LMFDB - Embedded newform 6001.2.a.d.1.5

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			1.5
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)

$f(q)$	$=$	$q-2.63308 q^{2} +2.70578 q^{3} +4.93313 q^{4} +2.79051 q^{5} -7.12456 q^{6} -5.09743 q^{7} -7.72317 q^{8} +4.32127 q^{9} +O(q^{10})$	\(q-2.63308 q^{2} +2.70578 q^{3} +4.93313 q^{4} +2.79051 q^{5} -7.12456 q^{6} -5.09743 q^{7} -7.72317 q^{8} +4.32127 q^{9} -7.34766 q^{10} -0.629200 q^{11} +13.3480 q^{12} -1.20129 q^{13} +13.4220 q^{14} +7.55053 q^{15} +10.4695 q^{16} +1.00000 q^{17} -11.3783 q^{18} -4.74739 q^{19} +13.7660 q^{20} -13.7925 q^{21} +1.65674 q^{22} -1.58864 q^{23} -20.8972 q^{24} +2.78697 q^{25} +3.16309 q^{26} +3.57506 q^{27} -25.1463 q^{28} -6.31747 q^{29} -19.8812 q^{30} +9.25295 q^{31} -12.1207 q^{32} -1.70248 q^{33} -2.63308 q^{34} -14.2245 q^{35} +21.3174 q^{36} +3.59230 q^{37} +12.5003 q^{38} -3.25043 q^{39} -21.5516 q^{40} +5.58238 q^{41} +36.3169 q^{42} +8.15637 q^{43} -3.10393 q^{44} +12.0586 q^{45} +4.18303 q^{46} +2.64958 q^{47} +28.3282 q^{48} +18.9838 q^{49} -7.33832 q^{50} +2.70578 q^{51} -5.92611 q^{52} -10.7493 q^{53} -9.41344 q^{54} -1.75579 q^{55} +39.3683 q^{56} -12.8454 q^{57} +16.6344 q^{58} +5.28430 q^{59} +37.2477 q^{60} +9.37335 q^{61} -24.3638 q^{62} -22.0274 q^{63} +10.9759 q^{64} -3.35221 q^{65} +4.48277 q^{66} -0.944014 q^{67} +4.93313 q^{68} -4.29852 q^{69} +37.4542 q^{70} +13.8769 q^{71} -33.3739 q^{72} -5.11346 q^{73} -9.45884 q^{74} +7.54094 q^{75} -23.4195 q^{76} +3.20730 q^{77} +8.55865 q^{78} +12.7727 q^{79} +29.2153 q^{80} -3.29045 q^{81} -14.6989 q^{82} +14.5151 q^{83} -68.0404 q^{84} +2.79051 q^{85} -21.4764 q^{86} -17.0937 q^{87} +4.85942 q^{88} +10.3474 q^{89} -31.7512 q^{90} +6.12349 q^{91} -7.83698 q^{92} +25.0365 q^{93} -6.97657 q^{94} -13.2477 q^{95} -32.7961 q^{96} -6.69361 q^{97} -49.9859 q^{98} -2.71894 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) $ 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9} + 19 q^{10} + 48 q^{11} + 43 q^{12} + 6 q^{13} + 40 q^{14} + 49 q^{15} + 135 q^{16} + 121 q^{17} + 30 q^{19} + 50 q^{20} + 18 q^{21} + 24 q^{22} + 75 q^{23} + 24 q^{24} + 128 q^{25} + 59 q^{26} + 75 q^{27} + 52 q^{28} + 49 q^{29} - 34 q^{30} + 101 q^{31} + 47 q^{32} + 20 q^{33} + 9 q^{34} + 47 q^{35} + 138 q^{36} + 32 q^{37} + 30 q^{38} + 101 q^{39} + 36 q^{40} + 83 q^{41} - 11 q^{42} + 8 q^{43} + 98 q^{44} + 49 q^{45} + 45 q^{46} + 135 q^{47} + 54 q^{48} + 116 q^{49} + 3 q^{50} + 21 q^{51} - 5 q^{52} + 28 q^{53} + 10 q^{54} + 37 q^{55} + 75 q^{56} + 31 q^{58} + 150 q^{59} + 50 q^{60} + 36 q^{61} + 34 q^{62} + 118 q^{63} + 110 q^{64} + 18 q^{65} - 28 q^{66} - 6 q^{67} + 127 q^{68} + 25 q^{69} - 22 q^{70} + 223 q^{71} + q^{72} + 38 q^{73} - 10 q^{74} + 88 q^{75} - 4 q^{76} + 38 q^{77} + 42 q^{78} + 74 q^{79} + 106 q^{80} + 133 q^{81} + 28 q^{82} + 55 q^{83} + 10 q^{84} + 27 q^{85} + 64 q^{86} + 14 q^{87} + 56 q^{88} + 118 q^{89} + 51 q^{90} + 73 q^{91} + 82 q^{92} + 31 q^{93} + 33 q^{94} + 106 q^{95} + 38 q^{96} + 37 q^{97} + 88 q^{98} + 81 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9 + 19 * q^10 + 48 * q^11 + 43 * q^12 + 6 * q^13 + 40 * q^14 + 49 * q^15 + 135 * q^16 + 121 * q^17 + 30 * q^19 + 50 * q^20 + 18 * q^21 + 24 * q^22 + 75 * q^23 + 24 * q^24 + 128 * q^25 + 59 * q^26 + 75 * q^27 + 52 * q^28 + 49 * q^29 - 34 * q^30 + 101 * q^31 + 47 * q^32 + 20 * q^33 + 9 * q^34 + 47 * q^35 + 138 * q^36 + 32 * q^37 + 30 * q^38 + 101 * q^39 + 36 * q^40 + 83 * q^41 - 11 * q^42 + 8 * q^43 + 98 * q^44 + 49 * q^45 + 45 * q^46 + 135 * q^47 + 54 * q^48 + 116 * q^49 + 3 * q^50 + 21 * q^51 - 5 * q^52 + 28 * q^53 + 10 * q^54 + 37 * q^55 + 75 * q^56 + 31 * q^58 + 150 * q^59 + 50 * q^60 + 36 * q^61 + 34 * q^62 + 118 * q^63 + 110 * q^64 + 18 * q^65 - 28 * q^66 - 6 * q^67 + 127 * q^68 + 25 * q^69 - 22 * q^70 + 223 * q^71 + q^72 + 38 * q^73 - 10 * q^74 + 88 * q^75 - 4 * q^76 + 38 * q^77 + 42 * q^78 + 74 * q^79 + 106 * q^80 + 133 * q^81 + 28 * q^82 + 55 * q^83 + 10 * q^84 + 27 * q^85 + 64 * q^86 + 14 * q^87 + 56 * q^88 + 118 * q^89 + 51 * q^90 + 73 * q^91 + 82 * q^92 + 31 * q^93 + 33 * q^94 + 106 * q^95 + 38 * q^96 + 37 * q^97 + 88 * q^98 + 81 * 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 $

$2$	−2.63308	−1.86187	−0.930936	−	0.365183i	$-0.881006\pi$
$2$	−2.63308	−1.86187	−0.930936	+	0.365183i	$0.881006\pi$
$3$	2.70578	1.56219	0.781093	−	0.624415i	$-0.214663\pi$
$3$	2.70578	1.56219	0.781093	+	0.624415i	$0.214663\pi$
$4$	4.93313	2.46656
$5$	2.79051	1.24796	0.623978	−	0.781442i	$-0.285516\pi$
$5$	2.79051	1.24796	0.623978	+	0.781442i	$0.285516\pi$
$6$	−7.12456	−2.90859
$7$	−5.09743	−1.92665	−0.963324	−	0.268342i	$-0.913524\pi$
$7$	−5.09743	−1.92665	−0.963324	+	0.268342i	$0.913524\pi$
$8$	−7.72317	−2.73055
$9$	4.32127	1.44042
$10$	−7.34766	−2.32353
$11$	−0.629200	−0.189711	−0.0948555	−	0.995491i	$-0.530239\pi$
$11$	−0.629200	−0.189711	−0.0948555	+	0.995491i	$0.530239\pi$
$12$	13.3480	3.85323
$13$	−1.20129	−0.333178	−0.166589	−	0.986026i	$-0.553275\pi$
$13$	−1.20129	−0.333178	−0.166589	+	0.986026i	$0.553275\pi$
$14$	13.4220	3.58717
$15$	7.55053	1.94954
$16$	10.4695	2.61738
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−11.3783	−2.68188
$19$	−4.74739	−1.08913	−0.544563	−	0.838720i	$-0.683305\pi$
$19$	−4.74739	−1.08913	−0.544563	+	0.838720i	$0.683305\pi$
$20$	13.7660	3.07816
$21$	−13.7925	−3.00978
$22$	1.65674	0.353217
$23$	−1.58864	−0.331255	−0.165627	−	0.986188i	$-0.552965\pi$
$23$	−1.58864	−0.331255	−0.165627	+	0.986188i	$0.552965\pi$
$24$	−20.8972	−4.26563
$25$	2.78697	0.557394
$26$	3.16309	0.620334
$27$	3.57506	0.688022
$28$	−25.1463	−4.75220
$29$	−6.31747	−1.17312	−0.586562	−	0.809904i	$-0.699519\pi$
$29$	−6.31747	−1.17312	−0.586562	+	0.809904i	$0.699519\pi$
$30$	−19.8812	−3.62979
$31$	9.25295	1.66188	0.830939	−	0.556363i	$-0.187804\pi$
$31$	9.25295	1.66188	0.830939	+	0.556363i	$0.187804\pi$
$32$	−12.1207	−2.14266
$33$	−1.70248	−0.296364
$34$	−2.63308	−0.451570
$35$	−14.2245	−2.40437
$36$	21.3174	3.55290
$37$	3.59230	0.590571	0.295286	−	0.955409i	$-0.404585\pi$
$37$	3.59230	0.590571	0.295286	+	0.955409i	$0.404585\pi$
$38$	12.5003	2.02781
$39$	−3.25043	−0.520485
$40$	−21.5516	−3.40761
$41$	5.58238	0.871822	0.435911	−	0.899990i	$-0.356426\pi$
$41$	5.58238	0.871822	0.435911	+	0.899990i	$0.356426\pi$
$42$	36.3169	5.60382
$43$	8.15637	1.24384	0.621918	−	0.783083i	$-0.286354\pi$
$43$	8.15637	1.24384	0.621918	+	0.783083i	$0.286354\pi$
$44$	−3.10393	−0.467934
$45$	12.0586	1.79758
$46$	4.18303	0.616754
$47$	2.64958	0.386481	0.193241	−	0.981151i	$-0.438100\pi$
$47$	2.64958	0.386481	0.193241	+	0.981151i	$0.438100\pi$
$48$	28.3282	4.08883
$49$	18.9838	2.71197
$50$	−7.33832	−1.03780
$51$	2.70578	0.378886
$52$	−5.92611	−0.821804
$53$	−10.7493	−1.47653	−0.738267	−	0.674508i	$-0.764356\pi$
$53$	−10.7493	−1.47653	−0.738267	+	0.674508i	$0.764356\pi$
$54$	−9.41344	−1.28101
$55$	−1.75579	−0.236751
$56$	39.3683	5.26082
$57$	−12.8454	−1.70142
$58$	16.6344	2.18421
$59$	5.28430	0.687958	0.343979	−	0.938977i	$-0.388225\pi$
$59$	5.28430	0.687958	0.343979	+	0.938977i	$0.388225\pi$
$60$	37.2477	4.80866
$61$	9.37335	1.20013	0.600067	−	0.799950i	$-0.295141\pi$
$61$	9.37335	1.20013	0.600067	+	0.799950i	$0.295141\pi$
$62$	−24.3638	−3.09420
$63$	−22.0274	−2.77519
$64$	10.9759	1.37199
$65$	−3.35221	−0.415791
$66$	4.48277	0.551791
$67$	−0.944014	−0.115330	−0.0576648	−	0.998336i	$-0.518365\pi$
$67$	−0.944014	−0.115330	−0.0576648	+	0.998336i	$0.518365\pi$
$68$	4.93313	0.598230
$69$	−4.29852	−0.517481
$70$	37.4542	4.47663
$71$	13.8769	1.64688	0.823440	−	0.567403i	$-0.192052\pi$
$71$	13.8769	1.64688	0.823440	+	0.567403i	$0.192052\pi$
$72$	−33.3739	−3.93315
$73$	−5.11346	−0.598485	−0.299242	−	0.954177i	$-0.596734\pi$
$73$	−5.11346	−0.598485	−0.299242	+	0.954177i	$0.596734\pi$
$74$	−9.45884	−1.09957
$75$	7.54094	0.870752
$76$	−23.4195	−2.68640
$77$	3.20730	0.365506
$78$	8.55865	0.969076
$79$	12.7727	1.43704	0.718518	−	0.695508i	$-0.244821\pi$
$79$	12.7727	1.43704	0.718518	+	0.695508i	$0.244821\pi$
$80$	29.2153	3.26637
$81$	−3.29045	−0.365605
$82$	−14.6989	−1.62322
$83$	14.5151	1.59324	0.796620	−	0.604480i	$-0.206619\pi$
$83$	14.5151	1.59324	0.796620	+	0.604480i	$0.206619\pi$
$84$	−68.0404	−7.42382
$85$	2.79051	0.302674
$86$	−21.4764	−2.31586
$87$	−17.0937	−1.83264
$88$	4.85942	0.518016
$89$	10.3474	1.09682	0.548411	−	0.836209i	$-0.315233\pi$
$89$	10.3474	1.09682	0.548411	+	0.836209i	$0.315233\pi$
$90$	−31.7512	−3.34687
$91$	6.12349	0.641916
$92$	−7.83698	−0.817062
$93$	25.0365	2.59616
$94$	−6.97657	−0.719578
$95$	−13.2477	−1.35918
$96$	−32.7961	−3.34724
$97$	−6.69361	−0.679633	−0.339816	−	0.940492i	$-0.610365\pi$
$97$	−6.69361	−0.679633	−0.339816	+	0.940492i	$0.610365\pi$
$98$	−49.9859	−5.04934
$99$	−2.71894	−0.273264
$100$	13.7485	1.37485
$101$	2.61584	0.260286	0.130143	−	0.991495i	$-0.458456\pi$
$101$	2.61584	0.260286	0.130143	+	0.991495i	$0.458456\pi$
$102$	−7.12456	−0.705436
$103$	−12.3409	−1.21598	−0.607992	−	0.793943i	$-0.708025\pi$
$103$	−12.3409	−1.21598	−0.607992	+	0.793943i	$0.708025\pi$
$104$	9.27776	0.909759
$105$	−38.4883	−3.75607
$106$	28.3039	2.74912
$107$	1.23460	0.119354	0.0596768	−	0.998218i	$-0.480993\pi$
$107$	1.23460	0.119354	0.0596768	+	0.998218i	$0.480993\pi$
$108$	17.6363	1.69705
$109$	16.5492	1.58513	0.792563	−	0.609791i	$-0.208746\pi$
$109$	16.5492	1.58513	0.792563	+	0.609791i	$0.208746\pi$
$110$	4.62315	0.440800
$111$	9.72000	0.922581
$112$	−53.3676	−5.04276
$113$	−14.9594	−1.40726	−0.703632	−	0.710565i	$-0.748440\pi$
$113$	−14.9594	−1.40726	−0.703632	+	0.710565i	$0.748440\pi$
$114$	33.8231	3.16782
$115$	−4.43313	−0.413391
$116$	−31.1649	−2.89359
$117$	−5.19109	−0.479916
$118$	−13.9140	−1.28089
$119$	−5.09743	−0.467281
$120$	−58.3140	−5.32332
$121$	−10.6041	−0.964010
$122$	−24.6808	−2.23450
$123$	15.1047	1.36195
$124$	45.6460	4.09913
$125$	−6.17549	−0.552353
$126$	57.9999	5.16704
$127$	−7.77864	−0.690242	−0.345121	−	0.938558i	$-0.612162\pi$
$127$	−7.77864	−0.690242	−0.345121	+	0.938558i	$0.612162\pi$
$128$	−4.65898	−0.411799
$129$	22.0694	1.94310
$130$	8.82666	0.774149
$131$	−7.38141	−0.644917	−0.322458	−	0.946584i	$-0.604509\pi$
$131$	−7.38141	−0.644917	−0.322458	+	0.946584i	$0.604509\pi$
$132$	−8.39855	−0.731000
$133$	24.1995	2.09836
$134$	2.48567	0.214729
$135$	9.97627	0.858621
$136$	−7.72317	−0.662257
$137$	7.11938	0.608250	0.304125	−	0.952632i	$-0.401636\pi$
$137$	7.11938	0.608250	0.304125	+	0.952632i	$0.401636\pi$
$138$	11.3184	0.963484
$139$	4.08365	0.346370	0.173185	−	0.984889i	$-0.444594\pi$
$139$	4.08365	0.346370	0.173185	+	0.984889i	$0.444594\pi$
$140$	−70.1711	−5.93054
$141$	7.16919	0.603755
$142$	−36.5389	−3.06628
$143$	0.755851	0.0632074
$144$	45.2415	3.77013
$145$	−17.6290	−1.46401
$146$	13.4642	1.11430
$147$	51.3661	4.23660
$148$	17.7213	1.45668
$149$	15.6416	1.28141	0.640706	−	0.767786i	$-0.278642\pi$
$149$	15.6416	1.28141	0.640706	+	0.767786i	$0.278642\pi$
$150$	−19.8559	−1.62123
$151$	13.5726	1.10452	0.552261	−	0.833671i	$-0.313765\pi$
$151$	13.5726	1.10452	0.552261	+	0.833671i	$0.313765\pi$
$152$	36.6650	2.97392
$153$	4.32127	0.349354
$154$	−8.44510	−0.680525
$155$	25.8205	2.07395
$156$	−16.0348	−1.28381
$157$	17.4093	1.38941	0.694706	−	0.719293i	$-0.255534\pi$
$157$	17.4093	1.38941	0.694706	+	0.719293i	$0.255534\pi$
$158$	−33.6315	−2.67558
$159$	−29.0854	−2.30662
$160$	−33.8231	−2.67395
$161$	8.09800	0.638211
$162$	8.66403	0.680710
$163$	20.6814	1.61989	0.809944	−	0.586507i	$-0.199497\pi$
$163$	20.6814	1.61989	0.809944	+	0.586507i	$0.199497\pi$
$164$	27.5386	2.15040
$165$	−4.75079	−0.369849
$166$	−38.2195	−2.96641
$167$	18.1352	1.40335	0.701673	−	0.712500i	$-0.252437\pi$
$167$	18.1352	1.40335	0.701673	+	0.712500i	$0.252437\pi$
$168$	106.522	8.21837
$169$	−11.5569	−0.888993
$170$	−7.34766	−0.563540
$171$	−20.5148	−1.56880
$172$	40.2364	3.06800
$173$	17.3581	1.31971	0.659855	−	0.751393i	$-0.270618\pi$
$173$	17.3581	1.31971	0.659855	+	0.751393i	$0.270618\pi$
$174$	45.0092	3.41214
$175$	−14.2064	−1.07390
$176$	−6.58741	−0.496545
$177$	14.2982	1.07472
$178$	−27.2455	−2.04214
$179$	4.46749	0.333916	0.166958	−	0.985964i	$-0.446606\pi$
$179$	4.46749	0.333916	0.166958	+	0.985964i	$0.446606\pi$
$180$	59.4864	4.43386
$181$	−12.2531	−0.910766	−0.455383	−	0.890296i	$-0.650498\pi$
$181$	−12.2531	−0.910766	−0.455383	+	0.890296i	$0.650498\pi$
$182$	−16.1236	−1.19516
$183$	25.3623	1.87483
$184$	12.2694	0.904510
$185$	10.0244	0.737007
$186$	−65.9231	−4.83372
$187$	−0.629200	−0.0460117
$188$	13.0707	0.953280
$189$	−18.2236	−1.32558
$190$	34.8822	2.53062
$191$	−7.99654	−0.578609	−0.289305	−	0.957237i	$-0.593424\pi$
$191$	−7.99654	−0.578609	−0.289305	+	0.957237i	$0.593424\pi$
$192$	29.6984	2.14330
$193$	14.7125	1.05903	0.529516	−	0.848300i	$-0.322374\pi$
$193$	14.7125	1.05903	0.529516	+	0.848300i	$0.322374\pi$
$194$	17.6248	1.26539
$195$	−9.07036	−0.649542
$196$	93.6495	6.68925
$197$	−18.2213	−1.29822	−0.649108	−	0.760696i	$-0.724858\pi$
$197$	−18.2213	−1.29822	−0.649108	+	0.760696i	$0.724858\pi$
$198$	7.15920	0.508782
$199$	18.2708	1.29518	0.647590	−	0.761989i	$-0.275777\pi$
$199$	18.2708	1.29518	0.647590	+	0.761989i	$0.275777\pi$
$200$	−21.5242	−1.52199
$201$	−2.55430	−0.180166
$202$	−6.88773	−0.484619
$203$	32.2029	2.26020
$204$	13.3480	0.934546
$205$	15.5777	1.08800
$206$	32.4946	2.26400
$207$	−6.86495	−0.477147
$208$	−12.5769	−0.872051
$209$	2.98706	0.206619
$210$	101.343	6.99332
$211$	−17.2474	−1.18736	−0.593681	−	0.804700i	$-0.702326\pi$
$211$	−17.2474	−1.18736	−0.593681	+	0.804700i	$0.702326\pi$
$212$	−53.0279	−3.64197
$213$	37.5478	2.57273
$214$	−3.25081	−0.222221
$215$	22.7605	1.55225
$216$	−27.6108	−1.87868
$217$	−47.1662	−3.20185
$218$	−43.5754	−2.95130
$219$	−13.8359	−0.934944
$220$	−8.66155	−0.583961
$221$	−1.20129	−0.0808074
$222$	−25.5936	−1.71773
$223$	1.93787	0.129769	0.0648847	−	0.997893i	$-0.479332\pi$
$223$	1.93787	0.129769	0.0648847	+	0.997893i	$0.479332\pi$
$224$	61.7846	4.12816
$225$	12.0432	0.802883
$226$	39.3894	2.62014
$227$	21.0477	1.39698	0.698492	−	0.715618i	$-0.253855\pi$
$227$	21.0477	1.39698	0.698492	+	0.715618i	$0.253855\pi$
$228$	−63.3681	−4.19666
$229$	−1.28845	−0.0851431	−0.0425715	−	0.999093i	$-0.513555\pi$
$229$	−1.28845	−0.0851431	−0.0425715	+	0.999093i	$0.513555\pi$
$230$	11.6728	0.769682
$231$	8.67827	0.570988
$232$	48.7909	3.20328
$233$	−7.00149	−0.458683	−0.229341	−	0.973346i	$-0.573657\pi$
$233$	−7.00149	−0.458683	−0.229341	+	0.973346i	$0.573657\pi$
$234$	13.6686	0.893543
$235$	7.39369	0.482311
$236$	26.0681	1.69689
$237$	34.5601	2.24492
$238$	13.4220	0.870016
$239$	−10.0232	−0.648344	−0.324172	−	0.945998i	$-0.605086\pi$
$239$	−10.0232	−0.648344	−0.324172	+	0.945998i	$0.605086\pi$
$240$	79.0503	5.10267
$241$	−23.6446	−1.52308	−0.761541	−	0.648117i	$-0.775557\pi$
$241$	−23.6446	−1.52308	−0.761541	+	0.648117i	$0.775557\pi$
$242$	27.9215	1.79486
$243$	−19.6284	−1.25916
$244$	46.2399	2.96021
$245$	52.9746	3.38442
$246$	−39.7720	−2.53577
$247$	5.70299	0.362873
$248$	−71.4621	−4.53785
$249$	39.2748	2.48894
$250$	16.2606	1.02841
$251$	11.9889	0.756733	0.378366	−	0.925656i	$-0.376486\pi$
$251$	11.9889	0.756733	0.378366	+	0.925656i	$0.376486\pi$
$252$	−108.664	−6.84518
$253$	0.999574	0.0628427
$254$	20.4818	1.28514
$255$	7.55053	0.472832
$256$	−9.68431	−0.605269
$257$	28.2659	1.76318	0.881589	−	0.472017i	$-0.156474\pi$
$257$	28.2659	1.76318	0.881589	+	0.472017i	$0.156474\pi$
$258$	−58.1105	−3.61780
$259$	−18.3115	−1.13782
$260$	−16.5369	−1.02557
$261$	−27.2995	−1.68980
$262$	19.4359	1.20075
$263$	−7.93940	−0.489565	−0.244782	−	0.969578i	$-0.578716\pi$
$263$	−7.93940	−0.489565	−0.244782	+	0.969578i	$0.578716\pi$
$264$	13.1485	0.809237
$265$	−29.9962	−1.84265
$266$	−63.7193	−3.90688
$267$	27.9978	1.71344
$268$	−4.65694	−0.284468
$269$	23.2796	1.41938	0.709690	−	0.704514i	$-0.248835\pi$
$269$	23.2796	1.41938	0.709690	+	0.704514i	$0.248835\pi$
$270$	−26.2684	−1.59864
$271$	−6.93319	−0.421162	−0.210581	−	0.977576i	$-0.567536\pi$
$271$	−6.93319	−0.421162	−0.210581	+	0.977576i	$0.567536\pi$
$272$	10.4695	0.634807
$273$	16.5688	1.00279
$274$	−18.7459	−1.13248
$275$	−1.75356	−0.105744
$276$	−21.2052	−1.27640
$277$	4.55603	0.273745	0.136873	−	0.990589i	$-0.456295\pi$
$277$	4.55603	0.273745	0.136873	+	0.990589i	$0.456295\pi$
$278$	−10.7526	−0.644897
$279$	39.9845	2.39381
$280$	109.858	6.56527
$281$	−12.9068	−0.769956	−0.384978	−	0.922926i	$-0.625791\pi$
$281$	−12.9068	−0.769956	−0.384978	+	0.922926i	$0.625791\pi$
$282$	−18.8771	−1.12411
$283$	12.4555	0.740404	0.370202	−	0.928951i	$-0.379288\pi$
$283$	12.4555	0.740404	0.370202	+	0.928951i	$0.379288\pi$
$284$	68.4564	4.06214
$285$	−35.8453	−2.12329
$286$	−1.99022	−0.117684
$287$	−28.4558	−1.67969
$288$	−52.3769	−3.08634
$289$	1.00000	0.0588235
$290$	46.4186	2.72579
$291$	−18.1115	−1.06171
$292$	−25.2253	−1.47620
$293$	−14.0921	−0.823267	−0.411633	−	0.911350i	$-0.635042\pi$
$293$	−14.0921	−0.823267	−0.411633	+	0.911350i	$0.635042\pi$
$294$	−135.251	−7.88801
$295$	14.7459	0.858541
$296$	−27.7440	−1.61259
$297$	−2.24943	−0.130525
$298$	−41.1857	−2.38582
$299$	1.90842	0.110367
$300$	37.2004	2.14777
$301$	−41.5765	−2.39643
$302$	−35.7378	−2.05648
$303$	7.07791	0.406615
$304$	−49.7029	−2.85065
$305$	26.1565	1.49771
$306$	−11.3783	−0.650452
$307$	−8.67457	−0.495084	−0.247542	−	0.968877i	$-0.579623\pi$
$307$	−8.67457	−0.495084	−0.247542	+	0.968877i	$0.579623\pi$
$308$	15.8220	0.901545
$309$	−33.3918	−1.89959
$310$	−67.9875	−3.86143
$311$	−6.16714	−0.349707	−0.174853	−	0.984594i	$-0.555945\pi$
$311$	−6.16714	−0.349707	−0.174853	+	0.984594i	$0.555945\pi$
$312$	25.1036	1.42121
$313$	3.33188	0.188329	0.0941645	−	0.995557i	$-0.469982\pi$
$313$	3.33188	0.188329	0.0941645	+	0.995557i	$0.469982\pi$
$314$	−45.8401	−2.58691
$315$	−61.4677	−3.46331
$316$	63.0092	3.54454
$317$	19.2978	1.08387	0.541936	−	0.840420i	$-0.317692\pi$
$317$	19.2978	1.08387	0.541936	+	0.840420i	$0.317692\pi$
$318$	76.5842	4.29463
$319$	3.97495	0.222555
$320$	30.6284	1.71218
$321$	3.34057	0.186452
$322$	−21.3227	−1.18827
$323$	−4.74739	−0.264152
$324$	−16.2322	−0.901789
$325$	−3.34795	−0.185711
$326$	−54.4557	−3.01602
$327$	44.7785	2.47626
$328$	−43.1137	−2.38056
$329$	−13.5061	−0.744613
$330$	12.5092	0.688611
$331$	−17.0096	−0.934930	−0.467465	−	0.884012i	$-0.654833\pi$
$331$	−17.0096	−0.934930	−0.467465	+	0.884012i	$0.654833\pi$
$332$	71.6049	3.92983
$333$	15.5233	0.850672
$334$	−47.7515	−2.61285
$335$	−2.63428	−0.143926
$336$	−144.401	−7.87773
$337$	−11.5670	−0.630093	−0.315046	−	0.949076i	$-0.602020\pi$
$337$	−11.5670	−0.630093	−0.315046	+	0.949076i	$0.602020\pi$
$338$	30.4303	1.65519
$339$	−40.4770	−2.19841
$340$	13.7660	0.746564
$341$	−5.82195	−0.315277
$342$	54.0171	2.92091
$343$	−61.0866	−3.29836
$344$	−62.9931	−3.39636
$345$	−11.9951	−0.645794
$346$	−45.7053	−2.45713
$347$	−6.69435	−0.359372	−0.179686	−	0.983724i	$-0.557508\pi$
$347$	−6.69435	−0.359372	−0.179686	+	0.983724i	$0.557508\pi$
$348$	−84.3255	−4.52032
$349$	29.5670	1.58268	0.791341	−	0.611374i	$-0.209383\pi$
$349$	29.5670	1.58268	0.791341	+	0.611374i	$0.209383\pi$
$350$	37.4066	1.99947
$351$	−4.29469	−0.229233
$352$	7.62637	0.406487
$353$	−1.00000	−0.0532246
$353$	−1.00000	−0.0532246
$354$	−37.6483	−2.00098
$355$	38.7236	2.05523
$356$	51.0450	2.70538
$357$	−13.7925	−0.729979
$358$	−11.7633	−0.621709
$359$	20.6343	1.08904	0.544518	−	0.838749i	$-0.316713\pi$
$359$	20.6343	1.08904	0.544518	+	0.838749i	$0.316713\pi$
$360$	−93.1303	−4.90840
$361$	3.53775	0.186197
$362$	32.2635	1.69573
$363$	−28.6924	−1.50596
$364$	30.2079	1.58333
$365$	−14.2692	−0.746883
$366$	−66.7809	−3.49070
$367$	−21.1046	−1.10165	−0.550825	−	0.834621i	$-0.685687\pi$
$367$	−21.1046	−1.10165	−0.550825	+	0.834621i	$0.685687\pi$
$368$	−16.6323	−0.867019
$369$	24.1230	1.25579
$370$	−26.3950	−1.37221
$371$	54.7940	2.84476
$372$	123.508	6.40360
$373$	3.49642	0.181038	0.0905189	−	0.995895i	$-0.471147\pi$
$373$	3.49642	0.181038	0.0905189	+	0.995895i	$0.471147\pi$
$374$	1.65674	0.0856678
$375$	−16.7096	−0.862878
$376$	−20.4632	−1.05531
$377$	7.58911	0.390859
$378$	47.9844	2.46805
$379$	−19.8239	−1.01828	−0.509142	−	0.860683i	$-0.670037\pi$
$379$	−19.8239	−1.01828	−0.509142	+	0.860683i	$0.670037\pi$
$380$	−65.3525	−3.35251
$381$	−21.0473	−1.07829
$382$	21.0556	1.07730
$383$	−2.69266	−0.137589	−0.0687943	−	0.997631i	$-0.521915\pi$
$383$	−2.69266	−0.137589	−0.0687943	+	0.997631i	$0.521915\pi$
$384$	−12.6062	−0.643307
$385$	8.95003	0.456136
$386$	−38.7394	−1.97178
$387$	35.2459	1.79165
$388$	−33.0204	−1.67636
$389$	14.2518	0.722594	0.361297	−	0.932451i	$-0.382334\pi$
$389$	14.2518	0.722594	0.361297	+	0.932451i	$0.382334\pi$
$390$	23.8830	1.20936
$391$	−1.58864	−0.0803411
$392$	−146.615	−7.40518
$393$	−19.9725	−1.00748
$394$	47.9783	2.41711
$395$	35.6423	1.79336
$396$	−13.4129	−0.674023
$397$	−15.7945	−0.792703	−0.396351	−	0.918099i	$-0.629724\pi$
$397$	−15.7945	−0.792703	−0.396351	+	0.918099i	$0.629724\pi$
$398$	−48.1085	−2.41146
$399$	65.4787	3.27803
$400$	29.1782	1.45891
$401$	−0.423162	−0.0211317	−0.0105658	−	0.999944i	$-0.503363\pi$
$401$	−0.423162	−0.0211317	−0.0105658	+	0.999944i	$0.503363\pi$
$402$	6.72568	0.335446
$403$	−11.1155	−0.553700
$404$	12.9043	0.642012
$405$	−9.18204	−0.456259
$406$	−84.7928	−4.20820
$407$	−2.26028	−0.112038
$408$	−20.8972	−1.03457
$409$	−18.8010	−0.929648	−0.464824	−	0.885403i	$-0.653882\pi$
$409$	−18.8010	−0.929648	−0.464824	+	0.885403i	$0.653882\pi$
$410$	−41.0174	−2.02571
$411$	19.2635	0.950199
$412$	−60.8792	−2.99930
$413$	−26.9364	−1.32545
$414$	18.0760	0.888386
$415$	40.5046	1.98829
$416$	14.5605	0.713887
$417$	11.0495	0.541095
$418$	−7.86518	−0.384699
$419$	−3.04013	−0.148520	−0.0742599	−	0.997239i	$-0.523659\pi$
$419$	−3.04013	−0.148520	−0.0742599	+	0.997239i	$0.523659\pi$
$420$	−189.868	−9.26460
$421$	19.1728	0.934423	0.467211	−	0.884146i	$-0.345259\pi$
$421$	19.1728	0.934423	0.467211	+	0.884146i	$0.345259\pi$
$422$	45.4139	2.21072
$423$	11.4495	0.556696
$424$	83.0190	4.03176
$425$	2.78697	0.135188
$426$	−98.8665	−4.79010
$427$	−47.7800	−2.31224
$428$	6.09046	0.294393
$429$	2.04517	0.0987417
$430$	−59.9302	−2.89009
$431$	11.9769	0.576906	0.288453	−	0.957494i	$-0.406859\pi$
$431$	11.9769	0.576906	0.288453	+	0.957494i	$0.406859\pi$
$432$	37.4292	1.80081
$433$	14.5934	0.701313	0.350657	−	0.936504i	$-0.385958\pi$
$433$	14.5934	0.701313	0.350657	+	0.936504i	$0.385958\pi$
$434$	124.193	5.96144
$435$	−47.7002	−2.28705
$436$	81.6393	3.90981
$437$	7.54191	0.360779
$438$	36.4311	1.74075
$439$	7.81298	0.372893	0.186447	−	0.982465i	$-0.440303\pi$
$439$	7.81298	0.372893	0.186447	+	0.982465i	$0.440303\pi$
$440$	13.5603	0.646461
$441$	82.0341	3.90638
$442$	3.16309	0.150453
$443$	21.1567	1.00518	0.502591	−	0.864524i	$-0.332380\pi$
$443$	21.1567	1.00518	0.502591	+	0.864524i	$0.332380\pi$
$444$	47.9500	2.27561
$445$	28.8745	1.36878
$446$	−5.10257	−0.241614
$447$	42.3229	2.00180
$448$	−55.9489	−2.64333
$449$	−17.9303	−0.846185	−0.423093	−	0.906086i	$-0.639055\pi$
$449$	−17.9303	−0.846185	−0.423093	+	0.906086i	$0.639055\pi$
$450$	−31.7109	−1.49486
$451$	−3.51244	−0.165394
$452$	−73.7967	−3.47111
$453$	36.7245	1.72547
$454$	−55.4203	−2.60100
$455$	17.0877	0.801082
$456$	99.2074	4.64581
$457$	7.42332	0.347248	0.173624	−	0.984812i	$-0.444452\pi$
$457$	7.42332	0.347248	0.173624	+	0.984812i	$0.444452\pi$
$458$	3.39259	0.158525
$459$	3.57506	0.166870
$460$	−21.8692	−1.01966
$461$	9.33948	0.434983	0.217492	−	0.976062i	$-0.430213\pi$
$461$	9.33948	0.434983	0.217492	+	0.976062i	$0.430213\pi$
$462$	−22.8506	−1.06311
$463$	16.4791	0.765850	0.382925	−	0.923779i	$-0.374917\pi$
$463$	16.4791	0.765850	0.382925	+	0.923779i	$0.374917\pi$
$464$	−66.1408	−3.07051
$465$	69.8646	3.23989
$466$	18.4355	0.854008
$467$	−7.02063	−0.324876	−0.162438	−	0.986719i	$-0.551936\pi$
$467$	−7.02063	−0.324876	−0.162438	+	0.986719i	$0.551936\pi$
$468$	−25.6083	−1.18374
$469$	4.81204	0.222200
$470$	−19.4682	−0.898001
$471$	47.1058	2.17052
$472$	−40.8116	−1.87851
$473$	−5.13199	−0.235969
$474$	−90.9995	−4.17975
$475$	−13.2308	−0.607073
$476$	−25.1463	−1.15258
$477$	−46.4508	−2.12683
$478$	26.3918	1.20713
$479$	11.3866	0.520268	0.260134	−	0.965572i	$-0.416233\pi$
$479$	11.3866	0.520268	0.260134	+	0.965572i	$0.416233\pi$
$480$	−91.5179	−4.17720
$481$	−4.31539	−0.196765
$482$	62.2582	2.83578
$483$	21.9114	0.997004
$484$	−52.3114	−2.37779
$485$	−18.6786	−0.848152
$486$	51.6833	2.34440
$487$	−31.7884	−1.44047	−0.720235	−	0.693730i	$-0.755966\pi$
$487$	−31.7884	−1.44047	−0.720235	+	0.693730i	$0.755966\pi$
$488$	−72.3920	−3.27703
$489$	55.9593	2.53057
$490$	−139.486	−6.30135
$491$	14.9969	0.676799	0.338400	−	0.941002i	$-0.390114\pi$
$491$	14.9969	0.676799	0.338400	+	0.941002i	$0.390114\pi$
$492$	74.5136	3.35933
$493$	−6.31747	−0.284525
$494$	−15.0165	−0.675622
$495$	−7.58725	−0.341021
$496$	96.8738	4.34976
$497$	−70.7363	−3.17296
$498$	−103.414	−4.63408
$499$	−17.2507	−0.772248	−0.386124	−	0.922447i	$-0.626186\pi$
$499$	−17.2507	−0.772248	−0.386124	+	0.922447i	$0.626186\pi$
$500$	−30.4645	−1.36241
$501$	49.0700	2.19228
$502$	−31.5678	−1.40894
$503$	−34.6405	−1.54454	−0.772271	−	0.635293i	$-0.780879\pi$
$503$	−34.6405	−1.54454	−0.772271	+	0.635293i	$0.780879\pi$
$504$	170.121	7.57780
$505$	7.29955	0.324826
$506$	−2.63196	−0.117005
$507$	−31.2705	−1.38877
$508$	−38.3730	−1.70253
$509$	4.86172	0.215492	0.107746	−	0.994178i	$-0.465637\pi$
$509$	4.86172	0.215492	0.107746	+	0.994178i	$0.465637\pi$
$510$	−19.8812	−0.880353
$511$	26.0655	1.15307
$512$	34.8175	1.53873
$513$	−16.9722	−0.749343
$514$	−74.4265	−3.28281
$515$	−34.4374	−1.51749
$516$	108.871	4.79278
$517$	−1.66712	−0.0733197
$518$	48.2158	2.11848
$519$	46.9672	2.06163
$520$	25.8897	1.13534
$521$	−32.1808	−1.40987	−0.704934	−	0.709273i	$-0.749023\pi$
$521$	−32.1808	−1.40987	−0.704934	+	0.709273i	$0.749023\pi$
$522$	71.8818	3.14618
$523$	7.36268	0.321948	0.160974	−	0.986959i	$-0.448537\pi$
$523$	7.36268	0.321948	0.160974	+	0.986959i	$0.448537\pi$
$524$	−36.4135	−1.59073
$525$	−38.4394	−1.67763
$526$	20.9051	0.911506
$527$	9.25295	0.403065
$528$	−17.8241	−0.775695
$529$	−20.4762	−0.890270
$530$	78.9824	3.43078
$531$	22.8349	0.990950
$532$	119.379	5.17575
$533$	−6.70605	−0.290471
$534$	−73.7206	−3.19020
$535$	3.44518	0.148948
$536$	7.29078	0.314914
$537$	12.0881	0.521639
$538$	−61.2970	−2.64270
$539$	−11.9446	−0.514491
$540$	49.2142	2.11784
$541$	−21.2582	−0.913962	−0.456981	−	0.889477i	$-0.651069\pi$
$541$	−21.2582	−0.913962	−0.456981	+	0.889477i	$0.651069\pi$
$542$	18.2557	0.784149
$543$	−33.1543	−1.42279
$544$	−12.1207	−0.519672
$545$	46.1808	1.97817
$546$	−43.6271	−1.86707
$547$	−32.8677	−1.40532	−0.702661	−	0.711525i	$-0.748005\pi$
$547$	−32.8677	−1.40532	−0.702661	+	0.711525i	$0.748005\pi$
$548$	35.1208	1.50029
$549$	40.5047	1.72870
$550$	4.61727	0.196881
$551$	29.9915	1.27768
$552$	33.1983	1.41301
$553$	−65.1077	−2.76866
$554$	−11.9964	−0.509678
$555$	27.1238	1.15134
$556$	20.1452	0.854345
$557$	39.3424	1.66699	0.833496	−	0.552525i	$-0.186336\pi$
$557$	39.3424	1.66699	0.833496	+	0.552525i	$0.186336\pi$
$558$	−105.282	−4.45696
$559$	−9.79816	−0.414418
$560$	−148.923	−6.29314
$561$	−1.70248	−0.0718787
$562$	33.9847	1.43356
$563$	−27.6562	−1.16557	−0.582785	−	0.812626i	$-0.698037\pi$
$563$	−27.6562	−1.16557	−0.582785	+	0.812626i	$0.698037\pi$
$564$	35.3666	1.48920
$565$	−41.7445	−1.75620
$566$	−32.7964	−1.37854
$567$	16.7728	0.704393
$568$	−107.173	−4.49690
$569$	−32.2565	−1.35226	−0.676132	−	0.736780i	$-0.736345\pi$
$569$	−32.2565	−1.35226	−0.676132	+	0.736780i	$0.736345\pi$
$570$	94.3838	3.95330
$571$	20.0863	0.840585	0.420292	−	0.907389i	$-0.361927\pi$
$571$	20.0863	0.840585	0.420292	+	0.907389i	$0.361927\pi$
$572$	3.72871	0.155905
$573$	−21.6369	−0.903895
$574$	74.9265	3.12737
$575$	−4.42750	−0.184639
$576$	47.4298	1.97624
$577$	12.7216	0.529609	0.264804	−	0.964302i	$-0.414693\pi$
$577$	12.7216	0.529609	0.264804	+	0.964302i	$0.414693\pi$
$578$	−2.63308	−0.109522
$579$	39.8090	1.65440
$580$	−86.9661	−3.61107
$581$	−73.9898	−3.06961
$582$	47.6890	1.97677
$583$	6.76348	0.280115
$584$	39.4921	1.63420
$585$	−14.4858	−0.598915
$586$	37.1056	1.53282
$587$	30.8908	1.27500	0.637499	−	0.770451i	$-0.279969\pi$
$587$	30.8908	1.27500	0.637499	+	0.770451i	$0.279969\pi$
$588$	253.395	10.4498
$589$	−43.9274	−1.81000
$590$	−38.8272	−1.59849
$591$	−49.3030	−2.02805
$592$	37.6096	1.54575
$593$	18.4540	0.757815	0.378908	−	0.925435i	$-0.376300\pi$
$593$	18.4540	0.757815	0.378908	+	0.925435i	$0.376300\pi$
$594$	5.92294	0.243021
$595$	−14.2245	−0.583146
$596$	77.1622	3.16069
$597$	49.4368	2.02331
$598$	−5.02503	−0.205489
$599$	47.3061	1.93287	0.966437	−	0.256902i	$-0.0827019\pi$
$599$	47.3061	1.93287	0.966437	+	0.256902i	$0.0827019\pi$
$600$	−58.2400	−2.37764
$601$	−39.6256	−1.61636	−0.808181	−	0.588934i	$-0.799548\pi$
$601$	−39.6256	−1.61636	−0.808181	+	0.588934i	$0.799548\pi$
$602$	109.475	4.46185
$603$	−4.07933	−0.166123
$604$	66.9554	2.72438
$605$	−29.5909	−1.20304
$606$	−18.6367	−0.757065
$607$	38.9455	1.58075	0.790374	−	0.612625i	$-0.209886\pi$
$607$	38.9455	1.58075	0.790374	+	0.612625i	$0.209886\pi$
$608$	57.5419	2.33363
$609$	87.1340	3.53085
$610$	−68.8721	−2.78855
$611$	−3.18291	−0.128767
$612$	21.3174	0.861704
$613$	−23.7534	−0.959391	−0.479695	−	0.877435i	$-0.659253\pi$
$613$	−23.7534	−0.959391	−0.479695	+	0.877435i	$0.659253\pi$
$614$	22.8409	0.921782
$615$	42.1499	1.69965
$616$	−24.7706	−0.998034
$617$	−1.45981	−0.0587697	−0.0293848	−	0.999568i	$-0.509355\pi$
$617$	−1.45981	−0.0587697	−0.0293848	+	0.999568i	$0.509355\pi$
$618$	87.9233	3.53679
$619$	−33.9880	−1.36609	−0.683046	−	0.730376i	$-0.739345\pi$
$619$	−33.9880	−1.36609	−0.683046	+	0.730376i	$0.739345\pi$
$620$	127.376	5.11553
$621$	−5.67950	−0.227911
$622$	16.2386	0.651109
$623$	−52.7451	−2.11319
$624$	−34.0304	−1.36231
$625$	−31.1676	−1.24671
$626$	−8.77312	−0.350644
$627$	8.08234	0.322778
$628$	85.8823	3.42708
$629$	3.59230	0.143235
$630$	161.849	6.44824
$631$	−8.84464	−0.352100	−0.176050	−	0.984381i	$-0.556332\pi$
$631$	−8.84464	−0.352100	−0.176050	+	0.984381i	$0.556332\pi$
$632$	−98.6455	−3.92391
$633$	−46.6678	−1.85488
$634$	−50.8127	−2.01803
$635$	−21.7064	−0.861392
$636$	−143.482	−5.68943
$637$	−22.8050	−0.903568
$638$	−10.4664	−0.414368
$639$	59.9656	2.37220
$640$	−13.0009	−0.513908
$641$	3.82470	0.151067	0.0755334	−	0.997143i	$-0.475934\pi$
$641$	3.82470	0.151067	0.0755334	+	0.997143i	$0.475934\pi$
$642$	−8.79600	−0.347150
$643$	−11.4785	−0.452669	−0.226335	−	0.974050i	$-0.572674\pi$
$643$	−11.4785	−0.452669	−0.226335	+	0.974050i	$0.572674\pi$
$644$	39.9485	1.57419
$645$	61.5849	2.42490
$646$	12.5003	0.491817
$647$	−18.4076	−0.723678	−0.361839	−	0.932241i	$-0.617851\pi$
$647$	−18.4076	−0.723678	−0.361839	+	0.932241i	$0.617851\pi$
$648$	25.4127	0.998306
$649$	−3.32488	−0.130513
$650$	8.81544	0.345770
$651$	−127.622	−5.00189
$652$	102.024	3.99556
$653$	−14.4054	−0.563726	−0.281863	−	0.959455i	$-0.590952\pi$
$653$	−14.4054	−0.563726	−0.281863	+	0.959455i	$0.590952\pi$
$654$	−117.906	−4.61048
$655$	−20.5979	−0.804828
$656$	58.4448	2.28189
$657$	−22.0966	−0.862071
$658$	35.5626	1.38637
$659$	24.5298	0.955546	0.477773	−	0.878483i	$-0.341444\pi$
$659$	24.5298	0.955546	0.477773	+	0.878483i	$0.341444\pi$
$660$	−23.4363	−0.912256
$661$	−31.9769	−1.24376	−0.621878	−	0.783114i	$-0.713630\pi$
$661$	−31.9769	−1.24376	−0.621878	+	0.783114i	$0.713630\pi$
$662$	44.7876	1.74072
$663$	−3.25043	−0.126236
$664$	−112.103	−4.35043
$665$	67.5291	2.61867
$666$	−40.8742	−1.58384
$667$	10.0362	0.388603
$668$	89.4634	3.46144
$669$	5.24346	0.202724
$670$	6.93629	0.267972
$671$	−5.89771	−0.227679
$672$	167.176	6.44895
$673$	3.84789	0.148325	0.0741626	−	0.997246i	$-0.476372\pi$
$673$	3.84789	0.148325	0.0741626	+	0.997246i	$0.476372\pi$
$674$	30.4568	1.17315
$675$	9.96359	0.383499
$676$	−57.0117	−2.19276
$677$	−27.5568	−1.05910	−0.529548	−	0.848280i	$-0.677638\pi$
$677$	−27.5568	−1.05910	−0.529548	+	0.848280i	$0.677638\pi$
$678$	106.579	4.09315
$679$	34.1202	1.30941
$680$	−21.5516	−0.826467
$681$	56.9505	2.18235
$682$	15.3297	0.587004
$683$	34.6126	1.32441	0.662207	−	0.749321i	$-0.269620\pi$
$683$	34.6126	1.32441	0.662207	+	0.749321i	$0.269620\pi$
$684$	−101.202	−3.86955
$685$	19.8667	0.759069
$686$	160.846	6.14113
$687$	−3.48626	−0.133009
$688$	85.3932	3.25559
$689$	12.9131	0.491948
$690$	31.5841	1.20239
$691$	−8.73729	−0.332382	−0.166191	−	0.986094i	$-0.553147\pi$
$691$	−8.73729	−0.332382	−0.166191	+	0.986094i	$0.553147\pi$
$692$	85.6297	3.25515
$693$	13.8596	0.526483
$694$	17.6268	0.669104
$695$	11.3955	0.432255
$696$	132.018	5.00412
$697$	5.58238	0.211448
$698$	−77.8523	−2.94675
$699$	−18.9445	−0.716547
$700$	−70.0819	−2.64885
$701$	16.9615	0.640629	0.320314	−	0.947311i	$-0.396211\pi$
$701$	16.9615	0.640629	0.320314	+	0.947311i	$0.396211\pi$
$702$	11.3083	0.426803
$703$	−17.0541	−0.643207
$704$	−6.90603	−0.260281
$705$	20.0057	0.753460
$706$	2.63308	0.0990974
$707$	−13.3341	−0.501480
$708$	70.5348	2.65086
$709$	−7.22766	−0.271441	−0.135720	−	0.990747i	$-0.543335\pi$
$709$	−7.22766	−0.271441	−0.135720	+	0.990747i	$0.543335\pi$
$710$	−101.962	−3.82658
$711$	55.1941	2.06994
$712$	−79.9147	−2.99493
$713$	−14.6996	−0.550505
$714$	36.3169	1.35913
$715$	2.10921	0.0788801
$716$	22.0387	0.823625
$717$	−27.1205	−1.01283
$718$	−54.3318	−2.02764
$719$	32.2279	1.20190	0.600948	−	0.799288i	$-0.294790\pi$
$719$	32.2279	1.20190	0.600948	+	0.799288i	$0.294790\pi$
$720$	126.247	4.70495
$721$	62.9068	2.34277
$722$	−9.31519	−0.346676
$723$	−63.9771	−2.37934
$724$	−60.4462	−2.24646
$725$	−17.6066	−0.653892
$726$	75.5496	2.80391
$727$	−22.4636	−0.833130	−0.416565	−	0.909106i	$-0.636766\pi$
$727$	−22.4636	−0.833130	−0.416565	+	0.909106i	$0.636766\pi$
$728$	−47.2927	−1.75279
$729$	−43.2390	−1.60144
$730$	37.5719	1.39060
$731$	8.15637	0.301674
$732$	125.115	4.62439
$733$	−39.6452	−1.46433	−0.732165	−	0.681128i	$-0.761490\pi$
$733$	−39.6452	−1.46433	−0.732165	+	0.681128i	$0.761490\pi$
$734$	55.5701	2.05113
$735$	143.338	5.28709
$736$	19.2555	0.709768
$737$	0.593973	0.0218793
$738$	−63.5178	−2.33812
$739$	31.3222	1.15221	0.576103	−	0.817377i	$-0.304573\pi$
$739$	31.3222	1.15221	0.576103	+	0.817377i	$0.304573\pi$
$740$	49.4515	1.81787
$741$	15.4311	0.566874
$742$	−144.277	−5.29658
$743$	33.5752	1.23176	0.615878	−	0.787842i	$-0.288802\pi$
$743$	33.5752	1.23176	0.615878	+	0.787842i	$0.288802\pi$
$744$	−193.361	−7.08896
$745$	43.6482	1.59915
$746$	−9.20637	−0.337069
$747$	62.7237	2.29494
$748$	−3.10393	−0.113491
$749$	−6.29330	−0.229952
$750$	43.9977	1.60657
$751$	−20.7154	−0.755915	−0.377957	−	0.925823i	$-0.623373\pi$
$751$	−20.7154	−0.755915	−0.377957	+	0.925823i	$0.623373\pi$
$752$	27.7398	1.01157
$753$	32.4394	1.18216
$754$	−19.9828	−0.727729
$755$	37.8745	1.37840
$756$	−89.8996	−3.26962
$757$	−24.4176	−0.887474	−0.443737	−	0.896157i	$-0.646348\pi$
$757$	−24.4176	−0.887474	−0.443737	+	0.896157i	$0.646348\pi$
$758$	52.1979	1.89591
$759$	2.70463	0.0981719
$760$	102.314	3.71132
$761$	−8.06229	−0.292258	−0.146129	−	0.989266i	$-0.546681\pi$
$761$	−8.06229	−0.292258	−0.146129	+	0.989266i	$0.546681\pi$
$762$	55.4193	2.00763
$763$	−84.3584	−3.05398
$764$	−39.4480	−1.42718
$765$	12.0586	0.435978
$766$	7.09001	0.256172
$767$	−6.34797	−0.229212
$768$	−26.2036	−0.945542
$769$	10.4938	0.378417	0.189208	−	0.981937i	$-0.439408\pi$
$769$	10.4938	0.378417	0.189208	+	0.981937i	$0.439408\pi$
$770$	−23.5662	−0.849266
$771$	76.4814	2.75441
$772$	72.5789	2.61217
$773$	−10.4408	−0.375529	−0.187765	−	0.982214i	$-0.560124\pi$
$773$	−10.4408	−0.375529	−0.187765	+	0.982214i	$0.560124\pi$
$774$	−92.8053	−3.33582
$775$	25.7877	0.926321
$776$	51.6959	1.85577
$777$	−49.5470	−1.77749
$778$	−37.5261	−1.34538
$779$	−26.5018	−0.949525
$780$	−44.7453	−1.60214
$781$	−8.73132	−0.312431
$782$	4.18303	0.149585
$783$	−22.5854	−0.807135
$784$	198.751	7.09825
$785$	48.5809	1.73393
$786$	52.5893	1.87580
$787$	−11.9673	−0.426588	−0.213294	−	0.976988i	$-0.568419\pi$
$787$	−11.9673	−0.426588	−0.213294	+	0.976988i	$0.568419\pi$
$788$	−89.8882	−3.20213
$789$	−21.4823	−0.764790
$790$	−93.8491	−3.33900
$791$	76.2546	2.71130
$792$	20.9989	0.746162
$793$	−11.2601	−0.399858
$794$	41.5882	1.47591
$795$	−81.1632	−2.87856
$796$	90.1321	3.19465
$797$	−21.4467	−0.759683	−0.379841	−	0.925052i	$-0.624021\pi$
$797$	−21.4467	−0.759683	−0.379841	+	0.925052i	$0.624021\pi$
$798$	−172.411	−6.10327
$799$	2.64958	0.0937354
$800$	−33.7801	−1.19431
$801$	44.7138	1.57989
$802$	1.11422	0.0393445
$803$	3.21739	0.113539
$804$	−12.6007	−0.444392
$805$	22.5976	0.796460
$806$	29.2679	1.03092
$807$	62.9895	2.21733
$808$	−20.2026	−0.710725
$809$	24.9347	0.876657	0.438328	−	0.898815i	$-0.355571\pi$
$809$	24.9347	0.876657	0.438328	+	0.898815i	$0.355571\pi$
$810$	24.1771	0.849496
$811$	13.6818	0.480435	0.240217	−	0.970719i	$-0.422781\pi$
$811$	13.6818	0.480435	0.240217	+	0.970719i	$0.422781\pi$
$812$	158.861	5.57493
$813$	−18.7597	−0.657932
$814$	5.95150	0.208600
$815$	57.7116	2.02155
$816$	28.3282	0.991686
$817$	−38.7215	−1.35469
$818$	49.5045	1.73088
$819$	26.4612	0.924630
$820$	76.8469	2.68361
$821$	13.1310	0.458274	0.229137	−	0.973394i	$-0.426410\pi$
$821$	13.1310	0.458274	0.229137	+	0.973394i	$0.426410\pi$
$822$	−50.7224	−1.76915
$823$	13.9871	0.487559	0.243779	−	0.969831i	$-0.421613\pi$
$823$	13.9871	0.487559	0.243779	+	0.969831i	$0.421613\pi$
$824$	95.3108	3.32031
$825$	−4.74476	−0.165191
$826$	70.9257	2.46782
$827$	2.39687	0.0833472	0.0416736	−	0.999131i	$-0.486731\pi$
$827$	2.39687	0.0833472	0.0416736	+	0.999131i	$0.486731\pi$
$828$	−33.8657	−1.17691
$829$	23.3984	0.812660	0.406330	−	0.913727i	$-0.366808\pi$
$829$	23.3984	0.812660	0.406330	+	0.913727i	$0.366808\pi$
$830$	−106.652	−3.70195
$831$	12.3276	0.427641
$832$	−13.1852	−0.457115
$833$	18.9838	0.657750
$834$	−29.0942	−1.00745
$835$	50.6066	1.75131
$836$	14.7356	0.509640
$837$	33.0799	1.14341
$838$	8.00491	0.276525
$839$	−18.7964	−0.648924	−0.324462	−	0.945899i	$-0.605183\pi$
$839$	−18.7964	−0.648924	−0.324462	+	0.945899i	$0.605183\pi$
$840$	297.252	10.2562
$841$	10.9104	0.376222
$842$	−50.4835	−1.73977
$843$	−34.9231	−1.20281
$844$	−85.0838	−2.92871
$845$	−32.2497	−1.10942
$846$	−30.1476	−1.03650
$847$	54.0537	1.85731
$848$	−112.540	−3.86465
$849$	33.7020	1.15665
$850$	−7.33832	−0.251702
$851$	−5.70689	−0.195630
$852$	185.228	6.34581
$853$	40.8049	1.39713	0.698566	−	0.715545i	$-0.253822\pi$
$853$	40.8049	1.39713	0.698566	+	0.715545i	$0.253822\pi$
$854$	125.809	4.30509
$855$	−57.2467	−1.95780
$856$	−9.53505	−0.325901
$857$	−52.1108	−1.78007	−0.890035	−	0.455893i	$-0.849320\pi$
$857$	−52.1108	−1.78007	−0.890035	+	0.455893i	$0.849320\pi$
$858$	−5.38510	−0.183844
$859$	37.2242	1.27007	0.635037	−	0.772482i	$-0.280985\pi$
$859$	37.2242	1.27007	0.635037	+	0.772482i	$0.280985\pi$
$860$	112.280	3.82873
$861$	−76.9953	−2.62399
$862$	−31.5361	−1.07412
$863$	23.5426	0.801400	0.400700	−	0.916209i	$-0.368767\pi$
$863$	23.5426	0.801400	0.400700	+	0.916209i	$0.368767\pi$
$864$	−43.3324	−1.47420
$865$	48.4380	1.64694
$866$	−38.4256	−1.30575
$867$	2.70578	0.0918932
$868$	−232.677	−7.89758
$869$	−8.03656	−0.272622
$870$	125.599	4.25820
$871$	1.13403	0.0384252
$872$	−127.812	−4.32827
$873$	−28.9249	−0.978959
$874$	−19.8585	−0.671723
$875$	31.4792	1.06419
$876$	−68.2543	−2.30610
$877$	−2.93054	−0.0989573	−0.0494786	−	0.998775i	$-0.515756\pi$
$877$	−2.93054	−0.0989573	−0.0494786	+	0.998775i	$0.515756\pi$
$878$	−20.5722	−0.694279
$879$	−38.1301	−1.28609
$880$	−18.3823	−0.619666
$881$	−17.9111	−0.603440	−0.301720	−	0.953397i	$-0.597561\pi$
$881$	−17.9111	−0.603440	−0.301720	+	0.953397i	$0.597561\pi$
$882$	−216.003	−7.27318
$883$	−53.4075	−1.79731	−0.898653	−	0.438661i	$-0.855453\pi$
$883$	−53.4075	−1.79731	−0.898653	+	0.438661i	$0.855453\pi$
$884$	−5.92611	−0.199317
$885$	39.8993	1.34120
$886$	−55.7072	−1.87152
$887$	−3.12584	−0.104955	−0.0524777	−	0.998622i	$-0.516712\pi$
$887$	−3.12584	−0.104955	−0.0524777	+	0.998622i	$0.516712\pi$
$888$	−75.0692	−2.51916
$889$	39.6511	1.32985
$890$	−76.0291	−2.54850
$891$	2.07035	0.0693594
$892$	9.55976	0.320084
$893$	−12.5786	−0.420927
$894$	−111.440	−3.72710
$895$	12.4666	0.416712
$896$	23.7488	0.793392
$897$	5.16377	0.172413
$898$	47.2121	1.57549
$899$	−58.4552	−1.94959
$900$	59.4108	1.98036
$901$	−10.7493	−0.358112
$902$	9.24854	0.307943
$903$	−112.497	−3.74367
$904$	115.534	3.84261
$905$	−34.1925	−1.13660
$906$	−96.6988	−3.21260
$907$	9.83541	0.326579	0.163290	−	0.986578i	$-0.447789\pi$
$907$	9.83541	0.326579	0.163290	+	0.986578i	$0.447789\pi$
$908$	103.831	3.44575
$909$	11.3038	0.374922
$910$	−44.9933	−1.49151
$911$	27.9397	0.925683	0.462842	−	0.886441i	$-0.346830\pi$
$911$	27.9397	0.925683	0.462842	+	0.886441i	$0.346830\pi$
$912$	−134.485	−4.45325
$913$	−9.13291	−0.302255
$914$	−19.5462	−0.646532
$915$	70.7737	2.33971
$916$	−6.35608	−0.210011
$917$	37.6262	1.24253
$918$	−9.41344	−0.310690
$919$	−23.2793	−0.767913	−0.383957	−	0.923351i	$-0.625439\pi$
$919$	−23.2793	−0.767913	−0.383957	+	0.923351i	$0.625439\pi$
$920$	34.2378	1.12879
$921$	−23.4715	−0.773412
$922$	−24.5916	−0.809883
$923$	−16.6701	−0.548704
$924$	42.8110	1.40838
$925$	10.0116	0.329181
$926$	−43.3909	−1.42591
$927$	−53.3283	−1.75153
$928$	76.5724	2.51361
$929$	−11.1442	−0.365629	−0.182815	−	0.983147i	$-0.558521\pi$
$929$	−11.1442	−0.365629	−0.182815	+	0.983147i	$0.558521\pi$
$930$	−183.959	−6.03227
$931$	−90.1236	−2.95368
$932$	−34.5392	−1.13137
$933$	−16.6870	−0.546306
$934$	18.4859	0.604877
$935$	−1.75579	−0.0574205
$936$	40.0917	1.31044
$937$	12.2398	0.399855	0.199928	−	0.979811i	$-0.435929\pi$
$937$	12.2398	0.399855	0.199928	+	0.979811i	$0.435929\pi$
$938$	−12.6705	−0.413707
$939$	9.01535	0.294205
$940$	36.4740	1.18965
$941$	−30.0195	−0.978608	−0.489304	−	0.872113i	$-0.662749\pi$
$941$	−30.0195	−0.978608	−0.489304	+	0.872113i	$0.662749\pi$
$942$	−124.033	−4.04123
$943$	−8.86841	−0.288795
$944$	55.3240	1.80064
$945$	−50.8533	−1.65426
$946$	13.5130	0.439344
$947$	11.4160	0.370971	0.185486	−	0.982647i	$-0.440614\pi$
$947$	11.4160	0.370971	0.185486	+	0.982647i	$0.440614\pi$
$948$	170.489	5.53723
$949$	6.14274	0.199402
$950$	34.8379	1.13029
$951$	52.2156	1.69321
$952$	39.3683	1.27594
$953$	−24.3550	−0.788935	−0.394468	−	0.918910i	$-0.629071\pi$
$953$	−24.3550	−0.788935	−0.394468	+	0.918910i	$0.629071\pi$
$954$	122.309	3.95989
$955$	−22.3145	−0.722079
$956$	−49.4455	−1.59918
$957$	10.7554	0.347672
$958$	−29.9819	−0.968672
$959$	−36.2905	−1.17188
$960$	82.8738	2.67474
$961$	54.6170	1.76184
$962$	11.3628	0.366351
$963$	5.33505	0.171920
$964$	−116.642	−3.75678
$965$	41.0556	1.32163
$966$	−57.6946	−1.85629
$967$	−28.0613	−0.902392	−0.451196	−	0.892425i	$-0.649002\pi$
$967$	−28.0613	−0.902392	−0.451196	+	0.892425i	$0.649002\pi$
$968$	81.8974	2.63228
$969$	−12.8454	−0.412654
$970$	49.1823	1.57915
$971$	44.1080	1.41549	0.707746	−	0.706467i	$-0.249712\pi$
$971$	44.1080	1.41549	0.707746	+	0.706467i	$0.249712\pi$
$972$	−96.8296	−3.10581
$973$	−20.8161	−0.667334
$974$	83.7015	2.68197
$975$	−9.05884	−0.290115
$976$	98.1343	3.14120
$977$	−2.74982	−0.0879747	−0.0439873	−	0.999032i	$-0.514006\pi$
$977$	−2.74982	−0.0879747	−0.0439873	+	0.999032i	$0.514006\pi$
$978$	−147.345	−4.71159
$979$	−6.51058	−0.208079
$980$	261.330	8.34789
$981$	71.5135	2.28325
$982$	−39.4880	−1.26011
$983$	−27.7878	−0.886294	−0.443147	−	0.896449i	$-0.646138\pi$
$983$	−27.7878	−0.886294	−0.443147	+	0.896449i	$0.646138\pi$
$984$	−116.656	−3.71887
$985$	−50.8469	−1.62012
$986$	16.6344	0.529748
$987$	−36.5445	−1.16322
$988$	28.1336	0.895049
$989$	−12.9576	−0.412027
$990$	19.9779	0.634938
$991$	53.8238	1.70977	0.854885	−	0.518818i	$-0.173628\pi$
$991$	53.8238	1.70977	0.854885	+	0.518818i	$0.173628\pi$
$992$	−112.152	−3.56085
$993$	−46.0242	−1.46053
$994$	186.255	5.90764
$995$	50.9848	1.61633
$996$	193.747	6.13912
$997$	−40.7736	−1.29131	−0.645656	−	0.763628i	$-0.723416\pi$
$997$	−40.7736	−1.29131	−0.645656	+	0.763628i	$0.723416\pi$
$998$	45.4226	1.43783
$999$	12.8427	0.406326

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.d.1.5	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.d.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-2.63308 q^{2} +2.70578 q^{3} +4.93313 q^{4} +2.79051 q^{5} -7.12456 q^{6} -5.09743 q^{7} -7.72317 q^{8} +4.32127 q^{9} +O(q^{10})\)	\(q-2.63308 q^{2} +2.70578 q^{3} +4.93313 q^{4} +2.79051 q^{5} -7.12456 q^{6} -5.09743 q^{7} -7.72317 q^{8} +4.32127 q^{9} -7.34766 q^{10} -0.629200 q^{11} +13.3480 q^{12} -1.20129 q^{13} +13.4220 q^{14} +7.55053 q^{15} +10.4695 q^{16} +1.00000 q^{17} -11.3783 q^{18} -4.74739 q^{19} +13.7660 q^{20} -13.7925 q^{21} +1.65674 q^{22} -1.58864 q^{23} -20.8972 q^{24} +2.78697 q^{25} +3.16309 q^{26} +3.57506 q^{27} -25.1463 q^{28} -6.31747 q^{29} -19.8812 q^{30} +9.25295 q^{31} -12.1207 q^{32} -1.70248 q^{33} -2.63308 q^{34} -14.2245 q^{35} +21.3174 q^{36} +3.59230 q^{37} +12.5003 q^{38} -3.25043 q^{39} -21.5516 q^{40} +5.58238 q^{41} +36.3169 q^{42} +8.15637 q^{43} -3.10393 q^{44} +12.0586 q^{45} +4.18303 q^{46} +2.64958 q^{47} +28.3282 q^{48} +18.9838 q^{49} -7.33832 q^{50} +2.70578 q^{51} -5.92611 q^{52} -10.7493 q^{53} -9.41344 q^{54} -1.75579 q^{55} +39.3683 q^{56} -12.8454 q^{57} +16.6344 q^{58} +5.28430 q^{59} +37.2477 q^{60} +9.37335 q^{61} -24.3638 q^{62} -22.0274 q^{63} +10.9759 q^{64} -3.35221 q^{65} +4.48277 q^{66} -0.944014 q^{67} +4.93313 q^{68} -4.29852 q^{69} +37.4542 q^{70} +13.8769 q^{71} -33.3739 q^{72} -5.11346 q^{73} -9.45884 q^{74} +7.54094 q^{75} -23.4195 q^{76} +3.20730 q^{77} +8.55865 q^{78} +12.7727 q^{79} +29.2153 q^{80} -3.29045 q^{81} -14.6989 q^{82} +14.5151 q^{83} -68.0404 q^{84} +2.79051 q^{85} -21.4764 q^{86} -17.0937 q^{87} +4.85942 q^{88} +10.3474 q^{89} -31.7512 q^{90} +6.12349 q^{91} -7.83698 q^{92} +25.0365 q^{93} -6.97657 q^{94} -13.2477 q^{95} -32.7961 q^{96} -6.69361 q^{97} -49.9859 q^{98} -2.71894 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9} + 19 q^{10} + 48 q^{11} + 43 q^{12} + 6 q^{13} + 40 q^{14} + 49 q^{15} + 135 q^{16} + 121 q^{17} + 30 q^{19} + 50 q^{20} + 18 q^{21} + 24 q^{22} + 75 q^{23} + 24 q^{24} + 128 q^{25} + 59 q^{26} + 75 q^{27} + 52 q^{28} + 49 q^{29} - 34 q^{30} + 101 q^{31} + 47 q^{32} + 20 q^{33} + 9 q^{34} + 47 q^{35} + 138 q^{36} + 32 q^{37} + 30 q^{38} + 101 q^{39} + 36 q^{40} + 83 q^{41} - 11 q^{42} + 8 q^{43} + 98 q^{44} + 49 q^{45} + 45 q^{46} + 135 q^{47} + 54 q^{48} + 116 q^{49} + 3 q^{50} + 21 q^{51} - 5 q^{52} + 28 q^{53} + 10 q^{54} + 37 q^{55} + 75 q^{56} + 31 q^{58} + 150 q^{59} + 50 q^{60} + 36 q^{61} + 34 q^{62} + 118 q^{63} + 110 q^{64} + 18 q^{65} - 28 q^{66} - 6 q^{67} + 127 q^{68} + 25 q^{69} - 22 q^{70} + 223 q^{71} + q^{72} + 38 q^{73} - 10 q^{74} + 88 q^{75} - 4 q^{76} + 38 q^{77} + 42 q^{78} + 74 q^{79} + 106 q^{80} + 133 q^{81} + 28 q^{82} + 55 q^{83} + 10 q^{84} + 27 q^{85} + 64 q^{86} + 14 q^{87} + 56 q^{88} + 118 q^{89} + 51 q^{90} + 73 q^{91} + 82 q^{92} + 31 q^{93} + 33 q^{94} + 106 q^{95} + 38 q^{96} + 37 q^{97} + 88 q^{98} + 81 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9 + 19 * q^10 + 48 * q^11 + 43 * q^12 + 6 * q^13 + 40 * q^14 + 49 * q^15 + 135 * q^16 + 121 * q^17 + 30 * q^19 + 50 * q^20 + 18 * q^21 + 24 * q^22 + 75 * q^23 + 24 * q^24 + 128 * q^25 + 59 * q^26 + 75 * q^27 + 52 * q^28 + 49 * q^29 - 34 * q^30 + 101 * q^31 + 47 * q^32 + 20 * q^33 + 9 * q^34 + 47 * q^35 + 138 * q^36 + 32 * q^37 + 30 * q^38 + 101 * q^39 + 36 * q^40 + 83 * q^41 - 11 * q^42 + 8 * q^43 + 98 * q^44 + 49 * q^45 + 45 * q^46 + 135 * q^47 + 54 * q^48 + 116 * q^49 + 3 * q^50 + 21 * q^51 - 5 * q^52 + 28 * q^53 + 10 * q^54 + 37 * q^55 + 75 * q^56 + 31 * q^58 + 150 * q^59 + 50 * q^60 + 36 * q^61 + 34 * q^62 + 118 * q^63 + 110 * q^64 + 18 * q^65 - 28 * q^66 - 6 * q^67 + 127 * q^68 + 25 * q^69 - 22 * q^70 + 223 * q^71 + q^72 + 38 * q^73 - 10 * q^74 + 88 * q^75 - 4 * q^76 + 38 * q^77 + 42 * q^78 + 74 * q^79 + 106 * q^80 + 133 * q^81 + 28 * q^82 + 55 * q^83 + 10 * q^84 + 27 * q^85 + 64 * q^86 + 14 * q^87 + 56 * q^88 + 118 * q^89 + 51 * q^90 + 73 * q^91 + 82 * q^92 + 31 * q^93 + 33 * q^94 + 106 * q^95 + 38 * q^96 + 37 * q^97 + 88 * q^98 + 81 * q^99

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