LMFDB - Embedded newform 5586.2.a.bw.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5586,2,Mod(1,5586)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5586, 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("5586.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5586.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:	$44.6044345691$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.29268.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 9x^{2} + 5x + 16 $ x^4 - x^3 - 9x^2 + 5x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 798)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.85121$ of defining polynomial
Character	$\chi$	$=$	5586.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.46130 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.46130 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +3.46130 q^{10} +0.278197 q^{11} -1.00000 q^{12} +6.92261 q^{13} +3.46130 q^{15} +1.00000 q^{16} +5.79751 q^{17} -1.00000 q^{18} +1.00000 q^{19} -3.46130 q^{20} -0.278197 q^{22} +3.09233 q^{23} +1.00000 q^{24} +6.98062 q^{25} -6.92261 q^{26} -1.00000 q^{27} -8.55364 q^{29} -3.46130 q^{30} +7.34959 q^{31} -1.00000 q^{32} -0.278197 q^{33} -5.79751 q^{34} +1.00000 q^{36} -5.24112 q^{37} -1.00000 q^{38} -6.92261 q^{39} +3.46130 q^{40} +8.88553 q^{41} +10.3705 q^{43} +0.278197 q^{44} -3.46130 q^{45} -3.09233 q^{46} -1.79320 q^{47} -1.00000 q^{48} -6.98062 q^{50} -5.79751 q^{51} +6.92261 q^{52} +8.38823 q^{53} +1.00000 q^{54} -0.962923 q^{55} -1.00000 q^{57} +8.55364 q^{58} -7.79476 q^{59} +3.46130 q^{60} +9.12941 q^{61} -7.34959 q^{62} +1.00000 q^{64} -23.9612 q^{65} +0.278197 q^{66} -13.7378 q^{67} +5.79751 q^{68} -3.09233 q^{69} +0.684727 q^{71} -1.00000 q^{72} -1.92536 q^{73} +5.24112 q^{74} -6.98062 q^{75} +1.00000 q^{76} +6.92261 q^{78} +1.40761 q^{79} -3.46130 q^{80} +1.00000 q^{81} -8.88553 q^{82} -0.146030 q^{83} -20.0670 q^{85} -10.3705 q^{86} +8.55364 q^{87} -0.278197 q^{88} -13.7007 q^{89} +3.46130 q^{90} +3.09233 q^{92} -7.34959 q^{93} +1.79320 q^{94} -3.46130 q^{95} +1.00000 q^{96} +4.09233 q^{97} +0.278197 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{6} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^6 - 4 * q^8 + 4 * q^9	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{6} - 4 q^{8} + 4 q^{9} - 2 q^{11} - 4 q^{12} + 4 q^{16} + 10 q^{17} - 4 q^{18} + 4 q^{19} + 2 q^{22} - 5 q^{23} + 4 q^{24} + 4 q^{25} - 4 q^{27} - 3 q^{29} + 9 q^{31} - 4 q^{32} + 2 q^{33} - 10 q^{34} + 4 q^{36} - 14 q^{37} - 4 q^{38} + 4 q^{41} + 21 q^{43} - 2 q^{44} + 5 q^{46} + 7 q^{47} - 4 q^{48} - 4 q^{50} - 10 q^{51} - 7 q^{53} + 4 q^{54} - 4 q^{57} + 3 q^{58} + 7 q^{59} + 23 q^{61} - 9 q^{62} + 4 q^{64} - 48 q^{65} - 2 q^{66} + 6 q^{67} + 10 q^{68} + 5 q^{69} + 2 q^{71} - 4 q^{72} - 5 q^{73} + 14 q^{74} - 4 q^{75} + 4 q^{76} - 11 q^{79} + 4 q^{81} - 4 q^{82} + 14 q^{83} + 6 q^{85} - 21 q^{86} + 3 q^{87} + 2 q^{88} + 10 q^{89} - 5 q^{92} - 9 q^{93} - 7 q^{94} + 4 q^{96} - q^{97} - 2 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^6 - 4 * q^8 + 4 * q^9 - 2 * q^11 - 4 * q^12 + 4 * q^16 + 10 * q^17 - 4 * q^18 + 4 * q^19 + 2 * q^22 - 5 * q^23 + 4 * q^24 + 4 * q^25 - 4 * q^27 - 3 * q^29 + 9 * q^31 - 4 * q^32 + 2 * q^33 - 10 * q^34 + 4 * q^36 - 14 * q^37 - 4 * q^38 + 4 * q^41 + 21 * q^43 - 2 * q^44 + 5 * q^46 + 7 * q^47 - 4 * q^48 - 4 * q^50 - 10 * q^51 - 7 * q^53 + 4 * q^54 - 4 * q^57 + 3 * q^58 + 7 * q^59 + 23 * q^61 - 9 * q^62 + 4 * q^64 - 48 * q^65 - 2 * q^66 + 6 * q^67 + 10 * q^68 + 5 * q^69 + 2 * q^71 - 4 * q^72 - 5 * q^73 + 14 * q^74 - 4 * q^75 + 4 * q^76 - 11 * q^79 + 4 * q^81 - 4 * q^82 + 14 * q^83 + 6 * q^85 - 21 * q^86 + 3 * q^87 + 2 * q^88 + 10 * q^89 - 5 * q^92 - 9 * q^93 - 7 * q^94 + 4 * q^96 - q^97 - 2 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−3.46130	−1.54794	−0.773971	−	0.633221i	$-0.781732\pi$
$5$	−3.46130	−1.54794	−0.773971	+	0.633221i	$0.781732\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	3.46130	1.09456
$11$	0.278197	0.0838795	0.0419397	−	0.999120i	$-0.486646\pi$
$11$	0.278197	0.0838795	0.0419397	+	0.999120i	$0.486646\pi$
$12$	−1.00000	−0.288675
$13$	6.92261	1.91999	0.959993	−	0.280025i	$-0.0903427\pi$
$13$	6.92261	1.91999	0.959993	+	0.280025i	$0.0903427\pi$
$14$	0	0
$15$	3.46130	0.893705
$16$	1.00000	0.250000
$17$	5.79751	1.40610	0.703052	−	0.711139i	$-0.251820\pi$
$17$	5.79751	1.40610	0.703052	+	0.711139i	$0.251820\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−3.46130	−0.773971
$21$	0	0
$22$	−0.278197	−0.0593118
$23$	3.09233	0.644796	0.322398	−	0.946604i	$-0.395511\pi$
$23$	3.09233	0.644796	0.322398	+	0.946604i	$0.395511\pi$
$24$	1.00000	0.204124
$25$	6.98062	1.39612
$26$	−6.92261	−1.35763
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−8.55364	−1.58837	−0.794185	−	0.607676i	$-0.792102\pi$
$29$	−8.55364	−1.58837	−0.794185	+	0.607676i	$0.792102\pi$
$30$	−3.46130	−0.631945
$31$	7.34959	1.32003	0.660013	−	0.751254i	$-0.270551\pi$
$31$	7.34959	1.32003	0.660013	+	0.751254i	$0.270551\pi$
$32$	−1.00000	−0.176777
$33$	−0.278197	−0.0484278
$34$	−5.79751	−0.994265
$35$	0	0
$36$	1.00000	0.166667
$37$	−5.24112	−0.861635	−0.430817	−	0.902439i	$-0.641775\pi$
$37$	−5.24112	−0.861635	−0.430817	+	0.902439i	$0.641775\pi$
$38$	−1.00000	−0.162221
$39$	−6.92261	−1.10850
$40$	3.46130	0.547280
$41$	8.88553	1.38769	0.693843	−	0.720126i	$-0.255916\pi$
$41$	8.88553	1.38769	0.693843	+	0.720126i	$0.255916\pi$
$42$	0	0
$43$	10.3705	1.58149	0.790745	−	0.612145i	$-0.209693\pi$
$43$	10.3705	1.58149	0.790745	+	0.612145i	$0.209693\pi$
$44$	0.278197	0.0419397
$45$	−3.46130	−0.515981
$46$	−3.09233	−0.455939
$47$	−1.79320	−0.261565	−0.130782	−	0.991411i	$-0.541749\pi$
$47$	−1.79320	−0.261565	−0.130782	+	0.991411i	$0.541749\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	−6.98062	−0.987209
$51$	−5.79751	−0.811814
$52$	6.92261	0.959993
$53$	8.38823	1.15221	0.576106	−	0.817375i	$-0.304572\pi$
$53$	8.38823	1.15221	0.576106	+	0.817375i	$0.304572\pi$
$54$	1.00000	0.136083
$55$	−0.962923	−0.129841
$56$	0	0
$57$	−1.00000	−0.132453
$58$	8.55364	1.12315
$59$	−7.79476	−1.01479	−0.507395	−	0.861713i	$-0.669392\pi$
$59$	−7.79476	−1.01479	−0.507395	+	0.861713i	$0.669392\pi$
$60$	3.46130	0.446852
$61$	9.12941	1.16890	0.584450	−	0.811429i	$-0.301310\pi$
$61$	9.12941	1.16890	0.584450	+	0.811429i	$0.301310\pi$
$62$	−7.34959	−0.933399
$63$	0	0
$64$	1.00000	0.125000
$65$	−23.9612	−2.97203
$66$	0.278197	0.0342437
$67$	−13.7378	−1.67834	−0.839171	−	0.543868i	$-0.816959\pi$
$67$	−13.7378	−1.67834	−0.839171	+	0.543868i	$0.816959\pi$
$68$	5.79751	0.703052
$69$	−3.09233	−0.372273
$70$	0	0
$71$	0.684727	0.0812621	0.0406311	−	0.999174i	$-0.487063\pi$
$71$	0.684727	0.0812621	0.0406311	+	0.999174i	$0.487063\pi$
$72$	−1.00000	−0.117851
$73$	−1.92536	−0.225347	−0.112673	−	0.993632i	$-0.535941\pi$
$73$	−1.92536	−0.225347	−0.112673	+	0.993632i	$0.535941\pi$
$74$	5.24112	0.609268
$75$	−6.98062	−0.806053
$76$	1.00000	0.114708
$77$	0	0
$78$	6.92261	0.783831
$79$	1.40761	0.158368	0.0791840	−	0.996860i	$-0.474769\pi$
$79$	1.40761	0.158368	0.0791840	+	0.996860i	$0.474769\pi$
$80$	−3.46130	−0.386985
$81$	1.00000	0.111111
$82$	−8.88553	−0.981243
$83$	−0.146030	−0.0160289	−0.00801443	−	0.999968i	$-0.502551\pi$
$83$	−0.146030	−0.0160289	−0.00801443	+	0.999968i	$0.502551\pi$
$84$	0	0
$85$	−20.0670	−2.17657
$86$	−10.3705	−1.11828
$87$	8.55364	0.917046
$88$	−0.278197	−0.0296559
$89$	−13.7007	−1.45228	−0.726138	−	0.687549i	$-0.758687\pi$
$89$	−13.7007	−1.45228	−0.726138	+	0.687549i	$0.758687\pi$
$90$	3.46130	0.364853
$91$	0	0
$92$	3.09233	0.322398
$93$	−7.34959	−0.762117
$94$	1.79320	0.184954
$95$	−3.46130	−0.355122
$96$	1.00000	0.102062
$97$	4.09233	0.415513	0.207757	−	0.978181i	$-0.433384\pi$
$97$	4.09233	0.415513	0.207757	+	0.978181i	$0.433384\pi$
$98$	0	0
$99$	0.278197	0.0279598
$100$	6.98062	0.698062
$101$	−2.45699	−0.244479	−0.122240	−	0.992501i	$-0.539008\pi$
$101$	−2.45699	−0.244479	−0.122240	+	0.992501i	$0.539008\pi$
$102$	5.79751	0.574039
$103$	17.3468	1.70923	0.854617	−	0.519259i	$-0.173792\pi$
$103$	17.3468	1.70923	0.854617	+	0.519259i	$0.173792\pi$
$104$	−6.92261	−0.678817
$105$	0	0
$106$	−8.38823	−0.814737
$107$	−11.4779	−1.10961	−0.554806	−	0.831979i	$-0.687208\pi$
$107$	−11.4779	−1.10961	−0.554806	+	0.831979i	$0.687208\pi$
$108$	−1.00000	−0.0962250
$109$	−18.6814	−1.78935	−0.894675	−	0.446718i	$-0.852593\pi$
$109$	−18.6814	−1.78935	−0.894675	+	0.446718i	$0.852593\pi$
$110$	0.962923	0.0918112
$111$	5.24112	0.497465
$112$	0	0
$113$	3.29913	0.310356	0.155178	−	0.987886i	$-0.450405\pi$
$113$	3.29913	0.310356	0.155178	+	0.987886i	$0.450405\pi$
$114$	1.00000	0.0936586
$115$	−10.7035	−0.998106
$116$	−8.55364	−0.794185
$117$	6.92261	0.639995
$118$	7.79476	0.717565
$119$	0	0
$120$	−3.46130	−0.315972
$121$	−10.9226	−0.992964
$122$	−9.12941	−0.826538
$123$	−8.88553	−0.801181
$124$	7.34959	0.660013
$125$	−6.85553	−0.613177
$126$	0	0
$127$	−3.45699	−0.306758	−0.153379	−	0.988167i	$-0.549016\pi$
$127$	−3.45699	−0.306758	−0.153379	+	0.988167i	$0.549016\pi$
$128$	−1.00000	−0.0883883
$129$	−10.3705	−0.913074
$130$	23.9612	2.10154
$131$	18.4956	1.61597	0.807985	−	0.589203i	$-0.200558\pi$
$131$	18.4956	1.61597	0.807985	+	0.589203i	$0.200558\pi$
$132$	−0.278197	−0.0242139
$133$	0	0
$134$	13.7378	1.18677
$135$	3.46130	0.297902
$136$	−5.79751	−0.497133
$137$	−12.1680	−1.03959	−0.519793	−	0.854292i	$-0.673991\pi$
$137$	−12.1680	−1.03959	−0.519793	+	0.854292i	$0.673991\pi$
$138$	3.09233	0.263237
$139$	−2.91829	−0.247526	−0.123763	−	0.992312i	$-0.539496\pi$
$139$	−2.91829	−0.247526	−0.123763	+	0.992312i	$0.539496\pi$
$140$	0	0
$141$	1.79320	0.151015
$142$	−0.684727	−0.0574610
$143$	1.92585	0.161047
$144$	1.00000	0.0833333
$145$	29.6067	2.45870
$146$	1.92536	0.159344
$147$	0	0
$148$	−5.24112	−0.430817
$149$	−4.16493	−0.341204	−0.170602	−	0.985340i	$-0.554571\pi$
$149$	−4.16493	−0.341204	−0.170602	+	0.985340i	$0.554571\pi$
$150$	6.98062	0.569965
$151$	19.2754	1.56861	0.784306	−	0.620374i	$-0.213019\pi$
$151$	19.2754	1.56861	0.784306	+	0.620374i	$0.213019\pi$
$152$	−1.00000	−0.0811107
$153$	5.79751	0.468701
$154$	0	0
$155$	−25.4392	−2.04332
$156$	−6.92261	−0.554252
$157$	−21.4569	−1.71244	−0.856222	−	0.516608i	$-0.827194\pi$
$157$	−21.4569	−1.71244	−0.856222	+	0.516608i	$0.827194\pi$
$158$	−1.40761	−0.111983
$159$	−8.38823	−0.665230
$160$	3.46130	0.273640
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	15.9446	1.24888	0.624439	−	0.781073i	$-0.285327\pi$
$163$	15.9446	1.24888	0.624439	+	0.781073i	$0.285327\pi$
$164$	8.88553	0.693843
$165$	0.962923	0.0749635
$166$	0.146030	0.0113341
$167$	17.6073	1.36250	0.681248	−	0.732053i	$-0.261437\pi$
$167$	17.6073	1.36250	0.681248	+	0.732053i	$0.261437\pi$
$168$	0	0
$169$	34.9225	2.68634
$170$	20.0670	1.53907
$171$	1.00000	0.0764719
$172$	10.3705	0.790745
$173$	10.0106	0.761094	0.380547	−	0.924762i	$-0.375736\pi$
$173$	10.0106	0.761094	0.380547	+	0.924762i	$0.375736\pi$
$174$	−8.55364	−0.648449
$175$	0	0
$176$	0.278197	0.0209699
$177$	7.79476	0.585890
$178$	13.7007	1.02691
$179$	6.25882	0.467806	0.233903	−	0.972260i	$-0.424850\pi$
$179$	6.25882	0.467806	0.233903	+	0.972260i	$0.424850\pi$
$180$	−3.46130	−0.257990
$181$	−4.25019	−0.315914	−0.157957	−	0.987446i	$-0.550491\pi$
$181$	−4.25019	−0.315914	−0.157957	+	0.987446i	$0.550491\pi$
$182$	0	0
$183$	−9.12941	−0.674865
$184$	−3.09233	−0.227970
$185$	18.1411	1.33376
$186$	7.34959	0.538898
$187$	1.61285	0.117943
$188$	−1.79320	−0.130782
$189$	0	0
$190$	3.46130	0.251109
$191$	−10.9479	−0.792159	−0.396080	−	0.918216i	$-0.629630\pi$
$191$	−10.9479	−0.792159	−0.396080	+	0.918216i	$0.629630\pi$
$192$	−1.00000	−0.0721688
$193$	21.2899	1.53248	0.766240	−	0.642554i	$-0.222125\pi$
$193$	21.2899	1.53248	0.766240	+	0.642554i	$0.222125\pi$
$194$	−4.09233	−0.293812
$195$	23.9612	1.71590
$196$	0	0
$197$	−6.63103	−0.472441	−0.236221	−	0.971699i	$-0.575909\pi$
$197$	−6.63103	−0.472441	−0.236221	+	0.971699i	$0.575909\pi$
$198$	−0.278197	−0.0197706
$199$	−7.87047	−0.557923	−0.278961	−	0.960302i	$-0.589990\pi$
$199$	−7.87047	−0.557923	−0.278961	+	0.960302i	$0.589990\pi$
$200$	−6.98062	−0.493604
$201$	13.7378	0.968991
$202$	2.45699	0.172873
$203$	0	0
$204$	−5.79751	−0.405907
$205$	−30.7555	−2.14806
$206$	−17.3468	−1.20861
$207$	3.09233	0.214932
$208$	6.92261	0.479996
$209$	0.278197	0.0192433
$210$	0	0
$211$	14.9123	1.02660	0.513302	−	0.858208i	$-0.328422\pi$
$211$	14.9123	1.02660	0.513302	+	0.858208i	$0.328422\pi$
$212$	8.38823	0.576106
$213$	−0.684727	−0.0469167
$214$	11.4779	0.784615
$215$	−35.8955	−2.44806
$216$	1.00000	0.0680414
$217$	0	0
$218$	18.6814	1.26526
$219$	1.92536	0.130104
$220$	−0.962923	−0.0649203
$221$	40.1339	2.69970
$222$	−5.24112	−0.351761
$223$	3.92861	0.263079	0.131539	−	0.991311i	$-0.458008\pi$
$223$	3.92861	0.263079	0.131539	+	0.991311i	$0.458008\pi$
$224$	0	0
$225$	6.98062	0.465375
$226$	−3.29913	−0.219455
$227$	−7.03971	−0.467242	−0.233621	−	0.972328i	$-0.575057\pi$
$227$	−7.03971	−0.467242	−0.233621	+	0.972328i	$0.575057\pi$
$228$	−1.00000	−0.0662266
$229$	5.88397	0.388824	0.194412	−	0.980920i	$-0.437720\pi$
$229$	5.88397	0.388824	0.194412	+	0.980920i	$0.437720\pi$
$230$	10.7035	0.705768
$231$	0	0
$232$	8.55364	0.561574
$233$	2.80658	0.183865	0.0919326	−	0.995765i	$-0.470696\pi$
$233$	2.80658	0.183865	0.0919326	+	0.995765i	$0.470696\pi$
$234$	−6.92261	−0.452545
$235$	6.20680	0.404887
$236$	−7.79476	−0.507395
$237$	−1.40761	−0.0914338
$238$	0	0
$239$	−12.4016	−0.802193	−0.401097	−	0.916036i	$-0.631371\pi$
$239$	−12.4016	−0.802193	−0.401097	+	0.916036i	$0.631371\pi$
$240$	3.46130	0.223426
$241$	−15.1965	−0.978892	−0.489446	−	0.872034i	$-0.662801\pi$
$241$	−15.1965	−0.978892	−0.489446	+	0.872034i	$0.662801\pi$
$242$	10.9226	0.702132
$243$	−1.00000	−0.0641500
$244$	9.12941	0.584450
$245$	0	0
$246$	8.88553	0.566521
$247$	6.92261	0.440475
$248$	−7.34959	−0.466700
$249$	0.146030	0.00925427
$250$	6.85553	0.433582
$251$	5.91198	0.373161	0.186581	−	0.982440i	$-0.440259\pi$
$251$	5.91198	0.373161	0.186581	+	0.982440i	$0.440259\pi$
$252$	0	0
$253$	0.860277	0.0540851
$254$	3.45699	0.216911
$255$	20.0670	1.25664
$256$	1.00000	0.0625000
$257$	1.40485	0.0876320	0.0438160	−	0.999040i	$-0.486048\pi$
$257$	1.40485	0.0876320	0.0438160	+	0.999040i	$0.486048\pi$
$258$	10.3705	0.645641
$259$	0	0
$260$	−23.9612	−1.48601
$261$	−8.55364	−0.529457
$262$	−18.4956	−1.14266
$263$	−10.7781	−0.664608	−0.332304	−	0.943172i	$-0.607826\pi$
$263$	−10.7781	−0.664608	−0.332304	+	0.943172i	$0.607826\pi$
$264$	0.278197	0.0171218
$265$	−29.0342	−1.78356
$266$	0	0
$267$	13.7007	0.838472
$268$	−13.7378	−0.839171
$269$	22.4462	1.36857	0.684286	−	0.729214i	$-0.260114\pi$
$269$	22.4462	1.36857	0.684286	+	0.729214i	$0.260114\pi$
$270$	−3.46130	−0.210648
$271$	−2.27651	−0.138288	−0.0691442	−	0.997607i	$-0.522027\pi$
$271$	−2.27651	−0.138288	−0.0691442	+	0.997607i	$0.522027\pi$
$272$	5.79751	0.351526
$273$	0	0
$274$	12.1680	0.735098
$275$	1.94199	0.117106
$276$	−3.09233	−0.186137
$277$	27.4521	1.64943	0.824717	−	0.565545i	$-0.191334\pi$
$277$	27.4521	1.64943	0.824717	+	0.565545i	$0.191334\pi$
$278$	2.91829	0.175027
$279$	7.34959	0.440009
$280$	0	0
$281$	8.14279	0.485758	0.242879	−	0.970057i	$-0.421908\pi$
$281$	8.14279	0.485758	0.242879	+	0.970057i	$0.421908\pi$
$282$	−1.79320	−0.106783
$283$	−8.18586	−0.486599	−0.243300	−	0.969951i	$-0.578230\pi$
$283$	−8.18586	−0.486599	−0.243300	+	0.969951i	$0.578230\pi$
$284$	0.684727	0.0406311
$285$	3.46130	0.205030
$286$	−1.92585	−0.113878
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	16.6112	0.977127
$290$	−29.6067	−1.73857
$291$	−4.09233	−0.239897
$292$	−1.92536	−0.112673
$293$	−19.3421	−1.12998	−0.564988	−	0.825099i	$-0.691119\pi$
$293$	−19.3421	−1.12998	−0.564988	+	0.825099i	$0.691119\pi$
$294$	0	0
$295$	26.9800	1.57084
$296$	5.24112	0.304634
$297$	−0.278197	−0.0161426
$298$	4.16493	0.241268
$299$	21.4070	1.23800
$300$	−6.98062	−0.403026
$301$	0	0
$302$	−19.2754	−1.10918
$303$	2.45699	0.141150
$304$	1.00000	0.0573539
$305$	−31.5997	−1.80939
$306$	−5.79751	−0.331422
$307$	−11.7007	−0.667797	−0.333898	−	0.942609i	$-0.608364\pi$
$307$	−11.7007	−0.667797	−0.333898	+	0.942609i	$0.608364\pi$
$308$	0	0
$309$	−17.3468	−0.986827
$310$	25.4392	1.44485
$311$	13.8555	0.785675	0.392837	−	0.919608i	$-0.371494\pi$
$311$	13.8555	0.785675	0.392837	+	0.919608i	$0.371494\pi$
$312$	6.92261	0.391915
$313$	−1.97199	−0.111463	−0.0557317	−	0.998446i	$-0.517749\pi$
$313$	−1.97199	−0.111463	−0.0557317	+	0.998446i	$0.517749\pi$
$314$	21.4569	1.21088
$315$	0	0
$316$	1.40761	0.0791840
$317$	19.9005	1.11772	0.558861	−	0.829261i	$-0.311239\pi$
$317$	19.9005	1.11772	0.558861	+	0.829261i	$0.311239\pi$
$318$	8.38823	0.470388
$319$	−2.37959	−0.133232
$320$	−3.46130	−0.193493
$321$	11.4779	0.640635
$322$	0	0
$323$	5.79751	0.322582
$324$	1.00000	0.0555556
$325$	48.3241	2.68054
$326$	−15.9446	−0.883091
$327$	18.6814	1.03308
$328$	−8.88553	−0.490621
$329$	0	0
$330$	−0.962923	−0.0530072
$331$	−4.66762	−0.256556	−0.128278	−	0.991738i	$-0.540945\pi$
$331$	−4.66762	−0.256556	−0.128278	+	0.991738i	$0.540945\pi$
$332$	−0.146030	−0.00801443
$333$	−5.24112	−0.287212
$334$	−17.6073	−0.963430
$335$	47.5508	2.59798
$336$	0	0
$337$	−11.4639	−0.624480	−0.312240	−	0.950003i	$-0.601079\pi$
$337$	−11.4639	−0.624480	−0.312240	+	0.950003i	$0.601079\pi$
$338$	−34.9225	−1.89953
$339$	−3.29913	−0.179184
$340$	−20.0670	−1.08828
$341$	2.04463	0.110723
$342$	−1.00000	−0.0540738
$343$	0	0
$344$	−10.3705	−0.559141
$345$	10.7035	0.576257
$346$	−10.0106	−0.538174
$347$	7.84258	0.421012	0.210506	−	0.977593i	$-0.432489\pi$
$347$	7.84258	0.421012	0.210506	+	0.977593i	$0.432489\pi$
$348$	8.55364	0.458523
$349$	21.2991	1.14012	0.570058	−	0.821604i	$-0.306921\pi$
$349$	21.2991	1.14012	0.570058	+	0.821604i	$0.306921\pi$
$350$	0	0
$351$	−6.92261	−0.369501
$352$	−0.278197	−0.0148279
$353$	8.71701	0.463959	0.231980	−	0.972721i	$-0.425480\pi$
$353$	8.71701	0.463959	0.231980	+	0.972721i	$0.425480\pi$
$354$	−7.79476	−0.414287
$355$	−2.37005	−0.125789
$356$	−13.7007	−0.726138
$357$	0	0
$358$	−6.25882	−0.330789
$359$	1.17128	0.0618180	0.0309090	−	0.999522i	$-0.490160\pi$
$359$	1.17128	0.0618180	0.0309090	+	0.999522i	$0.490160\pi$
$360$	3.46130	0.182427
$361$	1.00000	0.0526316
$362$	4.25019	0.223385
$363$	10.9226	0.573288
$364$	0	0
$365$	6.66427	0.348824
$366$	9.12941	0.477202
$367$	5.01295	0.261674	0.130837	−	0.991404i	$-0.458234\pi$
$367$	5.01295	0.261674	0.130837	+	0.991404i	$0.458234\pi$
$368$	3.09233	0.161199
$369$	8.88553	0.462562
$370$	−18.1411	−0.943111
$371$	0	0
$372$	−7.34959	−0.381059
$373$	1.86584	0.0966096	0.0483048	−	0.998833i	$-0.484618\pi$
$373$	1.86584	0.0966096	0.0483048	+	0.998833i	$0.484618\pi$
$374$	−1.61285	−0.0833985
$375$	6.85553	0.354018
$376$	1.79320	0.0924771
$377$	−59.2135	−3.04965
$378$	0	0
$379$	−11.8065	−0.606457	−0.303228	−	0.952918i	$-0.598065\pi$
$379$	−11.8065	−0.606457	−0.303228	+	0.952918i	$0.598065\pi$
$380$	−3.46130	−0.177561
$381$	3.45699	0.177107
$382$	10.9479	0.560141
$383$	5.52639	0.282385	0.141193	−	0.989982i	$-0.454906\pi$
$383$	5.52639	0.282385	0.141193	+	0.989982i	$0.454906\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−21.2899	−1.08363
$387$	10.3705	0.527164
$388$	4.09233	0.207757
$389$	1.26421	0.0640979	0.0320490	−	0.999486i	$-0.489797\pi$
$389$	1.26421	0.0640979	0.0320490	+	0.999486i	$0.489797\pi$
$390$	−23.9612	−1.21332
$391$	17.9278	0.906650
$392$	0	0
$393$	−18.4956	−0.932981
$394$	6.63103	0.334066
$395$	−4.87215	−0.245144
$396$	0.278197	0.0139799
$397$	−1.40485	−0.0705073	−0.0352536	−	0.999378i	$-0.511224\pi$
$397$	−1.40485	−0.0705073	−0.0352536	+	0.999378i	$0.511224\pi$
$398$	7.87047	0.394511
$399$	0	0
$400$	6.98062	0.349031
$401$	−4.77119	−0.238262	−0.119131	−	0.992879i	$-0.538011\pi$
$401$	−4.77119	−0.238262	−0.119131	+	0.992879i	$0.538011\pi$
$402$	−13.7378	−0.685180
$403$	50.8783	2.53443
$404$	−2.45699	−0.122240
$405$	−3.46130	−0.171994
$406$	0	0
$407$	−1.45806	−0.0722735
$408$	5.79751	0.287020
$409$	−18.0890	−0.894442	−0.447221	−	0.894424i	$-0.647586\pi$
$409$	−18.0890	−0.894442	−0.447221	+	0.894424i	$0.647586\pi$
$410$	30.7555	1.51891
$411$	12.1680	0.600205
$412$	17.3468	0.854617
$413$	0	0
$414$	−3.09233	−0.151980
$415$	0.505454	0.0248118
$416$	−6.92261	−0.339409
$417$	2.91829	0.142909
$418$	−0.278197	−0.0136071
$419$	2.70518	0.132157	0.0660784	−	0.997814i	$-0.478951\pi$
$419$	2.70518	0.132157	0.0660784	+	0.997814i	$0.478951\pi$
$420$	0	0
$421$	6.14064	0.299276	0.149638	−	0.988741i	$-0.452189\pi$
$421$	6.14064	0.299276	0.149638	+	0.988741i	$0.452189\pi$
$422$	−14.9123	−0.725919
$423$	−1.79320	−0.0871883
$424$	−8.38823	−0.407368
$425$	40.4702	1.96310
$426$	0.684727	0.0331751
$427$	0	0
$428$	−11.4779	−0.554806
$429$	−1.92585	−0.0929808
$430$	35.8955	1.73104
$431$	21.2765	1.02485	0.512427	−	0.858731i	$-0.328747\pi$
$431$	21.2765	1.02485	0.512427	+	0.858731i	$0.328747\pi$
$432$	−1.00000	−0.0481125
$433$	−9.42099	−0.452744	−0.226372	−	0.974041i	$-0.572686\pi$
$433$	−9.42099	−0.452744	−0.226372	+	0.974041i	$0.572686\pi$
$434$	0	0
$435$	−29.6067	−1.41953
$436$	−18.6814	−0.894675
$437$	3.09233	0.147926
$438$	−1.92536	−0.0919975
$439$	12.5924	0.601002	0.300501	−	0.953781i	$-0.402846\pi$
$439$	12.5924	0.601002	0.300501	+	0.953781i	$0.402846\pi$
$440$	0.962923	0.0459056
$441$	0	0
$442$	−40.1339	−1.90898
$443$	−23.2947	−1.10676	−0.553382	−	0.832927i	$-0.686663\pi$
$443$	−23.2947	−1.10676	−0.553382	+	0.832927i	$0.686663\pi$
$444$	5.24112	0.248733
$445$	47.4224	2.24804
$446$	−3.92861	−0.186025
$447$	4.16493	0.196994
$448$	0	0
$449$	−0.486074	−0.0229393	−0.0114696	−	0.999934i	$-0.503651\pi$
$449$	−0.486074	−0.0229393	−0.0114696	+	0.999934i	$0.503651\pi$
$450$	−6.98062	−0.329070
$451$	2.47193	0.116398
$452$	3.29913	0.155178
$453$	−19.2754	−0.905639
$454$	7.03971	0.330390
$455$	0	0
$456$	1.00000	0.0468293
$457$	14.4597	0.676398	0.338199	−	0.941075i	$-0.390182\pi$
$457$	14.4597	0.676398	0.338199	+	0.941075i	$0.390182\pi$
$458$	−5.88397	−0.274940
$459$	−5.79751	−0.270605
$460$	−10.7035	−0.499053
$461$	18.0188	0.839218	0.419609	−	0.907705i	$-0.362167\pi$
$461$	18.0188	0.839218	0.419609	+	0.907705i	$0.362167\pi$
$462$	0	0
$463$	23.3408	1.08474	0.542370	−	0.840140i	$-0.317527\pi$
$463$	23.3408	1.08474	0.542370	+	0.840140i	$0.317527\pi$
$464$	−8.55364	−0.397093
$465$	25.4392	1.17971
$466$	−2.80658	−0.130012
$467$	−8.14879	−0.377081	−0.188540	−	0.982065i	$-0.560376\pi$
$467$	−8.14879	−0.377081	−0.188540	+	0.982065i	$0.560376\pi$
$468$	6.92261	0.319998
$469$	0	0
$470$	−6.20680	−0.286298
$471$	21.4569	0.988680
$472$	7.79476	0.358783
$473$	2.88505	0.132655
$474$	1.40761	0.0646535
$475$	6.98062	0.320293
$476$	0	0
$477$	8.38823	0.384070
$478$	12.4016	0.567236
$479$	27.1627	1.24109	0.620547	−	0.784170i	$-0.286911\pi$
$479$	27.1627	1.24109	0.620547	+	0.784170i	$0.286911\pi$
$480$	−3.46130	−0.157986
$481$	−36.2822	−1.65433
$482$	15.1965	0.692181
$483$	0	0
$484$	−10.9226	−0.496482
$485$	−14.1648	−0.643191
$486$	1.00000	0.0453609
$487$	−11.9423	−0.541159	−0.270580	−	0.962698i	$-0.587215\pi$
$487$	−11.9423	−0.541159	−0.270580	+	0.962698i	$0.587215\pi$
$488$	−9.12941	−0.413269
$489$	−15.9446	−0.721041
$490$	0	0
$491$	−7.00863	−0.316295	−0.158148	−	0.987415i	$-0.550552\pi$
$491$	−7.00863	−0.316295	−0.158148	+	0.987415i	$0.550552\pi$
$492$	−8.88553	−0.400591
$493$	−49.5898	−2.23341
$494$	−6.92261	−0.311463
$495$	−0.962923	−0.0432802
$496$	7.34959	0.330006
$497$	0	0
$498$	−0.146030	−0.00654376
$499$	−9.12604	−0.408538	−0.204269	−	0.978915i	$-0.565482\pi$
$499$	−9.12604	−0.408538	−0.204269	+	0.978915i	$0.565482\pi$
$500$	−6.85553	−0.306589
$501$	−17.6073	−0.786638
$502$	−5.91198	−0.263865
$503$	−24.1190	−1.07541	−0.537706	−	0.843133i	$-0.680709\pi$
$503$	−24.1190	−1.07541	−0.537706	+	0.843133i	$0.680709\pi$
$504$	0	0
$505$	8.50438	0.378440
$506$	−0.860277	−0.0382440
$507$	−34.9225	−1.55096
$508$	−3.45699	−0.153379
$509$	−37.5061	−1.66243	−0.831215	−	0.555951i	$-0.812354\pi$
$509$	−37.5061	−1.66243	−0.831215	+	0.555951i	$0.812354\pi$
$510$	−20.0670	−0.888580
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	−1.40485	−0.0619651
$515$	−60.0427	−2.64580
$516$	−10.3705	−0.456537
$517$	−0.498862	−0.0219399
$518$	0	0
$519$	−10.0106	−0.439418
$520$	23.9612	1.05077
$521$	42.2049	1.84903	0.924516	−	0.381143i	$-0.124469\pi$
$521$	42.2049	1.84903	0.924516	+	0.381143i	$0.124469\pi$
$522$	8.55364	0.374382
$523$	19.0938	0.834915	0.417458	−	0.908696i	$-0.362921\pi$
$523$	19.0938	0.834915	0.417458	+	0.908696i	$0.362921\pi$
$524$	18.4956	0.807985
$525$	0	0
$526$	10.7781	0.469949
$527$	42.6094	1.85609
$528$	−0.278197	−0.0121070
$529$	−13.4375	−0.584238
$530$	29.0342	1.26116
$531$	−7.79476	−0.338264
$532$	0	0
$533$	61.5110	2.66434
$534$	−13.7007	−0.592889
$535$	39.7286	1.71762
$536$	13.7378	0.593383
$537$	−6.25882	−0.270088
$538$	−22.4462	−0.967726
$539$	0	0
$540$	3.46130	0.148951
$541$	0.786124	0.0337981	0.0168991	−	0.999857i	$-0.494621\pi$
$541$	0.786124	0.0337981	0.0168991	+	0.999857i	$0.494621\pi$
$542$	2.27651	0.0977846
$543$	4.25019	0.182393
$544$	−5.79751	−0.248566
$545$	64.6619	2.76981
$546$	0	0
$547$	0.670738	0.0286787	0.0143394	−	0.999897i	$-0.495435\pi$
$547$	0.670738	0.0286787	0.0143394	+	0.999897i	$0.495435\pi$
$548$	−12.1680	−0.519793
$549$	9.12941	0.389634
$550$	−1.94199	−0.0828066
$551$	−8.55364	−0.364397
$552$	3.09233	0.131618
$553$	0	0
$554$	−27.4521	−1.16633
$555$	−18.1411	−0.770047
$556$	−2.91829	−0.123763
$557$	6.15298	0.260710	0.130355	−	0.991467i	$-0.458388\pi$
$557$	6.15298	0.260710	0.130355	+	0.991467i	$0.458388\pi$
$558$	−7.34959	−0.311133
$559$	71.7911	3.03644
$560$	0	0
$561$	−1.61285	−0.0680946
$562$	−8.14279	−0.343483
$563$	−23.6754	−0.997798	−0.498899	−	0.866660i	$-0.666262\pi$
$563$	−23.6754	−0.997798	−0.498899	+	0.866660i	$0.666262\pi$
$564$	1.79320	0.0755073
$565$	−11.4193	−0.480414
$566$	8.18586	0.344078
$567$	0	0
$568$	−0.684727	−0.0287305
$569$	36.6691	1.53725	0.768623	−	0.639702i	$-0.220942\pi$
$569$	36.6691	1.53725	0.768623	+	0.639702i	$0.220942\pi$
$570$	−3.46130	−0.144978
$571$	−17.7280	−0.741893	−0.370947	−	0.928654i	$-0.620967\pi$
$571$	−17.7280	−0.741893	−0.370947	+	0.928654i	$0.620967\pi$
$572$	1.92585	0.0805237
$573$	10.9479	0.457353
$574$	0	0
$575$	21.5864	0.900215
$576$	1.00000	0.0416667
$577$	−1.23206	−0.0512911	−0.0256456	−	0.999671i	$-0.508164\pi$
$577$	−1.23206	−0.0512911	−0.0256456	+	0.999671i	$0.508164\pi$
$578$	−16.6112	−0.690933
$579$	−21.2899	−0.884778
$580$	29.6067	1.22935
$581$	0	0
$582$	4.09233	0.169633
$583$	2.33358	0.0966469
$584$	1.92536	0.0796722
$585$	−23.9612	−0.990675
$586$	19.3421	0.799014
$587$	−10.0714	−0.415691	−0.207845	−	0.978162i	$-0.566645\pi$
$587$	−10.0714	−0.415691	−0.207845	+	0.978162i	$0.566645\pi$
$588$	0	0
$589$	7.34959	0.302835
$590$	−26.9800	−1.11075
$591$	6.63103	0.272764
$592$	−5.24112	−0.215409
$593$	28.2634	1.16064	0.580320	−	0.814388i	$-0.302927\pi$
$593$	28.2634	1.16064	0.580320	+	0.814388i	$0.302927\pi$
$594$	0.278197	0.0114146
$595$	0	0
$596$	−4.16493	−0.170602
$597$	7.87047	0.322117
$598$	−21.4070	−0.875397
$599$	4.27975	0.174866	0.0874330	−	0.996170i	$-0.472134\pi$
$599$	4.27975	0.174866	0.0874330	+	0.996170i	$0.472134\pi$
$600$	6.98062	0.284983
$601$	−47.6366	−1.94314	−0.971569	−	0.236757i	$-0.923915\pi$
$601$	−47.6366	−1.94314	−0.971569	+	0.236757i	$0.923915\pi$
$602$	0	0
$603$	−13.7378	−0.559447
$604$	19.2754	0.784306
$605$	37.8065	1.53705
$606$	−2.45699	−0.0998083
$607$	−20.6931	−0.839905	−0.419953	−	0.907546i	$-0.637953\pi$
$607$	−20.6931	−0.839905	−0.419953	+	0.907546i	$0.637953\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	31.5997	1.27943
$611$	−12.4136	−0.502201
$612$	5.79751	0.234351
$613$	1.67398	0.0676114	0.0338057	−	0.999428i	$-0.489237\pi$
$613$	1.67398	0.0676114	0.0338057	+	0.999428i	$0.489237\pi$
$614$	11.7007	0.472203
$615$	30.7555	1.24018
$616$	0	0
$617$	−13.5252	−0.544504	−0.272252	−	0.962226i	$-0.587768\pi$
$617$	−13.5252	−0.544504	−0.272252	+	0.962226i	$0.587768\pi$
$618$	17.3468	0.697792
$619$	45.1559	1.81497	0.907485	−	0.420085i	$-0.138000\pi$
$619$	45.1559	1.81497	0.907485	+	0.420085i	$0.138000\pi$
$620$	−25.4392	−1.02166
$621$	−3.09233	−0.124091
$622$	−13.8555	−0.555556
$623$	0	0
$624$	−6.92261	−0.277126
$625$	−11.1740	−0.446962
$626$	1.97199	0.0788165
$627$	−0.278197	−0.0111101
$628$	−21.4569	−0.856222
$629$	−30.3855	−1.21155
$630$	0	0
$631$	−3.01542	−0.120042	−0.0600210	−	0.998197i	$-0.519117\pi$
$631$	−3.01542	−0.120042	−0.0600210	+	0.998197i	$0.519117\pi$
$632$	−1.40761	−0.0559915
$633$	−14.9123	−0.592710
$634$	−19.9005	−0.790349
$635$	11.9657	0.474844
$636$	−8.38823	−0.332615
$637$	0	0
$638$	2.37959	0.0942090
$639$	0.684727	0.0270874
$640$	3.46130	0.136820
$641$	15.9962	0.631811	0.315905	−	0.948791i	$-0.397692\pi$
$641$	15.9962	0.631811	0.315905	+	0.948791i	$0.397692\pi$
$642$	−11.4779	−0.452998
$643$	−20.9315	−0.825460	−0.412730	−	0.910854i	$-0.635425\pi$
$643$	−20.9315	−0.825460	−0.412730	+	0.910854i	$0.635425\pi$
$644$	0	0
$645$	35.8955	1.41339
$646$	−5.79751	−0.228100
$647$	43.4198	1.70701	0.853504	−	0.521086i	$-0.174473\pi$
$647$	43.4198	1.70701	0.853504	+	0.521086i	$0.174473\pi$
$648$	−1.00000	−0.0392837
$649$	−2.16848	−0.0851201
$650$	−48.3241	−1.89543
$651$	0	0
$652$	15.9446	0.624439
$653$	−6.06220	−0.237232	−0.118616	−	0.992940i	$-0.537846\pi$
$653$	−6.06220	−0.237232	−0.118616	+	0.992940i	$0.537846\pi$
$654$	−18.6814	−0.730499
$655$	−64.0190	−2.50143
$656$	8.88553	0.346922
$657$	−1.92536	−0.0751156
$658$	0	0
$659$	−0.570382	−0.0222189	−0.0111095	−	0.999938i	$-0.503536\pi$
$659$	−0.570382	−0.0222189	−0.0111095	+	0.999938i	$0.503536\pi$
$660$	0.962923	0.0374817
$661$	−17.6396	−0.686101	−0.343051	−	0.939317i	$-0.611460\pi$
$661$	−17.6396	−0.686101	−0.343051	+	0.939317i	$0.611460\pi$
$662$	4.66762	0.181412
$663$	−40.1339	−1.55867
$664$	0.146030	0.00566706
$665$	0	0
$666$	5.24112	0.203089
$667$	−26.4507	−1.02417
$668$	17.6073	0.681248
$669$	−3.92861	−0.151889
$670$	−47.5508	−1.83705
$671$	2.53977	0.0980468
$672$	0	0
$673$	−39.1296	−1.50833	−0.754167	−	0.656682i	$-0.771959\pi$
$673$	−39.1296	−1.50833	−0.754167	+	0.656682i	$0.771959\pi$
$674$	11.4639	0.441574
$675$	−6.98062	−0.268684
$676$	34.9225	1.34317
$677$	35.4149	1.36110	0.680552	−	0.732700i	$-0.261740\pi$
$677$	35.4149	1.36110	0.680552	+	0.732700i	$0.261740\pi$
$678$	3.29913	0.126702
$679$	0	0
$680$	20.0670	0.769533
$681$	7.03971	0.269762
$682$	−2.04463	−0.0782930
$683$	−36.2898	−1.38859	−0.694295	−	0.719691i	$-0.744284\pi$
$683$	−36.2898	−1.38859	−0.694295	+	0.719691i	$0.744284\pi$
$684$	1.00000	0.0382360
$685$	42.1173	1.60922
$686$	0	0
$687$	−5.88397	−0.224488
$688$	10.3705	0.395373
$689$	58.0684	2.21223
$690$	−10.7035	−0.407475
$691$	33.7147	1.28257	0.641284	−	0.767303i	$-0.278402\pi$
$691$	33.7147	1.28257	0.641284	+	0.767303i	$0.278402\pi$
$692$	10.0106	0.380547
$693$	0	0
$694$	−7.84258	−0.297700
$695$	10.1011	0.383156
$696$	−8.55364	−0.324225
$697$	51.5140	1.95123
$698$	−21.2991	−0.806184
$699$	−2.80658	−0.106155
$700$	0	0
$701$	12.6976	0.479583	0.239791	−	0.970824i	$-0.422921\pi$
$701$	12.6976	0.479583	0.239791	+	0.970824i	$0.422921\pi$
$702$	6.92261	0.261277
$703$	−5.24112	−0.197673
$704$	0.278197	0.0104849
$705$	−6.20680	−0.233762
$706$	−8.71701	−0.328069
$707$	0	0
$708$	7.79476	0.292945
$709$	−21.2791	−0.799155	−0.399578	−	0.916699i	$-0.630843\pi$
$709$	−21.2791	−0.799155	−0.399578	+	0.916699i	$0.630843\pi$
$710$	2.37005	0.0889463
$711$	1.40761	0.0527893
$712$	13.7007	0.513457
$713$	22.7274	0.851147
$714$	0	0
$715$	−6.66594	−0.249292
$716$	6.25882	0.233903
$717$	12.4016	0.463146
$718$	−1.17128	−0.0437119
$719$	48.2232	1.79842	0.899210	−	0.437516i	$-0.144142\pi$
$719$	48.2232	1.79842	0.899210	+	0.437516i	$0.144142\pi$
$720$	−3.46130	−0.128995
$721$	0	0
$722$	−1.00000	−0.0372161
$723$	15.1965	0.565163
$724$	−4.25019	−0.157957
$725$	−59.7097	−2.21756
$726$	−10.9226	−0.405376
$727$	49.2945	1.82823	0.914116	−	0.405452i	$-0.132886\pi$
$727$	49.2945	1.82823	0.914116	+	0.405452i	$0.132886\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−6.66427	−0.246656
$731$	60.1233	2.22374
$732$	−9.12941	−0.337433
$733$	−0.924289	−0.0341394	−0.0170697	−	0.999854i	$-0.505434\pi$
$733$	−0.924289	−0.0341394	−0.0170697	+	0.999854i	$0.505434\pi$
$734$	−5.01295	−0.185031
$735$	0	0
$736$	−3.09233	−0.113985
$737$	−3.82182	−0.140778
$738$	−8.88553	−0.327081
$739$	2.35176	0.0865108	0.0432554	−	0.999064i	$-0.486227\pi$
$739$	2.35176	0.0865108	0.0432554	+	0.999064i	$0.486227\pi$
$740$	18.1411	0.666880
$741$	−6.92261	−0.254308
$742$	0	0
$743$	−50.4616	−1.85126	−0.925628	−	0.378433i	$-0.876463\pi$
$743$	−50.4616	−1.85126	−0.925628	+	0.378433i	$0.876463\pi$
$744$	7.34959	0.269449
$745$	14.4161	0.528164
$746$	−1.86584	−0.0683133
$747$	−0.146030	−0.00534296
$748$	1.61285	0.0589716
$749$	0	0
$750$	−6.85553	−0.250328
$751$	−6.22282	−0.227074	−0.113537	−	0.993534i	$-0.536218\pi$
$751$	−6.22282	−0.227074	−0.113537	+	0.993534i	$0.536218\pi$
$752$	−1.79320	−0.0653912
$753$	−5.91198	−0.215445
$754$	59.2135	2.15643
$755$	−66.7181	−2.42812
$756$	0	0
$757$	19.9762	0.726047	0.363023	−	0.931780i	$-0.381745\pi$
$757$	19.9762	0.726047	0.363023	+	0.931780i	$0.381745\pi$
$758$	11.8065	0.428830
$759$	−0.860277	−0.0312261
$760$	3.46130	0.125555
$761$	15.3054	0.554822	0.277411	−	0.960751i	$-0.410524\pi$
$761$	15.3054	0.554822	0.277411	+	0.960751i	$0.410524\pi$
$762$	−3.45699	−0.125233
$763$	0	0
$764$	−10.9479	−0.396080
$765$	−20.0670	−0.725522
$766$	−5.52639	−0.199677
$767$	−53.9600	−1.94838
$768$	−1.00000	−0.0360844
$769$	−18.0461	−0.650761	−0.325380	−	0.945583i	$-0.605492\pi$
$769$	−18.0461	−0.650761	−0.325380	+	0.945583i	$0.605492\pi$
$770$	0	0
$771$	−1.40485	−0.0505943
$772$	21.2899	0.766240
$773$	−40.2781	−1.44870	−0.724351	−	0.689432i	$-0.757860\pi$
$773$	−40.2781	−1.44870	−0.724351	+	0.689432i	$0.757860\pi$
$774$	−10.3705	−0.372761
$775$	51.3047	1.84292
$776$	−4.09233	−0.146906
$777$	0	0
$778$	−1.26421	−0.0453241
$779$	8.88553	0.318357
$780$	23.9612	0.857950
$781$	0.190489	0.00681622
$782$	−17.9278	−0.641098
$783$	8.55364	0.305682
$784$	0	0
$785$	74.2687	2.65076
$786$	18.4956	0.659717
$787$	−22.2856	−0.794395	−0.397198	−	0.917733i	$-0.630017\pi$
$787$	−22.2856	−0.794395	−0.397198	+	0.917733i	$0.630017\pi$
$788$	−6.63103	−0.236221
$789$	10.7781	0.383712
$790$	4.87215	0.173343
$791$	0	0
$792$	−0.278197	−0.00988529
$793$	63.1993	2.24427
$794$	1.40485	0.0498562
$795$	29.0342	1.02974
$796$	−7.87047	−0.278961
$797$	−11.6159	−0.411457	−0.205728	−	0.978609i	$-0.565956\pi$
$797$	−11.6159	−0.411457	−0.205728	+	0.978609i	$0.565956\pi$
$798$	0	0
$799$	−10.3961	−0.367787
$800$	−6.98062	−0.246802
$801$	−13.7007	−0.484092
$802$	4.77119	0.168476
$803$	−0.535630	−0.0189020
$804$	13.7378	0.484495
$805$	0	0
$806$	−50.8783	−1.79211
$807$	−22.4462	−0.790145
$808$	2.45699	0.0864365
$809$	−21.9957	−0.773327	−0.386664	−	0.922221i	$-0.626373\pi$
$809$	−21.9957	−0.773327	−0.386664	+	0.922221i	$0.626373\pi$
$810$	3.46130	0.121618
$811$	24.2399	0.851177	0.425588	−	0.904917i	$-0.360067\pi$
$811$	24.2399	0.851177	0.425588	+	0.904917i	$0.360067\pi$
$812$	0	0
$813$	2.27651	0.0798408
$814$	1.45806	0.0511051
$815$	−55.1892	−1.93319
$816$	−5.79751	−0.202954
$817$	10.3705	0.362819
$818$	18.0890	0.632466
$819$	0	0
$820$	−30.7555	−1.07403
$821$	−13.4332	−0.468821	−0.234410	−	0.972138i	$-0.575316\pi$
$821$	−13.4332	−0.468821	−0.234410	+	0.972138i	$0.575316\pi$
$822$	−12.1680	−0.424409
$823$	9.53653	0.332423	0.166211	−	0.986090i	$-0.446847\pi$
$823$	9.53653	0.332423	0.166211	+	0.986090i	$0.446847\pi$
$824$	−17.3468	−0.604306
$825$	−1.94199	−0.0676113
$826$	0	0
$827$	46.7140	1.62440	0.812202	−	0.583376i	$-0.198268\pi$
$827$	46.7140	1.62440	0.812202	+	0.583376i	$0.198268\pi$
$828$	3.09233	0.107466
$829$	17.3276	0.601812	0.300906	−	0.953654i	$-0.402711\pi$
$829$	17.3276	0.601812	0.300906	+	0.953654i	$0.402711\pi$
$830$	−0.505454	−0.0175446
$831$	−27.4521	−0.952302
$832$	6.92261	0.239998
$833$	0	0
$834$	−2.91829	−0.101052
$835$	−60.9443	−2.10907
$836$	0.278197	0.00962164
$837$	−7.34959	−0.254039
$838$	−2.70518	−0.0934490
$839$	−26.5740	−0.917435	−0.458718	−	0.888582i	$-0.651691\pi$
$839$	−26.5740	−0.917435	−0.458718	+	0.888582i	$0.651691\pi$
$840$	0	0
$841$	44.1647	1.52292
$842$	−6.14064	−0.211620
$843$	−8.14279	−0.280453
$844$	14.9123	0.513302
$845$	−120.877	−4.15831
$846$	1.79320	0.0616514
$847$	0	0
$848$	8.38823	0.288053
$849$	8.18586	0.280938
$850$	−40.4702	−1.38812
$851$	−16.2073	−0.555579
$852$	−0.684727	−0.0234583
$853$	−4.35464	−0.149100	−0.0745500	−	0.997217i	$-0.523752\pi$
$853$	−4.35464	−0.149100	−0.0745500	+	0.997217i	$0.523752\pi$
$854$	0	0
$855$	−3.46130	−0.118374
$856$	11.4779	0.392307
$857$	−44.7011	−1.52696	−0.763480	−	0.645832i	$-0.776511\pi$
$857$	−44.7011	−1.52696	−0.763480	+	0.645832i	$0.776511\pi$
$858$	1.92585	0.0657473
$859$	5.42050	0.184945	0.0924726	−	0.995715i	$-0.470523\pi$
$859$	5.42050	0.184945	0.0924726	+	0.995715i	$0.470523\pi$
$860$	−35.8955	−1.22403
$861$	0	0
$862$	−21.2765	−0.724681
$863$	−41.7588	−1.42148	−0.710742	−	0.703453i	$-0.751641\pi$
$863$	−41.7588	−1.42148	−0.710742	+	0.703453i	$0.751641\pi$
$864$	1.00000	0.0340207
$865$	−34.6498	−1.17813
$866$	9.42099	0.320138
$867$	−16.6112	−0.564145
$868$	0	0
$869$	0.391591	0.0132838
$870$	29.6067	1.00376
$871$	−95.1015	−3.22239
$872$	18.6814	0.632631
$873$	4.09233	0.138504
$874$	−3.09233	−0.104600
$875$	0	0
$876$	1.92536	0.0650520
$877$	35.9401	1.21361	0.606805	−	0.794851i	$-0.292451\pi$
$877$	35.9401	1.21361	0.606805	+	0.794851i	$0.292451\pi$
$878$	−12.5924	−0.424973
$879$	19.3421	0.652392
$880$	−0.962923	−0.0324601
$881$	49.3541	1.66278	0.831391	−	0.555688i	$-0.187545\pi$
$881$	49.3541	1.66278	0.831391	+	0.555688i	$0.187545\pi$
$882$	0	0
$883$	12.0927	0.406951	0.203476	−	0.979080i	$-0.434776\pi$
$883$	12.0927	0.406951	0.203476	+	0.979080i	$0.434776\pi$
$884$	40.1339	1.34985
$885$	−26.9800	−0.906923
$886$	23.2947	0.782601
$887$	27.5621	0.925445	0.462722	−	0.886503i	$-0.346873\pi$
$887$	27.5621	0.925445	0.462722	+	0.886503i	$0.346873\pi$
$888$	−5.24112	−0.175880
$889$	0	0
$890$	−47.4224	−1.58960
$891$	0.278197	0.00931994
$892$	3.92861	0.131539
$893$	−1.79320	−0.0600071
$894$	−4.16493	−0.139296
$895$	−21.6637	−0.724136
$896$	0	0
$897$	−21.4070	−0.714759
$898$	0.486074	0.0162205
$899$	−62.8657	−2.09669
$900$	6.98062	0.232687
$901$	48.6309	1.62013
$902$	−2.47193	−0.0823061
$903$	0	0
$904$	−3.29913	−0.109728
$905$	14.7112	0.489016
$906$	19.2754	0.640384
$907$	40.3679	1.34039	0.670197	−	0.742183i	$-0.266210\pi$
$907$	40.3679	1.34039	0.670197	+	0.742183i	$0.266210\pi$
$908$	−7.03971	−0.233621
$909$	−2.45699	−0.0814931
$910$	0	0
$911$	−6.02988	−0.199779	−0.0998894	−	0.994999i	$-0.531849\pi$
$911$	−6.02988	−0.199779	−0.0998894	+	0.994999i	$0.531849\pi$
$912$	−1.00000	−0.0331133
$913$	−0.0406251	−0.00134449
$914$	−14.4597	−0.478286
$915$	31.5997	1.04465
$916$	5.88397	0.194412
$917$	0	0
$918$	5.79751	0.191346
$919$	51.5149	1.69932	0.849659	−	0.527332i	$-0.176807\pi$
$919$	51.5149	1.69932	0.849659	+	0.527332i	$0.176807\pi$
$920$	10.7035	0.352884
$921$	11.7007	0.385553
$922$	−18.0188	−0.593417
$923$	4.74009	0.156022
$924$	0	0
$925$	−36.5863	−1.20295
$926$	−23.3408	−0.767027
$927$	17.3468	0.569745
$928$	8.55364	0.280787
$929$	−8.68537	−0.284958	−0.142479	−	0.989798i	$-0.545507\pi$
$929$	−8.68537	−0.284958	−0.142479	+	0.989798i	$0.545507\pi$
$930$	−25.4392	−0.834183
$931$	0	0
$932$	2.80658	0.0919326
$933$	−13.8555	−0.453610
$934$	8.14879	0.266636
$935$	−5.58256	−0.182569
$936$	−6.92261	−0.226272
$937$	−59.2801	−1.93660	−0.968298	−	0.249799i	$-0.919635\pi$
$937$	−59.2801	−1.93660	−0.968298	+	0.249799i	$0.919635\pi$
$938$	0	0
$939$	1.97199	0.0643534
$940$	6.20680	0.202444
$941$	−14.2282	−0.463825	−0.231913	−	0.972737i	$-0.574498\pi$
$941$	−14.2282	−0.463825	−0.231913	+	0.972737i	$0.574498\pi$
$942$	−21.4569	−0.699102
$943$	27.4770	0.894775
$944$	−7.79476	−0.253698
$945$	0	0
$946$	−2.88505	−0.0938010
$947$	15.6081	0.507194	0.253597	−	0.967310i	$-0.418386\pi$
$947$	15.6081	0.507194	0.253597	+	0.967310i	$0.418386\pi$
$948$	−1.40761	−0.0457169
$949$	−13.3285	−0.432663
$950$	−6.98062	−0.226481
$951$	−19.9005	−0.645317
$952$	0	0
$953$	9.11279	0.295192	0.147596	−	0.989048i	$-0.452846\pi$
$953$	9.11279	0.295192	0.147596	+	0.989048i	$0.452846\pi$
$954$	−8.38823	−0.271579
$955$	37.8939	1.22622
$956$	−12.4016	−0.401097
$957$	2.37959	0.0769213
$958$	−27.1627	−0.877585
$959$	0	0
$960$	3.46130	0.111713
$961$	23.0165	0.742468
$962$	36.2822	1.16979
$963$	−11.4779	−0.369871
$964$	−15.1965	−0.489446
$965$	−73.6908	−2.37219
$966$	0	0
$967$	−4.04494	−0.130077	−0.0650383	−	0.997883i	$-0.520717\pi$
$967$	−4.04494	−0.130077	−0.0650383	+	0.997883i	$0.520717\pi$
$968$	10.9226	0.351066
$969$	−5.79751	−0.186243
$970$	14.1648	0.454804
$971$	18.0859	0.580403	0.290201	−	0.956966i	$-0.406278\pi$
$971$	18.0859	0.580403	0.290201	+	0.956966i	$0.406278\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	11.9423	0.382657
$975$	−48.3241	−1.54761
$976$	9.12941	0.292225
$977$	−43.1513	−1.38053	−0.690266	−	0.723556i	$-0.742507\pi$
$977$	−43.1513	−1.38053	−0.690266	+	0.723556i	$0.742507\pi$
$978$	15.9446	0.509853
$979$	−3.81150	−0.121816
$980$	0	0
$981$	−18.6814	−0.596450
$982$	7.00863	0.223654
$983$	−31.5917	−1.00762	−0.503809	−	0.863815i	$-0.668068\pi$
$983$	−31.5917	−1.00762	−0.503809	+	0.863815i	$0.668068\pi$
$984$	8.88553	0.283260
$985$	22.9520	0.731312
$986$	49.5898	1.57926
$987$	0	0
$988$	6.92261	0.220237
$989$	32.0691	1.01974
$990$	0.962923	0.0306037
$991$	36.7951	1.16883	0.584417	−	0.811453i	$-0.301323\pi$
$991$	36.7951	1.16883	0.584417	+	0.811453i	$0.301323\pi$
$992$	−7.34959	−0.233350
$993$	4.66762	0.148123
$994$	0	0
$995$	27.2421	0.863632
$996$	0.146030	0.00462714
$997$	−42.3123	−1.34005	−0.670023	−	0.742341i	$-0.733716\pi$
$997$	−42.3123	−1.34005	−0.670023	+	0.742341i	$0.733716\pi$
$998$	9.12604	0.288880
$999$	5.24112	0.165822

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5586.2.a.bw.1.1		4
7.2	even	3		798.2.j.l.571.4	yes	8
7.4	even	3		798.2.j.l.457.4	✓	8
7.6	odd	2		5586.2.a.bz.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.j.l.457.4	✓	8	7.4	even	3
798.2.j.l.571.4	yes	8	7.2	even	3
5586.2.a.bw.1.1		4	1.1	even	1	trivial
5586.2.a.bz.1.4		4	7.6	odd	2

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:	\( N \)	\(=\)	\( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5586.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.46130 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.46130 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +3.46130 q^{10} +0.278197 q^{11} -1.00000 q^{12} +6.92261 q^{13} +3.46130 q^{15} +1.00000 q^{16} +5.79751 q^{17} -1.00000 q^{18} +1.00000 q^{19} -3.46130 q^{20} -0.278197 q^{22} +3.09233 q^{23} +1.00000 q^{24} +6.98062 q^{25} -6.92261 q^{26} -1.00000 q^{27} -8.55364 q^{29} -3.46130 q^{30} +7.34959 q^{31} -1.00000 q^{32} -0.278197 q^{33} -5.79751 q^{34} +1.00000 q^{36} -5.24112 q^{37} -1.00000 q^{38} -6.92261 q^{39} +3.46130 q^{40} +8.88553 q^{41} +10.3705 q^{43} +0.278197 q^{44} -3.46130 q^{45} -3.09233 q^{46} -1.79320 q^{47} -1.00000 q^{48} -6.98062 q^{50} -5.79751 q^{51} +6.92261 q^{52} +8.38823 q^{53} +1.00000 q^{54} -0.962923 q^{55} -1.00000 q^{57} +8.55364 q^{58} -7.79476 q^{59} +3.46130 q^{60} +9.12941 q^{61} -7.34959 q^{62} +1.00000 q^{64} -23.9612 q^{65} +0.278197 q^{66} -13.7378 q^{67} +5.79751 q^{68} -3.09233 q^{69} +0.684727 q^{71} -1.00000 q^{72} -1.92536 q^{73} +5.24112 q^{74} -6.98062 q^{75} +1.00000 q^{76} +6.92261 q^{78} +1.40761 q^{79} -3.46130 q^{80} +1.00000 q^{81} -8.88553 q^{82} -0.146030 q^{83} -20.0670 q^{85} -10.3705 q^{86} +8.55364 q^{87} -0.278197 q^{88} -13.7007 q^{89} +3.46130 q^{90} +3.09233 q^{92} -7.34959 q^{93} +1.79320 q^{94} -3.46130 q^{95} +1.00000 q^{96} +4.09233 q^{97} +0.278197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{6} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^6 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{6} - 4 q^{8} + 4 q^{9} - 2 q^{11} - 4 q^{12} + 4 q^{16} + 10 q^{17} - 4 q^{18} + 4 q^{19} + 2 q^{22} - 5 q^{23} + 4 q^{24} + 4 q^{25} - 4 q^{27} - 3 q^{29} + 9 q^{31} - 4 q^{32} + 2 q^{33} - 10 q^{34} + 4 q^{36} - 14 q^{37} - 4 q^{38} + 4 q^{41} + 21 q^{43} - 2 q^{44} + 5 q^{46} + 7 q^{47} - 4 q^{48} - 4 q^{50} - 10 q^{51} - 7 q^{53} + 4 q^{54} - 4 q^{57} + 3 q^{58} + 7 q^{59} + 23 q^{61} - 9 q^{62} + 4 q^{64} - 48 q^{65} - 2 q^{66} + 6 q^{67} + 10 q^{68} + 5 q^{69} + 2 q^{71} - 4 q^{72} - 5 q^{73} + 14 q^{74} - 4 q^{75} + 4 q^{76} - 11 q^{79} + 4 q^{81} - 4 q^{82} + 14 q^{83} + 6 q^{85} - 21 q^{86} + 3 q^{87} + 2 q^{88} + 10 q^{89} - 5 q^{92} - 9 q^{93} - 7 q^{94} + 4 q^{96} - q^{97} - 2 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^6 - 4 * q^8 + 4 * q^9 - 2 * q^11 - 4 * q^12 + 4 * q^16 + 10 * q^17 - 4 * q^18 + 4 * q^19 + 2 * q^22 - 5 * q^23 + 4 * q^24 + 4 * q^25 - 4 * q^27 - 3 * q^29 + 9 * q^31 - 4 * q^32 + 2 * q^33 - 10 * q^34 + 4 * q^36 - 14 * q^37 - 4 * q^38 + 4 * q^41 + 21 * q^43 - 2 * q^44 + 5 * q^46 + 7 * q^47 - 4 * q^48 - 4 * q^50 - 10 * q^51 - 7 * q^53 + 4 * q^54 - 4 * q^57 + 3 * q^58 + 7 * q^59 + 23 * q^61 - 9 * q^62 + 4 * q^64 - 48 * q^65 - 2 * q^66 + 6 * q^67 + 10 * q^68 + 5 * q^69 + 2 * q^71 - 4 * q^72 - 5 * q^73 + 14 * q^74 - 4 * q^75 + 4 * q^76 - 11 * q^79 + 4 * q^81 - 4 * q^82 + 14 * q^83 + 6 * q^85 - 21 * q^86 + 3 * q^87 + 2 * q^88 + 10 * q^89 - 5 * q^92 - 9 * q^93 - 7 * q^94 + 4 * q^96 - q^97 - 2 * q^99

Introduction

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