LMFDB - Embedded newform 9025.2.a.cd.1.7

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:	$0$
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} - 12x^{7} - 4x^{6} + 48x^{5} + 27x^{4} - 72x^{3} - 51x^{2} + 27x + 19 $ x^9 - 12x^7 - 4x^6 + 48x^5 + 27x^4 - 72x^3 - 51x^2 + 27*x + 19
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			1.7
Root			$1.68361$ 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)

$f(q)$	$=$	$q+1.68361 q^{2} -3.25202 q^{3} +0.834534 q^{4} -5.47512 q^{6} +0.548389 q^{7} -1.96219 q^{8} +7.57562 q^{9} +O(q^{10})$	\(q+1.68361 q^{2} -3.25202 q^{3} +0.834534 q^{4} -5.47512 q^{6} +0.548389 q^{7} -1.96219 q^{8} +7.57562 q^{9} +0.331202 q^{11} -2.71392 q^{12} +4.82155 q^{13} +0.923272 q^{14} -4.97262 q^{16} -5.28074 q^{17} +12.7544 q^{18} -1.78337 q^{21} +0.557614 q^{22} +1.11005 q^{23} +6.38107 q^{24} +8.11760 q^{26} -14.8800 q^{27} +0.457649 q^{28} +3.20529 q^{29} +6.02121 q^{31} -4.44757 q^{32} -1.07707 q^{33} -8.89069 q^{34} +6.32211 q^{36} -6.67261 q^{37} -15.6798 q^{39} +7.91140 q^{41} -3.00250 q^{42} -1.63905 q^{43} +0.276399 q^{44} +1.86889 q^{46} +4.60129 q^{47} +16.1711 q^{48} -6.69927 q^{49} +17.1731 q^{51} +4.02375 q^{52} +6.72620 q^{53} -25.0521 q^{54} -1.07604 q^{56} +5.39645 q^{58} +6.80362 q^{59} +0.679648 q^{61} +10.1374 q^{62} +4.15439 q^{63} +2.45729 q^{64} -1.81337 q^{66} -7.77194 q^{67} -4.40696 q^{68} -3.60991 q^{69} +1.08685 q^{71} -14.8648 q^{72} -13.9512 q^{73} -11.2340 q^{74} +0.181627 q^{77} -26.3986 q^{78} +1.40438 q^{79} +25.6632 q^{81} +13.3197 q^{82} +0.854878 q^{83} -1.48828 q^{84} -2.75952 q^{86} -10.4237 q^{87} -0.649880 q^{88} -14.5520 q^{89} +2.64409 q^{91} +0.926377 q^{92} -19.5811 q^{93} +7.74677 q^{94} +14.4636 q^{96} -7.02143 q^{97} -11.2789 q^{98} +2.50906 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 3 q^{3} + 6 q^{4} - 12 q^{6} + 12 q^{8} + 6 q^{9}+O(q^{10}) $ 9 * q - 3 * q^3 + 6 * q^4 - 12 * q^6 + 12 * q^8 + 6 * q^9	$ 9 q - 3 q^{3} + 6 q^{4} - 12 q^{6} + 12 q^{8} + 6 q^{9} - 6 q^{12} + 3 q^{13} + 12 q^{14} - 12 q^{16} + 9 q^{17} - 6 q^{18} + 12 q^{21} - 12 q^{22} + 15 q^{24} + 21 q^{26} - 6 q^{27} + 15 q^{28} + 15 q^{29} + 30 q^{31} + 9 q^{32} - 9 q^{33} - 6 q^{36} - 30 q^{37} + 6 q^{39} + 18 q^{41} - 36 q^{42} + 6 q^{43} - 24 q^{44} + 21 q^{46} - 21 q^{47} - 15 q^{48} + 3 q^{49} + 18 q^{51} + 3 q^{52} + 9 q^{53} - 9 q^{54} + 36 q^{56} - 18 q^{58} + 27 q^{59} + 12 q^{61} + 6 q^{62} + 15 q^{63} + 24 q^{64} + 3 q^{66} - 36 q^{67} - 3 q^{68} + 27 q^{69} - 6 q^{71} - 12 q^{72} + 9 q^{73} - 9 q^{74} - 12 q^{77} - 54 q^{78} + 45 q^{79} - 15 q^{81} + 48 q^{82} - 12 q^{84} - 9 q^{86} - 45 q^{87} - 39 q^{88} - 9 q^{89} + 51 q^{91} + 54 q^{92} - 9 q^{93} + 33 q^{94} - 9 q^{96} - 45 q^{97} - 33 q^{98} + 12 q^{99}+O(q^{100}) $ 9 * q - 3 * q^3 + 6 * q^4 - 12 * q^6 + 12 * q^8 + 6 * q^9 - 6 * q^12 + 3 * q^13 + 12 * q^14 - 12 * q^16 + 9 * q^17 - 6 * q^18 + 12 * q^21 - 12 * q^22 + 15 * q^24 + 21 * q^26 - 6 * q^27 + 15 * q^28 + 15 * q^29 + 30 * q^31 + 9 * q^32 - 9 * q^33 - 6 * q^36 - 30 * q^37 + 6 * q^39 + 18 * q^41 - 36 * q^42 + 6 * q^43 - 24 * q^44 + 21 * q^46 - 21 * q^47 - 15 * q^48 + 3 * q^49 + 18 * q^51 + 3 * q^52 + 9 * q^53 - 9 * q^54 + 36 * q^56 - 18 * q^58 + 27 * q^59 + 12 * q^61 + 6 * q^62 + 15 * q^63 + 24 * q^64 + 3 * q^66 - 36 * q^67 - 3 * q^68 + 27 * q^69 - 6 * q^71 - 12 * q^72 + 9 * q^73 - 9 * q^74 - 12 * q^77 - 54 * q^78 + 45 * q^79 - 15 * q^81 + 48 * q^82 - 12 * q^84 - 9 * q^86 - 45 * q^87 - 39 * q^88 - 9 * q^89 + 51 * q^91 + 54 * q^92 - 9 * q^93 + 33 * q^94 - 9 * q^96 - 45 * q^97 - 33 * q^98 + 12 * 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 $

$2$	1.68361	1.19049	0.595245	−	0.803544i	$-0.297055\pi$
$2$	1.68361	1.19049	0.595245	+	0.803544i	$0.297055\pi$
$3$	−3.25202	−1.87755	−0.938777	−	0.344526i	$-0.888040\pi$
$3$	−3.25202	−1.87755	−0.938777	+	0.344526i	$0.888040\pi$
$4$	0.834534	0.417267
$5$	0	0
$5$	0	0
$6$	−5.47512	−2.23521
$7$	0.548389	0.207272	0.103636	−	0.994615i	$-0.466952\pi$
$7$	0.548389	0.207272	0.103636	+	0.994615i	$0.466952\pi$
$8$	−1.96219	−0.693738
$9$	7.57562	2.52521
$10$	0	0
$11$	0.331202	0.0998611	0.0499306	−	0.998753i	$-0.484100\pi$
$11$	0.331202	0.0998611	0.0499306	+	0.998753i	$0.484100\pi$
$12$	−2.71392	−0.783441
$13$	4.82155	1.33726	0.668629	−	0.743596i	$-0.266882\pi$
$13$	4.82155	1.33726	0.668629	+	0.743596i	$0.266882\pi$
$14$	0.923272	0.246755
$15$	0	0
$16$	−4.97262	−1.24316
$17$	−5.28074	−1.28077	−0.640384	−	0.768055i	$-0.721225\pi$
$17$	−5.28074	−1.28077	−0.640384	+	0.768055i	$0.721225\pi$
$18$	12.7544	3.00623
$19$	0	0
$19$	0	0
$20$	0	0
$21$	−1.78337	−0.389163
$22$	0.557614	0.118884
$23$	1.11005	0.231462	0.115731	−	0.993281i	$-0.463079\pi$
$23$	1.11005	0.231462	0.115731	+	0.993281i	$0.463079\pi$
$24$	6.38107	1.30253
$25$	0	0
$26$	8.11760	1.59199
$27$	−14.8800	−2.86366
$28$	0.457649	0.0864876
$29$	3.20529	0.595207	0.297604	−	0.954690i	$-0.403813\pi$
$29$	3.20529	0.595207	0.297604	+	0.954690i	$0.403813\pi$
$30$	0	0
$31$	6.02121	1.08144	0.540720	−	0.841202i	$-0.318152\pi$
$31$	6.02121	1.08144	0.540720	+	0.841202i	$0.318152\pi$
$32$	−4.44757	−0.786226
$33$	−1.07707	−0.187495
$34$	−8.89069	−1.52474
$35$	0	0
$36$	6.32211	1.05369
$37$	−6.67261	−1.09697	−0.548485	−	0.836161i	$-0.684795\pi$
$37$	−6.67261	−1.09697	−0.548485	+	0.836161i	$0.684795\pi$
$38$	0	0
$39$	−15.6798	−2.51077
$40$	0	0
$41$	7.91140	1.23555	0.617777	−	0.786354i	$-0.288034\pi$
$41$	7.91140	1.23555	0.617777	+	0.786354i	$0.288034\pi$
$42$	−3.00250	−0.463295
$43$	−1.63905	−0.249953	−0.124977	−	0.992160i	$-0.539886\pi$
$43$	−1.63905	−0.249953	−0.124977	+	0.992160i	$0.539886\pi$
$44$	0.276399	0.0416687
$45$	0	0
$46$	1.86889	0.275553
$47$	4.60129	0.671167	0.335584	−	0.942010i	$-0.391067\pi$
$47$	4.60129	0.671167	0.335584	+	0.942010i	$0.391067\pi$
$48$	16.1711	2.33409
$49$	−6.69927	−0.957039
$50$	0	0
$51$	17.1731	2.40471
$52$	4.02375	0.557993
$53$	6.72620	0.923914	0.461957	−	0.886902i	$-0.347147\pi$
$53$	6.72620	0.923914	0.461957	+	0.886902i	$0.347147\pi$
$54$	−25.0521	−3.40916
$55$	0	0
$56$	−1.07604	−0.143792
$57$	0	0
$58$	5.39645	0.708588
$59$	6.80362	0.885756	0.442878	−	0.896582i	$-0.353958\pi$
$59$	6.80362	0.885756	0.442878	+	0.896582i	$0.353958\pi$
$60$	0	0
$61$	0.679648	0.0870200	0.0435100	−	0.999053i	$-0.486146\pi$
$61$	0.679648	0.0870200	0.0435100	+	0.999053i	$0.486146\pi$
$62$	10.1374	1.28744
$63$	4.15439	0.523404
$64$	2.45729	0.307161
$65$	0	0
$66$	−1.81337	−0.223210
$67$	−7.77194	−0.949494	−0.474747	−	0.880122i	$-0.657460\pi$
$67$	−7.77194	−0.949494	−0.474747	+	0.880122i	$0.657460\pi$
$68$	−4.40696	−0.534422
$69$	−3.60991	−0.434583
$70$	0	0
$71$	1.08685	0.128985	0.0644926	−	0.997918i	$-0.479457\pi$
$71$	1.08685	0.128985	0.0644926	+	0.997918i	$0.479457\pi$
$72$	−14.8648	−1.75183
$73$	−13.9512	−1.63287	−0.816435	−	0.577437i	$-0.804053\pi$
$73$	−13.9512	−1.63287	−0.816435	+	0.577437i	$0.804053\pi$
$74$	−11.2340	−1.30593
$75$	0	0
$76$	0	0
$77$	0.181627	0.0206984
$78$	−26.3986	−2.98905
$79$	1.40438	0.158005	0.0790025	−	0.996874i	$-0.474826\pi$
$79$	1.40438	0.158005	0.0790025	+	0.996874i	$0.474826\pi$
$80$	0	0
$81$	25.6632	2.85146
$82$	13.3197	1.47091
$83$	0.854878	0.0938351	0.0469176	−	0.998899i	$-0.485060\pi$
$83$	0.854878	0.0938351	0.0469176	+	0.998899i	$0.485060\pi$
$84$	−1.48828	−0.162385
$85$	0	0
$86$	−2.75952	−0.297567
$87$	−10.4237	−1.11753
$88$	−0.649880	−0.0692775
$89$	−14.5520	−1.54251	−0.771257	−	0.636524i	$-0.780372\pi$
$89$	−14.5520	−1.54251	−0.771257	+	0.636524i	$0.780372\pi$
$90$	0	0
$91$	2.64409	0.277175
$92$	0.926377	0.0965815
$93$	−19.5811	−2.03046
$94$	7.74677	0.799018
$95$	0	0
$96$	14.4636	1.47618
$97$	−7.02143	−0.712918	−0.356459	−	0.934311i	$-0.616016\pi$
$97$	−7.02143	−0.712918	−0.356459	+	0.934311i	$0.616016\pi$
$98$	−11.2789	−1.13934
$99$	2.50906	0.252170
$100$	0	0
$101$	−7.20677	−0.717100	−0.358550	−	0.933510i	$-0.616729\pi$
$101$	−7.20677	−0.717100	−0.358550	+	0.933510i	$0.616729\pi$
$102$	28.9127	2.86278
$103$	7.07518	0.697138	0.348569	−	0.937283i	$-0.386668\pi$
$103$	7.07518	0.697138	0.348569	+	0.937283i	$0.386668\pi$
$104$	−9.46079	−0.927706
$105$	0	0
$106$	11.3243	1.09991
$107$	−6.50106	−0.628481	−0.314241	−	0.949343i	$-0.601750\pi$
$107$	−6.50106	−0.628481	−0.314241	+	0.949343i	$0.601750\pi$
$108$	−12.4179	−1.19491
$109$	17.6607	1.69159	0.845793	−	0.533512i	$-0.179128\pi$
$109$	17.6607	1.69159	0.845793	+	0.533512i	$0.179128\pi$
$110$	0	0
$111$	21.6994	2.05962
$112$	−2.72693	−0.257671
$113$	−4.86487	−0.457649	−0.228824	−	0.973468i	$-0.573488\pi$
$113$	−4.86487	−0.457649	−0.228824	+	0.973468i	$0.573488\pi$
$114$	0	0
$115$	0	0
$116$	2.67492	0.248360
$117$	36.5262	3.37685
$118$	11.4546	1.05448
$119$	−2.89590	−0.265467
$120$	0	0
$121$	−10.8903	−0.990028
$122$	1.14426	0.103596
$123$	−25.7280	−2.31982
$124$	5.02490	0.451250
$125$	0	0
$126$	6.99436	0.623107
$127$	−2.96929	−0.263482	−0.131741	−	0.991284i	$-0.542057\pi$
$127$	−2.96929	−0.263482	−0.131741	+	0.991284i	$0.542057\pi$
$128$	13.0322	1.15190
$129$	5.33023	0.469300
$130$	0	0
$131$	−7.99500	−0.698527	−0.349263	−	0.937025i	$-0.613568\pi$
$131$	−7.99500	−0.698527	−0.349263	+	0.937025i	$0.613568\pi$
$132$	−0.898855	−0.0782353
$133$	0	0
$134$	−13.0849	−1.13036
$135$	0	0
$136$	10.3618	0.888517
$137$	−0.920774	−0.0786671	−0.0393335	−	0.999226i	$-0.512523\pi$
$137$	−0.920774	−0.0786671	−0.0393335	+	0.999226i	$0.512523\pi$
$138$	−6.07768	−0.517366
$139$	−0.100054	−0.00848647	−0.00424323	−	0.999991i	$-0.501351\pi$
$139$	−0.100054	−0.00848647	−0.00424323	+	0.999991i	$0.501351\pi$
$140$	0	0
$141$	−14.9635	−1.26015
$142$	1.82983	0.153556
$143$	1.59691	0.133540
$144$	−37.6707	−3.13922
$145$	0	0
$146$	−23.4884	−1.94392
$147$	21.7861	1.79689
$148$	−5.56851	−0.457729
$149$	−17.2975	−1.41707	−0.708533	−	0.705678i	$-0.750643\pi$
$149$	−17.2975	−1.41707	−0.708533	+	0.705678i	$0.750643\pi$
$150$	0	0
$151$	19.2178	1.56393	0.781963	−	0.623325i	$-0.214219\pi$
$151$	19.2178	1.56393	0.781963	+	0.623325i	$0.214219\pi$
$152$	0	0
$153$	−40.0049	−3.23420
$154$	0.305789	0.0246412
$155$	0	0
$156$	−13.0853	−1.04766
$157$	6.58266	0.525353	0.262677	−	0.964884i	$-0.415395\pi$
$157$	6.58266	0.525353	0.262677	+	0.964884i	$0.415395\pi$
$158$	2.36442	0.188103
$159$	−21.8737	−1.73470
$160$	0	0
$161$	0.608741	0.0479755
$162$	43.2067	3.39464
$163$	14.5927	1.14299	0.571496	−	0.820605i	$-0.306363\pi$
$163$	14.5927	1.14299	0.571496	+	0.820605i	$0.306363\pi$
$164$	6.60233	0.515556
$165$	0	0
$166$	1.43928	0.111710
$167$	3.50963	0.271584	0.135792	−	0.990737i	$-0.456642\pi$
$167$	3.50963	0.271584	0.135792	+	0.990737i	$0.456642\pi$
$168$	3.49931	0.269977
$169$	10.2474	0.788258
$170$	0	0
$171$	0	0
$172$	−1.36784	−0.104297
$173$	2.50295	0.190296	0.0951478	−	0.995463i	$-0.469668\pi$
$173$	2.50295	0.190296	0.0951478	+	0.995463i	$0.469668\pi$
$174$	−17.5493	−1.33041
$175$	0	0
$176$	−1.64694	−0.124143
$177$	−22.1255	−1.66305
$178$	−24.4999	−1.83635
$179$	5.02058	0.375255	0.187628	−	0.982240i	$-0.439920\pi$
$179$	5.02058	0.375255	0.187628	+	0.982240i	$0.439920\pi$
$180$	0	0
$181$	5.42123	0.402957	0.201479	−	0.979493i	$-0.435425\pi$
$181$	5.42123	0.402957	0.201479	+	0.979493i	$0.435425\pi$
$182$	4.45160	0.329975
$183$	−2.21023	−0.163385
$184$	−2.17813	−0.160574
$185$	0	0
$186$	−32.9668	−2.41725
$187$	−1.74899	−0.127899
$188$	3.83993	0.280056
$189$	−8.16003	−0.593555
$190$	0	0
$191$	5.98517	0.433071	0.216536	−	0.976275i	$-0.430524\pi$
$191$	5.98517	0.433071	0.216536	+	0.976275i	$0.430524\pi$
$192$	−7.99114	−0.576711
$193$	2.16859	0.156099	0.0780494	−	0.996949i	$-0.475131\pi$
$193$	2.16859	0.156099	0.0780494	+	0.996949i	$0.475131\pi$
$194$	−11.8213	−0.848722
$195$	0	0
$196$	−5.59077	−0.399341
$197$	−16.5665	−1.18032	−0.590159	−	0.807287i	$-0.700935\pi$
$197$	−16.5665	−1.18032	−0.590159	+	0.807287i	$0.700935\pi$
$198$	4.22427	0.300206
$199$	13.9801	0.991025	0.495513	−	0.868601i	$-0.334980\pi$
$199$	13.9801	0.991025	0.495513	+	0.868601i	$0.334980\pi$
$200$	0	0
$201$	25.2745	1.78273
$202$	−12.1334	−0.853701
$203$	1.75775	0.123370
$204$	14.3315	1.00341
$205$	0	0
$206$	11.9118	0.829936
$207$	8.40935	0.584490
$208$	−23.9757	−1.66242
$209$	0	0
$210$	0	0
$211$	18.0813	1.24476	0.622382	−	0.782713i	$-0.286165\pi$
$211$	18.0813	1.24476	0.622382	+	0.782713i	$0.286165\pi$
$212$	5.61324	0.385519
$213$	−3.53445	−0.242176
$214$	−10.9452	−0.748201
$215$	0	0
$216$	29.1974	1.98663
$217$	3.30196	0.224152
$218$	29.7336	2.01382
$219$	45.3697	3.06580
$220$	0	0
$221$	−25.4614	−1.71272
$222$	36.5333	2.45196
$223$	26.2666	1.75894	0.879470	−	0.475954i	$-0.157897\pi$
$223$	26.2666	1.75894	0.879470	+	0.475954i	$0.157897\pi$
$224$	−2.43900	−0.162962
$225$	0	0
$226$	−8.19054	−0.544826
$227$	6.97401	0.462881	0.231441	−	0.972849i	$-0.425656\pi$
$227$	6.97401	0.462881	0.231441	+	0.972849i	$0.425656\pi$
$228$	0	0
$229$	2.62489	0.173458	0.0867288	−	0.996232i	$-0.472359\pi$
$229$	2.62489	0.173458	0.0867288	+	0.996232i	$0.472359\pi$
$230$	0	0
$231$	−0.590656	−0.0388623
$232$	−6.28938	−0.412918
$233$	26.6586	1.74646	0.873231	−	0.487306i	$-0.162020\pi$
$233$	26.6586	1.74646	0.873231	+	0.487306i	$0.162020\pi$
$234$	61.4959	4.02011
$235$	0	0
$236$	5.67785	0.369596
$237$	−4.56707	−0.296663
$238$	−4.87556	−0.316036
$239$	13.1074	0.847846	0.423923	−	0.905698i	$-0.360653\pi$
$239$	13.1074	0.847846	0.423923	+	0.905698i	$0.360653\pi$
$240$	0	0
$241$	15.1619	0.976666	0.488333	−	0.872657i	$-0.337605\pi$
$241$	15.1619	0.976666	0.488333	+	0.872657i	$0.337605\pi$
$242$	−18.3350	−1.17862
$243$	−38.8171	−2.49012
$244$	0.567189	0.0363106
$245$	0	0
$246$	−43.3159	−2.76172
$247$	0	0
$248$	−11.8147	−0.750237
$249$	−2.78008	−0.176180
$250$	0	0
$251$	19.0064	1.19967	0.599835	−	0.800124i	$-0.295233\pi$
$251$	19.0064	1.19967	0.599835	+	0.800124i	$0.295233\pi$
$252$	3.46698	0.218399
$253$	0.367652	0.0231141
$254$	−4.99913	−0.313673
$255$	0	0
$256$	17.0266	1.06416
$257$	21.8382	1.36223	0.681115	−	0.732176i	$-0.261495\pi$
$257$	21.8382	1.36223	0.681115	+	0.732176i	$0.261495\pi$
$258$	8.97401	0.558697
$259$	−3.65918	−0.227371
$260$	0	0
$261$	24.2821	1.50302
$262$	−13.4604	−0.831589
$263$	19.6212	1.20990	0.604948	−	0.796265i	$-0.293194\pi$
$263$	19.6212	1.20990	0.604948	+	0.796265i	$0.293194\pi$
$264$	2.11342	0.130072
$265$	0	0
$266$	0	0
$267$	47.3235	2.89615
$268$	−6.48595	−0.396192
$269$	1.69133	0.103122	0.0515611	−	0.998670i	$-0.483580\pi$
$269$	1.69133	0.103122	0.0515611	+	0.998670i	$0.483580\pi$
$270$	0	0
$271$	−7.93969	−0.482302	−0.241151	−	0.970488i	$-0.577525\pi$
$271$	−7.93969	−0.482302	−0.241151	+	0.970488i	$0.577525\pi$
$272$	26.2591	1.59219
$273$	−8.59861	−0.520412
$274$	−1.55022	−0.0936524
$275$	0	0
$276$	−3.01260	−0.181337
$277$	9.47395	0.569234	0.284617	−	0.958641i	$-0.408133\pi$
$277$	9.47395	0.569234	0.284617	+	0.958641i	$0.408133\pi$
$278$	−0.168452	−0.0101031
$279$	45.6144	2.73086
$280$	0	0
$281$	12.5701	0.749867	0.374933	−	0.927052i	$-0.377666\pi$
$281$	12.5701	0.749867	0.374933	+	0.927052i	$0.377666\pi$
$282$	−25.1926	−1.50020
$283$	18.5840	1.10470	0.552351	−	0.833612i	$-0.313731\pi$
$283$	18.5840	1.10470	0.552351	+	0.833612i	$0.313731\pi$
$284$	0.907012	0.0538212
$285$	0	0
$286$	2.68856	0.158978
$287$	4.33853	0.256095
$288$	−33.6931	−1.98538
$289$	10.8862	0.640366
$290$	0	0
$291$	22.8338	1.33854
$292$	−11.6428	−0.681343
$293$	−17.3651	−1.01448	−0.507239	−	0.861806i	$-0.669334\pi$
$293$	−17.3651	−1.01448	−0.507239	+	0.861806i	$0.669334\pi$
$294$	36.6793	2.13918
$295$	0	0
$296$	13.0929	0.761009
$297$	−4.92828	−0.285968
$298$	−29.1222	−1.68700
$299$	5.35218	0.309525
$300$	0	0
$301$	−0.898838	−0.0518082
$302$	32.3553	1.86184
$303$	23.4365	1.34639
$304$	0	0
$305$	0	0
$306$	−67.3525	−3.85029
$307$	−25.0504	−1.42970	−0.714851	−	0.699277i	$-0.753506\pi$
$307$	−25.0504	−1.42970	−0.714851	+	0.699277i	$0.753506\pi$
$308$	0.151574	0.00863675
$309$	−23.0086	−1.30891
$310$	0	0
$311$	−5.58411	−0.316646	−0.158323	−	0.987387i	$-0.550609\pi$
$311$	−5.58411	−0.316646	−0.158323	+	0.987387i	$0.550609\pi$
$312$	30.7666	1.74182
$313$	0.821107	0.0464117	0.0232059	−	0.999731i	$-0.492613\pi$
$313$	0.821107	0.0464117	0.0232059	+	0.999731i	$0.492613\pi$
$314$	11.0826	0.625428
$315$	0	0
$316$	1.17200	0.0659302
$317$	33.5325	1.88337	0.941686	−	0.336494i	$-0.109241\pi$
$317$	33.5325	1.88337	0.941686	+	0.336494i	$0.109241\pi$
$318$	−36.8268	−2.06514
$319$	1.06160	0.0594381
$320$	0	0
$321$	21.1416	1.18001
$322$	1.02488	0.0571144
$323$	0	0
$324$	21.4168	1.18982
$325$	0	0
$326$	24.5684	1.36072
$327$	−57.4328	−3.17604
$328$	−15.5237	−0.857150
$329$	2.52330	0.139114
$330$	0	0
$331$	−11.2673	−0.619306	−0.309653	−	0.950850i	$-0.600213\pi$
$331$	−11.2673	−0.619306	−0.309653	+	0.950850i	$0.600213\pi$
$332$	0.713425	0.0391543
$333$	−50.5491	−2.77008
$334$	5.90885	0.323318
$335$	0	0
$336$	8.86803	0.483791
$337$	6.29577	0.342952	0.171476	−	0.985188i	$-0.445146\pi$
$337$	6.29577	0.342952	0.171476	+	0.985188i	$0.445146\pi$
$338$	17.2525	0.938413
$339$	15.8207	0.859260
$340$	0	0
$341$	1.99424	0.107994
$342$	0	0
$343$	−7.51253	−0.405638
$344$	3.21613	0.173402
$345$	0	0
$346$	4.21398	0.226545
$347$	17.5564	0.942479	0.471239	−	0.882005i	$-0.343807\pi$
$347$	17.5564	0.942479	0.471239	+	0.882005i	$0.343807\pi$
$348$	−8.69890	−0.466310
$349$	12.5169	0.670013	0.335007	−	0.942216i	$-0.391261\pi$
$349$	12.5169	0.670013	0.335007	+	0.942216i	$0.391261\pi$
$350$	0	0
$351$	−71.7447	−3.82945
$352$	−1.47304	−0.0785134
$353$	−5.82818	−0.310203	−0.155101	−	0.987899i	$-0.549570\pi$
$353$	−5.82818	−0.310203	−0.155101	+	0.987899i	$0.549570\pi$
$354$	−37.2506	−1.97985
$355$	0	0
$356$	−12.1442	−0.643640
$357$	9.41752	0.498428
$358$	8.45268	0.446738
$359$	0.579539	0.0305869	0.0152934	−	0.999883i	$-0.495132\pi$
$359$	0.579539	0.0305869	0.0152934	+	0.999883i	$0.495132\pi$
$360$	0	0
$361$	0	0
$362$	9.12723	0.479717
$363$	35.4155	1.85883
$364$	2.20658	0.115656
$365$	0	0
$366$	−3.72115	−0.194508
$367$	7.90625	0.412703	0.206352	−	0.978478i	$-0.433841\pi$
$367$	7.90625	0.412703	0.206352	+	0.978478i	$0.433841\pi$
$368$	−5.51988	−0.287743
$369$	59.9338	3.12003
$370$	0	0
$371$	3.68857	0.191501
$372$	−16.3411	−0.847245
$373$	−8.30620	−0.430079	−0.215039	−	0.976605i	$-0.568988\pi$
$373$	−8.30620	−0.430079	−0.215039	+	0.976605i	$0.568988\pi$
$374$	−2.94461	−0.152262
$375$	0	0
$376$	−9.02859	−0.465614
$377$	15.4545	0.795945
$378$	−13.7383	−0.706621
$379$	−10.2928	−0.528707	−0.264354	−	0.964426i	$-0.585159\pi$
$379$	−10.2928	−0.528707	−0.264354	+	0.964426i	$0.585159\pi$
$380$	0	0
$381$	9.65620	0.494702
$382$	10.0767	0.515567
$383$	32.0284	1.63658	0.818288	−	0.574808i	$-0.194923\pi$
$383$	32.0284	1.63658	0.818288	+	0.574808i	$0.194923\pi$
$384$	−42.3811	−2.16275
$385$	0	0
$386$	3.65106	0.185834
$387$	−12.4168	−0.631183
$388$	−5.85962	−0.297477
$389$	−30.6083	−1.55190	−0.775950	−	0.630794i	$-0.782729\pi$
$389$	−30.6083	−1.55190	−0.775950	+	0.630794i	$0.782729\pi$
$390$	0	0
$391$	−5.86191	−0.296449
$392$	13.1452	0.663934
$393$	25.9999	1.31152
$394$	−27.8916	−1.40516
$395$	0	0
$396$	2.09390	0.105222
$397$	−10.6204	−0.533025	−0.266512	−	0.963831i	$-0.585871\pi$
$397$	−10.6204	−0.533025	−0.266512	+	0.963831i	$0.585871\pi$
$398$	23.5371	1.17981
$399$	0	0
$400$	0	0
$401$	15.2347	0.760782	0.380391	−	0.924826i	$-0.375789\pi$
$401$	15.2347	0.760782	0.380391	+	0.924826i	$0.375789\pi$
$402$	42.5523	2.12232
$403$	29.0316	1.44617
$404$	−6.01429	−0.299222
$405$	0	0
$406$	2.95935	0.146870
$407$	−2.20998	−0.109545
$408$	−33.6968	−1.66824
$409$	11.6641	0.576753	0.288377	−	0.957517i	$-0.406884\pi$
$409$	11.6641	0.576753	0.288377	+	0.957517i	$0.406884\pi$
$410$	0	0
$411$	2.99437	0.147702
$412$	5.90448	0.290893
$413$	3.73103	0.183592
$414$	14.1580	0.695830
$415$	0	0
$416$	−21.4442	−1.05139
$417$	0.325377	0.0159338
$418$	0	0
$419$	17.7028	0.864840	0.432420	−	0.901672i	$-0.357660\pi$
$419$	17.7028	0.864840	0.432420	+	0.901672i	$0.357660\pi$
$420$	0	0
$421$	−20.6023	−1.00410	−0.502048	−	0.864840i	$-0.667420\pi$
$421$	−20.6023	−1.00410	−0.502048	+	0.864840i	$0.667420\pi$
$422$	30.4417	1.48188
$423$	34.8576	1.69484
$424$	−13.1981	−0.640955
$425$	0	0
$426$	−5.95063	−0.288309
$427$	0.372711	0.0180368
$428$	−5.42535	−0.262244
$429$	−5.19317	−0.250729
$430$	0	0
$431$	−8.33155	−0.401317	−0.200658	−	0.979661i	$-0.564308\pi$
$431$	−8.33155	−0.401317	−0.200658	+	0.979661i	$0.564308\pi$
$432$	73.9926	3.55997
$433$	28.1941	1.35492	0.677460	−	0.735559i	$-0.263081\pi$
$433$	28.1941	1.35492	0.677460	+	0.735559i	$0.263081\pi$
$434$	5.55921	0.266851
$435$	0	0
$436$	14.7384	0.705843
$437$	0	0
$438$	76.3848	3.64981
$439$	−30.3824	−1.45007	−0.725037	−	0.688710i	$-0.758177\pi$
$439$	−30.3824	−1.45007	−0.725037	+	0.688710i	$0.758177\pi$
$440$	0	0
$441$	−50.7511	−2.41672
$442$	−42.8669	−2.03897
$443$	−24.5208	−1.16502	−0.582508	−	0.812825i	$-0.697929\pi$
$443$	−24.5208	−1.16502	−0.582508	+	0.812825i	$0.697929\pi$
$444$	18.1089	0.859411
$445$	0	0
$446$	44.2226	2.09400
$447$	56.2518	2.66062
$448$	1.34755	0.0636657
$449$	−24.6889	−1.16514	−0.582570	−	0.812781i	$-0.697953\pi$
$449$	−24.6889	−1.16514	−0.582570	+	0.812781i	$0.697953\pi$
$450$	0	0
$451$	2.62027	0.123384
$452$	−4.05990	−0.190962
$453$	−62.4968	−2.93635
$454$	11.7415	0.551056
$455$	0	0
$456$	0	0
$457$	−7.16480	−0.335155	−0.167578	−	0.985859i	$-0.553594\pi$
$457$	−7.16480	−0.335155	−0.167578	+	0.985859i	$0.553594\pi$
$458$	4.41929	0.206500
$459$	78.5774	3.66768
$460$	0	0
$461$	21.7204	1.01162	0.505811	−	0.862645i	$-0.331193\pi$
$461$	21.7204	1.01162	0.505811	+	0.862645i	$0.331193\pi$
$462$	−0.994432	−0.0462652
$463$	31.9283	1.48384	0.741918	−	0.670491i	$-0.233916\pi$
$463$	31.9283	1.48384	0.741918	+	0.670491i	$0.233916\pi$
$464$	−15.9387	−0.739935
$465$	0	0
$466$	44.8826	2.07915
$467$	19.5382	0.904121	0.452061	−	0.891987i	$-0.350689\pi$
$467$	19.5382	0.904121	0.452061	+	0.891987i	$0.350689\pi$
$468$	30.4824	1.40905
$469$	−4.26205	−0.196803
$470$	0	0
$471$	−21.4069	−0.986379
$472$	−13.3500	−0.614482
$473$	−0.542857	−0.0249606
$474$	−7.68914	−0.353174
$475$	0	0
$476$	−2.41673	−0.110770
$477$	50.9551	2.33308
$478$	22.0677	1.00935
$479$	−12.2388	−0.559203	−0.279601	−	0.960116i	$-0.590202\pi$
$479$	−12.2388	−0.559203	−0.279601	+	0.960116i	$0.590202\pi$
$480$	0	0
$481$	−32.1723	−1.46693
$482$	25.5267	1.16271
$483$	−1.97964	−0.0900766
$484$	−9.08833	−0.413106
$485$	0	0
$486$	−65.3527	−2.96446
$487$	−14.1017	−0.639010	−0.319505	−	0.947585i	$-0.603517\pi$
$487$	−14.1017	−0.639010	−0.319505	+	0.947585i	$0.603517\pi$
$488$	−1.33360	−0.0603691
$489$	−47.4559	−2.14603
$490$	0	0
$491$	−19.8867	−0.897474	−0.448737	−	0.893664i	$-0.648126\pi$
$491$	−19.8867	−0.897474	−0.448737	+	0.893664i	$0.648126\pi$
$492$	−21.4709	−0.967983
$493$	−16.9263	−0.762322
$494$	0	0
$495$	0	0
$496$	−29.9412	−1.34440
$497$	0.596016	0.0267350
$498$	−4.68056	−0.209741
$499$	−7.43742	−0.332945	−0.166472	−	0.986046i	$-0.553238\pi$
$499$	−7.43742	−0.332945	−0.166472	+	0.986046i	$0.553238\pi$
$500$	0	0
$501$	−11.4134	−0.509913
$502$	31.9992	1.42820
$503$	13.5121	0.602475	0.301237	−	0.953549i	$-0.402600\pi$
$503$	13.5121	0.602475	0.301237	+	0.953549i	$0.402600\pi$
$504$	−8.15169	−0.363105
$505$	0	0
$506$	0.618981	0.0275171
$507$	−33.3246	−1.48000
$508$	−2.47798	−0.109942
$509$	35.1737	1.55905	0.779523	−	0.626373i	$-0.215461\pi$
$509$	35.1737	1.55905	0.779523	+	0.626373i	$0.215461\pi$
$510$	0	0
$511$	−7.65071	−0.338448
$512$	2.60163	0.114977
$513$	0	0
$514$	36.7670	1.62172
$515$	0	0
$516$	4.44826	0.195824
$517$	1.52396	0.0670235
$518$	−6.16063	−0.270682
$519$	−8.13963	−0.357290
$520$	0	0
$521$	5.85595	0.256554	0.128277	−	0.991738i	$-0.459055\pi$
$521$	5.85595	0.256554	0.128277	+	0.991738i	$0.459055\pi$
$522$	40.8815	1.78933
$523$	11.5494	0.505021	0.252511	−	0.967594i	$-0.418744\pi$
$523$	11.5494	0.505021	0.252511	+	0.967594i	$0.418744\pi$
$524$	−6.67210	−0.291472
$525$	0	0
$526$	33.0344	1.44037
$527$	−31.7964	−1.38507
$528$	5.35588	0.233085
$529$	−21.7678	−0.946425
$530$	0	0
$531$	51.5416	2.23672
$532$	0	0
$533$	38.1452	1.65225
$534$	79.6742	3.44784
$535$	0	0
$536$	15.2500	0.658700
$537$	−16.3270	−0.704562
$538$	2.84754	0.122766
$539$	−2.21881	−0.0955709
$540$	0	0
$541$	11.7510	0.505216	0.252608	−	0.967569i	$-0.418712\pi$
$541$	11.7510	0.505216	0.252608	+	0.967569i	$0.418712\pi$
$542$	−13.3673	−0.574176
$543$	−17.6299	−0.756574
$544$	23.4864	1.00697
$545$	0	0
$546$	−14.4767	−0.619545
$547$	−28.9598	−1.23823	−0.619116	−	0.785300i	$-0.712509\pi$
$547$	−28.9598	−1.23823	−0.619116	+	0.785300i	$0.712509\pi$
$548$	−0.768417	−0.0328252
$549$	5.14875	0.219743
$550$	0	0
$551$	0	0
$552$	7.08333	0.301486
$553$	0.770146	0.0327499
$554$	15.9504	0.677668
$555$	0	0
$556$	−0.0834984	−0.00354112
$557$	24.2154	1.02604	0.513021	−	0.858376i	$-0.328526\pi$
$557$	24.2154	1.02604	0.513021	+	0.858376i	$0.328526\pi$
$558$	76.7967	3.25106
$559$	−7.90277	−0.334252
$560$	0	0
$561$	5.68775	0.240137
$562$	21.1630	0.892709
$563$	45.4464	1.91534	0.957669	−	0.287871i	$-0.0929473\pi$
$563$	45.4464	1.91534	0.957669	+	0.287871i	$0.0929473\pi$
$564$	−12.4875	−0.525820
$565$	0	0
$566$	31.2881	1.31514
$567$	14.0734	0.591027
$568$	−2.13260	−0.0894819
$569$	−28.1695	−1.18093	−0.590463	−	0.807065i	$-0.701055\pi$
$569$	−28.1695	−1.18093	−0.590463	+	0.807065i	$0.701055\pi$
$570$	0	0
$571$	18.2742	0.764752	0.382376	−	0.924007i	$-0.375106\pi$
$571$	18.2742	0.764752	0.382376	+	0.924007i	$0.375106\pi$
$572$	1.33267	0.0557218
$573$	−19.4639	−0.813115
$574$	7.30437	0.304879
$575$	0	0
$576$	18.6155	0.775644
$577$	20.1838	0.840263	0.420132	−	0.907463i	$-0.361984\pi$
$577$	20.1838	0.840263	0.420132	+	0.907463i	$0.361984\pi$
$578$	18.3281	0.762350
$579$	−7.05231	−0.293084
$580$	0	0
$581$	0.468806	0.0194493
$582$	38.4432	1.59352
$583$	2.22773	0.0922631
$584$	27.3750	1.13278
$585$	0	0
$586$	−29.2359	−1.20773
$587$	18.4923	0.763260	0.381630	−	0.924315i	$-0.375363\pi$
$587$	18.4923	0.763260	0.381630	+	0.924315i	$0.375363\pi$
$588$	18.1813	0.749783
$589$	0	0
$590$	0	0
$591$	53.8747	2.21611
$592$	33.1803	1.36370
$593$	5.10430	0.209608	0.104804	−	0.994493i	$-0.466578\pi$
$593$	5.10430	0.209608	0.104804	+	0.994493i	$0.466578\pi$
$594$	−8.29730	−0.340442
$595$	0	0
$596$	−14.4353	−0.591295
$597$	−45.4636	−1.86070
$598$	9.01097	0.368486
$599$	−35.7699	−1.46152	−0.730760	−	0.682635i	$-0.760834\pi$
$599$	−35.7699	−1.46152	−0.730760	+	0.682635i	$0.760834\pi$
$600$	0	0
$601$	−34.3352	−1.40056	−0.700281	−	0.713867i	$-0.746942\pi$
$601$	−34.3352	−1.40056	−0.700281	+	0.713867i	$0.746942\pi$
$602$	−1.51329	−0.0616771
$603$	−58.8773	−2.39767
$604$	16.0379	0.652575
$605$	0	0
$606$	39.4579	1.60287
$607$	−3.43239	−0.139316	−0.0696582	−	0.997571i	$-0.522191\pi$
$607$	−3.43239	−0.139316	−0.0696582	+	0.997571i	$0.522191\pi$
$608$	0	0
$609$	−5.71622	−0.231633
$610$	0	0
$611$	22.1854	0.897523
$612$	−33.3854	−1.34953
$613$	−28.1010	−1.13499	−0.567494	−	0.823378i	$-0.692087\pi$
$613$	−28.1010	−1.13499	−0.567494	+	0.823378i	$0.692087\pi$
$614$	−42.1750	−1.70205
$615$	0	0
$616$	−0.356387	−0.0143592
$617$	11.9234	0.480019	0.240009	−	0.970771i	$-0.422849\pi$
$617$	11.9234	0.480019	0.240009	+	0.970771i	$0.422849\pi$
$618$	−38.7375	−1.55825
$619$	−27.8914	−1.12105	−0.560525	−	0.828137i	$-0.689401\pi$
$619$	−27.8914	−1.12105	−0.560525	+	0.828137i	$0.689401\pi$
$620$	0	0
$621$	−16.5176	−0.662828
$622$	−9.40145	−0.376964
$623$	−7.98018	−0.319719
$624$	77.9696	3.12128
$625$	0	0
$626$	1.38242	0.0552527
$627$	0	0
$628$	5.49345	0.219212
$629$	35.2363	1.40496
$630$	0	0
$631$	18.7543	0.746598	0.373299	−	0.927711i	$-0.378227\pi$
$631$	18.7543	0.746598	0.373299	+	0.927711i	$0.378227\pi$
$632$	−2.75565	−0.109614
$633$	−58.8006	−2.33711
$634$	56.4555	2.24213
$635$	0	0
$636$	−18.2544	−0.723832
$637$	−32.3009	−1.27981
$638$	1.78731	0.0707604
$639$	8.23355	0.325714
$640$	0	0
$641$	21.8102	0.861450	0.430725	−	0.902483i	$-0.358258\pi$
$641$	21.8102	0.861450	0.430725	+	0.902483i	$0.358258\pi$
$642$	35.5941	1.40479
$643$	47.4901	1.87283	0.936413	−	0.350901i	$-0.114125\pi$
$643$	47.4901	1.87283	0.936413	+	0.350901i	$0.114125\pi$
$644$	0.508015	0.0200186
$645$	0	0
$646$	0	0
$647$	−35.0985	−1.37986	−0.689932	−	0.723874i	$-0.742360\pi$
$647$	−35.0985	−1.37986	−0.689932	+	0.723874i	$0.742360\pi$
$648$	−50.3560	−1.97817
$649$	2.25337	0.0884525
$650$	0	0
$651$	−10.7380	−0.420857
$652$	12.1781	0.476933
$653$	−46.5164	−1.82033	−0.910163	−	0.414250i	$-0.864044\pi$
$653$	−46.5164	−1.82033	−0.910163	+	0.414250i	$0.864044\pi$
$654$	−96.6943	−3.78105
$655$	0	0
$656$	−39.3404	−1.53598
$657$	−105.689	−4.12333
$658$	4.24824	0.165614
$659$	43.2332	1.68413	0.842063	−	0.539379i	$-0.181341\pi$
$659$	43.2332	1.68413	0.842063	+	0.539379i	$0.181341\pi$
$660$	0	0
$661$	46.9045	1.82437	0.912186	−	0.409776i	$-0.134393\pi$
$661$	46.9045	1.82437	0.912186	+	0.409776i	$0.134393\pi$
$662$	−18.9697	−0.737277
$663$	82.8008	3.21572
$664$	−1.67743	−0.0650970
$665$	0	0
$666$	−85.1049	−3.29775
$667$	3.55804	0.137768
$668$	2.92891	0.113323
$669$	−85.4194	−3.30250
$670$	0	0
$671$	0.225101	0.00868991
$672$	7.93166	0.305970
$673$	14.3118	0.551679	0.275839	−	0.961204i	$-0.411044\pi$
$673$	14.3118	0.551679	0.275839	+	0.961204i	$0.411044\pi$
$674$	10.5996	0.408281
$675$	0	0
$676$	8.55176	0.328914
$677$	−27.6860	−1.06406	−0.532029	−	0.846726i	$-0.678570\pi$
$677$	−27.6860	−1.06406	−0.532029	+	0.846726i	$0.678570\pi$
$678$	26.6358	1.02294
$679$	−3.85048	−0.147768
$680$	0	0
$681$	−22.6796	−0.869084
$682$	3.35751	0.128566
$683$	20.0771	0.768228	0.384114	−	0.923286i	$-0.374507\pi$
$683$	20.0771	0.768228	0.384114	+	0.923286i	$0.374507\pi$
$684$	0	0
$685$	0	0
$686$	−12.6481	−0.482909
$687$	−8.53619	−0.325676
$688$	8.15039	0.310731
$689$	32.4307	1.23551
$690$	0	0
$691$	−28.7356	−1.09315	−0.546577	−	0.837409i	$-0.684069\pi$
$691$	−28.7356	−1.09315	−0.546577	+	0.837409i	$0.684069\pi$
$692$	2.08880	0.0794041
$693$	1.37594	0.0522677
$694$	29.5581	1.12201
$695$	0	0
$696$	20.4532	0.775275
$697$	−41.7781	−1.58246
$698$	21.0735	0.797644
$699$	−86.6942	−3.27908
$700$	0	0
$701$	−26.9089	−1.01633	−0.508167	−	0.861259i	$-0.669677\pi$
$701$	−26.9089	−1.01633	−0.508167	+	0.861259i	$0.669677\pi$
$702$	−120.790	−4.55892
$703$	0	0
$704$	0.813858	0.0306734
$705$	0	0
$706$	−9.81237	−0.369293
$707$	−3.95211	−0.148634
$708$	−18.4645	−0.693937
$709$	−10.0327	−0.376786	−0.188393	−	0.982094i	$-0.560328\pi$
$709$	−10.0327	−0.376786	−0.188393	+	0.982094i	$0.560328\pi$
$710$	0	0
$711$	10.6390	0.398995
$712$	28.5538	1.07010
$713$	6.68386	0.250313
$714$	15.8554	0.593374
$715$	0	0
$716$	4.18984	0.156582
$717$	−42.6254	−1.59188
$718$	0.975715	0.0364134
$719$	26.3737	0.983572	0.491786	−	0.870716i	$-0.336344\pi$
$719$	26.3737	0.983572	0.491786	+	0.870716i	$0.336344\pi$
$720$	0	0
$721$	3.87995	0.144497
$722$	0	0
$723$	−49.3069	−1.83374
$724$	4.52420	0.168141
$725$	0	0
$726$	59.6257	2.21292
$727$	48.4127	1.79553	0.897765	−	0.440476i	$-0.145190\pi$
$727$	48.4127	1.79553	0.897765	+	0.440476i	$0.145190\pi$
$728$	−5.18819	−0.192287
$729$	49.2444	1.82386
$730$	0	0
$731$	8.65541	0.320132
$732$	−1.84451	−0.0681750
$733$	35.3375	1.30522	0.652610	−	0.757694i	$-0.273674\pi$
$733$	35.3375	1.30522	0.652610	+	0.757694i	$0.273674\pi$
$734$	13.3110	0.491319
$735$	0	0
$736$	−4.93704	−0.181982
$737$	−2.57408	−0.0948175
$738$	100.905	3.71436
$739$	19.4663	0.716080	0.358040	−	0.933706i	$-0.383445\pi$
$739$	19.4663	0.716080	0.358040	+	0.933706i	$0.383445\pi$
$740$	0	0
$741$	0	0
$742$	6.21011	0.227980
$743$	28.6013	1.04928	0.524640	−	0.851324i	$-0.324200\pi$
$743$	28.6013	1.04928	0.524640	+	0.851324i	$0.324200\pi$
$744$	38.4217	1.40861
$745$	0	0
$746$	−13.9844	−0.512005
$747$	6.47624	0.236953
$748$	−1.45959	−0.0533680
$749$	−3.56511	−0.130266
$750$	0	0
$751$	−47.5763	−1.73608	−0.868042	−	0.496490i	$-0.834622\pi$
$751$	−47.5763	−1.73608	−0.868042	+	0.496490i	$0.834622\pi$
$752$	−22.8805	−0.834365
$753$	−61.8090	−2.25245
$754$	26.0193	0.947565
$755$	0	0
$756$	−6.80982	−0.247671
$757$	−11.8767	−0.431665	−0.215832	−	0.976430i	$-0.569246\pi$
$757$	−11.8767	−0.431665	−0.215832	+	0.976430i	$0.569246\pi$
$758$	−17.3291	−0.629421
$759$	−1.19561	−0.0433979
$760$	0	0
$761$	28.1049	1.01880	0.509401	−	0.860530i	$-0.329867\pi$
$761$	28.1049	1.01880	0.509401	+	0.860530i	$0.329867\pi$
$762$	16.2572	0.588938
$763$	9.68492	0.350618
$764$	4.99482	0.180706
$765$	0	0
$766$	53.9233	1.94833
$767$	32.8040	1.18448
$768$	−55.3708	−1.99802
$769$	55.3734	1.99682	0.998408	−	0.0563960i	$-0.0179609\pi$
$769$	55.3734	1.99682	0.998408	+	0.0563960i	$0.0179609\pi$
$770$	0	0
$771$	−71.0183	−2.55766
$772$	1.80977	0.0651349
$773$	17.8883	0.643396	0.321698	−	0.946842i	$-0.395746\pi$
$773$	17.8883	0.643396	0.321698	+	0.946842i	$0.395746\pi$
$774$	−20.9051	−0.751418
$775$	0	0
$776$	13.7774	0.494578
$777$	11.8997	0.426900
$778$	−51.5323	−1.84752
$779$	0	0
$780$	0	0
$781$	0.359966	0.0128806
$782$	−9.86915	−0.352920
$783$	−47.6947	−1.70447
$784$	33.3129	1.18975
$785$	0	0
$786$	43.7736	1.56135
$787$	7.40295	0.263887	0.131943	−	0.991257i	$-0.457878\pi$
$787$	7.40295	0.263887	0.131943	+	0.991257i	$0.457878\pi$
$788$	−13.8253	−0.492508
$789$	−63.8086	−2.27165
$790$	0	0
$791$	−2.66784	−0.0948576
$792$	−4.92325	−0.174940
$793$	3.27696	0.116368
$794$	−17.8807	−0.634561
$795$	0	0
$796$	11.6669	0.413522
$797$	45.6568	1.61725	0.808624	−	0.588326i	$-0.200213\pi$
$797$	45.6568	1.61725	0.808624	+	0.588326i	$0.200213\pi$
$798$	0	0
$799$	−24.2982	−0.859609
$800$	0	0
$801$	−110.241	−3.89517
$802$	25.6492	0.905704
$803$	−4.62068	−0.163060
$804$	21.0924	0.743872
$805$	0	0
$806$	48.8778	1.72165
$807$	−5.50024	−0.193618
$808$	14.1410	0.497480
$809$	−19.3525	−0.680398	−0.340199	−	0.940353i	$-0.610494\pi$
$809$	−19.3525	−0.680398	−0.340199	+	0.940353i	$0.610494\pi$
$810$	0	0
$811$	−20.8363	−0.731661	−0.365831	−	0.930681i	$-0.619215\pi$
$811$	−20.8363	−0.731661	−0.365831	+	0.930681i	$0.619215\pi$
$812$	1.46690	0.0514780
$813$	25.8200	0.905547
$814$	−3.72074	−0.130412
$815$	0	0
$816$	−85.3951	−2.98943
$817$	0	0
$818$	19.6378	0.686619
$819$	20.0306	0.699925
$820$	0	0
$821$	−30.6430	−1.06945	−0.534723	−	0.845027i	$-0.679584\pi$
$821$	−30.6430	−1.06945	−0.534723	+	0.845027i	$0.679584\pi$
$822$	5.04135	0.175837
$823$	−8.07545	−0.281493	−0.140746	−	0.990046i	$-0.544950\pi$
$823$	−8.07545	−0.281493	−0.140746	+	0.990046i	$0.544950\pi$
$824$	−13.8828	−0.483631
$825$	0	0
$826$	6.28159	0.218564
$827$	−36.5412	−1.27066	−0.635332	−	0.772239i	$-0.719137\pi$
$827$	−36.5412	−1.27066	−0.635332	+	0.772239i	$0.719137\pi$
$828$	7.01788	0.243888
$829$	42.7028	1.48313	0.741564	−	0.670882i	$-0.234084\pi$
$829$	42.7028	1.48313	0.741564	+	0.670882i	$0.234084\pi$
$830$	0	0
$831$	−30.8095	−1.06877
$832$	11.8479	0.410753
$833$	35.3771	1.22574
$834$	0.547808	0.0189690
$835$	0	0
$836$	0	0
$837$	−89.5956	−3.09688
$838$	29.8046	1.02958
$839$	−48.1211	−1.66132	−0.830662	−	0.556776i	$-0.812038\pi$
$839$	−48.1211	−1.66132	−0.830662	+	0.556776i	$0.812038\pi$
$840$	0	0
$841$	−18.7261	−0.645728
$842$	−34.6862	−1.19537
$843$	−40.8781	−1.40792
$844$	15.0894	0.519399
$845$	0	0
$846$	58.6866	2.01769
$847$	−5.97212	−0.205205
$848$	−33.4468	−1.14857
$849$	−60.4354	−2.07414
$850$	0	0
$851$	−7.40695	−0.253907
$852$	−2.94962	−0.101052
$853$	−32.4486	−1.11102	−0.555510	−	0.831510i	$-0.687477\pi$
$853$	−32.4486	−1.11102	−0.555510	+	0.831510i	$0.687477\pi$
$854$	0.627500	0.0214726
$855$	0	0
$856$	12.7563	0.436001
$857$	30.1775	1.03084	0.515422	−	0.856936i	$-0.327635\pi$
$857$	30.1775	1.03084	0.515422	+	0.856936i	$0.327635\pi$
$858$	−8.74326	−0.298490
$859$	26.5675	0.906470	0.453235	−	0.891391i	$-0.350270\pi$
$859$	26.5675	0.906470	0.453235	+	0.891391i	$0.350270\pi$
$860$	0	0
$861$	−14.1090	−0.480832
$862$	−14.0271	−0.477764
$863$	11.5566	0.393391	0.196696	−	0.980465i	$-0.436979\pi$
$863$	11.5566	0.393391	0.196696	+	0.980465i	$0.436979\pi$
$864$	66.1798	2.25148
$865$	0	0
$866$	47.4677	1.61302
$867$	−35.4022	−1.20232
$868$	2.75560	0.0935312
$869$	0.465133	0.0157786
$870$	0	0
$871$	−37.4728	−1.26972
$872$	−34.6535	−1.17352
$873$	−53.1917	−1.80027
$874$	0	0
$875$	0	0
$876$	37.8626	1.27926
$877$	18.1665	0.613438	0.306719	−	0.951800i	$-0.400769\pi$
$877$	18.1665	0.613438	0.306719	+	0.951800i	$0.400769\pi$
$878$	−51.1521	−1.72630
$879$	56.4715	1.90474
$880$	0	0
$881$	−39.8613	−1.34296	−0.671480	−	0.741023i	$-0.734341\pi$
$881$	−39.8613	−1.34296	−0.671480	+	0.741023i	$0.734341\pi$
$882$	−85.4450	−2.87708
$883$	26.3518	0.886810	0.443405	−	0.896321i	$-0.353770\pi$
$883$	26.3518	0.886810	0.443405	+	0.896321i	$0.353770\pi$
$884$	−21.2484	−0.714660
$885$	0	0
$886$	−41.2833	−1.38694
$887$	55.9581	1.87889	0.939445	−	0.342700i	$-0.111341\pi$
$887$	55.9581	1.87889	0.939445	+	0.342700i	$0.111341\pi$
$888$	−42.5784	−1.42884
$889$	−1.62833	−0.0546124
$890$	0	0
$891$	8.49969	0.284750
$892$	21.9203	0.733947
$893$	0	0
$894$	94.7059	3.16744
$895$	0	0
$896$	7.14674	0.238756
$897$	−17.4054	−0.581149
$898$	−41.5664	−1.38709
$899$	19.2997	0.643681
$900$	0	0
$901$	−35.5193	−1.18332
$902$	4.41151	0.146887
$903$	2.92304	0.0972726
$904$	9.54580	0.317488
$905$	0	0
$906$	−105.220	−3.49570
$907$	−46.1120	−1.53113	−0.765563	−	0.643361i	$-0.777539\pi$
$907$	−46.1120	−1.53113	−0.765563	+	0.643361i	$0.777539\pi$
$908$	5.82005	0.193145
$909$	−54.5957	−1.81083
$910$	0	0
$911$	−1.40625	−0.0465912	−0.0232956	−	0.999729i	$-0.507416\pi$
$911$	−1.40625	−0.0465912	−0.0232956	+	0.999729i	$0.507416\pi$
$912$	0	0
$913$	0.283137	0.00937048
$914$	−12.0627	−0.398999
$915$	0	0
$916$	2.19056	0.0723781
$917$	−4.38437	−0.144785
$918$	132.294	4.36634
$919$	47.0354	1.55155	0.775777	−	0.631007i	$-0.217358\pi$
$919$	47.0354	1.55155	0.775777	+	0.631007i	$0.217358\pi$
$920$	0	0
$921$	81.4644	2.68434
$922$	36.5687	1.20433
$923$	5.24029	0.172486
$924$	−0.492922	−0.0162160
$925$	0	0
$926$	53.7548	1.76649
$927$	53.5989	1.76042
$928$	−14.2557	−0.467968
$929$	−0.987098	−0.0323856	−0.0161928	−	0.999869i	$-0.505155\pi$
$929$	−0.987098	−0.0323856	−0.0161928	+	0.999869i	$0.505155\pi$
$930$	0	0
$931$	0	0
$932$	22.2475	0.728741
$933$	18.1596	0.594520
$934$	32.8947	1.07635
$935$	0	0
$936$	−71.6713	−2.34265
$937$	10.6228	0.347032	0.173516	−	0.984831i	$-0.444487\pi$
$937$	10.6228	0.347032	0.173516	+	0.984831i	$0.444487\pi$
$938$	−7.17561	−0.234292
$939$	−2.67025	−0.0871405
$940$	0	0
$941$	10.5236	0.343059	0.171529	−	0.985179i	$-0.445129\pi$
$941$	10.5236	0.343059	0.171529	+	0.985179i	$0.445129\pi$
$942$	−36.0408	−1.17427
$943$	8.78208	0.285984
$944$	−33.8318	−1.10113
$945$	0	0
$946$	−0.913958	−0.0297153
$947$	−35.1113	−1.14096	−0.570482	−	0.821310i	$-0.693244\pi$
$947$	−35.1113	−1.14096	−0.570482	+	0.821310i	$0.693244\pi$
$948$	−3.81137	−0.123788
$949$	−67.2667	−2.18357
$950$	0	0
$951$	−109.048	−3.53613
$952$	5.68230	0.184164
$953$	21.0777	0.682775	0.341387	−	0.939923i	$-0.389103\pi$
$953$	21.0777	0.682775	0.341387	+	0.939923i	$0.389103\pi$
$954$	85.7884	2.77750
$955$	0	0
$956$	10.9386	0.353778
$957$	−3.45234	−0.111598
$958$	−20.6053	−0.665726
$959$	−0.504943	−0.0163054
$960$	0	0
$961$	5.25495	0.169514
$962$	−54.1655	−1.74637
$963$	−49.2496	−1.58705
$964$	12.6531	0.407530
$965$	0	0
$966$	−3.33293	−0.107235
$967$	−47.4060	−1.52448	−0.762238	−	0.647297i	$-0.775899\pi$
$967$	−47.4060	−1.52448	−0.762238	+	0.647297i	$0.775899\pi$
$968$	21.3688	0.686820
$969$	0	0
$970$	0	0
$971$	32.6009	1.04621	0.523106	−	0.852268i	$-0.324773\pi$
$971$	32.6009	1.04621	0.523106	+	0.852268i	$0.324773\pi$
$972$	−32.3942	−1.03904
$973$	−0.0548685	−0.00175900
$974$	−23.7418	−0.760736
$975$	0	0
$976$	−3.37963	−0.108179
$977$	−23.9914	−0.767553	−0.383777	−	0.923426i	$-0.625377\pi$
$977$	−23.9914	−0.767553	−0.383777	+	0.923426i	$0.625377\pi$
$978$	−79.8970	−2.55483
$979$	−4.81967	−0.154037
$980$	0	0
$981$	133.791	4.27160
$982$	−33.4814	−1.06843
$983$	4.28746	0.136749	0.0683743	−	0.997660i	$-0.478219\pi$
$983$	4.28746	0.136749	0.0683743	+	0.997660i	$0.478219\pi$
$984$	50.4832	1.60935
$985$	0	0
$986$	−28.4972	−0.907537
$987$	−8.20581	−0.261194
$988$	0	0
$989$	−1.81944	−0.0578547
$990$	0	0
$991$	45.7393	1.45296	0.726479	−	0.687189i	$-0.241155\pi$
$991$	45.7393	1.45296	0.726479	+	0.687189i	$0.241155\pi$
$992$	−26.7797	−0.850257
$993$	36.6414	1.16278
$994$	1.00346	0.0318277
$995$	0	0
$996$	−2.32007	−0.0735143
$997$	−11.9723	−0.379167	−0.189584	−	0.981865i	$-0.560714\pi$
$997$	−11.9723	−0.379167	−0.189584	+	0.981865i	$0.560714\pi$
$998$	−12.5217	−0.396367
$999$	99.2884	3.14135

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.cd.1.7		9
5.4	even	2		1805.2.a.u.1.3		9
19.2	odd	18		475.2.l.b.251.3		18
19.10	odd	18		475.2.l.b.176.3		18
19.18	odd	2		9025.2.a.ce.1.3		9
95.2	even	36		475.2.u.c.99.2		36
95.29	odd	18		95.2.k.b.81.1	yes	18
95.48	even	36		475.2.u.c.24.2		36
95.59	odd	18		95.2.k.b.61.1	✓	18
95.67	even	36		475.2.u.c.24.5		36
95.78	even	36		475.2.u.c.99.5		36
95.94	odd	2		1805.2.a.t.1.7		9
285.29	even	18		855.2.bs.b.271.3		18
285.59	even	18		855.2.bs.b.631.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.b.61.1	✓	18	95.59	odd	18
95.2.k.b.81.1	yes	18	95.29	odd	18
475.2.l.b.176.3		18	19.10	odd	18
475.2.l.b.251.3		18	19.2	odd	18
475.2.u.c.24.2		36	95.48	even	36
475.2.u.c.24.5		36	95.67	even	36
475.2.u.c.99.2		36	95.2	even	36
475.2.u.c.99.5		36	95.78	even	36
855.2.bs.b.271.3		18	285.29	even	18
855.2.bs.b.631.3		18	285.59	even	18
1805.2.a.t.1.7		9	95.94	odd	2
1805.2.a.u.1.3		9	5.4	even	2
9025.2.a.cd.1.7		9	1.1	even	1	trivial
9025.2.a.ce.1.3		9	19.18	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:	\( N \)	\(=\)	\( 9025 = 5^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9025.a (trivial)

\(f(q)\)	\(=\)	\(q+1.68361 q^{2} -3.25202 q^{3} +0.834534 q^{4} -5.47512 q^{6} +0.548389 q^{7} -1.96219 q^{8} +7.57562 q^{9} +O(q^{10})\)	\(q+1.68361 q^{2} -3.25202 q^{3} +0.834534 q^{4} -5.47512 q^{6} +0.548389 q^{7} -1.96219 q^{8} +7.57562 q^{9} +0.331202 q^{11} -2.71392 q^{12} +4.82155 q^{13} +0.923272 q^{14} -4.97262 q^{16} -5.28074 q^{17} +12.7544 q^{18} -1.78337 q^{21} +0.557614 q^{22} +1.11005 q^{23} +6.38107 q^{24} +8.11760 q^{26} -14.8800 q^{27} +0.457649 q^{28} +3.20529 q^{29} +6.02121 q^{31} -4.44757 q^{32} -1.07707 q^{33} -8.89069 q^{34} +6.32211 q^{36} -6.67261 q^{37} -15.6798 q^{39} +7.91140 q^{41} -3.00250 q^{42} -1.63905 q^{43} +0.276399 q^{44} +1.86889 q^{46} +4.60129 q^{47} +16.1711 q^{48} -6.69927 q^{49} +17.1731 q^{51} +4.02375 q^{52} +6.72620 q^{53} -25.0521 q^{54} -1.07604 q^{56} +5.39645 q^{58} +6.80362 q^{59} +0.679648 q^{61} +10.1374 q^{62} +4.15439 q^{63} +2.45729 q^{64} -1.81337 q^{66} -7.77194 q^{67} -4.40696 q^{68} -3.60991 q^{69} +1.08685 q^{71} -14.8648 q^{72} -13.9512 q^{73} -11.2340 q^{74} +0.181627 q^{77} -26.3986 q^{78} +1.40438 q^{79} +25.6632 q^{81} +13.3197 q^{82} +0.854878 q^{83} -1.48828 q^{84} -2.75952 q^{86} -10.4237 q^{87} -0.649880 q^{88} -14.5520 q^{89} +2.64409 q^{91} +0.926377 q^{92} -19.5811 q^{93} +7.74677 q^{94} +14.4636 q^{96} -7.02143 q^{97} -11.2789 q^{98} +2.50906 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 3 q^{3} + 6 q^{4} - 12 q^{6} + 12 q^{8} + 6 q^{9}+O(q^{10}) \) 9 * q - 3 * q^3 + 6 * q^4 - 12 * q^6 + 12 * q^8 + 6 * q^9	\( 9 q - 3 q^{3} + 6 q^{4} - 12 q^{6} + 12 q^{8} + 6 q^{9} - 6 q^{12} + 3 q^{13} + 12 q^{14} - 12 q^{16} + 9 q^{17} - 6 q^{18} + 12 q^{21} - 12 q^{22} + 15 q^{24} + 21 q^{26} - 6 q^{27} + 15 q^{28} + 15 q^{29} + 30 q^{31} + 9 q^{32} - 9 q^{33} - 6 q^{36} - 30 q^{37} + 6 q^{39} + 18 q^{41} - 36 q^{42} + 6 q^{43} - 24 q^{44} + 21 q^{46} - 21 q^{47} - 15 q^{48} + 3 q^{49} + 18 q^{51} + 3 q^{52} + 9 q^{53} - 9 q^{54} + 36 q^{56} - 18 q^{58} + 27 q^{59} + 12 q^{61} + 6 q^{62} + 15 q^{63} + 24 q^{64} + 3 q^{66} - 36 q^{67} - 3 q^{68} + 27 q^{69} - 6 q^{71} - 12 q^{72} + 9 q^{73} - 9 q^{74} - 12 q^{77} - 54 q^{78} + 45 q^{79} - 15 q^{81} + 48 q^{82} - 12 q^{84} - 9 q^{86} - 45 q^{87} - 39 q^{88} - 9 q^{89} + 51 q^{91} + 54 q^{92} - 9 q^{93} + 33 q^{94} - 9 q^{96} - 45 q^{97} - 33 q^{98} + 12 q^{99}+O(q^{100}) \) 9 * q - 3 * q^3 + 6 * q^4 - 12 * q^6 + 12 * q^8 + 6 * q^9 - 6 * q^12 + 3 * q^13 + 12 * q^14 - 12 * q^16 + 9 * q^17 - 6 * q^18 + 12 * q^21 - 12 * q^22 + 15 * q^24 + 21 * q^26 - 6 * q^27 + 15 * q^28 + 15 * q^29 + 30 * q^31 + 9 * q^32 - 9 * q^33 - 6 * q^36 - 30 * q^37 + 6 * q^39 + 18 * q^41 - 36 * q^42 + 6 * q^43 - 24 * q^44 + 21 * q^46 - 21 * q^47 - 15 * q^48 + 3 * q^49 + 18 * q^51 + 3 * q^52 + 9 * q^53 - 9 * q^54 + 36 * q^56 - 18 * q^58 + 27 * q^59 + 12 * q^61 + 6 * q^62 + 15 * q^63 + 24 * q^64 + 3 * q^66 - 36 * q^67 - 3 * q^68 + 27 * q^69 - 6 * q^71 - 12 * q^72 + 9 * q^73 - 9 * q^74 - 12 * q^77 - 54 * q^78 + 45 * q^79 - 15 * q^81 + 48 * q^82 - 12 * q^84 - 9 * q^86 - 45 * q^87 - 39 * q^88 - 9 * q^89 + 51 * q^91 + 54 * q^92 - 9 * q^93 + 33 * q^94 - 9 * q^96 - 45 * q^97 - 33 * q^98 + 12 * q^99

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