LMFDB - Embedded newform 4033.2.a.e.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.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:	$32.2036671352$
Analytic rank:	$0$
Dimension:	$82$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.92046 q^{2} +1.69690 q^{3} +1.68818 q^{4} -0.668171 q^{5} -3.25884 q^{6} +1.48884 q^{7} +0.598834 q^{8} -0.120514 q^{9} +O(q^{10})$	\(q-1.92046 q^{2} +1.69690 q^{3} +1.68818 q^{4} -0.668171 q^{5} -3.25884 q^{6} +1.48884 q^{7} +0.598834 q^{8} -0.120514 q^{9} +1.28320 q^{10} +0.205376 q^{11} +2.86469 q^{12} -0.291949 q^{13} -2.85927 q^{14} -1.13382 q^{15} -4.52640 q^{16} +0.0221940 q^{17} +0.231443 q^{18} -2.06520 q^{19} -1.12799 q^{20} +2.52643 q^{21} -0.394417 q^{22} -4.75410 q^{23} +1.01616 q^{24} -4.55355 q^{25} +0.560677 q^{26} -5.29522 q^{27} +2.51344 q^{28} +0.539101 q^{29} +2.17747 q^{30} +7.06835 q^{31} +7.49513 q^{32} +0.348504 q^{33} -0.0426229 q^{34} -0.994802 q^{35} -0.203450 q^{36} -1.00000 q^{37} +3.96614 q^{38} -0.495409 q^{39} -0.400123 q^{40} +6.30766 q^{41} -4.85191 q^{42} +6.85574 q^{43} +0.346712 q^{44} +0.0805242 q^{45} +9.13008 q^{46} +3.20986 q^{47} -7.68088 q^{48} -4.78335 q^{49} +8.74493 q^{50} +0.0376612 q^{51} -0.492862 q^{52} +9.68284 q^{53} +10.1693 q^{54} -0.137226 q^{55} +0.891570 q^{56} -3.50444 q^{57} -1.03532 q^{58} +8.05278 q^{59} -1.91410 q^{60} +3.29620 q^{61} -13.5745 q^{62} -0.179427 q^{63} -5.34132 q^{64} +0.195072 q^{65} -0.669289 q^{66} +9.51311 q^{67} +0.0374676 q^{68} -8.06726 q^{69} +1.91048 q^{70} -10.0208 q^{71} -0.0721681 q^{72} +9.53947 q^{73} +1.92046 q^{74} -7.72694 q^{75} -3.48643 q^{76} +0.305773 q^{77} +0.951415 q^{78} +1.80256 q^{79} +3.02441 q^{80} -8.62393 q^{81} -12.1136 q^{82} +13.2855 q^{83} +4.26507 q^{84} -0.0148294 q^{85} -13.1662 q^{86} +0.914803 q^{87} +0.122986 q^{88} +8.94737 q^{89} -0.154644 q^{90} -0.434666 q^{91} -8.02579 q^{92} +11.9943 q^{93} -6.16442 q^{94} +1.37990 q^{95} +12.7185 q^{96} -2.08850 q^{97} +9.18624 q^{98} -0.0247507 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9}+O(q^{10}) $ 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9	\( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9} + 13 q^{10} + 2 q^{11} + 36 q^{12} + 23 q^{13} + 24 q^{14} + 35 q^{15} + 104 q^{16} + 43 q^{17} + 42 q^{18} + 15 q^{19} + 59 q^{20} + 9 q^{21} + 6 q^{22} + 70 q^{23} + 15 q^{24} + 98 q^{25} + 10 q^{26} + 65 q^{27} + 37 q^{28} + 27 q^{29} + 17 q^{30} + 59 q^{31} + 46 q^{32} + 16 q^{33} - 16 q^{34} + 80 q^{35} + 88 q^{36} - 82 q^{37} + 82 q^{38} + 13 q^{39} + 14 q^{40} + 3 q^{41} + 62 q^{42} + 7 q^{43} - 11 q^{44} + 42 q^{45} - 11 q^{46} + 123 q^{47} + 45 q^{48} + 105 q^{49} + 27 q^{50} + 3 q^{51} - 30 q^{52} + 82 q^{53} - 27 q^{54} + 37 q^{55} + 66 q^{56} + 29 q^{57} - 34 q^{58} + 60 q^{59} + 94 q^{60} + 9 q^{61} - 2 q^{62} + 106 q^{63} + 93 q^{64} + 9 q^{65} + 63 q^{66} + 113 q^{68} + 48 q^{69} + 47 q^{70} + 59 q^{71} + 63 q^{72} + 21 q^{73} - 10 q^{74} + 77 q^{75} + 22 q^{76} + 30 q^{77} + 29 q^{78} + 55 q^{79} + 88 q^{80} + 42 q^{81} + 4 q^{82} + 92 q^{83} + 43 q^{84} - 7 q^{85} + 17 q^{86} + 147 q^{87} - 13 q^{88} + 100 q^{89} + 91 q^{90} + 28 q^{91} + 127 q^{92} + 3 q^{93} + 30 q^{94} + 48 q^{95} - 31 q^{96} + 53 q^{97} + 101 q^{98} - 20 q^{99}+O(q^{100}) \) 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9 + 13 * q^10 + 2 * q^11 + 36 * q^12 + 23 * q^13 + 24 * q^14 + 35 * q^15 + 104 * q^16 + 43 * q^17 + 42 * q^18 + 15 * q^19 + 59 * q^20 + 9 * q^21 + 6 * q^22 + 70 * q^23 + 15 * q^24 + 98 * q^25 + 10 * q^26 + 65 * q^27 + 37 * q^28 + 27 * q^29 + 17 * q^30 + 59 * q^31 + 46 * q^32 + 16 * q^33 - 16 * q^34 + 80 * q^35 + 88 * q^36 - 82 * q^37 + 82 * q^38 + 13 * q^39 + 14 * q^40 + 3 * q^41 + 62 * q^42 + 7 * q^43 - 11 * q^44 + 42 * q^45 - 11 * q^46 + 123 * q^47 + 45 * q^48 + 105 * q^49 + 27 * q^50 + 3 * q^51 - 30 * q^52 + 82 * q^53 - 27 * q^54 + 37 * q^55 + 66 * q^56 + 29 * q^57 - 34 * q^58 + 60 * q^59 + 94 * q^60 + 9 * q^61 - 2 * q^62 + 106 * q^63 + 93 * q^64 + 9 * q^65 + 63 * q^66 + 113 * q^68 + 48 * q^69 + 47 * q^70 + 59 * q^71 + 63 * q^72 + 21 * q^73 - 10 * q^74 + 77 * q^75 + 22 * q^76 + 30 * q^77 + 29 * q^78 + 55 * q^79 + 88 * q^80 + 42 * q^81 + 4 * q^82 + 92 * q^83 + 43 * q^84 - 7 * q^85 + 17 * q^86 + 147 * q^87 - 13 * q^88 + 100 * q^89 + 91 * q^90 + 28 * q^91 + 127 * q^92 + 3 * q^93 + 30 * q^94 + 48 * q^95 - 31 * q^96 + 53 * q^97 + 101 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.92046	−1.35797	−0.678987	−	0.734151i	$-0.737581\pi$
$2$	−1.92046	−1.35797	−0.678987	+	0.734151i	$0.737581\pi$
$3$	1.69690	0.979708	0.489854	−	0.871804i	$-0.337050\pi$
$3$	1.69690	0.979708	0.489854	+	0.871804i	$0.337050\pi$
$4$	1.68818	0.844091
$5$	−0.668171	−0.298815	−0.149408	−	0.988776i	$-0.547737\pi$
$5$	−0.668171	−0.298815	−0.149408	+	0.988776i	$0.547737\pi$
$6$	−3.25884	−1.33042
$7$	1.48884	0.562730	0.281365	−	0.959601i	$-0.409213\pi$
$7$	1.48884	0.562730	0.281365	+	0.959601i	$0.409213\pi$
$8$	0.598834	0.211720
$9$	−0.120514	−0.0401714
$10$	1.28320	0.405783
$11$	0.205376	0.0619232	0.0309616	−	0.999521i	$-0.490143\pi$
$11$	0.205376	0.0619232	0.0309616	+	0.999521i	$0.490143\pi$
$12$	2.86469	0.826963
$13$	−0.291949	−0.0809719	−0.0404860	−	0.999180i	$-0.512891\pi$
$13$	−0.291949	−0.0809719	−0.0404860	+	0.999180i	$0.512891\pi$
$14$	−2.85927	−0.764172
$15$	−1.13382	−0.292752
$16$	−4.52640	−1.13160
$17$	0.0221940	0.00538285	0.00269142	−	0.999996i	$-0.499143\pi$
$17$	0.0221940	0.00538285	0.00269142	+	0.999996i	$0.499143\pi$
$18$	0.231443	0.0545517
$19$	−2.06520	−0.473789	−0.236894	−	0.971535i	$-0.576129\pi$
$19$	−2.06520	−0.473789	−0.236894	+	0.971535i	$0.576129\pi$
$20$	−1.12799	−0.252227
$21$	2.52643	0.551311
$22$	−0.394417	−0.0840900
$23$	−4.75410	−0.991299	−0.495649	−	0.868523i	$-0.665070\pi$
$23$	−4.75410	−0.991299	−0.495649	+	0.868523i	$0.665070\pi$
$24$	1.01616	0.207424
$25$	−4.55355	−0.910710
$26$	0.560677	0.109958
$27$	−5.29522	−1.01906
$28$	2.51344	0.474995
$29$	0.539101	0.100109	0.0500543	−	0.998747i	$-0.484061\pi$
$29$	0.539101	0.100109	0.0500543	+	0.998747i	$0.484061\pi$
$30$	2.17747	0.397549
$31$	7.06835	1.26951	0.634756	−	0.772712i	$-0.281101\pi$
$31$	7.06835	1.26951	0.634756	+	0.772712i	$0.281101\pi$
$32$	7.49513	1.32496
$33$	0.348504	0.0606667
$34$	−0.0426229	−0.00730976
$35$	−0.994802	−0.168152
$36$	−0.203450	−0.0339084
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	3.96614	0.643392
$39$	−0.495409	−0.0793289
$40$	−0.400123	−0.0632651
$41$	6.30766	0.985090	0.492545	−	0.870287i	$-0.336067\pi$
$41$	6.30766	0.985090	0.492545	+	0.870287i	$0.336067\pi$
$42$	−4.85191	−0.748666
$43$	6.85574	1.04549	0.522745	−	0.852489i	$-0.324908\pi$
$43$	6.85574	1.04549	0.522745	+	0.852489i	$0.324908\pi$
$44$	0.346712	0.0522688
$45$	0.0805242	0.0120038
$46$	9.13008	1.34616
$47$	3.20986	0.468206	0.234103	−	0.972212i	$-0.424785\pi$
$47$	3.20986	0.468206	0.234103	+	0.972212i	$0.424785\pi$
$48$	−7.68088	−1.10864
$49$	−4.78335	−0.683335
$50$	8.74493	1.23672
$51$	0.0376612	0.00527362
$52$	−0.492862	−0.0683477
$53$	9.68284	1.33004	0.665020	−	0.746825i	$-0.268423\pi$
$53$	9.68284	1.33004	0.665020	+	0.746825i	$0.268423\pi$
$54$	10.1693	1.38386
$55$	−0.137226	−0.0185036
$56$	0.891570	0.119141
$57$	−3.50444	−0.464175
$58$	−1.03532	−0.135945
$59$	8.05278	1.04838	0.524192	−	0.851600i	$-0.324368\pi$
$59$	8.05278	1.04838	0.524192	+	0.851600i	$0.324368\pi$
$60$	−1.91410	−0.247109
$61$	3.29620	0.422035	0.211017	−	0.977482i	$-0.432322\pi$
$61$	3.29620	0.422035	0.211017	+	0.977482i	$0.432322\pi$
$62$	−13.5745	−1.72396
$63$	−0.179427	−0.0226057
$64$	−5.34132	−0.667665
$65$	0.195072	0.0241956
$66$	−0.669289	−0.0823837
$67$	9.51311	1.16221	0.581106	−	0.813828i	$-0.302620\pi$
$67$	9.51311	1.16221	0.581106	+	0.813828i	$0.302620\pi$
$68$	0.0374676	0.00454361
$69$	−8.06726	−0.971184
$70$	1.91048	0.228346
$71$	−10.0208	−1.18925	−0.594627	−	0.804002i	$-0.702700\pi$
$71$	−10.0208	−1.18925	−0.594627	+	0.804002i	$0.702700\pi$
$72$	−0.0721681	−0.00850509
$73$	9.53947	1.11651	0.558256	−	0.829669i	$-0.311471\pi$
$73$	9.53947	1.11651	0.558256	+	0.829669i	$0.311471\pi$
$74$	1.92046	0.223249
$75$	−7.72694	−0.892230
$76$	−3.48643	−0.399921
$77$	0.305773	0.0348460
$78$	0.951415	0.107727
$79$	1.80256	0.202804	0.101402	−	0.994846i	$-0.467667\pi$
$79$	1.80256	0.202804	0.101402	+	0.994846i	$0.467667\pi$
$80$	3.02441	0.338140
$81$	−8.62393	−0.958215
$82$	−12.1136	−1.33773
$83$	13.2855	1.45827	0.729135	−	0.684369i	$-0.239922\pi$
$83$	13.2855	1.45827	0.729135	+	0.684369i	$0.239922\pi$
$84$	4.26507	0.465357
$85$	−0.0148294	−0.00160848
$86$	−13.1662	−1.41975
$87$	0.914803	0.0980771
$88$	0.122986	0.0131104
$89$	8.94737	0.948420	0.474210	−	0.880412i	$-0.342734\pi$
$89$	8.94737	0.948420	0.474210	+	0.880412i	$0.342734\pi$
$90$	−0.154644	−0.0163009
$91$	−0.434666	−0.0455653
$92$	−8.02579	−0.836747
$93$	11.9943	1.24375
$94$	−6.16442	−0.635811
$95$	1.37990	0.141575
$96$	12.7185	1.29808
$97$	−2.08850	−0.212055	−0.106027	−	0.994363i	$-0.533813\pi$
$97$	−2.08850	−0.212055	−0.106027	+	0.994363i	$0.533813\pi$
$98$	9.18624	0.927951
$99$	−0.0247507	−0.00248754
$100$	−7.68722	−0.768722
$101$	8.62584	0.858303	0.429151	−	0.903233i	$-0.358813\pi$
$101$	8.62584	0.858303	0.429151	+	0.903233i	$0.358813\pi$
$102$	−0.0723269	−0.00716143
$103$	−17.3021	−1.70483	−0.852415	−	0.522866i	$-0.824863\pi$
$103$	−17.3021	−1.70483	−0.852415	+	0.522866i	$0.824863\pi$
$104$	−0.174829	−0.0171434
$105$	−1.68808	−0.164740
$106$	−18.5955	−1.80616
$107$	−6.35900	−0.614747	−0.307374	−	0.951589i	$-0.599450\pi$
$107$	−6.35900	−0.614747	−0.307374	+	0.951589i	$0.599450\pi$
$108$	−8.93929	−0.860184
$109$	1.00000	0.0957826
$109$	1.00000	0.0957826
$110$	0.263538	0.0251274
$111$	−1.69690	−0.161063
$112$	−6.73911	−0.636786
$113$	−3.57879	−0.336664	−0.168332	−	0.985730i	$-0.553838\pi$
$113$	−3.57879	−0.336664	−0.168332	+	0.985730i	$0.553838\pi$
$114$	6.73015	0.630337
$115$	3.17655	0.296215
$116$	0.910101	0.0845007
$117$	0.0351840	0.00325276
$118$	−15.4651	−1.42368
$119$	0.0330434	0.00302909
$120$	−0.678971	−0.0619813
$121$	−10.9578	−0.996166
$122$	−6.33023	−0.573112
$123$	10.7035	0.965101
$124$	11.9327	1.07158
$125$	6.38340	0.570949
$126$	0.344583	0.0306979
$127$	18.7828	1.66670	0.833351	−	0.552744i	$-0.186419\pi$
$127$	18.7828	1.66670	0.833351	+	0.552744i	$0.186419\pi$
$128$	−4.73245	−0.418293
$129$	11.6335	1.02428
$130$	−0.374628	−0.0328570
$131$	17.7039	1.54680	0.773399	−	0.633920i	$-0.218555\pi$
$131$	17.7039	1.54680	0.773399	+	0.633920i	$0.218555\pi$
$132$	0.588338	0.0512082
$133$	−3.07475	−0.266615
$134$	−18.2696	−1.57825
$135$	3.53811	0.304512
$136$	0.0132905	0.00113965
$137$	−0.132461	−0.0113169	−0.00565845	−	0.999984i	$-0.501801\pi$
$137$	−0.132461	−0.0113169	−0.00565845	+	0.999984i	$0.501801\pi$
$138$	15.4929	1.31884
$139$	−6.17401	−0.523672	−0.261836	−	0.965112i	$-0.584328\pi$
$139$	−6.17401	−0.523672	−0.261836	+	0.965112i	$0.584328\pi$
$140$	−1.67941	−0.141936
$141$	5.44683	0.458706
$142$	19.2446	1.61497
$143$	−0.0599592	−0.00501404
$144$	0.545496	0.0454580
$145$	−0.360212	−0.0299139
$146$	−18.3202	−1.51619
$147$	−8.11688	−0.669469
$148$	−1.68818	−0.138768
$149$	15.8421	1.29783	0.648916	−	0.760860i	$-0.275223\pi$
$149$	15.8421	1.29783	0.648916	+	0.760860i	$0.275223\pi$
$150$	14.8393	1.21162
$151$	2.73658	0.222700	0.111350	−	0.993781i	$-0.464483\pi$
$151$	2.73658	0.222700	0.111350	+	0.993781i	$0.464483\pi$
$152$	−1.23671	−0.100310
$153$	−0.00267470	−0.000216237 0
$154$	−0.587226	−0.0473200
$155$	−4.72286	−0.379350
$156$	−0.836341	−0.0669608
$157$	−4.42158	−0.352881	−0.176440	−	0.984311i	$-0.556458\pi$
$157$	−4.42158	−0.352881	−0.176440	+	0.984311i	$0.556458\pi$
$158$	−3.46175	−0.275402
$159$	16.4309	1.30305
$160$	−5.00803	−0.395919
$161$	−7.07811	−0.557833
$162$	16.5620	1.30123
$163$	9.09687	0.712522	0.356261	−	0.934386i	$-0.384051\pi$
$163$	9.09687	0.712522	0.356261	+	0.934386i	$0.384051\pi$
$164$	10.6485	0.831506
$165$	−0.232860	−0.0181281
$166$	−25.5143	−1.98029
$167$	−16.8724	−1.30563	−0.652814	−	0.757519i	$-0.726412\pi$
$167$	−16.8724	−1.30563	−0.652814	+	0.757519i	$0.726412\pi$
$168$	1.51291	0.116723
$169$	−12.9148	−0.993444
$170$	0.0284794	0.00218427
$171$	0.248886	0.0190328
$172$	11.5737	0.882489
$173$	9.86292	0.749864	0.374932	−	0.927052i	$-0.377666\pi$
$173$	9.86292	0.749864	0.374932	+	0.927052i	$0.377666\pi$
$174$	−1.75685	−0.133186
$175$	−6.77952	−0.512483
$176$	−0.929615	−0.0700724
$177$	13.6648	1.02711
$178$	−17.1831	−1.28793
$179$	1.88992	0.141260	0.0706298	−	0.997503i	$-0.477499\pi$
$179$	1.88992	0.141260	0.0706298	+	0.997503i	$0.477499\pi$
$180$	0.135939	0.0101323
$181$	7.03347	0.522793	0.261397	−	0.965231i	$-0.415817\pi$
$181$	7.03347	0.522793	0.261397	+	0.965231i	$0.415817\pi$
$182$	0.834760	0.0618765
$183$	5.59333	0.413471
$184$	−2.84692	−0.209878
$185$	0.668171	0.0491249
$186$	−23.0346	−1.68898
$187$	0.00455812	0.000333323 0
$188$	5.41883	0.395209
$189$	−7.88375	−0.573458
$190$	−2.65006	−0.192255
$191$	12.7269	0.920887	0.460443	−	0.887689i	$-0.347690\pi$
$191$	12.7269	0.920887	0.460443	+	0.887689i	$0.347690\pi$
$192$	−9.06371	−0.654117
$193$	4.39100	0.316071	0.158036	−	0.987433i	$-0.449484\pi$
$193$	4.39100	0.316071	0.158036	+	0.987433i	$0.449484\pi$
$194$	4.01088	0.287965
$195$	0.331018	0.0237047
$196$	−8.07516	−0.576797
$197$	21.2893	1.51680	0.758400	−	0.651790i	$-0.225981\pi$
$197$	21.2893	1.51680	0.758400	+	0.651790i	$0.225981\pi$
$198$	0.0475329	0.00337802
$199$	5.40260	0.382980	0.191490	−	0.981495i	$-0.438668\pi$
$199$	5.40260	0.382980	0.191490	+	0.981495i	$0.438668\pi$
$200$	−2.72682	−0.192815
$201$	16.1428	1.13863
$202$	−16.5656	−1.16555
$203$	0.802637	0.0563340
$204$	0.0635789	0.00445142
$205$	−4.21459	−0.294360
$206$	33.2281	2.31511
$207$	0.572937	0.0398219
$208$	1.32148	0.0916280
$209$	−0.424142	−0.0293385
$210$	3.24190	0.223713
$211$	12.1721	0.837963	0.418981	−	0.907995i	$-0.362387\pi$
$211$	12.1721	0.837963	0.418981	+	0.907995i	$0.362387\pi$
$212$	16.3464	1.12268
$213$	−17.0044	−1.16512
$214$	12.2122	0.834811
$215$	−4.58080	−0.312408
$216$	−3.17095	−0.215756
$217$	10.5237	0.714393
$218$	−1.92046	−0.130070
$219$	16.1876	1.09386
$220$	−0.231663	−0.0156187
$221$	−0.00647952	−0.000435859 0
$222$	3.25884	0.218719
$223$	−14.8331	−0.993295	−0.496647	−	0.867952i	$-0.665436\pi$
$223$	−14.8331	−0.993295	−0.496647	+	0.867952i	$0.665436\pi$
$224$	11.1591	0.745597
$225$	0.548768	0.0365845
$226$	6.87293	0.457181
$227$	2.55821	0.169794	0.0848970	−	0.996390i	$-0.472944\pi$
$227$	2.55821	0.169794	0.0848970	+	0.996390i	$0.472944\pi$
$228$	−5.91614	−0.391806
$229$	−6.77019	−0.447387	−0.223693	−	0.974660i	$-0.571811\pi$
$229$	−6.77019	−0.447387	−0.223693	+	0.974660i	$0.571811\pi$
$230$	−6.10046	−0.402252
$231$	0.518867	0.0341390
$232$	0.322832	0.0211950
$233$	−22.1344	−1.45007	−0.725035	−	0.688712i	$-0.758176\pi$
$233$	−22.1344	−1.45007	−0.725035	+	0.688712i	$0.758176\pi$
$234$	−0.0675696	−0.00441716
$235$	−2.14474	−0.139907
$236$	13.5946	0.884931
$237$	3.05877	0.198688
$238$	−0.0634588	−0.00411342
$239$	8.74156	0.565444	0.282722	−	0.959202i	$-0.408763\pi$
$239$	8.74156	0.565444	0.282722	+	0.959202i	$0.408763\pi$
$240$	5.13214	0.331278
$241$	19.1316	1.23237	0.616186	−	0.787601i	$-0.288677\pi$
$241$	19.1316	1.23237	0.616186	+	0.787601i	$0.288677\pi$
$242$	21.0441	1.35277
$243$	1.25165	0.0802936
$244$	5.56458	0.356236
$245$	3.19609	0.204191
$246$	−20.5557	−1.31058
$247$	0.602931	0.0383636
$248$	4.23277	0.268781
$249$	22.5442	1.42868
$250$	−12.2591	−0.775333
$251$	−8.52815	−0.538292	−0.269146	−	0.963099i	$-0.586741\pi$
$251$	−8.52815	−0.538292	−0.269146	+	0.963099i	$0.586741\pi$
$252$	−0.302905	−0.0190812
$253$	−0.976378	−0.0613844
$254$	−36.0717	−2.26334
$255$	−0.0251641	−0.00157584
$256$	19.7711	1.23570
$257$	9.80649	0.611712	0.305856	−	0.952078i	$-0.401057\pi$
$257$	9.80649	0.611712	0.305856	+	0.952078i	$0.401057\pi$
$258$	−22.3418	−1.39094
$259$	−1.48884	−0.0925122
$260$	0.329316	0.0204233
$261$	−0.0649694	−0.00402150
$262$	−33.9997	−2.10051
$263$	−10.1808	−0.627778	−0.313889	−	0.949460i	$-0.601632\pi$
$263$	−10.1808	−0.627778	−0.313889	+	0.949460i	$0.601632\pi$
$264$	0.208696	0.0128443
$265$	−6.46979	−0.397436
$266$	5.90495	0.362056
$267$	15.1828	0.929175
$268$	16.0599	0.981013
$269$	−16.5195	−1.00721	−0.503605	−	0.863934i	$-0.667993\pi$
$269$	−16.5195	−1.00721	−0.503605	+	0.863934i	$0.667993\pi$
$270$	−6.79481	−0.413519
$271$	−11.9901	−0.728345	−0.364172	−	0.931332i	$-0.618648\pi$
$271$	−11.9901	−0.728345	−0.364172	+	0.931332i	$0.618648\pi$
$272$	−0.100459	−0.00609123
$273$	−0.737586	−0.0446407
$274$	0.254387	0.0153681
$275$	−0.935189	−0.0563940
$276$	−13.6190	−0.819768
$277$	−10.5725	−0.635242	−0.317621	−	0.948218i	$-0.602884\pi$
$277$	−10.5725	−0.635242	−0.317621	+	0.948218i	$0.602884\pi$
$278$	11.8570	0.711133
$279$	−0.851837	−0.0509981
$280$	−0.595721	−0.0356011
$281$	6.59513	0.393432	0.196716	−	0.980460i	$-0.436972\pi$
$281$	6.59513	0.393432	0.196716	+	0.980460i	$0.436972\pi$
$282$	−10.4604	−0.622910
$283$	−1.84635	−0.109754	−0.0548770	−	0.998493i	$-0.517477\pi$
$283$	−1.84635	−0.109754	−0.0548770	+	0.998493i	$0.517477\pi$
$284$	−16.9170	−1.00384
$285$	2.34157	0.138702
$286$	0.115150	0.00680893
$287$	9.39111	0.554340
$288$	−0.903270	−0.0532257
$289$	−16.9995	−0.999971
$290$	0.691773	0.0406223
$291$	−3.54398	−0.207752
$292$	16.1044	0.942437
$293$	21.8540	1.27672	0.638362	−	0.769736i	$-0.279612\pi$
$293$	21.8540	1.27672	0.638362	+	0.769736i	$0.279612\pi$
$294$	15.5882	0.909121
$295$	−5.38064	−0.313273
$296$	−0.598834	−0.0348065
$297$	−1.08751	−0.0631037
$298$	−30.4241	−1.76242
$299$	1.38795	0.0802674
$300$	−13.0445	−0.753123
$301$	10.2071	0.588328
$302$	−5.25551	−0.302420
$303$	14.6372	0.840886
$304$	9.34791	0.536140
$305$	−2.20242	−0.126110
$306$	0.00513666	0.000293644 0
$307$	−16.1490	−0.921670	−0.460835	−	0.887486i	$-0.652450\pi$
$307$	−16.1490	−0.921670	−0.460835	+	0.887486i	$0.652450\pi$
$308$	0.516200	0.0294132
$309$	−29.3601	−1.67024
$310$	9.07009	0.515147
$311$	15.0634	0.854169	0.427084	−	0.904212i	$-0.359541\pi$
$311$	15.0634	0.854169	0.427084	+	0.904212i	$0.359541\pi$
$312$	−0.296668	−0.0167955
$313$	−6.29610	−0.355876	−0.177938	−	0.984042i	$-0.556943\pi$
$313$	−6.29610	−0.355876	−0.177938	+	0.984042i	$0.556943\pi$
$314$	8.49149	0.479203
$315$	0.119888	0.00675492
$316$	3.04305	0.171185
$317$	6.72704	0.377828	0.188914	−	0.981994i	$-0.439503\pi$
$317$	6.72704	0.377828	0.188914	+	0.981994i	$0.439503\pi$
$318$	−31.5549	−1.76951
$319$	0.110718	0.00619904
$320$	3.56891	0.199508
$321$	−10.7906	−0.602273
$322$	13.5933	0.757523
$323$	−0.0458351	−0.00255033
$324$	−14.5588	−0.808821
$325$	1.32940	0.0737419
$326$	−17.4702	−0.967586
$327$	1.69690	0.0938390
$328$	3.77724	0.208563
$329$	4.77898	0.263474
$330$	0.447199	0.0246175
$331$	34.2021	1.87992	0.939959	−	0.341286i	$-0.110863\pi$
$331$	34.2021	1.87992	0.939959	+	0.341286i	$0.110863\pi$
$332$	22.4283	1.23091
$333$	0.120514	0.00660414
$334$	32.4029	1.77301
$335$	−6.35638	−0.347286
$336$	−11.4356	−0.623864
$337$	10.2433	0.557986	0.278993	−	0.960293i	$-0.409999\pi$
$337$	10.2433	0.557986	0.278993	+	0.960293i	$0.409999\pi$
$338$	24.8023	1.34907
$339$	−6.07286	−0.329833
$340$	−0.0250348	−0.00135770
$341$	1.45167	0.0786123
$342$	−0.477976	−0.0258460
$343$	−17.5436	−0.947263
$344$	4.10545	0.221351
$345$	5.39031	0.290204
$346$	−18.9414	−1.01829
$347$	6.80076	0.365084	0.182542	−	0.983198i	$-0.441568\pi$
$347$	6.80076	0.365084	0.182542	+	0.983198i	$0.441568\pi$
$348$	1.54435	0.0827861
$349$	−12.0002	−0.642357	−0.321179	−	0.947019i	$-0.604079\pi$
$349$	−12.0002	−0.642357	−0.321179	+	0.947019i	$0.604079\pi$
$350$	13.0198	0.695939
$351$	1.54593	0.0825157
$352$	1.53932	0.0820460
$353$	23.1151	1.23029	0.615146	−	0.788413i	$-0.289097\pi$
$353$	23.1151	1.23029	0.615146	+	0.788413i	$0.289097\pi$
$354$	−26.2428	−1.39479
$355$	6.69563	0.355367
$356$	15.1048	0.800553
$357$	0.0560716	0.00296762
$358$	−3.62953	−0.191827
$359$	−6.90191	−0.364269	−0.182134	−	0.983274i	$-0.558301\pi$
$359$	−6.90191	−0.364269	−0.182134	+	0.983274i	$0.558301\pi$
$360$	0.0482206	0.00254145
$361$	−14.7350	−0.775524
$362$	−13.5075	−0.709939
$363$	−18.5944	−0.975952
$364$	−0.733795	−0.0384613
$365$	−6.37400	−0.333630
$366$	−10.7418	−0.561482
$367$	−32.5752	−1.70041	−0.850207	−	0.526449i	$-0.823523\pi$
$367$	−32.5752	−1.70041	−0.850207	+	0.526449i	$0.823523\pi$
$368$	21.5190	1.12175
$369$	−0.760163	−0.0395725
$370$	−1.28320	−0.0667103
$371$	14.4162	0.748453
$372$	20.2486	1.04984
$373$	−17.9391	−0.928853	−0.464427	−	0.885612i	$-0.653740\pi$
$373$	−17.9391	−0.928853	−0.464427	+	0.885612i	$0.653740\pi$
$374$	−0.00875371	−0.000452644 0
$375$	10.8320	0.559363
$376$	1.92217	0.0991285
$377$	−0.157390	−0.00810598
$378$	15.1405	0.778741
$379$	−10.8140	−0.555480	−0.277740	−	0.960656i	$-0.589585\pi$
$379$	−10.8140	−0.555480	−0.277740	+	0.960656i	$0.589585\pi$
$380$	2.32953	0.119502
$381$	31.8726	1.63288
$382$	−24.4416	−1.25054
$383$	24.9890	1.27688	0.638439	−	0.769672i	$-0.279580\pi$
$383$	24.9890	1.27688	0.638439	+	0.769672i	$0.279580\pi$
$384$	−8.03051	−0.409805
$385$	−0.204308	−0.0104125
$386$	−8.43276	−0.429216
$387$	−0.826214	−0.0419988
$388$	−3.52577	−0.178994
$389$	30.7316	1.55816	0.779078	−	0.626927i	$-0.215688\pi$
$389$	30.7316	1.55816	0.779078	+	0.626927i	$0.215688\pi$
$390$	−0.635708	−0.0321903
$391$	−0.105513	−0.00533601
$392$	−2.86443	−0.144676
$393$	30.0419	1.51541
$394$	−40.8853	−2.05977
$395$	−1.20442	−0.0606008
$396$	−0.0417838	−0.00209971
$397$	−21.9334	−1.10081	−0.550404	−	0.834898i	$-0.685526\pi$
$397$	−21.9334	−1.10081	−0.550404	+	0.834898i	$0.685526\pi$
$398$	−10.3755	−0.520077
$399$	−5.21756	−0.261205
$400$	20.6112	1.03056
$401$	−2.58524	−0.129101	−0.0645503	−	0.997914i	$-0.520561\pi$
$401$	−2.58524	−0.129101	−0.0645503	+	0.997914i	$0.520561\pi$
$402$	−31.0018	−1.54623
$403$	−2.06359	−0.102795
$404$	14.5620	0.724486
$405$	5.76226	0.286329
$406$	−1.54143	−0.0765001
$407$	−0.205376	−0.0101801
$408$	0.0225528	0.00111653
$409$	12.4825	0.617219	0.308610	−	0.951189i	$-0.400136\pi$
$409$	12.4825	0.617219	0.308610	+	0.951189i	$0.400136\pi$
$410$	8.09397	0.399733
$411$	−0.224774	−0.0110873
$412$	−29.2092	−1.43903
$413$	11.9893	0.589957
$414$	−1.10031	−0.0540771
$415$	−8.87697	−0.435753
$416$	−2.18819	−0.107285
$417$	−10.4767	−0.513046
$418$	0.814549	0.0398409
$419$	24.5824	1.20093	0.600464	−	0.799652i	$-0.294983\pi$
$419$	24.5824	1.20093	0.600464	+	0.799652i	$0.294983\pi$
$420$	−2.84979	−0.139056
$421$	21.8706	1.06591	0.532953	−	0.846145i	$-0.321082\pi$
$421$	21.8706	1.06591	0.532953	+	0.846145i	$0.321082\pi$
$422$	−23.3761	−1.13793
$423$	−0.386834	−0.0188085
$424$	5.79841	0.281596
$425$	−0.101062	−0.00490221
$426$	32.6563	1.58220
$427$	4.90752	0.237492
$428$	−10.7351	−0.518903
$429$	−0.101745	−0.00491230
$430$	8.79727	0.424242
$431$	2.36284	0.113814	0.0569071	−	0.998379i	$-0.481876\pi$
$431$	2.36284	0.113814	0.0569071	+	0.998379i	$0.481876\pi$
$432$	23.9683	1.15317
$433$	−12.5489	−0.603064	−0.301532	−	0.953456i	$-0.597498\pi$
$433$	−12.5489	−0.603064	−0.301532	+	0.953456i	$0.597498\pi$
$434$	−20.2103	−0.970126
$435$	−0.611245	−0.0293069
$436$	1.68818	0.0808493
$437$	9.81815	0.469666
$438$	−31.0877	−1.48543
$439$	11.9091	0.568389	0.284195	−	0.958767i	$-0.408274\pi$
$439$	11.9091	0.568389	0.284195	+	0.958767i	$0.408274\pi$
$440$	−0.0821758	−0.00391758
$441$	0.576462	0.0274506
$442$	0.0124437	0.000591886 0
$443$	−6.60657	−0.313888	−0.156944	−	0.987608i	$-0.550164\pi$
$443$	−6.60657	−0.313888	−0.156944	+	0.987608i	$0.550164\pi$
$444$	−2.86469	−0.135952
$445$	−5.97837	−0.283402
$446$	28.4864	1.34887
$447$	26.8825	1.27150
$448$	−7.95239	−0.375715
$449$	5.72789	0.270316	0.135158	−	0.990824i	$-0.456846\pi$
$449$	5.72789	0.270316	0.135158	+	0.990824i	$0.456846\pi$
$450$	−1.05389	−0.0496808
$451$	1.29544	0.0609999
$452$	−6.04165	−0.284175
$453$	4.64372	0.218181
$454$	−4.91294	−0.230576
$455$	0.290431	0.0136156
$456$	−2.09858	−0.0982749
$457$	−7.28262	−0.340666	−0.170333	−	0.985387i	$-0.554484\pi$
$457$	−7.28262	−0.340666	−0.170333	+	0.985387i	$0.554484\pi$
$458$	13.0019	0.607539
$459$	−0.117522	−0.00548547
$460$	5.36260	0.250033
$461$	15.8771	0.739471	0.369735	−	0.929137i	$-0.379448\pi$
$461$	15.8771	0.739471	0.369735	+	0.929137i	$0.379448\pi$
$462$	−0.996466	−0.0463598
$463$	22.2257	1.03292	0.516458	−	0.856313i	$-0.327250\pi$
$463$	22.2257	1.03292	0.516458	+	0.856313i	$0.327250\pi$
$464$	−2.44019	−0.113283
$465$	−8.01425	−0.371652
$466$	42.5082	1.96916
$467$	−33.2692	−1.53952	−0.769758	−	0.638336i	$-0.779623\pi$
$467$	−33.2692	−1.53952	−0.769758	+	0.638336i	$0.779623\pi$
$468$	0.0593970	0.00274563
$469$	14.1635	0.654011
$470$	4.11889	0.189990
$471$	−7.50300	−0.345720
$472$	4.82228	0.221963
$473$	1.40800	0.0647401
$474$	−5.87426	−0.269813
$475$	9.40397	0.431484
$476$	0.0557834	0.00255683
$477$	−1.16692	−0.0534296
$478$	−16.7879	−0.767858
$479$	29.4189	1.34418	0.672091	−	0.740468i	$-0.265396\pi$
$479$	29.4189	1.34418	0.672091	+	0.740468i	$0.265396\pi$
$480$	−8.49815	−0.387886
$481$	0.291949	0.0133117
$482$	−36.7415	−1.67353
$483$	−12.0109	−0.546514
$484$	−18.4988	−0.840855
$485$	1.39547	0.0633652
$486$	−2.40375	−0.109037
$487$	24.2965	1.10098	0.550491	−	0.834841i	$-0.314441\pi$
$487$	24.2965	1.10098	0.550491	+	0.834841i	$0.314441\pi$
$488$	1.97387	0.0893531
$489$	15.4365	0.698064
$490$	−6.13798	−0.277286
$491$	−32.9445	−1.48676	−0.743382	−	0.668867i	$-0.766780\pi$
$491$	−32.9445	−1.48676	−0.743382	+	0.668867i	$0.766780\pi$
$492$	18.0694	0.814634
$493$	0.0119648	0.000538869 0
$494$	−1.15791	−0.0520967
$495$	0.0165377	0.000743316 0
$496$	−31.9942	−1.43658
$497$	−14.9194	−0.669228
$498$	−43.2953	−1.94011
$499$	−7.49744	−0.335631	−0.167816	−	0.985818i	$-0.553671\pi$
$499$	−7.49744	−0.335631	−0.167816	+	0.985818i	$0.553671\pi$
$500$	10.7764	0.481933
$501$	−28.6309	−1.27913
$502$	16.3780	0.730987
$503$	−19.5379	−0.871153	−0.435577	−	0.900152i	$-0.643456\pi$
$503$	−19.5379	−0.871153	−0.435577	+	0.900152i	$0.643456\pi$
$504$	−0.107447	−0.00478607
$505$	−5.76353	−0.256474
$506$	1.87510	0.0833584
$507$	−21.9151	−0.973285
$508$	31.7088	1.40685
$509$	−2.84496	−0.126101	−0.0630504	−	0.998010i	$-0.520083\pi$
$509$	−2.84496	−0.126101	−0.0630504	+	0.998010i	$0.520083\pi$
$510$	0.0483268	0.00213994
$511$	14.2028	0.628294
$512$	−28.5049	−1.25975
$513$	10.9357	0.482821
$514$	−18.8330	−0.830689
$515$	11.5608	0.509429
$516$	19.6395	0.864582
$517$	0.659228	0.0289928
$518$	2.85927	0.125629
$519$	16.7364	0.734648
$520$	0.116815	0.00512270
$521$	7.88646	0.345512	0.172756	−	0.984965i	$-0.444733\pi$
$521$	7.88646	0.345512	0.172756	+	0.984965i	$0.444733\pi$
$522$	0.124771	0.00546109
$523$	11.6027	0.507350	0.253675	−	0.967290i	$-0.418361\pi$
$523$	11.6027	0.507350	0.253675	+	0.967290i	$0.418361\pi$
$524$	29.8874	1.30564
$525$	−11.5042	−0.502084
$526$	19.5520	0.852506
$527$	0.156875	0.00683359
$528$	−1.57747	−0.0686505
$529$	−0.398516	−0.0173268
$530$	12.4250	0.539708
$531$	−0.970476	−0.0421151
$532$	−5.19075	−0.225047
$533$	−1.84151	−0.0797647
$534$	−29.1581	−1.26179
$535$	4.24890	0.183696
$536$	5.69677	0.246063
$537$	3.20702	0.138393
$538$	31.7250	1.36776
$539$	−0.982384	−0.0423143
$540$	5.97297	0.257036
$541$	19.0182	0.817658	0.408829	−	0.912611i	$-0.365937\pi$
$541$	19.0182	0.817658	0.408829	+	0.912611i	$0.365937\pi$
$542$	23.0265	0.989073
$543$	11.9351	0.512185
$544$	0.166347	0.00713208
$545$	−0.668171	−0.0286213
$546$	1.41651	0.0606209
$547$	29.1343	1.24569	0.622847	−	0.782344i	$-0.285976\pi$
$547$	29.1343	1.24569	0.622847	+	0.782344i	$0.285976\pi$
$548$	−0.223618	−0.00955251
$549$	−0.397239	−0.0169537
$550$	1.79600	0.0765816
$551$	−1.11335	−0.0474303
$552$	−4.83095	−0.205619
$553$	2.68373	0.114124
$554$	20.3042	0.862642
$555$	1.13382	0.0481281
$556$	−10.4228	−0.442027
$557$	13.0120	0.551335	0.275667	−	0.961253i	$-0.411101\pi$
$557$	13.0120	0.551335	0.275667	+	0.961253i	$0.411101\pi$
$558$	1.63592	0.0692541
$559$	−2.00152	−0.0846554
$560$	4.50288	0.190281
$561$	0.00773470	0.000326559 0
$562$	−12.6657	−0.534271
$563$	−33.8098	−1.42491	−0.712457	−	0.701716i	$-0.752418\pi$
$563$	−33.8098	−1.42491	−0.712457	+	0.701716i	$0.752418\pi$
$564$	9.19524	0.387189
$565$	2.39124	0.100600
$566$	3.54585	0.149043
$567$	−12.8397	−0.539216
$568$	−6.00081	−0.251788
$569$	29.1496	1.22201	0.611006	−	0.791626i	$-0.290765\pi$
$569$	29.1496	1.22201	0.611006	+	0.791626i	$0.290765\pi$
$570$	−4.49689	−0.188354
$571$	43.1182	1.80444	0.902221	−	0.431274i	$-0.141936\pi$
$571$	43.1182	1.80444	0.902221	+	0.431274i	$0.141936\pi$
$572$	−0.101222	−0.00423231
$573$	21.5963	0.902200
$574$	−18.0353	−0.752778
$575$	21.6480	0.902785
$576$	0.643705	0.0268211
$577$	25.7612	1.07245	0.536227	−	0.844074i	$-0.319849\pi$
$577$	25.7612	1.07245	0.536227	+	0.844074i	$0.319849\pi$
$578$	32.6469	1.35793
$579$	7.45111	0.309657
$580$	−0.608103	−0.0252501
$581$	19.7800	0.820613
$582$	6.80609	0.282121
$583$	1.98862	0.0823603
$584$	5.71256	0.236387
$585$	−0.0235089	−0.000971974 0
$586$	−41.9698	−1.73376
$587$	−9.80060	−0.404514	−0.202257	−	0.979332i	$-0.564828\pi$
$587$	−9.80060	−0.404514	−0.202257	+	0.979332i	$0.564828\pi$
$588$	−13.7028	−0.565093
$589$	−14.5975	−0.601480
$590$	10.3333	0.425416
$591$	36.1259	1.48602
$592$	4.52640	0.186034
$593$	36.1450	1.48430	0.742148	−	0.670236i	$-0.233807\pi$
$593$	36.1450	1.48430	0.742148	+	0.670236i	$0.233807\pi$
$594$	2.08852	0.0856932
$595$	−0.0220787	−0.000905137 0
$596$	26.7443	1.09549
$597$	9.16770	0.375209
$598$	−2.66551	−0.109001
$599$	−21.3461	−0.872179	−0.436089	−	0.899903i	$-0.643637\pi$
$599$	−21.3461	−0.872179	−0.436089	+	0.899903i	$0.643637\pi$
$600$	−4.62715	−0.188903
$601$	−29.2630	−1.19366	−0.596830	−	0.802367i	$-0.703573\pi$
$601$	−29.2630	−1.19366	−0.596830	+	0.802367i	$0.703573\pi$
$602$	−19.6024	−0.798934
$603$	−1.14647	−0.0466877
$604$	4.61985	0.187979
$605$	7.32170	0.297669
$606$	−28.1103	−1.14190
$607$	1.08172	0.0439055	0.0219528	−	0.999759i	$-0.493012\pi$
$607$	1.08172	0.0439055	0.0219528	+	0.999759i	$0.493012\pi$
$608$	−15.4789	−0.627753
$609$	1.36200	0.0551909
$610$	4.22967	0.171254
$611$	−0.937114	−0.0379116
$612$	−0.00451538	−0.000182523 0
$613$	18.9443	0.765155	0.382577	−	0.923923i	$-0.375037\pi$
$613$	18.9443	0.765155	0.382577	+	0.923923i	$0.375037\pi$
$614$	31.0135	1.25160
$615$	−7.15176	−0.288387
$616$	0.183107	0.00737759
$617$	23.3251	0.939032	0.469516	−	0.882924i	$-0.344428\pi$
$617$	23.3251	0.939032	0.469516	+	0.882924i	$0.344428\pi$
$618$	56.3850	2.26814
$619$	−13.1777	−0.529656	−0.264828	−	0.964296i	$-0.585315\pi$
$619$	−13.1777	−0.529656	−0.264828	+	0.964296i	$0.585315\pi$
$620$	−7.97306	−0.320206
$621$	25.1740	1.01020
$622$	−28.9288	−1.15994
$623$	13.3212	0.533704
$624$	2.24242	0.0897687
$625$	18.5025	0.740101
$626$	12.0914	0.483271
$627$	−0.719728	−0.0287432
$628$	−7.46444	−0.297864
$629$	−0.0221940	−0.000884934 0
$630$	−0.230240	−0.00917299
$631$	−34.4858	−1.37286	−0.686429	−	0.727197i	$-0.740823\pi$
$631$	−34.4858	−1.37286	−0.686429	+	0.727197i	$0.740823\pi$
$632$	1.07943	0.0429375
$633$	20.6549	0.820959
$634$	−12.9190	−0.513081
$635$	−12.5501	−0.498036
$636$	27.7383	1.09989
$637$	1.39649	0.0553310
$638$	−0.212631	−0.00841813
$639$	1.20765	0.0477740
$640$	3.16208	0.124992
$641$	46.9074	1.85273	0.926366	−	0.376625i	$-0.122916\pi$
$641$	46.9074	1.85273	0.926366	+	0.376625i	$0.122916\pi$
$642$	20.7230	0.817871
$643$	37.8131	1.49120	0.745601	−	0.666393i	$-0.232163\pi$
$643$	37.8131	1.49120	0.745601	+	0.666393i	$0.232163\pi$
$644$	−11.9491	−0.470862
$645$	−7.77319	−0.306069
$646$	0.0880246	0.00346328
$647$	−20.6101	−0.810266	−0.405133	−	0.914258i	$-0.632775\pi$
$647$	−20.6101	−0.810266	−0.405133	+	0.914258i	$0.632775\pi$
$648$	−5.16430	−0.202873
$649$	1.65385	0.0649192
$650$	−2.55307	−0.100140
$651$	17.8576	0.699896
$652$	15.3572	0.601434
$653$	14.3670	0.562225	0.281112	−	0.959675i	$-0.409297\pi$
$653$	14.3670	0.562225	0.281112	+	0.959675i	$0.409297\pi$
$654$	−3.25884	−0.127431
$655$	−11.8292	−0.462207
$656$	−28.5510	−1.11473
$657$	−1.14964	−0.0448519
$658$	−9.17786	−0.357790
$659$	−37.8635	−1.47495	−0.737477	−	0.675373i	$-0.763983\pi$
$659$	−37.8635	−1.47495	−0.737477	+	0.675373i	$0.763983\pi$
$660$	−0.393110	−0.0153018
$661$	25.0975	0.976178	0.488089	−	0.872794i	$-0.337694\pi$
$661$	25.0975	0.976178	0.488089	+	0.872794i	$0.337694\pi$
$662$	−65.6840	−2.55288
$663$	−0.0109951	−0.000427015 0
$664$	7.95580	0.308745
$665$	2.05446	0.0796686
$666$	−0.231443	−0.00896825
$667$	−2.56294	−0.0992374
$668$	−28.4837	−1.10207
$669$	−25.1703	−0.973139
$670$	12.2072	0.471606
$671$	0.676960	0.0261337
$672$	18.9359	0.730468
$673$	34.4136	1.32655	0.663273	−	0.748378i	$-0.269167\pi$
$673$	34.4136	1.32655	0.663273	+	0.748378i	$0.269167\pi$
$674$	−19.6718	−0.757730
$675$	24.1120	0.928072
$676$	−21.8025	−0.838557
$677$	−11.3045	−0.434466	−0.217233	−	0.976120i	$-0.569703\pi$
$677$	−11.3045	−0.434466	−0.217233	+	0.976120i	$0.569703\pi$
$678$	11.6627	0.447904
$679$	−3.10945	−0.119330
$680$	−0.00888036	−0.000340546 0
$681$	4.34103	0.166349
$682$	−2.78788	−0.106753
$683$	−27.7988	−1.06369	−0.531846	−	0.846841i	$-0.678502\pi$
$683$	−27.7988	−1.06369	−0.531846	+	0.846841i	$0.678502\pi$
$684$	0.420165	0.0160654
$685$	0.0885066	0.00338166
$686$	33.6918	1.28636
$687$	−11.4884	−0.438309
$688$	−31.0318	−1.18308
$689$	−2.82689	−0.107696
$690$	−10.3519	−0.394090
$691$	−18.3811	−0.699250	−0.349625	−	0.936890i	$-0.613691\pi$
$691$	−18.3811	−0.699250	−0.349625	+	0.936890i	$0.613691\pi$
$692$	16.6504	0.632953
$693$	−0.0368500	−0.00139982
$694$	−13.0606	−0.495774
$695$	4.12529	0.156481
$696$	0.547815	0.0207649
$697$	0.139992	0.00530259
$698$	23.0460	0.872304
$699$	−37.5599	−1.42065
$700$	−11.4451	−0.432583
$701$	−1.53096	−0.0578235	−0.0289118	−	0.999582i	$-0.509204\pi$
$701$	−1.53096	−0.0578235	−0.0289118	+	0.999582i	$0.509204\pi$
$702$	−2.96890	−0.112054
$703$	2.06520	0.0778904
$704$	−1.09698	−0.0413439
$705$	−3.63941	−0.137068
$706$	−44.3917	−1.67070
$707$	12.8425	0.482993
$708$	23.0687	0.866975
$709$	−12.3701	−0.464569	−0.232285	−	0.972648i	$-0.574620\pi$
$709$	−12.3701	−0.464569	−0.232285	+	0.972648i	$0.574620\pi$
$710$	−12.8587	−0.482579
$711$	−0.217234	−0.00814691
$712$	5.35799	0.200799
$713$	−33.6036	−1.25847
$714$	−0.107683	−0.00402995
$715$	0.0400630	0.00149827
$716$	3.19054	0.119236
$717$	14.8336	0.553971
$718$	13.2549	0.494667
$719$	47.9595	1.78859	0.894295	−	0.447479i	$-0.147678\pi$
$719$	47.9595	1.78859	0.894295	+	0.447479i	$0.147678\pi$
$720$	−0.364485	−0.0135836
$721$	−25.7602	−0.959359
$722$	28.2980	1.05314
$723$	32.4644	1.20737
$724$	11.8738	0.441285
$725$	−2.45482	−0.0911698
$726$	35.7098	1.32532
$727$	−7.35786	−0.272888	−0.136444	−	0.990648i	$-0.543567\pi$
$727$	−7.35786	−0.272888	−0.136444	+	0.990648i	$0.543567\pi$
$728$	−0.260293	−0.00964708
$729$	27.9957	1.03688
$730$	12.2410	0.453061
$731$	0.152156	0.00562771
$732$	9.44256	0.349007
$733$	−41.8674	−1.54641	−0.773203	−	0.634158i	$-0.781347\pi$
$733$	−41.8674	−1.54641	−0.773203	+	0.634158i	$0.781347\pi$
$734$	62.5596	2.30912
$735$	5.42346	0.200048
$736$	−35.6326	−1.31344
$737$	1.95376	0.0719679
$738$	1.45987	0.0537384
$739$	−36.8839	−1.35679	−0.678397	−	0.734695i	$-0.737325\pi$
$739$	−36.8839	−1.35679	−0.678397	+	0.734695i	$0.737325\pi$
$740$	1.12799	0.0414659
$741$	1.02312	0.0375851
$742$	−27.6859	−1.01638
$743$	31.0186	1.13796	0.568981	−	0.822351i	$-0.307338\pi$
$743$	31.0186	1.13796	0.568981	+	0.822351i	$0.307338\pi$
$744$	7.18260	0.263327
$745$	−10.5852	−0.387812
$746$	34.4515	1.26136
$747$	−1.60109	−0.0585808
$748$	0.00769495	0.000281355 0
$749$	−9.46755	−0.345937
$750$	−20.8025	−0.759601
$751$	−44.2625	−1.61516	−0.807581	−	0.589757i	$-0.799224\pi$
$751$	−44.2625	−1.61516	−0.807581	+	0.589757i	$0.799224\pi$
$752$	−14.5291	−0.529823
$753$	−14.4715	−0.527369
$754$	0.302261	0.0110077
$755$	−1.82850	−0.0665461
$756$	−13.3092	−0.484051
$757$	6.67719	0.242687	0.121343	−	0.992611i	$-0.461280\pi$
$757$	6.67719	0.242687	0.121343	+	0.992611i	$0.461280\pi$
$758$	20.7680	0.754327
$759$	−1.65682	−0.0601388
$760$	0.826333	0.0299743
$761$	47.2669	1.71342	0.856712	−	0.515795i	$-0.172503\pi$
$761$	47.2669	1.71342	0.856712	+	0.515795i	$0.172503\pi$
$762$	−61.2102	−2.21741
$763$	1.48884	0.0538997
$764$	21.4853	0.777312
$765$	0.00178716	6.46148e−5 0
$766$	−47.9905	−1.73397
$767$	−2.35100	−0.0848896
$768$	33.5497	1.21062
$769$	−34.6269	−1.24868	−0.624338	−	0.781154i	$-0.714631\pi$
$769$	−34.6269	−1.24868	−0.624338	+	0.781154i	$0.714631\pi$
$770$	0.392367	0.0141399
$771$	16.6407	0.599300
$772$	7.41281	0.266793
$773$	−16.2381	−0.584043	−0.292022	−	0.956412i	$-0.594328\pi$
$773$	−16.2381	−0.584043	−0.292022	+	0.956412i	$0.594328\pi$
$774$	1.58671	0.0570333
$775$	−32.1861	−1.15616
$776$	−1.25066	−0.0448962
$777$	−2.52643	−0.0906350
$778$	−59.0190	−2.11593
$779$	−13.0265	−0.466724
$780$	0.558819	0.0200089
$781$	−2.05804	−0.0736424
$782$	0.202633	0.00724616
$783$	−2.85466	−0.102017
$784$	21.6514	0.773263
$785$	2.95437	0.105446
$786$	−57.6943	−2.05789
$787$	−51.2457	−1.82671	−0.913356	−	0.407162i	$-0.866518\pi$
$787$	−51.2457	−1.82671	−0.913356	+	0.407162i	$0.866518\pi$
$788$	35.9402	1.28032
$789$	−17.2759	−0.615039
$790$	2.31304	0.0822942
$791$	−5.32825	−0.189451
$792$	−0.0148216	−0.000526662 0
$793$	−0.962320	−0.0341730
$794$	42.1224	1.49487
$795$	−10.9786	−0.389372
$796$	9.12058	0.323270
$797$	−52.4428	−1.85762	−0.928809	−	0.370559i	$-0.879166\pi$
$797$	−52.4428	−1.85762	−0.928809	+	0.370559i	$0.879166\pi$
$798$	10.0201	0.354709
$799$	0.0712398	0.00252028
$800$	−34.1294	−1.20666
$801$	−1.07829	−0.0380994
$802$	4.96485	0.175315
$803$	1.95918	0.0691379
$804$	27.2521	0.961106
$805$	4.72939	0.166689
$806$	3.96306	0.139593
$807$	−28.0320	−0.986772
$808$	5.16544	0.181720
$809$	42.9616	1.51045	0.755225	−	0.655465i	$-0.227527\pi$
$809$	42.9616	1.51045	0.755225	+	0.655465i	$0.227527\pi$
$810$	−11.0662	−0.388827
$811$	20.4944	0.719655	0.359828	−	0.933019i	$-0.382836\pi$
$811$	20.4944	0.719655	0.359828	+	0.933019i	$0.382836\pi$
$812$	1.35500	0.0475511
$813$	−20.3460	−0.713566
$814$	0.394417	0.0138243
$815$	−6.07827	−0.212912
$816$	−0.170470	−0.00596763
$817$	−14.1584	−0.495341
$818$	−23.9722	−0.838167
$819$	0.0523834	0.00183042
$820$	−7.11500	−0.248467
$821$	−26.3721	−0.920392	−0.460196	−	0.887817i	$-0.652221\pi$
$821$	−26.3721	−0.920392	−0.460196	+	0.887817i	$0.652221\pi$
$822$	0.431670	0.0150562
$823$	9.29772	0.324098	0.162049	−	0.986783i	$-0.448190\pi$
$823$	9.29772	0.324098	0.162049	+	0.986783i	$0.448190\pi$
$824$	−10.3611	−0.360946
$825$	−1.58693	−0.0552497
$826$	−23.0251	−0.801145
$827$	41.4746	1.44221	0.721106	−	0.692825i	$-0.243634\pi$
$827$	41.4746	1.44221	0.721106	+	0.692825i	$0.243634\pi$
$828$	0.967223	0.0336133
$829$	−25.9880	−0.902600	−0.451300	−	0.892372i	$-0.649040\pi$
$829$	−25.9880	−0.902600	−0.451300	+	0.892372i	$0.649040\pi$
$830$	17.0479	0.591741
$831$	−17.9406	−0.622352
$832$	1.55939	0.0540621
$833$	−0.106162	−0.00367829
$834$	20.1201	0.696703
$835$	11.2737	0.390141
$836$	−0.716029	−0.0247644
$837$	−37.4284	−1.29372
$838$	−47.2096	−1.63083
$839$	−53.5394	−1.84839	−0.924193	−	0.381926i	$-0.875261\pi$
$839$	−53.5394	−1.84839	−0.924193	+	0.381926i	$0.875261\pi$
$840$	−1.01088	−0.0348787
$841$	−28.7094	−0.989978
$842$	−42.0016	−1.44747
$843$	11.1913	0.385449
$844$	20.5487	0.707317
$845$	8.62927	0.296856
$846$	0.742901	0.0255415
$847$	−16.3145	−0.560572
$848$	−43.8284	−1.50508
$849$	−3.13308	−0.107527
$850$	0.194085	0.00665707
$851$	4.75410	0.162969
$852$	−28.7065	−0.983469
$853$	46.0490	1.57669	0.788344	−	0.615235i	$-0.210939\pi$
$853$	46.0490	1.57669	0.788344	+	0.615235i	$0.210939\pi$
$854$	−9.42472	−0.322507
$855$	−0.166298	−0.00568728
$856$	−3.80798	−0.130154
$857$	−31.9819	−1.09248	−0.546241	−	0.837628i	$-0.683942\pi$
$857$	−31.9819	−1.09248	−0.546241	+	0.837628i	$0.683942\pi$
$858$	0.195398	0.00667077
$859$	−36.8866	−1.25855	−0.629277	−	0.777181i	$-0.716649\pi$
$859$	−36.8866	−1.25855	−0.629277	+	0.777181i	$0.716649\pi$
$860$	−7.73323	−0.263701
$861$	15.9358	0.543091
$862$	−4.53776	−0.154557
$863$	5.79854	0.197385	0.0986923	−	0.995118i	$-0.468534\pi$
$863$	5.79854	0.197385	0.0986923	+	0.995118i	$0.468534\pi$
$864$	−39.6883	−1.35022
$865$	−6.59011	−0.224071
$866$	24.0998	0.818944
$867$	−28.8465	−0.979680
$868$	17.7659	0.603013
$869$	0.370202	0.0125582
$870$	1.17387	0.0397980
$871$	−2.77734	−0.0941065
$872$	0.598834	0.0202791
$873$	0.251694	0.00851854
$874$	−18.8554	−0.637794
$875$	9.50389	0.321290
$876$	27.3276	0.923314
$877$	11.2322	0.379285	0.189643	−	0.981853i	$-0.439267\pi$
$877$	11.2322	0.379285	0.189643	+	0.981853i	$0.439267\pi$
$878$	−22.8710	−0.771857
$879$	37.0842	1.25082
$880$	0.621142	0.0209387
$881$	47.9849	1.61665	0.808327	−	0.588734i	$-0.200373\pi$
$881$	47.9849	1.61665	0.808327	+	0.588734i	$0.200373\pi$
$882$	−1.10707	−0.0372771
$883$	27.3207	0.919415	0.459707	−	0.888071i	$-0.347954\pi$
$883$	27.3207	0.919415	0.459707	+	0.888071i	$0.347954\pi$
$884$	−0.0109386	−0.000367905 0
$885$	−9.13043	−0.306916
$886$	12.6877	0.426251
$887$	−29.6507	−0.995572	−0.497786	−	0.867300i	$-0.665854\pi$
$887$	−29.6507	−0.995572	−0.497786	+	0.867300i	$0.665854\pi$
$888$	−1.01616	−0.0341002
$889$	27.9646	0.937903
$890$	11.4813	0.384853
$891$	−1.77115	−0.0593357
$892$	−25.0409	−0.838432
$893$	−6.62899	−0.221831
$894$	−51.6268	−1.72666
$895$	−1.26279	−0.0422105
$896$	−7.04587	−0.235386
$897$	2.35522	0.0786386
$898$	−11.0002	−0.367082
$899$	3.81055	0.127089
$900$	0.926420	0.0308807
$901$	0.214901	0.00715940
$902$	−2.48785	−0.0828363
$903$	17.3205	0.576390
$904$	−2.14310	−0.0712784
$905$	−4.69956	−0.156219
$906$	−8.91810	−0.296284
$907$	−26.1920	−0.869691	−0.434846	−	0.900505i	$-0.643197\pi$
$907$	−26.1920	−0.869691	−0.434846	+	0.900505i	$0.643197\pi$
$908$	4.31872	0.143322
$909$	−1.03954	−0.0344793
$910$	−0.557762	−0.0184896
$911$	−1.00308	−0.0332335	−0.0166167	−	0.999862i	$-0.505290\pi$
$911$	−1.00308	−0.0332335	−0.0166167	+	0.999862i	$0.505290\pi$
$912$	15.8625	0.525261
$913$	2.72852	0.0903008
$914$	13.9860	0.462616
$915$	−3.73730	−0.123551
$916$	−11.4293	−0.377635
$917$	26.3583	0.870429
$918$	0.225697	0.00744912
$919$	−10.5209	−0.347052	−0.173526	−	0.984829i	$-0.555516\pi$
$919$	−10.5209	−0.347052	−0.173526	+	0.984829i	$0.555516\pi$
$920$	1.90223	0.0627146
$921$	−27.4033	−0.902968
$922$	−30.4914	−1.00418
$923$	2.92557	0.0962962
$924$	0.875943	0.0288164
$925$	4.55355	0.149720
$926$	−42.6836	−1.40267
$927$	2.08516	0.0684855
$928$	4.04063	0.132640
$929$	−36.2744	−1.19012	−0.595062	−	0.803680i	$-0.702872\pi$
$929$	−36.2744	−1.19012	−0.595062	+	0.803680i	$0.702872\pi$
$930$	15.3911	0.504693
$931$	9.87855	0.323756
$932$	−37.3668	−1.22399
$933$	25.5612	0.836836
$934$	63.8923	2.09062
$935$	−0.00304561	−9.96020e−5 0
$936$	0.0210694	0.000688673 0
$937$	−25.1245	−0.820783	−0.410392	−	0.911909i	$-0.634608\pi$
$937$	−25.1245	−0.820783	−0.410392	+	0.911909i	$0.634608\pi$
$938$	−27.2006	−0.888130
$939$	−10.6839	−0.348655
$940$	−3.62070	−0.118094
$941$	0.927182	0.0302253	0.0151126	−	0.999886i	$-0.495189\pi$
$941$	0.927182	0.0302253	0.0151126	+	0.999886i	$0.495189\pi$
$942$	14.4093	0.469479
$943$	−29.9872	−0.976519
$944$	−36.4502	−1.18635
$945$	5.26769	0.171358
$946$	−2.70402	−0.0879153
$947$	6.36258	0.206756	0.103378	−	0.994642i	$-0.467035\pi$
$947$	6.36258	0.206756	0.103378	+	0.994642i	$0.467035\pi$
$948$	5.16376	0.167711
$949$	−2.78504	−0.0904061
$950$	−18.0600	−0.585943
$951$	11.4151	0.370162
$952$	0.0197875	0.000641318 0
$953$	50.1116	1.62327	0.811637	−	0.584163i	$-0.198577\pi$
$953$	50.1116	1.62327	0.811637	+	0.584163i	$0.198577\pi$
$954$	2.24103	0.0725560
$955$	−8.50375	−0.275175
$956$	14.7574	0.477287
$957$	0.187879	0.00607325
$958$	−56.4979	−1.82536
$959$	−0.197214	−0.00636836
$960$	6.05611	0.195460
$961$	18.9615	0.611662
$962$	−0.560677	−0.0180769
$963$	0.766350	0.0246953
$964$	32.2976	1.04023
$965$	−2.93394	−0.0944468
$966$	23.0665	0.742152
$967$	4.16919	0.134072	0.0670360	−	0.997751i	$-0.478646\pi$
$967$	4.16919	0.134072	0.0670360	+	0.997751i	$0.478646\pi$
$968$	−6.56191	−0.210908
$969$	−0.0777777	−0.00249858
$970$	−2.67996	−0.0860482
$971$	−10.4339	−0.334839	−0.167419	−	0.985886i	$-0.553543\pi$
$971$	−10.4339	−0.334839	−0.167419	+	0.985886i	$0.553543\pi$
$972$	2.11302	0.0677751
$973$	−9.19213	−0.294686
$974$	−46.6606	−1.49510
$975$	2.25587	0.0722456
$976$	−14.9199	−0.477575
$977$	−30.8008	−0.985405	−0.492702	−	0.870198i	$-0.663991\pi$
$977$	−30.8008	−0.985405	−0.492702	+	0.870198i	$0.663991\pi$
$978$	−29.6453	−0.947952
$979$	1.83758	0.0587292
$980$	5.39559	0.172356
$981$	−0.120514	−0.00384773
$982$	63.2687	2.01899
$983$	−8.28862	−0.264366	−0.132183	−	0.991225i	$-0.542199\pi$
$983$	−8.28862	−0.264366	−0.132183	+	0.991225i	$0.542199\pi$
$984$	6.40961	0.204331
$985$	−14.2249	−0.453243
$986$	−0.0229780	−0.000731769 0
$987$	8.10947	0.258127
$988$	1.01786	0.0323824
$989$	−32.5929	−1.03639
$990$	−0.0317601	−0.00100940
$991$	−34.7404	−1.10357	−0.551783	−	0.833988i	$-0.686052\pi$
$991$	−34.7404	−1.10357	−0.551783	+	0.833988i	$0.686052\pi$
$992$	52.9782	1.68206
$993$	58.0377	1.84177
$994$	28.6523	0.908794
$995$	−3.60986	−0.114440
$996$	38.0587	1.20594
$997$	−35.3284	−1.11886	−0.559431	−	0.828877i	$-0.688980\pi$
$997$	−35.3284	−1.11886	−0.559431	+	0.828877i	$0.688980\pi$
$998$	14.3986	0.455779
$999$	5.29522	0.167533

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.e.1.13	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.e.1.13	✓	82	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-1.92046 q^{2} +1.69690 q^{3} +1.68818 q^{4} -0.668171 q^{5} -3.25884 q^{6} +1.48884 q^{7} +0.598834 q^{8} -0.120514 q^{9} +O(q^{10})\)	\(q-1.92046 q^{2} +1.69690 q^{3} +1.68818 q^{4} -0.668171 q^{5} -3.25884 q^{6} +1.48884 q^{7} +0.598834 q^{8} -0.120514 q^{9} +1.28320 q^{10} +0.205376 q^{11} +2.86469 q^{12} -0.291949 q^{13} -2.85927 q^{14} -1.13382 q^{15} -4.52640 q^{16} +0.0221940 q^{17} +0.231443 q^{18} -2.06520 q^{19} -1.12799 q^{20} +2.52643 q^{21} -0.394417 q^{22} -4.75410 q^{23} +1.01616 q^{24} -4.55355 q^{25} +0.560677 q^{26} -5.29522 q^{27} +2.51344 q^{28} +0.539101 q^{29} +2.17747 q^{30} +7.06835 q^{31} +7.49513 q^{32} +0.348504 q^{33} -0.0426229 q^{34} -0.994802 q^{35} -0.203450 q^{36} -1.00000 q^{37} +3.96614 q^{38} -0.495409 q^{39} -0.400123 q^{40} +6.30766 q^{41} -4.85191 q^{42} +6.85574 q^{43} +0.346712 q^{44} +0.0805242 q^{45} +9.13008 q^{46} +3.20986 q^{47} -7.68088 q^{48} -4.78335 q^{49} +8.74493 q^{50} +0.0376612 q^{51} -0.492862 q^{52} +9.68284 q^{53} +10.1693 q^{54} -0.137226 q^{55} +0.891570 q^{56} -3.50444 q^{57} -1.03532 q^{58} +8.05278 q^{59} -1.91410 q^{60} +3.29620 q^{61} -13.5745 q^{62} -0.179427 q^{63} -5.34132 q^{64} +0.195072 q^{65} -0.669289 q^{66} +9.51311 q^{67} +0.0374676 q^{68} -8.06726 q^{69} +1.91048 q^{70} -10.0208 q^{71} -0.0721681 q^{72} +9.53947 q^{73} +1.92046 q^{74} -7.72694 q^{75} -3.48643 q^{76} +0.305773 q^{77} +0.951415 q^{78} +1.80256 q^{79} +3.02441 q^{80} -8.62393 q^{81} -12.1136 q^{82} +13.2855 q^{83} +4.26507 q^{84} -0.0148294 q^{85} -13.1662 q^{86} +0.914803 q^{87} +0.122986 q^{88} +8.94737 q^{89} -0.154644 q^{90} -0.434666 q^{91} -8.02579 q^{92} +11.9943 q^{93} -6.16442 q^{94} +1.37990 q^{95} +12.7185 q^{96} -2.08850 q^{97} +9.18624 q^{98} -0.0247507 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9}+O(q^{10}) \) 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9	\( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9} + 13 q^{10} + 2 q^{11} + 36 q^{12} + 23 q^{13} + 24 q^{14} + 35 q^{15} + 104 q^{16} + 43 q^{17} + 42 q^{18} + 15 q^{19} + 59 q^{20} + 9 q^{21} + 6 q^{22} + 70 q^{23} + 15 q^{24} + 98 q^{25} + 10 q^{26} + 65 q^{27} + 37 q^{28} + 27 q^{29} + 17 q^{30} + 59 q^{31} + 46 q^{32} + 16 q^{33} - 16 q^{34} + 80 q^{35} + 88 q^{36} - 82 q^{37} + 82 q^{38} + 13 q^{39} + 14 q^{40} + 3 q^{41} + 62 q^{42} + 7 q^{43} - 11 q^{44} + 42 q^{45} - 11 q^{46} + 123 q^{47} + 45 q^{48} + 105 q^{49} + 27 q^{50} + 3 q^{51} - 30 q^{52} + 82 q^{53} - 27 q^{54} + 37 q^{55} + 66 q^{56} + 29 q^{57} - 34 q^{58} + 60 q^{59} + 94 q^{60} + 9 q^{61} - 2 q^{62} + 106 q^{63} + 93 q^{64} + 9 q^{65} + 63 q^{66} + 113 q^{68} + 48 q^{69} + 47 q^{70} + 59 q^{71} + 63 q^{72} + 21 q^{73} - 10 q^{74} + 77 q^{75} + 22 q^{76} + 30 q^{77} + 29 q^{78} + 55 q^{79} + 88 q^{80} + 42 q^{81} + 4 q^{82} + 92 q^{83} + 43 q^{84} - 7 q^{85} + 17 q^{86} + 147 q^{87} - 13 q^{88} + 100 q^{89} + 91 q^{90} + 28 q^{91} + 127 q^{92} + 3 q^{93} + 30 q^{94} + 48 q^{95} - 31 q^{96} + 53 q^{97} + 101 q^{98} - 20 q^{99}+O(q^{100}) \) 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9 + 13 * q^10 + 2 * q^11 + 36 * q^12 + 23 * q^13 + 24 * q^14 + 35 * q^15 + 104 * q^16 + 43 * q^17 + 42 * q^18 + 15 * q^19 + 59 * q^20 + 9 * q^21 + 6 * q^22 + 70 * q^23 + 15 * q^24 + 98 * q^25 + 10 * q^26 + 65 * q^27 + 37 * q^28 + 27 * q^29 + 17 * q^30 + 59 * q^31 + 46 * q^32 + 16 * q^33 - 16 * q^34 + 80 * q^35 + 88 * q^36 - 82 * q^37 + 82 * q^38 + 13 * q^39 + 14 * q^40 + 3 * q^41 + 62 * q^42 + 7 * q^43 - 11 * q^44 + 42 * q^45 - 11 * q^46 + 123 * q^47 + 45 * q^48 + 105 * q^49 + 27 * q^50 + 3 * q^51 - 30 * q^52 + 82 * q^53 - 27 * q^54 + 37 * q^55 + 66 * q^56 + 29 * q^57 - 34 * q^58 + 60 * q^59 + 94 * q^60 + 9 * q^61 - 2 * q^62 + 106 * q^63 + 93 * q^64 + 9 * q^65 + 63 * q^66 + 113 * q^68 + 48 * q^69 + 47 * q^70 + 59 * q^71 + 63 * q^72 + 21 * q^73 - 10 * q^74 + 77 * q^75 + 22 * q^76 + 30 * q^77 + 29 * q^78 + 55 * q^79 + 88 * q^80 + 42 * q^81 + 4 * q^82 + 92 * q^83 + 43 * q^84 - 7 * q^85 + 17 * q^86 + 147 * q^87 - 13 * q^88 + 100 * q^89 + 91 * q^90 + 28 * q^91 + 127 * q^92 + 3 * q^93 + 30 * q^94 + 48 * q^95 - 31 * q^96 + 53 * q^97 + 101 * q^98 - 20 * q^99

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