LMFDB - Embedded newform 2254.4.a.z.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2254,4,Mod(1,2254)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2254, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2254.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2254 = 2 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2254.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:	$132.990305153$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 200x^{12} + 15521x^{10} - 598294x^{8} + 12167812x^{6} - 125559722x^{4} + 539505876x^{2} - 324615200 $ x^14 - 200x^12 + 15521x^10 - 598294x^8 + 12167812x^6 - 125559722x^4 + 539505876x^2 - 324615200
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 7^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-4.57720$ of defining polynomial
Character	$\chi$	$=$	2254.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00000 q^{2} -4.57720 q^{3} +4.00000 q^{4} +14.7602 q^{5} +9.15439 q^{6} -8.00000 q^{8} -6.04928 q^{9} -29.5203 q^{10} -32.4632 q^{11} -18.3088 q^{12} -56.9971 q^{13} -67.5602 q^{15} +16.0000 q^{16} +62.6276 q^{17} +12.0986 q^{18} -117.766 q^{19} +59.0407 q^{20} +64.9264 q^{22} +23.0000 q^{23} +36.6176 q^{24} +92.8627 q^{25} +113.994 q^{26} +151.273 q^{27} +255.065 q^{29} +135.120 q^{30} +119.130 q^{31} -32.0000 q^{32} +148.590 q^{33} -125.255 q^{34} -24.1971 q^{36} -53.9112 q^{37} +235.532 q^{38} +260.887 q^{39} -118.081 q^{40} +1.65538 q^{41} +511.471 q^{43} -129.853 q^{44} -89.2884 q^{45} -46.0000 q^{46} +175.407 q^{47} -73.2351 q^{48} -185.725 q^{50} -286.659 q^{51} -227.988 q^{52} -191.117 q^{53} -302.546 q^{54} -479.162 q^{55} +539.037 q^{57} -510.131 q^{58} +254.364 q^{59} -270.241 q^{60} -293.652 q^{61} -238.261 q^{62} +64.0000 q^{64} -841.287 q^{65} -297.181 q^{66} -768.998 q^{67} +250.511 q^{68} -105.275 q^{69} +640.408 q^{71} +48.3942 q^{72} -591.512 q^{73} +107.822 q^{74} -425.051 q^{75} -471.063 q^{76} -521.774 q^{78} +680.149 q^{79} +236.163 q^{80} -529.076 q^{81} -3.31076 q^{82} -167.146 q^{83} +924.395 q^{85} -1022.94 q^{86} -1167.48 q^{87} +259.706 q^{88} +451.747 q^{89} +178.577 q^{90} +92.0000 q^{92} -545.283 q^{93} -350.814 q^{94} -1738.24 q^{95} +146.470 q^{96} -1199.56 q^{97} +196.379 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 28 q^{2} + 56 q^{4} - 112 q^{8} + 22 q^{9} - 92 q^{11} - 268 q^{15} + 224 q^{16} - 44 q^{18} + 184 q^{22} + 322 q^{23} + 130 q^{25} + 196 q^{29} + 536 q^{30} - 448 q^{32} + 88 q^{36} + 628 q^{37}+ \cdots + 1800 q^{99}+O(q^{100}) $ 14 * q - 28 * q^2 + 56 * q^4 - 112 * q^8 + 22 * q^9 - 92 * q^11 - 268 * q^15 + 224 * q^16 - 44 * q^18 + 184 * q^22 + 322 * q^23 + 130 * q^25 + 196 * q^29 + 536 * q^30 - 448 * q^32 + 88 * q^36 + 628 * q^37 + 388 * q^39 + 640 * q^43 - 368 * q^44 - 644 * q^46 - 260 * q^50 + 656 * q^51 - 1260 * q^53 + 380 * q^57 - 392 * q^58 - 1072 * q^60 + 896 * q^64 - 204 * q^65 - 1564 * q^67 - 900 * q^71 - 176 * q^72 - 1256 * q^74 - 776 * q^78 - 404 * q^79 - 4278 * q^81 + 1512 * q^85 - 1280 * q^86 + 736 * q^88 + 1288 * q^92 - 2712 * q^93 - 4752 * q^95 + 1800 * q^99

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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	−4.57720	−0.880882	−0.440441	−	0.897782i	$-0.645178\pi$
$3$	−4.57720	−0.880882	−0.440441	+	0.897782i	$0.645178\pi$
$4$	4.00000	0.500000
$5$	14.7602	1.32019	0.660095	−	0.751182i	$-0.270516\pi$
$5$	14.7602	1.32019	0.660095	+	0.751182i	$0.270516\pi$
$6$	9.15439	0.622877
$7$	0	0
$7$	0	0
$8$	−8.00000	−0.353553
$9$	−6.04928	−0.224047
$10$	−29.5203	−0.933515
$11$	−32.4632	−0.889820	−0.444910	−	0.895575i	$-0.646764\pi$
$11$	−32.4632	−0.889820	−0.444910	+	0.895575i	$0.646764\pi$
$12$	−18.3088	−0.440441
$13$	−56.9971	−1.21601	−0.608006	−	0.793933i	$-0.708030\pi$
$13$	−56.9971	−1.21601	−0.608006	+	0.793933i	$0.708030\pi$
$14$	0	0
$15$	−67.5602	−1.16293
$16$	16.0000	0.250000
$17$	62.6276	0.893496	0.446748	−	0.894660i	$-0.352582\pi$
$17$	62.6276	0.893496	0.446748	+	0.894660i	$0.352582\pi$
$18$	12.0986	0.158425
$19$	−117.766	−1.42197	−0.710983	−	0.703210i	$-0.751750\pi$
$19$	−117.766	−1.42197	−0.710983	+	0.703210i	$0.751750\pi$
$20$	59.0407	0.660095
$21$	0	0
$22$	64.9264	0.629198
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	36.6176	0.311439
$25$	92.8627	0.742902
$26$	113.994	0.859850
$27$	151.273	1.07824
$28$	0	0
$29$	255.065	1.63326	0.816629	−	0.577164i	$-0.195841\pi$
$29$	255.065	1.63326	0.816629	+	0.577164i	$0.195841\pi$
$30$	135.120	0.822317
$31$	119.130	0.690208	0.345104	−	0.938564i	$-0.387844\pi$
$31$	119.130	0.690208	0.345104	+	0.938564i	$0.387844\pi$
$32$	−32.0000	−0.176777
$33$	148.590	0.783826
$34$	−125.255	−0.631797
$35$	0	0
$36$	−24.1971	−0.112024
$37$	−53.9112	−0.239539	−0.119770	−	0.992802i	$-0.538216\pi$
$37$	−53.9112	−0.239539	−0.119770	+	0.992802i	$0.538216\pi$
$38$	235.532	1.00548
$39$	260.887	1.07116
$40$	−118.081	−0.466758
$41$	1.65538	0.00630554	0.00315277	−	0.999995i	$-0.498996\pi$
$41$	1.65538	0.00630554	0.00315277	+	0.999995i	$0.498996\pi$
$42$	0	0
$43$	511.471	1.81392	0.906961	−	0.421215i	$-0.138396\pi$
$43$	511.471	1.81392	0.906961	+	0.421215i	$0.138396\pi$
$44$	−129.853	−0.444910
$45$	−89.2884	−0.295785
$46$	−46.0000	−0.147442
$47$	175.407	0.544377	0.272189	−	0.962244i	$-0.412252\pi$
$47$	175.407	0.544377	0.272189	+	0.962244i	$0.412252\pi$
$48$	−73.2351	−0.220220
$49$	0	0
$50$	−185.725	−0.525311
$51$	−286.659	−0.787064
$52$	−227.988	−0.608006
$53$	−191.117	−0.495320	−0.247660	−	0.968847i	$-0.579662\pi$
$53$	−191.117	−0.495320	−0.247660	+	0.968847i	$0.579662\pi$
$54$	−302.546	−0.762432
$55$	−479.162	−1.17473
$56$	0	0
$57$	539.037	1.25258
$58$	−510.131	−1.15489
$59$	254.364	0.561277	0.280638	−	0.959814i	$-0.409454\pi$
$59$	254.364	0.561277	0.280638	+	0.959814i	$0.409454\pi$
$60$	−270.241	−0.581466
$61$	−293.652	−0.616366	−0.308183	−	0.951327i	$-0.599721\pi$
$61$	−293.652	−0.616366	−0.308183	+	0.951327i	$0.599721\pi$
$62$	−238.261	−0.488051
$63$	0	0
$64$	64.0000	0.125000
$65$	−841.287	−1.60537
$66$	−297.181	−0.554249
$67$	−768.998	−1.40221	−0.701105	−	0.713058i	$-0.747310\pi$
$67$	−768.998	−1.40221	−0.701105	+	0.713058i	$0.747310\pi$
$68$	250.511	0.446748
$69$	−105.275	−0.183677
$70$	0	0
$71$	640.408	1.07046	0.535228	−	0.844707i	$-0.320226\pi$
$71$	640.408	1.07046	0.535228	+	0.844707i	$0.320226\pi$
$72$	48.3942	0.0792127
$73$	−591.512	−0.948373	−0.474186	−	0.880425i	$-0.657258\pi$
$73$	−591.512	−0.948373	−0.474186	+	0.880425i	$0.657258\pi$
$74$	107.822	0.169380
$75$	−425.051	−0.654408
$76$	−471.063	−0.710983
$77$	0	0
$78$	−521.774	−0.757426
$79$	680.149	0.968642	0.484321	−	0.874890i	$-0.339067\pi$
$79$	680.149	0.968642	0.484321	+	0.874890i	$0.339067\pi$
$80$	236.163	0.330047
$81$	−529.076	−0.725755
$82$	−3.31076	−0.00445869
$83$	−167.146	−0.221044	−0.110522	−	0.993874i	$-0.535252\pi$
$83$	−167.146	−0.221044	−0.110522	+	0.993874i	$0.535252\pi$
$84$	0	0
$85$	924.395	1.17958
$86$	−1022.94	−1.28264
$87$	−1167.48	−1.43871
$88$	259.706	0.314599
$89$	451.747	0.538034	0.269017	−	0.963135i	$-0.413301\pi$
$89$	451.747	0.538034	0.269017	+	0.963135i	$0.413301\pi$
$90$	178.577	0.209152
$91$	0	0
$92$	92.0000	0.104257
$93$	−545.283	−0.607992
$94$	−350.814	−0.384933
$95$	−1738.24	−1.87726
$96$	146.470	0.155719
$97$	−1199.56	−1.25564	−0.627818	−	0.778360i	$-0.716052\pi$
$97$	−1199.56	−1.25564	−0.627818	+	0.778360i	$0.716052\pi$
$98$	0	0
$99$	196.379	0.199362
$100$	371.451	0.371451
$101$	1204.42	1.18657	0.593287	−	0.804991i	$-0.297830\pi$
$101$	1204.42	1.18657	0.593287	+	0.804991i	$0.297830\pi$
$102$	573.318	0.556538
$103$	336.654	0.322054	0.161027	−	0.986950i	$-0.448519\pi$
$103$	336.654	0.322054	0.161027	+	0.986950i	$0.448519\pi$
$104$	455.977	0.429925
$105$	0	0
$106$	382.235	0.350244
$107$	1752.57	1.58343	0.791716	−	0.610889i	$-0.209188\pi$
$107$	1752.57	1.58343	0.791716	+	0.610889i	$0.209188\pi$
$108$	605.092	0.539120
$109$	−2102.48	−1.84753	−0.923766	−	0.382957i	$-0.874906\pi$
$109$	−2102.48	−1.84753	−0.923766	+	0.382957i	$0.874906\pi$
$110$	958.325	0.830661
$111$	246.762	0.211006
$112$	0	0
$113$	−1770.99	−1.47435	−0.737173	−	0.675705i	$-0.763840\pi$
$113$	−1770.99	−1.47435	−0.737173	+	0.675705i	$0.763840\pi$
$114$	−1078.07	−0.885710
$115$	339.484	0.275279
$116$	1020.26	0.816629
$117$	344.791	0.272444
$118$	−508.727	−0.396883
$119$	0	0
$120$	540.482	0.411158
$121$	−277.141	−0.208220
$122$	587.305	0.435837
$123$	−7.57700	−0.00555443
$124$	476.522	0.345104
$125$	−474.352	−0.339419
$126$	0	0
$127$	−1115.83	−0.779636	−0.389818	−	0.920892i	$-0.627462\pi$
$127$	−1115.83	−0.779636	−0.389818	+	0.920892i	$0.627462\pi$
$128$	−128.000	−0.0883883
$129$	−2341.10	−1.59785
$130$	1682.57	1.13517
$131$	−266.134	−0.177498	−0.0887490	−	0.996054i	$-0.528287\pi$
$131$	−266.134	−0.177498	−0.0887490	+	0.996054i	$0.528287\pi$
$132$	594.361	0.391913
$133$	0	0
$134$	1538.00	0.991513
$135$	2232.82	1.42348
$136$	−501.021	−0.315899
$137$	2454.72	1.53081	0.765403	−	0.643551i	$-0.222540\pi$
$137$	2454.72	1.53081	0.765403	+	0.643551i	$0.222540\pi$
$138$	210.551	0.129879
$139$	1068.85	0.652223	0.326111	−	0.945331i	$-0.394262\pi$
$139$	1068.85	0.652223	0.326111	+	0.945331i	$0.394262\pi$
$140$	0	0
$141$	−802.872	−0.479532
$142$	−1280.82	−0.756927
$143$	1850.31	1.08203
$144$	−96.7885	−0.0560119
$145$	3764.81	2.15621
$146$	1183.02	0.670601
$147$	0	0
$148$	−215.645	−0.119770
$149$	−2379.40	−1.30824	−0.654120	−	0.756391i	$-0.726961\pi$
$149$	−2379.40	−1.30824	−0.654120	+	0.756391i	$0.726961\pi$
$150$	850.101	0.462737
$151$	−1302.97	−0.702215	−0.351107	−	0.936335i	$-0.614195\pi$
$151$	−1302.97	−0.702215	−0.351107	+	0.936335i	$0.614195\pi$
$152$	942.127	0.502741
$153$	−378.852	−0.200185
$154$	0	0
$155$	1758.39	0.911206
$156$	1043.55	0.535581
$157$	−992.850	−0.504701	−0.252350	−	0.967636i	$-0.581204\pi$
$157$	−992.850	−0.504701	−0.252350	+	0.967636i	$0.581204\pi$
$158$	−1360.30	−0.684934
$159$	874.781	0.436319
$160$	−472.326	−0.233379
$161$	0	0
$162$	1058.15	0.513187
$163$	−392.005	−0.188370	−0.0941848	−	0.995555i	$-0.530024\pi$
$163$	−392.005	−0.188370	−0.0941848	+	0.995555i	$0.530024\pi$
$164$	6.62152	0.00315277
$165$	2193.22	1.03480
$166$	334.292	0.156302
$167$	3076.35	1.42548	0.712740	−	0.701428i	$-0.247454\pi$
$167$	3076.35	1.42548	0.712740	+	0.701428i	$0.247454\pi$
$168$	0	0
$169$	1051.67	0.478684
$170$	−1848.79	−0.834092
$171$	712.399	0.318588
$172$	2045.88	0.906961
$173$	1124.68	0.494264	0.247132	−	0.968982i	$-0.420512\pi$
$173$	1124.68	0.494264	0.247132	+	0.968982i	$0.420512\pi$
$174$	2334.97	1.01732
$175$	0	0
$176$	−519.411	−0.222455
$177$	−1164.27	−0.494419
$178$	−903.493	−0.380448
$179$	−3167.30	−1.32254	−0.661271	−	0.750147i	$-0.729983\pi$
$179$	−3167.30	−1.32254	−0.661271	+	0.750147i	$0.729983\pi$
$180$	−357.154	−0.147893
$181$	−1008.55	−0.414171	−0.207085	−	0.978323i	$-0.566398\pi$
$181$	−1008.55	−0.414171	−0.207085	+	0.978323i	$0.566398\pi$
$182$	0	0
$183$	1344.10	0.542946
$184$	−184.000	−0.0737210
$185$	−795.739	−0.316237
$186$	1090.57	0.429915
$187$	−2033.09	−0.795051
$188$	701.628	0.272189
$189$	0	0
$190$	3476.49	1.32743
$191$	−627.529	−0.237730	−0.118865	−	0.992910i	$-0.537926\pi$
$191$	−627.529	−0.237730	−0.118865	+	0.992910i	$0.537926\pi$
$192$	−292.941	−0.110110
$193$	−4334.60	−1.61664	−0.808320	−	0.588743i	$-0.799623\pi$
$193$	−4334.60	−1.61664	−0.808320	+	0.588743i	$0.799623\pi$
$194$	2399.12	0.887868
$195$	3850.73	1.41414
$196$	0	0
$197$	−3370.94	−1.21914	−0.609568	−	0.792734i	$-0.708657\pi$
$197$	−3370.94	−1.21914	−0.609568	+	0.792734i	$0.708657\pi$
$198$	−392.758	−0.140970
$199$	−2396.56	−0.853706	−0.426853	−	0.904321i	$-0.640378\pi$
$199$	−2396.56	−0.853706	−0.426853	+	0.904321i	$0.640378\pi$
$200$	−742.902	−0.262655
$201$	3519.86	1.23518
$202$	−2408.83	−0.839034
$203$	0	0
$204$	−1146.64	−0.393532
$205$	24.4337	0.00832451
$206$	−673.308	−0.227726
$207$	−139.133	−0.0467171
$208$	−911.953	−0.304003
$209$	3823.06	1.26529
$210$	0	0
$211$	3872.82	1.26358	0.631792	−	0.775138i	$-0.282320\pi$
$211$	3872.82	1.26358	0.631792	+	0.775138i	$0.282320\pi$
$212$	−764.469	−0.247660
$213$	−2931.27	−0.942946
$214$	−3505.14	−1.11966
$215$	7549.40	2.39472
$216$	−1210.18	−0.381216
$217$	0	0
$218$	4204.96	1.30640
$219$	2707.46	0.835404
$220$	−1916.65	−0.587366
$221$	−3569.59	−1.08650
$222$	−493.525	−0.149204
$223$	4603.83	1.38249	0.691244	−	0.722621i	$-0.257063\pi$
$223$	4603.83	1.38249	0.691244	+	0.722621i	$0.257063\pi$
$224$	0	0
$225$	−561.752	−0.166445
$226$	3541.99	1.04252
$227$	759.790	0.222154	0.111077	−	0.993812i	$-0.464570\pi$
$227$	759.790	0.222154	0.111077	+	0.993812i	$0.464570\pi$
$228$	2156.15	0.626292
$229$	3422.99	0.987761	0.493880	−	0.869530i	$-0.335578\pi$
$229$	3422.99	0.987761	0.493880	+	0.869530i	$0.335578\pi$
$230$	−678.968	−0.194651
$231$	0	0
$232$	−2040.52	−0.577444
$233$	−6.35709	−0.00178741	−0.000893706	−	1.00000i	$-0.500284\pi$
$233$	−6.35709	−0.00178741	−0.000893706		1.00000i	$0.500284\pi$
$234$	−689.583	−0.192647
$235$	2589.04	0.718682
$236$	1017.45	0.280638
$237$	−3113.18	−0.853259
$238$	0	0
$239$	−4893.62	−1.32444	−0.662222	−	0.749307i	$-0.730387\pi$
$239$	−4893.62	−1.32444	−0.662222	+	0.749307i	$0.730387\pi$
$240$	−1080.96	−0.290733
$241$	−3474.09	−0.928571	−0.464286	−	0.885685i	$-0.653689\pi$
$241$	−3474.09	−0.928571	−0.464286	+	0.885685i	$0.653689\pi$
$242$	554.283	0.147234
$243$	−1662.69	−0.438936
$244$	−1174.61	−0.308183
$245$	0	0
$246$	15.1540	0.00392758
$247$	6712.31	1.72913
$248$	−953.043	−0.244025
$249$	765.060	0.194714
$250$	948.704	0.240005
$251$	3531.41	0.888050	0.444025	−	0.896014i	$-0.353550\pi$
$251$	3531.41	0.888050	0.444025	+	0.896014i	$0.353550\pi$
$252$	0	0
$253$	−746.653	−0.185540
$254$	2231.66	0.551286
$255$	−4231.14	−1.03907
$256$	256.000	0.0625000
$257$	−3932.67	−0.954526	−0.477263	−	0.878761i	$-0.658371\pi$
$257$	−3932.67	−0.954526	−0.477263	+	0.878761i	$0.658371\pi$
$258$	4682.21	1.12985
$259$	0	0
$260$	−3365.15	−0.802683
$261$	−1542.96	−0.365927
$262$	532.268	0.125510
$263$	−3191.48	−0.748271	−0.374136	−	0.927374i	$-0.622061\pi$
$263$	−3191.48	−0.748271	−0.374136	+	0.927374i	$0.622061\pi$
$264$	−1188.72	−0.277124
$265$	−2820.92	−0.653917
$266$	0	0
$267$	−2067.73	−0.473945
$268$	−3075.99	−0.701105
$269$	3703.06	0.839330	0.419665	−	0.907679i	$-0.362148\pi$
$269$	3703.06	0.839330	0.419665	+	0.907679i	$0.362148\pi$
$270$	−4465.63	−1.00655
$271$	−3144.04	−0.704750	−0.352375	−	0.935859i	$-0.614626\pi$
$271$	−3144.04	−0.704750	−0.352375	+	0.935859i	$0.614626\pi$
$272$	1002.04	0.223374
$273$	0	0
$274$	−4909.43	−1.08244
$275$	−3014.62	−0.661049
$276$	−421.102	−0.0918383
$277$	−461.547	−0.100114	−0.0500571	−	0.998746i	$-0.515940\pi$
$277$	−461.547	−0.100114	−0.0500571	+	0.998746i	$0.515940\pi$
$278$	−2137.71	−0.461191
$279$	−720.653	−0.154639
$280$	0	0
$281$	4712.83	1.00051	0.500256	−	0.865878i	$-0.333239\pi$
$281$	4712.83	1.00051	0.500256	+	0.865878i	$0.333239\pi$
$282$	1605.74	0.339080
$283$	−757.248	−0.159059	−0.0795296	−	0.996833i	$-0.525342\pi$
$283$	−757.248	−0.159059	−0.0795296	+	0.996833i	$0.525342\pi$
$284$	2561.63	0.535228
$285$	7956.29	1.65365
$286$	−3700.61	−0.765112
$287$	0	0
$288$	193.577	0.0396064
$289$	−990.780	−0.201665
$290$	−7529.62	−1.52467
$291$	5490.61	1.10607
$292$	−2366.05	−0.474186
$293$	3865.33	0.770699	0.385350	−	0.922771i	$-0.374081\pi$
$293$	3865.33	0.770699	0.385350	+	0.922771i	$0.374081\pi$
$294$	0	0
$295$	3754.45	0.740992
$296$	431.290	0.0846899
$297$	−4910.80	−0.959440
$298$	4758.79	0.925065
$299$	−1310.93	−0.253556
$300$	−1700.20	−0.327204
$301$	0	0
$302$	2605.95	0.496541
$303$	−5512.85	−1.04523
$304$	−1884.25	−0.355491
$305$	−4334.36	−0.813720
$306$	757.704	0.141553
$307$	−5548.34	−1.03147	−0.515734	−	0.856749i	$-0.672481\pi$
$307$	−5548.34	−1.03147	−0.515734	+	0.856749i	$0.672481\pi$
$308$	0	0
$309$	−1540.93	−0.283691
$310$	−3516.77	−0.644320
$311$	−10295.0	−1.87709	−0.938545	−	0.345157i	$-0.887826\pi$
$311$	−10295.0	−1.87709	−0.938545	+	0.345157i	$0.887826\pi$
$312$	−2087.09	−0.378713
$313$	−9170.41	−1.65605	−0.828023	−	0.560694i	$-0.810534\pi$
$313$	−9170.41	−1.65605	−0.828023	+	0.560694i	$0.810534\pi$
$314$	1985.70	0.356877
$315$	0	0
$316$	2720.60	0.484321
$317$	6757.45	1.19728	0.598638	−	0.801020i	$-0.295709\pi$
$317$	6757.45	1.19728	0.598638	+	0.801020i	$0.295709\pi$
$318$	−1749.56	−0.308524
$319$	−8280.24	−1.45330
$320$	944.651	0.165024
$321$	−8021.85	−1.39482
$322$	0	0
$323$	−7375.40	−1.27052
$324$	−2116.30	−0.362878
$325$	−5292.90	−0.903377
$326$	784.011	0.133197
$327$	9623.46	1.62746
$328$	−13.2430	−0.00222934
$329$	0	0
$330$	−4386.44	−0.731714
$331$	−9900.16	−1.64399	−0.821997	−	0.569492i	$-0.807140\pi$
$331$	−9900.16	−1.64399	−0.821997	+	0.569492i	$0.807140\pi$
$332$	−668.584	−0.110522
$333$	326.124	0.0536682
$334$	−6152.70	−1.00797
$335$	−11350.5	−1.85118
$336$	0	0
$337$	−6662.09	−1.07688	−0.538438	−	0.842665i	$-0.680985\pi$
$337$	−6662.09	−1.07688	−0.538438	+	0.842665i	$0.680985\pi$
$338$	−2103.34	−0.338480
$339$	8106.18	1.29872
$340$	3697.58	0.589792
$341$	−3867.35	−0.614161
$342$	−1424.80	−0.225276
$343$	0	0
$344$	−4091.77	−0.641318
$345$	−1553.88	−0.242488
$346$	−2249.35	−0.349497
$347$	−5454.78	−0.843885	−0.421942	−	0.906623i	$-0.638652\pi$
$347$	−5454.78	−0.843885	−0.421942	+	0.906623i	$0.638652\pi$
$348$	−4669.94	−0.719353
$349$	11797.2	1.80943	0.904717	−	0.426014i	$-0.140082\pi$
$349$	11797.2	1.80943	0.904717	+	0.426014i	$0.140082\pi$
$350$	0	0
$351$	−8622.12	−1.31115
$352$	1038.82	0.157299
$353$	−1228.04	−0.185162	−0.0925810	−	0.995705i	$-0.529512\pi$
$353$	−1228.04	−0.185162	−0.0925810	+	0.995705i	$0.529512\pi$
$354$	2328.54	0.349607
$355$	9452.53	1.41321
$356$	1806.99	0.269017
$357$	0	0
$358$	6334.60	0.935179
$359$	−486.085	−0.0714613	−0.0357306	−	0.999361i	$-0.511376\pi$
$359$	−486.085	−0.0714613	−0.0357306	+	0.999361i	$0.511376\pi$
$360$	714.307	0.104576
$361$	7009.80	1.02199
$362$	2017.10	0.292863
$363$	1268.53	0.183417
$364$	0	0
$365$	−8730.81	−1.25203
$366$	−2688.21	−0.383920
$367$	−11500.6	−1.63577	−0.817883	−	0.575385i	$-0.804852\pi$
$367$	−11500.6	−1.63577	−0.817883	+	0.575385i	$0.804852\pi$
$368$	368.000	0.0521286
$369$	−10.0139	−0.00141274
$370$	1591.48	0.223614
$371$	0	0
$372$	−2181.13	−0.303996
$373$	−6355.96	−0.882303	−0.441152	−	0.897433i	$-0.645430\pi$
$373$	−6355.96	−0.882303	−0.441152	+	0.897433i	$0.645430\pi$
$374$	4066.19	0.562186
$375$	2171.20	0.298988
$376$	−1403.26	−0.192467
$377$	−14538.0	−1.98606
$378$	0	0
$379$	10701.7	1.45042	0.725209	−	0.688529i	$-0.241743\pi$
$379$	10701.7	1.45042	0.725209	+	0.688529i	$0.241743\pi$
$380$	−6952.98	−0.938632
$381$	5107.37	0.686767
$382$	1255.06	0.168100
$383$	8250.18	1.10069	0.550345	−	0.834937i	$-0.314496\pi$
$383$	8250.18	1.10069	0.550345	+	0.834937i	$0.314496\pi$
$384$	585.881	0.0778597
$385$	0	0
$386$	8669.21	1.14314
$387$	−3094.03	−0.406404
$388$	−4798.23	−0.627818
$389$	8580.74	1.11841	0.559204	−	0.829030i	$-0.311107\pi$
$389$	8580.74	1.11841	0.559204	+	0.829030i	$0.311107\pi$
$390$	−7701.47	−0.999946
$391$	1440.44	0.186307
$392$	0	0
$393$	1218.15	0.156355
$394$	6741.89	0.862060
$395$	10039.1	1.27879
$396$	785.516	0.0996809
$397$	1426.65	0.180357	0.0901784	−	0.995926i	$-0.471256\pi$
$397$	1426.65	0.180357	0.0901784	+	0.995926i	$0.471256\pi$
$398$	4793.11	0.603661
$399$	0	0
$400$	1485.80	0.185725
$401$	−7825.99	−0.974592	−0.487296	−	0.873237i	$-0.662017\pi$
$401$	−7825.99	−0.974592	−0.487296	+	0.873237i	$0.662017\pi$
$402$	−7039.71	−0.873405
$403$	−6790.09	−0.839301
$404$	4817.67	0.593287
$405$	−7809.25	−0.958135
$406$	0	0
$407$	1750.13	0.213147
$408$	2293.27	0.278269
$409$	−7324.00	−0.885449	−0.442724	−	0.896658i	$-0.645988\pi$
$409$	−7324.00	−0.885449	−0.442724	+	0.896658i	$0.645988\pi$
$410$	−48.8674	−0.00588631
$411$	−11235.7	−1.34846
$412$	1346.62	0.161027
$413$	0	0
$414$	278.267	0.0330340
$415$	−2467.10	−0.291820
$416$	1823.91	0.214962
$417$	−4892.35	−0.574531
$418$	−7646.11	−0.894697
$419$	12890.7	1.50299	0.751493	−	0.659741i	$-0.229334\pi$
$419$	12890.7	1.50299	0.751493	+	0.659741i	$0.229334\pi$
$420$	0	0
$421$	−2378.02	−0.275291	−0.137646	−	0.990482i	$-0.543953\pi$
$421$	−2378.02	−0.275291	−0.137646	+	0.990482i	$0.543953\pi$
$422$	−7745.65	−0.893489
$423$	−1061.09	−0.121966
$424$	1528.94	0.175122
$425$	5815.77	0.663780
$426$	5862.54	0.666763
$427$	0	0
$428$	7010.28	0.791716
$429$	−8469.22	−0.953142
$430$	−15098.8	−1.69332
$431$	−8171.19	−0.913208	−0.456604	−	0.889670i	$-0.650934\pi$
$431$	−8171.19	−0.913208	−0.456604	+	0.889670i	$0.650934\pi$
$432$	2420.37	0.269560
$433$	11344.7	1.25911	0.629553	−	0.776958i	$-0.283238\pi$
$433$	11344.7	1.25911	0.629553	+	0.776958i	$0.283238\pi$
$434$	0	0
$435$	−17232.3	−1.89937
$436$	−8409.92	−0.923766
$437$	−2708.61	−0.296500
$438$	−5414.93	−0.590720
$439$	6555.98	0.712756	0.356378	−	0.934342i	$-0.384012\pi$
$439$	6555.98	0.712756	0.356378	+	0.934342i	$0.384012\pi$
$440$	3833.30	0.415330
$441$	0	0
$442$	7139.19	0.768272
$443$	−9672.74	−1.03739	−0.518697	−	0.854958i	$-0.673583\pi$
$443$	−9672.74	−1.03739	−0.518697	+	0.854958i	$0.673583\pi$
$444$	987.049	0.105503
$445$	6667.86	0.710308
$446$	−9207.65	−0.977567
$447$	10891.0	1.15240
$448$	0	0
$449$	−9645.83	−1.01384	−0.506921	−	0.861993i	$-0.669216\pi$
$449$	−9645.83	−1.01384	−0.506921	+	0.861993i	$0.669216\pi$
$450$	1123.50	0.117695
$451$	−53.7389	−0.00561079
$452$	−7083.97	−0.737173
$453$	5963.96	0.618568
$454$	−1519.58	−0.157087
$455$	0	0
$456$	−4312.30	−0.442855
$457$	1359.12	0.139118	0.0695592	−	0.997578i	$-0.477841\pi$
$457$	1359.12	0.139118	0.0695592	+	0.997578i	$0.477841\pi$
$458$	−6845.97	−0.698452
$459$	9473.87	0.963404
$460$	1357.94	0.137639
$461$	−5752.64	−0.581187	−0.290593	−	0.956847i	$-0.593853\pi$
$461$	−5752.64	−0.581187	−0.290593	+	0.956847i	$0.593853\pi$
$462$	0	0
$463$	−143.715	−0.0144255	−0.00721274	−	0.999974i	$-0.502296\pi$
$463$	−143.715	−0.0144255	−0.00721274	+	0.999974i	$0.502296\pi$
$464$	4081.05	0.408314
$465$	−8048.47	−0.802665
$466$	12.7142	0.00126389
$467$	−3592.80	−0.356006	−0.178003	−	0.984030i	$-0.556964\pi$
$467$	−3592.80	−0.356006	−0.178003	+	0.984030i	$0.556964\pi$
$468$	1379.17	0.136222
$469$	0	0
$470$	−5178.08	−0.508185
$471$	4544.47	0.444582
$472$	−2034.91	−0.198441
$473$	−16604.0	−1.61406
$474$	6226.35	0.603345
$475$	−10936.1	−1.05638
$476$	0	0
$477$	1156.12	0.110975
$478$	9787.25	0.936524
$479$	−7129.94	−0.680115	−0.340058	−	0.940405i	$-0.610447\pi$
$479$	−7129.94	−0.680115	−0.340058	+	0.940405i	$0.610447\pi$
$480$	2161.93	0.205579
$481$	3072.78	0.291282
$482$	6948.18	0.656599
$483$	0	0
$484$	−1108.57	−0.104110
$485$	−17705.7	−1.65768
$486$	3325.38	0.310375
$487$	−13770.0	−1.28127	−0.640636	−	0.767845i	$-0.721329\pi$
$487$	−13770.0	−1.28127	−0.640636	+	0.767845i	$0.721329\pi$
$488$	2349.22	0.217918
$489$	1794.29	0.165931
$490$	0	0
$491$	−9724.40	−0.893800	−0.446900	−	0.894584i	$-0.647472\pi$
$491$	−9724.40	−0.893800	−0.446900	+	0.894584i	$0.647472\pi$
$492$	−30.3080	−0.00277722
$493$	15974.1	1.45931
$494$	−13424.6	−1.22268
$495$	2898.59	0.263196
$496$	1906.09	0.172552
$497$	0	0
$498$	−1530.12	−0.137683
$499$	−8186.81	−0.734453	−0.367227	−	0.930132i	$-0.619693\pi$
$499$	−8186.81	−0.734453	−0.367227	+	0.930132i	$0.619693\pi$
$500$	−1897.41	−0.169709
$501$	−14081.1	−1.25568
$502$	−7062.82	−0.627946
$503$	5711.49	0.506288	0.253144	−	0.967429i	$-0.418535\pi$
$503$	5711.49	0.506288	0.253144	+	0.967429i	$0.418535\pi$
$504$	0	0
$505$	17777.4	1.56650
$506$	1493.31	0.131197
$507$	−4813.69	−0.421664
$508$	−4463.31	−0.389818
$509$	−16390.5	−1.42730	−0.713649	−	0.700503i	$-0.752959\pi$
$509$	−16390.5	−1.42730	−0.713649	+	0.700503i	$0.752959\pi$
$510$	8462.27	0.734737
$511$	0	0
$512$	−512.000	−0.0441942
$513$	−17814.8	−1.53322
$514$	7865.34	0.674952
$515$	4969.07	0.425172
$516$	−9364.41	−0.798925
$517$	−5694.27	−0.484398
$518$	0	0
$519$	−5147.87	−0.435388
$520$	6730.29	0.567583
$521$	−4377.05	−0.368065	−0.184033	−	0.982920i	$-0.558915\pi$
$521$	−4377.05	−0.368065	−0.184033	+	0.982920i	$0.558915\pi$
$522$	3085.92	0.258749
$523$	14662.3	1.22589	0.612944	−	0.790127i	$-0.289985\pi$
$523$	14662.3	1.22589	0.612944	+	0.790127i	$0.289985\pi$
$524$	−1064.54	−0.0887490
$525$	0	0
$526$	6382.97	0.529108
$527$	7460.86	0.616698
$528$	2377.45	0.195957
$529$	529.000	0.0434783
$530$	5641.85	0.462389
$531$	−1538.72	−0.125753
$532$	0	0
$533$	−94.3519	−0.00766760
$534$	4135.47	0.335129
$535$	25868.2	2.09043
$536$	6151.99	0.495756
$537$	14497.4	1.16500
$538$	−7406.13	−0.593496
$539$	0	0
$540$	8931.26	0.711741
$541$	11007.9	0.874798	0.437399	−	0.899267i	$-0.355900\pi$
$541$	11007.9	0.874798	0.437399	+	0.899267i	$0.355900\pi$
$542$	6288.09	0.498333
$543$	4616.33	0.364836
$544$	−2004.08	−0.157949
$545$	−31033.0	−2.43909
$546$	0	0
$547$	−14669.3	−1.14664	−0.573321	−	0.819331i	$-0.694345\pi$
$547$	−14669.3	−1.14664	−0.573321	+	0.819331i	$0.694345\pi$
$548$	9818.86	0.765403
$549$	1776.39	0.138095
$550$	6029.24	0.467432
$551$	−30038.0	−2.32244
$552$	842.204	0.0649395
$553$	0	0
$554$	923.093	0.0707915
$555$	3642.25	0.278568
$556$	4275.41	0.326111
$557$	25015.9	1.90297	0.951487	−	0.307690i	$-0.0995559\pi$
$557$	25015.9	1.90297	0.951487	+	0.307690i	$0.0995559\pi$
$558$	1441.31	0.109347
$559$	−29152.4	−2.20575
$560$	0	0
$561$	9305.86	0.700346
$562$	−9425.66	−0.707469
$563$	8222.88	0.615548	0.307774	−	0.951460i	$-0.400416\pi$
$563$	8222.88	0.615548	0.307774	+	0.951460i	$0.400416\pi$
$564$	−3211.49	−0.239766
$565$	−26140.2	−1.94642
$566$	1514.50	0.112472
$567$	0	0
$568$	−5123.26	−0.378464
$569$	−10974.8	−0.808588	−0.404294	−	0.914629i	$-0.632483\pi$
$569$	−10974.8	−0.808588	−0.404294	+	0.914629i	$0.632483\pi$
$570$	−15912.6	−1.16931
$571$	−16486.9	−1.20832	−0.604162	−	0.796861i	$-0.706492\pi$
$571$	−16486.9	−1.20832	−0.604162	+	0.796861i	$0.706492\pi$
$572$	7401.23	0.541016
$573$	2872.32	0.209412
$574$	0	0
$575$	2135.84	0.154906
$576$	−387.154	−0.0280059
$577$	24532.2	1.77000	0.884999	−	0.465593i	$-0.154159\pi$
$577$	24532.2	1.77000	0.884999	+	0.465593i	$0.154159\pi$
$578$	1981.56	0.142599
$579$	19840.3	1.42407
$580$	15059.2	1.07810
$581$	0	0
$582$	−10981.2	−0.782107
$583$	6204.28	0.440746
$584$	4732.09	0.335300
$585$	5089.18	0.359678
$586$	−7730.66	−0.544967
$587$	14854.9	1.04451	0.522254	−	0.852790i	$-0.325091\pi$
$587$	14854.9	1.04451	0.522254	+	0.852790i	$0.325091\pi$
$588$	0	0
$589$	−14029.5	−0.981452
$590$	−7508.90	−0.523961
$591$	15429.5	1.07391
$592$	−862.580	−0.0598848
$593$	16350.0	1.13223	0.566116	−	0.824326i	$-0.308445\pi$
$593$	16350.0	1.13223	0.566116	+	0.824326i	$0.308445\pi$
$594$	9821.61	0.678427
$595$	0	0
$596$	−9517.58	−0.654120
$597$	10969.5	0.752014
$598$	2621.87	0.179291
$599$	24832.1	1.69384	0.846921	−	0.531719i	$-0.178454\pi$
$599$	24832.1	1.69384	0.846921	+	0.531719i	$0.178454\pi$
$600$	3400.41	0.231368
$601$	−4249.44	−0.288416	−0.144208	−	0.989547i	$-0.546063\pi$
$601$	−4249.44	−0.288416	−0.144208	+	0.989547i	$0.546063\pi$
$602$	0	0
$603$	4651.89	0.314162
$604$	−5211.89	−0.351107
$605$	−4090.65	−0.274890
$606$	11025.7	0.739090
$607$	2499.46	0.167133	0.0835666	−	0.996502i	$-0.473369\pi$
$607$	2499.46	0.167133	0.0835666	+	0.996502i	$0.473369\pi$
$608$	3768.51	0.251370
$609$	0	0
$610$	8668.72	0.575387
$611$	−9997.69	−0.661969
$612$	−1515.41	−0.100093
$613$	−21993.2	−1.44910	−0.724550	−	0.689222i	$-0.757952\pi$
$613$	−21993.2	−1.44910	−0.724550	+	0.689222i	$0.757952\pi$
$614$	11096.7	0.729358
$615$	−111.838	−0.00733290
$616$	0	0
$617$	6507.69	0.424619	0.212309	−	0.977203i	$-0.431902\pi$
$617$	6507.69	0.424619	0.212309	+	0.977203i	$0.431902\pi$
$618$	3081.86	0.200600
$619$	18867.1	1.22510	0.612548	−	0.790434i	$-0.290145\pi$
$619$	18867.1	1.22510	0.612548	+	0.790434i	$0.290145\pi$
$620$	7033.54	0.455603
$621$	3479.28	0.224829
$622$	20590.0	1.32730
$623$	0	0
$624$	4174.19	0.267791
$625$	−18609.4	−1.19100
$626$	18340.8	1.17100
$627$	−17498.9	−1.11457
$628$	−3971.40	−0.252350
$629$	−3376.33	−0.214027
$630$	0	0
$631$	−3625.78	−0.228748	−0.114374	−	0.993438i	$-0.536486\pi$
$631$	−3625.78	−0.228748	−0.114374	+	0.993438i	$0.536486\pi$
$632$	−5441.19	−0.342467
$633$	−17726.7	−1.11307
$634$	−13514.9	−0.846602
$635$	−16469.8	−1.02927
$636$	3499.13	0.218159
$637$	0	0
$638$	16560.5	1.02764
$639$	−3874.01	−0.239833
$640$	−1889.30	−0.116689
$641$	−19028.1	−1.17249	−0.586244	−	0.810134i	$-0.699394\pi$
$641$	−19028.1	−1.17249	−0.586244	+	0.810134i	$0.699394\pi$
$642$	16043.7	0.986284
$643$	16780.3	1.02916	0.514580	−	0.857442i	$-0.327948\pi$
$643$	16780.3	1.02916	0.514580	+	0.857442i	$0.327948\pi$
$644$	0	0
$645$	−34555.1	−2.10947
$646$	14750.8	0.898394
$647$	−16038.4	−0.974548	−0.487274	−	0.873249i	$-0.662009\pi$
$647$	−16038.4	−0.974548	−0.487274	+	0.873249i	$0.662009\pi$
$648$	4232.61	0.256593
$649$	−8257.46	−0.499435
$650$	10585.8	0.638784
$651$	0	0
$652$	−1568.02	−0.0941848
$653$	−10798.0	−0.647103	−0.323552	−	0.946211i	$-0.604877\pi$
$653$	−10798.0	−0.647103	−0.323552	+	0.946211i	$0.604877\pi$
$654$	−19246.9	−1.15079
$655$	−3928.18	−0.234331
$656$	26.4861	0.00157638
$657$	3578.22	0.212480
$658$	0	0
$659$	4711.90	0.278528	0.139264	−	0.990255i	$-0.455526\pi$
$659$	4711.90	0.278528	0.139264	+	0.990255i	$0.455526\pi$
$660$	8772.88	0.517400
$661$	−19090.0	−1.12332	−0.561661	−	0.827367i	$-0.689838\pi$
$661$	−19090.0	−1.12332	−0.561661	+	0.827367i	$0.689838\pi$
$662$	19800.3	1.16248
$663$	16338.7	0.957079
$664$	1337.17	0.0781509
$665$	0	0
$666$	−652.248	−0.0379491
$667$	5866.50	0.340558
$668$	12305.4	0.712740
$669$	−21072.6	−1.21781
$670$	22701.1	1.30898
$671$	9532.89	0.548455
$672$	0	0
$673$	−1755.90	−0.100572	−0.0502860	−	0.998735i	$-0.516013\pi$
$673$	−1755.90	−0.100572	−0.0502860	+	0.998735i	$0.516013\pi$
$674$	13324.2	0.761466
$675$	14047.6	0.801027
$676$	4206.67	0.239342
$677$	21551.3	1.22346	0.611732	−	0.791065i	$-0.290473\pi$
$677$	21551.3	1.22346	0.611732	+	0.791065i	$0.290473\pi$
$678$	−16212.4	−0.918336
$679$	0	0
$680$	−7395.16	−0.417046
$681$	−3477.71	−0.195692
$682$	7734.71	0.434277
$683$	−9417.76	−0.527615	−0.263807	−	0.964575i	$-0.584978\pi$
$683$	−9417.76	−0.527615	−0.263807	+	0.964575i	$0.584978\pi$
$684$	2849.59	0.159294
$685$	36232.0	2.02096
$686$	0	0
$687$	−15667.7	−0.870100
$688$	8183.54	0.453480
$689$	10893.1	0.602315
$690$	3107.77	0.171465
$691$	−9793.49	−0.539164	−0.269582	−	0.962978i	$-0.586885\pi$
$691$	−9793.49	−0.539164	−0.269582	+	0.962978i	$0.586885\pi$
$692$	4498.71	0.247132
$693$	0	0
$694$	10909.6	0.596717
$695$	15776.5	0.861058
$696$	9339.87	0.508659
$697$	103.673	0.00563397
$698$	−23594.5	−1.27946
$699$	29.0977	0.00157450
$700$	0	0
$701$	−10569.0	−0.569454	−0.284727	−	0.958609i	$-0.591903\pi$
$701$	−10569.0	−0.569454	−0.284727	+	0.958609i	$0.591903\pi$
$702$	17244.2	0.927125
$703$	6348.90	0.340617
$704$	−2077.64	−0.111228
$705$	−11850.5	−0.633074
$706$	2456.09	0.130929
$707$	0	0
$708$	−4657.09	−0.247209
$709$	20843.4	1.10408	0.552038	−	0.833819i	$-0.313851\pi$
$709$	20843.4	1.10408	0.552038	+	0.833819i	$0.313851\pi$
$710$	−18905.1	−0.999288
$711$	−4114.41	−0.217022
$712$	−3613.97	−0.190224
$713$	2740.00	0.143918
$714$	0	0
$715$	27310.9	1.42849
$716$	−12669.2	−0.661271
$717$	22399.1	1.16668
$718$	972.171	0.0505308
$719$	10184.3	0.528247	0.264123	−	0.964489i	$-0.414917\pi$
$719$	10184.3	0.528247	0.264123	+	0.964489i	$0.414917\pi$
$720$	−1428.61	−0.0739463
$721$	0	0
$722$	−14019.6	−0.722653
$723$	15901.6	0.817962
$724$	−4034.20	−0.207085
$725$	23686.1	1.21335
$726$	−2537.06	−0.129696
$727$	20161.4	1.02853	0.514266	−	0.857630i	$-0.328064\pi$
$727$	20161.4	1.02853	0.514266	+	0.857630i	$0.328064\pi$
$728$	0	0
$729$	21895.5	1.11241
$730$	17461.6	0.885320
$731$	32032.2	1.62073
$732$	5376.42	0.271473
$733$	−31634.2	−1.59404	−0.797022	−	0.603950i	$-0.793593\pi$
$733$	−31634.2	−1.59404	−0.797022	+	0.603950i	$0.793593\pi$
$734$	23001.2	1.15666
$735$	0	0
$736$	−736.000	−0.0368605
$737$	24964.1	1.24771
$738$	20.0277	0.000998957 0
$739$	−29119.2	−1.44948	−0.724740	−	0.689022i	$-0.758040\pi$
$739$	−29119.2	−1.44948	−0.724740	+	0.689022i	$0.758040\pi$
$740$	−3182.96	−0.158119
$741$	−30723.6	−1.52316
$742$	0	0
$743$	24914.9	1.23020	0.615100	−	0.788449i	$-0.289115\pi$
$743$	24914.9	1.23020	0.615100	+	0.788449i	$0.289115\pi$
$744$	4362.27	0.214958
$745$	−35120.3	−1.72712
$746$	12711.9	0.623883
$747$	1011.11	0.0495244
$748$	−8132.37	−0.397525
$749$	0	0
$750$	−4342.41	−0.211416
$751$	4730.39	0.229846	0.114923	−	0.993374i	$-0.463338\pi$
$751$	4730.39	0.229846	0.114923	+	0.993374i	$0.463338\pi$
$752$	2806.51	0.136094
$753$	−16164.0	−0.782267
$754$	29076.0	1.40436
$755$	−19232.1	−0.927057
$756$	0	0
$757$	18579.5	0.892052	0.446026	−	0.895020i	$-0.352839\pi$
$757$	18579.5	0.892052	0.446026	+	0.895020i	$0.352839\pi$
$758$	−21403.4	−1.02560
$759$	3417.58	0.163439
$760$	13906.0	0.663713
$761$	−29983.6	−1.42826	−0.714129	−	0.700014i	$-0.753177\pi$
$761$	−29983.6	−1.42826	−0.714129	+	0.700014i	$0.753177\pi$
$762$	−10214.7	−0.485618
$763$	0	0
$764$	−2510.12	−0.118865
$765$	−5591.92	−0.264283
$766$	−16500.4	−0.778306
$767$	−14498.0	−0.682519
$768$	−1171.76	−0.0550551
$769$	−14327.3	−0.671855	−0.335927	−	0.941888i	$-0.609050\pi$
$769$	−14327.3	−0.671855	−0.335927	+	0.941888i	$0.609050\pi$
$770$	0	0
$771$	18000.6	0.840824
$772$	−17338.4	−0.808320
$773$	−24571.3	−1.14330	−0.571649	−	0.820498i	$-0.693696\pi$
$773$	−24571.3	−1.14330	−0.571649	+	0.820498i	$0.693696\pi$
$774$	6188.06	0.287371
$775$	11062.8	0.512757
$776$	9596.46	0.443934
$777$	0	0
$778$	−17161.5	−0.790834
$779$	−194.947	−0.00896625
$780$	15402.9	0.707069
$781$	−20789.7	−0.952514
$782$	−2880.87	−0.131739
$783$	38584.5	1.76104
$784$	0	0
$785$	−14654.6	−0.666301
$786$	−2436.29	−0.110559
$787$	17350.1	0.785849	0.392924	−	0.919571i	$-0.371463\pi$
$787$	17350.1	0.785849	0.392924	+	0.919571i	$0.371463\pi$
$788$	−13483.8	−0.609568
$789$	14608.0	0.659138
$790$	−20078.2	−0.904242
$791$	0	0
$792$	−1571.03	−0.0704851
$793$	16737.3	0.749508
$794$	−2853.30	−0.127531
$795$	12911.9	0.576024
$796$	−9586.23	−0.426853
$797$	−27251.1	−1.21115	−0.605573	−	0.795789i	$-0.707056\pi$
$797$	−27251.1	−1.21115	−0.605573	+	0.795789i	$0.707056\pi$
$798$	0	0
$799$	10985.3	0.486399
$800$	−2971.61	−0.131328
$801$	−2732.74	−0.120545
$802$	15652.0	0.689140
$803$	19202.4	0.843881
$804$	14079.4	0.617591
$805$	0	0
$806$	13580.2	0.593475
$807$	−16949.7	−0.739351
$808$	−9635.33	−0.419517
$809$	30140.1	1.30985	0.654925	−	0.755694i	$-0.272700\pi$
$809$	30140.1	1.30985	0.654925	+	0.755694i	$0.272700\pi$
$810$	15618.5	0.677504
$811$	2021.30	0.0875183	0.0437591	−	0.999042i	$-0.486067\pi$
$811$	2021.30	0.0875183	0.0437591	+	0.999042i	$0.486067\pi$
$812$	0	0
$813$	14390.9	0.620801
$814$	−3500.26	−0.150718
$815$	−5786.07	−0.248684
$816$	−4586.54	−0.196766
$817$	−60233.8	−2.57933
$818$	14648.0	0.626107
$819$	0	0
$820$	97.7348	0.00416225
$821$	−31174.9	−1.32523	−0.662614	−	0.748961i	$-0.730553\pi$
$821$	−31174.9	−1.32523	−0.662614	+	0.748961i	$0.730553\pi$
$822$	22471.4	0.953505
$823$	13963.8	0.591431	0.295716	−	0.955276i	$-0.404442\pi$
$823$	13963.8	0.591431	0.295716	+	0.955276i	$0.404442\pi$
$824$	−2693.23	−0.113863
$825$	13798.5	0.582306
$826$	0	0
$827$	16597.3	0.697879	0.348939	−	0.937145i	$-0.386542\pi$
$827$	16597.3	0.697879	0.348939	+	0.937145i	$0.386542\pi$
$828$	−556.534	−0.0233586
$829$	−21082.7	−0.883273	−0.441637	−	0.897194i	$-0.645602\pi$
$829$	−21082.7	−0.883273	−0.441637	+	0.897194i	$0.645602\pi$
$830$	4934.21	0.206348
$831$	2112.59	0.0881888
$832$	−3647.81	−0.152001
$833$	0	0
$834$	9784.70	0.406255
$835$	45407.5	1.88190
$836$	15292.2	0.632647
$837$	18021.2	0.744211
$838$	−25781.4	−1.06277
$839$	−45857.1	−1.88696	−0.943482	−	0.331425i	$-0.892471\pi$
$839$	−45857.1	−1.88696	−0.943482	+	0.331425i	$0.892471\pi$
$840$	0	0
$841$	40669.4	1.66753
$842$	4756.04	0.194660
$843$	−21571.5	−0.881333
$844$	15491.3	0.631792
$845$	15522.8	0.631953
$846$	2122.17	0.0862433
$847$	0	0
$848$	−3057.88	−0.123830
$849$	3466.07	0.140112
$850$	−11631.5	−0.469363
$851$	−1239.96	−0.0499474
$852$	−11725.1	−0.471473
$853$	−9553.50	−0.383476	−0.191738	−	0.981446i	$-0.561412\pi$
$853$	−9553.50	−0.383476	−0.191738	+	0.981446i	$0.561412\pi$
$854$	0	0
$855$	10515.1	0.420596
$856$	−14020.6	−0.559828
$857$	36393.4	1.45061	0.725307	−	0.688426i	$-0.241698\pi$
$857$	36393.4	1.45061	0.725307	+	0.688426i	$0.241698\pi$
$858$	16938.4	0.673973
$859$	−4110.90	−0.163285	−0.0816426	−	0.996662i	$-0.526017\pi$
$859$	−4110.90	−0.163285	−0.0816426	+	0.996662i	$0.526017\pi$
$860$	30197.6	1.19736
$861$	0	0
$862$	16342.4	0.645735
$863$	920.302	0.0363006	0.0181503	−	0.999835i	$-0.494222\pi$
$863$	920.302	0.0363006	0.0181503	+	0.999835i	$0.494222\pi$
$864$	−4840.74	−0.190608
$865$	16600.4	0.652522
$866$	−22689.4	−0.890322
$867$	4534.99	0.177643
$868$	0	0
$869$	−22079.8	−0.861917
$870$	34464.5	1.34305
$871$	43830.7	1.70510
$872$	16819.8	0.653201
$873$	7256.46	0.281322
$874$	5417.23	0.209657
$875$	0	0
$876$	10829.9	0.417702
$877$	5197.13	0.200108	0.100054	−	0.994982i	$-0.468098\pi$
$877$	5197.13	0.200108	0.100054	+	0.994982i	$0.468098\pi$
$878$	−13112.0	−0.503995
$879$	−17692.4	−0.678895
$880$	−7666.60	−0.293683
$881$	−44377.9	−1.69708	−0.848541	−	0.529130i	$-0.822518\pi$
$881$	−44377.9	−1.69708	−0.848541	+	0.529130i	$0.822518\pi$
$882$	0	0
$883$	5826.13	0.222044	0.111022	−	0.993818i	$-0.464588\pi$
$883$	5826.13	0.222044	0.111022	+	0.993818i	$0.464588\pi$
$884$	−14278.4	−0.543251
$885$	−17184.9	−0.652726
$886$	19345.5	0.733549
$887$	−17722.9	−0.670887	−0.335444	−	0.942060i	$-0.608886\pi$
$887$	−17722.9	−0.670887	−0.335444	+	0.942060i	$0.608886\pi$
$888$	−1974.10	−0.0746018
$889$	0	0
$890$	−13335.7	−0.502263
$891$	17175.5	0.645792
$892$	18415.3	0.691244
$893$	−20657.0	−0.774086
$894$	−21781.9	−0.814873
$895$	−46749.9	−1.74601
$896$	0	0
$897$	6000.40	0.223353
$898$	19291.7	0.716895
$899$	30386.0	1.12729
$900$	−2247.01	−0.0832226
$901$	−11969.2	−0.442567
$902$	107.478	0.00396743
$903$	0	0
$904$	14167.9	0.521260
$905$	−14886.4	−0.546784
$906$	−11927.9	−0.437394
$907$	−20879.7	−0.764387	−0.382194	−	0.924082i	$-0.624831\pi$
$907$	−20879.7	−0.764387	−0.382194	+	0.924082i	$0.624831\pi$
$908$	3039.16	0.111077
$909$	−7285.85	−0.265849
$910$	0	0
$911$	−24033.6	−0.874061	−0.437031	−	0.899447i	$-0.643970\pi$
$911$	−24033.6	−0.874061	−0.437031	+	0.899447i	$0.643970\pi$
$912$	8624.60	0.313146
$913$	5426.09	0.196689
$914$	−2718.25	−0.0983716
$915$	19839.2	0.716791
$916$	13691.9	0.493880
$917$	0	0
$918$	−18947.7	−0.681229
$919$	−47109.2	−1.69096	−0.845479	−	0.534009i	$-0.820685\pi$
$919$	−47109.2	−1.69096	−0.845479	+	0.534009i	$0.820685\pi$
$920$	−2715.87	−0.0973257
$921$	25395.8	0.908601
$922$	11505.3	0.410961
$923$	−36501.4	−1.30169
$924$	0	0
$925$	−5006.34	−0.177954
$926$	287.430	0.0102004
$927$	−2036.52	−0.0721553
$928$	−8162.09	−0.288722
$929$	−30502.1	−1.07722	−0.538611	−	0.842554i	$-0.681051\pi$
$929$	−30502.1	−1.07722	−0.538611	+	0.842554i	$0.681051\pi$
$930$	16096.9	0.567570
$931$	0	0
$932$	−25.4284	−0.000893706 0
$933$	47122.1	1.65349
$934$	7185.60	0.251734
$935$	−30008.8	−1.04962
$936$	−2758.33	−0.0963236
$937$	−25258.4	−0.880637	−0.440318	−	0.897842i	$-0.645134\pi$
$937$	−25258.4	−0.880637	−0.440318	+	0.897842i	$0.645134\pi$
$938$	0	0
$939$	41974.8	1.45878
$940$	10356.2	0.359341
$941$	−8759.75	−0.303464	−0.151732	−	0.988422i	$-0.548485\pi$
$941$	−8759.75	−0.303464	−0.151732	+	0.988422i	$0.548485\pi$
$942$	−9088.94	−0.314367
$943$	38.0737	0.00131480
$944$	4069.82	0.140319
$945$	0	0
$946$	33208.0	1.14132
$947$	−26144.6	−0.897134	−0.448567	−	0.893749i	$-0.648066\pi$
$947$	−26144.6	−0.897134	−0.448567	+	0.893749i	$0.648066\pi$
$948$	−12452.7	−0.426630
$949$	33714.4	1.15323
$950$	21872.1	0.746974
$951$	−30930.2	−1.05466
$952$	0	0
$953$	−490.121	−0.0166596	−0.00832978	−	0.999965i	$-0.502651\pi$
$953$	−490.121	−0.0166596	−0.00832978	+	0.999965i	$0.502651\pi$
$954$	−2312.24	−0.0784714
$955$	−9262.44	−0.313849
$956$	−19574.5	−0.662222
$957$	37900.3	1.28019
$958$	14259.9	0.480914
$959$	0	0
$960$	−4323.85	−0.145366
$961$	−15598.9	−0.523613
$962$	−6145.57	−0.205968
$963$	−10601.8	−0.354764
$964$	−13896.4	−0.464286
$965$	−63979.5	−2.13427
$966$	0	0
$967$	−31156.9	−1.03613	−0.518065	−	0.855341i	$-0.673348\pi$
$967$	−31156.9	−1.03613	−0.518065	+	0.855341i	$0.673348\pi$
$968$	2217.13	0.0736170
$969$	33758.6	1.11918
$970$	35411.4	1.17215
$971$	37284.3	1.23224	0.616122	−	0.787651i	$-0.288703\pi$
$971$	37284.3	1.23224	0.616122	+	0.787651i	$0.288703\pi$
$972$	−6650.76	−0.219468
$973$	0	0
$974$	27540.1	0.905996
$975$	24226.7	0.795768
$976$	−4698.44	−0.154092
$977$	11949.2	0.391288	0.195644	−	0.980675i	$-0.437320\pi$
$977$	11949.2	0.391288	0.195644	+	0.980675i	$0.437320\pi$
$978$	−3588.57	−0.117331
$979$	−14665.1	−0.478754
$980$	0	0
$981$	12718.5	0.413935
$982$	19448.8	0.632012
$983$	−6061.02	−0.196660	−0.0983298	−	0.995154i	$-0.531350\pi$
$983$	−6061.02	−0.196660	−0.0983298	+	0.995154i	$0.531350\pi$
$984$	60.6160	0.00196379
$985$	−49755.7	−1.60949
$986$	−31948.3	−1.03189
$987$	0	0
$988$	26849.2	0.864563
$989$	11763.8	0.378229
$990$	−5797.17	−0.186107
$991$	18618.8	0.596816	0.298408	−	0.954438i	$-0.403544\pi$
$991$	18618.8	0.596816	0.298408	+	0.954438i	$0.403544\pi$
$992$	−3812.17	−0.122013
$993$	45315.0	1.44816
$994$	0	0
$995$	−35373.6	−1.12705
$996$	3060.24	0.0973569
$997$	−35778.7	−1.13653	−0.568266	−	0.822845i	$-0.692385\pi$
$997$	−35778.7	−1.13653	−0.568266	+	0.822845i	$0.692385\pi$
$998$	16373.6	0.519337
$999$	−8155.32	−0.258281

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2254.4.a.z.1.4	✓	14
7.6	odd	2	inner	2254.4.a.z.1.11	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2254.4.a.z.1.4	✓	14	1.1	even	1	trivial
2254.4.a.z.1.11	yes	14	7.6	odd	2	inner

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:	\( N \)	\(=\)	\( 2254 = 2 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2254.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -4.57720 q^{3} +4.00000 q^{4} +14.7602 q^{5} +9.15439 q^{6} -8.00000 q^{8} -6.04928 q^{9} -29.5203 q^{10} -32.4632 q^{11} -18.3088 q^{12} -56.9971 q^{13} -67.5602 q^{15} +16.0000 q^{16} +62.6276 q^{17} +12.0986 q^{18} -117.766 q^{19} +59.0407 q^{20} +64.9264 q^{22} +23.0000 q^{23} +36.6176 q^{24} +92.8627 q^{25} +113.994 q^{26} +151.273 q^{27} +255.065 q^{29} +135.120 q^{30} +119.130 q^{31} -32.0000 q^{32} +148.590 q^{33} -125.255 q^{34} -24.1971 q^{36} -53.9112 q^{37} +235.532 q^{38} +260.887 q^{39} -118.081 q^{40} +1.65538 q^{41} +511.471 q^{43} -129.853 q^{44} -89.2884 q^{45} -46.0000 q^{46} +175.407 q^{47} -73.2351 q^{48} -185.725 q^{50} -286.659 q^{51} -227.988 q^{52} -191.117 q^{53} -302.546 q^{54} -479.162 q^{55} +539.037 q^{57} -510.131 q^{58} +254.364 q^{59} -270.241 q^{60} -293.652 q^{61} -238.261 q^{62} +64.0000 q^{64} -841.287 q^{65} -297.181 q^{66} -768.998 q^{67} +250.511 q^{68} -105.275 q^{69} +640.408 q^{71} +48.3942 q^{72} -591.512 q^{73} +107.822 q^{74} -425.051 q^{75} -471.063 q^{76} -521.774 q^{78} +680.149 q^{79} +236.163 q^{80} -529.076 q^{81} -3.31076 q^{82} -167.146 q^{83} +924.395 q^{85} -1022.94 q^{86} -1167.48 q^{87} +259.706 q^{88} +451.747 q^{89} +178.577 q^{90} +92.0000 q^{92} -545.283 q^{93} -350.814 q^{94} -1738.24 q^{95} +146.470 q^{96} -1199.56 q^{97} +196.379 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 28 q^{2} + 56 q^{4} - 112 q^{8} + 22 q^{9} - 92 q^{11} - 268 q^{15} + 224 q^{16} - 44 q^{18} + 184 q^{22} + 322 q^{23} + 130 q^{25} + 196 q^{29} + 536 q^{30} - 448 q^{32} + 88 q^{36} + 628 q^{37}+ \cdots + 1800 q^{99}+O(q^{100}) \) 14 * q - 28 * q^2 + 56 * q^4 - 112 * q^8 + 22 * q^9 - 92 * q^11 - 268 * q^15 + 224 * q^16 - 44 * q^18 + 184 * q^22 + 322 * q^23 + 130 * q^25 + 196 * q^29 + 536 * q^30 - 448 * q^32 + 88 * q^36 + 628 * q^37 + 388 * q^39 + 640 * q^43 - 368 * q^44 - 644 * q^46 - 260 * q^50 + 656 * q^51 - 1260 * q^53 + 380 * q^57 - 392 * q^58 - 1072 * q^60 + 896 * q^64 - 204 * q^65 - 1564 * q^67 - 900 * q^71 - 176 * q^72 - 1256 * q^74 - 776 * q^78 - 404 * q^79 - 4278 * q^81 + 1512 * q^85 - 1280 * q^86 + 736 * q^88 + 1288 * q^92 - 2712 * q^93 - 4752 * q^95 + 1800 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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