LMFDB - Embedded newform 9025.2.a.bp.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9025,2,Mod(1,9025)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("9025.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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

Newform invariants

comment:select newform

sage:traces = [4,1,3,5,0,2,4,12,1,0,-2,6,7,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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			1.4
Root			$-0.491918$ 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)

$f(q)$	$=$	\(q+2.75802 q^{2} +1.49192 q^{3} +5.60665 q^{4} +4.11474 q^{6} +2.84864 q^{7} +9.94721 q^{8} -0.774179 q^{9} -0.864801 q^{11} +8.36467 q^{12} +0.643281 q^{13} +7.85659 q^{14} +16.2213 q^{16} -3.74185 q^{17} -2.13520 q^{18} +4.24993 q^{21} -2.38513 q^{22} -0.417460 q^{23} +14.8404 q^{24} +1.77418 q^{26} -5.63077 q^{27} +15.9713 q^{28} +9.70523 q^{29} -4.93349 q^{31} +24.8441 q^{32} -1.29021 q^{33} -10.3201 q^{34} -4.34056 q^{36} +6.36467 q^{37} +0.959723 q^{39} +4.01372 q^{41} +11.7214 q^{42} +2.05829 q^{43} -4.84864 q^{44} -1.15136 q^{46} +3.95396 q^{47} +24.2008 q^{48} +1.11474 q^{49} -5.58254 q^{51} +3.60665 q^{52} -10.9875 q^{53} -15.5297 q^{54} +28.3360 q^{56} +26.7672 q^{58} -2.45959 q^{59} +6.33479 q^{61} -13.6067 q^{62} -2.20536 q^{63} +36.0778 q^{64} -3.55843 q^{66} -2.53220 q^{67} -20.9793 q^{68} -0.622817 q^{69} +1.78213 q^{71} -7.70092 q^{72} +7.13090 q^{73} +17.5539 q^{74} -2.46350 q^{77} +2.64693 q^{78} -1.82452 q^{79} -6.07811 q^{81} +11.0699 q^{82} +7.43913 q^{83} +23.8279 q^{84} +5.67681 q^{86} +14.4794 q^{87} -8.60235 q^{88} -4.44588 q^{89} +1.83247 q^{91} -2.34056 q^{92} -7.36037 q^{93} +10.9051 q^{94} +37.0653 q^{96} -10.8541 q^{97} +3.07446 q^{98} +0.669511 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + 3 q^{3} + 5 q^{4} + 2 q^{6} + 4 q^{7} + 12 q^{8} + q^{9} - 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}+ \cdots + 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

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 $

$2$	2.75802	1.95021	0.975106	−	0.221739i	$-0.0711734\pi$
$2$	2.75802	1.95021	0.975106	+	0.221739i	$0.0711734\pi$
$3$	1.49192	0.861360	0.430680	−	0.902505i	$-0.358274\pi$
$3$	1.49192	0.861360	0.430680	+	0.902505i	$0.358274\pi$
$4$	5.60665	2.80333
$5$	0	0
$5$	0	0
$6$	4.11474	1.67983
$7$	2.84864	1.07668	0.538342	−	0.842727i	$-0.319051\pi$
$7$	2.84864	1.07668	0.538342	+	0.842727i	$0.319051\pi$
$8$	9.94721	3.51687
$9$	−0.774179	−0.258060
$10$	0	0
$11$	−0.864801	−0.260747	−0.130374	−	0.991465i	$-0.541618\pi$
$11$	−0.864801	−0.260747	−0.130374	+	0.991465i	$0.541618\pi$
$12$	8.36467	2.41467
$13$	0.643281	0.178414	0.0892070	−	0.996013i	$-0.471567\pi$
$13$	0.643281	0.178414	0.0892070	+	0.996013i	$0.471567\pi$
$14$	7.85659	2.09976
$15$	0	0
$16$	16.2213	4.05531
$17$	−3.74185	−0.907533	−0.453766	−	0.891121i	$-0.649920\pi$
$17$	−3.74185	−0.907533	−0.453766	+	0.891121i	$0.649920\pi$
$18$	−2.13520	−0.503271
$19$	0	0
$19$	0	0
$20$	0	0
$21$	4.24993	0.927412
$22$	−2.38513	−0.508512
$23$	−0.417460	−0.0870465	−0.0435233	−	0.999052i	$-0.513858\pi$
$23$	−0.417460	−0.0870465	−0.0435233	+	0.999052i	$0.513858\pi$
$24$	14.8404	3.02929
$25$	0	0
$26$	1.77418	0.347945
$27$	−5.63077	−1.08364
$28$	15.9713	3.01830
$29$	9.70523	1.80222	0.901108	−	0.433596i	$-0.142755\pi$
$29$	9.70523	1.80222	0.901108	+	0.433596i	$0.142755\pi$
$30$	0	0
$31$	−4.93349	−0.886081	−0.443041	−	0.896501i	$-0.646100\pi$
$31$	−4.93349	−0.886081	−0.443041	+	0.896501i	$0.646100\pi$
$32$	24.8441	4.39185
$33$	−1.29021	−0.224597
$34$	−10.3201	−1.76988
$35$	0	0
$36$	−4.34056	−0.723426
$37$	6.36467	1.04635	0.523173	−	0.852227i	$-0.324748\pi$
$37$	6.36467	1.04635	0.523173	+	0.852227i	$0.324748\pi$
$38$	0	0
$39$	0.959723	0.153679
$40$	0	0
$41$	4.01372	0.626837	0.313419	−	0.949615i	$-0.398526\pi$
$41$	4.01372	0.626837	0.313419	+	0.949615i	$0.398526\pi$
$42$	11.7214	1.80865
$43$	2.05829	0.313887	0.156944	−	0.987608i	$-0.449836\pi$
$43$	2.05829	0.313887	0.156944	+	0.987608i	$0.449836\pi$
$44$	−4.84864	−0.730960
$45$	0	0
$46$	−1.15136	−0.169759
$47$	3.95396	0.576744	0.288372	−	0.957518i	$-0.406886\pi$
$47$	3.95396	0.576744	0.288372	+	0.957518i	$0.406886\pi$
$48$	24.2008	3.49308
$49$	1.11474	0.159248
$50$	0	0
$51$	−5.58254	−0.781712
$52$	3.60665	0.500153
$53$	−10.9875	−1.50925	−0.754624	−	0.656158i	$-0.772181\pi$
$53$	−10.9875	−1.50925	−0.754624	+	0.656158i	$0.772181\pi$
$54$	−15.5297	−2.11333
$55$	0	0
$56$	28.3360	3.78656
$57$	0	0
$58$	26.7672	3.51470
$59$	−2.45959	−0.320212	−0.160106	−	0.987100i	$-0.551184\pi$
$59$	−2.45959	−0.320212	−0.160106	+	0.987100i	$0.551184\pi$
$60$	0	0
$61$	6.33479	0.811087	0.405543	−	0.914076i	$-0.367082\pi$
$61$	6.33479	0.811087	0.405543	+	0.914076i	$0.367082\pi$
$62$	−13.6067	−1.72805
$63$	−2.20536	−0.277849
$64$	36.0778	4.50973
$65$	0	0
$66$	−3.55843	−0.438012
$67$	−2.53220	−0.309357	−0.154678	−	0.987965i	$-0.549434\pi$
$67$	−2.53220	−0.309357	−0.154678	+	0.987965i	$0.549434\pi$
$68$	−20.9793	−2.54411
$69$	−0.622817	−0.0749783
$70$	0	0
$71$	1.78213	0.211500	0.105750	−	0.994393i	$-0.466276\pi$
$71$	1.78213	0.211500	0.105750	+	0.994393i	$0.466276\pi$
$72$	−7.70092	−0.907563
$73$	7.13090	0.834609	0.417304	−	0.908767i	$-0.362975\pi$
$73$	7.13090	0.834609	0.417304	+	0.908767i	$0.362975\pi$
$74$	17.5539	2.04060
$75$	0	0
$76$	0	0
$77$	−2.46350	−0.280742
$78$	2.64693	0.299706
$79$	−1.82452	−0.205275	−0.102637	−	0.994719i	$-0.532728\pi$
$79$	−1.82452	−0.205275	−0.102637	+	0.994719i	$0.532728\pi$
$80$	0	0
$81$	−6.07811	−0.675345
$82$	11.0699	1.22247
$83$	7.43913	0.816550	0.408275	−	0.912859i	$-0.366130\pi$
$83$	7.43913	0.816550	0.408275	+	0.912859i	$0.366130\pi$
$84$	23.8279	2.59984
$85$	0	0
$86$	5.67681	0.612146
$87$	14.4794	1.55236
$88$	−8.60235	−0.917014
$89$	−4.44588	−0.471262	−0.235631	−	0.971843i	$-0.575716\pi$
$89$	−4.44588	−0.471262	−0.235631	+	0.971843i	$0.575716\pi$
$90$	0	0
$91$	1.83247	0.192096
$92$	−2.34056	−0.244020
$93$	−7.36037	−0.763235
$94$	10.9051	1.12477
$95$	0	0
$96$	37.0653	3.78296
$97$	−10.8541	−1.10207	−0.551036	−	0.834482i	$-0.685767\pi$
$97$	−10.8541	−1.10207	−0.551036	+	0.834482i	$0.685767\pi$
$98$	3.07446	0.310567
$99$	0.669511	0.0672884
$100$	0	0
$101$	−5.29598	−0.526969	−0.263485	−	0.964664i	$-0.584872\pi$
$101$	−5.29598	−0.526969	−0.263485	+	0.964664i	$0.584872\pi$
$102$	−15.3967	−1.52450
$103$	−0.385134	−0.0379484	−0.0189742	−	0.999820i	$-0.506040\pi$
$103$	−0.385134	−0.0379484	−0.0189742	+	0.999820i	$0.506040\pi$
$104$	6.39885	0.627459
$105$	0	0
$106$	−30.3037	−2.94335
$107$	−6.43336	−0.621937	−0.310968	−	0.950420i	$-0.600653\pi$
$107$	−6.43336	−0.621937	−0.310968	+	0.950420i	$0.600653\pi$
$108$	−31.5698	−3.03780
$109$	−6.56882	−0.629179	−0.314590	−	0.949228i	$-0.601867\pi$
$109$	−6.56882	−0.629179	−0.314590	+	0.949228i	$0.601867\pi$
$110$	0	0
$111$	9.49557	0.901279
$112$	46.2085	4.36629
$113$	0.294513	0.0277054	0.0138527	−	0.999904i	$-0.495590\pi$
$113$	0.294513	0.0277054	0.0138527	+	0.999904i	$0.495590\pi$
$114$	0	0
$115$	0	0
$116$	54.4138	5.05220
$117$	−0.498015	−0.0460415
$118$	−6.78360	−0.624481
$119$	−10.6592	−0.977126
$120$	0	0
$121$	−10.2521	−0.932011
$122$	17.4715	1.58179
$123$	5.98814	0.539932
$124$	−27.6604	−2.48398
$125$	0	0
$126$	−6.08241	−0.541864
$127$	8.83492	0.783972	0.391986	−	0.919971i	$-0.371788\pi$
$127$	8.83492	0.783972	0.391986	+	0.919971i	$0.371788\pi$
$128$	49.8151	4.40308
$129$	3.07081	0.270370
$130$	0	0
$131$	20.9128	1.82716	0.913578	−	0.406662i	$-0.133307\pi$
$131$	20.9128	1.82716	0.913578	+	0.406662i	$0.133307\pi$
$132$	−7.23377	−0.629619
$133$	0	0
$134$	−6.98384	−0.603312
$135$	0	0
$136$	−37.2210	−3.19167
$137$	−5.21477	−0.445528	−0.222764	−	0.974872i	$-0.571508\pi$
$137$	−5.21477	−0.445528	−0.222764	+	0.974872i	$0.571508\pi$
$138$	−1.71774	−0.146224
$139$	−10.7238	−0.909584	−0.454792	−	0.890598i	$-0.650286\pi$
$139$	−10.7238	−0.909584	−0.454792	+	0.890598i	$0.650286\pi$
$140$	0	0
$141$	5.89898	0.496784
$142$	4.91514	0.412470
$143$	−0.556310	−0.0465210
$144$	−12.5582	−1.04651
$145$	0	0
$146$	19.6671	1.62766
$147$	1.66309	0.137170
$148$	35.6845	2.93325
$149$	−14.9116	−1.22160	−0.610801	−	0.791784i	$-0.709153\pi$
$149$	−14.9116	−1.22160	−0.610801	+	0.791784i	$0.709153\pi$
$150$	0	0
$151$	−21.4589	−1.74630	−0.873152	−	0.487448i	$-0.837928\pi$
$151$	−21.4589	−1.74630	−0.873152	+	0.487448i	$0.837928\pi$
$152$	0	0
$153$	2.89687	0.234198
$154$	−6.79438	−0.547507
$155$	0	0
$156$	5.38083	0.430811
$157$	2.43118	0.194029	0.0970145	−	0.995283i	$-0.469071\pi$
$157$	2.43118	0.194029	0.0970145	+	0.995283i	$0.469071\pi$
$158$	−5.03207	−0.400330
$159$	−16.3924	−1.30000
$160$	0	0
$161$	−1.18919	−0.0937216
$162$	−16.7635	−1.31707
$163$	−17.8175	−1.39558	−0.697788	−	0.716305i	$-0.745832\pi$
$163$	−17.8175	−1.39558	−0.697788	+	0.716305i	$0.745832\pi$
$164$	22.5035	1.75723
$165$	0	0
$166$	20.5172	1.59245
$167$	−0.405598	−0.0313861	−0.0156931	−	0.999877i	$-0.504995\pi$
$167$	−0.405598	−0.0313861	−0.0156931	+	0.999877i	$0.504995\pi$
$168$	42.2750	3.26159
$169$	−12.5862	−0.968168
$170$	0	0
$171$	0	0
$172$	11.5401	0.879928
$173$	18.0210	1.37011	0.685056	−	0.728490i	$-0.259778\pi$
$173$	18.0210	1.37011	0.685056	+	0.728490i	$0.259778\pi$
$174$	39.9344	3.02742
$175$	0	0
$176$	−14.0282	−1.05741
$177$	−3.66951	−0.275817
$178$	−12.2618	−0.919061
$179$	−20.1523	−1.50625	−0.753127	−	0.657875i	$-0.771455\pi$
$179$	−20.1523	−1.50625	−0.753127	+	0.657875i	$0.771455\pi$
$180$	0	0
$181$	17.1108	1.27184	0.635919	−	0.771756i	$-0.280621\pi$
$181$	17.1108	1.27184	0.635919	+	0.771756i	$0.280621\pi$
$182$	5.05399	0.374627
$183$	9.45099	0.698637
$184$	−4.15257	−0.306131
$185$	0	0
$186$	−20.3000	−1.48847
$187$	3.23596	0.236637
$188$	22.1685	1.61680
$189$	−16.0400	−1.16674
$190$	0	0
$191$	5.28080	0.382105	0.191053	−	0.981580i	$-0.438810\pi$
$191$	5.28080	0.382105	0.191053	+	0.981580i	$0.438810\pi$
$192$	53.8252	3.88450
$193$	18.0036	1.29593	0.647966	−	0.761670i	$-0.275620\pi$
$193$	18.0036	1.29593	0.647966	+	0.761670i	$0.275620\pi$
$194$	−29.9359	−2.14927
$195$	0	0
$196$	6.24993	0.446424
$197$	−8.07785	−0.575523	−0.287761	−	0.957702i	$-0.592911\pi$
$197$	−8.07785	−0.575523	−0.287761	+	0.957702i	$0.592911\pi$
$198$	1.84652	0.131227
$199$	1.40374	0.0995088	0.0497544	−	0.998761i	$-0.484156\pi$
$199$	1.40374	0.0995088	0.0497544	+	0.998761i	$0.484156\pi$
$200$	0	0
$201$	−3.77783	−0.266468
$202$	−14.6064	−1.02770
$203$	27.6467	1.94042
$204$	−31.2994	−2.19139
$205$	0	0
$206$	−1.06221	−0.0740074
$207$	0.323189	0.0224632
$208$	10.4348	0.723525
$209$	0	0
$210$	0	0
$211$	−18.9163	−1.30226	−0.651128	−	0.758968i	$-0.725704\pi$
$211$	−18.9163	−1.30226	−0.651128	+	0.758968i	$0.725704\pi$
$212$	−61.6030	−4.23091
$213$	2.65879	0.182178
$214$	−17.7433	−1.21291
$215$	0	0
$216$	−56.0104	−3.81103
$217$	−14.0537	−0.954030
$218$	−18.1169	−1.22703
$219$	10.6387	0.718898
$220$	0	0
$221$	−2.40706	−0.161917
$222$	26.1889	1.75769
$223$	−16.1480	−1.08135	−0.540675	−	0.841231i	$-0.681831\pi$
$223$	−16.1480	−1.08135	−0.540675	+	0.841231i	$0.681831\pi$
$224$	70.7718	4.72864
$225$	0	0
$226$	0.812271	0.0540315
$227$	26.3186	1.74683	0.873414	−	0.486978i	$-0.161901\pi$
$227$	26.3186	1.74683	0.873414	+	0.486978i	$0.161901\pi$
$228$	0	0
$229$	−13.3323	−0.881026	−0.440513	−	0.897746i	$-0.645203\pi$
$229$	−13.3323	−0.881026	−0.440513	+	0.897746i	$0.645203\pi$
$230$	0	0
$231$	−3.67535	−0.241820
$232$	96.5399	6.33816
$233$	−25.3094	−1.65808	−0.829038	−	0.559192i	$-0.811111\pi$
$233$	−25.3094	−1.65808	−0.829038	+	0.559192i	$0.811111\pi$
$234$	−1.37353	−0.0897907
$235$	0	0
$236$	−13.7901	−0.897658
$237$	−2.72204	−0.176815
$238$	−29.3982	−1.90560
$239$	−23.5500	−1.52332	−0.761660	−	0.647977i	$-0.775615\pi$
$239$	−23.5500	−1.52332	−0.761660	+	0.647977i	$0.775615\pi$
$240$	0	0
$241$	−8.38415	−0.540071	−0.270035	−	0.962850i	$-0.587035\pi$
$241$	−8.38415	−0.540071	−0.270035	+	0.962850i	$0.587035\pi$
$242$	−28.2755	−1.81762
$243$	7.82426	0.501927
$244$	35.5170	2.27374
$245$	0	0
$246$	16.5154	1.05298
$247$	0	0
$248$	−49.0745	−3.11623
$249$	11.0986	0.703343
$250$	0	0
$251$	18.2478	1.15179	0.575896	−	0.817523i	$-0.304653\pi$
$251$	18.2478	1.15179	0.575896	+	0.817523i	$0.304653\pi$
$252$	−12.3647	−0.778901
$253$	0.361020	0.0226971
$254$	24.3669	1.52891
$255$	0	0
$256$	65.2353	4.07720
$257$	14.0998	0.879520	0.439760	−	0.898115i	$-0.355064\pi$
$257$	14.0998	0.879520	0.439760	+	0.898115i	$0.355064\pi$
$258$	8.46934	0.527278
$259$	18.1306	1.12658
$260$	0	0
$261$	−7.51359	−0.465079
$262$	57.6778	3.56334
$263$	6.41071	0.395301	0.197651	−	0.980273i	$-0.436669\pi$
$263$	6.41071	0.395301	0.197651	+	0.980273i	$0.436669\pi$
$264$	−12.8340	−0.789879
$265$	0	0
$266$	0	0
$267$	−6.63288	−0.405926
$268$	−14.1971	−0.867229
$269$	−17.9911	−1.09694	−0.548469	−	0.836171i	$-0.684789\pi$
$269$	−17.9911	−1.09694	−0.548469	+	0.836171i	$0.684789\pi$
$270$	0	0
$271$	11.8819	0.721774	0.360887	−	0.932609i	$-0.382474\pi$
$271$	11.8819	0.721774	0.360887	+	0.932609i	$0.382474\pi$
$272$	−60.6976	−3.68033
$273$	2.73390	0.165463
$274$	−14.3824	−0.868874
$275$	0	0
$276$	−3.49192	−0.210189
$277$	−23.6240	−1.41943	−0.709715	−	0.704489i	$-0.751176\pi$
$277$	−23.6240	−1.41943	−0.709715	+	0.704489i	$0.751176\pi$
$278$	−29.5765	−1.77388
$279$	3.81941	0.228662
$280$	0	0
$281$	−13.8093	−0.823794	−0.411897	−	0.911230i	$-0.635134\pi$
$281$	−13.8093	−0.823794	−0.411897	+	0.911230i	$0.635134\pi$
$282$	16.2695	0.968834
$283$	11.7574	0.698903	0.349451	−	0.936954i	$-0.386368\pi$
$283$	11.7574	0.698903	0.349451	+	0.936954i	$0.386368\pi$
$284$	9.99179	0.592904
$285$	0	0
$286$	−1.53431	−0.0907257
$287$	11.4336	0.674905
$288$	−19.2338	−1.13336
$289$	−2.99854	−0.176384
$290$	0	0
$291$	−16.1935	−0.949279
$292$	39.9805	2.33968
$293$	−27.0576	−1.58072	−0.790362	−	0.612640i	$-0.790108\pi$
$293$	−27.0576	−1.58072	−0.790362	+	0.612640i	$0.790108\pi$
$294$	4.58684	0.267510
$295$	0	0
$296$	63.3107	3.67986
$297$	4.86949	0.282557
$298$	−41.1263	−2.38238
$299$	−0.268544	−0.0155303
$300$	0	0
$301$	5.86334	0.337957
$302$	−59.1841	−3.40566
$303$	−7.90117	−0.453910
$304$	0	0
$305$	0	0
$306$	7.98960	0.456735
$307$	8.83824	0.504425	0.252212	−	0.967672i	$-0.418842\pi$
$307$	8.83824	0.504425	0.252212	+	0.967672i	$0.418842\pi$
$308$	−13.8120	−0.787012
$309$	−0.574589	−0.0326872
$310$	0	0
$311$	−0.651493	−0.0369428	−0.0184714	−	0.999829i	$-0.505880\pi$
$311$	−0.651493	−0.0369428	−0.0184714	+	0.999829i	$0.505880\pi$
$312$	9.54656	0.540468
$313$	2.96556	0.167623	0.0838116	−	0.996482i	$-0.473291\pi$
$313$	2.96556	0.167623	0.0838116	+	0.996482i	$0.473291\pi$
$314$	6.70523	0.378398
$315$	0	0
$316$	−10.2295	−0.575453
$317$	−10.3799	−0.582991	−0.291495	−	0.956572i	$-0.594153\pi$
$317$	−10.3799	−0.582991	−0.291495	+	0.956572i	$0.594153\pi$
$318$	−45.2106	−2.53528
$319$	−8.39309	−0.469923
$320$	0	0
$321$	−9.59805	−0.535711
$322$	−3.27981	−0.182777
$323$	0	0
$324$	−34.0778	−1.89321
$325$	0	0
$326$	−49.1410	−2.72167
$327$	−9.80015	−0.541949
$328$	39.9253	2.20450
$329$	11.2634	0.620971
$330$	0	0
$331$	−15.0922	−0.829543	−0.414772	−	0.909926i	$-0.636139\pi$
$331$	−15.0922	−0.829543	−0.414772	+	0.909926i	$0.636139\pi$
$332$	41.7086	2.28906
$333$	−4.92740	−0.270020
$334$	−1.11865	−0.0612096
$335$	0	0
$336$	68.9393	3.76095
$337$	15.7974	0.860541	0.430271	−	0.902700i	$-0.358418\pi$
$337$	15.7974	0.860541	0.430271	+	0.902700i	$0.358418\pi$
$338$	−34.7129	−1.88813
$339$	0.439389	0.0238643
$340$	0	0
$341$	4.26649	0.231043
$342$	0	0
$343$	−16.7650	−0.905224
$344$	20.4743	1.10390
$345$	0	0
$346$	49.7023	2.67201
$347$	21.3522	1.14624	0.573122	−	0.819470i	$-0.305732\pi$
$347$	21.3522	1.14624	0.573122	+	0.819470i	$0.305732\pi$
$348$	81.1810	4.35176
$349$	−32.3897	−1.73378	−0.866891	−	0.498497i	$-0.833885\pi$
$349$	−32.3897	−1.73378	−0.866891	+	0.498497i	$0.833885\pi$
$350$	0	0
$351$	−3.62217	−0.193337
$352$	−21.4852	−1.14516
$353$	−0.730583	−0.0388850	−0.0194425	−	0.999811i	$-0.506189\pi$
$353$	−0.730583	−0.0388850	−0.0194425	+	0.999811i	$0.506189\pi$
$354$	−10.1206	−0.537902
$355$	0	0
$356$	−24.9265	−1.32110
$357$	−15.9026	−0.841657
$358$	−55.5804	−2.93751
$359$	−26.8496	−1.41707	−0.708533	−	0.705677i	$-0.750643\pi$
$359$	−26.8496	−1.41707	−0.708533	+	0.705677i	$0.750643\pi$
$360$	0	0
$361$	0	0
$362$	47.1919	2.48035
$363$	−15.2953	−0.802796
$364$	10.2740	0.538506
$365$	0	0
$366$	26.0660	1.36249
$367$	22.9643	1.19873	0.599364	−	0.800477i	$-0.295420\pi$
$367$	22.9643	1.19873	0.599364	+	0.800477i	$0.295420\pi$
$368$	−6.77173	−0.353001
$369$	−3.10734	−0.161761
$370$	0	0
$371$	−31.2994	−1.62498
$372$	−41.2670	−2.13960
$373$	29.5305	1.52903	0.764515	−	0.644606i	$-0.222979\pi$
$373$	29.5305	1.52903	0.764515	+	0.644606i	$0.222979\pi$
$374$	8.92482	0.461492
$375$	0	0
$376$	39.3308	2.02833
$377$	6.24319	0.321541
$378$	−44.2386	−2.27539
$379$	−17.5117	−0.899517	−0.449759	−	0.893150i	$-0.648490\pi$
$379$	−17.5117	−0.899517	−0.449759	+	0.893150i	$0.648490\pi$
$380$	0	0
$381$	13.1810	0.675282
$382$	14.5645	0.745186
$383$	8.10652	0.414224	0.207112	−	0.978317i	$-0.433594\pi$
$383$	8.10652	0.414224	0.207112	+	0.978317i	$0.433594\pi$
$384$	74.3201	3.79263
$385$	0	0
$386$	49.6544	2.52734
$387$	−1.59349	−0.0810016
$388$	−60.8554	−3.08947
$389$	17.3078	0.877542	0.438771	−	0.898599i	$-0.355414\pi$
$389$	17.3078	0.877542	0.438771	+	0.898599i	$0.355414\pi$
$390$	0	0
$391$	1.56208	0.0789976
$392$	11.0885	0.560054
$393$	31.2001	1.57384
$394$	−22.2788	−1.12239
$395$	0	0
$396$	3.75372	0.188631
$397$	11.3894	0.571619	0.285810	−	0.958286i	$-0.407737\pi$
$397$	11.3894	0.571619	0.285810	+	0.958286i	$0.407737\pi$
$398$	3.87155	0.194063
$399$	0	0
$400$	0	0
$401$	8.93861	0.446373	0.223186	−	0.974776i	$-0.428354\pi$
$401$	8.93861	0.446373	0.223186	+	0.974776i	$0.428354\pi$
$402$	−10.4193	−0.519668
$403$	−3.17362	−0.158089
$404$	−29.6927	−1.47727
$405$	0	0
$406$	76.2500	3.78422
$407$	−5.50417	−0.272832
$408$	−55.5307	−2.74918
$409$	6.54471	0.323615	0.161808	−	0.986822i	$-0.448268\pi$
$409$	6.54471	0.323615	0.161808	+	0.986822i	$0.448268\pi$
$410$	0	0
$411$	−7.78001	−0.383760
$412$	−2.15931	−0.106382
$413$	−7.00649	−0.344767
$414$	0.891361	0.0438080
$415$	0	0
$416$	15.9817	0.783568
$417$	−15.9991	−0.783479
$418$	0	0
$419$	21.8441	1.06715	0.533576	−	0.845752i	$-0.320848\pi$
$419$	21.8441	1.06715	0.533576	+	0.845752i	$0.320848\pi$
$420$	0	0
$421$	29.3434	1.43011	0.715054	−	0.699069i	$-0.246402\pi$
$421$	29.3434	1.43011	0.715054	+	0.699069i	$0.246402\pi$
$422$	−52.1716	−2.53967
$423$	−3.06107	−0.148834
$424$	−109.295	−5.30783
$425$	0	0
$426$	7.33299	0.355285
$427$	18.0455	0.873284
$428$	−36.0696	−1.74349
$429$	−0.829969	−0.0400713
$430$	0	0
$431$	12.8867	0.620732	0.310366	−	0.950617i	$-0.399548\pi$
$431$	12.8867	0.620732	0.310366	+	0.950617i	$0.399548\pi$
$432$	−91.3381	−4.39451
$433$	−13.8429	−0.665246	−0.332623	−	0.943060i	$-0.607934\pi$
$433$	−13.8429	−0.665246	−0.332623	+	0.943060i	$0.607934\pi$
$434$	−38.7604	−1.86056
$435$	0	0
$436$	−36.8291	−1.76379
$437$	0	0
$438$	29.3418	1.40200
$439$	0.0708081	0.00337948	0.00168974	−	0.999999i	$-0.499462\pi$
$439$	0.0708081	0.00337948	0.00168974	+	0.999999i	$0.499462\pi$
$440$	0	0
$441$	−0.863005	−0.0410955
$442$	−6.63872	−0.315772
$443$	3.78914	0.180027	0.0900137	−	0.995941i	$-0.471309\pi$
$443$	3.78914	0.180027	0.0900137	+	0.995941i	$0.471309\pi$
$444$	53.2384	2.52658
$445$	0	0
$446$	−44.5365	−2.10886
$447$	−22.2468	−1.05224
$448$	102.773	4.85555
$449$	26.5765	1.25422	0.627112	−	0.778929i	$-0.284237\pi$
$449$	26.5765	1.25422	0.627112	+	0.778929i	$0.284237\pi$
$450$	0	0
$451$	−3.47106	−0.163446
$452$	1.65123	0.0776674
$453$	−32.0150	−1.50420
$454$	72.5872	3.40669
$455$	0	0
$456$	0	0
$457$	33.1523	1.55080	0.775400	−	0.631471i	$-0.217548\pi$
$457$	33.1523	1.55080	0.775400	+	0.631471i	$0.217548\pi$
$458$	−36.7708	−1.71819
$459$	21.0695	0.983440
$460$	0	0
$461$	−19.2536	−0.896729	−0.448364	−	0.893851i	$-0.647993\pi$
$461$	−19.2536	−0.896729	−0.448364	+	0.893851i	$0.647993\pi$
$462$	−10.1367	−0.471600
$463$	−39.1713	−1.82044	−0.910222	−	0.414120i	$-0.864089\pi$
$463$	−39.1713	−1.82044	−0.910222	+	0.414120i	$0.864089\pi$
$464$	157.431	7.30855
$465$	0	0
$466$	−69.8038	−3.23360
$467$	39.0650	1.80771	0.903856	−	0.427836i	$-0.140724\pi$
$467$	39.0650	1.80771	0.903856	+	0.427836i	$0.140724\pi$
$468$	−2.79220	−0.129069
$469$	−7.21331	−0.333080
$470$	0	0
$471$	3.62712	0.167129
$472$	−24.4661	−1.12614
$473$	−1.78001	−0.0818452
$474$	−7.50743	−0.344828
$475$	0	0
$476$	−59.7623	−2.73920
$477$	8.50629	0.389476
$478$	−64.9512	−2.97080
$479$	−24.7550	−1.13109	−0.565543	−	0.824718i	$-0.691334\pi$
$479$	−24.7550	−1.13109	−0.565543	+	0.824718i	$0.691334\pi$
$480$	0	0
$481$	4.09427	0.186683
$482$	−23.1236	−1.05325
$483$	−1.77418	−0.0807280
$484$	−57.4801	−2.61273
$485$	0	0
$486$	21.5794	0.978863
$487$	21.8871	0.991797	0.495899	−	0.868380i	$-0.334839\pi$
$487$	21.8871	0.991797	0.495899	+	0.868380i	$0.334839\pi$
$488$	63.0135	2.85249
$489$	−26.5823	−1.20209
$490$	0	0
$491$	9.39553	0.424014	0.212007	−	0.977268i	$-0.432000\pi$
$491$	9.39553	0.424014	0.212007	+	0.977268i	$0.432000\pi$
$492$	33.5734	1.51361
$493$	−36.3155	−1.63557
$494$	0	0
$495$	0	0
$496$	−80.0275	−3.59334
$497$	5.07664	0.227719
$498$	30.6100	1.37167
$499$	24.9115	1.11519	0.557596	−	0.830112i	$-0.311724\pi$
$499$	24.9115	1.11519	0.557596	+	0.830112i	$0.311724\pi$
$500$	0	0
$501$	−0.605119	−0.0270347
$502$	50.3278	2.24624
$503$	31.3180	1.39640	0.698200	−	0.715903i	$-0.253985\pi$
$503$	31.3180	1.39640	0.698200	+	0.715903i	$0.253985\pi$
$504$	−21.9371	−0.977158
$505$	0	0
$506$	0.995699	0.0442642
$507$	−18.7776	−0.833941
$508$	49.5343	2.19773
$509$	9.66619	0.428446	0.214223	−	0.976785i	$-0.431278\pi$
$509$	9.66619	0.428446	0.214223	+	0.976785i	$0.431278\pi$
$510$	0	0
$511$	20.3133	0.898609
$512$	80.2896	3.54833
$513$	0	0
$514$	38.8874	1.71525
$515$	0	0
$516$	17.2170	0.757934
$517$	−3.41938	−0.150384
$518$	50.0046	2.19708
$519$	26.8859	1.18016
$520$	0	0
$521$	0.982633	0.0430499	0.0215250	−	0.999768i	$-0.493148\pi$
$521$	0.982633	0.0430499	0.0215250	+	0.999768i	$0.493148\pi$
$522$	−20.7226	−0.907003
$523$	39.7209	1.73687	0.868436	−	0.495801i	$-0.165125\pi$
$523$	39.7209	1.73687	0.868436	+	0.495801i	$0.165125\pi$
$524$	117.251	5.12212
$525$	0	0
$526$	17.6809	0.770922
$527$	18.4604	0.804148
$528$	−20.9289	−0.910812
$529$	−22.8257	−0.992423
$530$	0	0
$531$	1.90417	0.0826337
$532$	0	0
$533$	2.58195	0.111837
$534$	−18.2936	−0.791642
$535$	0	0
$536$	−25.1883	−1.08797
$537$	−30.0656	−1.29743
$538$	−49.6198	−2.13926
$539$	−0.964024	−0.0415234
$540$	0	0
$541$	30.7775	1.32323	0.661614	−	0.749845i	$-0.269872\pi$
$541$	30.7775	1.32323	0.661614	+	0.749845i	$0.269872\pi$
$542$	32.7705	1.40761
$543$	25.5280	1.09551
$544$	−92.9629	−3.98575
$545$	0	0
$546$	7.54015	0.322688
$547$	−17.8657	−0.763884	−0.381942	−	0.924186i	$-0.624745\pi$
$547$	−17.8657	−0.763884	−0.381942	+	0.924186i	$0.624745\pi$
$548$	−29.2374	−1.24896
$549$	−4.90426	−0.209309
$550$	0	0
$551$	0	0
$552$	−6.19529	−0.263689
$553$	−5.19741	−0.221016
$554$	−65.1554	−2.76819
$555$	0	0
$556$	−60.1248	−2.54986
$557$	10.6576	0.451575	0.225787	−	0.974177i	$-0.427505\pi$
$557$	10.6576	0.451575	0.225787	+	0.974177i	$0.427505\pi$
$558$	10.5340	0.445939
$559$	1.32406	0.0560019
$560$	0	0
$561$	4.82778	0.203829
$562$	−38.0863	−1.60657
$563$	7.75961	0.327029	0.163514	−	0.986541i	$-0.447717\pi$
$563$	7.75961	0.327029	0.163514	+	0.986541i	$0.447717\pi$
$564$	33.0735	1.39265
$565$	0	0
$566$	32.4270	1.36301
$567$	−17.3143	−0.727133
$568$	17.7272	0.743818
$569$	−5.72754	−0.240111	−0.120056	−	0.992767i	$-0.538307\pi$
$569$	−5.72754	−0.240111	−0.120056	+	0.992767i	$0.538307\pi$
$570$	0	0
$571$	−20.8347	−0.871903	−0.435952	−	0.899970i	$-0.643588\pi$
$571$	−20.8347	−0.871903	−0.435952	+	0.899970i	$0.643588\pi$
$572$	−3.11904	−0.130413
$573$	7.87852	0.329130
$574$	31.5341	1.31621
$575$	0	0
$576$	−27.9307	−1.16378
$577$	5.11190	0.212811	0.106406	−	0.994323i	$-0.466066\pi$
$577$	5.11190	0.212811	0.106406	+	0.994323i	$0.466066\pi$
$578$	−8.27001	−0.343987
$579$	26.8600	1.11626
$580$	0	0
$581$	21.1914	0.879167
$582$	−44.6619	−1.85130
$583$	9.50199	0.393532
$584$	70.9325	2.93521
$585$	0	0
$586$	−74.6254	−3.08275
$587$	10.6692	0.440367	0.220184	−	0.975458i	$-0.429334\pi$
$587$	10.6692	0.440367	0.220184	+	0.975458i	$0.429334\pi$
$588$	9.32439	0.384531
$589$	0	0
$590$	0	0
$591$	−12.0515	−0.495732
$592$	103.243	4.24326
$593$	17.0027	0.698216	0.349108	−	0.937083i	$-0.386485\pi$
$593$	17.0027	0.698216	0.349108	+	0.937083i	$0.386485\pi$
$594$	13.4301	0.551045
$595$	0	0
$596$	−83.6040	−3.42455
$597$	2.09427	0.0857128
$598$	−0.740650	−0.0302874
$599$	−28.6751	−1.17163	−0.585816	−	0.810444i	$-0.699226\pi$
$599$	−28.6751	−1.17163	−0.585816	+	0.810444i	$0.699226\pi$
$600$	0	0
$601$	−27.4370	−1.11918	−0.559590	−	0.828770i	$-0.689041\pi$
$601$	−27.4370	−1.11918	−0.559590	+	0.828770i	$0.689041\pi$
$602$	16.1712	0.659088
$603$	1.96037	0.0798326
$604$	−120.313	−4.89546
$605$	0	0
$606$	−21.7915	−0.885221
$607$	−17.7547	−0.720639	−0.360320	−	0.932829i	$-0.617332\pi$
$607$	−17.7547	−0.720639	−0.360320	+	0.932829i	$0.617332\pi$
$608$	0	0
$609$	41.2466	1.67140
$610$	0	0
$611$	2.54351	0.102899
$612$	16.2417	0.656533
$613$	−34.6391	−1.39906	−0.699530	−	0.714603i	$-0.746607\pi$
$613$	−34.6391	−1.39906	−0.699530	+	0.714603i	$0.746607\pi$
$614$	24.3760	0.983736
$615$	0	0
$616$	−24.5050	−0.987334
$617$	−4.46569	−0.179782	−0.0898909	−	0.995952i	$-0.528652\pi$
$617$	−4.46569	−0.179782	−0.0898909	+	0.995952i	$0.528652\pi$
$618$	−1.58472	−0.0637470
$619$	−17.9112	−0.719913	−0.359957	−	0.932969i	$-0.617209\pi$
$619$	−17.9112	−0.719913	−0.359957	+	0.932969i	$0.617209\pi$
$620$	0	0
$621$	2.35062	0.0943272
$622$	−1.79683	−0.0720463
$623$	−12.6647	−0.507400
$624$	15.5679	0.623215
$625$	0	0
$626$	8.17906	0.326901
$627$	0	0
$628$	13.6308	0.543927
$629$	−23.8157	−0.949593
$630$	0	0
$631$	4.96881	0.197805	0.0989026	−	0.995097i	$-0.468467\pi$
$631$	4.96881	0.197805	0.0989026	+	0.995097i	$0.468467\pi$
$632$	−18.1489	−0.721925
$633$	−28.2216	−1.12171
$634$	−28.6278	−1.13696
$635$	0	0
$636$	−91.9067	−3.64434
$637$	0.717088	0.0284121
$638$	−23.1483	−0.916449
$639$	−1.37969	−0.0545796
$640$	0	0
$641$	37.9521	1.49902	0.749508	−	0.661995i	$-0.230290\pi$
$641$	37.9521	1.49902	0.749508	+	0.661995i	$0.230290\pi$
$642$	−26.4716	−1.04475
$643$	−35.2502	−1.39013	−0.695067	−	0.718945i	$-0.744625\pi$
$643$	−35.2502	−1.39013	−0.695067	+	0.718945i	$0.744625\pi$
$644$	−6.66740	−0.262732
$645$	0	0
$646$	0	0
$647$	−35.5219	−1.39651	−0.698254	−	0.715850i	$-0.746040\pi$
$647$	−35.5219	−1.39651	−0.698254	+	0.715850i	$0.746040\pi$
$648$	−60.4602	−2.37510
$649$	2.12706	0.0834943
$650$	0	0
$651$	−20.9670	−0.821762
$652$	−99.8966	−3.91225
$653$	−8.02411	−0.314008	−0.157004	−	0.987598i	$-0.550184\pi$
$653$	−8.02411	−0.314008	−0.157004	+	0.987598i	$0.550184\pi$
$654$	−27.0290	−1.05692
$655$	0	0
$656$	65.1075	2.54202
$657$	−5.52059	−0.215379
$658$	31.0646	1.21102
$659$	47.2195	1.83941	0.919706	−	0.392608i	$-0.128427\pi$
$659$	47.2195	1.83941	0.919706	+	0.392608i	$0.128427\pi$
$660$	0	0
$661$	26.1159	1.01579	0.507896	−	0.861418i	$-0.330423\pi$
$661$	26.1159	1.01579	0.507896	+	0.861418i	$0.330423\pi$
$662$	−41.6246	−1.61778
$663$	−3.59114	−0.139468
$664$	73.9986	2.87170
$665$	0	0
$666$	−13.5898	−0.526596
$667$	−4.05155	−0.156877
$668$	−2.27405	−0.0879856
$669$	−24.0915	−0.931431
$670$	0	0
$671$	−5.47833	−0.211489
$672$	105.586	4.07306
$673$	15.3820	0.592931	0.296466	−	0.955044i	$-0.404192\pi$
$673$	15.3820	0.592931	0.296466	+	0.955044i	$0.404192\pi$
$674$	43.5696	1.67824
$675$	0	0
$676$	−70.5664	−2.71409
$677$	24.4763	0.940701	0.470350	−	0.882480i	$-0.344128\pi$
$677$	24.4763	0.940701	0.470350	+	0.882480i	$0.344128\pi$
$678$	1.21184	0.0465405
$679$	−30.9195	−1.18658
$680$	0	0
$681$	39.2652	1.50465
$682$	11.7670	0.450583
$683$	−17.8502	−0.683018	−0.341509	−	0.939879i	$-0.610938\pi$
$683$	−17.8502	−0.683018	−0.341509	+	0.939879i	$0.610938\pi$
$684$	0	0
$685$	0	0
$686$	−46.2381	−1.76538
$687$	−19.8908	−0.758880
$688$	33.3881	1.27291
$689$	−7.06804	−0.269271
$690$	0	0
$691$	−9.27242	−0.352739	−0.176370	−	0.984324i	$-0.556435\pi$
$691$	−9.27242	−0.352739	−0.176370	+	0.984324i	$0.556435\pi$
$692$	101.038	3.84087
$693$	1.90719	0.0724483
$694$	58.8896	2.23542
$695$	0	0
$696$	144.030	5.45943
$697$	−15.0187	−0.568875
$698$	−89.3314	−3.38124
$699$	−37.7596	−1.42820
$700$	0	0
$701$	−7.68906	−0.290412	−0.145206	−	0.989401i	$-0.546384\pi$
$701$	−7.68906	−0.290412	−0.145206	+	0.989401i	$0.546384\pi$
$702$	−9.98999	−0.377048
$703$	0	0
$704$	−31.2001	−1.17590
$705$	0	0
$706$	−2.01496	−0.0758340
$707$	−15.0863	−0.567379
$708$	−20.5737	−0.773206
$709$	24.4375	0.917769	0.458885	−	0.888496i	$-0.348249\pi$
$709$	24.4375	0.917769	0.458885	+	0.888496i	$0.348249\pi$
$710$	0	0
$711$	1.41251	0.0529732
$712$	−44.2241	−1.65737
$713$	2.05954	0.0771303
$714$	−43.8597	−1.64141
$715$	0	0
$716$	−112.987	−4.22252
$717$	−35.1346	−1.31213
$718$	−74.0516	−2.76358
$719$	−22.1126	−0.824662	−0.412331	−	0.911034i	$-0.635285\pi$
$719$	−22.1126	−0.824662	−0.412331	+	0.911034i	$0.635285\pi$
$720$	0	0
$721$	−1.09711	−0.0408584
$722$	0	0
$723$	−12.5085	−0.465195
$724$	95.9345	3.56538
$725$	0	0
$726$	−42.1848	−1.56562
$727$	29.0494	1.07738	0.538692	−	0.842503i	$-0.318919\pi$
$727$	29.0494	1.07738	0.538692	+	0.842503i	$0.318919\pi$
$728$	18.2280	0.675575
$729$	29.9075	1.10768
$730$	0	0
$731$	−7.70184	−0.284863
$732$	52.9884	1.95851
$733$	−14.5428	−0.537151	−0.268576	−	0.963259i	$-0.586553\pi$
$733$	−14.5428	−0.537151	−0.268576	+	0.963259i	$0.586553\pi$
$734$	63.3360	2.33777
$735$	0	0
$736$	−10.3714	−0.382296
$737$	2.18984	0.0806640
$738$	−8.57009	−0.315469
$739$	−4.75596	−0.174951	−0.0874754	−	0.996167i	$-0.527880\pi$
$739$	−4.75596	−0.174951	−0.0874754	+	0.996167i	$0.527880\pi$
$740$	0	0
$741$	0	0
$742$	−86.3242	−3.16906
$743$	5.87705	0.215608	0.107804	−	0.994172i	$-0.465618\pi$
$743$	5.87705	0.215608	0.107804	+	0.994172i	$0.465618\pi$
$744$	−73.2151	−2.68420
$745$	0	0
$746$	81.4455	2.98193
$747$	−5.75922	−0.210719
$748$	18.1429	0.663370
$749$	−18.3263	−0.669629
$750$	0	0
$751$	−1.62096	−0.0591498	−0.0295749	−	0.999563i	$-0.509415\pi$
$751$	−1.62096	−0.0591498	−0.0295749	+	0.999563i	$0.509415\pi$
$752$	64.1382	2.33888
$753$	27.2243	0.992107
$754$	17.2188	0.627072
$755$	0	0
$756$	−89.9308	−3.27075
$757$	28.1135	1.02180	0.510901	−	0.859639i	$-0.329312\pi$
$757$	28.1135	1.02180	0.510901	+	0.859639i	$0.329312\pi$
$758$	−48.2976	−1.75425
$759$	0.538612	0.0195504
$760$	0	0
$761$	20.1663	0.731027	0.365514	−	0.930806i	$-0.380893\pi$
$761$	20.1663	0.731027	0.365514	+	0.930806i	$0.380893\pi$
$762$	36.3534	1.31694
$763$	−18.7122	−0.677427
$764$	29.6076	1.07117
$765$	0	0
$766$	22.3579	0.807825
$767$	−1.58221	−0.0571303
$768$	97.3257	3.51194
$769$	45.3047	1.63373	0.816865	−	0.576829i	$-0.195710\pi$
$769$	45.3047	1.63373	0.816865	+	0.576829i	$0.195710\pi$
$770$	0	0
$771$	21.0357	0.757583
$772$	100.940	3.63292
$773$	−20.1762	−0.725686	−0.362843	−	0.931850i	$-0.618194\pi$
$773$	−20.1762	−0.725686	−0.362843	+	0.931850i	$0.618194\pi$
$774$	−4.39487	−0.157970
$775$	0	0
$776$	−107.968	−3.87584
$777$	27.0494	0.970393
$778$	47.7353	1.71139
$779$	0	0
$780$	0	0
$781$	−1.54119	−0.0551480
$782$	4.30823	0.154062
$783$	−54.6479	−1.95296
$784$	18.0824	0.645800
$785$	0	0
$786$	86.0505	3.06932
$787$	−46.1385	−1.64466	−0.822331	−	0.569010i	$-0.807327\pi$
$787$	−46.1385	−1.64466	−0.822331	+	0.569010i	$0.807327\pi$
$788$	−45.2897	−1.61338
$789$	9.56426	0.340497
$790$	0	0
$791$	0.838961	0.0298300
$792$	6.65976	0.236644
$793$	4.07505	0.144709
$794$	31.4122	1.11478
$795$	0	0
$796$	7.87031	0.278956
$797$	−1.86497	−0.0660606	−0.0330303	−	0.999454i	$-0.510516\pi$
$797$	−1.86497	−0.0660606	−0.0330303	+	0.999454i	$0.510516\pi$
$798$	0	0
$799$	−14.7951	−0.523414
$800$	0	0
$801$	3.44191	0.121614
$802$	24.6528	0.870522
$803$	−6.16681	−0.217622
$804$	−21.1810	−0.746996
$805$	0	0
$806$	−8.75290	−0.308308
$807$	−26.8413	−0.944859
$808$	−52.6802	−1.85328
$809$	18.2267	0.640816	0.320408	−	0.947280i	$-0.396180\pi$
$809$	18.2267	0.640816	0.320408	+	0.947280i	$0.396180\pi$
$810$	0	0
$811$	20.9779	0.736634	0.368317	−	0.929700i	$-0.379934\pi$
$811$	20.9779	0.736634	0.368317	+	0.929700i	$0.379934\pi$
$812$	155.005	5.43962
$813$	17.7268	0.621707
$814$	−15.1806	−0.532079
$815$	0	0
$816$	−90.5558	−3.17009
$817$	0	0
$818$	18.0504	0.631118
$819$	−1.41866	−0.0495721
$820$	0	0
$821$	−22.0867	−0.770829	−0.385415	−	0.922743i	$-0.625942\pi$
$821$	−22.0867	−0.770829	−0.385415	+	0.922743i	$0.625942\pi$
$822$	−21.4574	−0.748413
$823$	−15.9769	−0.556921	−0.278461	−	0.960448i	$-0.589824\pi$
$823$	−15.9769	−0.556921	−0.278461	+	0.960448i	$0.589824\pi$
$824$	−3.83101	−0.133460
$825$	0	0
$826$	−19.3240	−0.672368
$827$	49.2009	1.71088	0.855441	−	0.517901i	$-0.173286\pi$
$827$	49.2009	1.71088	0.855441	+	0.517901i	$0.173286\pi$
$828$	1.81201	0.0629717
$829$	35.8564	1.24534	0.622672	−	0.782483i	$-0.286047\pi$
$829$	35.8564	1.24534	0.622672	+	0.782483i	$0.286047\pi$
$830$	0	0
$831$	−35.2451	−1.22264
$832$	23.2082	0.804599
$833$	−4.17118	−0.144523
$834$	−44.1257	−1.52795
$835$	0	0
$836$	0	0
$837$	27.7794	0.960195
$838$	60.2463	2.08117
$839$	25.4830	0.879770	0.439885	−	0.898054i	$-0.355019\pi$
$839$	25.4830	0.879770	0.439885	+	0.898054i	$0.355019\pi$
$840$	0	0
$841$	65.1914	2.24798
$842$	80.9294	2.78901
$843$	−20.6024	−0.709583
$844$	−106.057	−3.65065
$845$	0	0
$846$	−8.44249	−0.290259
$847$	−29.2046	−1.00348
$848$	−178.231	−6.12047
$849$	17.5410	0.602007
$850$	0	0
$851$	−2.65700	−0.0910807
$852$	14.9069	0.510703
$853$	57.1622	1.95720	0.978598	−	0.205782i	$-0.0659737\pi$
$853$	57.1622	1.95720	0.978598	+	0.205782i	$0.0659737\pi$
$854$	49.7698	1.70309
$855$	0	0
$856$	−63.9940	−2.18727
$857$	26.1974	0.894885	0.447442	−	0.894313i	$-0.352335\pi$
$857$	26.1974	0.894885	0.447442	+	0.894313i	$0.352335\pi$
$858$	−2.28907	−0.0781475
$859$	−17.7449	−0.605449	−0.302724	−	0.953078i	$-0.597896\pi$
$859$	−17.7449	−0.605449	−0.302724	+	0.953078i	$0.597896\pi$
$860$	0	0
$861$	17.0580	0.581336
$862$	35.5418	1.21056
$863$	25.0867	0.853960	0.426980	−	0.904261i	$-0.359578\pi$
$863$	25.0867	0.853960	0.426980	+	0.904261i	$0.359578\pi$
$864$	−139.891	−4.75920
$865$	0	0
$866$	−38.1789	−1.29737
$867$	−4.47357	−0.151930
$868$	−78.7944	−2.67446
$869$	1.57785	0.0535249
$870$	0	0
$871$	−1.62891	−0.0551936
$872$	−65.3415	−2.21274
$873$	8.40305	0.284400
$874$	0	0
$875$	0	0
$876$	59.6476	2.01531
$877$	10.0157	0.338205	0.169103	−	0.985598i	$-0.445913\pi$
$877$	10.0157	0.338205	0.169103	+	0.985598i	$0.445913\pi$
$878$	0.195290	0.00659071
$879$	−40.3678	−1.36157
$880$	0	0
$881$	33.3473	1.12350	0.561750	−	0.827307i	$-0.310128\pi$
$881$	33.3473	1.12350	0.561750	+	0.827307i	$0.310128\pi$
$882$	−2.38018	−0.0801449
$883$	27.3570	0.920638	0.460319	−	0.887754i	$-0.347735\pi$
$883$	27.3570	0.920638	0.460319	+	0.887754i	$0.347735\pi$
$884$	−13.4956	−0.453905
$885$	0	0
$886$	10.4505	0.351092
$887$	17.1634	0.576292	0.288146	−	0.957586i	$-0.406961\pi$
$887$	17.1634	0.576292	0.288146	+	0.957586i	$0.406961\pi$
$888$	94.4544	3.16968
$889$	25.1675	0.844090
$890$	0	0
$891$	5.25635	0.176094
$892$	−90.5363	−3.03138
$893$	0	0
$894$	−61.3571	−2.05209
$895$	0	0
$896$	141.905	4.74072
$897$	−0.400646	−0.0133772
$898$	73.2985	2.44600
$899$	−47.8807	−1.59691
$900$	0	0
$901$	41.1136	1.36969
$902$	−9.57325	−0.318754
$903$	8.74762	0.291103
$904$	2.92958	0.0974364
$905$	0	0
$906$	−88.2979	−2.93350
$907$	3.02106	0.100313	0.0501563	−	0.998741i	$-0.484028\pi$
$907$	3.02106	0.100313	0.0501563	+	0.998741i	$0.484028\pi$
$908$	147.559	4.89693
$909$	4.10004	0.135990
$910$	0	0
$911$	19.5682	0.648324	0.324162	−	0.946002i	$-0.394918\pi$
$911$	19.5682	0.648324	0.324162	+	0.946002i	$0.394918\pi$
$912$	0	0
$913$	−6.43336	−0.212913
$914$	91.4346	3.02439
$915$	0	0
$916$	−74.7498	−2.46980
$917$	59.5729	1.96727
$918$	58.1100	1.91792
$919$	−1.81420	−0.0598448	−0.0299224	−	0.999552i	$-0.509526\pi$
$919$	−1.81420	−0.0598448	−0.0299224	+	0.999552i	$0.509526\pi$
$920$	0	0
$921$	13.1859	0.434491
$922$	−53.1017	−1.74881
$923$	1.14641	0.0377346
$924$	−20.6064	−0.677901
$925$	0	0
$926$	−108.035	−3.55025
$927$	0.298163	0.00979295
$928$	241.117	7.91507
$929$	−22.4754	−0.737395	−0.368698	−	0.929549i	$-0.620196\pi$
$929$	−22.4754	−0.737395	−0.368698	+	0.929549i	$0.620196\pi$
$930$	0	0
$931$	0	0
$932$	−141.901	−4.64813
$933$	−0.971975	−0.0318210
$934$	107.742	3.52542
$935$	0	0
$936$	−4.95386	−0.161922
$937$	−55.0385	−1.79803	−0.899015	−	0.437918i	$-0.855716\pi$
$937$	−55.0385	−1.79803	−0.899015	+	0.437918i	$0.855716\pi$
$938$	−19.8944	−0.649576
$939$	4.42437	0.144384
$940$	0	0
$941$	12.1956	0.397566	0.198783	−	0.980044i	$-0.436301\pi$
$941$	12.1956	0.397566	0.198783	+	0.980044i	$0.436301\pi$
$942$	10.0036	0.325937
$943$	−1.67557	−0.0545640
$944$	−39.8977	−1.29856
$945$	0	0
$946$	−4.90931	−0.159615
$947$	−30.4307	−0.988863	−0.494432	−	0.869216i	$-0.664624\pi$
$947$	−30.4307	−0.988863	−0.494432	+	0.869216i	$0.664624\pi$
$948$	−15.2615	−0.495672
$949$	4.58717	0.148906
$950$	0	0
$951$	−15.4859	−0.502164
$952$	−106.029	−3.43642
$953$	15.7378	0.509798	0.254899	−	0.966968i	$-0.417958\pi$
$953$	15.7378	0.509798	0.254899	+	0.966968i	$0.417958\pi$
$954$	23.4605	0.759561
$955$	0	0
$956$	−132.036	−4.27036
$957$	−12.5218	−0.404772
$958$	−68.2748	−2.20586
$959$	−14.8550	−0.479693
$960$	0	0
$961$	−6.66065	−0.214860
$962$	11.2921	0.364071
$963$	4.98058	0.160497
$964$	−47.0070	−1.51399
$965$	0	0
$966$	−4.89322	−0.157437
$967$	−30.6373	−0.985228	−0.492614	−	0.870248i	$-0.663958\pi$
$967$	−30.6373	−0.985228	−0.492614	+	0.870248i	$0.663958\pi$
$968$	−101.980	−3.27776
$969$	0	0
$970$	0	0
$971$	−16.4765	−0.528755	−0.264378	−	0.964419i	$-0.585167\pi$
$971$	−16.4765	−0.528755	−0.264378	+	0.964419i	$0.585167\pi$
$972$	43.8679	1.40706
$973$	−30.5483	−0.979334
$974$	60.3649	1.93422
$975$	0	0
$976$	102.758	3.28921
$977$	−2.77995	−0.0889383	−0.0444692	−	0.999011i	$-0.514160\pi$
$977$	−2.77995	−0.0889383	−0.0444692	+	0.999011i	$0.514160\pi$
$978$	−73.3144	−2.34433
$979$	3.84480	0.122880
$980$	0	0
$981$	5.08545	0.162366
$982$	25.9130	0.826918
$983$	−1.71171	−0.0545951	−0.0272976	−	0.999627i	$-0.508690\pi$
$983$	−1.71171	−0.0545951	−0.0272976	+	0.999627i	$0.508690\pi$
$984$	59.5653	1.89887
$985$	0	0
$986$	−100.159	−3.18971
$987$	16.8041	0.534879
$988$	0	0
$989$	−0.859257	−0.0273228
$990$	0	0
$991$	9.67421	0.307311	0.153656	−	0.988124i	$-0.450895\pi$
$991$	9.67421	0.307311	0.153656	+	0.988124i	$0.450895\pi$
$992$	−122.568	−3.89154
$993$	−22.5164	−0.714535
$994$	14.0015	0.444099
$995$	0	0
$996$	62.2259	1.97170
$997$	−22.7311	−0.719902	−0.359951	−	0.932971i	$-0.617207\pi$
$997$	−22.7311	−0.719902	−0.359951	+	0.932971i	$0.617207\pi$
$998$	68.7064	2.17486
$999$	−35.8380	−1.13386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.bp.1.4		4
5.4	even	2		1805.2.a.i.1.1		4
19.8	odd	6		475.2.e.e.26.4		8
19.12	odd	6		475.2.e.e.201.4		8
19.18	odd	2		9025.2.a.bg.1.1		4
95.8	even	12		475.2.j.c.349.8		16
95.12	even	12		475.2.j.c.49.8		16
95.27	even	12		475.2.j.c.349.1		16
95.69	odd	6		95.2.e.c.11.1	✓	8
95.84	odd	6		95.2.e.c.26.1	yes	8
95.88	even	12		475.2.j.c.49.1		16
95.94	odd	2		1805.2.a.o.1.4		4
285.164	even	6		855.2.k.h.676.4		8
285.179	even	6		855.2.k.h.406.4		8
380.179	even	6		1520.2.q.o.881.3		8
380.259	even	6		1520.2.q.o.961.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.c.11.1	✓	8	95.69	odd	6
95.2.e.c.26.1	yes	8	95.84	odd	6
475.2.e.e.26.4		8	19.8	odd	6
475.2.e.e.201.4		8	19.12	odd	6
475.2.j.c.49.1		16	95.88	even	12
475.2.j.c.49.8		16	95.12	even	12
475.2.j.c.349.1		16	95.27	even	12
475.2.j.c.349.8		16	95.8	even	12
855.2.k.h.406.4		8	285.179	even	6
855.2.k.h.676.4		8	285.164	even	6
1520.2.q.o.881.3		8	380.179	even	6
1520.2.q.o.961.3		8	380.259	even	6
1805.2.a.i.1.1		4	5.4	even	2
1805.2.a.o.1.4		4	95.94	odd	2
9025.2.a.bg.1.1		4	19.18	odd	2
9025.2.a.bp.1.4		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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+2.75802 q^{2} +1.49192 q^{3} +5.60665 q^{4} +4.11474 q^{6} +2.84864 q^{7} +9.94721 q^{8} -0.774179 q^{9} -0.864801 q^{11} +8.36467 q^{12} +0.643281 q^{13} +7.85659 q^{14} +16.2213 q^{16} -3.74185 q^{17} -2.13520 q^{18} +4.24993 q^{21} -2.38513 q^{22} -0.417460 q^{23} +14.8404 q^{24} +1.77418 q^{26} -5.63077 q^{27} +15.9713 q^{28} +9.70523 q^{29} -4.93349 q^{31} +24.8441 q^{32} -1.29021 q^{33} -10.3201 q^{34} -4.34056 q^{36} +6.36467 q^{37} +0.959723 q^{39} +4.01372 q^{41} +11.7214 q^{42} +2.05829 q^{43} -4.84864 q^{44} -1.15136 q^{46} +3.95396 q^{47} +24.2008 q^{48} +1.11474 q^{49} -5.58254 q^{51} +3.60665 q^{52} -10.9875 q^{53} -15.5297 q^{54} +28.3360 q^{56} +26.7672 q^{58} -2.45959 q^{59} +6.33479 q^{61} -13.6067 q^{62} -2.20536 q^{63} +36.0778 q^{64} -3.55843 q^{66} -2.53220 q^{67} -20.9793 q^{68} -0.622817 q^{69} +1.78213 q^{71} -7.70092 q^{72} +7.13090 q^{73} +17.5539 q^{74} -2.46350 q^{77} +2.64693 q^{78} -1.82452 q^{79} -6.07811 q^{81} +11.0699 q^{82} +7.43913 q^{83} +23.8279 q^{84} +5.67681 q^{86} +14.4794 q^{87} -8.60235 q^{88} -4.44588 q^{89} +1.83247 q^{91} -2.34056 q^{92} -7.36037 q^{93} +10.9051 q^{94} +37.0653 q^{96} -10.8541 q^{97} +3.07446 q^{98} +0.669511 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + 3 q^{3} + 5 q^{4} + 2 q^{6} + 4 q^{7} + 12 q^{8} + q^{9} - 2 q^{11} + 6 q^{12} + 7 q^{13} + q^{14} + 7 q^{16} + q^{17} - 10 q^{18} + 4 q^{21} + 2 q^{22} - 2 q^{23} + 23 q^{24} + 3 q^{26}+ \cdots + 38 q^{99}+O(q^{100}) \) 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

Introduction

L-functions

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