LMFDB - Embedded newform 3025.2.a.bk.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3025,2,Mod(1,3025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3025, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("3025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3025 = 5^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3025.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:	$24.1547466114$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	8.8.1480160000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 9x^{6} + 27x^{4} - 31x^{2} + 11 $ x^8 - 9x^6 + 27x^4 - 31*x^2 + 11
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.802699$ of defining polynomial
Character	$\chi$	$=$	3025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.802699 q^{2} +1.76074 q^{3} -1.35567 q^{4} -1.41335 q^{6} -0.592103 q^{7} +2.69360 q^{8} +0.100212 q^{9} +O(q^{10})$	\(q-0.802699 q^{2} +1.76074 q^{3} -1.35567 q^{4} -1.41335 q^{6} -0.592103 q^{7} +2.69360 q^{8} +0.100212 q^{9} -2.38699 q^{12} +1.79489 q^{13} +0.475281 q^{14} +0.549201 q^{16} -7.07712 q^{17} -0.0804405 q^{18} +2.28684 q^{19} -1.04254 q^{21} +1.49081 q^{23} +4.74273 q^{24} -1.44076 q^{26} -5.10578 q^{27} +0.802699 q^{28} -3.57549 q^{29} +6.16724 q^{31} -5.82804 q^{32} +5.68079 q^{34} -0.135855 q^{36} +7.33743 q^{37} -1.83565 q^{38} +3.16034 q^{39} -8.41020 q^{41} +0.836847 q^{42} -9.51936 q^{43} -1.19667 q^{46} +1.93165 q^{47} +0.967002 q^{48} -6.64941 q^{49} -12.4610 q^{51} -2.43329 q^{52} +2.38291 q^{53} +4.09840 q^{54} -1.59489 q^{56} +4.02654 q^{57} +2.87004 q^{58} -0.0382778 q^{59} +3.44158 q^{61} -4.95043 q^{62} -0.0593361 q^{63} +3.57976 q^{64} +6.79162 q^{67} +9.59426 q^{68} +2.62493 q^{69} -11.7935 q^{71} +0.269932 q^{72} -6.82275 q^{73} -5.88974 q^{74} -3.10021 q^{76} -2.53680 q^{78} -4.52605 q^{79} -9.29059 q^{81} +6.75086 q^{82} -5.94262 q^{83} +1.41335 q^{84} +7.64118 q^{86} -6.29552 q^{87} -6.21375 q^{89} -1.06276 q^{91} -2.02105 q^{92} +10.8589 q^{93} -1.55054 q^{94} -10.2617 q^{96} -5.37571 q^{97} +5.33748 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} - 6 q^{6} + 4 q^{9}+O(q^{10}) $ 8 * q + 2 * q^4 - 6 * q^6 + 4 * q^9	$ 8 q + 2 q^{4} - 6 q^{6} + 4 q^{9} - 4 q^{14} - 22 q^{16} - 12 q^{19} - 4 q^{21} - 2 q^{24} + 10 q^{26} - 24 q^{29} + 14 q^{31} + 8 q^{34} + 20 q^{36} - 30 q^{39} - 34 q^{41} - 24 q^{46} - 30 q^{49} - 54 q^{51} - 20 q^{54} - 10 q^{56} - 6 q^{59} - 20 q^{61} + 14 q^{64} + 32 q^{69} - 42 q^{71} + 4 q^{74} - 28 q^{76} - 16 q^{79} - 36 q^{81} + 6 q^{84} + 46 q^{86} - 12 q^{89} + 20 q^{91} + 42 q^{94} + 8 q^{96}+O(q^{100}) $ 8 * q + 2 * q^4 - 6 * q^6 + 4 * q^9 - 4 * q^14 - 22 * q^16 - 12 * q^19 - 4 * q^21 - 2 * q^24 + 10 * q^26 - 24 * q^29 + 14 * q^31 + 8 * q^34 + 20 * q^36 - 30 * q^39 - 34 * q^41 - 24 * q^46 - 30 * q^49 - 54 * q^51 - 20 * q^54 - 10 * q^56 - 6 * q^59 - 20 * q^61 + 14 * q^64 + 32 * q^69 - 42 * q^71 + 4 * q^74 - 28 * q^76 - 16 * q^79 - 36 * q^81 + 6 * q^84 + 46 * q^86 - 12 * q^89 + 20 * q^91 + 42 * q^94 + 8 * q^96

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 $

$2$	−0.802699	−0.567594	−0.283797	−	0.958884i	$-0.591594\pi$
$2$	−0.802699	−0.567594	−0.283797	+	0.958884i	$0.591594\pi$
$3$	1.76074	1.01656	0.508282	−	0.861190i	$-0.330281\pi$
$3$	1.76074	1.01656	0.508282	+	0.861190i	$0.330281\pi$
$4$	−1.35567	−0.677837
$5$	0	0
$5$	0	0
$6$	−1.41335	−0.576996
$7$	−0.592103	−0.223794	−0.111897	−	0.993720i	$-0.535693\pi$
$7$	−0.592103	−0.223794	−0.111897	+	0.993720i	$0.535693\pi$
$8$	2.69360	0.952330
$9$	0.100212	0.0334042
$10$	0	0
$11$	0	0
$11$	0	0
$12$	−2.38699	−0.689065
$13$	1.79489	0.497813	0.248906	−	0.968528i	$-0.419929\pi$
$13$	1.79489	0.497813	0.248906	+	0.968528i	$0.419929\pi$
$14$	0.475281	0.127024
$15$	0	0
$16$	0.549201	0.137300
$17$	−7.07712	−1.71645	−0.858226	−	0.513271i	$-0.828433\pi$
$17$	−7.07712	−1.71645	−0.858226	+	0.513271i	$0.828433\pi$
$18$	−0.0804405	−0.0189600
$19$	2.28684	0.524637	0.262319	−	0.964981i	$-0.415513\pi$
$19$	2.28684	0.524637	0.262319	+	0.964981i	$0.415513\pi$
$20$	0	0
$21$	−1.04254	−0.227501
$22$	0	0
$23$	1.49081	0.310855	0.155428	−	0.987847i	$-0.450324\pi$
$23$	1.49081	0.310855	0.155428	+	0.987847i	$0.450324\pi$
$24$	4.74273	0.968105
$25$	0	0
$26$	−1.44076	−0.282556
$27$	−5.10578	−0.982607
$28$	0.802699	0.151696
$29$	−3.57549	−0.663952	−0.331976	−	0.943288i	$-0.607715\pi$
$29$	−3.57549	−0.663952	−0.331976	+	0.943288i	$0.607715\pi$
$30$	0	0
$31$	6.16724	1.10767	0.553834	−	0.832627i	$-0.313164\pi$
$31$	6.16724	1.10767	0.553834	+	0.832627i	$0.313164\pi$
$32$	−5.82804	−1.03026
$33$	0	0
$34$	5.68079	0.974248
$35$	0	0
$36$	−0.135855	−0.0226426
$37$	7.33743	1.20627	0.603133	−	0.797641i	$-0.293919\pi$
$37$	7.33743	1.20627	0.603133	+	0.797641i	$0.293919\pi$
$38$	−1.83565	−0.297781
$39$	3.16034	0.506059
$40$	0	0
$41$	−8.41020	−1.31345	−0.656726	−	0.754129i	$-0.728059\pi$
$41$	−8.41020	−1.31345	−0.656726	+	0.754129i	$0.728059\pi$
$42$	0.836847	0.129128
$43$	−9.51936	−1.45169	−0.725844	−	0.687859i	$-0.758551\pi$
$43$	−9.51936	−1.45169	−0.725844	+	0.687859i	$0.758551\pi$
$44$	0	0
$45$	0	0
$46$	−1.19667	−0.176440
$47$	1.93165	0.281761	0.140880	−	0.990027i	$-0.455007\pi$
$47$	1.93165	0.281761	0.140880	+	0.990027i	$0.455007\pi$
$48$	0.967002	0.139575
$49$	−6.64941	−0.949916
$50$	0	0
$51$	−12.4610	−1.74489
$52$	−2.43329	−0.337436
$53$	2.38291	0.327318	0.163659	−	0.986517i	$-0.447670\pi$
$53$	2.38291	0.327318	0.163659	+	0.986517i	$0.447670\pi$
$54$	4.09840	0.557722
$55$	0	0
$56$	−1.59489	−0.213126
$57$	4.02654	0.533328
$58$	2.87004	0.376855
$59$	−0.0382778	−0.00498334	−0.00249167	−	0.999997i	$-0.500793\pi$
$59$	−0.0382778	−0.00498334	−0.00249167	+	0.999997i	$0.500793\pi$
$60$	0	0
$61$	3.44158	0.440649	0.220325	−	0.975427i	$-0.429288\pi$
$61$	3.44158	0.440649	0.220325	+	0.975427i	$0.429288\pi$
$62$	−4.95043	−0.628706
$63$	−0.0593361	−0.00747565
$64$	3.57976	0.447470
$65$	0	0
$66$	0	0
$67$	6.79162	0.829728	0.414864	−	0.909883i	$-0.363829\pi$
$67$	6.79162	0.829728	0.414864	+	0.909883i	$0.363829\pi$
$68$	9.59426	1.16348
$69$	2.62493	0.316005
$70$	0	0
$71$	−11.7935	−1.39963	−0.699816	−	0.714324i	$-0.746735\pi$
$71$	−11.7935	−1.39963	−0.699816	+	0.714324i	$0.746735\pi$
$72$	0.269932	0.0318118
$73$	−6.82275	−0.798543	−0.399271	−	0.916833i	$-0.630737\pi$
$73$	−6.82275	−0.798543	−0.399271	+	0.916833i	$0.630737\pi$
$74$	−5.88974	−0.684669
$75$	0	0
$76$	−3.10021	−0.355619
$77$	0	0
$78$	−2.53680	−0.287236
$79$	−4.52605	−0.509221	−0.254610	−	0.967044i	$-0.581947\pi$
$79$	−4.52605	−0.509221	−0.254610	+	0.967044i	$0.581947\pi$
$80$	0	0
$81$	−9.29059	−1.03229
$82$	6.75086	0.745508
$83$	−5.94262	−0.652288	−0.326144	−	0.945320i	$-0.605749\pi$
$83$	−5.94262	−0.652288	−0.326144	+	0.945320i	$0.605749\pi$
$84$	1.41335	0.154209
$85$	0	0
$86$	7.64118	0.823970
$87$	−6.29552	−0.674951
$88$	0	0
$89$	−6.21375	−0.658656	−0.329328	−	0.944216i	$-0.606822\pi$
$89$	−6.21375	−0.658656	−0.329328	+	0.944216i	$0.606822\pi$
$90$	0	0
$91$	−1.06276	−0.111407
$92$	−2.02105	−0.210709
$93$	10.8589	1.12602
$94$	−1.55054	−0.159926
$95$	0	0
$96$	−10.2617	−1.04733
$97$	−5.37571	−0.545821	−0.272910	−	0.962039i	$-0.587986\pi$
$97$	−5.37571	−0.545821	−0.272910	+	0.962039i	$0.587986\pi$
$98$	5.33748	0.539167
$99$	0	0
$100$	0	0
$101$	9.93130	0.988201	0.494101	−	0.869405i	$-0.335497\pi$
$101$	9.93130	0.988201	0.494101	+	0.869405i	$0.335497\pi$
$102$	10.0024	0.990386
$103$	13.5214	1.33230	0.666150	−	0.745818i	$-0.267941\pi$
$103$	13.5214	1.33230	0.666150	+	0.745818i	$0.267941\pi$
$104$	4.83471	0.474082
$105$	0	0
$106$	−1.91276	−0.185784
$107$	5.60440	0.541798	0.270899	−	0.962608i	$-0.412679\pi$
$107$	5.60440	0.541798	0.270899	+	0.962608i	$0.412679\pi$
$108$	6.92177	0.666048
$109$	−18.6001	−1.78157	−0.890784	−	0.454428i	$-0.849844\pi$
$109$	−18.6001	−1.78157	−0.890784	+	0.454428i	$0.849844\pi$
$110$	0	0
$111$	12.9193	1.22625
$112$	−0.325184	−0.0307270
$113$	−11.8014	−1.11018	−0.555091	−	0.831790i	$-0.687316\pi$
$113$	−11.8014	−1.11018	−0.555091	+	0.831790i	$0.687316\pi$
$114$	−3.23210	−0.302714
$115$	0	0
$116$	4.84720	0.450052
$117$	0.179870	0.0166290
$118$	0.0307255	0.00282851
$119$	4.19038	0.384132
$120$	0	0
$121$	0	0
$122$	−2.76255	−0.250110
$123$	−14.8082	−1.33521
$124$	−8.36076	−0.750819
$125$	0	0
$126$	0.0476291	0.00424313
$127$	16.0566	1.42479	0.712397	−	0.701777i	$-0.247610\pi$
$127$	16.0566	1.42479	0.712397	+	0.701777i	$0.247610\pi$
$128$	8.78261	0.776280
$129$	−16.7611	−1.47574
$130$	0	0
$131$	−18.0296	−1.57525	−0.787625	−	0.616154i	$-0.788690\pi$
$131$	−18.0296	−1.57525	−0.787625	+	0.616154i	$0.788690\pi$
$132$	0	0
$133$	−1.35405	−0.117411
$134$	−5.45162	−0.470949
$135$	0	0
$136$	−19.0629	−1.63463
$137$	−4.03208	−0.344483	−0.172242	−	0.985055i	$-0.555101\pi$
$137$	−4.03208	−0.344483	−0.172242	+	0.985055i	$0.555101\pi$
$138$	−2.10703	−0.179362
$139$	−7.93492	−0.673031	−0.336516	−	0.941678i	$-0.609248\pi$
$139$	−7.93492	−0.673031	−0.336516	+	0.941678i	$0.609248\pi$
$140$	0	0
$141$	3.40114	0.286428
$142$	9.46663	0.794422
$143$	0	0
$144$	0.0550368	0.00458640
$145$	0	0
$146$	5.47662	0.453248
$147$	−11.7079	−0.965652
$148$	−9.94716	−0.817652
$149$	−12.5009	−1.02411	−0.512056	−	0.858952i	$-0.671116\pi$
$149$	−12.5009	−1.02411	−0.512056	+	0.858952i	$0.671116\pi$
$150$	0	0
$151$	−8.40248	−0.683784	−0.341892	−	0.939739i	$-0.611068\pi$
$151$	−8.40248	−0.683784	−0.341892	+	0.939739i	$0.611068\pi$
$152$	6.15983	0.499628
$153$	−0.709215	−0.0573367
$154$	0	0
$155$	0	0
$156$	−4.28439	−0.343026
$157$	−13.9959	−1.11699	−0.558496	−	0.829507i	$-0.688621\pi$
$157$	−13.9959	−1.11699	−0.558496	+	0.829507i	$0.688621\pi$
$158$	3.63306	0.289031
$159$	4.19569	0.332740
$160$	0	0
$161$	−0.882713	−0.0695676
$162$	7.45755	0.585921
$163$	−11.8415	−0.927496	−0.463748	−	0.885967i	$-0.653496\pi$
$163$	−11.8415	−0.927496	−0.463748	+	0.885967i	$0.653496\pi$
$164$	11.4015	0.890307
$165$	0	0
$166$	4.77014	0.370235
$167$	8.72628	0.675260	0.337630	−	0.941279i	$-0.390375\pi$
$167$	8.72628	0.675260	0.337630	+	0.941279i	$0.390375\pi$
$168$	−2.80818	−0.216656
$169$	−9.77837	−0.752182
$170$	0	0
$171$	0.229170	0.0175251
$172$	12.9052	0.984009
$173$	−9.17861	−0.697837	−0.348918	−	0.937153i	$-0.613451\pi$
$173$	−9.17861	−0.697837	−0.348918	+	0.937153i	$0.613451\pi$
$174$	5.05341	0.383098
$175$	0	0
$176$	0	0
$177$	−0.0673973	−0.00506589
$178$	4.98777	0.373849
$179$	1.44816	0.108241	0.0541204	−	0.998534i	$-0.482765\pi$
$179$	1.44816	0.108241	0.0541204	+	0.998534i	$0.482765\pi$
$180$	0	0
$181$	0.793502	0.0589806	0.0294903	−	0.999565i	$-0.490612\pi$
$181$	0.793502	0.0589806	0.0294903	+	0.999565i	$0.490612\pi$
$182$	0.853076	0.0632342
$183$	6.05974	0.447949
$184$	4.01564	0.296037
$185$	0	0
$186$	−8.71644	−0.639120
$187$	0	0
$188$	−2.61869	−0.190988
$189$	3.02315	0.219902
$190$	0	0
$191$	−8.15029	−0.589735	−0.294867	−	0.955538i	$-0.595275\pi$
$191$	−8.15029	−0.589735	−0.294867	+	0.955538i	$0.595275\pi$
$192$	6.30303	0.454882
$193$	−4.36836	−0.314442	−0.157221	−	0.987563i	$-0.550253\pi$
$193$	−4.36836	−0.314442	−0.157221	+	0.987563i	$0.550253\pi$
$194$	4.31508	0.309804
$195$	0	0
$196$	9.01444	0.643889
$197$	15.6525	1.11520	0.557599	−	0.830111i	$-0.311723\pi$
$197$	15.6525	1.11520	0.557599	+	0.830111i	$0.311723\pi$
$198$	0	0
$199$	1.43830	0.101959	0.0509793	−	0.998700i	$-0.483766\pi$
$199$	1.43830	0.101959	0.0509793	+	0.998700i	$0.483766\pi$
$200$	0	0
$201$	11.9583	0.843472
$202$	−7.97185	−0.560897
$203$	2.11706	0.148589
$204$	16.8930	1.18275
$205$	0	0
$206$	−10.8536	−0.756206
$207$	0.149398	0.0103839
$208$	0.985756	0.0683499
$209$	0	0
$210$	0	0
$211$	−8.68130	−0.597646	−0.298823	−	0.954309i	$-0.596594\pi$
$211$	−8.68130	−0.597646	−0.298823	+	0.954309i	$0.596594\pi$
$212$	−3.23045	−0.221868
$213$	−20.7653	−1.42282
$214$	−4.49864	−0.307521
$215$	0	0
$216$	−13.7529	−0.935767
$217$	−3.65164	−0.247889
$218$	14.9303	1.01121
$219$	−12.0131	−0.811770
$220$	0	0
$221$	−12.7026	−0.854472
$222$	−10.3703	−0.696010
$223$	6.30604	0.422284	0.211142	−	0.977455i	$-0.432282\pi$
$223$	6.30604	0.422284	0.211142	+	0.977455i	$0.432282\pi$
$224$	3.45080	0.230566
$225$	0	0
$226$	9.47296	0.630132
$227$	−1.11681	−0.0741252	−0.0370626	−	0.999313i	$-0.511800\pi$
$227$	−1.11681	−0.0741252	−0.0370626	+	0.999313i	$0.511800\pi$
$228$	−5.45867	−0.361510
$229$	−4.19616	−0.277290	−0.138645	−	0.990342i	$-0.544275\pi$
$229$	−4.19616	−0.277290	−0.138645	+	0.990342i	$0.544275\pi$
$230$	0	0
$231$	0	0
$232$	−9.63094	−0.632302
$233$	−6.77947	−0.444138	−0.222069	−	0.975031i	$-0.571281\pi$
$233$	−6.77947	−0.444138	−0.222069	+	0.975031i	$0.571281\pi$
$234$	−0.144382	−0.00943853
$235$	0	0
$236$	0.0518922	0.00337789
$237$	−7.96921	−0.517656
$238$	−3.36362	−0.218031
$239$	−4.39808	−0.284488	−0.142244	−	0.989832i	$-0.545432\pi$
$239$	−4.39808	−0.284488	−0.142244	+	0.989832i	$0.545432\pi$
$240$	0	0
$241$	9.61218	0.619175	0.309587	−	0.950871i	$-0.399809\pi$
$241$	9.61218	0.619175	0.309587	+	0.950871i	$0.399809\pi$
$242$	0	0
$243$	−1.04101	−0.0667807
$244$	−4.66566	−0.298688
$245$	0	0
$246$	11.8865	0.757857
$247$	4.10463	0.261171
$248$	16.6120	1.05487
$249$	−10.4634	−0.663093
$250$	0	0
$251$	13.4206	0.847100	0.423550	−	0.905873i	$-0.360784\pi$
$251$	13.4206	0.847100	0.423550	+	0.905873i	$0.360784\pi$
$252$	0.0804405	0.00506727
$253$	0	0
$254$	−12.8886	−0.808704
$255$	0	0
$256$	−14.2093	−0.888081
$257$	10.8174	0.674769	0.337384	−	0.941367i	$-0.390458\pi$
$257$	10.8174	0.674769	0.337384	+	0.941367i	$0.390458\pi$
$258$	13.4541	0.837619
$259$	−4.34451	−0.269955
$260$	0	0
$261$	−0.358309	−0.0221788
$262$	14.4723	0.894103
$263$	24.6351	1.51906	0.759531	−	0.650471i	$-0.225428\pi$
$263$	24.6351	1.51906	0.759531	+	0.650471i	$0.225428\pi$
$264$	0	0
$265$	0	0
$266$	1.08689	0.0666416
$267$	−10.9408	−0.669566
$268$	−9.20722	−0.562420
$269$	−4.80101	−0.292723	−0.146361	−	0.989231i	$-0.546756\pi$
$269$	−4.80101	−0.292723	−0.146361	+	0.989231i	$0.546756\pi$
$270$	0	0
$271$	−23.3303	−1.41722	−0.708609	−	0.705602i	$-0.750677\pi$
$271$	−23.3303	−1.41722	−0.708609	+	0.705602i	$0.750677\pi$
$272$	−3.88676	−0.235670
$273$	−1.87125	−0.113253
$274$	3.23654	0.195527
$275$	0	0
$276$	−3.55855	−0.214200
$277$	−21.8973	−1.31568	−0.657840	−	0.753158i	$-0.728530\pi$
$277$	−21.8973	−1.31568	−0.657840	+	0.753158i	$0.728530\pi$
$278$	6.36935	0.382008
$279$	0.618034	0.0370007
$280$	0	0
$281$	−15.7754	−0.941084	−0.470542	−	0.882378i	$-0.655942\pi$
$281$	−15.7754	−0.941084	−0.470542	+	0.882378i	$0.655942\pi$
$282$	−2.73009	−0.162575
$283$	22.6091	1.34397	0.671987	−	0.740563i	$-0.265441\pi$
$283$	22.6091	1.34397	0.671987	+	0.740563i	$0.265441\pi$
$284$	15.9881	0.948722
$285$	0	0
$286$	0	0
$287$	4.97971	0.293943
$288$	−0.584042	−0.0344150
$289$	33.0856	1.94621
$290$	0	0
$291$	−9.46524	−0.554862
$292$	9.24943	0.541282
$293$	−13.2596	−0.774635	−0.387317	−	0.921946i	$-0.626598\pi$
$293$	−13.2596	−0.774635	−0.387317	+	0.921946i	$0.626598\pi$
$294$	9.39792	0.548098
$295$	0	0
$296$	19.7641	1.14876
$297$	0	0
$298$	10.0344	0.581280
$299$	2.67584	0.154748
$300$	0	0
$301$	5.63644	0.324879
$302$	6.74466	0.388112
$303$	17.4865	1.00457
$304$	1.25594	0.0720329
$305$	0	0
$306$	0.569286	0.0325439
$307$	10.0161	0.571650	0.285825	−	0.958282i	$-0.407732\pi$
$307$	10.0161	0.571650	0.285825	+	0.958282i	$0.407732\pi$
$308$	0	0
$309$	23.8076	1.35437
$310$	0	0
$311$	−3.40826	−0.193265	−0.0966323	−	0.995320i	$-0.530807\pi$
$311$	−3.40826	−0.193265	−0.0966323	+	0.995320i	$0.530807\pi$
$312$	8.51267	0.481935
$313$	−24.5008	−1.38487	−0.692434	−	0.721481i	$-0.743462\pi$
$313$	−24.5008	−1.38487	−0.692434	+	0.721481i	$0.743462\pi$
$314$	11.2345	0.633998
$315$	0	0
$316$	6.13586	0.345169
$317$	−6.98851	−0.392514	−0.196257	−	0.980553i	$-0.562879\pi$
$317$	−6.98851	−0.392514	−0.196257	+	0.980553i	$0.562879\pi$
$318$	−3.36787	−0.188861
$319$	0	0
$320$	0	0
$321$	9.86790	0.550772
$322$	0.708553	0.0394861
$323$	−16.1842	−0.900515
$324$	12.5950	0.699723
$325$	0	0
$326$	9.50514	0.526441
$327$	−32.7500	−1.81108
$328$	−22.6537	−1.25084
$329$	−1.14374	−0.0630563
$330$	0	0
$331$	5.64321	0.310179	0.155089	−	0.987900i	$-0.450433\pi$
$331$	5.64321	0.310179	0.155089	+	0.987900i	$0.450433\pi$
$332$	8.05626	0.442145
$333$	0.735302	0.0402943
$334$	−7.00458	−0.383273
$335$	0	0
$336$	−0.572565	−0.0312360
$337$	22.6164	1.23199	0.615996	−	0.787750i	$-0.288754\pi$
$337$	22.6164	1.23199	0.615996	+	0.787750i	$0.288754\pi$
$338$	7.84909	0.426934
$339$	−20.7792	−1.12857
$340$	0	0
$341$	0	0
$342$	−0.183955	−0.00994713
$343$	8.08186	0.436379
$344$	−25.6413	−1.38249
$345$	0	0
$346$	7.36766	0.396088
$347$	−0.182395	−0.00979145	−0.00489573	−	0.999988i	$-0.501558\pi$
$347$	−0.182395	−0.00979145	−0.00489573	+	0.999988i	$0.501558\pi$
$348$	8.53468	0.457507
$349$	15.4273	0.825803	0.412902	−	0.910776i	$-0.364515\pi$
$349$	15.4273	0.825803	0.412902	+	0.910776i	$0.364515\pi$
$350$	0	0
$351$	−9.16431	−0.489155
$352$	0	0
$353$	23.9103	1.27262	0.636308	−	0.771435i	$-0.280461\pi$
$353$	23.9103	1.27262	0.636308	+	0.771435i	$0.280461\pi$
$354$	0.0540997	0.00287537
$355$	0	0
$356$	8.42382	0.446461
$357$	7.37818	0.390495
$358$	−1.16244	−0.0614368
$359$	8.76734	0.462723	0.231361	−	0.972868i	$-0.425682\pi$
$359$	8.76734	0.462723	0.231361	+	0.972868i	$0.425682\pi$
$360$	0	0
$361$	−13.7704	−0.724756
$362$	−0.636943	−0.0334770
$363$	0	0
$364$	1.44076	0.0755161
$365$	0	0
$366$	−4.86414	−0.254253
$367$	−5.38232	−0.280955	−0.140477	−	0.990084i	$-0.544864\pi$
$367$	−5.38232	−0.280955	−0.140477	+	0.990084i	$0.544864\pi$
$368$	0.818755	0.0426806
$369$	−0.842807	−0.0438748
$370$	0	0
$371$	−1.41093	−0.0732517
$372$	−14.7211	−0.763256
$373$	−3.22450	−0.166958	−0.0834792	−	0.996510i	$-0.526603\pi$
$373$	−3.22450	−0.166958	−0.0834792	+	0.996510i	$0.526603\pi$
$374$	0	0
$375$	0	0
$376$	5.20309	0.268329
$377$	−6.41762	−0.330524
$378$	−2.42668	−0.124815
$379$	−19.6634	−1.01004	−0.505020	−	0.863108i	$-0.668515\pi$
$379$	−19.6634	−1.01004	−0.505020	+	0.863108i	$0.668515\pi$
$380$	0	0
$381$	28.2716	1.44840
$382$	6.54223	0.334730
$383$	−27.9751	−1.42946	−0.714731	−	0.699400i	$-0.753451\pi$
$383$	−27.9751	−1.42946	−0.714731	+	0.699400i	$0.753451\pi$
$384$	15.4639	0.789139
$385$	0	0
$386$	3.50648	0.178475
$387$	−0.953959	−0.0484924
$388$	7.28771	0.369977
$389$	13.0400	0.661154	0.330577	−	0.943779i	$-0.392757\pi$
$389$	13.0400	0.661154	0.330577	+	0.943779i	$0.392757\pi$
$390$	0	0
$391$	−10.5506	−0.533569
$392$	−17.9108	−0.904634
$393$	−31.7454	−1.60134
$394$	−12.5643	−0.632980
$395$	0	0
$396$	0	0
$397$	1.82243	0.0914651	0.0457325	−	0.998954i	$-0.485438\pi$
$397$	1.82243	0.0914651	0.0457325	+	0.998954i	$0.485438\pi$
$398$	−1.15452	−0.0578711
$399$	−2.38413	−0.119356
$400$	0	0
$401$	5.38085	0.268707	0.134353	−	0.990933i	$-0.457104\pi$
$401$	5.38085	0.268707	0.134353	+	0.990933i	$0.457104\pi$
$402$	−9.59890	−0.478750
$403$	11.0695	0.551411
$404$	−13.4636	−0.669840
$405$	0	0
$406$	−1.69936	−0.0843379
$407$	0	0
$408$	−33.5648	−1.66171
$409$	36.6821	1.81381	0.906906	−	0.421333i	$-0.138438\pi$
$409$	36.6821	1.81381	0.906906	+	0.421333i	$0.138438\pi$
$410$	0	0
$411$	−7.09944	−0.350190
$412$	−18.3306	−0.903083
$413$	0.0226644	0.00111524
$414$	−0.119921	−0.00589382
$415$	0	0
$416$	−10.4607	−0.512877
$417$	−13.9713	−0.684180
$418$	0	0
$419$	2.86630	0.140028	0.0700141	−	0.997546i	$-0.477696\pi$
$419$	2.86630	0.140028	0.0700141	+	0.997546i	$0.477696\pi$
$420$	0	0
$421$	4.65975	0.227102	0.113551	−	0.993532i	$-0.463777\pi$
$421$	4.65975	0.227102	0.113551	+	0.993532i	$0.463777\pi$
$422$	6.96847	0.339220
$423$	0.193576	0.00941198
$424$	6.41859	0.311714
$425$	0	0
$426$	16.6683	0.807582
$427$	−2.03777	−0.0986147
$428$	−7.59774	−0.367250
$429$	0	0
$430$	0	0
$431$	−20.7691	−1.00041	−0.500207	−	0.865906i	$-0.666743\pi$
$431$	−20.7691	−1.00041	−0.500207	+	0.865906i	$0.666743\pi$
$432$	−2.80410	−0.134912
$433$	12.7972	0.614993	0.307496	−	0.951549i	$-0.400509\pi$
$433$	12.7972	0.614993	0.307496	+	0.951549i	$0.400509\pi$
$434$	2.93117	0.140701
$435$	0	0
$436$	25.2157	1.20761
$437$	3.40925	0.163086
$438$	9.64291	0.460756
$439$	10.6208	0.506905	0.253452	−	0.967348i	$-0.418434\pi$
$439$	10.6208	0.506905	0.253452	+	0.967348i	$0.418434\pi$
$440$	0	0
$441$	−0.666354	−0.0317312
$442$	10.1964	0.484993
$443$	−6.59894	−0.313525	−0.156763	−	0.987636i	$-0.550106\pi$
$443$	−6.59894	−0.313525	−0.156763	+	0.987636i	$0.550106\pi$
$444$	−17.5144	−0.831196
$445$	0	0
$446$	−5.06185	−0.239686
$447$	−22.0108	−1.04108
$448$	−2.11958	−0.100141
$449$	13.6281	0.643147	0.321574	−	0.946885i	$-0.395788\pi$
$449$	13.6281	0.643147	0.321574	+	0.946885i	$0.395788\pi$
$450$	0	0
$451$	0	0
$452$	15.9988	0.752522
$453$	−14.7946	−0.695111
$454$	0.896462	0.0420730
$455$	0	0
$456$	10.8459	0.507904
$457$	−13.4999	−0.631498	−0.315749	−	0.948843i	$-0.602256\pi$
$457$	−13.4999	−0.631498	−0.315749	+	0.948843i	$0.602256\pi$
$458$	3.36825	0.157388
$459$	36.1342	1.68660
$460$	0	0
$461$	−11.3217	−0.527303	−0.263652	−	0.964618i	$-0.584927\pi$
$461$	−11.3217	−0.527303	−0.263652	+	0.964618i	$0.584927\pi$
$462$	0	0
$463$	4.82990	0.224464	0.112232	−	0.993682i	$-0.464200\pi$
$463$	4.82990	0.224464	0.112232	+	0.993682i	$0.464200\pi$
$464$	−1.96367	−0.0911609
$465$	0	0
$466$	5.44187	0.252090
$467$	−24.0173	−1.11139	−0.555694	−	0.831387i	$-0.687547\pi$
$467$	−24.0173	−1.11139	−0.555694	+	0.831387i	$0.687547\pi$
$468$	−0.243846	−0.0112718
$469$	−4.02134	−0.185688
$470$	0	0
$471$	−24.6431	−1.13550
$472$	−0.103105	−0.00474579
$473$	0	0
$474$	6.39688	0.293818
$475$	0	0
$476$	−5.68079	−0.260379
$477$	0.238797	0.0109338
$478$	3.53034	0.161474
$479$	−43.2250	−1.97500	−0.987501	−	0.157611i	$-0.949621\pi$
$479$	−43.2250	−1.97500	−0.987501	+	0.157611i	$0.949621\pi$
$480$	0	0
$481$	13.1699	0.600494
$482$	−7.71569	−0.351440
$483$	−1.55423	−0.0707199
$484$	0	0
$485$	0	0
$486$	0.835616	0.0379043
$487$	41.9609	1.90143	0.950715	−	0.310067i	$-0.100352\pi$
$487$	41.9609	1.90143	0.950715	+	0.310067i	$0.100352\pi$
$488$	9.27023	0.419644
$489$	−20.8498	−0.942860
$490$	0	0
$491$	9.05983	0.408864	0.204432	−	0.978881i	$-0.434465\pi$
$491$	9.05983	0.408864	0.204432	+	0.978881i	$0.434465\pi$
$492$	20.0751	0.905055
$493$	25.3042	1.13964
$494$	−3.29478	−0.148239
$495$	0	0
$496$	3.38705	0.152083
$497$	6.98297	0.313229
$498$	8.39898	0.376367
$499$	30.2793	1.35549	0.677744	−	0.735298i	$-0.262958\pi$
$499$	30.2793	1.35549	0.677744	+	0.735298i	$0.262958\pi$
$500$	0	0
$501$	15.3647	0.686446
$502$	−10.7727	−0.480809
$503$	18.0638	0.805426	0.402713	−	0.915326i	$-0.368067\pi$
$503$	18.0638	0.805426	0.402713	+	0.915326i	$0.368067\pi$
$504$	−0.159828	−0.00711929
$505$	0	0
$506$	0	0
$507$	−17.2172	−0.764642
$508$	−21.7675	−0.965778
$509$	−24.9157	−1.10437	−0.552184	−	0.833722i	$-0.686206\pi$
$509$	−24.9157	−1.10437	−0.552184	+	0.833722i	$0.686206\pi$
$510$	0	0
$511$	4.03977	0.178709
$512$	−6.15942	−0.272210
$513$	−11.6761	−0.515513
$514$	−8.68309	−0.382995
$515$	0	0
$516$	22.7226	1.00031
$517$	0	0
$518$	3.48734	0.153225
$519$	−16.1612	−0.709396
$520$	0	0
$521$	36.2831	1.58959	0.794797	−	0.606876i	$-0.207578\pi$
$521$	36.2831	1.58959	0.794797	+	0.606876i	$0.207578\pi$
$522$	0.287614	0.0125885
$523$	−24.7070	−1.08036	−0.540181	−	0.841549i	$-0.681644\pi$
$523$	−24.7070	−1.08036	−0.540181	+	0.841549i	$0.681644\pi$
$524$	24.4422	1.06776
$525$	0	0
$526$	−19.7745	−0.862211
$527$	−43.6462	−1.90126
$528$	0	0
$529$	−20.7775	−0.903369
$530$	0	0
$531$	−0.00383591	−0.000166464 0
$532$	1.83565	0.0795853
$533$	−15.0954	−0.653854
$534$	8.78217	0.380042
$535$	0	0
$536$	18.2939	0.790175
$537$	2.54984	0.110034
$538$	3.85376	0.166148
$539$	0	0
$540$	0	0
$541$	12.5420	0.539221	0.269610	−	0.962970i	$-0.413105\pi$
$541$	12.5420	0.539221	0.269610	+	0.962970i	$0.413105\pi$
$542$	18.7272	0.804404
$543$	1.39715	0.0599576
$544$	41.2457	1.76839
$545$	0	0
$546$	1.50205	0.0642817
$547$	30.7407	1.31438	0.657189	−	0.753726i	$-0.271745\pi$
$547$	30.7407	1.31438	0.657189	+	0.753726i	$0.271745\pi$
$548$	5.46618	0.233504
$549$	0.344889	0.0147195
$550$	0	0
$551$	−8.17659	−0.348334
$552$	7.07051	0.300941
$553$	2.67989	0.113961
$554$	17.5769	0.746772
$555$	0	0
$556$	10.7572	0.456206
$557$	13.4294	0.569021	0.284510	−	0.958673i	$-0.408169\pi$
$557$	13.4294	0.569021	0.284510	+	0.958673i	$0.408169\pi$
$558$	−0.496095	−0.0210014
$559$	−17.0862	−0.722669
$560$	0	0
$561$	0	0
$562$	12.6629	0.534154
$563$	30.5401	1.28711	0.643556	−	0.765399i	$-0.277458\pi$
$563$	30.5401	1.28711	0.643556	+	0.765399i	$0.277458\pi$
$564$	−4.61084	−0.194152
$565$	0	0
$566$	−18.1483	−0.762831
$567$	5.50099	0.231020
$568$	−31.7669	−1.33291
$569$	−25.7204	−1.07826	−0.539128	−	0.842224i	$-0.681246\pi$
$569$	−25.7204	−1.07826	−0.539128	+	0.842224i	$0.681246\pi$
$570$	0	0
$571$	27.1115	1.13458	0.567291	−	0.823518i	$-0.307992\pi$
$571$	27.1115	1.13458	0.567291	+	0.823518i	$0.307992\pi$
$572$	0	0
$573$	−14.3506	−0.599504
$574$	−3.99721	−0.166840
$575$	0	0
$576$	0.358736	0.0149473
$577$	−2.87015	−0.119486	−0.0597430	−	0.998214i	$-0.519028\pi$
$577$	−2.87015	−0.119486	−0.0597430	+	0.998214i	$0.519028\pi$
$578$	−26.5578	−1.10466
$579$	−7.69156	−0.319650
$580$	0	0
$581$	3.51865	0.145978
$582$	7.59774	0.314936
$583$	0	0
$584$	−18.3777	−0.760476
$585$	0	0
$586$	10.6435	0.439678
$587$	−44.8360	−1.85058	−0.925289	−	0.379262i	$-0.876178\pi$
$587$	−44.8360	−1.85058	−0.925289	+	0.379262i	$0.876178\pi$
$588$	15.8721	0.654554
$589$	14.1035	0.581124
$590$	0	0
$591$	27.5601	1.13367
$592$	4.02972	0.165621
$593$	−6.09322	−0.250219	−0.125109	−	0.992143i	$-0.539928\pi$
$593$	−6.09322	−0.250219	−0.125109	+	0.992143i	$0.539928\pi$
$594$	0	0
$595$	0	0
$596$	16.9471	0.694181
$597$	2.53248	0.103648
$598$	−2.14789	−0.0878339
$599$	−12.9337	−0.528457	−0.264229	−	0.964460i	$-0.585117\pi$
$599$	−12.9337	−0.528457	−0.264229	+	0.964460i	$0.585117\pi$
$600$	0	0
$601$	11.0471	0.450621	0.225310	−	0.974287i	$-0.427660\pi$
$601$	11.0471	0.450621	0.225310	+	0.974287i	$0.427660\pi$
$602$	−4.52437	−0.184399
$603$	0.680605	0.0277164
$604$	11.3910	0.463494
$605$	0	0
$606$	−14.0364	−0.570188
$607$	0.115912	0.00470474	0.00235237	−	0.999997i	$-0.499251\pi$
$607$	0.115912	0.00470474	0.00235237	+	0.999997i	$0.499251\pi$
$608$	−13.3278	−0.540514
$609$	3.72760	0.151050
$610$	0	0
$611$	3.46710	0.140264
$612$	0.961465	0.0388649
$613$	−19.0445	−0.769202	−0.384601	−	0.923083i	$-0.625661\pi$
$613$	−19.0445	−0.769202	−0.384601	+	0.923083i	$0.625661\pi$
$614$	−8.03993	−0.324465
$615$	0	0
$616$	0	0
$617$	−30.8894	−1.24356	−0.621780	−	0.783192i	$-0.713590\pi$
$617$	−30.8894	−1.24356	−0.621780	+	0.783192i	$0.713590\pi$
$618$	−19.1104	−0.768732
$619$	33.5697	1.34928	0.674639	−	0.738148i	$-0.264299\pi$
$619$	33.5697	1.34928	0.674639	+	0.738148i	$0.264299\pi$
$620$	0	0
$621$	−7.61174	−0.305449
$622$	2.73581	0.109696
$623$	3.67918	0.147403
$624$	1.73566	0.0694821
$625$	0	0
$626$	19.6668	0.786043
$627$	0	0
$628$	18.9738	0.757139
$629$	−51.9278	−2.07050
$630$	0	0
$631$	24.6573	0.981590	0.490795	−	0.871275i	$-0.336706\pi$
$631$	24.6573	0.981590	0.490795	+	0.871275i	$0.336706\pi$
$632$	−12.1914	−0.484946
$633$	−15.2855	−0.607546
$634$	5.60967	0.222788
$635$	0	0
$636$	−5.68799	−0.225543
$637$	−11.9350	−0.472880
$638$	0	0
$639$	−1.18186	−0.0467535
$640$	0	0
$641$	7.01647	0.277134	0.138567	−	0.990353i	$-0.455750\pi$
$641$	7.01647	0.277134	0.138567	+	0.990353i	$0.455750\pi$
$642$	−7.92095	−0.312615
$643$	−12.2525	−0.483192	−0.241596	−	0.970377i	$-0.577671\pi$
$643$	−12.2525	−0.483192	−0.241596	+	0.970377i	$0.577671\pi$
$644$	1.19667	0.0471555
$645$	0	0
$646$	12.9911	0.511127
$647$	−6.12014	−0.240608	−0.120304	−	0.992737i	$-0.538387\pi$
$647$	−6.12014	−0.240608	−0.120304	+	0.992737i	$0.538387\pi$
$648$	−25.0251	−0.983079
$649$	0	0
$650$	0	0
$651$	−6.42960	−0.251996
$652$	16.0532	0.628691
$653$	38.0316	1.48829	0.744145	−	0.668018i	$-0.232857\pi$
$653$	38.0316	1.48829	0.744145	+	0.668018i	$0.232857\pi$
$654$	26.2884	1.02796
$655$	0	0
$656$	−4.61889	−0.180338
$657$	−0.683725	−0.0266746
$658$	0.918077	0.0357904
$659$	−15.7879	−0.615011	−0.307505	−	0.951546i	$-0.599494\pi$
$659$	−15.7879	−0.615011	−0.307505	+	0.951546i	$0.599494\pi$
$660$	0	0
$661$	−24.5794	−0.956027	−0.478014	−	0.878352i	$-0.658643\pi$
$661$	−24.5794	−0.956027	−0.478014	+	0.878352i	$0.658643\pi$
$662$	−4.52980	−0.176056
$663$	−22.3661	−0.868626
$664$	−16.0070	−0.621193
$665$	0	0
$666$	−0.590226	−0.0228708
$667$	−5.33038	−0.206393
$668$	−11.8300	−0.457716
$669$	11.1033	0.429279
$670$	0	0
$671$	0	0
$672$	6.07597	0.234385
$673$	29.9733	1.15539	0.577693	−	0.816254i	$-0.303953\pi$
$673$	29.9733	1.15539	0.577693	+	0.816254i	$0.303953\pi$
$674$	−18.1541	−0.699271
$675$	0	0
$676$	13.2563	0.509857
$677$	3.75709	0.144397	0.0721984	−	0.997390i	$-0.476999\pi$
$677$	3.75709	0.144397	0.0721984	+	0.997390i	$0.476999\pi$
$678$	16.6794	0.640570
$679$	3.18297	0.122151
$680$	0	0
$681$	−1.96641	−0.0753531
$682$	0	0
$683$	−21.0157	−0.804144	−0.402072	−	0.915608i	$-0.631710\pi$
$683$	−21.0157	−0.804144	−0.402072	+	0.915608i	$0.631710\pi$
$684$	−0.310680	−0.0118791
$685$	0	0
$686$	−6.48730	−0.247686
$687$	−7.38836	−0.281883
$688$	−5.22805	−0.199317
$689$	4.27706	0.162943
$690$	0	0
$691$	−38.2825	−1.45633	−0.728167	−	0.685399i	$-0.759628\pi$
$691$	−38.2825	−1.45633	−0.728167	+	0.685399i	$0.759628\pi$
$692$	12.4432	0.473020
$693$	0	0
$694$	0.146408	0.00555757
$695$	0	0
$696$	−16.9576	−0.642776
$697$	59.5200	2.25448
$698$	−12.3835	−0.468721
$699$	−11.9369	−0.451495
$700$	0	0
$701$	34.2344	1.29302	0.646509	−	0.762907i	$-0.276228\pi$
$701$	34.2344	1.29302	0.646509	+	0.762907i	$0.276228\pi$
$702$	7.35618	0.277641
$703$	16.7795	0.632852
$704$	0	0
$705$	0	0
$706$	−19.1928	−0.722329
$707$	−5.88035	−0.221153
$708$	0.0913687	0.00343385
$709$	−4.12477	−0.154909	−0.0774545	−	0.996996i	$-0.524679\pi$
$709$	−4.12477	−0.154909	−0.0774545	+	0.996996i	$0.524679\pi$
$710$	0	0
$711$	−0.453567	−0.0170101
$712$	−16.7373	−0.627258
$713$	9.19418	0.344325
$714$	−5.92246	−0.221642
$715$	0	0
$716$	−1.96324	−0.0733697
$717$	−7.74389	−0.289201
$718$	−7.03754	−0.262639
$719$	29.3596	1.09493	0.547463	−	0.836830i	$-0.315594\pi$
$719$	29.3596	1.09493	0.547463	+	0.836830i	$0.315594\pi$
$720$	0	0
$721$	−8.00605	−0.298161
$722$	11.0535	0.411367
$723$	16.9246	0.629431
$724$	−1.07573	−0.0399792
$725$	0	0
$726$	0	0
$727$	44.0893	1.63518	0.817591	−	0.575799i	$-0.195309\pi$
$727$	44.0893	1.63518	0.817591	+	0.575799i	$0.195309\pi$
$728$	−2.86265	−0.106097
$729$	26.0388	0.964401
$730$	0	0
$731$	67.3696	2.49176
$732$	−8.21503	−0.303636
$733$	48.9490	1.80797	0.903987	−	0.427561i	$-0.140627\pi$
$733$	48.9490	1.80797	0.903987	+	0.427561i	$0.140627\pi$
$734$	4.32038	0.159468
$735$	0	0
$736$	−8.68849	−0.320262
$737$	0	0
$738$	0.676520	0.0249031
$739$	20.6622	0.760072	0.380036	−	0.924972i	$-0.375912\pi$
$739$	20.6622	0.760072	0.380036	+	0.924972i	$0.375912\pi$
$740$	0	0
$741$	7.22719	0.265498
$742$	1.13255	0.0415772
$743$	30.1631	1.10658	0.553288	−	0.832990i	$-0.313373\pi$
$743$	30.1631	1.10658	0.553288	+	0.832990i	$0.313373\pi$
$744$	29.2495	1.07234
$745$	0	0
$746$	2.58830	0.0947645
$747$	−0.595525	−0.0217891
$748$	0	0
$749$	−3.31838	−0.121251
$750$	0	0
$751$	12.0966	0.441412	0.220706	−	0.975340i	$-0.429164\pi$
$751$	12.0966	0.441412	0.220706	+	0.975340i	$0.429164\pi$
$752$	1.06087	0.0386858
$753$	23.6302	0.861133
$754$	5.15141	0.187603
$755$	0	0
$756$	−4.09840	−0.149057
$757$	−20.6101	−0.749086	−0.374543	−	0.927210i	$-0.622200\pi$
$757$	−20.6101	−0.749086	−0.374543	+	0.927210i	$0.622200\pi$
$758$	15.7838	0.573293
$759$	0	0
$760$	0	0
$761$	−20.8450	−0.755631	−0.377816	−	0.925881i	$-0.623325\pi$
$761$	−20.8450	−0.755631	−0.377816	+	0.925881i	$0.623325\pi$
$762$	−22.6935	−0.822100
$763$	11.0132	0.398704
$764$	11.0491	0.399744
$765$	0	0
$766$	22.4556	0.811354
$767$	−0.0687044	−0.00248077
$768$	−25.0189	−0.902792
$769$	−10.7167	−0.386455	−0.193228	−	0.981154i	$-0.561896\pi$
$769$	−10.7167	−0.386455	−0.193228	+	0.981154i	$0.561896\pi$
$770$	0	0
$771$	19.0466	0.685946
$772$	5.92207	0.213140
$773$	20.3563	0.732164	0.366082	−	0.930583i	$-0.380699\pi$
$773$	20.3563	0.732164	0.366082	+	0.930583i	$0.380699\pi$
$774$	0.765742	0.0275240
$775$	0	0
$776$	−14.4800	−0.519801
$777$	−7.64957	−0.274427
$778$	−10.4672	−0.375267
$779$	−19.2328	−0.689087
$780$	0	0
$781$	0	0
$782$	8.46898	0.302850
$783$	18.2557	0.652405
$784$	−3.65187	−0.130424
$785$	0	0
$786$	25.4820	0.908914
$787$	14.2222	0.506967	0.253484	−	0.967340i	$-0.418424\pi$
$787$	14.2222	0.506967	0.253484	+	0.967340i	$0.418424\pi$
$788$	−21.2198	−0.755923
$789$	43.3760	1.54423
$790$	0	0
$791$	6.98764	0.248452
$792$	0	0
$793$	6.17726	0.219361
$794$	−1.46286	−0.0519150
$795$	0	0
$796$	−1.94987	−0.0691113
$797$	45.0384	1.59534	0.797671	−	0.603093i	$-0.206065\pi$
$797$	45.0384	1.59534	0.797671	+	0.603093i	$0.206065\pi$
$798$	1.91374	0.0677455
$799$	−13.6705	−0.483629
$800$	0	0
$801$	−0.622695	−0.0220018
$802$	−4.31920	−0.152516
$803$	0	0
$804$	−16.2115	−0.571737
$805$	0	0
$806$	−8.88548	−0.312978
$807$	−8.45334	−0.297572
$808$	26.7509	0.941094
$809$	−23.7753	−0.835896	−0.417948	−	0.908471i	$-0.637251\pi$
$809$	−23.7753	−0.835896	−0.417948	+	0.908471i	$0.637251\pi$
$810$	0	0
$811$	8.19869	0.287895	0.143948	−	0.989585i	$-0.454020\pi$
$811$	8.19869	0.287895	0.143948	+	0.989585i	$0.454020\pi$
$812$	−2.87004	−0.100719
$813$	−41.0787	−1.44069
$814$	0	0
$815$	0	0
$816$	−6.84358	−0.239573
$817$	−21.7693	−0.761610
$818$	−29.4447	−1.02951
$819$	−0.106502	−0.00372147
$820$	0	0
$821$	43.4373	1.51597	0.757986	−	0.652271i	$-0.226184\pi$
$821$	43.4373	1.51597	0.757986	+	0.652271i	$0.226184\pi$
$822$	5.69872	0.198766
$823$	51.6801	1.80145	0.900727	−	0.434386i	$-0.143034\pi$
$823$	51.6801	1.80145	0.900727	+	0.434386i	$0.143034\pi$
$824$	36.4211	1.26879
$825$	0	0
$826$	−0.0181927	−0.000633004 0
$827$	25.3079	0.880042	0.440021	−	0.897987i	$-0.354971\pi$
$827$	25.3079	0.880042	0.440021	+	0.897987i	$0.354971\pi$
$828$	−0.202535	−0.00703857
$829$	−41.8760	−1.45441	−0.727207	−	0.686418i	$-0.759182\pi$
$829$	−41.8760	−1.45441	−0.727207	+	0.686418i	$0.759182\pi$
$830$	0	0
$831$	−38.5555	−1.33747
$832$	6.42527	0.222756
$833$	47.0587	1.63049
$834$	11.2148	0.388336
$835$	0	0
$836$	0	0
$837$	−31.4885	−1.08840
$838$	−2.30078	−0.0794791
$839$	−14.3848	−0.496619	−0.248309	−	0.968681i	$-0.579875\pi$
$839$	−14.3848	−0.496619	−0.248309	+	0.968681i	$0.579875\pi$
$840$	0	0
$841$	−16.2158	−0.559167
$842$	−3.74038	−0.128902
$843$	−27.7765	−0.956673
$844$	11.7690	0.405106
$845$	0	0
$846$	−0.155383	−0.00534218
$847$	0	0
$848$	1.30870	0.0449408
$849$	39.8088	1.36624
$850$	0	0
$851$	10.9387	0.374974
$852$	28.1510	0.964437
$853$	43.0014	1.47234	0.736170	−	0.676797i	$-0.236632\pi$
$853$	43.0014	1.47234	0.736170	+	0.676797i	$0.236632\pi$
$854$	1.63572	0.0559731
$855$	0	0
$856$	15.0960	0.515970
$857$	54.3052	1.85503	0.927516	−	0.373784i	$-0.121940\pi$
$857$	54.3052	1.85503	0.927516	+	0.373784i	$0.121940\pi$
$858$	0	0
$859$	24.3361	0.830336	0.415168	−	0.909745i	$-0.363723\pi$
$859$	24.3361	0.830336	0.415168	+	0.909745i	$0.363723\pi$
$860$	0	0
$861$	8.76798	0.298812
$862$	16.6714	0.567828
$863$	39.1501	1.33268	0.666342	−	0.745646i	$-0.267859\pi$
$863$	39.1501	1.33268	0.666342	+	0.745646i	$0.267859\pi$
$864$	29.7567	1.01234
$865$	0	0
$866$	−10.2723	−0.349066
$867$	58.2551	1.97845
$868$	4.95043	0.168029
$869$	0	0
$870$	0	0
$871$	12.1902	0.413049
$872$	−50.1012	−1.69664
$873$	−0.538713	−0.0182327
$874$	−2.73660	−0.0925668
$875$	0	0
$876$	16.2859	0.550248
$877$	−43.0882	−1.45499	−0.727493	−	0.686116i	$-0.759314\pi$
$877$	−43.0882	−1.45499	−0.727493	+	0.686116i	$0.759314\pi$
$878$	−8.52534	−0.287716
$879$	−23.3468	−0.787466
$880$	0	0
$881$	−38.1083	−1.28390	−0.641950	−	0.766746i	$-0.721874\pi$
$881$	−38.1083	−1.28390	−0.641950	+	0.766746i	$0.721874\pi$
$882$	0.534882	0.0180104
$883$	29.0261	0.976805	0.488403	−	0.872618i	$-0.337580\pi$
$883$	29.0261	0.976805	0.488403	+	0.872618i	$0.337580\pi$
$884$	17.2206	0.579193
$885$	0	0
$886$	5.29696	0.177955
$887$	−2.21174	−0.0742631	−0.0371315	−	0.999310i	$-0.511822\pi$
$887$	−2.21174	−0.0742631	−0.0371315	+	0.999310i	$0.511822\pi$
$888$	34.7994	1.16779
$889$	−9.50717	−0.318860
$890$	0	0
$891$	0	0
$892$	−8.54894	−0.286240
$893$	4.41739	0.147822
$894$	17.6681	0.590909
$895$	0	0
$896$	−5.20021	−0.173727
$897$	4.71146	0.157311
$898$	−10.9392	−0.365047
$899$	−22.0509	−0.735439
$900$	0	0
$901$	−16.8641	−0.561825
$902$	0	0
$903$	9.92432	0.330261
$904$	−31.7882	−1.05726
$905$	0	0
$906$	11.8756	0.394541
$907$	26.6863	0.886106	0.443053	−	0.896496i	$-0.353895\pi$
$907$	26.6863	0.886106	0.443053	+	0.896496i	$0.353895\pi$
$908$	1.51403	0.0502448
$909$	0.995240	0.0330100
$910$	0	0
$911$	−36.2736	−1.20180	−0.600899	−	0.799325i	$-0.705191\pi$
$911$	−36.2736	−1.20180	−0.600899	+	0.799325i	$0.705191\pi$
$912$	2.21138	0.0732261
$913$	0	0
$914$	10.8363	0.358434
$915$	0	0
$916$	5.68863	0.187958
$917$	10.6754	0.352532
$918$	−29.0049	−0.957303
$919$	29.6718	0.978781	0.489391	−	0.872065i	$-0.337219\pi$
$919$	29.6718	0.978781	0.489391	+	0.872065i	$0.337219\pi$
$920$	0	0
$921$	17.6358	0.581119
$922$	9.08790	0.299294
$923$	−21.1680	−0.696754
$924$	0	0
$925$	0	0
$926$	−3.87696	−0.127405
$927$	1.35501	0.0445044
$928$	20.8381	0.684044
$929$	27.7726	0.911189	0.455595	−	0.890187i	$-0.349427\pi$
$929$	27.7726	0.911189	0.455595	+	0.890187i	$0.349427\pi$
$930$	0	0
$931$	−15.2062	−0.498362
$932$	9.19075	0.301053
$933$	−6.00106	−0.196466
$934$	19.2786	0.630817
$935$	0	0
$936$	0.484498	0.0158363
$937$	−30.2421	−0.987967	−0.493983	−	0.869471i	$-0.664460\pi$
$937$	−30.2421	−0.987967	−0.493983	+	0.869471i	$0.664460\pi$
$938$	3.22792	0.105395
$939$	−43.1396	−1.40781
$940$	0	0
$941$	6.00672	0.195813	0.0979067	−	0.995196i	$-0.468785\pi$
$941$	6.00672	0.195813	0.0979067	+	0.995196i	$0.468785\pi$
$942$	19.7810	0.644500
$943$	−12.5380	−0.408294
$944$	−0.0210222	−0.000684214 0
$945$	0	0
$946$	0	0
$947$	−10.0218	−0.325665	−0.162833	−	0.986654i	$-0.552063\pi$
$947$	−10.0218	−0.325665	−0.162833	+	0.986654i	$0.552063\pi$
$948$	10.8037	0.350887
$949$	−12.2461	−0.397525
$950$	0	0
$951$	−12.3050	−0.399016
$952$	11.2872	0.365820
$953$	−9.78136	−0.316849	−0.158425	−	0.987371i	$-0.550641\pi$
$953$	−9.78136	−0.316849	−0.158425	+	0.987371i	$0.550641\pi$
$954$	−0.191682	−0.00620594
$955$	0	0
$956$	5.96237	0.192837
$957$	0	0
$958$	34.6967	1.12100
$959$	2.38740	0.0770933
$960$	0	0
$961$	7.03479	0.226929
$962$	−10.5714	−0.340837
$963$	0.561631	0.0180983
$964$	−13.0310	−0.419700
$965$	0	0
$966$	1.24758	0.0401402
$967$	−1.22635	−0.0394367	−0.0197184	−	0.999806i	$-0.506277\pi$
$967$	−1.22635	−0.0394367	−0.0197184	+	0.999806i	$0.506277\pi$
$968$	0	0
$969$	−28.4963	−0.915432
$970$	0	0
$971$	−44.6467	−1.43278	−0.716390	−	0.697700i	$-0.754207\pi$
$971$	−44.6467	−1.43278	−0.716390	+	0.697700i	$0.754207\pi$
$972$	1.41127	0.0452664
$973$	4.69829	0.150620
$974$	−33.6820	−1.07924
$975$	0	0
$976$	1.89012	0.0605013
$977$	47.2451	1.51151	0.755753	−	0.654857i	$-0.227271\pi$
$977$	47.2451	1.51151	0.755753	+	0.654857i	$0.227271\pi$
$978$	16.7361	0.535162
$979$	0	0
$980$	0	0
$981$	−1.86396	−0.0595118
$982$	−7.27232	−0.232069
$983$	−13.9351	−0.444459	−0.222230	−	0.974994i	$-0.571333\pi$
$983$	−13.9351	−0.444459	−0.222230	+	0.974994i	$0.571333\pi$
$984$	−39.8873	−1.27156
$985$	0	0
$986$	−20.3116	−0.646854
$987$	−2.01383	−0.0641008
$988$	−5.56454	−0.177032
$989$	−14.1916	−0.451265
$990$	0	0
$991$	36.5755	1.16186	0.580930	−	0.813953i	$-0.302689\pi$
$991$	36.5755	1.16186	0.580930	+	0.813953i	$0.302689\pi$
$992$	−35.9429	−1.14119
$993$	9.93623	0.315317
$994$	−5.60522	−0.177787
$995$	0	0
$996$	14.1850	0.449469
$997$	19.3415	0.612552	0.306276	−	0.951943i	$-0.400917\pi$
$997$	19.3415	0.612552	0.306276	+	0.951943i	$0.400917\pi$
$998$	−24.3052	−0.769367
$999$	−37.4633	−1.18529

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3025.2.a.bk.1.4		8
5.2	odd	4		605.2.b.f.364.4		8
5.3	odd	4		605.2.b.f.364.5		8
5.4	even	2	inner	3025.2.a.bk.1.5		8
11.7	odd	10		275.2.h.d.126.3		16
11.8	odd	10		275.2.h.d.251.3		16
11.10	odd	2		3025.2.a.bl.1.5		8
55.2	even	20		605.2.j.h.444.3		16
55.3	odd	20		605.2.j.d.9.3		16
55.7	even	20		55.2.j.a.49.2	yes	16
55.8	even	20		55.2.j.a.9.2	✓	16
55.13	even	20		605.2.j.h.444.2		16
55.17	even	20		605.2.j.h.124.2		16
55.18	even	20		55.2.j.a.49.3	yes	16
55.19	odd	10		275.2.h.d.251.2		16
55.27	odd	20		605.2.j.g.124.3		16
55.28	even	20		605.2.j.h.124.3		16
55.29	odd	10		275.2.h.d.126.2		16
55.32	even	4		605.2.b.g.364.5		8
55.37	odd	20		605.2.j.d.269.3		16
55.38	odd	20		605.2.j.g.124.2		16
55.42	odd	20		605.2.j.g.444.2		16
55.43	even	4		605.2.b.g.364.4		8
55.47	odd	20		605.2.j.d.9.2		16
55.48	odd	20		605.2.j.d.269.2		16
55.52	even	20		55.2.j.a.9.3	yes	16
55.53	odd	20		605.2.j.g.444.3		16
55.54	odd	2		3025.2.a.bl.1.4		8
165.8	odd	20		495.2.ba.a.64.3		16
165.62	odd	20		495.2.ba.a.379.3		16
165.107	odd	20		495.2.ba.a.64.2		16
165.128	odd	20		495.2.ba.a.379.2		16
220.7	odd	20		880.2.cd.c.49.3		16
220.63	odd	20		880.2.cd.c.449.3		16
220.107	odd	20		880.2.cd.c.449.2		16
220.183	odd	20		880.2.cd.c.49.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.j.a.9.2	✓	16	55.8	even	20
55.2.j.a.9.3	yes	16	55.52	even	20
55.2.j.a.49.2	yes	16	55.7	even	20
55.2.j.a.49.3	yes	16	55.18	even	20
275.2.h.d.126.2		16	55.29	odd	10
275.2.h.d.126.3		16	11.7	odd	10
275.2.h.d.251.2		16	55.19	odd	10
275.2.h.d.251.3		16	11.8	odd	10
495.2.ba.a.64.2		16	165.107	odd	20
495.2.ba.a.64.3		16	165.8	odd	20
495.2.ba.a.379.2		16	165.128	odd	20
495.2.ba.a.379.3		16	165.62	odd	20
605.2.b.f.364.4		8	5.2	odd	4
605.2.b.f.364.5		8	5.3	odd	4
605.2.b.g.364.4		8	55.43	even	4
605.2.b.g.364.5		8	55.32	even	4
605.2.j.d.9.2		16	55.47	odd	20
605.2.j.d.9.3		16	55.3	odd	20
605.2.j.d.269.2		16	55.48	odd	20
605.2.j.d.269.3		16	55.37	odd	20
605.2.j.g.124.2		16	55.38	odd	20
605.2.j.g.124.3		16	55.27	odd	20
605.2.j.g.444.2		16	55.42	odd	20
605.2.j.g.444.3		16	55.53	odd	20
605.2.j.h.124.2		16	55.17	even	20
605.2.j.h.124.3		16	55.28	even	20
605.2.j.h.444.2		16	55.13	even	20
605.2.j.h.444.3		16	55.2	even	20
880.2.cd.c.49.2		16	220.183	odd	20
880.2.cd.c.49.3		16	220.7	odd	20
880.2.cd.c.449.2		16	220.107	odd	20
880.2.cd.c.449.3		16	220.63	odd	20
3025.2.a.bk.1.4		8	1.1	even	1	trivial
3025.2.a.bk.1.5		8	5.4	even	2	inner
3025.2.a.bl.1.4		8	55.54	odd	2
3025.2.a.bl.1.5		8	11.10	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:	\( N \)	\(=\)	\( 3025 = 5^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3025.a (trivial)

\(f(q)\)	\(=\)	\(q-0.802699 q^{2} +1.76074 q^{3} -1.35567 q^{4} -1.41335 q^{6} -0.592103 q^{7} +2.69360 q^{8} +0.100212 q^{9} +O(q^{10})\)	\(q-0.802699 q^{2} +1.76074 q^{3} -1.35567 q^{4} -1.41335 q^{6} -0.592103 q^{7} +2.69360 q^{8} +0.100212 q^{9} -2.38699 q^{12} +1.79489 q^{13} +0.475281 q^{14} +0.549201 q^{16} -7.07712 q^{17} -0.0804405 q^{18} +2.28684 q^{19} -1.04254 q^{21} +1.49081 q^{23} +4.74273 q^{24} -1.44076 q^{26} -5.10578 q^{27} +0.802699 q^{28} -3.57549 q^{29} +6.16724 q^{31} -5.82804 q^{32} +5.68079 q^{34} -0.135855 q^{36} +7.33743 q^{37} -1.83565 q^{38} +3.16034 q^{39} -8.41020 q^{41} +0.836847 q^{42} -9.51936 q^{43} -1.19667 q^{46} +1.93165 q^{47} +0.967002 q^{48} -6.64941 q^{49} -12.4610 q^{51} -2.43329 q^{52} +2.38291 q^{53} +4.09840 q^{54} -1.59489 q^{56} +4.02654 q^{57} +2.87004 q^{58} -0.0382778 q^{59} +3.44158 q^{61} -4.95043 q^{62} -0.0593361 q^{63} +3.57976 q^{64} +6.79162 q^{67} +9.59426 q^{68} +2.62493 q^{69} -11.7935 q^{71} +0.269932 q^{72} -6.82275 q^{73} -5.88974 q^{74} -3.10021 q^{76} -2.53680 q^{78} -4.52605 q^{79} -9.29059 q^{81} +6.75086 q^{82} -5.94262 q^{83} +1.41335 q^{84} +7.64118 q^{86} -6.29552 q^{87} -6.21375 q^{89} -1.06276 q^{91} -2.02105 q^{92} +10.8589 q^{93} -1.55054 q^{94} -10.2617 q^{96} -5.37571 q^{97} +5.33748 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} - 6 q^{6} + 4 q^{9}+O(q^{10}) \) 8 * q + 2 * q^4 - 6 * q^6 + 4 * q^9	\( 8 q + 2 q^{4} - 6 q^{6} + 4 q^{9} - 4 q^{14} - 22 q^{16} - 12 q^{19} - 4 q^{21} - 2 q^{24} + 10 q^{26} - 24 q^{29} + 14 q^{31} + 8 q^{34} + 20 q^{36} - 30 q^{39} - 34 q^{41} - 24 q^{46} - 30 q^{49} - 54 q^{51} - 20 q^{54} - 10 q^{56} - 6 q^{59} - 20 q^{61} + 14 q^{64} + 32 q^{69} - 42 q^{71} + 4 q^{74} - 28 q^{76} - 16 q^{79} - 36 q^{81} + 6 q^{84} + 46 q^{86} - 12 q^{89} + 20 q^{91} + 42 q^{94} + 8 q^{96}+O(q^{100}) \) 8 * q + 2 * q^4 - 6 * q^6 + 4 * q^9 - 4 * q^14 - 22 * q^16 - 12 * q^19 - 4 * q^21 - 2 * q^24 + 10 * q^26 - 24 * q^29 + 14 * q^31 + 8 * q^34 + 20 * q^36 - 30 * q^39 - 34 * q^41 - 24 * q^46 - 30 * q^49 - 54 * q^51 - 20 * q^54 - 10 * q^56 - 6 * q^59 - 20 * q^61 + 14 * q^64 + 32 * q^69 - 42 * q^71 + 4 * q^74 - 28 * q^76 - 16 * q^79 - 36 * q^81 + 6 * q^84 + 46 * q^86 - 12 * q^89 + 20 * q^91 + 42 * q^94 + 8 * q^96

Introduction

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