LMFDB - Embedded newform 7225.2.a.bb.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7225,2,Mod(1,7225)] 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("7225.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7225, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 7225 = 5^{2} \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7225.a (trivial)

Newform invariants

comment:select newform

sage:traces = [6,-2,4,6,0,-4,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$57.6919154604$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.7718912.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 7x^{4} + 4x^{3} + 9x^{2} - 2x - 1 $ x^6 - 2x^5 - 7x^4 + 4x^3 + 9x^2 - 2*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 85)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.35757$ of defining polynomial
Character	$\chi$	$=$	7225.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.677603 q^{2} +2.35757 q^{3} -1.54085 q^{4} +1.59750 q^{6} +4.27746 q^{7} -2.39929 q^{8} +2.55814 q^{9} -1.65650 q^{11} -3.63267 q^{12} -6.21427 q^{13} +2.89842 q^{14} +1.45594 q^{16} +1.73340 q^{18} -3.38977 q^{19} +10.0844 q^{21} -1.12245 q^{22} -4.67439 q^{23} -5.65650 q^{24} -4.21081 q^{26} -1.04172 q^{27} -6.59095 q^{28} +3.64759 q^{29} -2.99963 q^{31} +5.78514 q^{32} -3.90532 q^{33} -3.94171 q^{36} -5.35017 q^{37} -2.29692 q^{38} -14.6506 q^{39} +2.18836 q^{41} +6.83324 q^{42} +0.998176 q^{43} +2.55243 q^{44} -3.16739 q^{46} -2.00393 q^{47} +3.43248 q^{48} +11.2967 q^{49} +9.57528 q^{52} +6.95444 q^{53} -0.705876 q^{54} -10.2629 q^{56} -7.99163 q^{57} +2.47162 q^{58} -6.30165 q^{59} -6.53502 q^{61} -2.03256 q^{62} +10.9423 q^{63} +1.00815 q^{64} -2.64626 q^{66} -5.80078 q^{67} -11.0202 q^{69} -13.5865 q^{71} -6.13772 q^{72} -9.92480 q^{73} -3.62530 q^{74} +5.22314 q^{76} -7.08564 q^{77} -9.92728 q^{78} +1.16097 q^{79} -10.1303 q^{81} +1.48284 q^{82} -3.65934 q^{83} -15.5386 q^{84} +0.676367 q^{86} +8.59945 q^{87} +3.97444 q^{88} -2.69634 q^{89} -26.5813 q^{91} +7.20256 q^{92} -7.07184 q^{93} -1.35787 q^{94} +13.6389 q^{96} +10.4701 q^{97} +7.65468 q^{98} -4.23756 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} + 4 q^{3} + 6 q^{4} - 4 q^{6} + 8 q^{7} - 6 q^{8} + 2 q^{9} + 8 q^{12} - 8 q^{14} + 2 q^{16} - 14 q^{18} - 12 q^{19} + 8 q^{21} + 16 q^{22} - 24 q^{24} - 12 q^{26} - 8 q^{27} - 8 q^{28} - 8 q^{29}+ \cdots - 20 q^{99}+O(q^{100}) $ 6 * q - 2 * q^2 + 4 * q^3 + 6 * q^4 - 4 * q^6 + 8 * q^7 - 6 * q^8 + 2 * q^9 + 8 * q^12 - 8 * q^14 + 2 * q^16 - 14 * q^18 - 12 * q^19 + 8 * q^21 + 16 * q^22 - 24 * q^24 - 12 * q^26 - 8 * q^27 - 8 * q^28 - 8 * q^29 - 4 * q^31 + 6 * q^32 + 8 * q^33 - 10 * q^36 + 16 * q^37 + 12 * q^38 - 28 * q^39 - 12 * q^41 + 8 * q^42 - 8 * q^43 + 4 * q^44 - 20 * q^46 - 24 * q^47 + 8 * q^48 - 10 * q^49 + 28 * q^52 + 12 * q^54 - 20 * q^56 - 16 * q^57 + 48 * q^58 - 16 * q^59 + 4 * q^61 - 40 * q^62 + 20 * q^63 - 14 * q^64 - 16 * q^66 + 4 * q^67 - 32 * q^71 + 10 * q^72 - 8 * q^73 + 8 * q^74 - 36 * q^76 - 24 * q^77 + 4 * q^78 - 36 * q^79 - 14 * q^81 - 28 * q^82 - 20 * q^83 - 48 * q^86 - 24 * q^87 + 12 * q^88 - 12 * q^89 - 12 * q^91 + 28 * q^92 - 36 * q^93 + 20 * q^94 + 44 * q^96 + 16 * q^97 + 22 * q^98 - 20 * 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 $

$2$	0.677603	0.479138	0.239569	−	0.970879i	$-0.422994\pi$
$2$	0.677603	0.479138	0.239569	+	0.970879i	$0.422994\pi$
$3$	2.35757	1.36114	0.680572	−	0.732681i	$-0.261731\pi$
$3$	2.35757	1.36114	0.680572	+	0.732681i	$0.261731\pi$
$4$	−1.54085	−0.770427
$5$	0	0
$5$	0	0
$6$	1.59750	0.652176
$7$	4.27746	1.61673	0.808365	−	0.588682i	$-0.200353\pi$
$7$	4.27746	1.61673	0.808365	+	0.588682i	$0.200353\pi$
$8$	−2.39929	−0.848279
$9$	2.55814	0.852712
$10$	0	0
$11$	−1.65650	−0.499455	−0.249727	−	0.968316i	$-0.580341\pi$
$11$	−1.65650	−0.499455	−0.249727	+	0.968316i	$0.580341\pi$
$12$	−3.63267	−1.04866
$13$	−6.21427	−1.72353	−0.861764	−	0.507309i	$-0.830640\pi$
$13$	−6.21427	−1.72353	−0.861764	+	0.507309i	$0.830640\pi$
$14$	2.89842	0.774636
$15$	0	0
$16$	1.45594	0.363984
$17$	0	0
$17$	0	0
$18$	1.73340	0.408567
$19$	−3.38977	−0.777667	−0.388834	−	0.921308i	$-0.627122\pi$
$19$	−3.38977	−0.777667	−0.388834	+	0.921308i	$0.627122\pi$
$20$	0	0
$21$	10.0844	2.20060
$22$	−1.12245	−0.239308
$23$	−4.67439	−0.974679	−0.487339	−	0.873213i	$-0.662033\pi$
$23$	−4.67439	−0.974679	−0.487339	+	0.873213i	$0.662033\pi$
$24$	−5.65650	−1.15463
$25$	0	0
$26$	−4.21081	−0.825808
$27$	−1.04172	−0.200480
$28$	−6.59095	−1.24557
$29$	3.64759	0.677340	0.338670	−	0.940905i	$-0.390023\pi$
$29$	3.64759	0.677340	0.338670	+	0.940905i	$0.390023\pi$
$30$	0	0
$31$	−2.99963	−0.538749	−0.269375	−	0.963035i	$-0.586817\pi$
$31$	−2.99963	−0.538749	−0.269375	+	0.963035i	$0.586817\pi$
$32$	5.78514	1.02268
$33$	−3.90532	−0.679830
$34$	0	0
$35$	0	0
$36$	−3.94171	−0.656952
$37$	−5.35017	−0.879563	−0.439782	−	0.898105i	$-0.644944\pi$
$37$	−5.35017	−0.879563	−0.439782	+	0.898105i	$0.644944\pi$
$38$	−2.29692	−0.372610
$39$	−14.6506	−2.34597
$40$	0	0
$41$	2.18836	0.341765	0.170882	−	0.985291i	$-0.445338\pi$
$41$	2.18836	0.341765	0.170882	+	0.985291i	$0.445338\pi$
$42$	6.83324	1.05439
$43$	0.998176	0.152220	0.0761102	−	0.997099i	$-0.475750\pi$
$43$	0.998176	0.152220	0.0761102	+	0.997099i	$0.475750\pi$
$44$	2.55243	0.384793
$45$	0	0
$46$	−3.16739	−0.467006
$47$	−2.00393	−0.292303	−0.146152	−	0.989262i	$-0.546689\pi$
$47$	−2.00393	−0.292303	−0.146152	+	0.989262i	$0.546689\pi$
$48$	3.43248	0.495435
$49$	11.2967	1.61381
$50$	0	0
$51$	0	0
$52$	9.57528	1.32785
$53$	6.95444	0.955266	0.477633	−	0.878560i	$-0.341495\pi$
$53$	6.95444	0.955266	0.477633	+	0.878560i	$0.341495\pi$
$54$	−0.705876	−0.0960575
$55$	0	0
$56$	−10.2629	−1.37144
$57$	−7.99163	−1.05852
$58$	2.47162	0.324539
$59$	−6.30165	−0.820405	−0.410202	−	0.911995i	$-0.634542\pi$
$59$	−6.30165	−0.820405	−0.410202	+	0.911995i	$0.634542\pi$
$60$	0	0
$61$	−6.53502	−0.836724	−0.418362	−	0.908280i	$-0.637396\pi$
$61$	−6.53502	−0.836724	−0.418362	+	0.908280i	$0.637396\pi$
$62$	−2.03256	−0.258135
$63$	10.9423	1.37860
$64$	1.00815	0.126019
$65$	0	0
$66$	−2.64626	−0.325732
$67$	−5.80078	−0.708678	−0.354339	−	0.935117i	$-0.615294\pi$
$67$	−5.80078	−0.708678	−0.354339	+	0.935117i	$0.615294\pi$
$68$	0	0
$69$	−11.0202	−1.32668
$70$	0	0
$71$	−13.5865	−1.61243	−0.806213	−	0.591625i	$-0.798486\pi$
$71$	−13.5865	−1.61243	−0.806213	+	0.591625i	$0.798486\pi$
$72$	−6.13772	−0.723337
$73$	−9.92480	−1.16161	−0.580805	−	0.814043i	$-0.697262\pi$
$73$	−9.92480	−1.16161	−0.580805	+	0.814043i	$0.697262\pi$
$74$	−3.62530	−0.421432
$75$	0	0
$76$	5.22314	0.599136
$77$	−7.08564	−0.807483
$78$	−9.92728	−1.12404
$79$	1.16097	0.130619	0.0653096	−	0.997865i	$-0.479197\pi$
$79$	1.16097	0.130619	0.0653096	+	0.997865i	$0.479197\pi$
$80$	0	0
$81$	−10.1303	−1.12559
$82$	1.48284	0.163752
$83$	−3.65934	−0.401665	−0.200832	−	0.979626i	$-0.564365\pi$
$83$	−3.65934	−0.401665	−0.200832	+	0.979626i	$0.564365\pi$
$84$	−15.5386	−1.69540
$85$	0	0
$86$	0.676367	0.0729346
$87$	8.59945	0.921958
$88$	3.97444	0.423677
$89$	−2.69634	−0.285811	−0.142906	−	0.989736i	$-0.545645\pi$
$89$	−2.69634	−0.285811	−0.142906	+	0.989736i	$0.545645\pi$
$90$	0	0
$91$	−26.5813	−2.78648
$92$	7.20256	0.750919
$93$	−7.07184	−0.733315
$94$	−1.35787	−0.140054
$95$	0	0
$96$	13.6389	1.39201
$97$	10.4701	1.06308	0.531539	−	0.847034i	$-0.321614\pi$
$97$	10.4701	1.06308	0.531539	+	0.847034i	$0.321614\pi$
$98$	7.65468	0.773239
$99$	−4.23756	−0.425891
$100$	0	0
$101$	11.5529	1.14956	0.574779	−	0.818309i	$-0.305088\pi$
$101$	11.5529	1.14956	0.574779	+	0.818309i	$0.305088\pi$
$102$	0	0
$103$	−11.3302	−1.11640	−0.558198	−	0.829708i	$-0.688507\pi$
$103$	−11.3302	−1.11640	−0.558198	+	0.829708i	$0.688507\pi$
$104$	14.9099	1.46203
$105$	0	0
$106$	4.71235	0.457704
$107$	−6.07097	−0.586903	−0.293451	−	0.955974i	$-0.594804\pi$
$107$	−6.07097	−0.586903	−0.293451	+	0.955974i	$0.594804\pi$
$108$	1.60514	0.154455
$109$	3.06935	0.293990	0.146995	−	0.989137i	$-0.453040\pi$
$109$	3.06935	0.293990	0.146995	+	0.989137i	$0.453040\pi$
$110$	0	0
$111$	−12.6134	−1.19721
$112$	6.22772	0.588464
$113$	−7.38421	−0.694648	−0.347324	−	0.937745i	$-0.612910\pi$
$113$	−7.38421	−0.694648	−0.347324	+	0.937745i	$0.612910\pi$
$114$	−5.41515	−0.507175
$115$	0	0
$116$	−5.62040	−0.521841
$117$	−15.8969	−1.46967
$118$	−4.27002	−0.393087
$119$	0	0
$120$	0	0
$121$	−8.25599	−0.750545
$122$	−4.42815	−0.400906
$123$	5.15921	0.465191
$124$	4.62199	0.415067
$125$	0	0
$126$	7.41456	0.660542
$127$	14.3835	1.27633	0.638164	−	0.769900i	$-0.279694\pi$
$127$	14.3835	1.27633	0.638164	+	0.769900i	$0.279694\pi$
$128$	−10.8871	−0.962297
$129$	2.35327	0.207194
$130$	0	0
$131$	4.66403	0.407498	0.203749	−	0.979023i	$-0.434687\pi$
$131$	4.66403	0.407498	0.203749	+	0.979023i	$0.434687\pi$
$132$	6.01753	0.523759
$133$	−14.4996	−1.25728
$134$	−3.93063	−0.339554
$135$	0	0
$136$	0	0
$137$	14.5618	1.24410	0.622049	−	0.782978i	$-0.286300\pi$
$137$	14.5618	1.24410	0.622049	+	0.782978i	$0.286300\pi$
$138$	−7.46733	−0.635662
$139$	−5.36952	−0.455437	−0.227718	−	0.973727i	$-0.573127\pi$
$139$	−5.36952	−0.455437	−0.227718	+	0.973727i	$0.573127\pi$
$140$	0	0
$141$	−4.72440	−0.397867
$142$	−9.20629	−0.772574
$143$	10.2940	0.860824
$144$	3.72449	0.310374
$145$	0	0
$146$	−6.72507	−0.556571
$147$	26.6328	2.19663
$148$	8.24384	0.677639
$149$	12.6885	1.03948	0.519741	−	0.854324i	$-0.326029\pi$
$149$	12.6885	1.03948	0.519741	+	0.854324i	$0.326029\pi$
$150$	0	0
$151$	−16.2607	−1.32327	−0.661637	−	0.749824i	$-0.730138\pi$
$151$	−16.2607	−1.32327	−0.661637	+	0.749824i	$0.730138\pi$
$152$	8.13306	0.659678
$153$	0	0
$154$	−4.80125	−0.386896
$155$	0	0
$156$	22.5744	1.80740
$157$	10.0238	0.799985	0.399993	−	0.916518i	$-0.369013\pi$
$157$	10.0238	0.799985	0.399993	+	0.916518i	$0.369013\pi$
$158$	0.786676	0.0625846
$159$	16.3956	1.30025
$160$	0	0
$161$	−19.9946	−1.57579
$162$	−6.86436	−0.539315
$163$	−8.04592	−0.630205	−0.315102	−	0.949058i	$-0.602039\pi$
$163$	−8.04592	−0.630205	−0.315102	+	0.949058i	$0.602039\pi$
$164$	−3.37194	−0.263305
$165$	0	0
$166$	−2.47958	−0.192453
$167$	−12.9027	−0.998444	−0.499222	−	0.866474i	$-0.666381\pi$
$167$	−12.9027	−0.998444	−0.499222	+	0.866474i	$0.666381\pi$
$168$	−24.1955	−1.86672
$169$	25.6171	1.97055
$170$	0	0
$171$	−8.67150	−0.663126
$172$	−1.53804	−0.117275
$173$	16.4632	1.25167	0.625836	−	0.779955i	$-0.284758\pi$
$173$	16.4632	1.25167	0.625836	+	0.779955i	$0.284758\pi$
$174$	5.82701	0.441745
$175$	0	0
$176$	−2.41177	−0.181794
$177$	−14.8566	−1.11669
$178$	−1.82705	−0.136943
$179$	−13.9304	−1.04121	−0.520603	−	0.853799i	$-0.674293\pi$
$179$	−13.9304	−1.04121	−0.520603	+	0.853799i	$0.674293\pi$
$180$	0	0
$181$	−13.0497	−0.969978	−0.484989	−	0.874520i	$-0.661176\pi$
$181$	−13.0497	−0.969978	−0.484989	+	0.874520i	$0.661176\pi$
$182$	−18.0116	−1.33511
$183$	−15.4068	−1.13890
$184$	11.2152	0.826799
$185$	0	0
$186$	−4.79190	−0.351359
$187$	0	0
$188$	3.08776	0.225198
$189$	−4.45594	−0.324122
$190$	0	0
$191$	−4.75563	−0.344105	−0.172053	−	0.985088i	$-0.555040\pi$
$191$	−4.75563	−0.344105	−0.172053	+	0.985088i	$0.555040\pi$
$192$	2.37679	0.171530
$193$	13.9400	1.00342	0.501711	−	0.865036i	$-0.332704\pi$
$193$	13.9400	1.00342	0.501711	+	0.865036i	$0.332704\pi$
$194$	7.09457	0.509361
$195$	0	0
$196$	−17.4066	−1.24333
$197$	15.1100	1.07655	0.538273	−	0.842771i	$-0.319077\pi$
$197$	15.1100	1.07655	0.538273	+	0.842771i	$0.319077\pi$
$198$	−2.87139	−0.204061
$199$	2.04982	0.145308	0.0726538	−	0.997357i	$-0.476853\pi$
$199$	2.04982	0.145308	0.0726538	+	0.997357i	$0.476853\pi$
$200$	0	0
$201$	−13.6757	−0.964612
$202$	7.82829	0.550797
$203$	15.6024	1.09508
$204$	0	0
$205$	0	0
$206$	−7.67737	−0.534907
$207$	−11.9577	−0.831120
$208$	−9.04759	−0.627337
$209$	5.61517	0.388410
$210$	0	0
$211$	0.438284	0.0301727	0.0150864	−	0.999886i	$-0.495198\pi$
$211$	0.438284	0.0301727	0.0150864	+	0.999886i	$0.495198\pi$
$212$	−10.7158	−0.735962
$213$	−32.0312	−2.19474
$214$	−4.11371	−0.281207
$215$	0	0
$216$	2.49940	0.170063
$217$	−12.8308	−0.871012
$218$	2.07980	0.140862
$219$	−23.3984	−1.58112
$220$	0	0
$221$	0	0
$222$	−8.54689	−0.573630
$223$	−27.2421	−1.82427	−0.912134	−	0.409893i	$-0.865566\pi$
$223$	−27.2421	−1.82427	−0.912134	+	0.409893i	$0.865566\pi$
$224$	24.7457	1.65339
$225$	0	0
$226$	−5.00357	−0.332832
$227$	−9.26138	−0.614699	−0.307350	−	0.951597i	$-0.599442\pi$
$227$	−9.26138	−0.614699	−0.307350	+	0.951597i	$0.599442\pi$
$228$	12.3139	0.815510
$229$	11.0731	0.731728	0.365864	−	0.930668i	$-0.380773\pi$
$229$	11.0731	0.731728	0.365864	+	0.930668i	$0.380773\pi$
$230$	0	0
$231$	−16.7049	−1.09910
$232$	−8.75164	−0.574573
$233$	−15.4853	−1.01448	−0.507239	−	0.861806i	$-0.669334\pi$
$233$	−15.4853	−1.01448	−0.507239	+	0.861806i	$0.669334\pi$
$234$	−10.7718	−0.704176
$235$	0	0
$236$	9.70992	0.632062
$237$	2.73706	0.177791
$238$	0	0
$239$	2.34216	0.151501	0.0757507	−	0.997127i	$-0.475865\pi$
$239$	2.34216	0.151501	0.0757507	+	0.997127i	$0.475865\pi$
$240$	0	0
$241$	30.5342	1.96688	0.983441	−	0.181227i	$-0.0580068\pi$
$241$	30.5342	1.96688	0.983441	+	0.181227i	$0.0580068\pi$
$242$	−5.59429	−0.359615
$243$	−20.7578	−1.33162
$244$	10.0695	0.644635
$245$	0	0
$246$	3.49590	0.222890
$247$	21.0650	1.34033
$248$	7.19699	0.457009
$249$	−8.62715	−0.546724
$250$	0	0
$251$	9.23001	0.582593	0.291297	−	0.956633i	$-0.405913\pi$
$251$	9.23001	0.582593	0.291297	+	0.956633i	$0.405913\pi$
$252$	−16.8605	−1.06211
$253$	7.74315	0.486808
$254$	9.74630	0.611537
$255$	0	0
$256$	−9.39347	−0.587092
$257$	−3.23036	−0.201504	−0.100752	−	0.994912i	$-0.532125\pi$
$257$	−3.23036	−0.201504	−0.100752	+	0.994912i	$0.532125\pi$
$258$	1.59458	0.0992744
$259$	−22.8852	−1.42202
$260$	0	0
$261$	9.33103	0.577576
$262$	3.16036	0.195248
$263$	−12.4719	−0.769051	−0.384526	−	0.923114i	$-0.625635\pi$
$263$	−12.4719	−0.769051	−0.384526	+	0.923114i	$0.625635\pi$
$264$	9.37002	0.576685
$265$	0	0
$266$	−9.82500	−0.602409
$267$	−6.35681	−0.389030
$268$	8.93815	0.545984
$269$	0.310023	0.0189024	0.00945120	−	0.999955i	$-0.496992\pi$
$269$	0.310023	0.0189024	0.00945120	+	0.999955i	$0.496992\pi$
$270$	0	0
$271$	−18.3441	−1.11433	−0.557164	−	0.830403i	$-0.688110\pi$
$271$	−18.3441	−1.11433	−0.557164	+	0.830403i	$0.688110\pi$
$272$	0	0
$273$	−62.6673	−3.79280
$274$	9.86712	0.596094
$275$	0	0
$276$	16.9805	1.02211
$277$	12.7545	0.766342	0.383171	−	0.923677i	$-0.374832\pi$
$277$	12.7545	0.766342	0.383171	+	0.923677i	$0.374832\pi$
$278$	−3.63840	−0.218217
$279$	−7.67346	−0.459398
$280$	0	0
$281$	31.1275	1.85691	0.928457	−	0.371441i	$-0.121136\pi$
$281$	31.1275	1.85691	0.928457	+	0.371441i	$0.121136\pi$
$282$	−3.20127	−0.190633
$283$	27.8553	1.65582	0.827912	−	0.560858i	$-0.189528\pi$
$283$	27.8553	1.65582	0.827912	+	0.560858i	$0.189528\pi$
$284$	20.9349	1.24226
$285$	0	0
$286$	6.97522	0.412454
$287$	9.36063	0.552541
$288$	14.7992	0.872049
$289$	0	0
$290$	0	0
$291$	24.6840	1.44700
$292$	15.2927	0.894935
$293$	31.4302	1.83617	0.918086	−	0.396381i	$-0.129734\pi$
$293$	31.4302	1.83617	0.918086	+	0.396381i	$0.129734\pi$
$294$	18.0464	1.05249
$295$	0	0
$296$	12.8366	0.746115
$297$	1.72562	0.100131
$298$	8.59776	0.498055
$299$	29.0479	1.67989
$300$	0	0
$301$	4.26966	0.246099
$302$	−11.0183	−0.634031
$303$	27.2368	1.56471
$304$	−4.93530	−0.283059
$305$	0	0
$306$	0	0
$307$	4.21985	0.240839	0.120420	−	0.992723i	$-0.461576\pi$
$307$	4.21985	0.240839	0.120420	+	0.992723i	$0.461576\pi$
$308$	10.9179	0.622107
$309$	−26.7117	−1.51957
$310$	0	0
$311$	−15.4099	−0.873818	−0.436909	−	0.899506i	$-0.643927\pi$
$311$	−15.4099	−0.873818	−0.436909	+	0.899506i	$0.643927\pi$
$312$	35.1510	1.99004
$313$	10.8608	0.613891	0.306945	−	0.951727i	$-0.400693\pi$
$313$	10.8608	0.613891	0.306945	+	0.951727i	$0.400693\pi$
$314$	6.79215	0.383303
$315$	0	0
$316$	−1.78888	−0.100633
$317$	−28.8872	−1.62247	−0.811233	−	0.584723i	$-0.801203\pi$
$317$	−28.8872	−1.62247	−0.811233	+	0.584723i	$0.801203\pi$
$318$	11.1097	0.623001
$319$	−6.04225	−0.338301
$320$	0	0
$321$	−14.3127	−0.798859
$322$	−13.5484	−0.755022
$323$	0	0
$324$	15.6094	0.867188
$325$	0	0
$326$	−5.45194	−0.301955
$327$	7.23620	0.400163
$328$	−5.25052	−0.289912
$329$	−8.57174	−0.472575
$330$	0	0
$331$	−7.29249	−0.400832	−0.200416	−	0.979711i	$-0.564229\pi$
$331$	−7.29249	−0.400832	−0.200416	+	0.979711i	$0.564229\pi$
$332$	5.63851	0.309453
$333$	−13.6865	−0.750014
$334$	−8.74294	−0.478392
$335$	0	0
$336$	14.6823	0.800985
$337$	13.4064	0.730295	0.365148	−	0.930950i	$-0.381018\pi$
$337$	13.4064	0.730295	0.365148	+	0.930950i	$0.381018\pi$
$338$	17.3583	0.944165
$339$	−17.4088	−0.945516
$340$	0	0
$341$	4.96890	0.269081
$342$	−5.87584	−0.317729
$343$	18.3790	0.992371
$344$	−2.39492	−0.129125
$345$	0	0
$346$	11.1555	0.599723
$347$	−33.4156	−1.79384	−0.896921	−	0.442190i	$-0.854202\pi$
$347$	−33.4156	−1.79384	−0.896921	+	0.442190i	$0.854202\pi$
$348$	−13.2505	−0.710301
$349$	−22.4213	−1.20019	−0.600093	−	0.799930i	$-0.704870\pi$
$349$	−22.4213	−1.20019	−0.600093	+	0.799930i	$0.704870\pi$
$350$	0	0
$351$	6.47356	0.345533
$352$	−9.58310	−0.510781
$353$	22.2555	1.18454	0.592270	−	0.805739i	$-0.298232\pi$
$353$	22.2555	1.18454	0.592270	+	0.805739i	$0.298232\pi$
$354$	−10.0669	−0.535048
$355$	0	0
$356$	4.15466	0.220197
$357$	0	0
$358$	−9.43927	−0.498881
$359$	−36.6674	−1.93523	−0.967617	−	0.252424i	$-0.918772\pi$
$359$	−36.6674	−1.93523	−0.967617	+	0.252424i	$0.918772\pi$
$360$	0	0
$361$	−7.50945	−0.395234
$362$	−8.84253	−0.464753
$363$	−19.4641	−1.02160
$364$	40.9579	2.14678
$365$	0	0
$366$	−10.4397	−0.545691
$367$	−0.135781	−0.00708768	−0.00354384	−	0.999994i	$-0.501128\pi$
$367$	−0.135781	−0.00708768	−0.00354384	+	0.999994i	$0.501128\pi$
$368$	−6.80563	−0.354768
$369$	5.59812	0.291427
$370$	0	0
$371$	29.7474	1.54441
$372$	10.8967	0.564966
$373$	0.927465	0.0480223	0.0240111	−	0.999712i	$-0.492356\pi$
$373$	0.927465	0.0480223	0.0240111	+	0.999712i	$0.492356\pi$
$374$	0	0
$375$	0	0
$376$	4.80802	0.247955
$377$	−22.6671	−1.16742
$378$	−3.01936	−0.155299
$379$	−8.38647	−0.430784	−0.215392	−	0.976528i	$-0.569103\pi$
$379$	−8.38647	−0.430784	−0.215392	+	0.976528i	$0.569103\pi$
$380$	0	0
$381$	33.9101	1.73727
$382$	−3.22243	−0.164874
$383$	−21.9106	−1.11958	−0.559789	−	0.828635i	$-0.689118\pi$
$383$	−21.9106	−1.11958	−0.559789	+	0.828635i	$0.689118\pi$
$384$	−25.6672	−1.30982
$385$	0	0
$386$	9.44577	0.480777
$387$	2.55347	0.129800
$388$	−16.1329	−0.819023
$389$	12.7622	0.647071	0.323536	−	0.946216i	$-0.395128\pi$
$389$	12.7622	0.647071	0.323536	+	0.946216i	$0.395128\pi$
$390$	0	0
$391$	0	0
$392$	−27.1041	−1.36896
$393$	10.9958	0.554663
$394$	10.2386	0.515814
$395$	0	0
$396$	6.52947	0.328118
$397$	25.1771	1.26360	0.631800	−	0.775131i	$-0.282316\pi$
$397$	25.1771	1.26360	0.631800	+	0.775131i	$0.282316\pi$
$398$	1.38896	0.0696223
$399$	−34.1839	−1.71133
$400$	0	0
$401$	−5.77896	−0.288588	−0.144294	−	0.989535i	$-0.546091\pi$
$401$	−5.77896	−0.288588	−0.144294	+	0.989535i	$0.546091\pi$
$402$	−9.26673	−0.462182
$403$	18.6405	0.928550
$404$	−17.8014	−0.885650
$405$	0	0
$406$	10.5723	0.524693
$407$	8.86259	0.439302
$408$	0	0
$409$	−15.4742	−0.765149	−0.382575	−	0.923925i	$-0.624963\pi$
$409$	−15.4742	−0.765149	−0.382575	+	0.923925i	$0.624963\pi$
$410$	0	0
$411$	34.3304	1.69340
$412$	17.4581	0.860101
$413$	−26.9551	−1.32637
$414$	−8.10260	−0.398221
$415$	0	0
$416$	−35.9504	−1.76261
$417$	−12.6590	−0.619915
$418$	3.80486	0.186102
$419$	18.1317	0.885790	0.442895	−	0.896574i	$-0.353952\pi$
$419$	18.1317	0.885790	0.442895	+	0.896574i	$0.353952\pi$
$420$	0	0
$421$	−9.81137	−0.478177	−0.239089	−	0.970998i	$-0.576849\pi$
$421$	−9.81137	−0.478177	−0.239089	+	0.970998i	$0.576849\pi$
$422$	0.296983	0.0144569
$423$	−5.12633	−0.249250
$424$	−16.6857	−0.810331
$425$	0	0
$426$	−21.7045	−1.05158
$427$	−27.9533	−1.35276
$428$	9.35448	0.452166
$429$	24.2687	1.17171
$430$	0	0
$431$	18.1257	0.873085	0.436542	−	0.899684i	$-0.356203\pi$
$431$	18.1257	0.873085	0.436542	+	0.899684i	$0.356203\pi$
$432$	−1.51669	−0.0729716
$433$	−12.8308	−0.616610	−0.308305	−	0.951287i	$-0.599762\pi$
$433$	−12.8308	−0.616610	−0.308305	+	0.951287i	$0.599762\pi$
$434$	−8.69420	−0.417335
$435$	0	0
$436$	−4.72942	−0.226498
$437$	15.8451	0.757976
$438$	−15.8548	−0.757573
$439$	−24.2848	−1.15905	−0.579526	−	0.814954i	$-0.696762\pi$
$439$	−24.2848	−1.15905	−0.579526	+	0.814954i	$0.696762\pi$
$440$	0	0
$441$	28.8985	1.37612
$442$	0	0
$443$	16.1216	0.765962	0.382981	−	0.923756i	$-0.374897\pi$
$443$	16.1216	0.765962	0.382981	+	0.923756i	$0.374897\pi$
$444$	19.4354	0.922364
$445$	0	0
$446$	−18.4594	−0.874076
$447$	29.9140	1.41488
$448$	4.31234	0.203739
$449$	−19.1265	−0.902634	−0.451317	−	0.892364i	$-0.649046\pi$
$449$	−19.1265	−0.902634	−0.451317	+	0.892364i	$0.649046\pi$
$450$	0	0
$451$	−3.62503	−0.170696
$452$	11.3780	0.535176
$453$	−38.3357	−1.80117
$454$	−6.27554	−0.294526
$455$	0	0
$456$	19.1743	0.897917
$457$	3.68314	0.172290	0.0861451	−	0.996283i	$-0.472545\pi$
$457$	3.68314	0.172290	0.0861451	+	0.996283i	$0.472545\pi$
$458$	7.50314	0.350599
$459$	0	0
$460$	0	0
$461$	−19.7569	−0.920172	−0.460086	−	0.887874i	$-0.652181\pi$
$461$	−19.7569	−0.920172	−0.460086	+	0.887874i	$0.652181\pi$
$462$	−11.3193	−0.526621
$463$	23.6496	1.09909	0.549545	−	0.835464i	$-0.314801\pi$
$463$	23.6496	1.09909	0.549545	+	0.835464i	$0.314801\pi$
$464$	5.31066	0.246541
$465$	0	0
$466$	−10.4929	−0.486074
$467$	5.50118	0.254564	0.127282	−	0.991867i	$-0.459375\pi$
$467$	5.50118	0.254564	0.127282	+	0.991867i	$0.459375\pi$
$468$	24.4949	1.13228
$469$	−24.8126	−1.14574
$470$	0	0
$471$	23.6318	1.08889
$472$	15.1195	0.695932
$473$	−1.65348	−0.0760272
$474$	1.85464	0.0851866
$475$	0	0
$476$	0	0
$477$	17.7904	0.814567
$478$	1.58705	0.0725901
$479$	11.1650	0.510143	0.255072	−	0.966922i	$-0.417901\pi$
$479$	11.1650	0.510143	0.255072	+	0.966922i	$0.417901\pi$
$480$	0	0
$481$	33.2474	1.51595
$482$	20.6901	0.942408
$483$	−47.1386	−2.14488
$484$	12.7213	0.578240
$485$	0	0
$486$	−14.0656	−0.638027
$487$	35.4428	1.60607	0.803034	−	0.595933i	$-0.203218\pi$
$487$	35.4428	1.60607	0.803034	+	0.595933i	$0.203218\pi$
$488$	15.6794	0.709775
$489$	−18.9688	−0.857799
$490$	0	0
$491$	−12.8558	−0.580175	−0.290087	−	0.957000i	$-0.593684\pi$
$491$	−12.8558	−0.580175	−0.290087	+	0.957000i	$0.593684\pi$
$492$	−7.94959	−0.358395
$493$	0	0
$494$	14.2737	0.642203
$495$	0	0
$496$	−4.36727	−0.196096
$497$	−58.1159	−2.60686
$498$	−5.84579	−0.261956
$499$	−18.5876	−0.832094	−0.416047	−	0.909343i	$-0.636585\pi$
$499$	−18.5876	−0.832094	−0.416047	+	0.909343i	$0.636585\pi$
$500$	0	0
$501$	−30.4191	−1.35903
$502$	6.25429	0.279143
$503$	−34.0067	−1.51628	−0.758142	−	0.652090i	$-0.773892\pi$
$503$	−34.0067	−1.51628	−0.758142	+	0.652090i	$0.773892\pi$
$504$	−26.2539	−1.16944
$505$	0	0
$506$	5.24679	0.233248
$507$	60.3942	2.68220
$508$	−22.1629	−0.983318
$509$	−29.8369	−1.32250	−0.661249	−	0.750167i	$-0.729973\pi$
$509$	−29.8369	−1.32250	−0.661249	+	0.750167i	$0.729973\pi$
$510$	0	0
$511$	−42.4530	−1.87801
$512$	15.4092	0.680999
$513$	3.53121	0.155907
$514$	−2.18890	−0.0965483
$515$	0	0
$516$	−3.62604	−0.159628
$517$	3.31952	0.145992
$518$	−15.5071	−0.681342
$519$	38.8131	1.70370
$520$	0	0
$521$	−38.4178	−1.68312	−0.841558	−	0.540167i	$-0.818361\pi$
$521$	−38.4178	−1.68312	−0.841558	+	0.540167i	$0.818361\pi$
$522$	6.32274	0.276739
$523$	20.2414	0.885093	0.442547	−	0.896745i	$-0.354075\pi$
$523$	20.2414	0.885093	0.442547	+	0.896745i	$0.354075\pi$
$524$	−7.18658	−0.313947
$525$	0	0
$526$	−8.45101	−0.368482
$527$	0	0
$528$	−5.68591	−0.247447
$529$	−1.15003	−0.0500014
$530$	0	0
$531$	−16.1205	−0.699569
$532$	22.3418	0.968640
$533$	−13.5991	−0.589041
$534$	−4.30739	−0.186399
$535$	0	0
$536$	13.9178	0.601156
$537$	−32.8418	−1.41723
$538$	0.210072	0.00905686
$539$	−18.7130	−0.806027
$540$	0	0
$541$	7.30589	0.314105	0.157052	−	0.987590i	$-0.449801\pi$
$541$	7.30589	0.314105	0.157052	+	0.987590i	$0.449801\pi$
$542$	−12.4301	−0.533916
$543$	−30.7656	−1.32028
$544$	0	0
$545$	0	0
$546$	−42.4636	−1.81727
$547$	43.7144	1.86909	0.934547	−	0.355841i	$-0.115806\pi$
$547$	43.7144	1.86909	0.934547	+	0.355841i	$0.115806\pi$
$548$	−22.4376	−0.958486
$549$	−16.7175	−0.713485
$550$	0	0
$551$	−12.3645	−0.526745
$552$	26.4407	1.12539
$553$	4.96600	0.211176
$554$	8.64247	0.367183
$555$	0	0
$556$	8.27364	0.350881
$557$	29.0497	1.23088	0.615438	−	0.788185i	$-0.288979\pi$
$557$	29.0497	1.23088	0.615438	+	0.788185i	$0.288979\pi$
$558$	−5.19956	−0.220115
$559$	−6.20293	−0.262356
$560$	0	0
$561$	0	0
$562$	21.0921	0.889718
$563$	−39.3006	−1.65632	−0.828162	−	0.560489i	$-0.810613\pi$
$563$	−39.3006	−1.65632	−0.828162	+	0.560489i	$0.810613\pi$
$564$	7.27962	0.306527
$565$	0	0
$566$	18.8748	0.793368
$567$	−43.3322	−1.81978
$568$	32.5981	1.36779
$569$	−14.3009	−0.599525	−0.299763	−	0.954014i	$-0.596907\pi$
$569$	−14.3009	−0.599525	−0.299763	+	0.954014i	$0.596907\pi$
$570$	0	0
$571$	−23.9174	−1.00091	−0.500455	−	0.865762i	$-0.666834\pi$
$571$	−23.9174	−1.00091	−0.500455	+	0.865762i	$0.666834\pi$
$572$	−15.8615	−0.663202
$573$	−11.2117	−0.468377
$574$	6.34280	0.264743
$575$	0	0
$576$	2.57899	0.107458
$577$	5.85190	0.243618	0.121809	−	0.992554i	$-0.461131\pi$
$577$	5.85190	0.243618	0.121809	+	0.992554i	$0.461131\pi$
$578$	0	0
$579$	32.8645	1.36580
$580$	0	0
$581$	−15.6527	−0.649384
$582$	16.7259	0.693313
$583$	−11.5201	−0.477112
$584$	23.8125	0.985369
$585$	0	0
$586$	21.2972	0.879779
$587$	2.30210	0.0950176	0.0475088	−	0.998871i	$-0.484872\pi$
$587$	2.30210	0.0950176	0.0475088	+	0.998871i	$0.484872\pi$
$588$	−41.0372	−1.69234
$589$	10.1681	0.418968
$590$	0	0
$591$	35.6230	1.46533
$592$	−7.78952	−0.320147
$593$	4.89325	0.200942	0.100471	−	0.994940i	$-0.467965\pi$
$593$	4.89325	0.200942	0.100471	+	0.994940i	$0.467965\pi$
$594$	1.16929	0.0479764
$595$	0	0
$596$	−19.5511	−0.800844
$597$	4.83258	0.197784
$598$	19.6830	0.804897
$599$	6.54372	0.267369	0.133685	−	0.991024i	$-0.457319\pi$
$599$	6.54372	0.267369	0.133685	+	0.991024i	$0.457319\pi$
$600$	0	0
$601$	16.0671	0.655390	0.327695	−	0.944784i	$-0.393728\pi$
$601$	16.0671	0.655390	0.327695	+	0.944784i	$0.393728\pi$
$602$	2.89314	0.117915
$603$	−14.8392	−0.604298
$604$	25.0553	1.01949
$605$	0	0
$606$	18.4557	0.749714
$607$	43.6245	1.77066	0.885331	−	0.464961i	$-0.153932\pi$
$607$	43.6245	1.77066	0.885331	+	0.464961i	$0.153932\pi$
$608$	−19.6103	−0.795302
$609$	36.7838	1.49056
$610$	0	0
$611$	12.4530	0.503793
$612$	0	0
$613$	24.9253	1.00672	0.503362	−	0.864076i	$-0.332096\pi$
$613$	24.9253	1.00672	0.503362	+	0.864076i	$0.332096\pi$
$614$	2.85938	0.115395
$615$	0	0
$616$	17.0005	0.684971
$617$	−17.8320	−0.717890	−0.358945	−	0.933359i	$-0.616863\pi$
$617$	−17.8320	−0.717890	−0.358945	+	0.933359i	$0.616863\pi$
$618$	−18.0999	−0.728086
$619$	−27.6196	−1.11012	−0.555062	−	0.831809i	$-0.687306\pi$
$619$	−27.6196	−1.11012	−0.555062	+	0.831809i	$0.687306\pi$
$620$	0	0
$621$	4.86943	0.195404
$622$	−10.4418	−0.418679
$623$	−11.5335	−0.462080
$624$	−21.3303	−0.853896
$625$	0	0
$626$	7.35934	0.294138
$627$	13.2382	0.528681
$628$	−15.4452	−0.616330
$629$	0	0
$630$	0	0
$631$	38.2023	1.52081	0.760406	−	0.649448i	$-0.225000\pi$
$631$	38.2023	1.52081	0.760406	+	0.649448i	$0.225000\pi$
$632$	−2.78550	−0.110801
$633$	1.03329	0.0410694
$634$	−19.5741	−0.777385
$635$	0	0
$636$	−25.2632	−1.00175
$637$	−70.2007	−2.78145
$638$	−4.09425	−0.162093
$639$	−34.7562	−1.37494
$640$	0	0
$641$	23.2598	0.918706	0.459353	−	0.888254i	$-0.348081\pi$
$641$	23.2598	0.918706	0.459353	+	0.888254i	$0.348081\pi$
$642$	−9.69836	−0.382764
$643$	6.84489	0.269936	0.134968	−	0.990850i	$-0.456907\pi$
$643$	6.84489	0.269936	0.134968	+	0.990850i	$0.456907\pi$
$644$	30.8087	1.21403
$645$	0	0
$646$	0	0
$647$	−39.1427	−1.53886	−0.769429	−	0.638732i	$-0.779459\pi$
$647$	−39.1427	−1.53886	−0.769429	+	0.638732i	$0.779459\pi$
$648$	24.3057	0.954817
$649$	10.4387	0.409755
$650$	0	0
$651$	−30.2495	−1.18557
$652$	12.3976	0.485527
$653$	13.7584	0.538409	0.269204	−	0.963083i	$-0.413239\pi$
$653$	13.7584	0.538409	0.269204	+	0.963083i	$0.413239\pi$
$654$	4.90327	0.191733
$655$	0	0
$656$	3.18612	0.124397
$657$	−25.3890	−0.990519
$658$	−5.80824	−0.226429
$659$	19.0767	0.743124	0.371562	−	0.928408i	$-0.378822\pi$
$659$	19.0767	0.743124	0.371562	+	0.928408i	$0.378822\pi$
$660$	0	0
$661$	−3.89804	−0.151616	−0.0758082	−	0.997122i	$-0.524154\pi$
$661$	−3.89804	−0.151616	−0.0758082	+	0.997122i	$0.524154\pi$
$662$	−4.94142	−0.192054
$663$	0	0
$664$	8.77984	0.340724
$665$	0	0
$666$	−9.27400	−0.359360
$667$	−17.0503	−0.660189
$668$	19.8812	0.769228
$669$	−64.2252	−2.48309
$670$	0	0
$671$	10.8253	0.417906
$672$	58.3398	2.25050
$673$	−8.97910	−0.346119	−0.173059	−	0.984911i	$-0.555365\pi$
$673$	−8.97910	−0.346119	−0.173059	+	0.984911i	$0.555365\pi$
$674$	9.08425	0.349912
$675$	0	0
$676$	−39.4723	−1.51816
$677$	−30.8503	−1.18567	−0.592836	−	0.805323i	$-0.701992\pi$
$677$	−30.8503	−1.18567	−0.592836	+	0.805323i	$0.701992\pi$
$678$	−11.7963	−0.453033
$679$	44.7855	1.71871
$680$	0	0
$681$	−21.8343	−0.836694
$682$	3.36694	0.128927
$683$	−4.46924	−0.171011	−0.0855055	−	0.996338i	$-0.527251\pi$
$683$	−4.46924	−0.171011	−0.0855055	+	0.996338i	$0.527251\pi$
$684$	13.3615	0.510890
$685$	0	0
$686$	12.4537	0.475483
$687$	26.1055	0.995988
$688$	1.45328	0.0554059
$689$	−43.2168	−1.64643
$690$	0	0
$691$	12.0975	0.460211	0.230105	−	0.973166i	$-0.426093\pi$
$691$	12.0975	0.460211	0.230105	+	0.973166i	$0.426093\pi$
$692$	−25.3673	−0.964321
$693$	−18.1260	−0.688551
$694$	−22.6425	−0.859498
$695$	0	0
$696$	−20.6326	−0.782077
$697$	0	0
$698$	−15.1928	−0.575054
$699$	−36.5077	−1.38085
$700$	0	0
$701$	8.83630	0.333742	0.166871	−	0.985979i	$-0.446634\pi$
$701$	8.83630	0.333742	0.166871	+	0.985979i	$0.446634\pi$
$702$	4.38650	0.165558
$703$	18.1359	0.684007
$704$	−1.67001	−0.0629408
$705$	0	0
$706$	15.0804	0.567558
$707$	49.4172	1.85852
$708$	22.8918	0.860327
$709$	−26.7907	−1.00615	−0.503073	−	0.864244i	$-0.667797\pi$
$709$	−26.7907	−1.00615	−0.503073	+	0.864244i	$0.667797\pi$
$710$	0	0
$711$	2.96992	0.111381
$712$	6.46931	0.242448
$713$	14.0214	0.525107
$714$	0	0
$715$	0	0
$716$	21.4647	0.802172
$717$	5.52180	0.206215
$718$	−24.8460	−0.927244
$719$	−43.9096	−1.63755	−0.818775	−	0.574114i	$-0.805347\pi$
$719$	−43.9096	−1.63755	−0.818775	+	0.574114i	$0.805347\pi$
$720$	0	0
$721$	−48.4644	−1.80491
$722$	−5.08842	−0.189372
$723$	71.9866	2.67721
$724$	20.1077	0.747297
$725$	0	0
$726$	−13.1889	−0.489487
$727$	−2.37306	−0.0880118	−0.0440059	−	0.999031i	$-0.514012\pi$
$727$	−2.37306	−0.0880118	−0.0440059	+	0.999031i	$0.514012\pi$
$728$	63.7764	2.36371
$729$	−18.5470	−0.686926
$730$	0	0
$731$	0	0
$732$	23.7396	0.877440
$733$	27.2035	1.00478	0.502391	−	0.864640i	$-0.332454\pi$
$733$	27.2035	1.00478	0.502391	+	0.864640i	$0.332454\pi$
$734$	−0.0920053	−0.00339598
$735$	0	0
$736$	−27.0420	−0.996782
$737$	9.60901	0.353952
$738$	3.79331	0.139634
$739$	−10.3375	−0.380270	−0.190135	−	0.981758i	$-0.560893\pi$
$739$	−10.3375	−0.380270	−0.190135	+	0.981758i	$0.560893\pi$
$740$	0	0
$741$	49.6621	1.82438
$742$	20.1569	0.739983
$743$	−11.8092	−0.433236	−0.216618	−	0.976256i	$-0.569503\pi$
$743$	−11.8092	−0.433236	−0.216618	+	0.976256i	$0.569503\pi$
$744$	16.9674	0.622056
$745$	0	0
$746$	0.628453	0.0230093
$747$	−9.36110	−0.342505
$748$	0	0
$749$	−25.9684	−0.948863
$750$	0	0
$751$	20.0214	0.730592	0.365296	−	0.930891i	$-0.380968\pi$
$751$	20.0214	0.730592	0.365296	+	0.930891i	$0.380968\pi$
$752$	−2.91760	−0.106394
$753$	21.7604	0.792993
$754$	−15.3593	−0.559353
$755$	0	0
$756$	6.86595	0.249712
$757$	4.41769	0.160564	0.0802818	−	0.996772i	$-0.474418\pi$
$757$	4.41769	0.160564	0.0802818	+	0.996772i	$0.474418\pi$
$758$	−5.68270	−0.206405
$759$	18.2550	0.662616
$760$	0	0
$761$	41.6749	1.51071	0.755357	−	0.655314i	$-0.227463\pi$
$761$	41.6749	1.51071	0.755357	+	0.655314i	$0.227463\pi$
$762$	22.9776	0.832390
$763$	13.1290	0.475303
$764$	7.32773	0.265108
$765$	0	0
$766$	−14.8467	−0.536432
$767$	39.1601	1.41399
$768$	−22.1458	−0.799116
$769$	30.7653	1.10942	0.554712	−	0.832043i	$-0.312829\pi$
$769$	30.7653	1.10942	0.554712	+	0.832043i	$0.312829\pi$
$770$	0	0
$771$	−7.61579	−0.274276
$772$	−21.4795	−0.773063
$773$	25.2932	0.909735	0.454867	−	0.890559i	$-0.349687\pi$
$773$	25.2932	0.909735	0.454867	+	0.890559i	$0.349687\pi$
$774$	1.73024	0.0621922
$775$	0	0
$776$	−25.1208	−0.901786
$777$	−53.9534	−1.93557
$778$	8.64773	0.310036
$779$	−7.41804	−0.265779
$780$	0	0
$781$	22.5062	0.805334
$782$	0	0
$783$	−3.79978	−0.135793
$784$	16.4473	0.587403
$785$	0	0
$786$	7.45077	0.265760
$787$	19.6586	0.700755	0.350377	−	0.936609i	$-0.386053\pi$
$787$	19.6586	0.700755	0.350377	+	0.936609i	$0.386053\pi$
$788$	−23.2823	−0.829399
$789$	−29.4034	−1.04679
$790$	0	0
$791$	−31.5857	−1.12306
$792$	10.1672	0.361274
$793$	40.6104	1.44212
$794$	17.0601	0.605439
$795$	0	0
$796$	−3.15847	−0.111949
$797$	−27.3888	−0.970159	−0.485080	−	0.874470i	$-0.661209\pi$
$797$	−27.3888	−0.970159	−0.485080	+	0.874470i	$0.661209\pi$
$798$	−23.1631	−0.819965
$799$	0	0
$800$	0	0
$801$	−6.89760	−0.243715
$802$	−3.91584	−0.138273
$803$	16.4405	0.580171
$804$	21.0723	0.743163
$805$	0	0
$806$	12.6309	0.444903
$807$	0.730900	0.0257289
$808$	−27.7188	−0.975145
$809$	3.76870	0.132500	0.0662502	−	0.997803i	$-0.478896\pi$
$809$	3.76870	0.132500	0.0662502	+	0.997803i	$0.478896\pi$
$810$	0	0
$811$	−33.9594	−1.19248	−0.596239	−	0.802807i	$-0.703339\pi$
$811$	−33.9594	−1.19248	−0.596239	+	0.802807i	$0.703339\pi$
$812$	−24.0411	−0.843676
$813$	−43.2476	−1.51676
$814$	6.00532	0.210486
$815$	0	0
$816$	0	0
$817$	−3.38359	−0.118377
$818$	−10.4854	−0.366612
$819$	−67.9986	−2.37606
$820$	0	0
$821$	−27.1413	−0.947236	−0.473618	−	0.880730i	$-0.657052\pi$
$821$	−27.1413	−0.947236	−0.473618	+	0.880730i	$0.657052\pi$
$822$	23.2624	0.811370
$823$	−1.93168	−0.0673340	−0.0336670	−	0.999433i	$-0.510719\pi$
$823$	−1.93168	−0.0673340	−0.0336670	+	0.999433i	$0.510719\pi$
$824$	27.1844	0.947015
$825$	0	0
$826$	−18.2648	−0.635515
$827$	19.6867	0.684574	0.342287	−	0.939595i	$-0.388799\pi$
$827$	19.6867	0.684574	0.342287	+	0.939595i	$0.388799\pi$
$828$	18.4251	0.640317
$829$	21.3907	0.742930	0.371465	−	0.928447i	$-0.378855\pi$
$829$	21.3907	0.742930	0.371465	+	0.928447i	$0.378855\pi$
$830$	0	0
$831$	30.0696	1.04310
$832$	−6.26493	−0.217197
$833$	0	0
$834$	−8.57779	−0.297025
$835$	0	0
$836$	−8.65216	−0.299241
$837$	3.12479	0.108008
$838$	12.2861	0.424415
$839$	28.8319	0.995389	0.497695	−	0.867352i	$-0.334180\pi$
$839$	28.8319	0.995389	0.497695	+	0.867352i	$0.334180\pi$
$840$	0	0
$841$	−15.6951	−0.541210
$842$	−6.64822	−0.229113
$843$	73.3854	2.52753
$844$	−0.675331	−0.0232459
$845$	0	0
$846$	−3.47362	−0.119425
$847$	−35.3147	−1.21343
$848$	10.1252	0.347702
$849$	65.6708	2.25382
$850$	0	0
$851$	25.0088	0.857292
$852$	49.3554	1.69089
$853$	11.5079	0.394023	0.197012	−	0.980401i	$-0.436876\pi$
$853$	11.5079	0.394023	0.197012	+	0.980401i	$0.436876\pi$
$854$	−18.9413	−0.648157
$855$	0	0
$856$	14.5660	0.497857
$857$	21.7731	0.743754	0.371877	−	0.928282i	$-0.378714\pi$
$857$	21.7731	0.743754	0.371877	+	0.928282i	$0.378714\pi$
$858$	16.4446	0.561409
$859$	−0.00614837	−0.000209780 0	−0.000104890	−	1.00000i	$-0.500033\pi$
$859$	−0.00614837	−0.000209780 0	−0.000104890		1.00000i	$0.500033\pi$
$860$	0	0
$861$	22.0683	0.752087
$862$	12.2820	0.418328
$863$	21.5322	0.732964	0.366482	−	0.930425i	$-0.380562\pi$
$863$	21.5322	0.732964	0.366482	+	0.930425i	$0.380562\pi$
$864$	−6.02652	−0.205026
$865$	0	0
$866$	−8.69421	−0.295441
$867$	0	0
$868$	19.7704	0.671051
$869$	−1.92315	−0.0652384
$870$	0	0
$871$	36.0476	1.22143
$872$	−7.36427	−0.249386
$873$	26.7839	0.906499
$874$	10.7367	0.363175
$875$	0	0
$876$	36.0535	1.21814
$877$	−1.11706	−0.0377205	−0.0188602	−	0.999822i	$-0.506004\pi$
$877$	−1.11706	−0.0377205	−0.0188602	+	0.999822i	$0.506004\pi$
$878$	−16.4555	−0.555345
$879$	74.0989	2.49929
$880$	0	0
$881$	−47.5945	−1.60350	−0.801750	−	0.597660i	$-0.796097\pi$
$881$	−47.5945	−1.60350	−0.801750	+	0.597660i	$0.796097\pi$
$882$	19.5817	0.659351
$883$	20.9432	0.704796	0.352398	−	0.935850i	$-0.385366\pi$
$883$	20.9432	0.704796	0.352398	+	0.935850i	$0.385366\pi$
$884$	0	0
$885$	0	0
$886$	10.9241	0.367001
$887$	19.0070	0.638193	0.319096	−	0.947722i	$-0.396621\pi$
$887$	19.0070	0.638193	0.319096	+	0.947722i	$0.396621\pi$
$888$	30.2633	1.01557
$889$	61.5249	2.06348
$890$	0	0
$891$	16.7810	0.562183
$892$	41.9761	1.40546
$893$	6.79286	0.227315
$894$	20.2698	0.677924
$895$	0	0
$896$	−46.5694	−1.55577
$897$	68.4826	2.28657
$898$	−12.9602	−0.432486
$899$	−10.9414	−0.364917
$900$	0	0
$901$	0	0
$902$	−2.45633	−0.0817869
$903$	10.0660	0.334976
$904$	17.7169	0.589255
$905$	0	0
$906$	−25.9764	−0.863007
$907$	−13.6294	−0.452556	−0.226278	−	0.974063i	$-0.572656\pi$
$907$	−13.6294	−0.452556	−0.226278	+	0.974063i	$0.572656\pi$
$908$	14.2704	0.473581
$909$	29.5539	0.980242
$910$	0	0
$911$	33.7729	1.11895	0.559473	−	0.828849i	$-0.311004\pi$
$911$	33.7729	1.11895	0.559473	+	0.828849i	$0.311004\pi$
$912$	−11.6353	−0.385284
$913$	6.06171	0.200613
$914$	2.49571	0.0825507
$915$	0	0
$916$	−17.0620	−0.563743
$917$	19.9502	0.658814
$918$	0	0
$919$	−31.7339	−1.04681	−0.523403	−	0.852085i	$-0.675338\pi$
$919$	−31.7339	−1.04681	−0.523403	+	0.852085i	$0.675338\pi$
$920$	0	0
$921$	9.94859	0.327817
$922$	−13.3874	−0.440889
$923$	84.4304	2.77906
$924$	25.7398	0.846777
$925$	0	0
$926$	16.0251	0.526616
$927$	−28.9841	−0.951964
$928$	21.1018	0.692701
$929$	8.44901	0.277203	0.138601	−	0.990348i	$-0.455739\pi$
$929$	8.44901	0.277203	0.138601	+	0.990348i	$0.455739\pi$
$930$	0	0
$931$	−38.2932	−1.25501
$932$	23.8606	0.781581
$933$	−36.3300	−1.18939
$934$	3.72762	0.121971
$935$	0	0
$936$	38.1415	1.24669
$937$	−18.0115	−0.588409	−0.294205	−	0.955742i	$-0.595055\pi$
$937$	−18.0115	−0.588409	−0.294205	+	0.955742i	$0.595055\pi$
$938$	−16.8131	−0.548968
$939$	25.6052	0.835593
$940$	0	0
$941$	−21.4128	−0.698036	−0.349018	−	0.937116i	$-0.613485\pi$
$941$	−21.4128	−0.698036	−0.349018	+	0.937116i	$0.613485\pi$
$942$	16.0130	0.521731
$943$	−10.2293	−0.333111
$944$	−9.17481	−0.298615
$945$	0	0
$946$	−1.12041	−0.0364275
$947$	46.7780	1.52008	0.760040	−	0.649876i	$-0.225179\pi$
$947$	46.7780	1.52008	0.760040	+	0.649876i	$0.225179\pi$
$948$	−4.21742	−0.136975
$949$	61.6754	2.00207
$950$	0	0
$951$	−68.1036	−2.20841
$952$	0	0
$953$	−8.60527	−0.278752	−0.139376	−	0.990240i	$-0.544510\pi$
$953$	−8.60527	−0.278752	−0.139376	+	0.990240i	$0.544510\pi$
$954$	12.0548	0.390290
$955$	0	0
$956$	−3.60892	−0.116721
$957$	−14.2450	−0.460476
$958$	7.56546	0.244429
$959$	62.2875	2.01137
$960$	0	0
$961$	−22.0022	−0.709749
$962$	22.5286	0.726350
$963$	−15.5304	−0.500459
$964$	−47.0488	−1.51534
$965$	0	0
$966$	−31.9412	−1.02769
$967$	−29.7257	−0.955913	−0.477957	−	0.878383i	$-0.658622\pi$
$967$	−29.7257	−0.955913	−0.477957	+	0.878383i	$0.658622\pi$
$968$	19.8086	0.636671
$969$	0	0
$970$	0	0
$971$	−5.92180	−0.190040	−0.0950198	−	0.995475i	$-0.530291\pi$
$971$	−5.92180	−0.190040	−0.0950198	+	0.995475i	$0.530291\pi$
$972$	31.9848	1.02591
$973$	−22.9679	−0.736318
$974$	24.0162	0.769528
$975$	0	0
$976$	−9.51459	−0.304555
$977$	51.4273	1.64530	0.822652	−	0.568545i	$-0.192493\pi$
$977$	51.4273	1.64530	0.822652	+	0.568545i	$0.192493\pi$
$978$	−12.8533	−0.411004
$979$	4.46650	0.142750
$980$	0	0
$981$	7.85181	0.250689
$982$	−8.71114	−0.277984
$983$	−13.6951	−0.436805	−0.218403	−	0.975859i	$-0.570085\pi$
$983$	−13.6951	−0.436805	−0.218403	+	0.975859i	$0.570085\pi$
$984$	−12.3785	−0.394611
$985$	0	0
$986$	0	0
$987$	−20.2085	−0.643243
$988$	−32.4580	−1.03263
$989$	−4.66587	−0.148366
$990$	0	0
$991$	53.4998	1.69948	0.849739	−	0.527203i	$-0.176759\pi$
$991$	53.4998	1.69948	0.849739	+	0.527203i	$0.176759\pi$
$992$	−17.3533	−0.550967
$993$	−17.1926	−0.545589
$994$	−39.3796	−1.24904
$995$	0	0
$996$	13.2932	0.421211
$997$	23.1517	0.733221	0.366610	−	0.930375i	$-0.380518\pi$
$997$	23.1517	0.733221	0.366610	+	0.930375i	$0.380518\pi$
$998$	−12.5950	−0.398688
$999$	5.57341	0.176335

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7225.2.a.bb.1.4		6
5.4	even	2		1445.2.a.n.1.3		6
17.2	even	8		425.2.e.f.276.4		12
17.9	even	8		425.2.e.f.251.3		12
17.16	even	2		7225.2.a.z.1.4		6
85.2	odd	8		425.2.j.c.174.3		12
85.4	even	4		1445.2.d.g.866.8		12
85.9	even	8		85.2.e.a.81.4	yes	12
85.19	even	8		85.2.e.a.21.3	✓	12
85.43	odd	8		425.2.j.c.149.3		12
85.53	odd	8		425.2.j.b.174.4		12
85.64	even	4		1445.2.d.g.866.7		12
85.77	odd	8		425.2.j.b.149.4		12
85.84	even	2		1445.2.a.o.1.3		6
255.104	odd	8		765.2.k.b.361.4		12
255.179	odd	8		765.2.k.b.676.3		12
340.19	odd	8		1360.2.bt.d.1041.5		12
340.179	odd	8		1360.2.bt.d.81.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.e.a.21.3	✓	12	85.19	even	8
85.2.e.a.81.4	yes	12	85.9	even	8
425.2.e.f.251.3		12	17.9	even	8
425.2.e.f.276.4		12	17.2	even	8
425.2.j.b.149.4		12	85.77	odd	8
425.2.j.b.174.4		12	85.53	odd	8
425.2.j.c.149.3		12	85.43	odd	8
425.2.j.c.174.3		12	85.2	odd	8
765.2.k.b.361.4		12	255.104	odd	8
765.2.k.b.676.3		12	255.179	odd	8
1360.2.bt.d.81.5		12	340.179	odd	8
1360.2.bt.d.1041.5		12	340.19	odd	8
1445.2.a.n.1.3		6	5.4	even	2
1445.2.a.o.1.3		6	85.84	even	2
1445.2.d.g.866.7		12	85.64	even	4
1445.2.d.g.866.8		12	85.4	even	4
7225.2.a.z.1.4		6	17.16	even	2
7225.2.a.bb.1.4		6	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 7225 = 5^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7225.a (trivial)

\(f(q)\)	\(=\)	\(q+0.677603 q^{2} +2.35757 q^{3} -1.54085 q^{4} +1.59750 q^{6} +4.27746 q^{7} -2.39929 q^{8} +2.55814 q^{9} -1.65650 q^{11} -3.63267 q^{12} -6.21427 q^{13} +2.89842 q^{14} +1.45594 q^{16} +1.73340 q^{18} -3.38977 q^{19} +10.0844 q^{21} -1.12245 q^{22} -4.67439 q^{23} -5.65650 q^{24} -4.21081 q^{26} -1.04172 q^{27} -6.59095 q^{28} +3.64759 q^{29} -2.99963 q^{31} +5.78514 q^{32} -3.90532 q^{33} -3.94171 q^{36} -5.35017 q^{37} -2.29692 q^{38} -14.6506 q^{39} +2.18836 q^{41} +6.83324 q^{42} +0.998176 q^{43} +2.55243 q^{44} -3.16739 q^{46} -2.00393 q^{47} +3.43248 q^{48} +11.2967 q^{49} +9.57528 q^{52} +6.95444 q^{53} -0.705876 q^{54} -10.2629 q^{56} -7.99163 q^{57} +2.47162 q^{58} -6.30165 q^{59} -6.53502 q^{61} -2.03256 q^{62} +10.9423 q^{63} +1.00815 q^{64} -2.64626 q^{66} -5.80078 q^{67} -11.0202 q^{69} -13.5865 q^{71} -6.13772 q^{72} -9.92480 q^{73} -3.62530 q^{74} +5.22314 q^{76} -7.08564 q^{77} -9.92728 q^{78} +1.16097 q^{79} -10.1303 q^{81} +1.48284 q^{82} -3.65934 q^{83} -15.5386 q^{84} +0.676367 q^{86} +8.59945 q^{87} +3.97444 q^{88} -2.69634 q^{89} -26.5813 q^{91} +7.20256 q^{92} -7.07184 q^{93} -1.35787 q^{94} +13.6389 q^{96} +10.4701 q^{97} +7.65468 q^{98} -4.23756 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} + 4 q^{3} + 6 q^{4} - 4 q^{6} + 8 q^{7} - 6 q^{8} + 2 q^{9} + 8 q^{12} - 8 q^{14} + 2 q^{16} - 14 q^{18} - 12 q^{19} + 8 q^{21} + 16 q^{22} - 24 q^{24} - 12 q^{26} - 8 q^{27} - 8 q^{28} - 8 q^{29}+ \cdots - 20 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 + 4 * q^3 + 6 * q^4 - 4 * q^6 + 8 * q^7 - 6 * q^8 + 2 * q^9 + 8 * q^12 - 8 * q^14 + 2 * q^16 - 14 * q^18 - 12 * q^19 + 8 * q^21 + 16 * q^22 - 24 * q^24 - 12 * q^26 - 8 * q^27 - 8 * q^28 - 8 * q^29 - 4 * q^31 + 6 * q^32 + 8 * q^33 - 10 * q^36 + 16 * q^37 + 12 * q^38 - 28 * q^39 - 12 * q^41 + 8 * q^42 - 8 * q^43 + 4 * q^44 - 20 * q^46 - 24 * q^47 + 8 * q^48 - 10 * q^49 + 28 * q^52 + 12 * q^54 - 20 * q^56 - 16 * q^57 + 48 * q^58 - 16 * q^59 + 4 * q^61 - 40 * q^62 + 20 * q^63 - 14 * q^64 - 16 * q^66 + 4 * q^67 - 32 * q^71 + 10 * q^72 - 8 * q^73 + 8 * q^74 - 36 * q^76 - 24 * q^77 + 4 * q^78 - 36 * q^79 - 14 * q^81 - 28 * q^82 - 20 * q^83 - 48 * q^86 - 24 * q^87 + 12 * q^88 - 12 * q^89 - 12 * q^91 + 28 * q^92 - 36 * q^93 + 20 * q^94 + 44 * q^96 + 16 * q^97 + 22 * q^98 - 20 * q^99

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