LMFDB - Embedded newform 5800.2.a.u.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5800,2,Mod(1,5800)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5800.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5800, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 5800 = 2^{3} \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5800.a (trivial)

Newform invariants

comment:select newform

sage:traces = [5,0,1,0,0,0,-7,0,12,0,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$46.3132331723$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.3145252.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 11x^{3} + 9x^{2} + 22x - 11 $ x^5 - 2x^4 - 11x^3 + 9x^2 + 22x - 11
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 1160)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.58684$ of defining polynomial
Character	$\chi$	$=$	5800.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q-0.959449 q^{3} -4.10933 q^{7} -2.07946 q^{9} +5.18879 q^{11} +0.586839 q^{13} +2.10933 q^{17} +0.372610 q^{19} +3.94270 q^{21} -6.13313 q^{23} +4.87348 q^{27} +1.00000 q^{29} -1.36411 q^{31} -4.97838 q^{33} +2.71997 q^{37} -0.563043 q^{39} +5.64250 q^{41} -11.0066 q^{43} +8.36247 q^{47} +9.88660 q^{49} -2.02380 q^{51} -3.16056 q^{53} -0.357501 q^{57} -6.58684 q^{59} +2.28708 q^{61} +8.54518 q^{63} -7.61725 q^{67} +5.88443 q^{69} +14.2085 q^{71} -2.46683 q^{73} -21.3224 q^{77} +5.30681 q^{79} +1.56251 q^{81} +14.8575 q^{83} -0.959449 q^{87} -3.91890 q^{89} -2.41152 q^{91} +1.30880 q^{93} +6.27069 q^{97} -10.7899 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{3} - 7 q^{7} + 12 q^{9} - 10 q^{11} - 3 q^{13} - 3 q^{17} + 2 q^{19} + 4 q^{21} - 13 q^{23} + 4 q^{27} + 5 q^{29} + 7 q^{31} - 12 q^{33} - 10 q^{37} - q^{39} + 4 q^{41} - 17 q^{43} - 6 q^{47}+ \cdots - 96 q^{99}+O(q^{100}) $ 5 * q + q^3 - 7 * q^7 + 12 * q^9 - 10 * q^11 - 3 * q^13 - 3 * q^17 + 2 * q^19 + 4 * q^21 - 13 * q^23 + 4 * q^27 + 5 * q^29 + 7 * q^31 - 12 * q^33 - 10 * q^37 - q^39 + 4 * q^41 - 17 * q^43 - 6 * q^47 + 28 * q^49 - 6 * q^51 - 5 * q^53 - 26 * q^57 - 27 * q^59 + 21 * q^61 - 54 * q^63 + 10 * q^67 + 25 * q^69 - 4 * q^71 - 23 * q^73 - 2 * q^77 - 3 * q^79 + 57 * q^81 + 12 * q^83 + q^87 - 8 * q^89 + 16 * q^91 - 46 * q^93 - 25 * q^97 - 96 * 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 $

$2$	0	0
$2$	0	0
$3$	−0.959449	−0.553938	−0.276969	−	0.960879i	$-0.589330\pi$
$3$	−0.959449	−0.553938	−0.276969	+	0.960879i	$0.589330\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	−4.10933	−1.55318	−0.776591	−	0.630006i	$-0.783053\pi$
$7$	−4.10933	−1.55318	−0.776591	+	0.630006i	$0.783053\pi$
$8$	0	0
$9$	−2.07946	−0.693152
$10$	0	0
$11$	5.18879	1.56448	0.782239	−	0.622978i	$-0.214077\pi$
$11$	5.18879	1.56448	0.782239	+	0.622978i	$0.214077\pi$
$12$	0	0
$13$	0.586839	0.162760	0.0813800	−	0.996683i	$-0.474067\pi$
$13$	0.586839	0.162760	0.0813800	+	0.996683i	$0.474067\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	2.10933	0.511588	0.255794	−	0.966731i	$-0.417663\pi$
$17$	2.10933	0.511588	0.255794	+	0.966731i	$0.417663\pi$
$18$	0	0
$19$	0.372610	0.0854827	0.0427413	−	0.999086i	$-0.486391\pi$
$19$	0.372610	0.0854827	0.0427413	+	0.999086i	$0.486391\pi$
$20$	0	0
$21$	3.94270	0.860367
$22$	0	0
$23$	−6.13313	−1.27885	−0.639423	−	0.768855i	$-0.720827\pi$
$23$	−6.13313	−1.27885	−0.639423	+	0.768855i	$0.720827\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	4.87348	0.937902
$28$	0	0
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	−1.36411	−0.245001	−0.122501	−	0.992468i	$-0.539091\pi$
$31$	−1.36411	−0.245001	−0.122501	+	0.992468i	$0.539091\pi$
$32$	0	0
$33$	−4.97838	−0.866625
$34$	0	0
$35$	0	0
$36$	0	0
$37$	2.71997	0.447160	0.223580	−	0.974686i	$-0.428226\pi$
$37$	2.71997	0.447160	0.223580	+	0.974686i	$0.428226\pi$
$38$	0	0
$39$	−0.563043	−0.0901590
$40$	0	0
$41$	5.64250	0.881210	0.440605	−	0.897701i	$-0.354764\pi$
$41$	5.64250	0.881210	0.440605	+	0.897701i	$0.354764\pi$
$42$	0	0
$43$	−11.0066	−1.67849	−0.839246	−	0.543752i	$-0.817003\pi$
$43$	−11.0066	−1.67849	−0.839246	+	0.543752i	$0.817003\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	8.36247	1.21979	0.609896	−	0.792482i	$-0.291211\pi$
$47$	8.36247	1.21979	0.609896	+	0.792482i	$0.291211\pi$
$48$	0	0
$49$	9.88660	1.41237
$50$	0	0
$51$	−2.02380	−0.283388
$52$	0	0
$53$	−3.16056	−0.434136	−0.217068	−	0.976156i	$-0.569649\pi$
$53$	−3.16056	−0.434136	−0.217068	+	0.976156i	$0.569649\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	−0.357501	−0.0473521
$58$	0	0
$59$	−6.58684	−0.857533	−0.428767	−	0.903415i	$-0.641052\pi$
$59$	−6.58684	−0.857533	−0.428767	+	0.903415i	$0.641052\pi$
$60$	0	0
$61$	2.28708	0.292830	0.146415	−	0.989223i	$-0.453227\pi$
$61$	2.28708	0.292830	0.146415	+	0.989223i	$0.453227\pi$
$62$	0	0
$63$	8.54518	1.07659
$64$	0	0
$65$	0	0
$66$	0	0
$67$	−7.61725	−0.930595	−0.465297	−	0.885154i	$-0.654053\pi$
$67$	−7.61725	−0.930595	−0.465297	+	0.885154i	$0.654053\pi$
$68$	0	0
$69$	5.88443	0.708402
$70$	0	0
$71$	14.2085	1.68624	0.843120	−	0.537725i	$-0.180716\pi$
$71$	14.2085	1.68624	0.843120	+	0.537725i	$0.180716\pi$
$72$	0	0
$73$	−2.46683	−0.288721	−0.144360	−	0.989525i	$-0.546112\pi$
$73$	−2.46683	−0.288721	−0.144360	+	0.989525i	$0.546112\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	−21.3224	−2.42992
$78$	0	0
$79$	5.30681	0.597062	0.298531	−	0.954400i	$-0.403503\pi$
$79$	5.30681	0.597062	0.298531	+	0.954400i	$0.403503\pi$
$80$	0	0
$81$	1.56251	0.173612
$82$	0	0
$83$	14.8575	1.63083	0.815413	−	0.578880i	$-0.196510\pi$
$83$	14.8575	1.63083	0.815413	+	0.578880i	$0.196510\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	−0.959449	−0.102864
$88$	0	0
$89$	−3.91890	−0.415402	−0.207701	−	0.978192i	$-0.566598\pi$
$89$	−3.91890	−0.415402	−0.207701	+	0.978192i	$0.566598\pi$
$90$	0	0
$91$	−2.41152	−0.252796
$92$	0	0
$93$	1.30880	0.135716
$94$	0	0
$95$	0	0
$96$	0	0
$97$	6.27069	0.636692	0.318346	−	0.947975i	$-0.396873\pi$
$97$	6.27069	0.636692	0.318346	+	0.947975i	$0.396873\pi$
$98$	0	0
$99$	−10.7899	−1.08442
$100$	0	0
$101$	−5.40302	−0.537620	−0.268810	−	0.963193i	$-0.586630\pi$
$101$	−5.40302	−0.537620	−0.268810	+	0.963193i	$0.586630\pi$
$102$	0	0
$103$	−13.2699	−1.30752	−0.653761	−	0.756702i	$-0.726810\pi$
$103$	−13.2699	−1.30752	−0.653761	+	0.756702i	$0.726810\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	12.9600	1.25289	0.626444	−	0.779466i	$-0.284510\pi$
$107$	12.9600	1.25289	0.626444	+	0.779466i	$0.284510\pi$
$108$	0	0
$109$	4.89728	0.469074	0.234537	−	0.972107i	$-0.424643\pi$
$109$	4.89728	0.469074	0.234537	+	0.972107i	$0.424643\pi$
$110$	0	0
$111$	−2.60967	−0.247699
$112$	0	0
$113$	13.5255	1.27237	0.636185	−	0.771537i	$-0.280512\pi$
$113$	13.5255	1.27237	0.636185	+	0.771537i	$0.280512\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	−1.22031	−0.112817
$118$	0	0
$119$	−8.66794	−0.794589
$120$	0	0
$121$	15.9235	1.44759
$122$	0	0
$123$	−5.41369	−0.488136
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−13.3001	−1.18019	−0.590097	−	0.807332i	$-0.700910\pi$
$127$	−13.3001	−1.18019	−0.590097	+	0.807332i	$0.700910\pi$
$128$	0	0
$129$	10.5603	0.929781
$130$	0	0
$131$	−14.5315	−1.26963	−0.634813	−	0.772666i	$-0.718923\pi$
$131$	−14.5315	−1.26963	−0.634813	+	0.772666i	$0.718923\pi$
$132$	0	0
$133$	−1.53118	−0.132770
$134$	0	0
$135$	0	0
$136$	0	0
$137$	5.11151	0.436706	0.218353	−	0.975870i	$-0.429932\pi$
$137$	5.11151	0.436706	0.218353	+	0.975870i	$0.429932\pi$
$138$	0	0
$139$	−13.2315	−1.12228	−0.561141	−	0.827720i	$-0.689638\pi$
$139$	−13.2315	−1.12228	−0.561141	+	0.827720i	$0.689638\pi$
$140$	0	0
$141$	−8.02336	−0.675689
$142$	0	0
$143$	3.04498	0.254634
$144$	0	0
$145$	0	0
$146$	0	0
$147$	−9.48570	−0.782367
$148$	0	0
$149$	−20.6438	−1.69121	−0.845604	−	0.533810i	$-0.820760\pi$
$149$	−20.6438	−1.69121	−0.845604	+	0.533810i	$0.820760\pi$
$150$	0	0
$151$	−8.87264	−0.722045	−0.361023	−	0.932557i	$-0.617572\pi$
$151$	−8.87264	−0.722045	−0.361023	+	0.932557i	$0.617572\pi$
$152$	0	0
$153$	−4.38626	−0.354608
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−17.4853	−1.39548	−0.697738	−	0.716353i	$-0.745810\pi$
$157$	−17.4853	−1.39548	−0.697738	+	0.716353i	$0.745810\pi$
$158$	0	0
$159$	3.03240	0.240485
$160$	0	0
$161$	25.2031	1.98628
$162$	0	0
$163$	−8.52467	−0.667704	−0.333852	−	0.942626i	$-0.608349\pi$
$163$	−8.52467	−0.667704	−0.333852	+	0.942626i	$0.608349\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−18.3178	−1.41748	−0.708739	−	0.705471i	$-0.750736\pi$
$167$	−18.3178	−1.41748	−0.708739	+	0.705471i	$0.750736\pi$
$168$	0	0
$169$	−12.6556	−0.973509
$170$	0	0
$171$	−0.774827	−0.0592525
$172$	0	0
$173$	25.4828	1.93742	0.968712	−	0.248187i	$-0.0798346\pi$
$173$	25.4828	1.93742	0.968712	+	0.248187i	$0.0798346\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	6.31974	0.475021
$178$	0	0
$179$	−8.51259	−0.636261	−0.318131	−	0.948047i	$-0.603055\pi$
$179$	−8.51259	−0.636261	−0.318131	+	0.948047i	$0.603055\pi$
$180$	0	0
$181$	−0.897279	−0.0666942	−0.0333471	−	0.999444i	$-0.510617\pi$
$181$	−0.897279	−0.0666942	−0.0333471	+	0.999444i	$0.510617\pi$
$182$	0	0
$183$	−2.19433	−0.162210
$184$	0	0
$185$	0	0
$186$	0	0
$187$	10.9449	0.800368
$188$	0	0
$189$	−20.0268	−1.45673
$190$	0	0
$191$	−12.8444	−0.929389	−0.464694	−	0.885471i	$-0.653836\pi$
$191$	−12.8444	−0.929389	−0.464694	+	0.885471i	$0.653836\pi$
$192$	0	0
$193$	−4.25459	−0.306252	−0.153126	−	0.988207i	$-0.548934\pi$
$193$	−4.25459	−0.306252	−0.153126	+	0.988207i	$0.548934\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−26.5214	−1.88957	−0.944786	−	0.327688i	$-0.893730\pi$
$197$	−26.5214	−1.88957	−0.944786	+	0.327688i	$0.893730\pi$
$198$	0	0
$199$	−12.0496	−0.854174	−0.427087	−	0.904211i	$-0.640460\pi$
$199$	−12.0496	−0.854174	−0.427087	+	0.904211i	$0.640460\pi$
$200$	0	0
$201$	7.30836	0.515492
$202$	0	0
$203$	−4.10933	−0.288419
$204$	0	0
$205$	0	0
$206$	0	0
$207$	12.7536	0.886435
$208$	0	0
$209$	1.93340	0.133736
$210$	0	0
$211$	−24.3116	−1.67368	−0.836839	−	0.547449i	$-0.815599\pi$
$211$	−24.3116	−1.67368	−0.836839	+	0.547449i	$0.815599\pi$
$212$	0	0
$213$	−13.6324	−0.934074
$214$	0	0
$215$	0	0
$216$	0	0
$217$	5.60558	0.380532
$218$	0	0
$219$	2.36680	0.159934
$220$	0	0
$221$	1.23784	0.0832660
$222$	0	0
$223$	−2.84813	−0.190725	−0.0953624	−	0.995443i	$-0.530401\pi$
$223$	−2.84813	−0.190725	−0.0953624	+	0.995443i	$0.530401\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	14.0627	0.933374	0.466687	−	0.884422i	$-0.345447\pi$
$227$	14.0627	0.933374	0.466687	+	0.884422i	$0.345447\pi$
$228$	0	0
$229$	−10.1822	−0.672857	−0.336429	−	0.941709i	$-0.609219\pi$
$229$	−10.1822	−0.672857	−0.336429	+	0.941709i	$0.609219\pi$
$230$	0	0
$231$	20.4578	1.34603
$232$	0	0
$233$	4.68547	0.306955	0.153478	−	0.988152i	$-0.450953\pi$
$233$	4.68547	0.306955	0.153478	+	0.988152i	$0.450953\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−5.09161	−0.330736
$238$	0	0
$239$	−18.5942	−1.20276	−0.601380	−	0.798963i	$-0.705382\pi$
$239$	−18.5942	−1.20276	−0.601380	+	0.798963i	$0.705382\pi$
$240$	0	0
$241$	4.37503	0.281821	0.140910	−	0.990022i	$-0.454997\pi$
$241$	4.37503	0.281821	0.140910	+	0.990022i	$0.454997\pi$
$242$	0	0
$243$	−16.1196	−1.03407
$244$	0	0
$245$	0	0
$246$	0	0
$247$	0.218662	0.0139131
$248$	0	0
$249$	−14.2550	−0.903377
$250$	0	0
$251$	−3.63425	−0.229392	−0.114696	−	0.993401i	$-0.536589\pi$
$251$	−3.63425	−0.229392	−0.114696	+	0.993401i	$0.536589\pi$
$252$	0	0
$253$	−31.8235	−2.00073
$254$	0	0
$255$	0	0
$256$	0	0
$257$	4.73508	0.295366	0.147683	−	0.989035i	$-0.452818\pi$
$257$	4.73508	0.295366	0.147683	+	0.989035i	$0.452818\pi$
$258$	0	0
$259$	−11.1772	−0.694520
$260$	0	0
$261$	−2.07946	−0.128715
$262$	0	0
$263$	−25.5877	−1.57781	−0.788903	−	0.614518i	$-0.789351\pi$
$263$	−25.5877	−1.57781	−0.788903	+	0.614518i	$0.789351\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	3.75999	0.230107
$268$	0	0
$269$	2.97700	0.181511	0.0907556	−	0.995873i	$-0.471072\pi$
$269$	2.97700	0.181511	0.0907556	+	0.995873i	$0.471072\pi$
$270$	0	0
$271$	2.91038	0.176793	0.0883964	−	0.996085i	$-0.471826\pi$
$271$	2.91038	0.176793	0.0883964	+	0.996085i	$0.471826\pi$
$272$	0	0
$273$	2.31373	0.140033
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−2.00686	−0.120580	−0.0602901	−	0.998181i	$-0.519203\pi$
$277$	−2.00686	−0.120580	−0.0602901	+	0.998181i	$0.519203\pi$
$278$	0	0
$279$	2.83661	0.169823
$280$	0	0
$281$	15.2646	0.910610	0.455305	−	0.890335i	$-0.349530\pi$
$281$	15.2646	0.910610	0.455305	+	0.890335i	$0.349530\pi$
$282$	0	0
$283$	−7.18879	−0.427329	−0.213665	−	0.976907i	$-0.568540\pi$
$283$	−7.18879	−0.427329	−0.213665	+	0.976907i	$0.568540\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	−23.1869	−1.36868
$288$	0	0
$289$	−12.5507	−0.738278
$290$	0	0
$291$	−6.01641	−0.352688
$292$	0	0
$293$	18.7433	1.09500	0.547499	−	0.836807i	$-0.315580\pi$
$293$	18.7433	1.09500	0.547499	+	0.836807i	$0.315580\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	25.2875	1.46733
$298$	0	0
$299$	−3.59916	−0.208145
$300$	0	0
$301$	45.2298	2.60700
$302$	0	0
$303$	5.18392	0.297809
$304$	0	0
$305$	0	0
$306$	0	0
$307$	9.10769	0.519803	0.259902	−	0.965635i	$-0.416310\pi$
$307$	9.10769	0.519803	0.259902	+	0.965635i	$0.416310\pi$
$308$	0	0
$309$	12.7318	0.724286
$310$	0	0
$311$	−31.5153	−1.78707	−0.893535	−	0.448993i	$-0.851783\pi$
$311$	−31.5153	−1.78707	−0.893535	+	0.448993i	$0.851783\pi$
$312$	0	0
$313$	23.6557	1.33710	0.668550	−	0.743667i	$-0.266915\pi$
$313$	23.6557	1.33710	0.668550	+	0.743667i	$0.266915\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	25.9371	1.45677	0.728386	−	0.685167i	$-0.240271\pi$
$317$	25.9371	1.45677	0.728386	+	0.685167i	$0.240271\pi$
$318$	0	0
$319$	5.18879	0.290516
$320$	0	0
$321$	−12.4344	−0.694023
$322$	0	0
$323$	0.785958	0.0437319
$324$	0	0
$325$	0	0
$326$	0	0
$327$	−4.69869	−0.259838
$328$	0	0
$329$	−34.3641	−1.89456
$330$	0	0
$331$	−20.6953	−1.13752	−0.568759	−	0.822504i	$-0.692576\pi$
$331$	−20.6953	−1.13752	−0.568759	+	0.822504i	$0.692576\pi$
$332$	0	0
$333$	−5.65605	−0.309950
$334$	0	0
$335$	0	0
$336$	0	0
$337$	5.05712	0.275479	0.137739	−	0.990469i	$-0.456016\pi$
$337$	5.05712	0.275479	0.137739	+	0.990469i	$0.456016\pi$
$338$	0	0
$339$	−12.9770	−0.704814
$340$	0	0
$341$	−7.07808	−0.383300
$342$	0	0
$343$	−11.8620	−0.640488
$344$	0	0
$345$	0	0
$346$	0	0
$347$	16.7026	0.896642	0.448321	−	0.893873i	$-0.352022\pi$
$347$	16.7026	0.896642	0.448321	+	0.893873i	$0.352022\pi$
$348$	0	0
$349$	−12.4757	−0.667808	−0.333904	−	0.942607i	$-0.608366\pi$
$349$	−12.4757	−0.667808	−0.333904	+	0.942607i	$0.608366\pi$
$350$	0	0
$351$	2.85995	0.152653
$352$	0	0
$353$	−24.4485	−1.30126	−0.650632	−	0.759393i	$-0.725496\pi$
$353$	−24.4485	−1.30126	−0.650632	+	0.759393i	$0.725496\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	8.31645	0.440153
$358$	0	0
$359$	2.81174	0.148398	0.0741991	−	0.997243i	$-0.476360\pi$
$359$	2.81174	0.148398	0.0741991	+	0.997243i	$0.476360\pi$
$360$	0	0
$361$	−18.8612	−0.992693
$362$	0	0
$363$	−15.2778	−0.801877
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−12.8112	−0.668740	−0.334370	−	0.942442i	$-0.608523\pi$
$367$	−12.8112	−0.668740	−0.334370	+	0.942442i	$0.608523\pi$
$368$	0	0
$369$	−11.7333	−0.610813
$370$	0	0
$371$	12.9878	0.674292
$372$	0	0
$373$	6.23375	0.322771	0.161386	−	0.986891i	$-0.448404\pi$
$373$	6.23375	0.322771	0.161386	+	0.986891i	$0.448404\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0.586839	0.0302238
$378$	0	0
$379$	11.9938	0.616078	0.308039	−	0.951374i	$-0.400327\pi$
$379$	11.9938	0.616078	0.308039	+	0.951374i	$0.400327\pi$
$380$	0	0
$381$	12.7608	0.653755
$382$	0	0
$383$	−2.92679	−0.149552	−0.0747759	−	0.997200i	$-0.523824\pi$
$383$	−2.92679	−0.149552	−0.0747759	+	0.997200i	$0.523824\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	22.8878	1.16345
$388$	0	0
$389$	16.1783	0.820272	0.410136	−	0.912024i	$-0.365481\pi$
$389$	16.1783	0.820272	0.410136	+	0.912024i	$0.365481\pi$
$390$	0	0
$391$	−12.9368	−0.654242
$392$	0	0
$393$	13.9423	0.703294
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−11.9389	−0.599195	−0.299597	−	0.954066i	$-0.596852\pi$
$397$	−11.9389	−0.599195	−0.299597	+	0.954066i	$0.596852\pi$
$398$	0	0
$399$	1.46909	0.0735464
$400$	0	0
$401$	37.9678	1.89602	0.948010	−	0.318241i	$-0.103092\pi$
$401$	37.9678	1.89602	0.948010	+	0.318241i	$0.103092\pi$
$402$	0	0
$403$	−0.800514	−0.0398764
$404$	0	0
$405$	0	0
$406$	0	0
$407$	14.1133	0.699572
$408$	0	0
$409$	−18.6035	−0.919882	−0.459941	−	0.887949i	$-0.652130\pi$
$409$	−18.6035	−0.919882	−0.459941	+	0.887949i	$0.652130\pi$
$410$	0	0
$411$	−4.90423	−0.241908
$412$	0	0
$413$	27.0675	1.33190
$414$	0	0
$415$	0	0
$416$	0	0
$417$	12.6950	0.621675
$418$	0	0
$419$	0.788560	0.0385237	0.0192618	−	0.999814i	$-0.493868\pi$
$419$	0.788560	0.0385237	0.0192618	+	0.999814i	$0.493868\pi$
$420$	0	0
$421$	−16.0463	−0.782050	−0.391025	−	0.920380i	$-0.627879\pi$
$421$	−16.0463	−0.782050	−0.391025	+	0.920380i	$0.627879\pi$
$422$	0	0
$423$	−17.3894	−0.845501
$424$	0	0
$425$	0	0
$426$	0	0
$427$	−9.39835	−0.454818
$428$	0	0
$429$	−2.92151	−0.141052
$430$	0	0
$431$	27.6340	1.33108	0.665540	−	0.746362i	$-0.268201\pi$
$431$	27.6340	1.33108	0.665540	+	0.746362i	$0.268201\pi$
$432$	0	0
$433$	−17.6543	−0.848412	−0.424206	−	0.905566i	$-0.639447\pi$
$433$	−17.6543	−0.848412	−0.424206	+	0.905566i	$0.639447\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	−2.28527	−0.109319
$438$	0	0
$439$	1.69338	0.0808207	0.0404103	−	0.999183i	$-0.487133\pi$
$439$	1.69338	0.0808207	0.0404103	+	0.999183i	$0.487133\pi$
$440$	0	0
$441$	−20.5588	−0.978989
$442$	0	0
$443$	9.36655	0.445018	0.222509	−	0.974931i	$-0.428575\pi$
$443$	9.36655	0.445018	0.222509	+	0.974931i	$0.428575\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	19.8067	0.936825
$448$	0	0
$449$	−21.4298	−1.01133	−0.505667	−	0.862729i	$-0.668754\pi$
$449$	−21.4298	−1.01133	−0.505667	+	0.862729i	$0.668754\pi$
$450$	0	0
$451$	29.2777	1.37863
$452$	0	0
$453$	8.51285	0.399968
$454$	0	0
$455$	0	0
$456$	0	0
$457$	21.3911	1.00063	0.500316	−	0.865843i	$-0.333217\pi$
$457$	21.3911	1.00063	0.500316	+	0.865843i	$0.333217\pi$
$458$	0	0
$459$	10.2798	0.479819
$460$	0	0
$461$	−16.5598	−0.771265	−0.385632	−	0.922653i	$-0.626017\pi$
$461$	−16.5598	−0.771265	−0.385632	+	0.922653i	$0.626017\pi$
$462$	0	0
$463$	6.45243	0.299870	0.149935	−	0.988696i	$-0.452094\pi$
$463$	6.45243	0.299870	0.149935	+	0.988696i	$0.452094\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	6.95015	0.321615	0.160807	−	0.986986i	$-0.448590\pi$
$467$	6.95015	0.321615	0.160807	+	0.986986i	$0.448590\pi$
$468$	0	0
$469$	31.3018	1.44538
$470$	0	0
$471$	16.7762	0.773008
$472$	0	0
$473$	−57.1110	−2.62596
$474$	0	0
$475$	0	0
$476$	0	0
$477$	6.57224	0.300922
$478$	0	0
$479$	30.8878	1.41130	0.705651	−	0.708560i	$-0.250655\pi$
$479$	30.8878	1.41130	0.705651	+	0.708560i	$0.250655\pi$
$480$	0	0
$481$	1.59618	0.0727797
$482$	0	0
$483$	−24.1811	−1.10028
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−35.9132	−1.62738	−0.813691	−	0.581298i	$-0.802545\pi$
$487$	−35.9132	−1.62738	−0.813691	+	0.581298i	$0.802545\pi$
$488$	0	0
$489$	8.17899	0.369867
$490$	0	0
$491$	−22.6986	−1.02437	−0.512187	−	0.858874i	$-0.671165\pi$
$491$	−22.6986	−1.02437	−0.512187	+	0.858874i	$0.671165\pi$
$492$	0	0
$493$	2.10933	0.0949995
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−58.3875	−2.61904
$498$	0	0
$499$	36.5137	1.63458	0.817288	−	0.576230i	$-0.195477\pi$
$499$	36.5137	1.63458	0.817288	+	0.576230i	$0.195477\pi$
$500$	0	0
$501$	17.5751	0.785195
$502$	0	0
$503$	−33.5450	−1.49570	−0.747849	−	0.663869i	$-0.768913\pi$
$503$	−33.5450	−1.49570	−0.747849	+	0.663869i	$0.768913\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	12.1424	0.539264
$508$	0	0
$509$	36.8770	1.63454	0.817272	−	0.576252i	$-0.195485\pi$
$509$	36.8770	1.63454	0.817272	+	0.576252i	$0.195485\pi$
$510$	0	0
$511$	10.1370	0.448436
$512$	0	0
$513$	1.81591	0.0801744
$514$	0	0
$515$	0	0
$516$	0	0
$517$	43.3911	1.90834
$518$	0	0
$519$	−24.4495	−1.07321
$520$	0	0
$521$	12.3218	0.539826	0.269913	−	0.962885i	$-0.413005\pi$
$521$	12.3218	0.539826	0.269913	+	0.962885i	$0.413005\pi$
$522$	0	0
$523$	−23.0266	−1.00688	−0.503441	−	0.864030i	$-0.667933\pi$
$523$	−23.0266	−1.00688	−0.503441	+	0.864030i	$0.667933\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−2.87736	−0.125340
$528$	0	0
$529$	14.6153	0.635446
$530$	0	0
$531$	13.6970	0.594401
$532$	0	0
$533$	3.31124	0.143426
$534$	0	0
$535$	0	0
$536$	0	0
$537$	8.16740	0.352449
$538$	0	0
$539$	51.2995	2.20963
$540$	0	0
$541$	−28.0391	−1.20550	−0.602749	−	0.797931i	$-0.705928\pi$
$541$	−28.0391	−1.20550	−0.602749	+	0.797931i	$0.705928\pi$
$542$	0	0
$543$	0.860894	0.0369445
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−5.22517	−0.223412	−0.111706	−	0.993741i	$-0.535632\pi$
$547$	−5.22517	−0.223412	−0.111706	+	0.993741i	$0.535632\pi$
$548$	0	0
$549$	−4.75588	−0.202976
$550$	0	0
$551$	0.372610	0.0158737
$552$	0	0
$553$	−21.8074	−0.927346
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−45.3186	−1.92021	−0.960106	−	0.279637i	$-0.909786\pi$
$557$	−45.3186	−1.92021	−0.960106	+	0.279637i	$0.909786\pi$
$558$	0	0
$559$	−6.45911	−0.273191
$560$	0	0
$561$	−10.5011	−0.443355
$562$	0	0
$563$	30.0314	1.26567	0.632836	−	0.774286i	$-0.281891\pi$
$563$	30.0314	1.26567	0.632836	+	0.774286i	$0.281891\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	−6.42087	−0.269651
$568$	0	0
$569$	8.97111	0.376089	0.188044	−	0.982161i	$-0.439785\pi$
$569$	8.97111	0.376089	0.188044	+	0.982161i	$0.439785\pi$
$570$	0	0
$571$	−4.33668	−0.181484	−0.0907422	−	0.995874i	$-0.528924\pi$
$571$	−4.33668	−0.181484	−0.0907422	+	0.995874i	$0.528924\pi$
$572$	0	0
$573$	12.3236	0.514824
$574$	0	0
$575$	0	0
$576$	0	0
$577$	−22.8907	−0.952953	−0.476477	−	0.879187i	$-0.658086\pi$
$577$	−22.8907	−0.952953	−0.476477	+	0.879187i	$0.658086\pi$
$578$	0	0
$579$	4.08207	0.169645
$580$	0	0
$581$	−61.0545	−2.53297
$582$	0	0
$583$	−16.3995	−0.679196
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−1.15528	−0.0476835	−0.0238418	−	0.999716i	$-0.507590\pi$
$587$	−1.15528	−0.0476835	−0.0238418	+	0.999716i	$0.507590\pi$
$588$	0	0
$589$	−0.508282	−0.0209434
$590$	0	0
$591$	25.4459	1.04671
$592$	0	0
$593$	30.9456	1.27078	0.635391	−	0.772191i	$-0.280839\pi$
$593$	30.9456	1.27078	0.635391	+	0.772191i	$0.280839\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	11.5610	0.473160
$598$	0	0
$599$	−16.7552	−0.684598	−0.342299	−	0.939591i	$-0.611206\pi$
$599$	−16.7552	−0.684598	−0.342299	+	0.939591i	$0.611206\pi$
$600$	0	0
$601$	−4.86217	−0.198332	−0.0991660	−	0.995071i	$-0.531617\pi$
$601$	−4.86217	−0.198332	−0.0991660	+	0.995071i	$0.531617\pi$
$602$	0	0
$603$	15.8397	0.645044
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−38.7400	−1.57241	−0.786205	−	0.617966i	$-0.787957\pi$
$607$	−38.7400	−1.57241	−0.786205	+	0.617966i	$0.787957\pi$
$608$	0	0
$609$	3.94270	0.159766
$610$	0	0
$611$	4.90742	0.198533
$612$	0	0
$613$	3.03145	0.122439	0.0612196	−	0.998124i	$-0.480501\pi$
$613$	3.03145	0.122439	0.0612196	+	0.998124i	$0.480501\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−37.4111	−1.50611	−0.753057	−	0.657955i	$-0.771422\pi$
$617$	−37.4111	−1.50611	−0.753057	+	0.657955i	$0.771422\pi$
$618$	0	0
$619$	36.4019	1.46312	0.731558	−	0.681779i	$-0.238793\pi$
$619$	36.4019	1.46312	0.731558	+	0.681779i	$0.238793\pi$
$620$	0	0
$621$	−29.8897	−1.19943
$622$	0	0
$623$	16.1041	0.645195
$624$	0	0
$625$	0	0
$626$	0	0
$627$	−1.85500	−0.0740814
$628$	0	0
$629$	5.73731	0.228762
$630$	0	0
$631$	−26.6478	−1.06083	−0.530416	−	0.847737i	$-0.677964\pi$
$631$	−26.6478	−1.06083	−0.530416	+	0.847737i	$0.677964\pi$
$632$	0	0
$633$	23.3257	0.927115
$634$	0	0
$635$	0	0
$636$	0	0
$637$	5.80185	0.229877
$638$	0	0
$639$	−29.5460	−1.16882
$640$	0	0
$641$	35.8277	1.41511	0.707554	−	0.706660i	$-0.249799\pi$
$641$	35.8277	1.41511	0.707554	+	0.706660i	$0.249799\pi$
$642$	0	0
$643$	−8.55091	−0.337215	−0.168607	−	0.985683i	$-0.553927\pi$
$643$	−8.55091	−0.337215	−0.168607	+	0.985683i	$0.553927\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	37.5481	1.47617	0.738084	−	0.674709i	$-0.235731\pi$
$647$	37.5481	1.47617	0.738084	+	0.674709i	$0.235731\pi$
$648$	0	0
$649$	−34.1777	−1.34159
$650$	0	0
$651$	−5.37827	−0.210791
$652$	0	0
$653$	−16.3281	−0.638968	−0.319484	−	0.947592i	$-0.603510\pi$
$653$	−16.3281	−0.638968	−0.319484	+	0.947592i	$0.603510\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	5.12967	0.200127
$658$	0	0
$659$	−35.7821	−1.39387	−0.696937	−	0.717132i	$-0.745454\pi$
$659$	−35.7821	−1.39387	−0.696937	+	0.717132i	$0.745454\pi$
$660$	0	0
$661$	48.4847	1.88584	0.942918	−	0.333024i	$-0.108069\pi$
$661$	48.4847	1.88584	0.942918	+	0.333024i	$0.108069\pi$
$662$	0	0
$663$	−1.18764	−0.0461242
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−6.13313	−0.237476
$668$	0	0
$669$	2.73264	0.105650
$670$	0	0
$671$	11.8672	0.458126
$672$	0	0
$673$	−26.5228	−1.02238	−0.511189	−	0.859468i	$-0.670795\pi$
$673$	−26.5228	−1.02238	−0.511189	+	0.859468i	$0.670795\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	−16.2249	−0.623574	−0.311787	−	0.950152i	$-0.600927\pi$
$677$	−16.2249	−0.623574	−0.311787	+	0.950152i	$0.600927\pi$
$678$	0	0
$679$	−25.7683	−0.988898
$680$	0	0
$681$	−13.4925	−0.517032
$682$	0	0
$683$	−27.6221	−1.05693	−0.528465	−	0.848955i	$-0.677232\pi$
$683$	−27.6221	−1.05693	−0.528465	+	0.848955i	$0.677232\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	9.76929	0.372721
$688$	0	0
$689$	−1.85474	−0.0706599
$690$	0	0
$691$	−16.1550	−0.614566	−0.307283	−	0.951618i	$-0.599420\pi$
$691$	−16.1550	−0.614566	−0.307283	+	0.951618i	$0.599420\pi$
$692$	0	0
$693$	44.3391	1.68430
$694$	0	0
$695$	0	0
$696$	0	0
$697$	11.9019	0.450817
$698$	0	0
$699$	−4.49547	−0.170034
$700$	0	0
$701$	−35.2897	−1.33287	−0.666436	−	0.745562i	$-0.732181\pi$
$701$	−35.2897	−1.33287	−0.666436	+	0.745562i	$0.732181\pi$
$702$	0	0
$703$	1.01349	0.0382244
$704$	0	0
$705$	0	0
$706$	0	0
$707$	22.2028	0.835022
$708$	0	0
$709$	−33.3822	−1.25369	−0.626847	−	0.779142i	$-0.715655\pi$
$709$	−33.3822	−1.25369	−0.626847	+	0.779142i	$0.715655\pi$
$710$	0	0
$711$	−11.0353	−0.413855
$712$	0	0
$713$	8.36626	0.313319
$714$	0	0
$715$	0	0
$716$	0	0
$717$	17.8402	0.666255
$718$	0	0
$719$	46.0474	1.71728	0.858639	−	0.512581i	$-0.171311\pi$
$719$	46.0474	1.71728	0.858639	+	0.512581i	$0.171311\pi$
$720$	0	0
$721$	54.5304	2.03082
$722$	0	0
$723$	−4.19762	−0.156111
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−41.2234	−1.52889	−0.764445	−	0.644689i	$-0.776987\pi$
$727$	−41.2234	−1.52889	−0.764445	+	0.644689i	$0.776987\pi$
$728$	0	0
$729$	10.7784	0.399200
$730$	0	0
$731$	−23.2166	−0.858696
$732$	0	0
$733$	−1.37038	−0.0506160	−0.0253080	−	0.999680i	$-0.508057\pi$
$733$	−1.37038	−0.0506160	−0.0253080	+	0.999680i	$0.508057\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−39.5243	−1.45590
$738$	0	0
$739$	−27.0991	−0.996858	−0.498429	−	0.866930i	$-0.666090\pi$
$739$	−27.0991	−0.996858	−0.498429	+	0.866930i	$0.666090\pi$
$740$	0	0
$741$	−0.209795	−0.00770703
$742$	0	0
$743$	2.75040	0.100902	0.0504512	−	0.998727i	$-0.483934\pi$
$743$	2.75040	0.100902	0.0504512	+	0.998727i	$0.483934\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−30.8956	−1.13041
$748$	0	0
$749$	−53.2569	−1.94596
$750$	0	0
$751$	34.7388	1.26764	0.633818	−	0.773482i	$-0.281487\pi$
$751$	34.7388	1.26764	0.633818	+	0.773482i	$0.281487\pi$
$752$	0	0
$753$	3.48687	0.127069
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−13.6435	−0.495881	−0.247940	−	0.968775i	$-0.579754\pi$
$757$	−13.6435	−0.495881	−0.247940	+	0.968775i	$0.579754\pi$
$758$	0	0
$759$	30.5330	1.10828
$760$	0	0
$761$	27.6320	1.00166	0.500830	−	0.865545i	$-0.333028\pi$
$761$	27.6320	1.00166	0.500830	+	0.865545i	$0.333028\pi$
$762$	0	0
$763$	−20.1245	−0.728557
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−3.86542	−0.139572
$768$	0	0
$769$	30.7173	1.10769	0.553847	−	0.832619i	$-0.313159\pi$
$769$	30.7173	1.10769	0.553847	+	0.832619i	$0.313159\pi$
$770$	0	0
$771$	−4.54307	−0.163615
$772$	0	0
$773$	−4.41536	−0.158809	−0.0794047	−	0.996842i	$-0.525302\pi$
$773$	−4.41536	−0.158809	−0.0794047	+	0.996842i	$0.525302\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	10.7240	0.384721
$778$	0	0
$779$	2.10245	0.0753282
$780$	0	0
$781$	73.7250	2.63809
$782$	0	0
$783$	4.87348	0.174164
$784$	0	0
$785$	0	0
$786$	0	0
$787$	45.2955	1.61461	0.807306	−	0.590133i	$-0.200925\pi$
$787$	45.2955	1.61461	0.807306	+	0.590133i	$0.200925\pi$
$788$	0	0
$789$	24.5501	0.874007
$790$	0	0
$791$	−55.5806	−1.97622
$792$	0	0
$793$	1.34215	0.0476610
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−20.0726	−0.711009	−0.355505	−	0.934675i	$-0.615691\pi$
$797$	−20.0726	−0.711009	−0.355505	+	0.934675i	$0.615691\pi$
$798$	0	0
$799$	17.6392	0.624030
$800$	0	0
$801$	8.14918	0.287937
$802$	0	0
$803$	−12.7999	−0.451698
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−2.85628	−0.100546
$808$	0	0
$809$	2.91231	0.102391	0.0511957	−	0.998689i	$-0.483697\pi$
$809$	2.91231	0.102391	0.0511957	+	0.998689i	$0.483697\pi$
$810$	0	0
$811$	48.6091	1.70690	0.853449	−	0.521176i	$-0.174507\pi$
$811$	48.6091	1.70690	0.853449	+	0.521176i	$0.174507\pi$
$812$	0	0
$813$	−2.79236	−0.0979323
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−4.10118	−0.143482
$818$	0	0
$819$	5.01464	0.175226
$820$	0	0
$821$	−9.86317	−0.344227	−0.172114	−	0.985077i	$-0.555060\pi$
$821$	−9.86317	−0.344227	−0.172114	+	0.985077i	$0.555060\pi$
$822$	0	0
$823$	38.0949	1.32790	0.663952	−	0.747775i	$-0.268878\pi$
$823$	38.0949	1.32790	0.663952	+	0.747775i	$0.268878\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	30.8871	1.07405	0.537025	−	0.843566i	$-0.319548\pi$
$827$	30.8871	1.07405	0.537025	+	0.843566i	$0.319548\pi$
$828$	0	0
$829$	1.77795	0.0617508	0.0308754	−	0.999523i	$-0.490171\pi$
$829$	1.77795	0.0617508	0.0308754	+	0.999523i	$0.490171\pi$
$830$	0	0
$831$	1.92548	0.0667940
$832$	0	0
$833$	20.8541	0.722552
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−6.64797	−0.229787
$838$	0	0
$839$	−52.4002	−1.80906	−0.904529	−	0.426413i	$-0.859777\pi$
$839$	−52.4002	−1.80906	−0.904529	+	0.426413i	$0.859777\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	0	0
$843$	−14.6456	−0.504422
$844$	0	0
$845$	0	0
$846$	0	0
$847$	−65.4350	−2.24837
$848$	0	0
$849$	6.89728	0.236714
$850$	0	0
$851$	−16.6819	−0.571848
$852$	0	0
$853$	37.2395	1.27505	0.637527	−	0.770428i	$-0.279957\pi$
$853$	37.2395	1.27505	0.637527	+	0.770428i	$0.279957\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−34.0157	−1.16195	−0.580977	−	0.813920i	$-0.697330\pi$
$857$	−34.0157	−1.16195	−0.580977	+	0.813920i	$0.697330\pi$
$858$	0	0
$859$	−56.0008	−1.91072	−0.955361	−	0.295441i	$-0.904533\pi$
$859$	−56.0008	−1.91072	−0.955361	+	0.295441i	$0.904533\pi$
$860$	0	0
$861$	22.2467	0.758164
$862$	0	0
$863$	1.26936	0.0432094	0.0216047	−	0.999767i	$-0.493122\pi$
$863$	1.26936	0.0432094	0.0216047	+	0.999767i	$0.493122\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	12.0418	0.408960
$868$	0	0
$869$	27.5359	0.934091
$870$	0	0
$871$	−4.47010	−0.151463
$872$	0	0
$873$	−13.0396	−0.441324
$874$	0	0
$875$	0	0
$876$	0	0
$877$	3.44338	0.116275	0.0581373	−	0.998309i	$-0.481484\pi$
$877$	3.44338	0.116275	0.0581373	+	0.998309i	$0.481484\pi$
$878$	0	0
$879$	−17.9833	−0.606561
$880$	0	0
$881$	−27.9269	−0.940880	−0.470440	−	0.882432i	$-0.655905\pi$
$881$	−27.9269	−0.940880	−0.470440	+	0.882432i	$0.655905\pi$
$882$	0	0
$883$	9.16611	0.308464	0.154232	−	0.988035i	$-0.450710\pi$
$883$	9.16611	0.308464	0.154232	+	0.988035i	$0.450710\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−1.85948	−0.0624354	−0.0312177	−	0.999513i	$-0.509939\pi$
$887$	−1.85948	−0.0624354	−0.0312177	+	0.999513i	$0.509939\pi$
$888$	0	0
$889$	54.6545	1.83305
$890$	0	0
$891$	8.10754	0.271613
$892$	0	0
$893$	3.11594	0.104271
$894$	0	0
$895$	0	0
$896$	0	0
$897$	3.45321	0.115299
$898$	0	0
$899$	−1.36411	−0.0454956
$900$	0	0
$901$	−6.66666	−0.222099
$902$	0	0
$903$	−43.3957	−1.44412
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−15.0204	−0.498743	−0.249372	−	0.968408i	$-0.580224\pi$
$907$	−15.0204	−0.498743	−0.249372	+	0.968408i	$0.580224\pi$
$908$	0	0
$909$	11.2353	0.372653
$910$	0	0
$911$	−17.4234	−0.577262	−0.288631	−	0.957440i	$-0.593200\pi$
$911$	−17.4234	−0.577262	−0.288631	+	0.957440i	$0.593200\pi$
$912$	0	0
$913$	77.0926	2.55139
$914$	0	0
$915$	0	0
$916$	0	0
$917$	59.7148	1.97196
$918$	0	0
$919$	−25.2788	−0.833872	−0.416936	−	0.908936i	$-0.636896\pi$
$919$	−25.2788	−0.833872	−0.416936	+	0.908936i	$0.636896\pi$
$920$	0	0
$921$	−8.73837	−0.287939
$922$	0	0
$923$	8.33812	0.274452
$924$	0	0
$925$	0	0
$926$	0	0
$927$	27.5942	0.906311
$928$	0	0
$929$	0.301140	0.00988007	0.00494004	−	0.999988i	$-0.498428\pi$
$929$	0.301140	0.00988007	0.00494004	+	0.999988i	$0.498428\pi$
$930$	0	0
$931$	3.68385	0.120733
$932$	0	0
$933$	30.2374	0.989927
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−51.2256	−1.67347	−0.836733	−	0.547611i	$-0.815538\pi$
$937$	−51.2256	−1.67347	−0.836733	+	0.547611i	$0.815538\pi$
$938$	0	0
$939$	−22.6965	−0.740671
$940$	0	0
$941$	−57.9926	−1.89050	−0.945252	−	0.326342i	$-0.894184\pi$
$941$	−57.9926	−1.89050	−0.945252	+	0.326342i	$0.894184\pi$
$942$	0	0
$943$	−34.6062	−1.12693
$944$	0	0
$945$	0	0
$946$	0	0
$947$	25.3754	0.824590	0.412295	−	0.911050i	$-0.364727\pi$
$947$	25.3754	0.824590	0.412295	+	0.911050i	$0.364727\pi$
$948$	0	0
$949$	−1.44763	−0.0469922
$950$	0	0
$951$	−24.8853	−0.806962
$952$	0	0
$953$	46.6922	1.51251	0.756254	−	0.654278i	$-0.227028\pi$
$953$	46.6922	1.51251	0.756254	+	0.654278i	$0.227028\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	−4.97838	−0.160928
$958$	0	0
$959$	−21.0049	−0.678283
$960$	0	0
$961$	−29.1392	−0.939974
$962$	0	0
$963$	−26.9497	−0.868443
$964$	0	0
$965$	0	0
$966$	0	0
$967$	38.0513	1.22365	0.611823	−	0.790994i	$-0.290436\pi$
$967$	38.0513	1.22365	0.611823	+	0.790994i	$0.290436\pi$
$968$	0	0
$969$	−0.754087	−0.0242248
$970$	0	0
$971$	−39.6675	−1.27299	−0.636496	−	0.771280i	$-0.719617\pi$
$971$	−39.6675	−1.27299	−0.636496	+	0.771280i	$0.719617\pi$
$972$	0	0
$973$	54.3727	1.74311
$974$	0	0
$975$	0	0
$976$	0	0
$977$	8.82940	0.282477	0.141239	−	0.989976i	$-0.454891\pi$
$977$	8.82940	0.282477	0.141239	+	0.989976i	$0.454891\pi$
$978$	0	0
$979$	−20.3343	−0.649888
$980$	0	0
$981$	−10.1837	−0.325140
$982$	0	0
$983$	31.1423	0.993284	0.496642	−	0.867956i	$-0.334566\pi$
$983$	31.1423	0.993284	0.496642	+	0.867956i	$0.334566\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	32.9707	1.04947
$988$	0	0
$989$	67.5049	2.14653
$990$	0	0
$991$	49.6229	1.57632	0.788162	−	0.615468i	$-0.211033\pi$
$991$	49.6229	1.57632	0.788162	+	0.615468i	$0.211033\pi$
$992$	0	0
$993$	19.8561	0.630115
$994$	0	0
$995$	0	0
$996$	0	0
$997$	8.81848	0.279284	0.139642	−	0.990202i	$-0.455405\pi$
$997$	8.81848	0.279284	0.139642	+	0.990202i	$0.455405\pi$
$998$	0	0
$999$	13.2557	0.419392

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5800.2.a.u.1.2		5
5.4	even	2		1160.2.a.h.1.4	✓	5
20.19	odd	2		2320.2.a.v.1.2		5
40.19	odd	2		9280.2.a.ci.1.4		5
40.29	even	2		9280.2.a.ck.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1160.2.a.h.1.4	✓	5	5.4	even	2
2320.2.a.v.1.2		5	20.19	odd	2
5800.2.a.u.1.2		5	1.1	even	1	trivial
9280.2.a.ci.1.4		5	40.19	odd	2
9280.2.a.ck.1.2		5	40.29	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5800 = 2^{3} \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5800.a (trivial)

\(f(q)\)	\(=\)	\(q-0.959449 q^{3} -4.10933 q^{7} -2.07946 q^{9} +5.18879 q^{11} +0.586839 q^{13} +2.10933 q^{17} +0.372610 q^{19} +3.94270 q^{21} -6.13313 q^{23} +4.87348 q^{27} +1.00000 q^{29} -1.36411 q^{31} -4.97838 q^{33} +2.71997 q^{37} -0.563043 q^{39} +5.64250 q^{41} -11.0066 q^{43} +8.36247 q^{47} +9.88660 q^{49} -2.02380 q^{51} -3.16056 q^{53} -0.357501 q^{57} -6.58684 q^{59} +2.28708 q^{61} +8.54518 q^{63} -7.61725 q^{67} +5.88443 q^{69} +14.2085 q^{71} -2.46683 q^{73} -21.3224 q^{77} +5.30681 q^{79} +1.56251 q^{81} +14.8575 q^{83} -0.959449 q^{87} -3.91890 q^{89} -2.41152 q^{91} +1.30880 q^{93} +6.27069 q^{97} -10.7899 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{3} - 7 q^{7} + 12 q^{9} - 10 q^{11} - 3 q^{13} - 3 q^{17} + 2 q^{19} + 4 q^{21} - 13 q^{23} + 4 q^{27} + 5 q^{29} + 7 q^{31} - 12 q^{33} - 10 q^{37} - q^{39} + 4 q^{41} - 17 q^{43} - 6 q^{47}+ \cdots - 96 q^{99}+O(q^{100}) \) 5 * q + q^3 - 7 * q^7 + 12 * q^9 - 10 * q^11 - 3 * q^13 - 3 * q^17 + 2 * q^19 + 4 * q^21 - 13 * q^23 + 4 * q^27 + 5 * q^29 + 7 * q^31 - 12 * q^33 - 10 * q^37 - q^39 + 4 * q^41 - 17 * q^43 - 6 * q^47 + 28 * q^49 - 6 * q^51 - 5 * q^53 - 26 * q^57 - 27 * q^59 + 21 * q^61 - 54 * q^63 + 10 * q^67 + 25 * q^69 - 4 * q^71 - 23 * q^73 - 2 * q^77 - 3 * q^79 + 57 * q^81 + 12 * q^83 + q^87 - 8 * q^89 + 16 * q^91 - 46 * q^93 - 25 * q^97 - 96 * q^99

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