LMFDB - Embedded newform 6027.2.a.u.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, 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("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.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:	$48.1258372982$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.8468.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 5x^{2} + 3x + 4 $ x^4 - x^3 - 5x^2 + 3x + 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.704624$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.704624 q^{2} +1.00000 q^{3} -1.50350 q^{4} -1.50350 q^{5} -0.704624 q^{6} +2.46865 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.704624 q^{2} +1.00000 q^{3} -1.50350 q^{4} -1.50350 q^{5} -0.704624 q^{6} +2.46865 q^{8} +1.00000 q^{9} +1.05941 q^{10} -4.26753 q^{11} -1.50350 q^{12} -2.30238 q^{13} -1.50350 q^{15} +1.26753 q^{16} -0.905744 q^{17} -0.704624 q^{18} -1.17328 q^{19} +2.26053 q^{20} +3.00701 q^{22} -0.893136 q^{23} +2.46865 q^{24} -2.73947 q^{25} +1.62232 q^{26} +1.00000 q^{27} +3.32694 q^{29} +1.05941 q^{30} +3.09426 q^{31} -5.83045 q^{32} -4.26753 q^{33} +0.638209 q^{34} -1.50350 q^{36} -2.36179 q^{37} +0.826721 q^{38} -2.30238 q^{39} -3.71163 q^{40} +1.00000 q^{41} -7.84305 q^{43} +6.41626 q^{44} -1.50350 q^{45} +0.629325 q^{46} +1.30567 q^{47} +1.26753 q^{48} +1.93030 q^{50} -0.905744 q^{51} +3.46165 q^{52} -6.64894 q^{53} -0.704624 q^{54} +6.41626 q^{55} -1.17328 q^{57} -2.34424 q^{58} +0.638209 q^{59} +2.26053 q^{60} +9.84305 q^{61} -2.18029 q^{62} +1.57320 q^{64} +3.46165 q^{65} +3.00701 q^{66} -13.4478 q^{67} +1.36179 q^{68} -0.893136 q^{69} -0.245293 q^{71} +2.46865 q^{72} +2.08725 q^{73} +1.66418 q^{74} -2.73947 q^{75} +1.76403 q^{76} +1.62232 q^{78} -14.5736 q^{79} -1.90574 q^{80} +1.00000 q^{81} -0.704624 q^{82} +6.41626 q^{83} +1.36179 q^{85} +5.52641 q^{86} +3.32694 q^{87} -10.5351 q^{88} +1.81149 q^{89} +1.05941 q^{90} +1.34283 q^{92} +3.09426 q^{93} -0.920006 q^{94} +1.76403 q^{95} -5.83045 q^{96} +6.29416 q^{97} -4.26753 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + 4 q^{3} + 3 q^{4} + 3 q^{5} + q^{6} + 3 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + q^2 + 4 * q^3 + 3 * q^4 + 3 * q^5 + q^6 + 3 * q^8 + 4 * q^9	$ 4 q + q^{2} + 4 q^{3} + 3 q^{4} + 3 q^{5} + q^{6} + 3 q^{8} + 4 q^{9} + 5 q^{10} - 5 q^{11} + 3 q^{12} + 5 q^{13} + 3 q^{15} - 7 q^{16} - 5 q^{17} + q^{18} + 6 q^{19} + 15 q^{20} - 6 q^{22} + 3 q^{23} + 3 q^{24} - 5 q^{25} - q^{26} + 4 q^{27} + 2 q^{29} + 5 q^{30} + 11 q^{31} - 3 q^{32} - 5 q^{33} + 16 q^{34} + 3 q^{36} + 4 q^{37} + 14 q^{38} + 5 q^{39} + 7 q^{40} + 4 q^{41} - 19 q^{43} + 3 q^{45} - 23 q^{46} + 4 q^{47} - 7 q^{48} + 12 q^{50} - 5 q^{51} + 25 q^{52} + 9 q^{53} + q^{54} + 6 q^{57} + 25 q^{58} + 16 q^{59} + 15 q^{60} + 27 q^{61} + 20 q^{62} - 7 q^{64} + 25 q^{65} - 6 q^{66} - 13 q^{67} - 8 q^{68} + 3 q^{69} + q^{71} + 3 q^{72} + 25 q^{73} - 21 q^{74} - 5 q^{75} + 4 q^{76} - q^{78} - q^{79} - 9 q^{80} + 4 q^{81} + q^{82} - 8 q^{85} + 16 q^{86} + 2 q^{87} - 18 q^{88} + 10 q^{89} + 5 q^{90} + 15 q^{92} + 11 q^{93} - 13 q^{94} + 4 q^{95} - 3 q^{96} - 15 q^{97} - 5 q^{99}+O(q^{100}) $ 4 * q + q^2 + 4 * q^3 + 3 * q^4 + 3 * q^5 + q^6 + 3 * q^8 + 4 * q^9 + 5 * q^10 - 5 * q^11 + 3 * q^12 + 5 * q^13 + 3 * q^15 - 7 * q^16 - 5 * q^17 + q^18 + 6 * q^19 + 15 * q^20 - 6 * q^22 + 3 * q^23 + 3 * q^24 - 5 * q^25 - q^26 + 4 * q^27 + 2 * q^29 + 5 * q^30 + 11 * q^31 - 3 * q^32 - 5 * q^33 + 16 * q^34 + 3 * q^36 + 4 * q^37 + 14 * q^38 + 5 * q^39 + 7 * q^40 + 4 * q^41 - 19 * q^43 + 3 * q^45 - 23 * q^46 + 4 * q^47 - 7 * q^48 + 12 * q^50 - 5 * q^51 + 25 * q^52 + 9 * q^53 + q^54 + 6 * q^57 + 25 * q^58 + 16 * q^59 + 15 * q^60 + 27 * q^61 + 20 * q^62 - 7 * q^64 + 25 * q^65 - 6 * q^66 - 13 * q^67 - 8 * q^68 + 3 * q^69 + q^71 + 3 * q^72 + 25 * q^73 - 21 * q^74 - 5 * q^75 + 4 * q^76 - q^78 - q^79 - 9 * q^80 + 4 * q^81 + q^82 - 8 * q^85 + 16 * q^86 + 2 * q^87 - 18 * q^88 + 10 * q^89 + 5 * q^90 + 15 * q^92 + 11 * q^93 - 13 * q^94 + 4 * q^95 - 3 * q^96 - 15 * q^97 - 5 * 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 $

$2$	−0.704624	−0.498245	−0.249122	−	0.968472i	$-0.580142\pi$
$2$	−0.704624	−0.498245	−0.249122	+	0.968472i	$0.580142\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.50350	−0.751752
$5$	−1.50350	−0.672388	−0.336194	−	0.941793i	$-0.609140\pi$
$5$	−1.50350	−0.672388	−0.336194	+	0.941793i	$0.609140\pi$
$6$	−0.704624	−0.287662
$7$	0	0
$7$	0	0
$8$	2.46865	0.872801
$9$	1.00000	0.333333
$10$	1.05941	0.335014
$11$	−4.26753	−1.28671	−0.643355	−	0.765568i	$-0.722458\pi$
$11$	−4.26753	−1.28671	−0.643355	+	0.765568i	$0.722458\pi$
$12$	−1.50350	−0.434024
$13$	−2.30238	−0.638567	−0.319283	−	0.947659i	$-0.603442\pi$
$13$	−2.30238	−0.638567	−0.319283	+	0.947659i	$0.603442\pi$
$14$	0	0
$15$	−1.50350	−0.388203
$16$	1.26753	0.316884
$17$	−0.905744	−0.219675	−0.109838	−	0.993950i	$-0.535033\pi$
$17$	−0.905744	−0.219675	−0.109838	+	0.993950i	$0.535033\pi$
$18$	−0.704624	−0.166082
$19$	−1.17328	−0.269169	−0.134584	−	0.990902i	$-0.542970\pi$
$19$	−1.17328	−0.269169	−0.134584	+	0.990902i	$0.542970\pi$
$20$	2.26053	0.505469
$21$	0	0
$22$	3.00701	0.641096
$23$	−0.893136	−0.186232	−0.0931159	−	0.995655i	$-0.529683\pi$
$23$	−0.893136	−0.186232	−0.0931159	+	0.995655i	$0.529683\pi$
$24$	2.46865	0.503912
$25$	−2.73947	−0.547895
$26$	1.62232	0.318162
$27$	1.00000	0.192450
$28$	0	0
$29$	3.32694	0.617797	0.308899	−	0.951095i	$-0.400040\pi$
$29$	3.32694	0.617797	0.308899	+	0.951095i	$0.400040\pi$
$30$	1.05941	0.193420
$31$	3.09426	0.555745	0.277872	−	0.960618i	$-0.410371\pi$
$31$	3.09426	0.555745	0.277872	+	0.960618i	$0.410371\pi$
$32$	−5.83045	−1.03069
$33$	−4.26753	−0.742882
$34$	0.638209	0.109452
$35$	0	0
$36$	−1.50350	−0.250584
$37$	−2.36179	−0.388276	−0.194138	−	0.980974i	$-0.562191\pi$
$37$	−2.36179	−0.388276	−0.194138	+	0.980974i	$0.562191\pi$
$38$	0.826721	0.134112
$39$	−2.30238	−0.368677
$40$	−3.71163	−0.586861
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−7.84305	−1.19605	−0.598027	−	0.801476i	$-0.704049\pi$
$43$	−7.84305	−1.19605	−0.598027	+	0.801476i	$0.704049\pi$
$44$	6.41626	0.967287
$45$	−1.50350	−0.224129
$46$	0.629325	0.0927890
$47$	1.30567	0.190451	0.0952257	−	0.995456i	$-0.469643\pi$
$47$	1.30567	0.190451	0.0952257	+	0.995456i	$0.469643\pi$
$48$	1.26753	0.182953
$49$	0	0
$50$	1.93030	0.272986
$51$	−0.905744	−0.126830
$52$	3.46165	0.480044
$53$	−6.64894	−0.913303	−0.456651	−	0.889646i	$-0.650951\pi$
$53$	−6.64894	−0.913303	−0.456651	+	0.889646i	$0.650951\pi$
$54$	−0.704624	−0.0958872
$55$	6.41626	0.865168
$56$	0	0
$57$	−1.17328	−0.155405
$58$	−2.34424	−0.307814
$59$	0.638209	0.0830878	0.0415439	−	0.999137i	$-0.486772\pi$
$59$	0.638209	0.0830878	0.0415439	+	0.999137i	$0.486772\pi$
$60$	2.26053	0.291833
$61$	9.84305	1.26027	0.630137	−	0.776484i	$-0.282999\pi$
$61$	9.84305	1.26027	0.630137	+	0.776484i	$0.282999\pi$
$62$	−2.18029	−0.276897
$63$	0	0
$64$	1.57320	0.196651
$65$	3.46165	0.429364
$66$	3.00701	0.370137
$67$	−13.4478	−1.64291	−0.821457	−	0.570271i	$-0.806838\pi$
$67$	−13.4478	−1.64291	−0.821457	+	0.570271i	$0.806838\pi$
$68$	1.36179	0.165141
$69$	−0.893136	−0.107521
$70$	0	0
$71$	−0.245293	−0.0291110	−0.0145555	−	0.999894i	$-0.504633\pi$
$71$	−0.245293	−0.0291110	−0.0145555	+	0.999894i	$0.504633\pi$
$72$	2.46865	0.290934
$73$	2.08725	0.244294	0.122147	−	0.992512i	$-0.461022\pi$
$73$	2.08725	0.244294	0.122147	+	0.992512i	$0.461022\pi$
$74$	1.66418	0.193456
$75$	−2.73947	−0.316327
$76$	1.76403	0.202348
$77$	0	0
$78$	1.62232	0.183691
$79$	−14.5736	−1.63966	−0.819832	−	0.572605i	$-0.805933\pi$
$79$	−14.5736	−1.63966	−0.819832	+	0.572605i	$0.805933\pi$
$80$	−1.90574	−0.213069
$81$	1.00000	0.111111
$82$	−0.704624	−0.0778127
$83$	6.41626	0.704276	0.352138	−	0.935948i	$-0.385455\pi$
$83$	6.41626	0.704276	0.352138	+	0.935948i	$0.385455\pi$
$84$	0	0
$85$	1.36179	0.147707
$86$	5.52641	0.595928
$87$	3.32694	0.356685
$88$	−10.5351	−1.12304
$89$	1.81149	0.192017	0.0960087	−	0.995380i	$-0.469392\pi$
$89$	1.81149	0.192017	0.0960087	+	0.995380i	$0.469392\pi$
$90$	1.05941	0.111671
$91$	0	0
$92$	1.34283	0.140000
$93$	3.09426	0.320859
$94$	−0.920006	−0.0948914
$95$	1.76403	0.180986
$96$	−5.83045	−0.595067
$97$	6.29416	0.639075	0.319538	−	0.947574i	$-0.396472\pi$
$97$	6.29416	0.639075	0.319538	+	0.947574i	$0.396472\pi$
$98$	0	0
$99$	−4.26753	−0.428903
$100$	4.11881	0.411881
$101$	−10.2816	−1.02305	−0.511526	−	0.859268i	$-0.670920\pi$
$101$	−10.2816	−1.02305	−0.511526	+	0.859268i	$0.670920\pi$
$102$	0.638209	0.0631922
$103$	8.68708	0.855963	0.427982	−	0.903787i	$-0.359225\pi$
$103$	8.68708	0.855963	0.427982	+	0.903787i	$0.359225\pi$
$104$	−5.68379	−0.557342
$105$	0	0
$106$	4.68501	0.455048
$107$	17.9551	1.73578	0.867890	−	0.496756i	$-0.165476\pi$
$107$	17.9551	1.73578	0.867890	+	0.496756i	$0.165476\pi$
$108$	−1.50350	−0.144675
$109$	−1.29866	−0.124389	−0.0621946	−	0.998064i	$-0.519810\pi$
$109$	−1.29866	−0.124389	−0.0621946	+	0.998064i	$0.519810\pi$
$110$	−4.52105	−0.431065
$111$	−2.36179	−0.224171
$112$	0	0
$113$	3.46493	0.325953	0.162977	−	0.986630i	$-0.447890\pi$
$113$	3.46493	0.325953	0.162977	+	0.986630i	$0.447890\pi$
$114$	0.826721	0.0774295
$115$	1.34283	0.125220
$116$	−5.00207	−0.464431
$117$	−2.30238	−0.212856
$118$	−0.449698	−0.0413981
$119$	0	0
$120$	−3.71163	−0.338824
$121$	7.21185	0.655623
$122$	−6.93566	−0.627925
$123$	1.00000	0.0901670
$124$	−4.65223	−0.417782
$125$	11.6363	1.04079
$126$	0	0
$127$	11.1398	0.988501	0.494250	−	0.869320i	$-0.335443\pi$
$127$	11.1398	0.988501	0.494250	+	0.869320i	$0.335443\pi$
$128$	10.5524	0.932707
$129$	−7.84305	−0.690542
$130$	−2.43916	−0.213928
$131$	−4.43850	−0.387793	−0.193897	−	0.981022i	$-0.562113\pi$
$131$	−4.43850	−0.387793	−0.193897	+	0.981022i	$0.562113\pi$
$132$	6.41626	0.558464
$133$	0	0
$134$	9.47566	0.818573
$135$	−1.50350	−0.129401
$136$	−2.23597	−0.191733
$137$	10.7362	0.917255	0.458627	−	0.888629i	$-0.348341\pi$
$137$	10.7362	0.917255	0.458627	+	0.888629i	$0.348341\pi$
$138$	0.629325	0.0535717
$139$	12.1836	1.03340	0.516699	−	0.856167i	$-0.327161\pi$
$139$	12.1836	1.03340	0.516699	+	0.856167i	$0.327161\pi$
$140$	0	0
$141$	1.30567	0.109957
$142$	0.172840	0.0145044
$143$	9.82551	0.821650
$144$	1.26753	0.105628
$145$	−5.00207	−0.415399
$146$	−1.47072	−0.121718
$147$	0	0
$148$	3.55096	0.291887
$149$	6.11716	0.501137	0.250569	−	0.968099i	$-0.419382\pi$
$149$	6.11716	0.501137	0.250569	+	0.968099i	$0.419382\pi$
$150$	1.93030	0.157608
$151$	−8.41626	−0.684905	−0.342453	−	0.939535i	$-0.611258\pi$
$151$	−8.41626	−0.684905	−0.342453	+	0.939535i	$0.611258\pi$
$152$	−2.89642	−0.234931
$153$	−0.905744	−0.0732251
$154$	0	0
$155$	−4.65223	−0.373676
$156$	3.46165	0.277153
$157$	−8.46372	−0.675478	−0.337739	−	0.941240i	$-0.609662\pi$
$157$	−8.46372	−0.675478	−0.337739	+	0.941240i	$0.609662\pi$
$158$	10.2689	0.816953
$159$	−6.64894	−0.527295
$160$	8.76610	0.693021
$161$	0	0
$162$	−0.704624	−0.0553605
$163$	8.70603	0.681909	0.340955	−	0.940080i	$-0.389250\pi$
$163$	8.70603	0.681909	0.340955	+	0.940080i	$0.389250\pi$
$164$	−1.50350	−0.117404
$165$	6.41626	0.499505
$166$	−4.52105	−0.350902
$167$	−7.09304	−0.548876	−0.274438	−	0.961605i	$-0.588492\pi$
$167$	−7.09304	−0.548876	−0.274438	+	0.961605i	$0.588492\pi$
$168$	0	0
$169$	−7.69903	−0.592233
$170$	−0.959551	−0.0735942
$171$	−1.17328	−0.0897229
$172$	11.7921	0.899137
$173$	16.8030	1.27751	0.638756	−	0.769409i	$-0.279449\pi$
$173$	16.8030	1.27751	0.638756	+	0.769409i	$0.279449\pi$
$174$	−2.34424	−0.177717
$175$	0	0
$176$	−5.40925	−0.407737
$177$	0.638209	0.0479708
$178$	−1.27642	−0.0956716
$179$	4.85663	0.363002	0.181501	−	0.983391i	$-0.441904\pi$
$179$	4.85663	0.363002	0.181501	+	0.983391i	$0.441904\pi$
$180$	2.26053	0.168490
$181$	−5.94597	−0.441961	−0.220980	−	0.975278i	$-0.570926\pi$
$181$	−5.94597	−0.441961	−0.220980	+	0.975278i	$0.570926\pi$
$182$	0	0
$183$	9.84305	0.727619
$184$	−2.20484	−0.162543
$185$	3.55096	0.261072
$186$	−2.18029	−0.159866
$187$	3.86530	0.282658
$188$	−1.96308	−0.143172
$189$	0	0
$190$	−1.24298	−0.0901752
$191$	−14.0854	−1.01918	−0.509591	−	0.860417i	$-0.670203\pi$
$191$	−14.0854	−1.01918	−0.509591	+	0.860417i	$0.670203\pi$
$192$	1.57320	0.113536
$193$	9.65924	0.695287	0.347644	−	0.937627i	$-0.386982\pi$
$193$	9.65924	0.695287	0.347644	+	0.937627i	$0.386982\pi$
$194$	−4.43502	−0.318416
$195$	3.46165	0.247894
$196$	0	0
$197$	−1.13984	−0.0812102	−0.0406051	−	0.999175i	$-0.512929\pi$
$197$	−1.13984	−0.0812102	−0.0406051	+	0.999175i	$0.512929\pi$
$198$	3.00701	0.213699
$199$	−6.81027	−0.482768	−0.241384	−	0.970430i	$-0.577601\pi$
$199$	−6.81027	−0.482768	−0.241384	+	0.970430i	$0.577601\pi$
$200$	−6.76282	−0.478203
$201$	−13.4478	−0.948536
$202$	7.24463	0.509731
$203$	0	0
$204$	1.36179	0.0953444
$205$	−1.50350	−0.105009
$206$	−6.12113	−0.426479
$207$	−0.893136	−0.0620772
$208$	−2.91835	−0.202351
$209$	5.00701	0.346342
$210$	0	0
$211$	3.45439	0.237810	0.118905	−	0.992906i	$-0.462062\pi$
$211$	3.45439	0.237810	0.118905	+	0.992906i	$0.462062\pi$
$212$	9.99672	0.686577
$213$	−0.245293	−0.0168072
$214$	−12.6516	−0.864843
$215$	11.7921	0.804212
$216$	2.46865	0.167971
$217$	0	0
$218$	0.915068	0.0619762
$219$	2.08725	0.141043
$220$	−9.64687	−0.650392
$221$	2.08537	0.140277
$222$	1.66418	0.111692
$223$	−3.01195	−0.201695	−0.100847	−	0.994902i	$-0.532155\pi$
$223$	−3.01195	−0.201695	−0.100847	+	0.994902i	$0.532155\pi$
$224$	0	0
$225$	−2.73947	−0.182632
$226$	−2.44147	−0.162404
$227$	−14.0619	−0.933322	−0.466661	−	0.884436i	$-0.654543\pi$
$227$	−14.0619	−0.933322	−0.466661	+	0.884436i	$0.654543\pi$
$228$	1.76403	0.116826
$229$	1.07999	0.0713680	0.0356840	−	0.999363i	$-0.488639\pi$
$229$	1.07999	0.0713680	0.0356840	+	0.999363i	$0.488639\pi$
$230$	−0.946193	−0.0623901
$231$	0	0
$232$	8.21307	0.539214
$233$	5.55030	0.363612	0.181806	−	0.983334i	$-0.441806\pi$
$233$	5.55030	0.363612	0.181806	+	0.983334i	$0.441806\pi$
$234$	1.62232	0.106054
$235$	−1.96308	−0.128057
$236$	−0.959551	−0.0624614
$237$	−14.5736	−0.946660
$238$	0	0
$239$	−1.45836	−0.0943335	−0.0471668	−	0.998887i	$-0.515019\pi$
$239$	−1.45836	−0.0943335	−0.0471668	+	0.998887i	$0.515019\pi$
$240$	−1.90574	−0.123015
$241$	−1.68335	−0.108434	−0.0542172	−	0.998529i	$-0.517266\pi$
$241$	−1.68335	−0.108434	−0.0542172	+	0.998529i	$0.517266\pi$
$242$	−5.08165	−0.326661
$243$	1.00000	0.0641500
$244$	−14.7991	−0.947414
$245$	0	0
$246$	−0.704624	−0.0449252
$247$	2.70134	0.171882
$248$	7.63865	0.485055
$249$	6.41626	0.406614
$250$	−8.19924	−0.518566
$251$	18.8882	1.19221	0.596106	−	0.802906i	$-0.296714\pi$
$251$	18.8882	1.19221	0.596106	+	0.802906i	$0.296714\pi$
$252$	0	0
$253$	3.81149	0.239626
$254$	−7.84940	−0.492515
$255$	1.36179	0.0852786
$256$	−10.5819	−0.661367
$257$	−15.1796	−0.946879	−0.473440	−	0.880826i	$-0.656988\pi$
$257$	−15.1796	−0.946879	−0.473440	+	0.880826i	$0.656988\pi$
$258$	5.52641	0.344059
$259$	0	0
$260$	−5.20460	−0.322776
$261$	3.32694	0.205932
$262$	3.12747	0.193216
$263$	−1.96021	−0.120872	−0.0604359	−	0.998172i	$-0.519249\pi$
$263$	−1.96021	−0.120872	−0.0604359	+	0.998172i	$0.519249\pi$
$264$	−10.5351	−0.648389
$265$	9.99672	0.614093
$266$	0	0
$267$	1.81149	0.110861
$268$	20.2189	1.23506
$269$	30.4771	1.85822	0.929110	−	0.369804i	$-0.120575\pi$
$269$	30.4771	1.85822	0.929110	+	0.369804i	$0.120575\pi$
$270$	1.05941	0.0644734
$271$	−5.84634	−0.355140	−0.177570	−	0.984108i	$-0.556824\pi$
$271$	−5.84634	−0.355140	−0.177570	+	0.984108i	$0.556824\pi$
$272$	−1.14806	−0.0696115
$273$	0	0
$274$	−7.56498	−0.457017
$275$	11.6908	0.704982
$276$	1.34283	0.0808291
$277$	7.11638	0.427582	0.213791	−	0.976879i	$-0.431419\pi$
$277$	7.11638	0.427582	0.213791	+	0.976879i	$0.431419\pi$
$278$	−8.58484	−0.514885
$279$	3.09426	0.185248
$280$	0	0
$281$	−4.47632	−0.267035	−0.133518	−	0.991046i	$-0.542627\pi$
$281$	−4.47632	−0.267035	−0.133518	+	0.991046i	$0.542627\pi$
$282$	−0.920006	−0.0547856
$283$	−0.675569	−0.0401584	−0.0200792	−	0.999798i	$-0.506392\pi$
$283$	−0.675569	−0.0401584	−0.0200792	+	0.999798i	$0.506392\pi$
$284$	0.368800	0.0218842
$285$	1.76403	0.104492
$286$	−6.92329	−0.409383
$287$	0	0
$288$	−5.83045	−0.343562
$289$	−16.1796	−0.951743
$290$	3.52458	0.206971
$291$	6.29416	0.368970
$292$	−3.13818	−0.183648
$293$	2.58722	0.151147	0.0755736	−	0.997140i	$-0.475921\pi$
$293$	2.58722	0.151147	0.0755736	+	0.997140i	$0.475921\pi$
$294$	0	0
$295$	−0.959551	−0.0558672
$296$	−5.83045	−0.338888
$297$	−4.26753	−0.247627
$298$	−4.31030	−0.249689
$299$	2.05634	0.118921
$300$	4.11881	0.237800
$301$	0	0
$302$	5.93030	0.341250
$303$	−10.2816	−0.590660
$304$	−1.48717	−0.0852952
$305$	−14.7991	−0.847393
$306$	0.638209	0.0364840
$307$	27.0130	1.54172	0.770858	−	0.637007i	$-0.219828\pi$
$307$	27.0130	1.54172	0.770858	+	0.637007i	$0.219828\pi$
$308$	0	0
$309$	8.68708	0.494191
$310$	3.27807	0.186182
$311$	29.6830	1.68317	0.841585	−	0.540125i	$-0.181623\pi$
$311$	29.6830	1.68317	0.841585	+	0.540125i	$0.181623\pi$
$312$	−5.68379	−0.321781
$313$	14.0091	0.791840	0.395920	−	0.918285i	$-0.370426\pi$
$313$	14.0091	0.791840	0.395920	+	0.918285i	$0.370426\pi$
$314$	5.96374	0.336553
$315$	0	0
$316$	21.9115	1.23262
$317$	21.2836	1.19541	0.597704	−	0.801717i	$-0.296080\pi$
$317$	21.2836	1.19541	0.597704	+	0.801717i	$0.296080\pi$
$318$	4.68501	0.262722
$319$	−14.1978	−0.794926
$320$	−2.36532	−0.132225
$321$	17.9551	1.00215
$322$	0	0
$323$	1.06269	0.0591297
$324$	−1.50350	−0.0835280
$325$	6.30732	0.349867
$326$	−6.13448	−0.339758
$327$	−1.29866	−0.0718161
$328$	2.46865	0.136309
$329$	0	0
$330$	−4.52105	−0.248876
$331$	8.80304	0.483859	0.241930	−	0.970294i	$-0.422220\pi$
$331$	8.80304	0.483859	0.241930	+	0.970294i	$0.422220\pi$
$332$	−9.64687	−0.529441
$333$	−2.36179	−0.129425
$334$	4.99793	0.273475
$335$	20.2189	1.10467
$336$	0	0
$337$	32.7158	1.78214	0.891072	−	0.453863i	$-0.149954\pi$
$337$	32.7158	1.78214	0.891072	+	0.453863i	$0.149954\pi$
$338$	5.42492	0.295077
$339$	3.46493	0.188189
$340$	−2.04746	−0.111039
$341$	−13.2048	−0.715082
$342$	0.826721	0.0447040
$343$	0	0
$344$	−19.3618	−1.04392
$345$	1.34283	0.0722957
$346$	−11.8398	−0.636513
$347$	32.9033	1.76634	0.883171	−	0.469051i	$-0.155404\pi$
$347$	32.9033	1.76634	0.883171	+	0.469051i	$0.155404\pi$
$348$	−5.00207	−0.268139
$349$	32.5250	1.74102	0.870511	−	0.492149i	$-0.163789\pi$
$349$	32.5250	1.74102	0.870511	+	0.492149i	$0.163789\pi$
$350$	0	0
$351$	−2.30238	−0.122892
$352$	24.8816	1.32620
$353$	7.58131	0.403513	0.201756	−	0.979436i	$-0.435335\pi$
$353$	7.58131	0.403513	0.201756	+	0.979436i	$0.435335\pi$
$354$	−0.449698	−0.0239012
$355$	0.368800	0.0195738
$356$	−2.72358	−0.144350
$357$	0	0
$358$	−3.42210	−0.180864
$359$	24.6482	1.30088	0.650440	−	0.759557i	$-0.274584\pi$
$359$	24.6482	1.30088	0.650440	+	0.759557i	$0.274584\pi$
$360$	−3.71163	−0.195620
$361$	−17.6234	−0.927548
$362$	4.18968	0.220205
$363$	7.21185	0.378524
$364$	0	0
$365$	−3.13818	−0.164260
$366$	−6.93566	−0.362533
$367$	−21.6318	−1.12917	−0.564586	−	0.825374i	$-0.690964\pi$
$367$	−21.6318	−1.12917	−0.564586	+	0.825374i	$0.690964\pi$
$368$	−1.13208	−0.0590138
$369$	1.00000	0.0520579
$370$	−2.50209	−0.130078
$371$	0	0
$372$	−4.65223	−0.241207
$373$	−32.2405	−1.66935	−0.834676	−	0.550741i	$-0.814345\pi$
$373$	−32.2405	−1.66935	−0.834676	+	0.550741i	$0.814345\pi$
$374$	−2.72358	−0.140833
$375$	11.6363	0.600898
$376$	3.22325	0.166226
$377$	−7.65990	−0.394505
$378$	0	0
$379$	28.8416	1.48149	0.740747	−	0.671784i	$-0.234472\pi$
$379$	28.8416	1.48149	0.740747	+	0.671784i	$0.234472\pi$
$380$	−2.65223	−0.136056
$381$	11.1398	0.570711
$382$	9.92490	0.507802
$383$	−31.1691	−1.59267	−0.796333	−	0.604858i	$-0.793230\pi$
$383$	−31.1691	−1.59267	−0.796333	+	0.604858i	$0.793230\pi$
$384$	10.5524	0.538498
$385$	0	0
$386$	−6.80613	−0.346423
$387$	−7.84305	−0.398685
$388$	−9.46330	−0.480426
$389$	0.0362595	0.00183843	0.000919215	−	1.00000i	$-0.499707\pi$
$389$	0.0362595	0.00183843	0.000919215		1.00000i	$0.499707\pi$
$390$	−2.43916	−0.123512
$391$	0.808953	0.0409105
$392$	0	0
$393$	−4.43850	−0.223893
$394$	0.803158	0.0404625
$395$	21.9115	1.10249
$396$	6.41626	0.322429
$397$	34.1952	1.71621	0.858104	−	0.513477i	$-0.171643\pi$
$397$	34.1952	1.71621	0.858104	+	0.513477i	$0.171643\pi$
$398$	4.79868	0.240536
$399$	0	0
$400$	−3.47238	−0.173619
$401$	20.3606	1.01676	0.508379	−	0.861133i	$-0.330245\pi$
$401$	20.3606	1.01676	0.508379	+	0.861133i	$0.330245\pi$
$402$	9.47566	0.472603
$403$	−7.12417	−0.354880
$404$	15.4584	0.769082
$405$	−1.50350	−0.0747097
$406$	0	0
$407$	10.0790	0.499599
$408$	−2.23597	−0.110697
$409$	−10.5257	−0.520465	−0.260232	−	0.965546i	$-0.583799\pi$
$409$	−10.5257	−0.520465	−0.260232	+	0.965546i	$0.583799\pi$
$410$	1.05941	0.0523203
$411$	10.7362	0.529577
$412$	−13.0611	−0.643472
$413$	0	0
$414$	0.629325	0.0309297
$415$	−9.64687	−0.473546
$416$	13.4239	0.658162
$417$	12.1836	0.596632
$418$	−3.52806	−0.172563
$419$	27.5895	1.34784	0.673919	−	0.738806i	$-0.264610\pi$
$419$	27.5895	1.34784	0.673919	+	0.738806i	$0.264610\pi$
$420$	0	0
$421$	33.0924	1.61282	0.806412	−	0.591354i	$-0.201406\pi$
$421$	33.0924	1.61282	0.806412	+	0.591354i	$0.201406\pi$
$422$	−2.43405	−0.118488
$423$	1.30567	0.0634838
$424$	−16.4139	−0.797132
$425$	2.48126	0.120359
$426$	0.172840	0.00837411
$427$	0	0
$428$	−26.9955	−1.30488
$429$	9.82551	0.474380
$430$	−8.30898	−0.400694
$431$	−4.91044	−0.236528	−0.118264	−	0.992982i	$-0.537733\pi$
$431$	−4.91044	−0.236528	−0.118264	+	0.992982i	$0.537733\pi$
$432$	1.26753	0.0609843
$433$	−12.2511	−0.588750	−0.294375	−	0.955690i	$-0.595111\pi$
$433$	−12.2511	−0.588750	−0.294375	+	0.955690i	$0.595111\pi$
$434$	0	0
$435$	−5.00207	−0.239831
$436$	1.95254	0.0935098
$437$	1.04790	0.0501277
$438$	−1.47072	−0.0702740
$439$	−15.5133	−0.740408	−0.370204	−	0.928951i	$-0.620712\pi$
$439$	−15.5133	−0.740408	−0.370204	+	0.928951i	$0.620712\pi$
$440$	15.8395	0.755120
$441$	0	0
$442$	−1.46940	−0.0698924
$443$	−18.4525	−0.876706	−0.438353	−	0.898803i	$-0.644438\pi$
$443$	−18.4525	−0.876706	−0.438353	+	0.898803i	$0.644438\pi$
$444$	3.55096	0.168521
$445$	−2.72358	−0.129110
$446$	2.12229	0.100493
$447$	6.11716	0.289332
$448$	0	0
$449$	−13.5643	−0.640140	−0.320070	−	0.947394i	$-0.603706\pi$
$449$	−13.5643	−0.640140	−0.320070	+	0.947394i	$0.603706\pi$
$450$	1.93030	0.0909952
$451$	−4.26753	−0.200950
$452$	−5.20954	−0.245036
$453$	−8.41626	−0.395430
$454$	9.90837	0.465023
$455$	0	0
$456$	−2.89642	−0.135637
$457$	−7.62298	−0.356588	−0.178294	−	0.983977i	$-0.557058\pi$
$457$	−7.62298	−0.356588	−0.178294	+	0.983977i	$0.557058\pi$
$458$	−0.760990	−0.0355587
$459$	−0.905744	−0.0422765
$460$	−2.01896	−0.0941343
$461$	10.5533	0.491518	0.245759	−	0.969331i	$-0.420963\pi$
$461$	10.5533	0.491518	0.245759	+	0.969331i	$0.420963\pi$
$462$	0	0
$463$	−22.4384	−1.04280	−0.521400	−	0.853312i	$-0.674590\pi$
$463$	−22.4384	−1.04280	−0.521400	+	0.853312i	$0.674590\pi$
$464$	4.21701	0.195770
$465$	−4.65223	−0.215742
$466$	−3.91088	−0.181168
$467$	25.3453	1.17284	0.586421	−	0.810006i	$-0.300536\pi$
$467$	25.3453	1.17284	0.586421	+	0.810006i	$0.300536\pi$
$468$	3.46165	0.160015
$469$	0	0
$470$	1.38323	0.0638038
$471$	−8.46372	−0.389987
$472$	1.57552	0.0725191
$473$	33.4705	1.53898
$474$	10.2689	0.471668
$475$	3.21417	0.147476
$476$	0	0
$477$	−6.64894	−0.304434
$478$	1.02760	0.0470012
$479$	37.6491	1.72023	0.860117	−	0.510098i	$-0.170391\pi$
$479$	37.6491	1.72023	0.860117	+	0.510098i	$0.170391\pi$
$480$	8.76610	0.400116
$481$	5.43775	0.247940
$482$	1.18613	0.0540268
$483$	0	0
$484$	−10.8431	−0.492866
$485$	−9.46330	−0.429706
$486$	−0.704624	−0.0319624
$487$	7.52337	0.340916	0.170458	−	0.985365i	$-0.445475\pi$
$487$	7.52337	0.340916	0.170458	+	0.985365i	$0.445475\pi$
$488$	24.2991	1.09997
$489$	8.70603	0.393700
$490$	0	0
$491$	19.8758	0.896982	0.448491	−	0.893787i	$-0.351962\pi$
$491$	19.8758	0.896982	0.448491	+	0.893787i	$0.351962\pi$
$492$	−1.50350	−0.0677832
$493$	−3.01336	−0.135715
$494$	−1.90343	−0.0856394
$495$	6.41626	0.288389
$496$	3.92208	0.176106
$497$	0	0
$498$	−4.52105	−0.202593
$499$	−37.6127	−1.68377	−0.841887	−	0.539654i	$-0.818555\pi$
$499$	−37.6127	−1.68377	−0.841887	+	0.539654i	$0.818555\pi$
$500$	−17.4953	−0.782413
$501$	−7.09304	−0.316894
$502$	−13.3091	−0.594013
$503$	15.2628	0.680536	0.340268	−	0.940328i	$-0.389482\pi$
$503$	15.2628	0.680536	0.340268	+	0.940328i	$0.389482\pi$
$504$	0	0
$505$	15.4584	0.687888
$506$	−2.68567	−0.119392
$507$	−7.69903	−0.341926
$508$	−16.7488	−0.743108
$509$	−11.1269	−0.493192	−0.246596	−	0.969118i	$-0.579312\pi$
$509$	−11.1269	−0.493192	−0.246596	+	0.969118i	$0.579312\pi$
$510$	−0.959551	−0.0424896
$511$	0	0
$512$	−13.6485	−0.603184
$513$	−1.17328	−0.0518015
$514$	10.6959	0.471777
$515$	−13.0611	−0.575539
$516$	11.7921	0.519117
$517$	−5.57199	−0.245056
$518$	0	0
$519$	16.8030	0.737572
$520$	8.54561	0.374750
$521$	17.0795	0.748265	0.374132	−	0.927375i	$-0.377941\pi$
$521$	17.0795	0.748265	0.374132	+	0.927375i	$0.377941\pi$
$522$	−2.34424	−0.102605
$523$	23.7322	1.03774	0.518869	−	0.854854i	$-0.326353\pi$
$523$	23.7322	1.03774	0.518869	+	0.854854i	$0.326353\pi$
$524$	6.67330	0.291525
$525$	0	0
$526$	1.38121	0.0602237
$527$	−2.80260	−0.122083
$528$	−5.40925	−0.235407
$529$	−22.2023	−0.965318
$530$	−7.04393	−0.305969
$531$	0.638209	0.0276959
$532$	0	0
$533$	−2.30238	−0.0997273
$534$	−1.27642	−0.0552360
$535$	−26.9955	−1.16712
$536$	−33.1980	−1.43394
$537$	4.85663	0.209579
$538$	−21.4749	−0.925848
$539$	0	0
$540$	2.26053	0.0972775
$541$	−27.4226	−1.17899	−0.589495	−	0.807772i	$-0.700673\pi$
$541$	−27.4226	−1.17899	−0.589495	+	0.807772i	$0.700673\pi$
$542$	4.11947	0.176946
$543$	−5.94597	−0.255166
$544$	5.28089	0.226416
$545$	1.95254	0.0836377
$546$	0	0
$547$	−21.2333	−0.907871	−0.453936	−	0.891034i	$-0.649980\pi$
$547$	−21.2333	−0.907871	−0.453936	+	0.891034i	$0.649980\pi$
$548$	−16.1419	−0.689548
$549$	9.84305	0.420091
$550$	−8.23762	−0.351253
$551$	−3.90343	−0.166292
$552$	−2.20484	−0.0938444
$553$	0	0
$554$	−5.01438	−0.213040
$555$	3.55096	0.150730
$556$	−18.3181	−0.776859
$557$	26.6920	1.13098	0.565489	−	0.824756i	$-0.308688\pi$
$557$	26.6920	1.13098	0.565489	+	0.824756i	$0.308688\pi$
$558$	−2.18029	−0.0922990
$559$	18.0577	0.763760
$560$	0	0
$561$	3.86530	0.163193
$562$	3.15413	0.133049
$563$	−5.72358	−0.241220	−0.120610	−	0.992700i	$-0.538485\pi$
$563$	−5.72358	−0.241220	−0.120610	+	0.992700i	$0.538485\pi$
$564$	−1.96308	−0.0826606
$565$	−5.20954	−0.219167
$566$	0.476022	0.0200087
$567$	0	0
$568$	−0.605544	−0.0254081
$569$	33.3248	1.39705	0.698523	−	0.715587i	$-0.253841\pi$
$569$	33.3248	1.39705	0.698523	+	0.715587i	$0.253841\pi$
$570$	−1.24298	−0.0520626
$571$	8.54252	0.357493	0.178747	−	0.983895i	$-0.442796\pi$
$571$	8.54252	0.357493	0.178747	+	0.983895i	$0.442796\pi$
$572$	−14.7727	−0.617677
$573$	−14.0854	−0.588425
$574$	0	0
$575$	2.44672	0.102035
$576$	1.57320	0.0655502
$577$	−6.13581	−0.255437	−0.127718	−	0.991810i	$-0.540765\pi$
$577$	−6.13581	−0.255437	−0.127718	+	0.991810i	$0.540765\pi$
$578$	11.4006	0.474201
$579$	9.65924	0.401424
$580$	7.52064	0.312277
$581$	0	0
$582$	−4.43502	−0.183837
$583$	28.3746	1.17516
$584$	5.15269	0.213220
$585$	3.46165	0.143121
$586$	−1.82302	−0.0753083
$587$	−39.5794	−1.63362	−0.816809	−	0.576908i	$-0.804259\pi$
$587$	−39.5794	−1.63362	−0.816809	+	0.576908i	$0.804259\pi$
$588$	0	0
$589$	−3.63043	−0.149589
$590$	0.676123	0.0278355
$591$	−1.13984	−0.0468867
$592$	−2.99365	−0.123038
$593$	−15.4883	−0.636027	−0.318014	−	0.948086i	$-0.603016\pi$
$593$	−15.4883	−0.636027	−0.318014	+	0.948086i	$0.603016\pi$
$594$	3.00701	0.123379
$595$	0	0
$596$	−9.19717	−0.376731
$597$	−6.81027	−0.278726
$598$	−1.44895	−0.0592519
$599$	4.22806	0.172754	0.0863768	−	0.996263i	$-0.472471\pi$
$599$	4.22806	0.172754	0.0863768	+	0.996263i	$0.472471\pi$
$600$	−6.76282	−0.276091
$601$	−35.7858	−1.45973	−0.729867	−	0.683589i	$-0.760418\pi$
$601$	−35.7858	−1.45973	−0.729867	+	0.683589i	$0.760418\pi$
$602$	0	0
$603$	−13.4478	−0.547638
$604$	12.6539	0.514879
$605$	−10.8431	−0.440833
$606$	7.24463	0.294293
$607$	3.30743	0.134244	0.0671222	−	0.997745i	$-0.478618\pi$
$607$	3.30743	0.134244	0.0671222	+	0.997745i	$0.478618\pi$
$608$	6.84074	0.277429
$609$	0	0
$610$	10.4278	0.422209
$611$	−3.00615	−0.121616
$612$	1.36179	0.0550471
$613$	21.8254	0.881519	0.440760	−	0.897625i	$-0.354709\pi$
$613$	21.8254	0.881519	0.440760	+	0.897625i	$0.354709\pi$
$614$	−19.0341	−0.768152
$615$	−1.50350	−0.0606272
$616$	0	0
$617$	36.3792	1.46457	0.732286	−	0.680997i	$-0.238453\pi$
$617$	36.3792	1.46457	0.732286	+	0.680997i	$0.238453\pi$
$618$	−6.12113	−0.246228
$619$	33.3671	1.34114	0.670568	−	0.741848i	$-0.266051\pi$
$619$	33.3671	1.34114	0.670568	+	0.741848i	$0.266051\pi$
$620$	6.99464	0.280912
$621$	−0.893136	−0.0358403
$622$	−20.9154	−0.838630
$623$	0	0
$624$	−2.91835	−0.116828
$625$	−3.79791	−0.151916
$626$	−9.87114	−0.394530
$627$	5.00701	0.199961
$628$	12.7252	0.507792
$629$	2.13918	0.0852946
$630$	0	0
$631$	35.8563	1.42742	0.713708	−	0.700443i	$-0.247014\pi$
$631$	35.8563	1.42742	0.713708	+	0.700443i	$0.247014\pi$
$632$	−35.9773	−1.43110
$633$	3.45439	0.137300
$634$	−14.9970	−0.595605
$635$	−16.7488	−0.664656
$636$	9.99672	0.396396
$637$	0	0
$638$	10.0041	0.396068
$639$	−0.245293	−0.00970365
$640$	−15.8655	−0.627141
$641$	29.4974	1.16508	0.582538	−	0.812803i	$-0.302060\pi$
$641$	29.4974	1.16508	0.582538	+	0.812803i	$0.302060\pi$
$642$	−12.6516	−0.499318
$643$	−39.6993	−1.56559	−0.782795	−	0.622280i	$-0.786207\pi$
$643$	−39.6993	−1.56559	−0.782795	+	0.622280i	$0.786207\pi$
$644$	0	0
$645$	11.7921	0.464312
$646$	−0.748798	−0.0294611
$647$	−28.2158	−1.10928	−0.554638	−	0.832092i	$-0.687143\pi$
$647$	−28.2158	−1.10928	−0.554638	+	0.832092i	$0.687143\pi$
$648$	2.46865	0.0969779
$649$	−2.72358	−0.106910
$650$	−4.44429	−0.174320
$651$	0	0
$652$	−13.0896	−0.512627
$653$	23.1901	0.907497	0.453748	−	0.891130i	$-0.350086\pi$
$653$	23.1901	0.907497	0.453748	+	0.891130i	$0.350086\pi$
$654$	0.915068	0.0357820
$655$	6.67330	0.260748
$656$	1.26753	0.0494889
$657$	2.08725	0.0814313
$658$	0	0
$659$	−14.5515	−0.566847	−0.283423	−	0.958995i	$-0.591470\pi$
$659$	−14.5515	−0.566847	−0.283423	+	0.958995i	$0.591470\pi$
$660$	−9.64687	−0.375504
$661$	26.5326	1.03200	0.516000	−	0.856589i	$-0.327420\pi$
$661$	26.5326	1.03200	0.516000	+	0.856589i	$0.327420\pi$
$662$	−6.20284	−0.241080
$663$	2.08537	0.0809891
$664$	15.8395	0.614693
$665$	0	0
$666$	1.66418	0.0644855
$667$	−2.97141	−0.115053
$668$	10.6644	0.412619
$669$	−3.01195	−0.116449
$670$	−14.2467	−0.550398
$671$	−42.0056	−1.62161
$672$	0	0
$673$	−17.9600	−0.692307	−0.346153	−	0.938178i	$-0.612512\pi$
$673$	−17.9600	−0.692307	−0.346153	+	0.938178i	$0.612512\pi$
$674$	−23.0523	−0.887943
$675$	−2.73947	−0.105442
$676$	11.5755	0.445212
$677$	7.79090	0.299429	0.149714	−	0.988729i	$-0.452165\pi$
$677$	7.79090	0.299429	0.149714	+	0.988729i	$0.452165\pi$
$678$	−2.44147	−0.0937643
$679$	0	0
$680$	3.36179	0.128919
$681$	−14.0619	−0.538854
$682$	9.30445	0.356286
$683$	−4.27880	−0.163724	−0.0818618	−	0.996644i	$-0.526087\pi$
$683$	−4.27880	−0.163724	−0.0818618	+	0.996644i	$0.526087\pi$
$684$	1.76403	0.0674494
$685$	−16.1419	−0.616751
$686$	0	0
$687$	1.07999	0.0412043
$688$	−9.94134	−0.379010
$689$	15.3084	0.583204
$690$	−0.946193	−0.0360210
$691$	23.8218	0.906222	0.453111	−	0.891454i	$-0.350314\pi$
$691$	23.8218	0.906222	0.453111	+	0.891454i	$0.350314\pi$
$692$	−25.2635	−0.960372
$693$	0	0
$694$	−23.1845	−0.880071
$695$	−18.3181	−0.694843
$696$	8.21307	0.311316
$697$	−0.905744	−0.0343075
$698$	−22.9179	−0.867455
$699$	5.55030	0.209932
$700$	0	0
$701$	9.77225	0.369093	0.184546	−	0.982824i	$-0.440918\pi$
$701$	9.77225	0.369093	0.184546	+	0.982824i	$0.440918\pi$
$702$	1.62232	0.0612304
$703$	2.77104	0.104512
$704$	−6.71370	−0.253032
$705$	−1.96308	−0.0739339
$706$	−5.34198	−0.201048
$707$	0	0
$708$	−0.959551	−0.0360621
$709$	−7.96953	−0.299302	−0.149651	−	0.988739i	$-0.547815\pi$
$709$	−7.96953	−0.299302	−0.149651	+	0.988739i	$0.547815\pi$
$710$	−0.259865	−0.00975256
$711$	−14.5736	−0.546554
$712$	4.47194	0.167593
$713$	−2.76359	−0.103497
$714$	0	0
$715$	−14.7727	−0.552467
$716$	−7.30197	−0.272887
$717$	−1.45836	−0.0544635
$718$	−17.3677	−0.648157
$719$	−3.66691	−0.136753	−0.0683763	−	0.997660i	$-0.521782\pi$
$719$	−3.66691	−0.136753	−0.0683763	+	0.997660i	$0.521782\pi$
$720$	−1.90574	−0.0710229
$721$	0	0
$722$	12.4179	0.462146
$723$	−1.68335	−0.0626046
$724$	8.93980	0.332245
$725$	−9.11407	−0.338488
$726$	−5.08165	−0.188598
$727$	−40.3400	−1.49613	−0.748064	−	0.663627i	$-0.769016\pi$
$727$	−40.3400	−1.49613	−0.748064	+	0.663627i	$0.769016\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	2.21124	0.0818417
$731$	7.10380	0.262744
$732$	−14.7991	−0.546990
$733$	−35.1684	−1.29898	−0.649488	−	0.760372i	$-0.725017\pi$
$733$	−35.1684	−1.29898	−0.649488	+	0.760372i	$0.725017\pi$
$734$	15.2423	0.562604
$735$	0	0
$736$	5.20738	0.191947
$737$	57.3891	2.11395
$738$	−0.704624	−0.0259376
$739$	1.71767	0.0631856	0.0315928	−	0.999501i	$-0.489942\pi$
$739$	1.71767	0.0631856	0.0315928	+	0.999501i	$0.489942\pi$
$740$	−5.33889	−0.196261
$741$	2.70134	0.0992362
$742$	0	0
$743$	−20.4571	−0.750500	−0.375250	−	0.926924i	$-0.622443\pi$
$743$	−20.4571	−0.750500	−0.375250	+	0.926924i	$0.622443\pi$
$744$	7.63865	0.280046
$745$	−9.19717	−0.336958
$746$	22.7175	0.831746
$747$	6.41626	0.234759
$748$	−5.81149	−0.212489
$749$	0	0
$750$	−8.19924	−0.299394
$751$	20.4502	0.746238	0.373119	−	0.927783i	$-0.378288\pi$
$751$	20.4502	0.746238	0.373119	+	0.927783i	$0.378288\pi$
$752$	1.65498	0.0603510
$753$	18.8882	0.688324
$754$	5.39735	0.196560
$755$	12.6539	0.460522
$756$	0	0
$757$	28.4022	1.03230	0.516148	−	0.856499i	$-0.327365\pi$
$757$	28.4022	1.03230	0.516148	+	0.856499i	$0.327365\pi$
$758$	−20.3225	−0.738147
$759$	3.81149	0.138348
$760$	4.35478	0.157965
$761$	10.0943	0.365916	0.182958	−	0.983121i	$-0.441433\pi$
$761$	10.0943	0.365916	0.182958	+	0.983121i	$0.441433\pi$
$762$	−7.84940	−0.284354
$763$	0	0
$764$	21.1774	0.766172
$765$	1.36179	0.0492356
$766$	21.9625	0.793537
$767$	−1.46940	−0.0530571
$768$	−10.5819	−0.381840
$769$	−39.5682	−1.42687	−0.713434	−	0.700723i	$-0.752861\pi$
$769$	−39.5682	−1.42687	−0.713434	+	0.700723i	$0.752861\pi$
$770$	0	0
$771$	−15.1796	−0.546681
$772$	−14.5227	−0.522684
$773$	−13.6450	−0.490776	−0.245388	−	0.969425i	$-0.578915\pi$
$773$	−13.6450	−0.490776	−0.245388	+	0.969425i	$0.578915\pi$
$774$	5.52641	0.198643
$775$	−8.47663	−0.304490
$776$	15.5381	0.557786
$777$	0	0
$778$	−0.0255493	−0.000915988 0
$779$	−1.17328	−0.0420371
$780$	−5.20460	−0.186355
$781$	1.04680	0.0374574
$782$	−0.570008	−0.0203834
$783$	3.32694	0.118895
$784$	0	0
$785$	12.7252	0.454183
$786$	3.12747	0.111553
$787$	−6.72052	−0.239561	−0.119780	−	0.992800i	$-0.538219\pi$
$787$	−6.72052	−0.239561	−0.119780	+	0.992800i	$0.538219\pi$
$788$	1.71375	0.0610499
$789$	−1.96021	−0.0697854
$790$	−15.4394	−0.549309
$791$	0	0
$792$	−10.5351	−0.374347
$793$	−22.6625	−0.804769
$794$	−24.0948	−0.855091
$795$	9.99672	0.354547
$796$	10.2393	0.362922
$797$	−1.63942	−0.0580714	−0.0290357	−	0.999578i	$-0.509244\pi$
$797$	−1.63942	−0.0580714	−0.0290357	+	0.999578i	$0.509244\pi$
$798$	0	0
$799$	−1.18260	−0.0418375
$800$	15.9724	0.564708
$801$	1.81149	0.0640058
$802$	−14.3466	−0.506595
$803$	−8.90740	−0.314335
$804$	20.2189	0.713064
$805$	0	0
$806$	5.01986	0.176817
$807$	30.4771	1.07284
$808$	−25.3816	−0.892922
$809$	−28.1798	−0.990750	−0.495375	−	0.868679i	$-0.664969\pi$
$809$	−28.1798	−0.990750	−0.495375	+	0.868679i	$0.664969\pi$
$810$	1.05941	0.0372237
$811$	−22.2848	−0.782526	−0.391263	−	0.920279i	$-0.627962\pi$
$811$	−22.2848	−0.782526	−0.391263	+	0.920279i	$0.627962\pi$
$812$	0	0
$813$	−5.84634	−0.205040
$814$	−7.10193	−0.248922
$815$	−13.0896	−0.458507
$816$	−1.14806	−0.0401902
$817$	9.20209	0.321940
$818$	7.41670	0.259319
$819$	0	0
$820$	2.26053	0.0789410
$821$	−29.0974	−1.01551	−0.507753	−	0.861503i	$-0.669524\pi$
$821$	−29.0974	−1.01551	−0.507753	+	0.861503i	$0.669524\pi$
$822$	−7.56498	−0.263859
$823$	−28.7398	−1.00181	−0.500903	−	0.865503i	$-0.666999\pi$
$823$	−28.7398	−1.00181	−0.500903	+	0.865503i	$0.666999\pi$
$824$	21.4454	0.747086
$825$	11.6908	0.407021
$826$	0	0
$827$	38.5448	1.34033	0.670167	−	0.742211i	$-0.266223\pi$
$827$	38.5448	1.34033	0.670167	+	0.742211i	$0.266223\pi$
$828$	1.34283	0.0466667
$829$	−42.9541	−1.49186	−0.745928	−	0.666026i	$-0.767994\pi$
$829$	−42.9541	−1.49186	−0.745928	+	0.666026i	$0.767994\pi$
$830$	6.79742	0.235942
$831$	7.11638	0.246865
$832$	−3.62212	−0.125574
$833$	0	0
$834$	−8.58484	−0.297269
$835$	10.6644	0.369057
$836$	−7.52806	−0.260363
$837$	3.09426	0.106953
$838$	−19.4403	−0.671553
$839$	−12.5023	−0.431627	−0.215813	−	0.976435i	$-0.569240\pi$
$839$	−12.5023	−0.431627	−0.215813	+	0.976435i	$0.569240\pi$
$840$	0	0
$841$	−17.9315	−0.618326
$842$	−23.3177	−0.803581
$843$	−4.47632	−0.154173
$844$	−5.19369	−0.178774
$845$	11.5755	0.398210
$846$	−0.920006	−0.0316305
$847$	0	0
$848$	−8.42777	−0.289411
$849$	−0.675569	−0.0231855
$850$	−1.74836	−0.0599682
$851$	2.10940	0.0723093
$852$	0.368800	0.0126349
$853$	−0.740028	−0.0253381	−0.0126690	−	0.999920i	$-0.504033\pi$
$853$	−0.740028	−0.0253381	−0.0126690	+	0.999920i	$0.504033\pi$
$854$	0	0
$855$	1.76403	0.0603286
$856$	44.3248	1.51499
$857$	55.2205	1.88630	0.943148	−	0.332374i	$-0.107850\pi$
$857$	55.2205	1.88630	0.943148	+	0.332374i	$0.107850\pi$
$858$	−6.92329	−0.236357
$859$	−48.3612	−1.65006	−0.825032	−	0.565087i	$-0.808843\pi$
$859$	−48.3612	−1.65006	−0.825032	+	0.565087i	$0.808843\pi$
$860$	−17.7294	−0.604568
$861$	0	0
$862$	3.46001	0.117849
$863$	−34.7431	−1.18267	−0.591334	−	0.806427i	$-0.701399\pi$
$863$	−34.7431	−1.18267	−0.591334	+	0.806427i	$0.701399\pi$
$864$	−5.83045	−0.198356
$865$	−25.2635	−0.858983
$866$	8.63241	0.293341
$867$	−16.1796	−0.549489
$868$	0	0
$869$	62.1935	2.10977
$870$	3.52458	0.119494
$871$	30.9621	1.04911
$872$	−3.20594	−0.108567
$873$	6.29416	0.213025
$874$	−0.738374	−0.0249759
$875$	0	0
$876$	−3.13818	−0.106029
$877$	−32.5538	−1.09926	−0.549632	−	0.835407i	$-0.685232\pi$
$877$	−32.5538	−1.09926	−0.549632	+	0.835407i	$0.685232\pi$
$878$	10.9310	0.368904
$879$	2.58722	0.0872648
$880$	8.13283	0.274158
$881$	−3.54142	−0.119313	−0.0596567	−	0.998219i	$-0.519001\pi$
$881$	−3.54142	−0.119313	−0.0596567	+	0.998219i	$0.519001\pi$
$882$	0	0
$883$	34.3909	1.15735	0.578673	−	0.815559i	$-0.303571\pi$
$883$	34.3909	1.15735	0.578673	+	0.815559i	$0.303571\pi$
$884$	−3.13537	−0.105454
$885$	−0.959551	−0.0322549
$886$	13.0021	0.436814
$887$	−10.8911	−0.365686	−0.182843	−	0.983142i	$-0.558530\pi$
$887$	−10.8911	−0.365686	−0.182843	+	0.983142i	$0.558530\pi$
$888$	−5.83045	−0.195657
$889$	0	0
$890$	1.91910	0.0643284
$891$	−4.26753	−0.142968
$892$	4.52848	0.151625
$893$	−1.53191	−0.0512636
$894$	−4.31030	−0.144158
$895$	−7.30197	−0.244078
$896$	0	0
$897$	2.05634	0.0686593
$898$	9.55775	0.318946
$899$	10.2944	0.343338
$900$	4.11881	0.137294
$901$	6.02224	0.200630
$902$	3.00701	0.100122
$903$	0	0
$904$	8.55372	0.284492
$905$	8.93980	0.297169
$906$	5.93030	0.197021
$907$	−32.4770	−1.07838	−0.539190	−	0.842184i	$-0.681269\pi$
$907$	−32.4770	−1.07838	−0.539190	+	0.842184i	$0.681269\pi$
$908$	21.1422	0.701627
$909$	−10.2816	−0.341018
$910$	0	0
$911$	14.4670	0.479314	0.239657	−	0.970858i	$-0.422965\pi$
$911$	14.4670	0.479314	0.239657	+	0.970858i	$0.422965\pi$
$912$	−1.48717	−0.0492452
$913$	−27.3816	−0.906199
$914$	5.37134	0.177668
$915$	−14.7991	−0.489242
$916$	−1.62378	−0.0536510
$917$	0	0
$918$	0.638209	0.0210641
$919$	−21.8298	−0.720097	−0.360049	−	0.932934i	$-0.617240\pi$
$919$	−21.8298	−0.720097	−0.360049	+	0.932934i	$0.617240\pi$
$920$	3.31499	0.109292
$921$	27.0130	0.890110
$922$	−7.43614	−0.244896
$923$	0.564759	0.0185893
$924$	0	0
$925$	6.47006	0.212734
$926$	15.8106	0.519570
$927$	8.68708	0.285321
$928$	−19.3975	−0.636756
$929$	−11.2589	−0.369392	−0.184696	−	0.982796i	$-0.559130\pi$
$929$	−11.2589	−0.369392	−0.184696	+	0.982796i	$0.559130\pi$
$930$	3.27807	0.107492
$931$	0	0
$932$	−8.34490	−0.273346
$933$	29.6830	0.971778
$934$	−17.8589	−0.584363
$935$	−5.81149	−0.190056
$936$	−5.68379	−0.185781
$937$	−27.7504	−0.906566	−0.453283	−	0.891367i	$-0.649747\pi$
$937$	−27.7504	−0.906566	−0.453283	+	0.891367i	$0.649747\pi$
$938$	0	0
$939$	14.0091	0.457169
$940$	2.95150	0.0962673
$941$	27.2563	0.888531	0.444266	−	0.895895i	$-0.353465\pi$
$941$	27.2563	0.888531	0.444266	+	0.895895i	$0.353465\pi$
$942$	5.96374	0.194309
$943$	−0.893136	−0.0290845
$944$	0.808953	0.0263292
$945$	0	0
$946$	−23.5841	−0.766786
$947$	−16.0528	−0.521645	−0.260823	−	0.965387i	$-0.583994\pi$
$947$	−16.0528	−0.521645	−0.260823	+	0.965387i	$0.583994\pi$
$948$	21.9115	0.711654
$949$	−4.80564	−0.155998
$950$	−2.26478	−0.0734792
$951$	21.2836	0.690169
$952$	0	0
$953$	−4.62507	−0.149821	−0.0749104	−	0.997190i	$-0.523867\pi$
$953$	−4.62507	−0.149821	−0.0749104	+	0.997190i	$0.523867\pi$
$954$	4.68501	0.151683
$955$	21.1774	0.685285
$956$	2.19265	0.0709154
$957$	−14.1978	−0.458951
$958$	−26.5285	−0.857097
$959$	0	0
$960$	−2.36532	−0.0763404
$961$	−21.4256	−0.691148
$962$	−3.83157	−0.123535
$963$	17.9551	0.578593
$964$	2.53093	0.0815157
$965$	−14.5227	−0.467502
$966$	0	0
$967$	0.867236	0.0278884	0.0139442	−	0.999903i	$-0.495561\pi$
$967$	0.867236	0.0278884	0.0139442	+	0.999903i	$0.495561\pi$
$968$	17.8036	0.572229
$969$	1.06269	0.0341385
$970$	6.66807	0.214099
$971$	45.9188	1.47360	0.736802	−	0.676109i	$-0.236335\pi$
$971$	45.9188	1.47360	0.736802	+	0.676109i	$0.236335\pi$
$972$	−1.50350	−0.0482249
$973$	0	0
$974$	−5.30115	−0.169860
$975$	6.30732	0.201996
$976$	12.4764	0.399360
$977$	−0.727989	−0.0232904	−0.0116452	−	0.999932i	$-0.503707\pi$
$977$	−0.727989	−0.0232904	−0.0116452	+	0.999932i	$0.503707\pi$
$978$	−6.13448	−0.196159
$979$	−7.73059	−0.247071
$980$	0	0
$981$	−1.29866	−0.0414630
$982$	−14.0050	−0.446916
$983$	26.3436	0.840230	0.420115	−	0.907471i	$-0.361990\pi$
$983$	26.3436	0.840230	0.420115	+	0.907471i	$0.361990\pi$
$984$	2.46865	0.0786978
$985$	1.71375	0.0546047
$986$	2.12329	0.0676192
$987$	0	0
$988$	−4.06148	−0.129213
$989$	7.00491	0.222743
$990$	−4.52105	−0.143688
$991$	29.2465	0.929044	0.464522	−	0.885561i	$-0.346226\pi$
$991$	29.2465	0.929044	0.464522	+	0.885561i	$0.346226\pi$
$992$	−18.0409	−0.572799
$993$	8.80304	0.279356
$994$	0	0
$995$	10.2393	0.324607
$996$	−9.64687	−0.305673
$997$	43.6374	1.38201	0.691005	−	0.722850i	$-0.257168\pi$
$997$	43.6374	1.38201	0.691005	+	0.722850i	$0.257168\pi$
$998$	26.5028	0.838931
$999$	−2.36179	−0.0747237

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.u.1.2		4
7.6	odd	2		861.2.a.i.1.2	✓	4
21.20	even	2		2583.2.a.o.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.a.i.1.2	✓	4	7.6	odd	2
2583.2.a.o.1.3		4	21.20	even	2
6027.2.a.u.1.2		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:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q-0.704624 q^{2} +1.00000 q^{3} -1.50350 q^{4} -1.50350 q^{5} -0.704624 q^{6} +2.46865 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.704624 q^{2} +1.00000 q^{3} -1.50350 q^{4} -1.50350 q^{5} -0.704624 q^{6} +2.46865 q^{8} +1.00000 q^{9} +1.05941 q^{10} -4.26753 q^{11} -1.50350 q^{12} -2.30238 q^{13} -1.50350 q^{15} +1.26753 q^{16} -0.905744 q^{17} -0.704624 q^{18} -1.17328 q^{19} +2.26053 q^{20} +3.00701 q^{22} -0.893136 q^{23} +2.46865 q^{24} -2.73947 q^{25} +1.62232 q^{26} +1.00000 q^{27} +3.32694 q^{29} +1.05941 q^{30} +3.09426 q^{31} -5.83045 q^{32} -4.26753 q^{33} +0.638209 q^{34} -1.50350 q^{36} -2.36179 q^{37} +0.826721 q^{38} -2.30238 q^{39} -3.71163 q^{40} +1.00000 q^{41} -7.84305 q^{43} +6.41626 q^{44} -1.50350 q^{45} +0.629325 q^{46} +1.30567 q^{47} +1.26753 q^{48} +1.93030 q^{50} -0.905744 q^{51} +3.46165 q^{52} -6.64894 q^{53} -0.704624 q^{54} +6.41626 q^{55} -1.17328 q^{57} -2.34424 q^{58} +0.638209 q^{59} +2.26053 q^{60} +9.84305 q^{61} -2.18029 q^{62} +1.57320 q^{64} +3.46165 q^{65} +3.00701 q^{66} -13.4478 q^{67} +1.36179 q^{68} -0.893136 q^{69} -0.245293 q^{71} +2.46865 q^{72} +2.08725 q^{73} +1.66418 q^{74} -2.73947 q^{75} +1.76403 q^{76} +1.62232 q^{78} -14.5736 q^{79} -1.90574 q^{80} +1.00000 q^{81} -0.704624 q^{82} +6.41626 q^{83} +1.36179 q^{85} +5.52641 q^{86} +3.32694 q^{87} -10.5351 q^{88} +1.81149 q^{89} +1.05941 q^{90} +1.34283 q^{92} +3.09426 q^{93} -0.920006 q^{94} +1.76403 q^{95} -5.83045 q^{96} +6.29416 q^{97} -4.26753 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + 4 q^{3} + 3 q^{4} + 3 q^{5} + q^{6} + 3 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + q^2 + 4 * q^3 + 3 * q^4 + 3 * q^5 + q^6 + 3 * q^8 + 4 * q^9	\( 4 q + q^{2} + 4 q^{3} + 3 q^{4} + 3 q^{5} + q^{6} + 3 q^{8} + 4 q^{9} + 5 q^{10} - 5 q^{11} + 3 q^{12} + 5 q^{13} + 3 q^{15} - 7 q^{16} - 5 q^{17} + q^{18} + 6 q^{19} + 15 q^{20} - 6 q^{22} + 3 q^{23} + 3 q^{24} - 5 q^{25} - q^{26} + 4 q^{27} + 2 q^{29} + 5 q^{30} + 11 q^{31} - 3 q^{32} - 5 q^{33} + 16 q^{34} + 3 q^{36} + 4 q^{37} + 14 q^{38} + 5 q^{39} + 7 q^{40} + 4 q^{41} - 19 q^{43} + 3 q^{45} - 23 q^{46} + 4 q^{47} - 7 q^{48} + 12 q^{50} - 5 q^{51} + 25 q^{52} + 9 q^{53} + q^{54} + 6 q^{57} + 25 q^{58} + 16 q^{59} + 15 q^{60} + 27 q^{61} + 20 q^{62} - 7 q^{64} + 25 q^{65} - 6 q^{66} - 13 q^{67} - 8 q^{68} + 3 q^{69} + q^{71} + 3 q^{72} + 25 q^{73} - 21 q^{74} - 5 q^{75} + 4 q^{76} - q^{78} - q^{79} - 9 q^{80} + 4 q^{81} + q^{82} - 8 q^{85} + 16 q^{86} + 2 q^{87} - 18 q^{88} + 10 q^{89} + 5 q^{90} + 15 q^{92} + 11 q^{93} - 13 q^{94} + 4 q^{95} - 3 q^{96} - 15 q^{97} - 5 q^{99}+O(q^{100}) \) 4 * q + q^2 + 4 * q^3 + 3 * q^4 + 3 * q^5 + q^6 + 3 * q^8 + 4 * q^9 + 5 * q^10 - 5 * q^11 + 3 * q^12 + 5 * q^13 + 3 * q^15 - 7 * q^16 - 5 * q^17 + q^18 + 6 * q^19 + 15 * q^20 - 6 * q^22 + 3 * q^23 + 3 * q^24 - 5 * q^25 - q^26 + 4 * q^27 + 2 * q^29 + 5 * q^30 + 11 * q^31 - 3 * q^32 - 5 * q^33 + 16 * q^34 + 3 * q^36 + 4 * q^37 + 14 * q^38 + 5 * q^39 + 7 * q^40 + 4 * q^41 - 19 * q^43 + 3 * q^45 - 23 * q^46 + 4 * q^47 - 7 * q^48 + 12 * q^50 - 5 * q^51 + 25 * q^52 + 9 * q^53 + q^54 + 6 * q^57 + 25 * q^58 + 16 * q^59 + 15 * q^60 + 27 * q^61 + 20 * q^62 - 7 * q^64 + 25 * q^65 - 6 * q^66 - 13 * q^67 - 8 * q^68 + 3 * q^69 + q^71 + 3 * q^72 + 25 * q^73 - 21 * q^74 - 5 * q^75 + 4 * q^76 - q^78 - q^79 - 9 * q^80 + 4 * q^81 + q^82 - 8 * q^85 + 16 * q^86 + 2 * q^87 - 18 * q^88 + 10 * q^89 + 5 * q^90 + 15 * q^92 + 11 * q^93 - 13 * q^94 + 4 * q^95 - 3 * q^96 - 15 * q^97 - 5 * q^99

Introduction

L-functions

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