LMFDB - Embedded newform 5800.2.a.u.1.5

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			1.5
Root			$-1.66804$ 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)

$f(q)$	$=$	$q+3.31966 q^{3} -4.86927 q^{7} +8.02012 q^{9} -4.15085 q^{11} -2.66804 q^{13} +2.86927 q^{17} -0.651620 q^{19} -16.1643 q^{21} +4.65573 q^{23} +16.6651 q^{27} +1.00000 q^{29} -4.17251 q^{31} -13.7794 q^{33} -11.3238 q^{37} -8.85697 q^{39} +3.83684 q^{41} -12.0094 q^{43} -7.48692 q^{47} +16.7098 q^{49} +9.52500 q^{51} -1.61919 q^{53} -2.16316 q^{57} -3.33196 q^{59} -11.0459 q^{61} -39.0522 q^{63} +6.18368 q^{67} +15.4554 q^{69} +0.903244 q^{71} -5.03243 q^{73} +20.2116 q^{77} -11.9918 q^{79} +31.2620 q^{81} -6.22453 q^{83} +3.31966 q^{87} +4.63931 q^{89} +12.9914 q^{91} -13.8513 q^{93} -11.5565 q^{97} -33.2903 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	3.31966	1.91660	0.958302	−	0.285756i	$-0.0922446\pi$
$3$	3.31966	1.91660	0.958302	+	0.285756i	$0.0922446\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	−4.86927	−1.84041	−0.920206	−	0.391434i	$-0.871979\pi$
$7$	−4.86927	−1.84041	−0.920206	+	0.391434i	$0.871979\pi$
$8$	0	0
$9$	8.02012	2.67337
$10$	0	0
$11$	−4.15085	−1.25153	−0.625764	−	0.780012i	$-0.715213\pi$
$11$	−4.15085	−1.25153	−0.625764	+	0.780012i	$0.715213\pi$
$12$	0	0
$13$	−2.66804	−0.739980	−0.369990	−	0.929036i	$-0.620639\pi$
$13$	−2.66804	−0.739980	−0.369990	+	0.929036i	$0.620639\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	2.86927	0.695901	0.347951	−	0.937513i	$-0.386878\pi$
$17$	2.86927	0.695901	0.347951	+	0.937513i	$0.386878\pi$
$18$	0	0
$19$	−0.651620	−0.149492	−0.0747460	−	0.997203i	$-0.523815\pi$
$19$	−0.651620	−0.149492	−0.0747460	+	0.997203i	$0.523815\pi$
$20$	0	0
$21$	−16.1643	−3.52734
$22$	0	0
$23$	4.65573	0.970787	0.485393	−	0.874296i	$-0.338676\pi$
$23$	4.65573	0.970787	0.485393	+	0.874296i	$0.338676\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	16.6651	3.20720
$28$	0	0
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	−4.17251	−0.749406	−0.374703	−	0.927145i	$-0.622255\pi$
$31$	−4.17251	−0.749406	−0.374703	+	0.927145i	$0.622255\pi$
$32$	0	0
$33$	−13.7794	−2.39869
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−11.3238	−1.86162	−0.930808	−	0.365509i	$-0.880895\pi$
$37$	−11.3238	−1.86162	−0.930808	+	0.365509i	$0.880895\pi$
$38$	0	0
$39$	−8.85697	−1.41825
$40$	0	0
$41$	3.83684	0.599214	0.299607	−	0.954063i	$-0.403144\pi$
$41$	3.83684	0.599214	0.299607	+	0.954063i	$0.403144\pi$
$42$	0	0
$43$	−12.0094	−1.83141	−0.915705	−	0.401851i	$-0.868367\pi$
$43$	−12.0094	−1.83141	−0.915705	+	0.401851i	$0.868367\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−7.48692	−1.09208	−0.546040	−	0.837759i	$-0.683865\pi$
$47$	−7.48692	−1.09208	−0.546040	+	0.837759i	$0.683865\pi$
$48$	0	0
$49$	16.7098	2.38712
$50$	0	0
$51$	9.52500	1.33377
$52$	0	0
$53$	−1.61919	−0.222413	−0.111206	−	0.993797i	$-0.535471\pi$
$53$	−1.61919	−0.222413	−0.111206	+	0.993797i	$0.535471\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	−2.16316	−0.286517
$58$	0	0
$59$	−3.33196	−0.433785	−0.216892	−	0.976196i	$-0.569592\pi$
$59$	−3.33196	−0.433785	−0.216892	+	0.976196i	$0.569592\pi$
$60$	0	0
$61$	−11.0459	−1.41428	−0.707141	−	0.707072i	$-0.750015\pi$
$61$	−11.0459	−1.41428	−0.707141	+	0.707072i	$0.750015\pi$
$62$	0	0
$63$	−39.0522	−4.92011
$64$	0	0
$65$	0	0
$66$	0	0
$67$	6.18368	0.755457	0.377729	−	0.925916i	$-0.376705\pi$
$67$	6.18368	0.755457	0.377729	+	0.925916i	$0.376705\pi$
$68$	0	0
$69$	15.4554	1.86062
$70$	0	0
$71$	0.903244	0.107195	0.0535977	−	0.998563i	$-0.482931\pi$
$71$	0.903244	0.107195	0.0535977	+	0.998563i	$0.482931\pi$
$72$	0	0
$73$	−5.03243	−0.589001	−0.294501	−	0.955651i	$-0.595153\pi$
$73$	−5.03243	−0.589001	−0.294501	+	0.955651i	$0.595153\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	20.2116	2.30333
$78$	0	0
$79$	−11.9918	−1.34918	−0.674592	−	0.738191i	$-0.735680\pi$
$79$	−11.9918	−1.34918	−0.674592	+	0.738191i	$0.735680\pi$
$80$	0	0
$81$	31.2620	3.47356
$82$	0	0
$83$	−6.22453	−0.683231	−0.341616	−	0.939840i	$-0.610974\pi$
$83$	−6.22453	−0.683231	−0.341616	+	0.939840i	$0.610974\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	3.31966	0.355905
$88$	0	0
$89$	4.63931	0.491766	0.245883	−	0.969299i	$-0.420922\pi$
$89$	4.63931	0.491766	0.245883	+	0.969299i	$0.420922\pi$
$90$	0	0
$91$	12.9914	1.36187
$92$	0	0
$93$	−13.8513	−1.43631
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−11.5565	−1.17338	−0.586692	−	0.809810i	$-0.699570\pi$
$97$	−11.5565	−1.17338	−0.586692	+	0.809810i	$0.699570\pi$
$98$	0	0
$99$	−33.2903	−3.34580
$100$	0	0
$101$	6.16727	0.613666	0.306833	−	0.951763i	$-0.400731\pi$
$101$	6.16727	0.613666	0.306833	+	0.951763i	$0.400731\pi$
$102$	0	0
$103$	−12.4885	−1.23052	−0.615262	−	0.788322i	$-0.710950\pi$
$103$	−12.4885	−1.23052	−0.615262	+	0.788322i	$0.710950\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−12.7247	−1.23014	−0.615072	−	0.788471i	$-0.710873\pi$
$107$	−12.7247	−1.23014	−0.615072	+	0.788471i	$0.710873\pi$
$108$	0	0
$109$	5.14008	0.492331	0.246165	−	0.969228i	$-0.420829\pi$
$109$	5.14008	0.492331	0.246165	+	0.969228i	$0.420829\pi$
$110$	0	0
$111$	−37.5910	−3.56798
$112$	0	0
$113$	−2.25326	−0.211969	−0.105984	−	0.994368i	$-0.533799\pi$
$113$	−2.25326	−0.211969	−0.105984	+	0.994368i	$0.533799\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	−21.3980	−1.97824
$118$	0	0
$119$	−13.9713	−1.28074
$120$	0	0
$121$	6.22956	0.566323
$122$	0	0
$123$	12.7370	1.14846
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−6.85891	−0.608630	−0.304315	−	0.952571i	$-0.598428\pi$
$127$	−6.85891	−0.608630	−0.304315	+	0.952571i	$0.598428\pi$
$128$	0	0
$129$	−39.8670	−3.51009
$130$	0	0
$131$	6.69187	0.584671	0.292336	−	0.956316i	$-0.405568\pi$
$131$	6.69187	0.584671	0.292336	+	0.956316i	$0.405568\pi$
$132$	0	0
$133$	3.17292	0.275127
$134$	0	0
$135$	0	0
$136$	0	0
$137$	3.12367	0.266873	0.133436	−	0.991057i	$-0.457399\pi$
$137$	3.12367	0.266873	0.133436	+	0.991057i	$0.457399\pi$
$138$	0	0
$139$	−5.42320	−0.459990	−0.229995	−	0.973192i	$-0.573871\pi$
$139$	−5.42320	−0.459990	−0.229995	+	0.973192i	$0.573871\pi$
$140$	0	0
$141$	−24.8540	−2.09309
$142$	0	0
$143$	11.0746	0.926106
$144$	0	0
$145$	0	0
$146$	0	0
$147$	55.4709	4.57516
$148$	0	0
$149$	19.6132	1.60677	0.803386	−	0.595458i	$-0.203029\pi$
$149$	19.6132	1.60677	0.803386	+	0.595458i	$0.203029\pi$
$150$	0	0
$151$	15.0393	1.22388	0.611941	−	0.790903i	$-0.290389\pi$
$151$	15.0393	1.22388	0.611941	+	0.790903i	$0.290389\pi$
$152$	0	0
$153$	23.0119	1.86040
$154$	0	0
$155$	0	0
$156$	0	0
$157$	19.0919	1.52370	0.761848	−	0.647755i	$-0.224292\pi$
$157$	19.0919	1.52370	0.761848	+	0.647755i	$0.224292\pi$
$158$	0	0
$159$	−5.37516	−0.426278
$160$	0	0
$161$	−22.6700	−1.78665
$162$	0	0
$163$	−9.79170	−0.766946	−0.383473	−	0.923552i	$-0.625272\pi$
$163$	−9.79170	−0.766946	−0.383473	+	0.923552i	$0.625272\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−5.77252	−0.446691	−0.223345	−	0.974739i	$-0.571698\pi$
$167$	−5.77252	−0.446691	−0.223345	+	0.974739i	$0.571698\pi$
$168$	0	0
$169$	−5.88158	−0.452429
$170$	0	0
$171$	−5.22608	−0.399648
$172$	0	0
$173$	15.1467	1.15158	0.575790	−	0.817598i	$-0.304695\pi$
$173$	15.1467	1.15158	0.575790	+	0.817598i	$0.304695\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−11.0610	−0.831394
$178$	0	0
$179$	25.7909	1.92770	0.963852	−	0.266438i	$-0.0858468\pi$
$179$	25.7909	1.92770	0.963852	+	0.266438i	$0.0858468\pi$
$180$	0	0
$181$	−1.14008	−0.0847418	−0.0423709	−	0.999102i	$-0.513491\pi$
$181$	−1.14008	−0.0847418	−0.0423709	+	0.999102i	$0.513491\pi$
$182$	0	0
$183$	−36.6686	−2.71062
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−11.9099	−0.870940
$188$	0	0
$189$	−81.1469	−5.90257
$190$	0	0
$191$	3.26927	0.236556	0.118278	−	0.992981i	$-0.462263\pi$
$191$	3.26927	0.236556	0.118278	+	0.992981i	$0.462263\pi$
$192$	0	0
$193$	−11.1893	−0.805426	−0.402713	−	0.915326i	$-0.631933\pi$
$193$	−11.1893	−0.805426	−0.402713	+	0.915326i	$0.631933\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−18.3258	−1.30566	−0.652831	−	0.757504i	$-0.726419\pi$
$197$	−18.3258	−1.30566	−0.652831	+	0.757504i	$0.726419\pi$
$198$	0	0
$199$	−18.9435	−1.34287	−0.671434	−	0.741064i	$-0.734321\pi$
$199$	−18.9435	−1.34287	−0.671434	+	0.741064i	$0.734321\pi$
$200$	0	0
$201$	20.5277	1.44791
$202$	0	0
$203$	−4.86927	−0.341756
$204$	0	0
$205$	0	0
$206$	0	0
$207$	37.3395	2.59528
$208$	0	0
$209$	2.70478	0.187093
$210$	0	0
$211$	5.75579	0.396245	0.198122	−	0.980177i	$-0.436516\pi$
$211$	5.75579	0.396245	0.198122	+	0.980177i	$0.436516\pi$
$212$	0	0
$213$	2.99846	0.205451
$214$	0	0
$215$	0	0
$216$	0	0
$217$	20.3171	1.37922
$218$	0	0
$219$	−16.7059	−1.12888
$220$	0	0
$221$	−7.65533	−0.514953
$222$	0	0
$223$	4.32942	0.289919	0.144960	−	0.989438i	$-0.453695\pi$
$223$	4.32942	0.289919	0.144960	+	0.989438i	$0.453695\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	−11.8648	−0.787493	−0.393747	−	0.919219i	$-0.628821\pi$
$227$	−11.8648	−0.787493	−0.393747	+	0.919219i	$0.628821\pi$
$228$	0	0
$229$	0.160208	0.0105868	0.00529342	−	0.999986i	$-0.498315\pi$
$229$	0.160208	0.0105868	0.00529342	+	0.999986i	$0.498315\pi$
$230$	0	0
$231$	67.0957	4.41457
$232$	0	0
$233$	−19.0820	−1.25011	−0.625053	−	0.780582i	$-0.714923\pi$
$233$	−19.0820	−1.25011	−0.625053	+	0.780582i	$0.714923\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−39.8087	−2.58585
$238$	0	0
$239$	28.5567	1.84718	0.923588	−	0.383386i	$-0.125242\pi$
$239$	28.5567	1.84718	0.923588	+	0.383386i	$0.125242\pi$
$240$	0	0
$241$	−22.8902	−1.47448	−0.737242	−	0.675628i	$-0.763872\pi$
$241$	−22.8902	−1.47448	−0.737242	+	0.675628i	$0.763872\pi$
$242$	0	0
$243$	53.7839	3.45024
$244$	0	0
$245$	0	0
$246$	0	0
$247$	1.73855	0.110621
$248$	0	0
$249$	−20.6633	−1.30948
$250$	0	0
$251$	17.8320	1.12554	0.562771	−	0.826613i	$-0.309735\pi$
$251$	17.8320	1.12554	0.562771	+	0.826613i	$0.309735\pi$
$252$	0	0
$253$	−19.3252	−1.21497
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−12.1385	−0.757182	−0.378591	−	0.925564i	$-0.623591\pi$
$257$	−12.1385	−0.757182	−0.378591	+	0.925564i	$0.623591\pi$
$258$	0	0
$259$	55.1385	3.42614
$260$	0	0
$261$	8.02012	0.496433
$262$	0	0
$263$	15.5920	0.961446	0.480723	−	0.876873i	$-0.340374\pi$
$263$	15.5920	0.961446	0.480723	+	0.876873i	$0.340374\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	15.4009	0.942522
$268$	0	0
$269$	−2.51996	−0.153645	−0.0768223	−	0.997045i	$-0.524477\pi$
$269$	−2.51996	−0.153645	−0.0768223	+	0.997045i	$0.524477\pi$
$270$	0	0
$271$	−29.6682	−1.80221	−0.901107	−	0.433597i	$-0.857244\pi$
$271$	−29.6682	−1.80221	−0.901107	+	0.433597i	$0.857244\pi$
$272$	0	0
$273$	43.1270	2.61016
$274$	0	0
$275$	0	0
$276$	0	0
$277$	20.4836	1.23074	0.615369	−	0.788239i	$-0.289007\pi$
$277$	20.4836	1.23074	0.615369	+	0.788239i	$0.289007\pi$
$278$	0	0
$279$	−33.4641	−2.00344
$280$	0	0
$281$	−24.9709	−1.48964	−0.744819	−	0.667266i	$-0.767464\pi$
$281$	−24.9709	−1.48964	−0.744819	+	0.667266i	$0.767464\pi$
$282$	0	0
$283$	2.15085	0.127855	0.0639274	−	0.997955i	$-0.479637\pi$
$283$	2.15085	0.127855	0.0639274	+	0.997955i	$0.479637\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	−18.6826	−1.10280
$288$	0	0
$289$	−8.76727	−0.515722
$290$	0	0
$291$	−38.3636	−2.24891
$292$	0	0
$293$	21.5303	1.25781	0.628905	−	0.777482i	$-0.283503\pi$
$293$	21.5303	1.25781	0.628905	+	0.777482i	$0.283503\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−69.1743	−4.01390
$298$	0	0
$299$	−12.4217	−0.718363
$300$	0	0
$301$	58.4768	3.37055
$302$	0	0
$303$	20.4732	1.17616
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−8.79016	−0.501681	−0.250841	−	0.968028i	$-0.580707\pi$
$307$	−8.79016	−0.501681	−0.250841	+	0.968028i	$0.580707\pi$
$308$	0	0
$309$	−41.4574	−2.35843
$310$	0	0
$311$	−0.911439	−0.0516830	−0.0258415	−	0.999666i	$-0.508227\pi$
$311$	−0.911439	−0.0516830	−0.0258415	+	0.999666i	$0.508227\pi$
$312$	0	0
$313$	23.8556	1.34840	0.674198	−	0.738551i	$-0.264489\pi$
$313$	23.8556	1.34840	0.674198	+	0.738551i	$0.264489\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	1.72932	0.0971284	0.0485642	−	0.998820i	$-0.484535\pi$
$317$	1.72932	0.0971284	0.0485642	+	0.998820i	$0.484535\pi$
$318$	0	0
$319$	−4.15085	−0.232403
$320$	0	0
$321$	−42.2416	−2.35770
$322$	0	0
$323$	−1.86968	−0.104032
$324$	0	0
$325$	0	0
$326$	0	0
$327$	17.0633	0.943604
$328$	0	0
$329$	36.4559	2.00988
$330$	0	0
$331$	17.5032	0.962061	0.481030	−	0.876704i	$-0.340263\pi$
$331$	17.5032	0.962061	0.481030	+	0.876704i	$0.340263\pi$
$332$	0	0
$333$	−90.8180	−4.97680
$334$	0	0
$335$	0	0
$336$	0	0
$337$	30.0504	1.63695	0.818475	−	0.574542i	$-0.194820\pi$
$337$	30.0504	1.63695	0.818475	+	0.574542i	$0.194820\pi$
$338$	0	0
$339$	−7.48004	−0.406260
$340$	0	0
$341$	17.3195	0.937902
$342$	0	0
$343$	−47.2798	−2.55287
$344$	0	0
$345$	0	0
$346$	0	0
$347$	20.0967	1.07885	0.539423	−	0.842035i	$-0.318642\pi$
$347$	20.0967	1.07885	0.539423	+	0.842035i	$0.318642\pi$
$348$	0	0
$349$	5.31065	0.284273	0.142136	−	0.989847i	$-0.454603\pi$
$349$	5.31065	0.284273	0.142136	+	0.989847i	$0.454603\pi$
$350$	0	0
$351$	−44.4631	−2.37326
$352$	0	0
$353$	0.497689	0.0264893	0.0132447	−	0.999912i	$-0.495784\pi$
$353$	0.497689	0.0264893	0.0132447	+	0.999912i	$0.495784\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	−46.3799	−2.45468
$358$	0	0
$359$	−9.25419	−0.488418	−0.244209	−	0.969723i	$-0.578528\pi$
$359$	−9.25419	−0.488418	−0.244209	+	0.969723i	$0.578528\pi$
$360$	0	0
$361$	−18.5754	−0.977652
$362$	0	0
$363$	20.6800	1.08542
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−22.1509	−1.15626	−0.578132	−	0.815943i	$-0.696218\pi$
$367$	−22.1509	−1.15626	−0.578132	+	0.815943i	$0.696218\pi$
$368$	0	0
$369$	30.7720	1.60192
$370$	0	0
$371$	7.88428	0.409332
$372$	0	0
$373$	−22.9292	−1.18723	−0.593616	−	0.804749i	$-0.702300\pi$
$373$	−22.9292	−1.18723	−0.593616	+	0.804749i	$0.702300\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−2.66804	−0.137411
$378$	0	0
$379$	22.3247	1.14674	0.573371	−	0.819296i	$-0.305635\pi$
$379$	22.3247	1.14674	0.573371	+	0.819296i	$0.305635\pi$
$380$	0	0
$381$	−22.7692	−1.16650
$382$	0	0
$383$	−2.69542	−0.137730	−0.0688648	−	0.997626i	$-0.521938\pi$
$383$	−2.69542	−0.137730	−0.0688648	+	0.997626i	$0.521938\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−96.3165	−4.89604
$388$	0	0
$389$	8.53280	0.432630	0.216315	−	0.976324i	$-0.430596\pi$
$389$	8.53280	0.432630	0.216315	+	0.976324i	$0.430596\pi$
$390$	0	0
$391$	13.3586	0.675572
$392$	0	0
$393$	22.2147	1.12058
$394$	0	0
$395$	0	0
$396$	0	0
$397$	24.0782	1.20845	0.604224	−	0.796815i	$-0.293483\pi$
$397$	24.0782	1.20845	0.604224	+	0.796815i	$0.293483\pi$
$398$	0	0
$399$	10.5330	0.527309
$400$	0	0
$401$	7.57376	0.378215	0.189108	−	0.981956i	$-0.439440\pi$
$401$	7.57376	0.378215	0.189108	+	0.981956i	$0.439440\pi$
$402$	0	0
$403$	11.1324	0.554545
$404$	0	0
$405$	0	0
$406$	0	0
$407$	47.0033	2.32987
$408$	0	0
$409$	30.8189	1.52390	0.761949	−	0.647638i	$-0.224243\pi$
$409$	30.8189	1.52390	0.761949	+	0.647638i	$0.224243\pi$
$410$	0	0
$411$	10.3695	0.511490
$412$	0	0
$413$	16.2242	0.798343
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−18.0032	−0.881619
$418$	0	0
$419$	−11.8881	−0.580770	−0.290385	−	0.956910i	$-0.593783\pi$
$419$	−11.8881	−0.580770	−0.290385	+	0.956910i	$0.593783\pi$
$420$	0	0
$421$	14.3754	0.700613	0.350307	−	0.936635i	$-0.386077\pi$
$421$	14.3754	0.700613	0.350307	+	0.936635i	$0.386077\pi$
$422$	0	0
$423$	−60.0461	−2.91954
$424$	0	0
$425$	0	0
$426$	0	0
$427$	53.7855	2.60286
$428$	0	0
$429$	36.7639	1.77498
$430$	0	0
$431$	−23.0884	−1.11213	−0.556064	−	0.831139i	$-0.687689\pi$
$431$	−23.0884	−1.11213	−0.556064	+	0.831139i	$0.687689\pi$
$432$	0	0
$433$	24.2968	1.16763	0.583815	−	0.811887i	$-0.301559\pi$
$433$	24.2968	1.16763	0.583815	+	0.811887i	$0.301559\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	−3.03377	−0.145125
$438$	0	0
$439$	14.1057	0.673229	0.336614	−	0.941643i	$-0.390718\pi$
$439$	14.1057	0.673229	0.336614	+	0.941643i	$0.390718\pi$
$440$	0	0
$441$	134.015	6.38166
$442$	0	0
$443$	13.7870	0.655040	0.327520	−	0.944844i	$-0.393787\pi$
$443$	13.7870	0.655040	0.327520	+	0.944844i	$0.393787\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	65.1090	3.07955
$448$	0	0
$449$	21.4828	1.01384	0.506919	−	0.861994i	$-0.330784\pi$
$449$	21.4828	1.01384	0.506919	+	0.861994i	$0.330784\pi$
$450$	0	0
$451$	−15.9262	−0.749934
$452$	0	0
$453$	49.9254	2.34570
$454$	0	0
$455$	0	0
$456$	0	0
$457$	9.07710	0.424609	0.212304	−	0.977204i	$-0.431903\pi$
$457$	9.07710	0.424609	0.212304	+	0.977204i	$0.431903\pi$
$458$	0	0
$459$	47.8167	2.23189
$460$	0	0
$461$	12.4619	0.580409	0.290204	−	0.956965i	$-0.406277\pi$
$461$	12.4619	0.580409	0.290204	+	0.956965i	$0.406277\pi$
$462$	0	0
$463$	6.66232	0.309624	0.154812	−	0.987944i	$-0.450523\pi$
$463$	6.66232	0.309624	0.154812	+	0.987944i	$0.450523\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	23.5494	1.08974	0.544869	−	0.838521i	$-0.316579\pi$
$467$	23.5494	1.08974	0.544869	+	0.838521i	$0.316579\pi$
$468$	0	0
$469$	−30.1100	−1.39035
$470$	0	0
$471$	63.3784	2.92032
$472$	0	0
$473$	49.8490	2.29206
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−12.9861	−0.594593
$478$	0	0
$479$	11.1199	0.508081	0.254040	−	0.967194i	$-0.418240\pi$
$479$	11.1199	0.508081	0.254040	+	0.967194i	$0.418240\pi$
$480$	0	0
$481$	30.2122	1.37756
$482$	0	0
$483$	−75.2567	−3.42430
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−16.2803	−0.737733	−0.368866	−	0.929482i	$-0.620254\pi$
$487$	−16.2803	−0.737733	−0.368866	+	0.929482i	$0.620254\pi$
$488$	0	0
$489$	−32.5051	−1.46993
$490$	0	0
$491$	−21.8157	−0.984529	−0.492265	−	0.870446i	$-0.663831\pi$
$491$	−21.8157	−0.984529	−0.492265	+	0.870446i	$0.663831\pi$
$492$	0	0
$493$	2.86927	0.129226
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−4.39814	−0.197284
$498$	0	0
$499$	−40.6010	−1.81755	−0.908775	−	0.417286i	$-0.862981\pi$
$499$	−40.6010	−1.81755	−0.908775	+	0.417286i	$0.862981\pi$
$500$	0	0
$501$	−19.1628	−0.856130
$502$	0	0
$503$	−18.6869	−0.833209	−0.416605	−	0.909088i	$-0.636780\pi$
$503$	−18.6869	−0.833209	−0.416605	+	0.909088i	$0.636780\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−19.5248	−0.867128
$508$	0	0
$509$	7.46948	0.331079	0.165539	−	0.986203i	$-0.447063\pi$
$509$	7.46948	0.331079	0.165539	+	0.986203i	$0.447063\pi$
$510$	0	0
$511$	24.5043	1.08401
$512$	0	0
$513$	−10.8593	−0.479450
$514$	0	0
$515$	0	0
$516$	0	0
$517$	31.0771	1.36677
$518$	0	0
$519$	50.2818	2.20712
$520$	0	0
$521$	24.9325	1.09231	0.546157	−	0.837683i	$-0.316090\pi$
$521$	24.9325	1.09231	0.546157	+	0.837683i	$0.316090\pi$
$522$	0	0
$523$	3.42948	0.149961	0.0749803	−	0.997185i	$-0.476111\pi$
$523$	3.42948	0.149961	0.0749803	+	0.997185i	$0.476111\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−11.9721	−0.521512
$528$	0	0
$529$	−1.32417	−0.0575727
$530$	0	0
$531$	−26.7228	−1.15967
$532$	0	0
$533$	−10.2368	−0.443407
$534$	0	0
$535$	0	0
$536$	0	0
$537$	85.6170	3.69465
$538$	0	0
$539$	−69.3600	−2.98755
$540$	0	0
$541$	37.0013	1.59081	0.795404	−	0.606079i	$-0.207259\pi$
$541$	37.0013	1.59081	0.795404	+	0.606079i	$0.207259\pi$
$542$	0	0
$543$	−3.78469	−0.162417
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−0.773925	−0.0330906	−0.0165453	−	0.999863i	$-0.505267\pi$
$547$	−0.773925	−0.0330906	−0.0165453	+	0.999863i	$0.505267\pi$
$548$	0	0
$549$	−88.5895	−3.78091
$550$	0	0
$551$	−0.651620	−0.0277600
$552$	0	0
$553$	58.3914	2.48305
$554$	0	0
$555$	0	0
$556$	0	0
$557$	12.1255	0.513772	0.256886	−	0.966442i	$-0.417303\pi$
$557$	12.1255	0.513772	0.256886	+	0.966442i	$0.417303\pi$
$558$	0	0
$559$	32.0414	1.35521
$560$	0	0
$561$	−39.5369	−1.66925
$562$	0	0
$563$	−9.19346	−0.387458	−0.193729	−	0.981055i	$-0.562058\pi$
$563$	−9.19346	−0.387458	−0.193729	+	0.981055i	$0.562058\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	−152.223	−6.39278
$568$	0	0
$569$	−23.8205	−0.998605	−0.499303	−	0.866428i	$-0.666410\pi$
$569$	−23.8205	−0.998605	−0.499303	+	0.866428i	$0.666410\pi$
$570$	0	0
$571$	2.10241	0.0879830	0.0439915	−	0.999032i	$-0.485993\pi$
$571$	2.10241	0.0879830	0.0439915	+	0.999032i	$0.485993\pi$
$572$	0	0
$573$	10.8529	0.453385
$574$	0	0
$575$	0	0
$576$	0	0
$577$	23.6447	0.984340	0.492170	−	0.870499i	$-0.336204\pi$
$577$	23.6447	0.984340	0.492170	+	0.870499i	$0.336204\pi$
$578$	0	0
$579$	−37.1448	−1.54368
$580$	0	0
$581$	30.3090	1.25743
$582$	0	0
$583$	6.72102	0.278356
$584$	0	0
$585$	0	0
$586$	0	0
$587$	39.8402	1.64438	0.822190	−	0.569213i	$-0.192752\pi$
$587$	39.8402	1.64438	0.822190	+	0.569213i	$0.192752\pi$
$588$	0	0
$589$	2.71890	0.112030
$590$	0	0
$591$	−60.8355	−2.50244
$592$	0	0
$593$	−24.9478	−1.02448	−0.512242	−	0.858841i	$-0.671185\pi$
$593$	−24.9478	−1.02448	−0.512242	+	0.858841i	$0.671185\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−62.8859	−2.57375
$598$	0	0
$599$	−7.24961	−0.296211	−0.148106	−	0.988972i	$-0.547318\pi$
$599$	−7.24961	−0.296211	−0.148106	+	0.988972i	$0.547318\pi$
$600$	0	0
$601$	−7.54069	−0.307591	−0.153796	−	0.988103i	$-0.549150\pi$
$601$	−7.54069	−0.307591	−0.153796	+	0.988103i	$0.549150\pi$
$602$	0	0
$603$	49.5939	2.01962
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−4.21138	−0.170934	−0.0854672	−	0.996341i	$-0.527238\pi$
$607$	−4.21138	−0.170934	−0.0854672	+	0.996341i	$0.527238\pi$
$608$	0	0
$609$	−16.1643	−0.655011
$610$	0	0
$611$	19.9754	0.808118
$612$	0	0
$613$	−48.0535	−1.94086	−0.970432	−	0.241374i	$-0.922402\pi$
$613$	−48.0535	−1.94086	−0.970432	+	0.241374i	$0.922402\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	23.2408	0.935638	0.467819	−	0.883824i	$-0.345040\pi$
$617$	23.2408	0.935638	0.467819	+	0.883824i	$0.345040\pi$
$618$	0	0
$619$	12.6213	0.507291	0.253646	−	0.967297i	$-0.418370\pi$
$619$	12.6213	0.507291	0.253646	+	0.967297i	$0.418370\pi$
$620$	0	0
$621$	77.5882	3.11351
$622$	0	0
$623$	−22.5901	−0.905053
$624$	0	0
$625$	0	0
$626$	0	0
$627$	8.97894	0.358584
$628$	0	0
$629$	−32.4910	−1.29550
$630$	0	0
$631$	9.33219	0.371508	0.185754	−	0.982596i	$-0.440527\pi$
$631$	9.33219	0.371508	0.185754	+	0.982596i	$0.440527\pi$
$632$	0	0
$633$	19.1073	0.759445
$634$	0	0
$635$	0	0
$636$	0	0
$637$	−44.5824	−1.76642
$638$	0	0
$639$	7.24413	0.286573
$640$	0	0
$641$	3.88607	0.153490	0.0767452	−	0.997051i	$-0.475547\pi$
$641$	3.88607	0.153490	0.0767452	+	0.997051i	$0.475547\pi$
$642$	0	0
$643$	0.118824	0.00468596	0.00234298	−	0.999997i	$-0.499254\pi$
$643$	0.118824	0.00468596	0.00234298	+	0.999997i	$0.499254\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	9.87034	0.388043	0.194022	−	0.980997i	$-0.437847\pi$
$647$	9.87034	0.388043	0.194022	+	0.980997i	$0.437847\pi$
$648$	0	0
$649$	13.8305	0.542894
$650$	0	0
$651$	67.4458	2.64341
$652$	0	0
$653$	−25.5818	−1.00109	−0.500547	−	0.865710i	$-0.666868\pi$
$653$	−25.5818	−1.00109	−0.500547	+	0.865710i	$0.666868\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−40.3607	−1.57462
$658$	0	0
$659$	−36.0505	−1.40433	−0.702165	−	0.712014i	$-0.747783\pi$
$659$	−36.0505	−1.40433	−0.702165	+	0.712014i	$0.747783\pi$
$660$	0	0
$661$	−21.7084	−0.844358	−0.422179	−	0.906512i	$-0.638735\pi$
$661$	−21.7084	−0.844358	−0.422179	+	0.906512i	$0.638735\pi$
$662$	0	0
$663$	−25.4131	−0.986962
$664$	0	0
$665$	0	0
$666$	0	0
$667$	4.65573	0.180271
$668$	0	0
$669$	14.3722	0.555661
$670$	0	0
$671$	45.8499	1.77001
$672$	0	0
$673$	−32.6252	−1.25761	−0.628804	−	0.777563i	$-0.716455\pi$
$673$	−32.6252	−1.25761	−0.628804	+	0.777563i	$0.716455\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	−7.41384	−0.284937	−0.142469	−	0.989799i	$-0.545504\pi$
$677$	−7.41384	−0.284937	−0.142469	+	0.989799i	$0.545504\pi$
$678$	0	0
$679$	56.2717	2.15951
$680$	0	0
$681$	−39.3870	−1.50931
$682$	0	0
$683$	38.6608	1.47931	0.739656	−	0.672985i	$-0.234988\pi$
$683$	38.6608	1.47931	0.739656	+	0.672985i	$0.234988\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0.531836	0.0202908
$688$	0	0
$689$	4.32006	0.164581
$690$	0	0
$691$	1.34724	0.0512515	0.0256258	−	0.999672i	$-0.491842\pi$
$691$	1.34724	0.0512515	0.0256258	+	0.999672i	$0.491842\pi$
$692$	0	0
$693$	162.100	6.15766
$694$	0	0
$695$	0	0
$696$	0	0
$697$	11.0090	0.416994
$698$	0	0
$699$	−63.3458	−2.39596
$700$	0	0
$701$	15.2328	0.575336	0.287668	−	0.957730i	$-0.407120\pi$
$701$	15.2328	0.575336	0.287668	+	0.957730i	$0.407120\pi$
$702$	0	0
$703$	7.37880	0.278297
$704$	0	0
$705$	0	0
$706$	0	0
$707$	−30.0301	−1.12940
$708$	0	0
$709$	−13.5672	−0.509526	−0.254763	−	0.967004i	$-0.581997\pi$
$709$	−13.5672	−0.509526	−0.254763	+	0.967004i	$0.581997\pi$
$710$	0	0
$711$	−96.1758	−3.60687
$712$	0	0
$713$	−19.4261	−0.727513
$714$	0	0
$715$	0	0
$716$	0	0
$717$	94.7983	3.54031
$718$	0	0
$719$	−27.1855	−1.01385	−0.506924	−	0.861991i	$-0.669217\pi$
$719$	−27.1855	−1.01385	−0.506924	+	0.861991i	$0.669217\pi$
$720$	0	0
$721$	60.8097	2.26467
$722$	0	0
$723$	−75.9875	−2.82600
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−20.7284	−0.768773	−0.384387	−	0.923172i	$-0.625587\pi$
$727$	−20.7284	−0.768773	−0.384387	+	0.923172i	$0.625587\pi$
$728$	0	0
$729$	84.7580	3.13919
$730$	0	0
$731$	−34.4581	−1.27448
$732$	0	0
$733$	−21.7008	−0.801538	−0.400769	−	0.916179i	$-0.631257\pi$
$733$	−21.7008	−0.801538	−0.400769	+	0.916179i	$0.631257\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−25.6675	−0.945476
$738$	0	0
$739$	39.7154	1.46095	0.730477	−	0.682937i	$-0.239298\pi$
$739$	39.7154	1.46095	0.730477	+	0.682937i	$0.239298\pi$
$740$	0	0
$741$	5.77138	0.212017
$742$	0	0
$743$	33.1821	1.21733	0.608667	−	0.793426i	$-0.291704\pi$
$743$	33.1821	1.21733	0.608667	+	0.793426i	$0.291704\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−49.9215	−1.82653
$748$	0	0
$749$	61.9600	2.26397
$750$	0	0
$751$	−7.11400	−0.259594	−0.129797	−	0.991541i	$-0.541432\pi$
$751$	−7.11400	−0.259594	−0.129797	+	0.991541i	$0.541432\pi$
$752$	0	0
$753$	59.1960	2.15722
$754$	0	0
$755$	0	0
$756$	0	0
$757$	10.0942	0.366880	0.183440	−	0.983031i	$-0.441277\pi$
$757$	10.0942	0.366880	0.183440	+	0.983031i	$0.441277\pi$
$758$	0	0
$759$	−64.1532	−2.32861
$760$	0	0
$761$	−46.1079	−1.67141	−0.835705	−	0.549178i	$-0.814941\pi$
$761$	−46.1079	−1.67141	−0.835705	+	0.549178i	$0.814941\pi$
$762$	0	0
$763$	−25.0285	−0.906092
$764$	0	0
$765$	0	0
$766$	0	0
$767$	8.88980	0.320992
$768$	0	0
$769$	−32.8015	−1.18285	−0.591426	−	0.806359i	$-0.701435\pi$
$769$	−32.8015	−1.18285	−0.591426	+	0.806359i	$0.701435\pi$
$770$	0	0
$771$	−40.2958	−1.45122
$772$	0	0
$773$	−32.7754	−1.17885	−0.589425	−	0.807823i	$-0.700646\pi$
$773$	−32.7754	−1.17885	−0.589425	+	0.807823i	$0.700646\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	183.041	6.56656
$778$	0	0
$779$	−2.50017	−0.0895777
$780$	0	0
$781$	−3.74923	−0.134158
$782$	0	0
$783$	16.6651	0.595562
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−5.78534	−0.206225	−0.103113	−	0.994670i	$-0.532880\pi$
$787$	−5.78534	−0.206225	−0.103113	+	0.994670i	$0.532880\pi$
$788$	0	0
$789$	51.7602	1.84271
$790$	0	0
$791$	10.9717	0.390110
$792$	0	0
$793$	29.4709	1.04654
$794$	0	0
$795$	0	0
$796$	0	0
$797$	41.1649	1.45814	0.729069	−	0.684441i	$-0.239954\pi$
$797$	41.1649	1.45814	0.729069	+	0.684441i	$0.239954\pi$
$798$	0	0
$799$	−21.4820	−0.759980
$800$	0	0
$801$	37.2079	1.31468
$802$	0	0
$803$	20.8889	0.737152
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−8.36540	−0.294476
$808$	0	0
$809$	21.2043	0.745505	0.372752	−	0.927931i	$-0.378414\pi$
$809$	21.2043	0.745505	0.372752	+	0.927931i	$0.378414\pi$
$810$	0	0
$811$	−23.6539	−0.830600	−0.415300	−	0.909684i	$-0.636323\pi$
$811$	−23.6539	−0.830600	−0.415300	+	0.909684i	$0.636323\pi$
$812$	0	0
$813$	−98.4882	−3.45413
$814$	0	0
$815$	0	0
$816$	0	0
$817$	7.82554	0.273781
$818$	0	0
$819$	104.193	3.64079
$820$	0	0
$821$	−39.5689	−1.38096	−0.690482	−	0.723350i	$-0.742601\pi$
$821$	−39.5689	−1.38096	−0.690482	+	0.723350i	$0.742601\pi$
$822$	0	0
$823$	−37.3564	−1.30216	−0.651082	−	0.759007i	$-0.725685\pi$
$823$	−37.3564	−1.30216	−0.651082	+	0.759007i	$0.725685\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−11.5482	−0.401571	−0.200786	−	0.979635i	$-0.564349\pi$
$827$	−11.5482	−0.401571	−0.200786	+	0.979635i	$0.564349\pi$
$828$	0	0
$829$	−44.0314	−1.52927	−0.764637	−	0.644461i	$-0.777082\pi$
$829$	−44.0314	−1.52927	−0.764637	+	0.644461i	$0.777082\pi$
$830$	0	0
$831$	67.9984	2.35884
$832$	0	0
$833$	47.9451	1.66120
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−69.5353	−2.40349
$838$	0	0
$839$	42.7875	1.47719	0.738595	−	0.674150i	$-0.235490\pi$
$839$	42.7875	1.47719	0.738595	+	0.674150i	$0.235490\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	0	0
$843$	−82.8948	−2.85505
$844$	0	0
$845$	0	0
$846$	0	0
$847$	−30.3334	−1.04227
$848$	0	0
$849$	7.14008	0.245047
$850$	0	0
$851$	−52.7204	−1.80723
$852$	0	0
$853$	−8.01745	−0.274512	−0.137256	−	0.990536i	$-0.543828\pi$
$853$	−8.01745	−0.274512	−0.137256	+	0.990536i	$0.543828\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−19.0264	−0.649928	−0.324964	−	0.945726i	$-0.605352\pi$
$857$	−19.0264	−0.649928	−0.324964	+	0.945726i	$0.605352\pi$
$858$	0	0
$859$	16.0665	0.548183	0.274091	−	0.961704i	$-0.411623\pi$
$859$	16.0665	0.548183	0.274091	+	0.961704i	$0.411623\pi$
$860$	0	0
$861$	−62.0200	−2.11363
$862$	0	0
$863$	21.8935	0.745264	0.372632	−	0.927979i	$-0.378455\pi$
$863$	21.8935	0.745264	0.372632	+	0.927979i	$0.378455\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−29.1043	−0.988435
$868$	0	0
$869$	49.7762	1.68854
$870$	0	0
$871$	−16.4983	−0.559023
$872$	0	0
$873$	−92.6845	−3.13690
$874$	0	0
$875$	0	0
$876$	0	0
$877$	1.03848	0.0350671	0.0175336	−	0.999846i	$-0.494419\pi$
$877$	1.03848	0.0350671	0.0175336	+	0.999846i	$0.494419\pi$
$878$	0	0
$879$	71.4731	2.41073
$880$	0	0
$881$	−9.77305	−0.329262	−0.164631	−	0.986355i	$-0.552643\pi$
$881$	−9.77305	−0.329262	−0.164631	+	0.986355i	$0.552643\pi$
$882$	0	0
$883$	−50.0428	−1.68407	−0.842037	−	0.539420i	$-0.818643\pi$
$883$	−50.0428	−1.68407	−0.842037	+	0.539420i	$0.818643\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−56.5443	−1.89857	−0.949287	−	0.314412i	$-0.898193\pi$
$887$	−56.5443	−1.89857	−0.949287	+	0.314412i	$0.898193\pi$
$888$	0	0
$889$	33.3979	1.12013
$890$	0	0
$891$	−129.764	−4.34725
$892$	0	0
$893$	4.87863	0.163257
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−41.2357	−1.37682
$898$	0	0
$899$	−4.17251	−0.139161
$900$	0	0
$901$	−4.64590	−0.154777
$902$	0	0
$903$	194.123	6.46001
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−26.7482	−0.888161	−0.444080	−	0.895987i	$-0.646470\pi$
$907$	−26.7482	−0.888161	−0.444080	+	0.895987i	$0.646470\pi$
$908$	0	0
$909$	49.4622	1.64056
$910$	0	0
$911$	−14.6243	−0.484525	−0.242262	−	0.970211i	$-0.577890\pi$
$911$	−14.6243	−0.484525	−0.242262	+	0.970211i	$0.577890\pi$
$912$	0	0
$913$	25.8371	0.855084
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−32.5845	−1.07604
$918$	0	0
$919$	−11.1194	−0.366794	−0.183397	−	0.983039i	$-0.558709\pi$
$919$	−11.1194	−0.366794	−0.183397	+	0.983039i	$0.558709\pi$
$920$	0	0
$921$	−29.1803	−0.961525
$922$	0	0
$923$	−2.40989	−0.0793224
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−100.159	−3.28965
$928$	0	0
$929$	24.6772	0.809633	0.404817	−	0.914398i	$-0.367335\pi$
$929$	24.6772	0.809633	0.404817	+	0.914398i	$0.367335\pi$
$930$	0	0
$931$	−10.8885	−0.356855
$932$	0	0
$933$	−3.02567	−0.0990559
$934$	0	0
$935$	0	0
$936$	0	0
$937$	15.5204	0.507030	0.253515	−	0.967332i	$-0.418413\pi$
$937$	15.5204	0.507030	0.253515	+	0.967332i	$0.418413\pi$
$938$	0	0
$939$	79.1923	2.58434
$940$	0	0
$941$	−40.1203	−1.30788	−0.653942	−	0.756545i	$-0.726886\pi$
$941$	−40.1203	−1.30788	−0.653942	+	0.756545i	$0.726886\pi$
$942$	0	0
$943$	17.8633	0.581709
$944$	0	0
$945$	0	0
$946$	0	0
$947$	37.2969	1.21199	0.605993	−	0.795470i	$-0.292776\pi$
$947$	37.2969	1.21199	0.605993	+	0.795470i	$0.292776\pi$
$948$	0	0
$949$	13.4267	0.435849
$950$	0	0
$951$	5.74076	0.186157
$952$	0	0
$953$	6.00495	0.194520	0.0972598	−	0.995259i	$-0.468992\pi$
$953$	6.00495	0.194520	0.0972598	+	0.995259i	$0.468992\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	−13.7794	−0.445425
$958$	0	0
$959$	−15.2100	−0.491156
$960$	0	0
$961$	−13.5901	−0.438391
$962$	0	0
$963$	−102.054	−3.28863
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−10.0255	−0.322397	−0.161199	−	0.986922i	$-0.551536\pi$
$967$	−10.0255	−0.322397	−0.161199	+	0.986922i	$0.551536\pi$
$968$	0	0
$969$	−6.20669	−0.199387
$970$	0	0
$971$	0.278092	0.00892439	0.00446220	−	0.999990i	$-0.498580\pi$
$971$	0.278092	0.00892439	0.00446220	+	0.999990i	$0.498580\pi$
$972$	0	0
$973$	26.4071	0.846571
$974$	0	0
$975$	0	0
$976$	0	0
$977$	2.51949	0.0806055	0.0403028	−	0.999188i	$-0.487168\pi$
$977$	2.51949	0.0806055	0.0403028	+	0.999188i	$0.487168\pi$
$978$	0	0
$979$	−19.2571	−0.615460
$980$	0	0
$981$	41.2241	1.31618
$982$	0	0
$983$	2.08907	0.0666311	0.0333155	−	0.999445i	$-0.489393\pi$
$983$	2.08907	0.0666311	0.0333155	+	0.999445i	$0.489393\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	121.021	3.85214
$988$	0	0
$989$	−55.9123	−1.77791
$990$	0	0
$991$	−14.8717	−0.472414	−0.236207	−	0.971703i	$-0.575904\pi$
$991$	−14.8717	−0.472414	−0.236207	+	0.971703i	$0.575904\pi$
$992$	0	0
$993$	58.1045	1.84389
$994$	0	0
$995$	0	0
$996$	0	0
$997$	59.7507	1.89232	0.946162	−	0.323694i	$-0.104925\pi$
$997$	59.7507	1.89232	0.946162	+	0.323694i	$0.104925\pi$
$998$	0	0
$999$	−188.712	−5.97057

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5800.2.a.u.1.5		5
5.4	even	2		1160.2.a.h.1.1	✓	5
20.19	odd	2		2320.2.a.v.1.5		5
40.19	odd	2		9280.2.a.ci.1.1		5
40.29	even	2		9280.2.a.ck.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1160.2.a.h.1.1	✓	5	5.4	even	2
2320.2.a.v.1.5		5	20.19	odd	2
5800.2.a.u.1.5		5	1.1	even	1	trivial
9280.2.a.ci.1.1		5	40.19	odd	2
9280.2.a.ck.1.5		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)

\(f(q)\)	\(=\)	\(q+3.31966 q^{3} -4.86927 q^{7} +8.02012 q^{9} -4.15085 q^{11} -2.66804 q^{13} +2.86927 q^{17} -0.651620 q^{19} -16.1643 q^{21} +4.65573 q^{23} +16.6651 q^{27} +1.00000 q^{29} -4.17251 q^{31} -13.7794 q^{33} -11.3238 q^{37} -8.85697 q^{39} +3.83684 q^{41} -12.0094 q^{43} -7.48692 q^{47} +16.7098 q^{49} +9.52500 q^{51} -1.61919 q^{53} -2.16316 q^{57} -3.33196 q^{59} -11.0459 q^{61} -39.0522 q^{63} +6.18368 q^{67} +15.4554 q^{69} +0.903244 q^{71} -5.03243 q^{73} +20.2116 q^{77} -11.9918 q^{79} +31.2620 q^{81} -6.22453 q^{83} +3.31966 q^{87} +4.63931 q^{89} +12.9914 q^{91} -13.8513 q^{93} -11.5565 q^{97} -33.2903 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{3} - 7 q^{7} + 12 q^{9} - 10 q^{11} - 3 q^{13} - 3 q^{17} + 2 q^{19} + 4 q^{21} - 13 q^{23} + 4 q^{27} + 5 q^{29} + 7 q^{31} - 12 q^{33} - 10 q^{37} - q^{39} + 4 q^{41} - 17 q^{43} - 6 q^{47}+ \cdots - 96 q^{99}+O(q^{100}) \) 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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