LMFDB - Embedded newform 6005.2.a.d.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$1$
Dimension:	$83$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.97272 q^{2} -2.98994 q^{3} +1.89163 q^{4} -1.00000 q^{5} +5.89832 q^{6} +0.991432 q^{7} +0.213787 q^{8} +5.93974 q^{9} +O(q^{10})$	\(q-1.97272 q^{2} -2.98994 q^{3} +1.89163 q^{4} -1.00000 q^{5} +5.89832 q^{6} +0.991432 q^{7} +0.213787 q^{8} +5.93974 q^{9} +1.97272 q^{10} -6.41871 q^{11} -5.65585 q^{12} -4.91111 q^{13} -1.95582 q^{14} +2.98994 q^{15} -4.20500 q^{16} +1.22630 q^{17} -11.7174 q^{18} -0.492096 q^{19} -1.89163 q^{20} -2.96432 q^{21} +12.6623 q^{22} +6.80564 q^{23} -0.639210 q^{24} +1.00000 q^{25} +9.68824 q^{26} -8.78964 q^{27} +1.87542 q^{28} -0.840164 q^{29} -5.89832 q^{30} +0.976308 q^{31} +7.86772 q^{32} +19.1916 q^{33} -2.41914 q^{34} -0.991432 q^{35} +11.2358 q^{36} -7.50952 q^{37} +0.970768 q^{38} +14.6839 q^{39} -0.213787 q^{40} +2.89791 q^{41} +5.84778 q^{42} +2.29432 q^{43} -12.1418 q^{44} -5.93974 q^{45} -13.4256 q^{46} -0.646799 q^{47} +12.5727 q^{48} -6.01706 q^{49} -1.97272 q^{50} -3.66656 q^{51} -9.28999 q^{52} -4.12697 q^{53} +17.3395 q^{54} +6.41871 q^{55} +0.211955 q^{56} +1.47134 q^{57} +1.65741 q^{58} -7.43276 q^{59} +5.65585 q^{60} +3.40551 q^{61} -1.92598 q^{62} +5.88885 q^{63} -7.11081 q^{64} +4.91111 q^{65} -37.8596 q^{66} +6.42229 q^{67} +2.31970 q^{68} -20.3484 q^{69} +1.95582 q^{70} -9.75451 q^{71} +1.26984 q^{72} +13.9521 q^{73} +14.8142 q^{74} -2.98994 q^{75} -0.930863 q^{76} -6.36372 q^{77} -28.9673 q^{78} -1.27958 q^{79} +4.20500 q^{80} +8.46128 q^{81} -5.71677 q^{82} +1.06443 q^{83} -5.60740 q^{84} -1.22630 q^{85} -4.52606 q^{86} +2.51204 q^{87} -1.37224 q^{88} -6.55019 q^{89} +11.7174 q^{90} -4.86903 q^{91} +12.8737 q^{92} -2.91910 q^{93} +1.27595 q^{94} +0.492096 q^{95} -23.5240 q^{96} -1.87672 q^{97} +11.8700 q^{98} -38.1255 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9}+O(q^{10}) $ 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9	\( 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9} - q^{10} - 26 q^{11} - 12 q^{12} - 15 q^{13} - 21 q^{14} + 4 q^{15} + 5 q^{16} + 8 q^{17} - 12 q^{18} - 79 q^{19} - 61 q^{20} - 34 q^{21} - 25 q^{22} + 31 q^{23} - 42 q^{24} + 83 q^{25} - 13 q^{26} - 25 q^{27} - 16 q^{28} - 16 q^{29} + 6 q^{30} - 40 q^{31} + 15 q^{32} - 33 q^{33} - 54 q^{34} - 2 q^{35} + 11 q^{36} - 45 q^{37} + 10 q^{38} - 54 q^{39} + 3 q^{40} - 27 q^{41} - 28 q^{42} - 101 q^{43} - 51 q^{44} - 61 q^{45} - 46 q^{46} + 71 q^{47} - 14 q^{48} + 23 q^{49} + q^{50} - 71 q^{51} - 34 q^{52} - 49 q^{53} - 25 q^{54} + 26 q^{55} - 41 q^{56} - 20 q^{57} - 43 q^{58} - 60 q^{59} + 12 q^{60} - 38 q^{61} - 2 q^{62} + 36 q^{63} - 113 q^{64} + 15 q^{65} - 42 q^{66} - 164 q^{67} + 10 q^{68} - 93 q^{69} + 21 q^{70} - 78 q^{71} + q^{72} - 18 q^{73} - 23 q^{74} - 4 q^{75} - 112 q^{76} - 35 q^{77} - 44 q^{78} - 124 q^{79} - 5 q^{80} - 45 q^{81} - 34 q^{82} + 5 q^{83} - 60 q^{84} - 8 q^{85} - 25 q^{86} + 12 q^{87} - 149 q^{88} - 44 q^{89} + 12 q^{90} - 192 q^{91} + 35 q^{92} - 13 q^{93} - 32 q^{94} + 79 q^{95} - 59 q^{96} - 31 q^{97} + 25 q^{98} - 134 q^{99}+O(q^{100}) \) 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9 - q^10 - 26 * q^11 - 12 * q^12 - 15 * q^13 - 21 * q^14 + 4 * q^15 + 5 * q^16 + 8 * q^17 - 12 * q^18 - 79 * q^19 - 61 * q^20 - 34 * q^21 - 25 * q^22 + 31 * q^23 - 42 * q^24 + 83 * q^25 - 13 * q^26 - 25 * q^27 - 16 * q^28 - 16 * q^29 + 6 * q^30 - 40 * q^31 + 15 * q^32 - 33 * q^33 - 54 * q^34 - 2 * q^35 + 11 * q^36 - 45 * q^37 + 10 * q^38 - 54 * q^39 + 3 * q^40 - 27 * q^41 - 28 * q^42 - 101 * q^43 - 51 * q^44 - 61 * q^45 - 46 * q^46 + 71 * q^47 - 14 * q^48 + 23 * q^49 + q^50 - 71 * q^51 - 34 * q^52 - 49 * q^53 - 25 * q^54 + 26 * q^55 - 41 * q^56 - 20 * q^57 - 43 * q^58 - 60 * q^59 + 12 * q^60 - 38 * q^61 - 2 * q^62 + 36 * q^63 - 113 * q^64 + 15 * q^65 - 42 * q^66 - 164 * q^67 + 10 * q^68 - 93 * q^69 + 21 * q^70 - 78 * q^71 + q^72 - 18 * q^73 - 23 * q^74 - 4 * q^75 - 112 * q^76 - 35 * q^77 - 44 * q^78 - 124 * q^79 - 5 * q^80 - 45 * q^81 - 34 * q^82 + 5 * q^83 - 60 * q^84 - 8 * q^85 - 25 * q^86 + 12 * q^87 - 149 * q^88 - 44 * q^89 + 12 * q^90 - 192 * q^91 + 35 * q^92 - 13 * q^93 - 32 * q^94 + 79 * q^95 - 59 * q^96 - 31 * q^97 + 25 * q^98 - 134 * 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 $

$2$	−1.97272	−1.39492	−0.697462	−	0.716622i	$-0.745688\pi$
$2$	−1.97272	−1.39492	−0.697462	+	0.716622i	$0.745688\pi$
$3$	−2.98994	−1.72624	−0.863121	−	0.504997i	$-0.831494\pi$
$3$	−2.98994	−1.72624	−0.863121	+	0.504997i	$0.831494\pi$
$4$	1.89163	0.945814
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	5.89832	2.40798
$7$	0.991432	0.374726	0.187363	−	0.982291i	$-0.440006\pi$
$7$	0.991432	0.374726	0.187363	+	0.982291i	$0.440006\pi$
$8$	0.213787	0.0755851
$9$	5.93974	1.97991
$10$	1.97272	0.623829
$11$	−6.41871	−1.93531	−0.967657	−	0.252268i	$-0.918823\pi$
$11$	−6.41871	−1.93531	−0.967657	+	0.252268i	$0.918823\pi$
$12$	−5.65585	−1.63270
$13$	−4.91111	−1.36210	−0.681048	−	0.732239i	$-0.738475\pi$
$13$	−4.91111	−1.36210	−0.681048	+	0.732239i	$0.738475\pi$
$14$	−1.95582	−0.522715
$15$	2.98994	0.771999
$16$	−4.20500	−1.05125
$17$	1.22630	0.297421	0.148711	−	0.988881i	$-0.452488\pi$
$17$	1.22630	0.297421	0.148711	+	0.988881i	$0.452488\pi$
$18$	−11.7174	−2.76183
$19$	−0.492096	−0.112895	−0.0564473	−	0.998406i	$-0.517977\pi$
$19$	−0.492096	−0.112895	−0.0564473	+	0.998406i	$0.517977\pi$
$20$	−1.89163	−0.422981
$21$	−2.96432	−0.646868
$22$	12.6623	2.69962
$23$	6.80564	1.41907	0.709537	−	0.704668i	$-0.248904\pi$
$23$	6.80564	1.41907	0.709537	+	0.704668i	$0.248904\pi$
$24$	−0.639210	−0.130478
$25$	1.00000	0.200000
$26$	9.68824	1.90002
$27$	−8.78964	−1.69157
$28$	1.87542	0.354421
$29$	−0.840164	−0.156014	−0.0780072	−	0.996953i	$-0.524856\pi$
$29$	−0.840164	−0.156014	−0.0780072	+	0.996953i	$0.524856\pi$
$30$	−5.89832	−1.07688
$31$	0.976308	0.175350	0.0876750	−	0.996149i	$-0.472056\pi$
$31$	0.976308	0.175350	0.0876750	+	0.996149i	$0.472056\pi$
$32$	7.86772	1.39083
$33$	19.1916	3.34082
$34$	−2.41914	−0.414880
$35$	−0.991432	−0.167583
$36$	11.2358	1.87263
$37$	−7.50952	−1.23456	−0.617278	−	0.786745i	$-0.711765\pi$
$37$	−7.50952	−1.23456	−0.617278	+	0.786745i	$0.711765\pi$
$38$	0.970768	0.157479
$39$	14.6839	2.35131
$40$	−0.213787	−0.0338027
$41$	2.89791	0.452577	0.226289	−	0.974060i	$-0.427341\pi$
$41$	2.89791	0.452577	0.226289	+	0.974060i	$0.427341\pi$
$42$	5.84778	0.902332
$43$	2.29432	0.349881	0.174941	−	0.984579i	$-0.444027\pi$
$43$	2.29432	0.349881	0.174941	+	0.984579i	$0.444027\pi$
$44$	−12.1418	−1.83045
$45$	−5.93974	−0.885444
$46$	−13.4256	−1.97950
$47$	−0.646799	−0.0943454	−0.0471727	−	0.998887i	$-0.515021\pi$
$47$	−0.646799	−0.0943454	−0.0471727	+	0.998887i	$0.515021\pi$
$48$	12.5727	1.81471
$49$	−6.01706	−0.859580
$50$	−1.97272	−0.278985
$51$	−3.66656	−0.513421
$52$	−9.28999	−1.28829
$53$	−4.12697	−0.566883	−0.283441	−	0.958990i	$-0.591476\pi$
$53$	−4.12697	−0.566883	−0.283441	+	0.958990i	$0.591476\pi$
$54$	17.3395	2.35961
$55$	6.41871	0.865499
$56$	0.211955	0.0283237
$57$	1.47134	0.194883
$58$	1.65741	0.217628
$59$	−7.43276	−0.967662	−0.483831	−	0.875161i	$-0.660755\pi$
$59$	−7.43276	−0.967662	−0.483831	+	0.875161i	$0.660755\pi$
$60$	5.65585	0.730168
$61$	3.40551	0.436032	0.218016	−	0.975945i	$-0.430042\pi$
$61$	3.40551	0.436032	0.218016	+	0.975945i	$0.430042\pi$
$62$	−1.92598	−0.244600
$63$	5.88885	0.741925
$64$	−7.11081	−0.888851
$65$	4.91111	0.609148
$66$	−37.8596	−4.66019
$67$	6.42229	0.784607	0.392304	−	0.919836i	$-0.371678\pi$
$67$	6.42229	0.784607	0.392304	+	0.919836i	$0.371678\pi$
$68$	2.31970	0.281305
$69$	−20.3484	−2.44967
$70$	1.95582	0.233765
$71$	−9.75451	−1.15765	−0.578824	−	0.815453i	$-0.696488\pi$
$71$	−9.75451	−1.15765	−0.578824	+	0.815453i	$0.696488\pi$
$72$	1.26984	0.149652
$73$	13.9521	1.63297	0.816487	−	0.577364i	$-0.195919\pi$
$73$	13.9521	1.63297	0.816487	+	0.577364i	$0.195919\pi$
$74$	14.8142	1.72211
$75$	−2.98994	−0.345248
$76$	−0.930863	−0.106777
$77$	−6.36372	−0.725213
$78$	−28.9673	−3.27990
$79$	−1.27958	−0.143964	−0.0719820	−	0.997406i	$-0.522932\pi$
$79$	−1.27958	−0.143964	−0.0719820	+	0.997406i	$0.522932\pi$
$80$	4.20500	0.470133
$81$	8.46128	0.940142
$82$	−5.71677	−0.631311
$83$	1.06443	0.116837	0.0584184	−	0.998292i	$-0.481394\pi$
$83$	1.06443	0.116837	0.0584184	+	0.998292i	$0.481394\pi$
$84$	−5.60740	−0.611817
$85$	−1.22630	−0.133011
$86$	−4.52606	−0.488058
$87$	2.51204	0.269319
$88$	−1.37224	−0.146281
$89$	−6.55019	−0.694318	−0.347159	−	0.937806i	$-0.612854\pi$
$89$	−6.55019	−0.694318	−0.347159	+	0.937806i	$0.612854\pi$
$90$	11.7174	1.23513
$91$	−4.86903	−0.510413
$92$	12.8737	1.34218
$93$	−2.91910	−0.302697
$94$	1.27595	0.131605
$95$	0.492096	0.0504880
$96$	−23.5240	−2.40091
$97$	−1.87672	−0.190552	−0.0952762	−	0.995451i	$-0.530373\pi$
$97$	−1.87672	−0.190552	−0.0952762	+	0.995451i	$0.530373\pi$
$98$	11.8700	1.19905
$99$	−38.1255	−3.83175
$100$	1.89163	0.189163
$101$	12.2647	1.22039	0.610193	−	0.792252i	$-0.291092\pi$
$101$	12.2647	1.22039	0.610193	+	0.792252i	$0.291092\pi$
$102$	7.23310	0.716183
$103$	−1.84833	−0.182121	−0.0910604	−	0.995845i	$-0.529026\pi$
$103$	−1.84833	−0.182121	−0.0910604	+	0.995845i	$0.529026\pi$
$104$	−1.04993	−0.102954
$105$	2.96432	0.289288
$106$	8.14136	0.790758
$107$	8.14252	0.787167	0.393583	−	0.919289i	$-0.371235\pi$
$107$	8.14252	0.787167	0.393583	+	0.919289i	$0.371235\pi$
$108$	−16.6267	−1.59991
$109$	−6.45716	−0.618483	−0.309242	−	0.950983i	$-0.600075\pi$
$109$	−6.45716	−0.618483	−0.309242	+	0.950983i	$0.600075\pi$
$110$	−12.6623	−1.20731
$111$	22.4530	2.13114
$112$	−4.16897	−0.393931
$113$	6.96171	0.654903	0.327451	−	0.944868i	$-0.393810\pi$
$113$	6.96171	0.654903	0.327451	+	0.944868i	$0.393810\pi$
$114$	−2.90254	−0.271848
$115$	−6.80564	−0.634629
$116$	−1.58928	−0.147561
$117$	−29.1707	−2.69683
$118$	14.6628	1.34982
$119$	1.21579	0.111451
$120$	0.639210	0.0583516
$121$	30.1999	2.74544
$122$	−6.71813	−0.608231
$123$	−8.66457	−0.781258
$124$	1.84681	0.165849
$125$	−1.00000	−0.0894427
$126$	−11.6171	−1.03493
$127$	−6.19405	−0.549633	−0.274816	−	0.961497i	$-0.588617\pi$
$127$	−6.19405	−0.549633	−0.274816	+	0.961497i	$0.588617\pi$
$128$	−1.70778	−0.150948
$129$	−6.85989	−0.603980
$130$	−9.68824	−0.849715
$131$	0.885328	0.0773515	0.0386757	−	0.999252i	$-0.487686\pi$
$131$	0.885328	0.0773515	0.0386757	+	0.999252i	$0.487686\pi$
$132$	36.3033	3.15980
$133$	−0.487880	−0.0423046
$134$	−12.6694	−1.09447
$135$	8.78964	0.756492
$136$	0.262167	0.0224806
$137$	22.0936	1.88759	0.943794	−	0.330535i	$-0.107229\pi$
$137$	22.0936	1.88759	0.943794	+	0.330535i	$0.107229\pi$
$138$	40.1418	3.41710
$139$	−18.4515	−1.56503	−0.782517	−	0.622630i	$-0.786064\pi$
$139$	−18.4515	−1.56503	−0.782517	+	0.622630i	$0.786064\pi$
$140$	−1.87542	−0.158502
$141$	1.93389	0.162863
$142$	19.2429	1.61483
$143$	31.5230	2.63608
$144$	−24.9766	−2.08138
$145$	0.840164	0.0697718
$146$	−27.5237	−2.27787
$147$	17.9907	1.48384
$148$	−14.2052	−1.16766
$149$	−1.14388	−0.0937103	−0.0468552	−	0.998902i	$-0.514920\pi$
$149$	−1.14388	−0.0937103	−0.0468552	+	0.998902i	$0.514920\pi$
$150$	5.89832	0.481596
$151$	3.01009	0.244958	0.122479	−	0.992471i	$-0.460916\pi$
$151$	3.01009	0.244958	0.122479	+	0.992471i	$0.460916\pi$
$152$	−0.105204	−0.00853315
$153$	7.28389	0.588868
$154$	12.5538	1.01162
$155$	−0.976308	−0.0784189
$156$	27.7765	2.22390
$157$	−3.09265	−0.246820	−0.123410	−	0.992356i	$-0.539383\pi$
$157$	−3.09265	−0.246820	−0.123410	+	0.992356i	$0.539383\pi$
$158$	2.52425	0.200819
$159$	12.3394	0.978577
$160$	−7.86772	−0.621998
$161$	6.74733	0.531764
$162$	−16.6917	−1.31143
$163$	16.2601	1.27359	0.636794	−	0.771034i	$-0.280260\pi$
$163$	16.2601	1.27359	0.636794	+	0.771034i	$0.280260\pi$
$164$	5.48177	0.428054
$165$	−19.1916	−1.49406
$166$	−2.09983	−0.162979
$167$	2.13124	0.164920	0.0824601	−	0.996594i	$-0.473722\pi$
$167$	2.13124	0.164920	0.0824601	+	0.996594i	$0.473722\pi$
$168$	−0.633733	−0.0488936
$169$	11.1190	0.855304
$170$	2.41914	0.185540
$171$	−2.92292	−0.223521
$172$	4.34001	0.330923
$173$	24.3120	1.84841	0.924204	−	0.381899i	$-0.124730\pi$
$173$	24.3120	1.84841	0.924204	+	0.381899i	$0.124730\pi$
$174$	−4.95555	−0.375679
$175$	0.991432	0.0749452
$176$	26.9907	2.03450
$177$	22.2235	1.67042
$178$	12.9217	0.968522
$179$	2.01480	0.150593	0.0752965	−	0.997161i	$-0.476010\pi$
$179$	2.01480	0.150593	0.0752965	+	0.997161i	$0.476010\pi$
$180$	−11.2358	−0.837466
$181$	−2.71557	−0.201847	−0.100923	−	0.994894i	$-0.532180\pi$
$181$	−2.71557	−0.201847	−0.100923	+	0.994894i	$0.532180\pi$
$182$	9.60523	0.711987
$183$	−10.1823	−0.752696
$184$	1.45496	0.107261
$185$	7.50952	0.552111
$186$	5.75857	0.422239
$187$	−7.87126	−0.575603
$188$	−1.22350	−0.0892332
$189$	−8.71433	−0.633875
$190$	−0.970768	−0.0704269
$191$	−4.46385	−0.322993	−0.161497	−	0.986873i	$-0.551632\pi$
$191$	−4.46385	−0.322993	−0.161497	+	0.986873i	$0.551632\pi$
$192$	21.2609	1.53437
$193$	−3.23110	−0.232580	−0.116290	−	0.993215i	$-0.537100\pi$
$193$	−3.23110	−0.232580	−0.116290	+	0.993215i	$0.537100\pi$
$194$	3.70225	0.265806
$195$	−14.6839	−1.05154
$196$	−11.3820	−0.813003
$197$	24.6998	1.75979	0.879895	−	0.475168i	$-0.157613\pi$
$197$	24.6998	1.75979	0.879895	+	0.475168i	$0.157613\pi$
$198$	75.2109	5.34501
$199$	20.2727	1.43709	0.718547	−	0.695479i	$-0.244808\pi$
$199$	20.2727	1.43709	0.718547	+	0.695479i	$0.244808\pi$
$200$	0.213787	0.0151170
$201$	−19.2023	−1.35442
$202$	−24.1949	−1.70235
$203$	−0.832965	−0.0584627
$204$	−6.93577	−0.485601
$205$	−2.89791	−0.202399
$206$	3.64623	0.254045
$207$	40.4237	2.80964
$208$	20.6512	1.43190
$209$	3.15862	0.218487
$210$	−5.84778	−0.403535
$211$	−5.67367	−0.390591	−0.195296	−	0.980744i	$-0.562567\pi$
$211$	−5.67367	−0.390591	−0.195296	+	0.980744i	$0.562567\pi$
$212$	−7.80669	−0.536166
$213$	29.1654	1.99838
$214$	−16.0629	−1.09804
$215$	−2.29432	−0.156472
$216$	−1.87911	−0.127857
$217$	0.967943	0.0657082
$218$	12.7382	0.862738
$219$	−41.7160	−2.81891
$220$	12.1418	0.818601
$221$	−6.02248	−0.405116
$222$	−44.2935	−2.97279
$223$	−2.64675	−0.177240	−0.0886199	−	0.996066i	$-0.528246\pi$
$223$	−2.64675	−0.177240	−0.0886199	+	0.996066i	$0.528246\pi$
$224$	7.80031	0.521180
$225$	5.93974	0.395983
$226$	−13.7335	−0.913540
$227$	18.8499	1.25111	0.625556	−	0.780179i	$-0.284872\pi$
$227$	18.8499	1.25111	0.625556	+	0.780179i	$0.284872\pi$
$228$	2.78322	0.184324
$229$	17.9706	1.18753	0.593766	−	0.804638i	$-0.297641\pi$
$229$	17.9706	1.18753	0.593766	+	0.804638i	$0.297641\pi$
$230$	13.4256	0.885260
$231$	19.0271	1.25189
$232$	−0.179616	−0.0117924
$233$	−9.70755	−0.635963	−0.317981	−	0.948097i	$-0.603005\pi$
$233$	−9.70755	−0.635963	−0.317981	+	0.948097i	$0.603005\pi$
$234$	57.5456	3.76188
$235$	0.646799	0.0421925
$236$	−14.0600	−0.915229
$237$	3.82587	0.248517
$238$	−2.39842	−0.155466
$239$	20.9193	1.35316	0.676578	−	0.736371i	$-0.263462\pi$
$239$	20.9193	1.35316	0.676578	+	0.736371i	$0.263462\pi$
$240$	−12.5727	−0.811564
$241$	0.319710	0.0205943	0.0102972	−	0.999947i	$-0.496722\pi$
$241$	0.319710	0.0205943	0.0102972	+	0.999947i	$0.496722\pi$
$242$	−59.5759	−3.82969
$243$	1.07020	0.0686536
$244$	6.44197	0.412405
$245$	6.01706	0.384416
$246$	17.0928	1.08980
$247$	2.41674	0.153773
$248$	0.208722	0.0132538
$249$	−3.18260	−0.201689
$250$	1.97272	0.124766
$251$	11.5644	0.729935	0.364968	−	0.931020i	$-0.381080\pi$
$251$	11.5644	0.729935	0.364968	+	0.931020i	$0.381080\pi$
$252$	11.1395	0.701723
$253$	−43.6834	−2.74635
$254$	12.2191	0.766696
$255$	3.66656	0.229609
$256$	17.5906	1.09941
$257$	0.338558	0.0211186	0.0105593	−	0.999944i	$-0.496639\pi$
$257$	0.338558	0.0211186	0.0105593	+	0.999944i	$0.496639\pi$
$258$	13.5327	0.842506
$259$	−7.44518	−0.462621
$260$	9.28999	0.576140
$261$	−4.99035	−0.308895
$262$	−1.74651	−0.107899
$263$	−22.0473	−1.35950	−0.679748	−	0.733446i	$-0.737911\pi$
$263$	−22.0473	−1.35950	−0.679748	+	0.733446i	$0.737911\pi$
$264$	4.10291	0.252516
$265$	4.12697	0.253518
$266$	0.962451	0.0590117
$267$	19.5847	1.19856
$268$	12.1486	0.742093
$269$	23.7911	1.45057	0.725284	−	0.688450i	$-0.241708\pi$
$269$	23.7911	1.45057	0.725284	+	0.688450i	$0.241708\pi$
$270$	−17.3395	−1.05525
$271$	−18.4695	−1.12194	−0.560971	−	0.827836i	$-0.689572\pi$
$271$	−18.4695	−1.12194	−0.560971	+	0.827836i	$0.689572\pi$
$272$	−5.15658	−0.312664
$273$	14.5581	0.881096
$274$	−43.5846	−2.63304
$275$	−6.41871	−0.387063
$276$	−38.4917	−2.31693
$277$	−7.98271	−0.479635	−0.239817	−	0.970818i	$-0.577088\pi$
$277$	−7.98271	−0.479635	−0.239817	+	0.970818i	$0.577088\pi$
$278$	36.3996	2.18310
$279$	5.79901	0.347178
$280$	−0.211955	−0.0126668
$281$	16.9300	1.00996	0.504980	−	0.863131i	$-0.331500\pi$
$281$	16.9300	1.00996	0.504980	+	0.863131i	$0.331500\pi$
$282$	−3.81503	−0.227182
$283$	−6.45240	−0.383556	−0.191778	−	0.981438i	$-0.561425\pi$
$283$	−6.45240	−0.383556	−0.191778	+	0.981438i	$0.561425\pi$
$284$	−18.4519	−1.09492
$285$	−1.47134	−0.0871545
$286$	−62.1860	−3.67714
$287$	2.87308	0.169593
$288$	46.7322	2.75372
$289$	−15.4962	−0.911541
$290$	−1.65741	−0.0973264
$291$	5.61129	0.328940
$292$	26.3922	1.54449
$293$	−6.20744	−0.362643	−0.181321	−	0.983424i	$-0.558037\pi$
$293$	−6.20744	−0.362643	−0.181321	+	0.983424i	$0.558037\pi$
$294$	−35.4905	−2.06985
$295$	7.43276	0.432752
$296$	−1.60544	−0.0933141
$297$	56.4182	3.27372
$298$	2.25656	0.130719
$299$	−33.4232	−1.93291
$300$	−5.65585	−0.326541
$301$	2.27467	0.131110
$302$	−5.93807	−0.341698
$303$	−36.6708	−2.10668
$304$	2.06926	0.118680
$305$	−3.40551	−0.194999
$306$	−14.3691	−0.821426
$307$	−17.2379	−0.983819	−0.491910	−	0.870646i	$-0.663701\pi$
$307$	−17.2379	−0.983819	−0.491910	+	0.870646i	$0.663701\pi$
$308$	−12.0378	−0.685917
$309$	5.52638	0.314385
$310$	1.92598	0.109388
$311$	2.04143	0.115759	0.0578795	−	0.998324i	$-0.481566\pi$
$311$	2.04143	0.115759	0.0578795	+	0.998324i	$0.481566\pi$
$312$	3.13923	0.177724
$313$	−5.02116	−0.283813	−0.141907	−	0.989880i	$-0.545323\pi$
$313$	−5.02116	−0.283813	−0.141907	+	0.989880i	$0.545323\pi$
$314$	6.10094	0.344296
$315$	−5.88885	−0.331799
$316$	−2.42049	−0.136163
$317$	11.7597	0.660491	0.330245	−	0.943895i	$-0.392869\pi$
$317$	11.7597	0.660491	0.330245	+	0.943895i	$0.392869\pi$
$318$	−24.3422	−1.36504
$319$	5.39277	0.301937
$320$	7.11081	0.397506
$321$	−24.3456	−1.35884
$322$	−13.3106	−0.741771
$323$	−0.603457	−0.0335772
$324$	16.0056	0.889200
$325$	−4.91111	−0.272419
$326$	−32.0766	−1.77656
$327$	19.3065	1.06765
$328$	0.619535	0.0342081
$329$	−0.641258	−0.0353537
$330$	37.8596	2.08410
$331$	−11.9128	−0.654788	−0.327394	−	0.944888i	$-0.606170\pi$
$331$	−11.9128	−0.654788	−0.327394	+	0.944888i	$0.606170\pi$
$332$	2.01351	0.110506
$333$	−44.6046	−2.44432
$334$	−4.20434	−0.230051
$335$	−6.42229	−0.350887
$336$	12.4650	0.680020
$337$	−28.6228	−1.55919	−0.779593	−	0.626287i	$-0.784574\pi$
$337$	−28.6228	−1.55919	−0.779593	+	0.626287i	$0.784574\pi$
$338$	−21.9346	−1.19308
$339$	−20.8151	−1.13052
$340$	−2.31970	−0.125803
$341$	−6.26664	−0.339357
$342$	5.76611	0.311796
$343$	−12.9055	−0.696833
$344$	0.490497	0.0264458
$345$	20.3484	1.09552
$346$	−47.9608	−2.57839
$347$	10.6724	0.572925	0.286463	−	0.958091i	$-0.407521\pi$
$347$	10.6724	0.572925	0.286463	+	0.958091i	$0.407521\pi$
$348$	4.75184	0.254726
$349$	15.9888	0.855861	0.427931	−	0.903812i	$-0.359243\pi$
$349$	15.9888	0.855861	0.427931	+	0.903812i	$0.359243\pi$
$350$	−1.95582	−0.104543
$351$	43.1669	2.30408
$352$	−50.5006	−2.69169
$353$	33.8445	1.80136	0.900681	−	0.434481i	$-0.143068\pi$
$353$	33.8445	1.80136	0.900681	+	0.434481i	$0.143068\pi$
$354$	−43.8407	−2.33011
$355$	9.75451	0.517716
$356$	−12.3905	−0.656696
$357$	−3.63514	−0.192392
$358$	−3.97463	−0.210066
$359$	−14.2312	−0.751094	−0.375547	−	0.926803i	$-0.622545\pi$
$359$	−14.2312	−0.751094	−0.375547	+	0.926803i	$0.622545\pi$
$360$	−1.26984	−0.0669264
$361$	−18.7578	−0.987255
$362$	5.35706	0.281561
$363$	−90.2958	−4.73930
$364$	−9.21039	−0.482756
$365$	−13.9521	−0.730288
$366$	20.0868	1.04995
$367$	26.6661	1.39196	0.695979	−	0.718062i	$-0.254971\pi$
$367$	26.6661	1.39196	0.695979	+	0.718062i	$0.254971\pi$
$368$	−28.6177	−1.49180
$369$	17.2128	0.896064
$370$	−14.8142	−0.770153
$371$	−4.09161	−0.212426
$372$	−5.52185	−0.286295
$373$	21.3291	1.10438	0.552190	−	0.833718i	$-0.313792\pi$
$373$	21.3291	1.10438	0.552190	+	0.833718i	$0.313792\pi$
$374$	15.5278	0.802923
$375$	2.98994	0.154400
$376$	−0.138277	−0.00713110
$377$	4.12613	0.212507
$378$	17.1910	0.884207
$379$	−2.12553	−0.109181	−0.0545906	−	0.998509i	$-0.517385\pi$
$379$	−2.12553	−0.109181	−0.0545906	+	0.998509i	$0.517385\pi$
$380$	0.930863	0.0477523
$381$	18.5198	0.948799
$382$	8.80594	0.450551
$383$	6.69375	0.342035	0.171017	−	0.985268i	$-0.445295\pi$
$383$	6.69375	0.342035	0.171017	+	0.985268i	$0.445295\pi$
$384$	5.10617	0.260573
$385$	6.36372	0.324325
$386$	6.37406	0.324431
$387$	13.6277	0.692734
$388$	−3.55006	−0.180227
$389$	33.5018	1.69861	0.849306	−	0.527902i	$-0.177021\pi$
$389$	33.5018	1.69861	0.849306	+	0.527902i	$0.177021\pi$
$390$	28.9673	1.46681
$391$	8.34574	0.422062
$392$	−1.28637	−0.0649715
$393$	−2.64708	−0.133527
$394$	−48.7259	−2.45477
$395$	1.27958	0.0643827
$396$	−72.1192	−3.62413
$397$	−20.7205	−1.03993	−0.519966	−	0.854187i	$-0.674055\pi$
$397$	−20.7205	−1.03993	−0.519966	+	0.854187i	$0.674055\pi$
$398$	−39.9924	−2.00464
$399$	1.45873	0.0730279
$400$	−4.20500	−0.210250
$401$	14.0785	0.703048	0.351524	−	0.936179i	$-0.385664\pi$
$401$	14.0785	0.703048	0.351524	+	0.936179i	$0.385664\pi$
$402$	37.8807	1.88932
$403$	−4.79475	−0.238843
$404$	23.2003	1.15426
$405$	−8.46128	−0.420444
$406$	1.64321	0.0815511
$407$	48.2014	2.38926
$408$	−0.783862	−0.0388070
$409$	−5.46561	−0.270257	−0.135129	−	0.990828i	$-0.543145\pi$
$409$	−5.46561	−0.270257	−0.135129	+	0.990828i	$0.543145\pi$
$410$	5.71677	0.282331
$411$	−66.0587	−3.25843
$412$	−3.49634	−0.172253
$413$	−7.36907	−0.362608
$414$	−79.7447	−3.91924
$415$	−1.06443	−0.0522510
$416$	−38.6392	−1.89444
$417$	55.1688	2.70163
$418$	−6.23108	−0.304772
$419$	−22.0499	−1.07721	−0.538604	−	0.842559i	$-0.681048\pi$
$419$	−22.0499	−1.07721	−0.538604	+	0.842559i	$0.681048\pi$
$420$	5.60740	0.273613
$421$	−32.2685	−1.57267	−0.786336	−	0.617799i	$-0.788025\pi$
$421$	−32.2685	−1.57267	−0.786336	+	0.617799i	$0.788025\pi$
$422$	11.1926	0.544845
$423$	−3.84182	−0.186796
$424$	−0.882292	−0.0428479
$425$	1.22630	0.0594842
$426$	−57.5352	−2.78759
$427$	3.37634	0.163392
$428$	15.4026	0.744514
$429$	−94.2518	−4.55052
$430$	4.52606	0.218266
$431$	−10.4006	−0.500978	−0.250489	−	0.968119i	$-0.580591\pi$
$431$	−10.4006	−0.500978	−0.250489	+	0.968119i	$0.580591\pi$
$432$	36.9604	1.77826
$433$	8.34740	0.401150	0.200575	−	0.979678i	$-0.435719\pi$
$433$	8.34740	0.401150	0.200575	+	0.979678i	$0.435719\pi$
$434$	−1.90948	−0.0916580
$435$	−2.51204	−0.120443
$436$	−12.2145	−0.584970
$437$	−3.34903	−0.160206
$438$	82.2941	3.93216
$439$	−30.9263	−1.47603	−0.738016	−	0.674783i	$-0.764237\pi$
$439$	−30.9263	−1.47603	−0.738016	+	0.674783i	$0.764237\pi$
$440$	1.37224	0.0654188
$441$	−35.7398	−1.70189
$442$	11.8807	0.565106
$443$	−37.8822	−1.79984	−0.899918	−	0.436060i	$-0.856374\pi$
$443$	−37.8822	−1.79984	−0.899918	+	0.436060i	$0.856374\pi$
$444$	42.4727	2.01567
$445$	6.55019	0.310509
$446$	5.22131	0.247236
$447$	3.42013	0.161767
$448$	−7.04989	−0.333076
$449$	−3.63798	−0.171687	−0.0858435	−	0.996309i	$-0.527359\pi$
$449$	−3.63798	−0.171687	−0.0858435	+	0.996309i	$0.527359\pi$
$450$	−11.7174	−0.552366
$451$	−18.6008	−0.875880
$452$	13.1690	0.619417
$453$	−8.99999	−0.422856
$454$	−37.1856	−1.74521
$455$	4.86903	0.228264
$456$	0.314553	0.0147303
$457$	13.7444	0.642935	0.321467	−	0.946921i	$-0.395824\pi$
$457$	13.7444	0.642935	0.321467	+	0.946921i	$0.395824\pi$
$458$	−35.4510	−1.65652
$459$	−10.7787	−0.503108
$460$	−12.8737	−0.600241
$461$	22.6426	1.05457	0.527285	−	0.849689i	$-0.323210\pi$
$461$	22.6426	1.05457	0.527285	+	0.849689i	$0.323210\pi$
$462$	−37.5352	−1.74630
$463$	−13.6147	−0.632730	−0.316365	−	0.948638i	$-0.602462\pi$
$463$	−13.6147	−0.632730	−0.316365	+	0.948638i	$0.602462\pi$
$464$	3.53289	0.164010
$465$	2.91910	0.135370
$466$	19.1503	0.887120
$467$	6.86769	0.317799	0.158899	−	0.987295i	$-0.449205\pi$
$467$	6.86769	0.317799	0.158899	+	0.987295i	$0.449205\pi$
$468$	−55.1801	−2.55070
$469$	6.36726	0.294013
$470$	−1.27595	−0.0588554
$471$	9.24684	0.426072
$472$	−1.58903	−0.0731409
$473$	−14.7266	−0.677130
$474$	−7.54737	−0.346662
$475$	−0.492096	−0.0225789
$476$	2.29983	0.105412
$477$	−24.5131	−1.12238
$478$	−41.2679	−1.88755
$479$	−6.67165	−0.304836	−0.152418	−	0.988316i	$-0.548706\pi$
$479$	−6.67165	−0.304836	−0.152418	+	0.988316i	$0.548706\pi$
$480$	23.5240	1.07372
$481$	36.8800	1.68158
$482$	−0.630699	−0.0287275
$483$	−20.1741	−0.917954
$484$	57.1269	2.59668
$485$	1.87672	0.0852176
$486$	−2.11121	−0.0957666
$487$	3.03804	0.137667	0.0688334	−	0.997628i	$-0.478072\pi$
$487$	3.03804	0.137667	0.0688334	+	0.997628i	$0.478072\pi$
$488$	0.728055	0.0329575
$489$	−48.6167	−2.19852
$490$	−11.8700	−0.536231
$491$	−22.5780	−1.01893	−0.509466	−	0.860491i	$-0.670157\pi$
$491$	−22.5780	−1.01893	−0.509466	+	0.860491i	$0.670157\pi$
$492$	−16.3902	−0.738925
$493$	−1.03029	−0.0464020
$494$	−4.76755	−0.214502
$495$	38.1255	1.71361
$496$	−4.10537	−0.184337
$497$	−9.67094	−0.433801
$498$	6.27837	0.281341
$499$	−40.4175	−1.80933	−0.904667	−	0.426119i	$-0.859881\pi$
$499$	−40.4175	−1.80933	−0.904667	+	0.426119i	$0.859881\pi$
$500$	−1.89163	−0.0845962
$501$	−6.37228	−0.284692
$502$	−22.8132	−1.01820
$503$	−43.4048	−1.93532	−0.967662	−	0.252250i	$-0.918830\pi$
$503$	−43.4048	−1.93532	−0.967662	+	0.252250i	$0.918830\pi$
$504$	1.25896	0.0560785
$505$	−12.2647	−0.545774
$506$	86.1752	3.83096
$507$	−33.2450	−1.47646
$508$	−11.7168	−0.519850
$509$	27.5939	1.22308	0.611538	−	0.791215i	$-0.290551\pi$
$509$	27.5939	1.22308	0.611538	+	0.791215i	$0.290551\pi$
$510$	−7.23310	−0.320287
$511$	13.8326	0.611918
$512$	−31.2858	−1.38265
$513$	4.32535	0.190969
$514$	−0.667880	−0.0294589
$515$	1.84833	0.0814469
$516$	−12.9764	−0.571253
$517$	4.15162	0.182588
$518$	14.6873	0.645321
$519$	−72.6915	−3.19080
$520$	1.04993	0.0460425
$521$	6.15236	0.269540	0.134770	−	0.990877i	$-0.456970\pi$
$521$	6.15236	0.269540	0.134770	+	0.990877i	$0.456970\pi$
$522$	9.84457	0.430885
$523$	8.17346	0.357401	0.178700	−	0.983904i	$-0.442811\pi$
$523$	8.17346	0.357401	0.178700	+	0.983904i	$0.442811\pi$
$524$	1.67471	0.0731601
$525$	−2.96432	−0.129374
$526$	43.4932	1.89639
$527$	1.19724	0.0521528
$528$	−80.7005	−3.51204
$529$	23.3167	1.01377
$530$	−8.14136	−0.353638
$531$	−44.1486	−1.91589
$532$	−0.922888	−0.0400123
$533$	−14.2319	−0.616454
$534$	−38.6351	−1.67190
$535$	−8.14252	−0.352032
$536$	1.37300	0.0593046
$537$	−6.02412	−0.259960
$538$	−46.9332	−2.02343
$539$	38.6218	1.66356
$540$	16.6267	0.715501
$541$	−4.33159	−0.186230	−0.0931148	−	0.995655i	$-0.529682\pi$
$541$	−4.33159	−0.186230	−0.0931148	+	0.995655i	$0.529682\pi$
$542$	36.4351	1.56502
$543$	8.11939	0.348436
$544$	9.64817	0.413662
$545$	6.45716	0.276594
$546$	−28.7191	−1.22906
$547$	−20.2382	−0.865323	−0.432661	−	0.901557i	$-0.642425\pi$
$547$	−20.2382	−0.865323	−0.432661	+	0.901557i	$0.642425\pi$
$548$	41.7930	1.78531
$549$	20.2279	0.863304
$550$	12.6623	0.539924
$551$	0.413441	0.0176132
$552$	−4.35023	−0.185158
$553$	−1.26862	−0.0539471
$554$	15.7477	0.669054
$555$	−22.4530	−0.953077
$556$	−34.9033	−1.48023
$557$	4.61542	0.195562	0.0977808	−	0.995208i	$-0.468826\pi$
$557$	4.61542	0.195562	0.0977808	+	0.995208i	$0.468826\pi$
$558$	−11.4398	−0.484287
$559$	−11.2677	−0.476572
$560$	4.16897	0.176171
$561$	23.5346	0.993631
$562$	−33.3982	−1.40882
$563$	−2.06476	−0.0870191	−0.0435095	−	0.999053i	$-0.513854\pi$
$563$	−2.06476	−0.0870191	−0.0435095	+	0.999053i	$0.513854\pi$
$564$	3.65820	0.154038
$565$	−6.96171	−0.292882
$566$	12.7288	0.535031
$567$	8.38879	0.352296
$568$	−2.08539	−0.0875009
$569$	−16.8124	−0.704814	−0.352407	−	0.935847i	$-0.614637\pi$
$569$	−16.8124	−0.704814	−0.352407	+	0.935847i	$0.614637\pi$
$570$	2.90254	0.121574
$571$	−17.3032	−0.724116	−0.362058	−	0.932156i	$-0.617926\pi$
$571$	−17.3032	−0.724116	−0.362058	+	0.932156i	$0.617926\pi$
$572$	59.6298	2.49325
$573$	13.3466	0.557564
$574$	−5.66779	−0.236569
$575$	6.80564	0.283815
$576$	−42.2364	−1.75985
$577$	15.8068	0.658048	0.329024	−	0.944322i	$-0.393280\pi$
$577$	15.8068	0.658048	0.329024	+	0.944322i	$0.393280\pi$
$578$	30.5697	1.27153
$579$	9.66079	0.401489
$580$	1.58928	0.0659912
$581$	1.05531	0.0437818
$582$	−11.0695	−0.458846
$583$	26.4898	1.09710
$584$	2.98278	0.123428
$585$	29.1707	1.20606
$586$	12.2456	0.505859
$587$	32.5466	1.34334	0.671670	−	0.740850i	$-0.265577\pi$
$587$	32.5466	1.34334	0.671670	+	0.740850i	$0.265577\pi$
$588$	34.0316	1.40344
$589$	−0.480437	−0.0197961
$590$	−14.6628	−0.603656
$591$	−73.8510	−3.03782
$592$	31.5775	1.29783
$593$	−21.7491	−0.893128	−0.446564	−	0.894752i	$-0.647352\pi$
$593$	−21.7491	−0.893128	−0.446564	+	0.894752i	$0.647352\pi$
$594$	−111.297	−4.56659
$595$	−1.21579	−0.0498426
$596$	−2.16380	−0.0886326
$597$	−60.6141	−2.48077
$598$	65.9347	2.69627
$599$	16.9455	0.692374	0.346187	−	0.938166i	$-0.387476\pi$
$599$	16.9455	0.692374	0.346187	+	0.938166i	$0.387476\pi$
$600$	−0.639210	−0.0260956
$601$	22.4684	0.916506	0.458253	−	0.888822i	$-0.348475\pi$
$601$	22.4684	0.916506	0.458253	+	0.888822i	$0.348475\pi$
$602$	−4.48728	−0.182888
$603$	38.1467	1.55345
$604$	5.69397	0.231684
$605$	−30.1999	−1.22780
$606$	72.3413	2.93866
$607$	−15.3447	−0.622821	−0.311410	−	0.950276i	$-0.600801\pi$
$607$	−15.3447	−0.622821	−0.311410	+	0.950276i	$0.600801\pi$
$608$	−3.87167	−0.157017
$609$	2.49052	0.100921
$610$	6.71813	0.272009
$611$	3.17650	0.128507
$612$	13.7784	0.556960
$613$	3.26961	0.132058	0.0660292	−	0.997818i	$-0.478967\pi$
$613$	3.26961	0.132058	0.0660292	+	0.997818i	$0.478967\pi$
$614$	34.0056	1.37235
$615$	8.66457	0.349389
$616$	−1.36048	−0.0548153
$617$	33.2340	1.33795	0.668976	−	0.743284i	$-0.266733\pi$
$617$	33.2340	1.33795	0.668976	+	0.743284i	$0.266733\pi$
$618$	−10.9020	−0.438543
$619$	20.6570	0.830275	0.415137	−	0.909759i	$-0.363733\pi$
$619$	20.6570	0.830275	0.415137	+	0.909759i	$0.363733\pi$
$620$	−1.84681	−0.0741697
$621$	−59.8191	−2.40046
$622$	−4.02718	−0.161475
$623$	−6.49407	−0.260179
$624$	−61.7458	−2.47181
$625$	1.00000	0.0400000
$626$	9.90536	0.395898
$627$	−9.44409	−0.377161
$628$	−5.85015	−0.233446
$629$	−9.20891	−0.367183
$630$	11.6171	0.462835
$631$	40.0942	1.59612	0.798062	−	0.602576i	$-0.205859\pi$
$631$	40.0942	1.59612	0.798062	+	0.602576i	$0.205859\pi$
$632$	−0.273557	−0.0108815
$633$	16.9639	0.674255
$634$	−23.1986	−0.921335
$635$	6.19405	0.245803
$636$	23.3415	0.925552
$637$	29.5504	1.17083
$638$	−10.6384	−0.421179
$639$	−57.9393	−2.29204
$640$	1.70778	0.0675061
$641$	35.6145	1.40669	0.703344	−	0.710850i	$-0.251689\pi$
$641$	35.6145	1.40669	0.703344	+	0.710850i	$0.251689\pi$
$642$	48.0271	1.89548
$643$	−27.8217	−1.09718	−0.548591	−	0.836091i	$-0.684835\pi$
$643$	−27.8217	−1.09718	−0.548591	+	0.836091i	$0.684835\pi$
$644$	12.7634	0.502950
$645$	6.85989	0.270108
$646$	1.19045	0.0468377
$647$	−3.23367	−0.127129	−0.0635643	−	0.997978i	$-0.520247\pi$
$647$	−3.23367	−0.127129	−0.0635643	+	0.997978i	$0.520247\pi$
$648$	1.80891	0.0710608
$649$	47.7087	1.87273
$650$	9.68824	0.380004
$651$	−2.89409	−0.113428
$652$	30.7581	1.20458
$653$	9.55320	0.373845	0.186923	−	0.982375i	$-0.440149\pi$
$653$	9.55320	0.373845	0.186923	+	0.982375i	$0.440149\pi$
$654$	−38.0864	−1.48929
$655$	−0.885328	−0.0345926
$656$	−12.1857	−0.475772
$657$	82.8720	3.23315
$658$	1.26502	0.0493157
$659$	50.7292	1.97613	0.988065	−	0.154038i	$-0.0492277\pi$
$659$	50.7292	1.97613	0.988065	+	0.154038i	$0.0492277\pi$
$660$	−36.3033	−1.41310
$661$	4.98365	0.193842	0.0969208	−	0.995292i	$-0.469101\pi$
$661$	4.98365	0.193842	0.0969208	+	0.995292i	$0.469101\pi$
$662$	23.5007	0.913380
$663$	18.0069	0.699328
$664$	0.227562	0.00883113
$665$	0.487880	0.0189192
$666$	87.9924	3.40964
$667$	−5.71785	−0.221396
$668$	4.03151	0.155984
$669$	7.91364	0.305959
$670$	12.6694	0.489461
$671$	−21.8590	−0.843858
$672$	−23.3224	−0.899683
$673$	−6.14057	−0.236702	−0.118351	−	0.992972i	$-0.537761\pi$
$673$	−6.14057	−0.236702	−0.118351	+	0.992972i	$0.537761\pi$
$674$	56.4649	2.17495
$675$	−8.78964	−0.338313
$676$	21.0329	0.808959
$677$	3.74220	0.143824	0.0719122	−	0.997411i	$-0.477090\pi$
$677$	3.74220	0.143824	0.0719122	+	0.997411i	$0.477090\pi$
$678$	41.0624	1.57699
$679$	−1.86064	−0.0714050
$680$	−0.262167	−0.0100536
$681$	−56.3601	−2.15972
$682$	12.3623	0.473378
$683$	−9.95696	−0.380992	−0.190496	−	0.981688i	$-0.561010\pi$
$683$	−9.95696	−0.380992	−0.190496	+	0.981688i	$0.561010\pi$
$684$	−5.52908	−0.211410
$685$	−22.0936	−0.844155
$686$	25.4590	0.972030
$687$	−53.7311	−2.04997
$688$	−9.64763	−0.367812
$689$	20.2680	0.772148
$690$	−40.1418	−1.52817
$691$	−1.60299	−0.0609807	−0.0304903	−	0.999535i	$-0.509707\pi$
$691$	−1.60299	−0.0609807	−0.0304903	+	0.999535i	$0.509707\pi$
$692$	45.9893	1.74825
$693$	−37.7988	−1.43586
$694$	−21.0537	−0.799187
$695$	18.4515	0.699904
$696$	0.537041	0.0203565
$697$	3.55370	0.134606
$698$	−31.5415	−1.19386
$699$	29.0250	1.09783
$700$	1.87542	0.0708843
$701$	−11.8254	−0.446639	−0.223320	−	0.974745i	$-0.571689\pi$
$701$	−11.8254	−0.446639	−0.223320	+	0.974745i	$0.571689\pi$
$702$	−85.1562	−3.21401
$703$	3.69540	0.139375
$704$	45.6423	1.72021
$705$	−1.93389	−0.0728345
$706$	−66.7658	−2.51276
$707$	12.1597	0.457311
$708$	42.0386	1.57991
$709$	32.1730	1.20828	0.604141	−	0.796878i	$-0.293517\pi$
$709$	32.1730	1.20828	0.604141	+	0.796878i	$0.293517\pi$
$710$	−19.2429	−0.722175
$711$	−7.60037	−0.285036
$712$	−1.40034	−0.0524801
$713$	6.64440	0.248835
$714$	7.17113	0.268373
$715$	−31.5230	−1.17889
$716$	3.81125	0.142433
$717$	−62.5474	−2.33587
$718$	28.0742	1.04772
$719$	−30.7405	−1.14643	−0.573214	−	0.819406i	$-0.694304\pi$
$719$	−30.7405	−1.14643	−0.573214	+	0.819406i	$0.694304\pi$
$720$	24.9766	0.930823
$721$	−1.83249	−0.0682455
$722$	37.0040	1.37715
$723$	−0.955913	−0.0355508
$724$	−5.13685	−0.190909
$725$	−0.840164	−0.0312029
$726$	178.128	6.61097
$727$	−15.7111	−0.582691	−0.291346	−	0.956618i	$-0.594103\pi$
$727$	−15.7111	−0.582691	−0.291346	+	0.956618i	$0.594103\pi$
$728$	−1.04093	−0.0385796
$729$	−28.5837	−1.05866
$730$	27.5237	1.01870
$731$	2.81353	0.104062
$732$	−19.2611	−0.711911
$733$	32.4482	1.19850	0.599250	−	0.800562i	$-0.295465\pi$
$733$	32.4482	1.19850	0.599250	+	0.800562i	$0.295465\pi$
$734$	−52.6047	−1.94168
$735$	−17.9907	−0.663595
$736$	53.5448	1.97369
$737$	−41.2228	−1.51846
$738$	−33.9561	−1.24994
$739$	35.2802	1.29780	0.648902	−	0.760872i	$-0.275228\pi$
$739$	35.2802	1.29780	0.648902	+	0.760872i	$0.275228\pi$
$740$	14.2052	0.522194
$741$	−7.22590	−0.265450
$742$	8.07160	0.296318
$743$	−27.9434	−1.02514	−0.512571	−	0.858645i	$-0.671307\pi$
$743$	−27.9434	−1.02514	−0.512571	+	0.858645i	$0.671307\pi$
$744$	−0.624066	−0.0228794
$745$	1.14388	0.0419085
$746$	−42.0764	−1.54053
$747$	6.32246	0.231327
$748$	−14.8895	−0.544414
$749$	8.07275	0.294972
$750$	−5.89832	−0.215376
$751$	29.3913	1.07251	0.536253	−	0.844058i	$-0.319839\pi$
$751$	29.3913	1.07251	0.536253	+	0.844058i	$0.319839\pi$
$752$	2.71979	0.0991805
$753$	−34.5767	−1.26005
$754$	−8.13971	−0.296431
$755$	−3.01009	−0.109548
$756$	−16.4843	−0.599528
$757$	−53.1859	−1.93308	−0.966538	−	0.256523i	$-0.917423\pi$
$757$	−53.1859	−1.93308	−0.966538	+	0.256523i	$0.917423\pi$
$758$	4.19308	0.152300
$759$	130.611	4.74087
$760$	0.105204	0.00381614
$761$	−12.8847	−0.467070	−0.233535	−	0.972348i	$-0.575029\pi$
$761$	−12.8847	−0.467070	−0.233535	+	0.972348i	$0.575029\pi$
$762$	−36.5344	−1.32350
$763$	−6.40183	−0.231762
$764$	−8.44395	−0.305491
$765$	−7.28389	−0.263350
$766$	−13.2049	−0.477113
$767$	36.5030	1.31805
$768$	−52.5948	−1.89785
$769$	−32.1961	−1.16102	−0.580510	−	0.814253i	$-0.697147\pi$
$769$	−32.1961	−1.16102	−0.580510	+	0.814253i	$0.697147\pi$
$770$	−12.5538	−0.452409
$771$	−1.01227	−0.0364559
$772$	−6.11204	−0.219977
$773$	−15.5883	−0.560671	−0.280336	−	0.959902i	$-0.590446\pi$
$773$	−15.5883	−0.560671	−0.280336	+	0.959902i	$0.590446\pi$
$774$	−26.8836	−0.966312
$775$	0.976308	0.0350700
$776$	−0.401219	−0.0144029
$777$	22.2606	0.798596
$778$	−66.0898	−2.36943
$779$	−1.42605	−0.0510935
$780$	−27.7765	−0.994558
$781$	62.6114	2.24041
$782$	−16.4638	−0.588745
$783$	7.38474	0.263909
$784$	25.3017	0.903634
$785$	3.09265	0.110381
$786$	5.22195	0.186261
$787$	−33.4794	−1.19341	−0.596707	−	0.802459i	$-0.703524\pi$
$787$	−33.4794	−1.19341	−0.596707	+	0.802459i	$0.703524\pi$
$788$	46.7229	1.66443
$789$	65.9201	2.34682
$790$	−2.52425	−0.0898089
$791$	6.90207	0.245409
$792$	−8.15073	−0.289624
$793$	−16.7248	−0.593917
$794$	40.8758	1.45063
$795$	−12.3394	−0.437633
$796$	38.3484	1.35922
$797$	−18.7484	−0.664104	−0.332052	−	0.943261i	$-0.607741\pi$
$797$	−18.7484	−0.664104	−0.332052	+	0.943261i	$0.607741\pi$
$798$	−2.87767	−0.101868
$799$	−0.793169	−0.0280603
$800$	7.86772	0.278166
$801$	−38.9064	−1.37469
$802$	−27.7730	−0.980698
$803$	−89.5547	−3.16032
$804$	−36.3235	−1.28103
$805$	−6.74733	−0.237812
$806$	9.45870	0.333169
$807$	−71.1339	−2.50403
$808$	2.62204	0.0922431
$809$	−39.4903	−1.38841	−0.694203	−	0.719779i	$-0.744243\pi$
$809$	−39.4903	−1.38841	−0.694203	+	0.719779i	$0.744243\pi$
$810$	16.6917	0.586488
$811$	−21.7902	−0.765156	−0.382578	−	0.923923i	$-0.624964\pi$
$811$	−21.7902	−0.765156	−0.382578	+	0.923923i	$0.624964\pi$
$812$	−1.57566	−0.0552949
$813$	55.2226	1.93674
$814$	−95.0880	−3.33283
$815$	−16.2601	−0.569566
$816$	15.4179	0.539734
$817$	−1.12903	−0.0394997
$818$	10.7821	0.376988
$819$	−28.9208	−1.01057
$820$	−5.48177	−0.191432
$821$	−54.0973	−1.88801	−0.944005	−	0.329932i	$-0.892974\pi$
$821$	−54.0973	−1.88801	−0.944005	+	0.329932i	$0.892974\pi$
$822$	130.315	4.54527
$823$	−48.4296	−1.68815	−0.844076	−	0.536224i	$-0.819850\pi$
$823$	−48.4296	−1.68815	−0.844076	+	0.536224i	$0.819850\pi$
$824$	−0.395148	−0.0137656
$825$	19.1916	0.668164
$826$	14.5371	0.505811
$827$	−28.2906	−0.983762	−0.491881	−	0.870662i	$-0.663691\pi$
$827$	−28.2906	−0.983762	−0.491881	+	0.870662i	$0.663691\pi$
$828$	76.4666	2.65740
$829$	−9.12898	−0.317063	−0.158531	−	0.987354i	$-0.550676\pi$
$829$	−9.12898	−0.317063	−0.158531	+	0.987354i	$0.550676\pi$
$830$	2.09983	0.0728862
$831$	23.8678	0.827966
$832$	34.9219	1.21070
$833$	−7.37871	−0.255657
$834$	−108.833	−3.76857
$835$	−2.13124	−0.0737546
$836$	5.97494	0.206648
$837$	−8.58139	−0.296616
$838$	43.4983	1.50262
$839$	−39.6033	−1.36726	−0.683629	−	0.729829i	$-0.739600\pi$
$839$	−39.6033	−1.36726	−0.683629	+	0.729829i	$0.739600\pi$
$840$	0.633733	0.0218659
$841$	−28.2941	−0.975659
$842$	63.6568	2.19376
$843$	−50.6197	−1.74344
$844$	−10.7325	−0.369427
$845$	−11.1190	−0.382504
$846$	7.57884	0.260566
$847$	29.9411	1.02879
$848$	17.3539	0.595935
$849$	19.2923	0.662110
$850$	−2.41914	−0.0829760
$851$	−51.1071	−1.75193
$852$	55.1701	1.89010
$853$	36.4631	1.24847	0.624236	−	0.781236i	$-0.285410\pi$
$853$	36.4631	1.24847	0.624236	+	0.781236i	$0.285410\pi$
$854$	−6.66057	−0.227920
$855$	2.92292	0.0999618
$856$	1.74076	0.0594981
$857$	31.2156	1.06631	0.533153	−	0.846019i	$-0.321007\pi$
$857$	31.2156	1.06631	0.533153	+	0.846019i	$0.321007\pi$
$858$	185.932	6.34763
$859$	5.72092	0.195195	0.0975977	−	0.995226i	$-0.468884\pi$
$859$	5.72092	0.195195	0.0975977	+	0.995226i	$0.468884\pi$
$860$	−4.34001	−0.147993
$861$	−8.59034	−0.292758
$862$	20.5174	0.698826
$863$	−19.8261	−0.674890	−0.337445	−	0.941345i	$-0.609563\pi$
$863$	−19.8261	−0.674890	−0.337445	+	0.941345i	$0.609563\pi$
$864$	−69.1544	−2.35268
$865$	−24.3120	−0.826633
$866$	−16.4671	−0.559574
$867$	46.3327	1.57354
$868$	1.83099	0.0621478
$869$	8.21326	0.278616
$870$	4.95555	0.168009
$871$	−31.5405	−1.06871
$872$	−1.38046	−0.0467481
$873$	−11.1473	−0.377277
$874$	6.60670	0.223475
$875$	−0.991432	−0.0335165
$876$	−78.9112	−2.66616
$877$	33.2904	1.12414	0.562068	−	0.827091i	$-0.310006\pi$
$877$	33.2904	1.12414	0.562068	+	0.827091i	$0.310006\pi$
$878$	61.0090	2.05895
$879$	18.5599	0.626009
$880$	−26.9907	−0.909856
$881$	35.1653	1.18475	0.592375	−	0.805663i	$-0.298191\pi$
$881$	35.1653	1.18475	0.592375	+	0.805663i	$0.298191\pi$
$882$	70.5046	2.37401
$883$	10.8756	0.365993	0.182996	−	0.983114i	$-0.441420\pi$
$883$	10.8756	0.365993	0.182996	+	0.983114i	$0.441420\pi$
$884$	−11.3923	−0.383164
$885$	−22.2235	−0.747034
$886$	74.7309	2.51063
$887$	−24.5579	−0.824573	−0.412286	−	0.911054i	$-0.635270\pi$
$887$	−24.5579	−0.824573	−0.412286	+	0.911054i	$0.635270\pi$
$888$	4.80016	0.161083
$889$	−6.14098	−0.205962
$890$	−12.9217	−0.433136
$891$	−54.3105	−1.81947
$892$	−5.00668	−0.167636
$893$	0.318287	0.0106511
$894$	−6.74697	−0.225652
$895$	−2.01480	−0.0673472
$896$	−1.69315	−0.0565643
$897$	99.9334	3.33668
$898$	7.17673	0.239491
$899$	−0.820258	−0.0273571
$900$	11.2358	0.374526
$901$	−5.06089	−0.168603
$902$	36.6943	1.22179
$903$	−6.80112	−0.226327
$904$	1.48832	0.0495009
$905$	2.71557	0.0902686
$906$	17.7545	0.589853
$907$	−57.6357	−1.91376	−0.956881	−	0.290481i	$-0.906185\pi$
$907$	−57.6357	−1.91376	−0.956881	+	0.290481i	$0.906185\pi$
$908$	35.6570	1.18332
$909$	72.8493	2.41626
$910$	−9.60523	−0.318410
$911$	−10.1867	−0.337502	−0.168751	−	0.985659i	$-0.553973\pi$
$911$	−10.1867	−0.337502	−0.168751	+	0.985659i	$0.553973\pi$
$912$	−6.18697	−0.204871
$913$	−6.83230	−0.226116
$914$	−27.1138	−0.896845
$915$	10.1823	0.336616
$916$	33.9937	1.12318
$917$	0.877743	0.0289856
$918$	21.2634	0.701797
$919$	55.8487	1.84228	0.921139	−	0.389233i	$-0.127260\pi$
$919$	55.8487	1.84228	0.921139	+	0.389233i	$0.127260\pi$
$920$	−1.45496	−0.0479685
$921$	51.5403	1.69831
$922$	−44.6675	−1.47104
$923$	47.9054	1.57683
$924$	35.9923	1.18406
$925$	−7.50952	−0.246911
$926$	26.8580	0.882610
$927$	−10.9786	−0.360584
$928$	−6.61017	−0.216989
$929$	−28.6109	−0.938693	−0.469346	−	0.883014i	$-0.655510\pi$
$929$	−28.6109	−0.938693	−0.469346	+	0.883014i	$0.655510\pi$
$930$	−5.75857	−0.188831
$931$	2.96097	0.0970420
$932$	−18.3631	−0.601502
$933$	−6.10376	−0.199828
$934$	−13.5480	−0.443305
$935$	7.87126	0.257418
$936$	−6.23631	−0.203840
$937$	−15.8208	−0.516842	−0.258421	−	0.966032i	$-0.583202\pi$
$937$	−15.8208	−0.516842	−0.258421	+	0.966032i	$0.583202\pi$
$938$	−12.5608	−0.410126
$939$	15.0130	0.489930
$940$	1.22350	0.0399063
$941$	−19.0784	−0.621939	−0.310970	−	0.950420i	$-0.600654\pi$
$941$	−19.0784	−0.621939	−0.310970	+	0.950420i	$0.600654\pi$
$942$	−18.2414	−0.594338
$943$	19.7221	0.642241
$944$	31.2547	1.01725
$945$	8.71433	0.283477
$946$	29.0515	0.944545
$947$	1.03377	0.0335930	0.0167965	−	0.999859i	$-0.494653\pi$
$947$	1.03377	0.0335930	0.0167965	+	0.999859i	$0.494653\pi$
$948$	7.23712	0.235051
$949$	−68.5204	−2.22427
$950$	0.970768	0.0314959
$951$	−35.1608	−1.14017
$952$	0.259920	0.00842407
$953$	−28.6738	−0.928835	−0.464417	−	0.885616i	$-0.653736\pi$
$953$	−28.6738	−0.928835	−0.464417	+	0.885616i	$0.653736\pi$
$954$	48.3575	1.56563
$955$	4.46385	0.144447
$956$	39.5715	1.27983
$957$	−16.1241	−0.521217
$958$	13.1613	0.425223
$959$	21.9043	0.707328
$960$	−21.2609	−0.686192
$961$	−30.0468	−0.969252
$962$	−72.7540	−2.34568
$963$	48.3644	1.55852
$964$	0.604772	0.0194784
$965$	3.23110	0.104013
$966$	39.7979	1.28048
$967$	19.8980	0.639876	0.319938	−	0.947438i	$-0.396338\pi$
$967$	19.8980	0.639876	0.319938	+	0.947438i	$0.396338\pi$
$968$	6.45634	0.207515
$969$	1.80430	0.0579624
$970$	−3.70225	−0.118872
$971$	22.5998	0.725263	0.362631	−	0.931933i	$-0.381878\pi$
$971$	22.5998	0.725263	0.362631	+	0.931933i	$0.381878\pi$
$972$	2.02443	0.0649336
$973$	−18.2934	−0.586459
$974$	−5.99320	−0.192035
$975$	14.6839	0.470261
$976$	−14.3202	−0.458378
$977$	−15.9214	−0.509369	−0.254685	−	0.967024i	$-0.581972\pi$
$977$	−15.9214	−0.509369	−0.254685	+	0.967024i	$0.581972\pi$
$978$	95.9072	3.06677
$979$	42.0438	1.34372
$980$	11.3820	0.363586
$981$	−38.3538	−1.22454
$982$	44.5402	1.42133
$983$	−41.8592	−1.33510	−0.667550	−	0.744565i	$-0.732657\pi$
$983$	−41.8592	−1.33510	−0.667550	+	0.744565i	$0.732657\pi$
$984$	−1.85237	−0.0590515
$985$	−24.6998	−0.787002
$986$	2.03248	0.0647273
$987$	1.91732	0.0610290
$988$	4.57157	0.145441
$989$	15.6143	0.496507
$990$	−75.2109	−2.39036
$991$	46.1662	1.46652	0.733259	−	0.679950i	$-0.237999\pi$
$991$	46.1662	1.46652	0.733259	+	0.679950i	$0.237999\pi$
$992$	7.68131	0.243882
$993$	35.6186	1.13032
$994$	19.0781	0.605120
$995$	−20.2727	−0.642688
$996$	−6.02029	−0.190760
$997$	−29.7630	−0.942605	−0.471302	−	0.881972i	$-0.656216\pi$
$997$	−29.7630	−0.942605	−0.471302	+	0.881972i	$0.656216\pi$
$998$	79.7324	2.52388
$999$	66.0060	2.08834

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.d.1.14	✓	83

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.d.1.14	✓	83	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-1.97272 q^{2} -2.98994 q^{3} +1.89163 q^{4} -1.00000 q^{5} +5.89832 q^{6} +0.991432 q^{7} +0.213787 q^{8} +5.93974 q^{9} +O(q^{10})\)	\(q-1.97272 q^{2} -2.98994 q^{3} +1.89163 q^{4} -1.00000 q^{5} +5.89832 q^{6} +0.991432 q^{7} +0.213787 q^{8} +5.93974 q^{9} +1.97272 q^{10} -6.41871 q^{11} -5.65585 q^{12} -4.91111 q^{13} -1.95582 q^{14} +2.98994 q^{15} -4.20500 q^{16} +1.22630 q^{17} -11.7174 q^{18} -0.492096 q^{19} -1.89163 q^{20} -2.96432 q^{21} +12.6623 q^{22} +6.80564 q^{23} -0.639210 q^{24} +1.00000 q^{25} +9.68824 q^{26} -8.78964 q^{27} +1.87542 q^{28} -0.840164 q^{29} -5.89832 q^{30} +0.976308 q^{31} +7.86772 q^{32} +19.1916 q^{33} -2.41914 q^{34} -0.991432 q^{35} +11.2358 q^{36} -7.50952 q^{37} +0.970768 q^{38} +14.6839 q^{39} -0.213787 q^{40} +2.89791 q^{41} +5.84778 q^{42} +2.29432 q^{43} -12.1418 q^{44} -5.93974 q^{45} -13.4256 q^{46} -0.646799 q^{47} +12.5727 q^{48} -6.01706 q^{49} -1.97272 q^{50} -3.66656 q^{51} -9.28999 q^{52} -4.12697 q^{53} +17.3395 q^{54} +6.41871 q^{55} +0.211955 q^{56} +1.47134 q^{57} +1.65741 q^{58} -7.43276 q^{59} +5.65585 q^{60} +3.40551 q^{61} -1.92598 q^{62} +5.88885 q^{63} -7.11081 q^{64} +4.91111 q^{65} -37.8596 q^{66} +6.42229 q^{67} +2.31970 q^{68} -20.3484 q^{69} +1.95582 q^{70} -9.75451 q^{71} +1.26984 q^{72} +13.9521 q^{73} +14.8142 q^{74} -2.98994 q^{75} -0.930863 q^{76} -6.36372 q^{77} -28.9673 q^{78} -1.27958 q^{79} +4.20500 q^{80} +8.46128 q^{81} -5.71677 q^{82} +1.06443 q^{83} -5.60740 q^{84} -1.22630 q^{85} -4.52606 q^{86} +2.51204 q^{87} -1.37224 q^{88} -6.55019 q^{89} +11.7174 q^{90} -4.86903 q^{91} +12.8737 q^{92} -2.91910 q^{93} +1.27595 q^{94} +0.492096 q^{95} -23.5240 q^{96} -1.87672 q^{97} +11.8700 q^{98} -38.1255 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9}+O(q^{10}) \) 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9	\( 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9} - q^{10} - 26 q^{11} - 12 q^{12} - 15 q^{13} - 21 q^{14} + 4 q^{15} + 5 q^{16} + 8 q^{17} - 12 q^{18} - 79 q^{19} - 61 q^{20} - 34 q^{21} - 25 q^{22} + 31 q^{23} - 42 q^{24} + 83 q^{25} - 13 q^{26} - 25 q^{27} - 16 q^{28} - 16 q^{29} + 6 q^{30} - 40 q^{31} + 15 q^{32} - 33 q^{33} - 54 q^{34} - 2 q^{35} + 11 q^{36} - 45 q^{37} + 10 q^{38} - 54 q^{39} + 3 q^{40} - 27 q^{41} - 28 q^{42} - 101 q^{43} - 51 q^{44} - 61 q^{45} - 46 q^{46} + 71 q^{47} - 14 q^{48} + 23 q^{49} + q^{50} - 71 q^{51} - 34 q^{52} - 49 q^{53} - 25 q^{54} + 26 q^{55} - 41 q^{56} - 20 q^{57} - 43 q^{58} - 60 q^{59} + 12 q^{60} - 38 q^{61} - 2 q^{62} + 36 q^{63} - 113 q^{64} + 15 q^{65} - 42 q^{66} - 164 q^{67} + 10 q^{68} - 93 q^{69} + 21 q^{70} - 78 q^{71} + q^{72} - 18 q^{73} - 23 q^{74} - 4 q^{75} - 112 q^{76} - 35 q^{77} - 44 q^{78} - 124 q^{79} - 5 q^{80} - 45 q^{81} - 34 q^{82} + 5 q^{83} - 60 q^{84} - 8 q^{85} - 25 q^{86} + 12 q^{87} - 149 q^{88} - 44 q^{89} + 12 q^{90} - 192 q^{91} + 35 q^{92} - 13 q^{93} - 32 q^{94} + 79 q^{95} - 59 q^{96} - 31 q^{97} + 25 q^{98} - 134 q^{99}+O(q^{100}) \) 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9 - q^10 - 26 * q^11 - 12 * q^12 - 15 * q^13 - 21 * q^14 + 4 * q^15 + 5 * q^16 + 8 * q^17 - 12 * q^18 - 79 * q^19 - 61 * q^20 - 34 * q^21 - 25 * q^22 + 31 * q^23 - 42 * q^24 + 83 * q^25 - 13 * q^26 - 25 * q^27 - 16 * q^28 - 16 * q^29 + 6 * q^30 - 40 * q^31 + 15 * q^32 - 33 * q^33 - 54 * q^34 - 2 * q^35 + 11 * q^36 - 45 * q^37 + 10 * q^38 - 54 * q^39 + 3 * q^40 - 27 * q^41 - 28 * q^42 - 101 * q^43 - 51 * q^44 - 61 * q^45 - 46 * q^46 + 71 * q^47 - 14 * q^48 + 23 * q^49 + q^50 - 71 * q^51 - 34 * q^52 - 49 * q^53 - 25 * q^54 + 26 * q^55 - 41 * q^56 - 20 * q^57 - 43 * q^58 - 60 * q^59 + 12 * q^60 - 38 * q^61 - 2 * q^62 + 36 * q^63 - 113 * q^64 + 15 * q^65 - 42 * q^66 - 164 * q^67 + 10 * q^68 - 93 * q^69 + 21 * q^70 - 78 * q^71 + q^72 - 18 * q^73 - 23 * q^74 - 4 * q^75 - 112 * q^76 - 35 * q^77 - 44 * q^78 - 124 * q^79 - 5 * q^80 - 45 * q^81 - 34 * q^82 + 5 * q^83 - 60 * q^84 - 8 * q^85 - 25 * q^86 + 12 * q^87 - 149 * q^88 - 44 * q^89 + 12 * q^90 - 192 * q^91 + 35 * q^92 - 13 * q^93 - 32 * q^94 + 79 * q^95 - 59 * q^96 - 31 * q^97 + 25 * q^98 - 134 * q^99

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