LMFDB - Embedded newform 4033.2.a.e.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.2036671352$
Analytic rank:	$0$
Dimension:	$82$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.32285 q^{2} +2.68333 q^{3} +3.39564 q^{4} -2.18288 q^{5} -6.23298 q^{6} +1.55979 q^{7} -3.24187 q^{8} +4.20026 q^{9} +O(q^{10})$	\(q-2.32285 q^{2} +2.68333 q^{3} +3.39564 q^{4} -2.18288 q^{5} -6.23298 q^{6} +1.55979 q^{7} -3.24187 q^{8} +4.20026 q^{9} +5.07050 q^{10} +2.77170 q^{11} +9.11162 q^{12} +1.99402 q^{13} -3.62315 q^{14} -5.85738 q^{15} +0.739095 q^{16} +5.84932 q^{17} -9.75658 q^{18} +6.51124 q^{19} -7.41226 q^{20} +4.18542 q^{21} -6.43824 q^{22} +3.96182 q^{23} -8.69900 q^{24} -0.235052 q^{25} -4.63181 q^{26} +3.22069 q^{27} +5.29647 q^{28} +8.28758 q^{29} +13.6058 q^{30} -7.81389 q^{31} +4.76693 q^{32} +7.43738 q^{33} -13.5871 q^{34} -3.40482 q^{35} +14.2626 q^{36} -1.00000 q^{37} -15.1247 q^{38} +5.35061 q^{39} +7.07659 q^{40} -2.68459 q^{41} -9.72211 q^{42} +4.38045 q^{43} +9.41169 q^{44} -9.16864 q^{45} -9.20271 q^{46} +3.89639 q^{47} +1.98323 q^{48} -4.56707 q^{49} +0.545991 q^{50} +15.6957 q^{51} +6.77098 q^{52} -1.01578 q^{53} -7.48118 q^{54} -6.05027 q^{55} -5.05662 q^{56} +17.4718 q^{57} -19.2508 q^{58} +6.59980 q^{59} -19.8895 q^{60} +9.58574 q^{61} +18.1505 q^{62} +6.55151 q^{63} -12.5511 q^{64} -4.35270 q^{65} -17.2759 q^{66} -15.2255 q^{67} +19.8622 q^{68} +10.6309 q^{69} +7.90889 q^{70} +2.25001 q^{71} -13.6167 q^{72} -9.61582 q^{73} +2.32285 q^{74} -0.630722 q^{75} +22.1098 q^{76} +4.32326 q^{77} -12.4287 q^{78} -2.62406 q^{79} -1.61335 q^{80} -3.95861 q^{81} +6.23590 q^{82} -1.26693 q^{83} +14.2122 q^{84} -12.7683 q^{85} -10.1751 q^{86} +22.2383 q^{87} -8.98548 q^{88} -9.75300 q^{89} +21.2974 q^{90} +3.11025 q^{91} +13.4529 q^{92} -20.9672 q^{93} -9.05073 q^{94} -14.2132 q^{95} +12.7912 q^{96} -5.73825 q^{97} +10.6086 q^{98} +11.6418 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9}+O(q^{10}) $ 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9	\( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9} + 13 q^{10} + 2 q^{11} + 36 q^{12} + 23 q^{13} + 24 q^{14} + 35 q^{15} + 104 q^{16} + 43 q^{17} + 42 q^{18} + 15 q^{19} + 59 q^{20} + 9 q^{21} + 6 q^{22} + 70 q^{23} + 15 q^{24} + 98 q^{25} + 10 q^{26} + 65 q^{27} + 37 q^{28} + 27 q^{29} + 17 q^{30} + 59 q^{31} + 46 q^{32} + 16 q^{33} - 16 q^{34} + 80 q^{35} + 88 q^{36} - 82 q^{37} + 82 q^{38} + 13 q^{39} + 14 q^{40} + 3 q^{41} + 62 q^{42} + 7 q^{43} - 11 q^{44} + 42 q^{45} - 11 q^{46} + 123 q^{47} + 45 q^{48} + 105 q^{49} + 27 q^{50} + 3 q^{51} - 30 q^{52} + 82 q^{53} - 27 q^{54} + 37 q^{55} + 66 q^{56} + 29 q^{57} - 34 q^{58} + 60 q^{59} + 94 q^{60} + 9 q^{61} - 2 q^{62} + 106 q^{63} + 93 q^{64} + 9 q^{65} + 63 q^{66} + 113 q^{68} + 48 q^{69} + 47 q^{70} + 59 q^{71} + 63 q^{72} + 21 q^{73} - 10 q^{74} + 77 q^{75} + 22 q^{76} + 30 q^{77} + 29 q^{78} + 55 q^{79} + 88 q^{80} + 42 q^{81} + 4 q^{82} + 92 q^{83} + 43 q^{84} - 7 q^{85} + 17 q^{86} + 147 q^{87} - 13 q^{88} + 100 q^{89} + 91 q^{90} + 28 q^{91} + 127 q^{92} + 3 q^{93} + 30 q^{94} + 48 q^{95} - 31 q^{96} + 53 q^{97} + 101 q^{98} - 20 q^{99}+O(q^{100}) \) 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9 + 13 * q^10 + 2 * q^11 + 36 * q^12 + 23 * q^13 + 24 * q^14 + 35 * q^15 + 104 * q^16 + 43 * q^17 + 42 * q^18 + 15 * q^19 + 59 * q^20 + 9 * q^21 + 6 * q^22 + 70 * q^23 + 15 * q^24 + 98 * q^25 + 10 * q^26 + 65 * q^27 + 37 * q^28 + 27 * q^29 + 17 * q^30 + 59 * q^31 + 46 * q^32 + 16 * q^33 - 16 * q^34 + 80 * q^35 + 88 * q^36 - 82 * q^37 + 82 * q^38 + 13 * q^39 + 14 * q^40 + 3 * q^41 + 62 * q^42 + 7 * q^43 - 11 * q^44 + 42 * q^45 - 11 * q^46 + 123 * q^47 + 45 * q^48 + 105 * q^49 + 27 * q^50 + 3 * q^51 - 30 * q^52 + 82 * q^53 - 27 * q^54 + 37 * q^55 + 66 * q^56 + 29 * q^57 - 34 * q^58 + 60 * q^59 + 94 * q^60 + 9 * q^61 - 2 * q^62 + 106 * q^63 + 93 * q^64 + 9 * q^65 + 63 * q^66 + 113 * q^68 + 48 * q^69 + 47 * q^70 + 59 * q^71 + 63 * q^72 + 21 * q^73 - 10 * q^74 + 77 * q^75 + 22 * q^76 + 30 * q^77 + 29 * q^78 + 55 * q^79 + 88 * q^80 + 42 * q^81 + 4 * q^82 + 92 * q^83 + 43 * q^84 - 7 * q^85 + 17 * q^86 + 147 * q^87 - 13 * q^88 + 100 * q^89 + 91 * q^90 + 28 * q^91 + 127 * q^92 + 3 * q^93 + 30 * q^94 + 48 * q^95 - 31 * q^96 + 53 * q^97 + 101 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.32285	−1.64250	−0.821252	−	0.570565i	$-0.806724\pi$
$2$	−2.32285	−1.64250	−0.821252	+	0.570565i	$0.806724\pi$
$3$	2.68333	1.54922	0.774611	−	0.632439i	$-0.217946\pi$
$3$	2.68333	1.54922	0.774611	+	0.632439i	$0.217946\pi$
$4$	3.39564	1.69782
$5$	−2.18288	−0.976212	−0.488106	−	0.872784i	$-0.662312\pi$
$5$	−2.18288	−0.976212	−0.488106	+	0.872784i	$0.662312\pi$
$6$	−6.23298	−2.54460
$7$	1.55979	0.589544	0.294772	−	0.955568i	$-0.404756\pi$
$7$	1.55979	0.589544	0.294772	+	0.955568i	$0.404756\pi$
$8$	−3.24187	−1.14617
$9$	4.20026	1.40009
$10$	5.07050	1.60343
$11$	2.77170	0.835699	0.417849	−	0.908516i	$-0.362784\pi$
$11$	2.77170	0.835699	0.417849	+	0.908516i	$0.362784\pi$
$12$	9.11162	2.63030
$13$	1.99402	0.553042	0.276521	−	0.961008i	$-0.410819\pi$
$13$	1.99402	0.553042	0.276521	+	0.961008i	$0.410819\pi$
$14$	−3.62315	−0.968328
$15$	−5.85738	−1.51237
$16$	0.739095	0.184774
$17$	5.84932	1.41867	0.709334	−	0.704872i	$-0.248996\pi$
$17$	5.84932	1.41867	0.709334	+	0.704872i	$0.248996\pi$
$18$	−9.75658	−2.29965
$19$	6.51124	1.49378	0.746891	−	0.664947i	$-0.231546\pi$
$19$	6.51124	1.49378	0.746891	+	0.664947i	$0.231546\pi$
$20$	−7.41226	−1.65743
$21$	4.18542	0.913334
$22$	−6.43824	−1.37264
$23$	3.96182	0.826096	0.413048	−	0.910709i	$-0.364464\pi$
$23$	3.96182	0.826096	0.413048	+	0.910709i	$0.364464\pi$
$24$	−8.69900	−1.77568
$25$	−0.235052	−0.0470104
$26$	−4.63181	−0.908373
$27$	3.22069	0.619821
$28$	5.29647	1.00094
$29$	8.28758	1.53896	0.769482	−	0.638668i	$-0.220514\pi$
$29$	8.28758	1.53896	0.769482	+	0.638668i	$0.220514\pi$
$30$	13.6058	2.48407
$31$	−7.81389	−1.40342	−0.701708	−	0.712465i	$-0.747579\pi$
$31$	−7.81389	−1.40342	−0.701708	+	0.712465i	$0.747579\pi$
$32$	4.76693	0.842681
$33$	7.43738	1.29468
$34$	−13.5871	−2.33017
$35$	−3.40482	−0.575520
$36$	14.2626	2.37709
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−15.1247	−2.45354
$39$	5.35061	0.856784
$40$	7.07659	1.11891
$41$	−2.68459	−0.419262	−0.209631	−	0.977781i	$-0.567226\pi$
$41$	−2.68459	−0.419262	−0.209631	+	0.977781i	$0.567226\pi$
$42$	−9.72211	−1.50015
$43$	4.38045	0.668013	0.334007	−	0.942571i	$-0.391599\pi$
$43$	4.38045	0.668013	0.334007	+	0.942571i	$0.391599\pi$
$44$	9.41169	1.41887
$45$	−9.16864	−1.36678
$46$	−9.20271	−1.35687
$47$	3.89639	0.568347	0.284173	−	0.958773i	$-0.408281\pi$
$47$	3.89639	0.568347	0.284173	+	0.958773i	$0.408281\pi$
$48$	1.98323	0.286255
$49$	−4.56707	−0.652438
$50$	0.545991	0.0772147
$51$	15.6957	2.19783
$52$	6.77098	0.938966
$53$	−1.01578	−0.139528	−0.0697638	−	0.997564i	$-0.522225\pi$
$53$	−1.01578	−0.139528	−0.0697638	+	0.997564i	$0.522225\pi$
$54$	−7.48118	−1.01806
$55$	−6.05027	−0.815819
$56$	−5.05662	−0.675719
$57$	17.4718	2.31420
$58$	−19.2508	−2.52776
$59$	6.59980	0.859220	0.429610	−	0.903014i	$-0.358651\pi$
$59$	6.59980	0.859220	0.429610	+	0.903014i	$0.358651\pi$
$60$	−19.8895	−2.56773
$61$	9.58574	1.22733	0.613664	−	0.789567i	$-0.289695\pi$
$61$	9.58574	1.22733	0.613664	+	0.789567i	$0.289695\pi$
$62$	18.1505	2.30512
$63$	6.55151	0.825412
$64$	−12.5511	−1.56888
$65$	−4.35270	−0.539886
$66$	−17.2759	−2.12652
$67$	−15.2255	−1.86009	−0.930043	−	0.367452i	$-0.880230\pi$
$67$	−15.2255	−1.86009	−0.930043	+	0.367452i	$0.880230\pi$
$68$	19.8622	2.40864
$69$	10.6309	1.27981
$70$	7.90889	0.945294
$71$	2.25001	0.267027	0.133513	−	0.991047i	$-0.457374\pi$
$71$	2.25001	0.267027	0.133513	+	0.991047i	$0.457374\pi$
$72$	−13.6167	−1.60474
$73$	−9.61582	−1.12545	−0.562724	−	0.826645i	$-0.690246\pi$
$73$	−9.61582	−1.12545	−0.562724	+	0.826645i	$0.690246\pi$
$74$	2.32285	0.270026
$75$	−0.630722	−0.0728295
$76$	22.1098	2.53617
$77$	4.32326	0.492681
$78$	−12.4287	−1.40727
$79$	−2.62406	−0.295230	−0.147615	−	0.989045i	$-0.547160\pi$
$79$	−2.62406	−0.295230	−0.147615	+	0.989045i	$0.547160\pi$
$80$	−1.61335	−0.180378
$81$	−3.95861	−0.439845
$82$	6.23590	0.688640
$83$	−1.26693	−0.139064	−0.0695320	−	0.997580i	$-0.522151\pi$
$83$	−1.26693	−0.139064	−0.0695320	+	0.997580i	$0.522151\pi$
$84$	14.2122	1.55068
$85$	−12.7683	−1.38492
$86$	−10.1751	−1.09721
$87$	22.2383	2.38420
$88$	−8.98548	−0.957855
$89$	−9.75300	−1.03382	−0.516908	−	0.856041i	$-0.672917\pi$
$89$	−9.75300	−1.03382	−0.516908	+	0.856041i	$0.672917\pi$
$90$	21.2974	2.24494
$91$	3.11025	0.326042
$92$	13.4529	1.40256
$93$	−20.9672	−2.17420
$94$	−9.05073	−0.933512
$95$	−14.2132	−1.45825
$96$	12.7912	1.30550
$97$	−5.73825	−0.582631	−0.291315	−	0.956627i	$-0.594093\pi$
$97$	−5.73825	−0.582631	−0.291315	+	0.956627i	$0.594093\pi$
$98$	10.6086	1.07163
$99$	11.6418	1.17005
$100$	−0.798152	−0.0798152
$101$	0.811261	0.0807235	0.0403618	−	0.999185i	$-0.487149\pi$
$101$	0.811261	0.0807235	0.0403618	+	0.999185i	$0.487149\pi$
$102$	−36.4587	−3.60995
$103$	−11.9575	−1.17820	−0.589102	−	0.808058i	$-0.700519\pi$
$103$	−11.9575	−1.17820	−0.589102	+	0.808058i	$0.700519\pi$
$104$	−6.46435	−0.633882
$105$	−9.13626	−0.891607
$106$	2.35950	0.229175
$107$	−3.61291	−0.349274	−0.174637	−	0.984633i	$-0.555875\pi$
$107$	−3.61291	−0.349274	−0.174637	+	0.984633i	$0.555875\pi$
$108$	10.9363	1.05235
$109$	1.00000	0.0957826
$109$	1.00000	0.0957826
$110$	14.0539	1.33999
$111$	−2.68333	−0.254690
$112$	1.15283	0.108932
$113$	4.98625	0.469067	0.234534	−	0.972108i	$-0.424644\pi$
$113$	4.98625	0.469067	0.234534	+	0.972108i	$0.424644\pi$
$114$	−40.5844	−3.80108
$115$	−8.64816	−0.806445
$116$	28.1416	2.61288
$117$	8.37540	0.774306
$118$	−15.3303	−1.41127
$119$	9.12369	0.836367
$120$	18.9888	1.73344
$121$	−3.31769	−0.301608
$122$	−22.2663	−2.01589
$123$	−7.20363	−0.649530
$124$	−26.5332	−2.38275
$125$	11.4275	1.02210
$126$	−15.2182	−1.35574
$127$	11.1411	0.988611	0.494305	−	0.869288i	$-0.335422\pi$
$127$	11.1411	0.988611	0.494305	+	0.869288i	$0.335422\pi$
$128$	19.6204	1.73421
$129$	11.7542	1.03490
$130$	10.1107	0.886765
$131$	−16.5526	−1.44621	−0.723104	−	0.690739i	$-0.757285\pi$
$131$	−16.5526	−1.44621	−0.723104	+	0.690739i	$0.757285\pi$
$132$	25.2547	2.19814
$133$	10.1561	0.880650
$134$	35.3665	3.05520
$135$	−7.03036	−0.605077
$136$	−18.9627	−1.62604
$137$	9.78292	0.835811	0.417906	−	0.908490i	$-0.362764\pi$
$137$	9.78292	0.835811	0.417906	+	0.908490i	$0.362764\pi$
$138$	−24.6939	−2.10209
$139$	8.84417	0.750153	0.375076	−	0.926994i	$-0.377616\pi$
$139$	8.84417	0.750153	0.375076	+	0.926994i	$0.377616\pi$
$140$	−11.5615	−0.977129
$141$	10.4553	0.880495
$142$	−5.22644	−0.438593
$143$	5.52682	0.462176
$144$	3.10439	0.258699
$145$	−18.0908	−1.50236
$146$	22.3361	1.84855
$147$	−12.2549	−1.01077
$148$	−3.39564	−0.279120
$149$	8.43459	0.690989	0.345494	−	0.938421i	$-0.387711\pi$
$149$	8.43459	0.690989	0.345494	+	0.938421i	$0.387711\pi$
$150$	1.46507	0.119623
$151$	22.7776	1.85362	0.926808	−	0.375535i	$-0.122541\pi$
$151$	22.7776	1.85362	0.926808	+	0.375535i	$0.122541\pi$
$152$	−21.1086	−1.71213
$153$	24.5686	1.98626
$154$	−10.0423	−0.809231
$155$	17.0568	1.37003
$156$	18.1688	1.45467
$157$	19.5578	1.56088	0.780442	−	0.625229i	$-0.214994\pi$
$157$	19.5578	1.56088	0.780442	+	0.625229i	$0.214994\pi$
$158$	6.09531	0.484917
$159$	−2.72566	−0.216159
$160$	−10.4056	−0.822636
$161$	6.17959	0.487020
$162$	9.19526	0.722448
$163$	−7.70902	−0.603817	−0.301908	−	0.953337i	$-0.597624\pi$
$163$	−7.70902	−0.603817	−0.301908	+	0.953337i	$0.597624\pi$
$164$	−9.11589	−0.711832
$165$	−16.2349	−1.26388
$166$	2.94290	0.228413
$167$	5.37116	0.415633	0.207817	−	0.978168i	$-0.433364\pi$
$167$	5.37116	0.415633	0.207817	+	0.978168i	$0.433364\pi$
$168$	−13.5686	−1.04684
$169$	−9.02388	−0.694145
$170$	29.6590	2.27474
$171$	27.3489	2.09142
$172$	14.8744	1.13417
$173$	11.3448	0.862526	0.431263	−	0.902226i	$-0.358068\pi$
$173$	11.3448	0.862526	0.431263	+	0.902226i	$0.358068\pi$
$174$	−51.6563	−3.91605
$175$	−0.366631	−0.0277147
$176$	2.04855	0.154415
$177$	17.7094	1.33112
$178$	22.6548	1.69805
$179$	12.8657	0.961629	0.480815	−	0.876822i	$-0.340341\pi$
$179$	12.8657	0.961629	0.480815	+	0.876822i	$0.340341\pi$
$180$	−31.1334	−2.32055
$181$	−5.71958	−0.425133	−0.212567	−	0.977147i	$-0.568182\pi$
$181$	−5.71958	−0.425133	−0.212567	+	0.977147i	$0.568182\pi$
$182$	−7.22464	−0.535526
$183$	25.7217	1.90140
$184$	−12.8437	−0.946849
$185$	2.18288	0.160488
$186$	48.7038	3.57114
$187$	16.2125	1.18558
$188$	13.2307	0.964951
$189$	5.02358	0.365412
$190$	33.0152	2.39518
$191$	−16.9881	−1.22922	−0.614609	−	0.788832i	$-0.710686\pi$
$191$	−16.9881	−1.22922	−0.614609	+	0.788832i	$0.710686\pi$
$192$	−33.6786	−2.43054
$193$	−17.3117	−1.24613	−0.623063	−	0.782172i	$-0.714112\pi$
$193$	−17.3117	−1.24613	−0.623063	+	0.782172i	$0.714112\pi$
$194$	13.3291	0.956974
$195$	−11.6797	−0.836403
$196$	−15.5081	−1.10772
$197$	−22.3313	−1.59104	−0.795520	−	0.605927i	$-0.792802\pi$
$197$	−22.3313	−1.59104	−0.795520	+	0.605927i	$0.792802\pi$
$198$	−27.0423	−1.92181
$199$	21.7618	1.54265	0.771327	−	0.636439i	$-0.219593\pi$
$199$	21.7618	1.54265	0.771327	+	0.636439i	$0.219593\pi$
$200$	0.762007	0.0538820
$201$	−40.8549	−2.88168
$202$	−1.88444	−0.132589
$203$	12.9268	0.907287
$204$	53.2968	3.73152
$205$	5.86012	0.409289
$206$	27.7754	1.93521
$207$	16.6407	1.15661
$208$	1.47377	0.102188
$209$	18.0472	1.24835
$210$	21.2222	1.46447
$211$	20.0375	1.37944	0.689721	−	0.724075i	$-0.257733\pi$
$211$	20.0375	1.37944	0.689721	+	0.724075i	$0.257733\pi$
$212$	−3.44921	−0.236893
$213$	6.03752	0.413684
$214$	8.39226	0.573683
$215$	−9.56199	−0.652122
$216$	−10.4410	−0.710423
$217$	−12.1880	−0.827375
$218$	−2.32285	−0.157323
$219$	−25.8024	−1.74357
$220$	−20.5446	−1.38511
$221$	11.6637	0.784583
$222$	6.23298	0.418330
$223$	−21.2643	−1.42396	−0.711982	−	0.702198i	$-0.752202\pi$
$223$	−21.2643	−1.42396	−0.711982	+	0.702198i	$0.752202\pi$
$224$	7.43539	0.496798
$225$	−0.987278	−0.0658186
$226$	−11.5823	−0.770445
$227$	11.0672	0.734554	0.367277	−	0.930112i	$-0.380290\pi$
$227$	11.0672	0.734554	0.367277	+	0.930112i	$0.380290\pi$
$228$	59.3280	3.92909
$229$	3.45156	0.228085	0.114043	−	0.993476i	$-0.463620\pi$
$229$	3.45156	0.228085	0.114043	+	0.993476i	$0.463620\pi$
$230$	20.0884	1.32459
$231$	11.6007	0.763272
$232$	−26.8672	−1.76392
$233$	−10.0170	−0.656238	−0.328119	−	0.944636i	$-0.606415\pi$
$233$	−10.0170	−0.656238	−0.328119	+	0.944636i	$0.606415\pi$
$234$	−19.4548	−1.27180
$235$	−8.50533	−0.554827
$236$	22.4105	1.45880
$237$	−7.04123	−0.457377
$238$	−21.1930	−1.37374
$239$	12.4624	0.806128	0.403064	−	0.915172i	$-0.367945\pi$
$239$	12.4624	0.806128	0.403064	+	0.915172i	$0.367945\pi$
$240$	−4.32916	−0.279446
$241$	−13.6382	−0.878514	−0.439257	−	0.898361i	$-0.644758\pi$
$241$	−13.6382	−0.878514	−0.439257	+	0.898361i	$0.644758\pi$
$242$	7.70650	0.495392
$243$	−20.2843	−1.30124
$244$	32.5497	2.08378
$245$	9.96934	0.636918
$246$	16.7330	1.06686
$247$	12.9835	0.826123
$248$	25.3316	1.60856
$249$	−3.39960	−0.215441
$250$	−26.5443	−1.67881
$251$	−6.08243	−0.383920	−0.191960	−	0.981403i	$-0.561484\pi$
$251$	−6.08243	−0.383920	−0.191960	+	0.981403i	$0.561484\pi$
$252$	22.2466	1.40140
$253$	10.9810	0.690367
$254$	−25.8791	−1.62380
$255$	−34.2617	−2.14555
$256$	−20.4731	−1.27957
$257$	3.55895	0.222001	0.111001	−	0.993820i	$-0.464594\pi$
$257$	3.55895	0.222001	0.111001	+	0.993820i	$0.464594\pi$
$258$	−27.3033	−1.69983
$259$	−1.55979	−0.0969204
$260$	−14.7802	−0.916629
$261$	34.8100	2.15468
$262$	38.4492	2.37540
$263$	21.6338	1.33400	0.667000	−	0.745058i	$-0.267578\pi$
$263$	21.6338	1.33400	0.667000	+	0.745058i	$0.267578\pi$
$264$	−24.1110	−1.48393
$265$	2.21731	0.136209
$266$	−23.5912	−1.44647
$267$	−26.1705	−1.60161
$268$	−51.7002	−3.15809
$269$	−30.6743	−1.87025	−0.935123	−	0.354323i	$-0.884711\pi$
$269$	−30.6743	−1.87025	−0.935123	+	0.354323i	$0.884711\pi$
$270$	16.3305	0.993842
$271$	−0.211536	−0.0128499	−0.00642495	−	0.999979i	$-0.502045\pi$
$271$	−0.211536	−0.0128499	−0.00642495	+	0.999979i	$0.502045\pi$
$272$	4.32320	0.262133
$273$	8.34582	0.505112
$274$	−22.7243	−1.37282
$275$	−0.651493	−0.0392865
$276$	36.0986	2.17288
$277$	−6.29216	−0.378059	−0.189030	−	0.981971i	$-0.560534\pi$
$277$	−6.29216	−0.378059	−0.189030	+	0.981971i	$0.560534\pi$
$278$	−20.5437	−1.23213
$279$	−32.8204	−1.96490
$280$	11.0380	0.659645
$281$	3.13854	0.187230	0.0936148	−	0.995608i	$-0.470158\pi$
$281$	3.13854	0.187230	0.0936148	+	0.995608i	$0.470158\pi$
$282$	−24.2861	−1.44622
$283$	−1.86409	−0.110809	−0.0554044	−	0.998464i	$-0.517645\pi$
$283$	−1.86409	−0.110809	−0.0554044	+	0.998464i	$0.517645\pi$
$284$	7.64022	0.453364
$285$	−38.1388	−2.25915
$286$	−12.8380	−0.759126
$287$	−4.18738	−0.247173
$288$	20.0223	1.17983
$289$	17.2145	1.01262
$290$	42.0221	2.46762
$291$	−15.3976	−0.902624
$292$	−32.6519	−1.91081
$293$	5.91446	0.345527	0.172763	−	0.984963i	$-0.444730\pi$
$293$	5.91446	0.345527	0.172763	+	0.984963i	$0.444730\pi$
$294$	28.4664	1.66020
$295$	−14.4065	−0.838781
$296$	3.24187	0.188430
$297$	8.92677	0.517984
$298$	−19.5923	−1.13495
$299$	7.89994	0.456866
$300$	−2.14170	−0.123651
$301$	6.83257	0.393823
$302$	−52.9090	−3.04457
$303$	2.17688	0.125059
$304$	4.81242	0.276011
$305$	−20.9245	−1.19813
$306$	−57.0693	−3.26244
$307$	11.0929	0.633107	0.316553	−	0.948575i	$-0.397474\pi$
$307$	11.0929	0.633107	0.316553	+	0.948575i	$0.397474\pi$
$308$	14.6802	0.836484
$309$	−32.0858	−1.82530
$310$	−39.6203	−2.25028
$311$	−14.5142	−0.823026	−0.411513	−	0.911404i	$-0.635000\pi$
$311$	−14.5142	−0.823026	−0.411513	+	0.911404i	$0.635000\pi$
$312$	−17.3460	−0.982023
$313$	−22.3789	−1.26493	−0.632466	−	0.774589i	$-0.717957\pi$
$313$	−22.3789	−1.26493	−0.632466	+	0.774589i	$0.717957\pi$
$314$	−45.4299	−2.56376
$315$	−14.3011	−0.805777
$316$	−8.91038	−0.501248
$317$	5.51995	0.310031	0.155016	−	0.987912i	$-0.450457\pi$
$317$	5.51995	0.310031	0.155016	+	0.987912i	$0.450457\pi$
$318$	6.33131	0.355042
$319$	22.9707	1.28611
$320$	27.3974	1.53156
$321$	−9.69464	−0.541102
$322$	−14.3543	−0.799932
$323$	38.0863	2.11918
$324$	−13.4420	−0.746779
$325$	−0.468698	−0.0259987
$326$	17.9069	0.991771
$327$	2.68333	0.148388
$328$	8.70307	0.480547
$329$	6.07753	0.335065
$330$	37.7112	2.07593
$331$	10.8892	0.598523	0.299261	−	0.954171i	$-0.403260\pi$
$331$	10.8892	0.598523	0.299261	+	0.954171i	$0.403260\pi$
$332$	−4.30205	−0.236106
$333$	−4.20026	−0.230173
$334$	−12.4764	−0.682679
$335$	33.2353	1.81584
$336$	3.09342	0.168760
$337$	5.14300	0.280157	0.140078	−	0.990140i	$-0.455265\pi$
$337$	5.14300	0.280157	0.140078	+	0.990140i	$0.455265\pi$
$338$	20.9611	1.14014
$339$	13.3798	0.726689
$340$	−43.3567	−2.35135
$341$	−21.6577	−1.17283
$342$	−63.5274	−3.43517
$343$	−18.0422	−0.974185
$344$	−14.2008	−0.765658
$345$	−23.2059	−1.24936
$346$	−26.3522	−1.41670
$347$	5.68049	0.304945	0.152472	−	0.988308i	$-0.451276\pi$
$347$	5.68049	0.304945	0.152472	+	0.988308i	$0.451276\pi$
$348$	75.5133	4.04794
$349$	22.9109	1.22639	0.613197	−	0.789930i	$-0.289883\pi$
$349$	22.9109	1.22639	0.613197	+	0.789930i	$0.289883\pi$
$350$	0.851629	0.0455215
$351$	6.42212	0.342787
$352$	13.2125	0.704228
$353$	21.4074	1.13940	0.569700	−	0.821852i	$-0.307059\pi$
$353$	21.4074	1.13940	0.569700	+	0.821852i	$0.307059\pi$
$354$	−41.1364	−2.18637
$355$	−4.91149	−0.260675
$356$	−33.1177	−1.75523
$357$	24.4819	1.29572
$358$	−29.8852	−1.57948
$359$	−24.4497	−1.29040	−0.645202	−	0.764012i	$-0.723227\pi$
$359$	−24.4497	−1.29040	−0.645202	+	0.764012i	$0.723227\pi$
$360$	29.7235	1.56657
$361$	23.3963	1.23138
$362$	13.2857	0.698283
$363$	−8.90245	−0.467257
$364$	10.5613	0.553561
$365$	20.9902	1.09867
$366$	−59.7477	−3.12306
$367$	0.393170	0.0205233	0.0102616	−	0.999947i	$-0.496734\pi$
$367$	0.393170	0.0205233	0.0102616	+	0.999947i	$0.496734\pi$
$368$	2.92816	0.152641
$369$	−11.2760	−0.587003
$370$	−5.07050	−0.263603
$371$	−1.58439	−0.0822577
$372$	−71.1972	−3.69140
$373$	0.507641	0.0262847	0.0131423	−	0.999914i	$-0.495817\pi$
$373$	0.507641	0.0262847	0.0131423	+	0.999914i	$0.495817\pi$
$374$	−37.6593	−1.94732
$375$	30.6637	1.58346
$376$	−12.6316	−0.651424
$377$	16.5256	0.851112
$378$	−11.6690	−0.600191
$379$	−33.9978	−1.74635	−0.873174	−	0.487409i	$-0.837942\pi$
$379$	−33.9978	−1.74635	−0.873174	+	0.487409i	$0.837942\pi$
$380$	−48.2630	−2.47584
$381$	29.8952	1.53158
$382$	39.4609	2.01900
$383$	−3.24865	−0.165998	−0.0829990	−	0.996550i	$-0.526450\pi$
$383$	−3.24865	−0.165998	−0.0829990	+	0.996550i	$0.526450\pi$
$384$	52.6480	2.68668
$385$	−9.43714	−0.480961
$386$	40.2126	2.04677
$387$	18.3990	0.935276
$388$	−19.4850	−0.989203
$389$	27.6781	1.40333	0.701666	−	0.712506i	$-0.252440\pi$
$389$	27.6781	1.40333	0.701666	+	0.712506i	$0.252440\pi$
$390$	27.1303	1.37379
$391$	23.1739	1.17196
$392$	14.8058	0.747807
$393$	−44.4161	−2.24050
$394$	51.8723	2.61329
$395$	5.72801	0.288207
$396$	39.5315	1.98653
$397$	15.0748	0.756581	0.378290	−	0.925687i	$-0.376512\pi$
$397$	15.0748	0.756581	0.378290	+	0.925687i	$0.376512\pi$
$398$	−50.5495	−2.53382
$399$	27.2523	1.36432
$400$	−0.173726	−0.00868628
$401$	−21.3938	−1.06836	−0.534179	−	0.845372i	$-0.679379\pi$
$401$	−21.3938	−1.06836	−0.534179	+	0.845372i	$0.679379\pi$
$402$	94.8999	4.73318
$403$	−15.5811	−0.776148
$404$	2.75475	0.137054
$405$	8.64115	0.429382
$406$	−30.0272	−1.49022
$407$	−2.77170	−0.137388
$408$	−50.8832	−2.51909
$409$	8.78134	0.434209	0.217105	−	0.976148i	$-0.430339\pi$
$409$	8.78134	0.434209	0.217105	+	0.976148i	$0.430339\pi$
$410$	−13.6122	−0.672258
$411$	26.2508	1.29486
$412$	−40.6033	−2.00038
$413$	10.2943	0.506548
$414$	−38.6538	−1.89973
$415$	2.76556	0.135756
$416$	9.50535	0.466038
$417$	23.7318	1.16215
$418$	−41.9210	−2.05042
$419$	−24.1527	−1.17994	−0.589968	−	0.807427i	$-0.700860\pi$
$419$	−24.1527	−1.17994	−0.589968	+	0.807427i	$0.700860\pi$
$420$	−31.0234	−1.51379
$421$	36.6979	1.78854	0.894272	−	0.447523i	$-0.147694\pi$
$421$	36.6979	1.78854	0.894272	+	0.447523i	$0.147694\pi$
$422$	−46.5442	−2.26574
$423$	16.3658	0.795734
$424$	3.29301	0.159923
$425$	−1.37489	−0.0666921
$426$	−14.0243	−0.679477
$427$	14.9517	0.723564
$428$	−12.2682	−0.593004
$429$	14.8303	0.716013
$430$	22.2111	1.07111
$431$	−19.2577	−0.927609	−0.463804	−	0.885938i	$-0.653516\pi$
$431$	−19.2577	−0.927609	−0.463804	+	0.885938i	$0.653516\pi$
$432$	2.38039	0.114527
$433$	27.7112	1.33172	0.665859	−	0.746078i	$-0.268065\pi$
$433$	27.7112	1.33172	0.665859	+	0.746078i	$0.268065\pi$
$434$	28.3109	1.35897
$435$	−48.5435	−2.32748
$436$	3.39564	0.162622
$437$	25.7963	1.23401
$438$	59.9352	2.86382
$439$	38.0232	1.81475	0.907374	−	0.420324i	$-0.138084\pi$
$439$	38.0232	1.81475	0.907374	+	0.420324i	$0.138084\pi$
$440$	19.6142	0.935069
$441$	−19.1829	−0.913469
$442$	−27.0930	−1.28868
$443$	−22.4262	−1.06550	−0.532750	−	0.846273i	$-0.678841\pi$
$443$	−22.4262	−1.06550	−0.532750	+	0.846273i	$0.678841\pi$
$444$	−9.11162	−0.432419
$445$	21.2896	1.00922
$446$	49.3938	2.33887
$447$	22.6328	1.07049
$448$	−19.5770	−0.924925
$449$	−3.00695	−0.141907	−0.0709533	−	0.997480i	$-0.522604\pi$
$449$	−3.00695	−0.141907	−0.0709533	+	0.997480i	$0.522604\pi$
$450$	2.29330	0.108107
$451$	−7.44087	−0.350377
$452$	16.9315	0.796392
$453$	61.1199	2.87166
$454$	−25.7074	−1.20651
$455$	−6.78928	−0.318286
$456$	−56.6413	−2.65247
$457$	−17.7816	−0.831787	−0.415894	−	0.909413i	$-0.636531\pi$
$457$	−17.7816	−0.831787	−0.415894	+	0.909413i	$0.636531\pi$
$458$	−8.01745	−0.374631
$459$	18.8388	0.879321
$460$	−29.3660	−1.36920
$461$	32.6453	1.52044	0.760222	−	0.649664i	$-0.225090\pi$
$461$	32.6453	1.52044	0.760222	+	0.649664i	$0.225090\pi$
$462$	−26.9468	−1.25368
$463$	1.01840	0.0473289	0.0236645	−	0.999720i	$-0.492467\pi$
$463$	1.01840	0.0473289	0.0236645	+	0.999720i	$0.492467\pi$
$464$	6.12530	0.284360
$465$	45.7689	2.12248
$466$	23.2681	1.07787
$467$	7.69968	0.356299	0.178149	−	0.984003i	$-0.442989\pi$
$467$	7.69968	0.356299	0.178149	+	0.984003i	$0.442989\pi$
$468$	28.4398	1.31463
$469$	−23.7485	−1.09660
$470$	19.7566	0.911305
$471$	52.4801	2.41815
$472$	−21.3957	−0.984815
$473$	12.1413	0.558257
$474$	16.3557	0.751243
$475$	−1.53048	−0.0702232
$476$	30.9808	1.42000
$477$	−4.26652	−0.195351
$478$	−28.9484	−1.32407
$479$	−37.2521	−1.70209	−0.851046	−	0.525091i	$-0.824031\pi$
$479$	−37.2521	−1.70209	−0.851046	+	0.525091i	$0.824031\pi$
$480$	−27.9217	−1.27444
$481$	−1.99402	−0.0909195
$482$	31.6795	1.44296
$483$	16.5819	0.754501
$484$	−11.2657	−0.512076
$485$	12.5259	0.568771
$486$	47.1175	2.13729
$487$	−27.6683	−1.25377	−0.626884	−	0.779113i	$-0.715670\pi$
$487$	−27.6683	−1.25377	−0.626884	+	0.779113i	$0.715670\pi$
$488$	−31.0757	−1.40673
$489$	−20.6858	−0.935446
$490$	−23.1573	−1.04614
$491$	36.0059	1.62492	0.812461	−	0.583015i	$-0.198127\pi$
$491$	36.0059	1.62492	0.812461	+	0.583015i	$0.198127\pi$
$492$	−24.4609	−1.10278
$493$	48.4767	2.18328
$494$	−30.1589	−1.35691
$495$	−25.4127	−1.14222
$496$	−5.77520	−0.259314
$497$	3.50953	0.157424
$498$	7.89676	0.353862
$499$	−39.7810	−1.78084	−0.890420	−	0.455139i	$-0.849589\pi$
$499$	−39.7810	−1.78084	−0.890420	+	0.455139i	$0.849589\pi$
$500$	38.8036	1.73535
$501$	14.4126	0.643908
$502$	14.1286	0.630590
$503$	−6.54184	−0.291686	−0.145843	−	0.989308i	$-0.546589\pi$
$503$	−6.54184	−0.291686	−0.145843	+	0.989308i	$0.546589\pi$
$504$	−21.2391	−0.946065
$505$	−1.77088	−0.0788033
$506$	−25.5071	−1.13393
$507$	−24.2141	−1.07538
$508$	37.8311	1.67848
$509$	−18.3782	−0.814597	−0.407299	−	0.913295i	$-0.633529\pi$
$509$	−18.3782	−0.814597	−0.407299	+	0.913295i	$0.633529\pi$
$510$	79.5848	3.52407
$511$	−14.9986	−0.663500
$512$	8.31530	0.367488
$513$	20.9707	0.925878
$514$	−8.26692	−0.364638
$515$	26.1017	1.15018
$516$	39.9130	1.75707
$517$	10.7996	0.474966
$518$	3.62315	0.159192
$519$	30.4417	1.33624
$520$	14.1109	0.618803
$521$	−27.2037	−1.19182	−0.595909	−	0.803052i	$-0.703208\pi$
$521$	−27.2037	−1.19182	−0.595909	+	0.803052i	$0.703208\pi$
$522$	−80.8584	−3.53907
$523$	24.2496	1.06036	0.530180	−	0.847885i	$-0.322124\pi$
$523$	24.2496	1.06036	0.530180	+	0.847885i	$0.322124\pi$
$524$	−56.2067	−2.45540
$525$	−0.983791	−0.0429362
$526$	−50.2522	−2.19110
$527$	−45.7059	−1.99098
$528$	5.49693	0.239223
$529$	−7.30401	−0.317566
$530$	−5.15049	−0.223723
$531$	27.7208	1.20298
$532$	34.4866	1.49518
$533$	−5.35312	−0.231869
$534$	60.7902	2.63065
$535$	7.88654	0.340965
$536$	49.3589	2.13198
$537$	34.5230	1.48978
$538$	71.2519	3.07189
$539$	−12.6585	−0.545241
$540$	−23.8726	−1.02731
$541$	−24.1121	−1.03666	−0.518330	−	0.855181i	$-0.673446\pi$
$541$	−24.1121	−1.03666	−0.518330	+	0.855181i	$0.673446\pi$
$542$	0.491367	0.0211060
$543$	−15.3475	−0.658626
$544$	27.8833	1.19549
$545$	−2.18288	−0.0935041
$546$	−19.3861	−0.829648
$547$	−18.8851	−0.807469	−0.403734	−	0.914876i	$-0.632288\pi$
$547$	−18.8851	−0.807469	−0.403734	+	0.914876i	$0.632288\pi$
$548$	33.2193	1.41906
$549$	40.2626	1.71836
$550$	1.51332	0.0645282
$551$	53.9624	2.29888
$552$	−34.4638	−1.46688
$553$	−4.09298	−0.174051
$554$	14.6158	0.620964
$555$	5.85738	0.248632
$556$	30.0316	1.27362
$557$	7.60229	0.322119	0.161060	−	0.986945i	$-0.448509\pi$
$557$	7.60229	0.322119	0.161060	+	0.986945i	$0.448509\pi$
$558$	76.2368	3.22736
$559$	8.73472	0.369439
$560$	−2.51648	−0.106341
$561$	43.5036	1.83672
$562$	−7.29036	−0.307525
$563$	1.41920	0.0598119	0.0299060	−	0.999553i	$-0.490479\pi$
$563$	1.41920	0.0598119	0.0299060	+	0.999553i	$0.490479\pi$
$564$	35.5024	1.49492
$565$	−10.8844	−0.457909
$566$	4.33001	0.182004
$567$	−6.17458	−0.259308
$568$	−7.29423	−0.306059
$569$	33.7927	1.41666	0.708332	−	0.705879i	$-0.249448\pi$
$569$	33.7927	1.41666	0.708332	+	0.705879i	$0.249448\pi$
$570$	88.5908	3.71066
$571$	−16.2490	−0.679999	−0.339999	−	0.940426i	$-0.610427\pi$
$571$	−16.2490	−0.679999	−0.339999	+	0.940426i	$0.610427\pi$
$572$	18.7671	0.784692
$573$	−45.5847	−1.90433
$574$	9.72667	0.405983
$575$	−0.931232	−0.0388351
$576$	−52.7177	−2.19657
$577$	−24.7735	−1.03133	−0.515667	−	0.856789i	$-0.672456\pi$
$577$	−24.7735	−1.03133	−0.515667	+	0.856789i	$0.672456\pi$
$578$	−39.9868	−1.66323
$579$	−46.4531	−1.93053
$580$	−61.4297	−2.55073
$581$	−1.97614	−0.0819843
$582$	35.7664	1.48256
$583$	−2.81543	−0.116603
$584$	31.1732	1.28996
$585$	−18.2825	−0.755887
$586$	−13.7384	−0.567529
$587$	8.44057	0.348380	0.174190	−	0.984712i	$-0.444269\pi$
$587$	8.44057	0.348380	0.174190	+	0.984712i	$0.444269\pi$
$588$	−41.6134	−1.71611
$589$	−50.8781	−2.09640
$590$	33.4642	1.37770
$591$	−59.9223	−2.46487
$592$	−0.739095	−0.0303766
$593$	−3.15706	−0.129645	−0.0648225	−	0.997897i	$-0.520648\pi$
$593$	−3.15706	−0.129645	−0.0648225	+	0.997897i	$0.520648\pi$
$594$	−20.7356	−0.850791
$595$	−19.9159	−0.816472
$596$	28.6409	1.17317
$597$	58.3941	2.38991
$598$	−18.3504	−0.750404
$599$	23.9470	0.978449	0.489225	−	0.872158i	$-0.337280\pi$
$599$	23.9470	0.978449	0.489225	+	0.872158i	$0.337280\pi$
$600$	2.04472	0.0834752
$601$	37.4753	1.52865	0.764324	−	0.644832i	$-0.223073\pi$
$601$	37.4753	1.52865	0.764324	+	0.644832i	$0.223073\pi$
$602$	−15.8711	−0.646856
$603$	−63.9508	−2.60428
$604$	77.3446	3.14711
$605$	7.24210	0.294433
$606$	−5.05657	−0.205409
$607$	29.6882	1.20501	0.602503	−	0.798116i	$-0.294170\pi$
$607$	29.6882	1.20501	0.602503	+	0.798116i	$0.294170\pi$
$608$	31.0386	1.25878
$609$	34.6870	1.40559
$610$	48.6045	1.96794
$611$	7.76948	0.314319
$612$	83.4263	3.37231
$613$	47.3276	1.91154	0.955772	−	0.294108i	$-0.0950225\pi$
$613$	47.3276	1.91154	0.955772	+	0.294108i	$0.0950225\pi$
$614$	−25.7672	−1.03988
$615$	15.7246	0.634079
$616$	−14.0154	−0.564698
$617$	16.5755	0.667305	0.333653	−	0.942696i	$-0.391719\pi$
$617$	16.5755	0.667305	0.333653	+	0.942696i	$0.391719\pi$
$618$	74.5307	2.99806
$619$	−34.4605	−1.38508	−0.692542	−	0.721377i	$-0.743509\pi$
$619$	−34.4605	−1.38508	−0.692542	+	0.721377i	$0.743509\pi$
$620$	57.9186	2.32607
$621$	12.7598	0.512032
$622$	33.7144	1.35182
$623$	−15.2126	−0.609480
$624$	3.95461	0.158311
$625$	−23.7695	−0.950780
$626$	51.9829	2.07765
$627$	48.4266	1.93397
$628$	66.4113	2.65010
$629$	−5.84932	−0.233228
$630$	33.2194	1.32349
$631$	−20.5242	−0.817056	−0.408528	−	0.912746i	$-0.633958\pi$
$631$	−20.5242	−0.817056	−0.408528	+	0.912746i	$0.633958\pi$
$632$	8.50686	0.338385
$633$	53.7673	2.13706
$634$	−12.8220	−0.509227
$635$	−24.3196	−0.965094
$636$	−9.25537	−0.366999
$637$	−9.10682	−0.360825
$638$	−53.3574	−2.11244
$639$	9.45062	0.373861
$640$	−42.8289	−1.69296
$641$	7.72873	0.305267	0.152633	−	0.988283i	$-0.451225\pi$
$641$	7.72873	0.305267	0.152633	+	0.988283i	$0.451225\pi$
$642$	22.5192	0.888762
$643$	−23.4707	−0.925593	−0.462797	−	0.886465i	$-0.653154\pi$
$643$	−23.4707	−0.925593	−0.462797	+	0.886465i	$0.653154\pi$
$644$	20.9837	0.826872
$645$	−25.6580	−1.01028
$646$	−88.4689	−3.48076
$647$	33.7914	1.32848	0.664238	−	0.747521i	$-0.268756\pi$
$647$	33.7914	1.32848	0.664238	+	0.747521i	$0.268756\pi$
$648$	12.8333	0.504139
$649$	18.2926	0.718049
$650$	1.08872	0.0427030
$651$	−32.7044	−1.28179
$652$	−26.1770	−1.02517
$653$	16.5313	0.646921	0.323460	−	0.946242i	$-0.395154\pi$
$653$	16.5313	0.646921	0.323460	+	0.946242i	$0.395154\pi$
$654$	−6.23298	−0.243729
$655$	36.1323	1.41181
$656$	−1.98416	−0.0774686
$657$	−40.3889	−1.57572
$658$	−14.1172	−0.550346
$659$	28.3668	1.10501	0.552507	−	0.833508i	$-0.313671\pi$
$659$	28.3668	1.10501	0.552507	+	0.833508i	$0.313671\pi$
$660$	−55.1278	−2.14585
$661$	35.3251	1.37399	0.686994	−	0.726663i	$-0.258930\pi$
$661$	35.3251	1.37399	0.686994	+	0.726663i	$0.258930\pi$
$662$	−25.2939	−0.983076
$663$	31.2974	1.21549
$664$	4.10723	0.159391
$665$	−22.1696	−0.859701
$666$	9.75658	0.378060
$667$	32.8339	1.27133
$668$	18.2385	0.705670
$669$	−57.0592	−2.20603
$670$	−77.2006	−2.98252
$671$	26.5688	1.02568
$672$	19.9516	0.769649
$673$	−17.8676	−0.688747	−0.344373	−	0.938833i	$-0.611909\pi$
$673$	−17.8676	−0.688747	−0.344373	+	0.938833i	$0.611909\pi$
$674$	−11.9464	−0.460159
$675$	−0.757028	−0.0291380
$676$	−30.6419	−1.17853
$677$	−18.1553	−0.697763	−0.348882	−	0.937167i	$-0.613438\pi$
$677$	−18.1553	−0.697763	−0.348882	+	0.937167i	$0.613438\pi$
$678$	−31.0792	−1.19359
$679$	−8.95044	−0.343487
$680$	41.3933	1.58736
$681$	29.6969	1.13799
$682$	50.3077	1.92638
$683$	34.2064	1.30887	0.654436	−	0.756117i	$-0.272906\pi$
$683$	34.2064	1.30887	0.654436	+	0.756117i	$0.272906\pi$
$684$	92.8670	3.55086
$685$	−21.3549	−0.815929
$686$	41.9092	1.60010
$687$	9.26166	0.353355
$688$	3.23757	0.123431
$689$	−2.02548	−0.0771646
$690$	53.9038	2.05208
$691$	49.7569	1.89284	0.946421	−	0.322937i	$-0.104670\pi$
$691$	49.7569	1.89284	0.946421	+	0.322937i	$0.104670\pi$
$692$	38.5227	1.46441
$693$	18.1588	0.689796
$694$	−13.1949	−0.500873
$695$	−19.3057	−0.732308
$696$	−72.0936	−2.73270
$697$	−15.7030	−0.594794
$698$	−53.2187	−2.01436
$699$	−26.8790	−1.01666
$700$	−1.24495	−0.0470545
$701$	6.27822	0.237125	0.118563	−	0.992947i	$-0.462171\pi$
$701$	6.27822	0.237125	0.118563	+	0.992947i	$0.462171\pi$
$702$	−14.9176	−0.563029
$703$	−6.51124	−0.245576
$704$	−34.7877	−1.31111
$705$	−22.8226	−0.859549
$706$	−49.7262	−1.87147
$707$	1.26539	0.0475901
$708$	60.1349	2.26001
$709$	1.42904	0.0536686	0.0268343	−	0.999640i	$-0.491457\pi$
$709$	1.42904	0.0536686	0.0268343	+	0.999640i	$0.491457\pi$
$710$	11.4087	0.428160
$711$	−11.0217	−0.413348
$712$	31.6179	1.18493
$713$	−30.9572	−1.15936
$714$	−56.8677	−2.12822
$715$	−12.0644	−0.451182
$716$	43.6874	1.63267
$717$	33.4408	1.24887
$718$	56.7930	2.11950
$719$	−42.9241	−1.60080	−0.800400	−	0.599467i	$-0.795379\pi$
$719$	−42.9241	−1.60080	−0.800400	+	0.599467i	$0.795379\pi$
$720$	−6.77649	−0.252545
$721$	−18.6511	−0.694604
$722$	−54.3461	−2.02255
$723$	−36.5958	−1.36101
$724$	−19.4217	−0.721800
$725$	−1.94801	−0.0723473
$726$	20.6791	0.767472
$727$	28.6465	1.06244	0.531220	−	0.847234i	$-0.321734\pi$
$727$	28.6465	1.06244	0.531220	+	0.847234i	$0.321734\pi$
$728$	−10.0830	−0.373701
$729$	−42.5537	−1.57606
$730$	−48.7570	−1.80458
$731$	25.6227	0.947689
$732$	87.3416	3.22824
$733$	−0.618293	−0.0228372	−0.0114186	−	0.999935i	$-0.503635\pi$
$733$	−0.618293	−0.0228372	−0.0114186	+	0.999935i	$0.503635\pi$
$734$	−0.913275	−0.0337096
$735$	26.7510	0.986726
$736$	18.8857	0.696136
$737$	−42.2004	−1.55447
$738$	26.1924	0.964155
$739$	−20.9015	−0.768873	−0.384436	−	0.923151i	$-0.625604\pi$
$739$	−20.9015	−0.768873	−0.384436	+	0.923151i	$0.625604\pi$
$740$	7.41226	0.272480
$741$	34.8391	1.27985
$742$	3.68031	0.135109
$743$	−0.885438	−0.0324836	−0.0162418	−	0.999868i	$-0.505170\pi$
$743$	−0.885438	−0.0324836	−0.0162418	+	0.999868i	$0.505170\pi$
$744$	67.9730	2.49201
$745$	−18.4117	−0.674552
$746$	−1.17917	−0.0431727
$747$	−5.32144	−0.194701
$748$	55.0520	2.01290
$749$	−5.63537	−0.205912
$750$	−71.2272	−2.60085
$751$	24.2920	0.886429	0.443214	−	0.896416i	$-0.353838\pi$
$751$	24.2920	0.886429	0.443214	+	0.896416i	$0.353838\pi$
$752$	2.87980	0.105015
$753$	−16.3212	−0.594777
$754$	−38.3865	−1.39795
$755$	−49.7207	−1.80952
$756$	17.0583	0.620404
$757$	3.22131	0.117080	0.0585402	−	0.998285i	$-0.481355\pi$
$757$	3.22131	0.117080	0.0585402	+	0.998285i	$0.481355\pi$
$758$	78.9718	2.86838
$759$	29.4655	1.06953
$760$	46.0774	1.67140
$761$	−22.8609	−0.828709	−0.414354	−	0.910116i	$-0.635993\pi$
$761$	−22.8609	−0.828709	−0.414354	+	0.910116i	$0.635993\pi$
$762$	−69.4421	−2.51562
$763$	1.55979	0.0564681
$764$	−57.6856	−2.08699
$765$	−53.6303	−1.93901
$766$	7.54612	0.272652
$767$	13.1601	0.475185
$768$	−54.9362	−1.98234
$769$	−9.57459	−0.345269	−0.172634	−	0.984986i	$-0.555228\pi$
$769$	−9.57459	−0.345269	−0.172634	+	0.984986i	$0.555228\pi$
$770$	21.9211	0.789980
$771$	9.54984	0.343929
$772$	−58.7844	−2.11570
$773$	10.9946	0.395448	0.197724	−	0.980258i	$-0.436645\pi$
$773$	10.9946	0.395448	0.197724	+	0.980258i	$0.436645\pi$
$774$	−42.7382	−1.53619
$775$	1.83667	0.0659751
$776$	18.6026	0.667796
$777$	−4.18542	−0.150151
$778$	−64.2920	−2.30498
$779$	−17.4800	−0.626286
$780$	−39.6602	−1.42006
$781$	6.23635	0.223154
$782$	−53.8296	−1.92494
$783$	26.6917	0.953883
$784$	−3.37549	−0.120553
$785$	−42.6923	−1.52375
$786$	103.172	3.68002
$787$	−45.6671	−1.62786	−0.813929	−	0.580965i	$-0.802675\pi$
$787$	−45.6671	−1.62786	−0.813929	+	0.580965i	$0.802675\pi$
$788$	−75.8291	−2.70130
$789$	58.0507	2.06666
$790$	−13.3053	−0.473382
$791$	7.77749	0.276536
$792$	−37.7413	−1.34108
$793$	19.1142	0.678764
$794$	−35.0165	−1.24269
$795$	5.94979	0.211017
$796$	73.8953	2.61915
$797$	10.2062	0.361524	0.180762	−	0.983527i	$-0.442144\pi$
$797$	10.2062	0.361524	0.180762	+	0.983527i	$0.442144\pi$
$798$	−63.3030	−2.24090
$799$	22.7912	0.806295
$800$	−1.12047	−0.0396148
$801$	−40.9651	−1.44743
$802$	49.6947	1.75478
$803$	−26.6522	−0.940534
$804$	−138.729	−4.89258
$805$	−13.4893	−0.475434
$806$	36.1925	1.27483
$807$	−82.3093	−2.89742
$808$	−2.63000	−0.0925231
$809$	−43.4761	−1.52854	−0.764268	−	0.644898i	$-0.776900\pi$
$809$	−43.4761	−1.52854	−0.764268	+	0.644898i	$0.776900\pi$
$810$	−20.0721	−0.705262
$811$	−38.3173	−1.34550	−0.672751	−	0.739869i	$-0.734887\pi$
$811$	−38.3173	−1.34550	−0.672751	+	0.739869i	$0.734887\pi$
$812$	43.8949	1.54041
$813$	−0.567621	−0.0199073
$814$	6.43824	0.225660
$815$	16.8278	0.589453
$816$	11.6006	0.406101
$817$	28.5222	0.997865
$818$	−20.3978	−0.713191
$819$	13.0638	0.456487
$820$	19.8989	0.694899
$821$	−23.3529	−0.815022	−0.407511	−	0.913200i	$-0.633603\pi$
$821$	−23.3529	−0.815022	−0.407511	+	0.913200i	$0.633603\pi$
$822$	−60.9767	−2.12681
$823$	−10.4424	−0.363999	−0.182000	−	0.983299i	$-0.558257\pi$
$823$	−10.4424	−0.363999	−0.182000	+	0.983299i	$0.558257\pi$
$824$	38.7645	1.35043
$825$	−1.74817	−0.0608635
$826$	−23.9121	−0.832007
$827$	25.2488	0.877987	0.438993	−	0.898490i	$-0.355335\pi$
$827$	25.2488	0.877987	0.438993	+	0.898490i	$0.355335\pi$
$828$	56.5057	1.96371
$829$	45.5315	1.58138	0.790688	−	0.612219i	$-0.209723\pi$
$829$	45.5315	1.58138	0.790688	+	0.612219i	$0.209723\pi$
$830$	−6.42398	−0.222980
$831$	−16.8839	−0.585697
$832$	−25.0271	−0.867657
$833$	−26.7142	−0.925593
$834$	−55.1255	−1.90884
$835$	−11.7246	−0.405746
$836$	61.2818	2.11948
$837$	−25.1661	−0.869868
$838$	56.1031	1.93805
$839$	−29.4422	−1.01646	−0.508229	−	0.861222i	$-0.669700\pi$
$839$	−29.4422	−1.01646	−0.508229	+	0.861222i	$0.669700\pi$
$840$	29.6185	1.02194
$841$	39.6839	1.36841
$842$	−85.2437	−2.93769
$843$	8.42174	0.290060
$844$	68.0403	2.34204
$845$	19.6980	0.677632
$846$	−38.0154	−1.30700
$847$	−5.17488	−0.177811
$848$	−0.750755	−0.0257810
$849$	−5.00197	−0.171667
$850$	3.19367	0.109542
$851$	−3.96182	−0.135809
$852$	20.5012	0.702361
$853$	1.02582	0.0351233	0.0175617	−	0.999846i	$-0.494410\pi$
$853$	1.02582	0.0351233	0.0175617	+	0.999846i	$0.494410\pi$
$854$	−34.7306	−1.18846
$855$	−59.6992	−2.04167
$856$	11.7126	0.400328
$857$	−8.11170	−0.277090	−0.138545	−	0.990356i	$-0.544243\pi$
$857$	−8.11170	−0.277090	−0.138545	+	0.990356i	$0.544243\pi$
$858$	−34.4486	−1.17605
$859$	4.71205	0.160773	0.0803866	−	0.996764i	$-0.474385\pi$
$859$	4.71205	0.160773	0.0803866	+	0.996764i	$0.474385\pi$
$860$	−32.4691	−1.10719
$861$	−11.2361	−0.382926
$862$	44.7327	1.52360
$863$	−33.7496	−1.14885	−0.574426	−	0.818557i	$-0.694775\pi$
$863$	−33.7496	−1.14885	−0.574426	+	0.818557i	$0.694775\pi$
$864$	15.3528	0.522312
$865$	−24.7642	−0.842008
$866$	−64.3691	−2.18735
$867$	46.1923	1.56877
$868$	−41.3861	−1.40473
$869$	−7.27311	−0.246723
$870$	112.759	3.82290
$871$	−30.3599	−1.02870
$872$	−3.24187	−0.109783
$873$	−24.1021	−0.815733
$874$	−59.9211	−2.02686
$875$	17.8244	0.602575
$876$	−87.6158	−2.96026
$877$	−24.4826	−0.826718	−0.413359	−	0.910568i	$-0.635645\pi$
$877$	−24.4826	−0.826718	−0.413359	+	0.910568i	$0.635645\pi$
$878$	−88.3223	−2.98073
$879$	15.8705	0.535297
$880$	−4.47173	−0.150742
$881$	−23.6035	−0.795221	−0.397610	−	0.917554i	$-0.630160\pi$
$881$	−23.6035	−0.795221	−0.397610	+	0.917554i	$0.630160\pi$
$882$	44.5589	1.50038
$883$	47.6203	1.60255	0.801275	−	0.598297i	$-0.204156\pi$
$883$	47.6203	1.60255	0.801275	+	0.598297i	$0.204156\pi$
$884$	39.6056	1.33208
$885$	−38.6575	−1.29946
$886$	52.0927	1.75009
$887$	43.3641	1.45602	0.728012	−	0.685564i	$-0.240445\pi$
$887$	43.3641	1.45602	0.728012	+	0.685564i	$0.240445\pi$
$888$	8.69900	0.291919
$889$	17.3777	0.582829
$890$	−49.4525	−1.65765
$891$	−10.9721	−0.367578
$892$	−72.2060	−2.41763
$893$	25.3703	0.848986
$894$	−52.5726	−1.75829
$895$	−28.0843	−0.938754
$896$	30.6036	1.02239
$897$	21.1982	0.707786
$898$	6.98469	0.233082
$899$	−64.7582	−2.15981
$900$	−3.35244	−0.111748
$901$	−5.94160	−0.197943
$902$	17.2840	0.575495
$903$	18.3340	0.610119
$904$	−16.1648	−0.537632
$905$	12.4851	0.415020
$906$	−141.972	−4.71672
$907$	−39.1921	−1.30135	−0.650676	−	0.759355i	$-0.725514\pi$
$907$	−39.1921	−1.30135	−0.650676	+	0.759355i	$0.725514\pi$
$908$	37.5801	1.24714
$909$	3.40751	0.113020
$910$	15.7705	0.522787
$911$	−46.2619	−1.53272	−0.766362	−	0.642409i	$-0.777935\pi$
$911$	−46.2619	−1.53272	−0.766362	+	0.642409i	$0.777935\pi$
$912$	12.9133	0.427603
$913$	−3.51156	−0.116216
$914$	41.3040	1.36621
$915$	−56.1473	−1.85617
$916$	11.7202	0.387248
$917$	−25.8185	−0.852603
$918$	−43.7598	−1.44429
$919$	−28.7263	−0.947594	−0.473797	−	0.880634i	$-0.657117\pi$
$919$	−28.7263	−0.947594	−0.473797	+	0.880634i	$0.657117\pi$
$920$	28.0362	0.924325
$921$	29.7660	0.980822
$922$	−75.8302	−2.49733
$923$	4.48656	0.147677
$924$	39.3919	1.29590
$925$	0.235052	0.00772846
$926$	−2.36559	−0.0777380
$927$	−50.2245	−1.64959
$928$	39.5063	1.29686
$929$	14.8819	0.488259	0.244130	−	0.969743i	$-0.421498\pi$
$929$	14.8819	0.488259	0.244130	+	0.969743i	$0.421498\pi$
$930$	−106.314	−3.48619
$931$	−29.7373	−0.974600
$932$	−34.0143	−1.11417
$933$	−38.9464	−1.27505
$934$	−17.8852	−0.585222
$935$	−35.3900	−1.15738
$936$	−27.1519	−0.887489
$937$	−2.04179	−0.0667022	−0.0333511	−	0.999444i	$-0.510618\pi$
$937$	−2.04179	−0.0667022	−0.0333511	+	0.999444i	$0.510618\pi$
$938$	55.1641	1.80117
$939$	−60.0500	−1.95966
$940$	−28.8811	−0.941996
$941$	20.9885	0.684205	0.342103	−	0.939663i	$-0.388861\pi$
$941$	20.9885	0.684205	0.342103	+	0.939663i	$0.388861\pi$
$942$	−121.903	−3.97183
$943$	−10.6358	−0.346351
$944$	4.87787	0.158761
$945$	−10.9659	−0.356719
$946$	−28.2024	−0.916940
$947$	19.0748	0.619849	0.309924	−	0.950761i	$-0.399696\pi$
$947$	19.0748	0.619849	0.309924	+	0.950761i	$0.399696\pi$
$948$	−23.9095	−0.776544
$949$	−19.1741	−0.622419
$950$	3.55508	0.115342
$951$	14.8118	0.480307
$952$	−29.5778	−0.958621
$953$	8.60118	0.278620	0.139310	−	0.990249i	$-0.455512\pi$
$953$	8.60118	0.278620	0.139310	+	0.990249i	$0.455512\pi$
$954$	9.91050	0.320864
$955$	37.0830	1.19998
$956$	42.3180	1.36866
$957$	61.6379	1.99247
$958$	86.5311	2.79569
$959$	15.2593	0.492747
$960$	73.5162	2.37273
$961$	30.0569	0.969577
$962$	4.63181	0.149336
$963$	−15.1752	−0.489013
$964$	−46.3105	−1.49156
$965$	37.7894	1.21648
$966$	−38.5172	−1.23927
$967$	−24.8051	−0.797677	−0.398839	−	0.917021i	$-0.630587\pi$
$967$	−24.8051	−0.797677	−0.398839	+	0.917021i	$0.630587\pi$
$968$	10.7555	0.345695
$969$	102.198	3.28308
$970$	−29.0958	−0.934209
$971$	46.9127	1.50550	0.752750	−	0.658306i	$-0.228727\pi$
$971$	46.9127	1.50550	0.752750	+	0.658306i	$0.228727\pi$
$972$	−68.8782	−2.20927
$973$	13.7950	0.442248
$974$	64.2693	2.05932
$975$	−1.25767	−0.0402777
$976$	7.08477	0.226778
$977$	9.64844	0.308681	0.154340	−	0.988018i	$-0.450675\pi$
$977$	9.64844	0.308681	0.154340	+	0.988018i	$0.450675\pi$
$978$	48.0501	1.53647
$979$	−27.0324	−0.863958
$980$	33.8523	1.08137
$981$	4.20026	0.134104
$982$	−83.6363	−2.66894
$983$	−29.2314	−0.932338	−0.466169	−	0.884696i	$-0.654366\pi$
$983$	−29.2314	−0.932338	−0.466169	+	0.884696i	$0.654366\pi$
$984$	23.3532	0.744473
$985$	48.7465	1.55319
$986$	−112.604	−3.58605
$987$	16.3080	0.519090
$988$	44.0875	1.40261
$989$	17.3546	0.551843
$990$	59.0300	1.87610
$991$	−62.4467	−1.98368	−0.991842	−	0.127471i	$-0.959314\pi$
$991$	−62.4467	−1.98368	−0.991842	+	0.127471i	$0.959314\pi$
$992$	−37.2482	−1.18263
$993$	29.2192	0.927244
$994$	−8.15213	−0.258570
$995$	−47.5034	−1.50596
$996$	−11.5438	−0.365780
$997$	−48.4771	−1.53528	−0.767642	−	0.640879i	$-0.778570\pi$
$997$	−48.4771	−1.53528	−0.767642	+	0.640879i	$0.778570\pi$
$998$	92.4053	2.92504
$999$	−3.22069	−0.101898

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.e.1.11	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.e.1.11	✓	82	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.32285 q^{2} +2.68333 q^{3} +3.39564 q^{4} -2.18288 q^{5} -6.23298 q^{6} +1.55979 q^{7} -3.24187 q^{8} +4.20026 q^{9} +O(q^{10})\)	\(q-2.32285 q^{2} +2.68333 q^{3} +3.39564 q^{4} -2.18288 q^{5} -6.23298 q^{6} +1.55979 q^{7} -3.24187 q^{8} +4.20026 q^{9} +5.07050 q^{10} +2.77170 q^{11} +9.11162 q^{12} +1.99402 q^{13} -3.62315 q^{14} -5.85738 q^{15} +0.739095 q^{16} +5.84932 q^{17} -9.75658 q^{18} +6.51124 q^{19} -7.41226 q^{20} +4.18542 q^{21} -6.43824 q^{22} +3.96182 q^{23} -8.69900 q^{24} -0.235052 q^{25} -4.63181 q^{26} +3.22069 q^{27} +5.29647 q^{28} +8.28758 q^{29} +13.6058 q^{30} -7.81389 q^{31} +4.76693 q^{32} +7.43738 q^{33} -13.5871 q^{34} -3.40482 q^{35} +14.2626 q^{36} -1.00000 q^{37} -15.1247 q^{38} +5.35061 q^{39} +7.07659 q^{40} -2.68459 q^{41} -9.72211 q^{42} +4.38045 q^{43} +9.41169 q^{44} -9.16864 q^{45} -9.20271 q^{46} +3.89639 q^{47} +1.98323 q^{48} -4.56707 q^{49} +0.545991 q^{50} +15.6957 q^{51} +6.77098 q^{52} -1.01578 q^{53} -7.48118 q^{54} -6.05027 q^{55} -5.05662 q^{56} +17.4718 q^{57} -19.2508 q^{58} +6.59980 q^{59} -19.8895 q^{60} +9.58574 q^{61} +18.1505 q^{62} +6.55151 q^{63} -12.5511 q^{64} -4.35270 q^{65} -17.2759 q^{66} -15.2255 q^{67} +19.8622 q^{68} +10.6309 q^{69} +7.90889 q^{70} +2.25001 q^{71} -13.6167 q^{72} -9.61582 q^{73} +2.32285 q^{74} -0.630722 q^{75} +22.1098 q^{76} +4.32326 q^{77} -12.4287 q^{78} -2.62406 q^{79} -1.61335 q^{80} -3.95861 q^{81} +6.23590 q^{82} -1.26693 q^{83} +14.2122 q^{84} -12.7683 q^{85} -10.1751 q^{86} +22.2383 q^{87} -8.98548 q^{88} -9.75300 q^{89} +21.2974 q^{90} +3.11025 q^{91} +13.4529 q^{92} -20.9672 q^{93} -9.05073 q^{94} -14.2132 q^{95} +12.7912 q^{96} -5.73825 q^{97} +10.6086 q^{98} +11.6418 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9}+O(q^{10}) \) 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9	\( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9} + 13 q^{10} + 2 q^{11} + 36 q^{12} + 23 q^{13} + 24 q^{14} + 35 q^{15} + 104 q^{16} + 43 q^{17} + 42 q^{18} + 15 q^{19} + 59 q^{20} + 9 q^{21} + 6 q^{22} + 70 q^{23} + 15 q^{24} + 98 q^{25} + 10 q^{26} + 65 q^{27} + 37 q^{28} + 27 q^{29} + 17 q^{30} + 59 q^{31} + 46 q^{32} + 16 q^{33} - 16 q^{34} + 80 q^{35} + 88 q^{36} - 82 q^{37} + 82 q^{38} + 13 q^{39} + 14 q^{40} + 3 q^{41} + 62 q^{42} + 7 q^{43} - 11 q^{44} + 42 q^{45} - 11 q^{46} + 123 q^{47} + 45 q^{48} + 105 q^{49} + 27 q^{50} + 3 q^{51} - 30 q^{52} + 82 q^{53} - 27 q^{54} + 37 q^{55} + 66 q^{56} + 29 q^{57} - 34 q^{58} + 60 q^{59} + 94 q^{60} + 9 q^{61} - 2 q^{62} + 106 q^{63} + 93 q^{64} + 9 q^{65} + 63 q^{66} + 113 q^{68} + 48 q^{69} + 47 q^{70} + 59 q^{71} + 63 q^{72} + 21 q^{73} - 10 q^{74} + 77 q^{75} + 22 q^{76} + 30 q^{77} + 29 q^{78} + 55 q^{79} + 88 q^{80} + 42 q^{81} + 4 q^{82} + 92 q^{83} + 43 q^{84} - 7 q^{85} + 17 q^{86} + 147 q^{87} - 13 q^{88} + 100 q^{89} + 91 q^{90} + 28 q^{91} + 127 q^{92} + 3 q^{93} + 30 q^{94} + 48 q^{95} - 31 q^{96} + 53 q^{97} + 101 q^{98} - 20 q^{99}+O(q^{100}) \) 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9 + 13 * q^10 + 2 * q^11 + 36 * q^12 + 23 * q^13 + 24 * q^14 + 35 * q^15 + 104 * q^16 + 43 * q^17 + 42 * q^18 + 15 * q^19 + 59 * q^20 + 9 * q^21 + 6 * q^22 + 70 * q^23 + 15 * q^24 + 98 * q^25 + 10 * q^26 + 65 * q^27 + 37 * q^28 + 27 * q^29 + 17 * q^30 + 59 * q^31 + 46 * q^32 + 16 * q^33 - 16 * q^34 + 80 * q^35 + 88 * q^36 - 82 * q^37 + 82 * q^38 + 13 * q^39 + 14 * q^40 + 3 * q^41 + 62 * q^42 + 7 * q^43 - 11 * q^44 + 42 * q^45 - 11 * q^46 + 123 * q^47 + 45 * q^48 + 105 * q^49 + 27 * q^50 + 3 * q^51 - 30 * q^52 + 82 * q^53 - 27 * q^54 + 37 * q^55 + 66 * q^56 + 29 * q^57 - 34 * q^58 + 60 * q^59 + 94 * q^60 + 9 * q^61 - 2 * q^62 + 106 * q^63 + 93 * q^64 + 9 * q^65 + 63 * q^66 + 113 * q^68 + 48 * q^69 + 47 * q^70 + 59 * q^71 + 63 * q^72 + 21 * q^73 - 10 * q^74 + 77 * q^75 + 22 * q^76 + 30 * q^77 + 29 * q^78 + 55 * q^79 + 88 * q^80 + 42 * q^81 + 4 * q^82 + 92 * q^83 + 43 * q^84 - 7 * q^85 + 17 * q^86 + 147 * q^87 - 13 * q^88 + 100 * q^89 + 91 * q^90 + 28 * q^91 + 127 * q^92 + 3 * q^93 + 30 * q^94 + 48 * q^95 - 31 * q^96 + 53 * q^97 + 101 * q^98 - 20 * q^99

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