LMFDB - Embedded newform 4235.2.a.z.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4235,2,Mod(1,4235)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, 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("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4235 = 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4235.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:	$33.8166452560$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.270017.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 7x^{2} + 7x - 3 $ x^5 - 2x^4 - 5x^3 + 7x^2 + 7x - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.64458$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.34922 q^{2} -1.64458 q^{3} +3.51886 q^{4} +1.00000 q^{5} +3.86349 q^{6} -1.00000 q^{7} -3.56813 q^{8} -0.295356 q^{9} +O(q^{10})$	\(q-2.34922 q^{2} -1.64458 q^{3} +3.51886 q^{4} +1.00000 q^{5} +3.86349 q^{6} -1.00000 q^{7} -3.56813 q^{8} -0.295356 q^{9} -2.34922 q^{10} -5.78704 q^{12} +0.774897 q^{13} +2.34922 q^{14} -1.64458 q^{15} +1.34463 q^{16} +4.83632 q^{17} +0.693857 q^{18} -6.49168 q^{19} +3.51886 q^{20} +1.64458 q^{21} -1.02098 q^{23} +5.86808 q^{24} +1.00000 q^{25} -1.82041 q^{26} +5.41948 q^{27} -3.51886 q^{28} -7.73776 q^{29} +3.86349 q^{30} +9.88022 q^{31} +3.97742 q^{32} -11.3616 q^{34} -1.00000 q^{35} -1.03931 q^{36} +1.89525 q^{37} +15.2504 q^{38} -1.27438 q^{39} -3.56813 q^{40} -9.56653 q^{41} -3.86349 q^{42} +2.28457 q^{43} -0.295356 q^{45} +2.39850 q^{46} +2.03094 q^{47} -2.21136 q^{48} +1.00000 q^{49} -2.34922 q^{50} -7.95371 q^{51} +2.72675 q^{52} +4.32092 q^{53} -12.7316 q^{54} +3.56813 q^{56} +10.6761 q^{57} +18.1777 q^{58} +1.32847 q^{59} -5.78704 q^{60} +0.894426 q^{61} -23.2109 q^{62} +0.295356 q^{63} -12.0331 q^{64} +0.774897 q^{65} -7.75874 q^{67} +17.0183 q^{68} +1.67908 q^{69} +2.34922 q^{70} +10.5821 q^{71} +1.05387 q^{72} -1.66533 q^{73} -4.45237 q^{74} -1.64458 q^{75} -22.8433 q^{76} +2.99380 q^{78} +1.15588 q^{79} +1.34463 q^{80} -8.02670 q^{81} +22.4739 q^{82} -13.8377 q^{83} +5.78704 q^{84} +4.83632 q^{85} -5.36696 q^{86} +12.7254 q^{87} -6.45237 q^{89} +0.693857 q^{90} -0.774897 q^{91} -3.59267 q^{92} -16.2488 q^{93} -4.77113 q^{94} -6.49168 q^{95} -6.54119 q^{96} -6.94752 q^{97} -2.34922 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} + 2 q^{3} + 4 q^{4} + 5 q^{5} + q^{6} - 5 q^{7} - q^{9}+O(q^{10}) $ 5 * q - 2 * q^2 + 2 * q^3 + 4 * q^4 + 5 * q^5 + q^6 - 5 * q^7 - q^9	$ 5 q - 2 q^{2} + 2 q^{3} + 4 q^{4} + 5 q^{5} + q^{6} - 5 q^{7} - q^{9} - 2 q^{10} - 3 q^{12} - 8 q^{13} + 2 q^{14} + 2 q^{15} + 2 q^{16} - 6 q^{17} - 11 q^{18} - 7 q^{19} + 4 q^{20} - 2 q^{21} + 3 q^{23} + 6 q^{24} + 5 q^{25} - 15 q^{26} + 5 q^{27} - 4 q^{28} - 17 q^{29} + q^{30} + 12 q^{31} + 3 q^{32} - 12 q^{34} - 5 q^{35} - 3 q^{36} - 2 q^{37} + 21 q^{38} - 14 q^{39} - 5 q^{41} - q^{42} - 4 q^{43} - q^{45} - 2 q^{46} - 12 q^{48} + 5 q^{49} - 2 q^{50} - 14 q^{51} - 2 q^{52} + 8 q^{53} - 22 q^{54} - 4 q^{57} + 6 q^{58} - 16 q^{59} - 3 q^{60} - 24 q^{61} - 9 q^{62} + q^{63} - 38 q^{64} - 8 q^{65} - 9 q^{67} - 19 q^{68} + 22 q^{69} + 2 q^{70} - 10 q^{71} - 4 q^{72} - 11 q^{73} + q^{74} + 2 q^{75} - 11 q^{76} - 5 q^{78} - 9 q^{79} + 2 q^{80} - 19 q^{81} + 44 q^{82} - 10 q^{83} + 3 q^{84} - 6 q^{85} + 15 q^{86} + 2 q^{87} - 9 q^{89} - 11 q^{90} + 8 q^{91} - 26 q^{92} - q^{93} - 34 q^{94} - 7 q^{95} + 18 q^{96} + 11 q^{97} - 2 q^{98}+O(q^{100}) $ 5 * q - 2 * q^2 + 2 * q^3 + 4 * q^4 + 5 * q^5 + q^6 - 5 * q^7 - q^9 - 2 * q^10 - 3 * q^12 - 8 * q^13 + 2 * q^14 + 2 * q^15 + 2 * q^16 - 6 * q^17 - 11 * q^18 - 7 * q^19 + 4 * q^20 - 2 * q^21 + 3 * q^23 + 6 * q^24 + 5 * q^25 - 15 * q^26 + 5 * q^27 - 4 * q^28 - 17 * q^29 + q^30 + 12 * q^31 + 3 * q^32 - 12 * q^34 - 5 * q^35 - 3 * q^36 - 2 * q^37 + 21 * q^38 - 14 * q^39 - 5 * q^41 - q^42 - 4 * q^43 - q^45 - 2 * q^46 - 12 * q^48 + 5 * q^49 - 2 * q^50 - 14 * q^51 - 2 * q^52 + 8 * q^53 - 22 * q^54 - 4 * q^57 + 6 * q^58 - 16 * q^59 - 3 * q^60 - 24 * q^61 - 9 * q^62 + q^63 - 38 * q^64 - 8 * q^65 - 9 * q^67 - 19 * q^68 + 22 * q^69 + 2 * q^70 - 10 * q^71 - 4 * q^72 - 11 * q^73 + q^74 + 2 * q^75 - 11 * q^76 - 5 * q^78 - 9 * q^79 + 2 * q^80 - 19 * q^81 + 44 * q^82 - 10 * q^83 + 3 * q^84 - 6 * q^85 + 15 * q^86 + 2 * q^87 - 9 * q^89 - 11 * q^90 + 8 * q^91 - 26 * q^92 - q^93 - 34 * q^94 - 7 * q^95 + 18 * q^96 + 11 * q^97 - 2 * 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 $

$2$	−2.34922	−1.66115	−0.830576	−	0.556905i	$-0.811989\pi$
$2$	−2.34922	−1.66115	−0.830576	+	0.556905i	$0.811989\pi$
$3$	−1.64458	−0.949499	−0.474749	−	0.880121i	$-0.657461\pi$
$3$	−1.64458	−0.949499	−0.474749	+	0.880121i	$0.657461\pi$
$4$	3.51886	1.75943
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	3.86349	1.57726
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.56813	−1.26153
$9$	−0.295356	−0.0984519
$10$	−2.34922	−0.742890
$11$	0	0
$11$	0	0
$12$	−5.78704	−1.67057
$13$	0.774897	0.214918	0.107459	−	0.994210i	$-0.465729\pi$
$13$	0.774897	0.214918	0.107459	+	0.994210i	$0.465729\pi$
$14$	2.34922	0.627857
$15$	−1.64458	−0.424629
$16$	1.34463	0.336158
$17$	4.83632	1.17298	0.586490	−	0.809957i	$-0.300509\pi$
$17$	4.83632	1.17298	0.586490	+	0.809957i	$0.300509\pi$
$18$	0.693857	0.163544
$19$	−6.49168	−1.48929	−0.744647	−	0.667458i	$-0.767382\pi$
$19$	−6.49168	−1.48929	−0.744647	+	0.667458i	$0.767382\pi$
$20$	3.51886	0.786840
$21$	1.64458	0.358877
$22$	0	0
$23$	−1.02098	−0.212888	−0.106444	−	0.994319i	$-0.533947\pi$
$23$	−1.02098	−0.212888	−0.106444	+	0.994319i	$0.533947\pi$
$24$	5.86808	1.19782
$25$	1.00000	0.200000
$26$	−1.82041	−0.357011
$27$	5.41948	1.04298
$28$	−3.51886	−0.665001
$29$	−7.73776	−1.43687	−0.718433	−	0.695596i	$-0.755140\pi$
$29$	−7.73776	−1.43687	−0.718433	+	0.695596i	$0.755140\pi$
$30$	3.86349	0.705373
$31$	9.88022	1.77454	0.887270	−	0.461250i	$-0.152599\pi$
$31$	9.88022	1.77454	0.887270	+	0.461250i	$0.152599\pi$
$32$	3.97742	0.703115
$33$	0	0
$34$	−11.3616	−1.94850
$35$	−1.00000	−0.169031
$36$	−1.03931	−0.173219
$37$	1.89525	0.311577	0.155789	−	0.987790i	$-0.450208\pi$
$37$	1.89525	0.311577	0.155789	+	0.987790i	$0.450208\pi$
$38$	15.2504	2.47395
$39$	−1.27438	−0.204064
$40$	−3.56813	−0.564171
$41$	−9.56653	−1.49404	−0.747020	−	0.664801i	$-0.768516\pi$
$41$	−9.56653	−1.49404	−0.747020	+	0.664801i	$0.768516\pi$
$42$	−3.86349	−0.596149
$43$	2.28457	0.348393	0.174197	−	0.984711i	$-0.444267\pi$
$43$	2.28457	0.348393	0.174197	+	0.984711i	$0.444267\pi$
$44$	0	0
$45$	−0.295356	−0.0440290
$46$	2.39850	0.353640
$47$	2.03094	0.296243	0.148121	−	0.988969i	$-0.452677\pi$
$47$	2.03094	0.296243	0.148121	+	0.988969i	$0.452677\pi$
$48$	−2.21136	−0.319182
$49$	1.00000	0.142857
$50$	−2.34922	−0.332231
$51$	−7.95371	−1.11374
$52$	2.72675	0.378132
$53$	4.32092	0.593524	0.296762	−	0.954951i	$-0.404093\pi$
$53$	4.32092	0.593524	0.296762	+	0.954951i	$0.404093\pi$
$54$	−12.7316	−1.73255
$55$	0	0
$56$	3.56813	0.476812
$57$	10.6761	1.41408
$58$	18.1777	2.38685
$59$	1.32847	0.172953	0.0864764	−	0.996254i	$-0.472439\pi$
$59$	1.32847	0.172953	0.0864764	+	0.996254i	$0.472439\pi$
$60$	−5.78704	−0.747104
$61$	0.894426	0.114520	0.0572598	−	0.998359i	$-0.481764\pi$
$61$	0.894426	0.114520	0.0572598	+	0.998359i	$0.481764\pi$
$62$	−23.2109	−2.94778
$63$	0.295356	0.0372113
$64$	−12.0331	−1.50414
$65$	0.774897	0.0961141
$66$	0	0
$67$	−7.75874	−0.947881	−0.473940	−	0.880557i	$-0.657169\pi$
$67$	−7.75874	−0.947881	−0.473940	+	0.880557i	$0.657169\pi$
$68$	17.0183	2.06377
$69$	1.67908	0.202137
$70$	2.34922	0.280786
$71$	10.5821	1.25586	0.627931	−	0.778269i	$-0.283902\pi$
$71$	10.5821	1.25586	0.627931	+	0.778269i	$0.283902\pi$
$72$	1.05387	0.124200
$73$	−1.66533	−0.194912	−0.0974561	−	0.995240i	$-0.531071\pi$
$73$	−1.66533	−0.194912	−0.0974561	+	0.995240i	$0.531071\pi$
$74$	−4.45237	−0.517577
$75$	−1.64458	−0.189900
$76$	−22.8433	−2.62031
$77$	0	0
$78$	2.99380	0.338982
$79$	1.15588	0.130047	0.0650236	−	0.997884i	$-0.479288\pi$
$79$	1.15588	0.130047	0.0650236	+	0.997884i	$0.479288\pi$
$80$	1.34463	0.150335
$81$	−8.02670	−0.891855
$82$	22.4739	2.48183
$83$	−13.8377	−1.51888	−0.759441	−	0.650576i	$-0.774527\pi$
$83$	−13.8377	−1.51888	−0.759441	+	0.650576i	$0.774527\pi$
$84$	5.78704	0.631418
$85$	4.83632	0.524572
$86$	−5.36696	−0.578735
$87$	12.7254	1.36430
$88$	0	0
$89$	−6.45237	−0.683950	−0.341975	−	0.939709i	$-0.611096\pi$
$89$	−6.45237	−0.683950	−0.341975	+	0.939709i	$0.611096\pi$
$90$	0.693857	0.0731390
$91$	−0.774897	−0.0812313
$92$	−3.59267	−0.374561
$93$	−16.2488	−1.68492
$94$	−4.77113	−0.492104
$95$	−6.49168	−0.666033
$96$	−6.54119	−0.667607
$97$	−6.94752	−0.705413	−0.352707	−	0.935734i	$-0.614739\pi$
$97$	−6.94752	−0.705413	−0.352707	+	0.935734i	$0.614739\pi$
$98$	−2.34922	−0.237308
$99$	0	0
$100$	3.51886	0.351886
$101$	−16.3390	−1.62579	−0.812896	−	0.582408i	$-0.802110\pi$
$101$	−16.3390	−1.62579	−0.812896	+	0.582408i	$0.802110\pi$
$102$	18.6851	1.85010
$103$	6.51484	0.641926	0.320963	−	0.947092i	$-0.395993\pi$
$103$	6.51484	0.641926	0.320963	+	0.947092i	$0.395993\pi$
$104$	−2.76493	−0.271124
$105$	1.64458	0.160495
$106$	−10.1508	−0.985935
$107$	15.6061	1.50870	0.754348	−	0.656475i	$-0.227953\pi$
$107$	15.6061	1.50870	0.754348	+	0.656475i	$0.227953\pi$
$108$	19.0704	1.83505
$109$	0.692852	0.0663632	0.0331816	−	0.999449i	$-0.489436\pi$
$109$	0.692852	0.0663632	0.0331816	+	0.999449i	$0.489436\pi$
$110$	0	0
$111$	−3.11689	−0.295842
$112$	−1.34463	−0.127056
$113$	−3.30567	−0.310971	−0.155486	−	0.987838i	$-0.549694\pi$
$113$	−3.30567	−0.310971	−0.155486	+	0.987838i	$0.549694\pi$
$114$	−25.0805	−2.34901
$115$	−1.02098	−0.0952065
$116$	−27.2281	−2.52806
$117$	−0.228870	−0.0211591
$118$	−3.12089	−0.287301
$119$	−4.83632	−0.443344
$120$	5.86808	0.535680
$121$	0	0
$122$	−2.10121	−0.190234
$123$	15.7329	1.41859
$124$	34.7671	3.12218
$125$	1.00000	0.0894427
$126$	−0.693857	−0.0618137
$127$	10.0792	0.894383	0.447192	−	0.894438i	$-0.352424\pi$
$127$	10.0792	0.894383	0.447192	+	0.894438i	$0.352424\pi$
$128$	20.3137	1.79549
$129$	−3.75716	−0.330799
$130$	−1.82041	−0.159660
$131$	15.7884	1.37944	0.689721	−	0.724076i	$-0.257733\pi$
$131$	15.7884	1.37944	0.689721	+	0.724076i	$0.257733\pi$
$132$	0	0
$133$	6.49168	0.562900
$134$	18.2270	1.57457
$135$	5.41948	0.466434
$136$	−17.2566	−1.47974
$137$	18.6436	1.59283	0.796413	−	0.604753i	$-0.206728\pi$
$137$	18.6436	1.59283	0.796413	+	0.604753i	$0.206728\pi$
$138$	−3.94453	−0.335781
$139$	−13.3279	−1.13046	−0.565228	−	0.824935i	$-0.691212\pi$
$139$	−13.3279	−1.13046	−0.565228	+	0.824935i	$0.691212\pi$
$140$	−3.51886	−0.297398
$141$	−3.34004	−0.281282
$142$	−24.8597	−2.08618
$143$	0	0
$144$	−0.397145	−0.0330954
$145$	−7.73776	−0.642586
$146$	3.91223	0.323779
$147$	−1.64458	−0.135643
$148$	6.66911	0.548198
$149$	19.5585	1.60229	0.801147	−	0.598467i	$-0.204223\pi$
$149$	19.5585	1.60229	0.801147	+	0.598467i	$0.204223\pi$
$150$	3.86349	0.315452
$151$	−11.9888	−0.975633	−0.487817	−	0.872946i	$-0.662207\pi$
$151$	−11.9888	−0.975633	−0.487817	+	0.872946i	$0.662207\pi$
$152$	23.1632	1.87878
$153$	−1.42843	−0.115482
$154$	0	0
$155$	9.88022	0.793599
$156$	−4.48436	−0.359036
$157$	−11.7811	−0.940232	−0.470116	−	0.882605i	$-0.655788\pi$
$157$	−11.7811	−0.940232	−0.470116	+	0.882605i	$0.655788\pi$
$158$	−2.71543	−0.216028
$159$	−7.10611	−0.563551
$160$	3.97742	0.314443
$161$	1.02098	0.0804642
$162$	18.8565	1.48151
$163$	4.49211	0.351849	0.175925	−	0.984404i	$-0.443708\pi$
$163$	4.49211	0.351849	0.175925	+	0.984404i	$0.443708\pi$
$164$	−33.6632	−2.62866
$165$	0	0
$166$	32.5078	2.52309
$167$	5.86030	0.453483	0.226742	−	0.973955i	$-0.427193\pi$
$167$	5.86030	0.453483	0.226742	+	0.973955i	$0.427193\pi$
$168$	−5.86808	−0.452732
$169$	−12.3995	−0.953810
$170$	−11.3616	−0.871394
$171$	1.91736	0.146624
$172$	8.03907	0.612973
$173$	4.45156	0.338446	0.169223	−	0.985578i	$-0.445874\pi$
$173$	4.45156	0.338446	0.169223	+	0.985578i	$0.445874\pi$
$174$	−29.8948	−2.26632
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	−2.18478	−0.164218
$178$	15.1581	1.13615
$179$	−6.79186	−0.507647	−0.253824	−	0.967251i	$-0.581688\pi$
$179$	−6.79186	−0.507647	−0.253824	+	0.967251i	$0.581688\pi$
$180$	−1.03931	−0.0774659
$181$	−5.10455	−0.379418	−0.189709	−	0.981840i	$-0.560754\pi$
$181$	−5.10455	−0.379418	−0.189709	+	0.981840i	$0.560754\pi$
$182$	1.82041	0.134938
$183$	−1.47096	−0.108736
$184$	3.64298	0.268564
$185$	1.89525	0.139342
$186$	38.1721	2.79892
$187$	0	0
$188$	7.14658	0.521218
$189$	−5.41948	−0.394209
$190$	15.2504	1.10638
$191$	1.64707	0.119178	0.0595888	−	0.998223i	$-0.481021\pi$
$191$	1.64707	0.119178	0.0595888	+	0.998223i	$0.481021\pi$
$192$	19.7894	1.42818
$193$	−10.4522	−0.752369	−0.376185	−	0.926545i	$-0.622764\pi$
$193$	−10.4522	−0.752369	−0.376185	+	0.926545i	$0.622764\pi$
$194$	16.3213	1.17180
$195$	−1.27438	−0.0912602
$196$	3.51886	0.251347
$197$	26.6710	1.90023	0.950116	−	0.311896i	$-0.100964\pi$
$197$	26.6710	1.90023	0.950116	+	0.311896i	$0.100964\pi$
$198$	0	0
$199$	16.1083	1.14189	0.570944	−	0.820989i	$-0.306577\pi$
$199$	16.1083	1.14189	0.570944	+	0.820989i	$0.306577\pi$
$200$	−3.56813	−0.252305
$201$	12.7599	0.900012
$202$	38.3840	2.70069
$203$	7.73776	0.543085
$204$	−27.9880	−1.95955
$205$	−9.56653	−0.668155
$206$	−15.3048	−1.06634
$207$	0.301551	0.0209593
$208$	1.04195	0.0722463
$209$	0	0
$210$	−3.86349	−0.266606
$211$	−22.4085	−1.54266	−0.771332	−	0.636433i	$-0.780409\pi$
$211$	−22.4085	−1.54266	−0.771332	+	0.636433i	$0.780409\pi$
$212$	15.2047	1.04426
$213$	−17.4031	−1.19244
$214$	−36.6622	−2.50617
$215$	2.28457	0.155806
$216$	−19.3374	−1.31574
$217$	−9.88022	−0.670713
$218$	−1.62766	−0.110239
$219$	2.73877	0.185069
$220$	0	0
$221$	3.74765	0.252094
$222$	7.32228	0.491439
$223$	5.95931	0.399065	0.199532	−	0.979891i	$-0.436058\pi$
$223$	5.95931	0.399065	0.199532	+	0.979891i	$0.436058\pi$
$224$	−3.97742	−0.265753
$225$	−0.295356	−0.0196904
$226$	7.76576	0.516571
$227$	16.1485	1.07181	0.535905	−	0.844278i	$-0.319970\pi$
$227$	16.1485	1.07181	0.535905	+	0.844278i	$0.319970\pi$
$228$	37.5676	2.48798
$229$	−3.95268	−0.261200	−0.130600	−	0.991435i	$-0.541690\pi$
$229$	−3.95268	−0.261200	−0.130600	+	0.991435i	$0.541690\pi$
$230$	2.39850	0.158152
$231$	0	0
$232$	27.6094	1.81264
$233$	−23.5799	−1.54477	−0.772385	−	0.635154i	$-0.780937\pi$
$233$	−23.5799	−1.54477	−0.772385	+	0.635154i	$0.780937\pi$
$234$	0.537668	0.0351484
$235$	2.03094	0.132484
$236$	4.67471	0.304298
$237$	−1.90094	−0.123480
$238$	11.3616	0.736463
$239$	18.0454	1.16726	0.583629	−	0.812021i	$-0.301632\pi$
$239$	18.0454	1.16726	0.583629	+	0.812021i	$0.301632\pi$
$240$	−2.21136	−0.142742
$241$	−12.1774	−0.784415	−0.392207	−	0.919877i	$-0.628288\pi$
$241$	−12.1774	−0.784415	−0.392207	+	0.919877i	$0.628288\pi$
$242$	0	0
$243$	−3.05788	−0.196163
$244$	3.14736	0.201489
$245$	1.00000	0.0638877
$246$	−36.9602	−2.35649
$247$	−5.03039	−0.320076
$248$	−35.2539	−2.23863
$249$	22.7572	1.44218
$250$	−2.34922	−0.148578
$251$	22.0217	1.39000	0.695000	−	0.719010i	$-0.255404\pi$
$251$	22.0217	1.39000	0.695000	+	0.719010i	$0.255404\pi$
$252$	1.03931	0.0654707
$253$	0	0
$254$	−23.6783	−1.48571
$255$	−7.95371	−0.498081
$256$	−23.6551	−1.47844
$257$	6.75244	0.421206	0.210603	−	0.977572i	$-0.432457\pi$
$257$	6.75244	0.421206	0.210603	+	0.977572i	$0.432457\pi$
$258$	8.82640	0.549508
$259$	−1.89525	−0.117765
$260$	2.72675	0.169106
$261$	2.28539	0.141462
$262$	−37.0906	−2.29146
$263$	13.4859	0.831579	0.415790	−	0.909461i	$-0.363505\pi$
$263$	13.4859	0.831579	0.415790	+	0.909461i	$0.363505\pi$
$264$	0	0
$265$	4.32092	0.265432
$266$	−15.2504	−0.935063
$267$	10.6114	0.649410
$268$	−27.3019	−1.66773
$269$	20.4589	1.24740	0.623701	−	0.781663i	$-0.285628\pi$
$269$	20.4589	1.24740	0.623701	+	0.781663i	$0.285628\pi$
$270$	−12.7316	−0.774819
$271$	30.1020	1.82857	0.914283	−	0.405076i	$-0.132755\pi$
$271$	30.1020	1.82857	0.914283	+	0.405076i	$0.132755\pi$
$272$	6.50307	0.394307
$273$	1.27438	0.0771290
$274$	−43.7979	−2.64593
$275$	0	0
$276$	5.90843	0.355646
$277$	−27.1624	−1.63203	−0.816014	−	0.578032i	$-0.803821\pi$
$277$	−27.1624	−1.63203	−0.816014	+	0.578032i	$0.803821\pi$
$278$	31.3102	1.87786
$279$	−2.91818	−0.174707
$280$	3.56813	0.213237
$281$	15.2378	0.909010	0.454505	−	0.890744i	$-0.349816\pi$
$281$	15.2378	0.909010	0.454505	+	0.890744i	$0.349816\pi$
$282$	7.84651	0.467253
$283$	−14.8916	−0.885213	−0.442606	−	0.896716i	$-0.645946\pi$
$283$	−14.8916	−0.885213	−0.442606	+	0.896716i	$0.645946\pi$
$284$	37.2368	2.20960
$285$	10.6761	0.632397
$286$	0	0
$287$	9.56653	0.564694
$288$	−1.17475	−0.0692231
$289$	6.38996	0.375880
$290$	18.1777	1.06743
$291$	11.4257	0.669789
$292$	−5.86005	−0.342934
$293$	−13.7864	−0.805413	−0.402706	−	0.915329i	$-0.631930\pi$
$293$	−13.7864	−0.805413	−0.402706	+	0.915329i	$0.631930\pi$
$294$	3.86349	0.225323
$295$	1.32847	0.0773468
$296$	−6.76251	−0.393063
$297$	0	0
$298$	−45.9473	−2.66166
$299$	−0.791151	−0.0457534
$300$	−5.78704	−0.334115
$301$	−2.28457	−0.131680
$302$	28.1643	1.62068
$303$	26.8708	1.54369
$304$	−8.72893	−0.500639
$305$	0.894426	0.0512147
$306$	3.35571	0.191833
$307$	−21.5698	−1.23106	−0.615528	−	0.788115i	$-0.711057\pi$
$307$	−21.5698	−1.23106	−0.615528	+	0.788115i	$0.711057\pi$
$308$	0	0
$309$	−10.7142	−0.609508
$310$	−23.2109	−1.31829
$311$	−28.3664	−1.60851	−0.804255	−	0.594284i	$-0.797436\pi$
$311$	−28.3664	−1.60851	−0.804255	+	0.594284i	$0.797436\pi$
$312$	4.54716	0.257432
$313$	1.36021	0.0768836	0.0384418	−	0.999261i	$-0.487761\pi$
$313$	1.36021	0.0768836	0.0384418	+	0.999261i	$0.487761\pi$
$314$	27.6764	1.56187
$315$	0.295356	0.0166414
$316$	4.06739	0.228809
$317$	−30.7876	−1.72920	−0.864602	−	0.502458i	$-0.832429\pi$
$317$	−30.7876	−1.72920	−0.864602	+	0.502458i	$0.832429\pi$
$318$	16.6938	0.936144
$319$	0	0
$320$	−12.0331	−0.672672
$321$	−25.6654	−1.43250
$322$	−2.39850	−0.133663
$323$	−31.3958	−1.74691
$324$	−28.2448	−1.56915
$325$	0.774897	0.0429835
$326$	−10.5530	−0.584475
$327$	−1.13945	−0.0630118
$328$	34.1346	1.88477
$329$	−2.03094	−0.111969
$330$	0	0
$331$	−31.3314	−1.72213	−0.861065	−	0.508494i	$-0.830202\pi$
$331$	−31.3314	−1.72213	−0.861065	+	0.508494i	$0.830202\pi$
$332$	−48.6928	−2.67236
$333$	−0.559773	−0.0306754
$334$	−13.7672	−0.753305
$335$	−7.75874	−0.423905
$336$	2.21136	0.120639
$337$	−27.8793	−1.51868	−0.759341	−	0.650693i	$-0.774479\pi$
$337$	−27.8793	−1.51868	−0.759341	+	0.650693i	$0.774479\pi$
$338$	29.1293	1.58442
$339$	5.43644	0.295267
$340$	17.0183	0.922947
$341$	0	0
$342$	−4.50430	−0.243565
$343$	−1.00000	−0.0539949
$344$	−8.15164	−0.439507
$345$	1.67908	0.0903984
$346$	−10.4577	−0.562210
$347$	−15.5821	−0.836490	−0.418245	−	0.908334i	$-0.637355\pi$
$347$	−15.5821	−0.836490	−0.418245	+	0.908334i	$0.637355\pi$
$348$	44.7787	2.40039
$349$	−20.5218	−1.09851	−0.549253	−	0.835656i	$-0.685088\pi$
$349$	−20.5218	−1.09851	−0.549253	+	0.835656i	$0.685088\pi$
$350$	2.34922	0.125571
$351$	4.19954	0.224155
$352$	0	0
$353$	−10.9327	−0.581887	−0.290944	−	0.956740i	$-0.593969\pi$
$353$	−10.9327	−0.581887	−0.290944	+	0.956740i	$0.593969\pi$
$354$	5.13255	0.272792
$355$	10.5821	0.561639
$356$	−22.7050	−1.20336
$357$	7.95371	0.420955
$358$	15.9556	0.843280
$359$	−5.38698	−0.284314	−0.142157	−	0.989844i	$-0.545404\pi$
$359$	−5.38698	−0.284314	−0.142157	+	0.989844i	$0.545404\pi$
$360$	1.05387	0.0555438
$361$	23.1420	1.21800
$362$	11.9917	0.630271
$363$	0	0
$364$	−2.72675	−0.142921
$365$	−1.66533	−0.0871673
$366$	3.45561	0.180627
$367$	19.5588	1.02096	0.510480	−	0.859890i	$-0.329468\pi$
$367$	19.5588	1.02096	0.510480	+	0.859890i	$0.329468\pi$
$368$	−1.37284	−0.0715641
$369$	2.82553	0.147091
$370$	−4.45237	−0.231468
$371$	−4.32092	−0.224331
$372$	−57.1772	−2.96450
$373$	−8.30055	−0.429786	−0.214893	−	0.976638i	$-0.568940\pi$
$373$	−8.30055	−0.429786	−0.214893	+	0.976638i	$0.568940\pi$
$374$	0	0
$375$	−1.64458	−0.0849258
$376$	−7.24666	−0.373718
$377$	−5.99597	−0.308808
$378$	12.7316	0.654841
$379$	−15.5009	−0.796226	−0.398113	−	0.917336i	$-0.630335\pi$
$379$	−15.5009	−0.796226	−0.398113	+	0.917336i	$0.630335\pi$
$380$	−22.8433	−1.17184
$381$	−16.5760	−0.849216
$382$	−3.86933	−0.197972
$383$	13.6798	0.699003	0.349502	−	0.936936i	$-0.386351\pi$
$383$	13.6798	0.699003	0.349502	+	0.936936i	$0.386351\pi$
$384$	−33.4074	−1.70482
$385$	0	0
$386$	24.5547	1.24980
$387$	−0.674761	−0.0343000
$388$	−24.4473	−1.24112
$389$	5.59773	0.283816	0.141908	−	0.989880i	$-0.454676\pi$
$389$	5.59773	0.283816	0.141908	+	0.989880i	$0.454676\pi$
$390$	2.99380	0.151597
$391$	−4.93776	−0.249713
$392$	−3.56813	−0.180218
$393$	−25.9653	−1.30978
$394$	−62.6562	−3.15658
$395$	1.15588	0.0581588
$396$	0	0
$397$	−21.5944	−1.08379	−0.541896	−	0.840446i	$-0.682293\pi$
$397$	−21.5944	−1.08379	−0.541896	+	0.840446i	$0.682293\pi$
$398$	−37.8420	−1.89685
$399$	−10.6761	−0.534473
$400$	1.34463	0.0672316
$401$	−21.5573	−1.07652	−0.538259	−	0.842779i	$-0.680918\pi$
$401$	−21.5573	−1.07652	−0.538259	+	0.842779i	$0.680918\pi$
$402$	−29.9758	−1.49506
$403$	7.65615	0.381380
$404$	−57.4946	−2.86046
$405$	−8.02670	−0.398850
$406$	−18.1777	−0.902146
$407$	0	0
$408$	28.3799	1.40501
$409$	30.1507	1.49086	0.745428	−	0.666586i	$-0.232245\pi$
$409$	30.1507	1.49086	0.745428	+	0.666586i	$0.232245\pi$
$410$	22.4739	1.10991
$411$	−30.6608	−1.51239
$412$	22.9248	1.12942
$413$	−1.32847	−0.0653700
$414$	−0.708411	−0.0348165
$415$	−13.8377	−0.679265
$416$	3.08209	0.151112
$417$	21.9188	1.07337
$418$	0	0
$419$	−23.7017	−1.15791	−0.578953	−	0.815361i	$-0.696538\pi$
$419$	−23.7017	−1.15791	−0.578953	+	0.815361i	$0.696538\pi$
$420$	5.78704	0.282379
$421$	−32.3444	−1.57637	−0.788184	−	0.615440i	$-0.788978\pi$
$421$	−32.3444	−1.57637	−0.788184	+	0.615440i	$0.788978\pi$
$422$	52.6426	2.56260
$423$	−0.599849	−0.0291657
$424$	−15.4176	−0.748746
$425$	4.83632	0.234596
$426$	40.8838	1.98083
$427$	−0.894426	−0.0432843
$428$	54.9155	2.65444
$429$	0	0
$430$	−5.36696	−0.258818
$431$	−24.0984	−1.16078	−0.580390	−	0.814339i	$-0.697100\pi$
$431$	−24.0984	−1.16078	−0.580390	+	0.814339i	$0.697100\pi$
$432$	7.28721	0.350606
$433$	−30.4734	−1.46446	−0.732229	−	0.681058i	$-0.761520\pi$
$433$	−30.4734	−1.46446	−0.732229	+	0.681058i	$0.761520\pi$
$434$	23.2109	1.11416
$435$	12.7254	0.610135
$436$	2.43805	0.116761
$437$	6.62785	0.317053
$438$	−6.43398	−0.307428
$439$	24.4600	1.16741	0.583706	−	0.811965i	$-0.301602\pi$
$439$	24.4600	1.16741	0.583706	+	0.811965i	$0.301602\pi$
$440$	0	0
$441$	−0.295356	−0.0140646
$442$	−8.80406	−0.418767
$443$	−38.3371	−1.82145	−0.910726	−	0.413010i	$-0.864477\pi$
$443$	−38.3371	−1.82145	−0.910726	+	0.413010i	$0.864477\pi$
$444$	−10.9679	−0.520513
$445$	−6.45237	−0.305872
$446$	−13.9998	−0.662908
$447$	−32.1655	−1.52138
$448$	12.0331	0.568511
$449$	7.96137	0.375720	0.187860	−	0.982196i	$-0.439845\pi$
$449$	7.96137	0.375720	0.187860	+	0.982196i	$0.439845\pi$
$450$	0.693857	0.0327087
$451$	0	0
$452$	−11.6322	−0.547131
$453$	19.7165	0.926363
$454$	−37.9363	−1.78044
$455$	−0.774897	−0.0363277
$456$	−38.0937	−1.78390
$457$	−4.28175	−0.200292	−0.100146	−	0.994973i	$-0.531931\pi$
$457$	−4.28175	−0.200292	−0.100146	+	0.994973i	$0.531931\pi$
$458$	9.28573	0.433894
$459$	26.2103	1.22339
$460$	−3.59267	−0.167509
$461$	−35.1353	−1.63641	−0.818207	−	0.574924i	$-0.805032\pi$
$461$	−35.1353	−1.63641	−0.818207	+	0.574924i	$0.805032\pi$
$462$	0	0
$463$	−35.6815	−1.65826	−0.829131	−	0.559054i	$-0.811164\pi$
$463$	−35.6815	−1.65826	−0.829131	+	0.559054i	$0.811164\pi$
$464$	−10.4044	−0.483014
$465$	−16.2488	−0.753521
$466$	55.3945	2.56610
$467$	−9.70921	−0.449289	−0.224644	−	0.974441i	$-0.572122\pi$
$467$	−9.70921	−0.449289	−0.224644	+	0.974441i	$0.572122\pi$
$468$	−0.805361	−0.0372278
$469$	7.75874	0.358265
$470$	−4.77113	−0.220076
$471$	19.3749	0.892749
$472$	−4.74017	−0.218184
$473$	0	0
$474$	4.46574	0.205118
$475$	−6.49168	−0.297859
$476$	−17.0183	−0.780033
$477$	−1.27621	−0.0584336
$478$	−42.3926	−1.93899
$479$	−13.0773	−0.597518	−0.298759	−	0.954329i	$-0.596573\pi$
$479$	−13.0773	−0.597518	−0.298759	+	0.954329i	$0.596573\pi$
$480$	−6.54119	−0.298563
$481$	1.46862	0.0669635
$482$	28.6074	1.30303
$483$	−1.67908	−0.0764006
$484$	0	0
$485$	−6.94752	−0.315470
$486$	7.18365	0.325857
$487$	34.2632	1.55262	0.776308	−	0.630354i	$-0.217090\pi$
$487$	34.2632	1.55262	0.776308	+	0.630354i	$0.217090\pi$
$488$	−3.19143	−0.144469
$489$	−7.38764	−0.334081
$490$	−2.34922	−0.106127
$491$	11.2481	0.507621	0.253810	−	0.967254i	$-0.418316\pi$
$491$	11.2481	0.507621	0.253810	+	0.967254i	$0.418316\pi$
$492$	55.3619	2.49591
$493$	−37.4223	−1.68541
$494$	11.8175	0.531695
$495$	0	0
$496$	13.2853	0.596526
$497$	−10.5821	−0.474672
$498$	−53.4617	−2.39568
$499$	−21.0915	−0.944183	−0.472092	−	0.881549i	$-0.656501\pi$
$499$	−21.0915	−0.944183	−0.472092	+	0.881549i	$0.656501\pi$
$500$	3.51886	0.157368
$501$	−9.63773	−0.430582
$502$	−51.7340	−2.30900
$503$	23.4394	1.04511	0.522556	−	0.852605i	$-0.324979\pi$
$503$	23.4394	1.04511	0.522556	+	0.852605i	$0.324979\pi$
$504$	−1.05387	−0.0469430
$505$	−16.3390	−0.727077
$506$	0	0
$507$	20.3920	0.905642
$508$	35.4672	1.57360
$509$	−37.0572	−1.64253	−0.821265	−	0.570547i	$-0.806731\pi$
$509$	−37.0572	−1.64253	−0.821265	+	0.570547i	$0.806731\pi$
$510$	18.6851	0.827388
$511$	1.66533	0.0736699
$512$	14.9438	0.660430
$513$	−35.1815	−1.55330
$514$	−15.8630	−0.699687
$515$	6.51484	0.287078
$516$	−13.2209	−0.582017
$517$	0	0
$518$	4.45237	0.195626
$519$	−7.32095	−0.321354
$520$	−2.76493	−0.121250
$521$	2.64273	0.115780	0.0578900	−	0.998323i	$-0.481563\pi$
$521$	2.64273	0.115780	0.0578900	+	0.998323i	$0.481563\pi$
$522$	−5.36890	−0.234990
$523$	29.9984	1.31174	0.655868	−	0.754875i	$-0.272303\pi$
$523$	29.9984	1.31174	0.655868	+	0.754875i	$0.272303\pi$
$524$	55.5572	2.42703
$525$	1.64458	0.0717754
$526$	−31.6815	−1.38138
$527$	47.7839	2.08150
$528$	0	0
$529$	−21.9576	−0.954679
$530$	−10.1508	−0.440923
$531$	−0.392373	−0.0170275
$532$	22.8433	0.990383
$533$	−7.41307	−0.321096
$534$	−24.9287	−1.07877
$535$	15.6061	0.674709
$536$	27.6842	1.19578
$537$	11.1698	0.482011
$538$	−48.0626	−2.07213
$539$	0	0
$540$	19.0704	0.820657
$541$	24.1862	1.03985	0.519923	−	0.854213i	$-0.325961\pi$
$541$	24.1862	1.03985	0.519923	+	0.854213i	$0.325961\pi$
$542$	−70.7163	−3.03753
$543$	8.39484	0.360257
$544$	19.2361	0.824740
$545$	0.692852	0.0296785
$546$	−2.99380	−0.128123
$547$	−8.66134	−0.370332	−0.185166	−	0.982707i	$-0.559282\pi$
$547$	−8.66134	−0.370332	−0.185166	+	0.982707i	$0.559282\pi$
$548$	65.6040	2.80246
$549$	−0.264174	−0.0112747
$550$	0	0
$551$	50.2311	2.13992
$552$	−5.99117	−0.255001
$553$	−1.15588	−0.0491532
$554$	63.8105	2.71105
$555$	−3.11689	−0.132305
$556$	−46.8989	−1.98896
$557$	39.1410	1.65846	0.829229	−	0.558909i	$-0.188780\pi$
$557$	39.1410	1.65846	0.829229	+	0.558909i	$0.188780\pi$
$558$	6.85546	0.290215
$559$	1.77031	0.0748759
$560$	−1.34463	−0.0568211
$561$	0	0
$562$	−35.7970	−1.51000
$563$	35.7761	1.50778	0.753892	−	0.656999i	$-0.228174\pi$
$563$	35.7761	1.50778	0.753892	+	0.656999i	$0.228174\pi$
$564$	−11.7531	−0.494896
$565$	−3.30567	−0.139071
$566$	34.9837	1.47047
$567$	8.02670	0.337090
$568$	−37.7583	−1.58430
$569$	−43.0304	−1.80393	−0.901965	−	0.431809i	$-0.857875\pi$
$569$	−43.0304	−1.80393	−0.901965	+	0.431809i	$0.857875\pi$
$570$	−25.0805	−1.05051
$571$	−5.54693	−0.232132	−0.116066	−	0.993242i	$-0.537028\pi$
$571$	−5.54693	−0.232132	−0.116066	+	0.993242i	$0.537028\pi$
$572$	0	0
$573$	−2.70873	−0.113159
$574$	−22.4739	−0.938043
$575$	−1.02098	−0.0425776
$576$	3.55405	0.148085
$577$	−15.5951	−0.649231	−0.324616	−	0.945846i	$-0.605235\pi$
$577$	−15.5951	−0.649231	−0.324616	+	0.945846i	$0.605235\pi$
$578$	−15.0115	−0.624394
$579$	17.1896	0.714374
$580$	−27.2281	−1.13058
$581$	13.8377	0.574083
$582$	−26.8416	−1.11262
$583$	0	0
$584$	5.94212	0.245887
$585$	−0.228870	−0.00946262
$586$	32.3874	1.33791
$587$	2.34805	0.0969143	0.0484572	−	0.998825i	$-0.484570\pi$
$587$	2.34805	0.0969143	0.0484572	+	0.998825i	$0.484570\pi$
$588$	−5.78704	−0.238654
$589$	−64.1393	−2.64281
$590$	−3.12089	−0.128485
$591$	−43.8626	−1.80427
$592$	2.54842	0.104739
$593$	12.1163	0.497559	0.248779	−	0.968560i	$-0.419971\pi$
$593$	12.1163	0.497559	0.248779	+	0.968560i	$0.419971\pi$
$594$	0	0
$595$	−4.83632	−0.198270
$596$	68.8235	2.81912
$597$	−26.4914	−1.08422
$598$	1.85859	0.0760034
$599$	−42.8223	−1.74967	−0.874836	−	0.484419i	$-0.839031\pi$
$599$	−42.8223	−1.74967	−0.874836	+	0.484419i	$0.839031\pi$
$600$	5.86808	0.239563
$601$	3.78918	0.154564	0.0772818	−	0.997009i	$-0.475376\pi$
$601$	3.78918	0.154564	0.0772818	+	0.997009i	$0.475376\pi$
$602$	5.36696	0.218741
$603$	2.29159	0.0933207
$604$	−42.1868	−1.71656
$605$	0	0
$606$	−63.1256	−2.56430
$607$	−22.3676	−0.907873	−0.453936	−	0.891034i	$-0.649981\pi$
$607$	−22.3676	−0.907873	−0.453936	+	0.891034i	$0.649981\pi$
$608$	−25.8202	−1.04715
$609$	−12.7254	−0.515658
$610$	−2.10121	−0.0850754
$611$	1.57377	0.0636678
$612$	−5.02645	−0.203182
$613$	−7.57985	−0.306147	−0.153074	−	0.988215i	$-0.548917\pi$
$613$	−7.57985	−0.306147	−0.153074	+	0.988215i	$0.548917\pi$
$614$	50.6724	2.04497
$615$	15.7329	0.634413
$616$	0	0
$617$	19.5185	0.785787	0.392893	−	0.919584i	$-0.371474\pi$
$617$	19.5185	0.785787	0.392893	+	0.919584i	$0.371474\pi$
$618$	25.1700	1.01249
$619$	−2.85702	−0.114833	−0.0574167	−	0.998350i	$-0.518286\pi$
$619$	−2.85702	−0.114833	−0.0574167	+	0.998350i	$0.518286\pi$
$620$	34.7671	1.39628
$621$	−5.53315	−0.222038
$622$	66.6390	2.67198
$623$	6.45237	0.258509
$624$	−1.71357	−0.0685978
$625$	1.00000	0.0400000
$626$	−3.19544	−0.127715
$627$	0	0
$628$	−41.4559	−1.65427
$629$	9.16603	0.365474
$630$	−0.693857	−0.0276439
$631$	22.3087	0.888093	0.444047	−	0.896004i	$-0.353542\pi$
$631$	22.3087	0.888093	0.444047	+	0.896004i	$0.353542\pi$
$632$	−4.12435	−0.164058
$633$	36.8526	1.46476
$634$	72.3270	2.87247
$635$	10.0792	0.399980
$636$	−25.0054	−0.991527
$637$	0.774897	0.0307025
$638$	0	0
$639$	−3.12548	−0.123642
$640$	20.3137	0.802968
$641$	25.3980	1.00316	0.501581	−	0.865111i	$-0.332752\pi$
$641$	25.3980	1.00316	0.501581	+	0.865111i	$0.332752\pi$
$642$	60.2939	2.37961
$643$	−19.0169	−0.749955	−0.374977	−	0.927034i	$-0.622350\pi$
$643$	−19.0169	−0.749955	−0.374977	+	0.927034i	$0.622350\pi$
$644$	3.59267	0.141571
$645$	−3.75716	−0.147938
$646$	73.7559	2.90189
$647$	−17.3436	−0.681847	−0.340923	−	0.940091i	$-0.610740\pi$
$647$	−17.3436	−0.681847	−0.340923	+	0.940091i	$0.610740\pi$
$648$	28.6403	1.12510
$649$	0	0
$650$	−1.82041	−0.0714022
$651$	16.2488	0.636841
$652$	15.8071	0.619054
$653$	18.1855	0.711655	0.355828	−	0.934552i	$-0.384199\pi$
$653$	18.1855	0.711655	0.355828	+	0.934552i	$0.384199\pi$
$654$	2.67683	0.104672
$655$	15.7884	0.616905
$656$	−12.8635	−0.502234
$657$	0.491865	0.0191895
$658$	4.77113	0.185998
$659$	−21.3285	−0.830839	−0.415419	−	0.909630i	$-0.636365\pi$
$659$	−21.3285	−0.830839	−0.415419	+	0.909630i	$0.636365\pi$
$660$	0	0
$661$	41.5555	1.61632	0.808161	−	0.588962i	$-0.200463\pi$
$661$	41.5555	1.61632	0.808161	+	0.588962i	$0.200463\pi$
$662$	73.6045	2.86072
$663$	−6.16331	−0.239363
$664$	49.3746	1.91611
$665$	6.49168	0.251737
$666$	1.31503	0.0509565
$667$	7.90007	0.305892
$668$	20.6215	0.797871
$669$	−9.80056	−0.378912
$670$	18.2270	0.704171
$671$	0	0
$672$	6.54119	0.252332
$673$	−32.3007	−1.24510	−0.622550	−	0.782580i	$-0.713903\pi$
$673$	−32.3007	−1.24510	−0.622550	+	0.782580i	$0.713903\pi$
$674$	65.4947	2.52276
$675$	5.41948	0.208596
$676$	−43.6322	−1.67816
$677$	−42.5686	−1.63604	−0.818022	−	0.575187i	$-0.804929\pi$
$677$	−42.5686	−1.63604	−0.818022	+	0.575187i	$0.804929\pi$
$678$	−12.7714	−0.490483
$679$	6.94752	0.266621
$680$	−17.2566	−0.661761
$681$	−26.5574	−1.01768
$682$	0	0
$683$	−39.9707	−1.52944	−0.764718	−	0.644365i	$-0.777122\pi$
$683$	−39.9707	−1.52944	−0.764718	+	0.644365i	$0.777122\pi$
$684$	6.74690	0.257974
$685$	18.6436	0.712334
$686$	2.34922	0.0896938
$687$	6.50050	0.248009
$688$	3.07191	0.117115
$689$	3.34827	0.127559
$690$	−3.94453	−0.150166
$691$	28.7051	1.09199	0.545996	−	0.837788i	$-0.316151\pi$
$691$	28.7051	1.09199	0.545996	+	0.837788i	$0.316151\pi$
$692$	15.6644	0.595471
$693$	0	0
$694$	36.6058	1.38954
$695$	−13.3279	−0.505555
$696$	−45.4058	−1.72110
$697$	−46.2668	−1.75248
$698$	48.2103	1.82479
$699$	38.7790	1.46676
$700$	−3.51886	−0.133000
$701$	−16.0028	−0.604418	−0.302209	−	0.953242i	$-0.597724\pi$
$701$	−16.0028	−0.604418	−0.302209	+	0.953242i	$0.597724\pi$
$702$	−9.86565	−0.372355
$703$	−12.3034	−0.464030
$704$	0	0
$705$	−3.34004	−0.125793
$706$	25.6833	0.966603
$707$	16.3390	0.614492
$708$	−7.68794	−0.288930
$709$	29.1537	1.09489	0.547445	−	0.836841i	$-0.315600\pi$
$709$	29.1537	1.09489	0.547445	+	0.836841i	$0.315600\pi$
$710$	−24.8597	−0.932968
$711$	−0.341397	−0.0128034
$712$	23.0229	0.862820
$713$	−10.0875	−0.377779
$714$	−18.6851	−0.699271
$715$	0	0
$716$	−23.8996	−0.893169
$717$	−29.6771	−1.10831
$718$	12.6552	0.472289
$719$	−27.2779	−1.01729	−0.508647	−	0.860975i	$-0.669854\pi$
$719$	−27.2779	−1.01729	−0.508647	+	0.860975i	$0.669854\pi$
$720$	−0.397145	−0.0148007
$721$	−6.51484	−0.242625
$722$	−54.3657	−2.02328
$723$	20.0267	0.744801
$724$	−17.9622	−0.667559
$725$	−7.73776	−0.287373
$726$	0	0
$727$	15.2591	0.565930	0.282965	−	0.959130i	$-0.408682\pi$
$727$	15.2591	0.565930	0.282965	+	0.959130i	$0.408682\pi$
$728$	2.76493	0.102475
$729$	29.1090	1.07811
$730$	3.91223	0.144798
$731$	11.0489	0.408658
$732$	−5.17608	−0.191313
$733$	−30.7784	−1.13683	−0.568413	−	0.822743i	$-0.692442\pi$
$733$	−30.7784	−1.13683	−0.568413	+	0.822743i	$0.692442\pi$
$734$	−45.9480	−1.69597
$735$	−1.64458	−0.0606613
$736$	−4.06085	−0.149685
$737$	0	0
$738$	−6.63780	−0.244341
$739$	−20.8534	−0.767105	−0.383553	−	0.923519i	$-0.625300\pi$
$739$	−20.8534	−0.767105	−0.383553	+	0.923519i	$0.625300\pi$
$740$	6.66911	0.245162
$741$	8.27287	0.303912
$742$	10.1508	0.372648
$743$	23.1969	0.851011	0.425506	−	0.904956i	$-0.360096\pi$
$743$	23.1969	0.851011	0.425506	+	0.904956i	$0.360096\pi$
$744$	57.9779	2.12557
$745$	19.5585	0.716568
$746$	19.4998	0.713940
$747$	4.08704	0.149537
$748$	0	0
$749$	−15.6061	−0.570233
$750$	3.86349	0.141075
$751$	−26.0579	−0.950866	−0.475433	−	0.879752i	$-0.657709\pi$
$751$	−26.0579	−0.950866	−0.475433	+	0.879752i	$0.657709\pi$
$752$	2.73087	0.0995844
$753$	−36.2165	−1.31980
$754$	14.0859	0.512977
$755$	−11.9888	−0.436317
$756$	−19.0704	−0.693582
$757$	19.5753	0.711475	0.355738	−	0.934586i	$-0.384230\pi$
$757$	19.5753	0.711475	0.355738	+	0.934586i	$0.384230\pi$
$758$	36.4150	1.32265
$759$	0	0
$760$	23.1632	0.840217
$761$	−10.0359	−0.363799	−0.181900	−	0.983317i	$-0.558225\pi$
$761$	−10.0359	−0.363799	−0.181900	+	0.983317i	$0.558225\pi$
$762$	38.9408	1.41068
$763$	−0.692852	−0.0250829
$764$	5.79579	0.209684
$765$	−1.42843	−0.0516452
$766$	−32.1368	−1.16115
$767$	1.02943	0.0371706
$768$	38.9027	1.40378
$769$	−19.1558	−0.690777	−0.345389	−	0.938460i	$-0.612253\pi$
$769$	−19.1558	−0.690777	−0.345389	+	0.938460i	$0.612253\pi$
$770$	0	0
$771$	−11.1049	−0.399934
$772$	−36.7799	−1.32374
$773$	40.4417	1.45459	0.727294	−	0.686326i	$-0.240778\pi$
$773$	40.4417	1.45459	0.727294	+	0.686326i	$0.240778\pi$
$774$	1.58516	0.0569776
$775$	9.88022	0.354908
$776$	24.7897	0.889897
$777$	3.11689	0.111818
$778$	−13.1503	−0.471462
$779$	62.1029	2.22507
$780$	−4.48436	−0.160566
$781$	0	0
$782$	11.5999	0.414812
$783$	−41.9346	−1.49862
$784$	1.34463	0.0480226
$785$	−11.7811	−0.420484
$786$	60.9984	2.17574
$787$	7.61129	0.271313	0.135657	−	0.990756i	$-0.456686\pi$
$787$	7.61129	0.271313	0.135657	+	0.990756i	$0.456686\pi$
$788$	93.8515	3.34332
$789$	−22.1787	−0.789583
$790$	−2.71543	−0.0966107
$791$	3.30567	0.117536
$792$	0	0
$793$	0.693088	0.0246123
$794$	50.7301	1.80034
$795$	−7.10611	−0.252028
$796$	56.6828	2.00907
$797$	12.9299	0.458002	0.229001	−	0.973426i	$-0.426454\pi$
$797$	12.9299	0.458002	0.229001	+	0.973426i	$0.426454\pi$
$798$	25.0805	0.887842
$799$	9.82226	0.347487
$800$	3.97742	0.140623
$801$	1.90574	0.0673362
$802$	50.6429	1.78826
$803$	0	0
$804$	44.9001	1.58351
$805$	1.02098	0.0359847
$806$	−17.9860	−0.633531
$807$	−33.6463	−1.18441
$808$	58.2998	2.05098
$809$	−49.8708	−1.75336	−0.876682	−	0.481070i	$-0.840248\pi$
$809$	−49.8708	−1.75336	−0.876682	+	0.481070i	$0.840248\pi$
$810$	18.8565	0.662550
$811$	24.6779	0.866558	0.433279	−	0.901260i	$-0.357356\pi$
$811$	24.6779	0.866558	0.433279	+	0.901260i	$0.357356\pi$
$812$	27.2281	0.955518
$813$	−49.5051	−1.73622
$814$	0	0
$815$	4.49211	0.157352
$816$	−10.6948	−0.374394
$817$	−14.8307	−0.518860
$818$	−70.8307	−2.47654
$819$	0.228870	0.00799737
$820$	−33.6632	−1.17557
$821$	8.95832	0.312648	0.156324	−	0.987706i	$-0.450036\pi$
$821$	8.95832	0.312648	0.156324	+	0.987706i	$0.450036\pi$
$822$	72.0291	2.51231
$823$	−18.0993	−0.630903	−0.315452	−	0.948942i	$-0.602156\pi$
$823$	−18.0993	−0.630903	−0.315452	+	0.948942i	$0.602156\pi$
$824$	−23.2458	−0.809806
$825$	0	0
$826$	3.12089	0.108590
$827$	16.2631	0.565525	0.282762	−	0.959190i	$-0.408749\pi$
$827$	16.2631	0.565525	0.282762	+	0.959190i	$0.408749\pi$
$828$	1.06111	0.0368763
$829$	9.43842	0.327810	0.163905	−	0.986476i	$-0.447591\pi$
$829$	9.43842	0.327810	0.163905	+	0.986476i	$0.447591\pi$
$830$	32.5078	1.12836
$831$	44.6707	1.54961
$832$	−9.32443	−0.323266
$833$	4.83632	0.167568
$834$	−51.4921	−1.78303
$835$	5.86030	0.202804
$836$	0	0
$837$	53.5456	1.85081
$838$	55.6807	1.92346
$839$	−36.9100	−1.27428	−0.637138	−	0.770750i	$-0.719882\pi$
$839$	−36.9100	−1.27428	−0.637138	+	0.770750i	$0.719882\pi$
$840$	−5.86808	−0.202468
$841$	30.8730	1.06459
$842$	75.9842	2.61859
$843$	−25.0598	−0.863104
$844$	−78.8522	−2.71421
$845$	−12.3995	−0.426557
$846$	1.40918	0.0484486
$847$	0	0
$848$	5.81005	0.199518
$849$	24.4904	0.840509
$850$	−11.3616	−0.389699
$851$	−1.93501	−0.0663311
$852$	−61.2390	−2.09801
$853$	−29.1282	−0.997331	−0.498666	−	0.866794i	$-0.666176\pi$
$853$	−29.1282	−0.997331	−0.498666	+	0.866794i	$0.666176\pi$
$854$	2.10121	0.0719019
$855$	1.91736	0.0655722
$856$	−55.6845	−1.90326
$857$	25.1149	0.857908	0.428954	−	0.903326i	$-0.358882\pi$
$857$	25.1149	0.857908	0.428954	+	0.903326i	$0.358882\pi$
$858$	0	0
$859$	−32.7727	−1.11819	−0.559096	−	0.829103i	$-0.688852\pi$
$859$	−32.7727	−1.11819	−0.559096	+	0.829103i	$0.688852\pi$
$860$	8.03907	0.274130
$861$	−15.7329	−0.536177
$862$	56.6126	1.92823
$863$	−52.8925	−1.80048	−0.900240	−	0.435393i	$-0.856609\pi$
$863$	−52.8925	−1.80048	−0.900240	+	0.435393i	$0.856609\pi$
$864$	21.5555	0.733334
$865$	4.45156	0.151358
$866$	71.5889	2.43269
$867$	−10.5088	−0.356898
$868$	−34.7671	−1.18007
$869$	0	0
$870$	−29.8948	−1.01353
$871$	−6.01222	−0.203716
$872$	−2.47219	−0.0837188
$873$	2.05199	0.0694493
$874$	−15.5703	−0.526674
$875$	−1.00000	−0.0338062
$876$	9.63733	0.325615
$877$	−3.12070	−0.105379	−0.0526893	−	0.998611i	$-0.516779\pi$
$877$	−3.12070	−0.105379	−0.0526893	+	0.998611i	$0.516779\pi$
$878$	−57.4620	−1.93925
$879$	22.6729	0.764738
$880$	0	0
$881$	40.5997	1.36784	0.683919	−	0.729558i	$-0.260274\pi$
$881$	40.5997	1.36784	0.683919	+	0.729558i	$0.260274\pi$
$882$	0.693857	0.0233634
$883$	−6.24459	−0.210147	−0.105074	−	0.994464i	$-0.533508\pi$
$883$	−6.24459	−0.210147	−0.105074	+	0.994464i	$0.533508\pi$
$884$	13.1874	0.443541
$885$	−2.18478	−0.0734407
$886$	90.0626	3.02571
$887$	9.51979	0.319643	0.159822	−	0.987146i	$-0.448908\pi$
$887$	9.51979	0.319643	0.159822	+	0.987146i	$0.448908\pi$
$888$	11.1215	0.373213
$889$	−10.0792	−0.338045
$890$	15.1581	0.508099
$891$	0	0
$892$	20.9699	0.702126
$893$	−13.1842	−0.441193
$894$	75.5640	2.52724
$895$	−6.79186	−0.227027
$896$	−20.3137	−0.678632
$897$	1.30111	0.0434428
$898$	−18.7030	−0.624128
$899$	−76.4508	−2.54978
$900$	−1.03931	−0.0346438
$901$	20.8974	0.696192
$902$	0	0
$903$	3.75716	0.125030
$904$	11.7951	0.392298
$905$	−5.10455	−0.169681
$906$	−46.3185	−1.53883
$907$	−37.0452	−1.23007	−0.615033	−	0.788501i	$-0.710857\pi$
$907$	−37.0452	−1.23007	−0.615033	+	0.788501i	$0.710857\pi$
$908$	56.8241	1.88577
$909$	4.82582	0.160062
$910$	1.82041	0.0603459
$911$	−54.2506	−1.79740	−0.898702	−	0.438561i	$-0.855488\pi$
$911$	−54.2506	−1.79740	−0.898702	+	0.438561i	$0.855488\pi$
$912$	14.3554	0.475356
$913$	0	0
$914$	10.0588	0.332715
$915$	−1.47096	−0.0486283
$916$	−13.9089	−0.459563
$917$	−15.7884	−0.521380
$918$	−61.5739	−2.03224
$919$	−11.8212	−0.389945	−0.194973	−	0.980809i	$-0.562462\pi$
$919$	−11.8212	−0.389945	−0.194973	+	0.980809i	$0.562462\pi$
$920$	3.64298	0.120105
$921$	35.4733	1.16889
$922$	82.5407	2.71833
$923$	8.20003	0.269907
$924$	0	0
$925$	1.89525	0.0623155
$926$	83.8240	2.75463
$927$	−1.92420	−0.0631989
$928$	−30.7763	−1.01028
$929$	−19.5730	−0.642168	−0.321084	−	0.947051i	$-0.604047\pi$
$929$	−19.5730	−0.642168	−0.321084	+	0.947051i	$0.604047\pi$
$930$	38.1721	1.25171
$931$	−6.49168	−0.212756
$932$	−82.9743	−2.71791
$933$	46.6508	1.52728
$934$	22.8091	0.746337
$935$	0	0
$936$	0.816639	0.0266927
$937$	−9.79791	−0.320084	−0.160042	−	0.987110i	$-0.551163\pi$
$937$	−9.79791	−0.320084	−0.160042	+	0.987110i	$0.551163\pi$
$938$	−18.2270	−0.595133
$939$	−2.23697	−0.0730009
$940$	7.14658	0.233096
$941$	34.1832	1.11434	0.557170	−	0.830399i	$-0.311887\pi$
$941$	34.1832	1.11434	0.557170	+	0.830399i	$0.311887\pi$
$942$	−45.5160	−1.48299
$943$	9.76719	0.318064
$944$	1.78631	0.0581395
$945$	−5.41948	−0.176296
$946$	0	0
$947$	−6.31904	−0.205341	−0.102671	−	0.994715i	$-0.532739\pi$
$947$	−6.31904	−0.205341	−0.102671	+	0.994715i	$0.532739\pi$
$948$	−6.68915	−0.217253
$949$	−1.29046	−0.0418901
$950$	15.2504	0.494789
$951$	50.6327	1.64188
$952$	17.2566	0.559290
$953$	1.16252	0.0376578	0.0188289	−	0.999823i	$-0.494006\pi$
$953$	1.16252	0.0376578	0.0188289	+	0.999823i	$0.494006\pi$
$954$	2.99810	0.0970672
$955$	1.64707	0.0532978
$956$	63.4990	2.05371
$957$	0	0
$958$	30.7216	0.992569
$959$	−18.6436	−0.602032
$960$	19.7894	0.638701
$961$	66.6188	2.14899
$962$	−3.45013	−0.111237
$963$	−4.60934	−0.148534
$964$	−42.8505	−1.38012
$965$	−10.4522	−0.336470
$966$	3.94453	0.126913
$967$	40.6151	1.30609	0.653046	−	0.757318i	$-0.273491\pi$
$967$	40.6151	1.30609	0.653046	+	0.757318i	$0.273491\pi$
$968$	0	0
$969$	51.6330	1.65869
$970$	16.3213	0.524045
$971$	35.3395	1.13410	0.567049	−	0.823684i	$-0.308085\pi$
$971$	35.3395	1.13410	0.567049	+	0.823684i	$0.308085\pi$
$972$	−10.7602	−0.345135
$973$	13.3279	0.427272
$974$	−80.4920	−2.57913
$975$	−1.27438	−0.0408128
$976$	1.20267	0.0384967
$977$	−25.7656	−0.824314	−0.412157	−	0.911113i	$-0.635224\pi$
$977$	−25.7656	−0.824314	−0.412157	+	0.911113i	$0.635224\pi$
$978$	17.3552	0.554959
$979$	0	0
$980$	3.51886	0.112406
$981$	−0.204638	−0.00653358
$982$	−26.4244	−0.843235
$983$	−36.4298	−1.16193	−0.580966	−	0.813928i	$-0.697325\pi$
$983$	−36.4298	−1.16193	−0.580966	+	0.813928i	$0.697325\pi$
$984$	−56.1372	−1.78959
$985$	26.6710	0.849810
$986$	87.9133	2.79973
$987$	3.34004	0.106315
$988$	−17.7012	−0.563150
$989$	−2.33249	−0.0741688
$990$	0	0
$991$	−34.0939	−1.08303	−0.541514	−	0.840692i	$-0.682149\pi$
$991$	−34.0939	−1.08303	−0.541514	+	0.840692i	$0.682149\pi$
$992$	39.2978	1.24771
$993$	51.5270	1.63516
$994$	24.8597	0.788502
$995$	16.1083	0.510668
$996$	80.0792	2.53741
$997$	48.2752	1.52889	0.764445	−	0.644689i	$-0.223013\pi$
$997$	48.2752	1.52889	0.764445	+	0.644689i	$0.223013\pi$
$998$	49.5486	1.56843
$999$	10.2713	0.324969

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.z.1.1	✓	5
11.10	odd	2		4235.2.a.bf.1.5	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.z.1.1	✓	5	1.1	even	1	trivial
4235.2.a.bf.1.5	yes	5	11.10	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:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q-2.34922 q^{2} -1.64458 q^{3} +3.51886 q^{4} +1.00000 q^{5} +3.86349 q^{6} -1.00000 q^{7} -3.56813 q^{8} -0.295356 q^{9} +O(q^{10})\)	\(q-2.34922 q^{2} -1.64458 q^{3} +3.51886 q^{4} +1.00000 q^{5} +3.86349 q^{6} -1.00000 q^{7} -3.56813 q^{8} -0.295356 q^{9} -2.34922 q^{10} -5.78704 q^{12} +0.774897 q^{13} +2.34922 q^{14} -1.64458 q^{15} +1.34463 q^{16} +4.83632 q^{17} +0.693857 q^{18} -6.49168 q^{19} +3.51886 q^{20} +1.64458 q^{21} -1.02098 q^{23} +5.86808 q^{24} +1.00000 q^{25} -1.82041 q^{26} +5.41948 q^{27} -3.51886 q^{28} -7.73776 q^{29} +3.86349 q^{30} +9.88022 q^{31} +3.97742 q^{32} -11.3616 q^{34} -1.00000 q^{35} -1.03931 q^{36} +1.89525 q^{37} +15.2504 q^{38} -1.27438 q^{39} -3.56813 q^{40} -9.56653 q^{41} -3.86349 q^{42} +2.28457 q^{43} -0.295356 q^{45} +2.39850 q^{46} +2.03094 q^{47} -2.21136 q^{48} +1.00000 q^{49} -2.34922 q^{50} -7.95371 q^{51} +2.72675 q^{52} +4.32092 q^{53} -12.7316 q^{54} +3.56813 q^{56} +10.6761 q^{57} +18.1777 q^{58} +1.32847 q^{59} -5.78704 q^{60} +0.894426 q^{61} -23.2109 q^{62} +0.295356 q^{63} -12.0331 q^{64} +0.774897 q^{65} -7.75874 q^{67} +17.0183 q^{68} +1.67908 q^{69} +2.34922 q^{70} +10.5821 q^{71} +1.05387 q^{72} -1.66533 q^{73} -4.45237 q^{74} -1.64458 q^{75} -22.8433 q^{76} +2.99380 q^{78} +1.15588 q^{79} +1.34463 q^{80} -8.02670 q^{81} +22.4739 q^{82} -13.8377 q^{83} +5.78704 q^{84} +4.83632 q^{85} -5.36696 q^{86} +12.7254 q^{87} -6.45237 q^{89} +0.693857 q^{90} -0.774897 q^{91} -3.59267 q^{92} -16.2488 q^{93} -4.77113 q^{94} -6.49168 q^{95} -6.54119 q^{96} -6.94752 q^{97} -2.34922 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} + 2 q^{3} + 4 q^{4} + 5 q^{5} + q^{6} - 5 q^{7} - q^{9}+O(q^{10}) \) 5 * q - 2 * q^2 + 2 * q^3 + 4 * q^4 + 5 * q^5 + q^6 - 5 * q^7 - q^9	\( 5 q - 2 q^{2} + 2 q^{3} + 4 q^{4} + 5 q^{5} + q^{6} - 5 q^{7} - q^{9} - 2 q^{10} - 3 q^{12} - 8 q^{13} + 2 q^{14} + 2 q^{15} + 2 q^{16} - 6 q^{17} - 11 q^{18} - 7 q^{19} + 4 q^{20} - 2 q^{21} + 3 q^{23} + 6 q^{24} + 5 q^{25} - 15 q^{26} + 5 q^{27} - 4 q^{28} - 17 q^{29} + q^{30} + 12 q^{31} + 3 q^{32} - 12 q^{34} - 5 q^{35} - 3 q^{36} - 2 q^{37} + 21 q^{38} - 14 q^{39} - 5 q^{41} - q^{42} - 4 q^{43} - q^{45} - 2 q^{46} - 12 q^{48} + 5 q^{49} - 2 q^{50} - 14 q^{51} - 2 q^{52} + 8 q^{53} - 22 q^{54} - 4 q^{57} + 6 q^{58} - 16 q^{59} - 3 q^{60} - 24 q^{61} - 9 q^{62} + q^{63} - 38 q^{64} - 8 q^{65} - 9 q^{67} - 19 q^{68} + 22 q^{69} + 2 q^{70} - 10 q^{71} - 4 q^{72} - 11 q^{73} + q^{74} + 2 q^{75} - 11 q^{76} - 5 q^{78} - 9 q^{79} + 2 q^{80} - 19 q^{81} + 44 q^{82} - 10 q^{83} + 3 q^{84} - 6 q^{85} + 15 q^{86} + 2 q^{87} - 9 q^{89} - 11 q^{90} + 8 q^{91} - 26 q^{92} - q^{93} - 34 q^{94} - 7 q^{95} + 18 q^{96} + 11 q^{97} - 2 q^{98}+O(q^{100}) \) 5 * q - 2 * q^2 + 2 * q^3 + 4 * q^4 + 5 * q^5 + q^6 - 5 * q^7 - q^9 - 2 * q^10 - 3 * q^12 - 8 * q^13 + 2 * q^14 + 2 * q^15 + 2 * q^16 - 6 * q^17 - 11 * q^18 - 7 * q^19 + 4 * q^20 - 2 * q^21 + 3 * q^23 + 6 * q^24 + 5 * q^25 - 15 * q^26 + 5 * q^27 - 4 * q^28 - 17 * q^29 + q^30 + 12 * q^31 + 3 * q^32 - 12 * q^34 - 5 * q^35 - 3 * q^36 - 2 * q^37 + 21 * q^38 - 14 * q^39 - 5 * q^41 - q^42 - 4 * q^43 - q^45 - 2 * q^46 - 12 * q^48 + 5 * q^49 - 2 * q^50 - 14 * q^51 - 2 * q^52 + 8 * q^53 - 22 * q^54 - 4 * q^57 + 6 * q^58 - 16 * q^59 - 3 * q^60 - 24 * q^61 - 9 * q^62 + q^63 - 38 * q^64 - 8 * q^65 - 9 * q^67 - 19 * q^68 + 22 * q^69 + 2 * q^70 - 10 * q^71 - 4 * q^72 - 11 * q^73 + q^74 + 2 * q^75 - 11 * q^76 - 5 * q^78 - 9 * q^79 + 2 * q^80 - 19 * q^81 + 44 * q^82 - 10 * q^83 + 3 * q^84 - 6 * q^85 + 15 * q^86 + 2 * q^87 - 9 * q^89 - 11 * q^90 + 8 * q^91 - 26 * q^92 - q^93 - 34 * q^94 - 7 * q^95 + 18 * q^96 + 11 * q^97 - 2 * q^98

Introduction

L-functions

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