LMFDB - Embedded newform 1815.4.a.bf.1.6

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 47x^{8} + 760x^{6} - 4899x^{4} + 10629x^{2} - 1452 $ x^10 - 47x^8 + 760x^6 - 4899x^4 + 10629x^2 - 1452
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.382418$ 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)

$f(q)$	$=$	$q+0.382418 q^{2} -3.00000 q^{3} -7.85376 q^{4} -5.00000 q^{5} -1.14725 q^{6} -2.52423 q^{7} -6.06276 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+0.382418 q^{2} -3.00000 q^{3} -7.85376 q^{4} -5.00000 q^{5} -1.14725 q^{6} -2.52423 q^{7} -6.06276 q^{8} +9.00000 q^{9} -1.91209 q^{10} +23.5613 q^{12} -73.6731 q^{13} -0.965312 q^{14} +15.0000 q^{15} +60.5115 q^{16} -25.9831 q^{17} +3.44176 q^{18} -5.76439 q^{19} +39.2688 q^{20} +7.57270 q^{21} -189.246 q^{23} +18.1883 q^{24} +25.0000 q^{25} -28.1739 q^{26} -27.0000 q^{27} +19.8247 q^{28} -270.799 q^{29} +5.73627 q^{30} -67.7978 q^{31} +71.6427 q^{32} -9.93639 q^{34} +12.6212 q^{35} -70.6838 q^{36} +339.759 q^{37} -2.20440 q^{38} +221.019 q^{39} +30.3138 q^{40} +72.3609 q^{41} +2.89594 q^{42} -341.631 q^{43} -45.0000 q^{45} -72.3711 q^{46} +165.626 q^{47} -181.535 q^{48} -336.628 q^{49} +9.56044 q^{50} +77.9492 q^{51} +578.611 q^{52} -519.432 q^{53} -10.3253 q^{54} +15.3038 q^{56} +17.2932 q^{57} -103.558 q^{58} -632.259 q^{59} -117.806 q^{60} -630.199 q^{61} -25.9271 q^{62} -22.7181 q^{63} -456.695 q^{64} +368.366 q^{65} -986.191 q^{67} +204.065 q^{68} +567.739 q^{69} +4.82656 q^{70} -632.308 q^{71} -54.5648 q^{72} -117.640 q^{73} +129.930 q^{74} -75.0000 q^{75} +45.2721 q^{76} +84.5217 q^{78} +43.4840 q^{79} -302.558 q^{80} +81.0000 q^{81} +27.6721 q^{82} +905.452 q^{83} -59.4742 q^{84} +129.915 q^{85} -130.646 q^{86} +812.397 q^{87} +4.55915 q^{89} -17.2088 q^{90} +185.968 q^{91} +1486.29 q^{92} +203.393 q^{93} +63.3382 q^{94} +28.8220 q^{95} -214.928 q^{96} +74.9609 q^{97} -128.733 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 30 q^{3} + 14 q^{4} - 50 q^{5} + 90 q^{9}+O(q^{10}) $ 10 * q - 30 * q^3 + 14 * q^4 - 50 * q^5 + 90 * q^9	$ 10 q - 30 q^{3} + 14 q^{4} - 50 q^{5} + 90 q^{9} - 42 q^{12} - 224 q^{14} + 150 q^{15} - 238 q^{16} - 70 q^{20} - 370 q^{23} + 250 q^{25} + 112 q^{26} - 270 q^{27} + 326 q^{31} - 510 q^{34} + 126 q^{36} + 984 q^{37} - 1152 q^{38} + 672 q^{42} - 450 q^{45} + 58 q^{47} + 714 q^{48} + 150 q^{49} + 138 q^{53} - 1380 q^{56} - 816 q^{58} + 192 q^{59} + 210 q^{60} - 1424 q^{64} - 480 q^{67} + 1110 q^{69} + 1120 q^{70} - 716 q^{71} - 750 q^{75} - 336 q^{78} + 1190 q^{80} + 810 q^{81} - 2976 q^{82} - 1584 q^{86} - 3160 q^{89} + 1840 q^{91} + 406 q^{92} - 978 q^{93} - 204 q^{97}+O(q^{100}) $ 10 * q - 30 * q^3 + 14 * q^4 - 50 * q^5 + 90 * q^9 - 42 * q^12 - 224 * q^14 + 150 * q^15 - 238 * q^16 - 70 * q^20 - 370 * q^23 + 250 * q^25 + 112 * q^26 - 270 * q^27 + 326 * q^31 - 510 * q^34 + 126 * q^36 + 984 * q^37 - 1152 * q^38 + 672 * q^42 - 450 * q^45 + 58 * q^47 + 714 * q^48 + 150 * q^49 + 138 * q^53 - 1380 * q^56 - 816 * q^58 + 192 * q^59 + 210 * q^60 - 1424 * q^64 - 480 * q^67 + 1110 * q^69 + 1120 * q^70 - 716 * q^71 - 750 * q^75 - 336 * q^78 + 1190 * q^80 + 810 * q^81 - 2976 * q^82 - 1584 * q^86 - 3160 * q^89 + 1840 * q^91 + 406 * q^92 - 978 * q^93 - 204 * q^97

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 $

$2$	0.382418	0.135205	0.0676025	−	0.997712i	$-0.478465\pi$
$2$	0.382418	0.135205	0.0676025	+	0.997712i	$0.478465\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−7.85376	−0.981720
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−1.14725	−0.0780607
$7$	−2.52423	−0.136296	−0.0681479	−	0.997675i	$-0.521709\pi$
$7$	−2.52423	−0.136296	−0.0681479	+	0.997675i	$0.521709\pi$
$8$	−6.06276	−0.267939
$9$	9.00000	0.333333
$10$	−1.91209	−0.0604655
$11$	0	0
$11$	0	0
$12$	23.5613	0.566796
$13$	−73.6731	−1.57179	−0.785894	−	0.618361i	$-0.787797\pi$
$13$	−73.6731	−1.57179	−0.785894	+	0.618361i	$0.787797\pi$
$14$	−0.965312	−0.0184279
$15$	15.0000	0.258199
$16$	60.5115	0.945493
$17$	−25.9831	−0.370695	−0.185348	−	0.982673i	$-0.559341\pi$
$17$	−25.9831	−0.370695	−0.185348	+	0.982673i	$0.559341\pi$
$18$	3.44176	0.0450684
$19$	−5.76439	−0.0696022	−0.0348011	−	0.999394i	$-0.511080\pi$
$19$	−5.76439	−0.0696022	−0.0348011	+	0.999394i	$0.511080\pi$
$20$	39.2688	0.439038
$21$	7.57270	0.0786904
$22$	0	0
$23$	−189.246	−1.71568	−0.857838	−	0.513920i	$-0.828193\pi$
$23$	−189.246	−1.71568	−0.857838	+	0.513920i	$0.828193\pi$
$24$	18.1883	0.154694
$25$	25.0000	0.200000
$26$	−28.1739	−0.212514
$27$	−27.0000	−0.192450
$28$	19.8247	0.133804
$29$	−270.799	−1.73400	−0.867002	−	0.498305i	$-0.833956\pi$
$29$	−270.799	−1.73400	−0.867002	+	0.498305i	$0.833956\pi$
$30$	5.73627	0.0349098
$31$	−67.7978	−0.392801	−0.196401	−	0.980524i	$-0.562925\pi$
$31$	−67.7978	−0.392801	−0.196401	+	0.980524i	$0.562925\pi$
$32$	71.6427	0.395774
$33$	0	0
$34$	−9.93639	−0.0501199
$35$	12.6212	0.0609533
$36$	−70.6838	−0.327240
$37$	339.759	1.50962	0.754812	−	0.655942i	$-0.227728\pi$
$37$	339.759	1.50962	0.754812	+	0.655942i	$0.227728\pi$
$38$	−2.20440	−0.00941057
$39$	221.019	0.907473
$40$	30.3138	0.119826
$41$	72.3609	0.275631	0.137815	−	0.990458i	$-0.455992\pi$
$41$	72.3609	0.275631	0.137815	+	0.990458i	$0.455992\pi$
$42$	2.89594	0.0106393
$43$	−341.631	−1.21159	−0.605793	−	0.795622i	$-0.707144\pi$
$43$	−341.631	−1.21159	−0.605793	+	0.795622i	$0.707144\pi$
$44$	0	0
$45$	−45.0000	−0.149071
$46$	−72.3711	−0.231968
$47$	165.626	0.514021	0.257010	−	0.966409i	$-0.417263\pi$
$47$	165.626	0.514021	0.257010	+	0.966409i	$0.417263\pi$
$48$	−181.535	−0.545881
$49$	−336.628	−0.981423
$50$	9.56044	0.0270410
$51$	77.9492	0.214021
$52$	578.611	1.54306
$53$	−519.432	−1.34622	−0.673108	−	0.739544i	$-0.735041\pi$
$53$	−519.432	−1.34622	−0.673108	+	0.739544i	$0.735041\pi$
$54$	−10.3253	−0.0260202
$55$	0	0
$56$	15.3038	0.0365189
$57$	17.2932	0.0401848
$58$	−103.558	−0.234446
$59$	−632.259	−1.39514	−0.697569	−	0.716518i	$-0.745735\pi$
$59$	−632.259	−1.39514	−0.697569	+	0.716518i	$0.745735\pi$
$60$	−117.806	−0.253479
$61$	−630.199	−1.32277	−0.661383	−	0.750048i	$-0.730030\pi$
$61$	−630.199	−1.32277	−0.661383	+	0.750048i	$0.730030\pi$
$62$	−25.9271	−0.0531088
$63$	−22.7181	−0.0454319
$64$	−456.695	−0.891982
$65$	368.366	0.702925
$66$	0	0
$67$	−986.191	−1.79824	−0.899122	−	0.437698i	$-0.855794\pi$
$67$	−986.191	−1.79824	−0.899122	+	0.437698i	$0.855794\pi$
$68$	204.065	0.363919
$69$	567.739	0.990546
$70$	4.82656	0.00824120
$71$	−632.308	−1.05692	−0.528459	−	0.848959i	$-0.677230\pi$
$71$	−632.308	−1.05692	−0.528459	+	0.848959i	$0.677230\pi$
$72$	−54.5648	−0.0893128
$73$	−117.640	−0.188613	−0.0943066	−	0.995543i	$-0.530063\pi$
$73$	−117.640	−0.188613	−0.0943066	+	0.995543i	$0.530063\pi$
$74$	129.930	0.204109
$75$	−75.0000	−0.115470
$76$	45.2721	0.0683298
$77$	0	0
$78$	84.5217	0.122695
$79$	43.4840	0.0619282	0.0309641	−	0.999520i	$-0.490142\pi$
$79$	43.4840	0.0619282	0.0309641	+	0.999520i	$0.490142\pi$
$80$	−302.558	−0.422837
$81$	81.0000	0.111111
$82$	27.6721	0.0372667
$83$	905.452	1.19743	0.598713	−	0.800964i	$-0.295679\pi$
$83$	905.452	1.19743	0.598713	+	0.800964i	$0.295679\pi$
$84$	−59.4742	−0.0772519
$85$	129.915	0.165780
$86$	−130.646	−0.163813
$87$	812.397	1.00113
$88$	0	0
$89$	4.55915	0.00542999	0.00271500	−	0.999996i	$-0.499136\pi$
$89$	4.55915	0.00542999	0.00271500	+	0.999996i	$0.499136\pi$
$90$	−17.2088	−0.0201552
$91$	185.968	0.214228
$92$	1486.29	1.68431
$93$	203.393	0.226784
$94$	63.3382	0.0694982
$95$	28.8220	0.0311271
$96$	−214.928	−0.228500
$97$	74.9609	0.0784652	0.0392326	−	0.999230i	$-0.487509\pi$
$97$	74.9609	0.0784652	0.0392326	+	0.999230i	$0.487509\pi$
$98$	−128.733	−0.132693
$99$	0	0
$100$	−196.344	−0.196344
$101$	−414.176	−0.408040	−0.204020	−	0.978967i	$-0.565401\pi$
$101$	−414.176	−0.408040	−0.204020	+	0.978967i	$0.565401\pi$
$102$	29.8092	0.0289367
$103$	−112.325	−0.107454	−0.0537269	−	0.998556i	$-0.517110\pi$
$103$	−112.325	−0.107454	−0.0537269	+	0.998556i	$0.517110\pi$
$104$	446.662	0.421143
$105$	−37.8635	−0.0351914
$106$	−198.640	−0.182015
$107$	−1193.38	−1.07821	−0.539105	−	0.842239i	$-0.681237\pi$
$107$	−1193.38	−1.07821	−0.539105	+	0.842239i	$0.681237\pi$
$108$	212.051	0.188932
$109$	−1355.98	−1.19155	−0.595776	−	0.803151i	$-0.703155\pi$
$109$	−1355.98	−1.19155	−0.595776	+	0.803151i	$0.703155\pi$
$110$	0	0
$111$	−1019.28	−0.871581
$112$	−152.745	−0.128867
$113$	1463.99	1.21876	0.609382	−	0.792877i	$-0.291418\pi$
$113$	1463.99	1.21876	0.609382	+	0.792877i	$0.291418\pi$
$114$	6.61321	0.00543320
$115$	946.231	0.767274
$116$	2126.79	1.70231
$117$	−663.058	−0.523930
$118$	−241.787	−0.188630
$119$	65.5874	0.0505242
$120$	−90.9414	−0.0691814
$121$	0	0
$122$	−240.999	−0.178845
$123$	−217.083	−0.159136
$124$	532.468	0.385621
$125$	−125.000	−0.0894427
$126$	−8.68781	−0.00614263
$127$	2476.36	1.73025	0.865124	−	0.501558i	$-0.167240\pi$
$127$	2476.36	1.73025	0.865124	+	0.501558i	$0.167240\pi$
$128$	−747.790	−0.516374
$129$	1024.89	0.699510
$130$	140.870	0.0950391
$131$	−443.172	−0.295573	−0.147787	−	0.989019i	$-0.547215\pi$
$131$	−443.172	−0.295573	−0.147787	+	0.989019i	$0.547215\pi$
$132$	0	0
$133$	14.5507	0.00948649
$134$	−377.137	−0.243132
$135$	135.000	0.0860663
$136$	157.529	0.0993236
$137$	1155.46	0.720567	0.360283	−	0.932843i	$-0.382680\pi$
$137$	1155.46	0.720567	0.360283	+	0.932843i	$0.382680\pi$
$138$	217.113	0.133927
$139$	−2459.43	−1.50076	−0.750381	−	0.661005i	$-0.770130\pi$
$139$	−2459.43	−1.50076	−0.750381	+	0.661005i	$0.770130\pi$
$140$	−99.1236	−0.0598391
$141$	−496.877	−0.296770
$142$	−241.806	−0.142901
$143$	0	0
$144$	544.604	0.315164
$145$	1353.99	0.775470
$146$	−44.9878	−0.0255015
$147$	1009.88	0.566625
$148$	−2668.39	−1.48203
$149$	−1588.30	−0.873280	−0.436640	−	0.899636i	$-0.643832\pi$
$149$	−1588.30	−0.873280	−0.436640	+	0.899636i	$0.643832\pi$
$150$	−28.6813	−0.0156121
$151$	576.599	0.310748	0.155374	−	0.987856i	$-0.450342\pi$
$151$	576.599	0.310748	0.155374	+	0.987856i	$0.450342\pi$
$152$	34.9481	0.0186491
$153$	−233.848	−0.123565
$154$	0	0
$155$	338.989	0.175666
$156$	−1735.83	−0.890884
$157$	−342.000	−0.173851	−0.0869253	−	0.996215i	$-0.527704\pi$
$157$	−342.000	−0.173851	−0.0869253	+	0.996215i	$0.527704\pi$
$158$	16.6290	0.00837300
$159$	1558.30	0.777239
$160$	−358.214	−0.176995
$161$	477.702	0.233840
$162$	30.9758	0.0150228
$163$	1199.43	0.576359	0.288180	−	0.957576i	$-0.406950\pi$
$163$	1199.43	0.576359	0.288180	+	0.957576i	$0.406950\pi$
$164$	−568.305	−0.270592
$165$	0	0
$166$	346.261	0.161898
$167$	2519.48	1.16745	0.583723	−	0.811953i	$-0.301595\pi$
$167$	2519.48	1.16745	0.583723	+	0.811953i	$0.301595\pi$
$168$	−45.9115	−0.0210842
$169$	3230.73	1.47052
$170$	49.6819	0.0224143
$171$	−51.8795	−0.0232007
$172$	2683.09	1.18944
$173$	−594.341	−0.261196	−0.130598	−	0.991435i	$-0.541690\pi$
$173$	−594.341	−0.261196	−0.130598	+	0.991435i	$0.541690\pi$
$174$	310.675	0.135357
$175$	−63.1059	−0.0272592
$176$	0	0
$177$	1896.78	0.805483
$178$	1.74350	0.000734163 0
$179$	2045.06	0.853937	0.426968	−	0.904267i	$-0.359582\pi$
$179$	2045.06	0.853937	0.426968	+	0.904267i	$0.359582\pi$
$180$	353.419	0.146346
$181$	23.9333	0.00982842	0.00491421	−	0.999988i	$-0.498436\pi$
$181$	23.9333	0.00982842	0.00491421	+	0.999988i	$0.498436\pi$
$182$	71.1175	0.0289647
$183$	1890.60	0.763699
$184$	1147.35	0.459696
$185$	−1698.80	−0.675124
$186$	77.7812	0.0306624
$187$	0	0
$188$	−1300.78	−0.504624
$189$	68.1543	0.0262301
$190$	11.0220	0.00420853
$191$	3177.28	1.20366	0.601832	−	0.798623i	$-0.294438\pi$
$191$	3177.28	1.20366	0.601832	+	0.798623i	$0.294438\pi$
$192$	1370.08	0.514986
$193$	4075.01	1.51982	0.759911	−	0.650027i	$-0.225243\pi$
$193$	4075.01	1.51982	0.759911	+	0.650027i	$0.225243\pi$
$194$	28.6664	0.0106089
$195$	−1105.10	−0.405834
$196$	2643.80	0.963483
$197$	−748.340	−0.270645	−0.135322	−	0.990802i	$-0.543207\pi$
$197$	−748.340	−0.270645	−0.135322	+	0.990802i	$0.543207\pi$
$198$	0	0
$199$	783.495	0.279098	0.139549	−	0.990215i	$-0.455435\pi$
$199$	783.495	0.279098	0.139549	+	0.990215i	$0.455435\pi$
$200$	−151.569	−0.0535877
$201$	2958.57	1.03822
$202$	−158.388	−0.0551691
$203$	683.560	0.236337
$204$	−612.194	−0.210109
$205$	−361.804	−0.123266
$206$	−42.9552	−0.0145283
$207$	−1703.22	−0.571892
$208$	−4458.08	−1.48612
$209$	0	0
$210$	−14.4797	−0.00475806
$211$	5316.59	1.73464	0.867319	−	0.497752i	$-0.165841\pi$
$211$	5316.59	1.73464	0.867319	+	0.497752i	$0.165841\pi$
$212$	4079.49	1.32161
$213$	1896.93	0.610212
$214$	−456.370	−0.145779
$215$	1708.15	0.541838
$216$	163.694	0.0515648
$217$	171.138	0.0535372
$218$	−518.550	−0.161104
$219$	352.921	0.108896
$220$	0	0
$221$	1914.26	0.582655
$222$	−389.790	−0.117842
$223$	1024.50	0.307649	0.153825	−	0.988098i	$-0.450841\pi$
$223$	1024.50	0.307649	0.153825	+	0.988098i	$0.450841\pi$
$224$	−180.843	−0.0539423
$225$	225.000	0.0666667
$226$	559.855	0.164783
$227$	−3478.11	−1.01696	−0.508480	−	0.861074i	$-0.669793\pi$
$227$	−3478.11	−1.01696	−0.508480	+	0.861074i	$0.669793\pi$
$228$	−135.816	−0.0394503
$229$	4359.58	1.25803	0.629015	−	0.777393i	$-0.283458\pi$
$229$	4359.58	1.25803	0.629015	+	0.777393i	$0.283458\pi$
$230$	361.855	0.103739
$231$	0	0
$232$	1641.79	0.464606
$233$	−2768.67	−0.778461	−0.389231	−	0.921140i	$-0.627259\pi$
$233$	−2768.67	−0.778461	−0.389231	+	0.921140i	$0.627259\pi$
$234$	−253.565	−0.0708379
$235$	−828.128	−0.229877
$236$	4965.61	1.36963
$237$	−130.452	−0.0357543
$238$	25.0818	0.00683113
$239$	979.032	0.264972	0.132486	−	0.991185i	$-0.457704\pi$
$239$	979.032	0.264972	0.132486	+	0.991185i	$0.457704\pi$
$240$	907.673	0.244125
$241$	−6567.39	−1.75537	−0.877683	−	0.479242i	$-0.840912\pi$
$241$	−6567.39	−1.75537	−0.877683	+	0.479242i	$0.840912\pi$
$242$	0	0
$243$	−243.000	−0.0641500
$244$	4949.43	1.29859
$245$	1683.14	0.438906
$246$	−83.0162	−0.0215159
$247$	424.681	0.109400
$248$	411.042	0.105247
$249$	−2716.36	−0.691334
$250$	−47.8022	−0.0120931
$251$	−3356.28	−0.844010	−0.422005	−	0.906594i	$-0.638673\pi$
$251$	−3356.28	−0.844010	−0.422005	+	0.906594i	$0.638673\pi$
$252$	178.422	0.0446014
$253$	0	0
$254$	947.004	0.233938
$255$	−389.746	−0.0957131
$256$	3367.59	0.822166
$257$	−1142.54	−0.277313	−0.138657	−	0.990341i	$-0.544278\pi$
$257$	−1142.54	−0.277313	−0.138657	+	0.990341i	$0.544278\pi$
$258$	391.937	0.0945773
$259$	−857.632	−0.205755
$260$	−2893.05	−0.690076
$261$	−2437.19	−0.578001
$262$	−169.477	−0.0399630
$263$	763.774	0.179074	0.0895368	−	0.995984i	$-0.471461\pi$
$263$	763.774	0.179074	0.0895368	+	0.995984i	$0.471461\pi$
$264$	0	0
$265$	2597.16	0.602046
$266$	5.56443	0.00128262
$267$	−13.6775	−0.00313501
$268$	7745.30	1.76537
$269$	2744.13	0.621980	0.310990	−	0.950413i	$-0.399340\pi$
$269$	2744.13	0.621980	0.310990	+	0.950413i	$0.399340\pi$
$270$	51.6264	0.0116366
$271$	−4617.54	−1.03504	−0.517520	−	0.855671i	$-0.673145\pi$
$271$	−4617.54	−1.03504	−0.517520	+	0.855671i	$0.673145\pi$
$272$	−1572.28	−0.350490
$273$	−557.905	−0.123685
$274$	441.869	0.0974243
$275$	0	0
$276$	−4458.88	−0.972439
$277$	−6329.55	−1.37294	−0.686472	−	0.727156i	$-0.740842\pi$
$277$	−6329.55	−1.37294	−0.686472	+	0.727156i	$0.740842\pi$
$278$	−940.529	−0.202911
$279$	−610.180	−0.130934
$280$	−76.5191	−0.0163318
$281$	8970.82	1.90446	0.952232	−	0.305377i	$-0.0987824\pi$
$281$	8970.82	1.90446	0.952232	+	0.305377i	$0.0987824\pi$
$282$	−190.014	−0.0401248
$283$	1075.96	0.226005	0.113003	−	0.993595i	$-0.463953\pi$
$283$	1075.96	0.226005	0.113003	+	0.993595i	$0.463953\pi$
$284$	4966.00	1.03760
$285$	−86.4659	−0.0179712
$286$	0	0
$287$	−182.656	−0.0375674
$288$	644.785	0.131925
$289$	−4237.88	−0.862585
$290$	517.791	0.104847
$291$	−224.883	−0.0453019
$292$	923.919	0.185165
$293$	−2870.12	−0.572266	−0.286133	−	0.958190i	$-0.592370\pi$
$293$	−2870.12	−0.572266	−0.286133	+	0.958190i	$0.592370\pi$
$294$	386.198	0.0766106
$295$	3161.29	0.623924
$296$	−2059.88	−0.404486
$297$	0	0
$298$	−607.394	−0.118072
$299$	13942.4	2.69668
$300$	589.032	0.113359
$301$	862.356	0.165134
$302$	220.502	0.0420147
$303$	1242.53	0.235582
$304$	−348.812	−0.0658084
$305$	3151.00	0.591559
$306$	−89.4275	−0.0167066
$307$	−2223.09	−0.413285	−0.206643	−	0.978416i	$-0.566254\pi$
$307$	−2223.09	−0.413285	−0.206643	+	0.978416i	$0.566254\pi$
$308$	0	0
$309$	336.976	0.0620385
$310$	129.635	0.0237510
$311$	−6149.31	−1.12121	−0.560603	−	0.828084i	$-0.689431\pi$
$311$	−6149.31	−1.12121	−0.560603	+	0.828084i	$0.689431\pi$
$312$	−1339.99	−0.243147
$313$	1906.85	0.344350	0.172175	−	0.985066i	$-0.444921\pi$
$313$	1906.85	0.344350	0.172175	+	0.985066i	$0.444921\pi$
$314$	−130.787	−0.0235055
$315$	113.591	0.0203178
$316$	−341.512	−0.0607961
$317$	5434.67	0.962907	0.481454	−	0.876472i	$-0.340109\pi$
$317$	5434.67	0.962907	0.481454	+	0.876472i	$0.340109\pi$
$318$	595.920	0.105087
$319$	0	0
$320$	2283.47	0.398907
$321$	3580.14	0.622504
$322$	182.682	0.0316163
$323$	149.777	0.0258012
$324$	−636.154	−0.109080
$325$	−1841.83	−0.314358
$326$	458.683	0.0779267
$327$	4067.93	0.687942
$328$	−438.706	−0.0738522
$329$	−418.078	−0.0700589
$330$	0	0
$331$	−6113.94	−1.01526	−0.507632	−	0.861574i	$-0.669479\pi$
$331$	−6113.94	−1.01526	−0.507632	+	0.861574i	$0.669479\pi$
$332$	−7111.20	−1.17554
$333$	3057.83	0.503208
$334$	963.495	0.157845
$335$	4930.95	0.804199
$336$	458.236	0.0744013
$337$	−5606.84	−0.906303	−0.453151	−	0.891434i	$-0.649700\pi$
$337$	−5606.84	−0.906303	−0.453151	+	0.891434i	$0.649700\pi$
$338$	1235.49	0.198822
$339$	−4391.96	−0.703654
$340$	−1020.32	−0.162749
$341$	0	0
$342$	−19.8396	−0.00313686
$343$	1715.54	0.270060
$344$	2071.22	0.324631
$345$	−2838.69	−0.442986
$346$	−227.287	−0.0353150
$347$	−148.094	−0.0229110	−0.0114555	−	0.999934i	$-0.503646\pi$
$347$	−148.094	−0.0229110	−0.0114555	+	0.999934i	$0.503646\pi$
$348$	−6380.37	−0.982826
$349$	5376.97	0.824706	0.412353	−	0.911024i	$-0.364707\pi$
$349$	5376.97	0.824706	0.412353	+	0.911024i	$0.364707\pi$
$350$	−24.1328	−0.00368558
$351$	1989.17	0.302491
$352$	0	0
$353$	−11942.0	−1.80059	−0.900297	−	0.435277i	$-0.856651\pi$
$353$	−11942.0	−1.80059	−0.900297	+	0.435277i	$0.856651\pi$
$354$	725.361	0.108905
$355$	3161.54	0.472668
$356$	−35.8065	−0.00533073
$357$	−196.762	−0.0291702
$358$	782.065	0.115457
$359$	−10991.7	−1.61593	−0.807964	−	0.589232i	$-0.799430\pi$
$359$	−10991.7	−1.61593	−0.807964	+	0.589232i	$0.799430\pi$
$360$	272.824	0.0399419
$361$	−6825.77	−0.995156
$362$	9.15250	0.00132885
$363$	0	0
$364$	−1460.55	−0.210312
$365$	588.202	0.0843504
$366$	722.998	0.103256
$367$	10778.9	1.53312	0.766561	−	0.642172i	$-0.221966\pi$
$367$	10778.9	1.53312	0.766561	+	0.642172i	$0.221966\pi$
$368$	−11451.6	−1.62216
$369$	651.248	0.0918770
$370$	−649.649	−0.0912802
$371$	1311.17	0.183484
$372$	−1597.40	−0.222638
$373$	−6702.69	−0.930435	−0.465217	−	0.885196i	$-0.654024\pi$
$373$	−6702.69	−0.930435	−0.465217	+	0.885196i	$0.654024\pi$
$374$	0	0
$375$	375.000	0.0516398
$376$	−1004.15	−0.137726
$377$	19950.6	2.72549
$378$	26.0634	0.00354645
$379$	10321.0	1.39883	0.699414	−	0.714716i	$-0.253444\pi$
$379$	10321.0	1.39883	0.699414	+	0.714716i	$0.253444\pi$
$380$	−226.361	−0.0305580
$381$	−7429.08	−0.998959
$382$	1215.05	0.162741
$383$	−2797.91	−0.373281	−0.186640	−	0.982428i	$-0.559760\pi$
$383$	−2797.91	−0.373281	−0.186640	+	0.982428i	$0.559760\pi$
$384$	2243.37	0.298129
$385$	0	0
$386$	1558.36	0.205488
$387$	−3074.68	−0.403862
$388$	−588.724	−0.0770308
$389$	1680.59	0.219047	0.109524	−	0.993984i	$-0.465067\pi$
$389$	1680.59	0.219047	0.109524	+	0.993984i	$0.465067\pi$
$390$	−422.609	−0.0548708
$391$	4917.20	0.635993
$392$	2040.90	0.262961
$393$	1329.52	0.170649
$394$	−286.179	−0.0365926
$395$	−217.420	−0.0276951
$396$	0	0
$397$	10170.8	1.28578	0.642892	−	0.765957i	$-0.277734\pi$
$397$	10170.8	1.28578	0.642892	+	0.765957i	$0.277734\pi$
$398$	299.622	0.0377355
$399$	−43.6520	−0.00547703
$400$	1512.79	0.189099
$401$	−5427.60	−0.675914	−0.337957	−	0.941162i	$-0.609736\pi$
$401$	−5427.60	−0.675914	−0.337957	+	0.941162i	$0.609736\pi$
$402$	1131.41	0.140372
$403$	4994.88	0.617401
$404$	3252.84	0.400581
$405$	−405.000	−0.0496904
$406$	261.405	0.0319540
$407$	0	0
$408$	−472.587	−0.0573445
$409$	6944.24	0.839537	0.419769	−	0.907631i	$-0.362111\pi$
$409$	6944.24	0.839537	0.419769	+	0.907631i	$0.362111\pi$
$410$	−138.360	−0.0166662
$411$	−3466.38	−0.416019
$412$	882.176	0.105490
$413$	1595.97	0.190151
$414$	−651.340	−0.0773227
$415$	−4527.26	−0.535505
$416$	−5278.15	−0.622073
$417$	7378.28	0.866465
$418$	0	0
$419$	−3123.22	−0.364151	−0.182076	−	0.983285i	$-0.558282\pi$
$419$	−3123.22	−0.364151	−0.182076	+	0.983285i	$0.558282\pi$
$420$	297.371	0.0345481
$421$	−1713.25	−0.198334	−0.0991670	−	0.995071i	$-0.531618\pi$
$421$	−1713.25	−0.198334	−0.0991670	+	0.995071i	$0.531618\pi$
$422$	2033.16	0.234532
$423$	1490.63	0.171340
$424$	3149.19	0.360703
$425$	−649.577	−0.0741391
$426$	725.418	0.0825038
$427$	1590.77	0.180287
$428$	9372.52	1.05850
$429$	0	0
$430$	653.228	0.0732592
$431$	1915.50	0.214075	0.107038	−	0.994255i	$-0.465863\pi$
$431$	1915.50	0.214075	0.107038	+	0.994255i	$0.465863\pi$
$432$	−1633.81	−0.181960
$433$	−7031.13	−0.780357	−0.390178	−	0.920739i	$-0.627587\pi$
$433$	−7031.13	−0.780357	−0.390178	+	0.920739i	$0.627587\pi$
$434$	65.4460	0.00723850
$435$	−4061.98	−0.447718
$436$	10649.5	1.16977
$437$	1090.89	0.119415
$438$	134.963	0.0147233
$439$	−11152.1	−1.21244	−0.606219	−	0.795297i	$-0.707315\pi$
$439$	−11152.1	−1.21244	−0.606219	+	0.795297i	$0.707315\pi$
$440$	0	0
$441$	−3029.65	−0.327141
$442$	732.045	0.0787779
$443$	2457.41	0.263555	0.131778	−	0.991279i	$-0.457932\pi$
$443$	2457.41	0.263555	0.131778	+	0.991279i	$0.457932\pi$
$444$	8005.16	0.855648
$445$	−22.7958	−0.00242837
$446$	391.788	0.0415958
$447$	4764.90	0.504188
$448$	1152.80	0.121573
$449$	−70.2970	−0.00738868	−0.00369434	−	0.999993i	$-0.501176\pi$
$449$	−70.2970	−0.00738868	−0.00369434	+	0.999993i	$0.501176\pi$
$450$	86.0440	0.00901367
$451$	0	0
$452$	−11497.8	−1.19648
$453$	−1729.80	−0.179410
$454$	−1330.09	−0.137498
$455$	−929.841	−0.0958058
$456$	−104.844	−0.0107671
$457$	−3306.56	−0.338456	−0.169228	−	0.985577i	$-0.554127\pi$
$457$	−3306.56	−0.338456	−0.169228	+	0.985577i	$0.554127\pi$
$458$	1667.18	0.170092
$459$	701.543	0.0713404
$460$	−7431.47	−0.753248
$461$	11824.6	1.19463	0.597316	−	0.802006i	$-0.296234\pi$
$461$	11824.6	1.19463	0.597316	+	0.802006i	$0.296234\pi$
$462$	0	0
$463$	1207.39	0.121192	0.0605961	−	0.998162i	$-0.480700\pi$
$463$	1207.39	0.121192	0.0605961	+	0.998162i	$0.480700\pi$
$464$	−16386.5	−1.63949
$465$	−1016.97	−0.101421
$466$	−1058.79	−0.105252
$467$	6686.44	0.662551	0.331276	−	0.943534i	$-0.392521\pi$
$467$	6686.44	0.662551	0.331276	+	0.943534i	$0.392521\pi$
$468$	5207.50	0.514352
$469$	2489.38	0.245093
$470$	−316.691	−0.0310805
$471$	1026.00	0.100373
$472$	3833.23	0.373811
$473$	0	0
$474$	−49.8871	−0.00483416
$475$	−144.110	−0.0139204
$476$	−515.107	−0.0496006
$477$	−4674.89	−0.448739
$478$	374.399	0.0358255
$479$	−16365.7	−1.56110	−0.780549	−	0.625094i	$-0.785061\pi$
$479$	−16365.7	−1.56110	−0.780549	+	0.625094i	$0.785061\pi$
$480$	1074.64	0.102188
$481$	−25031.1	−2.37281
$482$	−2511.49	−0.237334
$483$	−1433.11	−0.135007
$484$	0	0
$485$	−374.804	−0.0350907
$486$	−92.9275	−0.00867341
$487$	3641.39	0.338823	0.169412	−	0.985545i	$-0.445813\pi$
$487$	3641.39	0.338823	0.169412	+	0.985545i	$0.445813\pi$
$488$	3820.74	0.354420
$489$	−3598.29	−0.332761
$490$	643.663	0.0593423
$491$	−13475.4	−1.23856	−0.619281	−	0.785169i	$-0.712576\pi$
$491$	−13475.4	−1.23856	−0.619281	+	0.785169i	$0.712576\pi$
$492$	1704.91	0.156227
$493$	7036.19	0.642787
$494$	162.405	0.0147914
$495$	0	0
$496$	−4102.55	−0.371391
$497$	1596.09	0.144054
$498$	−1038.78	−0.0934718
$499$	4287.64	0.384652	0.192326	−	0.981331i	$-0.438397\pi$
$499$	4287.64	0.384652	0.192326	+	0.981331i	$0.438397\pi$
$500$	981.720	0.0878077
$501$	−7558.45	−0.674025
$502$	−1283.50	−0.114114
$503$	11773.4	1.04364	0.521820	−	0.853056i	$-0.325253\pi$
$503$	11773.4	1.04364	0.521820	+	0.853056i	$0.325253\pi$
$504$	137.734	0.0121730
$505$	2070.88	0.182481
$506$	0	0
$507$	−9692.20	−0.849005
$508$	−19448.7	−1.69862
$509$	−12585.7	−1.09598	−0.547990	−	0.836485i	$-0.684607\pi$
$509$	−12585.7	−1.09598	−0.547990	+	0.836485i	$0.684607\pi$
$510$	−149.046	−0.0129409
$511$	296.952	0.0257072
$512$	7270.15	0.627535
$513$	155.639	0.0133949
$514$	−436.927	−0.0374942
$515$	561.627	0.0480548
$516$	−8049.26	−0.686722
$517$	0	0
$518$	−327.973	−0.0278192
$519$	1783.02	0.150802
$520$	−2233.31	−0.188341
$521$	−14173.5	−1.19184	−0.595922	−	0.803042i	$-0.703213\pi$
$521$	−14173.5	−1.19184	−0.595922	+	0.803042i	$0.703213\pi$
$522$	−932.025	−0.0781487
$523$	13944.4	1.16586	0.582932	−	0.812521i	$-0.301905\pi$
$523$	13944.4	1.16586	0.582932	+	0.812521i	$0.301905\pi$
$524$	3480.56	0.290170
$525$	189.318	0.0157381
$526$	292.081	0.0242117
$527$	1761.60	0.145610
$528$	0	0
$529$	23647.1	1.94355
$530$	993.200	0.0813997
$531$	−5690.33	−0.465046
$532$	−114.277	−0.00931307
$533$	−5331.05	−0.433234
$534$	−5.23050	−0.000423869 0
$535$	5966.90	0.482190
$536$	5979.03	0.481819
$537$	−6135.17	−0.493020
$538$	1049.40	0.0840948
$539$	0	0
$540$	−1060.26	−0.0844930
$541$	−1074.46	−0.0853874	−0.0426937	−	0.999088i	$-0.513594\pi$
$541$	−1074.46	−0.0853874	−0.0426937	+	0.999088i	$0.513594\pi$
$542$	−1765.83	−0.139943
$543$	−71.7998	−0.00567444
$544$	−1861.50	−0.146712
$545$	6779.89	0.532878
$546$	−213.353	−0.0167228
$547$	−19860.4	−1.55241	−0.776207	−	0.630479i	$-0.782859\pi$
$547$	−19860.4	−1.55241	−0.776207	+	0.630479i	$0.782859\pi$
$548$	−9074.71	−0.707395
$549$	−5671.79	−0.440922
$550$	0	0
$551$	1560.99	0.120690
$552$	−3442.06	−0.265406
$553$	−109.764	−0.00844055
$554$	−2420.53	−0.185629
$555$	5096.39	0.389783
$556$	19315.7	1.47333
$557$	−6784.60	−0.516109	−0.258054	−	0.966130i	$-0.583081\pi$
$557$	−6784.60	−0.516109	−0.258054	+	0.966130i	$0.583081\pi$
$558$	−233.344	−0.0177029
$559$	25169.0	1.90436
$560$	763.727	0.0576310
$561$	0	0
$562$	3430.60	0.257493
$563$	−13760.1	−1.03005	−0.515027	−	0.857174i	$-0.672218\pi$
$563$	−13760.1	−1.03005	−0.515027	+	0.857174i	$0.672218\pi$
$564$	3902.35	0.291345
$565$	−7319.94	−0.545048
$566$	411.468	0.0305570
$567$	−204.463	−0.0151440
$568$	3833.53	0.283189
$569$	13449.1	0.990886	0.495443	−	0.868640i	$-0.335006\pi$
$569$	13449.1	0.990886	0.495443	+	0.868640i	$0.335006\pi$
$570$	−33.0661	−0.00242980
$571$	−8398.47	−0.615525	−0.307763	−	0.951463i	$-0.599580\pi$
$571$	−8398.47	−0.615525	−0.307763	+	0.951463i	$0.599580\pi$
$572$	0	0
$573$	−9531.84	−0.694936
$574$	−69.8508	−0.00507930
$575$	−4731.16	−0.343135
$576$	−4110.25	−0.297327
$577$	9868.12	0.711985	0.355992	−	0.934489i	$-0.384143\pi$
$577$	9868.12	0.711985	0.355992	+	0.934489i	$0.384143\pi$
$578$	−1620.64	−0.116626
$579$	−12225.0	−0.877469
$580$	−10633.9	−0.761294
$581$	−2285.57	−0.163204
$582$	−85.9991	−0.00612504
$583$	0	0
$584$	713.225	0.0505368
$585$	3315.29	0.234308
$586$	−1097.58	−0.0773733
$587$	27119.6	1.90689	0.953446	−	0.301562i	$-0.0975081\pi$
$587$	27119.6	1.90689	0.953446	+	0.301562i	$0.0975081\pi$
$588$	−7931.39	−0.556267
$589$	390.813	0.0273398
$590$	1208.93	0.0843577
$591$	2245.02	0.156257
$592$	20559.3	1.42734
$593$	−24189.0	−1.67508	−0.837540	−	0.546376i	$-0.816007\pi$
$593$	−24189.0	−1.67508	−0.837540	+	0.546376i	$0.816007\pi$
$594$	0	0
$595$	−327.937	−0.0225951
$596$	12474.1	0.857316
$597$	−2350.49	−0.161137
$598$	5331.81	0.364605
$599$	−18626.1	−1.27052	−0.635260	−	0.772298i	$-0.719107\pi$
$599$	−18626.1	−1.27052	−0.635260	+	0.772298i	$0.719107\pi$
$600$	454.707	0.0309389
$601$	27194.8	1.84576	0.922878	−	0.385092i	$-0.125830\pi$
$601$	27194.8	1.84576	0.922878	+	0.385092i	$0.125830\pi$
$602$	329.780	0.0223270
$603$	−8875.72	−0.599415
$604$	−4528.47	−0.305067
$605$	0	0
$606$	475.164	0.0318519
$607$	3938.11	0.263333	0.131666	−	0.991294i	$-0.457967\pi$
$607$	3938.11	0.263333	0.131666	+	0.991294i	$0.457967\pi$
$608$	−412.977	−0.0275467
$609$	−2050.68	−0.136449
$610$	1205.00	0.0799818
$611$	−12202.2	−0.807932
$612$	1836.58	0.121306
$613$	−11195.5	−0.737657	−0.368828	−	0.929498i	$-0.620241\pi$
$613$	−11195.5	−0.737657	−0.368828	+	0.929498i	$0.620241\pi$
$614$	−850.150	−0.0558782
$615$	1085.41	0.0711676
$616$	0	0
$617$	−8605.78	−0.561517	−0.280758	−	0.959778i	$-0.590586\pi$
$617$	−8605.78	−0.561517	−0.280758	+	0.959778i	$0.590586\pi$
$618$	128.866	0.00838792
$619$	21573.3	1.40082	0.700408	−	0.713743i	$-0.253001\pi$
$619$	21573.3	1.40082	0.700408	+	0.713743i	$0.253001\pi$
$620$	−2662.34	−0.172455
$621$	5109.65	0.330182
$622$	−2351.60	−0.151593
$623$	−11.5084	−0.000740085 0
$624$	13374.2	0.858009
$625$	625.000	0.0400000
$626$	729.214	0.0465579
$627$	0	0
$628$	2685.98	0.170672
$629$	−8827.99	−0.559610
$630$	43.4390	0.00274707
$631$	−980.650	−0.0618685	−0.0309343	−	0.999521i	$-0.509848\pi$
$631$	−980.650	−0.0618685	−0.0309343	+	0.999521i	$0.509848\pi$
$632$	−263.633	−0.0165929
$633$	−15949.8	−1.00149
$634$	2078.31	0.130190
$635$	−12381.8	−0.773791
$636$	−12238.5	−0.763030
$637$	24800.5	1.54259
$638$	0	0
$639$	−5690.78	−0.352306
$640$	3738.95	0.230930
$641$	−13102.7	−0.807370	−0.403685	−	0.914898i	$-0.632271\pi$
$641$	−13102.7	−0.807370	−0.403685	+	0.914898i	$0.632271\pi$
$642$	1369.11	0.0841657
$643$	1988.08	0.121932	0.0609659	−	0.998140i	$-0.480582\pi$
$643$	1988.08	0.121932	0.0609659	+	0.998140i	$0.480582\pi$
$644$	−3751.75	−0.229565
$645$	−5124.46	−0.312830
$646$	57.2772	0.00348846
$647$	4306.10	0.261654	0.130827	−	0.991405i	$-0.458237\pi$
$647$	4306.10	0.261654	0.130827	+	0.991405i	$0.458237\pi$
$648$	−491.083	−0.0297709
$649$	0	0
$650$	−704.348	−0.0425028
$651$	−513.413	−0.0309097
$652$	−9420.02	−0.565823
$653$	−17130.3	−1.02658	−0.513292	−	0.858214i	$-0.671574\pi$
$653$	−17130.3	−1.02658	−0.513292	+	0.858214i	$0.671574\pi$
$654$	1555.65	0.0930133
$655$	2215.86	0.132184
$656$	4378.67	0.260607
$657$	−1058.76	−0.0628711
$658$	−159.880	−0.00947232
$659$	19756.3	1.16782	0.583911	−	0.811818i	$-0.301522\pi$
$659$	19756.3	1.16782	0.583911	+	0.811818i	$0.301522\pi$
$660$	0	0
$661$	25854.5	1.52137	0.760683	−	0.649124i	$-0.224864\pi$
$661$	25854.5	1.52137	0.760683	+	0.649124i	$0.224864\pi$
$662$	−2338.08	−0.137269
$663$	−5742.77	−0.336396
$664$	−5489.54	−0.320836
$665$	−72.7534	−0.00424249
$666$	1169.37	0.0680362
$667$	51247.7	2.97499
$668$	−19787.4	−1.14610
$669$	−3073.51	−0.177622
$670$	1885.68	0.108732
$671$	0	0
$672$	542.529	0.0311436
$673$	27414.6	1.57022	0.785109	−	0.619357i	$-0.212607\pi$
$673$	27414.6	1.57022	0.785109	+	0.619357i	$0.212607\pi$
$674$	−2144.15	−0.122537
$675$	−675.000	−0.0384900
$676$	−25373.4	−1.44364
$677$	−8690.05	−0.493332	−0.246666	−	0.969101i	$-0.579335\pi$
$677$	−8690.05	−0.493332	−0.246666	+	0.969101i	$0.579335\pi$
$678$	−1679.56	−0.0951375
$679$	−189.219	−0.0106945
$680$	−787.645	−0.0444189
$681$	10434.3	0.587142
$682$	0	0
$683$	28280.0	1.58434	0.792171	−	0.610299i	$-0.208951\pi$
$683$	28280.0	1.58434	0.792171	+	0.610299i	$0.208951\pi$
$684$	407.449	0.0227766
$685$	−5777.30	−0.322247
$686$	656.053	0.0365134
$687$	−13078.7	−0.726324
$688$	−20672.6	−1.14555
$689$	38268.2	2.11597
$690$	−1085.57	−0.0598939
$691$	−6055.45	−0.333372	−0.166686	−	0.986010i	$-0.553307\pi$
$691$	−6055.45	−0.333372	−0.166686	+	0.986010i	$0.553307\pi$
$692$	4667.81	0.256421
$693$	0	0
$694$	−56.6339	−0.00309769
$695$	12297.1	0.671161
$696$	−4925.36	−0.268241
$697$	−1880.16	−0.102175
$698$	2056.25	0.111504
$699$	8306.00	0.449445
$700$	495.618	0.0267609
$701$	−26455.7	−1.42542	−0.712709	−	0.701460i	$-0.752532\pi$
$701$	−26455.7	−1.42542	−0.712709	+	0.701460i	$0.752532\pi$
$702$	760.696	0.0408983
$703$	−1958.50	−0.105073
$704$	0	0
$705$	2484.38	0.132720
$706$	−4566.84	−0.243449
$707$	1045.48	0.0556141
$708$	−14896.8	−0.790758
$709$	−9462.86	−0.501248	−0.250624	−	0.968084i	$-0.580636\pi$
$709$	−9462.86	−0.501248	−0.250624	+	0.968084i	$0.580636\pi$
$710$	1209.03	0.0639071
$711$	391.356	0.0206427
$712$	−27.6410	−0.00145490
$713$	12830.5	0.673920
$714$	−75.2453	−0.00394396
$715$	0	0
$716$	−16061.4	−0.838326
$717$	−2937.09	−0.152982
$718$	−4203.41	−0.218482
$719$	−33490.0	−1.73709	−0.868544	−	0.495612i	$-0.834944\pi$
$719$	−33490.0	−1.73709	−0.868544	+	0.495612i	$0.834944\pi$
$720$	−2723.02	−0.140946
$721$	283.536	0.0146455
$722$	−2610.30	−0.134550
$723$	19702.2	1.01346
$724$	−187.966	−0.00964876
$725$	−6769.97	−0.346801
$726$	0	0
$727$	15705.0	0.801191	0.400596	−	0.916255i	$-0.368803\pi$
$727$	15705.0	0.801191	0.400596	+	0.916255i	$0.368803\pi$
$728$	−1127.48	−0.0574000
$729$	729.000	0.0370370
$730$	224.939	0.0114046
$731$	8876.62	0.449129
$732$	−14848.3	−0.749739
$733$	12116.4	0.610546	0.305273	−	0.952265i	$-0.401252\pi$
$733$	12116.4	0.610546	0.305273	+	0.952265i	$0.401252\pi$
$734$	4122.05	0.207286
$735$	−5049.42	−0.253402
$736$	−13558.1	−0.679020
$737$	0	0
$738$	249.049	0.0124222
$739$	−27072.0	−1.34758	−0.673789	−	0.738924i	$-0.735334\pi$
$739$	−27072.0	−1.34758	−0.673789	+	0.738924i	$0.735334\pi$
$740$	13341.9	0.662782
$741$	−1274.04	−0.0631621
$742$	501.414	0.0248079
$743$	−21368.3	−1.05508	−0.527542	−	0.849529i	$-0.676886\pi$
$743$	−21368.3	−1.05508	−0.527542	+	0.849529i	$0.676886\pi$
$744$	−1233.12	−0.0607642
$745$	7941.51	0.390543
$746$	−2563.23	−0.125800
$747$	8149.07	0.399142
$748$	0	0
$749$	3012.37	0.146955
$750$	143.407	0.00698196
$751$	−15853.2	−0.770295	−0.385148	−	0.922855i	$-0.625849\pi$
$751$	−15853.2	−0.770295	−0.385148	+	0.922855i	$0.625849\pi$
$752$	10022.3	0.486003
$753$	10068.8	0.487289
$754$	7629.46	0.368500
$755$	−2882.99	−0.138971
$756$	−535.267	−0.0257506
$757$	32945.7	1.58181	0.790906	−	0.611938i	$-0.209610\pi$
$757$	32945.7	1.58181	0.790906	+	0.611938i	$0.209610\pi$
$758$	3946.95	0.189129
$759$	0	0
$760$	−174.740	−0.00834014
$761$	19496.3	0.928700	0.464350	−	0.885652i	$-0.346288\pi$
$761$	19496.3	0.928700	0.464350	+	0.885652i	$0.346288\pi$
$762$	−2841.01	−0.135064
$763$	3422.80	0.162403
$764$	−24953.6	−1.18166
$765$	1169.24	0.0552600
$766$	−1069.97	−0.0504694
$767$	46580.5	2.19286
$768$	−10102.8	−0.474678
$769$	−12743.7	−0.597592	−0.298796	−	0.954317i	$-0.596585\pi$
$769$	−12743.7	−0.597592	−0.298796	+	0.954317i	$0.596585\pi$
$770$	0	0
$771$	3427.61	0.160107
$772$	−32004.1	−1.49204
$773$	−28374.0	−1.32024	−0.660118	−	0.751162i	$-0.729494\pi$
$773$	−28374.0	−1.32024	−0.660118	+	0.751162i	$0.729494\pi$
$774$	−1175.81	−0.0546042
$775$	−1694.95	−0.0785603
$776$	−454.469	−0.0210238
$777$	2572.89	0.118793
$778$	642.688	0.0296163
$779$	−417.116	−0.0191845
$780$	8679.16	0.398415
$781$	0	0
$782$	1880.42	0.0859895
$783$	7311.57	0.333709
$784$	−20369.9	−0.927929
$785$	1710.00	0.0777483
$786$	508.430	0.0230726
$787$	−40513.1	−1.83499	−0.917495	−	0.397748i	$-0.869792\pi$
$787$	−40513.1	−1.83499	−0.917495	+	0.397748i	$0.869792\pi$
$788$	5877.28	0.265697
$789$	−2291.32	−0.103388
$790$	−83.1452	−0.00374452
$791$	−3695.45	−0.166112
$792$	0	0
$793$	46428.7	2.07911
$794$	3889.48	0.173845
$795$	−7791.48	−0.347592
$796$	−6153.38	−0.273996
$797$	−5829.68	−0.259094	−0.129547	−	0.991573i	$-0.541352\pi$
$797$	−5829.68	−0.259094	−0.129547	+	0.991573i	$0.541352\pi$
$798$	−16.6933	−0.000740522 0
$799$	−4303.46	−0.190545
$800$	1791.07	0.0791548
$801$	41.0324	0.00181000
$802$	−2075.61	−0.0913870
$803$	0	0
$804$	−23235.9	−1.01924
$805$	−2388.51	−0.104576
$806$	1910.13	0.0834757
$807$	−8232.39	−0.359100
$808$	2511.05	0.109330
$809$	−25366.8	−1.10241	−0.551205	−	0.834370i	$-0.685832\pi$
$809$	−25366.8	−1.10241	−0.551205	+	0.834370i	$0.685832\pi$
$810$	−154.879	−0.00671839
$811$	−14620.9	−0.633057	−0.316529	−	0.948583i	$-0.602517\pi$
$811$	−14620.9	−0.633057	−0.316529	+	0.948583i	$0.602517\pi$
$812$	−5368.51	−0.232017
$813$	13852.6	0.597580
$814$	0	0
$815$	−5997.15	−0.257756
$816$	4716.83	0.202355
$817$	1969.29	0.0843291
$818$	2655.60	0.113510
$819$	1673.71	0.0714094
$820$	2841.52	0.121013
$821$	−30119.3	−1.28036	−0.640178	−	0.768227i	$-0.721139\pi$
$821$	−30119.3	−1.28036	−0.640178	+	0.768227i	$0.721139\pi$
$822$	−1325.61	−0.0562479
$823$	19284.9	0.816801	0.408401	−	0.912803i	$-0.366087\pi$
$823$	19284.9	0.816801	0.408401	+	0.912803i	$0.366087\pi$
$824$	681.002	0.0287910
$825$	0	0
$826$	610.327	0.0257094
$827$	−15287.4	−0.642799	−0.321400	−	0.946944i	$-0.604153\pi$
$827$	−15287.4	−0.642799	−0.321400	+	0.946944i	$0.604153\pi$
$828$	13376.6	0.561438
$829$	43130.2	1.80696	0.903482	−	0.428627i	$-0.141003\pi$
$829$	43130.2	1.80696	0.903482	+	0.428627i	$0.141003\pi$
$830$	−1731.30	−0.0724030
$831$	18988.6	0.792670
$832$	33646.2	1.40201
$833$	8746.64	0.363809
$834$	2821.59	0.117151
$835$	−12597.4	−0.522098
$836$	0	0
$837$	1830.54	0.0755947
$838$	−1194.38	−0.0492351
$839$	−47072.6	−1.93698	−0.968489	−	0.249055i	$-0.919880\pi$
$839$	−47072.6	−1.93698	−0.968489	+	0.249055i	$0.919880\pi$
$840$	229.557	0.00942914
$841$	48943.1	2.00677
$842$	−655.176	−0.0268157
$843$	−26912.5	−1.09954
$844$	−41755.2	−1.70293
$845$	−16153.7	−0.657636
$846$	570.043	0.0231661
$847$	0	0
$848$	−31431.6	−1.27284
$849$	−3227.89	−0.130484
$850$	−248.410	−0.0100240
$851$	−64298.1	−2.59002
$852$	−14898.0	−0.599057
$853$	−10565.3	−0.424091	−0.212046	−	0.977260i	$-0.568013\pi$
$853$	−10565.3	−0.424091	−0.212046	+	0.977260i	$0.568013\pi$
$854$	608.339	0.0243758
$855$	259.398	0.0103757
$856$	7235.17	0.288894
$857$	42079.5	1.67726	0.838628	−	0.544705i	$-0.183358\pi$
$857$	42079.5	1.67726	0.838628	+	0.544705i	$0.183358\pi$
$858$	0	0
$859$	−7454.78	−0.296105	−0.148052	−	0.988980i	$-0.547300\pi$
$859$	−7454.78	−0.296105	−0.148052	+	0.988980i	$0.547300\pi$
$860$	−13415.4	−0.531933
$861$	547.967	0.0216895
$862$	732.522	0.0289441
$863$	−14963.8	−0.590236	−0.295118	−	0.955461i	$-0.595359\pi$
$863$	−14963.8	−0.590236	−0.295118	+	0.955461i	$0.595359\pi$
$864$	−1934.35	−0.0761667
$865$	2971.71	0.116810
$866$	−2688.83	−0.105508
$867$	12713.6	0.498014
$868$	−1344.07	−0.0525585
$869$	0	0
$870$	−1553.37	−0.0605337
$871$	72655.8	2.82646
$872$	8220.96	0.319262
$873$	674.648	0.0261551
$874$	417.175	0.0161455
$875$	315.529	0.0121907
$876$	−2771.76	−0.106905
$877$	36028.9	1.38724	0.693620	−	0.720341i	$-0.256015\pi$
$877$	36028.9	1.38724	0.693620	+	0.720341i	$0.256015\pi$
$878$	−4264.76	−0.163928
$879$	8610.35	0.330398
$880$	0	0
$881$	−24091.0	−0.921277	−0.460639	−	0.887588i	$-0.652380\pi$
$881$	−24091.0	−0.921277	−0.460639	+	0.887588i	$0.652380\pi$
$882$	−1158.59	−0.0442311
$883$	−8158.04	−0.310917	−0.155459	−	0.987842i	$-0.549686\pi$
$883$	−8158.04	−0.310917	−0.155459	+	0.987842i	$0.549686\pi$
$884$	−15034.1	−0.572004
$885$	−9483.88	−0.360223
$886$	939.756	0.0356340
$887$	−42817.1	−1.62081	−0.810405	−	0.585870i	$-0.800753\pi$
$887$	−42817.1	−1.62081	−0.810405	+	0.585870i	$0.800753\pi$
$888$	6179.63	0.233530
$889$	−6250.92	−0.235826
$890$	−8.71751	−0.000328327 0
$891$	0	0
$892$	−8046.20	−0.302026
$893$	−954.731	−0.0357770
$894$	1822.18	0.0681688
$895$	−10225.3	−0.381892
$896$	1887.60	0.0703797
$897$	−41827.1	−1.55693
$898$	−26.8828	−0.000998988 0
$899$	18359.6	0.681119
$900$	−1767.10	−0.0654480
$901$	13496.4	0.499036
$902$	0	0
$903$	−2587.07	−0.0953403
$904$	−8875.80	−0.326554
$905$	−119.666	−0.00439540
$906$	−661.505	−0.0242572
$907$	−2378.07	−0.0870589	−0.0435295	−	0.999052i	$-0.513860\pi$
$907$	−2378.07	−0.0870589	−0.0435295	+	0.999052i	$0.513860\pi$
$908$	27316.2	0.998370
$909$	−3727.58	−0.136013
$910$	−355.588	−0.0129534
$911$	−40183.8	−1.46141	−0.730707	−	0.682691i	$-0.760809\pi$
$911$	−40183.8	−1.46141	−0.730707	+	0.682691i	$0.760809\pi$
$912$	1046.44	0.0379945
$913$	0	0
$914$	−1264.49	−0.0457609
$915$	−9452.99	−0.341537
$916$	−34239.1	−1.23503
$917$	1118.67	0.0402854
$918$	268.282	0.00964558
$919$	−42705.5	−1.53289	−0.766444	−	0.642311i	$-0.777976\pi$
$919$	−42705.5	−1.53289	−0.766444	+	0.642311i	$0.777976\pi$
$920$	−5736.77	−0.205582
$921$	6669.28	0.238610
$922$	4521.93	0.161520
$923$	46584.2	1.66125
$924$	0	0
$925$	8493.98	0.301925
$926$	461.726	0.0163858
$927$	−1010.93	−0.0358180
$928$	−19400.8	−0.686273
$929$	32671.9	1.15385	0.576927	−	0.816796i	$-0.304252\pi$
$929$	32671.9	1.15385	0.576927	+	0.816796i	$0.304252\pi$
$930$	−388.906	−0.0137126
$931$	1940.46	0.0683092
$932$	21744.4	0.764231
$933$	18447.9	0.647329
$934$	2557.01	0.0895803
$935$	0	0
$936$	4019.96	0.140381
$937$	−30900.8	−1.07736	−0.538679	−	0.842511i	$-0.681076\pi$
$937$	−30900.8	−1.07736	−0.538679	+	0.842511i	$0.681076\pi$
$938$	951.981	0.0331378
$939$	−5720.55	−0.198811
$940$	6503.92	0.225675
$941$	−42323.0	−1.46619	−0.733097	−	0.680124i	$-0.761926\pi$
$941$	−42323.0	−1.46619	−0.733097	+	0.680124i	$0.761926\pi$
$942$	392.360	0.0135709
$943$	−13694.0	−0.472894
$944$	−38259.0	−1.31909
$945$	−340.772	−0.0117305
$946$	0	0
$947$	50460.8	1.73153	0.865764	−	0.500453i	$-0.166833\pi$
$947$	50460.8	1.73153	0.865764	+	0.500453i	$0.166833\pi$
$948$	1024.54	0.0351007
$949$	8666.94	0.296460
$950$	−55.1101	−0.00188211
$951$	−16304.0	−0.555935
$952$	−397.640	−0.0135374
$953$	36633.8	1.24521	0.622605	−	0.782536i	$-0.286074\pi$
$953$	36633.8	1.24521	0.622605	+	0.782536i	$0.286074\pi$
$954$	−1787.76	−0.0606718
$955$	−15886.4	−0.538295
$956$	−7689.08	−0.260128
$957$	0	0
$958$	−6258.52	−0.211068
$959$	−2916.65	−0.0982103
$960$	−6850.42	−0.230309
$961$	−25194.5	−0.845707
$962$	−9572.34	−0.320816
$963$	−10740.4	−0.359403
$964$	51578.7	1.72328
$965$	−20375.0	−0.679685
$966$	−548.045	−0.0182537
$967$	−51425.9	−1.71018	−0.855090	−	0.518479i	$-0.826498\pi$
$967$	−51425.9	−1.71018	−0.855090	+	0.518479i	$0.826498\pi$
$968$	0	0
$969$	−449.330	−0.0148963
$970$	−143.332	−0.00474444
$971$	19552.7	0.646215	0.323108	−	0.946362i	$-0.395272\pi$
$971$	19552.7	0.646215	0.323108	+	0.946362i	$0.395272\pi$
$972$	1908.46	0.0629773
$973$	6208.17	0.204548
$974$	1392.53	0.0458106
$975$	5525.49	0.181495
$976$	−38134.3	−1.25067
$977$	4877.64	0.159723	0.0798616	−	0.996806i	$-0.474552\pi$
$977$	4877.64	0.159723	0.0798616	+	0.996806i	$0.474552\pi$
$978$	−1376.05	−0.0449910
$979$	0	0
$980$	−13219.0	−0.430883
$981$	−12203.8	−0.397184
$982$	−5153.21	−0.167460
$983$	−32295.7	−1.04789	−0.523944	−	0.851753i	$-0.675540\pi$
$983$	−32295.7	−1.04789	−0.523944	+	0.851753i	$0.675540\pi$
$984$	1316.12	0.0426386
$985$	3741.70	0.121036
$986$	2690.76	0.0869081
$987$	1254.23	0.0404485
$988$	−3335.34	−0.107400
$989$	64652.3	2.07869
$990$	0	0
$991$	48086.2	1.54138	0.770690	−	0.637210i	$-0.219912\pi$
$991$	48086.2	1.54138	0.770690	+	0.637210i	$0.219912\pi$
$992$	−4857.22	−0.155461
$993$	18341.8	0.586163
$994$	610.375	0.0194768
$995$	−3917.48	−0.124816
$996$	21333.6	0.678696
$997$	−842.467	−0.0267615	−0.0133807	−	0.999910i	$-0.504259\pi$
$997$	−842.467	−0.0267615	−0.0133807	+	0.999910i	$0.504259\pi$
$998$	1639.67	0.0520068
$999$	−9173.50	−0.290527

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.4.a.bf.1.6	yes	10
11.10	odd	2	inner	1815.4.a.bf.1.5	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1815.4.a.bf.1.5	✓	10	11.10	odd	2	inner
1815.4.a.bf.1.6	yes	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1815.a (trivial)

\(f(q)\)	\(=\)	\(q+0.382418 q^{2} -3.00000 q^{3} -7.85376 q^{4} -5.00000 q^{5} -1.14725 q^{6} -2.52423 q^{7} -6.06276 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+0.382418 q^{2} -3.00000 q^{3} -7.85376 q^{4} -5.00000 q^{5} -1.14725 q^{6} -2.52423 q^{7} -6.06276 q^{8} +9.00000 q^{9} -1.91209 q^{10} +23.5613 q^{12} -73.6731 q^{13} -0.965312 q^{14} +15.0000 q^{15} +60.5115 q^{16} -25.9831 q^{17} +3.44176 q^{18} -5.76439 q^{19} +39.2688 q^{20} +7.57270 q^{21} -189.246 q^{23} +18.1883 q^{24} +25.0000 q^{25} -28.1739 q^{26} -27.0000 q^{27} +19.8247 q^{28} -270.799 q^{29} +5.73627 q^{30} -67.7978 q^{31} +71.6427 q^{32} -9.93639 q^{34} +12.6212 q^{35} -70.6838 q^{36} +339.759 q^{37} -2.20440 q^{38} +221.019 q^{39} +30.3138 q^{40} +72.3609 q^{41} +2.89594 q^{42} -341.631 q^{43} -45.0000 q^{45} -72.3711 q^{46} +165.626 q^{47} -181.535 q^{48} -336.628 q^{49} +9.56044 q^{50} +77.9492 q^{51} +578.611 q^{52} -519.432 q^{53} -10.3253 q^{54} +15.3038 q^{56} +17.2932 q^{57} -103.558 q^{58} -632.259 q^{59} -117.806 q^{60} -630.199 q^{61} -25.9271 q^{62} -22.7181 q^{63} -456.695 q^{64} +368.366 q^{65} -986.191 q^{67} +204.065 q^{68} +567.739 q^{69} +4.82656 q^{70} -632.308 q^{71} -54.5648 q^{72} -117.640 q^{73} +129.930 q^{74} -75.0000 q^{75} +45.2721 q^{76} +84.5217 q^{78} +43.4840 q^{79} -302.558 q^{80} +81.0000 q^{81} +27.6721 q^{82} +905.452 q^{83} -59.4742 q^{84} +129.915 q^{85} -130.646 q^{86} +812.397 q^{87} +4.55915 q^{89} -17.2088 q^{90} +185.968 q^{91} +1486.29 q^{92} +203.393 q^{93} +63.3382 q^{94} +28.8220 q^{95} -214.928 q^{96} +74.9609 q^{97} -128.733 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 30 q^{3} + 14 q^{4} - 50 q^{5} + 90 q^{9}+O(q^{10}) \) 10 * q - 30 * q^3 + 14 * q^4 - 50 * q^5 + 90 * q^9	\( 10 q - 30 q^{3} + 14 q^{4} - 50 q^{5} + 90 q^{9} - 42 q^{12} - 224 q^{14} + 150 q^{15} - 238 q^{16} - 70 q^{20} - 370 q^{23} + 250 q^{25} + 112 q^{26} - 270 q^{27} + 326 q^{31} - 510 q^{34} + 126 q^{36} + 984 q^{37} - 1152 q^{38} + 672 q^{42} - 450 q^{45} + 58 q^{47} + 714 q^{48} + 150 q^{49} + 138 q^{53} - 1380 q^{56} - 816 q^{58} + 192 q^{59} + 210 q^{60} - 1424 q^{64} - 480 q^{67} + 1110 q^{69} + 1120 q^{70} - 716 q^{71} - 750 q^{75} - 336 q^{78} + 1190 q^{80} + 810 q^{81} - 2976 q^{82} - 1584 q^{86} - 3160 q^{89} + 1840 q^{91} + 406 q^{92} - 978 q^{93} - 204 q^{97}+O(q^{100}) \) 10 * q - 30 * q^3 + 14 * q^4 - 50 * q^5 + 90 * q^9 - 42 * q^12 - 224 * q^14 + 150 * q^15 - 238 * q^16 - 70 * q^20 - 370 * q^23 + 250 * q^25 + 112 * q^26 - 270 * q^27 + 326 * q^31 - 510 * q^34 + 126 * q^36 + 984 * q^37 - 1152 * q^38 + 672 * q^42 - 450 * q^45 + 58 * q^47 + 714 * q^48 + 150 * q^49 + 138 * q^53 - 1380 * q^56 - 816 * q^58 + 192 * q^59 + 210 * q^60 - 1424 * q^64 - 480 * q^67 + 1110 * q^69 + 1120 * q^70 - 716 * q^71 - 750 * q^75 - 336 * q^78 + 1190 * q^80 + 810 * q^81 - 2976 * q^82 - 1584 * q^86 - 3160 * q^89 + 1840 * q^91 + 406 * q^92 - 978 * q^93 - 204 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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