LMFDB - Embedded newform 6023.2.a.b.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, 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("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$1$
Dimension:	$99$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.90532 q^{2} +0.192511 q^{3} +1.63023 q^{4} +0.483590 q^{5} -0.366795 q^{6} +3.15438 q^{7} +0.704532 q^{8} -2.96294 q^{9} +O(q^{10})$	\(q-1.90532 q^{2} +0.192511 q^{3} +1.63023 q^{4} +0.483590 q^{5} -0.366795 q^{6} +3.15438 q^{7} +0.704532 q^{8} -2.96294 q^{9} -0.921392 q^{10} +0.275963 q^{11} +0.313837 q^{12} -1.15979 q^{13} -6.01010 q^{14} +0.0930965 q^{15} -4.60281 q^{16} -4.88188 q^{17} +5.64534 q^{18} -1.00000 q^{19} +0.788362 q^{20} +0.607254 q^{21} -0.525797 q^{22} +7.55013 q^{23} +0.135630 q^{24} -4.76614 q^{25} +2.20976 q^{26} -1.14793 q^{27} +5.14237 q^{28} -1.37761 q^{29} -0.177378 q^{30} +1.85608 q^{31} +7.36075 q^{32} +0.0531260 q^{33} +9.30153 q^{34} +1.52543 q^{35} -4.83027 q^{36} +8.37268 q^{37} +1.90532 q^{38} -0.223272 q^{39} +0.340704 q^{40} +2.29793 q^{41} -1.15701 q^{42} -7.33007 q^{43} +0.449883 q^{44} -1.43285 q^{45} -14.3854 q^{46} +3.26360 q^{47} -0.886093 q^{48} +2.95014 q^{49} +9.08100 q^{50} -0.939817 q^{51} -1.89071 q^{52} -4.39939 q^{53} +2.18718 q^{54} +0.133453 q^{55} +2.22236 q^{56} -0.192511 q^{57} +2.62479 q^{58} +2.49711 q^{59} +0.151769 q^{60} +8.52919 q^{61} -3.53641 q^{62} -9.34625 q^{63} -4.81892 q^{64} -0.560860 q^{65} -0.101222 q^{66} -10.4770 q^{67} -7.95858 q^{68} +1.45348 q^{69} -2.90642 q^{70} -6.40455 q^{71} -2.08748 q^{72} +8.31413 q^{73} -15.9526 q^{74} -0.917536 q^{75} -1.63023 q^{76} +0.870493 q^{77} +0.425403 q^{78} -1.19875 q^{79} -2.22587 q^{80} +8.66783 q^{81} -4.37828 q^{82} -4.01360 q^{83} +0.989963 q^{84} -2.36083 q^{85} +13.9661 q^{86} -0.265206 q^{87} +0.194425 q^{88} -14.4394 q^{89} +2.73003 q^{90} -3.65841 q^{91} +12.3084 q^{92} +0.357316 q^{93} -6.21819 q^{94} -0.483590 q^{95} +1.41703 q^{96} +3.23977 q^{97} -5.62094 q^{98} -0.817662 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9}+O(q^{10}) $ 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9} - 6 q^{10} - 9 q^{11} - 27 q^{12} - 28 q^{13} - 13 q^{14} - 10 q^{15} + 38 q^{16} - 36 q^{17} - 14 q^{18} - 99 q^{19} - 34 q^{20} - 20 q^{21} - 53 q^{22} - 38 q^{23} - 25 q^{24} - 8 q^{25} - 3 q^{26} - 3 q^{27} - 63 q^{28} - 34 q^{29} - 30 q^{30} - 16 q^{31} - 43 q^{32} - 41 q^{33} - 14 q^{34} - 25 q^{35} - 16 q^{36} - 80 q^{37} + 4 q^{38} - 48 q^{39} - 10 q^{40} - 32 q^{41} - 37 q^{42} - 76 q^{43} - 21 q^{44} - 53 q^{45} - 23 q^{46} - 31 q^{47} - 74 q^{48} - 32 q^{49} - 29 q^{50} - 30 q^{51} - 71 q^{52} - 35 q^{53} - 80 q^{54} - 45 q^{55} - 33 q^{56} + 3 q^{57} - 91 q^{58} + 12 q^{59} - 56 q^{60} - 61 q^{61} - 46 q^{62} - 43 q^{63} - 30 q^{64} - 46 q^{65} - 75 q^{66} - 26 q^{67} - 55 q^{68} - 45 q^{69} - 76 q^{70} - 41 q^{71} - 77 q^{72} - 143 q^{73} - 64 q^{74} - 8 q^{75} - 80 q^{76} - 58 q^{77} - 34 q^{78} - 22 q^{79} - 36 q^{80} - 81 q^{81} - 109 q^{82} - 7 q^{83} - 6 q^{84} - 80 q^{85} + 32 q^{86} - 57 q^{87} - 120 q^{88} - 28 q^{89} - 12 q^{90} - 30 q^{91} - 107 q^{92} - 121 q^{93} + 8 q^{94} + 15 q^{95} + 4 q^{96} - 128 q^{97} + 54 q^{98} - 34 q^{99}+O(q^{100}) \) 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9 - 6 * q^10 - 9 * q^11 - 27 * q^12 - 28 * q^13 - 13 * q^14 - 10 * q^15 + 38 * q^16 - 36 * q^17 - 14 * q^18 - 99 * q^19 - 34 * q^20 - 20 * q^21 - 53 * q^22 - 38 * q^23 - 25 * q^24 - 8 * q^25 - 3 * q^26 - 3 * q^27 - 63 * q^28 - 34 * q^29 - 30 * q^30 - 16 * q^31 - 43 * q^32 - 41 * q^33 - 14 * q^34 - 25 * q^35 - 16 * q^36 - 80 * q^37 + 4 * q^38 - 48 * q^39 - 10 * q^40 - 32 * q^41 - 37 * q^42 - 76 * q^43 - 21 * q^44 - 53 * q^45 - 23 * q^46 - 31 * q^47 - 74 * q^48 - 32 * q^49 - 29 * q^50 - 30 * q^51 - 71 * q^52 - 35 * q^53 - 80 * q^54 - 45 * q^55 - 33 * q^56 + 3 * q^57 - 91 * q^58 + 12 * q^59 - 56 * q^60 - 61 * q^61 - 46 * q^62 - 43 * q^63 - 30 * q^64 - 46 * q^65 - 75 * q^66 - 26 * q^67 - 55 * q^68 - 45 * q^69 - 76 * q^70 - 41 * q^71 - 77 * q^72 - 143 * q^73 - 64 * q^74 - 8 * q^75 - 80 * q^76 - 58 * q^77 - 34 * q^78 - 22 * q^79 - 36 * q^80 - 81 * q^81 - 109 * q^82 - 7 * q^83 - 6 * q^84 - 80 * q^85 + 32 * q^86 - 57 * q^87 - 120 * q^88 - 28 * q^89 - 12 * q^90 - 30 * q^91 - 107 * q^92 - 121 * q^93 + 8 * q^94 + 15 * q^95 + 4 * q^96 - 128 * q^97 + 54 * q^98 - 34 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.90532	−1.34726	−0.673631	−	0.739068i	$-0.735266\pi$
$2$	−1.90532	−1.34726	−0.673631	+	0.739068i	$0.735266\pi$
$3$	0.192511	0.111146	0.0555732	−	0.998455i	$-0.482301\pi$
$3$	0.192511	0.111146	0.0555732	+	0.998455i	$0.482301\pi$
$4$	1.63023	0.815114
$5$	0.483590	0.216268	0.108134	−	0.994136i	$-0.465512\pi$
$5$	0.483590	0.216268	0.108134	+	0.994136i	$0.465512\pi$
$6$	−0.366795	−0.149743
$7$	3.15438	1.19224	0.596122	−	0.802894i	$-0.296707\pi$
$7$	3.15438	1.19224	0.596122	+	0.802894i	$0.296707\pi$
$8$	0.704532	0.249090
$9$	−2.96294	−0.987646
$10$	−0.921392	−0.291370
$11$	0.275963	0.0832060	0.0416030	−	0.999134i	$-0.486754\pi$
$11$	0.275963	0.0832060	0.0416030	+	0.999134i	$0.486754\pi$
$12$	0.313837	0.0905970
$13$	−1.15979	−0.321667	−0.160833	−	0.986982i	$-0.551418\pi$
$13$	−1.15979	−0.321667	−0.160833	+	0.986982i	$0.551418\pi$
$14$	−6.01010	−1.60627
$15$	0.0930965	0.0240374
$16$	−4.60281	−1.15070
$17$	−4.88188	−1.18403	−0.592015	−	0.805927i	$-0.701667\pi$
$17$	−4.88188	−1.18403	−0.592015	+	0.805927i	$0.701667\pi$
$18$	5.64534	1.33062
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0.788362	0.176283
$21$	0.607254	0.132514
$22$	−0.525797	−0.112100
$23$	7.55013	1.57431	0.787155	−	0.616755i	$-0.211553\pi$
$23$	7.55013	1.57431	0.787155	+	0.616755i	$0.211553\pi$
$24$	0.135630	0.0276854
$25$	−4.76614	−0.953228
$26$	2.20976	0.433369
$27$	−1.14793	−0.220920
$28$	5.14237	0.971816
$29$	−1.37761	−0.255816	−0.127908	−	0.991786i	$-0.540826\pi$
$29$	−1.37761	−0.255816	−0.127908	+	0.991786i	$0.540826\pi$
$30$	−0.177378	−0.0323847
$31$	1.85608	0.333361	0.166681	−	0.986011i	$-0.446695\pi$
$31$	1.85608	0.333361	0.166681	+	0.986011i	$0.446695\pi$
$32$	7.36075	1.30121
$33$	0.0531260	0.00924805
$34$	9.30153	1.59520
$35$	1.52543	0.257844
$36$	−4.83027	−0.805045
$37$	8.37268	1.37646	0.688230	−	0.725493i	$-0.258388\pi$
$37$	8.37268	1.37646	0.688230	+	0.725493i	$0.258388\pi$
$38$	1.90532	0.309083
$39$	−0.223272	−0.0357521
$40$	0.340704	0.0538701
$41$	2.29793	0.358876	0.179438	−	0.983769i	$-0.442572\pi$
$41$	2.29793	0.358876	0.179438	+	0.983769i	$0.442572\pi$
$42$	−1.15701	−0.178531
$43$	−7.33007	−1.11782	−0.558912	−	0.829227i	$-0.688781\pi$
$43$	−7.33007	−1.11782	−0.558912	+	0.829227i	$0.688781\pi$
$44$	0.449883	0.0678224
$45$	−1.43285	−0.213596
$46$	−14.3854	−2.12101
$47$	3.26360	0.476045	0.238023	−	0.971260i	$-0.423501\pi$
$47$	3.26360	0.476045	0.238023	+	0.971260i	$0.423501\pi$
$48$	−0.886093	−0.127897
$49$	2.95014	0.421448
$50$	9.08100	1.28425
$51$	−0.939817	−0.131601
$52$	−1.89071	−0.262195
$53$	−4.39939	−0.604303	−0.302151	−	0.953260i	$-0.597705\pi$
$53$	−4.39939	−0.604303	−0.302151	+	0.953260i	$0.597705\pi$
$54$	2.18718	0.297637
$55$	0.133453	0.0179948
$56$	2.22236	0.296976
$57$	−0.192511	−0.0254987
$58$	2.62479	0.344651
$59$	2.49711	0.325097	0.162548	−	0.986701i	$-0.448029\pi$
$59$	2.49711	0.325097	0.162548	+	0.986701i	$0.448029\pi$
$60$	0.151769	0.0195932
$61$	8.52919	1.09205	0.546026	−	0.837768i	$-0.316140\pi$
$61$	8.52919	1.09205	0.546026	+	0.837768i	$0.316140\pi$
$62$	−3.53641	−0.449125
$63$	−9.34625	−1.17752
$64$	−4.81892	−0.602366
$65$	−0.560860	−0.0695662
$66$	−0.101222	−0.0124595
$67$	−10.4770	−1.27996	−0.639982	−	0.768390i	$-0.721058\pi$
$67$	−10.4770	−1.27996	−0.639982	+	0.768390i	$0.721058\pi$
$68$	−7.95858	−0.965120
$69$	1.45348	0.174979
$70$	−2.90642	−0.347384
$71$	−6.40455	−0.760081	−0.380040	−	0.924970i	$-0.624090\pi$
$71$	−6.40455	−0.760081	−0.380040	+	0.924970i	$0.624090\pi$
$72$	−2.08748	−0.246012
$73$	8.31413	0.973096	0.486548	−	0.873654i	$-0.338256\pi$
$73$	8.31413	0.973096	0.486548	+	0.873654i	$0.338256\pi$
$74$	−15.9526	−1.85445
$75$	−0.917536	−0.105948
$76$	−1.63023	−0.187000
$77$	0.870493	0.0992019
$78$	0.425403	0.0481674
$79$	−1.19875	−0.134870	−0.0674350	−	0.997724i	$-0.521482\pi$
$79$	−1.19875	−0.134870	−0.0674350	+	0.997724i	$0.521482\pi$
$80$	−2.22587	−0.248860
$81$	8.66783	0.963092
$82$	−4.37828	−0.483500
$83$	−4.01360	−0.440550	−0.220275	−	0.975438i	$-0.570695\pi$
$83$	−4.01360	−0.440550	−0.220275	+	0.975438i	$0.570695\pi$
$84$	0.989963	0.108014
$85$	−2.36083	−0.256068
$86$	13.9661	1.50600
$87$	−0.265206	−0.0284330
$88$	0.194425	0.0207257
$89$	−14.4394	−1.53058	−0.765289	−	0.643687i	$-0.777404\pi$
$89$	−14.4394	−1.53058	−0.765289	+	0.643687i	$0.777404\pi$
$90$	2.73003	0.287770
$91$	−3.65841	−0.383505
$92$	12.3084	1.28324
$93$	0.357316	0.0370519
$94$	−6.21819	−0.641358
$95$	−0.483590	−0.0496153
$96$	1.41703	0.144625
$97$	3.23977	0.328949	0.164475	−	0.986381i	$-0.447407\pi$
$97$	3.23977	0.328949	0.164475	+	0.986381i	$0.447407\pi$
$98$	−5.62094	−0.567801
$99$	−0.817662	−0.0821781
$100$	−7.76990	−0.776990
$101$	−10.9631	−1.09087	−0.545437	−	0.838152i	$-0.683636\pi$
$101$	−10.9631	−1.09087	−0.545437	+	0.838152i	$0.683636\pi$
$102$	1.79065	0.177301
$103$	8.05610	0.793791	0.396896	−	0.917864i	$-0.370087\pi$
$103$	8.05610	0.793791	0.396896	+	0.917864i	$0.370087\pi$
$104$	−0.817105	−0.0801238
$105$	0.293662	0.0286585
$106$	8.38223	0.814154
$107$	−10.7610	−1.04031	−0.520153	−	0.854073i	$-0.674125\pi$
$107$	−10.7610	−1.04031	−0.520153	+	0.854073i	$0.674125\pi$
$108$	−1.87139	−0.180075
$109$	−14.4526	−1.38431	−0.692154	−	0.721750i	$-0.743338\pi$
$109$	−14.4526	−1.38431	−0.692154	+	0.721750i	$0.743338\pi$
$110$	−0.254270	−0.0242437
$111$	1.61184	0.152989
$112$	−14.5190	−1.37192
$113$	−14.2216	−1.33786	−0.668928	−	0.743327i	$-0.733246\pi$
$113$	−14.2216	−1.33786	−0.668928	+	0.743327i	$0.733246\pi$
$114$	0.366795	0.0343535
$115$	3.65117	0.340473
$116$	−2.24582	−0.208519
$117$	3.43637	0.317693
$118$	−4.75779	−0.437990
$119$	−15.3993	−1.41165
$120$	0.0655894	0.00598747
$121$	−10.9238	−0.993077
$122$	−16.2508	−1.47128
$123$	0.442377	0.0398878
$124$	3.02583	0.271728
$125$	−4.72281	−0.422421
$126$	17.8076	1.58642
$127$	8.13952	0.722266	0.361133	−	0.932514i	$-0.382390\pi$
$127$	8.13952	0.722266	0.361133	+	0.932514i	$0.382390\pi$
$128$	−5.53992	−0.489665
$129$	−1.41112	−0.124242
$130$	1.06862	0.0937238
$131$	4.55518	0.397988	0.198994	−	0.980001i	$-0.436233\pi$
$131$	4.55518	0.397988	0.198994	+	0.980001i	$0.436233\pi$
$132$	0.0866075	0.00753822
$133$	−3.15438	−0.273520
$134$	19.9619	1.72445
$135$	−0.555129	−0.0477779
$136$	−3.43944	−0.294930
$137$	19.9708	1.70622	0.853111	−	0.521729i	$-0.174713\pi$
$137$	19.9708	1.70622	0.853111	+	0.521729i	$0.174713\pi$
$138$	−2.76935	−0.235743
$139$	−6.98302	−0.592292	−0.296146	−	0.955143i	$-0.595701\pi$
$139$	−6.98302	−0.592292	−0.296146	+	0.955143i	$0.595701\pi$
$140$	2.48680	0.210173
$141$	0.628280	0.0529108
$142$	12.2027	1.02403
$143$	−0.320058	−0.0267646
$144$	13.6379	1.13649
$145$	−0.666199	−0.0553248
$146$	−15.8411	−1.31101
$147$	0.567934	0.0468424
$148$	13.6494	1.12197
$149$	6.68046	0.547285	0.273642	−	0.961832i	$-0.411772\pi$
$149$	6.68046	0.547285	0.273642	+	0.961832i	$0.411772\pi$
$150$	1.74820	0.142740
$151$	−11.7844	−0.959003	−0.479501	−	0.877541i	$-0.659182\pi$
$151$	−11.7844	−0.959003	−0.479501	+	0.877541i	$0.659182\pi$
$152$	−0.704532	−0.0571451
$153$	14.4647	1.16940
$154$	−1.65856	−0.133651
$155$	0.897581	0.0720954
$156$	−0.363984	−0.0291420
$157$	1.62321	0.129547	0.0647733	−	0.997900i	$-0.479368\pi$
$157$	1.62321	0.129547	0.0647733	+	0.997900i	$0.479368\pi$
$158$	2.28400	0.181705
$159$	−0.846933	−0.0671661
$160$	3.55958	0.281410
$161$	23.8160	1.87696
$162$	−16.5150	−1.29754
$163$	6.52174	0.510822	0.255411	−	0.966833i	$-0.417789\pi$
$163$	6.52174	0.510822	0.255411	+	0.966833i	$0.417789\pi$
$164$	3.74615	0.292525
$165$	0.0256912	0.00200006
$166$	7.64717	0.593536
$167$	21.7814	1.68549	0.842747	−	0.538310i	$-0.180937\pi$
$167$	21.7814	1.68549	0.842747	+	0.538310i	$0.180937\pi$
$168$	0.427830	0.0330078
$169$	−11.6549	−0.896531
$170$	4.49812	0.344990
$171$	2.96294	0.226582
$172$	−11.9497	−0.911155
$173$	1.37783	0.104755	0.0523773	−	0.998627i	$-0.483320\pi$
$173$	1.37783	0.104755	0.0523773	+	0.998627i	$0.483320\pi$
$174$	0.505301	0.0383068
$175$	−15.0342	−1.13648
$176$	−1.27021	−0.0957454
$177$	0.480723	0.0361333
$178$	27.5117	2.06209
$179$	14.9624	1.11834	0.559170	−	0.829053i	$-0.311120\pi$
$179$	14.9624	1.11834	0.559170	+	0.829053i	$0.311120\pi$
$180$	−2.33587	−0.174105
$181$	−12.2335	−0.909311	−0.454655	−	0.890667i	$-0.650238\pi$
$181$	−12.2335	−0.909311	−0.454655	+	0.890667i	$0.650238\pi$
$182$	6.97042	0.516682
$183$	1.64197	0.121378
$184$	5.31931	0.392144
$185$	4.04894	0.297684
$186$	−0.680800	−0.0499187
$187$	−1.34722	−0.0985184
$188$	5.32042	0.388031
$189$	−3.62102	−0.263391
$190$	0.921392	0.0668448
$191$	−6.10667	−0.441863	−0.220932	−	0.975289i	$-0.570910\pi$
$191$	−6.10667	−0.441863	−0.220932	+	0.975289i	$0.570910\pi$
$192$	−0.927697	−0.0669508
$193$	−11.2876	−0.812498	−0.406249	−	0.913762i	$-0.633163\pi$
$193$	−11.2876	−0.812498	−0.406249	+	0.913762i	$0.633163\pi$
$194$	−6.17279	−0.443181
$195$	−0.107972	−0.00773203
$196$	4.80939	0.343528
$197$	16.2734	1.15943	0.579717	−	0.814818i	$-0.303163\pi$
$197$	16.2734	1.15943	0.579717	+	0.814818i	$0.303163\pi$
$198$	1.55790	0.110715
$199$	−24.9455	−1.76834	−0.884169	−	0.467168i	$-0.845274\pi$
$199$	−24.9455	−1.76834	−0.884169	+	0.467168i	$0.845274\pi$
$200$	−3.35790	−0.237439
$201$	−2.01693	−0.142263
$202$	20.8882	1.46969
$203$	−4.34552	−0.304995
$204$	−1.53212	−0.107270
$205$	1.11125	0.0776134
$206$	−15.3494	−1.06944
$207$	−22.3706	−1.55486
$208$	5.33827	0.370143
$209$	−0.275963	−0.0190888
$210$	−0.559519	−0.0386105
$211$	−7.56706	−0.520938	−0.260469	−	0.965482i	$-0.583877\pi$
$211$	−7.56706	−0.520938	−0.260469	+	0.965482i	$0.583877\pi$
$212$	−7.17201	−0.492576
$213$	−1.23295	−0.0844803
$214$	20.5031	1.40156
$215$	−3.54475	−0.241750
$216$	−0.808755	−0.0550288
$217$	5.85478	0.397448
$218$	27.5368	1.86502
$219$	1.60056	0.108156
$220$	0.217559	0.0146678
$221$	5.66193	0.380863
$222$	−3.07106	−0.206116
$223$	−21.3191	−1.42763	−0.713817	−	0.700332i	$-0.753035\pi$
$223$	−21.3191	−1.42763	−0.713817	+	0.700332i	$0.753035\pi$
$224$	23.2186	1.55136
$225$	14.1218	0.941452
$226$	27.0966	1.80244
$227$	15.6393	1.03801	0.519007	−	0.854770i	$-0.326302\pi$
$227$	15.6393	1.03801	0.519007	+	0.854770i	$0.326302\pi$
$228$	−0.313837	−0.0207844
$229$	−6.15833	−0.406954	−0.203477	−	0.979080i	$-0.565224\pi$
$229$	−6.15833	−0.406954	−0.203477	+	0.979080i	$0.565224\pi$
$230$	−6.95662	−0.458706
$231$	0.167580	0.0110259
$232$	−0.970571	−0.0637211
$233$	−13.4709	−0.882509	−0.441255	−	0.897382i	$-0.645466\pi$
$233$	−13.4709	−0.882509	−0.441255	+	0.897382i	$0.645466\pi$
$234$	−6.54738	−0.428015
$235$	1.57825	0.102953
$236$	4.07087	0.264991
$237$	−0.230773	−0.0149903
$238$	29.3406	1.90187
$239$	10.7874	0.697780	0.348890	−	0.937164i	$-0.386559\pi$
$239$	10.7874	0.697780	0.348890	+	0.937164i	$0.386559\pi$
$240$	−0.428506	−0.0276599
$241$	−12.0072	−0.773450	−0.386725	−	0.922195i	$-0.626394\pi$
$241$	−12.0072	−0.773450	−0.386725	+	0.922195i	$0.626394\pi$
$242$	20.8134	1.33793
$243$	5.11245	0.327964
$244$	13.9045	0.890147
$245$	1.42666	0.0911457
$246$	−0.842868	−0.0537393
$247$	1.15979	0.0737954
$248$	1.30767	0.0830369
$249$	−0.772663	−0.0489655
$250$	8.99844	0.569111
$251$	−18.3238	−1.15659	−0.578295	−	0.815828i	$-0.696282\pi$
$251$	−18.3238	−1.15659	−0.578295	+	0.815828i	$0.696282\pi$
$252$	−15.2365	−0.959810
$253$	2.08356	0.130992
$254$	−15.5084	−0.973081
$255$	−0.454486	−0.0284610
$256$	20.1932	1.26207
$257$	9.04924	0.564476	0.282238	−	0.959344i	$-0.408923\pi$
$257$	9.04924	0.564476	0.282238	+	0.959344i	$0.408923\pi$
$258$	2.68863	0.167387
$259$	26.4106	1.64108
$260$	−0.914331	−0.0567044
$261$	4.08178	0.252656
$262$	−8.67905	−0.536194
$263$	−19.1515	−1.18093	−0.590465	−	0.807063i	$-0.701056\pi$
$263$	−19.1515	−1.18093	−0.590465	+	0.807063i	$0.701056\pi$
$264$	0.0374290	0.00230359
$265$	−2.12750	−0.130691
$266$	6.01010	0.368503
$267$	−2.77976	−0.170118
$268$	−17.0798	−1.04332
$269$	9.03702	0.550997	0.275498	−	0.961302i	$-0.411157\pi$
$269$	9.03702	0.550997	0.275498	+	0.961302i	$0.411157\pi$
$270$	1.05770	0.0643693
$271$	−26.0810	−1.58431	−0.792153	−	0.610323i	$-0.791040\pi$
$271$	−26.0810	−1.58431	−0.792153	+	0.610323i	$0.791040\pi$
$272$	22.4704	1.36247
$273$	−0.704285	−0.0426252
$274$	−38.0507	−2.29873
$275$	−1.31528	−0.0793143
$276$	2.36951	0.142628
$277$	19.5523	1.17478	0.587392	−	0.809303i	$-0.300155\pi$
$277$	19.5523	1.17478	0.587392	+	0.809303i	$0.300155\pi$
$278$	13.3049	0.797972
$279$	−5.49945	−0.329243
$280$	1.07471	0.0642264
$281$	13.9768	0.833785	0.416892	−	0.908956i	$-0.363119\pi$
$281$	13.9768	0.833785	0.416892	+	0.908956i	$0.363119\pi$
$282$	−1.19707	−0.0712846
$283$	−15.5358	−0.923508	−0.461754	−	0.887008i	$-0.652780\pi$
$283$	−15.5358	−0.923508	−0.461754	+	0.887008i	$0.652780\pi$
$284$	−10.4409	−0.619552
$285$	−0.0930965	−0.00551456
$286$	0.609811	0.0360589
$287$	7.24855	0.427868
$288$	−21.8094	−1.28513
$289$	6.83277	0.401928
$290$	1.26932	0.0745370
$291$	0.623693	0.0365615
$292$	13.5539	0.793184
$293$	26.8607	1.56922	0.784610	−	0.619990i	$-0.212863\pi$
$293$	26.8607	1.56922	0.784610	+	0.619990i	$0.212863\pi$
$294$	−1.08209	−0.0631090
$295$	1.20758	0.0703080
$296$	5.89882	0.342862
$297$	−0.316787	−0.0183819
$298$	−12.7284	−0.737336
$299$	−8.75653	−0.506403
$300$	−1.49579	−0.0863596
$301$	−23.1218	−1.33272
$302$	22.4530	1.29203
$303$	−2.11053	−0.121247
$304$	4.60281	0.263989
$305$	4.12463	0.236176
$306$	−27.5599	−1.57549
$307$	−14.6776	−0.837696	−0.418848	−	0.908056i	$-0.637566\pi$
$307$	−14.6776	−0.837696	−0.418848	+	0.908056i	$0.637566\pi$
$308$	1.41910	0.0808609
$309$	1.55089	0.0882271
$310$	−1.71017	−0.0971314
$311$	−3.49593	−0.198236	−0.0991181	−	0.995076i	$-0.531602\pi$
$311$	−3.49593	−0.198236	−0.0991181	+	0.995076i	$0.531602\pi$
$312$	−0.157302	−0.00890547
$313$	−18.3347	−1.03634	−0.518168	−	0.855279i	$-0.673386\pi$
$313$	−18.3347	−1.03634	−0.518168	+	0.855279i	$0.673386\pi$
$314$	−3.09274	−0.174533
$315$	−4.51975	−0.254659
$316$	−1.95424	−0.109934
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	1.61367	0.0904903
$319$	−0.380170	−0.0212854
$320$	−2.33038	−0.130272
$321$	−2.07162	−0.115626
$322$	−45.3770	−2.52876
$323$	4.88188	0.271635
$324$	14.1305	0.785030
$325$	5.52770	0.306622
$326$	−12.4260	−0.688211
$327$	−2.78229	−0.153861
$328$	1.61896	0.0893923
$329$	10.2947	0.567563
$330$	−0.0489498	−0.00269460
$331$	6.95525	0.382295	0.191148	−	0.981561i	$-0.438779\pi$
$331$	6.95525	0.382295	0.191148	+	0.981561i	$0.438779\pi$
$332$	−6.54308	−0.359098
$333$	−24.8077	−1.35946
$334$	−41.5004	−2.27080
$335$	−5.06655	−0.276815
$336$	−2.79508	−0.152484
$337$	−1.25226	−0.0682151	−0.0341076	−	0.999418i	$-0.510859\pi$
$337$	−1.25226	−0.0682151	−0.0341076	+	0.999418i	$0.510859\pi$
$338$	22.2063	1.20786
$339$	−2.73782	−0.148698
$340$	−3.84869	−0.208725
$341$	0.512209	0.0277377
$342$	−5.64534	−0.305265
$343$	−12.7748	−0.689776
$344$	−5.16426	−0.278438
$345$	0.702891	0.0378424
$346$	−2.62520	−0.141132
$347$	30.5851	1.64190	0.820948	−	0.571002i	$-0.193445\pi$
$347$	30.5851	1.64190	0.820948	+	0.571002i	$0.193445\pi$
$348$	−0.432346	−0.0231762
$349$	7.79138	0.417063	0.208532	−	0.978016i	$-0.433132\pi$
$349$	7.79138	0.417063	0.208532	+	0.978016i	$0.433132\pi$
$350$	28.6450	1.53114
$351$	1.33136	0.0710625
$352$	2.03129	0.108268
$353$	17.5016	0.931516	0.465758	−	0.884912i	$-0.345782\pi$
$353$	17.5016	0.931516	0.465758	+	0.884912i	$0.345782\pi$
$354$	−0.915929	−0.0486811
$355$	−3.09718	−0.164381
$356$	−23.5396	−1.24760
$357$	−2.96454	−0.156900
$358$	−28.5080	−1.50670
$359$	−31.8635	−1.68169	−0.840846	−	0.541275i	$-0.817942\pi$
$359$	−31.8635	−1.68169	−0.840846	+	0.541275i	$0.817942\pi$
$360$	−1.00949	−0.0532046
$361$	1.00000	0.0526316
$362$	23.3087	1.22508
$363$	−2.10296	−0.110377
$364$	−5.96404	−0.312601
$365$	4.02063	0.210449
$366$	−3.12846	−0.163527
$367$	−20.0046	−1.04423	−0.522117	−	0.852874i	$-0.674858\pi$
$367$	−20.0046	−1.04423	−0.522117	+	0.852874i	$0.674858\pi$
$368$	−34.7518	−1.81156
$369$	−6.80862	−0.354443
$370$	−7.71452	−0.401059
$371$	−13.8774	−0.720477
$372$	0.582507	0.0302016
$373$	5.25846	0.272273	0.136136	−	0.990690i	$-0.456531\pi$
$373$	5.25846	0.272273	0.136136	+	0.990690i	$0.456531\pi$
$374$	2.56688	0.132730
$375$	−0.909194	−0.0469506
$376$	2.29931	0.118578
$377$	1.59773	0.0822875
$378$	6.89919	0.354856
$379$	19.7180	1.01285	0.506423	−	0.862285i	$-0.330967\pi$
$379$	19.7180	1.01285	0.506423	+	0.862285i	$0.330967\pi$
$380$	−0.788362	−0.0404421
$381$	1.56695	0.0802773
$382$	11.6351	0.595305
$383$	−1.80538	−0.0922507	−0.0461253	−	0.998936i	$-0.514687\pi$
$383$	−1.80538	−0.0922507	−0.0461253	+	0.998936i	$0.514687\pi$
$384$	−1.06650	−0.0544245
$385$	0.420962	0.0214542
$386$	21.5064	1.09465
$387$	21.7185	1.10402
$388$	5.28157	0.268131
$389$	15.7186	0.796965	0.398483	−	0.917176i	$-0.369537\pi$
$389$	15.7186	0.796965	0.398483	+	0.917176i	$0.369537\pi$
$390$	0.205721	0.0104171
$391$	−36.8588	−1.86403
$392$	2.07846	0.104978
$393$	0.876923	0.0442349
$394$	−31.0060	−1.56206
$395$	−0.579703	−0.0291680
$396$	−1.33298	−0.0669845
$397$	−17.4261	−0.874591	−0.437295	−	0.899318i	$-0.644064\pi$
$397$	−17.4261	−0.874591	−0.437295	+	0.899318i	$0.644064\pi$
$398$	47.5290	2.38241
$399$	−0.607254	−0.0304007
$400$	21.9377	1.09688
$401$	8.64815	0.431868	0.215934	−	0.976408i	$-0.430720\pi$
$401$	8.64815	0.431868	0.215934	+	0.976408i	$0.430720\pi$
$402$	3.84289	0.191666
$403$	−2.15265	−0.107231
$404$	−17.8724	−0.889186
$405$	4.19167	0.208286
$406$	8.27958	0.410909
$407$	2.31055	0.114530
$408$	−0.662131	−0.0327804
$409$	2.61074	0.129093	0.0645463	−	0.997915i	$-0.479440\pi$
$409$	2.61074	0.129093	0.0645463	+	0.997915i	$0.479440\pi$
$410$	−2.11729	−0.104566
$411$	3.84461	0.189641
$412$	13.1333	0.647031
$413$	7.87686	0.387595
$414$	42.6230	2.09481
$415$	−1.94094	−0.0952768
$416$	−8.53689	−0.418555
$417$	−1.34431	−0.0658311
$418$	0.525797	0.0257176
$419$	−34.5804	−1.68936	−0.844681	−	0.535270i	$-0.820210\pi$
$419$	−34.5804	−1.68936	−0.844681	+	0.535270i	$0.820210\pi$
$420$	0.478736	0.0233599
$421$	3.83716	0.187012	0.0935060	−	0.995619i	$-0.470193\pi$
$421$	3.83716	0.187012	0.0935060	+	0.995619i	$0.470193\pi$
$422$	14.4176	0.701840
$423$	−9.66986	−0.470165
$424$	−3.09951	−0.150526
$425$	23.2677	1.12865
$426$	2.34916	0.113817
$427$	26.9043	1.30199
$428$	−17.5429	−0.847968
$429$	−0.0616147	−0.00297479
$430$	6.75386	0.325700
$431$	−16.7423	−0.806449	−0.403225	−	0.915101i	$-0.632111\pi$
$431$	−16.7423	−0.806449	−0.403225	+	0.915101i	$0.632111\pi$
$432$	5.28372	0.254213
$433$	−2.86215	−0.137546	−0.0687730	−	0.997632i	$-0.521908\pi$
$433$	−2.86215	−0.137546	−0.0687730	+	0.997632i	$0.521908\pi$
$434$	−11.1552	−0.535467
$435$	−0.128251	−0.00614916
$436$	−23.5610	−1.12837
$437$	−7.55013	−0.361172
$438$	−3.04958	−0.145715
$439$	13.9130	0.664034	0.332017	−	0.943273i	$-0.392271\pi$
$439$	13.9130	0.664034	0.332017	+	0.943273i	$0.392271\pi$
$440$	0.0940218	0.00448232
$441$	−8.74107	−0.416242
$442$	−10.7878	−0.513122
$443$	−24.0423	−1.14228	−0.571141	−	0.820852i	$-0.693499\pi$
$443$	−24.0423	−1.14228	−0.571141	+	0.820852i	$0.693499\pi$
$444$	2.62766	0.124703
$445$	−6.98277	−0.331015
$446$	40.6196	1.92340
$447$	1.28606	0.0608288
$448$	−15.2007	−0.718167
$449$	6.22590	0.293818	0.146909	−	0.989150i	$-0.453068\pi$
$449$	6.22590	0.293818	0.146909	+	0.989150i	$0.453068\pi$
$450$	−26.9065	−1.26838
$451$	0.634143	0.0298606
$452$	−23.1845	−1.09051
$453$	−2.26863	−0.106590
$454$	−29.7977	−1.39848
$455$	−1.76917	−0.0829399
$456$	−0.135630	−0.00635147
$457$	20.7843	0.972250	0.486125	−	0.873889i	$-0.338410\pi$
$457$	20.7843	0.972250	0.486125	+	0.873889i	$0.338410\pi$
$458$	11.7336	0.548274
$459$	5.60407	0.261576
$460$	5.95223	0.277524
$461$	−23.0718	−1.07456	−0.537281	−	0.843403i	$-0.680548\pi$
$461$	−23.0718	−1.07456	−0.537281	+	0.843403i	$0.680548\pi$
$462$	−0.319292	−0.0148548
$463$	−23.8808	−1.10983	−0.554917	−	0.831906i	$-0.687250\pi$
$463$	−23.8808	−1.10983	−0.554917	+	0.831906i	$0.687250\pi$
$464$	6.34089	0.294368
$465$	0.172794	0.00801315
$466$	25.6664	1.18897
$467$	−31.0463	−1.43665	−0.718326	−	0.695707i	$-0.755091\pi$
$467$	−31.0463	−1.43665	−0.718326	+	0.695707i	$0.755091\pi$
$468$	5.60207	0.258956
$469$	−33.0483	−1.52603
$470$	−3.00706	−0.138705
$471$	0.312487	0.0143986
$472$	1.75930	0.0809782
$473$	−2.02283	−0.0930097
$474$	0.439695	0.0201959
$475$	4.76614	0.218686
$476$	−25.1044	−1.15066
$477$	13.0351	0.596838
$478$	−20.5534	−0.940093
$479$	−37.9564	−1.73427	−0.867137	−	0.498070i	$-0.834042\pi$
$479$	−37.9564	−1.73427	−0.867137	+	0.498070i	$0.834042\pi$
$480$	0.685260	0.0312777
$481$	−9.71051	−0.442761
$482$	22.8775	1.04204
$483$	4.58485	0.208618
$484$	−17.8084	−0.809471
$485$	1.56672	0.0711412
$486$	−9.74084	−0.441853
$487$	−26.8893	−1.21847	−0.609236	−	0.792989i	$-0.708524\pi$
$487$	−26.8893	−1.21847	−0.609236	+	0.792989i	$0.708524\pi$
$488$	6.00909	0.272019
$489$	1.25551	0.0567761
$490$	−2.71823	−0.122797
$491$	−31.1045	−1.40373	−0.701863	−	0.712312i	$-0.747648\pi$
$491$	−31.1045	−1.40373	−0.701863	+	0.712312i	$0.747648\pi$
$492$	0.721176	0.0325131
$493$	6.72534	0.302894
$494$	−2.20976	−0.0994217
$495$	−0.395413	−0.0177725
$496$	−8.54318	−0.383600
$497$	−20.2024	−0.906202
$498$	1.47217	0.0659694
$499$	−6.15626	−0.275592	−0.137796	−	0.990461i	$-0.544002\pi$
$499$	−6.15626	−0.275592	−0.137796	+	0.990461i	$0.544002\pi$
$500$	−7.69925	−0.344321
$501$	4.19316	0.187337
$502$	34.9127	1.55823
$503$	−33.9425	−1.51342	−0.756710	−	0.653750i	$-0.773195\pi$
$503$	−33.9425	−1.51342	−0.756710	+	0.653750i	$0.773195\pi$
$504$	−6.58473	−0.293307
$505$	−5.30166	−0.235921
$506$	−3.96983	−0.176481
$507$	−2.24370	−0.0996462
$508$	13.2693	0.588729
$509$	3.12900	0.138690	0.0693452	−	0.997593i	$-0.477909\pi$
$509$	3.12900	0.138690	0.0693452	+	0.997593i	$0.477909\pi$
$510$	0.865940	0.0383445
$511$	26.2260	1.16017
$512$	−27.3945	−1.21068
$513$	1.14793	0.0506825
$514$	−17.2417	−0.760497
$515$	3.89585	0.171672
$516$	−2.30045	−0.101272
$517$	0.900634	0.0396098
$518$	−50.3206	−2.21096
$519$	0.265248	0.0116431
$520$	−0.395144	−0.0173282
$521$	31.8977	1.39746	0.698732	−	0.715383i	$-0.253748\pi$
$521$	31.8977	1.39746	0.698732	+	0.715383i	$0.253748\pi$
$522$	−7.77708	−0.340394
$523$	7.24919	0.316985	0.158492	−	0.987360i	$-0.449337\pi$
$523$	7.24919	0.316985	0.158492	+	0.987360i	$0.449337\pi$
$524$	7.42598	0.324406
$525$	−2.89426	−0.126316
$526$	36.4896	1.59102
$527$	−9.06115	−0.394710
$528$	−0.244529	−0.0106418
$529$	34.0044	1.47845
$530$	4.05356	0.176076
$531$	−7.39880	−0.321081
$532$	−5.14237	−0.222950
$533$	−2.66510	−0.115438
$534$	5.29631	0.229194
$535$	−5.20392	−0.224985
$536$	−7.38135	−0.318826
$537$	2.88042	0.124299
$538$	−17.2184	−0.742337
$539$	0.814128	0.0350670
$540$	−0.904987	−0.0389444
$541$	−23.4682	−1.00898	−0.504489	−	0.863418i	$-0.668319\pi$
$541$	−23.4682	−1.00898	−0.504489	+	0.863418i	$0.668319\pi$
$542$	49.6925	2.13447
$543$	−2.35509	−0.101067
$544$	−35.9343	−1.54067
$545$	−6.98913	−0.299381
$546$	1.34188	0.0574274
$547$	−4.06876	−0.173968	−0.0869838	−	0.996210i	$-0.527723\pi$
$547$	−4.06876	−0.173968	−0.0869838	+	0.996210i	$0.527723\pi$
$548$	32.5570	1.39077
$549$	−25.2715	−1.07856
$550$	2.50602	0.106857
$551$	1.37761	0.0586882
$552$	1.02403	0.0435855
$553$	−3.78132	−0.160798
$554$	−37.2533	−1.58274
$555$	0.779467	0.0330865
$556$	−11.3839	−0.482785
$557$	13.7567	0.582889	0.291444	−	0.956588i	$-0.405864\pi$
$557$	13.7567	0.582889	0.291444	+	0.956588i	$0.405864\pi$
$558$	10.4782	0.443577
$559$	8.50130	0.359567
$560$	−7.02126	−0.296702
$561$	−0.259355	−0.0109500
$562$	−26.6302	−1.12333
$563$	21.5907	0.909939	0.454969	−	0.890507i	$-0.349650\pi$
$563$	21.5907	0.909939	0.454969	+	0.890507i	$0.349650\pi$
$564$	1.02424	0.0431283
$565$	−6.87742	−0.289335
$566$	29.6006	1.24421
$567$	27.3417	1.14824
$568$	−4.51221	−0.189328
$569$	−10.5882	−0.443879	−0.221940	−	0.975060i	$-0.571239\pi$
$569$	−10.5882	−0.443879	−0.221940	+	0.975060i	$0.571239\pi$
$570$	0.177378	0.00742956
$571$	−10.6935	−0.447510	−0.223755	−	0.974645i	$-0.571832\pi$
$571$	−10.6935	−0.447510	−0.223755	+	0.974645i	$0.571832\pi$
$572$	−0.521767	−0.0218162
$573$	−1.17560	−0.0491115
$574$	−13.8108	−0.576450
$575$	−35.9850	−1.50068
$576$	14.2782	0.594924
$577$	−31.9517	−1.33016	−0.665082	−	0.746770i	$-0.731604\pi$
$577$	−31.9517	−1.33016	−0.665082	+	0.746770i	$0.731604\pi$
$578$	−13.0186	−0.541502
$579$	−2.17299	−0.0903063
$580$	−1.08606	−0.0450960
$581$	−12.6604	−0.525243
$582$	−1.18833	−0.0492580
$583$	−1.21407	−0.0502816
$584$	5.85757	0.242388
$585$	1.66180	0.0687068
$586$	−51.1782	−2.11415
$587$	5.49886	0.226962	0.113481	−	0.993540i	$-0.463800\pi$
$587$	5.49886	0.226962	0.113481	+	0.993540i	$0.463800\pi$
$588$	0.925863	0.0381819
$589$	−1.85608	−0.0764784
$590$	−2.30082	−0.0947233
$591$	3.13282	0.128867
$592$	−38.5379	−1.58390
$593$	13.5925	0.558178	0.279089	−	0.960265i	$-0.409968\pi$
$593$	13.5925	0.558178	0.279089	+	0.960265i	$0.409968\pi$
$594$	0.603580	0.0247652
$595$	−7.44696	−0.305296
$596$	10.8907	0.446100
$597$	−4.80228	−0.196544
$598$	16.6840	0.682257
$599$	34.4227	1.40647	0.703236	−	0.710957i	$-0.251738\pi$
$599$	34.4227	1.40647	0.703236	+	0.710957i	$0.251738\pi$
$600$	−0.646433	−0.0263905
$601$	−5.73276	−0.233844	−0.116922	−	0.993141i	$-0.537303\pi$
$601$	−5.73276	−0.233844	−0.116922	+	0.993141i	$0.537303\pi$
$602$	44.0544	1.79552
$603$	31.0426	1.26415
$604$	−19.2113	−0.781697
$605$	−5.28266	−0.214771
$606$	4.02122	0.163351
$607$	43.9158	1.78249	0.891244	−	0.453524i	$-0.149833\pi$
$607$	43.9158	1.78249	0.891244	+	0.453524i	$0.149833\pi$
$608$	−7.36075	−0.298518
$609$	−0.836561	−0.0338992
$610$	−7.85873	−0.318191
$611$	−3.78508	−0.153128
$612$	23.5808	0.953197
$613$	7.03264	0.284046	0.142023	−	0.989863i	$-0.454639\pi$
$613$	7.03264	0.284046	0.142023	+	0.989863i	$0.454639\pi$
$614$	27.9655	1.12860
$615$	0.213929	0.00862645
$616$	0.613290	0.0247102
$617$	−38.7033	−1.55814	−0.779068	−	0.626940i	$-0.784307\pi$
$617$	−38.7033	−1.55814	−0.779068	+	0.626940i	$0.784307\pi$
$618$	−2.95494	−0.118865
$619$	−45.5247	−1.82979	−0.914896	−	0.403690i	$-0.867728\pi$
$619$	−45.5247	−1.82979	−0.914896	+	0.403690i	$0.867728\pi$
$620$	1.46326	0.0587660
$621$	−8.66704	−0.347796
$622$	6.66086	0.267076
$623$	−45.5475	−1.82482
$624$	1.02768	0.0411400
$625$	21.5468	0.861872
$626$	34.9333	1.39622
$627$	−0.0531260	−0.00212165
$628$	2.64621	0.105595
$629$	−40.8744	−1.62977
$630$	8.61155	0.343092
$631$	43.2374	1.72125	0.860627	−	0.509236i	$-0.170072\pi$
$631$	43.2374	1.72125	0.860627	+	0.509236i	$0.170072\pi$
$632$	−0.844558	−0.0335947
$633$	−1.45674	−0.0579004
$634$	1.90532	0.0756698
$635$	3.93619	0.156203
$636$	−1.38069	−0.0547481
$637$	−3.42152	−0.135566
$638$	0.724344	0.0286770
$639$	18.9763	0.750691
$640$	−2.67905	−0.105899
$641$	22.6887	0.896148	0.448074	−	0.893996i	$-0.352110\pi$
$641$	22.6887	0.896148	0.448074	+	0.893996i	$0.352110\pi$
$642$	3.94708	0.155779
$643$	32.4261	1.27876	0.639379	−	0.768891i	$-0.279191\pi$
$643$	32.4261	1.27876	0.639379	+	0.768891i	$0.279191\pi$
$644$	38.8255	1.52994
$645$	−0.682404	−0.0268696
$646$	−9.30153	−0.365964
$647$	19.2569	0.757066	0.378533	−	0.925588i	$-0.376429\pi$
$647$	19.2569	0.757066	0.378533	+	0.925588i	$0.376429\pi$
$648$	6.10676	0.239896
$649$	0.689111	0.0270500
$650$	−10.5320	−0.413100
$651$	1.12711	0.0441750
$652$	10.6319	0.416378
$653$	−10.3758	−0.406036	−0.203018	−	0.979175i	$-0.565075\pi$
$653$	−10.3758	−0.406036	−0.203018	+	0.979175i	$0.565075\pi$
$654$	5.30114	0.207291
$655$	2.20284	0.0860720
$656$	−10.5769	−0.412960
$657$	−24.6343	−0.961075
$658$	−19.6146	−0.764656
$659$	11.6409	0.453466	0.226733	−	0.973957i	$-0.427195\pi$
$659$	11.6409	0.453466	0.226733	+	0.973957i	$0.427195\pi$
$660$	0.0418825	0.00163027
$661$	−41.2231	−1.60339	−0.801696	−	0.597733i	$-0.796068\pi$
$661$	−41.2231	−1.60339	−0.801696	+	0.597733i	$0.796068\pi$
$662$	−13.2520	−0.515052
$663$	1.08999	0.0423316
$664$	−2.82771	−0.109736
$665$	−1.52543	−0.0591536
$666$	47.2666	1.83154
$667$	−10.4011	−0.402734
$668$	35.5086	1.37387
$669$	−4.10417	−0.158676
$670$	9.65338	0.372942
$671$	2.35374	0.0908652
$672$	4.46985	0.172428
$673$	34.2744	1.32118	0.660591	−	0.750746i	$-0.270306\pi$
$673$	34.2744	1.32118	0.660591	+	0.750746i	$0.270306\pi$
$674$	2.38596	0.0919036
$675$	5.47121	0.210587
$676$	−19.0001	−0.730775
$677$	20.4310	0.785228	0.392614	−	0.919703i	$-0.371571\pi$
$677$	20.4310	0.785228	0.392614	+	0.919703i	$0.371571\pi$
$678$	5.21641	0.200335
$679$	10.2195	0.392188
$680$	−1.66328	−0.0637838
$681$	3.01074	0.115372
$682$	−0.975920	−0.0373699
$683$	−22.2896	−0.852888	−0.426444	−	0.904514i	$-0.640234\pi$
$683$	−22.2896	−0.852888	−0.426444	+	0.904514i	$0.640234\pi$
$684$	4.83027	0.184690
$685$	9.65769	0.369001
$686$	24.3401	0.929308
$687$	−1.18555	−0.0452315
$688$	33.7389	1.28628
$689$	5.10235	0.194384
$690$	−1.33923	−0.0509836
$691$	−7.67977	−0.292152	−0.146076	−	0.989273i	$-0.546664\pi$
$691$	−7.67977	−0.292152	−0.146076	+	0.989273i	$0.546664\pi$
$692$	2.24618	0.0853869
$693$	−2.57922	−0.0979764
$694$	−58.2744	−2.21206
$695$	−3.37692	−0.128094
$696$	−0.186846	−0.00708238
$697$	−11.2182	−0.424920
$698$	−14.8450	−0.561893
$699$	−2.59330	−0.0980878
$700$	−24.5092	−0.926362
$701$	21.3710	0.807173	0.403587	−	0.914941i	$-0.367763\pi$
$701$	21.3710	0.807173	0.403587	+	0.914941i	$0.367763\pi$
$702$	−2.53665	−0.0957398
$703$	−8.37268	−0.315782
$704$	−1.32985	−0.0501204
$705$	0.303830	0.0114429
$706$	−33.3461	−1.25500
$707$	−34.5820	−1.30059
$708$	0.783688	0.0294528
$709$	−7.56456	−0.284093	−0.142046	−	0.989860i	$-0.545368\pi$
$709$	−7.56456	−0.284093	−0.142046	+	0.989860i	$0.545368\pi$
$710$	5.90110	0.221464
$711$	3.55182	0.133204
$712$	−10.1730	−0.381251
$713$	14.0136	0.524814
$714$	5.64839	0.211386
$715$	−0.154777	−0.00578832
$716$	24.3921	0.911574
$717$	2.07670	0.0775558
$718$	60.7100	2.26568
$719$	34.6906	1.29374	0.646870	−	0.762600i	$-0.276077\pi$
$719$	34.6906	1.29374	0.646870	+	0.762600i	$0.276077\pi$
$720$	6.59513	0.245786
$721$	25.4120	0.946394
$722$	−1.90532	−0.0709085
$723$	−2.31152	−0.0859662
$724$	−19.9434	−0.741192
$725$	6.56589	0.243851
$726$	4.00681	0.148707
$727$	−11.1343	−0.412949	−0.206475	−	0.978452i	$-0.566199\pi$
$727$	−11.1343	−0.412949	−0.206475	+	0.978452i	$0.566199\pi$
$728$	−2.57746	−0.0955272
$729$	−25.0193	−0.926640
$730$	−7.66057	−0.283531
$731$	35.7845	1.32354
$732$	2.67678	0.0989366
$733$	−42.0339	−1.55256	−0.776279	−	0.630390i	$-0.782895\pi$
$733$	−42.0339	−1.55256	−0.776279	+	0.630390i	$0.782895\pi$
$734$	38.1152	1.40686
$735$	0.274647	0.0101305
$736$	55.5746	2.04851
$737$	−2.89125	−0.106501
$738$	12.9726	0.477527
$739$	13.7933	0.507394	0.253697	−	0.967284i	$-0.418353\pi$
$739$	13.7933	0.507394	0.253697	+	0.967284i	$0.418353\pi$
$740$	6.60070	0.242647
$741$	0.223272	0.00820209
$742$	26.4408	0.970671
$743$	−46.6466	−1.71130	−0.855648	−	0.517558i	$-0.826841\pi$
$743$	−46.6466	−1.71130	−0.855648	+	0.517558i	$0.826841\pi$
$744$	0.251740	0.00922925
$745$	3.23060	0.118360
$746$	−10.0190	−0.366823
$747$	11.8921	0.435107
$748$	−2.19627	−0.0803038
$749$	−33.9444	−1.24030
$750$	1.73230	0.0632547
$751$	32.0437	1.16929	0.584646	−	0.811289i	$-0.301233\pi$
$751$	32.0437	1.16929	0.584646	+	0.811289i	$0.301233\pi$
$752$	−15.0218	−0.547787
$753$	−3.52754	−0.128551
$754$	−3.04419	−0.110863
$755$	−5.69883	−0.207402
$756$	−5.90309	−0.214693
$757$	−15.9303	−0.578996	−0.289498	−	0.957179i	$-0.593488\pi$
$757$	−15.9303	−0.578996	−0.289498	+	0.957179i	$0.593488\pi$
$758$	−37.5690	−1.36457
$759$	0.401108	0.0145593
$760$	−0.340704	−0.0123586
$761$	−32.0099	−1.16036	−0.580178	−	0.814489i	$-0.697017\pi$
$761$	−32.0099	−1.16036	−0.580178	+	0.814489i	$0.697017\pi$
$762$	−2.98553	−0.108154
$763$	−45.5890	−1.65043
$764$	−9.95527	−0.360169
$765$	6.99499	0.252905
$766$	3.43982	0.124286
$767$	−2.89612	−0.104573
$768$	3.88741	0.140275
$769$	−47.5896	−1.71613	−0.858063	−	0.513545i	$-0.828332\pi$
$769$	−47.5896	−1.71613	−0.858063	+	0.513545i	$0.828332\pi$
$770$	−0.802065	−0.0289044
$771$	1.74208	0.0627395
$772$	−18.4013	−0.662279
$773$	24.1627	0.869073	0.434537	−	0.900654i	$-0.356912\pi$
$773$	24.1627	0.869073	0.434537	+	0.900654i	$0.356912\pi$
$774$	−41.3807	−1.48740
$775$	−8.84633	−0.317770
$776$	2.28252	0.0819378
$777$	5.08435	0.182400
$778$	−29.9489	−1.07372
$779$	−2.29793	−0.0823318
$780$	−0.176019	−0.00630249
$781$	−1.76742	−0.0632433
$782$	70.2277	2.51134
$783$	1.58141	0.0565148
$784$	−13.5789	−0.484961
$785$	0.784970	0.0280168
$786$	−1.67082	−0.0595960
$787$	−36.4965	−1.30096	−0.650479	−	0.759524i	$-0.725432\pi$
$787$	−36.4965	−1.30096	−0.650479	+	0.759524i	$0.725432\pi$
$788$	26.5294	0.945072
$789$	−3.68687	−0.131256
$790$	1.10452	0.0392970
$791$	−44.8604	−1.59505
$792$	−0.576069	−0.0204697
$793$	−9.89203	−0.351276
$794$	33.2022	1.17830
$795$	−0.409568	−0.0145259
$796$	−40.6668	−1.44140
$797$	−56.1672	−1.98954	−0.994771	−	0.102126i	$-0.967435\pi$
$797$	−56.1672	−1.98954	−0.994771	+	0.102126i	$0.967435\pi$
$798$	1.15701	0.0409578
$799$	−15.9325	−0.563652
$800$	−35.0824	−1.24035
$801$	42.7832	1.51167
$802$	−16.4775	−0.581840
$803$	2.29439	0.0809674
$804$	−3.28806	−0.115961
$805$	11.5172	0.405927
$806$	4.10148	0.144469
$807$	1.73973	0.0612413
$808$	−7.72388	−0.271725
$809$	33.5262	1.17872	0.589359	−	0.807872i	$-0.299381\pi$
$809$	33.5262	1.17872	0.589359	+	0.807872i	$0.299381\pi$
$810$	−7.98646	−0.280616
$811$	−2.38310	−0.0836819	−0.0418409	−	0.999124i	$-0.513322\pi$
$811$	−2.38310	−0.0836819	−0.0418409	+	0.999124i	$0.513322\pi$
$812$	−7.08418	−0.248606
$813$	−5.02088	−0.176090
$814$	−4.40233	−0.154302
$815$	3.15385	0.110474
$816$	4.32580	0.151433
$817$	7.33007	0.256447
$818$	−4.97428	−0.173922
$819$	10.8396	0.378768
$820$	1.81160	0.0632638
$821$	−28.5564	−0.996625	−0.498312	−	0.866998i	$-0.666047\pi$
$821$	−28.5564	−0.996625	−0.498312	+	0.866998i	$0.666047\pi$
$822$	−7.32519	−0.255495
$823$	29.2610	1.01998	0.509988	−	0.860182i	$-0.329650\pi$
$823$	29.2610	1.01998	0.509988	+	0.860182i	$0.329650\pi$
$824$	5.67578	0.197725
$825$	−0.253206	−0.00881550
$826$	−15.0079	−0.522192
$827$	40.6414	1.41324	0.706620	−	0.707593i	$-0.250219\pi$
$827$	40.6414	1.41324	0.706620	+	0.707593i	$0.250219\pi$
$828$	−36.4691	−1.26739
$829$	−46.1735	−1.60367	−0.801836	−	0.597545i	$-0.796143\pi$
$829$	−46.1735	−1.60367	−0.801836	+	0.597545i	$0.796143\pi$
$830$	3.69810	0.128363
$831$	3.76404	0.130573
$832$	5.58892	0.193761
$833$	−14.4022	−0.499007
$834$	2.56133	0.0886918
$835$	10.5333	0.364518
$836$	−0.449883	−0.0155595
$837$	−2.13065	−0.0736461
$838$	65.8866	2.27601
$839$	−39.8820	−1.37688	−0.688439	−	0.725294i	$-0.741704\pi$
$839$	−39.8820	−1.37688	−0.688439	+	0.725294i	$0.741704\pi$
$840$	0.206894	0.00713853
$841$	−27.1022	−0.934558
$842$	−7.31101	−0.251954
$843$	2.69069	0.0926722
$844$	−12.3360	−0.424624
$845$	−5.63619	−0.193891
$846$	18.4241	0.633435
$847$	−34.4580	−1.18399
$848$	20.2496	0.695373
$849$	−2.99082	−0.102645
$850$	−44.3324	−1.52059
$851$	63.2148	2.16698
$852$	−2.00999	−0.0688611
$853$	−12.0596	−0.412911	−0.206456	−	0.978456i	$-0.566193\pi$
$853$	−12.0596	−0.412911	−0.206456	+	0.978456i	$0.566193\pi$
$854$	−51.2613	−1.75412
$855$	1.43285	0.0490024
$856$	−7.58148	−0.259129
$857$	−14.5354	−0.496520	−0.248260	−	0.968693i	$-0.579859\pi$
$857$	−14.5354	−0.496520	−0.248260	+	0.968693i	$0.579859\pi$
$858$	0.117396	0.00400782
$859$	33.3997	1.13958	0.569792	−	0.821789i	$-0.307024\pi$
$859$	33.3997	1.13958	0.569792	+	0.821789i	$0.307024\pi$
$860$	−5.77875	−0.197054
$861$	1.39543	0.0475560
$862$	31.8994	1.08650
$863$	−38.8927	−1.32392	−0.661962	−	0.749537i	$-0.730276\pi$
$863$	−38.8927	−1.32392	−0.661962	+	0.749537i	$0.730276\pi$
$864$	−8.44965	−0.287463
$865$	0.666305	0.0226550
$866$	5.45330	0.185311
$867$	1.31539	0.0446728
$868$	9.54463	0.323966
$869$	−0.330811	−0.0112220
$870$	0.244358	0.00828452
$871$	12.1510	0.411721
$872$	−10.1823	−0.344817
$873$	−9.59925	−0.324886
$874$	14.3854	0.486593
$875$	−14.8975	−0.503629
$876$	2.60929	0.0881596
$877$	−51.0238	−1.72295	−0.861475	−	0.507799i	$-0.830459\pi$
$877$	−51.0238	−1.72295	−0.861475	+	0.507799i	$0.830459\pi$
$878$	−26.5087	−0.894627
$879$	5.17099	0.174413
$880$	−0.614259	−0.0207067
$881$	7.84432	0.264282	0.132141	−	0.991231i	$-0.457815\pi$
$881$	7.84432	0.264282	0.132141	+	0.991231i	$0.457815\pi$
$882$	16.6545	0.560786
$883$	31.0420	1.04465	0.522323	−	0.852748i	$-0.325066\pi$
$883$	31.0420	1.04465	0.522323	+	0.852748i	$0.325066\pi$
$884$	9.23025	0.310447
$885$	0.232473	0.00781448
$886$	45.8081	1.53895
$887$	7.90835	0.265536	0.132768	−	0.991147i	$-0.457613\pi$
$887$	7.90835	0.265536	0.132768	+	0.991147i	$0.457613\pi$
$888$	1.13559	0.0381079
$889$	25.6752	0.861118
$890$	13.3044	0.445964
$891$	2.39200	0.0801350
$892$	−34.7550	−1.16368
$893$	−3.26360	−0.109212
$894$	−2.45036	−0.0819523
$895$	7.23565	0.241861
$896$	−17.4750	−0.583800
$897$	−1.68573	−0.0562849
$898$	−11.8623	−0.395850
$899$	−2.55695	−0.0852792
$900$	23.0217	0.767391
$901$	21.4773	0.715513
$902$	−1.20824	−0.0402301
$903$	−4.45121	−0.148127
$904$	−10.0196	−0.333246
$905$	−5.91601	−0.196655
$906$	4.32247	0.143604
$907$	−16.6993	−0.554492	−0.277246	−	0.960799i	$-0.589422\pi$
$907$	−16.6993	−0.554492	−0.277246	+	0.960799i	$0.589422\pi$
$908$	25.4956	0.846101
$909$	32.4831	1.07740
$910$	3.37083	0.111742
$911$	−6.94656	−0.230150	−0.115075	−	0.993357i	$-0.536711\pi$
$911$	−6.94656	−0.230150	−0.115075	+	0.993357i	$0.536711\pi$
$912$	0.886093	0.0293415
$913$	−1.10761	−0.0366564
$914$	−39.6007	−1.30988
$915$	0.794038	0.0262501
$916$	−10.0395	−0.331714
$917$	14.3688	0.474499
$918$	−10.6775	−0.352411
$919$	−19.6077	−0.646798	−0.323399	−	0.946263i	$-0.604826\pi$
$919$	−19.6077	−0.646798	−0.323399	+	0.946263i	$0.604826\pi$
$920$	2.57236	0.0848083
$921$	−2.82561	−0.0931069
$922$	43.9591	1.44772
$923$	7.42791	0.244492
$924$	0.273193	0.00898740
$925$	−39.9054	−1.31208
$926$	45.5004	1.49524
$927$	−23.8697	−0.783985
$928$	−10.1403	−0.332870
$929$	−13.9927	−0.459085	−0.229542	−	0.973299i	$-0.573723\pi$
$929$	−13.9927	−0.459085	−0.229542	+	0.973299i	$0.573723\pi$
$930$	−0.329228	−0.0107958
$931$	−2.95014	−0.0966868
$932$	−21.9607	−0.719346
$933$	−0.673007	−0.0220332
$934$	59.1530	1.93555
$935$	−0.651502	−0.0213064
$936$	2.42103	0.0791340
$937$	−41.9479	−1.37038	−0.685190	−	0.728365i	$-0.740281\pi$
$937$	−41.9479	−1.37038	−0.685190	+	0.728365i	$0.740281\pi$
$938$	62.9675	2.05596
$939$	−3.52963	−0.115185
$940$	2.57290	0.0839188
$941$	22.0640	0.719265	0.359633	−	0.933094i	$-0.382902\pi$
$941$	22.0640	0.719265	0.359633	+	0.933094i	$0.382902\pi$
$942$	−0.595386	−0.0193987
$943$	17.3497	0.564982
$944$	−11.4937	−0.374090
$945$	−1.75109	−0.0569629
$946$	3.85413	0.125308
$947$	−12.5010	−0.406227	−0.203113	−	0.979155i	$-0.565106\pi$
$947$	−12.5010	−0.406227	−0.203113	+	0.979155i	$0.565106\pi$
$948$	−0.376213	−0.0122188
$949$	−9.64261	−0.313012
$950$	−9.08100	−0.294627
$951$	−0.192511	−0.00624261
$952$	−10.8493	−0.351628
$953$	−34.5045	−1.11771	−0.558856	−	0.829265i	$-0.688759\pi$
$953$	−34.5045	−1.11771	−0.558856	+	0.829265i	$0.688759\pi$
$954$	−24.8360	−0.804097
$955$	−2.95312	−0.0955608
$956$	17.5860	0.568771
$957$	−0.0731870	−0.00236580
$958$	72.3190	2.33652
$959$	62.9956	2.03423
$960$	−0.448625	−0.0144793
$961$	−27.5550	−0.888870
$962$	18.5016	0.596515
$963$	31.8842	1.02745
$964$	−19.5744	−0.630450
$965$	−5.45856	−0.175717
$966$	−8.73559	−0.281063
$967$	−1.17818	−0.0378878	−0.0189439	−	0.999821i	$-0.506030\pi$
$967$	−1.17818	−0.0378878	−0.0189439	+	0.999821i	$0.506030\pi$
$968$	−7.69620	−0.247365
$969$	0.939817	0.0301913
$970$	−2.98510	−0.0958458
$971$	37.2248	1.19460	0.597301	−	0.802017i	$-0.296240\pi$
$971$	37.2248	1.19460	0.597301	+	0.802017i	$0.296240\pi$
$972$	8.33447	0.267328
$973$	−22.0271	−0.706157
$974$	51.2327	1.64160
$975$	1.06414	0.0340799
$976$	−39.2583	−1.25663
$977$	−12.6335	−0.404182	−0.202091	−	0.979367i	$-0.564774\pi$
$977$	−12.6335	−0.404182	−0.202091	+	0.979367i	$0.564774\pi$
$978$	−2.39214	−0.0764922
$979$	−3.98475	−0.127353
$980$	2.32577	0.0742942
$981$	42.8222	1.36721
$982$	59.2639	1.89119
$983$	22.7119	0.724398	0.362199	−	0.932101i	$-0.382026\pi$
$983$	22.7119	0.724398	0.362199	+	0.932101i	$0.382026\pi$
$984$	0.311669	0.00993564
$985$	7.86967	0.250749
$986$	−12.8139	−0.408077
$987$	1.98184	0.0630826
$988$	1.89071	0.0601516
$989$	−55.3429	−1.75980
$990$	0.753387	0.0239442
$991$	−3.85710	−0.122525	−0.0612623	−	0.998122i	$-0.519513\pi$
$991$	−3.85710	−0.122525	−0.0612623	+	0.998122i	$0.519513\pi$
$992$	13.6621	0.433773
$993$	1.33896	0.0424907
$994$	38.4920	1.22089
$995$	−12.0634	−0.382435
$996$	−1.25962	−0.0399125
$997$	−24.1860	−0.765977	−0.382989	−	0.923753i	$-0.625105\pi$
$997$	−24.1860	−0.765977	−0.382989	+	0.923753i	$0.625105\pi$
$998$	11.7296	0.371294
$999$	−9.61128	−0.304087

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.b.1.19	✓	99

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.b.1.19	✓	99	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-1.90532 q^{2} +0.192511 q^{3} +1.63023 q^{4} +0.483590 q^{5} -0.366795 q^{6} +3.15438 q^{7} +0.704532 q^{8} -2.96294 q^{9} +O(q^{10})\)	\(q-1.90532 q^{2} +0.192511 q^{3} +1.63023 q^{4} +0.483590 q^{5} -0.366795 q^{6} +3.15438 q^{7} +0.704532 q^{8} -2.96294 q^{9} -0.921392 q^{10} +0.275963 q^{11} +0.313837 q^{12} -1.15979 q^{13} -6.01010 q^{14} +0.0930965 q^{15} -4.60281 q^{16} -4.88188 q^{17} +5.64534 q^{18} -1.00000 q^{19} +0.788362 q^{20} +0.607254 q^{21} -0.525797 q^{22} +7.55013 q^{23} +0.135630 q^{24} -4.76614 q^{25} +2.20976 q^{26} -1.14793 q^{27} +5.14237 q^{28} -1.37761 q^{29} -0.177378 q^{30} +1.85608 q^{31} +7.36075 q^{32} +0.0531260 q^{33} +9.30153 q^{34} +1.52543 q^{35} -4.83027 q^{36} +8.37268 q^{37} +1.90532 q^{38} -0.223272 q^{39} +0.340704 q^{40} +2.29793 q^{41} -1.15701 q^{42} -7.33007 q^{43} +0.449883 q^{44} -1.43285 q^{45} -14.3854 q^{46} +3.26360 q^{47} -0.886093 q^{48} +2.95014 q^{49} +9.08100 q^{50} -0.939817 q^{51} -1.89071 q^{52} -4.39939 q^{53} +2.18718 q^{54} +0.133453 q^{55} +2.22236 q^{56} -0.192511 q^{57} +2.62479 q^{58} +2.49711 q^{59} +0.151769 q^{60} +8.52919 q^{61} -3.53641 q^{62} -9.34625 q^{63} -4.81892 q^{64} -0.560860 q^{65} -0.101222 q^{66} -10.4770 q^{67} -7.95858 q^{68} +1.45348 q^{69} -2.90642 q^{70} -6.40455 q^{71} -2.08748 q^{72} +8.31413 q^{73} -15.9526 q^{74} -0.917536 q^{75} -1.63023 q^{76} +0.870493 q^{77} +0.425403 q^{78} -1.19875 q^{79} -2.22587 q^{80} +8.66783 q^{81} -4.37828 q^{82} -4.01360 q^{83} +0.989963 q^{84} -2.36083 q^{85} +13.9661 q^{86} -0.265206 q^{87} +0.194425 q^{88} -14.4394 q^{89} +2.73003 q^{90} -3.65841 q^{91} +12.3084 q^{92} +0.357316 q^{93} -6.21819 q^{94} -0.483590 q^{95} +1.41703 q^{96} +3.23977 q^{97} -5.62094 q^{98} -0.817662 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9}+O(q^{10}) \) 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9} - 6 q^{10} - 9 q^{11} - 27 q^{12} - 28 q^{13} - 13 q^{14} - 10 q^{15} + 38 q^{16} - 36 q^{17} - 14 q^{18} - 99 q^{19} - 34 q^{20} - 20 q^{21} - 53 q^{22} - 38 q^{23} - 25 q^{24} - 8 q^{25} - 3 q^{26} - 3 q^{27} - 63 q^{28} - 34 q^{29} - 30 q^{30} - 16 q^{31} - 43 q^{32} - 41 q^{33} - 14 q^{34} - 25 q^{35} - 16 q^{36} - 80 q^{37} + 4 q^{38} - 48 q^{39} - 10 q^{40} - 32 q^{41} - 37 q^{42} - 76 q^{43} - 21 q^{44} - 53 q^{45} - 23 q^{46} - 31 q^{47} - 74 q^{48} - 32 q^{49} - 29 q^{50} - 30 q^{51} - 71 q^{52} - 35 q^{53} - 80 q^{54} - 45 q^{55} - 33 q^{56} + 3 q^{57} - 91 q^{58} + 12 q^{59} - 56 q^{60} - 61 q^{61} - 46 q^{62} - 43 q^{63} - 30 q^{64} - 46 q^{65} - 75 q^{66} - 26 q^{67} - 55 q^{68} - 45 q^{69} - 76 q^{70} - 41 q^{71} - 77 q^{72} - 143 q^{73} - 64 q^{74} - 8 q^{75} - 80 q^{76} - 58 q^{77} - 34 q^{78} - 22 q^{79} - 36 q^{80} - 81 q^{81} - 109 q^{82} - 7 q^{83} - 6 q^{84} - 80 q^{85} + 32 q^{86} - 57 q^{87} - 120 q^{88} - 28 q^{89} - 12 q^{90} - 30 q^{91} - 107 q^{92} - 121 q^{93} + 8 q^{94} + 15 q^{95} + 4 q^{96} - 128 q^{97} + 54 q^{98} - 34 q^{99}+O(q^{100}) \) 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9 - 6 * q^10 - 9 * q^11 - 27 * q^12 - 28 * q^13 - 13 * q^14 - 10 * q^15 + 38 * q^16 - 36 * q^17 - 14 * q^18 - 99 * q^19 - 34 * q^20 - 20 * q^21 - 53 * q^22 - 38 * q^23 - 25 * q^24 - 8 * q^25 - 3 * q^26 - 3 * q^27 - 63 * q^28 - 34 * q^29 - 30 * q^30 - 16 * q^31 - 43 * q^32 - 41 * q^33 - 14 * q^34 - 25 * q^35 - 16 * q^36 - 80 * q^37 + 4 * q^38 - 48 * q^39 - 10 * q^40 - 32 * q^41 - 37 * q^42 - 76 * q^43 - 21 * q^44 - 53 * q^45 - 23 * q^46 - 31 * q^47 - 74 * q^48 - 32 * q^49 - 29 * q^50 - 30 * q^51 - 71 * q^52 - 35 * q^53 - 80 * q^54 - 45 * q^55 - 33 * q^56 + 3 * q^57 - 91 * q^58 + 12 * q^59 - 56 * q^60 - 61 * q^61 - 46 * q^62 - 43 * q^63 - 30 * q^64 - 46 * q^65 - 75 * q^66 - 26 * q^67 - 55 * q^68 - 45 * q^69 - 76 * q^70 - 41 * q^71 - 77 * q^72 - 143 * q^73 - 64 * q^74 - 8 * q^75 - 80 * q^76 - 58 * q^77 - 34 * q^78 - 22 * q^79 - 36 * q^80 - 81 * q^81 - 109 * q^82 - 7 * q^83 - 6 * q^84 - 80 * q^85 + 32 * q^86 - 57 * q^87 - 120 * q^88 - 28 * q^89 - 12 * q^90 - 30 * q^91 - 107 * q^92 - 121 * q^93 + 8 * q^94 + 15 * q^95 + 4 * q^96 - 128 * q^97 + 54 * q^98 - 34 * q^99

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