LMFDB - Embedded newform 9200.2.a.da.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9200,2,Mod(1,9200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9200, 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("9200.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9200 = 2^{4} \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9200.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:	$73.4623698596$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 12x^{5} + 9x^{4} + 43x^{3} - 14x^{2} - 49x - 9 $ x^7 - x^6 - 12x^5 + 9x^4 + 43x^3 - 14x^2 - 49*x - 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 575)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.07994$ of defining polynomial
Character	$\chi$	$=$	9200.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.06928 q^{3} -2.95289 q^{7} -1.85663 q^{9} +O(q^{10})$	$q+1.06928 q^{3} -2.95289 q^{7} -1.85663 q^{9} -5.89337 q^{11} +3.64965 q^{13} -4.68638 q^{17} -5.73350 q^{19} -3.15748 q^{21} +1.00000 q^{23} -5.19312 q^{27} +10.3864 q^{29} -7.29495 q^{31} -6.30169 q^{33} +0.612908 q^{37} +3.90251 q^{39} -9.10447 q^{41} +1.58385 q^{43} +6.22567 q^{47} +1.71954 q^{49} -5.01108 q^{51} -3.17878 q^{53} -6.13074 q^{57} -1.38576 q^{59} +6.02130 q^{61} +5.48242 q^{63} +13.3807 q^{67} +1.06928 q^{69} +6.22567 q^{71} +4.48063 q^{73} +17.4024 q^{77} +7.01303 q^{79} +0.0169706 q^{81} +2.46049 q^{83} +11.1060 q^{87} +2.15663 q^{89} -10.7770 q^{91} -7.80038 q^{93} -17.7687 q^{97} +10.9418 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 3 q^{7} + 15 q^{9}+O(q^{10}) $ 7 * q - 3 * q^7 + 15 * q^9	$ 7 q - 3 q^{7} + 15 q^{9} + q^{11} - 3 q^{13} + 10 q^{17} - 15 q^{19} + 2 q^{21} + 7 q^{23} + 3 q^{29} - 14 q^{31} + 6 q^{33} - 10 q^{37} + 8 q^{39} + 19 q^{41} - 5 q^{43} + 14 q^{47} + 40 q^{49} - 2 q^{51} + 4 q^{53} - 4 q^{57} + 16 q^{59} + 40 q^{61} - 53 q^{63} + 4 q^{67} + 14 q^{71} - 3 q^{73} - 17 q^{77} + q^{79} + 47 q^{81} - 17 q^{83} + 56 q^{87} + 16 q^{89} - 25 q^{91} + 14 q^{93} - 24 q^{97} + 53 q^{99}+O(q^{100}) $ 7 * q - 3 * q^7 + 15 * q^9 + q^11 - 3 * q^13 + 10 * q^17 - 15 * q^19 + 2 * q^21 + 7 * q^23 + 3 * q^29 - 14 * q^31 + 6 * q^33 - 10 * q^37 + 8 * q^39 + 19 * q^41 - 5 * q^43 + 14 * q^47 + 40 * q^49 - 2 * q^51 + 4 * q^53 - 4 * q^57 + 16 * q^59 + 40 * q^61 - 53 * q^63 + 4 * q^67 + 14 * q^71 - 3 * q^73 - 17 * q^77 + q^79 + 47 * q^81 - 17 * q^83 + 56 * q^87 + 16 * q^89 - 25 * q^91 + 14 * q^93 - 24 * q^97 + 53 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0	0
$2$	0	0
$3$	1.06928	0.617352	0.308676	−	0.951167i	$-0.400114\pi$
$3$	1.06928	0.617352	0.308676	+	0.951167i	$0.400114\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	−2.95289	−1.11609	−0.558043	−	0.829812i	$-0.688448\pi$
$7$	−2.95289	−1.11609	−0.558043	+	0.829812i	$0.688448\pi$
$8$	0	0
$9$	−1.85663	−0.618877
$10$	0	0
$11$	−5.89337	−1.77692	−0.888459	−	0.458956i	$-0.848223\pi$
$11$	−5.89337	−1.77692	−0.888459	+	0.458956i	$0.848223\pi$
$12$	0	0
$13$	3.64965	1.01223	0.506115	−	0.862466i	$-0.331081\pi$
$13$	3.64965	1.01223	0.506115	+	0.862466i	$0.331081\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−4.68638	−1.13661	−0.568307	−	0.822816i	$-0.692402\pi$
$17$	−4.68638	−1.13661	−0.568307	+	0.822816i	$0.692402\pi$
$18$	0	0
$19$	−5.73350	−1.31535	−0.657677	−	0.753300i	$-0.728461\pi$
$19$	−5.73350	−1.31535	−0.657677	+	0.753300i	$0.728461\pi$
$20$	0	0
$21$	−3.15748	−0.689018
$22$	0	0
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−5.19312	−0.999416
$28$	0	0
$29$	10.3864	1.92871	0.964354	−	0.264617i	$-0.0852455\pi$
$29$	10.3864	1.92871	0.964354	+	0.264617i	$0.0852455\pi$
$30$	0	0
$31$	−7.29495	−1.31021	−0.655106	−	0.755537i	$-0.727376\pi$
$31$	−7.29495	−1.31021	−0.655106	+	0.755537i	$0.727376\pi$
$32$	0	0
$33$	−6.30169	−1.09698
$34$	0	0
$35$	0	0
$36$	0	0
$37$	0.612908	0.100761	0.0503807	−	0.998730i	$-0.483957\pi$
$37$	0.612908	0.100761	0.0503807	+	0.998730i	$0.483957\pi$
$38$	0	0
$39$	3.90251	0.624902
$40$	0	0
$41$	−9.10447	−1.42188	−0.710940	−	0.703253i	$-0.751730\pi$
$41$	−9.10447	−1.42188	−0.710940	+	0.703253i	$0.751730\pi$
$42$	0	0
$43$	1.58385	0.241535	0.120768	−	0.992681i	$-0.461464\pi$
$43$	1.58385	0.241535	0.120768	+	0.992681i	$0.461464\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	6.22567	0.908107	0.454053	−	0.890974i	$-0.349978\pi$
$47$	6.22567	0.908107	0.454053	+	0.890974i	$0.349978\pi$
$48$	0	0
$49$	1.71954	0.245648
$50$	0	0
$51$	−5.01108	−0.701691
$52$	0	0
$53$	−3.17878	−0.436639	−0.218319	−	0.975877i	$-0.570057\pi$
$53$	−3.17878	−0.436639	−0.218319	+	0.975877i	$0.570057\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	−6.13074	−0.812036
$58$	0	0
$59$	−1.38576	−0.180411	−0.0902056	−	0.995923i	$-0.528752\pi$
$59$	−1.38576	−0.180411	−0.0902056	+	0.995923i	$0.528752\pi$
$60$	0	0
$61$	6.02130	0.770949	0.385474	−	0.922719i	$-0.374038\pi$
$61$	6.02130	0.770949	0.385474	+	0.922719i	$0.374038\pi$
$62$	0	0
$63$	5.48242	0.690720
$64$	0	0
$65$	0	0
$66$	0	0
$67$	13.3807	1.63472	0.817359	−	0.576129i	$-0.195437\pi$
$67$	13.3807	1.63472	0.817359	+	0.576129i	$0.195437\pi$
$68$	0	0
$69$	1.06928	0.128727
$70$	0	0
$71$	6.22567	0.738851	0.369425	−	0.929260i	$-0.379555\pi$
$71$	6.22567	0.738851	0.369425	+	0.929260i	$0.379555\pi$
$72$	0	0
$73$	4.48063	0.524418	0.262209	−	0.965011i	$-0.415549\pi$
$73$	4.48063	0.524418	0.262209	+	0.965011i	$0.415549\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	17.4024	1.98319
$78$	0	0
$79$	7.01303	0.789028	0.394514	−	0.918890i	$-0.370913\pi$
$79$	7.01303	0.789028	0.394514	+	0.918890i	$0.370913\pi$
$80$	0	0
$81$	0.0169706	0.00188563
$82$	0	0
$83$	2.46049	0.270074	0.135037	−	0.990841i	$-0.456885\pi$
$83$	2.46049	0.270074	0.135037	+	0.990841i	$0.456885\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	11.1060	1.19069
$88$	0	0
$89$	2.15663	0.228602	0.114301	−	0.993446i	$-0.463537\pi$
$89$	2.15663	0.228602	0.114301	+	0.993446i	$0.463537\pi$
$90$	0	0
$91$	−10.7770	−1.12974
$92$	0	0
$93$	−7.80038	−0.808861
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−17.7687	−1.80414	−0.902068	−	0.431594i	$-0.857951\pi$
$97$	−17.7687	−1.80414	−0.902068	+	0.431594i	$0.857951\pi$
$98$	0	0
$99$	10.9418	1.09969
$100$	0	0
$101$	3.18653	0.317072	0.158536	−	0.987353i	$-0.449323\pi$
$101$	3.18653	0.317072	0.158536	+	0.987353i	$0.449323\pi$
$102$	0	0
$103$	−12.6204	−1.24352	−0.621761	−	0.783207i	$-0.713582\pi$
$103$	−12.6204	−1.24352	−0.621761	+	0.783207i	$0.713582\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	1.68553	0.162947	0.0814733	−	0.996676i	$-0.474037\pi$
$107$	1.68553	0.162947	0.0814733	+	0.996676i	$0.474037\pi$
$108$	0	0
$109$	−5.80929	−0.556429	−0.278215	−	0.960519i	$-0.589743\pi$
$109$	−5.80929	−0.556429	−0.278215	+	0.960519i	$0.589743\pi$
$110$	0	0
$111$	0.655373	0.0622052
$112$	0	0
$113$	9.40374	0.884630	0.442315	−	0.896860i	$-0.354157\pi$
$113$	9.40374	0.884630	0.442315	+	0.896860i	$0.354157\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	−6.77604	−0.626446
$118$	0	0
$119$	13.8384	1.26856
$120$	0	0
$121$	23.7318	2.15744
$122$	0	0
$123$	−9.73527	−0.877799
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−15.8267	−1.40440	−0.702198	−	0.711982i	$-0.747798\pi$
$127$	−15.8267	−1.40440	−0.702198	+	0.711982i	$0.747798\pi$
$128$	0	0
$129$	1.69359	0.149112
$130$	0	0
$131$	6.97506	0.609414	0.304707	−	0.952446i	$-0.401442\pi$
$131$	6.97506	0.609414	0.304707	+	0.952446i	$0.401442\pi$
$132$	0	0
$133$	16.9304	1.46805
$134$	0	0
$135$	0	0
$136$	0	0
$137$	3.70809	0.316803	0.158402	−	0.987375i	$-0.449366\pi$
$137$	3.70809	0.316803	0.158402	+	0.987375i	$0.449366\pi$
$138$	0	0
$139$	1.28393	0.108902	0.0544509	−	0.998516i	$-0.482659\pi$
$139$	1.28393	0.108902	0.0544509	+	0.998516i	$0.482659\pi$
$140$	0	0
$141$	6.65701	0.560621
$142$	0	0
$143$	−21.5087	−1.79865
$144$	0	0
$145$	0	0
$146$	0	0
$147$	1.83868	0.151651
$148$	0	0
$149$	−0.734825	−0.0601992	−0.0300996	−	0.999547i	$-0.509582\pi$
$149$	−0.734825	−0.0601992	−0.0300996	+	0.999547i	$0.509582\pi$
$150$	0	0
$151$	12.8604	1.04656	0.523281	−	0.852160i	$-0.324708\pi$
$151$	12.8604	1.04656	0.523281	+	0.852160i	$0.324708\pi$
$152$	0	0
$153$	8.70088	0.703425
$154$	0	0
$155$	0	0
$156$	0	0
$157$	13.9303	1.11176	0.555878	−	0.831264i	$-0.312382\pi$
$157$	13.9303	1.11176	0.555878	+	0.831264i	$0.312382\pi$
$158$	0	0
$159$	−3.39902	−0.269560
$160$	0	0
$161$	−2.95289	−0.232720
$162$	0	0
$163$	12.6677	0.992212	0.496106	−	0.868262i	$-0.334763\pi$
$163$	12.6677	0.992212	0.496106	+	0.868262i	$0.334763\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−6.67811	−0.516768	−0.258384	−	0.966042i	$-0.583190\pi$
$167$	−6.67811	−0.516768	−0.258384	+	0.966042i	$0.583190\pi$
$168$	0	0
$169$	0.319911	0.0246085
$170$	0	0
$171$	10.6450	0.814042
$172$	0	0
$173$	−15.7354	−1.19634	−0.598171	−	0.801369i	$-0.704106\pi$
$173$	−15.7354	−1.19634	−0.598171	+	0.801369i	$0.704106\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−1.48178	−0.111377
$178$	0	0
$179$	7.77154	0.580872	0.290436	−	0.956894i	$-0.406200\pi$
$179$	7.77154	0.580872	0.290436	+	0.956894i	$0.406200\pi$
$180$	0	0
$181$	−2.46939	−0.183548	−0.0917741	−	0.995780i	$-0.529254\pi$
$181$	−2.46939	−0.183548	−0.0917741	+	0.995780i	$0.529254\pi$
$182$	0	0
$183$	6.43849	0.475947
$184$	0	0
$185$	0	0
$186$	0	0
$187$	27.6186	2.01967
$188$	0	0
$189$	15.3347	1.11543
$190$	0	0
$191$	9.74202	0.704908	0.352454	−	0.935829i	$-0.385347\pi$
$191$	9.74202	0.704908	0.352454	+	0.935829i	$0.385347\pi$
$192$	0	0
$193$	1.54038	0.110879	0.0554394	−	0.998462i	$-0.482344\pi$
$193$	1.54038	0.110879	0.0554394	+	0.998462i	$0.482344\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	14.7266	1.04923	0.524614	−	0.851340i	$-0.324210\pi$
$197$	14.7266	1.04923	0.524614	+	0.851340i	$0.324210\pi$
$198$	0	0
$199$	19.3914	1.37462	0.687309	−	0.726365i	$-0.258792\pi$
$199$	19.3914	1.37462	0.687309	+	0.726365i	$0.258792\pi$
$200$	0	0
$201$	14.3078	1.00920
$202$	0	0
$203$	−30.6699	−2.15260
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−1.85663	−0.129045
$208$	0	0
$209$	33.7896	2.33728
$210$	0	0
$211$	−23.0986	−1.59017	−0.795086	−	0.606497i	$-0.792574\pi$
$211$	−23.0986	−1.59017	−0.795086	+	0.606497i	$0.792574\pi$
$212$	0	0
$213$	6.65701	0.456131
$214$	0	0
$215$	0	0
$216$	0	0
$217$	21.5412	1.46231
$218$	0	0
$219$	4.79107	0.323751
$220$	0	0
$221$	−17.1036	−1.15052
$222$	0	0
$223$	2.17546	0.145679	0.0728396	−	0.997344i	$-0.476794\pi$
$223$	2.17546	0.145679	0.0728396	+	0.997344i	$0.476794\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	13.4985	0.895928	0.447964	−	0.894051i	$-0.352149\pi$
$227$	13.4985	0.895928	0.447964	+	0.894051i	$0.352149\pi$
$228$	0	0
$229$	9.00063	0.594778	0.297389	−	0.954756i	$-0.403884\pi$
$229$	9.00063	0.594778	0.297389	+	0.954756i	$0.403884\pi$
$230$	0	0
$231$	18.6082	1.22433
$232$	0	0
$233$	−19.1523	−1.25471	−0.627354	−	0.778734i	$-0.715862\pi$
$233$	−19.1523	−1.25471	−0.627354	+	0.778734i	$0.715862\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	7.49892	0.487107
$238$	0	0
$239$	−11.4712	−0.742009	−0.371005	−	0.928631i	$-0.620987\pi$
$239$	−11.4712	−0.742009	−0.371005	+	0.928631i	$0.620987\pi$
$240$	0	0
$241$	26.4633	1.70465	0.852325	−	0.523012i	$-0.175192\pi$
$241$	26.4633	1.70465	0.852325	+	0.523012i	$0.175192\pi$
$242$	0	0
$243$	15.5975	1.00058
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−20.9252	−1.33144
$248$	0	0
$249$	2.63096	0.166731
$250$	0	0
$251$	−19.3419	−1.22085	−0.610426	−	0.792073i	$-0.709002\pi$
$251$	−19.3419	−1.22085	−0.610426	+	0.792073i	$0.709002\pi$
$252$	0	0
$253$	−5.89337	−0.370513
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−10.7563	−0.670959	−0.335480	−	0.942047i	$-0.608898\pi$
$257$	−10.7563	−0.670959	−0.335480	+	0.942047i	$0.608898\pi$
$258$	0	0
$259$	−1.80985	−0.112458
$260$	0	0
$261$	−19.2837	−1.19363
$262$	0	0
$263$	−14.9372	−0.921069	−0.460535	−	0.887642i	$-0.652342\pi$
$263$	−14.9372	−0.921069	−0.460535	+	0.887642i	$0.652342\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	2.30605	0.141128
$268$	0	0
$269$	14.1731	0.864146	0.432073	−	0.901839i	$-0.357782\pi$
$269$	14.1731	0.864146	0.432073	+	0.901839i	$0.357782\pi$
$270$	0	0
$271$	6.12384	0.371996	0.185998	−	0.982550i	$-0.440448\pi$
$271$	6.12384	0.371996	0.185998	+	0.982550i	$0.440448\pi$
$272$	0	0
$273$	−11.5237	−0.697444
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−2.95941	−0.177814	−0.0889068	−	0.996040i	$-0.528337\pi$
$277$	−2.95941	−0.177814	−0.0889068	+	0.996040i	$0.528337\pi$
$278$	0	0
$279$	13.5440	0.810860
$280$	0	0
$281$	−27.1304	−1.61846	−0.809231	−	0.587490i	$-0.800116\pi$
$281$	−27.1304	−1.61846	−0.809231	+	0.587490i	$0.800116\pi$
$282$	0	0
$283$	−3.50760	−0.208505	−0.104253	−	0.994551i	$-0.533245\pi$
$283$	−3.50760	−0.208505	−0.104253	+	0.994551i	$0.533245\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	26.8845	1.58694
$288$	0	0
$289$	4.96219	0.291893
$290$	0	0
$291$	−18.9998	−1.11379
$292$	0	0
$293$	−1.47172	−0.0859787	−0.0429894	−	0.999076i	$-0.513688\pi$
$293$	−1.47172	−0.0859787	−0.0429894	+	0.999076i	$0.513688\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	30.6050	1.77588
$298$	0	0
$299$	3.64965	0.211064
$300$	0	0
$301$	−4.67693	−0.269574
$302$	0	0
$303$	3.40731	0.195745
$304$	0	0
$305$	0	0
$306$	0	0
$307$	18.4258	1.05162	0.525808	−	0.850604i	$-0.323763\pi$
$307$	18.4258	1.05162	0.525808	+	0.850604i	$0.323763\pi$
$308$	0	0
$309$	−13.4948	−0.767690
$310$	0	0
$311$	14.0373	0.795985	0.397992	−	0.917389i	$-0.369707\pi$
$311$	14.0373	0.795985	0.397992	+	0.917389i	$0.369707\pi$
$312$	0	0
$313$	4.85733	0.274553	0.137276	−	0.990533i	$-0.456165\pi$
$313$	4.85733	0.274553	0.137276	+	0.990533i	$0.456165\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−20.5571	−1.15460	−0.577302	−	0.816531i	$-0.695895\pi$
$317$	−20.5571	−1.15460	−0.577302	+	0.816531i	$0.695895\pi$
$318$	0	0
$319$	−61.2109	−3.42715
$320$	0	0
$321$	1.80231	0.100595
$322$	0	0
$323$	26.8694	1.49505
$324$	0	0
$325$	0	0
$326$	0	0
$327$	−6.21178	−0.343512
$328$	0	0
$329$	−18.3837	−1.01353
$330$	0	0
$331$	28.5828	1.57105	0.785525	−	0.618830i	$-0.212393\pi$
$331$	28.5828	1.57105	0.785525	+	0.618830i	$0.212393\pi$
$332$	0	0
$333$	−1.13794	−0.0623589
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−3.73357	−0.203381	−0.101690	−	0.994816i	$-0.532425\pi$
$337$	−3.73357	−0.203381	−0.101690	+	0.994816i	$0.532425\pi$
$338$	0	0
$339$	10.0553	0.546128
$340$	0	0
$341$	42.9918	2.32814
$342$	0	0
$343$	15.5926	0.841921
$344$	0	0
$345$	0	0
$346$	0	0
$347$	26.2237	1.40776	0.703880	−	0.710319i	$-0.251449\pi$
$347$	26.2237	1.40776	0.703880	+	0.710319i	$0.251449\pi$
$348$	0	0
$349$	28.6776	1.53507	0.767537	−	0.641004i	$-0.221482\pi$
$349$	28.6776	1.53507	0.767537	+	0.641004i	$0.221482\pi$
$350$	0	0
$351$	−18.9530	−1.01164
$352$	0	0
$353$	−0.121347	−0.00645865	−0.00322933	−	0.999995i	$-0.501028\pi$
$353$	−0.121347	−0.00645865	−0.00322933	+	0.999995i	$0.501028\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	14.7971	0.783148
$358$	0	0
$359$	23.2795	1.22865	0.614324	−	0.789054i	$-0.289429\pi$
$359$	23.2795	1.22865	0.614324	+	0.789054i	$0.289429\pi$
$360$	0	0
$361$	13.8730	0.730157
$362$	0	0
$363$	25.3760	1.33190
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−28.8647	−1.50673	−0.753363	−	0.657605i	$-0.771570\pi$
$367$	−28.8647	−1.50673	−0.753363	+	0.657605i	$0.771570\pi$
$368$	0	0
$369$	16.9036	0.879968
$370$	0	0
$371$	9.38657	0.487327
$372$	0	0
$373$	−25.2116	−1.30541	−0.652703	−	0.757614i	$-0.726365\pi$
$373$	−25.2116	−1.30541	−0.652703	+	0.757614i	$0.726365\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	37.9067	1.95229
$378$	0	0
$379$	−7.32791	−0.376409	−0.188205	−	0.982130i	$-0.560267\pi$
$379$	−7.32791	−0.376409	−0.188205	+	0.982130i	$0.560267\pi$
$380$	0	0
$381$	−16.9233	−0.867006
$382$	0	0
$383$	−4.37082	−0.223338	−0.111669	−	0.993745i	$-0.535620\pi$
$383$	−4.37082	−0.223338	−0.111669	+	0.993745i	$0.535620\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−2.94063	−0.149480
$388$	0	0
$389$	−16.6902	−0.846226	−0.423113	−	0.906077i	$-0.639063\pi$
$389$	−16.6902	−0.846226	−0.423113	+	0.906077i	$0.639063\pi$
$390$	0	0
$391$	−4.68638	−0.237001
$392$	0	0
$393$	7.45832	0.376222
$394$	0	0
$395$	0	0
$396$	0	0
$397$	18.2264	0.914754	0.457377	−	0.889273i	$-0.348789\pi$
$397$	18.2264	0.914754	0.457377	+	0.889273i	$0.348789\pi$
$398$	0	0
$399$	18.1034	0.906302
$400$	0	0
$401$	−23.9721	−1.19711	−0.598554	−	0.801082i	$-0.704258\pi$
$401$	−23.9721	−1.19711	−0.598554	+	0.801082i	$0.704258\pi$
$402$	0	0
$403$	−26.6240	−1.32624
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−3.61209	−0.179045
$408$	0	0
$409$	33.7235	1.66752	0.833760	−	0.552127i	$-0.186184\pi$
$409$	33.7235	1.66752	0.833760	+	0.552127i	$0.186184\pi$
$410$	0	0
$411$	3.96500	0.195579
$412$	0	0
$413$	4.09200	0.201354
$414$	0	0
$415$	0	0
$416$	0	0
$417$	1.37289	0.0672307
$418$	0	0
$419$	−3.62819	−0.177249	−0.0886244	−	0.996065i	$-0.528247\pi$
$419$	−3.62819	−0.177249	−0.0886244	+	0.996065i	$0.528247\pi$
$420$	0	0
$421$	15.3678	0.748982	0.374491	−	0.927231i	$-0.377818\pi$
$421$	15.3678	0.748982	0.374491	+	0.927231i	$0.377818\pi$
$422$	0	0
$423$	−11.5588	−0.562006
$424$	0	0
$425$	0	0
$426$	0	0
$427$	−17.7802	−0.860445
$428$	0	0
$429$	−22.9989	−1.11040
$430$	0	0
$431$	14.0199	0.675313	0.337656	−	0.941269i	$-0.390366\pi$
$431$	14.0199	0.675313	0.337656	+	0.941269i	$0.390366\pi$
$432$	0	0
$433$	22.9911	1.10488	0.552441	−	0.833552i	$-0.313697\pi$
$433$	22.9911	1.10488	0.552441	+	0.833552i	$0.313697\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	−5.73350	−0.274270
$438$	0	0
$439$	−3.54418	−0.169154	−0.0845772	−	0.996417i	$-0.526954\pi$
$439$	−3.54418	−0.169154	−0.0845772	+	0.996417i	$0.526954\pi$
$440$	0	0
$441$	−3.19255	−0.152026
$442$	0	0
$443$	4.89648	0.232639	0.116319	−	0.993212i	$-0.462890\pi$
$443$	4.89648	0.232639	0.116319	+	0.993212i	$0.462890\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−0.785737	−0.0371641
$448$	0	0
$449$	−33.5702	−1.58427	−0.792137	−	0.610344i	$-0.791031\pi$
$449$	−33.5702	−1.58427	−0.792137	+	0.610344i	$0.791031\pi$
$450$	0	0
$451$	53.6560	2.52656
$452$	0	0
$453$	13.7514	0.646096
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−35.2502	−1.64893	−0.824467	−	0.565910i	$-0.808525\pi$
$457$	−35.2502	−1.64893	−0.824467	+	0.565910i	$0.808525\pi$
$458$	0	0
$459$	24.3369	1.13595
$460$	0	0
$461$	−30.3269	−1.41247	−0.706233	−	0.707979i	$-0.749607\pi$
$461$	−30.3269	−1.41247	−0.706233	+	0.707979i	$0.749607\pi$
$462$	0	0
$463$	−21.7155	−1.00920	−0.504602	−	0.863352i	$-0.668361\pi$
$463$	−21.7155	−1.00920	−0.504602	+	0.863352i	$0.668361\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−16.4780	−0.762511	−0.381255	−	0.924470i	$-0.624508\pi$
$467$	−16.4780	−0.762511	−0.381255	+	0.924470i	$0.624508\pi$
$468$	0	0
$469$	−39.5118	−1.82449
$470$	0	0
$471$	14.8954	0.686344
$472$	0	0
$473$	−9.33422	−0.429188
$474$	0	0
$475$	0	0
$476$	0	0
$477$	5.90182	0.270226
$478$	0	0
$479$	33.3508	1.52384	0.761919	−	0.647672i	$-0.224257\pi$
$479$	33.3508	1.52384	0.761919	+	0.647672i	$0.224257\pi$
$480$	0	0
$481$	2.23690	0.101994
$482$	0	0
$483$	−3.15748	−0.143670
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−19.9386	−0.903506	−0.451753	−	0.892143i	$-0.649201\pi$
$487$	−19.9386	−0.903506	−0.451753	+	0.892143i	$0.649201\pi$
$488$	0	0
$489$	13.5454	0.612544
$490$	0	0
$491$	9.51846	0.429562	0.214781	−	0.976662i	$-0.431096\pi$
$491$	9.51846	0.429562	0.214781	+	0.976662i	$0.431096\pi$
$492$	0	0
$493$	−48.6747	−2.19220
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−18.3837	−0.824621
$498$	0	0
$499$	27.6987	1.23997	0.619983	−	0.784616i	$-0.287140\pi$
$499$	27.6987	1.23997	0.619983	+	0.784616i	$0.287140\pi$
$500$	0	0
$501$	−7.14080	−0.319027
$502$	0	0
$503$	−0.761780	−0.0339661	−0.0169831	−	0.999856i	$-0.505406\pi$
$503$	−0.761780	−0.0339661	−0.0169831	+	0.999856i	$0.505406\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	0.342076	0.0151921
$508$	0	0
$509$	10.2481	0.454239	0.227119	−	0.973867i	$-0.427069\pi$
$509$	10.2481	0.454239	0.227119	+	0.973867i	$0.427069\pi$
$510$	0	0
$511$	−13.2308	−0.585296
$512$	0	0
$513$	29.7747	1.31459
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−36.6901	−1.61363
$518$	0	0
$519$	−16.8256	−0.738563
$520$	0	0
$521$	1.36360	0.0597405	0.0298702	−	0.999554i	$-0.490491\pi$
$521$	1.36360	0.0597405	0.0298702	+	0.999554i	$0.490491\pi$
$522$	0	0
$523$	−2.50258	−0.109430	−0.0547150	−	0.998502i	$-0.517425\pi$
$523$	−2.50258	−0.109430	−0.0547150	+	0.998502i	$0.517425\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	34.1869	1.48921
$528$	0	0
$529$	1.00000	0.0434783
$530$	0	0
$531$	2.57285	0.111652
$532$	0	0
$533$	−33.2281	−1.43927
$534$	0	0
$535$	0	0
$536$	0	0
$537$	8.30999	0.358603
$538$	0	0
$539$	−10.1339	−0.436497
$540$	0	0
$541$	14.4910	0.623019	0.311509	−	0.950243i	$-0.399166\pi$
$541$	14.4910	0.623019	0.311509	+	0.950243i	$0.399166\pi$
$542$	0	0
$543$	−2.64048	−0.113314
$544$	0	0
$545$	0	0
$546$	0	0
$547$	25.9898	1.11124	0.555622	−	0.831435i	$-0.312480\pi$
$547$	25.9898	1.11124	0.555622	+	0.831435i	$0.312480\pi$
$548$	0	0
$549$	−11.1793	−0.477122
$550$	0	0
$551$	−59.5504	−2.53693
$552$	0	0
$553$	−20.7087	−0.880623
$554$	0	0
$555$	0	0
$556$	0	0
$557$	6.12731	0.259623	0.129811	−	0.991539i	$-0.458563\pi$
$557$	6.12731	0.259623	0.129811	+	0.991539i	$0.458563\pi$
$558$	0	0
$559$	5.78049	0.244489
$560$	0	0
$561$	29.5321	1.24685
$562$	0	0
$563$	22.2228	0.936579	0.468289	−	0.883575i	$-0.344870\pi$
$563$	22.2228	0.936579	0.468289	+	0.883575i	$0.344870\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	−0.0501123	−0.00210452
$568$	0	0
$569$	−2.78729	−0.116849	−0.0584247	−	0.998292i	$-0.518608\pi$
$569$	−2.78729	−0.116849	−0.0584247	+	0.998292i	$0.518608\pi$
$570$	0	0
$571$	22.7888	0.953683	0.476842	−	0.878989i	$-0.341782\pi$
$571$	22.7888	0.953683	0.476842	+	0.878989i	$0.341782\pi$
$572$	0	0
$573$	10.4170	0.435176
$574$	0	0
$575$	0	0
$576$	0	0
$577$	24.8664	1.03520	0.517601	−	0.855622i	$-0.326825\pi$
$577$	24.8664	1.03520	0.517601	+	0.855622i	$0.326825\pi$
$578$	0	0
$579$	1.64710	0.0684512
$580$	0	0
$581$	−7.26555	−0.301426
$582$	0	0
$583$	18.7337	0.775871
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−40.7204	−1.68071	−0.840356	−	0.542035i	$-0.817654\pi$
$587$	−40.7204	−1.68071	−0.840356	+	0.542035i	$0.817654\pi$
$588$	0	0
$589$	41.8256	1.72339
$590$	0	0
$591$	15.7469	0.647742
$592$	0	0
$593$	10.8793	0.446761	0.223380	−	0.974731i	$-0.428291\pi$
$593$	10.8793	0.446761	0.223380	+	0.974731i	$0.428291\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	20.7349	0.848623
$598$	0	0
$599$	−4.34005	−0.177330	−0.0886648	−	0.996062i	$-0.528260\pi$
$599$	−4.34005	−0.177330	−0.0886648	+	0.996062i	$0.528260\pi$
$600$	0	0
$601$	2.35747	0.0961633	0.0480817	−	0.998843i	$-0.484689\pi$
$601$	2.35747	0.0961633	0.0480817	+	0.998843i	$0.484689\pi$
$602$	0	0
$603$	−24.8431	−1.01169
$604$	0	0
$605$	0	0
$606$	0	0
$607$	21.0552	0.854603	0.427301	−	0.904109i	$-0.359464\pi$
$607$	21.0552	0.854603	0.427301	+	0.904109i	$0.359464\pi$
$608$	0	0
$609$	−32.7948	−1.32891
$610$	0	0
$611$	22.7215	0.919212
$612$	0	0
$613$	5.65525	0.228414	0.114207	−	0.993457i	$-0.463567\pi$
$613$	5.65525	0.228414	0.114207	+	0.993457i	$0.463567\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−26.9891	−1.08654	−0.543270	−	0.839558i	$-0.682814\pi$
$617$	−26.9891	−1.08654	−0.543270	+	0.839558i	$0.682814\pi$
$618$	0	0
$619$	19.0549	0.765883	0.382941	−	0.923773i	$-0.374911\pi$
$619$	19.0549	0.765883	0.382941	+	0.923773i	$0.374911\pi$
$620$	0	0
$621$	−5.19312	−0.208393
$622$	0	0
$623$	−6.36827	−0.255139
$624$	0	0
$625$	0	0
$626$	0	0
$627$	36.1307	1.44292
$628$	0	0
$629$	−2.87232	−0.114527
$630$	0	0
$631$	−29.9572	−1.19258	−0.596288	−	0.802771i	$-0.703358\pi$
$631$	−29.9572	−1.19258	−0.596288	+	0.802771i	$0.703358\pi$
$632$	0	0
$633$	−24.6989	−0.981695
$634$	0	0
$635$	0	0
$636$	0	0
$637$	6.27571	0.248653
$638$	0	0
$639$	−11.5588	−0.457258
$640$	0	0
$641$	−21.3875	−0.844755	−0.422378	−	0.906420i	$-0.638804\pi$
$641$	−21.3875	−0.844755	−0.422378	+	0.906420i	$0.638804\pi$
$642$	0	0
$643$	−47.7440	−1.88284	−0.941420	−	0.337236i	$-0.890508\pi$
$643$	−47.7440	−1.88284	−0.941420	+	0.337236i	$0.890508\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	13.2144	0.519510	0.259755	−	0.965675i	$-0.416358\pi$
$647$	13.2144	0.519510	0.259755	+	0.965675i	$0.416358\pi$
$648$	0	0
$649$	8.16682	0.320576
$650$	0	0
$651$	23.0336	0.902759
$652$	0	0
$653$	−24.5353	−0.960142	−0.480071	−	0.877230i	$-0.659389\pi$
$653$	−24.5353	−0.960142	−0.480071	+	0.877230i	$0.659389\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−8.31888	−0.324550
$658$	0	0
$659$	−17.7100	−0.689883	−0.344941	−	0.938624i	$-0.612101\pi$
$659$	−17.7100	−0.689883	−0.344941	+	0.938624i	$0.612101\pi$
$660$	0	0
$661$	−30.9074	−1.20216	−0.601078	−	0.799190i	$-0.705262\pi$
$661$	−30.9074	−1.20216	−0.601078	+	0.799190i	$0.705262\pi$
$662$	0	0
$663$	−18.2887	−0.710272
$664$	0	0
$665$	0	0
$666$	0	0
$667$	10.3864	0.402163
$668$	0	0
$669$	2.32618	0.0899353
$670$	0	0
$671$	−35.4858	−1.36991
$672$	0	0
$673$	−18.8356	−0.726059	−0.363029	−	0.931778i	$-0.618258\pi$
$673$	−18.8356	−0.726059	−0.363029	+	0.931778i	$0.618258\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	9.47784	0.364263	0.182132	−	0.983274i	$-0.441700\pi$
$677$	9.47784	0.364263	0.182132	+	0.983274i	$0.441700\pi$
$678$	0	0
$679$	52.4689	2.01357
$680$	0	0
$681$	14.4338	0.553103
$682$	0	0
$683$	14.0831	0.538874	0.269437	−	0.963018i	$-0.413162\pi$
$683$	14.0831	0.538874	0.269437	+	0.963018i	$0.413162\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	9.62423	0.367187
$688$	0	0
$689$	−11.6014	−0.441979
$690$	0	0
$691$	14.8398	0.564531	0.282265	−	0.959336i	$-0.408914\pi$
$691$	14.8398	0.564531	0.282265	+	0.959336i	$0.408914\pi$
$692$	0	0
$693$	−32.3099	−1.22735
$694$	0	0
$695$	0	0
$696$	0	0
$697$	42.6670	1.61613
$698$	0	0
$699$	−20.4793	−0.774597
$700$	0	0
$701$	2.93446	0.110833	0.0554165	−	0.998463i	$-0.482351\pi$
$701$	2.93446	0.110833	0.0554165	+	0.998463i	$0.482351\pi$
$702$	0	0
$703$	−3.51410	−0.132537
$704$	0	0
$705$	0	0
$706$	0	0
$707$	−9.40947	−0.353879
$708$	0	0
$709$	25.8990	0.972656	0.486328	−	0.873776i	$-0.338336\pi$
$709$	25.8990	0.972656	0.486328	+	0.873776i	$0.338336\pi$
$710$	0	0
$711$	−13.0206	−0.488311
$712$	0	0
$713$	−7.29495	−0.273198
$714$	0	0
$715$	0	0
$716$	0	0
$717$	−12.2660	−0.458081
$718$	0	0
$719$	26.5304	0.989418	0.494709	−	0.869059i	$-0.335275\pi$
$719$	26.5304	0.989418	0.494709	+	0.869059i	$0.335275\pi$
$720$	0	0
$721$	37.2665	1.38788
$722$	0	0
$723$	28.2968	1.05237
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−15.6397	−0.580045	−0.290022	−	0.957020i	$-0.593663\pi$
$727$	−15.6397	−0.580045	−0.290022	+	0.957020i	$0.593663\pi$
$728$	0	0
$729$	16.6273	0.615824
$730$	0	0
$731$	−7.42253	−0.274532
$732$	0	0
$733$	−42.0912	−1.55468	−0.777338	−	0.629084i	$-0.783430\pi$
$733$	−42.0912	−1.55468	−0.777338	+	0.629084i	$0.783430\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−78.8576	−2.90476
$738$	0	0
$739$	−10.2699	−0.377783	−0.188892	−	0.981998i	$-0.560490\pi$
$739$	−10.2699	−0.377783	−0.188892	+	0.981998i	$0.560490\pi$
$740$	0	0
$741$	−22.3750	−0.821967
$742$	0	0
$743$	−40.4417	−1.48366	−0.741832	−	0.670586i	$-0.766043\pi$
$743$	−40.4417	−1.48366	−0.741832	+	0.670586i	$0.766043\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−4.56822	−0.167143
$748$	0	0
$749$	−4.97719	−0.181863
$750$	0	0
$751$	15.3636	0.560625	0.280312	−	0.959909i	$-0.409562\pi$
$751$	15.3636	0.560625	0.280312	+	0.959909i	$0.409562\pi$
$752$	0	0
$753$	−20.6820	−0.753695
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−2.10127	−0.0763720	−0.0381860	−	0.999271i	$-0.512158\pi$
$757$	−2.10127	−0.0763720	−0.0381860	+	0.999271i	$0.512158\pi$
$758$	0	0
$759$	−6.30169	−0.228737
$760$	0	0
$761$	−5.01242	−0.181700	−0.0908501	−	0.995865i	$-0.528958\pi$
$761$	−5.01242	−0.181700	−0.0908501	+	0.995865i	$0.528958\pi$
$762$	0	0
$763$	17.1542	0.621023
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−5.05755	−0.182617
$768$	0	0
$769$	−9.51281	−0.343041	−0.171520	−	0.985181i	$-0.554868\pi$
$769$	−9.51281	−0.343041	−0.171520	+	0.985181i	$0.554868\pi$
$770$	0	0
$771$	−11.5015	−0.414218
$772$	0	0
$773$	−19.0278	−0.684384	−0.342192	−	0.939630i	$-0.611169\pi$
$773$	−19.0278	−0.684384	−0.342192	+	0.939630i	$0.611169\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	−1.93524	−0.0694264
$778$	0	0
$779$	52.2004	1.87027
$780$	0	0
$781$	−36.6901	−1.31288
$782$	0	0
$783$	−53.9378	−1.92758
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−26.8205	−0.956048	−0.478024	−	0.878347i	$-0.658647\pi$
$787$	−26.8205	−0.956048	−0.478024	+	0.878347i	$0.658647\pi$
$788$	0	0
$789$	−15.9721	−0.568624
$790$	0	0
$791$	−27.7682	−0.987323
$792$	0	0
$793$	21.9756	0.780377
$794$	0	0
$795$	0	0
$796$	0	0
$797$	50.4220	1.78604	0.893019	−	0.450019i	$-0.148583\pi$
$797$	50.4220	1.78604	0.893019	+	0.450019i	$0.148583\pi$
$798$	0	0
$799$	−29.1759	−1.03217
$800$	0	0
$801$	−4.00406	−0.141476
$802$	0	0
$803$	−26.4060	−0.931848
$804$	0	0
$805$	0	0
$806$	0	0
$807$	15.1550	0.533482
$808$	0	0
$809$	49.3793	1.73608	0.868042	−	0.496490i	$-0.165378\pi$
$809$	49.3793	1.73608	0.868042	+	0.496490i	$0.165378\pi$
$810$	0	0
$811$	16.3987	0.575835	0.287918	−	0.957655i	$-0.407037\pi$
$811$	16.3987	0.575835	0.287918	+	0.957655i	$0.407037\pi$
$812$	0	0
$813$	6.54812	0.229653
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−9.08100	−0.317704
$818$	0	0
$819$	20.0089	0.699167
$820$	0	0
$821$	−1.68535	−0.0588190	−0.0294095	−	0.999567i	$-0.509363\pi$
$821$	−1.68535	−0.0588190	−0.0294095	+	0.999567i	$0.509363\pi$
$822$	0	0
$823$	16.2573	0.566693	0.283347	−	0.959018i	$-0.408555\pi$
$823$	16.2573	0.566693	0.283347	+	0.959018i	$0.408555\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−53.9104	−1.87465	−0.937324	−	0.348460i	$-0.886705\pi$
$827$	−53.9104	−1.87465	−0.937324	+	0.348460i	$0.886705\pi$
$828$	0	0
$829$	23.9588	0.832123	0.416062	−	0.909336i	$-0.363410\pi$
$829$	23.9588	0.832123	0.416062	+	0.909336i	$0.363410\pi$
$830$	0	0
$831$	−3.16445	−0.109773
$832$	0	0
$833$	−8.05842	−0.279208
$834$	0	0
$835$	0	0
$836$	0	0
$837$	37.8836	1.30945
$838$	0	0
$839$	4.56491	0.157598	0.0787991	−	0.996891i	$-0.474891\pi$
$839$	4.56491	0.157598	0.0787991	+	0.996891i	$0.474891\pi$
$840$	0	0
$841$	78.8774	2.71991
$842$	0	0
$843$	−29.0101	−0.999160
$844$	0	0
$845$	0	0
$846$	0	0
$847$	−70.0773	−2.40788
$848$	0	0
$849$	−3.75063	−0.128721
$850$	0	0
$851$	0.612908	0.0210102
$852$	0	0
$853$	−2.86000	−0.0979244	−0.0489622	−	0.998801i	$-0.515591\pi$
$853$	−2.86000	−0.0979244	−0.0489622	+	0.998801i	$0.515591\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	42.6985	1.45855	0.729276	−	0.684219i	$-0.239857\pi$
$857$	42.6985	1.45855	0.729276	+	0.684219i	$0.239857\pi$
$858$	0	0
$859$	16.7846	0.572683	0.286341	−	0.958128i	$-0.407561\pi$
$859$	16.7846	0.572683	0.286341	+	0.958128i	$0.407561\pi$
$860$	0	0
$861$	28.7471	0.979700
$862$	0	0
$863$	21.0775	0.717487	0.358743	−	0.933436i	$-0.383205\pi$
$863$	21.0775	0.717487	0.358743	+	0.933436i	$0.383205\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	5.30599	0.180201
$868$	0	0
$869$	−41.3304	−1.40204
$870$	0	0
$871$	48.8349	1.65471
$872$	0	0
$873$	32.9899	1.11654
$874$	0	0
$875$	0	0
$876$	0	0
$877$	45.1822	1.52570	0.762848	−	0.646578i	$-0.223800\pi$
$877$	45.1822	1.52570	0.762848	+	0.646578i	$0.223800\pi$
$878$	0	0
$879$	−1.57369	−0.0530791
$880$	0	0
$881$	8.33503	0.280814	0.140407	−	0.990094i	$-0.455159\pi$
$881$	8.33503	0.280814	0.140407	+	0.990094i	$0.455159\pi$
$882$	0	0
$883$	12.6224	0.424779	0.212390	−	0.977185i	$-0.431875\pi$
$883$	12.6224	0.424779	0.212390	+	0.977185i	$0.431875\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	38.9112	1.30651	0.653256	−	0.757137i	$-0.273403\pi$
$887$	38.9112	1.30651	0.653256	+	0.757137i	$0.273403\pi$
$888$	0	0
$889$	46.7346	1.56743
$890$	0	0
$891$	−0.100014	−0.00335060
$892$	0	0
$893$	−35.6948	−1.19448
$894$	0	0
$895$	0	0
$896$	0	0
$897$	3.90251	0.130301
$898$	0	0
$899$	−75.7683	−2.52701
$900$	0	0
$901$	14.8970	0.496290
$902$	0	0
$903$	−5.00097	−0.166422
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−46.5114	−1.54438	−0.772192	−	0.635389i	$-0.780840\pi$
$907$	−46.5114	−1.54438	−0.772192	+	0.635389i	$0.780840\pi$
$908$	0	0
$909$	−5.91621	−0.196228
$910$	0	0
$911$	−1.59191	−0.0527422	−0.0263711	−	0.999652i	$-0.508395\pi$
$911$	−1.59191	−0.0527422	−0.0263711	+	0.999652i	$0.508395\pi$
$912$	0	0
$913$	−14.5006	−0.479899
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−20.5966	−0.680158
$918$	0	0
$919$	10.4308	0.344080	0.172040	−	0.985090i	$-0.444964\pi$
$919$	10.4308	0.344080	0.172040	+	0.985090i	$0.444964\pi$
$920$	0	0
$921$	19.7024	0.649216
$922$	0	0
$923$	22.7215	0.747886
$924$	0	0
$925$	0	0
$926$	0	0
$927$	23.4314	0.769587
$928$	0	0
$929$	36.7943	1.20718	0.603592	−	0.797294i	$-0.293736\pi$
$929$	36.7943	1.20718	0.603592	+	0.797294i	$0.293736\pi$
$930$	0	0
$931$	−9.85897	−0.323115
$932$	0	0
$933$	15.0099	0.491403
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−13.3700	−0.436779	−0.218389	−	0.975862i	$-0.570080\pi$
$937$	−13.3700	−0.436779	−0.218389	+	0.975862i	$0.570080\pi$
$938$	0	0
$939$	5.19387	0.169496
$940$	0	0
$941$	−53.3116	−1.73791	−0.868955	−	0.494891i	$-0.835208\pi$
$941$	−53.3116	−1.73791	−0.868955	+	0.494891i	$0.835208\pi$
$942$	0	0
$943$	−9.10447	−0.296482
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−30.5958	−0.994230	−0.497115	−	0.867685i	$-0.665607\pi$
$947$	−30.5958	−0.994230	−0.497115	+	0.867685i	$0.665607\pi$
$948$	0	0
$949$	16.3527	0.530832
$950$	0	0
$951$	−21.9814	−0.712797
$952$	0	0
$953$	40.5905	1.31485	0.657427	−	0.753518i	$-0.271645\pi$
$953$	40.5905	1.31485	0.657427	+	0.753518i	$0.271645\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	−65.4519	−2.11576
$958$	0	0
$959$	−10.9496	−0.353580
$960$	0	0
$961$	22.2163	0.716655
$962$	0	0
$963$	−3.12941	−0.100844
$964$	0	0
$965$	0	0
$966$	0	0
$967$	12.0775	0.388387	0.194194	−	0.980963i	$-0.437791\pi$
$967$	12.0775	0.388387	0.194194	+	0.980963i	$0.437791\pi$
$968$	0	0
$969$	28.7310	0.922972
$970$	0	0
$971$	−25.8205	−0.828621	−0.414310	−	0.910136i	$-0.635977\pi$
$971$	−25.8205	−0.828621	−0.414310	+	0.910136i	$0.635977\pi$
$972$	0	0
$973$	−3.79131	−0.121544
$974$	0	0
$975$	0	0
$976$	0	0
$977$	13.8713	0.443783	0.221892	−	0.975071i	$-0.428777\pi$
$977$	13.8713	0.443783	0.221892	+	0.975071i	$0.428777\pi$
$978$	0	0
$979$	−12.7098	−0.406207
$980$	0	0
$981$	10.7857	0.344361
$982$	0	0
$983$	0.852788	0.0271997	0.0135999	−	0.999908i	$-0.495671\pi$
$983$	0.852788	0.0271997	0.0135999	+	0.999908i	$0.495671\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	−19.6574	−0.625702
$988$	0	0
$989$	1.58385	0.0503635
$990$	0	0
$991$	57.0162	1.81118	0.905589	−	0.424156i	$-0.139429\pi$
$991$	57.0162	1.81118	0.905589	+	0.424156i	$0.139429\pi$
$992$	0	0
$993$	30.5631	0.969891
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−21.2745	−0.673770	−0.336885	−	0.941546i	$-0.609373\pi$
$997$	−21.2745	−0.673770	−0.336885	+	0.941546i	$0.609373\pi$
$998$	0	0
$999$	−3.18290	−0.100703

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9200.2.a.da.1.5		7
4.3	odd	2		575.2.a.k.1.5	✓	7
5.4	even	2		9200.2.a.db.1.3		7
12.11	even	2		5175.2.a.cg.1.3		7
20.3	even	4		575.2.b.f.24.6		14
20.7	even	4		575.2.b.f.24.9		14
20.19	odd	2		575.2.a.l.1.3	yes	7
60.59	even	2		5175.2.a.cb.1.5		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
575.2.a.k.1.5	✓	7	4.3	odd	2
575.2.a.l.1.3	yes	7	20.19	odd	2
575.2.b.f.24.6		14	20.3	even	4
575.2.b.f.24.9		14	20.7	even	4
5175.2.a.cb.1.5		7	60.59	even	2
5175.2.a.cg.1.3		7	12.11	even	2
9200.2.a.da.1.5		7	1.1	even	1	trivial
9200.2.a.db.1.3		7	5.4	even	2

Overview	Random
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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:	\( N \)	\(=\)	\( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9200.a (trivial)

\(f(q)\)	\(=\)	\(q+1.06928 q^{3} -2.95289 q^{7} -1.85663 q^{9} +O(q^{10})\)	\(q+1.06928 q^{3} -2.95289 q^{7} -1.85663 q^{9} -5.89337 q^{11} +3.64965 q^{13} -4.68638 q^{17} -5.73350 q^{19} -3.15748 q^{21} +1.00000 q^{23} -5.19312 q^{27} +10.3864 q^{29} -7.29495 q^{31} -6.30169 q^{33} +0.612908 q^{37} +3.90251 q^{39} -9.10447 q^{41} +1.58385 q^{43} +6.22567 q^{47} +1.71954 q^{49} -5.01108 q^{51} -3.17878 q^{53} -6.13074 q^{57} -1.38576 q^{59} +6.02130 q^{61} +5.48242 q^{63} +13.3807 q^{67} +1.06928 q^{69} +6.22567 q^{71} +4.48063 q^{73} +17.4024 q^{77} +7.01303 q^{79} +0.0169706 q^{81} +2.46049 q^{83} +11.1060 q^{87} +2.15663 q^{89} -10.7770 q^{91} -7.80038 q^{93} -17.7687 q^{97} +10.9418 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 3 q^{7} + 15 q^{9}+O(q^{10}) \) 7 * q - 3 * q^7 + 15 * q^9	\( 7 q - 3 q^{7} + 15 q^{9} + q^{11} - 3 q^{13} + 10 q^{17} - 15 q^{19} + 2 q^{21} + 7 q^{23} + 3 q^{29} - 14 q^{31} + 6 q^{33} - 10 q^{37} + 8 q^{39} + 19 q^{41} - 5 q^{43} + 14 q^{47} + 40 q^{49} - 2 q^{51} + 4 q^{53} - 4 q^{57} + 16 q^{59} + 40 q^{61} - 53 q^{63} + 4 q^{67} + 14 q^{71} - 3 q^{73} - 17 q^{77} + q^{79} + 47 q^{81} - 17 q^{83} + 56 q^{87} + 16 q^{89} - 25 q^{91} + 14 q^{93} - 24 q^{97} + 53 q^{99}+O(q^{100}) \) 7 * q - 3 * q^7 + 15 * q^9 + q^11 - 3 * q^13 + 10 * q^17 - 15 * q^19 + 2 * q^21 + 7 * q^23 + 3 * q^29 - 14 * q^31 + 6 * q^33 - 10 * q^37 + 8 * q^39 + 19 * q^41 - 5 * q^43 + 14 * q^47 + 40 * q^49 - 2 * q^51 + 4 * q^53 - 4 * q^57 + 16 * q^59 + 40 * q^61 - 53 * q^63 + 4 * q^67 + 14 * q^71 - 3 * q^73 - 17 * q^77 + q^79 + 47 * q^81 - 17 * q^83 + 56 * q^87 + 16 * q^89 - 25 * q^91 + 14 * q^93 - 24 * q^97 + 53 * q^99

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