LMFDB - Embedded newform 6031.2.a.d.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, 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("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.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:	$48.1577774590$
Analytic rank:	$0$
Dimension:	$133$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.45235 q^{2} -2.50002 q^{3} +4.01402 q^{4} -3.16357 q^{5} +6.13092 q^{6} -0.556288 q^{7} -4.93908 q^{8} +3.25009 q^{9} +O(q^{10})$	\(q-2.45235 q^{2} -2.50002 q^{3} +4.01402 q^{4} -3.16357 q^{5} +6.13092 q^{6} -0.556288 q^{7} -4.93908 q^{8} +3.25009 q^{9} +7.75817 q^{10} +0.948061 q^{11} -10.0351 q^{12} -4.46540 q^{13} +1.36421 q^{14} +7.90897 q^{15} +4.08431 q^{16} +0.621048 q^{17} -7.97035 q^{18} +3.59352 q^{19} -12.6986 q^{20} +1.39073 q^{21} -2.32498 q^{22} +4.39121 q^{23} +12.3478 q^{24} +5.00815 q^{25} +10.9507 q^{26} -0.625218 q^{27} -2.23295 q^{28} +0.608404 q^{29} -19.3956 q^{30} +5.87987 q^{31} -0.138001 q^{32} -2.37017 q^{33} -1.52303 q^{34} +1.75985 q^{35} +13.0459 q^{36} -1.00000 q^{37} -8.81257 q^{38} +11.1636 q^{39} +15.6251 q^{40} +4.96366 q^{41} -3.41055 q^{42} -12.0167 q^{43} +3.80554 q^{44} -10.2819 q^{45} -10.7688 q^{46} +9.02763 q^{47} -10.2108 q^{48} -6.69054 q^{49} -12.2817 q^{50} -1.55263 q^{51} -17.9242 q^{52} +0.333636 q^{53} +1.53325 q^{54} -2.99925 q^{55} +2.74755 q^{56} -8.98387 q^{57} -1.49202 q^{58} +4.14371 q^{59} +31.7467 q^{60} +3.73513 q^{61} -14.4195 q^{62} -1.80798 q^{63} -7.83020 q^{64} +14.1266 q^{65} +5.81248 q^{66} -0.200881 q^{67} +2.49290 q^{68} -10.9781 q^{69} -4.31577 q^{70} +16.0585 q^{71} -16.0524 q^{72} +6.90138 q^{73} +2.45235 q^{74} -12.5205 q^{75} +14.4245 q^{76} -0.527395 q^{77} -27.3770 q^{78} +16.1956 q^{79} -12.9210 q^{80} -8.18720 q^{81} -12.1726 q^{82} -4.01716 q^{83} +5.58241 q^{84} -1.96473 q^{85} +29.4692 q^{86} -1.52102 q^{87} -4.68255 q^{88} -9.80757 q^{89} +25.2147 q^{90} +2.48405 q^{91} +17.6264 q^{92} -14.6998 q^{93} -22.1389 q^{94} -11.3683 q^{95} +0.345005 q^{96} -9.24184 q^{97} +16.4076 q^{98} +3.08128 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9}+O(q^{10}) $ 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9} + 9 q^{10} + 23 q^{11} + 24 q^{12} + 23 q^{13} + 31 q^{14} + 9 q^{15} + 168 q^{16} + 98 q^{17} + 38 q^{18} + 29 q^{19} + 83 q^{20} + 26 q^{21} + 2 q^{22} + 34 q^{23} + 75 q^{24} + 177 q^{25} + 67 q^{26} + 32 q^{27} + 32 q^{28} + 91 q^{29} + 12 q^{30} + 24 q^{31} + 88 q^{32} + 27 q^{33} + 23 q^{34} + 66 q^{35} + 232 q^{36} - 133 q^{37} + 26 q^{38} + 28 q^{39} + 41 q^{40} + 132 q^{41} + 13 q^{42} + 11 q^{43} + 65 q^{44} + 107 q^{45} + 20 q^{46} + 10 q^{47} + 27 q^{48} + 229 q^{49} + 78 q^{50} + 19 q^{51} + 71 q^{52} + 7 q^{53} + 43 q^{54} + 41 q^{55} + 67 q^{56} + 45 q^{57} + 25 q^{58} + 97 q^{59} - 42 q^{60} + 65 q^{61} + 24 q^{62} + 39 q^{63} + 200 q^{64} + 60 q^{65} + 35 q^{66} + 25 q^{67} + 227 q^{68} + 120 q^{69} + 37 q^{70} + 26 q^{71} + 93 q^{72} + 55 q^{73} - 14 q^{74} + 5 q^{75} + 34 q^{76} + 21 q^{77} - 2 q^{78} + 50 q^{79} + 162 q^{80} + 341 q^{81} + 66 q^{82} + 30 q^{83} - 89 q^{84} + 30 q^{85} - 12 q^{86} + 80 q^{87} - 85 q^{88} + 225 q^{89} - 86 q^{90} + q^{91} + 82 q^{92} + 42 q^{93} - 17 q^{94} + 70 q^{95} + 55 q^{96} + 12 q^{97} + 90 q^{98} + 17 q^{99}+O(q^{100}) \) 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9 + 9 * q^10 + 23 * q^11 + 24 * q^12 + 23 * q^13 + 31 * q^14 + 9 * q^15 + 168 * q^16 + 98 * q^17 + 38 * q^18 + 29 * q^19 + 83 * q^20 + 26 * q^21 + 2 * q^22 + 34 * q^23 + 75 * q^24 + 177 * q^25 + 67 * q^26 + 32 * q^27 + 32 * q^28 + 91 * q^29 + 12 * q^30 + 24 * q^31 + 88 * q^32 + 27 * q^33 + 23 * q^34 + 66 * q^35 + 232 * q^36 - 133 * q^37 + 26 * q^38 + 28 * q^39 + 41 * q^40 + 132 * q^41 + 13 * q^42 + 11 * q^43 + 65 * q^44 + 107 * q^45 + 20 * q^46 + 10 * q^47 + 27 * q^48 + 229 * q^49 + 78 * q^50 + 19 * q^51 + 71 * q^52 + 7 * q^53 + 43 * q^54 + 41 * q^55 + 67 * q^56 + 45 * q^57 + 25 * q^58 + 97 * q^59 - 42 * q^60 + 65 * q^61 + 24 * q^62 + 39 * q^63 + 200 * q^64 + 60 * q^65 + 35 * q^66 + 25 * q^67 + 227 * q^68 + 120 * q^69 + 37 * q^70 + 26 * q^71 + 93 * q^72 + 55 * q^73 - 14 * q^74 + 5 * q^75 + 34 * q^76 + 21 * q^77 - 2 * q^78 + 50 * q^79 + 162 * q^80 + 341 * q^81 + 66 * q^82 + 30 * q^83 - 89 * q^84 + 30 * q^85 - 12 * q^86 + 80 * q^87 - 85 * q^88 + 225 * q^89 - 86 * q^90 + q^91 + 82 * q^92 + 42 * q^93 - 17 * q^94 + 70 * q^95 + 55 * q^96 + 12 * q^97 + 90 * q^98 + 17 * 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 $

$2$	−2.45235	−1.73407	−0.867037	−	0.498245i	$-0.833978\pi$
$2$	−2.45235	−1.73407	−0.867037	+	0.498245i	$0.833978\pi$
$3$	−2.50002	−1.44339	−0.721693	−	0.692214i	$-0.756636\pi$
$3$	−2.50002	−1.44339	−0.721693	+	0.692214i	$0.756636\pi$
$4$	4.01402	2.00701
$5$	−3.16357	−1.41479	−0.707395	−	0.706819i	$-0.750130\pi$
$5$	−3.16357	−1.41479	−0.707395	+	0.706819i	$0.750130\pi$
$6$	6.13092	2.50294
$7$	−0.556288	−0.210257	−0.105129	−	0.994459i	$-0.533525\pi$
$7$	−0.556288	−0.210257	−0.105129	+	0.994459i	$0.533525\pi$
$8$	−4.93908	−1.74623
$9$	3.25009	1.08336
$10$	7.75817	2.45335
$11$	0.948061	0.285851	0.142926	−	0.989733i	$-0.454349\pi$
$11$	0.948061	0.285851	0.142926	+	0.989733i	$0.454349\pi$
$12$	−10.0351	−2.89689
$13$	−4.46540	−1.23848	−0.619240	−	0.785202i	$-0.712559\pi$
$13$	−4.46540	−1.23848	−0.619240	+	0.785202i	$0.712559\pi$
$14$	1.36421	0.364601
$15$	7.90897	2.04209
$16$	4.08431	1.02108
$17$	0.621048	0.150626	0.0753132	−	0.997160i	$-0.476004\pi$
$17$	0.621048	0.150626	0.0753132	+	0.997160i	$0.476004\pi$
$18$	−7.97035	−1.87863
$19$	3.59352	0.824411	0.412205	−	0.911091i	$-0.364759\pi$
$19$	3.59352	0.824411	0.412205	+	0.911091i	$0.364759\pi$
$20$	−12.6986	−2.83950
$21$	1.39073	0.303482
$22$	−2.32498	−0.495687
$23$	4.39121	0.915631	0.457815	−	0.889047i	$-0.348632\pi$
$23$	4.39121	0.915631	0.457815	+	0.889047i	$0.348632\pi$
$24$	12.3478	2.52048
$25$	5.00815	1.00163
$26$	10.9507	2.14762
$27$	−0.625218	−0.120323
$28$	−2.23295	−0.421988
$29$	0.608404	0.112978	0.0564889	−	0.998403i	$-0.482009\pi$
$29$	0.608404	0.112978	0.0564889	+	0.998403i	$0.482009\pi$
$30$	−19.3956	−3.54113
$31$	5.87987	1.05606	0.528028	−	0.849227i	$-0.322932\pi$
$31$	5.87987	1.05606	0.528028	+	0.849227i	$0.322932\pi$
$32$	−0.138001	−0.0243954
$33$	−2.37017	−0.412594
$34$	−1.52303	−0.261197
$35$	1.75985	0.297469
$36$	13.0459	2.17432
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−8.81257	−1.42959
$39$	11.1636	1.78760
$40$	15.6251	2.47055
$41$	4.96366	0.775194	0.387597	−	0.921829i	$-0.373305\pi$
$41$	4.96366	0.775194	0.387597	+	0.921829i	$0.373305\pi$
$42$	−3.41055	−0.526260
$43$	−12.0167	−1.83253	−0.916265	−	0.400573i	$-0.868811\pi$
$43$	−12.0167	−1.83253	−0.916265	+	0.400573i	$0.868811\pi$
$44$	3.80554	0.573706
$45$	−10.2819	−1.53273
$46$	−10.7688	−1.58777
$47$	9.02763	1.31682	0.658408	−	0.752662i	$-0.271230\pi$
$47$	9.02763	1.31682	0.658408	+	0.752662i	$0.271230\pi$
$48$	−10.2108	−1.47381
$49$	−6.69054	−0.955792
$50$	−12.2817	−1.73690
$51$	−1.55263	−0.217412
$52$	−17.9242	−2.48564
$53$	0.333636	0.0458284	0.0229142	−	0.999737i	$-0.492706\pi$
$53$	0.333636	0.0458284	0.0229142	+	0.999737i	$0.492706\pi$
$54$	1.53325	0.208649
$55$	−2.99925	−0.404419
$56$	2.74755	0.367157
$57$	−8.98387	−1.18994
$58$	−1.49202	−0.195912
$59$	4.14371	0.539465	0.269733	−	0.962935i	$-0.413065\pi$
$59$	4.14371	0.539465	0.269733	+	0.962935i	$0.413065\pi$
$60$	31.7467	4.09849
$61$	3.73513	0.478234	0.239117	−	0.970991i	$-0.423142\pi$
$61$	3.73513	0.478234	0.239117	+	0.970991i	$0.423142\pi$
$62$	−14.4195	−1.83128
$63$	−1.80798	−0.227784
$64$	−7.83020	−0.978774
$65$	14.1266	1.75219
$66$	5.81248	0.715467
$67$	−0.200881	−0.0245416	−0.0122708	−	0.999925i	$-0.503906\pi$
$67$	−0.200881	−0.0245416	−0.0122708	+	0.999925i	$0.503906\pi$
$68$	2.49290	0.302308
$69$	−10.9781	−1.32161
$70$	−4.31577	−0.515834
$71$	16.0585	1.90580	0.952898	−	0.303292i	$-0.0980857\pi$
$71$	16.0585	1.90580	0.952898	+	0.303292i	$0.0980857\pi$
$72$	−16.0524	−1.89180
$73$	6.90138	0.807746	0.403873	−	0.914815i	$-0.367664\pi$
$73$	6.90138	0.807746	0.403873	+	0.914815i	$0.367664\pi$
$74$	2.45235	0.285080
$75$	−12.5205	−1.44574
$76$	14.4245	1.65460
$77$	−0.527395	−0.0601022
$78$	−27.3770	−3.09984
$79$	16.1956	1.82215	0.911075	−	0.412241i	$-0.135254\pi$
$79$	16.1956	1.82215	0.911075	+	0.412241i	$0.135254\pi$
$80$	−12.9210	−1.44461
$81$	−8.18720	−0.909689
$82$	−12.1726	−1.34424
$83$	−4.01716	−0.440941	−0.220470	−	0.975394i	$-0.570759\pi$
$83$	−4.01716	−0.440941	−0.220470	+	0.975394i	$0.570759\pi$
$84$	5.58241	0.609091
$85$	−1.96473	−0.213105
$86$	29.4692	3.17774
$87$	−1.52102	−0.163071
$88$	−4.68255	−0.499162
$89$	−9.80757	−1.03960	−0.519800	−	0.854288i	$-0.673994\pi$
$89$	−9.80757	−1.03960	−0.519800	+	0.854288i	$0.673994\pi$
$90$	25.2147	2.65786
$91$	2.48405	0.260399
$92$	17.6264	1.83768
$93$	−14.6998	−1.52429
$94$	−22.1389	−2.28345
$95$	−11.3683	−1.16637
$96$	0.345005	0.0352119
$97$	−9.24184	−0.938367	−0.469184	−	0.883101i	$-0.655452\pi$
$97$	−9.24184	−0.938367	−0.469184	+	0.883101i	$0.655452\pi$
$98$	16.4076	1.65741
$99$	3.08128	0.309680
$100$	20.1028	2.01028
$101$	9.01552	0.897078	0.448539	−	0.893763i	$-0.351944\pi$
$101$	9.01552	0.897078	0.448539	+	0.893763i	$0.351944\pi$
$102$	3.80759	0.377008
$103$	8.88180	0.875150	0.437575	−	0.899182i	$-0.355838\pi$
$103$	8.88180	0.875150	0.437575	+	0.899182i	$0.355838\pi$
$104$	22.0550	2.16267
$105$	−4.39966	−0.429363
$106$	−0.818192	−0.0794699
$107$	−5.71407	−0.552400	−0.276200	−	0.961100i	$-0.589075\pi$
$107$	−5.71407	−0.552400	−0.276200	+	0.961100i	$0.589075\pi$
$108$	−2.50964	−0.241490
$109$	3.89873	0.373430	0.186715	−	0.982414i	$-0.440216\pi$
$109$	3.89873	0.373430	0.186715	+	0.982414i	$0.440216\pi$
$110$	7.35522	0.701293
$111$	2.50002	0.237291
$112$	−2.27205	−0.214689
$113$	14.6331	1.37657	0.688284	−	0.725442i	$-0.258364\pi$
$113$	14.6331	1.37657	0.688284	+	0.725442i	$0.258364\pi$
$114$	22.0316	2.06345
$115$	−13.8919	−1.29542
$116$	2.44215	0.226748
$117$	−14.5129	−1.34172
$118$	−10.1618	−0.935472
$119$	−0.345481	−0.0316702
$120$	−39.0630	−3.56595
$121$	−10.1012	−0.918289
$122$	−9.15984	−0.829293
$123$	−12.4092	−1.11890
$124$	23.6019	2.11951
$125$	−0.0257707	−0.00230500
$126$	4.43381	0.394995
$127$	−15.6325	−1.38716	−0.693578	−	0.720381i	$-0.743967\pi$
$127$	−15.6325	−1.38716	−0.693578	+	0.720381i	$0.743967\pi$
$128$	19.4784	1.72166
$129$	30.0420	2.64505
$130$	−34.6434	−3.03842
$131$	−0.388080	−0.0339067	−0.0169534	−	0.999856i	$-0.505397\pi$
$131$	−0.388080	−0.0339067	−0.0169534	+	0.999856i	$0.505397\pi$
$132$	−9.51391	−0.828079
$133$	−1.99903	−0.173338
$134$	0.492632	0.0425569
$135$	1.97792	0.170232
$136$	−3.06741	−0.263028
$137$	8.69332	0.742721	0.371360	−	0.928489i	$-0.378891\pi$
$137$	8.69332	0.742721	0.371360	+	0.928489i	$0.378891\pi$
$138$	26.9221	2.29176
$139$	16.1711	1.37161	0.685807	−	0.727784i	$-0.259450\pi$
$139$	16.1711	1.37161	0.685807	+	0.727784i	$0.259450\pi$
$140$	7.06408	0.597024
$141$	−22.5692	−1.90067
$142$	−39.3811	−3.30479
$143$	−4.23348	−0.354021
$144$	13.2744	1.10620
$145$	−1.92473	−0.159840
$146$	−16.9246	−1.40069
$147$	16.7265	1.37958
$148$	−4.01402	−0.329950
$149$	−11.2259	−0.919661	−0.459830	−	0.888007i	$-0.652090\pi$
$149$	−11.2259	−0.919661	−0.459830	+	0.888007i	$0.652090\pi$
$150$	30.7045	2.50701
$151$	−19.9777	−1.62576	−0.812881	−	0.582429i	$-0.802102\pi$
$151$	−19.9777	−1.62576	−0.812881	+	0.582429i	$0.802102\pi$
$152$	−17.7487	−1.43961
$153$	2.01846	0.163183
$154$	1.29336	0.104222
$155$	−18.6013	−1.49410
$156$	44.8108	3.58774
$157$	−22.4663	−1.79301	−0.896504	−	0.443035i	$-0.853902\pi$
$157$	−22.4663	−1.79301	−0.896504	+	0.443035i	$0.853902\pi$
$158$	−39.7173	−3.15974
$159$	−0.834096	−0.0661481
$160$	0.436576	0.0345143
$161$	−2.44278	−0.192518
$162$	20.0779	1.57747
$163$	1.00000	0.0783260
$163$	1.00000	0.0783260
$164$	19.9242	1.55582
$165$	7.49819	0.583733
$166$	9.85149	0.764624
$167$	−1.68205	−0.130161	−0.0650805	−	0.997880i	$-0.520730\pi$
$167$	−1.68205	−0.130161	−0.0650805	+	0.997880i	$0.520730\pi$
$168$	−6.86892	−0.529949
$169$	6.93983	0.533833
$170$	4.81820	0.369539
$171$	11.6793	0.893135
$172$	−48.2353	−3.67790
$173$	−16.9837	−1.29124	−0.645622	−	0.763658i	$-0.723402\pi$
$173$	−16.9837	−1.29124	−0.645622	+	0.763658i	$0.723402\pi$
$174$	3.73008	0.282776
$175$	−2.78597	−0.210600
$176$	3.87218	0.291876
$177$	−10.3593	−0.778656
$178$	24.0516	1.80274
$179$	8.47960	0.633795	0.316898	−	0.948460i	$-0.397359\pi$
$179$	8.47960	0.633795	0.316898	+	0.948460i	$0.397359\pi$
$180$	−41.2716	−3.07620
$181$	−24.1537	−1.79533	−0.897664	−	0.440680i	$-0.854737\pi$
$181$	−24.1537	−1.79533	−0.897664	+	0.440680i	$0.854737\pi$
$182$	−6.09176	−0.451551
$183$	−9.33789	−0.690276
$184$	−21.6885	−1.59890
$185$	3.16357	0.232590
$186$	36.0490	2.64324
$187$	0.588792	0.0430567
$188$	36.2371	2.64286
$189$	0.347801	0.0252988
$190$	27.8792	2.02257
$191$	15.9993	1.15767	0.578833	−	0.815446i	$-0.303508\pi$
$191$	15.9993	1.15767	0.578833	+	0.815446i	$0.303508\pi$
$192$	19.5756	1.41275
$193$	21.4051	1.54077	0.770385	−	0.637579i	$-0.220064\pi$
$193$	21.4051	1.54077	0.770385	+	0.637579i	$0.220064\pi$
$194$	22.6642	1.62720
$195$	−35.3167	−2.52908
$196$	−26.8560	−1.91828
$197$	−16.7343	−1.19227	−0.596134	−	0.802885i	$-0.703297\pi$
$197$	−16.7343	−1.19227	−0.596134	+	0.802885i	$0.703297\pi$
$198$	−7.55638	−0.537008
$199$	−20.1377	−1.42752	−0.713761	−	0.700389i	$-0.753010\pi$
$199$	−20.1377	−1.42752	−0.713761	+	0.700389i	$0.753010\pi$
$200$	−24.7356	−1.74907
$201$	0.502207	0.0354230
$202$	−22.1092	−1.55560
$203$	−0.338448	−0.0237544
$204$	−6.23229	−0.436348
$205$	−15.7029	−1.09674
$206$	−21.7813	−1.51757
$207$	14.2718	0.991959
$208$	−18.2381	−1.26458
$209$	3.40688	0.235659
$210$	10.7895	0.744547
$211$	4.08421	0.281169	0.140584	−	0.990069i	$-0.455102\pi$
$211$	4.08421	0.281169	0.140584	+	0.990069i	$0.455102\pi$
$212$	1.33922	0.0919781
$213$	−40.1466	−2.75080
$214$	14.0129	0.957902
$215$	38.0156	2.59264
$216$	3.08800	0.210112
$217$	−3.27090	−0.222043
$218$	−9.56104	−0.647555
$219$	−17.2536	−1.16589
$220$	−12.0391	−0.811674
$221$	−2.77323	−0.186548
$222$	−6.13092	−0.411480
$223$	11.4014	0.763491	0.381745	−	0.924267i	$-0.375323\pi$
$223$	11.4014	0.763491	0.381745	+	0.924267i	$0.375323\pi$
$224$	0.0767683	0.00512930
$225$	16.2769	1.08513
$226$	−35.8855	−2.38707
$227$	−15.9466	−1.05841	−0.529206	−	0.848493i	$-0.677510\pi$
$227$	−15.9466	−1.05841	−0.529206	+	0.848493i	$0.677510\pi$
$228$	−36.0614	−2.38823
$229$	−10.8155	−0.714706	−0.357353	−	0.933969i	$-0.616321\pi$
$229$	−10.8155	−0.714706	−0.357353	+	0.933969i	$0.616321\pi$
$230$	34.0677	2.24636
$231$	1.31850	0.0867507
$232$	−3.00496	−0.197285
$233$	−17.1471	−1.12335	−0.561673	−	0.827359i	$-0.689842\pi$
$233$	−17.1471	−1.12335	−0.561673	+	0.827359i	$0.689842\pi$
$234$	35.5908	2.32664
$235$	−28.5595	−1.86302
$236$	16.6329	1.08271
$237$	−40.4893	−2.63006
$238$	0.847241	0.0549185
$239$	20.1793	1.30529	0.652645	−	0.757663i	$-0.273659\pi$
$239$	20.1793	1.30529	0.652645	+	0.757663i	$0.273659\pi$
$240$	32.3027	2.08513
$241$	6.87226	0.442681	0.221340	−	0.975197i	$-0.428957\pi$
$241$	6.87226	0.442681	0.221340	+	0.975197i	$0.428957\pi$
$242$	24.7716	1.59238
$243$	22.3438	1.43336
$244$	14.9929	0.959821
$245$	21.1660	1.35224
$246$	30.4318	1.94026
$247$	−16.0465	−1.02102
$248$	−29.0411	−1.84411
$249$	10.0430	0.636448
$250$	0.0631987	0.00399704
$251$	−25.8974	−1.63463	−0.817315	−	0.576191i	$-0.804538\pi$
$251$	−25.8974	−1.63463	−0.817315	+	0.576191i	$0.804538\pi$
$252$	−7.25728	−0.457165
$253$	4.16314	0.261734
$254$	38.3363	2.40543
$255$	4.91185	0.307592
$256$	−32.1074	−2.00671
$257$	13.1215	0.818494	0.409247	−	0.912424i	$-0.365791\pi$
$257$	13.1215	0.818494	0.409247	+	0.912424i	$0.365791\pi$
$258$	−73.6734	−4.58670
$259$	0.556288	0.0345660
$260$	56.7044	3.51666
$261$	1.97737	0.122396
$262$	0.951708	0.0587967
$263$	−11.0032	−0.678487	−0.339243	−	0.940699i	$-0.610171\pi$
$263$	−11.0032	−0.678487	−0.339243	+	0.940699i	$0.610171\pi$
$264$	11.7065	0.720483
$265$	−1.05548	−0.0648376
$266$	4.90233	0.300581
$267$	24.5191	1.50054
$268$	−0.806342	−0.0492552
$269$	16.8350	1.02645	0.513223	−	0.858255i	$-0.328451\pi$
$269$	16.8350	1.02645	0.513223	+	0.858255i	$0.328451\pi$
$270$	−4.85054	−0.295195
$271$	18.5243	1.12527	0.562635	−	0.826705i	$-0.309788\pi$
$271$	18.5243	1.12527	0.562635	+	0.826705i	$0.309788\pi$
$272$	2.53655	0.153801
$273$	−6.21017	−0.375856
$274$	−21.3191	−1.28793
$275$	4.74803	0.286317
$276$	−44.0663	−2.65248
$277$	0.405043	0.0243367	0.0121683	−	0.999926i	$-0.496127\pi$
$277$	0.405043	0.0243367	0.0121683	+	0.999926i	$0.496127\pi$
$278$	−39.6572	−2.37848
$279$	19.1101	1.14409
$280$	−8.69205	−0.519449
$281$	−22.2049	−1.32464	−0.662318	−	0.749223i	$-0.730427\pi$
$281$	−22.2049	−1.32464	−0.662318	+	0.749223i	$0.730427\pi$
$282$	55.3476	3.29590
$283$	10.8694	0.646117	0.323059	−	0.946379i	$-0.395289\pi$
$283$	10.8694	0.646117	0.323059	+	0.946379i	$0.395289\pi$
$284$	64.4592	3.82495
$285$	28.4210	1.68352
$286$	10.3820	0.613898
$287$	−2.76122	−0.162990
$288$	−0.448515	−0.0264290
$289$	−16.6143	−0.977312
$290$	4.72010	0.277174
$291$	23.1048	1.35443
$292$	27.7023	1.62115
$293$	2.25054	0.131478	0.0657390	−	0.997837i	$-0.479060\pi$
$293$	2.25054	0.131478	0.0657390	+	0.997837i	$0.479060\pi$
$294$	−41.0192	−2.39229
$295$	−13.1089	−0.763230
$296$	4.93908	0.287078
$297$	−0.592745	−0.0343945
$298$	27.5298	1.59476
$299$	−19.6085	−1.13399
$300$	−50.2573	−2.90161
$301$	6.68474	0.385302
$302$	48.9923	2.81919
$303$	−22.5390	−1.29483
$304$	14.6771	0.841787
$305$	−11.8163	−0.676601
$306$	−4.94997	−0.282971
$307$	19.8687	1.13397	0.566985	−	0.823728i	$-0.308110\pi$
$307$	19.8687	1.13397	0.566985	+	0.823728i	$0.308110\pi$
$308$	−2.11697	−0.120626
$309$	−22.2047	−1.26318
$310$	45.6170	2.59087
$311$	−1.52261	−0.0863395	−0.0431697	−	0.999068i	$-0.513746\pi$
$311$	−1.52261	−0.0863395	−0.0431697	+	0.999068i	$0.513746\pi$
$312$	−55.1378	−3.12157
$313$	15.8357	0.895085	0.447543	−	0.894263i	$-0.352299\pi$
$313$	15.8357	0.895085	0.447543	+	0.894263i	$0.352299\pi$
$314$	55.0953	3.10921
$315$	5.71967	0.322267
$316$	65.0095	3.65707
$317$	−3.55705	−0.199784	−0.0998920	−	0.994998i	$-0.531850\pi$
$317$	−3.55705	−0.199784	−0.0998920	+	0.994998i	$0.531850\pi$
$318$	2.04549	0.114706
$319$	0.576805	0.0322949
$320$	24.7713	1.38476
$321$	14.2853	0.797326
$322$	5.99054	0.333840
$323$	2.23175	0.124178
$324$	−32.8636	−1.82575
$325$	−22.3634	−1.24050
$326$	−2.45235	−0.135823
$327$	−9.74688	−0.539004
$328$	−24.5159	−1.35367
$329$	−5.02196	−0.276870
$330$	−18.3882	−1.01224
$331$	−26.8565	−1.47617	−0.738083	−	0.674710i	$-0.764269\pi$
$331$	−26.8565	−1.47617	−0.738083	+	0.674710i	$0.764269\pi$
$332$	−16.1250	−0.884972
$333$	−3.25009	−0.178104
$334$	4.12498	0.225709
$335$	0.635502	0.0347212
$336$	5.68017	0.309879
$337$	−31.2241	−1.70089	−0.850444	−	0.526066i	$-0.823667\pi$
$337$	−31.2241	−1.70089	−0.850444	+	0.526066i	$0.823667\pi$
$338$	−17.0189	−0.925706
$339$	−36.5830	−1.98692
$340$	−7.88645	−0.427703
$341$	5.57447	0.301875
$342$	−28.6416	−1.54876
$343$	7.61588	0.411219
$344$	59.3514	3.20001
$345$	34.7299	1.86980
$346$	41.6499	2.23911
$347$	5.31829	0.285501	0.142750	−	0.989759i	$-0.454405\pi$
$347$	5.31829	0.285501	0.142750	+	0.989759i	$0.454405\pi$
$348$	−6.10541	−0.327284
$349$	0.0607852	0.00325376	0.00162688	−	0.999999i	$-0.499482\pi$
$349$	0.0607852	0.00325376	0.00162688	+	0.999999i	$0.499482\pi$
$350$	6.83217	0.365195
$351$	2.79185	0.149018
$352$	−0.130834	−0.00697345
$353$	−15.3660	−0.817847	−0.408924	−	0.912569i	$-0.634096\pi$
$353$	−15.3660	−0.817847	−0.408924	+	0.912569i	$0.634096\pi$
$354$	25.4047	1.35025
$355$	−50.8022	−2.69630
$356$	−39.3678	−2.08649
$357$	0.863710	0.0457124
$358$	−20.7950	−1.09905
$359$	13.6250	0.719102	0.359551	−	0.933125i	$-0.382930\pi$
$359$	13.6250	0.719102	0.359551	+	0.933125i	$0.382930\pi$
$360$	50.7829	2.67649
$361$	−6.08660	−0.320347
$362$	59.2332	3.11323
$363$	25.2531	1.32545
$364$	9.97102	0.522624
$365$	−21.8330	−1.14279
$366$	22.8998	1.19699
$367$	2.44722	0.127744	0.0638718	−	0.997958i	$-0.479655\pi$
$367$	2.44722	0.127744	0.0638718	+	0.997958i	$0.479655\pi$
$368$	17.9351	0.934930
$369$	16.1323	0.839815
$370$	−7.75817	−0.403328
$371$	−0.185598	−0.00963575
$372$	−59.0051	−3.05927
$373$	31.6569	1.63913	0.819567	−	0.572984i	$-0.194214\pi$
$373$	31.6569	1.63913	0.819567	+	0.572984i	$0.194214\pi$
$374$	−1.44392	−0.0746635
$375$	0.0644272	0.00332700
$376$	−44.5882	−2.29946
$377$	−2.71677	−0.139921
$378$	−0.852930	−0.0438700
$379$	−23.8632	−1.22577	−0.612884	−	0.790173i	$-0.709991\pi$
$379$	−23.8632	−1.22577	−0.612884	+	0.790173i	$0.709991\pi$
$380$	−45.6327	−2.34091
$381$	39.0814	2.00220
$382$	−39.2358	−2.00748
$383$	−32.3630	−1.65367	−0.826836	−	0.562443i	$-0.809861\pi$
$383$	−32.3630	−1.65367	−0.826836	+	0.562443i	$0.809861\pi$
$384$	−48.6963	−2.48502
$385$	1.66845	0.0850320
$386$	−52.4927	−2.67181
$387$	−39.0553	−1.98529
$388$	−37.0969	−1.88331
$389$	−2.28838	−0.116026	−0.0580128	−	0.998316i	$-0.518476\pi$
$389$	−2.28838	−0.116026	−0.0580128	+	0.998316i	$0.518476\pi$
$390$	86.6090	4.38562
$391$	2.72715	0.137918
$392$	33.0451	1.66903
$393$	0.970207	0.0489405
$394$	41.0383	2.06748
$395$	−51.2359	−2.57796
$396$	12.3683	0.621531
$397$	7.70007	0.386455	0.193228	−	0.981154i	$-0.438104\pi$
$397$	7.70007	0.386455	0.193228	+	0.981154i	$0.438104\pi$
$398$	49.3846	2.47543
$399$	4.99761	0.250194
$400$	20.4548	1.02274
$401$	−1.60522	−0.0801608	−0.0400804	−	0.999196i	$-0.512761\pi$
$401$	−1.60522	−0.0801608	−0.0400804	+	0.999196i	$0.512761\pi$
$402$	−1.23159	−0.0614260
$403$	−26.2560	−1.30790
$404$	36.1885	1.80044
$405$	25.9007	1.28702
$406$	0.829993	0.0411918
$407$	−0.948061	−0.0469937
$408$	7.66857	0.379651
$409$	−9.08886	−0.449415	−0.224708	−	0.974426i	$-0.572143\pi$
$409$	−9.08886	−0.449415	−0.224708	+	0.974426i	$0.572143\pi$
$410$	38.5089	1.90182
$411$	−21.7335	−1.07203
$412$	35.6517	1.75643
$413$	−2.30510	−0.113426
$414$	−34.9995	−1.72013
$415$	12.7086	0.623838
$416$	0.616231	0.0302132
$417$	−40.4280	−1.97977
$418$	−8.35486	−0.408650
$419$	23.8976	1.16747	0.583737	−	0.811943i	$-0.301590\pi$
$419$	23.8976	1.16747	0.583737	+	0.811943i	$0.301590\pi$
$420$	−17.6603	−0.861736
$421$	32.9620	1.60647	0.803235	−	0.595662i	$-0.203110\pi$
$421$	32.9620	1.60647	0.803235	+	0.595662i	$0.203110\pi$
$422$	−10.0159	−0.487567
$423$	29.3406	1.42659
$424$	−1.64785	−0.0800269
$425$	3.11030	0.150872
$426$	98.4534	4.77008
$427$	−2.07781	−0.100552
$428$	−22.9364	−1.10867
$429$	10.5838	0.510989
$430$	−93.2276	−4.49583
$431$	−13.9182	−0.670417	−0.335209	−	0.942144i	$-0.608807\pi$
$431$	−13.9182	−0.670417	−0.335209	+	0.942144i	$0.608807\pi$
$432$	−2.55358	−0.122859
$433$	10.3590	0.497822	0.248911	−	0.968526i	$-0.419927\pi$
$433$	10.3590	0.497822	0.248911	+	0.968526i	$0.419927\pi$
$434$	8.02138	0.385039
$435$	4.81185	0.230711
$436$	15.6496	0.749478
$437$	15.7799	0.754855
$438$	42.3118	2.02174
$439$	38.2486	1.82551	0.912753	−	0.408512i	$-0.133952\pi$
$439$	38.2486	1.82551	0.912753	+	0.408512i	$0.133952\pi$
$440$	14.8136	0.706208
$441$	−21.7448	−1.03547
$442$	6.80093	0.323487
$443$	28.6492	1.36117	0.680583	−	0.732671i	$-0.261727\pi$
$443$	28.6492	1.36117	0.680583	+	0.732671i	$0.261727\pi$
$444$	10.0351	0.476246
$445$	31.0269	1.47081
$446$	−27.9601	−1.32395
$447$	28.0649	1.32742
$448$	4.35584	0.205794
$449$	11.2527	0.531049	0.265525	−	0.964104i	$-0.414455\pi$
$449$	11.2527	0.531049	0.265525	+	0.964104i	$0.414455\pi$
$450$	−39.9167	−1.88169
$451$	4.70586	0.221590
$452$	58.7376	2.76278
$453$	49.9446	2.34660
$454$	39.1066	1.83536
$455$	−7.85845	−0.368410
$456$	44.3720	2.07791
$457$	−15.3755	−0.719235	−0.359618	−	0.933100i	$-0.617093\pi$
$457$	−15.3755	−0.719235	−0.359618	+	0.933100i	$0.617093\pi$
$458$	26.5233	1.23935
$459$	−0.388290	−0.0181238
$460$	−55.7623	−2.59993
$461$	34.3222	1.59854	0.799272	−	0.600970i	$-0.205219\pi$
$461$	34.3222	1.59854	0.799272	+	0.600970i	$0.205219\pi$
$462$	−3.23341	−0.150432
$463$	−18.2991	−0.850433	−0.425217	−	0.905092i	$-0.639802\pi$
$463$	−18.2991	−0.850433	−0.425217	+	0.905092i	$0.639802\pi$
$464$	2.48491	0.115359
$465$	46.5037	2.15656
$466$	42.0508	1.94797
$467$	15.5999	0.721878	0.360939	−	0.932589i	$-0.382456\pi$
$467$	15.5999	0.721878	0.360939	+	0.932589i	$0.382456\pi$
$468$	−58.2552	−2.69285
$469$	0.111748	0.00516004
$470$	70.0379	3.23061
$471$	56.1662	2.58800
$472$	−20.4661	−0.942029
$473$	−11.3926	−0.523831
$474$	99.2940	4.56072
$475$	17.9969	0.825754
$476$	−1.38677	−0.0635625
$477$	1.08435	0.0496488
$478$	−49.4867	−2.26347
$479$	7.69371	0.351534	0.175767	−	0.984432i	$-0.443759\pi$
$479$	7.69371	0.351534	0.175767	+	0.984432i	$0.443759\pi$
$480$	−1.09145	−0.0498175
$481$	4.46540	0.203605
$482$	−16.8532	−0.767641
$483$	6.10698	0.277877
$484$	−40.5463	−1.84301
$485$	29.2372	1.32759
$486$	−54.7948	−2.48554
$487$	−36.8071	−1.66789	−0.833944	−	0.551850i	$-0.813922\pi$
$487$	−36.8071	−1.66789	−0.833944	+	0.551850i	$0.813922\pi$
$488$	−18.4481	−0.835106
$489$	−2.50002	−0.113055
$490$	−51.9064	−2.34489
$491$	16.3533	0.738015	0.369008	−	0.929426i	$-0.379698\pi$
$491$	16.3533	0.738015	0.369008	+	0.929426i	$0.379698\pi$
$492$	−49.8109	−2.24565
$493$	0.377848	0.0170174
$494$	39.3517	1.77052
$495$	−9.74783	−0.438132
$496$	24.0152	1.07831
$497$	−8.93316	−0.400707
$498$	−24.6289	−1.10365
$499$	22.2652	0.996726	0.498363	−	0.866968i	$-0.333935\pi$
$499$	22.2652	0.996726	0.498363	+	0.866968i	$0.333935\pi$
$500$	−0.103444	−0.00462616
$501$	4.20516	0.187873
$502$	63.5095	2.83457
$503$	3.53657	0.157688	0.0788440	−	0.996887i	$-0.474877\pi$
$503$	3.53657	0.157688	0.0788440	+	0.996887i	$0.474877\pi$
$504$	8.92977	0.397764
$505$	−28.5212	−1.26918
$506$	−10.2095	−0.453866
$507$	−17.3497	−0.770527
$508$	−62.7490	−2.78404
$509$	−9.99790	−0.443149	−0.221574	−	0.975143i	$-0.571120\pi$
$509$	−9.99790	−0.443149	−0.221574	+	0.975143i	$0.571120\pi$
$510$	−12.0456	−0.533387
$511$	−3.83915	−0.169834
$512$	39.7818	1.75813
$513$	−2.24673	−0.0991957
$514$	−32.1784	−1.41933
$515$	−28.0982	−1.23815
$516$	120.589	5.30863
$517$	8.55875	0.376413
$518$	−1.36421	−0.0599400
$519$	42.4594	1.86376
$520$	−69.7724	−3.05972
$521$	30.4533	1.33418	0.667092	−	0.744975i	$-0.267539\pi$
$521$	30.4533	1.33418	0.667092	+	0.744975i	$0.267539\pi$
$522$	−4.84919	−0.212243
$523$	−18.8954	−0.826238	−0.413119	−	0.910677i	$-0.635561\pi$
$523$	−18.8954	−0.826238	−0.413119	+	0.910677i	$0.635561\pi$
$524$	−1.55776	−0.0680511
$525$	6.96497	0.303976
$526$	26.9837	1.17655
$527$	3.65168	0.159070
$528$	−9.68051	−0.421290
$529$	−3.71728	−0.161621
$530$	2.58840	0.112433
$531$	13.4674	0.584436
$532$	−8.02415	−0.347891
$533$	−22.1648	−0.960062
$534$	−60.1294	−2.60205
$535$	18.0768	0.781530
$536$	0.992169	0.0428552
$537$	−21.1992	−0.914811
$538$	−41.2852	−1.77993
$539$	−6.34305	−0.273214
$540$	7.93940	0.341657
$541$	28.7619	1.23657	0.618285	−	0.785954i	$-0.287828\pi$
$541$	28.7619	1.23657	0.618285	+	0.785954i	$0.287828\pi$
$542$	−45.4280	−1.95130
$543$	60.3846	2.59135
$544$	−0.0857053	−0.00367459
$545$	−12.3339	−0.528325
$546$	15.2295	0.651762
$547$	23.8934	1.02161	0.510803	−	0.859698i	$-0.329348\pi$
$547$	23.8934	1.02161	0.510803	+	0.859698i	$0.329348\pi$
$548$	34.8952	1.49065
$549$	12.1395	0.518101
$550$	−11.6438	−0.496495
$551$	2.18631	0.0931401
$552$	54.2217	2.30783
$553$	−9.00942	−0.383120
$554$	−0.993306	−0.0422015
$555$	−7.90897	−0.335717
$556$	64.9110	2.75284
$557$	−8.50151	−0.360221	−0.180110	−	0.983646i	$-0.557645\pi$
$557$	−8.50151	−0.360221	−0.180110	+	0.983646i	$0.557645\pi$
$558$	−46.8646	−1.98394
$559$	53.6594	2.26955
$560$	7.18779	0.303739
$561$	−1.47199	−0.0621474
$562$	54.4543	2.29701
$563$	11.0886	0.467327	0.233664	−	0.972318i	$-0.424929\pi$
$563$	11.0886	0.467327	0.233664	+	0.972318i	$0.424929\pi$
$564$	−90.5933	−3.81467
$565$	−46.2928	−1.94755
$566$	−26.6555	−1.12041
$567$	4.55444	0.191268
$568$	−79.3143	−3.32795
$569$	−27.9618	−1.17222	−0.586110	−	0.810232i	$-0.699341\pi$
$569$	−27.9618	−1.17222	−0.586110	+	0.810232i	$0.699341\pi$
$570$	−69.6984	−2.91934
$571$	−4.92636	−0.206162	−0.103081	−	0.994673i	$-0.532870\pi$
$571$	−4.92636	−0.206162	−0.103081	+	0.994673i	$0.532870\pi$
$572$	−16.9933	−0.710524
$573$	−39.9985	−1.67096
$574$	6.77149	0.282636
$575$	21.9918	0.917122
$576$	−25.4488	−1.06037
$577$	33.3049	1.38650	0.693250	−	0.720697i	$-0.256178\pi$
$577$	33.3049	1.38650	0.693250	+	0.720697i	$0.256178\pi$
$578$	40.7441	1.69473
$579$	−53.5130	−2.22392
$580$	−7.72589	−0.320800
$581$	2.23470	0.0927109
$582$	−56.6610	−2.34867
$583$	0.316307	0.0131001
$584$	−34.0865	−1.41051
$585$	45.9126	1.89825
$586$	−5.51912	−0.227993
$587$	20.7393	0.856005	0.428002	−	0.903778i	$-0.359218\pi$
$587$	20.7393	0.856005	0.428002	+	0.903778i	$0.359218\pi$
$588$	67.1404	2.76882
$589$	21.1294	0.870623
$590$	32.1476	1.32350
$591$	41.8360	1.72090
$592$	−4.08431	−0.167864
$593$	12.3311	0.506376	0.253188	−	0.967417i	$-0.418521\pi$
$593$	12.3311	0.506376	0.253188	+	0.967417i	$0.418521\pi$
$594$	1.45362	0.0596426
$595$	1.09295	0.0448067
$596$	−45.0609	−1.84577
$597$	50.3445	2.06046
$598$	48.0870	1.96642
$599$	−28.1193	−1.14892	−0.574461	−	0.818532i	$-0.694788\pi$
$599$	−28.1193	−1.14892	−0.574461	+	0.818532i	$0.694788\pi$
$600$	61.8395	2.52459
$601$	39.3077	1.60339	0.801696	−	0.597732i	$-0.203931\pi$
$601$	39.3077	1.60339	0.801696	+	0.597732i	$0.203931\pi$
$602$	−16.3933	−0.668142
$603$	−0.652882	−0.0265874
$604$	−80.1909	−3.26292
$605$	31.9557	1.29919
$606$	55.2734	2.24533
$607$	−33.8307	−1.37315	−0.686574	−	0.727060i	$-0.740886\pi$
$607$	−33.8307	−1.37315	−0.686574	+	0.727060i	$0.740886\pi$
$608$	−0.495910	−0.0201118
$609$	0.846125	0.0342867
$610$	28.9778	1.17328
$611$	−40.3120	−1.63085
$612$	8.10214	0.327509
$613$	−12.9780	−0.524175	−0.262088	−	0.965044i	$-0.584411\pi$
$613$	−12.9780	−0.524175	−0.262088	+	0.965044i	$0.584411\pi$
$614$	−48.7251	−1.96639
$615$	39.2574	1.58301
$616$	2.60485	0.104952
$617$	−11.3411	−0.456576	−0.228288	−	0.973594i	$-0.573313\pi$
$617$	−11.3411	−0.456576	−0.228288	+	0.973594i	$0.573313\pi$
$618$	54.4536	2.19044
$619$	−9.98612	−0.401376	−0.200688	−	0.979655i	$-0.564318\pi$
$619$	−9.98612	−0.401376	−0.200688	+	0.979655i	$0.564318\pi$
$620$	−74.6661	−2.99866
$621$	−2.74546	−0.110172
$622$	3.73398	0.149719
$623$	5.45583	0.218583
$624$	45.5956	1.82528
$625$	−24.9592	−0.998368
$626$	−38.8346	−1.55214
$627$	−8.51726	−0.340146
$628$	−90.1803	−3.59859
$629$	−0.621048	−0.0247628
$630$	−14.0266	−0.558834
$631$	−29.8938	−1.19005	−0.595026	−	0.803707i	$-0.702858\pi$
$631$	−29.8938	−1.19005	−0.595026	+	0.803707i	$0.702858\pi$
$632$	−79.9914	−3.18189
$633$	−10.2106	−0.405835
$634$	8.72314	0.346440
$635$	49.4543	1.96253
$636$	−3.34808	−0.132760
$637$	29.8760	1.18373
$638$	−1.41453	−0.0560016
$639$	52.1916	2.06467
$640$	−61.6211	−2.43579
$641$	28.0591	1.10827	0.554134	−	0.832428i	$-0.313050\pi$
$641$	28.0591	1.10827	0.554134	+	0.832428i	$0.313050\pi$
$642$	−35.0325	−1.38262
$643$	−15.7198	−0.619929	−0.309965	−	0.950748i	$-0.600317\pi$
$643$	−15.7198	−0.619929	−0.309965	+	0.950748i	$0.600317\pi$
$644$	−9.80535	−0.386385
$645$	−95.0397	−3.74218
$646$	−5.47303	−0.215334
$647$	−31.6461	−1.24414	−0.622068	−	0.782963i	$-0.713707\pi$
$647$	−31.6461	−1.24414	−0.622068	+	0.782963i	$0.713707\pi$
$648$	40.4372	1.58852
$649$	3.92849	0.154207
$650$	54.8429	2.15111
$651$	8.17730	0.320494
$652$	4.01402	0.157201
$653$	26.5789	1.04011	0.520055	−	0.854133i	$-0.325911\pi$
$653$	26.5789	1.04011	0.520055	+	0.854133i	$0.325911\pi$
$654$	23.9028	0.934672
$655$	1.22772	0.0479709
$656$	20.2731	0.791533
$657$	22.4301	0.875081
$658$	12.3156	0.480112
$659$	−7.49464	−0.291950	−0.145975	−	0.989288i	$-0.546632\pi$
$659$	−7.49464	−0.291950	−0.145975	+	0.989288i	$0.546632\pi$
$660$	30.0979	1.17156
$661$	28.2757	1.09980	0.549898	−	0.835232i	$-0.314667\pi$
$661$	28.2757	1.09980	0.549898	+	0.835232i	$0.314667\pi$
$662$	65.8615	2.55978
$663$	6.93312	0.269260
$664$	19.8411	0.769983
$665$	6.32407	0.245237
$666$	7.97035	0.308845
$667$	2.67163	0.103446
$668$	−6.75179	−0.261234
$669$	−28.5036	−1.10201
$670$	−1.55847	−0.0602090
$671$	3.54113	0.136704
$672$	−0.191922	−0.00740356
$673$	25.4612	0.981458	0.490729	−	0.871312i	$-0.336731\pi$
$673$	25.4612	0.981458	0.490729	+	0.871312i	$0.336731\pi$
$674$	76.5725	2.94946
$675$	−3.13118	−0.120519
$676$	27.8566	1.07141
$677$	40.8394	1.56959	0.784793	−	0.619758i	$-0.212769\pi$
$677$	40.8394	1.56959	0.784793	+	0.619758i	$0.212769\pi$
$678$	89.7144	3.44546
$679$	5.14112	0.197298
$680$	9.70394	0.372129
$681$	39.8667	1.52770
$682$	−13.6706	−0.523473
$683$	−5.75268	−0.220120	−0.110060	−	0.993925i	$-0.535104\pi$
$683$	−5.75268	−0.220120	−0.110060	+	0.993925i	$0.535104\pi$
$684$	46.8807	1.79253
$685$	−27.5019	−1.05079
$686$	−18.6768	−0.713084
$687$	27.0388	1.03160
$688$	−49.0799	−1.87116
$689$	−1.48982	−0.0567576
$690$	−85.1699	−3.24236
$691$	24.5318	0.933234	0.466617	−	0.884459i	$-0.345473\pi$
$691$	24.5318	0.933234	0.466617	+	0.884459i	$0.345473\pi$
$692$	−68.1727	−2.59154
$693$	−1.71408	−0.0651125
$694$	−13.0423	−0.495079
$695$	−51.1583	−1.94054
$696$	7.51244	0.284758
$697$	3.08267	0.116765
$698$	−0.149067	−0.00564225
$699$	42.8682	1.62142
$700$	−11.1829	−0.422675
$701$	−5.38410	−0.203355	−0.101677	−	0.994817i	$-0.532421\pi$
$701$	−5.38410	−0.203355	−0.101677	+	0.994817i	$0.532421\pi$
$702$	−6.84659	−0.258408
$703$	−3.59352	−0.135532
$704$	−7.42351	−0.279784
$705$	71.3992	2.68905
$706$	37.6827	1.41821
$707$	−5.01523	−0.188617
$708$	−41.5826	−1.56277
$709$	8.49291	0.318958	0.159479	−	0.987201i	$-0.449019\pi$
$709$	8.49291	0.318958	0.159479	+	0.987201i	$0.449019\pi$
$710$	124.585	4.67558
$711$	52.6371	1.97405
$712$	48.4403	1.81538
$713$	25.8197	0.966956
$714$	−2.11812	−0.0792686
$715$	13.3929	0.500865
$716$	34.0373	1.27203
$717$	−50.4486	−1.88404
$718$	−33.4134	−1.24698
$719$	−10.0594	−0.375151	−0.187576	−	0.982250i	$-0.560063\pi$
$719$	−10.0594	−0.375151	−0.187576	+	0.982250i	$0.560063\pi$
$720$	−41.9943	−1.56504
$721$	−4.94084	−0.184006
$722$	14.9265	0.555506
$723$	−17.1808	−0.638959
$724$	−96.9533	−3.60324
$725$	3.04698	0.113162
$726$	−61.9295	−2.29842
$727$	37.2385	1.38110	0.690550	−	0.723285i	$-0.257369\pi$
$727$	37.2385	1.38110	0.690550	+	0.723285i	$0.257369\pi$
$728$	−12.2689	−0.454716
$729$	−31.2983	−1.15920
$730$	53.5421	1.98168
$731$	−7.46295	−0.276027
$732$	−37.4824	−1.38539
$733$	−2.68782	−0.0992771	−0.0496385	−	0.998767i	$-0.515807\pi$
$733$	−2.68782	−0.0992771	−0.0496385	+	0.998767i	$0.515807\pi$
$734$	−6.00143	−0.221517
$735$	−52.9153	−1.95181
$736$	−0.605992	−0.0223372
$737$	−0.190448	−0.00701524
$738$	−39.5621	−1.45630
$739$	30.0418	1.10511	0.552553	−	0.833478i	$-0.313654\pi$
$739$	30.0418	1.10511	0.552553	+	0.833478i	$0.313654\pi$
$740$	12.6986	0.466810
$741$	40.1166	1.47372
$742$	0.455150	0.0167091
$743$	10.0355	0.368168	0.184084	−	0.982910i	$-0.441068\pi$
$743$	10.0355	0.368168	0.184084	+	0.982910i	$0.441068\pi$
$744$	72.6033	2.66177
$745$	35.5138	1.30113
$746$	−77.6339	−2.84238
$747$	−13.0561	−0.477698
$748$	2.36342	0.0864152
$749$	3.17867	0.116146
$750$	−0.157998	−0.00576927
$751$	0.980624	0.0357835	0.0178917	−	0.999840i	$-0.494305\pi$
$751$	0.980624	0.0357835	0.0178917	+	0.999840i	$0.494305\pi$
$752$	36.8716	1.34457
$753$	64.7440	2.35940
$754$	6.66247	0.242633
$755$	63.2008	2.30011
$756$	1.39608	0.0507749
$757$	29.1983	1.06123	0.530616	−	0.847612i	$-0.321961\pi$
$757$	29.1983	1.06123	0.530616	+	0.847612i	$0.321961\pi$
$758$	58.5208	2.12557
$759$	−10.4079	−0.377783
$760$	56.1491	2.03674
$761$	−4.70124	−0.170420	−0.0852099	−	0.996363i	$-0.527156\pi$
$761$	−4.70124	−0.170420	−0.0852099	+	0.996363i	$0.527156\pi$
$762$	−95.8413	−3.47196
$763$	−2.16881	−0.0785163
$764$	64.2214	2.32345
$765$	−6.38553	−0.230869
$766$	79.3654	2.86759
$767$	−18.5033	−0.668117
$768$	80.2691	2.89646
$769$	44.3979	1.60103	0.800515	−	0.599312i	$-0.204559\pi$
$769$	44.3979	1.60103	0.800515	+	0.599312i	$0.204559\pi$
$770$	−4.09162	−0.147452
$771$	−32.8039	−1.18140
$772$	85.9203	3.09234
$773$	−23.3478	−0.839761	−0.419881	−	0.907579i	$-0.637928\pi$
$773$	−23.3478	−0.839761	−0.419881	+	0.907579i	$0.637928\pi$
$774$	95.7773	3.44264
$775$	29.4472	1.05778
$776$	45.6462	1.63860
$777$	−1.39073	−0.0498921
$778$	5.61192	0.201197
$779$	17.8370	0.639078
$780$	−141.762	−5.07590
$781$	15.2245	0.544774
$782$	−6.68793	−0.239160
$783$	−0.380385	−0.0135939
$784$	−27.3263	−0.975938
$785$	71.0737	2.53673
$786$	−2.37929	−0.0848663
$787$	−32.3704	−1.15388	−0.576940	−	0.816787i	$-0.695753\pi$
$787$	−32.3704	−1.15388	−0.576940	+	0.816787i	$0.695753\pi$
$788$	−67.1717	−2.39289
$789$	27.5082	0.979318
$790$	125.648	4.47037
$791$	−8.14022	−0.289433
$792$	−15.2187	−0.540773
$793$	−16.6789	−0.592284
$794$	−18.8833	−0.670142
$795$	2.63872	0.0935856
$796$	−80.8330	−2.86505
$797$	−16.5771	−0.587192	−0.293596	−	0.955930i	$-0.594852\pi$
$797$	−16.5771	−0.587192	−0.293596	+	0.955930i	$0.594852\pi$
$798$	−12.2559	−0.433854
$799$	5.60659	0.198347
$800$	−0.691130	−0.0244351
$801$	−31.8754	−1.12626
$802$	3.93656	0.139005
$803$	6.54293	0.230895
$804$	2.01587	0.0710942
$805$	7.72788	0.272372
$806$	64.3888	2.26800
$807$	−42.0877	−1.48156
$808$	−44.5284	−1.56650
$809$	16.5622	0.582296	0.291148	−	0.956678i	$-0.405963\pi$
$809$	16.5622	0.582296	0.291148	+	0.956678i	$0.405963\pi$
$810$	−63.5177	−2.23178
$811$	−28.6788	−1.00705	−0.503525	−	0.863981i	$-0.667964\pi$
$811$	−28.6788	−1.00705	−0.503525	+	0.863981i	$0.667964\pi$
$812$	−1.35854	−0.0476753
$813$	−46.3110	−1.62420
$814$	2.32498	0.0814904
$815$	−3.16357	−0.110815
$816$	−6.34143	−0.221994
$817$	−43.1823	−1.51076
$818$	22.2891	0.779319
$819$	8.07337	0.282106
$820$	−63.0316	−2.20116
$821$	−9.95255	−0.347346	−0.173673	−	0.984803i	$-0.555564\pi$
$821$	−9.95255	−0.347346	−0.173673	+	0.984803i	$0.555564\pi$
$822$	53.2980	1.85898
$823$	−4.01530	−0.139964	−0.0699822	−	0.997548i	$-0.522294\pi$
$823$	−4.01530	−0.139964	−0.0699822	+	0.997548i	$0.522294\pi$
$824$	−43.8679	−1.52821
$825$	−11.8702	−0.413266
$826$	5.65290	0.196690
$827$	50.7656	1.76529	0.882646	−	0.470039i	$-0.155760\pi$
$827$	50.7656	1.76529	0.882646	+	0.470039i	$0.155760\pi$
$828$	57.2873	1.99087
$829$	−15.7327	−0.546418	−0.273209	−	0.961955i	$-0.588085\pi$
$829$	−15.7327	−0.546418	−0.273209	+	0.961955i	$0.588085\pi$
$830$	−31.1658	−1.08178
$831$	−1.01261	−0.0351272
$832$	34.9650	1.21219
$833$	−4.15515	−0.143967
$834$	99.1436	3.43306
$835$	5.32128	0.184150
$836$	13.6753	0.472969
$837$	−3.67620	−0.127068
$838$	−58.6053	−2.02449
$839$	39.7538	1.37245	0.686227	−	0.727387i	$-0.259266\pi$
$839$	39.7538	1.37245	0.686227	+	0.727387i	$0.259266\pi$
$840$	21.7303	0.749766
$841$	−28.6298	−0.987236
$842$	−80.8344	−2.78574
$843$	55.5127	1.91196
$844$	16.3941	0.564308
$845$	−21.9546	−0.755261
$846$	−71.9533	−2.47381
$847$	5.61916	0.193077
$848$	1.36267	0.0467944
$849$	−27.1736	−0.932596
$850$	−7.62754	−0.261623
$851$	−4.39121	−0.150529
$852$	−161.149	−5.52088
$853$	27.1508	0.929625	0.464813	−	0.885409i	$-0.346122\pi$
$853$	27.1508	0.929625	0.464813	+	0.885409i	$0.346122\pi$
$854$	5.09551	0.174365
$855$	−36.9481	−1.26360
$856$	28.2222	0.964616
$857$	34.0867	1.16438	0.582189	−	0.813053i	$-0.302196\pi$
$857$	34.0867	1.16438	0.582189	+	0.813053i	$0.302196\pi$
$858$	−25.9551	−0.886092
$859$	24.4139	0.832992	0.416496	−	0.909137i	$-0.363258\pi$
$859$	24.4139	0.832992	0.416496	+	0.909137i	$0.363258\pi$
$860$	152.595	5.20346
$861$	6.90311	0.235257
$862$	34.1323	1.16255
$863$	−45.0763	−1.53441	−0.767207	−	0.641400i	$-0.778354\pi$
$863$	−45.0763	−1.53441	−0.767207	+	0.641400i	$0.778354\pi$
$864$	0.0862807	0.00293533
$865$	53.7289	1.82684
$866$	−25.4039	−0.863260
$867$	41.5360	1.41064
$868$	−13.1294	−0.445642
$869$	15.3544	0.520864
$870$	−11.8003	−0.400069
$871$	0.897017	0.0303943
$872$	−19.2561	−0.652094
$873$	−30.0368	−1.01659
$874$	−38.6979	−1.30897
$875$	0.0143359	0.000484643 0
$876$	−69.2562	−2.33995
$877$	−45.2647	−1.52848	−0.764240	−	0.644932i	$-0.776886\pi$
$877$	−45.2647	−1.52848	−0.764240	+	0.644932i	$0.776886\pi$
$878$	−93.7989	−3.16556
$879$	−5.62639	−0.189774
$880$	−12.2499	−0.412944
$881$	−41.3400	−1.39278	−0.696390	−	0.717663i	$-0.745212\pi$
$881$	−41.3400	−1.39278	−0.696390	+	0.717663i	$0.745212\pi$
$882$	53.3259	1.79558
$883$	7.22939	0.243288	0.121644	−	0.992574i	$-0.461183\pi$
$883$	7.22939	0.243288	0.121644	+	0.992574i	$0.461183\pi$
$884$	−11.1318	−0.374403
$885$	32.7725	1.10163
$886$	−70.2579	−2.36036
$887$	24.7830	0.832132	0.416066	−	0.909334i	$-0.363409\pi$
$887$	24.7830	0.832132	0.416066	+	0.909334i	$0.363409\pi$
$888$	−12.3478	−0.414364
$889$	8.69615	0.291659
$890$	−76.0887	−2.55050
$891$	−7.76197	−0.260036
$892$	45.7652	1.53233
$893$	32.4410	1.08560
$894$	−68.8250	−2.30185
$895$	−26.8258	−0.896687
$896$	−10.8356	−0.361991
$897$	49.0216	1.63679
$898$	−27.5956	−0.920878
$899$	3.57734	0.119311
$900$	65.3358	2.17786
$901$	0.207204	0.00690297
$902$	−11.5404	−0.384254
$903$	−16.7120	−0.556140
$904$	−72.2741	−2.40380
$905$	76.4117	2.54001
$906$	−122.482	−4.06918
$907$	−51.7026	−1.71676	−0.858378	−	0.513018i	$-0.828527\pi$
$907$	−51.7026	−1.71676	−0.858378	+	0.513018i	$0.828527\pi$
$908$	−64.0099	−2.12424
$909$	29.3012	0.971860
$910$	19.2717	0.638850
$911$	36.5303	1.21030	0.605152	−	0.796110i	$-0.293112\pi$
$911$	36.5303	1.21030	0.605152	+	0.796110i	$0.293112\pi$
$912$	−36.6929	−1.21502
$913$	−3.80852	−0.126043
$914$	37.7061	1.24721
$915$	29.5410	0.976596
$916$	−43.4135	−1.43442
$917$	0.215884	0.00712912
$918$	0.952224	0.0314281
$919$	23.0844	0.761483	0.380741	−	0.924682i	$-0.375669\pi$
$919$	23.0844	0.761483	0.380741	+	0.924682i	$0.375669\pi$
$920$	68.6131	2.26211
$921$	−49.6722	−1.63675
$922$	−84.1700	−2.77199
$923$	−71.7078	−2.36029
$924$	5.29247	0.174109
$925$	−5.00815	−0.164667
$926$	44.8759	1.47471
$927$	28.8666	0.948104
$928$	−0.0839605	−0.00275614
$929$	18.3149	0.600894	0.300447	−	0.953799i	$-0.402864\pi$
$929$	18.3149	0.600894	0.300447	+	0.953799i	$0.402864\pi$
$930$	−114.043	−3.73963
$931$	−24.0426	−0.787965
$932$	−68.8290	−2.25457
$933$	3.80656	0.124621
$934$	−38.2564	−1.25179
$935$	−1.86268	−0.0609162
$936$	71.6806	2.34295
$937$	36.4602	1.19110	0.595552	−	0.803317i	$-0.296933\pi$
$937$	36.4602	1.19110	0.595552	+	0.803317i	$0.296933\pi$
$938$	−0.274045	−0.00894788
$939$	−39.5895	−1.29195
$940$	−114.638	−3.73909
$941$	−9.64613	−0.314455	−0.157227	−	0.987562i	$-0.550256\pi$
$941$	−9.64613	−0.314455	−0.157227	+	0.987562i	$0.550256\pi$
$942$	−137.739	−4.48779
$943$	21.7965	0.709791
$944$	16.9242	0.550836
$945$	−1.10029	−0.0357925
$946$	27.9386	0.908361
$947$	34.6949	1.12743	0.563717	−	0.825968i	$-0.309371\pi$
$947$	34.6949	1.12743	0.563717	+	0.825968i	$0.309371\pi$
$948$	−162.525	−5.27856
$949$	−30.8175	−1.00038
$950$	−44.1347	−1.43192
$951$	8.89269	0.288365
$952$	1.70636	0.0553035
$953$	46.4095	1.50335	0.751676	−	0.659533i	$-0.229246\pi$
$953$	46.4095	1.50335	0.751676	+	0.659533i	$0.229246\pi$
$954$	−2.65919	−0.0860946
$955$	−50.6148	−1.63785
$956$	81.0001	2.61973
$957$	−1.44202	−0.0466139
$958$	−18.8677	−0.609586
$959$	−4.83599	−0.156162
$960$	−61.9288	−1.99874
$961$	3.57283	0.115253
$962$	−10.9507	−0.353066
$963$	−18.5712	−0.598449
$964$	27.5854	0.888465
$965$	−67.7163	−2.17986
$966$	−14.9765	−0.481860
$967$	34.3735	1.10538	0.552689	−	0.833388i	$-0.313602\pi$
$967$	34.3735	1.10538	0.552689	+	0.833388i	$0.313602\pi$
$968$	49.8905	1.60354
$969$	−5.57941	−0.179237
$970$	−71.6998	−2.30214
$971$	−48.1365	−1.54477	−0.772387	−	0.635152i	$-0.780937\pi$
$971$	−48.1365	−1.54477	−0.772387	+	0.635152i	$0.780937\pi$
$972$	89.6884	2.87676
$973$	−8.99578	−0.288391
$974$	90.2638	2.89224
$975$	55.9089	1.79052
$976$	15.2554	0.488314
$977$	−41.0575	−1.31355	−0.656773	−	0.754089i	$-0.728079\pi$
$977$	−41.0575	−1.31355	−0.656773	+	0.754089i	$0.728079\pi$
$978$	6.13092	0.196045
$979$	−9.29817	−0.297171
$980$	84.9606	2.71397
$981$	12.6712	0.404560
$982$	−40.1041	−1.27977
$983$	−0.291337	−0.00929220	−0.00464610	−	0.999989i	$-0.501479\pi$
$983$	−0.291337	−0.00929220	−0.00464610	+	0.999989i	$0.501479\pi$
$984$	61.2902	1.95386
$985$	52.9400	1.68681
$986$	−0.926616	−0.0295095
$987$	12.5550	0.399630
$988$	−64.4111	−2.04919
$989$	−52.7679	−1.67792
$990$	23.9051	0.759754
$991$	−35.8599	−1.13913	−0.569563	−	0.821948i	$-0.692888\pi$
$991$	−35.8599	−1.13913	−0.569563	+	0.821948i	$0.692888\pi$
$992$	−0.811428	−0.0257629
$993$	67.1416	2.13068
$994$	21.9072	0.694855
$995$	63.7069	2.01964
$996$	40.3127	1.27736
$997$	28.4075	0.899673	0.449837	−	0.893111i	$-0.351482\pi$
$997$	28.4075	0.899673	0.449837	+	0.893111i	$0.351482\pi$
$998$	−54.6020	−1.72840
$999$	0.625218	0.0197810

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.d.1.10	✓	133

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.d.1.10	✓	133	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:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.45235 q^{2} -2.50002 q^{3} +4.01402 q^{4} -3.16357 q^{5} +6.13092 q^{6} -0.556288 q^{7} -4.93908 q^{8} +3.25009 q^{9} +O(q^{10})\)	\(q-2.45235 q^{2} -2.50002 q^{3} +4.01402 q^{4} -3.16357 q^{5} +6.13092 q^{6} -0.556288 q^{7} -4.93908 q^{8} +3.25009 q^{9} +7.75817 q^{10} +0.948061 q^{11} -10.0351 q^{12} -4.46540 q^{13} +1.36421 q^{14} +7.90897 q^{15} +4.08431 q^{16} +0.621048 q^{17} -7.97035 q^{18} +3.59352 q^{19} -12.6986 q^{20} +1.39073 q^{21} -2.32498 q^{22} +4.39121 q^{23} +12.3478 q^{24} +5.00815 q^{25} +10.9507 q^{26} -0.625218 q^{27} -2.23295 q^{28} +0.608404 q^{29} -19.3956 q^{30} +5.87987 q^{31} -0.138001 q^{32} -2.37017 q^{33} -1.52303 q^{34} +1.75985 q^{35} +13.0459 q^{36} -1.00000 q^{37} -8.81257 q^{38} +11.1636 q^{39} +15.6251 q^{40} +4.96366 q^{41} -3.41055 q^{42} -12.0167 q^{43} +3.80554 q^{44} -10.2819 q^{45} -10.7688 q^{46} +9.02763 q^{47} -10.2108 q^{48} -6.69054 q^{49} -12.2817 q^{50} -1.55263 q^{51} -17.9242 q^{52} +0.333636 q^{53} +1.53325 q^{54} -2.99925 q^{55} +2.74755 q^{56} -8.98387 q^{57} -1.49202 q^{58} +4.14371 q^{59} +31.7467 q^{60} +3.73513 q^{61} -14.4195 q^{62} -1.80798 q^{63} -7.83020 q^{64} +14.1266 q^{65} +5.81248 q^{66} -0.200881 q^{67} +2.49290 q^{68} -10.9781 q^{69} -4.31577 q^{70} +16.0585 q^{71} -16.0524 q^{72} +6.90138 q^{73} +2.45235 q^{74} -12.5205 q^{75} +14.4245 q^{76} -0.527395 q^{77} -27.3770 q^{78} +16.1956 q^{79} -12.9210 q^{80} -8.18720 q^{81} -12.1726 q^{82} -4.01716 q^{83} +5.58241 q^{84} -1.96473 q^{85} +29.4692 q^{86} -1.52102 q^{87} -4.68255 q^{88} -9.80757 q^{89} +25.2147 q^{90} +2.48405 q^{91} +17.6264 q^{92} -14.6998 q^{93} -22.1389 q^{94} -11.3683 q^{95} +0.345005 q^{96} -9.24184 q^{97} +16.4076 q^{98} +3.08128 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9}+O(q^{10}) \) 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9} + 9 q^{10} + 23 q^{11} + 24 q^{12} + 23 q^{13} + 31 q^{14} + 9 q^{15} + 168 q^{16} + 98 q^{17} + 38 q^{18} + 29 q^{19} + 83 q^{20} + 26 q^{21} + 2 q^{22} + 34 q^{23} + 75 q^{24} + 177 q^{25} + 67 q^{26} + 32 q^{27} + 32 q^{28} + 91 q^{29} + 12 q^{30} + 24 q^{31} + 88 q^{32} + 27 q^{33} + 23 q^{34} + 66 q^{35} + 232 q^{36} - 133 q^{37} + 26 q^{38} + 28 q^{39} + 41 q^{40} + 132 q^{41} + 13 q^{42} + 11 q^{43} + 65 q^{44} + 107 q^{45} + 20 q^{46} + 10 q^{47} + 27 q^{48} + 229 q^{49} + 78 q^{50} + 19 q^{51} + 71 q^{52} + 7 q^{53} + 43 q^{54} + 41 q^{55} + 67 q^{56} + 45 q^{57} + 25 q^{58} + 97 q^{59} - 42 q^{60} + 65 q^{61} + 24 q^{62} + 39 q^{63} + 200 q^{64} + 60 q^{65} + 35 q^{66} + 25 q^{67} + 227 q^{68} + 120 q^{69} + 37 q^{70} + 26 q^{71} + 93 q^{72} + 55 q^{73} - 14 q^{74} + 5 q^{75} + 34 q^{76} + 21 q^{77} - 2 q^{78} + 50 q^{79} + 162 q^{80} + 341 q^{81} + 66 q^{82} + 30 q^{83} - 89 q^{84} + 30 q^{85} - 12 q^{86} + 80 q^{87} - 85 q^{88} + 225 q^{89} - 86 q^{90} + q^{91} + 82 q^{92} + 42 q^{93} - 17 q^{94} + 70 q^{95} + 55 q^{96} + 12 q^{97} + 90 q^{98} + 17 q^{99}+O(q^{100}) \) 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9 + 9 * q^10 + 23 * q^11 + 24 * q^12 + 23 * q^13 + 31 * q^14 + 9 * q^15 + 168 * q^16 + 98 * q^17 + 38 * q^18 + 29 * q^19 + 83 * q^20 + 26 * q^21 + 2 * q^22 + 34 * q^23 + 75 * q^24 + 177 * q^25 + 67 * q^26 + 32 * q^27 + 32 * q^28 + 91 * q^29 + 12 * q^30 + 24 * q^31 + 88 * q^32 + 27 * q^33 + 23 * q^34 + 66 * q^35 + 232 * q^36 - 133 * q^37 + 26 * q^38 + 28 * q^39 + 41 * q^40 + 132 * q^41 + 13 * q^42 + 11 * q^43 + 65 * q^44 + 107 * q^45 + 20 * q^46 + 10 * q^47 + 27 * q^48 + 229 * q^49 + 78 * q^50 + 19 * q^51 + 71 * q^52 + 7 * q^53 + 43 * q^54 + 41 * q^55 + 67 * q^56 + 45 * q^57 + 25 * q^58 + 97 * q^59 - 42 * q^60 + 65 * q^61 + 24 * q^62 + 39 * q^63 + 200 * q^64 + 60 * q^65 + 35 * q^66 + 25 * q^67 + 227 * q^68 + 120 * q^69 + 37 * q^70 + 26 * q^71 + 93 * q^72 + 55 * q^73 - 14 * q^74 + 5 * q^75 + 34 * q^76 + 21 * q^77 - 2 * q^78 + 50 * q^79 + 162 * q^80 + 341 * q^81 + 66 * q^82 + 30 * q^83 - 89 * q^84 + 30 * q^85 - 12 * q^86 + 80 * q^87 - 85 * q^88 + 225 * q^89 - 86 * q^90 + q^91 + 82 * q^92 + 42 * q^93 - 17 * q^94 + 70 * q^95 + 55 * q^96 + 12 * q^97 + 90 * q^98 + 17 * q^99

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