LMFDB - Embedded newform 1815.4.a.y.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1815,4,Mod(1,1815)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1815, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1815.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1815 = 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1815.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:	$107.088466660$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 30x^{3} + 15x^{2} + 181x - 22 $ x^5 - x^4 - 30x^3 + 15x^2 + 181*x - 22
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-4.40676$ of defining polynomial
Character	$\chi$	$=$	1815.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.40676 q^{2} +3.00000 q^{3} +11.4195 q^{4} -5.00000 q^{5} -13.2203 q^{6} -17.2681 q^{7} -15.0689 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-4.40676 q^{2} +3.00000 q^{3} +11.4195 q^{4} -5.00000 q^{5} -13.2203 q^{6} -17.2681 q^{7} -15.0689 q^{8} +9.00000 q^{9} +22.0338 q^{10} +34.2585 q^{12} -25.9525 q^{13} +76.0965 q^{14} -15.0000 q^{15} -24.9510 q^{16} -45.4853 q^{17} -39.6608 q^{18} -17.3463 q^{19} -57.0975 q^{20} -51.8044 q^{21} -54.3698 q^{23} -45.2067 q^{24} +25.0000 q^{25} +114.366 q^{26} +27.0000 q^{27} -197.194 q^{28} -201.607 q^{29} +66.1013 q^{30} +71.2055 q^{31} +230.504 q^{32} +200.443 q^{34} +86.3407 q^{35} +102.776 q^{36} +30.1189 q^{37} +76.4411 q^{38} -77.8574 q^{39} +75.3446 q^{40} -339.153 q^{41} +228.290 q^{42} -142.554 q^{43} -45.0000 q^{45} +239.595 q^{46} +387.767 q^{47} -74.8530 q^{48} -44.8112 q^{49} -110.169 q^{50} -136.456 q^{51} -296.364 q^{52} +207.201 q^{53} -118.982 q^{54} +260.212 q^{56} -52.0390 q^{57} +888.433 q^{58} -683.032 q^{59} -171.293 q^{60} -173.523 q^{61} -313.785 q^{62} -155.413 q^{63} -816.168 q^{64} +129.762 q^{65} +35.1423 q^{67} -519.420 q^{68} -163.110 q^{69} -380.483 q^{70} +331.264 q^{71} -135.620 q^{72} -1049.92 q^{73} -132.727 q^{74} +75.0000 q^{75} -198.087 q^{76} +343.099 q^{78} +302.376 q^{79} +124.755 q^{80} +81.0000 q^{81} +1494.56 q^{82} +831.525 q^{83} -591.581 q^{84} +227.427 q^{85} +628.200 q^{86} -604.821 q^{87} +18.4662 q^{89} +198.304 q^{90} +448.151 q^{91} -620.876 q^{92} +213.616 q^{93} -1708.80 q^{94} +86.7317 q^{95} +691.513 q^{96} -1174.28 q^{97} +197.472 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} + 15 q^{3} + 21 q^{4} - 25 q^{5} + 3 q^{6} - 14 q^{7} + 30 q^{8} + 45 q^{9}+O(q^{10}) $ 5 * q + q^2 + 15 * q^3 + 21 * q^4 - 25 * q^5 + 3 * q^6 - 14 * q^7 + 30 * q^8 + 45 * q^9	\( 5 q + q^{2} + 15 q^{3} + 21 q^{4} - 25 q^{5} + 3 q^{6} - 14 q^{7} + 30 q^{8} + 45 q^{9} - 5 q^{10} + 63 q^{12} + 6 q^{13} - 64 q^{14} - 75 q^{15} - 7 q^{16} - 135 q^{17} + 9 q^{18} - 84 q^{19} - 105 q^{20} - 42 q^{21} + 285 q^{23} + 90 q^{24} + 125 q^{25} + 184 q^{26} + 135 q^{27} - 124 q^{28} + 114 q^{29} - 15 q^{30} - 245 q^{31} + 251 q^{32} + 229 q^{34} + 70 q^{35} + 189 q^{36} + 36 q^{37} + 178 q^{38} + 18 q^{39} - 150 q^{40} - 284 q^{41} - 192 q^{42} + 904 q^{43} - 225 q^{45} + 847 q^{46} + 437 q^{47} - 21 q^{48} + 663 q^{49} + 25 q^{50} - 405 q^{51} + 484 q^{52} - 343 q^{53} + 27 q^{54} + 2006 q^{56} - 252 q^{57} + 1272 q^{58} + 1388 q^{59} - 315 q^{60} - 243 q^{61} - 1799 q^{62} - 126 q^{63} - 684 q^{64} - 30 q^{65} + 1000 q^{67} + 1009 q^{68} + 855 q^{69} + 320 q^{70} + 1246 q^{71} + 270 q^{72} - 1926 q^{73} + 1018 q^{74} + 375 q^{75} + 832 q^{76} + 552 q^{78} + 205 q^{79} + 35 q^{80} + 405 q^{81} - 1708 q^{82} - 176 q^{83} - 372 q^{84} + 675 q^{85} + 1112 q^{86} + 342 q^{87} + 576 q^{89} - 45 q^{90} - 580 q^{91} + 1931 q^{92} - 735 q^{93} - 1253 q^{94} + 420 q^{95} + 753 q^{96} - 846 q^{97} + 253 q^{98}+O(q^{100}) \) 5 * q + q^2 + 15 * q^3 + 21 * q^4 - 25 * q^5 + 3 * q^6 - 14 * q^7 + 30 * q^8 + 45 * q^9 - 5 * q^10 + 63 * q^12 + 6 * q^13 - 64 * q^14 - 75 * q^15 - 7 * q^16 - 135 * q^17 + 9 * q^18 - 84 * q^19 - 105 * q^20 - 42 * q^21 + 285 * q^23 + 90 * q^24 + 125 * q^25 + 184 * q^26 + 135 * q^27 - 124 * q^28 + 114 * q^29 - 15 * q^30 - 245 * q^31 + 251 * q^32 + 229 * q^34 + 70 * q^35 + 189 * q^36 + 36 * q^37 + 178 * q^38 + 18 * q^39 - 150 * q^40 - 284 * q^41 - 192 * q^42 + 904 * q^43 - 225 * q^45 + 847 * q^46 + 437 * q^47 - 21 * q^48 + 663 * q^49 + 25 * q^50 - 405 * q^51 + 484 * q^52 - 343 * q^53 + 27 * q^54 + 2006 * q^56 - 252 * q^57 + 1272 * q^58 + 1388 * q^59 - 315 * q^60 - 243 * q^61 - 1799 * q^62 - 126 * q^63 - 684 * q^64 - 30 * q^65 + 1000 * q^67 + 1009 * q^68 + 855 * q^69 + 320 * q^70 + 1246 * q^71 + 270 * q^72 - 1926 * q^73 + 1018 * q^74 + 375 * q^75 + 832 * q^76 + 552 * q^78 + 205 * q^79 + 35 * q^80 + 405 * q^81 - 1708 * q^82 - 176 * q^83 - 372 * q^84 + 675 * q^85 + 1112 * q^86 + 342 * q^87 + 576 * q^89 - 45 * q^90 - 580 * q^91 + 1931 * q^92 - 735 * q^93 - 1253 * q^94 + 420 * q^95 + 753 * q^96 - 846 * q^97 + 253 * q^98

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 $

$2$	−4.40676	−1.55802	−0.779012	−	0.627009i	$-0.784279\pi$
$2$	−4.40676	−1.55802	−0.779012	+	0.627009i	$0.784279\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	11.4195	1.42744
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−13.2203	−0.899525
$7$	−17.2681	−0.932392	−0.466196	−	0.884681i	$-0.654376\pi$
$7$	−17.2681	−0.932392	−0.466196	+	0.884681i	$0.654376\pi$
$8$	−15.0689	−0.665958
$9$	9.00000	0.333333
$10$	22.0338	0.696769
$11$	0	0
$11$	0	0
$12$	34.2585	0.824132
$13$	−25.9525	−0.553686	−0.276843	−	0.960915i	$-0.589288\pi$
$13$	−25.9525	−0.553686	−0.276843	+	0.960915i	$0.589288\pi$
$14$	76.0965	1.45269
$15$	−15.0000	−0.258199
$16$	−24.9510	−0.389859
$17$	−45.4853	−0.648930	−0.324465	−	0.945898i	$-0.605184\pi$
$17$	−45.4853	−0.648930	−0.324465	+	0.945898i	$0.605184\pi$
$18$	−39.6608	−0.519341
$19$	−17.3463	−0.209449	−0.104724	−	0.994501i	$-0.533396\pi$
$19$	−17.3463	−0.209449	−0.104724	+	0.994501i	$0.533396\pi$
$20$	−57.0975	−0.638370
$21$	−51.8044	−0.538317
$22$	0	0
$23$	−54.3698	−0.492908	−0.246454	−	0.969154i	$-0.579266\pi$
$23$	−54.3698	−0.492908	−0.246454	+	0.969154i	$0.579266\pi$
$24$	−45.2067	−0.384491
$25$	25.0000	0.200000
$26$	114.366	0.862656
$27$	27.0000	0.192450
$28$	−197.194	−1.33093
$29$	−201.607	−1.29095	−0.645474	−	0.763783i	$-0.723340\pi$
$29$	−201.607	−1.29095	−0.645474	+	0.763783i	$0.723340\pi$
$30$	66.1013	0.402280
$31$	71.2055	0.412544	0.206272	−	0.978495i	$-0.433867\pi$
$31$	71.2055	0.412544	0.206272	+	0.978495i	$0.433867\pi$
$32$	230.504	1.27337
$33$	0	0
$34$	200.443	1.01105
$35$	86.3407	0.416978
$36$	102.776	0.475813
$37$	30.1189	0.133825	0.0669124	−	0.997759i	$-0.478685\pi$
$37$	30.1189	0.133825	0.0669124	+	0.997759i	$0.478685\pi$
$38$	76.4411	0.326326
$39$	−77.8574	−0.319671
$40$	75.3446	0.297826
$41$	−339.153	−1.29187	−0.645936	−	0.763392i	$-0.723533\pi$
$41$	−339.153	−1.29187	−0.645936	+	0.763392i	$0.723533\pi$
$42$	228.290	0.838710
$43$	−142.554	−0.505564	−0.252782	−	0.967523i	$-0.581346\pi$
$43$	−142.554	−0.505564	−0.252782	+	0.967523i	$0.581346\pi$
$44$	0	0
$45$	−45.0000	−0.149071
$46$	239.595	0.767963
$47$	387.767	1.20344	0.601720	−	0.798707i	$-0.294482\pi$
$47$	387.767	1.20344	0.601720	+	0.798707i	$0.294482\pi$
$48$	−74.8530	−0.225085
$49$	−44.8112	−0.130645
$50$	−110.169	−0.311605
$51$	−136.456	−0.374660
$52$	−296.364	−0.790353
$53$	207.201	0.537004	0.268502	−	0.963279i	$-0.413471\pi$
$53$	207.201	0.537004	0.268502	+	0.963279i	$0.413471\pi$
$54$	−118.982	−0.299842
$55$	0	0
$56$	260.212	0.620934
$57$	−52.0390	−0.120925
$58$	888.433	2.01133
$59$	−683.032	−1.50717	−0.753586	−	0.657349i	$-0.771678\pi$
$59$	−683.032	−1.50717	−0.753586	+	0.657349i	$0.771678\pi$
$60$	−171.293	−0.368563
$61$	−173.523	−0.364218	−0.182109	−	0.983278i	$-0.558292\pi$
$61$	−173.523	−0.364218	−0.182109	+	0.983278i	$0.558292\pi$
$62$	−313.785	−0.642754
$63$	−155.413	−0.310797
$64$	−816.168	−1.59408
$65$	129.762	0.247616
$66$	0	0
$67$	35.1423	0.0640793	0.0320397	−	0.999487i	$-0.489800\pi$
$67$	35.1423	0.0640793	0.0320397	+	0.999487i	$0.489800\pi$
$68$	−519.420	−0.926307
$69$	−163.110	−0.284581
$70$	−380.483	−0.649662
$71$	331.264	0.553716	0.276858	−	0.960911i	$-0.410707\pi$
$71$	331.264	0.553716	0.276858	+	0.960911i	$0.410707\pi$
$72$	−135.620	−0.221986
$73$	−1049.92	−1.68335	−0.841673	−	0.539987i	$-0.818429\pi$
$73$	−1049.92	−1.68335	−0.841673	+	0.539987i	$0.818429\pi$
$74$	−132.727	−0.208502
$75$	75.0000	0.115470
$76$	−198.087	−0.298975
$77$	0	0
$78$	343.099	0.498055
$79$	302.376	0.430633	0.215316	−	0.976544i	$-0.430922\pi$
$79$	302.376	0.430633	0.215316	+	0.976544i	$0.430922\pi$
$80$	124.755	0.174350
$81$	81.0000	0.111111
$82$	1494.56	2.01277
$83$	831.525	1.09966	0.549829	−	0.835277i	$-0.314693\pi$
$83$	831.525	1.09966	0.549829	+	0.835277i	$0.314693\pi$
$84$	−591.581	−0.768414
$85$	227.427	0.290210
$86$	628.200	0.787680
$87$	−604.821	−0.745329
$88$	0	0
$89$	18.4662	0.0219934	0.0109967	−	0.999940i	$-0.496500\pi$
$89$	18.4662	0.0219934	0.0109967	+	0.999940i	$0.496500\pi$
$90$	198.304	0.232256
$91$	448.151	0.516253
$92$	−620.876	−0.703596
$93$	213.616	0.238183
$94$	−1708.80	−1.87499
$95$	86.7317	0.0936683
$96$	691.513	0.735179
$97$	−1174.28	−1.22917	−0.614586	−	0.788850i	$-0.710677\pi$
$97$	−1174.28	−1.22917	−0.614586	+	0.788850i	$0.710677\pi$
$98$	197.472	0.203548
$99$	0	0
$100$	285.488	0.285488
$101$	−766.438	−0.755084	−0.377542	−	0.925993i	$-0.623231\pi$
$101$	−766.438	−0.755084	−0.377542	+	0.925993i	$0.623231\pi$
$102$	601.328	0.583729
$103$	−128.534	−0.122959	−0.0614797	−	0.998108i	$-0.519582\pi$
$103$	−128.534	−0.122959	−0.0614797	+	0.998108i	$0.519582\pi$
$104$	391.075	0.368732
$105$	259.022	0.240743
$106$	−913.083	−0.836665
$107$	2012.45	1.81824	0.909118	−	0.416539i	$-0.136757\pi$
$107$	2012.45	1.81824	0.909118	+	0.416539i	$0.136757\pi$
$108$	308.327	0.274711
$109$	−33.5794	−0.0295076	−0.0147538	−	0.999891i	$-0.504696\pi$
$109$	−33.5794	−0.0295076	−0.0147538	+	0.999891i	$0.504696\pi$
$110$	0	0
$111$	90.3567	0.0772638
$112$	430.857	0.363502
$113$	2068.36	1.72190	0.860949	−	0.508691i	$-0.169870\pi$
$113$	2068.36	1.72190	0.860949	+	0.508691i	$0.169870\pi$
$114$	229.323	0.188404
$115$	271.849	0.220435
$116$	−2302.25	−1.84275
$117$	−233.572	−0.184562
$118$	3009.96	2.34821
$119$	785.447	0.605057
$120$	226.034	0.171950
$121$	0	0
$122$	764.672	0.567460
$123$	−1017.46	−0.745863
$124$	813.131	0.588881
$125$	−125.000	−0.0894427
$126$	684.869	0.484230
$127$	−1805.49	−1.26151	−0.630753	−	0.775983i	$-0.717254\pi$
$127$	−1805.49	−1.26151	−0.630753	+	0.775983i	$0.717254\pi$
$128$	1752.62	1.21024
$129$	−427.661	−0.291887
$130$	−571.831	−0.385792
$131$	192.802	0.128590	0.0642948	−	0.997931i	$-0.479520\pi$
$131$	192.802	0.128590	0.0642948	+	0.997931i	$0.479520\pi$
$132$	0	0
$133$	299.539	0.195288
$134$	−154.864	−0.0998371
$135$	−135.000	−0.0860663
$136$	685.414	0.432160
$137$	2554.29	1.59291	0.796453	−	0.604701i	$-0.206707\pi$
$137$	2554.29	1.59291	0.796453	+	0.604701i	$0.206707\pi$
$138$	718.784	0.443384
$139$	207.349	0.126526	0.0632629	−	0.997997i	$-0.479849\pi$
$139$	207.349	0.126526	0.0632629	+	0.997997i	$0.479849\pi$
$140$	985.968	0.595211
$141$	1163.30	0.694806
$142$	−1459.80	−0.862702
$143$	0	0
$144$	−224.559	−0.129953
$145$	1008.03	0.577329
$146$	4626.76	2.62269
$147$	−134.434	−0.0754278
$148$	343.943	0.191027
$149$	−2421.25	−1.33125	−0.665627	−	0.746285i	$-0.731836\pi$
$149$	−2421.25	−1.33125	−0.665627	+	0.746285i	$0.731836\pi$
$150$	−330.507	−0.179905
$151$	1155.49	0.622731	0.311366	−	0.950290i	$-0.399214\pi$
$151$	1155.49	0.622731	0.311366	+	0.950290i	$0.399214\pi$
$152$	261.391	0.139484
$153$	−409.368	−0.216310
$154$	0	0
$155$	−356.027	−0.184495
$156$	−889.093	−0.456310
$157$	−3595.97	−1.82796	−0.913980	−	0.405758i	$-0.867008\pi$
$157$	−3595.97	−1.82796	−0.913980	+	0.405758i	$0.867008\pi$
$158$	−1332.50	−0.670936
$159$	621.602	0.310039
$160$	−1152.52	−0.569467
$161$	938.866	0.459584
$162$	−356.947	−0.173114
$163$	−656.832	−0.315626	−0.157813	−	0.987469i	$-0.550444\pi$
$163$	−656.832	−0.315626	−0.157813	+	0.987469i	$0.550444\pi$
$164$	−3872.95	−1.84407
$165$	0	0
$166$	−3664.33	−1.71329
$167$	275.865	0.127827	0.0639134	−	0.997955i	$-0.479642\pi$
$167$	275.865	0.127827	0.0639134	+	0.997955i	$0.479642\pi$
$168$	780.636	0.358496
$169$	−1523.47	−0.693432
$170$	−1002.21	−0.452154
$171$	−156.117	−0.0698162
$172$	−1627.89	−0.721661
$173$	3945.09	1.73375	0.866877	−	0.498522i	$-0.166124\pi$
$173$	3945.09	1.73375	0.866877	+	0.498522i	$0.166124\pi$
$174$	2665.30	1.16124
$175$	−431.704	−0.186478
$176$	0	0
$177$	−2049.10	−0.870167
$178$	−81.3761	−0.0342663
$179$	−2266.87	−0.946558	−0.473279	−	0.880913i	$-0.656930\pi$
$179$	−2266.87	−0.946558	−0.473279	+	0.880913i	$0.656930\pi$
$180$	−513.878	−0.212790
$181$	959.963	0.394218	0.197109	−	0.980382i	$-0.436845\pi$
$181$	959.963	0.394218	0.197109	+	0.980382i	$0.436845\pi$
$182$	−1974.89	−0.804334
$183$	−520.568	−0.210281
$184$	819.294	0.328256
$185$	−150.595	−0.0598483
$186$	−941.355	−0.371094
$187$	0	0
$188$	4428.11	1.71783
$189$	−466.240	−0.179439
$190$	−382.206	−0.145937
$191$	2830.64	1.07235	0.536173	−	0.844108i	$-0.319870\pi$
$191$	2830.64	1.07235	0.536173	+	0.844108i	$0.319870\pi$
$192$	−2448.50	−0.920342
$193$	−2707.04	−1.00962	−0.504811	−	0.863230i	$-0.668438\pi$
$193$	−2707.04	−1.00962	−0.504811	+	0.863230i	$0.668438\pi$
$194$	5174.75	1.91508
$195$	389.287	0.142961
$196$	−511.721	−0.186487
$197$	−3972.45	−1.43668	−0.718339	−	0.695693i	$-0.755097\pi$
$197$	−3972.45	−1.43668	−0.718339	+	0.695693i	$0.755097\pi$
$198$	0	0
$199$	−2201.27	−0.784141	−0.392070	−	0.919935i	$-0.628241\pi$
$199$	−2201.27	−0.784141	−0.392070	+	0.919935i	$0.628241\pi$
$200$	−376.723	−0.133192
$201$	105.427	0.0369962
$202$	3377.51	1.17644
$203$	3481.38	1.20367
$204$	−1558.26	−0.534804
$205$	1695.76	0.577743
$206$	566.417	0.191574
$207$	−489.329	−0.164303
$208$	647.540	0.215860
$209$	0	0
$210$	−1141.45	−0.375083
$211$	1443.87	0.471091	0.235546	−	0.971863i	$-0.424312\pi$
$211$	1443.87	0.471091	0.235546	+	0.971863i	$0.424312\pi$
$212$	2366.13	0.766540
$213$	993.792	0.319688
$214$	−8868.39	−2.83285
$215$	712.769	0.226095
$216$	−406.861	−0.128164
$217$	−1229.59	−0.384653
$218$	147.976	0.0459735
$219$	−3149.77	−0.971881
$220$	0	0
$221$	1180.46	0.359303
$222$	−398.180	−0.120379
$223$	−3669.53	−1.10193	−0.550964	−	0.834529i	$-0.685740\pi$
$223$	−3669.53	−1.10193	−0.550964	+	0.834529i	$0.685740\pi$
$224$	−3980.38	−1.18728
$225$	225.000	0.0666667
$226$	−9114.74	−2.68276
$227$	2428.16	0.709968	0.354984	−	0.934872i	$-0.384486\pi$
$227$	2428.16	0.709968	0.354984	+	0.934872i	$0.384486\pi$
$228$	−594.260	−0.172613
$229$	775.003	0.223640	0.111820	−	0.993728i	$-0.464332\pi$
$229$	775.003	0.223640	0.111820	+	0.993728i	$0.464332\pi$
$230$	−1197.97	−0.343444
$231$	0	0
$232$	3038.00	0.859717
$233$	−5704.53	−1.60393	−0.801967	−	0.597369i	$-0.796213\pi$
$233$	−5704.53	−1.60393	−0.801967	+	0.597369i	$0.796213\pi$
$234$	1029.30	0.287552
$235$	−1938.84	−0.538195
$236$	−7799.88	−2.15140
$237$	907.129	0.248626
$238$	−3461.27	−0.942693
$239$	−1125.02	−0.304483	−0.152242	−	0.988343i	$-0.548649\pi$
$239$	−1125.02	−0.304483	−0.152242	+	0.988343i	$0.548649\pi$
$240$	374.265	0.100661
$241$	2080.62	0.556119	0.278060	−	0.960564i	$-0.410309\pi$
$241$	2080.62	0.556119	0.278060	+	0.960564i	$0.410309\pi$
$242$	0	0
$243$	243.000	0.0641500
$244$	−1981.54	−0.519898
$245$	224.056	0.0584261
$246$	4483.69	1.16207
$247$	450.181	0.115969
$248$	−1072.99	−0.274737
$249$	2494.57	0.634888
$250$	550.845	0.139354
$251$	−2526.70	−0.635394	−0.317697	−	0.948192i	$-0.602909\pi$
$251$	−2526.70	−0.635394	−0.317697	+	0.948192i	$0.602909\pi$
$252$	−1774.74	−0.443644
$253$	0	0
$254$	7956.35	1.96546
$255$	682.280	0.167553
$256$	−1194.02	−0.291510
$257$	3237.81	0.785872	0.392936	−	0.919566i	$-0.371459\pi$
$257$	3237.81	0.785872	0.392936	+	0.919566i	$0.371459\pi$
$258$	1884.60	0.454768
$259$	−520.098	−0.124777
$260$	1481.82	0.353456
$261$	−1814.46	−0.430316
$262$	−849.634	−0.200346
$263$	5376.00	1.26045	0.630225	−	0.776412i	$-0.282962\pi$
$263$	5376.00	1.26045	0.630225	+	0.776412i	$0.282962\pi$
$264$	0	0
$265$	−1036.00	−0.240155
$266$	−1320.00	−0.304264
$267$	55.3986	0.0126979
$268$	401.308	0.0914693
$269$	5083.61	1.15224	0.576122	−	0.817364i	$-0.304565\pi$
$269$	5083.61	1.15224	0.576122	+	0.817364i	$0.304565\pi$
$270$	594.912	0.134093
$271$	−3200.15	−0.717325	−0.358662	−	0.933467i	$-0.616767\pi$
$271$	−3200.15	−0.717325	−0.358662	+	0.933467i	$0.616767\pi$
$272$	1134.90	0.252991
$273$	1344.45	0.298059
$274$	−11256.2	−2.48178
$275$	0	0
$276$	−1862.63	−0.406221
$277$	2445.09	0.530365	0.265182	−	0.964198i	$-0.414568\pi$
$277$	2445.09	0.530365	0.265182	+	0.964198i	$0.414568\pi$
$278$	−913.735	−0.197130
$279$	640.849	0.137515
$280$	−1301.06	−0.277690
$281$	4378.00	0.929429	0.464715	−	0.885461i	$-0.346157\pi$
$281$	4378.00	0.929429	0.464715	+	0.885461i	$0.346157\pi$
$282$	−5126.39	−1.08252
$283$	8084.72	1.69819	0.849093	−	0.528244i	$-0.177149\pi$
$283$	8084.72	1.69819	0.849093	+	0.528244i	$0.177149\pi$
$284$	3782.87	0.790395
$285$	260.195	0.0540794
$286$	0	0
$287$	5856.54	1.20453
$288$	2074.54	0.424456
$289$	−2844.09	−0.578890
$290$	−4442.16	−0.899492
$291$	−3522.83	−0.709663
$292$	−11989.6	−2.40287
$293$	2003.75	0.399523	0.199762	−	0.979845i	$-0.435983\pi$
$293$	2003.75	0.399523	0.199762	+	0.979845i	$0.435983\pi$
$294$	592.416	0.117518
$295$	3415.16	0.674028
$296$	−453.859	−0.0891217
$297$	0	0
$298$	10669.9	2.07412
$299$	1411.03	0.272917
$300$	856.463	0.164826
$301$	2461.64	0.471384
$302$	−5091.96	−0.970230
$303$	−2299.31	−0.435948
$304$	432.809	0.0816555
$305$	867.613	0.162883
$306$	1803.98	0.337016
$307$	6804.87	1.26506	0.632532	−	0.774534i	$-0.282016\pi$
$307$	6804.87	1.26506	0.632532	+	0.774534i	$0.282016\pi$
$308$	0	0
$309$	−385.601	−0.0709906
$310$	1568.93	0.287448
$311$	5093.98	0.928788	0.464394	−	0.885629i	$-0.346272\pi$
$311$	5093.98	0.928788	0.464394	+	0.885629i	$0.346272\pi$
$312$	1173.23	0.212887
$313$	3901.20	0.704501	0.352250	−	0.935906i	$-0.385417\pi$
$313$	3901.20	0.704501	0.352250	+	0.935906i	$0.385417\pi$
$314$	15846.6	2.84801
$315$	777.067	0.138993
$316$	3452.99	0.614701
$317$	−10503.9	−1.86106	−0.930531	−	0.366212i	$-0.880654\pi$
$317$	−10503.9	−1.86106	−0.930531	+	0.366212i	$0.880654\pi$
$318$	−2739.25	−0.483049
$319$	0	0
$320$	4080.84	0.712893
$321$	6037.36	1.04976
$322$	−4137.35	−0.716043
$323$	789.004	0.135918
$324$	924.980	0.158604
$325$	−648.812	−0.110737
$326$	2894.50	0.491753
$327$	−100.738	−0.0170362
$328$	5110.66	0.860333
$329$	−6696.02	−1.12208
$330$	0	0
$331$	120.142	0.0199505	0.00997524	−	0.999950i	$-0.496825\pi$
$331$	120.142	0.0199505	0.00997524	+	0.999950i	$0.496825\pi$
$332$	9495.60	1.56969
$333$	271.070	0.0446083
$334$	−1215.67	−0.199157
$335$	−175.712	−0.0286572
$336$	1292.57	0.209868
$337$	5231.06	0.845561	0.422780	−	0.906232i	$-0.361054\pi$
$337$	5231.06	0.845561	0.422780	+	0.906232i	$0.361054\pi$
$338$	6713.56	1.08038
$339$	6205.07	0.994138
$340$	2597.10	0.414257
$341$	0	0
$342$	687.970	0.108775
$343$	6696.78	1.05420
$344$	2148.13	0.336684
$345$	815.548	0.127268
$346$	−17385.0	−2.70123
$347$	−169.607	−0.0262391	−0.0131195	−	0.999914i	$-0.504176\pi$
$347$	−169.607	−0.0262391	−0.0131195	+	0.999914i	$0.504176\pi$
$348$	−6906.75	−1.06391
$349$	635.896	0.0975322	0.0487661	−	0.998810i	$-0.484471\pi$
$349$	635.896	0.0975322	0.0487661	+	0.998810i	$0.484471\pi$
$350$	1902.41	0.290538
$351$	−700.717	−0.106557
$352$	0	0
$353$	4978.87	0.750704	0.375352	−	0.926882i	$-0.377522\pi$
$353$	4978.87	0.750704	0.375352	+	0.926882i	$0.377522\pi$
$354$	9029.87	1.35574
$355$	−1656.32	−0.247629
$356$	210.875	0.0313942
$357$	2356.34	0.349330
$358$	9989.55	1.47476
$359$	10320.4	1.51725	0.758624	−	0.651529i	$-0.225872\pi$
$359$	10320.4	1.51725	0.758624	+	0.651529i	$0.225872\pi$
$360$	678.101	0.0992752
$361$	−6558.10	−0.956131
$362$	−4230.32	−0.614201
$363$	0	0
$364$	5117.66	0.736919
$365$	5249.62	0.752816
$366$	2294.01	0.327623
$367$	8933.97	1.27071	0.635353	−	0.772222i	$-0.280854\pi$
$367$	8933.97	1.27071	0.635353	+	0.772222i	$0.280854\pi$
$368$	1356.58	0.192165
$369$	−3052.37	−0.430624
$370$	663.634	0.0932450
$371$	−3577.97	−0.500698
$372$	2439.39	0.339991
$373$	12126.2	1.68331	0.841653	−	0.540019i	$-0.181583\pi$
$373$	12126.2	1.68331	0.841653	+	0.540019i	$0.181583\pi$
$374$	0	0
$375$	−375.000	−0.0516398
$376$	−5843.23	−0.801440
$377$	5232.20	0.714780
$378$	2054.61	0.279570
$379$	−8026.43	−1.08784	−0.543918	−	0.839138i	$-0.683060\pi$
$379$	−8026.43	−1.08784	−0.543918	+	0.839138i	$0.683060\pi$
$380$	990.433	0.133706
$381$	−5416.47	−0.728331
$382$	−12473.9	−1.67074
$383$	1748.62	0.233290	0.116645	−	0.993174i	$-0.462786\pi$
$383$	1748.62	0.233290	0.116645	+	0.993174i	$0.462786\pi$
$384$	5257.86	0.698735
$385$	0	0
$386$	11929.3	1.57302
$387$	−1282.98	−0.168521
$388$	−13409.7	−1.75457
$389$	−3854.03	−0.502332	−0.251166	−	0.967944i	$-0.580814\pi$
$389$	−3854.03	−0.502332	−0.251166	+	0.967944i	$0.580814\pi$
$390$	−1715.49	−0.222737
$391$	2473.03	0.319863
$392$	675.256	0.0870040
$393$	578.407	0.0742412
$394$	17505.6	2.23838
$395$	−1511.88	−0.192585
$396$	0	0
$397$	4767.12	0.602657	0.301329	−	0.953520i	$-0.402570\pi$
$397$	4767.12	0.602657	0.301329	+	0.953520i	$0.402570\pi$
$398$	9700.47	1.22171
$399$	898.618	0.112750
$400$	−623.775	−0.0779718
$401$	2382.23	0.296666	0.148333	−	0.988937i	$-0.452609\pi$
$401$	2382.23	0.296666	0.148333	+	0.988937i	$0.452609\pi$
$402$	−464.591	−0.0576410
$403$	−1847.96	−0.228420
$404$	−8752.34	−1.07783
$405$	−405.000	−0.0496904
$406$	−15341.6	−1.87534
$407$	0	0
$408$	2056.24	0.249508
$409$	15694.5	1.89742	0.948709	−	0.316152i	$-0.102391\pi$
$409$	15694.5	1.89742	0.948709	+	0.316152i	$0.102391\pi$
$410$	−7472.82	−0.900137
$411$	7662.88	0.919664
$412$	−1467.79	−0.175517
$413$	11794.7	1.40528
$414$	2156.35	0.255988
$415$	−4157.62	−0.491782
$416$	−5982.15	−0.705046
$417$	622.046	0.0730497
$418$	0	0
$419$	−10683.1	−1.24559	−0.622795	−	0.782385i	$-0.714003\pi$
$419$	−10683.1	−1.24559	−0.622795	+	0.782385i	$0.714003\pi$
$420$	2957.90	0.343645
$421$	15184.3	1.75781	0.878905	−	0.476996i	$-0.158275\pi$
$421$	15184.3	1.75781	0.878905	+	0.476996i	$0.158275\pi$
$422$	−6362.79	−0.733971
$423$	3489.90	0.401146
$424$	−3122.29	−0.357622
$425$	−1137.13	−0.129786
$426$	−4379.40	−0.498081
$427$	2996.41	0.339594
$428$	22981.2	2.59542
$429$	0	0
$430$	−3141.00	−0.352261
$431$	6124.43	0.684463	0.342232	−	0.939616i	$-0.388817\pi$
$431$	6124.43	0.684463	0.342232	+	0.939616i	$0.388817\pi$
$432$	−673.677	−0.0750284
$433$	11982.6	1.32990	0.664950	−	0.746888i	$-0.268453\pi$
$433$	11982.6	1.32990	0.664950	+	0.746888i	$0.268453\pi$
$434$	5418.49	0.599299
$435$	3024.10	0.333321
$436$	−383.460	−0.0421202
$437$	943.118	0.103239
$438$	13880.3	1.51421
$439$	−8105.40	−0.881206	−0.440603	−	0.897702i	$-0.645235\pi$
$439$	−8105.40	−0.881206	−0.440603	+	0.897702i	$0.645235\pi$
$440$	0	0
$441$	−403.301	−0.0435483
$442$	−5201.98	−0.559803
$443$	5682.85	0.609482	0.304741	−	0.952435i	$-0.401430\pi$
$443$	5682.85	0.609482	0.304741	+	0.952435i	$0.401430\pi$
$444$	1031.83	0.110289
$445$	−92.3310	−0.00983575
$446$	16170.7	1.71683
$447$	−7263.76	−0.768599
$448$	14093.7	1.48631
$449$	−13885.2	−1.45943	−0.729714	−	0.683752i	$-0.760347\pi$
$449$	−13885.2	−1.45943	−0.729714	+	0.683752i	$0.760347\pi$
$450$	−991.520	−0.103868
$451$	0	0
$452$	23619.6	2.45790
$453$	3466.47	0.359534
$454$	−10700.3	−1.10615
$455$	−2240.76	−0.230875
$456$	784.172	0.0805312
$457$	13548.6	1.38682	0.693411	−	0.720542i	$-0.256107\pi$
$457$	13548.6	1.38682	0.693411	+	0.720542i	$0.256107\pi$
$458$	−3415.25	−0.348437
$459$	−1228.10	−0.124887
$460$	3104.38	0.314658
$461$	10455.0	1.05626	0.528130	−	0.849163i	$-0.322893\pi$
$461$	10455.0	1.05626	0.528130	+	0.849163i	$0.322893\pi$
$462$	0	0
$463$	−11848.9	−1.18934	−0.594668	−	0.803971i	$-0.702717\pi$
$463$	−11848.9	−1.18934	−0.594668	+	0.803971i	$0.702717\pi$
$464$	5030.29	0.503288
$465$	−1068.08	−0.106519
$466$	25138.5	2.49897
$467$	−3376.08	−0.334532	−0.167266	−	0.985912i	$-0.553494\pi$
$467$	−3376.08	−0.334532	−0.167266	+	0.985912i	$0.553494\pi$
$468$	−2667.28	−0.263451
$469$	−606.842	−0.0597471
$470$	8543.98	0.838520
$471$	−10787.9	−1.05537
$472$	10292.5	1.00371
$473$	0	0
$474$	−3997.50	−0.387365
$475$	−433.659	−0.0418897
$476$	8969.41	0.863681
$477$	1864.81	0.179001
$478$	4957.69	0.474392
$479$	−23.8322	−0.00227332	−0.00113666	−	0.999999i	$-0.500362\pi$
$479$	−23.8322	−0.00227332	−0.00113666	+	0.999999i	$0.500362\pi$
$480$	−3457.56	−0.328782
$481$	−781.660	−0.0740970
$482$	−9168.80	−0.866447
$483$	2816.60	0.265341
$484$	0	0
$485$	5871.38	0.549703
$486$	−1070.84	−0.0999473
$487$	−11095.7	−1.03243	−0.516215	−	0.856459i	$-0.672659\pi$
$487$	−11095.7	−1.03243	−0.516215	+	0.856459i	$0.672659\pi$
$488$	2614.80	0.242554
$489$	−1970.49	−0.182227
$490$	−987.360	−0.0910293
$491$	1189.42	0.109323	0.0546617	−	0.998505i	$-0.482592\pi$
$491$	1189.42	0.109323	0.0546617	+	0.998505i	$0.482592\pi$
$492$	−11618.9	−1.06467
$493$	9170.15	0.837734
$494$	−1983.84	−0.180682
$495$	0	0
$496$	−1776.65	−0.160834
$497$	−5720.32	−0.516280
$498$	−10993.0	−0.989171
$499$	20051.6	1.79886	0.899432	−	0.437061i	$-0.143981\pi$
$499$	20051.6	1.79886	0.899432	+	0.437061i	$0.143981\pi$
$500$	−1427.44	−0.127674
$501$	827.595	0.0738009
$502$	11134.6	0.989959
$503$	18520.0	1.64168	0.820839	−	0.571159i	$-0.193506\pi$
$503$	18520.0	1.64168	0.820839	+	0.571159i	$0.193506\pi$
$504$	2341.91	0.206978
$505$	3832.19	0.337684
$506$	0	0
$507$	−4570.41	−0.400353
$508$	−20617.8	−1.80072
$509$	7591.08	0.661039	0.330519	−	0.943799i	$-0.392776\pi$
$509$	7591.08	0.661039	0.330519	+	0.943799i	$0.392776\pi$
$510$	−3006.64	−0.261051
$511$	18130.2	1.56954
$512$	−8759.18	−0.756064
$513$	−468.351	−0.0403084
$514$	−14268.2	−1.22441
$515$	642.669	0.0549891
$516$	−4883.68	−0.416651
$517$	0	0
$518$	2291.94	0.194406
$519$	11835.3	1.00098
$520$	−1955.38	−0.164902
$521$	6338.56	0.533008	0.266504	−	0.963834i	$-0.414131\pi$
$521$	6338.56	0.533008	0.266504	+	0.963834i	$0.414131\pi$
$522$	7995.89	0.670442
$523$	2702.19	0.225925	0.112962	−	0.993599i	$-0.463966\pi$
$523$	2702.19	0.225925	0.112962	+	0.993599i	$0.463966\pi$
$524$	2201.71	0.183554
$525$	−1295.11	−0.107663
$526$	−23690.7	−1.96381
$527$	−3238.80	−0.267712
$528$	0	0
$529$	−9210.92	−0.757041
$530$	4565.42	0.374168
$531$	−6147.29	−0.502391
$532$	3420.59	0.278762
$533$	8801.85	0.715292
$534$	−244.128	−0.0197836
$535$	−10062.3	−0.813140
$536$	−529.556	−0.0426742
$537$	−6800.61	−0.546496
$538$	−22402.2	−1.79522
$539$	0	0
$540$	−1541.63	−0.122854
$541$	−18227.6	−1.44855	−0.724274	−	0.689512i	$-0.757825\pi$
$541$	−18227.6	−1.44855	−0.724274	+	0.689512i	$0.757825\pi$
$542$	14102.3	1.11761
$543$	2879.89	0.227602
$544$	−10484.6	−0.826327
$545$	167.897	0.0131962
$546$	−5924.68	−0.464382
$547$	−6151.07	−0.480806	−0.240403	−	0.970673i	$-0.577280\pi$
$547$	−6151.07	−0.480806	−0.240403	+	0.970673i	$0.577280\pi$
$548$	29168.8	2.27377
$549$	−1561.70	−0.121406
$550$	0	0
$551$	3497.14	0.270387
$552$	2457.88	0.189519
$553$	−5221.48	−0.401519
$554$	−10774.9	−0.826321
$555$	−451.784	−0.0345534
$556$	2367.82	0.180608
$557$	14422.4	1.09712	0.548561	−	0.836111i	$-0.315176\pi$
$557$	14422.4	1.09712	0.548561	+	0.836111i	$0.315176\pi$
$558$	−2824.07	−0.214251
$559$	3699.62	0.279924
$560$	−2154.29	−0.162563
$561$	0	0
$562$	−19292.8	−1.44807
$563$	−2612.79	−0.195588	−0.0977940	−	0.995207i	$-0.531179\pi$
$563$	−2612.79	−0.195588	−0.0977940	+	0.995207i	$0.531179\pi$
$564$	13284.3	0.991792
$565$	−10341.8	−0.770056
$566$	−35627.4	−2.64581
$567$	−1398.72	−0.103599
$568$	−4991.79	−0.368751
$569$	−5437.19	−0.400595	−0.200298	−	0.979735i	$-0.564191\pi$
$569$	−5437.19	−0.400595	−0.200298	+	0.979735i	$0.564191\pi$
$570$	−1146.62	−0.0842570
$571$	−22747.0	−1.66713	−0.833567	−	0.552419i	$-0.813705\pi$
$571$	−22747.0	−1.66713	−0.833567	+	0.552419i	$0.813705\pi$
$572$	0	0
$573$	8491.92	0.619119
$574$	−25808.3	−1.87669
$575$	−1359.25	−0.0985817
$576$	−7345.51	−0.531359
$577$	−14121.4	−1.01886	−0.509429	−	0.860513i	$-0.670143\pi$
$577$	−14121.4	−1.01886	−0.509429	+	0.860513i	$0.670143\pi$
$578$	12533.2	0.901924
$579$	−8121.13	−0.582906
$580$	11511.3	0.824101
$581$	−14358.9	−1.02531
$582$	15524.3	1.10567
$583$	0	0
$584$	15821.2	1.12104
$585$	1167.86	0.0825387
$586$	−8830.04	−0.622467
$587$	18666.7	1.31253	0.656265	−	0.754530i	$-0.272135\pi$
$587$	18666.7	1.31253	0.656265	+	0.754530i	$0.272135\pi$
$588$	−1535.16	−0.107669
$589$	−1235.15	−0.0864069
$590$	−15049.8	−1.05015
$591$	−11917.4	−0.829466
$592$	−751.497	−0.0521728
$593$	12449.1	0.862098	0.431049	−	0.902329i	$-0.358144\pi$
$593$	12449.1	0.862098	0.431049	+	0.902329i	$0.358144\pi$
$594$	0	0
$595$	−3927.23	−0.270590
$596$	−27649.5	−1.90028
$597$	−6603.81	−0.452724
$598$	−6218.07	−0.425211
$599$	6986.28	0.476547	0.238274	−	0.971198i	$-0.423419\pi$
$599$	6986.28	0.476547	0.238274	+	0.971198i	$0.423419\pi$
$600$	−1130.17	−0.0768982
$601$	10551.9	0.716174	0.358087	−	0.933688i	$-0.383429\pi$
$601$	10551.9	0.716174	0.358087	+	0.933688i	$0.383429\pi$
$602$	−10847.8	−0.734427
$603$	316.281	0.0213598
$604$	13195.1	0.888910
$605$	0	0
$606$	10132.5	0.679217
$607$	−3483.36	−0.232925	−0.116462	−	0.993195i	$-0.537155\pi$
$607$	−3483.36	−0.232925	−0.116462	+	0.993195i	$0.537155\pi$
$608$	−3998.41	−0.266705
$609$	10444.1	0.694939
$610$	−3823.36	−0.253776
$611$	−10063.5	−0.666328
$612$	−4674.78	−0.308769
$613$	20645.3	1.36029	0.680144	−	0.733079i	$-0.261917\pi$
$613$	20645.3	1.36029	0.680144	+	0.733079i	$0.261917\pi$
$614$	−29987.4	−1.97100
$615$	5087.29	0.333560
$616$	0	0
$617$	15804.3	1.03121	0.515606	−	0.856826i	$-0.327567\pi$
$617$	15804.3	1.03121	0.515606	+	0.856826i	$0.327567\pi$
$618$	1699.25	0.110605
$619$	3126.34	0.203002	0.101501	−	0.994835i	$-0.467636\pi$
$619$	3126.34	0.203002	0.101501	+	0.994835i	$0.467636\pi$
$620$	−4065.65	−0.263356
$621$	−1467.99	−0.0948603
$622$	−22447.9	−1.44707
$623$	−318.877	−0.0205065
$624$	1942.62	0.124627
$625$	625.000	0.0400000
$626$	−17191.6	−1.09763
$627$	0	0
$628$	−41064.2	−2.60930
$629$	−1369.97	−0.0868429
$630$	−3424.34	−0.216554
$631$	9740.71	0.614535	0.307268	−	0.951623i	$-0.400585\pi$
$631$	9740.71	0.614535	0.307268	+	0.951623i	$0.400585\pi$
$632$	−4556.48	−0.286783
$633$	4331.62	0.271985
$634$	46288.1	2.89958
$635$	9027.45	0.564163
$636$	7098.39	0.442562
$637$	1162.96	0.0723362
$638$	0	0
$639$	2981.38	0.184572
$640$	−8763.10	−0.541237
$641$	15919.2	0.980919	0.490460	−	0.871464i	$-0.336829\pi$
$641$	15919.2	0.980919	0.490460	+	0.871464i	$0.336829\pi$
$642$	−26605.2	−1.63555
$643$	30839.6	1.89144	0.945719	−	0.324987i	$-0.105360\pi$
$643$	30839.6	1.89144	0.945719	+	0.324987i	$0.105360\pi$
$644$	10721.4	0.656028
$645$	2138.31	0.130536
$646$	−3476.95	−0.211763
$647$	8710.68	0.529292	0.264646	−	0.964346i	$-0.414745\pi$
$647$	8710.68	0.529292	0.264646	+	0.964346i	$0.414745\pi$
$648$	−1220.58	−0.0739953
$649$	0	0
$650$	2859.16	0.172531
$651$	−3688.76	−0.222080
$652$	−7500.69	−0.450536
$653$	−28870.6	−1.73016	−0.865078	−	0.501637i	$-0.832731\pi$
$653$	−28870.6	−1.73016	−0.865078	+	0.501637i	$0.832731\pi$
$654$	443.929	0.0265428
$655$	−964.012	−0.0575070
$656$	8462.19	0.503648
$657$	−9449.32	−0.561116
$658$	29507.7	1.74822
$659$	13960.9	0.825252	0.412626	−	0.910901i	$-0.364612\pi$
$659$	13960.9	0.825252	0.412626	+	0.910901i	$0.364612\pi$
$660$	0	0
$661$	−13524.8	−0.795842	−0.397921	−	0.917420i	$-0.630268\pi$
$661$	−13524.8	−0.795842	−0.397921	+	0.917420i	$0.630268\pi$
$662$	−529.437	−0.0310833
$663$	3541.37	0.207444
$664$	−12530.2	−0.732327
$665$	−1497.70	−0.0873356
$666$	−1194.54	−0.0695007
$667$	10961.3	0.636319
$668$	3150.24	0.182465
$669$	−11008.6	−0.636198
$670$	774.318	0.0446485
$671$	0	0
$672$	−11941.1	−0.685476
$673$	9709.59	0.556133	0.278066	−	0.960562i	$-0.410307\pi$
$673$	9709.59	0.556133	0.278066	+	0.960562i	$0.410307\pi$
$674$	−23052.0	−1.31740
$675$	675.000	0.0384900
$676$	−17397.3	−0.989830
$677$	−28005.4	−1.58986	−0.794929	−	0.606703i	$-0.792492\pi$
$677$	−28005.4	−1.58986	−0.794929	+	0.606703i	$0.792492\pi$
$678$	−27344.2	−1.54889
$679$	20277.6	1.14607
$680$	−3427.07	−0.193268
$681$	7284.49	0.409901
$682$	0	0
$683$	−26790.6	−1.50090	−0.750449	−	0.660929i	$-0.770163\pi$
$683$	−26790.6	−1.50090	−0.750449	+	0.660929i	$0.770163\pi$
$684$	−1782.78	−0.0996583
$685$	−12771.5	−0.712369
$686$	−29511.1	−1.64248
$687$	2325.01	0.129119
$688$	3556.86	0.197099
$689$	−5377.37	−0.297332
$690$	−3593.92	−0.198287
$691$	−9726.16	−0.535456	−0.267728	−	0.963494i	$-0.586273\pi$
$691$	−9726.16	−0.535456	−0.267728	+	0.963494i	$0.586273\pi$
$692$	45050.9	2.47483
$693$	0	0
$694$	747.416	0.0408811
$695$	−1036.74	−0.0565840
$696$	9113.99	0.496358
$697$	15426.5	0.838334
$698$	−2802.24	−0.151957
$699$	−17113.6	−0.926031
$700$	−4929.84	−0.266186
$701$	−18359.7	−0.989209	−0.494604	−	0.869118i	$-0.664687\pi$
$701$	−18359.7	−0.989209	−0.494604	+	0.869118i	$0.664687\pi$
$702$	3087.89	0.166018
$703$	−522.453	−0.0280294
$704$	0	0
$705$	−5816.51	−0.310727
$706$	−21940.7	−1.16961
$707$	13235.0	0.704034
$708$	−23399.7	−1.24211
$709$	16955.7	0.898147	0.449073	−	0.893495i	$-0.351754\pi$
$709$	16955.7	0.898147	0.449073	+	0.893495i	$0.351754\pi$
$710$	7299.00	0.385812
$711$	2721.39	0.143544
$712$	−278.266	−0.0146467
$713$	−3871.43	−0.203347
$714$	−10383.8	−0.544264
$715$	0	0
$716$	−25886.5	−1.35115
$717$	−3375.06	−0.175793
$718$	−45479.7	−2.36391
$719$	−14796.1	−0.767454	−0.383727	−	0.923446i	$-0.625360\pi$
$719$	−14796.1	−0.767454	−0.383727	+	0.923446i	$0.625360\pi$
$720$	1122.79	0.0581168
$721$	2219.54	0.114646
$722$	28900.0	1.48968
$723$	6241.87	0.321076
$724$	10962.3	0.562722
$725$	−5040.17	−0.258189
$726$	0	0
$727$	−21718.1	−1.10795	−0.553974	−	0.832534i	$-0.686889\pi$
$727$	−21718.1	−1.10795	−0.553974	+	0.832534i	$0.686889\pi$
$728$	−6753.15	−0.343803
$729$	729.000	0.0370370
$730$	−23133.8	−1.17290
$731$	6484.10	0.328075
$732$	−5944.62	−0.300163
$733$	3803.06	0.191636	0.0958181	−	0.995399i	$-0.469453\pi$
$733$	3803.06	0.191636	0.0958181	+	0.995399i	$0.469453\pi$
$734$	−39369.8	−1.97979
$735$	672.168	0.0337323
$736$	−12532.5	−0.627654
$737$	0	0
$738$	13451.1	0.670922
$739$	−34354.2	−1.71007	−0.855034	−	0.518572i	$-0.826464\pi$
$739$	−34354.2	−1.71007	−0.855034	+	0.518572i	$0.826464\pi$
$740$	−1719.71	−0.0854297
$741$	1350.54	0.0669547
$742$	15767.3	0.780100
$743$	−2128.50	−0.105097	−0.0525486	−	0.998618i	$-0.516734\pi$
$743$	−2128.50	−0.105097	−0.0525486	+	0.998618i	$0.516734\pi$
$744$	−3218.97	−0.158620
$745$	12106.3	0.595355
$746$	−53437.4	−2.62263
$747$	7483.72	0.366553
$748$	0	0
$749$	−34751.3	−1.69531
$750$	1652.53	0.0804560
$751$	14337.1	0.696629	0.348314	−	0.937378i	$-0.386754\pi$
$751$	14337.1	0.696629	0.348314	+	0.937378i	$0.386754\pi$
$752$	−9675.18	−0.469172
$753$	−7580.10	−0.366845
$754$	−23057.0	−1.11364
$755$	−5777.45	−0.278494
$756$	−5324.23	−0.256138
$757$	−17730.4	−0.851286	−0.425643	−	0.904891i	$-0.639952\pi$
$757$	−17730.4	−0.851286	−0.425643	+	0.904891i	$0.639952\pi$
$758$	35370.5	1.69488
$759$	0	0
$760$	−1306.95	−0.0623792
$761$	1786.97	0.0851218	0.0425609	−	0.999094i	$-0.486448\pi$
$761$	1786.97	0.0851218	0.0425609	+	0.999094i	$0.486448\pi$
$762$	23869.1	1.13476
$763$	579.854	0.0275126
$764$	32324.5	1.53071
$765$	2046.84	0.0967368
$766$	−7705.72	−0.363471
$767$	17726.4	0.834501
$768$	−3582.07	−0.168303
$769$	30714.7	1.44031	0.720157	−	0.693811i	$-0.244070\pi$
$769$	30714.7	1.44031	0.720157	+	0.693811i	$0.244070\pi$
$770$	0	0
$771$	9713.43	0.453723
$772$	−30913.1	−1.44117
$773$	−11252.7	−0.523588	−0.261794	−	0.965124i	$-0.584314\pi$
$773$	−11252.7	−0.523588	−0.261794	+	0.965124i	$0.584314\pi$
$774$	5653.80	0.262560
$775$	1780.14	0.0825089
$776$	17695.1	0.818577
$777$	−1560.29	−0.0720402
$778$	16983.8	0.782645
$779$	5883.06	0.270581
$780$	4445.46	0.204068
$781$	0	0
$782$	−10898.0	−0.498354
$783$	−5443.39	−0.248443
$784$	1118.08	0.0509331
$785$	17979.9	0.817489
$786$	−2548.90	−0.115670
$787$	26404.2	1.19594	0.597972	−	0.801517i	$-0.295973\pi$
$787$	26404.2	1.19594	0.597972	+	0.801517i	$0.295973\pi$
$788$	−45363.4	−2.05077
$789$	16128.0	0.727722
$790$	6662.49	0.300052
$791$	−35716.7	−1.60548
$792$	0	0
$793$	4503.34	0.201662
$794$	−21007.5	−0.938954
$795$	−3108.01	−0.138654
$796$	−25137.4	−1.11931
$797$	31752.2	1.41119	0.705597	−	0.708613i	$-0.250679\pi$
$797$	31752.2	1.41119	0.705597	+	0.708613i	$0.250679\pi$
$798$	−3959.99	−0.175667
$799$	−17637.7	−0.780948
$800$	5762.61	0.254674
$801$	166.196	0.00733114
$802$	−10497.9	−0.462212
$803$	0	0
$804$	1203.92	0.0528098
$805$	−4694.33	−0.205532
$806$	8143.50	0.355884
$807$	15250.8	0.665248
$808$	11549.4	0.502854
$809$	703.110	0.0305563	0.0152781	−	0.999883i	$-0.495137\pi$
$809$	703.110	0.0305563	0.0152781	+	0.999883i	$0.495137\pi$
$810$	1784.74	0.0774188
$811$	−2813.77	−0.121831	−0.0609154	−	0.998143i	$-0.519402\pi$
$811$	−2813.77	−0.121831	−0.0609154	+	0.998143i	$0.519402\pi$
$812$	39755.6	1.71816
$813$	−9600.44	−0.414148
$814$	0	0
$815$	3284.16	0.141152
$816$	3404.71	0.146065
$817$	2472.79	0.105890
$818$	−69161.9	−2.95622
$819$	4033.36	0.172084
$820$	19364.8	0.824692
$821$	−16337.2	−0.694485	−0.347242	−	0.937775i	$-0.612882\pi$
$821$	−16337.2	−0.694485	−0.347242	+	0.937775i	$0.612882\pi$
$822$	−33768.5	−1.43286
$823$	−23570.6	−0.998324	−0.499162	−	0.866509i	$-0.666359\pi$
$823$	−23570.6	−0.998324	−0.499162	+	0.866509i	$0.666359\pi$
$824$	1936.86	0.0818858
$825$	0	0
$826$	−51976.3	−2.18945
$827$	40003.0	1.68203	0.841016	−	0.541011i	$-0.181958\pi$
$827$	40003.0	1.68203	0.841016	+	0.541011i	$0.181958\pi$
$828$	−5587.89	−0.234532
$829$	3230.70	0.135352	0.0676760	−	0.997707i	$-0.478442\pi$
$829$	3230.70	0.135352	0.0676760	+	0.997707i	$0.478442\pi$
$830$	18321.6	0.766209
$831$	7335.26	0.306206
$832$	21181.6	0.882619
$833$	2038.25	0.0847793
$834$	−2741.20	−0.113813
$835$	−1379.33	−0.0571659
$836$	0	0
$837$	1922.55	0.0793942
$838$	47077.7	1.94066
$839$	29047.9	1.19529	0.597643	−	0.801762i	$-0.296104\pi$
$839$	29047.9	1.19529	0.597643	+	0.801762i	$0.296104\pi$
$840$	−3903.18	−0.160325
$841$	16256.4	0.666545
$842$	−66913.6	−2.73871
$843$	13134.0	0.536606
$844$	16488.3	0.672453
$845$	7617.35	0.310112
$846$	−15379.2	−0.624996
$847$	0	0
$848$	−5169.86	−0.209356
$849$	24254.1	0.980448
$850$	5011.07	0.202210
$851$	−1637.56	−0.0659634
$852$	11348.6	0.456335
$853$	−8928.12	−0.358374	−0.179187	−	0.983815i	$-0.557347\pi$
$853$	−8928.12	−0.358374	−0.179187	+	0.983815i	$0.557347\pi$
$854$	−13204.5	−0.529095
$855$	780.586	0.0312228
$856$	−30325.5	−1.21087
$857$	−15643.0	−0.623516	−0.311758	−	0.950162i	$-0.600918\pi$
$857$	−15643.0	−0.623516	−0.311758	+	0.950162i	$0.600918\pi$
$858$	0	0
$859$	18677.0	0.741853	0.370926	−	0.928662i	$-0.379040\pi$
$859$	18677.0	0.741853	0.370926	+	0.928662i	$0.379040\pi$
$860$	8139.47	0.322737
$861$	17569.6	0.695436
$862$	−26988.9	−1.06641
$863$	10385.3	0.409639	0.204820	−	0.978800i	$-0.434339\pi$
$863$	10385.3	0.409639	0.204820	+	0.978800i	$0.434339\pi$
$864$	6223.61	0.245060
$865$	−19725.4	−0.775358
$866$	−52804.3	−2.07201
$867$	−8532.26	−0.334222
$868$	−14041.3	−0.549068
$869$	0	0
$870$	−13326.5	−0.519322
$871$	−912.030	−0.0354798
$872$	506.005	0.0196508
$873$	−10568.5	−0.409724
$874$	−4156.09	−0.160849
$875$	2158.52	0.0833957
$876$	−35968.8	−1.38730
$877$	−28636.4	−1.10260	−0.551302	−	0.834306i	$-0.685869\pi$
$877$	−28636.4	−1.10260	−0.551302	+	0.834306i	$0.685869\pi$
$878$	35718.5	1.37294
$879$	6011.25	0.230665
$880$	0	0
$881$	−23560.1	−0.900976	−0.450488	−	0.892782i	$-0.648750\pi$
$881$	−23560.1	−0.900976	−0.450488	+	0.892782i	$0.648750\pi$
$882$	1777.25	0.0678492
$883$	−8251.01	−0.314460	−0.157230	−	0.987562i	$-0.550256\pi$
$883$	−8251.01	−0.314460	−0.157230	+	0.987562i	$0.550256\pi$
$884$	13480.2	0.512883
$885$	10245.5	0.389150
$886$	−25043.0	−0.949588
$887$	−37994.8	−1.43827	−0.719133	−	0.694873i	$-0.755461\pi$
$887$	−37994.8	−1.43827	−0.719133	+	0.694873i	$0.755461\pi$
$888$	−1361.58	−0.0514545
$889$	31177.5	1.17622
$890$	406.880	0.0153243
$891$	0	0
$892$	−41904.2	−1.57293
$893$	−6726.35	−0.252059
$894$	32009.6	1.19750
$895$	11334.4	0.423314
$896$	−30264.5	−1.12842
$897$	4233.09	0.157568
$898$	61188.7	2.27382
$899$	−14355.5	−0.532573
$900$	2569.39	0.0951625
$901$	−9424.59	−0.348478
$902$	0	0
$903$	7384.92	0.272154
$904$	−31167.9	−1.14671
$905$	−4799.81	−0.176300
$906$	−15275.9	−0.560162
$907$	35805.6	1.31081	0.655405	−	0.755278i	$-0.272498\pi$
$907$	35805.6	1.31081	0.655405	+	0.755278i	$0.272498\pi$
$908$	27728.4	1.01344
$909$	−6897.94	−0.251695
$910$	9874.46	0.359709
$911$	−19846.0	−0.721763	−0.360882	−	0.932612i	$-0.617524\pi$
$911$	−19846.0	−0.721763	−0.360882	+	0.932612i	$0.617524\pi$
$912$	1298.43	0.0471438
$913$	0	0
$914$	−59705.5	−2.16070
$915$	2602.84	0.0940406
$916$	8850.14	0.319232
$917$	−3329.34	−0.119896
$918$	5411.95	0.194576
$919$	−26202.7	−0.940529	−0.470264	−	0.882526i	$-0.655841\pi$
$919$	−26202.7	−0.940529	−0.470264	+	0.882526i	$0.655841\pi$
$920$	−4096.47	−0.146801
$921$	20414.6	0.730385
$922$	−46072.5	−1.64568
$923$	−8597.12	−0.306585
$924$	0	0
$925$	752.973	0.0267650
$926$	52215.0	1.85301
$927$	−1156.80	−0.0409864
$928$	−46471.3	−1.64385
$929$	44085.2	1.55693	0.778466	−	0.627687i	$-0.215998\pi$
$929$	44085.2	1.55693	0.778466	+	0.627687i	$0.215998\pi$
$930$	4706.78	0.165958
$931$	777.310	0.0273634
$932$	−65142.9	−2.28952
$933$	15281.9	0.536236
$934$	14877.6	0.521209
$935$	0	0
$936$	3519.68	0.122911
$937$	−4515.66	−0.157439	−0.0787194	−	0.996897i	$-0.525083\pi$
$937$	−4515.66	−0.157439	−0.0787194	+	0.996897i	$0.525083\pi$
$938$	2674.21	0.0930874
$939$	11703.6	0.406744
$940$	−22140.5	−0.768239
$941$	−2866.89	−0.0993177	−0.0496589	−	0.998766i	$-0.515813\pi$
$941$	−2866.89	−0.0993177	−0.0496589	+	0.998766i	$0.515813\pi$
$942$	47539.7	1.64430
$943$	18439.7	0.636775
$944$	17042.3	0.587585
$945$	2331.20	0.0802475
$946$	0	0
$947$	47495.1	1.62976	0.814880	−	0.579630i	$-0.196803\pi$
$947$	47495.1	1.62976	0.814880	+	0.579630i	$0.196803\pi$
$948$	10359.0	0.354898
$949$	27248.1	0.932046
$950$	1911.03	0.0652652
$951$	−31511.7	−1.07449
$952$	−11835.8	−0.402943
$953$	3804.18	0.129307	0.0646535	−	0.997908i	$-0.479406\pi$
$953$	3804.18	0.129307	0.0646535	+	0.997908i	$0.479406\pi$
$954$	−8217.75	−0.278888
$955$	−14153.2	−0.479567
$956$	−12847.2	−0.434631
$957$	0	0
$958$	105.023	0.00354189
$959$	−44107.9	−1.48521
$960$	12242.5	0.411589
$961$	−24720.8	−0.829807
$962$	3444.59	0.115445
$963$	18112.1	0.606079
$964$	23759.7	0.793826
$965$	13535.2	0.451517
$966$	−12412.1	−0.413407
$967$	−14966.8	−0.497726	−0.248863	−	0.968539i	$-0.580057\pi$
$967$	−14966.8	−0.497726	−0.248863	+	0.968539i	$0.580057\pi$
$968$	0	0
$969$	2367.01	0.0784720
$970$	−25873.8	−0.856450
$971$	24248.6	0.801414	0.400707	−	0.916206i	$-0.368764\pi$
$971$	24248.6	0.801414	0.400707	+	0.916206i	$0.368764\pi$
$972$	2774.94	0.0915702
$973$	−3580.53	−0.117972
$974$	48896.0	1.60855
$975$	−1946.44	−0.0639342
$976$	4329.56	0.141994
$977$	−5632.90	−0.184455	−0.0922275	−	0.995738i	$-0.529399\pi$
$977$	−5632.90	−0.184455	−0.0922275	+	0.995738i	$0.529399\pi$
$978$	8683.49	0.283913
$979$	0	0
$980$	2558.61	0.0833997
$981$	−302.215	−0.00983586
$982$	−5241.49	−0.170328
$983$	−34965.9	−1.13453	−0.567264	−	0.823536i	$-0.691998\pi$
$983$	−34965.9	−1.13453	−0.567264	+	0.823536i	$0.691998\pi$
$984$	15332.0	0.496713
$985$	19862.3	0.642502
$986$	−40410.6	−1.30521
$987$	−20088.1	−0.647832
$988$	5140.84	0.165538
$989$	7750.63	0.249197
$990$	0	0
$991$	2331.24	0.0747267	0.0373634	−	0.999302i	$-0.488104\pi$
$991$	2331.24	0.0747267	0.0373634	+	0.999302i	$0.488104\pi$
$992$	16413.2	0.525321
$993$	360.426	0.0115184
$994$	25208.0	0.804377
$995$	11006.4	0.350678
$996$	28486.8	0.906263
$997$	−13163.2	−0.418136	−0.209068	−	0.977901i	$-0.567043\pi$
$997$	−13163.2	−0.418136	−0.209068	+	0.977901i	$0.567043\pi$
$998$	−88362.5	−2.80267
$999$	813.211	0.0257546

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.4.a.y.1.1	yes	5
11.10	odd	2		1815.4.a.x.1.5	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1815.4.a.x.1.5	✓	5	11.10	odd	2
1815.4.a.y.1.1	yes	5	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:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1815.a (trivial)

\(f(q)\)	\(=\)	\(q-4.40676 q^{2} +3.00000 q^{3} +11.4195 q^{4} -5.00000 q^{5} -13.2203 q^{6} -17.2681 q^{7} -15.0689 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-4.40676 q^{2} +3.00000 q^{3} +11.4195 q^{4} -5.00000 q^{5} -13.2203 q^{6} -17.2681 q^{7} -15.0689 q^{8} +9.00000 q^{9} +22.0338 q^{10} +34.2585 q^{12} -25.9525 q^{13} +76.0965 q^{14} -15.0000 q^{15} -24.9510 q^{16} -45.4853 q^{17} -39.6608 q^{18} -17.3463 q^{19} -57.0975 q^{20} -51.8044 q^{21} -54.3698 q^{23} -45.2067 q^{24} +25.0000 q^{25} +114.366 q^{26} +27.0000 q^{27} -197.194 q^{28} -201.607 q^{29} +66.1013 q^{30} +71.2055 q^{31} +230.504 q^{32} +200.443 q^{34} +86.3407 q^{35} +102.776 q^{36} +30.1189 q^{37} +76.4411 q^{38} -77.8574 q^{39} +75.3446 q^{40} -339.153 q^{41} +228.290 q^{42} -142.554 q^{43} -45.0000 q^{45} +239.595 q^{46} +387.767 q^{47} -74.8530 q^{48} -44.8112 q^{49} -110.169 q^{50} -136.456 q^{51} -296.364 q^{52} +207.201 q^{53} -118.982 q^{54} +260.212 q^{56} -52.0390 q^{57} +888.433 q^{58} -683.032 q^{59} -171.293 q^{60} -173.523 q^{61} -313.785 q^{62} -155.413 q^{63} -816.168 q^{64} +129.762 q^{65} +35.1423 q^{67} -519.420 q^{68} -163.110 q^{69} -380.483 q^{70} +331.264 q^{71} -135.620 q^{72} -1049.92 q^{73} -132.727 q^{74} +75.0000 q^{75} -198.087 q^{76} +343.099 q^{78} +302.376 q^{79} +124.755 q^{80} +81.0000 q^{81} +1494.56 q^{82} +831.525 q^{83} -591.581 q^{84} +227.427 q^{85} +628.200 q^{86} -604.821 q^{87} +18.4662 q^{89} +198.304 q^{90} +448.151 q^{91} -620.876 q^{92} +213.616 q^{93} -1708.80 q^{94} +86.7317 q^{95} +691.513 q^{96} -1174.28 q^{97} +197.472 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} + 15 q^{3} + 21 q^{4} - 25 q^{5} + 3 q^{6} - 14 q^{7} + 30 q^{8} + 45 q^{9}+O(q^{10}) \) 5 * q + q^2 + 15 * q^3 + 21 * q^4 - 25 * q^5 + 3 * q^6 - 14 * q^7 + 30 * q^8 + 45 * q^9	\( 5 q + q^{2} + 15 q^{3} + 21 q^{4} - 25 q^{5} + 3 q^{6} - 14 q^{7} + 30 q^{8} + 45 q^{9} - 5 q^{10} + 63 q^{12} + 6 q^{13} - 64 q^{14} - 75 q^{15} - 7 q^{16} - 135 q^{17} + 9 q^{18} - 84 q^{19} - 105 q^{20} - 42 q^{21} + 285 q^{23} + 90 q^{24} + 125 q^{25} + 184 q^{26} + 135 q^{27} - 124 q^{28} + 114 q^{29} - 15 q^{30} - 245 q^{31} + 251 q^{32} + 229 q^{34} + 70 q^{35} + 189 q^{36} + 36 q^{37} + 178 q^{38} + 18 q^{39} - 150 q^{40} - 284 q^{41} - 192 q^{42} + 904 q^{43} - 225 q^{45} + 847 q^{46} + 437 q^{47} - 21 q^{48} + 663 q^{49} + 25 q^{50} - 405 q^{51} + 484 q^{52} - 343 q^{53} + 27 q^{54} + 2006 q^{56} - 252 q^{57} + 1272 q^{58} + 1388 q^{59} - 315 q^{60} - 243 q^{61} - 1799 q^{62} - 126 q^{63} - 684 q^{64} - 30 q^{65} + 1000 q^{67} + 1009 q^{68} + 855 q^{69} + 320 q^{70} + 1246 q^{71} + 270 q^{72} - 1926 q^{73} + 1018 q^{74} + 375 q^{75} + 832 q^{76} + 552 q^{78} + 205 q^{79} + 35 q^{80} + 405 q^{81} - 1708 q^{82} - 176 q^{83} - 372 q^{84} + 675 q^{85} + 1112 q^{86} + 342 q^{87} + 576 q^{89} - 45 q^{90} - 580 q^{91} + 1931 q^{92} - 735 q^{93} - 1253 q^{94} + 420 q^{95} + 753 q^{96} - 846 q^{97} + 253 q^{98}+O(q^{100}) \) 5 * q + q^2 + 15 * q^3 + 21 * q^4 - 25 * q^5 + 3 * q^6 - 14 * q^7 + 30 * q^8 + 45 * q^9 - 5 * q^10 + 63 * q^12 + 6 * q^13 - 64 * q^14 - 75 * q^15 - 7 * q^16 - 135 * q^17 + 9 * q^18 - 84 * q^19 - 105 * q^20 - 42 * q^21 + 285 * q^23 + 90 * q^24 + 125 * q^25 + 184 * q^26 + 135 * q^27 - 124 * q^28 + 114 * q^29 - 15 * q^30 - 245 * q^31 + 251 * q^32 + 229 * q^34 + 70 * q^35 + 189 * q^36 + 36 * q^37 + 178 * q^38 + 18 * q^39 - 150 * q^40 - 284 * q^41 - 192 * q^42 + 904 * q^43 - 225 * q^45 + 847 * q^46 + 437 * q^47 - 21 * q^48 + 663 * q^49 + 25 * q^50 - 405 * q^51 + 484 * q^52 - 343 * q^53 + 27 * q^54 + 2006 * q^56 - 252 * q^57 + 1272 * q^58 + 1388 * q^59 - 315 * q^60 - 243 * q^61 - 1799 * q^62 - 126 * q^63 - 684 * q^64 - 30 * q^65 + 1000 * q^67 + 1009 * q^68 + 855 * q^69 + 320 * q^70 + 1246 * q^71 + 270 * q^72 - 1926 * q^73 + 1018 * q^74 + 375 * q^75 + 832 * q^76 + 552 * q^78 + 205 * q^79 + 35 * q^80 + 405 * q^81 - 1708 * q^82 - 176 * q^83 - 372 * q^84 + 675 * q^85 + 1112 * q^86 + 342 * q^87 + 576 * q^89 - 45 * q^90 - 580 * q^91 + 1931 * q^92 - 735 * q^93 - 1253 * q^94 + 420 * q^95 + 753 * q^96 - 846 * q^97 + 253 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more