LMFDB - Embedded newform 4029.2.a.k.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.22001 q^{2} +1.00000 q^{3} +2.92842 q^{4} -1.63428 q^{5} -2.22001 q^{6} -1.90265 q^{7} -2.06110 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.22001 q^{2} +1.00000 q^{3} +2.92842 q^{4} -1.63428 q^{5} -2.22001 q^{6} -1.90265 q^{7} -2.06110 q^{8} +1.00000 q^{9} +3.62811 q^{10} -4.46342 q^{11} +2.92842 q^{12} -1.29449 q^{13} +4.22389 q^{14} -1.63428 q^{15} -1.28119 q^{16} +1.00000 q^{17} -2.22001 q^{18} -6.67824 q^{19} -4.78587 q^{20} -1.90265 q^{21} +9.90882 q^{22} +5.41253 q^{23} -2.06110 q^{24} -2.32912 q^{25} +2.87378 q^{26} +1.00000 q^{27} -5.57176 q^{28} -0.385878 q^{29} +3.62811 q^{30} -4.16741 q^{31} +6.96645 q^{32} -4.46342 q^{33} -2.22001 q^{34} +3.10947 q^{35} +2.92842 q^{36} -6.13298 q^{37} +14.8257 q^{38} -1.29449 q^{39} +3.36842 q^{40} -9.88644 q^{41} +4.22389 q^{42} +2.00780 q^{43} -13.0708 q^{44} -1.63428 q^{45} -12.0158 q^{46} +3.04402 q^{47} -1.28119 q^{48} -3.37992 q^{49} +5.17066 q^{50} +1.00000 q^{51} -3.79083 q^{52} +11.1495 q^{53} -2.22001 q^{54} +7.29449 q^{55} +3.92156 q^{56} -6.67824 q^{57} +0.856651 q^{58} +3.07457 q^{59} -4.78587 q^{60} +11.5138 q^{61} +9.25168 q^{62} -1.90265 q^{63} -12.9032 q^{64} +2.11557 q^{65} +9.90882 q^{66} -10.5512 q^{67} +2.92842 q^{68} +5.41253 q^{69} -6.90303 q^{70} -9.15147 q^{71} -2.06110 q^{72} -3.90855 q^{73} +13.6152 q^{74} -2.32912 q^{75} -19.5567 q^{76} +8.49233 q^{77} +2.87378 q^{78} +1.00000 q^{79} +2.09382 q^{80} +1.00000 q^{81} +21.9480 q^{82} +9.32483 q^{83} -5.57176 q^{84} -1.63428 q^{85} -4.45732 q^{86} -0.385878 q^{87} +9.19958 q^{88} -2.90621 q^{89} +3.62811 q^{90} +2.46297 q^{91} +15.8502 q^{92} -4.16741 q^{93} -6.75775 q^{94} +10.9141 q^{95} +6.96645 q^{96} -0.111051 q^{97} +7.50345 q^{98} -4.46342 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * 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 $

$2$	−2.22001	−1.56978	−0.784890	−	0.619635i	$-0.787281\pi$
$2$	−2.22001	−1.56978	−0.784890	+	0.619635i	$0.787281\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.92842	1.46421
$5$	−1.63428	−0.730873	−0.365437	−	0.930836i	$-0.619080\pi$
$5$	−1.63428	−0.730873	−0.365437	+	0.930836i	$0.619080\pi$
$6$	−2.22001	−0.906313
$7$	−1.90265	−0.719134	−0.359567	−	0.933119i	$-0.617076\pi$
$7$	−1.90265	−0.719134	−0.359567	+	0.933119i	$0.617076\pi$
$8$	−2.06110	−0.728710
$9$	1.00000	0.333333
$10$	3.62811	1.14731
$11$	−4.46342	−1.34577	−0.672886	−	0.739746i	$-0.734946\pi$
$11$	−4.46342	−1.34577	−0.672886	+	0.739746i	$0.734946\pi$
$12$	2.92842	0.845363
$13$	−1.29449	−0.359028	−0.179514	−	0.983755i	$-0.557453\pi$
$13$	−1.29449	−0.359028	−0.179514	+	0.983755i	$0.557453\pi$
$14$	4.22389	1.12888
$15$	−1.63428	−0.421970
$16$	−1.28119	−0.320296
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.22001	−0.523260
$19$	−6.67824	−1.53209	−0.766047	−	0.642785i	$-0.777779\pi$
$19$	−6.67824	−1.53209	−0.766047	+	0.642785i	$0.777779\pi$
$20$	−4.78587	−1.07015
$21$	−1.90265	−0.415192
$22$	9.90882	2.11257
$23$	5.41253	1.12859	0.564295	−	0.825573i	$-0.309148\pi$
$23$	5.41253	1.12859	0.564295	+	0.825573i	$0.309148\pi$
$24$	−2.06110	−0.420721
$25$	−2.32912	−0.465824
$26$	2.87378	0.563596
$27$	1.00000	0.192450
$28$	−5.57176	−1.05296
$29$	−0.385878	−0.0716557	−0.0358278	−	0.999358i	$-0.511407\pi$
$29$	−0.385878	−0.0716557	−0.0358278	+	0.999358i	$0.511407\pi$
$30$	3.62811	0.662400
$31$	−4.16741	−0.748490	−0.374245	−	0.927330i	$-0.622098\pi$
$31$	−4.16741	−0.748490	−0.374245	+	0.927330i	$0.622098\pi$
$32$	6.96645	1.23151
$33$	−4.46342	−0.776982
$34$	−2.22001	−0.380728
$35$	3.10947	0.525596
$36$	2.92842	0.488070
$37$	−6.13298	−1.00826	−0.504128	−	0.863629i	$-0.668186\pi$
$37$	−6.13298	−1.00826	−0.504128	+	0.863629i	$0.668186\pi$
$38$	14.8257	2.40505
$39$	−1.29449	−0.207285
$40$	3.36842	0.532595
$41$	−9.88644	−1.54400	−0.772002	−	0.635621i	$-0.780744\pi$
$41$	−9.88644	−1.54400	−0.772002	+	0.635621i	$0.780744\pi$
$42$	4.22389	0.651761
$43$	2.00780	0.306187	0.153093	−	0.988212i	$-0.451077\pi$
$43$	2.00780	0.306187	0.153093	+	0.988212i	$0.451077\pi$
$44$	−13.0708	−1.97050
$45$	−1.63428	−0.243624
$46$	−12.0158	−1.77164
$47$	3.04402	0.444017	0.222008	−	0.975045i	$-0.428739\pi$
$47$	3.04402	0.444017	0.222008	+	0.975045i	$0.428739\pi$
$48$	−1.28119	−0.184923
$49$	−3.37992	−0.482846
$50$	5.17066	0.731242
$51$	1.00000	0.140028
$52$	−3.79083	−0.525693
$53$	11.1495	1.53151	0.765754	−	0.643133i	$-0.222366\pi$
$53$	11.1495	1.53151	0.765754	+	0.643133i	$0.222366\pi$
$54$	−2.22001	−0.302104
$55$	7.29449	0.983589
$56$	3.92156	0.524040
$57$	−6.67824	−0.884555
$58$	0.856651	0.112484
$59$	3.07457	0.400275	0.200137	−	0.979768i	$-0.435861\pi$
$59$	3.07457	0.400275	0.200137	+	0.979768i	$0.435861\pi$
$60$	−4.78587	−0.617853
$61$	11.5138	1.47420	0.737099	−	0.675785i	$-0.236195\pi$
$61$	11.5138	1.47420	0.737099	+	0.675785i	$0.236195\pi$
$62$	9.25168	1.17496
$63$	−1.90265	−0.239711
$64$	−12.9032	−1.61290
$65$	2.11557	0.262404
$66$	9.90882	1.21969
$67$	−10.5512	−1.28904	−0.644519	−	0.764588i	$-0.722942\pi$
$67$	−10.5512	−1.28904	−0.644519	+	0.764588i	$0.722942\pi$
$68$	2.92842	0.355123
$69$	5.41253	0.651592
$70$	−6.90303	−0.825070
$71$	−9.15147	−1.08608	−0.543040	−	0.839707i	$-0.682727\pi$
$71$	−9.15147	−1.08608	−0.543040	+	0.839707i	$0.682727\pi$
$72$	−2.06110	−0.242903
$73$	−3.90855	−0.457461	−0.228730	−	0.973490i	$-0.573457\pi$
$73$	−3.90855	−0.457461	−0.228730	+	0.973490i	$0.573457\pi$
$74$	13.6152	1.58274
$75$	−2.32912	−0.268944
$76$	−19.5567	−2.24331
$77$	8.49233	0.967791
$78$	2.87378	0.325392
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	2.09382	0.234096
$81$	1.00000	0.111111
$82$	21.9480	2.42375
$83$	9.32483	1.02353	0.511766	−	0.859125i	$-0.328991\pi$
$83$	9.32483	1.02353	0.511766	+	0.859125i	$0.328991\pi$
$84$	−5.57176	−0.607929
$85$	−1.63428	−0.177263
$86$	−4.45732	−0.480646
$87$	−0.385878	−0.0413704
$88$	9.19958	0.980678
$89$	−2.90621	−0.308058	−0.154029	−	0.988066i	$-0.549225\pi$
$89$	−2.90621	−0.308058	−0.154029	+	0.988066i	$0.549225\pi$
$90$	3.62811	0.382437
$91$	2.46297	0.258189
$92$	15.8502	1.65249
$93$	−4.16741	−0.432141
$94$	−6.75775	−0.697009
$95$	10.9141	1.11977
$96$	6.96645	0.711010
$97$	−0.111051	−0.0112755	−0.00563777	−	0.999984i	$-0.501795\pi$
$97$	−0.111051	−0.0112755	−0.00563777	+	0.999984i	$0.501795\pi$
$98$	7.50345	0.757963
$99$	−4.46342	−0.448591
$100$	−6.82066	−0.682066
$101$	−4.06378	−0.404361	−0.202181	−	0.979348i	$-0.564803\pi$
$101$	−4.06378	−0.404361	−0.202181	+	0.979348i	$0.564803\pi$
$102$	−2.22001	−0.219813
$103$	2.71058	0.267082	0.133541	−	0.991043i	$-0.457365\pi$
$103$	2.71058	0.267082	0.133541	+	0.991043i	$0.457365\pi$
$104$	2.66809	0.261628
$105$	3.10947	0.303453
$106$	−24.7521	−2.40413
$107$	−14.6277	−1.41411	−0.707056	−	0.707157i	$-0.749977\pi$
$107$	−14.6277	−1.41411	−0.707056	+	0.707157i	$0.749977\pi$
$108$	2.92842	0.281788
$109$	−1.86669	−0.178797	−0.0893983	−	0.995996i	$-0.528494\pi$
$109$	−1.86669	−0.178797	−0.0893983	+	0.995996i	$0.528494\pi$
$110$	−16.1938	−1.54402
$111$	−6.13298	−0.582117
$112$	2.43765	0.230336
$113$	14.1312	1.32935	0.664674	−	0.747133i	$-0.268570\pi$
$113$	14.1312	1.32935	0.664674	+	0.747133i	$0.268570\pi$
$114$	14.8257	1.38856
$115$	−8.84560	−0.824856
$116$	−1.13001	−0.104919
$117$	−1.29449	−0.119676
$118$	−6.82556	−0.628343
$119$	−1.90265	−0.174416
$120$	3.36842	0.307494
$121$	8.92215	0.811104
$122$	−25.5608	−2.31417
$123$	−9.88644	−0.891431
$124$	−12.2039	−1.09595
$125$	11.9779	1.07133
$126$	4.22389	0.376294
$127$	−4.97589	−0.441539	−0.220769	−	0.975326i	$-0.570857\pi$
$127$	−4.97589	−0.441539	−0.220769	+	0.975326i	$0.570857\pi$
$128$	14.7122	1.30039
$129$	2.00780	0.176777
$130$	−4.69657	−0.411917
$131$	17.1743	1.50052	0.750261	−	0.661142i	$-0.229928\pi$
$131$	17.1743	1.50052	0.750261	+	0.661142i	$0.229928\pi$
$132$	−13.0708	−1.13767
$133$	12.7064	1.10178
$134$	23.4238	2.02351
$135$	−1.63428	−0.140657
$136$	−2.06110	−0.176738
$137$	6.69309	0.571829	0.285915	−	0.958255i	$-0.407703\pi$
$137$	6.69309	0.571829	0.285915	+	0.958255i	$0.407703\pi$
$138$	−12.0158	−1.02286
$139$	14.9696	1.26970	0.634852	−	0.772634i	$-0.281061\pi$
$139$	14.9696	1.26970	0.634852	+	0.772634i	$0.281061\pi$
$140$	9.10583	0.769583
$141$	3.04402	0.256353
$142$	20.3163	1.70491
$143$	5.77788	0.483170
$144$	−1.28119	−0.106765
$145$	0.630633	0.0523712
$146$	8.67700	0.718113
$147$	−3.37992	−0.278771
$148$	−17.9600	−1.47630
$149$	−7.16380	−0.586882	−0.293441	−	0.955977i	$-0.594800\pi$
$149$	−7.16380	−0.586882	−0.293441	+	0.955977i	$0.594800\pi$
$150$	5.17066	0.422183
$151$	21.9170	1.78358	0.891790	−	0.452450i	$-0.149450\pi$
$151$	21.9170	1.78358	0.891790	+	0.452450i	$0.149450\pi$
$152$	13.7645	1.11645
$153$	1.00000	0.0808452
$154$	−18.8530	−1.51922
$155$	6.81073	0.547051
$156$	−3.79083	−0.303509
$157$	−17.8477	−1.42440	−0.712200	−	0.701977i	$-0.752301\pi$
$157$	−17.8477	−1.42440	−0.712200	+	0.701977i	$0.752301\pi$
$158$	−2.22001	−0.176614
$159$	11.1495	0.884217
$160$	−11.3851	−0.900074
$161$	−10.2981	−0.811607
$162$	−2.22001	−0.174420
$163$	9.39482	0.735859	0.367930	−	0.929854i	$-0.380067\pi$
$163$	9.39482	0.735859	0.367930	+	0.929854i	$0.380067\pi$
$164$	−28.9517	−2.26075
$165$	7.29449	0.567875
$166$	−20.7012	−1.60672
$167$	−4.89296	−0.378628	−0.189314	−	0.981917i	$-0.560626\pi$
$167$	−4.89296	−0.378628	−0.189314	+	0.981917i	$0.560626\pi$
$168$	3.92156	0.302555
$169$	−11.3243	−0.871099
$170$	3.62811	0.278264
$171$	−6.67824	−0.510698
$172$	5.87968	0.448322
$173$	22.1087	1.68090	0.840448	−	0.541891i	$-0.182292\pi$
$173$	22.1087	1.68090	0.840448	+	0.541891i	$0.182292\pi$
$174$	0.856651	0.0649425
$175$	4.43150	0.334990
$176$	5.71847	0.431046
$177$	3.07457	0.231099
$178$	6.45180	0.483583
$179$	−15.7268	−1.17547	−0.587737	−	0.809052i	$-0.699981\pi$
$179$	−15.7268	−1.17547	−0.587737	+	0.809052i	$0.699981\pi$
$180$	−4.78587	−0.356718
$181$	15.6878	1.16606	0.583031	−	0.812450i	$-0.301867\pi$
$181$	15.6878	1.16606	0.583031	+	0.812450i	$0.301867\pi$
$182$	−5.46781	−0.405301
$183$	11.5138	0.851128
$184$	−11.1558	−0.822415
$185$	10.0230	0.736907
$186$	9.25168	0.678366
$187$	−4.46342	−0.326398
$188$	8.91419	0.650134
$189$	−1.90265	−0.138397
$190$	−24.2294	−1.75779
$191$	19.6849	1.42435	0.712176	−	0.702001i	$-0.247710\pi$
$191$	19.6849	1.42435	0.712176	+	0.702001i	$0.247710\pi$
$192$	−12.9032	−0.931206
$193$	4.07050	0.293001	0.146500	−	0.989211i	$-0.453199\pi$
$193$	4.07050	0.293001	0.146500	+	0.989211i	$0.453199\pi$
$194$	0.246534	0.0177001
$195$	2.11557	0.151499
$196$	−9.89785	−0.706989
$197$	−20.3233	−1.44797	−0.723987	−	0.689814i	$-0.757692\pi$
$197$	−20.3233	−1.44797	−0.723987	+	0.689814i	$0.757692\pi$
$198$	9.90882	0.704189
$199$	−10.5630	−0.748789	−0.374395	−	0.927269i	$-0.622149\pi$
$199$	−10.5630	−0.748789	−0.374395	+	0.927269i	$0.622149\pi$
$200$	4.80056	0.339451
$201$	−10.5512	−0.744227
$202$	9.02162	0.634759
$203$	0.734190	0.0515300
$204$	2.92842	0.205031
$205$	16.1572	1.12847
$206$	−6.01751	−0.419260
$207$	5.41253	0.376197
$208$	1.65849	0.114995
$209$	29.8078	2.06185
$210$	−6.90303	−0.476354
$211$	19.0212	1.30947	0.654735	−	0.755858i	$-0.272780\pi$
$211$	19.0212	1.30947	0.654735	+	0.755858i	$0.272780\pi$
$212$	32.6506	2.24245
$213$	−9.15147	−0.627048
$214$	32.4736	2.21985
$215$	−3.28131	−0.223783
$216$	−2.06110	−0.140240
$217$	7.92913	0.538264
$218$	4.14406	0.280671
$219$	−3.90855	−0.264115
$220$	21.3614	1.44018
$221$	−1.29449	−0.0870771
$222$	13.6152	0.913795
$223$	8.55625	0.572969	0.286485	−	0.958085i	$-0.407513\pi$
$223$	8.55625	0.572969	0.286485	+	0.958085i	$0.407513\pi$
$224$	−13.2547	−0.885617
$225$	−2.32912	−0.155275
$226$	−31.3713	−2.08679
$227$	8.88220	0.589532	0.294766	−	0.955569i	$-0.404758\pi$
$227$	8.88220	0.589532	0.294766	+	0.955569i	$0.404758\pi$
$228$	−19.5567	−1.29518
$229$	−29.3221	−1.93766	−0.968830	−	0.247725i	$-0.920317\pi$
$229$	−29.3221	−1.93766	−0.968830	+	0.247725i	$0.920317\pi$
$230$	19.6373	1.29484
$231$	8.49233	0.558754
$232$	0.795334	0.0522162
$233$	2.85833	0.187256	0.0936278	−	0.995607i	$-0.470154\pi$
$233$	2.85833	0.187256	0.0936278	+	0.995607i	$0.470154\pi$
$234$	2.87378	0.187865
$235$	−4.97479	−0.324520
$236$	9.00363	0.586087
$237$	1.00000	0.0649570
$238$	4.22389	0.273794
$239$	−24.0944	−1.55854	−0.779270	−	0.626689i	$-0.784410\pi$
$239$	−24.0944	−1.55854	−0.779270	+	0.626689i	$0.784410\pi$
$240$	2.09382	0.135155
$241$	0.357116	0.0230039	0.0115019	−	0.999934i	$-0.496339\pi$
$241$	0.357116	0.0230039	0.0115019	+	0.999934i	$0.496339\pi$
$242$	−19.8072	−1.27326
$243$	1.00000	0.0641500
$244$	33.7174	2.15854
$245$	5.52375	0.352899
$246$	21.9480	1.39935
$247$	8.64495	0.550065
$248$	8.58947	0.545432
$249$	9.32483	0.590937
$250$	−26.5909	−1.68176
$251$	−9.94112	−0.627478	−0.313739	−	0.949509i	$-0.601582\pi$
$251$	−9.94112	−0.627478	−0.313739	+	0.949509i	$0.601582\pi$
$252$	−5.57176	−0.350988
$253$	−24.1584	−1.51883
$254$	11.0465	0.693119
$255$	−1.63428	−0.102343
$256$	−6.85486	−0.428429
$257$	−30.7848	−1.92030	−0.960150	−	0.279485i	$-0.909836\pi$
$257$	−30.7848	−1.92030	−0.960150	+	0.279485i	$0.909836\pi$
$258$	−4.45732	−0.277501
$259$	11.6689	0.725071
$260$	6.19528	0.384215
$261$	−0.385878	−0.0238852
$262$	−38.1269	−2.35549
$263$	−14.0747	−0.867885	−0.433943	−	0.900941i	$-0.642878\pi$
$263$	−14.0747	−0.867885	−0.433943	+	0.900941i	$0.642878\pi$
$264$	9.19958	0.566195
$265$	−18.2215	−1.11934
$266$	−28.2082	−1.72955
$267$	−2.90621	−0.177857
$268$	−30.8985	−1.88743
$269$	−29.9446	−1.82575	−0.912877	−	0.408235i	$-0.866144\pi$
$269$	−29.9446	−1.82575	−0.912877	+	0.408235i	$0.866144\pi$
$270$	3.62811	0.220800
$271$	22.7835	1.38400	0.692000	−	0.721898i	$-0.256730\pi$
$271$	22.7835	1.38400	0.692000	+	0.721898i	$0.256730\pi$
$272$	−1.28119	−0.0776833
$273$	2.46297	0.149066
$274$	−14.8587	−0.897646
$275$	10.3959	0.626894
$276$	15.8502	0.954068
$277$	26.0724	1.56654	0.783269	−	0.621682i	$-0.213551\pi$
$277$	26.0724	1.56654	0.783269	+	0.621682i	$0.213551\pi$
$278$	−33.2326	−1.99316
$279$	−4.16741	−0.249497
$280$	−6.40893	−0.383007
$281$	31.1424	1.85780	0.928898	−	0.370335i	$-0.120757\pi$
$281$	31.1424	1.85780	0.928898	+	0.370335i	$0.120757\pi$
$282$	−6.75775	−0.402418
$283$	−4.82456	−0.286791	−0.143395	−	0.989665i	$-0.545802\pi$
$283$	−4.82456	−0.286791	−0.143395	+	0.989665i	$0.545802\pi$
$284$	−26.7994	−1.59025
$285$	10.9141	0.646497
$286$	−12.8269	−0.758472
$287$	18.8104	1.11035
$288$	6.96645	0.410502
$289$	1.00000	0.0588235
$290$	−1.40001	−0.0822113
$291$	−0.111051	−0.00650993
$292$	−11.4459	−0.669820
$293$	14.7399	0.861115	0.430557	−	0.902563i	$-0.358317\pi$
$293$	14.7399	0.861115	0.430557	+	0.902563i	$0.358317\pi$
$294$	7.50345	0.437610
$295$	−5.02471	−0.292550
$296$	12.6407	0.734726
$297$	−4.46342	−0.258994
$298$	15.9037	0.921275
$299$	−7.00649	−0.405196
$300$	−6.82066	−0.393791
$301$	−3.82014	−0.220189
$302$	−48.6558	−2.79983
$303$	−4.06378	−0.233458
$304$	8.55607	0.490724
$305$	−18.8169	−1.07745
$306$	−2.22001	−0.126909
$307$	−9.51663	−0.543143	−0.271571	−	0.962418i	$-0.587543\pi$
$307$	−9.51663	−0.543143	−0.271571	+	0.962418i	$0.587543\pi$
$308$	24.8691	1.41705
$309$	2.71058	0.154200
$310$	−15.1199	−0.858750
$311$	10.6710	0.605098	0.302549	−	0.953134i	$-0.402162\pi$
$311$	10.6710	0.605098	0.302549	+	0.953134i	$0.402162\pi$
$312$	2.66809	0.151051
$313$	−20.8019	−1.17579	−0.587897	−	0.808936i	$-0.700044\pi$
$313$	−20.8019	−1.17579	−0.587897	+	0.808936i	$0.700044\pi$
$314$	39.6219	2.23600
$315$	3.10947	0.175199
$316$	2.92842	0.164737
$317$	17.2323	0.967861	0.483930	−	0.875106i	$-0.339209\pi$
$317$	17.2323	0.967861	0.483930	+	0.875106i	$0.339209\pi$
$318$	−24.7521	−1.38803
$319$	1.72234	0.0964323
$320$	21.0874	1.17882
$321$	−14.6277	−0.816438
$322$	22.8619	1.27405
$323$	−6.67824	−0.371587
$324$	2.92842	0.162690
$325$	3.01504	0.167244
$326$	−20.8566	−1.15514
$327$	−1.86669	−0.103228
$328$	20.3770	1.12513
$329$	−5.79171	−0.319307
$330$	−16.1938	−0.891440
$331$	26.6575	1.46523	0.732614	−	0.680645i	$-0.238300\pi$
$331$	26.6575	1.46523	0.732614	+	0.680645i	$0.238300\pi$
$332$	27.3070	1.49867
$333$	−6.13298	−0.336085
$334$	10.8624	0.594363
$335$	17.2437	0.942124
$336$	2.43765	0.132985
$337$	−12.8716	−0.701163	−0.350582	−	0.936532i	$-0.614016\pi$
$337$	−12.8716	−0.701163	−0.350582	+	0.936532i	$0.614016\pi$
$338$	25.1400	1.36743
$339$	14.1312	0.767500
$340$	−4.78587	−0.259550
$341$	18.6009	1.00730
$342$	14.8257	0.801684
$343$	19.7494	1.06637
$344$	−4.13828	−0.223121
$345$	−8.84560	−0.476231
$346$	−49.0815	−2.63864
$347$	19.9735	1.07223	0.536117	−	0.844144i	$-0.319891\pi$
$347$	19.9735	1.07223	0.536117	+	0.844144i	$0.319891\pi$
$348$	−1.13001	−0.0605751
$349$	−16.2872	−0.871833	−0.435916	−	0.899987i	$-0.643576\pi$
$349$	−16.2872	−0.871833	−0.435916	+	0.899987i	$0.643576\pi$
$350$	−9.83796	−0.525861
$351$	−1.29449	−0.0690950
$352$	−31.0942	−1.65733
$353$	−14.3591	−0.764258	−0.382129	−	0.924109i	$-0.624809\pi$
$353$	−14.3591	−0.764258	−0.382129	+	0.924109i	$0.624809\pi$
$354$	−6.82556	−0.362774
$355$	14.9561	0.793786
$356$	−8.51062	−0.451062
$357$	−1.90265	−0.100699
$358$	34.9135	1.84524
$359$	9.07260	0.478834	0.239417	−	0.970917i	$-0.423044\pi$
$359$	9.07260	0.478834	0.239417	+	0.970917i	$0.423044\pi$
$360$	3.36842	0.177532
$361$	25.5989	1.34731
$362$	−34.8269	−1.83046
$363$	8.92215	0.468291
$364$	7.21262	0.378044
$365$	6.38767	0.334346
$366$	−25.5608	−1.33608
$367$	−22.8469	−1.19260	−0.596299	−	0.802762i	$-0.703363\pi$
$367$	−22.8469	−1.19260	−0.596299	+	0.802762i	$0.703363\pi$
$368$	−6.93445	−0.361483
$369$	−9.88644	−0.514668
$370$	−22.2511	−1.15678
$371$	−21.2137	−1.10136
$372$	−12.2039	−0.632745
$373$	−17.2152	−0.891369	−0.445684	−	0.895190i	$-0.647040\pi$
$373$	−17.2152	−0.891369	−0.445684	+	0.895190i	$0.647040\pi$
$374$	9.90882	0.512373
$375$	11.9779	0.618534
$376$	−6.27405	−0.323559
$377$	0.499517	0.0257264
$378$	4.22389	0.217254
$379$	−2.54211	−0.130580	−0.0652898	−	0.997866i	$-0.520797\pi$
$379$	−2.54211	−0.130580	−0.0652898	+	0.997866i	$0.520797\pi$
$380$	31.9612	1.63957
$381$	−4.97589	−0.254923
$382$	−43.7007	−2.23592
$383$	30.8515	1.57644	0.788220	−	0.615394i	$-0.211003\pi$
$383$	30.8515	1.57644	0.788220	+	0.615394i	$0.211003\pi$
$384$	14.7122	0.750780
$385$	−13.8789	−0.707332
$386$	−9.03653	−0.459947
$387$	2.00780	0.102062
$388$	−0.325205	−0.0165098
$389$	9.85490	0.499663	0.249832	−	0.968289i	$-0.419625\pi$
$389$	9.85490	0.499663	0.249832	+	0.968289i	$0.419625\pi$
$390$	−4.69657	−0.237820
$391$	5.41253	0.273723
$392$	6.96637	0.351855
$393$	17.1743	0.866326
$394$	45.1178	2.27300
$395$	−1.63428	−0.0822297
$396$	−13.0708	−0.656832
$397$	18.2723	0.917061	0.458531	−	0.888679i	$-0.348376\pi$
$397$	18.2723	0.917061	0.458531	+	0.888679i	$0.348376\pi$
$398$	23.4499	1.17544
$399$	12.7064	0.636113
$400$	2.98404	0.149202
$401$	10.6339	0.531030	0.265515	−	0.964107i	$-0.414458\pi$
$401$	10.6339	0.531030	0.265515	+	0.964107i	$0.414458\pi$
$402$	23.4238	1.16827
$403$	5.39469	0.268729
$404$	−11.9005	−0.592071
$405$	−1.63428	−0.0812081
$406$	−1.62991	−0.0808909
$407$	27.3741	1.35688
$408$	−2.06110	−0.102040
$409$	20.1190	0.994822	0.497411	−	0.867515i	$-0.334284\pi$
$409$	20.1190	0.994822	0.497411	+	0.867515i	$0.334284\pi$
$410$	−35.8691	−1.77145
$411$	6.69309	0.330146
$412$	7.93774	0.391064
$413$	−5.84982	−0.287851
$414$	−12.0158	−0.590546
$415$	−15.2394	−0.748072
$416$	−9.01803	−0.442145
$417$	14.9696	0.733064
$418$	−66.1735	−3.23665
$419$	18.7028	0.913690	0.456845	−	0.889546i	$-0.348979\pi$
$419$	18.7028	0.913690	0.456845	+	0.889546i	$0.348979\pi$
$420$	9.10583	0.444319
$421$	12.0322	0.586415	0.293208	−	0.956049i	$-0.405277\pi$
$421$	12.0322	0.586415	0.293208	+	0.956049i	$0.405277\pi$
$422$	−42.2271	−2.05558
$423$	3.04402	0.148006
$424$	−22.9804	−1.11603
$425$	−2.32912	−0.112979
$426$	20.3163	0.984328
$427$	−21.9068	−1.06015
$428$	−42.8361	−2.07056
$429$	5.77788	0.278959
$430$	7.28453	0.351291
$431$	32.4481	1.56297	0.781484	−	0.623925i	$-0.214463\pi$
$431$	32.4481	1.56297	0.781484	+	0.623925i	$0.214463\pi$
$432$	−1.28119	−0.0616411
$433$	−33.4347	−1.60677	−0.803384	−	0.595461i	$-0.796969\pi$
$433$	−33.4347	−1.60677	−0.803384	+	0.595461i	$0.796969\pi$
$434$	−17.6027	−0.844957
$435$	0.630633	0.0302365
$436$	−5.46646	−0.261796
$437$	−36.1462	−1.72911
$438$	8.67700	0.414603
$439$	13.4602	0.642421	0.321210	−	0.947008i	$-0.395910\pi$
$439$	13.4602	0.642421	0.321210	+	0.947008i	$0.395910\pi$
$440$	−15.0347	−0.716751
$441$	−3.37992	−0.160949
$442$	2.87378	0.136692
$443$	24.6866	1.17289	0.586447	−	0.809988i	$-0.300526\pi$
$443$	24.6866	1.17289	0.586447	+	0.809988i	$0.300526\pi$
$444$	−17.9600	−0.852342
$445$	4.74957	0.225151
$446$	−18.9949	−0.899436
$447$	−7.16380	−0.338836
$448$	24.5502	1.15989
$449$	33.3851	1.57554	0.787769	−	0.615971i	$-0.211236\pi$
$449$	33.3851	1.57554	0.787769	+	0.615971i	$0.211236\pi$
$450$	5.17066	0.243747
$451$	44.1274	2.07788
$452$	41.3821	1.94645
$453$	21.9170	1.02975
$454$	−19.7185	−0.925437
$455$	−4.02519	−0.188704
$456$	13.7645	0.644584
$457$	14.2678	0.667418	0.333709	−	0.942676i	$-0.391700\pi$
$457$	14.2678	0.667418	0.333709	+	0.942676i	$0.391700\pi$
$458$	65.0953	3.04170
$459$	1.00000	0.0466760
$460$	−25.9036	−1.20776
$461$	−8.54505	−0.397983	−0.198991	−	0.980001i	$-0.563767\pi$
$461$	−8.54505	−0.397983	−0.198991	+	0.980001i	$0.563767\pi$
$462$	−18.8530	−0.877122
$463$	6.34967	0.295094	0.147547	−	0.989055i	$-0.452862\pi$
$463$	6.34967	0.295094	0.147547	+	0.989055i	$0.452862\pi$
$464$	0.494381	0.0229511
$465$	6.81073	0.315840
$466$	−6.34551	−0.293950
$467$	5.83527	0.270024	0.135012	−	0.990844i	$-0.456893\pi$
$467$	5.83527	0.270024	0.135012	+	0.990844i	$0.456893\pi$
$468$	−3.79083	−0.175231
$469$	20.0753	0.926991
$470$	11.0441	0.509425
$471$	−17.8477	−0.822378
$472$	−6.33700	−0.291684
$473$	−8.96166	−0.412057
$474$	−2.22001	−0.101968
$475$	15.5544	0.713687
$476$	−5.57176	−0.255381
$477$	11.1495	0.510503
$478$	53.4898	2.44657
$479$	10.9464	0.500155	0.250077	−	0.968226i	$-0.419544\pi$
$479$	10.9464	0.500155	0.250077	+	0.968226i	$0.419544\pi$
$480$	−11.3851	−0.519658
$481$	7.93911	0.361992
$482$	−0.792799	−0.0361110
$483$	−10.2981	−0.468582
$484$	26.1278	1.18763
$485$	0.181489	0.00824099
$486$	−2.22001	−0.100701
$487$	−7.31707	−0.331568	−0.165784	−	0.986162i	$-0.553015\pi$
$487$	−7.31707	−0.331568	−0.165784	+	0.986162i	$0.553015\pi$
$488$	−23.7312	−1.07426
$489$	9.39482	0.424849
$490$	−12.2628	−0.553975
$491$	−11.9953	−0.541339	−0.270670	−	0.962672i	$-0.587245\pi$
$491$	−11.9953	−0.541339	−0.270670	+	0.962672i	$0.587245\pi$
$492$	−28.9517	−1.30524
$493$	−0.385878	−0.0173791
$494$	−19.1918	−0.863481
$495$	7.29449	0.327863
$496$	5.33923	0.239738
$497$	17.4120	0.781036
$498$	−20.7012	−0.927641
$499$	14.1153	0.631889	0.315945	−	0.948778i	$-0.397679\pi$
$499$	14.1153	0.631889	0.315945	+	0.948778i	$0.397679\pi$
$500$	35.0762	1.56866
$501$	−4.89296	−0.218601
$502$	22.0693	0.985002
$503$	23.3365	1.04052	0.520261	−	0.854007i	$-0.325835\pi$
$503$	23.3365	1.04052	0.520261	+	0.854007i	$0.325835\pi$
$504$	3.92156	0.174680
$505$	6.64137	0.295537
$506$	53.6318	2.38422
$507$	−11.3243	−0.502929
$508$	−14.5715	−0.646506
$509$	32.1813	1.42641	0.713206	−	0.700954i	$-0.247242\pi$
$509$	32.1813	1.42641	0.713206	+	0.700954i	$0.247242\pi$
$510$	3.62811	0.160656
$511$	7.43660	0.328976
$512$	−14.2066	−0.627850
$513$	−6.67824	−0.294852
$514$	68.3423	3.01445
$515$	−4.42986	−0.195203
$516$	5.87968	0.258839
$517$	−13.5868	−0.597545
$518$	−25.9050	−1.13820
$519$	22.1087	0.970466
$520$	−4.36041	−0.191217
$521$	11.4869	0.503251	0.251625	−	0.967825i	$-0.419035\pi$
$521$	11.4869	0.503251	0.251625	+	0.967825i	$0.419035\pi$
$522$	0.856651	0.0374946
$523$	3.23156	0.141306	0.0706531	−	0.997501i	$-0.477492\pi$
$523$	3.23156	0.141306	0.0706531	+	0.997501i	$0.477492\pi$
$524$	50.2935	2.19708
$525$	4.43150	0.193407
$526$	31.2460	1.36239
$527$	−4.16741	−0.181535
$528$	5.71847	0.248865
$529$	6.29545	0.273715
$530$	40.4518	1.75712
$531$	3.07457	0.133425
$532$	37.2096	1.61324
$533$	12.7979	0.554341
$534$	6.45180	0.279197
$535$	23.9058	1.03354
$536$	21.7472	0.939336
$537$	−15.7268	−0.678660
$538$	66.4771	2.86603
$539$	15.0860	0.649802
$540$	−4.78587	−0.205951
$541$	−5.01331	−0.215539	−0.107770	−	0.994176i	$-0.534371\pi$
$541$	−5.01331	−0.215539	−0.107770	+	0.994176i	$0.534371\pi$
$542$	−50.5795	−2.17258
$543$	15.6878	0.673226
$544$	6.96645	0.298684
$545$	3.05070	0.130678
$546$	−5.46781	−0.234000
$547$	−22.2531	−0.951472	−0.475736	−	0.879588i	$-0.657818\pi$
$547$	−22.2531	−0.951472	−0.475736	+	0.879588i	$0.657818\pi$
$548$	19.6002	0.837279
$549$	11.5138	0.491399
$550$	−23.0789	−0.984086
$551$	2.57698	0.109783
$552$	−11.1558	−0.474821
$553$	−1.90265	−0.0809089
$554$	−57.8809	−2.45912
$555$	10.0230	0.425453
$556$	43.8373	1.85912
$557$	−0.355109	−0.0150464	−0.00752322	−	0.999972i	$-0.502395\pi$
$557$	−0.355109	−0.0150464	−0.00752322	+	0.999972i	$0.502395\pi$
$558$	9.25168	0.391655
$559$	−2.59909	−0.109930
$560$	−3.98380	−0.168346
$561$	−4.46342	−0.188446
$562$	−69.1362	−2.91633
$563$	−38.8358	−1.63673	−0.818367	−	0.574697i	$-0.805120\pi$
$563$	−38.8358	−1.63673	−0.818367	+	0.574697i	$0.805120\pi$
$564$	8.91419	0.375355
$565$	−23.0943	−0.971585
$566$	10.7106	0.450198
$567$	−1.90265	−0.0799038
$568$	18.8621	0.791437
$569$	8.40024	0.352156	0.176078	−	0.984376i	$-0.443659\pi$
$569$	8.40024	0.352156	0.176078	+	0.984376i	$0.443659\pi$
$570$	−24.2294	−1.01486
$571$	15.9096	0.665797	0.332899	−	0.942963i	$-0.391973\pi$
$571$	15.9096	0.665797	0.332899	+	0.942963i	$0.391973\pi$
$572$	16.9201	0.707464
$573$	19.6849	0.822350
$574$	−41.7593	−1.74300
$575$	−12.6064	−0.525725
$576$	−12.9032	−0.537632
$577$	10.4062	0.433216	0.216608	−	0.976259i	$-0.430501\pi$
$577$	10.4062	0.433216	0.216608	+	0.976259i	$0.430501\pi$
$578$	−2.22001	−0.0923400
$579$	4.07050	0.169164
$580$	1.84676	0.0766825
$581$	−17.7419	−0.736057
$582$	0.246534	0.0102192
$583$	−49.7652	−2.06106
$584$	8.05592	0.333356
$585$	2.11557	0.0874680
$586$	−32.7227	−1.35176
$587$	29.6498	1.22378	0.611888	−	0.790944i	$-0.290410\pi$
$587$	29.6498	1.22378	0.611888	+	0.790944i	$0.290410\pi$
$588$	−9.89785	−0.408180
$589$	27.8310	1.14676
$590$	11.1549	0.459239
$591$	−20.3233	−0.835988
$592$	7.85748	0.322941
$593$	44.7799	1.83889	0.919445	−	0.393219i	$-0.128639\pi$
$593$	44.7799	1.83889	0.919445	+	0.393219i	$0.128639\pi$
$594$	9.90882	0.406564
$595$	3.10947	0.127476
$596$	−20.9786	−0.859319
$597$	−10.5630	−0.432314
$598$	15.5544	0.636068
$599$	−24.6038	−1.00529	−0.502643	−	0.864494i	$-0.667639\pi$
$599$	−24.6038	−1.00529	−0.502643	+	0.864494i	$0.667639\pi$
$600$	4.80056	0.195982
$601$	20.3776	0.831219	0.415609	−	0.909543i	$-0.363568\pi$
$601$	20.3776	0.831219	0.415609	+	0.909543i	$0.363568\pi$
$602$	8.48073	0.345649
$603$	−10.5512	−0.429680
$604$	64.1822	2.61154
$605$	−14.5813	−0.592814
$606$	9.02162	0.366478
$607$	4.01090	0.162797	0.0813987	−	0.996682i	$-0.474061\pi$
$607$	4.01090	0.162797	0.0813987	+	0.996682i	$0.474061\pi$
$608$	−46.5236	−1.88678
$609$	0.734190	0.0297509
$610$	41.7736	1.69136
$611$	−3.94047	−0.159414
$612$	2.92842	0.118374
$613$	−19.0827	−0.770743	−0.385372	−	0.922761i	$-0.625927\pi$
$613$	−19.0827	−0.770743	−0.385372	+	0.922761i	$0.625927\pi$
$614$	21.1270	0.852615
$615$	16.1572	0.651523
$616$	−17.5036	−0.705239
$617$	−43.6562	−1.75753	−0.878767	−	0.477251i	$-0.841633\pi$
$617$	−43.6562	−1.75753	−0.878767	+	0.477251i	$0.841633\pi$
$618$	−6.01751	−0.242060
$619$	21.0467	0.845937	0.422969	−	0.906144i	$-0.360988\pi$
$619$	21.0467	0.845937	0.422969	+	0.906144i	$0.360988\pi$
$620$	19.9447	0.800998
$621$	5.41253	0.217197
$622$	−23.6897	−0.949870
$623$	5.52950	0.221535
$624$	1.65849	0.0663926
$625$	−7.92958	−0.317183
$626$	46.1803	1.84574
$627$	29.8078	1.19041
$628$	−52.2655	−2.08562
$629$	−6.13298	−0.244538
$630$	−6.90303	−0.275023
$631$	−23.1984	−0.923513	−0.461757	−	0.887007i	$-0.652781\pi$
$631$	−23.1984	−0.923513	−0.461757	+	0.887007i	$0.652781\pi$
$632$	−2.06110	−0.0819863
$633$	19.0212	0.756023
$634$	−38.2557	−1.51933
$635$	8.13201	0.322709
$636$	32.6506	1.29468
$637$	4.37529	0.173355
$638$	−3.82359	−0.151378
$639$	−9.15147	−0.362026
$640$	−24.0439	−0.950419
$641$	4.56317	0.180234	0.0901172	−	0.995931i	$-0.471276\pi$
$641$	4.56317	0.180234	0.0901172	+	0.995931i	$0.471276\pi$
$642$	32.4736	1.28163
$643$	38.5256	1.51930	0.759651	−	0.650331i	$-0.225370\pi$
$643$	38.5256	1.51930	0.759651	+	0.650331i	$0.225370\pi$
$644$	−30.1573	−1.18836
$645$	−3.28131	−0.129201
$646$	14.8257	0.583311
$647$	−40.2058	−1.58065	−0.790326	−	0.612687i	$-0.790089\pi$
$647$	−40.2058	−1.58065	−0.790326	+	0.612687i	$0.790089\pi$
$648$	−2.06110	−0.0809678
$649$	−13.7231	−0.538679
$650$	−6.69340	−0.262537
$651$	7.92913	0.310767
$652$	27.5120	1.07745
$653$	46.1148	1.80461	0.902305	−	0.431098i	$-0.141874\pi$
$653$	46.1148	1.80461	0.902305	+	0.431098i	$0.141874\pi$
$654$	4.14406	0.162046
$655$	−28.0676	−1.09669
$656$	12.6664	0.494539
$657$	−3.90855	−0.152487
$658$	12.8576	0.501243
$659$	8.17654	0.318513	0.159256	−	0.987237i	$-0.449090\pi$
$659$	8.17654	0.318513	0.159256	+	0.987237i	$0.449090\pi$
$660$	21.3614	0.831490
$661$	−1.66625	−0.0648096	−0.0324048	−	0.999475i	$-0.510317\pi$
$661$	−1.66625	−0.0648096	−0.0324048	+	0.999475i	$0.510317\pi$
$662$	−59.1797	−2.30009
$663$	−1.29449	−0.0502740
$664$	−19.2194	−0.745859
$665$	−20.7658	−0.805262
$666$	13.6152	0.527580
$667$	−2.08857	−0.0808699
$668$	−14.3286	−0.554392
$669$	8.55625	0.330804
$670$	−38.2811	−1.47893
$671$	−51.3912	−1.98393
$672$	−13.2547	−0.511311
$673$	−28.9598	−1.11632	−0.558159	−	0.829734i	$-0.688492\pi$
$673$	−28.9598	−1.11632	−0.558159	+	0.829734i	$0.688492\pi$
$674$	28.5751	1.10067
$675$	−2.32912	−0.0896480
$676$	−33.1623	−1.27547
$677$	−27.2001	−1.04539	−0.522693	−	0.852521i	$-0.675073\pi$
$677$	−27.2001	−1.04539	−0.522693	+	0.852521i	$0.675073\pi$
$678$	−31.3713	−1.20481
$679$	0.211291	0.00810862
$680$	3.36842	0.129173
$681$	8.88220	0.340367
$682$	−41.2942	−1.58124
$683$	−2.31369	−0.0885307	−0.0442654	−	0.999020i	$-0.514095\pi$
$683$	−2.31369	−0.0885307	−0.0442654	+	0.999020i	$0.514095\pi$
$684$	−19.5567	−0.747770
$685$	−10.9384	−0.417935
$686$	−43.8437	−1.67396
$687$	−29.3221	−1.11871
$688$	−2.57236	−0.0980704
$689$	−14.4330	−0.549855
$690$	19.6373	0.747578
$691$	−12.9395	−0.492243	−0.246122	−	0.969239i	$-0.579156\pi$
$691$	−12.9395	−0.492243	−0.246122	+	0.969239i	$0.579156\pi$
$692$	64.7438	2.46119
$693$	8.49233	0.322597
$694$	−44.3413	−1.68317
$695$	−24.4645	−0.927993
$696$	0.795334	0.0301471
$697$	−9.88644	−0.374476
$698$	36.1576	1.36859
$699$	2.85833	0.108112
$700$	12.9773	0.490496
$701$	−17.5815	−0.664043	−0.332021	−	0.943272i	$-0.607731\pi$
$701$	−17.5815	−0.664043	−0.332021	+	0.943272i	$0.607731\pi$
$702$	2.87378	0.108464
$703$	40.9575	1.54474
$704$	57.5923	2.17059
$705$	−4.97479	−0.187362
$706$	31.8773	1.19972
$707$	7.73195	0.290790
$708$	9.00363	0.338377
$709$	−24.5669	−0.922628	−0.461314	−	0.887237i	$-0.652622\pi$
$709$	−24.5669	−0.922628	−0.461314	+	0.887237i	$0.652622\pi$
$710$	−33.2026	−1.24607
$711$	1.00000	0.0375029
$712$	5.99000	0.224485
$713$	−22.5562	−0.844738
$714$	4.22389	0.158075
$715$	−9.44268	−0.353136
$716$	−46.0546	−1.72114
$717$	−24.0944	−0.899823
$718$	−20.1412	−0.751664
$719$	−37.4207	−1.39556	−0.697778	−	0.716314i	$-0.745828\pi$
$719$	−37.4207	−1.39556	−0.697778	+	0.716314i	$0.745828\pi$
$720$	2.09382	0.0780320
$721$	−5.15729	−0.192068
$722$	−56.8297	−2.11498
$723$	0.357116	0.0132813
$724$	45.9404	1.70736
$725$	0.898756	0.0333790
$726$	−19.8072	−0.735115
$727$	−13.6349	−0.505692	−0.252846	−	0.967507i	$-0.581367\pi$
$727$	−13.6349	−0.505692	−0.252846	+	0.967507i	$0.581367\pi$
$728$	−5.07644	−0.188145
$729$	1.00000	0.0370370
$730$	−14.1807	−0.524850
$731$	2.00780	0.0742611
$732$	33.7174	1.24623
$733$	14.8079	0.546944	0.273472	−	0.961880i	$-0.411828\pi$
$733$	14.8079	0.546944	0.273472	+	0.961880i	$0.411828\pi$
$734$	50.7203	1.87212
$735$	5.52375	0.203747
$736$	37.7061	1.38986
$737$	47.0946	1.73475
$738$	21.9480	0.807915
$739$	−9.86864	−0.363024	−0.181512	−	0.983389i	$-0.558099\pi$
$739$	−9.86864	−0.363024	−0.181512	+	0.983389i	$0.558099\pi$
$740$	29.3516	1.07899
$741$	8.64495	0.317580
$742$	47.0945	1.72889
$743$	26.6119	0.976295	0.488148	−	0.872761i	$-0.337673\pi$
$743$	26.6119	0.976295	0.488148	+	0.872761i	$0.337673\pi$
$744$	8.58947	0.314905
$745$	11.7077	0.428936
$746$	38.2178	1.39925
$747$	9.32483	0.341178
$748$	−13.0708	−0.477915
$749$	27.8314	1.01694
$750$	−26.5909	−0.970962
$751$	−32.8146	−1.19742	−0.598712	−	0.800965i	$-0.704320\pi$
$751$	−32.8146	−1.19742	−0.598712	+	0.800965i	$0.704320\pi$
$752$	−3.89996	−0.142217
$753$	−9.94112	−0.362274
$754$	−1.10893	−0.0403848
$755$	−35.8185	−1.30357
$756$	−5.57176	−0.202643
$757$	−42.5526	−1.54660	−0.773300	−	0.634040i	$-0.781395\pi$
$757$	−42.5526	−1.54660	−0.773300	+	0.634040i	$0.781395\pi$
$758$	5.64351	0.204981
$759$	−24.1584	−0.876894
$760$	−22.4952	−0.815985
$761$	20.5221	0.743924	0.371962	−	0.928248i	$-0.378685\pi$
$761$	20.5221	0.743924	0.371962	+	0.928248i	$0.378685\pi$
$762$	11.0465	0.400172
$763$	3.55166	0.128579
$764$	57.6458	2.08555
$765$	−1.63428	−0.0590876
$766$	−68.4906	−2.47466
$767$	−3.98001	−0.143710
$768$	−6.85486	−0.247353
$769$	13.8634	0.499928	0.249964	−	0.968255i	$-0.419581\pi$
$769$	13.8634	0.499928	0.249964	+	0.968255i	$0.419581\pi$
$770$	30.8111	1.11036
$771$	−30.7848	−1.10869
$772$	11.9201	0.429015
$773$	16.6664	0.599447	0.299724	−	0.954026i	$-0.403106\pi$
$773$	16.6664	0.599447	0.299724	+	0.954026i	$0.403106\pi$
$774$	−4.45732	−0.160215
$775$	9.70642	0.348665
$776$	0.228888	0.00821660
$777$	11.6689	0.418620
$778$	−21.8779	−0.784361
$779$	66.0241	2.36556
$780$	6.19528	0.221827
$781$	40.8469	1.46162
$782$	−12.0158	−0.429685
$783$	−0.385878	−0.0137901
$784$	4.33031	0.154654
$785$	29.1681	1.04106
$786$	−38.1269	−1.35994
$787$	38.5395	1.37379	0.686893	−	0.726759i	$-0.258974\pi$
$787$	38.5395	1.37379	0.686893	+	0.726759i	$0.258974\pi$
$788$	−59.5152	−2.12014
$789$	−14.0747	−0.501074
$790$	3.62811	0.129083
$791$	−26.8867	−0.955980
$792$	9.19958	0.326893
$793$	−14.9046	−0.529278
$794$	−40.5646	−1.43958
$795$	−18.2215	−0.646250
$796$	−30.9329	−1.09639
$797$	49.0978	1.73913	0.869566	−	0.493817i	$-0.164399\pi$
$797$	49.0978	1.73913	0.869566	+	0.493817i	$0.164399\pi$
$798$	−28.2082	−0.998558
$799$	3.04402	0.107690
$800$	−16.2257	−0.573665
$801$	−2.90621	−0.102686
$802$	−23.6072	−0.833600
$803$	17.4455	0.615639
$804$	−30.8985	−1.08971
$805$	16.8301	0.593182
$806$	−11.9762	−0.421845
$807$	−29.9446	−1.05410
$808$	8.37588	0.294662
$809$	−27.4817	−0.966204	−0.483102	−	0.875564i	$-0.660490\pi$
$809$	−27.4817	−0.966204	−0.483102	+	0.875564i	$0.660490\pi$
$810$	3.62811	0.127479
$811$	−20.6161	−0.723930	−0.361965	−	0.932192i	$-0.617894\pi$
$811$	−20.6161	−0.723930	−0.361965	+	0.932192i	$0.617894\pi$
$812$	2.15002	0.0754509
$813$	22.7835	0.799052
$814$	−60.7706	−2.13001
$815$	−15.3538	−0.537820
$816$	−1.28119	−0.0448505
$817$	−13.4086	−0.469106
$818$	−44.6643	−1.56165
$819$	2.46297	0.0860631
$820$	47.3152	1.65232
$821$	−52.2856	−1.82478	−0.912391	−	0.409321i	$-0.865766\pi$
$821$	−52.2856	−1.82478	−0.912391	+	0.409321i	$0.865766\pi$
$822$	−14.8587	−0.518256
$823$	−2.33779	−0.0814903	−0.0407451	−	0.999170i	$-0.512973\pi$
$823$	−2.33779	−0.0814903	−0.0407451	+	0.999170i	$0.512973\pi$
$824$	−5.58679	−0.194625
$825$	10.3959	0.361937
$826$	12.9866	0.451863
$827$	26.2013	0.911107	0.455553	−	0.890208i	$-0.349441\pi$
$827$	26.2013	0.911107	0.455553	+	0.890208i	$0.349441\pi$
$828$	15.8502	0.550831
$829$	22.0549	0.766000	0.383000	−	0.923748i	$-0.374891\pi$
$829$	22.0549	0.766000	0.383000	+	0.923748i	$0.374891\pi$
$830$	33.8315	1.17431
$831$	26.0724	0.904442
$832$	16.7031	0.579075
$833$	−3.37992	−0.117107
$834$	−33.2326	−1.15075
$835$	7.99647	0.276729
$836$	87.2899	3.01898
$837$	−4.16741	−0.144047
$838$	−41.5203	−1.43429
$839$	−16.5348	−0.570843	−0.285422	−	0.958402i	$-0.592134\pi$
$839$	−16.5348	−0.570843	−0.285422	+	0.958402i	$0.592134\pi$
$840$	−6.40893	−0.221129
$841$	−28.8511	−0.994865
$842$	−26.7116	−0.920543
$843$	31.1424	1.07260
$844$	55.7020	1.91734
$845$	18.5071	0.636663
$846$	−6.75775	−0.232336
$847$	−16.9757	−0.583293
$848$	−14.2846	−0.490537
$849$	−4.82456	−0.165579
$850$	5.17066	0.177352
$851$	−33.1949	−1.13791
$852$	−26.7994	−0.918131
$853$	43.3295	1.48357	0.741787	−	0.670636i	$-0.233979\pi$
$853$	43.3295	1.48357	0.741787	+	0.670636i	$0.233979\pi$
$854$	48.6332	1.66420
$855$	10.9141	0.373255
$856$	30.1492	1.03048
$857$	1.52979	0.0522565	0.0261283	−	0.999659i	$-0.491682\pi$
$857$	1.52979	0.0522565	0.0261283	+	0.999659i	$0.491682\pi$
$858$	−12.8269	−0.437904
$859$	5.96544	0.203538	0.101769	−	0.994808i	$-0.467550\pi$
$859$	5.96544	0.203538	0.101769	+	0.994808i	$0.467550\pi$
$860$	−9.60906	−0.327666
$861$	18.8104	0.641058
$862$	−72.0349	−2.45352
$863$	−4.67341	−0.159085	−0.0795423	−	0.996831i	$-0.525346\pi$
$863$	−4.67341	−0.159085	−0.0795423	+	0.996831i	$0.525346\pi$
$864$	6.96645	0.237003
$865$	−36.1319	−1.22852
$866$	74.2251	2.52227
$867$	1.00000	0.0339618
$868$	23.2198	0.788133
$869$	−4.46342	−0.151411
$870$	−1.40001	−0.0474647
$871$	13.6585	0.462801
$872$	3.84744	0.130291
$873$	−0.111051	−0.00375851
$874$	80.2447	2.71432
$875$	−22.7897	−0.770431
$876$	−11.4459	−0.386721
$877$	26.2398	0.886055	0.443027	−	0.896508i	$-0.353904\pi$
$877$	26.2398	0.886055	0.443027	+	0.896508i	$0.353904\pi$
$878$	−29.8817	−1.00846
$879$	14.7399	0.497165
$880$	−9.34560	−0.315040
$881$	−39.1655	−1.31952	−0.659760	−	0.751477i	$-0.729342\pi$
$881$	−39.1655	−1.31952	−0.659760	+	0.751477i	$0.729342\pi$
$882$	7.50345	0.252654
$883$	−48.0021	−1.61540	−0.807700	−	0.589594i	$-0.799288\pi$
$883$	−48.0021	−1.61540	−0.807700	+	0.589594i	$0.799288\pi$
$884$	−3.79083	−0.127499
$885$	−5.02471	−0.168904
$886$	−54.8043	−1.84119
$887$	15.5810	0.523158	0.261579	−	0.965182i	$-0.415757\pi$
$887$	15.5810	0.523158	0.261579	+	0.965182i	$0.415757\pi$
$888$	12.6407	0.424194
$889$	9.46737	0.317526
$890$	−10.5441	−0.353438
$891$	−4.46342	−0.149530
$892$	25.0563	0.838948
$893$	−20.3287	−0.680275
$894$	15.9037	0.531899
$895$	25.7020	0.859122
$896$	−27.9922	−0.935154
$897$	−7.00649	−0.233940
$898$	−74.1150	−2.47325
$899$	1.60811	0.0536335
$900$	−6.82066	−0.227355
$901$	11.1495	0.371445
$902$	−97.9630	−3.26181
$903$	−3.82014	−0.127126
$904$	−29.1258	−0.968710
$905$	−25.6382	−0.852243
$906$	−48.6558	−1.61648
$907$	6.98488	0.231929	0.115965	−	0.993253i	$-0.463004\pi$
$907$	6.98488	0.231929	0.115965	+	0.993253i	$0.463004\pi$
$908$	26.0108	0.863200
$909$	−4.06378	−0.134787
$910$	8.93594	0.296223
$911$	−45.3891	−1.50381	−0.751905	−	0.659272i	$-0.770865\pi$
$911$	−45.3891	−1.50381	−0.751905	+	0.659272i	$0.770865\pi$
$912$	8.55607	0.283320
$913$	−41.6206	−1.37744
$914$	−31.6745	−1.04770
$915$	−18.8169	−0.622067
$916$	−85.8676	−2.83715
$917$	−32.6766	−1.07908
$918$	−2.22001	−0.0732711
$919$	0.150106	0.00495153	0.00247577	−	0.999997i	$-0.499212\pi$
$919$	0.150106	0.00495153	0.00247577	+	0.999997i	$0.499212\pi$
$920$	18.2317	0.601081
$921$	−9.51663	−0.313584
$922$	18.9701	0.624746
$923$	11.8465	0.389933
$924$	24.8691	0.818134
$925$	14.2845	0.469670
$926$	−14.0963	−0.463233
$927$	2.71058	0.0890273
$928$	−2.68820	−0.0882444
$929$	34.2867	1.12491	0.562455	−	0.826828i	$-0.309857\pi$
$929$	34.2867	1.12491	0.562455	+	0.826828i	$0.309857\pi$
$930$	−15.1199	−0.495799
$931$	22.5720	0.739766
$932$	8.37040	0.274182
$933$	10.6710	0.349353
$934$	−12.9543	−0.423879
$935$	7.29449	0.238555
$936$	2.66809	0.0872092
$937$	58.5314	1.91214	0.956069	−	0.293143i	$-0.0947011\pi$
$937$	58.5314	1.91214	0.956069	+	0.293143i	$0.0947011\pi$
$938$	−44.5673	−1.45517
$939$	−20.8019	−0.678844
$940$	−14.5683	−0.475166
$941$	−7.10197	−0.231518	−0.115759	−	0.993277i	$-0.536930\pi$
$941$	−7.10197	−0.231518	−0.115759	+	0.993277i	$0.536930\pi$
$942$	39.6219	1.29095
$943$	−53.5106	−1.74255
$944$	−3.93909	−0.128206
$945$	3.10947	0.101151
$946$	19.8949	0.646840
$947$	20.7604	0.674623	0.337312	−	0.941393i	$-0.390482\pi$
$947$	20.7604	0.674623	0.337312	+	0.941393i	$0.390482\pi$
$948$	2.92842	0.0951108
$949$	5.05960	0.164241
$950$	−34.5309	−1.12033
$951$	17.2323	0.558795
$952$	3.92156	0.127098
$953$	2.03780	0.0660108	0.0330054	−	0.999455i	$-0.489492\pi$
$953$	2.03780	0.0660108	0.0330054	+	0.999455i	$0.489492\pi$
$954$	−24.7521	−0.801377
$955$	−32.1708	−1.04102
$956$	−70.5587	−2.28203
$957$	1.72234	0.0556752
$958$	−24.3011	−0.785134
$959$	−12.7346	−0.411222
$960$	21.0874	0.680594
$961$	−13.6327	−0.439763
$962$	−17.6249	−0.568248
$963$	−14.6277	−0.471371
$964$	1.04579	0.0336825
$965$	−6.65234	−0.214146
$966$	22.8619	0.735570
$967$	−45.6011	−1.46643	−0.733216	−	0.679996i	$-0.761982\pi$
$967$	−45.6011	−1.46643	−0.733216	+	0.679996i	$0.761982\pi$
$968$	−18.3895	−0.591060
$969$	−6.67824	−0.214536
$970$	−0.402906	−0.0129365
$971$	16.9241	0.543121	0.271561	−	0.962421i	$-0.412460\pi$
$971$	16.9241	0.543121	0.271561	+	0.962421i	$0.412460\pi$
$972$	2.92842	0.0939292
$973$	−28.4819	−0.913087
$974$	16.2439	0.520489
$975$	3.01504	0.0965584
$976$	−14.7514	−0.472180
$977$	8.46580	0.270845	0.135422	−	0.990788i	$-0.456761\pi$
$977$	8.46580	0.270845	0.135422	+	0.990788i	$0.456761\pi$
$978$	−20.8566	−0.666919
$979$	12.9717	0.414576
$980$	16.1759	0.516719
$981$	−1.86669	−0.0595988
$982$	26.6296	0.849784
$983$	−51.5719	−1.64489	−0.822444	−	0.568846i	$-0.807390\pi$
$983$	−51.5719	−1.64489	−0.822444	+	0.568846i	$0.807390\pi$
$984$	20.3770	0.649594
$985$	33.2140	1.05829
$986$	0.856651	0.0272813
$987$	−5.79171	−0.184352
$988$	25.3161	0.805411
$989$	10.8673	0.345559
$990$	−16.1938	−0.514673
$991$	15.8735	0.504237	0.252118	−	0.967696i	$-0.418873\pi$
$991$	15.8735	0.504237	0.252118	+	0.967696i	$0.418873\pi$
$992$	−29.0321	−0.921769
$993$	26.6575	0.845949
$994$	−38.6548	−1.22606
$995$	17.2629	0.547270
$996$	27.3070	0.865256
$997$	11.4346	0.362139	0.181069	−	0.983470i	$-0.442044\pi$
$997$	11.4346	0.362139	0.181069	+	0.983470i	$0.442044\pi$
$998$	−31.3361	−0.991927
$999$	−6.13298	−0.194039

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.k.1.5	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.k.1.5	✓	31	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.22001 q^{2} +1.00000 q^{3} +2.92842 q^{4} -1.63428 q^{5} -2.22001 q^{6} -1.90265 q^{7} -2.06110 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.22001 q^{2} +1.00000 q^{3} +2.92842 q^{4} -1.63428 q^{5} -2.22001 q^{6} -1.90265 q^{7} -2.06110 q^{8} +1.00000 q^{9} +3.62811 q^{10} -4.46342 q^{11} +2.92842 q^{12} -1.29449 q^{13} +4.22389 q^{14} -1.63428 q^{15} -1.28119 q^{16} +1.00000 q^{17} -2.22001 q^{18} -6.67824 q^{19} -4.78587 q^{20} -1.90265 q^{21} +9.90882 q^{22} +5.41253 q^{23} -2.06110 q^{24} -2.32912 q^{25} +2.87378 q^{26} +1.00000 q^{27} -5.57176 q^{28} -0.385878 q^{29} +3.62811 q^{30} -4.16741 q^{31} +6.96645 q^{32} -4.46342 q^{33} -2.22001 q^{34} +3.10947 q^{35} +2.92842 q^{36} -6.13298 q^{37} +14.8257 q^{38} -1.29449 q^{39} +3.36842 q^{40} -9.88644 q^{41} +4.22389 q^{42} +2.00780 q^{43} -13.0708 q^{44} -1.63428 q^{45} -12.0158 q^{46} +3.04402 q^{47} -1.28119 q^{48} -3.37992 q^{49} +5.17066 q^{50} +1.00000 q^{51} -3.79083 q^{52} +11.1495 q^{53} -2.22001 q^{54} +7.29449 q^{55} +3.92156 q^{56} -6.67824 q^{57} +0.856651 q^{58} +3.07457 q^{59} -4.78587 q^{60} +11.5138 q^{61} +9.25168 q^{62} -1.90265 q^{63} -12.9032 q^{64} +2.11557 q^{65} +9.90882 q^{66} -10.5512 q^{67} +2.92842 q^{68} +5.41253 q^{69} -6.90303 q^{70} -9.15147 q^{71} -2.06110 q^{72} -3.90855 q^{73} +13.6152 q^{74} -2.32912 q^{75} -19.5567 q^{76} +8.49233 q^{77} +2.87378 q^{78} +1.00000 q^{79} +2.09382 q^{80} +1.00000 q^{81} +21.9480 q^{82} +9.32483 q^{83} -5.57176 q^{84} -1.63428 q^{85} -4.45732 q^{86} -0.385878 q^{87} +9.19958 q^{88} -2.90621 q^{89} +3.62811 q^{90} +2.46297 q^{91} +15.8502 q^{92} -4.16741 q^{93} -6.75775 q^{94} +10.9141 q^{95} +6.96645 q^{96} -0.111051 q^{97} +7.50345 q^{98} -4.46342 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * q^99

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