LMFDB - Embedded newform 5800.2.a.u.1.3

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			1.3
Root			$-2.28850$ 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)

$f(q)$	$=$	$q-0.184115 q^{3} +1.70985 q^{7} -2.96610 q^{9} +0.256255 q^{11} -3.28850 q^{13} -3.70985 q^{17} +3.47261 q^{19} -0.314808 q^{21} +2.39289 q^{23} +1.09845 q^{27} +1.00000 q^{29} +10.6551 q^{31} -0.0471803 q^{33} -9.68138 q^{37} +0.605462 q^{39} +5.36064 q^{41} +1.29444 q^{43} -4.32075 q^{47} -4.07642 q^{49} +0.683038 q^{51} -5.59787 q^{53} -0.639360 q^{57} -2.71150 q^{59} +8.49942 q^{61} -5.07158 q^{63} +11.2660 q^{67} -0.440566 q^{69} -13.2131 q^{71} +3.07049 q^{73} +0.438156 q^{77} -10.9699 q^{79} +8.69606 q^{81} -10.7328 q^{83} -0.184115 q^{87} -2.36823 q^{89} -5.62283 q^{91} -1.96176 q^{93} -15.4443 q^{97} -0.760078 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.184115	−0.106299	−0.0531494	−	0.998587i	$-0.516926\pi$
$3$	−0.184115	−0.106299	−0.0531494	+	0.998587i	$0.516926\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	1.70985	0.646261	0.323131	−	0.946354i	$-0.395265\pi$
$7$	1.70985	0.646261	0.323131	+	0.946354i	$0.395265\pi$
$8$	0	0
$9$	−2.96610	−0.988701
$10$	0	0
$11$	0.256255	0.0772637	0.0386319	−	0.999254i	$-0.487700\pi$
$11$	0.256255	0.0772637	0.0386319	+	0.999254i	$0.487700\pi$
$12$	0	0
$13$	−3.28850	−0.912066	−0.456033	−	0.889963i	$-0.650730\pi$
$13$	−3.28850	−0.912066	−0.456033	+	0.889963i	$0.650730\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−3.70985	−0.899770	−0.449885	−	0.893086i	$-0.648535\pi$
$17$	−3.70985	−0.899770	−0.449885	+	0.893086i	$0.648535\pi$
$18$	0	0
$19$	3.47261	0.796672	0.398336	−	0.917239i	$-0.369588\pi$
$19$	3.47261	0.796672	0.398336	+	0.917239i	$0.369588\pi$
$20$	0	0
$21$	−0.314808	−0.0686968
$22$	0	0
$23$	2.39289	0.498951	0.249476	−	0.968381i	$-0.419742\pi$
$23$	2.39289	0.498951	0.249476	+	0.968381i	$0.419742\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	1.09845	0.211396
$28$	0	0
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	10.6551	1.91371	0.956854	−	0.290569i	$-0.0938445\pi$
$31$	10.6551	1.91371	0.956854	+	0.290569i	$0.0938445\pi$
$32$	0	0
$33$	−0.0471803	−0.00821304
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−9.68138	−1.59161	−0.795805	−	0.605553i	$-0.792952\pi$
$37$	−9.68138	−1.59161	−0.795805	+	0.605553i	$0.792952\pi$
$38$	0	0
$39$	0.605462	0.0969515
$40$	0	0
$41$	5.36064	0.837191	0.418596	−	0.908173i	$-0.362522\pi$
$41$	5.36064	0.837191	0.418596	+	0.908173i	$0.362522\pi$
$42$	0	0
$43$	1.29444	0.197400	0.0986999	−	0.995117i	$-0.468532\pi$
$43$	1.29444	0.197400	0.0986999	+	0.995117i	$0.468532\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−4.32075	−0.630245	−0.315123	−	0.949051i	$-0.602046\pi$
$47$	−4.32075	−0.630245	−0.315123	+	0.949051i	$0.602046\pi$
$48$	0	0
$49$	−4.07642	−0.582346
$50$	0	0
$51$	0.683038	0.0956445
$52$	0	0
$53$	−5.59787	−0.768927	−0.384463	−	0.923140i	$-0.625614\pi$
$53$	−5.59787	−0.768927	−0.384463	+	0.923140i	$0.625614\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	−0.639360	−0.0846853
$58$	0	0
$59$	−2.71150	−0.353007	−0.176504	−	0.984300i	$-0.556479\pi$
$59$	−2.71150	−0.353007	−0.176504	+	0.984300i	$0.556479\pi$
$60$	0	0
$61$	8.49942	1.08824	0.544120	−	0.839008i	$-0.316864\pi$
$61$	8.49942	1.08824	0.544120	+	0.839008i	$0.316864\pi$
$62$	0	0
$63$	−5.07158	−0.638959
$64$	0	0
$65$	0	0
$66$	0	0
$67$	11.2660	1.37636	0.688179	−	0.725541i	$-0.258410\pi$
$67$	11.2660	1.37636	0.688179	+	0.725541i	$0.258410\pi$
$68$	0	0
$69$	−0.440566	−0.0530379
$70$	0	0
$71$	−13.2131	−1.56810	−0.784050	−	0.620697i	$-0.786850\pi$
$71$	−13.2131	−1.56810	−0.784050	+	0.620697i	$0.786850\pi$
$72$	0	0
$73$	3.07049	0.359373	0.179687	−	0.983724i	$-0.442492\pi$
$73$	3.07049	0.359373	0.179687	+	0.983724i	$0.442492\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0.438156	0.0499326
$78$	0	0
$79$	−10.9699	−1.23421	−0.617104	−	0.786881i	$-0.711694\pi$
$79$	−10.9699	−1.23421	−0.617104	+	0.786881i	$0.711694\pi$
$80$	0	0
$81$	8.69606	0.966229
$82$	0	0
$83$	−10.7328	−1.17808	−0.589042	−	0.808103i	$-0.700495\pi$
$83$	−10.7328	−1.17808	−0.589042	+	0.808103i	$0.700495\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	−0.184115	−0.0197392
$88$	0	0
$89$	−2.36823	−0.251032	−0.125516	−	0.992092i	$-0.540059\pi$
$89$	−2.36823	−0.251032	−0.125516	+	0.992092i	$0.540059\pi$
$90$	0	0
$91$	−5.62283	−0.589433
$92$	0	0
$93$	−1.96176	−0.203425
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−15.4443	−1.56814	−0.784068	−	0.620675i	$-0.786859\pi$
$97$	−15.4443	−1.56814	−0.784068	+	0.620675i	$0.786859\pi$
$98$	0	0
$99$	−0.760078	−0.0763907
$100$	0	0
$101$	6.50486	0.647258	0.323629	−	0.946184i	$-0.395097\pi$
$101$	6.50486	0.647258	0.323629	+	0.946184i	$0.395097\pi$
$102$	0	0
$103$	−9.88802	−0.974296	−0.487148	−	0.873319i	$-0.661963\pi$
$103$	−9.88802	−0.974296	−0.487148	+	0.873319i	$0.661963\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	3.88259	0.375344	0.187672	−	0.982232i	$-0.439906\pi$
$107$	3.88259	0.375344	0.187672	+	0.982232i	$0.439906\pi$
$108$	0	0
$109$	−1.58459	−0.151776	−0.0758881	−	0.997116i	$-0.524179\pi$
$109$	−1.58459	−0.151776	−0.0758881	+	0.997116i	$0.524179\pi$
$110$	0	0
$111$	1.78249	0.169186
$112$	0	0
$113$	−14.3896	−1.35366	−0.676829	−	0.736140i	$-0.736646\pi$
$113$	−14.3896	−1.35366	−0.676829	+	0.736140i	$0.736646\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	9.75403	0.901760
$118$	0	0
$119$	−6.34327	−0.581487
$120$	0	0
$121$	−10.9343	−0.994030
$122$	0	0
$123$	−0.986974	−0.0889924
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−15.5545	−1.38024	−0.690121	−	0.723694i	$-0.742443\pi$
$127$	−15.5545	−1.38024	−0.690121	+	0.723694i	$0.742443\pi$
$128$	0	0
$129$	−0.238325	−0.0209834
$130$	0	0
$131$	−19.4048	−1.69541	−0.847703	−	0.530470i	$-0.822015\pi$
$131$	−19.4048	−1.69541	−0.847703	+	0.530470i	$0.822015\pi$
$132$	0	0
$133$	5.93764	0.514859
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−8.34570	−0.713022	−0.356511	−	0.934291i	$-0.616034\pi$
$137$	−8.34570	−0.713022	−0.356511	+	0.934291i	$0.616034\pi$
$138$	0	0
$139$	−1.43628	−0.121824	−0.0609119	−	0.998143i	$-0.519401\pi$
$139$	−1.43628	−0.121824	−0.0609119	+	0.998143i	$0.519401\pi$
$140$	0	0
$141$	0.795514	0.0669943
$142$	0	0
$143$	−0.842694	−0.0704696
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0.750530	0.0619027
$148$	0	0
$149$	6.27326	0.513926	0.256963	−	0.966421i	$-0.417278\pi$
$149$	6.27326	0.513926	0.256963	+	0.966421i	$0.417278\pi$
$150$	0	0
$151$	13.8996	1.13113	0.565566	−	0.824703i	$-0.308658\pi$
$151$	13.8996	1.13113	0.565566	+	0.824703i	$0.308658\pi$
$152$	0	0
$153$	11.0038	0.889603
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−1.13699	−0.0907420	−0.0453710	−	0.998970i	$-0.514447\pi$
$157$	−1.13699	−0.0907420	−0.0453710	+	0.998970i	$0.514447\pi$
$158$	0	0
$159$	1.03065	0.0817360
$160$	0	0
$161$	4.09147	0.322453
$162$	0	0
$163$	1.05720	0.0828067	0.0414033	−	0.999143i	$-0.486817\pi$
$163$	1.05720	0.0828067	0.0414033	+	0.999143i	$0.486817\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	14.9229	1.15477	0.577384	−	0.816472i	$-0.304073\pi$
$167$	14.9229	1.15477	0.577384	+	0.816472i	$0.304073\pi$
$168$	0	0
$169$	−2.18577	−0.168136
$170$	0	0
$171$	−10.3001	−0.787671
$172$	0	0
$173$	−9.98361	−0.759040	−0.379520	−	0.925184i	$-0.623911\pi$
$173$	−9.98361	−0.759040	−0.379520	+	0.925184i	$0.623911\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	0.499228	0.0375242
$178$	0	0
$179$	−17.5418	−1.31113	−0.655566	−	0.755138i	$-0.727570\pi$
$179$	−17.5418	−1.31113	−0.655566	+	0.755138i	$0.727570\pi$
$180$	0	0
$181$	5.58459	0.415099	0.207550	−	0.978224i	$-0.433451\pi$
$181$	5.58459	0.415099	0.207550	+	0.978224i	$0.433451\pi$
$182$	0	0
$183$	−1.56487	−0.115679
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−0.950666	−0.0695196
$188$	0	0
$189$	1.87818	0.136617
$190$	0	0
$191$	2.55798	0.185089	0.0925444	−	0.995709i	$-0.470500\pi$
$191$	2.55798	0.185089	0.0925444	+	0.995709i	$0.470500\pi$
$192$	0	0
$193$	−18.6988	−1.34597	−0.672983	−	0.739658i	$-0.734987\pi$
$193$	−18.6988	−1.34597	−0.672983	+	0.739658i	$0.734987\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	21.1758	1.50872	0.754358	−	0.656463i	$-0.227948\pi$
$197$	21.1758	1.50872	0.754358	+	0.656463i	$0.227948\pi$
$198$	0	0
$199$	17.1453	1.21540	0.607698	−	0.794169i	$-0.292093\pi$
$199$	17.1453	1.21540	0.607698	+	0.794169i	$0.292093\pi$
$200$	0	0
$201$	−2.07423	−0.146305
$202$	0	0
$203$	1.70985	0.120008
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−7.09754	−0.493313
$208$	0	0
$209$	0.889874	0.0615539
$210$	0	0
$211$	−15.7140	−1.08180	−0.540898	−	0.841088i	$-0.681915\pi$
$211$	−15.7140	−1.08180	−0.540898	+	0.841088i	$0.681915\pi$
$212$	0	0
$213$	2.43272	0.166687
$214$	0	0
$215$	0	0
$216$	0	0
$217$	18.2185	1.23676
$218$	0	0
$219$	−0.565322	−0.0382009
$220$	0	0
$221$	12.1998	0.820649
$222$	0	0
$223$	5.11416	0.342470	0.171235	−	0.985230i	$-0.445224\pi$
$223$	5.11416	0.342470	0.171235	+	0.985230i	$0.445224\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	11.4672	0.761103	0.380552	−	0.924760i	$-0.375734\pi$
$227$	11.4672	0.761103	0.380552	+	0.924760i	$0.375734\pi$
$228$	0	0
$229$	−17.5507	−1.15978	−0.579891	−	0.814694i	$-0.696905\pi$
$229$	−17.5507	−1.15978	−0.579891	+	0.814694i	$0.696905\pi$
$230$	0	0
$231$	−0.0806711	−0.00530777
$232$	0	0
$233$	24.2971	1.59176	0.795879	−	0.605456i	$-0.207009\pi$
$233$	24.2971	1.59176	0.795879	+	0.605456i	$0.207009\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	2.01972	0.131195
$238$	0	0
$239$	−20.8720	−1.35010	−0.675049	−	0.737773i	$-0.735877\pi$
$239$	−20.8720	−1.35010	−0.675049	+	0.737773i	$0.735877\pi$
$240$	0	0
$241$	26.5932	1.71302	0.856510	−	0.516131i	$-0.172628\pi$
$241$	26.5932	1.71302	0.856510	+	0.516131i	$0.172628\pi$
$242$	0	0
$243$	−4.89642	−0.314105
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−11.4197	−0.726618
$248$	0	0
$249$	1.97608	0.125229
$250$	0	0
$251$	−14.9894	−0.946123	−0.473062	−	0.881029i	$-0.656851\pi$
$251$	−14.9894	−0.946123	−0.473062	+	0.881029i	$0.656851\pi$
$252$	0	0
$253$	0.613188	0.0385508
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−4.84813	−0.302418	−0.151209	−	0.988502i	$-0.548317\pi$
$257$	−4.84813	−0.302418	−0.151209	+	0.988502i	$0.548317\pi$
$258$	0	0
$259$	−16.5537	−1.02860
$260$	0	0
$261$	−2.96610	−0.183597
$262$	0	0
$263$	−25.7524	−1.58796	−0.793981	−	0.607942i	$-0.791995\pi$
$263$	−25.7524	−1.58796	−0.793981	+	0.607942i	$0.791995\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0.436026	0.0266844
$268$	0	0
$269$	−12.6493	−0.771244	−0.385622	−	0.922657i	$-0.626013\pi$
$269$	−12.6493	−0.771244	−0.385622	+	0.922657i	$0.626013\pi$
$270$	0	0
$271$	23.0278	1.39884	0.699421	−	0.714710i	$-0.253441\pi$
$271$	23.0278	1.39884	0.699421	+	0.714710i	$0.253441\pi$
$272$	0	0
$273$	1.03525	0.0626560
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−16.4620	−0.989107	−0.494554	−	0.869147i	$-0.664668\pi$
$277$	−16.4620	−0.989107	−0.494554	+	0.869147i	$0.664668\pi$
$278$	0	0
$279$	−31.6040	−1.89208
$280$	0	0
$281$	−2.45144	−0.146241	−0.0731203	−	0.997323i	$-0.523296\pi$
$281$	−2.45144	−0.146241	−0.0731203	+	0.997323i	$0.523296\pi$
$282$	0	0
$283$	−2.25625	−0.134120	−0.0670602	−	0.997749i	$-0.521362\pi$
$283$	−2.25625	−0.134120	−0.0670602	+	0.997749i	$0.521362\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	9.16587	0.541044
$288$	0	0
$289$	−3.23704	−0.190414
$290$	0	0
$291$	2.84353	0.166691
$292$	0	0
$293$	−2.47690	−0.144702	−0.0723510	−	0.997379i	$-0.523050\pi$
$293$	−2.47690	−0.144702	−0.0723510	+	0.997379i	$0.523050\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	0.281483	0.0163333
$298$	0	0
$299$	−7.86900	−0.455076
$300$	0	0
$301$	2.21329	0.127572
$302$	0	0
$303$	−1.19764	−0.0688027
$304$	0	0
$305$	0	0
$306$	0	0
$307$	2.62448	0.149787	0.0748936	−	0.997192i	$-0.476138\pi$
$307$	2.62448	0.149787	0.0748936	+	0.997192i	$0.476138\pi$
$308$	0	0
$309$	1.82053	0.103566
$310$	0	0
$311$	12.1829	0.690831	0.345416	−	0.938450i	$-0.387738\pi$
$311$	12.1829	0.690831	0.345416	+	0.938450i	$0.387738\pi$
$312$	0	0
$313$	−1.22823	−0.0694239	−0.0347119	−	0.999397i	$-0.511051\pi$
$313$	−1.22823	−0.0694239	−0.0347119	+	0.999397i	$0.511051\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−13.1807	−0.740305	−0.370152	−	0.928971i	$-0.620695\pi$
$317$	−13.1807	−0.740305	−0.370152	+	0.928971i	$0.620695\pi$
$318$	0	0
$319$	0.256255	0.0143475
$320$	0	0
$321$	−0.714842	−0.0398986
$322$	0	0
$323$	−12.8829	−0.716822
$324$	0	0
$325$	0	0
$326$	0	0
$327$	0.291747	0.0161336
$328$	0	0
$329$	−7.38781	−0.407303
$330$	0	0
$331$	7.99639	0.439521	0.219761	−	0.975554i	$-0.429472\pi$
$331$	7.99639	0.439521	0.219761	+	0.975554i	$0.429472\pi$
$332$	0	0
$333$	28.7160	1.57363
$334$	0	0
$335$	0	0
$336$	0	0
$337$	29.9588	1.63196	0.815980	−	0.578081i	$-0.196198\pi$
$337$	29.9588	1.63196	0.815980	+	0.578081i	$0.196198\pi$
$338$	0	0
$339$	2.64934	0.143892
$340$	0	0
$341$	2.73041	0.147860
$342$	0	0
$343$	−18.9390	−1.02261
$344$	0	0
$345$	0	0
$346$	0	0
$347$	15.3512	0.824096	0.412048	−	0.911162i	$-0.364814\pi$
$347$	15.3512	0.824096	0.412048	+	0.911162i	$0.364814\pi$
$348$	0	0
$349$	−34.3997	−1.84137	−0.920686	−	0.390304i	$-0.872370\pi$
$349$	−34.3997	−1.84137	−0.920686	+	0.390304i	$0.872370\pi$
$350$	0	0
$351$	−3.61225	−0.192807
$352$	0	0
$353$	−0.350920	−0.0186776	−0.00933879	−	0.999956i	$-0.502973\pi$
$353$	−0.350920	−0.0186776	−0.00933879	+	0.999956i	$0.502973\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	1.16789	0.0618113
$358$	0	0
$359$	−0.557781	−0.0294386	−0.0147193	−	0.999892i	$-0.504685\pi$
$359$	−0.557781	−0.0294386	−0.0147193	+	0.999892i	$0.504685\pi$
$360$	0	0
$361$	−6.94095	−0.365313
$362$	0	0
$363$	2.01317	0.105664
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−17.7437	−0.926216	−0.463108	−	0.886302i	$-0.653266\pi$
$367$	−17.7437	−0.926216	−0.463108	+	0.886302i	$0.653266\pi$
$368$	0	0
$369$	−15.9002	−0.827732
$370$	0	0
$371$	−9.57150	−0.496928
$372$	0	0
$373$	34.2009	1.77085	0.885427	−	0.464779i	$-0.153866\pi$
$373$	34.2009	1.77085	0.885427	+	0.464779i	$0.153866\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−3.28850	−0.169366
$378$	0	0
$379$	−0.150413	−0.00772618	−0.00386309	−	0.999993i	$-0.501230\pi$
$379$	−0.150413	−0.00772618	−0.00386309	+	0.999993i	$0.501230\pi$
$380$	0	0
$381$	2.86382	0.146718
$382$	0	0
$383$	−14.1843	−0.724784	−0.362392	−	0.932026i	$-0.618040\pi$
$383$	−14.1843	−0.724784	−0.362392	+	0.932026i	$0.618040\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−3.83943	−0.195169
$388$	0	0
$389$	−16.8796	−0.855828	−0.427914	−	0.903819i	$-0.640751\pi$
$389$	−16.8796	−0.855828	−0.427914	+	0.903819i	$0.640751\pi$
$390$	0	0
$391$	−8.87724	−0.448941
$392$	0	0
$393$	3.57272	0.180220
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−14.6554	−0.735532	−0.367766	−	0.929918i	$-0.619877\pi$
$397$	−14.6554	−0.735532	−0.367766	+	0.929918i	$0.619877\pi$
$398$	0	0
$399$	−1.09321	−0.0547289
$400$	0	0
$401$	−26.1891	−1.30782	−0.653910	−	0.756572i	$-0.726872\pi$
$401$	−26.1891	−1.30782	−0.653910	+	0.756572i	$0.726872\pi$
$402$	0	0
$403$	−35.0392	−1.74543
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−2.48090	−0.122974
$408$	0	0
$409$	29.7331	1.47021	0.735104	−	0.677954i	$-0.237133\pi$
$409$	29.7331	1.47021	0.735104	+	0.677954i	$0.237133\pi$
$410$	0	0
$411$	1.53657	0.0757933
$412$	0	0
$413$	−4.63625	−0.228135
$414$	0	0
$415$	0	0
$416$	0	0
$417$	0.264441	0.0129497
$418$	0	0
$419$	2.43687	0.119049	0.0595244	−	0.998227i	$-0.481042\pi$
$419$	2.43687	0.119049	0.0595244	+	0.998227i	$0.481042\pi$
$420$	0	0
$421$	14.4766	0.705546	0.352773	−	0.935709i	$-0.385239\pi$
$421$	14.4766	0.705546	0.352773	+	0.935709i	$0.385239\pi$
$422$	0	0
$423$	12.8158	0.623124
$424$	0	0
$425$	0	0
$426$	0	0
$427$	14.5327	0.703287
$428$	0	0
$429$	0.155153	0.00749083
$430$	0	0
$431$	−25.0975	−1.20890	−0.604451	−	0.796642i	$-0.706608\pi$
$431$	−25.0975	−1.20890	−0.604451	+	0.796642i	$0.706608\pi$
$432$	0	0
$433$	−18.8626	−0.906477	−0.453238	−	0.891389i	$-0.649731\pi$
$433$	−18.8626	−0.906477	−0.453238	+	0.891389i	$0.649731\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	8.30957	0.397501
$438$	0	0
$439$	−2.67410	−0.127628	−0.0638139	−	0.997962i	$-0.520326\pi$
$439$	−2.67410	−0.127628	−0.0638139	+	0.997962i	$0.520326\pi$
$440$	0	0
$441$	12.0911	0.575766
$442$	0	0
$443$	−20.3218	−0.965517	−0.482759	−	0.875754i	$-0.660365\pi$
$443$	−20.3218	−0.965517	−0.482759	+	0.875754i	$0.660365\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−1.15500	−0.0546297
$448$	0	0
$449$	19.1561	0.904034	0.452017	−	0.892009i	$-0.350705\pi$
$449$	19.1561	0.904034	0.452017	+	0.892009i	$0.350705\pi$
$450$	0	0
$451$	1.37369	0.0646845
$452$	0	0
$453$	−2.55912	−0.120238
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−23.1072	−1.08091	−0.540455	−	0.841373i	$-0.681748\pi$
$457$	−23.1072	−1.08091	−0.540455	+	0.841373i	$0.681748\pi$
$458$	0	0
$459$	−4.07507	−0.190208
$460$	0	0
$461$	−14.0632	−0.654989	−0.327494	−	0.944853i	$-0.606204\pi$
$461$	−14.0632	−0.654989	−0.327494	+	0.944853i	$0.606204\pi$
$462$	0	0
$463$	−14.0061	−0.650920	−0.325460	−	0.945556i	$-0.605519\pi$
$463$	−14.0061	−0.650920	−0.325460	+	0.945556i	$0.605519\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	9.38880	0.434462	0.217231	−	0.976120i	$-0.430298\pi$
$467$	9.38880	0.434462	0.217231	+	0.976120i	$0.430298\pi$
$468$	0	0
$469$	19.2631	0.889487
$470$	0	0
$471$	0.209338	0.00964577
$472$	0	0
$473$	0.331706	0.0152518
$474$	0	0
$475$	0	0
$476$	0	0
$477$	16.6039	0.760238
$478$	0	0
$479$	−3.48034	−0.159021	−0.0795104	−	0.996834i	$-0.525336\pi$
$479$	−3.48034	−0.159021	−0.0795104	+	0.996834i	$0.525336\pi$
$480$	0	0
$481$	31.8372	1.45165
$482$	0	0
$483$	−0.753300	−0.0342763
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−13.9163	−0.630607	−0.315304	−	0.948991i	$-0.602106\pi$
$487$	−13.9163	−0.630607	−0.315304	+	0.948991i	$0.602106\pi$
$488$	0	0
$489$	−0.194647	−0.00880225
$490$	0	0
$491$	4.66505	0.210531	0.105265	−	0.994444i	$-0.466431\pi$
$491$	4.66505	0.210531	0.105265	+	0.994444i	$0.466431\pi$
$492$	0	0
$493$	−3.70985	−0.167083
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−22.5923	−1.01340
$498$	0	0
$499$	28.9387	1.29547	0.647737	−	0.761864i	$-0.275716\pi$
$499$	28.9387	1.29547	0.647737	+	0.761864i	$0.275716\pi$
$500$	0	0
$501$	−2.74753	−0.122751
$502$	0	0
$503$	−3.78510	−0.168769	−0.0843846	−	0.996433i	$-0.526892\pi$
$503$	−3.78510	−0.168769	−0.0843846	+	0.996433i	$0.526892\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	0.402432	0.0178727
$508$	0	0
$509$	−1.17131	−0.0519174	−0.0259587	−	0.999663i	$-0.508264\pi$
$509$	−1.17131	−0.0519174	−0.0259587	+	0.999663i	$0.508264\pi$
$510$	0	0
$511$	5.25006	0.232249
$512$	0	0
$513$	3.81449	0.168414
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−1.10721	−0.0486951
$518$	0	0
$519$	1.83813	0.0806850
$520$	0	0
$521$	−17.2800	−0.757049	−0.378524	−	0.925591i	$-0.623568\pi$
$521$	−17.2800	−0.757049	−0.378524	+	0.925591i	$0.623568\pi$
$522$	0	0
$523$	−14.9927	−0.655586	−0.327793	−	0.944750i	$-0.606305\pi$
$523$	−14.9927	−0.655586	−0.327793	+	0.944750i	$0.606305\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−39.5287	−1.72190
$528$	0	0
$529$	−17.2741	−0.751048
$530$	0	0
$531$	8.04258	0.349018
$532$	0	0
$533$	−17.6285	−0.763574
$534$	0	0
$535$	0	0
$536$	0	0
$537$	3.22970	0.139372
$538$	0	0
$539$	−1.04460	−0.0449942
$540$	0	0
$541$	44.2382	1.90195	0.950974	−	0.309271i	$-0.100085\pi$
$541$	44.2382	1.90195	0.950974	+	0.309271i	$0.100085\pi$
$542$	0	0
$543$	−1.02821	−0.0441246
$544$	0	0
$545$	0	0
$546$	0	0
$547$	4.30013	0.183860	0.0919301	−	0.995765i	$-0.470696\pi$
$547$	4.30013	0.183860	0.0919301	+	0.995765i	$0.470696\pi$
$548$	0	0
$549$	−25.2102	−1.07594
$550$	0	0
$551$	3.47261	0.147938
$552$	0	0
$553$	−18.7568	−0.797621
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−30.5320	−1.29368	−0.646842	−	0.762624i	$-0.723911\pi$
$557$	−30.5320	−1.29368	−0.646842	+	0.762624i	$0.723911\pi$
$558$	0	0
$559$	−4.25676	−0.180042
$560$	0	0
$561$	0.175032	0.00738985
$562$	0	0
$563$	29.6766	1.25072	0.625360	−	0.780337i	$-0.284952\pi$
$563$	29.6766	1.25072	0.625360	+	0.780337i	$0.284952\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	14.8689	0.624437
$568$	0	0
$569$	−23.3004	−0.976804	−0.488402	−	0.872619i	$-0.662420\pi$
$569$	−23.3004	−0.976804	−0.488402	+	0.872619i	$0.662420\pi$
$570$	0	0
$571$	18.6458	0.780304	0.390152	−	0.920750i	$-0.372422\pi$
$571$	18.6458	0.780304	0.390152	+	0.920750i	$0.372422\pi$
$572$	0	0
$573$	−0.470962	−0.0196747
$574$	0	0
$575$	0	0
$576$	0	0
$577$	23.0346	0.958942	0.479471	−	0.877558i	$-0.340829\pi$
$577$	23.0346	0.958942	0.479471	+	0.877558i	$0.340829\pi$
$578$	0	0
$579$	3.44272	0.143075
$580$	0	0
$581$	−18.3515	−0.761350
$582$	0	0
$583$	−1.43448	−0.0594102
$584$	0	0
$585$	0	0
$586$	0	0
$587$	10.7416	0.443353	0.221676	−	0.975120i	$-0.428847\pi$
$587$	10.7416	0.443353	0.221676	+	0.975120i	$0.428847\pi$
$588$	0	0
$589$	37.0010	1.52460
$590$	0	0
$591$	−3.89879	−0.160375
$592$	0	0
$593$	43.7342	1.79595	0.897975	−	0.440046i	$-0.145038\pi$
$593$	43.7342	1.79595	0.897975	+	0.440046i	$0.145038\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−3.15670	−0.129195
$598$	0	0
$599$	39.7623	1.62464	0.812322	−	0.583210i	$-0.198203\pi$
$599$	39.7623	1.62464	0.812322	+	0.583210i	$0.198203\pi$
$600$	0	0
$601$	−28.0823	−1.14550	−0.572751	−	0.819730i	$-0.694124\pi$
$601$	−28.0823	−1.14550	−0.572751	+	0.819730i	$0.694124\pi$
$602$	0	0
$603$	−33.4160	−1.36081
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−16.1918	−0.657203	−0.328602	−	0.944469i	$-0.606577\pi$
$607$	−16.1918	−0.657203	−0.328602	+	0.944469i	$0.606577\pi$
$608$	0	0
$609$	−0.314808	−0.0127567
$610$	0	0
$611$	14.2088	0.574825
$612$	0	0
$613$	−3.55339	−0.143520	−0.0717600	−	0.997422i	$-0.522862\pi$
$613$	−3.55339	−0.143520	−0.0717600	+	0.997422i	$0.522862\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−19.5532	−0.787184	−0.393592	−	0.919285i	$-0.628768\pi$
$617$	−19.5532	−0.787184	−0.393592	+	0.919285i	$0.628768\pi$
$618$	0	0
$619$	−21.2594	−0.854486	−0.427243	−	0.904137i	$-0.640515\pi$
$619$	−21.2594	−0.854486	−0.427243	+	0.904137i	$0.640515\pi$
$620$	0	0
$621$	2.62846	0.105476
$622$	0	0
$623$	−4.04931	−0.162232
$624$	0	0
$625$	0	0
$626$	0	0
$627$	−0.163839	−0.00654310
$628$	0	0
$629$	35.9165	1.43208
$630$	0	0
$631$	−25.7430	−1.02481	−0.512406	−	0.858743i	$-0.671246\pi$
$631$	−25.7430	−1.02481	−0.512406	+	0.858743i	$0.671246\pi$
$632$	0	0
$633$	2.89318	0.114994
$634$	0	0
$635$	0	0
$636$	0	0
$637$	13.4053	0.531138
$638$	0	0
$639$	39.1913	1.55038
$640$	0	0
$641$	16.9431	0.669212	0.334606	−	0.942358i	$-0.391397\pi$
$641$	16.9431	0.669212	0.334606	+	0.942358i	$0.391397\pi$
$642$	0	0
$643$	21.4069	0.844208	0.422104	−	0.906547i	$-0.361292\pi$
$643$	21.4069	0.844208	0.422104	+	0.906547i	$0.361292\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−32.5971	−1.28153	−0.640763	−	0.767739i	$-0.721382\pi$
$647$	−32.5971	−1.28153	−0.640763	+	0.767739i	$0.721382\pi$
$648$	0	0
$649$	−0.694835	−0.0272747
$650$	0	0
$651$	−3.35431	−0.131466
$652$	0	0
$653$	15.5435	0.608266	0.304133	−	0.952630i	$-0.401633\pi$
$653$	15.5435	0.608266	0.304133	+	0.952630i	$0.401633\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−9.10738	−0.355313
$658$	0	0
$659$	−20.9033	−0.814277	−0.407138	−	0.913366i	$-0.633473\pi$
$659$	−20.9033	−0.814277	−0.407138	+	0.913366i	$0.633473\pi$
$660$	0	0
$661$	−21.9190	−0.852552	−0.426276	−	0.904593i	$-0.640175\pi$
$661$	−21.9190	−0.852552	−0.426276	+	0.904593i	$0.640175\pi$
$662$	0	0
$663$	−2.24617	−0.0872340
$664$	0	0
$665$	0	0
$666$	0	0
$667$	2.39289	0.0926529
$668$	0	0
$669$	−0.941594	−0.0364041
$670$	0	0
$671$	2.17802	0.0840815
$672$	0	0
$673$	10.4793	0.403949	0.201974	−	0.979391i	$-0.435264\pi$
$673$	10.4793	0.403949	0.201974	+	0.979391i	$0.435264\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	−16.7307	−0.643014	−0.321507	−	0.946907i	$-0.604189\pi$
$677$	−16.7307	−0.643014	−0.321507	+	0.946907i	$0.604189\pi$
$678$	0	0
$679$	−26.4075	−1.01343
$680$	0	0
$681$	−2.11128	−0.0809044
$682$	0	0
$683$	−46.9752	−1.79746	−0.898729	−	0.438505i	$-0.855508\pi$
$683$	−46.9752	−1.79746	−0.898729	+	0.438505i	$0.855508\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	3.23134	0.123283
$688$	0	0
$689$	18.4086	0.701312
$690$	0	0
$691$	22.4981	0.855866	0.427933	−	0.903810i	$-0.359242\pi$
$691$	22.4981	0.855866	0.427933	+	0.903810i	$0.359242\pi$
$692$	0	0
$693$	−1.29962	−0.0493684
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−19.8872	−0.753280
$698$	0	0
$699$	−4.47346	−0.169202
$700$	0	0
$701$	42.3257	1.59862	0.799310	−	0.600919i	$-0.205199\pi$
$701$	42.3257	1.59862	0.799310	+	0.600919i	$0.205199\pi$
$702$	0	0
$703$	−33.6197	−1.26799
$704$	0	0
$705$	0	0
$706$	0	0
$707$	11.1223	0.418298
$708$	0	0
$709$	1.79005	0.0672269	0.0336134	−	0.999435i	$-0.489298\pi$
$709$	1.79005	0.0672269	0.0336134	+	0.999435i	$0.489298\pi$
$710$	0	0
$711$	32.5378	1.22026
$712$	0	0
$713$	25.4964	0.954847
$714$	0	0
$715$	0	0
$716$	0	0
$717$	3.84285	0.143514
$718$	0	0
$719$	−1.07965	−0.0402640	−0.0201320	−	0.999797i	$-0.506409\pi$
$719$	−1.07965	−0.0402640	−0.0201320	+	0.999797i	$0.506409\pi$
$720$	0	0
$721$	−16.9070	−0.629650
$722$	0	0
$723$	−4.89621	−0.182092
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−26.6510	−0.988433	−0.494216	−	0.869339i	$-0.664545\pi$
$727$	−26.6510	−0.988433	−0.494216	+	0.869339i	$0.664545\pi$
$728$	0	0
$729$	−25.1867	−0.932840
$730$	0	0
$731$	−4.80216	−0.177614
$732$	0	0
$733$	35.2920	1.30354	0.651769	−	0.758417i	$-0.274027\pi$
$733$	35.2920	1.30354	0.651769	+	0.758417i	$0.274027\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	2.88696	0.106343
$738$	0	0
$739$	31.8336	1.17102	0.585509	−	0.810666i	$-0.300895\pi$
$739$	31.8336	1.17102	0.585509	+	0.810666i	$0.300895\pi$
$740$	0	0
$741$	2.10254	0.0772386
$742$	0	0
$743$	37.6987	1.38303	0.691515	−	0.722362i	$-0.256943\pi$
$743$	37.6987	1.38303	0.691515	+	0.722362i	$0.256943\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	31.8347	1.16477
$748$	0	0
$749$	6.63863	0.242570
$750$	0	0
$751$	−12.9188	−0.471412	−0.235706	−	0.971824i	$-0.575740\pi$
$751$	−12.9188	−0.471412	−0.235706	+	0.971824i	$0.575740\pi$
$752$	0	0
$753$	2.75977	0.100572
$754$	0	0
$755$	0	0
$756$	0	0
$757$	25.6157	0.931019	0.465510	−	0.885043i	$-0.345871\pi$
$757$	25.6157	0.931019	0.465510	+	0.885043i	$0.345871\pi$
$758$	0	0
$759$	−0.112897	−0.00409791
$760$	0	0
$761$	−15.7323	−0.570295	−0.285148	−	0.958484i	$-0.592043\pi$
$761$	−15.7323	−0.570295	−0.285148	+	0.958484i	$0.592043\pi$
$762$	0	0
$763$	−2.70941	−0.0980871
$764$	0	0
$765$	0	0
$766$	0	0
$767$	8.91677	0.321966
$768$	0	0
$769$	19.2989	0.695936	0.347968	−	0.937506i	$-0.386872\pi$
$769$	19.2989	0.695936	0.347968	+	0.937506i	$0.386872\pi$
$770$	0	0
$771$	0.892613	0.0321467
$772$	0	0
$773$	36.1347	1.29967	0.649837	−	0.760074i	$-0.274837\pi$
$773$	36.1347	1.29967	0.649837	+	0.760074i	$0.274837\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	3.04778	0.109339
$778$	0	0
$779$	18.6154	0.666967
$780$	0	0
$781$	−3.38591	−0.121157
$782$	0	0
$783$	1.09845	0.0392553
$784$	0	0
$785$	0	0
$786$	0	0
$787$	21.1127	0.752586	0.376293	−	0.926501i	$-0.377199\pi$
$787$	21.1127	0.752586	0.376293	+	0.926501i	$0.377199\pi$
$788$	0	0
$789$	4.74141	0.168799
$790$	0	0
$791$	−24.6040	−0.874817
$792$	0	0
$793$	−27.9504	−0.992546
$794$	0	0
$795$	0	0
$796$	0	0
$797$	8.45303	0.299422	0.149711	−	0.988730i	$-0.452166\pi$
$797$	8.45303	0.299422	0.149711	+	0.988730i	$0.452166\pi$
$798$	0	0
$799$	16.0293	0.567076
$800$	0	0
$801$	7.02441	0.248195
$802$	0	0
$803$	0.786827	0.0277665
$804$	0	0
$805$	0	0
$806$	0	0
$807$	2.32893	0.0819823
$808$	0	0
$809$	−23.1246	−0.813019	−0.406510	−	0.913647i	$-0.633254\pi$
$809$	−23.1246	−0.813019	−0.406510	+	0.913647i	$0.633254\pi$
$810$	0	0
$811$	−24.7956	−0.870692	−0.435346	−	0.900263i	$-0.643374\pi$
$811$	−24.7956	−0.870692	−0.435346	+	0.900263i	$0.643374\pi$
$812$	0	0
$813$	−4.23977	−0.148695
$814$	0	0
$815$	0	0
$816$	0	0
$817$	4.49508	0.157263
$818$	0	0
$819$	16.6779	0.582773
$820$	0	0
$821$	25.8382	0.901761	0.450880	−	0.892584i	$-0.351110\pi$
$821$	25.8382	0.901761	0.450880	+	0.892584i	$0.351110\pi$
$822$	0	0
$823$	−36.8190	−1.28343	−0.641715	−	0.766943i	$-0.721777\pi$
$823$	−36.8190	−1.28343	−0.641715	+	0.766943i	$0.721777\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	45.4094	1.57904	0.789519	−	0.613726i	$-0.210330\pi$
$827$	45.4094	1.57904	0.789519	+	0.613726i	$0.210330\pi$
$828$	0	0
$829$	26.5024	0.920465	0.460232	−	0.887798i	$-0.347766\pi$
$829$	26.5024	0.920465	0.460232	+	0.887798i	$0.347766\pi$
$830$	0	0
$831$	3.03090	0.105141
$832$	0	0
$833$	15.1229	0.523978
$834$	0	0
$835$	0	0
$836$	0	0
$837$	11.7041	0.404551
$838$	0	0
$839$	43.2554	1.49334	0.746672	−	0.665192i	$-0.231651\pi$
$839$	43.2554	1.49334	0.746672	+	0.665192i	$0.231651\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	0	0
$843$	0.451346	0.0155452
$844$	0	0
$845$	0	0
$846$	0	0
$847$	−18.6960	−0.642403
$848$	0	0
$849$	0.415410	0.0142568
$850$	0	0
$851$	−23.1664	−0.794135
$852$	0	0
$853$	−13.4921	−0.461959	−0.230980	−	0.972959i	$-0.574193\pi$
$853$	−13.4921	−0.461959	−0.230980	+	0.972959i	$0.574193\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−39.1449	−1.33716	−0.668582	−	0.743639i	$-0.733098\pi$
$857$	−39.1449	−1.33716	−0.668582	+	0.743639i	$0.733098\pi$
$858$	0	0
$859$	24.6899	0.842409	0.421205	−	0.906966i	$-0.361607\pi$
$859$	24.6899	0.842409	0.421205	+	0.906966i	$0.361607\pi$
$860$	0	0
$861$	−1.68757	−0.0575124
$862$	0	0
$863$	6.18955	0.210695	0.105347	−	0.994435i	$-0.466405\pi$
$863$	6.18955	0.210695	0.105347	+	0.994435i	$0.466405\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	0.595987	0.0202408
$868$	0	0
$869$	−2.81109	−0.0953595
$870$	0	0
$871$	−37.0482	−1.25533
$872$	0	0
$873$	45.8095	1.55042
$874$	0	0
$875$	0	0
$876$	0	0
$877$	12.9550	0.437460	0.218730	−	0.975785i	$-0.429809\pi$
$877$	12.9550	0.437460	0.218730	+	0.975785i	$0.429809\pi$
$878$	0	0
$879$	0.456034	0.0153816
$880$	0	0
$881$	49.3474	1.66256	0.831278	−	0.555856i	$-0.187610\pi$
$881$	49.3474	1.66256	0.831278	+	0.555856i	$0.187610\pi$
$882$	0	0
$883$	37.7367	1.26994	0.634970	−	0.772537i	$-0.281012\pi$
$883$	37.7367	1.26994	0.634970	+	0.772537i	$0.281012\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−4.23239	−0.142110	−0.0710548	−	0.997472i	$-0.522637\pi$
$887$	−4.23239	−0.142110	−0.0710548	+	0.997472i	$0.522637\pi$
$888$	0	0
$889$	−26.5959	−0.891997
$890$	0	0
$891$	2.22841	0.0746545
$892$	0	0
$893$	−15.0043	−0.502099
$894$	0	0
$895$	0	0
$896$	0	0
$897$	1.44880	0.0483740
$898$	0	0
$899$	10.6551	0.355367
$900$	0	0
$901$	20.7672	0.691857
$902$	0	0
$903$	−0.407499	−0.0135607
$904$	0	0
$905$	0	0
$906$	0	0
$907$	41.9450	1.39276	0.696381	−	0.717673i	$-0.254793\pi$
$907$	41.9450	1.39276	0.696381	+	0.717673i	$0.254793\pi$
$908$	0	0
$909$	−19.2941	−0.639944
$910$	0	0
$911$	−59.4552	−1.96984	−0.984919	−	0.173017i	$-0.944648\pi$
$911$	−59.4552	−1.96984	−0.984919	+	0.173017i	$0.944648\pi$
$912$	0	0
$913$	−2.75034	−0.0910231
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−33.1793	−1.09568
$918$	0	0
$919$	−34.9442	−1.15270	−0.576351	−	0.817202i	$-0.695524\pi$
$919$	−34.9442	−1.15270	−0.576351	+	0.817202i	$0.695524\pi$
$920$	0	0
$921$	−0.483207	−0.0159222
$922$	0	0
$923$	43.4511	1.43021
$924$	0	0
$925$	0	0
$926$	0	0
$927$	29.3289	0.963287
$928$	0	0
$929$	0.908593	0.0298100	0.0149050	−	0.999889i	$-0.495255\pi$
$929$	0.908593	0.0298100	0.0149050	+	0.999889i	$0.495255\pi$
$930$	0	0
$931$	−14.1558	−0.463939
$932$	0	0
$933$	−2.24306	−0.0734345
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−2.29791	−0.0750695	−0.0375347	−	0.999295i	$-0.511950\pi$
$937$	−2.29791	−0.0750695	−0.0375347	+	0.999295i	$0.511950\pi$
$938$	0	0
$939$	0.226136	0.00737967
$940$	0	0
$941$	−43.1124	−1.40542	−0.702712	−	0.711475i	$-0.748028\pi$
$941$	−43.1124	−1.40542	−0.702712	+	0.711475i	$0.748028\pi$
$942$	0	0
$943$	12.8274	0.417717
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−13.6389	−0.443206	−0.221603	−	0.975137i	$-0.571129\pi$
$947$	−13.6389	−0.443206	−0.221603	+	0.975137i	$0.571129\pi$
$948$	0	0
$949$	−10.0973	−0.327772
$950$	0	0
$951$	2.42677	0.0786935
$952$	0	0
$953$	−34.5290	−1.11851	−0.559253	−	0.828997i	$-0.688912\pi$
$953$	−34.5290	−1.11851	−0.559253	+	0.828997i	$0.688912\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	−0.0471803	−0.00152512
$958$	0	0
$959$	−14.2699	−0.460798
$960$	0	0
$961$	82.5307	2.66228
$962$	0	0
$963$	−11.5162	−0.371103
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−5.43670	−0.174832	−0.0874162	−	0.996172i	$-0.527861\pi$
$967$	−5.43670	−0.174832	−0.0874162	+	0.996172i	$0.527861\pi$
$968$	0	0
$969$	2.37193	0.0761973
$970$	0	0
$971$	−16.2737	−0.522247	−0.261124	−	0.965305i	$-0.584093\pi$
$971$	−16.2737	−0.522247	−0.261124	+	0.965305i	$0.584093\pi$
$972$	0	0
$973$	−2.45582	−0.0787301
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−23.8052	−0.761597	−0.380798	−	0.924658i	$-0.624351\pi$
$977$	−23.8052	−0.761597	−0.380798	+	0.924658i	$0.624351\pi$
$978$	0	0
$979$	−0.606870	−0.0193957
$980$	0	0
$981$	4.70005	0.150061
$982$	0	0
$983$	15.0193	0.479041	0.239520	−	0.970891i	$-0.423010\pi$
$983$	15.0193	0.479041	0.239520	+	0.970891i	$0.423010\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	1.36021	0.0432958
$988$	0	0
$989$	3.09744	0.0984928
$990$	0	0
$991$	42.4588	1.34875	0.674375	−	0.738389i	$-0.264413\pi$
$991$	42.4588	1.34875	0.674375	+	0.738389i	$0.264413\pi$
$992$	0	0
$993$	−1.47225	−0.0467206
$994$	0	0
$995$	0	0
$996$	0	0
$997$	41.0913	1.30138	0.650688	−	0.759345i	$-0.274481\pi$
$997$	41.0913	1.30138	0.650688	+	0.759345i	$0.274481\pi$
$998$	0	0
$999$	−10.6345	−0.336461

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5800.2.a.u.1.3		5
5.4	even	2		1160.2.a.h.1.3	✓	5
20.19	odd	2		2320.2.a.v.1.3		5
40.19	odd	2		9280.2.a.ci.1.3		5
40.29	even	2		9280.2.a.ck.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1160.2.a.h.1.3	✓	5	5.4	even	2
2320.2.a.v.1.3		5	20.19	odd	2
5800.2.a.u.1.3		5	1.1	even	1	trivial
9280.2.a.ci.1.3		5	40.19	odd	2
9280.2.a.ck.1.3		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)

\(f(q)\)	\(=\)	\(q-0.184115 q^{3} +1.70985 q^{7} -2.96610 q^{9} +0.256255 q^{11} -3.28850 q^{13} -3.70985 q^{17} +3.47261 q^{19} -0.314808 q^{21} +2.39289 q^{23} +1.09845 q^{27} +1.00000 q^{29} +10.6551 q^{31} -0.0471803 q^{33} -9.68138 q^{37} +0.605462 q^{39} +5.36064 q^{41} +1.29444 q^{43} -4.32075 q^{47} -4.07642 q^{49} +0.683038 q^{51} -5.59787 q^{53} -0.639360 q^{57} -2.71150 q^{59} +8.49942 q^{61} -5.07158 q^{63} +11.2660 q^{67} -0.440566 q^{69} -13.2131 q^{71} +3.07049 q^{73} +0.438156 q^{77} -10.9699 q^{79} +8.69606 q^{81} -10.7328 q^{83} -0.184115 q^{87} -2.36823 q^{89} -5.62283 q^{91} -1.96176 q^{93} -15.4443 q^{97} -0.760078 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{3} - 7 q^{7} + 12 q^{9} - 10 q^{11} - 3 q^{13} - 3 q^{17} + 2 q^{19} + 4 q^{21} - 13 q^{23} + 4 q^{27} + 5 q^{29} + 7 q^{31} - 12 q^{33} - 10 q^{37} - q^{39} + 4 q^{41} - 17 q^{43} - 6 q^{47}+ \cdots - 96 q^{99}+O(q^{100}) \) 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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