LMFDB - Embedded newform 5800.2.a.q.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5800,2,Mod(1,5800)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$46.3132331723$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.229.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 4x - 1 $ x^3 - 4*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1160)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.86081$ 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)

$f(q)$	$=$	$q+0.462598 q^{3} +2.86081 q^{7} -2.78600 q^{9} +5.72161 q^{11} -0.462598 q^{13} -1.93561 q^{17} -8.36842 q^{19} +1.32340 q^{21} -8.18421 q^{23} -2.67660 q^{27} -1.00000 q^{29} +3.78600 q^{31} +2.64681 q^{33} -3.07480 q^{37} -0.213997 q^{39} +3.72161 q^{41} -9.78600 q^{43} -8.64681 q^{47} +1.18421 q^{49} -0.895410 q^{51} +2.58242 q^{53} -3.87122 q^{57} +11.7562 q^{59} -9.62743 q^{61} -7.97021 q^{63} -13.2936 q^{67} -3.78600 q^{69} -5.29362 q^{71} -9.63640 q^{73} +16.3684 q^{77} -5.90582 q^{79} +7.11982 q^{81} -4.92520 q^{83} -0.462598 q^{87} -5.07480 q^{89} -1.32340 q^{91} +1.75140 q^{93} +1.66618 q^{97} -15.9404 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{3} + 3 q^{7} + 2 q^{9} + 6 q^{11} + q^{13} - 5 q^{17} + 2 q^{19} - 4 q^{21} - 11 q^{23} - 16 q^{27} - 3 q^{29} + q^{31} - 8 q^{33} - 14 q^{37} - 11 q^{39} - 19 q^{43} - 10 q^{47} - 10 q^{49}+ \cdots + 9 q^{97}+O(q^{100}) $ 3 * q - q^3 + 3 * q^7 + 2 * q^9 + 6 * q^11 + q^13 - 5 * q^17 + 2 * q^19 - 4 * q^21 - 11 * q^23 - 16 * q^27 - 3 * q^29 + q^31 - 8 * q^33 - 14 * q^37 - 11 * q^39 - 19 * q^43 - 10 * q^47 - 10 * q^49 + 26 * q^51 - 9 * q^53 - 10 * q^57 + q^59 + 7 * q^61 - 8 * q^67 - q^69 + 16 * q^71 - 9 * q^73 + 22 * q^77 + 7 * q^79 + 7 * q^81 - 10 * q^83 + q^87 - 20 * q^89 + 4 * q^91 + 18 * q^93 + 9 * q^97

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
$3$	0.462598	0.267081	0.133541	−	0.991043i	$-0.457365\pi$
$3$	0.462598	0.267081	0.133541	+	0.991043i	$0.457365\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	2.86081	1.08128	0.540641	−	0.841253i	$-0.318182\pi$
$7$	2.86081	1.08128	0.540641	+	0.841253i	$0.318182\pi$
$8$	0	0
$9$	−2.78600	−0.928668
$10$	0	0
$11$	5.72161	1.72513	0.862565	−	0.505946i	$-0.168856\pi$
$11$	5.72161	1.72513	0.862565	+	0.505946i	$0.168856\pi$
$12$	0	0
$13$	−0.462598	−0.128302	−0.0641509	−	0.997940i	$-0.520434\pi$
$13$	−0.462598	−0.128302	−0.0641509	+	0.997940i	$0.520434\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−1.93561	−0.469454	−0.234727	−	0.972061i	$-0.575420\pi$
$17$	−1.93561	−0.469454	−0.234727	+	0.972061i	$0.575420\pi$
$18$	0	0
$19$	−8.36842	−1.91985	−0.959924	−	0.280262i	$-0.909579\pi$
$19$	−8.36842	−1.91985	−0.959924	+	0.280262i	$0.909579\pi$
$20$	0	0
$21$	1.32340	0.288790
$22$	0	0
$23$	−8.18421	−1.70653	−0.853263	−	0.521481i	$-0.825380\pi$
$23$	−8.18421	−1.70653	−0.853263	+	0.521481i	$0.825380\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−2.67660	−0.515111
$28$	0	0
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0	0
$31$	3.78600	0.679986	0.339993	−	0.940428i	$-0.389575\pi$
$31$	3.78600	0.679986	0.339993	+	0.940428i	$0.389575\pi$
$32$	0	0
$33$	2.64681	0.460750
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−3.07480	−0.505495	−0.252747	−	0.967532i	$-0.581334\pi$
$37$	−3.07480	−0.505495	−0.252747	+	0.967532i	$0.581334\pi$
$38$	0	0
$39$	−0.213997	−0.0342670
$40$	0	0
$41$	3.72161	0.581218	0.290609	−	0.956842i	$-0.406142\pi$
$41$	3.72161	0.581218	0.290609	+	0.956842i	$0.406142\pi$
$42$	0	0
$43$	−9.78600	−1.49235	−0.746176	−	0.665749i	$-0.768112\pi$
$43$	−9.78600	−1.49235	−0.746176	+	0.665749i	$0.768112\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−8.64681	−1.26127	−0.630633	−	0.776081i	$-0.717205\pi$
$47$	−8.64681	−1.26127	−0.630633	+	0.776081i	$0.717205\pi$
$48$	0	0
$49$	1.18421	0.169173
$50$	0	0
$51$	−0.895410	−0.125382
$52$	0	0
$53$	2.58242	0.354722	0.177361	−	0.984146i	$-0.443244\pi$
$53$	2.58242	0.354722	0.177361	+	0.984146i	$0.443244\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	−3.87122	−0.512755
$58$	0	0
$59$	11.7562	1.53053	0.765264	−	0.643716i	$-0.222608\pi$
$59$	11.7562	1.53053	0.765264	+	0.643716i	$0.222608\pi$
$60$	0	0
$61$	−9.62743	−1.23267	−0.616333	−	0.787485i	$-0.711383\pi$
$61$	−9.62743	−1.23267	−0.616333	+	0.787485i	$0.711383\pi$
$62$	0	0
$63$	−7.97021	−1.00415
$64$	0	0
$65$	0	0
$66$	0	0
$67$	−13.2936	−1.62407	−0.812037	−	0.583606i	$-0.801641\pi$
$67$	−13.2936	−1.62407	−0.812037	+	0.583606i	$0.801641\pi$
$68$	0	0
$69$	−3.78600	−0.455781
$70$	0	0
$71$	−5.29362	−0.628237	−0.314118	−	0.949384i	$-0.601709\pi$
$71$	−5.29362	−0.628237	−0.314118	+	0.949384i	$0.601709\pi$
$72$	0	0
$73$	−9.63640	−1.12785	−0.563927	−	0.825824i	$-0.690710\pi$
$73$	−9.63640	−1.12785	−0.563927	+	0.825824i	$0.690710\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	16.3684	1.86535
$78$	0	0
$79$	−5.90582	−0.664457	−0.332228	−	0.943199i	$-0.607800\pi$
$79$	−5.90582	−0.664457	−0.332228	+	0.943199i	$0.607800\pi$
$80$	0	0
$81$	7.11982	0.791091
$82$	0	0
$83$	−4.92520	−0.540611	−0.270305	−	0.962775i	$-0.587125\pi$
$83$	−4.92520	−0.540611	−0.270305	+	0.962775i	$0.587125\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	−0.462598	−0.0495958
$88$	0	0
$89$	−5.07480	−0.537928	−0.268964	−	0.963150i	$-0.586681\pi$
$89$	−5.07480	−0.537928	−0.268964	+	0.963150i	$0.586681\pi$
$90$	0	0
$91$	−1.32340	−0.138730
$92$	0	0
$93$	1.75140	0.181612
$94$	0	0
$95$	0	0
$96$	0	0
$97$	1.66618	0.169175	0.0845877	−	0.996416i	$-0.473043\pi$
$97$	1.66618	0.169175	0.0845877	+	0.996416i	$0.473043\pi$
$98$	0	0
$99$	−15.9404	−1.60207
$100$	0	0
$101$	−13.2590	−1.31932	−0.659661	−	0.751564i	$-0.729300\pi$
$101$	−13.2590	−1.31932	−0.659661	+	0.751564i	$0.729300\pi$
$102$	0	0
$103$	14.8864	1.46681	0.733403	−	0.679795i	$-0.237931\pi$
$103$	14.8864	1.46681	0.733403	+	0.679795i	$0.237931\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−1.48197	−0.143268	−0.0716339	−	0.997431i	$-0.522821\pi$
$107$	−1.48197	−0.143268	−0.0716339	+	0.997431i	$0.522821\pi$
$108$	0	0
$109$	17.0152	1.62976	0.814882	−	0.579627i	$-0.196802\pi$
$109$	17.0152	1.62976	0.814882	+	0.579627i	$0.196802\pi$
$110$	0	0
$111$	−1.42240	−0.135008
$112$	0	0
$113$	5.40862	0.508800	0.254400	−	0.967099i	$-0.418122\pi$
$113$	5.40862	0.508800	0.254400	+	0.967099i	$0.418122\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	1.28880	0.119150
$118$	0	0
$119$	−5.53740	−0.507613
$120$	0	0
$121$	21.7368	1.97608
$122$	0	0
$123$	1.72161	0.155232
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−12.0900	−1.07282	−0.536408	−	0.843959i	$-0.680219\pi$
$127$	−12.0900	−1.07282	−0.536408	+	0.843959i	$0.680219\pi$
$128$	0	0
$129$	−4.52699	−0.398579
$130$	0	0
$131$	8.49720	0.742404	0.371202	−	0.928552i	$-0.378946\pi$
$131$	8.49720	0.742404	0.371202	+	0.928552i	$0.378946\pi$
$132$	0	0
$133$	−23.9404	−2.07590
$134$	0	0
$135$	0	0
$136$	0	0
$137$	3.25901	0.278436	0.139218	−	0.990262i	$-0.455541\pi$
$137$	3.25901	0.278436	0.139218	+	0.990262i	$0.455541\pi$
$138$	0	0
$139$	22.6724	1.92305	0.961526	−	0.274714i	$-0.0885831\pi$
$139$	22.6724	1.92305	0.961526	+	0.274714i	$0.0885831\pi$
$140$	0	0
$141$	−4.00000	−0.336861
$142$	0	0
$143$	−2.64681	−0.221337
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0.547814	0.0451829
$148$	0	0
$149$	11.6620	0.955391	0.477696	−	0.878525i	$-0.341472\pi$
$149$	11.6620	0.955391	0.477696	+	0.878525i	$0.341472\pi$
$150$	0	0
$151$	4.66763	0.379847	0.189923	−	0.981799i	$-0.439176\pi$
$151$	4.66763	0.379847	0.189923	+	0.981799i	$0.439176\pi$
$152$	0	0
$153$	5.39261	0.435967
$154$	0	0
$155$	0	0
$156$	0	0
$157$	15.3836	1.22775	0.613874	−	0.789404i	$-0.289610\pi$
$157$	15.3836	1.22775	0.613874	+	0.789404i	$0.289610\pi$
$158$	0	0
$159$	1.19462	0.0947397
$160$	0	0
$161$	−23.4134	−1.84524
$162$	0	0
$163$	0.646809	0.0506620	0.0253310	−	0.999679i	$-0.491936\pi$
$163$	0.646809	0.0506620	0.0253310	+	0.999679i	$0.491936\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	14.5616	1.12681	0.563405	−	0.826181i	$-0.309491\pi$
$167$	14.5616	1.12681	0.563405	+	0.826181i	$0.309491\pi$
$168$	0	0
$169$	−12.7860	−0.983539
$170$	0	0
$171$	23.3144	1.78290
$172$	0	0
$173$	−6.98062	−0.530727	−0.265364	−	0.964148i	$-0.585492\pi$
$173$	−6.98062	−0.530727	−0.265364	+	0.964148i	$0.585492\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	5.43841	0.408776
$178$	0	0
$179$	−11.7562	−0.878701	−0.439350	−	0.898316i	$-0.644791\pi$
$179$	−11.7562	−0.878701	−0.439350	+	0.898316i	$0.644791\pi$
$180$	0	0
$181$	−5.57201	−0.414164	−0.207082	−	0.978324i	$-0.566397\pi$
$181$	−5.57201	−0.414164	−0.207082	+	0.978324i	$0.566397\pi$
$182$	0	0
$183$	−4.45364	−0.329222
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−11.0748	−0.809870
$188$	0	0
$189$	−7.65722	−0.556981
$190$	0	0
$191$	−13.0796	−0.946408	−0.473204	−	0.880953i	$-0.656903\pi$
$191$	−13.0796	−0.946408	−0.473204	+	0.880953i	$0.656903\pi$
$192$	0	0
$193$	4.18421	0.301186	0.150593	−	0.988596i	$-0.451882\pi$
$193$	4.18421	0.301186	0.150593	+	0.988596i	$0.451882\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	1.28880	0.0918232	0.0459116	−	0.998946i	$-0.485381\pi$
$197$	1.28880	0.0918232	0.0459116	+	0.998946i	$0.485381\pi$
$198$	0	0
$199$	3.87122	0.274423	0.137212	−	0.990542i	$-0.456186\pi$
$199$	3.87122	0.274423	0.137212	+	0.990542i	$0.456186\pi$
$200$	0	0
$201$	−6.14961	−0.433760
$202$	0	0
$203$	−2.86081	−0.200789
$204$	0	0
$205$	0	0
$206$	0	0
$207$	22.8012	1.58480
$208$	0	0
$209$	−47.8809	−3.31199
$210$	0	0
$211$	25.1648	1.73242	0.866209	−	0.499681i	$-0.166550\pi$
$211$	25.1648	1.73242	0.866209	+	0.499681i	$0.166550\pi$
$212$	0	0
$213$	−2.44882	−0.167790
$214$	0	0
$215$	0	0
$216$	0	0
$217$	10.8310	0.735257
$218$	0	0
$219$	−4.45778	−0.301229
$220$	0	0
$221$	0.895410	0.0602318
$222$	0	0
$223$	5.96540	0.399472	0.199736	−	0.979850i	$-0.435991\pi$
$223$	5.96540	0.399472	0.199736	+	0.979850i	$0.435991\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	−12.7964	−0.849328	−0.424664	−	0.905351i	$-0.639608\pi$
$227$	−12.7964	−0.849328	−0.424664	+	0.905351i	$0.639608\pi$
$228$	0	0
$229$	−11.3788	−0.751934	−0.375967	−	0.926633i	$-0.622689\pi$
$229$	−11.3788	−0.751934	−0.375967	+	0.926633i	$0.622689\pi$
$230$	0	0
$231$	7.57201	0.498201
$232$	0	0
$233$	−18.0000	−1.17922	−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000	−1.17922	−0.589610	+	0.807688i	$0.700718\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−2.73202	−0.177464
$238$	0	0
$239$	−8.79641	−0.568993	−0.284496	−	0.958677i	$-0.591826\pi$
$239$	−8.79641	−0.568993	−0.284496	+	0.958677i	$0.591826\pi$
$240$	0	0
$241$	−5.62743	−0.362495	−0.181247	−	0.983438i	$-0.558013\pi$
$241$	−5.62743	−0.362495	−0.181247	+	0.983438i	$0.558013\pi$
$242$	0	0
$243$	11.3234	0.726397
$244$	0	0
$245$	0	0
$246$	0	0
$247$	3.87122	0.246320
$248$	0	0
$249$	−2.27839	−0.144387
$250$	0	0
$251$	−11.0748	−0.699035	−0.349518	−	0.936930i	$-0.613655\pi$
$251$	−11.0748	−0.699035	−0.349518	+	0.936930i	$0.613655\pi$
$252$	0	0
$253$	−46.8269	−2.94398
$254$	0	0
$255$	0	0
$256$	0	0
$257$	13.8712	0.865263	0.432631	−	0.901571i	$-0.357585\pi$
$257$	13.8712	0.865263	0.432631	+	0.901571i	$0.357585\pi$
$258$	0	0
$259$	−8.79641	−0.546583
$260$	0	0
$261$	2.78600	0.172449
$262$	0	0
$263$	8.09003	0.498853	0.249426	−	0.968394i	$-0.419758\pi$
$263$	8.09003	0.498853	0.249426	+	0.968394i	$0.419758\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−2.34760	−0.143671
$268$	0	0
$269$	4.80123	0.292736	0.146368	−	0.989230i	$-0.453242\pi$
$269$	4.80123	0.292736	0.146368	+	0.989230i	$0.453242\pi$
$270$	0	0
$271$	−25.0361	−1.52083	−0.760416	−	0.649436i	$-0.775005\pi$
$271$	−25.0361	−1.52083	−0.760416	+	0.649436i	$0.775005\pi$
$272$	0	0
$273$	−0.612205	−0.0370523
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−22.1801	−1.33267	−0.666335	−	0.745652i	$-0.732138\pi$
$277$	−22.1801	−1.33267	−0.666335	+	0.745652i	$0.732138\pi$
$278$	0	0
$279$	−10.5478	−0.631481
$280$	0	0
$281$	−3.80683	−0.227096	−0.113548	−	0.993532i	$-0.536222\pi$
$281$	−3.80683	−0.227096	−0.113548	+	0.993532i	$0.536222\pi$
$282$	0	0
$283$	4.92520	0.292773	0.146386	−	0.989228i	$-0.453236\pi$
$283$	4.92520	0.292773	0.146386	+	0.989228i	$0.453236\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	10.6468	0.628461
$288$	0	0
$289$	−13.2534	−0.779613
$290$	0	0
$291$	0.770774	0.0451836
$292$	0	0
$293$	−22.2188	−1.29804	−0.649018	−	0.760773i	$-0.724820\pi$
$293$	−22.2188	−1.29804	−0.649018	+	0.760773i	$0.724820\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−15.3144	−0.888634
$298$	0	0
$299$	3.78600	0.218950
$300$	0	0
$301$	−27.9959	−1.61365
$302$	0	0
$303$	−6.13360	−0.352366
$304$	0	0
$305$	0	0
$306$	0	0
$307$	21.9404	1.25221	0.626103	−	0.779740i	$-0.284649\pi$
$307$	21.9404	1.25221	0.626103	+	0.779740i	$0.284649\pi$
$308$	0	0
$309$	6.88645	0.391756
$310$	0	0
$311$	19.1994	1.08870	0.544350	−	0.838858i	$-0.316776\pi$
$311$	19.1994	1.08870	0.544350	+	0.838858i	$0.316776\pi$
$312$	0	0
$313$	8.88645	0.502292	0.251146	−	0.967949i	$-0.419193\pi$
$313$	8.88645	0.502292	0.251146	+	0.967949i	$0.419193\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−3.87122	−0.217429	−0.108715	−	0.994073i	$-0.534673\pi$
$317$	−3.87122	−0.217429	−0.108715	+	0.994073i	$0.534673\pi$
$318$	0	0
$319$	−5.72161	−0.320349
$320$	0	0
$321$	−0.685559	−0.0382641
$322$	0	0
$323$	16.1980	0.901280
$324$	0	0
$325$	0	0
$326$	0	0
$327$	7.87122	0.435279
$328$	0	0
$329$	−24.7368	−1.36379
$330$	0	0
$331$	21.4224	1.17748	0.588741	−	0.808322i	$-0.299624\pi$
$331$	21.4224	1.17748	0.588741	+	0.808322i	$0.299624\pi$
$332$	0	0
$333$	8.56641	0.469436
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−27.1004	−1.47626	−0.738128	−	0.674661i	$-0.764290\pi$
$337$	−27.1004	−1.47626	−0.738128	+	0.674661i	$0.764290\pi$
$338$	0	0
$339$	2.50202	0.135891
$340$	0	0
$341$	21.6620	1.17307
$342$	0	0
$343$	−16.6378	−0.898359
$344$	0	0
$345$	0	0
$346$	0	0
$347$	−26.5180	−1.42356	−0.711781	−	0.702401i	$-0.752111\pi$
$347$	−26.5180	−1.42356	−0.711781	+	0.702401i	$0.752111\pi$
$348$	0	0
$349$	−27.2340	−1.45780	−0.728902	−	0.684618i	$-0.759969\pi$
$349$	−27.2340	−1.45780	−0.728902	+	0.684618i	$0.759969\pi$
$350$	0	0
$351$	1.23819	0.0660896
$352$	0	0
$353$	−34.6773	−1.84568	−0.922842	−	0.385178i	$-0.874140\pi$
$353$	−34.6773	−1.84568	−0.922842	+	0.385178i	$0.874140\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	−2.56159	−0.135574
$358$	0	0
$359$	−20.9806	−1.10732	−0.553658	−	0.832744i	$-0.686768\pi$
$359$	−20.9806	−1.10732	−0.553658	+	0.832744i	$0.686768\pi$
$360$	0	0
$361$	51.0305	2.68581
$362$	0	0
$363$	10.0554	0.527773
$364$	0	0
$365$	0	0
$366$	0	0
$367$	3.97918	0.207711	0.103856	−	0.994592i	$-0.466882\pi$
$367$	3.97918	0.207711	0.103856	+	0.994592i	$0.466882\pi$
$368$	0	0
$369$	−10.3684	−0.539758
$370$	0	0
$371$	7.38780	0.383555
$372$	0	0
$373$	17.1697	0.889011	0.444505	−	0.895776i	$-0.353379\pi$
$373$	17.1697	0.889011	0.444505	+	0.895776i	$0.353379\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0.462598	0.0238250
$378$	0	0
$379$	7.27279	0.373578	0.186789	−	0.982400i	$-0.440192\pi$
$379$	7.27279	0.373578	0.186789	+	0.982400i	$0.440192\pi$
$380$	0	0
$381$	−5.59283	−0.286529
$382$	0	0
$383$	18.5616	0.948453	0.474227	−	0.880403i	$-0.342728\pi$
$383$	18.5616	0.948453	0.474227	+	0.880403i	$0.342728\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	27.2638	1.38590
$388$	0	0
$389$	4.40717	0.223452	0.111726	−	0.993739i	$-0.464362\pi$
$389$	4.40717	0.223452	0.111726	+	0.993739i	$0.464362\pi$
$390$	0	0
$391$	15.8414	0.801136
$392$	0	0
$393$	3.93079	0.198282
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−29.1697	−1.46398	−0.731991	−	0.681314i	$-0.761409\pi$
$397$	−29.1697	−1.46398	−0.731991	+	0.681314i	$0.761409\pi$
$398$	0	0
$399$	−11.0748	−0.554434
$400$	0	0
$401$	−24.3338	−1.21517	−0.607586	−	0.794254i	$-0.707862\pi$
$401$	−24.3338	−1.21517	−0.607586	+	0.794254i	$0.707862\pi$
$402$	0	0
$403$	−1.75140	−0.0872434
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−17.5928	−0.872044
$408$	0	0
$409$	12.9044	0.638080	0.319040	−	0.947741i	$-0.396640\pi$
$409$	12.9044	0.638080	0.319040	+	0.947741i	$0.396640\pi$
$410$	0	0
$411$	1.50761	0.0743651
$412$	0	0
$413$	33.6323	1.65493
$414$	0	0
$415$	0	0
$416$	0	0
$417$	10.4882	0.513611
$418$	0	0
$419$	−10.3732	−0.506766	−0.253383	−	0.967366i	$-0.581543\pi$
$419$	−10.3732	−0.506766	−0.253383	+	0.967366i	$0.581543\pi$
$420$	0	0
$421$	−5.74244	−0.279869	−0.139935	−	0.990161i	$-0.544689\pi$
$421$	−5.74244	−0.279869	−0.139935	+	0.990161i	$0.544689\pi$
$422$	0	0
$423$	24.0900	1.17130
$424$	0	0
$425$	0	0
$426$	0	0
$427$	−27.5422	−1.33286
$428$	0	0
$429$	−1.22441	−0.0591150
$430$	0	0
$431$	−2.81724	−0.135702	−0.0678508	−	0.997695i	$-0.521614\pi$
$431$	−2.81724	−0.135702	−0.0678508	+	0.997695i	$0.521614\pi$
$432$	0	0
$433$	−18.6468	−0.896108	−0.448054	−	0.894006i	$-0.647883\pi$
$433$	−18.6468	−0.896108	−0.448054	+	0.894006i	$0.647883\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	68.4889	3.27627
$438$	0	0
$439$	40.4197	1.92913	0.964564	−	0.263851i	$-0.0849926\pi$
$439$	40.4197	1.92913	0.964564	+	0.263851i	$0.0849926\pi$
$440$	0	0
$441$	−3.29921	−0.157105
$442$	0	0
$443$	39.1607	1.86058	0.930290	−	0.366824i	$-0.119555\pi$
$443$	39.1607	1.86058	0.930290	+	0.366824i	$0.119555\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	5.39484	0.255167
$448$	0	0
$449$	5.61365	0.264925	0.132462	−	0.991188i	$-0.457712\pi$
$449$	5.61365	0.264925	0.132462	+	0.991188i	$0.457712\pi$
$450$	0	0
$451$	21.2936	1.00268
$452$	0	0
$453$	2.15924	0.101450
$454$	0	0
$455$	0	0
$456$	0	0
$457$	8.32967	0.389646	0.194823	−	0.980838i	$-0.437587\pi$
$457$	8.32967	0.389646	0.194823	+	0.980838i	$0.437587\pi$
$458$	0	0
$459$	5.18084	0.241821
$460$	0	0
$461$	30.1365	1.40360	0.701798	−	0.712376i	$-0.252381\pi$
$461$	30.1365	1.40360	0.701798	+	0.712376i	$0.252381\pi$
$462$	0	0
$463$	15.1857	0.705737	0.352869	−	0.935673i	$-0.385206\pi$
$463$	15.1857	0.705737	0.352869	+	0.935673i	$0.385206\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−13.7860	−0.637940	−0.318970	−	0.947765i	$-0.603337\pi$
$467$	−13.7860	−0.637940	−0.318970	+	0.947765i	$0.603337\pi$
$468$	0	0
$469$	−38.0305	−1.75608
$470$	0	0
$471$	7.11645	0.327909
$472$	0	0
$473$	−55.9917	−2.57450
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−7.19462	−0.329419
$478$	0	0
$479$	17.7652	0.811712	0.405856	−	0.913937i	$-0.366973\pi$
$479$	17.7652	0.811712	0.405856	+	0.913937i	$0.366973\pi$
$480$	0	0
$481$	1.42240	0.0648558
$482$	0	0
$483$	−10.8310	−0.492828
$484$	0	0
$485$	0	0
$486$	0	0
$487$	7.62743	0.345632	0.172816	−	0.984954i	$-0.444713\pi$
$487$	7.62743	0.345632	0.172816	+	0.984954i	$0.444713\pi$
$488$	0	0
$489$	0.299213	0.0135309
$490$	0	0
$491$	−16.1801	−0.730196	−0.365098	−	0.930969i	$-0.618965\pi$
$491$	−16.1801	−0.730196	−0.365098	+	0.930969i	$0.618965\pi$
$492$	0	0
$493$	1.93561	0.0871754
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−15.1440	−0.679302
$498$	0	0
$499$	−33.3074	−1.49104	−0.745522	−	0.666481i	$-0.767800\pi$
$499$	−33.3074	−1.49104	−0.745522	+	0.666481i	$0.767800\pi$
$500$	0	0
$501$	6.73617	0.300950
$502$	0	0
$503$	−28.2701	−1.26050	−0.630251	−	0.776392i	$-0.717048\pi$
$503$	−28.2701	−1.26050	−0.630251	+	0.776392i	$0.717048\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−5.91478	−0.262685
$508$	0	0
$509$	12.7160	0.563628	0.281814	−	0.959469i	$-0.409064\pi$
$509$	12.7160	0.563628	0.281814	+	0.959469i	$0.409064\pi$
$510$	0	0
$511$	−27.5679	−1.21953
$512$	0	0
$513$	22.3989	0.988935
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−49.4737	−2.17585
$518$	0	0
$519$	−3.22923	−0.141747
$520$	0	0
$521$	−11.2084	−0.491049	−0.245524	−	0.969390i	$-0.578960\pi$
$521$	−11.2084	−0.491049	−0.245524	+	0.969390i	$0.578960\pi$
$522$	0	0
$523$	−39.5541	−1.72958	−0.864790	−	0.502134i	$-0.832548\pi$
$523$	−39.5541	−1.72958	−0.864790	+	0.502134i	$0.832548\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−7.32822	−0.319222
$528$	0	0
$529$	43.9813	1.91223
$530$	0	0
$531$	−32.7528	−1.42135
$532$	0	0
$533$	−1.72161	−0.0745713
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−5.43841	−0.234685
$538$	0	0
$539$	6.77559	0.291845
$540$	0	0
$541$	30.1365	1.29567	0.647835	−	0.761781i	$-0.275675\pi$
$541$	30.1365	1.29567	0.647835	+	0.761781i	$0.275675\pi$
$542$	0	0
$543$	−2.57760	−0.110615
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−44.5485	−1.90476	−0.952378	−	0.304920i	$-0.901370\pi$
$547$	−44.5485	−1.90476	−0.952378	+	0.304920i	$0.901370\pi$
$548$	0	0
$549$	26.8221	1.14474
$550$	0	0
$551$	8.36842	0.356507
$552$	0	0
$553$	−16.8954	−0.718466
$554$	0	0
$555$	0	0
$556$	0	0
$557$	23.3490	0.989331	0.494665	−	0.869084i	$-0.335291\pi$
$557$	23.3490	0.989331	0.494665	+	0.869084i	$0.335291\pi$
$558$	0	0
$559$	4.52699	0.191471
$560$	0	0
$561$	−5.12319	−0.216301
$562$	0	0
$563$	−39.1607	−1.65043	−0.825213	−	0.564821i	$-0.808945\pi$
$563$	−39.1607	−1.65043	−0.825213	+	0.564821i	$0.808945\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	20.3684	0.855393
$568$	0	0
$569$	47.2340	1.98015	0.990077	−	0.140526i	$-0.0448792\pi$
$569$	47.2340	1.98015	0.990077	+	0.140526i	$0.0448792\pi$
$570$	0	0
$571$	−27.3795	−1.14580	−0.572898	−	0.819626i	$-0.694181\pi$
$571$	−27.3795	−1.14580	−0.572898	+	0.819626i	$0.694181\pi$
$572$	0	0
$573$	−6.05061	−0.252768
$574$	0	0
$575$	0	0
$576$	0	0
$577$	19.6572	0.818341	0.409170	−	0.912458i	$-0.365818\pi$
$577$	19.6572	0.818341	0.409170	+	0.912458i	$0.365818\pi$
$578$	0	0
$579$	1.93561	0.0804412
$580$	0	0
$581$	−14.0900	−0.584553
$582$	0	0
$583$	14.7756	0.611942
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−26.9460	−1.11218	−0.556091	−	0.831122i	$-0.687699\pi$
$587$	−26.9460	−1.11218	−0.556091	+	0.831122i	$0.687699\pi$
$588$	0	0
$589$	−31.6829	−1.30547
$590$	0	0
$591$	0.596197	0.0245243
$592$	0	0
$593$	−3.73954	−0.153564	−0.0767822	−	0.997048i	$-0.524465\pi$
$593$	−3.73954	−0.153564	−0.0767822	+	0.997048i	$0.524465\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	1.79082	0.0732934
$598$	0	0
$599$	−21.2084	−0.866552	−0.433276	−	0.901261i	$-0.642642\pi$
$599$	−21.2084	−0.866552	−0.433276	+	0.901261i	$0.642642\pi$
$600$	0	0
$601$	−32.1413	−1.31107	−0.655536	−	0.755164i	$-0.727557\pi$
$601$	−32.1413	−1.31107	−0.655536	+	0.755164i	$0.727557\pi$
$602$	0	0
$603$	37.0361	1.50822
$604$	0	0
$605$	0	0
$606$	0	0
$607$	5.76036	0.233806	0.116903	−	0.993143i	$-0.462703\pi$
$607$	5.76036	0.233806	0.116903	+	0.993143i	$0.462703\pi$
$608$	0	0
$609$	−1.32340	−0.0536270
$610$	0	0
$611$	4.00000	0.161823
$612$	0	0
$613$	26.4633	1.06884	0.534421	−	0.845219i	$-0.320530\pi$
$613$	26.4633	1.06884	0.534421	+	0.845219i	$0.320530\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	16.8221	0.677230	0.338615	−	0.940925i	$-0.390042\pi$
$617$	16.8221	0.677230	0.338615	+	0.940925i	$0.390042\pi$
$618$	0	0
$619$	−25.8325	−1.03829	−0.519147	−	0.854685i	$-0.673750\pi$
$619$	−25.8325	−1.03829	−0.519147	+	0.854685i	$0.673750\pi$
$620$	0	0
$621$	21.9058	0.879050
$622$	0	0
$623$	−14.5180	−0.581652
$624$	0	0
$625$	0	0
$626$	0	0
$627$	−22.1496	−0.884570
$628$	0	0
$629$	5.95162	0.237306
$630$	0	0
$631$	38.0900	1.51634	0.758170	−	0.652057i	$-0.226094\pi$
$631$	38.0900	1.51634	0.758170	+	0.652057i	$0.226094\pi$
$632$	0	0
$633$	11.6412	0.462697
$634$	0	0
$635$	0	0
$636$	0	0
$637$	−0.547814	−0.0217052
$638$	0	0
$639$	14.7480	0.583423
$640$	0	0
$641$	14.5664	0.575339	0.287669	−	0.957730i	$-0.407120\pi$
$641$	14.5664	0.575339	0.287669	+	0.957730i	$0.407120\pi$
$642$	0	0
$643$	40.5664	1.59978	0.799892	−	0.600145i	$-0.204890\pi$
$643$	40.5664	1.59978	0.799892	+	0.600145i	$0.204890\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	40.7368	1.60153	0.800765	−	0.598978i	$-0.204426\pi$
$647$	40.7368	1.60153	0.800765	+	0.598978i	$0.204426\pi$
$648$	0	0
$649$	67.2645	2.64036
$650$	0	0
$651$	5.01041	0.196374
$652$	0	0
$653$	−33.1648	−1.29784	−0.648920	−	0.760857i	$-0.724779\pi$
$653$	−33.1648	−1.29784	−0.648920	+	0.760857i	$0.724779\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	26.8470	1.04740
$658$	0	0
$659$	4.12878	0.160835	0.0804173	−	0.996761i	$-0.474375\pi$
$659$	4.12878	0.160835	0.0804173	+	0.996761i	$0.474375\pi$
$660$	0	0
$661$	6.66763	0.259341	0.129670	−	0.991557i	$-0.458608\pi$
$661$	6.66763	0.259341	0.129670	+	0.991557i	$0.458608\pi$
$662$	0	0
$663$	0.414215	0.0160868
$664$	0	0
$665$	0	0
$666$	0	0
$667$	8.18421	0.316894
$668$	0	0
$669$	2.75958	0.106692
$670$	0	0
$671$	−55.0844	−2.12651
$672$	0	0
$673$	10.4280	0.401970	0.200985	−	0.979594i	$-0.435586\pi$
$673$	10.4280	0.401970	0.200985	+	0.979594i	$0.435586\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	−43.3657	−1.66668	−0.833340	−	0.552761i	$-0.813574\pi$
$677$	−43.3657	−1.66668	−0.833340	+	0.552761i	$0.813574\pi$
$678$	0	0
$679$	4.76663	0.182926
$680$	0	0
$681$	−5.91960	−0.226840
$682$	0	0
$683$	6.81724	0.260854	0.130427	−	0.991458i	$-0.458365\pi$
$683$	6.81724	0.260854	0.130427	+	0.991458i	$0.458365\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	−5.26383	−0.200828
$688$	0	0
$689$	−1.19462	−0.0455115
$690$	0	0
$691$	−0.950838	−0.0361716	−0.0180858	−	0.999836i	$-0.505757\pi$
$691$	−0.950838	−0.0361716	−0.0180858	+	0.999836i	$0.505757\pi$
$692$	0	0
$693$	−45.6025	−1.73229
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−7.20359	−0.272855
$698$	0	0
$699$	−8.32677	−0.314947
$700$	0	0
$701$	−49.2132	−1.85876	−0.929379	−	0.369127i	$-0.879657\pi$
$701$	−49.2132	−1.85876	−0.929379	+	0.369127i	$0.879657\pi$
$702$	0	0
$703$	25.7312	0.970472
$704$	0	0
$705$	0	0
$706$	0	0
$707$	−37.9315	−1.42656
$708$	0	0
$709$	39.6204	1.48797	0.743987	−	0.668194i	$-0.232932\pi$
$709$	39.6204	1.48797	0.743987	+	0.668194i	$0.232932\pi$
$710$	0	0
$711$	16.4536	0.617060
$712$	0	0
$713$	−30.9854	−1.16041
$714$	0	0
$715$	0	0
$716$	0	0
$717$	−4.06921	−0.151967
$718$	0	0
$719$	3.33237	0.124276	0.0621382	−	0.998068i	$-0.480208\pi$
$719$	3.33237	0.124276	0.0621382	+	0.998068i	$0.480208\pi$
$720$	0	0
$721$	42.5872	1.58603
$722$	0	0
$723$	−2.60324	−0.0968156
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−2.36842	−0.0878398	−0.0439199	−	0.999035i	$-0.513985\pi$
$727$	−2.36842	−0.0878398	−0.0439199	+	0.999035i	$0.513985\pi$
$728$	0	0
$729$	−16.1213	−0.597084
$730$	0	0
$731$	18.9419	0.700591
$732$	0	0
$733$	−30.3297	−1.12025	−0.560126	−	0.828407i	$-0.689247\pi$
$733$	−30.3297	−1.12025	−0.560126	+	0.828407i	$0.689247\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−76.0609	−2.80174
$738$	0	0
$739$	33.5928	1.23573	0.617866	−	0.786283i	$-0.287997\pi$
$739$	33.5928	1.23573	0.617866	+	0.786283i	$0.287997\pi$
$740$	0	0
$741$	1.79082	0.0657874
$742$	0	0
$743$	21.9404	0.804916	0.402458	−	0.915438i	$-0.368156\pi$
$743$	21.9404	0.804916	0.402458	+	0.915438i	$0.368156\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	13.7216	0.502048
$748$	0	0
$749$	−4.23964	−0.154913
$750$	0	0
$751$	40.9944	1.49591	0.747954	−	0.663751i	$-0.231037\pi$
$751$	40.9944	1.49591	0.747954	+	0.663751i	$0.231037\pi$
$752$	0	0
$753$	−5.12319	−0.186699
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−14.0388	−0.510247	−0.255124	−	0.966908i	$-0.582116\pi$
$757$	−14.0388	−0.510247	−0.255124	+	0.966908i	$0.582116\pi$
$758$	0	0
$759$	−21.6620	−0.786282
$760$	0	0
$761$	−28.9300	−1.04871	−0.524356	−	0.851499i	$-0.675694\pi$
$761$	−28.9300	−1.04871	−0.524356	+	0.851499i	$0.675694\pi$
$762$	0	0
$763$	48.6773	1.76224
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−5.43841	−0.196369
$768$	0	0
$769$	−16.7756	−0.604943	−0.302472	−	0.953158i	$-0.597812\pi$
$769$	−16.7756	−0.604943	−0.302472	+	0.953158i	$0.597812\pi$
$770$	0	0
$771$	6.41680	0.231096
$772$	0	0
$773$	8.05957	0.289883	0.144941	−	0.989440i	$-0.453701\pi$
$773$	8.05957	0.289883	0.144941	+	0.989440i	$0.453701\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	−4.06921	−0.145982
$778$	0	0
$779$	−31.1440	−1.11585
$780$	0	0
$781$	−30.2880	−1.08379
$782$	0	0
$783$	2.67660	0.0956537
$784$	0	0
$785$	0	0
$786$	0	0
$787$	33.0636	1.17859	0.589295	−	0.807918i	$-0.299405\pi$
$787$	33.0636	1.17859	0.589295	+	0.807918i	$0.299405\pi$
$788$	0	0
$789$	3.74244	0.133234
$790$	0	0
$791$	15.4730	0.550157
$792$	0	0
$793$	4.45364	0.158153
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−21.2936	−0.754259	−0.377129	−	0.926161i	$-0.623089\pi$
$797$	−21.2936	−0.754259	−0.377129	+	0.926161i	$0.623089\pi$
$798$	0	0
$799$	16.7368	0.592107
$800$	0	0
$801$	14.1384	0.499556
$802$	0	0
$803$	−55.1357	−1.94570
$804$	0	0
$805$	0	0
$806$	0	0
$807$	2.22104	0.0781844
$808$	0	0
$809$	11.3532	0.399157	0.199578	−	0.979882i	$-0.436043\pi$
$809$	11.3532	0.399157	0.199578	+	0.979882i	$0.436043\pi$
$810$	0	0
$811$	14.2445	0.500190	0.250095	−	0.968221i	$-0.419538\pi$
$811$	14.2445	0.500190	0.250095	+	0.968221i	$0.419538\pi$
$812$	0	0
$813$	−11.5816	−0.406186
$814$	0	0
$815$	0	0
$816$	0	0
$817$	81.8934	2.86509
$818$	0	0
$819$	3.68701	0.128834
$820$	0	0
$821$	−20.2188	−0.705641	−0.352821	−	0.935691i	$-0.614777\pi$
$821$	−20.2188	−0.705641	−0.352821	+	0.935691i	$0.614777\pi$
$822$	0	0
$823$	2.00000	0.0697156	0.0348578	−	0.999392i	$-0.488902\pi$
$823$	2.00000	0.0697156	0.0348578	+	0.999392i	$0.488902\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	15.5589	0.541036	0.270518	−	0.962715i	$-0.412805\pi$
$827$	15.5589	0.541036	0.270518	+	0.962715i	$0.412805\pi$
$828$	0	0
$829$	−27.5589	−0.957160	−0.478580	−	0.878044i	$-0.658848\pi$
$829$	−27.5589	−0.957160	−0.478580	+	0.878044i	$0.658848\pi$
$830$	0	0
$831$	−10.2605	−0.355932
$832$	0	0
$833$	−2.29217	−0.0794189
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−10.1336	−0.350268
$838$	0	0
$839$	3.95835	0.136657	0.0683287	−	0.997663i	$-0.478233\pi$
$839$	3.95835	0.136657	0.0683287	+	0.997663i	$0.478233\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	0	0
$843$	−1.76103	−0.0606532
$844$	0	0
$845$	0	0
$846$	0	0
$847$	62.1849	2.13670
$848$	0	0
$849$	2.27839	0.0781941
$850$	0	0
$851$	25.1648	0.862639
$852$	0	0
$853$	−3.63158	−0.124343	−0.0621715	−	0.998065i	$-0.519803\pi$
$853$	−3.63158	−0.124343	−0.0621715	+	0.998065i	$0.519803\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	39.9196	1.36363	0.681814	−	0.731526i	$-0.261191\pi$
$857$	39.9196	1.36363	0.681814	+	0.731526i	$0.261191\pi$
$858$	0	0
$859$	26.1772	0.893153	0.446577	−	0.894745i	$-0.352643\pi$
$859$	26.1772	0.893153	0.446577	+	0.894745i	$0.352643\pi$
$860$	0	0
$861$	4.92520	0.167850
$862$	0	0
$863$	24.9211	0.848322	0.424161	−	0.905587i	$-0.360569\pi$
$863$	24.9211	0.848322	0.424161	+	0.905587i	$0.360569\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−6.13101	−0.208220
$868$	0	0
$869$	−33.7908	−1.14628
$870$	0	0
$871$	6.14961	0.208371
$872$	0	0
$873$	−4.64199	−0.157108
$874$	0	0
$875$	0	0
$876$	0	0
$877$	45.6371	1.54105	0.770527	−	0.637407i	$-0.219993\pi$
$877$	45.6371	1.54105	0.770527	+	0.637407i	$0.219993\pi$
$878$	0	0
$879$	−10.2784	−0.346681
$880$	0	0
$881$	−39.7216	−1.33826	−0.669128	−	0.743148i	$-0.733332\pi$
$881$	−39.7216	−1.33826	−0.669128	+	0.743148i	$0.733332\pi$
$882$	0	0
$883$	−55.2132	−1.85807	−0.929036	−	0.369988i	$-0.879362\pi$
$883$	−55.2132	−1.85807	−0.929036	+	0.369988i	$0.879362\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−8.13168	−0.273035	−0.136518	−	0.990638i	$-0.543591\pi$
$887$	−8.13168	−0.273035	−0.136518	+	0.990638i	$0.543591\pi$
$888$	0	0
$889$	−34.5872	−1.16002
$890$	0	0
$891$	40.7368	1.36474
$892$	0	0
$893$	72.3601	2.42144
$894$	0	0
$895$	0	0
$896$	0	0
$897$	1.75140	0.0584775
$898$	0	0
$899$	−3.78600	−0.126270
$900$	0	0
$901$	−4.99855	−0.166526
$902$	0	0
$903$	−12.9508	−0.430977
$904$	0	0
$905$	0	0
$906$	0	0
$907$	9.78600	0.324939	0.162469	−	0.986714i	$-0.448054\pi$
$907$	9.78600	0.324939	0.162469	+	0.986714i	$0.448054\pi$
$908$	0	0
$909$	36.9396	1.22521
$910$	0	0
$911$	39.3795	1.30470	0.652351	−	0.757917i	$-0.273783\pi$
$911$	39.3795	1.30470	0.652351	+	0.757917i	$0.273783\pi$
$912$	0	0
$913$	−28.1801	−0.932624
$914$	0	0
$915$	0	0
$916$	0	0
$917$	24.3088	0.802749
$918$	0	0
$919$	−0.994404	−0.0328024	−0.0164012	−	0.999865i	$-0.505221\pi$
$919$	−0.994404	−0.0328024	−0.0164012	+	0.999865i	$0.505221\pi$
$920$	0	0
$921$	10.1496	0.334441
$922$	0	0
$923$	2.44882	0.0806039
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−41.4737	−1.36217
$928$	0	0
$929$	22.6933	0.744542	0.372271	−	0.928124i	$-0.378579\pi$
$929$	22.6933	0.744542	0.372271	+	0.928124i	$0.378579\pi$
$930$	0	0
$931$	−9.90997	−0.324786
$932$	0	0
$933$	8.88163	0.290772
$934$	0	0
$935$	0	0
$936$	0	0
$937$	34.0096	1.11105	0.555523	−	0.831501i	$-0.312518\pi$
$937$	34.0096	1.11105	0.555523	+	0.831501i	$0.312518\pi$
$938$	0	0
$939$	4.11086	0.134153
$940$	0	0
$941$	−31.3532	−1.02208	−0.511042	−	0.859555i	$-0.670740\pi$
$941$	−31.3532	−1.02208	−0.511042	+	0.859555i	$0.670740\pi$
$942$	0	0
$943$	−30.4585	−0.991864
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−2.24378	−0.0729132	−0.0364566	−	0.999335i	$-0.511607\pi$
$947$	−2.24378	−0.0729132	−0.0364566	+	0.999335i	$0.511607\pi$
$948$	0	0
$949$	4.45778	0.144706
$950$	0	0
$951$	−1.79082	−0.0580713
$952$	0	0
$953$	1.56237	0.0506102	0.0253051	−	0.999680i	$-0.491944\pi$
$953$	1.56237	0.0506102	0.0253051	+	0.999680i	$0.491944\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	−2.64681	−0.0855592
$958$	0	0
$959$	9.32340	0.301068
$960$	0	0
$961$	−16.6662	−0.537619
$962$	0	0
$963$	4.12878	0.133048
$964$	0	0
$965$	0	0
$966$	0	0
$967$	58.8060	1.89108	0.945538	−	0.325513i	$-0.105537\pi$
$967$	58.8060	1.89108	0.945538	+	0.325513i	$0.105537\pi$
$968$	0	0
$969$	7.49316	0.240715
$970$	0	0
$971$	−15.5541	−0.499154	−0.249577	−	0.968355i	$-0.580292\pi$
$971$	−15.5541	−0.499154	−0.249577	+	0.968355i	$0.580292\pi$
$972$	0	0
$973$	64.8615	2.07936
$974$	0	0
$975$	0	0
$976$	0	0
$977$	35.9612	1.15050	0.575251	−	0.817977i	$-0.304904\pi$
$977$	35.9612	1.15050	0.575251	+	0.817977i	$0.304904\pi$
$978$	0	0
$979$	−29.0361	−0.927996
$980$	0	0
$981$	−47.4045	−1.51351
$982$	0	0
$983$	50.0609	1.59670	0.798348	−	0.602197i	$-0.205708\pi$
$983$	50.0609	1.59670	0.798348	+	0.602197i	$0.205708\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	−11.4432	−0.364242
$988$	0	0
$989$	80.0907	2.54674
$990$	0	0
$991$	20.0096	0.635627	0.317813	−	0.948153i	$-0.397051\pi$
$991$	20.0096	0.635627	0.317813	+	0.948153i	$0.397051\pi$
$992$	0	0
$993$	9.90997	0.314483
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−19.7521	−0.625554	−0.312777	−	0.949827i	$-0.601259\pi$
$997$	−19.7521	−0.625554	−0.312777	+	0.949827i	$0.601259\pi$
$998$	0	0
$999$	8.23000	0.260386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5800.2.a.q.1.2		3
5.4	even	2		1160.2.a.g.1.2	✓	3
20.19	odd	2		2320.2.a.p.1.2		3
40.19	odd	2		9280.2.a.bq.1.2		3
40.29	even	2		9280.2.a.bo.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1160.2.a.g.1.2	✓	3	5.4	even	2
2320.2.a.p.1.2		3	20.19	odd	2
5800.2.a.q.1.2		3	1.1	even	1	trivial
9280.2.a.bo.1.2		3	40.29	even	2
9280.2.a.bq.1.2		3	40.19	odd	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+0.462598 q^{3} +2.86081 q^{7} -2.78600 q^{9} +5.72161 q^{11} -0.462598 q^{13} -1.93561 q^{17} -8.36842 q^{19} +1.32340 q^{21} -8.18421 q^{23} -2.67660 q^{27} -1.00000 q^{29} +3.78600 q^{31} +2.64681 q^{33} -3.07480 q^{37} -0.213997 q^{39} +3.72161 q^{41} -9.78600 q^{43} -8.64681 q^{47} +1.18421 q^{49} -0.895410 q^{51} +2.58242 q^{53} -3.87122 q^{57} +11.7562 q^{59} -9.62743 q^{61} -7.97021 q^{63} -13.2936 q^{67} -3.78600 q^{69} -5.29362 q^{71} -9.63640 q^{73} +16.3684 q^{77} -5.90582 q^{79} +7.11982 q^{81} -4.92520 q^{83} -0.462598 q^{87} -5.07480 q^{89} -1.32340 q^{91} +1.75140 q^{93} +1.66618 q^{97} -15.9404 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{3} + 3 q^{7} + 2 q^{9} + 6 q^{11} + q^{13} - 5 q^{17} + 2 q^{19} - 4 q^{21} - 11 q^{23} - 16 q^{27} - 3 q^{29} + q^{31} - 8 q^{33} - 14 q^{37} - 11 q^{39} - 19 q^{43} - 10 q^{47} - 10 q^{49}+ \cdots + 9 q^{97}+O(q^{100}) \) 3 * q - q^3 + 3 * q^7 + 2 * q^9 + 6 * q^11 + q^13 - 5 * q^17 + 2 * q^19 - 4 * q^21 - 11 * q^23 - 16 * q^27 - 3 * q^29 + q^31 - 8 * q^33 - 14 * q^37 - 11 * q^39 - 19 * q^43 - 10 * q^47 - 10 * q^49 + 26 * q^51 - 9 * q^53 - 10 * q^57 + q^59 + 7 * q^61 - 8 * q^67 - q^69 + 16 * q^71 - 9 * q^73 + 22 * q^77 + 7 * q^79 + 7 * q^81 - 10 * q^83 + q^87 - 20 * q^89 + 4 * q^91 + 18 * q^93 + 9 * q^97

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