LMFDB - Embedded newform 9025.2.a.bp.1.1

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:	$4$
Coefficient field:	4.4.7537.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 5x^{2} + 4x + 3 $ x^4 - x^3 - 5x^2 + 4x + 3
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			1.1
Root			$2.15976$ 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)

$f(q)$	$=$	$q-1.66454 q^{2} -1.15976 q^{3} +0.770710 q^{4} +1.93047 q^{6} +2.43525 q^{7} +2.04621 q^{8} -1.65497 q^{9} +O(q^{10})$	\(q-1.66454 q^{2} -1.15976 q^{3} +0.770710 q^{4} +1.93047 q^{6} +2.43525 q^{7} +2.04621 q^{8} -1.65497 q^{9} -5.75477 q^{11} -0.893835 q^{12} -1.59501 q^{13} -4.05359 q^{14} -4.94743 q^{16} +5.98406 q^{17} +2.75477 q^{18} -2.82430 q^{21} +9.57907 q^{22} +0.940044 q^{23} -2.37310 q^{24} +2.65497 q^{26} +5.39862 q^{27} +1.87687 q^{28} -2.61834 q^{29} +5.26913 q^{31} +4.14280 q^{32} +6.67412 q^{33} -9.96073 q^{34} -1.27550 q^{36} -2.89384 q^{37} +1.84982 q^{39} +6.31534 q^{41} +4.70118 q^{42} -4.53922 q^{43} -4.43525 q^{44} -1.56475 q^{46} -8.95437 q^{47} +5.73781 q^{48} -1.06953 q^{49} -6.94004 q^{51} -1.22929 q^{52} -2.19639 q^{53} -8.98625 q^{54} +4.98304 q^{56} +4.35834 q^{58} +10.7988 q^{59} -10.5287 q^{61} -8.77071 q^{62} -4.03027 q^{63} +2.99898 q^{64} -11.1094 q^{66} +1.00958 q^{67} +4.61197 q^{68} -1.09022 q^{69} -8.83388 q^{71} -3.38641 q^{72} +10.2500 q^{73} +4.81692 q^{74} -14.0143 q^{77} -3.07911 q^{78} -7.60459 q^{79} -1.29619 q^{81} -10.5122 q^{82} -3.11355 q^{83} -2.17672 q^{84} +7.55574 q^{86} +3.03663 q^{87} -11.7755 q^{88} +11.1141 q^{89} -3.88426 q^{91} +0.724501 q^{92} -6.11091 q^{93} +14.9049 q^{94} -4.80463 q^{96} +4.05776 q^{97} +1.78029 q^{98} +9.52395 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + 3 q^{3} + 5 q^{4} + 2 q^{6} + 4 q^{7} + 12 q^{8} + q^{9}+O(q^{10}) $ 4 * q + q^2 + 3 * q^3 + 5 * q^4 + 2 * q^6 + 4 * q^7 + 12 * q^8 + q^9	$ 4 q + q^{2} + 3 q^{3} + 5 q^{4} + 2 q^{6} + 4 q^{7} + 12 q^{8} + q^{9} - 2 q^{11} + 6 q^{12} + 7 q^{13} + q^{14} + 7 q^{16} + q^{17} - 10 q^{18} + 4 q^{21} + 2 q^{22} - 2 q^{23} + 23 q^{24} + 3 q^{26} + 12 q^{27} + 19 q^{28} + q^{29} + 30 q^{32} + 19 q^{33} - 15 q^{34} - 7 q^{36} - 2 q^{37} + 15 q^{39} + 8 q^{41} + 15 q^{42} - q^{43} - 12 q^{44} - 12 q^{46} + 12 q^{47} + 23 q^{48} - 10 q^{49} - 22 q^{51} - 3 q^{52} - 5 q^{53} - 34 q^{54} + 41 q^{56} + 27 q^{58} + 5 q^{59} - 37 q^{62} + 3 q^{63} + 56 q^{64} - 31 q^{66} + 4 q^{67} - 16 q^{68} + 9 q^{69} - 20 q^{71} + 17 q^{72} + 20 q^{73} + 25 q^{74} - 14 q^{77} - 18 q^{78} - 17 q^{79} + 12 q^{81} - 21 q^{82} - q^{83} + 20 q^{84} - 8 q^{86} + 16 q^{87} - 7 q^{88} - 11 q^{89} - 6 q^{91} + q^{92} + 8 q^{93} + 31 q^{94} + 21 q^{96} + q^{97} + 9 q^{98} + 38 q^{99}+O(q^{100}) $ 4 * q + q^2 + 3 * q^3 + 5 * q^4 + 2 * q^6 + 4 * q^7 + 12 * q^8 + q^9 - 2 * q^11 + 6 * q^12 + 7 * q^13 + q^14 + 7 * q^16 + q^17 - 10 * q^18 + 4 * q^21 + 2 * q^22 - 2 * q^23 + 23 * q^24 + 3 * q^26 + 12 * q^27 + 19 * q^28 + q^29 + 30 * q^32 + 19 * q^33 - 15 * q^34 - 7 * q^36 - 2 * q^37 + 15 * q^39 + 8 * q^41 + 15 * q^42 - q^43 - 12 * q^44 - 12 * q^46 + 12 * q^47 + 23 * q^48 - 10 * q^49 - 22 * q^51 - 3 * q^52 - 5 * q^53 - 34 * q^54 + 41 * q^56 + 27 * q^58 + 5 * q^59 - 37 * q^62 + 3 * q^63 + 56 * q^64 - 31 * q^66 + 4 * q^67 - 16 * q^68 + 9 * q^69 - 20 * q^71 + 17 * q^72 + 20 * q^73 + 25 * q^74 - 14 * q^77 - 18 * q^78 - 17 * q^79 + 12 * q^81 - 21 * q^82 - q^83 + 20 * q^84 - 8 * q^86 + 16 * q^87 - 7 * q^88 - 11 * q^89 - 6 * q^91 + q^92 + 8 * q^93 + 31 * q^94 + 21 * q^96 + q^97 + 9 * q^98 + 38 * 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 $

$2$	−1.66454	−1.17701	−0.588506	−	0.808493i	$-0.700283\pi$
$2$	−1.66454	−1.17701	−0.588506	+	0.808493i	$0.700283\pi$
$3$	−1.15976	−0.669585	−0.334793	−	0.942292i	$-0.608666\pi$
$3$	−1.15976	−0.669585	−0.334793	+	0.942292i	$0.608666\pi$
$4$	0.770710	0.385355
$5$	0	0
$5$	0	0
$6$	1.93047	0.788109
$7$	2.43525	0.920440	0.460220	−	0.887805i	$-0.347771\pi$
$7$	2.43525	0.920440	0.460220	+	0.887805i	$0.347771\pi$
$8$	2.04621	0.723444
$9$	−1.65497	−0.551656
$10$	0	0
$11$	−5.75477	−1.73513	−0.867564	−	0.497326i	$-0.834315\pi$
$11$	−5.75477	−1.73513	−0.867564	+	0.497326i	$0.834315\pi$
$12$	−0.893835	−0.258028
$13$	−1.59501	−0.442376	−0.221188	−	0.975231i	$-0.570993\pi$
$13$	−1.59501	−0.442376	−0.221188	+	0.975231i	$0.570993\pi$
$14$	−4.05359	−1.08337
$15$	0	0
$16$	−4.94743	−1.23686
$17$	5.98406	1.45135	0.725673	−	0.688039i	$-0.241528\pi$
$17$	5.98406	1.45135	0.725673	+	0.688039i	$0.241528\pi$
$18$	2.75477	0.649305
$19$	0	0
$19$	0	0
$20$	0	0
$21$	−2.82430	−0.616313
$22$	9.57907	2.04226
$23$	0.940044	0.196013	0.0980064	−	0.995186i	$-0.468753\pi$
$23$	0.940044	0.196013	0.0980064	+	0.995186i	$0.468753\pi$
$24$	−2.37310	−0.484407
$25$	0	0
$26$	2.65497	0.520682
$27$	5.39862	1.03897
$28$	1.87687	0.354696
$29$	−2.61834	−0.486213	−0.243106	−	0.970000i	$-0.578166\pi$
$29$	−2.61834	−0.486213	−0.243106	+	0.970000i	$0.578166\pi$
$30$	0	0
$31$	5.26913	0.946364	0.473182	−	0.880965i	$-0.343105\pi$
$31$	5.26913	0.946364	0.473182	+	0.880965i	$0.343105\pi$
$32$	4.14280	0.732350
$33$	6.67412	1.16182
$34$	−9.96073	−1.70825
$35$	0	0
$36$	−1.27550	−0.212583
$37$	−2.89384	−0.475744	−0.237872	−	0.971297i	$-0.576450\pi$
$37$	−2.89384	−0.475744	−0.237872	+	0.971297i	$0.576450\pi$
$38$	0	0
$39$	1.84982	0.296209
$40$	0	0
$41$	6.31534	0.986291	0.493145	−	0.869947i	$-0.335847\pi$
$41$	6.31534	0.986291	0.493145	+	0.869947i	$0.335847\pi$
$42$	4.70118	0.725407
$43$	−4.53922	−0.692225	−0.346113	−	0.938193i	$-0.612498\pi$
$43$	−4.53922	−0.692225	−0.346113	+	0.938193i	$0.612498\pi$
$44$	−4.43525	−0.668640
$45$	0	0
$46$	−1.56475	−0.230709
$47$	−8.95437	−1.30613	−0.653064	−	0.757303i	$-0.726517\pi$
$47$	−8.95437	−1.30613	−0.653064	+	0.757303i	$0.726517\pi$
$48$	5.73781	0.828181
$49$	−1.06953	−0.152791
$50$	0	0
$51$	−6.94004	−0.971801
$52$	−1.22929	−0.170472
$53$	−2.19639	−0.301697	−0.150848	−	0.988557i	$-0.548201\pi$
$53$	−2.19639	−0.301697	−0.150848	+	0.988557i	$0.548201\pi$
$54$	−8.98625	−1.22287
$55$	0	0
$56$	4.98304	0.665887
$57$	0	0
$58$	4.35834	0.572278
$59$	10.7988	1.40588	0.702941	−	0.711249i	$-0.251870\pi$
$59$	10.7988	1.40588	0.702941	+	0.711249i	$0.251870\pi$
$60$	0	0
$61$	−10.5287	−1.34806	−0.674030	−	0.738704i	$-0.735438\pi$
$61$	−10.5287	−1.34806	−0.674030	+	0.738704i	$0.735438\pi$
$62$	−8.77071	−1.11388
$63$	−4.03027	−0.507766
$64$	2.99898	0.374873
$65$	0	0
$66$	−11.1094	−1.36747
$67$	1.00958	0.123340	0.0616698	−	0.998097i	$-0.480357\pi$
$67$	1.00958	0.123340	0.0616698	+	0.998097i	$0.480357\pi$
$68$	4.61197	0.559284
$69$	−1.09022	−0.131247
$70$	0	0
$71$	−8.83388	−1.04839	−0.524194	−	0.851599i	$-0.675633\pi$
$71$	−8.83388	−1.04839	−0.524194	+	0.851599i	$0.675633\pi$
$72$	−3.38641	−0.399092
$73$	10.2500	1.19967	0.599835	−	0.800124i	$-0.295233\pi$
$73$	10.2500	1.19967	0.599835	+	0.800124i	$0.295233\pi$
$74$	4.81692	0.559955
$75$	0	0
$76$	0	0
$77$	−14.0143	−1.59708
$78$	−3.07911	−0.348641
$79$	−7.60459	−0.855583	−0.427792	−	0.903877i	$-0.640708\pi$
$79$	−7.60459	−0.855583	−0.427792	+	0.903877i	$0.640708\pi$
$80$	0	0
$81$	−1.29619	−0.144021
$82$	−10.5122	−1.16088
$83$	−3.11355	−0.341756	−0.170878	−	0.985292i	$-0.554660\pi$
$83$	−3.11355	−0.341756	−0.170878	+	0.985292i	$0.554660\pi$
$84$	−2.17672	−0.237499
$85$	0	0
$86$	7.55574	0.814757
$87$	3.03663	0.325561
$88$	−11.7755	−1.25527
$89$	11.1141	1.17809	0.589047	−	0.808099i	$-0.299503\pi$
$89$	11.1141	1.17809	0.589047	+	0.808099i	$0.299503\pi$
$90$	0	0
$91$	−3.88426	−0.407181
$92$	0.724501	0.0755345
$93$	−6.11091	−0.633672
$94$	14.9049	1.53733
$95$	0	0
$96$	−4.80463	−0.490371
$97$	4.05776	0.412003	0.206002	−	0.978552i	$-0.433955\pi$
$97$	4.05776	0.412003	0.206002	+	0.978552i	$0.433955\pi$
$98$	1.78029	0.179836
$99$	9.52395	0.957193
$100$	0	0
$101$	−11.1301	−1.10748	−0.553741	−	0.832689i	$-0.686800\pi$
$101$	−11.1301	−1.10748	−0.553741	+	0.832689i	$0.686800\pi$
$102$	11.5520	1.14382
$103$	11.5791	1.14092	0.570460	−	0.821326i	$-0.306765\pi$
$103$	11.5791	1.14092	0.570460	+	0.821326i	$0.306765\pi$
$104$	−3.26372	−0.320035
$105$	0	0
$106$	3.65598	0.355101
$107$	17.9177	1.73217	0.866086	−	0.499894i	$-0.166628\pi$
$107$	17.9177	1.73217	0.866086	+	0.499894i	$0.166628\pi$
$108$	4.16077	0.400371
$109$	−5.62470	−0.538749	−0.269374	−	0.963036i	$-0.586817\pi$
$109$	−5.62470	−0.538749	−0.269374	+	0.963036i	$0.586817\pi$
$110$	0	0
$111$	3.35614	0.318551
$112$	−12.0482	−1.13845
$113$	−15.6789	−1.47494	−0.737472	−	0.675378i	$-0.763981\pi$
$113$	−15.6789	−1.47494	−0.737472	+	0.675378i	$0.763981\pi$
$114$	0	0
$115$	0	0
$116$	−2.01798	−0.187364
$117$	2.63969	0.244039
$118$	−17.9751	−1.65474
$119$	14.5727	1.33588
$120$	0	0
$121$	22.1173	2.01067
$122$	17.5255	1.58668
$123$	−7.32425	−0.660406
$124$	4.06097	0.364686
$125$	0	0
$126$	6.70856	0.597646
$127$	6.11991	0.543054	0.271527	−	0.962431i	$-0.412471\pi$
$127$	6.11991	0.543054	0.271527	+	0.962431i	$0.412471\pi$
$128$	−13.2775	−1.17358
$129$	5.26439	0.463504
$130$	0	0
$131$	−14.8811	−1.30017	−0.650084	−	0.759862i	$-0.725266\pi$
$131$	−14.8811	−1.30017	−0.650084	+	0.759862i	$0.725266\pi$
$132$	5.14381	0.447711
$133$	0	0
$134$	−1.68049	−0.145172
$135$	0	0
$136$	12.2446	1.04997
$137$	−17.3504	−1.48234	−0.741170	−	0.671317i	$-0.765729\pi$
$137$	−17.3504	−1.48234	−0.741170	+	0.671317i	$0.765729\pi$
$138$	1.81472	0.154479
$139$	−6.70534	−0.568740	−0.284370	−	0.958715i	$-0.591784\pi$
$139$	−6.70534	−0.568740	−0.284370	+	0.958715i	$0.591784\pi$
$140$	0	0
$141$	10.3849	0.874564
$142$	14.7044	1.23396
$143$	9.17891	0.767579
$144$	8.18782	0.682319
$145$	0	0
$146$	−17.0615	−1.41202
$147$	1.24040	0.102306
$148$	−2.23031	−0.183330
$149$	14.3928	1.17911	0.589553	−	0.807729i	$-0.299304\pi$
$149$	14.3928	1.17911	0.589553	+	0.807729i	$0.299304\pi$
$150$	0	0
$151$	−12.7219	−1.03529	−0.517645	−	0.855595i	$-0.673191\pi$
$151$	−12.7219	−1.03529	−0.517645	+	0.855595i	$0.673191\pi$
$152$	0	0
$153$	−9.90341	−0.800644
$154$	23.3275	1.87978
$155$	0	0
$156$	1.42568	0.114145
$157$	3.37530	0.269378	0.134689	−	0.990888i	$-0.456996\pi$
$157$	3.37530	0.269378	0.134689	+	0.990888i	$0.456996\pi$
$158$	12.6582	1.00703
$159$	2.54727	0.202012
$160$	0	0
$161$	2.28925	0.180418
$162$	2.15756	0.169514
$163$	−0.307960	−0.0241213	−0.0120607	−	0.999927i	$-0.503839\pi$
$163$	−0.307960	−0.0241213	−0.0120607	+	0.999927i	$0.503839\pi$
$164$	4.86730	0.380072
$165$	0	0
$166$	5.18264	0.402251
$167$	14.2643	1.10380	0.551902	−	0.833909i	$-0.313902\pi$
$167$	14.2643	1.10380	0.551902	+	0.833909i	$0.313902\pi$
$168$	−5.77911	−0.445868
$169$	−10.4559	−0.804303
$170$	0	0
$171$	0	0
$172$	−3.49842	−0.266752
$173$	13.3471	1.01476	0.507382	−	0.861721i	$-0.330613\pi$
$173$	13.3471	1.01476	0.507382	+	0.861721i	$0.330613\pi$
$174$	−5.05461	−0.383189
$175$	0	0
$176$	28.4713	2.14610
$177$	−12.5239	−0.941357
$178$	−18.5000	−1.38663
$179$	14.2207	1.06291	0.531454	−	0.847087i	$-0.321646\pi$
$179$	14.2207	1.06291	0.531454	+	0.847087i	$0.321646\pi$
$180$	0	0
$181$	−9.88263	−0.734570	−0.367285	−	0.930108i	$-0.619713\pi$
$181$	−9.88263	−0.734570	−0.367285	+	0.930108i	$0.619713\pi$
$182$	6.46552	0.479256
$183$	12.2107	0.902641
$184$	1.92353	0.141804
$185$	0	0
$186$	10.1719	0.745839
$187$	−34.4368	−2.51827
$188$	−6.90122	−0.503323
$189$	13.1470	0.956305
$190$	0	0
$191$	−12.9942	−0.940228	−0.470114	−	0.882606i	$-0.655787\pi$
$191$	−12.9942	−0.940228	−0.470114	+	0.882606i	$0.655787\pi$
$192$	−3.47809	−0.251009
$193$	14.5159	1.04488	0.522439	−	0.852677i	$-0.325022\pi$
$193$	14.5159	1.04488	0.522439	+	0.852677i	$0.325022\pi$
$194$	−6.75432	−0.484932
$195$	0	0
$196$	−0.824301	−0.0588786
$197$	25.0010	1.78125	0.890624	−	0.454740i	$-0.150268\pi$
$197$	25.0010	1.78125	0.890624	+	0.454740i	$0.150268\pi$
$198$	−15.8530	−1.12663
$199$	−2.25539	−0.159880	−0.0799401	−	0.996800i	$-0.525473\pi$
$199$	−2.25539	−0.159880	−0.0799401	+	0.996800i	$0.525473\pi$
$200$	0	0
$201$	−1.17086	−0.0825864
$202$	18.5265	1.30352
$203$	−6.37632	−0.447530
$204$	−5.34876	−0.374488
$205$	0	0
$206$	−19.2739	−1.34287
$207$	−1.55574	−0.108131
$208$	7.89120	0.547156
$209$	0	0
$210$	0	0
$211$	−22.2161	−1.52942	−0.764710	−	0.644374i	$-0.777118\pi$
$211$	−22.2161	−1.52942	−0.764710	+	0.644374i	$0.777118\pi$
$212$	−1.69278	−0.116260
$213$	10.2451	0.701986
$214$	−29.8249	−2.03879
$215$	0	0
$216$	11.0467	0.751634
$217$	12.8317	0.871071
$218$	9.36257	0.634113
$219$	−11.8875	−0.803281
$220$	0	0
$221$	−9.54463	−0.642041
$222$	−5.58645	−0.374938
$223$	10.2160	0.684113	0.342056	−	0.939679i	$-0.388877\pi$
$223$	10.2160	0.684113	0.342056	+	0.939679i	$0.388877\pi$
$224$	10.0888	0.674084
$225$	0	0
$226$	26.0982	1.73602
$227$	4.15180	0.275565	0.137782	−	0.990463i	$-0.456003\pi$
$227$	4.15180	0.275565	0.137782	+	0.990463i	$0.456003\pi$
$228$	0	0
$229$	6.53286	0.431703	0.215852	−	0.976426i	$-0.430747\pi$
$229$	6.53286	0.431703	0.215852	+	0.976426i	$0.430747\pi$
$230$	0	0
$231$	16.2532	1.06938
$232$	−5.35766	−0.351748
$233$	−5.14820	−0.337270	−0.168635	−	0.985679i	$-0.553936\pi$
$233$	−5.14820	−0.337270	−0.168635	+	0.985679i	$0.553936\pi$
$234$	−4.39388	−0.287237
$235$	0	0
$236$	8.32272	0.541763
$237$	8.81947	0.572886
$238$	−24.2569	−1.57234
$239$	13.9962	0.905338	0.452669	−	0.891679i	$-0.350472\pi$
$239$	13.9962	0.905338	0.452669	+	0.891679i	$0.350472\pi$
$240$	0	0
$241$	−15.2257	−0.980773	−0.490387	−	0.871505i	$-0.663144\pi$
$241$	−15.2257	−0.980773	−0.490387	+	0.871505i	$0.663144\pi$
$242$	−36.8153	−2.36658
$243$	−14.6926	−0.942532
$244$	−8.11456	−0.519482
$245$	0	0
$246$	12.1916	0.777305
$247$	0	0
$248$	10.7817	0.684642
$249$	3.61095	0.228835
$250$	0	0
$251$	−6.11259	−0.385823	−0.192912	−	0.981216i	$-0.561793\pi$
$251$	−6.11259	−0.385823	−0.192912	+	0.981216i	$0.561793\pi$
$252$	−3.10616	−0.195670
$253$	−5.40973	−0.340107
$254$	−10.1869	−0.639181
$255$	0	0
$256$	16.1031	1.00644
$257$	0.122683	0.00765274	0.00382637	−	0.999993i	$-0.498782\pi$
$257$	0.122683	0.00765274	0.00382637	+	0.999993i	$0.498782\pi$
$258$	−8.76281	−0.545549
$259$	−7.04723	−0.437893
$260$	0	0
$261$	4.33326	0.268222
$262$	24.7703	1.53031
$263$	10.0605	0.620359	0.310179	−	0.950678i	$-0.399611\pi$
$263$	10.0605	0.620359	0.310179	+	0.950678i	$0.399611\pi$
$264$	13.6566	0.840509
$265$	0	0
$266$	0	0
$267$	−12.8897	−0.788835
$268$	0.778092	0.0475295
$269$	−5.71228	−0.348284	−0.174142	−	0.984721i	$-0.555715\pi$
$269$	−5.71228	−0.348284	−0.174142	+	0.984721i	$0.555715\pi$
$270$	0	0
$271$	−12.7112	−0.772150	−0.386075	−	0.922467i	$-0.626169\pi$
$271$	−12.7112	−0.772150	−0.386075	+	0.922467i	$0.626169\pi$
$272$	−29.6057	−1.79511
$273$	4.50479	0.272642
$274$	28.8804	1.74473
$275$	0	0
$276$	−0.840244	−0.0505768
$277$	−17.6019	−1.05760	−0.528799	−	0.848747i	$-0.677358\pi$
$277$	−17.6019	−1.05760	−0.528799	+	0.848747i	$0.677358\pi$
$278$	11.1613	0.669413
$279$	−8.72024	−0.522067
$280$	0	0
$281$	20.5004	1.22295	0.611476	−	0.791263i	$-0.290576\pi$
$281$	20.5004	1.22295	0.611476	+	0.791263i	$0.290576\pi$
$282$	−17.2861	−1.02937
$283$	11.8561	0.704772	0.352386	−	0.935855i	$-0.385370\pi$
$283$	11.8561	0.704772	0.352386	+	0.935855i	$0.385370\pi$
$284$	−6.80836	−0.404002
$285$	0	0
$286$	−15.2787	−0.903449
$287$	15.3795	0.907821
$288$	−6.85619	−0.404005
$289$	18.8089	1.10641
$290$	0	0
$291$	−4.70601	−0.275871
$292$	7.89976	0.462298
$293$	−24.9814	−1.45943	−0.729715	−	0.683751i	$-0.760347\pi$
$293$	−24.9814	−1.45943	−0.729715	+	0.683751i	$0.760347\pi$
$294$	−2.06470	−0.120416
$295$	0	0
$296$	−5.92139	−0.344174
$297$	−31.0678	−1.80274
$298$	−23.9575	−1.38782
$299$	−1.49938	−0.0867114
$300$	0	0
$301$	−11.0542	−0.637151
$302$	21.1761	1.21855
$303$	12.9082	0.741554
$304$	0	0
$305$	0	0
$306$	16.4847	0.942366
$307$	16.9199	0.965671	0.482836	−	0.875711i	$-0.339607\pi$
$307$	16.9199	0.965671	0.482836	+	0.875711i	$0.339607\pi$
$308$	−10.8010	−0.615443
$309$	−13.4289	−0.763943
$310$	0	0
$311$	−15.2133	−0.862670	−0.431335	−	0.902192i	$-0.641957\pi$
$311$	−15.2133	−0.862670	−0.431335	+	0.902192i	$0.641957\pi$
$312$	3.78512	0.214290
$313$	−24.9273	−1.40898	−0.704488	−	0.709716i	$-0.748823\pi$
$313$	−24.9273	−1.40898	−0.704488	+	0.709716i	$0.748823\pi$
$314$	−5.61834	−0.317061
$315$	0	0
$316$	−5.86093	−0.329703
$317$	−25.2304	−1.41708	−0.708541	−	0.705669i	$-0.750646\pi$
$317$	−25.2304	−1.41708	−0.708541	+	0.705669i	$0.750646\pi$
$318$	−4.24005	−0.237770
$319$	15.0679	0.843641
$320$	0	0
$321$	−20.7802	−1.15984
$322$	−3.81055	−0.212354
$323$	0	0
$324$	−0.998983	−0.0554991
$325$	0	0
$326$	0.512614	0.0283911
$327$	6.52328	0.360738
$328$	12.9225	0.713526
$329$	−21.8062	−1.20221
$330$	0	0
$331$	20.2063	1.11064	0.555320	−	0.831637i	$-0.312596\pi$
$331$	20.2063	1.11064	0.555320	+	0.831637i	$0.312596\pi$
$332$	−2.39964	−0.131697
$333$	4.78920	0.262447
$334$	−23.7436	−1.29919
$335$	0	0
$336$	13.9730	0.762291
$337$	−31.8247	−1.73360	−0.866800	−	0.498657i	$-0.833827\pi$
$337$	−31.8247	−1.73360	−0.866800	+	0.498657i	$0.833827\pi$
$338$	17.4044	0.946674
$339$	18.1837	0.987601
$340$	0	0
$341$	−30.3226	−1.64206
$342$	0	0
$343$	−19.6514	−1.06107
$344$	−9.28820	−0.500786
$345$	0	0
$346$	−22.2169	−1.19439
$347$	3.30255	0.177290	0.0886451	−	0.996063i	$-0.471746\pi$
$347$	3.30255	0.177290	0.0886451	+	0.996063i	$0.471746\pi$
$348$	2.34036	0.125457
$349$	17.8486	0.955416	0.477708	−	0.878519i	$-0.341468\pi$
$349$	17.8486	0.955416	0.477708	+	0.878519i	$0.341468\pi$
$350$	0	0
$351$	−8.61086	−0.459614
$352$	−23.8408	−1.27072
$353$	8.29523	0.441511	0.220755	−	0.975329i	$-0.429148\pi$
$353$	8.29523	0.441511	0.220755	+	0.975329i	$0.429148\pi$
$354$	20.8467	1.10799
$355$	0	0
$356$	8.56576	0.453984
$357$	−16.9008	−0.894484
$358$	−23.6710	−1.25105
$359$	8.35022	0.440708	0.220354	−	0.975420i	$-0.429279\pi$
$359$	8.35022	0.440708	0.220354	+	0.975420i	$0.429279\pi$
$360$	0	0
$361$	0	0
$362$	16.4501	0.864598
$363$	−25.6507	−1.34631
$364$	−2.99363	−0.156909
$365$	0	0
$366$	−20.3253	−1.06242
$367$	−14.4198	−0.752705	−0.376353	−	0.926477i	$-0.622822\pi$
$367$	−14.4198	−0.752705	−0.376353	+	0.926477i	$0.622822\pi$
$368$	−4.65080	−0.242440
$369$	−10.4517	−0.544093
$370$	0	0
$371$	−5.34876	−0.277694
$372$	−4.70974	−0.244188
$373$	−24.1157	−1.24866	−0.624332	−	0.781159i	$-0.714629\pi$
$373$	−24.1157	−1.24866	−0.624332	+	0.781159i	$0.714629\pi$
$374$	57.3217	2.96403
$375$	0	0
$376$	−18.3225	−0.944911
$377$	4.17627	0.215089
$378$	−21.8838	−1.12558
$379$	−16.6757	−0.856571	−0.428285	−	0.903644i	$-0.640882\pi$
$379$	−16.6757	−0.856571	−0.428285	+	0.903644i	$0.640882\pi$
$380$	0	0
$381$	−7.09760	−0.363621
$382$	21.6294	1.10666
$383$	−10.8779	−0.555834	−0.277917	−	0.960605i	$-0.589644\pi$
$383$	−10.8779	−0.555834	−0.277917	+	0.960605i	$0.589644\pi$
$384$	15.3987	0.785811
$385$	0	0
$386$	−24.1624	−1.22983
$387$	7.51226	0.381870
$388$	3.12736	0.158767
$389$	36.4543	1.84831	0.924154	−	0.382021i	$-0.124772\pi$
$389$	36.4543	1.84831	0.924154	+	0.382021i	$0.124772\pi$
$390$	0	0
$391$	5.62528	0.284482
$392$	−2.18849	−0.110535
$393$	17.2584	0.870573
$394$	−41.6153	−2.09655
$395$	0	0
$396$	7.34020	0.368859
$397$	−8.58381	−0.430809	−0.215405	−	0.976525i	$-0.569107\pi$
$397$	−8.58381	−0.430809	−0.215405	+	0.976525i	$0.569107\pi$
$398$	3.75419	0.188181
$399$	0	0
$400$	0	0
$401$	17.0557	0.851721	0.425860	−	0.904789i	$-0.359971\pi$
$401$	17.0557	0.851721	0.425860	+	0.904789i	$0.359971\pi$
$402$	1.94896	0.0972051
$403$	−8.40432	−0.418649
$404$	−8.57805	−0.426774
$405$	0	0
$406$	10.6137	0.526747
$407$	16.6533	0.825476
$408$	−14.2008	−0.703043
$409$	11.7940	0.583178	0.291589	−	0.956544i	$-0.405816\pi$
$409$	11.7940	0.583178	0.291589	+	0.956544i	$0.405816\pi$
$410$	0	0
$411$	20.1222	0.992553
$412$	8.92410	0.439659
$413$	26.2978	1.29403
$414$	2.58960	0.127272
$415$	0	0
$416$	−6.60780	−0.323974
$417$	7.77656	0.380820
$418$	0	0
$419$	1.14280	0.0558292	0.0279146	−	0.999610i	$-0.491113\pi$
$419$	1.14280	0.0558292	0.0279146	+	0.999610i	$0.491113\pi$
$420$	0	0
$421$	−19.5189	−0.951292	−0.475646	−	0.879637i	$-0.657786\pi$
$421$	−19.5189	−0.951292	−0.475646	+	0.879637i	$0.657786\pi$
$422$	36.9797	1.80014
$423$	14.8192	0.720533
$424$	−4.49426	−0.218261
$425$	0	0
$426$	−17.0535	−0.826245
$427$	−25.6400	−1.24081
$428$	13.8094	0.667501
$429$	−10.6453	−0.513960
$430$	0	0
$431$	36.8785	1.77637	0.888187	−	0.459483i	$-0.151965\pi$
$431$	36.8785	1.77637	0.888187	+	0.459483i	$0.151965\pi$
$432$	−26.7093	−1.28505
$433$	0.368933	0.0177298	0.00886490	−	0.999961i	$-0.497178\pi$
$433$	0.368933	0.0177298	0.00886490	+	0.999961i	$0.497178\pi$
$434$	−21.3589	−1.02526
$435$	0	0
$436$	−4.33501	−0.207609
$437$	0	0
$438$	19.7872	0.945470
$439$	2.26439	0.108073	0.0540367	−	0.998539i	$-0.482791\pi$
$439$	2.26439	0.108073	0.0540367	+	0.998539i	$0.482791\pi$
$440$	0	0
$441$	1.77004	0.0842878
$442$	15.8875	0.755690
$443$	16.4627	0.782169	0.391084	−	0.920355i	$-0.372100\pi$
$443$	16.4627	0.782169	0.391084	+	0.920355i	$0.372100\pi$
$444$	2.58661	0.122755
$445$	0	0
$446$	−17.0050	−0.805209
$447$	−16.6922	−0.789513
$448$	7.30329	0.345048
$449$	−14.1613	−0.668315	−0.334158	−	0.942517i	$-0.608452\pi$
$449$	−14.1613	−0.668315	−0.334158	+	0.942517i	$0.608452\pi$
$450$	0	0
$451$	−36.3433	−1.71134
$452$	−12.0839	−0.568377
$453$	14.7543	0.693215
$454$	−6.91086	−0.324343
$455$	0	0
$456$	0	0
$457$	−1.22073	−0.0571033	−0.0285516	−	0.999592i	$-0.509090\pi$
$457$	−1.22073	−0.0571033	−0.0285516	+	0.999592i	$0.509090\pi$
$458$	−10.8742	−0.508120
$459$	32.3057	1.50790
$460$	0	0
$461$	−8.69160	−0.404808	−0.202404	−	0.979302i	$-0.564875\pi$
$461$	−8.69160	−0.404808	−0.202404	+	0.979302i	$0.564875\pi$
$462$	−27.0542	−1.25867
$463$	19.7149	0.916229	0.458114	−	0.888893i	$-0.348525\pi$
$463$	19.7149	0.916229	0.458114	+	0.888893i	$0.348525\pi$
$464$	12.9540	0.601375
$465$	0	0
$466$	8.56942	0.396971
$467$	11.4795	0.531207	0.265604	−	0.964082i	$-0.414429\pi$
$467$	11.4795	0.531207	0.265604	+	0.964082i	$0.414429\pi$
$468$	2.03443	0.0940418
$469$	2.45858	0.113527
$470$	0	0
$471$	−3.91452	−0.180372
$472$	22.0966	1.01708
$473$	26.1222	1.20110
$474$	−14.6804	−0.674293
$475$	0	0
$476$	11.2313	0.514787
$477$	3.63495	0.166433
$478$	−23.2973	−1.06559
$479$	39.2631	1.79398	0.896989	−	0.442053i	$-0.145750\pi$
$479$	39.2631	1.79398	0.896989	+	0.442053i	$0.145750\pi$
$480$	0	0
$481$	4.61570	0.210458
$482$	25.3439	1.15438
$483$	−2.65497	−0.120805
$484$	17.0460	0.774820
$485$	0	0
$486$	24.4565	1.10937
$487$	31.5943	1.43168	0.715838	−	0.698266i	$-0.246045\pi$
$487$	31.5943	1.43168	0.715838	+	0.698266i	$0.246045\pi$
$488$	−21.5439	−0.975246
$489$	0.357159	0.0161513
$490$	0	0
$491$	−11.0637	−0.499300	−0.249650	−	0.968336i	$-0.580316\pi$
$491$	−11.0637	−0.499300	−0.249650	+	0.968336i	$0.580316\pi$
$492$	−5.64487	−0.254491
$493$	−15.6683	−0.705663
$494$	0	0
$495$	0	0
$496$	−26.0686	−1.17052
$497$	−21.5127	−0.964979
$498$	−6.01060	−0.269341
$499$	−20.3735	−0.912045	−0.456023	−	0.889968i	$-0.650726\pi$
$499$	−20.3735	−0.912045	−0.456023	+	0.889968i	$0.650726\pi$
$500$	0	0
$501$	−16.5431	−0.739091
$502$	10.1747	0.454118
$503$	13.6724	0.609624	0.304812	−	0.952413i	$-0.401406\pi$
$503$	13.6724	0.609624	0.304812	+	0.952413i	$0.401406\pi$
$504$	−8.24676	−0.367340
$505$	0	0
$506$	9.00474	0.400310
$507$	12.1263	0.538550
$508$	4.71668	0.209269
$509$	7.72393	0.342357	0.171179	−	0.985240i	$-0.445243\pi$
$509$	7.72393	0.342357	0.171179	+	0.985240i	$0.445243\pi$
$510$	0	0
$511$	24.9613	1.10422
$512$	−0.249240	−0.0110150
$513$	0	0
$514$	−0.204211	−0.00900736
$515$	0	0
$516$	4.05732	0.178613
$517$	51.5303	2.26630
$518$	11.7304	0.515405
$519$	−15.4794	−0.679471
$520$	0	0
$521$	2.16876	0.0950151	0.0475075	−	0.998871i	$-0.484872\pi$
$521$	2.16876	0.0950151	0.0475075	+	0.998871i	$0.484872\pi$
$522$	−7.21290	−0.315700
$523$	−23.8932	−1.04478	−0.522389	−	0.852707i	$-0.674959\pi$
$523$	−23.8932	−1.04478	−0.522389	+	0.852707i	$0.674959\pi$
$524$	−11.4690	−0.501026
$525$	0	0
$526$	−16.7462	−0.730169
$527$	31.5308	1.37350
$528$	−33.0197	−1.43700
$529$	−22.1163	−0.961579
$530$	0	0
$531$	−17.8716	−0.775562
$532$	0	0
$533$	−10.0730	−0.436312
$534$	21.4554	0.928467
$535$	0	0
$536$	2.06581	0.0892293
$537$	−16.4926	−0.711707
$538$	9.50835	0.409934
$539$	6.15492	0.265111
$540$	0	0
$541$	42.4550	1.82528	0.912641	−	0.408762i	$-0.134039\pi$
$541$	42.4550	1.82528	0.912641	+	0.408762i	$0.134039\pi$
$542$	21.1584	0.908829
$543$	11.4614	0.491858
$544$	24.7907	1.06289
$545$	0	0
$546$	−7.49842	−0.320903
$547$	12.0307	0.514396	0.257198	−	0.966359i	$-0.417201\pi$
$547$	12.0307	0.514396	0.257198	+	0.966359i	$0.417201\pi$
$548$	−13.3721	−0.571227
$549$	17.4246	0.743665
$550$	0	0
$551$	0	0
$552$	−2.23082	−0.0949500
$553$	−18.5191	−0.787513
$554$	29.2992	1.24481
$555$	0	0
$556$	−5.16787	−0.219167
$557$	8.75270	0.370864	0.185432	−	0.982657i	$-0.440632\pi$
$557$	8.75270	0.370864	0.185432	+	0.982657i	$0.440632\pi$
$558$	14.5152	0.614479
$559$	7.24011	0.306224
$560$	0	0
$561$	39.9383	1.68620
$562$	−34.1238	−1.43943
$563$	−35.9707	−1.51598	−0.757991	−	0.652265i	$-0.773819\pi$
$563$	−35.9707	−1.51598	−0.757991	+	0.652265i	$0.773819\pi$
$564$	8.00373	0.337018
$565$	0	0
$566$	−19.7350	−0.829524
$567$	−3.15654	−0.132562
$568$	−18.0760	−0.758450
$569$	20.3125	0.851543	0.425772	−	0.904831i	$-0.360003\pi$
$569$	20.3125	0.851543	0.425772	+	0.904831i	$0.360003\pi$
$570$	0	0
$571$	10.1773	0.425906	0.212953	−	0.977062i	$-0.431692\pi$
$571$	10.1773	0.425906	0.212953	+	0.977062i	$0.431692\pi$
$572$	7.07428	0.295790
$573$	15.0701	0.629563
$574$	−25.5998	−1.06852
$575$	0	0
$576$	−4.96322	−0.206801
$577$	32.7441	1.36316	0.681578	−	0.731745i	$-0.261294\pi$
$577$	32.7441	1.36316	0.681578	+	0.731745i	$0.261294\pi$
$578$	−31.3083	−1.30225
$579$	−16.8349	−0.699634
$580$	0	0
$581$	−7.58228	−0.314566
$582$	7.83337	0.324703
$583$	12.6397	0.523482
$584$	20.9736	0.867893
$585$	0	0
$586$	41.5827	1.71777
$587$	−8.77326	−0.362111	−0.181056	−	0.983473i	$-0.557951\pi$
$587$	−8.77326	−0.362111	−0.181056	+	0.983473i	$0.557951\pi$
$588$	0.955987	0.0394243
$589$	0	0
$590$	0	0
$591$	−28.9951	−1.19270
$592$	14.3170	0.588427
$593$	32.3207	1.32725	0.663625	−	0.748065i	$-0.269017\pi$
$593$	32.3207	1.32725	0.663625	+	0.748065i	$0.269017\pi$
$594$	51.7138	2.12184
$595$	0	0
$596$	11.0927	0.454375
$597$	2.61570	0.107053
$598$	2.49579	0.102060
$599$	19.5504	0.798807	0.399404	−	0.916775i	$-0.369217\pi$
$599$	19.5504	0.798807	0.399404	+	0.916775i	$0.369217\pi$
$600$	0	0
$601$	0.401837	0.0163913	0.00819564	−	0.999966i	$-0.497391\pi$
$601$	0.401837	0.0163913	0.00819564	+	0.999966i	$0.497391\pi$
$602$	18.4002	0.749934
$603$	−1.67082	−0.0680410
$604$	−9.80486	−0.398954
$605$	0	0
$606$	−21.4862	−0.872817
$607$	13.4453	0.545727	0.272863	−	0.962053i	$-0.412029\pi$
$607$	13.4453	0.545727	0.272863	+	0.962053i	$0.412029\pi$
$608$	0	0
$609$	7.39497	0.299659
$610$	0	0
$611$	14.2823	0.577800
$612$	−7.63266	−0.308532
$613$	20.7053	0.836280	0.418140	−	0.908383i	$-0.362682\pi$
$613$	20.7053	0.836280	0.418140	+	0.908383i	$0.362682\pi$
$614$	−28.1640	−1.13661
$615$	0	0
$616$	−28.6762	−1.15540
$617$	9.27871	0.373547	0.186773	−	0.982403i	$-0.440197\pi$
$617$	9.27871	0.373547	0.186773	+	0.982403i	$0.440197\pi$
$618$	22.3530	0.899169
$619$	−2.89129	−0.116211	−0.0581053	−	0.998310i	$-0.518506\pi$
$619$	−2.89129	−0.116211	−0.0581053	+	0.998310i	$0.518506\pi$
$620$	0	0
$621$	5.07494	0.203650
$622$	25.3233	1.01537
$623$	27.0657	1.08437
$624$	−9.15186	−0.366368
$625$	0	0
$626$	41.4926	1.65838
$627$	0	0
$628$	2.60138	0.103806
$629$	−17.3169	−0.690469
$630$	0	0
$631$	30.4540	1.21236	0.606178	−	0.795329i	$-0.292702\pi$
$631$	30.4540	1.21236	0.606178	+	0.795329i	$0.292702\pi$
$632$	−15.5606	−0.618966
$633$	25.7653	1.02408
$634$	41.9972	1.66792
$635$	0	0
$636$	1.96321	0.0778462
$637$	1.70592	0.0675910
$638$	−25.0812	−0.992975
$639$	14.6198	0.578349
$640$	0	0
$641$	20.0738	0.792869	0.396434	−	0.918063i	$-0.370247\pi$
$641$	20.0738	0.792869	0.396434	+	0.918063i	$0.370247\pi$
$642$	34.5896	1.36514
$643$	2.08913	0.0823874	0.0411937	−	0.999151i	$-0.486884\pi$
$643$	2.08913	0.0823874	0.0411937	+	0.999151i	$0.486884\pi$
$644$	1.76434	0.0695249
$645$	0	0
$646$	0	0
$647$	2.10623	0.0828043	0.0414021	−	0.999143i	$-0.486818\pi$
$647$	2.10623	0.0828043	0.0414021	+	0.999143i	$0.486818\pi$
$648$	−2.65227	−0.104191
$649$	−62.1444	−2.43938
$650$	0	0
$651$	−14.8816	−0.583257
$652$	−0.237348	−0.00929527
$653$	−1.83067	−0.0716395	−0.0358197	−	0.999358i	$-0.511404\pi$
$653$	−1.83067	−0.0716395	−0.0358197	+	0.999358i	$0.511404\pi$
$654$	−10.8583	−0.424593
$655$	0	0
$656$	−31.2447	−1.21990
$657$	−16.9634	−0.661804
$658$	36.2973	1.41502
$659$	−24.0536	−0.936994	−0.468497	−	0.883465i	$-0.655204\pi$
$659$	−24.0536	−0.936994	−0.468497	+	0.883465i	$0.655204\pi$
$660$	0	0
$661$	17.4422	0.678423	0.339211	−	0.940710i	$-0.389840\pi$
$661$	17.4422	0.678423	0.339211	+	0.940710i	$0.389840\pi$
$662$	−33.6343	−1.30723
$663$	11.0694	0.429902
$664$	−6.37097	−0.247241
$665$	0	0
$666$	−7.97184	−0.308902
$667$	−2.46135	−0.0953039
$668$	10.9936	0.425356
$669$	−11.8480	−0.458072
$670$	0	0
$671$	60.5901	2.33906
$672$	−11.7005	−0.451357
$673$	47.5187	1.83171	0.915856	−	0.401506i	$-0.131513\pi$
$673$	47.5187	1.83171	0.915856	+	0.401506i	$0.131513\pi$
$674$	52.9736	2.04047
$675$	0	0
$676$	−8.05850	−0.309942
$677$	14.5531	0.559321	0.279661	−	0.960099i	$-0.409778\pi$
$677$	14.5531	0.559321	0.279661	+	0.960099i	$0.409778\pi$
$678$	−30.2675	−1.16242
$679$	9.88168	0.379224
$680$	0	0
$681$	−4.81507	−0.184514
$682$	50.4734	1.93273
$683$	3.33714	0.127692	0.0638460	−	0.997960i	$-0.479663\pi$
$683$	3.33714	0.127692	0.0638460	+	0.997960i	$0.479663\pi$
$684$	0	0
$685$	0	0
$686$	32.7106	1.24890
$687$	−7.57652	−0.289062
$688$	22.4575	0.856183
$689$	3.50326	0.133464
$690$	0	0
$691$	−19.3318	−0.735415	−0.367708	−	0.929941i	$-0.619857\pi$
$691$	−19.3318	−0.735415	−0.367708	+	0.929941i	$0.619857\pi$
$692$	10.2868	0.391044
$693$	23.1932	0.881038
$694$	−5.49724	−0.208673
$695$	0	0
$696$	6.21358	0.235525
$697$	37.7914	1.43145
$698$	−29.7099	−1.12454
$699$	5.97066	0.225831
$700$	0	0
$701$	9.93785	0.375347	0.187674	−	0.982231i	$-0.439905\pi$
$701$	9.93785	0.375347	0.187674	+	0.982231i	$0.439905\pi$
$702$	14.3332	0.540971
$703$	0	0
$704$	−17.2584	−0.650452
$705$	0	0
$706$	−13.8078	−0.519663
$707$	−27.1045	−1.01937
$708$	−9.65233	−0.362757
$709$	37.2119	1.39752	0.698760	−	0.715356i	$-0.253735\pi$
$709$	37.2119	1.39752	0.698760	+	0.715356i	$0.253735\pi$
$710$	0	0
$711$	12.5853	0.471987
$712$	22.7418	0.852285
$713$	4.95322	0.185499
$714$	28.1321	1.05282
$715$	0	0
$716$	10.9601	0.409596
$717$	−16.2322	−0.606201
$718$	−13.8993	−0.518718
$719$	−2.64218	−0.0985365	−0.0492683	−	0.998786i	$-0.515689\pi$
$719$	−2.64218	−0.0985365	−0.0492683	+	0.998786i	$0.515689\pi$
$720$	0	0
$721$	28.1980	1.05015
$722$	0	0
$723$	17.6581	0.656711
$724$	−7.61664	−0.283070
$725$	0	0
$726$	42.6968	1.58463
$727$	10.1731	0.377298	0.188649	−	0.982045i	$-0.439589\pi$
$727$	10.1731	0.377298	0.188649	+	0.982045i	$0.439589\pi$
$728$	−7.94800	−0.294572
$729$	20.9284	0.775126
$730$	0	0
$731$	−27.1630	−1.00466
$732$	9.41091	0.347837
$733$	−14.8222	−0.547472	−0.273736	−	0.961805i	$-0.588259\pi$
$733$	−14.8222	−0.547472	−0.273736	+	0.961805i	$0.588259\pi$
$734$	24.0023	0.885942
$735$	0	0
$736$	3.89441	0.143550
$737$	−5.80989	−0.214010
$738$	17.3973	0.640403
$739$	35.4866	1.30539	0.652697	−	0.757619i	$-0.273637\pi$
$739$	35.4866	1.30539	0.652697	+	0.757619i	$0.273637\pi$
$740$	0	0
$741$	0	0
$742$	8.90325	0.326849
$743$	−8.73882	−0.320596	−0.160298	−	0.987069i	$-0.551246\pi$
$743$	−8.73882	−0.320596	−0.160298	+	0.987069i	$0.551246\pi$
$744$	−12.5042	−0.458426
$745$	0	0
$746$	40.1417	1.46969
$747$	5.15282	0.188532
$748$	−26.5408	−0.970428
$749$	43.6342	1.59436
$750$	0	0
$751$	−13.0991	−0.477994	−0.238997	−	0.971020i	$-0.576819\pi$
$751$	−13.0991	−0.477994	−0.238997	+	0.971020i	$0.576819\pi$
$752$	44.3011	1.61549
$753$	7.08911	0.258342
$754$	−6.95160	−0.253162
$755$	0	0
$756$	10.1325	0.368517
$757$	16.4380	0.597450	0.298725	−	0.954339i	$-0.403439\pi$
$757$	16.4380	0.597450	0.298725	+	0.954339i	$0.403439\pi$
$758$	27.7574	1.00819
$759$	6.27397	0.227731
$760$	0	0
$761$	16.3918	0.594203	0.297101	−	0.954846i	$-0.403980\pi$
$761$	16.3918	0.594203	0.297101	+	0.954846i	$0.403980\pi$
$762$	11.8143	0.427986
$763$	−13.6976	−0.495886
$764$	−10.0148	−0.362321
$765$	0	0
$766$	18.1067	0.654223
$767$	−17.2242	−0.621929
$768$	−18.6756	−0.673899
$769$	−50.0421	−1.80456	−0.902282	−	0.431147i	$-0.858109\pi$
$769$	−50.0421	−1.80456	−0.902282	+	0.431147i	$0.858109\pi$
$770$	0	0
$771$	−0.142282	−0.00512416
$772$	11.1875	0.402649
$773$	48.6873	1.75116	0.875580	−	0.483074i	$-0.160480\pi$
$773$	48.6873	1.75116	0.875580	+	0.483074i	$0.160480\pi$
$774$	−12.5045	−0.449465
$775$	0	0
$776$	8.30302	0.298061
$777$	8.17306	0.293207
$778$	−60.6799	−2.17548
$779$	0	0
$780$	0	0
$781$	50.8369	1.81909
$782$	−9.36352	−0.334839
$783$	−14.1354	−0.505158
$784$	5.29144	0.188980
$785$	0	0
$786$	−28.7275	−1.02467
$787$	6.51678	0.232298	0.116149	−	0.993232i	$-0.462945\pi$
$787$	6.51678	0.232298	0.116149	+	0.993232i	$0.462945\pi$
$788$	19.2685	0.686413
$789$	−11.6678	−0.415383
$790$	0	0
$791$	−38.1820	−1.35760
$792$	19.4880	0.692475
$793$	16.7934	0.596350
$794$	14.2881	0.507067
$795$	0	0
$796$	−1.73825	−0.0616106
$797$	38.3796	1.35947	0.679737	−	0.733456i	$-0.262094\pi$
$797$	38.3796	1.35947	0.679737	+	0.733456i	$0.262094\pi$
$798$	0	0
$799$	−53.5834	−1.89565
$800$	0	0
$801$	−18.3935	−0.649902
$802$	−28.3900	−1.00248
$803$	−58.9862	−2.08158
$804$	−0.902397	−0.0318251
$805$	0	0
$806$	13.9894	0.492755
$807$	6.62485	0.233206
$808$	−22.7744	−0.801202
$809$	25.1409	0.883906	0.441953	−	0.897038i	$-0.354286\pi$
$809$	25.1409	0.883906	0.441953	+	0.897038i	$0.354286\pi$
$810$	0	0
$811$	47.0106	1.65077	0.825383	−	0.564573i	$-0.190959\pi$
$811$	47.0106	1.65077	0.825383	+	0.564573i	$0.190959\pi$
$812$	−4.91429	−0.172458
$813$	14.7419	0.517020
$814$	−27.7202	−0.971594
$815$	0	0
$816$	34.3354	1.20198
$817$	0	0
$818$	−19.6317	−0.686406
$819$	6.42832	0.224624
$820$	0	0
$821$	−19.8204	−0.691737	−0.345869	−	0.938283i	$-0.612416\pi$
$821$	−19.8204	−0.691737	−0.345869	+	0.938283i	$0.612416\pi$
$822$	−33.4943	−1.16825
$823$	39.2168	1.36701	0.683505	−	0.729946i	$-0.260455\pi$
$823$	39.2168	1.36701	0.683505	+	0.729946i	$0.260455\pi$
$824$	23.6932	0.825391
$825$	0	0
$826$	−43.7738	−1.52309
$827$	−11.8435	−0.411839	−0.205920	−	0.978569i	$-0.566019\pi$
$827$	−11.8435	−0.411839	−0.205920	+	0.978569i	$0.566019\pi$
$828$	−1.19903	−0.0416690
$829$	−46.9321	−1.63002	−0.815010	−	0.579447i	$-0.803269\pi$
$829$	−46.9321	−1.63002	−0.815010	+	0.579447i	$0.803269\pi$
$830$	0	0
$831$	20.4140	0.708153
$832$	−4.78341	−0.165835
$833$	−6.40015	−0.221752
$834$	−12.9444	−0.448229
$835$	0	0
$836$	0	0
$837$	28.4461	0.983240
$838$	−1.90223	−0.0657116
$839$	53.1339	1.83438	0.917192	−	0.398445i	$-0.130450\pi$
$839$	53.1339	1.83438	0.917192	+	0.398445i	$0.130450\pi$
$840$	0	0
$841$	−22.1443	−0.763597
$842$	32.4901	1.11968
$843$	−23.7755	−0.818870
$844$	−17.1222	−0.589370
$845$	0	0
$846$	−24.6672	−0.848075
$847$	53.8613	1.85070
$848$	10.8665	0.373156
$849$	−13.7502	−0.471905
$850$	0	0
$851$	−2.72033	−0.0932518
$852$	7.89603	0.270514
$853$	−42.2998	−1.44832	−0.724159	−	0.689633i	$-0.757772\pi$
$853$	−42.2998	−1.44832	−0.724159	+	0.689633i	$0.757772\pi$
$854$	42.6790	1.46045
$855$	0	0
$856$	36.6634	1.25313
$857$	23.5384	0.804056	0.402028	−	0.915627i	$-0.368305\pi$
$857$	23.5384	0.804056	0.402028	+	0.915627i	$0.368305\pi$
$858$	17.7196	0.604936
$859$	9.48124	0.323496	0.161748	−	0.986832i	$-0.448287\pi$
$859$	9.48124	0.323496	0.161748	+	0.986832i	$0.448287\pi$
$860$	0	0
$861$	−17.8364	−0.607864
$862$	−61.3859	−2.09081
$863$	22.8204	0.776816	0.388408	−	0.921487i	$-0.373025\pi$
$863$	22.8204	0.776816	0.388408	+	0.921487i	$0.373025\pi$
$864$	22.3654	0.760886
$865$	0	0
$866$	−0.614106	−0.0208682
$867$	−21.8138	−0.740834
$868$	9.88950	0.335672
$869$	43.7626	1.48455
$870$	0	0
$871$	−1.61029	−0.0545625
$872$	−11.5093	−0.389755
$873$	−6.71546	−0.227284
$874$	0	0
$875$	0	0
$876$	−9.16179	−0.309548
$877$	−25.2942	−0.854124	−0.427062	−	0.904222i	$-0.640451\pi$
$877$	−25.2942	−0.854124	−0.427062	+	0.904222i	$0.640451\pi$
$878$	−3.76918	−0.127204
$879$	28.9723	0.977213
$880$	0	0
$881$	−33.2871	−1.12147	−0.560736	−	0.827995i	$-0.689482\pi$
$881$	−33.2871	−1.12147	−0.560736	+	0.827995i	$0.689482\pi$
$882$	−2.94632	−0.0992077
$883$	15.3109	0.515252	0.257626	−	0.966245i	$-0.417060\pi$
$883$	15.3109	0.515252	0.257626	+	0.966245i	$0.417060\pi$
$884$	−7.35614	−0.247414
$885$	0	0
$886$	−27.4030	−0.920621
$887$	43.2055	1.45070	0.725349	−	0.688381i	$-0.241678\pi$
$887$	43.2055	1.45070	0.725349	+	0.688381i	$0.241678\pi$
$888$	6.86737	0.230454
$889$	14.9035	0.499849
$890$	0	0
$891$	7.45925	0.249894
$892$	7.87356	0.263626
$893$	0	0
$894$	27.7849	0.929265
$895$	0	0
$896$	−32.3342	−1.08021
$897$	1.73891	0.0580607
$898$	23.5722	0.786614
$899$	−13.7964	−0.460134
$900$	0	0
$901$	−13.1433	−0.437867
$902$	60.4951	2.01427
$903$	12.8201	0.426627
$904$	−32.0822	−1.06704
$905$	0	0
$906$	−24.5591	−0.815922
$907$	14.3278	0.475748	0.237874	−	0.971296i	$-0.423549\pi$
$907$	14.3278	0.475748	0.237874	+	0.971296i	$0.423549\pi$
$908$	3.19983	0.106190
$909$	18.4199	0.610949
$910$	0	0
$911$	4.61162	0.152790	0.0763949	−	0.997078i	$-0.475659\pi$
$911$	4.61162	0.152790	0.0763949	+	0.997078i	$0.475659\pi$
$912$	0	0
$913$	17.9177	0.592990
$914$	2.03196	0.0672112
$915$	0	0
$916$	5.03494	0.166359
$917$	−36.2393	−1.19673
$918$	−53.7742	−1.77481
$919$	26.4921	0.873892	0.436946	−	0.899488i	$-0.356060\pi$
$919$	26.4921	0.873892	0.436946	+	0.899488i	$0.356060\pi$
$920$	0	0
$921$	−19.6230	−0.646599
$922$	14.4676	0.476464
$923$	14.0901	0.463782
$924$	12.5265	0.412091
$925$	0	0
$926$	−32.8163	−1.07841
$927$	−19.1630	−0.629394
$928$	−10.8472	−0.356078
$929$	−4.75725	−0.156080	−0.0780402	−	0.996950i	$-0.524866\pi$
$929$	−4.75725	−0.156080	−0.0780402	+	0.996950i	$0.524866\pi$
$930$	0	0
$931$	0	0
$932$	−3.96777	−0.129969
$933$	17.6438	0.577631
$934$	−19.1081	−0.625237
$935$	0	0
$936$	5.40135	0.176549
$937$	11.9367	0.389954	0.194977	−	0.980808i	$-0.437537\pi$
$937$	11.9367	0.389954	0.194977	+	0.980808i	$0.437537\pi$
$938$	−4.09242	−0.133622
$939$	28.9096	0.943429
$940$	0	0
$941$	17.9943	0.586597	0.293299	−	0.956021i	$-0.405247\pi$
$941$	17.9943	0.586597	0.293299	+	0.956021i	$0.405247\pi$
$942$	6.51590	0.212299
$943$	5.93670	0.193326
$944$	−53.4262	−1.73887
$945$	0	0
$946$	−43.4815	−1.41371
$947$	25.2191	0.819511	0.409755	−	0.912195i	$-0.365614\pi$
$947$	25.2191	0.819511	0.409755	+	0.912195i	$0.365614\pi$
$948$	6.79725	0.220764
$949$	−16.3488	−0.530705
$950$	0	0
$951$	29.2611	0.948858
$952$	29.8188	0.966433
$953$	42.3179	1.37081	0.685405	−	0.728162i	$-0.259625\pi$
$953$	42.3179	1.37081	0.685405	+	0.728162i	$0.259625\pi$
$954$	−6.05053	−0.195893
$955$	0	0
$956$	10.7870	0.348876
$957$	−17.4751	−0.564890
$958$	−65.3552	−2.11153
$959$	−42.2525	−1.36441
$960$	0	0
$961$	−3.23623	−0.104395
$962$	−7.68304	−0.247711
$963$	−29.6533	−0.955563
$964$	−11.7346	−0.377946
$965$	0	0
$966$	4.41931	0.142189
$967$	13.6964	0.440447	0.220223	−	0.975449i	$-0.429321\pi$
$967$	13.6964	0.440447	0.220223	+	0.975449i	$0.429321\pi$
$968$	45.2567	1.45460
$969$	0	0
$970$	0	0
$971$	38.5812	1.23813	0.619065	−	0.785339i	$-0.287512\pi$
$971$	38.5812	1.23813	0.619065	+	0.785339i	$0.287512\pi$
$972$	−11.3237	−0.363209
$973$	−16.3292	−0.523491
$974$	−52.5902	−1.68510
$975$	0	0
$976$	52.0899	1.66736
$977$	−17.4592	−0.558568	−0.279284	−	0.960209i	$-0.590097\pi$
$977$	−17.4592	−0.558568	−0.279284	+	0.960209i	$0.590097\pi$
$978$	−0.594507	−0.0190102
$979$	−63.9592	−2.04414
$980$	0	0
$981$	9.30869	0.297204
$982$	18.4161	0.587681
$983$	43.9161	1.40071	0.700353	−	0.713796i	$-0.253026\pi$
$983$	43.9161	1.40071	0.700353	+	0.713796i	$0.253026\pi$
$984$	−14.9870	−0.477767
$985$	0	0
$986$	26.0805	0.830574
$987$	25.2898	0.804984
$988$	0	0
$989$	−4.26707	−0.135685
$990$	0	0
$991$	−46.3462	−1.47224	−0.736118	−	0.676853i	$-0.763343\pi$
$991$	−46.3462	−1.47224	−0.736118	+	0.676853i	$0.763343\pi$
$992$	21.8289	0.693070
$993$	−23.4344	−0.743668
$994$	35.8089	1.13579
$995$	0	0
$996$	2.78300	0.0881827
$997$	−11.7371	−0.371719	−0.185859	−	0.982576i	$-0.559507\pi$
$997$	−11.7371	−0.371719	−0.185859	+	0.982576i	$0.559507\pi$
$998$	33.9127	1.07349
$999$	−15.6227	−0.494281

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.bp.1.1		4
5.4	even	2		1805.2.a.i.1.4		4
19.8	odd	6		475.2.e.e.26.1		8
19.12	odd	6		475.2.e.e.201.1		8
19.18	odd	2		9025.2.a.bg.1.4		4
95.8	even	12		475.2.j.c.349.2		16
95.12	even	12		475.2.j.c.49.2		16
95.27	even	12		475.2.j.c.349.7		16
95.69	odd	6		95.2.e.c.11.4	✓	8
95.84	odd	6		95.2.e.c.26.4	yes	8
95.88	even	12		475.2.j.c.49.7		16
95.94	odd	2		1805.2.a.o.1.1		4
285.164	even	6		855.2.k.h.676.1		8
285.179	even	6		855.2.k.h.406.1		8
380.179	even	6		1520.2.q.o.881.1		8
380.259	even	6		1520.2.q.o.961.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.c.11.4	✓	8	95.69	odd	6
95.2.e.c.26.4	yes	8	95.84	odd	6
475.2.e.e.26.1		8	19.8	odd	6
475.2.e.e.201.1		8	19.12	odd	6
475.2.j.c.49.2		16	95.12	even	12
475.2.j.c.49.7		16	95.88	even	12
475.2.j.c.349.2		16	95.8	even	12
475.2.j.c.349.7		16	95.27	even	12
855.2.k.h.406.1		8	285.179	even	6
855.2.k.h.676.1		8	285.164	even	6
1520.2.q.o.881.1		8	380.179	even	6
1520.2.q.o.961.1		8	380.259	even	6
1805.2.a.i.1.4		4	5.4	even	2
1805.2.a.o.1.1		4	95.94	odd	2
9025.2.a.bg.1.4		4	19.18	odd	2
9025.2.a.bp.1.1		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.66454 q^{2} -1.15976 q^{3} +0.770710 q^{4} +1.93047 q^{6} +2.43525 q^{7} +2.04621 q^{8} -1.65497 q^{9} +O(q^{10})\)	\(q-1.66454 q^{2} -1.15976 q^{3} +0.770710 q^{4} +1.93047 q^{6} +2.43525 q^{7} +2.04621 q^{8} -1.65497 q^{9} -5.75477 q^{11} -0.893835 q^{12} -1.59501 q^{13} -4.05359 q^{14} -4.94743 q^{16} +5.98406 q^{17} +2.75477 q^{18} -2.82430 q^{21} +9.57907 q^{22} +0.940044 q^{23} -2.37310 q^{24} +2.65497 q^{26} +5.39862 q^{27} +1.87687 q^{28} -2.61834 q^{29} +5.26913 q^{31} +4.14280 q^{32} +6.67412 q^{33} -9.96073 q^{34} -1.27550 q^{36} -2.89384 q^{37} +1.84982 q^{39} +6.31534 q^{41} +4.70118 q^{42} -4.53922 q^{43} -4.43525 q^{44} -1.56475 q^{46} -8.95437 q^{47} +5.73781 q^{48} -1.06953 q^{49} -6.94004 q^{51} -1.22929 q^{52} -2.19639 q^{53} -8.98625 q^{54} +4.98304 q^{56} +4.35834 q^{58} +10.7988 q^{59} -10.5287 q^{61} -8.77071 q^{62} -4.03027 q^{63} +2.99898 q^{64} -11.1094 q^{66} +1.00958 q^{67} +4.61197 q^{68} -1.09022 q^{69} -8.83388 q^{71} -3.38641 q^{72} +10.2500 q^{73} +4.81692 q^{74} -14.0143 q^{77} -3.07911 q^{78} -7.60459 q^{79} -1.29619 q^{81} -10.5122 q^{82} -3.11355 q^{83} -2.17672 q^{84} +7.55574 q^{86} +3.03663 q^{87} -11.7755 q^{88} +11.1141 q^{89} -3.88426 q^{91} +0.724501 q^{92} -6.11091 q^{93} +14.9049 q^{94} -4.80463 q^{96} +4.05776 q^{97} +1.78029 q^{98} +9.52395 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + 3 q^{3} + 5 q^{4} + 2 q^{6} + 4 q^{7} + 12 q^{8} + q^{9}+O(q^{10}) \) 4 * q + q^2 + 3 * q^3 + 5 * q^4 + 2 * q^6 + 4 * q^7 + 12 * q^8 + q^9	\( 4 q + q^{2} + 3 q^{3} + 5 q^{4} + 2 q^{6} + 4 q^{7} + 12 q^{8} + q^{9} - 2 q^{11} + 6 q^{12} + 7 q^{13} + q^{14} + 7 q^{16} + q^{17} - 10 q^{18} + 4 q^{21} + 2 q^{22} - 2 q^{23} + 23 q^{24} + 3 q^{26} + 12 q^{27} + 19 q^{28} + q^{29} + 30 q^{32} + 19 q^{33} - 15 q^{34} - 7 q^{36} - 2 q^{37} + 15 q^{39} + 8 q^{41} + 15 q^{42} - q^{43} - 12 q^{44} - 12 q^{46} + 12 q^{47} + 23 q^{48} - 10 q^{49} - 22 q^{51} - 3 q^{52} - 5 q^{53} - 34 q^{54} + 41 q^{56} + 27 q^{58} + 5 q^{59} - 37 q^{62} + 3 q^{63} + 56 q^{64} - 31 q^{66} + 4 q^{67} - 16 q^{68} + 9 q^{69} - 20 q^{71} + 17 q^{72} + 20 q^{73} + 25 q^{74} - 14 q^{77} - 18 q^{78} - 17 q^{79} + 12 q^{81} - 21 q^{82} - q^{83} + 20 q^{84} - 8 q^{86} + 16 q^{87} - 7 q^{88} - 11 q^{89} - 6 q^{91} + q^{92} + 8 q^{93} + 31 q^{94} + 21 q^{96} + q^{97} + 9 q^{98} + 38 q^{99}+O(q^{100}) \) 4 * q + q^2 + 3 * q^3 + 5 * q^4 + 2 * q^6 + 4 * q^7 + 12 * q^8 + q^9 - 2 * q^11 + 6 * q^12 + 7 * q^13 + q^14 + 7 * q^16 + q^17 - 10 * q^18 + 4 * q^21 + 2 * q^22 - 2 * q^23 + 23 * q^24 + 3 * q^26 + 12 * q^27 + 19 * q^28 + q^29 + 30 * q^32 + 19 * q^33 - 15 * q^34 - 7 * q^36 - 2 * q^37 + 15 * q^39 + 8 * q^41 + 15 * q^42 - q^43 - 12 * q^44 - 12 * q^46 + 12 * q^47 + 23 * q^48 - 10 * q^49 - 22 * q^51 - 3 * q^52 - 5 * q^53 - 34 * q^54 + 41 * q^56 + 27 * q^58 + 5 * q^59 - 37 * q^62 + 3 * q^63 + 56 * q^64 - 31 * q^66 + 4 * q^67 - 16 * q^68 + 9 * q^69 - 20 * q^71 + 17 * q^72 + 20 * q^73 + 25 * q^74 - 14 * q^77 - 18 * q^78 - 17 * q^79 + 12 * q^81 - 21 * q^82 - q^83 + 20 * q^84 - 8 * q^86 + 16 * q^87 - 7 * q^88 - 11 * q^89 - 6 * q^91 + q^92 + 8 * q^93 + 31 * q^94 + 21 * q^96 + q^97 + 9 * q^98 + 38 * q^99

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