	−78.5360	−1.12046	−0.560229	+	0.828338i	$0.689287\pi$
$18$	7.84213	0.102689
$19$	−73.3278	−0.885398	−0.442699	−	0.896670i	$-0.645979\pi$
$19$	−73.3278	−0.885398	−0.442699	+	0.896670i	$0.645979\pi$
$20$	41.7472	0.466748
$21$	−184.761	−1.91991
$22$	0	0
$23$	47.4408	0.430091	0.215045	−	0.976604i	$-0.431010\pi$
$23$	47.4408	0.430091	0.215045	+	0.976604i	$0.431010\pi$
$24$	−47.6833	−0.405555
$25$	−96.3111	−0.770489
$26$	−5.89764	−0.0444855
$27$	−64.6434	−0.460764
$28$	216.395	1.46053
$29$	−69.5988	−0.445661	−0.222831	−	0.974857i	$-0.571530\pi$
$29$	−69.5988	−0.445661	−0.222831	+	0.974857i	$0.571530\pi$
$30$	−16.1706	−0.0984110
$31$	273.316	1.58352	0.791759	−	0.610834i	$-0.209166\pi$
$31$	273.316	1.58352	0.791759	+	0.610834i	$0.209166\pi$
$32$	84.1350	0.464784
$33$	0	0
$34$	−35.6290	−0.179715
$35$	148.708	0.718176
$36$	−134.732	−0.623758
$37$	−234.731	−1.04296	−0.521481	−	0.853263i	$-0.674620\pi$
$37$	−234.731	−1.04296	−0.521481	+	0.853263i	$0.674620\pi$
$38$	−33.2662	−0.142013
$39$	−86.5122	−0.355206
$40$	38.3786	0.151705
$41$	309.491	1.17889	0.589443	−	0.807810i	$-0.299347\pi$
$41$	309.491	1.17889	0.589443	+	0.807810i	$0.299347\pi$
$42$	−83.8195	−0.307944
$43$	375.060	1.33014	0.665070	−	0.746781i	$-0.268402\pi$
$43$	375.060	1.33014	0.665070	+	0.746781i	$0.268402\pi$
$44$	0	0
$45$	−92.5882	−0.306716
$46$	21.5222	0.0689842
$47$	−502.720	−1.56020	−0.780098	−	0.625657i	$-0.784831\pi$
$47$	−502.720	−1.56020	−0.780098	+	0.625657i	$0.784831\pi$
$48$	393.317	1.18272
$49$	427.819	1.24729
$50$	−43.6929	−0.123582
$51$	−522.640	−1.43499
$52$	101.324	0.270215
$53$	391.238	1.01397	0.506987	−	0.861953i	$-0.330759\pi$
$53$	391.238	1.01397	0.506987	+	0.861953i	$0.330759\pi$
$54$	−29.3264	−0.0739041
$55$	0	0
$56$	198.934	0.474708
$57$	−487.981	−1.13394
$58$	−31.5745	−0.0714817
$59$	738.325	1.62918	0.814591	−	0.580036i	$-0.196961\pi$
$59$	738.325	1.62918	0.814591	+	0.580036i	$0.196961\pi$
$60$	277.819	0.597771
$61$	−908.609	−1.90714	−0.953570	−	0.301173i	$-0.902622\pi$
$61$	−908.609	−1.90714	−0.953570	+	0.301173i	$0.902622\pi$
$62$	123.994	0.253988
$63$	−479.927	−0.959764
$64$	−434.654	−0.848934
$65$	69.6306	0.132871
$66$	0	0
$67$	235.932	0.430205	0.215102	−	0.976592i	$-0.430992\pi$
$67$	235.932	0.430205	0.215102	+	0.976592i	$0.430992\pi$
$68$	612.124	1.09163
$69$	315.708	0.550823
$70$	67.4633	0.115192
$71$	336.883	0.563108	0.281554	−	0.959545i	$-0.409150\pi$
$71$	336.883	0.563108	0.281554	+	0.959545i	$0.409150\pi$
$72$	−123.860	−0.202737
$73$	472.190	0.757064	0.378532	−	0.925588i	$-0.376429\pi$
$73$	472.190	0.757064	0.378532	+	0.925588i	$0.376429\pi$
$74$	−106.489	−0.167285
$75$	−640.930	−0.986776
$76$	571.531	0.862620
$77$	0	0
$78$	−39.2475	−0.0569732
$79$	145.435	0.207122	0.103561	−	0.994623i	$-0.466976\pi$
$79$	145.435	0.207122	0.103561	+	0.994623i	$0.466976\pi$
$80$	−316.567	−0.442416
$81$	−896.915	−1.23034
$82$	140.405	0.189087
$83$	−1189.92	−1.57362	−0.786809	−	0.617197i	$-0.788268\pi$
$83$	−1189.92	−1.57362	−0.786809	+	0.617197i	$0.788268\pi$
$84$	1440.06	1.87052
$85$	420.654	0.536781
$86$	170.151	0.213347
$87$	−463.165	−0.570765
$88$	0	0
$89$	−354.291	−0.421964	−0.210982	−	0.977490i	$-0.567666\pi$
$89$	−354.291	−0.421964	−0.210982	+	0.977490i	$0.567666\pi$
$90$	−42.0040	−0.0491956
$91$	360.927	0.415774
$92$	−369.762	−0.419026
$93$	1818.86	2.02803
$94$	−228.066	−0.250247
$95$	392.758	0.424170
$96$	559.900	0.595256
$97$	705.353	0.738327	0.369164	−	0.929364i	$-0.379644\pi$
$97$	705.353	0.738327	0.369164	+	0.929364i	$0.379644\pi$
$98$	194.086	0.200058
$99$	0	0
$100$	750.667	0.750667
$101$	1520.04	1.49752	0.748760	−	0.662841i	$-0.230650\pi$
$101$	1520.04	1.49752	0.748760	+	0.662841i	$0.230650\pi$
$102$	−237.103	−0.230164
$103$	443.751	0.424505	0.212253	−	0.977215i	$-0.431920\pi$
$103$	443.751	0.424505	0.212253	+	0.977215i	$0.431920\pi$
$104$	93.1484	0.0878265
$105$	989.617	0.919778
$106$	177.491	0.162636
$107$	−947.259	−0.855841	−0.427920	−	0.903816i	$-0.640754\pi$
$107$	−947.259	−0.855841	−0.427920	+	0.903816i	$0.640754\pi$
$108$	503.843	0.448910
$109$	94.6412	0.0831649	0.0415825	−	0.999135i	$-0.486760\pi$
$109$	94.6412	0.0831649	0.0415825	+	0.999135i	$0.486760\pi$
$110$	0	0
$111$	−1562.09	−1.33574
$112$	−1640.91	−1.38439
$113$	2021.01	1.68249	0.841244	−	0.540656i	$-0.181824\pi$
$113$	2021.01	1.68249	0.841244	+	0.540656i	$0.181824\pi$
$114$	−221.380	−0.181878
$115$	−254.102	−0.206045
$116$	542.466	0.434196
$117$	−224.720	−0.177568
$118$	334.952	0.261312
$119$	2180.45	1.67967
$120$	255.401	0.194290
$121$	0	0
$122$	−412.204	−0.305895
$123$	2059.59	1.50982
$124$	−2130.28	−1.54278
$125$	1185.39	0.848193
$126$	−217.726	−0.153941
$127$	353.990	0.247335	0.123668	−	0.992324i	$-0.460534\pi$
$127$	353.990	0.247335	0.123668	+	0.992324i	$0.460534\pi$
$128$	−870.267	−0.600949
$129$	2495.94	1.70353
$130$	31.5889	0.0213118
$131$	791.809	0.528097	0.264049	−	0.964509i	$-0.414942\pi$
$131$	791.809	0.528097	0.264049	+	0.964509i	$0.414942\pi$
$132$	0	0
$133$	2035.85	1.32730
$134$	107.034	0.0690025
$135$	346.243	0.220740
$136$	562.731	0.354807
$137$	151.662	0.0945792	0.0472896	−	0.998881i	$-0.484942\pi$
$137$	151.662	0.0945792	0.0472896	+	0.998881i	$0.484942\pi$
$138$	143.226	0.0883491
$139$	−190.145	−0.116028	−0.0580139	−	0.998316i	$-0.518477\pi$
$139$	−190.145	−0.116028	−0.0580139	+	0.998316i	$0.518477\pi$
$140$	−1159.05	−0.699700
$141$	−3345.49	−1.99817
$142$	152.832	0.0903194
$143$	0	0
$144$	1021.66	0.591240
$145$	372.785	0.213504
$146$	214.216	0.121429
$147$	2847.05	1.59742
$148$	1829.54	1.01613
$149$	−188.884	−0.103852	−0.0519262	−	0.998651i	$-0.516536\pi$
$149$	−188.884	−0.103852	−0.0519262	+	0.998651i	$0.516536\pi$
$150$	−290.767	−0.158274
$151$	−1065.99	−0.574497	−0.287248	−	0.957856i	$-0.592740\pi$
$151$	−1065.99	−0.574497	−0.287248	+	0.957856i	$0.592740\pi$
$152$	525.413	0.280373
$153$	−1357.59	−0.717349
$154$	0	0
$155$	−1463.94	−0.758620
$156$	674.293	0.346068
$157$	1784.01	0.906874	0.453437	−	0.891288i	$-0.350198\pi$
$157$	1784.01	0.906874	0.453437	+	0.891288i	$0.350198\pi$
$158$	65.9785	0.0332213
$159$	2603.60	1.29861
$160$	−450.644	−0.222666
$161$	−1317.13	−0.644747
$162$	−406.898	−0.197339
$163$	−941.444	−0.452390	−0.226195	−	0.974082i	$-0.572629\pi$
$163$	−941.444	−0.452390	−0.226195	+	0.974082i	$0.572629\pi$
$164$	−2412.23	−1.14856
$165$	0	0
$166$	−539.823	−0.252400
$167$	−2534.00	−1.17417	−0.587087	−	0.809524i	$-0.699725\pi$
$167$	−2534.00	−1.17417	−0.587087	+	0.809524i	$0.699725\pi$
$168$	1323.86	0.607965
$169$	169.000	0.0769231
$170$	190.836	0.0860968
$171$	−1267.56	−0.566857
$172$	−2923.28	−1.29592
$173$	−745.890	−0.327798	−0.163899	−	0.986477i	$-0.552407\pi$
$173$	−745.890	−0.327798	−0.163899	+	0.986477i	$0.552407\pi$
$174$	−210.122	−0.0915476
$175$	2673.95	1.15504
$176$	0	0
$177$	4913.40	2.08652
$178$	−160.729	−0.0676808
$179$	600.188	0.250616	0.125308	−	0.992118i	$-0.460008\pi$
$179$	600.188	0.250616	0.125308	+	0.992118i	$0.460008\pi$
$180$	721.650	0.298826
$181$	2782.12	1.14250	0.571252	−	0.820775i	$-0.306458\pi$
$181$	2782.12	1.14250	0.571252	+	0.820775i	$0.306458\pi$
$182$	163.740	0.0666880
$183$	−6046.60	−2.44250
$184$	−339.925	−0.136194
$185$	1257.27	0.499655
$186$	825.152	0.325286
$187$	0	0
$188$	3918.29	1.52006
$189$	1794.74	0.690729
$190$	178.181	0.0680346
$191$	66.0343	0.0250161	0.0125081	−	0.999922i	$-0.496018\pi$
$191$	66.0343	0.0250161	0.0125081	+	0.999922i	$0.496018\pi$
$192$	−2892.53	−1.08724
$193$	3191.62	1.19035	0.595176	−	0.803595i	$-0.297082\pi$
$193$	3191.62	1.19035	0.595176	+	0.803595i	$0.297082\pi$
$194$	319.994	0.118424
$195$	463.377	0.170170
$196$	−3334.51	−1.21520
$197$	2042.32	0.738626	0.369313	−	0.929305i	$-0.379593\pi$
$197$	2042.32	0.738626	0.369313	+	0.929305i	$0.379593\pi$
$198$	0	0
$199$	5176.41	1.84395	0.921974	−	0.387251i	$-0.126575\pi$
$199$	5176.41	1.84395	0.921974	+	0.387251i	$0.126575\pi$
$200$	690.095	0.243985
$201$	1570.08	0.550969
$202$	689.587	0.240194
$203$	1932.32	0.668089
$204$	4073.56	1.39807
$205$	−1657.69	−0.564772
$206$	201.314	0.0680884
$207$	820.070	0.275356
$208$	−768.337	−0.256128
$209$	0	0
$210$	448.954	0.147527
$211$	−865.256	−0.282307	−0.141153	−	0.989988i	$-0.545081\pi$
$211$	−865.256	−0.282307	−0.141153	+	0.989988i	$0.545081\pi$
$212$	−3049.38	−0.987889
$213$	2241.88	0.721180
$214$	−429.738	−0.137272
$215$	−2008.89	−0.637234
$216$	463.187	0.145907
$217$	−7588.25	−2.37384
$218$	42.9353	0.0133392
$219$	3142.33	0.969583
$220$	0	0
$221$	1020.97	0.310759
$222$	−708.663	−0.214245
$223$	−2582.37	−0.775462	−0.387731	−	0.921773i	$-0.626741\pi$
$223$	−2582.37	−0.775462	−0.387731	+	0.921773i	$0.626741\pi$
$224$	−2335.89	−0.696756
$225$	−1664.85	−0.493289
$226$	916.863	0.269862
$227$	648.168	0.189517	0.0947587	−	0.995500i	$-0.469792\pi$
$227$	648.168	0.189517	0.0947587	+	0.995500i	$0.469792\pi$
$228$	3803.42	1.10477
$229$	−6528.01	−1.88377	−0.941884	−	0.335939i	$-0.890946\pi$
$229$	−6528.01	−1.88377	−0.941884	+	0.335939i	$0.890946\pi$
$230$	−115.277	−0.0330485
$231$	0	0
$232$	498.694	0.141124
$233$	−1331.88	−0.374481	−0.187241	−	0.982314i	$-0.559954\pi$
$233$	−1331.88	−0.374481	−0.187241	+	0.982314i	$0.559954\pi$
$234$	−101.948	−0.0284809
$235$	2692.67	0.747448
$236$	−5754.65	−1.58727
$237$	967.836	0.265265
$238$	989.190	0.269410
$239$	−3934.89	−1.06497	−0.532483	−	0.846441i	$-0.678741\pi$
$239$	−3934.89	−1.06497	−0.532483	+	0.846441i	$0.678741\pi$
$240$	−2106.68	−0.566608
$241$	5733.57	1.53250	0.766249	−	0.642544i	$-0.222121\pi$
$241$	5733.57	1.53250	0.766249	+	0.642544i	$0.222121\pi$
$242$	0	0
$243$	−4223.40	−1.11494
$244$	7081.87	1.85808
$245$	−2291.49	−0.597541
$246$	934.365	0.242166
$247$	953.262	0.245565
$248$	−1958.38	−0.501441
$249$	−7918.64	−2.01535
$250$	537.768	0.136046
$251$	−2427.49	−0.610445	−0.305223	−	0.952281i	$-0.598731\pi$
$251$	−2427.49	−0.610445	−0.305223	+	0.952281i	$0.598731\pi$
$252$	3740.64	0.935073
$253$	0	0
$254$	160.593	0.0396712
$255$	2799.37	0.687463
$256$	3082.42	0.752545
$257$	−625.909	−0.151919	−0.0759594	−	0.997111i	$-0.524202\pi$
$257$	−625.909	−0.151919	−0.0759594	+	0.997111i	$0.524202\pi$
$258$	1132.32	0.273237
$259$	6516.99	1.56350
$260$	−542.714	−0.129453
$261$	−1203.10	−0.285325
$262$	359.216	0.0847039
$263$	−6051.97	−1.41894	−0.709469	−	0.704737i	$-0.751065\pi$
$263$	−6051.97	−1.41894	−0.709469	+	0.704737i	$0.751065\pi$
$264$	0	0
$265$	−2095.55	−0.485768
$266$	923.592	0.212891
$267$	−2357.73	−0.540416
$268$	−1838.90	−0.419137
$269$	2859.04	0.648026	0.324013	−	0.946053i	$-0.394968\pi$
$269$	2859.04	0.648026	0.324013	+	0.946053i	$0.394968\pi$
$270$	157.078	0.0354054
$271$	−217.644	−0.0487857	−0.0243929	−	0.999702i	$-0.507765\pi$
$271$	−217.644	−0.0487857	−0.0243929	+	0.999702i	$0.507765\pi$
$272$	−4641.70	−1.03472
$273$	2401.89	0.532488
$274$	68.8036	0.0151700
$275$	0	0
$276$	−2460.69	−0.536652
$277$	−1093.12	−0.237109	−0.118555	−	0.992948i	$-0.537826\pi$
$277$	−1093.12	−0.237109	−0.118555	+	0.992948i	$0.537826\pi$
$278$	−86.2619	−0.0186102
$279$	4724.59	1.01381
$280$	−1065.53	−0.227420
$281$	−8732.09	−1.85378	−0.926892	−	0.375329i	$-0.877530\pi$
$281$	−8732.09	−1.85378	−0.926892	+	0.375329i	$0.877530\pi$
$282$	−1517.73	−0.320495
$283$	5378.63	1.12978	0.564888	−	0.825168i	$-0.308919\pi$
$283$	5378.63	1.12978	0.564888	+	0.825168i	$0.308919\pi$
$284$	−2625.73	−0.548621
$285$	2613.72	0.543241
$286$	0	0
$287$	−8592.59	−1.76726
$288$	1454.37	0.297568
$289$	1254.90	0.255425
$290$	169.119	0.0342449
$291$	4693.97	0.945586
$292$	−3680.34	−0.737588
$293$	−1671.91	−0.333359	−0.166680	−	0.986011i	$-0.553305\pi$
$293$	−1671.91	−0.333359	−0.166680	+	0.986011i	$0.553305\pi$
$294$	1291.60	0.256217
$295$	−3954.62	−0.780497
$296$	1681.91	0.330267
$297$	0	0
$298$	−85.6901	−0.0166574
$299$	−616.730	−0.119286
$300$	4995.53	0.961390
$301$	−10413.0	−1.99401
$302$	−483.602	−0.0921462
$303$	10115.5	1.91789
$304$	−4333.89	−0.817649
$305$	4866.69	0.913659
$306$	−615.889	−0.115059
$307$	−3955.81	−0.735408	−0.367704	−	0.929943i	$-0.619856\pi$
$307$	−3955.81	−0.735408	−0.367704	+	0.929943i	$0.619856\pi$
$308$	0	0
$309$	2953.07	0.543670
$310$	−664.136	−0.121679
$311$	7107.61	1.29593	0.647967	−	0.761668i	$-0.275619\pi$
$311$	7107.61	1.29593	0.647967	+	0.761668i	$0.275619\pi$
$312$	619.883	0.112481
$313$	2743.42	0.495423	0.247711	−	0.968834i	$-0.420322\pi$
$313$	2743.42	0.495423	0.247711	+	0.968834i	$0.420322\pi$
$314$	809.341	0.145458
$315$	2570.59	0.459797
$316$	−1133.55	−0.201794
$317$	3143.16	0.556901	0.278451	−	0.960451i	$-0.410179\pi$
$317$	3143.16	0.556901	0.278451	+	0.960451i	$0.410179\pi$
$318$	1181.16	0.208290
$319$	0	0
$320$	2328.09	0.406701
$321$	−6303.80	−1.09609
$322$	−597.534	−0.103414
$323$	5758.88	0.992051
$324$	6990.72	1.19868
$325$	1252.04	0.213695
$326$	−427.100	−0.0725609
$327$	629.817	0.106511
$328$	−2217.58	−0.373309
$329$	13957.3	2.33888
$330$	0	0
$331$	−10264.1	−1.70443	−0.852215	−	0.523191i	$-0.824741\pi$
$331$	−10264.1	−1.70443	−0.852215	+	0.523191i	$0.824741\pi$
$332$	9274.43	1.53313
$333$	−4057.61	−0.667734
$334$	−1149.59	−0.188331
$335$	−1263.70	−0.206099
$336$	−10919.9	−1.77301
$337$	6861.92	1.10918	0.554588	−	0.832125i	$-0.312876\pi$
$337$	6861.92	1.10918	0.554588	+	0.832125i	$0.312876\pi$
$338$	76.6693	0.0123380
$339$	13449.4	2.15479
$340$	−3278.66	−0.522971
$341$	0	0
$342$	−575.046	−0.0909209
$343$	−2354.90	−0.370707
$344$	−2687.40	−0.421206
$345$	−1691.00	−0.263884
$346$	−338.384	−0.0525770
$347$	1149.36	0.177813	0.0889063	−	0.996040i	$-0.471663\pi$
$347$	1149.36	0.177813	0.0889063	+	0.996040i	$0.471663\pi$
$348$	3610.00	0.556081
$349$	−9973.96	−1.52978	−0.764891	−	0.644160i	$-0.777207\pi$
$349$	−9973.96	−1.52978	−0.764891	+	0.644160i	$0.777207\pi$
$350$	1213.07	0.185262
$351$	840.364	0.127793
$352$	0	0
$353$	2486.72	0.374943	0.187472	−	0.982270i	$-0.439971\pi$
$353$	2486.72	0.374943	0.187472	+	0.982270i	$0.439971\pi$
$354$	2229.03	0.334666
$355$	−1804.41	−0.269770
$356$	2761.41	0.411109
$357$	14510.4	2.15118
$358$	272.284	0.0401974
$359$	231.647	0.0340553	0.0170276	−	0.999855i	$-0.494580\pi$
$359$	231.647	0.0340553	0.0170276	+	0.999855i	$0.494580\pi$
$360$	663.419	0.0971257
$361$	−1482.03	−0.216071
$362$	1262.15	0.183251
$363$	0	0
$364$	−2813.14	−0.405078
$365$	−2529.14	−0.362689
$366$	−2743.13	−0.391764
$367$	2747.28	0.390754	0.195377	−	0.980728i	$-0.437407\pi$
$367$	2747.28	0.390754	0.195377	+	0.980728i	$0.437407\pi$
$368$	2803.89	0.397181
$369$	5349.91	0.754757
$370$	570.377	0.0801419
$371$	−10862.2	−1.52004
$372$	−14176.5	−1.97586
$373$	11569.0	1.60595	0.802974	−	0.596015i	$-0.203250\pi$
$373$	11569.0	1.60595	0.802974	+	0.596015i	$0.203250\pi$
$374$	0	0
$375$	7888.49	1.08629
$376$	3602.12	0.494056
$377$	904.785	0.123604
$378$	814.208	0.110789
$379$	3408.39	0.461945	0.230972	−	0.972960i	$-0.425809\pi$
$379$	3408.39	0.461945	0.230972	+	0.972960i	$0.425809\pi$
$380$	−3061.23	−0.413258
$381$	2355.73	0.316766
$382$	29.9574	0.00401245
$383$	−7031.38	−0.938085	−0.469043	−	0.883175i	$-0.655401\pi$
$383$	−7031.38	−0.938085	−0.469043	+	0.883175i	$0.655401\pi$
$384$	−5791.44	−0.769644
$385$	0	0
$386$	1447.93	0.190926
$387$	6483.35	0.851594
$388$	−5497.65	−0.719333
$389$	−11318.6	−1.47527	−0.737633	−	0.675202i	$-0.764056\pi$
$389$	−11318.6	−1.47527	−0.737633	+	0.675202i	$0.764056\pi$
$390$	210.218	0.0272943
$391$	−3725.81	−0.481898
$392$	−3065.44	−0.394969
$393$	5269.32	0.676341
$394$	926.528	0.118472
$395$	−778.977	−0.0992268
$396$	0	0
$397$	8467.04	1.07040	0.535200	−	0.844726i	$-0.320236\pi$
$397$	8467.04	1.07040	0.535200	+	0.844726i	$0.320236\pi$
$398$	2348.35	0.295759
$399$	13548.1	1.69989
$400$	−5692.27	−0.711533
$401$	−1295.65	−0.161351	−0.0806755	−	0.996740i	$-0.525708\pi$
$401$	−1295.65	−0.161351	−0.0806755	+	0.996740i	$0.525708\pi$
$402$	712.289	0.0883725
$403$	−3553.11	−0.439189
$404$	−11847.5	−1.45899
$405$	4804.05	0.589421
$406$	876.623	0.107158
$407$	0	0
$408$	3744.86	0.454407
$409$	−10618.4	−1.28373	−0.641865	−	0.766817i	$-0.721839\pi$
$409$	−10618.4	−1.28373	−0.641865	+	0.766817i	$0.721839\pi$
$410$	−752.037	−0.0905865
$411$	1009.28	0.121129
$412$	−3458.68	−0.413584
$413$	−20498.6	−2.44230
$414$	372.036	0.0441657
$415$	6373.43	0.753877
$416$	−1093.75	−0.128908
$417$	−1265.37	−0.148598
$418$	0	0
$419$	6836.68	0.797121	0.398561	−	0.917142i	$-0.369510\pi$
$419$	6836.68	0.797121	0.398561	+	0.917142i	$0.369510\pi$
$420$	−7713.26	−0.896116
$421$	7179.09	0.831086	0.415543	−	0.909573i	$-0.363592\pi$
$421$	7179.09	0.831086	0.415543	+	0.909573i	$0.363592\pi$
$422$	−392.536	−0.0452805
$423$	−8690.11	−0.998883
$424$	−2803.32	−0.321088
$425$	7563.89	0.863300
$426$	1017.06	0.115673
$427$	25226.3	2.85898
$428$	7383.11	0.833823
$429$	0	0
$430$	−911.363	−0.102209
$431$	8276.69	0.924998	0.462499	−	0.886620i	$-0.346953\pi$
$431$	8276.69	0.924998	0.462499	+	0.886620i	$0.346953\pi$
$432$	−3820.61	−0.425508
$433$	15647.8	1.73668	0.868342	−	0.495966i	$-0.165186\pi$
$433$	15647.8	1.73668	0.868342	+	0.495966i	$0.165186\pi$
$434$	−3442.52	−0.380752
$435$	2480.81	0.273438
$436$	−737.651	−0.0810254
$437$	−3478.73	−0.380801
$438$	1425.56	0.155516
$439$	−4861.37	−0.528520	−0.264260	−	0.964451i	$-0.585128\pi$
$439$	−4861.37	−0.528520	−0.264260	+	0.964451i	$0.585128\pi$
$440$	0	0
$441$	7395.36	0.798549
$442$	463.177	0.0498441
$443$	−1659.80	−0.178012	−0.0890061	−	0.996031i	$-0.528369\pi$
$443$	−1659.80	−0.178012	−0.0890061	+	0.996031i	$0.528369\pi$
$444$	12175.2	1.30137
$445$	1897.66	0.202152
$446$	−1171.53	−0.124380
$447$	−1256.98	−0.133005
$448$	12067.6	1.27263
$449$	−1030.81	−0.108345	−0.0541724	−	0.998532i	$-0.517252\pi$
$449$	−1030.81	−0.108345	−0.0541724	+	0.998532i	$0.517252\pi$
$450$	−755.284	−0.0791210
$451$	0	0
$452$	−15752.2	−1.63920
$453$	−7093.93	−0.735766
$454$	294.051	0.0303976
$455$	−1933.20	−0.199186
$456$	3496.51	0.359077
$457$	4199.41	0.429847	0.214923	−	0.976631i	$-0.431050\pi$
$457$	4199.41	0.429847	0.214923	+	0.976631i	$0.431050\pi$
$458$	−2961.52	−0.302146
$459$	5076.83	0.516267
$460$	1980.52	0.200744
$461$	−5550.99	−0.560815	−0.280407	−	0.959881i	$-0.590470\pi$
$461$	−5550.99	−0.560815	−0.280407	+	0.959881i	$0.590470\pi$
$462$	0	0
$463$	−1984.25	−0.199171	−0.0995853	−	0.995029i	$-0.531752\pi$
$463$	−1984.25	−0.199171	−0.0995853	+	0.995029i	$0.531752\pi$
$464$	−4113.49	−0.411560
$465$	−9742.18	−0.971576
$466$	−604.225	−0.0600648
$467$	8682.92	0.860381	0.430190	−	0.902738i	$-0.358446\pi$
$467$	8682.92	0.860381	0.430190	+	0.902738i	$0.358446\pi$
$468$	1751.51	0.172999
$469$	−6550.34	−0.644918
$470$	1221.57	0.119887
$471$	11872.2	1.16145
$472$	−5290.29	−0.515901
$473$	0	0
$474$	439.073	0.0425470
$475$	7062.29	0.682189
$476$	−16994.8	−1.63646
$477$	6763.01	0.649176
$478$	−1785.12	−0.170815
$479$	−4654.14	−0.443952	−0.221976	−	0.975052i	$-0.571251\pi$
$479$	−4654.14	−0.443952	−0.221976	+	0.975052i	$0.571251\pi$
$480$	−2998.94	−0.285171
$481$	3051.51	0.289265
$482$	2601.12	0.245804
$483$	−8765.21	−0.825736
$484$	0	0
$485$	−3778.01	−0.353713
$486$	−1916.01	−0.178831
$487$	3041.03	0.282961	0.141481	−	0.989941i	$-0.454814\pi$
$487$	3041.03	0.282961	0.141481	+	0.989941i	$0.454814\pi$
$488$	6510.42	0.603920
$489$	−6265.11	−0.579382
$490$	−1039.57	−0.0958424
$491$	18798.6	1.72784	0.863921	−	0.503628i	$-0.168002\pi$
$491$	18798.6	1.72784	0.863921	+	0.503628i	$0.168002\pi$
$492$	−16052.9	−1.47097
$493$	5466.01	0.499345
$494$	432.461	0.0393873
$495$	0	0
$496$	16153.8	1.46235
$497$	−9353.09	−0.844152
$498$	−3592.40	−0.323252
$499$	791.590	0.0710149	0.0355075	−	0.999369i	$-0.488695\pi$
$499$	791.590	0.0710149	0.0355075	+	0.999369i	$0.488695\pi$
$500$	−9239.12	−0.826372
$501$	−16863.2	−1.50378
$502$	−1101.27	−0.0979121
$503$	9524.31	0.844270	0.422135	−	0.906533i	$-0.361281\pi$
$503$	9524.31	0.844270	0.422135	+	0.906533i	$0.361281\pi$
$504$	3438.80	0.303922
$505$	−8141.63	−0.717421
$506$	0	0
$507$	1124.66	0.0985165
$508$	−2759.07	−0.240972
$509$	−18628.4	−1.62218	−0.811091	−	0.584920i	$-0.801126\pi$
$509$	−18628.4	−1.62218	−0.811091	+	0.584920i	$0.801126\pi$
$510$	1269.97	0.110265
$511$	−13109.7	−1.13491
$512$	8360.52	0.721653
$513$	4740.16	0.407959
$514$	−283.953	−0.0243670
$515$	−2376.82	−0.203369
$516$	−19453.8	−1.65970
$517$	0	0
$518$	2956.53	0.250777
$519$	−4963.74	−0.419815
$520$	−498.921	−0.0420753
$521$	−16166.3	−1.35942	−0.679711	−	0.733480i	$-0.737895\pi$
$521$	−16166.3	−1.35942	−0.679711	+	0.733480i	$0.737895\pi$
$522$	−545.803	−0.0457646
$523$	18862.1	1.57702	0.788510	−	0.615022i	$-0.210853\pi$
$523$	18862.1	1.57702	0.788510	+	0.615022i	$0.210853\pi$
$524$	−6171.51	−0.514511
$525$	17794.5	1.47927
$526$	−2745.57	−0.227590
$527$	−21465.2	−1.77426
$528$	0	0
$529$	−9916.37	−0.815022
$530$	−950.676	−0.0779145
$531$	12762.8	1.04305
$532$	−15867.8	−1.29315
$533$	−4023.38	−0.326964
$534$	−1069.62	−0.0866798
$535$	5073.71	0.410010
$536$	−1690.52	−0.136230
$537$	3994.12	0.320967
$538$	1297.05	0.103940
$539$	0	0
$540$	−2698.68	−0.215061
$541$	13053.1	1.03733	0.518664	−	0.854978i	$-0.326429\pi$
$541$	13053.1	1.03733	0.518664	+	0.854978i	$0.326429\pi$
$542$	−98.7373	−0.00782497
$543$	18514.4	1.46322
$544$	−6607.63	−0.520771
$545$	−506.917	−0.0398421
$546$	1089.65	0.0854082
$547$	13472.9	1.05313	0.526564	−	0.850135i	$-0.323480\pi$
$547$	13472.9	1.05313	0.526564	+	0.850135i	$0.323480\pi$
$548$	−1182.08	−0.0921460
$549$	−15706.4	−1.22101
$550$	0	0
$551$	5103.53	0.394588
$552$	−2262.13	−0.174425
$553$	−4037.79	−0.310496
$554$	−495.910	−0.0380311
$555$	8366.84	0.639915
$556$	1482.02	0.113043
$557$	13907.4	1.05794	0.528972	−	0.848639i	$-0.322578\pi$
$557$	13907.4	1.05794	0.528972	+	0.848639i	$0.322578\pi$
$558$	2143.38	0.162610
$559$	−4875.77	−0.368915
$560$	8789.04	0.663223
$561$	0	0
$562$	−3961.44	−0.297337
$563$	5303.13	0.396981	0.198491	−	0.980103i	$-0.436396\pi$
$563$	5303.13	0.396981	0.198491	+	0.980103i	$0.436396\pi$
$564$	26075.4	1.94676
$565$	−10825.0	−0.806034
$566$	2440.09	0.181210
$567$	24901.6	1.84439
$568$	−2413.85	−0.178315
$569$	378.295	0.0278716	0.0139358	−	0.999903i	$-0.495564\pi$
$569$	378.295	0.0278716	0.0139358	+	0.999903i	$0.495564\pi$
$570$	1185.75	0.0871329
$571$	15271.3	1.11923	0.559617	−	0.828751i	$-0.310948\pi$
$571$	15271.3	1.11923	0.559617	+	0.828751i	$0.310948\pi$
$572$	0	0
$573$	439.444	0.0320385
$574$	−3898.15	−0.283459
$575$	−4569.07	−0.331380
$576$	−7513.51	−0.543512
$577$	11644.0	0.840111	0.420055	−	0.907498i	$-0.362011\pi$
$577$	11644.0	0.840111	0.420055	+	0.907498i	$0.362011\pi$
$578$	569.306	0.0409688
$579$	21239.6	1.52450
$580$	−2905.56	−0.208012
$581$	33036.4	2.35900
$582$	2129.49	0.151667
$583$	0	0
$584$	−3383.37	−0.239734
$585$	1203.65	0.0850678
$586$	−758.488	−0.0534690
$587$	−10313.3	−0.725170	−0.362585	−	0.931951i	$-0.618106\pi$
$587$	−10313.3	−0.725170	−0.362585	+	0.931951i	$0.618106\pi$
$588$	−22190.4	−1.55632
$589$	−20041.7	−1.40204
$590$	−1794.07	−0.125188
$591$	13591.2	0.945969
$592$	−13873.3	−0.963157
$593$	−16503.8	−1.14288	−0.571441	−	0.820643i	$-0.693615\pi$
$593$	−16503.8	−1.14288	−0.571441	+	0.820643i	$0.693615\pi$
$594$	0	0
$595$	−11678.9	−0.804686
$596$	1472.20	0.101181
$597$	34447.9	2.36157
$598$	−279.788	−0.0191328
$599$	−7924.92	−0.540573	−0.270287	−	0.962780i	$-0.587118\pi$
$599$	−7924.92	−0.540573	−0.270287	+	0.962780i	$0.587118\pi$
$600$	4592.43	0.312475
$601$	−15799.8	−1.07236	−0.536180	−	0.844104i	$-0.680133\pi$
$601$	−15799.8	−1.07236	−0.536180	+	0.844104i	$0.680133\pi$
$602$	−4724.02	−0.319828
$603$	4078.37	0.275429
$604$	8308.52	0.559717
$605$	0	0
$606$	4589.06	0.307620
$607$	−3749.05	−0.250691	−0.125345	−	0.992113i	$-0.540004\pi$
$607$	−3749.05	−0.250691	−0.125345	+	0.992113i	$0.540004\pi$
$608$	−6169.44	−0.411519
$609$	12859.2	0.855631
$610$	2207.84	0.146546
$611$	6535.36	0.432721
$612$	10581.3	0.698894
$613$	−7004.99	−0.461548	−0.230774	−	0.973007i	$-0.574126\pi$
$613$	−7004.99	−0.461548	−0.230774	+	0.973007i	$0.574126\pi$
$614$	−1794.61	−0.117955
$615$	−11031.6	−0.723312
$616$	0	0
$617$	12326.0	0.804256	0.402128	−	0.915583i	$-0.368271\pi$
$617$	12326.0	0.804256	0.402128	+	0.915583i	$0.368271\pi$
$618$	1339.70	0.0872017
$619$	−13557.3	−0.880312	−0.440156	−	0.897921i	$-0.645077\pi$
$619$	−13557.3	−0.880312	−0.440156	+	0.897921i	$0.645077\pi$
$620$	11410.2	0.739104
$621$	−3066.73	−0.198170
$622$	3224.47	0.207861
$623$	9836.42	0.632565
$624$	−5113.12	−0.328027
$625$	5689.73	0.364143
$626$	1244.59	0.0794631
$627$	0	0
$628$	−13904.9	−0.883544
$629$	18434.9	1.16859
$630$	1166.18	0.0737490
$631$	−10971.4	−0.692177	−0.346089	−	0.938202i	$-0.612490\pi$
$631$	−10971.4	−0.692177	−0.346089	+	0.938202i	$0.612490\pi$
$632$	−1042.08	−0.0655880
$633$	−5758.10	−0.361554
$634$	1425.94	0.0893239
$635$	−1896.04	−0.118492
$636$	−20293.0	−1.26520
$637$	−5561.65	−0.345935
$638$	0	0
$639$	5823.42	0.360518
$640$	4661.32	0.287898
$641$	6770.60	0.417196	0.208598	−	0.978001i	$-0.433110\pi$
$641$	6770.60	0.417196	0.208598	+	0.978001i	$0.433110\pi$
$642$	−2859.81	−0.175807
$643$	25384.1	1.55684	0.778421	−	0.627742i	$-0.216021\pi$
$643$	25384.1	1.55684	0.778421	+	0.627742i	$0.216021\pi$
$644$	10265.9	0.628160
$645$	−13368.8	−0.816115
$646$	2612.60	0.159120
$647$	−30086.3	−1.82815	−0.914077	−	0.405541i	$-0.867083\pi$
$647$	−30086.3	−1.82815	−0.914077	+	0.405541i	$0.867083\pi$
$648$	6426.63	0.389602
$649$	0	0
$650$	568.008	0.0342756
$651$	−50498.2	−3.04021
$652$	7337.79	0.440752
$653$	32193.5	1.92929	0.964647	−	0.263545i	$-0.0848917\pi$
$653$	32193.5	1.92929	0.964647	+	0.263545i	$0.0848917\pi$
$654$	285.725	0.0170837
$655$	−4241.09	−0.252997
$656$	18291.8	1.08868
$657$	8162.37	0.484694
$658$	6331.95	0.375144
$659$	26788.6	1.58352	0.791758	−	0.610835i	$-0.209166\pi$
$659$	26788.6	1.58352	0.791758	+	0.610835i	$0.209166\pi$
$660$	0	0
$661$	−32586.1	−1.91748	−0.958739	−	0.284286i	$-0.908243\pi$
$661$	−32586.1	−1.91748	−0.958739	+	0.284286i	$0.908243\pi$
$662$	−4656.46	−0.273381
$663$	6794.32	0.397994
$664$	8526.06	0.498306
$665$	−10904.4	−0.635872
$666$	−1840.79	−0.107101
$667$	−3301.82	−0.191675
$668$	19750.5	1.14397
$669$	−17185.1	−0.993145
$670$	−573.296	−0.0330572
$671$	0	0
$672$	−15544.9	−0.892346
$673$	5814.89	0.333057	0.166529	−	0.986037i	$-0.446744\pi$
$673$	5814.89	0.333057	0.166529	+	0.986037i	$0.446744\pi$
$674$	3113.01	0.177906
$675$	6225.88	0.355014
$676$	−1317.22	−0.0749441
$677$	−17002.5	−0.965230	−0.482615	−	0.875833i	$-0.660313\pi$
$677$	−17002.5	−0.965230	−0.482615	+	0.875833i	$0.660313\pi$
$678$	6101.52	0.345616
$679$	−19583.2	−1.10682
$680$	−3014.10	−0.169979
$681$	4313.42	0.242718
$682$	0	0
$683$	−13386.1	−0.749936	−0.374968	−	0.927038i	$-0.622346\pi$
$683$	−13386.1	−0.749936	−0.374968	+	0.927038i	$0.622346\pi$
$684$	9879.59	0.552274
$685$	−812.331	−0.0453103
$686$	−1068.33	−0.0594594
$687$	−43442.5	−2.41257
$688$	22167.1	1.22836
$689$	−5086.09	−0.281226
$690$	−767.144	−0.0423256
$691$	−12976.3	−0.714386	−0.357193	−	0.934031i	$-0.616266\pi$
$691$	−12976.3	−0.714386	−0.357193	+	0.934031i	$0.616266\pi$
$692$	5813.61	0.319364
$693$	0	0
$694$	521.425	0.0285202
$695$	1018.45	0.0555858
$696$	3318.70	0.180740
$697$	−24306.2	−1.32089
$698$	−4524.83	−0.245369
$699$	−8863.36	−0.479604
$700$	−20841.3	−1.12532
$701$	19414.7	1.04605	0.523026	−	0.852316i	$-0.324803\pi$
$701$	19414.7	1.04605	0.523026	+	0.852316i	$0.324803\pi$
$702$	381.243	0.0204973
$703$	17212.3	0.923436
$704$	0	0
$705$	17919.1	0.957267
$706$	1128.14	0.0601389
$707$	−42201.8	−2.24492
$708$	−38295.9	−2.03284
$709$	14686.7	0.777954	0.388977	−	0.921247i	$-0.372829\pi$
$709$	14686.7	0.777954	0.388977	+	0.921247i	$0.372829\pi$
$710$	−818.597	−0.0432696
$711$	2514.01	0.132606
$712$	2538.59	0.133620
$713$	12966.3	0.681056
$714$	6582.85	0.345038
$715$	0	0
$716$	−4677.98	−0.244168
$717$	−26185.9	−1.36392
$718$	105.090	0.00546228
$719$	−34870.4	−1.80869	−0.904343	−	0.426807i	$-0.859638\pi$
$719$	−34870.4	−1.80869	−0.904343	+	0.426807i	$0.859638\pi$
$720$	−5472.23	−0.283247
$721$	−12320.1	−0.636374
$722$	−672.344	−0.0346566
$723$	38155.7	1.96269
$724$	−21684.4	−1.11311
$725$	6703.14	0.343377
$726$	0	0
$727$	−33713.2	−1.71988	−0.859941	−	0.510394i	$-0.829500\pi$
$727$	−33713.2	−1.71988	−0.859941	+	0.510394i	$0.829500\pi$
$728$	−2586.14	−0.131660
$729$	−3889.16	−0.197590
$730$	−1147.38	−0.0581734
$731$	−29455.7	−1.49037
$732$	47128.3	2.37966
$733$	14895.1	0.750566	0.375283	−	0.926910i	$-0.377546\pi$
$733$	14895.1	0.750566	0.375283	+	0.926910i	$0.377546\pi$
$734$	1246.34	0.0626748
$735$	−15249.3	−0.765280
$736$	3991.43	0.199899
$737$	0	0
$738$	2427.07	0.121059
$739$	−26805.4	−1.33431	−0.667154	−	0.744920i	$-0.732488\pi$
$739$	−26805.4	−1.33431	−0.667154	+	0.744920i	$0.732488\pi$
$740$	−9799.37	−0.486800
$741$	6343.75	0.314499
$742$	−4927.79	−0.243807
$743$	−9229.50	−0.455717	−0.227858	−	0.973694i	$-0.573172\pi$
$743$	−9229.50	−0.455717	−0.227858	+	0.973694i	$0.573172\pi$
$744$	−13032.6	−0.642203
$745$	1011.70	0.0497529
$746$	5248.43	0.257585
$747$	−20569.1	−1.00748
$748$	0	0
$749$	26299.3	1.28299
$750$	3578.73	0.174236
$751$	11269.0	0.547554	0.273777	−	0.961793i	$-0.411727\pi$
$751$	11269.0	0.547554	0.273777	+	0.961793i	$0.411727\pi$
$752$	−29712.2	−1.44081
$753$	−16154.4	−0.781806
$754$	410.469	0.0198254
$755$	5709.65	0.275226
$756$	−13988.5	−0.672959
$757$	10487.5	0.503535	0.251768	−	0.967788i	$-0.418988\pi$
$757$	10487.5	0.503535	0.251768	+	0.967788i	$0.418988\pi$
$758$	1546.26	0.0740935
$759$	0	0
$760$	−2814.22	−0.134319
$761$	1173.99	0.0559227	0.0279613	−	0.999609i	$-0.491098\pi$
$761$	1173.99	0.0559227	0.0279613	+	0.999609i	$0.491098\pi$
$762$	1068.71	0.0508075
$763$	−2627.58	−0.124672
$764$	−514.684	−0.0243725
$765$	7271.51	0.343663
$766$	−3189.89	−0.150464
$767$	−9598.23	−0.451854
$768$	20512.9	0.963795
$769$	−23092.5	−1.08288	−0.541441	−	0.840739i	$-0.682121\pi$
$769$	−23092.5	−1.08288	−0.541441	+	0.840739i	$0.682121\pi$
$770$	0	0
$771$	−4165.29	−0.194565
$772$	−24876.1	−1.15973
$773$	33139.3	1.54196	0.770981	−	0.636859i	$-0.219767\pi$
$773$	33139.3	1.54196	0.770981	+	0.636859i	$0.219767\pi$
$774$	2941.26	0.136591
$775$	−26323.4	−1.22008
$776$	−5054.04	−0.233801
$777$	43369.2	2.00239
$778$	−5134.87	−0.236625
$779$	−22694.3	−1.04378
$780$	−3611.64	−0.165792
$781$	0	0
$782$	−1690.27	−0.0772939
$783$	4499.10	0.205345
$784$	25285.4	1.15185
$785$	−9555.50	−0.434459
$786$	2390.50	0.108482
$787$	23666.0	1.07192	0.535960	−	0.844243i	$-0.319950\pi$
$787$	23666.0	1.07192	0.535960	+	0.844243i	$0.319950\pi$
$788$	−15918.2	−0.719624
$789$	−40274.6	−1.81725
$790$	−353.394	−0.0159154
$791$	−56110.7	−2.52221
$792$	0	0
$793$	11811.9	0.528945
$794$	3841.19	0.171686
$795$	−13945.4	−0.622130
$796$	−40345.9	−1.79651
$797$	8982.04	0.399197	0.199599	−	0.979878i	$-0.436036\pi$
$797$	8982.04	0.399197	0.199599	+	0.979878i	$0.436036\pi$
$798$	6146.30	0.272653
$799$	39481.6	1.74813
$800$	−8103.14	−0.358111
$801$	−6124.35	−0.270154
$802$	−587.791	−0.0258798
$803$	0	0
$804$	−12237.5	−0.536795
$805$	7054.80	0.308881
$806$	−1611.92	−0.0704435
$807$	19026.3	0.829936
$808$	−10891.5	−0.474209
$809$	1287.28	0.0559436	0.0279718	−	0.999609i	$-0.491095\pi$
$809$	1287.28	0.0559436	0.0279718	+	0.999609i	$0.491095\pi$
$810$	2179.43	0.0945399
$811$	−20428.0	−0.884494	−0.442247	−	0.896893i	$-0.645819\pi$
$811$	−20428.0	−0.884494	−0.442247	+	0.896893i	$0.645819\pi$
$812$	−15060.8	−0.650901
$813$	−1448.37	−0.0624806
$814$	0	0
$815$	5042.56	0.216728
$816$	−30889.6	−1.32518
$817$	−27502.3	−1.17770
$818$	−4817.19	−0.205904
$819$	6239.05	0.266191
$820$	12920.4	0.550243
$821$	−28518.2	−1.21229	−0.606146	−	0.795353i	$-0.707285\pi$
$821$	−28518.2	−1.21229	−0.606146	+	0.795353i	$0.707285\pi$
$822$	457.873	0.0194284
$823$	29722.3	1.25888	0.629438	−	0.777050i	$-0.283285\pi$
$823$	29722.3	1.25888	0.629438	+	0.777050i	$0.283285\pi$
$824$	−3179.59	−0.134425
$825$	0	0
$826$	−9299.48	−0.391732
$827$	27923.0	1.17410	0.587049	−	0.809551i	$-0.300290\pi$
$827$	27923.0	1.17410	0.587049	+	0.809551i	$0.300290\pi$
$828$	−6391.78	−0.268272
$829$	−22210.6	−0.930526	−0.465263	−	0.885173i	$-0.654040\pi$
$829$	−22210.6	−0.930526	−0.465263	+	0.885173i	$0.654040\pi$
$830$	2891.40	0.120918
$831$	−7274.49	−0.303669
$832$	5650.50	0.235452
$833$	−33599.2	−1.39753
$834$	−574.054	−0.0238344
$835$	13572.6	0.562515
$836$	0	0
$837$	−17668.1	−0.729628
$838$	3101.56	0.127854
$839$	13387.3	0.550871	0.275435	−	0.961320i	$-0.411178\pi$
$839$	13387.3	0.550871	0.275435	+	0.961320i	$0.411178\pi$
$840$	−7090.86	−0.291260
$841$	−19545.0	−0.801386
$842$	3256.90	0.133302
$843$	−58110.2	−2.37417
$844$	6743.97	0.275044
$845$	−905.198	−0.0368518
$846$	−3942.39	−0.160215
$847$	0	0
$848$	23123.3	0.936388
$849$	35793.7	1.44692
$850$	3431.47	0.138469
$851$	−11135.8	−0.448568
$852$	−17473.7	−0.702626
$853$	−14078.2	−0.565096	−0.282548	−	0.959253i	$-0.591180\pi$
$853$	−14078.2	−0.565096	−0.282548	+	0.959253i	$0.591180\pi$
$854$	11444.3	0.458566
$855$	6789.29	0.271566
$856$	6787.36	0.271013
$857$	−32491.5	−1.29508	−0.647542	−	0.762030i	$-0.724203\pi$
$857$	−32491.5	−1.29508	−0.647542	+	0.762030i	$0.724203\pi$
$858$	0	0
$859$	−6213.65	−0.246807	−0.123403	−	0.992357i	$-0.539381\pi$
$859$	−6213.65	−0.246807	−0.123403	+	0.992357i	$0.539381\pi$
$860$	15657.7	0.620841
$861$	−57181.8	−2.26336
$862$	3754.84	0.148365
$863$	7937.17	0.313076	0.156538	−	0.987672i	$-0.449967\pi$
$863$	7937.17	0.313076	0.156538	+	0.987672i	$0.449967\pi$
$864$	−5438.77	−0.214156
$865$	3995.13	0.157039
$866$	7098.84	0.278555
$867$	8351.12	0.327127
$868$	59144.3	2.31277
$869$	0	0
$870$	1125.45	0.0438580
$871$	−3067.12	−0.119317
$872$	−678.129	−0.0263352
$873$	12192.9	0.472698
$874$	−1578.18	−0.0610785
$875$	−32910.6	−1.27152
$876$	−24491.9	−0.944639
$877$	16319.9	0.628374	0.314187	−	0.949361i	$-0.398268\pi$
$877$	16319.9	0.628374	0.314187	+	0.949361i	$0.398268\pi$
$878$	−2205.43	−0.0847718
$879$	−11126.2	−0.426938
$880$	0	0
$881$	2347.74	0.0897814	0.0448907	−	0.998992i	$-0.485706\pi$
$881$	2347.74	0.0897814	0.0448907	+	0.998992i	$0.485706\pi$
$882$	3355.01	0.128083
$883$	−43204.4	−1.64659	−0.823297	−	0.567610i	$-0.807868\pi$
$883$	−43204.4	−1.64659	−0.823297	+	0.567610i	$0.807868\pi$
$884$	−7957.62	−0.302764
$885$	−26317.1	−0.999594
$886$	−752.991	−0.0285522
$887$	19055.8	0.721344	0.360672	−	0.932693i	$-0.382547\pi$
$887$	19055.8	0.721344	0.360672	+	0.932693i	$0.382547\pi$
$888$	11192.8	0.422978
$889$	−9828.06	−0.370779
$890$	860.899	0.0324240
$891$	0	0
$892$	20127.5	0.755512
$893$	36863.4	1.38139
$894$	−570.249	−0.0213333
$895$	−3214.73	−0.120063
$896$	24161.8	0.900880
$897$	−4104.21	−0.152771
$898$	−467.641	−0.0173779
$899$	−19022.5	−0.705712
$900$	12976.2	0.480599
$901$	−30726.3	−1.13612
$902$	0	0
$903$	−69296.4	−2.55375
$904$	−14481.1	−0.532781
$905$	−14901.6	−0.547343
$906$	−3218.27	−0.118013
$907$	−28170.6	−1.03130	−0.515650	−	0.856799i	$-0.672450\pi$
$907$	−28170.6	−1.03130	−0.515650	+	0.856799i	$0.672450\pi$
$908$	−5051.94	−0.184642
$909$	26275.7	0.958755
$910$	−877.023	−0.0319484
$911$	−26521.1	−0.964527	−0.482263	−	0.876026i	$-0.660185\pi$
$911$	−26521.1	−0.964527	−0.482263	+	0.876026i	$0.660185\pi$
$912$	−28841.1	−1.04718
$913$	0	0
$914$	1905.12	0.0689451
$915$	32386.8	1.17014
$916$	50880.5	1.83530
$917$	−21983.5	−0.791668
$918$	2303.18	0.0828064
$919$	4347.49	0.156050	0.0780252	−	0.996951i	$-0.475139\pi$
$919$	4347.49	0.156050	0.0780252	+	0.996951i	$0.475139\pi$
$920$	1820.71	0.0652467
$921$	−26325.1	−0.941847
$922$	−2518.29	−0.0899516
$923$	−4379.48	−0.156178
$924$	0	0
$925$	22607.2	0.803590
$926$	−900.185	−0.0319459
$927$	7670.75	0.271781
$928$	−5855.70	−0.207136
$929$	53264.1	1.88109	0.940547	−	0.339663i	$-0.110313\pi$
$929$	53264.1	1.88109	0.940547	+	0.339663i	$0.110313\pi$
$930$	−4419.68	−0.155835
$931$	−31371.1	−1.10435
$932$	10380.9	0.364847
$933$	47299.6	1.65972
$934$	3939.13	0.138000
$935$	0	0
$936$	1610.18	0.0562290
$937$	16296.0	0.568160	0.284080	−	0.958801i	$-0.408312\pi$
$937$	16296.0	0.568160	0.284080	+	0.958801i	$0.408312\pi$
$938$	−2971.65	−0.103441
$939$	18256.9	0.634495
$940$	−20987.2	−0.728219
$941$	29317.3	1.01564	0.507821	−	0.861463i	$-0.330451\pi$
$941$	29317.3	1.01564	0.507821	+	0.861463i	$0.330451\pi$
$942$	5385.99	0.186290
$943$	14682.5	0.507028
$944$	43637.1	1.50452
$945$	−9612.96	−0.330910
$946$	0	0
$947$	23214.8	0.796598	0.398299	−	0.917256i	$-0.369601\pi$
$947$	23214.8	0.796598	0.398299	+	0.917256i	$0.369601\pi$
$948$	−7543.50	−0.258440
$949$	−6138.47	−0.209972
$950$	3203.91	0.109420
$951$	20917.1	0.713231
$952$	−15623.5	−0.531890
$953$	13759.8	0.467707	0.233853	−	0.972272i	$-0.424866\pi$
$953$	13759.8	0.467707	0.233853	+	0.972272i	$0.424866\pi$
$954$	3068.14	0.104124
$955$	−353.693	−0.0119845
$956$	30669.3	1.03757
$957$	0	0
$958$	−2111.42	−0.0712075
$959$	−4210.69	−0.141783
$960$	15493.0	0.520868
$961$	44910.7	1.50753
$962$	1384.36	0.0463966
$963$	−16374.5	−0.547934
$964$	−44688.6	−1.49307
$965$	−17095.0	−0.570265
$966$	−3976.46	−0.132444
$967$	25212.8	0.838460	0.419230	−	0.907880i	$-0.362300\pi$
$967$	25212.8	0.838460	0.419230	+	0.907880i	$0.362300\pi$
$968$	0	0
$969$	38324.1	1.27053
$970$	−1713.95	−0.0567336
$971$	34578.2	1.14281	0.571405	−	0.820668i	$-0.306399\pi$
$971$	34578.2	1.14281	0.571405	+	0.820668i	$0.306399\pi$
$972$	32918.0	1.08626
$973$	5279.11	0.173937
$974$	1379.61	0.0453854
$975$	8332.09	0.273683
$976$	−53701.4	−1.76121
$977$	−22372.0	−0.732594	−0.366297	−	0.930498i	$-0.619375\pi$
$977$	−22372.0	−0.732594	−0.366297	+	0.930498i	$0.619375\pi$
$978$	−2842.26	−0.0929298
$979$	0	0
$980$	17860.3	0.582169
$981$	1635.98	0.0532446
$982$	8528.27	0.277136
$983$	10075.5	0.326917	0.163458	−	0.986550i	$-0.447735\pi$
$983$	10075.5	0.326917	0.163458	+	0.986550i	$0.447735\pi$
$984$	−14757.5	−0.478103
$985$	−10939.1	−0.353856
$986$	2479.74	0.0800922
$987$	92883.1	2.99544
$988$	−7429.90	−0.239248
$989$	17793.1	0.572081
$990$	0	0
$991$	−21119.4	−0.676973	−0.338487	−	0.940971i	$-0.609915\pi$
$991$	−21119.4	−0.676973	−0.338487	+	0.940971i	$0.609915\pi$
$992$	22995.4	0.735994
$993$	−68305.5	−2.18289
$994$	−4243.17	−0.135397
$995$	−27725.9	−0.883386
$996$	61719.3	1.96351
$997$	46382.8	1.47338	0.736689	−	0.676231i	$-0.236388\pi$
$997$	46382.8	1.47338	0.736689	+	0.676231i	$0.236388\pi$
$998$	359.116	0.0113904
$999$	15173.8	0.480559

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.4.a.q.1.20		38
11.5	even	5		143.4.h.b.14.10	✓	76
11.9	even	5		143.4.h.b.92.10	yes	76
11.10	odd	2		1573.4.a.r.1.19		38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.b.14.10	✓	76	11.5	even	5
143.4.h.b.92.10	yes	76	11.9	even	5
1573.4.a.q.1.20		38	1.1	even	1	trivial
1573.4.a.r.1.19		38	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:	\( N \)	\(=\)	\( 1573 = 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1573.a (trivial)

\(f(q)\)	\(=\)	\(q+0.453664 q^{2} +6.65479 q^{3} -7.79419 q^{4} -5.35620 q^{5} +3.01904 q^{6} -27.7636 q^{7} -7.16526 q^{8} +17.2862 q^{9} +O(q^{10})\)	\(q+0.453664 q^{2} +6.65479 q^{3} -7.79419 q^{4} -5.35620 q^{5} +3.01904 q^{6} -27.7636 q^{7} -7.16526 q^{8} +17.2862 q^{9} -2.42992 q^{10} -51.8687 q^{12} -13.0000 q^{13} -12.5954 q^{14} -35.6444 q^{15} +59.1029 q^{16} -78.5360 q^{17} +7.84213 q^{18} -73.3278 q^{19} +41.7472 q^{20} -184.761 q^{21} +47.4408 q^{23} -47.6833 q^{24} -96.3111 q^{25} -5.89764 q^{26} -64.6434 q^{27} +216.395 q^{28} -69.5988 q^{29} -16.1706 q^{30} +273.316 q^{31} +84.1350 q^{32} -35.6290 q^{34} +148.708 q^{35} -134.732 q^{36} -234.731 q^{37} -33.2662 q^{38} -86.5122 q^{39} +38.3786 q^{40} +309.491 q^{41} -83.8195 q^{42} +375.060 q^{43} -92.5882 q^{45} +21.5222 q^{46} -502.720 q^{47} +393.317 q^{48} +427.819 q^{49} -43.6929 q^{50} -522.640 q^{51} +101.324 q^{52} +391.238 q^{53} -29.3264 q^{54} +198.934 q^{56} -487.981 q^{57} -31.5745 q^{58} +738.325 q^{59} +277.819 q^{60} -908.609 q^{61} +123.994 q^{62} -479.927 q^{63} -434.654 q^{64} +69.6306 q^{65} +235.932 q^{67} +612.124 q^{68} +315.708 q^{69} +67.4633 q^{70} +336.883 q^{71} -123.860 q^{72} +472.190 q^{73} -106.489 q^{74} -640.930 q^{75} +571.531 q^{76} -39.2475 q^{78} +145.435 q^{79} -316.567 q^{80} -896.915 q^{81} +140.405 q^{82} -1189.92 q^{83} +1440.06 q^{84} +420.654 q^{85} +170.151 q^{86} -463.165 q^{87} -354.291 q^{89} -42.0040 q^{90} +360.927 q^{91} -369.762 q^{92} +1818.86 q^{93} -228.066 q^{94} +392.758 q^{95} +559.900 q^{96} +705.353 q^{97} +194.086 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 3 q^{2} + 19 q^{3} + 181 q^{4} + 52 q^{5} - 104 q^{6} - 12 q^{7} - 57 q^{8} + 477 q^{9}+O(q^{10}) \) 38 * q - 3 * q^2 + 19 * q^3 + 181 * q^4 + 52 * q^5 - 104 * q^6 - 12 * q^7 - 57 * q^8 + 477 * q^9	\( 38 q - 3 q^{2} + 19 q^{3} + 181 q^{4} + 52 q^{5} - 104 q^{6} - 12 q^{7} - 57 q^{8} + 477 q^{9} + 30 q^{10} + 122 q^{12} - 494 q^{13} + 181 q^{14} + 264 q^{15} + 961 q^{16} + 33 q^{17} - 28 q^{18} - 107 q^{19} + 595 q^{20} - 148 q^{21} + 840 q^{23} - 968 q^{24} + 1428 q^{25} + 39 q^{26} + 1108 q^{27} + 353 q^{28} + 162 q^{29} + 48 q^{30} + 62 q^{31} - 1204 q^{32} - 58 q^{34} + 352 q^{35} + 3357 q^{36} + 304 q^{37} + 963 q^{38} - 247 q^{39} + 571 q^{40} - 361 q^{41} + 587 q^{42} - 483 q^{43} + 1136 q^{45} + 1860 q^{46} + 2892 q^{47} + 945 q^{48} + 2270 q^{49} + 782 q^{50} + 682 q^{51} - 2353 q^{52} + 1622 q^{53} - 3273 q^{54} + 3269 q^{56} - 62 q^{57} + 1683 q^{58} + 3417 q^{59} + 4279 q^{60} + 1714 q^{61} - 508 q^{62} - 3730 q^{63} + 4823 q^{64} - 676 q^{65} + 4939 q^{67} + 3699 q^{68} + 1818 q^{69} + 592 q^{70} + 1544 q^{71} + 5570 q^{72} - 617 q^{73} + 1398 q^{74} + 5457 q^{75} - 3316 q^{76} + 1352 q^{78} + 3176 q^{79} + 5091 q^{80} + 5994 q^{81} + 1238 q^{82} - 1659 q^{83} - 5157 q^{84} - 1074 q^{85} + 1144 q^{86} + 906 q^{87} + 3727 q^{89} + 6753 q^{90} + 156 q^{91} + 11004 q^{92} + 6956 q^{93} + 9255 q^{94} - 1768 q^{95} - 4812 q^{96} + 5723 q^{97} - 2043 q^{98}+O(q^{100}) \) 38 * q - 3 * q^2 + 19 * q^3 + 181 * q^4 + 52 * q^5 - 104 * q^6 - 12 * q^7 - 57 * q^8 + 477 * q^9 + 30 * q^10 + 122 * q^12 - 494 * q^13 + 181 * q^14 + 264 * q^15 + 961 * q^16 + 33 * q^17 - 28 * q^18 - 107 * q^19 + 595 * q^20 - 148 * q^21 + 840 * q^23 - 968 * q^24 + 1428 * q^25 + 39 * q^26 + 1108 * q^27 + 353 * q^28 + 162 * q^29 + 48 * q^30 + 62 * q^31 - 1204 * q^32 - 58 * q^34 + 352 * q^35 + 3357 * q^36 + 304 * q^37 + 963 * q^38 - 247 * q^39 + 571 * q^40 - 361 * q^41 + 587 * q^42 - 483 * q^43 + 1136 * q^45 + 1860 * q^46 + 2892 * q^47 + 945 * q^48 + 2270 * q^49 + 782 * q^50 + 682 * q^51 - 2353 * q^52 + 1622 * q^53 - 3273 * q^54 + 3269 * q^56 - 62 * q^57 + 1683 * q^58 + 3417 * q^59 + 4279 * q^60 + 1714 * q^61 - 508 * q^62 - 3730 * q^63 + 4823 * q^64 - 676 * q^65 + 4939 * q^67 + 3699 * q^68 + 1818 * q^69 + 592 * q^70 + 1544 * q^71 + 5570 * q^72 - 617 * q^73 + 1398 * q^74 + 5457 * q^75 - 3316 * q^76 + 1352 * q^78 + 3176 * q^79 + 5091 * q^80 + 5994 * q^81 + 1238 * q^82 - 1659 * q^83 - 5157 * q^84 - 1074 * q^85 + 1144 * q^86 + 906 * q^87 + 3727 * q^89 + 6753 * q^90 + 156 * q^91 + 11004 * q^92 + 6956 * q^93 + 9255 * q^94 - 1768 * q^95 - 4812 * q^96 + 5723 * q^97 - 2043 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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