LMFDB - Embedded newform 6019.2.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, 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("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.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:	$48.0619569766$
Analytic rank:	$1$
Dimension:	$101$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.59744 q^{2} +2.60815 q^{3} +4.74669 q^{4} -0.0717768 q^{5} -6.77450 q^{6} +0.808846 q^{7} -7.13437 q^{8} +3.80242 q^{9} +O(q^{10})$	\(q-2.59744 q^{2} +2.60815 q^{3} +4.74669 q^{4} -0.0717768 q^{5} -6.77450 q^{6} +0.808846 q^{7} -7.13437 q^{8} +3.80242 q^{9} +0.186436 q^{10} -1.73869 q^{11} +12.3801 q^{12} +1.00000 q^{13} -2.10093 q^{14} -0.187204 q^{15} +9.03770 q^{16} -8.05779 q^{17} -9.87656 q^{18} +3.65312 q^{19} -0.340702 q^{20} +2.10959 q^{21} +4.51614 q^{22} -5.38750 q^{23} -18.6075 q^{24} -4.99485 q^{25} -2.59744 q^{26} +2.09283 q^{27} +3.83934 q^{28} +0.715020 q^{29} +0.486252 q^{30} +8.21765 q^{31} -9.20615 q^{32} -4.53476 q^{33} +20.9296 q^{34} -0.0580563 q^{35} +18.0489 q^{36} +2.27692 q^{37} -9.48876 q^{38} +2.60815 q^{39} +0.512082 q^{40} -9.71961 q^{41} -5.47952 q^{42} +8.81960 q^{43} -8.25303 q^{44} -0.272925 q^{45} +13.9937 q^{46} +1.00176 q^{47} +23.5716 q^{48} -6.34577 q^{49} +12.9738 q^{50} -21.0159 q^{51} +4.74669 q^{52} -2.84358 q^{53} -5.43600 q^{54} +0.124798 q^{55} -5.77060 q^{56} +9.52787 q^{57} -1.85722 q^{58} -2.84179 q^{59} -0.888601 q^{60} +3.56239 q^{61} -21.3448 q^{62} +3.07557 q^{63} +5.83701 q^{64} -0.0717768 q^{65} +11.7788 q^{66} -15.8323 q^{67} -38.2479 q^{68} -14.0514 q^{69} +0.150798 q^{70} +8.97175 q^{71} -27.1279 q^{72} +10.0646 q^{73} -5.91415 q^{74} -13.0273 q^{75} +17.3402 q^{76} -1.40633 q^{77} -6.77450 q^{78} -13.7629 q^{79} -0.648697 q^{80} -5.94886 q^{81} +25.2461 q^{82} +13.1692 q^{83} +10.0136 q^{84} +0.578362 q^{85} -22.9084 q^{86} +1.86488 q^{87} +12.4045 q^{88} +5.27736 q^{89} +0.708907 q^{90} +0.808846 q^{91} -25.5728 q^{92} +21.4328 q^{93} -2.60202 q^{94} -0.262209 q^{95} -24.0110 q^{96} -1.33441 q^{97} +16.4828 q^{98} -6.61123 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) $ 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9 - 19 * q^10 - 42 * q^11 - 28 * q^12 + 101 * q^13 - 45 * q^14 - 15 * q^15 + 48 * q^16 - 83 * q^17 - 4 * q^18 - 18 * q^19 - 51 * q^20 - 50 * q^21 - 20 * q^22 - 64 * q^23 - 23 * q^24 + 46 * q^25 - 8 * q^26 - 37 * q^27 - 11 * q^28 - 117 * q^29 - 28 * q^30 - 10 * q^31 - 36 * q^32 - 20 * q^33 - 10 * q^34 - 53 * q^35 - 16 * q^36 - 27 * q^37 - 68 * q^38 - 13 * q^39 - 42 * q^40 - 60 * q^41 - 31 * q^42 - 16 * q^43 - 89 * q^44 - 56 * q^45 + 5 * q^46 - 23 * q^47 - 37 * q^48 + 48 * q^49 - 30 * q^50 - 68 * q^51 + 86 * q^52 - 189 * q^53 - 23 * q^54 + 3 * q^55 - 106 * q^56 - 25 * q^57 - 82 * q^59 + 6 * q^60 - 68 * q^61 - 57 * q^62 + 3 * q^63 - 2 * q^64 - 43 * q^65 - 40 * q^66 - 13 * q^67 - 138 * q^68 - 92 * q^69 + 18 * q^70 - 39 * q^71 - 20 * q^72 + 19 * q^73 - 88 * q^74 - 21 * q^75 - 53 * q^76 - 147 * q^77 - 10 * q^78 - 19 * q^79 - 104 * q^80 - 55 * q^81 + 27 * q^82 - 49 * q^83 - 59 * q^84 - 27 * q^85 - 99 * q^86 - 33 * q^87 - 41 * q^88 - 70 * q^89 - 49 * q^90 - q^91 - 111 * q^92 - 84 * q^93 + 4 * q^94 - 82 * q^95 - 7 * q^96 + 25 * q^97 - 37 * q^98 - 41 * 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 $

$2$	−2.59744	−1.83667	−0.918334	−	0.395807i	$-0.870465\pi$
$2$	−2.59744	−1.83667	−0.918334	+	0.395807i	$0.870465\pi$
$3$	2.60815	1.50581	0.752907	−	0.658127i	$-0.228651\pi$
$3$	2.60815	1.50581	0.752907	+	0.658127i	$0.228651\pi$
$4$	4.74669	2.37335
$5$	−0.0717768	−0.0320995	−0.0160498	−	0.999871i	$-0.505109\pi$
$5$	−0.0717768	−0.0320995	−0.0160498	+	0.999871i	$0.505109\pi$
$6$	−6.77450	−2.76568
$7$	0.808846	0.305715	0.152857	−	0.988248i	$-0.451152\pi$
$7$	0.808846	0.305715	0.152857	+	0.988248i	$0.451152\pi$
$8$	−7.13437	−2.52238
$9$	3.80242	1.26747
$10$	0.186436	0.0589562
$11$	−1.73869	−0.524235	−0.262117	−	0.965036i	$-0.584421\pi$
$11$	−1.73869	−0.524235	−0.262117	+	0.965036i	$0.584421\pi$
$12$	12.3801	3.57382
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−2.10093	−0.561497
$15$	−0.187204	−0.0483359
$16$	9.03770	2.25943
$17$	−8.05779	−1.95430	−0.977151	−	0.212548i	$-0.931824\pi$
$17$	−8.05779	−1.95430	−0.977151	+	0.212548i	$0.931824\pi$
$18$	−9.87656	−2.32793
$19$	3.65312	0.838083	0.419042	−	0.907967i	$-0.362366\pi$
$19$	3.65312	0.838083	0.419042	+	0.907967i	$0.362366\pi$
$20$	−0.340702	−0.0761833
$21$	2.10959	0.460350
$22$	4.51614	0.962845
$23$	−5.38750	−1.12337	−0.561686	−	0.827351i	$-0.689847\pi$
$23$	−5.38750	−1.12337	−0.561686	+	0.827351i	$0.689847\pi$
$24$	−18.6075	−3.79823
$25$	−4.99485	−0.998970
$26$	−2.59744	−0.509400
$27$	2.09283	0.402765
$28$	3.83934	0.725567
$29$	0.715020	0.132776	0.0663880	−	0.997794i	$-0.478853\pi$
$29$	0.715020	0.132776	0.0663880	+	0.997794i	$0.478853\pi$
$30$	0.486252	0.0887770
$31$	8.21765	1.47593	0.737966	−	0.674837i	$-0.235786\pi$
$31$	8.21765	1.47593	0.737966	+	0.674837i	$0.235786\pi$
$32$	−9.20615	−1.62743
$33$	−4.53476	−0.789400
$34$	20.9296	3.58940
$35$	−0.0580563	−0.00981331
$36$	18.0489	3.00815
$37$	2.27692	0.374323	0.187161	−	0.982329i	$-0.440071\pi$
$37$	2.27692	0.374323	0.187161	+	0.982329i	$0.440071\pi$
$38$	−9.48876	−1.53928
$39$	2.60815	0.417637
$40$	0.512082	0.0809672
$41$	−9.71961	−1.51795	−0.758974	−	0.651121i	$-0.774299\pi$
$41$	−9.71961	−1.51795	−0.758974	+	0.651121i	$0.774299\pi$
$42$	−5.47952	−0.845509
$43$	8.81960	1.34498	0.672488	−	0.740108i	$-0.265226\pi$
$43$	8.81960	1.34498	0.672488	+	0.740108i	$0.265226\pi$
$44$	−8.25303	−1.24419
$45$	−0.272925	−0.0406853
$46$	13.9937	2.06326
$47$	1.00176	0.146122	0.0730610	−	0.997327i	$-0.476723\pi$
$47$	1.00176	0.146122	0.0730610	+	0.997327i	$0.476723\pi$
$48$	23.5716	3.40227
$49$	−6.34577	−0.906538
$50$	12.9738	1.83477
$51$	−21.0159	−2.94281
$52$	4.74669	0.658248
$53$	−2.84358	−0.390596	−0.195298	−	0.980744i	$-0.562567\pi$
$53$	−2.84358	−0.390596	−0.195298	+	0.980744i	$0.562567\pi$
$54$	−5.43600	−0.739746
$55$	0.124798	0.0168277
$56$	−5.77060	−0.771129
$57$	9.52787	1.26200
$58$	−1.85722	−0.243865
$59$	−2.84179	−0.369969	−0.184985	−	0.982741i	$-0.559224\pi$
$59$	−2.84179	−0.369969	−0.184985	+	0.982741i	$0.559224\pi$
$60$	−0.888601	−0.114718
$61$	3.56239	0.456118	0.228059	−	0.973647i	$-0.426762\pi$
$61$	3.56239	0.456118	0.228059	+	0.973647i	$0.426762\pi$
$62$	−21.3448	−2.71080
$63$	3.07557	0.387486
$64$	5.83701	0.729626
$65$	−0.0717768	−0.00890281
$66$	11.7788	1.44986
$67$	−15.8323	−1.93422	−0.967112	−	0.254352i	$-0.918138\pi$
$67$	−15.8323	−1.93422	−0.967112	+	0.254352i	$0.918138\pi$
$68$	−38.2479	−4.63823
$69$	−14.0514	−1.69159
$70$	0.150798	0.0180238
$71$	8.97175	1.06475	0.532375	−	0.846508i	$-0.321299\pi$
$71$	8.97175	1.06475	0.532375	+	0.846508i	$0.321299\pi$
$72$	−27.1279	−3.19705
$73$	10.0646	1.17797	0.588986	−	0.808143i	$-0.299527\pi$
$73$	10.0646	1.17797	0.588986	+	0.808143i	$0.299527\pi$
$74$	−5.91415	−0.687506
$75$	−13.0273	−1.50426
$76$	17.3402	1.98906
$77$	−1.40633	−0.160266
$78$	−6.77450	−0.767061
$79$	−13.7629	−1.54845	−0.774224	−	0.632912i	$-0.781859\pi$
$79$	−13.7629	−1.54845	−0.774224	+	0.632912i	$0.781859\pi$
$80$	−0.648697	−0.0725265
$81$	−5.94886	−0.660984
$82$	25.2461	2.78797
$83$	13.1692	1.44551	0.722755	−	0.691104i	$-0.242875\pi$
$83$	13.1692	1.44551	0.722755	+	0.691104i	$0.242875\pi$
$84$	10.0136	1.09257
$85$	0.578362	0.0627322
$86$	−22.9084	−2.47027
$87$	1.86488	0.199936
$88$	12.4045	1.32232
$89$	5.27736	0.559399	0.279700	−	0.960088i	$-0.409765\pi$
$89$	5.27736	0.559399	0.279700	+	0.960088i	$0.409765\pi$
$90$	0.708907	0.0747254
$91$	0.808846	0.0847901
$92$	−25.5728	−2.66615
$93$	21.4328	2.22248
$94$	−2.60202	−0.268377
$95$	−0.262209	−0.0269021
$96$	−24.0110	−2.45061
$97$	−1.33441	−0.135489	−0.0677444	−	0.997703i	$-0.521580\pi$
$97$	−1.33441	−0.135489	−0.0677444	+	0.997703i	$0.521580\pi$
$98$	16.4828	1.66501
$99$	−6.61123	−0.664454
$100$	−23.7090	−2.37090
$101$	−11.1155	−1.10603	−0.553015	−	0.833172i	$-0.686523\pi$
$101$	−11.1155	−1.10603	−0.553015	+	0.833172i	$0.686523\pi$
$102$	54.5875	5.40497
$103$	−15.0725	−1.48514	−0.742569	−	0.669770i	$-0.766393\pi$
$103$	−15.0725	−1.48514	−0.742569	+	0.669770i	$0.766393\pi$
$104$	−7.13437	−0.699582
$105$	−0.151419	−0.0147770
$106$	7.38603	0.717394
$107$	12.7342	1.23106	0.615531	−	0.788113i	$-0.288942\pi$
$107$	12.7342	1.23106	0.615531	+	0.788113i	$0.288942\pi$
$108$	9.93402	0.955901
$109$	−1.97313	−0.188992	−0.0944958	−	0.995525i	$-0.530124\pi$
$109$	−1.97313	−0.188992	−0.0944958	+	0.995525i	$0.530124\pi$
$110$	−0.324154	−0.0309069
$111$	5.93853	0.563660
$112$	7.31010	0.690740
$113$	2.03744	0.191666	0.0958330	−	0.995397i	$-0.469449\pi$
$113$	2.03744	0.191666	0.0958330	+	0.995397i	$0.469449\pi$
$114$	−24.7481	−2.31787
$115$	0.386697	0.0360597
$116$	3.39398	0.315123
$117$	3.80242	0.351534
$118$	7.38137	0.679511
$119$	−6.51751	−0.597459
$120$	1.33558	0.121922
$121$	−7.97696	−0.725178
$122$	−9.25310	−0.837737
$123$	−25.3502	−2.28575
$124$	39.0066	3.50290
$125$	0.717398	0.0641660
$126$	−7.98861	−0.711682
$127$	8.31869	0.738164	0.369082	−	0.929397i	$-0.379672\pi$
$127$	8.31869	0.738164	0.369082	+	0.929397i	$0.379672\pi$
$128$	3.25101	0.287352
$129$	23.0028	2.02528
$130$	0.186436	0.0163515
$131$	−21.8566	−1.90962	−0.954811	−	0.297215i	$-0.903942\pi$
$131$	−21.8566	−1.90962	−0.954811	+	0.297215i	$0.903942\pi$
$132$	−21.5251	−1.87352
$133$	2.95481	0.256214
$134$	41.1234	3.55252
$135$	−0.150217	−0.0129286
$136$	57.4872	4.92949
$137$	−10.9943	−0.939308	−0.469654	−	0.882851i	$-0.655621\pi$
$137$	−10.9943	−0.939308	−0.469654	+	0.882851i	$0.655621\pi$
$138$	36.4976	3.10688
$139$	−9.35352	−0.793356	−0.396678	−	0.917958i	$-0.629837\pi$
$139$	−9.35352	−0.793356	−0.396678	+	0.917958i	$0.629837\pi$
$140$	−0.275575	−0.0232904
$141$	2.61274	0.220032
$142$	−23.3036	−1.95559
$143$	−1.73869	−0.145397
$144$	34.3651	2.86376
$145$	−0.0513218	−0.00426205
$146$	−26.1422	−2.16354
$147$	−16.5507	−1.36508
$148$	10.8078	0.888398
$149$	−9.34658	−0.765702	−0.382851	−	0.923810i	$-0.625058\pi$
$149$	−9.34658	−0.765702	−0.382851	+	0.923810i	$0.625058\pi$
$150$	33.8376	2.76283
$151$	−3.51256	−0.285848	−0.142924	−	0.989734i	$-0.545650\pi$
$151$	−3.51256	−0.285848	−0.142924	+	0.989734i	$0.545650\pi$
$152$	−26.0627	−2.11396
$153$	−30.6391	−2.47703
$154$	3.65286	0.294356
$155$	−0.589836	−0.0473768
$156$	12.3801	0.991198
$157$	19.7447	1.57580	0.787898	−	0.615805i	$-0.211169\pi$
$157$	19.7447	1.57580	0.787898	+	0.615805i	$0.211169\pi$
$158$	35.7483	2.84398
$159$	−7.41647	−0.588164
$160$	0.660788	0.0522398
$161$	−4.35765	−0.343431
$162$	15.4518	1.21401
$163$	−16.8302	−1.31824	−0.659122	−	0.752036i	$-0.729072\pi$
$163$	−16.8302	−1.31824	−0.659122	+	0.752036i	$0.729072\pi$
$164$	−46.1360	−3.60262
$165$	0.325490	0.0253394
$166$	−34.2063	−2.65492
$167$	4.84028	0.374552	0.187276	−	0.982307i	$-0.440034\pi$
$167$	4.84028	0.374552	0.187276	+	0.982307i	$0.440034\pi$
$168$	−15.0506	−1.16118
$169$	1.00000	0.0769231
$170$	−1.50226	−0.115218
$171$	13.8907	1.06225
$172$	41.8639	3.19209
$173$	20.8807	1.58753	0.793763	−	0.608227i	$-0.208119\pi$
$173$	20.8807	1.58753	0.793763	+	0.608227i	$0.208119\pi$
$174$	−4.84390	−0.367215
$175$	−4.04006	−0.305400
$176$	−15.7138	−1.18447
$177$	−7.41180	−0.557105
$178$	−13.7076	−1.02743
$179$	−8.38823	−0.626966	−0.313483	−	0.949594i	$-0.601496\pi$
$179$	−8.38823	−0.626966	−0.313483	+	0.949594i	$0.601496\pi$
$180$	−1.29549	−0.0965604
$181$	1.04457	0.0776422	0.0388211	−	0.999246i	$-0.487640\pi$
$181$	1.04457	0.0776422	0.0388211	+	0.999246i	$0.487640\pi$
$182$	−2.10093	−0.155731
$183$	9.29124	0.686828
$184$	38.4364	2.83357
$185$	−0.163430	−0.0120156
$186$	−55.6704	−4.08195
$187$	14.0100	1.02451
$188$	4.75505	0.346798
$189$	1.69278	0.123131
$190$	0.681072	0.0494102
$191$	−9.25592	−0.669735	−0.334867	−	0.942265i	$-0.608692\pi$
$191$	−9.25592	−0.669735	−0.334867	+	0.942265i	$0.608692\pi$
$192$	15.2238	1.09868
$193$	−24.2278	−1.74395	−0.871976	−	0.489548i	$-0.837162\pi$
$193$	−24.2278	−1.74395	−0.871976	+	0.489548i	$0.837162\pi$
$194$	3.46605	0.248848
$195$	−0.187204	−0.0134060
$196$	−30.1214	−2.15153
$197$	−25.1639	−1.79286	−0.896428	−	0.443190i	$-0.853847\pi$
$197$	−25.1639	−1.79286	−0.896428	+	0.443190i	$0.853847\pi$
$198$	17.1723	1.22038
$199$	−17.5442	−1.24367	−0.621836	−	0.783148i	$-0.713613\pi$
$199$	−17.5442	−1.24367	−0.621836	+	0.783148i	$0.713613\pi$
$200$	35.6351	2.51978
$201$	−41.2929	−2.91258
$202$	28.8717	2.03141
$203$	0.578341	0.0405916
$204$	−99.7559	−6.98431
$205$	0.697642	0.0487254
$206$	39.1499	2.72770
$207$	−20.4855	−1.42384
$208$	9.03770	0.626652
$209$	−6.35164	−0.439352
$210$	0.393303	0.0271405
$211$	−16.1970	−1.11505	−0.557524	−	0.830161i	$-0.688248\pi$
$211$	−16.1970	−1.11505	−0.557524	+	0.830161i	$0.688248\pi$
$212$	−13.4976	−0.927019
$213$	23.3996	1.60332
$214$	−33.0763	−2.26105
$215$	−0.633042	−0.0431731
$216$	−14.9310	−1.01593
$217$	6.64681	0.451215
$218$	5.12509	0.347115
$219$	26.2499	1.77381
$220$	0.592376	0.0399380
$221$	−8.05779	−0.542026
$222$	−15.4250	−1.03526
$223$	−17.7798	−1.19063	−0.595313	−	0.803494i	$-0.702972\pi$
$223$	−17.7798	−1.19063	−0.595313	+	0.803494i	$0.702972\pi$
$224$	−7.44635	−0.497530
$225$	−18.9925	−1.26617
$226$	−5.29212	−0.352027
$227$	−16.9981	−1.12820	−0.564101	−	0.825706i	$-0.690777\pi$
$227$	−16.9981	−1.12820	−0.564101	+	0.825706i	$0.690777\pi$
$228$	45.2258	2.99515
$229$	−18.8219	−1.24379	−0.621893	−	0.783102i	$-0.713636\pi$
$229$	−18.8219	−1.24379	−0.621893	+	0.783102i	$0.713636\pi$
$230$	−1.00442	−0.0662297
$231$	−3.66792	−0.241331
$232$	−5.10122	−0.334911
$233$	16.2962	1.06760	0.533800	−	0.845611i	$-0.320764\pi$
$233$	16.2962	1.06760	0.533800	+	0.845611i	$0.320764\pi$
$234$	−9.87656	−0.645651
$235$	−0.0719032	−0.00469045
$236$	−13.4891	−0.878065
$237$	−35.8956	−2.33167
$238$	16.9288	1.09733
$239$	−7.00649	−0.453212	−0.226606	−	0.973986i	$-0.572763\pi$
$239$	−7.00649	−0.453212	−0.226606	+	0.973986i	$0.572763\pi$
$240$	−1.69190	−0.109211
$241$	17.2041	1.10822	0.554108	−	0.832445i	$-0.313059\pi$
$241$	17.2041	1.10822	0.554108	+	0.832445i	$0.313059\pi$
$242$	20.7197	1.33191
$243$	−21.7940	−1.39808
$244$	16.9096	1.08253
$245$	0.455479	0.0290995
$246$	65.8455	4.19816
$247$	3.65312	0.232442
$248$	−58.6277	−3.72286
$249$	34.3473	2.17667
$250$	−1.86340	−0.117852
$251$	−17.7248	−1.11878	−0.559391	−	0.828904i	$-0.688965\pi$
$251$	−17.7248	−1.11878	−0.559391	+	0.828904i	$0.688965\pi$
$252$	14.5988	0.919637
$253$	9.36719	0.588910
$254$	−21.6073	−1.35576
$255$	1.50845	0.0944630
$256$	−20.1183	−1.25740
$257$	−8.46346	−0.527936	−0.263968	−	0.964531i	$-0.585031\pi$
$257$	−8.46346	−0.527936	−0.263968	+	0.964531i	$0.585031\pi$
$258$	−59.7484	−3.71977
$259$	1.84167	0.114436
$260$	−0.340702	−0.0211295
$261$	2.71881	0.168290
$262$	56.7712	3.50734
$263$	22.4335	1.38331	0.691654	−	0.722229i	$-0.256882\pi$
$263$	22.4335	1.38331	0.691654	+	0.722229i	$0.256882\pi$
$264$	32.3526	1.99117
$265$	0.204103	0.0125379
$266$	−7.67494	−0.470581
$267$	13.7641	0.842350
$268$	−75.1511	−4.59058
$269$	6.45852	0.393783	0.196892	−	0.980425i	$-0.436915\pi$
$269$	6.45852	0.393783	0.196892	+	0.980425i	$0.436915\pi$
$270$	0.390178	0.0237455
$271$	−20.7421	−1.25999	−0.629996	−	0.776598i	$-0.716943\pi$
$271$	−20.7421	−1.25999	−0.629996	+	0.776598i	$0.716943\pi$
$272$	−72.8239	−4.41560
$273$	2.10959	0.127678
$274$	28.5571	1.72520
$275$	8.68449	0.523695
$276$	−66.6976	−4.01472
$277$	2.11064	0.126816	0.0634080	−	0.997988i	$-0.479803\pi$
$277$	2.11064	0.126816	0.0634080	+	0.997988i	$0.479803\pi$
$278$	24.2952	1.45713
$279$	31.2469	1.87071
$280$	0.414195	0.0247529
$281$	24.3904	1.45501	0.727506	−	0.686101i	$-0.240679\pi$
$281$	24.3904	1.45501	0.727506	+	0.686101i	$0.240679\pi$
$282$	−6.78643	−0.404126
$283$	9.65537	0.573952	0.286976	−	0.957938i	$-0.407350\pi$
$283$	9.65537	0.573952	0.286976	+	0.957938i	$0.407350\pi$
$284$	42.5861	2.52702
$285$	−0.683879	−0.0405095
$286$	4.51614	0.267045
$287$	−7.86166	−0.464059
$288$	−35.0056	−2.06273
$289$	47.9280	2.81929
$290$	0.133305	0.00782796
$291$	−3.48034	−0.204021
$292$	47.7736	2.79574
$293$	5.86309	0.342526	0.171263	−	0.985225i	$-0.445215\pi$
$293$	5.86309	0.342526	0.171263	+	0.985225i	$0.445215\pi$
$294$	42.9894	2.50719
$295$	0.203974	0.0118758
$296$	−16.2444	−0.944184
$297$	−3.63878	−0.211144
$298$	24.2772	1.40634
$299$	−5.38750	−0.311567
$300$	−61.8365	−3.57013
$301$	7.13369	0.411179
$302$	9.12367	0.525008
$303$	−28.9907	−1.66547
$304$	33.0158	1.89359
$305$	−0.255697	−0.0146412
$306$	79.5832	4.54947
$307$	−18.9749	−1.08295	−0.541477	−	0.840716i	$-0.682135\pi$
$307$	−18.9749	−1.08295	−0.541477	+	0.840716i	$0.682135\pi$
$308$	−6.67543	−0.380368
$309$	−39.3113	−2.23634
$310$	1.53206	0.0870154
$311$	−13.8718	−0.786599	−0.393299	−	0.919410i	$-0.628666\pi$
$311$	−13.8718	−0.786599	−0.393299	+	0.919410i	$0.628666\pi$
$312$	−18.6075	−1.05344
$313$	−17.1416	−0.968898	−0.484449	−	0.874820i	$-0.660980\pi$
$313$	−17.1416	−0.968898	−0.484449	+	0.874820i	$0.660980\pi$
$314$	−51.2856	−2.89421
$315$	−0.220755	−0.0124381
$316$	−65.3282	−3.67500
$317$	27.8063	1.56176	0.780880	−	0.624681i	$-0.214771\pi$
$317$	27.8063	1.56176	0.780880	+	0.624681i	$0.214771\pi$
$318$	19.2638	1.08026
$319$	−1.24320	−0.0696058
$320$	−0.418962	−0.0234207
$321$	33.2126	1.85375
$322$	11.3187	0.630769
$323$	−29.4361	−1.63787
$324$	−28.2374	−1.56874
$325$	−4.99485	−0.277064
$326$	43.7155	2.42118
$327$	−5.14621	−0.284586
$328$	69.3433	3.82884
$329$	0.810271	0.0446717
$330$	−0.845441	−0.0465400
$331$	−24.3611	−1.33901	−0.669503	−	0.742809i	$-0.733493\pi$
$331$	−24.3611	−1.33901	−0.669503	+	0.742809i	$0.733493\pi$
$332$	62.5103	3.43070
$333$	8.65780	0.474444
$334$	−12.5723	−0.687928
$335$	1.13639	0.0620877
$336$	19.0658	1.04013
$337$	−11.0505	−0.601957	−0.300978	−	0.953631i	$-0.597313\pi$
$337$	−11.0505	−0.601957	−0.300978	+	0.953631i	$0.597313\pi$
$338$	−2.59744	−0.141282
$339$	5.31393	0.288613
$340$	2.74531	0.148885
$341$	−14.2879	−0.773736
$342$	−36.0802	−1.95100
$343$	−10.7947	−0.582857
$344$	−62.9222	−3.39254
$345$	1.00856	0.0542992
$346$	−54.2362	−2.91576
$347$	30.4020	1.63206	0.816031	−	0.578008i	$-0.196170\pi$
$347$	30.4020	1.63206	0.816031	+	0.578008i	$0.196170\pi$
$348$	8.85199	0.474517
$349$	28.5079	1.52599	0.762997	−	0.646403i	$-0.223727\pi$
$349$	28.5079	1.52599	0.762997	+	0.646403i	$0.223727\pi$
$350$	10.4938	0.560918
$351$	2.09283	0.111707
$352$	16.0066	0.853157
$353$	13.2730	0.706452	0.353226	−	0.935538i	$-0.385085\pi$
$353$	13.2730	0.706452	0.353226	+	0.935538i	$0.385085\pi$
$354$	19.2517	1.02322
$355$	−0.643963	−0.0341780
$356$	25.0500	1.32765
$357$	−16.9986	−0.899662
$358$	21.7879	1.15153
$359$	26.0096	1.37273	0.686367	−	0.727255i	$-0.259204\pi$
$359$	26.0096	1.37273	0.686367	+	0.727255i	$0.259204\pi$
$360$	1.94715	0.102624
$361$	−5.65472	−0.297617
$362$	−2.71320	−0.142603
$363$	−20.8051	−1.09198
$364$	3.83934	0.201236
$365$	−0.722405	−0.0378124
$366$	−24.1334	−1.26148
$367$	−2.52550	−0.131830	−0.0659150	−	0.997825i	$-0.520997\pi$
$367$	−2.52550	−0.131830	−0.0659150	+	0.997825i	$0.520997\pi$
$368$	−48.6906	−2.53817
$369$	−36.9580	−1.92396
$370$	0.424499	0.0220686
$371$	−2.30002	−0.119411
$372$	101.735	5.27471
$373$	27.0972	1.40304	0.701521	−	0.712649i	$-0.252505\pi$
$373$	27.0972	1.40304	0.701521	+	0.712649i	$0.252505\pi$
$374$	−36.3901	−1.88169
$375$	1.87108	0.0966220
$376$	−7.14693	−0.368575
$377$	0.715020	0.0368254
$378$	−4.39688	−0.226151
$379$	−17.9152	−0.920242	−0.460121	−	0.887856i	$-0.652194\pi$
$379$	−17.9152	−0.920242	−0.460121	+	0.887856i	$0.652194\pi$
$380$	−1.24463	−0.0638480
$381$	21.6963	1.11154
$382$	24.0417	1.23008
$383$	32.8776	1.67997	0.839984	−	0.542611i	$-0.182564\pi$
$383$	32.8776	1.67997	0.839984	+	0.542611i	$0.182564\pi$
$384$	8.47911	0.432698
$385$	0.100942	0.00514448
$386$	62.9302	3.20306
$387$	33.5358	1.70472
$388$	−6.33404	−0.321562
$389$	−18.5000	−0.937987	−0.468994	−	0.883202i	$-0.655383\pi$
$389$	−18.5000	−0.937987	−0.468994	+	0.883202i	$0.655383\pi$
$390$	0.486252	0.0246223
$391$	43.4113	2.19541
$392$	45.2730	2.28663
$393$	−57.0052	−2.87553
$394$	65.3618	3.29288
$395$	0.987857	0.0497045
$396$	−31.3815	−1.57698
$397$	12.9141	0.648142	0.324071	−	0.946033i	$-0.394948\pi$
$397$	12.9141	0.648142	0.324071	+	0.946033i	$0.394948\pi$
$398$	45.5699	2.28421
$399$	7.70657	0.385811
$400$	−45.1419	−2.25710
$401$	−35.7276	−1.78415	−0.892075	−	0.451886i	$-0.850751\pi$
$401$	−35.7276	−1.78415	−0.892075	+	0.451886i	$0.850751\pi$
$402$	107.256	5.34944
$403$	8.21765	0.409350
$404$	−52.7616	−2.62499
$405$	0.426990	0.0212173
$406$	−1.50221	−0.0745532
$407$	−3.95885	−0.196233
$408$	149.935	7.42289
$409$	17.9473	0.887435	0.443717	−	0.896167i	$-0.353659\pi$
$409$	17.9473	0.887435	0.443717	+	0.896167i	$0.353659\pi$
$410$	−1.81208	−0.0894924
$411$	−28.6748	−1.41442
$412$	−71.5445	−3.52475
$413$	−2.29857	−0.113105
$414$	53.2099	2.61513
$415$	−0.945245	−0.0464002
$416$	−9.20615	−0.451369
$417$	−24.3953	−1.19465
$418$	16.4980	0.806944
$419$	27.1617	1.32694	0.663469	−	0.748204i	$-0.269084\pi$
$419$	27.1617	1.32694	0.663469	+	0.748204i	$0.269084\pi$
$420$	−0.718741	−0.0350710
$421$	29.9522	1.45978	0.729891	−	0.683564i	$-0.239571\pi$
$421$	29.9522	1.45978	0.729891	+	0.683564i	$0.239571\pi$
$422$	42.0707	2.04797
$423$	3.80912	0.185206
$424$	20.2871	0.985231
$425$	40.2474	1.95229
$426$	−60.7791	−2.94476
$427$	2.88143	0.139442
$428$	60.4453	2.92174
$429$	−4.53476	−0.218940
$430$	1.64429	0.0792946
$431$	−13.7698	−0.663269	−0.331635	−	0.943408i	$-0.607600\pi$
$431$	−13.7698	−0.663269	−0.331635	+	0.943408i	$0.607600\pi$
$432$	18.9144	0.910018
$433$	−21.1583	−1.01680	−0.508401	−	0.861120i	$-0.669763\pi$
$433$	−21.1583	−1.01680	−0.508401	+	0.861120i	$0.669763\pi$
$434$	−17.2647	−0.828731
$435$	−0.133855	−0.00641785
$436$	−9.36584	−0.448542
$437$	−19.6812	−0.941478
$438$	−68.1827	−3.25789
$439$	−1.61165	−0.0769200	−0.0384600	−	0.999260i	$-0.512245\pi$
$439$	−1.61165	−0.0769200	−0.0384600	+	0.999260i	$0.512245\pi$
$440$	−0.890352	−0.0424459
$441$	−24.1293	−1.14901
$442$	20.9296	0.995521
$443$	12.7253	0.604595	0.302298	−	0.953214i	$-0.402246\pi$
$443$	12.7253	0.604595	0.302298	+	0.953214i	$0.402246\pi$
$444$	28.1884	1.33776
$445$	−0.378792	−0.0179565
$446$	46.1820	2.18678
$447$	−24.3772	−1.15300
$448$	4.72124	0.223058
$449$	−14.0757	−0.664272	−0.332136	−	0.943232i	$-0.607769\pi$
$449$	−14.0757	−0.664272	−0.332136	+	0.943232i	$0.607769\pi$
$450$	49.3319	2.32553
$451$	16.8994	0.795761
$452$	9.67109	0.454890
$453$	−9.16127	−0.430434
$454$	44.1515	2.07213
$455$	−0.0580563	−0.00272172
$456$	−67.9753	−3.18323
$457$	−4.14600	−0.193942	−0.0969709	−	0.995287i	$-0.530915\pi$
$457$	−4.14600	−0.193942	−0.0969709	+	0.995287i	$0.530915\pi$
$458$	48.8888	2.28442
$459$	−16.8636	−0.787125
$460$	1.83553	0.0855822
$461$	5.98849	0.278912	0.139456	−	0.990228i	$-0.455465\pi$
$461$	5.98849	0.278912	0.139456	+	0.990228i	$0.455465\pi$
$462$	9.52720	0.443245
$463$	1.00000	0.0464739
$463$	1.00000	0.0464739
$464$	6.46214	0.299997
$465$	−1.53838	−0.0713406
$466$	−42.3284	−1.96082
$467$	5.14198	0.237943	0.118971	−	0.992898i	$-0.462040\pi$
$467$	5.14198	0.237943	0.118971	+	0.992898i	$0.462040\pi$
$468$	18.0489	0.834312
$469$	−12.8059	−0.591321
$470$	0.186764	0.00861479
$471$	51.4970	2.37286
$472$	20.2744	0.933203
$473$	−15.3346	−0.705083
$474$	93.2368	4.28251
$475$	−18.2468	−0.837220
$476$	−30.9366	−1.41798
$477$	−10.8125	−0.495070
$478$	18.1989	0.832400
$479$	−8.89941	−0.406624	−0.203312	−	0.979114i	$-0.565171\pi$
$479$	−8.89941	−0.406624	−0.203312	+	0.979114i	$0.565171\pi$
$480$	1.72343	0.0786634
$481$	2.27692	0.103818
$482$	−44.6867	−2.03542
$483$	−11.3654	−0.517143
$484$	−37.8641	−1.72110
$485$	0.0957797	0.00434913
$486$	56.6085	2.56782
$487$	33.7585	1.52974	0.764871	−	0.644184i	$-0.222803\pi$
$487$	33.7585	1.52974	0.764871	+	0.644184i	$0.222803\pi$
$488$	−25.4154	−1.15050
$489$	−43.8956	−1.98503
$490$	−1.18308	−0.0534460
$491$	14.9638	0.675307	0.337653	−	0.941271i	$-0.390367\pi$
$491$	14.9638	0.675307	0.337653	+	0.941271i	$0.390367\pi$
$492$	−120.329	−5.42487
$493$	−5.76148	−0.259484
$494$	−9.48876	−0.426919
$495$	0.474533	0.0213287
$496$	74.2686	3.33476
$497$	7.25676	0.325510
$498$	−89.2149	−3.99782
$499$	42.5262	1.90374	0.951868	−	0.306509i	$-0.0991611\pi$
$499$	42.5262	1.90374	0.951868	+	0.306509i	$0.0991611\pi$
$500$	3.40527	0.152288
$501$	12.6242	0.564006
$502$	46.0392	2.05483
$503$	−26.7097	−1.19093	−0.595464	−	0.803382i	$-0.703032\pi$
$503$	−26.7097	−1.19093	−0.595464	+	0.803382i	$0.703032\pi$
$504$	−21.9423	−0.977386
$505$	0.797832	0.0355030
$506$	−24.3307	−1.08163
$507$	2.60815	0.115832
$508$	39.4863	1.75192
$509$	−7.38104	−0.327159	−0.163579	−	0.986530i	$-0.552304\pi$
$509$	−7.38104	−0.327159	−0.163579	+	0.986530i	$0.552304\pi$
$510$	−3.91811	−0.173497
$511$	8.14071	0.360124
$512$	45.7541	2.02207
$513$	7.64536	0.337551
$514$	21.9833	0.969643
$515$	1.08186	0.0476722
$516$	109.187	4.80670
$517$	−1.74175	−0.0766022
$518$	−4.78364	−0.210181
$519$	54.4598	2.39052
$520$	0.512082	0.0224563
$521$	−38.3569	−1.68045	−0.840224	−	0.542239i	$-0.817577\pi$
$521$	−38.3569	−1.68045	−0.840224	+	0.542239i	$0.817577\pi$
$522$	−7.06194	−0.309093
$523$	21.0182	0.919062	0.459531	−	0.888162i	$-0.348017\pi$
$523$	21.0182	0.919062	0.459531	+	0.888162i	$0.348017\pi$
$524$	−103.747	−4.53219
$525$	−10.5371	−0.459875
$526$	−58.2696	−2.54068
$527$	−66.2161	−2.88442
$528$	−40.9838	−1.78359
$529$	6.02514	0.261963
$530$	−0.530145	−0.0230280
$531$	−10.8057	−0.468926
$532$	14.0256	0.608086
$533$	−9.71961	−0.421003
$534$	−35.7515	−1.54712
$535$	−0.914020	−0.0395165
$536$	112.953	4.87884
$537$	−21.8777	−0.944094
$538$	−16.7756	−0.723248
$539$	11.0333	0.475239
$540$	−0.713032	−0.0306840
$541$	−4.24866	−0.182664	−0.0913320	−	0.995821i	$-0.529112\pi$
$541$	−4.24866	−0.182664	−0.0913320	+	0.995821i	$0.529112\pi$
$542$	53.8763	2.31419
$543$	2.72439	0.116915
$544$	74.1812	3.18049
$545$	0.141625	0.00606654
$546$	−5.47952	−0.234502
$547$	−14.3040	−0.611594	−0.305797	−	0.952097i	$-0.598923\pi$
$547$	−14.3040	−0.611594	−0.305797	+	0.952097i	$0.598923\pi$
$548$	−52.1866	−2.22930
$549$	13.5457	0.578117
$550$	−22.5575	−0.961853
$551$	2.61205	0.111277
$552$	100.248	4.26682
$553$	−11.1321	−0.473383
$554$	−5.48226	−0.232919
$555$	−0.426248	−0.0180932
$556$	−44.3983	−1.88291
$557$	14.5796	0.617758	0.308879	−	0.951101i	$-0.400046\pi$
$557$	14.5796	0.617758	0.308879	+	0.951101i	$0.400046\pi$
$558$	−81.1621	−3.43586
$559$	8.81960	0.373029
$560$	−0.524696	−0.0221724
$561$	36.5401	1.54273
$562$	−63.3527	−2.67237
$563$	−23.2918	−0.981631	−0.490815	−	0.871264i	$-0.663301\pi$
$563$	−23.2918	−0.981631	−0.490815	+	0.871264i	$0.663301\pi$
$564$	12.4019	0.522213
$565$	−0.146241	−0.00615239
$566$	−25.0792	−1.05416
$567$	−4.81171	−0.202073
$568$	−64.0078	−2.68571
$569$	−12.2361	−0.512963	−0.256481	−	0.966549i	$-0.582563\pi$
$569$	−12.2361	−0.512963	−0.256481	+	0.966549i	$0.582563\pi$
$570$	1.77634	0.0744025
$571$	6.29019	0.263236	0.131618	−	0.991300i	$-0.457983\pi$
$571$	6.29019	0.263236	0.131618	+	0.991300i	$0.457983\pi$
$572$	−8.25303	−0.345076
$573$	−24.1408	−1.00850
$574$	20.4202	0.852323
$575$	26.9097	1.12221
$576$	22.1948	0.924782
$577$	32.6533	1.35937	0.679687	−	0.733502i	$-0.262116\pi$
$577$	32.6533	1.35937	0.679687	+	0.733502i	$0.262116\pi$
$578$	−124.490	−5.17810
$579$	−63.1895	−2.62607
$580$	−0.243609	−0.0101153
$581$	10.6519	0.441914
$582$	9.03996	0.374719
$583$	4.94411	0.204764
$584$	−71.8046	−2.97129
$585$	−0.272925	−0.0112841
$586$	−15.2290	−0.629105
$587$	30.9828	1.27880	0.639399	−	0.768875i	$-0.279183\pi$
$587$	30.9828	1.27880	0.639399	+	0.768875i	$0.279183\pi$
$588$	−78.5610	−3.23980
$589$	30.0200	1.23695
$590$	−0.529811	−0.0218120
$591$	−65.6312	−2.69970
$592$	20.5781	0.845754
$593$	−21.5589	−0.885320	−0.442660	−	0.896690i	$-0.645965\pi$
$593$	−21.5589	−0.885320	−0.442660	+	0.896690i	$0.645965\pi$
$594$	9.45152	0.387800
$595$	0.467806	0.0191782
$596$	−44.3654	−1.81728
$597$	−45.7577	−1.87274
$598$	13.9937	0.572245
$599$	−1.30416	−0.0532867	−0.0266433	−	0.999645i	$-0.508482\pi$
$599$	−1.30416	−0.0532867	−0.0266433	+	0.999645i	$0.508482\pi$
$600$	92.9414	3.79432
$601$	6.14171	0.250525	0.125263	−	0.992124i	$-0.460023\pi$
$601$	6.14171	0.250525	0.125263	+	0.992124i	$0.460023\pi$
$602$	−18.5293	−0.755199
$603$	−60.2011	−2.45158
$604$	−16.6731	−0.678417
$605$	0.572560	0.0232779
$606$	75.3016	3.05892
$607$	35.9048	1.45733	0.728666	−	0.684869i	$-0.240140\pi$
$607$	35.9048	1.45733	0.728666	+	0.684869i	$0.240140\pi$
$608$	−33.6312	−1.36392
$609$	1.50840	0.0611233
$610$	0.664158	0.0268910
$611$	1.00176	0.0405269
$612$	−145.434	−5.87884
$613$	−38.7779	−1.56623	−0.783113	−	0.621879i	$-0.786369\pi$
$613$	−38.7779	−1.56623	−0.783113	+	0.621879i	$0.786369\pi$
$614$	49.2861	1.98902
$615$	1.81955	0.0733714
$616$	10.0333	0.404253
$617$	2.31128	0.0930488	0.0465244	−	0.998917i	$-0.485185\pi$
$617$	2.31128	0.0930488	0.0465244	+	0.998917i	$0.485185\pi$
$618$	102.109	4.10741
$619$	38.4040	1.54359	0.771793	−	0.635874i	$-0.219360\pi$
$619$	38.4040	1.54359	0.771793	+	0.635874i	$0.219360\pi$
$620$	−2.79977	−0.112441
$621$	−11.2751	−0.452455
$622$	36.0312	1.44472
$623$	4.26857	0.171017
$624$	23.5716	0.943621
$625$	24.9227	0.996910
$626$	44.5242	1.77954
$627$	−16.5660	−0.661583
$628$	93.7219	3.73991
$629$	−18.3469	−0.731540
$630$	0.573397	0.0228447
$631$	−39.6826	−1.57974	−0.789870	−	0.613275i	$-0.789852\pi$
$631$	−39.6826	−1.57974	−0.789870	+	0.613275i	$0.789852\pi$
$632$	98.1896	3.90577
$633$	−42.2441	−1.67905
$634$	−72.2253	−2.86843
$635$	−0.597089	−0.0236947
$636$	−35.2037	−1.39592
$637$	−6.34577	−0.251429
$638$	3.22913	0.127843
$639$	34.1144	1.34954
$640$	−0.233347	−0.00922386
$641$	−32.4645	−1.28227	−0.641136	−	0.767427i	$-0.721537\pi$
$641$	−32.4645	−1.28227	−0.641136	+	0.767427i	$0.721537\pi$
$642$	−86.2678	−3.40472
$643$	21.9887	0.867148	0.433574	−	0.901118i	$-0.357252\pi$
$643$	21.9887	0.867148	0.433574	+	0.901118i	$0.357252\pi$
$644$	−20.6844	−0.815081
$645$	−1.65107	−0.0650107
$646$	76.4584	3.00822
$647$	−33.1874	−1.30473	−0.652366	−	0.757904i	$-0.726223\pi$
$647$	−33.1874	−1.30473	−0.652366	+	0.757904i	$0.726223\pi$
$648$	42.4413	1.66725
$649$	4.94099	0.193951
$650$	12.9738	0.508875
$651$	17.3358	0.679445
$652$	−79.8878	−3.12865
$653$	49.4215	1.93401	0.967006	−	0.254755i	$-0.0819947\pi$
$653$	49.4215	1.93401	0.967006	+	0.254755i	$0.0819947\pi$
$654$	13.3670	0.522690
$655$	1.56880	0.0612980
$656$	−87.8429	−3.42969
$657$	38.2699	1.49305
$658$	−2.10463	−0.0820470
$659$	31.9443	1.24437	0.622187	−	0.782868i	$-0.286244\pi$
$659$	31.9443	1.24437	0.622187	+	0.782868i	$0.286244\pi$
$660$	1.54500	0.0601391
$661$	−35.3659	−1.37557	−0.687787	−	0.725913i	$-0.741418\pi$
$661$	−35.3659	−1.37557	−0.687787	+	0.725913i	$0.741418\pi$
$662$	63.2764	2.45931
$663$	−21.0159	−0.816189
$664$	−93.9541	−3.64613
$665$	−0.212087	−0.00822437
$666$	−22.4881	−0.871396
$667$	−3.85217	−0.149157
$668$	22.9753	0.888942
$669$	−46.3724	−1.79286
$670$	−2.95171	−0.114034
$671$	−6.19390	−0.239113
$672$	−19.4212	−0.749188
$673$	4.05227	0.156204	0.0781018	−	0.996945i	$-0.475114\pi$
$673$	4.05227	0.156204	0.0781018	+	0.996945i	$0.475114\pi$
$674$	28.7029	1.10559
$675$	−10.4534	−0.402350
$676$	4.74669	0.182565
$677$	13.1539	0.505547	0.252774	−	0.967525i	$-0.418657\pi$
$677$	13.1539	0.505547	0.252774	+	0.967525i	$0.418657\pi$
$678$	−13.8026	−0.530087
$679$	−1.07933	−0.0414210
$680$	−4.12625	−0.158234
$681$	−44.3335	−1.69886
$682$	37.1121	1.42109
$683$	−40.7067	−1.55760	−0.778798	−	0.627274i	$-0.784171\pi$
$683$	−40.7067	−1.55760	−0.778798	+	0.627274i	$0.784171\pi$
$684$	65.9349	2.52108
$685$	0.789136	0.0301513
$686$	28.0385	1.07051
$687$	−49.0903	−1.87291
$688$	79.7089	3.03887
$689$	−2.84358	−0.108332
$690$	−2.61968	−0.0997295
$691$	−2.64731	−0.100709	−0.0503543	−	0.998731i	$-0.516035\pi$
$691$	−2.64731	−0.100709	−0.0503543	+	0.998731i	$0.516035\pi$
$692$	99.1140	3.76775
$693$	−5.34747	−0.203133
$694$	−78.9672	−2.99756
$695$	0.671366	0.0254664
$696$	−13.3047	−0.504314
$697$	78.3186	2.96653
$698$	−74.0476	−2.80274
$699$	42.5028	1.60761
$700$	−19.1769	−0.724820
$701$	25.5399	0.964629	0.482314	−	0.875998i	$-0.339796\pi$
$701$	25.5399	0.964629	0.482314	+	0.875998i	$0.339796\pi$
$702$	−5.43600	−0.205169
$703$	8.31785	0.313714
$704$	−10.1488	−0.382496
$705$	−0.187534	−0.00706294
$706$	−34.4759	−1.29752
$707$	−8.99069	−0.338130
$708$	−35.1815	−1.32220
$709$	30.3817	1.14101	0.570505	−	0.821294i	$-0.306748\pi$
$709$	30.3817	1.14101	0.570505	+	0.821294i	$0.306748\pi$
$710$	1.67266	0.0627736
$711$	−52.3323	−1.96262
$712$	−37.6506	−1.41102
$713$	−44.2726	−1.65802
$714$	44.1529	1.65238
$715$	0.124798	0.00466717
$716$	−39.8164	−1.48801
$717$	−18.2739	−0.682453
$718$	−67.5584	−2.52126
$719$	−16.3209	−0.608666	−0.304333	−	0.952566i	$-0.598433\pi$
$719$	−16.3209	−0.608666	−0.304333	+	0.952566i	$0.598433\pi$
$720$	−2.46662	−0.0919254
$721$	−12.1913	−0.454029
$722$	14.6878	0.546623
$723$	44.8709	1.66877
$724$	4.95824	0.184272
$725$	−3.57142	−0.132639
$726$	54.0399	2.00561
$727$	10.3708	0.384633	0.192316	−	0.981333i	$-0.438400\pi$
$727$	10.3708	0.384633	0.192316	+	0.981333i	$0.438400\pi$
$728$	−5.77060	−0.213873
$729$	−38.9953	−1.44427
$730$	1.87640	0.0694488
$731$	−71.0665	−2.62849
$732$	44.1027	1.63008
$733$	−37.5477	−1.38686	−0.693428	−	0.720526i	$-0.743901\pi$
$733$	−37.5477	−1.38686	−0.693428	+	0.720526i	$0.743901\pi$
$734$	6.55983	0.242128
$735$	1.18795	0.0438184
$736$	49.5981	1.82821
$737$	27.5275	1.01399
$738$	95.9963	3.53367
$739$	9.34251	0.343670	0.171835	−	0.985126i	$-0.445030\pi$
$739$	9.34251	0.343670	0.171835	+	0.985126i	$0.445030\pi$
$740$	−0.775751	−0.0285172
$741$	9.52787	0.350015
$742$	5.97416	0.219318
$743$	−26.5312	−0.973334	−0.486667	−	0.873588i	$-0.661787\pi$
$743$	−26.5312	−0.973334	−0.486667	+	0.873588i	$0.661787\pi$
$744$	−152.910	−5.60594
$745$	0.670868	0.0245787
$746$	−70.3834	−2.57692
$747$	50.0750	1.83215
$748$	66.5012	2.43152
$749$	10.3000	0.376354
$750$	−4.86001	−0.177463
$751$	42.2150	1.54045	0.770224	−	0.637774i	$-0.220145\pi$
$751$	42.2150	1.54045	0.770224	+	0.637774i	$0.220145\pi$
$752$	9.05362	0.330152
$753$	−46.2289	−1.68468
$754$	−1.85722	−0.0676360
$755$	0.252120	0.00917560
$756$	8.03509	0.292233
$757$	−33.8782	−1.23133	−0.615663	−	0.788010i	$-0.711112\pi$
$757$	−33.8782	−1.23133	−0.615663	+	0.788010i	$0.711112\pi$
$758$	46.5337	1.69018
$759$	24.4310	0.886789
$760$	1.87070	0.0678573
$761$	47.1438	1.70896	0.854480	−	0.519484i	$-0.173876\pi$
$761$	47.1438	1.70896	0.854480	+	0.519484i	$0.173876\pi$
$762$	−56.3550	−2.04152
$763$	−1.59596	−0.0577775
$764$	−43.9350	−1.58951
$765$	2.19918	0.0795114
$766$	−85.3976	−3.08554
$767$	−2.84179	−0.102611
$768$	−52.4715	−1.89340
$769$	36.1044	1.30196	0.650980	−	0.759095i	$-0.274358\pi$
$769$	36.1044	1.30196	0.650980	+	0.759095i	$0.274358\pi$
$770$	−0.262191	−0.00944870
$771$	−22.0739	−0.794973
$772$	−115.002	−4.13900
$773$	10.4084	0.374364	0.187182	−	0.982325i	$-0.440065\pi$
$773$	10.4084	0.374364	0.187182	+	0.982325i	$0.440065\pi$
$774$	−87.1073	−3.13101
$775$	−41.0459	−1.47441
$776$	9.52017	0.341754
$777$	4.80335	0.172319
$778$	48.0526	1.72277
$779$	−35.5069	−1.27217
$780$	−0.888601	−0.0318170
$781$	−15.5991	−0.558180
$782$	−112.758	−4.03223
$783$	1.49642	0.0534775
$784$	−57.3512	−2.04826
$785$	−1.41721	−0.0505824
$786$	148.068	5.28140
$787$	19.4090	0.691856	0.345928	−	0.938261i	$-0.387564\pi$
$787$	19.4090	0.691856	0.345928	+	0.938261i	$0.387564\pi$
$788$	−119.445	−4.25507
$789$	58.5098	2.08300
$790$	−2.56590	−0.0912905
$791$	1.64797	0.0585952
$792$	47.1670	1.67600
$793$	3.56239	0.126504
$794$	−33.5437	−1.19042
$795$	0.532330	0.0188798
$796$	−83.2767	−2.95166
$797$	−4.12883	−0.146251	−0.0731254	−	0.997323i	$-0.523297\pi$
$797$	−4.12883	−0.146251	−0.0731254	+	0.997323i	$0.523297\pi$
$798$	−20.0174	−0.708607
$799$	−8.07199	−0.285566
$800$	45.9833	1.62576
$801$	20.0667	0.709023
$802$	92.8003	3.27689
$803$	−17.4992	−0.617534
$804$	−196.005	−6.91256
$805$	0.312778	0.0110240
$806$	−21.3448	−0.751840
$807$	16.8448	0.592964
$808$	79.3017	2.78983
$809$	−29.2758	−1.02928	−0.514641	−	0.857406i	$-0.672075\pi$
$809$	−29.2758	−1.02928	−0.514641	+	0.857406i	$0.672075\pi$
$810$	−1.10908	−0.0389691
$811$	−34.5219	−1.21223	−0.606114	−	0.795378i	$-0.707273\pi$
$811$	−34.5219	−1.21223	−0.606114	+	0.795378i	$0.707273\pi$
$812$	2.74521	0.0963379
$813$	−54.0984	−1.89731
$814$	10.2829	0.360415
$815$	1.20802	0.0423150
$816$	−189.935	−6.64907
$817$	32.2190	1.12720
$818$	−46.6169	−1.62992
$819$	3.07557	0.107469
$820$	3.31149	0.115642
$821$	15.1533	0.528853	0.264427	−	0.964406i	$-0.414817\pi$
$821$	15.1533	0.528853	0.264427	+	0.964406i	$0.414817\pi$
$822$	74.4810	2.59782
$823$	−41.6366	−1.45136	−0.725681	−	0.688032i	$-0.758475\pi$
$823$	−41.6366	−1.45136	−0.725681	+	0.688032i	$0.758475\pi$
$824$	107.533	3.74608
$825$	22.6504	0.788586
$826$	5.97039	0.207737
$827$	54.7471	1.90374	0.951871	−	0.306497i	$-0.0991571\pi$
$827$	54.7471	1.90374	0.951871	+	0.306497i	$0.0991571\pi$
$828$	−97.2385	−3.37927
$829$	−5.40446	−0.187705	−0.0938523	−	0.995586i	$-0.529918\pi$
$829$	−5.40446	−0.187705	−0.0938523	+	0.995586i	$0.529918\pi$
$830$	2.45522	0.0852218
$831$	5.50485	0.190961
$832$	5.83701	0.202362
$833$	51.1329	1.77165
$834$	63.3654	2.19417
$835$	−0.347420	−0.0120230
$836$	−30.1493	−1.04274
$837$	17.1981	0.594454
$838$	−70.5510	−2.43714
$839$	20.0800	0.693239	0.346620	−	0.938006i	$-0.387329\pi$
$839$	20.0800	0.693239	0.346620	+	0.938006i	$0.387329\pi$
$840$	1.08028	0.0372732
$841$	−28.4887	−0.982371
$842$	−77.7991	−2.68113
$843$	63.6138	2.19098
$844$	−76.8822	−2.64639
$845$	−0.0717768	−0.00246920
$846$	−9.89396	−0.340161
$847$	−6.45213	−0.221698
$848$	−25.6994	−0.882522
$849$	25.1826	0.864265
$850$	−104.540	−3.58570
$851$	−12.2669	−0.420503
$852$	111.071	3.80522
$853$	−39.7621	−1.36143	−0.680715	−	0.732549i	$-0.738331\pi$
$853$	−39.7621	−1.36143	−0.680715	+	0.732549i	$0.738331\pi$
$854$	−7.48433	−0.256109
$855$	−0.997029	−0.0340977
$856$	−90.8505	−3.10520
$857$	−29.8311	−1.01901	−0.509505	−	0.860467i	$-0.670172\pi$
$857$	−29.8311	−1.01901	−0.509505	+	0.860467i	$0.670172\pi$
$858$	11.7788	0.402120
$859$	9.69987	0.330955	0.165478	−	0.986214i	$-0.447083\pi$
$859$	9.69987	0.330955	0.165478	+	0.986214i	$0.447083\pi$
$860$	−3.00486	−0.102465
$861$	−20.5044	−0.698787
$862$	35.7663	1.21820
$863$	−47.9707	−1.63294	−0.816471	−	0.577386i	$-0.804073\pi$
$863$	−47.9707	−1.63294	−0.816471	+	0.577386i	$0.804073\pi$
$864$	−19.2669	−0.655473
$865$	−1.49875	−0.0509589
$866$	54.9574	1.86753
$867$	125.003	4.24533
$868$	31.5503	1.07089
$869$	23.9294	0.811750
$870$	0.347680	0.0117874
$871$	−15.8323	−0.536457
$872$	14.0770	0.476708
$873$	−5.07399	−0.171729
$874$	51.1207	1.72918
$875$	0.580264	0.0196165
$876$	124.600	4.20986
$877$	34.5687	1.16730	0.583652	−	0.812004i	$-0.301623\pi$
$877$	34.5687	1.16730	0.583652	+	0.812004i	$0.301623\pi$
$878$	4.18617	0.141276
$879$	15.2918	0.515780
$880$	1.12788	0.0380209
$881$	−23.9844	−0.808056	−0.404028	−	0.914747i	$-0.632390\pi$
$881$	−23.9844	−0.808056	−0.404028	+	0.914747i	$0.632390\pi$
$882$	62.6743	2.11036
$883$	37.0421	1.24657	0.623284	−	0.781996i	$-0.285798\pi$
$883$	37.0421	1.24657	0.623284	+	0.781996i	$0.285798\pi$
$884$	−38.2479	−1.28641
$885$	0.531995	0.0178828
$886$	−33.0531	−1.11044
$887$	−13.6001	−0.456648	−0.228324	−	0.973585i	$-0.573325\pi$
$887$	−13.6001	−0.456648	−0.228324	+	0.973585i	$0.573325\pi$
$888$	−42.3676	−1.42177
$889$	6.72854	0.225668
$890$	0.983889	0.0329800
$891$	10.3432	0.346511
$892$	−84.3954	−2.82577
$893$	3.65956	0.122462
$894$	63.3184	2.11768
$895$	0.602080	0.0201253
$896$	2.62957	0.0878477
$897$	−14.0514	−0.469162
$898$	36.5607	1.22005
$899$	5.87578	0.195968
$900$	−90.1516	−3.00505
$901$	22.9130	0.763342
$902$	−43.8952	−1.46155
$903$	18.6057	0.619159
$904$	−14.5358	−0.483454
$905$	−0.0749757	−0.00249228
$906$	23.7959	0.790564
$907$	−31.0365	−1.03055	−0.515275	−	0.857025i	$-0.672310\pi$
$907$	−31.0365	−1.03055	−0.515275	+	0.857025i	$0.672310\pi$
$908$	−80.6847	−2.67761
$909$	−42.2656	−1.40186
$910$	0.150798	0.00499890
$911$	6.67578	0.221178	0.110589	−	0.993866i	$-0.464726\pi$
$911$	6.67578	0.221178	0.110589	+	0.993866i	$0.464726\pi$
$912$	86.1100	2.85139
$913$	−22.8972	−0.757787
$914$	10.7690	0.356206
$915$	−0.666895	−0.0220469
$916$	−89.3418	−2.95194
$917$	−17.6786	−0.583800
$918$	43.8021	1.44569
$919$	9.65092	0.318354	0.159177	−	0.987250i	$-0.449116\pi$
$919$	9.65092	0.318354	0.159177	+	0.987250i	$0.449116\pi$
$920$	−2.75884	−0.0909562
$921$	−49.4892	−1.63073
$922$	−15.5548	−0.512269
$923$	8.97175	0.295309
$924$	−17.4105	−0.572763
$925$	−11.3729	−0.373937
$926$	−2.59744	−0.0853572
$927$	−57.3120	−1.88237
$928$	−6.58258	−0.216084
$929$	−34.3674	−1.12756	−0.563779	−	0.825925i	$-0.690653\pi$
$929$	−34.3674	−1.12756	−0.563779	+	0.825925i	$0.690653\pi$
$930$	3.99584	0.131029
$931$	−23.1819	−0.759754
$932$	77.3530	2.53378
$933$	−36.1797	−1.18447
$934$	−13.3560	−0.437021
$935$	−1.00559	−0.0328864
$936$	−27.1279	−0.886702
$937$	−47.4418	−1.54986	−0.774928	−	0.632050i	$-0.782214\pi$
$937$	−47.4418	−1.54986	−0.774928	+	0.632050i	$0.782214\pi$
$938$	33.2625	1.08606
$939$	−44.7077	−1.45898
$940$	−0.341302	−0.0111321
$941$	−13.4773	−0.439346	−0.219673	−	0.975574i	$-0.570499\pi$
$941$	−13.4773	−0.439346	−0.219673	+	0.975574i	$0.570499\pi$
$942$	−133.760	−4.35815
$943$	52.3644	1.70522
$944$	−25.6832	−0.835918
$945$	−0.121502	−0.00395246
$946$	39.8306	1.29500
$947$	−0.761036	−0.0247304	−0.0123652	−	0.999924i	$-0.503936\pi$
$947$	−0.761036	−0.0247304	−0.0123652	+	0.999924i	$0.503936\pi$
$948$	−170.386	−5.53387
$949$	10.0646	0.326711
$950$	47.3949	1.53769
$951$	72.5230	2.35172
$952$	46.4983	1.50702
$953$	−15.7730	−0.510938	−0.255469	−	0.966817i	$-0.582230\pi$
$953$	−15.7730	−0.510938	−0.255469	+	0.966817i	$0.582230\pi$
$954$	28.0848	0.909278
$955$	0.664360	0.0214982
$956$	−33.2577	−1.07563
$957$	−3.24244	−0.104813
$958$	23.1157	0.746834
$959$	−8.89270	−0.287160
$960$	−1.09271	−0.0352672
$961$	36.5297	1.17838
$962$	−5.91415	−0.190680
$963$	48.4208	1.56034
$964$	81.6628	2.63018
$965$	1.73899	0.0559801
$966$	29.5209	0.949820
$967$	−42.4557	−1.36528	−0.682642	−	0.730753i	$-0.739169\pi$
$967$	−42.4557	−1.36528	−0.682642	+	0.730753i	$0.739169\pi$
$968$	56.9105	1.82917
$969$	−76.7736	−2.46632
$970$	−0.248782	−0.00798791
$971$	−54.9167	−1.76236	−0.881180	−	0.472780i	$-0.843250\pi$
$971$	−54.9167	−1.76236	−0.881180	+	0.472780i	$0.843250\pi$
$972$	−103.449	−3.31814
$973$	−7.56556	−0.242541
$974$	−87.6856	−2.80963
$975$	−13.0273	−0.417207
$976$	32.1959	1.03056
$977$	−18.1736	−0.581426	−0.290713	−	0.956810i	$-0.593893\pi$
$977$	−18.1736	−0.581426	−0.290713	+	0.956810i	$0.593893\pi$
$978$	114.016	3.64584
$979$	−9.17570	−0.293256
$980$	2.16202	0.0690631
$981$	−7.50267	−0.239542
$982$	−38.8675	−1.24031
$983$	−47.3146	−1.50910	−0.754550	−	0.656243i	$-0.772145\pi$
$983$	−47.3146	−1.50910	−0.754550	+	0.656243i	$0.772145\pi$
$984$	180.857	5.76552
$985$	1.80618	0.0575498
$986$	14.9651	0.476586
$987$	2.11330	0.0672672
$988$	17.3402	0.551666
$989$	−47.5156	−1.51091
$990$	−1.23257	−0.0391737
$991$	18.5944	0.590670	0.295335	−	0.955394i	$-0.404569\pi$
$991$	18.5944	0.590670	0.295335	+	0.955394i	$0.404569\pi$
$992$	−75.6529	−2.40198
$993$	−63.5372	−2.01629
$994$	−18.8490	−0.597854
$995$	1.25926	0.0399213
$996$	163.036	5.16599
$997$	46.7005	1.47902	0.739510	−	0.673146i	$-0.235057\pi$
$997$	46.7005	1.47902	0.739510	+	0.673146i	$0.235057\pi$
$998$	−110.459	−3.49653
$999$	4.76520	0.150764

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.b.1.5	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.b.1.5	✓	101	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.59744 q^{2} +2.60815 q^{3} +4.74669 q^{4} -0.0717768 q^{5} -6.77450 q^{6} +0.808846 q^{7} -7.13437 q^{8} +3.80242 q^{9} +O(q^{10})\)	\(q-2.59744 q^{2} +2.60815 q^{3} +4.74669 q^{4} -0.0717768 q^{5} -6.77450 q^{6} +0.808846 q^{7} -7.13437 q^{8} +3.80242 q^{9} +0.186436 q^{10} -1.73869 q^{11} +12.3801 q^{12} +1.00000 q^{13} -2.10093 q^{14} -0.187204 q^{15} +9.03770 q^{16} -8.05779 q^{17} -9.87656 q^{18} +3.65312 q^{19} -0.340702 q^{20} +2.10959 q^{21} +4.51614 q^{22} -5.38750 q^{23} -18.6075 q^{24} -4.99485 q^{25} -2.59744 q^{26} +2.09283 q^{27} +3.83934 q^{28} +0.715020 q^{29} +0.486252 q^{30} +8.21765 q^{31} -9.20615 q^{32} -4.53476 q^{33} +20.9296 q^{34} -0.0580563 q^{35} +18.0489 q^{36} +2.27692 q^{37} -9.48876 q^{38} +2.60815 q^{39} +0.512082 q^{40} -9.71961 q^{41} -5.47952 q^{42} +8.81960 q^{43} -8.25303 q^{44} -0.272925 q^{45} +13.9937 q^{46} +1.00176 q^{47} +23.5716 q^{48} -6.34577 q^{49} +12.9738 q^{50} -21.0159 q^{51} +4.74669 q^{52} -2.84358 q^{53} -5.43600 q^{54} +0.124798 q^{55} -5.77060 q^{56} +9.52787 q^{57} -1.85722 q^{58} -2.84179 q^{59} -0.888601 q^{60} +3.56239 q^{61} -21.3448 q^{62} +3.07557 q^{63} +5.83701 q^{64} -0.0717768 q^{65} +11.7788 q^{66} -15.8323 q^{67} -38.2479 q^{68} -14.0514 q^{69} +0.150798 q^{70} +8.97175 q^{71} -27.1279 q^{72} +10.0646 q^{73} -5.91415 q^{74} -13.0273 q^{75} +17.3402 q^{76} -1.40633 q^{77} -6.77450 q^{78} -13.7629 q^{79} -0.648697 q^{80} -5.94886 q^{81} +25.2461 q^{82} +13.1692 q^{83} +10.0136 q^{84} +0.578362 q^{85} -22.9084 q^{86} +1.86488 q^{87} +12.4045 q^{88} +5.27736 q^{89} +0.708907 q^{90} +0.808846 q^{91} -25.5728 q^{92} +21.4328 q^{93} -2.60202 q^{94} -0.262209 q^{95} -24.0110 q^{96} -1.33441 q^{97} +16.4828 q^{98} -6.61123 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9 - 19 * q^10 - 42 * q^11 - 28 * q^12 + 101 * q^13 - 45 * q^14 - 15 * q^15 + 48 * q^16 - 83 * q^17 - 4 * q^18 - 18 * q^19 - 51 * q^20 - 50 * q^21 - 20 * q^22 - 64 * q^23 - 23 * q^24 + 46 * q^25 - 8 * q^26 - 37 * q^27 - 11 * q^28 - 117 * q^29 - 28 * q^30 - 10 * q^31 - 36 * q^32 - 20 * q^33 - 10 * q^34 - 53 * q^35 - 16 * q^36 - 27 * q^37 - 68 * q^38 - 13 * q^39 - 42 * q^40 - 60 * q^41 - 31 * q^42 - 16 * q^43 - 89 * q^44 - 56 * q^45 + 5 * q^46 - 23 * q^47 - 37 * q^48 + 48 * q^49 - 30 * q^50 - 68 * q^51 + 86 * q^52 - 189 * q^53 - 23 * q^54 + 3 * q^55 - 106 * q^56 - 25 * q^57 - 82 * q^59 + 6 * q^60 - 68 * q^61 - 57 * q^62 + 3 * q^63 - 2 * q^64 - 43 * q^65 - 40 * q^66 - 13 * q^67 - 138 * q^68 - 92 * q^69 + 18 * q^70 - 39 * q^71 - 20 * q^72 + 19 * q^73 - 88 * q^74 - 21 * q^75 - 53 * q^76 - 147 * q^77 - 10 * q^78 - 19 * q^79 - 104 * q^80 - 55 * q^81 + 27 * q^82 - 49 * q^83 - 59 * q^84 - 27 * q^85 - 99 * q^86 - 33 * q^87 - 41 * q^88 - 70 * q^89 - 49 * q^90 - q^91 - 111 * q^92 - 84 * q^93 + 4 * q^94 - 82 * q^95 - 7 * q^96 + 25 * q^97 - 37 * q^98 - 41 * q^99

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