LMFDB - Embedded newform 1441.4.a.a.1.9

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			1.9
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)

$f(q)$	$=$	$q-4.63574 q^{2} -1.60774 q^{3} +13.4901 q^{4} +19.3385 q^{5} +7.45306 q^{6} -5.00186 q^{7} -25.4508 q^{8} -24.4152 q^{9} +O(q^{10})$	\(q-4.63574 q^{2} -1.60774 q^{3} +13.4901 q^{4} +19.3385 q^{5} +7.45306 q^{6} -5.00186 q^{7} -25.4508 q^{8} -24.4152 q^{9} -89.6483 q^{10} -11.0000 q^{11} -21.6886 q^{12} -16.3551 q^{13} +23.1874 q^{14} -31.0912 q^{15} +10.0626 q^{16} +4.49664 q^{17} +113.183 q^{18} +15.3457 q^{19} +260.879 q^{20} +8.04168 q^{21} +50.9932 q^{22} -75.9804 q^{23} +40.9183 q^{24} +248.977 q^{25} +75.8181 q^{26} +82.6621 q^{27} -67.4758 q^{28} +201.644 q^{29} +144.131 q^{30} -190.540 q^{31} +156.959 q^{32} +17.6851 q^{33} -20.8453 q^{34} -96.7285 q^{35} -329.364 q^{36} +289.485 q^{37} -71.1386 q^{38} +26.2947 q^{39} -492.181 q^{40} +321.615 q^{41} -37.2792 q^{42} -268.156 q^{43} -148.391 q^{44} -472.153 q^{45} +352.226 q^{46} -137.058 q^{47} -16.1780 q^{48} -317.981 q^{49} -1154.19 q^{50} -7.22942 q^{51} -220.633 q^{52} +311.068 q^{53} -383.200 q^{54} -212.723 q^{55} +127.302 q^{56} -24.6718 q^{57} -934.770 q^{58} -456.827 q^{59} -419.424 q^{60} -205.807 q^{61} +883.295 q^{62} +122.121 q^{63} -808.124 q^{64} -316.283 q^{65} -81.9837 q^{66} +331.121 q^{67} +60.6602 q^{68} +122.157 q^{69} +448.408 q^{70} +264.835 q^{71} +621.387 q^{72} -949.272 q^{73} -1341.98 q^{74} -400.290 q^{75} +207.015 q^{76} +55.0205 q^{77} -121.896 q^{78} +626.144 q^{79} +194.595 q^{80} +526.311 q^{81} -1490.93 q^{82} -1297.35 q^{83} +108.483 q^{84} +86.9582 q^{85} +1243.10 q^{86} -324.191 q^{87} +279.959 q^{88} -832.633 q^{89} +2188.78 q^{90} +81.8060 q^{91} -1024.99 q^{92} +306.338 q^{93} +635.364 q^{94} +296.762 q^{95} -252.349 q^{96} -73.8368 q^{97} +1474.08 q^{98} +268.567 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.63574	−1.63898	−0.819492	−	0.573091i	$-0.805744\pi$
$2$	−4.63574	−1.63898	−0.819492	+	0.573091i	$0.805744\pi$
$3$	−1.60774	−0.309409	−0.154705	−	0.987961i	$-0.549443\pi$
$3$	−1.60774	−0.309409	−0.154705	+	0.987961i	$0.549443\pi$
$4$	13.4901	1.68627
$5$	19.3385	1.72969	0.864843	−	0.502042i	$-0.167418\pi$
$5$	19.3385	1.72969	0.864843	+	0.502042i	$0.167418\pi$
$6$	7.45306	0.507117
$7$	−5.00186	−0.270075	−0.135038	−	0.990840i	$-0.543116\pi$
$7$	−5.00186	−0.270075	−0.135038	+	0.990840i	$0.543116\pi$
$8$	−25.4508	−1.12478
$9$	−24.4152	−0.904266
$10$	−89.6483	−2.83493
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−21.6886	−0.521746
$13$	−16.3551	−0.348930	−0.174465	−	0.984663i	$-0.555820\pi$
$13$	−16.3551	−0.348930	−0.174465	+	0.984663i	$0.555820\pi$
$14$	23.1874	0.442649
$15$	−31.0912	−0.535181
$16$	10.0626	0.157228
$17$	4.49664	0.0641527	0.0320763	−	0.999485i	$-0.489788\pi$
$17$	4.49664	0.0641527	0.0320763	+	0.999485i	$0.489788\pi$
$18$	113.183	1.48208
$19$	15.3457	0.185291	0.0926457	−	0.995699i	$-0.470468\pi$
$19$	15.3457	0.185291	0.0926457	+	0.995699i	$0.470468\pi$
$20$	260.879	2.91671
$21$	8.04168	0.0835638
$22$	50.9932	0.494172
$23$	−75.9804	−0.688826	−0.344413	−	0.938818i	$-0.611922\pi$
$23$	−75.9804	−0.688826	−0.344413	+	0.938818i	$0.611922\pi$
$24$	40.9183	0.348017
$25$	248.977	1.99182
$26$	75.8181	0.571891
$27$	82.6621	0.589197
$28$	−67.4758	−0.455419
$29$	201.644	1.29118	0.645592	−	0.763682i	$-0.276611\pi$
$29$	201.644	1.29118	0.645592	+	0.763682i	$0.276611\pi$
$30$	144.131	0.877153
$31$	−190.540	−1.10394	−0.551968	−	0.833866i	$-0.686123\pi$
$31$	−190.540	−1.10394	−0.551968	+	0.833866i	$0.686123\pi$
$32$	156.959	0.867085
$33$	17.6851	0.0932904
$34$	−20.8453	−0.105145
$35$	−96.7285	−0.467146
$36$	−329.364	−1.52483
$37$	289.485	1.28625	0.643123	−	0.765763i	$-0.277638\pi$
$37$	289.485	1.28625	0.643123	+	0.765763i	$0.277638\pi$
$38$	−71.1386	−0.303689
$39$	26.2947	0.107962
$40$	−492.181	−1.94551
$41$	321.615	1.22507	0.612535	−	0.790443i	$-0.290150\pi$
$41$	321.615	1.22507	0.612535	+	0.790443i	$0.290150\pi$
$42$	−37.2792	−0.136960
$43$	−268.156	−0.951011	−0.475505	−	0.879713i	$-0.657735\pi$
$43$	−268.156	−0.951011	−0.475505	+	0.879713i	$0.657735\pi$
$44$	−148.391	−0.508428
$45$	−472.153	−1.56410
$46$	352.226	1.12897
$47$	−137.058	−0.425360	−0.212680	−	0.977122i	$-0.568219\pi$
$47$	−137.058	−0.425360	−0.212680	+	0.977122i	$0.568219\pi$
$48$	−16.1780	−0.0486477
$49$	−317.981	−0.927059
$50$	−1154.19	−3.26455
$51$	−7.22942	−0.0198494
$52$	−220.633	−0.588389
$53$	311.068	0.806197	0.403098	−	0.915157i	$-0.367933\pi$
$53$	311.068	0.806197	0.403098	+	0.915157i	$0.367933\pi$
$54$	−383.200	−0.965685
$55$	−212.723	−0.521520
$56$	127.302	0.303775
$57$	−24.6718	−0.0573309
$58$	−934.770	−2.11623
$59$	−456.827	−1.00803	−0.504016	−	0.863694i	$-0.668145\pi$
$59$	−456.827	−1.00803	−0.504016	+	0.863694i	$0.668145\pi$
$60$	−419.424	−0.902458
$61$	−205.807	−0.431982	−0.215991	−	0.976395i	$-0.569298\pi$
$61$	−205.807	−0.431982	−0.215991	+	0.976395i	$0.569298\pi$
$62$	883.295	1.80933
$63$	122.121	0.244220
$64$	−808.124	−1.57837
$65$	−316.283	−0.603540
$66$	−81.9837	−0.152901
$67$	331.121	0.603775	0.301887	−	0.953344i	$-0.402383\pi$
$67$	331.121	0.603775	0.301887	+	0.953344i	$0.402383\pi$
$68$	60.6602	0.108178
$69$	122.157	0.213129
$70$	448.408	0.765644
$71$	264.835	0.442677	0.221339	−	0.975197i	$-0.428957\pi$
$71$	264.835	0.442677	0.221339	+	0.975197i	$0.428957\pi$
$72$	621.387	1.01710
$73$	−949.272	−1.52197	−0.760985	−	0.648769i	$-0.775284\pi$
$73$	−949.272	−1.52197	−0.760985	+	0.648769i	$0.775284\pi$
$74$	−1341.98	−2.10814
$75$	−400.290	−0.616286
$76$	207.015	0.312451
$77$	55.0205	0.0814307
$78$	−121.896	−0.176948
$79$	626.144	0.891731	0.445866	−	0.895100i	$-0.352896\pi$
$79$	626.144	0.891731	0.445866	+	0.895100i	$0.352896\pi$
$80$	194.595	0.271955
$81$	526.311	0.721963
$82$	−1490.93	−2.00787
$83$	−1297.35	−1.71570	−0.857848	−	0.513903i	$-0.828199\pi$
$83$	−1297.35	−1.71570	−0.857848	+	0.513903i	$0.828199\pi$
$84$	108.483	0.140911
$85$	86.9582	0.110964
$86$	1243.10	1.55869
$87$	−324.191	−0.399504
$88$	279.959	0.339134
$89$	−832.633	−0.991674	−0.495837	−	0.868416i	$-0.665139\pi$
$89$	−832.633	−0.991674	−0.495837	+	0.868416i	$0.665139\pi$
$90$	2188.78	2.56353
$91$	81.8060	0.0942374
$92$	−1024.99	−1.16154
$93$	306.338	0.341568
$94$	635.364	0.697158
$95$	296.762	0.320496
$96$	−252.349	−0.268284
$97$	−73.8368	−0.0772885	−0.0386443	−	0.999253i	$-0.512304\pi$
$97$	−73.8368	−0.0772885	−0.0386443	+	0.999253i	$0.512304\pi$
$98$	1474.08	1.51943
$99$	268.567	0.272646
$100$	3358.73	3.35873
$101$	1431.71	1.41050	0.705249	−	0.708959i	$-0.250835\pi$
$101$	1431.71	1.41050	0.705249	+	0.708959i	$0.250835\pi$
$102$	33.5137	0.0325329
$103$	−1733.14	−1.65798	−0.828989	−	0.559265i	$-0.811084\pi$
$103$	−1733.14	−1.65798	−0.828989	+	0.559265i	$0.811084\pi$
$104$	416.251	0.392469
$105$	155.514	0.144539
$106$	−1442.03	−1.32134
$107$	776.844	0.701872	0.350936	−	0.936399i	$-0.385863\pi$
$107$	776.844	0.701872	0.350936	+	0.936399i	$0.385863\pi$
$108$	1115.12	0.993544
$109$	769.511	0.676200	0.338100	−	0.941110i	$-0.390216\pi$
$109$	769.511	0.676200	0.338100	+	0.941110i	$0.390216\pi$
$110$	986.131	0.854763
$111$	−465.416	−0.397976
$112$	−50.3316	−0.0424633
$113$	1607.69	1.33840	0.669199	−	0.743084i	$-0.266638\pi$
$113$	1607.69	1.33840	0.669199	+	0.743084i	$0.266638\pi$
$114$	114.372	0.0939643
$115$	−1469.35	−1.19145
$116$	2720.20	2.17728
$117$	399.313	0.315526
$118$	2117.74	1.65215
$119$	−22.4916	−0.0173260
$120$	791.297	0.601960
$121$	121.000	0.0909091
$122$	954.068	0.708010
$123$	−517.073	−0.379048
$124$	−2570.41	−1.86153
$125$	2397.53	1.71553
$126$	−566.124	−0.400272
$127$	253.126	0.176861	0.0884304	−	0.996082i	$-0.471815\pi$
$127$	253.126	0.176861	0.0884304	+	0.996082i	$0.471815\pi$
$128$	2490.58	1.71983
$129$	431.125	0.294251
$130$	1466.21	0.989192
$131$	131.000	0.0873704
$131$	131.000	0.0873704
$132$	238.574	0.157312
$133$	−76.7569	−0.0500426
$134$	−1534.99	−0.989577
$135$	1598.56	1.01913
$136$	−114.443	−0.0721576
$137$	−2733.03	−1.70437	−0.852184	−	0.523242i	$-0.824722\pi$
$137$	−2733.03	−1.70437	−0.852184	+	0.523242i	$0.824722\pi$
$138$	−566.287	−0.349315
$139$	592.003	0.361245	0.180622	−	0.983553i	$-0.442189\pi$
$139$	592.003	0.361245	0.180622	+	0.983553i	$0.442189\pi$
$140$	−1304.88	−0.787732
$141$	220.353	0.131610
$142$	−1227.71	−0.725541
$143$	179.906	0.105206
$144$	−245.679	−0.142176
$145$	3899.49	2.23334
$146$	4400.58	2.49448
$147$	511.231	0.286841
$148$	3905.19	2.16895
$149$	−183.070	−0.100655	−0.0503277	−	0.998733i	$-0.516027\pi$
$149$	−183.070	−0.100655	−0.0503277	+	0.998733i	$0.516027\pi$
$150$	1855.64	1.01008
$151$	−1127.14	−0.607452	−0.303726	−	0.952759i	$-0.598231\pi$
$151$	−1127.14	−0.607452	−0.303726	+	0.952759i	$0.598231\pi$
$152$	−390.560	−0.208412
$153$	−109.786	−0.0580111
$154$	−255.061	−0.133464
$155$	−3684.75	−1.90946
$156$	354.719	0.182053
$157$	1547.26	0.786529	0.393265	−	0.919425i	$-0.371346\pi$
$157$	1547.26	0.786529	0.393265	+	0.919425i	$0.371346\pi$
$158$	−2902.65	−1.46153
$159$	−500.115	−0.249445
$160$	3035.35	1.49979
$161$	380.044	0.186035
$162$	−2439.84	−1.18328
$163$	−1823.01	−0.876008	−0.438004	−	0.898973i	$-0.644314\pi$
$163$	−1823.01	−0.876008	−0.438004	+	0.898973i	$0.644314\pi$
$164$	4338.63	2.06579
$165$	342.003	0.161363
$166$	6014.19	2.81200
$167$	318.899	0.147767	0.0738837	−	0.997267i	$-0.476461\pi$
$167$	318.899	0.147767	0.0738837	+	0.997267i	$0.476461\pi$
$168$	−204.668	−0.0939908
$169$	−1929.51	−0.878248
$170$	−403.116	−0.181868
$171$	−374.667	−0.167553
$172$	−3617.46	−1.60366
$173$	616.894	0.271107	0.135554	−	0.990770i	$-0.456719\pi$
$173$	616.894	0.271107	0.135554	+	0.990770i	$0.456719\pi$
$174$	1502.87	0.654781
$175$	−1245.35	−0.537940
$176$	−110.688	−0.0474059
$177$	734.459	0.311894
$178$	3859.88	1.62534
$179$	−4416.17	−1.84402	−0.922012	−	0.387162i	$-0.873455\pi$
$179$	−4416.17	−1.84402	−0.922012	+	0.387162i	$0.873455\pi$
$180$	−6369.40	−2.63748
$181$	−4276.19	−1.75606	−0.878030	−	0.478606i	$-0.841142\pi$
$181$	−4276.19	−1.75606	−0.878030	+	0.478606i	$0.841142\pi$
$182$	−379.232	−0.154454
$183$	330.883	0.133659
$184$	1933.77	0.774777
$185$	5598.21	2.22480
$186$	−1420.11	−0.559824
$187$	−49.4630	−0.0193428
$188$	−1848.93	−0.717270
$189$	−413.465	−0.159128
$190$	−1375.71	−0.525288
$191$	−2589.01	−0.980806	−0.490403	−	0.871496i	$-0.663150\pi$
$191$	−2589.01	−0.980806	−0.490403	+	0.871496i	$0.663150\pi$
$192$	1299.25	0.488361
$193$	−2127.72	−0.793557	−0.396778	−	0.917914i	$-0.629872\pi$
$193$	−2127.72	−0.793557	−0.396778	+	0.917914i	$0.629872\pi$
$194$	342.288	0.126675
$195$	508.500	0.186741
$196$	−4289.61	−1.56327
$197$	−3505.87	−1.26793	−0.633967	−	0.773360i	$-0.718574\pi$
$197$	−3505.87	−1.26793	−0.633967	+	0.773360i	$0.718574\pi$
$198$	−1245.01	−0.446863
$199$	2121.28	0.755644	0.377822	−	0.925878i	$-0.376673\pi$
$199$	2121.28	0.755644	0.377822	+	0.925878i	$0.376673\pi$
$200$	−6336.67	−2.24035
$201$	−532.356	−0.186814
$202$	−6637.04	−2.31178
$203$	−1008.60	−0.348717
$204$	−97.5258	−0.0334714
$205$	6219.55	2.11899
$206$	8034.41	2.71740
$207$	1855.08	0.622882
$208$	−164.574	−0.0548615
$209$	−168.802	−0.0558675
$210$	−720.923	−0.236897
$211$	−2603.72	−0.849514	−0.424757	−	0.905307i	$-0.639641\pi$
$211$	−2603.72	−0.849514	−0.424757	+	0.905307i	$0.639641\pi$
$212$	4196.34	1.35946
$213$	−425.784	−0.136968
$214$	−3601.25	−1.15036
$215$	−5185.74	−1.64495
$216$	−2103.82	−0.662717
$217$	953.055	0.298146
$218$	−3567.26	−1.10828
$219$	1526.18	0.470912
$220$	−2869.67	−0.879422
$221$	−73.5430	−0.0223848
$222$	2157.55	0.652277
$223$	5780.12	1.73572	0.867860	−	0.496809i	$-0.165495\pi$
$223$	5780.12	1.73572	0.867860	+	0.496809i	$0.165495\pi$
$224$	−785.089	−0.234178
$225$	−6078.82	−1.80113
$226$	−7452.85	−2.19361
$227$	3202.37	0.936337	0.468169	−	0.883639i	$-0.344914\pi$
$227$	3202.37	0.936337	0.468169	+	0.883639i	$0.344914\pi$
$228$	−332.826	−0.0966751
$229$	−4284.67	−1.23641	−0.618207	−	0.786015i	$-0.712141\pi$
$229$	−4284.67	−1.23641	−0.618207	+	0.786015i	$0.712141\pi$
$230$	6811.51	1.95277
$231$	−88.4585	−0.0251954
$232$	−5132.01	−1.45230
$233$	57.4138	0.0161429	0.00807147	−	0.999967i	$-0.497431\pi$
$233$	57.4138	0.0161429	0.00807147	+	0.999967i	$0.497431\pi$
$234$	−1851.11	−0.517141
$235$	−2650.49	−0.735739
$236$	−6162.66	−1.69981
$237$	−1006.68	−0.275910
$238$	104.265	0.0283971
$239$	4472.95	1.21059	0.605296	−	0.796001i	$-0.293055\pi$
$239$	4472.95	1.21059	0.605296	+	0.796001i	$0.293055\pi$
$240$	−312.857	−0.0841452
$241$	314.290	0.0840050	0.0420025	−	0.999118i	$-0.486626\pi$
$241$	314.290	0.0840050	0.0420025	+	0.999118i	$0.486626\pi$
$242$	−560.925	−0.148998
$243$	−3078.05	−0.812579
$244$	−2776.36	−0.728436
$245$	−6149.28	−1.60352
$246$	2397.02	0.621253
$247$	−250.980	−0.0646537
$248$	4849.40	1.24168
$249$	2085.80	0.530852
$250$	−11114.3	−2.81172
$251$	572.567	0.143984	0.0719922	−	0.997405i	$-0.477064\pi$
$251$	572.567	0.143984	0.0719922	+	0.997405i	$0.477064\pi$
$252$	1647.43	0.411820
$253$	835.784	0.207689
$254$	−1173.43	−0.289872
$255$	−139.806	−0.0343333
$256$	−5080.71	−1.24041
$257$	−4854.55	−1.17828	−0.589141	−	0.808030i	$-0.700534\pi$
$257$	−4854.55	−1.17828	−0.589141	+	0.808030i	$0.700534\pi$
$258$	−1998.59	−0.482273
$259$	−1447.97	−0.347383
$260$	−4266.70	−1.01773
$261$	−4923.18	−1.16757
$262$	−607.283	−0.143199
$263$	1188.83	0.278732	0.139366	−	0.990241i	$-0.455494\pi$
$263$	1188.83	0.278732	0.139366	+	0.990241i	$0.455494\pi$
$264$	−450.101	−0.104931
$265$	6015.58	1.39447
$266$	355.825	0.0820190
$267$	1338.66	0.306833
$268$	4466.87	1.01813
$269$	−4295.47	−0.973604	−0.486802	−	0.873512i	$-0.661837\pi$
$269$	−4295.47	−0.973604	−0.486802	+	0.873512i	$0.661837\pi$
$270$	−7410.52	−1.67033
$271$	−8096.53	−1.81487	−0.907433	−	0.420196i	$-0.861961\pi$
$271$	−8096.53	−1.81487	−0.907433	+	0.420196i	$0.861961\pi$
$272$	45.2477	0.0100866
$273$	−131.523	−0.0291579
$274$	12669.6	2.79343
$275$	−2738.75	−0.600555
$276$	1647.91	0.359393
$277$	4671.58	1.01331	0.506657	−	0.862148i	$-0.330881\pi$
$277$	4671.58	1.01331	0.506657	+	0.862148i	$0.330881\pi$
$278$	−2744.37	−0.592074
$279$	4652.07	0.998251
$280$	2461.82	0.525435
$281$	−62.2967	−0.0132253	−0.00661265	−	0.999978i	$-0.502105\pi$
$281$	−62.2967	−0.0132253	−0.00661265	+	0.999978i	$0.502105\pi$
$282$	−1021.50	−0.215707
$283$	1932.37	0.405893	0.202946	−	0.979190i	$-0.434948\pi$
$283$	1932.37	0.405893	0.202946	+	0.979190i	$0.434948\pi$
$284$	3572.65	0.746472
$285$	−477.115	−0.0991644
$286$	−833.999	−0.172432
$287$	−1608.68	−0.330861
$288$	−3832.19	−0.784076
$289$	−4892.78	−0.995884
$290$	−18077.0	−3.66041
$291$	118.710	0.0239138
$292$	−12805.8	−2.56645
$293$	−3262.52	−0.650507	−0.325254	−	0.945627i	$-0.605450\pi$
$293$	−3262.52	−0.650507	−0.325254	+	0.945627i	$0.605450\pi$
$294$	−2369.93	−0.470127
$295$	−8834.35	−1.74358
$296$	−7367.64	−1.44674
$297$	−909.283	−0.177650
$298$	848.665	0.164973
$299$	1242.67	0.240352
$300$	−5399.96	−1.03922
$301$	1341.28	0.256844
$302$	5225.13	0.995604
$303$	−2301.81	−0.436421
$304$	154.417	0.0291329
$305$	−3979.99	−0.747193
$306$	508.941	0.0950792
$307$	3687.64	0.685554	0.342777	−	0.939417i	$-0.388633\pi$
$307$	3687.64	0.685554	0.342777	+	0.939417i	$0.388633\pi$
$308$	742.234	0.137314
$309$	2786.44	0.512994
$310$	17081.6	3.12958
$311$	4208.08	0.767262	0.383631	−	0.923487i	$-0.374673\pi$
$311$	4208.08	0.767262	0.383631	+	0.923487i	$0.374673\pi$
$312$	−669.223	−0.121434
$313$	7872.82	1.42172	0.710859	−	0.703334i	$-0.248306\pi$
$313$	7872.82	1.42172	0.710859	+	0.703334i	$0.248306\pi$
$314$	−7172.72	−1.28911
$315$	2361.64	0.422424
$316$	8446.77	1.50370
$317$	−2368.57	−0.419660	−0.209830	−	0.977738i	$-0.567291\pi$
$317$	−2368.57	−0.419660	−0.209830	+	0.977738i	$0.567291\pi$
$318$	2318.41	0.408836
$319$	−2218.08	−0.389307
$320$	−15627.9	−2.73008
$321$	−1248.96	−0.217166
$322$	−1761.78	−0.304908
$323$	69.0039	0.0118869
$324$	7100.00	1.21742
$325$	−4072.05	−0.695004
$326$	8451.02	1.43576
$327$	−1237.17	−0.209222
$328$	−8185.38	−1.37793
$329$	685.544	0.114879
$330$	−1585.44	−0.264471
$331$	−7011.93	−1.16438	−0.582191	−	0.813052i	$-0.697805\pi$
$331$	−7011.93	−1.16438	−0.582191	+	0.813052i	$0.697805\pi$
$332$	−17501.4	−2.89312
$333$	−7067.84	−1.16311
$334$	−1478.34	−0.242188
$335$	6403.39	1.04434
$336$	80.9200	0.0131385
$337$	−5145.65	−0.831756	−0.415878	−	0.909420i	$-0.636526\pi$
$337$	−5145.65	−0.831756	−0.415878	+	0.909420i	$0.636526\pi$
$338$	8944.72	1.43943
$339$	−2584.75	−0.414112
$340$	1173.08	0.187115
$341$	2095.94	0.332849
$342$	1736.86	0.274616
$343$	3306.14	0.520451
$344$	6824.80	1.06968
$345$	2362.32	0.368647
$346$	−2859.76	−0.444340
$347$	5800.05	0.897300	0.448650	−	0.893708i	$-0.351905\pi$
$347$	5800.05	0.897300	0.448650	+	0.893708i	$0.351905\pi$
$348$	−4373.37	−0.673671
$349$	10023.6	1.53739	0.768694	−	0.639617i	$-0.220907\pi$
$349$	10023.6	1.53739	0.768694	+	0.639617i	$0.220907\pi$
$350$	5773.12	0.881675
$351$	−1351.95	−0.205589
$352$	−1726.55	−0.261436
$353$	−3751.01	−0.565569	−0.282785	−	0.959183i	$-0.591258\pi$
$353$	−3751.01	−0.565569	−0.282785	+	0.959183i	$0.591258\pi$
$354$	−3404.76	−0.511189
$355$	5121.50	0.765693
$356$	−11232.3	−1.67223
$357$	36.1605	0.00536084
$358$	20472.2	3.02232
$359$	−4436.61	−0.652244	−0.326122	−	0.945328i	$-0.605742\pi$
$359$	−4436.61	−0.652244	−0.326122	+	0.945328i	$0.605742\pi$
$360$	12016.7	1.75926
$361$	−6623.51	−0.965667
$362$	19823.3	2.87815
$363$	−194.536	−0.0281281
$364$	1103.57	0.158909
$365$	−18357.5	−2.63253
$366$	−1533.89	−0.219065
$367$	3664.44	0.521205	0.260602	−	0.965446i	$-0.416079\pi$
$367$	3664.44	0.521205	0.260602	+	0.965446i	$0.416079\pi$
$368$	−764.558	−0.108303
$369$	−7852.30	−1.10779
$370$	−25951.9	−3.64641
$371$	−1555.92	−0.217734
$372$	4132.54	0.575974
$373$	12011.9	1.66744	0.833719	−	0.552189i	$-0.186207\pi$
$373$	12011.9	1.66744	0.833719	+	0.552189i	$0.186207\pi$
$374$	229.298	0.0317024
$375$	−3854.59	−0.530801
$376$	3488.23	0.478436
$377$	−3297.91	−0.450533
$378$	1916.72	0.260808
$379$	3612.45	0.489602	0.244801	−	0.969573i	$-0.421277\pi$
$379$	3612.45	0.489602	0.244801	+	0.969573i	$0.421277\pi$
$380$	4003.36	0.540442
$381$	−406.960	−0.0547224
$382$	12002.0	1.60753
$383$	−149.443	−0.0199377	−0.00996887	−	0.999950i	$-0.503173\pi$
$383$	−149.443	−0.0199377	−0.00996887	+	0.999950i	$0.503173\pi$
$384$	−4004.20	−0.532131
$385$	1064.01	0.140850
$386$	9863.55	1.30063
$387$	6547.08	0.859966
$388$	−996.067	−0.130329
$389$	−10508.5	−1.36968	−0.684838	−	0.728695i	$-0.740127\pi$
$389$	−10508.5	−1.36968	−0.684838	+	0.728695i	$0.740127\pi$
$390$	−2357.28	−0.306065
$391$	−341.656	−0.0441900
$392$	8092.89	1.04274
$393$	−210.614	−0.0270332
$394$	16252.3	2.07812
$395$	12108.7	1.54242
$396$	3623.00	0.459754
$397$	1791.58	0.226491	0.113246	−	0.993567i	$-0.463875\pi$
$397$	1791.58	0.226491	0.113246	+	0.993567i	$0.463875\pi$
$398$	−9833.69	−1.23849
$399$	123.405	0.0154836
$400$	2505.35	0.313168
$401$	−6553.94	−0.816180	−0.408090	−	0.912942i	$-0.633805\pi$
$401$	−6553.94	−0.816180	−0.408090	+	0.912942i	$0.633805\pi$
$402$	2467.87	0.306184
$403$	3116.30	0.385196
$404$	19313.9	2.37848
$405$	10178.1	1.24877
$406$	4675.59	0.571541
$407$	−3184.34	−0.387818
$408$	183.995	0.0223262
$409$	−13324.0	−1.61083	−0.805413	−	0.592713i	$-0.798057\pi$
$409$	−13324.0	−1.61083	−0.805413	+	0.592713i	$0.798057\pi$
$410$	−28832.3	−3.47299
$411$	4393.99	0.527347
$412$	−23380.3	−2.79579
$413$	2284.99	0.272244
$414$	−8599.65	−1.02089
$415$	−25088.8	−2.96762
$416$	−2567.09	−0.302552
$417$	−951.785	−0.111772
$418$	782.524	0.0915658
$419$	−8061.76	−0.939959	−0.469980	−	0.882677i	$-0.655739\pi$
$419$	−8061.76	−0.939959	−0.469980	+	0.882677i	$0.655739\pi$
$420$	2097.90	0.243731
$421$	−3228.11	−0.373702	−0.186851	−	0.982388i	$-0.559828\pi$
$421$	−3228.11	−0.373702	−0.186851	+	0.982388i	$0.559828\pi$
$422$	12070.2	1.39234
$423$	3346.29	0.384639
$424$	−7916.93	−0.906793
$425$	1119.56	0.127780
$426$	1973.83	0.224489
$427$	1029.42	0.116668
$428$	10479.7	1.18354
$429$	−289.242	−0.0325518
$430$	24039.8	2.69605
$431$	−5217.42	−0.583095	−0.291548	−	0.956556i	$-0.594170\pi$
$431$	−5217.42	−0.583095	−0.291548	+	0.956556i	$0.594170\pi$
$432$	831.793	0.0926381
$433$	12839.0	1.42495	0.712476	−	0.701696i	$-0.247574\pi$
$433$	12839.0	1.42495	0.712476	+	0.701696i	$0.247574\pi$
$434$	−4418.12	−0.488656
$435$	−6269.36	−0.691017
$436$	10380.8	1.14025
$437$	−1165.97	−0.127634
$438$	−7074.98	−0.771816
$439$	−5215.19	−0.566987	−0.283493	−	0.958974i	$-0.591493\pi$
$439$	−5215.19	−0.566987	−0.283493	+	0.958974i	$0.591493\pi$
$440$	5413.99	0.586595
$441$	7763.57	0.838308
$442$	340.927	0.0366883
$443$	−15995.7	−1.71553	−0.857765	−	0.514042i	$-0.828148\pi$
$443$	−15995.7	−1.71553	−0.857765	+	0.514042i	$0.828148\pi$
$444$	−6278.53	−0.671094
$445$	−16101.9	−1.71528
$446$	−26795.2	−2.84482
$447$	294.328	0.0311437
$448$	4042.12	0.426278
$449$	4912.10	0.516295	0.258148	−	0.966106i	$-0.416888\pi$
$449$	4912.10	0.516295	0.258148	+	0.966106i	$0.416888\pi$
$450$	28179.8	2.95202
$451$	−3537.77	−0.369373
$452$	21688.0	2.25689
$453$	1812.14	0.187951
$454$	−14845.4	−1.53464
$455$	1582.00	0.163001
$456$	627.918	0.0644846
$457$	6727.53	0.688623	0.344311	−	0.938856i	$-0.388112\pi$
$457$	6727.53	0.688623	0.344311	+	0.938856i	$0.388112\pi$
$458$	19862.6	2.02646
$459$	371.702	0.0377986
$460$	−19821.7	−2.00911
$461$	11577.7	1.16969	0.584846	−	0.811144i	$-0.301155\pi$
$461$	11577.7	1.16969	0.584846	+	0.811144i	$0.301155\pi$
$462$	410.071	0.0412949
$463$	−13161.2	−1.32107	−0.660533	−	0.750797i	$-0.729670\pi$
$463$	−13161.2	−1.32107	−0.660533	+	0.750797i	$0.729670\pi$
$464$	2029.06	0.203010
$465$	5924.12	0.590805
$466$	−266.156	−0.0264580
$467$	−6805.76	−0.674374	−0.337187	−	0.941438i	$-0.609476\pi$
$467$	−6805.76	−0.674374	−0.337187	+	0.941438i	$0.609476\pi$
$468$	5386.78	0.532060
$469$	−1656.22	−0.163065
$470$	12287.0	1.20586
$471$	−2487.59	−0.243359
$472$	11626.6	1.13381
$473$	2949.72	0.286740
$474$	4666.69	0.452212
$475$	3820.72	0.369066
$476$	−303.414	−0.0292163
$477$	−7594.77	−0.729016
$478$	−20735.5	−1.98414
$479$	−18483.1	−1.76308	−0.881538	−	0.472113i	$-0.843492\pi$
$479$	−18483.1	−1.76308	−0.881538	+	0.472113i	$0.843492\pi$
$480$	−4880.05	−0.464048
$481$	−4734.56	−0.448810
$482$	−1456.97	−0.137683
$483$	−611.010	−0.0575609
$484$	1632.31	0.153297
$485$	−1427.89	−0.133685
$486$	14269.0	1.33180
$487$	19768.5	1.83941	0.919707	−	0.392605i	$-0.128426\pi$
$487$	19768.5	1.83941	0.919707	+	0.392605i	$0.128426\pi$
$488$	5237.96	0.485884
$489$	2930.92	0.271045
$490$	28506.5	2.62815
$491$	−16413.0	−1.50857	−0.754287	−	0.656545i	$-0.772017\pi$
$491$	−16413.0	−1.50857	−0.754287	+	0.656545i	$0.772017\pi$
$492$	−6975.38	−0.639176
$493$	906.720	0.0828329
$494$	1163.48	0.105966
$495$	5193.68	0.471593
$496$	−1917.32	−0.173569
$497$	−1324.67	−0.119556
$498$	−9669.24	−0.870058
$499$	10751.3	0.964514	0.482257	−	0.876030i	$-0.339817\pi$
$499$	10751.3	0.964514	0.482257	+	0.876030i	$0.339817\pi$
$500$	32342.9	2.89284
$501$	−512.706	−0.0457206
$502$	−2654.27	−0.235988
$503$	−19135.6	−1.69625	−0.848125	−	0.529796i	$-0.822269\pi$
$503$	−19135.6	−1.69625	−0.848125	+	0.529796i	$0.822269\pi$
$504$	−3108.09	−0.274693
$505$	27687.1	2.43972
$506$	−3874.48	−0.340399
$507$	3102.15	0.271738
$508$	3414.71	0.298234
$509$	−9714.68	−0.845964	−0.422982	−	0.906138i	$-0.639017\pi$
$509$	−9714.68	−0.845964	−0.422982	+	0.906138i	$0.639017\pi$
$510$	648.105	0.0562717
$511$	4748.13	0.411046
$512$	3628.22	0.313176
$513$	1268.50	0.109173
$514$	22504.5	1.93119
$515$	−33516.4	−2.86778
$516$	5815.93	0.496186
$517$	1507.63	0.128251
$518$	6712.40	0.569355
$519$	−991.803	−0.0838831
$520$	8049.67	0.678849
$521$	−2095.27	−0.176191	−0.0880955	−	0.996112i	$-0.528078\pi$
$521$	−2095.27	−0.176191	−0.0880955	+	0.996112i	$0.528078\pi$
$522$	22822.6	1.91363
$523$	446.947	0.0373683	0.0186842	−	0.999825i	$-0.494052\pi$
$523$	446.947	0.0373683	0.0186842	+	0.999825i	$0.494052\pi$
$524$	1767.21	0.147330
$525$	2002.19	0.166444
$526$	−5511.12	−0.456837
$527$	−856.790	−0.0708204
$528$	177.958	0.0146678
$529$	−6393.98	−0.525518
$530$	−27886.7	−2.28551
$531$	11153.5	0.911529
$532$	−1035.46	−0.0843852
$533$	−5260.05	−0.427464
$534$	−6205.67	−0.502894
$535$	15023.0	1.21402
$536$	−8427.32	−0.679113
$537$	7100.05	0.570558
$538$	19912.7	1.59572
$539$	3497.79	0.279519
$540$	21564.8	1.71852
$541$	7518.14	0.597468	0.298734	−	0.954336i	$-0.403436\pi$
$541$	7518.14	0.597468	0.298734	+	0.954336i	$0.403436\pi$
$542$	37533.4	2.97454
$543$	6874.99	0.543341
$544$	705.789	0.0556258
$545$	14881.2	1.16961
$546$	609.705	0.0477893
$547$	1758.62	0.137465	0.0687323	−	0.997635i	$-0.478105\pi$
$547$	1758.62	0.137465	0.0687323	+	0.997635i	$0.478105\pi$
$548$	−36868.9	−2.87402
$549$	5024.81	0.390626
$550$	12696.1	0.984300
$551$	3094.36	0.239245
$552$	−3108.99	−0.239723
$553$	−3131.89	−0.240834
$554$	−21656.2	−1.66080
$555$	−9000.45	−0.688374
$556$	7986.20	0.609155
$557$	−22485.9	−1.71052	−0.855258	−	0.518202i	$-0.826601\pi$
$557$	−22485.9	−1.71052	−0.855258	+	0.518202i	$0.826601\pi$
$558$	−21565.8	−1.63612
$559$	4385.73	0.331836
$560$	−973.337	−0.0734482
$561$	79.5236	0.00598483
$562$	288.792	0.0216761
$563$	6728.40	0.503673	0.251837	−	0.967770i	$-0.418965\pi$
$563$	6728.40	0.503673	0.251837	+	0.967770i	$0.418965\pi$
$564$	2972.59	0.221930
$565$	31090.3	2.31501
$566$	−8957.98	−0.665251
$567$	−2632.54	−0.194984
$568$	−6740.26	−0.497914
$569$	10504.1	0.773910	0.386955	−	0.922099i	$-0.373527\pi$
$569$	10504.1	0.773910	0.386955	+	0.922099i	$0.373527\pi$
$570$	2211.78	0.162529
$571$	9520.20	0.697737	0.348869	−	0.937172i	$-0.386566\pi$
$571$	9520.20	0.697737	0.348869	+	0.937172i	$0.386566\pi$
$572$	2426.96	0.177406
$573$	4162.44	0.303471
$574$	7457.41	0.542276
$575$	−18917.4	−1.37202
$576$	19730.5	1.42726
$577$	−1717.81	−0.123940	−0.0619701	−	0.998078i	$-0.519738\pi$
$577$	−1717.81	−0.123940	−0.0619701	+	0.998078i	$0.519738\pi$
$578$	22681.7	1.63224
$579$	3420.81	0.245534
$580$	52604.6	3.76601
$581$	6489.17	0.463367
$582$	−550.310	−0.0391943
$583$	−3421.74	−0.243077
$584$	24159.8	1.71188
$585$	7722.11	0.545760
$586$	15124.2	1.06617
$587$	11116.2	0.781627	0.390813	−	0.920470i	$-0.372194\pi$
$587$	11116.2	0.781627	0.390813	+	0.920470i	$0.372194\pi$
$588$	6896.57	0.483690
$589$	−2923.96	−0.204550
$590$	40953.8	2.85770
$591$	5636.52	0.392310
$592$	2912.97	0.202233
$593$	−19119.3	−1.32401	−0.662003	−	0.749501i	$-0.730293\pi$
$593$	−19119.3	−1.32401	−0.662003	+	0.749501i	$0.730293\pi$
$594$	4215.21	0.291165
$595$	−434.953	−0.0299686
$596$	−2469.63	−0.169732
$597$	−3410.45	−0.233803
$598$	−5760.69	−0.393933
$599$	−3266.21	−0.222794	−0.111397	−	0.993776i	$-0.535532\pi$
$599$	−3266.21	−0.222794	−0.111397	+	0.993776i	$0.535532\pi$
$600$	10187.7	0.693186
$601$	−1640.05	−0.111313	−0.0556564	−	0.998450i	$-0.517725\pi$
$601$	−1640.05	−0.111313	−0.0556564	+	0.998450i	$0.517725\pi$
$602$	−6217.84	−0.420964
$603$	−8084.39	−0.545973
$604$	−15205.2	−1.02433
$605$	2339.96	0.157244
$606$	10670.6	0.715287
$607$	−5767.93	−0.385689	−0.192844	−	0.981229i	$-0.561771\pi$
$607$	−5767.93	−0.385689	−0.192844	+	0.981229i	$0.561771\pi$
$608$	2408.64	0.160663
$609$	1621.56	0.107896
$610$	18450.2	1.22464
$611$	2241.59	0.148421
$612$	−1481.03	−0.0978221
$613$	−10013.1	−0.659749	−0.329875	−	0.944025i	$-0.607007\pi$
$613$	−10013.1	−0.659749	−0.329875	+	0.944025i	$0.607007\pi$
$614$	−17095.0	−1.12361
$615$	−9999.41	−0.655634
$616$	−1400.32	−0.0915916
$617$	−20935.2	−1.36600	−0.682998	−	0.730420i	$-0.739324\pi$
$617$	−20935.2	−1.36600	−0.682998	+	0.730420i	$0.739324\pi$
$618$	−12917.2	−0.840788
$619$	−20559.1	−1.33496	−0.667481	−	0.744626i	$-0.732628\pi$
$619$	−20559.1	−1.33496	−0.667481	+	0.744626i	$0.732628\pi$
$620$	−49707.8	−3.21986
$621$	−6280.70	−0.405855
$622$	−19507.6	−1.25753
$623$	4164.72	0.267827
$624$	264.592	0.0169746
$625$	15242.4	0.975513
$626$	−36496.4	−2.33017
$627$	271.390	0.0172859
$628$	20872.8	1.32630
$629$	1301.71	0.0825161
$630$	−10948.0	−0.692345
$631$	11190.5	0.705999	0.352999	−	0.935624i	$-0.385162\pi$
$631$	11190.5	0.705999	0.352999	+	0.935624i	$0.385162\pi$
$632$	−15935.9	−1.00300
$633$	4186.10	0.262848
$634$	10980.1	0.687816
$635$	4895.08	0.305914
$636$	−6746.62	−0.420630
$637$	5200.62	0.323479
$638$	10282.5	0.638067
$639$	−6465.98	−0.400298
$640$	48164.0	2.97477
$641$	13913.3	0.857321	0.428661	−	0.903466i	$-0.358986\pi$
$641$	13913.3	0.857321	0.428661	+	0.903466i	$0.358986\pi$
$642$	5789.87	0.355931
$643$	−17345.6	−1.06383	−0.531915	−	0.846798i	$-0.678527\pi$
$643$	−17345.6	−1.06383	−0.531915	+	0.846798i	$0.678527\pi$
$644$	5126.84	0.313704
$645$	8337.30	0.508963
$646$	−319.884	−0.0194825
$647$	−11773.4	−0.715394	−0.357697	−	0.933838i	$-0.616438\pi$
$647$	−11773.4	−0.715394	−0.357697	+	0.933838i	$0.616438\pi$
$648$	−13395.1	−0.812049
$649$	5025.10	0.303933
$650$	18877.0	1.13910
$651$	−1532.26	−0.0922490
$652$	−24592.7	−1.47718
$653$	−12068.3	−0.723231	−0.361615	−	0.932327i	$-0.617775\pi$
$653$	−12068.3	−0.723231	−0.361615	+	0.932327i	$0.617775\pi$
$654$	5735.21	0.342912
$655$	2533.34	0.151123
$656$	3236.28	0.192615
$657$	23176.6	1.37627
$658$	−3178.01	−0.188285
$659$	−16830.3	−0.994866	−0.497433	−	0.867502i	$-0.665724\pi$
$659$	−16830.3	−0.994866	−0.497433	+	0.867502i	$0.665724\pi$
$660$	4613.67	0.272101
$661$	−24497.7	−1.44153	−0.720765	−	0.693180i	$-0.756209\pi$
$661$	−24497.7	−1.44153	−0.720765	+	0.693180i	$0.756209\pi$
$662$	32505.5	1.90840
$663$	118.238	0.00692606
$664$	33018.7	1.92978
$665$	−1484.36	−0.0865580
$666$	32764.7	1.90631
$667$	−15321.0	−0.889402
$668$	4301.99	0.249175
$669$	−9292.92	−0.537048
$670$	−29684.5	−1.71166
$671$	2263.88	0.130247
$672$	1262.22	0.0724569
$673$	16353.1	0.936648	0.468324	−	0.883557i	$-0.344858\pi$
$673$	16353.1	0.936648	0.468324	+	0.883557i	$0.344858\pi$
$674$	23853.9	1.36323
$675$	20581.0	1.17357
$676$	−26029.3	−1.48096
$677$	23556.3	1.33729	0.668643	−	0.743583i	$-0.266875\pi$
$677$	23556.3	1.33729	0.668643	+	0.743583i	$0.266875\pi$
$678$	11982.2	0.678723
$679$	369.321	0.0208737
$680$	−2213.16	−0.124810
$681$	−5148.56	−0.289711
$682$	−9716.24	−0.545534
$683$	−8542.51	−0.478580	−0.239290	−	0.970948i	$-0.576915\pi$
$683$	−8542.51	−0.478580	−0.239290	+	0.970948i	$0.576915\pi$
$684$	−5054.31	−0.282538
$685$	−52852.6	−2.94802
$686$	−15326.4	−0.853011
$687$	6888.62	0.382558
$688$	−2698.34	−0.149525
$689$	−5087.55	−0.281306
$690$	−10951.1	−0.604206
$691$	−9123.09	−0.502256	−0.251128	−	0.967954i	$-0.580801\pi$
$691$	−9123.09	−0.502256	−0.251128	+	0.967954i	$0.580801\pi$
$692$	8321.98	0.457159
$693$	−1343.34	−0.0736351
$694$	−26887.6	−1.47066
$695$	11448.4	0.624840
$696$	8250.93	0.449354
$697$	1446.19	0.0785915
$698$	−46466.6	−2.51975
$699$	−92.3063	−0.00499477
$700$	−16799.9	−0.907110
$701$	−23688.8	−1.27634	−0.638169	−	0.769896i	$-0.720308\pi$
$701$	−23688.8	−1.27634	−0.638169	+	0.769896i	$0.720308\pi$
$702$	6267.29	0.336957
$703$	4442.34	0.238330
$704$	8889.36	0.475895
$705$	4261.29	0.227645
$706$	17388.7	0.926959
$707$	−7161.21	−0.380941
$708$	9907.94	0.525937
$709$	31550.8	1.67125	0.835623	−	0.549303i	$-0.185107\pi$
$709$	31550.8	1.67125	0.835623	+	0.549303i	$0.185107\pi$
$710$	−23742.0	−1.25496
$711$	−15287.4	−0.806362
$712$	21191.2	1.11541
$713$	14477.3	0.760420
$714$	−167.631	−0.00878632
$715$	3479.11	0.181974
$716$	−59574.7	−3.10951
$717$	−7191.34	−0.374568
$718$	20567.0	1.06902
$719$	−216.313	−0.0112199	−0.00560996	−	0.999984i	$-0.501786\pi$
$719$	−216.313	−0.0112199	−0.00560996	+	0.999984i	$0.501786\pi$
$720$	−4751.07	−0.245919
$721$	8668.95	0.447779
$722$	30704.9	1.58271
$723$	−505.296	−0.0259919
$724$	−57686.4	−2.96118
$725$	50204.7	2.57180
$726$	901.820	0.0461015
$727$	−18696.1	−0.953781	−0.476890	−	0.878963i	$-0.658236\pi$
$727$	−18696.1	−0.953781	−0.476890	+	0.878963i	$0.658236\pi$
$728$	−2082.03	−0.105996
$729$	−9261.70	−0.470543
$730$	85100.6	4.31468
$731$	−1205.80	−0.0610099
$732$	4463.66	0.225385
$733$	24078.2	1.21330	0.606649	−	0.794970i	$-0.292513\pi$
$733$	24078.2	1.21330	0.606649	+	0.794970i	$0.292513\pi$
$734$	−16987.4	−0.854246
$735$	9886.42	0.496145
$736$	−11925.8	−0.597271
$737$	−3642.34	−0.182045
$738$	36401.2	1.81565
$739$	35287.3	1.75652	0.878258	−	0.478187i	$-0.158706\pi$
$739$	35287.3	1.75652	0.878258	+	0.478187i	$0.158706\pi$
$740$	75520.5	3.75161
$741$	403.510	0.0200045
$742$	7212.84	0.356862
$743$	−26167.3	−1.29204	−0.646021	−	0.763320i	$-0.723568\pi$
$743$	−26167.3	−1.29204	−0.646021	+	0.763320i	$0.723568\pi$
$744$	−7796.57	−0.384188
$745$	−3540.29	−0.174102
$746$	−55684.2	−2.73290
$747$	31675.1	1.55145
$748$	−667.263	−0.0326170
$749$	−3885.67	−0.189558
$750$	17868.9	0.869974
$751$	5901.50	0.286749	0.143375	−	0.989668i	$-0.454205\pi$
$751$	5901.50	0.286749	0.143375	+	0.989668i	$0.454205\pi$
$752$	−1379.15	−0.0668783
$753$	−920.537	−0.0445501
$754$	15288.3	0.738416
$755$	−21797.2	−1.05070
$756$	−5577.69	−0.268332
$757$	11712.4	0.562343	0.281172	−	0.959657i	$-0.409277\pi$
$757$	11712.4	0.562343	0.281172	+	0.959657i	$0.409277\pi$
$758$	−16746.4	−0.802449
$759$	−1343.72	−0.0642609
$760$	−7552.84	−0.360487
$761$	36285.6	1.72845	0.864227	−	0.503102i	$-0.167808\pi$
$761$	36285.6	1.72845	0.864227	+	0.503102i	$0.167808\pi$
$762$	1886.56	0.0896890
$763$	−3848.99	−0.182625
$764$	−34926.0	−1.65390
$765$	−2123.10	−0.100341
$766$	692.778	0.0326776
$767$	7471.46	0.351733
$768$	8168.44	0.383793
$769$	8915.59	0.418081	0.209041	−	0.977907i	$-0.432966\pi$
$769$	8915.59	0.418081	0.209041	+	0.977907i	$0.432966\pi$
$770$	−4932.49	−0.230850
$771$	7804.85	0.364572
$772$	−28703.2	−1.33815
$773$	19761.5	0.919497	0.459749	−	0.888049i	$-0.347940\pi$
$773$	19761.5	0.919497	0.459749	+	0.888049i	$0.347940\pi$
$774$	−30350.6	−1.40947
$775$	−47440.1	−2.19884
$776$	1879.21	0.0869325
$777$	2327.95	0.107484
$778$	48714.9	2.24488
$779$	4935.40	0.226995
$780$	6859.73	0.314895
$781$	−2913.18	−0.133472
$782$	1583.83	0.0724267
$783$	16668.3	0.760763
$784$	−3199.71	−0.145759
$785$	29921.7	1.36045
$786$	976.351	0.0443070
$787$	−13891.5	−0.629196	−0.314598	−	0.949225i	$-0.601870\pi$
$787$	−13891.5	−0.629196	−0.314598	+	0.949225i	$0.601870\pi$
$788$	−47294.6	−2.13807
$789$	−1911.33	−0.0862422
$790$	−56132.8	−2.52799
$791$	−8041.45	−0.361468
$792$	−6835.26	−0.306667
$793$	3365.99	0.150731
$794$	−8305.32	−0.371215
$795$	−9671.47	−0.431461
$796$	28616.3	1.27422
$797$	3945.96	0.175374	0.0876870	−	0.996148i	$-0.472052\pi$
$797$	3945.96	0.175374	0.0876870	+	0.996148i	$0.472052\pi$
$798$	−572.074	−0.0253774
$799$	−616.299	−0.0272880
$800$	39079.2	1.72707
$801$	20328.9	0.896737
$802$	30382.4	1.33770
$803$	10442.0	0.458891
$804$	−7181.56	−0.315017
$805$	7349.47	0.321782
$806$	−14446.4	−0.631330
$807$	6905.99	0.301242
$808$	−36438.2	−1.58650
$809$	−23415.9	−1.01762	−0.508812	−	0.860878i	$-0.669915\pi$
$809$	−23415.9	−1.01762	−0.508812	+	0.860878i	$0.669915\pi$
$810$	−47182.9	−2.04671
$811$	−34041.4	−1.47393	−0.736964	−	0.675932i	$-0.763741\pi$
$811$	−34041.4	−1.47393	−0.736964	+	0.675932i	$0.763741\pi$
$812$	−13606.1	−0.588030
$813$	13017.1	0.561537
$814$	14761.8	0.635627
$815$	−35254.3	−1.51522
$816$	−72.7465	−0.00312088
$817$	−4115.04	−0.176214
$818$	61766.5	2.64012
$819$	−1997.31	−0.0852157
$820$	83902.6	3.57318
$821$	−25335.8	−1.07701	−0.538506	−	0.842622i	$-0.681011\pi$
$821$	−25335.8	−1.07701	−0.538506	+	0.842622i	$0.681011\pi$
$822$	−20369.4	−0.864313
$823$	25030.2	1.06015	0.530073	−	0.847952i	$-0.322165\pi$
$823$	25030.2	1.06015	0.530073	+	0.847952i	$0.322165\pi$
$824$	44110.0	1.86486
$825$	4403.19	0.185817
$826$	−10592.6	−0.446204
$827$	−36947.7	−1.55357	−0.776783	−	0.629769i	$-0.783150\pi$
$827$	−36947.7	−1.55357	−0.776783	+	0.629769i	$0.783150\pi$
$828$	25025.2	1.05035
$829$	17206.4	0.720874	0.360437	−	0.932784i	$-0.382628\pi$
$829$	17206.4	0.720874	0.360437	+	0.932784i	$0.382628\pi$
$830$	116305.	4.86387
$831$	−7510.67	−0.313529
$832$	13216.9	0.550740
$833$	−1429.85	−0.0594733
$834$	4412.23	0.183193
$835$	6167.03	0.255591
$836$	−2277.16	−0.0942074
$837$	−15750.4	−0.650436
$838$	37372.3	1.54058
$839$	27750.9	1.14191	0.570957	−	0.820980i	$-0.306572\pi$
$839$	27750.9	1.14191	0.570957	+	0.820980i	$0.306572\pi$
$840$	−3957.96	−0.162575
$841$	16271.3	0.667158
$842$	14964.7	0.612491
$843$	100.157	0.00409203
$844$	−35124.5	−1.43251
$845$	−37313.8	−1.51909
$846$	−15512.5	−0.630416
$847$	−605.225	−0.0245523
$848$	3130.14	0.126756
$849$	−3106.75	−0.125587
$850$	−5189.99	−0.209430
$851$	−21995.2	−0.886000
$852$	−5743.89	−0.230965
$853$	−26526.0	−1.06475	−0.532376	−	0.846508i	$-0.678701\pi$
$853$	−26526.0	−1.06475	−0.532376	+	0.846508i	$0.678701\pi$
$854$	−4772.12	−0.191216
$855$	−7245.49	−0.289814
$856$	−19771.3	−0.789451
$857$	20437.4	0.814618	0.407309	−	0.913290i	$-0.366467\pi$
$857$	20437.4	0.814618	0.407309	+	0.913290i	$0.366467\pi$
$858$	1340.85	0.0533519
$859$	−13618.6	−0.540932	−0.270466	−	0.962729i	$-0.587178\pi$
$859$	−13618.6	−0.540932	−0.270466	+	0.962729i	$0.587178\pi$
$860$	−69956.3	−2.77382
$861$	2586.33	0.102371
$862$	24186.6	0.955683
$863$	37824.7	1.49197	0.745985	−	0.665963i	$-0.231979\pi$
$863$	37824.7	1.49197	0.745985	+	0.665963i	$0.231979\pi$
$864$	12974.6	0.510885
$865$	11929.8	0.468931
$866$	−59518.5	−2.33547
$867$	7866.31	0.308136
$868$	12856.8	0.502753
$869$	−6887.59	−0.268867
$870$	29063.1	1.13257
$871$	−5415.53	−0.210675
$872$	−19584.7	−0.760575
$873$	1802.74	0.0698894
$874$	5405.14	0.209189
$875$	−11992.1	−0.463322
$876$	20588.4	0.794082
$877$	5516.90	0.212420	0.106210	−	0.994344i	$-0.466128\pi$
$877$	5516.90	0.212420	0.106210	+	0.994344i	$0.466128\pi$
$878$	24176.3	0.929282
$879$	5245.28	0.201273
$880$	−2140.54	−0.0819974
$881$	3781.00	0.144591	0.0722957	−	0.997383i	$-0.476967\pi$
$881$	3781.00	0.144591	0.0722957	+	0.997383i	$0.476967\pi$
$882$	−35989.9	−1.37397
$883$	−35472.0	−1.35190	−0.675950	−	0.736948i	$-0.736266\pi$
$883$	−35472.0	−1.35190	−0.675950	+	0.736948i	$0.736266\pi$
$884$	−992.105	−0.0377467
$885$	14203.3	0.539479
$886$	74152.1	2.81173
$887$	−18080.8	−0.684434	−0.342217	−	0.939621i	$-0.611178\pi$
$887$	−18080.8	−0.684434	−0.342217	+	0.939621i	$0.611178\pi$
$888$	11845.2	0.447635
$889$	−1266.10	−0.0477657
$890$	74644.2	2.81132
$891$	−5789.42	−0.217680
$892$	77974.6	2.92689
$893$	−2103.24	−0.0788155
$894$	−1364.43	−0.0510440
$895$	−85402.1	−3.18958
$896$	−12457.5	−0.464484
$897$	−1997.88	−0.0743672
$898$	−22771.3	−0.846199
$899$	−38421.3	−1.42538
$900$	−82004.0	−3.03719
$901$	1398.76	0.0517197
$902$	16400.2	0.605395
$903$	−2156.43	−0.0794700
$904$	−40917.1	−1.50540
$905$	−82695.1	−3.03743
$906$	−8400.63	−0.308049
$907$	−17444.3	−0.638622	−0.319311	−	0.947650i	$-0.603451\pi$
$907$	−17444.3	−0.638622	−0.319311	+	0.947650i	$0.603451\pi$
$908$	43200.3	1.57891
$909$	−34955.4	−1.27547
$910$	−7333.77	−0.267156
$911$	−28422.0	−1.03366	−0.516830	−	0.856088i	$-0.672888\pi$
$911$	−28422.0	−1.03366	−0.516830	+	0.856088i	$0.672888\pi$
$912$	−248.262	−0.00901400
$913$	14270.9	0.517302
$914$	−31187.1	−1.12864
$915$	6398.78	0.231188
$916$	−57800.7	−2.08492
$917$	−655.244	−0.0235966
$918$	−1723.11	−0.0619512
$919$	14755.8	0.529650	0.264825	−	0.964296i	$-0.414686\pi$
$919$	14755.8	0.529650	0.264825	+	0.964296i	$0.414686\pi$
$920$	37396.1	1.34012
$921$	−5928.76	−0.212117
$922$	−53671.3	−1.91711
$923$	−4331.40	−0.154463
$924$	−1193.32	−0.0424862
$925$	72075.2	2.56196
$926$	61012.1	2.16521
$927$	42315.0	1.49925
$928$	31649.9	1.11957
$929$	−2756.18	−0.0973385	−0.0486693	−	0.998815i	$-0.515498\pi$
$929$	−2756.18	−0.0973385	−0.0486693	+	0.998815i	$0.515498\pi$
$930$	−27462.7	−0.968320
$931$	−4879.63	−0.171776
$932$	774.520	0.0272213
$933$	−6765.49	−0.237398
$934$	31549.7	1.10529
$935$	−956.540	−0.0334569
$936$	−10162.9	−0.354897
$937$	12213.3	0.425818	0.212909	−	0.977072i	$-0.431706\pi$
$937$	12213.3	0.425818	0.212909	+	0.977072i	$0.431706\pi$
$938$	7677.83	0.267260
$939$	−12657.4	−0.439893
$940$	−35755.4	−1.24065
$941$	−35285.0	−1.22238	−0.611190	−	0.791484i	$-0.709309\pi$
$941$	−35285.0	−1.22238	−0.611190	+	0.791484i	$0.709309\pi$
$942$	11531.9	0.398862
$943$	−24436.5	−0.843861
$944$	−4596.86	−0.158490
$945$	−7995.78	−0.275241
$946$	−13674.1	−0.469963
$947$	13708.8	0.470409	0.235205	−	0.971946i	$-0.424424\pi$
$947$	13708.8	0.470409	0.235205	+	0.971946i	$0.424424\pi$
$948$	−13580.2	−0.465257
$949$	15525.4	0.531061
$950$	−17711.9	−0.604893
$951$	3808.04	0.129847
$952$	572.429	0.0194880
$953$	−21440.7	−0.728785	−0.364392	−	0.931245i	$-0.618723\pi$
$953$	−21440.7	−0.728785	−0.364392	+	0.931245i	$0.618723\pi$
$954$	35207.4	1.19485
$955$	−50067.5	−1.69649
$956$	60340.7	2.04138
$957$	3566.10	0.120455
$958$	85682.9	2.88965
$959$	13670.2	0.460308
$960$	25125.5	0.844712
$961$	6514.49	0.218673
$962$	21948.2	0.735592
$963$	−18966.8	−0.634679
$964$	4239.82	0.141655
$965$	−41146.8	−1.37260
$966$	2832.49	0.0943414
$967$	31445.1	1.04572	0.522858	−	0.852420i	$-0.324866\pi$
$967$	31445.1	1.04572	0.522858	+	0.852420i	$0.324866\pi$
$968$	−3079.55	−0.102253
$969$	−110.940	−0.00367793
$970$	6619.34	0.219107
$971$	12323.2	0.407280	0.203640	−	0.979046i	$-0.434723\pi$
$971$	12323.2	0.407280	0.203640	+	0.979046i	$0.434723\pi$
$972$	−41523.3	−1.37023
$973$	−2961.12	−0.0975633
$974$	−91641.6	−3.01477
$975$	6546.78	0.215041
$976$	−2070.95	−0.0679194
$977$	54375.2	1.78057	0.890285	−	0.455403i	$-0.150505\pi$
$977$	54375.2	1.78057	0.890285	+	0.455403i	$0.150505\pi$
$978$	−13587.0	−0.444238
$979$	9158.97	0.299001
$980$	−82954.5	−2.70397
$981$	−18787.7	−0.611464
$982$	76086.7	2.47253
$983$	28072.6	0.910860	0.455430	−	0.890272i	$-0.349485\pi$
$983$	28072.6	0.910860	0.455430	+	0.890272i	$0.349485\pi$
$984$	13159.9	0.426345
$985$	−67798.2	−2.19313
$986$	−4203.32	−0.135762
$987$	−1102.17	−0.0355447
$988$	−3385.75	−0.109023
$989$	20374.6	0.655081
$990$	−24076.6	−0.772933
$991$	−17858.7	−0.572454	−0.286227	−	0.958162i	$-0.592401\pi$
$991$	−17858.7	−0.572454	−0.286227	+	0.958162i	$0.592401\pi$
$992$	−29907.0	−0.957206
$993$	11273.3	0.360271
$994$	6140.82	0.195951
$995$	41022.2	1.30703
$996$	28137.7	0.895158
$997$	5382.99	0.170994	0.0854970	−	0.996338i	$-0.472752\pi$
$997$	5382.99	0.170994	0.0854970	+	0.996338i	$0.472752\pi$
$998$	−49840.1	−1.58082
$999$	23929.5	0.757853

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.4.a.a.1.9	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.4.a.a.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-4.63574 q^{2} -1.60774 q^{3} +13.4901 q^{4} +19.3385 q^{5} +7.45306 q^{6} -5.00186 q^{7} -25.4508 q^{8} -24.4152 q^{9} +O(q^{10})\)	\(q-4.63574 q^{2} -1.60774 q^{3} +13.4901 q^{4} +19.3385 q^{5} +7.45306 q^{6} -5.00186 q^{7} -25.4508 q^{8} -24.4152 q^{9} -89.6483 q^{10} -11.0000 q^{11} -21.6886 q^{12} -16.3551 q^{13} +23.1874 q^{14} -31.0912 q^{15} +10.0626 q^{16} +4.49664 q^{17} +113.183 q^{18} +15.3457 q^{19} +260.879 q^{20} +8.04168 q^{21} +50.9932 q^{22} -75.9804 q^{23} +40.9183 q^{24} +248.977 q^{25} +75.8181 q^{26} +82.6621 q^{27} -67.4758 q^{28} +201.644 q^{29} +144.131 q^{30} -190.540 q^{31} +156.959 q^{32} +17.6851 q^{33} -20.8453 q^{34} -96.7285 q^{35} -329.364 q^{36} +289.485 q^{37} -71.1386 q^{38} +26.2947 q^{39} -492.181 q^{40} +321.615 q^{41} -37.2792 q^{42} -268.156 q^{43} -148.391 q^{44} -472.153 q^{45} +352.226 q^{46} -137.058 q^{47} -16.1780 q^{48} -317.981 q^{49} -1154.19 q^{50} -7.22942 q^{51} -220.633 q^{52} +311.068 q^{53} -383.200 q^{54} -212.723 q^{55} +127.302 q^{56} -24.6718 q^{57} -934.770 q^{58} -456.827 q^{59} -419.424 q^{60} -205.807 q^{61} +883.295 q^{62} +122.121 q^{63} -808.124 q^{64} -316.283 q^{65} -81.9837 q^{66} +331.121 q^{67} +60.6602 q^{68} +122.157 q^{69} +448.408 q^{70} +264.835 q^{71} +621.387 q^{72} -949.272 q^{73} -1341.98 q^{74} -400.290 q^{75} +207.015 q^{76} +55.0205 q^{77} -121.896 q^{78} +626.144 q^{79} +194.595 q^{80} +526.311 q^{81} -1490.93 q^{82} -1297.35 q^{83} +108.483 q^{84} +86.9582 q^{85} +1243.10 q^{86} -324.191 q^{87} +279.959 q^{88} -832.633 q^{89} +2188.78 q^{90} +81.8060 q^{91} -1024.99 q^{92} +306.338 q^{93} +635.364 q^{94} +296.762 q^{95} -252.349 q^{96} -73.8368 q^{97} +1474.08 q^{98} +268.567 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 14 q^{2} - 10 q^{3} + 296 q^{4} - 42 q^{5} - 13 q^{6} - 59 q^{7} - 150 q^{8} + 541 q^{9}+O(q^{10}) \) 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