LMFDB - Embedded newform 1859.4.a.o.1.15

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:	$1$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q-1.63650 q^{2} -2.06438 q^{3} -5.32187 q^{4} -14.3735 q^{5} +3.37836 q^{6} -27.7797 q^{7} +21.8012 q^{8} -22.7383 q^{9} +O(q^{10})$	\(q-1.63650 q^{2} -2.06438 q^{3} -5.32187 q^{4} -14.3735 q^{5} +3.37836 q^{6} -27.7797 q^{7} +21.8012 q^{8} -22.7383 q^{9} +23.5223 q^{10} -11.0000 q^{11} +10.9863 q^{12} +45.4616 q^{14} +29.6724 q^{15} +6.89718 q^{16} -44.5391 q^{17} +37.2113 q^{18} -53.2551 q^{19} +76.4940 q^{20} +57.3479 q^{21} +18.0015 q^{22} -100.658 q^{23} -45.0060 q^{24} +81.5982 q^{25} +102.679 q^{27} +147.840 q^{28} -269.052 q^{29} -48.5589 q^{30} +124.206 q^{31} -185.697 q^{32} +22.7082 q^{33} +72.8883 q^{34} +399.293 q^{35} +121.010 q^{36} -202.566 q^{37} +87.1520 q^{38} -313.361 q^{40} +360.709 q^{41} -93.8499 q^{42} -174.690 q^{43} +58.5405 q^{44} +326.830 q^{45} +164.727 q^{46} +342.031 q^{47} -14.2384 q^{48} +428.714 q^{49} -133.536 q^{50} +91.9456 q^{51} +594.854 q^{53} -168.034 q^{54} +158.109 q^{55} -605.633 q^{56} +109.939 q^{57} +440.304 q^{58} +648.751 q^{59} -157.912 q^{60} +217.807 q^{61} -203.262 q^{62} +631.665 q^{63} +248.716 q^{64} -37.1619 q^{66} +730.955 q^{67} +237.031 q^{68} +207.796 q^{69} -653.443 q^{70} -1013.98 q^{71} -495.724 q^{72} -233.315 q^{73} +331.499 q^{74} -168.450 q^{75} +283.417 q^{76} +305.577 q^{77} +183.229 q^{79} -99.1368 q^{80} +401.967 q^{81} -590.300 q^{82} -547.870 q^{83} -305.198 q^{84} +640.184 q^{85} +285.880 q^{86} +555.426 q^{87} -239.814 q^{88} +1169.47 q^{89} -534.858 q^{90} +535.688 q^{92} -256.407 q^{93} -559.735 q^{94} +765.464 q^{95} +383.349 q^{96} +1747.75 q^{97} -701.590 q^{98} +250.122 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q - 23 q^{3} + 114 q^{4} + 23 q^{5} + 77 q^{6} - 4 q^{7} - 21 q^{8} + 260 q^{9}+O(q^{10}) $ 39 * q - 23 * q^3 + 114 * q^4 + 23 * q^5 + 77 * q^6 - 4 * q^7 - 21 * q^8 + 260 * q^9	\( 39 q - 23 q^{3} + 114 q^{4} + 23 q^{5} + 77 q^{6} - 4 q^{7} - 21 q^{8} + 260 q^{9} - 158 q^{10} - 429 q^{11} - 351 q^{12} - 176 q^{14} + 30 q^{15} + 230 q^{16} - 244 q^{17} + 21 q^{18} - 70 q^{19} + 366 q^{20} - 142 q^{21} - 47 q^{23} + 846 q^{24} + 322 q^{25} - 416 q^{27} + 1131 q^{28} - 838 q^{29} - 293 q^{30} + 507 q^{31} - 1433 q^{32} + 253 q^{33} + 166 q^{34} - 498 q^{35} + 815 q^{36} + 89 q^{37} + 81 q^{38} - 2917 q^{40} + 618 q^{41} - 318 q^{42} - 1064 q^{43} - 1254 q^{44} + 238 q^{45} - 1331 q^{46} + 1499 q^{47} - 1460 q^{48} - 413 q^{49} - 2459 q^{50} - 2350 q^{51} - 2745 q^{53} - 845 q^{54} - 253 q^{55} - 2904 q^{56} + 1450 q^{57} - 2509 q^{58} + 2285 q^{59} - 3566 q^{60} - 6218 q^{61} - 911 q^{62} - 1930 q^{63} + 67 q^{64} - 847 q^{66} + 546 q^{67} - 170 q^{68} - 5254 q^{69} - 2195 q^{70} - 263 q^{71} - 2393 q^{72} - 1148 q^{73} + 775 q^{74} - 5385 q^{75} - 7247 q^{76} + 44 q^{77} - 3666 q^{79} + 5594 q^{80} - 1901 q^{81} - 4414 q^{82} + 2722 q^{83} - 9971 q^{84} + 1858 q^{85} + 2478 q^{86} - 2284 q^{87} + 231 q^{88} + 13 q^{89} - 6771 q^{90} - 2232 q^{92} - 1082 q^{93} - 7330 q^{94} - 2352 q^{95} + 5770 q^{96} - 1197 q^{97} + 6813 q^{98} - 2860 q^{99}+O(q^{100}) \) 39 * q - 23 * q^3 + 114 * q^4 + 23 * q^5 + 77 * q^6 - 4 * q^7 - 21 * q^8 + 260 * q^9 - 158 * q^10 - 429 * q^11 - 351 * q^12 - 176 * q^14 + 30 * q^15 + 230 * q^16 - 244 * q^17 + 21 * q^18 - 70 * q^19 + 366 * q^20 - 142 * q^21 - 47 * q^23 + 846 * q^24 + 322 * q^25 - 416 * q^27 + 1131 * q^28 - 838 * q^29 - 293 * q^30 + 507 * q^31 - 1433 * q^32 + 253 * q^33 + 166 * q^34 - 498 * q^35 + 815 * q^36 + 89 * q^37 + 81 * q^38 - 2917 * q^40 + 618 * q^41 - 318 * q^42 - 1064 * q^43 - 1254 * q^44 + 238 * q^45 - 1331 * q^46 + 1499 * q^47 - 1460 * q^48 - 413 * q^49 - 2459 * q^50 - 2350 * q^51 - 2745 * q^53 - 845 * q^54 - 253 * q^55 - 2904 * q^56 + 1450 * q^57 - 2509 * q^58 + 2285 * q^59 - 3566 * q^60 - 6218 * q^61 - 911 * q^62 - 1930 * q^63 + 67 * q^64 - 847 * q^66 + 546 * q^67 - 170 * q^68 - 5254 * q^69 - 2195 * q^70 - 263 * q^71 - 2393 * q^72 - 1148 * q^73 + 775 * q^74 - 5385 * q^75 - 7247 * q^76 + 44 * q^77 - 3666 * q^79 + 5594 * q^80 - 1901 * q^81 - 4414 * q^82 + 2722 * q^83 - 9971 * q^84 + 1858 * q^85 + 2478 * q^86 - 2284 * q^87 + 231 * q^88 + 13 * q^89 - 6771 * q^90 - 2232 * q^92 - 1082 * q^93 - 7330 * q^94 - 2352 * q^95 + 5770 * q^96 - 1197 * q^97 + 6813 * q^98 - 2860 * 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 $

$2$	−1.63650	−0.578590	−0.289295	−	0.957240i	$-0.593421\pi$
$2$	−1.63650	−0.578590	−0.289295	+	0.957240i	$0.593421\pi$
$3$	−2.06438	−0.397290	−0.198645	−	0.980072i	$-0.563654\pi$
$3$	−2.06438	−0.397290	−0.198645	+	0.980072i	$0.563654\pi$
$4$	−5.32187	−0.665233
$5$	−14.3735	−1.28561	−0.642804	−	0.766031i	$-0.722229\pi$
$5$	−14.3735	−1.28561	−0.642804	+	0.766031i	$0.722229\pi$
$6$	3.37836	0.229868
$7$	−27.7797	−1.49996	−0.749982	−	0.661458i	$-0.769938\pi$
$7$	−27.7797	−1.49996	−0.749982	+	0.661458i	$0.769938\pi$
$8$	21.8012	0.963488
$9$	−22.7383	−0.842161
$10$	23.5223	0.743840
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	10.9863	0.264290
$13$	0	0
$13$	0	0
$14$	45.4616	0.867865
$15$	29.6724	0.510759
$16$	6.89718	0.107768
$17$	−44.5391	−0.635431	−0.317715	−	0.948186i	$-0.602916\pi$
$17$	−44.5391	−0.635431	−0.317715	+	0.948186i	$0.602916\pi$
$18$	37.2113	0.487266
$19$	−53.2551	−0.643030	−0.321515	−	0.946905i	$-0.604192\pi$
$19$	−53.2551	−0.643030	−0.321515	+	0.946905i	$0.604192\pi$
$20$	76.4940	0.855229
$21$	57.3479	0.595921
$22$	18.0015	0.174452
$23$	−100.658	−0.912550	−0.456275	−	0.889839i	$-0.650817\pi$
$23$	−100.658	−0.912550	−0.456275	+	0.889839i	$0.650817\pi$
$24$	−45.0060	−0.382784
$25$	81.5982	0.652786
$26$	0	0
$27$	102.679	0.731872
$28$	147.840	0.997826
$29$	−269.052	−1.72282	−0.861410	−	0.507910i	$-0.830418\pi$
$29$	−269.052	−1.72282	−0.861410	+	0.507910i	$0.830418\pi$
$30$	−48.5589	−0.295520
$31$	124.206	0.719612	0.359806	−	0.933027i	$-0.382843\pi$
$31$	124.206	0.719612	0.359806	+	0.933027i	$0.382843\pi$
$32$	−185.697	−1.02584
$33$	22.7082	0.119787
$34$	72.8883	0.367654
$35$	399.293	1.92837
$36$	121.010	0.560233
$37$	−202.566	−0.900044	−0.450022	−	0.893017i	$-0.648584\pi$
$37$	−202.566	−0.900044	−0.450022	+	0.893017i	$0.648584\pi$
$38$	87.1520	0.372051
$39$	0	0
$40$	−313.361	−1.23867
$41$	360.709	1.37398	0.686990	−	0.726666i	$-0.258931\pi$
$41$	360.709	1.37398	0.686990	+	0.726666i	$0.258931\pi$
$42$	−93.8499	−0.344794
$43$	−174.690	−0.619533	−0.309766	−	0.950813i	$-0.600251\pi$
$43$	−174.690	−0.619533	−0.309766	+	0.950813i	$0.600251\pi$
$44$	58.5405	0.200575
$45$	326.830	1.08269
$46$	164.727	0.527992
$47$	342.031	1.06150	0.530749	−	0.847529i	$-0.321911\pi$
$47$	342.031	1.06150	0.530749	+	0.847529i	$0.321911\pi$
$48$	−14.2384	−0.0428153
$49$	428.714	1.24989
$50$	−133.536	−0.377695
$51$	91.9456	0.252450
$52$	0	0
$53$	594.854	1.54169	0.770844	−	0.637023i	$-0.219835\pi$
$53$	594.854	1.54169	0.770844	+	0.637023i	$0.219835\pi$
$54$	−168.034	−0.423454
$55$	158.109	0.387625
$56$	−605.633	−1.44520
$57$	109.939	0.255469
$58$	440.304	0.996807
$59$	648.751	1.43153	0.715765	−	0.698341i	$-0.246078\pi$
$59$	648.751	1.43153	0.715765	+	0.698341i	$0.246078\pi$
$60$	−157.912	−0.339774
$61$	217.807	0.457169	0.228584	−	0.973524i	$-0.426590\pi$
$61$	217.807	0.457169	0.228584	+	0.973524i	$0.426590\pi$
$62$	−203.262	−0.416361
$63$	631.665	1.26321
$64$	248.716	0.485774
$65$	0	0
$66$	−37.1619	−0.0693078
$67$	730.955	1.33284	0.666420	−	0.745576i	$-0.267826\pi$
$67$	730.955	1.33284	0.666420	+	0.745576i	$0.267826\pi$
$68$	237.031	0.422710
$69$	207.796	0.362547
$70$	−653.443	−1.11573
$71$	−1013.98	−1.69489	−0.847443	−	0.530887i	$-0.821859\pi$
$71$	−1013.98	−1.69489	−0.847443	+	0.530887i	$0.821859\pi$
$72$	−495.724	−0.811412
$73$	−233.315	−0.374075	−0.187038	−	0.982353i	$-0.559889\pi$
$73$	−233.315	−0.374075	−0.187038	+	0.982353i	$0.559889\pi$
$74$	331.499	0.520757
$75$	−168.450	−0.259345
$76$	283.417	0.427765
$77$	305.577	0.452256
$78$	0	0
$79$	183.229	0.260948	0.130474	−	0.991452i	$-0.458350\pi$
$79$	183.229	0.260948	0.130474	+	0.991452i	$0.458350\pi$
$80$	−99.1368	−0.138548
$81$	401.967	0.551396
$82$	−590.300	−0.794972
$83$	−547.870	−0.724536	−0.362268	−	0.932074i	$-0.617998\pi$
$83$	−547.870	−0.724536	−0.362268	+	0.932074i	$0.617998\pi$
$84$	−305.198	−0.396426
$85$	640.184	0.816915
$86$	285.880	0.358456
$87$	555.426	0.684459
$88$	−239.814	−0.290503
$89$	1169.47	1.39285	0.696423	−	0.717632i	$-0.254774\pi$
$89$	1169.47	1.39285	0.696423	+	0.717632i	$0.254774\pi$
$90$	−534.858	−0.626433
$91$	0	0
$92$	535.688	0.607058
$93$	−256.407	−0.285895
$94$	−559.735	−0.614173
$95$	765.464	0.826683
$96$	383.349	0.407556
$97$	1747.75	1.82945	0.914727	−	0.404071i	$-0.132405\pi$
$97$	1747.75	1.82945	0.914727	+	0.404071i	$0.132405\pi$
$98$	−701.590	−0.723177
$99$	250.122	0.253921
$100$	−434.255	−0.434255
$101$	−655.909	−0.646192	−0.323096	−	0.946366i	$-0.604724\pi$
$101$	−655.909	−0.646192	−0.323096	+	0.946366i	$0.604724\pi$
$102$	−150.469	−0.146065
$103$	−470.017	−0.449632	−0.224816	−	0.974401i	$-0.572178\pi$
$103$	−470.017	−0.449632	−0.224816	+	0.974401i	$0.572178\pi$
$104$	0	0
$105$	−824.291	−0.766120
$106$	−973.479	−0.892006
$107$	1144.75	1.03428	0.517138	−	0.855902i	$-0.326997\pi$
$107$	1144.75	1.03428	0.517138	+	0.855902i	$0.326997\pi$
$108$	−546.443	−0.486865
$109$	−1685.58	−1.48118	−0.740592	−	0.671955i	$-0.765455\pi$
$109$	−1685.58	−1.48118	−0.740592	+	0.671955i	$0.765455\pi$
$110$	−258.745	−0.224276
$111$	418.173	0.357578
$112$	−191.602	−0.161649
$113$	−621.707	−0.517569	−0.258785	−	0.965935i	$-0.583322\pi$
$113$	−621.707	−0.517569	−0.258785	+	0.965935i	$0.583322\pi$
$114$	−179.915	−0.147812
$115$	1446.81	1.17318
$116$	1431.86	1.14608
$117$	0	0
$118$	−1061.68	−0.828269
$119$	1237.29	0.953124
$120$	646.895	0.492110
$121$	121.000	0.0909091
$122$	−356.441	−0.264514
$123$	−744.639	−0.545869
$124$	−661.005	−0.478710
$125$	623.837	0.446381
$126$	−1033.72	−0.730882
$127$	−2436.32	−1.70227	−0.851134	−	0.524948i	$-0.824085\pi$
$127$	−2436.32	−1.70227	−0.851134	+	0.524948i	$0.824085\pi$
$128$	1078.55	0.744778
$129$	360.625	0.246134
$130$	0	0
$131$	−577.749	−0.385329	−0.192665	−	0.981265i	$-0.561713\pi$
$131$	−577.749	−0.385329	−0.192665	+	0.981265i	$0.561713\pi$
$132$	−120.850	−0.0796865
$133$	1479.41	0.964522
$134$	−1196.21	−0.771169
$135$	−1475.86	−0.940900
$136$	−971.008	−0.612230
$137$	−1870.99	−1.16678	−0.583391	−	0.812191i	$-0.698275\pi$
$137$	−1870.99	−1.16678	−0.583391	+	0.812191i	$0.698275\pi$
$138$	−340.059	−0.209766
$139$	−1541.16	−0.940426	−0.470213	−	0.882553i	$-0.655823\pi$
$139$	−1541.16	−0.940426	−0.470213	+	0.882553i	$0.655823\pi$
$140$	−2124.98	−1.28281
$141$	−706.082	−0.421722
$142$	1659.37	0.980644
$143$	0	0
$144$	−156.830	−0.0907583
$145$	3867.23	2.21487
$146$	381.821	0.216436
$147$	−885.027	−0.496570
$148$	1078.03	0.598739
$149$	−1199.38	−0.659446	−0.329723	−	0.944078i	$-0.606955\pi$
$149$	−1199.38	−0.659446	−0.329723	+	0.944078i	$0.606955\pi$
$150$	275.668	0.150055
$151$	968.971	0.522210	0.261105	−	0.965310i	$-0.415913\pi$
$151$	968.971	0.522210	0.261105	+	0.965310i	$0.415913\pi$
$152$	−1161.03	−0.619551
$153$	1012.75	0.535135
$154$	−500.077	−0.261671
$155$	−1785.27	−0.925138
$156$	0	0
$157$	637.219	0.323921	0.161961	−	0.986797i	$-0.448218\pi$
$157$	637.219	0.323921	0.161961	+	0.986797i	$0.448218\pi$
$158$	−299.854	−0.150982
$159$	−1228.00	−0.612497
$160$	2669.12	1.31883
$161$	2796.25	1.36879
$162$	−657.820	−0.319032
$163$	496.865	0.238758	0.119379	−	0.992849i	$-0.461910\pi$
$163$	496.865	0.238758	0.119379	+	0.992849i	$0.461910\pi$
$164$	−1919.64	−0.914018
$165$	−326.396	−0.154000
$166$	896.589	0.419210
$167$	−833.281	−0.386115	−0.193057	−	0.981187i	$-0.561840\pi$
$167$	−833.281	−0.386115	−0.193057	+	0.981187i	$0.561840\pi$
$168$	1250.26	0.574162
$169$	0	0
$170$	−1047.66	−0.472659
$171$	1210.93	0.541534
$172$	929.674	0.412134
$173$	−2056.79	−0.903902	−0.451951	−	0.892043i	$-0.649272\pi$
$173$	−2056.79	−0.903902	−0.451951	+	0.892043i	$0.649272\pi$
$174$	−908.955	−0.396021
$175$	−2266.78	−0.979155
$176$	−75.8690	−0.0324934
$177$	−1339.27	−0.568732
$178$	−1913.83	−0.805887
$179$	−102.937	−0.0429825	−0.0214912	−	0.999769i	$-0.506841\pi$
$179$	−102.937	−0.0429825	−0.0214912	+	0.999769i	$0.506841\pi$
$180$	−1739.35	−0.720240
$181$	−1999.85	−0.821258	−0.410629	−	0.911802i	$-0.634691\pi$
$181$	−1999.85	−0.821258	−0.410629	+	0.911802i	$0.634691\pi$
$182$	0	0
$183$	−449.636	−0.181629
$184$	−2194.47	−0.879230
$185$	2911.59	1.15710
$186$	419.611	0.165416
$187$	489.930	0.191590
$188$	−1820.25	−0.706144
$189$	−2852.39	−1.09778
$190$	−1252.68	−0.478311
$191$	1947.71	0.737862	0.368931	−	0.929457i	$-0.379724\pi$
$191$	1947.71	0.737862	0.368931	+	0.929457i	$0.379724\pi$
$192$	−513.444	−0.192993
$193$	3355.80	1.25159	0.625793	−	0.779989i	$-0.284776\pi$
$193$	3355.80	1.25159	0.625793	+	0.779989i	$0.284776\pi$
$194$	−2860.19	−1.05850
$195$	0	0
$196$	−2281.56	−0.831471
$197$	−1386.47	−0.501431	−0.250716	−	0.968061i	$-0.580666\pi$
$197$	−1386.47	−0.501431	−0.250716	+	0.968061i	$0.580666\pi$
$198$	−409.324	−0.146916
$199$	−595.907	−0.212275	−0.106138	−	0.994351i	$-0.533848\pi$
$199$	−595.907	−0.212275	−0.106138	+	0.994351i	$0.533848\pi$
$200$	1778.94	0.628951
$201$	−1508.97	−0.529524
$202$	1073.40	0.373881
$203$	7474.20	2.58417
$204$	−489.322	−0.167938
$205$	−5184.65	−1.76640
$206$	769.183	0.260153
$207$	2288.80	0.768514
$208$	0	0
$209$	585.806	0.193881
$210$	1348.95	0.443270
$211$	−1892.57	−0.617486	−0.308743	−	0.951145i	$-0.599908\pi$
$211$	−1892.57	−0.617486	−0.308743	+	0.951145i	$0.599908\pi$
$212$	−3165.73	−1.02558
$213$	2093.23	0.673361
$214$	−1873.39	−0.598422
$215$	2510.90	0.796476
$216$	2238.52	0.705150
$217$	−3450.40	−1.07939
$218$	2758.45	0.856999
$219$	481.651	0.148616
$220$	−841.434	−0.257861
$221$	0	0
$222$	−684.340	−0.206891
$223$	4611.48	1.38479	0.692394	−	0.721520i	$-0.256556\pi$
$223$	4611.48	1.38479	0.692394	+	0.721520i	$0.256556\pi$
$224$	5158.62	1.53873
$225$	−1855.41	−0.549751
$226$	1017.42	0.299460
$227$	−4311.75	−1.26071	−0.630354	−	0.776308i	$-0.717090\pi$
$227$	−4311.75	−1.26071	−0.630354	+	0.776308i	$0.717090\pi$
$228$	−585.079	−0.169947
$229$	1516.41	0.437586	0.218793	−	0.975771i	$-0.429788\pi$
$229$	1516.41	0.437586	0.218793	+	0.975771i	$0.429788\pi$
$230$	−2367.71	−0.678791
$231$	−630.827	−0.179677
$232$	−5865.68	−1.65992
$233$	4540.98	1.27678	0.638389	−	0.769714i	$-0.279601\pi$
$233$	4540.98	1.27678	0.638389	+	0.769714i	$0.279601\pi$
$234$	0	0
$235$	−4916.20	−1.36467
$236$	−3452.57	−0.952301
$237$	−378.254	−0.103672
$238$	−2024.82	−0.551468
$239$	−721.749	−0.195339	−0.0976696	−	0.995219i	$-0.531139\pi$
$239$	−721.749	−0.195339	−0.0976696	+	0.995219i	$0.531139\pi$
$240$	204.656	0.0550437
$241$	4802.43	1.28362	0.641808	−	0.766865i	$-0.278184\pi$
$241$	4802.43	1.28362	0.641808	+	0.766865i	$0.278184\pi$
$242$	−198.017	−0.0525991
$243$	−3602.14	−0.950936
$244$	−1159.14	−0.304124
$245$	−6162.13	−1.60687
$246$	1218.60	0.315834
$247$	0	0
$248$	2707.83	0.693337
$249$	1131.01	0.287851
$250$	−1020.91	−0.258272
$251$	−2154.72	−0.541852	−0.270926	−	0.962600i	$-0.587330\pi$
$251$	−2154.72	−0.541852	−0.270926	+	0.962600i	$0.587330\pi$
$252$	−3361.64	−0.840330
$253$	1107.24	0.275144
$254$	3987.03	0.984916
$255$	−1321.58	−0.324552
$256$	−3754.78	−0.916695
$257$	−1879.69	−0.456234	−0.228117	−	0.973634i	$-0.573257\pi$
$257$	−1879.69	−0.456234	−0.228117	+	0.973634i	$0.573257\pi$
$258$	−590.164	−0.142411
$259$	5627.23	1.35003
$260$	0	0
$261$	6117.81	1.45089
$262$	945.486	0.222948
$263$	−7779.67	−1.82401	−0.912005	−	0.410178i	$-0.865467\pi$
$263$	−7779.67	−1.82401	−0.912005	+	0.410178i	$0.865467\pi$
$264$	495.066	0.115414
$265$	−8550.15	−1.98201
$266$	−2421.06	−0.558063
$267$	−2414.22	−0.553363
$268$	−3890.04	−0.886650
$269$	2860.78	0.648419	0.324210	−	0.945985i	$-0.394902\pi$
$269$	2860.78	0.648419	0.324210	+	0.945985i	$0.394902\pi$
$270$	2415.24	0.544395
$271$	8298.59	1.86016	0.930080	−	0.367356i	$-0.119737\pi$
$271$	8298.59	1.86016	0.930080	+	0.367356i	$0.119737\pi$
$272$	−307.194	−0.0684794
$273$	0	0
$274$	3061.87	0.675089
$275$	−897.580	−0.196822
$276$	−1105.86	−0.241178
$277$	1669.61	0.362156	0.181078	−	0.983469i	$-0.442041\pi$
$277$	1669.61	0.362156	0.181078	+	0.983469i	$0.442041\pi$
$278$	2522.11	0.544122
$279$	−2824.23	−0.606029
$280$	8705.08	1.85796
$281$	−206.207	−0.0437768	−0.0218884	−	0.999760i	$-0.506968\pi$
$281$	−206.207	−0.0437768	−0.0218884	+	0.999760i	$0.506968\pi$
$282$	1155.50	0.244004
$283$	1750.59	0.367709	0.183854	−	0.982953i	$-0.441143\pi$
$283$	1750.59	0.367709	0.183854	+	0.982953i	$0.441143\pi$
$284$	5396.25	1.12749
$285$	−1580.21	−0.328433
$286$	0	0
$287$	−10020.4	−2.06092
$288$	4222.45	0.863924
$289$	−2929.27	−0.596227
$290$	−6328.73	−1.28150
$291$	−3608.02	−0.726824
$292$	1241.67	0.248847
$293$	8996.37	1.79377	0.896883	−	0.442268i	$-0.145826\pi$
$293$	8996.37	1.79377	0.896883	+	0.442268i	$0.145826\pi$
$294$	1448.35	0.287311
$295$	−9324.85	−1.84038
$296$	−4416.19	−0.867182
$297$	−1129.47	−0.220668
$298$	1962.79	0.381549
$299$	0	0
$300$	896.466	0.172525
$301$	4852.83	0.929277
$302$	−1585.72	−0.302146
$303$	1354.05	0.256726
$304$	−367.310	−0.0692983
$305$	−3130.65	−0.587740
$306$	−1657.36	−0.309624
$307$	7161.37	1.33134	0.665669	−	0.746247i	$-0.268146\pi$
$307$	7161.37	1.33134	0.665669	+	0.746247i	$0.268146\pi$
$308$	−1626.24	−0.300856
$309$	970.293	0.178634
$310$	2921.60	0.535276
$311$	−8110.37	−1.47877	−0.739384	−	0.673284i	$-0.764883\pi$
$311$	−8110.37	−1.47877	−0.739384	+	0.673284i	$0.764883\pi$
$312$	0	0
$313$	3709.75	0.669927	0.334964	−	0.942231i	$-0.391276\pi$
$313$	3709.75	0.669927	0.334964	+	0.942231i	$0.391276\pi$
$314$	−1042.81	−0.187418
$315$	−9079.25	−1.62399
$316$	−975.119	−0.173591
$317$	−7001.37	−1.24049	−0.620246	−	0.784407i	$-0.712967\pi$
$317$	−7001.37	−1.24049	−0.620246	+	0.784407i	$0.712967\pi$
$318$	2009.63	0.354385
$319$	2959.58	0.519450
$320$	−3574.93	−0.624514
$321$	−2363.21	−0.410907
$322$	−4576.07	−0.791970
$323$	2371.94	0.408601
$324$	−2139.22	−0.366807
$325$	0	0
$326$	−813.120	−0.138143
$327$	3479.67	0.588459
$328$	7863.90	1.32381
$329$	−9501.54	−1.59221
$330$	534.148	0.0891026
$331$	9461.80	1.57120	0.785600	−	0.618734i	$-0.212354\pi$
$331$	9461.80	1.57120	0.785600	+	0.618734i	$0.212354\pi$
$332$	2915.69	0.481986
$333$	4606.01	0.757982
$334$	1363.66	0.223402
$335$	−10506.4	−1.71351
$336$	395.539	0.0642214
$337$	−11914.2	−1.92584	−0.962922	−	0.269781i	$-0.913049\pi$
$337$	−11914.2	−1.92584	−0.962922	+	0.269781i	$0.913049\pi$
$338$	0	0
$339$	1283.44	0.205625
$340$	−3406.97	−0.543439
$341$	−1366.26	−0.216971
$342$	−1981.69	−0.313327
$343$	−2381.10	−0.374832
$344$	−3808.45	−0.596912
$345$	−2986.76	−0.466093
$346$	3365.94	0.522989
$347$	4922.38	0.761519	0.380759	−	0.924674i	$-0.375663\pi$
$347$	4922.38	0.761519	0.380759	+	0.924674i	$0.375663\pi$
$348$	−2955.90	−0.455325
$349$	−368.762	−0.0565598	−0.0282799	−	0.999600i	$-0.509003\pi$
$349$	−368.762	−0.0565598	−0.0282799	+	0.999600i	$0.509003\pi$
$350$	3709.58	0.566530
$351$	0	0
$352$	2042.67	0.309303
$353$	800.427	0.120687	0.0603434	−	0.998178i	$-0.480780\pi$
$353$	800.427	0.120687	0.0603434	+	0.998178i	$0.480780\pi$
$354$	2191.71	0.329063
$355$	14574.4	2.17896
$356$	−6223.74	−0.926567
$357$	−2554.23	−0.378666
$358$	168.456	0.0248693
$359$	−7884.10	−1.15907	−0.579536	−	0.814947i	$-0.696766\pi$
$359$	−7884.10	−1.15907	−0.579536	+	0.814947i	$0.696766\pi$
$360$	7125.30	1.04316
$361$	−4022.89	−0.586513
$362$	3272.76	0.475172
$363$	−249.790	−0.0361173
$364$	0	0
$365$	3353.56	0.480914
$366$	735.829	0.105089
$367$	6869.60	0.977085	0.488543	−	0.872540i	$-0.337529\pi$
$367$	6869.60	0.977085	0.488543	+	0.872540i	$0.337529\pi$
$368$	−694.256	−0.0983440
$369$	−8201.92	−1.15711
$370$	−4764.81	−0.669489
$371$	−16524.9	−2.31248
$372$	1364.56	0.190187
$373$	−1391.07	−0.193101	−0.0965504	−	0.995328i	$-0.530781\pi$
$373$	−1391.07	−0.193101	−0.0965504	+	0.995328i	$0.530781\pi$
$374$	−801.772	−0.110852
$375$	−1287.84	−0.177343
$376$	7456.71	1.02274
$377$	0	0
$378$	4667.94	0.635166
$379$	−5764.39	−0.781258	−0.390629	−	0.920548i	$-0.627742\pi$
$379$	−5764.39	−0.781258	−0.390629	+	0.920548i	$0.627742\pi$
$380$	−4073.70	−0.549937
$381$	5029.48	0.676294
$382$	−3187.43	−0.426920
$383$	9188.10	1.22582	0.612911	−	0.790152i	$-0.289998\pi$
$383$	9188.10	1.22582	0.612911	+	0.790152i	$0.289998\pi$
$384$	−2226.54	−0.295893
$385$	−4392.22	−0.581424
$386$	−5491.77	−0.724155
$387$	3972.15	0.521746
$388$	−9301.29	−1.21701
$389$	13599.4	1.77253	0.886267	−	0.463174i	$-0.153289\pi$
$389$	13599.4	1.77253	0.886267	+	0.463174i	$0.153289\pi$
$390$	0	0
$391$	4483.22	0.579862
$392$	9346.49	1.20426
$393$	1192.69	0.153087
$394$	2268.96	0.290123
$395$	−2633.64	−0.335476
$396$	−1331.11	−0.168917
$397$	−3448.43	−0.435950	−0.217975	−	0.975954i	$-0.569945\pi$
$397$	−3448.43	−0.435950	−0.217975	+	0.975954i	$0.569945\pi$
$398$	975.203	0.122820
$399$	−3054.07	−0.383195
$400$	562.797	0.0703497
$401$	6520.07	0.811962	0.405981	−	0.913882i	$-0.366930\pi$
$401$	6520.07	0.811962	0.405981	+	0.913882i	$0.366930\pi$
$402$	2469.43	0.306377
$403$	0	0
$404$	3490.66	0.429869
$405$	−5777.69	−0.708878
$406$	−12231.5	−1.49518
$407$	2228.23	0.271374
$408$	2004.53	0.243233
$409$	6867.18	0.830221	0.415110	−	0.909771i	$-0.363743\pi$
$409$	6867.18	0.830221	0.415110	+	0.909771i	$0.363743\pi$
$410$	8484.69	1.02202
$411$	3862.43	0.463551
$412$	2501.37	0.299110
$413$	−18022.1	−2.14724
$414$	−3745.62	−0.444655
$415$	7874.82	0.931469
$416$	0	0
$417$	3181.53	0.373622
$418$	−958.672	−0.112178
$419$	8109.75	0.945554	0.472777	−	0.881182i	$-0.343252\pi$
$419$	8109.75	0.945554	0.472777	+	0.881182i	$0.343252\pi$
$420$	4386.77	0.509648
$421$	−7217.72	−0.835558	−0.417779	−	0.908549i	$-0.637191\pi$
$421$	−7217.72	−0.835558	−0.417779	+	0.908549i	$0.637191\pi$
$422$	3097.19	0.357272
$423$	−7777.23	−0.893952
$424$	12968.6	1.48540
$425$	−3634.31	−0.414800
$426$	−3425.57	−0.389600
$427$	−6050.62	−0.685737
$428$	−6092.23	−0.688035
$429$	0	0
$430$	−4109.10	−0.460833
$431$	12120.6	1.35460	0.677298	−	0.735709i	$-0.263151\pi$
$431$	12120.6	1.35460	0.677298	+	0.735709i	$0.263151\pi$
$432$	708.194	0.0788727
$433$	−1150.16	−0.127652	−0.0638261	−	0.997961i	$-0.520330\pi$
$433$	−1150.16	−0.127652	−0.0638261	+	0.997961i	$0.520330\pi$
$434$	5646.58	0.624526
$435$	−7983.43	−0.879945
$436$	8970.42	0.985333
$437$	5360.55	0.586796
$438$	−788.222	−0.0859880
$439$	10545.9	1.14653	0.573267	−	0.819369i	$-0.305676\pi$
$439$	10545.9	1.14653	0.573267	+	0.819369i	$0.305676\pi$
$440$	3446.97	0.373472
$441$	−9748.24	−1.05261
$442$	0	0
$443$	14148.5	1.51741	0.758706	−	0.651433i	$-0.225832\pi$
$443$	14148.5	1.51741	0.758706	+	0.651433i	$0.225832\pi$
$444$	−2225.46	−0.237873
$445$	−16809.4	−1.79065
$446$	−7546.69	−0.801225
$447$	2475.98	0.261991
$448$	−6909.27	−0.728643
$449$	−13065.7	−1.37329	−0.686645	−	0.726993i	$-0.740917\pi$
$449$	−13065.7	−1.37329	−0.686645	+	0.726993i	$0.740917\pi$
$450$	3036.38	0.318080
$451$	−3967.79	−0.414271
$452$	3308.64	0.344304
$453$	−2000.32	−0.207469
$454$	7056.18	0.729434
$455$	0	0
$456$	2396.80	0.246141
$457$	−15117.1	−1.54737	−0.773683	−	0.633573i	$-0.781588\pi$
$457$	−15117.1	−1.54737	−0.773683	+	0.633573i	$0.781588\pi$
$458$	−2481.60	−0.253183
$459$	−4573.22	−0.465054
$460$	−7699.73	−0.780438
$461$	−3520.72	−0.355697	−0.177849	−	0.984058i	$-0.556914\pi$
$461$	−3520.72	−0.355697	−0.177849	+	0.984058i	$0.556914\pi$
$462$	1032.35	0.103959
$463$	−9470.73	−0.950631	−0.475315	−	0.879815i	$-0.657666\pi$
$463$	−9470.73	−0.950631	−0.475315	+	0.879815i	$0.657666\pi$
$464$	−1855.70	−0.185666
$465$	3685.48	0.367548
$466$	−7431.31	−0.738732
$467$	946.266	0.0937643	0.0468822	−	0.998900i	$-0.485071\pi$
$467$	946.266	0.0937643	0.0468822	+	0.998900i	$0.485071\pi$
$468$	0	0
$469$	−20305.7	−1.99921
$470$	8045.36	0.789585
$471$	−1315.46	−0.128691
$472$	14143.6	1.37926
$473$	1921.58	0.186796
$474$	619.012	0.0599835
$475$	−4345.52	−0.419761
$476$	−6584.67	−0.634050
$477$	−13526.0	−1.29835
$478$	1181.14	0.113021
$479$	−1087.44	−0.103729	−0.0518645	−	0.998654i	$-0.516516\pi$
$479$	−1087.44	−0.103729	−0.0518645	+	0.998654i	$0.516516\pi$
$480$	−5510.08	−0.523957
$481$	0	0
$482$	−7859.18	−0.742688
$483$	−5772.52	−0.543807
$484$	−643.946	−0.0604757
$485$	−25121.3	−2.35196
$486$	5894.90	0.550202
$487$	−20259.4	−1.88510	−0.942549	−	0.334067i	$-0.891579\pi$
$487$	−20259.4	−1.88510	−0.942549	+	0.334067i	$0.891579\pi$
$488$	4748.46	0.440477
$489$	−1025.72	−0.0948560
$490$	10084.3	0.929721
$491$	−169.175	−0.0155494	−0.00777470	−	0.999970i	$-0.502475\pi$
$491$	−169.175	−0.0155494	−0.00777470	+	0.999970i	$0.502475\pi$
$492$	3962.87	0.363130
$493$	11983.4	1.09473
$494$	0	0
$495$	−3595.13	−0.326443
$496$	856.668	0.0775514
$497$	28168.0	2.54227
$498$	−1850.90	−0.166548
$499$	−3237.96	−0.290483	−0.145241	−	0.989396i	$-0.546396\pi$
$499$	−3237.96	−0.290483	−0.145241	+	0.989396i	$0.546396\pi$
$500$	−3319.98	−0.296948
$501$	1720.21	0.153400
$502$	3526.21	0.313510
$503$	3422.21	0.303357	0.151679	−	0.988430i	$-0.451532\pi$
$503$	3422.21	0.303357	0.151679	+	0.988430i	$0.451532\pi$
$504$	13771.1	1.21709
$505$	9427.73	0.830749
$506$	−1812.00	−0.159196
$507$	0	0
$508$	12965.7	1.13241
$509$	−5565.28	−0.484630	−0.242315	−	0.970198i	$-0.577907\pi$
$509$	−5565.28	−0.484630	−0.242315	+	0.970198i	$0.577907\pi$
$510$	2162.77	0.187783
$511$	6481.44	0.561100
$512$	−2483.72	−0.214387
$513$	−5468.17	−0.470615
$514$	3076.12	0.263973
$515$	6755.80	0.578051
$516$	−1919.20	−0.163737
$517$	−3762.35	−0.320054
$518$	−9208.96	−0.781117
$519$	4246.00	0.359111
$520$	0	0
$521$	13893.6	1.16831	0.584154	−	0.811643i	$-0.301426\pi$
$521$	13893.6	1.16831	0.584154	+	0.811643i	$0.301426\pi$
$522$	−10011.8	−0.839472
$523$	−4836.43	−0.404364	−0.202182	−	0.979348i	$-0.564803\pi$
$523$	−4836.43	−0.404364	−0.202182	+	0.979348i	$0.564803\pi$
$524$	3074.70	0.256334
$525$	4679.48	0.389009
$526$	12731.4	1.05536
$527$	−5532.01	−0.457264
$528$	156.622	0.0129093
$529$	−2034.97	−0.167253
$530$	13992.3	1.14677
$531$	−14751.5	−1.20558
$532$	−7873.24	−0.641632
$533$	0	0
$534$	3950.88	0.320171
$535$	−16454.2	−1.32967
$536$	15935.7	1.28418
$537$	212.501	0.0170765
$538$	−4681.67	−0.375169
$539$	−4715.85	−0.376857
$540$	7854.31	0.625918
$541$	12017.2	0.955007	0.477503	−	0.878630i	$-0.341542\pi$
$541$	12017.2	0.955007	0.477503	+	0.878630i	$0.341542\pi$
$542$	−13580.7	−1.07627
$543$	4128.45	0.326277
$544$	8270.79	0.651852
$545$	24227.7	1.90422
$546$	0	0
$547$	−12138.3	−0.948803	−0.474401	−	0.880309i	$-0.657335\pi$
$547$	−12138.3	−0.948803	−0.474401	+	0.880309i	$0.657335\pi$
$548$	9957.14	0.776183
$549$	−4952.57	−0.385010
$550$	1468.89	0.113879
$551$	14328.4	1.10782
$552$	4530.21	0.349309
$553$	−5090.05	−0.391412
$554$	−2732.32	−0.209540
$555$	−6010.62	−0.459705
$556$	8201.83	0.625603
$557$	−21867.5	−1.66347	−0.831737	−	0.555169i	$-0.812653\pi$
$557$	−21867.5	−1.66347	−0.831737	+	0.555169i	$0.812653\pi$
$558$	4621.85	0.350643
$559$	0	0
$560$	2753.99	0.207817
$561$	−1011.40	−0.0761166
$562$	337.458	0.0253288
$563$	2972.86	0.222542	0.111271	−	0.993790i	$-0.464508\pi$
$563$	2972.86	0.222542	0.111271	+	0.993790i	$0.464508\pi$
$564$	3757.67	0.280544
$565$	8936.13	0.665391
$566$	−2864.84	−0.212753
$567$	−11166.5	−0.827074
$568$	−22105.9	−1.63300
$569$	12642.2	0.931438	0.465719	−	0.884933i	$-0.345796\pi$
$569$	12642.2	0.931438	0.465719	+	0.884933i	$0.345796\pi$
$570$	2586.01	0.190028
$571$	−679.187	−0.0497778	−0.0248889	−	0.999690i	$-0.507923\pi$
$571$	−679.187	−0.0497778	−0.0248889	+	0.999690i	$0.507923\pi$
$572$	0	0
$573$	−4020.82	−0.293145
$574$	16398.4	1.19243
$575$	−8213.51	−0.595699
$576$	−5655.39	−0.409100
$577$	2991.45	0.215833	0.107916	−	0.994160i	$-0.465582\pi$
$577$	2991.45	0.215833	0.107916	+	0.994160i	$0.465582\pi$
$578$	4793.75	0.344971
$579$	−6927.65	−0.497242
$580$	−20580.9	−1.47340
$581$	15219.7	1.08678
$582$	5904.52	0.420533
$583$	−6543.40	−0.464837
$584$	−5086.56	−0.360417
$585$	0	0
$586$	−14722.6	−1.03786
$587$	3475.61	0.244385	0.122192	−	0.992506i	$-0.461007\pi$
$587$	3475.61	0.244385	0.122192	+	0.992506i	$0.461007\pi$
$588$	4710.00	0.330335
$589$	−6614.58	−0.462732
$590$	15260.1	1.06483
$591$	2862.20	0.199214
$592$	−1397.13	−0.0969964
$593$	20295.7	1.40547	0.702737	−	0.711449i	$-0.251961\pi$
$593$	20295.7	1.40547	0.702737	+	0.711449i	$0.251961\pi$
$594$	1848.37	0.127676
$595$	−17784.2	−1.22534
$596$	6382.96	0.438685
$597$	1230.18	0.0843347
$598$	0	0
$599$	−19439.6	−1.32601	−0.663004	−	0.748616i	$-0.730719\pi$
$599$	−19439.6	−1.32601	−0.663004	+	0.748616i	$0.730719\pi$
$600$	−3672.41	−0.249876
$601$	17119.1	1.16190	0.580950	−	0.813939i	$-0.302681\pi$
$601$	17119.1	1.16190	0.580950	+	0.813939i	$0.302681\pi$
$602$	−7941.66	−0.537671
$603$	−16620.7	−1.12247
$604$	−5156.74	−0.347392
$605$	−1739.20	−0.116873
$606$	−2215.90	−0.148539
$607$	5051.89	0.337809	0.168904	−	0.985632i	$-0.445977\pi$
$607$	5051.89	0.337809	0.168904	+	0.985632i	$0.445977\pi$
$608$	9889.32	0.659647
$609$	−15429.6	−1.02666
$610$	5123.31	0.340060
$611$	0	0
$612$	−5389.70	−0.355990
$613$	−17948.2	−1.18258	−0.591291	−	0.806458i	$-0.701382\pi$
$613$	−17948.2	−1.18258	−0.591291	+	0.806458i	$0.701382\pi$
$614$	−11719.6	−0.770300
$615$	10703.1	0.701773
$616$	6661.96	0.435744
$617$	21331.5	1.39186	0.695929	−	0.718111i	$-0.254993\pi$
$617$	21331.5	1.39186	0.695929	+	0.718111i	$0.254993\pi$
$618$	−1587.88	−0.103356
$619$	−17332.1	−1.12542	−0.562710	−	0.826655i	$-0.690241\pi$
$619$	−17332.1	−1.12542	−0.562710	+	0.826655i	$0.690241\pi$
$620$	9500.97	0.615433
$621$	−10335.4	−0.667869
$622$	13272.6	0.855601
$623$	−32487.5	−2.08922
$624$	0	0
$625$	−19166.5	−1.22666
$626$	−6071.00	−0.387613
$627$	−1209.33	−0.0770268
$628$	−3391.19	−0.215483
$629$	9022.11	0.571916
$630$	14858.2	0.939627
$631$	12375.7	0.780776	0.390388	−	0.920650i	$-0.372341\pi$
$631$	12375.7	0.780776	0.390388	+	0.920650i	$0.372341\pi$
$632$	3994.62	0.251420
$633$	3906.97	0.245321
$634$	11457.7	0.717737
$635$	35018.4	2.18845
$636$	6535.27	0.407454
$637$	0	0
$638$	−4843.35	−0.300549
$639$	23056.1	1.42737
$640$	−15502.6	−0.957492
$641$	2693.16	0.165949	0.0829745	−	0.996552i	$-0.473558\pi$
$641$	2693.16	0.165949	0.0829745	+	0.996552i	$0.473558\pi$
$642$	3867.39	0.237747
$643$	−3462.40	−0.212354	−0.106177	−	0.994347i	$-0.533861\pi$
$643$	−3462.40	−0.212354	−0.106177	+	0.994347i	$0.533861\pi$
$644$	−14881.3	−0.910566
$645$	−5183.46	−0.316432
$646$	−3881.68	−0.236413
$647$	18923.9	1.14988	0.574942	−	0.818194i	$-0.305025\pi$
$647$	18923.9	1.14988	0.574942	+	0.818194i	$0.305025\pi$
$648$	8763.39	0.531263
$649$	−7136.27	−0.431622
$650$	0	0
$651$	7122.92	0.428832
$652$	−2644.25	−0.158829
$653$	27543.1	1.65060	0.825302	−	0.564692i	$-0.191005\pi$
$653$	27543.1	1.65060	0.825302	+	0.564692i	$0.191005\pi$
$654$	−5694.48	−0.340477
$655$	8304.29	0.495382
$656$	2487.87	0.148072
$657$	5305.20	0.315032
$658$	15549.3	0.921237
$659$	28264.3	1.67075	0.835373	−	0.549684i	$-0.185252\pi$
$659$	28264.3	1.67075	0.835373	+	0.549684i	$0.185252\pi$
$660$	1737.04	0.102446
$661$	−21695.0	−1.27661	−0.638304	−	0.769784i	$-0.720364\pi$
$661$	−21695.0	−1.27661	−0.638304	+	0.769784i	$0.720364\pi$
$662$	−15484.2	−0.909081
$663$	0	0
$664$	−11944.2	−0.698082
$665$	−21264.4	−1.24000
$666$	−7537.74	−0.438561
$667$	27082.3	1.57216
$668$	4434.61	0.256856
$669$	−9519.85	−0.550162
$670$	17193.7	0.991420
$671$	−2395.88	−0.137842
$672$	−10649.3	−0.611320
$673$	−19053.4	−1.09132	−0.545658	−	0.838008i	$-0.683720\pi$
$673$	−19053.4	−1.09132	−0.545658	+	0.838008i	$0.683720\pi$
$674$	19497.6	1.11427
$675$	8378.40	0.477755
$676$	0	0
$677$	9094.81	0.516310	0.258155	−	0.966103i	$-0.416885\pi$
$677$	9094.81	0.516310	0.258155	+	0.966103i	$0.416885\pi$
$678$	−2100.35	−0.118973
$679$	−48552.0	−2.74412
$680$	13956.8	0.787087
$681$	8901.08	0.500867
$682$	2235.89	0.125537
$683$	−8382.14	−0.469596	−0.234798	−	0.972044i	$-0.575443\pi$
$683$	−8382.14	−0.469596	−0.234798	+	0.972044i	$0.575443\pi$
$684$	−6444.42	−0.360247
$685$	26892.7	1.50002
$686$	3896.68	0.216874
$687$	−3130.44	−0.173848
$688$	−1204.87	−0.0667661
$689$	0	0
$690$	4887.84	0.269677
$691$	17056.7	0.939028	0.469514	−	0.882925i	$-0.344429\pi$
$691$	17056.7	0.939028	0.469514	+	0.882925i	$0.344429\pi$
$692$	10946.0	0.601306
$693$	−6948.32	−0.380873
$694$	−8055.47	−0.440607
$695$	22151.9	1.20902
$696$	12109.0	0.659468
$697$	−16065.6	−0.873070
$698$	603.479	0.0327250
$699$	−9374.30	−0.507251
$700$	12063.5	0.651367
$701$	22108.7	1.19120	0.595601	−	0.803280i	$-0.296914\pi$
$701$	22108.7	1.19120	0.595601	+	0.803280i	$0.296914\pi$
$702$	0	0
$703$	10787.7	0.578755
$704$	−2735.88	−0.146466
$705$	10148.9	0.542169
$706$	−1309.90	−0.0698282
$707$	18221.0	0.969266
$708$	7127.41	0.378340
$709$	−13292.7	−0.704118	−0.352059	−	0.935978i	$-0.614518\pi$
$709$	−13292.7	−0.704118	−0.352059	+	0.935978i	$0.614518\pi$
$710$	−23851.0	−1.26072
$711$	−4166.32	−0.219760
$712$	25495.8	1.34199
$713$	−12502.3	−0.656682
$714$	4179.99	0.219093
$715$	0	0
$716$	547.817	0.0285934
$717$	1489.96	0.0776063
$718$	12902.3	0.670628
$719$	15790.0	0.819007	0.409503	−	0.912309i	$-0.365702\pi$
$719$	15790.0	0.819007	0.409503	+	0.912309i	$0.365702\pi$
$720$	2254.21	0.116680
$721$	13056.9	0.674433
$722$	6583.47	0.339351
$723$	−9914.03	−0.509968
$724$	10642.9	0.546328
$725$	−21954.2	−1.12463
$726$	408.781	0.0208971
$727$	−33105.0	−1.68885	−0.844427	−	0.535670i	$-0.820059\pi$
$727$	−33105.0	−1.68885	−0.844427	+	0.535670i	$0.820059\pi$
$728$	0	0
$729$	−3416.94	−0.173599
$730$	−5488.11	−0.278252
$731$	7780.52	0.393670
$732$	2392.90	0.120825
$733$	12116.4	0.610544	0.305272	−	0.952265i	$-0.401253\pi$
$733$	12116.4	0.610544	0.305272	+	0.952265i	$0.401253\pi$
$734$	−11242.1	−0.565332
$735$	12721.0	0.638394
$736$	18691.9	0.936131
$737$	−8040.50	−0.401867
$738$	13422.4	0.669494
$739$	−14578.8	−0.725696	−0.362848	−	0.931848i	$-0.618196\pi$
$739$	−14578.8	−0.725696	−0.362848	+	0.931848i	$0.618196\pi$
$740$	−15495.1	−0.769744
$741$	0	0
$742$	27043.0	1.33798
$743$	4683.14	0.231235	0.115618	−	0.993294i	$-0.463115\pi$
$743$	4683.14	0.231235	0.115618	+	0.993294i	$0.463115\pi$
$744$	−5590.00	−0.275456
$745$	17239.4	0.847788
$746$	2276.48	0.111726
$747$	12457.7	0.610176
$748$	−2607.34	−0.127452
$749$	−31801.0	−1.55138
$750$	2107.54	0.102609
$751$	−5817.64	−0.282675	−0.141337	−	0.989961i	$-0.545140\pi$
$751$	−5817.64	−0.282675	−0.141337	+	0.989961i	$0.545140\pi$
$752$	2359.05	0.114396
$753$	4448.16	0.215272
$754$	0	0
$755$	−13927.5	−0.671357
$756$	15180.0	0.730281
$757$	28501.8	1.36845	0.684224	−	0.729272i	$-0.260141\pi$
$757$	28501.8	1.36845	0.684224	+	0.729272i	$0.260141\pi$
$758$	9433.43	0.452028
$759$	−2285.76	−0.109312
$760$	16688.1	0.796499
$761$	−9957.24	−0.474310	−0.237155	−	0.971472i	$-0.576215\pi$
$761$	−9957.24	−0.474310	−0.237155	+	0.971472i	$0.576215\pi$
$762$	−8230.74	−0.391297
$763$	46824.9	2.22172
$764$	−10365.5	−0.490850
$765$	−14556.7	−0.687973
$766$	−15036.3	−0.709249
$767$	0	0
$768$	7751.29	0.364194
$769$	23769.4	1.11463	0.557313	−	0.830302i	$-0.311832\pi$
$769$	23769.4	1.11463	0.557313	+	0.830302i	$0.311832\pi$
$770$	7187.87	0.336406
$771$	3880.40	0.181257
$772$	−17859.1	−0.832596
$773$	32180.2	1.49734	0.748669	−	0.662944i	$-0.230693\pi$
$773$	32180.2	1.49734	0.748669	+	0.662944i	$0.230693\pi$
$774$	−6500.43	−0.301877
$775$	10134.9	0.469752
$776$	38103.1	1.76266
$777$	−11616.7	−0.536355
$778$	−22255.4	−1.02557
$779$	−19209.6	−0.883510
$780$	0	0
$781$	11153.7	0.511027
$782$	−7336.79	−0.335503
$783$	−27626.0	−1.26088
$784$	2956.92	0.134699
$785$	−9159.09	−0.416435
$786$	−1951.84	−0.0885749
$787$	−4982.68	−0.225684	−0.112842	−	0.993613i	$-0.535995\pi$
$787$	−4982.68	−0.225684	−0.112842	+	0.993613i	$0.535995\pi$
$788$	7378.61	0.333569
$789$	16060.2	0.724661
$790$	4309.96	0.194103
$791$	17270.9	0.776335
$792$	5452.96	0.244650
$793$	0	0
$794$	5643.37	0.252236
$795$	17650.7	0.787431
$796$	3171.34	0.141212
$797$	−12038.5	−0.535038	−0.267519	−	0.963553i	$-0.586204\pi$
$797$	−12038.5	−0.535038	−0.267519	+	0.963553i	$0.586204\pi$
$798$	4997.99	0.221713
$799$	−15233.8	−0.674509
$800$	−15152.6	−0.669655
$801$	−26591.7	−1.17300
$802$	−10670.1	−0.469793
$803$	2566.47	0.112788
$804$	8030.52	0.352257
$805$	−40192.0	−1.75973
$806$	0	0
$807$	−5905.73	−0.257610
$808$	−14299.6	−0.622598
$809$	−16334.9	−0.709896	−0.354948	−	0.934886i	$-0.615501\pi$
$809$	−16334.9	−0.709896	−0.354948	+	0.934886i	$0.615501\pi$
$810$	9455.19	0.410150
$811$	−28993.7	−1.25537	−0.627686	−	0.778467i	$-0.715998\pi$
$811$	−28993.7	−1.25537	−0.627686	+	0.778467i	$0.715998\pi$
$812$	−39776.7	−1.71908
$813$	−17131.4	−0.739023
$814$	−3646.49	−0.157014
$815$	−7141.70	−0.306948
$816$	634.165	0.0272062
$817$	9303.11	0.398378
$818$	−11238.1	−0.480358
$819$	0	0
$820$	27592.0	1.17507
$821$	38690.3	1.64470	0.822351	−	0.568981i	$-0.192662\pi$
$821$	38690.3	1.64470	0.822351	+	0.568981i	$0.192662\pi$
$822$	−6320.86	−0.268206
$823$	−897.775	−0.0380249	−0.0190124	−	0.999819i	$-0.506052\pi$
$823$	−897.775	−0.0380249	−0.0190124	+	0.999819i	$0.506052\pi$
$824$	−10247.0	−0.433215
$825$	1852.95	0.0781955
$826$	29493.3	1.24237
$827$	8584.91	0.360975	0.180488	−	0.983577i	$-0.442232\pi$
$827$	8584.91	0.360975	0.180488	+	0.983577i	$0.442232\pi$
$828$	−12180.7	−0.511241
$829$	−31623.4	−1.32488	−0.662440	−	0.749115i	$-0.730479\pi$
$829$	−31623.4	−1.32488	−0.662440	+	0.749115i	$0.730479\pi$
$830$	−12887.1	−0.538939
$831$	−3446.71	−0.143881
$832$	0	0
$833$	−19094.5	−0.794221
$834$	−5206.58	−0.216174
$835$	11977.2	0.496392
$836$	−3117.58	−0.128976
$837$	12753.3	0.526664
$838$	−13271.6	−0.547088
$839$	7130.98	0.293431	0.146716	−	0.989179i	$-0.453130\pi$
$839$	7130.98	0.293431	0.146716	+	0.989179i	$0.453130\pi$
$840$	−17970.6	−0.738147
$841$	48000.2	1.96811
$842$	11811.8	0.483446
$843$	425.689	0.0173921
$844$	10072.0	0.410773
$845$	0	0
$846$	12727.4	0.517232
$847$	−3361.35	−0.136360
$848$	4102.82	0.166145
$849$	−3613.87	−0.146087
$850$	5947.56	0.239999
$851$	20389.9	0.821335
$852$	−11139.9	−0.447942
$853$	43949.7	1.76414	0.882070	−	0.471119i	$-0.156150\pi$
$853$	43949.7	1.76414	0.882070	+	0.471119i	$0.156150\pi$
$854$	9901.84	0.396761
$855$	−17405.4	−0.696200
$856$	24957.1	0.996513
$857$	−14735.8	−0.587357	−0.293679	−	0.955904i	$-0.594880\pi$
$857$	−14735.8	−0.587357	−0.293679	+	0.955904i	$0.594880\pi$
$858$	0	0
$859$	22628.4	0.898802	0.449401	−	0.893330i	$-0.351637\pi$
$859$	22628.4	0.898802	0.449401	+	0.893330i	$0.351637\pi$
$860$	−13362.7	−0.529842
$861$	20685.9	0.818784
$862$	−19835.4	−0.783756
$863$	21686.0	0.855390	0.427695	−	0.903923i	$-0.359326\pi$
$863$	21686.0	0.855390	0.427695	+	0.903923i	$0.359326\pi$
$864$	−19067.2	−0.750784
$865$	29563.4	1.16206
$866$	1882.24	0.0738583
$867$	6047.11	0.236875
$868$	18362.5	0.718048
$869$	−2015.52	−0.0786787
$870$	13064.9	0.509128
$871$	0	0
$872$	−36747.7	−1.42710
$873$	−39740.9	−1.54070
$874$	−8772.55	−0.339515
$875$	−17330.0	−0.669556
$876$	−2563.28	−0.0988645
$877$	8443.41	0.325101	0.162551	−	0.986700i	$-0.448028\pi$
$877$	8443.41	0.325101	0.162551	+	0.986700i	$0.448028\pi$
$878$	−17258.4	−0.663373
$879$	−18571.9	−0.712645
$880$	1090.50	0.0417737
$881$	−14490.6	−0.554143	−0.277072	−	0.960849i	$-0.589364\pi$
$881$	−14490.6	−0.554143	−0.277072	+	0.960849i	$0.589364\pi$
$882$	15953.0	0.609031
$883$	−2909.59	−0.110890	−0.0554449	−	0.998462i	$-0.517658\pi$
$883$	−2909.59	−0.110890	−0.0554449	+	0.998462i	$0.517658\pi$
$884$	0	0
$885$	19250.0	0.731166
$886$	−23154.0	−0.877960
$887$	−12652.0	−0.478931	−0.239466	−	0.970905i	$-0.576972\pi$
$887$	−12652.0	−0.478931	−0.239466	+	0.970905i	$0.576972\pi$
$888$	9116.69	0.344522
$889$	67680.2	2.55334
$890$	27508.5	1.03605
$891$	−4421.64	−0.166252
$892$	−24541.7	−0.921207
$893$	−18214.9	−0.682575
$894$	−4051.95	−0.151585
$895$	1479.57	0.0552586
$896$	−29961.9	−1.11714
$897$	0	0
$898$	21382.0	0.794573
$899$	−33417.8	−1.23976
$900$	9874.23	0.365712
$901$	−26494.3	−0.979637
$902$	6493.30	0.239693
$903$	−10018.1	−0.369192
$904$	−13554.0	−0.498672
$905$	28744.9	1.05582
$906$	3273.53	0.120039
$907$	36770.6	1.34614	0.673070	−	0.739579i	$-0.264975\pi$
$907$	36770.6	1.34614	0.673070	+	0.739579i	$0.264975\pi$
$908$	22946.6	0.838665
$909$	14914.3	0.544198
$910$	0	0
$911$	10124.6	0.368212	0.184106	−	0.982906i	$-0.441061\pi$
$911$	10124.6	0.368212	0.184106	+	0.982906i	$0.441061\pi$
$912$	758.267	0.0275315
$913$	6026.57	0.218456
$914$	24739.1	0.895291
$915$	6462.85	0.233503
$916$	−8070.12	−0.291096
$917$	16049.7	0.577981
$918$	7484.08	0.269076
$919$	39242.0	1.40857	0.704283	−	0.709919i	$-0.251269\pi$
$919$	39242.0	1.40857	0.704283	+	0.709919i	$0.251269\pi$
$920$	31542.3	1.13034
$921$	−14783.8	−0.528927
$922$	5761.66	0.205803
$923$	0	0
$924$	3357.18	0.119527
$925$	−16529.0	−0.587536
$926$	15498.9	0.550026
$927$	10687.4	0.378663
$928$	49962.3	1.76734
$929$	44260.9	1.56314	0.781569	−	0.623819i	$-0.214420\pi$
$929$	44260.9	1.56314	0.781569	+	0.623819i	$0.214420\pi$
$930$	−6031.28	−0.212660
$931$	−22831.2	−0.803719
$932$	−24166.5	−0.849355
$933$	16742.9	0.587499
$934$	−1548.56	−0.0542511
$935$	−7042.03	−0.246309
$936$	0	0
$937$	−2012.16	−0.0701542	−0.0350771	−	0.999385i	$-0.511168\pi$
$937$	−2012.16	−0.0701542	−0.0350771	+	0.999385i	$0.511168\pi$
$938$	33230.3	1.15673
$939$	−7658.32	−0.266155
$940$	26163.3	0.907823
$941$	−951.484	−0.0329623	−0.0164811	−	0.999864i	$-0.505246\pi$
$941$	−951.484	−0.0329623	−0.0164811	+	0.999864i	$0.505246\pi$
$942$	2152.75	0.0744591
$943$	−36308.2	−1.25383
$944$	4474.56	0.154274
$945$	40998.9	1.41132
$946$	−3144.67	−0.108078
$947$	10913.6	0.374493	0.187246	−	0.982313i	$-0.440044\pi$
$947$	10913.6	0.374493	0.187246	+	0.982313i	$0.440044\pi$
$948$	2013.02	0.0689659
$949$	0	0
$950$	7111.45	0.242869
$951$	14453.5	0.492835
$952$	26974.4	0.918323
$953$	17230.8	0.585688	0.292844	−	0.956160i	$-0.405398\pi$
$953$	17230.8	0.585688	0.292844	+	0.956160i	$0.405398\pi$
$954$	22135.3	0.751213
$955$	−27995.5	−0.948600
$956$	3841.05	0.129946
$957$	−6109.69	−0.206372
$958$	1779.59	0.0600166
$959$	51975.5	1.75013
$960$	7380.00	0.248113
$961$	−14364.0	−0.482159
$962$	0	0
$963$	−26029.8	−0.871027
$964$	−25557.9	−0.853904
$965$	−48234.7	−1.60905
$966$	9446.74	0.314642
$967$	25951.5	0.863025	0.431512	−	0.902107i	$-0.357980\pi$
$967$	25951.5	0.863025	0.431512	+	0.902107i	$0.357980\pi$
$968$	2637.95	0.0875898
$969$	−4896.58	−0.162333
$970$	41111.1	1.36082
$971$	36677.0	1.21218	0.606088	−	0.795398i	$-0.292738\pi$
$971$	36677.0	1.21218	0.606088	+	0.795398i	$0.292738\pi$
$972$	19170.1	0.632594
$973$	42813.0	1.41061
$974$	33154.6	1.09070
$975$	0	0
$976$	1502.25	0.0492684
$977$	−7573.95	−0.248017	−0.124008	−	0.992281i	$-0.539575\pi$
$977$	−7573.95	−0.248017	−0.124008	+	0.992281i	$0.539575\pi$
$978$	1678.59	0.0548827
$979$	−12864.1	−0.419959
$980$	32794.0	1.06895
$981$	38327.2	1.24740
$982$	276.855	0.00899673
$983$	42683.4	1.38493	0.692466	−	0.721450i	$-0.256524\pi$
$983$	42683.4	1.38493	0.692466	+	0.721450i	$0.256524\pi$
$984$	−16234.1	−0.525938
$985$	19928.5	0.644644
$986$	−19610.8	−0.633402
$987$	19614.8	0.632569
$988$	0	0
$989$	17583.9	0.565354
$990$	5883.43	0.188877
$991$	−46026.3	−1.47535	−0.737676	−	0.675155i	$-0.764077\pi$
$991$	−46026.3	−1.47535	−0.737676	+	0.675155i	$0.764077\pi$
$992$	−23064.6	−0.738208
$993$	−19532.7	−0.624222
$994$	−46096.9	−1.47093
$995$	8565.29	0.272902
$996$	−6019.09	−0.191488
$997$	50484.3	1.60367	0.801833	−	0.597548i	$-0.203858\pi$
$997$	50484.3	1.60367	0.801833	+	0.597548i	$0.203858\pi$
$998$	5298.92	0.168071
$999$	−20799.2	−0.658717

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.o.1.15	yes	39
13.12	even	2		1859.4.a.n.1.25	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.n.1.25	✓	39	13.12	even	2
1859.4.a.o.1.15	yes	39	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)

\(f(q)\)	\(=\)	\(q-1.63650 q^{2} -2.06438 q^{3} -5.32187 q^{4} -14.3735 q^{5} +3.37836 q^{6} -27.7797 q^{7} +21.8012 q^{8} -22.7383 q^{9} +O(q^{10})\)	\(q-1.63650 q^{2} -2.06438 q^{3} -5.32187 q^{4} -14.3735 q^{5} +3.37836 q^{6} -27.7797 q^{7} +21.8012 q^{8} -22.7383 q^{9} +23.5223 q^{10} -11.0000 q^{11} +10.9863 q^{12} +45.4616 q^{14} +29.6724 q^{15} +6.89718 q^{16} -44.5391 q^{17} +37.2113 q^{18} -53.2551 q^{19} +76.4940 q^{20} +57.3479 q^{21} +18.0015 q^{22} -100.658 q^{23} -45.0060 q^{24} +81.5982 q^{25} +102.679 q^{27} +147.840 q^{28} -269.052 q^{29} -48.5589 q^{30} +124.206 q^{31} -185.697 q^{32} +22.7082 q^{33} +72.8883 q^{34} +399.293 q^{35} +121.010 q^{36} -202.566 q^{37} +87.1520 q^{38} -313.361 q^{40} +360.709 q^{41} -93.8499 q^{42} -174.690 q^{43} +58.5405 q^{44} +326.830 q^{45} +164.727 q^{46} +342.031 q^{47} -14.2384 q^{48} +428.714 q^{49} -133.536 q^{50} +91.9456 q^{51} +594.854 q^{53} -168.034 q^{54} +158.109 q^{55} -605.633 q^{56} +109.939 q^{57} +440.304 q^{58} +648.751 q^{59} -157.912 q^{60} +217.807 q^{61} -203.262 q^{62} +631.665 q^{63} +248.716 q^{64} -37.1619 q^{66} +730.955 q^{67} +237.031 q^{68} +207.796 q^{69} -653.443 q^{70} -1013.98 q^{71} -495.724 q^{72} -233.315 q^{73} +331.499 q^{74} -168.450 q^{75} +283.417 q^{76} +305.577 q^{77} +183.229 q^{79} -99.1368 q^{80} +401.967 q^{81} -590.300 q^{82} -547.870 q^{83} -305.198 q^{84} +640.184 q^{85} +285.880 q^{86} +555.426 q^{87} -239.814 q^{88} +1169.47 q^{89} -534.858 q^{90} +535.688 q^{92} -256.407 q^{93} -559.735 q^{94} +765.464 q^{95} +383.349 q^{96} +1747.75 q^{97} -701.590 q^{98} +250.122 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 23 q^{3} + 114 q^{4} + 23 q^{5} + 77 q^{6} - 4 q^{7} - 21 q^{8} + 260 q^{9}+O(q^{10}) \) 39 * q - 23 * q^3 + 114 * q^4 + 23 * q^5 + 77 * q^6 - 4 * q^7 - 21 * q^8 + 260 * q^9	\( 39 q - 23 q^{3} + 114 q^{4} + 23 q^{5} + 77 q^{6} - 4 q^{7} - 21 q^{8} + 260 q^{9} - 158 q^{10} - 429 q^{11} - 351 q^{12} - 176 q^{14} + 30 q^{15} + 230 q^{16} - 244 q^{17} + 21 q^{18} - 70 q^{19} + 366 q^{20} - 142 q^{21} - 47 q^{23} + 846 q^{24} + 322 q^{25} - 416 q^{27} + 1131 q^{28} - 838 q^{29} - 293 q^{30} + 507 q^{31} - 1433 q^{32} + 253 q^{33} + 166 q^{34} - 498 q^{35} + 815 q^{36} + 89 q^{37} + 81 q^{38} - 2917 q^{40} + 618 q^{41} - 318 q^{42} - 1064 q^{43} - 1254 q^{44} + 238 q^{45} - 1331 q^{46} + 1499 q^{47} - 1460 q^{48} - 413 q^{49} - 2459 q^{50} - 2350 q^{51} - 2745 q^{53} - 845 q^{54} - 253 q^{55} - 2904 q^{56} + 1450 q^{57} - 2509 q^{58} + 2285 q^{59} - 3566 q^{60} - 6218 q^{61} - 911 q^{62} - 1930 q^{63} + 67 q^{64} - 847 q^{66} + 546 q^{67} - 170 q^{68} - 5254 q^{69} - 2195 q^{70} - 263 q^{71} - 2393 q^{72} - 1148 q^{73} + 775 q^{74} - 5385 q^{75} - 7247 q^{76} + 44 q^{77} - 3666 q^{79} + 5594 q^{80} - 1901 q^{81} - 4414 q^{82} + 2722 q^{83} - 9971 q^{84} + 1858 q^{85} + 2478 q^{86} - 2284 q^{87} + 231 q^{88} + 13 q^{89} - 6771 q^{90} - 2232 q^{92} - 1082 q^{93} - 7330 q^{94} - 2352 q^{95} + 5770 q^{96} - 1197 q^{97} + 6813 q^{98} - 2860 q^{99}+O(q^{100}) \) 39 * q - 23 * q^3 + 114 * q^4 + 23 * q^5 + 77 * q^6 - 4 * q^7 - 21 * q^8 + 260 * q^9 - 158 * q^10 - 429 * q^11 - 351 * q^12 - 176 * q^14 + 30 * q^15 + 230 * q^16 - 244 * q^17 + 21 * q^18 - 70 * q^19 + 366 * q^20 - 142 * q^21 - 47 * q^23 + 846 * q^24 + 322 * q^25 - 416 * q^27 + 1131 * q^28 - 838 * q^29 - 293 * q^30 + 507 * q^31 - 1433 * q^32 + 253 * q^33 + 166 * q^34 - 498 * q^35 + 815 * q^36 + 89 * q^37 + 81 * q^38 - 2917 * q^40 + 618 * q^41 - 318 * q^42 - 1064 * q^43 - 1254 * q^44 + 238 * q^45 - 1331 * q^46 + 1499 * q^47 - 1460 * q^48 - 413 * q^49 - 2459 * q^50 - 2350 * q^51 - 2745 * q^53 - 845 * q^54 - 253 * q^55 - 2904 * q^56 + 1450 * q^57 - 2509 * q^58 + 2285 * q^59 - 3566 * q^60 - 6218 * q^61 - 911 * q^62 - 1930 * q^63 + 67 * q^64 - 847 * q^66 + 546 * q^67 - 170 * q^68 - 5254 * q^69 - 2195 * q^70 - 263 * q^71 - 2393 * q^72 - 1148 * q^73 + 775 * q^74 - 5385 * q^75 - 7247 * q^76 + 44 * q^77 - 3666 * q^79 + 5594 * q^80 - 1901 * q^81 - 4414 * q^82 + 2722 * q^83 - 9971 * q^84 + 1858 * q^85 + 2478 * q^86 - 2284 * q^87 + 231 * q^88 + 13 * q^89 - 6771 * q^90 - 2232 * q^92 - 1082 * q^93 - 7330 * q^94 - 2352 * q^95 + 5770 * q^96 - 1197 * q^97 + 6813 * q^98 - 2860 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more