LMFDB - Embedded newform 4011.2.a.m.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, 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("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.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:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.76452 q^{2} +1.00000 q^{3} +5.64259 q^{4} +4.23744 q^{5} -2.76452 q^{6} -1.00000 q^{7} -10.0700 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.76452 q^{2} +1.00000 q^{3} +5.64259 q^{4} +4.23744 q^{5} -2.76452 q^{6} -1.00000 q^{7} -10.0700 q^{8} +1.00000 q^{9} -11.7145 q^{10} -2.70022 q^{11} +5.64259 q^{12} -6.67663 q^{13} +2.76452 q^{14} +4.23744 q^{15} +16.5536 q^{16} -0.826285 q^{17} -2.76452 q^{18} +3.05936 q^{19} +23.9101 q^{20} -1.00000 q^{21} +7.46482 q^{22} +0.807645 q^{23} -10.0700 q^{24} +12.9559 q^{25} +18.4577 q^{26} +1.00000 q^{27} -5.64259 q^{28} +3.57161 q^{29} -11.7145 q^{30} -0.0466552 q^{31} -25.6229 q^{32} -2.70022 q^{33} +2.28428 q^{34} -4.23744 q^{35} +5.64259 q^{36} -11.6029 q^{37} -8.45766 q^{38} -6.67663 q^{39} -42.6711 q^{40} +10.8515 q^{41} +2.76452 q^{42} +3.44546 q^{43} -15.2362 q^{44} +4.23744 q^{45} -2.23275 q^{46} +6.58946 q^{47} +16.5536 q^{48} +1.00000 q^{49} -35.8168 q^{50} -0.826285 q^{51} -37.6735 q^{52} -6.86921 q^{53} -2.76452 q^{54} -11.4420 q^{55} +10.0700 q^{56} +3.05936 q^{57} -9.87380 q^{58} +7.92099 q^{59} +23.9101 q^{60} +11.5097 q^{61} +0.128979 q^{62} -1.00000 q^{63} +37.7277 q^{64} -28.2918 q^{65} +7.46482 q^{66} -5.61997 q^{67} -4.66239 q^{68} +0.807645 q^{69} +11.7145 q^{70} +16.2746 q^{71} -10.0700 q^{72} +3.18825 q^{73} +32.0765 q^{74} +12.9559 q^{75} +17.2627 q^{76} +2.70022 q^{77} +18.4577 q^{78} -10.7834 q^{79} +70.1450 q^{80} +1.00000 q^{81} -29.9992 q^{82} -1.35646 q^{83} -5.64259 q^{84} -3.50133 q^{85} -9.52507 q^{86} +3.57161 q^{87} +27.1913 q^{88} +6.57078 q^{89} -11.7145 q^{90} +6.67663 q^{91} +4.55721 q^{92} -0.0466552 q^{93} -18.2167 q^{94} +12.9638 q^{95} -25.6229 q^{96} +7.76134 q^{97} -2.76452 q^{98} -2.70022 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9} + 11 q^{11} + 40 q^{12} + 13 q^{13} - 6 q^{14} + 22 q^{15} + 58 q^{16} + 17 q^{17} + 6 q^{18} + 3 q^{19} + 52 q^{20} - 29 q^{21} + 17 q^{22} + 36 q^{23} + 15 q^{24} + 57 q^{25} + 25 q^{26} + 29 q^{27} - 40 q^{28} + 20 q^{29} + 6 q^{31} + 46 q^{32} + 11 q^{33} + 18 q^{34} - 22 q^{35} + 40 q^{36} + 22 q^{37} + 8 q^{38} + 13 q^{39} + 6 q^{40} + 26 q^{41} - 6 q^{42} + 21 q^{43} + 22 q^{44} + 22 q^{45} + 28 q^{46} + 41 q^{47} + 58 q^{48} + 29 q^{49} + 18 q^{50} + 17 q^{51} + 2 q^{52} + 37 q^{53} + 6 q^{54} + 7 q^{55} - 15 q^{56} + 3 q^{57} + 9 q^{58} + 27 q^{59} + 52 q^{60} + 20 q^{61} - 12 q^{62} - 29 q^{63} + 59 q^{64} + 3 q^{65} + 17 q^{66} + 30 q^{67} + 33 q^{68} + 36 q^{69} + 68 q^{71} + 15 q^{72} + q^{73} + 21 q^{74} + 57 q^{75} + 11 q^{76} - 11 q^{77} + 25 q^{78} + 34 q^{79} + 110 q^{80} + 29 q^{81} - 49 q^{82} + 13 q^{83} - 40 q^{84} + 27 q^{85} + 35 q^{86} + 20 q^{87} + 17 q^{88} + 61 q^{89} - 13 q^{91} + 86 q^{92} + 6 q^{93} - 19 q^{94} + 25 q^{95} + 46 q^{96} - 3 q^{97} + 6 q^{98} + 11 q^{99}+O(q^{100}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9 + 11 * q^11 + 40 * q^12 + 13 * q^13 - 6 * q^14 + 22 * q^15 + 58 * q^16 + 17 * q^17 + 6 * q^18 + 3 * q^19 + 52 * q^20 - 29 * q^21 + 17 * q^22 + 36 * q^23 + 15 * q^24 + 57 * q^25 + 25 * q^26 + 29 * q^27 - 40 * q^28 + 20 * q^29 + 6 * q^31 + 46 * q^32 + 11 * q^33 + 18 * q^34 - 22 * q^35 + 40 * q^36 + 22 * q^37 + 8 * q^38 + 13 * q^39 + 6 * q^40 + 26 * q^41 - 6 * q^42 + 21 * q^43 + 22 * q^44 + 22 * q^45 + 28 * q^46 + 41 * q^47 + 58 * q^48 + 29 * q^49 + 18 * q^50 + 17 * q^51 + 2 * q^52 + 37 * q^53 + 6 * q^54 + 7 * q^55 - 15 * q^56 + 3 * q^57 + 9 * q^58 + 27 * q^59 + 52 * q^60 + 20 * q^61 - 12 * q^62 - 29 * q^63 + 59 * q^64 + 3 * q^65 + 17 * q^66 + 30 * q^67 + 33 * q^68 + 36 * q^69 + 68 * q^71 + 15 * q^72 + q^73 + 21 * q^74 + 57 * q^75 + 11 * q^76 - 11 * q^77 + 25 * q^78 + 34 * q^79 + 110 * q^80 + 29 * q^81 - 49 * q^82 + 13 * q^83 - 40 * q^84 + 27 * q^85 + 35 * q^86 + 20 * q^87 + 17 * q^88 + 61 * q^89 - 13 * q^91 + 86 * q^92 + 6 * q^93 - 19 * q^94 + 25 * q^95 + 46 * q^96 - 3 * q^97 + 6 * q^98 + 11 * 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 $

$2$	−2.76452	−1.95481	−0.977407	−	0.211368i	$-0.932208\pi$
$2$	−2.76452	−1.95481	−0.977407	+	0.211368i	$0.932208\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.64259	2.82129
$5$	4.23744	1.89504	0.947520	−	0.319698i	$-0.103581\pi$
$5$	4.23744	1.89504	0.947520	+	0.319698i	$0.103581\pi$
$6$	−2.76452	−1.12861
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−10.0700	−3.56029
$9$	1.00000	0.333333
$10$	−11.7145	−3.70445
$11$	−2.70022	−0.814147	−0.407073	−	0.913396i	$-0.633451\pi$
$11$	−2.70022	−0.814147	−0.407073	+	0.913396i	$0.633451\pi$
$12$	5.64259	1.62888
$13$	−6.67663	−1.85176	−0.925882	−	0.377814i	$-0.876676\pi$
$13$	−6.67663	−1.85176	−0.925882	+	0.377814i	$0.876676\pi$
$14$	2.76452	0.738850
$15$	4.23744	1.09410
$16$	16.5536	4.13841
$17$	−0.826285	−0.200404	−0.100202	−	0.994967i	$-0.531949\pi$
$17$	−0.826285	−0.200404	−0.100202	+	0.994967i	$0.531949\pi$
$18$	−2.76452	−0.651604
$19$	3.05936	0.701865	0.350932	−	0.936401i	$-0.385865\pi$
$19$	3.05936	0.701865	0.350932	+	0.936401i	$0.385865\pi$
$20$	23.9101	5.34646
$21$	−1.00000	−0.218218
$22$	7.46482	1.59150
$23$	0.807645	0.168406	0.0842028	−	0.996449i	$-0.473166\pi$
$23$	0.807645	0.168406	0.0842028	+	0.996449i	$0.473166\pi$
$24$	−10.0700	−2.05553
$25$	12.9559	2.59117
$26$	18.4577	3.61985
$27$	1.00000	0.192450
$28$	−5.64259	−1.06635
$29$	3.57161	0.663232	0.331616	−	0.943415i	$-0.392406\pi$
$29$	3.57161	0.663232	0.331616	+	0.943415i	$0.392406\pi$
$30$	−11.7145	−2.13876
$31$	−0.0466552	−0.00837952	−0.00418976	−	0.999991i	$-0.501334\pi$
$31$	−0.0466552	−0.00837952	−0.00418976	+	0.999991i	$0.501334\pi$
$32$	−25.6229	−4.52953
$33$	−2.70022	−0.470048
$34$	2.28428	0.391752
$35$	−4.23744	−0.716258
$36$	5.64259	0.940432
$37$	−11.6029	−1.90751	−0.953753	−	0.300591i	$-0.902816\pi$
$37$	−11.6029	−1.90751	−0.953753	+	0.300591i	$0.902816\pi$
$38$	−8.45766	−1.37201
$39$	−6.67663	−1.06912
$40$	−42.6711	−6.74689
$41$	10.8515	1.69472	0.847358	−	0.531022i	$-0.178192\pi$
$41$	10.8515	1.69472	0.847358	+	0.531022i	$0.178192\pi$
$42$	2.76452	0.426575
$43$	3.44546	0.525428	0.262714	−	0.964874i	$-0.415382\pi$
$43$	3.44546	0.525428	0.262714	+	0.964874i	$0.415382\pi$
$44$	−15.2362	−2.29695
$45$	4.23744	0.631680
$46$	−2.23275	−0.329202
$47$	6.58946	0.961171	0.480586	−	0.876948i	$-0.340424\pi$
$47$	6.58946	0.961171	0.480586	+	0.876948i	$0.340424\pi$
$48$	16.5536	2.38931
$49$	1.00000	0.142857
$50$	−35.8168	−5.06526
$51$	−0.826285	−0.115703
$52$	−37.6735	−5.22437
$53$	−6.86921	−0.943559	−0.471779	−	0.881717i	$-0.656388\pi$
$53$	−6.86921	−0.943559	−0.471779	+	0.881717i	$0.656388\pi$
$54$	−2.76452	−0.376204
$55$	−11.4420	−1.54284
$56$	10.0700	1.34566
$57$	3.05936	0.405222
$58$	−9.87380	−1.29649
$59$	7.92099	1.03122	0.515612	−	0.856822i	$-0.327564\pi$
$59$	7.92099	1.03122	0.515612	+	0.856822i	$0.327564\pi$
$60$	23.9101	3.08678
$61$	11.5097	1.47367	0.736835	−	0.676072i	$-0.236319\pi$
$61$	11.5097	1.47367	0.736835	+	0.676072i	$0.236319\pi$
$62$	0.128979	0.0163804
$63$	−1.00000	−0.125988
$64$	37.7277	4.71597
$65$	−28.2918	−3.50916
$66$	7.46482	0.918856
$67$	−5.61997	−0.686588	−0.343294	−	0.939228i	$-0.611543\pi$
$67$	−5.61997	−0.686588	−0.343294	+	0.939228i	$0.611543\pi$
$68$	−4.66239	−0.565398
$69$	0.807645	0.0972291
$70$	11.7145	1.40015
$71$	16.2746	1.93144	0.965720	−	0.259585i	$-0.0835859\pi$
$71$	16.2746	1.93144	0.965720	+	0.259585i	$0.0835859\pi$
$72$	−10.0700	−1.18676
$73$	3.18825	0.373156	0.186578	−	0.982440i	$-0.440260\pi$
$73$	3.18825	0.373156	0.186578	+	0.982440i	$0.440260\pi$
$74$	32.0765	3.72882
$75$	12.9559	1.49601
$76$	17.2627	1.98017
$77$	2.70022	0.307718
$78$	18.4577	2.08992
$79$	−10.7834	−1.21323	−0.606613	−	0.794997i	$-0.707472\pi$
$79$	−10.7834	−1.21323	−0.606613	+	0.794997i	$0.707472\pi$
$80$	70.1450	7.84245
$81$	1.00000	0.111111
$82$	−29.9992	−3.31285
$83$	−1.35646	−0.148891	−0.0744454	−	0.997225i	$-0.523719\pi$
$83$	−1.35646	−0.148891	−0.0744454	+	0.997225i	$0.523719\pi$
$84$	−5.64259	−0.615657
$85$	−3.50133	−0.379773
$86$	−9.52507	−1.02711
$87$	3.57161	0.382917
$88$	27.1913	2.89860
$89$	6.57078	0.696502	0.348251	−	0.937401i	$-0.386776\pi$
$89$	6.57078	0.696502	0.348251	+	0.937401i	$0.386776\pi$
$90$	−11.7145	−1.23482
$91$	6.67663	0.699901
$92$	4.55721	0.475122
$93$	−0.0466552	−0.00483792
$94$	−18.2167	−1.87891
$95$	12.9638	1.33006
$96$	−25.6229	−2.61512
$97$	7.76134	0.788045	0.394022	−	0.919101i	$-0.371083\pi$
$97$	7.76134	0.788045	0.394022	+	0.919101i	$0.371083\pi$
$98$	−2.76452	−0.279259
$99$	−2.70022	−0.271382
$100$	73.1047	7.31047
$101$	−0.199324	−0.0198335	−0.00991674	−	0.999951i	$-0.503157\pi$
$101$	−0.199324	−0.0198335	−0.00991674	+	0.999951i	$0.503157\pi$
$102$	2.28428	0.226178
$103$	13.8117	1.36090	0.680451	−	0.732793i	$-0.261784\pi$
$103$	13.8117	1.36090	0.680451	+	0.732793i	$0.261784\pi$
$104$	67.2338	6.59282
$105$	−4.23744	−0.413531
$106$	18.9901	1.84448
$107$	15.1513	1.46474	0.732368	−	0.680909i	$-0.238415\pi$
$107$	15.1513	1.46474	0.732368	+	0.680909i	$0.238415\pi$
$108$	5.64259	0.542958
$109$	4.52396	0.433317	0.216658	−	0.976247i	$-0.430484\pi$
$109$	4.52396	0.433317	0.216658	+	0.976247i	$0.430484\pi$
$110$	31.6317	3.01596
$111$	−11.6029	−1.10130
$112$	−16.5536	−1.56417
$113$	8.04204	0.756532	0.378266	−	0.925697i	$-0.376521\pi$
$113$	8.04204	0.756532	0.378266	+	0.925697i	$0.376521\pi$
$114$	−8.45766	−0.792133
$115$	3.42235	0.319135
$116$	20.1531	1.87117
$117$	−6.67663	−0.617254
$118$	−21.8978	−2.01585
$119$	0.826285	0.0757454
$120$	−42.6711	−3.89532
$121$	−3.70882	−0.337165
$122$	−31.8189	−2.88075
$123$	10.8515	0.978445
$124$	−0.263256	−0.0236411
$125$	33.7125	3.01534
$126$	2.76452	0.246283
$127$	−9.65014	−0.856312	−0.428156	−	0.903705i	$-0.640837\pi$
$127$	−9.65014	−0.856312	−0.428156	+	0.903705i	$0.640837\pi$
$128$	−53.0535	−4.68931
$129$	3.44546	0.303356
$130$	78.2133	6.85976
$131$	−12.6749	−1.10741	−0.553706	−	0.832712i	$-0.686787\pi$
$131$	−12.6749	−1.10741	−0.553706	+	0.832712i	$0.686787\pi$
$132$	−15.2362	−1.32614
$133$	−3.05936	−0.265280
$134$	15.5365	1.34215
$135$	4.23744	0.364700
$136$	8.32071	0.713495
$137$	5.45702	0.466225	0.233112	−	0.972450i	$-0.425109\pi$
$137$	5.45702	0.466225	0.233112	+	0.972450i	$0.425109\pi$
$138$	−2.23275	−0.190065
$139$	−21.4011	−1.81522	−0.907609	−	0.419817i	$-0.862094\pi$
$139$	−21.4011	−1.81522	−0.907609	+	0.419817i	$0.862094\pi$
$140$	−23.9101	−2.02077
$141$	6.58946	0.554933
$142$	−44.9915	−3.77561
$143$	18.0284	1.50761
$144$	16.5536	1.37947
$145$	15.1345	1.25685
$146$	−8.81398	−0.729451
$147$	1.00000	0.0824786
$148$	−65.4704	−5.38164
$149$	13.8047	1.13092	0.565462	−	0.824774i	$-0.308698\pi$
$149$	13.8047	1.13092	0.565462	+	0.824774i	$0.308698\pi$
$150$	−35.8168	−2.92443
$151$	−1.56330	−0.127220	−0.0636100	−	0.997975i	$-0.520261\pi$
$151$	−1.56330	−0.127220	−0.0636100	+	0.997975i	$0.520261\pi$
$152$	−30.8078	−2.49884
$153$	−0.826285	−0.0668012
$154$	−7.46482	−0.601532
$155$	−0.197698	−0.0158795
$156$	−37.6735	−3.01629
$157$	2.46473	0.196707	0.0983534	−	0.995152i	$-0.468642\pi$
$157$	2.46473	0.196707	0.0983534	+	0.995152i	$0.468642\pi$
$158$	29.8110	2.37163
$159$	−6.86921	−0.544764
$160$	−108.575	−8.58363
$161$	−0.807645	−0.0636514
$162$	−2.76452	−0.217201
$163$	18.4794	1.44742	0.723708	−	0.690106i	$-0.242436\pi$
$163$	18.4794	1.44742	0.723708	+	0.690106i	$0.242436\pi$
$164$	61.2304	4.78129
$165$	−11.4420	−0.890759
$166$	3.74997	0.291054
$167$	16.9740	1.31349	0.656746	−	0.754112i	$-0.271932\pi$
$167$	16.9740	1.31349	0.656746	+	0.754112i	$0.271932\pi$
$168$	10.0700	0.776919
$169$	31.5774	2.42903
$170$	9.67951	0.742385
$171$	3.05936	0.233955
$172$	19.4413	1.48239
$173$	3.37925	0.256920	0.128460	−	0.991715i	$-0.458997\pi$
$173$	3.37925	0.256920	0.128460	+	0.991715i	$0.458997\pi$
$174$	−9.87380	−0.748531
$175$	−12.9559	−0.979372
$176$	−44.6984	−3.36927
$177$	7.92099	0.595378
$178$	−18.1651	−1.36153
$179$	−8.47469	−0.633428	−0.316714	−	0.948521i	$-0.602580\pi$
$179$	−8.47469	−0.633428	−0.316714	+	0.948521i	$0.602580\pi$
$180$	23.9101	1.78215
$181$	12.5898	0.935790	0.467895	−	0.883784i	$-0.345013\pi$
$181$	12.5898	0.935790	0.467895	+	0.883784i	$0.345013\pi$
$182$	−18.4577	−1.36818
$183$	11.5097	0.850824
$184$	−8.13301	−0.599573
$185$	−49.1666	−3.61480
$186$	0.128979	0.00945722
$187$	2.23115	0.163158
$188$	37.1816	2.71175
$189$	−1.00000	−0.0727393
$190$	−35.8388	−2.60002
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	37.7277	2.72277
$193$	2.18383	0.157195	0.0785977	−	0.996906i	$-0.474956\pi$
$193$	2.18383	0.157195	0.0785977	+	0.996906i	$0.474956\pi$
$194$	−21.4564	−1.54048
$195$	−28.2918	−2.02602
$196$	5.64259	0.403042
$197$	20.2723	1.44434	0.722170	−	0.691715i	$-0.243145\pi$
$197$	20.2723	1.44434	0.722170	+	0.691715i	$0.243145\pi$
$198$	7.46482	0.530501
$199$	7.76964	0.550775	0.275387	−	0.961333i	$-0.411194\pi$
$199$	7.76964	0.550775	0.275387	+	0.961333i	$0.411194\pi$
$200$	−130.466	−9.22533
$201$	−5.61997	−0.396402
$202$	0.551036	0.0387708
$203$	−3.57161	−0.250678
$204$	−4.66239	−0.326432
$205$	45.9825	3.21155
$206$	−38.1826	−2.66031
$207$	0.807645	0.0561352
$208$	−110.522	−7.66335
$209$	−8.26093	−0.571421
$210$	11.7145	0.808377
$211$	−23.9605	−1.64951	−0.824753	−	0.565494i	$-0.808686\pi$
$211$	−23.9605	−1.64951	−0.824753	+	0.565494i	$0.808686\pi$
$212$	−38.7601	−2.66206
$213$	16.2746	1.11512
$214$	−41.8862	−2.86328
$215$	14.5999	0.995707
$216$	−10.0700	−0.685178
$217$	0.0466552	0.00316716
$218$	−12.5066	−0.847054
$219$	3.18825	0.215442
$220$	−64.5625	−4.35281
$221$	5.51680	0.371100
$222$	32.0765	2.15283
$223$	−9.25538	−0.619786	−0.309893	−	0.950771i	$-0.600293\pi$
$223$	−9.25538	−0.619786	−0.309893	+	0.950771i	$0.600293\pi$
$224$	25.6229	1.71200
$225$	12.9559	0.863725
$226$	−22.2324	−1.47888
$227$	−5.43176	−0.360519	−0.180259	−	0.983619i	$-0.557694\pi$
$227$	−5.43176	−0.360519	−0.180259	+	0.983619i	$0.557694\pi$
$228$	17.2627	1.14325
$229$	−19.6049	−1.29552	−0.647762	−	0.761842i	$-0.724295\pi$
$229$	−19.6049	−1.29552	−0.647762	+	0.761842i	$0.724295\pi$
$230$	−9.46116	−0.623850
$231$	2.70022	0.177661
$232$	−35.9662	−2.36130
$233$	21.2819	1.39422	0.697111	−	0.716964i	$-0.254469\pi$
$233$	21.2819	1.39422	0.697111	+	0.716964i	$0.254469\pi$
$234$	18.4577	1.20662
$235$	27.9224	1.82146
$236$	44.6949	2.90939
$237$	−10.7834	−0.700457
$238$	−2.28428	−0.148068
$239$	−9.58324	−0.619888	−0.309944	−	0.950755i	$-0.600310\pi$
$239$	−9.58324	−0.619888	−0.309944	+	0.950755i	$0.600310\pi$
$240$	70.1450	4.52784
$241$	−19.1630	−1.23440	−0.617200	−	0.786807i	$-0.711733\pi$
$241$	−19.1630	−1.23440	−0.617200	+	0.786807i	$0.711733\pi$
$242$	10.2531	0.659095
$243$	1.00000	0.0641500
$244$	64.9447	4.15766
$245$	4.23744	0.270720
$246$	−29.9992	−1.91268
$247$	−20.4262	−1.29969
$248$	0.469819	0.0298335
$249$	−1.35646	−0.0859622
$250$	−93.1990	−5.89442
$251$	1.10916	0.0700094	0.0350047	−	0.999387i	$-0.488855\pi$
$251$	1.10916	0.0700094	0.0350047	+	0.999387i	$0.488855\pi$
$252$	−5.64259	−0.355450
$253$	−2.18082	−0.137107
$254$	26.6780	1.67393
$255$	−3.50133	−0.219262
$256$	71.2121	4.45076
$257$	3.75758	0.234391	0.117196	−	0.993109i	$-0.462610\pi$
$257$	3.75758	0.234391	0.117196	+	0.993109i	$0.462610\pi$
$258$	−9.52507	−0.593005
$259$	11.6029	0.720970
$260$	−159.639	−9.90039
$261$	3.57161	0.221077
$262$	35.0401	2.16478
$263$	0.860818	0.0530803	0.0265402	−	0.999648i	$-0.491551\pi$
$263$	0.860818	0.0530803	0.0265402	+	0.999648i	$0.491551\pi$
$264$	27.1913	1.67351
$265$	−29.1078	−1.78808
$266$	8.45766	0.518573
$267$	6.57078	0.402125
$268$	−31.7112	−1.93707
$269$	9.23324	0.562960	0.281480	−	0.959567i	$-0.409175\pi$
$269$	9.23324	0.562960	0.281480	+	0.959567i	$0.409175\pi$
$270$	−11.7145	−0.712921
$271$	13.6135	0.826959	0.413479	−	0.910513i	$-0.364313\pi$
$271$	13.6135	0.826959	0.413479	+	0.910513i	$0.364313\pi$
$272$	−13.6780	−0.829352
$273$	6.67663	0.404088
$274$	−15.0861	−0.911382
$275$	−34.9837	−2.10960
$276$	4.55721	0.274312
$277$	8.02131	0.481954	0.240977	−	0.970531i	$-0.422532\pi$
$277$	8.02131	0.481954	0.240977	+	0.970531i	$0.422532\pi$
$278$	59.1638	3.54841
$279$	−0.0466552	−0.00279317
$280$	42.6711	2.55009
$281$	−20.0619	−1.19679	−0.598395	−	0.801201i	$-0.704195\pi$
$281$	−20.0619	−1.19679	−0.598395	+	0.801201i	$0.704195\pi$
$282$	−18.2167	−1.08479
$283$	14.2707	0.848306	0.424153	−	0.905591i	$-0.360572\pi$
$283$	14.2707	0.848306	0.424153	+	0.905591i	$0.360572\pi$
$284$	91.8309	5.44916
$285$	12.9638	0.767911
$286$	−49.8398	−2.94709
$287$	−10.8515	−0.640543
$288$	−25.6229	−1.50984
$289$	−16.3173	−0.959838
$290$	−41.8396	−2.45691
$291$	7.76134	0.454978
$292$	17.9900	1.05278
$293$	16.3062	0.952618	0.476309	−	0.879278i	$-0.341974\pi$
$293$	16.3062	0.952618	0.476309	+	0.879278i	$0.341974\pi$
$294$	−2.76452	−0.161230
$295$	33.5647	1.95421
$296$	116.842	6.79128
$297$	−2.70022	−0.156683
$298$	−38.1634	−2.21075
$299$	−5.39235	−0.311848
$300$	73.1047	4.22070
$301$	−3.44546	−0.198593
$302$	4.32179	0.248691
$303$	−0.199324	−0.0114509
$304$	50.6435	2.90460
$305$	48.7718	2.79266
$306$	2.28428	0.130584
$307$	10.1327	0.578304	0.289152	−	0.957283i	$-0.406627\pi$
$307$	10.1327	0.578304	0.289152	+	0.957283i	$0.406627\pi$
$308$	15.2362	0.868165
$309$	13.8117	0.785718
$310$	0.546542	0.0310415
$311$	−15.3731	−0.871726	−0.435863	−	0.900013i	$-0.643557\pi$
$311$	−15.3731	−0.871726	−0.435863	+	0.900013i	$0.643557\pi$
$312$	67.2338	3.80636
$313$	−3.42572	−0.193633	−0.0968166	−	0.995302i	$-0.530866\pi$
$313$	−3.42572	−0.193633	−0.0968166	+	0.995302i	$0.530866\pi$
$314$	−6.81380	−0.384525
$315$	−4.23744	−0.238753
$316$	−60.8463	−3.42287
$317$	−0.689591	−0.0387313	−0.0193657	−	0.999812i	$-0.506165\pi$
$317$	−0.689591	−0.0387313	−0.0193657	+	0.999812i	$0.506165\pi$
$318$	18.9901	1.06491
$319$	−9.64413	−0.539968
$320$	159.869	8.93695
$321$	15.1513	0.845666
$322$	2.23275	0.124427
$323$	−2.52790	−0.140656
$324$	5.64259	0.313477
$325$	−86.5015	−4.79824
$326$	−51.0867	−2.82943
$327$	4.52396	0.250176
$328$	−109.275	−6.03368
$329$	−6.58946	−0.363289
$330$	31.6317	1.74127
$331$	−13.0657	−0.718154	−0.359077	−	0.933308i	$-0.616908\pi$
$331$	−13.0657	−0.718154	−0.359077	+	0.933308i	$0.616908\pi$
$332$	−7.65395	−0.420065
$333$	−11.6029	−0.635835
$334$	−46.9252	−2.56763
$335$	−23.8143	−1.30111
$336$	−16.5536	−0.903075
$337$	−32.6188	−1.77686	−0.888430	−	0.459012i	$-0.848204\pi$
$337$	−32.6188	−1.77686	−0.888430	+	0.459012i	$0.848204\pi$
$338$	−87.2963	−4.74830
$339$	8.04204	0.436784
$340$	−19.7566	−1.07145
$341$	0.125979	0.00682215
$342$	−8.45766	−0.457338
$343$	−1.00000	−0.0539949
$344$	−34.6959	−1.87068
$345$	3.42235	0.184253
$346$	−9.34202	−0.502230
$347$	−6.21559	−0.333670	−0.166835	−	0.985985i	$-0.553355\pi$
$347$	−6.21559	−0.333670	−0.166835	+	0.985985i	$0.553355\pi$
$348$	20.1531	1.08032
$349$	19.5954	1.04892	0.524460	−	0.851435i	$-0.324267\pi$
$349$	19.5954	1.04892	0.524460	+	0.851435i	$0.324267\pi$
$350$	35.8168	1.91449
$351$	−6.67663	−0.356372
$352$	69.1873	3.68770
$353$	−28.3122	−1.50690	−0.753452	−	0.657503i	$-0.771613\pi$
$353$	−28.3122	−1.50690	−0.753452	+	0.657503i	$0.771613\pi$
$354$	−21.8978	−1.16385
$355$	68.9626	3.66016
$356$	37.0762	1.96504
$357$	0.826285	0.0437316
$358$	23.4285	1.23823
$359$	2.69296	0.142129	0.0710646	−	0.997472i	$-0.477360\pi$
$359$	2.69296	0.142129	0.0710646	+	0.997472i	$0.477360\pi$
$360$	−42.6711	−2.24896
$361$	−9.64033	−0.507386
$362$	−34.8047	−1.82929
$363$	−3.70882	−0.194663
$364$	37.6735	1.97463
$365$	13.5100	0.707146
$366$	−31.8189	−1.66320
$367$	18.7201	0.977182	0.488591	−	0.872513i	$-0.337511\pi$
$367$	18.7201	0.977182	0.488591	+	0.872513i	$0.337511\pi$
$368$	13.3695	0.696932
$369$	10.8515	0.564905
$370$	135.922	7.06626
$371$	6.86921	0.356632
$372$	−0.263256	−0.0136492
$373$	−0.134406	−0.00695927	−0.00347964	−	0.999994i	$-0.501108\pi$
$373$	−0.134406	−0.00695927	−0.00347964	+	0.999994i	$0.501108\pi$
$374$	−6.16807	−0.318943
$375$	33.7125	1.74091
$376$	−66.3560	−3.42205
$377$	−23.8463	−1.22815
$378$	2.76452	0.142192
$379$	−8.70471	−0.447131	−0.223565	−	0.974689i	$-0.571770\pi$
$379$	−8.70471	−0.447131	−0.223565	+	0.974689i	$0.571770\pi$
$380$	73.1496	3.75249
$381$	−9.65014	−0.494392
$382$	2.76452	0.141445
$383$	−10.2546	−0.523986	−0.261993	−	0.965070i	$-0.584380\pi$
$383$	−10.2546	−0.523986	−0.261993	+	0.965070i	$0.584380\pi$
$384$	−53.0535	−2.70737
$385$	11.4420	0.583139
$386$	−6.03725	−0.307288
$387$	3.44546	0.175143
$388$	43.7941	2.22331
$389$	14.0827	0.714019	0.357009	−	0.934101i	$-0.383796\pi$
$389$	14.0827	0.714019	0.357009	+	0.934101i	$0.383796\pi$
$390$	78.2133	3.96048
$391$	−0.667345	−0.0337491
$392$	−10.0700	−0.508613
$393$	−12.6749	−0.639365
$394$	−56.0432	−2.82342
$395$	−45.6940	−2.29911
$396$	−15.2362	−0.765649
$397$	25.2723	1.26838	0.634191	−	0.773176i	$-0.281333\pi$
$397$	25.2723	1.26838	0.634191	+	0.773176i	$0.281333\pi$
$398$	−21.4793	−1.07666
$399$	−3.05936	−0.153159
$400$	214.467	10.7233
$401$	16.6661	0.832263	0.416132	−	0.909304i	$-0.363386\pi$
$401$	16.6661	0.832263	0.416132	+	0.909304i	$0.363386\pi$
$402$	15.5365	0.774892
$403$	0.311499	0.0155169
$404$	−1.12470	−0.0559561
$405$	4.23744	0.210560
$406$	9.87380	0.490029
$407$	31.3304	1.55299
$408$	8.32071	0.411937
$409$	36.6006	1.80979	0.904893	−	0.425640i	$-0.139951\pi$
$409$	36.6006	1.80979	0.904893	+	0.425640i	$0.139951\pi$
$410$	−127.120	−6.27799
$411$	5.45702	0.269175
$412$	77.9335	3.83951
$413$	−7.92099	−0.389766
$414$	−2.23275	−0.109734
$415$	−5.74792	−0.282154
$416$	171.074	8.38761
$417$	−21.4011	−1.04802
$418$	22.8375	1.11702
$419$	−7.08576	−0.346162	−0.173081	−	0.984908i	$-0.555372\pi$
$419$	−7.08576	−0.346162	−0.173081	+	0.984908i	$0.555372\pi$
$420$	−23.9101	−1.16669
$421$	−5.68251	−0.276949	−0.138474	−	0.990366i	$-0.544220\pi$
$421$	−5.68251	−0.276949	−0.138474	+	0.990366i	$0.544220\pi$
$422$	66.2392	3.22448
$423$	6.58946	0.320390
$424$	69.1731	3.35934
$425$	−10.7052	−0.519281
$426$	−44.9915	−2.17985
$427$	−11.5097	−0.556995
$428$	85.4928	4.13245
$429$	18.0284	0.870417
$430$	−40.3619	−1.94642
$431$	−37.5602	−1.80921	−0.904606	−	0.426249i	$-0.859835\pi$
$431$	−37.5602	−1.80921	−0.904606	+	0.426249i	$0.859835\pi$
$432$	16.5536	0.796437
$433$	−33.6048	−1.61494	−0.807472	−	0.589906i	$-0.799165\pi$
$433$	−33.6048	−1.61494	−0.807472	+	0.589906i	$0.799165\pi$
$434$	−0.128979	−0.00619121
$435$	15.1345	0.725643
$436$	25.5269	1.22251
$437$	2.47088	0.118198
$438$	−8.81398	−0.421148
$439$	13.2577	0.632755	0.316378	−	0.948633i	$-0.397533\pi$
$439$	13.2577	0.632755	0.316378	+	0.948633i	$0.397533\pi$
$440$	115.221	5.49296
$441$	1.00000	0.0476190
$442$	−15.2513	−0.725431
$443$	−29.0827	−1.38176	−0.690880	−	0.722970i	$-0.742777\pi$
$443$	−29.0827	−1.38176	−0.690880	+	0.722970i	$0.742777\pi$
$444$	−65.4704	−3.10709
$445$	27.8433	1.31990
$446$	25.5867	1.21157
$447$	13.8047	0.652940
$448$	−37.7277	−1.78247
$449$	−17.3445	−0.818537	−0.409268	−	0.912414i	$-0.634216\pi$
$449$	−17.3445	−0.818537	−0.409268	+	0.912414i	$0.634216\pi$
$450$	−35.8168	−1.68842
$451$	−29.3014	−1.37975
$452$	45.3779	2.13440
$453$	−1.56330	−0.0734505
$454$	15.0162	0.704747
$455$	28.2918	1.32634
$456$	−30.8078	−1.44271
$457$	1.14937	0.0537651	0.0268825	−	0.999639i	$-0.491442\pi$
$457$	1.14937	0.0537651	0.0268825	+	0.999639i	$0.491442\pi$
$458$	54.1981	2.53251
$459$	−0.826285	−0.0385677
$460$	19.3109	0.900375
$461$	31.9254	1.48691	0.743457	−	0.668784i	$-0.233185\pi$
$461$	31.9254	1.48691	0.743457	+	0.668784i	$0.233185\pi$
$462$	−7.46482	−0.347295
$463$	−7.45475	−0.346452	−0.173226	−	0.984882i	$-0.555419\pi$
$463$	−7.45475	−0.346452	−0.173226	+	0.984882i	$0.555419\pi$
$464$	59.1232	2.74472
$465$	−0.197698	−0.00916804
$466$	−58.8342	−2.72544
$467$	−19.3236	−0.894189	−0.447094	−	0.894487i	$-0.647541\pi$
$467$	−19.3236	−0.894189	−0.447094	+	0.894487i	$0.647541\pi$
$468$	−37.6735	−1.74146
$469$	5.61997	0.259506
$470$	−77.1922	−3.56061
$471$	2.46473	0.113569
$472$	−79.7646	−3.67146
$473$	−9.30351	−0.427776
$474$	29.8110	1.36926
$475$	39.6366	1.81865
$476$	4.66239	0.213700
$477$	−6.86921	−0.314520
$478$	26.4931	1.21177
$479$	7.52525	0.343837	0.171919	−	0.985111i	$-0.445003\pi$
$479$	7.52525	0.343837	0.171919	+	0.985111i	$0.445003\pi$
$480$	−108.575	−4.95576
$481$	77.4683	3.53225
$482$	52.9767	2.41302
$483$	−0.807645	−0.0367491
$484$	−20.9273	−0.951243
$485$	32.8882	1.49338
$486$	−2.76452	−0.125401
$487$	−29.7716	−1.34908	−0.674541	−	0.738237i	$-0.735658\pi$
$487$	−29.7716	−1.34908	−0.674541	+	0.738237i	$0.735658\pi$
$488$	−115.903	−5.24670
$489$	18.4794	0.835666
$490$	−11.7145	−0.529207
$491$	−18.3564	−0.828413	−0.414206	−	0.910183i	$-0.635941\pi$
$491$	−18.3564	−0.828413	−0.414206	+	0.910183i	$0.635941\pi$
$492$	61.2304	2.76048
$493$	−2.95117	−0.132914
$494$	56.4687	2.54065
$495$	−11.4420	−0.514280
$496$	−0.772313	−0.0346779
$497$	−16.2746	−0.730016
$498$	3.74997	0.168040
$499$	41.1114	1.84040	0.920200	−	0.391450i	$-0.128026\pi$
$499$	41.1114	1.84040	0.920200	+	0.391450i	$0.128026\pi$
$500$	190.226	8.50715
$501$	16.9740	0.758345
$502$	−3.06629	−0.136855
$503$	−4.02243	−0.179351	−0.0896756	−	0.995971i	$-0.528583\pi$
$503$	−4.02243	−0.179351	−0.0896756	+	0.995971i	$0.528583\pi$
$504$	10.0700	0.448555
$505$	−0.844623	−0.0375852
$506$	6.02893	0.268018
$507$	31.5774	1.40240
$508$	−54.4518	−2.41591
$509$	28.8841	1.28026	0.640132	−	0.768265i	$-0.278880\pi$
$509$	28.8841	1.28026	0.640132	+	0.768265i	$0.278880\pi$
$510$	9.67951	0.428616
$511$	−3.18825	−0.141040
$512$	−90.7606	−4.01109
$513$	3.05936	0.135074
$514$	−10.3879	−0.458191
$515$	58.5260	2.57896
$516$	19.4413	0.855857
$517$	−17.7930	−0.782534
$518$	−32.0765	−1.40936
$519$	3.37925	0.148333
$520$	284.899	12.4936
$521$	7.74715	0.339409	0.169704	−	0.985495i	$-0.445719\pi$
$521$	7.74715	0.339409	0.169704	+	0.985495i	$0.445719\pi$
$522$	−9.87380	−0.432165
$523$	4.71002	0.205955	0.102977	−	0.994684i	$-0.467163\pi$
$523$	4.71002	0.205955	0.102977	+	0.994684i	$0.467163\pi$
$524$	−71.5193	−3.12434
$525$	−12.9559	−0.565441
$526$	−2.37975	−0.103762
$527$	0.0385505	0.00167929
$528$	−44.6984	−1.94525
$529$	−22.3477	−0.971640
$530$	80.4693	3.49536
$531$	7.92099	0.343742
$532$	−17.2627	−0.748433
$533$	−72.4513	−3.13821
$534$	−18.1651	−0.786080
$535$	64.2029	2.77573
$536$	56.5932	2.44445
$537$	−8.47469	−0.365710
$538$	−25.5255	−1.10048
$539$	−2.70022	−0.116307
$540$	23.9101	1.02893
$541$	35.4673	1.52486	0.762429	−	0.647072i	$-0.224007\pi$
$541$	35.4673	1.52486	0.762429	+	0.647072i	$0.224007\pi$
$542$	−37.6347	−1.61655
$543$	12.5898	0.540279
$544$	21.1718	0.907733
$545$	19.1700	0.821153
$546$	−18.4577	−0.789916
$547$	−5.56809	−0.238074	−0.119037	−	0.992890i	$-0.537981\pi$
$547$	−5.56809	−0.238074	−0.119037	+	0.992890i	$0.537981\pi$
$548$	30.7917	1.31536
$549$	11.5097	0.491223
$550$	96.7132	4.12386
$551$	10.9268	0.465499
$552$	−8.13301	−0.346164
$553$	10.7834	0.458557
$554$	−22.1751	−0.942129
$555$	−49.1666	−2.08701
$556$	−120.758	−5.12126
$557$	3.30906	0.140209	0.0701047	−	0.997540i	$-0.477667\pi$
$557$	3.30906	0.140209	0.0701047	+	0.997540i	$0.477667\pi$
$558$	0.128979	0.00546013
$559$	−23.0041	−0.972969
$560$	−70.1450	−2.96417
$561$	2.23115	0.0941993
$562$	55.4615	2.33950
$563$	−23.6178	−0.995372	−0.497686	−	0.867357i	$-0.665817\pi$
$563$	−23.6178	−0.995372	−0.497686	+	0.867357i	$0.665817\pi$
$564$	37.1816	1.56563
$565$	34.0776	1.43366
$566$	−39.4517	−1.65828
$567$	−1.00000	−0.0419961
$568$	−163.886	−6.87649
$569$	−21.0514	−0.882521	−0.441260	−	0.897379i	$-0.645468\pi$
$569$	−21.0514	−0.882521	−0.441260	+	0.897379i	$0.645468\pi$
$570$	−35.8388	−1.50112
$571$	17.0316	0.712752	0.356376	−	0.934343i	$-0.384012\pi$
$571$	17.0316	0.712752	0.356376	+	0.934343i	$0.384012\pi$
$572$	101.727	4.25340
$573$	−1.00000	−0.0417756
$574$	29.9992	1.25214
$575$	10.4637	0.436368
$576$	37.7277	1.57199
$577$	9.22855	0.384189	0.192095	−	0.981376i	$-0.438472\pi$
$577$	9.22855	0.384189	0.192095	+	0.981376i	$0.438472\pi$
$578$	45.1094	1.87630
$579$	2.18383	0.0907568
$580$	85.3976	3.54594
$581$	1.35646	0.0562755
$582$	−21.4564	−0.889397
$583$	18.5484	0.768195
$584$	−32.1057	−1.32854
$585$	−28.2918	−1.16972
$586$	−45.0789	−1.86219
$587$	5.06503	0.209056	0.104528	−	0.994522i	$-0.466667\pi$
$587$	5.06503	0.209056	0.104528	+	0.994522i	$0.466667\pi$
$588$	5.64259	0.232696
$589$	−0.142735	−0.00588129
$590$	−92.7904	−3.82012
$591$	20.2723	0.833890
$592$	−192.070	−7.89404
$593$	0.425021	0.0174535	0.00872675	−	0.999962i	$-0.497222\pi$
$593$	0.425021	0.0174535	0.00872675	+	0.999962i	$0.497222\pi$
$594$	7.46482	0.306285
$595$	3.50133	0.143541
$596$	77.8942	3.19067
$597$	7.76964	0.317990
$598$	14.9073	0.609604
$599$	−35.4573	−1.44875	−0.724373	−	0.689408i	$-0.757871\pi$
$599$	−35.4573	−1.44875	−0.724373	+	0.689408i	$0.757871\pi$
$600$	−130.466	−5.32625
$601$	4.44706	0.181399	0.0906996	−	0.995878i	$-0.471090\pi$
$601$	4.44706	0.181399	0.0906996	+	0.995878i	$0.471090\pi$
$602$	9.52507	0.388213
$603$	−5.61997	−0.228863
$604$	−8.82109	−0.358925
$605$	−15.7159	−0.638942
$606$	0.551036	0.0223843
$607$	−8.45148	−0.343035	−0.171517	−	0.985181i	$-0.554867\pi$
$607$	−8.45148	−0.343035	−0.171517	+	0.985181i	$0.554867\pi$
$608$	−78.3895	−3.17911
$609$	−3.57161	−0.144729
$610$	−134.831	−5.45914
$611$	−43.9954	−1.77986
$612$	−4.66239	−0.188466
$613$	−3.28309	−0.132603	−0.0663014	−	0.997800i	$-0.521120\pi$
$613$	−3.28309	−0.132603	−0.0663014	+	0.997800i	$0.521120\pi$
$614$	−28.0121	−1.13048
$615$	45.9825	1.85419
$616$	−27.1913	−1.09557
$617$	−26.3533	−1.06094	−0.530472	−	0.847702i	$-0.677985\pi$
$617$	−26.3533	−1.06094	−0.530472	+	0.847702i	$0.677985\pi$
$618$	−38.1826	−1.53593
$619$	−1.45751	−0.0585824	−0.0292912	−	0.999571i	$-0.509325\pi$
$619$	−1.45751	−0.0585824	−0.0292912	+	0.999571i	$0.509325\pi$
$620$	−1.11553	−0.0448008
$621$	0.807645	0.0324097
$622$	42.4992	1.70406
$623$	−6.57078	−0.263253
$624$	−110.522	−4.42444
$625$	78.0752	3.12301
$626$	9.47049	0.378517
$627$	−8.26093	−0.329910
$628$	13.9075	0.554968
$629$	9.58731	0.382271
$630$	11.7145	0.466717
$631$	−20.2289	−0.805300	−0.402650	−	0.915354i	$-0.631911\pi$
$631$	−20.2289	−0.805300	−0.402650	+	0.915354i	$0.631911\pi$
$632$	108.589	4.31944
$633$	−23.9605	−0.952342
$634$	1.90639	0.0757125
$635$	−40.8919	−1.62274
$636$	−38.7601	−1.53694
$637$	−6.67663	−0.264538
$638$	26.6614	1.05554
$639$	16.2746	0.643813
$640$	−224.811	−8.88643
$641$	−11.2059	−0.442606	−0.221303	−	0.975205i	$-0.571031\pi$
$641$	−11.2059	−0.442606	−0.221303	+	0.975205i	$0.571031\pi$
$642$	−41.8862	−1.65312
$643$	15.0178	0.592246	0.296123	−	0.955150i	$-0.404306\pi$
$643$	15.0178	0.592246	0.296123	+	0.955150i	$0.404306\pi$
$644$	−4.55721	−0.179579
$645$	14.5999	0.574872
$646$	6.98844	0.274957
$647$	−10.3683	−0.407622	−0.203811	−	0.979010i	$-0.565333\pi$
$647$	−10.3683	−0.407622	−0.203811	+	0.979010i	$0.565333\pi$
$648$	−10.0700	−0.395588
$649$	−21.3884	−0.839568
$650$	239.135	9.37966
$651$	0.0466552	0.00182856
$652$	104.272	4.08359
$653$	−17.7736	−0.695537	−0.347768	−	0.937581i	$-0.613060\pi$
$653$	−17.7736	−0.695537	−0.347768	+	0.937581i	$0.613060\pi$
$654$	−12.5066	−0.489047
$655$	−53.7091	−2.09859
$656$	179.631	7.01343
$657$	3.18825	0.124385
$658$	18.2167	0.710161
$659$	−41.1867	−1.60441	−0.802203	−	0.597051i	$-0.796339\pi$
$659$	−41.1867	−1.60441	−0.802203	+	0.597051i	$0.796339\pi$
$660$	−64.5625	−2.51309
$661$	−29.9271	−1.16403	−0.582015	−	0.813178i	$-0.697735\pi$
$661$	−29.9271	−1.16403	−0.582015	+	0.813178i	$0.697735\pi$
$662$	36.1203	1.40386
$663$	5.51680	0.214255
$664$	13.6596	0.530095
$665$	−12.9638	−0.502716
$666$	32.0765	1.24294
$667$	2.88460	0.111692
$668$	95.7776	3.70575
$669$	−9.25538	−0.357834
$670$	65.8351	2.54343
$671$	−31.0788	−1.19978
$672$	25.6229	0.988424
$673$	6.78759	0.261642	0.130821	−	0.991406i	$-0.458239\pi$
$673$	6.78759	0.261642	0.130821	+	0.991406i	$0.458239\pi$
$674$	90.1755	3.47343
$675$	12.9559	0.498672
$676$	178.178	6.85300
$677$	39.5240	1.51903	0.759516	−	0.650489i	$-0.225436\pi$
$677$	39.5240	1.51903	0.759516	+	0.650489i	$0.225436\pi$
$678$	−22.2324	−0.853831
$679$	−7.76134	−0.297853
$680$	35.2585	1.35210
$681$	−5.43176	−0.208146
$682$	−0.348272	−0.0133360
$683$	−19.8756	−0.760518	−0.380259	−	0.924880i	$-0.624165\pi$
$683$	−19.8756	−0.760518	−0.380259	+	0.924880i	$0.624165\pi$
$684$	17.2627	0.660056
$685$	23.1238	0.883514
$686$	2.76452	0.105550
$687$	−19.6049	−0.747972
$688$	57.0350	2.17444
$689$	45.8632	1.74725
$690$	−9.46116	−0.360180
$691$	7.16184	0.272449	0.136225	−	0.990678i	$-0.456503\pi$
$691$	7.16184	0.272449	0.136225	+	0.990678i	$0.456503\pi$
$692$	19.0677	0.724847
$693$	2.70022	0.102573
$694$	17.1831	0.652263
$695$	−90.6858	−3.43991
$696$	−35.9662	−1.36330
$697$	−8.96642	−0.339627
$698$	−54.1721	−2.05044
$699$	21.2819	0.804954
$700$	−73.1047	−2.76310
$701$	−31.8464	−1.20282	−0.601410	−	0.798940i	$-0.705394\pi$
$701$	−31.8464	−1.20282	−0.601410	+	0.798940i	$0.705394\pi$
$702$	18.4577	0.696641
$703$	−35.4974	−1.33881
$704$	−101.873	−3.83949
$705$	27.9224	1.05162
$706$	78.2696	2.94572
$707$	0.199324	0.00749635
$708$	44.6949	1.67974
$709$	26.4999	0.995223	0.497611	−	0.867400i	$-0.334211\pi$
$709$	26.4999	0.995223	0.497611	+	0.867400i	$0.334211\pi$
$710$	−190.649	−7.15492
$711$	−10.7834	−0.404409
$712$	−66.1679	−2.47975
$713$	−0.0376808	−0.00141116
$714$	−2.28428	−0.0854872
$715$	76.3940	2.85697
$716$	−47.8192	−1.78709
$717$	−9.58324	−0.357893
$718$	−7.44476	−0.277836
$719$	−49.0731	−1.83012	−0.915058	−	0.403322i	$-0.867856\pi$
$719$	−49.0731	−1.83012	−0.915058	+	0.403322i	$0.867856\pi$
$720$	70.1450	2.61415
$721$	−13.8117	−0.514373
$722$	26.6509	0.991845
$723$	−19.1630	−0.712681
$724$	71.0389	2.64014
$725$	46.2733	1.71855
$726$	10.2531	0.380529
$727$	−48.1223	−1.78476	−0.892379	−	0.451287i	$-0.850965\pi$
$727$	−48.1223	−1.78476	−0.892379	+	0.451287i	$0.850965\pi$
$728$	−67.2338	−2.49185
$729$	1.00000	0.0370370
$730$	−37.3487	−1.38234
$731$	−2.84694	−0.105298
$732$	64.9447	2.40043
$733$	−3.33839	−0.123306	−0.0616532	−	0.998098i	$-0.519637\pi$
$733$	−3.33839	−0.123306	−0.0616532	+	0.998098i	$0.519637\pi$
$734$	−51.7522	−1.91021
$735$	4.23744	0.156300
$736$	−20.6942	−0.762798
$737$	15.1751	0.558984
$738$	−29.9992	−1.10428
$739$	20.9551	0.770846	0.385423	−	0.922740i	$-0.374056\pi$
$739$	20.9551	0.770846	0.385423	+	0.922740i	$0.374056\pi$
$740$	−277.427	−10.1984
$741$	−20.4262	−0.750375
$742$	−18.9901	−0.697148
$743$	18.3846	0.674464	0.337232	−	0.941422i	$-0.390509\pi$
$743$	18.3846	0.674464	0.337232	+	0.941422i	$0.390509\pi$
$744$	0.469819	0.0172244
$745$	58.4965	2.14315
$746$	0.371568	0.0136041
$747$	−1.35646	−0.0496303
$748$	12.5895	0.460317
$749$	−15.1513	−0.553618
$750$	−93.1990	−3.40315
$751$	−37.5739	−1.37109	−0.685545	−	0.728030i	$-0.740436\pi$
$751$	−37.5739	−1.37109	−0.685545	+	0.728030i	$0.740436\pi$
$752$	109.080	3.97772
$753$	1.10916	0.0404199
$754$	65.9237	2.40080
$755$	−6.62440	−0.241087
$756$	−5.64259	−0.205219
$757$	52.5391	1.90957	0.954783	−	0.297305i	$-0.0960878\pi$
$757$	52.5391	1.90957	0.954783	+	0.297305i	$0.0960878\pi$
$758$	24.0644	0.874058
$759$	−2.18082	−0.0791587
$760$	−130.546	−4.73540
$761$	−18.6740	−0.676932	−0.338466	−	0.940979i	$-0.609908\pi$
$761$	−18.6740	−0.676932	−0.338466	+	0.940979i	$0.609908\pi$
$762$	26.6780	0.966444
$763$	−4.52396	−0.163778
$764$	−5.64259	−0.204142
$765$	−3.50133	−0.126591
$766$	28.3491	1.02429
$767$	−52.8855	−1.90958
$768$	71.2121	2.56965
$769$	0.165093	0.00595341	0.00297671	−	0.999996i	$-0.499052\pi$
$769$	0.165093	0.00595341	0.00297671	+	0.999996i	$0.499052\pi$
$770$	−31.6317	−1.13993
$771$	3.75758	0.135326
$772$	12.3225	0.443495
$773$	15.7710	0.567243	0.283621	−	0.958936i	$-0.408464\pi$
$773$	15.7710	0.567243	0.283621	+	0.958936i	$0.408464\pi$
$774$	−9.52507	−0.342371
$775$	−0.604458	−0.0217128
$776$	−78.1569	−2.80567
$777$	11.6029	0.416252
$778$	−38.9318	−1.39577
$779$	33.1985	1.18946
$780$	−159.639	−5.71599
$781$	−43.9450	−1.57248
$782$	1.84489	0.0659732
$783$	3.57161	0.127639
$784$	16.5536	0.591201
$785$	10.4441	0.372767
$786$	35.0401	1.24984
$787$	−28.8309	−1.02771	−0.513856	−	0.857877i	$-0.671783\pi$
$787$	−28.8309	−1.02771	−0.513856	+	0.857877i	$0.671783\pi$
$788$	114.388	4.07491
$789$	0.860818	0.0306459
$790$	126.322	4.49434
$791$	−8.04204	−0.285942
$792$	27.1913	0.966200
$793$	−76.8462	−2.72889
$794$	−69.8659	−2.47945
$795$	−29.1078	−1.03235
$796$	43.8409	1.55390
$797$	−8.95588	−0.317234	−0.158617	−	0.987340i	$-0.550703\pi$
$797$	−8.95588	−0.317234	−0.158617	+	0.987340i	$0.550703\pi$
$798$	8.45766	0.299398
$799$	−5.44477	−0.192622
$800$	−331.967	−11.7368
$801$	6.57078	0.232167
$802$	−46.0737	−1.62692
$803$	−8.60897	−0.303804
$804$	−31.7112	−1.11837
$805$	−3.42235	−0.120622
$806$	−0.861147	−0.0303326
$807$	9.23324	0.325025
$808$	2.00720	0.0706130
$809$	28.7648	1.01132	0.505659	−	0.862733i	$-0.331249\pi$
$809$	28.7648	1.01132	0.505659	+	0.862733i	$0.331249\pi$
$810$	−11.7145	−0.411605
$811$	−20.6864	−0.726399	−0.363199	−	0.931711i	$-0.618316\pi$
$811$	−20.6864	−0.726399	−0.363199	+	0.931711i	$0.618316\pi$
$812$	−20.1531	−0.707236
$813$	13.6135	0.477445
$814$	−86.6136	−3.03580
$815$	78.3052	2.74291
$816$	−13.6780	−0.478827
$817$	10.5409	0.368780
$818$	−101.183	−3.53779
$819$	6.67663	0.233300
$820$	259.460	9.06074
$821$	−14.4441	−0.504103	−0.252051	−	0.967714i	$-0.581105\pi$
$821$	−14.4441	−0.504103	−0.252051	+	0.967714i	$0.581105\pi$
$822$	−15.0861	−0.526187
$823$	37.1082	1.29351	0.646755	−	0.762698i	$-0.276126\pi$
$823$	37.1082	1.29351	0.646755	+	0.762698i	$0.276126\pi$
$824$	−139.084	−4.84521
$825$	−34.9837	−1.21798
$826$	21.8978	0.761921
$827$	36.1274	1.25627	0.628137	−	0.778103i	$-0.283818\pi$
$827$	36.1274	1.25627	0.628137	+	0.778103i	$0.283818\pi$
$828$	4.55721	0.158374
$829$	15.0684	0.523347	0.261674	−	0.965156i	$-0.415726\pi$
$829$	15.0684	0.523347	0.261674	+	0.965156i	$0.415726\pi$
$830$	15.8902	0.551559
$831$	8.02131	0.278256
$832$	−251.894	−8.73286
$833$	−0.826285	−0.0286291
$834$	59.1638	2.04868
$835$	71.9265	2.48912
$836$	−46.6131	−1.61215
$837$	−0.0466552	−0.00161264
$838$	19.5888	0.676682
$839$	−13.6932	−0.472741	−0.236371	−	0.971663i	$-0.575958\pi$
$839$	−13.6932	−0.472741	−0.236371	+	0.971663i	$0.575958\pi$
$840$	42.6711	1.47229
$841$	−16.2436	−0.560124
$842$	15.7094	0.541383
$843$	−20.0619	−0.690967
$844$	−135.199	−4.65374
$845$	133.807	4.60310
$846$	−18.2167	−0.626303
$847$	3.70882	0.127437
$848$	−113.710	−3.90483
$849$	14.2707	0.489769
$850$	29.5949	1.01510
$851$	−9.37103	−0.321235
$852$	91.8309	3.14608
$853$	−1.58581	−0.0542971	−0.0271485	−	0.999631i	$-0.508643\pi$
$853$	−1.58581	−0.0542971	−0.0271485	+	0.999631i	$0.508643\pi$
$854$	31.8189	1.08882
$855$	12.9638	0.443354
$856$	−152.574	−5.21489
$857$	43.9717	1.50204	0.751022	−	0.660277i	$-0.229561\pi$
$857$	43.9717	1.50204	0.751022	+	0.660277i	$0.229561\pi$
$858$	−49.8398	−1.70150
$859$	−48.1723	−1.64362	−0.821809	−	0.569763i	$-0.807035\pi$
$859$	−48.1723	−1.64362	−0.821809	+	0.569763i	$0.807035\pi$
$860$	82.3814	2.80918
$861$	−10.8515	−0.369817
$862$	103.836	3.53667
$863$	−19.8649	−0.676210	−0.338105	−	0.941108i	$-0.609786\pi$
$863$	−19.8649	−0.676210	−0.338105	+	0.941108i	$0.609786\pi$
$864$	−25.6229	−0.871708
$865$	14.3194	0.486873
$866$	92.9013	3.15691
$867$	−16.3173	−0.554163
$868$	0.263256	0.00893549
$869$	29.1175	0.987745
$870$	−41.8396	−1.41850
$871$	37.5224	1.27140
$872$	−45.5564	−1.54273
$873$	7.76134	0.262682
$874$	−6.83079	−0.231055
$875$	−33.7125	−1.13969
$876$	17.9900	0.607825
$877$	37.2658	1.25838	0.629188	−	0.777253i	$-0.283387\pi$
$877$	37.2658	1.25838	0.629188	+	0.777253i	$0.283387\pi$
$878$	−36.6512	−1.23692
$879$	16.3062	0.549994
$880$	−189.407	−6.38490
$881$	−9.85069	−0.331878	−0.165939	−	0.986136i	$-0.553066\pi$
$881$	−9.85069	−0.331878	−0.165939	+	0.986136i	$0.553066\pi$
$882$	−2.76452	−0.0930863
$883$	31.9950	1.07672	0.538359	−	0.842716i	$-0.319045\pi$
$883$	31.9950	1.07672	0.538359	+	0.842716i	$0.319045\pi$
$884$	31.1290	1.04698
$885$	33.5647	1.12826
$886$	80.3997	2.70108
$887$	−47.0987	−1.58142	−0.790709	−	0.612192i	$-0.790288\pi$
$887$	−47.0987	−1.58142	−0.790709	+	0.612192i	$0.790288\pi$
$888$	116.842	3.92095
$889$	9.65014	0.323655
$890$	−76.9734	−2.58015
$891$	−2.70022	−0.0904607
$892$	−52.2243	−1.74860
$893$	20.1595	0.674612
$894$	−38.1634	−1.27638
$895$	−35.9110	−1.20037
$896$	53.0535	1.77239
$897$	−5.39235	−0.180045
$898$	47.9492	1.60009
$899$	−0.166634	−0.00555756
$900$	73.1047	2.43682
$901$	5.67593	0.189093
$902$	81.0043	2.69715
$903$	−3.44546	−0.114658
$904$	−80.9835	−2.69347
$905$	53.3483	1.77336
$906$	4.32179	0.143582
$907$	25.5818	0.849429	0.424714	−	0.905327i	$-0.360375\pi$
$907$	25.5818	0.849429	0.424714	+	0.905327i	$0.360375\pi$
$908$	−30.6492	−1.01713
$909$	−0.199324	−0.00661116
$910$	−78.2133	−2.59275
$911$	44.7001	1.48098	0.740489	−	0.672068i	$-0.234594\pi$
$911$	44.7001	1.48098	0.740489	+	0.672068i	$0.234594\pi$
$912$	50.6435	1.67697
$913$	3.66274	0.121219
$914$	−3.17745	−0.105101
$915$	48.7718	1.61234
$916$	−110.622	−3.65506
$917$	12.6749	0.418562
$918$	2.28428	0.0753926
$919$	43.0045	1.41859	0.709294	−	0.704913i	$-0.249014\pi$
$919$	43.0045	1.41859	0.709294	+	0.704913i	$0.249014\pi$
$920$	−34.4631	−1.13621
$921$	10.1327	0.333884
$922$	−88.2585	−2.90664
$923$	−108.659	−3.57657
$924$	15.2362	0.501235
$925$	−150.326	−4.94268
$926$	20.6088	0.677248
$927$	13.8117	0.453634
$928$	−91.5149	−3.00412
$929$	−24.1345	−0.791829	−0.395914	−	0.918287i	$-0.629572\pi$
$929$	−24.1345	−0.791829	−0.395914	+	0.918287i	$0.629572\pi$
$930$	0.546542	0.0179218
$931$	3.05936	0.100266
$932$	120.085	3.93351
$933$	−15.3731	−0.503291
$934$	53.4205	1.74797
$935$	9.45436	0.309191
$936$	67.2338	2.19761
$937$	−3.22078	−0.105218	−0.0526091	−	0.998615i	$-0.516754\pi$
$937$	−3.22078	−0.105218	−0.0526091	+	0.998615i	$0.516754\pi$
$938$	−15.5365	−0.507286
$939$	−3.42572	−0.111794
$940$	157.555	5.13887
$941$	48.7079	1.58783	0.793916	−	0.608027i	$-0.208039\pi$
$941$	48.7079	1.58783	0.793916	+	0.608027i	$0.208039\pi$
$942$	−6.81380	−0.222006
$943$	8.76415	0.285400
$944$	131.121	4.26763
$945$	−4.23744	−0.137844
$946$	25.7198	0.836222
$947$	35.1917	1.14358	0.571788	−	0.820401i	$-0.306250\pi$
$947$	35.1917	1.14358	0.571788	+	0.820401i	$0.306250\pi$
$948$	−60.8463	−1.97620
$949$	−21.2867	−0.690997
$950$	−109.576	−3.55513
$951$	−0.689591	−0.0223615
$952$	−8.32071	−0.269676
$953$	−11.3566	−0.367876	−0.183938	−	0.982938i	$-0.558885\pi$
$953$	−11.3566	−0.367876	−0.183938	+	0.982938i	$0.558885\pi$
$954$	18.9901	0.614827
$955$	−4.23744	−0.137120
$956$	−54.0743	−1.74889
$957$	−9.64413	−0.311751
$958$	−20.8037	−0.672138
$959$	−5.45702	−0.176216
$960$	159.869	5.15975
$961$	−30.9978	−0.999930
$962$	−214.163	−6.90489
$963$	15.1513	0.488245
$964$	−108.129	−3.48260
$965$	9.25384	0.297892
$966$	2.23275	0.0718377
$967$	−25.2247	−0.811173	−0.405587	−	0.914057i	$-0.632933\pi$
$967$	−25.2247	−0.811173	−0.405587	+	0.914057i	$0.632933\pi$
$968$	37.3479	1.20041
$969$	−2.52790	−0.0812079
$970$	−90.9202	−2.91927
$971$	55.6112	1.78465	0.892325	−	0.451394i	$-0.149073\pi$
$971$	55.6112	1.78465	0.892325	+	0.451394i	$0.149073\pi$
$972$	5.64259	0.180986
$973$	21.4011	0.686088
$974$	82.3044	2.63720
$975$	−86.5015	−2.77027
$976$	190.528	6.09865
$977$	18.1318	0.580087	0.290043	−	0.957013i	$-0.406330\pi$
$977$	18.1318	0.580087	0.290043	+	0.957013i	$0.406330\pi$
$978$	−51.0867	−1.63357
$979$	−17.7426	−0.567054
$980$	23.9101	0.763781
$981$	4.52396	0.144439
$982$	50.7467	1.61939
$983$	3.48353	0.111107	0.0555537	−	0.998456i	$-0.482308\pi$
$983$	3.48353	0.111107	0.0555537	+	0.998456i	$0.482308\pi$
$984$	−109.275	−3.48355
$985$	85.9025	2.73708
$986$	8.15858	0.259822
$987$	−6.58946	−0.209745
$988$	−115.257	−3.66680
$989$	2.78271	0.0884851
$990$	31.6317	1.00532
$991$	4.99788	0.158763	0.0793815	−	0.996844i	$-0.474705\pi$
$991$	4.99788	0.158763	0.0793815	+	0.996844i	$0.474705\pi$
$992$	1.19544	0.0379552
$993$	−13.0657	−0.414626
$994$	44.9915	1.42704
$995$	32.9233	1.04374
$996$	−7.65395	−0.242525
$997$	2.16443	0.0685480	0.0342740	−	0.999412i	$-0.489088\pi$
$997$	2.16443	0.0685480	0.0342740	+	0.999412i	$0.489088\pi$
$998$	−113.653	−3.59764
$999$	−11.6029	−0.367100

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.m.1.1	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.m.1.1	✓	29	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.76452 q^{2} +1.00000 q^{3} +5.64259 q^{4} +4.23744 q^{5} -2.76452 q^{6} -1.00000 q^{7} -10.0700 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.76452 q^{2} +1.00000 q^{3} +5.64259 q^{4} +4.23744 q^{5} -2.76452 q^{6} -1.00000 q^{7} -10.0700 q^{8} +1.00000 q^{9} -11.7145 q^{10} -2.70022 q^{11} +5.64259 q^{12} -6.67663 q^{13} +2.76452 q^{14} +4.23744 q^{15} +16.5536 q^{16} -0.826285 q^{17} -2.76452 q^{18} +3.05936 q^{19} +23.9101 q^{20} -1.00000 q^{21} +7.46482 q^{22} +0.807645 q^{23} -10.0700 q^{24} +12.9559 q^{25} +18.4577 q^{26} +1.00000 q^{27} -5.64259 q^{28} +3.57161 q^{29} -11.7145 q^{30} -0.0466552 q^{31} -25.6229 q^{32} -2.70022 q^{33} +2.28428 q^{34} -4.23744 q^{35} +5.64259 q^{36} -11.6029 q^{37} -8.45766 q^{38} -6.67663 q^{39} -42.6711 q^{40} +10.8515 q^{41} +2.76452 q^{42} +3.44546 q^{43} -15.2362 q^{44} +4.23744 q^{45} -2.23275 q^{46} +6.58946 q^{47} +16.5536 q^{48} +1.00000 q^{49} -35.8168 q^{50} -0.826285 q^{51} -37.6735 q^{52} -6.86921 q^{53} -2.76452 q^{54} -11.4420 q^{55} +10.0700 q^{56} +3.05936 q^{57} -9.87380 q^{58} +7.92099 q^{59} +23.9101 q^{60} +11.5097 q^{61} +0.128979 q^{62} -1.00000 q^{63} +37.7277 q^{64} -28.2918 q^{65} +7.46482 q^{66} -5.61997 q^{67} -4.66239 q^{68} +0.807645 q^{69} +11.7145 q^{70} +16.2746 q^{71} -10.0700 q^{72} +3.18825 q^{73} +32.0765 q^{74} +12.9559 q^{75} +17.2627 q^{76} +2.70022 q^{77} +18.4577 q^{78} -10.7834 q^{79} +70.1450 q^{80} +1.00000 q^{81} -29.9992 q^{82} -1.35646 q^{83} -5.64259 q^{84} -3.50133 q^{85} -9.52507 q^{86} +3.57161 q^{87} +27.1913 q^{88} +6.57078 q^{89} -11.7145 q^{90} +6.67663 q^{91} +4.55721 q^{92} -0.0466552 q^{93} -18.2167 q^{94} +12.9638 q^{95} -25.6229 q^{96} +7.76134 q^{97} -2.76452 q^{98} -2.70022 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9} + 11 q^{11} + 40 q^{12} + 13 q^{13} - 6 q^{14} + 22 q^{15} + 58 q^{16} + 17 q^{17} + 6 q^{18} + 3 q^{19} + 52 q^{20} - 29 q^{21} + 17 q^{22} + 36 q^{23} + 15 q^{24} + 57 q^{25} + 25 q^{26} + 29 q^{27} - 40 q^{28} + 20 q^{29} + 6 q^{31} + 46 q^{32} + 11 q^{33} + 18 q^{34} - 22 q^{35} + 40 q^{36} + 22 q^{37} + 8 q^{38} + 13 q^{39} + 6 q^{40} + 26 q^{41} - 6 q^{42} + 21 q^{43} + 22 q^{44} + 22 q^{45} + 28 q^{46} + 41 q^{47} + 58 q^{48} + 29 q^{49} + 18 q^{50} + 17 q^{51} + 2 q^{52} + 37 q^{53} + 6 q^{54} + 7 q^{55} - 15 q^{56} + 3 q^{57} + 9 q^{58} + 27 q^{59} + 52 q^{60} + 20 q^{61} - 12 q^{62} - 29 q^{63} + 59 q^{64} + 3 q^{65} + 17 q^{66} + 30 q^{67} + 33 q^{68} + 36 q^{69} + 68 q^{71} + 15 q^{72} + q^{73} + 21 q^{74} + 57 q^{75} + 11 q^{76} - 11 q^{77} + 25 q^{78} + 34 q^{79} + 110 q^{80} + 29 q^{81} - 49 q^{82} + 13 q^{83} - 40 q^{84} + 27 q^{85} + 35 q^{86} + 20 q^{87} + 17 q^{88} + 61 q^{89} - 13 q^{91} + 86 q^{92} + 6 q^{93} - 19 q^{94} + 25 q^{95} + 46 q^{96} - 3 q^{97} + 6 q^{98} + 11 q^{99}+O(q^{100}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9 + 11 * q^11 + 40 * q^12 + 13 * q^13 - 6 * q^14 + 22 * q^15 + 58 * q^16 + 17 * q^17 + 6 * q^18 + 3 * q^19 + 52 * q^20 - 29 * q^21 + 17 * q^22 + 36 * q^23 + 15 * q^24 + 57 * q^25 + 25 * q^26 + 29 * q^27 - 40 * q^28 + 20 * q^29 + 6 * q^31 + 46 * q^32 + 11 * q^33 + 18 * q^34 - 22 * q^35 + 40 * q^36 + 22 * q^37 + 8 * q^38 + 13 * q^39 + 6 * q^40 + 26 * q^41 - 6 * q^42 + 21 * q^43 + 22 * q^44 + 22 * q^45 + 28 * q^46 + 41 * q^47 + 58 * q^48 + 29 * q^49 + 18 * q^50 + 17 * q^51 + 2 * q^52 + 37 * q^53 + 6 * q^54 + 7 * q^55 - 15 * q^56 + 3 * q^57 + 9 * q^58 + 27 * q^59 + 52 * q^60 + 20 * q^61 - 12 * q^62 - 29 * q^63 + 59 * q^64 + 3 * q^65 + 17 * q^66 + 30 * q^67 + 33 * q^68 + 36 * q^69 + 68 * q^71 + 15 * q^72 + q^73 + 21 * q^74 + 57 * q^75 + 11 * q^76 - 11 * q^77 + 25 * q^78 + 34 * q^79 + 110 * q^80 + 29 * q^81 - 49 * q^82 + 13 * q^83 - 40 * q^84 + 27 * q^85 + 35 * q^86 + 20 * q^87 + 17 * q^88 + 61 * q^89 - 13 * q^91 + 86 * q^92 + 6 * q^93 - 19 * q^94 + 25 * q^95 + 46 * q^96 - 3 * q^97 + 6 * q^98 + 11 * q^99

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