LMFDB - Embedded newform 4015.2.a.g.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$1$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.71308 q^{2} +1.21665 q^{3} +0.934626 q^{4} -1.00000 q^{5} -2.08421 q^{6} -4.29501 q^{7} +1.82507 q^{8} -1.51977 q^{9} +O(q^{10})$	\(q-1.71308 q^{2} +1.21665 q^{3} +0.934626 q^{4} -1.00000 q^{5} -2.08421 q^{6} -4.29501 q^{7} +1.82507 q^{8} -1.51977 q^{9} +1.71308 q^{10} -1.00000 q^{11} +1.13711 q^{12} -3.59162 q^{13} +7.35767 q^{14} -1.21665 q^{15} -4.99573 q^{16} +5.70569 q^{17} +2.60347 q^{18} +2.87347 q^{19} -0.934626 q^{20} -5.22552 q^{21} +1.71308 q^{22} +5.29655 q^{23} +2.22046 q^{24} +1.00000 q^{25} +6.15271 q^{26} -5.49897 q^{27} -4.01423 q^{28} +7.75556 q^{29} +2.08421 q^{30} -2.46936 q^{31} +4.90792 q^{32} -1.21665 q^{33} -9.77427 q^{34} +4.29501 q^{35} -1.42041 q^{36} +5.15927 q^{37} -4.92247 q^{38} -4.36973 q^{39} -1.82507 q^{40} +4.71319 q^{41} +8.95170 q^{42} -2.15550 q^{43} -0.934626 q^{44} +1.51977 q^{45} -9.07339 q^{46} +8.55818 q^{47} -6.07804 q^{48} +11.4471 q^{49} -1.71308 q^{50} +6.94182 q^{51} -3.35682 q^{52} +1.11252 q^{53} +9.42014 q^{54} +1.00000 q^{55} -7.83867 q^{56} +3.49601 q^{57} -13.2859 q^{58} +3.59848 q^{59} -1.13711 q^{60} -13.4705 q^{61} +4.23020 q^{62} +6.52741 q^{63} +1.58381 q^{64} +3.59162 q^{65} +2.08421 q^{66} -12.3490 q^{67} +5.33269 q^{68} +6.44404 q^{69} -7.35767 q^{70} +6.62414 q^{71} -2.77367 q^{72} -1.00000 q^{73} -8.83822 q^{74} +1.21665 q^{75} +2.68562 q^{76} +4.29501 q^{77} +7.48568 q^{78} +0.822249 q^{79} +4.99573 q^{80} -2.13101 q^{81} -8.07405 q^{82} -9.59601 q^{83} -4.88391 q^{84} -5.70569 q^{85} +3.69254 q^{86} +9.43579 q^{87} -1.82507 q^{88} -11.5309 q^{89} -2.60347 q^{90} +15.4260 q^{91} +4.95030 q^{92} -3.00434 q^{93} -14.6608 q^{94} -2.87347 q^{95} +5.97122 q^{96} -14.8763 q^{97} -19.6098 q^{98} +1.51977 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9}+O(q^{10}) $ 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9} + 5 q^{10} - 32 q^{11} - 24 q^{12} - q^{13} - 5 q^{14} + 7 q^{15} + 47 q^{16} - 30 q^{17} - 11 q^{18} + 16 q^{19} - 37 q^{20} + q^{21} + 5 q^{22} - 26 q^{23} - 21 q^{24} + 32 q^{25} - q^{26} - 31 q^{27} - 24 q^{28} - 10 q^{29} + 3 q^{30} - 2 q^{31} - 31 q^{32} + 7 q^{33} - 14 q^{34} + 38 q^{36} - 28 q^{37} - 63 q^{38} - 2 q^{39} + 18 q^{40} - 62 q^{41} - 9 q^{42} + 8 q^{43} - 37 q^{44} - 29 q^{45} + 19 q^{46} - 21 q^{47} - 79 q^{48} + 34 q^{49} - 5 q^{50} + 17 q^{51} + 15 q^{52} - 32 q^{53} + 5 q^{54} + 32 q^{55} - 52 q^{56} - 57 q^{57} + 4 q^{58} - 37 q^{59} + 24 q^{60} + 15 q^{61} - 22 q^{62} + 5 q^{63} + 70 q^{64} + q^{65} + 3 q^{66} - 42 q^{67} - 81 q^{68} - 8 q^{69} + 5 q^{70} - 40 q^{71} - 27 q^{72} - 32 q^{73} - 17 q^{74} - 7 q^{75} + 21 q^{76} - 105 q^{78} + 18 q^{79} - 47 q^{80} + 12 q^{81} - 70 q^{82} - 26 q^{83} + 22 q^{84} + 30 q^{85} - 45 q^{86} - 18 q^{87} + 18 q^{88} - 83 q^{89} + 11 q^{90} - 18 q^{91} - 73 q^{92} - 68 q^{93} + 56 q^{94} - 16 q^{95} - 35 q^{96} - 99 q^{97} - 61 q^{98} - 29 q^{99}+O(q^{100}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9 + 5 * q^10 - 32 * q^11 - 24 * q^12 - q^13 - 5 * q^14 + 7 * q^15 + 47 * q^16 - 30 * q^17 - 11 * q^18 + 16 * q^19 - 37 * q^20 + q^21 + 5 * q^22 - 26 * q^23 - 21 * q^24 + 32 * q^25 - q^26 - 31 * q^27 - 24 * q^28 - 10 * q^29 + 3 * q^30 - 2 * q^31 - 31 * q^32 + 7 * q^33 - 14 * q^34 + 38 * q^36 - 28 * q^37 - 63 * q^38 - 2 * q^39 + 18 * q^40 - 62 * q^41 - 9 * q^42 + 8 * q^43 - 37 * q^44 - 29 * q^45 + 19 * q^46 - 21 * q^47 - 79 * q^48 + 34 * q^49 - 5 * q^50 + 17 * q^51 + 15 * q^52 - 32 * q^53 + 5 * q^54 + 32 * q^55 - 52 * q^56 - 57 * q^57 + 4 * q^58 - 37 * q^59 + 24 * q^60 + 15 * q^61 - 22 * q^62 + 5 * q^63 + 70 * q^64 + q^65 + 3 * q^66 - 42 * q^67 - 81 * q^68 - 8 * q^69 + 5 * q^70 - 40 * q^71 - 27 * q^72 - 32 * q^73 - 17 * q^74 - 7 * q^75 + 21 * q^76 - 105 * q^78 + 18 * q^79 - 47 * q^80 + 12 * q^81 - 70 * q^82 - 26 * q^83 + 22 * q^84 + 30 * q^85 - 45 * q^86 - 18 * q^87 + 18 * q^88 - 83 * q^89 + 11 * q^90 - 18 * q^91 - 73 * q^92 - 68 * q^93 + 56 * q^94 - 16 * q^95 - 35 * q^96 - 99 * q^97 - 61 * q^98 - 29 * 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 $

$2$	−1.71308	−1.21133	−0.605664	−	0.795721i	$-0.707092\pi$
$2$	−1.71308	−1.21133	−0.605664	+	0.795721i	$0.707092\pi$
$3$	1.21665	0.702432	0.351216	−	0.936294i	$-0.385768\pi$
$3$	1.21665	0.702432	0.351216	+	0.936294i	$0.385768\pi$
$4$	0.934626	0.467313
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.08421	−0.850875
$7$	−4.29501	−1.62336	−0.811680	−	0.584102i	$-0.801447\pi$
$7$	−4.29501	−1.62336	−0.811680	+	0.584102i	$0.801447\pi$
$8$	1.82507	0.645258
$9$	−1.51977	−0.506589
$10$	1.71308	0.541722
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.13711	0.328256
$13$	−3.59162	−0.996135	−0.498067	−	0.867138i	$-0.665957\pi$
$13$	−3.59162	−0.996135	−0.498067	+	0.867138i	$0.665957\pi$
$14$	7.35767	1.96642
$15$	−1.21665	−0.314137
$16$	−4.99573	−1.24893
$17$	5.70569	1.38383	0.691916	−	0.721978i	$-0.256767\pi$
$17$	5.70569	1.38383	0.691916	+	0.721978i	$0.256767\pi$
$18$	2.60347	0.613645
$19$	2.87347	0.659220	0.329610	−	0.944117i	$-0.393083\pi$
$19$	2.87347	0.659220	0.329610	+	0.944117i	$0.393083\pi$
$20$	−0.934626	−0.208989
$21$	−5.22552	−1.14030
$22$	1.71308	0.365229
$23$	5.29655	1.10441	0.552204	−	0.833709i	$-0.313787\pi$
$23$	5.29655	1.10441	0.552204	+	0.833709i	$0.313787\pi$
$24$	2.22046	0.453250
$25$	1.00000	0.200000
$26$	6.15271	1.20665
$27$	−5.49897	−1.05828
$28$	−4.01423	−0.758618
$29$	7.75556	1.44017	0.720086	−	0.693885i	$-0.244103\pi$
$29$	7.75556	1.44017	0.720086	+	0.693885i	$0.244103\pi$
$30$	2.08421	0.380523
$31$	−2.46936	−0.443510	−0.221755	−	0.975102i	$-0.571179\pi$
$31$	−2.46936	−0.443510	−0.221755	+	0.975102i	$0.571179\pi$
$32$	4.90792	0.867607
$33$	−1.21665	−0.211791
$34$	−9.77427	−1.67627
$35$	4.29501	0.725989
$36$	−1.42041	−0.236736
$37$	5.15927	0.848179	0.424090	−	0.905620i	$-0.360594\pi$
$37$	5.15927	0.848179	0.424090	+	0.905620i	$0.360594\pi$
$38$	−4.92247	−0.798531
$39$	−4.36973	−0.699717
$40$	−1.82507	−0.288568
$41$	4.71319	0.736077	0.368038	−	0.929811i	$-0.380030\pi$
$41$	4.71319	0.736077	0.368038	+	0.929811i	$0.380030\pi$
$42$	8.95170	1.38128
$43$	−2.15550	−0.328711	−0.164356	−	0.986401i	$-0.552554\pi$
$43$	−2.15550	−0.328711	−0.164356	+	0.986401i	$0.552554\pi$
$44$	−0.934626	−0.140900
$45$	1.51977	0.226553
$46$	−9.07339	−1.33780
$47$	8.55818	1.24834	0.624169	−	0.781289i	$-0.285438\pi$
$47$	8.55818	1.24834	0.624169	+	0.781289i	$0.285438\pi$
$48$	−6.07804	−0.877290
$49$	11.4471	1.63530
$50$	−1.71308	−0.242265
$51$	6.94182	0.972049
$52$	−3.35682	−0.465507
$53$	1.11252	0.152817	0.0764084	−	0.997077i	$-0.475655\pi$
$53$	1.11252	0.152817	0.0764084	+	0.997077i	$0.475655\pi$
$54$	9.42014	1.28192
$55$	1.00000	0.134840
$56$	−7.83867	−1.04749
$57$	3.49601	0.463057
$58$	−13.2859	−1.74452
$59$	3.59848	0.468482	0.234241	−	0.972179i	$-0.424739\pi$
$59$	3.59848	0.468482	0.234241	+	0.972179i	$0.424739\pi$
$60$	−1.13711	−0.146800
$61$	−13.4705	−1.72472	−0.862358	−	0.506298i	$-0.831013\pi$
$61$	−13.4705	−1.72472	−0.862358	+	0.506298i	$0.831013\pi$
$62$	4.23020	0.537236
$63$	6.52741	0.822376
$64$	1.58381	0.197976
$65$	3.59162	0.445485
$66$	2.08421	0.256549
$67$	−12.3490	−1.50867	−0.754337	−	0.656488i	$-0.772041\pi$
$67$	−12.3490	−1.50867	−0.754337	+	0.656488i	$0.772041\pi$
$68$	5.33269	0.646683
$69$	6.44404	0.775771
$70$	−7.35767	−0.879410
$71$	6.62414	0.786140	0.393070	−	0.919508i	$-0.371413\pi$
$71$	6.62414	0.786140	0.393070	+	0.919508i	$0.371413\pi$
$72$	−2.77367	−0.326880
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	−8.83822	−1.02742
$75$	1.21665	0.140486
$76$	2.68562	0.308062
$77$	4.29501	0.489462
$78$	7.48568	0.847587
$79$	0.822249	0.0925102	0.0462551	−	0.998930i	$-0.485271\pi$
$79$	0.822249	0.0925102	0.0462551	+	0.998930i	$0.485271\pi$
$80$	4.99573	0.558539
$81$	−2.13101	−0.236779
$82$	−8.07405	−0.891629
$83$	−9.59601	−1.05330	−0.526649	−	0.850083i	$-0.676552\pi$
$83$	−9.59601	−1.05330	−0.526649	+	0.850083i	$0.676552\pi$
$84$	−4.88391	−0.532878
$85$	−5.70569	−0.618869
$86$	3.69254	0.398177
$87$	9.43579	1.01162
$88$	−1.82507	−0.194553
$89$	−11.5309	−1.22227	−0.611136	−	0.791525i	$-0.709287\pi$
$89$	−11.5309	−1.22227	−0.611136	+	0.791525i	$0.709287\pi$
$90$	−2.60347	−0.274430
$91$	15.4260	1.61709
$92$	4.95030	0.516104
$93$	−3.00434	−0.311536
$94$	−14.6608	−1.51215
$95$	−2.87347	−0.294812
$96$	5.97122	0.609435
$97$	−14.8763	−1.51046	−0.755228	−	0.655462i	$-0.772474\pi$
$97$	−14.8763	−1.51046	−0.755228	+	0.655462i	$0.772474\pi$
$98$	−19.6098	−1.98088
$99$	1.51977	0.152742
$100$	0.934626	0.0934626
$101$	−14.3862	−1.43148	−0.715742	−	0.698365i	$-0.753911\pi$
$101$	−14.3862	−1.43148	−0.715742	+	0.698365i	$0.753911\pi$
$102$	−11.8919	−1.17747
$103$	−5.34767	−0.526921	−0.263461	−	0.964670i	$-0.584864\pi$
$103$	−5.34767	−0.526921	−0.263461	+	0.964670i	$0.584864\pi$
$104$	−6.55493	−0.642764
$105$	5.22552	0.509958
$106$	−1.90584	−0.185111
$107$	6.84373	0.661608	0.330804	−	0.943699i	$-0.392680\pi$
$107$	6.84373	0.661608	0.330804	+	0.943699i	$0.392680\pi$
$108$	−5.13948	−0.494547
$109$	15.6034	1.49454	0.747268	−	0.664523i	$-0.231365\pi$
$109$	15.6034	1.49454	0.747268	+	0.664523i	$0.231365\pi$
$110$	−1.71308	−0.163335
$111$	6.27702	0.595788
$112$	21.4567	2.02747
$113$	−6.59536	−0.620440	−0.310220	−	0.950665i	$-0.600403\pi$
$113$	−6.59536	−0.620440	−0.310220	+	0.950665i	$0.600403\pi$
$114$	−5.98892	−0.560914
$115$	−5.29655	−0.493906
$116$	7.24855	0.673011
$117$	5.45842	0.504631
$118$	−6.16447	−0.567485
$119$	−24.5060	−2.24646
$120$	−2.22046	−0.202700
$121$	1.00000	0.0909091
$122$	23.0759	2.08920
$123$	5.73430	0.517044
$124$	−2.30793	−0.207258
$125$	−1.00000	−0.0894427
$126$	−11.1819	−0.996167
$127$	1.83725	0.163030	0.0815150	−	0.996672i	$-0.474024\pi$
$127$	1.83725	0.163030	0.0815150	+	0.996672i	$0.474024\pi$
$128$	−12.5290	−1.10742
$129$	−2.62249	−0.230898
$130$	−6.15271	−0.539628
$131$	−6.39607	−0.558827	−0.279413	−	0.960171i	$-0.590140\pi$
$131$	−6.39607	−0.558827	−0.279413	+	0.960171i	$0.590140\pi$
$132$	−1.13711	−0.0989729
$133$	−12.3416	−1.07015
$134$	21.1548	1.82750
$135$	5.49897	0.473276
$136$	10.4133	0.892929
$137$	−17.0994	−1.46090	−0.730451	−	0.682965i	$-0.760690\pi$
$137$	−17.0994	−1.46090	−0.730451	+	0.682965i	$0.760690\pi$
$138$	−11.0391	−0.939713
$139$	1.10283	0.0935407	0.0467703	−	0.998906i	$-0.485107\pi$
$139$	1.10283	0.0935407	0.0467703	+	0.998906i	$0.485107\pi$
$140$	4.01423	0.339264
$141$	10.4123	0.876873
$142$	−11.3476	−0.952273
$143$	3.59162	0.300346
$144$	7.59234	0.632695
$145$	−7.75556	−0.644064
$146$	1.71308	0.141775
$147$	13.9271	1.14869
$148$	4.82199	0.396365
$149$	−21.1325	−1.73124	−0.865620	−	0.500702i	$-0.833075\pi$
$149$	−21.1325	−1.73124	−0.865620	+	0.500702i	$0.833075\pi$
$150$	−2.08421	−0.170175
$151$	14.0390	1.14248	0.571240	−	0.820783i	$-0.306462\pi$
$151$	14.0390	1.14248	0.571240	+	0.820783i	$0.306462\pi$
$152$	5.24427	0.425367
$153$	−8.67131	−0.701034
$154$	−7.35767	−0.592898
$155$	2.46936	0.198344
$156$	−4.08407	−0.326987
$157$	−13.1673	−1.05087	−0.525434	−	0.850834i	$-0.676097\pi$
$157$	−13.1673	−1.05087	−0.525434	+	0.850834i	$0.676097\pi$
$158$	−1.40857	−0.112060
$159$	1.35355	0.107344
$160$	−4.90792	−0.388005
$161$	−22.7487	−1.79285
$162$	3.65058	0.286817
$163$	−15.0972	−1.18250	−0.591251	−	0.806487i	$-0.701366\pi$
$163$	−15.0972	−1.18250	−0.591251	+	0.806487i	$0.701366\pi$
$164$	4.40507	0.343978
$165$	1.21665	0.0947160
$166$	16.4387	1.27589
$167$	6.64984	0.514580	0.257290	−	0.966334i	$-0.417170\pi$
$167$	6.64984	0.514580	0.257290	+	0.966334i	$0.417170\pi$
$168$	−9.53691	−0.735789
$169$	−0.100298	−0.00771525
$170$	9.77427	0.749653
$171$	−4.36701	−0.333953
$172$	−2.01459	−0.153611
$173$	−0.994095	−0.0755796	−0.0377898	−	0.999286i	$-0.512032\pi$
$173$	−0.994095	−0.0755796	−0.0377898	+	0.999286i	$0.512032\pi$
$174$	−16.1642	−1.22541
$175$	−4.29501	−0.324672
$176$	4.99573	0.376567
$177$	4.37809	0.329077
$178$	19.7533	1.48057
$179$	10.1031	0.755143	0.377572	−	0.925980i	$-0.376759\pi$
$179$	10.1031	0.755143	0.377572	+	0.925980i	$0.376759\pi$
$180$	1.42041	0.105871
$181$	2.26215	0.168144	0.0840721	−	0.996460i	$-0.473207\pi$
$181$	2.26215	0.168144	0.0840721	+	0.996460i	$0.473207\pi$
$182$	−26.4259	−1.95882
$183$	−16.3888	−1.21150
$184$	9.66655	0.712628
$185$	−5.15927	−0.379317
$186$	5.14667	0.377372
$187$	−5.70569	−0.417241
$188$	7.99870	0.583365
$189$	23.6181	1.71797
$190$	4.92247	0.357114
$191$	−4.26757	−0.308790	−0.154395	−	0.988009i	$-0.549343\pi$
$191$	−4.26757	−0.308790	−0.154395	+	0.988009i	$0.549343\pi$
$192$	1.92694	0.139065
$193$	−13.7135	−0.987119	−0.493560	−	0.869712i	$-0.664305\pi$
$193$	−13.7135	−0.987119	−0.493560	+	0.869712i	$0.664305\pi$
$194$	25.4842	1.82966
$195$	4.36973	0.312923
$196$	10.6988	0.764198
$197$	26.5484	1.89150	0.945749	−	0.324897i	$-0.105330\pi$
$197$	26.5484	1.89150	0.945749	+	0.324897i	$0.105330\pi$
$198$	−2.60347	−0.185021
$199$	−10.4900	−0.743614	−0.371807	−	0.928310i	$-0.621262\pi$
$199$	−10.4900	−0.743614	−0.371807	+	0.928310i	$0.621262\pi$
$200$	1.82507	0.129052
$201$	−15.0244	−1.05974
$202$	24.6447	1.73399
$203$	−33.3102	−2.33792
$204$	6.48801	0.454251
$205$	−4.71319	−0.329183
$206$	9.16095	0.638274
$207$	−8.04952	−0.559480
$208$	17.9427	1.24410
$209$	−2.87347	−0.198762
$210$	−8.95170	−0.617726
$211$	26.0227	1.79148	0.895740	−	0.444579i	$-0.146647\pi$
$211$	26.0227	1.79148	0.895740	+	0.444579i	$0.146647\pi$
$212$	1.03979	0.0714133
$213$	8.05925	0.552211
$214$	−11.7238	−0.801424
$215$	2.15550	0.147004
$216$	−10.0360	−0.682862
$217$	10.6059	0.719977
$218$	−26.7298	−1.81037
$219$	−1.21665	−0.0822135
$220$	0.934626	0.0630125
$221$	−20.4926	−1.37848
$222$	−10.7530	−0.721695
$223$	−22.4124	−1.50084	−0.750422	−	0.660959i	$-0.770150\pi$
$223$	−22.4124	−1.50084	−0.750422	+	0.660959i	$0.770150\pi$
$224$	−21.0796	−1.40844
$225$	−1.51977	−0.101318
$226$	11.2984	0.751555
$227$	−4.14632	−0.275201	−0.137600	−	0.990488i	$-0.543939\pi$
$227$	−4.14632	−0.275201	−0.137600	+	0.990488i	$0.543939\pi$
$228$	3.26746	0.216393
$229$	−0.884997	−0.0584822	−0.0292411	−	0.999572i	$-0.509309\pi$
$229$	−0.884997	−0.0584822	−0.0292411	+	0.999572i	$0.509309\pi$
$230$	9.07339	0.598282
$231$	5.22552	0.343814
$232$	14.1544	0.929282
$233$	9.22286	0.604210	0.302105	−	0.953275i	$-0.402311\pi$
$233$	9.22286	0.604210	0.302105	+	0.953275i	$0.402311\pi$
$234$	−9.35068	−0.611273
$235$	−8.55818	−0.558274
$236$	3.36323	0.218928
$237$	1.00039	0.0649822
$238$	41.9806	2.72120
$239$	−10.2391	−0.662313	−0.331156	−	0.943576i	$-0.607439\pi$
$239$	−10.2391	−0.662313	−0.331156	+	0.943576i	$0.607439\pi$
$240$	6.07804	0.392336
$241$	21.1283	1.36099	0.680495	−	0.732752i	$-0.261765\pi$
$241$	21.1283	1.36099	0.680495	+	0.732752i	$0.261765\pi$
$242$	−1.71308	−0.110121
$243$	13.9042	0.891955
$244$	−12.5899	−0.805983
$245$	−11.4471	−0.731329
$246$	−9.82328	−0.626309
$247$	−10.3204	−0.656672
$248$	−4.50674	−0.286179
$249$	−11.6750	−0.739871
$250$	1.71308	0.108344
$251$	−2.36900	−0.149530	−0.0747651	−	0.997201i	$-0.523821\pi$
$251$	−2.36900	−0.149530	−0.0747651	+	0.997201i	$0.523821\pi$
$252$	6.10069	0.384307
$253$	−5.29655	−0.332991
$254$	−3.14735	−0.197483
$255$	−6.94182	−0.434714
$256$	18.2956	1.14347
$257$	−29.6651	−1.85046	−0.925230	−	0.379407i	$-0.876128\pi$
$257$	−29.6651	−1.85046	−0.925230	+	0.379407i	$0.876128\pi$
$258$	4.49253	0.279692
$259$	−22.1591	−1.37690
$260$	3.35682	0.208181
$261$	−11.7866	−0.729574
$262$	10.9569	0.676922
$263$	19.0369	1.17386	0.586932	−	0.809636i	$-0.300336\pi$
$263$	19.0369	1.17386	0.586932	+	0.809636i	$0.300336\pi$
$264$	−2.22046	−0.136660
$265$	−1.11252	−0.0683418
$266$	21.1421	1.29630
$267$	−14.0291	−0.858564
$268$	−11.5417	−0.705023
$269$	26.5672	1.61983	0.809917	−	0.586545i	$-0.199512\pi$
$269$	26.5672	1.61983	0.809917	+	0.586545i	$0.199512\pi$
$270$	−9.42014	−0.573292
$271$	−27.3498	−1.66138	−0.830691	−	0.556734i	$-0.812054\pi$
$271$	−27.3498	−1.66138	−0.830691	+	0.556734i	$0.812054\pi$
$272$	−28.5041	−1.72831
$273$	18.7680	1.13589
$274$	29.2926	1.76963
$275$	−1.00000	−0.0603023
$276$	6.02277	0.362528
$277$	−7.24350	−0.435220	−0.217610	−	0.976036i	$-0.569826\pi$
$277$	−7.24350	−0.435220	−0.217610	+	0.976036i	$0.569826\pi$
$278$	−1.88923	−0.113308
$279$	3.75285	0.224677
$280$	7.83867	0.468450
$281$	32.4343	1.93487	0.967434	−	0.253125i	$-0.0814584\pi$
$281$	32.4343	1.93487	0.967434	+	0.253125i	$0.0814584\pi$
$282$	−17.8370	−1.06218
$283$	−2.36037	−0.140309	−0.0701547	−	0.997536i	$-0.522349\pi$
$283$	−2.36037	−0.140309	−0.0701547	+	0.997536i	$0.522349\pi$
$284$	6.19109	0.367374
$285$	−3.49601	−0.207086
$286$	−6.15271	−0.363817
$287$	−20.2432	−1.19492
$288$	−7.45890	−0.439520
$289$	15.5549	0.914993
$290$	13.2859	0.780172
$291$	−18.0992	−1.06099
$292$	−0.934626	−0.0546949
$293$	4.24262	0.247857	0.123928	−	0.992291i	$-0.460451\pi$
$293$	4.24262	0.247857	0.123928	+	0.992291i	$0.460451\pi$
$294$	−23.8582	−1.39144
$295$	−3.59848	−0.209512
$296$	9.41601	0.547294
$297$	5.49897	0.319082
$298$	36.2015	2.09710
$299$	−19.0232	−1.10014
$300$	1.13711	0.0656512
$301$	9.25791	0.533617
$302$	−24.0499	−1.38392
$303$	−17.5030	−1.00552
$304$	−14.3551	−0.823320
$305$	13.4705	0.771317
$306$	14.8546	0.849182
$307$	22.2230	1.26833	0.634167	−	0.773196i	$-0.281343\pi$
$307$	22.2230	1.26833	0.634167	+	0.773196i	$0.281343\pi$
$308$	4.01423	0.228732
$309$	−6.50623	−0.370127
$310$	−4.23020	−0.240259
$311$	22.5168	1.27681	0.638404	−	0.769701i	$-0.279595\pi$
$311$	22.5168	1.27681	0.638404	+	0.769701i	$0.279595\pi$
$312$	−7.97505	−0.451498
$313$	−0.0369569	−0.00208893	−0.00104446	−	0.999999i	$-0.500332\pi$
$313$	−0.0369569	−0.00208893	−0.00104446	+	0.999999i	$0.500332\pi$
$314$	22.5566	1.27294
$315$	−6.52741	−0.367778
$316$	0.768496	0.0432313
$317$	27.7967	1.56122	0.780608	−	0.625020i	$-0.214909\pi$
$317$	27.7967	1.56122	0.780608	+	0.625020i	$0.214909\pi$
$318$	−2.31873	−0.130028
$319$	−7.75556	−0.434228
$320$	−1.58381	−0.0885377
$321$	8.32641	0.464735
$322$	38.9703	2.17173
$323$	16.3951	0.912250
$324$	−1.99170	−0.110650
$325$	−3.59162	−0.199227
$326$	25.8626	1.43240
$327$	18.9839	1.04981
$328$	8.60188	0.474959
$329$	−36.7574	−2.02650
$330$	−2.08421	−0.114732
$331$	5.32678	0.292786	0.146393	−	0.989227i	$-0.453234\pi$
$331$	5.32678	0.292786	0.146393	+	0.989227i	$0.453234\pi$
$332$	−8.96868	−0.492220
$333$	−7.84089	−0.429678
$334$	−11.3917	−0.623325
$335$	12.3490	0.674699
$336$	26.1053	1.42416
$337$	10.0800	0.549091	0.274546	−	0.961574i	$-0.411473\pi$
$337$	10.0800	0.549091	0.274546	+	0.961574i	$0.411473\pi$
$338$	0.171819	0.00934570
$339$	−8.02424	−0.435817
$340$	−5.33269	−0.289206
$341$	2.46936	0.133723
$342$	7.48101	0.404527
$343$	−19.1004	−1.03132
$344$	−3.93394	−0.212104
$345$	−6.44404	−0.346936
$346$	1.70296	0.0915516
$347$	5.57021	0.299025	0.149512	−	0.988760i	$-0.452230\pi$
$347$	5.57021	0.299025	0.149512	+	0.988760i	$0.452230\pi$
$348$	8.81894	0.472745
$349$	−1.36565	−0.0731015	−0.0365507	−	0.999332i	$-0.511637\pi$
$349$	−1.36565	−0.0731015	−0.0365507	+	0.999332i	$0.511637\pi$
$350$	7.35767	0.393284
$351$	19.7502	1.05419
$352$	−4.90792	−0.261593
$353$	−21.2628	−1.13171	−0.565853	−	0.824506i	$-0.691453\pi$
$353$	−21.2628	−1.13171	−0.565853	+	0.824506i	$0.691453\pi$
$354$	−7.49999	−0.398620
$355$	−6.62414	−0.351573
$356$	−10.7771	−0.571184
$357$	−29.8152	−1.57799
$358$	−17.3074	−0.914726
$359$	13.8050	0.728598	0.364299	−	0.931282i	$-0.381309\pi$
$359$	13.8050	0.728598	0.364299	+	0.931282i	$0.381309\pi$
$360$	2.77367	0.146185
$361$	−10.7432	−0.565429
$362$	−3.87523	−0.203678
$363$	1.21665	0.0638575
$364$	14.4176	0.755686
$365$	1.00000	0.0523424
$366$	28.0753	1.46752
$367$	14.3781	0.750529	0.375264	−	0.926918i	$-0.377552\pi$
$367$	14.3781	0.750529	0.375264	+	0.926918i	$0.377552\pi$
$368$	−26.4601	−1.37933
$369$	−7.16295	−0.372888
$370$	8.83822	0.459477
$371$	−4.77830	−0.248077
$372$	−2.80794	−0.145585
$373$	−2.24348	−0.116163	−0.0580816	−	0.998312i	$-0.518498\pi$
$373$	−2.24348	−0.116163	−0.0580816	+	0.998312i	$0.518498\pi$
$374$	9.77427	0.505416
$375$	−1.21665	−0.0628275
$376$	15.6192	0.805500
$377$	−27.8550	−1.43460
$378$	−40.4596	−2.08102
$379$	−3.97176	−0.204016	−0.102008	−	0.994784i	$-0.532527\pi$
$379$	−3.97176	−0.204016	−0.102008	+	0.994784i	$0.532527\pi$
$380$	−2.68562	−0.137770
$381$	2.23529	0.114518
$382$	7.31066	0.374046
$383$	−32.7489	−1.67339	−0.836695	−	0.547669i	$-0.815515\pi$
$383$	−32.7489	−1.67339	−0.836695	+	0.547669i	$0.815515\pi$
$384$	−15.2434	−0.777888
$385$	−4.29501	−0.218894
$386$	23.4923	1.19572
$387$	3.27586	0.166521
$388$	−13.9037	−0.705856
$389$	22.5464	1.14315	0.571573	−	0.820551i	$-0.306333\pi$
$389$	22.5464	1.14315	0.571573	+	0.820551i	$0.306333\pi$
$390$	−7.48568	−0.379052
$391$	30.2205	1.52832
$392$	20.8917	1.05519
$393$	−7.78177	−0.392538
$394$	−45.4795	−2.29122
$395$	−0.822249	−0.0413718
$396$	1.42041	0.0713785
$397$	−21.5236	−1.08024	−0.540120	−	0.841588i	$-0.681621\pi$
$397$	−21.5236	−1.08024	−0.540120	+	0.841588i	$0.681621\pi$
$398$	17.9701	0.900760
$399$	−15.0154	−0.751709
$400$	−4.99573	−0.249786
$401$	−27.8151	−1.38902	−0.694510	−	0.719483i	$-0.744379\pi$
$401$	−27.8151	−1.38902	−0.694510	+	0.719483i	$0.744379\pi$
$402$	25.7380	1.28369
$403$	8.86899	0.441796
$404$	−13.4457	−0.668951
$405$	2.13101	0.105891
$406$	57.0629	2.83198
$407$	−5.15927	−0.255736
$408$	12.6693	0.627222
$409$	−12.5231	−0.619228	−0.309614	−	0.950862i	$-0.600200\pi$
$409$	−12.5231	−0.619228	−0.309614	+	0.950862i	$0.600200\pi$
$410$	8.07405	0.398749
$411$	−20.8040	−1.02618
$412$	−4.99807	−0.246237
$413$	−15.4555	−0.760516
$414$	13.7894	0.677714
$415$	9.59601	0.471049
$416$	−17.6274	−0.864253
$417$	1.34175	0.0657060
$418$	4.92247	0.240766
$419$	−21.1036	−1.03098	−0.515490	−	0.856895i	$-0.672390\pi$
$419$	−21.1036	−1.03098	−0.515490	+	0.856895i	$0.672390\pi$
$420$	4.88391	0.238310
$421$	−18.9056	−0.921403	−0.460702	−	0.887555i	$-0.652402\pi$
$421$	−18.9056	−0.921403	−0.460702	+	0.887555i	$0.652402\pi$
$422$	−44.5789	−2.17007
$423$	−13.0064	−0.632394
$424$	2.03043	0.0986063
$425$	5.70569	0.276767
$426$	−13.8061	−0.668908
$427$	57.8558	2.79984
$428$	6.39633	0.309178
$429$	4.36973	0.210973
$430$	−3.69254	−0.178070
$431$	16.6017	0.799676	0.399838	−	0.916586i	$-0.369066\pi$
$431$	16.6017	0.799676	0.399838	+	0.916586i	$0.369066\pi$
$432$	27.4713	1.32172
$433$	−21.6663	−1.04122	−0.520608	−	0.853796i	$-0.674295\pi$
$433$	−21.6663	−1.04122	−0.520608	+	0.853796i	$0.674295\pi$
$434$	−18.1687	−0.872128
$435$	−9.43579	−0.452411
$436$	14.5834	0.698416
$437$	15.2195	0.728047
$438$	2.08421	0.0995874
$439$	33.6957	1.60821	0.804104	−	0.594488i	$-0.202645\pi$
$439$	33.6957	1.60821	0.804104	+	0.594488i	$0.202645\pi$
$440$	1.82507	0.0870066
$441$	−17.3969	−0.828425
$442$	35.1054	1.66980
$443$	−13.8158	−0.656410	−0.328205	−	0.944607i	$-0.606444\pi$
$443$	−13.8158	−0.656410	−0.328205	+	0.944607i	$0.606444\pi$
$444$	5.86667	0.278420
$445$	11.5309	0.546617
$446$	38.3941	1.81801
$447$	−25.7108	−1.21608
$448$	−6.80248	−0.321387
$449$	−16.6570	−0.786095	−0.393047	−	0.919518i	$-0.628579\pi$
$449$	−16.6570	−0.786095	−0.393047	+	0.919518i	$0.628579\pi$
$450$	2.60347	0.122729
$451$	−4.71319	−0.221935
$452$	−6.16420	−0.289940
$453$	17.0806	0.802515
$454$	7.10296	0.333358
$455$	−15.4260	−0.723183
$456$	6.38044	0.298791
$457$	−9.37860	−0.438712	−0.219356	−	0.975645i	$-0.570396\pi$
$457$	−9.37860	−0.438712	−0.219356	+	0.975645i	$0.570396\pi$
$458$	1.51607	0.0708411
$459$	−31.3754	−1.46448
$460$	−4.95030	−0.230809
$461$	−23.5022	−1.09461	−0.547303	−	0.836934i	$-0.684345\pi$
$461$	−23.5022	−1.09461	−0.547303	+	0.836934i	$0.684345\pi$
$462$	−8.95170	−0.416471
$463$	−34.7190	−1.61353	−0.806765	−	0.590872i	$-0.798784\pi$
$463$	−34.7190	−1.61353	−0.806765	+	0.590872i	$0.798784\pi$
$464$	−38.7446	−1.79868
$465$	3.00434	0.139323
$466$	−15.7995	−0.731895
$467$	0.423754	0.0196090	0.00980449	−	0.999952i	$-0.496879\pi$
$467$	0.423754	0.0196090	0.00980449	+	0.999952i	$0.496879\pi$
$468$	5.10158	0.235821
$469$	53.0392	2.44912
$470$	14.6608	0.676252
$471$	−16.0200	−0.738164
$472$	6.56746	0.302292
$473$	2.15550	0.0991102
$474$	−1.71374	−0.0787147
$475$	2.87347	0.131844
$476$	−22.9039	−1.04980
$477$	−1.69078	−0.0774153
$478$	17.5404	0.802277
$479$	6.78250	0.309900	0.154950	−	0.987922i	$-0.450478\pi$
$479$	6.78250	0.309900	0.154950	+	0.987922i	$0.450478\pi$
$480$	−5.97122	−0.272548
$481$	−18.5301	−0.844901
$482$	−36.1943	−1.64860
$483$	−27.6772	−1.25936
$484$	0.934626	0.0424830
$485$	14.8763	0.675496
$486$	−23.8190	−1.08045
$487$	−37.2432	−1.68765	−0.843824	−	0.536620i	$-0.819701\pi$
$487$	−37.2432	−1.68765	−0.843824	+	0.536620i	$0.819701\pi$
$488$	−24.5845	−1.11289
$489$	−18.3680	−0.830628
$490$	19.6098	0.885878
$491$	−18.4899	−0.834439	−0.417219	−	0.908806i	$-0.636995\pi$
$491$	−18.4899	−0.834439	−0.417219	+	0.908806i	$0.636995\pi$
$492$	5.35942	0.241621
$493$	44.2508	1.99296
$494$	17.6796	0.795444
$495$	−1.51977	−0.0683084
$496$	12.3362	0.553914
$497$	−28.4507	−1.27619
$498$	20.0001	0.896226
$499$	8.64215	0.386876	0.193438	−	0.981113i	$-0.438036\pi$
$499$	8.64215	0.386876	0.193438	+	0.981113i	$0.438036\pi$
$500$	−0.934626	−0.0417978
$501$	8.09052	0.361458
$502$	4.05828	0.181130
$503$	−37.4727	−1.67082	−0.835412	−	0.549624i	$-0.814771\pi$
$503$	−37.4727	−1.67082	−0.835412	+	0.549624i	$0.814771\pi$
$504$	11.9129	0.530645
$505$	14.3862	0.640179
$506$	9.07339	0.403361
$507$	−0.122028	−0.00541944
$508$	1.71715	0.0761860
$509$	10.3746	0.459848	0.229924	−	0.973209i	$-0.426152\pi$
$509$	10.3746	0.459848	0.229924	+	0.973209i	$0.426152\pi$
$510$	11.8919	0.526580
$511$	4.29501	0.190000
$512$	−6.28359	−0.277698
$513$	−15.8011	−0.697637
$514$	50.8186	2.24151
$515$	5.34767	0.235646
$516$	−2.45105	−0.107901
$517$	−8.55818	−0.376388
$518$	37.9602	1.66788
$519$	−1.20946	−0.0530896
$520$	6.55493	0.287453
$521$	−23.5959	−1.03376	−0.516878	−	0.856059i	$-0.672906\pi$
$521$	−23.5959	−1.03376	−0.516878	+	0.856059i	$0.672906\pi$
$522$	20.1914	0.883753
$523$	−37.2441	−1.62857	−0.814285	−	0.580465i	$-0.802871\pi$
$523$	−37.2441	−1.62857	−0.814285	+	0.580465i	$0.802871\pi$
$524$	−5.97793	−0.261147
$525$	−5.22552	−0.228060
$526$	−32.6116	−1.42193
$527$	−14.0894	−0.613744
$528$	6.07804	0.264513
$529$	5.05345	0.219715
$530$	1.90584	0.0827842
$531$	−5.46885	−0.237328
$532$	−11.5348	−0.500096
$533$	−16.9280	−0.733232
$534$	24.0328	1.04000
$535$	−6.84373	−0.295880
$536$	−22.5378	−0.973484
$537$	12.2920	0.530437
$538$	−45.5117	−1.96215
$539$	−11.4471	−0.493062
$540$	5.13948	0.221168
$541$	14.1444	0.608116	0.304058	−	0.952653i	$-0.401658\pi$
$541$	14.1444	0.608116	0.304058	+	0.952653i	$0.401658\pi$
$542$	46.8522	2.01248
$543$	2.75224	0.118110
$544$	28.0031	1.20062
$545$	−15.6034	−0.668377
$546$	−32.1511	−1.37594
$547$	34.4739	1.47400	0.736999	−	0.675894i	$-0.236242\pi$
$547$	34.4739	1.47400	0.736999	+	0.675894i	$0.236242\pi$
$548$	−15.9816	−0.682699
$549$	20.4720	0.873722
$550$	1.71308	0.0730458
$551$	22.2854	0.949389
$552$	11.7608	0.500573
$553$	−3.53157	−0.150178
$554$	12.4087	0.527193
$555$	−6.27702	−0.266445
$556$	1.03073	0.0437128
$557$	−31.0521	−1.31572	−0.657860	−	0.753140i	$-0.728538\pi$
$557$	−31.0521	−1.31572	−0.657860	+	0.753140i	$0.728538\pi$
$558$	−6.42891	−0.272158
$559$	7.74174	0.327441
$560$	−21.4567	−0.906711
$561$	−6.94182	−0.293084
$562$	−55.5624	−2.34376
$563$	−32.1840	−1.35639	−0.678197	−	0.734880i	$-0.737239\pi$
$563$	−32.1840	−1.35639	−0.678197	+	0.734880i	$0.737239\pi$
$564$	9.73160	0.409774
$565$	6.59536	0.277469
$566$	4.04349	0.169961
$567$	9.15272	0.384378
$568$	12.0895	0.507263
$569$	−11.6923	−0.490168	−0.245084	−	0.969502i	$-0.578815\pi$
$569$	−11.6923	−0.490168	−0.245084	+	0.969502i	$0.578815\pi$
$570$	5.98892	0.250848
$571$	−11.5421	−0.483020	−0.241510	−	0.970398i	$-0.577643\pi$
$571$	−11.5421	−0.483020	−0.241510	+	0.970398i	$0.577643\pi$
$572$	3.35682	0.140356
$573$	−5.19213	−0.216904
$574$	34.6781	1.44744
$575$	5.29655	0.220881
$576$	−2.40702	−0.100293
$577$	32.7588	1.36377	0.681884	−	0.731460i	$-0.261161\pi$
$577$	32.7588	1.36377	0.681884	+	0.731460i	$0.261161\pi$
$578$	−26.6467	−1.10836
$579$	−16.6845	−0.693385
$580$	−7.24855	−0.300980
$581$	41.2149	1.70988
$582$	31.0053	1.28521
$583$	−1.11252	−0.0460760
$584$	−1.82507	−0.0755217
$585$	−5.45842	−0.225678
$586$	−7.26793	−0.300236
$587$	−18.4827	−0.762862	−0.381431	−	0.924397i	$-0.624569\pi$
$587$	−18.4827	−0.762862	−0.381431	+	0.924397i	$0.624569\pi$
$588$	13.0166	0.536797
$589$	−7.09564	−0.292371
$590$	6.16447	0.253787
$591$	32.3001	1.32865
$592$	−25.7743	−1.05932
$593$	−27.0797	−1.11203	−0.556015	−	0.831172i	$-0.687670\pi$
$593$	−27.0797	−1.11203	−0.556015	+	0.831172i	$0.687670\pi$
$594$	−9.42014	−0.386513
$595$	24.5060	1.00465
$596$	−19.7510	−0.809031
$597$	−12.7626	−0.522339
$598$	32.5881	1.33263
$599$	−2.77232	−0.113274	−0.0566370	−	0.998395i	$-0.518038\pi$
$599$	−2.77232	−0.113274	−0.0566370	+	0.998395i	$0.518038\pi$
$600$	2.22046	0.0906500
$601$	2.98332	0.121692	0.0608461	−	0.998147i	$-0.480620\pi$
$601$	2.98332	0.121692	0.0608461	+	0.998147i	$0.480620\pi$
$602$	−15.8595	−0.646385
$603$	18.7676	0.764277
$604$	13.1213	0.533896
$605$	−1.00000	−0.0406558
$606$	29.9839	1.21801
$607$	13.3405	0.541475	0.270737	−	0.962653i	$-0.412733\pi$
$607$	13.3405	0.541475	0.270737	+	0.962653i	$0.412733\pi$
$608$	14.1028	0.571943
$609$	−40.5268	−1.64223
$610$	−23.0759	−0.934317
$611$	−30.7377	−1.24351
$612$	−8.10444	−0.327602
$613$	−8.13498	−0.328569	−0.164284	−	0.986413i	$-0.552531\pi$
$613$	−8.13498	−0.328569	−0.164284	+	0.986413i	$0.552531\pi$
$614$	−38.0697	−1.53637
$615$	−5.73430	−0.231229
$616$	7.83867	0.315829
$617$	−21.1187	−0.850207	−0.425104	−	0.905145i	$-0.639762\pi$
$617$	−21.1187	−0.850207	−0.425104	+	0.905145i	$0.639762\pi$
$618$	11.1457	0.448344
$619$	25.8962	1.04085	0.520427	−	0.853906i	$-0.325773\pi$
$619$	25.8962	1.04085	0.520427	+	0.853906i	$0.325773\pi$
$620$	2.30793	0.0926887
$621$	−29.1256	−1.16877
$622$	−38.5729	−1.54663
$623$	49.5253	1.98419
$624$	21.8300	0.873899
$625$	1.00000	0.0400000
$626$	0.0633100	0.00253038
$627$	−3.49601	−0.139617
$628$	−12.3065	−0.491084
$629$	29.4372	1.17374
$630$	11.1819	0.445499
$631$	−18.6342	−0.741817	−0.370908	−	0.928669i	$-0.620954\pi$
$631$	−18.6342	−0.741817	−0.370908	+	0.928669i	$0.620954\pi$
$632$	1.50066	0.0596930
$633$	31.6605	1.25839
$634$	−47.6178	−1.89114
$635$	−1.83725	−0.0729092
$636$	1.26506	0.0501630
$637$	−41.1136	−1.62898
$638$	13.2859	0.525992
$639$	−10.0671	−0.398250
$640$	12.5290	0.495254
$641$	−6.59401	−0.260448	−0.130224	−	0.991485i	$-0.541570\pi$
$641$	−6.59401	−0.260448	−0.130224	+	0.991485i	$0.541570\pi$
$642$	−14.2638	−0.562946
$643$	−41.4464	−1.63449	−0.817243	−	0.576293i	$-0.804499\pi$
$643$	−41.4464	−1.63449	−0.817243	+	0.576293i	$0.804499\pi$
$644$	−21.2616	−0.837823
$645$	2.62249	0.103261
$646$	−28.0861	−1.10503
$647$	−4.80025	−0.188717	−0.0943587	−	0.995538i	$-0.530080\pi$
$647$	−4.80025	−0.188717	−0.0943587	+	0.995538i	$0.530080\pi$
$648$	−3.88924	−0.152784
$649$	−3.59848	−0.141253
$650$	6.15271	0.241329
$651$	12.9037	0.505735
$652$	−14.1102	−0.552599
$653$	29.8626	1.16861	0.584307	−	0.811533i	$-0.301366\pi$
$653$	29.8626	1.16861	0.584307	+	0.811533i	$0.301366\pi$
$654$	−32.5208	−1.27166
$655$	6.39607	0.249915
$656$	−23.5458	−0.919309
$657$	1.51977	0.0592917
$658$	62.9683	2.45476
$659$	−25.1573	−0.979988	−0.489994	−	0.871726i	$-0.663001\pi$
$659$	−25.1573	−0.979988	−0.489994	+	0.871726i	$0.663001\pi$
$660$	1.13711	0.0442620
$661$	−11.6782	−0.454227	−0.227114	−	0.973868i	$-0.572929\pi$
$661$	−11.6782	−0.454227	−0.227114	+	0.973868i	$0.572929\pi$
$662$	−9.12517	−0.354660
$663$	−24.9323	−0.968292
$664$	−17.5133	−0.679649
$665$	12.3416	0.478586
$666$	13.4320	0.520480
$667$	41.0777	1.59054
$668$	6.21512	0.240470
$669$	−27.2680	−1.05424
$670$	−21.1548	−0.817282
$671$	13.4705	0.520022
$672$	−25.6464	−0.989333
$673$	7.58670	0.292446	0.146223	−	0.989252i	$-0.453288\pi$
$673$	7.58670	0.292446	0.146223	+	0.989252i	$0.453288\pi$
$674$	−17.2678	−0.665129
$675$	−5.49897	−0.211655
$676$	−0.0937414	−0.00360544
$677$	−49.8133	−1.91448	−0.957240	−	0.289295i	$-0.906579\pi$
$677$	−49.8133	−1.91448	−0.957240	+	0.289295i	$0.906579\pi$
$678$	13.7461	0.527917
$679$	63.8937	2.45202
$680$	−10.4133	−0.399330
$681$	−5.04461	−0.193310
$682$	−4.23020	−0.161983
$683$	31.8874	1.22014	0.610068	−	0.792349i	$-0.291142\pi$
$683$	31.8874	1.22014	0.610068	+	0.792349i	$0.291142\pi$
$684$	−4.08152	−0.156061
$685$	17.0994	0.653335
$686$	32.7203	1.24927
$687$	−1.07673	−0.0410798
$688$	10.7683	0.410538
$689$	−3.99576	−0.152226
$690$	11.0391	0.420252
$691$	−23.4044	−0.890347	−0.445173	−	0.895444i	$-0.646858\pi$
$691$	−23.4044	−0.890347	−0.445173	+	0.895444i	$0.646858\pi$
$692$	−0.929107	−0.0353194
$693$	−6.52741	−0.247956
$694$	−9.54220	−0.362217
$695$	−1.10283	−0.0418327
$696$	17.2209	0.652758
$697$	26.8920	1.01861
$698$	2.33946	0.0885498
$699$	11.2210	0.424416
$700$	−4.01423	−0.151724
$701$	20.7852	0.785047	0.392524	−	0.919742i	$-0.371602\pi$
$701$	20.7852	0.785047	0.392524	+	0.919742i	$0.371602\pi$
$702$	−33.8335	−1.27696
$703$	14.8250	0.559136
$704$	−1.58381	−0.0596921
$705$	−10.4123	−0.392150
$706$	36.4248	1.37087
$707$	61.7890	2.32381
$708$	4.09188	0.153782
$709$	26.6573	1.00113	0.500567	−	0.865698i	$-0.333125\pi$
$709$	26.6573	1.00113	0.500567	+	0.865698i	$0.333125\pi$
$710$	11.3476	0.425870
$711$	−1.24963	−0.0468646
$712$	−21.0446	−0.788681
$713$	−13.0791	−0.489816
$714$	51.0756	1.91146
$715$	−3.59162	−0.134319
$716$	9.44265	0.352888
$717$	−12.4574	−0.465230
$718$	−23.6489	−0.882571
$719$	26.9584	1.00538	0.502690	−	0.864467i	$-0.332344\pi$
$719$	26.9584	1.00538	0.502690	+	0.864467i	$0.332344\pi$
$720$	−7.59234	−0.282950
$721$	22.9683	0.855383
$722$	18.4038	0.684920
$723$	25.7057	0.956004
$724$	2.11426	0.0785760
$725$	7.75556	0.288034
$726$	−2.08421	−0.0773523
$727$	3.59144	0.133199	0.0665995	−	0.997780i	$-0.478785\pi$
$727$	3.59144	0.133199	0.0665995	+	0.997780i	$0.478785\pi$
$728$	28.1535	1.04344
$729$	23.3096	0.863318
$730$	−1.71308	−0.0634038
$731$	−12.2986	−0.454882
$732$	−15.3174	−0.566148
$733$	−16.5494	−0.611266	−0.305633	−	0.952149i	$-0.598868\pi$
$733$	−16.5494	−0.611266	−0.305633	+	0.952149i	$0.598868\pi$
$734$	−24.6307	−0.909136
$735$	−13.9271	−0.513709
$736$	25.9951	0.958191
$737$	12.3490	0.454882
$738$	12.2707	0.451689
$739$	−4.81546	−0.177139	−0.0885697	−	0.996070i	$-0.528230\pi$
$739$	−4.81546	−0.177139	−0.0885697	+	0.996070i	$0.528230\pi$
$740$	−4.82199	−0.177260
$741$	−12.5563	−0.461268
$742$	8.18559	0.300502
$743$	−18.2930	−0.671107	−0.335553	−	0.942021i	$-0.608923\pi$
$743$	−18.2930	−0.671107	−0.335553	+	0.942021i	$0.608923\pi$
$744$	−5.48312	−0.201021
$745$	21.1325	0.774234
$746$	3.84326	0.140712
$747$	14.5837	0.533589
$748$	−5.33269	−0.194982
$749$	−29.3939	−1.07403
$750$	2.08421	0.0761046
$751$	13.9193	0.507924	0.253962	−	0.967214i	$-0.418266\pi$
$751$	13.9193	0.507924	0.253962	+	0.967214i	$0.418266\pi$
$752$	−42.7543	−1.55909
$753$	−2.88224	−0.105035
$754$	47.7177	1.73778
$755$	−14.0390	−0.510933
$756$	22.0741	0.802828
$757$	−44.6092	−1.62135	−0.810674	−	0.585498i	$-0.800899\pi$
$757$	−44.6092	−1.62135	−0.810674	+	0.585498i	$0.800899\pi$
$758$	6.80392	0.247130
$759$	−6.44404	−0.233904
$760$	−5.24427	−0.190230
$761$	−17.5425	−0.635916	−0.317958	−	0.948105i	$-0.602997\pi$
$761$	−17.5425	−0.635916	−0.317958	+	0.948105i	$0.602997\pi$
$762$	−3.82922	−0.138718
$763$	−67.0168	−2.42617
$764$	−3.98858	−0.144302
$765$	8.67131	0.313512
$766$	56.1013	2.02702
$767$	−12.9244	−0.466672
$768$	22.2593	0.803212
$769$	−35.6915	−1.28707	−0.643535	−	0.765417i	$-0.722533\pi$
$769$	−35.6915	−1.28707	−0.643535	+	0.765417i	$0.722533\pi$
$770$	7.35767	0.265152
$771$	−36.0920	−1.29982
$772$	−12.8170	−0.461294
$773$	33.8271	1.21668	0.608338	−	0.793678i	$-0.291836\pi$
$773$	33.8271	1.21668	0.608338	+	0.793678i	$0.291836\pi$
$774$	−5.61180	−0.201712
$775$	−2.46936	−0.0887020
$776$	−27.1502	−0.974634
$777$	−26.9599	−0.967180
$778$	−38.6236	−1.38472
$779$	13.5432	0.485236
$780$	4.08407	0.146233
$781$	−6.62414	−0.237030
$782$	−51.7699	−1.85129
$783$	−42.6476	−1.52410
$784$	−57.1866	−2.04238
$785$	13.1673	0.469963
$786$	13.3308	0.475492
$787$	11.9903	0.427407	0.213704	−	0.976899i	$-0.431447\pi$
$787$	11.9903	0.427407	0.213704	+	0.976899i	$0.431447\pi$
$788$	24.8129	0.883922
$789$	23.1612	0.824560
$790$	1.40857	0.0501148
$791$	28.3272	1.00720
$792$	2.77367	0.0985582
$793$	48.3807	1.71805
$794$	36.8716	1.30852
$795$	−1.35355	−0.0480055
$796$	−9.80420	−0.347501
$797$	−6.45387	−0.228608	−0.114304	−	0.993446i	$-0.536464\pi$
$797$	−6.45387	−0.228608	−0.114304	+	0.993446i	$0.536464\pi$
$798$	25.7225	0.910566
$799$	48.8303	1.72749
$800$	4.90792	0.173521
$801$	17.5243	0.619190
$802$	47.6494	1.68256
$803$	1.00000	0.0352892
$804$	−14.0422	−0.495231
$805$	22.7487	0.801788
$806$	−15.1933	−0.535159
$807$	32.3230	1.13782
$808$	−26.2558	−0.923676
$809$	40.8361	1.43572	0.717860	−	0.696187i	$-0.245122\pi$
$809$	40.8361	1.43572	0.717860	+	0.696187i	$0.245122\pi$
$810$	−3.65058	−0.128268
$811$	−25.5272	−0.896381	−0.448191	−	0.893938i	$-0.647931\pi$
$811$	−25.5272	−0.896381	−0.448191	+	0.893938i	$0.647931\pi$
$812$	−31.1326	−1.09254
$813$	−33.2751	−1.16701
$814$	8.83822	0.309779
$815$	15.0972	0.528831
$816$	−34.6794	−1.21402
$817$	−6.19378	−0.216693
$818$	21.4530	0.750088
$819$	−23.4439	−0.819198
$820$	−4.40507	−0.153832
$821$	−27.6511	−0.965030	−0.482515	−	0.875888i	$-0.660277\pi$
$821$	−27.6511	−0.965030	−0.482515	+	0.875888i	$0.660277\pi$
$822$	35.6388	1.24305
$823$	52.1554	1.81802	0.909011	−	0.416773i	$-0.136839\pi$
$823$	52.1554	1.81802	0.909011	+	0.416773i	$0.136839\pi$
$824$	−9.75984	−0.340000
$825$	−1.21665	−0.0423583
$826$	26.4764	0.921234
$827$	−29.2873	−1.01842	−0.509210	−	0.860642i	$-0.670062\pi$
$827$	−29.2873	−1.01842	−0.509210	+	0.860642i	$0.670062\pi$
$828$	−7.52329	−0.261452
$829$	−47.3679	−1.64516	−0.822578	−	0.568652i	$-0.807465\pi$
$829$	−47.3679	−1.64516	−0.822578	+	0.568652i	$0.807465\pi$
$830$	−16.4387	−0.570595
$831$	−8.81280	−0.305712
$832$	−5.68844	−0.197211
$833$	65.3136	2.26298
$834$	−2.29853	−0.0795914
$835$	−6.64984	−0.230127
$836$	−2.68562	−0.0928842
$837$	13.5789	0.469357
$838$	36.1521	1.24885
$839$	12.0903	0.417402	0.208701	−	0.977979i	$-0.433076\pi$
$839$	12.0903	0.417402	0.208701	+	0.977979i	$0.433076\pi$
$840$	9.53691	0.329055
$841$	31.1487	1.07409
$842$	32.3867	1.11612
$843$	39.4611	1.35911
$844$	24.3215	0.837182
$845$	0.100298	0.00345037
$846$	22.2810	0.766036
$847$	−4.29501	−0.147578
$848$	−5.55786	−0.190858
$849$	−2.87174	−0.0985578
$850$	−9.77427	−0.335255
$851$	27.3263	0.936735
$852$	7.53238	0.258055
$853$	23.7741	0.814010	0.407005	−	0.913426i	$-0.366573\pi$
$853$	23.7741	0.814010	0.407005	+	0.913426i	$0.366573\pi$
$854$	−99.1113	−3.39152
$855$	4.36701	0.149348
$856$	12.4903	0.426908
$857$	−4.54280	−0.155179	−0.0775895	−	0.996985i	$-0.524722\pi$
$857$	−4.54280	−0.155179	−0.0775895	+	0.996985i	$0.524722\pi$
$858$	−7.48568	−0.255557
$859$	31.0135	1.05817	0.529084	−	0.848570i	$-0.322536\pi$
$859$	31.0135	1.05817	0.529084	+	0.848570i	$0.322536\pi$
$860$	2.01459	0.0686970
$861$	−24.6289	−0.839349
$862$	−28.4400	−0.968669
$863$	−12.7612	−0.434395	−0.217197	−	0.976128i	$-0.569692\pi$
$863$	−12.7612	−0.434395	−0.217197	+	0.976128i	$0.569692\pi$
$864$	−26.9885	−0.918168
$865$	0.994095	0.0338002
$866$	37.1160	1.26125
$867$	18.9248	0.642721
$868$	9.91258	0.336455
$869$	−0.822249	−0.0278929
$870$	16.1642	0.548018
$871$	44.3530	1.50284
$872$	28.4773	0.964362
$873$	22.6084	0.765180
$874$	−26.0721	−0.881903
$875$	4.29501	0.145198
$876$	−1.13711	−0.0384194
$877$	14.3581	0.484837	0.242419	−	0.970172i	$-0.422059\pi$
$877$	14.3581	0.484837	0.242419	+	0.970172i	$0.422059\pi$
$878$	−57.7233	−1.94807
$879$	5.16178	0.174103
$880$	−4.99573	−0.168406
$881$	−28.9337	−0.974800	−0.487400	−	0.873179i	$-0.662055\pi$
$881$	−28.9337	−0.974800	−0.487400	+	0.873179i	$0.662055\pi$
$882$	29.8022	1.00349
$883$	20.8890	0.702970	0.351485	−	0.936194i	$-0.385677\pi$
$883$	20.8890	0.702970	0.351485	+	0.936194i	$0.385677\pi$
$884$	−19.1530	−0.644184
$885$	−4.37809	−0.147168
$886$	23.6676	0.795127
$887$	37.6352	1.26367	0.631833	−	0.775104i	$-0.282303\pi$
$887$	37.6352	1.26367	0.631833	+	0.775104i	$0.282303\pi$
$888$	11.4560	0.384437
$889$	−7.89102	−0.264656
$890$	−19.7533	−0.662132
$891$	2.13101	0.0713916
$892$	−20.9472	−0.701364
$893$	24.5917	0.822929
$894$	44.0445	1.47307
$895$	−10.1031	−0.337710
$896$	53.8123	1.79774
$897$	−23.1445	−0.772773
$898$	28.5348	0.952218
$899$	−19.1513	−0.638731
$900$	−1.42041	−0.0473471
$901$	6.34771	0.211473
$902$	8.07405	0.268836
$903$	11.2636	0.374830
$904$	−12.0370	−0.400344
$905$	−2.26215	−0.0751964
$906$	−29.2603	−0.972109
$907$	1.94180	0.0644764	0.0322382	−	0.999480i	$-0.489736\pi$
$907$	1.94180	0.0644764	0.0322382	+	0.999480i	$0.489736\pi$
$908$	−3.87526	−0.128605
$909$	21.8637	0.725173
$910$	26.4259	0.876011
$911$	2.21382	0.0733470	0.0366735	−	0.999327i	$-0.488324\pi$
$911$	2.21382	0.0733470	0.0366735	+	0.999327i	$0.488324\pi$
$912$	−17.4651	−0.578327
$913$	9.59601	0.317581
$914$	16.0662	0.531424
$915$	16.3888	0.541798
$916$	−0.827141	−0.0273295
$917$	27.4712	0.907178
$918$	53.7484	1.77396
$919$	−25.1240	−0.828764	−0.414382	−	0.910103i	$-0.636002\pi$
$919$	−25.1240	−0.828764	−0.414382	+	0.910103i	$0.636002\pi$
$920$	−9.66655	−0.318697
$921$	27.0376	0.890920
$922$	40.2610	1.32593
$923$	−23.7914	−0.783102
$924$	4.88391	0.160669
$925$	5.15927	0.169636
$926$	59.4763	1.95451
$927$	8.12720	0.266932
$928$	38.0637	1.24950
$929$	24.7199	0.811034	0.405517	−	0.914087i	$-0.367091\pi$
$929$	24.7199	0.811034	0.405517	+	0.914087i	$0.367091\pi$
$930$	−5.14667	−0.168766
$931$	32.8929	1.07802
$932$	8.61993	0.282355
$933$	27.3950	0.896872
$934$	−0.725922	−0.0237529
$935$	5.70569	0.186596
$936$	9.96196	0.325617
$937$	−57.2454	−1.87013	−0.935063	−	0.354481i	$-0.884658\pi$
$937$	−57.2454	−1.87013	−0.935063	+	0.354481i	$0.884658\pi$
$938$	−90.8601	−2.96669
$939$	−0.0449636	−0.00146733
$940$	−7.99870	−0.260889
$941$	8.62268	0.281091	0.140546	−	0.990074i	$-0.455114\pi$
$941$	8.62268	0.281091	0.140546	+	0.990074i	$0.455114\pi$
$942$	27.4435	0.894158
$943$	24.9637	0.812928
$944$	−17.9770	−0.585102
$945$	−23.6181	−0.768297
$946$	−3.69254	−0.120055
$947$	−19.1888	−0.623552	−0.311776	−	0.950156i	$-0.600924\pi$
$947$	−19.1888	−0.623552	−0.311776	+	0.950156i	$0.600924\pi$
$948$	0.934989	0.0303670
$949$	3.59162	0.116589
$950$	−4.92247	−0.159706
$951$	33.8188	1.09665
$952$	−44.7250	−1.44955
$953$	4.66207	0.151019	0.0755097	−	0.997145i	$-0.475942\pi$
$953$	4.66207	0.151019	0.0755097	+	0.997145i	$0.475942\pi$
$954$	2.89643	0.0937752
$955$	4.26757	0.138095
$956$	−9.56974	−0.309507
$957$	−9.43579	−0.305016
$958$	−11.6189	−0.375390
$959$	73.4422	2.37157
$960$	−1.92694	−0.0621918
$961$	−24.9023	−0.803299
$962$	31.7435	1.02345
$963$	−10.4009	−0.335163
$964$	19.7470	0.636009
$965$	13.7135	0.441453
$966$	47.4132	1.52549
$967$	−38.6423	−1.24265	−0.621326	−	0.783552i	$-0.713406\pi$
$967$	−38.6423	−1.24265	−0.621326	+	0.783552i	$0.713406\pi$
$968$	1.82507	0.0586598
$969$	19.9471	0.640794
$970$	−25.4842	−0.818247
$971$	36.8258	1.18180	0.590898	−	0.806746i	$-0.298774\pi$
$971$	36.8258	1.18180	0.590898	+	0.806746i	$0.298774\pi$
$972$	12.9952	0.416822
$973$	−4.73666	−0.151850
$974$	63.8003	2.04429
$975$	−4.36973	−0.139943
$976$	67.2948	2.15405
$977$	11.8527	0.379202	0.189601	−	0.981861i	$-0.439281\pi$
$977$	11.8527	0.379202	0.189601	+	0.981861i	$0.439281\pi$
$978$	31.4657	1.00616
$979$	11.5309	0.368529
$980$	−10.6988	−0.341760
$981$	−23.7135	−0.757115
$982$	31.6746	1.01078
$983$	−30.6730	−0.978317	−0.489158	−	0.872195i	$-0.662696\pi$
$983$	−30.6730	−0.978317	−0.489158	+	0.872195i	$0.662696\pi$
$984$	10.4655	0.333627
$985$	−26.5484	−0.845904
$986$	−75.8050	−2.41412
$987$	−44.7209	−1.42348
$988$	−9.64572	−0.306871
$989$	−11.4167	−0.363031
$990$	2.60347	0.0827438
$991$	35.7422	1.13539	0.567694	−	0.823239i	$-0.307836\pi$
$991$	35.7422	1.13539	0.567694	+	0.823239i	$0.307836\pi$
$992$	−12.1194	−0.384792
$993$	6.48081	0.205662
$994$	48.7382	1.54588
$995$	10.4900	0.332554
$996$	−10.9117	−0.345751
$997$	35.5975	1.12738	0.563692	−	0.825985i	$-0.309380\pi$
$997$	35.5975	1.12738	0.563692	+	0.825985i	$0.309380\pi$
$998$	−14.8047	−0.468633
$999$	−28.3707	−0.897608

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.g.1.10	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.g.1.10	✓	32	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.71308 q^{2} +1.21665 q^{3} +0.934626 q^{4} -1.00000 q^{5} -2.08421 q^{6} -4.29501 q^{7} +1.82507 q^{8} -1.51977 q^{9} +O(q^{10})\)	\(q-1.71308 q^{2} +1.21665 q^{3} +0.934626 q^{4} -1.00000 q^{5} -2.08421 q^{6} -4.29501 q^{7} +1.82507 q^{8} -1.51977 q^{9} +1.71308 q^{10} -1.00000 q^{11} +1.13711 q^{12} -3.59162 q^{13} +7.35767 q^{14} -1.21665 q^{15} -4.99573 q^{16} +5.70569 q^{17} +2.60347 q^{18} +2.87347 q^{19} -0.934626 q^{20} -5.22552 q^{21} +1.71308 q^{22} +5.29655 q^{23} +2.22046 q^{24} +1.00000 q^{25} +6.15271 q^{26} -5.49897 q^{27} -4.01423 q^{28} +7.75556 q^{29} +2.08421 q^{30} -2.46936 q^{31} +4.90792 q^{32} -1.21665 q^{33} -9.77427 q^{34} +4.29501 q^{35} -1.42041 q^{36} +5.15927 q^{37} -4.92247 q^{38} -4.36973 q^{39} -1.82507 q^{40} +4.71319 q^{41} +8.95170 q^{42} -2.15550 q^{43} -0.934626 q^{44} +1.51977 q^{45} -9.07339 q^{46} +8.55818 q^{47} -6.07804 q^{48} +11.4471 q^{49} -1.71308 q^{50} +6.94182 q^{51} -3.35682 q^{52} +1.11252 q^{53} +9.42014 q^{54} +1.00000 q^{55} -7.83867 q^{56} +3.49601 q^{57} -13.2859 q^{58} +3.59848 q^{59} -1.13711 q^{60} -13.4705 q^{61} +4.23020 q^{62} +6.52741 q^{63} +1.58381 q^{64} +3.59162 q^{65} +2.08421 q^{66} -12.3490 q^{67} +5.33269 q^{68} +6.44404 q^{69} -7.35767 q^{70} +6.62414 q^{71} -2.77367 q^{72} -1.00000 q^{73} -8.83822 q^{74} +1.21665 q^{75} +2.68562 q^{76} +4.29501 q^{77} +7.48568 q^{78} +0.822249 q^{79} +4.99573 q^{80} -2.13101 q^{81} -8.07405 q^{82} -9.59601 q^{83} -4.88391 q^{84} -5.70569 q^{85} +3.69254 q^{86} +9.43579 q^{87} -1.82507 q^{88} -11.5309 q^{89} -2.60347 q^{90} +15.4260 q^{91} +4.95030 q^{92} -3.00434 q^{93} -14.6608 q^{94} -2.87347 q^{95} +5.97122 q^{96} -14.8763 q^{97} -19.6098 q^{98} +1.51977 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9}+O(q^{10}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9} + 5 q^{10} - 32 q^{11} - 24 q^{12} - q^{13} - 5 q^{14} + 7 q^{15} + 47 q^{16} - 30 q^{17} - 11 q^{18} + 16 q^{19} - 37 q^{20} + q^{21} + 5 q^{22} - 26 q^{23} - 21 q^{24} + 32 q^{25} - q^{26} - 31 q^{27} - 24 q^{28} - 10 q^{29} + 3 q^{30} - 2 q^{31} - 31 q^{32} + 7 q^{33} - 14 q^{34} + 38 q^{36} - 28 q^{37} - 63 q^{38} - 2 q^{39} + 18 q^{40} - 62 q^{41} - 9 q^{42} + 8 q^{43} - 37 q^{44} - 29 q^{45} + 19 q^{46} - 21 q^{47} - 79 q^{48} + 34 q^{49} - 5 q^{50} + 17 q^{51} + 15 q^{52} - 32 q^{53} + 5 q^{54} + 32 q^{55} - 52 q^{56} - 57 q^{57} + 4 q^{58} - 37 q^{59} + 24 q^{60} + 15 q^{61} - 22 q^{62} + 5 q^{63} + 70 q^{64} + q^{65} + 3 q^{66} - 42 q^{67} - 81 q^{68} - 8 q^{69} + 5 q^{70} - 40 q^{71} - 27 q^{72} - 32 q^{73} - 17 q^{74} - 7 q^{75} + 21 q^{76} - 105 q^{78} + 18 q^{79} - 47 q^{80} + 12 q^{81} - 70 q^{82} - 26 q^{83} + 22 q^{84} + 30 q^{85} - 45 q^{86} - 18 q^{87} + 18 q^{88} - 83 q^{89} + 11 q^{90} - 18 q^{91} - 73 q^{92} - 68 q^{93} + 56 q^{94} - 16 q^{95} - 35 q^{96} - 99 q^{97} - 61 q^{98} - 29 q^{99}+O(q^{100}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9 + 5 * q^10 - 32 * q^11 - 24 * q^12 - q^13 - 5 * q^14 + 7 * q^15 + 47 * q^16 - 30 * q^17 - 11 * q^18 + 16 * q^19 - 37 * q^20 + q^21 + 5 * q^22 - 26 * q^23 - 21 * q^24 + 32 * q^25 - q^26 - 31 * q^27 - 24 * q^28 - 10 * q^29 + 3 * q^30 - 2 * q^31 - 31 * q^32 + 7 * q^33 - 14 * q^34 + 38 * q^36 - 28 * q^37 - 63 * q^38 - 2 * q^39 + 18 * q^40 - 62 * q^41 - 9 * q^42 + 8 * q^43 - 37 * q^44 - 29 * q^45 + 19 * q^46 - 21 * q^47 - 79 * q^48 + 34 * q^49 - 5 * q^50 + 17 * q^51 + 15 * q^52 - 32 * q^53 + 5 * q^54 + 32 * q^55 - 52 * q^56 - 57 * q^57 + 4 * q^58 - 37 * q^59 + 24 * q^60 + 15 * q^61 - 22 * q^62 + 5 * q^63 + 70 * q^64 + q^65 + 3 * q^66 - 42 * q^67 - 81 * q^68 - 8 * q^69 + 5 * q^70 - 40 * q^71 - 27 * q^72 - 32 * q^73 - 17 * q^74 - 7 * q^75 + 21 * q^76 - 105 * q^78 + 18 * q^79 - 47 * q^80 + 12 * q^81 - 70 * q^82 - 26 * q^83 + 22 * q^84 + 30 * q^85 - 45 * q^86 - 18 * q^87 + 18 * q^88 - 83 * q^89 + 11 * q^90 - 18 * q^91 - 73 * q^92 - 68 * q^93 + 56 * q^94 - 16 * q^95 - 35 * q^96 - 99 * q^97 - 61 * q^98 - 29 * q^99

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