LMFDB - Embedded newform 1859.4.a.b.1.1

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:	$4$
Coefficient field:	4.4.297133.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 19x^{2} - 2x + 52 $ x^4 - 19x^2 - 2x + 52
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$4.03811$ of defining polynomial
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)

$f(q)$	$=$	$q-4.03811 q^{2} -3.27078 q^{3} +8.30634 q^{4} +16.3826 q^{5} +13.2078 q^{6} +1.85898 q^{7} -1.23702 q^{8} -16.3020 q^{9} +O(q^{10})$	\(q-4.03811 q^{2} -3.27078 q^{3} +8.30634 q^{4} +16.3826 q^{5} +13.2078 q^{6} +1.85898 q^{7} -1.23702 q^{8} -16.3020 q^{9} -66.1546 q^{10} +11.0000 q^{11} -27.1682 q^{12} -7.50677 q^{14} -53.5838 q^{15} -61.4555 q^{16} +7.54352 q^{17} +65.8292 q^{18} -9.26432 q^{19} +136.079 q^{20} -6.08032 q^{21} -44.4192 q^{22} -45.7988 q^{23} +4.04603 q^{24} +143.388 q^{25} +141.631 q^{27} +15.4413 q^{28} +116.106 q^{29} +216.377 q^{30} +233.181 q^{31} +258.060 q^{32} -35.9786 q^{33} -30.4616 q^{34} +30.4549 q^{35} -135.410 q^{36} +20.9457 q^{37} +37.4103 q^{38} -20.2656 q^{40} -248.144 q^{41} +24.5530 q^{42} -375.029 q^{43} +91.3697 q^{44} -267.068 q^{45} +184.941 q^{46} -481.865 q^{47} +201.007 q^{48} -339.544 q^{49} -579.017 q^{50} -24.6732 q^{51} -28.2350 q^{53} -571.923 q^{54} +180.208 q^{55} -2.29960 q^{56} +30.3016 q^{57} -468.849 q^{58} +187.126 q^{59} -445.085 q^{60} -310.893 q^{61} -941.610 q^{62} -30.3051 q^{63} -550.432 q^{64} +145.286 q^{66} -97.2371 q^{67} +62.6591 q^{68} +149.798 q^{69} -122.980 q^{70} +407.302 q^{71} +20.1659 q^{72} +1040.38 q^{73} -84.5811 q^{74} -468.992 q^{75} -76.9525 q^{76} +20.4488 q^{77} -626.344 q^{79} -1006.80 q^{80} -23.0916 q^{81} +1002.03 q^{82} -528.688 q^{83} -50.5052 q^{84} +123.582 q^{85} +1514.41 q^{86} -379.757 q^{87} -13.6072 q^{88} -1088.06 q^{89} +1078.45 q^{90} -380.420 q^{92} -762.683 q^{93} +1945.83 q^{94} -151.773 q^{95} -844.058 q^{96} -38.2951 q^{97} +1371.12 q^{98} -179.322 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 6 q^{4} + 6 q^{5} + 13 q^{6} + 17 q^{7} - 6 q^{8} - 44 q^{9}+O(q^{10}) $ 4 * q - 4 * q^3 + 6 * q^4 + 6 * q^5 + 13 * q^6 + 17 * q^7 - 6 * q^8 - 44 * q^9	\( 4 q - 4 q^{3} + 6 q^{4} + 6 q^{5} + 13 q^{6} + 17 q^{7} - 6 q^{8} - 44 q^{9} - 82 q^{10} + 44 q^{11} + 17 q^{12} - 40 q^{14} - 9 q^{15} - 142 q^{16} - 41 q^{17} + 75 q^{18} + 41 q^{19} + 174 q^{20} + 179 q^{21} - 136 q^{23} + 171 q^{24} - 162 q^{25} + 11 q^{27} + 56 q^{28} - 207 q^{29} + 305 q^{30} + 348 q^{31} + 2 q^{32} - 44 q^{33} - 197 q^{34} + 136 q^{35} - 153 q^{36} + 333 q^{37} - 110 q^{38} + 142 q^{40} + 198 q^{41} + 317 q^{42} - 252 q^{43} + 66 q^{44} - 303 q^{45} - 345 q^{46} - 561 q^{47} + q^{48} - 431 q^{49} - 958 q^{50} + 375 q^{51} + 343 q^{53} - 803 q^{54} + 66 q^{55} + 888 q^{56} - 797 q^{57} - 753 q^{58} + 541 q^{59} - 669 q^{60} - 801 q^{61} + 50 q^{62} - 895 q^{63} - 214 q^{64} + 143 q^{66} + 863 q^{67} + 221 q^{68} - 238 q^{69} + 184 q^{70} - 781 q^{71} - 711 q^{72} + 1306 q^{73} + 1347 q^{74} - 779 q^{75} - 1160 q^{76} + 187 q^{77} - 278 q^{79} - 874 q^{80} - 596 q^{81} + 1675 q^{82} - 437 q^{83} - 439 q^{84} + 615 q^{85} - 234 q^{86} - 818 q^{87} - 66 q^{88} - 2552 q^{89} + 899 q^{90} - 1391 q^{92} + 876 q^{93} - 415 q^{94} - 940 q^{95} - 3077 q^{96} + 2504 q^{97} + 144 q^{98} - 484 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 + 6 * q^4 + 6 * q^5 + 13 * q^6 + 17 * q^7 - 6 * q^8 - 44 * q^9 - 82 * q^10 + 44 * q^11 + 17 * q^12 - 40 * q^14 - 9 * q^15 - 142 * q^16 - 41 * q^17 + 75 * q^18 + 41 * q^19 + 174 * q^20 + 179 * q^21 - 136 * q^23 + 171 * q^24 - 162 * q^25 + 11 * q^27 + 56 * q^28 - 207 * q^29 + 305 * q^30 + 348 * q^31 + 2 * q^32 - 44 * q^33 - 197 * q^34 + 136 * q^35 - 153 * q^36 + 333 * q^37 - 110 * q^38 + 142 * q^40 + 198 * q^41 + 317 * q^42 - 252 * q^43 + 66 * q^44 - 303 * q^45 - 345 * q^46 - 561 * q^47 + q^48 - 431 * q^49 - 958 * q^50 + 375 * q^51 + 343 * q^53 - 803 * q^54 + 66 * q^55 + 888 * q^56 - 797 * q^57 - 753 * q^58 + 541 * q^59 - 669 * q^60 - 801 * q^61 + 50 * q^62 - 895 * q^63 - 214 * q^64 + 143 * q^66 + 863 * q^67 + 221 * q^68 - 238 * q^69 + 184 * q^70 - 781 * q^71 - 711 * q^72 + 1306 * q^73 + 1347 * q^74 - 779 * q^75 - 1160 * q^76 + 187 * q^77 - 278 * q^79 - 874 * q^80 - 596 * q^81 + 1675 * q^82 - 437 * q^83 - 439 * q^84 + 615 * q^85 - 234 * q^86 - 818 * q^87 - 66 * q^88 - 2552 * q^89 + 899 * q^90 - 1391 * q^92 + 876 * q^93 - 415 * q^94 - 940 * q^95 - 3077 * q^96 + 2504 * q^97 + 144 * q^98 - 484 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−4.03811	−1.42769	−0.713844	−	0.700305i	$-0.753047\pi$
$2$	−4.03811	−1.42769	−0.713844	+	0.700305i	$0.753047\pi$
$3$	−3.27078	−0.629462	−0.314731	−	0.949181i	$-0.601914\pi$
$3$	−3.27078	−0.629462	−0.314731	+	0.949181i	$0.601914\pi$
$4$	8.30634	1.03829
$5$	16.3826	1.46530	0.732650	−	0.680605i	$-0.238283\pi$
$5$	16.3826	1.46530	0.732650	+	0.680605i	$0.238283\pi$
$6$	13.2078	0.898676
$7$	1.85898	0.100376	0.0501878	−	0.998740i	$-0.484018\pi$
$7$	1.85898	0.100376	0.0501878	+	0.998740i	$0.484018\pi$
$8$	−1.23702	−0.0546692
$9$	−16.3020	−0.603777
$10$	−66.1546	−2.09199
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−27.1682	−0.653566
$13$	0	0
$13$	0	0
$14$	−7.50677	−0.143305
$15$	−53.5838	−0.922351
$16$	−61.4555	−0.960242
$17$	7.54352	0.107622	0.0538110	−	0.998551i	$-0.482863\pi$
$17$	7.54352	0.107622	0.0538110	+	0.998551i	$0.482863\pi$
$18$	65.8292	0.862005
$19$	−9.26432	−0.111862	−0.0559310	−	0.998435i	$-0.517813\pi$
$19$	−9.26432	−0.111862	−0.0559310	+	0.998435i	$0.517813\pi$
$20$	136.079	1.52141
$21$	−6.08032	−0.0631826
$22$	−44.4192	−0.430464
$23$	−45.7988	−0.415205	−0.207602	−	0.978213i	$-0.566566\pi$
$23$	−45.7988	−0.415205	−0.207602	+	0.978213i	$0.566566\pi$
$24$	4.04603	0.0344122
$25$	143.388	1.14711
$26$	0	0
$27$	141.631	1.00952
$28$	15.4413	0.104219
$29$	116.106	0.743460	0.371730	−	0.928341i	$-0.378765\pi$
$29$	116.106	0.743460	0.371730	+	0.928341i	$0.378765\pi$
$30$	216.377	1.31683
$31$	233.181	1.35098	0.675492	−	0.737367i	$-0.263931\pi$
$31$	233.181	1.35098	0.675492	+	0.737367i	$0.263931\pi$
$32$	258.060	1.42559
$33$	−35.9786	−0.189790
$34$	−30.4616	−0.153651
$35$	30.4549	0.147080
$36$	−135.410	−0.626897
$37$	20.9457	0.0930663	0.0465332	−	0.998917i	$-0.485183\pi$
$37$	20.9457	0.0930663	0.0465332	+	0.998917i	$0.485183\pi$
$38$	37.4103	0.159704
$39$	0	0
$40$	−20.2656	−0.0801068
$41$	−248.144	−0.945208	−0.472604	−	0.881275i	$-0.656686\pi$
$41$	−248.144	−0.945208	−0.472604	+	0.881275i	$0.656686\pi$
$42$	24.5530	0.0902050
$43$	−375.029	−1.33003	−0.665016	−	0.746829i	$-0.731575\pi$
$43$	−375.029	−1.33003	−0.665016	+	0.746829i	$0.731575\pi$
$44$	91.3697	0.313057
$45$	−267.068	−0.884715
$46$	184.941	0.592783
$47$	−481.865	−1.49547	−0.747737	−	0.663995i	$-0.768860\pi$
$47$	−481.865	−1.49547	−0.747737	+	0.663995i	$0.768860\pi$
$48$	201.007	0.604436
$49$	−339.544	−0.989925
$50$	−579.017	−1.63771
$51$	−24.6732	−0.0677440
$52$	0	0
$53$	−28.2350	−0.0731768	−0.0365884	−	0.999330i	$-0.511649\pi$
$53$	−28.2350	−0.0731768	−0.0365884	+	0.999330i	$0.511649\pi$
$54$	−571.923	−1.44128
$55$	180.208	0.441805
$56$	−2.29960	−0.00548745
$57$	30.3016	0.0704130
$58$	−468.849	−1.06143
$59$	187.126	0.412911	0.206456	−	0.978456i	$-0.433807\pi$
$59$	187.126	0.412911	0.206456	+	0.978456i	$0.433807\pi$
$60$	−445.085	−0.957670
$61$	−310.893	−0.652554	−0.326277	−	0.945274i	$-0.605794\pi$
$61$	−310.893	−0.652554	−0.326277	+	0.945274i	$0.605794\pi$
$62$	−941.610	−1.92878
$63$	−30.3051	−0.0606045
$64$	−550.432	−1.07506
$65$	0	0
$66$	145.286	0.270961
$67$	−97.2371	−0.177305	−0.0886523	−	0.996063i	$-0.528256\pi$
$67$	−97.2371	−0.177305	−0.0886523	+	0.996063i	$0.528256\pi$
$68$	62.6591	0.111743
$69$	149.798	0.261356
$70$	−122.980	−0.209985
$71$	407.302	0.680815	0.340407	−	0.940278i	$-0.389435\pi$
$71$	407.302	0.680815	0.340407	+	0.940278i	$0.389435\pi$
$72$	20.1659	0.0330080
$73$	1040.38	1.66804	0.834019	−	0.551735i	$-0.186034\pi$
$73$	1040.38	1.66804	0.834019	+	0.551735i	$0.186034\pi$
$74$	−84.5811	−0.132870
$75$	−468.992	−0.722060
$76$	−76.9525	−0.116146
$77$	20.4488	0.0302644
$78$	0	0
$79$	−626.344	−0.892015	−0.446008	−	0.895029i	$-0.647155\pi$
$79$	−626.344	−0.892015	−0.446008	+	0.895029i	$0.647155\pi$
$80$	−1006.80	−1.40704
$81$	−23.0916	−0.0316758
$82$	1002.03	1.34946
$83$	−528.688	−0.699169	−0.349585	−	0.936905i	$-0.613677\pi$
$83$	−528.688	−0.699169	−0.349585	+	0.936905i	$0.613677\pi$
$84$	−50.5052	−0.0656020
$85$	123.582	0.157699
$86$	1514.41	1.89887
$87$	−379.757	−0.467980
$88$	−13.6072	−0.0164834
$89$	−1088.06	−1.29589	−0.647943	−	0.761689i	$-0.724370\pi$
$89$	−1088.06	−1.29589	−0.647943	+	0.761689i	$0.724370\pi$
$90$	1078.45	1.26310
$91$	0	0
$92$	−380.420	−0.431104
$93$	−762.683	−0.850393
$94$	1945.83	2.13507
$95$	−151.773	−0.163912
$96$	−844.058	−0.897358
$97$	−38.2951	−0.0400853	−0.0200427	−	0.999799i	$-0.506380\pi$
$97$	−38.2951	−0.0400853	−0.0200427	+	0.999799i	$0.506380\pi$
$98$	1371.12	1.41330
$99$	−179.322	−0.182046
$100$	1191.03	1.19103
$101$	−937.027	−0.923145	−0.461573	−	0.887102i	$-0.652715\pi$
$101$	−937.027	−0.923145	−0.461573	+	0.887102i	$0.652715\pi$
$102$	99.6332	0.0967172
$103$	1746.55	1.67080	0.835402	−	0.549639i	$-0.185235\pi$
$103$	1746.55	1.67080	0.835402	+	0.549639i	$0.185235\pi$
$104$	0	0
$105$	−99.6112	−0.0925815
$106$	114.016	0.104474
$107$	−438.872	−0.396517	−0.198259	−	0.980150i	$-0.563529\pi$
$107$	−438.872	−0.396517	−0.198259	+	0.980150i	$0.563529\pi$
$108$	1176.44	1.04817
$109$	539.093	0.473723	0.236861	−	0.971543i	$-0.423881\pi$
$109$	539.093	0.473723	0.236861	+	0.971543i	$0.423881\pi$
$110$	−727.700	−0.630759
$111$	−68.5089	−0.0585817
$112$	−114.245	−0.0963847
$113$	−1769.43	−1.47304	−0.736522	−	0.676414i	$-0.763533\pi$
$113$	−1769.43	−1.47304	−0.736522	+	0.676414i	$0.763533\pi$
$114$	−122.361	−0.100528
$115$	−750.302	−0.608400
$116$	964.416	0.771929
$117$	0	0
$118$	−755.637	−0.589509
$119$	14.0233	0.0108026
$120$	66.2843	0.0504242
$121$	121.000	0.0909091
$122$	1255.42	0.931644
$123$	811.624	0.594973
$124$	1936.88	1.40272
$125$	301.246	0.215554
$126$	122.375	0.0865242
$127$	−710.173	−0.496202	−0.248101	−	0.968734i	$-0.579806\pi$
$127$	−710.173	−0.496202	−0.248101	+	0.968734i	$0.579806\pi$
$128$	158.223	0.109258
$129$	1226.64	0.837205
$130$	0	0
$131$	−1361.63	−0.908140	−0.454070	−	0.890966i	$-0.650028\pi$
$131$	−1361.63	−0.908140	−0.454070	+	0.890966i	$0.650028\pi$
$132$	−298.850	−0.197057
$133$	−17.2222	−0.0112282
$134$	392.654	0.253136
$135$	2320.28	1.47925
$136$	−9.33151	−0.00588360
$137$	2143.68	1.33684	0.668421	−	0.743784i	$-0.266971\pi$
$137$	2143.68	1.33684	0.668421	+	0.743784i	$0.266971\pi$
$138$	−604.901	−0.373134
$139$	681.558	0.415892	0.207946	−	0.978140i	$-0.433322\pi$
$139$	681.558	0.415892	0.207946	+	0.978140i	$0.433322\pi$
$140$	252.968	0.152712
$141$	1576.08	0.941345
$142$	−1644.73	−0.971991
$143$	0	0
$144$	1001.85	0.579772
$145$	1902.11	1.08939
$146$	−4201.15	−2.38144
$147$	1110.57	0.623120
$148$	173.982	0.0966300
$149$	496.644	0.273065	0.136532	−	0.990636i	$-0.456404\pi$
$149$	496.644	0.273065	0.136532	+	0.990636i	$0.456404\pi$
$150$	1893.84	1.03088
$151$	1542.12	0.831098	0.415549	−	0.909571i	$-0.363590\pi$
$151$	1542.12	0.831098	0.415549	+	0.909571i	$0.363590\pi$
$152$	11.4602	0.00611541
$153$	−122.974	−0.0649797
$154$	−82.5745	−0.0432080
$155$	3820.10	1.97960
$156$	0	0
$157$	−3199.82	−1.62658	−0.813292	−	0.581856i	$-0.802327\pi$
$157$	−3199.82	−1.62658	−0.813292	+	0.581856i	$0.802327\pi$
$158$	2529.25	1.27352
$159$	92.3504	0.0460621
$160$	4227.69	2.08892
$161$	−85.1391	−0.0416764
$162$	93.2465	0.0452231
$163$	−4046.54	−1.94447	−0.972237	−	0.233997i	$-0.924819\pi$
$163$	−4046.54	−1.94447	−0.972237	+	0.233997i	$0.924819\pi$
$164$	−2061.16	−0.981402
$165$	−589.422	−0.278099
$166$	2134.90	0.998195
$167$	2465.29	1.14234	0.571168	−	0.820833i	$-0.306490\pi$
$167$	2465.29	1.14234	0.571168	+	0.820833i	$0.306490\pi$
$168$	7.52149	0.00345414
$169$	0	0
$170$	−499.039	−0.225144
$171$	151.027	0.0675398
$172$	−3115.12	−1.38096
$173$	4349.75	1.91159	0.955797	−	0.294028i	$-0.0949960\pi$
$173$	4349.75	1.91159	0.955797	+	0.294028i	$0.0949960\pi$
$174$	1533.50	0.668129
$175$	266.556	0.115141
$176$	−676.010	−0.289524
$177$	−612.049	−0.259912
$178$	4393.69	1.85012
$179$	3357.75	1.40207	0.701034	−	0.713128i	$-0.252722\pi$
$179$	3357.75	1.40207	0.701034	+	0.713128i	$0.252722\pi$
$180$	−2218.36	−0.918593
$181$	1063.72	0.436826	0.218413	−	0.975856i	$-0.429912\pi$
$181$	1063.72	0.436826	0.218413	+	0.975856i	$0.429912\pi$
$182$	0	0
$183$	1016.86	0.410758
$184$	56.6541	0.0226989
$185$	343.144	0.136370
$186$	3079.80	1.21410
$187$	82.9788	0.0324492
$188$	−4002.54	−1.55274
$189$	263.290	0.101331
$190$	612.877	0.234015
$191$	−40.4465	−0.0153226	−0.00766128	−	0.999971i	$-0.502439\pi$
$191$	−40.4465	−0.0153226	−0.00766128	+	0.999971i	$0.502439\pi$
$192$	1800.34	0.676711
$193$	4868.07	1.81560	0.907801	−	0.419400i	$-0.137760\pi$
$193$	4868.07	1.81560	0.907801	+	0.419400i	$0.137760\pi$
$194$	154.640	0.0572293
$195$	0	0
$196$	−2820.37	−1.02783
$197$	−1019.61	−0.368754	−0.184377	−	0.982856i	$-0.559027\pi$
$197$	−1019.61	−0.368754	−0.184377	+	0.982856i	$0.559027\pi$
$198$	724.121	0.259904
$199$	2855.51	1.01720	0.508598	−	0.861004i	$-0.330164\pi$
$199$	2855.51	1.01720	0.508598	+	0.861004i	$0.330164\pi$
$200$	−177.374	−0.0627113
$201$	318.041	0.111607
$202$	3783.82	1.31796
$203$	215.839	0.0746252
$204$	−204.944	−0.0703380
$205$	−4065.23	−1.38501
$206$	−7052.77	−2.38539
$207$	746.612	0.250691
$208$	0	0
$209$	−101.907	−0.0337277
$210$	402.241	0.132177
$211$	−200.577	−0.0654422	−0.0327211	−	0.999465i	$-0.510417\pi$
$211$	−200.577	−0.0654422	−0.0327211	+	0.999465i	$0.510417\pi$
$212$	−234.529	−0.0759789
$213$	−1332.20	−0.428547
$214$	1772.21	0.566103
$215$	−6143.94	−1.94890
$216$	−175.201	−0.0551895
$217$	433.478	0.135606
$218$	−2176.92	−0.676328
$219$	−3402.84	−1.04997
$220$	1496.87	0.458722
$221$	0	0
$222$	276.646	0.0836364
$223$	−2581.40	−0.775173	−0.387587	−	0.921833i	$-0.626691\pi$
$223$	−2581.40	−0.775173	−0.387587	+	0.921833i	$0.626691\pi$
$224$	479.729	0.143095
$225$	−2337.51	−0.692596
$226$	7145.15	2.10305
$227$	−5177.66	−1.51389	−0.756946	−	0.653477i	$-0.773310\pi$
$227$	−5177.66	−1.51389	−0.756946	+	0.653477i	$0.773310\pi$
$228$	251.695	0.0731092
$229$	−790.863	−0.228217	−0.114109	−	0.993468i	$-0.536401\pi$
$229$	−790.863	−0.228217	−0.114109	+	0.993468i	$0.536401\pi$
$230$	3029.80	0.868605
$231$	−66.8835	−0.0190503
$232$	−143.626	−0.0406443
$233$	−4339.73	−1.22019	−0.610097	−	0.792326i	$-0.708870\pi$
$233$	−4339.73	−1.22019	−0.610097	+	0.792326i	$0.708870\pi$
$234$	0	0
$235$	−7894.19	−2.19132
$236$	1554.33	0.428723
$237$	2048.64	0.561490
$238$	−56.6275	−0.0154228
$239$	−5359.99	−1.45067	−0.725333	−	0.688399i	$-0.758314\pi$
$239$	−5359.99	−1.45067	−0.725333	+	0.688399i	$0.758314\pi$
$240$	3293.02	0.885680
$241$	−5191.20	−1.38753	−0.693765	−	0.720202i	$-0.744049\pi$
$241$	−5191.20	−1.38753	−0.693765	+	0.720202i	$0.744049\pi$
$242$	−488.611	−0.129790
$243$	−3748.52	−0.989579
$244$	−2582.38	−0.677542
$245$	−5562.60	−1.45054
$246$	−3277.43	−0.849435
$247$	0	0
$248$	−288.450	−0.0738571
$249$	1729.22	0.440101
$250$	−1216.46	−0.307744
$251$	2885.35	0.725584	0.362792	−	0.931870i	$-0.381824\pi$
$251$	2885.35	0.725584	0.362792	+	0.931870i	$0.381824\pi$
$252$	−251.724	−0.0629251
$253$	−503.787	−0.125189
$254$	2867.76	0.708421
$255$	−404.211	−0.0992653
$256$	3764.53	0.919075
$257$	−614.295	−0.149100	−0.0745499	−	0.997217i	$-0.523752\pi$
$257$	−614.295	−0.149100	−0.0745499	+	0.997217i	$0.523752\pi$
$258$	−4953.30	−1.19527
$259$	38.9377	0.00934158
$260$	0	0
$261$	−1892.76	−0.448884
$262$	5498.42	1.29654
$263$	5611.59	1.31569	0.657844	−	0.753155i	$-0.271469\pi$
$263$	5611.59	1.31569	0.657844	+	0.753155i	$0.271469\pi$
$264$	44.5063	0.0103757
$265$	−462.561	−0.107226
$266$	69.5451	0.0160304
$267$	3558.80	0.815711
$268$	−807.684	−0.184094
$269$	822.550	0.186438	0.0932188	−	0.995646i	$-0.470284\pi$
$269$	822.550	0.186438	0.0932188	+	0.995646i	$0.470284\pi$
$270$	−9369.56	−2.11190
$271$	3537.69	0.792986	0.396493	−	0.918038i	$-0.370227\pi$
$271$	3537.69	0.792986	0.396493	+	0.918038i	$0.370227\pi$
$272$	−463.591	−0.103343
$273$	0	0
$274$	−8656.43	−1.90859
$275$	1577.27	0.345865
$276$	1244.27	0.271364
$277$	2847.74	0.617704	0.308852	−	0.951110i	$-0.400055\pi$
$277$	2847.74	0.617704	0.308852	+	0.951110i	$0.400055\pi$
$278$	−2752.21	−0.593764
$279$	−3801.31	−0.815693
$280$	−37.6733	−0.00804076
$281$	−1435.53	−0.304756	−0.152378	−	0.988322i	$-0.548693\pi$
$281$	−1435.53	−0.304756	−0.152378	+	0.988322i	$0.548693\pi$
$282$	−6364.37	−1.34395
$283$	6403.92	1.34514	0.672568	−	0.740036i	$-0.265191\pi$
$283$	6403.92	1.34514	0.672568	+	0.740036i	$0.265191\pi$
$284$	3383.19	0.706885
$285$	496.417	0.103176
$286$	0	0
$287$	−461.294	−0.0948757
$288$	−4206.89	−0.860741
$289$	−4856.10	−0.988418
$290$	−7680.94	−1.55531
$291$	125.255	0.0252322
$292$	8641.71	1.73191
$293$	−5540.09	−1.10463	−0.552313	−	0.833637i	$-0.686255\pi$
$293$	−5540.09	−1.10463	−0.552313	+	0.833637i	$0.686255\pi$
$294$	−4484.62	−0.889621
$295$	3065.61	0.605039
$296$	−25.9103	−0.00508786
$297$	1557.94	0.304381
$298$	−2005.50	−0.389851
$299$	0	0
$300$	−3895.60	−0.749709
$301$	−697.172	−0.133503
$302$	−6227.24	−1.18655
$303$	3064.81	0.581085
$304$	569.343	0.107415
$305$	−5093.23	−0.956188
$306$	496.584	0.0927707
$307$	6147.58	1.14287	0.571435	−	0.820647i	$-0.306387\pi$
$307$	6147.58	1.14287	0.571435	+	0.820647i	$0.306387\pi$
$308$	169.855	0.0314232
$309$	−5712.59	−1.05171
$310$	−15426.0	−2.82625
$311$	−8260.58	−1.50616	−0.753078	−	0.657932i	$-0.771432\pi$
$311$	−8260.58	−1.50616	−0.753078	+	0.657932i	$0.771432\pi$
$312$	0	0
$313$	−9265.62	−1.67324	−0.836619	−	0.547785i	$-0.815471\pi$
$313$	−9265.62	−1.67324	−0.836619	+	0.547785i	$0.815471\pi$
$314$	12921.2	2.32225
$315$	−496.475	−0.0888037
$316$	−5202.63	−0.926173
$317$	4553.94	0.806861	0.403431	−	0.915010i	$-0.367818\pi$
$317$	4553.94	0.806861	0.403431	+	0.915010i	$0.367818\pi$
$318$	−372.921	−0.0657622
$319$	1277.17	0.224162
$320$	−9017.48	−1.57529
$321$	1435.45	0.249593
$322$	343.801	0.0595009
$323$	−69.8856	−0.0120388
$324$	−191.807	−0.0328887
$325$	0	0
$326$	16340.4	2.77610
$327$	−1763.26	−0.298191
$328$	306.959	0.0516737
$329$	−895.778	−0.150109
$330$	2380.15	0.397039
$331$	−255.838	−0.0424838	−0.0212419	−	0.999774i	$-0.506762\pi$
$331$	−255.838	−0.0424838	−0.0212419	+	0.999774i	$0.506762\pi$
$332$	−4391.46	−0.725942
$333$	−341.457	−0.0561913
$334$	−9955.13	−1.63090
$335$	−1592.99	−0.259805
$336$	373.669	0.0606706
$337$	−8161.42	−1.31923	−0.659615	−	0.751603i	$-0.729281\pi$
$337$	−8161.42	−1.31923	−0.659615	+	0.751603i	$0.729281\pi$
$338$	0	0
$339$	5787.42	0.927226
$340$	1026.52	0.163737
$341$	2564.99	0.407337
$342$	−609.863	−0.0964257
$343$	−1268.84	−0.199740
$344$	463.919	0.0727118
$345$	2454.07	0.382965
$346$	−17564.8	−2.72916
$347$	−7294.88	−1.12856	−0.564279	−	0.825584i	$-0.690846\pi$
$347$	−7294.88	−1.12856	−0.564279	+	0.825584i	$0.690846\pi$
$348$	−3154.39	−0.485900
$349$	−3837.24	−0.588547	−0.294274	−	0.955721i	$-0.595078\pi$
$349$	−3837.24	−0.588547	−0.294274	+	0.955721i	$0.595078\pi$
$350$	−1076.38	−0.164386
$351$	0	0
$352$	2838.66	0.429833
$353$	358.484	0.0540515	0.0270257	−	0.999635i	$-0.491396\pi$
$353$	358.484	0.0540515	0.0270257	+	0.999635i	$0.491396\pi$
$354$	2471.52	0.371073
$355$	6672.65	0.997598
$356$	−9037.76	−1.34551
$357$	−45.8670	−0.00679984
$358$	−13559.0	−2.00171
$359$	−3034.07	−0.446051	−0.223026	−	0.974813i	$-0.571593\pi$
$359$	−3034.07	−0.446051	−0.223026	+	0.974813i	$0.571593\pi$
$360$	330.369	0.0483666
$361$	−6773.17	−0.987487
$362$	−4295.41	−0.623652
$363$	−395.765	−0.0572238
$364$	0	0
$365$	17044.0	2.44418
$366$	−4106.21	−0.586435
$367$	−9505.57	−1.35201	−0.676004	−	0.736898i	$-0.736290\pi$
$367$	−9505.57	−1.35201	−0.676004	+	0.736898i	$0.736290\pi$
$368$	2814.59	0.398697
$369$	4045.23	0.570695
$370$	−1385.66	−0.194694
$371$	−52.4883	−0.00734516
$372$	−6335.10	−0.882957
$373$	−577.135	−0.0801151	−0.0400575	−	0.999197i	$-0.512754\pi$
$373$	−577.135	−0.0801151	−0.0400575	+	0.999197i	$0.512754\pi$
$374$	−335.077	−0.0463274
$375$	−985.309	−0.135683
$376$	596.078	0.0817563
$377$	0	0
$378$	−1063.19	−0.144669
$379$	6416.36	0.869620	0.434810	−	0.900522i	$-0.356815\pi$
$379$	6416.36	0.869620	0.434810	+	0.900522i	$0.356815\pi$
$380$	−1260.68	−0.170188
$381$	2322.82	0.312340
$382$	163.328	0.0218758
$383$	1893.70	0.252646	0.126323	−	0.991989i	$-0.459682\pi$
$383$	1893.70	0.252646	0.126323	+	0.991989i	$0.459682\pi$
$384$	−517.512	−0.0687739
$385$	335.003	0.0443464
$386$	−19657.8	−2.59211
$387$	6113.72	0.803043
$388$	−318.092	−0.0416203
$389$	−8781.50	−1.14458	−0.572288	−	0.820053i	$-0.693944\pi$
$389$	−8781.50	−1.14458	−0.572288	+	0.820053i	$0.693944\pi$
$390$	0	0
$391$	−345.484	−0.0446852
$392$	420.024	0.0541184
$393$	4453.60	0.571640
$394$	4117.31	0.526465
$395$	−10261.1	−1.30707
$396$	−1489.51	−0.189017
$397$	105.396	0.0133241	0.00666203	−	0.999978i	$-0.497879\pi$
$397$	105.396	0.0133241	0.00666203	+	0.999978i	$0.497879\pi$
$398$	−11530.9	−1.45224
$399$	56.3300	0.00706774
$400$	−8811.99	−1.10150
$401$	4945.96	0.615934	0.307967	−	0.951397i	$-0.400351\pi$
$401$	4945.96	0.615934	0.307967	+	0.951397i	$0.400351\pi$
$402$	−1284.29	−0.159339
$403$	0	0
$404$	−7783.26	−0.958495
$405$	−378.300	−0.0464145
$406$	−871.581	−0.106541
$407$	230.403	0.0280606
$408$	30.5213	0.00370351
$409$	629.086	0.0760545	0.0380272	−	0.999277i	$-0.487893\pi$
$409$	629.086	0.0760545	0.0380272	+	0.999277i	$0.487893\pi$
$410$	16415.8	1.97737
$411$	−7011.52	−0.841491
$412$	14507.4	1.73478
$413$	347.864	0.0414462
$414$	−3014.90	−0.357909
$415$	−8661.26	−1.02449
$416$	0	0
$417$	−2229.23	−0.261788
$418$	411.514	0.0481526
$419$	−8803.86	−1.02648	−0.513242	−	0.858244i	$-0.671556\pi$
$419$	−8803.86	−1.02648	−0.513242	+	0.858244i	$0.671556\pi$
$420$	−827.404	−0.0961266
$421$	−12008.0	−1.39011	−0.695054	−	0.718958i	$-0.744619\pi$
$421$	−12008.0	−1.39011	−0.695054	+	0.718958i	$0.744619\pi$
$422$	809.952	0.0934310
$423$	7855.36	0.902933
$424$	34.9273	0.00400052
$425$	1081.65	0.123454
$426$	5379.55	0.611832
$427$	−577.945	−0.0655005
$428$	−3645.42	−0.411701
$429$	0	0
$430$	24809.9	2.78242
$431$	9684.95	1.08238	0.541192	−	0.840899i	$-0.317973\pi$
$431$	9684.95	1.08238	0.541192	+	0.840899i	$0.317973\pi$
$432$	−8704.02	−0.969380
$433$	−11452.0	−1.27101	−0.635503	−	0.772098i	$-0.719207\pi$
$433$	−11452.0	−1.27101	−0.635503	+	0.772098i	$0.719207\pi$
$434$	−1750.43	−0.193603
$435$	−6221.40	−0.685731
$436$	4477.89	0.491863
$437$	424.295	0.0464457
$438$	13741.1	1.49903
$439$	−41.4665	−0.00450817	−0.00225409	−	0.999997i	$-0.500717\pi$
$439$	−41.4665	−0.00450817	−0.00225409	+	0.999997i	$0.500717\pi$
$440$	−222.921	−0.0241531
$441$	5535.24	0.597694
$442$	0	0
$443$	9297.53	0.997153	0.498577	−	0.866846i	$-0.333856\pi$
$443$	9297.53	0.997153	0.498577	+	0.866846i	$0.333856\pi$
$444$	−569.058	−0.0608250
$445$	−17825.2	−1.89886
$446$	10424.0	1.10671
$447$	−1624.41	−0.171884
$448$	−1023.24	−0.107910
$449$	−6117.63	−0.643004	−0.321502	−	0.946909i	$-0.604188\pi$
$449$	−6117.63	−0.643004	−0.321502	+	0.946909i	$0.604188\pi$
$450$	9439.13	0.988811
$451$	−2729.58	−0.284991
$452$	−14697.5	−1.52945
$453$	−5043.93	−0.523145
$454$	20908.0	2.16137
$455$	0	0
$456$	−37.4837	−0.00384942
$457$	2714.98	0.277903	0.138951	−	0.990299i	$-0.455627\pi$
$457$	2714.98	0.277903	0.138951	+	0.990299i	$0.455627\pi$
$458$	3193.59	0.325823
$459$	1068.40	0.108646
$460$	−6232.26	−0.631697
$461$	5447.36	0.550344	0.275172	−	0.961395i	$-0.411265\pi$
$461$	5447.36	0.550344	0.275172	+	0.961395i	$0.411265\pi$
$462$	270.083	0.0271978
$463$	−4992.41	−0.501117	−0.250558	−	0.968101i	$-0.580614\pi$
$463$	−4992.41	−0.501117	−0.250558	+	0.968101i	$0.580614\pi$
$464$	−7135.35	−0.713901
$465$	−12494.7	−1.24608
$466$	17524.3	1.74206
$467$	911.269	0.0902966	0.0451483	−	0.998980i	$-0.485624\pi$
$467$	911.269	0.0902966	0.0451483	+	0.998980i	$0.485624\pi$
$468$	0	0
$469$	−180.762	−0.0177970
$470$	31877.6	3.12852
$471$	10465.9	1.02387
$472$	−231.479	−0.0225735
$473$	−4125.32	−0.401020
$474$	−8272.61	−0.801632
$475$	−1328.39	−0.128318
$476$	116.482	0.0112163
$477$	460.286	0.0441825
$478$	21644.2	2.07110
$479$	14540.6	1.38700	0.693502	−	0.720455i	$-0.256067\pi$
$479$	14540.6	1.38700	0.693502	+	0.720455i	$0.256067\pi$
$480$	−13827.8	−1.31490
$481$	0	0
$482$	20962.6	1.98096
$483$	278.471	0.0262337
$484$	1005.07	0.0943902
$485$	−627.372	−0.0587371
$486$	15136.9	1.41281
$487$	−5648.73	−0.525602	−0.262801	−	0.964850i	$-0.584646\pi$
$487$	−5648.73	−0.525602	−0.262801	+	0.964850i	$0.584646\pi$
$488$	384.582	0.0356746
$489$	13235.3	1.22397
$490$	22462.4	2.07091
$491$	11289.7	1.03768	0.518838	−	0.854873i	$-0.326365\pi$
$491$	11289.7	1.03768	0.518838	+	0.854873i	$0.326365\pi$
$492$	6741.62	0.617755
$493$	875.848	0.0800126
$494$	0	0
$495$	−2937.75	−0.266752
$496$	−14330.2	−1.29727
$497$	757.166	0.0683371
$498$	−6982.79	−0.628326
$499$	−14960.3	−1.34212	−0.671058	−	0.741405i	$-0.734160\pi$
$499$	−14960.3	−1.34212	−0.671058	+	0.741405i	$0.734160\pi$
$500$	2502.25	0.223808
$501$	−8063.44	−0.719058
$502$	−11651.3	−1.03591
$503$	−10788.2	−0.956310	−0.478155	−	0.878276i	$-0.658694\pi$
$503$	−10788.2	−0.956310	−0.478155	+	0.878276i	$0.658694\pi$
$504$	37.4880	0.00331319
$505$	−15350.9	−1.35269
$506$	2034.35	0.178731
$507$	0	0
$508$	−5898.93	−0.515203
$509$	1236.50	0.107676	0.0538378	−	0.998550i	$-0.482855\pi$
$509$	1236.50	0.107676	0.0538378	+	0.998550i	$0.482855\pi$
$510$	1632.25	0.141720
$511$	1934.04	0.167430
$512$	−16467.4	−1.42141
$513$	−1312.12	−0.112927
$514$	2480.59	0.212868
$515$	28613.0	2.44823
$516$	10188.9	0.869264
$517$	−5300.52	−0.450902
$518$	−157.235	−0.0133369
$519$	−14227.1	−1.20328
$520$	0	0
$521$	−15996.2	−1.34511	−0.672557	−	0.740046i	$-0.734804\pi$
$521$	−15996.2	−1.34511	−0.672557	+	0.740046i	$0.734804\pi$
$522$	7643.17	0.640867
$523$	1164.25	0.0973403	0.0486702	−	0.998815i	$-0.484502\pi$
$523$	1164.25	0.0973403	0.0486702	+	0.998815i	$0.484502\pi$
$524$	−11310.2	−0.942914
$525$	−871.846	−0.0724771
$526$	−22660.2	−1.87839
$527$	1759.00	0.145396
$528$	2211.08	0.182244
$529$	−10069.5	−0.827605
$530$	1867.87	0.153085
$531$	−3050.53	−0.249307
$532$	−143.053	−0.0116582
$533$	0	0
$534$	−14370.8	−1.16458
$535$	−7189.85	−0.581017
$536$	120.284	0.00969309
$537$	−10982.5	−0.882549
$538$	−3321.55	−0.266175
$539$	−3734.99	−0.298474
$540$	19273.1	1.53589
$541$	22457.9	1.78473	0.892366	−	0.451313i	$-0.149044\pi$
$541$	22457.9	1.78473	0.892366	+	0.451313i	$0.149044\pi$
$542$	−14285.6	−1.13214
$543$	−3479.19	−0.274966
$544$	1946.68	0.153425
$545$	8831.73	0.694146
$546$	0	0
$547$	−726.285	−0.0567710	−0.0283855	−	0.999597i	$-0.509037\pi$
$547$	−726.285	−0.0567710	−0.0283855	+	0.999597i	$0.509037\pi$
$548$	17806.2	1.38803
$549$	5068.18	0.393997
$550$	−6369.19	−0.493788
$551$	−1075.64	−0.0831650
$552$	−185.303	−0.0142881
$553$	−1164.36	−0.0895365
$554$	−11499.5	−0.881888
$555$	−1122.35	−0.0858399
$556$	5661.25	0.431817
$557$	−13761.1	−1.04681	−0.523407	−	0.852083i	$-0.675339\pi$
$557$	−13761.1	−1.04681	−0.523407	+	0.852083i	$0.675339\pi$
$558$	15350.1	1.16456
$559$	0	0
$560$	−1871.62	−0.141233
$561$	−271.405	−0.0204256
$562$	5796.83	0.435097
$563$	−8959.48	−0.670687	−0.335344	−	0.942096i	$-0.608852\pi$
$563$	−8959.48	−0.670687	−0.335344	+	0.942096i	$0.608852\pi$
$564$	13091.4	0.977391
$565$	−28987.8	−2.15845
$566$	−25859.7	−1.92043
$567$	−42.9269	−0.00317947
$568$	−503.841	−0.0372196
$569$	24897.5	1.83437	0.917185	−	0.398461i	$-0.130456\pi$
$569$	24897.5	1.83437	0.917185	+	0.398461i	$0.130456\pi$
$570$	−2004.59	−0.147303
$571$	−10360.2	−0.759299	−0.379650	−	0.925130i	$-0.623955\pi$
$571$	−10360.2	−0.759299	−0.379650	+	0.925130i	$0.623955\pi$
$572$	0	0
$573$	132.292	0.00964497
$574$	1862.76	0.135453
$575$	−6567.01	−0.476284
$576$	8973.13	0.649098
$577$	15870.3	1.14504	0.572520	−	0.819891i	$-0.305966\pi$
$577$	15870.3	1.14504	0.572520	+	0.819891i	$0.305966\pi$
$578$	19609.4	1.41115
$579$	−15922.4	−1.14285
$580$	15799.6	1.13111
$581$	−982.821	−0.0701795
$582$	−505.793	−0.0360237
$583$	−310.585	−0.0220636
$584$	−1286.97	−0.0911903
$585$	0	0
$586$	22371.5	1.57706
$587$	−11597.9	−0.815500	−0.407750	−	0.913094i	$-0.633686\pi$
$587$	−11597.9	−0.815500	−0.407750	+	0.913094i	$0.633686\pi$
$588$	9224.81	0.646981
$589$	−2160.26	−0.151124
$590$	−12379.3	−0.863807
$591$	3334.94	0.232117
$592$	−1287.23	−0.0893662
$593$	19959.4	1.38218	0.691090	−	0.722769i	$-0.257131\pi$
$593$	19959.4	1.38218	0.691090	+	0.722769i	$0.257131\pi$
$594$	−6291.15	−0.434561
$595$	229.737	0.0158291
$596$	4125.29	0.283521
$597$	−9339.76	−0.640286
$598$	0	0
$599$	−636.509	−0.0434174	−0.0217087	−	0.999764i	$-0.506911\pi$
$599$	−636.509	−0.0434174	−0.0217087	+	0.999764i	$0.506911\pi$
$600$	580.153	0.0394744
$601$	−3328.12	−0.225885	−0.112942	−	0.993602i	$-0.536028\pi$
$601$	−3328.12	−0.225885	−0.112942	+	0.993602i	$0.536028\pi$
$602$	2815.26	0.190600
$603$	1585.16	0.107052
$604$	12809.3	0.862922
$605$	1982.29	0.133209
$606$	−12376.0	−0.829608
$607$	−8335.47	−0.557374	−0.278687	−	0.960382i	$-0.589899\pi$
$607$	−8335.47	−0.557374	−0.278687	+	0.960382i	$0.589899\pi$
$608$	−2390.75	−0.159470
$609$	−705.962	−0.0469737
$610$	20567.0	1.36514
$611$	0	0
$612$	−1021.47	−0.0674679
$613$	18334.4	1.20803	0.604014	−	0.796974i	$-0.293567\pi$
$613$	18334.4	1.20803	0.604014	+	0.796974i	$0.293567\pi$
$614$	−24824.6	−1.63166
$615$	13296.5	0.871814
$616$	−25.2956	−0.00165453
$617$	233.854	0.0152587	0.00762935	−	0.999971i	$-0.497571\pi$
$617$	233.854	0.0152587	0.00762935	+	0.999971i	$0.497571\pi$
$618$	23068.1	1.50151
$619$	−14028.9	−0.910933	−0.455466	−	0.890253i	$-0.650528\pi$
$619$	−14028.9	−0.910933	−0.455466	+	0.890253i	$0.650528\pi$
$620$	31731.0	2.05540
$621$	−6486.55	−0.419156
$622$	33357.1	2.15032
$623$	−2022.68	−0.130075
$624$	0	0
$625$	−12988.3	−0.831254
$626$	37415.6	2.38886
$627$	333.317	0.0212303
$628$	−26578.8	−1.68887
$629$	158.005	0.0100160
$630$	2004.82	0.126784
$631$	−28655.2	−1.80784	−0.903918	−	0.427706i	$-0.859322\pi$
$631$	−28655.2	−1.80784	−0.903918	+	0.427706i	$0.859322\pi$
$632$	774.802	0.0487657
$633$	656.044	0.0411934
$634$	−18389.3	−1.15195
$635$	−11634.4	−0.727085
$636$	767.094	0.0478259
$637$	0	0
$638$	−5157.34	−0.320033
$639$	−6639.83	−0.411060
$640$	2592.09	0.160096
$641$	−4872.13	−0.300215	−0.150107	−	0.988670i	$-0.547962\pi$
$641$	−4872.13	−0.300215	−0.150107	+	0.988670i	$0.547962\pi$
$642$	−5796.52	−0.356340
$643$	24080.5	1.47689	0.738447	−	0.674312i	$-0.235560\pi$
$643$	24080.5	1.47689	0.738447	+	0.674312i	$0.235560\pi$
$644$	−707.194	−0.0432723
$645$	20095.5	1.22676
$646$	282.206	0.0171877
$647$	15462.8	0.939575	0.469787	−	0.882780i	$-0.344331\pi$
$647$	15462.8	0.939575	0.469787	+	0.882780i	$0.344331\pi$
$648$	28.5648	0.00173169
$649$	2058.39	0.124497
$650$	0	0
$651$	−1417.81	−0.0853587
$652$	−33611.9	−2.01893
$653$	−1810.67	−0.108510	−0.0542550	−	0.998527i	$-0.517278\pi$
$653$	−1810.67	−0.108510	−0.0542550	+	0.998527i	$0.517278\pi$
$654$	7120.23	0.425723
$655$	−22307.0	−1.33070
$656$	15249.8	0.907628
$657$	−16960.2	−1.00712
$658$	3617.25	0.214309
$659$	7651.57	0.452296	0.226148	−	0.974093i	$-0.427387\pi$
$659$	7651.57	0.452296	0.226148	+	0.974093i	$0.427387\pi$
$660$	−4895.93	−0.288748
$661$	−14611.9	−0.859812	−0.429906	−	0.902874i	$-0.641453\pi$
$661$	−14611.9	−0.859812	−0.429906	+	0.902874i	$0.641453\pi$
$662$	1033.10	0.0606536
$663$	0	0
$664$	653.999	0.0382230
$665$	−282.143	−0.0164527
$666$	1378.84	0.0802237
$667$	−5317.52	−0.308688
$668$	20477.6	1.18608
$669$	8443.21	0.487942
$670$	6432.68	0.370920
$671$	−3419.83	−0.196753
$672$	−1569.09	−0.0900728
$673$	−9375.13	−0.536976	−0.268488	−	0.963283i	$-0.586524\pi$
$673$	−9375.13	−0.536976	−0.268488	+	0.963283i	$0.586524\pi$
$674$	32956.7	1.88345
$675$	20308.3	1.15802
$676$	0	0
$677$	−32268.7	−1.83189	−0.915944	−	0.401307i	$-0.868556\pi$
$677$	−32268.7	−1.83189	−0.915944	+	0.401307i	$0.868556\pi$
$678$	−23370.2	−1.32379
$679$	−71.1898	−0.00402359
$680$	−152.874	−0.00862125
$681$	16935.0	0.952938
$682$	−10357.7	−0.581550
$683$	31691.3	1.77545	0.887726	−	0.460373i	$-0.152284\pi$
$683$	31691.3	1.77545	0.887726	+	0.460373i	$0.152284\pi$
$684$	1254.48	0.0701260
$685$	35119.0	1.95887
$686$	5123.70	0.285166
$687$	2586.74	0.143654
$688$	23047.6	1.27715
$689$	0	0
$690$	−9909.82	−0.546754
$691$	−35700.9	−1.96545	−0.982724	−	0.185075i	$-0.940747\pi$
$691$	−35700.9	−1.96545	−0.982724	+	0.185075i	$0.940747\pi$
$692$	36130.5	1.98479
$693$	−333.356	−0.0182729
$694$	29457.6	1.61123
$695$	11165.7	0.609406
$696$	469.768	0.0255841
$697$	−1871.88	−0.101725
$698$	15495.2	0.840261
$699$	14194.3	0.768067
$700$	2214.10	0.119550
$701$	27126.8	1.46157	0.730787	−	0.682605i	$-0.239153\pi$
$701$	27126.8	1.46157	0.730787	+	0.682605i	$0.239153\pi$
$702$	0	0
$703$	−194.048	−0.0104106
$704$	−6054.75	−0.324143
$705$	25820.2	1.37935
$706$	−1447.60	−0.0771686
$707$	−1741.92	−0.0926612
$708$	−5083.89	−0.269865
$709$	−27816.1	−1.47342	−0.736711	−	0.676208i	$-0.763622\pi$
$709$	−27816.1	−1.47342	−0.736711	+	0.676208i	$0.763622\pi$
$710$	−26944.9	−1.42426
$711$	10210.7	0.538579
$712$	1345.95	0.0708450
$713$	−10679.4	−0.560935
$714$	185.216	0.00970804
$715$	0	0
$716$	27890.6	1.45576
$717$	17531.4	0.913139
$718$	12251.9	0.636822
$719$	17189.5	0.891597	0.445799	−	0.895133i	$-0.352920\pi$
$719$	17189.5	0.891597	0.445799	+	0.895133i	$0.352920\pi$
$720$	16412.8	0.849540
$721$	3246.81	0.167708
$722$	27350.8	1.40982
$723$	16979.3	0.873397
$724$	8835.61	0.453553
$725$	16648.2	0.852827
$726$	1598.14	0.0816978
$727$	−89.3588	−0.00455864	−0.00227932	−	0.999997i	$-0.500726\pi$
$727$	−89.3588	−0.00455864	−0.00227932	+	0.999997i	$0.500726\pi$
$728$	0	0
$729$	12884.1	0.654578
$730$	−68825.6	−3.48952
$731$	−2829.04	−0.143141
$732$	8446.42	0.426487
$733$	30332.1	1.52844	0.764218	−	0.644959i	$-0.223125\pi$
$733$	30332.1	1.52844	0.764218	+	0.644959i	$0.223125\pi$
$734$	38384.5	1.93024
$735$	18194.1	0.913058
$736$	−11818.8	−0.591914
$737$	−1069.61	−0.0534593
$738$	−16335.1	−0.814774
$739$	−28779.4	−1.43257	−0.716283	−	0.697810i	$-0.754158\pi$
$739$	−28779.4	−1.43257	−0.716283	+	0.697810i	$0.754158\pi$
$740$	2850.27	0.141592
$741$	0	0
$742$	211.953	0.0104866
$743$	−14384.6	−0.710255	−0.355127	−	0.934818i	$-0.615562\pi$
$743$	−14384.6	−0.710255	−0.355127	+	0.934818i	$0.615562\pi$
$744$	943.456	0.0464903
$745$	8136.29	0.400122
$746$	2330.54	0.114379
$747$	8618.66	0.422142
$748$	689.250	0.0336918
$749$	−815.855	−0.0398006
$750$	3978.79	0.193713
$751$	−271.131	−0.0131740	−0.00658702	−	0.999978i	$-0.502097\pi$
$751$	−271.131	−0.0131740	−0.00658702	+	0.999978i	$0.502097\pi$
$752$	29613.3	1.43602
$753$	−9437.34	−0.456727
$754$	0	0
$755$	25263.8	1.21781
$756$	2186.97	0.105211
$757$	−31412.9	−1.50822	−0.754108	−	0.656750i	$-0.771930\pi$
$757$	−31412.9	−1.50822	−0.754108	+	0.656750i	$0.771930\pi$
$758$	−25910.0	−1.24155
$759$	1647.78	0.0788017
$760$	187.747	0.00896091
$761$	−8886.46	−0.423303	−0.211652	−	0.977345i	$-0.567884\pi$
$761$	−8886.46	−0.423303	−0.211652	+	0.977345i	$0.567884\pi$
$762$	−9379.80	−0.445924
$763$	1002.16	0.0475502
$764$	−335.962	−0.0159093
$765$	−2014.64	−0.0952148
$766$	−7646.97	−0.360700
$767$	0	0
$768$	−12313.0	−0.578523
$769$	−42491.3	−1.99256	−0.996279	−	0.0861871i	$-0.972532\pi$
$769$	−42491.3	−1.99256	−0.996279	+	0.0861871i	$0.972532\pi$
$770$	−1352.78	−0.0633128
$771$	2009.22	0.0938527
$772$	40435.8	1.88513
$773$	11300.9	0.525830	0.262915	−	0.964819i	$-0.415316\pi$
$773$	11300.9	0.525830	0.262915	+	0.964819i	$0.415316\pi$
$774$	−24687.9	−1.14650
$775$	33435.4	1.54972
$776$	47.3719	0.00219143
$777$	−127.357	−0.00588017
$778$	35460.7	1.63410
$779$	2298.88	0.105733
$780$	0	0
$781$	4480.32	0.205273
$782$	1395.10	0.0637965
$783$	16444.2	0.750536
$784$	20866.8	0.950567
$785$	−52421.3	−2.38343
$786$	−17984.1	−0.816123
$787$	10274.7	0.465381	0.232690	−	0.972551i	$-0.425247\pi$
$787$	10274.7	0.465381	0.232690	+	0.972551i	$0.425247\pi$
$788$	−8469.26	−0.382874
$789$	−18354.3	−0.828175
$790$	41435.5	1.86609
$791$	−3289.34	−0.147858
$792$	221.825	0.00995229
$793$	0	0
$794$	−425.599	−0.0190226
$795$	1512.94	0.0674948
$796$	23718.9	1.05615
$797$	30719.0	1.36528	0.682638	−	0.730757i	$-0.260833\pi$
$797$	30719.0	1.36528	0.682638	+	0.730757i	$0.260833\pi$
$798$	−227.467	−0.0100905
$799$	−3634.96	−0.160946
$800$	37002.8	1.63531
$801$	17737.5	0.782426
$802$	−19972.3	−0.879361
$803$	11444.1	0.502933
$804$	2641.76	0.115880
$805$	−1394.80	−0.0610685
$806$	0	0
$807$	−2690.38	−0.117355
$808$	1159.12	0.0504676
$809$	−16945.8	−0.736445	−0.368222	−	0.929738i	$-0.620034\pi$
$809$	−16945.8	−0.736445	−0.368222	+	0.929738i	$0.620034\pi$
$810$	1527.62	0.0662654
$811$	13023.2	0.563878	0.281939	−	0.959432i	$-0.409022\pi$
$811$	13023.2	0.563878	0.281939	+	0.959432i	$0.409022\pi$
$812$	1792.83	0.0774827
$813$	−11571.0	−0.499155
$814$	−930.392	−0.0400617
$815$	−66292.7	−2.84924
$816$	1516.30	0.0650506
$817$	3474.39	0.148780
$818$	−2540.32	−0.108582
$819$	0	0
$820$	−33767.1	−1.43805
$821$	−32285.0	−1.37242	−0.686208	−	0.727405i	$-0.740726\pi$
$821$	−32285.0	−1.37242	−0.686208	+	0.727405i	$0.740726\pi$
$822$	28313.3	1.20139
$823$	796.081	0.0337177	0.0168588	−	0.999858i	$-0.494633\pi$
$823$	796.081	0.0337177	0.0168588	+	0.999858i	$0.494633\pi$
$824$	−2160.52	−0.0913415
$825$	−5158.91	−0.217709
$826$	−1404.71	−0.0591722
$827$	39560.3	1.66342	0.831709	−	0.555212i	$-0.187363\pi$
$827$	39560.3	1.66342	0.831709	+	0.555212i	$0.187363\pi$
$828$	6201.61	0.260291
$829$	−44087.8	−1.84708	−0.923541	−	0.383499i	$-0.874719\pi$
$829$	−44087.8	−1.84708	−0.923541	+	0.383499i	$0.874719\pi$
$830$	34975.1	1.46266
$831$	−9314.33	−0.388821
$832$	0	0
$833$	−2561.36	−0.106538
$834$	9001.86	0.373752
$835$	40387.8	1.67387
$836$	−846.478	−0.0350192
$837$	33025.7	1.36384
$838$	35550.9	1.46550
$839$	−40141.6	−1.65178	−0.825889	−	0.563832i	$-0.809326\pi$
$839$	−40141.6	−1.65178	−0.825889	+	0.563832i	$0.809326\pi$
$840$	123.221	0.00506135
$841$	−10908.4	−0.447267
$842$	48489.7	1.98464
$843$	4695.30	0.191833
$844$	−1666.06	−0.0679481
$845$	0	0
$846$	−31720.8	−1.28911
$847$	224.937	0.00912505
$848$	1735.19	0.0702674
$849$	−20945.8	−0.846712
$850$	−4367.83	−0.176253
$851$	−959.289	−0.0386416
$852$	−11065.7	−0.444957
$853$	−21194.1	−0.850731	−0.425366	−	0.905022i	$-0.639854\pi$
$853$	−21194.1	−0.850731	−0.425366	+	0.905022i	$0.639854\pi$
$854$	2333.80	0.0935142
$855$	2474.20	0.0989661
$856$	542.894	0.0216773
$857$	−31521.0	−1.25640	−0.628201	−	0.778051i	$-0.716208\pi$
$857$	−31521.0	−1.25640	−0.628201	+	0.778051i	$0.716208\pi$
$858$	0	0
$859$	−39404.6	−1.56516	−0.782578	−	0.622553i	$-0.786096\pi$
$859$	−39404.6	−1.56516	−0.782578	+	0.622553i	$0.786096\pi$
$860$	−51033.6	−2.02352
$861$	1508.79	0.0597207
$862$	−39108.9	−1.54531
$863$	5139.53	0.202725	0.101362	−	0.994850i	$-0.467680\pi$
$863$	5139.53	0.202725	0.101362	+	0.994850i	$0.467680\pi$
$864$	36549.4	1.43916
$865$	71260.1	2.80106
$866$	46244.3	1.81460
$867$	15883.2	0.622172
$868$	3600.62	0.140798
$869$	−6889.79	−0.268953
$870$	25122.7	0.979010
$871$	0	0
$872$	−666.870	−0.0258980
$873$	624.286	0.0242026
$874$	−1713.35	−0.0663099
$875$	560.010	0.0216363
$876$	−28265.2	−1.09017
$877$	−39662.0	−1.52713	−0.763564	−	0.645732i	$-0.776552\pi$
$877$	−39662.0	−1.52713	−0.763564	+	0.645732i	$0.776552\pi$
$878$	167.446	0.00643626
$879$	18120.4	0.695320
$880$	−11074.8	−0.424239
$881$	−1761.39	−0.0673585	−0.0336792	−	0.999433i	$-0.510722\pi$
$881$	−1761.39	−0.0673585	−0.0336792	+	0.999433i	$0.510722\pi$
$882$	−22351.9	−0.853320
$883$	−46135.5	−1.75830	−0.879152	−	0.476541i	$-0.841890\pi$
$883$	−46135.5	−1.75830	−0.879152	+	0.476541i	$0.841890\pi$
$884$	0	0
$885$	−10026.9	−0.380849
$886$	−37544.4	−1.42362
$887$	15925.5	0.602849	0.301425	−	0.953490i	$-0.402538\pi$
$887$	15925.5	0.602849	0.301425	+	0.953490i	$0.402538\pi$
$888$	84.7470	0.00320262
$889$	−1320.20	−0.0498065
$890$	71979.9	2.71098
$891$	−254.008	−0.00955060
$892$	−21442.0	−0.804856
$893$	4464.15	0.167287
$894$	6559.56	0.245396
$895$	55008.5	2.05445
$896$	294.133	0.0109668
$897$	0	0
$898$	24703.7	0.918009
$899$	27073.7	1.00440
$900$	−19416.2	−0.719117
$901$	−212.991	−0.00787543
$902$	11022.3	0.406878
$903$	2280.30	0.0840349
$904$	2188.82	0.0805301
$905$	17426.4	0.640082
$906$	20367.9	0.746887
$907$	−27086.7	−0.991619	−0.495809	−	0.868431i	$-0.665128\pi$
$907$	−27086.7	−0.991619	−0.495809	+	0.868431i	$0.665128\pi$
$908$	−43007.4	−1.57186
$909$	15275.4	0.557374
$910$	0	0
$911$	−2553.66	−0.0928722	−0.0464361	−	0.998921i	$-0.514786\pi$
$911$	−2553.66	−0.0928722	−0.0464361	+	0.998921i	$0.514786\pi$
$912$	−1862.20	−0.0676135
$913$	−5815.57	−0.210807
$914$	−10963.4	−0.396758
$915$	16658.8	0.601884
$916$	−6569.18	−0.236956
$917$	−2531.25	−0.0911550
$918$	−4314.32	−0.155113
$919$	4268.04	0.153199	0.0765994	−	0.997062i	$-0.475594\pi$
$919$	4268.04	0.153199	0.0765994	+	0.997062i	$0.475594\pi$
$920$	928.140	0.0332607
$921$	−20107.4	−0.719393
$922$	−21997.0	−0.785720
$923$	0	0
$924$	−555.557	−0.0197797
$925$	3003.37	0.106757
$926$	20159.9	0.715439
$927$	−28472.3	−1.00879
$928$	29962.3	1.05987
$929$	−44710.9	−1.57903	−0.789515	−	0.613732i	$-0.789668\pi$
$929$	−44710.9	−1.57903	−0.789515	+	0.613732i	$0.789668\pi$
$930$	50455.0	1.77902
$931$	3145.64	0.110735
$932$	−36047.3	−1.26692
$933$	27018.5	0.948068
$934$	−3679.81	−0.128915
$935$	1359.40	0.0475479
$936$	0	0
$937$	48002.7	1.67362	0.836808	−	0.547496i	$-0.184419\pi$
$937$	48002.7	1.67362	0.836808	+	0.547496i	$0.184419\pi$
$938$	729.937	0.0254086
$939$	30305.8	1.05324
$940$	−65571.8	−2.27523
$941$	−41444.7	−1.43577	−0.717884	−	0.696163i	$-0.754889\pi$
$941$	−41444.7	−1.43577	−0.717884	+	0.696163i	$0.754889\pi$
$942$	−42262.6	−1.46177
$943$	11364.7	0.392455
$944$	−11499.9	−0.396495
$945$	4313.36	0.148480
$946$	16658.5	0.572531
$947$	34653.5	1.18911	0.594554	−	0.804055i	$-0.297328\pi$
$947$	34653.5	1.18911	0.594554	+	0.804055i	$0.297328\pi$
$948$	17016.7	0.582991
$949$	0	0
$950$	5364.20	0.183198
$951$	−14895.0	−0.507889
$952$	−17.3471	−0.000590570 0
$953$	−9034.94	−0.307104	−0.153552	−	0.988141i	$-0.549071\pi$
$953$	−9034.94	−0.307104	−0.153552	+	0.988141i	$0.549071\pi$
$954$	−1858.69	−0.0630788
$955$	−662.617	−0.0224521
$956$	−44521.9	−1.50621
$957$	−4177.33	−0.141101
$958$	−58716.4	−1.98021
$959$	3985.07	0.134186
$960$	29494.2	0.991585
$961$	24582.2	0.825157
$962$	0	0
$963$	7154.49	0.239408
$964$	−43119.9	−1.44066
$965$	79751.4	2.66040
$966$	−1124.50	−0.0374536
$967$	10965.2	0.364651	0.182325	−	0.983238i	$-0.441638\pi$
$967$	10965.2	0.364651	0.182325	+	0.983238i	$0.441638\pi$
$968$	−149.680	−0.00496992
$969$	228.581	0.00757798
$970$	2533.40	0.0838582
$971$	−45042.1	−1.48864	−0.744321	−	0.667822i	$-0.767227\pi$
$971$	−45042.1	−1.48864	−0.744321	+	0.667822i	$0.767227\pi$
$972$	−31136.5	−1.02747
$973$	1267.00	0.0417454
$974$	22810.2	0.750396
$975$	0	0
$976$	19106.1	0.626610
$977$	−48979.4	−1.60388	−0.801940	−	0.597404i	$-0.796199\pi$
$977$	−48979.4	−1.60388	−0.801940	+	0.597404i	$0.796199\pi$
$978$	−53445.8	−1.74745
$979$	−11968.6	−0.390724
$980$	−46204.8	−1.50608
$981$	−8788.29	−0.286023
$982$	−45589.2	−1.48148
$983$	−8876.81	−0.288023	−0.144011	−	0.989576i	$-0.546000\pi$
$983$	−8876.81	−0.288023	−0.144011	+	0.989576i	$0.546000\pi$
$984$	−1004.00	−0.0325267
$985$	−16703.9	−0.540335
$986$	−3536.77	−0.114233
$987$	2929.90	0.0944880
$988$	0	0
$989$	17175.9	0.552236
$990$	11863.0	0.380838
$991$	35228.0	1.12922	0.564609	−	0.825358i	$-0.309027\pi$
$991$	35228.0	1.12922	0.564609	+	0.825358i	$0.309027\pi$
$992$	60174.6	1.92595
$993$	836.791	0.0267419
$994$	−3057.52	−0.0975641
$995$	46780.6	1.49050
$996$	14363.5	0.456953
$997$	30904.5	0.981701	0.490850	−	0.871244i	$-0.336686\pi$
$997$	30904.5	0.981701	0.490850	+	0.871244i	$0.336686\pi$
$998$	60411.5	1.91612
$999$	2966.57	0.0939521

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.b.1.1		4
13.12	even	2		143.4.a.a.1.4	✓	4
39.38	odd	2		1287.4.a.b.1.1		4
52.51	odd	2		2288.4.a.i.1.3		4
143.142	odd	2		1573.4.a.c.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.a.a.1.4	✓	4	13.12	even	2
1287.4.a.b.1.1		4	39.38	odd	2
1573.4.a.c.1.1		4	143.142	odd	2
1859.4.a.b.1.1		4	1.1	even	1	trivial
2288.4.a.i.1.3		4	52.51	odd	2

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)

\(f(q)\)	\(=\)	\(q-4.03811 q^{2} -3.27078 q^{3} +8.30634 q^{4} +16.3826 q^{5} +13.2078 q^{6} +1.85898 q^{7} -1.23702 q^{8} -16.3020 q^{9} +O(q^{10})\)	\(q-4.03811 q^{2} -3.27078 q^{3} +8.30634 q^{4} +16.3826 q^{5} +13.2078 q^{6} +1.85898 q^{7} -1.23702 q^{8} -16.3020 q^{9} -66.1546 q^{10} +11.0000 q^{11} -27.1682 q^{12} -7.50677 q^{14} -53.5838 q^{15} -61.4555 q^{16} +7.54352 q^{17} +65.8292 q^{18} -9.26432 q^{19} +136.079 q^{20} -6.08032 q^{21} -44.4192 q^{22} -45.7988 q^{23} +4.04603 q^{24} +143.388 q^{25} +141.631 q^{27} +15.4413 q^{28} +116.106 q^{29} +216.377 q^{30} +233.181 q^{31} +258.060 q^{32} -35.9786 q^{33} -30.4616 q^{34} +30.4549 q^{35} -135.410 q^{36} +20.9457 q^{37} +37.4103 q^{38} -20.2656 q^{40} -248.144 q^{41} +24.5530 q^{42} -375.029 q^{43} +91.3697 q^{44} -267.068 q^{45} +184.941 q^{46} -481.865 q^{47} +201.007 q^{48} -339.544 q^{49} -579.017 q^{50} -24.6732 q^{51} -28.2350 q^{53} -571.923 q^{54} +180.208 q^{55} -2.29960 q^{56} +30.3016 q^{57} -468.849 q^{58} +187.126 q^{59} -445.085 q^{60} -310.893 q^{61} -941.610 q^{62} -30.3051 q^{63} -550.432 q^{64} +145.286 q^{66} -97.2371 q^{67} +62.6591 q^{68} +149.798 q^{69} -122.980 q^{70} +407.302 q^{71} +20.1659 q^{72} +1040.38 q^{73} -84.5811 q^{74} -468.992 q^{75} -76.9525 q^{76} +20.4488 q^{77} -626.344 q^{79} -1006.80 q^{80} -23.0916 q^{81} +1002.03 q^{82} -528.688 q^{83} -50.5052 q^{84} +123.582 q^{85} +1514.41 q^{86} -379.757 q^{87} -13.6072 q^{88} -1088.06 q^{89} +1078.45 q^{90} -380.420 q^{92} -762.683 q^{93} +1945.83 q^{94} -151.773 q^{95} -844.058 q^{96} -38.2951 q^{97} +1371.12 q^{98} -179.322 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 6 q^{4} + 6 q^{5} + 13 q^{6} + 17 q^{7} - 6 q^{8} - 44 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 + 6 * q^4 + 6 * q^5 + 13 * q^6 + 17 * q^7 - 6 * q^8 - 44 * q^9	\( 4 q - 4 q^{3} + 6 q^{4} + 6 q^{5} + 13 q^{6} + 17 q^{7} - 6 q^{8} - 44 q^{9} - 82 q^{10} + 44 q^{11} + 17 q^{12} - 40 q^{14} - 9 q^{15} - 142 q^{16} - 41 q^{17} + 75 q^{18} + 41 q^{19} + 174 q^{20} + 179 q^{21} - 136 q^{23} + 171 q^{24} - 162 q^{25} + 11 q^{27} + 56 q^{28} - 207 q^{29} + 305 q^{30} + 348 q^{31} + 2 q^{32} - 44 q^{33} - 197 q^{34} + 136 q^{35} - 153 q^{36} + 333 q^{37} - 110 q^{38} + 142 q^{40} + 198 q^{41} + 317 q^{42} - 252 q^{43} + 66 q^{44} - 303 q^{45} - 345 q^{46} - 561 q^{47} + q^{48} - 431 q^{49} - 958 q^{50} + 375 q^{51} + 343 q^{53} - 803 q^{54} + 66 q^{55} + 888 q^{56} - 797 q^{57} - 753 q^{58} + 541 q^{59} - 669 q^{60} - 801 q^{61} + 50 q^{62} - 895 q^{63} - 214 q^{64} + 143 q^{66} + 863 q^{67} + 221 q^{68} - 238 q^{69} + 184 q^{70} - 781 q^{71} - 711 q^{72} + 1306 q^{73} + 1347 q^{74} - 779 q^{75} - 1160 q^{76} + 187 q^{77} - 278 q^{79} - 874 q^{80} - 596 q^{81} + 1675 q^{82} - 437 q^{83} - 439 q^{84} + 615 q^{85} - 234 q^{86} - 818 q^{87} - 66 q^{88} - 2552 q^{89} + 899 q^{90} - 1391 q^{92} + 876 q^{93} - 415 q^{94} - 940 q^{95} - 3077 q^{96} + 2504 q^{97} + 144 q^{98} - 484 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 + 6 * q^4 + 6 * q^5 + 13 * q^6 + 17 * q^7 - 6 * q^8 - 44 * q^9 - 82 * q^10 + 44 * q^11 + 17 * q^12 - 40 * q^14 - 9 * q^15 - 142 * q^16 - 41 * q^17 + 75 * q^18 + 41 * q^19 + 174 * q^20 + 179 * q^21 - 136 * q^23 + 171 * q^24 - 162 * q^25 + 11 * q^27 + 56 * q^28 - 207 * q^29 + 305 * q^30 + 348 * q^31 + 2 * q^32 - 44 * q^33 - 197 * q^34 + 136 * q^35 - 153 * q^36 + 333 * q^37 - 110 * q^38 + 142 * q^40 + 198 * q^41 + 317 * q^42 - 252 * q^43 + 66 * q^44 - 303 * q^45 - 345 * q^46 - 561 * q^47 + q^48 - 431 * q^49 - 958 * q^50 + 375 * q^51 + 343 * q^53 - 803 * q^54 + 66 * q^55 + 888 * q^56 - 797 * q^57 - 753 * q^58 + 541 * q^59 - 669 * q^60 - 801 * q^61 + 50 * q^62 - 895 * q^63 - 214 * q^64 + 143 * q^66 + 863 * q^67 + 221 * q^68 - 238 * q^69 + 184 * q^70 - 781 * q^71 - 711 * q^72 + 1306 * q^73 + 1347 * q^74 - 779 * q^75 - 1160 * q^76 + 187 * q^77 - 278 * q^79 - 874 * q^80 - 596 * q^81 + 1675 * q^82 - 437 * q^83 - 439 * q^84 + 615 * q^85 - 234 * q^86 - 818 * q^87 - 66 * q^88 - 2552 * q^89 + 899 * q^90 - 1391 * q^92 + 876 * q^93 - 415 * q^94 - 940 * q^95 - 3077 * q^96 + 2504 * q^97 + 144 * q^98 - 484 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more