LMFDB - Embedded newform 7406.2.a.bb.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7406,2,Mod(1,7406)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7406, 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("7406.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7406 = 2 \cdot 7 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7406.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:	$59.1372077370$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.4352.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 6x^{2} - 4x + 2 $ x^4 - 6x^2 - 4x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.27133$ of defining polynomial
Character	$\chi$	$=$	7406.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.68554 q^{3} +1.00000 q^{4} -2.52660 q^{5} +2.68554 q^{6} +1.00000 q^{7} +1.00000 q^{8} +4.21215 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.68554 q^{3} +1.00000 q^{4} -2.52660 q^{5} +2.68554 q^{6} +1.00000 q^{7} +1.00000 q^{8} +4.21215 q^{9} -2.52660 q^{10} -3.41421 q^{11} +2.68554 q^{12} -0.744728 q^{13} +1.00000 q^{14} -6.78530 q^{15} +1.00000 q^{16} +0.526602 q^{17} +4.21215 q^{18} -7.37109 q^{19} -2.52660 q^{20} +2.68554 q^{21} -3.41421 q^{22} +2.68554 q^{24} +1.38372 q^{25} -0.744728 q^{26} +3.25527 q^{27} +1.00000 q^{28} -4.92638 q^{29} -6.78530 q^{30} -5.73875 q^{31} +1.00000 q^{32} -9.16902 q^{33} +0.526602 q^{34} -2.52660 q^{35} +4.21215 q^{36} -2.18165 q^{37} -7.37109 q^{38} -2.00000 q^{39} -2.52660 q^{40} -10.9670 q^{41} +2.68554 q^{42} +5.68897 q^{43} -3.41421 q^{44} -10.6424 q^{45} +2.62455 q^{47} +2.68554 q^{48} +1.00000 q^{49} +1.38372 q^{50} +1.41421 q^{51} -0.744728 q^{52} -6.27476 q^{53} +3.25527 q^{54} +8.62636 q^{55} +1.00000 q^{56} -19.7954 q^{57} -4.92638 q^{58} +7.73875 q^{59} -6.78530 q^{60} -12.5013 q^{61} -5.73875 q^{62} +4.21215 q^{63} +1.00000 q^{64} +1.88163 q^{65} -9.16902 q^{66} -12.1817 q^{67} +0.526602 q^{68} -2.52660 q^{70} -0.603650 q^{71} +4.21215 q^{72} +15.2754 q^{73} -2.18165 q^{74} +3.71604 q^{75} -7.37109 q^{76} -3.41421 q^{77} -2.00000 q^{78} +0.631207 q^{79} -2.52660 q^{80} -3.89426 q^{81} -10.9670 q^{82} +4.74473 q^{83} +2.68554 q^{84} -1.33051 q^{85} +5.68897 q^{86} -13.2300 q^{87} -3.41421 q^{88} +13.6931 q^{89} -10.6424 q^{90} -0.744728 q^{91} -15.4117 q^{93} +2.62455 q^{94} +18.6238 q^{95} +2.68554 q^{96} +16.5240 q^{97} +1.00000 q^{98} -14.3812 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{4} - 4 q^{5} + 4 q^{7} + 4 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^4 - 4 * q^5 + 4 * q^7 + 4 * q^8	$ 4 q + 4 q^{2} + 4 q^{4} - 4 q^{5} + 4 q^{7} + 4 q^{8} - 4 q^{10} - 8 q^{11} - 4 q^{13} + 4 q^{14} + 4 q^{16} - 4 q^{17} - 8 q^{19} - 4 q^{20} - 8 q^{22} - 4 q^{26} + 12 q^{27} + 4 q^{28} - 4 q^{29} + 4 q^{32} - 4 q^{33} - 4 q^{34} - 4 q^{35} + 8 q^{37} - 8 q^{38} - 8 q^{39} - 4 q^{40} - 8 q^{43} - 8 q^{44} - 16 q^{45} + 4 q^{49} - 4 q^{52} + 12 q^{54} + 12 q^{55} + 4 q^{56} - 24 q^{57} - 4 q^{58} + 8 q^{59} - 12 q^{61} + 4 q^{64} - 16 q^{65} - 4 q^{66} - 32 q^{67} - 4 q^{68} - 4 q^{70} + 8 q^{71} + 4 q^{73} + 8 q^{74} + 4 q^{75} - 8 q^{76} - 8 q^{77} - 8 q^{78} - 16 q^{79} - 4 q^{80} - 8 q^{81} + 20 q^{83} - 12 q^{85} - 8 q^{86} - 20 q^{87} - 8 q^{88} - 28 q^{89} - 16 q^{90} - 4 q^{91} - 12 q^{93} + 8 q^{95} + 16 q^{97} + 4 q^{98} - 8 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^4 - 4 * q^5 + 4 * q^7 + 4 * q^8 - 4 * q^10 - 8 * q^11 - 4 * q^13 + 4 * q^14 + 4 * q^16 - 4 * q^17 - 8 * q^19 - 4 * q^20 - 8 * q^22 - 4 * q^26 + 12 * q^27 + 4 * q^28 - 4 * q^29 + 4 * q^32 - 4 * q^33 - 4 * q^34 - 4 * q^35 + 8 * q^37 - 8 * q^38 - 8 * q^39 - 4 * q^40 - 8 * q^43 - 8 * q^44 - 16 * q^45 + 4 * q^49 - 4 * q^52 + 12 * q^54 + 12 * q^55 + 4 * q^56 - 24 * q^57 - 4 * q^58 + 8 * q^59 - 12 * q^61 + 4 * q^64 - 16 * q^65 - 4 * q^66 - 32 * q^67 - 4 * q^68 - 4 * q^70 + 8 * q^71 + 4 * q^73 + 8 * q^74 + 4 * q^75 - 8 * q^76 - 8 * q^77 - 8 * q^78 - 16 * q^79 - 4 * q^80 - 8 * q^81 + 20 * q^83 - 12 * q^85 - 8 * q^86 - 20 * q^87 - 8 * q^88 - 28 * q^89 - 16 * q^90 - 4 * q^91 - 12 * q^93 + 8 * q^95 + 16 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.68554	1.55050	0.775250	−	0.631655i	$-0.217624\pi$
$3$	2.68554	1.55050	0.775250	+	0.631655i	$0.217624\pi$
$4$	1.00000	0.500000
$5$	−2.52660	−1.12993	−0.564965	−	0.825115i	$-0.691111\pi$
$5$	−2.52660	−1.12993	−0.564965	+	0.825115i	$0.691111\pi$
$6$	2.68554	1.09637
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	4.21215	1.40405
$10$	−2.52660	−0.798982
$11$	−3.41421	−1.02942	−0.514712	−	0.857363i	$-0.672101\pi$
$11$	−3.41421	−1.02942	−0.514712	+	0.857363i	$0.672101\pi$
$12$	2.68554	0.775250
$13$	−0.744728	−0.206550	−0.103275	−	0.994653i	$-0.532932\pi$
$13$	−0.744728	−0.206550	−0.103275	+	0.994653i	$0.532932\pi$
$14$	1.00000	0.267261
$15$	−6.78530	−1.75196
$16$	1.00000	0.250000
$17$	0.526602	0.127720	0.0638599	−	0.997959i	$-0.479659\pi$
$17$	0.526602	0.127720	0.0638599	+	0.997959i	$0.479659\pi$
$18$	4.21215	0.992812
$19$	−7.37109	−1.69104	−0.845522	−	0.533941i	$-0.820710\pi$
$19$	−7.37109	−1.69104	−0.845522	+	0.533941i	$0.820710\pi$
$20$	−2.52660	−0.564965
$21$	2.68554	0.586034
$22$	−3.41421	−0.727913
$23$	0	0
$23$	0	0
$24$	2.68554	0.548184
$25$	1.38372	0.276744
$26$	−0.744728	−0.146053
$27$	3.25527	0.626477
$28$	1.00000	0.188982
$29$	−4.92638	−0.914806	−0.457403	−	0.889260i	$-0.651220\pi$
$29$	−4.92638	−0.914806	−0.457403	+	0.889260i	$0.651220\pi$
$30$	−6.78530	−1.23882
$31$	−5.73875	−1.03071	−0.515355	−	0.856977i	$-0.672340\pi$
$31$	−5.73875	−1.03071	−0.515355	+	0.856977i	$0.672340\pi$
$32$	1.00000	0.176777
$33$	−9.16902	−1.59612
$34$	0.526602	0.0903115
$35$	−2.52660	−0.427074
$36$	4.21215	0.702024
$37$	−2.18165	−0.358661	−0.179331	−	0.983789i	$-0.557393\pi$
$37$	−2.18165	−0.358661	−0.179331	+	0.983789i	$0.557393\pi$
$38$	−7.37109	−1.19575
$39$	−2.00000	−0.320256
$40$	−2.52660	−0.399491
$41$	−10.9670	−1.71275	−0.856375	−	0.516354i	$-0.827289\pi$
$41$	−10.9670	−1.71275	−0.856375	+	0.516354i	$0.827289\pi$
$42$	2.68554	0.414388
$43$	5.68897	0.867560	0.433780	−	0.901019i	$-0.357180\pi$
$43$	5.68897	0.867560	0.433780	+	0.901019i	$0.357180\pi$
$44$	−3.41421	−0.514712
$45$	−10.6424	−1.58648
$46$	0	0
$47$	2.62455	0.382831	0.191415	−	0.981509i	$-0.438692\pi$
$47$	2.62455	0.382831	0.191415	+	0.981509i	$0.438692\pi$
$48$	2.68554	0.387625
$49$	1.00000	0.142857
$50$	1.38372	0.195687
$51$	1.41421	0.198030
$52$	−0.744728	−0.103275
$53$	−6.27476	−0.861904	−0.430952	−	0.902375i	$-0.641822\pi$
$53$	−6.27476	−0.861904	−0.430952	+	0.902375i	$0.641822\pi$
$54$	3.25527	0.442986
$55$	8.62636	1.16318
$56$	1.00000	0.133631
$57$	−19.7954	−2.62196
$58$	−4.92638	−0.646865
$59$	7.73875	1.00750	0.503750	−	0.863850i	$-0.331953\pi$
$59$	7.73875	1.00750	0.503750	+	0.863850i	$0.331953\pi$
$60$	−6.78530	−0.875979
$61$	−12.5013	−1.60063	−0.800316	−	0.599578i	$-0.795335\pi$
$61$	−12.5013	−1.60063	−0.800316	+	0.599578i	$0.795335\pi$
$62$	−5.73875	−0.728822
$63$	4.21215	0.530681
$64$	1.00000	0.125000
$65$	1.88163	0.233388
$66$	−9.16902	−1.12863
$67$	−12.1817	−1.48823	−0.744113	−	0.668054i	$-0.767128\pi$
$67$	−12.1817	−1.48823	−0.744113	+	0.668054i	$0.767128\pi$
$68$	0.526602	0.0638599
$69$	0	0
$70$	−2.52660	−0.301987
$71$	−0.603650	−0.0716400	−0.0358200	−	0.999358i	$-0.511404\pi$
$71$	−0.603650	−0.0716400	−0.0358200	+	0.999358i	$0.511404\pi$
$72$	4.21215	0.496406
$73$	15.2754	1.78785	0.893927	−	0.448213i	$-0.147939\pi$
$73$	15.2754	1.78785	0.893927	+	0.448213i	$0.147939\pi$
$74$	−2.18165	−0.253612
$75$	3.71604	0.429091
$76$	−7.37109	−0.845522
$77$	−3.41421	−0.389086
$78$	−2.00000	−0.226455
$79$	0.631207	0.0710163	0.0355081	−	0.999369i	$-0.488695\pi$
$79$	0.631207	0.0710163	0.0355081	+	0.999369i	$0.488695\pi$
$80$	−2.52660	−0.282483
$81$	−3.89426	−0.432696
$82$	−10.9670	−1.21110
$83$	4.74473	0.520802	0.260401	−	0.965501i	$-0.416145\pi$
$83$	4.74473	0.520802	0.260401	+	0.965501i	$0.416145\pi$
$84$	2.68554	0.293017
$85$	−1.33051	−0.144315
$86$	5.68897	0.613458
$87$	−13.2300	−1.41841
$88$	−3.41421	−0.363956
$89$	13.6931	1.45146	0.725731	−	0.687978i	$-0.241502\pi$
$89$	13.6931	1.45146	0.725731	+	0.687978i	$0.241502\pi$
$90$	−10.6424	−1.12181
$91$	−0.744728	−0.0780687
$92$	0	0
$93$	−15.4117	−1.59811
$94$	2.62455	0.270702
$95$	18.6238	1.91076
$96$	2.68554	0.274092
$97$	16.5240	1.67776	0.838882	−	0.544314i	$-0.183210\pi$
$97$	16.5240	1.67776	0.838882	+	0.544314i	$0.183210\pi$
$98$	1.00000	0.101015
$99$	−14.3812	−1.44536
$100$	1.38372	0.138372
$101$	0.141078	0.0140378	0.00701891	−	0.999975i	$-0.497766\pi$
$101$	0.141078	0.0140378	0.00701891	+	0.999975i	$0.497766\pi$
$102$	1.41421	0.140028
$103$	12.9670	1.27767	0.638836	−	0.769343i	$-0.279416\pi$
$103$	12.9670	1.27767	0.638836	+	0.769343i	$0.279416\pi$
$104$	−0.744728	−0.0730266
$105$	−6.78530	−0.662178
$106$	−6.27476	−0.609458
$107$	11.0279	1.06611	0.533056	−	0.846080i	$-0.321044\pi$
$107$	11.0279	1.06611	0.533056	+	0.846080i	$0.321044\pi$
$108$	3.25527	0.313239
$109$	−9.35322	−0.895876	−0.447938	−	0.894065i	$-0.647842\pi$
$109$	−9.35322	−0.895876	−0.447938	+	0.894065i	$0.647842\pi$
$110$	8.62636	0.822491
$111$	−5.85892	−0.556104
$112$	1.00000	0.0944911
$113$	−8.36101	−0.786538	−0.393269	−	0.919424i	$-0.628656\pi$
$113$	−8.36101	−0.786538	−0.393269	+	0.919424i	$0.628656\pi$
$114$	−19.7954	−1.85401
$115$	0	0
$116$	−4.92638	−0.457403
$117$	−3.13690	−0.290007
$118$	7.73875	0.712410
$119$	0.526602	0.0482736
$120$	−6.78530	−0.619410
$121$	0.656854	0.0597140
$122$	−12.5013	−1.13182
$123$	−29.4522	−2.65562
$124$	−5.73875	−0.515355
$125$	9.13690	0.817230
$126$	4.21215	0.375248
$127$	−18.8353	−1.67136	−0.835680	−	0.549216i	$-0.814926\pi$
$127$	−18.8353	−1.67136	−0.835680	+	0.549216i	$0.814926\pi$
$128$	1.00000	0.0883883
$129$	15.2780	1.34515
$130$	1.88163	0.165030
$131$	−18.3041	−1.59924	−0.799619	−	0.600507i	$-0.794965\pi$
$131$	−18.3041	−1.59924	−0.799619	+	0.600507i	$0.794965\pi$
$132$	−9.16902	−0.798061
$133$	−7.37109	−0.639154
$134$	−12.1817	−1.05233
$135$	−8.22478	−0.707876
$136$	0.526602	0.0451558
$137$	0.903670	0.0772057	0.0386029	−	0.999255i	$-0.487709\pi$
$137$	0.903670	0.0772057	0.0386029	+	0.999255i	$0.487709\pi$
$138$	0	0
$139$	0.710806	0.0602898	0.0301449	−	0.999546i	$-0.490403\pi$
$139$	0.710806	0.0602898	0.0301449	+	0.999546i	$0.490403\pi$
$140$	−2.52660	−0.213537
$141$	7.04836	0.593579
$142$	−0.603650	−0.0506572
$143$	2.54266	0.212628
$144$	4.21215	0.351012
$145$	12.4470	1.03367
$146$	15.2754	1.26420
$147$	2.68554	0.221500
$148$	−2.18165	−0.179331
$149$	19.8587	1.62689	0.813443	−	0.581645i	$-0.197591\pi$
$149$	19.8587	1.62689	0.813443	+	0.581645i	$0.197591\pi$
$150$	3.71604	0.303413
$151$	23.6027	1.92076	0.960381	−	0.278690i	$-0.0899003\pi$
$151$	23.6027	1.92076	0.960381	+	0.278690i	$0.0899003\pi$
$152$	−7.37109	−0.597874
$153$	2.21813	0.179325
$154$	−3.41421	−0.275125
$155$	14.4995	1.16463
$156$	−2.00000	−0.160128
$157$	−19.6635	−1.56932	−0.784659	−	0.619927i	$-0.787162\pi$
$157$	−19.6635	−1.56932	−0.784659	+	0.619927i	$0.787162\pi$
$158$	0.631207	0.0502161
$159$	−16.8511	−1.33638
$160$	−2.52660	−0.199745
$161$	0	0
$162$	−3.89426	−0.305962
$163$	−17.0279	−1.33373	−0.666866	−	0.745178i	$-0.732365\pi$
$163$	−17.0279	−1.33373	−0.666866	+	0.745178i	$0.732365\pi$
$164$	−10.9670	−0.856375
$165$	23.1665	1.80351
$166$	4.74473	0.368262
$167$	18.5098	1.43233	0.716166	−	0.697930i	$-0.245896\pi$
$167$	18.5098	1.43233	0.716166	+	0.697930i	$0.245896\pi$
$168$	2.68554	0.207194
$169$	−12.4454	−0.957337
$170$	−1.33051	−0.102046
$171$	−31.0481	−2.37431
$172$	5.68897	0.433780
$173$	17.2394	1.31069	0.655344	−	0.755330i	$-0.272524\pi$
$173$	17.2394	1.31069	0.655344	+	0.755330i	$0.272524\pi$
$174$	−13.2300	−1.00296
$175$	1.38372	0.104599
$176$	−3.41421	−0.257356
$177$	20.7827	1.56213
$178$	13.6931	1.02634
$179$	−21.8087	−1.63006	−0.815029	−	0.579420i	$-0.803279\pi$
$179$	−21.8087	−1.63006	−0.815029	+	0.579420i	$0.803279\pi$
$180$	−10.6424	−0.793239
$181$	−23.4099	−1.74004	−0.870020	−	0.493016i	$-0.835895\pi$
$181$	−23.4099	−1.74004	−0.870020	+	0.493016i	$0.835895\pi$
$182$	−0.744728	−0.0552029
$183$	−33.5729	−2.48178
$184$	0	0
$185$	5.51217	0.405263
$186$	−15.4117	−1.13004
$187$	−1.79793	−0.131478
$188$	2.62455	0.191415
$189$	3.25527	0.236786
$190$	18.6238	1.35111
$191$	−0.478427	−0.0346178	−0.0173089	−	0.999850i	$-0.505510\pi$
$191$	−0.478427	−0.0346178	−0.0173089	+	0.999850i	$0.505510\pi$
$192$	2.68554	0.193812
$193$	7.25272	0.522062	0.261031	−	0.965330i	$-0.415937\pi$
$193$	7.25272	0.522062	0.261031	+	0.965330i	$0.415937\pi$
$194$	16.5240	1.18636
$195$	5.05320	0.361867
$196$	1.00000	0.0714286
$197$	−6.10641	−0.435064	−0.217532	−	0.976053i	$-0.569801\pi$
$197$	−6.10641	−0.435064	−0.217532	+	0.976053i	$0.569801\pi$
$198$	−14.3812	−1.02203
$199$	20.8843	1.48045	0.740225	−	0.672359i	$-0.234719\pi$
$199$	20.8843	1.48045	0.740225	+	0.672359i	$0.234719\pi$
$200$	1.38372	0.0978437
$201$	−32.7144	−2.30749
$202$	0.141078	0.00992624
$203$	−4.92638	−0.345764
$204$	1.41421	0.0990148
$205$	27.7091	1.93529
$206$	12.9670	0.903450
$207$	0	0
$208$	−0.744728	−0.0516376
$209$	25.1665	1.74080
$210$	−6.78530	−0.468230
$211$	−3.93901	−0.271173	−0.135586	−	0.990766i	$-0.543292\pi$
$211$	−3.93901	−0.271173	−0.135586	+	0.990766i	$0.543292\pi$
$212$	−6.27476	−0.430952
$213$	−1.62113	−0.111078
$214$	11.0279	0.753855
$215$	−14.3738	−0.980283
$216$	3.25527	0.221493
$217$	−5.73875	−0.389572
$218$	−9.35322	−0.633480
$219$	41.0228	2.77207
$220$	8.62636	0.581589
$221$	−0.392176	−0.0263806
$222$	−5.85892	−0.393225
$223$	−25.7564	−1.72477	−0.862387	−	0.506250i	$-0.831031\pi$
$223$	−25.7564	−1.72477	−0.862387	+	0.506250i	$0.831031\pi$
$224$	1.00000	0.0668153
$225$	5.82843	0.388562
$226$	−8.36101	−0.556166
$227$	−15.4573	−1.02594	−0.512970	−	0.858407i	$-0.671455\pi$
$227$	−15.4573	−1.02594	−0.512970	+	0.858407i	$0.671455\pi$
$228$	−19.7954	−1.31098
$229$	−10.5107	−0.694570	−0.347285	−	0.937760i	$-0.612896\pi$
$229$	−10.5107	−0.694570	−0.347285	+	0.937760i	$0.612896\pi$
$230$	0	0
$231$	−9.16902	−0.603277
$232$	−4.92638	−0.323433
$233$	12.4039	0.812605	0.406302	−	0.913739i	$-0.366818\pi$
$233$	12.4039	0.812605	0.406302	+	0.913739i	$0.366818\pi$
$234$	−3.13690	−0.205066
$235$	−6.63121	−0.432572
$236$	7.73875	0.503750
$237$	1.69513	0.110111
$238$	0.526602	0.0341346
$239$	−2.03212	−0.131447	−0.0657234	−	0.997838i	$-0.520935\pi$
$239$	−2.03212	−0.131447	−0.0657234	+	0.997838i	$0.520935\pi$
$240$	−6.78530	−0.437989
$241$	8.99858	0.579650	0.289825	−	0.957080i	$-0.406403\pi$
$241$	8.99858	0.579650	0.289825	+	0.957080i	$0.406403\pi$
$242$	0.656854	0.0422242
$243$	−20.2240	−1.29737
$244$	−12.5013	−0.800316
$245$	−2.52660	−0.161419
$246$	−29.4522	−1.87781
$247$	5.48946	0.349286
$248$	−5.73875	−0.364411
$249$	12.7422	0.807503
$250$	9.13690	0.577869
$251$	−5.95458	−0.375850	−0.187925	−	0.982183i	$-0.560176\pi$
$251$	−5.95458	−0.375850	−0.187925	+	0.982183i	$0.560176\pi$
$252$	4.21215	0.265340
$253$	0	0
$254$	−18.8353	−1.18183
$255$	−3.57316	−0.223760
$256$	1.00000	0.0625000
$257$	−8.30231	−0.517884	−0.258942	−	0.965893i	$-0.583374\pi$
$257$	−8.30231	−0.517884	−0.258942	+	0.965893i	$0.583374\pi$
$258$	15.2780	0.951166
$259$	−2.18165	−0.135561
$260$	1.88163	0.116694
$261$	−20.7506	−1.28443
$262$	−18.3041	−1.13083
$263$	−1.52062	−0.0937656	−0.0468828	−	0.998900i	$-0.514929\pi$
$263$	−1.52062	−0.0937656	−0.0468828	+	0.998900i	$0.514929\pi$
$264$	−9.16902	−0.564314
$265$	15.8538	0.973892
$266$	−7.37109	−0.451950
$267$	36.7733	2.25049
$268$	−12.1817	−0.744113
$269$	2.14724	0.130920	0.0654598	−	0.997855i	$-0.479149\pi$
$269$	2.14724	0.130920	0.0654598	+	0.997855i	$0.479149\pi$
$270$	−8.22478	−0.500544
$271$	2.88400	0.175191	0.0875953	−	0.996156i	$-0.472082\pi$
$271$	2.88400	0.175191	0.0875953	+	0.996156i	$0.472082\pi$
$272$	0.526602	0.0319300
$273$	−2.00000	−0.121046
$274$	0.903670	0.0545927
$275$	−4.72431	−0.284887
$276$	0	0
$277$	11.9507	0.718049	0.359024	−	0.933328i	$-0.383109\pi$
$277$	11.9507	0.718049	0.359024	+	0.933328i	$0.383109\pi$
$278$	0.710806	0.0426313
$279$	−24.1724	−1.44717
$280$	−2.52660	−0.150993
$281$	8.47066	0.505317	0.252659	−	0.967555i	$-0.418695\pi$
$281$	8.47066	0.505317	0.252659	+	0.967555i	$0.418695\pi$
$282$	7.04836	0.419724
$283$	6.51740	0.387419	0.193710	−	0.981059i	$-0.437948\pi$
$283$	6.51740	0.387419	0.193710	+	0.981059i	$0.437948\pi$
$284$	−0.603650	−0.0358200
$285$	50.0151	2.96264
$286$	2.54266	0.150351
$287$	−10.9670	−0.647359
$288$	4.21215	0.248203
$289$	−16.7227	−0.983688
$290$	12.4470	0.730913
$291$	44.3761	2.60137
$292$	15.2754	0.893927
$293$	7.71148	0.450509	0.225255	−	0.974300i	$-0.427679\pi$
$293$	7.71148	0.450509	0.225255	+	0.974300i	$0.427679\pi$
$294$	2.68554	0.156624
$295$	−19.5527	−1.13840
$296$	−2.18165	−0.126806
$297$	−11.1142	−0.644911
$298$	19.8587	1.15038
$299$	0	0
$300$	3.71604	0.214546
$301$	5.68897	0.327907
$302$	23.6027	1.35818
$303$	0.378872	0.0217656
$304$	−7.37109	−0.422761
$305$	31.5859	1.80860
$306$	2.21813	0.126802
$307$	7.94406	0.453391	0.226696	−	0.973966i	$-0.427208\pi$
$307$	7.94406	0.453391	0.226696	+	0.973966i	$0.427208\pi$
$308$	−3.41421	−0.194543
$309$	34.8233	1.98103
$310$	14.4995	0.823518
$311$	−8.52245	−0.483264	−0.241632	−	0.970368i	$-0.577683\pi$
$311$	−8.52245	−0.483264	−0.241632	+	0.970368i	$0.577683\pi$
$312$	−2.00000	−0.113228
$313$	13.5701	0.767028	0.383514	−	0.923535i	$-0.374714\pi$
$313$	13.5701	0.767028	0.383514	+	0.923535i	$0.374714\pi$
$314$	−19.6635	−1.10968
$315$	−10.6424	−0.599632
$316$	0.631207	0.0355081
$317$	−1.98830	−0.111674	−0.0558370	−	0.998440i	$-0.517783\pi$
$317$	−1.98830	−0.111674	−0.0558370	+	0.998440i	$0.517783\pi$
$318$	−16.8511	−0.944965
$319$	16.8197	0.941723
$320$	−2.52660	−0.141241
$321$	29.6160	1.65301
$322$	0	0
$323$	−3.88163	−0.215980
$324$	−3.89426	−0.216348
$325$	−1.03049	−0.0571615
$326$	−17.0279	−0.943090
$327$	−25.1185	−1.38906
$328$	−10.9670	−0.605549
$329$	2.62455	0.144696
$330$	23.1665	1.27527
$331$	17.9375	0.985935	0.492968	−	0.870048i	$-0.335912\pi$
$331$	17.9375	0.985935	0.492968	+	0.870048i	$0.335912\pi$
$332$	4.74473	0.260401
$333$	−9.18944	−0.503578
$334$	18.5098	1.01281
$335$	30.7782	1.68159
$336$	2.68554	0.146508
$337$	−27.7880	−1.51371	−0.756854	−	0.653584i	$-0.773265\pi$
$337$	−27.7880	−1.51371	−0.756854	+	0.653584i	$0.773265\pi$
$338$	−12.4454	−0.676939
$339$	−22.4539	−1.21953
$340$	−1.33051	−0.0721573
$341$	19.5933	1.06104
$342$	−31.0481	−1.67889
$343$	1.00000	0.0539949
$344$	5.68897	0.306729
$345$	0	0
$346$	17.2394	0.926797
$347$	−11.2394	−0.603363	−0.301682	−	0.953409i	$-0.597548\pi$
$347$	−11.2394	−0.603363	−0.301682	+	0.953409i	$0.597548\pi$
$348$	−13.2300	−0.709203
$349$	−8.52709	−0.456445	−0.228222	−	0.973609i	$-0.573291\pi$
$349$	−8.52709	−0.456445	−0.228222	+	0.973609i	$0.573291\pi$
$350$	1.38372	0.0739629
$351$	−2.42429	−0.129399
$352$	−3.41421	−0.181978
$353$	25.9365	1.38046	0.690229	−	0.723591i	$-0.257510\pi$
$353$	25.9365	1.38046	0.690229	+	0.723591i	$0.257510\pi$
$354$	20.7827	1.10459
$355$	1.52518	0.0809483
$356$	13.6931	0.725731
$357$	1.41421	0.0748481
$358$	−21.8087	−1.15262
$359$	−10.0564	−0.530758	−0.265379	−	0.964144i	$-0.585497\pi$
$359$	−10.0564	−0.530758	−0.265379	+	0.964144i	$0.585497\pi$
$360$	−10.6424	−0.560905
$361$	35.3329	1.85963
$362$	−23.4099	−1.23039
$363$	1.76401	0.0925866
$364$	−0.744728	−0.0390344
$365$	−38.5949	−2.02015
$366$	−33.5729	−1.75488
$367$	−8.33735	−0.435206	−0.217603	−	0.976037i	$-0.569824\pi$
$367$	−8.33735	−0.435206	−0.217603	+	0.976037i	$0.569824\pi$
$368$	0	0
$369$	−46.1944	−2.40478
$370$	5.51217	0.286564
$371$	−6.27476	−0.325769
$372$	−15.4117	−0.799057
$373$	−14.5605	−0.753915	−0.376958	−	0.926230i	$-0.623030\pi$
$373$	−14.5605	−0.753915	−0.376958	+	0.926230i	$0.623030\pi$
$374$	−1.79793	−0.0929689
$375$	24.5376	1.26711
$376$	2.62455	0.135351
$377$	3.66881	0.188954
$378$	3.25527	0.167433
$379$	7.47845	0.384142	0.192071	−	0.981381i	$-0.438480\pi$
$379$	7.47845	0.384142	0.192071	+	0.981381i	$0.438480\pi$
$380$	18.6238	0.955381
$381$	−50.5830	−2.59144
$382$	−0.478427	−0.0244784
$383$	−11.5291	−0.589108	−0.294554	−	0.955635i	$-0.595171\pi$
$383$	−11.5291	−0.589108	−0.294554	+	0.955635i	$0.595171\pi$
$384$	2.68554	0.137046
$385$	8.62636	0.439640
$386$	7.25272	0.369154
$387$	23.9628	1.21810
$388$	16.5240	0.838882
$389$	−22.6922	−1.15054	−0.575270	−	0.817964i	$-0.695103\pi$
$389$	−22.6922	−1.15054	−0.575270	+	0.817964i	$0.695103\pi$
$390$	5.05320	0.255879
$391$	0	0
$392$	1.00000	0.0505076
$393$	−49.1565	−2.47962
$394$	−6.10641	−0.307636
$395$	−1.59481	−0.0802435
$396$	−14.3812	−0.722681
$397$	−2.73787	−0.137410	−0.0687050	−	0.997637i	$-0.521887\pi$
$397$	−2.73787	−0.137410	−0.0687050	+	0.997637i	$0.521887\pi$
$398$	20.8843	1.04684
$399$	−19.7954	−0.991009
$400$	1.38372	0.0691860
$401$	30.4995	1.52307	0.761537	−	0.648121i	$-0.224445\pi$
$401$	30.4995	1.52307	0.761537	+	0.648121i	$0.224445\pi$
$402$	−32.7144	−1.63164
$403$	4.27381	0.212894
$404$	0.141078	0.00701891
$405$	9.83925	0.488916
$406$	−4.92638	−0.244492
$407$	7.44862	0.369215
$408$	1.41421	0.0700140
$409$	−29.4497	−1.45619	−0.728097	−	0.685475i	$-0.759595\pi$
$409$	−29.4497	−1.45619	−0.728097	+	0.685475i	$0.759595\pi$
$410$	27.7091	1.36846
$411$	2.42684	0.119707
$412$	12.9670	0.638836
$413$	7.73875	0.380799
$414$	0	0
$415$	−11.9880	−0.588470
$416$	−0.744728	−0.0365133
$417$	1.90890	0.0934793
$418$	25.1665	1.23093
$419$	27.7834	1.35731	0.678654	−	0.734458i	$-0.262563\pi$
$419$	27.7834	1.35731	0.678654	+	0.734458i	$0.262563\pi$
$420$	−6.78530	−0.331089
$421$	−6.25594	−0.304896	−0.152448	−	0.988311i	$-0.548716\pi$
$421$	−6.25594	−0.304896	−0.152448	+	0.988311i	$0.548716\pi$
$422$	−3.93901	−0.191748
$423$	11.0550	0.537513
$424$	−6.27476	−0.304729
$425$	0.728670	0.0353457
$426$	−1.62113	−0.0785439
$427$	−12.5013	−0.604982
$428$	11.0279	0.533056
$429$	6.82843	0.329680
$430$	−14.3738	−0.693165
$431$	−30.7468	−1.48102	−0.740510	−	0.672046i	$-0.765416\pi$
$431$	−30.7468	−1.48102	−0.740510	+	0.672046i	$0.765416\pi$
$432$	3.25527	0.156619
$433$	8.07089	0.387862	0.193931	−	0.981015i	$-0.437876\pi$
$433$	8.07089	0.387862	0.193931	+	0.981015i	$0.437876\pi$
$434$	−5.73875	−0.275469
$435$	33.4270	1.60270
$436$	−9.35322	−0.447938
$437$	0	0
$438$	41.0228	1.96015
$439$	3.81425	0.182044	0.0910221	−	0.995849i	$-0.470987\pi$
$439$	3.81425	0.182044	0.0910221	+	0.995849i	$0.470987\pi$
$440$	8.62636	0.411246
$441$	4.21215	0.200578
$442$	−0.392176	−0.0186539
$443$	12.1518	0.577351	0.288675	−	0.957427i	$-0.406785\pi$
$443$	12.1518	0.577351	0.288675	+	0.957427i	$0.406785\pi$
$444$	−5.85892	−0.278052
$445$	−34.5969	−1.64005
$446$	−25.7564	−1.21960
$447$	53.3313	2.52248
$448$	1.00000	0.0472456
$449$	−26.0795	−1.23077	−0.615385	−	0.788227i	$-0.710999\pi$
$449$	−26.0795	−1.23077	−0.615385	+	0.788227i	$0.710999\pi$
$450$	5.82843	0.274755
$451$	37.4435	1.76315
$452$	−8.36101	−0.393269
$453$	63.3861	2.97814
$454$	−15.4573	−0.725449
$455$	1.88163	0.0882123
$456$	−19.7954	−0.927004
$457$	−35.3637	−1.65424	−0.827122	−	0.562023i	$-0.810023\pi$
$457$	−35.3637	−1.65424	−0.827122	+	0.562023i	$0.810023\pi$
$458$	−10.5107	−0.491135
$459$	1.71423	0.0800136
$460$	0	0
$461$	−0.757744	−0.0352917	−0.0176458	−	0.999844i	$-0.505617\pi$
$461$	−0.757744	−0.0352917	−0.0176458	+	0.999844i	$0.505617\pi$
$462$	−9.16902	−0.426581
$463$	5.44404	0.253006	0.126503	−	0.991966i	$-0.459625\pi$
$463$	5.44404	0.253006	0.126503	+	0.991966i	$0.459625\pi$
$464$	−4.92638	−0.228701
$465$	38.9391	1.80576
$466$	12.4039	0.574598
$467$	−8.54266	−0.395307	−0.197654	−	0.980272i	$-0.563332\pi$
$467$	−8.54266	−0.395307	−0.197654	+	0.980272i	$0.563332\pi$
$468$	−3.13690	−0.145003
$469$	−12.1817	−0.562496
$470$	−6.63121	−0.305875
$471$	−52.8072	−2.43323
$472$	7.73875	0.356205
$473$	−19.4234	−0.893087
$474$	1.69513	0.0778600
$475$	−10.1995	−0.467986
$476$	0.526602	0.0241368
$477$	−26.4302	−1.21016
$478$	−2.03212	−0.0929469
$479$	−15.6280	−0.714061	−0.357030	−	0.934093i	$-0.616211\pi$
$479$	−15.6280	−0.714061	−0.357030	+	0.934093i	$0.616211\pi$
$480$	−6.78530	−0.309705
$481$	1.62474	0.0740816
$482$	8.99858	0.409874
$483$	0	0
$484$	0.656854	0.0298570
$485$	−41.7497	−1.89576
$486$	−20.2240	−0.917381
$487$	6.26411	0.283854	0.141927	−	0.989877i	$-0.454670\pi$
$487$	6.26411	0.283854	0.141927	+	0.989877i	$0.454670\pi$
$488$	−12.5013	−0.565909
$489$	−45.7293	−2.06795
$490$	−2.52660	−0.114140
$491$	30.2518	1.36524	0.682622	−	0.730772i	$-0.260840\pi$
$491$	30.2518	1.36524	0.682622	+	0.730772i	$0.260840\pi$
$492$	−29.4522	−1.32781
$493$	−2.59424	−0.116839
$494$	5.48946	0.246982
$495$	36.3355	1.63316
$496$	−5.73875	−0.257677
$497$	−0.603650	−0.0270774
$498$	12.7422	0.570991
$499$	12.4445	0.557090	0.278545	−	0.960423i	$-0.410148\pi$
$499$	12.4445	0.557090	0.278545	+	0.960423i	$0.410148\pi$
$500$	9.13690	0.408615
$501$	49.7089	2.22083
$502$	−5.95458	−0.265766
$503$	−30.2518	−1.34886	−0.674430	−	0.738339i	$-0.735611\pi$
$503$	−30.2518	−1.34886	−0.674430	+	0.738339i	$0.735611\pi$
$504$	4.21215	0.187624
$505$	−0.356449	−0.0158618
$506$	0	0
$507$	−33.4226	−1.48435
$508$	−18.8353	−0.835680
$509$	−7.83111	−0.347108	−0.173554	−	0.984824i	$-0.555525\pi$
$509$	−7.83111	−0.347108	−0.173554	+	0.984824i	$0.555525\pi$
$510$	−3.57316	−0.158222
$511$	15.2754	0.675745
$512$	1.00000	0.0441942
$513$	−23.9949	−1.05940
$514$	−8.30231	−0.366199
$515$	−32.7623	−1.44368
$516$	15.2780	0.672576
$517$	−8.96079	−0.394095
$518$	−2.18165	−0.0958563
$519$	46.2972	2.03222
$520$	1.88163	0.0825150
$521$	25.9850	1.13842	0.569212	−	0.822191i	$-0.307248\pi$
$521$	25.9850	1.13842	0.569212	+	0.822191i	$0.307248\pi$
$522$	−20.7506	−0.908230
$523$	42.6086	1.86315	0.931573	−	0.363554i	$-0.118437\pi$
$523$	42.6086	1.86315	0.931573	+	0.363554i	$0.118437\pi$
$524$	−18.3041	−0.799619
$525$	3.71604	0.162181
$526$	−1.52062	−0.0663023
$527$	−3.02204	−0.131642
$528$	−9.16902	−0.399030
$529$	0	0
$530$	15.8538	0.688646
$531$	32.5967	1.41458
$532$	−7.37109	−0.319577
$533$	8.16740	0.353769
$534$	36.7733	1.59134
$535$	−27.8632	−1.20463
$536$	−12.1817	−0.526167
$537$	−58.5682	−2.52740
$538$	2.14724	0.0925741
$539$	−3.41421	−0.147061
$540$	−8.22478	−0.353938
$541$	12.7493	0.548135	0.274067	−	0.961710i	$-0.411631\pi$
$541$	12.7493	0.548135	0.274067	+	0.961710i	$0.411631\pi$
$542$	2.88400	0.123878
$543$	−62.8682	−2.69793
$544$	0.526602	0.0225779
$545$	23.6319	1.01228
$546$	−2.00000	−0.0855921
$547$	−14.8068	−0.633092	−0.316546	−	0.948577i	$-0.602523\pi$
$547$	−14.8068	−0.633092	−0.316546	+	0.948577i	$0.602523\pi$
$548$	0.903670	0.0386029
$549$	−52.6575	−2.24737
$550$	−4.72431	−0.201445
$551$	36.3128	1.54698
$552$	0	0
$553$	0.631207	0.0268416
$554$	11.9507	0.507737
$555$	14.8032	0.628359
$556$	0.710806	0.0301449
$557$	−20.2556	−0.858256	−0.429128	−	0.903244i	$-0.641179\pi$
$557$	−20.2556	−0.858256	−0.429128	+	0.903244i	$0.641179\pi$
$558$	−24.1724	−1.02330
$559$	−4.23674	−0.179195
$560$	−2.52660	−0.106768
$561$	−4.82843	−0.203856
$562$	8.47066	0.357313
$563$	−11.9390	−0.503169	−0.251585	−	0.967835i	$-0.580952\pi$
$563$	−11.9390	−0.503169	−0.251585	+	0.967835i	$0.580952\pi$
$564$	7.04836	0.296789
$565$	21.1249	0.888733
$566$	6.51740	0.273947
$567$	−3.89426	−0.163544
$568$	−0.603650	−0.0253286
$569$	35.5541	1.49050	0.745252	−	0.666783i	$-0.232329\pi$
$569$	35.5541	1.49050	0.745252	+	0.666783i	$0.232329\pi$
$570$	50.0151	2.09490
$571$	−15.3004	−0.640302	−0.320151	−	0.947367i	$-0.603734\pi$
$571$	−15.3004	−0.640302	−0.320151	+	0.947367i	$0.603734\pi$
$572$	2.54266	0.106314
$573$	−1.28484	−0.0536748
$574$	−10.9670	−0.457752
$575$	0	0
$576$	4.21215	0.175506
$577$	−4.01947	−0.167333	−0.0836663	−	0.996494i	$-0.526663\pi$
$577$	−4.01947	−0.167333	−0.0836663	+	0.996494i	$0.526663\pi$
$578$	−16.7227	−0.695572
$579$	19.4775	0.809457
$580$	12.4470	0.516834
$581$	4.74473	0.196844
$582$	44.3761	1.83945
$583$	21.4234	0.887265
$584$	15.2754	0.632102
$585$	7.92571	0.327688
$586$	7.71148	0.318558
$587$	−9.73189	−0.401678	−0.200839	−	0.979624i	$-0.564367\pi$
$587$	−9.73189	−0.401678	−0.200839	+	0.979624i	$0.564367\pi$
$588$	2.68554	0.110750
$589$	42.3008	1.74297
$590$	−19.5527	−0.804974
$591$	−16.3990	−0.674566
$592$	−2.18165	−0.0896653
$593$	5.35454	0.219885	0.109942	−	0.993938i	$-0.464933\pi$
$593$	5.35454	0.219885	0.109942	+	0.993938i	$0.464933\pi$
$594$	−11.1142	−0.456021
$595$	−1.33051	−0.0545458
$596$	19.8587	0.813443
$597$	56.0857	2.29544
$598$	0	0
$599$	44.9738	1.83758	0.918790	−	0.394747i	$-0.129168\pi$
$599$	44.9738	1.83758	0.918790	+	0.394747i	$0.129168\pi$
$600$	3.71604	0.151707
$601$	−29.5226	−1.20425	−0.602127	−	0.798401i	$-0.705680\pi$
$601$	−29.5226	−1.20425	−0.602127	+	0.798401i	$0.705680\pi$
$602$	5.68897	0.231865
$603$	−51.3109	−2.08954
$604$	23.6027	0.960381
$605$	−1.65961	−0.0674727
$606$	0.378872	0.0153906
$607$	7.75793	0.314885	0.157442	−	0.987528i	$-0.449675\pi$
$607$	7.75793	0.314885	0.157442	+	0.987528i	$0.449675\pi$
$608$	−7.37109	−0.298937
$609$	−13.2300	−0.536107
$610$	31.5859	1.27888
$611$	−1.95458	−0.0790738
$612$	2.21813	0.0896624
$613$	−22.9187	−0.925678	−0.462839	−	0.886442i	$-0.653169\pi$
$613$	−22.9187	−0.925678	−0.462839	+	0.886442i	$0.653169\pi$
$614$	7.94406	0.320596
$615$	74.4141	3.00067
$616$	−3.41421	−0.137563
$617$	35.7137	1.43778	0.718889	−	0.695124i	$-0.244651\pi$
$617$	35.7137	1.43778	0.718889	+	0.695124i	$0.244651\pi$
$618$	34.8233	1.40080
$619$	2.86634	0.115208	0.0576040	−	0.998340i	$-0.481654\pi$
$619$	2.86634	0.115208	0.0576040	+	0.998340i	$0.481654\pi$
$620$	14.4995	0.582315
$621$	0	0
$622$	−8.52245	−0.341719
$623$	13.6931	0.548601
$624$	−2.00000	−0.0800641
$625$	−30.0039	−1.20016
$626$	13.5701	0.542371
$627$	67.5857	2.69911
$628$	−19.6635	−0.784659
$629$	−1.14886	−0.0458082
$630$	−10.6424	−0.424004
$631$	−8.85825	−0.352641	−0.176321	−	0.984333i	$-0.556420\pi$
$631$	−8.85825	−0.352641	−0.176321	+	0.984333i	$0.556420\pi$
$632$	0.631207	0.0251081
$633$	−10.5784	−0.420453
$634$	−1.98830	−0.0789654
$635$	47.5893	1.88852
$636$	−16.8511	−0.668191
$637$	−0.744728	−0.0295072
$638$	16.8197	0.665899
$639$	−2.54266	−0.100586
$640$	−2.52660	−0.0998727
$641$	−0.861859	−0.0340414	−0.0170207	−	0.999855i	$-0.505418\pi$
$641$	−0.861859	−0.0340414	−0.0170207	+	0.999855i	$0.505418\pi$
$642$	29.6160	1.16885
$643$	2.45316	0.0967434	0.0483717	−	0.998829i	$-0.484597\pi$
$643$	2.45316	0.0967434	0.0483717	+	0.998829i	$0.484597\pi$
$644$	0	0
$645$	−38.6014	−1.51993
$646$	−3.88163	−0.152721
$647$	−40.3048	−1.58455	−0.792273	−	0.610167i	$-0.791102\pi$
$647$	−40.3048	−1.58455	−0.792273	+	0.610167i	$0.791102\pi$
$648$	−3.89426	−0.152981
$649$	−26.4217	−1.03714
$650$	−1.03049	−0.0404193
$651$	−15.4117	−0.604031
$652$	−17.0279	−0.666866
$653$	−29.5771	−1.15744	−0.578720	−	0.815526i	$-0.696447\pi$
$653$	−29.5771	−1.15744	−0.578720	+	0.815526i	$0.696447\pi$
$654$	−25.1185	−0.982211
$655$	46.2472	1.80703
$656$	−10.9670	−0.428188
$657$	64.3423	2.51023
$658$	2.62455	0.102316
$659$	26.4087	1.02874	0.514369	−	0.857569i	$-0.328026\pi$
$659$	26.4087	1.02874	0.514369	+	0.857569i	$0.328026\pi$
$660$	23.1665	0.901754
$661$	10.5490	0.410310	0.205155	−	0.978730i	$-0.434230\pi$
$661$	10.5490	0.410310	0.205155	+	0.978730i	$0.434230\pi$
$662$	17.9375	0.697161
$663$	−1.05320	−0.0409031
$664$	4.74473	0.184131
$665$	18.6238	0.722200
$666$	−9.18944	−0.356083
$667$	0	0
$668$	18.5098	0.716166
$669$	−69.1698	−2.67426
$670$	30.7782	1.18907
$671$	42.6822	1.64773
$672$	2.68554	0.103597
$673$	−43.8175	−1.68904	−0.844521	−	0.535522i	$-0.820115\pi$
$673$	−43.8175	−1.68904	−0.844521	+	0.535522i	$0.820115\pi$
$674$	−27.7880	−1.07035
$675$	4.50438	0.173374
$676$	−12.4454	−0.478668
$677$	17.3586	0.667147	0.333573	−	0.942724i	$-0.391746\pi$
$677$	17.3586	0.667147	0.333573	+	0.942724i	$0.391746\pi$
$678$	−22.4539	−0.862335
$679$	16.5240	0.634135
$680$	−1.33051	−0.0510229
$681$	−41.5114	−1.59072
$682$	19.5933	0.750267
$683$	32.7202	1.25200	0.626001	−	0.779822i	$-0.284691\pi$
$683$	32.7202	1.25200	0.626001	+	0.779822i	$0.284691\pi$
$684$	−31.0481	−1.18715
$685$	−2.28321	−0.0872371
$686$	1.00000	0.0381802
$687$	−28.2271	−1.07693
$688$	5.68897	0.216890
$689$	4.67299	0.178027
$690$	0	0
$691$	−1.58262	−0.0602056	−0.0301028	−	0.999547i	$-0.509583\pi$
$691$	−1.58262	−0.0602056	−0.0301028	+	0.999547i	$0.509583\pi$
$692$	17.2394	0.655344
$693$	−14.3812	−0.546295
$694$	−11.2394	−0.426642
$695$	−1.79593	−0.0681233
$696$	−13.2300	−0.501482
$697$	−5.77522	−0.218752
$698$	−8.52709	−0.322755
$699$	33.3112	1.25994
$700$	1.38372	0.0522997
$701$	−13.4954	−0.509713	−0.254856	−	0.966979i	$-0.582028\pi$
$701$	−13.4954	−0.509713	−0.254856	+	0.966979i	$0.582028\pi$
$702$	−2.42429	−0.0914990
$703$	16.0811	0.606512
$704$	−3.41421	−0.128678
$705$	−17.8084	−0.670703
$706$	25.9365	0.976131
$707$	0.141078	0.00530580
$708$	20.7827	0.781064
$709$	−4.04637	−0.151965	−0.0759823	−	0.997109i	$-0.524209\pi$
$709$	−4.04637	−0.151965	−0.0759823	+	0.997109i	$0.524209\pi$
$710$	1.52518	0.0572391
$711$	2.65873	0.0997103
$712$	13.6931	0.513170
$713$	0	0
$714$	1.41421	0.0529256
$715$	−6.42429	−0.240255
$716$	−21.8087	−0.815029
$717$	−5.45734	−0.203808
$718$	−10.0564	−0.375303
$719$	46.0785	1.71844	0.859220	−	0.511607i	$-0.170949\pi$
$719$	46.0785	1.71844	0.859220	+	0.511607i	$0.170949\pi$
$720$	−10.6424	−0.396620
$721$	12.9670	0.482915
$722$	35.3329	1.31496
$723$	24.1661	0.898746
$724$	−23.4099	−0.870020
$725$	−6.81673	−0.253167
$726$	1.76401	0.0654686
$727$	8.71330	0.323159	0.161579	−	0.986860i	$-0.448341\pi$
$727$	8.71330	0.323159	0.161579	+	0.986860i	$0.448341\pi$
$728$	−0.744728	−0.0276015
$729$	−42.6297	−1.57888
$730$	−38.5949	−1.42846
$731$	2.99583	0.110805
$732$	−33.5729	−1.24089
$733$	30.4031	1.12297	0.561483	−	0.827489i	$-0.310231\pi$
$733$	30.4031	1.12297	0.561483	+	0.827489i	$0.310231\pi$
$734$	−8.33735	−0.307737
$735$	−6.78530	−0.250280
$736$	0	0
$737$	41.5908	1.53202
$738$	−46.1944	−1.70044
$739$	17.4302	0.641181	0.320590	−	0.947218i	$-0.396119\pi$
$739$	17.4302	0.641181	0.320590	+	0.947218i	$0.396119\pi$
$740$	5.51217	0.202631
$741$	14.7422	0.541567
$742$	−6.27476	−0.230354
$743$	6.65136	0.244015	0.122007	−	0.992529i	$-0.461067\pi$
$743$	6.65136	0.244015	0.122007	+	0.992529i	$0.461067\pi$
$744$	−15.4117	−0.565019
$745$	−50.1749	−1.83827
$746$	−14.5605	−0.533099
$747$	19.9855	0.731231
$748$	−1.79793	−0.0657389
$749$	11.0279	0.402952
$750$	24.5376	0.895985
$751$	51.0861	1.86416	0.932080	−	0.362254i	$-0.117993\pi$
$751$	51.0861	1.86416	0.932080	+	0.362254i	$0.117993\pi$
$752$	2.62455	0.0957077
$753$	−15.9913	−0.582755
$754$	3.66881	0.133610
$755$	−59.6347	−2.17033
$756$	3.25527	0.118393
$757$	5.29126	0.192314	0.0961570	−	0.995366i	$-0.469345\pi$
$757$	5.29126	0.192314	0.0961570	+	0.995366i	$0.469345\pi$
$758$	7.47845	0.271629
$759$	0	0
$760$	18.6238	0.675556
$761$	28.2021	1.02232	0.511162	−	0.859484i	$-0.329215\pi$
$761$	28.2021	1.02232	0.511162	+	0.859484i	$0.329215\pi$
$762$	−50.5830	−1.83243
$763$	−9.35322	−0.338609
$764$	−0.478427	−0.0173089
$765$	−5.60432	−0.202625
$766$	−11.5291	−0.416563
$767$	−5.76326	−0.208099
$768$	2.68554	0.0969062
$769$	−21.2853	−0.767568	−0.383784	−	0.923423i	$-0.625379\pi$
$769$	−21.2853	−0.767568	−0.383784	+	0.923423i	$0.625379\pi$
$770$	8.62636	0.310872
$771$	−22.2962	−0.802979
$772$	7.25272	0.261031
$773$	14.5746	0.524211	0.262106	−	0.965039i	$-0.415583\pi$
$773$	14.5746	0.524211	0.262106	+	0.965039i	$0.415583\pi$
$774$	23.9628	0.861324
$775$	−7.94082	−0.285243
$776$	16.5240	0.593179
$777$	−5.85892	−0.210188
$778$	−22.6922	−0.813555
$779$	80.8384	2.89634
$780$	5.05320	0.180934
$781$	2.06099	0.0737480
$782$	0	0
$783$	−16.0367	−0.573105
$784$	1.00000	0.0357143
$785$	49.6819	1.77322
$786$	−49.1565	−1.75335
$787$	−2.96492	−0.105688	−0.0528439	−	0.998603i	$-0.516829\pi$
$787$	−2.96492	−0.105688	−0.0528439	+	0.998603i	$0.516829\pi$
$788$	−6.10641	−0.217532
$789$	−4.08370	−0.145384
$790$	−1.59481	−0.0567407
$791$	−8.36101	−0.297283
$792$	−14.3812	−0.511013
$793$	9.31010	0.330611
$794$	−2.73787	−0.0971635
$795$	42.5761	1.51002
$796$	20.8843	0.740225
$797$	5.92550	0.209892	0.104946	−	0.994478i	$-0.466533\pi$
$797$	5.92550	0.209892	0.104946	+	0.994478i	$0.466533\pi$
$798$	−19.7954	−0.700749
$799$	1.38210	0.0488951
$800$	1.38372	0.0489219
$801$	57.6772	2.03792
$802$	30.4995	1.07698
$803$	−52.1536	−1.84046
$804$	−32.7144	−1.15375
$805$	0	0
$806$	4.27381	0.150538
$807$	5.76651	0.202991
$808$	0.141078	0.00496312
$809$	−22.1811	−0.779846	−0.389923	−	0.920847i	$-0.627498\pi$
$809$	−22.1811	−0.779846	−0.389923	+	0.920847i	$0.627498\pi$
$810$	9.83925	0.345716
$811$	32.8023	1.15185	0.575923	−	0.817504i	$-0.304643\pi$
$811$	32.8023	1.15185	0.575923	+	0.817504i	$0.304643\pi$
$812$	−4.92638	−0.172882
$813$	7.74511	0.271633
$814$	7.44862	0.261074
$815$	43.0228	1.50702
$816$	1.41421	0.0495074
$817$	−41.9339	−1.46708
$818$	−29.4497	−1.02968
$819$	−3.13690	−0.109612
$820$	27.7091	0.967645
$821$	−32.9654	−1.15050	−0.575249	−	0.817978i	$-0.695095\pi$
$821$	−32.9654	−1.15050	−0.575249	+	0.817978i	$0.695095\pi$
$822$	2.42684	0.0846459
$823$	−47.7604	−1.66482	−0.832412	−	0.554157i	$-0.813041\pi$
$823$	−47.7604	−1.66482	−0.832412	+	0.554157i	$0.813041\pi$
$824$	12.9670	0.451725
$825$	−12.6873	−0.441717
$826$	7.73875	0.269265
$827$	24.4957	0.851801	0.425900	−	0.904770i	$-0.359957\pi$
$827$	24.4957	0.851801	0.425900	+	0.904770i	$0.359957\pi$
$828$	0	0
$829$	24.5715	0.853405	0.426702	−	0.904392i	$-0.359675\pi$
$829$	24.5715	0.853405	0.426702	+	0.904392i	$0.359675\pi$
$830$	−11.9880	−0.416111
$831$	32.0942	1.11333
$832$	−0.744728	−0.0258188
$833$	0.526602	0.0182457
$834$	1.90890	0.0660999
$835$	−46.7669	−1.61844
$836$	25.1665	0.870401
$837$	−18.6812	−0.645716
$838$	27.7834	0.959762
$839$	−23.7571	−0.820186	−0.410093	−	0.912044i	$-0.634504\pi$
$839$	−23.7571	−0.820186	−0.410093	+	0.912044i	$0.634504\pi$
$840$	−6.78530	−0.234115
$841$	−4.73078	−0.163130
$842$	−6.25594	−0.215594
$843$	22.7483	0.783494
$844$	−3.93901	−0.135586
$845$	31.4445	1.08172
$846$	11.0550	0.380079
$847$	0.656854	0.0225698
$848$	−6.27476	−0.215476
$849$	17.5028	0.600693
$850$	0.728670	0.0249932
$851$	0	0
$852$	−1.62113	−0.0555389
$853$	−34.0144	−1.16463	−0.582315	−	0.812963i	$-0.697853\pi$
$853$	−34.0144	−1.16463	−0.582315	+	0.812963i	$0.697853\pi$
$854$	−12.5013	−0.427787
$855$	78.4462	2.68280
$856$	11.0279	0.376927
$857$	9.04996	0.309141	0.154570	−	0.987982i	$-0.450601\pi$
$857$	9.04996	0.309141	0.154570	+	0.987982i	$0.450601\pi$
$858$	6.82843	0.233119
$859$	3.94698	0.134669	0.0673346	−	0.997730i	$-0.478551\pi$
$859$	3.94698	0.134669	0.0673346	+	0.997730i	$0.478551\pi$
$860$	−14.3738	−0.490141
$861$	−29.4522	−1.00373
$862$	−30.7468	−1.04724
$863$	24.6322	0.838488	0.419244	−	0.907874i	$-0.362295\pi$
$863$	24.6322	0.838488	0.419244	+	0.907874i	$0.362295\pi$
$864$	3.25527	0.110747
$865$	−43.5571	−1.48099
$866$	8.07089	0.274260
$867$	−44.9095	−1.52521
$868$	−5.73875	−0.194786
$869$	−2.15507	−0.0731059
$870$	33.4270	1.13328
$871$	9.07202	0.307394
$872$	−9.35322	−0.316740
$873$	69.6017	2.35566
$874$	0	0
$875$	9.13690	0.308884
$876$	41.0228	1.38603
$877$	−8.11352	−0.273974	−0.136987	−	0.990573i	$-0.543742\pi$
$877$	−8.11352	−0.273974	−0.136987	+	0.990573i	$0.543742\pi$
$878$	3.81425	0.128725
$879$	20.7095	0.698515
$880$	8.62636	0.290795
$881$	13.3839	0.450915	0.225458	−	0.974253i	$-0.427612\pi$
$881$	13.3839	0.450915	0.225458	+	0.974253i	$0.427612\pi$
$882$	4.21215	0.141830
$883$	−43.5078	−1.46415	−0.732076	−	0.681223i	$-0.761449\pi$
$883$	−43.5078	−1.46415	−0.732076	+	0.681223i	$0.761449\pi$
$884$	−0.392176	−0.0131903
$885$	−52.5097	−1.76510
$886$	12.1518	0.408249
$887$	6.36511	0.213719	0.106860	−	0.994274i	$-0.465920\pi$
$887$	6.36511	0.213719	0.106860	+	0.994274i	$0.465920\pi$
$888$	−5.85892	−0.196613
$889$	−18.8353	−0.631715
$890$	−34.5969	−1.15969
$891$	13.2958	0.445428
$892$	−25.7564	−0.862387
$893$	−19.3458	−0.647383
$894$	53.3313	1.78367
$895$	55.1019	1.84185
$896$	1.00000	0.0334077
$897$	0	0
$898$	−26.0795	−0.870286
$899$	28.2713	0.942899
$900$	5.82843	0.194281
$901$	−3.30430	−0.110082
$902$	37.4435	1.24673
$903$	15.2780	0.508419
$904$	−8.36101	−0.278083
$905$	59.1474	1.96613
$906$	63.3861	2.10586
$907$	1.23715	0.0410789	0.0205395	−	0.999789i	$-0.493462\pi$
$907$	1.23715	0.0410789	0.0205395	+	0.999789i	$0.493462\pi$
$908$	−15.4573	−0.512970
$909$	0.594243	0.0197098
$910$	1.88163	0.0623755
$911$	−13.4629	−0.446045	−0.223023	−	0.974813i	$-0.571592\pi$
$911$	−13.4629	−0.446045	−0.223023	+	0.974813i	$0.571592\pi$
$912$	−19.7954	−0.655491
$913$	−16.1995	−0.536126
$914$	−35.3637	−1.16973
$915$	84.8254	2.80424
$916$	−10.5107	−0.347285
$917$	−18.3041	−0.604455
$918$	1.71423	0.0565781
$919$	−46.2921	−1.52703	−0.763517	−	0.645787i	$-0.776529\pi$
$919$	−46.2921	−1.52703	−0.763517	+	0.645787i	$0.776529\pi$
$920$	0	0
$921$	21.3341	0.702983
$922$	−0.757744	−0.0249550
$923$	0.449555	0.0147973
$924$	−9.16902	−0.301639
$925$	−3.01879	−0.0992573
$926$	5.44404	0.178902
$927$	54.6187	1.79391
$928$	−4.92638	−0.161716
$929$	35.0409	1.14965	0.574827	−	0.818275i	$-0.305069\pi$
$929$	35.0409	1.14965	0.574827	+	0.818275i	$0.305069\pi$
$930$	38.9391	1.27686
$931$	−7.37109	−0.241578
$932$	12.4039	0.406302
$933$	−22.8874	−0.749300
$934$	−8.54266	−0.279524
$935$	4.54266	0.148561
$936$	−3.13690	−0.102533
$937$	44.0275	1.43832	0.719158	−	0.694847i	$-0.244528\pi$
$937$	44.0275	1.43832	0.719158	+	0.694847i	$0.244528\pi$
$938$	−12.1817	−0.397745
$939$	36.4431	1.18928
$940$	−6.63121	−0.216286
$941$	−37.3474	−1.21749	−0.608745	−	0.793366i	$-0.708327\pi$
$941$	−37.3474	−1.21749	−0.608745	+	0.793366i	$0.708327\pi$
$942$	−52.8072	−1.72055
$943$	0	0
$944$	7.73875	0.251875
$945$	−8.22478	−0.267552
$946$	−19.4234	−0.631508
$947$	48.5649	1.57815	0.789074	−	0.614298i	$-0.210561\pi$
$947$	48.5649	1.57815	0.789074	+	0.614298i	$0.210561\pi$
$948$	1.69513	0.0550554
$949$	−11.3760	−0.369282
$950$	−10.1995	−0.330916
$951$	−5.33966	−0.173150
$952$	0.526602	0.0170673
$953$	15.8147	0.512290	0.256145	−	0.966638i	$-0.417548\pi$
$953$	15.8147	0.512290	0.256145	+	0.966638i	$0.417548\pi$
$954$	−26.4302	−0.855709
$955$	1.20879	0.0391157
$956$	−2.03212	−0.0657234
$957$	45.1701	1.46014
$958$	−15.6280	−0.504917
$959$	0.903670	0.0291810
$960$	−6.78530	−0.218995
$961$	1.93323	0.0623624
$962$	1.62474	0.0523836
$963$	46.4513	1.49687
$964$	8.99858	0.289825
$965$	−18.3247	−0.589894
$966$	0	0
$967$	−51.1210	−1.64394	−0.821971	−	0.569529i	$-0.807126\pi$
$967$	−51.1210	−1.64394	−0.821971	+	0.569529i	$0.807126\pi$
$968$	0.656854	0.0211121
$969$	−10.4243	−0.334877
$970$	−41.7497	−1.34050
$971$	−47.9386	−1.53842	−0.769211	−	0.638995i	$-0.779351\pi$
$971$	−47.9386	−1.53842	−0.769211	+	0.638995i	$0.779351\pi$
$972$	−20.2240	−0.648686
$973$	0.710806	0.0227874
$974$	6.26411	0.200715
$975$	−2.76744	−0.0886290
$976$	−12.5013	−0.400158
$977$	32.2793	1.03271	0.516354	−	0.856375i	$-0.327289\pi$
$977$	32.2793	1.03271	0.516354	+	0.856375i	$0.327289\pi$
$978$	−45.7293	−1.46226
$979$	−46.7511	−1.49417
$980$	−2.52660	−0.0807093
$981$	−39.3971	−1.25785
$982$	30.2518	0.965373
$983$	31.9566	1.01926	0.509629	−	0.860394i	$-0.329783\pi$
$983$	31.9566	1.01926	0.509629	+	0.860394i	$0.329783\pi$
$984$	−29.4522	−0.938903
$985$	15.4285	0.491592
$986$	−2.59424	−0.0826175
$987$	7.04836	0.224352
$988$	5.48946	0.174643
$989$	0	0
$990$	36.3355	1.15482
$991$	−43.1019	−1.36918	−0.684588	−	0.728930i	$-0.740018\pi$
$991$	−43.1019	−1.36918	−0.684588	+	0.728930i	$0.740018\pi$
$992$	−5.73875	−0.182205
$993$	48.1720	1.52869
$994$	−0.603650	−0.0191466
$995$	−52.7663	−1.67281
$996$	12.7422	0.403751
$997$	21.8798	0.692939	0.346470	−	0.938061i	$-0.387380\pi$
$997$	21.8798	0.692939	0.346470	+	0.938061i	$0.387380\pi$
$998$	12.4445	0.393922
$999$	−7.10187	−0.224693

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7406.2.a.bb.1.4	✓	4
23.22	odd	2		7406.2.a.bc.1.4	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7406.2.a.bb.1.4	✓	4	1.1	even	1	trivial
7406.2.a.bc.1.4	yes	4	23.22	odd	2

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7406 = 2 \cdot 7 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7406.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.68554 q^{3} +1.00000 q^{4} -2.52660 q^{5} +2.68554 q^{6} +1.00000 q^{7} +1.00000 q^{8} +4.21215 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.68554 q^{3} +1.00000 q^{4} -2.52660 q^{5} +2.68554 q^{6} +1.00000 q^{7} +1.00000 q^{8} +4.21215 q^{9} -2.52660 q^{10} -3.41421 q^{11} +2.68554 q^{12} -0.744728 q^{13} +1.00000 q^{14} -6.78530 q^{15} +1.00000 q^{16} +0.526602 q^{17} +4.21215 q^{18} -7.37109 q^{19} -2.52660 q^{20} +2.68554 q^{21} -3.41421 q^{22} +2.68554 q^{24} +1.38372 q^{25} -0.744728 q^{26} +3.25527 q^{27} +1.00000 q^{28} -4.92638 q^{29} -6.78530 q^{30} -5.73875 q^{31} +1.00000 q^{32} -9.16902 q^{33} +0.526602 q^{34} -2.52660 q^{35} +4.21215 q^{36} -2.18165 q^{37} -7.37109 q^{38} -2.00000 q^{39} -2.52660 q^{40} -10.9670 q^{41} +2.68554 q^{42} +5.68897 q^{43} -3.41421 q^{44} -10.6424 q^{45} +2.62455 q^{47} +2.68554 q^{48} +1.00000 q^{49} +1.38372 q^{50} +1.41421 q^{51} -0.744728 q^{52} -6.27476 q^{53} +3.25527 q^{54} +8.62636 q^{55} +1.00000 q^{56} -19.7954 q^{57} -4.92638 q^{58} +7.73875 q^{59} -6.78530 q^{60} -12.5013 q^{61} -5.73875 q^{62} +4.21215 q^{63} +1.00000 q^{64} +1.88163 q^{65} -9.16902 q^{66} -12.1817 q^{67} +0.526602 q^{68} -2.52660 q^{70} -0.603650 q^{71} +4.21215 q^{72} +15.2754 q^{73} -2.18165 q^{74} +3.71604 q^{75} -7.37109 q^{76} -3.41421 q^{77} -2.00000 q^{78} +0.631207 q^{79} -2.52660 q^{80} -3.89426 q^{81} -10.9670 q^{82} +4.74473 q^{83} +2.68554 q^{84} -1.33051 q^{85} +5.68897 q^{86} -13.2300 q^{87} -3.41421 q^{88} +13.6931 q^{89} -10.6424 q^{90} -0.744728 q^{91} -15.4117 q^{93} +2.62455 q^{94} +18.6238 q^{95} +2.68554 q^{96} +16.5240 q^{97} +1.00000 q^{98} -14.3812 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{4} - 4 q^{5} + 4 q^{7} + 4 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^4 - 4 * q^5 + 4 * q^7 + 4 * q^8	\( 4 q + 4 q^{2} + 4 q^{4} - 4 q^{5} + 4 q^{7} + 4 q^{8} - 4 q^{10} - 8 q^{11} - 4 q^{13} + 4 q^{14} + 4 q^{16} - 4 q^{17} - 8 q^{19} - 4 q^{20} - 8 q^{22} - 4 q^{26} + 12 q^{27} + 4 q^{28} - 4 q^{29} + 4 q^{32} - 4 q^{33} - 4 q^{34} - 4 q^{35} + 8 q^{37} - 8 q^{38} - 8 q^{39} - 4 q^{40} - 8 q^{43} - 8 q^{44} - 16 q^{45} + 4 q^{49} - 4 q^{52} + 12 q^{54} + 12 q^{55} + 4 q^{56} - 24 q^{57} - 4 q^{58} + 8 q^{59} - 12 q^{61} + 4 q^{64} - 16 q^{65} - 4 q^{66} - 32 q^{67} - 4 q^{68} - 4 q^{70} + 8 q^{71} + 4 q^{73} + 8 q^{74} + 4 q^{75} - 8 q^{76} - 8 q^{77} - 8 q^{78} - 16 q^{79} - 4 q^{80} - 8 q^{81} + 20 q^{83} - 12 q^{85} - 8 q^{86} - 20 q^{87} - 8 q^{88} - 28 q^{89} - 16 q^{90} - 4 q^{91} - 12 q^{93} + 8 q^{95} + 16 q^{97} + 4 q^{98} - 8 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^4 - 4 * q^5 + 4 * q^7 + 4 * q^8 - 4 * q^10 - 8 * q^11 - 4 * q^13 + 4 * q^14 + 4 * q^16 - 4 * q^17 - 8 * q^19 - 4 * q^20 - 8 * q^22 - 4 * q^26 + 12 * q^27 + 4 * q^28 - 4 * q^29 + 4 * q^32 - 4 * q^33 - 4 * q^34 - 4 * q^35 + 8 * q^37 - 8 * q^38 - 8 * q^39 - 4 * q^40 - 8 * q^43 - 8 * q^44 - 16 * q^45 + 4 * q^49 - 4 * q^52 + 12 * q^54 + 12 * q^55 + 4 * q^56 - 24 * q^57 - 4 * q^58 + 8 * q^59 - 12 * q^61 + 4 * q^64 - 16 * q^65 - 4 * q^66 - 32 * q^67 - 4 * q^68 - 4 * q^70 + 8 * q^71 + 4 * q^73 + 8 * q^74 + 4 * q^75 - 8 * q^76 - 8 * q^77 - 8 * q^78 - 16 * q^79 - 4 * q^80 - 8 * q^81 + 20 * q^83 - 12 * q^85 - 8 * q^86 - 20 * q^87 - 8 * q^88 - 28 * q^89 - 16 * q^90 - 4 * q^91 - 12 * q^93 + 8 * q^95 + 16 * q^97 + 4 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

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Database

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