LMFDB - Embedded newform 1573.4.a.p.1.19

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			1.19
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)

$f(q)$	$=$	$q+0.568087 q^{2} +6.42425 q^{3} -7.67728 q^{4} +4.18544 q^{5} +3.64954 q^{6} +32.4879 q^{7} -8.90606 q^{8} +14.2710 q^{9} +O(q^{10})$	\(q+0.568087 q^{2} +6.42425 q^{3} -7.67728 q^{4} +4.18544 q^{5} +3.64954 q^{6} +32.4879 q^{7} -8.90606 q^{8} +14.2710 q^{9} +2.37769 q^{10} -49.3208 q^{12} -13.0000 q^{13} +18.4560 q^{14} +26.8883 q^{15} +56.3588 q^{16} -85.8370 q^{17} +8.10719 q^{18} -100.072 q^{19} -32.1328 q^{20} +208.711 q^{21} -82.5402 q^{23} -57.2148 q^{24} -107.482 q^{25} -7.38513 q^{26} -81.7741 q^{27} -249.419 q^{28} -259.438 q^{29} +15.2749 q^{30} -78.3795 q^{31} +103.265 q^{32} -48.7629 q^{34} +135.976 q^{35} -109.563 q^{36} -54.5209 q^{37} -56.8497 q^{38} -83.5153 q^{39} -37.2757 q^{40} +185.381 q^{41} +118.566 q^{42} -337.190 q^{43} +59.7305 q^{45} -46.8900 q^{46} -42.0820 q^{47} +362.063 q^{48} +712.465 q^{49} -61.0592 q^{50} -551.439 q^{51} +99.8046 q^{52} +389.569 q^{53} -46.4548 q^{54} -289.339 q^{56} -642.889 q^{57} -147.383 q^{58} -789.000 q^{59} -206.429 q^{60} +589.423 q^{61} -44.5264 q^{62} +463.636 q^{63} -392.207 q^{64} -54.4107 q^{65} -482.088 q^{67} +658.994 q^{68} -530.259 q^{69} +77.2463 q^{70} +249.887 q^{71} -127.099 q^{72} +285.786 q^{73} -30.9726 q^{74} -690.492 q^{75} +768.282 q^{76} -47.4440 q^{78} +339.447 q^{79} +235.886 q^{80} -910.655 q^{81} +105.312 q^{82} +186.130 q^{83} -1602.33 q^{84} -359.265 q^{85} -191.553 q^{86} -1666.70 q^{87} -423.425 q^{89} +33.9321 q^{90} -422.343 q^{91} +633.684 q^{92} -503.530 q^{93} -23.9062 q^{94} -418.845 q^{95} +663.402 q^{96} +874.897 q^{97} +404.742 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.568087	0.200849	0.100425	−	0.994945i	$-0.467980\pi$
$2$	0.568087	0.200849	0.100425	+	0.994945i	$0.467980\pi$
$3$	6.42425	1.23635	0.618174	−	0.786041i	$-0.287873\pi$
$3$	6.42425	1.23635	0.618174	+	0.786041i	$0.287873\pi$
$4$	−7.67728	−0.959660
$5$	4.18544	0.374357	0.187178	−	0.982326i	$-0.440066\pi$
$5$	4.18544	0.374357	0.187178	+	0.982326i	$0.440066\pi$
$6$	3.64954	0.248319
$7$	32.4879	1.75418	0.877091	−	0.480324i	$-0.159481\pi$
$7$	32.4879	1.75418	0.877091	+	0.480324i	$0.159481\pi$
$8$	−8.90606	−0.393596
$9$	14.2710	0.528557
$10$	2.37769	0.0751892
$11$	0	0
$11$	0	0
$12$	−49.3208	−1.18647
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	18.4560	0.352326
$15$	26.8883	0.462835
$16$	56.3588	0.880606
$17$	−85.8370	−1.22462	−0.612310	−	0.790618i	$-0.709759\pi$
$17$	−85.8370	−1.22462	−0.612310	+	0.790618i	$0.709759\pi$
$18$	8.10719	0.106160
$19$	−100.072	−1.20832	−0.604161	−	0.796862i	$-0.706492\pi$
$19$	−100.072	−1.20832	−0.604161	+	0.796862i	$0.706492\pi$
$20$	−32.1328	−0.359255
$21$	208.711	2.16878
$22$	0	0
$23$	−82.5402	−0.748297	−0.374148	−	0.927369i	$-0.622065\pi$
$23$	−82.5402	−0.748297	−0.374148	+	0.927369i	$0.622065\pi$
$24$	−57.2148	−0.486622
$25$	−107.482	−0.859857
$26$	−7.38513	−0.0557055
$27$	−81.7741	−0.582868
$28$	−249.419	−1.68342
$29$	−259.438	−1.66126	−0.830628	−	0.556827i	$-0.812018\pi$
$29$	−259.438	−1.66126	−0.830628	+	0.556827i	$0.812018\pi$
$30$	15.2749	0.0929601
$31$	−78.3795	−0.454109	−0.227054	−	0.973882i	$-0.572910\pi$
$31$	−78.3795	−0.454109	−0.227054	+	0.973882i	$0.572910\pi$
$32$	103.265	0.570465
$33$	0	0
$34$	−48.7629	−0.245964
$35$	135.976	0.656690
$36$	−109.563	−0.507235
$37$	−54.5209	−0.242248	−0.121124	−	0.992637i	$-0.538650\pi$
$37$	−54.5209	−0.242248	−0.121124	+	0.992637i	$0.538650\pi$
$38$	−56.8497	−0.242690
$39$	−83.5153	−0.342901
$40$	−37.2757	−0.147345
$41$	185.381	0.706137	0.353069	−	0.935597i	$-0.385138\pi$
$41$	185.381	0.706137	0.353069	+	0.935597i	$0.385138\pi$
$42$	118.566	0.435598
$43$	−337.190	−1.19584	−0.597919	−	0.801557i	$-0.704006\pi$
$43$	−337.190	−1.19584	−0.597919	+	0.801557i	$0.704006\pi$
$44$	0	0
$45$	59.7305	0.197869
$46$	−46.8900	−0.150295
$47$	−42.0820	−0.130602	−0.0653009	−	0.997866i	$-0.520801\pi$
$47$	−42.0820	−0.130602	−0.0653009	+	0.997866i	$0.520801\pi$
$48$	362.063	1.08874
$49$	712.465	2.07716
$50$	−61.0592	−0.172701
$51$	−551.439	−1.51406
$52$	99.8046	0.266162
$53$	389.569	1.00965	0.504825	−	0.863222i	$-0.331557\pi$
$53$	389.569	1.00965	0.504825	+	0.863222i	$0.331557\pi$
$54$	−46.4548	−0.117068
$55$	0	0
$56$	−289.339	−0.690439
$57$	−642.889	−1.49391
$58$	−147.383	−0.333662
$59$	−789.000	−1.74100	−0.870500	−	0.492168i	$-0.836205\pi$
$59$	−789.000	−1.74100	−0.870500	+	0.492168i	$0.836205\pi$
$60$	−206.429	−0.444164
$61$	589.423	1.23718	0.618589	−	0.785715i	$-0.287705\pi$
$61$	589.423	1.23718	0.618589	+	0.785715i	$0.287705\pi$
$62$	−44.5264	−0.0912073
$63$	463.636	0.927186
$64$	−392.207	−0.766029
$65$	−54.4107	−0.103828
$66$	0	0
$67$	−482.088	−0.879051	−0.439526	−	0.898230i	$-0.644853\pi$
$67$	−482.088	−0.879051	−0.439526	+	0.898230i	$0.644853\pi$
$68$	658.994	1.17522
$69$	−530.259	−0.925155
$70$	77.2463	0.131896
$71$	249.887	0.417692	0.208846	−	0.977949i	$-0.433029\pi$
$71$	249.887	0.417692	0.208846	+	0.977949i	$0.433029\pi$
$72$	−127.099	−0.208038
$73$	285.786	0.458202	0.229101	−	0.973403i	$-0.426421\pi$
$73$	285.786	0.458202	0.229101	+	0.973403i	$0.426421\pi$
$74$	−30.9726	−0.0486553
$75$	−690.492	−1.06308
$76$	768.282	1.15958
$77$	0	0
$78$	−47.4440	−0.0688714
$79$	339.447	0.483428	0.241714	−	0.970348i	$-0.422290\pi$
$79$	339.447	0.483428	0.241714	+	0.970348i	$0.422290\pi$
$80$	235.886	0.329661
$81$	−910.655	−1.24918
$82$	105.312	0.141827
$83$	186.130	0.246149	0.123075	−	0.992397i	$-0.460725\pi$
$83$	186.130	0.246149	0.123075	+	0.992397i	$0.460725\pi$
$84$	−1602.33	−2.08129
$85$	−359.265	−0.458445
$86$	−191.553	−0.240183
$87$	−1666.70	−2.05389
$88$	0	0
$89$	−423.425	−0.504303	−0.252151	−	0.967688i	$-0.581138\pi$
$89$	−423.425	−0.504303	−0.252151	+	0.967688i	$0.581138\pi$
$90$	33.9321	0.0397418
$91$	−422.343	−0.486523
$92$	633.684	0.718110
$93$	−503.530	−0.561437
$94$	−23.9062	−0.0262313
$95$	−418.845	−0.452344
$96$	663.402	0.705293
$97$	874.897	0.915798	0.457899	−	0.889004i	$-0.348602\pi$
$97$	874.897	0.915798	0.457899	+	0.889004i	$0.348602\pi$
$98$	404.742	0.417195
$99$	0	0
$100$	825.170	0.825170
$101$	1125.62	1.10895	0.554475	−	0.832201i	$-0.312919\pi$
$101$	1125.62	1.10895	0.554475	+	0.832201i	$0.312919\pi$
$102$	−313.265	−0.304097
$103$	−1775.91	−1.69889	−0.849445	−	0.527678i	$-0.823063\pi$
$103$	−1775.91	−1.69889	−0.849445	+	0.527678i	$0.823063\pi$
$104$	115.779	0.109164
$105$	873.545	0.811898
$106$	221.309	0.202787
$107$	1900.89	1.71744	0.858720	−	0.512445i	$-0.171260\pi$
$107$	1900.89	1.71744	0.858720	+	0.512445i	$0.171260\pi$
$108$	627.802	0.559355
$109$	691.667	0.607796	0.303898	−	0.952705i	$-0.401712\pi$
$109$	691.667	0.607796	0.303898	+	0.952705i	$0.401712\pi$
$110$	0	0
$111$	−350.256	−0.299503
$112$	1830.98	1.54474
$113$	985.138	0.820124	0.410062	−	0.912058i	$-0.365507\pi$
$113$	985.138	0.820124	0.410062	+	0.912058i	$0.365507\pi$
$114$	−365.217	−0.300050
$115$	−345.467	−0.280130
$116$	1991.78	1.59424
$117$	−185.524	−0.146595
$118$	−448.221	−0.349678
$119$	−2788.67	−2.14821
$120$	−239.469	−0.182170
$121$	0	0
$122$	334.843	0.248486
$123$	1190.93	0.873032
$124$	601.741	0.435790
$125$	−973.039	−0.696250
$126$	263.386	0.186224
$127$	−1744.50	−1.21890	−0.609448	−	0.792826i	$-0.708609\pi$
$127$	−1744.50	−1.21890	−0.609448	+	0.792826i	$0.708609\pi$
$128$	−1048.93	−0.724321
$129$	−2166.20	−1.47847
$130$	−30.9100	−0.0208537
$131$	−1217.27	−0.811857	−0.405929	−	0.913905i	$-0.633052\pi$
$131$	−1217.27	−0.811857	−0.405929	+	0.913905i	$0.633052\pi$
$132$	0	0
$133$	−3251.14	−2.11962
$134$	−273.868	−0.176557
$135$	−342.260	−0.218200
$136$	764.469	0.482005
$137$	−1247.75	−0.778120	−0.389060	−	0.921213i	$-0.627200\pi$
$137$	−1247.75	−0.778120	−0.389060	+	0.921213i	$0.627200\pi$
$138$	−301.233	−0.185817
$139$	1577.36	0.962517	0.481259	−	0.876579i	$-0.340180\pi$
$139$	1577.36	0.962517	0.481259	+	0.876579i	$0.340180\pi$
$140$	−1043.93	−0.630199
$141$	−270.345	−0.161469
$142$	141.958	0.0838931
$143$	0	0
$144$	804.299	0.465451
$145$	−1085.86	−0.621903
$146$	162.352	0.0920295
$147$	4577.06	2.56809
$148$	418.572	0.232476
$149$	−129.118	−0.0709915	−0.0354958	−	0.999370i	$-0.511301\pi$
$149$	−129.118	−0.0709915	−0.0354958	+	0.999370i	$0.511301\pi$
$150$	−392.260	−0.213519
$151$	2631.22	1.41805	0.709026	−	0.705183i	$-0.249135\pi$
$151$	2631.22	1.41805	0.709026	+	0.705183i	$0.249135\pi$
$152$	891.248	0.475591
$153$	−1224.98	−0.647281
$154$	0	0
$155$	−328.052	−0.169999
$156$	641.170	0.329069
$157$	−1829.70	−0.930104	−0.465052	−	0.885283i	$-0.653964\pi$
$157$	−1829.70	−0.930104	−0.465052	+	0.885283i	$0.653964\pi$
$158$	192.836	0.0970961
$159$	2502.69	1.24828
$160$	432.210	0.213557
$161$	−2681.56	−1.31265
$162$	−517.332	−0.250898
$163$	−3118.26	−1.49841	−0.749207	−	0.662336i	$-0.769565\pi$
$163$	−3118.26	−1.49841	−0.749207	+	0.662336i	$0.769565\pi$
$164$	−1423.22	−0.677651
$165$	0	0
$166$	105.738	0.0494389
$167$	−4155.01	−1.92530	−0.962648	−	0.270754i	$-0.912727\pi$
$167$	−4155.01	−1.92530	−0.962648	+	0.270754i	$0.912727\pi$
$168$	−1858.79	−0.853623
$169$	169.000	0.0769231
$170$	−204.094	−0.0920782
$171$	−1428.13	−0.638667
$172$	2588.70	1.14760
$173$	−141.547	−0.0622058	−0.0311029	−	0.999516i	$-0.509902\pi$
$173$	−141.547	−0.0622058	−0.0311029	+	0.999516i	$0.509902\pi$
$174$	−946.828	−0.412522
$175$	−3491.87	−1.50835
$176$	0	0
$177$	−5068.74	−2.15248
$178$	−240.542	−0.101289
$179$	−1057.43	−0.441540	−0.220770	−	0.975326i	$-0.570857\pi$
$179$	−1057.43	−0.441540	−0.220770	+	0.975326i	$0.570857\pi$
$180$	−458.568	−0.189887
$181$	803.891	0.330126	0.165063	−	0.986283i	$-0.447217\pi$
$181$	803.891	0.330126	0.165063	+	0.986283i	$0.447217\pi$
$182$	−239.928	−0.0977177
$183$	3786.60	1.52958
$184$	735.108	0.294526
$185$	−228.194	−0.0906872
$186$	−286.049	−0.112764
$187$	0	0
$188$	323.075	0.125333
$189$	−2656.67	−1.02246
$190$	−237.941	−0.0908528
$191$	2455.20	0.930114	0.465057	−	0.885281i	$-0.346034\pi$
$191$	2455.20	0.930114	0.465057	+	0.885281i	$0.346034\pi$
$192$	−2519.64	−0.947079
$193$	4998.26	1.86416	0.932080	−	0.362252i	$-0.117992\pi$
$193$	4998.26	1.86416	0.932080	+	0.362252i	$0.117992\pi$
$194$	497.018	0.183937
$195$	−349.548	−0.128367
$196$	−5469.79	−1.99336
$197$	−3641.05	−1.31682	−0.658411	−	0.752658i	$-0.728771\pi$
$197$	−3641.05	−1.31682	−0.658411	+	0.752658i	$0.728771\pi$
$198$	0	0
$199$	256.117	0.0912343	0.0456171	−	0.998959i	$-0.485475\pi$
$199$	256.117	0.0912343	0.0456171	+	0.998959i	$0.485475\pi$
$200$	957.242	0.338436
$201$	−3097.06	−1.08681
$202$	639.453	0.222731
$203$	−8428.60	−2.91415
$204$	4233.55	1.45298
$205$	775.900	0.264347
$206$	−1008.87	−0.341220
$207$	−1177.93	−0.395517
$208$	−732.664	−0.244236
$209$	0	0
$210$	496.250	0.163069
$211$	3459.32	1.12867	0.564335	−	0.825546i	$-0.309133\pi$
$211$	3459.32	1.12867	0.564335	+	0.825546i	$0.309133\pi$
$212$	−2990.83	−0.968920
$213$	1605.34	0.516413
$214$	1079.87	0.344946
$215$	−1411.29	−0.447670
$216$	728.285	0.229414
$217$	−2546.39	−0.796590
$218$	392.927	0.122075
$219$	1835.96	0.566498
$220$	0	0
$221$	1115.88	0.339648
$222$	−198.976	−0.0601549
$223$	621.018	0.186486	0.0932431	−	0.995643i	$-0.470277\pi$
$223$	621.018	0.186486	0.0932431	+	0.995643i	$0.470277\pi$
$224$	3354.87	1.00070
$225$	−1533.88	−0.454483
$226$	559.644	0.164721
$227$	−3235.16	−0.945924	−0.472962	−	0.881083i	$-0.656815\pi$
$227$	−3235.16	−0.945924	−0.472962	+	0.881083i	$0.656815\pi$
$228$	4935.64	1.43364
$229$	2093.34	0.604068	0.302034	−	0.953297i	$-0.402334\pi$
$229$	2093.34	0.604068	0.302034	+	0.953297i	$0.402334\pi$
$230$	−196.255	−0.0562638
$231$	0	0
$232$	2310.57	0.653864
$233$	794.125	0.223283	0.111641	−	0.993749i	$-0.464389\pi$
$233$	794.125	0.223283	0.111641	+	0.993749i	$0.464389\pi$
$234$	−105.394	−0.0294435
$235$	−176.131	−0.0488917
$236$	6057.37	1.67077
$237$	2180.70	0.597685
$238$	−1584.20	−0.431465
$239$	−2385.58	−0.645649	−0.322825	−	0.946459i	$-0.604632\pi$
$239$	−2385.58	−0.645649	−0.322825	+	0.946459i	$0.604632\pi$
$240$	1515.39	0.407576
$241$	2327.78	0.622179	0.311090	−	0.950381i	$-0.399306\pi$
$241$	2327.78	0.622179	0.311090	+	0.950381i	$0.399306\pi$
$242$	0	0
$243$	−3642.38	−0.961559
$244$	−4525.16	−1.18727
$245$	2981.98	0.777598
$246$	676.554	0.175348
$247$	1300.94	0.335128
$248$	698.052	0.178735
$249$	1195.74	0.304326
$250$	−552.771	−0.139841
$251$	−2849.78	−0.716640	−0.358320	−	0.933599i	$-0.616650\pi$
$251$	−2849.78	−0.716640	−0.358320	+	0.933599i	$0.616650\pi$
$252$	−3559.47	−0.889783
$253$	0	0
$254$	−991.030	−0.244814
$255$	−2308.01	−0.566797
$256$	2541.77	0.620550
$257$	−2377.15	−0.576974	−0.288487	−	0.957484i	$-0.593152\pi$
$257$	−2377.15	−0.576974	−0.288487	+	0.957484i	$0.593152\pi$
$258$	−1230.59	−0.296950
$259$	−1771.27	−0.424947
$260$	417.726	0.0996394
$261$	−3702.45	−0.878069
$262$	−691.515	−0.163061
$263$	−1059.76	−0.248469	−0.124235	−	0.992253i	$-0.539648\pi$
$263$	−1059.76	−0.248469	−0.124235	+	0.992253i	$0.539648\pi$
$264$	0	0
$265$	1630.52	0.377969
$266$	−1846.93	−0.425723
$267$	−2720.19	−0.623494
$268$	3701.12	0.843590
$269$	−316.929	−0.0718346	−0.0359173	−	0.999355i	$-0.511435\pi$
$269$	−316.929	−0.0718346	−0.0359173	+	0.999355i	$0.511435\pi$
$270$	−194.434	−0.0438254
$271$	1487.41	0.333409	0.166704	−	0.986007i	$-0.446687\pi$
$271$	1487.41	0.333409	0.166704	+	0.986007i	$0.446687\pi$
$272$	−4837.67	−1.07841
$273$	−2713.24	−0.601512
$274$	−708.830	−0.156285
$275$	0	0
$276$	4070.95	0.887834
$277$	−7236.87	−1.56975	−0.784876	−	0.619653i	$-0.787273\pi$
$277$	−7236.87	−1.56975	−0.784876	+	0.619653i	$0.787273\pi$
$278$	896.078	0.193321
$279$	−1118.56	−0.240022
$280$	−1211.01	−0.258471
$281$	5045.57	1.07115	0.535575	−	0.844487i	$-0.320095\pi$
$281$	5045.57	1.07115	0.535575	+	0.844487i	$0.320095\pi$
$282$	−153.580	−0.0324310
$283$	7225.86	1.51778	0.758892	−	0.651216i	$-0.225741\pi$
$283$	7225.86	1.51778	0.758892	+	0.651216i	$0.225741\pi$
$284$	−1918.45	−0.400842
$285$	−2690.77	−0.559254
$286$	0	0
$287$	6022.64	1.23869
$288$	1473.70	0.301523
$289$	2454.99	0.499693
$290$	−616.864	−0.124909
$291$	5620.56	1.13224
$292$	−2194.06	−0.439718
$293$	−3718.22	−0.741368	−0.370684	−	0.928759i	$-0.620877\pi$
$293$	−3718.22	−0.741368	−0.370684	+	0.928759i	$0.620877\pi$
$294$	2600.17	0.515798
$295$	−3302.31	−0.651755
$296$	485.566	0.0953478
$297$	0	0
$298$	−73.3501	−0.0142586
$299$	1073.02	0.207540
$300$	5301.10	1.02020
$301$	−10954.6	−2.09772
$302$	1494.76	0.284814
$303$	7231.30	1.37105
$304$	−5639.95	−1.06406
$305$	2466.99	0.463146
$306$	−695.897	−0.130006
$307$	−55.8315	−0.0103794	−0.00518970	−	0.999987i	$-0.501652\pi$
$307$	−55.8315	−0.0103794	−0.00518970	+	0.999987i	$0.501652\pi$
$308$	0	0
$309$	−11408.9	−2.10042
$310$	−186.362	−0.0341441
$311$	7481.59	1.36412	0.682061	−	0.731295i	$-0.261084\pi$
$311$	7481.59	1.36412	0.682061	+	0.731295i	$0.261084\pi$
$312$	743.792	0.134965
$313$	8131.78	1.46848	0.734241	−	0.678889i	$-0.237538\pi$
$313$	8131.78	1.46848	0.734241	+	0.678889i	$0.237538\pi$
$314$	−1039.43	−0.186810
$315$	1940.52	0.347098
$316$	−2606.03	−0.463926
$317$	−4504.93	−0.798177	−0.399089	−	0.916912i	$-0.630673\pi$
$317$	−4504.93	−0.798177	−0.399089	+	0.916912i	$0.630673\pi$
$318$	1421.75	0.250716
$319$	0	0
$320$	−1641.56	−0.286768
$321$	12211.8	2.12335
$322$	−1523.36	−0.263644
$323$	8589.89	1.47973
$324$	6991.35	1.19879
$325$	1397.27	0.238481
$326$	−1771.45	−0.300955
$327$	4443.45	0.751447
$328$	−1651.01	−0.277933
$329$	−1367.16	−0.229100
$330$	0	0
$331$	−8036.89	−1.33458	−0.667292	−	0.744796i	$-0.732547\pi$
$331$	−8036.89	−1.33458	−0.667292	+	0.744796i	$0.732547\pi$
$332$	−1428.97	−0.236220
$333$	−778.069	−0.128042
$334$	−2360.41	−0.386694
$335$	−2017.75	−0.329079
$336$	11762.7	1.90984
$337$	−4854.75	−0.784734	−0.392367	−	0.919809i	$-0.628344\pi$
$337$	−4854.75	−0.784734	−0.392367	+	0.919809i	$0.628344\pi$
$338$	96.0067	0.0154499
$339$	6328.78	1.01396
$340$	2758.18	0.439951
$341$	0	0
$342$	−811.304	−0.128276
$343$	12003.1	1.88953
$344$	3003.04	0.470677
$345$	−2219.37	−0.346338
$346$	−80.4109	−0.0124940
$347$	411.674	0.0636883	0.0318442	−	0.999493i	$-0.489862\pi$
$347$	411.674	0.0636883	0.0318442	+	0.999493i	$0.489862\pi$
$348$	12795.7	1.97104
$349$	11420.6	1.75167	0.875835	−	0.482611i	$-0.160311\pi$
$349$	11420.6	1.75167	0.875835	+	0.482611i	$0.160311\pi$
$350$	−1983.69	−0.302950
$351$	1063.06	0.161658
$352$	0	0
$353$	−1875.22	−0.282742	−0.141371	−	0.989957i	$-0.545151\pi$
$353$	−1875.22	−0.282742	−0.141371	+	0.989957i	$0.545151\pi$
$354$	−2879.48	−0.432324
$355$	1045.89	0.156366
$356$	3250.75	0.483959
$357$	−17915.1	−2.65593
$358$	−600.710	−0.0886829
$359$	−908.487	−0.133560	−0.0667801	−	0.997768i	$-0.521273\pi$
$359$	−908.487	−0.133560	−0.0667801	+	0.997768i	$0.521273\pi$
$360$	−531.963	−0.0778804
$361$	3155.43	0.460043
$362$	456.680	0.0663054
$363$	0	0
$364$	3242.44	0.466896
$365$	1196.14	0.171531
$366$	2151.12	0.307215
$367$	−11987.7	−1.70505	−0.852526	−	0.522685i	$-0.824930\pi$
$367$	−11987.7	−1.70505	−0.852526	+	0.522685i	$0.824930\pi$
$368$	−4651.87	−0.658955
$369$	2645.58	0.373234
$370$	−129.634	−0.0182144
$371$	12656.3	1.77111
$372$	3865.74	0.538788
$373$	2789.19	0.387181	0.193591	−	0.981082i	$-0.437987\pi$
$373$	2789.19	0.387181	0.193591	+	0.981082i	$0.437987\pi$
$374$	0	0
$375$	−6251.05	−0.860808
$376$	374.785	0.0514043
$377$	3372.69	0.460750
$378$	−1509.22	−0.205359
$379$	−4274.52	−0.579334	−0.289667	−	0.957128i	$-0.593545\pi$
$379$	−4274.52	−0.579334	−0.289667	+	0.957128i	$0.593545\pi$
$380$	3215.59	0.434096
$381$	−11207.1	−1.50698
$382$	1394.77	0.186813
$383$	−6703.92	−0.894398	−0.447199	−	0.894435i	$-0.647578\pi$
$383$	−6703.92	−0.894398	−0.447199	+	0.894435i	$0.647578\pi$
$384$	−6738.59	−0.895513
$385$	0	0
$386$	2839.45	0.374415
$387$	−4812.05	−0.632068
$388$	−6716.83	−0.878854
$389$	13052.3	1.70123	0.850615	−	0.525789i	$-0.176230\pi$
$389$	13052.3	1.70123	0.850615	+	0.525789i	$0.176230\pi$
$390$	−198.574	−0.0257825
$391$	7085.00	0.916379
$392$	−6345.25	−0.817560
$393$	−7820.05	−1.00374
$394$	−2068.43	−0.264483
$395$	1420.74	0.180975
$396$	0	0
$397$	−6965.68	−0.880598	−0.440299	−	0.897851i	$-0.645128\pi$
$397$	−6965.68	−0.880598	−0.440299	+	0.897851i	$0.645128\pi$
$398$	145.496	0.0183243
$399$	−20886.1	−2.62059
$400$	−6057.56	−0.757195
$401$	13411.9	1.67022	0.835108	−	0.550087i	$-0.185405\pi$
$401$	13411.9	1.67022	0.835108	+	0.550087i	$0.185405\pi$
$402$	−1759.40	−0.218286
$403$	1018.93	0.125947
$404$	−8641.73	−1.06421
$405$	−3811.49	−0.467641
$406$	−4788.18	−0.585304
$407$	0	0
$408$	4911.14	0.595926
$409$	−10107.8	−1.22200	−0.611002	−	0.791629i	$-0.709233\pi$
$409$	−10107.8	−1.22200	−0.611002	+	0.791629i	$0.709233\pi$
$410$	440.779	0.0530939
$411$	−8015.86	−0.962027
$412$	13634.2	1.63036
$413$	−25633.0	−3.05403
$414$	−669.169	−0.0794393
$415$	779.034	0.0921477
$416$	−1342.45	−0.158218
$417$	10133.4	1.19001
$418$	0	0
$419$	2991.26	0.348765	0.174382	−	0.984678i	$-0.444207\pi$
$419$	2991.26	0.348765	0.174382	+	0.984678i	$0.444207\pi$
$420$	−6706.45	−0.779146
$421$	−9457.60	−1.09486	−0.547429	−	0.836852i	$-0.684393\pi$
$421$	−9457.60	−1.09486	−0.547429	+	0.836852i	$0.684393\pi$
$422$	1965.19	0.226692
$423$	−600.554	−0.0690305
$424$	−3469.52	−0.397394
$425$	9225.94	1.05300
$426$	911.972	0.103721
$427$	19149.1	2.17024
$428$	−14593.7	−1.64816
$429$	0	0
$430$	−801.734	−0.0899141
$431$	3068.28	0.342909	0.171454	−	0.985192i	$-0.445153\pi$
$431$	3068.28	0.342909	0.171454	+	0.985192i	$0.445153\pi$
$432$	−4608.69	−0.513277
$433$	−3591.74	−0.398633	−0.199316	−	0.979935i	$-0.563872\pi$
$433$	−3591.74	−0.398633	−0.199316	+	0.979935i	$0.563872\pi$
$434$	−1446.57	−0.159994
$435$	−6975.85	−0.768888
$436$	−5310.12	−0.583277
$437$	8259.98	0.904184
$438$	1042.99	0.113781
$439$	6956.83	0.756335	0.378168	−	0.925737i	$-0.376554\pi$
$439$	6956.83	0.756335	0.378168	+	0.925737i	$0.376554\pi$
$440$	0	0
$441$	10167.6	1.09790
$442$	633.918	0.0682181
$443$	−16130.4	−1.72997	−0.864985	−	0.501798i	$-0.832672\pi$
$443$	−16130.4	−1.72997	−0.864985	+	0.501798i	$0.832672\pi$
$444$	2689.01	0.287421
$445$	−1772.22	−0.188789
$446$	352.792	0.0374556
$447$	−829.485	−0.0877702
$448$	−12742.0	−1.34375
$449$	5809.50	0.610617	0.305309	−	0.952253i	$-0.401240\pi$
$449$	5809.50	0.610617	0.305309	+	0.952253i	$0.401240\pi$
$450$	−871.378	−0.0912826
$451$	0	0
$452$	−7563.18	−0.787040
$453$	16903.6	1.75320
$454$	−1837.85	−0.189988
$455$	−1767.69	−0.182133
$456$	5725.60	0.587996
$457$	4111.46	0.420844	0.210422	−	0.977611i	$-0.432516\pi$
$457$	4111.46	0.420844	0.210422	+	0.977611i	$0.432516\pi$
$458$	1189.20	0.121327
$459$	7019.24	0.713791
$460$	2652.24	0.268829
$461$	8061.13	0.814413	0.407207	−	0.913336i	$-0.366503\pi$
$461$	8061.13	0.814413	0.407207	+	0.913336i	$0.366503\pi$
$462$	0	0
$463$	−14037.9	−1.40907	−0.704533	−	0.709671i	$-0.748844\pi$
$463$	−14037.9	−1.40907	−0.704533	+	0.709671i	$0.748844\pi$
$464$	−14621.6	−1.46291
$465$	−2107.49	−0.210178
$466$	451.132	0.0448461
$467$	10130.6	1.00383	0.501916	−	0.864917i	$-0.332629\pi$
$467$	10130.6	1.00383	0.501916	+	0.864917i	$0.332629\pi$
$468$	1424.32	0.140682
$469$	−15662.0	−1.54202
$470$	−100.058	−0.00981985
$471$	−11754.5	−1.14993
$472$	7026.88	0.685251
$473$	0	0
$474$	1238.83	0.120045
$475$	10756.0	1.03898
$476$	21409.4	2.06155
$477$	5559.55	0.533657
$478$	−1355.22	−0.129678
$479$	−4139.90	−0.394900	−0.197450	−	0.980313i	$-0.563266\pi$
$479$	−4139.90	−0.394900	−0.197450	+	0.980313i	$0.563266\pi$
$480$	2776.62	0.264031
$481$	708.771	0.0671875
$482$	1322.38	0.124964
$483$	−17227.0	−1.62289
$484$	0	0
$485$	3661.83	0.342835
$486$	−2069.19	−0.193128
$487$	−13909.4	−1.29424	−0.647119	−	0.762389i	$-0.724026\pi$
$487$	−13909.4	−1.29424	−0.647119	+	0.762389i	$0.724026\pi$
$488$	−5249.43	−0.486948
$489$	−20032.5	−1.85256
$490$	1694.02	0.156180
$491$	360.876	0.0331693	0.0165846	−	0.999862i	$-0.494721\pi$
$491$	360.876	0.0331693	0.0165846	+	0.999862i	$0.494721\pi$
$492$	−9143.13	−0.837813
$493$	22269.4	2.03441
$494$	739.046	0.0673102
$495$	0	0
$496$	−4417.37	−0.399891
$497$	8118.31	0.732708
$498$	679.287	0.0611237
$499$	6602.77	0.592346	0.296173	−	0.955134i	$-0.404289\pi$
$499$	6602.77	0.592346	0.296173	+	0.955134i	$0.404289\pi$
$500$	7470.29	0.668163
$501$	−26692.9	−2.38034
$502$	−1618.92	−0.143937
$503$	−12582.0	−1.11531	−0.557657	−	0.830071i	$-0.688300\pi$
$503$	−12582.0	−1.11531	−0.557657	+	0.830071i	$0.688300\pi$
$504$	−4129.17	−0.364936
$505$	4711.23	0.415143
$506$	0	0
$507$	1085.70	0.0951037
$508$	13393.0	1.16972
$509$	2384.89	0.207678	0.103839	−	0.994594i	$-0.466887\pi$
$509$	2384.89	0.207678	0.103839	+	0.994594i	$0.466887\pi$
$510$	−1311.15	−0.113841
$511$	9284.61	0.803771
$512$	9835.38	0.848958
$513$	8183.31	0.704292
$514$	−1350.43	−0.115885
$515$	−7432.96	−0.635991
$516$	16630.5	1.41883
$517$	0	0
$518$	−1006.24	−0.0853503
$519$	−909.332	−0.0769080
$520$	484.585	0.0408662
$521$	35.2464	0.00296387	0.00148193	−	0.999999i	$-0.499528\pi$
$521$	35.2464	0.00296387	0.00148193	+	0.999999i	$0.499528\pi$
$522$	−2103.31	−0.176359
$523$	−1298.38	−0.108555	−0.0542776	−	0.998526i	$-0.517286\pi$
$523$	−1298.38	−0.108555	−0.0542776	+	0.998526i	$0.517286\pi$
$524$	9345.31	0.779107
$525$	−22432.7	−1.86484
$526$	−602.035	−0.0499049
$527$	6727.86	0.556111
$528$	0	0
$529$	−5354.11	−0.440052
$530$	926.275	0.0759147
$531$	−11259.9	−0.920218
$532$	24959.9	2.03411
$533$	−2409.95	−0.195847
$534$	−1545.30	−0.125228
$535$	7956.06	0.642935
$536$	4293.50	0.345991
$537$	−6793.17	−0.545897
$538$	−180.043	−0.0144279
$539$	0	0
$540$	2627.63	0.209398
$541$	−9642.86	−0.766320	−0.383160	−	0.923682i	$-0.625164\pi$
$541$	−9642.86	−0.766320	−0.383160	+	0.923682i	$0.625164\pi$
$542$	844.978	0.0669648
$543$	5164.40	0.408150
$544$	−8863.97	−0.698602
$545$	2894.93	0.227532
$546$	−1541.36	−0.120813
$547$	10845.7	0.847767	0.423883	−	0.905717i	$-0.360667\pi$
$547$	10845.7	0.847767	0.423883	+	0.905717i	$0.360667\pi$
$548$	9579.31	0.746730
$549$	8411.67	0.653919
$550$	0	0
$551$	25962.5	2.00733
$552$	4722.52	0.364137
$553$	11027.9	0.848021
$554$	−4111.17	−0.315283
$555$	−1465.97	−0.112121
$556$	−12109.8	−0.923689
$557$	−12675.1	−0.964200	−0.482100	−	0.876116i	$-0.660126\pi$
$557$	−12675.1	−0.964200	−0.482100	+	0.876116i	$0.660126\pi$
$558$	−635.438	−0.0482083
$559$	4383.47	0.331666
$560$	7663.45	0.578285
$561$	0	0
$562$	2866.32	0.215140
$563$	7266.10	0.543925	0.271962	−	0.962308i	$-0.412327\pi$
$563$	7266.10	0.543925	0.271962	+	0.962308i	$0.412327\pi$
$564$	2075.52	0.154956
$565$	4123.23	0.307019
$566$	4104.92	0.304846
$567$	−29585.3	−2.19130
$568$	−2225.51	−0.164402
$569$	−3699.17	−0.272543	−0.136272	−	0.990672i	$-0.543512\pi$
$569$	−3699.17	−0.272543	−0.136272	+	0.990672i	$0.543512\pi$
$570$	−1528.59	−0.112326
$571$	7214.65	0.528763	0.264381	−	0.964418i	$-0.414832\pi$
$571$	7214.65	0.528763	0.264381	+	0.964418i	$0.414832\pi$
$572$	0	0
$573$	15772.8	1.14994
$574$	3421.38	0.248791
$575$	8871.60	0.643428
$576$	−5597.20	−0.404890
$577$	−10256.4	−0.739996	−0.369998	−	0.929033i	$-0.620642\pi$
$577$	−10256.4	−0.739996	−0.369998	+	0.929033i	$0.620642\pi$
$578$	1394.65	0.100363
$579$	32110.1	2.30475
$580$	8336.46	0.596815
$581$	6046.97	0.431791
$582$	3192.97	0.227410
$583$	0	0
$584$	−2545.23	−0.180347
$585$	−776.497	−0.0548790
$586$	−2112.27	−0.148903
$587$	−25492.1	−1.79245	−0.896227	−	0.443596i	$-0.853703\pi$
$587$	−25492.1	−1.79245	−0.896227	+	0.443596i	$0.853703\pi$
$588$	−35139.3	−2.46449
$589$	7843.60	0.548710
$590$	−1876.00	−0.130904
$591$	−23391.0	−1.62805
$592$	−3072.73	−0.213325
$593$	−14443.5	−1.00021	−0.500103	−	0.865966i	$-0.666704\pi$
$593$	−14443.5	−1.00021	−0.500103	+	0.865966i	$0.666704\pi$
$594$	0	0
$595$	−11671.8	−0.804196
$596$	991.273	0.0681277
$597$	1645.36	0.112797
$598$	609.570	0.0416843
$599$	5312.50	0.362375	0.181188	−	0.983449i	$-0.442006\pi$
$599$	5312.50	0.362375	0.181188	+	0.983449i	$0.442006\pi$
$600$	6149.57	0.418425
$601$	−13351.0	−0.906157	−0.453079	−	0.891471i	$-0.649674\pi$
$601$	−13351.0	−0.906157	−0.453079	+	0.891471i	$0.649674\pi$
$602$	−6223.17	−0.421325
$603$	−6879.90	−0.464629
$604$	−20200.6	−1.36085
$605$	0	0
$606$	4108.01	0.275374
$607$	−3099.94	−0.207286	−0.103643	−	0.994615i	$-0.533050\pi$
$607$	−3099.94	−0.207286	−0.103643	+	0.994615i	$0.533050\pi$
$608$	−10334.0	−0.689305
$609$	−54147.5	−3.60290
$610$	1401.47	0.0930224
$611$	547.066	0.0362224
$612$	9404.54	0.621170
$613$	−2112.57	−0.139194	−0.0695971	−	0.997575i	$-0.522171\pi$
$613$	−2112.57	−0.139194	−0.0695971	+	0.997575i	$0.522171\pi$
$614$	−31.7172	−0.00208469
$615$	4984.58	0.326825
$616$	0	0
$617$	5317.81	0.346981	0.173490	−	0.984836i	$-0.444495\pi$
$617$	5317.81	0.346981	0.173490	+	0.984836i	$0.444495\pi$
$618$	−6481.25	−0.421867
$619$	29031.6	1.88510	0.942551	−	0.334063i	$-0.108420\pi$
$619$	29031.6	1.88510	0.942551	+	0.334063i	$0.108420\pi$
$620$	2518.55	0.163141
$621$	6749.65	0.436158
$622$	4250.20	0.273983
$623$	−13756.2	−0.884639
$624$	−4706.82	−0.301961
$625$	9362.67	0.599211
$626$	4619.56	0.294943
$627$	0	0
$628$	14047.1	0.892583
$629$	4679.91	0.296662
$630$	1102.38	0.0697144
$631$	18985.2	1.19777	0.598883	−	0.800837i	$-0.295612\pi$
$631$	18985.2	1.19777	0.598883	+	0.800837i	$0.295612\pi$
$632$	−3023.14	−0.190275
$633$	22223.5	1.39543
$634$	−2559.19	−0.160313
$635$	−7301.51	−0.456302
$636$	−19213.8	−1.19792
$637$	−9262.04	−0.576100
$638$	0	0
$639$	3566.15	0.220774
$640$	−4390.22	−0.271154
$641$	−7269.06	−0.447911	−0.223955	−	0.974599i	$-0.571897\pi$
$641$	−7269.06	−0.447911	−0.223955	+	0.974599i	$0.571897\pi$
$642$	6937.37	0.426474
$643$	−6225.84	−0.381840	−0.190920	−	0.981606i	$-0.561147\pi$
$643$	−6225.84	−0.381840	−0.190920	+	0.981606i	$0.561147\pi$
$644$	20587.1	1.25970
$645$	−9066.47	−0.553476
$646$	4879.81	0.297203
$647$	2226.28	0.135277	0.0676385	−	0.997710i	$-0.478454\pi$
$647$	2226.28	0.135277	0.0676385	+	0.997710i	$0.478454\pi$
$648$	8110.35	0.491674
$649$	0	0
$650$	793.770	0.0478988
$651$	−16358.6	−0.984863
$652$	23939.8	1.43797
$653$	−26268.1	−1.57420	−0.787099	−	0.616827i	$-0.788418\pi$
$653$	−26268.1	−1.57420	−0.787099	+	0.616827i	$0.788418\pi$
$654$	2524.26	0.150927
$655$	−5094.80	−0.303924
$656$	10447.8	0.621829
$657$	4078.47	0.242186
$658$	−776.664	−0.0460144
$659$	3537.57	0.209111	0.104556	−	0.994519i	$-0.466658\pi$
$659$	3537.57	0.209111	0.104556	+	0.994519i	$0.466658\pi$
$660$	0	0
$661$	1798.05	0.105803	0.0529016	−	0.998600i	$-0.483153\pi$
$661$	1798.05	0.105803	0.0529016	+	0.998600i	$0.483153\pi$
$662$	−4565.65	−0.268050
$663$	7168.70	0.419924
$664$	−1657.68	−0.0968833
$665$	−13607.4	−0.793493
$666$	−442.011	−0.0257171
$667$	21414.1	1.24311
$668$	31899.2	1.84763
$669$	3989.58	0.230562
$670$	−1146.26	−0.0660952
$671$	0	0
$672$	21552.5	1.23721
$673$	−16423.1	−0.940657	−0.470329	−	0.882491i	$-0.655865\pi$
$673$	−16423.1	−0.940657	−0.470329	+	0.882491i	$0.655865\pi$
$674$	−2757.92	−0.157613
$675$	8789.25	0.501183
$676$	−1297.46	−0.0738200
$677$	19597.1	1.11252	0.556260	−	0.831008i	$-0.312236\pi$
$677$	19597.1	1.11252	0.556260	+	0.831008i	$0.312236\pi$
$678$	3595.30	0.203653
$679$	28423.6	1.60648
$680$	3199.64	0.180442
$681$	−20783.5	−1.16949
$682$	0	0
$683$	−29697.4	−1.66375	−0.831873	−	0.554966i	$-0.812731\pi$
$683$	−29697.4	−1.66375	−0.831873	+	0.554966i	$0.812731\pi$
$684$	10964.2	0.612903
$685$	−5222.37	−0.291294
$686$	6818.83	0.379511
$687$	13448.1	0.746838
$688$	−19003.6	−1.05306
$689$	−5064.40	−0.280026
$690$	−1260.79	−0.0695617
$691$	17663.1	0.972412	0.486206	−	0.873844i	$-0.338381\pi$
$691$	17663.1	0.972412	0.486206	+	0.873844i	$0.338381\pi$
$692$	1086.69	0.0596964
$693$	0	0
$694$	233.867	0.0127917
$695$	6601.94	0.360325
$696$	14843.7	0.808403
$697$	−15912.5	−0.864749
$698$	6487.92	0.351821
$699$	5101.66	0.276055
$700$	26808.1	1.44750
$701$	−19817.4	−1.06775	−0.533875	−	0.845564i	$-0.679265\pi$
$701$	−19817.4	−1.06775	−0.533875	+	0.845564i	$0.679265\pi$
$702$	603.912	0.0324689
$703$	5456.02	0.292714
$704$	0	0
$705$	−1131.51	−0.0604472
$706$	−1065.29	−0.0567884
$707$	36569.2	1.94530
$708$	38914.1	2.06565
$709$	−21364.6	−1.13168	−0.565842	−	0.824513i	$-0.691449\pi$
$709$	−21364.6	−1.13168	−0.565842	+	0.824513i	$0.691449\pi$
$710$	594.155	0.0314059
$711$	4844.27	0.255519
$712$	3771.04	0.198491
$713$	6469.46	0.339808
$714$	−10177.3	−0.533441
$715$	0	0
$716$	8118.15	0.423728
$717$	−15325.5	−0.798247
$718$	−516.100	−0.0268254
$719$	12088.4	0.627014	0.313507	−	0.949586i	$-0.398496\pi$
$719$	12088.4	0.627014	0.313507	+	0.949586i	$0.398496\pi$
$720$	3366.34	0.174245
$721$	−57695.6	−2.98016
$722$	1792.56	0.0923991
$723$	14954.2	0.769230
$724$	−6171.69	−0.316808
$725$	27885.0	1.42844
$726$	0	0
$727$	29354.8	1.49754	0.748769	−	0.662832i	$-0.230645\pi$
$727$	29354.8	1.49754	0.748769	+	0.662832i	$0.230645\pi$
$728$	3761.41	0.191493
$729$	1188.11	0.0603622
$730$	679.512	0.0344519
$731$	28943.4	1.46445
$732$	−29070.8	−1.46788
$733$	−2841.12	−0.143164	−0.0715820	−	0.997435i	$-0.522805\pi$
$733$	−2841.12	−0.143164	−0.0715820	+	0.997435i	$0.522805\pi$
$734$	−6810.07	−0.342458
$735$	19157.0	0.961382
$736$	−8523.53	−0.426877
$737$	0	0
$738$	1502.92	0.0749637
$739$	5059.82	0.251865	0.125933	−	0.992039i	$-0.459808\pi$
$739$	5059.82	0.251865	0.125933	+	0.992039i	$0.459808\pi$
$740$	1751.91	0.0870288
$741$	8357.55	0.414335
$742$	7189.87	0.355726
$743$	34229.2	1.69011	0.845053	−	0.534682i	$-0.179569\pi$
$743$	34229.2	1.69011	0.845053	+	0.534682i	$0.179569\pi$
$744$	4484.47	0.220979
$745$	−540.414	−0.0265762
$746$	1584.50	0.0777650
$747$	2656.26	0.130104
$748$	0	0
$749$	61756.0	3.01270
$750$	−3551.14	−0.172892
$751$	−27557.4	−1.33899	−0.669497	−	0.742815i	$-0.733490\pi$
$751$	−27557.4	−1.33899	−0.669497	+	0.742815i	$0.733490\pi$
$752$	−2371.69	−0.115009
$753$	−18307.7	−0.886017
$754$	1915.98	0.0925411
$755$	11012.8	0.530857
$756$	20396.0	0.981210
$757$	21181.5	1.01698	0.508491	−	0.861067i	$-0.330204\pi$
$757$	21181.5	1.01698	0.508491	+	0.861067i	$0.330204\pi$
$758$	−2428.30	−0.116359
$759$	0	0
$760$	3730.26	0.178041
$761$	−10751.5	−0.512146	−0.256073	−	0.966657i	$-0.582429\pi$
$761$	−10751.5	−0.512146	−0.256073	+	0.966657i	$0.582429\pi$
$762$	−6366.63	−0.302675
$763$	22470.8	1.06618
$764$	−18849.2	−0.892593
$765$	−5127.09	−0.242314
$766$	−3808.41	−0.179639
$767$	10257.0	0.482867
$768$	16329.0	0.767216
$769$	32893.0	1.54246	0.771231	−	0.636556i	$-0.219641\pi$
$769$	32893.0	1.54246	0.771231	+	0.636556i	$0.219641\pi$
$770$	0	0
$771$	−15271.4	−0.713341
$772$	−38373.1	−1.78896
$773$	14258.3	0.663435	0.331717	−	0.943379i	$-0.392372\pi$
$773$	14258.3	0.663435	0.331717	+	0.943379i	$0.392372\pi$
$774$	−2733.67	−0.126950
$775$	8424.40	0.390469
$776$	−7791.89	−0.360454
$777$	−11379.1	−0.525383
$778$	7414.85	0.341691
$779$	−18551.5	−0.853241
$780$	2683.58	0.123189
$781$	0	0
$782$	4024.90	0.184054
$783$	21215.3	0.968293
$784$	40153.7	1.82916
$785$	−7658.11	−0.348191
$786$	−4442.47	−0.201600
$787$	11624.7	0.526526	0.263263	−	0.964724i	$-0.415201\pi$
$787$	11624.7	0.526526	0.263263	+	0.964724i	$0.415201\pi$
$788$	27953.3	1.26370
$789$	−6808.15	−0.307195
$790$	807.101	0.0363486
$791$	32005.1	1.43865
$792$	0	0
$793$	−7662.49	−0.343131
$794$	−3957.11	−0.176867
$795$	10474.8	0.467301
$796$	−1966.28	−0.0875539
$797$	17100.8	0.760029	0.380014	−	0.924981i	$-0.375919\pi$
$797$	17100.8	0.760029	0.380014	+	0.924981i	$0.375919\pi$
$798$	−11865.1	−0.526342
$799$	3612.19	0.159938
$800$	−11099.2	−0.490518
$801$	−6042.71	−0.266553
$802$	7619.10	0.335461
$803$	0	0
$804$	23777.0	1.04297
$805$	−11223.5	−0.491399
$806$	578.843	0.0252964
$807$	−2036.03	−0.0888126
$808$	−10024.9	−0.436478
$809$	15381.3	0.668451	0.334226	−	0.942493i	$-0.391525\pi$
$809$	15381.3	0.668451	0.334226	+	0.942493i	$0.391525\pi$
$810$	−2165.26	−0.0939252
$811$	−7928.02	−0.343268	−0.171634	−	0.985161i	$-0.554905\pi$
$811$	−7928.02	−0.343268	−0.171634	+	0.985161i	$0.554905\pi$
$812$	64708.7	2.79659
$813$	9555.50	0.412209
$814$	0	0
$815$	−13051.3	−0.560941
$816$	−31078.4	−1.33329
$817$	33743.3	1.44496
$818$	−5742.12	−0.245438
$819$	−6027.27	−0.257155
$820$	−5956.80	−0.253683
$821$	−14001.0	−0.595175	−0.297588	−	0.954694i	$-0.596182\pi$
$821$	−14001.0	−0.595175	−0.297588	+	0.954694i	$0.596182\pi$
$822$	−4553.70	−0.193222
$823$	17654.6	0.747752	0.373876	−	0.927479i	$-0.378029\pi$
$823$	17654.6	0.747752	0.373876	+	0.927479i	$0.378029\pi$
$824$	15816.4	0.668676
$825$	0	0
$826$	−14561.8	−0.613400
$827$	−5848.98	−0.245936	−0.122968	−	0.992411i	$-0.539241\pi$
$827$	−5848.98	−0.245936	−0.122968	+	0.992411i	$0.539241\pi$
$828$	9043.33	0.379562
$829$	46305.5	1.94000	0.969999	−	0.243110i	$-0.0781675\pi$
$829$	46305.5	1.94000	0.969999	+	0.243110i	$0.0781675\pi$
$830$	442.559	0.0185078
$831$	−46491.5	−1.94076
$832$	5098.69	0.212458
$833$	−61155.9	−2.54373
$834$	5756.63	0.239012
$835$	−17390.5	−0.720748
$836$	0	0
$837$	6409.41	0.264685
$838$	1699.29	0.0700491
$839$	−15982.0	−0.657641	−0.328820	−	0.944392i	$-0.606651\pi$
$839$	−15982.0	−0.657641	−0.328820	+	0.944392i	$0.606651\pi$
$840$	−7779.84	−0.319560
$841$	42919.1	1.75977
$842$	−5372.74	−0.219901
$843$	32414.0	1.32432
$844$	−26558.1	−1.08314
$845$	707.339	0.0287967
$846$	−341.167	−0.0138647
$847$	0	0
$848$	21955.6	0.889104
$849$	46420.8	1.87651
$850$	5241.14	0.211494
$851$	4500.16	0.181273
$852$	−12324.6	−0.495581
$853$	16186.3	0.649719	0.324859	−	0.945762i	$-0.394683\pi$
$853$	16186.3	0.649719	0.324859	+	0.945762i	$0.394683\pi$
$854$	10878.4	0.435890
$855$	−5977.36	−0.239089
$856$	−16929.4	−0.675977
$857$	29309.8	1.16827	0.584134	−	0.811657i	$-0.301434\pi$
$857$	29309.8	1.16827	0.584134	+	0.811657i	$0.301434\pi$
$858$	0	0
$859$	−32694.4	−1.29862	−0.649312	−	0.760522i	$-0.724943\pi$
$859$	−32694.4	−1.29862	−0.649312	+	0.760522i	$0.724943\pi$
$860$	10834.8	0.429611
$861$	38691.0	1.53146
$862$	1743.05	0.0688729
$863$	39009.6	1.53870	0.769352	−	0.638825i	$-0.220579\pi$
$863$	39009.6	1.53870	0.769352	+	0.638825i	$0.220579\pi$
$864$	−8444.41	−0.332506
$865$	−592.435	−0.0232872
$866$	−2040.42	−0.0800650
$867$	15771.5	0.617794
$868$	19549.3	0.764455
$869$	0	0
$870$	−3962.89	−0.154430
$871$	6267.15	0.243805
$872$	−6160.03	−0.239226
$873$	12485.7	0.484051
$874$	4692.38	0.181604
$875$	−31612.0	−1.22135
$876$	−14095.2	−0.543645
$877$	−11086.6	−0.426873	−0.213436	−	0.976957i	$-0.568466\pi$
$877$	−11086.6	−0.426873	−0.213436	+	0.976957i	$0.568466\pi$
$878$	3952.08	0.151909
$879$	−23886.8	−0.916589
$880$	0	0
$881$	20837.0	0.796839	0.398419	−	0.917203i	$-0.369559\pi$
$881$	20837.0	0.796839	0.398419	+	0.917203i	$0.369559\pi$
$882$	5776.09	0.220511
$883$	14623.4	0.557325	0.278662	−	0.960389i	$-0.410109\pi$
$883$	14623.4	0.557325	0.278662	+	0.960389i	$0.410109\pi$
$884$	−8566.93	−0.325947
$885$	−21214.9	−0.805797
$886$	−9163.45	−0.347463
$887$	−45726.5	−1.73094	−0.865470	−	0.500960i	$-0.832980\pi$
$887$	−45726.5	−1.73094	−0.865470	+	0.500960i	$0.832980\pi$
$888$	3119.40	0.117883
$889$	−56675.3	−2.13817
$890$	−1006.77	−0.0379181
$891$	0	0
$892$	−4767.72	−0.178963
$893$	4211.23	0.157809
$894$	−471.220	−0.0176286
$895$	−4425.79	−0.165294
$896$	−34077.5	−1.27059
$897$	6893.37	0.256592
$898$	3300.30	0.122642
$899$	20334.6	0.754391
$900$	11776.0	0.436149
$901$	−33439.4	−1.23644
$902$	0	0
$903$	−70375.2	−2.59351
$904$	−8773.70	−0.322797
$905$	3364.63	0.123585
$906$	9602.73	0.352130
$907$	14024.7	0.513433	0.256717	−	0.966487i	$-0.417359\pi$
$907$	14024.7	0.513433	0.256717	+	0.966487i	$0.417359\pi$
$908$	24837.2	0.907765
$909$	16063.8	0.586143
$910$	−1004.20	−0.0365813
$911$	13376.5	0.486480	0.243240	−	0.969966i	$-0.421790\pi$
$911$	13376.5	0.486480	0.243240	+	0.969966i	$0.421790\pi$
$912$	−36232.4	−1.31554
$913$	0	0
$914$	2335.67	0.0845262
$915$	15848.6	0.572610
$916$	−16071.1	−0.579700
$917$	−39546.5	−1.42415
$918$	3987.54	0.143364
$919$	−30652.3	−1.10025	−0.550124	−	0.835083i	$-0.685419\pi$
$919$	−30652.3	−1.10025	−0.550124	+	0.835083i	$0.685419\pi$
$920$	3076.75	0.110258
$921$	−358.676	−0.0128325
$922$	4579.43	0.163574
$923$	−3248.53	−0.115847
$924$	0	0
$925$	5860.02	0.208299
$926$	−7974.76	−0.283010
$927$	−25344.1	−0.897960
$928$	−26790.9	−0.947688
$929$	34219.7	1.20852	0.604258	−	0.796789i	$-0.293470\pi$
$929$	34219.7	1.20852	0.604258	+	0.796789i	$0.293470\pi$
$930$	−1197.24	−0.0422140
$931$	−71297.9	−2.50988
$932$	−6096.72	−0.214275
$933$	48063.7	1.68653
$934$	5755.08	0.201619
$935$	0	0
$936$	1652.28	0.0576993
$937$	−39605.3	−1.38084	−0.690421	−	0.723408i	$-0.742575\pi$
$937$	−39605.3	−1.38084	−0.690421	+	0.723408i	$0.742575\pi$
$938$	−8897.40	−0.309713
$939$	52240.6	1.81556
$940$	1352.21	0.0469194
$941$	−17412.2	−0.603209	−0.301605	−	0.953433i	$-0.597522\pi$
$941$	−17412.2	−0.603209	−0.301605	+	0.953433i	$0.597522\pi$
$942$	−6677.57	−0.230963
$943$	−15301.4	−0.528400
$944$	−44467.1	−1.53314
$945$	−11119.3	−0.382763
$946$	0	0
$947$	10359.2	0.355468	0.177734	−	0.984079i	$-0.443123\pi$
$947$	10359.2	0.355468	0.177734	+	0.984079i	$0.443123\pi$
$948$	−16741.8	−0.573575
$949$	−3715.22	−0.127082
$950$	6110.32	0.208679
$951$	−28940.8	−0.986825
$952$	24836.0	0.845525
$953$	24795.6	0.842822	0.421411	−	0.906870i	$-0.361535\pi$
$953$	24795.6	0.842822	0.421411	+	0.906870i	$0.361535\pi$
$954$	3158.31	0.107185
$955$	10276.1	0.348194
$956$	18314.7	0.619603
$957$	0	0
$958$	−2351.83	−0.0793153
$959$	−40536.8	−1.36496
$960$	−10545.8	−0.354545
$961$	−23647.7	−0.793785
$962$	402.644	0.0134945
$963$	27127.7	0.907765
$964$	−17871.0	−0.597080
$965$	20919.9	0.697861
$966$	−9786.45	−0.325956
$967$	−3588.30	−0.119330	−0.0596650	−	0.998218i	$-0.519003\pi$
$967$	−3588.30	−0.119330	−0.0596650	+	0.998218i	$0.519003\pi$
$968$	0	0
$969$	55183.6	1.82947
$970$	2080.24	0.0688581
$971$	−50018.9	−1.65312	−0.826562	−	0.562846i	$-0.809706\pi$
$971$	−50018.9	−1.65312	−0.826562	+	0.562846i	$0.809706\pi$
$972$	27963.6	0.922770
$973$	51245.1	1.68843
$974$	−7901.74	−0.259947
$975$	8976.40	0.294846
$976$	33219.2	1.08947
$977$	−42985.4	−1.40760	−0.703800	−	0.710398i	$-0.748515\pi$
$977$	−42985.4	−1.40760	−0.703800	+	0.710398i	$0.748515\pi$
$978$	−11380.2	−0.372085
$979$	0	0
$980$	−22893.5	−0.746229
$981$	9870.81	0.321255
$982$	205.009	0.00666202
$983$	−4518.78	−0.146619	−0.0733097	−	0.997309i	$-0.523356\pi$
$983$	−4518.78	−0.146619	−0.0733097	+	0.997309i	$0.523356\pi$
$984$	−10606.5	−0.343622
$985$	−15239.4	−0.492961
$986$	12650.9	0.408609
$987$	−8782.96	−0.283247
$988$	−9987.66	−0.321609
$989$	27831.8	0.894841
$990$	0	0
$991$	36723.5	1.17715	0.588577	−	0.808441i	$-0.299688\pi$
$991$	36723.5	1.17715	0.588577	+	0.808441i	$0.299688\pi$
$992$	−8093.87	−0.259053
$993$	−51631.0	−1.65001
$994$	4611.91	0.147164
$995$	1071.96	0.0341542
$996$	−9180.06	−0.292050
$997$	8541.14	0.271315	0.135657	−	0.990756i	$-0.456685\pi$
$997$	8541.14	0.271315	0.135657	+	0.990756i	$0.456685\pi$
$998$	3750.95	0.118972
$999$	4458.39	0.141198

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.4.a.p.1.19		34
11.7	odd	10		143.4.h.a.27.8	✓	68
11.8	odd	10		143.4.h.a.53.8	yes	68
11.10	odd	2		1573.4.a.o.1.16		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.a.27.8	✓	68	11.7	odd	10
143.4.h.a.53.8	yes	68	11.8	odd	10
1573.4.a.o.1.16		34	11.10	odd	2
1573.4.a.p.1.19		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)

\(f(q)\)	\(=\)	\(q+0.568087 q^{2} +6.42425 q^{3} -7.67728 q^{4} +4.18544 q^{5} +3.64954 q^{6} +32.4879 q^{7} -8.90606 q^{8} +14.2710 q^{9} +O(q^{10})\)	\(q+0.568087 q^{2} +6.42425 q^{3} -7.67728 q^{4} +4.18544 q^{5} +3.64954 q^{6} +32.4879 q^{7} -8.90606 q^{8} +14.2710 q^{9} +2.37769 q^{10} -49.3208 q^{12} -13.0000 q^{13} +18.4560 q^{14} +26.8883 q^{15} +56.3588 q^{16} -85.8370 q^{17} +8.10719 q^{18} -100.072 q^{19} -32.1328 q^{20} +208.711 q^{21} -82.5402 q^{23} -57.2148 q^{24} -107.482 q^{25} -7.38513 q^{26} -81.7741 q^{27} -249.419 q^{28} -259.438 q^{29} +15.2749 q^{30} -78.3795 q^{31} +103.265 q^{32} -48.7629 q^{34} +135.976 q^{35} -109.563 q^{36} -54.5209 q^{37} -56.8497 q^{38} -83.5153 q^{39} -37.2757 q^{40} +185.381 q^{41} +118.566 q^{42} -337.190 q^{43} +59.7305 q^{45} -46.8900 q^{46} -42.0820 q^{47} +362.063 q^{48} +712.465 q^{49} -61.0592 q^{50} -551.439 q^{51} +99.8046 q^{52} +389.569 q^{53} -46.4548 q^{54} -289.339 q^{56} -642.889 q^{57} -147.383 q^{58} -789.000 q^{59} -206.429 q^{60} +589.423 q^{61} -44.5264 q^{62} +463.636 q^{63} -392.207 q^{64} -54.4107 q^{65} -482.088 q^{67} +658.994 q^{68} -530.259 q^{69} +77.2463 q^{70} +249.887 q^{71} -127.099 q^{72} +285.786 q^{73} -30.9726 q^{74} -690.492 q^{75} +768.282 q^{76} -47.4440 q^{78} +339.447 q^{79} +235.886 q^{80} -910.655 q^{81} +105.312 q^{82} +186.130 q^{83} -1602.33 q^{84} -359.265 q^{85} -191.553 q^{86} -1666.70 q^{87} -423.425 q^{89} +33.9321 q^{90} -422.343 q^{91} +633.684 q^{92} -503.530 q^{93} -23.9062 q^{94} -418.845 q^{95} +663.402 q^{96} +874.897 q^{97} +404.742 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} - 36 q^{6} + 36 q^{7} + 57 q^{8} + 265 q^{9}+O(q^{10}) \) 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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