LMFDB - Embedded newform 4235.2.a.bf.1.5

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:	$0$
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			1.5
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	$-0.188011\pi$
$2$	2.34922	1.66115	0.830576	+	0.556905i	$0.188011\pi$
$3$	−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	$-0.534271\pi$
$13$	−0.774897	−0.214918	−0.107459	+	0.994210i	$0.534271\pi$
$14$	2.34922	0.627857
$15$	−1.64458	−0.424629
$16$	1.34463	0.336158
$17$	−4.83632	−1.17298	−0.586490	−	0.809957i	$-0.699491\pi$
$17$	−4.83632	−1.17298	−0.586490	+	0.809957i	$0.699491\pi$
$18$	−0.693857	−0.163544
$19$	6.49168	1.48929	0.744647	−	0.667458i	$-0.232618\pi$
$19$	6.49168	1.48929	0.744647	+	0.667458i	$0.232618\pi$
$20$	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	$-0.244860\pi$
$29$	7.73776	1.43687	0.718433	+	0.695596i	$0.244860\pi$
$30$	−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	$-0.231484\pi$
$41$	9.56653	1.49404	0.747020	+	0.664801i	$0.231484\pi$
$42$	−3.86349	−0.596149
$43$	−2.28457	−0.348393	−0.174197	−	0.984711i	$-0.555733\pi$
$43$	−2.28457	−0.348393	−0.174197	+	0.984711i	$0.555733\pi$
$44$	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	$-0.518236\pi$
$61$	−0.894426	−0.114520	−0.0572598	+	0.998359i	$0.518236\pi$
$62$	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	$-0.468929\pi$
$73$	1.66533	0.194912	0.0974561	+	0.995240i	$0.468929\pi$
$74$	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	$-0.520712\pi$
$79$	−1.15588	−0.130047	−0.0650236	+	0.997884i	$0.520712\pi$
$80$	1.34463	0.150335
$81$	−8.02670	−0.891855
$82$	22.4739	2.48183
$83$	13.8377	1.51888	0.759441	−	0.650576i	$-0.225473\pi$
$83$	13.8377	1.51888	0.759441	+	0.650576i	$0.225473\pi$
$84$	−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	$-0.197890\pi$
$101$	16.3390	1.62579	0.812896	+	0.582408i	$0.197890\pi$
$102$	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	$-0.772047\pi$
$107$	−15.6061	−1.50870	−0.754348	+	0.656475i	$0.772047\pi$
$108$	19.0704	1.83505
$109$	−0.692852	−0.0663632	−0.0331816	−	0.999449i	$-0.510564\pi$
$109$	−0.692852	−0.0663632	−0.0331816	+	0.999449i	$0.510564\pi$
$110$	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	$-0.647576\pi$
$127$	−10.0792	−0.894383	−0.447192	+	0.894438i	$0.647576\pi$
$128$	−20.3137	−1.79549
$129$	3.75716	0.330799
$130$	−1.82041	−0.159660
$131$	−15.7884	−1.37944	−0.689721	−	0.724076i	$-0.742267\pi$
$131$	−15.7884	−1.37944	−0.689721	+	0.724076i	$0.742267\pi$
$132$	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	$-0.308788\pi$
$139$	13.3279	1.13046	0.565228	+	0.824935i	$0.308788\pi$
$140$	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	$-0.795777\pi$
$149$	−19.5585	−1.60229	−0.801147	+	0.598467i	$0.795777\pi$
$150$	−3.86349	−0.315452
$151$	11.9888	0.975633	0.487817	−	0.872946i	$-0.337793\pi$
$151$	11.9888	0.975633	0.487817	+	0.872946i	$0.337793\pi$
$152$	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	$-0.572807\pi$
$167$	−5.86030	−0.453483	−0.226742	+	0.973955i	$0.572807\pi$
$168$	−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	$-0.554126\pi$
$173$	−4.45156	−0.338446	−0.169223	+	0.985578i	$0.554126\pi$
$174$	−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	$-0.377236\pi$
$193$	10.4522	0.752369	0.376185	+	0.926545i	$0.377236\pi$
$194$	−16.3213	−1.17180
$195$	1.27438	0.0912602
$196$	3.51886	0.251347
$197$	−26.6710	−1.90023	−0.950116	−	0.311896i	$-0.899036\pi$
$197$	−26.6710	−1.90023	−0.950116	+	0.311896i	$0.899036\pi$
$198$	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	$-0.219591\pi$
$211$	22.4085	1.54266	0.771332	+	0.636433i	$0.219591\pi$
$212$	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	$-0.680030\pi$
$227$	−16.1485	−1.07181	−0.535905	+	0.844278i	$0.680030\pi$
$228$	−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	$-0.219063\pi$
$233$	23.5799	1.54477	0.772385	+	0.635154i	$0.219063\pi$
$234$	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	$-0.698368\pi$
$239$	−18.0454	−1.16726	−0.583629	+	0.812021i	$0.698368\pi$
$240$	−2.21136	−0.142742
$241$	12.1774	0.784415	0.392207	−	0.919877i	$-0.371712\pi$
$241$	12.1774	0.784415	0.392207	+	0.919877i	$0.371712\pi$
$242$	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	$-0.636495\pi$
$263$	−13.4859	−0.831579	−0.415790	+	0.909461i	$0.636495\pi$
$264$	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	$-0.867245\pi$
$271$	−30.1020	−1.82857	−0.914283	+	0.405076i	$0.867245\pi$
$272$	−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	$-0.196179\pi$
$277$	27.1624	1.63203	0.816014	+	0.578032i	$0.196179\pi$
$278$	31.3102	1.87786
$279$	−2.91818	−0.174707
$280$	3.56813	0.213237
$281$	−15.2378	−0.909010	−0.454505	−	0.890744i	$-0.650184\pi$
$281$	−15.2378	−0.909010	−0.454505	+	0.890744i	$0.650184\pi$
$282$	−7.84651	−0.467253
$283$	14.8916	0.885213	0.442606	−	0.896716i	$-0.354054\pi$
$283$	14.8916	0.885213	0.442606	+	0.896716i	$0.354054\pi$
$284$	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	$-0.368070\pi$
$293$	13.7864	0.805413	0.402706	+	0.915329i	$0.368070\pi$
$294$	−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	$-0.288943\pi$
$307$	21.5698	1.23106	0.615528	+	0.788115i	$0.288943\pi$
$308$	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	$-0.225521\pi$
$337$	27.8793	1.51868	0.759341	+	0.650693i	$0.225521\pi$
$338$	−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	$-0.362645\pi$
$347$	15.5821	0.836490	0.418245	+	0.908334i	$0.362645\pi$
$348$	−44.7787	−2.40039
$349$	20.5218	1.09851	0.549253	−	0.835656i	$-0.314912\pi$
$349$	20.5218	1.09851	0.549253	+	0.835656i	$0.314912\pi$
$350$	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	$-0.454596\pi$
$359$	5.38698	0.284314	0.142157	+	0.989844i	$0.454596\pi$
$360$	−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	$-0.431060\pi$
$373$	8.30055	0.429786	0.214893	+	0.976638i	$0.431060\pi$
$374$	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	$-0.767755\pi$
$409$	−30.1507	−1.49086	−0.745428	+	0.666586i	$0.767755\pi$
$410$	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	$-0.302900\pi$
$431$	24.0984	1.16078	0.580390	+	0.814339i	$0.302900\pi$
$432$	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	$-0.698398\pi$
$439$	−24.4600	−1.16741	−0.583706	+	0.811965i	$0.698398\pi$
$440$	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	$-0.468069\pi$
$457$	4.28175	0.200292	0.100146	+	0.994973i	$0.468069\pi$
$458$	−9.28573	−0.433894
$459$	−26.2103	−1.22339
$460$	−3.59267	−0.167509
$461$	35.1353	1.63641	0.818207	−	0.574924i	$-0.194968\pi$
$461$	35.1353	1.63641	0.818207	+	0.574924i	$0.194968\pi$
$462$	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	$-0.403427\pi$
$479$	13.0773	0.597518	0.298759	+	0.954329i	$0.403427\pi$
$480$	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	$-0.581684\pi$
$491$	−11.2481	−0.507621	−0.253810	+	0.967254i	$0.581684\pi$
$492$	−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	$-0.675021\pi$
$503$	−23.4394	−1.04511	−0.522556	+	0.852605i	$0.675021\pi$
$504$	−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	$-0.727697\pi$
$523$	−29.9984	−1.31174	−0.655868	+	0.754875i	$0.727697\pi$
$524$	−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	$-0.674039\pi$
$541$	−24.1862	−1.03985	−0.519923	+	0.854213i	$0.674039\pi$
$542$	−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	$-0.440718\pi$
$547$	8.66134	0.370332	0.185166	+	0.982707i	$0.440718\pi$
$548$	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	$-0.811220\pi$
$557$	−39.1410	−1.65846	−0.829229	+	0.558909i	$0.811220\pi$
$558$	−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	$-0.771826\pi$
$563$	−35.7761	−1.50778	−0.753892	+	0.656999i	$0.771826\pi$
$564$	−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	$-0.142125\pi$
$569$	43.0304	1.80393	0.901965	+	0.431809i	$0.142125\pi$
$570$	−25.0805	−1.05051
$571$	5.54693	0.232132	0.116066	−	0.993242i	$-0.462972\pi$
$571$	5.54693	0.232132	0.116066	+	0.993242i	$0.462972\pi$
$572$	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	$-0.580029\pi$
$593$	−12.1163	−0.497559	−0.248779	+	0.968560i	$0.580029\pi$
$594$	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	$-0.524624\pi$
$601$	−3.78918	−0.154564	−0.0772818	+	0.997009i	$0.524624\pi$
$602$	−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	$-0.350019\pi$
$607$	22.3676	0.907873	0.453936	+	0.891034i	$0.350019\pi$
$608$	−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	$-0.451083\pi$
$613$	7.57985	0.306147	0.153074	+	0.988215i	$0.451083\pi$
$614$	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	$-0.363635\pi$
$659$	21.3285	0.830839	0.415419	+	0.909630i	$0.363635\pi$
$660$	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	$-0.286097\pi$
$673$	32.3007	1.24510	0.622550	+	0.782580i	$0.286097\pi$
$674$	65.4947	2.52276
$675$	5.41948	0.208596
$676$	−43.6322	−1.67816
$677$	42.5686	1.63604	0.818022	−	0.575187i	$-0.195071\pi$
$677$	42.5686	1.63604	0.818022	+	0.575187i	$0.195071\pi$
$678$	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	$-0.402276\pi$
$701$	16.0028	0.604418	0.302209	+	0.953242i	$0.402276\pi$
$702$	−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	$-0.307558\pi$
$733$	30.7784	1.13683	0.568413	+	0.822743i	$0.307558\pi$
$734$	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	$-0.374700\pi$
$739$	20.8534	0.767105	0.383553	+	0.923519i	$0.374700\pi$
$740$	6.66911	0.245162
$741$	8.27287	0.303912
$742$	10.1508	0.372648
$743$	−23.1969	−0.851011	−0.425506	−	0.904956i	$-0.639904\pi$
$743$	−23.1969	−0.851011	−0.425506	+	0.904956i	$0.639904\pi$
$744$	−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	$-0.441775\pi$
$761$	10.0359	0.363799	0.181900	+	0.983317i	$0.441775\pi$
$762$	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	$-0.387747\pi$
$769$	19.1558	0.690777	0.345389	+	0.938460i	$0.387747\pi$
$770$	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	$-0.543314\pi$
$787$	−7.61129	−0.271313	−0.135657	+	0.990756i	$0.543314\pi$
$788$	−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	$-0.159752\pi$
$809$	49.8708	1.75336	0.876682	+	0.481070i	$0.159752\pi$
$810$	−18.8565	−0.662550
$811$	−24.6779	−0.866558	−0.433279	−	0.901260i	$-0.642644\pi$
$811$	−24.6779	−0.866558	−0.433279	+	0.901260i	$0.642644\pi$
$812$	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	$-0.549964\pi$
$821$	−8.95832	−0.312648	−0.156324	+	0.987706i	$0.549964\pi$
$822$	−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	$-0.591251\pi$
$827$	−16.2631	−0.565525	−0.282762	+	0.959190i	$0.591251\pi$
$828$	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	$-0.333824\pi$
$853$	29.1282	0.997331	0.498666	+	0.866794i	$0.333824\pi$
$854$	−2.10121	−0.0719019
$855$	−1.91736	−0.0655722
$856$	−55.6845	−1.90326
$857$	−25.1149	−0.857908	−0.428954	−	0.903326i	$-0.641118\pi$
$857$	−25.1149	−0.857908	−0.428954	+	0.903326i	$0.641118\pi$
$858$	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	$-0.483221\pi$
$877$	3.12070	0.105379	0.0526893	+	0.998611i	$0.483221\pi$
$878$	−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	$-0.551092\pi$
$887$	−9.51979	−0.319643	−0.159822	+	0.987146i	$0.551092\pi$
$888$	−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	$-0.437538\pi$
$919$	11.8212	0.389945	0.194973	+	0.980809i	$0.437538\pi$
$920$	−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	$-0.448837\pi$
$937$	9.79791	0.320084	0.160042	+	0.987110i	$0.448837\pi$
$938$	−18.2270	−0.595133
$939$	−2.23697	−0.0730009
$940$	7.14658	0.233096
$941$	−34.1832	−1.11434	−0.557170	−	0.830399i	$-0.688113\pi$
$941$	−34.1832	−1.11434	−0.557170	+	0.830399i	$0.688113\pi$
$942$	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	$-0.505994\pi$
$953$	−1.16252	−0.0376578	−0.0188289	+	0.999823i	$0.505994\pi$
$954$	−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	$-0.726509\pi$
$967$	−40.6151	−1.30609	−0.653046	+	0.757318i	$0.726509\pi$
$968$	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	$-0.776987\pi$
$997$	−48.2752	−1.52889	−0.764445	+	0.644689i	$0.776987\pi$
$998$	−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.bf.1.5	yes	5
11.10	odd	2		4235.2.a.z.1.1	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.z.1.1	✓	5	11.10	odd	2
4235.2.a.bf.1.5	yes	5	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:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
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

Modular forms

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Database

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