LMFDB - Embedded newform 4598.2.a.bi.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4598,2,Mod(1,4598)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4598, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4598.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4598 = 2 \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4598.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:	$36.7152148494$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	4598.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.23607 q^{3} +1.00000 q^{4} +0.618034 q^{5} -2.23607 q^{6} +2.85410 q^{7} +1.00000 q^{8} +2.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.23607 q^{3} +1.00000 q^{4} +0.618034 q^{5} -2.23607 q^{6} +2.85410 q^{7} +1.00000 q^{8} +2.00000 q^{9} +0.618034 q^{10} -2.23607 q^{12} +1.61803 q^{13} +2.85410 q^{14} -1.38197 q^{15} +1.00000 q^{16} -6.23607 q^{17} +2.00000 q^{18} +1.00000 q^{19} +0.618034 q^{20} -6.38197 q^{21} -0.236068 q^{23} -2.23607 q^{24} -4.61803 q^{25} +1.61803 q^{26} +2.23607 q^{27} +2.85410 q^{28} -10.4721 q^{29} -1.38197 q^{30} -10.7082 q^{31} +1.00000 q^{32} -6.23607 q^{34} +1.76393 q^{35} +2.00000 q^{36} -7.85410 q^{37} +1.00000 q^{38} -3.61803 q^{39} +0.618034 q^{40} +4.09017 q^{41} -6.38197 q^{42} +3.70820 q^{43} +1.23607 q^{45} -0.236068 q^{46} +11.4721 q^{47} -2.23607 q^{48} +1.14590 q^{49} -4.61803 q^{50} +13.9443 q^{51} +1.61803 q^{52} +5.94427 q^{53} +2.23607 q^{54} +2.85410 q^{56} -2.23607 q^{57} -10.4721 q^{58} -13.0902 q^{59} -1.38197 q^{60} -4.38197 q^{61} -10.7082 q^{62} +5.70820 q^{63} +1.00000 q^{64} +1.00000 q^{65} -6.09017 q^{67} -6.23607 q^{68} +0.527864 q^{69} +1.76393 q^{70} -3.76393 q^{71} +2.00000 q^{72} +1.32624 q^{73} -7.85410 q^{74} +10.3262 q^{75} +1.00000 q^{76} -3.61803 q^{78} +3.00000 q^{79} +0.618034 q^{80} -11.0000 q^{81} +4.09017 q^{82} +1.09017 q^{83} -6.38197 q^{84} -3.85410 q^{85} +3.70820 q^{86} +23.4164 q^{87} -9.18034 q^{89} +1.23607 q^{90} +4.61803 q^{91} -0.236068 q^{92} +23.9443 q^{93} +11.4721 q^{94} +0.618034 q^{95} -2.23607 q^{96} +16.4164 q^{97} +1.14590 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{4} - q^{5} - q^{7} + 2 q^{8} + 4 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^4 - q^5 - q^7 + 2 * q^8 + 4 * q^9	$ 2 q + 2 q^{2} + 2 q^{4} - q^{5} - q^{7} + 2 q^{8} + 4 q^{9} - q^{10} + q^{13} - q^{14} - 5 q^{15} + 2 q^{16} - 8 q^{17} + 4 q^{18} + 2 q^{19} - q^{20} - 15 q^{21} + 4 q^{23} - 7 q^{25} + q^{26} - q^{28} - 12 q^{29} - 5 q^{30} - 8 q^{31} + 2 q^{32} - 8 q^{34} + 8 q^{35} + 4 q^{36} - 9 q^{37} + 2 q^{38} - 5 q^{39} - q^{40} - 3 q^{41} - 15 q^{42} - 6 q^{43} - 2 q^{45} + 4 q^{46} + 14 q^{47} + 9 q^{49} - 7 q^{50} + 10 q^{51} + q^{52} - 6 q^{53} - q^{56} - 12 q^{58} - 15 q^{59} - 5 q^{60} - 11 q^{61} - 8 q^{62} - 2 q^{63} + 2 q^{64} + 2 q^{65} - q^{67} - 8 q^{68} + 10 q^{69} + 8 q^{70} - 12 q^{71} + 4 q^{72} - 13 q^{73} - 9 q^{74} + 5 q^{75} + 2 q^{76} - 5 q^{78} + 6 q^{79} - q^{80} - 22 q^{81} - 3 q^{82} - 9 q^{83} - 15 q^{84} - q^{85} - 6 q^{86} + 20 q^{87} + 4 q^{89} - 2 q^{90} + 7 q^{91} + 4 q^{92} + 30 q^{93} + 14 q^{94} - q^{95} + 6 q^{97} + 9 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^4 - q^5 - q^7 + 2 * q^8 + 4 * q^9 - q^10 + q^13 - q^14 - 5 * q^15 + 2 * q^16 - 8 * q^17 + 4 * q^18 + 2 * q^19 - q^20 - 15 * q^21 + 4 * q^23 - 7 * q^25 + q^26 - q^28 - 12 * q^29 - 5 * q^30 - 8 * q^31 + 2 * q^32 - 8 * q^34 + 8 * q^35 + 4 * q^36 - 9 * q^37 + 2 * q^38 - 5 * q^39 - q^40 - 3 * q^41 - 15 * q^42 - 6 * q^43 - 2 * q^45 + 4 * q^46 + 14 * q^47 + 9 * q^49 - 7 * q^50 + 10 * q^51 + q^52 - 6 * q^53 - q^56 - 12 * q^58 - 15 * q^59 - 5 * q^60 - 11 * q^61 - 8 * q^62 - 2 * q^63 + 2 * q^64 + 2 * q^65 - q^67 - 8 * q^68 + 10 * q^69 + 8 * q^70 - 12 * q^71 + 4 * q^72 - 13 * q^73 - 9 * q^74 + 5 * q^75 + 2 * q^76 - 5 * q^78 + 6 * q^79 - q^80 - 22 * q^81 - 3 * q^82 - 9 * q^83 - 15 * q^84 - q^85 - 6 * q^86 + 20 * q^87 + 4 * q^89 - 2 * q^90 + 7 * q^91 + 4 * q^92 + 30 * q^93 + 14 * q^94 - q^95 + 6 * q^97 + 9 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.23607	−1.29099	−0.645497	−	0.763763i	$-0.723350\pi$
$3$	−2.23607	−1.29099	−0.645497	+	0.763763i	$0.723350\pi$
$4$	1.00000	0.500000
$5$	0.618034	0.276393	0.138197	−	0.990405i	$-0.455869\pi$
$5$	0.618034	0.276393	0.138197	+	0.990405i	$0.455869\pi$
$6$	−2.23607	−0.912871
$7$	2.85410	1.07875	0.539375	−	0.842066i	$-0.318661\pi$
$7$	2.85410	1.07875	0.539375	+	0.842066i	$0.318661\pi$
$8$	1.00000	0.353553
$9$	2.00000	0.666667
$10$	0.618034	0.195440
$11$	0	0
$11$	0	0
$12$	−2.23607	−0.645497
$13$	1.61803	0.448762	0.224381	−	0.974502i	$-0.427964\pi$
$13$	1.61803	0.448762	0.224381	+	0.974502i	$0.427964\pi$
$14$	2.85410	0.762791
$15$	−1.38197	−0.356822
$16$	1.00000	0.250000
$17$	−6.23607	−1.51247	−0.756234	−	0.654301i	$-0.772963\pi$
$17$	−6.23607	−1.51247	−0.756234	+	0.654301i	$0.772963\pi$
$18$	2.00000	0.471405
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0.618034	0.138197
$21$	−6.38197	−1.39266
$22$	0	0
$23$	−0.236068	−0.0492236	−0.0246118	−	0.999697i	$-0.507835\pi$
$23$	−0.236068	−0.0492236	−0.0246118	+	0.999697i	$0.507835\pi$
$24$	−2.23607	−0.456435
$25$	−4.61803	−0.923607
$26$	1.61803	0.317323
$27$	2.23607	0.430331
$28$	2.85410	0.539375
$29$	−10.4721	−1.94463	−0.972313	−	0.233681i	$-0.924923\pi$
$29$	−10.4721	−1.94463	−0.972313	+	0.233681i	$0.924923\pi$
$30$	−1.38197	−0.252311
$31$	−10.7082	−1.92325	−0.961625	−	0.274367i	$-0.911532\pi$
$31$	−10.7082	−1.92325	−0.961625	+	0.274367i	$0.911532\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−6.23607	−1.06948
$35$	1.76393	0.298159
$36$	2.00000	0.333333
$37$	−7.85410	−1.29121	−0.645603	−	0.763673i	$-0.723394\pi$
$37$	−7.85410	−1.29121	−0.645603	+	0.763673i	$0.723394\pi$
$38$	1.00000	0.162221
$39$	−3.61803	−0.579349
$40$	0.618034	0.0977198
$41$	4.09017	0.638777	0.319389	−	0.947624i	$-0.396522\pi$
$41$	4.09017	0.638777	0.319389	+	0.947624i	$0.396522\pi$
$42$	−6.38197	−0.984759
$43$	3.70820	0.565496	0.282748	−	0.959194i	$-0.408754\pi$
$43$	3.70820	0.565496	0.282748	+	0.959194i	$0.408754\pi$
$44$	0	0
$45$	1.23607	0.184262
$46$	−0.236068	−0.0348063
$47$	11.4721	1.67338	0.836692	−	0.547674i	$-0.184487\pi$
$47$	11.4721	1.67338	0.836692	+	0.547674i	$0.184487\pi$
$48$	−2.23607	−0.322749
$49$	1.14590	0.163700
$50$	−4.61803	−0.653089
$51$	13.9443	1.95259
$52$	1.61803	0.224381
$53$	5.94427	0.816509	0.408254	−	0.912868i	$-0.366138\pi$
$53$	5.94427	0.816509	0.408254	+	0.912868i	$0.366138\pi$
$54$	2.23607	0.304290
$55$	0	0
$56$	2.85410	0.381395
$57$	−2.23607	−0.296174
$58$	−10.4721	−1.37506
$59$	−13.0902	−1.70419	−0.852097	−	0.523383i	$-0.824670\pi$
$59$	−13.0902	−1.70419	−0.852097	+	0.523383i	$0.824670\pi$
$60$	−1.38197	−0.178411
$61$	−4.38197	−0.561053	−0.280527	−	0.959846i	$-0.590509\pi$
$61$	−4.38197	−0.561053	−0.280527	+	0.959846i	$0.590509\pi$
$62$	−10.7082	−1.35994
$63$	5.70820	0.719166
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	0	0
$67$	−6.09017	−0.744033	−0.372016	−	0.928226i	$-0.621333\pi$
$67$	−6.09017	−0.744033	−0.372016	+	0.928226i	$0.621333\pi$
$68$	−6.23607	−0.756234
$69$	0.527864	0.0635474
$70$	1.76393	0.210830
$71$	−3.76393	−0.446697	−0.223348	−	0.974739i	$-0.571699\pi$
$71$	−3.76393	−0.446697	−0.223348	+	0.974739i	$0.571699\pi$
$72$	2.00000	0.235702
$73$	1.32624	0.155224	0.0776122	−	0.996984i	$-0.475270\pi$
$73$	1.32624	0.155224	0.0776122	+	0.996984i	$0.475270\pi$
$74$	−7.85410	−0.913021
$75$	10.3262	1.19237
$76$	1.00000	0.114708
$77$	0	0
$78$	−3.61803	−0.409662
$79$	3.00000	0.337526	0.168763	−	0.985657i	$-0.446023\pi$
$79$	3.00000	0.337526	0.168763	+	0.985657i	$0.446023\pi$
$80$	0.618034	0.0690983
$81$	−11.0000	−1.22222
$82$	4.09017	0.451684
$83$	1.09017	0.119662	0.0598308	−	0.998209i	$-0.480944\pi$
$83$	1.09017	0.119662	0.0598308	+	0.998209i	$0.480944\pi$
$84$	−6.38197	−0.696330
$85$	−3.85410	−0.418036
$86$	3.70820	0.399866
$87$	23.4164	2.51050
$88$	0	0
$89$	−9.18034	−0.973114	−0.486557	−	0.873649i	$-0.661747\pi$
$89$	−9.18034	−0.973114	−0.486557	+	0.873649i	$0.661747\pi$
$90$	1.23607	0.130293
$91$	4.61803	0.484102
$92$	−0.236068	−0.0246118
$93$	23.9443	2.48291
$94$	11.4721	1.18326
$95$	0.618034	0.0634089
$96$	−2.23607	−0.228218
$97$	16.4164	1.66683	0.833417	−	0.552645i	$-0.186381\pi$
$97$	16.4164	1.66683	0.833417	+	0.552645i	$0.186381\pi$
$98$	1.14590	0.115753
$99$	0	0
$100$	−4.61803	−0.461803
$101$	−0.527864	−0.0525244	−0.0262622	−	0.999655i	$-0.508360\pi$
$101$	−0.527864	−0.0525244	−0.0262622	+	0.999655i	$0.508360\pi$
$102$	13.9443	1.38069
$103$	−8.56231	−0.843669	−0.421835	−	0.906673i	$-0.638614\pi$
$103$	−8.56231	−0.843669	−0.421835	+	0.906673i	$0.638614\pi$
$104$	1.61803	0.158661
$105$	−3.94427	−0.384922
$106$	5.94427	0.577359
$107$	3.00000	0.290021	0.145010	−	0.989430i	$-0.453678\pi$
$107$	3.00000	0.290021	0.145010	+	0.989430i	$0.453678\pi$
$108$	2.23607	0.215166
$109$	10.3262	0.989074	0.494537	−	0.869157i	$-0.335338\pi$
$109$	10.3262	0.989074	0.494537	+	0.869157i	$0.335338\pi$
$110$	0	0
$111$	17.5623	1.66694
$112$	2.85410	0.269687
$113$	16.4164	1.54433	0.772163	−	0.635425i	$-0.219175\pi$
$113$	16.4164	1.54433	0.772163	+	0.635425i	$0.219175\pi$
$114$	−2.23607	−0.209427
$115$	−0.145898	−0.0136051
$116$	−10.4721	−0.972313
$117$	3.23607	0.299175
$118$	−13.0902	−1.20505
$119$	−17.7984	−1.63157
$120$	−1.38197	−0.126156
$121$	0	0
$122$	−4.38197	−0.396725
$123$	−9.14590	−0.824658
$124$	−10.7082	−0.961625
$125$	−5.94427	−0.531672
$126$	5.70820	0.508527
$127$	−19.1803	−1.70198	−0.850990	−	0.525182i	$-0.823997\pi$
$127$	−19.1803	−1.70198	−0.850990	+	0.525182i	$0.823997\pi$
$128$	1.00000	0.0883883
$129$	−8.29180	−0.730052
$130$	1.00000	0.0877058
$131$	−16.6525	−1.45493	−0.727467	−	0.686143i	$-0.759302\pi$
$131$	−16.6525	−1.45493	−0.727467	+	0.686143i	$0.759302\pi$
$132$	0	0
$133$	2.85410	0.247482
$134$	−6.09017	−0.526111
$135$	1.38197	0.118941
$136$	−6.23607	−0.534738
$137$	1.47214	0.125773	0.0628865	−	0.998021i	$-0.479969\pi$
$137$	1.47214	0.125773	0.0628865	+	0.998021i	$0.479969\pi$
$138$	0.527864	0.0449348
$139$	−4.85410	−0.411720	−0.205860	−	0.978581i	$-0.565999\pi$
$139$	−4.85410	−0.411720	−0.205860	+	0.978581i	$0.565999\pi$
$140$	1.76393	0.149079
$141$	−25.6525	−2.16033
$142$	−3.76393	−0.315862
$143$	0	0
$144$	2.00000	0.166667
$145$	−6.47214	−0.537482
$146$	1.32624	0.109760
$147$	−2.56231	−0.211335
$148$	−7.85410	−0.645603
$149$	17.7639	1.45528	0.727639	−	0.685960i	$-0.240618\pi$
$149$	17.7639	1.45528	0.727639	+	0.685960i	$0.240618\pi$
$150$	10.3262	0.843134
$151$	0.291796	0.0237460	0.0118730	−	0.999930i	$-0.496221\pi$
$151$	0.291796	0.0237460	0.0118730	+	0.999930i	$0.496221\pi$
$152$	1.00000	0.0811107
$153$	−12.4721	−1.00831
$154$	0	0
$155$	−6.61803	−0.531573
$156$	−3.61803	−0.289675
$157$	−3.70820	−0.295947	−0.147973	−	0.988991i	$-0.547275\pi$
$157$	−3.70820	−0.295947	−0.147973	+	0.988991i	$0.547275\pi$
$158$	3.00000	0.238667
$159$	−13.2918	−1.05411
$160$	0.618034	0.0488599
$161$	−0.673762	−0.0530999
$162$	−11.0000	−0.864242
$163$	−5.03444	−0.394328	−0.197164	−	0.980371i	$-0.563173\pi$
$163$	−5.03444	−0.394328	−0.197164	+	0.980371i	$0.563173\pi$
$164$	4.09017	0.319389
$165$	0	0
$166$	1.09017	0.0846136
$167$	−8.38197	−0.648616	−0.324308	−	0.945952i	$-0.605131\pi$
$167$	−8.38197	−0.648616	−0.324308	+	0.945952i	$0.605131\pi$
$168$	−6.38197	−0.492379
$169$	−10.3820	−0.798613
$170$	−3.85410	−0.295596
$171$	2.00000	0.152944
$172$	3.70820	0.282748
$173$	8.79837	0.668928	0.334464	−	0.942409i	$-0.391445\pi$
$173$	8.79837	0.668928	0.334464	+	0.942409i	$0.391445\pi$
$174$	23.4164	1.77519
$175$	−13.1803	−0.996340
$176$	0	0
$177$	29.2705	2.20011
$178$	−9.18034	−0.688096
$179$	−17.2361	−1.28828	−0.644142	−	0.764906i	$-0.722785\pi$
$179$	−17.2361	−1.28828	−0.644142	+	0.764906i	$0.722785\pi$
$180$	1.23607	0.0921311
$181$	4.05573	0.301460	0.150730	−	0.988575i	$-0.451838\pi$
$181$	4.05573	0.301460	0.150730	+	0.988575i	$0.451838\pi$
$182$	4.61803	0.342311
$183$	9.79837	0.724317
$184$	−0.236068	−0.0174032
$185$	−4.85410	−0.356881
$186$	23.9443	1.75568
$187$	0	0
$188$	11.4721	0.836692
$189$	6.38197	0.464220
$190$	0.618034	0.0448369
$191$	15.9443	1.15369	0.576844	−	0.816855i	$-0.304284\pi$
$191$	15.9443	1.15369	0.576844	+	0.816855i	$0.304284\pi$
$192$	−2.23607	−0.161374
$193$	−25.5623	−1.84002	−0.920008	−	0.391901i	$-0.871818\pi$
$193$	−25.5623	−1.84002	−0.920008	+	0.391901i	$0.871818\pi$
$194$	16.4164	1.17863
$195$	−2.23607	−0.160128
$196$	1.14590	0.0818499
$197$	0.819660	0.0583984	0.0291992	−	0.999574i	$-0.490704\pi$
$197$	0.819660	0.0583984	0.0291992	+	0.999574i	$0.490704\pi$
$198$	0	0
$199$	−21.8885	−1.55164	−0.775819	−	0.630956i	$-0.782663\pi$
$199$	−21.8885	−1.55164	−0.775819	+	0.630956i	$0.782663\pi$
$200$	−4.61803	−0.326544
$201$	13.6180	0.960542
$202$	−0.527864	−0.0371404
$203$	−29.8885	−2.09776
$204$	13.9443	0.976294
$205$	2.52786	0.176554
$206$	−8.56231	−0.596564
$207$	−0.472136	−0.0328157
$208$	1.61803	0.112190
$209$	0	0
$210$	−3.94427	−0.272181
$211$	−8.05573	−0.554579	−0.277290	−	0.960786i	$-0.589436\pi$
$211$	−8.05573	−0.554579	−0.277290	+	0.960786i	$0.589436\pi$
$212$	5.94427	0.408254
$213$	8.41641	0.576683
$214$	3.00000	0.205076
$215$	2.29180	0.156299
$216$	2.23607	0.152145
$217$	−30.5623	−2.07470
$218$	10.3262	0.699381
$219$	−2.96556	−0.200394
$220$	0	0
$221$	−10.0902	−0.678738
$222$	17.5623	1.17870
$223$	−20.0000	−1.33930	−0.669650	−	0.742677i	$-0.733556\pi$
$223$	−20.0000	−1.33930	−0.669650	+	0.742677i	$0.733556\pi$
$224$	2.85410	0.190698
$225$	−9.23607	−0.615738
$226$	16.4164	1.09200
$227$	13.0344	0.865126	0.432563	−	0.901604i	$-0.357609\pi$
$227$	13.0344	0.865126	0.432563	+	0.901604i	$0.357609\pi$
$228$	−2.23607	−0.148087
$229$	4.43769	0.293251	0.146626	−	0.989192i	$-0.453159\pi$
$229$	4.43769	0.293251	0.146626	+	0.989192i	$0.453159\pi$
$230$	−0.145898	−0.00962023
$231$	0	0
$232$	−10.4721	−0.687529
$233$	−7.65248	−0.501330	−0.250665	−	0.968074i	$-0.580649\pi$
$233$	−7.65248	−0.501330	−0.250665	+	0.968074i	$0.580649\pi$
$234$	3.23607	0.211548
$235$	7.09017	0.462512
$236$	−13.0902	−0.852097
$237$	−6.70820	−0.435745
$238$	−17.7984	−1.15370
$239$	21.9787	1.42168	0.710842	−	0.703351i	$-0.248314\pi$
$239$	21.9787	1.42168	0.710842	+	0.703351i	$0.248314\pi$
$240$	−1.38197	−0.0892055
$241$	−7.32624	−0.471924	−0.235962	−	0.971762i	$-0.575824\pi$
$241$	−7.32624	−0.471924	−0.235962	+	0.971762i	$0.575824\pi$
$242$	0	0
$243$	17.8885	1.14755
$244$	−4.38197	−0.280527
$245$	0.708204	0.0452455
$246$	−9.14590	−0.583121
$247$	1.61803	0.102953
$248$	−10.7082	−0.679972
$249$	−2.43769	−0.154483
$250$	−5.94427	−0.375949
$251$	3.05573	0.192876	0.0964379	−	0.995339i	$-0.469255\pi$
$251$	3.05573	0.192876	0.0964379	+	0.995339i	$0.469255\pi$
$252$	5.70820	0.359583
$253$	0	0
$254$	−19.1803	−1.20348
$255$	8.61803	0.539682
$256$	1.00000	0.0625000
$257$	6.32624	0.394620	0.197310	−	0.980341i	$-0.436779\pi$
$257$	6.32624	0.394620	0.197310	+	0.980341i	$0.436779\pi$
$258$	−8.29180	−0.516225
$259$	−22.4164	−1.39289
$260$	1.00000	0.0620174
$261$	−20.9443	−1.29642
$262$	−16.6525	−1.02879
$263$	−13.0344	−0.803738	−0.401869	−	0.915697i	$-0.631639\pi$
$263$	−13.0344	−0.803738	−0.401869	+	0.915697i	$0.631639\pi$
$264$	0	0
$265$	3.67376	0.225677
$266$	2.85410	0.174996
$267$	20.5279	1.25628
$268$	−6.09017	−0.372016
$269$	27.9443	1.70379	0.851896	−	0.523711i	$-0.175453\pi$
$269$	27.9443	1.70379	0.851896	+	0.523711i	$0.175453\pi$
$270$	1.38197	0.0841038
$271$	−7.70820	−0.468240	−0.234120	−	0.972208i	$-0.575221\pi$
$271$	−7.70820	−0.468240	−0.234120	+	0.972208i	$0.575221\pi$
$272$	−6.23607	−0.378117
$273$	−10.3262	−0.624972
$274$	1.47214	0.0889350
$275$	0	0
$276$	0.527864	0.0317737
$277$	−12.8541	−0.772328	−0.386164	−	0.922430i	$-0.626200\pi$
$277$	−12.8541	−0.772328	−0.386164	+	0.922430i	$0.626200\pi$
$278$	−4.85410	−0.291130
$279$	−21.4164	−1.28217
$280$	1.76393	0.105415
$281$	−1.03444	−0.0617096	−0.0308548	−	0.999524i	$-0.509823\pi$
$281$	−1.03444	−0.0617096	−0.0308548	+	0.999524i	$0.509823\pi$
$282$	−25.6525	−1.52758
$283$	−5.29180	−0.314565	−0.157282	−	0.987554i	$-0.550273\pi$
$283$	−5.29180	−0.314565	−0.157282	+	0.987554i	$0.550273\pi$
$284$	−3.76393	−0.223348
$285$	−1.38197	−0.0818606
$286$	0	0
$287$	11.6738	0.689080
$288$	2.00000	0.117851
$289$	21.8885	1.28756
$290$	−6.47214	−0.380057
$291$	−36.7082	−2.15187
$292$	1.32624	0.0776122
$293$	10.5279	0.615044	0.307522	−	0.951541i	$-0.400500\pi$
$293$	10.5279	0.615044	0.307522	+	0.951541i	$0.400500\pi$
$294$	−2.56231	−0.149437
$295$	−8.09017	−0.471028
$296$	−7.85410	−0.456510
$297$	0	0
$298$	17.7639	1.02904
$299$	−0.381966	−0.0220897
$300$	10.3262	0.596186
$301$	10.5836	0.610028
$302$	0.291796	0.0167910
$303$	1.18034	0.0678088
$304$	1.00000	0.0573539
$305$	−2.70820	−0.155071
$306$	−12.4721	−0.712985
$307$	−18.2361	−1.04079	−0.520394	−	0.853926i	$-0.674215\pi$
$307$	−18.2361	−1.04079	−0.520394	+	0.853926i	$0.674215\pi$
$308$	0	0
$309$	19.1459	1.08917
$310$	−6.61803	−0.375879
$311$	16.4721	0.934049	0.467025	−	0.884244i	$-0.345326\pi$
$311$	16.4721	0.934049	0.467025	+	0.884244i	$0.345326\pi$
$312$	−3.61803	−0.204831
$313$	9.94427	0.562083	0.281042	−	0.959696i	$-0.409320\pi$
$313$	9.94427	0.562083	0.281042	+	0.959696i	$0.409320\pi$
$314$	−3.70820	−0.209266
$315$	3.52786	0.198773
$316$	3.00000	0.168763
$317$	−3.00000	−0.168497	−0.0842484	−	0.996445i	$-0.526849\pi$
$317$	−3.00000	−0.168497	−0.0842484	+	0.996445i	$0.526849\pi$
$318$	−13.2918	−0.745367
$319$	0	0
$320$	0.618034	0.0345492
$321$	−6.70820	−0.374415
$322$	−0.673762	−0.0375473
$323$	−6.23607	−0.346984
$324$	−11.0000	−0.611111
$325$	−7.47214	−0.414480
$326$	−5.03444	−0.278832
$327$	−23.0902	−1.27689
$328$	4.09017	0.225842
$329$	32.7426	1.80516
$330$	0	0
$331$	9.70820	0.533611	0.266806	−	0.963750i	$-0.414032\pi$
$331$	9.70820	0.533611	0.266806	+	0.963750i	$0.414032\pi$
$332$	1.09017	0.0598308
$333$	−15.7082	−0.860804
$334$	−8.38197	−0.458641
$335$	−3.76393	−0.205646
$336$	−6.38197	−0.348165
$337$	−15.1803	−0.826926	−0.413463	−	0.910521i	$-0.635681\pi$
$337$	−15.1803	−0.826926	−0.413463	+	0.910521i	$0.635681\pi$
$338$	−10.3820	−0.564705
$339$	−36.7082	−1.99372
$340$	−3.85410	−0.209018
$341$	0	0
$342$	2.00000	0.108148
$343$	−16.7082	−0.902158
$344$	3.70820	0.199933
$345$	0.326238	0.0175641
$346$	8.79837	0.473004
$347$	−25.5967	−1.37411	−0.687053	−	0.726608i	$-0.741096\pi$
$347$	−25.5967	−1.37411	−0.687053	+	0.726608i	$0.741096\pi$
$348$	23.4164	1.25525
$349$	−12.6738	−0.678411	−0.339205	−	0.940712i	$-0.610158\pi$
$349$	−12.6738	−0.678411	−0.339205	+	0.940712i	$0.610158\pi$
$350$	−13.1803	−0.704519
$351$	3.61803	0.193116
$352$	0	0
$353$	26.9443	1.43410	0.717049	−	0.697022i	$-0.245492\pi$
$353$	26.9443	1.43410	0.717049	+	0.697022i	$0.245492\pi$
$354$	29.2705	1.55571
$355$	−2.32624	−0.123464
$356$	−9.18034	−0.486557
$357$	39.7984	2.10635
$358$	−17.2361	−0.910954
$359$	−19.8541	−1.04786	−0.523930	−	0.851762i	$-0.675535\pi$
$359$	−19.8541	−1.04786	−0.523930	+	0.851762i	$0.675535\pi$
$360$	1.23607	0.0651465
$361$	1.00000	0.0526316
$362$	4.05573	0.213164
$363$	0	0
$364$	4.61803	0.242051
$365$	0.819660	0.0429030
$366$	9.79837	0.512169
$367$	13.4377	0.701442	0.350721	−	0.936480i	$-0.385937\pi$
$367$	13.4377	0.701442	0.350721	+	0.936480i	$0.385937\pi$
$368$	−0.236068	−0.0123059
$369$	8.18034	0.425851
$370$	−4.85410	−0.252353
$371$	16.9656	0.880808
$372$	23.9443	1.24145
$373$	−19.1246	−0.990235	−0.495117	−	0.868826i	$-0.664875\pi$
$373$	−19.1246	−0.990235	−0.495117	+	0.868826i	$0.664875\pi$
$374$	0	0
$375$	13.2918	0.686385
$376$	11.4721	0.591630
$377$	−16.9443	−0.872674
$378$	6.38197	0.328253
$379$	21.8541	1.12257	0.561285	−	0.827623i	$-0.310307\pi$
$379$	21.8541	1.12257	0.561285	+	0.827623i	$0.310307\pi$
$380$	0.618034	0.0317045
$381$	42.8885	2.19725
$382$	15.9443	0.815780
$383$	−14.6180	−0.746947	−0.373473	−	0.927641i	$-0.621833\pi$
$383$	−14.6180	−0.746947	−0.373473	+	0.927641i	$0.621833\pi$
$384$	−2.23607	−0.114109
$385$	0	0
$386$	−25.5623	−1.30109
$387$	7.41641	0.376997
$388$	16.4164	0.833417
$389$	28.0689	1.42315	0.711574	−	0.702611i	$-0.247982\pi$
$389$	28.0689	1.42315	0.711574	+	0.702611i	$0.247982\pi$
$390$	−2.23607	−0.113228
$391$	1.47214	0.0744491
$392$	1.14590	0.0578766
$393$	37.2361	1.87831
$394$	0.819660	0.0412939
$395$	1.85410	0.0932900
$396$	0	0
$397$	29.8328	1.49727	0.748633	−	0.662985i	$-0.230711\pi$
$397$	29.8328	1.49727	0.748633	+	0.662985i	$0.230711\pi$
$398$	−21.8885	−1.09717
$399$	−6.38197	−0.319498
$400$	−4.61803	−0.230902
$401$	−29.4721	−1.47177	−0.735884	−	0.677107i	$-0.763233\pi$
$401$	−29.4721	−1.47177	−0.735884	+	0.677107i	$0.763233\pi$
$402$	13.6180	0.679206
$403$	−17.3262	−0.863081
$404$	−0.527864	−0.0262622
$405$	−6.79837	−0.337814
$406$	−29.8885	−1.48334
$407$	0	0
$408$	13.9443	0.690344
$409$	−3.00000	−0.148340	−0.0741702	−	0.997246i	$-0.523631\pi$
$409$	−3.00000	−0.148340	−0.0741702	+	0.997246i	$0.523631\pi$
$410$	2.52786	0.124842
$411$	−3.29180	−0.162372
$412$	−8.56231	−0.421835
$413$	−37.3607	−1.83840
$414$	−0.472136	−0.0232042
$415$	0.673762	0.0330737
$416$	1.61803	0.0793306
$417$	10.8541	0.531528
$418$	0	0
$419$	31.4164	1.53479	0.767396	−	0.641173i	$-0.221552\pi$
$419$	31.4164	1.53479	0.767396	+	0.641173i	$0.221552\pi$
$420$	−3.94427	−0.192461
$421$	−10.4164	−0.507665	−0.253832	−	0.967248i	$-0.581691\pi$
$421$	−10.4164	−0.507665	−0.253832	+	0.967248i	$0.581691\pi$
$422$	−8.05573	−0.392147
$423$	22.9443	1.11559
$424$	5.94427	0.288679
$425$	28.7984	1.39693
$426$	8.41641	0.407776
$427$	−12.5066	−0.605236
$428$	3.00000	0.145010
$429$	0	0
$430$	2.29180	0.110520
$431$	−27.0344	−1.30220	−0.651102	−	0.758991i	$-0.725693\pi$
$431$	−27.0344	−1.30220	−0.651102	+	0.758991i	$0.725693\pi$
$432$	2.23607	0.107583
$433$	−32.4721	−1.56051	−0.780256	−	0.625461i	$-0.784911\pi$
$433$	−32.4721	−1.56051	−0.780256	+	0.625461i	$0.784911\pi$
$434$	−30.5623	−1.46704
$435$	14.4721	0.693886
$436$	10.3262	0.494537
$437$	−0.236068	−0.0112927
$438$	−2.96556	−0.141700
$439$	26.8541	1.28168	0.640838	−	0.767676i	$-0.278587\pi$
$439$	26.8541	1.28168	0.640838	+	0.767676i	$0.278587\pi$
$440$	0	0
$441$	2.29180	0.109133
$442$	−10.0902	−0.479940
$443$	1.85410	0.0880910	0.0440455	−	0.999030i	$-0.485975\pi$
$443$	1.85410	0.0880910	0.0440455	+	0.999030i	$0.485975\pi$
$444$	17.5623	0.833470
$445$	−5.67376	−0.268962
$446$	−20.0000	−0.947027
$447$	−39.7214	−1.87876
$448$	2.85410	0.134844
$449$	12.7082	0.599737	0.299869	−	0.953981i	$-0.403057\pi$
$449$	12.7082	0.599737	0.299869	+	0.953981i	$0.403057\pi$
$450$	−9.23607	−0.435392
$451$	0	0
$452$	16.4164	0.772163
$453$	−0.652476	−0.0306560
$454$	13.0344	0.611737
$455$	2.85410	0.133802
$456$	−2.23607	−0.104713
$457$	9.00000	0.421002	0.210501	−	0.977594i	$-0.432490\pi$
$457$	9.00000	0.421002	0.210501	+	0.977594i	$0.432490\pi$
$458$	4.43769	0.207360
$459$	−13.9443	−0.650863
$460$	−0.145898	−0.00680253
$461$	−32.3050	−1.50459	−0.752296	−	0.658825i	$-0.771054\pi$
$461$	−32.3050	−1.50459	−0.752296	+	0.658825i	$0.771054\pi$
$462$	0	0
$463$	−16.1459	−0.750364	−0.375182	−	0.926951i	$-0.622420\pi$
$463$	−16.1459	−0.750364	−0.375182	+	0.926951i	$0.622420\pi$
$464$	−10.4721	−0.486157
$465$	14.7984	0.686258
$466$	−7.65248	−0.354494
$467$	−16.5066	−0.763833	−0.381917	−	0.924197i	$-0.624736\pi$
$467$	−16.5066	−0.763833	−0.381917	+	0.924197i	$0.624736\pi$
$468$	3.23607	0.149587
$469$	−17.3820	−0.802625
$470$	7.09017	0.327045
$471$	8.29180	0.382066
$472$	−13.0902	−0.602524
$473$	0	0
$474$	−6.70820	−0.308118
$475$	−4.61803	−0.211890
$476$	−17.7984	−0.815787
$477$	11.8885	0.544339
$478$	21.9787	1.00528
$479$	−8.23607	−0.376316	−0.188158	−	0.982139i	$-0.560252\pi$
$479$	−8.23607	−0.376316	−0.188158	+	0.982139i	$0.560252\pi$
$480$	−1.38197	−0.0630778
$481$	−12.7082	−0.579444
$482$	−7.32624	−0.333701
$483$	1.50658	0.0685517
$484$	0	0
$485$	10.1459	0.460701
$486$	17.8885	0.811441
$487$	−1.94427	−0.0881034	−0.0440517	−	0.999029i	$-0.514027\pi$
$487$	−1.94427	−0.0881034	−0.0440517	+	0.999029i	$0.514027\pi$
$488$	−4.38197	−0.198362
$489$	11.2574	0.509075
$490$	0.708204	0.0319934
$491$	−28.8541	−1.30217	−0.651084	−	0.759006i	$-0.725685\pi$
$491$	−28.8541	−1.30217	−0.651084	+	0.759006i	$0.725685\pi$
$492$	−9.14590	−0.412329
$493$	65.3050	2.94119
$494$	1.61803	0.0727988
$495$	0	0
$496$	−10.7082	−0.480813
$497$	−10.7426	−0.481874
$498$	−2.43769	−0.109236
$499$	31.0000	1.38775	0.693875	−	0.720095i	$-0.255902\pi$
$499$	31.0000	1.38775	0.693875	+	0.720095i	$0.255902\pi$
$500$	−5.94427	−0.265836
$501$	18.7426	0.837360
$502$	3.05573	0.136384
$503$	18.7984	0.838178	0.419089	−	0.907945i	$-0.362350\pi$
$503$	18.7984	0.838178	0.419089	+	0.907945i	$0.362350\pi$
$504$	5.70820	0.254264
$505$	−0.326238	−0.0145174
$506$	0	0
$507$	23.2148	1.03100
$508$	−19.1803	−0.850990
$509$	27.5410	1.22073	0.610367	−	0.792119i	$-0.291022\pi$
$509$	27.5410	1.22073	0.610367	+	0.792119i	$0.291022\pi$
$510$	8.61803	0.381613
$511$	3.78522	0.167448
$512$	1.00000	0.0441942
$513$	2.23607	0.0987248
$514$	6.32624	0.279038
$515$	−5.29180	−0.233184
$516$	−8.29180	−0.365026
$517$	0	0
$518$	−22.4164	−0.984920
$519$	−19.6738	−0.863582
$520$	1.00000	0.0438529
$521$	15.4721	0.677847	0.338923	−	0.940814i	$-0.389937\pi$
$521$	15.4721	0.677847	0.338923	+	0.940814i	$0.389937\pi$
$522$	−20.9443	−0.916706
$523$	−5.74265	−0.251108	−0.125554	−	0.992087i	$-0.540071\pi$
$523$	−5.74265	−0.251108	−0.125554	+	0.992087i	$0.540071\pi$
$524$	−16.6525	−0.727467
$525$	29.4721	1.28627
$526$	−13.0344	−0.568329
$527$	66.7771	2.90886
$528$	0	0
$529$	−22.9443	−0.997577
$530$	3.67376	0.159578
$531$	−26.1803	−1.13613
$532$	2.85410	0.123741
$533$	6.61803	0.286659
$534$	20.5279	0.888328
$535$	1.85410	0.0801598
$536$	−6.09017	−0.263055
$537$	38.5410	1.66317
$538$	27.9443	1.20476
$539$	0	0
$540$	1.38197	0.0594703
$541$	24.6869	1.06137	0.530687	−	0.847568i	$-0.321934\pi$
$541$	24.6869	1.06137	0.530687	+	0.847568i	$0.321934\pi$
$542$	−7.70820	−0.331096
$543$	−9.06888	−0.389183
$544$	−6.23607	−0.267369
$545$	6.38197	0.273373
$546$	−10.3262	−0.441922
$547$	18.7984	0.803760	0.401880	−	0.915692i	$-0.368357\pi$
$547$	18.7984	0.803760	0.401880	+	0.915692i	$0.368357\pi$
$548$	1.47214	0.0628865
$549$	−8.76393	−0.374036
$550$	0	0
$551$	−10.4721	−0.446128
$552$	0.527864	0.0224674
$553$	8.56231	0.364106
$554$	−12.8541	−0.546118
$555$	10.8541	0.460731
$556$	−4.85410	−0.205860
$557$	−26.9443	−1.14167	−0.570833	−	0.821066i	$-0.693380\pi$
$557$	−26.9443	−1.14167	−0.570833	+	0.821066i	$0.693380\pi$
$558$	−21.4164	−0.906629
$559$	6.00000	0.253773
$560$	1.76393	0.0745397
$561$	0	0
$562$	−1.03444	−0.0436353
$563$	12.5967	0.530890	0.265445	−	0.964126i	$-0.414481\pi$
$563$	12.5967	0.530890	0.265445	+	0.964126i	$0.414481\pi$
$564$	−25.6525	−1.08016
$565$	10.1459	0.426841
$566$	−5.29180	−0.222431
$567$	−31.3951	−1.31847
$568$	−3.76393	−0.157931
$569$	−5.52786	−0.231740	−0.115870	−	0.993264i	$-0.536966\pi$
$569$	−5.52786	−0.231740	−0.115870	+	0.993264i	$0.536966\pi$
$570$	−1.38197	−0.0578842
$571$	10.8885	0.455671	0.227836	−	0.973700i	$-0.426835\pi$
$571$	10.8885	0.455671	0.227836	+	0.973700i	$0.426835\pi$
$572$	0	0
$573$	−35.6525	−1.48940
$574$	11.6738	0.487253
$575$	1.09017	0.0454632
$576$	2.00000	0.0833333
$577$	16.2148	0.675030	0.337515	−	0.941320i	$-0.390414\pi$
$577$	16.2148	0.675030	0.337515	+	0.941320i	$0.390414\pi$
$578$	21.8885	0.910443
$579$	57.1591	2.37545
$580$	−6.47214	−0.268741
$581$	3.11146	0.129085
$582$	−36.7082	−1.52160
$583$	0	0
$584$	1.32624	0.0548801
$585$	2.00000	0.0826898
$586$	10.5279	0.434902
$587$	−7.58359	−0.313008	−0.156504	−	0.987677i	$-0.550022\pi$
$587$	−7.58359	−0.313008	−0.156504	+	0.987677i	$0.550022\pi$
$588$	−2.56231	−0.105668
$589$	−10.7082	−0.441224
$590$	−8.09017	−0.333067
$591$	−1.83282	−0.0753920
$592$	−7.85410	−0.322802
$593$	28.4164	1.16692	0.583461	−	0.812141i	$-0.301698\pi$
$593$	28.4164	1.16692	0.583461	+	0.812141i	$0.301698\pi$
$594$	0	0
$595$	−11.0000	−0.450956
$596$	17.7639	0.727639
$597$	48.9443	2.00316
$598$	−0.381966	−0.0156198
$599$	10.8541	0.443487	0.221743	−	0.975105i	$-0.428825\pi$
$599$	10.8541	0.443487	0.221743	+	0.975105i	$0.428825\pi$
$600$	10.3262	0.421567
$601$	37.2705	1.52030	0.760148	−	0.649750i	$-0.225126\pi$
$601$	37.2705	1.52030	0.760148	+	0.649750i	$0.225126\pi$
$602$	10.5836	0.431355
$603$	−12.1803	−0.496022
$604$	0.291796	0.0118730
$605$	0	0
$606$	1.18034	0.0479480
$607$	3.00000	0.121766	0.0608831	−	0.998145i	$-0.480608\pi$
$607$	3.00000	0.121766	0.0608831	+	0.998145i	$0.480608\pi$
$608$	1.00000	0.0405554
$609$	66.8328	2.70820
$610$	−2.70820	−0.109652
$611$	18.5623	0.750951
$612$	−12.4721	−0.504156
$613$	−21.1246	−0.853215	−0.426608	−	0.904437i	$-0.640291\pi$
$613$	−21.1246	−0.853215	−0.426608	+	0.904437i	$0.640291\pi$
$614$	−18.2361	−0.735948
$615$	−5.65248	−0.227930
$616$	0	0
$617$	−11.6180	−0.467724	−0.233862	−	0.972270i	$-0.575136\pi$
$617$	−11.6180	−0.467724	−0.233862	+	0.972270i	$0.575136\pi$
$618$	19.1459	0.770161
$619$	−0.909830	−0.0365692	−0.0182846	−	0.999833i	$-0.505820\pi$
$619$	−0.909830	−0.0365692	−0.0182846	+	0.999833i	$0.505820\pi$
$620$	−6.61803	−0.265787
$621$	−0.527864	−0.0211825
$622$	16.4721	0.660472
$623$	−26.2016	−1.04975
$624$	−3.61803	−0.144837
$625$	19.4164	0.776656
$626$	9.94427	0.397453
$627$	0	0
$628$	−3.70820	−0.147973
$629$	48.9787	1.95291
$630$	3.52786	0.140553
$631$	−2.14590	−0.0854269	−0.0427134	−	0.999087i	$-0.513600\pi$
$631$	−2.14590	−0.0854269	−0.0427134	+	0.999087i	$0.513600\pi$
$632$	3.00000	0.119334
$633$	18.0132	0.715959
$634$	−3.00000	−0.119145
$635$	−11.8541	−0.470416
$636$	−13.2918	−0.527054
$637$	1.85410	0.0734622
$638$	0	0
$639$	−7.52786	−0.297798
$640$	0.618034	0.0244299
$641$	−37.4853	−1.48058	−0.740290	−	0.672288i	$-0.765312\pi$
$641$	−37.4853	−1.48058	−0.740290	+	0.672288i	$0.765312\pi$
$642$	−6.70820	−0.264752
$643$	25.4164	1.00233	0.501163	−	0.865353i	$-0.332906\pi$
$643$	25.4164	1.00233	0.501163	+	0.865353i	$0.332906\pi$
$644$	−0.673762	−0.0265499
$645$	−5.12461	−0.201781
$646$	−6.23607	−0.245355
$647$	−0.618034	−0.0242974	−0.0121487	−	0.999926i	$-0.503867\pi$
$647$	−0.618034	−0.0242974	−0.0121487	+	0.999926i	$0.503867\pi$
$648$	−11.0000	−0.432121
$649$	0	0
$650$	−7.47214	−0.293081
$651$	68.3394	2.67843
$652$	−5.03444	−0.197164
$653$	32.3262	1.26502	0.632512	−	0.774551i	$-0.282024\pi$
$653$	32.3262	1.26502	0.632512	+	0.774551i	$0.282024\pi$
$654$	−23.0902	−0.902897
$655$	−10.2918	−0.402134
$656$	4.09017	0.159694
$657$	2.65248	0.103483
$658$	32.7426	1.27644
$659$	−40.5279	−1.57874	−0.789371	−	0.613917i	$-0.789593\pi$
$659$	−40.5279	−1.57874	−0.789371	+	0.613917i	$0.789593\pi$
$660$	0	0
$661$	−46.6180	−1.81323	−0.906616	−	0.421957i	$-0.861343\pi$
$661$	−46.6180	−1.81323	−0.906616	+	0.421957i	$0.861343\pi$
$662$	9.70820	0.377320
$663$	22.5623	0.876247
$664$	1.09017	0.0423068
$665$	1.76393	0.0684023
$666$	−15.7082	−0.608681
$667$	2.47214	0.0957215
$668$	−8.38197	−0.324308
$669$	44.7214	1.72903
$670$	−3.76393	−0.145413
$671$	0	0
$672$	−6.38197	−0.246190
$673$	−6.72949	−0.259403	−0.129701	−	0.991553i	$-0.541402\pi$
$673$	−6.72949	−0.259403	−0.129701	+	0.991553i	$0.541402\pi$
$674$	−15.1803	−0.584725
$675$	−10.3262	−0.397457
$676$	−10.3820	−0.399306
$677$	−2.63932	−0.101437	−0.0507187	−	0.998713i	$-0.516151\pi$
$677$	−2.63932	−0.101437	−0.0507187	+	0.998713i	$0.516151\pi$
$678$	−36.7082	−1.40977
$679$	46.8541	1.79810
$680$	−3.85410	−0.147798
$681$	−29.1459	−1.11687
$682$	0	0
$683$	23.2148	0.888289	0.444144	−	0.895955i	$-0.353508\pi$
$683$	23.2148	0.888289	0.444144	+	0.895955i	$0.353508\pi$
$684$	2.00000	0.0764719
$685$	0.909830	0.0347628
$686$	−16.7082	−0.637922
$687$	−9.92299	−0.378586
$688$	3.70820	0.141374
$689$	9.61803	0.366418
$690$	0.326238	0.0124197
$691$	27.2361	1.03611	0.518054	−	0.855348i	$-0.326656\pi$
$691$	27.2361	1.03611	0.518054	+	0.855348i	$0.326656\pi$
$692$	8.79837	0.334464
$693$	0	0
$694$	−25.5967	−0.971639
$695$	−3.00000	−0.113796
$696$	23.4164	0.887597
$697$	−25.5066	−0.966131
$698$	−12.6738	−0.479709
$699$	17.1115	0.647215
$700$	−13.1803	−0.498170
$701$	−19.1459	−0.723131	−0.361565	−	0.932347i	$-0.617758\pi$
$701$	−19.1459	−0.723131	−0.361565	+	0.932347i	$0.617758\pi$
$702$	3.61803	0.136554
$703$	−7.85410	−0.296223
$704$	0	0
$705$	−15.8541	−0.597100
$706$	26.9443	1.01406
$707$	−1.50658	−0.0566607
$708$	29.2705	1.10005
$709$	−31.7639	−1.19292	−0.596460	−	0.802643i	$-0.703426\pi$
$709$	−31.7639	−1.19292	−0.596460	+	0.802643i	$0.703426\pi$
$710$	−2.32624	−0.0873022
$711$	6.00000	0.225018
$712$	−9.18034	−0.344048
$713$	2.52786	0.0946693
$714$	39.7984	1.48942
$715$	0	0
$716$	−17.2361	−0.644142
$717$	−49.1459	−1.83539
$718$	−19.8541	−0.740949
$719$	25.1459	0.937784	0.468892	−	0.883256i	$-0.344653\pi$
$719$	25.1459	0.937784	0.468892	+	0.883256i	$0.344653\pi$
$720$	1.23607	0.0460655
$721$	−24.4377	−0.910107
$722$	1.00000	0.0372161
$723$	16.3820	0.609252
$724$	4.05573	0.150730
$725$	48.3607	1.79607
$726$	0	0
$727$	7.83282	0.290503	0.145252	−	0.989395i	$-0.453601\pi$
$727$	7.83282	0.290503	0.145252	+	0.989395i	$0.453601\pi$
$728$	4.61803	0.171156
$729$	−7.00000	−0.259259
$730$	0.819660	0.0303370
$731$	−23.1246	−0.855295
$732$	9.79837	0.362158
$733$	−5.43769	−0.200846	−0.100423	−	0.994945i	$-0.532020\pi$
$733$	−5.43769	−0.200846	−0.100423	+	0.994945i	$0.532020\pi$
$734$	13.4377	0.495994
$735$	−1.58359	−0.0584117
$736$	−0.236068	−0.00870158
$737$	0	0
$738$	8.18034	0.301122
$739$	15.1246	0.556368	0.278184	−	0.960528i	$-0.410268\pi$
$739$	15.1246	0.556368	0.278184	+	0.960528i	$0.410268\pi$
$740$	−4.85410	−0.178440
$741$	−3.61803	−0.132912
$742$	16.9656	0.622825
$743$	24.1803	0.887091	0.443545	−	0.896252i	$-0.353721\pi$
$743$	24.1803	0.887091	0.443545	+	0.896252i	$0.353721\pi$
$744$	23.9443	0.877840
$745$	10.9787	0.402229
$746$	−19.1246	−0.700202
$747$	2.18034	0.0797745
$748$	0	0
$749$	8.56231	0.312860
$750$	13.2918	0.485348
$751$	−48.8885	−1.78397	−0.891984	−	0.452067i	$-0.850687\pi$
$751$	−48.8885	−1.78397	−0.891984	+	0.452067i	$0.850687\pi$
$752$	11.4721	0.418346
$753$	−6.83282	−0.249002
$754$	−16.9443	−0.617074
$755$	0.180340	0.00656324
$756$	6.38197	0.232110
$757$	13.9230	0.506040	0.253020	−	0.967461i	$-0.418576\pi$
$757$	13.9230	0.506040	0.253020	+	0.967461i	$0.418576\pi$
$758$	21.8541	0.793777
$759$	0	0
$760$	0.618034	0.0224184
$761$	−50.8885	−1.84471	−0.922354	−	0.386346i	$-0.873737\pi$
$761$	−50.8885	−1.84471	−0.922354	+	0.386346i	$0.873737\pi$
$762$	42.8885	1.55369
$763$	29.4721	1.06696
$764$	15.9443	0.576844
$765$	−7.70820	−0.278691
$766$	−14.6180	−0.528171
$767$	−21.1803	−0.764778
$768$	−2.23607	−0.0806872
$769$	35.2918	1.27265	0.636327	−	0.771419i	$-0.280453\pi$
$769$	35.2918	1.27265	0.636327	+	0.771419i	$0.280453\pi$
$770$	0	0
$771$	−14.1459	−0.509452
$772$	−25.5623	−0.920008
$773$	5.49342	0.197585	0.0987923	−	0.995108i	$-0.468502\pi$
$773$	5.49342	0.197585	0.0987923	+	0.995108i	$0.468502\pi$
$774$	7.41641	0.266577
$775$	49.4508	1.77633
$776$	16.4164	0.589315
$777$	50.1246	1.79821
$778$	28.0689	1.00632
$779$	4.09017	0.146546
$780$	−2.23607	−0.0800641
$781$	0	0
$782$	1.47214	0.0526435
$783$	−23.4164	−0.836834
$784$	1.14590	0.0409249
$785$	−2.29180	−0.0817977
$786$	37.2361	1.32817
$787$	29.5967	1.05501	0.527505	−	0.849552i	$-0.323128\pi$
$787$	29.5967	1.05501	0.527505	+	0.849552i	$0.323128\pi$
$788$	0.819660	0.0291992
$789$	29.1459	1.03762
$790$	1.85410	0.0659660
$791$	46.8541	1.66594
$792$	0	0
$793$	−7.09017	−0.251779
$794$	29.8328	1.05873
$795$	−8.21478	−0.291348
$796$	−21.8885	−0.775819
$797$	10.2016	0.361360	0.180680	−	0.983542i	$-0.442170\pi$
$797$	10.2016	0.361360	0.180680	+	0.983542i	$0.442170\pi$
$798$	−6.38197	−0.225919
$799$	−71.5410	−2.53094
$800$	−4.61803	−0.163272
$801$	−18.3607	−0.648743
$802$	−29.4721	−1.04070
$803$	0	0
$804$	13.6180	0.480271
$805$	−0.416408	−0.0146764
$806$	−17.3262	−0.610291
$807$	−62.4853	−2.19959
$808$	−0.527864	−0.0185702
$809$	20.9443	0.736361	0.368181	−	0.929754i	$-0.379981\pi$
$809$	20.9443	0.736361	0.368181	+	0.929754i	$0.379981\pi$
$810$	−6.79837	−0.238871
$811$	54.4721	1.91278	0.956388	−	0.292100i	$-0.0943541\pi$
$811$	54.4721	1.91278	0.956388	+	0.292100i	$0.0943541\pi$
$812$	−29.8885	−1.04888
$813$	17.2361	0.604495
$814$	0	0
$815$	−3.11146	−0.108990
$816$	13.9443	0.488147
$817$	3.70820	0.129734
$818$	−3.00000	−0.104893
$819$	9.23607	0.322734
$820$	2.52786	0.0882768
$821$	0.437694	0.0152756	0.00763781	−	0.999971i	$-0.497569\pi$
$821$	0.437694	0.0152756	0.00763781	+	0.999971i	$0.497569\pi$
$822$	−3.29180	−0.114815
$823$	−16.7639	−0.584354	−0.292177	−	0.956364i	$-0.594380\pi$
$823$	−16.7639	−0.584354	−0.292177	+	0.956364i	$0.594380\pi$
$824$	−8.56231	−0.298282
$825$	0	0
$826$	−37.3607	−1.29994
$827$	28.2016	0.980667	0.490333	−	0.871535i	$-0.336875\pi$
$827$	28.2016	0.980667	0.490333	+	0.871535i	$0.336875\pi$
$828$	−0.472136	−0.0164079
$829$	32.3607	1.12393	0.561966	−	0.827160i	$-0.310045\pi$
$829$	32.3607	1.12393	0.561966	+	0.827160i	$0.310045\pi$
$830$	0.673762	0.0233866
$831$	28.7426	0.997071
$832$	1.61803	0.0560952
$833$	−7.14590	−0.247591
$834$	10.8541	0.375847
$835$	−5.18034	−0.179273
$836$	0	0
$837$	−23.9443	−0.827635
$838$	31.4164	1.08526
$839$	27.1591	0.937635	0.468817	−	0.883295i	$-0.344680\pi$
$839$	27.1591	0.937635	0.468817	+	0.883295i	$0.344680\pi$
$840$	−3.94427	−0.136090
$841$	80.6656	2.78157
$842$	−10.4164	−0.358973
$843$	2.31308	0.0796668
$844$	−8.05573	−0.277290
$845$	−6.41641	−0.220731
$846$	22.9443	0.788840
$847$	0	0
$848$	5.94427	0.204127
$849$	11.8328	0.406101
$850$	28.7984	0.987776
$851$	1.85410	0.0635578
$852$	8.41641	0.288341
$853$	3.61803	0.123879	0.0619396	−	0.998080i	$-0.480271\pi$
$853$	3.61803	0.123879	0.0619396	+	0.998080i	$0.480271\pi$
$854$	−12.5066	−0.427966
$855$	1.23607	0.0422726
$856$	3.00000	0.102538
$857$	22.9098	0.782585	0.391292	−	0.920266i	$-0.372028\pi$
$857$	22.9098	0.782585	0.391292	+	0.920266i	$0.372028\pi$
$858$	0	0
$859$	−2.52786	−0.0862496	−0.0431248	−	0.999070i	$-0.513731\pi$
$859$	−2.52786	−0.0862496	−0.0431248	+	0.999070i	$0.513731\pi$
$860$	2.29180	0.0781496
$861$	−26.1033	−0.889599
$862$	−27.0344	−0.920797
$863$	−30.1803	−1.02735	−0.513675	−	0.857985i	$-0.671716\pi$
$863$	−30.1803	−1.02735	−0.513675	+	0.857985i	$0.671716\pi$
$864$	2.23607	0.0760726
$865$	5.43769	0.184887
$866$	−32.4721	−1.10345
$867$	−48.9443	−1.66223
$868$	−30.5623	−1.03735
$869$	0	0
$870$	14.4721	0.490651
$871$	−9.85410	−0.333894
$872$	10.3262	0.349691
$873$	32.8328	1.11122
$874$	−0.236068	−0.00798512
$875$	−16.9656	−0.573541
$876$	−2.96556	−0.100197
$877$	−34.5066	−1.16520	−0.582602	−	0.812757i	$-0.697965\pi$
$877$	−34.5066	−1.16520	−0.582602	+	0.812757i	$0.697965\pi$
$878$	26.8541	0.906282
$879$	−23.5410	−0.794019
$880$	0	0
$881$	−23.0557	−0.776767	−0.388384	−	0.921498i	$-0.626966\pi$
$881$	−23.0557	−0.776767	−0.388384	+	0.921498i	$0.626966\pi$
$882$	2.29180	0.0771688
$883$	12.5410	0.422039	0.211019	−	0.977482i	$-0.432322\pi$
$883$	12.5410	0.422039	0.211019	+	0.977482i	$0.432322\pi$
$884$	−10.0902	−0.339369
$885$	18.0902	0.608094
$886$	1.85410	0.0622898
$887$	−44.5967	−1.49741	−0.748706	−	0.662902i	$-0.769325\pi$
$887$	−44.5967	−1.49741	−0.748706	+	0.662902i	$0.769325\pi$
$888$	17.5623	0.589352
$889$	−54.7426	−1.83601
$890$	−5.67376	−0.190185
$891$	0	0
$892$	−20.0000	−0.669650
$893$	11.4721	0.383900
$894$	−39.7214	−1.32848
$895$	−10.6525	−0.356073
$896$	2.85410	0.0953489
$897$	0.854102	0.0285176
$898$	12.7082	0.424078
$899$	112.138	3.74000
$900$	−9.23607	−0.307869
$901$	−37.0689	−1.23494
$902$	0	0
$903$	−23.6656	−0.787543
$904$	16.4164	0.546002
$905$	2.50658	0.0833215
$906$	−0.652476	−0.0216771
$907$	−51.1459	−1.69827	−0.849136	−	0.528175i	$-0.822877\pi$
$907$	−51.1459	−1.69827	−0.849136	+	0.528175i	$0.822877\pi$
$908$	13.0344	0.432563
$909$	−1.05573	−0.0350163
$910$	2.85410	0.0946126
$911$	20.3607	0.674579	0.337290	−	0.941401i	$-0.390490\pi$
$911$	20.3607	0.674579	0.337290	+	0.941401i	$0.390490\pi$
$912$	−2.23607	−0.0740436
$913$	0	0
$914$	9.00000	0.297694
$915$	6.05573	0.200196
$916$	4.43769	0.146626
$917$	−47.5279	−1.56951
$918$	−13.9443	−0.460230
$919$	16.4164	0.541527	0.270764	−	0.962646i	$-0.412724\pi$
$919$	16.4164	0.541527	0.270764	+	0.962646i	$0.412724\pi$
$920$	−0.145898	−0.00481012
$921$	40.7771	1.34365
$922$	−32.3050	−1.06391
$923$	−6.09017	−0.200460
$924$	0	0
$925$	36.2705	1.19257
$926$	−16.1459	−0.530587
$927$	−17.1246	−0.562446
$928$	−10.4721	−0.343765
$929$	29.9443	0.982440	0.491220	−	0.871036i	$-0.336551\pi$
$929$	29.9443	0.982440	0.491220	+	0.871036i	$0.336551\pi$
$930$	14.7984	0.485258
$931$	1.14590	0.0375553
$932$	−7.65248	−0.250665
$933$	−36.8328	−1.20585
$934$	−16.5066	−0.540112
$935$	0	0
$936$	3.23607	0.105774
$937$	−3.70820	−0.121142	−0.0605709	−	0.998164i	$-0.519292\pi$
$937$	−3.70820	−0.121142	−0.0605709	+	0.998164i	$0.519292\pi$
$938$	−17.3820	−0.567541
$939$	−22.2361	−0.725647
$940$	7.09017	0.231256
$941$	39.9443	1.30215	0.651073	−	0.759015i	$-0.274319\pi$
$941$	39.9443	1.30215	0.651073	+	0.759015i	$0.274319\pi$
$942$	8.29180	0.270161
$943$	−0.965558	−0.0314429
$944$	−13.0902	−0.426049
$945$	3.94427	0.128307
$946$	0	0
$947$	5.94427	0.193163	0.0965814	−	0.995325i	$-0.469209\pi$
$947$	5.94427	0.193163	0.0965814	+	0.995325i	$0.469209\pi$
$948$	−6.70820	−0.217872
$949$	2.14590	0.0696588
$950$	−4.61803	−0.149829
$951$	6.70820	0.217528
$952$	−17.7984	−0.576849
$953$	−46.0689	−1.49232	−0.746159	−	0.665768i	$-0.768104\pi$
$953$	−46.0689	−1.49232	−0.746159	+	0.665768i	$0.768104\pi$
$954$	11.8885	0.384906
$955$	9.85410	0.318871
$956$	21.9787	0.710842
$957$	0	0
$958$	−8.23607	−0.266095
$959$	4.20163	0.135678
$960$	−1.38197	−0.0446028
$961$	83.6656	2.69889
$962$	−12.7082	−0.409729
$963$	6.00000	0.193347
$964$	−7.32624	−0.235962
$965$	−15.7984	−0.508568
$966$	1.50658	0.0484733
$967$	−54.3951	−1.74923	−0.874615	−	0.484819i	$-0.838886\pi$
$967$	−54.3951	−1.74923	−0.874615	+	0.484819i	$0.838886\pi$
$968$	0	0
$969$	13.9443	0.447955
$970$	10.1459	0.325765
$971$	−38.0344	−1.22058	−0.610292	−	0.792177i	$-0.708948\pi$
$971$	−38.0344	−1.22058	−0.610292	+	0.792177i	$0.708948\pi$
$972$	17.8885	0.573775
$973$	−13.8541	−0.444142
$974$	−1.94427	−0.0622985
$975$	16.7082	0.535091
$976$	−4.38197	−0.140263
$977$	21.5967	0.690941	0.345471	−	0.938430i	$-0.387719\pi$
$977$	21.5967	0.690941	0.345471	+	0.938430i	$0.387719\pi$
$978$	11.2574	0.359970
$979$	0	0
$980$	0.708204	0.0226227
$981$	20.6525	0.659383
$982$	−28.8541	−0.920771
$983$	−18.5410	−0.591367	−0.295683	−	0.955286i	$-0.595547\pi$
$983$	−18.5410	−0.591367	−0.295683	+	0.955286i	$0.595547\pi$
$984$	−9.14590	−0.291561
$985$	0.506578	0.0161409
$986$	65.3050	2.07973
$987$	−73.2148	−2.33045
$988$	1.61803	0.0514765
$989$	−0.875388	−0.0278357
$990$	0	0
$991$	0.167184	0.00531078	0.00265539	−	0.999996i	$-0.499155\pi$
$991$	0.167184	0.00531078	0.00265539	+	0.999996i	$0.499155\pi$
$992$	−10.7082	−0.339986
$993$	−21.7082	−0.688889
$994$	−10.7426	−0.340736
$995$	−13.5279	−0.428862
$996$	−2.43769	−0.0772413
$997$	27.4721	0.870051	0.435026	−	0.900418i	$-0.356739\pi$
$997$	27.4721	0.870051	0.435026	+	0.900418i	$0.356739\pi$
$998$	31.0000	0.981288
$999$	−17.5623	−0.555647

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.bi.1.1		2
11.3	even	5		418.2.f.e.229.1	yes	4
11.4	even	5		418.2.f.e.115.1	✓	4
11.10	odd	2		4598.2.a.ba.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.e.115.1	✓	4	11.4	even	5
418.2.f.e.229.1	yes	4	11.3	even	5
4598.2.a.ba.1.1		2	11.10	odd	2
4598.2.a.bi.1.1		2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.23607 q^{3} +1.00000 q^{4} +0.618034 q^{5} -2.23607 q^{6} +2.85410 q^{7} +1.00000 q^{8} +2.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.23607 q^{3} +1.00000 q^{4} +0.618034 q^{5} -2.23607 q^{6} +2.85410 q^{7} +1.00000 q^{8} +2.00000 q^{9} +0.618034 q^{10} -2.23607 q^{12} +1.61803 q^{13} +2.85410 q^{14} -1.38197 q^{15} +1.00000 q^{16} -6.23607 q^{17} +2.00000 q^{18} +1.00000 q^{19} +0.618034 q^{20} -6.38197 q^{21} -0.236068 q^{23} -2.23607 q^{24} -4.61803 q^{25} +1.61803 q^{26} +2.23607 q^{27} +2.85410 q^{28} -10.4721 q^{29} -1.38197 q^{30} -10.7082 q^{31} +1.00000 q^{32} -6.23607 q^{34} +1.76393 q^{35} +2.00000 q^{36} -7.85410 q^{37} +1.00000 q^{38} -3.61803 q^{39} +0.618034 q^{40} +4.09017 q^{41} -6.38197 q^{42} +3.70820 q^{43} +1.23607 q^{45} -0.236068 q^{46} +11.4721 q^{47} -2.23607 q^{48} +1.14590 q^{49} -4.61803 q^{50} +13.9443 q^{51} +1.61803 q^{52} +5.94427 q^{53} +2.23607 q^{54} +2.85410 q^{56} -2.23607 q^{57} -10.4721 q^{58} -13.0902 q^{59} -1.38197 q^{60} -4.38197 q^{61} -10.7082 q^{62} +5.70820 q^{63} +1.00000 q^{64} +1.00000 q^{65} -6.09017 q^{67} -6.23607 q^{68} +0.527864 q^{69} +1.76393 q^{70} -3.76393 q^{71} +2.00000 q^{72} +1.32624 q^{73} -7.85410 q^{74} +10.3262 q^{75} +1.00000 q^{76} -3.61803 q^{78} +3.00000 q^{79} +0.618034 q^{80} -11.0000 q^{81} +4.09017 q^{82} +1.09017 q^{83} -6.38197 q^{84} -3.85410 q^{85} +3.70820 q^{86} +23.4164 q^{87} -9.18034 q^{89} +1.23607 q^{90} +4.61803 q^{91} -0.236068 q^{92} +23.9443 q^{93} +11.4721 q^{94} +0.618034 q^{95} -2.23607 q^{96} +16.4164 q^{97} +1.14590 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{4} - q^{5} - q^{7} + 2 q^{8} + 4 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^4 - q^5 - q^7 + 2 * q^8 + 4 * q^9	\( 2 q + 2 q^{2} + 2 q^{4} - q^{5} - q^{7} + 2 q^{8} + 4 q^{9} - q^{10} + q^{13} - q^{14} - 5 q^{15} + 2 q^{16} - 8 q^{17} + 4 q^{18} + 2 q^{19} - q^{20} - 15 q^{21} + 4 q^{23} - 7 q^{25} + q^{26} - q^{28} - 12 q^{29} - 5 q^{30} - 8 q^{31} + 2 q^{32} - 8 q^{34} + 8 q^{35} + 4 q^{36} - 9 q^{37} + 2 q^{38} - 5 q^{39} - q^{40} - 3 q^{41} - 15 q^{42} - 6 q^{43} - 2 q^{45} + 4 q^{46} + 14 q^{47} + 9 q^{49} - 7 q^{50} + 10 q^{51} + q^{52} - 6 q^{53} - q^{56} - 12 q^{58} - 15 q^{59} - 5 q^{60} - 11 q^{61} - 8 q^{62} - 2 q^{63} + 2 q^{64} + 2 q^{65} - q^{67} - 8 q^{68} + 10 q^{69} + 8 q^{70} - 12 q^{71} + 4 q^{72} - 13 q^{73} - 9 q^{74} + 5 q^{75} + 2 q^{76} - 5 q^{78} + 6 q^{79} - q^{80} - 22 q^{81} - 3 q^{82} - 9 q^{83} - 15 q^{84} - q^{85} - 6 q^{86} + 20 q^{87} + 4 q^{89} - 2 q^{90} + 7 q^{91} + 4 q^{92} + 30 q^{93} + 14 q^{94} - q^{95} + 6 q^{97} + 9 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^4 - q^5 - q^7 + 2 * q^8 + 4 * q^9 - q^10 + q^13 - q^14 - 5 * q^15 + 2 * q^16 - 8 * q^17 + 4 * q^18 + 2 * q^19 - q^20 - 15 * q^21 + 4 * q^23 - 7 * q^25 + q^26 - q^28 - 12 * q^29 - 5 * q^30 - 8 * q^31 + 2 * q^32 - 8 * q^34 + 8 * q^35 + 4 * q^36 - 9 * q^37 + 2 * q^38 - 5 * q^39 - q^40 - 3 * q^41 - 15 * q^42 - 6 * q^43 - 2 * q^45 + 4 * q^46 + 14 * q^47 + 9 * q^49 - 7 * q^50 + 10 * q^51 + q^52 - 6 * q^53 - q^56 - 12 * q^58 - 15 * q^59 - 5 * q^60 - 11 * q^61 - 8 * q^62 - 2 * q^63 + 2 * q^64 + 2 * q^65 - q^67 - 8 * q^68 + 10 * q^69 + 8 * q^70 - 12 * q^71 + 4 * q^72 - 13 * q^73 - 9 * q^74 + 5 * q^75 + 2 * q^76 - 5 * q^78 + 6 * q^79 - q^80 - 22 * q^81 - 3 * q^82 - 9 * q^83 - 15 * q^84 - q^85 - 6 * q^86 + 20 * q^87 + 4 * q^89 - 2 * q^90 + 7 * q^91 + 4 * q^92 + 30 * q^93 + 14 * q^94 - q^95 + 6 * q^97 + 9 * q^98

Introduction

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