LMFDB - Embedded newform 1441.4.a.a.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,4,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, 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("1441.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1441.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:	$85.0217523183$
Analytic rank:	$1$
Dimension:	$77$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.50745 q^{2} -6.76078 q^{3} +12.3171 q^{4} +12.7660 q^{5} +30.4739 q^{6} -21.9914 q^{7} -19.4592 q^{8} +18.7082 q^{9} +O(q^{10})$	\(q-4.50745 q^{2} -6.76078 q^{3} +12.3171 q^{4} +12.7660 q^{5} +30.4739 q^{6} -21.9914 q^{7} -19.4592 q^{8} +18.7082 q^{9} -57.5420 q^{10} -11.0000 q^{11} -83.2733 q^{12} +27.2605 q^{13} +99.1253 q^{14} -86.3079 q^{15} -10.8256 q^{16} +97.8427 q^{17} -84.3262 q^{18} -138.783 q^{19} +157.240 q^{20} +148.679 q^{21} +49.5820 q^{22} +13.0353 q^{23} +131.559 q^{24} +37.9700 q^{25} -122.875 q^{26} +56.0592 q^{27} -270.871 q^{28} +240.666 q^{29} +389.029 q^{30} +178.870 q^{31} +204.469 q^{32} +74.3686 q^{33} -441.021 q^{34} -280.742 q^{35} +230.431 q^{36} -434.646 q^{37} +625.557 q^{38} -184.302 q^{39} -248.416 q^{40} -216.517 q^{41} -670.164 q^{42} -408.696 q^{43} -135.488 q^{44} +238.828 q^{45} -58.7562 q^{46} -473.877 q^{47} +73.1893 q^{48} +140.623 q^{49} -171.148 q^{50} -661.493 q^{51} +335.771 q^{52} +577.705 q^{53} -252.684 q^{54} -140.426 q^{55} +427.935 q^{56} +938.280 q^{57} -1084.79 q^{58} +598.961 q^{59} -1063.07 q^{60} +342.662 q^{61} -806.249 q^{62} -411.419 q^{63} -835.031 q^{64} +348.007 q^{65} -335.213 q^{66} -674.759 q^{67} +1205.14 q^{68} -88.1291 q^{69} +1265.43 q^{70} -298.956 q^{71} -364.046 q^{72} +47.4339 q^{73} +1959.15 q^{74} -256.707 q^{75} -1709.40 q^{76} +241.906 q^{77} +830.734 q^{78} +2.47600 q^{79} -138.199 q^{80} -884.125 q^{81} +975.941 q^{82} +1099.70 q^{83} +1831.30 q^{84} +1249.06 q^{85} +1842.18 q^{86} -1627.09 q^{87} +214.051 q^{88} +543.214 q^{89} -1076.51 q^{90} -599.497 q^{91} +160.558 q^{92} -1209.30 q^{93} +2135.98 q^{94} -1771.70 q^{95} -1382.37 q^{96} +1375.32 q^{97} -633.850 q^{98} -205.790 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 77 q - 14 q^{2} - 10 q^{3} + 296 q^{4} - 42 q^{5} - 13 q^{6} - 59 q^{7} - 150 q^{8} + 541 q^{9}+O(q^{10}) $ 77 * q - 14 * q^2 - 10 * q^3 + 296 * q^4 - 42 * q^5 - 13 * q^6 - 59 * q^7 - 150 * q^8 + 541 * q^9	\( 77 q - 14 q^{2} - 10 q^{3} + 296 q^{4} - 42 q^{5} - 13 q^{6} - 59 q^{7} - 150 q^{8} + 541 q^{9} + 2 q^{10} - 847 q^{11} - 88 q^{12} - 20 q^{13} - 282 q^{14} - 330 q^{15} + 936 q^{16} - 56 q^{17} - 343 q^{18} - 157 q^{19} - 450 q^{20} - 122 q^{21} + 154 q^{22} - 764 q^{23} - 346 q^{24} + 1413 q^{25} - 408 q^{26} - 358 q^{27} - 228 q^{28} - 557 q^{29} - 267 q^{30} - 780 q^{31} - 1739 q^{32} + 110 q^{33} - 1104 q^{34} - 1254 q^{35} + 375 q^{36} - 541 q^{37} - 2133 q^{38} - 1458 q^{39} - 554 q^{40} - 1723 q^{41} - 5 q^{42} - 688 q^{43} - 3256 q^{44} - 1588 q^{45} + 276 q^{46} - 3086 q^{47} - 4280 q^{48} + 2452 q^{49} - 2234 q^{50} - 1570 q^{51} - 715 q^{52} - 1230 q^{53} - 5166 q^{54} + 462 q^{55} - 3203 q^{56} + 1024 q^{57} - 3016 q^{58} - 5408 q^{59} - 8221 q^{60} + 566 q^{61} - 3642 q^{62} - 3035 q^{63} + 1084 q^{64} - 1794 q^{65} + 143 q^{66} - 1925 q^{67} - 1105 q^{68} - 3710 q^{69} - 5875 q^{70} - 9614 q^{71} - 2198 q^{72} - 384 q^{73} - 2378 q^{74} - 3888 q^{75} - 2809 q^{76} + 649 q^{77} - 1731 q^{78} - 1086 q^{79} - 4357 q^{80} + 2329 q^{81} - 3167 q^{82} - 3045 q^{83} - 5359 q^{84} + 2582 q^{85} - 6468 q^{86} - 4432 q^{87} + 1650 q^{88} - 2831 q^{89} + 512 q^{90} - 6002 q^{91} - 7134 q^{92} - 4428 q^{93} + 1697 q^{94} - 10434 q^{95} + 195 q^{96} - 2506 q^{97} - 3435 q^{98} - 5951 q^{99}+O(q^{100}) \) 77 * q - 14 * q^2 - 10 * q^3 + 296 * q^4 - 42 * q^5 - 13 * q^6 - 59 * q^7 - 150 * q^8 + 541 * q^9 + 2 * q^10 - 847 * q^11 - 88 * q^12 - 20 * q^13 - 282 * q^14 - 330 * q^15 + 936 * q^16 - 56 * q^17 - 343 * q^18 - 157 * q^19 - 450 * q^20 - 122 * q^21 + 154 * q^22 - 764 * q^23 - 346 * q^24 + 1413 * q^25 - 408 * q^26 - 358 * q^27 - 228 * q^28 - 557 * q^29 - 267 * q^30 - 780 * q^31 - 1739 * q^32 + 110 * q^33 - 1104 * q^34 - 1254 * q^35 + 375 * q^36 - 541 * q^37 - 2133 * q^38 - 1458 * q^39 - 554 * q^40 - 1723 * q^41 - 5 * q^42 - 688 * q^43 - 3256 * q^44 - 1588 * q^45 + 276 * q^46 - 3086 * q^47 - 4280 * q^48 + 2452 * q^49 - 2234 * q^50 - 1570 * q^51 - 715 * q^52 - 1230 * q^53 - 5166 * q^54 + 462 * q^55 - 3203 * q^56 + 1024 * q^57 - 3016 * q^58 - 5408 * q^59 - 8221 * q^60 + 566 * q^61 - 3642 * q^62 - 3035 * q^63 + 1084 * q^64 - 1794 * q^65 + 143 * q^66 - 1925 * q^67 - 1105 * q^68 - 3710 * q^69 - 5875 * q^70 - 9614 * q^71 - 2198 * q^72 - 384 * q^73 - 2378 * q^74 - 3888 * q^75 - 2809 * q^76 + 649 * q^77 - 1731 * q^78 - 1086 * q^79 - 4357 * q^80 + 2329 * q^81 - 3167 * q^82 - 3045 * q^83 - 5359 * q^84 + 2582 * q^85 - 6468 * q^86 - 4432 * q^87 + 1650 * q^88 - 2831 * q^89 + 512 * q^90 - 6002 * q^91 - 7134 * q^92 - 4428 * q^93 + 1697 * q^94 - 10434 * q^95 + 195 * q^96 - 2506 * q^97 - 3435 * q^98 - 5951 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−4.50745	−1.59362	−0.796812	−	0.604227i	$-0.793482\pi$
$2$	−4.50745	−1.59362	−0.796812	+	0.604227i	$0.793482\pi$
$3$	−6.76078	−1.30111	−0.650557	−	0.759458i	$-0.725464\pi$
$3$	−6.76078	−1.30111	−0.650557	+	0.759458i	$0.725464\pi$
$4$	12.3171	1.53964
$5$	12.7660	1.14182	0.570912	−	0.821012i	$-0.306590\pi$
$5$	12.7660	1.14182	0.570912	+	0.821012i	$0.306590\pi$
$6$	30.4739	2.07349
$7$	−21.9914	−1.18743	−0.593713	−	0.804677i	$-0.702338\pi$
$7$	−21.9914	−1.18743	−0.593713	+	0.804677i	$0.702338\pi$
$8$	−19.4592	−0.859983
$9$	18.7082	0.692895
$10$	−57.5420	−1.81964
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−83.2733	−2.00325
$13$	27.2605	0.581593	0.290796	−	0.956785i	$-0.406080\pi$
$13$	27.2605	0.581593	0.290796	+	0.956785i	$0.406080\pi$
$14$	99.1253	1.89231
$15$	−86.3079	−1.48564
$16$	−10.8256	−0.169149
$17$	97.8427	1.39590	0.697951	−	0.716145i	$-0.254095\pi$
$17$	97.8427	1.39590	0.697951	+	0.716145i	$0.254095\pi$
$18$	−84.3262	−1.10422
$19$	−138.783	−1.67573	−0.837867	−	0.545874i	$-0.816198\pi$
$19$	−138.783	−1.67573	−0.837867	+	0.545874i	$0.816198\pi$
$20$	157.240	1.75800
$21$	148.679	1.54497
$22$	49.5820	0.480496
$23$	13.0353	0.118176	0.0590882	−	0.998253i	$-0.481181\pi$
$23$	13.0353	0.118176	0.0590882	+	0.998253i	$0.481181\pi$
$24$	131.559	1.11894
$25$	37.9700	0.303760
$26$	−122.875	−0.926840
$27$	56.0592	0.399578
$28$	−270.871	−1.82821
$29$	240.666	1.54105	0.770525	−	0.637409i	$-0.219994\pi$
$29$	240.666	1.54105	0.770525	+	0.637409i	$0.219994\pi$
$30$	389.029	2.36755
$31$	178.870	1.03632	0.518162	−	0.855283i	$-0.326617\pi$
$31$	178.870	1.03632	0.518162	+	0.855283i	$0.326617\pi$
$32$	204.469	1.12954
$33$	74.3686	0.392300
$34$	−441.021	−2.22455
$35$	−280.742	−1.35583
$36$	230.431	1.06681
$37$	−434.646	−1.93123	−0.965613	−	0.259983i	$-0.916283\pi$
$37$	−434.646	−1.93123	−0.965613	+	0.259983i	$0.916283\pi$
$38$	625.557	2.67049
$39$	−184.302	−0.756718
$40$	−248.416	−0.981949
$41$	−216.517	−0.824739	−0.412370	−	0.911017i	$-0.635299\pi$
$41$	−216.517	−0.824739	−0.412370	+	0.911017i	$0.635299\pi$
$42$	−670.164	−2.46211
$43$	−408.696	−1.44943	−0.724716	−	0.689048i	$-0.758029\pi$
$43$	−408.696	−1.44943	−0.724716	+	0.689048i	$0.758029\pi$
$44$	−135.488	−0.464219
$45$	238.828	0.791164
$46$	−58.7562	−0.188329
$47$	−473.877	−1.47068	−0.735341	−	0.677698i	$-0.762978\pi$
$47$	−473.877	−1.47068	−0.735341	+	0.677698i	$0.762978\pi$
$48$	73.1893	0.220082
$49$	140.623	0.409979
$50$	−171.148	−0.484079
$51$	−661.493	−1.81623
$52$	335.771	0.895443
$53$	577.705	1.49724	0.748621	−	0.662998i	$-0.230716\pi$
$53$	577.705	1.49724	0.748621	+	0.662998i	$0.230716\pi$
$54$	−252.684	−0.636777
$55$	−140.426	−0.344273
$56$	427.935	1.02117
$57$	938.280	2.18032
$58$	−1084.79	−2.45586
$59$	598.961	1.32166	0.660831	−	0.750534i	$-0.270204\pi$
$59$	598.961	1.32166	0.660831	+	0.750534i	$0.270204\pi$
$60$	−1063.07	−2.28735
$61$	342.662	0.719235	0.359618	−	0.933100i	$-0.382907\pi$
$61$	342.662	0.719235	0.359618	+	0.933100i	$0.382907\pi$
$62$	−806.249	−1.65151
$63$	−411.419	−0.822761
$64$	−835.031	−1.63092
$65$	348.007	0.664076
$66$	−335.213	−0.625180
$67$	−674.759	−1.23037	−0.615186	−	0.788382i	$-0.710919\pi$
$67$	−674.759	−1.23037	−0.615186	+	0.788382i	$0.710919\pi$
$68$	1205.14	2.14919
$69$	−88.1291	−0.153761
$70$	1265.43	2.16068
$71$	−298.956	−0.499712	−0.249856	−	0.968283i	$-0.580383\pi$
$71$	−298.956	−0.499712	−0.249856	+	0.968283i	$0.580383\pi$
$72$	−364.046	−0.595878
$73$	47.4339	0.0760509	0.0380255	−	0.999277i	$-0.487893\pi$
$73$	47.4339	0.0760509	0.0380255	+	0.999277i	$0.487893\pi$
$74$	1959.15	3.07765
$75$	−256.707	−0.395226
$76$	−1709.40	−2.58003
$77$	241.906	0.358022
$78$	830.734	1.20592
$79$	2.47600	0.00352622	0.00176311	−	0.999998i	$-0.499439\pi$
$79$	2.47600	0.00352622	0.00176311	+	0.999998i	$0.499439\pi$
$80$	−138.199	−0.193139
$81$	−884.125	−1.21279
$82$	975.941	1.31432
$83$	1099.70	1.45432	0.727158	−	0.686470i	$-0.240841\pi$
$83$	1099.70	1.45432	0.727158	+	0.686470i	$0.240841\pi$
$84$	1831.30	2.37870
$85$	1249.06	1.59387
$86$	1842.18	2.30985
$87$	−1627.09	−2.00508
$88$	214.051	0.259295
$89$	543.214	0.646973	0.323486	−	0.946233i	$-0.395145\pi$
$89$	543.214	0.646973	0.323486	+	0.946233i	$0.395145\pi$
$90$	−1076.51	−1.26082
$91$	−599.497	−0.690598
$92$	160.558	0.181949
$93$	−1209.30	−1.34837
$94$	2135.98	2.34371
$95$	−1771.70	−1.91339
$96$	−1382.37	−1.46966
$97$	1375.32	1.43962	0.719809	−	0.694172i	$-0.244229\pi$
$97$	1375.32	1.43962	0.719809	+	0.694172i	$0.244229\pi$
$98$	−633.850	−0.653352
$99$	−205.790	−0.208916
$100$	467.681	0.467681
$101$	−1135.10	−1.11828	−0.559140	−	0.829074i	$-0.688868\pi$
$101$	−1135.10	−1.11828	−0.559140	+	0.829074i	$0.688868\pi$
$102$	2981.65	2.89438
$103$	334.782	0.320263	0.160132	−	0.987096i	$-0.448808\pi$
$103$	334.782	0.320263	0.160132	+	0.987096i	$0.448808\pi$
$104$	−530.468	−0.500160
$105$	1898.03	1.76409
$106$	−2603.98	−2.38604
$107$	158.790	0.143466	0.0717328	−	0.997424i	$-0.477147\pi$
$107$	158.790	0.143466	0.0717328	+	0.997424i	$0.477147\pi$
$108$	690.488	0.615206
$109$	−653.227	−0.574017	−0.287008	−	0.957928i	$-0.592661\pi$
$109$	−653.227	−0.574017	−0.287008	+	0.957928i	$0.592661\pi$
$110$	632.962	0.548641
$111$	2938.55	2.51274
$112$	238.070	0.200852
$113$	2346.98	1.95386	0.976928	−	0.213569i	$-0.0685090\pi$
$113$	2346.98	1.95386	0.976928	+	0.213569i	$0.0685090\pi$
$114$	−4229.25	−3.47461
$115$	166.409	0.134937
$116$	2964.31	2.37266
$117$	509.994	0.402983
$118$	−2699.79	−2.10623
$119$	−2151.70	−1.65753
$120$	1679.48	1.27763
$121$	121.000	0.0909091
$122$	−1544.53	−1.14619
$123$	1463.83	1.07308
$124$	2203.16	1.59556
$125$	−1111.02	−0.794983
$126$	1854.45	1.31117
$127$	2021.55	1.41247	0.706234	−	0.707979i	$-0.250393\pi$
$127$	2021.55	1.41247	0.706234	+	0.707979i	$0.250393\pi$
$128$	2128.11	1.46953
$129$	2763.10	1.88587
$130$	−1568.62	−1.05829
$131$	131.000	0.0873704
$131$	131.000	0.0873704
$132$	916.007	0.604001
$133$	3052.03	1.98981
$134$	3041.44	1.96075
$135$	715.651	0.456247
$136$	−1903.94	−1.20045
$137$	1117.78	0.697068	0.348534	−	0.937296i	$-0.386680\pi$
$137$	1117.78	0.697068	0.348534	+	0.937296i	$0.386680\pi$
$138$	397.238	0.245037
$139$	1152.52	0.703279	0.351639	−	0.936136i	$-0.385624\pi$
$139$	1152.52	0.703279	0.351639	+	0.936136i	$0.385624\pi$
$140$	−3457.93	−2.08749
$141$	3203.78	1.91352
$142$	1347.53	0.796353
$143$	−299.866	−0.175357
$144$	−202.526	−0.117203
$145$	3072.33	1.75961
$146$	−213.806	−0.121197
$147$	−950.719	−0.533429
$148$	−5353.59	−2.97339
$149$	93.2938	0.0512948	0.0256474	−	0.999671i	$-0.491835\pi$
$149$	93.2938	0.0512948	0.0256474	+	0.999671i	$0.491835\pi$
$150$	1157.09	0.629842
$151$	−1687.55	−0.909475	−0.454738	−	0.890625i	$-0.650267\pi$
$151$	−1687.55	−0.909475	−0.454738	+	0.890625i	$0.650267\pi$
$152$	2700.60	1.44110
$153$	1830.46	0.967214
$154$	−1090.38	−0.570553
$155$	2283.45	1.18330
$156$	−2270.07	−1.16507
$157$	−2602.01	−1.32269	−0.661346	−	0.750081i	$-0.730015\pi$
$157$	−2602.01	−1.32269	−0.661346	+	0.750081i	$0.730015\pi$
$158$	−11.1604	−0.00561948
$159$	−3905.74	−1.94808
$160$	2610.25	1.28974
$161$	−286.666	−0.140326
$162$	3985.15	1.93273
$163$	1094.30	0.525841	0.262920	−	0.964818i	$-0.415314\pi$
$163$	1094.30	0.525841	0.262920	+	0.964818i	$0.415314\pi$
$164$	−2666.87	−1.26980
$165$	949.387	0.447938
$166$	−4956.86	−2.31763
$167$	3768.03	1.74598	0.872990	−	0.487737i	$-0.162178\pi$
$167$	3768.03	1.74598	0.872990	+	0.487737i	$0.162178\pi$
$168$	−2893.18	−1.32865
$169$	−1453.86	−0.661750
$170$	−5630.07	−2.54004
$171$	−2596.37	−1.16111
$172$	−5033.96	−2.23160
$173$	1652.77	0.726345	0.363173	−	0.931722i	$-0.381694\pi$
$173$	1652.77	0.726345	0.363173	+	0.931722i	$0.381694\pi$
$174$	7334.02	3.19535
$175$	−835.014	−0.360692
$176$	119.081	0.0510005
$177$	−4049.45	−1.71963
$178$	−2448.51	−1.03103
$179$	537.833	0.224579	0.112289	−	0.993676i	$-0.464182\pi$
$179$	537.833	0.224579	0.112289	+	0.993676i	$0.464182\pi$
$180$	2941.67	1.21811
$181$	−386.612	−0.158766	−0.0793831	−	0.996844i	$-0.525295\pi$
$181$	−386.612	−0.158766	−0.0793831	+	0.996844i	$0.525295\pi$
$182$	2702.21	1.10055
$183$	−2316.66	−0.935807
$184$	−253.657	−0.101630
$185$	−5548.68	−2.20512
$186$	5450.87	2.14880
$187$	−1076.27	−0.420881
$188$	−5836.80	−2.26432
$189$	−1232.82	−0.474469
$190$	7985.84	3.04923
$191$	672.583	0.254798	0.127399	−	0.991852i	$-0.459337\pi$
$191$	672.583	0.254798	0.127399	+	0.991852i	$0.459337\pi$
$192$	5645.46	2.12201
$193$	−665.131	−0.248068	−0.124034	−	0.992278i	$-0.539583\pi$
$193$	−665.131	−0.248068	−0.124034	+	0.992278i	$0.539583\pi$
$194$	−6199.20	−2.29421
$195$	−2352.80	−0.864038
$196$	1732.07	0.631220
$197$	4497.28	1.62649	0.813243	−	0.581924i	$-0.197700\pi$
$197$	4497.28	1.62649	0.813243	+	0.581924i	$0.197700\pi$
$198$	927.588	0.332933
$199$	−5222.52	−1.86038	−0.930188	−	0.367083i	$-0.880357\pi$
$199$	−5222.52	−1.86038	−0.930188	+	0.367083i	$0.880357\pi$
$200$	−738.866	−0.261228
$201$	4561.90	1.60085
$202$	5116.39	1.78212
$203$	−5292.58	−1.82988
$204$	−8147.69	−2.79634
$205$	−2764.05	−0.941706
$206$	−1509.02	−0.510379
$207$	243.867	0.0818839
$208$	−295.110	−0.0983760
$209$	1526.61	0.505253
$210$	−8555.30	−2.81129
$211$	5207.43	1.69903	0.849513	−	0.527567i	$-0.176896\pi$
$211$	5207.43	1.69903	0.849513	+	0.527567i	$0.176896\pi$
$212$	7115.66	2.30521
$213$	2021.18	0.650182
$214$	−715.739	−0.228630
$215$	−5217.40	−1.65499
$216$	−1090.87	−0.343630
$217$	−3933.61	−1.23056
$218$	2944.39	0.914767
$219$	−320.690	−0.0989509
$220$	−1729.64	−0.530056
$221$	2667.24	0.811847
$222$	−13245.4	−4.00437
$223$	−3261.81	−0.979494	−0.489747	−	0.871865i	$-0.662911\pi$
$223$	−3261.81	−0.979494	−0.489747	+	0.871865i	$0.662911\pi$
$224$	−4496.57	−1.34125
$225$	710.349	0.210474
$226$	−10578.9	−3.11371
$227$	573.166	0.167588	0.0837938	−	0.996483i	$-0.473296\pi$
$227$	573.166	0.167588	0.0837938	+	0.996483i	$0.473296\pi$
$228$	11556.9	3.35691
$229$	−2723.80	−0.785998	−0.392999	−	0.919539i	$-0.628562\pi$
$229$	−2723.80	−0.785998	−0.392999	+	0.919539i	$0.628562\pi$
$230$	−750.080	−0.215038
$231$	−1635.47	−0.465827
$232$	−4683.16	−1.32528
$233$	−5313.58	−1.49401	−0.747005	−	0.664818i	$-0.768509\pi$
$233$	−5313.58	−1.49401	−0.747005	+	0.664818i	$0.768509\pi$
$234$	−2298.77	−0.642203
$235$	−6049.50	−1.67926
$236$	7377.47	2.03488
$237$	−16.7397	−0.00458801
$238$	9698.69	2.64148
$239$	−5614.88	−1.51965	−0.759825	−	0.650128i	$-0.774715\pi$
$239$	−5614.88	−1.51965	−0.759825	+	0.650128i	$0.774715\pi$
$240$	934.332	0.251295
$241$	1572.61	0.420335	0.210168	−	0.977665i	$-0.432599\pi$
$241$	1572.61	0.420335	0.210168	+	0.977665i	$0.432599\pi$
$242$	−545.402	−0.144875
$243$	4463.78	1.17840
$244$	4220.61	1.10736
$245$	1795.19	0.468123
$246$	−6598.12	−1.71008
$247$	−3783.29	−0.974595
$248$	−3480.67	−0.891221
$249$	−7434.86	−1.89223
$250$	5007.88	1.26690
$251$	−2167.46	−0.545055	−0.272528	−	0.962148i	$-0.587860\pi$
$251$	−2167.46	−0.545055	−0.272528	+	0.962148i	$0.587860\pi$
$252$	−5067.50	−1.26676
$253$	−143.389	−0.0356315
$254$	−9112.03	−2.25094
$255$	−8444.60	−2.07381
$256$	−2912.09	−0.710959
$257$	−4595.57	−1.11542	−0.557712	−	0.830035i	$-0.688321\pi$
$257$	−4595.57	−1.11542	−0.557712	+	0.830035i	$0.688321\pi$
$258$	−12454.6	−3.00538
$259$	9558.49	2.29319
$260$	4286.44	1.02244
$261$	4502.41	1.06779
$262$	−590.476	−0.139236
$263$	6463.61	1.51545	0.757725	−	0.652574i	$-0.226311\pi$
$263$	6463.61	1.51545	0.757725	+	0.652574i	$0.226311\pi$
$264$	−1447.15	−0.337372
$265$	7374.96	1.70959
$266$	−13756.9	−3.17101
$267$	−3672.55	−0.841785
$268$	−8311.09	−1.89433
$269$	−823.429	−0.186637	−0.0933184	−	0.995636i	$-0.529747\pi$
$269$	−823.429	−0.186637	−0.0933184	+	0.995636i	$0.529747\pi$
$270$	−3225.76	−0.727087
$271$	−1677.32	−0.375977	−0.187988	−	0.982171i	$-0.560197\pi$
$271$	−1677.32	−0.375977	−0.187988	+	0.982171i	$0.560197\pi$
$272$	−1059.20	−0.236116
$273$	4053.07	0.898546
$274$	−5038.33	−1.11086
$275$	−417.670	−0.0915871
$276$	−1085.50	−0.236736
$277$	6916.02	1.50016	0.750078	−	0.661349i	$-0.230016\pi$
$277$	6916.02	1.50016	0.750078	+	0.661349i	$0.230016\pi$
$278$	−5194.94	−1.12076
$279$	3346.33	0.718064
$280$	5463.01	1.16599
$281$	−3494.20	−0.741802	−0.370901	−	0.928672i	$-0.620951\pi$
$281$	−3494.20	−0.741802	−0.370901	+	0.928672i	$0.620951\pi$
$282$	−14440.9	−3.04944
$283$	−5405.62	−1.13545	−0.567723	−	0.823220i	$-0.692175\pi$
$283$	−5405.62	−1.13545	−0.567723	+	0.823220i	$0.692175\pi$
$284$	−3682.28	−0.769376
$285$	11978.1	2.48954
$286$	1351.63	0.279453
$287$	4761.52	0.979316
$288$	3825.25	0.782656
$289$	4660.20	0.948545
$290$	−13848.4	−2.80415
$291$	−9298.26	−1.87311
$292$	584.249	0.117091
$293$	−4449.28	−0.887132	−0.443566	−	0.896242i	$-0.646287\pi$
$293$	−4449.28	−0.887132	−0.443566	+	0.896242i	$0.646287\pi$
$294$	4285.32	0.850085
$295$	7646.32	1.50910
$296$	8457.86	1.66082
$297$	−616.652	−0.120477
$298$	−420.517	−0.0817446
$299$	355.350	0.0687305
$300$	−3161.89	−0.608506
$301$	8987.81	1.72109
$302$	7606.54	1.44936
$303$	7674.13	1.45501
$304$	1502.40	0.283450
$305$	4374.41	0.821240
$306$	−8250.70	−1.54138
$307$	−1631.88	−0.303375	−0.151687	−	0.988429i	$-0.548471\pi$
$307$	−1631.88	−0.303375	−0.151687	+	0.988429i	$0.548471\pi$
$308$	2979.58	0.551225
$309$	−2263.39	−0.416698
$310$	−10292.5	−1.88573
$311$	−8955.65	−1.63289	−0.816445	−	0.577424i	$-0.804058\pi$
$311$	−8955.65	−1.63289	−0.816445	+	0.577424i	$0.804058\pi$
$312$	3586.38	0.650764
$313$	−763.304	−0.137842	−0.0689209	−	0.997622i	$-0.521956\pi$
$313$	−763.304	−0.137842	−0.0689209	+	0.997622i	$0.521956\pi$
$314$	11728.4	2.10788
$315$	−5252.17	−0.939448
$316$	30.4972	0.00542911
$317$	−329.515	−0.0583830	−0.0291915	−	0.999574i	$-0.509293\pi$
$317$	−329.515	−0.0583830	−0.0291915	+	0.999574i	$0.509293\pi$
$318$	17604.9	3.10451
$319$	−2647.32	−0.464644
$320$	−10660.0	−1.86222
$321$	−1073.55	−0.186665
$322$	1292.13	0.223626
$323$	−13578.9	−2.33916
$324$	−10889.9	−1.86726
$325$	1035.08	0.176665
$326$	−4932.50	−0.837993
$327$	4416.33	0.746861
$328$	4213.25	0.709262
$329$	10421.2	1.74632
$330$	−4279.32	−0.713844
$331$	−1891.27	−0.314059	−0.157029	−	0.987594i	$-0.550192\pi$
$331$	−1891.27	−0.314059	−0.157029	+	0.987594i	$0.550192\pi$
$332$	13545.2	2.23912
$333$	−8131.43	−1.33814
$334$	−16984.2	−2.78244
$335$	−8613.96	−1.40487
$336$	−1609.54	−0.261332
$337$	−7376.65	−1.19238	−0.596190	−	0.802844i	$-0.703319\pi$
$337$	−7376.65	−1.19238	−0.596190	+	0.802844i	$0.703319\pi$
$338$	6553.22	1.05458
$339$	−15867.4	−2.54219
$340$	15384.8	2.45399
$341$	−1967.57	−0.312463
$342$	11703.0	1.85037
$343$	4450.56	0.700606
$344$	7952.89	1.24649
$345$	−1125.05	−0.175568
$346$	−7449.78	−1.15752
$347$	2496.80	0.386269	0.193134	−	0.981172i	$-0.438135\pi$
$347$	2496.80	0.386269	0.193134	+	0.981172i	$0.438135\pi$
$348$	−20041.0	−3.08710
$349$	−6061.22	−0.929656	−0.464828	−	0.885401i	$-0.653884\pi$
$349$	−6061.22	−0.929656	−0.464828	+	0.885401i	$0.653884\pi$
$350$	3763.79	0.574808
$351$	1528.20	0.232392
$352$	−2249.16	−0.340570
$353$	7953.18	1.19917	0.599583	−	0.800313i	$-0.295333\pi$
$353$	7953.18	1.19917	0.599583	+	0.800313i	$0.295333\pi$
$354$	18252.7	2.74045
$355$	−3816.46	−0.570583
$356$	6690.83	0.996105
$357$	14547.2	2.15663
$358$	−2424.26	−0.357894
$359$	11643.0	1.71168	0.855839	−	0.517242i	$-0.173041\pi$
$359$	11643.0	1.71168	0.855839	+	0.517242i	$0.173041\pi$
$360$	−4647.40	−0.680388
$361$	12401.7	1.80809
$362$	1742.64	0.253014
$363$	−818.055	−0.118283
$364$	−7384.08	−1.06327
$365$	605.540	0.0868367
$366$	10442.2	1.49132
$367$	−4019.57	−0.571717	−0.285858	−	0.958272i	$-0.592279\pi$
$367$	−4019.57	−0.571717	−0.285858	+	0.958272i	$0.592279\pi$
$368$	−141.115	−0.0199895
$369$	−4050.64	−0.571458
$370$	25010.4	3.51413
$371$	−12704.6	−1.77786
$372$	−14895.1	−2.07601
$373$	5307.12	0.736709	0.368354	−	0.929686i	$-0.379921\pi$
$373$	5307.12	0.736709	0.368354	+	0.929686i	$0.379921\pi$
$374$	4851.23	0.670726
$375$	7511.38	1.03436
$376$	9221.26	1.26476
$377$	6560.66	0.896264
$378$	5556.89	0.756125
$379$	−2538.89	−0.344100	−0.172050	−	0.985088i	$-0.555039\pi$
$379$	−2538.89	−0.344100	−0.172050	+	0.985088i	$0.555039\pi$
$380$	−21822.2	−2.94594
$381$	−13667.2	−1.83778
$382$	−3031.64	−0.406052
$383$	−8045.40	−1.07337	−0.536685	−	0.843783i	$-0.680324\pi$
$383$	−8045.40	−1.07337	−0.536685	+	0.843783i	$0.680324\pi$
$384$	−14387.7	−1.91202
$385$	3088.16	0.408798
$386$	2998.04	0.395328
$387$	−7645.95	−1.00430
$388$	16940.0	2.21649
$389$	8277.02	1.07882	0.539411	−	0.842043i	$-0.318647\pi$
$389$	8277.02	1.07882	0.539411	+	0.842043i	$0.318647\pi$
$390$	10605.1	1.37695
$391$	1275.41	0.164963
$392$	−2736.40	−0.352575
$393$	−885.662	−0.113679
$394$	−20271.3	−2.59201
$395$	31.6085	0.00402632
$396$	−2534.74	−0.321655
$397$	−7055.04	−0.891896	−0.445948	−	0.895059i	$-0.647133\pi$
$397$	−7055.04	−0.891896	−0.445948	+	0.895059i	$0.647133\pi$
$398$	23540.3	2.96474
$399$	−20634.1	−2.58897
$400$	−411.047	−0.0513808
$401$	−12537.8	−1.56137	−0.780685	−	0.624925i	$-0.785130\pi$
$401$	−12537.8	−1.56137	−0.780685	+	0.624925i	$0.785130\pi$
$402$	−20562.5	−2.55116
$403$	4876.09	0.602718
$404$	−13981.1	−1.72175
$405$	−11286.7	−1.38479
$406$	23856.0	2.91615
$407$	4781.11	0.582287
$408$	12872.1	1.56192
$409$	5408.79	0.653905	0.326953	−	0.945041i	$-0.393978\pi$
$409$	5408.79	0.653905	0.326953	+	0.945041i	$0.393978\pi$
$410$	12458.8	1.50073
$411$	−7557.06	−0.906964
$412$	4123.55	0.493090
$413$	−13172.0	−1.56938
$414$	−1099.22	−0.130492
$415$	14038.8	1.66057
$416$	5573.94	0.656934
$417$	−7791.96	−0.915045
$418$	−6881.13	−0.805184
$419$	−10923.7	−1.27364	−0.636822	−	0.771011i	$-0.719751\pi$
$419$	−10923.7	−1.27364	−0.636822	+	0.771011i	$0.719751\pi$
$420$	23378.3	2.71606
$421$	−10266.9	−1.18855	−0.594274	−	0.804263i	$-0.702560\pi$
$421$	−10266.9	−1.18855	−0.594274	+	0.804263i	$0.702560\pi$
$422$	−23472.3	−2.70761
$423$	−8865.37	−1.01903
$424$	−11241.7	−1.28760
$425$	3715.09	0.424019
$426$	−9110.35	−1.03615
$427$	−7535.62	−0.854038
$428$	1955.84	0.220885
$429$	2027.33	0.228159
$430$	23517.2	2.63744
$431$	−15420.1	−1.72334	−0.861669	−	0.507470i	$-0.830581\pi$
$431$	−15420.1	−1.72334	−0.861669	+	0.507470i	$0.830581\pi$
$432$	−606.873	−0.0675884
$433$	14217.5	1.57795	0.788973	−	0.614428i	$-0.210613\pi$
$433$	14217.5	1.57795	0.788973	+	0.614428i	$0.210613\pi$
$434$	17730.6	1.96105
$435$	−20771.3	−2.28945
$436$	−8045.88	−0.883779
$437$	−1809.08	−0.198032
$438$	1445.50	0.157691
$439$	−6437.72	−0.699899	−0.349950	−	0.936769i	$-0.613801\pi$
$439$	−6437.72	−0.699899	−0.349950	+	0.936769i	$0.613801\pi$
$440$	2732.57	0.296069
$441$	2630.79	0.284072
$442$	−12022.5	−1.29378
$443$	1192.25	0.127868	0.0639342	−	0.997954i	$-0.479635\pi$
$443$	1192.25	0.127868	0.0639342	+	0.997954i	$0.479635\pi$
$444$	36194.4	3.86872
$445$	6934.66	0.738729
$446$	14702.5	1.56095
$447$	−630.739	−0.0667403
$448$	18363.5	1.93659
$449$	−11523.5	−1.21119	−0.605597	−	0.795772i	$-0.707065\pi$
$449$	−11523.5	−1.21119	−0.605597	+	0.795772i	$0.707065\pi$
$450$	−3201.87	−0.335416
$451$	2381.69	0.248668
$452$	28908.1	3.00823
$453$	11409.2	1.18333
$454$	−2583.52	−0.267072
$455$	−7653.17	−0.788540
$456$	−18258.2	−1.87504
$457$	6274.11	0.642211	0.321105	−	0.947043i	$-0.395946\pi$
$457$	6274.11	0.642211	0.321105	+	0.947043i	$0.395946\pi$
$458$	12277.4	1.25259
$459$	5484.99	0.557772
$460$	2049.68	0.207754
$461$	13649.8	1.37903	0.689515	−	0.724272i	$-0.257824\pi$
$461$	13649.8	1.37903	0.689515	+	0.724272i	$0.257824\pi$
$462$	7371.81	0.742354
$463$	12499.3	1.25463	0.627313	−	0.778767i	$-0.284155\pi$
$463$	12499.3	1.25463	0.627313	+	0.778767i	$0.284155\pi$
$464$	−2605.34	−0.260668
$465$	−15437.9	−1.53960
$466$	23950.7	2.38089
$467$	10930.1	1.08305	0.541526	−	0.840684i	$-0.317847\pi$
$467$	10930.1	1.08305	0.541526	+	0.840684i	$0.317847\pi$
$468$	6281.66	0.620448
$469$	14838.9	1.46098
$470$	27267.8	2.67611
$471$	17591.6	1.72097
$472$	−11655.3	−1.13661
$473$	4495.66	0.437020
$474$	75.4533	0.00731157
$475$	−5269.58	−0.509021
$476$	−26502.8	−2.55200
$477$	10807.8	1.03743
$478$	25308.8	2.42175
$479$	17191.1	1.63984	0.819919	−	0.572480i	$-0.194019\pi$
$479$	17191.1	1.63984	0.819919	+	0.572480i	$0.194019\pi$
$480$	−17647.3	−1.67810
$481$	−11848.7	−1.12319
$482$	−7088.47	−0.669857
$483$	1938.08	0.182579
$484$	1490.37	0.139967
$485$	17557.3	1.64379
$486$	−20120.3	−1.87793
$487$	−9212.72	−0.857224	−0.428612	−	0.903489i	$-0.640997\pi$
$487$	−9212.72	−0.857224	−0.428612	+	0.903489i	$0.640997\pi$
$488$	−6667.92	−0.618530
$489$	−7398.31	−0.684178
$490$	−8091.71	−0.746013
$491$	−5666.67	−0.520842	−0.260421	−	0.965495i	$-0.583861\pi$
$491$	−5666.67	−0.520842	−0.260421	+	0.965495i	$0.583861\pi$
$492$	18030.1	1.65215
$493$	23547.4	2.15116
$494$	17053.0	1.55314
$495$	−2627.11	−0.238545
$496$	−1936.37	−0.175294
$497$	6574.47	0.593371
$498$	33512.3	3.01550
$499$	687.426	0.0616702	0.0308351	−	0.999524i	$-0.490183\pi$
$499$	687.426	0.0616702	0.0308351	+	0.999524i	$0.490183\pi$
$500$	−13684.6	−1.22399
$501$	−25474.8	−2.27172
$502$	9769.73	0.868614
$503$	−6757.71	−0.599028	−0.299514	−	0.954092i	$-0.596825\pi$
$503$	−6757.71	−0.599028	−0.299514	+	0.954092i	$0.596825\pi$
$504$	8005.89	0.707561
$505$	−14490.6	−1.27688
$506$	646.318	0.0567833
$507$	9829.26	0.861012
$508$	24899.6	2.17469
$509$	−13703.2	−1.19329	−0.596646	−	0.802505i	$-0.703500\pi$
$509$	−13703.2	−1.19329	−0.596646	+	0.802505i	$0.703500\pi$
$510$	38063.6	3.30488
$511$	−1043.14	−0.0903048
$512$	−3898.75	−0.336527
$513$	−7780.06	−0.669587
$514$	20714.3	1.77757
$515$	4273.82	0.365684
$516$	34033.5	2.90357
$517$	5212.64	0.443427
$518$	−43084.4	−3.65448
$519$	−11174.0	−0.945057
$520$	−6771.93	−0.571094
$521$	−17124.5	−1.44000	−0.719998	−	0.693976i	$-0.755857\pi$
$521$	−17124.5	−1.44000	−0.719998	+	0.693976i	$0.755857\pi$
$522$	−20294.4	−1.70165
$523$	13771.6	1.15141	0.575706	−	0.817657i	$-0.304727\pi$
$523$	13771.6	1.15141	0.575706	+	0.817657i	$0.304727\pi$
$524$	1613.54	0.134519
$525$	5645.35	0.469302
$526$	−29134.4	−2.41506
$527$	17501.1	1.44661
$528$	−805.082	−0.0663574
$529$	−11997.1	−0.986034
$530$	−33242.3	−2.72444
$531$	11205.5	0.915774
$532$	37592.2	3.06359
$533$	−5902.37	−0.479662
$534$	16553.9	1.34149
$535$	2027.11	0.163812
$536$	13130.3	1.05810
$537$	−3636.17	−0.292202
$538$	3711.56	0.297429
$539$	−1546.85	−0.123613
$540$	8814.75	0.702457
$541$	−20385.5	−1.62004	−0.810020	−	0.586402i	$-0.800544\pi$
$541$	−20385.5	−1.62004	−0.810020	+	0.586402i	$0.800544\pi$
$542$	7560.42	0.599166
$543$	2613.80	0.206573
$544$	20005.8	1.57673
$545$	−8339.08	−0.655426
$546$	−18269.0	−1.43194
$547$	−24302.8	−1.89965	−0.949827	−	0.312774i	$-0.898742\pi$
$547$	−24302.8	−1.89965	−0.949827	+	0.312774i	$0.898742\pi$
$548$	13767.8	1.07323
$549$	6410.58	0.498355
$550$	1882.63	0.145955
$551$	−33400.2	−2.58239
$552$	1714.92	0.132232
$553$	−54.4507	−0.00418713
$554$	−31173.6	−2.39069
$555$	37513.4	2.86911
$556$	14195.8	1.08280
$557$	−9961.50	−0.757778	−0.378889	−	0.925442i	$-0.623694\pi$
$557$	−9961.50	−0.757778	−0.378889	+	0.925442i	$0.623694\pi$
$558$	−15083.4	−1.14432
$559$	−11141.3	−0.842979
$560$	3039.19	0.229338
$561$	7276.43	0.547613
$562$	15749.9	1.18215
$563$	3130.09	0.234312	0.117156	−	0.993114i	$-0.462622\pi$
$563$	3130.09	0.234312	0.117156	+	0.993114i	$0.462622\pi$
$564$	39461.3	2.94614
$565$	29961.5	2.23096
$566$	24365.6	1.80947
$567$	19443.2	1.44010
$568$	5817.44	0.429744
$569$	−9406.17	−0.693018	−0.346509	−	0.938047i	$-0.612633\pi$
$569$	−9406.17	−0.693018	−0.346509	+	0.938047i	$0.612633\pi$
$570$	−53990.5	−3.96739
$571$	−6600.31	−0.483738	−0.241869	−	0.970309i	$-0.577760\pi$
$571$	−6600.31	−0.483738	−0.241869	+	0.970309i	$0.577760\pi$
$572$	−3693.48	−0.269986
$573$	−4547.19	−0.331521
$574$	−21462.3	−1.56066
$575$	494.952	0.0358973
$576$	−15621.9	−1.13006
$577$	900.866	0.0649975	0.0324987	−	0.999472i	$-0.489654\pi$
$577$	900.866	0.0649975	0.0324987	+	0.999472i	$0.489654\pi$
$578$	−21005.6	−1.51162
$579$	4496.80	0.322765
$580$	37842.2	2.70916
$581$	−24184.1	−1.72689
$582$	41911.5	2.98503
$583$	−6354.75	−0.451436
$584$	−923.026	−0.0654025
$585$	6510.57	0.460135
$586$	20054.9	1.41376
$587$	6838.61	0.480851	0.240426	−	0.970668i	$-0.422713\pi$
$587$	6838.61	0.480851	0.240426	+	0.970668i	$0.422713\pi$
$588$	−11710.1	−0.821288
$589$	−24824.1	−1.73660
$590$	−34465.4	−2.40495
$591$	−30405.1	−2.11624
$592$	4705.29	0.326666
$593$	−13776.7	−0.954032	−0.477016	−	0.878895i	$-0.658282\pi$
$593$	−13776.7	−0.954032	−0.477016	+	0.878895i	$0.658282\pi$
$594$	2779.53	0.191996
$595$	−27468.6	−1.89261
$596$	1149.11	0.0789755
$597$	35308.4	2.42056
$598$	−1601.72	−0.109531
$599$	−4660.14	−0.317877	−0.158939	−	0.987288i	$-0.550807\pi$
$599$	−4660.14	−0.317877	−0.158939	+	0.987288i	$0.550807\pi$
$600$	4995.31	0.339888
$601$	−2280.04	−0.154750	−0.0773751	−	0.997002i	$-0.524654\pi$
$601$	−2280.04	−0.154750	−0.0773751	+	0.997002i	$0.524654\pi$
$602$	−40512.1	−2.74277
$603$	−12623.5	−0.852519
$604$	−20785.7	−1.40026
$605$	1544.68	0.103802
$606$	−34590.8	−2.31874
$607$	−20394.2	−1.36372	−0.681859	−	0.731484i	$-0.738828\pi$
$607$	−20394.2	−1.36372	−0.681859	+	0.731484i	$0.738828\pi$
$608$	−28376.8	−1.89282
$609$	35782.0	2.38088
$610$	−19717.4	−1.30875
$611$	−12918.1	−0.855337
$612$	22546.0	1.48916
$613$	8649.48	0.569901	0.284950	−	0.958542i	$-0.408023\pi$
$613$	8649.48	0.569901	0.284950	+	0.958542i	$0.408023\pi$
$614$	7355.60	0.483466
$615$	18687.2	1.22527
$616$	−4707.29	−0.307893
$617$	−14263.5	−0.930678	−0.465339	−	0.885133i	$-0.654068\pi$
$617$	−14263.5	−0.930678	−0.465339	+	0.885133i	$0.654068\pi$
$618$	10202.1	0.664061
$619$	9193.10	0.596934	0.298467	−	0.954420i	$-0.403525\pi$
$619$	9193.10	0.596934	0.298467	+	0.954420i	$0.403525\pi$
$620$	28125.5	1.82185
$621$	730.751	0.0472207
$622$	40367.2	2.60221
$623$	−11946.1	−0.768232
$624$	1995.18	0.127998
$625$	−18929.5	−1.21149
$626$	3440.56	0.219668
$627$	−10321.1	−0.657391
$628$	−32049.2	−2.03647
$629$	−42527.0	−2.69580
$630$	23673.9	1.49713
$631$	18011.9	1.13636	0.568179	−	0.822905i	$-0.307648\pi$
$631$	18011.9	1.13636	0.568179	+	0.822905i	$0.307648\pi$
$632$	−48.1809	−0.00303249
$633$	−35206.3	−2.21063
$634$	1485.27	0.0930406
$635$	25807.0	1.61279
$636$	−48107.4	−2.99934
$637$	3833.45	0.238441
$638$	11932.7	0.740468
$639$	−5592.92	−0.346248
$640$	27167.3	1.67794
$641$	4509.23	0.277853	0.138926	−	0.990303i	$-0.455635\pi$
$641$	4509.23	0.277853	0.138926	+	0.990303i	$0.455635\pi$
$642$	4838.95	0.297474
$643$	−17240.2	−1.05736	−0.528682	−	0.848820i	$-0.677314\pi$
$643$	−17240.2	−1.05736	−0.528682	+	0.848820i	$0.677314\pi$
$644$	−3530.90	−0.216051
$645$	35273.7	2.15333
$646$	61206.2	3.72775
$647$	−10158.3	−0.617252	−0.308626	−	0.951183i	$-0.599869\pi$
$647$	−10158.3	−0.617252	−0.308626	+	0.951183i	$0.599869\pi$
$648$	17204.4	1.04298
$649$	−6588.57	−0.398496
$650$	−4665.58	−0.281537
$651$	26594.3	1.60109
$652$	13478.6	0.809605
$653$	10228.0	0.612944	0.306472	−	0.951880i	$-0.400851\pi$
$653$	10228.0	0.612944	0.306472	+	0.951880i	$0.400851\pi$
$654$	−19906.4	−1.19022
$655$	1672.34	0.0997615
$656$	2343.92	0.139504
$657$	887.402	0.0526953
$658$	−46973.2	−2.78299
$659$	23475.6	1.38768	0.693839	−	0.720130i	$-0.255918\pi$
$659$	23475.6	1.38768	0.693839	+	0.720130i	$0.255918\pi$
$660$	11693.7	0.689663
$661$	−11830.0	−0.696115	−0.348058	−	0.937473i	$-0.613159\pi$
$661$	−11830.0	−0.696115	−0.348058	+	0.937473i	$0.613159\pi$
$662$	8524.80	0.500492
$663$	−18032.6	−1.05630
$664$	−21399.4	−1.25069
$665$	38962.1	2.27201
$666$	36652.0	2.13249
$667$	3137.16	0.182116
$668$	46411.3	2.68818
$669$	22052.4	1.27443
$670$	38827.0	2.23883
$671$	−3769.28	−0.216858
$672$	30400.3	1.74512
$673$	−18548.7	−1.06241	−0.531204	−	0.847244i	$-0.678260\pi$
$673$	−18548.7	−1.06241	−0.531204	+	0.847244i	$0.678260\pi$
$674$	33249.9	1.90021
$675$	2128.57	0.121376
$676$	−17907.4	−1.01886
$677$	−14079.0	−0.799262	−0.399631	−	0.916676i	$-0.630862\pi$
$677$	−14079.0	−0.799262	−0.399631	+	0.916676i	$0.630862\pi$
$678$	71521.8	4.05129
$679$	−30245.3	−1.70944
$680$	−24305.7	−1.37070
$681$	−3875.05	−0.218050
$682$	8868.73	0.497949
$683$	−10601.8	−0.593948	−0.296974	−	0.954886i	$-0.595977\pi$
$683$	−10601.8	−0.593948	−0.296974	+	0.954886i	$0.595977\pi$
$684$	−31979.8	−1.78769
$685$	14269.5	0.795928
$686$	−20060.7	−1.11650
$687$	18415.0	1.02267
$688$	4424.36	0.245170
$689$	15748.5	0.870785
$690$	5071.12	0.279789
$691$	−10554.9	−0.581084	−0.290542	−	0.956862i	$-0.593836\pi$
$691$	−10554.9	−0.581084	−0.290542	+	0.956862i	$0.593836\pi$
$692$	20357.4	1.11831
$693$	4525.61	0.248072
$694$	−11254.2	−0.615567
$695$	14713.1	0.803020
$696$	31661.8	1.72434
$697$	−21184.6	−1.15126
$698$	27320.7	1.48152
$699$	35924.0	1.94388
$700$	−10285.0	−0.555336
$701$	17979.8	0.968743	0.484372	−	0.874862i	$-0.339048\pi$
$701$	17979.8	0.968743	0.484372	+	0.874862i	$0.339048\pi$
$702$	−6888.30	−0.370345
$703$	60321.4	3.23622
$704$	9185.34	0.491741
$705$	40899.3	2.18490
$706$	−35848.6	−1.91102
$707$	24962.4	1.32787
$708$	−49877.5	−2.64761
$709$	−32458.7	−1.71934	−0.859671	−	0.510848i	$-0.829331\pi$
$709$	−32458.7	−1.71934	−0.859671	+	0.510848i	$0.829331\pi$
$710$	17202.5	0.909295
$711$	46.3214	0.00244330
$712$	−10570.5	−0.556386
$713$	2331.63	0.122469
$714$	−65570.7	−3.43687
$715$	−3828.07	−0.200226
$716$	6624.56	0.345770
$717$	37961.0	1.97724
$718$	−52480.1	−2.72777
$719$	5113.84	0.265249	0.132625	−	0.991166i	$-0.457660\pi$
$719$	5113.84	0.265249	0.132625	+	0.991166i	$0.457660\pi$
$720$	−2585.45	−0.133825
$721$	−7362.34	−0.380288
$722$	−55899.9	−2.88141
$723$	−10632.1	−0.546904
$724$	−4761.95	−0.244443
$725$	9138.07	0.468110
$726$	3687.34	0.188499
$727$	15870.0	0.809607	0.404804	−	0.914404i	$-0.367340\pi$
$727$	15870.0	0.809607	0.404804	+	0.914404i	$0.367340\pi$
$728$	11665.7	0.593902
$729$	−6307.25	−0.320441
$730$	−2729.44	−0.138385
$731$	−39987.9	−2.02327
$732$	−28534.6	−1.44080
$733$	−35891.1	−1.80855	−0.904275	−	0.426951i	$-0.859588\pi$
$733$	−35891.1	−1.80855	−0.904275	+	0.426951i	$0.859588\pi$
$734$	18118.0	0.911102
$735$	−12136.9	−0.609081
$736$	2665.33	0.133485
$737$	7422.35	0.370971
$738$	18258.1	0.910689
$739$	−30160.3	−1.50130	−0.750652	−	0.660698i	$-0.770261\pi$
$739$	−30160.3	−1.50130	−0.750652	+	0.660698i	$0.770261\pi$
$740$	−68343.7	−3.39509
$741$	25578.0	1.26806
$742$	57265.1	2.83325
$743$	−10230.4	−0.505135	−0.252568	−	0.967579i	$-0.581275\pi$
$743$	−10230.4	−0.505135	−0.252568	+	0.967579i	$0.581275\pi$
$744$	23532.0	1.15958
$745$	1190.99	0.0585696
$746$	−23921.6	−1.17404
$747$	20573.4	1.00769
$748$	−13256.5	−0.648004
$749$	−3492.02	−0.170355
$750$	−33857.2	−1.64839
$751$	33101.6	1.60838	0.804190	−	0.594372i	$-0.202599\pi$
$751$	33101.6	1.60838	0.804190	+	0.594372i	$0.202599\pi$
$752$	5129.98	0.248765
$753$	14653.7	0.709179
$754$	−29571.9	−1.42831
$755$	−21543.2	−1.03846
$756$	−15184.8	−0.730511
$757$	−24971.8	−1.19896	−0.599482	−	0.800388i	$-0.704627\pi$
$757$	−24971.8	−1.19896	−0.599482	+	0.800388i	$0.704627\pi$
$758$	11443.9	0.548366
$759$	969.420	0.0463606
$760$	34475.8	1.64549
$761$	3735.87	0.177957	0.0889785	−	0.996034i	$-0.471640\pi$
$761$	3735.87	0.177957	0.0889785	+	0.996034i	$0.471640\pi$
$762$	61604.4	2.92873
$763$	14365.4	0.681602
$764$	8284.28	0.392297
$765$	23367.6	1.10439
$766$	36264.3	1.71055
$767$	16328.0	0.768669
$768$	19688.0	0.925039
$769$	41316.7	1.93748	0.968738	−	0.248087i	$-0.0798020\pi$
$769$	41316.7	1.93748	0.968738	+	0.248087i	$0.0798020\pi$
$770$	−13919.7	−0.651471
$771$	31069.7	1.45129
$772$	−8192.49	−0.381936
$773$	−27648.3	−1.28647	−0.643235	−	0.765669i	$-0.722408\pi$
$773$	−27648.3	−1.28647	−0.643235	+	0.765669i	$0.722408\pi$
$774$	34463.8	1.60048
$775$	6791.70	0.314794
$776$	−26762.7	−1.23805
$777$	−64622.8	−2.98370
$778$	−37308.3	−1.71924
$779$	30048.9	1.38204
$780$	−28979.7	−1.33031
$781$	3288.52	0.150669
$782$	−5748.86	−0.262889
$783$	13491.5	0.615770
$784$	−1522.32	−0.0693477
$785$	−33217.1	−1.51028
$786$	3992.08	0.181161
$787$	−14702.9	−0.665948	−0.332974	−	0.942936i	$-0.608052\pi$
$787$	−14702.9	−0.665948	−0.332974	+	0.942936i	$0.608052\pi$
$788$	55393.5	2.50420
$789$	−43699.1	−1.97177
$790$	−142.474	−0.00641645
$791$	−51613.5	−2.32006
$792$	4004.51	0.179664
$793$	9341.14	0.418302
$794$	31800.3	1.42135
$795$	−49860.5	−2.22437
$796$	−64326.4	−2.86431
$797$	31272.9	1.38989	0.694944	−	0.719063i	$-0.255429\pi$
$797$	31272.9	1.38989	0.694944	+	0.719063i	$0.255429\pi$
$798$	93007.3	4.12584
$799$	−46365.4	−2.05293
$800$	7763.70	0.343110
$801$	10162.5	0.448284
$802$	56513.7	2.48824
$803$	−521.773	−0.0229302
$804$	56189.5	2.46474
$805$	−3659.57	−0.160227
$806$	−21978.7	−0.960506
$807$	5567.02	0.242836
$808$	22088.0	0.961701
$809$	−21846.3	−0.949413	−0.474707	−	0.880144i	$-0.657446\pi$
$809$	−21846.3	−0.949413	−0.474707	+	0.880144i	$0.657446\pi$
$810$	50874.3	2.20684
$811$	−16401.2	−0.710142	−0.355071	−	0.934839i	$-0.615543\pi$
$811$	−16401.2	−0.710142	−0.355071	+	0.934839i	$0.615543\pi$
$812$	−65189.3	−2.81736
$813$	11340.0	0.489188
$814$	−21550.6	−0.927946
$815$	13969.8	0.600417
$816$	7161.04	0.307214
$817$	56720.0	2.42886
$818$	−24379.8	−1.04208
$819$	−11215.5	−0.478512
$820$	−34045.2	−1.44989
$821$	−41987.8	−1.78488	−0.892439	−	0.451167i	$-0.851008\pi$
$821$	−41987.8	−1.78488	−0.892439	+	0.451167i	$0.851008\pi$
$822$	34063.1	1.44536
$823$	16161.8	0.684528	0.342264	−	0.939604i	$-0.388806\pi$
$823$	16161.8	0.684528	0.342264	+	0.939604i	$0.388806\pi$
$824$	−6514.60	−0.275421
$825$	2823.78	0.119165
$826$	59372.2	2.50100
$827$	−18531.3	−0.779197	−0.389599	−	0.920985i	$-0.627386\pi$
$827$	−18531.3	−0.779197	−0.389599	+	0.920985i	$0.627386\pi$
$828$	3003.74	0.126072
$829$	−10381.9	−0.434956	−0.217478	−	0.976065i	$-0.569783\pi$
$829$	−10381.9	−0.434956	−0.217478	+	0.976065i	$0.569783\pi$
$830$	−63279.1	−2.64633
$831$	−46757.7	−1.95187
$832$	−22763.4	−0.948531
$833$	13758.9	0.572290
$834$	35121.9	1.45824
$835$	48102.5	1.99360
$836$	18803.4	0.777908
$837$	10027.3	0.414092
$838$	49237.9	2.02971
$839$	−30624.0	−1.26014	−0.630071	−	0.776537i	$-0.716974\pi$
$839$	−30624.0	−1.26014	−0.630071	+	0.776537i	$0.716974\pi$
$840$	−36934.2	−1.51709
$841$	33530.9	1.37484
$842$	46277.6	1.89410
$843$	23623.5	0.965169
$844$	64140.6	2.61589
$845$	−18560.0	−0.755601
$846$	39960.2	1.62395
$847$	−2660.96	−0.107948
$848$	−6253.98	−0.253258
$849$	36546.2	1.47734
$850$	−16745.6	−0.675728
$851$	−5665.76	−0.228225
$852$	24895.1	1.00105
$853$	468.325	0.0187985	0.00939926	−	0.999956i	$-0.497008\pi$
$853$	468.325	0.0187985	0.00939926	+	0.999956i	$0.497008\pi$
$854$	33966.5	1.36102
$855$	−33145.2	−1.32578
$856$	−3089.93	−0.123378
$857$	25709.6	1.02477	0.512383	−	0.858757i	$-0.328763\pi$
$857$	25709.6	1.02477	0.512383	+	0.858757i	$0.328763\pi$
$858$	−9138.07	−0.363600
$859$	1733.93	0.0688717	0.0344358	−	0.999407i	$-0.489037\pi$
$859$	1733.93	0.0688717	0.0344358	+	0.999407i	$0.489037\pi$
$860$	−64263.3	−2.54809
$861$	−32191.6	−1.27420
$862$	69505.2	2.74635
$863$	18010.2	0.710398	0.355199	−	0.934791i	$-0.384413\pi$
$863$	18010.2	0.710398	0.355199	+	0.934791i	$0.384413\pi$
$864$	11462.4	0.451341
$865$	21099.2	0.829358
$866$	−64084.8	−2.51465
$867$	−31506.6	−1.23416
$868$	−48450.7	−1.89461
$869$	−27.2360	−0.00106320
$870$	93625.8	3.64852
$871$	−18394.3	−0.715576
$872$	12711.3	0.493645
$873$	25729.8	0.997504
$874$	8154.35	0.315589
$875$	24433.0	0.943983
$876$	−3949.98	−0.152349
$877$	−2735.53	−0.105327	−0.0526637	−	0.998612i	$-0.516771\pi$
$877$	−2735.53	−0.105327	−0.0526637	+	0.998612i	$0.516771\pi$
$878$	29017.7	1.11538
$879$	30080.6	1.15426
$880$	1520.19	0.0582335
$881$	−49024.1	−1.87476	−0.937381	−	0.348307i	$-0.886757\pi$
$881$	−49024.1	−1.87476	−0.937381	+	0.348307i	$0.886757\pi$
$882$	−11858.2	−0.452705
$883$	−33709.8	−1.28474	−0.642369	−	0.766395i	$-0.722048\pi$
$883$	−33709.8	−1.28474	−0.642369	+	0.766395i	$0.722048\pi$
$884$	32852.7	1.24995
$885$	−51695.1	−1.96352
$886$	−5374.03	−0.203774
$887$	−19543.8	−0.739814	−0.369907	−	0.929069i	$-0.620611\pi$
$887$	−19543.8	−0.739814	−0.369907	+	0.929069i	$0.620611\pi$
$888$	−57181.8	−2.16092
$889$	−44456.7	−1.67720
$890$	−31257.6	−1.17726
$891$	9725.37	0.365670
$892$	−40176.1	−1.50807
$893$	65765.9	2.46447
$894$	2843.02	0.106359
$895$	6865.97	0.256429
$896$	−46800.1	−1.74496
$897$	−2402.44	−0.0894262
$898$	51941.4	1.93019
$899$	43047.9	1.59703
$900$	8749.46	0.324054
$901$	56524.2	2.09001
$902$	−10735.3	−0.396284
$903$	−60764.6	−2.23933
$904$	−45670.4	−1.68028
$905$	−4935.48	−0.181283
$906$	−51426.2	−1.88578
$907$	−13471.3	−0.493173	−0.246587	−	0.969121i	$-0.579309\pi$
$907$	−13471.3	−0.493173	−0.246587	+	0.969121i	$0.579309\pi$
$908$	7059.76	0.258025
$909$	−21235.6	−0.774850
$910$	34496.3	1.25664
$911$	30209.4	1.09866	0.549331	−	0.835605i	$-0.314883\pi$
$911$	30209.4	1.09866	0.549331	+	0.835605i	$0.314883\pi$
$912$	−10157.4	−0.368800
$913$	−12096.7	−0.438493
$914$	−28280.2	−1.02344
$915$	−29574.4	−1.06853
$916$	−33549.3	−1.21015
$917$	−2880.88	−0.103746
$918$	−24723.3	−0.888879
$919$	16032.6	0.575480	0.287740	−	0.957709i	$-0.407096\pi$
$919$	16032.6	0.575480	0.287740	+	0.957709i	$0.407096\pi$
$920$	−3238.18	−0.116043
$921$	11032.8	0.394725
$922$	−61525.6	−2.19766
$923$	−8149.69	−0.290629
$924$	−20144.3	−0.717206
$925$	−16503.5	−0.586629
$926$	−56340.0	−1.99940
$927$	6263.17	0.221909
$928$	49208.7	1.74068
$929$	18739.6	0.661816	0.330908	−	0.943663i	$-0.392645\pi$
$929$	18739.6	0.661816	0.330908	+	0.943663i	$0.392645\pi$
$930$	69585.7	2.45355
$931$	−19516.0	−0.687016
$932$	−65448.0	−2.30024
$933$	60547.2	2.12457
$934$	−49266.9	−1.72598
$935$	−13739.6	−0.480571
$936$	−9924.08	−0.346558
$937$	40972.2	1.42850	0.714249	−	0.699891i	$-0.246768\pi$
$937$	40972.2	1.42850	0.714249	+	0.699891i	$0.246768\pi$
$938$	−66885.7	−2.32825
$939$	5160.53	0.179348
$940$	−74512.4	−2.58545
$941$	−8996.37	−0.311661	−0.155831	−	0.987784i	$-0.549805\pi$
$941$	−8996.37	−0.311661	−0.155831	+	0.987784i	$0.549805\pi$
$942$	−79293.3	−2.74258
$943$	−2822.38	−0.0974647
$944$	−6484.09	−0.223558
$945$	−15738.2	−0.541760
$946$	−20263.9	−0.696446
$947$	−52524.0	−1.80232	−0.901161	−	0.433484i	$-0.857284\pi$
$947$	−52524.0	−1.80232	−0.901161	+	0.433484i	$0.857284\pi$
$948$	−206.185	−0.00706389
$949$	1293.07	0.0442307
$950$	23752.4	0.811189
$951$	2227.78	0.0759629
$952$	41870.4	1.42545
$953$	44153.6	1.50081	0.750407	−	0.660976i	$-0.229858\pi$
$953$	44153.6	1.50081	0.750407	+	0.660976i	$0.229858\pi$
$954$	−48715.6	−1.65328
$955$	8586.18	0.290934
$956$	−69159.1	−2.33971
$957$	17898.0	0.604555
$958$	−77488.1	−2.61328
$959$	−24581.5	−0.827716
$960$	72069.8	2.42296
$961$	2203.54	0.0739665
$962$	53407.3	1.78994
$963$	2970.67	0.0994066
$964$	19370.0	0.647165
$965$	−8491.04	−0.283250
$966$	−8735.82	−0.290963
$967$	−53830.3	−1.79014	−0.895070	−	0.445926i	$-0.852874\pi$
$967$	−53830.3	−1.79014	−0.895070	+	0.445926i	$0.852874\pi$
$968$	−2354.56	−0.0781803
$969$	91803.9	3.04352
$970$	−79138.8	−2.61958
$971$	−28498.7	−0.941881	−0.470941	−	0.882165i	$-0.656085\pi$
$971$	−28498.7	−0.941881	−0.470941	+	0.882165i	$0.656085\pi$
$972$	54980.9	1.81431
$973$	−25345.6	−0.835091
$974$	41525.9	1.36609
$975$	−6997.96	−0.229861
$976$	−3709.51	−0.121658
$977$	9229.39	0.302225	0.151113	−	0.988517i	$-0.451714\pi$
$977$	9229.39	0.302225	0.151113	+	0.988517i	$0.451714\pi$
$978$	33347.5	1.09032
$979$	−5975.36	−0.195070
$980$	22111.5	0.720741
$981$	−12220.7	−0.397733
$982$	25542.2	0.830026
$983$	−8010.32	−0.259908	−0.129954	−	0.991520i	$-0.541483\pi$
$983$	−8010.32	−0.259908	−0.129954	+	0.991520i	$0.541483\pi$
$984$	−28484.9	−0.922830
$985$	57412.1	1.85716
$986$	−106139.	−3.42814
$987$	−70455.6	−2.27217
$988$	−46599.2	−1.50053
$989$	−5327.49	−0.171289
$990$	11841.6	0.380151
$991$	4968.71	0.159270	0.0796348	−	0.996824i	$-0.474625\pi$
$991$	4968.71	0.159270	0.0796348	+	0.996824i	$0.474625\pi$
$992$	36573.4	1.17057
$993$	12786.5	0.408626
$994$	−29634.1	−0.945610
$995$	−66670.6	−2.12422
$996$	−91576.0	−2.91335
$997$	36568.5	1.16162	0.580811	−	0.814038i	$-0.302735\pi$
$997$	36568.5	1.16162	0.580811	+	0.814038i	$0.302735\pi$
$998$	−3098.54	−0.0982791
$999$	−24365.9	−0.771675

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.4.a.a.1.11	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.4.a.a.1.11	✓	77	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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-4.50745 q^{2} -6.76078 q^{3} +12.3171 q^{4} +12.7660 q^{5} +30.4739 q^{6} -21.9914 q^{7} -19.4592 q^{8} +18.7082 q^{9} +O(q^{10})\)	\(q-4.50745 q^{2} -6.76078 q^{3} +12.3171 q^{4} +12.7660 q^{5} +30.4739 q^{6} -21.9914 q^{7} -19.4592 q^{8} +18.7082 q^{9} -57.5420 q^{10} -11.0000 q^{11} -83.2733 q^{12} +27.2605 q^{13} +99.1253 q^{14} -86.3079 q^{15} -10.8256 q^{16} +97.8427 q^{17} -84.3262 q^{18} -138.783 q^{19} +157.240 q^{20} +148.679 q^{21} +49.5820 q^{22} +13.0353 q^{23} +131.559 q^{24} +37.9700 q^{25} -122.875 q^{26} +56.0592 q^{27} -270.871 q^{28} +240.666 q^{29} +389.029 q^{30} +178.870 q^{31} +204.469 q^{32} +74.3686 q^{33} -441.021 q^{34} -280.742 q^{35} +230.431 q^{36} -434.646 q^{37} +625.557 q^{38} -184.302 q^{39} -248.416 q^{40} -216.517 q^{41} -670.164 q^{42} -408.696 q^{43} -135.488 q^{44} +238.828 q^{45} -58.7562 q^{46} -473.877 q^{47} +73.1893 q^{48} +140.623 q^{49} -171.148 q^{50} -661.493 q^{51} +335.771 q^{52} +577.705 q^{53} -252.684 q^{54} -140.426 q^{55} +427.935 q^{56} +938.280 q^{57} -1084.79 q^{58} +598.961 q^{59} -1063.07 q^{60} +342.662 q^{61} -806.249 q^{62} -411.419 q^{63} -835.031 q^{64} +348.007 q^{65} -335.213 q^{66} -674.759 q^{67} +1205.14 q^{68} -88.1291 q^{69} +1265.43 q^{70} -298.956 q^{71} -364.046 q^{72} +47.4339 q^{73} +1959.15 q^{74} -256.707 q^{75} -1709.40 q^{76} +241.906 q^{77} +830.734 q^{78} +2.47600 q^{79} -138.199 q^{80} -884.125 q^{81} +975.941 q^{82} +1099.70 q^{83} +1831.30 q^{84} +1249.06 q^{85} +1842.18 q^{86} -1627.09 q^{87} +214.051 q^{88} +543.214 q^{89} -1076.51 q^{90} -599.497 q^{91} +160.558 q^{92} -1209.30 q^{93} +2135.98 q^{94} -1771.70 q^{95} -1382.37 q^{96} +1375.32 q^{97} -633.850 q^{98} -205.790 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 14 q^{2} - 10 q^{3} + 296 q^{4} - 42 q^{5} - 13 q^{6} - 59 q^{7} - 150 q^{8} + 541 q^{9}+O(q^{10}) \) 77 * q - 14 * q^2 - 10 * q^3 + 296 * q^4 - 42 * q^5 - 13 * q^6 - 59 * q^7 - 150 * q^8 + 541 * q^9	\( 77 q - 14 q^{2} - 10 q^{3} + 296 q^{4} - 42 q^{5} - 13 q^{6} - 59 q^{7} - 150 q^{8} + 541 q^{9} + 2 q^{10} - 847 q^{11} - 88 q^{12} - 20 q^{13} - 282 q^{14} - 330 q^{15} + 936 q^{16} - 56 q^{17} - 343 q^{18} - 157 q^{19} - 450 q^{20} - 122 q^{21} + 154 q^{22} - 764 q^{23} - 346 q^{24} + 1413 q^{25} - 408 q^{26} - 358 q^{27} - 228 q^{28} - 557 q^{29} - 267 q^{30} - 780 q^{31} - 1739 q^{32} + 110 q^{33} - 1104 q^{34} - 1254 q^{35} + 375 q^{36} - 541 q^{37} - 2133 q^{38} - 1458 q^{39} - 554 q^{40} - 1723 q^{41} - 5 q^{42} - 688 q^{43} - 3256 q^{44} - 1588 q^{45} + 276 q^{46} - 3086 q^{47} - 4280 q^{48} + 2452 q^{49} - 2234 q^{50} - 1570 q^{51} - 715 q^{52} - 1230 q^{53} - 5166 q^{54} + 462 q^{55} - 3203 q^{56} + 1024 q^{57} - 3016 q^{58} - 5408 q^{59} - 8221 q^{60} + 566 q^{61} - 3642 q^{62} - 3035 q^{63} + 1084 q^{64} - 1794 q^{65} + 143 q^{66} - 1925 q^{67} - 1105 q^{68} - 3710 q^{69} - 5875 q^{70} - 9614 q^{71} - 2198 q^{72} - 384 q^{73} - 2378 q^{74} - 3888 q^{75} - 2809 q^{76} + 649 q^{77} - 1731 q^{78} - 1086 q^{79} - 4357 q^{80} + 2329 q^{81} - 3167 q^{82} - 3045 q^{83} - 5359 q^{84} + 2582 q^{85} - 6468 q^{86} - 4432 q^{87} + 1650 q^{88} - 2831 q^{89} + 512 q^{90} - 6002 q^{91} - 7134 q^{92} - 4428 q^{93} + 1697 q^{94} - 10434 q^{95} + 195 q^{96} - 2506 q^{97} - 3435 q^{98} - 5951 q^{99}+O(q^{100}) \) 77 * q - 14 * q^2 - 10 * q^3 + 296 * q^4 - 42 * q^5 - 13 * q^6 - 59 * q^7 - 150 * q^8 + 541 * q^9 + 2 * q^10 - 847 * q^11 - 88 * q^12 - 20 * q^13 - 282 * q^14 - 330 * q^15 + 936 * q^16 - 56 * q^17 - 343 * q^18 - 157 * q^19 - 450 * q^20 - 122 * q^21 + 154 * q^22 - 764 * q^23 - 346 * q^24 + 1413 * q^25 - 408 * q^26 - 358 * q^27 - 228 * q^28 - 557 * q^29 - 267 * q^30 - 780 * q^31 - 1739 * q^32 + 110 * q^33 - 1104 * q^34 - 1254 * q^35 + 375 * q^36 - 541 * q^37 - 2133 * q^38 - 1458 * q^39 - 554 * q^40 - 1723 * q^41 - 5 * q^42 - 688 * q^43 - 3256 * q^44 - 1588 * q^45 + 276 * q^46 - 3086 * q^47 - 4280 * q^48 + 2452 * q^49 - 2234 * q^50 - 1570 * q^51 - 715 * q^52 - 1230 * q^53 - 5166 * q^54 + 462 * q^55 - 3203 * q^56 + 1024 * q^57 - 3016 * q^58 - 5408 * q^59 - 8221 * q^60 + 566 * q^61 - 3642 * q^62 - 3035 * q^63 + 1084 * q^64 - 1794 * q^65 + 143 * q^66 - 1925 * q^67 - 1105 * q^68 - 3710 * q^69 - 5875 * q^70 - 9614 * q^71 - 2198 * q^72 - 384 * q^73 - 2378 * q^74 - 3888 * q^75 - 2809 * q^76 + 649 * q^77 - 1731 * q^78 - 1086 * q^79 - 4357 * q^80 + 2329 * q^81 - 3167 * q^82 - 3045 * q^83 - 5359 * q^84 + 2582 * q^85 - 6468 * q^86 - 4432 * q^87 + 1650 * q^88 - 2831 * q^89 + 512 * q^90 - 6002 * q^91 - 7134 * q^92 - 4428 * q^93 + 1697 * q^94 - 10434 * q^95 + 195 * q^96 - 2506 * q^97 - 3435 * q^98 - 5951 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more