LMFDB - Embedded newform 9025.2.a.cc.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9025,2,Mod(1,9025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9025, 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("9025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9025 = 5^{2} \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9025.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:	$72.0649878242$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 6x^{7} + 16x^{6} + 12x^{5} - 27x^{4} - 8x^{3} + 15x^{2} - 1 $ x^9 - 3x^8 - 6x^7 + 16x^6 + 12x^5 - 27x^4 - 8x^3 + 15*x^2 - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.256961$ of defining polynomial
Character	$\chi$	$=$	9025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.25696 q^{2} -3.01225 q^{3} -0.420048 q^{4} +3.78628 q^{6} -3.72392 q^{7} +3.04191 q^{8} +6.07366 q^{9} +O(q^{10})$	\(q-1.25696 q^{2} -3.01225 q^{3} -0.420048 q^{4} +3.78628 q^{6} -3.72392 q^{7} +3.04191 q^{8} +6.07366 q^{9} -3.35588 q^{11} +1.26529 q^{12} -4.84131 q^{13} +4.68082 q^{14} -2.98346 q^{16} +2.67526 q^{17} -7.63436 q^{18} +11.2174 q^{21} +4.21821 q^{22} -1.87703 q^{23} -9.16299 q^{24} +6.08534 q^{26} -9.25865 q^{27} +1.56423 q^{28} -5.25131 q^{29} -3.11891 q^{31} -2.33372 q^{32} +10.1087 q^{33} -3.36269 q^{34} -2.55123 q^{36} -0.992927 q^{37} +14.5832 q^{39} +0.416383 q^{41} -14.0998 q^{42} +7.21877 q^{43} +1.40963 q^{44} +2.35935 q^{46} -2.24086 q^{47} +8.98694 q^{48} +6.86757 q^{49} -8.05854 q^{51} +2.03358 q^{52} -0.260252 q^{53} +11.6378 q^{54} -11.3278 q^{56} +6.60069 q^{58} -5.18883 q^{59} +0.768938 q^{61} +3.92035 q^{62} -22.6178 q^{63} +8.90032 q^{64} -12.7063 q^{66} -10.7775 q^{67} -1.12374 q^{68} +5.65409 q^{69} +2.00146 q^{71} +18.4755 q^{72} -4.56262 q^{73} +1.24807 q^{74} +12.4970 q^{77} -18.3306 q^{78} -12.0521 q^{79} +9.66841 q^{81} -0.523377 q^{82} +13.5711 q^{83} -4.71184 q^{84} -9.07371 q^{86} +15.8183 q^{87} -10.2083 q^{88} -7.66941 q^{89} +18.0286 q^{91} +0.788443 q^{92} +9.39494 q^{93} +2.81668 q^{94} +7.02975 q^{96} +7.22894 q^{97} -8.63226 q^{98} -20.3825 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 6 q^{2} - 9 q^{3} + 6 q^{4} + 12 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 9 * q - 6 * q^2 - 9 * q^3 + 6 * q^4 + 12 * q^6 - 6 * q^8 + 6 * q^9	$ 9 q - 6 q^{2} - 9 q^{3} + 6 q^{4} + 12 q^{6} - 6 q^{8} + 6 q^{9} - 18 q^{12} - 9 q^{13} + 12 q^{16} + 9 q^{17} - 24 q^{18} + 12 q^{21} - 24 q^{22} + 12 q^{23} + 3 q^{24} - 3 q^{26} - 24 q^{27} + 15 q^{28} + 9 q^{29} + 18 q^{31} - 3 q^{32} + 9 q^{33} - 24 q^{34} + 18 q^{36} - 18 q^{37} + 18 q^{39} + 6 q^{41} + 12 q^{43} + 48 q^{44} - 9 q^{46} - 15 q^{47} + 21 q^{48} - 9 q^{49} - 6 q^{51} - 33 q^{52} - 15 q^{53} + 63 q^{54} - 6 q^{58} + 21 q^{59} - 12 q^{61} + 36 q^{62} - 21 q^{63} - 36 q^{64} + 3 q^{66} - 60 q^{67} + 51 q^{68} - 15 q^{69} - 18 q^{71} - 27 q^{73} + 27 q^{74} + 30 q^{77} + 6 q^{78} + 15 q^{79} + 33 q^{81} - 24 q^{82} - 48 q^{84} - 39 q^{86} - 15 q^{87} - 27 q^{88} - 39 q^{89} + 21 q^{91} + 6 q^{92} - 15 q^{93} + 15 q^{94} - 33 q^{96} - 15 q^{97} + 15 q^{98} - 36 q^{99}+O(q^{100}) $ 9 * q - 6 * q^2 - 9 * q^3 + 6 * q^4 + 12 * q^6 - 6 * q^8 + 6 * q^9 - 18 * q^12 - 9 * q^13 + 12 * q^16 + 9 * q^17 - 24 * q^18 + 12 * q^21 - 24 * q^22 + 12 * q^23 + 3 * q^24 - 3 * q^26 - 24 * q^27 + 15 * q^28 + 9 * q^29 + 18 * q^31 - 3 * q^32 + 9 * q^33 - 24 * q^34 + 18 * q^36 - 18 * q^37 + 18 * q^39 + 6 * q^41 + 12 * q^43 + 48 * q^44 - 9 * q^46 - 15 * q^47 + 21 * q^48 - 9 * q^49 - 6 * q^51 - 33 * q^52 - 15 * q^53 + 63 * q^54 - 6 * q^58 + 21 * q^59 - 12 * q^61 + 36 * q^62 - 21 * q^63 - 36 * q^64 + 3 * q^66 - 60 * q^67 + 51 * q^68 - 15 * q^69 - 18 * q^71 - 27 * q^73 + 27 * q^74 + 30 * q^77 + 6 * q^78 + 15 * q^79 + 33 * q^81 - 24 * q^82 - 48 * q^84 - 39 * q^86 - 15 * q^87 - 27 * q^88 - 39 * q^89 + 21 * q^91 + 6 * q^92 - 15 * q^93 + 15 * q^94 - 33 * q^96 - 15 * q^97 + 15 * q^98 - 36 * 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 $

$2$	−1.25696	−0.888806	−0.444403	−	0.895827i	$-0.646584\pi$
$2$	−1.25696	−0.888806	−0.444403	+	0.895827i	$0.646584\pi$
$3$	−3.01225	−1.73912	−0.869562	−	0.493823i	$-0.835599\pi$
$3$	−3.01225	−1.73912	−0.869562	+	0.493823i	$0.835599\pi$
$4$	−0.420048	−0.210024
$5$	0	0
$5$	0	0
$6$	3.78628	1.54574
$7$	−3.72392	−1.40751	−0.703754	−	0.710443i	$-0.748494\pi$
$7$	−3.72392	−1.40751	−0.703754	+	0.710443i	$0.748494\pi$
$8$	3.04191	1.07548
$9$	6.07366	2.02455
$10$	0	0
$11$	−3.35588	−1.01183	−0.505917	−	0.862582i	$-0.668846\pi$
$11$	−3.35588	−1.01183	−0.505917	+	0.862582i	$0.668846\pi$
$12$	1.26529	0.365258
$13$	−4.84131	−1.34274	−0.671369	−	0.741124i	$-0.734293\pi$
$13$	−4.84131	−1.34274	−0.671369	+	0.741124i	$0.734293\pi$
$14$	4.68082	1.25100
$15$	0	0
$16$	−2.98346	−0.745866
$17$	2.67526	0.648845	0.324422	−	0.945912i	$-0.394830\pi$
$17$	2.67526	0.648845	0.324422	+	0.945912i	$0.394830\pi$
$18$	−7.63436	−1.79944
$19$	0	0
$19$	0	0
$20$	0	0
$21$	11.2174	2.44783
$22$	4.21821	0.899325
$23$	−1.87703	−0.391388	−0.195694	−	0.980665i	$-0.562696\pi$
$23$	−1.87703	−0.391388	−0.195694	+	0.980665i	$0.562696\pi$
$24$	−9.16299	−1.87039
$25$	0	0
$26$	6.08534	1.19343
$27$	−9.25865	−1.78183
$28$	1.56423	0.295611
$29$	−5.25131	−0.975143	−0.487572	−	0.873083i	$-0.662117\pi$
$29$	−5.25131	−0.975143	−0.487572	+	0.873083i	$0.662117\pi$
$30$	0	0
$31$	−3.11891	−0.560173	−0.280086	−	0.959975i	$-0.590363\pi$
$31$	−3.11891	−0.560173	−0.280086	+	0.959975i	$0.590363\pi$
$32$	−2.33372	−0.412547
$33$	10.1087	1.75971
$34$	−3.36269	−0.576697
$35$	0	0
$36$	−2.55123	−0.425206
$37$	−0.992927	−0.163236	−0.0816181	−	0.996664i	$-0.526009\pi$
$37$	−0.992927	−0.163236	−0.0816181	+	0.996664i	$0.526009\pi$
$38$	0	0
$39$	14.5832	2.33519
$40$	0	0
$41$	0.416383	0.0650281	0.0325140	−	0.999471i	$-0.489649\pi$
$41$	0.416383	0.0650281	0.0325140	+	0.999471i	$0.489649\pi$
$42$	−14.0998	−2.17565
$43$	7.21877	1.10085	0.550426	−	0.834884i	$-0.314465\pi$
$43$	7.21877	1.10085	0.550426	+	0.834884i	$0.314465\pi$
$44$	1.40963	0.212510
$45$	0	0
$46$	2.35935	0.347868
$47$	−2.24086	−0.326864	−0.163432	−	0.986555i	$-0.552256\pi$
$47$	−2.24086	−0.326864	−0.163432	+	0.986555i	$0.552256\pi$
$48$	8.98694	1.29715
$49$	6.86757	0.981081
$50$	0	0
$51$	−8.05854	−1.12842
$52$	2.03358	0.282007
$53$	−0.260252	−0.0357483	−0.0178742	−	0.999840i	$-0.505690\pi$
$53$	−0.260252	−0.0357483	−0.0178742	+	0.999840i	$0.505690\pi$
$54$	11.6378	1.58370
$55$	0	0
$56$	−11.3278	−1.51374
$57$	0	0
$58$	6.60069	0.866713
$59$	−5.18883	−0.675528	−0.337764	−	0.941231i	$-0.609671\pi$
$59$	−5.18883	−0.675528	−0.337764	+	0.941231i	$0.609671\pi$
$60$	0	0
$61$	0.768938	0.0984524	0.0492262	−	0.998788i	$-0.484324\pi$
$61$	0.768938	0.0984524	0.0492262	+	0.998788i	$0.484324\pi$
$62$	3.92035	0.497885
$63$	−22.6178	−2.84958
$64$	8.90032	1.11254
$65$	0	0
$66$	−12.7063	−1.56404
$67$	−10.7775	−1.31668	−0.658339	−	0.752722i	$-0.728740\pi$
$67$	−10.7775	−1.31668	−0.658339	+	0.752722i	$0.728740\pi$
$68$	−1.12374	−0.136273
$69$	5.65409	0.680672
$70$	0	0
$71$	2.00146	0.237529	0.118765	−	0.992922i	$-0.462107\pi$
$71$	2.00146	0.237529	0.118765	+	0.992922i	$0.462107\pi$
$72$	18.4755	2.17736
$73$	−4.56262	−0.534015	−0.267007	−	0.963694i	$-0.586035\pi$
$73$	−4.56262	−0.534015	−0.267007	+	0.963694i	$0.586035\pi$
$74$	1.24807	0.145085
$75$	0	0
$76$	0	0
$77$	12.4970	1.42417
$78$	−18.3306	−2.07553
$79$	−12.0521	−1.35596	−0.677981	−	0.735079i	$-0.737145\pi$
$79$	−12.0521	−1.35596	−0.677981	+	0.735079i	$0.737145\pi$
$80$	0	0
$81$	9.66841	1.07427
$82$	−0.523377	−0.0577973
$83$	13.5711	1.48962	0.744809	−	0.667278i	$-0.232541\pi$
$83$	13.5711	1.48962	0.744809	+	0.667278i	$0.232541\pi$
$84$	−4.71184	−0.514104
$85$	0	0
$86$	−9.07371	−0.978443
$87$	15.8183	1.69590
$88$	−10.2083	−1.08820
$89$	−7.66941	−0.812956	−0.406478	−	0.913661i	$-0.633243\pi$
$89$	−7.66941	−0.812956	−0.406478	+	0.913661i	$0.633243\pi$
$90$	0	0
$91$	18.0286	1.88991
$92$	0.788443	0.0822009
$93$	9.39494	0.974210
$94$	2.81668	0.290518
$95$	0	0
$96$	7.02975	0.717471
$97$	7.22894	0.733988	0.366994	−	0.930223i	$-0.380387\pi$
$97$	7.22894	0.733988	0.366994	+	0.930223i	$0.380387\pi$
$98$	−8.63226	−0.871990
$99$	−20.3825	−2.04852
$100$	0	0
$101$	4.49184	0.446955	0.223477	−	0.974709i	$-0.428259\pi$
$101$	4.49184	0.446955	0.223477	+	0.974709i	$0.428259\pi$
$102$	10.1293	1.00295
$103$	−10.7445	−1.05869	−0.529345	−	0.848407i	$-0.677562\pi$
$103$	−10.7445	−1.05869	−0.529345	+	0.848407i	$0.677562\pi$
$104$	−14.7268	−1.44408
$105$	0	0
$106$	0.327127	0.0317733
$107$	−1.37863	−0.133277	−0.0666386	−	0.997777i	$-0.521227\pi$
$107$	−1.37863	−0.133277	−0.0666386	+	0.997777i	$0.521227\pi$
$108$	3.88908	0.374227
$109$	9.49878	0.909818	0.454909	−	0.890538i	$-0.349672\pi$
$109$	9.49878	0.909818	0.454909	+	0.890538i	$0.349672\pi$
$110$	0	0
$111$	2.99095	0.283888
$112$	11.1102	1.04981
$113$	17.0436	1.60333	0.801666	−	0.597772i	$-0.203947\pi$
$113$	17.0436	1.60333	0.801666	+	0.597772i	$0.203947\pi$
$114$	0	0
$115$	0	0
$116$	2.20580	0.204804
$117$	−29.4045	−2.71844
$118$	6.52216	0.600413
$119$	−9.96243	−0.913255
$120$	0	0
$121$	0.261910	0.0238100
$122$	−0.966525	−0.0875051
$123$	−1.25425	−0.113092
$124$	1.31009	0.117650
$125$	0	0
$126$	28.4297	2.53272
$127$	−19.8598	−1.76227	−0.881137	−	0.472860i	$-0.843221\pi$
$127$	−19.8598	−1.76227	−0.881137	+	0.472860i	$0.843221\pi$
$128$	−6.51992	−0.576285
$129$	−21.7447	−1.91452
$130$	0	0
$131$	5.42317	0.473824	0.236912	−	0.971531i	$-0.423865\pi$
$131$	5.42317	0.473824	0.236912	+	0.971531i	$0.423865\pi$
$132$	−4.24616	−0.369581
$133$	0	0
$134$	13.5469	1.17027
$135$	0	0
$136$	8.13788	0.697817
$137$	18.5615	1.58581	0.792906	−	0.609344i	$-0.208567\pi$
$137$	18.5615	1.58581	0.792906	+	0.609344i	$0.208567\pi$
$138$	−7.10697	−0.604985
$139$	−10.5127	−0.891675	−0.445838	−	0.895114i	$-0.647094\pi$
$139$	−10.5127	−0.891675	−0.445838	+	0.895114i	$0.647094\pi$
$140$	0	0
$141$	6.75005	0.568457
$142$	−2.51575	−0.211117
$143$	16.2468	1.35863
$144$	−18.1205	−1.51005
$145$	0	0
$146$	5.73504	0.474635
$147$	−20.6868	−1.70622
$148$	0.417077	0.0342835
$149$	15.1409	1.24039	0.620196	−	0.784447i	$-0.287053\pi$
$149$	15.1409	1.24039	0.620196	+	0.784447i	$0.287053\pi$
$150$	0	0
$151$	11.3432	0.923095	0.461548	−	0.887115i	$-0.347294\pi$
$151$	11.3432	0.923095	0.461548	+	0.887115i	$0.347294\pi$
$152$	0	0
$153$	16.2486	1.31362
$154$	−15.7083	−1.26581
$155$	0	0
$156$	−6.12567	−0.490446
$157$	4.21528	0.336416	0.168208	−	0.985752i	$-0.446202\pi$
$157$	4.21528	0.336416	0.168208	+	0.985752i	$0.446202\pi$
$158$	15.1490	1.20519
$159$	0.783944	0.0621708
$160$	0	0
$161$	6.98990	0.550882
$162$	−12.1528	−0.954815
$163$	13.9056	1.08917	0.544585	−	0.838706i	$-0.316687\pi$
$163$	13.9056	1.08917	0.544585	+	0.838706i	$0.316687\pi$
$164$	−0.174901	−0.0136575
$165$	0	0
$166$	−17.0583	−1.32398
$167$	−17.6222	−1.36365	−0.681824	−	0.731516i	$-0.738813\pi$
$167$	−17.6222	−1.36365	−0.681824	+	0.731516i	$0.738813\pi$
$168$	34.1222	2.63259
$169$	10.4383	0.802943
$170$	0	0
$171$	0	0
$172$	−3.03223	−0.231206
$173$	13.3182	1.01256	0.506282	−	0.862368i	$-0.331019\pi$
$173$	13.3182	1.01256	0.506282	+	0.862368i	$0.331019\pi$
$174$	−19.8829	−1.50732
$175$	0	0
$176$	10.0121	0.754693
$177$	15.6301	1.17483
$178$	9.64015	0.722560
$179$	14.6264	1.09323	0.546616	−	0.837383i	$-0.315916\pi$
$179$	14.6264	1.09323	0.546616	+	0.837383i	$0.315916\pi$
$180$	0	0
$181$	−8.78476	−0.652966	−0.326483	−	0.945203i	$-0.605864\pi$
$181$	−8.78476	−0.652966	−0.326483	+	0.945203i	$0.605864\pi$
$182$	−22.6613	−1.67977
$183$	−2.31623	−0.171221
$184$	−5.70975	−0.420928
$185$	0	0
$186$	−11.8091	−0.865883
$187$	−8.97783	−0.656524
$188$	0.941271	0.0686493
$189$	34.4785	2.50794
$190$	0	0
$191$	−9.70737	−0.702401	−0.351200	−	0.936300i	$-0.614226\pi$
$191$	−9.70737	−0.702401	−0.351200	+	0.936300i	$0.614226\pi$
$192$	−26.8100	−1.93485
$193$	20.2546	1.45796	0.728981	−	0.684534i	$-0.239994\pi$
$193$	20.2546	1.45796	0.728981	+	0.684534i	$0.239994\pi$
$194$	−9.08650	−0.652373
$195$	0	0
$196$	−2.88471	−0.206051
$197$	9.26182	0.659877	0.329939	−	0.944002i	$-0.392972\pi$
$197$	9.26182	0.659877	0.329939	+	0.944002i	$0.392972\pi$
$198$	25.6200	1.82073
$199$	18.1521	1.28676	0.643382	−	0.765545i	$-0.277531\pi$
$199$	18.1521	1.28676	0.643382	+	0.765545i	$0.277531\pi$
$200$	0	0
$201$	32.4644	2.28987
$202$	−5.64607	−0.397256
$203$	19.5554	1.37252
$204$	3.38498	0.236996
$205$	0	0
$206$	13.5055	0.940970
$207$	−11.4004	−0.792386
$208$	14.4439	1.00150
$209$	0	0
$210$	0	0
$211$	17.3820	1.19662	0.598311	−	0.801264i	$-0.295839\pi$
$211$	17.3820	1.19662	0.598311	+	0.801264i	$0.295839\pi$
$212$	0.109318	0.00750802
$213$	−6.02889	−0.413093
$214$	1.73288	0.118458
$215$	0	0
$216$	−28.1640	−1.91631
$217$	11.6146	0.788448
$218$	−11.9396	−0.808651
$219$	13.7438	0.928718
$220$	0	0
$221$	−12.9517	−0.871228
$222$	−3.75950	−0.252321
$223$	8.72670	0.584383	0.292191	−	0.956360i	$-0.405616\pi$
$223$	8.72670	0.584383	0.292191	+	0.956360i	$0.405616\pi$
$224$	8.69057	0.580663
$225$	0	0
$226$	−21.4232	−1.42505
$227$	20.1154	1.33510	0.667552	−	0.744563i	$-0.267342\pi$
$227$	20.1154	1.33510	0.667552	+	0.744563i	$0.267342\pi$
$228$	0	0
$229$	−20.8410	−1.37721	−0.688607	−	0.725135i	$-0.741778\pi$
$229$	−20.8410	−1.37721	−0.688607	+	0.725135i	$0.741778\pi$
$230$	0	0
$231$	−37.6442	−2.47680
$232$	−15.9740	−1.04874
$233$	−0.544051	−0.0356420	−0.0178210	−	0.999841i	$-0.505673\pi$
$233$	−0.544051	−0.0356420	−0.0178210	+	0.999841i	$0.505673\pi$
$234$	36.9603	2.41617
$235$	0	0
$236$	2.17956	0.141877
$237$	36.3038	2.35819
$238$	12.5224	0.811706
$239$	−22.2235	−1.43752	−0.718758	−	0.695260i	$-0.755289\pi$
$239$	−22.2235	−1.43752	−0.718758	+	0.695260i	$0.755289\pi$
$240$	0	0
$241$	21.7336	1.39998	0.699991	−	0.714152i	$-0.253187\pi$
$241$	21.7336	1.39998	0.699991	+	0.714152i	$0.253187\pi$
$242$	−0.329211	−0.0211625
$243$	−1.34772	−0.0864565
$244$	−0.322991	−0.0206774
$245$	0	0
$246$	1.57654	0.100517
$247$	0	0
$248$	−9.48743	−0.602452
$249$	−40.8795	−2.59063
$250$	0	0
$251$	17.8239	1.12504	0.562518	−	0.826785i	$-0.309833\pi$
$251$	17.8239	1.12504	0.562518	+	0.826785i	$0.309833\pi$
$252$	9.50058	0.598481
$253$	6.29908	0.396020
$254$	24.9630	1.56632
$255$	0	0
$256$	−9.60535	−0.600334
$257$	−15.7239	−0.980829	−0.490414	−	0.871489i	$-0.663155\pi$
$257$	−15.7239	−0.980829	−0.490414	+	0.871489i	$0.663155\pi$
$258$	27.3323	1.70163
$259$	3.69758	0.229756
$260$	0	0
$261$	−31.8947	−1.97423
$262$	−6.81671	−0.421138
$263$	30.4504	1.87765	0.938826	−	0.344391i	$-0.111915\pi$
$263$	30.4504	1.87765	0.938826	+	0.344391i	$0.111915\pi$
$264$	30.7499	1.89252
$265$	0	0
$266$	0	0
$267$	23.1022	1.41383
$268$	4.52706	0.276534
$269$	2.61192	0.159251	0.0796257	−	0.996825i	$-0.474627\pi$
$269$	2.61192	0.159251	0.0796257	+	0.996825i	$0.474627\pi$
$270$	0	0
$271$	−9.60823	−0.583658	−0.291829	−	0.956470i	$-0.594264\pi$
$271$	−9.60823	−0.583658	−0.291829	+	0.956470i	$0.594264\pi$
$272$	−7.98152	−0.483951
$273$	−54.3068	−3.28680
$274$	−23.3310	−1.40948
$275$	0	0
$276$	−2.37499	−0.142958
$277$	−20.0672	−1.20572	−0.602860	−	0.797847i	$-0.705972\pi$
$277$	−20.0672	−1.20572	−0.602860	+	0.797847i	$0.705972\pi$
$278$	13.2140	0.792526
$279$	−18.9432	−1.13410
$280$	0	0
$281$	26.5556	1.58417	0.792086	−	0.610409i	$-0.208995\pi$
$281$	26.5556	1.58417	0.792086	+	0.610409i	$0.208995\pi$
$282$	−8.48455	−0.505247
$283$	16.7788	0.997397	0.498699	−	0.866776i	$-0.333811\pi$
$283$	16.7788	0.997397	0.498699	+	0.866776i	$0.333811\pi$
$284$	−0.840709	−0.0498869
$285$	0	0
$286$	−20.4216	−1.20756
$287$	−1.55058	−0.0915276
$288$	−14.1742	−0.835224
$289$	−9.84301	−0.579000
$290$	0	0
$291$	−21.7754	−1.27650
$292$	1.91652	0.112156
$293$	−13.3788	−0.781597	−0.390799	−	0.920476i	$-0.627801\pi$
$293$	−13.3788	−0.781597	−0.390799	+	0.920476i	$0.627801\pi$
$294$	26.0026	1.51650
$295$	0	0
$296$	−3.02039	−0.175557
$297$	31.0709	1.80292
$298$	−19.0315	−1.10247
$299$	9.08728	0.525531
$300$	0	0
$301$	−26.8821	−1.54946
$302$	−14.2579	−0.820452
$303$	−13.5305	−0.777310
$304$	0	0
$305$	0	0
$306$	−20.4239	−1.16755
$307$	−27.9723	−1.59646	−0.798232	−	0.602350i	$-0.794231\pi$
$307$	−27.9723	−1.59646	−0.798232	+	0.602350i	$0.794231\pi$
$308$	−5.24935	−0.299109
$309$	32.3653	1.84119
$310$	0	0
$311$	24.8350	1.40826	0.704132	−	0.710069i	$-0.251336\pi$
$311$	24.8350	1.40826	0.704132	+	0.710069i	$0.251336\pi$
$312$	44.3609	2.51144
$313$	22.2726	1.25892	0.629462	−	0.777031i	$-0.283275\pi$
$313$	22.2726	1.25892	0.629462	+	0.777031i	$0.283275\pi$
$314$	−5.29845	−0.299009
$315$	0	0
$316$	5.06245	0.284785
$317$	14.0757	0.790568	0.395284	−	0.918559i	$-0.370646\pi$
$317$	14.0757	0.790568	0.395284	+	0.918559i	$0.370646\pi$
$318$	−0.985388	−0.0552578
$319$	17.6227	0.986684
$320$	0	0
$321$	4.15278	0.231786
$322$	−8.78604	−0.489627
$323$	0	0
$324$	−4.06120	−0.225622
$325$	0	0
$326$	−17.4788	−0.968061
$327$	−28.6127	−1.58229
$328$	1.26660	0.0699362
$329$	8.34479	0.460063
$330$	0	0
$331$	−5.28549	−0.290517	−0.145258	−	0.989394i	$-0.546401\pi$
$331$	−5.28549	−0.290517	−0.145258	+	0.989394i	$0.546401\pi$
$332$	−5.70050	−0.312856
$333$	−6.03070	−0.330481
$334$	22.1505	1.21202
$335$	0	0
$336$	−33.4666	−1.82575
$337$	−23.8881	−1.30127	−0.650633	−	0.759392i	$-0.725496\pi$
$337$	−23.8881	−1.30127	−0.650633	+	0.759392i	$0.725496\pi$
$338$	−13.1205	−0.713660
$339$	−51.3398	−2.78839
$340$	0	0
$341$	10.4667	0.566802
$342$	0	0
$343$	0.493173	0.0266288
$344$	21.9588	1.18394
$345$	0	0
$346$	−16.7405	−0.899973
$347$	8.76704	0.470639	0.235320	−	0.971918i	$-0.424386\pi$
$347$	8.76704	0.470639	0.235320	+	0.971918i	$0.424386\pi$
$348$	−6.64444	−0.356179
$349$	2.04011	0.109205	0.0546023	−	0.998508i	$-0.482611\pi$
$349$	2.04011	0.109205	0.0546023	+	0.998508i	$0.482611\pi$
$350$	0	0
$351$	44.8240	2.39253
$352$	7.83167	0.417429
$353$	−9.06450	−0.482455	−0.241227	−	0.970469i	$-0.577550\pi$
$353$	−9.06450	−0.482455	−0.241227	+	0.970469i	$0.577550\pi$
$354$	−19.6464	−1.04419
$355$	0	0
$356$	3.22152	0.170740
$357$	30.0094	1.58826
$358$	−18.3849	−0.971671
$359$	−23.6209	−1.24667	−0.623333	−	0.781956i	$-0.714222\pi$
$359$	−23.6209	−1.24667	−0.623333	+	0.781956i	$0.714222\pi$
$360$	0	0
$361$	0	0
$362$	11.0421	0.580360
$363$	−0.788939	−0.0414086
$364$	−7.57290	−0.396928
$365$	0	0
$366$	2.91142	0.152182
$367$	−10.4211	−0.543977	−0.271988	−	0.962301i	$-0.587681\pi$
$367$	−10.4211	−0.543977	−0.271988	+	0.962301i	$0.587681\pi$
$368$	5.60005	0.291923
$369$	2.52897	0.131653
$370$	0	0
$371$	0.969157	0.0503161
$372$	−3.94633	−0.204608
$373$	−9.20454	−0.476593	−0.238297	−	0.971192i	$-0.576589\pi$
$373$	−9.20454	−0.476593	−0.238297	+	0.971192i	$0.576589\pi$
$374$	11.2848	0.583522
$375$	0	0
$376$	−6.81650	−0.351534
$377$	25.4232	1.30936
$378$	−43.3381	−2.22907
$379$	12.6143	0.647954	0.323977	−	0.946065i	$-0.394980\pi$
$379$	12.6143	0.647954	0.323977	+	0.946065i	$0.394980\pi$
$380$	0	0
$381$	59.8228	3.06482
$382$	12.2018	0.624298
$383$	−0.529736	−0.0270682	−0.0135341	−	0.999908i	$-0.504308\pi$
$383$	−0.529736	−0.0270682	−0.0135341	+	0.999908i	$0.504308\pi$
$384$	19.6396	1.00223
$385$	0	0
$386$	−25.4593	−1.29584
$387$	43.8444	2.22873
$388$	−3.03651	−0.154155
$389$	30.3866	1.54066	0.770331	−	0.637644i	$-0.220091\pi$
$389$	30.3866	1.54066	0.770331	+	0.637644i	$0.220091\pi$
$390$	0	0
$391$	−5.02153	−0.253950
$392$	20.8905	1.05513
$393$	−16.3359	−0.824040
$394$	−11.6417	−0.586503
$395$	0	0
$396$	8.56163	0.430238
$397$	12.1258	0.608577	0.304288	−	0.952580i	$-0.401581\pi$
$397$	12.1258	0.608577	0.304288	+	0.952580i	$0.401581\pi$
$398$	−22.8164	−1.14368
$399$	0	0
$400$	0	0
$401$	−11.5906	−0.578806	−0.289403	−	0.957207i	$-0.593457\pi$
$401$	−11.5906	−0.578806	−0.289403	+	0.957207i	$0.593457\pi$
$402$	−40.8066	−2.03525
$403$	15.0996	0.752164
$404$	−1.88679	−0.0938713
$405$	0	0
$406$	−24.5804	−1.21991
$407$	3.33214	0.165168
$408$	−24.5133	−1.21359
$409$	4.83657	0.239153	0.119577	−	0.992825i	$-0.461846\pi$
$409$	4.83657	0.239153	0.119577	+	0.992825i	$0.461846\pi$
$410$	0	0
$411$	−55.9118	−2.75793
$412$	4.51323	0.222351
$413$	19.3228	0.950812
$414$	14.3299	0.704277
$415$	0	0
$416$	11.2982	0.553942
$417$	31.6669	1.55073
$418$	0	0
$419$	12.4329	0.607385	0.303693	−	0.952770i	$-0.401780\pi$
$419$	12.4329	0.607385	0.303693	+	0.952770i	$0.401780\pi$
$420$	0	0
$421$	27.6160	1.34592	0.672961	−	0.739678i	$-0.265022\pi$
$421$	27.6160	1.34592	0.672961	+	0.739678i	$0.265022\pi$
$422$	−21.8484	−1.06357
$423$	−13.6103	−0.661753
$424$	−0.791662	−0.0384465
$425$	0	0
$426$	7.57809	0.367159
$427$	−2.86346	−0.138573
$428$	0.579091	0.0279914
$429$	−48.9396	−2.36282
$430$	0	0
$431$	7.09165	0.341593	0.170796	−	0.985306i	$-0.445366\pi$
$431$	7.09165	0.341593	0.170796	+	0.985306i	$0.445366\pi$
$432$	27.6228	1.32900
$433$	6.58386	0.316400	0.158200	−	0.987407i	$-0.449431\pi$
$433$	6.58386	0.316400	0.158200	+	0.987407i	$0.449431\pi$
$434$	−14.5991	−0.700777
$435$	0	0
$436$	−3.98995	−0.191084
$437$	0	0
$438$	−17.2754	−0.825450
$439$	4.42825	0.211349	0.105674	−	0.994401i	$-0.466300\pi$
$439$	4.42825	0.211349	0.105674	+	0.994401i	$0.466300\pi$
$440$	0	0
$441$	41.7113	1.98625
$442$	16.2798	0.774352
$443$	2.77214	0.131708	0.0658541	−	0.997829i	$-0.479023\pi$
$443$	2.77214	0.131708	0.0658541	+	0.997829i	$0.479023\pi$
$444$	−1.25634	−0.0596234
$445$	0	0
$446$	−10.9691	−0.519403
$447$	−45.6083	−2.15720
$448$	−33.1441	−1.56591
$449$	26.3569	1.24386	0.621930	−	0.783073i	$-0.286349\pi$
$449$	26.3569	1.24386	0.621930	+	0.783073i	$0.286349\pi$
$450$	0	0
$451$	−1.39733	−0.0657977
$452$	−7.15916	−0.336739
$453$	−34.1685	−1.60538
$454$	−25.2842	−1.18665
$455$	0	0
$456$	0	0
$457$	−33.5784	−1.57073	−0.785366	−	0.619032i	$-0.787525\pi$
$457$	−33.5784	−1.57073	−0.785366	+	0.619032i	$0.787525\pi$
$458$	26.1964	1.22408
$459$	−24.7693	−1.15613
$460$	0	0
$461$	30.4525	1.41831	0.709156	−	0.705051i	$-0.249076\pi$
$461$	30.4525	1.41831	0.709156	+	0.705051i	$0.249076\pi$
$462$	47.3172	2.20140
$463$	28.5762	1.32805	0.664025	−	0.747710i	$-0.268847\pi$
$463$	28.5762	1.32805	0.664025	+	0.747710i	$0.268847\pi$
$464$	15.6671	0.727326
$465$	0	0
$466$	0.683851	0.0316788
$467$	11.2173	0.519073	0.259536	−	0.965733i	$-0.416430\pi$
$467$	11.2173	0.519073	0.259536	+	0.965733i	$0.416430\pi$
$468$	12.3513	0.570939
$469$	40.1344	1.85323
$470$	0	0
$471$	−12.6975	−0.585070
$472$	−15.7839	−0.726515
$473$	−24.2253	−1.11388
$474$	−45.6325	−2.09597
$475$	0	0
$476$	4.18470	0.191806
$477$	−1.58068	−0.0723745
$478$	27.9340	1.27767
$479$	−17.3905	−0.794594	−0.397297	−	0.917690i	$-0.630052\pi$
$479$	−17.3905	−0.794594	−0.397297	+	0.917690i	$0.630052\pi$
$480$	0	0
$481$	4.80706	0.219183
$482$	−27.3182	−1.24431
$483$	−21.0554	−0.958052
$484$	−0.110015	−0.00500068
$485$	0	0
$486$	1.69404	0.0768430
$487$	−15.3473	−0.695451	−0.347726	−	0.937596i	$-0.613046\pi$
$487$	−15.3473	−0.695451	−0.347726	+	0.937596i	$0.613046\pi$
$488$	2.33904	0.105883
$489$	−41.8872	−1.89420
$490$	0	0
$491$	8.35401	0.377011	0.188506	−	0.982072i	$-0.439636\pi$
$491$	8.35401	0.377011	0.188506	+	0.982072i	$0.439636\pi$
$492$	0.526846	0.0237520
$493$	−14.0486	−0.632717
$494$	0	0
$495$	0	0
$496$	9.30515	0.417813
$497$	−7.45326	−0.334324
$498$	51.3839	2.30257
$499$	0.270833	0.0121241	0.00606207	−	0.999982i	$-0.498070\pi$
$499$	0.270833	0.0121241	0.00606207	+	0.999982i	$0.498070\pi$
$500$	0	0
$501$	53.0826	2.37156
$502$	−22.4040	−0.999939
$503$	−41.5995	−1.85483	−0.927415	−	0.374034i	$-0.877974\pi$
$503$	−41.5995	−1.85483	−0.927415	+	0.374034i	$0.877974\pi$
$504$	−68.8013	−3.06466
$505$	0	0
$506$	−7.91770	−0.351985
$507$	−31.4427	−1.39642
$508$	8.34209	0.370120
$509$	1.62776	0.0721493	0.0360747	−	0.999349i	$-0.488515\pi$
$509$	1.62776	0.0721493	0.0360747	+	0.999349i	$0.488515\pi$
$510$	0	0
$511$	16.9908	0.751630
$512$	25.1134	1.10987
$513$	0	0
$514$	19.7643	0.871766
$515$	0	0
$516$	9.13385	0.402095
$517$	7.52006	0.330732
$518$	−4.64771	−0.204209
$519$	−40.1178	−1.76098
$520$	0	0
$521$	−9.14124	−0.400485	−0.200243	−	0.979746i	$-0.564173\pi$
$521$	−9.14124	−0.400485	−0.200243	+	0.979746i	$0.564173\pi$
$522$	40.0904	1.75471
$523$	−37.2995	−1.63099	−0.815497	−	0.578762i	$-0.803536\pi$
$523$	−37.2995	−1.63099	−0.815497	+	0.578762i	$0.803536\pi$
$524$	−2.27799	−0.0995146
$525$	0	0
$526$	−38.2750	−1.66887
$527$	−8.34388	−0.363465
$528$	−30.1591	−1.31251
$529$	−19.4768	−0.846816
$530$	0	0
$531$	−31.5152	−1.36764
$532$	0	0
$533$	−2.01584	−0.0873156
$534$	−29.0386	−1.25662
$535$	0	0
$536$	−32.7841	−1.41606
$537$	−44.0585	−1.90127
$538$	−3.28308	−0.141544
$539$	−23.0467	−0.992692
$540$	0	0
$541$	−36.2441	−1.55826	−0.779128	−	0.626864i	$-0.784338\pi$
$541$	−36.2441	−1.55826	−0.779128	+	0.626864i	$0.784338\pi$
$542$	12.0772	0.518759
$543$	26.4619	1.13559
$544$	−6.24329	−0.267679
$545$	0	0
$546$	68.2615	2.92132
$547$	15.1033	0.645772	0.322886	−	0.946438i	$-0.395347\pi$
$547$	15.1033	0.645772	0.322886	+	0.946438i	$0.395347\pi$
$548$	−7.79671	−0.333059
$549$	4.67027	0.199322
$550$	0	0
$551$	0	0
$552$	17.1992	0.732047
$553$	44.8809	1.90853
$554$	25.2236	1.07165
$555$	0	0
$556$	4.41584	0.187273
$557$	9.36275	0.396712	0.198356	−	0.980130i	$-0.436440\pi$
$557$	9.36275	0.396712	0.198356	+	0.980130i	$0.436440\pi$
$558$	23.8109	1.00799
$559$	−34.9483	−1.47815
$560$	0	0
$561$	27.0435	1.14178
$562$	−33.3793	−1.40802
$563$	14.4454	0.608802	0.304401	−	0.952544i	$-0.401544\pi$
$563$	14.4454	0.608802	0.304401	+	0.952544i	$0.401544\pi$
$564$	−2.83535	−0.119390
$565$	0	0
$566$	−21.0903	−0.886492
$567$	−36.0044	−1.51204
$568$	6.08825	0.255457
$569$	−37.8642	−1.58735	−0.793675	−	0.608342i	$-0.791835\pi$
$569$	−37.8642	−1.58735	−0.793675	+	0.608342i	$0.791835\pi$
$570$	0	0
$571$	−18.5203	−0.775048	−0.387524	−	0.921860i	$-0.626670\pi$
$571$	−18.5203	−0.775048	−0.387524	+	0.921860i	$0.626670\pi$
$572$	−6.82446	−0.285345
$573$	29.2411	1.22156
$574$	1.94901	0.0813502
$575$	0	0
$576$	54.0575	2.25240
$577$	9.08095	0.378045	0.189022	−	0.981973i	$-0.439468\pi$
$577$	9.08095	0.378045	0.189022	+	0.981973i	$0.439468\pi$
$578$	12.3723	0.514619
$579$	−61.0121	−2.53558
$580$	0	0
$581$	−50.5375	−2.09665
$582$	27.3708	1.13456
$583$	0.873373	0.0361714
$584$	−13.8791	−0.574320
$585$	0	0
$586$	16.8166	0.694688
$587$	23.0373	0.950852	0.475426	−	0.879756i	$-0.342294\pi$
$587$	23.0373	0.950852	0.475426	+	0.879756i	$0.342294\pi$
$588$	8.68948	0.358348
$589$	0	0
$590$	0	0
$591$	−27.8989	−1.14761
$592$	2.96236	0.121752
$593$	−40.2431	−1.65259	−0.826294	−	0.563239i	$-0.809555\pi$
$593$	−40.2431	−1.65259	−0.826294	+	0.563239i	$0.809555\pi$
$594$	−39.0549	−1.60244
$595$	0	0
$596$	−6.35992	−0.260512
$597$	−54.6786	−2.23784
$598$	−11.4224	−0.467095
$599$	−37.7691	−1.54320	−0.771602	−	0.636106i	$-0.780544\pi$
$599$	−37.7691	−1.54320	−0.771602	+	0.636106i	$0.780544\pi$
$600$	0	0
$601$	43.8389	1.78823	0.894113	−	0.447841i	$-0.147807\pi$
$601$	43.8389	1.78823	0.894113	+	0.447841i	$0.147807\pi$
$602$	33.7898	1.37717
$603$	−65.4587	−2.66568
$604$	−4.76469	−0.193872
$605$	0	0
$606$	17.0074	0.690877
$607$	7.80810	0.316921	0.158461	−	0.987365i	$-0.449347\pi$
$607$	7.80810	0.316921	0.158461	+	0.987365i	$0.449347\pi$
$608$	0	0
$609$	−58.9059	−2.38699
$610$	0	0
$611$	10.8487	0.438892
$612$	−6.82520	−0.275892
$613$	38.8957	1.57098	0.785491	−	0.618873i	$-0.212410\pi$
$613$	38.8957	1.57098	0.785491	+	0.618873i	$0.212410\pi$
$614$	35.1601	1.41895
$615$	0	0
$616$	38.0147	1.53166
$617$	−12.4615	−0.501681	−0.250841	−	0.968028i	$-0.580707\pi$
$617$	−12.4615	−0.501681	−0.250841	+	0.968028i	$0.580707\pi$
$618$	−40.6819	−1.63646
$619$	−2.75741	−0.110830	−0.0554148	−	0.998463i	$-0.517648\pi$
$619$	−2.75741	−0.110830	−0.0554148	+	0.998463i	$0.517648\pi$
$620$	0	0
$621$	17.3788	0.697386
$622$	−31.2167	−1.25167
$623$	28.5602	1.14424
$624$	−43.5085	−1.74174
$625$	0	0
$626$	−27.9958	−1.11894
$627$	0	0
$628$	−1.77062	−0.0706555
$629$	−2.65633	−0.105915
$630$	0	0
$631$	−39.9220	−1.58927	−0.794636	−	0.607087i	$-0.792338\pi$
$631$	−39.9220	−1.58927	−0.794636	+	0.607087i	$0.792338\pi$
$632$	−36.6612	−1.45831
$633$	−52.3588	−2.08108
$634$	−17.6926	−0.702661
$635$	0	0
$636$	−0.329295	−0.0130574
$637$	−33.2480	−1.31733
$638$	−22.1511	−0.876970
$639$	12.1562	0.480891
$640$	0	0
$641$	−5.01268	−0.197989	−0.0989945	−	0.995088i	$-0.531563\pi$
$641$	−5.01268	−0.197989	−0.0989945	+	0.995088i	$0.531563\pi$
$642$	−5.21989	−0.206012
$643$	−49.9753	−1.97083	−0.985417	−	0.170157i	$-0.945572\pi$
$643$	−49.9753	−1.97083	−0.985417	+	0.170157i	$0.945572\pi$
$644$	−2.93610	−0.115698
$645$	0	0
$646$	0	0
$647$	−32.7681	−1.28825	−0.644123	−	0.764922i	$-0.722777\pi$
$647$	−32.7681	−1.28825	−0.644123	+	0.764922i	$0.722777\pi$
$648$	29.4104	1.15535
$649$	17.4131	0.683523
$650$	0	0
$651$	−34.9860	−1.37121
$652$	−5.84102	−0.228752
$653$	−15.7996	−0.618284	−0.309142	−	0.951016i	$-0.600042\pi$
$653$	−15.7996	−0.618284	−0.309142	+	0.951016i	$0.600042\pi$
$654$	35.9651	1.40635
$655$	0	0
$656$	−1.24226	−0.0485022
$657$	−27.7118	−1.08114
$658$	−10.4891	−0.408907
$659$	−13.5485	−0.527773	−0.263887	−	0.964554i	$-0.585004\pi$
$659$	−13.5485	−0.527773	−0.263887	+	0.964554i	$0.585004\pi$
$660$	0	0
$661$	3.65778	0.142271	0.0711355	−	0.997467i	$-0.477338\pi$
$661$	3.65778	0.142271	0.0711355	+	0.997467i	$0.477338\pi$
$662$	6.64365	0.258213
$663$	39.0139	1.51517
$664$	41.2819	1.60205
$665$	0	0
$666$	7.58036	0.293733
$667$	9.85686	0.381659
$668$	7.40219	0.286399
$669$	−26.2870	−1.01631
$670$	0	0
$671$	−2.58046	−0.0996176
$672$	−26.1782	−1.00985
$673$	26.9303	1.03809	0.519043	−	0.854748i	$-0.326288\pi$
$673$	26.9303	1.03809	0.519043	+	0.854748i	$0.326288\pi$
$674$	30.0264	1.15657
$675$	0	0
$676$	−4.38457	−0.168637
$677$	−20.6933	−0.795308	−0.397654	−	0.917535i	$-0.630176\pi$
$677$	−20.6933	−0.795308	−0.397654	+	0.917535i	$0.630176\pi$
$678$	64.5321	2.47834
$679$	−26.9200	−1.03309
$680$	0	0
$681$	−60.5926	−2.32191
$682$	−13.1562	−0.503777
$683$	−26.9573	−1.03149	−0.515745	−	0.856742i	$-0.672485\pi$
$683$	−26.9573	−1.03149	−0.515745	+	0.856742i	$0.672485\pi$
$684$	0	0
$685$	0	0
$686$	−0.619899	−0.0236679
$687$	62.7785	2.39515
$688$	−21.5369	−0.821087
$689$	1.25996	0.0480006
$690$	0	0
$691$	8.70043	0.330980	0.165490	−	0.986211i	$-0.447079\pi$
$691$	8.70043	0.330980	0.165490	+	0.986211i	$0.447079\pi$
$692$	−5.59429	−0.212663
$693$	75.9027	2.88330
$694$	−11.0198	−0.418307
$695$	0	0
$696$	48.1177	1.82390
$697$	1.11393	0.0421931
$698$	−2.56434	−0.0970616
$699$	1.63882	0.0619858
$700$	0	0
$701$	−0.403070	−0.0152237	−0.00761187	−	0.999971i	$-0.502423\pi$
$701$	−0.403070	−0.0152237	−0.00761187	+	0.999971i	$0.502423\pi$
$702$	−56.3420	−2.12649
$703$	0	0
$704$	−29.8684	−1.12571
$705$	0	0
$706$	11.3937	0.428808
$707$	−16.7272	−0.629092
$708$	−6.56538	−0.246742
$709$	40.0543	1.50427	0.752135	−	0.659010i	$-0.229024\pi$
$709$	40.0543	1.50427	0.752135	+	0.659010i	$0.229024\pi$
$710$	0	0
$711$	−73.2002	−2.74522
$712$	−23.3296	−0.874315
$713$	5.85428	0.219245
$714$	−37.7206	−1.41166
$715$	0	0
$716$	−6.14382	−0.229605
$717$	66.9427	2.50002
$718$	29.6906	1.10804
$719$	18.0756	0.674108	0.337054	−	0.941485i	$-0.390570\pi$
$719$	18.0756	0.674108	0.337054	+	0.941485i	$0.390570\pi$
$720$	0	0
$721$	40.0118	1.49012
$722$	0	0
$723$	−65.4670	−2.43474
$724$	3.69002	0.137139
$725$	0	0
$726$	0.991666	0.0368042
$727$	−26.3614	−0.977689	−0.488844	−	0.872371i	$-0.662581\pi$
$727$	−26.3614	−0.977689	−0.488844	+	0.872371i	$0.662581\pi$
$728$	54.8414	2.03256
$729$	−24.9455	−0.923909
$730$	0	0
$731$	19.3120	0.714282
$732$	0.972931	0.0359606
$733$	3.30919	0.122228	0.0611139	−	0.998131i	$-0.480535\pi$
$733$	3.30919	0.122228	0.0611139	+	0.998131i	$0.480535\pi$
$734$	13.0989	0.483490
$735$	0	0
$736$	4.38046	0.161466
$737$	36.1678	1.33226
$738$	−3.17882	−0.117014
$739$	17.6943	0.650894	0.325447	−	0.945560i	$-0.394485\pi$
$739$	17.6943	0.650894	0.325447	+	0.945560i	$0.394485\pi$
$740$	0	0
$741$	0	0
$742$	−1.21819	−0.0447212
$743$	−37.2532	−1.36669	−0.683343	−	0.730097i	$-0.739475\pi$
$743$	−37.2532	−1.36669	−0.683343	+	0.730097i	$0.739475\pi$
$744$	28.5785	1.04774
$745$	0	0
$746$	11.5698	0.423599
$747$	82.4261	3.01581
$748$	3.77112	0.137886
$749$	5.13391	0.187589
$750$	0	0
$751$	−13.5647	−0.494982	−0.247491	−	0.968890i	$-0.579606\pi$
$751$	−13.5647	−0.494982	−0.247491	+	0.968890i	$0.579606\pi$
$752$	6.68553	0.243796
$753$	−53.6902	−1.95658
$754$	−31.9560	−1.16377
$755$	0	0
$756$	−14.4826	−0.526728
$757$	−12.5370	−0.455665	−0.227833	−	0.973700i	$-0.573164\pi$
$757$	−12.5370	−0.455665	−0.227833	+	0.973700i	$0.573164\pi$
$758$	−15.8557	−0.575905
$759$	−18.9744	−0.688728
$760$	0	0
$761$	−27.2282	−0.987022	−0.493511	−	0.869740i	$-0.664287\pi$
$761$	−27.2282	−0.987022	−0.493511	+	0.869740i	$0.664287\pi$
$762$	−75.1950	−2.72403
$763$	−35.3727	−1.28058
$764$	4.07757	0.147521
$765$	0	0
$766$	0.665858	0.0240584
$767$	25.1207	0.907056
$768$	28.9337	1.04406
$769$	−0.920184	−0.0331827	−0.0165913	−	0.999862i	$-0.505281\pi$
$769$	−0.920184	−0.0331827	−0.0165913	+	0.999862i	$0.505281\pi$
$770$	0	0
$771$	47.3643	1.70578
$772$	−8.50793	−0.306207
$773$	1.82987	0.0658157	0.0329079	−	0.999458i	$-0.489523\pi$
$773$	1.82987	0.0658157	0.0329079	+	0.999458i	$0.489523\pi$
$774$	−55.1107	−1.98091
$775$	0	0
$776$	21.9898	0.789387
$777$	−11.1380	−0.399575
$778$	−38.1948	−1.36935
$779$	0	0
$780$	0	0
$781$	−6.71664	−0.240340
$782$	6.31187	0.225712
$783$	48.6200	1.73754
$784$	−20.4891	−0.731754
$785$	0	0
$786$	20.5337	0.732411
$787$	2.90489	0.103548	0.0517740	−	0.998659i	$-0.483512\pi$
$787$	2.90489	0.103548	0.0517740	+	0.998659i	$0.483512\pi$
$788$	−3.89041	−0.138590
$789$	−91.7243	−3.26547
$790$	0	0
$791$	−63.4692	−2.25670
$792$	−62.0016	−2.20313
$793$	−3.72266	−0.132196
$794$	−15.2417	−0.540907
$795$	0	0
$796$	−7.62474	−0.270252
$797$	−19.9042	−0.705044	−0.352522	−	0.935804i	$-0.614676\pi$
$797$	−19.9042	−0.705044	−0.352522	+	0.935804i	$0.614676\pi$
$798$	0	0
$799$	−5.99488	−0.212084
$800$	0	0
$801$	−46.5814	−1.64587
$802$	14.5689	0.514447
$803$	15.3116	0.540335
$804$	−13.6366	−0.480927
$805$	0	0
$806$	−18.9796	−0.668528
$807$	−7.86775	−0.276958
$808$	13.6638	0.480689
$809$	44.4186	1.56168	0.780838	−	0.624734i	$-0.214792\pi$
$809$	44.4186	1.56168	0.780838	+	0.624734i	$0.214792\pi$
$810$	0	0
$811$	34.0494	1.19564	0.597819	−	0.801631i	$-0.296034\pi$
$811$	34.0494	1.19564	0.597819	+	0.801631i	$0.296034\pi$
$812$	−8.21423	−0.288263
$813$	28.9424	1.01505
$814$	−4.18837	−0.146802
$815$	0	0
$816$	24.0424	0.841651
$817$	0	0
$818$	−6.07938	−0.212561
$819$	109.500	3.82623
$820$	0	0
$821$	−26.8065	−0.935553	−0.467776	−	0.883847i	$-0.654945\pi$
$821$	−26.8065	−0.935553	−0.467776	+	0.883847i	$0.654945\pi$
$822$	70.2790	2.45126
$823$	−11.0407	−0.384853	−0.192426	−	0.981311i	$-0.561636\pi$
$823$	−11.0407	−0.384853	−0.192426	+	0.981311i	$0.561636\pi$
$824$	−32.6839	−1.13860
$825$	0	0
$826$	−24.2880	−0.845087
$827$	−11.8987	−0.413757	−0.206878	−	0.978367i	$-0.566330\pi$
$827$	−11.8987	−0.413757	−0.206878	+	0.978367i	$0.566330\pi$
$828$	4.78874	0.166420
$829$	11.2194	0.389665	0.194832	−	0.980837i	$-0.437584\pi$
$829$	11.2194	0.389665	0.194832	+	0.980837i	$0.437584\pi$
$830$	0	0
$831$	60.4474	2.09690
$832$	−43.0892	−1.49385
$833$	18.3725	0.636569
$834$	−39.8040	−1.37830
$835$	0	0
$836$	0	0
$837$	28.8769	0.998132
$838$	−15.6276	−0.539848
$839$	−35.8294	−1.23697	−0.618484	−	0.785797i	$-0.712253\pi$
$839$	−35.8294	−1.23697	−0.618484	+	0.785797i	$0.712253\pi$
$840$	0	0
$841$	−1.42378	−0.0490959
$842$	−34.7123	−1.19626
$843$	−79.9921	−2.75507
$844$	−7.30126	−0.251320
$845$	0	0
$846$	17.1076	0.588170
$847$	−0.975332	−0.0335128
$848$	0.776452	0.0266635
$849$	−50.5420	−1.73460
$850$	0	0
$851$	1.86375	0.0638886
$852$	2.53243	0.0867595
$853$	−13.0632	−0.447276	−0.223638	−	0.974672i	$-0.571793\pi$
$853$	−13.0632	−0.447276	−0.223638	+	0.974672i	$0.571793\pi$
$854$	3.59926	0.123164
$855$	0	0
$856$	−4.19366	−0.143337
$857$	24.1902	0.826323	0.413161	−	0.910658i	$-0.364425\pi$
$857$	24.1902	0.826323	0.413161	+	0.910658i	$0.364425\pi$
$858$	61.5151	2.10009
$859$	54.1525	1.84766	0.923830	−	0.382804i	$-0.125041\pi$
$859$	54.1525	1.84766	0.923830	+	0.382804i	$0.125041\pi$
$860$	0	0
$861$	4.67072	0.159178
$862$	−8.91393	−0.303610
$863$	−49.6852	−1.69131	−0.845653	−	0.533733i	$-0.820789\pi$
$863$	−49.6852	−1.69131	−0.845653	+	0.533733i	$0.820789\pi$
$864$	21.6071	0.735088
$865$	0	0
$866$	−8.27566	−0.281218
$867$	29.6496	1.00695
$868$	−4.87868	−0.165593
$869$	40.4452	1.37201
$870$	0	0
$871$	52.1770	1.76795
$872$	28.8944	0.978488
$873$	43.9062	1.48600
$874$	0	0
$875$	0	0
$876$	−5.77305	−0.195053
$877$	8.27138	0.279305	0.139652	−	0.990201i	$-0.455402\pi$
$877$	8.27138	0.279305	0.139652	+	0.990201i	$0.455402\pi$
$878$	−5.56614	−0.187848
$879$	40.3003	1.35929
$880$	0	0
$881$	−24.5193	−0.826075	−0.413037	−	0.910714i	$-0.635532\pi$
$881$	−24.5193	−0.826075	−0.413037	+	0.910714i	$0.635532\pi$
$882$	−52.4295	−1.76539
$883$	−49.1833	−1.65515	−0.827575	−	0.561355i	$-0.810280\pi$
$883$	−49.1833	−1.65515	−0.827575	+	0.561355i	$0.810280\pi$
$884$	5.44036	0.182979
$885$	0	0
$886$	−3.48447	−0.117063
$887$	−21.6466	−0.726821	−0.363411	−	0.931629i	$-0.618388\pi$
$887$	−21.6466	−0.726821	−0.363411	+	0.931629i	$0.618388\pi$
$888$	9.09818	0.305315
$889$	73.9564	2.48042
$890$	0	0
$891$	−32.4460	−1.08698
$892$	−3.66564	−0.122735
$893$	0	0
$894$	57.3278	1.91733
$895$	0	0
$896$	24.2796	0.811126
$897$	−27.3732	−0.913964
$898$	−33.1296	−1.10555
$899$	16.3783	0.546248
$900$	0	0
$901$	−0.696240	−0.0231951
$902$	1.75639	0.0584813
$903$	80.9757	2.69470
$904$	51.8452	1.72435
$905$	0	0
$906$	42.9485	1.42687
$907$	−13.4933	−0.448039	−0.224020	−	0.974585i	$-0.571918\pi$
$907$	−13.4933	−0.448039	−0.224020	+	0.974585i	$0.571918\pi$
$908$	−8.44943	−0.280404
$909$	27.2819	0.904884
$910$	0	0
$911$	16.2069	0.536958	0.268479	−	0.963286i	$-0.413479\pi$
$911$	16.2069	0.536958	0.268479	+	0.963286i	$0.413479\pi$
$912$	0	0
$913$	−45.5428	−1.50725
$914$	42.2068	1.39608
$915$	0	0
$916$	8.75424	0.289248
$917$	−20.1954	−0.666912
$918$	31.1340	1.02758
$919$	19.7373	0.651075	0.325537	−	0.945529i	$-0.394455\pi$
$919$	19.7373	0.651075	0.325537	+	0.945529i	$0.394455\pi$
$920$	0	0
$921$	84.2596	2.77645
$922$	−38.2776	−1.26060
$923$	−9.68967	−0.318939
$924$	15.8124	0.520189
$925$	0	0
$926$	−35.9192	−1.18038
$927$	−65.2587	−2.14338
$928$	12.2551	0.402292
$929$	6.48784	0.212859	0.106430	−	0.994320i	$-0.466058\pi$
$929$	6.48784	0.212859	0.106430	+	0.994320i	$0.466058\pi$
$930$	0	0
$931$	0	0
$932$	0.228528	0.00748568
$933$	−74.8094	−2.44915
$934$	−14.0997	−0.461355
$935$	0	0
$936$	−89.4457	−2.92362
$937$	7.40129	0.241790	0.120895	−	0.992665i	$-0.461424\pi$
$937$	7.40129	0.241790	0.120895	+	0.992665i	$0.461424\pi$
$938$	−50.4474	−1.64717
$939$	−67.0908	−2.18943
$940$	0	0
$941$	53.1005	1.73103	0.865513	−	0.500887i	$-0.166993\pi$
$941$	53.1005	1.73103	0.865513	+	0.500887i	$0.166993\pi$
$942$	15.9603	0.520013
$943$	−0.781563	−0.0254512
$944$	15.4807	0.503853
$945$	0	0
$946$	30.4503	0.990023
$947$	−15.2771	−0.496438	−0.248219	−	0.968704i	$-0.579845\pi$
$947$	−15.2771	−0.496438	−0.248219	+	0.968704i	$0.579845\pi$
$948$	−15.2494	−0.495277
$949$	22.0891	0.717041
$950$	0	0
$951$	−42.3994	−1.37490
$952$	−30.3048	−0.982184
$953$	16.9121	0.547836	0.273918	−	0.961753i	$-0.411680\pi$
$953$	16.9121	0.547836	0.273918	+	0.961753i	$0.411680\pi$
$954$	1.98686	0.0643269
$955$	0	0
$956$	9.33494	0.301913
$957$	−53.0841	−1.71597
$958$	21.8592	0.706240
$959$	−69.1214	−2.23205
$960$	0	0
$961$	−21.2724	−0.686207
$962$	−6.04229	−0.194811
$963$	−8.37334	−0.269827
$964$	−9.12915	−0.294030
$965$	0	0
$966$	26.4658	0.851522
$967$	−14.5256	−0.467110	−0.233555	−	0.972344i	$-0.575036\pi$
$967$	−14.5256	−0.467110	−0.233555	+	0.972344i	$0.575036\pi$
$968$	0.796706	0.0256071
$969$	0	0
$970$	0	0
$971$	30.6047	0.982151	0.491076	−	0.871117i	$-0.336604\pi$
$971$	30.6047	0.982151	0.491076	+	0.871117i	$0.336604\pi$
$972$	0.566109	0.0181580
$973$	39.1484	1.25504
$974$	19.2909	0.618121
$975$	0	0
$976$	−2.29410	−0.0734323
$977$	44.0014	1.40773	0.703865	−	0.710333i	$-0.251456\pi$
$977$	44.0014	1.40773	0.703865	+	0.710333i	$0.251456\pi$
$978$	52.6505	1.68358
$979$	25.7376	0.822577
$980$	0	0
$981$	57.6924	1.84198
$982$	−10.5007	−0.335090
$983$	−35.3620	−1.12787	−0.563936	−	0.825819i	$-0.690714\pi$
$983$	−35.3620	−1.12787	−0.563936	+	0.825819i	$0.690714\pi$
$984$	−3.81531	−0.121628
$985$	0	0
$986$	17.6585	0.562362
$987$	−25.1366	−0.800108
$988$	0	0
$989$	−13.5498	−0.430860
$990$	0	0
$991$	32.1513	1.02132	0.510660	−	0.859783i	$-0.329401\pi$
$991$	32.1513	1.02132	0.510660	+	0.859783i	$0.329401\pi$
$992$	7.27865	0.231097
$993$	15.9212	0.505245
$994$	9.36846	0.297150
$995$	0	0
$996$	17.1714	0.544095
$997$	8.31350	0.263291	0.131646	−	0.991297i	$-0.457974\pi$
$997$	8.31350	0.263291	0.131646	+	0.991297i	$0.457974\pi$
$998$	−0.340427	−0.0107760
$999$	9.19316	0.290859

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.cc.1.4		9
5.4	even	2		1805.2.a.v.1.6		9
19.9	even	9		475.2.l.c.176.2		18
19.17	even	9		475.2.l.c.251.2		18
19.18	odd	2		9025.2.a.cf.1.6		9
95.9	even	18		95.2.k.a.81.2	yes	18
95.17	odd	36		475.2.u.b.99.2		36
95.28	odd	36		475.2.u.b.24.2		36
95.47	odd	36		475.2.u.b.24.5		36
95.74	even	18		95.2.k.a.61.2	✓	18
95.93	odd	36		475.2.u.b.99.5		36
95.94	odd	2		1805.2.a.s.1.4		9
285.74	odd	18		855.2.bs.c.631.2		18
285.104	odd	18		855.2.bs.c.271.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.61.2	✓	18	95.74	even	18
95.2.k.a.81.2	yes	18	95.9	even	18
475.2.l.c.176.2		18	19.9	even	9
475.2.l.c.251.2		18	19.17	even	9
475.2.u.b.24.2		36	95.28	odd	36
475.2.u.b.24.5		36	95.47	odd	36
475.2.u.b.99.2		36	95.17	odd	36
475.2.u.b.99.5		36	95.93	odd	36
855.2.bs.c.271.2		18	285.104	odd	18
855.2.bs.c.631.2		18	285.74	odd	18
1805.2.a.s.1.4		9	95.94	odd	2
1805.2.a.v.1.6		9	5.4	even	2
9025.2.a.cc.1.4		9	1.1	even	1	trivial
9025.2.a.cf.1.6		9	19.18	odd	2

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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:	\( N \)	\(=\)	\( 9025 = 5^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9025.a (trivial)

\(f(q)\)	\(=\)	\(q-1.25696 q^{2} -3.01225 q^{3} -0.420048 q^{4} +3.78628 q^{6} -3.72392 q^{7} +3.04191 q^{8} +6.07366 q^{9} +O(q^{10})\)	\(q-1.25696 q^{2} -3.01225 q^{3} -0.420048 q^{4} +3.78628 q^{6} -3.72392 q^{7} +3.04191 q^{8} +6.07366 q^{9} -3.35588 q^{11} +1.26529 q^{12} -4.84131 q^{13} +4.68082 q^{14} -2.98346 q^{16} +2.67526 q^{17} -7.63436 q^{18} +11.2174 q^{21} +4.21821 q^{22} -1.87703 q^{23} -9.16299 q^{24} +6.08534 q^{26} -9.25865 q^{27} +1.56423 q^{28} -5.25131 q^{29} -3.11891 q^{31} -2.33372 q^{32} +10.1087 q^{33} -3.36269 q^{34} -2.55123 q^{36} -0.992927 q^{37} +14.5832 q^{39} +0.416383 q^{41} -14.0998 q^{42} +7.21877 q^{43} +1.40963 q^{44} +2.35935 q^{46} -2.24086 q^{47} +8.98694 q^{48} +6.86757 q^{49} -8.05854 q^{51} +2.03358 q^{52} -0.260252 q^{53} +11.6378 q^{54} -11.3278 q^{56} +6.60069 q^{58} -5.18883 q^{59} +0.768938 q^{61} +3.92035 q^{62} -22.6178 q^{63} +8.90032 q^{64} -12.7063 q^{66} -10.7775 q^{67} -1.12374 q^{68} +5.65409 q^{69} +2.00146 q^{71} +18.4755 q^{72} -4.56262 q^{73} +1.24807 q^{74} +12.4970 q^{77} -18.3306 q^{78} -12.0521 q^{79} +9.66841 q^{81} -0.523377 q^{82} +13.5711 q^{83} -4.71184 q^{84} -9.07371 q^{86} +15.8183 q^{87} -10.2083 q^{88} -7.66941 q^{89} +18.0286 q^{91} +0.788443 q^{92} +9.39494 q^{93} +2.81668 q^{94} +7.02975 q^{96} +7.22894 q^{97} -8.63226 q^{98} -20.3825 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 6 q^{2} - 9 q^{3} + 6 q^{4} + 12 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 9 * q - 6 * q^2 - 9 * q^3 + 6 * q^4 + 12 * q^6 - 6 * q^8 + 6 * q^9	\( 9 q - 6 q^{2} - 9 q^{3} + 6 q^{4} + 12 q^{6} - 6 q^{8} + 6 q^{9} - 18 q^{12} - 9 q^{13} + 12 q^{16} + 9 q^{17} - 24 q^{18} + 12 q^{21} - 24 q^{22} + 12 q^{23} + 3 q^{24} - 3 q^{26} - 24 q^{27} + 15 q^{28} + 9 q^{29} + 18 q^{31} - 3 q^{32} + 9 q^{33} - 24 q^{34} + 18 q^{36} - 18 q^{37} + 18 q^{39} + 6 q^{41} + 12 q^{43} + 48 q^{44} - 9 q^{46} - 15 q^{47} + 21 q^{48} - 9 q^{49} - 6 q^{51} - 33 q^{52} - 15 q^{53} + 63 q^{54} - 6 q^{58} + 21 q^{59} - 12 q^{61} + 36 q^{62} - 21 q^{63} - 36 q^{64} + 3 q^{66} - 60 q^{67} + 51 q^{68} - 15 q^{69} - 18 q^{71} - 27 q^{73} + 27 q^{74} + 30 q^{77} + 6 q^{78} + 15 q^{79} + 33 q^{81} - 24 q^{82} - 48 q^{84} - 39 q^{86} - 15 q^{87} - 27 q^{88} - 39 q^{89} + 21 q^{91} + 6 q^{92} - 15 q^{93} + 15 q^{94} - 33 q^{96} - 15 q^{97} + 15 q^{98} - 36 q^{99}+O(q^{100}) \) 9 * q - 6 * q^2 - 9 * q^3 + 6 * q^4 + 12 * q^6 - 6 * q^8 + 6 * q^9 - 18 * q^12 - 9 * q^13 + 12 * q^16 + 9 * q^17 - 24 * q^18 + 12 * q^21 - 24 * q^22 + 12 * q^23 + 3 * q^24 - 3 * q^26 - 24 * q^27 + 15 * q^28 + 9 * q^29 + 18 * q^31 - 3 * q^32 + 9 * q^33 - 24 * q^34 + 18 * q^36 - 18 * q^37 + 18 * q^39 + 6 * q^41 + 12 * q^43 + 48 * q^44 - 9 * q^46 - 15 * q^47 + 21 * q^48 - 9 * q^49 - 6 * q^51 - 33 * q^52 - 15 * q^53 + 63 * q^54 - 6 * q^58 + 21 * q^59 - 12 * q^61 + 36 * q^62 - 21 * q^63 - 36 * q^64 + 3 * q^66 - 60 * q^67 + 51 * q^68 - 15 * q^69 - 18 * q^71 - 27 * q^73 + 27 * q^74 + 30 * q^77 + 6 * q^78 + 15 * q^79 + 33 * q^81 - 24 * q^82 - 48 * q^84 - 39 * q^86 - 15 * q^87 - 27 * q^88 - 39 * q^89 + 21 * q^91 + 6 * q^92 - 15 * q^93 + 15 * q^94 - 33 * q^96 - 15 * q^97 + 15 * q^98 - 36 * q^99

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