LMFDB - Embedded newform 1815.4.a.x.1.5

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			1.5
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	$-0.215721\pi$
$2$	4.40676	1.55802	0.779012	+	0.627009i	$0.215721\pi$
$3$	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	$-0.345624\pi$
$7$	17.2681	0.932392	0.466196	+	0.884681i	$0.345624\pi$
$8$	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	$-0.410712\pi$
$13$	25.9525	0.553686	0.276843	+	0.960915i	$0.410712\pi$
$14$	76.0965	1.45269
$15$	−15.0000	−0.258199
$16$	−24.9510	−0.389859
$17$	45.4853	0.648930	0.324465	−	0.945898i	$-0.394816\pi$
$17$	45.4853	0.648930	0.324465	+	0.945898i	$0.394816\pi$
$18$	39.6608	0.519341
$19$	17.3463	0.209449	0.104724	−	0.994501i	$-0.466604\pi$
$19$	17.3463	0.209449	0.104724	+	0.994501i	$0.466604\pi$
$20$	−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	$-0.276660\pi$
$29$	201.607	1.29095	0.645474	+	0.763783i	$0.276660\pi$
$30$	−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	$-0.276467\pi$
$41$	339.153	1.29187	0.645936	+	0.763392i	$0.276467\pi$
$42$	228.290	0.838710
$43$	142.554	0.505564	0.252782	−	0.967523i	$-0.418654\pi$
$43$	142.554	0.505564	0.252782	+	0.967523i	$0.418654\pi$
$44$	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	$-0.441708\pi$
$61$	173.523	0.364218	0.182109	+	0.983278i	$0.441708\pi$
$62$	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	$-0.181571\pi$
$73$	1049.92	1.68335	0.841673	+	0.539987i	$0.181571\pi$
$74$	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	$-0.569078\pi$
$79$	−302.376	−0.430633	−0.215316	+	0.976544i	$0.569078\pi$
$80$	124.755	0.174350
$81$	81.0000	0.111111
$82$	1494.56	2.01277
$83$	−831.525	−1.09966	−0.549829	−	0.835277i	$-0.685307\pi$
$83$	−831.525	−1.09966	−0.549829	+	0.835277i	$0.685307\pi$
$84$	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	$-0.376769\pi$
$101$	766.438	0.755084	0.377542	+	0.925993i	$0.376769\pi$
$102$	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	$-0.863243\pi$
$107$	−2012.45	−1.81824	−0.909118	+	0.416539i	$0.863243\pi$
$108$	308.327	0.274711
$109$	33.5794	0.0295076	0.0147538	−	0.999891i	$-0.495304\pi$
$109$	33.5794	0.0295076	0.0147538	+	0.999891i	$0.495304\pi$
$110$	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	$-0.282746\pi$
$127$	1805.49	1.26151	0.630753	+	0.775983i	$0.282746\pi$
$128$	−1752.62	−1.21024
$129$	427.661	0.291887
$130$	−571.831	−0.385792
$131$	−192.802	−0.128590	−0.0642948	−	0.997931i	$-0.520480\pi$
$131$	−192.802	−0.128590	−0.0642948	+	0.997931i	$0.520480\pi$
$132$	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	$-0.520151\pi$
$139$	−207.349	−0.126526	−0.0632629	+	0.997997i	$0.520151\pi$
$140$	−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	$-0.268164\pi$
$149$	2421.25	1.33125	0.665627	+	0.746285i	$0.268164\pi$
$150$	330.507	0.179905
$151$	−1155.49	−0.622731	−0.311366	−	0.950290i	$-0.600786\pi$
$151$	−1155.49	−0.622731	−0.311366	+	0.950290i	$0.600786\pi$
$152$	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	$-0.520358\pi$
$167$	−275.865	−0.127827	−0.0639134	+	0.997955i	$0.520358\pi$
$168$	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	$-0.833876\pi$
$173$	−3945.09	−1.73375	−0.866877	+	0.498522i	$0.833876\pi$
$174$	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	$-0.331562\pi$
$193$	2707.04	1.00962	0.504811	+	0.863230i	$0.331562\pi$
$194$	−5174.75	−1.91508
$195$	−389.287	−0.142961
$196$	−511.721	−0.186487
$197$	3972.45	1.43668	0.718339	−	0.695693i	$-0.244903\pi$
$197$	3972.45	1.43668	0.718339	+	0.695693i	$0.244903\pi$
$198$	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	$-0.575688\pi$
$211$	−1443.87	−0.471091	−0.235546	+	0.971863i	$0.575688\pi$
$212$	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	$-0.615514\pi$
$227$	−2428.16	−0.709968	−0.354984	+	0.934872i	$0.615514\pi$
$228$	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	$-0.203787\pi$
$233$	5704.53	1.60393	0.801967	+	0.597369i	$0.203787\pi$
$234$	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	$-0.451351\pi$
$239$	1125.02	0.304483	0.152242	+	0.988343i	$0.451351\pi$
$240$	374.265	0.100661
$241$	−2080.62	−0.556119	−0.278060	−	0.960564i	$-0.589691\pi$
$241$	−2080.62	−0.556119	−0.278060	+	0.960564i	$0.589691\pi$
$242$	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	$-0.717038\pi$
$263$	−5376.00	−1.26045	−0.630225	+	0.776412i	$0.717038\pi$
$264$	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	$-0.383233\pi$
$271$	3200.15	0.717325	0.358662	+	0.933467i	$0.383233\pi$
$272$	−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	$-0.585432\pi$
$277$	−2445.09	−0.530365	−0.265182	+	0.964198i	$0.585432\pi$
$278$	−913.735	−0.197130
$279$	640.849	0.137515
$280$	−1301.06	−0.277690
$281$	−4378.00	−0.929429	−0.464715	−	0.885461i	$-0.653843\pi$
$281$	−4378.00	−0.929429	−0.464715	+	0.885461i	$0.653843\pi$
$282$	5126.39	1.08252
$283$	−8084.72	−1.69819	−0.849093	−	0.528244i	$-0.822851\pi$
$283$	−8084.72	−1.69819	−0.849093	+	0.528244i	$0.822851\pi$
$284$	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	$-0.564017\pi$
$293$	−2003.75	−0.399523	−0.199762	+	0.979845i	$0.564017\pi$
$294$	−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	$-0.717984\pi$
$307$	−6804.87	−1.26506	−0.632532	+	0.774534i	$0.717984\pi$
$308$	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	$-0.638946\pi$
$337$	−5231.06	−0.845561	−0.422780	+	0.906232i	$0.638946\pi$
$338$	−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	$-0.495824\pi$
$347$	169.607	0.0262391	0.0131195	+	0.999914i	$0.495824\pi$
$348$	6906.75	1.06391
$349$	−635.896	−0.0975322	−0.0487661	−	0.998810i	$-0.515529\pi$
$349$	−635.896	−0.0975322	−0.0487661	+	0.998810i	$0.515529\pi$
$350$	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	$-0.774128\pi$
$359$	−10320.4	−1.51725	−0.758624	+	0.651529i	$0.774128\pi$
$360$	−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	$-0.818417\pi$
$373$	−12126.2	−1.68331	−0.841653	+	0.540019i	$0.818417\pi$
$374$	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	$-0.897609\pi$
$409$	−15694.5	−1.89742	−0.948709	+	0.316152i	$0.897609\pi$
$410$	−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	$-0.611183\pi$
$431$	−6124.43	−0.684463	−0.342232	+	0.939616i	$0.611183\pi$
$432$	−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	$-0.354765\pi$
$439$	8105.40	0.881206	0.440603	+	0.897702i	$0.354765\pi$
$440$	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	$-0.743893\pi$
$457$	−13548.6	−1.38682	−0.693411	+	0.720542i	$0.743893\pi$
$458$	3415.25	0.348437
$459$	1228.10	0.124887
$460$	3104.38	0.314658
$461$	−10455.0	−1.05626	−0.528130	−	0.849163i	$-0.677107\pi$
$461$	−10455.0	−1.05626	−0.528130	+	0.849163i	$0.677107\pi$
$462$	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	$-0.499638\pi$
$479$	23.8322	0.00227332	0.00113666	+	0.999999i	$0.499638\pi$
$480$	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	$-0.517408\pi$
$491$	−1189.42	−0.109323	−0.0546617	+	0.998505i	$0.517408\pi$
$492$	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	$-0.806494\pi$
$503$	−18520.0	−1.64168	−0.820839	+	0.571159i	$0.806494\pi$
$504$	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	$-0.536034\pi$
$523$	−2702.19	−0.225925	−0.112962	+	0.993599i	$0.536034\pi$
$524$	−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	$-0.242175\pi$
$541$	18227.6	1.44855	0.724274	+	0.689512i	$0.242175\pi$
$542$	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	$-0.422720\pi$
$547$	6151.07	0.480806	0.240403	+	0.970673i	$0.422720\pi$
$548$	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	$-0.684824\pi$
$557$	−14422.4	−1.09712	−0.548561	+	0.836111i	$0.684824\pi$
$558$	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	$-0.468821\pi$
$563$	2612.79	0.195588	0.0977940	+	0.995207i	$0.468821\pi$
$564$	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	$-0.435809\pi$
$569$	5437.19	0.400595	0.200298	+	0.979735i	$0.435809\pi$
$570$	−1146.62	−0.0842570
$571$	22747.0	1.66713	0.833567	−	0.552419i	$-0.186295\pi$
$571$	22747.0	1.66713	0.833567	+	0.552419i	$0.186295\pi$
$572$	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	$-0.641856\pi$
$593$	−12449.1	−0.862098	−0.431049	+	0.902329i	$0.641856\pi$
$594$	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	$-0.616571\pi$
$601$	−10551.9	−0.716174	−0.358087	+	0.933688i	$0.616571\pi$
$602$	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	$-0.462845\pi$
$607$	3483.36	0.232925	0.116462	+	0.993195i	$0.462845\pi$
$608$	−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	$-0.738083\pi$
$613$	−20645.3	−1.36029	−0.680144	+	0.733079i	$0.738083\pi$
$614$	−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	$-0.635388\pi$
$659$	−13960.9	−0.825252	−0.412626	+	0.910901i	$0.635388\pi$
$660$	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	$-0.589693\pi$
$673$	−9709.59	−0.556133	−0.278066	+	0.960562i	$0.589693\pi$
$674$	−23052.0	−1.31740
$675$	675.000	0.0384900
$676$	−17397.3	−0.989830
$677$	28005.4	1.58986	0.794929	−	0.606703i	$-0.207508\pi$
$677$	28005.4	1.58986	0.794929	+	0.606703i	$0.207508\pi$
$678$	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	$-0.335313\pi$
$701$	18359.7	0.989209	0.494604	+	0.869118i	$0.335313\pi$
$702$	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	$-0.530547\pi$
$733$	−3803.06	−0.191636	−0.0958181	+	0.995399i	$0.530547\pi$
$734$	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	$-0.173536\pi$
$739$	34354.2	1.71007	0.855034	+	0.518572i	$0.173536\pi$
$740$	−1719.71	−0.0854297
$741$	1350.54	0.0669547
$742$	15767.3	0.780100
$743$	2128.50	0.105097	0.0525486	−	0.998618i	$-0.483266\pi$
$743$	2128.50	0.105097	0.0525486	+	0.998618i	$0.483266\pi$
$744$	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	$-0.513552\pi$
$761$	−1786.97	−0.0851218	−0.0425609	+	0.999094i	$0.513552\pi$
$762$	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	$-0.755930\pi$
$769$	−30714.7	−1.44031	−0.720157	+	0.693811i	$0.755930\pi$
$770$	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	$-0.704027\pi$
$787$	−26404.2	−1.19594	−0.597972	+	0.801517i	$0.704027\pi$
$788$	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	$-0.504863\pi$
$809$	−703.110	−0.0305563	−0.0152781	+	0.999883i	$0.504863\pi$
$810$	−1784.74	−0.0774188
$811$	2813.77	0.121831	0.0609154	−	0.998143i	$-0.480598\pi$
$811$	2813.77	0.121831	0.0609154	+	0.998143i	$0.480598\pi$
$812$	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	$-0.387118\pi$
$821$	16337.2	0.694485	0.347242	+	0.937775i	$0.387118\pi$
$822$	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	$-0.818042\pi$
$827$	−40003.0	−1.68203	−0.841016	+	0.541011i	$0.818042\pi$
$828$	−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	$-0.442653\pi$
$853$	8928.12	0.358374	0.179187	+	0.983815i	$0.442653\pi$
$854$	13204.5	0.529095
$855$	−780.586	−0.0312228
$856$	−30325.5	−1.21087
$857$	15643.0	0.623516	0.311758	−	0.950162i	$-0.399082\pi$
$857$	15643.0	0.623516	0.311758	+	0.950162i	$0.399082\pi$
$858$	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	$-0.314131\pi$
$877$	28636.4	1.10260	0.551302	+	0.834306i	$0.314131\pi$
$878$	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	$-0.244539\pi$
$887$	37994.8	1.43827	0.719133	+	0.694873i	$0.244539\pi$
$888$	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	$-0.344159\pi$
$919$	26202.7	0.940529	0.470264	+	0.882526i	$0.344159\pi$
$920$	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	$-0.474917\pi$
$937$	4515.66	0.157439	0.0787194	+	0.996897i	$0.474917\pi$
$938$	2674.21	0.0930874
$939$	11703.6	0.406744
$940$	−22140.5	−0.768239
$941$	2866.89	0.0993177	0.0496589	−	0.998766i	$-0.484187\pi$
$941$	2866.89	0.0993177	0.0496589	+	0.998766i	$0.484187\pi$
$942$	−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	$-0.520594\pi$
$953$	−3804.18	−0.129307	−0.0646535	+	0.997908i	$0.520594\pi$
$954$	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	$-0.419943\pi$
$967$	14966.8	0.497726	0.248863	+	0.968539i	$0.419943\pi$
$968$	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	$-0.432957\pi$
$997$	13163.2	0.418136	0.209068	+	0.977901i	$0.432957\pi$
$998$	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.x.1.5	✓	5
11.10	odd	2		1815.4.a.y.1.1	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1815.4.a.x.1.5	✓	5	1.1	even	1	trivial
1815.4.a.y.1.1	yes	5	11.10	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:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
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

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