LMFDB - Embedded newform 3525.2.a.u.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,2,Mod(1,3525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3525.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:	$28.1472667125$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.14656.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 4x^{2} + 4x + 2 $ x^4 - 2x^3 - 4x^2 + 4*x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 705)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.59286$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.59286 q^{2} +1.00000 q^{3} +4.72294 q^{4} -2.59286 q^{6} -0.255601 q^{7} -7.06020 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.59286 q^{2} +1.00000 q^{3} +4.72294 q^{4} -2.59286 q^{6} -0.255601 q^{7} -7.06020 q^{8} +1.00000 q^{9} +5.72294 q^{11} +4.72294 q^{12} -0.592862 q^{13} +0.662739 q^{14} +8.86025 q^{16} +2.08166 q^{17} -2.59286 q^{18} -0.922885 q^{19} -0.255601 q^{21} -14.8388 q^{22} +5.19027 q^{23} -7.06020 q^{24} +1.53721 q^{26} +1.00000 q^{27} -1.20719 q^{28} +5.00000 q^{29} +2.05296 q^{31} -8.85301 q^{32} +5.72294 q^{33} -5.39746 q^{34} +4.72294 q^{36} -4.13731 q^{37} +2.39291 q^{38} -0.592862 q^{39} +1.27706 q^{41} +0.662739 q^{42} +9.95707 q^{43} +27.0291 q^{44} -13.4577 q^{46} -1.00000 q^{47} +8.86025 q^{48} -6.93467 q^{49} +2.08166 q^{51} -2.80005 q^{52} +3.57140 q^{53} -2.59286 q^{54} +1.80460 q^{56} -0.922885 q^{57} -12.9643 q^{58} +0.151536 q^{59} -13.7858 q^{61} -5.32304 q^{62} -0.255601 q^{63} +5.23414 q^{64} -14.8388 q^{66} -7.23868 q^{67} +9.83154 q^{68} +5.19027 q^{69} -12.2290 q^{71} -7.06020 q^{72} +12.7420 q^{73} +10.7275 q^{74} -4.35872 q^{76} -1.46279 q^{77} +1.53721 q^{78} -3.41986 q^{79} +1.00000 q^{81} -3.31125 q^{82} +12.1113 q^{83} -1.20719 q^{84} -25.8173 q^{86} +5.00000 q^{87} -40.4050 q^{88} +15.0021 q^{89} +0.151536 q^{91} +24.5133 q^{92} +2.05296 q^{93} +2.59286 q^{94} -8.85301 q^{96} +17.0460 q^{97} +17.9806 q^{98} +5.72294 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 4 q^{3} + 4 q^{4} - 2 q^{6} - 6 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 4 * q^3 + 4 * q^4 - 2 * q^6 - 6 * q^8 + 4 * q^9	$ 4 q - 2 q^{2} + 4 q^{3} + 4 q^{4} - 2 q^{6} - 6 q^{8} + 4 q^{9} + 8 q^{11} + 4 q^{12} + 6 q^{13} + 10 q^{14} + 4 q^{16} + 2 q^{17} - 2 q^{18} + 2 q^{19} - 12 q^{22} - 8 q^{23} - 6 q^{24} + 8 q^{26} + 4 q^{27} - 4 q^{28} + 20 q^{29} - 4 q^{31} - 14 q^{32} + 8 q^{33} + 8 q^{34} + 4 q^{36} - 8 q^{38} + 6 q^{39} + 20 q^{41} + 10 q^{42} + 8 q^{43} + 32 q^{44} - 2 q^{46} - 4 q^{47} + 4 q^{48} + 2 q^{51} - 2 q^{52} - 10 q^{53} - 2 q^{54} - 14 q^{56} + 2 q^{57} - 10 q^{58} + 10 q^{59} - 20 q^{61} + 12 q^{62} + 4 q^{64} - 12 q^{66} + 2 q^{68} - 8 q^{69} + 18 q^{71} - 6 q^{72} + 4 q^{73} + 16 q^{74} - 26 q^{76} - 4 q^{77} + 8 q^{78} + 20 q^{79} + 4 q^{81} - 2 q^{82} + 28 q^{83} - 4 q^{84} - 40 q^{86} + 20 q^{87} - 40 q^{88} + 10 q^{91} + 36 q^{92} - 4 q^{93} + 2 q^{94} - 14 q^{96} + 20 q^{97} - 4 q^{98} + 8 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 4 * q^3 + 4 * q^4 - 2 * q^6 - 6 * q^8 + 4 * q^9 + 8 * q^11 + 4 * q^12 + 6 * q^13 + 10 * q^14 + 4 * q^16 + 2 * q^17 - 2 * q^18 + 2 * q^19 - 12 * q^22 - 8 * q^23 - 6 * q^24 + 8 * q^26 + 4 * q^27 - 4 * q^28 + 20 * q^29 - 4 * q^31 - 14 * q^32 + 8 * q^33 + 8 * q^34 + 4 * q^36 - 8 * q^38 + 6 * q^39 + 20 * q^41 + 10 * q^42 + 8 * q^43 + 32 * q^44 - 2 * q^46 - 4 * q^47 + 4 * q^48 + 2 * q^51 - 2 * q^52 - 10 * q^53 - 2 * q^54 - 14 * q^56 + 2 * q^57 - 10 * q^58 + 10 * q^59 - 20 * q^61 + 12 * q^62 + 4 * q^64 - 12 * q^66 + 2 * q^68 - 8 * q^69 + 18 * q^71 - 6 * q^72 + 4 * q^73 + 16 * q^74 - 26 * q^76 - 4 * q^77 + 8 * q^78 + 20 * q^79 + 4 * q^81 - 2 * q^82 + 28 * q^83 - 4 * q^84 - 40 * q^86 + 20 * q^87 - 40 * q^88 + 10 * q^91 + 36 * q^92 - 4 * q^93 + 2 * q^94 - 14 * q^96 + 20 * q^97 - 4 * q^98 + 8 * 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 $

$2$	−2.59286	−1.83343	−0.916715	−	0.399541i	$-0.869169\pi$
$2$	−2.59286	−1.83343	−0.916715	+	0.399541i	$0.869169\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.72294	2.36147
$5$	0	0
$5$	0	0
$6$	−2.59286	−1.05853
$7$	−0.255601	−0.0966082	−0.0483041	−	0.998833i	$-0.515382\pi$
$7$	−0.255601	−0.0966082	−0.0483041	+	0.998833i	$0.515382\pi$
$8$	−7.06020	−2.49616
$9$	1.00000	0.333333
$10$	0	0
$11$	5.72294	1.72553	0.862765	−	0.505605i	$-0.168731\pi$
$11$	5.72294	1.72553	0.862765	+	0.505605i	$0.168731\pi$
$12$	4.72294	1.36339
$13$	−0.592862	−0.164430	−0.0822152	−	0.996615i	$-0.526199\pi$
$13$	−0.592862	−0.164430	−0.0822152	+	0.996615i	$0.526199\pi$
$14$	0.662739	0.177124
$15$	0	0
$16$	8.86025	2.21506
$17$	2.08166	0.504877	0.252438	−	0.967613i	$-0.418768\pi$
$17$	2.08166	0.504877	0.252438	+	0.967613i	$0.418768\pi$
$18$	−2.59286	−0.611144
$19$	−0.922885	−0.211724	−0.105862	−	0.994381i	$-0.533760\pi$
$19$	−0.922885	−0.211724	−0.105862	+	0.994381i	$0.533760\pi$
$20$	0	0
$21$	−0.255601	−0.0557768
$22$	−14.8388	−3.16364
$23$	5.19027	1.08225	0.541123	−	0.840943i	$-0.317999\pi$
$23$	5.19027	1.08225	0.541123	+	0.840943i	$0.317999\pi$
$24$	−7.06020	−1.44116
$25$	0	0
$26$	1.53721	0.301472
$27$	1.00000	0.192450
$28$	−1.20719	−0.228137
$29$	5.00000	0.928477	0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000	0.928477	0.464238	+	0.885710i	$0.346328\pi$
$30$	0	0
$31$	2.05296	0.368722	0.184361	−	0.982859i	$-0.440978\pi$
$31$	2.05296	0.368722	0.184361	+	0.982859i	$0.440978\pi$
$32$	−8.85301	−1.56501
$33$	5.72294	0.996235
$34$	−5.39746	−0.925656
$35$	0	0
$36$	4.72294	0.787156
$37$	−4.13731	−0.680170	−0.340085	−	0.940395i	$-0.610456\pi$
$37$	−4.13731	−0.680170	−0.340085	+	0.940395i	$0.610456\pi$
$38$	2.39291	0.388182
$39$	−0.592862	−0.0949340
$40$	0	0
$41$	1.27706	0.199444	0.0997220	−	0.995015i	$-0.468205\pi$
$41$	1.27706	0.199444	0.0997220	+	0.995015i	$0.468205\pi$
$42$	0.662739	0.102263
$43$	9.95707	1.51844	0.759220	−	0.650834i	$-0.225581\pi$
$43$	9.95707	1.51844	0.759220	+	0.650834i	$0.225581\pi$
$44$	27.0291	4.07478
$45$	0	0
$46$	−13.4577	−1.98422
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	8.86025	1.27887
$49$	−6.93467	−0.990667
$50$	0	0
$51$	2.08166	0.291491
$52$	−2.80005	−0.388297
$53$	3.57140	0.490569	0.245285	−	0.969451i	$-0.421119\pi$
$53$	3.57140	0.490569	0.245285	+	0.969451i	$0.421119\pi$
$54$	−2.59286	−0.352844
$55$	0	0
$56$	1.80460	0.241149
$57$	−0.922885	−0.122239
$58$	−12.9643	−1.70230
$59$	0.151536	0.0197284	0.00986418	−	0.999951i	$-0.496860\pi$
$59$	0.151536	0.0197284	0.00986418	+	0.999951i	$0.496860\pi$
$60$	0	0
$61$	−13.7858	−1.76509	−0.882547	−	0.470224i	$-0.844173\pi$
$61$	−13.7858	−1.76509	−0.882547	+	0.470224i	$0.844173\pi$
$62$	−5.32304	−0.676026
$63$	−0.255601	−0.0322027
$64$	5.23414	0.654267
$65$	0	0
$66$	−14.8388	−1.82653
$67$	−7.23868	−0.884346	−0.442173	−	0.896930i	$-0.645792\pi$
$67$	−7.23868	−0.884346	−0.442173	+	0.896930i	$0.645792\pi$
$68$	9.83154	1.19225
$69$	5.19027	0.624835
$70$	0	0
$71$	−12.2290	−1.45132	−0.725658	−	0.688056i	$-0.758464\pi$
$71$	−12.2290	−1.45132	−0.725658	+	0.688056i	$0.758464\pi$
$72$	−7.06020	−0.832052
$73$	12.7420	1.49133	0.745667	−	0.666319i	$-0.232131\pi$
$73$	12.7420	1.49133	0.745667	+	0.666319i	$0.232131\pi$
$74$	10.7275	1.24704
$75$	0	0
$76$	−4.35872	−0.499980
$77$	−1.46279	−0.166700
$78$	1.53721	0.174055
$79$	−3.41986	−0.384765	−0.192382	−	0.981320i	$-0.561621\pi$
$79$	−3.41986	−0.384765	−0.192382	+	0.981320i	$0.561621\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−3.31125	−0.365667
$83$	12.1113	1.32939	0.664694	−	0.747116i	$-0.268562\pi$
$83$	12.1113	1.32939	0.664694	+	0.747116i	$0.268562\pi$
$84$	−1.20719	−0.131715
$85$	0	0
$86$	−25.8173	−2.78395
$87$	5.00000	0.536056
$88$	−40.4050	−4.30719
$89$	15.0021	1.59022	0.795110	−	0.606465i	$-0.207413\pi$
$89$	15.0021	1.59022	0.795110	+	0.606465i	$0.207413\pi$
$90$	0	0
$91$	0.151536	0.0158853
$92$	24.5133	2.55569
$93$	2.05296	0.212882
$94$	2.59286	0.267433
$95$	0	0
$96$	−8.85301	−0.903556
$97$	17.0460	1.73076	0.865378	−	0.501119i	$-0.167078\pi$
$97$	17.0460	1.73076	0.865378	+	0.501119i	$0.167078\pi$
$98$	17.9806	1.81632
$99$	5.72294	0.575177
$100$	0	0
$101$	6.88171	0.684756	0.342378	−	0.939562i	$-0.388768\pi$
$101$	6.88171	0.684756	0.342378	+	0.939562i	$0.388768\pi$
$102$	−5.39746	−0.534428
$103$	−10.1419	−0.999307	−0.499653	−	0.866225i	$-0.666539\pi$
$103$	−10.1419	−0.999307	−0.499653	+	0.866225i	$0.666539\pi$
$104$	4.18572	0.410444
$105$	0	0
$106$	−9.26015	−0.899425
$107$	−9.95707	−0.962587	−0.481293	−	0.876560i	$-0.659833\pi$
$107$	−9.95707	−0.962587	−0.481293	+	0.876560i	$0.659833\pi$
$108$	4.72294	0.454465
$109$	4.06744	0.389590	0.194795	−	0.980844i	$-0.437596\pi$
$109$	4.06744	0.389590	0.194795	+	0.980844i	$0.437596\pi$
$110$	0	0
$111$	−4.13731	−0.392696
$112$	−2.26469	−0.213993
$113$	−5.98308	−0.562841	−0.281420	−	0.959585i	$-0.590806\pi$
$113$	−5.98308	−0.562841	−0.281420	+	0.959585i	$0.590806\pi$
$114$	2.39291	0.224117
$115$	0	0
$116$	23.6147	2.19257
$117$	−0.592862	−0.0548101
$118$	−0.392913	−0.0361706
$119$	−0.532075	−0.0487752
$120$	0	0
$121$	21.7520	1.97745
$122$	35.7447	3.23618
$123$	1.27706	0.115149
$124$	9.69599	0.870725
$125$	0	0
$126$	0.662739	0.0590415
$127$	−18.3805	−1.63101	−0.815505	−	0.578751i	$-0.803540\pi$
$127$	−18.3805	−1.63101	−0.815505	+	0.578751i	$0.803540\pi$
$128$	4.13462	0.365452
$129$	9.95707	0.876671
$130$	0	0
$131$	12.9785	1.13394	0.566970	−	0.823738i	$-0.308116\pi$
$131$	12.9785	1.13394	0.566970	+	0.823738i	$0.308116\pi$
$132$	27.0291	2.35258
$133$	0.235890	0.0204543
$134$	18.7689	1.62139
$135$	0	0
$136$	−14.6969	−1.26025
$137$	−0.163320	−0.0139533	−0.00697667	−	0.999976i	$-0.502221\pi$
$137$	−0.163320	−0.0139533	−0.00697667	+	0.999976i	$0.502221\pi$
$138$	−13.4577	−1.14559
$139$	−5.23599	−0.444111	−0.222055	−	0.975034i	$-0.571277\pi$
$139$	−5.23599	−0.444111	−0.222055	+	0.975034i	$0.571277\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	31.7081	2.66089
$143$	−3.39291	−0.283730
$144$	8.86025	0.738354
$145$	0	0
$146$	−33.0381	−2.73426
$147$	−6.93467	−0.571962
$148$	−19.5403	−1.60620
$149$	−6.17780	−0.506105	−0.253052	−	0.967453i	$-0.581435\pi$
$149$	−6.17780	−0.506105	−0.253052	+	0.967453i	$0.581435\pi$
$150$	0	0
$151$	14.1086	1.14814	0.574071	−	0.818805i	$-0.305363\pi$
$151$	14.1086	1.14814	0.574071	+	0.818805i	$0.305363\pi$
$152$	6.51575	0.528497
$153$	2.08166	0.168292
$154$	3.79281	0.305633
$155$	0	0
$156$	−2.80005	−0.224183
$157$	9.58562	0.765016	0.382508	−	0.923952i	$-0.375060\pi$
$157$	9.58562	0.765016	0.382508	+	0.923952i	$0.375060\pi$
$158$	8.86723	0.705439
$159$	3.57140	0.283230
$160$	0	0
$161$	−1.32664	−0.104554
$162$	−2.59286	−0.203715
$163$	3.44587	0.269901	0.134951	−	0.990852i	$-0.456912\pi$
$163$	3.44587	0.269901	0.134951	+	0.990852i	$0.456912\pi$
$164$	6.03149	0.470981
$165$	0	0
$166$	−31.4029	−2.43734
$167$	−13.4818	−1.04325	−0.521627	−	0.853174i	$-0.674675\pi$
$167$	−13.4818	−1.04325	−0.521627	+	0.853174i	$0.674675\pi$
$168$	1.80460	0.139228
$169$	−12.6485	−0.972963
$170$	0	0
$171$	−0.922885	−0.0705748
$172$	47.0266	3.58575
$173$	−9.83060	−0.747407	−0.373703	−	0.927548i	$-0.621912\pi$
$173$	−9.83060	−0.747407	−0.373703	+	0.927548i	$0.621912\pi$
$174$	−12.9643	−0.982822
$175$	0	0
$176$	50.7066	3.82216
$177$	0.151536	0.0113902
$178$	−38.8984	−2.91556
$179$	1.47971	0.110599	0.0552993	−	0.998470i	$-0.482389\pi$
$179$	1.47971	0.110599	0.0552993	+	0.998470i	$0.482389\pi$
$180$	0	0
$181$	−26.1734	−1.94545	−0.972725	−	0.231962i	$-0.925486\pi$
$181$	−26.1734	−1.94545	−0.972725	+	0.231962i	$0.925486\pi$
$182$	−0.392913	−0.0291246
$183$	−13.7858	−1.01908
$184$	−36.6443	−2.70146
$185$	0	0
$186$	−5.32304	−0.390304
$187$	11.9132	0.871180
$188$	−4.72294	−0.344455
$189$	−0.255601	−0.0185923
$190$	0	0
$191$	12.3705	0.895099	0.447549	−	0.894259i	$-0.352297\pi$
$191$	12.3705	0.895099	0.447549	+	0.894259i	$0.352297\pi$
$192$	5.23414	0.377741
$193$	12.3276	0.887359	0.443679	−	0.896186i	$-0.353673\pi$
$193$	12.3276	0.887359	0.443679	+	0.896186i	$0.353673\pi$
$194$	−44.1979	−3.17322
$195$	0	0
$196$	−32.7520	−2.33943
$197$	0.230502	0.0164226	0.00821129	−	0.999966i	$-0.497386\pi$
$197$	0.230502	0.0164226	0.00821129	+	0.999966i	$0.497386\pi$
$198$	−14.8388	−1.05455
$199$	−6.02626	−0.427190	−0.213595	−	0.976922i	$-0.568517\pi$
$199$	−6.02626	−0.427190	−0.213595	+	0.976922i	$0.568517\pi$
$200$	0	0
$201$	−7.23868	−0.510577
$202$	−17.8433	−1.25545
$203$	−1.27801	−0.0896985
$204$	9.83154	0.688346
$205$	0	0
$206$	26.2964	1.83216
$207$	5.19027	0.360749
$208$	−5.25291	−0.364224
$209$	−5.28161	−0.365337
$210$	0	0
$211$	6.19271	0.426324	0.213162	−	0.977017i	$-0.431624\pi$
$211$	6.19271	0.426324	0.213162	+	0.977017i	$0.431624\pi$
$212$	16.8675	1.15846
$213$	−12.2290	−0.837917
$214$	25.8173	1.76484
$215$	0	0
$216$	−7.06020	−0.480386
$217$	−0.524739	−0.0356216
$218$	−10.5463	−0.714286
$219$	12.7420	0.861022
$220$	0	0
$221$	−1.23414	−0.0830171
$222$	10.7275	0.719981
$223$	−18.8817	−1.26441	−0.632206	−	0.774800i	$-0.717851\pi$
$223$	−18.8817	−1.26441	−0.632206	+	0.774800i	$0.717851\pi$
$224$	2.26284	0.151192
$225$	0	0
$226$	15.5133	1.03193
$227$	−13.1564	−0.873223	−0.436612	−	0.899650i	$-0.643822\pi$
$227$	−13.1564	−0.873223	−0.436612	+	0.899650i	$0.643822\pi$
$228$	−4.35872	−0.288664
$229$	27.3071	1.80450	0.902251	−	0.431212i	$-0.141914\pi$
$229$	27.3071	1.80450	0.902251	+	0.431212i	$0.141914\pi$
$230$	0	0
$231$	−1.46279	−0.0962445
$232$	−35.3010	−2.31762
$233$	20.1888	1.32261	0.661305	−	0.750117i	$-0.270003\pi$
$233$	20.1888	1.32261	0.661305	+	0.750117i	$0.270003\pi$
$234$	1.53721	0.100491
$235$	0	0
$236$	0.715696	0.0465879
$237$	−3.41986	−0.222144
$238$	1.37960	0.0894260
$239$	12.9785	0.839512	0.419756	−	0.907637i	$-0.362116\pi$
$239$	12.9785	0.839512	0.419756	+	0.907637i	$0.362116\pi$
$240$	0	0
$241$	−10.5427	−0.679115	−0.339557	−	0.940585i	$-0.610277\pi$
$241$	−10.5427	−0.679115	−0.339557	+	0.940585i	$0.610277\pi$
$242$	−56.3999	−3.62552
$243$	1.00000	0.0641500
$244$	−65.1096	−4.16821
$245$	0	0
$246$	−3.31125	−0.211118
$247$	0.547144	0.0348139
$248$	−14.4943	−0.920388
$249$	12.1113	0.767523
$250$	0	0
$251$	10.6782	0.673999	0.337000	−	0.941505i	$-0.390588\pi$
$251$	10.6782	0.673999	0.337000	+	0.941505i	$0.390588\pi$
$252$	−1.20719	−0.0760457
$253$	29.7036	1.86745
$254$	47.6582	2.99034
$255$	0	0
$256$	−21.1888	−1.32430
$257$	−19.1404	−1.19394	−0.596971	−	0.802263i	$-0.703629\pi$
$257$	−19.1404	−1.19394	−0.596971	+	0.802263i	$0.703629\pi$
$258$	−25.8173	−1.60732
$259$	1.05750	0.0657100
$260$	0	0
$261$	5.00000	0.309492
$262$	−33.6516	−2.07900
$263$	−8.25920	−0.509284	−0.254642	−	0.967035i	$-0.581958\pi$
$263$	−8.25920	−0.509284	−0.254642	+	0.967035i	$0.581958\pi$
$264$	−40.4050	−2.48676
$265$	0	0
$266$	−0.611632	−0.0375015
$267$	15.0021	0.918114
$268$	−34.1878	−2.08835
$269$	4.01448	0.244767	0.122384	−	0.992483i	$-0.460946\pi$
$269$	4.01448	0.244767	0.122384	+	0.992483i	$0.460946\pi$
$270$	0	0
$271$	23.3297	1.41718	0.708589	−	0.705622i	$-0.249332\pi$
$271$	23.3297	1.41718	0.708589	+	0.705622i	$0.249332\pi$
$272$	18.4440	1.11833
$273$	0.151536	0.00917140
$274$	0.423465	0.0255825
$275$	0	0
$276$	24.5133	1.47553
$277$	13.8578	0.832635	0.416317	−	0.909219i	$-0.363321\pi$
$277$	13.8578	0.832635	0.416317	+	0.909219i	$0.363321\pi$
$278$	13.5762	0.814246
$279$	2.05296	0.122907
$280$	0	0
$281$	−6.96616	−0.415566	−0.207783	−	0.978175i	$-0.566625\pi$
$281$	−6.96616	−0.415566	−0.207783	+	0.978175i	$0.566625\pi$
$282$	2.59286	0.154403
$283$	9.33996	0.555203	0.277601	−	0.960696i	$-0.410461\pi$
$283$	9.33996	0.555203	0.277601	+	0.960696i	$0.410461\pi$
$284$	−57.7568	−3.42723
$285$	0	0
$286$	8.79736	0.520199
$287$	−0.326419	−0.0192679
$288$	−8.85301	−0.521669
$289$	−12.6667	−0.745100
$290$	0	0
$291$	17.0460	0.999253
$292$	60.1794	3.52174
$293$	−24.4041	−1.42570	−0.712852	−	0.701315i	$-0.752597\pi$
$293$	−24.4041	−1.42570	−0.712852	+	0.701315i	$0.752597\pi$
$294$	17.9806	1.04865
$295$	0	0
$296$	29.2102	1.69781
$297$	5.72294	0.332078
$298$	16.0182	0.927908
$299$	−3.07712	−0.177954
$300$	0	0
$301$	−2.54504	−0.146694
$302$	−36.5817	−2.10504
$303$	6.88171	0.395344
$304$	−8.17699	−0.468982
$305$	0	0
$306$	−5.39746	−0.308552
$307$	7.68455	0.438581	0.219290	−	0.975660i	$-0.429626\pi$
$307$	7.68455	0.438581	0.219290	+	0.975660i	$0.429626\pi$
$308$	−6.90866	−0.393657
$309$	−10.1419	−0.576950
$310$	0	0
$311$	2.67696	0.151797	0.0758983	−	0.997116i	$-0.475818\pi$
$311$	2.67696	0.151797	0.0758983	+	0.997116i	$0.475818\pi$
$312$	4.18572	0.236970
$313$	−25.4123	−1.43639	−0.718194	−	0.695843i	$-0.755031\pi$
$313$	−25.4123	−1.43639	−0.718194	+	0.695843i	$0.755031\pi$
$314$	−24.8542	−1.40260
$315$	0	0
$316$	−16.1518	−0.908609
$317$	−9.01702	−0.506446	−0.253223	−	0.967408i	$-0.581491\pi$
$317$	−9.01702	−0.506446	−0.253223	+	0.967408i	$0.581491\pi$
$318$	−9.26015	−0.519283
$319$	28.6147	1.60211
$320$	0	0
$321$	−9.95707	−0.555750
$322$	3.43979	0.191692
$323$	−1.92113	−0.106895
$324$	4.72294	0.262385
$325$	0	0
$326$	−8.93467	−0.494845
$327$	4.06744	0.224930
$328$	−9.01633	−0.497843
$329$	0.255601	0.0140918
$330$	0	0
$331$	−30.4865	−1.67569	−0.837844	−	0.545910i	$-0.816184\pi$
$331$	−30.4865	−1.67569	−0.837844	+	0.545910i	$0.816184\pi$
$332$	57.2009	3.13931
$333$	−4.13731	−0.226723
$334$	34.9565	1.91273
$335$	0	0
$336$	−2.26469	−0.123549
$337$	23.9026	1.30206	0.651029	−	0.759053i	$-0.274338\pi$
$337$	23.9026	1.30206	0.651029	+	0.759053i	$0.274338\pi$
$338$	32.7959	1.78386
$339$	−5.98308	−0.324956
$340$	0	0
$341$	11.7489	0.636241
$342$	2.39291	0.129394
$343$	3.56172	0.192315
$344$	−70.2989	−3.79026
$345$	0	0
$346$	25.4894	1.37032
$347$	−11.0980	−0.595771	−0.297886	−	0.954602i	$-0.596281\pi$
$347$	−11.0980	−0.595771	−0.297886	+	0.954602i	$0.596281\pi$
$348$	23.6147	1.26588
$349$	19.2767	1.03186	0.515930	−	0.856631i	$-0.327447\pi$
$349$	19.2767	1.03186	0.515930	+	0.856631i	$0.327447\pi$
$350$	0	0
$351$	−0.592862	−0.0316447
$352$	−50.6652	−2.70046
$353$	29.4039	1.56501	0.782505	−	0.622644i	$-0.213941\pi$
$353$	29.4039	1.56501	0.782505	+	0.622644i	$0.213941\pi$
$354$	−0.392913	−0.0208831
$355$	0	0
$356$	70.8540	3.75525
$357$	−0.532075	−0.0281604
$358$	−3.83668	−0.202775
$359$	11.3635	0.599744	0.299872	−	0.953979i	$-0.403056\pi$
$359$	11.3635	0.599744	0.299872	+	0.953979i	$0.403056\pi$
$360$	0	0
$361$	−18.1483	−0.955173
$362$	67.8639	3.56685
$363$	21.7520	1.14168
$364$	0.715696	0.0375127
$365$	0	0
$366$	35.7447	1.86841
$367$	12.4489	0.649828	0.324914	−	0.945744i	$-0.394665\pi$
$367$	12.4489	0.649828	0.324914	+	0.945744i	$0.394665\pi$
$368$	45.9871	2.39724
$369$	1.27706	0.0664813
$370$	0	0
$371$	−0.912854	−0.0473930
$372$	9.69599	0.502713
$373$	36.1540	1.87198	0.935991	−	0.352023i	$-0.114506\pi$
$373$	36.1540	1.87198	0.935991	+	0.352023i	$0.114506\pi$
$374$	−30.8893	−1.59725
$375$	0	0
$376$	7.06020	0.364102
$377$	−2.96431	−0.152670
$378$	0.662739	0.0340876
$379$	23.6891	1.21683	0.608414	−	0.793620i	$-0.291806\pi$
$379$	23.6891	1.21683	0.608414	+	0.793620i	$0.291806\pi$
$380$	0	0
$381$	−18.3805	−0.941664
$382$	−32.0750	−1.64110
$383$	38.3621	1.96021	0.980106	−	0.198473i	$-0.0635982\pi$
$383$	38.3621	1.96021	0.980106	+	0.198473i	$0.0635982\pi$
$384$	4.13462	0.210994
$385$	0	0
$386$	−31.9637	−1.62691
$387$	9.95707	0.506146
$388$	80.5070	4.08712
$389$	−27.6480	−1.40181	−0.700904	−	0.713256i	$-0.747220\pi$
$389$	−27.6480	−1.40181	−0.700904	+	0.713256i	$0.747220\pi$
$390$	0	0
$391$	10.8044	0.546401
$392$	48.9601	2.47286
$393$	12.9785	0.654681
$394$	−0.597660	−0.0301097
$395$	0	0
$396$	27.0291	1.35826
$397$	31.4713	1.57950	0.789750	−	0.613429i	$-0.210210\pi$
$397$	31.4713	1.57950	0.789750	+	0.613429i	$0.210210\pi$
$398$	15.6253	0.783224
$399$	0.235890	0.0118093
$400$	0	0
$401$	37.5681	1.87606	0.938032	−	0.346549i	$-0.112647\pi$
$401$	37.5681	1.87606	0.938032	+	0.346549i	$0.112647\pi$
$402$	18.7689	0.936108
$403$	−1.21712	−0.0606291
$404$	32.5019	1.61703
$405$	0	0
$406$	3.31369	0.164456
$407$	−23.6776	−1.17365
$408$	−14.6969	−0.727606
$409$	9.65306	0.477313	0.238657	−	0.971104i	$-0.423293\pi$
$409$	9.65306	0.477313	0.238657	+	0.971104i	$0.423293\pi$
$410$	0	0
$411$	−0.163320	−0.00805597
$412$	−47.8993	−2.35983
$413$	−0.0387329	−0.00190592
$414$	−13.4577	−0.661408
$415$	0	0
$416$	5.24862	0.257335
$417$	−5.23599	−0.256407
$418$	13.6945	0.669819
$419$	−8.30307	−0.405632	−0.202816	−	0.979217i	$-0.565009\pi$
$419$	−8.30307	−0.405632	−0.202816	+	0.979217i	$0.565009\pi$
$420$	0	0
$421$	16.7895	0.818271	0.409136	−	0.912474i	$-0.365830\pi$
$421$	16.7895	0.818271	0.409136	+	0.912474i	$0.365830\pi$
$422$	−16.0568	−0.781635
$423$	−1.00000	−0.0486217
$424$	−25.2148	−1.22454
$425$	0	0
$426$	31.7081	1.53626
$427$	3.52367	0.170523
$428$	−47.0266	−2.27312
$429$	−3.39291	−0.163811
$430$	0	0
$431$	1.75164	0.0843734	0.0421867	−	0.999110i	$-0.486568\pi$
$431$	1.75164	0.0843734	0.0421867	+	0.999110i	$0.486568\pi$
$432$	8.86025	0.426289
$433$	−9.66240	−0.464345	−0.232173	−	0.972675i	$-0.574583\pi$
$433$	−9.66240	−0.464345	−0.232173	+	0.972675i	$0.574583\pi$
$434$	1.36057	0.0653097
$435$	0	0
$436$	19.2102	0.920003
$437$	−4.79002	−0.229138
$438$	−33.0381	−1.57862
$439$	25.6425	1.22385	0.611924	−	0.790916i	$-0.290396\pi$
$439$	25.6425	1.22385	0.611924	+	0.790916i	$0.290396\pi$
$440$	0	0
$441$	−6.93467	−0.330222
$442$	3.19995	0.152206
$443$	30.8309	1.46482	0.732409	−	0.680865i	$-0.238396\pi$
$443$	30.8309	1.46482	0.732409	+	0.680865i	$0.238396\pi$
$444$	−19.5403	−0.927339
$445$	0	0
$446$	48.9577	2.31821
$447$	−6.17780	−0.292200
$448$	−1.33785	−0.0632076
$449$	29.4634	1.39046	0.695232	−	0.718786i	$-0.255302\pi$
$449$	29.4634	1.39046	0.695232	+	0.718786i	$0.255302\pi$
$450$	0	0
$451$	7.30856	0.344147
$452$	−28.2577	−1.32913
$453$	14.1086	0.662880
$454$	34.1128	1.60099
$455$	0	0
$456$	6.51575	0.305128
$457$	−33.8693	−1.58434	−0.792170	−	0.610300i	$-0.791049\pi$
$457$	−33.8693	−1.58434	−0.792170	+	0.610300i	$0.791049\pi$
$458$	−70.8034	−3.30843
$459$	2.08166	0.0971636
$460$	0	0
$461$	−5.90317	−0.274938	−0.137469	−	0.990506i	$-0.543897\pi$
$461$	−5.90317	−0.274938	−0.137469	+	0.990506i	$0.543897\pi$
$462$	3.79281	0.176458
$463$	−40.2562	−1.87086	−0.935432	−	0.353506i	$-0.884989\pi$
$463$	−40.2562	−1.87086	−0.935432	+	0.353506i	$0.884989\pi$
$464$	44.3012	2.05663
$465$	0	0
$466$	−52.3467	−2.42491
$467$	−9.42685	−0.436223	−0.218111	−	0.975924i	$-0.569990\pi$
$467$	−9.42685	−0.436223	−0.218111	+	0.975924i	$0.569990\pi$
$468$	−2.80005	−0.129432
$469$	1.85022	0.0854351
$470$	0	0
$471$	9.58562	0.441682
$472$	−1.06988	−0.0492451
$473$	56.9837	2.62011
$474$	8.86723	0.407285
$475$	0	0
$476$	−2.51296	−0.115181
$477$	3.57140	0.163523
$478$	−33.6516	−1.53919
$479$	0.821612	0.0375404	0.0187702	−	0.999824i	$-0.494025\pi$
$479$	0.821612	0.0375404	0.0187702	+	0.999824i	$0.494025\pi$
$480$	0	0
$481$	2.45286	0.111841
$482$	27.3358	1.24511
$483$	−1.32664	−0.0603642
$484$	102.733	4.66969
$485$	0	0
$486$	−2.59286	−0.117615
$487$	−7.36512	−0.333745	−0.166873	−	0.985978i	$-0.553367\pi$
$487$	−7.36512	−0.333745	−0.166873	+	0.985978i	$0.553367\pi$
$488$	97.3306	4.40595
$489$	3.44587	0.155828
$490$	0	0
$491$	−15.3753	−0.693878	−0.346939	−	0.937888i	$-0.612779\pi$
$491$	−15.3753	−0.693878	−0.346939	+	0.937888i	$0.612779\pi$
$492$	6.03149	0.271921
$493$	10.4083	0.468766
$494$	−1.41867	−0.0638289
$495$	0	0
$496$	18.1897	0.816742
$497$	3.12575	0.140209
$498$	−31.4029	−1.40720
$499$	−39.6364	−1.77437	−0.887184	−	0.461415i	$-0.847342\pi$
$499$	−39.6364	−1.77437	−0.887184	+	0.461415i	$0.847342\pi$
$500$	0	0
$501$	−13.4818	−0.602323
$502$	−27.6870	−1.23573
$503$	16.6361	0.741769	0.370884	−	0.928679i	$-0.379055\pi$
$503$	16.6361	0.741769	0.370884	+	0.928679i	$0.379055\pi$
$504$	1.80460	0.0803831
$505$	0	0
$506$	−77.0173	−3.42384
$507$	−12.6485	−0.561740
$508$	−86.8101	−3.85158
$509$	−0.851158	−0.0377269	−0.0188635	−	0.999822i	$-0.506005\pi$
$509$	−0.851158	−0.0377269	−0.0188635	+	0.999822i	$0.506005\pi$
$510$	0	0
$511$	−3.25686	−0.144075
$512$	46.6703	2.06256
$513$	−0.922885	−0.0407464
$514$	49.6283	2.18901
$515$	0	0
$516$	47.0266	2.07023
$517$	−5.72294	−0.251694
$518$	−2.74196	−0.120475
$519$	−9.83060	−0.431516
$520$	0	0
$521$	32.6552	1.43065	0.715324	−	0.698793i	$-0.246279\pi$
$521$	32.6552	1.43065	0.715324	+	0.698793i	$0.246279\pi$
$522$	−12.9643	−0.567433
$523$	20.1249	0.880002	0.440001	−	0.897997i	$-0.354978\pi$
$523$	20.1249	0.880002	0.440001	+	0.897997i	$0.354978\pi$
$524$	61.2968	2.67776
$525$	0	0
$526$	21.4150	0.933737
$527$	4.27356	0.186159
$528$	50.7066	2.20672
$529$	3.93889	0.171256
$530$	0	0
$531$	0.151536	0.00657612
$532$	1.11410	0.0483022
$533$	−0.757124	−0.0327947
$534$	−38.8984	−1.68330
$535$	0	0
$536$	51.1065	2.20747
$537$	1.47971	0.0638541
$538$	−10.4090	−0.448763
$539$	−39.6867	−1.70943
$540$	0	0
$541$	25.7405	1.10667	0.553334	−	0.832959i	$-0.313355\pi$
$541$	25.7405	1.10667	0.553334	+	0.832959i	$0.313355\pi$
$542$	−60.4907	−2.59830
$543$	−26.1734	−1.12321
$544$	−18.4290	−0.790135
$545$	0	0
$546$	−0.392913	−0.0168151
$547$	39.5989	1.69313	0.846564	−	0.532287i	$-0.178667\pi$
$547$	39.5989	1.69313	0.846564	+	0.532287i	$0.178667\pi$
$548$	−0.771348	−0.0329504
$549$	−13.7858	−0.588365
$550$	0	0
$551$	−4.61442	−0.196581
$552$	−36.6443	−1.55969
$553$	0.874121	0.0371714
$554$	−35.9314	−1.52658
$555$	0	0
$556$	−24.7292	−1.04875
$557$	20.9582	0.888029	0.444014	−	0.896020i	$-0.353554\pi$
$557$	20.9582	0.888029	0.444014	+	0.896020i	$0.353554\pi$
$558$	−5.32304	−0.225342
$559$	−5.90317	−0.249678
$560$	0	0
$561$	11.9132	0.502976
$562$	18.0623	0.761912
$563$	−18.2408	−0.768757	−0.384379	−	0.923175i	$-0.625584\pi$
$563$	−18.2408	−0.768757	−0.384379	+	0.923175i	$0.625584\pi$
$564$	−4.72294	−0.198871
$565$	0	0
$566$	−24.2172	−1.01793
$567$	−0.255601	−0.0107342
$568$	86.3392	3.62271
$569$	−11.3490	−0.475777	−0.237888	−	0.971293i	$-0.576455\pi$
$569$	−11.3490	−0.475777	−0.237888	+	0.971293i	$0.576455\pi$
$570$	0	0
$571$	−9.06659	−0.379425	−0.189713	−	0.981840i	$-0.560756\pi$
$571$	−9.06659	−0.379425	−0.189713	+	0.981840i	$0.560756\pi$
$572$	−16.0245	−0.670018
$573$	12.3705	0.516785
$574$	0.846360	0.0353264
$575$	0	0
$576$	5.23414	0.218089
$577$	−33.1680	−1.38080	−0.690401	−	0.723427i	$-0.742566\pi$
$577$	−33.1680	−1.38080	−0.690401	+	0.723427i	$0.742566\pi$
$578$	32.8430	1.36609
$579$	12.3276	0.512317
$580$	0	0
$581$	−3.09566	−0.128430
$582$	−44.1979	−1.83206
$583$	20.4389	0.846492
$584$	−89.9607	−3.72260
$585$	0	0
$586$	63.2765	2.61393
$587$	−21.6328	−0.892879	−0.446440	−	0.894814i	$-0.647308\pi$
$587$	−21.6328	−0.892879	−0.446440	+	0.894814i	$0.647308\pi$
$588$	−32.7520	−1.35067
$589$	−1.89464	−0.0780674
$590$	0	0
$591$	0.230502	0.00948158
$592$	−36.6576	−1.50662
$593$	−18.9467	−0.778048	−0.389024	−	0.921228i	$-0.627188\pi$
$593$	−18.9467	−0.778048	−0.389024	+	0.921228i	$0.627188\pi$
$594$	−14.8388	−0.608843
$595$	0	0
$596$	−29.1773	−1.19515
$597$	−6.02626	−0.246638
$598$	7.97854	0.326267
$599$	31.0551	1.26888	0.634438	−	0.772974i	$-0.281232\pi$
$599$	31.0551	1.26888	0.634438	+	0.772974i	$0.281232\pi$
$600$	0	0
$601$	−14.6170	−0.596241	−0.298120	−	0.954528i	$-0.596360\pi$
$601$	−14.6170	−0.596241	−0.298120	+	0.954528i	$0.596360\pi$
$602$	6.59894	0.268953
$603$	−7.23868	−0.294782
$604$	66.6340	2.71130
$605$	0	0
$606$	−17.8433	−0.724836
$607$	26.9795	1.09506	0.547532	−	0.836785i	$-0.315568\pi$
$607$	26.9795	1.09506	0.547532	+	0.836785i	$0.315568\pi$
$608$	8.17031	0.331350
$609$	−1.27801	−0.0517874
$610$	0	0
$611$	0.592862	0.0239846
$612$	9.83154	0.397417
$613$	−12.2383	−0.494302	−0.247151	−	0.968977i	$-0.579494\pi$
$613$	−12.2383	−0.494302	−0.247151	+	0.968977i	$0.579494\pi$
$614$	−19.9250	−0.804107
$615$	0	0
$616$	10.3276	0.416110
$617$	14.9501	0.601868	0.300934	−	0.953645i	$-0.402702\pi$
$617$	14.9501	0.601868	0.300934	+	0.953645i	$0.402702\pi$
$618$	26.2964	1.05780
$619$	−34.8917	−1.40242	−0.701209	−	0.712956i	$-0.747356\pi$
$619$	−34.8917	−1.40242	−0.701209	+	0.712956i	$0.747356\pi$
$620$	0	0
$621$	5.19027	0.208278
$622$	−6.94100	−0.278309
$623$	−3.83456	−0.153628
$624$	−5.25291	−0.210285
$625$	0	0
$626$	65.8906	2.63352
$627$	−5.28161	−0.210927
$628$	45.2723	1.80656
$629$	−8.61248	−0.343402
$630$	0	0
$631$	38.7601	1.54302	0.771508	−	0.636219i	$-0.219503\pi$
$631$	38.7601	1.54302	0.771508	+	0.636219i	$0.219503\pi$
$632$	24.1449	0.960433
$633$	6.19271	0.246138
$634$	23.3799	0.928534
$635$	0	0
$636$	16.8675	0.668839
$637$	4.11130	0.162896
$638$	−74.1939	−2.93737
$639$	−12.2290	−0.483772
$640$	0	0
$641$	−36.6570	−1.44787	−0.723933	−	0.689870i	$-0.757668\pi$
$641$	−36.6570	−1.44787	−0.723933	+	0.689870i	$0.757668\pi$
$642$	25.8173	1.01893
$643$	−7.87927	−0.310728	−0.155364	−	0.987857i	$-0.549655\pi$
$643$	−7.87927	−0.310728	−0.155364	+	0.987857i	$0.549655\pi$
$644$	−6.26563	−0.246900
$645$	0	0
$646$	4.98123	0.195984
$647$	−2.71394	−0.106696	−0.0533481	−	0.998576i	$-0.516989\pi$
$647$	−2.71394	−0.106696	−0.0533481	+	0.998576i	$0.516989\pi$
$648$	−7.06020	−0.277351
$649$	0.867233	0.0340419
$650$	0	0
$651$	−0.524739	−0.0205661
$652$	16.2746	0.637363
$653$	16.6164	0.650251	0.325126	−	0.945671i	$-0.394593\pi$
$653$	16.6164	0.650251	0.325126	+	0.945671i	$0.394593\pi$
$654$	−10.5463	−0.412393
$655$	0	0
$656$	11.3151	0.441781
$657$	12.7420	0.497111
$658$	−0.662739	−0.0258363
$659$	36.7746	1.43254	0.716268	−	0.697826i	$-0.245849\pi$
$659$	36.7746	1.43254	0.716268	+	0.697826i	$0.245849\pi$
$660$	0	0
$661$	−4.58806	−0.178455	−0.0892275	−	0.996011i	$-0.528440\pi$
$661$	−4.58806	−0.178455	−0.0892275	+	0.996011i	$0.528440\pi$
$662$	79.0472	3.07226
$663$	−1.23414	−0.0479299
$664$	−85.5082	−3.31836
$665$	0	0
$666$	10.7275	0.415681
$667$	25.9513	1.00484
$668$	−63.6737	−2.46361
$669$	−18.8817	−0.730009
$670$	0	0
$671$	−78.8954	−3.04572
$672$	2.26284	0.0872910
$673$	1.50396	0.0579735	0.0289868	−	0.999580i	$-0.490772\pi$
$673$	1.50396	0.0579735	0.0289868	+	0.999580i	$0.490772\pi$
$674$	−61.9762	−2.38723
$675$	0	0
$676$	−59.7381	−2.29762
$677$	33.0303	1.26946	0.634729	−	0.772735i	$-0.281112\pi$
$677$	33.0303	1.26946	0.634729	+	0.772735i	$0.281112\pi$
$678$	15.5133	0.595785
$679$	−4.35697	−0.167205
$680$	0	0
$681$	−13.1564	−0.504156
$682$	−30.4634	−1.16650
$683$	−44.3575	−1.69729	−0.848646	−	0.528961i	$-0.822582\pi$
$683$	−44.3575	−1.69729	−0.848646	+	0.528961i	$0.822582\pi$
$684$	−4.35872	−0.166660
$685$	0	0
$686$	−9.23505	−0.352596
$687$	27.3071	1.04183
$688$	88.2221	3.36344
$689$	−2.11735	−0.0806645
$690$	0	0
$691$	28.4227	1.08125	0.540624	−	0.841264i	$-0.318188\pi$
$691$	28.4227	1.08125	0.540624	+	0.841264i	$0.318188\pi$
$692$	−46.4293	−1.76498
$693$	−1.46279	−0.0555668
$694$	28.7756	1.09231
$695$	0	0
$696$	−35.3010	−1.33808
$697$	2.65841	0.100695
$698$	−49.9819	−1.89184
$699$	20.1888	0.763609
$700$	0	0
$701$	−21.7652	−0.822061	−0.411030	−	0.911622i	$-0.634831\pi$
$701$	−21.7652	−0.822061	−0.411030	+	0.911622i	$0.634831\pi$
$702$	1.53721	0.0580183
$703$	3.81826	0.144008
$704$	29.9546	1.12896
$705$	0	0
$706$	−76.2402	−2.86934
$707$	−1.75897	−0.0661530
$708$	0.715696	0.0268975
$709$	−41.0786	−1.54274	−0.771370	−	0.636387i	$-0.780428\pi$
$709$	−41.0786	−1.54274	−0.771370	+	0.636387i	$0.780428\pi$
$710$	0	0
$711$	−3.41986	−0.128255
$712$	−105.918	−3.96944
$713$	10.6554	0.399048
$714$	1.37960	0.0516301
$715$	0	0
$716$	6.98857	0.261175
$717$	12.9785	0.484692
$718$	−29.4640	−1.09959
$719$	−1.09159	−0.0407095	−0.0203548	−	0.999793i	$-0.506480\pi$
$719$	−1.09159	−0.0407095	−0.0203548	+	0.999793i	$0.506480\pi$
$720$	0	0
$721$	2.59227	0.0965412
$722$	47.0560	1.75124
$723$	−10.5427	−0.392087
$724$	−123.615	−4.59412
$725$	0	0
$726$	−56.3999	−2.09320
$727$	−35.2796	−1.30845	−0.654223	−	0.756302i	$-0.727004\pi$
$727$	−35.2796	−1.30845	−0.654223	+	0.756302i	$0.727004\pi$
$728$	−1.06988	−0.0396523
$729$	1.00000	0.0370370
$730$	0	0
$731$	20.7272	0.766625
$732$	−65.1096	−2.40652
$733$	4.48519	0.165664	0.0828322	−	0.996564i	$-0.473603\pi$
$733$	4.48519	0.165664	0.0828322	+	0.996564i	$0.473603\pi$
$734$	−32.2783	−1.19141
$735$	0	0
$736$	−45.9495	−1.69372
$737$	−41.4265	−1.52597
$738$	−3.31125	−0.121889
$739$	45.9468	1.69018	0.845090	−	0.534624i	$-0.179547\pi$
$739$	45.9468	1.69018	0.845090	+	0.534624i	$0.179547\pi$
$740$	0	0
$741$	0.547144	0.0200998
$742$	2.36690	0.0868918
$743$	−41.0446	−1.50578	−0.752890	−	0.658147i	$-0.771341\pi$
$743$	−41.0446	−1.50578	−0.752890	+	0.658147i	$0.771341\pi$
$744$	−14.4943	−0.531386
$745$	0	0
$746$	−93.7423	−3.43215
$747$	12.1113	0.443129
$748$	56.2653	2.05726
$749$	2.54504	0.0929938
$750$	0	0
$751$	1.94529	0.0709846	0.0354923	−	0.999370i	$-0.488700\pi$
$751$	1.94529	0.0709846	0.0354923	+	0.999370i	$0.488700\pi$
$752$	−8.86025	−0.323100
$753$	10.6782	0.389134
$754$	7.68605	0.279910
$755$	0	0
$756$	−1.20719	−0.0439050
$757$	−37.1043	−1.34858	−0.674290	−	0.738467i	$-0.735550\pi$
$757$	−37.1043	−1.34858	−0.674290	+	0.738467i	$0.735550\pi$
$758$	−61.4226	−2.23097
$759$	29.7036	1.07817
$760$	0	0
$761$	32.4865	1.17763	0.588817	−	0.808267i	$-0.299594\pi$
$761$	32.4865	1.17763	0.588817	+	0.808267i	$0.299594\pi$
$762$	47.6582	1.72647
$763$	−1.03964	−0.0376376
$764$	58.4251	2.11375
$765$	0	0
$766$	−99.4677	−3.59391
$767$	−0.0898402	−0.00324394
$768$	−21.1888	−0.764584
$769$	19.2294	0.693428	0.346714	−	0.937971i	$-0.387297\pi$
$769$	19.2294	0.693428	0.346714	+	0.937971i	$0.387297\pi$
$770$	0	0
$771$	−19.1404	−0.689323
$772$	58.2224	2.09547
$773$	20.6071	0.741185	0.370593	−	0.928795i	$-0.379155\pi$
$773$	20.6071	0.741185	0.370593	+	0.928795i	$0.379155\pi$
$774$	−25.8173	−0.927984
$775$	0	0
$776$	−120.348	−4.32024
$777$	1.05750	0.0379377
$778$	71.6873	2.57012
$779$	−1.17858	−0.0422271
$780$	0	0
$781$	−69.9858	−2.50429
$782$	−28.0143	−1.00179
$783$	5.00000	0.178685
$784$	−61.4429	−2.19439
$785$	0	0
$786$	−33.6516	−1.20031
$787$	35.2935	1.25808	0.629039	−	0.777374i	$-0.283449\pi$
$787$	35.2935	1.25808	0.629039	+	0.777374i	$0.283449\pi$
$788$	1.08865	0.0387814
$789$	−8.25920	−0.294035
$790$	0	0
$791$	1.52928	0.0543750
$792$	−40.4050	−1.43573
$793$	8.17310	0.290235
$794$	−81.6008	−2.89590
$795$	0	0
$796$	−28.4616	−1.00880
$797$	8.32069	0.294734	0.147367	−	0.989082i	$-0.452920\pi$
$797$	8.32069	0.294734	0.147367	+	0.989082i	$0.452920\pi$
$798$	−0.611632	−0.0216515
$799$	−2.08166	−0.0736438
$800$	0	0
$801$	15.0021	0.530073
$802$	−97.4090	−3.43963
$803$	72.9214	2.57334
$804$	−34.1878	−1.20571
$805$	0	0
$806$	3.15583	0.111159
$807$	4.01448	0.141316
$808$	−48.5862	−1.70926
$809$	−25.2044	−0.886140	−0.443070	−	0.896487i	$-0.646111\pi$
$809$	−25.2044	−0.886140	−0.443070	+	0.896487i	$0.646111\pi$
$810$	0	0
$811$	24.2317	0.850890	0.425445	−	0.904984i	$-0.360118\pi$
$811$	24.2317	0.850890	0.425445	+	0.904984i	$0.360118\pi$
$812$	−6.03594	−0.211820
$813$	23.3297	0.818208
$814$	61.3927	2.15181
$815$	0	0
$816$	18.4440	0.645670
$817$	−9.18923	−0.321490
$818$	−25.0291	−0.875120
$819$	0.151536	0.00529511
$820$	0	0
$821$	26.8506	0.937092	0.468546	−	0.883439i	$-0.344778\pi$
$821$	26.8506	0.937092	0.468546	+	0.883439i	$0.344778\pi$
$822$	0.423465	0.0147701
$823$	22.9116	0.798648	0.399324	−	0.916810i	$-0.369245\pi$
$823$	22.9116	0.798648	0.399324	+	0.916810i	$0.369245\pi$
$824$	71.6035	2.49443
$825$	0	0
$826$	0.100429	0.00349437
$827$	6.89989	0.239933	0.119966	−	0.992778i	$-0.461721\pi$
$827$	6.89989	0.239933	0.119966	+	0.992778i	$0.461721\pi$
$828$	24.5133	0.851896
$829$	−29.7133	−1.03199	−0.515993	−	0.856593i	$-0.672577\pi$
$829$	−29.7133	−1.03199	−0.515993	+	0.856593i	$0.672577\pi$
$830$	0	0
$831$	13.8578	0.480722
$832$	−3.10312	−0.107581
$833$	−14.4356	−0.500165
$834$	13.5762	0.470105
$835$	0	0
$836$	−24.9447	−0.862730
$837$	2.05296	0.0709606
$838$	21.5287	0.743697
$839$	10.1398	0.350063	0.175032	−	0.984563i	$-0.443997\pi$
$839$	10.1398	0.350063	0.175032	+	0.984563i	$0.443997\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	−43.5329	−1.50024
$843$	−6.96616	−0.239927
$844$	29.2478	1.00675
$845$	0	0
$846$	2.59286	0.0891444
$847$	−5.55984	−0.191038
$848$	31.6435	1.08664
$849$	9.33996	0.320546
$850$	0	0
$851$	−21.4738	−0.736111
$852$	−57.7568	−1.97871
$853$	−45.9039	−1.57172	−0.785859	−	0.618405i	$-0.787779\pi$
$853$	−45.9039	−1.57172	−0.785859	+	0.618405i	$0.787779\pi$
$854$	−9.13640	−0.312641
$855$	0	0
$856$	70.2989	2.40277
$857$	−19.0811	−0.651797	−0.325898	−	0.945405i	$-0.605667\pi$
$857$	−19.0811	−0.651797	−0.325898	+	0.945405i	$0.605667\pi$
$858$	8.79736	0.300337
$859$	11.4523	0.390746	0.195373	−	0.980729i	$-0.437408\pi$
$859$	11.4523	0.390746	0.195373	+	0.980729i	$0.437408\pi$
$860$	0	0
$861$	−0.326419	−0.0111243
$862$	−4.54176	−0.154693
$863$	−37.8374	−1.28800	−0.644000	−	0.765026i	$-0.722726\pi$
$863$	−37.8374	−1.28800	−0.644000	+	0.765026i	$0.722726\pi$
$864$	−8.85301	−0.301185
$865$	0	0
$866$	25.0533	0.851345
$867$	−12.6667	−0.430183
$868$	−2.47831	−0.0841192
$869$	−19.5717	−0.663923
$870$	0	0
$871$	4.29154	0.145413
$872$	−28.7169	−0.972477
$873$	17.0460	0.576919
$874$	12.4199	0.420108
$875$	0	0
$876$	60.1794	2.03327
$877$	−42.0213	−1.41896	−0.709478	−	0.704727i	$-0.751069\pi$
$877$	−42.0213	−1.41896	−0.709478	+	0.704727i	$0.751069\pi$
$878$	−66.4874	−2.24384
$879$	−24.4041	−0.823130
$880$	0	0
$881$	−9.80589	−0.330369	−0.165184	−	0.986263i	$-0.552822\pi$
$881$	−9.80589	−0.330369	−0.165184	+	0.986263i	$0.552822\pi$
$882$	17.9806	0.605440
$883$	−11.6264	−0.391261	−0.195631	−	0.980678i	$-0.562675\pi$
$883$	−11.6264	−0.391261	−0.195631	+	0.980678i	$0.562675\pi$
$884$	−5.82875	−0.196042
$885$	0	0
$886$	−79.9402	−2.68564
$887$	−0.340611	−0.0114366	−0.00571830	−	0.999984i	$-0.501820\pi$
$887$	−0.340611	−0.0114366	−0.00571830	+	0.999984i	$0.501820\pi$
$888$	29.2102	0.980231
$889$	4.69809	0.157569
$890$	0	0
$891$	5.72294	0.191726
$892$	−89.1771	−2.98587
$893$	0.922885	0.0308832
$894$	16.0182	0.535728
$895$	0	0
$896$	−1.05681	−0.0353057
$897$	−3.07712	−0.102742
$898$	−76.3945	−2.54932
$899$	10.2648	0.342350
$900$	0	0
$901$	7.43444	0.247677
$902$	−18.9501	−0.630969
$903$	−2.54504	−0.0846936
$904$	42.2417	1.40494
$905$	0	0
$906$	−36.5817	−1.21534
$907$	24.4184	0.810798	0.405399	−	0.914140i	$-0.367133\pi$
$907$	24.4184	0.810798	0.405399	+	0.914140i	$0.367133\pi$
$908$	−62.1370	−2.06209
$909$	6.88171	0.228252
$910$	0	0
$911$	−16.3204	−0.540718	−0.270359	−	0.962760i	$-0.587142\pi$
$911$	−16.3204	−0.540718	−0.270359	+	0.962760i	$0.587142\pi$
$912$	−8.17699	−0.270767
$913$	69.3122	2.29390
$914$	87.8185	2.90478
$915$	0	0
$916$	128.969	4.26127
$917$	−3.31733	−0.109548
$918$	−5.39746	−0.178143
$919$	−36.7155	−1.21113	−0.605566	−	0.795795i	$-0.707053\pi$
$919$	−36.7155	−1.21113	−0.605566	+	0.795795i	$0.707053\pi$
$920$	0	0
$921$	7.68455	0.253215
$922$	15.3061	0.504080
$923$	7.25012	0.238640
$924$	−6.90866	−0.227278
$925$	0	0
$926$	104.379	3.43010
$927$	−10.1419	−0.333102
$928$	−44.2650	−1.45307
$929$	−4.04713	−0.132782	−0.0663911	−	0.997794i	$-0.521148\pi$
$929$	−4.04713	−0.132782	−0.0663911	+	0.997794i	$0.521148\pi$
$930$	0	0
$931$	6.39990	0.209748
$932$	95.3503	3.12330
$933$	2.67696	0.0876399
$934$	24.4425	0.799784
$935$	0	0
$936$	4.18572	0.136815
$937$	−36.5551	−1.19420	−0.597101	−	0.802166i	$-0.703681\pi$
$937$	−36.5551	−1.19420	−0.597101	+	0.802166i	$0.703681\pi$
$938$	−4.79736	−0.156639
$939$	−25.4123	−0.829299
$940$	0	0
$941$	−4.05252	−0.132108	−0.0660542	−	0.997816i	$-0.521041\pi$
$941$	−4.05252	−0.132108	−0.0660542	+	0.997816i	$0.521041\pi$
$942$	−24.8542	−0.809794
$943$	6.62831	0.215847
$944$	1.34265	0.0436995
$945$	0	0
$946$	−147.751	−4.80379
$947$	−36.8551	−1.19763	−0.598816	−	0.800887i	$-0.704362\pi$
$947$	−36.8551	−1.19763	−0.598816	+	0.800887i	$0.704362\pi$
$948$	−16.1518	−0.524586
$949$	−7.55423	−0.245221
$950$	0	0
$951$	−9.01702	−0.292397
$952$	3.75655	0.121751
$953$	40.3878	1.30829	0.654145	−	0.756369i	$-0.273029\pi$
$953$	40.3878	1.30829	0.654145	+	0.756369i	$0.273029\pi$
$954$	−9.26015	−0.299808
$955$	0	0
$956$	61.2968	1.98248
$957$	28.6147	0.924981
$958$	−2.13033	−0.0688277
$959$	0.0417447	0.00134801
$960$	0	0
$961$	−26.7854	−0.864044
$962$	−6.35992	−0.205052
$963$	−9.95707	−0.320862
$964$	−49.7925	−1.60371
$965$	0	0
$966$	3.43979	0.110674
$967$	−9.09429	−0.292453	−0.146226	−	0.989251i	$-0.546713\pi$
$967$	−9.09429	−0.292453	−0.146226	+	0.989251i	$0.546713\pi$
$968$	−153.573	−4.93603
$969$	−1.92113	−0.0617157
$970$	0	0
$971$	−44.3322	−1.42269	−0.711344	−	0.702844i	$-0.751913\pi$
$971$	−44.3322	−1.42269	−0.711344	+	0.702844i	$0.751913\pi$
$972$	4.72294	0.151488
$973$	1.33833	0.0429047
$974$	19.0967	0.611899
$975$	0	0
$976$	−122.146	−3.90979
$977$	29.3486	0.938943	0.469472	−	0.882948i	$-0.344444\pi$
$977$	29.3486	0.938943	0.469472	+	0.882948i	$0.344444\pi$
$978$	−8.93467	−0.285699
$979$	85.8561	2.74397
$980$	0	0
$981$	4.06744	0.129863
$982$	39.8661	1.27218
$983$	20.5133	0.654273	0.327136	−	0.944977i	$-0.393916\pi$
$983$	20.5133	0.654273	0.327136	+	0.944977i	$0.393916\pi$
$984$	−9.01633	−0.287430
$985$	0	0
$986$	−26.9873	−0.859450
$987$	0.255601	0.00813588
$988$	2.58412	0.0822119
$989$	51.6799	1.64332
$990$	0	0
$991$	33.6486	1.06888	0.534442	−	0.845205i	$-0.320522\pi$
$991$	33.6486	1.06888	0.534442	+	0.845205i	$0.320522\pi$
$992$	−18.1749	−0.577052
$993$	−30.4865	−0.967458
$994$	−8.10464	−0.257063
$995$	0	0
$996$	57.2009	1.81248
$997$	34.7387	1.10019	0.550093	−	0.835103i	$-0.314592\pi$
$997$	34.7387	1.10019	0.550093	+	0.835103i	$0.314592\pi$
$998$	102.772	3.25318
$999$	−4.13731	−0.130899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.u.1.1		4
5.4	even	2		705.2.a.j.1.4	✓	4
15.14	odd	2		2115.2.a.p.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.2.a.j.1.4	✓	4	5.4	even	2
2115.2.a.p.1.1		4	15.14	odd	2
3525.2.a.u.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:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q-2.59286 q^{2} +1.00000 q^{3} +4.72294 q^{4} -2.59286 q^{6} -0.255601 q^{7} -7.06020 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.59286 q^{2} +1.00000 q^{3} +4.72294 q^{4} -2.59286 q^{6} -0.255601 q^{7} -7.06020 q^{8} +1.00000 q^{9} +5.72294 q^{11} +4.72294 q^{12} -0.592862 q^{13} +0.662739 q^{14} +8.86025 q^{16} +2.08166 q^{17} -2.59286 q^{18} -0.922885 q^{19} -0.255601 q^{21} -14.8388 q^{22} +5.19027 q^{23} -7.06020 q^{24} +1.53721 q^{26} +1.00000 q^{27} -1.20719 q^{28} +5.00000 q^{29} +2.05296 q^{31} -8.85301 q^{32} +5.72294 q^{33} -5.39746 q^{34} +4.72294 q^{36} -4.13731 q^{37} +2.39291 q^{38} -0.592862 q^{39} +1.27706 q^{41} +0.662739 q^{42} +9.95707 q^{43} +27.0291 q^{44} -13.4577 q^{46} -1.00000 q^{47} +8.86025 q^{48} -6.93467 q^{49} +2.08166 q^{51} -2.80005 q^{52} +3.57140 q^{53} -2.59286 q^{54} +1.80460 q^{56} -0.922885 q^{57} -12.9643 q^{58} +0.151536 q^{59} -13.7858 q^{61} -5.32304 q^{62} -0.255601 q^{63} +5.23414 q^{64} -14.8388 q^{66} -7.23868 q^{67} +9.83154 q^{68} +5.19027 q^{69} -12.2290 q^{71} -7.06020 q^{72} +12.7420 q^{73} +10.7275 q^{74} -4.35872 q^{76} -1.46279 q^{77} +1.53721 q^{78} -3.41986 q^{79} +1.00000 q^{81} -3.31125 q^{82} +12.1113 q^{83} -1.20719 q^{84} -25.8173 q^{86} +5.00000 q^{87} -40.4050 q^{88} +15.0021 q^{89} +0.151536 q^{91} +24.5133 q^{92} +2.05296 q^{93} +2.59286 q^{94} -8.85301 q^{96} +17.0460 q^{97} +17.9806 q^{98} +5.72294 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 4 q^{3} + 4 q^{4} - 2 q^{6} - 6 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 4 * q^3 + 4 * q^4 - 2 * q^6 - 6 * q^8 + 4 * q^9	\( 4 q - 2 q^{2} + 4 q^{3} + 4 q^{4} - 2 q^{6} - 6 q^{8} + 4 q^{9} + 8 q^{11} + 4 q^{12} + 6 q^{13} + 10 q^{14} + 4 q^{16} + 2 q^{17} - 2 q^{18} + 2 q^{19} - 12 q^{22} - 8 q^{23} - 6 q^{24} + 8 q^{26} + 4 q^{27} - 4 q^{28} + 20 q^{29} - 4 q^{31} - 14 q^{32} + 8 q^{33} + 8 q^{34} + 4 q^{36} - 8 q^{38} + 6 q^{39} + 20 q^{41} + 10 q^{42} + 8 q^{43} + 32 q^{44} - 2 q^{46} - 4 q^{47} + 4 q^{48} + 2 q^{51} - 2 q^{52} - 10 q^{53} - 2 q^{54} - 14 q^{56} + 2 q^{57} - 10 q^{58} + 10 q^{59} - 20 q^{61} + 12 q^{62} + 4 q^{64} - 12 q^{66} + 2 q^{68} - 8 q^{69} + 18 q^{71} - 6 q^{72} + 4 q^{73} + 16 q^{74} - 26 q^{76} - 4 q^{77} + 8 q^{78} + 20 q^{79} + 4 q^{81} - 2 q^{82} + 28 q^{83} - 4 q^{84} - 40 q^{86} + 20 q^{87} - 40 q^{88} + 10 q^{91} + 36 q^{92} - 4 q^{93} + 2 q^{94} - 14 q^{96} + 20 q^{97} - 4 q^{98} + 8 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 4 * q^3 + 4 * q^4 - 2 * q^6 - 6 * q^8 + 4 * q^9 + 8 * q^11 + 4 * q^12 + 6 * q^13 + 10 * q^14 + 4 * q^16 + 2 * q^17 - 2 * q^18 + 2 * q^19 - 12 * q^22 - 8 * q^23 - 6 * q^24 + 8 * q^26 + 4 * q^27 - 4 * q^28 + 20 * q^29 - 4 * q^31 - 14 * q^32 + 8 * q^33 + 8 * q^34 + 4 * q^36 - 8 * q^38 + 6 * q^39 + 20 * q^41 + 10 * q^42 + 8 * q^43 + 32 * q^44 - 2 * q^46 - 4 * q^47 + 4 * q^48 + 2 * q^51 - 2 * q^52 - 10 * q^53 - 2 * q^54 - 14 * q^56 + 2 * q^57 - 10 * q^58 + 10 * q^59 - 20 * q^61 + 12 * q^62 + 4 * q^64 - 12 * q^66 + 2 * q^68 - 8 * q^69 + 18 * q^71 - 6 * q^72 + 4 * q^73 + 16 * q^74 - 26 * q^76 - 4 * q^77 + 8 * q^78 + 20 * q^79 + 4 * q^81 - 2 * q^82 + 28 * q^83 - 4 * q^84 - 40 * q^86 + 20 * q^87 - 40 * q^88 + 10 * q^91 + 36 * q^92 - 4 * q^93 + 2 * q^94 - 14 * q^96 + 20 * q^97 - 4 * q^98 + 8 * q^99

Introduction

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