LMFDB - Embedded newform 4019.2.a.a.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4019,2,Mod(1,4019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4019, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4019.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:	$32.0918765724$
Analytic rank:	$1$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	4019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.36640 q^{2} +0.537231 q^{3} +3.59984 q^{4} -0.969490 q^{5} -1.27130 q^{6} +3.20883 q^{7} -3.78587 q^{8} -2.71138 q^{9} +O(q^{10})$	\(q-2.36640 q^{2} +0.537231 q^{3} +3.59984 q^{4} -0.969490 q^{5} -1.27130 q^{6} +3.20883 q^{7} -3.78587 q^{8} -2.71138 q^{9} +2.29420 q^{10} +3.66106 q^{11} +1.93395 q^{12} -0.862250 q^{13} -7.59336 q^{14} -0.520841 q^{15} +1.75918 q^{16} -1.44829 q^{17} +6.41621 q^{18} -0.811375 q^{19} -3.49001 q^{20} +1.72388 q^{21} -8.66352 q^{22} +2.89522 q^{23} -2.03389 q^{24} -4.06009 q^{25} +2.04043 q^{26} -3.06833 q^{27} +11.5513 q^{28} +8.12591 q^{29} +1.23252 q^{30} -5.72998 q^{31} +3.40881 q^{32} +1.96683 q^{33} +3.42724 q^{34} -3.11093 q^{35} -9.76055 q^{36} -8.37839 q^{37} +1.92004 q^{38} -0.463228 q^{39} +3.67036 q^{40} -8.89121 q^{41} -4.07939 q^{42} +3.98967 q^{43} +13.1792 q^{44} +2.62866 q^{45} -6.85124 q^{46} +7.11721 q^{47} +0.945088 q^{48} +3.29657 q^{49} +9.60779 q^{50} -0.778068 q^{51} -3.10396 q^{52} -8.76352 q^{53} +7.26090 q^{54} -3.54936 q^{55} -12.1482 q^{56} -0.435896 q^{57} -19.2291 q^{58} -4.55866 q^{59} -1.87494 q^{60} +4.67288 q^{61} +13.5594 q^{62} -8.70036 q^{63} -11.5850 q^{64} +0.835943 q^{65} -4.65431 q^{66} -7.22865 q^{67} -5.21363 q^{68} +1.55540 q^{69} +7.36169 q^{70} -6.49221 q^{71} +10.2649 q^{72} -7.85154 q^{73} +19.8266 q^{74} -2.18121 q^{75} -2.92082 q^{76} +11.7477 q^{77} +1.09618 q^{78} +8.29530 q^{79} -1.70551 q^{80} +6.48574 q^{81} +21.0401 q^{82} -9.63926 q^{83} +6.20570 q^{84} +1.40411 q^{85} -9.44115 q^{86} +4.36549 q^{87} -13.8603 q^{88} -5.40996 q^{89} -6.22045 q^{90} -2.76681 q^{91} +10.4223 q^{92} -3.07832 q^{93} -16.8421 q^{94} +0.786620 q^{95} +1.83132 q^{96} +2.54683 q^{97} -7.80099 q^{98} -9.92652 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9}+O(q^{10}) $ 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9} - 58 q^{10} - 33 q^{11} - 33 q^{12} - 107 q^{13} - 28 q^{14} - 24 q^{15} + 74 q^{16} - 39 q^{17} - 33 q^{18} - 93 q^{19} - 63 q^{20} - 113 q^{21} - 38 q^{22} - 11 q^{23} - 130 q^{24} + 85 q^{25} - 33 q^{26} - 30 q^{27} - 94 q^{28} - 85 q^{29} - 16 q^{30} - 129 q^{31} - 35 q^{32} - 64 q^{33} - 78 q^{34} - 27 q^{35} + 79 q^{36} - 135 q^{37} - 11 q^{38} - 73 q^{39} - 146 q^{40} - 101 q^{41} + 4 q^{42} - 55 q^{43} - 82 q^{44} - 168 q^{45} - 113 q^{46} - 40 q^{47} - 65 q^{48} + 27 q^{49} - 5 q^{50} - 49 q^{51} - 177 q^{52} - 32 q^{53} - 155 q^{54} - 128 q^{55} - 44 q^{56} - 47 q^{57} - 46 q^{58} - 53 q^{59} - 11 q^{60} - 347 q^{61} - 11 q^{62} - 73 q^{63} + q^{64} - 31 q^{65} - 37 q^{66} - 40 q^{67} - 80 q^{68} - 175 q^{69} - 61 q^{70} - 31 q^{71} - 68 q^{72} - 193 q^{73} - 33 q^{74} - 56 q^{75} - 248 q^{76} - 84 q^{77} + 40 q^{78} - 111 q^{79} - 54 q^{80} + 49 q^{81} - 74 q^{82} - 24 q^{83} - 159 q^{84} - 258 q^{85} - q^{86} - 66 q^{87} - 97 q^{88} - 76 q^{89} - 75 q^{90} - 134 q^{91} + 31 q^{92} - 97 q^{93} - 111 q^{94} - 14 q^{95} - 216 q^{96} - 140 q^{97} - 13 q^{98} - 116 q^{99}+O(q^{100}) \) 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9 - 58 * q^10 - 33 * q^11 - 33 * q^12 - 107 * q^13 - 28 * q^14 - 24 * q^15 + 74 * q^16 - 39 * q^17 - 33 * q^18 - 93 * q^19 - 63 * q^20 - 113 * q^21 - 38 * q^22 - 11 * q^23 - 130 * q^24 + 85 * q^25 - 33 * q^26 - 30 * q^27 - 94 * q^28 - 85 * q^29 - 16 * q^30 - 129 * q^31 - 35 * q^32 - 64 * q^33 - 78 * q^34 - 27 * q^35 + 79 * q^36 - 135 * q^37 - 11 * q^38 - 73 * q^39 - 146 * q^40 - 101 * q^41 + 4 * q^42 - 55 * q^43 - 82 * q^44 - 168 * q^45 - 113 * q^46 - 40 * q^47 - 65 * q^48 + 27 * q^49 - 5 * q^50 - 49 * q^51 - 177 * q^52 - 32 * q^53 - 155 * q^54 - 128 * q^55 - 44 * q^56 - 47 * q^57 - 46 * q^58 - 53 * q^59 - 11 * q^60 - 347 * q^61 - 11 * q^62 - 73 * q^63 + q^64 - 31 * q^65 - 37 * q^66 - 40 * q^67 - 80 * q^68 - 175 * q^69 - 61 * q^70 - 31 * q^71 - 68 * q^72 - 193 * q^73 - 33 * q^74 - 56 * q^75 - 248 * q^76 - 84 * q^77 + 40 * q^78 - 111 * q^79 - 54 * q^80 + 49 * q^81 - 74 * q^82 - 24 * q^83 - 159 * q^84 - 258 * q^85 - q^86 - 66 * q^87 - 97 * q^88 - 76 * q^89 - 75 * q^90 - 134 * q^91 + 31 * q^92 - 97 * q^93 - 111 * q^94 - 14 * q^95 - 216 * q^96 - 140 * q^97 - 13 * q^98 - 116 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.36640	−1.67330	−0.836648	−	0.547741i	$-0.815488\pi$
$2$	−2.36640	−1.67330	−0.836648	+	0.547741i	$0.815488\pi$
$3$	0.537231	0.310171	0.155085	−	0.987901i	$-0.450435\pi$
$3$	0.537231	0.310171	0.155085	+	0.987901i	$0.450435\pi$
$4$	3.59984	1.79992
$5$	−0.969490	−0.433569	−0.216785	−	0.976219i	$-0.569557\pi$
$5$	−0.969490	−0.433569	−0.216785	+	0.976219i	$0.569557\pi$
$6$	−1.27130	−0.519007
$7$	3.20883	1.21282	0.606411	−	0.795151i	$-0.292609\pi$
$7$	3.20883	1.21282	0.606411	+	0.795151i	$0.292609\pi$
$8$	−3.78587	−1.33851
$9$	−2.71138	−0.903794
$10$	2.29420	0.725490
$11$	3.66106	1.10385	0.551925	−	0.833894i	$-0.313893\pi$
$11$	3.66106	1.10385	0.551925	+	0.833894i	$0.313893\pi$
$12$	1.93395	0.558283
$13$	−0.862250	−0.239145	−0.119573	−	0.992825i	$-0.538152\pi$
$13$	−0.862250	−0.239145	−0.119573	+	0.992825i	$0.538152\pi$
$14$	−7.59336	−2.02941
$15$	−0.520841	−0.134480
$16$	1.75918	0.439796
$17$	−1.44829	−0.351263	−0.175631	−	0.984456i	$-0.556197\pi$
$17$	−1.44829	−0.351263	−0.175631	+	0.984456i	$0.556197\pi$
$18$	6.41621	1.51232
$19$	−0.811375	−0.186142	−0.0930710	−	0.995659i	$-0.529668\pi$
$19$	−0.811375	−0.186142	−0.0930710	+	0.995659i	$0.529668\pi$
$20$	−3.49001	−0.780390
$21$	1.72388	0.376182
$22$	−8.66352	−1.84707
$23$	2.89522	0.603695	0.301847	−	0.953356i	$-0.402397\pi$
$23$	2.89522	0.603695	0.301847	+	0.953356i	$0.402397\pi$
$24$	−2.03389	−0.415165
$25$	−4.06009	−0.812018
$26$	2.04043	0.400161
$27$	−3.06833	−0.590501
$28$	11.5513	2.18298
$29$	8.12591	1.50894	0.754472	−	0.656332i	$-0.227893\pi$
$29$	8.12591	1.50894	0.754472	+	0.656332i	$0.227893\pi$
$30$	1.23252	0.225026
$31$	−5.72998	−1.02913	−0.514567	−	0.857450i	$-0.672047\pi$
$31$	−5.72998	−1.02913	−0.514567	+	0.857450i	$0.672047\pi$
$32$	3.40881	0.602597
$33$	1.96683	0.342382
$34$	3.42724	0.587767
$35$	−3.11093	−0.525842
$36$	−9.76055	−1.62676
$37$	−8.37839	−1.37740	−0.688699	−	0.725047i	$-0.741818\pi$
$37$	−8.37839	−1.37740	−0.688699	+	0.725047i	$0.741818\pi$
$38$	1.92004	0.311471
$39$	−0.463228	−0.0741758
$40$	3.67036	0.580335
$41$	−8.89121	−1.38857	−0.694287	−	0.719698i	$-0.744280\pi$
$41$	−8.89121	−1.38857	−0.694287	+	0.719698i	$0.744280\pi$
$42$	−4.07939	−0.629464
$43$	3.98967	0.608419	0.304209	−	0.952605i	$-0.401608\pi$
$43$	3.98967	0.608419	0.304209	+	0.952605i	$0.401608\pi$
$44$	13.1792	1.98684
$45$	2.62866	0.391857
$46$	−6.85124	−1.01016
$47$	7.11721	1.03815	0.519076	−	0.854728i	$-0.326276\pi$
$47$	7.11721	1.03815	0.519076	+	0.854728i	$0.326276\pi$
$48$	0.945088	0.136412
$49$	3.29657	0.470938
$50$	9.60779	1.35875
$51$	−0.778068	−0.108951
$52$	−3.10396	−0.430442
$53$	−8.76352	−1.20376	−0.601881	−	0.798586i	$-0.705582\pi$
$53$	−8.76352	−1.20376	−0.601881	+	0.798586i	$0.705582\pi$
$54$	7.26090	0.988083
$55$	−3.54936	−0.478595
$56$	−12.1482	−1.62337
$57$	−0.435896	−0.0577358
$58$	−19.2291	−2.52491
$59$	−4.55866	−0.593487	−0.296743	−	0.954957i	$-0.595901\pi$
$59$	−4.55866	−0.593487	−0.296743	+	0.954957i	$0.595901\pi$
$60$	−1.87494	−0.242054
$61$	4.67288	0.598301	0.299151	−	0.954206i	$-0.403297\pi$
$61$	4.67288	0.598301	0.299151	+	0.954206i	$0.403297\pi$
$62$	13.5594	1.72205
$63$	−8.70036	−1.09614
$64$	−11.5850	−1.44812
$65$	0.835943	0.103686
$66$	−4.65431	−0.572906
$67$	−7.22865	−0.883120	−0.441560	−	0.897232i	$-0.645575\pi$
$67$	−7.22865	−0.883120	−0.441560	+	0.897232i	$0.645575\pi$
$68$	−5.21363	−0.632245
$69$	1.55540	0.187248
$70$	7.36169	0.879890
$71$	−6.49221	−0.770483	−0.385242	−	0.922816i	$-0.625882\pi$
$71$	−6.49221	−0.770483	−0.385242	+	0.922816i	$0.625882\pi$
$72$	10.2649	1.20973
$73$	−7.85154	−0.918953	−0.459477	−	0.888190i	$-0.651963\pi$
$73$	−7.85154	−0.918953	−0.459477	+	0.888190i	$0.651963\pi$
$74$	19.8266	2.30480
$75$	−2.18121	−0.251864
$76$	−2.92082	−0.335041
$77$	11.7477	1.33877
$78$	1.09618	0.124118
$79$	8.29530	0.933294	0.466647	−	0.884444i	$-0.345462\pi$
$79$	8.29530	0.933294	0.466647	+	0.884444i	$0.345462\pi$
$80$	−1.70551	−0.190682
$81$	6.48574	0.720638
$82$	21.0401	2.32350
$83$	−9.63926	−1.05805	−0.529023	−	0.848608i	$-0.677441\pi$
$83$	−9.63926	−1.05805	−0.529023	+	0.848608i	$0.677441\pi$
$84$	6.20570	0.677098
$85$	1.40411	0.152297
$86$	−9.44115	−1.01806
$87$	4.36549	0.468030
$88$	−13.8603	−1.47751
$89$	−5.40996	−0.573454	−0.286727	−	0.958012i	$-0.592567\pi$
$89$	−5.40996	−0.573454	−0.286727	+	0.958012i	$0.592567\pi$
$90$	−6.22045	−0.655693
$91$	−2.76681	−0.290040
$92$	10.4223	1.08660
$93$	−3.07832	−0.319207
$94$	−16.8421	−1.73713
$95$	0.786620	0.0807055
$96$	1.83132	0.186908
$97$	2.54683	0.258591	0.129296	−	0.991606i	$-0.458728\pi$
$97$	2.54683	0.258591	0.129296	+	0.991606i	$0.458728\pi$
$98$	−7.80099	−0.788019
$99$	−9.92652	−0.997653
$100$	−14.6157	−1.46157
$101$	−5.98532	−0.595562	−0.297781	−	0.954634i	$-0.596246\pi$
$101$	−5.98532	−0.595562	−0.297781	+	0.954634i	$0.596246\pi$
$102$	1.84122	0.182308
$103$	−0.769888	−0.0758593	−0.0379297	−	0.999280i	$-0.512076\pi$
$103$	−0.769888	−0.0758593	−0.0379297	+	0.999280i	$0.512076\pi$
$104$	3.26436	0.320097
$105$	−1.67129	−0.163101
$106$	20.7380	2.01425
$107$	13.5296	1.30796	0.653980	−	0.756512i	$-0.273098\pi$
$107$	13.5296	1.30796	0.653980	+	0.756512i	$0.273098\pi$
$108$	−11.0455	−1.06286
$109$	7.11006	0.681020	0.340510	−	0.940241i	$-0.389400\pi$
$109$	7.11006	0.681020	0.340510	+	0.940241i	$0.389400\pi$
$110$	8.39920	0.800832
$111$	−4.50113	−0.427229
$112$	5.64491	0.533394
$113$	0.268577	0.0252656	0.0126328	−	0.999920i	$-0.495979\pi$
$113$	0.268577	0.0252656	0.0126328	+	0.999920i	$0.495979\pi$
$114$	1.03150	0.0966091
$115$	−2.80689	−0.261743
$116$	29.2520	2.71598
$117$	2.33789	0.216138
$118$	10.7876	0.993079
$119$	−4.64732	−0.426019
$120$	1.97183	0.180003
$121$	2.40333	0.218484
$122$	−11.0579	−1.00114
$123$	−4.77664	−0.430695
$124$	−20.6270	−1.85236
$125$	8.78367	0.785635
$126$	20.5885	1.83417
$127$	−13.2503	−1.17578	−0.587888	−	0.808942i	$-0.700041\pi$
$127$	−13.2503	−1.17578	−0.587888	+	0.808942i	$0.700041\pi$
$128$	20.5970	1.82054
$129$	2.14337	0.188714
$130$	−1.97817	−0.173497
$131$	−4.89585	−0.427753	−0.213876	−	0.976861i	$-0.568609\pi$
$131$	−4.89585	−0.427753	−0.213876	+	0.976861i	$0.568609\pi$
$132$	7.08029	0.616260
$133$	−2.60356	−0.225757
$134$	17.1059	1.47772
$135$	2.97472	0.256023
$136$	5.48304	0.470167
$137$	−9.72135	−0.830551	−0.415276	−	0.909696i	$-0.636315\pi$
$137$	−9.72135	−0.830551	−0.415276	+	0.909696i	$0.636315\pi$
$138$	−3.68070	−0.313322
$139$	−22.8315	−1.93654	−0.968270	−	0.249905i	$-0.919601\pi$
$139$	−22.8315	−1.93654	−0.968270	+	0.249905i	$0.919601\pi$
$140$	−11.1988	−0.946475
$141$	3.82359	0.322004
$142$	15.3632	1.28925
$143$	−3.15674	−0.263980
$144$	−4.76982	−0.397485
$145$	−7.87799	−0.654232
$146$	18.5799	1.53768
$147$	1.77102	0.146071
$148$	−30.1609	−2.47921
$149$	17.3779	1.42365	0.711826	−	0.702355i	$-0.247868\pi$
$149$	17.3779	1.42365	0.711826	+	0.702355i	$0.247868\pi$
$150$	5.16161	0.421443
$151$	18.3068	1.48979	0.744895	−	0.667182i	$-0.232500\pi$
$151$	18.3068	1.48979	0.744895	+	0.667182i	$0.232500\pi$
$152$	3.07175	0.249152
$153$	3.92688	0.317469
$154$	−27.7997	−2.24017
$155$	5.55516	0.446201
$156$	−1.66755	−0.133511
$157$	−18.5834	−1.48312	−0.741560	−	0.670887i	$-0.765914\pi$
$157$	−18.5834	−1.48312	−0.741560	+	0.670887i	$0.765914\pi$
$158$	−19.6300	−1.56168
$159$	−4.70804	−0.373372
$160$	−3.30480	−0.261268
$161$	9.29025	0.732174
$162$	−15.3479	−1.20584
$163$	−22.3146	−1.74781	−0.873907	−	0.486093i	$-0.838422\pi$
$163$	−22.3146	−1.74781	−0.873907	+	0.486093i	$0.838422\pi$
$164$	−32.0070	−2.49932
$165$	−1.90683	−0.148446
$166$	22.8103	1.77042
$167$	−4.46962	−0.345869	−0.172935	−	0.984933i	$-0.555325\pi$
$167$	−4.46962	−0.345869	−0.172935	+	0.984933i	$0.555325\pi$
$168$	−6.52639	−0.503522
$169$	−12.2565	−0.942810
$170$	−3.32267	−0.254838
$171$	2.19995	0.168234
$172$	14.3622	1.09511
$173$	11.1800	0.849999	0.425000	−	0.905194i	$-0.360274\pi$
$173$	11.1800	0.849999	0.425000	+	0.905194i	$0.360274\pi$
$174$	−10.3305	−0.783153
$175$	−13.0281	−0.984833
$176$	6.44046	0.485468
$177$	−2.44905	−0.184082
$178$	12.8021	0.959559
$179$	22.8433	1.70739	0.853694	−	0.520774i	$-0.174357\pi$
$179$	22.8433	1.70739	0.853694	+	0.520774i	$0.174357\pi$
$180$	9.46276	0.705312
$181$	9.10982	0.677128	0.338564	−	0.940943i	$-0.390059\pi$
$181$	9.10982	0.677128	0.338564	+	0.940943i	$0.390059\pi$
$182$	6.54738	0.485324
$183$	2.51042	0.185576
$184$	−10.9609	−0.808049
$185$	8.12277	0.597198
$186$	7.28454	0.534128
$187$	−5.30228	−0.387741
$188$	25.6208	1.86859
$189$	−9.84575	−0.716173
$190$	−1.86146	−0.135044
$191$	21.6754	1.56837	0.784187	−	0.620525i	$-0.213080\pi$
$191$	21.6754	1.56837	0.784187	+	0.620525i	$0.213080\pi$
$192$	−6.22380	−0.449164
$193$	11.3417	0.816391	0.408196	−	0.912894i	$-0.366158\pi$
$193$	11.3417	0.816391	0.408196	+	0.912894i	$0.366158\pi$
$194$	−6.02681	−0.432700
$195$	0.449095	0.0321603
$196$	11.8671	0.847652
$197$	22.8297	1.62655	0.813274	−	0.581881i	$-0.197683\pi$
$197$	22.8297	1.62655	0.813274	+	0.581881i	$0.197683\pi$
$198$	23.4901	1.66937
$199$	−14.5562	−1.03186	−0.515929	−	0.856631i	$-0.672553\pi$
$199$	−14.5562	−1.03186	−0.515929	+	0.856631i	$0.672553\pi$
$200$	15.3710	1.08689
$201$	−3.88346	−0.273918
$202$	14.1637	0.996551
$203$	26.0746	1.83008
$204$	−2.80092	−0.196104
$205$	8.61994	0.602043
$206$	1.82186	0.126935
$207$	−7.85004	−0.545616
$208$	−1.51685	−0.105175
$209$	−2.97049	−0.205473
$210$	3.95493	0.272916
$211$	−22.0031	−1.51476	−0.757378	−	0.652976i	$-0.773520\pi$
$211$	−22.0031	−1.51476	−0.757378	+	0.652976i	$0.773520\pi$
$212$	−31.5473	−2.16668
$213$	−3.48782	−0.238981
$214$	−32.0165	−2.18860
$215$	−3.86794	−0.263792
$216$	11.6163	0.790389
$217$	−18.3865	−1.24816
$218$	−16.8252	−1.13955
$219$	−4.21809	−0.285032
$220$	−12.7771	−0.861434
$221$	1.24879	0.0840027
$222$	10.6515	0.714880
$223$	−5.99564	−0.401497	−0.200749	−	0.979643i	$-0.564337\pi$
$223$	−5.99564	−0.401497	−0.200749	+	0.979643i	$0.564337\pi$
$224$	10.9383	0.730844
$225$	11.0085	0.733897
$226$	−0.635559	−0.0422768
$227$	10.5281	0.698774	0.349387	−	0.936979i	$-0.386390\pi$
$227$	10.5281	0.698774	0.349387	+	0.936979i	$0.386390\pi$
$228$	−1.56916	−0.103920
$229$	−13.7619	−0.909411	−0.454705	−	0.890642i	$-0.650255\pi$
$229$	−13.7619	−0.909411	−0.454705	+	0.890642i	$0.650255\pi$
$230$	6.64221	0.437974
$231$	6.31123	0.415248
$232$	−30.7636	−2.01973
$233$	23.0110	1.50750	0.753749	−	0.657162i	$-0.228243\pi$
$233$	23.0110	1.50750	0.753749	+	0.657162i	$0.228243\pi$
$234$	−5.53238	−0.361663
$235$	−6.90006	−0.450110
$236$	−16.4105	−1.06823
$237$	4.45649	0.289480
$238$	10.9974	0.712857
$239$	−6.90925	−0.446922	−0.223461	−	0.974713i	$-0.571736\pi$
$239$	−6.90925	−0.446922	−0.223461	+	0.974713i	$0.571736\pi$
$240$	−0.916253	−0.0591439
$241$	−7.21289	−0.464623	−0.232311	−	0.972641i	$-0.574629\pi$
$241$	−7.21289	−0.464623	−0.232311	+	0.972641i	$0.574629\pi$
$242$	−5.68723	−0.365589
$243$	12.6893	0.814022
$244$	16.8216	1.07690
$245$	−3.19599	−0.204184
$246$	11.3034	0.720680
$247$	0.699607	0.0445150
$248$	21.6929	1.37750
$249$	−5.17851	−0.328175
$250$	−20.7857	−1.31460
$251$	−26.5762	−1.67748	−0.838738	−	0.544535i	$-0.816706\pi$
$251$	−26.5762	−1.67748	−0.838738	+	0.544535i	$0.816706\pi$
$252$	−31.3199	−1.97297
$253$	10.5996	0.666388
$254$	31.3556	1.96742
$255$	0.754330	0.0472380
$256$	−25.5708	−1.59818
$257$	−14.4005	−0.898281	−0.449141	−	0.893461i	$-0.648270\pi$
$257$	−14.4005	−0.898281	−0.449141	+	0.893461i	$0.648270\pi$
$258$	−5.07208	−0.315774
$259$	−26.8848	−1.67054
$260$	3.00926	0.186627
$261$	−22.0325	−1.36377
$262$	11.5855	0.715757
$263$	−15.8236	−0.975722	−0.487861	−	0.872921i	$-0.662223\pi$
$263$	−15.8236	−0.975722	−0.487861	+	0.872921i	$0.662223\pi$
$264$	−7.44617	−0.458280
$265$	8.49615	0.521914
$266$	6.16106	0.377759
$267$	−2.90640	−0.177869
$268$	−26.0220	−1.58955
$269$	−12.1560	−0.741164	−0.370582	−	0.928800i	$-0.620842\pi$
$269$	−12.1560	−0.741164	−0.370582	+	0.928800i	$0.620842\pi$
$270$	−7.03937	−0.428403
$271$	−0.209899	−0.0127505	−0.00637524	−	0.999980i	$-0.502029\pi$
$271$	−0.209899	−0.0127505	−0.00637524	+	0.999980i	$0.502029\pi$
$272$	−2.54781	−0.154484
$273$	−1.48642	−0.0899620
$274$	23.0046	1.38976
$275$	−14.8642	−0.896346
$276$	5.59920	0.337032
$277$	15.6154	0.938241	0.469121	−	0.883134i	$-0.344571\pi$
$277$	15.6154	0.938241	0.469121	+	0.883134i	$0.344571\pi$
$278$	54.0284	3.24041
$279$	15.5362	0.930125
$280$	11.7775	0.703843
$281$	32.0738	1.91336	0.956681	−	0.291138i	$-0.0940337\pi$
$281$	32.0738	1.91336	0.956681	+	0.291138i	$0.0940337\pi$
$282$	−9.04813	−0.538808
$283$	21.4379	1.27435	0.637175	−	0.770719i	$-0.280103\pi$
$283$	21.4379	1.27435	0.637175	+	0.770719i	$0.280103\pi$
$284$	−23.3709	−1.38681
$285$	0.422597	0.0250325
$286$	7.47012	0.441717
$287$	−28.5304	−1.68409
$288$	−9.24257	−0.544624
$289$	−14.9024	−0.876615
$290$	18.6425	1.09472
$291$	1.36824	0.0802074
$292$	−28.2643	−1.65404
$293$	19.6968	1.15070	0.575351	−	0.817907i	$-0.304866\pi$
$293$	19.6968	1.15070	0.575351	+	0.817907i	$0.304866\pi$
$294$	−4.19094	−0.244420
$295$	4.41957	0.257318
$296$	31.7195	1.84366
$297$	−11.2333	−0.651825
$298$	−41.1230	−2.38219
$299$	−2.49640	−0.144371
$300$	−7.85200	−0.453336
$301$	12.8022	0.737904
$302$	−43.3213	−2.49286
$303$	−3.21550	−0.184726
$304$	−1.42736	−0.0818645
$305$	−4.53031	−0.259405
$306$	−9.29256	−0.531220
$307$	9.01924	0.514755	0.257377	−	0.966311i	$-0.417142\pi$
$307$	9.01924	0.514755	0.257377	+	0.966311i	$0.417142\pi$
$308$	42.2898	2.40969
$309$	−0.413608	−0.0235293
$310$	−13.1457	−0.746626
$311$	−12.4209	−0.704327	−0.352164	−	0.935938i	$-0.614554\pi$
$311$	−12.4209	−0.704327	−0.352164	+	0.935938i	$0.614554\pi$
$312$	1.75372	0.0992847
$313$	11.0557	0.624908	0.312454	−	0.949933i	$-0.398849\pi$
$313$	11.0557	0.624908	0.312454	+	0.949933i	$0.398849\pi$
$314$	43.9758	2.48170
$315$	8.43491	0.475253
$316$	29.8618	1.67986
$317$	−13.5754	−0.762468	−0.381234	−	0.924479i	$-0.624501\pi$
$317$	−13.5754	−0.762468	−0.381234	+	0.924479i	$0.624501\pi$
$318$	11.1411	0.624762
$319$	29.7494	1.66565
$320$	11.2315	0.627860
$321$	7.26855	0.405691
$322$	−21.9844	−1.22514
$323$	1.17511	0.0653848
$324$	23.3477	1.29709
$325$	3.50081	0.194190
$326$	52.8052	2.92461
$327$	3.81974	0.211232
$328$	33.6609	1.85861
$329$	22.8379	1.25909
$330$	4.51231	0.248395
$331$	−4.42553	−0.243249	−0.121624	−	0.992576i	$-0.538810\pi$
$331$	−4.42553	−0.243249	−0.121624	+	0.992576i	$0.538810\pi$
$332$	−34.6998	−1.90440
$333$	22.7170	1.24488
$334$	10.5769	0.578742
$335$	7.00811	0.382894
$336$	3.03262	0.165443
$337$	−11.7190	−0.638373	−0.319187	−	0.947692i	$-0.603410\pi$
$337$	−11.7190	−0.638373	−0.319187	+	0.947692i	$0.603410\pi$
$338$	29.0038	1.57760
$339$	0.144288	0.00783663
$340$	5.05456	0.274122
$341$	−20.9778	−1.13601
$342$	−5.20595	−0.281506
$343$	−11.8837	−0.641658
$344$	−15.1043	−0.814372
$345$	−1.50795	−0.0811851
$346$	−26.4563	−1.42230
$347$	−11.4673	−0.615598	−0.307799	−	0.951451i	$-0.599592\pi$
$347$	−11.4673	−0.615598	−0.307799	+	0.951451i	$0.599592\pi$
$348$	15.7151	0.842417
$349$	−13.8875	−0.743381	−0.371690	−	0.928357i	$-0.621222\pi$
$349$	−13.8875	−0.743381	−0.371690	+	0.928357i	$0.621222\pi$
$350$	30.8297	1.64792
$351$	2.64567	0.141215
$352$	12.4798	0.665177
$353$	6.04181	0.321573	0.160787	−	0.986989i	$-0.448597\pi$
$353$	6.04181	0.321573	0.160787	+	0.986989i	$0.448597\pi$
$354$	5.79544	0.308024
$355$	6.29413	0.334058
$356$	−19.4750	−1.03217
$357$	−2.49669	−0.132139
$358$	−54.0564	−2.85697
$359$	−11.9016	−0.628143	−0.314071	−	0.949399i	$-0.601693\pi$
$359$	−11.9016	−0.628143	−0.314071	+	0.949399i	$0.601693\pi$
$360$	−9.95175	−0.524503
$361$	−18.3417	−0.965351
$362$	−21.5575	−1.13304
$363$	1.29114	0.0677675
$364$	−9.96008	−0.522050
$365$	7.61199	0.398430
$366$	−5.94065	−0.310523
$367$	26.9352	1.40600	0.703002	−	0.711188i	$-0.251843\pi$
$367$	26.9352	1.40600	0.703002	+	0.711188i	$0.251843\pi$
$368$	5.09322	0.265502
$369$	24.1075	1.25498
$370$	−19.2217	−0.999289
$371$	−28.1206	−1.45995
$372$	−11.0815	−0.574548
$373$	−23.5616	−1.21998	−0.609988	−	0.792411i	$-0.708826\pi$
$373$	−23.5616	−1.21998	−0.609988	+	0.792411i	$0.708826\pi$
$374$	12.5473	0.648806
$375$	4.71886	0.243681
$376$	−26.9448	−1.38957
$377$	−7.00656	−0.360856
$378$	23.2990	1.19837
$379$	20.9263	1.07491	0.537457	−	0.843291i	$-0.319385\pi$
$379$	20.9263	1.07491	0.537457	+	0.843291i	$0.319385\pi$
$380$	2.83171	0.145264
$381$	−7.11849	−0.364692
$382$	−51.2925	−2.62435
$383$	−18.7904	−0.960145	−0.480073	−	0.877229i	$-0.659390\pi$
$383$	−18.7904	−0.960145	−0.480073	+	0.877229i	$0.659390\pi$
$384$	11.0654	0.564677
$385$	−11.3893	−0.580451
$386$	−26.8389	−1.36606
$387$	−10.8175	−0.549885
$388$	9.16819	0.465444
$389$	−26.8037	−1.35900	−0.679500	−	0.733676i	$-0.737803\pi$
$389$	−26.8037	−1.35900	−0.679500	+	0.733676i	$0.737803\pi$
$390$	−1.06274	−0.0538138
$391$	−4.19312	−0.212055
$392$	−12.4804	−0.630353
$393$	−2.63020	−0.132676
$394$	−54.0241	−2.72170
$395$	−8.04221	−0.404648
$396$	−35.7339	−1.79570
$397$	31.8407	1.59804	0.799021	−	0.601304i	$-0.205352\pi$
$397$	31.8407	1.59804	0.799021	+	0.601304i	$0.205352\pi$
$398$	34.4457	1.72661
$399$	−1.39871	−0.0700233
$400$	−7.14244	−0.357122
$401$	−38.9046	−1.94280	−0.971401	−	0.237444i	$-0.923690\pi$
$401$	−38.9046	−1.94280	−0.971401	+	0.237444i	$0.923690\pi$
$402$	9.18981	0.458346
$403$	4.94067	0.246112
$404$	−21.5462	−1.07196
$405$	−6.28786	−0.312446
$406$	−61.7030	−3.06227
$407$	−30.6737	−1.52044
$408$	2.94566	0.145832
$409$	−25.2514	−1.24860	−0.624301	−	0.781184i	$-0.714616\pi$
$409$	−25.2514	−1.24860	−0.624301	+	0.781184i	$0.714616\pi$
$410$	−20.3982	−1.00740
$411$	−5.22261	−0.257613
$412$	−2.77148	−0.136541
$413$	−14.6279	−0.719794
$414$	18.5763	0.912977
$415$	9.34516	0.458736
$416$	−2.93924	−0.144108
$417$	−12.2658	−0.600658
$418$	7.02936	0.343817
$419$	−34.4304	−1.68203	−0.841017	−	0.541009i	$-0.818043\pi$
$419$	−34.4304	−1.68203	−0.841017	+	0.541009i	$0.818043\pi$
$420$	−6.01637	−0.293569
$421$	34.8872	1.70030	0.850150	−	0.526540i	$-0.176511\pi$
$421$	34.8872	1.70030	0.850150	+	0.526540i	$0.176511\pi$
$422$	52.0681	2.53464
$423$	−19.2975	−0.938275
$424$	33.1775	1.61124
$425$	5.88020	0.285232
$426$	8.25357	0.399887
$427$	14.9945	0.725633
$428$	48.7046	2.35422
$429$	−1.69590	−0.0818789
$430$	9.15310	0.441402
$431$	−9.51851	−0.458491	−0.229245	−	0.973369i	$-0.573626\pi$
$431$	−9.51851	−0.458491	−0.229245	+	0.973369i	$0.573626\pi$
$432$	−5.39776	−0.259700
$433$	−17.1651	−0.824902	−0.412451	−	0.910980i	$-0.635327\pi$
$433$	−17.1651	−0.824902	−0.412451	+	0.910980i	$0.635327\pi$
$434$	43.5098	2.08854
$435$	−4.23230	−0.202923
$436$	25.5951	1.22578
$437$	−2.34911	−0.112373
$438$	9.98169	0.476944
$439$	23.7532	1.13368	0.566839	−	0.823829i	$-0.308166\pi$
$439$	23.7532	1.13368	0.566839	+	0.823829i	$0.308166\pi$
$440$	13.4374	0.640603
$441$	−8.93826	−0.425631
$442$	−2.95514	−0.140561
$443$	−19.3245	−0.918137	−0.459068	−	0.888401i	$-0.651817\pi$
$443$	−19.3245	−0.918137	−0.459068	+	0.888401i	$0.651817\pi$
$444$	−16.2034	−0.768978
$445$	5.24490	0.248632
$446$	14.1881	0.671824
$447$	9.33595	0.441575
$448$	−37.1741	−1.75631
$449$	−8.24472	−0.389092	−0.194546	−	0.980893i	$-0.562323\pi$
$449$	−8.24472	−0.389092	−0.194546	+	0.980893i	$0.562323\pi$
$450$	−26.0504	−1.22803
$451$	−32.5512	−1.53278
$452$	0.966833	0.0454760
$453$	9.83501	0.462089
$454$	−24.9136	−1.16926
$455$	2.68240	0.125753
$456$	1.65024	0.0772797
$457$	−1.21002	−0.0566024	−0.0283012	−	0.999599i	$-0.509010\pi$
$457$	−1.21002	−0.0566024	−0.0283012	+	0.999599i	$0.509010\pi$
$458$	32.5661	1.52171
$459$	4.44385	0.207421
$460$	−10.1043	−0.471118
$461$	7.20622	0.335627	0.167814	−	0.985819i	$-0.446329\pi$
$461$	7.20622	0.335627	0.167814	+	0.985819i	$0.446329\pi$
$462$	−14.9349	−0.694834
$463$	4.74153	0.220358	0.110179	−	0.993912i	$-0.464858\pi$
$463$	4.74153	0.220358	0.110179	+	0.993912i	$0.464858\pi$
$464$	14.2950	0.663627
$465$	2.98440	0.138398
$466$	−54.4531	−2.52249
$467$	−37.1032	−1.71693	−0.858465	−	0.512872i	$-0.828581\pi$
$467$	−37.1032	−1.71693	−0.858465	+	0.512872i	$0.828581\pi$
$468$	8.41603	0.389031
$469$	−23.1955	−1.07107
$470$	16.3283	0.753168
$471$	−9.98360	−0.460020
$472$	17.2585	0.794385
$473$	14.6064	0.671603
$474$	−10.5458	−0.484387
$475$	3.29425	0.151151
$476$	−16.7296	−0.766801
$477$	23.7613	1.08795
$478$	16.3500	0.747833
$479$	−38.7321	−1.76972	−0.884858	−	0.465862i	$-0.845744\pi$
$479$	−38.7321	−1.76972	−0.884858	+	0.465862i	$0.845744\pi$
$480$	−1.77544	−0.0810376
$481$	7.22426	0.329398
$482$	17.0686	0.777452
$483$	4.99101	0.227099
$484$	8.65161	0.393255
$485$	−2.46913	−0.112117
$486$	−30.0280	−1.36210
$487$	−34.0657	−1.54367	−0.771833	−	0.635826i	$-0.780660\pi$
$487$	−34.0657	−1.54367	−0.771833	+	0.635826i	$0.780660\pi$
$488$	−17.6909	−0.800830
$489$	−11.9881	−0.542121
$490$	7.56299	0.341661
$491$	37.2632	1.68166	0.840832	−	0.541296i	$-0.182066\pi$
$491$	37.2632	1.68166	0.840832	+	0.541296i	$0.182066\pi$
$492$	−17.1951	−0.775217
$493$	−11.7687	−0.530036
$494$	−1.65555	−0.0744867
$495$	9.62367	0.432552
$496$	−10.0801	−0.452609
$497$	−20.8324	−0.934459
$498$	12.2544	0.549134
$499$	−31.7317	−1.42050	−0.710252	−	0.703947i	$-0.751419\pi$
$499$	−31.7317	−1.42050	−0.710252	+	0.703947i	$0.751419\pi$
$500$	31.6198	1.41408
$501$	−2.40122	−0.107279
$502$	62.8900	2.80692
$503$	−19.3733	−0.863814	−0.431907	−	0.901918i	$-0.642159\pi$
$503$	−19.3733	−0.863814	−0.431907	+	0.901918i	$0.642159\pi$
$504$	32.9384	1.46719
$505$	5.80271	0.258217
$506$	−25.0828	−1.11507
$507$	−6.58459	−0.292432
$508$	−47.6991	−2.11631
$509$	−25.7299	−1.14046	−0.570229	−	0.821486i	$-0.693146\pi$
$509$	−25.7299	−1.14046	−0.570229	+	0.821486i	$0.693146\pi$
$510$	−1.78504	−0.0790431
$511$	−25.1942	−1.11453
$512$	19.3168	0.853688
$513$	2.48957	0.109917
$514$	34.0774	1.50309
$515$	0.746399	0.0328903
$516$	7.71581	0.339670
$517$	26.0565	1.14596
$518$	63.6201	2.79531
$519$	6.00624	0.263645
$520$	−3.16477	−0.138784
$521$	3.88213	0.170079	0.0850395	−	0.996378i	$-0.472898\pi$
$521$	3.88213	0.170079	0.0850395	+	0.996378i	$0.472898\pi$
$522$	52.1376	2.28200
$523$	12.1409	0.530886	0.265443	−	0.964127i	$-0.414482\pi$
$523$	12.1409	0.530886	0.265443	+	0.964127i	$0.414482\pi$
$524$	−17.6243	−0.769921
$525$	−6.99911	−0.305466
$526$	37.4448	1.63267
$527$	8.29869	0.361496
$528$	3.46002	0.150578
$529$	−14.6177	−0.635553
$530$	−20.1053	−0.873317
$531$	12.3603	0.536390
$532$	−9.37241	−0.406345
$533$	7.66644	0.332071
$534$	6.87770	0.297627
$535$	−13.1169	−0.567091
$536$	27.3667	1.18206
$537$	12.2721	0.529582
$538$	28.7659	1.24019
$539$	12.0689	0.519845
$540$	10.7085	0.460821
$541$	−17.0143	−0.731500	−0.365750	−	0.930713i	$-0.619188\pi$
$541$	−17.0143	−0.731500	−0.365750	+	0.930713i	$0.619188\pi$
$542$	0.496706	0.0213353
$543$	4.89408	0.210025
$544$	−4.93695	−0.211670
$545$	−6.89313	−0.295269
$546$	3.51746	0.150533
$547$	−36.7562	−1.57158	−0.785790	−	0.618493i	$-0.787743\pi$
$547$	−36.7562	−1.57158	−0.785790	+	0.618493i	$0.787743\pi$
$548$	−34.9953	−1.49493
$549$	−12.6700	−0.540741
$550$	35.1746	1.49985
$551$	−6.59316	−0.280878
$552$	−5.88854	−0.250633
$553$	26.6182	1.13192
$554$	−36.9524	−1.56996
$555$	4.36380	0.185233
$556$	−82.1897	−3.48562
$557$	20.3292	0.861378	0.430689	−	0.902500i	$-0.358271\pi$
$557$	20.3292	0.861378	0.430689	+	0.902500i	$0.358271\pi$
$558$	−36.7647	−1.55638
$559$	−3.44009	−0.145500
$560$	−5.47269	−0.231263
$561$	−2.84855	−0.120266
$562$	−75.8994	−3.20162
$563$	−4.63711	−0.195431	−0.0977155	−	0.995214i	$-0.531154\pi$
$563$	−4.63711	−0.195431	−0.0977155	+	0.995214i	$0.531154\pi$
$564$	13.7643	0.579582
$565$	−0.260382	−0.0109544
$566$	−50.7306	−2.13237
$567$	20.8116	0.874006
$568$	24.5786	1.03130
$569$	−14.6500	−0.614162	−0.307081	−	0.951683i	$-0.599352\pi$
$569$	−14.6500	−0.614162	−0.307081	+	0.951683i	$0.599352\pi$
$570$	−1.00003	−0.0418867
$571$	−20.6959	−0.866097	−0.433049	−	0.901371i	$-0.642562\pi$
$571$	−20.6959	−0.866097	−0.433049	+	0.901371i	$0.642562\pi$
$572$	−11.3638	−0.475144
$573$	11.6447	0.486464
$574$	67.5142	2.81799
$575$	−11.7548	−0.490211
$576$	31.4112	1.30880
$577$	−10.6227	−0.442227	−0.221114	−	0.975248i	$-0.570969\pi$
$577$	−10.6227	−0.442227	−0.221114	+	0.975248i	$0.570969\pi$
$578$	35.2651	1.46684
$579$	6.09310	0.253221
$580$	−28.3595	−1.17757
$581$	−30.9307	−1.28322
$582$	−3.23779	−0.134211
$583$	−32.0837	−1.32877
$584$	29.7249	1.23002
$585$	−2.26656	−0.0937107
$586$	−46.6106	−1.92546
$587$	46.7242	1.92851	0.964256	−	0.264972i	$-0.0853626\pi$
$587$	46.7242	1.92851	0.964256	+	0.264972i	$0.0853626\pi$
$588$	6.37539	0.262917
$589$	4.64916	0.191565
$590$	−10.4585	−0.430569
$591$	12.2648	0.504507
$592$	−14.7391	−0.605774
$593$	−2.81849	−0.115742	−0.0578708	−	0.998324i	$-0.518431\pi$
$593$	−2.81849	−0.115742	−0.0578708	+	0.998324i	$0.518431\pi$
$594$	26.5826	1.09070
$595$	4.50553	0.184709
$596$	62.5577	2.56246
$597$	−7.82002	−0.320052
$598$	5.90748	0.241575
$599$	1.27280	0.0520052	0.0260026	−	0.999662i	$-0.491722\pi$
$599$	1.27280	0.0520052	0.0260026	+	0.999662i	$0.491722\pi$
$600$	8.25776	0.337121
$601$	40.3081	1.64420	0.822101	−	0.569342i	$-0.192802\pi$
$601$	40.3081	1.64420	0.822101	+	0.569342i	$0.192802\pi$
$602$	−30.2950	−1.23473
$603$	19.5996	0.798159
$604$	65.9018	2.68150
$605$	−2.33000	−0.0947281
$606$	7.60916	0.309101
$607$	−12.7978	−0.519445	−0.259722	−	0.965683i	$-0.583631\pi$
$607$	−12.7978	−0.519445	−0.259722	+	0.965683i	$0.583631\pi$
$608$	−2.76582	−0.112169
$609$	14.0081	0.567637
$610$	10.7205	0.434062
$611$	−6.13681	−0.248269
$612$	14.1361	0.571420
$613$	−26.8599	−1.08486	−0.542431	−	0.840100i	$-0.682496\pi$
$613$	−26.8599	−1.08486	−0.542431	+	0.840100i	$0.682496\pi$
$614$	−21.3431	−0.861338
$615$	4.63090	0.186736
$616$	−44.4752	−1.79196
$617$	7.59587	0.305798	0.152899	−	0.988242i	$-0.451139\pi$
$617$	7.59587	0.305798	0.152899	+	0.988242i	$0.451139\pi$
$618$	0.978761	0.0393716
$619$	−34.8359	−1.40017	−0.700086	−	0.714059i	$-0.746855\pi$
$619$	−34.8359	−1.40017	−0.700086	+	0.714059i	$0.746855\pi$
$620$	19.9977	0.803126
$621$	−8.88349	−0.356482
$622$	29.3929	1.17855
$623$	−17.3596	−0.695498
$624$	−0.814902	−0.0326222
$625$	11.7848	0.471391
$626$	−26.1623	−1.04566
$627$	−1.59584	−0.0637317
$628$	−66.8974	−2.66950
$629$	12.1344	0.483829
$630$	−19.9604	−0.795240
$631$	−7.25226	−0.288708	−0.144354	−	0.989526i	$-0.546110\pi$
$631$	−7.25226	−0.288708	−0.144354	+	0.989526i	$0.546110\pi$
$632$	−31.4049	−1.24922
$633$	−11.8208	−0.469833
$634$	32.1247	1.27584
$635$	12.8461	0.509781
$636$	−16.9482	−0.672040
$637$	−2.84246	−0.112623
$638$	−70.3990	−2.78712
$639$	17.6029	0.696358
$640$	−19.9686	−0.789328
$641$	45.5370	1.79861	0.899303	−	0.437327i	$-0.144075\pi$
$641$	45.5370	1.79861	0.899303	+	0.437327i	$0.144075\pi$
$642$	−17.2003	−0.678841
$643$	−35.6591	−1.40626	−0.703128	−	0.711063i	$-0.748214\pi$
$643$	−35.6591	−1.40626	−0.703128	+	0.711063i	$0.748214\pi$
$644$	33.4434	1.31786
$645$	−2.07798	−0.0818204
$646$	−2.78077	−0.109408
$647$	−44.2283	−1.73879	−0.869397	−	0.494114i	$-0.835493\pi$
$647$	−44.2283	−1.73879	−0.869397	+	0.494114i	$0.835493\pi$
$648$	−24.5541	−0.964578
$649$	−16.6895	−0.655120
$650$	−8.28431	−0.324938
$651$	−9.87780	−0.387142
$652$	−80.3291	−3.14593
$653$	−17.8375	−0.698036	−0.349018	−	0.937116i	$-0.613485\pi$
$653$	−17.8375	−0.698036	−0.349018	+	0.937116i	$0.613485\pi$
$654$	−9.03904	−0.353454
$655$	4.74648	0.185460
$656$	−15.6413	−0.610689
$657$	21.2885	0.830544
$658$	−54.0435	−2.10684
$659$	33.5312	1.30619	0.653094	−	0.757276i	$-0.273470\pi$
$659$	33.5312	1.30619	0.653094	+	0.757276i	$0.273470\pi$
$660$	−6.86427	−0.267192
$661$	−45.1352	−1.75556	−0.877778	−	0.479067i	$-0.840975\pi$
$661$	−45.1352	−1.75556	−0.877778	+	0.479067i	$0.840975\pi$
$662$	10.4726	0.407028
$663$	0.670889	0.0260552
$664$	36.4929	1.41620
$665$	2.52413	0.0978814
$666$	−53.7575	−2.08306
$667$	23.5263	0.910941
$668$	−16.0899	−0.622538
$669$	−3.22104	−0.124533
$670$	−16.5840	−0.640695
$671$	17.1077	0.660435
$672$	5.87638	0.226686
$673$	18.4082	0.709585	0.354792	−	0.934945i	$-0.384552\pi$
$673$	18.4082	0.709585	0.354792	+	0.934945i	$0.384552\pi$
$674$	27.7318	1.06819
$675$	12.4577	0.479497
$676$	−44.1216	−1.69698
$677$	20.0403	0.770212	0.385106	−	0.922872i	$-0.374165\pi$
$677$	20.0403	0.770212	0.385106	+	0.922872i	$0.374165\pi$
$678$	−0.341442	−0.0131130
$679$	8.17233	0.313625
$680$	−5.31576	−0.203850
$681$	5.65602	0.216739
$682$	49.6417	1.90088
$683$	−8.35648	−0.319752	−0.159876	−	0.987137i	$-0.551109\pi$
$683$	−8.35648	−0.319752	−0.159876	+	0.987137i	$0.551109\pi$
$684$	7.91946	0.302808
$685$	9.42475	0.360101
$686$	28.1215	1.07368
$687$	−7.39331	−0.282072
$688$	7.01855	0.267580
$689$	7.55634	0.287874
$690$	3.56840	0.135847
$691$	46.0517	1.75189	0.875945	−	0.482411i	$-0.160239\pi$
$691$	46.0517	1.75189	0.875945	+	0.482411i	$0.160239\pi$
$692$	40.2462	1.52993
$693$	−31.8525	−1.20998
$694$	27.1363	1.03008
$695$	22.1349	0.839624
$696$	−16.5272	−0.626461
$697$	12.8771	0.487754
$698$	32.8634	1.24390
$699$	12.3622	0.467582
$700$	−46.8992	−1.77262
$701$	−6.35324	−0.239959	−0.119979	−	0.992776i	$-0.538283\pi$
$701$	−6.35324	−0.239959	−0.119979	+	0.992776i	$0.538283\pi$
$702$	−6.26071	−0.236295
$703$	6.79801	0.256392
$704$	−42.4132	−1.59851
$705$	−3.70693	−0.139611
$706$	−14.2973	−0.538087
$707$	−19.2059	−0.722310
$708$	−8.81621	−0.331333
$709$	−4.34681	−0.163248	−0.0816240	−	0.996663i	$-0.526011\pi$
$709$	−4.34681	−0.163248	−0.0816240	+	0.996663i	$0.526011\pi$
$710$	−14.8944	−0.558978
$711$	−22.4917	−0.843506
$712$	20.4814	0.767572
$713$	−16.5895	−0.621283
$714$	5.90816	0.221107
$715$	3.06043	0.114454
$716$	82.2323	3.07317
$717$	−3.71186	−0.138622
$718$	28.1640	1.05107
$719$	7.75934	0.289375	0.144687	−	0.989477i	$-0.453782\pi$
$719$	7.75934	0.289375	0.144687	+	0.989477i	$0.453782\pi$
$720$	4.62429	0.172337
$721$	−2.47044	−0.0920039
$722$	43.4037	1.61532
$723$	−3.87499	−0.144112
$724$	32.7939	1.21878
$725$	−32.9919	−1.22529
$726$	−3.05536	−0.113395
$727$	−14.4127	−0.534536	−0.267268	−	0.963622i	$-0.586121\pi$
$727$	−14.4127	−0.534536	−0.267268	+	0.963622i	$0.586121\pi$
$728$	10.4748	0.388221
$729$	−12.6401	−0.468152
$730$	−18.0130	−0.666691
$731$	−5.77821	−0.213715
$732$	9.03712	0.334021
$733$	24.2626	0.896159	0.448080	−	0.893994i	$-0.352108\pi$
$733$	24.2626	0.896159	0.448080	+	0.893994i	$0.352108\pi$
$734$	−63.7393	−2.35266
$735$	−1.71699	−0.0633320
$736$	9.86923	0.363785
$737$	−26.4645	−0.974832
$738$	−57.0479	−2.09996
$739$	−13.5693	−0.499154	−0.249577	−	0.968355i	$-0.580292\pi$
$739$	−13.5693	−0.499154	−0.249577	+	0.968355i	$0.580292\pi$
$740$	29.2407	1.07491
$741$	0.375851	0.0138072
$742$	66.5446	2.44293
$743$	3.41214	0.125179	0.0625896	−	0.998039i	$-0.480064\pi$
$743$	3.41214	0.125179	0.0625896	+	0.998039i	$0.480064\pi$
$744$	11.6541	0.427261
$745$	−16.8477	−0.617252
$746$	55.7562	2.04138
$747$	26.1357	0.956256
$748$	−19.0874	−0.697904
$749$	43.4143	1.58632
$750$	−11.1667	−0.407750
$751$	−7.95791	−0.290388	−0.145194	−	0.989403i	$-0.546381\pi$
$751$	−7.95791	−0.290388	−0.145194	+	0.989403i	$0.546381\pi$
$752$	12.5205	0.456574
$753$	−14.2776	−0.520304
$754$	16.5803	0.603820
$755$	−17.7483	−0.645927
$756$	−35.4432	−1.28905
$757$	51.8991	1.88630	0.943152	−	0.332361i	$-0.107845\pi$
$757$	51.8991	1.88630	0.943152	+	0.332361i	$0.107845\pi$
$758$	−49.5200	−1.79865
$759$	5.69441	0.206694
$760$	−2.97804	−0.108025
$761$	−40.0739	−1.45268	−0.726338	−	0.687337i	$-0.758779\pi$
$761$	−40.0739	−1.45268	−0.726338	+	0.687337i	$0.758779\pi$
$762$	16.8452	0.610237
$763$	22.8149	0.825956
$764$	78.0279	2.82295
$765$	−3.80707	−0.137645
$766$	44.4656	1.60661
$767$	3.93070	0.141929
$768$	−13.7375	−0.495708
$769$	17.0710	0.615596	0.307798	−	0.951452i	$-0.400408\pi$
$769$	17.0710	0.615596	0.307798	+	0.951452i	$0.400408\pi$
$770$	26.9516	0.971267
$771$	−7.73642	−0.278620
$772$	40.8282	1.46944
$773$	25.3194	0.910675	0.455338	−	0.890319i	$-0.349519\pi$
$773$	25.3194	0.910675	0.455338	+	0.890319i	$0.349519\pi$
$774$	25.5986	0.920121
$775$	23.2642	0.835675
$776$	−9.64195	−0.346126
$777$	−14.4434	−0.518152
$778$	63.4281	2.27401
$779$	7.21410	0.258472
$780$	1.61667	0.0578861
$781$	−23.7683	−0.850498
$782$	9.92260	0.354832
$783$	−24.9330	−0.891033
$784$	5.79926	0.207117
$785$	18.0165	0.643035
$786$	6.22411	0.222007
$787$	−29.6988	−1.05865	−0.529324	−	0.848420i	$-0.677555\pi$
$787$	−29.6988	−1.05865	−0.529324	+	0.848420i	$0.677555\pi$
$788$	82.1833	2.92766
$789$	−8.50091	−0.302640
$790$	19.0311	0.677095
$791$	0.861815	0.0306426
$792$	37.5805	1.33536
$793$	−4.02919	−0.143081
$794$	−75.3479	−2.67400
$795$	4.56440	0.161882
$796$	−52.3999	−1.85726
$797$	28.9917	1.02694	0.513469	−	0.858108i	$-0.328360\pi$
$797$	28.9917	1.02694	0.513469	+	0.858108i	$0.328360\pi$
$798$	3.30992	0.117170
$799$	−10.3078	−0.364664
$800$	−13.8401	−0.489320
$801$	14.6685	0.518285
$802$	92.0638	3.25088
$803$	−28.7449	−1.01439
$804$	−13.9798	−0.493031
$805$	−9.00681	−0.317448
$806$	−11.6916	−0.411819
$807$	−6.53058	−0.229887
$808$	22.6596	0.797162
$809$	−6.69426	−0.235358	−0.117679	−	0.993052i	$-0.537545\pi$
$809$	−6.69426	−0.235358	−0.117679	+	0.993052i	$0.537545\pi$
$810$	14.8796	0.522816
$811$	−34.5095	−1.21179	−0.605895	−	0.795544i	$-0.707185\pi$
$811$	−34.5095	−1.21179	−0.605895	+	0.795544i	$0.707185\pi$
$812$	93.8646	3.29400
$813$	−0.112765	−0.00395482
$814$	72.5863	2.54415
$815$	21.6338	0.757799
$816$	−1.36876	−0.0479163
$817$	−3.23712	−0.113252
$818$	59.7549	2.08928
$819$	7.50188	0.262137
$820$	31.0304	1.08363
$821$	3.78274	0.132019	0.0660093	−	0.997819i	$-0.478973\pi$
$821$	3.78274	0.132019	0.0660093	+	0.997819i	$0.478973\pi$
$822$	12.3588	0.431062
$823$	15.0426	0.524353	0.262176	−	0.965020i	$-0.415560\pi$
$823$	15.0426	0.524353	0.262176	+	0.965020i	$0.415560\pi$
$824$	2.91469	0.101538
$825$	−7.98552	−0.278020
$826$	34.6155	1.20443
$827$	40.7321	1.41640	0.708198	−	0.706014i	$-0.249509\pi$
$827$	40.7321	1.41640	0.708198	+	0.706014i	$0.249509\pi$
$828$	−28.2589	−0.982065
$829$	38.0532	1.32164	0.660821	−	0.750543i	$-0.270208\pi$
$829$	38.0532	1.32164	0.660821	+	0.750543i	$0.270208\pi$
$830$	−22.1144	−0.767601
$831$	8.38911	0.291015
$832$	9.98913	0.346311
$833$	−4.77440	−0.165423
$834$	29.0257	1.00508
$835$	4.33325	0.149958
$836$	−10.6933	−0.369835
$837$	17.5815	0.607705
$838$	81.4760	2.81454
$839$	39.5841	1.36659	0.683297	−	0.730140i	$-0.260545\pi$
$839$	39.5841	1.36659	0.683297	+	0.730140i	$0.260545\pi$
$840$	6.32727	0.218311
$841$	37.0304	1.27691
$842$	−82.5571	−2.84511
$843$	17.2310	0.593469
$844$	−79.2078	−2.72644
$845$	11.8826	0.408773
$846$	45.6655	1.57001
$847$	7.71187	0.264983
$848$	−15.4166	−0.529409
$849$	11.5171	0.395266
$850$	−13.9149	−0.477277
$851$	−24.2573	−0.831528
$852$	−12.5556	−0.430148
$853$	49.2149	1.68509	0.842544	−	0.538628i	$-0.181057\pi$
$853$	49.2149	1.68509	0.842544	+	0.538628i	$0.181057\pi$
$854$	−35.4829	−1.21420
$855$	−2.13283	−0.0729411
$856$	−51.2214	−1.75071
$857$	−2.04667	−0.0699128	−0.0349564	−	0.999389i	$-0.511129\pi$
$857$	−2.04667	−0.0699128	−0.0349564	+	0.999389i	$0.511129\pi$
$858$	4.01318	0.137008
$859$	28.2244	0.963006	0.481503	−	0.876445i	$-0.340091\pi$
$859$	28.2244	0.963006	0.481503	+	0.876445i	$0.340091\pi$
$860$	−13.9240	−0.474804
$861$	−15.3274	−0.522356
$862$	22.5246	0.767191
$863$	39.5864	1.34754	0.673768	−	0.738943i	$-0.264675\pi$
$863$	39.5864	1.34754	0.673768	+	0.738943i	$0.264675\pi$
$864$	−10.4594	−0.355834
$865$	−10.8389	−0.368533
$866$	40.6195	1.38031
$867$	−8.00606	−0.271900
$868$	−66.1885	−2.24658
$869$	30.3695	1.03022
$870$	10.0153	0.339551
$871$	6.23290	0.211194
$872$	−26.9177	−0.911549
$873$	−6.90543	−0.233713
$874$	5.55892	0.188033
$875$	28.1853	0.952836
$876$	−15.1845	−0.513036
$877$	32.2459	1.08887	0.544433	−	0.838804i	$-0.316745\pi$
$877$	32.2459	1.08887	0.544433	+	0.838804i	$0.316745\pi$
$878$	−56.2095	−1.89698
$879$	10.5818	0.356914
$880$	−6.24397	−0.210484
$881$	−11.9538	−0.402734	−0.201367	−	0.979516i	$-0.564538\pi$
$881$	−11.9538	−0.402734	−0.201367	+	0.979516i	$0.564538\pi$
$882$	21.1515	0.712207
$883$	8.87864	0.298790	0.149395	−	0.988778i	$-0.452267\pi$
$883$	8.87864	0.298790	0.149395	+	0.988778i	$0.452267\pi$
$884$	4.49545	0.151198
$885$	2.37433	0.0798124
$886$	45.7296	1.53631
$887$	−22.8776	−0.768154	−0.384077	−	0.923301i	$-0.625480\pi$
$887$	−22.8776	−0.768154	−0.384077	+	0.923301i	$0.625480\pi$
$888$	17.0407	0.571848
$889$	−42.5180	−1.42601
$890$	−12.4115	−0.416035
$891$	23.7447	0.795476
$892$	−21.5833	−0.722664
$893$	−5.77472	−0.193244
$894$	−22.0926	−0.738886
$895$	−22.1464	−0.740271
$896$	66.0922	2.20799
$897$	−1.34114	−0.0447795
$898$	19.5103	0.651067
$899$	−46.5613	−1.55291
$900$	39.6287	1.32096
$901$	12.6921	0.422837
$902$	77.0292	2.56479
$903$	6.87772	0.228876
$904$	−1.01679	−0.0338181
$905$	−8.83188	−0.293582
$906$	−23.2736	−0.773212
$907$	34.5349	1.14671	0.573356	−	0.819306i	$-0.305641\pi$
$907$	34.5349	1.14671	0.573356	+	0.819306i	$0.305641\pi$
$908$	37.8994	1.25774
$909$	16.2285	0.538265
$910$	−6.34762	−0.210421
$911$	−5.50026	−0.182232	−0.0911158	−	0.995840i	$-0.529043\pi$
$911$	−5.50026	−0.182232	−0.0911158	+	0.995840i	$0.529043\pi$
$912$	−0.766820	−0.0253920
$913$	−35.2899	−1.16792
$914$	2.86339	0.0947126
$915$	−2.43383	−0.0804598
$916$	−49.5406	−1.63687
$917$	−15.7099	−0.518788
$918$	−10.5159	−0.347077
$919$	−6.46397	−0.213227	−0.106613	−	0.994301i	$-0.534001\pi$
$919$	−6.46397	−0.213227	−0.106613	+	0.994301i	$0.534001\pi$
$920$	10.6265	0.350345
$921$	4.84542	0.159662
$922$	−17.0528	−0.561604
$923$	5.59790	0.184257
$924$	22.7194	0.747414
$925$	34.0170	1.11847
$926$	−11.2203	−0.368723
$927$	2.08746	0.0685612
$928$	27.6996	0.909285
$929$	−27.4671	−0.901166	−0.450583	−	0.892735i	$-0.648784\pi$
$929$	−27.4671	−0.901166	−0.450583	+	0.892735i	$0.648784\pi$
$930$	−7.06229	−0.231582
$931$	−2.67475	−0.0876614
$932$	82.8358	2.71338
$933$	−6.67292	−0.218462
$934$	87.8009	2.87293
$935$	5.14051	0.168113
$936$	−8.85093	−0.289302
$937$	43.8053	1.43106	0.715528	−	0.698584i	$-0.246186\pi$
$937$	43.8053	1.43106	0.715528	+	0.698584i	$0.246186\pi$
$938$	54.8898	1.79221
$939$	5.93949	0.193828
$940$	−24.8391	−0.810163
$941$	39.7282	1.29510	0.647552	−	0.762022i	$-0.275793\pi$
$941$	39.7282	1.29510	0.647552	+	0.762022i	$0.275793\pi$
$942$	23.6252	0.769750
$943$	−25.7420	−0.838275
$944$	−8.01951	−0.261013
$945$	9.54536	0.310511
$946$	−34.5646	−1.12379
$947$	−20.5460	−0.667654	−0.333827	−	0.942634i	$-0.608340\pi$
$947$	−20.5460	−0.667654	−0.333827	+	0.942634i	$0.608340\pi$
$948$	16.0427	0.521042
$949$	6.76999	0.219763
$950$	−7.79551	−0.252920
$951$	−7.29311	−0.236495
$952$	17.5941	0.570229
$953$	−19.1422	−0.620078	−0.310039	−	0.950724i	$-0.600342\pi$
$953$	−19.1422	−0.620078	−0.310039	+	0.950724i	$0.600342\pi$
$954$	−56.2286	−1.82047
$955$	−21.0140	−0.679999
$956$	−24.8722	−0.804424
$957$	15.9823	0.516635
$958$	91.6556	2.96126
$959$	−31.1941	−1.00731
$960$	6.03391	0.194744
$961$	1.83262	0.0591169
$962$	−17.0955	−0.551181
$963$	−36.6840	−1.18213
$964$	−25.9653	−0.836285
$965$	−10.9956	−0.353962
$966$	−11.8107	−0.380004
$967$	14.8404	0.477236	0.238618	−	0.971113i	$-0.423306\pi$
$967$	14.8404	0.477236	0.238618	+	0.971113i	$0.423306\pi$
$968$	−9.09868	−0.292443
$969$	0.631305	0.0202804
$970$	5.84294	0.187605
$971$	16.7101	0.536254	0.268127	−	0.963384i	$-0.413595\pi$
$971$	16.7101	0.536254	0.268127	+	0.963384i	$0.413595\pi$
$972$	45.6796	1.46518
$973$	−73.2623	−2.34868
$974$	80.6131	2.58301
$975$	1.88075	0.0602320
$976$	8.22045	0.263130
$977$	9.39460	0.300560	0.150280	−	0.988643i	$-0.451983\pi$
$977$	9.39460	0.300560	0.150280	+	0.988643i	$0.451983\pi$
$978$	28.3686	0.907129
$979$	−19.8062	−0.633007
$980$	−11.5051	−0.367516
$981$	−19.2781	−0.615502
$982$	−88.1796	−2.81392
$983$	2.07551	0.0661983	0.0330992	−	0.999452i	$-0.489462\pi$
$983$	2.07551	0.0661983	0.0330992	+	0.999452i	$0.489462\pi$
$984$	18.0837	0.576488
$985$	−22.1332	−0.705221
$986$	27.8494	0.886907
$987$	12.2692	0.390534
$988$	2.51848	0.0801234
$989$	11.5510	0.367299
$990$	−22.7734	−0.723787
$991$	0.759317	0.0241205	0.0120602	−	0.999927i	$-0.496161\pi$
$991$	0.759317	0.0241205	0.0120602	+	0.999927i	$0.496161\pi$
$992$	−19.5324	−0.620153
$993$	−2.37753	−0.0754487
$994$	49.2977	1.56363
$995$	14.1121	0.447382
$996$	−18.6418	−0.590689
$997$	−42.3679	−1.34180	−0.670902	−	0.741546i	$-0.734093\pi$
$997$	−42.3679	−1.34180	−0.670902	+	0.741546i	$0.734093\pi$
$998$	75.0898	2.37692
$999$	25.7077	0.813355

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4019.2.a.a.1.15	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4019.2.a.a.1.15	✓	149	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:	\( N \)	\(=\)	\( 4019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.36640 q^{2} +0.537231 q^{3} +3.59984 q^{4} -0.969490 q^{5} -1.27130 q^{6} +3.20883 q^{7} -3.78587 q^{8} -2.71138 q^{9} +O(q^{10})\)	\(q-2.36640 q^{2} +0.537231 q^{3} +3.59984 q^{4} -0.969490 q^{5} -1.27130 q^{6} +3.20883 q^{7} -3.78587 q^{8} -2.71138 q^{9} +2.29420 q^{10} +3.66106 q^{11} +1.93395 q^{12} -0.862250 q^{13} -7.59336 q^{14} -0.520841 q^{15} +1.75918 q^{16} -1.44829 q^{17} +6.41621 q^{18} -0.811375 q^{19} -3.49001 q^{20} +1.72388 q^{21} -8.66352 q^{22} +2.89522 q^{23} -2.03389 q^{24} -4.06009 q^{25} +2.04043 q^{26} -3.06833 q^{27} +11.5513 q^{28} +8.12591 q^{29} +1.23252 q^{30} -5.72998 q^{31} +3.40881 q^{32} +1.96683 q^{33} +3.42724 q^{34} -3.11093 q^{35} -9.76055 q^{36} -8.37839 q^{37} +1.92004 q^{38} -0.463228 q^{39} +3.67036 q^{40} -8.89121 q^{41} -4.07939 q^{42} +3.98967 q^{43} +13.1792 q^{44} +2.62866 q^{45} -6.85124 q^{46} +7.11721 q^{47} +0.945088 q^{48} +3.29657 q^{49} +9.60779 q^{50} -0.778068 q^{51} -3.10396 q^{52} -8.76352 q^{53} +7.26090 q^{54} -3.54936 q^{55} -12.1482 q^{56} -0.435896 q^{57} -19.2291 q^{58} -4.55866 q^{59} -1.87494 q^{60} +4.67288 q^{61} +13.5594 q^{62} -8.70036 q^{63} -11.5850 q^{64} +0.835943 q^{65} -4.65431 q^{66} -7.22865 q^{67} -5.21363 q^{68} +1.55540 q^{69} +7.36169 q^{70} -6.49221 q^{71} +10.2649 q^{72} -7.85154 q^{73} +19.8266 q^{74} -2.18121 q^{75} -2.92082 q^{76} +11.7477 q^{77} +1.09618 q^{78} +8.29530 q^{79} -1.70551 q^{80} +6.48574 q^{81} +21.0401 q^{82} -9.63926 q^{83} +6.20570 q^{84} +1.40411 q^{85} -9.44115 q^{86} +4.36549 q^{87} -13.8603 q^{88} -5.40996 q^{89} -6.22045 q^{90} -2.76681 q^{91} +10.4223 q^{92} -3.07832 q^{93} -16.8421 q^{94} +0.786620 q^{95} +1.83132 q^{96} +2.54683 q^{97} -7.80099 q^{98} -9.92652 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9}+O(q^{10}) \) 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9} - 58 q^{10} - 33 q^{11} - 33 q^{12} - 107 q^{13} - 28 q^{14} - 24 q^{15} + 74 q^{16} - 39 q^{17} - 33 q^{18} - 93 q^{19} - 63 q^{20} - 113 q^{21} - 38 q^{22} - 11 q^{23} - 130 q^{24} + 85 q^{25} - 33 q^{26} - 30 q^{27} - 94 q^{28} - 85 q^{29} - 16 q^{30} - 129 q^{31} - 35 q^{32} - 64 q^{33} - 78 q^{34} - 27 q^{35} + 79 q^{36} - 135 q^{37} - 11 q^{38} - 73 q^{39} - 146 q^{40} - 101 q^{41} + 4 q^{42} - 55 q^{43} - 82 q^{44} - 168 q^{45} - 113 q^{46} - 40 q^{47} - 65 q^{48} + 27 q^{49} - 5 q^{50} - 49 q^{51} - 177 q^{52} - 32 q^{53} - 155 q^{54} - 128 q^{55} - 44 q^{56} - 47 q^{57} - 46 q^{58} - 53 q^{59} - 11 q^{60} - 347 q^{61} - 11 q^{62} - 73 q^{63} + q^{64} - 31 q^{65} - 37 q^{66} - 40 q^{67} - 80 q^{68} - 175 q^{69} - 61 q^{70} - 31 q^{71} - 68 q^{72} - 193 q^{73} - 33 q^{74} - 56 q^{75} - 248 q^{76} - 84 q^{77} + 40 q^{78} - 111 q^{79} - 54 q^{80} + 49 q^{81} - 74 q^{82} - 24 q^{83} - 159 q^{84} - 258 q^{85} - q^{86} - 66 q^{87} - 97 q^{88} - 76 q^{89} - 75 q^{90} - 134 q^{91} + 31 q^{92} - 97 q^{93} - 111 q^{94} - 14 q^{95} - 216 q^{96} - 140 q^{97} - 13 q^{98} - 116 q^{99}+O(q^{100}) \) 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9 - 58 * q^10 - 33 * q^11 - 33 * q^12 - 107 * q^13 - 28 * q^14 - 24 * q^15 + 74 * q^16 - 39 * q^17 - 33 * q^18 - 93 * q^19 - 63 * q^20 - 113 * q^21 - 38 * q^22 - 11 * q^23 - 130 * q^24 + 85 * q^25 - 33 * q^26 - 30 * q^27 - 94 * q^28 - 85 * q^29 - 16 * q^30 - 129 * q^31 - 35 * q^32 - 64 * q^33 - 78 * q^34 - 27 * q^35 + 79 * q^36 - 135 * q^37 - 11 * q^38 - 73 * q^39 - 146 * q^40 - 101 * q^41 + 4 * q^42 - 55 * q^43 - 82 * q^44 - 168 * q^45 - 113 * q^46 - 40 * q^47 - 65 * q^48 + 27 * q^49 - 5 * q^50 - 49 * q^51 - 177 * q^52 - 32 * q^53 - 155 * q^54 - 128 * q^55 - 44 * q^56 - 47 * q^57 - 46 * q^58 - 53 * q^59 - 11 * q^60 - 347 * q^61 - 11 * q^62 - 73 * q^63 + q^64 - 31 * q^65 - 37 * q^66 - 40 * q^67 - 80 * q^68 - 175 * q^69 - 61 * q^70 - 31 * q^71 - 68 * q^72 - 193 * q^73 - 33 * q^74 - 56 * q^75 - 248 * q^76 - 84 * q^77 + 40 * q^78 - 111 * q^79 - 54 * q^80 + 49 * q^81 - 74 * q^82 - 24 * q^83 - 159 * q^84 - 258 * q^85 - q^86 - 66 * q^87 - 97 * q^88 - 76 * q^89 - 75 * q^90 - 134 * q^91 + 31 * q^92 - 97 * q^93 - 111 * q^94 - 14 * q^95 - 216 * q^96 - 140 * q^97 - 13 * q^98 - 116 * q^99

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