LMFDB - Embedded newform 6033.2.a.b.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6033,2,Mod(1,6033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6033, 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("6033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6033 = 3 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6033.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:	$48.1737475394$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.93019 q^{2} +1.00000 q^{3} +1.72562 q^{4} -2.39497 q^{5} -1.93019 q^{6} +3.37261 q^{7} +0.529608 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.93019 q^{2} +1.00000 q^{3} +1.72562 q^{4} -2.39497 q^{5} -1.93019 q^{6} +3.37261 q^{7} +0.529608 q^{8} +1.00000 q^{9} +4.62273 q^{10} +5.66629 q^{11} +1.72562 q^{12} -1.61075 q^{13} -6.50976 q^{14} -2.39497 q^{15} -4.47348 q^{16} +1.67690 q^{17} -1.93019 q^{18} +1.90430 q^{19} -4.13280 q^{20} +3.37261 q^{21} -10.9370 q^{22} -1.55923 q^{23} +0.529608 q^{24} +0.735861 q^{25} +3.10904 q^{26} +1.00000 q^{27} +5.81984 q^{28} -6.60080 q^{29} +4.62273 q^{30} -2.85301 q^{31} +7.57543 q^{32} +5.66629 q^{33} -3.23673 q^{34} -8.07728 q^{35} +1.72562 q^{36} -9.59153 q^{37} -3.67565 q^{38} -1.61075 q^{39} -1.26839 q^{40} +8.16568 q^{41} -6.50976 q^{42} -12.1689 q^{43} +9.77786 q^{44} -2.39497 q^{45} +3.00961 q^{46} +4.44396 q^{47} -4.47348 q^{48} +4.37449 q^{49} -1.42035 q^{50} +1.67690 q^{51} -2.77953 q^{52} -9.92553 q^{53} -1.93019 q^{54} -13.5706 q^{55} +1.78616 q^{56} +1.90430 q^{57} +12.7408 q^{58} -6.98181 q^{59} -4.13280 q^{60} +2.14829 q^{61} +5.50684 q^{62} +3.37261 q^{63} -5.67503 q^{64} +3.85768 q^{65} -10.9370 q^{66} -10.2088 q^{67} +2.89369 q^{68} -1.55923 q^{69} +15.5907 q^{70} +2.41370 q^{71} +0.529608 q^{72} -11.8892 q^{73} +18.5134 q^{74} +0.735861 q^{75} +3.28609 q^{76} +19.1102 q^{77} +3.10904 q^{78} -12.0065 q^{79} +10.7138 q^{80} +1.00000 q^{81} -15.7613 q^{82} -14.5677 q^{83} +5.81984 q^{84} -4.01611 q^{85} +23.4882 q^{86} -6.60080 q^{87} +3.00092 q^{88} -13.8310 q^{89} +4.62273 q^{90} -5.43241 q^{91} -2.69064 q^{92} -2.85301 q^{93} -8.57767 q^{94} -4.56073 q^{95} +7.57543 q^{96} -14.2220 q^{97} -8.44358 q^{98} +5.66629 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9}+O(q^{10}) $ 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9	\( 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9} - 41 q^{10} - 18 q^{11} + 53 q^{12} - 67 q^{13} - 7 q^{14} - 8 q^{15} + 21 q^{16} - 25 q^{17} - 11 q^{18} - 43 q^{19} - 8 q^{20} - 46 q^{21} - 49 q^{22} - 75 q^{23} - 33 q^{24} + 19 q^{25} + 71 q^{27} - 89 q^{28} - 35 q^{29} - 41 q^{30} - 82 q^{31} - 62 q^{32} - 18 q^{33} - 28 q^{34} - 51 q^{35} + 53 q^{36} - 66 q^{37} - 29 q^{38} - 67 q^{39} - 102 q^{40} + q^{41} - 7 q^{42} - 112 q^{43} - 25 q^{44} - 8 q^{45} - 36 q^{46} - 67 q^{47} + 21 q^{48} + 7 q^{49} - 24 q^{50} - 25 q^{51} - 134 q^{52} - 40 q^{53} - 11 q^{54} - 112 q^{55} + 9 q^{56} - 43 q^{57} - 47 q^{58} - 18 q^{59} - 8 q^{60} - 144 q^{61} - 19 q^{62} - 46 q^{63} - 17 q^{64} - 31 q^{65} - 49 q^{66} - 85 q^{67} - 22 q^{68} - 75 q^{69} - 11 q^{70} - 44 q^{71} - 33 q^{72} - 98 q^{73} + 6 q^{74} + 19 q^{75} - 85 q^{76} - 39 q^{77} - 126 q^{79} + 21 q^{80} + 71 q^{81} - 69 q^{82} - 43 q^{83} - 89 q^{84} - 112 q^{85} + 32 q^{86} - 35 q^{87} - 85 q^{88} + 8 q^{89} - 41 q^{90} - 40 q^{91} - 96 q^{92} - 82 q^{93} - 99 q^{94} - 103 q^{95} - 62 q^{96} - 67 q^{97} - 11 q^{98} - 18 q^{99}+O(q^{100}) \) 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9 - 41 * q^10 - 18 * q^11 + 53 * q^12 - 67 * q^13 - 7 * q^14 - 8 * q^15 + 21 * q^16 - 25 * q^17 - 11 * q^18 - 43 * q^19 - 8 * q^20 - 46 * q^21 - 49 * q^22 - 75 * q^23 - 33 * q^24 + 19 * q^25 + 71 * q^27 - 89 * q^28 - 35 * q^29 - 41 * q^30 - 82 * q^31 - 62 * q^32 - 18 * q^33 - 28 * q^34 - 51 * q^35 + 53 * q^36 - 66 * q^37 - 29 * q^38 - 67 * q^39 - 102 * q^40 + q^41 - 7 * q^42 - 112 * q^43 - 25 * q^44 - 8 * q^45 - 36 * q^46 - 67 * q^47 + 21 * q^48 + 7 * q^49 - 24 * q^50 - 25 * q^51 - 134 * q^52 - 40 * q^53 - 11 * q^54 - 112 * q^55 + 9 * q^56 - 43 * q^57 - 47 * q^58 - 18 * q^59 - 8 * q^60 - 144 * q^61 - 19 * q^62 - 46 * q^63 - 17 * q^64 - 31 * q^65 - 49 * q^66 - 85 * q^67 - 22 * q^68 - 75 * q^69 - 11 * q^70 - 44 * q^71 - 33 * q^72 - 98 * q^73 + 6 * q^74 + 19 * q^75 - 85 * q^76 - 39 * q^77 - 126 * q^79 + 21 * q^80 + 71 * q^81 - 69 * q^82 - 43 * q^83 - 89 * q^84 - 112 * q^85 + 32 * q^86 - 35 * q^87 - 85 * q^88 + 8 * q^89 - 41 * q^90 - 40 * q^91 - 96 * q^92 - 82 * q^93 - 99 * q^94 - 103 * q^95 - 62 * q^96 - 67 * q^97 - 11 * q^98 - 18 * 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 $

$2$	−1.93019	−1.36485	−0.682424	−	0.730957i	$-0.739074\pi$
$2$	−1.93019	−1.36485	−0.682424	+	0.730957i	$0.739074\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.72562	0.862809
$5$	−2.39497	−1.07106	−0.535531	−	0.844516i	$-0.679888\pi$
$5$	−2.39497	−1.07106	−0.535531	+	0.844516i	$0.679888\pi$
$6$	−1.93019	−0.787995
$7$	3.37261	1.27473	0.637363	−	0.770564i	$-0.280025\pi$
$7$	3.37261	1.27473	0.637363	+	0.770564i	$0.280025\pi$
$8$	0.529608	0.187245
$9$	1.00000	0.333333
$10$	4.62273	1.46184
$11$	5.66629	1.70845	0.854226	−	0.519902i	$-0.174032\pi$
$11$	5.66629	1.70845	0.854226	+	0.519902i	$0.174032\pi$
$12$	1.72562	0.498143
$13$	−1.61075	−0.446740	−0.223370	−	0.974734i	$-0.571706\pi$
$13$	−1.61075	−0.446740	−0.223370	+	0.974734i	$0.571706\pi$
$14$	−6.50976	−1.73981
$15$	−2.39497	−0.618378
$16$	−4.47348	−1.11837
$17$	1.67690	0.406708	0.203354	−	0.979105i	$-0.434816\pi$
$17$	1.67690	0.406708	0.203354	+	0.979105i	$0.434816\pi$
$18$	−1.93019	−0.454949
$19$	1.90430	0.436876	0.218438	−	0.975851i	$-0.429904\pi$
$19$	1.90430	0.436876	0.218438	+	0.975851i	$0.429904\pi$
$20$	−4.13280	−0.924121
$21$	3.37261	0.735964
$22$	−10.9370	−2.33178
$23$	−1.55923	−0.325123	−0.162561	−	0.986698i	$-0.551976\pi$
$23$	−1.55923	−0.325123	−0.162561	+	0.986698i	$0.551976\pi$
$24$	0.529608	0.108106
$25$	0.735861	0.147172
$26$	3.10904	0.609733
$27$	1.00000	0.192450
$28$	5.81984	1.09985
$29$	−6.60080	−1.22574	−0.612869	−	0.790184i	$-0.709985\pi$
$29$	−6.60080	−1.22574	−0.612869	+	0.790184i	$0.709985\pi$
$30$	4.62273	0.843991
$31$	−2.85301	−0.512416	−0.256208	−	0.966622i	$-0.582473\pi$
$31$	−2.85301	−0.512416	−0.256208	+	0.966622i	$0.582473\pi$
$32$	7.57543	1.33916
$33$	5.66629	0.986375
$34$	−3.23673	−0.555094
$35$	−8.07728	−1.36531
$36$	1.72562	0.287603
$37$	−9.59153	−1.57684	−0.788419	−	0.615138i	$-0.789100\pi$
$37$	−9.59153	−1.57684	−0.788419	+	0.615138i	$0.789100\pi$
$38$	−3.67565	−0.596270
$39$	−1.61075	−0.257926
$40$	−1.26839	−0.200551
$41$	8.16568	1.27526	0.637632	−	0.770341i	$-0.279914\pi$
$41$	8.16568	1.27526	0.637632	+	0.770341i	$0.279914\pi$
$42$	−6.50976	−1.00448
$43$	−12.1689	−1.85574	−0.927870	−	0.372905i	$-0.878362\pi$
$43$	−12.1689	−1.85574	−0.927870	+	0.372905i	$0.878362\pi$
$44$	9.77786	1.47407
$45$	−2.39497	−0.357020
$46$	3.00961	0.443743
$47$	4.44396	0.648219	0.324109	−	0.946020i	$-0.394935\pi$
$47$	4.44396	0.648219	0.324109	+	0.946020i	$0.394935\pi$
$48$	−4.47348	−0.645691
$49$	4.37449	0.624928
$50$	−1.42035	−0.200868
$51$	1.67690	0.234813
$52$	−2.77953	−0.385452
$53$	−9.92553	−1.36338	−0.681688	−	0.731643i	$-0.738754\pi$
$53$	−9.92553	−1.36338	−0.681688	+	0.731643i	$0.738754\pi$
$54$	−1.93019	−0.262665
$55$	−13.5706	−1.82986
$56$	1.78616	0.238686
$57$	1.90430	0.252231
$58$	12.7408	1.67295
$59$	−6.98181	−0.908954	−0.454477	−	0.890759i	$-0.650174\pi$
$59$	−6.98181	−0.908954	−0.454477	+	0.890759i	$0.650174\pi$
$60$	−4.13280	−0.533542
$61$	2.14829	0.275060	0.137530	−	0.990498i	$-0.456084\pi$
$61$	2.14829	0.275060	0.137530	+	0.990498i	$0.456084\pi$
$62$	5.50684	0.699369
$63$	3.37261	0.424909
$64$	−5.67503	−0.709379
$65$	3.85768	0.478486
$66$	−10.9370	−1.34625
$67$	−10.2088	−1.24720	−0.623599	−	0.781744i	$-0.714330\pi$
$67$	−10.2088	−1.24720	−0.623599	+	0.781744i	$0.714330\pi$
$68$	2.89369	0.350911
$69$	−1.55923	−0.187710
$70$	15.5907	1.86344
$71$	2.41370	0.286453	0.143227	−	0.989690i	$-0.454252\pi$
$71$	2.41370	0.286453	0.143227	+	0.989690i	$0.454252\pi$
$72$	0.529608	0.0624149
$73$	−11.8892	−1.39152	−0.695761	−	0.718273i	$-0.744933\pi$
$73$	−11.8892	−1.39152	−0.695761	+	0.718273i	$0.744933\pi$
$74$	18.5134	2.15214
$75$	0.735861	0.0849699
$76$	3.28609	0.376941
$77$	19.1102	2.17781
$78$	3.10904	0.352029
$79$	−12.0065	−1.35083	−0.675417	−	0.737436i	$-0.736036\pi$
$79$	−12.0065	−1.35083	−0.675417	+	0.737436i	$0.736036\pi$
$80$	10.7138	1.19784
$81$	1.00000	0.111111
$82$	−15.7613	−1.74054
$83$	−14.5677	−1.59901	−0.799505	−	0.600660i	$-0.794905\pi$
$83$	−14.5677	−1.59901	−0.799505	+	0.600660i	$0.794905\pi$
$84$	5.81984	0.634996
$85$	−4.01611	−0.435609
$86$	23.4882	2.53280
$87$	−6.60080	−0.707680
$88$	3.00092	0.319899
$89$	−13.8310	−1.46609	−0.733043	−	0.680183i	$-0.761900\pi$
$89$	−13.8310	−1.46609	−0.733043	+	0.680183i	$0.761900\pi$
$90$	4.62273	0.487278
$91$	−5.43241	−0.569472
$92$	−2.69064	−0.280519
$93$	−2.85301	−0.295843
$94$	−8.57767	−0.884720
$95$	−4.56073	−0.467921
$96$	7.57543	0.773164
$97$	−14.2220	−1.44403	−0.722013	−	0.691879i	$-0.756783\pi$
$97$	−14.2220	−1.44403	−0.722013	+	0.691879i	$0.756783\pi$
$98$	−8.44358	−0.852931
$99$	5.66629	0.569484
$100$	1.26982	0.126982
$101$	0.284630	0.0283217	0.0141608	−	0.999900i	$-0.495492\pi$
$101$	0.284630	0.0283217	0.0141608	+	0.999900i	$0.495492\pi$
$102$	−3.23673	−0.320484
$103$	−11.3789	−1.12120	−0.560599	−	0.828088i	$-0.689429\pi$
$103$	−11.3789	−1.12120	−0.560599	+	0.828088i	$0.689429\pi$
$104$	−0.853064	−0.0836498
$105$	−8.07728	−0.788262
$106$	19.1581	1.86080
$107$	11.3754	1.09970	0.549851	−	0.835263i	$-0.314684\pi$
$107$	11.3754	1.09970	0.549851	+	0.835263i	$0.314684\pi$
$108$	1.72562	0.166048
$109$	9.50926	0.910822	0.455411	−	0.890281i	$-0.349492\pi$
$109$	9.50926	0.910822	0.455411	+	0.890281i	$0.349492\pi$
$110$	26.1937	2.49748
$111$	−9.59153	−0.910388
$112$	−15.0873	−1.42562
$113$	6.19740	0.583003	0.291501	−	0.956570i	$-0.405845\pi$
$113$	6.19740	0.583003	0.291501	+	0.956570i	$0.405845\pi$
$114$	−3.67565	−0.344256
$115$	3.73431	0.348226
$116$	−11.3905	−1.05758
$117$	−1.61075	−0.148913
$118$	13.4762	1.24058
$119$	5.65552	0.518441
$120$	−1.26839	−0.115788
$121$	21.1069	1.91881
$122$	−4.14659	−0.375415
$123$	8.16568	0.736274
$124$	−4.92320	−0.442117
$125$	10.2125	0.913431
$126$	−6.50976	−0.579936
$127$	5.89193	0.522824	0.261412	−	0.965227i	$-0.415812\pi$
$127$	5.89193	0.522824	0.261412	+	0.965227i	$0.415812\pi$
$128$	−4.19699	−0.370965
$129$	−12.1689	−1.07141
$130$	−7.44604	−0.653061
$131$	−19.7837	−1.72851	−0.864254	−	0.503055i	$-0.832209\pi$
$131$	−19.7837	−1.72851	−0.864254	+	0.503055i	$0.832209\pi$
$132$	9.77786	0.851053
$133$	6.42246	0.556898
$134$	19.7048	1.70224
$135$	−2.39497	−0.206126
$136$	0.888099	0.0761539
$137$	−14.5845	−1.24603	−0.623017	−	0.782208i	$-0.714093\pi$
$137$	−14.5845	−1.24603	−0.623017	+	0.782208i	$0.714093\pi$
$138$	3.00961	0.256195
$139$	15.2942	1.29724	0.648618	−	0.761114i	$-0.275347\pi$
$139$	15.2942	1.29724	0.648618	+	0.761114i	$0.275347\pi$
$140$	−13.9383	−1.17800
$141$	4.44396	0.374249
$142$	−4.65889	−0.390965
$143$	−9.12696	−0.763234
$144$	−4.47348	−0.372790
$145$	15.8087	1.31284
$146$	22.9483	1.89922
$147$	4.37449	0.360802
$148$	−16.5513	−1.36051
$149$	5.25889	0.430825	0.215412	−	0.976523i	$-0.430890\pi$
$149$	5.25889	0.430825	0.215412	+	0.976523i	$0.430890\pi$
$150$	−1.42035	−0.115971
$151$	−6.75449	−0.549673	−0.274836	−	0.961491i	$-0.588624\pi$
$151$	−6.75449	−0.549673	−0.274836	+	0.961491i	$0.588624\pi$
$152$	1.00853	0.0818028
$153$	1.67690	0.135569
$154$	−36.8862	−2.97238
$155$	6.83286	0.548828
$156$	−2.77953	−0.222541
$157$	7.42128	0.592283	0.296141	−	0.955144i	$-0.404300\pi$
$157$	7.42128	0.592283	0.296141	+	0.955144i	$0.404300\pi$
$158$	23.1747	1.84368
$159$	−9.92553	−0.787146
$160$	−18.1429	−1.43432
$161$	−5.25869	−0.414443
$162$	−1.93019	−0.151650
$163$	25.0432	1.96154	0.980768	−	0.195178i	$-0.0625286\pi$
$163$	25.0432	1.96154	0.980768	+	0.195178i	$0.0625286\pi$
$164$	14.0908	1.10031
$165$	−13.5706	−1.05647
$166$	28.1183	2.18240
$167$	12.3477	0.955491	0.477745	−	0.878498i	$-0.341454\pi$
$167$	12.3477	0.955491	0.477745	+	0.878498i	$0.341454\pi$
$168$	1.78616	0.137805
$169$	−10.4055	−0.800423
$170$	7.75185	0.594539
$171$	1.90430	0.145625
$172$	−20.9989	−1.60115
$173$	5.39423	0.410116	0.205058	−	0.978750i	$-0.434262\pi$
$173$	5.39423	0.410116	0.205058	+	0.978750i	$0.434262\pi$
$174$	12.7408	0.965876
$175$	2.48177	0.187604
$176$	−25.3480	−1.91068
$177$	−6.98181	−0.524785
$178$	26.6964	2.00098
$179$	12.9658	0.969113	0.484557	−	0.874760i	$-0.338981\pi$
$179$	12.9658	0.969113	0.484557	+	0.874760i	$0.338981\pi$
$180$	−4.13280	−0.308040
$181$	−12.9114	−0.959694	−0.479847	−	0.877352i	$-0.659308\pi$
$181$	−12.9114	−0.959694	−0.479847	+	0.877352i	$0.659308\pi$
$182$	10.4856	0.777242
$183$	2.14829	0.158806
$184$	−0.825783	−0.0608775
$185$	22.9714	1.68889
$186$	5.50684	0.403781
$187$	9.50180	0.694840
$188$	7.66858	0.559289
$189$	3.37261	0.245321
$190$	8.80306	0.638641
$191$	23.3957	1.69285	0.846425	−	0.532508i	$-0.178750\pi$
$191$	23.3957	1.69285	0.846425	+	0.532508i	$0.178750\pi$
$192$	−5.67503	−0.409560
$193$	−8.87765	−0.639027	−0.319514	−	0.947582i	$-0.603520\pi$
$193$	−8.87765	−0.639027	−0.319514	+	0.947582i	$0.603520\pi$
$194$	27.4511	1.97088
$195$	3.85768	0.276254
$196$	7.54870	0.539193
$197$	5.52760	0.393825	0.196912	−	0.980421i	$-0.436909\pi$
$197$	5.52760	0.393825	0.196912	+	0.980421i	$0.436909\pi$
$198$	−10.9370	−0.777259
$199$	−2.51257	−0.178111	−0.0890557	−	0.996027i	$-0.528385\pi$
$199$	−2.51257	−0.178111	−0.0890557	+	0.996027i	$0.528385\pi$
$200$	0.389718	0.0275572
$201$	−10.2088	−0.720070
$202$	−0.549388	−0.0386548
$203$	−22.2619	−1.56248
$204$	2.89369	0.202599
$205$	−19.5565	−1.36589
$206$	21.9634	1.53026
$207$	−1.55923	−0.108374
$208$	7.20564	0.499621
$209$	10.7903	0.746382
$210$	15.5907	1.07586
$211$	22.2043	1.52860	0.764302	−	0.644858i	$-0.223084\pi$
$211$	22.2043	1.52860	0.764302	+	0.644858i	$0.223084\pi$
$212$	−17.1277	−1.17633
$213$	2.41370	0.165384
$214$	−21.9567	−1.50093
$215$	29.1441	1.98761
$216$	0.529608	0.0360353
$217$	−9.62208	−0.653190
$218$	−18.3546	−1.24313
$219$	−11.8892	−0.803396
$220$	−23.4176	−1.57882
$221$	−2.70106	−0.181693
$222$	18.5134	1.24254
$223$	−21.8205	−1.46121	−0.730603	−	0.682802i	$-0.760761\pi$
$223$	−21.8205	−1.46121	−0.730603	+	0.682802i	$0.760761\pi$
$224$	25.5490	1.70706
$225$	0.735861	0.0490574
$226$	−11.9621	−0.795710
$227$	23.0322	1.52870	0.764351	−	0.644800i	$-0.223059\pi$
$227$	23.0322	1.52870	0.764351	+	0.644800i	$0.223059\pi$
$228$	3.28609	0.217627
$229$	−17.1919	−1.13607	−0.568035	−	0.823004i	$-0.692296\pi$
$229$	−17.1919	−1.13607	−0.568035	+	0.823004i	$0.692296\pi$
$230$	−7.20792	−0.475276
$231$	19.1102	1.25736
$232$	−3.49584	−0.229513
$233$	18.7797	1.23030	0.615150	−	0.788410i	$-0.289096\pi$
$233$	18.7797	1.23030	0.615150	+	0.788410i	$0.289096\pi$
$234$	3.10904	0.203244
$235$	−10.6431	−0.694282
$236$	−12.0479	−0.784254
$237$	−12.0065	−0.779905
$238$	−10.9162	−0.707593
$239$	−7.78265	−0.503418	−0.251709	−	0.967803i	$-0.580993\pi$
$239$	−7.78265	−0.503418	−0.251709	+	0.967803i	$0.580993\pi$
$240$	10.7138	0.691575
$241$	−18.7057	−1.20494	−0.602471	−	0.798141i	$-0.705817\pi$
$241$	−18.7057	−1.20494	−0.602471	+	0.798141i	$0.705817\pi$
$242$	−40.7402	−2.61888
$243$	1.00000	0.0641500
$244$	3.70712	0.237324
$245$	−10.4768	−0.669336
$246$	−15.7613	−1.00490
$247$	−3.06734	−0.195170
$248$	−1.51098	−0.0959471
$249$	−14.5677	−0.923188
$250$	−19.7120	−1.24669
$251$	−4.43855	−0.280159	−0.140079	−	0.990140i	$-0.544736\pi$
$251$	−4.43855	−0.280159	−0.140079	+	0.990140i	$0.544736\pi$
$252$	5.81984	0.366615
$253$	−8.83508	−0.555456
$254$	−11.3725	−0.713575
$255$	−4.01611	−0.251499
$256$	19.4510	1.21569
$257$	−12.6404	−0.788484	−0.394242	−	0.919007i	$-0.628993\pi$
$257$	−12.6404	−0.788484	−0.394242	+	0.919007i	$0.628993\pi$
$258$	23.4882	1.46231
$259$	−32.3485	−2.01004
$260$	6.65688	0.412842
$261$	−6.60080	−0.408579
$262$	38.1862	2.35915
$263$	−19.3710	−1.19447	−0.597233	−	0.802067i	$-0.703733\pi$
$263$	−19.3710	−1.19447	−0.597233	+	0.802067i	$0.703733\pi$
$264$	3.00092	0.184694
$265$	23.7713	1.46026
$266$	−12.3965	−0.760081
$267$	−13.8310	−0.846445
$268$	−17.6164	−1.07609
$269$	11.9607	0.729259	0.364629	−	0.931153i	$-0.381196\pi$
$269$	11.9607	0.729259	0.364629	+	0.931153i	$0.381196\pi$
$270$	4.62273	0.281330
$271$	16.4438	0.998890	0.499445	−	0.866345i	$-0.333537\pi$
$271$	16.4438	0.998890	0.499445	+	0.866345i	$0.333537\pi$
$272$	−7.50157	−0.454849
$273$	−5.43241	−0.328785
$274$	28.1507	1.70065
$275$	4.16961	0.251437
$276$	−2.69064	−0.161958
$277$	−30.7318	−1.84650	−0.923249	−	0.384203i	$-0.874476\pi$
$277$	−30.7318	−1.84650	−0.923249	+	0.384203i	$0.874476\pi$
$278$	−29.5206	−1.77053
$279$	−2.85301	−0.170805
$280$	−4.27780	−0.255647
$281$	−2.63860	−0.157406	−0.0787028	−	0.996898i	$-0.525078\pi$
$281$	−2.63860	−0.157406	−0.0787028	+	0.996898i	$0.525078\pi$
$282$	−8.57767	−0.510793
$283$	4.08442	0.242793	0.121397	−	0.992604i	$-0.461263\pi$
$283$	4.08442	0.242793	0.121397	+	0.992604i	$0.461263\pi$
$284$	4.16512	0.247154
$285$	−4.56073	−0.270155
$286$	17.6167	1.04170
$287$	27.5396	1.62561
$288$	7.57543	0.446386
$289$	−14.1880	−0.834589
$290$	−30.5137	−1.79183
$291$	−14.2220	−0.833709
$292$	−20.5162	−1.20062
$293$	9.77650	0.571149	0.285574	−	0.958357i	$-0.407816\pi$
$293$	9.77650	0.571149	0.285574	+	0.958357i	$0.407816\pi$
$294$	−8.44358	−0.492440
$295$	16.7212	0.973545
$296$	−5.07976	−0.295255
$297$	5.66629	0.328792
$298$	−10.1506	−0.588010
$299$	2.51153	0.145245
$300$	1.26982	0.0733128
$301$	−41.0409	−2.36556
$302$	13.0374	0.750220
$303$	0.284630	0.0163515
$304$	−8.51884	−0.488589
$305$	−5.14507	−0.294606
$306$	−3.23673	−0.185031
$307$	33.9529	1.93780	0.968898	−	0.247459i	$-0.0795955\pi$
$307$	33.9529	1.93780	0.968898	+	0.247459i	$0.0795955\pi$
$308$	32.9769	1.87903
$309$	−11.3789	−0.647324
$310$	−13.1887	−0.749067
$311$	−17.1834	−0.974383	−0.487191	−	0.873295i	$-0.661979\pi$
$311$	−17.1834	−0.974383	−0.487191	+	0.873295i	$0.661979\pi$
$312$	−0.853064	−0.0482952
$313$	10.0867	0.570133	0.285067	−	0.958508i	$-0.407984\pi$
$313$	10.0867	0.570133	0.285067	+	0.958508i	$0.407984\pi$
$314$	−14.3245	−0.808376
$315$	−8.07728	−0.455103
$316$	−20.7186	−1.16551
$317$	−12.8819	−0.723520	−0.361760	−	0.932271i	$-0.617824\pi$
$317$	−12.8819	−0.723520	−0.361760	+	0.932271i	$0.617824\pi$
$318$	19.1581	1.07433
$319$	−37.4021	−2.09412
$320$	13.5915	0.759788
$321$	11.3754	0.634914
$322$	10.1502	0.565651
$323$	3.19332	0.177681
$324$	1.72562	0.0958677
$325$	−1.18528	−0.0657478
$326$	−48.3381	−2.67720
$327$	9.50926	0.525863
$328$	4.32461	0.238787
$329$	14.9877	0.826301
$330$	26.1937	1.44192
$331$	20.2962	1.11558	0.557789	−	0.829983i	$-0.311650\pi$
$331$	20.2962	1.11558	0.557789	+	0.829983i	$0.311650\pi$
$332$	−25.1382	−1.37964
$333$	−9.59153	−0.525613
$334$	−23.8333	−1.30410
$335$	24.4496	1.33583
$336$	−15.0873	−0.823079
$337$	−11.1769	−0.608846	−0.304423	−	0.952537i	$-0.598464\pi$
$337$	−11.1769	−0.608846	−0.304423	+	0.952537i	$0.598464\pi$
$338$	20.0845	1.09246
$339$	6.19740	0.336597
$340$	−6.93028	−0.375847
$341$	−16.1660	−0.875437
$342$	−3.67565	−0.198757
$343$	−8.85481	−0.478115
$344$	−6.44475	−0.347478
$345$	3.73431	0.201049
$346$	−10.4119	−0.559745
$347$	−6.81049	−0.365606	−0.182803	−	0.983150i	$-0.558517\pi$
$347$	−6.81049	−0.365606	−0.182803	+	0.983150i	$0.558517\pi$
$348$	−11.3905	−0.610593
$349$	−3.66292	−0.196072	−0.0980358	−	0.995183i	$-0.531256\pi$
$349$	−3.66292	−0.196072	−0.0980358	+	0.995183i	$0.531256\pi$
$350$	−4.79028	−0.256051
$351$	−1.61075	−0.0859752
$352$	42.9246	2.28789
$353$	−33.6252	−1.78969	−0.894844	−	0.446379i	$-0.852713\pi$
$353$	−33.6252	−1.78969	−0.894844	+	0.446379i	$0.852713\pi$
$354$	13.4762	0.716251
$355$	−5.78072	−0.306809
$356$	−23.8671	−1.26495
$357$	5.65552	0.299322
$358$	−25.0265	−1.32269
$359$	0.554468	0.0292637	0.0146319	−	0.999893i	$-0.495342\pi$
$359$	0.554468	0.0292637	0.0146319	+	0.999893i	$0.495342\pi$
$360$	−1.26839	−0.0668502
$361$	−15.3736	−0.809139
$362$	24.9213	1.30984
$363$	21.1069	1.10782
$364$	−9.37427	−0.491345
$365$	28.4742	1.49041
$366$	−4.14659	−0.216746
$367$	1.64047	0.0856320	0.0428160	−	0.999083i	$-0.486367\pi$
$367$	1.64047	0.0856320	0.0428160	+	0.999083i	$0.486367\pi$
$368$	6.97520	0.363607
$369$	8.16568	0.425088
$370$	−44.3391	−2.30508
$371$	−33.4749	−1.73793
$372$	−4.92320	−0.255256
$373$	37.5744	1.94553	0.972765	−	0.231792i	$-0.0744589\pi$
$373$	37.5744	1.94553	0.972765	+	0.231792i	$0.0744589\pi$
$374$	−18.3402	−0.948351
$375$	10.2125	0.527370
$376$	2.35356	0.121376
$377$	10.6322	0.547587
$378$	−6.50976	−0.334826
$379$	1.50004	0.0770516	0.0385258	−	0.999258i	$-0.487734\pi$
$379$	1.50004	0.0770516	0.0385258	+	0.999258i	$0.487734\pi$
$380$	−7.87008	−0.403727
$381$	5.89193	0.301852
$382$	−45.1580	−2.31048
$383$	−14.4209	−0.736875	−0.368437	−	0.929653i	$-0.620107\pi$
$383$	−14.4209	−0.736875	−0.368437	+	0.929653i	$0.620107\pi$
$384$	−4.19699	−0.214177
$385$	−45.7683	−2.33257
$386$	17.1355	0.872175
$387$	−12.1689	−0.618580
$388$	−24.5418	−1.24592
$389$	−25.9903	−1.31776	−0.658880	−	0.752248i	$-0.728970\pi$
$389$	−25.9903	−1.31776	−0.658880	+	0.752248i	$0.728970\pi$
$390$	−7.44604	−0.377045
$391$	−2.61468	−0.132230
$392$	2.31677	0.117014
$393$	−19.7837	−0.997955
$394$	−10.6693	−0.537511
$395$	28.7551	1.44683
$396$	9.77786	0.491356
$397$	−5.22713	−0.262342	−0.131171	−	0.991360i	$-0.541874\pi$
$397$	−5.22713	−0.262342	−0.131171	+	0.991360i	$0.541874\pi$
$398$	4.84973	0.243095
$399$	6.42246	0.321525
$400$	−3.29186	−0.164593
$401$	0.945540	0.0472180	0.0236090	−	0.999721i	$-0.492484\pi$
$401$	0.945540	0.0472180	0.0236090	+	0.999721i	$0.492484\pi$
$402$	19.7048	0.982786
$403$	4.59547	0.228917
$404$	0.491162	0.0244362
$405$	−2.39497	−0.119007
$406$	42.9697	2.13255
$407$	−54.3484	−2.69395
$408$	0.888099	0.0439675
$409$	11.2403	0.555798	0.277899	−	0.960610i	$-0.410362\pi$
$409$	11.2403	0.555798	0.277899	+	0.960610i	$0.410362\pi$
$410$	37.7477	1.86423
$411$	−14.5845	−0.719399
$412$	−19.6357	−0.967379
$413$	−23.5469	−1.15867
$414$	3.00961	0.147914
$415$	34.8891	1.71264
$416$	−12.2021	−0.598257
$417$	15.2942	0.748960
$418$	−20.8273	−1.01870
$419$	1.70247	0.0831710	0.0415855	−	0.999135i	$-0.486759\pi$
$419$	1.70247	0.0831710	0.0415855	+	0.999135i	$0.486759\pi$
$420$	−13.9383	−0.680120
$421$	3.79505	0.184959	0.0924797	−	0.995715i	$-0.470521\pi$
$421$	3.79505	0.184959	0.0924797	+	0.995715i	$0.470521\pi$
$422$	−42.8584	−2.08631
$423$	4.44396	0.216073
$424$	−5.25664	−0.255285
$425$	1.23396	0.0598561
$426$	−4.65889	−0.225724
$427$	7.24533	0.350626
$428$	19.6296	0.948833
$429$	−9.12696	−0.440654
$430$	−56.2535	−2.71279
$431$	35.4000	1.70516	0.852580	−	0.522597i	$-0.175037\pi$
$431$	35.4000	1.70516	0.852580	+	0.522597i	$0.175037\pi$
$432$	−4.47348	−0.215230
$433$	9.45734	0.454491	0.227245	−	0.973838i	$-0.427028\pi$
$433$	9.45734	0.454491	0.227245	+	0.973838i	$0.427028\pi$
$434$	18.5724	0.891504
$435$	15.8087	0.757969
$436$	16.4093	0.785865
$437$	−2.96925	−0.142038
$438$	22.9483	1.09651
$439$	18.4142	0.878863	0.439431	−	0.898276i	$-0.355180\pi$
$439$	18.4142	0.878863	0.439431	+	0.898276i	$0.355180\pi$
$440$	−7.18709	−0.342631
$441$	4.37449	0.208309
$442$	5.21354	0.247983
$443$	6.41651	0.304858	0.152429	−	0.988314i	$-0.451291\pi$
$443$	6.41651	0.304858	0.152429	+	0.988314i	$0.451291\pi$
$444$	−16.5513	−0.785491
$445$	33.1248	1.57027
$446$	42.1175	1.99432
$447$	5.25889	0.248737
$448$	−19.1397	−0.904264
$449$	9.51527	0.449053	0.224527	−	0.974468i	$-0.427916\pi$
$449$	9.51527	0.449053	0.224527	+	0.974468i	$0.427916\pi$
$450$	−1.42035	−0.0669559
$451$	46.2691	2.17873
$452$	10.6944	0.503020
$453$	−6.75449	−0.317354
$454$	−44.4565	−2.08645
$455$	13.0104	0.609939
$456$	1.00853	0.0472289
$457$	17.5593	0.821391	0.410696	−	0.911772i	$-0.365286\pi$
$457$	17.5593	0.821391	0.410696	+	0.911772i	$0.365286\pi$
$458$	33.1835	1.55056
$459$	1.67690	0.0782709
$460$	6.44399	0.300453
$461$	14.1749	0.660192	0.330096	−	0.943947i	$-0.392919\pi$
$461$	14.1749	0.660192	0.330096	+	0.943947i	$0.392919\pi$
$462$	−36.8862	−1.71610
$463$	−30.9019	−1.43613	−0.718067	−	0.695974i	$-0.754973\pi$
$463$	−30.9019	−1.43613	−0.718067	+	0.695974i	$0.754973\pi$
$464$	29.5286	1.37083
$465$	6.83286	0.316866
$466$	−36.2483	−1.67917
$467$	18.5519	0.858477	0.429239	−	0.903191i	$-0.358782\pi$
$467$	18.5519	0.858477	0.429239	+	0.903191i	$0.358782\pi$
$468$	−2.77953	−0.128484
$469$	−34.4301	−1.58984
$470$	20.5432	0.947589
$471$	7.42128	0.341955
$472$	−3.69762	−0.170197
$473$	−68.9525	−3.17044
$474$	23.1747	1.06445
$475$	1.40130	0.0642961
$476$	9.75927	0.447315
$477$	−9.92553	−0.454459
$478$	15.0220	0.687089
$479$	−37.9361	−1.73335	−0.866673	−	0.498876i	$-0.833746\pi$
$479$	−37.9361	−1.73335	−0.866673	+	0.498876i	$0.833746\pi$
$480$	−18.1429	−0.828106
$481$	15.4495	0.704437
$482$	36.1055	1.64456
$483$	−5.25869	−0.239278
$484$	36.4224	1.65556
$485$	34.0612	1.54664
$486$	−1.93019	−0.0875550
$487$	−27.3845	−1.24091	−0.620455	−	0.784242i	$-0.713052\pi$
$487$	−27.3845	−1.24091	−0.620455	+	0.784242i	$0.713052\pi$
$488$	1.13775	0.0515035
$489$	25.0432	1.13249
$490$	20.2221	0.913541
$491$	34.1295	1.54024	0.770122	−	0.637897i	$-0.220195\pi$
$491$	34.1295	1.54024	0.770122	+	0.637897i	$0.220195\pi$
$492$	14.0908	0.635264
$493$	−11.0689	−0.498517
$494$	5.92054	0.266378
$495$	−13.5706	−0.609952
$496$	12.7629	0.573070
$497$	8.14046	0.365150
$498$	28.1183	1.26001
$499$	−11.5563	−0.517331	−0.258665	−	0.965967i	$-0.583283\pi$
$499$	−11.5563	−0.517331	−0.258665	+	0.965967i	$0.583283\pi$
$500$	17.6228	0.788116
$501$	12.3477	0.551653
$502$	8.56723	0.382374
$503$	8.63052	0.384816	0.192408	−	0.981315i	$-0.438370\pi$
$503$	8.63052	0.384816	0.192408	+	0.981315i	$0.438370\pi$
$504$	1.78616	0.0795620
$505$	−0.681678	−0.0303343
$506$	17.0533	0.758113
$507$	−10.4055	−0.462124
$508$	10.1672	0.451097
$509$	31.1875	1.38236	0.691180	−	0.722683i	$-0.257091\pi$
$509$	31.1875	1.38236	0.691180	+	0.722683i	$0.257091\pi$
$510$	7.75185	0.343258
$511$	−40.0975	−1.77381
$512$	−29.1501	−1.28827
$513$	1.90430	0.0840769
$514$	24.3983	1.07616
$515$	27.2521	1.20087
$516$	−20.9989	−0.924424
$517$	25.1808	1.10745
$518$	62.4386	2.74340
$519$	5.39423	0.236780
$520$	2.04306	0.0895941
$521$	−24.9180	−1.09168	−0.545838	−	0.837891i	$-0.683789\pi$
$521$	−24.9180	−1.09168	−0.545838	+	0.837891i	$0.683789\pi$
$522$	12.7408	0.557649
$523$	9.01641	0.394260	0.197130	−	0.980377i	$-0.436838\pi$
$523$	9.01641	0.394260	0.197130	+	0.980377i	$0.436838\pi$
$524$	−34.1391	−1.49137
$525$	2.48177	0.108313
$526$	37.3896	1.63027
$527$	−4.78421	−0.208403
$528$	−25.3480	−1.10313
$529$	−20.5688	−0.894295
$530$	−45.8830	−1.99303
$531$	−6.98181	−0.302985
$532$	11.0827	0.480496
$533$	−13.1528	−0.569712
$534$	26.6964	1.15527
$535$	−27.2437	−1.17785
$536$	−5.40664	−0.233531
$537$	12.9658	0.559518
$538$	−23.0864	−0.995327
$539$	24.7872	1.06766
$540$	−4.13280	−0.177847
$541$	−11.6053	−0.498949	−0.249475	−	0.968381i	$-0.580258\pi$
$541$	−11.6053	−0.498949	−0.249475	+	0.968381i	$0.580258\pi$
$542$	−31.7396	−1.36333
$543$	−12.9114	−0.554079
$544$	12.7032	0.544646
$545$	−22.7743	−0.975546
$546$	10.4856	0.448741
$547$	36.4181	1.55712	0.778562	−	0.627567i	$-0.215949\pi$
$547$	36.4181	1.55712	0.778562	+	0.627567i	$0.215949\pi$
$548$	−25.1672	−1.07509
$549$	2.14829	0.0916866
$550$	−8.04811	−0.343173
$551$	−12.5699	−0.535496
$552$	−0.825783	−0.0351477
$553$	−40.4932	−1.72194
$554$	59.3182	2.52019
$555$	22.9714	0.975081
$556$	26.3919	1.11927
$557$	−25.7433	−1.09078	−0.545389	−	0.838183i	$-0.683618\pi$
$557$	−25.7433	−1.09078	−0.545389	+	0.838183i	$0.683618\pi$
$558$	5.50684	0.233123
$559$	19.6010	0.829034
$560$	36.1336	1.52692
$561$	9.50180	0.401166
$562$	5.09299	0.214835
$563$	−12.5132	−0.527367	−0.263684	−	0.964609i	$-0.584938\pi$
$563$	−12.5132	−0.527367	−0.263684	+	0.964609i	$0.584938\pi$
$564$	7.66858	0.322906
$565$	−14.8426	−0.624432
$566$	−7.88368	−0.331376
$567$	3.37261	0.141636
$568$	1.27831	0.0536369
$569$	0.347081	0.0145504	0.00727520	−	0.999974i	$-0.497684\pi$
$569$	0.347081	0.0145504	0.00727520	+	0.999974i	$0.497684\pi$
$570$	8.80306	0.368720
$571$	21.7556	0.910443	0.455222	−	0.890378i	$-0.349560\pi$
$571$	21.7556	0.910443	0.455222	+	0.890378i	$0.349560\pi$
$572$	−15.7496	−0.658526
$573$	23.3957	0.977368
$574$	−53.1566	−2.21872
$575$	−1.14738	−0.0478490
$576$	−5.67503	−0.236460
$577$	33.9926	1.41513	0.707566	−	0.706648i	$-0.249793\pi$
$577$	33.9926	1.41513	0.707566	+	0.706648i	$0.249793\pi$
$578$	27.3855	1.13909
$579$	−8.87765	−0.368943
$580$	27.2798	1.13273
$581$	−49.1310	−2.03830
$582$	27.4511	1.13789
$583$	−56.2410	−2.32926
$584$	−6.29660	−0.260555
$585$	3.85768	0.159495
$586$	−18.8705	−0.779531
$587$	−18.2005	−0.751217	−0.375608	−	0.926778i	$-0.622566\pi$
$587$	−18.2005	−0.751217	−0.375608	+	0.926778i	$0.622566\pi$
$588$	7.54870	0.311303
$589$	−5.43298	−0.223862
$590$	−32.2750	−1.32874
$591$	5.52760	0.227375
$592$	42.9075	1.76349
$593$	−32.9822	−1.35442	−0.677209	−	0.735791i	$-0.736811\pi$
$593$	−32.9822	−1.35442	−0.677209	+	0.735791i	$0.736811\pi$
$594$	−10.9370	−0.448751
$595$	−13.5448	−0.555282
$596$	9.07483	0.371719
$597$	−2.51257	−0.102833
$598$	−4.84772	−0.198238
$599$	11.8927	0.485924	0.242962	−	0.970036i	$-0.421881\pi$
$599$	11.8927	0.485924	0.242962	+	0.970036i	$0.421881\pi$
$600$	0.389718	0.0159102
$601$	−29.3296	−1.19638	−0.598189	−	0.801355i	$-0.704113\pi$
$601$	−29.3296	−1.19638	−0.598189	+	0.801355i	$0.704113\pi$
$602$	79.2166	3.22863
$603$	−10.2088	−0.415733
$604$	−11.6557	−0.474263
$605$	−50.5503	−2.05516
$606$	−0.549388	−0.0223174
$607$	21.6993	0.880747	0.440374	−	0.897815i	$-0.354846\pi$
$607$	21.6993	0.880747	0.440374	+	0.897815i	$0.354846\pi$
$608$	14.4259	0.585047
$609$	−22.2619	−0.902099
$610$	9.93094	0.402092
$611$	−7.15809	−0.289585
$612$	2.89369	0.116970
$613$	19.3618	0.782016	0.391008	−	0.920387i	$-0.372126\pi$
$613$	19.3618	0.782016	0.391008	+	0.920387i	$0.372126\pi$
$614$	−65.5355	−2.64480
$615$	−19.5565	−0.788595
$616$	10.1209	0.407783
$617$	−22.3001	−0.897768	−0.448884	−	0.893590i	$-0.648178\pi$
$617$	−22.3001	−0.897768	−0.448884	+	0.893590i	$0.648178\pi$
$618$	21.9634	0.883498
$619$	−24.4322	−0.982015	−0.491007	−	0.871155i	$-0.663371\pi$
$619$	−24.4322	−0.982015	−0.491007	+	0.871155i	$0.663371\pi$
$620$	11.7909	0.473534
$621$	−1.55923	−0.0625699
$622$	33.1672	1.32988
$623$	−46.6466	−1.86886
$624$	7.20564	0.288456
$625$	−28.1378	−1.12551
$626$	−19.4692	−0.778145
$627$	10.7903	0.430924
$628$	12.8063	0.511027
$629$	−16.0840	−0.641312
$630$	15.5907	0.621147
$631$	21.1046	0.840159	0.420080	−	0.907487i	$-0.362002\pi$
$631$	21.1046	0.840159	0.420080	+	0.907487i	$0.362002\pi$
$632$	−6.35873	−0.252937
$633$	22.2043	0.882540
$634$	24.8645	0.987494
$635$	−14.1110	−0.559976
$636$	−17.1277	−0.679156
$637$	−7.04619	−0.279180
$638$	72.1930	2.85815
$639$	2.41370	0.0954844
$640$	10.0517	0.397327
$641$	11.5772	0.457273	0.228636	−	0.973512i	$-0.426573\pi$
$641$	11.5772	0.457273	0.228636	+	0.973512i	$0.426573\pi$
$642$	−21.9567	−0.866560
$643$	38.3623	1.51286	0.756430	−	0.654074i	$-0.226942\pi$
$643$	38.3623	1.51286	0.756430	+	0.654074i	$0.226942\pi$
$644$	−9.07448	−0.357585
$645$	29.1441	1.14755
$646$	−6.16370	−0.242507
$647$	−37.1204	−1.45935	−0.729676	−	0.683793i	$-0.760329\pi$
$647$	−37.1204	−1.45935	−0.729676	+	0.683793i	$0.760329\pi$
$648$	0.529608	0.0208050
$649$	−39.5610	−1.55290
$650$	2.28782	0.0897357
$651$	−9.62208	−0.377119
$652$	43.2150	1.69243
$653$	19.9967	0.782532	0.391266	−	0.920278i	$-0.372037\pi$
$653$	19.9967	0.782532	0.391266	+	0.920278i	$0.372037\pi$
$654$	−18.3546	−0.717723
$655$	47.3813	1.85134
$656$	−36.5290	−1.42622
$657$	−11.8892	−0.463841
$658$	−28.9291	−1.12778
$659$	41.5001	1.61661	0.808307	−	0.588761i	$-0.200384\pi$
$659$	41.5001	1.61661	0.808307	+	0.588761i	$0.200384\pi$
$660$	−23.4176	−0.911530
$661$	5.16269	0.200805	0.100403	−	0.994947i	$-0.467987\pi$
$661$	5.16269	0.200805	0.100403	+	0.994947i	$0.467987\pi$
$662$	−39.1754	−1.52259
$663$	−2.70106	−0.104900
$664$	−7.71516	−0.299406
$665$	−15.3816	−0.596472
$666$	18.5134	0.717381
$667$	10.2922	0.398515
$668$	21.3073	0.824406
$669$	−21.8205	−0.843628
$670$	−47.1923	−1.82320
$671$	12.1728	0.469926
$672$	25.5490	0.985573
$673$	3.95617	0.152499	0.0762496	−	0.997089i	$-0.475705\pi$
$673$	3.95617	0.152499	0.0762496	+	0.997089i	$0.475705\pi$
$674$	21.5735	0.830982
$675$	0.735861	0.0283233
$676$	−17.9559	−0.690612
$677$	36.2923	1.39483	0.697413	−	0.716670i	$-0.254334\pi$
$677$	36.2923	1.39483	0.697413	+	0.716670i	$0.254334\pi$
$678$	−11.9621	−0.459403
$679$	−47.9653	−1.84074
$680$	−2.12697	−0.0815655
$681$	23.0322	0.882597
$682$	31.2034	1.19484
$683$	14.3340	0.548473	0.274237	−	0.961662i	$-0.411575\pi$
$683$	14.3340	0.548473	0.274237	+	0.961662i	$0.411575\pi$
$684$	3.28609	0.125647
$685$	34.9293	1.33458
$686$	17.0914	0.652554
$687$	−17.1919	−0.655911
$688$	54.4373	2.07540
$689$	15.9875	0.609075
$690$	−7.20792	−0.274401
$691$	6.45006	0.245372	0.122686	−	0.992446i	$-0.460849\pi$
$691$	6.45006	0.245372	0.122686	+	0.992446i	$0.460849\pi$
$692$	9.30838	0.353851
$693$	19.1102	0.725936
$694$	13.1455	0.498997
$695$	−36.6291	−1.38942
$696$	−3.49584	−0.132509
$697$	13.6930	0.518660
$698$	7.07011	0.267608
$699$	18.7797	0.710314
$700$	4.28259	0.161867
$701$	−32.0010	−1.20866	−0.604331	−	0.796733i	$-0.706560\pi$
$701$	−32.0010	−1.20866	−0.604331	+	0.796733i	$0.706560\pi$
$702$	3.10904	0.117343
$703$	−18.2652	−0.688883
$704$	−32.1564	−1.21194
$705$	−10.6431	−0.400844
$706$	64.9028	2.44265
$707$	0.959944	0.0361024
$708$	−12.0479	−0.452789
$709$	−20.8831	−0.784282	−0.392141	−	0.919905i	$-0.628265\pi$
$709$	−20.8831	−0.784282	−0.392141	+	0.919905i	$0.628265\pi$
$710$	11.1579	0.418747
$711$	−12.0065	−0.450278
$712$	−7.32502	−0.274517
$713$	4.44851	0.166598
$714$	−10.9162	−0.408529
$715$	21.8587	0.817471
$716$	22.3741	0.836159
$717$	−7.78265	−0.290648
$718$	−1.07023	−0.0399405
$719$	−7.23388	−0.269778	−0.134889	−	0.990861i	$-0.543068\pi$
$719$	−7.23388	−0.269778	−0.134889	+	0.990861i	$0.543068\pi$
$720$	10.7138	0.399281
$721$	−38.3766	−1.42922
$722$	29.6740	1.10435
$723$	−18.7057	−0.695674
$724$	−22.2801	−0.828032
$725$	−4.85727	−0.180395
$726$	−40.7402	−1.51201
$727$	−42.0277	−1.55872	−0.779361	−	0.626575i	$-0.784456\pi$
$727$	−42.0277	−1.55872	−0.779361	+	0.626575i	$0.784456\pi$
$728$	−2.87705	−0.106631
$729$	1.00000	0.0370370
$730$	−54.9604	−2.03418
$731$	−20.4060	−0.754743
$732$	3.70712	0.137019
$733$	−23.3097	−0.860963	−0.430481	−	0.902599i	$-0.641656\pi$
$733$	−23.3097	−0.860963	−0.430481	+	0.902599i	$0.641656\pi$
$734$	−3.16642	−0.116875
$735$	−10.4768	−0.386441
$736$	−11.8119	−0.435391
$737$	−57.8458	−2.13078
$738$	−15.7613	−0.580181
$739$	28.6388	1.05350	0.526748	−	0.850022i	$-0.323411\pi$
$739$	28.6388	1.05350	0.526748	+	0.850022i	$0.323411\pi$
$740$	39.6399	1.45719
$741$	−3.06734	−0.112682
$742$	64.6129	2.37201
$743$	47.6260	1.74723	0.873614	−	0.486619i	$-0.161770\pi$
$743$	47.6260	1.74723	0.873614	+	0.486619i	$0.161770\pi$
$744$	−1.51098	−0.0553951
$745$	−12.5949	−0.461440
$746$	−72.5257	−2.65535
$747$	−14.5677	−0.533003
$748$	16.3965	0.599514
$749$	38.3648	1.40182
$750$	−19.7120	−0.719779
$751$	−46.2279	−1.68688	−0.843441	−	0.537222i	$-0.819474\pi$
$751$	−46.2279	−1.68688	−0.843441	+	0.537222i	$0.819474\pi$
$752$	−19.8800	−0.724948
$753$	−4.43855	−0.161750
$754$	−20.5222	−0.747373
$755$	16.1768	0.588733
$756$	5.81984	0.211665
$757$	2.07526	0.0754266	0.0377133	−	0.999289i	$-0.487993\pi$
$757$	2.07526	0.0754266	0.0377133	+	0.999289i	$0.487993\pi$
$758$	−2.89535	−0.105164
$759$	−8.83508	−0.320693
$760$	−2.41540	−0.0876158
$761$	24.4122	0.884943	0.442471	−	0.896783i	$-0.354102\pi$
$761$	24.4122	0.884943	0.442471	+	0.896783i	$0.354102\pi$
$762$	−11.3725	−0.411983
$763$	32.0710	1.16105
$764$	40.3720	1.46061
$765$	−4.01611	−0.145203
$766$	27.8351	1.00572
$767$	11.2459	0.406066
$768$	19.4510	0.701879
$769$	−23.5097	−0.847782	−0.423891	−	0.905713i	$-0.639336\pi$
$769$	−23.5097	−0.847782	−0.423891	+	0.905713i	$0.639336\pi$
$770$	88.3413	3.18360
$771$	−12.6404	−0.455232
$772$	−15.3194	−0.551359
$773$	−32.5839	−1.17196	−0.585981	−	0.810325i	$-0.699291\pi$
$773$	−32.5839	−1.17196	−0.585981	+	0.810325i	$0.699291\pi$
$774$	23.4882	0.844267
$775$	−2.09942	−0.0754133
$776$	−7.53209	−0.270386
$777$	−32.3485	−1.16050
$778$	50.1661	1.79854
$779$	15.5499	0.557133
$780$	6.65688	0.238355
$781$	13.6767	0.489392
$782$	5.04681	0.180474
$783$	−6.60080	−0.235893
$784$	−19.5692	−0.698900
$785$	−17.7737	−0.634371
$786$	38.1862	1.36206
$787$	41.1459	1.46669	0.733347	−	0.679854i	$-0.237957\pi$
$787$	41.1459	1.46669	0.733347	+	0.679854i	$0.237957\pi$
$788$	9.53852	0.339796
$789$	−19.3710	−0.689626
$790$	−55.5027	−1.97470
$791$	20.9014	0.743169
$792$	3.00092	0.106633
$793$	−3.46034	−0.122880
$794$	10.0893	0.358057
$795$	23.7713	0.843081
$796$	−4.33574	−0.153676
$797$	−5.84092	−0.206896	−0.103448	−	0.994635i	$-0.532988\pi$
$797$	−5.84092	−0.206896	−0.103448	+	0.994635i	$0.532988\pi$
$798$	−12.3965	−0.438833
$799$	7.45207	0.263635
$800$	5.57446	0.197087
$801$	−13.8310	−0.488695
$802$	−1.82507	−0.0644454
$803$	−67.3675	−2.37735
$804$	−17.6164	−0.621283
$805$	12.5944	0.443893
$806$	−8.87011	−0.312436
$807$	11.9607	0.421038
$808$	0.150742	0.00530309
$809$	3.29706	0.115918	0.0579592	−	0.998319i	$-0.481541\pi$
$809$	3.29706	0.115918	0.0579592	+	0.998319i	$0.481541\pi$
$810$	4.62273	0.162426
$811$	−44.4464	−1.56072	−0.780361	−	0.625329i	$-0.784965\pi$
$811$	−44.4464	−1.56072	−0.780361	+	0.625329i	$0.784965\pi$
$812$	−38.4156	−1.34812
$813$	16.4438	0.576710
$814$	104.903	3.67683
$815$	−59.9776	−2.10092
$816$	−7.50157	−0.262607
$817$	−23.1732	−0.810729
$818$	−21.6959	−0.758580
$819$	−5.43241	−0.189824
$820$	−33.7471	−1.17850
$821$	−36.3328	−1.26802	−0.634011	−	0.773324i	$-0.718593\pi$
$821$	−36.3328	−1.26802	−0.634011	+	0.773324i	$0.718593\pi$
$822$	28.1507	0.981869
$823$	−49.2155	−1.71555	−0.857773	−	0.514029i	$-0.828153\pi$
$823$	−49.2155	−1.71555	−0.857773	+	0.514029i	$0.828153\pi$
$824$	−6.02637	−0.209938
$825$	4.16961	0.145167
$826$	45.4499	1.58140
$827$	44.1637	1.53572	0.767862	−	0.640616i	$-0.221321\pi$
$827$	44.1637	1.53572	0.767862	+	0.640616i	$0.221321\pi$
$828$	−2.69064	−0.0935063
$829$	6.20682	0.215572	0.107786	−	0.994174i	$-0.465624\pi$
$829$	6.20682	0.215572	0.107786	+	0.994174i	$0.465624\pi$
$830$	−67.3424	−2.33749
$831$	−30.7318	−1.06608
$832$	9.14103	0.316908
$833$	7.33558	0.254163
$834$	−29.5206	−1.02222
$835$	−29.5722	−1.02339
$836$	18.6200	0.643985
$837$	−2.85301	−0.0986144
$838$	−3.28608	−0.113516
$839$	13.2131	0.456166	0.228083	−	0.973642i	$-0.426754\pi$
$839$	13.2131	0.456166	0.228083	+	0.973642i	$0.426754\pi$
$840$	−4.27780	−0.147598
$841$	14.5706	0.502435
$842$	−7.32515	−0.252441
$843$	−2.63860	−0.0908782
$844$	38.3161	1.31889
$845$	24.9208	0.857302
$846$	−8.57767	−0.294907
$847$	71.1853	2.44595
$848$	44.4016	1.52476
$849$	4.08442	0.140177
$850$	−2.38178	−0.0816944
$851$	14.9554	0.512666
$852$	4.16512	0.142695
$853$	−28.8500	−0.987804	−0.493902	−	0.869518i	$-0.664430\pi$
$853$	−28.8500	−0.987804	−0.493902	+	0.869518i	$0.664430\pi$
$854$	−13.9848	−0.478551
$855$	−4.56073	−0.155974
$856$	6.02451	0.205914
$857$	22.9835	0.785103	0.392551	−	0.919730i	$-0.371592\pi$
$857$	22.9835	0.785103	0.392551	+	0.919730i	$0.371592\pi$
$858$	17.6167	0.601425
$859$	42.2350	1.44104	0.720521	−	0.693434i	$-0.243903\pi$
$859$	42.2350	1.44104	0.720521	+	0.693434i	$0.243903\pi$
$860$	50.2916	1.71493
$861$	27.5396	0.938549
$862$	−68.3286	−2.32728
$863$	−15.8643	−0.540027	−0.270013	−	0.962857i	$-0.587028\pi$
$863$	−15.8643	−0.540027	−0.270013	+	0.962857i	$0.587028\pi$
$864$	7.57543	0.257721
$865$	−12.9190	−0.439259
$866$	−18.2544	−0.620311
$867$	−14.1880	−0.481850
$868$	−16.6040	−0.563578
$869$	−68.0323	−2.30784
$870$	−30.5137	−1.03451
$871$	16.4437	0.557174
$872$	5.03618	0.170547
$873$	−14.2220	−0.481342
$874$	5.73120	0.193861
$875$	34.4427	1.16437
$876$	−20.5162	−0.693177
$877$	−50.2150	−1.69564	−0.847821	−	0.530283i	$-0.822086\pi$
$877$	−50.2150	−1.69564	−0.847821	+	0.530283i	$0.822086\pi$
$878$	−35.5429	−1.19951
$879$	9.77650	0.329753
$880$	60.7077	2.04646
$881$	−31.8771	−1.07397	−0.536983	−	0.843593i	$-0.680436\pi$
$881$	−31.8771	−1.07397	−0.536983	+	0.843593i	$0.680436\pi$
$882$	−8.44358	−0.284310
$883$	32.0333	1.07801	0.539004	−	0.842303i	$-0.318801\pi$
$883$	32.0333	1.07801	0.539004	+	0.842303i	$0.318801\pi$
$884$	−4.66099	−0.156766
$885$	16.7212	0.562077
$886$	−12.3851	−0.416084
$887$	29.0301	0.974734	0.487367	−	0.873197i	$-0.337957\pi$
$887$	29.0301	0.974734	0.487367	+	0.873197i	$0.337957\pi$
$888$	−5.07976	−0.170465
$889$	19.8712	0.666457
$890$	−63.9371	−2.14318
$891$	5.66629	0.189828
$892$	−37.6538	−1.26074
$893$	8.46264	0.283191
$894$	−10.1506	−0.339488
$895$	−31.0528	−1.03798
$896$	−14.1548	−0.472879
$897$	2.51153	0.0838575
$898$	−18.3662	−0.612889
$899$	18.8322	0.628087
$900$	1.26982	0.0423272
$901$	−16.6441	−0.554496
$902$	−89.3080	−2.97363
$903$	−41.0409	−1.36576
$904$	3.28220	0.109164
$905$	30.9223	1.02789
$906$	13.0374	0.433140
$907$	−42.3090	−1.40485	−0.702424	−	0.711759i	$-0.747899\pi$
$907$	−42.3090	−1.40485	−0.702424	+	0.711759i	$0.747899\pi$
$908$	39.7448	1.31898
$909$	0.284630	0.00944057
$910$	−25.1126	−0.832474
$911$	54.7951	1.81544	0.907722	−	0.419572i	$-0.137820\pi$
$911$	54.7951	1.81544	0.907722	+	0.419572i	$0.137820\pi$
$912$	−8.51884	−0.282087
$913$	−82.5447	−2.73183
$914$	−33.8928	−1.12107
$915$	−5.14507	−0.170091
$916$	−29.6666	−0.980212
$917$	−66.7226	−2.20338
$918$	−3.23673	−0.106828
$919$	6.83115	0.225339	0.112669	−	0.993633i	$-0.464060\pi$
$919$	6.83115	0.225339	0.112669	+	0.993633i	$0.464060\pi$
$920$	1.97772	0.0652036
$921$	33.9529	1.11879
$922$	−27.3603	−0.901062
$923$	−3.88785	−0.127970
$924$	32.9769	1.08486
$925$	−7.05804	−0.232067
$926$	59.6465	1.96010
$927$	−11.3789	−0.373733
$928$	−50.0039	−1.64146
$929$	19.2805	0.632573	0.316287	−	0.948664i	$-0.397564\pi$
$929$	19.2805	0.632573	0.316287	+	0.948664i	$0.397564\pi$
$930$	−13.1887	−0.432474
$931$	8.33035	0.273016
$932$	32.4066	1.06151
$933$	−17.1834	−0.562560
$934$	−35.8085	−1.17169
$935$	−22.7565	−0.744216
$936$	−0.853064	−0.0278833
$937$	45.4103	1.48349	0.741744	−	0.670683i	$-0.233999\pi$
$937$	45.4103	1.48349	0.741744	+	0.670683i	$0.233999\pi$
$938$	66.4566	2.16988
$939$	10.0867	0.329166
$940$	−18.3660	−0.599033
$941$	38.0428	1.24016	0.620080	−	0.784539i	$-0.287100\pi$
$941$	38.0428	1.24016	0.620080	+	0.784539i	$0.287100\pi$
$942$	−14.3245	−0.466716
$943$	−12.7322	−0.414618
$944$	31.2330	1.01655
$945$	−8.07728	−0.262754
$946$	133.091	4.32717
$947$	19.5530	0.635389	0.317694	−	0.948193i	$-0.397091\pi$
$947$	19.5530	0.635389	0.317694	+	0.948193i	$0.397091\pi$
$948$	−20.7186	−0.672909
$949$	19.1504	0.621649
$950$	−2.70477	−0.0877543
$951$	−12.8819	−0.417724
$952$	2.99521	0.0970754
$953$	19.1945	0.621771	0.310886	−	0.950447i	$-0.399374\pi$
$953$	19.1945	0.621771	0.310886	+	0.950447i	$0.399374\pi$
$954$	19.1581	0.620267
$955$	−56.0318	−1.81315
$956$	−13.4299	−0.434353
$957$	−37.4021	−1.20904
$958$	73.2238	2.36575
$959$	−49.1877	−1.58835
$960$	13.5915	0.438664
$961$	−22.8603	−0.737430
$962$	−29.8204	−0.961450
$963$	11.3754	0.366568
$964$	−32.2790	−1.03964
$965$	21.2617	0.684437
$966$	10.1502	0.326579
$967$	−56.4813	−1.81632	−0.908158	−	0.418627i	$-0.862511\pi$
$967$	−56.4813	−1.81632	−0.908158	+	0.418627i	$0.862511\pi$
$968$	11.1784	0.359287
$969$	3.19332	0.102584
$970$	−65.7445	−2.11093
$971$	46.4826	1.49170	0.745848	−	0.666116i	$-0.232044\pi$
$971$	46.4826	1.49170	0.745848	+	0.666116i	$0.232044\pi$
$972$	1.72562	0.0553492
$973$	51.5813	1.65362
$974$	52.8572	1.69365
$975$	−1.18528	−0.0379595
$976$	−9.61031	−0.307618
$977$	−1.94553	−0.0622429	−0.0311214	−	0.999516i	$-0.509908\pi$
$977$	−1.94553	−0.0622429	−0.0311214	+	0.999516i	$0.509908\pi$
$978$	−48.3381	−1.54568
$979$	−78.3706	−2.50474
$980$	−18.0789	−0.577509
$981$	9.50926	0.303607
$982$	−65.8763	−2.10220
$983$	−40.0987	−1.27895	−0.639474	−	0.768812i	$-0.720848\pi$
$983$	−40.0987	−1.27895	−0.639474	+	0.768812i	$0.720848\pi$
$984$	4.32461	0.137864
$985$	−13.2384	−0.421811
$986$	21.3650	0.680400
$987$	14.9877	0.477065
$988$	−5.29306	−0.168395
$989$	18.9742	0.603343
$990$	26.1937	0.832492
$991$	−32.1061	−1.01988	−0.509942	−	0.860209i	$-0.670333\pi$
$991$	−32.1061	−1.01988	−0.509942	+	0.860209i	$0.670333\pi$
$992$	−21.6128	−0.686206
$993$	20.2962	0.644080
$994$	−15.7126	−0.498373
$995$	6.01752	0.190768
$996$	−25.1382	−0.796535
$997$	−43.1040	−1.36512	−0.682558	−	0.730831i	$-0.739133\pi$
$997$	−43.1040	−1.36512	−0.682558	+	0.730831i	$0.739133\pi$
$998$	22.3058	0.706078
$999$	−9.59153	−0.303463

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.b.1.15	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.b.1.15	✓	71	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:	\( N \)	\(=\)	\( 6033 = 3 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6033.a (trivial)

\(f(q)\)	\(=\)	\(q-1.93019 q^{2} +1.00000 q^{3} +1.72562 q^{4} -2.39497 q^{5} -1.93019 q^{6} +3.37261 q^{7} +0.529608 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.93019 q^{2} +1.00000 q^{3} +1.72562 q^{4} -2.39497 q^{5} -1.93019 q^{6} +3.37261 q^{7} +0.529608 q^{8} +1.00000 q^{9} +4.62273 q^{10} +5.66629 q^{11} +1.72562 q^{12} -1.61075 q^{13} -6.50976 q^{14} -2.39497 q^{15} -4.47348 q^{16} +1.67690 q^{17} -1.93019 q^{18} +1.90430 q^{19} -4.13280 q^{20} +3.37261 q^{21} -10.9370 q^{22} -1.55923 q^{23} +0.529608 q^{24} +0.735861 q^{25} +3.10904 q^{26} +1.00000 q^{27} +5.81984 q^{28} -6.60080 q^{29} +4.62273 q^{30} -2.85301 q^{31} +7.57543 q^{32} +5.66629 q^{33} -3.23673 q^{34} -8.07728 q^{35} +1.72562 q^{36} -9.59153 q^{37} -3.67565 q^{38} -1.61075 q^{39} -1.26839 q^{40} +8.16568 q^{41} -6.50976 q^{42} -12.1689 q^{43} +9.77786 q^{44} -2.39497 q^{45} +3.00961 q^{46} +4.44396 q^{47} -4.47348 q^{48} +4.37449 q^{49} -1.42035 q^{50} +1.67690 q^{51} -2.77953 q^{52} -9.92553 q^{53} -1.93019 q^{54} -13.5706 q^{55} +1.78616 q^{56} +1.90430 q^{57} +12.7408 q^{58} -6.98181 q^{59} -4.13280 q^{60} +2.14829 q^{61} +5.50684 q^{62} +3.37261 q^{63} -5.67503 q^{64} +3.85768 q^{65} -10.9370 q^{66} -10.2088 q^{67} +2.89369 q^{68} -1.55923 q^{69} +15.5907 q^{70} +2.41370 q^{71} +0.529608 q^{72} -11.8892 q^{73} +18.5134 q^{74} +0.735861 q^{75} +3.28609 q^{76} +19.1102 q^{77} +3.10904 q^{78} -12.0065 q^{79} +10.7138 q^{80} +1.00000 q^{81} -15.7613 q^{82} -14.5677 q^{83} +5.81984 q^{84} -4.01611 q^{85} +23.4882 q^{86} -6.60080 q^{87} +3.00092 q^{88} -13.8310 q^{89} +4.62273 q^{90} -5.43241 q^{91} -2.69064 q^{92} -2.85301 q^{93} -8.57767 q^{94} -4.56073 q^{95} +7.57543 q^{96} -14.2220 q^{97} -8.44358 q^{98} +5.66629 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9}+O(q^{10}) \) 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9	\( 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9} - 41 q^{10} - 18 q^{11} + 53 q^{12} - 67 q^{13} - 7 q^{14} - 8 q^{15} + 21 q^{16} - 25 q^{17} - 11 q^{18} - 43 q^{19} - 8 q^{20} - 46 q^{21} - 49 q^{22} - 75 q^{23} - 33 q^{24} + 19 q^{25} + 71 q^{27} - 89 q^{28} - 35 q^{29} - 41 q^{30} - 82 q^{31} - 62 q^{32} - 18 q^{33} - 28 q^{34} - 51 q^{35} + 53 q^{36} - 66 q^{37} - 29 q^{38} - 67 q^{39} - 102 q^{40} + q^{41} - 7 q^{42} - 112 q^{43} - 25 q^{44} - 8 q^{45} - 36 q^{46} - 67 q^{47} + 21 q^{48} + 7 q^{49} - 24 q^{50} - 25 q^{51} - 134 q^{52} - 40 q^{53} - 11 q^{54} - 112 q^{55} + 9 q^{56} - 43 q^{57} - 47 q^{58} - 18 q^{59} - 8 q^{60} - 144 q^{61} - 19 q^{62} - 46 q^{63} - 17 q^{64} - 31 q^{65} - 49 q^{66} - 85 q^{67} - 22 q^{68} - 75 q^{69} - 11 q^{70} - 44 q^{71} - 33 q^{72} - 98 q^{73} + 6 q^{74} + 19 q^{75} - 85 q^{76} - 39 q^{77} - 126 q^{79} + 21 q^{80} + 71 q^{81} - 69 q^{82} - 43 q^{83} - 89 q^{84} - 112 q^{85} + 32 q^{86} - 35 q^{87} - 85 q^{88} + 8 q^{89} - 41 q^{90} - 40 q^{91} - 96 q^{92} - 82 q^{93} - 99 q^{94} - 103 q^{95} - 62 q^{96} - 67 q^{97} - 11 q^{98} - 18 q^{99}+O(q^{100}) \) 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9 - 41 * q^10 - 18 * q^11 + 53 * q^12 - 67 * q^13 - 7 * q^14 - 8 * q^15 + 21 * q^16 - 25 * q^17 - 11 * q^18 - 43 * q^19 - 8 * q^20 - 46 * q^21 - 49 * q^22 - 75 * q^23 - 33 * q^24 + 19 * q^25 + 71 * q^27 - 89 * q^28 - 35 * q^29 - 41 * q^30 - 82 * q^31 - 62 * q^32 - 18 * q^33 - 28 * q^34 - 51 * q^35 + 53 * q^36 - 66 * q^37 - 29 * q^38 - 67 * q^39 - 102 * q^40 + q^41 - 7 * q^42 - 112 * q^43 - 25 * q^44 - 8 * q^45 - 36 * q^46 - 67 * q^47 + 21 * q^48 + 7 * q^49 - 24 * q^50 - 25 * q^51 - 134 * q^52 - 40 * q^53 - 11 * q^54 - 112 * q^55 + 9 * q^56 - 43 * q^57 - 47 * q^58 - 18 * q^59 - 8 * q^60 - 144 * q^61 - 19 * q^62 - 46 * q^63 - 17 * q^64 - 31 * q^65 - 49 * q^66 - 85 * q^67 - 22 * q^68 - 75 * q^69 - 11 * q^70 - 44 * q^71 - 33 * q^72 - 98 * q^73 + 6 * q^74 + 19 * q^75 - 85 * q^76 - 39 * q^77 - 126 * q^79 + 21 * q^80 + 71 * q^81 - 69 * q^82 - 43 * q^83 - 89 * q^84 - 112 * q^85 + 32 * q^86 - 35 * q^87 - 85 * q^88 + 8 * q^89 - 41 * q^90 - 40 * q^91 - 96 * q^92 - 82 * q^93 - 99 * q^94 - 103 * q^95 - 62 * q^96 - 67 * q^97 - 11 * q^98 - 18 * q^99

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