LMFDB - Embedded newform 1859.4.a.q.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,4,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, 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("1859.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1859.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:	$109.684550701$
Analytic rank:	$0$
Dimension:	$51$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.57359 q^{2} -4.93113 q^{3} +4.77054 q^{4} +6.17910 q^{5} +17.6218 q^{6} +19.8272 q^{7} +11.5408 q^{8} -2.68401 q^{9} +O(q^{10})$	\(q-3.57359 q^{2} -4.93113 q^{3} +4.77054 q^{4} +6.17910 q^{5} +17.6218 q^{6} +19.8272 q^{7} +11.5408 q^{8} -2.68401 q^{9} -22.0816 q^{10} +11.0000 q^{11} -23.5241 q^{12} -70.8543 q^{14} -30.4699 q^{15} -79.4063 q^{16} -80.2618 q^{17} +9.59153 q^{18} -25.3151 q^{19} +29.4777 q^{20} -97.7704 q^{21} -39.3095 q^{22} -148.473 q^{23} -56.9089 q^{24} -86.8187 q^{25} +146.376 q^{27} +94.5865 q^{28} -203.801 q^{29} +108.887 q^{30} +331.165 q^{31} +191.439 q^{32} -54.2424 q^{33} +286.823 q^{34} +122.514 q^{35} -12.8042 q^{36} -110.637 q^{37} +90.4657 q^{38} +71.3115 q^{40} +190.734 q^{41} +349.391 q^{42} +532.829 q^{43} +52.4760 q^{44} -16.5847 q^{45} +530.582 q^{46} -161.291 q^{47} +391.562 q^{48} +50.1180 q^{49} +310.254 q^{50} +395.781 q^{51} -646.526 q^{53} -523.086 q^{54} +67.9701 q^{55} +228.821 q^{56} +124.832 q^{57} +728.300 q^{58} +535.991 q^{59} -145.358 q^{60} -426.609 q^{61} -1183.45 q^{62} -53.2163 q^{63} -48.8755 q^{64} +193.840 q^{66} +125.191 q^{67} -382.892 q^{68} +732.139 q^{69} -437.816 q^{70} -413.434 q^{71} -30.9755 q^{72} -823.632 q^{73} +395.371 q^{74} +428.114 q^{75} -120.767 q^{76} +218.099 q^{77} +545.273 q^{79} -490.659 q^{80} -649.328 q^{81} -681.605 q^{82} +1356.76 q^{83} -466.418 q^{84} -495.946 q^{85} -1904.11 q^{86} +1004.97 q^{87} +126.948 q^{88} -148.141 q^{89} +59.2671 q^{90} -708.297 q^{92} -1633.02 q^{93} +576.389 q^{94} -156.424 q^{95} -944.011 q^{96} +3.17029 q^{97} -179.101 q^{98} -29.5241 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9}+O(q^{10}) $ 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9	\( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9} + 212 q^{10} + 561 q^{11} + 209 q^{12} + 280 q^{14} + 284 q^{15} + 1246 q^{16} + 164 q^{17} - 189 q^{18} + 26 q^{19} + 438 q^{20} + 134 q^{21} + 373 q^{23} - 354 q^{24} + 2048 q^{25} + 1470 q^{27} - 1245 q^{28} + 898 q^{29} + 427 q^{30} + 767 q^{31} + 1127 q^{32} + 231 q^{33} + 206 q^{34} + 54 q^{35} + 3415 q^{36} + 395 q^{37} + 1577 q^{38} + 3253 q^{40} - 354 q^{41} + 942 q^{42} + 484 q^{43} + 2574 q^{44} + 1452 q^{45} - 2117 q^{46} + 1925 q^{47} + 1780 q^{48} + 4535 q^{49} - 1093 q^{50} + 230 q^{51} + 1387 q^{53} - 5271 q^{54} + 451 q^{55} + 2568 q^{56} - 5738 q^{57} + 3695 q^{58} + 1145 q^{59} - 1590 q^{60} + 5382 q^{61} - 395 q^{62} + 710 q^{63} + 9839 q^{64} - 803 q^{66} - 210 q^{67} + 1742 q^{68} + 7028 q^{69} - 6747 q^{70} + 3693 q^{71} - 12481 q^{72} + 968 q^{73} + 1735 q^{74} - 727 q^{75} - 2801 q^{76} + 44 q^{77} + 4234 q^{79} + 2390 q^{80} + 7743 q^{81} + 4770 q^{82} - 2798 q^{83} + 14821 q^{84} - 1802 q^{85} + 6558 q^{86} + 1896 q^{87} - 231 q^{88} + 3927 q^{89} + 1927 q^{90} + 1984 q^{92} - 1332 q^{93} + 7590 q^{94} + 4944 q^{95} - 7280 q^{96} + 3913 q^{97} - 15201 q^{98} + 6534 q^{99}+O(q^{100}) \) 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9 + 212 * q^10 + 561 * q^11 + 209 * q^12 + 280 * q^14 + 284 * q^15 + 1246 * q^16 + 164 * q^17 - 189 * q^18 + 26 * q^19 + 438 * q^20 + 134 * q^21 + 373 * q^23 - 354 * q^24 + 2048 * q^25 + 1470 * q^27 - 1245 * q^28 + 898 * q^29 + 427 * q^30 + 767 * q^31 + 1127 * q^32 + 231 * q^33 + 206 * q^34 + 54 * q^35 + 3415 * q^36 + 395 * q^37 + 1577 * q^38 + 3253 * q^40 - 354 * q^41 + 942 * q^42 + 484 * q^43 + 2574 * q^44 + 1452 * q^45 - 2117 * q^46 + 1925 * q^47 + 1780 * q^48 + 4535 * q^49 - 1093 * q^50 + 230 * q^51 + 1387 * q^53 - 5271 * q^54 + 451 * q^55 + 2568 * q^56 - 5738 * q^57 + 3695 * q^58 + 1145 * q^59 - 1590 * q^60 + 5382 * q^61 - 395 * q^62 + 710 * q^63 + 9839 * q^64 - 803 * q^66 - 210 * q^67 + 1742 * q^68 + 7028 * q^69 - 6747 * q^70 + 3693 * q^71 - 12481 * q^72 + 968 * q^73 + 1735 * q^74 - 727 * q^75 - 2801 * q^76 + 44 * q^77 + 4234 * q^79 + 2390 * q^80 + 7743 * q^81 + 4770 * q^82 - 2798 * q^83 + 14821 * q^84 - 1802 * q^85 + 6558 * q^86 + 1896 * q^87 - 231 * q^88 + 3927 * q^89 + 1927 * q^90 + 1984 * q^92 - 1332 * q^93 + 7590 * q^94 + 4944 * q^95 - 7280 * q^96 + 3913 * q^97 - 15201 * q^98 + 6534 * 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 $

$2$	−3.57359	−1.26345	−0.631727	−	0.775191i	$-0.717654\pi$
$2$	−3.57359	−1.26345	−0.631727	+	0.775191i	$0.717654\pi$
$3$	−4.93113	−0.948995	−0.474498	−	0.880257i	$-0.657370\pi$
$3$	−4.93113	−0.948995	−0.474498	+	0.880257i	$0.657370\pi$
$4$	4.77054	0.596318
$5$	6.17910	0.552676	0.276338	−	0.961061i	$-0.410879\pi$
$5$	6.17910	0.552676	0.276338	+	0.961061i	$0.410879\pi$
$6$	17.6218	1.19901
$7$	19.8272	1.07057	0.535284	−	0.844672i	$-0.320205\pi$
$7$	19.8272	1.07057	0.535284	+	0.844672i	$0.320205\pi$
$8$	11.5408	0.510034
$9$	−2.68401	−0.0994076
$10$	−22.0816	−0.698281
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−23.5241	−0.565903
$13$	0	0
$13$	0	0
$14$	−70.8543	−1.35261
$15$	−30.4699	−0.524487
$16$	−79.4063	−1.24072
$17$	−80.2618	−1.14508	−0.572540	−	0.819877i	$-0.694042\pi$
$17$	−80.2618	−1.14508	−0.572540	+	0.819877i	$0.694042\pi$
$18$	9.59153	0.125597
$19$	−25.3151	−0.305667	−0.152834	−	0.988252i	$-0.548840\pi$
$19$	−25.3151	−0.305667	−0.152834	+	0.988252i	$0.548840\pi$
$20$	29.4777	0.329570
$21$	−97.7704	−1.01596
$22$	−39.3095	−0.380946
$23$	−148.473	−1.34603	−0.673017	−	0.739627i	$-0.735002\pi$
$23$	−148.473	−1.34603	−0.673017	+	0.739627i	$0.735002\pi$
$24$	−56.9089	−0.484020
$25$	−86.8187	−0.694550
$26$	0	0
$27$	146.376	1.04333
$28$	94.5865	0.638399
$29$	−203.801	−1.30499	−0.652497	−	0.757791i	$-0.726278\pi$
$29$	−203.801	−1.30499	−0.652497	+	0.757791i	$0.726278\pi$
$30$	108.887	0.662665
$31$	331.165	1.91868	0.959338	−	0.282258i	$-0.0910836\pi$
$31$	331.165	1.91868	0.959338	+	0.282258i	$0.0910836\pi$
$32$	191.439	1.05756
$33$	−54.2424	−0.286133
$34$	286.823	1.44676
$35$	122.514	0.591677
$36$	−12.8042	−0.0592785
$37$	−110.637	−0.491584	−0.245792	−	0.969323i	$-0.579048\pi$
$37$	−110.637	−0.491584	−0.245792	+	0.969323i	$0.579048\pi$
$38$	90.4657	0.386197
$39$	0	0
$40$	71.3115	0.281883
$41$	190.734	0.726528	0.363264	−	0.931686i	$-0.381662\pi$
$41$	190.734	0.726528	0.363264	+	0.931686i	$0.381662\pi$
$42$	349.391	1.28363
$43$	532.829	1.88967	0.944834	−	0.327550i	$-0.106223\pi$
$43$	532.829	1.88967	0.944834	+	0.327550i	$0.106223\pi$
$44$	52.4760	0.179797
$45$	−16.5847	−0.0549402
$46$	530.582	1.70065
$47$	−161.291	−0.500570	−0.250285	−	0.968172i	$-0.580524\pi$
$47$	−161.291	−0.500570	−0.250285	+	0.968172i	$0.580524\pi$
$48$	391.562	1.17744
$49$	50.1180	0.146117
$50$	310.254	0.877532
$51$	395.781	1.08668
$52$	0	0
$53$	−646.526	−1.67561	−0.837803	−	0.545972i	$-0.816160\pi$
$53$	−646.526	−1.67561	−0.837803	+	0.545972i	$0.816160\pi$
$54$	−523.086	−1.31820
$55$	67.9701	0.166638
$56$	228.821	0.546026
$57$	124.832	0.290077
$58$	728.300	1.64880
$59$	535.991	1.18271	0.591357	−	0.806410i	$-0.298593\pi$
$59$	535.991	1.18271	0.591357	+	0.806410i	$0.298593\pi$
$60$	−145.358	−0.312761
$61$	−426.609	−0.895437	−0.447718	−	0.894175i	$-0.647763\pi$
$61$	−426.609	−0.895437	−0.447718	+	0.894175i	$0.647763\pi$
$62$	−1183.45	−2.42416
$63$	−53.2163	−0.106423
$64$	−48.8755	−0.0954600
$65$	0	0
$66$	193.840	0.361516
$67$	125.191	0.228276	0.114138	−	0.993465i	$-0.463589\pi$
$67$	125.191	0.228276	0.114138	+	0.993465i	$0.463589\pi$
$68$	−382.892	−0.682831
$69$	732.139	1.27738
$70$	−437.816	−0.747557
$71$	−413.434	−0.691065	−0.345533	−	0.938407i	$-0.612302\pi$
$71$	−413.434	−0.691065	−0.345533	+	0.938407i	$0.612302\pi$
$72$	−30.9755	−0.0507013
$73$	−823.632	−1.32053	−0.660266	−	0.751032i	$-0.729556\pi$
$73$	−823.632	−1.32053	−0.660266	+	0.751032i	$0.729556\pi$
$74$	395.371	0.621094
$75$	428.114	0.659125
$76$	−120.767	−0.182275
$77$	218.099	0.322789
$78$	0	0
$79$	545.273	0.776557	0.388279	−	0.921542i	$-0.373070\pi$
$79$	545.273	0.776557	0.388279	+	0.921542i	$0.373070\pi$
$80$	−490.659	−0.685717
$81$	−649.328	−0.890711
$82$	−681.605	−0.917936
$83$	1356.76	1.79426	0.897130	−	0.441767i	$-0.145648\pi$
$83$	1356.76	1.79426	0.897130	+	0.441767i	$0.145648\pi$
$84$	−466.418	−0.605838
$85$	−495.946	−0.632857
$86$	−1904.11	−2.38751
$87$	1004.97	1.23843
$88$	126.948	0.153781
$89$	−148.141	−0.176438	−0.0882188	−	0.996101i	$-0.528117\pi$
$89$	−148.141	−0.176438	−0.0882188	+	0.996101i	$0.528117\pi$
$90$	59.2671	0.0694144
$91$	0	0
$92$	−708.297	−0.802663
$93$	−1633.02	−1.82082
$94$	576.389	0.632447
$95$	−156.424	−0.168935
$96$	−944.011	−1.00362
$97$	3.17029	0.00331850	0.00165925	−	0.999999i	$-0.499472\pi$
$97$	3.17029	0.00331850	0.00165925	+	0.999999i	$0.499472\pi$
$98$	−179.101	−0.184612
$99$	−29.5241	−0.0299725
$100$	−414.172	−0.414172
$101$	141.983	0.139880	0.0699398	−	0.997551i	$-0.477719\pi$
$101$	141.983	0.139880	0.0699398	+	0.997551i	$0.477719\pi$
$102$	−1414.36	−1.37296
$103$	381.541	0.364993	0.182497	−	0.983206i	$-0.441582\pi$
$103$	381.541	0.364993	0.182497	+	0.983206i	$0.441582\pi$
$104$	0	0
$105$	−604.133	−0.561499
$106$	2310.42	2.11705
$107$	500.945	0.452600	0.226300	−	0.974058i	$-0.427337\pi$
$107$	500.945	0.452600	0.226300	+	0.974058i	$0.427337\pi$
$108$	698.291	0.622158
$109$	−62.7161	−0.0551111	−0.0275556	−	0.999620i	$-0.508772\pi$
$109$	−62.7161	−0.0551111	−0.0275556	+	0.999620i	$0.508772\pi$
$110$	−242.897	−0.210539
$111$	545.565	0.466511
$112$	−1574.40	−1.32828
$113$	542.597	0.451710	0.225855	−	0.974161i	$-0.427482\pi$
$113$	542.597	0.451710	0.225855	+	0.974161i	$0.427482\pi$
$114$	−446.098	−0.366499
$115$	−917.430	−0.743920
$116$	−972.239	−0.778191
$117$	0	0
$118$	−1915.41	−1.49430
$119$	−1591.37	−1.22589
$120$	−351.646	−0.267506
$121$	121.000	0.0909091
$122$	1524.52	1.13134
$123$	−940.534	−0.689472
$124$	1579.84	1.14414
$125$	−1308.85	−0.936536
$126$	190.173	0.134460
$127$	−1016.16	−0.709999	−0.354999	−	0.934867i	$-0.615519\pi$
$127$	−1016.16	−0.709999	−0.354999	+	0.934867i	$0.615519\pi$
$128$	−1356.85	−0.936954
$129$	−2627.45	−1.79329
$130$	0	0
$131$	−655.740	−0.437346	−0.218673	−	0.975798i	$-0.570173\pi$
$131$	−655.740	−0.437346	−0.218673	+	0.975798i	$0.570173\pi$
$132$	−258.766	−0.170626
$133$	−501.927	−0.327238
$134$	−447.381	−0.288417
$135$	904.469	0.576625
$136$	−926.282	−0.584030
$137$	1000.01	0.623628	0.311814	−	0.950143i	$-0.399063\pi$
$137$	1000.01	0.623628	0.311814	+	0.950143i	$0.399063\pi$
$138$	−2616.36	−1.61391
$139$	1440.93	0.879269	0.439634	−	0.898177i	$-0.355108\pi$
$139$	1440.93	0.879269	0.439634	+	0.898177i	$0.355108\pi$
$140$	584.460	0.352827
$141$	795.348	0.475038
$142$	1477.45	0.873130
$143$	0	0
$144$	213.127	0.123337
$145$	−1259.30	−0.721238
$146$	2943.32	1.66843
$147$	−247.138	−0.138664
$148$	−527.798	−0.293140
$149$	651.515	0.358216	0.179108	−	0.983829i	$-0.442679\pi$
$149$	651.515	0.358216	0.179108	+	0.983829i	$0.442679\pi$
$150$	−1529.90	−0.832774
$151$	−1162.49	−0.626503	−0.313251	−	0.949670i	$-0.601418\pi$
$151$	−1162.49	−0.626503	−0.313251	+	0.949670i	$0.601418\pi$
$152$	−292.155	−0.155901
$153$	215.423	0.113830
$154$	−779.397	−0.407829
$155$	2046.30	1.06041
$156$	0	0
$157$	3235.98	1.64496	0.822482	−	0.568791i	$-0.192589\pi$
$157$	3235.98	1.64496	0.822482	+	0.568791i	$0.192589\pi$
$158$	−1948.58	−0.981145
$159$	3188.10	1.59014
$160$	1182.92	0.584489
$161$	−2943.80	−1.44102
$162$	2320.43	1.12537
$163$	−2506.26	−1.20433	−0.602164	−	0.798372i	$-0.705695\pi$
$163$	−2506.26	−1.20433	−0.602164	+	0.798372i	$0.705695\pi$
$164$	909.905	0.433242
$165$	−335.169	−0.158139
$166$	−4848.50	−2.26697
$167$	1524.50	0.706403	0.353202	−	0.935547i	$-0.385093\pi$
$167$	1524.50	0.706403	0.353202	+	0.935547i	$0.385093\pi$
$168$	−1128.34	−0.518177
$169$	0	0
$170$	1772.31	0.799587
$171$	67.9458	0.0303857
$172$	2541.88	1.12684
$173$	−3038.98	−1.33555	−0.667774	−	0.744364i	$-0.732753\pi$
$173$	−3038.98	−1.33555	−0.667774	+	0.744364i	$0.732753\pi$
$174$	−3591.34	−1.56470
$175$	−1721.37	−0.743563
$176$	−873.469	−0.374092
$177$	−2643.04	−1.12239
$178$	529.396	0.222921
$179$	−3852.21	−1.60853	−0.804266	−	0.594269i	$-0.797442\pi$
$179$	−3852.21	−1.60853	−0.804266	+	0.594269i	$0.797442\pi$
$180$	−79.1182	−0.0327618
$181$	−3947.84	−1.62122	−0.810609	−	0.585587i	$-0.800864\pi$
$181$	−3947.84	−1.62122	−0.810609	+	0.585587i	$0.800864\pi$
$182$	0	0
$183$	2103.66	0.849765
$184$	−1713.49	−0.686523
$185$	−683.637	−0.271686
$186$	5835.73	2.30052
$187$	−882.880	−0.345254
$188$	−769.447	−0.298499
$189$	2902.22	1.11696
$190$	558.997	0.213442
$191$	3284.52	1.24429	0.622145	−	0.782902i	$-0.286261\pi$
$191$	3284.52	1.24429	0.622145	+	0.782902i	$0.286261\pi$
$192$	241.011	0.0905911
$193$	4528.65	1.68901	0.844506	−	0.535545i	$-0.179894\pi$
$193$	4528.65	1.68901	0.844506	+	0.535545i	$0.179894\pi$
$194$	−11.3293	−0.00419277
$195$	0	0
$196$	239.090	0.0871319
$197$	3743.45	1.35386	0.676929	−	0.736048i	$-0.263310\pi$
$197$	3743.45	1.35386	0.676929	+	0.736048i	$0.263310\pi$
$198$	105.507	0.0378689
$199$	−106.802	−0.0380453	−0.0190226	−	0.999819i	$-0.506055\pi$
$199$	−106.802	−0.0380453	−0.0190226	+	0.999819i	$0.506055\pi$
$200$	−1001.95	−0.354244
$201$	−617.332	−0.216633
$202$	−507.389	−0.176731
$203$	−4040.80	−1.39708
$204$	1888.09	0.648004
$205$	1178.57	0.401534
$206$	−1363.47	−0.461153
$207$	398.502	0.133806
$208$	0	0
$209$	−278.466	−0.0921622
$210$	2158.92	0.709428
$211$	−2767.72	−0.903022	−0.451511	−	0.892266i	$-0.649115\pi$
$211$	−2767.72	−0.903022	−0.451511	+	0.892266i	$0.649115\pi$
$212$	−3084.28	−0.999194
$213$	2038.70	0.655818
$214$	−1790.17	−0.571840
$215$	3292.41	1.04437
$216$	1689.28	0.532135
$217$	6566.07	2.05407
$218$	224.122	0.0696304
$219$	4061.43	1.25318
$220$	324.254	0.0993692
$221$	0	0
$222$	−1949.62	−0.589415
$223$	4028.18	1.20963	0.604814	−	0.796367i	$-0.293247\pi$
$223$	4028.18	1.20963	0.604814	+	0.796367i	$0.293247\pi$
$224$	3795.71	1.13219
$225$	233.022	0.0690435
$226$	−1939.02	−0.570715
$227$	665.679	0.194637	0.0973186	−	0.995253i	$-0.468973\pi$
$227$	665.679	0.194637	0.0973186	+	0.995253i	$0.468973\pi$
$228$	595.516	0.172978
$229$	−3770.53	−1.08805	−0.544025	−	0.839069i	$-0.683100\pi$
$229$	−3770.53	−1.08805	−0.544025	+	0.839069i	$0.683100\pi$
$230$	3278.52	0.939909
$231$	−1075.47	−0.306325
$232$	−2352.01	−0.665591
$233$	3203.67	0.900769	0.450384	−	0.892835i	$-0.351287\pi$
$233$	3203.67	0.900769	0.450384	+	0.892835i	$0.351287\pi$
$234$	0	0
$235$	−996.636	−0.276653
$236$	2556.97	0.705273
$237$	−2688.81	−0.736950
$238$	5686.89	1.54885
$239$	5984.88	1.61979	0.809895	−	0.586575i	$-0.199524\pi$
$239$	5984.88	1.61979	0.809895	+	0.586575i	$0.199524\pi$
$240$	2419.50	0.650743
$241$	−555.137	−0.148380	−0.0741898	−	0.997244i	$-0.523637\pi$
$241$	−555.137	−0.148380	−0.0741898	+	0.997244i	$0.523637\pi$
$242$	−432.404	−0.114860
$243$	−750.222	−0.198053
$244$	−2035.15	−0.533965
$245$	309.684	0.0807551
$246$	3361.08	0.871117
$247$	0	0
$248$	3821.89	0.978591
$249$	−6690.35	−1.70274
$250$	4677.29	1.18327
$251$	−3529.14	−0.887480	−0.443740	−	0.896156i	$-0.646349\pi$
$251$	−3529.14	−0.887480	−0.443740	+	0.896156i	$0.646349\pi$
$252$	−253.871	−0.0634617
$253$	−1633.20	−0.405844
$254$	3631.35	0.897051
$255$	2445.57	0.600579
$256$	5239.84	1.27926
$257$	−582.587	−0.141404	−0.0707019	−	0.997497i	$-0.522524\pi$
$257$	−582.587	−0.141404	−0.0707019	+	0.997497i	$0.522524\pi$
$258$	9389.42	2.26574
$259$	−2193.62	−0.526274
$260$	0	0
$261$	547.002	0.129726
$262$	2343.35	0.552566
$263$	−3297.45	−0.773115	−0.386558	−	0.922265i	$-0.626336\pi$
$263$	−3297.45	−0.773115	−0.386558	+	0.922265i	$0.626336\pi$
$264$	−625.998	−0.145938
$265$	−3994.95	−0.926067
$266$	1793.68	0.413450
$267$	730.503	0.167438
$268$	597.228	0.136125
$269$	−5078.74	−1.15114	−0.575569	−	0.817753i	$-0.695219\pi$
$269$	−5078.74	−1.15114	−0.575569	+	0.817753i	$0.695219\pi$
$270$	−3232.20	−0.728539
$271$	6364.65	1.42666	0.713330	−	0.700828i	$-0.247186\pi$
$271$	6364.65	1.42666	0.713330	+	0.700828i	$0.247186\pi$
$272$	6373.29	1.42073
$273$	0	0
$274$	−3573.64	−0.787925
$275$	−955.006	−0.209415
$276$	3492.70	0.761724
$277$	6050.26	1.31236	0.656182	−	0.754602i	$-0.272170\pi$
$277$	6050.26	1.31236	0.656182	+	0.754602i	$0.272170\pi$
$278$	−5149.30	−1.11092
$279$	−888.849	−0.190731
$280$	1413.91	0.301775
$281$	6931.17	1.47145	0.735727	−	0.677278i	$-0.236841\pi$
$281$	6931.17	1.47145	0.735727	+	0.677278i	$0.236841\pi$
$282$	−2842.25	−0.600189
$283$	−2072.74	−0.435376	−0.217688	−	0.976018i	$-0.569852\pi$
$283$	−2072.74	−0.435376	−0.217688	+	0.976018i	$0.569852\pi$
$284$	−1972.31	−0.412095
$285$	771.349	0.160318
$286$	0	0
$287$	3781.72	0.777798
$288$	−513.824	−0.105130
$289$	1528.96	0.311207
$290$	4500.24	0.911252
$291$	−15.6331	−0.00314924
$292$	−3929.17	−0.787457
$293$	−4392.97	−0.875905	−0.437952	−	0.898998i	$-0.644296\pi$
$293$	−4392.97	−0.875905	−0.437952	+	0.898998i	$0.644296\pi$
$294$	883.170	0.175196
$295$	3311.94	0.653657
$296$	−1276.83	−0.250725
$297$	1610.13	0.314577
$298$	−2328.25	−0.452590
$299$	0	0
$300$	2042.34	0.393048
$301$	10564.5	2.02302
$302$	4154.26	0.791558
$303$	−700.136	−0.132745
$304$	2010.18	0.379248
$305$	−2636.06	−0.494886
$306$	−769.834	−0.143819
$307$	614.557	0.114250	0.0571248	−	0.998367i	$-0.481807\pi$
$307$	614.557	0.114250	0.0571248	+	0.998367i	$0.481807\pi$
$308$	1040.45	0.192485
$309$	−1881.42	−0.346377
$310$	−7312.64	−1.33977
$311$	−308.775	−0.0562990	−0.0281495	−	0.999604i	$-0.508961\pi$
$311$	−308.775	−0.0562990	−0.0281495	+	0.999604i	$0.508961\pi$
$312$	0	0
$313$	2349.52	0.424290	0.212145	−	0.977238i	$-0.431955\pi$
$313$	2349.52	0.424290	0.212145	+	0.977238i	$0.431955\pi$
$314$	−11564.1	−2.07834
$315$	−328.829	−0.0588172
$316$	2601.25	0.463075
$317$	−3185.72	−0.564441	−0.282220	−	0.959350i	$-0.591071\pi$
$317$	−3185.72	−0.564441	−0.282220	+	0.959350i	$0.591071\pi$
$318$	−11393.0	−2.00907
$319$	−2241.81	−0.393470
$320$	−302.007	−0.0527584
$321$	−2470.22	−0.429515
$322$	10519.9	1.82066
$323$	2031.83	0.350013
$324$	−3097.65	−0.531147
$325$	0	0
$326$	8956.35	1.52161
$327$	309.261	0.0523002
$328$	2201.22	0.370554
$329$	−3197.96	−0.535894
$330$	1197.76	0.199801
$331$	6733.00	1.11806	0.559032	−	0.829146i	$-0.311173\pi$
$331$	6733.00	1.11806	0.559032	+	0.829146i	$0.311173\pi$
$332$	6472.47	1.06995
$333$	296.950	0.0488672
$334$	−5447.94	−0.892508
$335$	773.567	0.126163
$336$	7763.58	1.26053
$337$	5682.33	0.918505	0.459252	−	0.888306i	$-0.348117\pi$
$337$	5682.33	0.918505	0.459252	+	0.888306i	$0.348117\pi$
$338$	0	0
$339$	−2675.61	−0.428671
$340$	−2365.93	−0.377384
$341$	3642.81	0.578503
$342$	−242.811	−0.0383909
$343$	−5807.03	−0.914141
$344$	6149.25	0.963795
$345$	4523.96	0.705976
$346$	10860.1	1.68740
$347$	−5159.06	−0.798135	−0.399067	−	0.916922i	$-0.630666\pi$
$347$	−5159.06	−0.798135	−0.399067	+	0.916922i	$0.630666\pi$
$348$	4794.23	0.738500
$349$	8194.66	1.25688	0.628438	−	0.777859i	$-0.283694\pi$
$349$	8194.66	1.25688	0.628438	+	0.777859i	$0.283694\pi$
$350$	6151.48	0.939458
$351$	0	0
$352$	2105.83	0.318867
$353$	−5618.16	−0.847096	−0.423548	−	0.905874i	$-0.639215\pi$
$353$	−5618.16	−0.847096	−0.423548	+	0.905874i	$0.639215\pi$
$354$	9445.13	1.41809
$355$	−2554.65	−0.381935
$356$	−706.714	−0.105213
$357$	7847.23	1.16336
$358$	13766.2	2.03231
$359$	1111.92	0.163467	0.0817336	−	0.996654i	$-0.473954\pi$
$359$	1111.92	0.163467	0.0817336	+	0.996654i	$0.473954\pi$
$360$	−191.400	−0.0280214
$361$	−6218.15	−0.906567
$362$	14108.0	2.04834
$363$	−596.666	−0.0862723
$364$	0	0
$365$	−5089.30	−0.729826
$366$	−7517.62	−1.07364
$367$	6062.15	0.862239	0.431119	−	0.902295i	$-0.358119\pi$
$367$	6062.15	0.862239	0.431119	+	0.902295i	$0.358119\pi$
$368$	11789.7	1.67005
$369$	−511.931	−0.0722225
$370$	2443.04	0.343264
$371$	−12818.8	−1.79385
$372$	−7790.37	−1.08578
$373$	6526.78	0.906016	0.453008	−	0.891506i	$-0.350351\pi$
$373$	6526.78	0.906016	0.453008	+	0.891506i	$0.350351\pi$
$374$	3155.05	0.436213
$375$	6454.10	0.888769
$376$	−1861.42	−0.255308
$377$	0	0
$378$	−10371.3	−1.41123
$379$	8138.85	1.10307	0.551536	−	0.834151i	$-0.314042\pi$
$379$	8138.85	1.10307	0.551536	+	0.834151i	$0.314042\pi$
$380$	−746.229	−0.100739
$381$	5010.82	0.673786
$382$	−11737.5	−1.57210
$383$	1349.63	0.180059	0.0900297	−	0.995939i	$-0.471304\pi$
$383$	1349.63	0.180059	0.0900297	+	0.995939i	$0.471304\pi$
$384$	6690.82	0.889165
$385$	1347.66	0.178397
$386$	−16183.5	−2.13399
$387$	−1430.12	−0.187847
$388$	15.1240	0.00197888
$389$	14170.6	1.84698	0.923492	−	0.383617i	$-0.125322\pi$
$389$	14170.6	1.84698	0.923492	+	0.383617i	$0.125322\pi$
$390$	0	0
$391$	11916.7	1.54131
$392$	578.400	0.0745245
$393$	3233.54	0.415039
$394$	−13377.6	−1.71054
$395$	3369.30	0.429184
$396$	−140.846	−0.0178731
$397$	158.202	0.0199998	0.00999992	−	0.999950i	$-0.496817\pi$
$397$	158.202	0.0199998	0.00999992	+	0.999950i	$0.496817\pi$
$398$	381.667	0.0480685
$399$	2475.07	0.310547
$400$	6893.95	0.861744
$401$	−5377.53	−0.669678	−0.334839	−	0.942275i	$-0.608682\pi$
$401$	−5377.53	−0.669678	−0.334839	+	0.942275i	$0.608682\pi$
$402$	2206.09	0.273706
$403$	0	0
$404$	677.336	0.0834127
$405$	−4012.26	−0.492274
$406$	14440.1	1.76515
$407$	−1217.01	−0.148218
$408$	4567.61	0.554241
$409$	−2884.01	−0.348668	−0.174334	−	0.984687i	$-0.555777\pi$
$409$	−2884.01	−0.348668	−0.174334	+	0.984687i	$0.555777\pi$
$410$	−4211.71	−0.507321
$411$	−4931.19	−0.591820
$412$	1820.16	0.217652
$413$	10627.2	1.26618
$414$	−1424.08	−0.169058
$415$	8383.55	0.991644
$416$	0	0
$417$	−7105.42	−0.834422
$418$	995.123	0.116443
$419$	11911.1	1.38877	0.694386	−	0.719603i	$-0.255676\pi$
$419$	11911.1	1.38877	0.694386	+	0.719603i	$0.255676\pi$
$420$	−2882.04	−0.334832
$421$	−8346.54	−0.966236	−0.483118	−	0.875555i	$-0.660496\pi$
$421$	−8346.54	−0.966236	−0.483118	+	0.875555i	$0.660496\pi$
$422$	9890.69	1.14093
$423$	432.907	0.0497604
$424$	−7461.40	−0.854617
$425$	6968.23	0.795315
$426$	−7285.47	−0.828596
$427$	−8458.46	−0.958626
$428$	2389.78	0.269894
$429$	0	0
$430$	−11765.7	−1.31952
$431$	−5146.07	−0.575122	−0.287561	−	0.957762i	$-0.592844\pi$
$431$	−5146.07	−0.575122	−0.287561	+	0.957762i	$0.592844\pi$
$432$	−11623.1	−1.29449
$433$	−11433.8	−1.26899	−0.634497	−	0.772926i	$-0.718793\pi$
$433$	−11433.8	−1.26899	−0.634497	+	0.772926i	$0.718793\pi$
$434$	−23464.5	−2.59523
$435$	6209.79	0.684452
$436$	−299.190	−0.0328637
$437$	3758.61	0.411438
$438$	−14513.9	−1.58333
$439$	13742.9	1.49411	0.747055	−	0.664762i	$-0.231467\pi$
$439$	13742.9	1.49411	0.747055	+	0.664762i	$0.231467\pi$
$440$	784.426	0.0849911
$441$	−134.517	−0.0145251
$442$	0	0
$443$	−11486.8	−1.23196	−0.615978	−	0.787763i	$-0.711239\pi$
$443$	−11486.8	−1.23196	−0.615978	+	0.787763i	$0.711239\pi$
$444$	2602.64	0.278189
$445$	−915.380	−0.0975127
$446$	−14395.1	−1.52831
$447$	−3212.70	−0.339945
$448$	−969.065	−0.102196
$449$	3411.92	0.358616	0.179308	−	0.983793i	$-0.442614\pi$
$449$	3411.92	0.358616	0.179308	+	0.983793i	$0.442614\pi$
$450$	−832.725	−0.0872334
$451$	2098.08	0.219057
$452$	2588.48	0.269363
$453$	5732.37	0.594548
$454$	−2378.86	−0.245915
$455$	0	0
$456$	1440.65	0.147949
$457$	9543.80	0.976893	0.488447	−	0.872594i	$-0.337564\pi$
$457$	9543.80	0.976893	0.488447	+	0.872594i	$0.337564\pi$
$458$	13474.3	1.37470
$459$	−11748.4	−1.19470
$460$	−4376.64	−0.443612
$461$	5200.37	0.525392	0.262696	−	0.964879i	$-0.415388\pi$
$461$	5200.37	0.525392	0.262696	+	0.964879i	$0.415388\pi$
$462$	3843.30	0.387028
$463$	2529.29	0.253879	0.126939	−	0.991910i	$-0.459485\pi$
$463$	2529.29	0.253879	0.126939	+	0.991910i	$0.459485\pi$
$464$	16183.0	1.61914
$465$	−10090.6	−1.00632
$466$	−11448.6	−1.13808
$467$	−17278.0	−1.71206	−0.856028	−	0.516929i	$-0.827075\pi$
$467$	−17278.0	−1.71206	−0.856028	+	0.516929i	$0.827075\pi$
$468$	0	0
$469$	2482.19	0.244385
$470$	3561.57	0.349538
$471$	−15957.0	−1.56106
$472$	6185.74	0.603224
$473$	5861.12	0.569756
$474$	9608.71	0.931102
$475$	2197.82	0.212301
$476$	−7591.68	−0.731017
$477$	1735.28	0.166568
$478$	−21387.5	−2.04653
$479$	−8126.91	−0.775215	−0.387607	−	0.921825i	$-0.626698\pi$
$479$	−8126.91	−0.775215	−0.387607	+	0.921825i	$0.626698\pi$
$480$	−5833.14	−0.554678
$481$	0	0
$482$	1983.83	0.187471
$483$	14516.3	1.36752
$484$	577.236	0.0542107
$485$	19.5896	0.00183405
$486$	2680.99	0.250230
$487$	14243.1	1.32529	0.662644	−	0.748934i	$-0.269434\pi$
$487$	14243.1	1.32529	0.662644	+	0.748934i	$0.269434\pi$
$488$	−4923.39	−0.456703
$489$	12358.7	1.14290
$490$	−1106.68	−0.102030
$491$	6445.00	0.592381	0.296190	−	0.955129i	$-0.404284\pi$
$491$	6445.00	0.592381	0.296190	+	0.955129i	$0.404284\pi$
$492$	−4486.86	−0.411144
$493$	16357.4	1.49432
$494$	0	0
$495$	−182.432	−0.0165651
$496$	−26296.6	−2.38055
$497$	−8197.25	−0.739833
$498$	23908.5	2.15134
$499$	18231.4	1.63557	0.817783	−	0.575526i	$-0.195203\pi$
$499$	18231.4	1.63557	0.817783	+	0.575526i	$0.195203\pi$
$500$	−6243.92	−0.558473
$501$	−7517.50	−0.670373
$502$	12611.7	1.12129
$503$	−13439.0	−1.19128	−0.595641	−	0.803251i	$-0.703102\pi$
$503$	−13439.0	−1.19128	−0.595641	+	0.803251i	$0.703102\pi$
$504$	−614.157	−0.0542792
$505$	877.327	0.0773080
$506$	5836.40	0.512766
$507$	0	0
$508$	−4847.65	−0.423385
$509$	402.288	0.0350316	0.0175158	−	0.999847i	$-0.494424\pi$
$509$	402.288	0.0350316	0.0175158	+	0.999847i	$0.494424\pi$
$510$	−8739.47	−0.758804
$511$	−16330.3	−1.41372
$512$	−7870.22	−0.679331
$513$	−3705.51	−0.318913
$514$	2081.93	0.178657
$515$	2357.58	0.201723
$516$	−12534.4	−1.06937
$517$	−1774.21	−0.150927
$518$	7839.10	0.664924
$519$	14985.6	1.26743
$520$	0	0
$521$	9753.71	0.820188	0.410094	−	0.912043i	$-0.365496\pi$
$521$	9753.71	0.820188	0.410094	+	0.912043i	$0.365496\pi$
$522$	−1954.76	−0.163903
$523$	−1520.00	−0.127084	−0.0635422	−	0.997979i	$-0.520240\pi$
$523$	−1520.00	−0.127084	−0.0635422	+	0.997979i	$0.520240\pi$
$524$	−3128.24	−0.260797
$525$	8488.30	0.705638
$526$	11783.7	0.976796
$527$	−26579.9	−2.19704
$528$	4307.18	0.355012
$529$	9877.23	0.811805
$530$	14276.3	1.17004
$531$	−1438.60	−0.117571
$532$	−2394.47	−0.195138
$533$	0	0
$534$	−2610.52	−0.211551
$535$	3095.39	0.250141
$536$	1444.80	0.116429
$537$	18995.7	1.52649
$538$	18149.3	1.45441
$539$	551.298	0.0440558
$540$	4314.81	0.343851
$541$	14782.7	1.17478	0.587391	−	0.809303i	$-0.300155\pi$
$541$	14782.7	1.17478	0.587391	+	0.809303i	$0.300155\pi$
$542$	−22744.6	−1.80252
$543$	19467.3	1.53853
$544$	−15365.3	−1.21099
$545$	−387.529	−0.0304586
$546$	0	0
$547$	−3639.97	−0.284523	−0.142261	−	0.989829i	$-0.545437\pi$
$547$	−3639.97	−0.284523	−0.142261	+	0.989829i	$0.545437\pi$
$548$	4770.61	0.371880
$549$	1145.02	0.0890132
$550$	3412.80	0.264586
$551$	5159.23	0.398894
$552$	8449.44	0.651507
$553$	10811.2	0.831358
$554$	−21621.2	−1.65811
$555$	3371.10	0.257829
$556$	6874.03	0.524324
$557$	13496.6	1.02670	0.513349	−	0.858180i	$-0.328405\pi$
$557$	13496.6	1.02670	0.513349	+	0.858180i	$0.328405\pi$
$558$	3176.38	0.240980
$559$	0	0
$560$	−9728.40	−0.734107
$561$	4353.59	0.327645
$562$	−24769.1	−1.85912
$563$	−20637.9	−1.54491	−0.772454	−	0.635070i	$-0.780971\pi$
$563$	−20637.9	−1.54491	−0.772454	+	0.635070i	$0.780971\pi$
$564$	3794.24	0.283274
$565$	3352.76	0.249649
$566$	7407.11	0.550078
$567$	−12874.4	−0.953566
$568$	−4771.35	−0.352467
$569$	−22445.2	−1.65369	−0.826845	−	0.562429i	$-0.809867\pi$
$569$	−22445.2	−1.65369	−0.826845	+	0.562429i	$0.809867\pi$
$570$	−2756.48	−0.202555
$571$	17452.2	1.27908	0.639539	−	0.768759i	$-0.279125\pi$
$571$	17452.2	1.27908	0.639539	+	0.768759i	$0.279125\pi$
$572$	0	0
$573$	−16196.4	−1.18083
$574$	−13514.3	−0.982713
$575$	12890.2	0.934887
$576$	131.182	0.00948945
$577$	−11709.3	−0.844827	−0.422414	−	0.906403i	$-0.638817\pi$
$577$	−11709.3	−0.844827	−0.422414	+	0.906403i	$0.638817\pi$
$578$	−5463.87	−0.393196
$579$	−22331.3	−1.60287
$580$	−6007.56	−0.430087
$581$	26900.7	1.92088
$582$	55.8663	0.00397892
$583$	−7111.78	−0.505214
$584$	−9505.34	−0.673516
$585$	0	0
$586$	15698.7	1.10667
$587$	24624.4	1.73145	0.865723	−	0.500524i	$-0.166859\pi$
$587$	24624.4	1.73145	0.865723	+	0.500524i	$0.166859\pi$
$588$	−1178.98	−0.0826878
$589$	−8383.47	−0.586477
$590$	−11835.5	−0.825865
$591$	−18459.4	−1.28481
$592$	8785.27	0.609920
$593$	4505.72	0.312020	0.156010	−	0.987755i	$-0.450137\pi$
$593$	4505.72	0.312020	0.156010	+	0.987755i	$0.450137\pi$
$594$	−5753.95	−0.397453
$595$	−9833.22	−0.677517
$596$	3108.08	0.213611
$597$	526.655	0.0361048
$598$	0	0
$599$	15338.3	1.04625	0.523127	−	0.852255i	$-0.324766\pi$
$599$	15338.3	1.04625	0.523127	+	0.852255i	$0.324766\pi$
$600$	4940.76	0.336176
$601$	−12604.5	−0.855486	−0.427743	−	0.903900i	$-0.640691\pi$
$601$	−12604.5	−0.855486	−0.427743	+	0.903900i	$0.640691\pi$
$602$	−37753.2	−2.55599
$603$	−336.013	−0.0226924
$604$	−5545.70	−0.373595
$605$	747.671	0.0502432
$606$	2502.00	0.167717
$607$	6147.34	0.411059	0.205530	−	0.978651i	$-0.434108\pi$
$607$	6147.34	0.411059	0.205530	+	0.978651i	$0.434108\pi$
$608$	−4846.30	−0.323262
$609$	19925.7	1.32583
$610$	9420.19	0.625266
$611$	0	0
$612$	1027.69	0.0678786
$613$	10721.2	0.706403	0.353202	−	0.935547i	$-0.385093\pi$
$613$	10721.2	0.706403	0.353202	+	0.935547i	$0.385093\pi$
$614$	−2196.17	−0.144349
$615$	−5811.65	−0.381054
$616$	2517.03	0.164633
$617$	17913.2	1.16881	0.584406	−	0.811461i	$-0.301328\pi$
$617$	17913.2	1.16881	0.584406	+	0.811461i	$0.301328\pi$
$618$	6723.44	0.437632
$619$	18738.9	1.21677	0.608384	−	0.793642i	$-0.291818\pi$
$619$	18738.9	1.21677	0.608384	+	0.793642i	$0.291818\pi$
$620$	9761.97	0.632339
$621$	−21732.8	−1.40436
$622$	1103.43	0.0711313
$623$	−2937.23	−0.188888
$624$	0	0
$625$	2764.83	0.176949
$626$	−8396.22	−0.536071
$627$	1373.15	0.0874615
$628$	15437.4	0.980921
$629$	8879.92	0.562903
$630$	1175.10	0.0743129
$631$	22657.9	1.42947	0.714737	−	0.699393i	$-0.246546\pi$
$631$	22657.9	1.42947	0.714737	+	0.699393i	$0.246546\pi$
$632$	6292.87	0.396071
$633$	13648.0	0.856964
$634$	11384.4	0.713145
$635$	−6278.97	−0.392399
$636$	15209.0	0.948231
$637$	0	0
$638$	8011.30	0.497132
$639$	1109.66	0.0686972
$640$	−8384.14	−0.517831
$641$	−6623.42	−0.408127	−0.204063	−	0.978958i	$-0.565415\pi$
$641$	−6623.42	−0.408127	−0.204063	+	0.978958i	$0.565415\pi$
$642$	8827.57	0.542673
$643$	−12633.4	−0.774826	−0.387413	−	0.921906i	$-0.626631\pi$
$643$	−12633.4	−0.774826	−0.387413	+	0.921906i	$0.626631\pi$
$644$	−14043.5	−0.859306
$645$	−16235.3	−0.991105
$646$	−7260.94	−0.442226
$647$	−10406.8	−0.632357	−0.316178	−	0.948700i	$-0.602400\pi$
$647$	−10406.8	−0.632357	−0.316178	+	0.948700i	$0.602400\pi$
$648$	−7493.74	−0.454293
$649$	5895.90	0.356601
$650$	0	0
$651$	−32378.1	−1.94931
$652$	−11956.2	−0.718163
$653$	−14074.5	−0.843457	−0.421728	−	0.906722i	$-0.638576\pi$
$653$	−14074.5	−0.843457	−0.421728	+	0.906722i	$0.638576\pi$
$654$	−1105.17	−0.0660789
$655$	−4051.88	−0.241710
$656$	−15145.5	−0.901420
$657$	2210.63	0.131271
$658$	11428.2	0.677078
$659$	20373.5	1.20431	0.602154	−	0.798380i	$-0.294309\pi$
$659$	20373.5	1.20431	0.602154	+	0.798380i	$0.294309\pi$
$660$	−1598.94	−0.0943009
$661$	−1629.78	−0.0959017	−0.0479508	−	0.998850i	$-0.515269\pi$
$661$	−1629.78	−0.0959017	−0.0479508	+	0.998850i	$0.515269\pi$
$662$	−24061.0	−1.41262
$663$	0	0
$664$	15658.0	0.915134
$665$	−3101.46	−0.180856
$666$	−1061.18	−0.0617415
$667$	30258.9	1.75656
$668$	7272.69	0.421241
$669$	−19863.5	−1.14793
$670$	−2764.41	−0.159401
$671$	−4692.70	−0.269984
$672$	−18717.1	−1.07445
$673$	−19855.4	−1.13725	−0.568625	−	0.822597i	$-0.692524\pi$
$673$	−19855.4	−1.13725	−0.568625	+	0.822597i	$0.692524\pi$
$674$	−20306.3	−1.16049
$675$	−12708.1	−0.724647
$676$	0	0
$677$	−11153.6	−0.633188	−0.316594	−	0.948561i	$-0.602539\pi$
$677$	−11153.6	−0.633188	−0.316594	+	0.948561i	$0.602539\pi$
$678$	9561.55	0.541606
$679$	62.8580	0.00355268
$680$	−5723.59	−0.322779
$681$	−3282.54	−0.184710
$682$	−13017.9	−0.730912
$683$	28225.6	1.58129	0.790647	−	0.612272i	$-0.209744\pi$
$683$	28225.6	1.58129	0.790647	+	0.612272i	$0.209744\pi$
$684$	324.138	0.0181195
$685$	6179.19	0.344664
$686$	20751.9	1.15498
$687$	18592.9	1.03255
$688$	−42310.0	−2.34455
$689$	0	0
$690$	−16166.8	−0.891969
$691$	26964.1	1.48446	0.742231	−	0.670145i	$-0.233768\pi$
$691$	26964.1	1.48446	0.742231	+	0.670145i	$0.233768\pi$
$692$	−14497.6	−0.796411
$693$	−585.380	−0.0320876
$694$	18436.4	1.00841
$695$	8903.67	0.485950
$696$	11598.1	0.631643
$697$	−15308.7	−0.831933
$698$	−29284.3	−1.58801
$699$	−15797.7	−0.854825
$700$	−8211.88	−0.443400
$701$	−2951.14	−0.159005	−0.0795027	−	0.996835i	$-0.525333\pi$
$701$	−2951.14	−0.159005	−0.0795027	+	0.996835i	$0.525333\pi$
$702$	0	0
$703$	2800.78	0.150261
$704$	−537.631	−0.0287823
$705$	4914.54	0.262542
$706$	20077.0	1.07027
$707$	2815.13	0.149751
$708$	−12608.7	−0.669301
$709$	−11882.4	−0.629412	−0.314706	−	0.949189i	$-0.601906\pi$
$709$	−11882.4	−0.629412	−0.314706	+	0.949189i	$0.601906\pi$
$710$	9129.28	0.482558
$711$	−1463.52	−0.0771957
$712$	−1709.66	−0.0899892
$713$	−49169.1	−2.58260
$714$	−28042.8	−1.46985
$715$	0	0
$716$	−18377.1	−0.959197
$717$	−29512.2	−1.53717
$718$	−3973.53	−0.206533
$719$	19756.5	1.02475	0.512374	−	0.858763i	$-0.328766\pi$
$719$	19756.5	1.02475	0.512374	+	0.858763i	$0.328766\pi$
$720$	1316.93	0.0681655
$721$	7564.88	0.390750
$722$	22221.1	1.14541
$723$	2737.45	0.140812
$724$	−18833.3	−0.966761
$725$	17693.7	0.906383
$726$	2132.24	0.109001
$727$	−26914.8	−1.37306	−0.686531	−	0.727101i	$-0.740867\pi$
$727$	−26914.8	−1.37306	−0.686531	+	0.727101i	$0.740867\pi$
$728$	0	0
$729$	21231.3	1.07866
$730$	18187.1	0.922102
$731$	−42765.8	−2.16382
$732$	10035.6	0.506730
$733$	−2109.16	−0.106281	−0.0531403	−	0.998587i	$-0.516923\pi$
$733$	−2109.16	−0.106281	−0.0531403	+	0.998587i	$0.516923\pi$
$734$	−21663.6	−1.08940
$735$	−1527.09	−0.0766362
$736$	−28423.6	−1.42351
$737$	1377.10	0.0688278
$738$	1829.43	0.0912498
$739$	16871.9	0.839840	0.419920	−	0.907561i	$-0.362058\pi$
$739$	16871.9	0.839840	0.419920	+	0.907561i	$0.362058\pi$
$740$	−3261.32	−0.162011
$741$	0	0
$742$	45809.1	2.26645
$743$	−20175.8	−0.996204	−0.498102	−	0.867119i	$-0.665969\pi$
$743$	−20175.8	−0.996204	−0.498102	+	0.867119i	$0.665969\pi$
$744$	−18846.2	−0.928678
$745$	4025.78	0.197977
$746$	−23324.0	−1.14471
$747$	−3641.55	−0.178363
$748$	−4211.82	−0.205881
$749$	9932.35	0.484539
$750$	−23064.3	−1.12292
$751$	37873.6	1.84025	0.920125	−	0.391624i	$-0.128087\pi$
$751$	37873.6	1.84025	0.920125	+	0.391624i	$0.128087\pi$
$752$	12807.5	0.621068
$753$	17402.6	0.842215
$754$	0	0
$755$	−7183.13	−0.346253
$756$	13845.2	0.666063
$757$	−20891.5	−1.00306	−0.501528	−	0.865141i	$-0.667229\pi$
$757$	−20891.5	−1.00306	−0.501528	+	0.865141i	$0.667229\pi$
$758$	−29084.9	−1.39368
$759$	8053.53	0.385144
$760$	−1805.26	−0.0861626
$761$	−21011.1	−1.00086	−0.500429	−	0.865777i	$-0.666824\pi$
$761$	−21011.1	−1.00086	−0.500429	+	0.865777i	$0.666824\pi$
$762$	−17906.6	−0.851298
$763$	−1243.48	−0.0590002
$764$	15668.9	0.741992
$765$	1331.12	0.0629108
$766$	−4823.01	−0.227497
$767$	0	0
$768$	−25838.3	−1.21401
$769$	−17916.7	−0.840171	−0.420086	−	0.907485i	$-0.638000\pi$
$769$	−17916.7	−0.840171	−0.420086	+	0.907485i	$0.638000\pi$
$770$	−4815.97	−0.225397
$771$	2872.81	0.134191
$772$	21604.1	1.00719
$773$	−5403.15	−0.251407	−0.125704	−	0.992068i	$-0.540119\pi$
$773$	−5403.15	−0.251407	−0.125704	+	0.992068i	$0.540119\pi$
$774$	5110.65	0.237337
$775$	−28751.3	−1.33262
$776$	36.5876	0.00169255
$777$	10817.0	0.499432
$778$	−50639.8	−2.33358
$779$	−4828.45	−0.222076
$780$	0	0
$781$	−4547.78	−0.208364
$782$	−42585.4	−1.94738
$783$	−29831.4	−1.36154
$784$	−3979.68	−0.181290
$785$	19995.4	0.909131
$786$	−11555.3	−0.524383
$787$	−2670.61	−0.120962	−0.0604810	−	0.998169i	$-0.519263\pi$
$787$	−2670.61	−0.120962	−0.0604810	+	0.998169i	$0.519263\pi$
$788$	17858.3	0.807330
$789$	16260.1	0.733683
$790$	−12040.5	−0.542255
$791$	10758.2	0.483586
$792$	−340.730	−0.0152870
$793$	0	0
$794$	−565.349	−0.0252689
$795$	19699.6	0.878833
$796$	−509.504	−0.0226871
$797$	3994.89	0.177549	0.0887744	−	0.996052i	$-0.471705\pi$
$797$	3994.89	0.177549	0.0887744	+	0.996052i	$0.471705\pi$
$798$	−8844.87	−0.392362
$799$	12945.5	0.573192
$800$	−16620.5	−0.734530
$801$	397.612	0.0175392
$802$	19217.1	0.846108
$803$	−9059.95	−0.398155
$804$	−2945.01	−0.129182
$805$	−18190.1	−0.796417
$806$	0	0
$807$	25043.9	1.09242
$808$	1638.59	0.0713434
$809$	25404.8	1.10406	0.552031	−	0.833823i	$-0.313853\pi$
$809$	25404.8	1.10406	0.552031	+	0.833823i	$0.313853\pi$
$810$	14338.2	0.621966
$811$	23543.6	1.01939	0.509697	−	0.860354i	$-0.329758\pi$
$811$	23543.6	1.01939	0.509697	+	0.860354i	$0.329758\pi$
$812$	−19276.8	−0.833107
$813$	−31384.9	−1.35389
$814$	4349.08	0.187267
$815$	−15486.4	−0.665603
$816$	−31427.5	−1.34826
$817$	−13488.6	−0.577610
$818$	10306.3	0.440526
$819$	0	0
$820$	5622.39	0.239442
$821$	−7684.07	−0.326646	−0.163323	−	0.986573i	$-0.552221\pi$
$821$	−7684.07	−0.326646	−0.163323	+	0.986573i	$0.552221\pi$
$822$	17622.1	0.747737
$823$	35617.5	1.50856	0.754282	−	0.656550i	$-0.227985\pi$
$823$	35617.5	1.50856	0.754282	+	0.656550i	$0.227985\pi$
$824$	4403.27	0.186159
$825$	4709.25	0.198734
$826$	−37977.3	−1.59976
$827$	8738.50	0.367433	0.183717	−	0.982979i	$-0.441187\pi$
$827$	8738.50	0.367433	0.183717	+	0.982979i	$0.441187\pi$
$828$	1901.07	0.0797909
$829$	26974.7	1.13012	0.565061	−	0.825049i	$-0.308853\pi$
$829$	26974.7	1.13012	0.565061	+	0.825049i	$0.308853\pi$
$830$	−29959.4	−1.25290
$831$	−29834.6	−1.24543
$832$	0	0
$833$	−4022.56	−0.167315
$834$	25391.9	1.05425
$835$	9420.04	0.390412
$836$	−1328.43	−0.0549579
$837$	48474.5	2.00182
$838$	−42565.4	−1.75465
$839$	−30217.5	−1.24341	−0.621706	−	0.783250i	$-0.713560\pi$
$839$	−30217.5	−1.24341	−0.621706	+	0.783250i	$0.713560\pi$
$840$	−6972.15	−0.286384
$841$	17145.7	0.703009
$842$	29827.1	1.22080
$843$	−34178.4	−1.39640
$844$	−13203.5	−0.538488
$845$	0	0
$846$	−1547.03	−0.0628700
$847$	2399.09	0.0973244
$848$	51338.2	2.07896
$849$	10220.9	0.413170
$850$	−24901.6	−1.00484
$851$	16426.6	0.661688
$852$	9725.69	0.391076
$853$	1732.56	0.0695449	0.0347724	−	0.999395i	$-0.488929\pi$
$853$	1732.56	0.0695449	0.0347724	+	0.999395i	$0.488929\pi$
$854$	30227.1	1.21118
$855$	419.844	0.0167934
$856$	5781.29	0.230842
$857$	−24577.4	−0.979636	−0.489818	−	0.871825i	$-0.662937\pi$
$857$	−24577.4	−0.979636	−0.489818	+	0.871825i	$0.662937\pi$
$858$	0	0
$859$	20400.7	0.810316	0.405158	−	0.914247i	$-0.367216\pi$
$859$	20400.7	0.810316	0.405158	+	0.914247i	$0.367216\pi$
$860$	15706.6	0.622778
$861$	−18648.2	−0.738127
$862$	18389.9	0.726640
$863$	25180.4	0.993222	0.496611	−	0.867973i	$-0.334578\pi$
$863$	25180.4	0.993222	0.496611	+	0.867973i	$0.334578\pi$
$864$	28022.0	1.10339
$865$	−18778.2	−0.738124
$866$	40859.8	1.60332
$867$	−7539.49	−0.295334
$868$	31323.7	1.22488
$869$	5998.01	0.234141
$870$	−22191.2	−0.864774
$871$	0	0
$872$	−723.791	−0.0281086
$873$	−8.50908	−0.000329884 0
$874$	−13431.7	−0.519834
$875$	−25950.8	−1.00263
$876$	19375.2	0.747293
$877$	−43112.5	−1.65998	−0.829992	−	0.557776i	$-0.811655\pi$
$877$	−43112.5	−1.65998	−0.829992	+	0.557776i	$0.811655\pi$
$878$	−49111.6	−1.88774
$879$	21662.3	0.831230
$880$	−5397.25	−0.206752
$881$	11116.7	0.425119	0.212560	−	0.977148i	$-0.431820\pi$
$881$	11116.7	0.425119	0.212560	+	0.977148i	$0.431820\pi$
$882$	480.708	0.0183518
$883$	−28160.6	−1.07325	−0.536625	−	0.843821i	$-0.680301\pi$
$883$	−28160.6	−1.07325	−0.536625	+	0.843821i	$0.680301\pi$
$884$	0	0
$885$	−16331.6	−0.620317
$886$	41049.3	1.55652
$887$	32671.4	1.23675	0.618376	−	0.785882i	$-0.287791\pi$
$887$	32671.4	1.23675	0.618376	+	0.785882i	$0.287791\pi$
$888$	6296.23	0.237937
$889$	−20147.7	−0.760102
$890$	3271.19	0.123203
$891$	−7142.61	−0.268559
$892$	19216.6	0.721323
$893$	4083.11	0.153008
$894$	11480.9	0.429506
$895$	−23803.2	−0.888997
$896$	−26902.6	−1.00307
$897$	0	0
$898$	−12192.8	−0.453095
$899$	−67491.6	−2.50386
$900$	1111.64	0.0411719
$901$	51891.3	1.91870
$902$	−7497.66	−0.276768
$903$	−52094.9	−1.91984
$904$	6261.98	0.230388
$905$	−24394.1	−0.896008
$906$	−20485.2	−0.751185
$907$	−17515.0	−0.641208	−0.320604	−	0.947213i	$-0.603886\pi$
$907$	−17515.0	−0.641208	−0.320604	+	0.947213i	$0.603886\pi$
$908$	3175.65	0.116066
$909$	−381.083	−0.0139051
$910$	0	0
$911$	44444.5	1.61637	0.808184	−	0.588930i	$-0.200451\pi$
$911$	44444.5	1.61637	0.808184	+	0.588930i	$0.200451\pi$
$912$	−9912.43	−0.359905
$913$	14924.3	0.540990
$914$	−34105.6	−1.23426
$915$	12998.7	0.469645
$916$	−17987.5	−0.648823
$917$	−13001.5	−0.468208
$918$	41983.8	1.50945
$919$	−37795.7	−1.35665	−0.678327	−	0.734760i	$-0.737295\pi$
$919$	−37795.7	−1.35665	−0.678327	+	0.734760i	$0.737295\pi$
$920$	−10587.8	−0.379424
$921$	−3030.46	−0.108422
$922$	−18584.0	−0.663809
$923$	0	0
$924$	−5130.60	−0.182667
$925$	9605.36	0.341430
$926$	−9038.63	−0.320764
$927$	−1024.06	−0.0362831
$928$	−39015.4	−1.38011
$929$	3116.61	0.110068	0.0550338	−	0.998484i	$-0.482473\pi$
$929$	3116.61	0.110068	0.0550338	+	0.998484i	$0.482473\pi$
$930$	36059.6	1.27144
$931$	−1268.74	−0.0446631
$932$	15283.2	0.537144
$933$	1522.61	0.0534275
$934$	61744.5	2.16311
$935$	−5455.40	−0.190814
$936$	0	0
$937$	7975.52	0.278067	0.139034	−	0.990288i	$-0.455600\pi$
$937$	7975.52	0.278067	0.139034	+	0.990288i	$0.455600\pi$
$938$	−8870.31	−0.308770
$939$	−11585.8	−0.402649
$940$	−4754.49	−0.164973
$941$	56232.0	1.94805	0.974023	−	0.226447i	$-0.0727110\pi$
$941$	56232.0	1.94805	0.974023	+	0.226447i	$0.0727110\pi$
$942$	57023.8	1.97233
$943$	−28318.9	−0.977931
$944$	−42561.0	−1.46742
$945$	17933.1	0.617316
$946$	−20945.2	−0.719861
$947$	2340.85	0.0803247	0.0401624	−	0.999193i	$-0.487212\pi$
$947$	2340.85	0.0803247	0.0401624	+	0.999193i	$0.487212\pi$
$948$	−12827.1	−0.439456
$949$	0	0
$950$	−7854.12	−0.268233
$951$	15709.2	0.535652
$952$	−18365.6	−0.625244
$953$	−313.425	−0.0106536	−0.00532678	−	0.999986i	$-0.501696\pi$
$953$	−313.425	−0.0106536	−0.00532678	+	0.999986i	$0.501696\pi$
$954$	−6201.17	−0.210451
$955$	20295.4	0.687688
$956$	28551.1	0.965910
$957$	11054.6	0.373402
$958$	29042.2	0.979449
$959$	19827.5	0.667636
$960$	1489.23	0.0500675
$961$	79879.2	2.68132
$962$	0	0
$963$	−1344.54	−0.0449919
$964$	−2648.30	−0.0884814
$965$	27983.0	0.933476
$966$	−51875.2	−1.72780
$967$	40979.4	1.36278	0.681391	−	0.731920i	$-0.261375\pi$
$967$	40979.4	1.36278	0.681391	+	0.731920i	$0.261375\pi$
$968$	1396.43	0.0463667
$969$	−10019.2	−0.332161
$970$	−70.0050	−0.00231724
$971$	50792.6	1.67869	0.839347	−	0.543596i	$-0.182938\pi$
$971$	50792.6	1.67869	0.839347	+	0.543596i	$0.182938\pi$
$972$	−3578.97	−0.118102
$973$	28569.7	0.941317
$974$	−50898.9	−1.67444
$975$	0	0
$976$	33875.4	1.11099
$977$	22336.9	0.731444	0.365722	−	0.930724i	$-0.380822\pi$
$977$	22336.9	0.731444	0.365722	+	0.930724i	$0.380822\pi$
$978$	−44164.9	−1.44401
$979$	−1629.55	−0.0531979
$980$	1477.36	0.0481557
$981$	168.330	0.00547847
$982$	−23031.8	−0.748446
$983$	−30931.5	−1.00362	−0.501811	−	0.864977i	$-0.667333\pi$
$983$	−30931.5	−1.00362	−0.501811	+	0.864977i	$0.667333\pi$
$984$	−10854.5	−0.351654
$985$	23131.2	0.748244
$986$	−58454.6	−1.88801
$987$	15769.5	0.508561
$988$	0	0
$989$	−79110.8	−2.54356
$990$	651.938	0.0209292
$991$	−22371.6	−0.717112	−0.358556	−	0.933508i	$-0.616731\pi$
$991$	−22371.6	−0.717112	−0.358556	+	0.933508i	$0.616731\pi$
$992$	63398.0	2.02912
$993$	−33201.3	−1.06104
$994$	29293.6	0.934745
$995$	−659.942	−0.0210267
$996$	−31916.6	−1.01538
$997$	−23159.1	−0.735663	−0.367831	−	0.929893i	$-0.619900\pi$
$997$	−23159.1	−0.735663	−0.367831	+	0.929893i	$0.619900\pi$
$998$	−65151.4	−2.06646
$999$	−16194.5	−0.512886

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.q.1.12	yes	51
13.12	even	2		1859.4.a.p.1.40	✓	51

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.p.1.40	✓	51	13.12	even	2
1859.4.a.q.1.12	yes	51	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:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-3.57359 q^{2} -4.93113 q^{3} +4.77054 q^{4} +6.17910 q^{5} +17.6218 q^{6} +19.8272 q^{7} +11.5408 q^{8} -2.68401 q^{9} +O(q^{10})\)	\(q-3.57359 q^{2} -4.93113 q^{3} +4.77054 q^{4} +6.17910 q^{5} +17.6218 q^{6} +19.8272 q^{7} +11.5408 q^{8} -2.68401 q^{9} -22.0816 q^{10} +11.0000 q^{11} -23.5241 q^{12} -70.8543 q^{14} -30.4699 q^{15} -79.4063 q^{16} -80.2618 q^{17} +9.59153 q^{18} -25.3151 q^{19} +29.4777 q^{20} -97.7704 q^{21} -39.3095 q^{22} -148.473 q^{23} -56.9089 q^{24} -86.8187 q^{25} +146.376 q^{27} +94.5865 q^{28} -203.801 q^{29} +108.887 q^{30} +331.165 q^{31} +191.439 q^{32} -54.2424 q^{33} +286.823 q^{34} +122.514 q^{35} -12.8042 q^{36} -110.637 q^{37} +90.4657 q^{38} +71.3115 q^{40} +190.734 q^{41} +349.391 q^{42} +532.829 q^{43} +52.4760 q^{44} -16.5847 q^{45} +530.582 q^{46} -161.291 q^{47} +391.562 q^{48} +50.1180 q^{49} +310.254 q^{50} +395.781 q^{51} -646.526 q^{53} -523.086 q^{54} +67.9701 q^{55} +228.821 q^{56} +124.832 q^{57} +728.300 q^{58} +535.991 q^{59} -145.358 q^{60} -426.609 q^{61} -1183.45 q^{62} -53.2163 q^{63} -48.8755 q^{64} +193.840 q^{66} +125.191 q^{67} -382.892 q^{68} +732.139 q^{69} -437.816 q^{70} -413.434 q^{71} -30.9755 q^{72} -823.632 q^{73} +395.371 q^{74} +428.114 q^{75} -120.767 q^{76} +218.099 q^{77} +545.273 q^{79} -490.659 q^{80} -649.328 q^{81} -681.605 q^{82} +1356.76 q^{83} -466.418 q^{84} -495.946 q^{85} -1904.11 q^{86} +1004.97 q^{87} +126.948 q^{88} -148.141 q^{89} +59.2671 q^{90} -708.297 q^{92} -1633.02 q^{93} +576.389 q^{94} -156.424 q^{95} -944.011 q^{96} +3.17029 q^{97} -179.101 q^{98} -29.5241 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9}+O(q^{10}) \) 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9	\( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9} + 212 q^{10} + 561 q^{11} + 209 q^{12} + 280 q^{14} + 284 q^{15} + 1246 q^{16} + 164 q^{17} - 189 q^{18} + 26 q^{19} + 438 q^{20} + 134 q^{21} + 373 q^{23} - 354 q^{24} + 2048 q^{25} + 1470 q^{27} - 1245 q^{28} + 898 q^{29} + 427 q^{30} + 767 q^{31} + 1127 q^{32} + 231 q^{33} + 206 q^{34} + 54 q^{35} + 3415 q^{36} + 395 q^{37} + 1577 q^{38} + 3253 q^{40} - 354 q^{41} + 942 q^{42} + 484 q^{43} + 2574 q^{44} + 1452 q^{45} - 2117 q^{46} + 1925 q^{47} + 1780 q^{48} + 4535 q^{49} - 1093 q^{50} + 230 q^{51} + 1387 q^{53} - 5271 q^{54} + 451 q^{55} + 2568 q^{56} - 5738 q^{57} + 3695 q^{58} + 1145 q^{59} - 1590 q^{60} + 5382 q^{61} - 395 q^{62} + 710 q^{63} + 9839 q^{64} - 803 q^{66} - 210 q^{67} + 1742 q^{68} + 7028 q^{69} - 6747 q^{70} + 3693 q^{71} - 12481 q^{72} + 968 q^{73} + 1735 q^{74} - 727 q^{75} - 2801 q^{76} + 44 q^{77} + 4234 q^{79} + 2390 q^{80} + 7743 q^{81} + 4770 q^{82} - 2798 q^{83} + 14821 q^{84} - 1802 q^{85} + 6558 q^{86} + 1896 q^{87} - 231 q^{88} + 3927 q^{89} + 1927 q^{90} + 1984 q^{92} - 1332 q^{93} + 7590 q^{94} + 4944 q^{95} - 7280 q^{96} + 3913 q^{97} - 15201 q^{98} + 6534 q^{99}+O(q^{100}) \) 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9 + 212 * q^10 + 561 * q^11 + 209 * q^12 + 280 * q^14 + 284 * q^15 + 1246 * q^16 + 164 * q^17 - 189 * q^18 + 26 * q^19 + 438 * q^20 + 134 * q^21 + 373 * q^23 - 354 * q^24 + 2048 * q^25 + 1470 * q^27 - 1245 * q^28 + 898 * q^29 + 427 * q^30 + 767 * q^31 + 1127 * q^32 + 231 * q^33 + 206 * q^34 + 54 * q^35 + 3415 * q^36 + 395 * q^37 + 1577 * q^38 + 3253 * q^40 - 354 * q^41 + 942 * q^42 + 484 * q^43 + 2574 * q^44 + 1452 * q^45 - 2117 * q^46 + 1925 * q^47 + 1780 * q^48 + 4535 * q^49 - 1093 * q^50 + 230 * q^51 + 1387 * q^53 - 5271 * q^54 + 451 * q^55 + 2568 * q^56 - 5738 * q^57 + 3695 * q^58 + 1145 * q^59 - 1590 * q^60 + 5382 * q^61 - 395 * q^62 + 710 * q^63 + 9839 * q^64 - 803 * q^66 - 210 * q^67 + 1742 * q^68 + 7028 * q^69 - 6747 * q^70 + 3693 * q^71 - 12481 * q^72 + 968 * q^73 + 1735 * q^74 - 727 * q^75 - 2801 * q^76 + 44 * q^77 + 4234 * q^79 + 2390 * q^80 + 7743 * q^81 + 4770 * q^82 - 2798 * q^83 + 14821 * q^84 - 1802 * q^85 + 6558 * q^86 + 1896 * q^87 - 231 * q^88 + 3927 * q^89 + 1927 * q^90 + 1984 * q^92 - 1332 * q^93 + 7590 * q^94 + 4944 * q^95 - 7280 * q^96 + 3913 * q^97 - 15201 * q^98 + 6534 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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