LMFDB - Embedded newform 5586.2.a.ca.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:	$1$
Dimension:	$4$
Coefficient field:	4.4.202932.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 12x^{2} + 12x + 33 $ x^4 - 2x^3 - 12x^2 + 12*x + 33
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			$3.71730$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.71730 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.71730 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -3.71730 q^{10} -0.383715 q^{11} -1.00000 q^{12} -2.00000 q^{13} +3.71730 q^{15} +1.00000 q^{16} +0.717299 q^{17} +1.00000 q^{18} -1.00000 q^{19} -3.71730 q^{20} -0.383715 q^{22} +7.64741 q^{23} -1.00000 q^{24} +8.81831 q^{25} -2.00000 q^{26} -1.00000 q^{27} -3.16268 q^{29} +3.71730 q^{30} +5.65563 q^{31} +1.00000 q^{32} +0.383715 q^{33} +0.717299 q^{34} +1.00000 q^{36} +2.71730 q^{37} -1.00000 q^{38} +2.00000 q^{39} -3.71730 q^{40} +4.42638 q^{41} -8.26370 q^{43} -0.383715 q^{44} -3.71730 q^{45} +7.64741 q^{46} -3.87177 q^{47} -1.00000 q^{48} +8.81831 q^{50} -0.717299 q^{51} -2.00000 q^{52} +6.88820 q^{53} -1.00000 q^{54} +1.42638 q^{55} +1.00000 q^{57} -3.16268 q^{58} +13.5166 q^{59} +3.71730 q^{60} -14.8577 q^{61} +5.65563 q^{62} +1.00000 q^{64} +7.43460 q^{65} +0.383715 q^{66} -13.3113 q^{67} +0.717299 q^{68} -7.64741 q^{69} -14.1519 q^{71} +1.00000 q^{72} -1.83732 q^{73} +2.71730 q^{74} -8.81831 q^{75} -1.00000 q^{76} +2.00000 q^{78} +7.36471 q^{79} -3.71730 q^{80} +1.00000 q^{81} +4.42638 q^{82} -11.2020 q^{83} -2.66642 q^{85} -8.26370 q^{86} +3.16268 q^{87} -0.383715 q^{88} +4.10101 q^{89} -3.71730 q^{90} +7.64741 q^{92} -5.65563 q^{93} -3.87177 q^{94} +3.71730 q^{95} -1.00000 q^{96} +3.75664 q^{97} -0.383715 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} - 2 q^{10} - 4 q^{12} - 8 q^{13} + 2 q^{15} + 4 q^{16} - 10 q^{17} + 4 q^{18} - 4 q^{19} - 2 q^{20} + 7 q^{23} - 4 q^{24} + 8 q^{25} - 8 q^{26} - 4 q^{27} - 5 q^{29} + 2 q^{30} + 3 q^{31} + 4 q^{32} - 10 q^{34} + 4 q^{36} - 2 q^{37} - 4 q^{38} + 8 q^{39} - 2 q^{40} - 12 q^{41} - 11 q^{43} - 2 q^{45} + 7 q^{46} + 9 q^{47} - 4 q^{48} + 8 q^{50} + 10 q^{51} - 8 q^{52} + 11 q^{53} - 4 q^{54} - 24 q^{55} + 4 q^{57} - 5 q^{58} - 21 q^{59} + 2 q^{60} - 11 q^{61} + 3 q^{62} + 4 q^{64} + 4 q^{65} - 14 q^{67} - 10 q^{68} - 7 q^{69} - 18 q^{71} + 4 q^{72} - 15 q^{73} - 2 q^{74} - 8 q^{75} - 4 q^{76} + 8 q^{78} - 7 q^{79} - 2 q^{80} + 4 q^{81} - 12 q^{82} - 16 q^{83} - 22 q^{85} - 11 q^{86} + 5 q^{87} + 2 q^{89} - 2 q^{90} + 7 q^{92} - 3 q^{93} + 9 q^{94} + 2 q^{95} - 4 q^{96} - 19 q^{97}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 - 2 * q^10 - 4 * q^12 - 8 * q^13 + 2 * q^15 + 4 * q^16 - 10 * q^17 + 4 * q^18 - 4 * q^19 - 2 * q^20 + 7 * q^23 - 4 * q^24 + 8 * q^25 - 8 * q^26 - 4 * q^27 - 5 * q^29 + 2 * q^30 + 3 * q^31 + 4 * q^32 - 10 * q^34 + 4 * q^36 - 2 * q^37 - 4 * q^38 + 8 * q^39 - 2 * q^40 - 12 * q^41 - 11 * q^43 - 2 * q^45 + 7 * q^46 + 9 * q^47 - 4 * q^48 + 8 * q^50 + 10 * q^51 - 8 * q^52 + 11 * q^53 - 4 * q^54 - 24 * q^55 + 4 * q^57 - 5 * q^58 - 21 * q^59 + 2 * q^60 - 11 * q^61 + 3 * q^62 + 4 * q^64 + 4 * q^65 - 14 * q^67 - 10 * q^68 - 7 * q^69 - 18 * q^71 + 4 * q^72 - 15 * q^73 - 2 * q^74 - 8 * q^75 - 4 * q^76 + 8 * q^78 - 7 * q^79 - 2 * q^80 + 4 * q^81 - 12 * q^82 - 16 * q^83 - 22 * q^85 - 11 * q^86 + 5 * q^87 + 2 * q^89 - 2 * q^90 + 7 * q^92 - 3 * q^93 + 9 * q^94 + 2 * q^95 - 4 * q^96 - 19 * q^97

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
$5$	−3.71730	−1.66243	−0.831213	−	0.555954i	$-0.812353\pi$
$5$	−3.71730	−1.66243	−0.831213	+	0.555954i	$0.812353\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.71730	−1.17551
$11$	−0.383715	−0.115694	−0.0578471	−	0.998325i	$-0.518424\pi$
$11$	−0.383715	−0.115694	−0.0578471	+	0.998325i	$0.518424\pi$
$12$	−1.00000	−0.288675
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	0	0
$15$	3.71730	0.959803
$16$	1.00000	0.250000
$17$	0.717299	0.173971	0.0869853	−	0.996210i	$-0.472277\pi$
$17$	0.717299	0.173971	0.0869853	+	0.996210i	$0.472277\pi$
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−3.71730	−0.831213
$21$	0	0
$22$	−0.383715	−0.0818082
$23$	7.64741	1.59460	0.797298	−	0.603586i	$-0.206262\pi$
$23$	7.64741	1.59460	0.797298	+	0.603586i	$0.206262\pi$
$24$	−1.00000	−0.204124
$25$	8.81831	1.76366
$26$	−2.00000	−0.392232
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−3.16268	−0.587296	−0.293648	−	0.955914i	$-0.594869\pi$
$29$	−3.16268	−0.587296	−0.293648	+	0.955914i	$0.594869\pi$
$30$	3.71730	0.678683
$31$	5.65563	1.01578	0.507890	−	0.861422i	$-0.330425\pi$
$31$	5.65563	1.01578	0.507890	+	0.861422i	$0.330425\pi$
$32$	1.00000	0.176777
$33$	0.383715	0.0667961
$34$	0.717299	0.123016
$35$	0	0
$36$	1.00000	0.166667
$37$	2.71730	0.446721	0.223361	−	0.974736i	$-0.428297\pi$
$37$	2.71730	0.446721	0.223361	+	0.974736i	$0.428297\pi$
$38$	−1.00000	−0.162221
$39$	2.00000	0.320256
$40$	−3.71730	−0.587757
$41$	4.42638	0.691285	0.345642	−	0.938366i	$-0.387661\pi$
$41$	4.42638	0.691285	0.345642	+	0.938366i	$0.387661\pi$
$42$	0	0
$43$	−8.26370	−1.26020	−0.630101	−	0.776513i	$-0.716987\pi$
$43$	−8.26370	−1.26020	−0.630101	+	0.776513i	$0.716987\pi$
$44$	−0.383715	−0.0578471
$45$	−3.71730	−0.554142
$46$	7.64741	1.12755
$47$	−3.87177	−0.564755	−0.282378	−	0.959303i	$-0.591123\pi$
$47$	−3.87177	−0.564755	−0.282378	+	0.959303i	$0.591123\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	8.81831	1.24710
$51$	−0.717299	−0.100442
$52$	−2.00000	−0.277350
$53$	6.88820	0.946167	0.473084	−	0.881018i	$-0.343141\pi$
$53$	6.88820	0.946167	0.473084	+	0.881018i	$0.343141\pi$
$54$	−1.00000	−0.136083
$55$	1.42638	0.192333
$56$	0	0
$57$	1.00000	0.132453
$58$	−3.16268	−0.415281
$59$	13.5166	1.75971	0.879856	−	0.475240i	$-0.157639\pi$
$59$	13.5166	1.75971	0.879856	+	0.475240i	$0.157639\pi$
$60$	3.71730	0.479901
$61$	−14.8577	−1.90233	−0.951164	−	0.308686i	$-0.900111\pi$
$61$	−14.8577	−1.90233	−0.951164	+	0.308686i	$0.900111\pi$
$62$	5.65563	0.718266
$63$	0	0
$64$	1.00000	0.125000
$65$	7.43460	0.922148
$66$	0.383715	0.0472320
$67$	−13.3113	−1.62623	−0.813114	−	0.582104i	$-0.802230\pi$
$67$	−13.3113	−1.62623	−0.813114	+	0.582104i	$0.802230\pi$
$68$	0.717299	0.0869853
$69$	−7.64741	−0.920640
$70$	0	0
$71$	−14.1519	−1.67952	−0.839761	−	0.542957i	$-0.817305\pi$
$71$	−14.1519	−1.67952	−0.839761	+	0.542957i	$0.817305\pi$
$72$	1.00000	0.117851
$73$	−1.83732	−0.215042	−0.107521	−	0.994203i	$-0.534291\pi$
$73$	−1.83732	−0.215042	−0.107521	+	0.994203i	$0.534291\pi$
$74$	2.71730	0.315880
$75$	−8.81831	−1.01825
$76$	−1.00000	−0.114708
$77$	0	0
$78$	2.00000	0.226455
$79$	7.36471	0.828595	0.414297	−	0.910142i	$-0.364027\pi$
$79$	7.36471	0.828595	0.414297	+	0.910142i	$0.364027\pi$
$80$	−3.71730	−0.415607
$81$	1.00000	0.111111
$82$	4.42638	0.488812
$83$	−11.2020	−1.22958	−0.614791	−	0.788690i	$-0.710760\pi$
$83$	−11.2020	−1.22958	−0.614791	+	0.788690i	$0.710760\pi$
$84$	0	0
$85$	−2.66642	−0.289213
$86$	−8.26370	−0.891097
$87$	3.16268	0.339075
$88$	−0.383715	−0.0409041
$89$	4.10101	0.434707	0.217353	−	0.976093i	$-0.430258\pi$
$89$	4.10101	0.434707	0.217353	+	0.976093i	$0.430258\pi$
$90$	−3.71730	−0.391838
$91$	0	0
$92$	7.64741	0.797298
$93$	−5.65563	−0.586461
$94$	−3.87177	−0.399342
$95$	3.71730	0.381387
$96$	−1.00000	−0.102062
$97$	3.75664	0.381429	0.190715	−	0.981646i	$-0.438919\pi$
$97$	3.75664	0.381429	0.190715	+	0.981646i	$0.438919\pi$
$98$	0	0
$99$	−0.383715	−0.0385648
$100$	8.81831	0.881831
$101$	−4.31383	−0.429242	−0.214621	−	0.976697i	$-0.568852\pi$
$101$	−4.31383	−0.429242	−0.214621	+	0.976697i	$0.568852\pi$
$102$	−0.717299	−0.0710232
$103$	0.616285	0.0607244	0.0303622	−	0.999539i	$-0.490334\pi$
$103$	0.616285	0.0607244	0.0303622	+	0.999539i	$0.490334\pi$
$104$	−2.00000	−0.196116
$105$	0	0
$106$	6.88820	0.669041
$107$	−8.37293	−0.809441	−0.404721	−	0.914440i	$-0.632631\pi$
$107$	−8.37293	−0.809441	−0.404721	+	0.914440i	$0.632631\pi$
$108$	−1.00000	−0.0962250
$109$	−12.1519	−1.16394	−0.581970	−	0.813210i	$-0.697718\pi$
$109$	−12.1519	−1.16394	−0.581970	+	0.813210i	$0.697718\pi$
$110$	1.42638	0.136000
$111$	−2.71730	−0.257915
$112$	0	0
$113$	4.86844	0.457985	0.228992	−	0.973428i	$-0.426457\pi$
$113$	4.86844	0.457985	0.228992	+	0.973428i	$0.426457\pi$
$114$	1.00000	0.0936586
$115$	−28.4277	−2.65090
$116$	−3.16268	−0.293648
$117$	−2.00000	−0.184900
$118$	13.5166	1.24430
$119$	0	0
$120$	3.71730	0.339341
$121$	−10.8528	−0.986615
$122$	−14.8577	−1.34515
$123$	−4.42638	−0.399113
$124$	5.65563	0.507890
$125$	−14.1938	−1.26953
$126$	0	0
$127$	−3.45360	−0.306458	−0.153229	−	0.988191i	$-0.548967\pi$
$127$	−3.45360	−0.306458	−0.153229	+	0.988191i	$0.548967\pi$
$128$	1.00000	0.0883883
$129$	8.26370	0.727578
$130$	7.43460	0.652057
$131$	0.871766	0.0761666	0.0380833	−	0.999275i	$-0.487875\pi$
$131$	0.871766	0.0761666	0.0380833	+	0.999275i	$0.487875\pi$
$132$	0.383715	0.0333981
$133$	0	0
$134$	−13.3113	−1.14992
$135$	3.71730	0.319934
$136$	0.717299	0.0615079
$137$	10.3138	0.881170	0.440585	−	0.897711i	$-0.354771\pi$
$137$	10.3138	0.881170	0.440585	+	0.897711i	$0.354771\pi$
$138$	−7.64741	−0.650991
$139$	−18.5891	−1.57670	−0.788352	−	0.615224i	$-0.789065\pi$
$139$	−18.5891	−1.57670	−0.788352	+	0.615224i	$0.789065\pi$
$140$	0	0
$141$	3.87177	0.326062
$142$	−14.1519	−1.18760
$143$	0.767429	0.0641756
$144$	1.00000	0.0833333
$145$	11.7566	0.976336
$146$	−1.83732	−0.152057
$147$	0	0
$148$	2.71730	0.223361
$149$	−5.32280	−0.436061	−0.218030	−	0.975942i	$-0.569963\pi$
$149$	−5.32280	−0.436061	−0.218030	+	0.975942i	$0.569963\pi$
$150$	−8.81831	−0.720012
$151$	24.1830	1.96799	0.983993	−	0.178206i	$-0.0570292\pi$
$151$	24.1830	1.96799	0.983993	+	0.178206i	$0.0570292\pi$
$152$	−1.00000	−0.0811107
$153$	0.717299	0.0579902
$154$	0	0
$155$	−21.0237	−1.68866
$156$	2.00000	0.160128
$157$	1.87177	0.149383	0.0746916	−	0.997207i	$-0.476203\pi$
$157$	1.87177	0.149383	0.0746916	+	0.997207i	$0.476203\pi$
$158$	7.36471	0.585905
$159$	−6.88820	−0.546270
$160$	−3.71730	−0.293878
$161$	0	0
$162$	1.00000	0.0785674
$163$	4.77897	0.374318	0.187159	−	0.982330i	$-0.440072\pi$
$163$	4.77897	0.374318	0.187159	+	0.982330i	$0.440072\pi$
$164$	4.42638	0.345642
$165$	−1.42638	−0.111044
$166$	−11.2020	−0.869446
$167$	−14.1519	−1.09511	−0.547553	−	0.836771i	$-0.684441\pi$
$167$	−14.1519	−1.09511	−0.547553	+	0.836771i	$0.684441\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	−2.66642	−0.204505
$171$	−1.00000	−0.0764719
$172$	−8.26370	−0.630101
$173$	−3.04191	−0.231272	−0.115636	−	0.993292i	$-0.536891\pi$
$173$	−3.04191	−0.231272	−0.115636	+	0.993292i	$0.536891\pi$
$174$	3.16268	0.239762
$175$	0	0
$176$	−0.383715	−0.0289236
$177$	−13.5166	−1.01597
$178$	4.10101	0.307384
$179$	−15.1946	−1.13570	−0.567848	−	0.823134i	$-0.692224\pi$
$179$	−15.1946	−1.13570	−0.567848	+	0.823134i	$0.692224\pi$
$180$	−3.71730	−0.277071
$181$	−14.0000	−1.04061	−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000	−1.04061	−0.520306	+	0.853980i	$0.674182\pi$
$182$	0	0
$183$	14.8577	1.09831
$184$	7.64741	0.563775
$185$	−10.1010	−0.742641
$186$	−5.65563	−0.414691
$187$	−0.275238	−0.0201274
$188$	−3.87177	−0.282378
$189$	0	0
$190$	3.71730	0.269681
$191$	0.857656	0.0620578	0.0310289	−	0.999518i	$-0.490122\pi$
$191$	0.857656	0.0620578	0.0310289	+	0.999518i	$0.490122\pi$
$192$	−1.00000	−0.0721688
$193$	−12.7986	−0.921260	−0.460630	−	0.887592i	$-0.652377\pi$
$193$	−12.7986	−0.921260	−0.460630	+	0.887592i	$0.652377\pi$
$194$	3.75664	0.269711
$195$	−7.43460	−0.532403
$196$	0	0
$197$	15.7829	1.12448	0.562242	−	0.826973i	$-0.309939\pi$
$197$	15.7829	1.12448	0.562242	+	0.826973i	$0.309939\pi$
$198$	−0.383715	−0.0272694
$199$	0.879229	0.0623269	0.0311635	−	0.999514i	$-0.490079\pi$
$199$	0.879229	0.0623269	0.0311635	+	0.999514i	$0.490079\pi$
$200$	8.81831	0.623549
$201$	13.3113	0.938904
$202$	−4.31383	−0.303520
$203$	0	0
$204$	−0.717299	−0.0502210
$205$	−16.4542	−1.14921
$206$	0.616285	0.0429386
$207$	7.64741	0.531532
$208$	−2.00000	−0.138675
$209$	0.383715	0.0265421
$210$	0	0
$211$	−22.9702	−1.58133	−0.790667	−	0.612246i	$-0.790266\pi$
$211$	−22.9702	−1.58133	−0.790667	+	0.612246i	$0.790266\pi$
$212$	6.88820	0.473084
$213$	14.1519	0.969672
$214$	−8.37293	−0.572362
$215$	30.7186	2.09499
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−12.1519	−0.823030
$219$	1.83732	0.124154
$220$	1.42638	0.0961666
$221$	−1.43460	−0.0965015
$222$	−2.71730	−0.182373
$223$	−12.6137	−0.844677	−0.422338	−	0.906438i	$-0.638791\pi$
$223$	−12.6137	−0.844677	−0.422338	+	0.906438i	$0.638791\pi$
$224$	0	0
$225$	8.81831	0.587888
$226$	4.86844	0.323844
$227$	23.6678	1.57088	0.785442	−	0.618935i	$-0.212436\pi$
$227$	23.6678	1.57088	0.785442	+	0.618935i	$0.212436\pi$
$228$	1.00000	0.0662266
$229$	13.6202	0.900048	0.450024	−	0.893017i	$-0.351415\pi$
$229$	13.6202	0.900048	0.450024	+	0.893017i	$0.351415\pi$
$230$	−28.4277	−1.87447
$231$	0	0
$232$	−3.16268	−0.207640
$233$	−0.767429	−0.0502759	−0.0251380	−	0.999684i	$-0.508003\pi$
$233$	−0.767429	−0.0502759	−0.0251380	+	0.999684i	$0.508003\pi$
$234$	−2.00000	−0.130744
$235$	14.3925	0.938864
$236$	13.5166	0.879856
$237$	−7.36471	−0.478389
$238$	0	0
$239$	−6.76743	−0.437749	−0.218874	−	0.975753i	$-0.570238\pi$
$239$	−6.76743	−0.437749	−0.218874	+	0.975753i	$0.570238\pi$
$240$	3.71730	0.239951
$241$	−0.647412	−0.0417035	−0.0208517	−	0.999783i	$-0.506638\pi$
$241$	−0.647412	−0.0417035	−0.0208517	+	0.999783i	$0.506638\pi$
$242$	−10.8528	−0.697642
$243$	−1.00000	−0.0641500
$244$	−14.8577	−0.951164
$245$	0	0
$246$	−4.42638	−0.282216
$247$	2.00000	0.127257
$248$	5.65563	0.359133
$249$	11.2020	0.709900
$250$	−14.1938	−0.897695
$251$	18.2224	1.15019	0.575093	−	0.818088i	$-0.304966\pi$
$251$	18.2224	1.15019	0.575093	+	0.818088i	$0.304966\pi$
$252$	0	0
$253$	−2.93442	−0.184486
$254$	−3.45360	−0.216698
$255$	2.66642	0.166977
$256$	1.00000	0.0625000
$257$	6.65074	0.414862	0.207431	−	0.978250i	$-0.433490\pi$
$257$	6.65074	0.414862	0.207431	+	0.978250i	$0.433490\pi$
$258$	8.26370	0.514475
$259$	0	0
$260$	7.43460	0.461074
$261$	−3.16268	−0.195765
$262$	0.871766	0.0538579
$263$	−24.1417	−1.48864	−0.744320	−	0.667823i	$-0.767226\pi$
$263$	−24.1417	−1.48864	−0.744320	+	0.667823i	$0.767226\pi$
$264$	0.383715	0.0236160
$265$	−25.6055	−1.57293
$266$	0	0
$267$	−4.10101	−0.250978
$268$	−13.3113	−0.813114
$269$	6.13214	0.373883	0.186942	−	0.982371i	$-0.440142\pi$
$269$	6.13214	0.373883	0.186942	+	0.982371i	$0.440142\pi$
$270$	3.71730	0.226228
$271$	5.51527	0.335029	0.167514	−	0.985870i	$-0.446426\pi$
$271$	5.51527	0.335029	0.167514	+	0.985870i	$0.446426\pi$
$272$	0.717299	0.0434926
$273$	0	0
$274$	10.3138	0.623081
$275$	−3.38371	−0.204046
$276$	−7.64741	−0.460320
$277$	−18.6399	−1.11997	−0.559983	−	0.828504i	$-0.689192\pi$
$277$	−18.6399	−1.11997	−0.559983	+	0.828504i	$0.689192\pi$
$278$	−18.5891	−1.11490
$279$	5.65563	0.338594
$280$	0	0
$281$	−24.2643	−1.44749	−0.723743	−	0.690070i	$-0.757580\pi$
$281$	−24.2643	−1.44749	−0.723743	+	0.690070i	$0.757580\pi$
$282$	3.87177	0.230560
$283$	−11.1545	−0.663064	−0.331532	−	0.943444i	$-0.607566\pi$
$283$	−11.1545	−0.663064	−0.331532	+	0.943444i	$0.607566\pi$
$284$	−14.1519	−0.839761
$285$	−3.71730	−0.220194
$286$	0.767429	0.0453790
$287$	0	0
$288$	1.00000	0.0589256
$289$	−16.4855	−0.969734
$290$	11.7566	0.690374
$291$	−3.75664	−0.220218
$292$	−1.83732	−0.107521
$293$	17.3811	1.01542	0.507709	−	0.861529i	$-0.330493\pi$
$293$	17.3811	1.01542	0.507709	+	0.861529i	$0.330493\pi$
$294$	0	0
$295$	−50.2453	−2.92539
$296$	2.71730	0.157940
$297$	0.383715	0.0222654
$298$	−5.32280	−0.308341
$299$	−15.2948	−0.884523
$300$	−8.81831	−0.509126
$301$	0	0
$302$	24.1830	1.39158
$303$	4.31383	0.247823
$304$	−1.00000	−0.0573539
$305$	55.2304	3.16248
$306$	0.717299	0.0410053
$307$	−30.6068	−1.74682	−0.873412	−	0.486982i	$-0.838098\pi$
$307$	−30.6068	−1.74682	−0.873412	+	0.486982i	$0.838098\pi$
$308$	0	0
$309$	−0.616285	−0.0350593
$310$	−21.0237	−1.19406
$311$	−29.3743	−1.66566	−0.832831	−	0.553528i	$-0.813281\pi$
$311$	−29.3743	−1.66566	−0.832831	+	0.553528i	$0.813281\pi$
$312$	2.00000	0.113228
$313$	−19.0293	−1.07560	−0.537800	−	0.843072i	$-0.680744\pi$
$313$	−19.0293	−1.07560	−0.537800	+	0.843072i	$0.680744\pi$
$314$	1.87177	0.105630
$315$	0	0
$316$	7.36471	0.414297
$317$	18.2848	1.02698	0.513488	−	0.858097i	$-0.328353\pi$
$317$	18.2848	1.02698	0.513488	+	0.858097i	$0.328353\pi$
$318$	−6.88820	−0.386271
$319$	1.21357	0.0679467
$320$	−3.71730	−0.207803
$321$	8.37293	0.467331
$322$	0	0
$323$	−0.717299	−0.0399116
$324$	1.00000	0.0555556
$325$	−17.6366	−0.978304
$326$	4.77897	0.264683
$327$	12.1519	0.672001
$328$	4.42638	0.244406
$329$	0	0
$330$	−1.42638	−0.0785197
$331$	7.21024	0.396311	0.198155	−	0.980171i	$-0.436505\pi$
$331$	7.21024	0.396311	0.198155	+	0.980171i	$0.436505\pi$
$332$	−11.2020	−0.614791
$333$	2.71730	0.148907
$334$	−14.1519	−0.774357
$335$	49.4819	2.70349
$336$	0	0
$337$	−4.56873	−0.248874	−0.124437	−	0.992227i	$-0.539713\pi$
$337$	−4.56873	−0.248874	−0.124437	+	0.992227i	$0.539713\pi$
$338$	−9.00000	−0.489535
$339$	−4.86844	−0.264418
$340$	−2.66642	−0.144607
$341$	−2.17015	−0.117520
$342$	−1.00000	−0.0540738
$343$	0	0
$344$	−8.26370	−0.445549
$345$	28.4277	1.53050
$346$	−3.04191	−0.163534
$347$	16.2414	0.871882	0.435941	−	0.899975i	$-0.356416\pi$
$347$	16.2414	0.871882	0.435941	+	0.899975i	$0.356416\pi$
$348$	3.16268	0.169538
$349$	−31.4189	−1.68182	−0.840908	−	0.541178i	$-0.817979\pi$
$349$	−31.4189	−1.68182	−0.840908	+	0.541178i	$0.817979\pi$
$350$	0	0
$351$	2.00000	0.106752
$352$	−0.383715	−0.0204521
$353$	−6.70087	−0.356651	−0.178326	−	0.983972i	$-0.557068\pi$
$353$	−6.70087	−0.356651	−0.178326	+	0.983972i	$0.557068\pi$
$354$	−13.5166	−0.718400
$355$	52.6068	2.79208
$356$	4.10101	0.217353
$357$	0	0
$358$	−15.1946	−0.803058
$359$	−25.1666	−1.32824	−0.664121	−	0.747625i	$-0.731194\pi$
$359$	−25.1666	−1.32824	−0.664121	+	0.747625i	$0.731194\pi$
$360$	−3.71730	−0.195919
$361$	1.00000	0.0526316
$362$	−14.0000	−0.735824
$363$	10.8528	0.569622
$364$	0	0
$365$	6.82985	0.357491
$366$	14.8577	0.776622
$367$	25.0237	1.30622	0.653112	−	0.757261i	$-0.273463\pi$
$367$	25.0237	1.30622	0.653112	+	0.757261i	$0.273463\pi$
$368$	7.64741	0.398649
$369$	4.42638	0.230428
$370$	−10.1010	−0.525127
$371$	0	0
$372$	−5.65563	−0.293231
$373$	36.1260	1.87053	0.935267	−	0.353943i	$-0.115159\pi$
$373$	36.1260	1.87053	0.935267	+	0.353943i	$0.115159\pi$
$374$	−0.275238	−0.0142322
$375$	14.1938	0.732965
$376$	−3.87177	−0.199671
$377$	6.32537	0.325773
$378$	0	0
$379$	−9.23257	−0.474245	−0.237123	−	0.971480i	$-0.576204\pi$
$379$	−9.23257	−0.474245	−0.237123	+	0.971480i	$0.576204\pi$
$380$	3.71730	0.190693
$381$	3.45360	0.176933
$382$	0.857656	0.0438815
$383$	−25.5822	−1.30719	−0.653594	−	0.756845i	$-0.726740\pi$
$383$	−25.5822	−1.30719	−0.653594	+	0.756845i	$0.726740\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−12.7986	−0.651429
$387$	−8.26370	−0.420067
$388$	3.75664	0.190715
$389$	27.5364	1.39615	0.698075	−	0.716025i	$-0.254040\pi$
$389$	27.5364	1.39615	0.698075	+	0.716025i	$0.254040\pi$
$390$	−7.43460	−0.376466
$391$	5.48548	0.277413
$392$	0	0
$393$	−0.871766	−0.0439748
$394$	15.7829	0.795130
$395$	−27.3768	−1.37748
$396$	−0.383715	−0.0192824
$397$	−7.98357	−0.400684	−0.200342	−	0.979726i	$-0.564205\pi$
$397$	−7.98357	−0.400684	−0.200342	+	0.979726i	$0.564205\pi$
$398$	0.879229	0.0440718
$399$	0	0
$400$	8.81831	0.440916
$401$	−32.0853	−1.60227	−0.801133	−	0.598487i	$-0.795769\pi$
$401$	−32.0853	−1.60227	−0.801133	+	0.598487i	$0.795769\pi$
$402$	13.3113	0.663905
$403$	−11.3113	−0.563454
$404$	−4.31383	−0.214621
$405$	−3.71730	−0.184714
$406$	0	0
$407$	−1.04267	−0.0516831
$408$	−0.717299	−0.0355116
$409$	−12.9728	−0.641463	−0.320731	−	0.947170i	$-0.603929\pi$
$409$	−12.9728	−0.641463	−0.320731	+	0.947170i	$0.603929\pi$
$410$	−16.4542	−0.812614
$411$	−10.3138	−0.508744
$412$	0.616285	0.0303622
$413$	0	0
$414$	7.64741	0.375850
$415$	41.6413	2.04409
$416$	−2.00000	−0.0980581
$417$	18.5891	0.910310
$418$	0.383715	0.0187681
$419$	36.7688	1.79627	0.898136	−	0.439718i	$-0.144922\pi$
$419$	36.7688	1.79627	0.898136	+	0.439718i	$0.144922\pi$
$420$	0	0
$421$	2.60608	0.127013	0.0635063	−	0.997981i	$-0.479772\pi$
$421$	2.60608	0.127013	0.0635063	+	0.997981i	$0.479772\pi$
$422$	−22.9702	−1.11817
$423$	−3.87177	−0.188252
$424$	6.88820	0.334521
$425$	6.32537	0.306825
$426$	14.1519	0.685662
$427$	0	0
$428$	−8.37293	−0.404721
$429$	−0.767429	−0.0370518
$430$	30.7186	1.48138
$431$	−11.1378	−0.536488	−0.268244	−	0.963351i	$-0.586443\pi$
$431$	−11.1378	−0.536488	−0.268244	+	0.963351i	$0.586443\pi$
$432$	−1.00000	−0.0481125
$433$	−6.80188	−0.326877	−0.163439	−	0.986553i	$-0.552259\pi$
$433$	−6.80188	−0.326877	−0.163439	+	0.986553i	$0.552259\pi$
$434$	0	0
$435$	−11.7566	−0.563688
$436$	−12.1519	−0.581970
$437$	−7.64741	−0.365825
$438$	1.83732	0.0877904
$439$	36.8846	1.76041	0.880204	−	0.474596i	$-0.157406\pi$
$439$	36.8846	1.76041	0.880204	+	0.474596i	$0.157406\pi$
$440$	1.42638	0.0680001
$441$	0	0
$442$	−1.43460	−0.0682369
$443$	−6.37368	−0.302823	−0.151411	−	0.988471i	$-0.548382\pi$
$443$	−6.37368	−0.302823	−0.151411	+	0.988471i	$0.548382\pi$
$444$	−2.71730	−0.128957
$445$	−15.2447	−0.722668
$446$	−12.6137	−0.597277
$447$	5.32280	0.251760
$448$	0	0
$449$	−13.7212	−0.647544	−0.323772	−	0.946135i	$-0.604951\pi$
$449$	−13.7212	−0.647544	−0.323772	+	0.946135i	$0.604951\pi$
$450$	8.81831	0.415699
$451$	−1.69847	−0.0799777
$452$	4.86844	0.228992
$453$	−24.1830	−1.13622
$454$	23.6678	1.11078
$455$	0	0
$456$	1.00000	0.0468293
$457$	−30.4690	−1.42528	−0.712641	−	0.701529i	$-0.752501\pi$
$457$	−30.4690	−1.42528	−0.712641	+	0.701529i	$0.752501\pi$
$458$	13.6202	0.636430
$459$	−0.717299	−0.0334807
$460$	−28.4277	−1.32545
$461$	1.66974	0.0777675	0.0388838	−	0.999244i	$-0.487620\pi$
$461$	1.66974	0.0777675	0.0388838	+	0.999244i	$0.487620\pi$
$462$	0	0
$463$	11.1208	0.516826	0.258413	−	0.966035i	$-0.416800\pi$
$463$	11.1208	0.516826	0.258413	+	0.966035i	$0.416800\pi$
$464$	−3.16268	−0.146824
$465$	21.0237	0.974949
$466$	−0.767429	−0.0355505
$467$	5.82088	0.269358	0.134679	−	0.990889i	$-0.457000\pi$
$467$	5.82088	0.269358	0.134679	+	0.990889i	$0.457000\pi$
$468$	−2.00000	−0.0924500
$469$	0	0
$470$	14.3925	0.663877
$471$	−1.87177	−0.0862464
$472$	13.5166	0.622152
$473$	3.17090	0.145798
$474$	−7.36471	−0.338272
$475$	−8.81831	−0.404612
$476$	0	0
$477$	6.88820	0.315389
$478$	−6.76743	−0.309535
$479$	33.0597	1.51054	0.755268	−	0.655416i	$-0.227507\pi$
$479$	33.0597	1.51054	0.755268	+	0.655416i	$0.227507\pi$
$480$	3.71730	0.169671
$481$	−5.43460	−0.247796
$482$	−0.647412	−0.0294888
$483$	0	0
$484$	−10.8528	−0.493307
$485$	−13.9646	−0.634098
$486$	−1.00000	−0.0453609
$487$	−27.2758	−1.23599	−0.617993	−	0.786184i	$-0.712054\pi$
$487$	−27.2758	−1.23599	−0.617993	+	0.786184i	$0.712054\pi$
$488$	−14.8577	−0.672574
$489$	−4.77897	−0.216112
$490$	0	0
$491$	29.8692	1.34798	0.673989	−	0.738741i	$-0.264580\pi$
$491$	29.8692	1.34798	0.673989	+	0.738741i	$0.264580\pi$
$492$	−4.42638	−0.199557
$493$	−2.26859	−0.102172
$494$	2.00000	0.0899843
$495$	1.42638	0.0641111
$496$	5.65563	0.253945
$497$	0	0
$498$	11.2020	0.501975
$499$	−32.3940	−1.45016	−0.725078	−	0.688667i	$-0.758196\pi$
$499$	−32.3940	−1.45016	−0.725078	+	0.688667i	$0.758196\pi$
$500$	−14.1938	−0.634767
$501$	14.1519	0.632260
$502$	18.2224	0.813304
$503$	−36.5573	−1.63001	−0.815004	−	0.579455i	$-0.803266\pi$
$503$	−36.5573	−1.63001	−0.815004	+	0.579455i	$0.803266\pi$
$504$	0	0
$505$	16.0358	0.713583
$506$	−2.93442	−0.130451
$507$	9.00000	0.399704
$508$	−3.45360	−0.153229
$509$	−32.1336	−1.42430	−0.712149	−	0.702028i	$-0.752278\pi$
$509$	−32.1336	−1.42430	−0.712149	+	0.702028i	$0.752278\pi$
$510$	2.66642	0.118071
$511$	0	0
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	6.65074	0.293351
$515$	−2.29092	−0.100950
$516$	8.26370	0.363789
$517$	1.48565	0.0653389
$518$	0	0
$519$	3.04191	0.133525
$520$	7.43460	0.326029
$521$	−16.4041	−0.718675	−0.359337	−	0.933208i	$-0.616997\pi$
$521$	−16.4041	−0.718675	−0.359337	+	0.933208i	$0.616997\pi$
$522$	−3.16268	−0.138427
$523$	−14.4671	−0.632600	−0.316300	−	0.948659i	$-0.602441\pi$
$523$	−14.4671	−0.632600	−0.316300	+	0.948659i	$0.602441\pi$
$524$	0.871766	0.0380833
$525$	0	0
$526$	−24.1417	−1.05263
$527$	4.05678	0.176716
$528$	0.383715	0.0166990
$529$	35.4829	1.54274
$530$	−25.6055	−1.11223
$531$	13.5166	0.586571
$532$	0	0
$533$	−8.85276	−0.383456
$534$	−4.10101	−0.177468
$535$	31.1247	1.34564
$536$	−13.3113	−0.574959
$537$	15.1946	0.655694
$538$	6.13214	0.264375
$539$	0	0
$540$	3.71730	0.159967
$541$	−11.3385	−0.487479	−0.243740	−	0.969841i	$-0.578374\pi$
$541$	−11.3385	−0.487479	−0.243740	+	0.969841i	$0.578374\pi$
$542$	5.51527	0.236901
$543$	14.0000	0.600798
$544$	0.717299	0.0307539
$545$	45.1722	1.93497
$546$	0	0
$547$	21.3794	0.914117	0.457059	−	0.889437i	$-0.348903\pi$
$547$	21.3794	0.914117	0.457059	+	0.889437i	$0.348903\pi$
$548$	10.3138	0.440585
$549$	−14.8577	−0.634109
$550$	−3.38371	−0.144282
$551$	3.16268	0.134735
$552$	−7.64741	−0.325495
$553$	0	0
$554$	−18.6399	−0.791936
$555$	10.1010	0.428764
$556$	−18.5891	−0.788352
$557$	36.9561	1.56588	0.782940	−	0.622097i	$-0.213719\pi$
$557$	36.9561	1.56588	0.782940	+	0.622097i	$0.213719\pi$
$558$	5.65563	0.239422
$559$	16.5274	0.699034
$560$	0	0
$561$	0.275238	0.0116206
$562$	−24.2643	−1.02353
$563$	−6.68542	−0.281757	−0.140878	−	0.990027i	$-0.544993\pi$
$563$	−6.68542	−0.281757	−0.140878	+	0.990027i	$0.544993\pi$
$564$	3.87177	0.163031
$565$	−18.0975	−0.761366
$566$	−11.1545	−0.468857
$567$	0	0
$568$	−14.1519	−0.593800
$569$	11.0548	0.463441	0.231720	−	0.972782i	$-0.425565\pi$
$569$	11.0548	0.463441	0.231720	+	0.972782i	$0.425565\pi$
$570$	−3.71730	−0.155701
$571$	10.9931	0.460048	0.230024	−	0.973185i	$-0.426120\pi$
$571$	10.9931	0.460048	0.230024	+	0.973185i	$0.426120\pi$
$572$	0.767429	0.0320878
$573$	−0.857656	−0.0358291
$574$	0	0
$575$	67.4373	2.81233
$576$	1.00000	0.0416667
$577$	−8.63663	−0.359547	−0.179774	−	0.983708i	$-0.557537\pi$
$577$	−8.63663	−0.359547	−0.179774	+	0.983708i	$0.557537\pi$
$578$	−16.4855	−0.685706
$579$	12.7986	0.531890
$580$	11.7566	0.488168
$581$	0	0
$582$	−3.75664	−0.155718
$583$	−2.64310	−0.109466
$584$	−1.83732	−0.0760287
$585$	7.43460	0.307383
$586$	17.3811	0.718008
$587$	14.4117	0.594834	0.297417	−	0.954748i	$-0.403875\pi$
$587$	14.4117	0.594834	0.297417	+	0.954748i	$0.403875\pi$
$588$	0	0
$589$	−5.65563	−0.233036
$590$	−50.2453	−2.06857
$591$	−15.7829	−0.649221
$592$	2.71730	0.111680
$593$	17.5871	0.722215	0.361107	−	0.932524i	$-0.382399\pi$
$593$	17.5871	0.722215	0.361107	+	0.932524i	$0.382399\pi$
$594$	0.383715	0.0157440
$595$	0	0
$596$	−5.32280	−0.218030
$597$	−0.879229	−0.0359845
$598$	−15.2948	−0.625452
$599$	−11.1824	−0.456902	−0.228451	−	0.973555i	$-0.573366\pi$
$599$	−11.1824	−0.456902	−0.228451	+	0.973555i	$0.573366\pi$
$600$	−8.81831	−0.360006
$601$	35.1748	1.43481	0.717405	−	0.696656i	$-0.245330\pi$
$601$	35.1748	1.43481	0.717405	+	0.696656i	$0.245330\pi$
$602$	0	0
$603$	−13.3113	−0.542076
$604$	24.1830	0.983993
$605$	40.3430	1.64017
$606$	4.31383	0.175237
$607$	−21.8921	−0.888573	−0.444287	−	0.895885i	$-0.646543\pi$
$607$	−21.8921	−0.888573	−0.444287	+	0.895885i	$0.646543\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	55.2304	2.23621
$611$	7.74353	0.313270
$612$	0.717299	0.0289951
$613$	−27.7607	−1.12124	−0.560622	−	0.828072i	$-0.689438\pi$
$613$	−27.7607	−1.12124	−0.560622	+	0.828072i	$0.689438\pi$
$614$	−30.6068	−1.23519
$615$	16.4542	0.663497
$616$	0	0
$617$	14.0617	0.566102	0.283051	−	0.959105i	$-0.408654\pi$
$617$	14.0617	0.566102	0.283051	+	0.959105i	$0.408654\pi$
$618$	−0.616285	−0.0247906
$619$	19.7551	0.794023	0.397012	−	0.917814i	$-0.370047\pi$
$619$	19.7551	0.794023	0.397012	+	0.917814i	$0.370047\pi$
$620$	−21.0237	−0.844331
$621$	−7.64741	−0.306880
$622$	−29.3743	−1.17780
$623$	0	0
$624$	2.00000	0.0800641
$625$	8.67108	0.346843
$626$	−19.0293	−0.760564
$627$	−0.383715	−0.0153241
$628$	1.87177	0.0746916
$629$	1.94912	0.0777164
$630$	0	0
$631$	9.47062	0.377019	0.188510	−	0.982071i	$-0.439634\pi$
$631$	9.47062	0.377019	0.188510	+	0.982071i	$0.439634\pi$
$632$	7.36471	0.292952
$633$	22.9702	0.912984
$634$	18.2848	0.726182
$635$	12.8381	0.509463
$636$	−6.88820	−0.273135
$637$	0	0
$638$	1.21357	0.0480456
$639$	−14.1519	−0.559840
$640$	−3.71730	−0.146939
$641$	37.6374	1.48659	0.743294	−	0.668965i	$-0.233263\pi$
$641$	37.6374	1.48659	0.743294	+	0.668965i	$0.233263\pi$
$642$	8.37293	0.330453
$643$	23.3680	0.921545	0.460773	−	0.887518i	$-0.347572\pi$
$643$	23.3680	0.921545	0.460773	+	0.887518i	$0.347572\pi$
$644$	0	0
$645$	−30.7186	−1.20955
$646$	−0.717299	−0.0282218
$647$	21.5852	0.848600	0.424300	−	0.905522i	$-0.360520\pi$
$647$	21.5852	0.848600	0.424300	+	0.905522i	$0.360520\pi$
$648$	1.00000	0.0392837
$649$	−5.18652	−0.203589
$650$	−17.6366	−0.691765
$651$	0	0
$652$	4.77897	0.187159
$653$	20.8710	0.816746	0.408373	−	0.912815i	$-0.366096\pi$
$653$	20.8710	0.816746	0.408373	+	0.912815i	$0.366096\pi$
$654$	12.1519	0.475177
$655$	−3.24062	−0.126621
$656$	4.42638	0.172821
$657$	−1.83732	−0.0716805
$658$	0	0
$659$	42.4169	1.65233	0.826165	−	0.563429i	$-0.190518\pi$
$659$	42.4169	1.65233	0.826165	+	0.563429i	$0.190518\pi$
$660$	−1.42638	−0.0555218
$661$	22.4557	0.873425	0.436713	−	0.899601i	$-0.356143\pi$
$661$	22.4557	0.873425	0.436713	+	0.899601i	$0.356143\pi$
$662$	7.21024	0.280234
$663$	1.43460	0.0557152
$664$	−11.2020	−0.434723
$665$	0	0
$666$	2.71730	0.105293
$667$	−24.1863	−0.936499
$668$	−14.1519	−0.547553
$669$	12.6137	0.487674
$670$	49.4819	1.91165
$671$	5.70110	0.220088
$672$	0	0
$673$	22.2727	0.858548	0.429274	−	0.903174i	$-0.358769\pi$
$673$	22.2727	0.858548	0.429274	+	0.903174i	$0.358769\pi$
$674$	−4.56873	−0.175981
$675$	−8.81831	−0.339417
$676$	−9.00000	−0.346154
$677$	−38.4704	−1.47854	−0.739269	−	0.673411i	$-0.764829\pi$
$677$	−38.4704	−1.47854	−0.739269	+	0.673411i	$0.764829\pi$
$678$	−4.86844	−0.186971
$679$	0	0
$680$	−2.66642	−0.102252
$681$	−23.6678	−0.906950
$682$	−2.17015	−0.0830992
$683$	−15.3326	−0.586686	−0.293343	−	0.956007i	$-0.594768\pi$
$683$	−15.3326	−0.586686	−0.293343	+	0.956007i	$0.594768\pi$
$684$	−1.00000	−0.0382360
$685$	−38.3396	−1.46488
$686$	0	0
$687$	−13.6202	−0.519643
$688$	−8.26370	−0.315051
$689$	−13.7764	−0.524839
$690$	28.4277	1.08222
$691$	40.7646	1.55076	0.775380	−	0.631495i	$-0.217558\pi$
$691$	40.7646	1.55076	0.775380	+	0.631495i	$0.217558\pi$
$692$	−3.04191	−0.115636
$693$	0	0
$694$	16.2414	0.616514
$695$	69.1011	2.62115
$696$	3.16268	0.119881
$697$	3.17504	0.120263
$698$	−31.4189	−1.18922
$699$	0.767429	0.0290268
$700$	0	0
$701$	17.8915	0.675754	0.337877	−	0.941190i	$-0.390291\pi$
$701$	17.8915	0.675754	0.337877	+	0.941190i	$0.390291\pi$
$702$	2.00000	0.0754851
$703$	−2.71730	−0.102485
$704$	−0.383715	−0.0144618
$705$	−14.3925	−0.542053
$706$	−6.70087	−0.252190
$707$	0	0
$708$	−13.5166	−0.507985
$709$	−28.0350	−1.05288	−0.526439	−	0.850213i	$-0.676473\pi$
$709$	−28.0350	−1.05288	−0.526439	+	0.850213i	$0.676473\pi$
$710$	52.6068	1.97430
$711$	7.36471	0.276198
$712$	4.10101	0.153692
$713$	43.2509	1.61976
$714$	0	0
$715$	−2.85276	−0.106687
$716$	−15.1946	−0.567848
$717$	6.76743	0.252734
$718$	−25.1666	−0.939209
$719$	−42.7309	−1.59359	−0.796797	−	0.604247i	$-0.793474\pi$
$719$	−42.7309	−1.59359	−0.796797	+	0.604247i	$0.793474\pi$
$720$	−3.71730	−0.138536
$721$	0	0
$722$	1.00000	0.0372161
$723$	0.647412	0.0240775
$724$	−14.0000	−0.520306
$725$	−27.8895	−1.03579
$726$	10.8528	0.402784
$727$	25.5724	0.948427	0.474214	−	0.880410i	$-0.342732\pi$
$727$	25.5724	0.948427	0.474214	+	0.880410i	$0.342732\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	6.82985	0.252784
$731$	−5.92754	−0.219238
$732$	14.8577	0.549155
$733$	49.4530	1.82659	0.913293	−	0.407303i	$-0.133531\pi$
$733$	49.4530	1.82659	0.913293	+	0.407303i	$0.133531\pi$
$734$	25.0237	0.923640
$735$	0	0
$736$	7.64741	0.281887
$737$	5.10772	0.188145
$738$	4.42638	0.162937
$739$	−39.4632	−1.45168	−0.725838	−	0.687866i	$-0.758548\pi$
$739$	−39.4632	−1.45168	−0.725838	+	0.687866i	$0.758548\pi$
$740$	−10.1010	−0.371321
$741$	−2.00000	−0.0734718
$742$	0	0
$743$	48.6061	1.78318	0.891592	−	0.452839i	$-0.149589\pi$
$743$	48.6061	1.78318	0.891592	+	0.452839i	$0.149589\pi$
$744$	−5.65563	−0.207345
$745$	19.7864	0.724919
$746$	36.1260	1.32267
$747$	−11.2020	−0.409861
$748$	−0.275238	−0.0100637
$749$	0	0
$750$	14.1938	0.518285
$751$	42.4195	1.54791	0.773955	−	0.633241i	$-0.218276\pi$
$751$	42.4195	1.54791	0.773955	+	0.633241i	$0.218276\pi$
$752$	−3.87177	−0.141189
$753$	−18.2224	−0.664060
$754$	6.32537	0.230356
$755$	−89.8955	−3.27163
$756$	0	0
$757$	2.91285	0.105869	0.0529347	−	0.998598i	$-0.483142\pi$
$757$	2.91285	0.105869	0.0529347	+	0.998598i	$0.483142\pi$
$758$	−9.23257	−0.335342
$759$	2.93442	0.106513
$760$	3.71730	0.134841
$761$	−26.2084	−0.950055	−0.475027	−	0.879971i	$-0.657562\pi$
$761$	−26.2084	−0.950055	−0.475027	+	0.879971i	$0.657562\pi$
$762$	3.45360	0.125111
$763$	0	0
$764$	0.857656	0.0310289
$765$	−2.66642	−0.0964045
$766$	−25.5822	−0.924322
$767$	−27.0332	−0.976113
$768$	−1.00000	−0.0360844
$769$	9.09670	0.328036	0.164018	−	0.986457i	$-0.447555\pi$
$769$	9.09670	0.328036	0.164018	+	0.986457i	$0.447555\pi$
$770$	0	0
$771$	−6.65074	−0.239520
$772$	−12.7986	−0.460630
$773$	15.5924	0.560819	0.280410	−	0.959880i	$-0.409530\pi$
$773$	15.5924	0.560819	0.280410	+	0.959880i	$0.409530\pi$
$774$	−8.26370	−0.297032
$775$	49.8731	1.79149
$776$	3.75664	0.134856
$777$	0	0
$778$	27.5364	0.987227
$779$	−4.42638	−0.158592
$780$	−7.43460	−0.266201
$781$	5.43029	0.194311
$782$	5.48548	0.196160
$783$	3.16268	0.113025
$784$	0	0
$785$	−6.95792	−0.248339
$786$	−0.871766	−0.0310949
$787$	−12.4651	−0.444334	−0.222167	−	0.975009i	$-0.571313\pi$
$787$	−12.4651	−0.444334	−0.222167	+	0.975009i	$0.571313\pi$
$788$	15.7829	0.562242
$789$	24.1417	0.859467
$790$	−27.3768	−0.974024
$791$	0	0
$792$	−0.383715	−0.0136347
$793$	29.7153	1.05522
$794$	−7.98357	−0.283326
$795$	25.6055	0.908133
$796$	0.879229	0.0311635
$797$	−36.6544	−1.29837	−0.649183	−	0.760633i	$-0.724889\pi$
$797$	−36.6544	−1.29837	−0.649183	+	0.760633i	$0.724889\pi$
$798$	0	0
$799$	−2.77721	−0.0982508
$800$	8.81831	0.311774
$801$	4.10101	0.144902
$802$	−32.0853	−1.13297
$803$	0.705005	0.0248791
$804$	13.3113	0.469452
$805$	0	0
$806$	−11.3113	−0.398422
$807$	−6.13214	−0.215862
$808$	−4.31383	−0.151760
$809$	−28.8862	−1.01559	−0.507793	−	0.861479i	$-0.669538\pi$
$809$	−28.8862	−1.01559	−0.507793	+	0.861479i	$0.669538\pi$
$810$	−3.71730	−0.130613
$811$	10.1190	0.355325	0.177662	−	0.984092i	$-0.443147\pi$
$811$	10.1190	0.355325	0.177662	+	0.984092i	$0.443147\pi$
$812$	0	0
$813$	−5.51527	−0.193429
$814$	−1.04267	−0.0365455
$815$	−17.7649	−0.622276
$816$	−0.717299	−0.0251105
$817$	8.26370	0.289110
$818$	−12.9728	−0.453583
$819$	0	0
$820$	−16.4542	−0.574605
$821$	−30.5814	−1.06730	−0.533650	−	0.845706i	$-0.679180\pi$
$821$	−30.5814	−1.06730	−0.533650	+	0.845706i	$0.679180\pi$
$822$	−10.3138	−0.359736
$823$	40.4563	1.41022	0.705109	−	0.709099i	$-0.250898\pi$
$823$	40.4563	1.41022	0.705109	+	0.709099i	$0.250898\pi$
$824$	0.616285	0.0214693
$825$	3.38371	0.117806
$826$	0	0
$827$	3.07969	0.107091	0.0535456	−	0.998565i	$-0.482948\pi$
$827$	3.07969	0.107091	0.0535456	+	0.998565i	$0.482948\pi$
$828$	7.64741	0.265766
$829$	19.5199	0.677955	0.338978	−	0.940794i	$-0.389919\pi$
$829$	19.5199	0.677955	0.338978	+	0.940794i	$0.389919\pi$
$830$	41.6413	1.44539
$831$	18.6399	0.646613
$832$	−2.00000	−0.0693375
$833$	0	0
$834$	18.5891	0.643687
$835$	52.6068	1.82053
$836$	0.383715	0.0132710
$837$	−5.65563	−0.195487
$838$	36.7688	1.27016
$839$	−5.46315	−0.188609	−0.0943045	−	0.995543i	$-0.530063\pi$
$839$	−5.46315	−0.188609	−0.0943045	+	0.995543i	$0.530063\pi$
$840$	0	0
$841$	−18.9974	−0.655084
$842$	2.60608	0.0898115
$843$	24.2643	0.835706
$844$	−22.9702	−0.790667
$845$	33.4557	1.15091
$846$	−3.87177	−0.133114
$847$	0	0
$848$	6.88820	0.236542
$849$	11.1545	0.382820
$850$	6.32537	0.216958
$851$	20.7803	0.712340
$852$	14.1519	0.484836
$853$	−11.8659	−0.406280	−0.203140	−	0.979150i	$-0.565115\pi$
$853$	−11.8659	−0.406280	−0.203140	+	0.979150i	$0.565115\pi$
$854$	0	0
$855$	3.71730	0.127129
$856$	−8.37293	−0.286181
$857$	−36.4730	−1.24589	−0.622946	−	0.782265i	$-0.714064\pi$
$857$	−36.4730	−1.24589	−0.622946	+	0.782265i	$0.714064\pi$
$858$	−0.767429	−0.0261996
$859$	36.8592	1.25762	0.628809	−	0.777560i	$-0.283543\pi$
$859$	36.8592	1.25762	0.628809	+	0.777560i	$0.283543\pi$
$860$	30.7186	1.04750
$861$	0	0
$862$	−11.1378	−0.379355
$863$	−6.67264	−0.227139	−0.113570	−	0.993530i	$-0.536229\pi$
$863$	−6.67264	−0.227139	−0.113570	+	0.993530i	$0.536229\pi$
$864$	−1.00000	−0.0340207
$865$	11.3077	0.384473
$866$	−6.80188	−0.231137
$867$	16.4855	0.559876
$868$	0	0
$869$	−2.82595	−0.0958637
$870$	−11.7566	−0.398588
$871$	26.6225	0.902070
$872$	−12.1519	−0.411515
$873$	3.75664	0.127143
$874$	−7.64741	−0.258678
$875$	0	0
$876$	1.83732	0.0620772
$877$	−46.2470	−1.56165	−0.780825	−	0.624749i	$-0.785201\pi$
$877$	−46.2470	−1.56165	−0.780825	+	0.624749i	$0.785201\pi$
$878$	36.8846	1.24480
$879$	−17.3811	−0.586251
$880$	1.42638	0.0480833
$881$	−14.5885	−0.491498	−0.245749	−	0.969333i	$-0.579034\pi$
$881$	−14.5885	−0.491498	−0.245749	+	0.969333i	$0.579034\pi$
$882$	0	0
$883$	−56.7595	−1.91011	−0.955054	−	0.296431i	$-0.904204\pi$
$883$	−56.7595	−1.91011	−0.955054	+	0.296431i	$0.904204\pi$
$884$	−1.43460	−0.0482508
$885$	50.2453	1.68898
$886$	−6.37368	−0.214128
$887$	41.6883	1.39975	0.699877	−	0.714263i	$-0.253238\pi$
$887$	41.6883	1.39975	0.699877	+	0.714263i	$0.253238\pi$
$888$	−2.71730	−0.0911866
$889$	0	0
$890$	−15.2447	−0.511003
$891$	−0.383715	−0.0128549
$892$	−12.6137	−0.422338
$893$	3.87177	0.129564
$894$	5.32280	0.178021
$895$	56.4827	1.88801
$896$	0	0
$897$	15.2948	0.510679
$898$	−13.7212	−0.457883
$899$	−17.8870	−0.596564
$900$	8.81831	0.293944
$901$	4.94090	0.164605
$902$	−1.69847	−0.0565528
$903$	0	0
$904$	4.86844	0.161922
$905$	52.0422	1.72994
$906$	−24.1830	−0.803427
$907$	−23.3958	−0.776846	−0.388423	−	0.921481i	$-0.626980\pi$
$907$	−23.3958	−0.776846	−0.388423	+	0.921481i	$0.626980\pi$
$908$	23.6678	0.785442
$909$	−4.31383	−0.143081
$910$	0	0
$911$	−29.5744	−0.979843	−0.489921	−	0.871767i	$-0.662975\pi$
$911$	−29.5744	−0.979843	−0.489921	+	0.871767i	$0.662975\pi$
$912$	1.00000	0.0331133
$913$	4.29838	0.142256
$914$	−30.4690	−1.00783
$915$	−55.2304	−1.82586
$916$	13.6202	0.450024
$917$	0	0
$918$	−0.717299	−0.0236744
$919$	1.63680	0.0539929	0.0269965	−	0.999636i	$-0.491406\pi$
$919$	1.63680	0.0539929	0.0269965	+	0.999636i	$0.491406\pi$
$920$	−28.4277	−0.937234
$921$	30.6068	1.00853
$922$	1.66974	0.0549899
$923$	28.3038	0.931631
$924$	0	0
$925$	23.9620	0.787865
$926$	11.1208	0.365451
$927$	0.616285	0.0202415
$928$	−3.16268	−0.103820
$929$	−1.83656	−0.0602557	−0.0301278	−	0.999546i	$-0.509591\pi$
$929$	−1.83656	−0.0602557	−0.0301278	+	0.999546i	$0.509591\pi$
$930$	21.0237	0.689393
$931$	0	0
$932$	−0.767429	−0.0251380
$933$	29.3743	0.961670
$934$	5.82088	0.190465
$935$	1.02314	0.0334603
$936$	−2.00000	−0.0653720
$937$	−50.0497	−1.63505	−0.817525	−	0.575893i	$-0.804655\pi$
$937$	−50.0497	−1.63505	−0.817525	+	0.575893i	$0.804655\pi$
$938$	0	0
$939$	19.0293	0.620998
$940$	14.3925	0.469432
$941$	−32.8122	−1.06965	−0.534823	−	0.844964i	$-0.679622\pi$
$941$	−32.8122	−1.06965	−0.534823	+	0.844964i	$0.679622\pi$
$942$	−1.87177	−0.0609854
$943$	33.8504	1.10232
$944$	13.5166	0.439928
$945$	0	0
$946$	3.17090	0.103095
$947$	−41.8300	−1.35929	−0.679645	−	0.733541i	$-0.737866\pi$
$947$	−41.8300	−1.35929	−0.679645	+	0.733541i	$0.737866\pi$
$948$	−7.36471	−0.239195
$949$	3.67463	0.119284
$950$	−8.81831	−0.286104
$951$	−18.2848	−0.592925
$952$	0	0
$953$	24.6061	0.797069	0.398535	−	0.917153i	$-0.369519\pi$
$953$	24.6061	0.797069	0.398535	+	0.917153i	$0.369519\pi$
$954$	6.88820	0.223014
$955$	−3.18816	−0.103167
$956$	−6.76743	−0.218874
$957$	−1.21357	−0.0392291
$958$	33.0597	1.06811
$959$	0	0
$960$	3.71730	0.119975
$961$	0.986137	0.0318109
$962$	−5.43460	−0.175218
$963$	−8.37293	−0.269814
$964$	−0.647412	−0.0208517
$965$	47.5761	1.53153
$966$	0	0
$967$	−49.8662	−1.60359	−0.801795	−	0.597599i	$-0.796121\pi$
$967$	−49.8662	−1.60359	−0.801795	+	0.597599i	$0.796121\pi$
$968$	−10.8528	−0.348821
$969$	0.717299	0.0230430
$970$	−13.9646	−0.448375
$971$	9.29664	0.298343	0.149172	−	0.988811i	$-0.452339\pi$
$971$	9.29664	0.298343	0.149172	+	0.988811i	$0.452339\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−27.2758	−0.873974
$975$	17.6366	0.564824
$976$	−14.8577	−0.475582
$977$	−31.1894	−0.997838	−0.498919	−	0.866649i	$-0.666270\pi$
$977$	−31.1894	−0.997838	−0.498919	+	0.866649i	$0.666270\pi$
$978$	−4.77897	−0.152815
$979$	−1.57362	−0.0502931
$980$	0	0
$981$	−12.1519	−0.387980
$982$	29.8692	0.953164
$983$	37.8073	1.20587	0.602933	−	0.797792i	$-0.293999\pi$
$983$	37.8073	1.20587	0.602933	+	0.797792i	$0.293999\pi$
$984$	−4.42638	−0.141108
$985$	−58.6697	−1.86937
$986$	−2.26859	−0.0722466
$987$	0	0
$988$	2.00000	0.0636285
$989$	−63.1959	−2.00951
$990$	1.42638	0.0453334
$991$	−51.4845	−1.63546	−0.817729	−	0.575603i	$-0.804767\pi$
$991$	−51.4845	−1.63546	−0.817729	+	0.575603i	$0.804767\pi$
$992$	5.65563	0.179566
$993$	−7.21024	−0.228810
$994$	0	0
$995$	−3.26836	−0.103614
$996$	11.2020	0.354950
$997$	9.51328	0.301289	0.150644	−	0.988588i	$-0.451865\pi$
$997$	9.51328	0.301289	0.150644	+	0.988588i	$0.451865\pi$
$998$	−32.3940	−1.02541
$999$	−2.71730	−0.0859715

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5586.2.a.ca.1.1		4
7.3	odd	6		798.2.j.k.457.1	✓	8
7.5	odd	6		798.2.j.k.571.1	yes	8
7.6	odd	2		5586.2.a.cb.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.j.k.457.1	✓	8	7.3	odd	6
798.2.j.k.571.1	yes	8	7.5	odd	6
5586.2.a.ca.1.1		4	1.1	even	1	trivial
5586.2.a.cb.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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.71730 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.71730 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -3.71730 q^{10} -0.383715 q^{11} -1.00000 q^{12} -2.00000 q^{13} +3.71730 q^{15} +1.00000 q^{16} +0.717299 q^{17} +1.00000 q^{18} -1.00000 q^{19} -3.71730 q^{20} -0.383715 q^{22} +7.64741 q^{23} -1.00000 q^{24} +8.81831 q^{25} -2.00000 q^{26} -1.00000 q^{27} -3.16268 q^{29} +3.71730 q^{30} +5.65563 q^{31} +1.00000 q^{32} +0.383715 q^{33} +0.717299 q^{34} +1.00000 q^{36} +2.71730 q^{37} -1.00000 q^{38} +2.00000 q^{39} -3.71730 q^{40} +4.42638 q^{41} -8.26370 q^{43} -0.383715 q^{44} -3.71730 q^{45} +7.64741 q^{46} -3.87177 q^{47} -1.00000 q^{48} +8.81831 q^{50} -0.717299 q^{51} -2.00000 q^{52} +6.88820 q^{53} -1.00000 q^{54} +1.42638 q^{55} +1.00000 q^{57} -3.16268 q^{58} +13.5166 q^{59} +3.71730 q^{60} -14.8577 q^{61} +5.65563 q^{62} +1.00000 q^{64} +7.43460 q^{65} +0.383715 q^{66} -13.3113 q^{67} +0.717299 q^{68} -7.64741 q^{69} -14.1519 q^{71} +1.00000 q^{72} -1.83732 q^{73} +2.71730 q^{74} -8.81831 q^{75} -1.00000 q^{76} +2.00000 q^{78} +7.36471 q^{79} -3.71730 q^{80} +1.00000 q^{81} +4.42638 q^{82} -11.2020 q^{83} -2.66642 q^{85} -8.26370 q^{86} +3.16268 q^{87} -0.383715 q^{88} +4.10101 q^{89} -3.71730 q^{90} +7.64741 q^{92} -5.65563 q^{93} -3.87177 q^{94} +3.71730 q^{95} -1.00000 q^{96} +3.75664 q^{97} -0.383715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} - 2 q^{10} - 4 q^{12} - 8 q^{13} + 2 q^{15} + 4 q^{16} - 10 q^{17} + 4 q^{18} - 4 q^{19} - 2 q^{20} + 7 q^{23} - 4 q^{24} + 8 q^{25} - 8 q^{26} - 4 q^{27} - 5 q^{29} + 2 q^{30} + 3 q^{31} + 4 q^{32} - 10 q^{34} + 4 q^{36} - 2 q^{37} - 4 q^{38} + 8 q^{39} - 2 q^{40} - 12 q^{41} - 11 q^{43} - 2 q^{45} + 7 q^{46} + 9 q^{47} - 4 q^{48} + 8 q^{50} + 10 q^{51} - 8 q^{52} + 11 q^{53} - 4 q^{54} - 24 q^{55} + 4 q^{57} - 5 q^{58} - 21 q^{59} + 2 q^{60} - 11 q^{61} + 3 q^{62} + 4 q^{64} + 4 q^{65} - 14 q^{67} - 10 q^{68} - 7 q^{69} - 18 q^{71} + 4 q^{72} - 15 q^{73} - 2 q^{74} - 8 q^{75} - 4 q^{76} + 8 q^{78} - 7 q^{79} - 2 q^{80} + 4 q^{81} - 12 q^{82} - 16 q^{83} - 22 q^{85} - 11 q^{86} + 5 q^{87} + 2 q^{89} - 2 q^{90} + 7 q^{92} - 3 q^{93} + 9 q^{94} + 2 q^{95} - 4 q^{96} - 19 q^{97}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 - 2 * q^10 - 4 * q^12 - 8 * q^13 + 2 * q^15 + 4 * q^16 - 10 * q^17 + 4 * q^18 - 4 * q^19 - 2 * q^20 + 7 * q^23 - 4 * q^24 + 8 * q^25 - 8 * q^26 - 4 * q^27 - 5 * q^29 + 2 * q^30 + 3 * q^31 + 4 * q^32 - 10 * q^34 + 4 * q^36 - 2 * q^37 - 4 * q^38 + 8 * q^39 - 2 * q^40 - 12 * q^41 - 11 * q^43 - 2 * q^45 + 7 * q^46 + 9 * q^47 - 4 * q^48 + 8 * q^50 + 10 * q^51 - 8 * q^52 + 11 * q^53 - 4 * q^54 - 24 * q^55 + 4 * q^57 - 5 * q^58 - 21 * q^59 + 2 * q^60 - 11 * q^61 + 3 * q^62 + 4 * q^64 + 4 * q^65 - 14 * q^67 - 10 * q^68 - 7 * q^69 - 18 * q^71 + 4 * q^72 - 15 * q^73 - 2 * q^74 - 8 * q^75 - 4 * q^76 + 8 * q^78 - 7 * q^79 - 2 * q^80 + 4 * q^81 - 12 * q^82 - 16 * q^83 - 22 * q^85 - 11 * q^86 + 5 * q^87 + 2 * q^89 - 2 * q^90 + 7 * q^92 - 3 * q^93 + 9 * q^94 + 2 * q^95 - 4 * q^96 - 19 * q^97

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