LMFDB - Embedded newform 6001.2.a.c.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, 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("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.60140 q^{2} -0.594038 q^{3} +4.76726 q^{4} +2.91382 q^{5} +1.54533 q^{6} +0.0965456 q^{7} -7.19873 q^{8} -2.64712 q^{9} +O(q^{10})$	\(q-2.60140 q^{2} -0.594038 q^{3} +4.76726 q^{4} +2.91382 q^{5} +1.54533 q^{6} +0.0965456 q^{7} -7.19873 q^{8} -2.64712 q^{9} -7.57999 q^{10} -5.88337 q^{11} -2.83193 q^{12} -6.12764 q^{13} -0.251153 q^{14} -1.73092 q^{15} +9.19224 q^{16} -1.00000 q^{17} +6.88620 q^{18} -4.93625 q^{19} +13.8909 q^{20} -0.0573517 q^{21} +15.3050 q^{22} -3.35293 q^{23} +4.27632 q^{24} +3.49033 q^{25} +15.9404 q^{26} +3.35460 q^{27} +0.460258 q^{28} -7.11347 q^{29} +4.50280 q^{30} +0.393923 q^{31} -9.51518 q^{32} +3.49495 q^{33} +2.60140 q^{34} +0.281316 q^{35} -12.6195 q^{36} +3.55488 q^{37} +12.8411 q^{38} +3.64005 q^{39} -20.9758 q^{40} -2.14336 q^{41} +0.149194 q^{42} -7.34995 q^{43} -28.0476 q^{44} -7.71322 q^{45} +8.72229 q^{46} +7.47327 q^{47} -5.46054 q^{48} -6.99068 q^{49} -9.07973 q^{50} +0.594038 q^{51} -29.2121 q^{52} +0.693284 q^{53} -8.72665 q^{54} -17.1431 q^{55} -0.695006 q^{56} +2.93232 q^{57} +18.5050 q^{58} -9.55778 q^{59} -8.25173 q^{60} -4.59984 q^{61} -1.02475 q^{62} -0.255568 q^{63} +6.36827 q^{64} -17.8548 q^{65} -9.09174 q^{66} -5.40208 q^{67} -4.76726 q^{68} +1.99177 q^{69} -0.731815 q^{70} +10.2893 q^{71} +19.0559 q^{72} +0.189896 q^{73} -9.24764 q^{74} -2.07339 q^{75} -23.5324 q^{76} -0.568014 q^{77} -9.46921 q^{78} +3.39840 q^{79} +26.7845 q^{80} +5.94860 q^{81} +5.57573 q^{82} +3.43728 q^{83} -0.273410 q^{84} -2.91382 q^{85} +19.1201 q^{86} +4.22567 q^{87} +42.3529 q^{88} +18.6068 q^{89} +20.0651 q^{90} -0.591597 q^{91} -15.9843 q^{92} -0.234005 q^{93} -19.4409 q^{94} -14.3833 q^{95} +5.65237 q^{96} -13.6214 q^{97} +18.1855 q^{98} +15.5740 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) $ 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9} - q^{10} + 40 q^{11} + 41 q^{12} + 14 q^{13} + 32 q^{14} + 49 q^{15} + 135 q^{16} - 121 q^{17} + 28 q^{18} + 34 q^{19} + 64 q^{20} + 34 q^{21} - 18 q^{22} + 37 q^{23} + 54 q^{24} + 128 q^{25} + 91 q^{26} + 55 q^{27} - 28 q^{28} + 45 q^{29} + 30 q^{30} + 67 q^{31} + 47 q^{32} + 40 q^{33} - 9 q^{34} + 59 q^{35} + 138 q^{36} - 16 q^{37} + 30 q^{38} + 37 q^{39} + 14 q^{40} + 89 q^{41} + 33 q^{42} + 16 q^{43} + 90 q^{44} + 83 q^{45} - 9 q^{46} + 135 q^{47} + 96 q^{48} + 128 q^{49} + 71 q^{50} - 13 q^{51} + 47 q^{52} + 52 q^{53} + 90 q^{54} + 93 q^{55} + 69 q^{56} - 4 q^{57} + 5 q^{58} + 170 q^{59} + 78 q^{60} - 2 q^{61} + 46 q^{62} - 10 q^{63} + 182 q^{64} + 50 q^{65} + 68 q^{66} + 46 q^{67} - 127 q^{68} + 97 q^{69} + 46 q^{70} + 191 q^{71} + 57 q^{72} - 12 q^{73} + 68 q^{74} + 86 q^{75} + 108 q^{76} + 62 q^{77} - 10 q^{78} + 130 q^{80} + 149 q^{81} + 14 q^{82} + 83 q^{83} + 126 q^{84} - 21 q^{85} + 132 q^{86} + 50 q^{87} - 42 q^{88} + 144 q^{89} + 9 q^{90} + 13 q^{91} + 50 q^{92} + 43 q^{93} + 41 q^{94} + 82 q^{95} + 110 q^{96} - 3 q^{97} + 36 q^{98} + 89 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9 - q^10 + 40 * q^11 + 41 * q^12 + 14 * q^13 + 32 * q^14 + 49 * q^15 + 135 * q^16 - 121 * q^17 + 28 * q^18 + 34 * q^19 + 64 * q^20 + 34 * q^21 - 18 * q^22 + 37 * q^23 + 54 * q^24 + 128 * q^25 + 91 * q^26 + 55 * q^27 - 28 * q^28 + 45 * q^29 + 30 * q^30 + 67 * q^31 + 47 * q^32 + 40 * q^33 - 9 * q^34 + 59 * q^35 + 138 * q^36 - 16 * q^37 + 30 * q^38 + 37 * q^39 + 14 * q^40 + 89 * q^41 + 33 * q^42 + 16 * q^43 + 90 * q^44 + 83 * q^45 - 9 * q^46 + 135 * q^47 + 96 * q^48 + 128 * q^49 + 71 * q^50 - 13 * q^51 + 47 * q^52 + 52 * q^53 + 90 * q^54 + 93 * q^55 + 69 * q^56 - 4 * q^57 + 5 * q^58 + 170 * q^59 + 78 * q^60 - 2 * q^61 + 46 * q^62 - 10 * q^63 + 182 * q^64 + 50 * q^65 + 68 * q^66 + 46 * q^67 - 127 * q^68 + 97 * q^69 + 46 * q^70 + 191 * q^71 + 57 * q^72 - 12 * q^73 + 68 * q^74 + 86 * q^75 + 108 * q^76 + 62 * q^77 - 10 * q^78 + 130 * q^80 + 149 * q^81 + 14 * q^82 + 83 * q^83 + 126 * q^84 - 21 * q^85 + 132 * q^86 + 50 * q^87 - 42 * q^88 + 144 * q^89 + 9 * q^90 + 13 * q^91 + 50 * q^92 + 43 * q^93 + 41 * q^94 + 82 * q^95 + 110 * q^96 - 3 * q^97 + 36 * q^98 + 89 * 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 $

$2$	−2.60140	−1.83946	−0.919732	−	0.392546i	$-0.871594\pi$
$2$	−2.60140	−1.83946	−0.919732	+	0.392546i	$0.871594\pi$
$3$	−0.594038	−0.342968	−0.171484	−	0.985187i	$-0.554856\pi$
$3$	−0.594038	−0.342968	−0.171484	+	0.985187i	$0.554856\pi$
$4$	4.76726	2.38363
$5$	2.91382	1.30310	0.651549	−	0.758606i	$-0.274119\pi$
$5$	2.91382	1.30310	0.651549	+	0.758606i	$0.274119\pi$
$6$	1.54533	0.630877
$7$	0.0965456	0.0364908	0.0182454	−	0.999834i	$-0.494192\pi$
$7$	0.0965456	0.0364908	0.0182454	+	0.999834i	$0.494192\pi$
$8$	−7.19873	−2.54514
$9$	−2.64712	−0.882373
$10$	−7.57999	−2.39700
$11$	−5.88337	−1.77390	−0.886952	−	0.461861i	$-0.847182\pi$
$11$	−5.88337	−1.77390	−0.886952	+	0.461861i	$0.847182\pi$
$12$	−2.83193	−0.817508
$13$	−6.12764	−1.69950	−0.849751	−	0.527183i	$-0.823248\pi$
$13$	−6.12764	−1.69950	−0.849751	+	0.527183i	$0.823248\pi$
$14$	−0.251153	−0.0671235
$15$	−1.73092	−0.446921
$16$	9.19224	2.29806
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	6.88620	1.62309
$19$	−4.93625	−1.13245	−0.566226	−	0.824250i	$-0.691597\pi$
$19$	−4.93625	−1.13245	−0.566226	+	0.824250i	$0.691597\pi$
$20$	13.8909	3.10610
$21$	−0.0573517	−0.0125152
$22$	15.3050	3.26303
$23$	−3.35293	−0.699134	−0.349567	−	0.936911i	$-0.613671\pi$
$23$	−3.35293	−0.699134	−0.349567	+	0.936911i	$0.613671\pi$
$24$	4.27632	0.872900
$25$	3.49033	0.698066
$26$	15.9404	3.12618
$27$	3.35460	0.645593
$28$	0.460258	0.0869805
$29$	−7.11347	−1.32094	−0.660469	−	0.750853i	$-0.729643\pi$
$29$	−7.11347	−1.32094	−0.660469	+	0.750853i	$0.729643\pi$
$30$	4.50280	0.822095
$31$	0.393923	0.0707507	0.0353753	−	0.999374i	$-0.488737\pi$
$31$	0.393923	0.0707507	0.0353753	+	0.999374i	$0.488737\pi$
$32$	−9.51518	−1.68206
$33$	3.49495	0.608392
$34$	2.60140	0.446136
$35$	0.281316	0.0475511
$36$	−12.6195	−2.10325
$37$	3.55488	0.584418	0.292209	−	0.956354i	$-0.405610\pi$
$37$	3.55488	0.584418	0.292209	+	0.956354i	$0.405610\pi$
$38$	12.8411	2.08311
$39$	3.64005	0.582875
$40$	−20.9758	−3.31656
$41$	−2.14336	−0.334737	−0.167369	−	0.985894i	$-0.553527\pi$
$41$	−2.14336	−0.334737	−0.167369	+	0.985894i	$0.553527\pi$
$42$	0.149194	0.0230212
$43$	−7.34995	−1.12086	−0.560429	−	0.828203i	$-0.689364\pi$
$43$	−7.34995	−1.12086	−0.560429	+	0.828203i	$0.689364\pi$
$44$	−28.0476	−4.22833
$45$	−7.71322	−1.14982
$46$	8.72229	1.28603
$47$	7.47327	1.09009	0.545045	−	0.838407i	$-0.316513\pi$
$47$	7.47327	1.09009	0.545045	+	0.838407i	$0.316513\pi$
$48$	−5.46054	−0.788160
$49$	−6.99068	−0.998668
$50$	−9.07973	−1.28407
$51$	0.594038	0.0831819
$52$	−29.2121	−4.05099
$53$	0.693284	0.0952299	0.0476150	−	0.998866i	$-0.484838\pi$
$53$	0.693284	0.0952299	0.0476150	+	0.998866i	$0.484838\pi$
$54$	−8.72665	−1.18755
$55$	−17.1431	−2.31157
$56$	−0.695006	−0.0928741
$57$	2.93232	0.388395
$58$	18.5050	2.42982
$59$	−9.55778	−1.24432	−0.622158	−	0.782892i	$-0.713744\pi$
$59$	−9.55778	−1.24432	−0.622158	+	0.782892i	$0.713744\pi$
$60$	−8.25173	−1.06529
$61$	−4.59984	−0.588949	−0.294475	−	0.955659i	$-0.595145\pi$
$61$	−4.59984	−0.588949	−0.294475	+	0.955659i	$0.595145\pi$
$62$	−1.02475	−0.130143
$63$	−0.255568	−0.0321985
$64$	6.36827	0.796033
$65$	−17.8548	−2.21462
$66$	−9.09174	−1.11912
$67$	−5.40208	−0.659970	−0.329985	−	0.943986i	$-0.607044\pi$
$67$	−5.40208	−0.659970	−0.329985	+	0.943986i	$0.607044\pi$
$68$	−4.76726	−0.578115
$69$	1.99177	0.239780
$70$	−0.731815	−0.0874686
$71$	10.2893	1.22112	0.610559	−	0.791971i	$-0.290945\pi$
$71$	10.2893	1.22112	0.610559	+	0.791971i	$0.290945\pi$
$72$	19.0559	2.24576
$73$	0.189896	0.0222257	0.0111128	−	0.999938i	$-0.496463\pi$
$73$	0.189896	0.0222257	0.0111128	+	0.999938i	$0.496463\pi$
$74$	−9.24764	−1.07502
$75$	−2.07339	−0.239414
$76$	−23.5324	−2.69935
$77$	−0.568014	−0.0647312
$78$	−9.46921	−1.07218
$79$	3.39840	0.382350	0.191175	−	0.981556i	$-0.438770\pi$
$79$	3.39840	0.382350	0.191175	+	0.981556i	$0.438770\pi$
$80$	26.7845	2.99460
$81$	5.94860	0.660955
$82$	5.57573	0.615737
$83$	3.43728	0.377290	0.188645	−	0.982045i	$-0.439590\pi$
$83$	3.43728	0.377290	0.188645	+	0.982045i	$0.439590\pi$
$84$	−0.273410	−0.0298315
$85$	−2.91382	−0.316048
$86$	19.1201	2.06178
$87$	4.22567	0.453039
$88$	42.3529	4.51483
$89$	18.6068	1.97232	0.986160	−	0.165795i	$-0.0530190\pi$
$89$	18.6068	1.97232	0.986160	+	0.165795i	$0.0530190\pi$
$90$	20.0651	2.11505
$91$	−0.591597	−0.0620162
$92$	−15.9843	−1.66648
$93$	−0.234005	−0.0242652
$94$	−19.4409	−2.00518
$95$	−14.3833	−1.47570
$96$	5.65237	0.576893
$97$	−13.6214	−1.38304	−0.691522	−	0.722355i	$-0.743060\pi$
$97$	−13.6214	−1.38304	−0.691522	+	0.722355i	$0.743060\pi$
$98$	18.1855	1.83702
$99$	15.5740	1.56525
$100$	16.6393	1.66393
$101$	4.37565	0.435394	0.217697	−	0.976016i	$-0.430146\pi$
$101$	4.37565	0.435394	0.217697	+	0.976016i	$0.430146\pi$
$102$	−1.54533	−0.153010
$103$	11.8346	1.16610	0.583049	−	0.812437i	$-0.301860\pi$
$103$	11.8346	1.16610	0.583049	+	0.812437i	$0.301860\pi$
$104$	44.1113	4.32547
$105$	−0.167112	−0.0163085
$106$	−1.80351	−0.175172
$107$	−12.6559	−1.22349	−0.611746	−	0.791055i	$-0.709532\pi$
$107$	−12.6559	−1.22349	−0.611746	+	0.791055i	$0.709532\pi$
$108$	15.9923	1.53886
$109$	−15.0594	−1.44243	−0.721213	−	0.692713i	$-0.756415\pi$
$109$	−15.0594	−1.44243	−0.721213	+	0.692713i	$0.756415\pi$
$110$	44.5959	4.25205
$111$	−2.11173	−0.200437
$112$	0.887470	0.0838580
$113$	−3.35416	−0.315533	−0.157767	−	0.987476i	$-0.550429\pi$
$113$	−3.35416	−0.315533	−0.157767	+	0.987476i	$0.550429\pi$
$114$	−7.62811	−0.714438
$115$	−9.76982	−0.911040
$116$	−33.9118	−3.14863
$117$	16.2206	1.49960
$118$	24.8636	2.28888
$119$	−0.0965456	−0.00885032
$120$	12.4604	1.13747
$121$	23.6141	2.14674
$122$	11.9660	1.08335
$123$	1.27324	0.114804
$124$	1.87793	0.168643
$125$	−4.39890	−0.393450
$126$	0.664833	0.0592280
$127$	3.19000	0.283067	0.141533	−	0.989933i	$-0.454797\pi$
$127$	3.19000	0.283067	0.141533	+	0.989933i	$0.454797\pi$
$128$	2.46398	0.217787
$129$	4.36615	0.384418
$130$	46.4475	4.07371
$131$	11.8416	1.03460	0.517302	−	0.855803i	$-0.326936\pi$
$131$	11.8416	1.03460	0.517302	+	0.855803i	$0.326936\pi$
$132$	16.6613	1.45018
$133$	−0.476573	−0.0413241
$134$	14.0530	1.21399
$135$	9.77470	0.841272
$136$	7.19873	0.617286
$137$	5.29476	0.452362	0.226181	−	0.974085i	$-0.427376\pi$
$137$	5.29476	0.452362	0.226181	+	0.974085i	$0.427376\pi$
$138$	−5.18137	−0.441067
$139$	10.8321	0.918767	0.459383	−	0.888238i	$-0.348070\pi$
$139$	10.8321	0.918767	0.459383	+	0.888238i	$0.348070\pi$
$140$	1.34111	0.113344
$141$	−4.43941	−0.373865
$142$	−26.7666	−2.24620
$143$	36.0512	3.01476
$144$	−24.3330	−2.02775
$145$	−20.7274	−1.72131
$146$	−0.493995	−0.0408833
$147$	4.15273	0.342511
$148$	16.9470	1.39304
$149$	6.50773	0.533134	0.266567	−	0.963816i	$-0.414111\pi$
$149$	6.50773	0.533134	0.266567	+	0.963816i	$0.414111\pi$
$150$	5.39370	0.440394
$151$	12.6987	1.03340	0.516702	−	0.856165i	$-0.327160\pi$
$151$	12.6987	1.03340	0.516702	+	0.856165i	$0.327160\pi$
$152$	35.5347	2.88225
$153$	2.64712	0.214007
$154$	1.47763	0.119071
$155$	1.14782	0.0921951
$156$	17.3531	1.38936
$157$	−24.3493	−1.94329	−0.971643	−	0.236452i	$-0.924015\pi$
$157$	−24.3493	−1.94329	−0.971643	+	0.236452i	$0.924015\pi$
$158$	−8.84059	−0.703319
$159$	−0.411837	−0.0326608
$160$	−27.7255	−2.19189
$161$	−0.323710	−0.0255119
$162$	−15.4747	−1.21580
$163$	−5.57305	−0.436515	−0.218257	−	0.975891i	$-0.570037\pi$
$163$	−5.57305	−0.436515	−0.218257	+	0.975891i	$0.570037\pi$
$164$	−10.2180	−0.797889
$165$	10.1836	0.792795
$166$	−8.94172	−0.694012
$167$	−5.09973	−0.394629	−0.197314	−	0.980340i	$-0.563222\pi$
$167$	−5.09973	−0.394629	−0.197314	+	0.980340i	$0.563222\pi$
$168$	0.412860	0.0318528
$169$	24.5480	1.88831
$170$	7.57999	0.581359
$171$	13.0668	0.999246
$172$	−35.0391	−2.67171
$173$	13.5722	1.03188	0.515939	−	0.856625i	$-0.327443\pi$
$173$	13.5722	1.03188	0.515939	+	0.856625i	$0.327443\pi$
$174$	−10.9926	−0.833350
$175$	0.336976	0.0254730
$176$	−54.0814	−4.07654
$177$	5.67768	0.426760
$178$	−48.4037	−3.62801
$179$	−7.68763	−0.574600	−0.287300	−	0.957841i	$-0.592758\pi$
$179$	−7.68763	−0.574600	−0.287300	+	0.957841i	$0.592758\pi$
$180$	−36.7709	−2.74074
$181$	14.6003	1.08523	0.542617	−	0.839980i	$-0.317433\pi$
$181$	14.6003	1.08523	0.542617	+	0.839980i	$0.317433\pi$
$182$	1.53898	0.114077
$183$	2.73248	0.201991
$184$	24.1368	1.77939
$185$	10.3583	0.761554
$186$	0.608740	0.0446350
$187$	5.88337	0.430235
$188$	35.6270	2.59837
$189$	0.323872	0.0235582
$190$	37.4167	2.71449
$191$	1.48118	0.107174	0.0535871	−	0.998563i	$-0.482935\pi$
$191$	1.48118	0.107174	0.0535871	+	0.998563i	$0.482935\pi$
$192$	−3.78299	−0.273014
$193$	8.36763	0.602315	0.301158	−	0.953574i	$-0.402627\pi$
$193$	8.36763	0.602315	0.301158	+	0.953574i	$0.402627\pi$
$194$	35.4347	2.54406
$195$	10.6064	0.759543
$196$	−33.3264	−2.38046
$197$	−19.2631	−1.37244	−0.686219	−	0.727395i	$-0.740731\pi$
$197$	−19.2631	−1.37244	−0.686219	+	0.727395i	$0.740731\pi$
$198$	−40.5141	−2.87921
$199$	13.7499	0.974703	0.487352	−	0.873206i	$-0.337963\pi$
$199$	13.7499	0.974703	0.487352	+	0.873206i	$0.337963\pi$
$200$	−25.1260	−1.77667
$201$	3.20904	0.226348
$202$	−11.3828	−0.800891
$203$	−0.686774	−0.0482021
$204$	2.83193	0.198275
$205$	−6.24537	−0.436195
$206$	−30.7865	−2.14499
$207$	8.87560	0.616897
$208$	−56.3268	−3.90556
$209$	29.0418	2.00886
$210$	0.434725	0.0299989
$211$	5.43837	0.374393	0.187197	−	0.982322i	$-0.440060\pi$
$211$	5.43837	0.374393	0.187197	+	0.982322i	$0.440060\pi$
$212$	3.30507	0.226993
$213$	−6.11224	−0.418804
$214$	32.9230	2.25057
$215$	−21.4164	−1.46059
$216$	−24.1489	−1.64312
$217$	0.0380315	0.00258175
$218$	39.1754	2.65329
$219$	−0.112806	−0.00762269
$220$	−81.7255	−5.50993
$221$	6.12764	0.412190
$222$	5.49345	0.368696
$223$	−3.96192	−0.265310	−0.132655	−	0.991162i	$-0.542350\pi$
$223$	−3.96192	−0.265310	−0.132655	+	0.991162i	$0.542350\pi$
$224$	−0.918648	−0.0613798
$225$	−9.23932	−0.615955
$226$	8.72550	0.580412
$227$	−2.92267	−0.193985	−0.0969923	−	0.995285i	$-0.530922\pi$
$227$	−2.92267	−0.193985	−0.0969923	+	0.995285i	$0.530922\pi$
$228$	13.9791	0.925789
$229$	−9.55345	−0.631310	−0.315655	−	0.948874i	$-0.602224\pi$
$229$	−9.55345	−0.631310	−0.315655	+	0.948874i	$0.602224\pi$
$230$	25.4152	1.67583
$231$	0.337422	0.0222007
$232$	51.2080	3.36197
$233$	−16.3832	−1.07330	−0.536649	−	0.843806i	$-0.680310\pi$
$233$	−16.3832	−1.07330	−0.536649	+	0.843806i	$0.680310\pi$
$234$	−42.1962	−2.75845
$235$	21.7758	1.42049
$236$	−45.5644	−2.96599
$237$	−2.01878	−0.131134
$238$	0.251153	0.0162798
$239$	−5.17377	−0.334663	−0.167332	−	0.985901i	$-0.553515\pi$
$239$	−5.17377	−0.334663	−0.167332	+	0.985901i	$0.553515\pi$
$240$	−15.9110	−1.02705
$241$	14.1529	0.911671	0.455836	−	0.890064i	$-0.349340\pi$
$241$	14.1529	0.911671	0.455836	+	0.890064i	$0.349340\pi$
$242$	−61.4296	−3.94884
$243$	−13.5975	−0.872280
$244$	−21.9286	−1.40384
$245$	−20.3696	−1.30136
$246$	−3.31220	−0.211178
$247$	30.2476	1.92461
$248$	−2.83575	−0.180070
$249$	−2.04187	−0.129398
$250$	11.4433	0.723737
$251$	18.7472	1.18331	0.591655	−	0.806191i	$-0.298475\pi$
$251$	18.7472	1.18331	0.591655	+	0.806191i	$0.298475\pi$
$252$	−1.21836	−0.0767493
$253$	19.7265	1.24020
$254$	−8.29845	−0.520691
$255$	1.73092	0.108394
$256$	−19.1463	−1.19664
$257$	−13.1385	−0.819557	−0.409778	−	0.912185i	$-0.634394\pi$
$257$	−13.1385	−0.819557	−0.409778	+	0.912185i	$0.634394\pi$
$258$	−11.3581	−0.707123
$259$	0.343208	0.0213259
$260$	−85.1186	−5.27883
$261$	18.8302	1.16556
$262$	−30.8047	−1.90312
$263$	17.0269	1.04992	0.524961	−	0.851126i	$-0.324080\pi$
$263$	17.0269	1.04992	0.524961	+	0.851126i	$0.324080\pi$
$264$	−25.1592	−1.54844
$265$	2.02010	0.124094
$266$	1.23975	0.0760142
$267$	−11.0532	−0.676442
$268$	−25.7531	−1.57312
$269$	−2.88860	−0.176121	−0.0880605	−	0.996115i	$-0.528067\pi$
$269$	−2.88860	−0.176121	−0.0880605	+	0.996115i	$0.528067\pi$
$270$	−25.4278	−1.54749
$271$	−24.1335	−1.46600	−0.733002	−	0.680226i	$-0.761882\pi$
$271$	−24.1335	−1.46600	−0.733002	+	0.680226i	$0.761882\pi$
$272$	−9.19224	−0.557361
$273$	0.351431	0.0212696
$274$	−13.7738	−0.832104
$275$	−20.5349	−1.23830
$276$	9.49526	0.571547
$277$	5.71280	0.343249	0.171624	−	0.985162i	$-0.445098\pi$
$277$	5.71280	0.343249	0.171624	+	0.985162i	$0.445098\pi$
$278$	−28.1786	−1.69004
$279$	−1.04276	−0.0624285
$280$	−2.02512	−0.121024
$281$	14.9592	0.892390	0.446195	−	0.894936i	$-0.352779\pi$
$281$	14.9592	0.892390	0.446195	+	0.894936i	$0.352779\pi$
$282$	11.5487	0.687712
$283$	14.7111	0.874483	0.437242	−	0.899344i	$-0.355955\pi$
$283$	14.7111	0.874483	0.437242	+	0.899344i	$0.355955\pi$
$284$	49.0519	2.91069
$285$	8.54423	0.506117
$286$	−93.7835	−5.54554
$287$	−0.206932	−0.0122148
$288$	25.1878	1.48421
$289$	1.00000	0.0588235
$290$	53.9200	3.16629
$291$	8.09163	0.474340
$292$	0.905284	0.0529778
$293$	−31.2324	−1.82462	−0.912309	−	0.409503i	$-0.865702\pi$
$293$	−31.2324	−1.82462	−0.912309	+	0.409503i	$0.865702\pi$
$294$	−10.8029	−0.630037
$295$	−27.8496	−1.62147
$296$	−25.5906	−1.48742
$297$	−19.7364	−1.14522
$298$	−16.9292	−0.980680
$299$	20.5455	1.18818
$300$	−9.88437	−0.570675
$301$	−0.709605	−0.0409010
$302$	−33.0343	−1.90091
$303$	−2.59930	−0.149326
$304$	−45.3751	−2.60244
$305$	−13.4031	−0.767459
$306$	−6.88620	−0.393658
$307$	−32.3893	−1.84855	−0.924277	−	0.381722i	$-0.875331\pi$
$307$	−32.3893	−1.84855	−0.924277	+	0.381722i	$0.875331\pi$
$308$	−2.70787	−0.154295
$309$	−7.03019	−0.399934
$310$	−2.98593	−0.169590
$311$	17.2861	0.980202	0.490101	−	0.871666i	$-0.336960\pi$
$311$	17.2861	0.980202	0.490101	+	0.871666i	$0.336960\pi$
$312$	−26.2038	−1.48350
$313$	7.84740	0.443561	0.221781	−	0.975097i	$-0.428813\pi$
$313$	7.84740	0.443561	0.221781	+	0.975097i	$0.428813\pi$
$314$	63.3422	3.57461
$315$	−0.744677	−0.0419578
$316$	16.2011	0.911381
$317$	26.8678	1.50905	0.754524	−	0.656273i	$-0.227868\pi$
$317$	26.8678	1.50905	0.754524	+	0.656273i	$0.227868\pi$
$318$	1.07135	0.0600784
$319$	41.8512	2.34322
$320$	18.5560	1.03731
$321$	7.51808	0.419618
$322$	0.842099	0.0469283
$323$	4.93625	0.274660
$324$	28.3585	1.57547
$325$	−21.3875	−1.18637
$326$	14.4977	0.802954
$327$	8.94583	0.494706
$328$	15.4295	0.851952
$329$	0.721512	0.0397782
$330$	−26.4917	−1.45832
$331$	−25.8415	−1.42038	−0.710188	−	0.704012i	$-0.751390\pi$
$331$	−25.8415	−1.42038	−0.710188	+	0.704012i	$0.751390\pi$
$332$	16.3864	0.899320
$333$	−9.41018	−0.515675
$334$	13.2664	0.725905
$335$	−15.7407	−0.860005
$336$	−0.527191	−0.0287606
$337$	−33.1463	−1.80560	−0.902798	−	0.430064i	$-0.858491\pi$
$337$	−33.1463	−1.80560	−0.902798	+	0.430064i	$0.858491\pi$
$338$	−63.8591	−3.47348
$339$	1.99250	0.108218
$340$	−13.8909	−0.753341
$341$	−2.31760	−0.125505
$342$	−33.9920	−1.83808
$343$	−1.35074	−0.0729330
$344$	52.9103	2.85273
$345$	5.80364	0.312457
$346$	−35.3068	−1.89810
$347$	3.98066	0.213693	0.106847	−	0.994276i	$-0.465925\pi$
$347$	3.98066	0.213693	0.106847	+	0.994276i	$0.465925\pi$
$348$	20.1449	1.07988
$349$	−27.3366	−1.46330	−0.731649	−	0.681682i	$-0.761249\pi$
$349$	−27.3366	−1.46330	−0.731649	+	0.681682i	$0.761249\pi$
$350$	−0.876608	−0.0468567
$351$	−20.5558	−1.09719
$352$	55.9814	2.98382
$353$	1.00000	0.0532246
$353$	1.00000	0.0532246
$354$	−14.7699	−0.785011
$355$	29.9812	1.59124
$356$	88.7036	4.70128
$357$	0.0573517	0.00303537
$358$	19.9986	1.05696
$359$	3.38626	0.178720	0.0893600	−	0.995999i	$-0.471518\pi$
$359$	3.38626	0.178720	0.0893600	+	0.995999i	$0.471518\pi$
$360$	55.5254	2.92645
$361$	5.36652	0.282448
$362$	−37.9812	−1.99625
$363$	−14.0277	−0.736261
$364$	−2.82030	−0.147824
$365$	0.553323	0.0289622
$366$	−7.10826	−0.371555
$367$	−21.0107	−1.09675	−0.548376	−	0.836232i	$-0.684754\pi$
$367$	−21.0107	−1.09675	−0.548376	+	0.836232i	$0.684754\pi$
$368$	−30.8209	−1.60665
$369$	5.67374	0.295363
$370$	−26.9459	−1.40085
$371$	0.0669335	0.00347502
$372$	−1.11556	−0.0578393
$373$	1.86261	0.0964423	0.0482212	−	0.998837i	$-0.484645\pi$
$373$	1.86261	0.0964423	0.0482212	+	0.998837i	$0.484645\pi$
$374$	−15.3050	−0.791402
$375$	2.61311	0.134941
$376$	−53.7981	−2.77443
$377$	43.5888	2.24494
$378$	−0.842519	−0.0433345
$379$	17.2952	0.888394	0.444197	−	0.895929i	$-0.353489\pi$
$379$	17.2952	0.888394	0.444197	+	0.895929i	$0.353489\pi$
$380$	−68.5690	−3.51752
$381$	−1.89498	−0.0970827
$382$	−3.85313	−0.197143
$383$	18.4168	0.941053	0.470526	−	0.882386i	$-0.344064\pi$
$383$	18.4168	0.941053	0.470526	+	0.882386i	$0.344064\pi$
$384$	−1.46370	−0.0746939
$385$	−1.65509	−0.0843511
$386$	−21.7675	−1.10794
$387$	19.4562	0.989014
$388$	−64.9368	−3.29667
$389$	12.1797	0.617536	0.308768	−	0.951137i	$-0.400083\pi$
$389$	12.1797	0.617536	0.308768	+	0.951137i	$0.400083\pi$
$390$	−27.5916	−1.39715
$391$	3.35293	0.169565
$392$	50.3240	2.54175
$393$	−7.03435	−0.354836
$394$	50.1109	2.52455
$395$	9.90232	0.498240
$396$	74.2453	3.73096
$397$	−16.3869	−0.822432	−0.411216	−	0.911538i	$-0.634896\pi$
$397$	−16.3869	−0.822432	−0.411216	+	0.911538i	$0.634896\pi$
$398$	−35.7689	−1.79293
$399$	0.283102	0.0141728
$400$	32.0839	1.60420
$401$	−16.2906	−0.813512	−0.406756	−	0.913537i	$-0.633340\pi$
$401$	−16.2906	−0.813512	−0.406756	+	0.913537i	$0.633340\pi$
$402$	−8.34799	−0.416360
$403$	−2.41382	−0.120241
$404$	20.8599	1.03782
$405$	17.3331	0.861290
$406$	1.78657	0.0886660
$407$	−20.9147	−1.03670
$408$	−4.27632	−0.211709
$409$	−21.3513	−1.05575	−0.527877	−	0.849321i	$-0.677012\pi$
$409$	−21.3513	−1.05575	−0.527877	+	0.849321i	$0.677012\pi$
$410$	16.2467	0.802366
$411$	−3.14529	−0.155146
$412$	56.4186	2.77954
$413$	−0.922761	−0.0454061
$414$	−23.0889	−1.13476
$415$	10.0156	0.491646
$416$	58.3056	2.85867
$417$	−6.43467	−0.315107
$418$	−75.5492	−3.69523
$419$	−10.1001	−0.493424	−0.246712	−	0.969089i	$-0.579350\pi$
$419$	−10.1001	−0.493424	−0.246712	+	0.969089i	$0.579350\pi$
$420$	−0.796668	−0.0388734
$421$	16.1278	0.786019	0.393010	−	0.919534i	$-0.371434\pi$
$421$	16.1278	0.786019	0.393010	+	0.919534i	$0.371434\pi$
$422$	−14.1474	−0.688683
$423$	−19.7826	−0.961865
$424$	−4.99077	−0.242373
$425$	−3.49033	−0.169306
$426$	15.9004	0.770375
$427$	−0.444094	−0.0214912
$428$	−60.3339	−2.91635
$429$	−21.4158	−1.03396
$430$	55.7126	2.68670
$431$	34.2769	1.65106	0.825530	−	0.564358i	$-0.190876\pi$
$431$	34.2769	1.65106	0.825530	+	0.564358i	$0.190876\pi$
$432$	30.8363	1.48361
$433$	24.1431	1.16025	0.580123	−	0.814529i	$-0.303005\pi$
$433$	24.1431	1.16025	0.580123	+	0.814529i	$0.303005\pi$
$434$	−0.0989351	−0.00474903
$435$	12.3128	0.590355
$436$	−71.7919	−3.43821
$437$	16.5509	0.791736
$438$	0.293452	0.0140217
$439$	15.2900	0.729752	0.364876	−	0.931056i	$-0.381111\pi$
$439$	15.2900	0.729752	0.364876	+	0.931056i	$0.381111\pi$
$440$	123.408	5.88327
$441$	18.5052	0.881198
$442$	−15.9404	−0.758209
$443$	4.65373	0.221105	0.110553	−	0.993870i	$-0.464738\pi$
$443$	4.65373	0.221105	0.110553	+	0.993870i	$0.464738\pi$
$444$	−10.0672	−0.477766
$445$	54.2169	2.57013
$446$	10.3065	0.488028
$447$	−3.86583	−0.182848
$448$	0.614828	0.0290479
$449$	35.4108	1.67114	0.835568	−	0.549386i	$-0.185138\pi$
$449$	35.4108	1.67114	0.835568	+	0.549386i	$0.185138\pi$
$450$	24.0351	1.13303
$451$	12.6102	0.593791
$452$	−15.9902	−0.752114
$453$	−7.54350	−0.354424
$454$	7.60303	0.356828
$455$	−1.72381	−0.0808133
$456$	−21.1090	−0.988518
$457$	10.4265	0.487733	0.243866	−	0.969809i	$-0.421584\pi$
$457$	10.4265	0.487733	0.243866	+	0.969809i	$0.421584\pi$
$458$	24.8523	1.16127
$459$	−3.35460	−0.156579
$460$	−46.5752	−2.17158
$461$	−8.07999	−0.376323	−0.188161	−	0.982138i	$-0.560253\pi$
$461$	−8.07999	−0.376323	−0.188161	+	0.982138i	$0.560253\pi$
$462$	−0.877767	−0.0408374
$463$	1.75782	0.0816929	0.0408465	−	0.999165i	$-0.486995\pi$
$463$	1.75782	0.0816929	0.0408465	+	0.999165i	$0.486995\pi$
$464$	−65.3887	−3.03560
$465$	−0.681848	−0.0316200
$466$	42.6191	1.97429
$467$	33.0952	1.53146	0.765731	−	0.643161i	$-0.222378\pi$
$467$	33.0952	1.53146	0.765731	+	0.643161i	$0.222378\pi$
$468$	77.3278	3.57448
$469$	−0.521547	−0.0240828
$470$	−56.6473	−2.61295
$471$	14.4644	0.666485
$472$	68.8039	3.16696
$473$	43.2425	1.98829
$474$	5.25164	0.241216
$475$	−17.2291	−0.790526
$476$	−0.460258	−0.0210959
$477$	−1.83521	−0.0840283
$478$	13.4590	0.615601
$479$	8.31229	0.379798	0.189899	−	0.981804i	$-0.439184\pi$
$479$	8.31229	0.379798	0.189899	+	0.981804i	$0.439184\pi$
$480$	16.4700	0.751749
$481$	−21.7830	−0.993220
$482$	−36.8174	−1.67699
$483$	0.192296	0.00874978
$484$	112.575	5.11702
$485$	−39.6903	−1.80224
$486$	35.3725	1.60453
$487$	−29.6958	−1.34564	−0.672822	−	0.739804i	$-0.734918\pi$
$487$	−29.6958	−1.34564	−0.672822	+	0.739804i	$0.734918\pi$
$488$	33.1130	1.49896
$489$	3.31060	0.149711
$490$	52.9893	2.39381
$491$	−1.27799	−0.0576748	−0.0288374	−	0.999584i	$-0.509181\pi$
$491$	−1.27799	−0.0576748	−0.0288374	+	0.999584i	$0.509181\pi$
$492$	6.06986	0.273650
$493$	7.11347	0.320375
$494$	−78.6859	−3.54024
$495$	45.3798	2.03967
$496$	3.62103	0.162589
$497$	0.993388	0.0445596
$498$	5.31172	0.238024
$499$	−10.0392	−0.449415	−0.224708	−	0.974426i	$-0.572143\pi$
$499$	−10.0392	−0.449415	−0.224708	+	0.974426i	$0.572143\pi$
$500$	−20.9707	−0.937839
$501$	3.02943	0.135345
$502$	−48.7688	−2.17666
$503$	25.7517	1.14821	0.574105	−	0.818782i	$-0.305350\pi$
$503$	25.7517	1.14821	0.574105	+	0.818782i	$0.305350\pi$
$504$	1.83976	0.0819496
$505$	12.7499	0.567361
$506$	−51.3165	−2.28130
$507$	−14.5825	−0.647630
$508$	15.2075	0.674726
$509$	11.8926	0.527132	0.263566	−	0.964641i	$-0.415101\pi$
$509$	11.8926	0.527132	0.263566	+	0.964641i	$0.415101\pi$
$510$	−4.50280	−0.199387
$511$	0.0183336	0.000811033 0
$512$	44.8792	1.98340
$513$	−16.5591	−0.731104
$514$	34.1784	1.50755
$515$	34.4838	1.51954
$516$	20.8146	0.916310
$517$	−43.9681	−1.93371
$518$	−0.892819	−0.0392282
$519$	−8.06242	−0.353901
$520$	128.532	5.63651
$521$	−33.9733	−1.48840	−0.744199	−	0.667959i	$-0.767168\pi$
$521$	−33.9733	−1.48840	−0.744199	+	0.667959i	$0.767168\pi$
$522$	−48.9848	−2.14401
$523$	−2.55327	−0.111647	−0.0558235	−	0.998441i	$-0.517778\pi$
$523$	−2.55327	−0.111647	−0.0558235	+	0.998441i	$0.517778\pi$
$524$	56.4519	2.46611
$525$	−0.200176	−0.00873641
$526$	−44.2937	−1.93130
$527$	−0.393923	−0.0171596
$528$	32.1264	1.39812
$529$	−11.7579	−0.511212
$530$	−5.25509	−0.228266
$531$	25.3006	1.09795
$532$	−2.27195	−0.0985013
$533$	13.1338	0.568887
$534$	28.7536	1.24429
$535$	−36.8770	−1.59433
$536$	38.8882	1.67971
$537$	4.56674	0.197069
$538$	7.51439	0.323968
$539$	41.1288	1.77154
$540$	46.5985	2.00528
$541$	−45.7502	−1.96695	−0.983477	−	0.181034i	$-0.942056\pi$
$541$	−45.7502	−1.96695	−0.983477	+	0.181034i	$0.942056\pi$
$542$	62.7807	2.69666
$543$	−8.67315	−0.372200
$544$	9.51518	0.407960
$545$	−43.8802	−1.87962
$546$	−0.914211	−0.0391246
$547$	−23.4709	−1.00354	−0.501771	−	0.865001i	$-0.667318\pi$
$547$	−23.4709	−1.00354	−0.501771	+	0.865001i	$0.667318\pi$
$548$	25.2415	1.07826
$549$	12.1763	0.519673
$550$	53.4194	2.27781
$551$	35.1138	1.49590
$552$	−14.3382	−0.610274
$553$	0.328101	0.0139523
$554$	−14.8612	−0.631394
$555$	−6.15320	−0.261189
$556$	51.6394	2.19000
$557$	−7.32903	−0.310541	−0.155270	−	0.987872i	$-0.549625\pi$
$557$	−7.32903	−0.310541	−0.155270	+	0.987872i	$0.549625\pi$
$558$	2.71263	0.114835
$559$	45.0379	1.90490
$560$	2.58593	0.109275
$561$	−3.49495	−0.147557
$562$	−38.9148	−1.64152
$563$	−2.99664	−0.126293	−0.0631467	−	0.998004i	$-0.520114\pi$
$563$	−2.99664	−0.126293	−0.0631467	+	0.998004i	$0.520114\pi$
$564$	−21.1638	−0.891157
$565$	−9.77342	−0.411171
$566$	−38.2693	−1.60858
$567$	0.574311	0.0241188
$568$	−74.0701	−3.10791
$569$	8.24896	0.345814	0.172907	−	0.984938i	$-0.444684\pi$
$569$	8.24896	0.345814	0.172907	+	0.984938i	$0.444684\pi$
$570$	−22.2269	−0.930984
$571$	−7.82418	−0.327432	−0.163716	−	0.986508i	$-0.552348\pi$
$571$	−7.82418	−0.327432	−0.163716	+	0.986508i	$0.552348\pi$
$572$	171.866	7.18606
$573$	−0.879875	−0.0367573
$574$	0.538313	0.0224687
$575$	−11.7028	−0.488041
$576$	−16.8576	−0.702398
$577$	−12.9244	−0.538049	−0.269024	−	0.963133i	$-0.586701\pi$
$577$	−12.9244	−0.538049	−0.269024	+	0.963133i	$0.586701\pi$
$578$	−2.60140	−0.108204
$579$	−4.97069	−0.206575
$580$	−98.8127	−4.10297
$581$	0.331854	0.0137676
$582$	−21.0495	−0.872531
$583$	−4.07885	−0.168929
$584$	−1.36701	−0.0565674
$585$	47.2639	1.95412
$586$	81.2479	3.35632
$587$	−37.8714	−1.56312	−0.781561	−	0.623829i	$-0.785576\pi$
$587$	−37.8714	−1.56312	−0.781561	+	0.623829i	$0.785576\pi$
$588$	19.7971	0.816420
$589$	−1.94450	−0.0801218
$590$	72.4478	2.98263
$591$	11.4430	0.470702
$592$	32.6773	1.34303
$593$	−18.0687	−0.741995	−0.370997	−	0.928634i	$-0.620984\pi$
$593$	−18.0687	−0.741995	−0.370997	+	0.928634i	$0.620984\pi$
$594$	51.3421	2.10659
$595$	−0.281316	−0.0115328
$596$	31.0240	1.27079
$597$	−8.16795	−0.334292
$598$	−53.4471	−2.18561
$599$	4.86304	0.198699	0.0993493	−	0.995053i	$-0.468324\pi$
$599$	4.86304	0.198699	0.0993493	+	0.995053i	$0.468324\pi$
$600$	14.9258	0.609342
$601$	7.30595	0.298016	0.149008	−	0.988836i	$-0.452392\pi$
$601$	7.30595	0.298016	0.149008	+	0.988836i	$0.452392\pi$
$602$	1.84596	0.0752359
$603$	14.3000	0.582339
$604$	60.5379	2.46325
$605$	68.8072	2.79741
$606$	6.76181	0.274680
$607$	−47.6739	−1.93502	−0.967511	−	0.252828i	$-0.918639\pi$
$607$	−47.6739	−1.93502	−0.967511	+	0.252828i	$0.918639\pi$
$608$	46.9693	1.90485
$609$	0.407970	0.0165318
$610$	34.8667	1.41171
$611$	−45.7936	−1.85261
$612$	12.6195	0.510113
$613$	−23.9024	−0.965408	−0.482704	−	0.875783i	$-0.660345\pi$
$613$	−23.9024	−0.965408	−0.482704	+	0.875783i	$0.660345\pi$
$614$	84.2573	3.40035
$615$	3.70998	0.149601
$616$	4.08898	0.164750
$617$	−44.4516	−1.78955	−0.894777	−	0.446513i	$-0.852666\pi$
$617$	−44.4516	−1.78955	−0.894777	+	0.446513i	$0.852666\pi$
$618$	18.2883	0.735664
$619$	−9.88717	−0.397399	−0.198700	−	0.980060i	$-0.563672\pi$
$619$	−9.88717	−0.397399	−0.198700	+	0.980060i	$0.563672\pi$
$620$	5.47195	0.219759
$621$	−11.2477	−0.451356
$622$	−44.9679	−1.80305
$623$	1.79641	0.0719716
$624$	33.4602	1.33948
$625$	−30.2692	−1.21077
$626$	−20.4142	−0.815915
$627$	−17.2519	−0.688975
$628$	−116.079	−4.63207
$629$	−3.55488	−0.141742
$630$	1.93720	0.0771799
$631$	13.9588	0.555691	0.277845	−	0.960626i	$-0.410380\pi$
$631$	13.9588	0.555691	0.277845	+	0.960626i	$0.410380\pi$
$632$	−24.4642	−0.973133
$633$	−3.23060	−0.128405
$634$	−69.8938	−2.77584
$635$	9.29507	0.368864
$636$	−1.96333	−0.0778512
$637$	42.8364	1.69724
$638$	−108.872	−4.31027
$639$	−27.2371	−1.07748
$640$	7.17958	0.283798
$641$	30.3452	1.19856	0.599281	−	0.800539i	$-0.295453\pi$
$641$	30.3452	1.19856	0.599281	+	0.800539i	$0.295453\pi$
$642$	−19.5575	−0.771873
$643$	44.2362	1.74451	0.872253	−	0.489055i	$-0.162658\pi$
$643$	44.2362	1.74451	0.872253	+	0.489055i	$0.162658\pi$
$644$	−1.54321	−0.0608110
$645$	12.7222	0.500934
$646$	−12.8411	−0.505227
$647$	−34.6869	−1.36368	−0.681842	−	0.731499i	$-0.738821\pi$
$647$	−34.6869	−1.36368	−0.681842	+	0.731499i	$0.738821\pi$
$648$	−42.8224	−1.68222
$649$	56.2320	2.20730
$650$	55.6374	2.18228
$651$	−0.0225922	−0.000885457 0
$652$	−26.5682	−1.04049
$653$	8.47926	0.331819	0.165910	−	0.986141i	$-0.446944\pi$
$653$	8.47926	0.331819	0.165910	+	0.986141i	$0.446944\pi$
$654$	−23.2716	−0.909993
$655$	34.5042	1.34819
$656$	−19.7023	−0.769246
$657$	−0.502678	−0.0196113
$658$	−1.87694	−0.0731706
$659$	−31.3378	−1.22075	−0.610373	−	0.792114i	$-0.708980\pi$
$659$	−31.3378	−1.22075	−0.610373	+	0.792114i	$0.708980\pi$
$660$	48.5480	1.88973
$661$	−26.7529	−1.04057	−0.520283	−	0.853994i	$-0.674174\pi$
$661$	−26.7529	−1.04057	−0.520283	+	0.853994i	$0.674174\pi$
$662$	67.2239	2.61273
$663$	−3.64005	−0.141368
$664$	−24.7440	−0.960255
$665$	−1.38865	−0.0538494
$666$	24.4796	0.948565
$667$	23.8510	0.923513
$668$	−24.3117	−0.940649
$669$	2.35353	0.0909928
$670$	40.9477	1.58195
$671$	27.0626	1.04474
$672$	0.545712	0.0210513
$673$	−35.5911	−1.37194	−0.685968	−	0.727632i	$-0.740621\pi$
$673$	−35.5911	−1.37194	−0.685968	+	0.727632i	$0.740621\pi$
$674$	86.2268	3.32133
$675$	11.7087	0.450667
$676$	117.027	4.50103
$677$	−11.3778	−0.437285	−0.218643	−	0.975805i	$-0.570163\pi$
$677$	−11.3778	−0.437285	−0.218643	+	0.975805i	$0.570163\pi$
$678$	−5.18328	−0.199063
$679$	−1.31509	−0.0504684
$680$	20.9758	0.804385
$681$	1.73618	0.0665305
$682$	6.02899	0.230862
$683$	3.52772	0.134985	0.0674923	−	0.997720i	$-0.478500\pi$
$683$	3.52772	0.134985	0.0674923	+	0.997720i	$0.478500\pi$
$684$	62.2930	2.38183
$685$	15.4280	0.589472
$686$	3.51380	0.134158
$687$	5.67511	0.216519
$688$	−67.5625	−2.57580
$689$	−4.24820	−0.161844
$690$	−15.0976	−0.574754
$691$	36.6744	1.39516	0.697581	−	0.716506i	$-0.254260\pi$
$691$	36.6744	1.39516	0.697581	+	0.716506i	$0.254260\pi$
$692$	64.7024	2.45962
$693$	1.50360	0.0571171
$694$	−10.3553	−0.393081
$695$	31.5628	1.19724
$696$	−30.4195	−1.15305
$697$	2.14336	0.0811857
$698$	71.1134	2.69168
$699$	9.73222	0.368106
$700$	1.60645	0.0607182
$701$	−20.2947	−0.766520	−0.383260	−	0.923641i	$-0.625199\pi$
$701$	−20.2947	−0.766520	−0.383260	+	0.923641i	$0.625199\pi$
$702$	53.4738	2.01824
$703$	−17.5477	−0.661826
$704$	−37.4669	−1.41209
$705$	−12.9356	−0.487184
$706$	−2.60140	−0.0979048
$707$	0.422450	0.0158879
$708$	27.0670	1.01724
$709$	−24.3849	−0.915794	−0.457897	−	0.889005i	$-0.651397\pi$
$709$	−24.3849	−0.915794	−0.457897	+	0.889005i	$0.651397\pi$
$710$	−77.9930	−2.92702
$711$	−8.99597	−0.337375
$712$	−133.946	−5.01983
$713$	−1.32080	−0.0494642
$714$	−0.149194	−0.00558346
$715$	105.047	3.92852
$716$	−36.6489	−1.36963
$717$	3.07341	0.114779
$718$	−8.80900	−0.328749
$719$	1.43916	0.0536718	0.0268359	−	0.999640i	$-0.491457\pi$
$719$	1.43916	0.0536718	0.0268359	+	0.999640i	$0.491457\pi$
$720$	−70.9018	−2.64235
$721$	1.14258	0.0425518
$722$	−13.9604	−0.519554
$723$	−8.40738	−0.312674
$724$	69.6036	2.58680
$725$	−24.8284	−0.922102
$726$	36.4915	1.35433
$727$	22.0538	0.817931	0.408966	−	0.912550i	$-0.365890\pi$
$727$	22.0538	0.817931	0.408966	+	0.912550i	$0.365890\pi$
$728$	4.25875	0.157840
$729$	−9.76837	−0.361791
$730$	−1.43941	−0.0532750
$731$	7.34995	0.271848
$732$	13.0264	0.481471
$733$	39.2232	1.44874	0.724370	−	0.689411i	$-0.242131\pi$
$733$	39.2232	1.44874	0.724370	+	0.689411i	$0.242131\pi$
$734$	54.6573	2.01744
$735$	12.1003	0.446326
$736$	31.9037	1.17599
$737$	31.7825	1.17072
$738$	−14.7596	−0.543310
$739$	−45.6411	−1.67893	−0.839467	−	0.543411i	$-0.817132\pi$
$739$	−45.6411	−1.67893	−0.839467	+	0.543411i	$0.817132\pi$
$740$	49.3805	1.81526
$741$	−17.9682	−0.660078
$742$	−0.174121	−0.00639217
$743$	30.4687	1.11779	0.558894	−	0.829239i	$-0.311226\pi$
$743$	30.4687	1.11779	0.558894	+	0.829239i	$0.311226\pi$
$744$	1.68454	0.0617583
$745$	18.9623	0.694726
$746$	−4.84539	−0.177402
$747$	−9.09888	−0.332911
$748$	28.0476	1.02552
$749$	−1.22187	−0.0446462
$750$	−6.79774	−0.248218
$751$	−7.01430	−0.255955	−0.127978	−	0.991777i	$-0.540849\pi$
$751$	−7.01430	−0.255955	−0.127978	+	0.991777i	$0.540849\pi$
$752$	68.6961	2.50509
$753$	−11.1365	−0.405838
$754$	−113.392	−4.12948
$755$	37.0016	1.34663
$756$	1.54398	0.0561541
$757$	18.1582	0.659970	0.329985	−	0.943986i	$-0.392956\pi$
$757$	18.1582	0.659970	0.329985	+	0.943986i	$0.392956\pi$
$758$	−44.9916	−1.63417
$759$	−11.7183	−0.425347
$760$	103.542	3.75585
$761$	42.3977	1.53692	0.768458	−	0.639900i	$-0.221024\pi$
$761$	42.3977	1.53692	0.768458	+	0.639900i	$0.221024\pi$
$762$	4.92959	0.178580
$763$	−1.45392	−0.0526353
$764$	7.06115	0.255464
$765$	7.71322	0.278872
$766$	−47.9093	−1.73103
$767$	58.5667	2.11472
$768$	11.3736	0.410411
$769$	−40.9219	−1.47568	−0.737842	−	0.674974i	$-0.764155\pi$
$769$	−40.9219	−1.47568	−0.737842	+	0.674974i	$0.764155\pi$
$770$	4.30554	0.155161
$771$	7.80476	0.281082
$772$	39.8907	1.43570
$773$	−4.01430	−0.144384	−0.0721921	−	0.997391i	$-0.522999\pi$
$773$	−4.01430	−0.144384	−0.0721921	+	0.997391i	$0.522999\pi$
$774$	−50.6133	−1.81926
$775$	1.37492	0.0493886
$776$	98.0569	3.52004
$777$	−0.203878	−0.00731409
$778$	−31.6842	−1.13594
$779$	10.5802	0.379074
$780$	50.5637	1.81047
$781$	−60.5359	−2.16615
$782$	−8.72229	−0.311908
$783$	−23.8629	−0.852789
$784$	−64.2600	−2.29500
$785$	−70.9494	−2.53229
$786$	18.2991	0.652708
$787$	−0.215377	−0.00767738	−0.00383869	−	0.999993i	$-0.501222\pi$
$787$	−0.215377	−0.00767738	−0.00383869	+	0.999993i	$0.501222\pi$
$788$	−91.8321	−3.27138
$789$	−10.1146	−0.360090
$790$	−25.7599	−0.916494
$791$	−0.323830	−0.0115141
$792$	−112.113	−3.98376
$793$	28.1862	1.00092
$794$	42.6287	1.51284
$795$	−1.20002	−0.0425602
$796$	65.5492	2.32333
$797$	−30.0690	−1.06510	−0.532550	−	0.846399i	$-0.678766\pi$
$797$	−30.0690	−1.06510	−0.532550	+	0.846399i	$0.678766\pi$
$798$	−0.736461	−0.0260704
$799$	−7.47327	−0.264385
$800$	−33.2111	−1.17419
$801$	−49.2545	−1.74032
$802$	42.3782	1.49643
$803$	−1.11723	−0.0394262
$804$	15.2983	0.539530
$805$	−0.943233	−0.0332446
$806$	6.27930	0.221179
$807$	1.71594	0.0604038
$808$	−31.4992	−1.10814
$809$	−25.0323	−0.880090	−0.440045	−	0.897976i	$-0.645038\pi$
$809$	−25.0323	−0.880090	−0.440045	+	0.897976i	$0.645038\pi$
$810$	−45.0903	−1.58431
$811$	6.01133	0.211086	0.105543	−	0.994415i	$-0.466342\pi$
$811$	6.01133	0.211086	0.105543	+	0.994415i	$0.466342\pi$
$812$	−3.27403	−0.114896
$813$	14.3362	0.502792
$814$	54.4073	1.90698
$815$	−16.2388	−0.568822
$816$	5.46054	0.191157
$817$	36.2812	1.26932
$818$	55.5432	1.94202
$819$	1.56603	0.0547214
$820$	−29.7733	−1.03973
$821$	14.2946	0.498887	0.249443	−	0.968389i	$-0.419752\pi$
$821$	14.2946	0.498887	0.249443	+	0.968389i	$0.419752\pi$
$822$	8.18214	0.285385
$823$	−32.0531	−1.11730	−0.558651	−	0.829403i	$-0.688681\pi$
$823$	−32.0531	−1.11730	−0.558651	+	0.829403i	$0.688681\pi$
$824$	−85.1941	−2.96788
$825$	12.1985	0.424698
$826$	2.40047	0.0835229
$827$	−7.53481	−0.262011	−0.131006	−	0.991382i	$-0.541821\pi$
$827$	−7.53481	−0.262011	−0.131006	+	0.991382i	$0.541821\pi$
$828$	42.3123	1.47045
$829$	0.0267258	0.000928224 0	0.000464112	−	1.00000i	$-0.499852\pi$
$829$	0.0267258	0.000928224 0	0.000464112		1.00000i	$0.499852\pi$
$830$	−26.0545	−0.904366
$831$	−3.39362	−0.117723
$832$	−39.0225	−1.35286
$833$	6.99068	0.242213
$834$	16.7391	0.579629
$835$	−14.8597	−0.514240
$836$	138.450	4.78838
$837$	1.32145	0.0456762
$838$	26.2744	0.907635
$839$	28.1519	0.971912	0.485956	−	0.873983i	$-0.338472\pi$
$839$	28.1519	0.971912	0.485956	+	0.873983i	$0.338472\pi$
$840$	1.20300	0.0415074
$841$	21.6015	0.744878
$842$	−41.9547	−1.44585
$843$	−8.88632	−0.306061
$844$	25.9261	0.892415
$845$	71.5285	2.46065
$846$	51.4625	1.76932
$847$	2.27984	0.0783361
$848$	6.37284	0.218844
$849$	−8.73894	−0.299920
$850$	9.07973	0.311432
$851$	−11.9192	−0.408586
$852$	−29.1386	−0.998274
$853$	2.05776	0.0704563	0.0352282	−	0.999379i	$-0.488784\pi$
$853$	2.05776	0.0704563	0.0352282	+	0.999379i	$0.488784\pi$
$854$	1.15526	0.0395323
$855$	38.0744	1.30212
$856$	91.1064	3.11395
$857$	6.45929	0.220645	0.110323	−	0.993896i	$-0.464812\pi$
$857$	6.45929	0.220645	0.110323	+	0.993896i	$0.464812\pi$
$858$	55.7109	1.90194
$859$	11.4239	0.389780	0.194890	−	0.980825i	$-0.437565\pi$
$859$	11.4239	0.389780	0.194890	+	0.980825i	$0.437565\pi$
$860$	−102.098	−3.48150
$861$	0.122926	0.00418929
$862$	−89.1678	−3.03707
$863$	−24.3603	−0.829233	−0.414617	−	0.909996i	$-0.636084\pi$
$863$	−24.3603	−0.829233	−0.414617	+	0.909996i	$0.636084\pi$
$864$	−31.9196	−1.08593
$865$	39.5470	1.34464
$866$	−62.8059	−2.13423
$867$	−0.594038	−0.0201746
$868$	0.181306	0.00615393
$869$	−19.9941	−0.678252
$870$	−32.0305	−1.08594
$871$	33.1020	1.12162
$872$	108.408	3.67117
$873$	36.0575	1.22036
$874$	−43.0554	−1.45637
$875$	−0.424695	−0.0143573
$876$	−0.537773	−0.0181697
$877$	38.1336	1.28768	0.643840	−	0.765160i	$-0.277340\pi$
$877$	38.1336	1.28768	0.643840	+	0.765160i	$0.277340\pi$
$878$	−39.7754	−1.34235
$879$	18.5532	0.625785
$880$	−157.583	−5.31213
$881$	55.0889	1.85599	0.927995	−	0.372592i	$-0.121531\pi$
$881$	55.0889	1.85599	0.927995	+	0.372592i	$0.121531\pi$
$882$	−48.1392	−1.62093
$883$	17.6494	0.593949	0.296975	−	0.954885i	$-0.404022\pi$
$883$	17.6494	0.593949	0.296975	+	0.954885i	$0.404022\pi$
$884$	29.2121	0.982508
$885$	16.5437	0.556111
$886$	−12.1062	−0.406715
$887$	−4.37660	−0.146952	−0.0734759	−	0.997297i	$-0.523409\pi$
$887$	−4.37660	−0.146952	−0.0734759	+	0.997297i	$0.523409\pi$
$888$	15.2018	0.510139
$889$	0.307980	0.0103293
$890$	−141.040	−4.72766
$891$	−34.9978	−1.17247
$892$	−18.8875	−0.632400
$893$	−36.8899	−1.23447
$894$	10.0566	0.336342
$895$	−22.4003	−0.748761
$896$	0.237886	0.00794722
$897$	−12.2048	−0.407507
$898$	−92.1174	−3.07400
$899$	−2.80216	−0.0934573
$900$	−44.0462	−1.46821
$901$	−0.693284	−0.0230967
$902$	−32.8041	−1.09226
$903$	0.421532	0.0140277
$904$	24.1457	0.803075
$905$	42.5427	1.41417
$906$	19.6236	0.651951
$907$	5.14101	0.170704	0.0853522	−	0.996351i	$-0.472798\pi$
$907$	5.14101	0.170704	0.0853522	+	0.996351i	$0.472798\pi$
$908$	−13.9331	−0.462388
$909$	−11.5829	−0.384180
$910$	4.48430	0.148653
$911$	32.7655	1.08557	0.542785	−	0.839872i	$-0.317370\pi$
$911$	32.7655	1.08557	0.542785	+	0.839872i	$0.317370\pi$
$912$	26.9545	0.892554
$913$	−20.2228	−0.669277
$914$	−27.1235	−0.897167
$915$	7.96194	0.263214
$916$	−45.5438	−1.50481
$917$	1.14325	0.0377535
$918$	8.72665	0.288022
$919$	8.18478	0.269991	0.134996	−	0.990846i	$-0.456898\pi$
$919$	8.18478	0.269991	0.134996	+	0.990846i	$0.456898\pi$
$920$	70.3303	2.31872
$921$	19.2405	0.633995
$922$	21.0192	0.692232
$923$	−63.0493	−2.07529
$924$	1.60858	0.0529183
$925$	12.4077	0.407962
$926$	−4.57279	−0.150271
$927$	−31.3276	−1.02893
$928$	67.6859	2.22190
$929$	−34.3966	−1.12851	−0.564257	−	0.825599i	$-0.690837\pi$
$929$	−34.3966	−1.12851	−0.564257	+	0.825599i	$0.690837\pi$
$930$	1.77376	0.0581638
$931$	34.5077	1.13094
$932$	−78.1028	−2.55834
$933$	−10.2686	−0.336178
$934$	−86.0936	−2.81707
$935$	17.1431	0.560639
$936$	−116.768	−3.81668
$937$	21.2946	0.695663	0.347831	−	0.937557i	$-0.386918\pi$
$937$	21.2946	0.695663	0.347831	+	0.937557i	$0.386918\pi$
$938$	1.35675	0.0442995
$939$	−4.66165	−0.152127
$940$	103.811	3.38593
$941$	6.56001	0.213850	0.106925	−	0.994267i	$-0.465899\pi$
$941$	6.56001	0.213850	0.106925	+	0.994267i	$0.465899\pi$
$942$	−37.6276	−1.22597
$943$	7.18654	0.234026
$944$	−87.8573	−2.85951
$945$	0.943704	0.0306987
$946$	−112.491	−3.65739
$947$	−30.2130	−0.981790	−0.490895	−	0.871219i	$-0.663330\pi$
$947$	−30.2130	−0.981790	−0.490895	+	0.871219i	$0.663330\pi$
$948$	−9.62404	−0.312574
$949$	−1.16362	−0.0377726
$950$	44.8198	1.45415
$951$	−15.9605	−0.517555
$952$	0.695006	0.0225253
$953$	57.4331	1.86044	0.930221	−	0.367000i	$-0.119615\pi$
$953$	57.4331	1.86044	0.930221	+	0.367000i	$0.119615\pi$
$954$	4.77410	0.154567
$955$	4.31588	0.139659
$956$	−24.6647	−0.797713
$957$	−24.8612	−0.803648
$958$	−21.6236	−0.698626
$959$	0.511186	0.0165070
$960$	−11.0229	−0.355764
$961$	−30.8448	−0.994994
$962$	56.6662	1.82699
$963$	33.5017	1.07958
$964$	67.4708	2.17309
$965$	24.3817	0.784876
$966$	−0.500238	−0.0160949
$967$	8.17074	0.262753	0.131377	−	0.991333i	$-0.458060\pi$
$967$	8.17074	0.262753	0.131377	+	0.991333i	$0.458060\pi$
$968$	−169.992	−5.46374
$969$	−2.93232	−0.0941996
$970$	103.250	3.31516
$971$	47.1619	1.51350	0.756749	−	0.653705i	$-0.226786\pi$
$971$	47.1619	1.51350	0.756749	+	0.653705i	$0.226786\pi$
$972$	−64.8228	−2.07919
$973$	1.04579	0.0335265
$974$	77.2505	2.47526
$975$	12.7050	0.406885
$976$	−42.2828	−1.35344
$977$	−35.8745	−1.14773	−0.573863	−	0.818951i	$-0.694556\pi$
$977$	−35.8745	−1.14773	−0.573863	+	0.818951i	$0.694556\pi$
$978$	−8.61218	−0.275387
$979$	−109.471	−3.49871
$980$	−97.1070	−3.10197
$981$	39.8639	1.27276
$982$	3.32456	0.106091
$983$	22.1069	0.705100	0.352550	−	0.935793i	$-0.385315\pi$
$983$	22.1069	0.705100	0.352550	+	0.935793i	$0.385315\pi$
$984$	−9.16570	−0.292192
$985$	−56.1291	−1.78842
$986$	−18.5050	−0.589318
$987$	−0.428605	−0.0136427
$988$	144.198	4.58755
$989$	24.6439	0.783629
$990$	−118.051	−3.75190
$991$	22.2463	0.706677	0.353338	−	0.935496i	$-0.385046\pi$
$991$	22.2463	0.706677	0.353338	+	0.935496i	$0.385046\pi$
$992$	−3.74825	−0.119007
$993$	15.3508	0.487144
$994$	−2.58420	−0.0819657
$995$	40.0646	1.27013
$996$	−9.73413	−0.308438
$997$	4.69283	0.148624	0.0743118	−	0.997235i	$-0.476324\pi$
$997$	4.69283	0.148624	0.0743118	+	0.997235i	$0.476324\pi$
$998$	26.1159	0.826683
$999$	11.9252	0.377296

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.c.1.6	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.c.1.6	✓	121	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.60140 q^{2} -0.594038 q^{3} +4.76726 q^{4} +2.91382 q^{5} +1.54533 q^{6} +0.0965456 q^{7} -7.19873 q^{8} -2.64712 q^{9} +O(q^{10})\)	\(q-2.60140 q^{2} -0.594038 q^{3} +4.76726 q^{4} +2.91382 q^{5} +1.54533 q^{6} +0.0965456 q^{7} -7.19873 q^{8} -2.64712 q^{9} -7.57999 q^{10} -5.88337 q^{11} -2.83193 q^{12} -6.12764 q^{13} -0.251153 q^{14} -1.73092 q^{15} +9.19224 q^{16} -1.00000 q^{17} +6.88620 q^{18} -4.93625 q^{19} +13.8909 q^{20} -0.0573517 q^{21} +15.3050 q^{22} -3.35293 q^{23} +4.27632 q^{24} +3.49033 q^{25} +15.9404 q^{26} +3.35460 q^{27} +0.460258 q^{28} -7.11347 q^{29} +4.50280 q^{30} +0.393923 q^{31} -9.51518 q^{32} +3.49495 q^{33} +2.60140 q^{34} +0.281316 q^{35} -12.6195 q^{36} +3.55488 q^{37} +12.8411 q^{38} +3.64005 q^{39} -20.9758 q^{40} -2.14336 q^{41} +0.149194 q^{42} -7.34995 q^{43} -28.0476 q^{44} -7.71322 q^{45} +8.72229 q^{46} +7.47327 q^{47} -5.46054 q^{48} -6.99068 q^{49} -9.07973 q^{50} +0.594038 q^{51} -29.2121 q^{52} +0.693284 q^{53} -8.72665 q^{54} -17.1431 q^{55} -0.695006 q^{56} +2.93232 q^{57} +18.5050 q^{58} -9.55778 q^{59} -8.25173 q^{60} -4.59984 q^{61} -1.02475 q^{62} -0.255568 q^{63} +6.36827 q^{64} -17.8548 q^{65} -9.09174 q^{66} -5.40208 q^{67} -4.76726 q^{68} +1.99177 q^{69} -0.731815 q^{70} +10.2893 q^{71} +19.0559 q^{72} +0.189896 q^{73} -9.24764 q^{74} -2.07339 q^{75} -23.5324 q^{76} -0.568014 q^{77} -9.46921 q^{78} +3.39840 q^{79} +26.7845 q^{80} +5.94860 q^{81} +5.57573 q^{82} +3.43728 q^{83} -0.273410 q^{84} -2.91382 q^{85} +19.1201 q^{86} +4.22567 q^{87} +42.3529 q^{88} +18.6068 q^{89} +20.0651 q^{90} -0.591597 q^{91} -15.9843 q^{92} -0.234005 q^{93} -19.4409 q^{94} -14.3833 q^{95} +5.65237 q^{96} -13.6214 q^{97} +18.1855 q^{98} +15.5740 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9} - q^{10} + 40 q^{11} + 41 q^{12} + 14 q^{13} + 32 q^{14} + 49 q^{15} + 135 q^{16} - 121 q^{17} + 28 q^{18} + 34 q^{19} + 64 q^{20} + 34 q^{21} - 18 q^{22} + 37 q^{23} + 54 q^{24} + 128 q^{25} + 91 q^{26} + 55 q^{27} - 28 q^{28} + 45 q^{29} + 30 q^{30} + 67 q^{31} + 47 q^{32} + 40 q^{33} - 9 q^{34} + 59 q^{35} + 138 q^{36} - 16 q^{37} + 30 q^{38} + 37 q^{39} + 14 q^{40} + 89 q^{41} + 33 q^{42} + 16 q^{43} + 90 q^{44} + 83 q^{45} - 9 q^{46} + 135 q^{47} + 96 q^{48} + 128 q^{49} + 71 q^{50} - 13 q^{51} + 47 q^{52} + 52 q^{53} + 90 q^{54} + 93 q^{55} + 69 q^{56} - 4 q^{57} + 5 q^{58} + 170 q^{59} + 78 q^{60} - 2 q^{61} + 46 q^{62} - 10 q^{63} + 182 q^{64} + 50 q^{65} + 68 q^{66} + 46 q^{67} - 127 q^{68} + 97 q^{69} + 46 q^{70} + 191 q^{71} + 57 q^{72} - 12 q^{73} + 68 q^{74} + 86 q^{75} + 108 q^{76} + 62 q^{77} - 10 q^{78} + 130 q^{80} + 149 q^{81} + 14 q^{82} + 83 q^{83} + 126 q^{84} - 21 q^{85} + 132 q^{86} + 50 q^{87} - 42 q^{88} + 144 q^{89} + 9 q^{90} + 13 q^{91} + 50 q^{92} + 43 q^{93} + 41 q^{94} + 82 q^{95} + 110 q^{96} - 3 q^{97} + 36 q^{98} + 89 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9 - q^10 + 40 * q^11 + 41 * q^12 + 14 * q^13 + 32 * q^14 + 49 * q^15 + 135 * q^16 - 121 * q^17 + 28 * q^18 + 34 * q^19 + 64 * q^20 + 34 * q^21 - 18 * q^22 + 37 * q^23 + 54 * q^24 + 128 * q^25 + 91 * q^26 + 55 * q^27 - 28 * q^28 + 45 * q^29 + 30 * q^30 + 67 * q^31 + 47 * q^32 + 40 * q^33 - 9 * q^34 + 59 * q^35 + 138 * q^36 - 16 * q^37 + 30 * q^38 + 37 * q^39 + 14 * q^40 + 89 * q^41 + 33 * q^42 + 16 * q^43 + 90 * q^44 + 83 * q^45 - 9 * q^46 + 135 * q^47 + 96 * q^48 + 128 * q^49 + 71 * q^50 - 13 * q^51 + 47 * q^52 + 52 * q^53 + 90 * q^54 + 93 * q^55 + 69 * q^56 - 4 * q^57 + 5 * q^58 + 170 * q^59 + 78 * q^60 - 2 * q^61 + 46 * q^62 - 10 * q^63 + 182 * q^64 + 50 * q^65 + 68 * q^66 + 46 * q^67 - 127 * q^68 + 97 * q^69 + 46 * q^70 + 191 * q^71 + 57 * q^72 - 12 * q^73 + 68 * q^74 + 86 * q^75 + 108 * q^76 + 62 * q^77 - 10 * q^78 + 130 * q^80 + 149 * q^81 + 14 * q^82 + 83 * q^83 + 126 * q^84 - 21 * q^85 + 132 * q^86 + 50 * q^87 - 42 * q^88 + 144 * q^89 + 9 * q^90 + 13 * q^91 + 50 * q^92 + 43 * q^93 + 41 * q^94 + 82 * q^95 + 110 * q^96 - 3 * q^97 + 36 * q^98 + 89 * q^99

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