LMFDB - Embedded newform 1617.2.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,2,Mod(1,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, 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("1617.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1617.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:	$12.9118100068$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{21}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 5 $ x^2 - x - 5
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 231)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.79129$ of defining polynomial
Character	$\chi$	$=$	1617.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.79129 q^{2} +1.00000 q^{3} +5.79129 q^{4} -3.00000 q^{5} -2.79129 q^{6} -10.5826 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.79129 q^{2} +1.00000 q^{3} +5.79129 q^{4} -3.00000 q^{5} -2.79129 q^{6} -10.5826 q^{8} +1.00000 q^{9} +8.37386 q^{10} -1.00000 q^{11} +5.79129 q^{12} -1.00000 q^{13} -3.00000 q^{15} +17.9564 q^{16} +1.58258 q^{17} -2.79129 q^{18} -2.58258 q^{19} -17.3739 q^{20} +2.79129 q^{22} +3.58258 q^{23} -10.5826 q^{24} +4.00000 q^{25} +2.79129 q^{26} +1.00000 q^{27} +10.1652 q^{29} +8.37386 q^{30} +5.58258 q^{31} -28.9564 q^{32} -1.00000 q^{33} -4.41742 q^{34} +5.79129 q^{36} +1.00000 q^{37} +7.20871 q^{38} -1.00000 q^{39} +31.7477 q^{40} -7.16515 q^{41} -7.58258 q^{43} -5.79129 q^{44} -3.00000 q^{45} -10.0000 q^{46} -10.5826 q^{47} +17.9564 q^{48} -11.1652 q^{50} +1.58258 q^{51} -5.79129 q^{52} -0.417424 q^{53} -2.79129 q^{54} +3.00000 q^{55} -2.58258 q^{57} -28.3739 q^{58} +4.58258 q^{59} -17.3739 q^{60} -10.0000 q^{61} -15.5826 q^{62} +44.9129 q^{64} +3.00000 q^{65} +2.79129 q^{66} -0.582576 q^{67} +9.16515 q^{68} +3.58258 q^{69} -7.16515 q^{71} -10.5826 q^{72} -7.00000 q^{73} -2.79129 q^{74} +4.00000 q^{75} -14.9564 q^{76} +2.79129 q^{78} -11.1652 q^{79} -53.8693 q^{80} +1.00000 q^{81} +20.0000 q^{82} +2.41742 q^{83} -4.74773 q^{85} +21.1652 q^{86} +10.1652 q^{87} +10.5826 q^{88} +9.16515 q^{89} +8.37386 q^{90} +20.7477 q^{92} +5.58258 q^{93} +29.5390 q^{94} +7.74773 q^{95} -28.9564 q^{96} +11.5826 q^{97} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 2 q^{3} + 7 q^{4} - 6 q^{5} - q^{6} - 12 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - q^2 + 2 * q^3 + 7 * q^4 - 6 * q^5 - q^6 - 12 * q^8 + 2 * q^9	$ 2 q - q^{2} + 2 q^{3} + 7 q^{4} - 6 q^{5} - q^{6} - 12 q^{8} + 2 q^{9} + 3 q^{10} - 2 q^{11} + 7 q^{12} - 2 q^{13} - 6 q^{15} + 13 q^{16} - 6 q^{17} - q^{18} + 4 q^{19} - 21 q^{20} + q^{22} - 2 q^{23} - 12 q^{24} + 8 q^{25} + q^{26} + 2 q^{27} + 2 q^{29} + 3 q^{30} + 2 q^{31} - 35 q^{32} - 2 q^{33} - 18 q^{34} + 7 q^{36} + 2 q^{37} + 19 q^{38} - 2 q^{39} + 36 q^{40} + 4 q^{41} - 6 q^{43} - 7 q^{44} - 6 q^{45} - 20 q^{46} - 12 q^{47} + 13 q^{48} - 4 q^{50} - 6 q^{51} - 7 q^{52} - 10 q^{53} - q^{54} + 6 q^{55} + 4 q^{57} - 43 q^{58} - 21 q^{60} - 20 q^{61} - 22 q^{62} + 44 q^{64} + 6 q^{65} + q^{66} + 8 q^{67} - 2 q^{69} + 4 q^{71} - 12 q^{72} - 14 q^{73} - q^{74} + 8 q^{75} - 7 q^{76} + q^{78} - 4 q^{79} - 39 q^{80} + 2 q^{81} + 40 q^{82} + 14 q^{83} + 18 q^{85} + 24 q^{86} + 2 q^{87} + 12 q^{88} + 3 q^{90} + 14 q^{92} + 2 q^{93} + 27 q^{94} - 12 q^{95} - 35 q^{96} + 14 q^{97} - 2 q^{99}+O(q^{100}) $ 2 * q - q^2 + 2 * q^3 + 7 * q^4 - 6 * q^5 - q^6 - 12 * q^8 + 2 * q^9 + 3 * q^10 - 2 * q^11 + 7 * q^12 - 2 * q^13 - 6 * q^15 + 13 * q^16 - 6 * q^17 - q^18 + 4 * q^19 - 21 * q^20 + q^22 - 2 * q^23 - 12 * q^24 + 8 * q^25 + q^26 + 2 * q^27 + 2 * q^29 + 3 * q^30 + 2 * q^31 - 35 * q^32 - 2 * q^33 - 18 * q^34 + 7 * q^36 + 2 * q^37 + 19 * q^38 - 2 * q^39 + 36 * q^40 + 4 * q^41 - 6 * q^43 - 7 * q^44 - 6 * q^45 - 20 * q^46 - 12 * q^47 + 13 * q^48 - 4 * q^50 - 6 * q^51 - 7 * q^52 - 10 * q^53 - q^54 + 6 * q^55 + 4 * q^57 - 43 * q^58 - 21 * q^60 - 20 * q^61 - 22 * q^62 + 44 * q^64 + 6 * q^65 + q^66 + 8 * q^67 - 2 * q^69 + 4 * q^71 - 12 * q^72 - 14 * q^73 - q^74 + 8 * q^75 - 7 * q^76 + q^78 - 4 * q^79 - 39 * q^80 + 2 * q^81 + 40 * q^82 + 14 * q^83 + 18 * q^85 + 24 * q^86 + 2 * q^87 + 12 * q^88 + 3 * q^90 + 14 * q^92 + 2 * q^93 + 27 * q^94 - 12 * q^95 - 35 * q^96 + 14 * 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 $

$2$	−2.79129	−1.97374	−0.986869	−	0.161521i	$-0.948360\pi$
$2$	−2.79129	−1.97374	−0.986869	+	0.161521i	$0.948360\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.79129	2.89564
$5$	−3.00000	−1.34164	−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000	−1.34164	−0.670820	+	0.741620i	$0.734058\pi$
$6$	−2.79129	−1.13954
$7$	0	0
$7$	0	0
$8$	−10.5826	−3.74151
$9$	1.00000	0.333333
$10$	8.37386	2.64805
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	5.79129	1.67180
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	0	0
$15$	−3.00000	−0.774597
$16$	17.9564	4.48911
$17$	1.58258	0.383831	0.191915	−	0.981411i	$-0.438530\pi$
$17$	1.58258	0.383831	0.191915	+	0.981411i	$0.438530\pi$
$18$	−2.79129	−0.657913
$19$	−2.58258	−0.592483	−0.296242	−	0.955113i	$-0.595733\pi$
$19$	−2.58258	−0.592483	−0.296242	+	0.955113i	$0.595733\pi$
$20$	−17.3739	−3.88491
$21$	0	0
$22$	2.79129	0.595105
$23$	3.58258	0.747019	0.373509	−	0.927626i	$-0.378154\pi$
$23$	3.58258	0.747019	0.373509	+	0.927626i	$0.378154\pi$
$24$	−10.5826	−2.16016
$25$	4.00000	0.800000
$26$	2.79129	0.547417
$27$	1.00000	0.192450
$28$	0	0
$29$	10.1652	1.88762	0.943811	−	0.330487i	$-0.107213\pi$
$29$	10.1652	1.88762	0.943811	+	0.330487i	$0.107213\pi$
$30$	8.37386	1.52885
$31$	5.58258	1.00266	0.501330	−	0.865256i	$-0.332844\pi$
$31$	5.58258	1.00266	0.501330	+	0.865256i	$0.332844\pi$
$32$	−28.9564	−5.11882
$33$	−1.00000	−0.174078
$34$	−4.41742	−0.757582
$35$	0	0
$36$	5.79129	0.965215
$37$	1.00000	0.164399	0.0821995	−	0.996616i	$-0.473806\pi$
$37$	1.00000	0.164399	0.0821995	+	0.996616i	$0.473806\pi$
$38$	7.20871	1.16941
$39$	−1.00000	−0.160128
$40$	31.7477	5.01976
$41$	−7.16515	−1.11901	−0.559504	−	0.828827i	$-0.689008\pi$
$41$	−7.16515	−1.11901	−0.559504	+	0.828827i	$0.689008\pi$
$42$	0	0
$43$	−7.58258	−1.15633	−0.578166	−	0.815919i	$-0.696231\pi$
$43$	−7.58258	−1.15633	−0.578166	+	0.815919i	$0.696231\pi$
$44$	−5.79129	−0.873069
$45$	−3.00000	−0.447214
$46$	−10.0000	−1.47442
$47$	−10.5826	−1.54363	−0.771814	−	0.635849i	$-0.780650\pi$
$47$	−10.5826	−1.54363	−0.771814	+	0.635849i	$0.780650\pi$
$48$	17.9564	2.59179
$49$	0	0
$50$	−11.1652	−1.57899
$51$	1.58258	0.221605
$52$	−5.79129	−0.803107
$53$	−0.417424	−0.0573376	−0.0286688	−	0.999589i	$-0.509127\pi$
$53$	−0.417424	−0.0573376	−0.0286688	+	0.999589i	$0.509127\pi$
$54$	−2.79129	−0.379846
$55$	3.00000	0.404520
$56$	0	0
$57$	−2.58258	−0.342071
$58$	−28.3739	−3.72567
$59$	4.58258	0.596601	0.298300	−	0.954472i	$-0.403580\pi$
$59$	4.58258	0.596601	0.298300	+	0.954472i	$0.403580\pi$
$60$	−17.3739	−2.24296
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	−15.5826	−1.97899
$63$	0	0
$64$	44.9129	5.61411
$65$	3.00000	0.372104
$66$	2.79129	0.343584
$67$	−0.582576	−0.0711729	−0.0355865	−	0.999367i	$-0.511330\pi$
$67$	−0.582576	−0.0711729	−0.0355865	+	0.999367i	$0.511330\pi$
$68$	9.16515	1.11144
$69$	3.58258	0.431291
$70$	0	0
$71$	−7.16515	−0.850347	−0.425174	−	0.905112i	$-0.639787\pi$
$71$	−7.16515	−0.850347	−0.425174	+	0.905112i	$0.639787\pi$
$72$	−10.5826	−1.24717
$73$	−7.00000	−0.819288	−0.409644	−	0.912245i	$-0.634347\pi$
$73$	−7.00000	−0.819288	−0.409644	+	0.912245i	$0.634347\pi$
$74$	−2.79129	−0.324481
$75$	4.00000	0.461880
$76$	−14.9564	−1.71562
$77$	0	0
$78$	2.79129	0.316051
$79$	−11.1652	−1.25618	−0.628089	−	0.778142i	$-0.716163\pi$
$79$	−11.1652	−1.25618	−0.628089	+	0.778142i	$0.716163\pi$
$80$	−53.8693	−6.02277
$81$	1.00000	0.111111
$82$	20.0000	2.20863
$83$	2.41742	0.265347	0.132673	−	0.991160i	$-0.457644\pi$
$83$	2.41742	0.265347	0.132673	+	0.991160i	$0.457644\pi$
$84$	0	0
$85$	−4.74773	−0.514963
$86$	21.1652	2.28230
$87$	10.1652	1.08982
$88$	10.5826	1.12811
$89$	9.16515	0.971504	0.485752	−	0.874097i	$-0.338546\pi$
$89$	9.16515	0.971504	0.485752	+	0.874097i	$0.338546\pi$
$90$	8.37386	0.882683
$91$	0	0
$92$	20.7477	2.16310
$93$	5.58258	0.578886
$94$	29.5390	3.04672
$95$	7.74773	0.794900
$96$	−28.9564	−2.95535
$97$	11.5826	1.17603	0.588016	−	0.808849i	$-0.299909\pi$
$97$	11.5826	1.17603	0.588016	+	0.808849i	$0.299909\pi$
$98$	0	0
$99$	−1.00000	−0.100504
$100$	23.1652	2.31652
$101$	−2.41742	−0.240543	−0.120271	−	0.992741i	$-0.538376\pi$
$101$	−2.41742	−0.240543	−0.120271	+	0.992741i	$0.538376\pi$
$102$	−4.41742	−0.437390
$103$	−17.1652	−1.69133	−0.845666	−	0.533712i	$-0.820797\pi$
$103$	−17.1652	−1.69133	−0.845666	+	0.533712i	$0.820797\pi$
$104$	10.5826	1.03771
$105$	0	0
$106$	1.16515	0.113170
$107$	−3.41742	−0.330375	−0.165187	−	0.986262i	$-0.552823\pi$
$107$	−3.41742	−0.330375	−0.165187	+	0.986262i	$0.552823\pi$
$108$	5.79129	0.557267
$109$	−5.58258	−0.534714	−0.267357	−	0.963598i	$-0.586150\pi$
$109$	−5.58258	−0.534714	−0.267357	+	0.963598i	$0.586150\pi$
$110$	−8.37386	−0.798417
$111$	1.00000	0.0949158
$112$	0	0
$113$	−9.16515	−0.862185	−0.431092	−	0.902308i	$-0.641872\pi$
$113$	−9.16515	−0.862185	−0.431092	+	0.902308i	$0.641872\pi$
$114$	7.20871	0.675158
$115$	−10.7477	−1.00223
$116$	58.8693	5.46588
$117$	−1.00000	−0.0924500
$118$	−12.7913	−1.17753
$119$	0	0
$120$	31.7477	2.89816
$121$	1.00000	0.0909091
$122$	27.9129	2.52711
$123$	−7.16515	−0.646060
$124$	32.3303	2.90335
$125$	3.00000	0.268328
$126$	0	0
$127$	−2.41742	−0.214512	−0.107256	−	0.994231i	$-0.534206\pi$
$127$	−2.41742	−0.214512	−0.107256	+	0.994231i	$0.534206\pi$
$128$	−67.4519	−5.96196
$129$	−7.58258	−0.667609
$130$	−8.37386	−0.734436
$131$	16.0000	1.39793	0.698963	−	0.715158i	$-0.253645\pi$
$131$	16.0000	1.39793	0.698963	+	0.715158i	$0.253645\pi$
$132$	−5.79129	−0.504067
$133$	0	0
$134$	1.62614	0.140477
$135$	−3.00000	−0.258199
$136$	−16.7477	−1.43611
$137$	−2.41742	−0.206534	−0.103267	−	0.994654i	$-0.532930\pi$
$137$	−2.41742	−0.206534	−0.103267	+	0.994654i	$0.532930\pi$
$138$	−10.0000	−0.851257
$139$	7.16515	0.607740	0.303870	−	0.952713i	$-0.401721\pi$
$139$	7.16515	0.607740	0.303870	+	0.952713i	$0.401721\pi$
$140$	0	0
$141$	−10.5826	−0.891214
$142$	20.0000	1.67836
$143$	1.00000	0.0836242
$144$	17.9564	1.49637
$145$	−30.4955	−2.53251
$146$	19.5390	1.61706
$147$	0	0
$148$	5.79129	0.476041
$149$	−12.1652	−0.996608	−0.498304	−	0.867002i	$-0.666044\pi$
$149$	−12.1652	−0.996608	−0.498304	+	0.867002i	$0.666044\pi$
$150$	−11.1652	−0.911631
$151$	−5.58258	−0.454304	−0.227152	−	0.973859i	$-0.572941\pi$
$151$	−5.58258	−0.454304	−0.227152	+	0.973859i	$0.572941\pi$
$152$	27.3303	2.21678
$153$	1.58258	0.127944
$154$	0	0
$155$	−16.7477	−1.34521
$156$	−5.79129	−0.463674
$157$	−0.834849	−0.0666282	−0.0333141	−	0.999445i	$-0.510606\pi$
$157$	−0.834849	−0.0666282	−0.0333141	+	0.999445i	$0.510606\pi$
$158$	31.1652	2.47937
$159$	−0.417424	−0.0331039
$160$	86.8693	6.86762
$161$	0	0
$162$	−2.79129	−0.219304
$163$	−0.582576	−0.0456309	−0.0228154	−	0.999740i	$-0.507263\pi$
$163$	−0.582576	−0.0456309	−0.0228154	+	0.999740i	$0.507263\pi$
$164$	−41.4955	−3.24025
$165$	3.00000	0.233550
$166$	−6.74773	−0.523725
$167$	−22.7477	−1.76027	−0.880136	−	0.474722i	$-0.842549\pi$
$167$	−22.7477	−1.76027	−0.880136	+	0.474722i	$0.842549\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	13.2523	1.01640
$171$	−2.58258	−0.197494
$172$	−43.9129	−3.34833
$173$	−11.1652	−0.848871	−0.424435	−	0.905458i	$-0.639527\pi$
$173$	−11.1652	−0.848871	−0.424435	+	0.905458i	$0.639527\pi$
$174$	−28.3739	−2.15102
$175$	0	0
$176$	−17.9564	−1.35352
$177$	4.58258	0.344447
$178$	−25.5826	−1.91750
$179$	−22.3303	−1.66905	−0.834523	−	0.550974i	$-0.814256\pi$
$179$	−22.3303	−1.66905	−0.834523	+	0.550974i	$0.814256\pi$
$180$	−17.3739	−1.29497
$181$	−3.58258	−0.266291	−0.133145	−	0.991097i	$-0.542508\pi$
$181$	−3.58258	−0.266291	−0.133145	+	0.991097i	$0.542508\pi$
$182$	0	0
$183$	−10.0000	−0.739221
$184$	−37.9129	−2.79497
$185$	−3.00000	−0.220564
$186$	−15.5826	−1.14257
$187$	−1.58258	−0.115729
$188$	−61.2867	−4.46980
$189$	0	0
$190$	−21.6261	−1.56892
$191$	2.41742	0.174919	0.0874593	−	0.996168i	$-0.472125\pi$
$191$	2.41742	0.174919	0.0874593	+	0.996168i	$0.472125\pi$
$192$	44.9129	3.24131
$193$	−11.5826	−0.833732	−0.416866	−	0.908968i	$-0.636872\pi$
$193$	−11.5826	−0.833732	−0.416866	+	0.908968i	$0.636872\pi$
$194$	−32.3303	−2.32118
$195$	3.00000	0.214834
$196$	0	0
$197$	−13.1652	−0.937978	−0.468989	−	0.883204i	$-0.655382\pi$
$197$	−13.1652	−0.937978	−0.468989	+	0.883204i	$0.655382\pi$
$198$	2.79129	0.198368
$199$	0.417424	0.0295904	0.0147952	−	0.999891i	$-0.495290\pi$
$199$	0.417424	0.0295904	0.0147952	+	0.999891i	$0.495290\pi$
$200$	−42.3303	−2.99320
$201$	−0.582576	−0.0410917
$202$	6.74773	0.474768
$203$	0	0
$204$	9.16515	0.641689
$205$	21.4955	1.50131
$206$	47.9129	3.33825
$207$	3.58258	0.249006
$208$	−17.9564	−1.24506
$209$	2.58258	0.178640
$210$	0	0
$211$	5.16515	0.355584	0.177792	−	0.984068i	$-0.443105\pi$
$211$	5.16515	0.355584	0.177792	+	0.984068i	$0.443105\pi$
$212$	−2.41742	−0.166029
$213$	−7.16515	−0.490948
$214$	9.53901	0.652074
$215$	22.7477	1.55138
$216$	−10.5826	−0.720053
$217$	0	0
$218$	15.5826	1.05539
$219$	−7.00000	−0.473016
$220$	17.3739	1.17135
$221$	−1.58258	−0.106456
$222$	−2.79129	−0.187339
$223$	−6.00000	−0.401790	−0.200895	−	0.979613i	$-0.564385\pi$
$223$	−6.00000	−0.401790	−0.200895	+	0.979613i	$0.564385\pi$
$224$	0	0
$225$	4.00000	0.266667
$226$	25.5826	1.70173
$227$	22.0000	1.46019	0.730096	−	0.683345i	$-0.239475\pi$
$227$	22.0000	1.46019	0.730096	+	0.683345i	$0.239475\pi$
$228$	−14.9564	−0.990514
$229$	26.7477	1.76754	0.883770	−	0.467922i	$-0.154997\pi$
$229$	26.7477	1.76754	0.883770	+	0.467922i	$0.154997\pi$
$230$	30.0000	1.97814
$231$	0	0
$232$	−107.573	−7.06255
$233$	−14.0000	−0.917170	−0.458585	−	0.888650i	$-0.651644\pi$
$233$	−14.0000	−0.917170	−0.458585	+	0.888650i	$0.651644\pi$
$234$	2.79129	0.182472
$235$	31.7477	2.07099
$236$	26.5390	1.72754
$237$	−11.1652	−0.725255
$238$	0	0
$239$	7.41742	0.479793	0.239897	−	0.970798i	$-0.422886\pi$
$239$	7.41742	0.479793	0.239897	+	0.970798i	$0.422886\pi$
$240$	−53.8693	−3.47725
$241$	−8.16515	−0.525964	−0.262982	−	0.964801i	$-0.584706\pi$
$241$	−8.16515	−0.525964	−0.262982	+	0.964801i	$0.584706\pi$
$242$	−2.79129	−0.179431
$243$	1.00000	0.0641500
$244$	−57.9129	−3.70749
$245$	0	0
$246$	20.0000	1.27515
$247$	2.58258	0.164325
$248$	−59.0780	−3.75146
$249$	2.41742	0.153198
$250$	−8.37386	−0.529610
$251$	−16.5826	−1.04668	−0.523341	−	0.852123i	$-0.675315\pi$
$251$	−16.5826	−1.04668	−0.523341	+	0.852123i	$0.675315\pi$
$252$	0	0
$253$	−3.58258	−0.225235
$254$	6.74773	0.423390
$255$	−4.74773	−0.297314
$256$	98.4519	6.15324
$257$	−19.0000	−1.18519	−0.592594	−	0.805502i	$-0.701896\pi$
$257$	−19.0000	−1.18519	−0.592594	+	0.805502i	$0.701896\pi$
$258$	21.1652	1.31768
$259$	0	0
$260$	17.3739	1.07748
$261$	10.1652	0.629207
$262$	−44.6606	−2.75914
$263$	22.9129	1.41287	0.706434	−	0.707779i	$-0.250303\pi$
$263$	22.9129	1.41287	0.706434	+	0.707779i	$0.250303\pi$
$264$	10.5826	0.651313
$265$	1.25227	0.0769265
$266$	0	0
$267$	9.16515	0.560898
$268$	−3.37386	−0.206092
$269$	−10.0000	−0.609711	−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000	−0.609711	−0.304855	+	0.952399i	$0.598608\pi$
$270$	8.37386	0.509617
$271$	−14.5826	−0.885828	−0.442914	−	0.896564i	$-0.646055\pi$
$271$	−14.5826	−0.885828	−0.442914	+	0.896564i	$0.646055\pi$
$272$	28.4174	1.72306
$273$	0	0
$274$	6.74773	0.407645
$275$	−4.00000	−0.241209
$276$	20.7477	1.24887
$277$	−0.834849	−0.0501612	−0.0250806	−	0.999685i	$-0.507984\pi$
$277$	−0.834849	−0.0501612	−0.0250806	+	0.999685i	$0.507984\pi$
$278$	−20.0000	−1.19952
$279$	5.58258	0.334220
$280$	0	0
$281$	9.33030	0.556599	0.278300	−	0.960494i	$-0.410229\pi$
$281$	9.33030	0.556599	0.278300	+	0.960494i	$0.410229\pi$
$282$	29.5390	1.75902
$283$	−0.252273	−0.0149961	−0.00749803	−	0.999972i	$-0.502387\pi$
$283$	−0.252273	−0.0149961	−0.00749803	+	0.999972i	$0.502387\pi$
$284$	−41.4955	−2.46230
$285$	7.74773	0.458936
$286$	−2.79129	−0.165052
$287$	0	0
$288$	−28.9564	−1.70627
$289$	−14.4955	−0.852674
$290$	85.1216	4.99851
$291$	11.5826	0.678983
$292$	−40.5390	−2.37237
$293$	0	0		−	1.00000i	$-0.5\pi$
$293$	0	0			1.00000i	$0.5\pi$
$294$	0	0
$295$	−13.7477	−0.800424
$296$	−10.5826	−0.615100
$297$	−1.00000	−0.0580259
$298$	33.9564	1.96704
$299$	−3.58258	−0.207186
$300$	23.1652	1.33744
$301$	0	0
$302$	15.5826	0.896676
$303$	−2.41742	−0.138877
$304$	−46.3739	−2.65972
$305$	30.0000	1.71780
$306$	−4.41742	−0.252527
$307$	0	0		−	1.00000i	$-0.5\pi$
$307$	0	0			1.00000i	$0.5\pi$
$308$	0	0
$309$	−17.1652	−0.976491
$310$	46.7477	2.65509
$311$	22.3303	1.26624	0.633118	−	0.774056i	$-0.281775\pi$
$311$	22.3303	1.26624	0.633118	+	0.774056i	$0.281775\pi$
$312$	10.5826	0.599120
$313$	−10.4174	−0.588828	−0.294414	−	0.955678i	$-0.595124\pi$
$313$	−10.4174	−0.588828	−0.294414	+	0.955678i	$0.595124\pi$
$314$	2.33030	0.131507
$315$	0	0
$316$	−64.6606	−3.63744
$317$	−31.5826	−1.77385	−0.886927	−	0.461909i	$-0.847165\pi$
$317$	−31.5826	−1.77385	−0.886927	+	0.461909i	$0.847165\pi$
$318$	1.16515	0.0653384
$319$	−10.1652	−0.569139
$320$	−134.739	−7.53212
$321$	−3.41742	−0.190742
$322$	0	0
$323$	−4.08712	−0.227414
$324$	5.79129	0.321738
$325$	−4.00000	−0.221880
$326$	1.62614	0.0900634
$327$	−5.58258	−0.308717
$328$	75.8258	4.18678
$329$	0	0
$330$	−8.37386	−0.460966
$331$	15.1652	0.833552	0.416776	−	0.909009i	$-0.363160\pi$
$331$	15.1652	0.833552	0.416776	+	0.909009i	$0.363160\pi$
$332$	14.0000	0.768350
$333$	1.00000	0.0547997
$334$	63.4955	3.47432
$335$	1.74773	0.0954885
$336$	0	0
$337$	8.41742	0.458526	0.229263	−	0.973364i	$-0.426368\pi$
$337$	8.41742	0.458526	0.229263	+	0.973364i	$0.426368\pi$
$338$	33.4955	1.82191
$339$	−9.16515	−0.497783
$340$	−27.4955	−1.49115
$341$	−5.58258	−0.302313
$342$	7.20871	0.389803
$343$	0	0
$344$	80.2432	4.32642
$345$	−10.7477	−0.578638
$346$	31.1652	1.67545
$347$	−10.3303	−0.554560	−0.277280	−	0.960789i	$-0.589433\pi$
$347$	−10.3303	−0.554560	−0.277280	+	0.960789i	$0.589433\pi$
$348$	58.8693	3.15573
$349$	15.0000	0.802932	0.401466	−	0.915874i	$-0.368501\pi$
$349$	15.0000	0.802932	0.401466	+	0.915874i	$0.368501\pi$
$350$	0	0
$351$	−1.00000	−0.0533761
$352$	28.9564	1.54338
$353$	−5.83485	−0.310558	−0.155279	−	0.987871i	$-0.549628\pi$
$353$	−5.83485	−0.310558	−0.155279	+	0.987871i	$0.549628\pi$
$354$	−12.7913	−0.679849
$355$	21.4955	1.14086
$356$	53.0780	2.81313
$357$	0	0
$358$	62.3303	3.29426
$359$	−27.1652	−1.43372	−0.716861	−	0.697216i	$-0.754422\pi$
$359$	−27.1652	−1.43372	−0.716861	+	0.697216i	$0.754422\pi$
$360$	31.7477	1.67325
$361$	−12.3303	−0.648963
$362$	10.0000	0.525588
$363$	1.00000	0.0524864
$364$	0	0
$365$	21.0000	1.09919
$366$	27.9129	1.45903
$367$	−22.0000	−1.14839	−0.574195	−	0.818718i	$-0.694685\pi$
$367$	−22.0000	−1.14839	−0.574195	+	0.818718i	$0.694685\pi$
$368$	64.3303	3.35345
$369$	−7.16515	−0.373003
$370$	8.37386	0.435336
$371$	0	0
$372$	32.3303	1.67625
$373$	−7.25227	−0.375508	−0.187754	−	0.982216i	$-0.560121\pi$
$373$	−7.25227	−0.375508	−0.187754	+	0.982216i	$0.560121\pi$
$374$	4.41742	0.228420
$375$	3.00000	0.154919
$376$	111.991	5.77549
$377$	−10.1652	−0.523532
$378$	0	0
$379$	−3.41742	−0.175541	−0.0877706	−	0.996141i	$-0.527974\pi$
$379$	−3.41742	−0.175541	−0.0877706	+	0.996141i	$0.527974\pi$
$380$	44.8693	2.30175
$381$	−2.41742	−0.123848
$382$	−6.74773	−0.345244
$383$	26.3303	1.34542	0.672708	−	0.739908i	$-0.265131\pi$
$383$	26.3303	1.34542	0.672708	+	0.739908i	$0.265131\pi$
$384$	−67.4519	−3.44214
$385$	0	0
$386$	32.3303	1.64557
$387$	−7.58258	−0.385444
$388$	67.0780	3.40537
$389$	10.3303	0.523767	0.261884	−	0.965099i	$-0.415656\pi$
$389$	10.3303	0.523767	0.261884	+	0.965099i	$0.415656\pi$
$390$	−8.37386	−0.424027
$391$	5.66970	0.286729
$392$	0	0
$393$	16.0000	0.807093
$394$	36.7477	1.85132
$395$	33.4955	1.68534
$396$	−5.79129	−0.291023
$397$	22.4174	1.12510	0.562549	−	0.826764i	$-0.309821\pi$
$397$	22.4174	1.12510	0.562549	+	0.826764i	$0.309821\pi$
$398$	−1.16515	−0.0584038
$399$	0	0
$400$	71.8258	3.59129
$401$	−13.9129	−0.694776	−0.347388	−	0.937721i	$-0.612931\pi$
$401$	−13.9129	−0.694776	−0.347388	+	0.937721i	$0.612931\pi$
$402$	1.62614	0.0811043
$403$	−5.58258	−0.278088
$404$	−14.0000	−0.696526
$405$	−3.00000	−0.149071
$406$	0	0
$407$	−1.00000	−0.0495682
$408$	−16.7477	−0.829136
$409$	28.3303	1.40084	0.700422	−	0.713729i	$-0.252995\pi$
$409$	28.3303	1.40084	0.700422	+	0.713729i	$0.252995\pi$
$410$	−60.0000	−2.96319
$411$	−2.41742	−0.119243
$412$	−99.4083	−4.89750
$413$	0	0
$414$	−10.0000	−0.491473
$415$	−7.25227	−0.356000
$416$	28.9564	1.41971
$417$	7.16515	0.350879
$418$	−7.20871	−0.352590
$419$	6.58258	0.321580	0.160790	−	0.986989i	$-0.448596\pi$
$419$	6.58258	0.321580	0.160790	+	0.986989i	$0.448596\pi$
$420$	0	0
$421$	39.6606	1.93294	0.966470	−	0.256780i	$-0.0826617\pi$
$421$	39.6606	1.93294	0.966470	+	0.256780i	$0.0826617\pi$
$422$	−14.4174	−0.701829
$423$	−10.5826	−0.514542
$424$	4.41742	0.214529
$425$	6.33030	0.307065
$426$	20.0000	0.969003
$427$	0	0
$428$	−19.7913	−0.956648
$429$	1.00000	0.0482805
$430$	−63.4955	−3.06202
$431$	−9.74773	−0.469531	−0.234766	−	0.972052i	$-0.575432\pi$
$431$	−9.74773	−0.469531	−0.234766	+	0.972052i	$0.575432\pi$
$432$	17.9564	0.863930
$433$	−7.16515	−0.344335	−0.172168	−	0.985068i	$-0.555077\pi$
$433$	−7.16515	−0.344335	−0.172168	+	0.985068i	$0.555077\pi$
$434$	0	0
$435$	−30.4955	−1.46215
$436$	−32.3303	−1.54834
$437$	−9.25227	−0.442596
$438$	19.5390	0.933610
$439$	−26.5826	−1.26872	−0.634359	−	0.773039i	$-0.718736\pi$
$439$	−26.5826	−1.26872	−0.634359	+	0.773039i	$0.718736\pi$
$440$	−31.7477	−1.51351
$441$	0	0
$442$	4.41742	0.210115
$443$	−4.83485	−0.229711	−0.114855	−	0.993382i	$-0.536640\pi$
$443$	−4.83485	−0.229711	−0.114855	+	0.993382i	$0.536640\pi$
$444$	5.79129	0.274842
$445$	−27.4955	−1.30341
$446$	16.7477	0.793028
$447$	−12.1652	−0.575392
$448$	0	0
$449$	18.3303	0.865060	0.432530	−	0.901619i	$-0.357621\pi$
$449$	18.3303	0.865060	0.432530	+	0.901619i	$0.357621\pi$
$450$	−11.1652	−0.526330
$451$	7.16515	0.337394
$452$	−53.0780	−2.49658
$453$	−5.58258	−0.262292
$454$	−61.4083	−2.88204
$455$	0	0
$456$	27.3303	1.27986
$457$	25.9129	1.21215	0.606077	−	0.795406i	$-0.292742\pi$
$457$	25.9129	1.21215	0.606077	+	0.795406i	$0.292742\pi$
$458$	−74.6606	−3.48866
$459$	1.58258	0.0738683
$460$	−62.2432	−2.90210
$461$	18.3303	0.853727	0.426864	−	0.904316i	$-0.359618\pi$
$461$	18.3303	0.853727	0.426864	+	0.904316i	$0.359618\pi$
$462$	0	0
$463$	−0.582576	−0.0270746	−0.0135373	−	0.999908i	$-0.504309\pi$
$463$	−0.582576	−0.0270746	−0.0135373	+	0.999908i	$0.504309\pi$
$464$	182.530	8.47374
$465$	−16.7477	−0.776657
$466$	39.0780	1.81025
$467$	29.4174	1.36128	0.680638	−	0.732620i	$-0.261703\pi$
$467$	29.4174	1.36128	0.680638	+	0.732620i	$0.261703\pi$
$468$	−5.79129	−0.267702
$469$	0	0
$470$	−88.6170	−4.08760
$471$	−0.834849	−0.0384678
$472$	−48.4955	−2.23218
$473$	7.58258	0.348647
$474$	31.1652	1.43146
$475$	−10.3303	−0.473987
$476$	0	0
$477$	−0.417424	−0.0191125
$478$	−20.7042	−0.946987
$479$	6.41742	0.293220	0.146610	−	0.989194i	$-0.453164\pi$
$479$	6.41742	0.293220	0.146610	+	0.989194i	$0.453164\pi$
$480$	86.8693	3.96502
$481$	−1.00000	−0.0455961
$482$	22.7913	1.03811
$483$	0	0
$484$	5.79129	0.263240
$485$	−34.7477	−1.57781
$486$	−2.79129	−0.126615
$487$	−26.3303	−1.19314	−0.596570	−	0.802561i	$-0.703470\pi$
$487$	−26.3303	−1.19314	−0.596570	+	0.802561i	$0.703470\pi$
$488$	105.826	4.79051
$489$	−0.582576	−0.0263450
$490$	0	0
$491$	22.9129	1.03404	0.517022	−	0.855972i	$-0.327041\pi$
$491$	22.9129	1.03404	0.517022	+	0.855972i	$0.327041\pi$
$492$	−41.4955	−1.87076
$493$	16.0871	0.724528
$494$	−7.20871	−0.324335
$495$	3.00000	0.134840
$496$	100.243	4.50105
$497$	0	0
$498$	−6.74773	−0.302373
$499$	14.2523	0.638019	0.319010	−	0.947751i	$-0.396650\pi$
$499$	14.2523	0.638019	0.319010	+	0.947751i	$0.396650\pi$
$500$	17.3739	0.776983
$501$	−22.7477	−1.01629
$502$	46.2867	2.06588
$503$	−26.7477	−1.19262	−0.596311	−	0.802753i	$-0.703368\pi$
$503$	−26.7477	−1.19262	−0.596311	+	0.802753i	$0.703368\pi$
$504$	0	0
$505$	7.25227	0.322722
$506$	10.0000	0.444554
$507$	−12.0000	−0.532939
$508$	−14.0000	−0.621150
$509$	−6.00000	−0.265945	−0.132973	−	0.991120i	$-0.542452\pi$
$509$	−6.00000	−0.265945	−0.132973	+	0.991120i	$0.542452\pi$
$510$	13.2523	0.586821
$511$	0	0
$512$	−139.904	−6.18293
$513$	−2.58258	−0.114024
$514$	53.0345	2.33925
$515$	51.4955	2.26916
$516$	−43.9129	−1.93316
$517$	10.5826	0.465421
$518$	0	0
$519$	−11.1652	−0.490096
$520$	−31.7477	−1.39223
$521$	−34.1652	−1.49680	−0.748401	−	0.663246i	$-0.769178\pi$
$521$	−34.1652	−1.49680	−0.748401	+	0.663246i	$0.769178\pi$
$522$	−28.3739	−1.24189
$523$	−24.5826	−1.07492	−0.537460	−	0.843289i	$-0.680616\pi$
$523$	−24.5826	−1.07492	−0.537460	+	0.843289i	$0.680616\pi$
$524$	92.6606	4.04790
$525$	0	0
$526$	−63.9564	−2.78863
$527$	8.83485	0.384852
$528$	−17.9564	−0.781454
$529$	−10.1652	−0.441963
$530$	−3.49545	−0.151833
$531$	4.58258	0.198867
$532$	0	0
$533$	7.16515	0.310357
$534$	−25.5826	−1.10707
$535$	10.2523	0.443244
$536$	6.16515	0.266294
$537$	−22.3303	−0.963624
$538$	27.9129	1.20341
$539$	0	0
$540$	−17.3739	−0.747652
$541$	−18.3303	−0.788081	−0.394041	−	0.919093i	$-0.628923\pi$
$541$	−18.3303	−0.788081	−0.394041	+	0.919093i	$0.628923\pi$
$542$	40.7042	1.74839
$543$	−3.58258	−0.153743
$544$	−45.8258	−1.96476
$545$	16.7477	0.717394
$546$	0	0
$547$	8.00000	0.342055	0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000	0.342055	0.171028	+	0.985266i	$0.445291\pi$
$548$	−14.0000	−0.598050
$549$	−10.0000	−0.426790
$550$	11.1652	0.476084
$551$	−26.2523	−1.11838
$552$	−37.9129	−1.61368
$553$	0	0
$554$	2.33030	0.0990051
$555$	−3.00000	−0.127343
$556$	41.4955	1.75980
$557$	−27.3303	−1.15802	−0.579011	−	0.815320i	$-0.696561\pi$
$557$	−27.3303	−1.15802	−0.579011	+	0.815320i	$0.696561\pi$
$558$	−15.5826	−0.659663
$559$	7.58258	0.320709
$560$	0	0
$561$	−1.58258	−0.0668164
$562$	−26.0436	−1.09858
$563$	28.4174	1.19765	0.598826	−	0.800879i	$-0.295634\pi$
$563$	28.4174	1.19765	0.598826	+	0.800879i	$0.295634\pi$
$564$	−61.2867	−2.58064
$565$	27.4955	1.15674
$566$	0.704166	0.0295983
$567$	0	0
$568$	75.8258	3.18158
$569$	46.6606	1.95611	0.978057	−	0.208337i	$-0.0668050\pi$
$569$	46.6606	1.95611	0.978057	+	0.208337i	$0.0668050\pi$
$570$	−21.6261	−0.905819
$571$	47.1652	1.97380	0.986900	−	0.161333i	$-0.0515792\pi$
$571$	47.1652	1.97380	0.986900	+	0.161333i	$0.0515792\pi$
$572$	5.79129	0.242146
$573$	2.41742	0.100989
$574$	0	0
$575$	14.3303	0.597615
$576$	44.9129	1.87137
$577$	−23.9129	−0.995506	−0.497753	−	0.867319i	$-0.665841\pi$
$577$	−23.9129	−0.995506	−0.497753	+	0.867319i	$0.665841\pi$
$578$	40.4610	1.68296
$579$	−11.5826	−0.481355
$580$	−176.608	−7.33325
$581$	0	0
$582$	−32.3303	−1.34013
$583$	0.417424	0.0172879
$584$	74.0780	3.06537
$585$	3.00000	0.124035
$586$	0	0
$587$	−10.2523	−0.423157	−0.211578	−	0.977361i	$-0.567860\pi$
$587$	−10.2523	−0.423157	−0.211578	+	0.977361i	$0.567860\pi$
$588$	0	0
$589$	−14.4174	−0.594060
$590$	38.3739	1.57983
$591$	−13.1652	−0.541542
$592$	17.9564	0.738005
$593$	−16.0000	−0.657041	−0.328521	−	0.944497i	$-0.606550\pi$
$593$	−16.0000	−0.657041	−0.328521	+	0.944497i	$0.606550\pi$
$594$	2.79129	0.114528
$595$	0	0
$596$	−70.4519	−2.88582
$597$	0.417424	0.0170840
$598$	10.0000	0.408930
$599$	−11.1652	−0.456196	−0.228098	−	0.973638i	$-0.573251\pi$
$599$	−11.1652	−0.456196	−0.228098	+	0.973638i	$0.573251\pi$
$600$	−42.3303	−1.72813
$601$	30.4955	1.24394	0.621968	−	0.783043i	$-0.286333\pi$
$601$	30.4955	1.24394	0.621968	+	0.783043i	$0.286333\pi$
$602$	0	0
$603$	−0.582576	−0.0237243
$604$	−32.3303	−1.31550
$605$	−3.00000	−0.121967
$606$	6.74773	0.274108
$607$	−5.74773	−0.233293	−0.116647	−	0.993173i	$-0.537214\pi$
$607$	−5.74773	−0.233293	−0.116647	+	0.993173i	$0.537214\pi$
$608$	74.7822	3.03282
$609$	0	0
$610$	−83.7386	−3.39048
$611$	10.5826	0.428125
$612$	9.16515	0.370479
$613$	0.747727	0.0302004	0.0151002	−	0.999886i	$-0.495193\pi$
$613$	0.747727	0.0302004	0.0151002	+	0.999886i	$0.495193\pi$
$614$	0	0
$615$	21.4955	0.866780
$616$	0	0
$617$	21.1652	0.852077	0.426038	−	0.904705i	$-0.359909\pi$
$617$	21.1652	0.852077	0.426038	+	0.904705i	$0.359909\pi$
$618$	47.9129	1.92734
$619$	−35.0780	−1.40991	−0.704953	−	0.709254i	$-0.749032\pi$
$619$	−35.0780	−1.40991	−0.704953	+	0.709254i	$0.749032\pi$
$620$	−96.9909	−3.89525
$621$	3.58258	0.143764
$622$	−62.3303	−2.49922
$623$	0	0
$624$	−17.9564	−0.718833
$625$	−29.0000	−1.16000
$626$	29.0780	1.16219
$627$	2.58258	0.103138
$628$	−4.83485	−0.192931
$629$	1.58258	0.0631014
$630$	0	0
$631$	4.83485	0.192472	0.0962361	−	0.995359i	$-0.469320\pi$
$631$	4.83485	0.192472	0.0962361	+	0.995359i	$0.469320\pi$
$632$	118.156	4.70000
$633$	5.16515	0.205296
$634$	88.1561	3.50112
$635$	7.25227	0.287798
$636$	−2.41742	−0.0958571
$637$	0	0
$638$	28.3739	1.12333
$639$	−7.16515	−0.283449
$640$	202.356	7.99881
$641$	34.4174	1.35941	0.679703	−	0.733487i	$-0.262109\pi$
$641$	34.4174	1.35941	0.679703	+	0.733487i	$0.262109\pi$
$642$	9.53901	0.376475
$643$	44.2432	1.74478	0.872390	−	0.488810i	$-0.162569\pi$
$643$	44.2432	1.74478	0.872390	+	0.488810i	$0.162569\pi$
$644$	0	0
$645$	22.7477	0.895691
$646$	11.4083	0.448855
$647$	−34.9129	−1.37257	−0.686283	−	0.727334i	$-0.740759\pi$
$647$	−34.9129	−1.37257	−0.686283	+	0.727334i	$0.740759\pi$
$648$	−10.5826	−0.415723
$649$	−4.58258	−0.179882
$650$	11.1652	0.437933
$651$	0	0
$652$	−3.37386	−0.132131
$653$	6.33030	0.247724	0.123862	−	0.992299i	$-0.460472\pi$
$653$	6.33030	0.247724	0.123862	+	0.992299i	$0.460472\pi$
$654$	15.5826	0.609327
$655$	−48.0000	−1.87552
$656$	−128.661	−5.02335
$657$	−7.00000	−0.273096
$658$	0	0
$659$	−19.4174	−0.756395	−0.378198	−	0.925725i	$-0.623456\pi$
$659$	−19.4174	−0.756395	−0.378198	+	0.925725i	$0.623456\pi$
$660$	17.3739	0.676277
$661$	−25.0780	−0.975422	−0.487711	−	0.873005i	$-0.662168\pi$
$661$	−25.0780	−0.975422	−0.487711	+	0.873005i	$0.662168\pi$
$662$	−42.3303	−1.64521
$663$	−1.58258	−0.0614621
$664$	−25.5826	−0.992796
$665$	0	0
$666$	−2.79129	−0.108160
$667$	36.4174	1.41009
$668$	−131.739	−5.09712
$669$	−6.00000	−0.231973
$670$	−4.87841	−0.188469
$671$	10.0000	0.386046
$672$	0	0
$673$	38.7477	1.49362	0.746808	−	0.665040i	$-0.231586\pi$
$673$	38.7477	1.49362	0.746808	+	0.665040i	$0.231586\pi$
$674$	−23.4955	−0.905011
$675$	4.00000	0.153960
$676$	−69.4955	−2.67290
$677$	26.8348	1.03135	0.515674	−	0.856785i	$-0.327542\pi$
$677$	26.8348	1.03135	0.515674	+	0.856785i	$0.327542\pi$
$678$	25.5826	0.982493
$679$	0	0
$680$	50.2432	1.92674
$681$	22.0000	0.843042
$682$	15.5826	0.596688
$683$	31.0780	1.18917	0.594584	−	0.804034i	$-0.297317\pi$
$683$	31.0780	1.18917	0.594584	+	0.804034i	$0.297317\pi$
$684$	−14.9564	−0.571874
$685$	7.25227	0.277095
$686$	0	0
$687$	26.7477	1.02049
$688$	−136.156	−5.19090
$689$	0.417424	0.0159026
$690$	30.0000	1.14208
$691$	−10.0000	−0.380418	−0.190209	−	0.981744i	$-0.560917\pi$
$691$	−10.0000	−0.380418	−0.190209	+	0.981744i	$0.560917\pi$
$692$	−64.6606	−2.45803
$693$	0	0
$694$	28.8348	1.09456
$695$	−21.4955	−0.815369
$696$	−107.573	−4.07756
$697$	−11.3394	−0.429510
$698$	−41.8693	−1.58478
$699$	−14.0000	−0.529529
$700$	0	0
$701$	10.0000	0.377695	0.188847	−	0.982006i	$-0.439525\pi$
$701$	10.0000	0.377695	0.188847	+	0.982006i	$0.439525\pi$
$702$	2.79129	0.105350
$703$	−2.58258	−0.0974037
$704$	−44.9129	−1.69272
$705$	31.7477	1.19569
$706$	16.2867	0.612960
$707$	0	0
$708$	26.5390	0.997397
$709$	−45.6606	−1.71482	−0.857410	−	0.514634i	$-0.827928\pi$
$709$	−45.6606	−1.71482	−0.857410	+	0.514634i	$0.827928\pi$
$710$	−60.0000	−2.25176
$711$	−11.1652	−0.418726
$712$	−96.9909	−3.63489
$713$	20.0000	0.749006
$714$	0	0
$715$	−3.00000	−0.112194
$716$	−129.321	−4.83296
$717$	7.41742	0.277009
$718$	75.8258	2.82979
$719$	−50.0780	−1.86760	−0.933798	−	0.357801i	$-0.883526\pi$
$719$	−50.0780	−1.86760	−0.933798	+	0.357801i	$0.883526\pi$
$720$	−53.8693	−2.00759
$721$	0	0
$722$	34.4174	1.28088
$723$	−8.16515	−0.303665
$724$	−20.7477	−0.771083
$725$	40.6606	1.51010
$726$	−2.79129	−0.103594
$727$	−29.9129	−1.10941	−0.554704	−	0.832048i	$-0.687168\pi$
$727$	−29.9129	−1.10941	−0.554704	+	0.832048i	$0.687168\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−58.6170	−2.16951
$731$	−12.0000	−0.443836
$732$	−57.9129	−2.14052
$733$	34.0000	1.25582	0.627909	−	0.778287i	$-0.283911\pi$
$733$	34.0000	1.25582	0.627909	+	0.778287i	$0.283911\pi$
$734$	61.4083	2.26662
$735$	0	0
$736$	−103.739	−3.82386
$737$	0.582576	0.0214595
$738$	20.0000	0.736210
$739$	13.9129	0.511794	0.255897	−	0.966704i	$-0.417629\pi$
$739$	13.9129	0.511794	0.255897	+	0.966704i	$0.417629\pi$
$740$	−17.3739	−0.638676
$741$	2.58258	0.0948733
$742$	0	0
$743$	29.2432	1.07283	0.536414	−	0.843955i	$-0.319779\pi$
$743$	29.2432	1.07283	0.536414	+	0.843955i	$0.319779\pi$
$744$	−59.0780	−2.16591
$745$	36.4955	1.33709
$746$	20.2432	0.741156
$747$	2.41742	0.0884489
$748$	−9.16515	−0.335111
$749$	0	0
$750$	−8.37386	−0.305770
$751$	36.9129	1.34697	0.673485	−	0.739201i	$-0.264797\pi$
$751$	36.9129	1.34697	0.673485	+	0.739201i	$0.264797\pi$
$752$	−190.025	−6.92951
$753$	−16.5826	−0.604303
$754$	28.3739	1.03332
$755$	16.7477	0.609512
$756$	0	0
$757$	−9.33030	−0.339116	−0.169558	−	0.985520i	$-0.554234\pi$
$757$	−9.33030	−0.339116	−0.169558	+	0.985520i	$0.554234\pi$
$758$	9.53901	0.346473
$759$	−3.58258	−0.130039
$760$	−81.9909	−2.97412
$761$	−5.66970	−0.205526	−0.102763	−	0.994706i	$-0.532768\pi$
$761$	−5.66970	−0.205526	−0.102763	+	0.994706i	$0.532768\pi$
$762$	6.74773	0.244444
$763$	0	0
$764$	14.0000	0.506502
$765$	−4.74773	−0.171654
$766$	−73.4955	−2.65550
$767$	−4.58258	−0.165467
$768$	98.4519	3.55258
$769$	48.4955	1.74879	0.874395	−	0.485214i	$-0.161258\pi$
$769$	48.4955	1.74879	0.874395	+	0.485214i	$0.161258\pi$
$770$	0	0
$771$	−19.0000	−0.684268
$772$	−67.0780	−2.41419
$773$	12.1652	0.437550	0.218775	−	0.975775i	$-0.429794\pi$
$773$	12.1652	0.437550	0.218775	+	0.975775i	$0.429794\pi$
$774$	21.1652	0.760766
$775$	22.3303	0.802128
$776$	−122.573	−4.40013
$777$	0	0
$778$	−28.8348	−1.03378
$779$	18.5045	0.662994
$780$	17.3739	0.622084
$781$	7.16515	0.256389
$782$	−15.8258	−0.565928
$783$	10.1652	0.363273
$784$	0	0
$785$	2.50455	0.0893911
$786$	−44.6606	−1.59299
$787$	−29.4174	−1.04862	−0.524309	−	0.851528i	$-0.675676\pi$
$787$	−29.4174	−1.04862	−0.524309	+	0.851528i	$0.675676\pi$
$788$	−76.2432	−2.71605
$789$	22.9129	0.815720
$790$	−93.4955	−3.32642
$791$	0	0
$792$	10.5826	0.376035
$793$	10.0000	0.355110
$794$	−62.5735	−2.22065
$795$	1.25227	0.0444135
$796$	2.41742	0.0856833
$797$	−2.49545	−0.0883935	−0.0441968	−	0.999023i	$-0.514073\pi$
$797$	−2.49545	−0.0883935	−0.0441968	+	0.999023i	$0.514073\pi$
$798$	0	0
$799$	−16.7477	−0.592492
$800$	−115.826	−4.09506
$801$	9.16515	0.323835
$802$	38.8348	1.37131
$803$	7.00000	0.247025
$804$	−3.37386	−0.118987
$805$	0	0
$806$	15.5826	0.548873
$807$	−10.0000	−0.352017
$808$	25.5826	0.899992
$809$	−27.3303	−0.960882	−0.480441	−	0.877027i	$-0.659523\pi$
$809$	−27.3303	−0.960882	−0.480441	+	0.877027i	$0.659523\pi$
$810$	8.37386	0.294228
$811$	29.7477	1.04458	0.522292	−	0.852767i	$-0.325077\pi$
$811$	29.7477	1.04458	0.522292	+	0.852767i	$0.325077\pi$
$812$	0	0
$813$	−14.5826	−0.511433
$814$	2.79129	0.0978346
$815$	1.74773	0.0612202
$816$	28.4174	0.994809
$817$	19.5826	0.685108
$818$	−79.0780	−2.76490
$819$	0	0
$820$	124.486	4.34725
$821$	−47.0000	−1.64031	−0.820156	−	0.572140i	$-0.806113\pi$
$821$	−47.0000	−1.64031	−0.820156	+	0.572140i	$0.806113\pi$
$822$	6.74773	0.235354
$823$	−21.4174	−0.746564	−0.373282	−	0.927718i	$-0.621768\pi$
$823$	−21.4174	−0.746564	−0.373282	+	0.927718i	$0.621768\pi$
$824$	181.652	6.32813
$825$	−4.00000	−0.139262
$826$	0	0
$827$	−36.9129	−1.28359	−0.641793	−	0.766878i	$-0.721809\pi$
$827$	−36.9129	−1.28359	−0.641793	+	0.766878i	$0.721809\pi$
$828$	20.7477	0.721033
$829$	40.0000	1.38926	0.694629	−	0.719368i	$-0.255569\pi$
$829$	40.0000	1.38926	0.694629	+	0.719368i	$0.255569\pi$
$830$	20.2432	0.702651
$831$	−0.834849	−0.0289606
$832$	−44.9129	−1.55707
$833$	0	0
$834$	−20.0000	−0.692543
$835$	68.2432	2.36165
$836$	14.9564	0.517279
$837$	5.58258	0.192962
$838$	−18.3739	−0.634715
$839$	−52.9129	−1.82676	−0.913378	−	0.407113i	$-0.866535\pi$
$839$	−52.9129	−1.82676	−0.913378	+	0.407113i	$0.866535\pi$
$840$	0	0
$841$	74.3303	2.56311
$842$	−110.704	−3.81512
$843$	9.33030	0.321353
$844$	29.9129	1.02964
$845$	36.0000	1.23844
$846$	29.5390	1.01557
$847$	0	0
$848$	−7.49545	−0.257395
$849$	−0.252273	−0.00865798
$850$	−17.6697	−0.606066
$851$	3.58258	0.122809
$852$	−41.4955	−1.42161
$853$	1.16515	0.0398940	0.0199470	−	0.999801i	$-0.493650\pi$
$853$	1.16515	0.0398940	0.0199470	+	0.999801i	$0.493650\pi$
$854$	0	0
$855$	7.74773	0.264967
$856$	36.1652	1.23610
$857$	44.3303	1.51429	0.757147	−	0.653244i	$-0.226593\pi$
$857$	44.3303	1.51429	0.757147	+	0.653244i	$0.226593\pi$
$858$	−2.79129	−0.0952930
$859$	−12.0000	−0.409435	−0.204717	−	0.978821i	$-0.565628\pi$
$859$	−12.0000	−0.409435	−0.204717	+	0.978821i	$0.565628\pi$
$860$	131.739	4.49225
$861$	0	0
$862$	27.2087	0.926732
$863$	23.5826	0.802760	0.401380	−	0.915912i	$-0.368531\pi$
$863$	23.5826	0.802760	0.401380	+	0.915912i	$0.368531\pi$
$864$	−28.9564	−0.985118
$865$	33.4955	1.13888
$866$	20.0000	0.679628
$867$	−14.4955	−0.492291
$868$	0	0
$869$	11.1652	0.378752
$870$	85.1216	2.88589
$871$	0.582576	0.0197398
$872$	59.0780	2.00063
$873$	11.5826	0.392011
$874$	25.8258	0.873569
$875$	0	0
$876$	−40.5390	−1.36969
$877$	−45.4955	−1.53627	−0.768136	−	0.640287i	$-0.778816\pi$
$877$	−45.4955	−1.53627	−0.768136	+	0.640287i	$0.778816\pi$
$878$	74.1996	2.50412
$879$	0	0
$880$	53.8693	1.81593
$881$	−35.6606	−1.20144	−0.600718	−	0.799461i	$-0.705119\pi$
$881$	−35.6606	−1.20144	−0.600718	+	0.799461i	$0.705119\pi$
$882$	0	0
$883$	−28.2523	−0.950765	−0.475382	−	0.879779i	$-0.657690\pi$
$883$	−28.2523	−0.950765	−0.475382	+	0.879779i	$0.657690\pi$
$884$	−9.16515	−0.308257
$885$	−13.7477	−0.462125
$886$	13.4955	0.453389
$887$	−11.2523	−0.377814	−0.188907	−	0.981995i	$-0.560495\pi$
$887$	−11.2523	−0.377814	−0.188907	+	0.981995i	$0.560495\pi$
$888$	−10.5826	−0.355128
$889$	0	0
$890$	76.7477	2.57259
$891$	−1.00000	−0.0335013
$892$	−34.7477	−1.16344
$893$	27.3303	0.914574
$894$	33.9564	1.13567
$895$	66.9909	2.23926
$896$	0	0
$897$	−3.58258	−0.119619
$898$	−51.1652	−1.70740
$899$	56.7477	1.89264
$900$	23.1652	0.772172
$901$	−0.660606	−0.0220080
$902$	−20.0000	−0.665927
$903$	0	0
$904$	96.9909	3.22587
$905$	10.7477	0.357267
$906$	15.5826	0.517696
$907$	5.66970	0.188259	0.0941296	−	0.995560i	$-0.469993\pi$
$907$	5.66970	0.188259	0.0941296	+	0.995560i	$0.469993\pi$
$908$	127.408	4.22819
$909$	−2.41742	−0.0801809
$910$	0	0
$911$	51.4955	1.70612	0.853060	−	0.521812i	$-0.174744\pi$
$911$	51.4955	1.70612	0.853060	+	0.521812i	$0.174744\pi$
$912$	−46.3739	−1.53559
$913$	−2.41742	−0.0800051
$914$	−72.3303	−2.39247
$915$	30.0000	0.991769
$916$	154.904	5.11817
$917$	0	0
$918$	−4.41742	−0.145797
$919$	−53.9129	−1.77842	−0.889211	−	0.457498i	$-0.848746\pi$
$919$	−53.9129	−1.77842	−0.889211	+	0.457498i	$0.848746\pi$
$920$	113.739	3.74985
$921$	0	0
$922$	−51.1652	−1.68503
$923$	7.16515	0.235844
$924$	0	0
$925$	4.00000	0.131519
$926$	1.62614	0.0534382
$927$	−17.1652	−0.563778
$928$	−294.347	−9.66240
$929$	−15.3303	−0.502971	−0.251485	−	0.967861i	$-0.580919\pi$
$929$	−15.3303	−0.502971	−0.251485	+	0.967861i	$0.580919\pi$
$930$	46.7477	1.53292
$931$	0	0
$932$	−81.0780	−2.65580
$933$	22.3303	0.731061
$934$	−82.1125	−2.68680
$935$	4.74773	0.155267
$936$	10.5826	0.345902
$937$	−10.0000	−0.326686	−0.163343	−	0.986569i	$-0.552228\pi$
$937$	−10.0000	−0.326686	−0.163343	+	0.986569i	$0.552228\pi$
$938$	0	0
$939$	−10.4174	−0.339960
$940$	183.860	5.99686
$941$	−16.8348	−0.548800	−0.274400	−	0.961616i	$-0.588479\pi$
$941$	−16.8348	−0.548800	−0.274400	+	0.961616i	$0.588479\pi$
$942$	2.33030	0.0759254
$943$	−25.6697	−0.835920
$944$	82.2867	2.67821
$945$	0	0
$946$	−21.1652	−0.688138
$947$	26.8348	0.872015	0.436008	−	0.899943i	$-0.356392\pi$
$947$	26.8348	0.872015	0.436008	+	0.899943i	$0.356392\pi$
$948$	−64.6606	−2.10008
$949$	7.00000	0.227230
$950$	28.8348	0.935526
$951$	−31.5826	−1.02414
$952$	0	0
$953$	−9.83485	−0.318582	−0.159291	−	0.987232i	$-0.550921\pi$
$953$	−9.83485	−0.318582	−0.159291	+	0.987232i	$0.550921\pi$
$954$	1.16515	0.0377232
$955$	−7.25227	−0.234678
$956$	42.9564	1.38931
$957$	−10.1652	−0.328593
$958$	−17.9129	−0.578739
$959$	0	0
$960$	−134.739	−4.34867
$961$	0.165151	0.00532746
$962$	2.79129	0.0899947
$963$	−3.41742	−0.110125
$964$	−47.2867	−1.52300
$965$	34.7477	1.11857
$966$	0	0
$967$	5.16515	0.166100	0.0830500	−	0.996545i	$-0.473534\pi$
$967$	5.16515	0.166100	0.0830500	+	0.996545i	$0.473534\pi$
$968$	−10.5826	−0.340137
$969$	−4.08712	−0.131297
$970$	96.9909	3.11419
$971$	3.41742	0.109670	0.0548352	−	0.998495i	$-0.482537\pi$
$971$	3.41742	0.109670	0.0548352	+	0.998495i	$0.482537\pi$
$972$	5.79129	0.185756
$973$	0	0
$974$	73.4955	2.35495
$975$	−4.00000	−0.128103
$976$	−179.564	−5.74772
$977$	50.7477	1.62356	0.811782	−	0.583961i	$-0.198498\pi$
$977$	50.7477	1.62356	0.811782	+	0.583961i	$0.198498\pi$
$978$	1.62614	0.0519981
$979$	−9.16515	−0.292920
$980$	0	0
$981$	−5.58258	−0.178238
$982$	−63.9564	−2.04093
$983$	23.1652	0.738854	0.369427	−	0.929260i	$-0.379554\pi$
$983$	23.1652	0.738854	0.369427	+	0.929260i	$0.379554\pi$
$984$	75.8258	2.41724
$985$	39.4955	1.25843
$986$	−44.9038	−1.43003
$987$	0	0
$988$	14.9564	0.475828
$989$	−27.1652	−0.863802
$990$	−8.37386	−0.266139
$991$	−47.7477	−1.51676	−0.758378	−	0.651815i	$-0.774008\pi$
$991$	−47.7477	−1.51676	−0.758378	+	0.651815i	$0.774008\pi$
$992$	−161.652	−5.13244
$993$	15.1652	0.481252
$994$	0	0
$995$	−1.25227	−0.0396997
$996$	14.0000	0.443607
$997$	62.6606	1.98448	0.992241	−	0.124332i	$-0.0396789\pi$
$997$	62.6606	1.98448	0.992241	+	0.124332i	$0.0396789\pi$
$998$	−39.7822	−1.25928
$999$	1.00000	0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.2.a.o.1.1		2
3.2	odd	2		4851.2.a.ba.1.2		2
7.6	odd	2		231.2.a.b.1.1	✓	2
21.20	even	2		693.2.a.j.1.2		2
28.27	even	2		3696.2.a.bl.1.1		2
35.34	odd	2		5775.2.a.bn.1.2		2
77.76	even	2		2541.2.a.z.1.2		2
231.230	odd	2		7623.2.a.bf.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.a.b.1.1	✓	2	7.6	odd	2
693.2.a.j.1.2		2	21.20	even	2
1617.2.a.o.1.1		2	1.1	even	1	trivial
2541.2.a.z.1.2		2	77.76	even	2
3696.2.a.bl.1.1		2	28.27	even	2
4851.2.a.ba.1.2		2	3.2	odd	2
5775.2.a.bn.1.2		2	35.34	odd	2
7623.2.a.bf.1.1		2	231.230	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:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1617.a (trivial)

\(f(q)\)	\(=\)	\(q-2.79129 q^{2} +1.00000 q^{3} +5.79129 q^{4} -3.00000 q^{5} -2.79129 q^{6} -10.5826 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.79129 q^{2} +1.00000 q^{3} +5.79129 q^{4} -3.00000 q^{5} -2.79129 q^{6} -10.5826 q^{8} +1.00000 q^{9} +8.37386 q^{10} -1.00000 q^{11} +5.79129 q^{12} -1.00000 q^{13} -3.00000 q^{15} +17.9564 q^{16} +1.58258 q^{17} -2.79129 q^{18} -2.58258 q^{19} -17.3739 q^{20} +2.79129 q^{22} +3.58258 q^{23} -10.5826 q^{24} +4.00000 q^{25} +2.79129 q^{26} +1.00000 q^{27} +10.1652 q^{29} +8.37386 q^{30} +5.58258 q^{31} -28.9564 q^{32} -1.00000 q^{33} -4.41742 q^{34} +5.79129 q^{36} +1.00000 q^{37} +7.20871 q^{38} -1.00000 q^{39} +31.7477 q^{40} -7.16515 q^{41} -7.58258 q^{43} -5.79129 q^{44} -3.00000 q^{45} -10.0000 q^{46} -10.5826 q^{47} +17.9564 q^{48} -11.1652 q^{50} +1.58258 q^{51} -5.79129 q^{52} -0.417424 q^{53} -2.79129 q^{54} +3.00000 q^{55} -2.58258 q^{57} -28.3739 q^{58} +4.58258 q^{59} -17.3739 q^{60} -10.0000 q^{61} -15.5826 q^{62} +44.9129 q^{64} +3.00000 q^{65} +2.79129 q^{66} -0.582576 q^{67} +9.16515 q^{68} +3.58258 q^{69} -7.16515 q^{71} -10.5826 q^{72} -7.00000 q^{73} -2.79129 q^{74} +4.00000 q^{75} -14.9564 q^{76} +2.79129 q^{78} -11.1652 q^{79} -53.8693 q^{80} +1.00000 q^{81} +20.0000 q^{82} +2.41742 q^{83} -4.74773 q^{85} +21.1652 q^{86} +10.1652 q^{87} +10.5826 q^{88} +9.16515 q^{89} +8.37386 q^{90} +20.7477 q^{92} +5.58258 q^{93} +29.5390 q^{94} +7.74773 q^{95} -28.9564 q^{96} +11.5826 q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 2 q^{3} + 7 q^{4} - 6 q^{5} - q^{6} - 12 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - q^2 + 2 * q^3 + 7 * q^4 - 6 * q^5 - q^6 - 12 * q^8 + 2 * q^9	\( 2 q - q^{2} + 2 q^{3} + 7 q^{4} - 6 q^{5} - q^{6} - 12 q^{8} + 2 q^{9} + 3 q^{10} - 2 q^{11} + 7 q^{12} - 2 q^{13} - 6 q^{15} + 13 q^{16} - 6 q^{17} - q^{18} + 4 q^{19} - 21 q^{20} + q^{22} - 2 q^{23} - 12 q^{24} + 8 q^{25} + q^{26} + 2 q^{27} + 2 q^{29} + 3 q^{30} + 2 q^{31} - 35 q^{32} - 2 q^{33} - 18 q^{34} + 7 q^{36} + 2 q^{37} + 19 q^{38} - 2 q^{39} + 36 q^{40} + 4 q^{41} - 6 q^{43} - 7 q^{44} - 6 q^{45} - 20 q^{46} - 12 q^{47} + 13 q^{48} - 4 q^{50} - 6 q^{51} - 7 q^{52} - 10 q^{53} - q^{54} + 6 q^{55} + 4 q^{57} - 43 q^{58} - 21 q^{60} - 20 q^{61} - 22 q^{62} + 44 q^{64} + 6 q^{65} + q^{66} + 8 q^{67} - 2 q^{69} + 4 q^{71} - 12 q^{72} - 14 q^{73} - q^{74} + 8 q^{75} - 7 q^{76} + q^{78} - 4 q^{79} - 39 q^{80} + 2 q^{81} + 40 q^{82} + 14 q^{83} + 18 q^{85} + 24 q^{86} + 2 q^{87} + 12 q^{88} + 3 q^{90} + 14 q^{92} + 2 q^{93} + 27 q^{94} - 12 q^{95} - 35 q^{96} + 14 q^{97} - 2 q^{99}+O(q^{100}) \) 2 * q - q^2 + 2 * q^3 + 7 * q^4 - 6 * q^5 - q^6 - 12 * q^8 + 2 * q^9 + 3 * q^10 - 2 * q^11 + 7 * q^12 - 2 * q^13 - 6 * q^15 + 13 * q^16 - 6 * q^17 - q^18 + 4 * q^19 - 21 * q^20 + q^22 - 2 * q^23 - 12 * q^24 + 8 * q^25 + q^26 + 2 * q^27 + 2 * q^29 + 3 * q^30 + 2 * q^31 - 35 * q^32 - 2 * q^33 - 18 * q^34 + 7 * q^36 + 2 * q^37 + 19 * q^38 - 2 * q^39 + 36 * q^40 + 4 * q^41 - 6 * q^43 - 7 * q^44 - 6 * q^45 - 20 * q^46 - 12 * q^47 + 13 * q^48 - 4 * q^50 - 6 * q^51 - 7 * q^52 - 10 * q^53 - q^54 + 6 * q^55 + 4 * q^57 - 43 * q^58 - 21 * q^60 - 20 * q^61 - 22 * q^62 + 44 * q^64 + 6 * q^65 + q^66 + 8 * q^67 - 2 * q^69 + 4 * q^71 - 12 * q^72 - 14 * q^73 - q^74 + 8 * q^75 - 7 * q^76 + q^78 - 4 * q^79 - 39 * q^80 + 2 * q^81 + 40 * q^82 + 14 * q^83 + 18 * q^85 + 24 * q^86 + 2 * q^87 + 12 * q^88 + 3 * q^90 + 14 * q^92 + 2 * q^93 + 27 * q^94 - 12 * q^95 - 35 * q^96 + 14 * q^97 - 2 * q^99

Introduction

L-functions

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