LMFDB - Embedded newform 6002.2.a.c.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6002,2,Mod(1,6002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6002 = 2 \cdot 3001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6002.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:	$47.9262112932$
Analytic rank:	$0$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.36851 q^{3} +1.00000 q^{4} +0.212949 q^{5} +1.36851 q^{6} -1.32734 q^{7} -1.00000 q^{8} -1.12718 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.36851 q^{3} +1.00000 q^{4} +0.212949 q^{5} +1.36851 q^{6} -1.32734 q^{7} -1.00000 q^{8} -1.12718 q^{9} -0.212949 q^{10} +1.59735 q^{11} -1.36851 q^{12} -2.31374 q^{13} +1.32734 q^{14} -0.291422 q^{15} +1.00000 q^{16} -4.84113 q^{17} +1.12718 q^{18} -8.22828 q^{19} +0.212949 q^{20} +1.81647 q^{21} -1.59735 q^{22} -0.469705 q^{23} +1.36851 q^{24} -4.95465 q^{25} +2.31374 q^{26} +5.64809 q^{27} -1.32734 q^{28} +3.08525 q^{29} +0.291422 q^{30} -8.47839 q^{31} -1.00000 q^{32} -2.18599 q^{33} +4.84113 q^{34} -0.282654 q^{35} -1.12718 q^{36} -6.55413 q^{37} +8.22828 q^{38} +3.16637 q^{39} -0.212949 q^{40} -2.29950 q^{41} -1.81647 q^{42} +2.17849 q^{43} +1.59735 q^{44} -0.240032 q^{45} +0.469705 q^{46} -7.41710 q^{47} -1.36851 q^{48} -5.23818 q^{49} +4.95465 q^{50} +6.62514 q^{51} -2.31374 q^{52} +12.4867 q^{53} -5.64809 q^{54} +0.340153 q^{55} +1.32734 q^{56} +11.2605 q^{57} -3.08525 q^{58} +0.0533622 q^{59} -0.291422 q^{60} +13.7078 q^{61} +8.47839 q^{62} +1.49615 q^{63} +1.00000 q^{64} -0.492708 q^{65} +2.18599 q^{66} -7.30748 q^{67} -4.84113 q^{68} +0.642796 q^{69} +0.282654 q^{70} +8.12634 q^{71} +1.12718 q^{72} -12.3717 q^{73} +6.55413 q^{74} +6.78049 q^{75} -8.22828 q^{76} -2.12022 q^{77} -3.16637 q^{78} -10.9580 q^{79} +0.212949 q^{80} -4.34791 q^{81} +2.29950 q^{82} +16.1285 q^{83} +1.81647 q^{84} -1.03091 q^{85} -2.17849 q^{86} -4.22219 q^{87} -1.59735 q^{88} -16.5138 q^{89} +0.240032 q^{90} +3.07111 q^{91} -0.469705 q^{92} +11.6028 q^{93} +7.41710 q^{94} -1.75220 q^{95} +1.36851 q^{96} +19.4801 q^{97} +5.23818 q^{98} -1.80050 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q - 69 q^{2} + 11 q^{3} + 69 q^{4} - 2 q^{5} - 11 q^{6} + 23 q^{7} - 69 q^{8} + 72 q^{9}+O(q^{10}) $ 69 * q - 69 * q^2 + 11 * q^3 + 69 * q^4 - 2 * q^5 - 11 * q^6 + 23 * q^7 - 69 * q^8 + 72 * q^9	\( 69 q - 69 q^{2} + 11 q^{3} + 69 q^{4} - 2 q^{5} - 11 q^{6} + 23 q^{7} - 69 q^{8} + 72 q^{9} + 2 q^{10} - 14 q^{11} + 11 q^{12} + 31 q^{13} - 23 q^{14} + 34 q^{15} + 69 q^{16} - 4 q^{17} - 72 q^{18} + 17 q^{19} - 2 q^{20} - 11 q^{21} + 14 q^{22} + 33 q^{23} - 11 q^{24} + 119 q^{25} - 31 q^{26} + 44 q^{27} + 23 q^{28} - 25 q^{29} - 34 q^{30} + 49 q^{31} - 69 q^{32} + 10 q^{33} + 4 q^{34} - 11 q^{35} + 72 q^{36} + 73 q^{37} - 17 q^{38} + 31 q^{39} + 2 q^{40} - 46 q^{41} + 11 q^{42} + 76 q^{43} - 14 q^{44} + 9 q^{45} - 33 q^{46} + 23 q^{47} + 11 q^{48} + 100 q^{49} - 119 q^{50} + 25 q^{51} + 31 q^{52} + 30 q^{53} - 44 q^{54} + 81 q^{55} - 23 q^{56} + 12 q^{57} + 25 q^{58} - 3 q^{59} + 34 q^{60} + 13 q^{61} - 49 q^{62} + 65 q^{63} + 69 q^{64} - 27 q^{65} - 10 q^{66} + 105 q^{67} - 4 q^{68} + 19 q^{69} + 11 q^{70} + 51 q^{71} - 72 q^{72} + 43 q^{73} - 73 q^{74} + 77 q^{75} + 17 q^{76} - 19 q^{77} - 31 q^{78} + 89 q^{79} - 2 q^{80} + 73 q^{81} + 46 q^{82} - 10 q^{83} - 11 q^{84} + 44 q^{85} - 76 q^{86} + 57 q^{87} + 14 q^{88} - 28 q^{89} - 9 q^{90} + 76 q^{91} + 33 q^{92} + 59 q^{93} - 23 q^{94} + 72 q^{95} - 11 q^{96} + 89 q^{97} - 100 q^{98} - 17 q^{99}+O(q^{100}) \) 69 * q - 69 * q^2 + 11 * q^3 + 69 * q^4 - 2 * q^5 - 11 * q^6 + 23 * q^7 - 69 * q^8 + 72 * q^9 + 2 * q^10 - 14 * q^11 + 11 * q^12 + 31 * q^13 - 23 * q^14 + 34 * q^15 + 69 * q^16 - 4 * q^17 - 72 * q^18 + 17 * q^19 - 2 * q^20 - 11 * q^21 + 14 * q^22 + 33 * q^23 - 11 * q^24 + 119 * q^25 - 31 * q^26 + 44 * q^27 + 23 * q^28 - 25 * q^29 - 34 * q^30 + 49 * q^31 - 69 * q^32 + 10 * q^33 + 4 * q^34 - 11 * q^35 + 72 * q^36 + 73 * q^37 - 17 * q^38 + 31 * q^39 + 2 * q^40 - 46 * q^41 + 11 * q^42 + 76 * q^43 - 14 * q^44 + 9 * q^45 - 33 * q^46 + 23 * q^47 + 11 * q^48 + 100 * q^49 - 119 * q^50 + 25 * q^51 + 31 * q^52 + 30 * q^53 - 44 * q^54 + 81 * q^55 - 23 * q^56 + 12 * q^57 + 25 * q^58 - 3 * q^59 + 34 * q^60 + 13 * q^61 - 49 * q^62 + 65 * q^63 + 69 * q^64 - 27 * q^65 - 10 * q^66 + 105 * q^67 - 4 * q^68 + 19 * q^69 + 11 * q^70 + 51 * q^71 - 72 * q^72 + 43 * q^73 - 73 * q^74 + 77 * q^75 + 17 * q^76 - 19 * q^77 - 31 * q^78 + 89 * q^79 - 2 * q^80 + 73 * q^81 + 46 * q^82 - 10 * q^83 - 11 * q^84 + 44 * q^85 - 76 * q^86 + 57 * q^87 + 14 * q^88 - 28 * q^89 - 9 * q^90 + 76 * q^91 + 33 * q^92 + 59 * q^93 - 23 * q^94 + 72 * q^95 - 11 * q^96 + 89 * q^97 - 100 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.36851	−0.790109	−0.395055	−	0.918658i	$-0.629274\pi$
$3$	−1.36851	−0.790109	−0.395055	+	0.918658i	$0.629274\pi$
$4$	1.00000	0.500000
$5$	0.212949	0.0952335	0.0476168	−	0.998866i	$-0.484837\pi$
$5$	0.212949	0.0952335	0.0476168	+	0.998866i	$0.484837\pi$
$6$	1.36851	0.558692
$7$	−1.32734	−0.501686	−0.250843	−	0.968028i	$-0.580708\pi$
$7$	−1.32734	−0.501686	−0.250843	+	0.968028i	$0.580708\pi$
$8$	−1.00000	−0.353553
$9$	−1.12718	−0.375728
$10$	−0.212949	−0.0673403
$11$	1.59735	0.481619	0.240809	−	0.970572i	$-0.422587\pi$
$11$	1.59735	0.481619	0.240809	+	0.970572i	$0.422587\pi$
$12$	−1.36851	−0.395055
$13$	−2.31374	−0.641716	−0.320858	−	0.947127i	$-0.603971\pi$
$13$	−2.31374	−0.641716	−0.320858	+	0.947127i	$0.603971\pi$
$14$	1.32734	0.354746
$15$	−0.291422	−0.0752449
$16$	1.00000	0.250000
$17$	−4.84113	−1.17415	−0.587074	−	0.809533i	$-0.699720\pi$
$17$	−4.84113	−1.17415	−0.587074	+	0.809533i	$0.699720\pi$
$18$	1.12718	0.265679
$19$	−8.22828	−1.88770	−0.943848	−	0.330379i	$-0.892823\pi$
$19$	−8.22828	−1.88770	−0.943848	+	0.330379i	$0.892823\pi$
$20$	0.212949	0.0476168
$21$	1.81647	0.396387
$22$	−1.59735	−0.340556
$23$	−0.469705	−0.0979402	−0.0489701	−	0.998800i	$-0.515594\pi$
$23$	−0.469705	−0.0979402	−0.0489701	+	0.998800i	$0.515594\pi$
$24$	1.36851	0.279346
$25$	−4.95465	−0.990931
$26$	2.31374	0.453762
$27$	5.64809	1.08697
$28$	−1.32734	−0.250843
$29$	3.08525	0.572916	0.286458	−	0.958093i	$-0.407522\pi$
$29$	3.08525	0.572916	0.286458	+	0.958093i	$0.407522\pi$
$30$	0.291422	0.0532062
$31$	−8.47839	−1.52276	−0.761382	−	0.648304i	$-0.775479\pi$
$31$	−8.47839	−1.52276	−0.761382	+	0.648304i	$0.775479\pi$
$32$	−1.00000	−0.176777
$33$	−2.18599	−0.380531
$34$	4.84113	0.830248
$35$	−0.282654	−0.0477773
$36$	−1.12718	−0.187864
$37$	−6.55413	−1.07749	−0.538746	−	0.842468i	$-0.681102\pi$
$37$	−6.55413	−1.07749	−0.538746	+	0.842468i	$0.681102\pi$
$38$	8.22828	1.33480
$39$	3.16637	0.507026
$40$	−0.212949	−0.0336701
$41$	−2.29950	−0.359122	−0.179561	−	0.983747i	$-0.557468\pi$
$41$	−2.29950	−0.359122	−0.179561	+	0.983747i	$0.557468\pi$
$42$	−1.81647	−0.280288
$43$	2.17849	0.332217	0.166109	−	0.986107i	$-0.446880\pi$
$43$	2.17849	0.332217	0.166109	+	0.986107i	$0.446880\pi$
$44$	1.59735	0.240809
$45$	−0.240032	−0.0357818
$46$	0.469705	0.0692542
$47$	−7.41710	−1.08189	−0.540947	−	0.841056i	$-0.681934\pi$
$47$	−7.41710	−1.08189	−0.540947	+	0.841056i	$0.681934\pi$
$48$	−1.36851	−0.197527
$49$	−5.23818	−0.748311
$50$	4.95465	0.700694
$51$	6.62514	0.927705
$52$	−2.31374	−0.320858
$53$	12.4867	1.71518	0.857591	−	0.514332i	$-0.171960\pi$
$53$	12.4867	1.71518	0.857591	+	0.514332i	$0.171960\pi$
$54$	−5.64809	−0.768607
$55$	0.340153	0.0458663
$56$	1.32734	0.177373
$57$	11.2605	1.49149
$58$	−3.08525	−0.405113
$59$	0.0533622	0.00694716	0.00347358	−	0.999994i	$-0.498894\pi$
$59$	0.0533622	0.00694716	0.00347358	+	0.999994i	$0.498894\pi$
$60$	−0.291422	−0.0376224
$61$	13.7078	1.75510	0.877551	−	0.479483i	$-0.159176\pi$
$61$	13.7078	1.75510	0.877551	+	0.479483i	$0.159176\pi$
$62$	8.47839	1.07676
$63$	1.49615	0.188497
$64$	1.00000	0.125000
$65$	−0.492708	−0.0611129
$66$	2.18599	0.269076
$67$	−7.30748	−0.892751	−0.446376	−	0.894846i	$-0.647285\pi$
$67$	−7.30748	−0.892751	−0.446376	+	0.894846i	$0.647285\pi$
$68$	−4.84113	−0.587074
$69$	0.642796	0.0773835
$70$	0.282654	0.0337837
$71$	8.12634	0.964419	0.482209	−	0.876056i	$-0.339834\pi$
$71$	8.12634	0.964419	0.482209	+	0.876056i	$0.339834\pi$
$72$	1.12718	0.132840
$73$	−12.3717	−1.44800	−0.724000	−	0.689800i	$-0.757698\pi$
$73$	−12.3717	−1.44800	−0.724000	+	0.689800i	$0.757698\pi$
$74$	6.55413	0.761903
$75$	6.78049	0.782943
$76$	−8.22828	−0.943848
$77$	−2.12022	−0.241621
$78$	−3.16637	−0.358521
$79$	−10.9580	−1.23287	−0.616435	−	0.787405i	$-0.711424\pi$
$79$	−10.9580	−1.23287	−0.616435	+	0.787405i	$0.711424\pi$
$80$	0.212949	0.0238084
$81$	−4.34791	−0.483101
$82$	2.29950	0.253938
$83$	16.1285	1.77033	0.885167	−	0.465274i	$-0.154044\pi$
$83$	16.1285	1.77033	0.885167	+	0.465274i	$0.154044\pi$
$84$	1.81647	0.198193
$85$	−1.03091	−0.111818
$86$	−2.17849	−0.234913
$87$	−4.22219	−0.452666
$88$	−1.59735	−0.170278
$89$	−16.5138	−1.75045	−0.875227	−	0.483712i	$-0.839288\pi$
$89$	−16.5138	−1.75045	−0.875227	+	0.483712i	$0.839288\pi$
$90$	0.240032	0.0253016
$91$	3.07111	0.321940
$92$	−0.469705	−0.0489701
$93$	11.6028	1.20315
$94$	7.41710	0.765015
$95$	−1.75220	−0.179772
$96$	1.36851	0.139673
$97$	19.4801	1.97791	0.988953	−	0.148227i	$-0.0473565\pi$
$97$	19.4801	1.97791	0.988953	+	0.148227i	$0.0473565\pi$
$98$	5.23818	0.529136
$99$	−1.80050	−0.180957
$100$	−4.95465	−0.495465
$101$	−11.9934	−1.19339	−0.596693	−	0.802470i	$-0.703519\pi$
$101$	−11.9934	−1.19339	−0.596693	+	0.802470i	$0.703519\pi$
$102$	−6.62514	−0.655986
$103$	−10.9104	−1.07504	−0.537518	−	0.843252i	$-0.680638\pi$
$103$	−10.9104	−1.07504	−0.537518	+	0.843252i	$0.680638\pi$
$104$	2.31374	0.226881
$105$	0.386815	0.0377493
$106$	−12.4867	−1.21282
$107$	2.92538	0.282807	0.141403	−	0.989952i	$-0.454839\pi$
$107$	2.92538	0.282807	0.141403	+	0.989952i	$0.454839\pi$
$108$	5.64809	0.543487
$109$	7.24929	0.694356	0.347178	−	0.937799i	$-0.387140\pi$
$109$	7.24929	0.694356	0.347178	+	0.937799i	$0.387140\pi$
$110$	−0.340153	−0.0324323
$111$	8.96939	0.851337
$112$	−1.32734	−0.125421
$113$	−13.7018	−1.28895	−0.644477	−	0.764623i	$-0.722925\pi$
$113$	−13.7018	−1.28895	−0.644477	+	0.764623i	$0.722925\pi$
$114$	−11.2605	−1.05464
$115$	−0.100023	−0.00932719
$116$	3.08525	0.286458
$117$	2.60801	0.241110
$118$	−0.0533622	−0.00491238
$119$	6.42581	0.589053
$120$	0.291422	0.0266031
$121$	−8.44848	−0.768043
$122$	−13.7078	−1.24104
$123$	3.14689	0.283746
$124$	−8.47839	−0.761382
$125$	−2.11983	−0.189603
$126$	−1.49615	−0.133288
$127$	21.9647	1.94905	0.974524	−	0.224282i	$-0.0720036\pi$
$127$	21.9647	1.94905	0.974524	+	0.224282i	$0.0720036\pi$
$128$	−1.00000	−0.0883883
$129$	−2.98129	−0.262488
$130$	0.492708	0.0432133
$131$	−0.121567	−0.0106214	−0.00531069	−	0.999986i	$-0.501690\pi$
$131$	−0.121567	−0.0106214	−0.00531069	+	0.999986i	$0.501690\pi$
$132$	−2.18599	−0.190266
$133$	10.9217	0.947031
$134$	7.30748	0.631270
$135$	1.20275	0.103516
$136$	4.84113	0.415124
$137$	23.1207	1.97534	0.987668	−	0.156561i	$-0.0500409\pi$
$137$	23.1207	1.97534	0.987668	+	0.156561i	$0.0500409\pi$
$138$	−0.642796	−0.0547184
$139$	15.7535	1.33619	0.668097	−	0.744074i	$-0.267109\pi$
$139$	15.7535	1.33619	0.668097	+	0.744074i	$0.267109\pi$
$140$	−0.282654	−0.0238887
$141$	10.1504	0.854815
$142$	−8.12634	−0.681947
$143$	−3.69585	−0.309063
$144$	−1.12718	−0.0939319
$145$	0.656999	0.0545608
$146$	12.3717	1.02389
$147$	7.16850	0.591248
$148$	−6.55413	−0.538746
$149$	−22.8646	−1.87314	−0.936571	−	0.350478i	$-0.886019\pi$
$149$	−22.8646	−1.87314	−0.936571	+	0.350478i	$0.886019\pi$
$150$	−6.78049	−0.553625
$151$	−23.2458	−1.89172	−0.945858	−	0.324580i	$-0.894777\pi$
$151$	−23.2458	−1.89172	−0.945858	+	0.324580i	$0.894777\pi$
$152$	8.22828	0.667401
$153$	5.45684	0.441160
$154$	2.12022	0.170852
$155$	−1.80546	−0.145018
$156$	3.16637	0.253513
$157$	8.91507	0.711500	0.355750	−	0.934581i	$-0.384225\pi$
$157$	8.91507	0.711500	0.355750	+	0.934581i	$0.384225\pi$
$158$	10.9580	0.871771
$159$	−17.0882	−1.35518
$160$	−0.212949	−0.0168351
$161$	0.623456	0.0491353
$162$	4.34791	0.341604
$163$	1.98060	0.155133	0.0775663	−	0.996987i	$-0.475285\pi$
$163$	1.98060	0.155133	0.0775663	+	0.996987i	$0.475285\pi$
$164$	−2.29950	−0.179561
$165$	−0.465503	−0.0362393
$166$	−16.1285	−1.25182
$167$	−16.9030	−1.30799	−0.653996	−	0.756498i	$-0.726909\pi$
$167$	−16.9030	−1.30799	−0.653996	+	0.756498i	$0.726909\pi$
$168$	−1.81647	−0.140144
$169$	−7.64661	−0.588201
$170$	1.03091	0.0790674
$171$	9.27477	0.709259
$172$	2.17849	0.166109
$173$	−16.0351	−1.21912	−0.609562	−	0.792738i	$-0.708655\pi$
$173$	−16.0351	−1.21912	−0.609562	+	0.792738i	$0.708655\pi$
$174$	4.22219	0.320083
$175$	6.57649	0.497136
$176$	1.59735	0.120405
$177$	−0.0730266	−0.00548902
$178$	16.5138	1.23776
$179$	20.3378	1.52012	0.760059	−	0.649854i	$-0.225170\pi$
$179$	20.3378	1.52012	0.760059	+	0.649854i	$0.225170\pi$
$180$	−0.240032	−0.0178909
$181$	26.2606	1.95194	0.975969	−	0.217910i	$-0.0699239\pi$
$181$	26.2606	1.95194	0.975969	+	0.217910i	$0.0699239\pi$
$182$	−3.07111	−0.227646
$183$	−18.7592	−1.38672
$184$	0.469705	0.0346271
$185$	−1.39569	−0.102613
$186$	−11.6028	−0.850755
$187$	−7.73298	−0.565492
$188$	−7.41710	−0.540947
$189$	−7.49691	−0.545320
$190$	1.75220	0.127118
$191$	12.1112	0.876335	0.438168	−	0.898893i	$-0.355628\pi$
$191$	12.1112	0.876335	0.438168	+	0.898893i	$0.355628\pi$
$192$	−1.36851	−0.0987636
$193$	3.28598	0.236530	0.118265	−	0.992982i	$-0.462267\pi$
$193$	3.28598	0.236530	0.118265	+	0.992982i	$0.462267\pi$
$194$	−19.4801	−1.39859
$195$	0.674275	0.0482858
$196$	−5.23818	−0.374156
$197$	−11.0590	−0.787922	−0.393961	−	0.919127i	$-0.628895\pi$
$197$	−11.0590	−0.787922	−0.393961	+	0.919127i	$0.628895\pi$
$198$	1.80050	0.127956
$199$	−1.20854	−0.0856714	−0.0428357	−	0.999082i	$-0.513639\pi$
$199$	−1.20854	−0.0856714	−0.0428357	+	0.999082i	$0.513639\pi$
$200$	4.95465	0.350347
$201$	10.0004	0.705371
$202$	11.9934	0.843851
$203$	−4.09516	−0.287424
$204$	6.62514	0.463852
$205$	−0.489676	−0.0342004
$206$	10.9104	0.760165
$207$	0.529443	0.0367988
$208$	−2.31374	−0.160429
$209$	−13.1434	−0.909150
$210$	−0.386815	−0.0266928
$211$	−6.82828	−0.470078	−0.235039	−	0.971986i	$-0.575522\pi$
$211$	−6.82828	−0.470078	−0.235039	+	0.971986i	$0.575522\pi$
$212$	12.4867	0.857591
$213$	−11.1210	−0.761996
$214$	−2.92538	−0.199975
$215$	0.463907	0.0316382
$216$	−5.64809	−0.384304
$217$	11.2537	0.763949
$218$	−7.24929	−0.490984
$219$	16.9308	1.14408
$220$	0.340153	0.0229331
$221$	11.2011	0.753469
$222$	−8.96939	−0.601986
$223$	−16.7584	−1.12222	−0.561111	−	0.827740i	$-0.689626\pi$
$223$	−16.7584	−1.12222	−0.561111	+	0.827740i	$0.689626\pi$
$224$	1.32734	0.0886864
$225$	5.58480	0.372320
$226$	13.7018	0.911429
$227$	−2.96896	−0.197057	−0.0985283	−	0.995134i	$-0.531413\pi$
$227$	−2.96896	−0.197057	−0.0985283	+	0.995134i	$0.531413\pi$
$228$	11.2605	0.745743
$229$	−18.2340	−1.20493	−0.602467	−	0.798144i	$-0.705815\pi$
$229$	−18.2340	−1.20493	−0.602467	+	0.798144i	$0.705815\pi$
$230$	0.100023	0.00659532
$231$	2.90154	0.190907
$232$	−3.08525	−0.202556
$233$	−13.4222	−0.879314	−0.439657	−	0.898166i	$-0.644900\pi$
$233$	−13.4222	−0.879314	−0.439657	+	0.898166i	$0.644900\pi$
$234$	−2.60801	−0.170491
$235$	−1.57946	−0.103033
$236$	0.0533622	0.00347358
$237$	14.9961	0.974103
$238$	−6.42581	−0.416524
$239$	−3.54010	−0.228990	−0.114495	−	0.993424i	$-0.536525\pi$
$239$	−3.54010	−0.228990	−0.114495	+	0.993424i	$0.536525\pi$
$240$	−0.291422	−0.0188112
$241$	2.91480	0.187759	0.0938795	−	0.995584i	$-0.470073\pi$
$241$	2.91480	0.187759	0.0938795	+	0.995584i	$0.470073\pi$
$242$	8.44848	0.543089
$243$	−10.9941	−0.705272
$244$	13.7078	0.877551
$245$	−1.11546	−0.0712643
$246$	−3.14689	−0.200638
$247$	19.0381	1.21137
$248$	8.47839	0.538378
$249$	−22.0720	−1.39876
$250$	2.11983	0.134070
$251$	−27.7956	−1.75444	−0.877222	−	0.480085i	$-0.840606\pi$
$251$	−27.7956	−1.75444	−0.877222	+	0.480085i	$0.840606\pi$
$252$	1.49615	0.0942486
$253$	−0.750283	−0.0471699
$254$	−21.9647	−1.37819
$255$	1.41081	0.0883486
$256$	1.00000	0.0625000
$257$	1.02652	0.0640323	0.0320162	−	0.999487i	$-0.489807\pi$
$257$	1.02652	0.0640323	0.0320162	+	0.999487i	$0.489807\pi$
$258$	2.98129	0.185607
$259$	8.69954	0.540563
$260$	−0.492708	−0.0305564
$261$	−3.47763	−0.215260
$262$	0.121567	0.00751045
$263$	−0.598797	−0.0369234	−0.0184617	−	0.999830i	$-0.505877\pi$
$263$	−0.598797	−0.0369234	−0.0184617	+	0.999830i	$0.505877\pi$
$264$	2.18599	0.134538
$265$	2.65903	0.163343
$266$	−10.9217	−0.669652
$267$	22.5992	1.38305
$268$	−7.30748	−0.446376
$269$	18.3297	1.11758	0.558790	−	0.829309i	$-0.311266\pi$
$269$	18.3297	1.11758	0.558790	+	0.829309i	$0.311266\pi$
$270$	−1.20275	−0.0731972
$271$	17.5748	1.06759	0.533797	−	0.845613i	$-0.320765\pi$
$271$	17.5748	1.06759	0.533797	+	0.845613i	$0.320765\pi$
$272$	−4.84113	−0.293537
$273$	−4.20284	−0.254368
$274$	−23.1207	−1.39677
$275$	−7.91431	−0.477251
$276$	0.642796	0.0386917
$277$	12.6741	0.761514	0.380757	−	0.924675i	$-0.375663\pi$
$277$	12.6741	0.761514	0.380757	+	0.924675i	$0.375663\pi$
$278$	−15.7535	−0.944831
$279$	9.55669	0.572144
$280$	0.282654	0.0168918
$281$	8.57436	0.511503	0.255752	−	0.966742i	$-0.417677\pi$
$281$	8.57436	0.511503	0.255752	+	0.966742i	$0.417677\pi$
$282$	−10.1504	−0.604445
$283$	30.4095	1.80766	0.903829	−	0.427894i	$-0.140744\pi$
$283$	30.4095	1.80766	0.903829	+	0.427894i	$0.140744\pi$
$284$	8.12634	0.482209
$285$	2.39790	0.142039
$286$	3.69585	0.218540
$287$	3.05221	0.180166
$288$	1.12718	0.0664199
$289$	6.43658	0.378623
$290$	−0.656999	−0.0385803
$291$	−26.6587	−1.56276
$292$	−12.3717	−0.724000
$293$	7.72776	0.451461	0.225730	−	0.974190i	$-0.427523\pi$
$293$	7.72776	0.451461	0.225730	+	0.974190i	$0.427523\pi$
$294$	−7.16850	−0.418075
$295$	0.0113634	0.000661603 0
$296$	6.55413	0.380951
$297$	9.02197	0.523508
$298$	22.8646	1.32451
$299$	1.08678	0.0628498
$300$	6.78049	0.391472
$301$	−2.89159	−0.166669
$302$	23.2458	1.33765
$303$	16.4131	0.942905
$304$	−8.22828	−0.471924
$305$	2.91905	0.167145
$306$	−5.45684	−0.311947
$307$	−2.21630	−0.126491	−0.0632456	−	0.997998i	$-0.520145\pi$
$307$	−2.21630	−0.126491	−0.0632456	+	0.997998i	$0.520145\pi$
$308$	−2.12022	−0.120811
$309$	14.9310	0.849395
$310$	1.80546	0.102543
$311$	−6.71998	−0.381055	−0.190527	−	0.981682i	$-0.561020\pi$
$311$	−6.71998	−0.381055	−0.190527	+	0.981682i	$0.561020\pi$
$312$	−3.16637	−0.179261
$313$	17.4062	0.983858	0.491929	−	0.870635i	$-0.336292\pi$
$313$	17.4062	0.983858	0.491929	+	0.870635i	$0.336292\pi$
$314$	−8.91507	−0.503107
$315$	0.318603	0.0179513
$316$	−10.9580	−0.616435
$317$	1.59302	0.0894731	0.0447365	−	0.998999i	$-0.485755\pi$
$317$	1.59302	0.0894731	0.0447365	+	0.998999i	$0.485755\pi$
$318$	17.0882	0.958258
$319$	4.92821	0.275927
$320$	0.212949	0.0119042
$321$	−4.00341	−0.223448
$322$	−0.623456	−0.0347439
$323$	39.8342	2.21643
$324$	−4.34791	−0.241551
$325$	11.4638	0.635896
$326$	−1.98060	−0.109695
$327$	−9.92072	−0.548617
$328$	2.29950	0.126969
$329$	9.84498	0.542771
$330$	0.465503	0.0256251
$331$	−12.6917	−0.697597	−0.348798	−	0.937198i	$-0.613410\pi$
$331$	−12.6917	−0.697597	−0.348798	+	0.937198i	$0.613410\pi$
$332$	16.1285	0.885167
$333$	7.38770	0.404844
$334$	16.9030	0.924890
$335$	−1.55612	−0.0850198
$336$	1.81647	0.0990967
$337$	8.43182	0.459310	0.229655	−	0.973272i	$-0.426240\pi$
$337$	8.43182	0.459310	0.229655	+	0.973272i	$0.426240\pi$
$338$	7.64661	0.415921
$339$	18.7510	1.01842
$340$	−1.03091	−0.0559091
$341$	−13.5429	−0.733392
$342$	−9.27477	−0.501522
$343$	16.2442	0.877103
$344$	−2.17849	−0.117457
$345$	0.136882	0.00736950
$346$	16.0351	0.862051
$347$	30.1133	1.61657	0.808285	−	0.588792i	$-0.200396\pi$
$347$	30.1133	1.61657	0.808285	+	0.588792i	$0.200396\pi$
$348$	−4.22219	−0.226333
$349$	−29.5639	−1.58252	−0.791261	−	0.611479i	$-0.790575\pi$
$349$	−29.5639	−1.58252	−0.791261	+	0.611479i	$0.790575\pi$
$350$	−6.57649	−0.351528
$351$	−13.0682	−0.697529
$352$	−1.59735	−0.0851390
$353$	−25.6827	−1.36695	−0.683477	−	0.729972i	$-0.739533\pi$
$353$	−25.6827	−1.36695	−0.683477	+	0.729972i	$0.739533\pi$
$354$	0.0730266	0.00388132
$355$	1.73049	0.0918450
$356$	−16.5138	−0.875227
$357$	−8.79379	−0.465417
$358$	−20.3378	−1.07489
$359$	−0.830194	−0.0438160	−0.0219080	−	0.999760i	$-0.506974\pi$
$359$	−0.830194	−0.0438160	−0.0219080	+	0.999760i	$0.506974\pi$
$360$	0.240032	0.0126508
$361$	48.7046	2.56340
$362$	−26.2606	−1.38023
$363$	11.5618	0.606838
$364$	3.07111	0.160970
$365$	−2.63454	−0.137898
$366$	18.7592	0.980561
$367$	8.82226	0.460518	0.230259	−	0.973129i	$-0.426043\pi$
$367$	8.82226	0.460518	0.230259	+	0.973129i	$0.426043\pi$
$368$	−0.469705	−0.0244851
$369$	2.59196	0.134932
$370$	1.39569	0.0725587
$371$	−16.5741	−0.860483
$372$	11.6028	0.601575
$373$	−22.0294	−1.14064	−0.570319	−	0.821423i	$-0.693180\pi$
$373$	−22.0294	−1.14064	−0.570319	+	0.821423i	$0.693180\pi$
$374$	7.73298	0.399863
$375$	2.90101	0.149807
$376$	7.41710	0.382508
$377$	−7.13846	−0.367649
$378$	7.49691	0.385600
$379$	−1.91057	−0.0981395	−0.0490698	−	0.998795i	$-0.515626\pi$
$379$	−1.91057	−0.0981395	−0.0490698	+	0.998795i	$0.515626\pi$
$380$	−1.75220	−0.0898860
$381$	−30.0588	−1.53996
$382$	−12.1112	−0.619663
$383$	16.9908	0.868188	0.434094	−	0.900868i	$-0.357069\pi$
$383$	16.9908	0.868188	0.434094	+	0.900868i	$0.357069\pi$
$384$	1.36851	0.0698364
$385$	−0.451498	−0.0230105
$386$	−3.28598	−0.167252
$387$	−2.45556	−0.124823
$388$	19.4801	0.988953
$389$	−33.6393	−1.70558	−0.852791	−	0.522252i	$-0.825092\pi$
$389$	−33.6393	−1.70558	−0.852791	+	0.522252i	$0.825092\pi$
$390$	−0.674275	−0.0341432
$391$	2.27390	0.114996
$392$	5.23818	0.264568
$393$	0.166366	0.00839205
$394$	11.0590	0.557145
$395$	−2.33349	−0.117411
$396$	−1.80050	−0.0904787
$397$	2.77808	0.139428	0.0697140	−	0.997567i	$-0.477791\pi$
$397$	2.77808	0.139428	0.0697140	+	0.997567i	$0.477791\pi$
$398$	1.20854	0.0605789
$399$	−14.9464	−0.748258
$400$	−4.95465	−0.247733
$401$	−11.8701	−0.592765	−0.296382	−	0.955069i	$-0.595780\pi$
$401$	−11.8701	−0.592765	−0.296382	+	0.955069i	$0.595780\pi$
$402$	−10.0004	−0.498772
$403$	19.6168	0.977182
$404$	−11.9934	−0.596693
$405$	−0.925882	−0.0460074
$406$	4.09516	0.203239
$407$	−10.4692	−0.518941
$408$	−6.62514	−0.327993
$409$	−29.3187	−1.44972	−0.724859	−	0.688897i	$-0.758095\pi$
$409$	−29.3187	−1.44972	−0.724859	+	0.688897i	$0.758095\pi$
$410$	0.489676	0.0241834
$411$	−31.6409	−1.56073
$412$	−10.9104	−0.537518
$413$	−0.0708295	−0.00348529
$414$	−0.529443	−0.0260207
$415$	3.43454	0.168595
$416$	2.31374	0.113440
$417$	−21.5588	−1.05574
$418$	13.1434	0.642866
$419$	14.1194	0.689777	0.344889	−	0.938644i	$-0.387917\pi$
$419$	14.1194	0.689777	0.344889	+	0.938644i	$0.387917\pi$
$420$	0.386815	0.0188746
$421$	27.4877	1.33967	0.669834	−	0.742511i	$-0.266365\pi$
$421$	27.4877	1.33967	0.669834	+	0.742511i	$0.266365\pi$
$422$	6.82828	0.332395
$423$	8.36042	0.406498
$424$	−12.4867	−0.606409
$425$	23.9861	1.16350
$426$	11.1210	0.538813
$427$	−18.1948	−0.880510
$428$	2.92538	0.141403
$429$	5.05781	0.244193
$430$	−0.463907	−0.0223716
$431$	12.7215	0.612771	0.306386	−	0.951907i	$-0.400880\pi$
$431$	12.7215	0.612771	0.306386	+	0.951907i	$0.400880\pi$
$432$	5.64809	0.271744
$433$	−27.8917	−1.34039	−0.670195	−	0.742185i	$-0.733790\pi$
$433$	−27.8917	−1.34039	−0.670195	+	0.742185i	$0.733790\pi$
$434$	−11.2537	−0.540194
$435$	−0.899109	−0.0431090
$436$	7.24929	0.347178
$437$	3.86486	0.184881
$438$	−16.9308	−0.808985
$439$	−3.70196	−0.176685	−0.0883425	−	0.996090i	$-0.528157\pi$
$439$	−3.70196	−0.176685	−0.0883425	+	0.996090i	$0.528157\pi$
$440$	−0.340153	−0.0162162
$441$	5.90438	0.281161
$442$	−11.2011	−0.532783
$443$	27.9384	1.32739	0.663696	−	0.748003i	$-0.268987\pi$
$443$	27.9384	1.32739	0.663696	+	0.748003i	$0.268987\pi$
$444$	8.96939	0.425669
$445$	−3.51658	−0.166702
$446$	16.7584	0.793531
$447$	31.2904	1.47999
$448$	−1.32734	−0.0627107
$449$	30.4436	1.43672	0.718361	−	0.695671i	$-0.244893\pi$
$449$	30.4436	1.43672	0.718361	+	0.695671i	$0.244893\pi$
$450$	−5.58480	−0.263270
$451$	−3.67311	−0.172960
$452$	−13.7018	−0.644477
$453$	31.8121	1.49466
$454$	2.96896	0.139340
$455$	0.653989	0.0306595
$456$	−11.2605	−0.527320
$457$	34.7731	1.62662	0.813308	−	0.581833i	$-0.197664\pi$
$457$	34.7731	1.62662	0.813308	+	0.581833i	$0.197664\pi$
$458$	18.2340	0.852017
$459$	−27.3432	−1.27627
$460$	−0.100023	−0.00466360
$461$	−17.3257	−0.806936	−0.403468	−	0.914994i	$-0.632195\pi$
$461$	−17.3257	−0.806936	−0.403468	+	0.914994i	$0.632195\pi$
$462$	−2.90154	−0.134992
$463$	12.9817	0.603311	0.301655	−	0.953417i	$-0.402461\pi$
$463$	12.9817	0.603311	0.301655	+	0.953417i	$0.402461\pi$
$464$	3.08525	0.143229
$465$	2.47079	0.114580
$466$	13.4222	0.621769
$467$	13.0650	0.604575	0.302288	−	0.953217i	$-0.402250\pi$
$467$	13.0650	0.604575	0.302288	+	0.953217i	$0.402250\pi$
$468$	2.60801	0.120555
$469$	9.69949	0.447881
$470$	1.57946	0.0728551
$471$	−12.2004	−0.562163
$472$	−0.0533622	−0.00245619
$473$	3.47981	0.160002
$474$	−14.9961	−0.688795
$475$	40.7683	1.87058
$476$	6.42581	0.294527
$477$	−14.0748	−0.644441
$478$	3.54010	0.161921
$479$	−27.7403	−1.26749	−0.633744	−	0.773543i	$-0.718483\pi$
$479$	−27.7403	−1.26749	−0.633744	+	0.773543i	$0.718483\pi$
$480$	0.291422	0.0133015
$481$	15.1646	0.691444
$482$	−2.91480	−0.132766
$483$	−0.853206	−0.0388222
$484$	−8.44848	−0.384022
$485$	4.14827	0.188363
$486$	10.9941	0.498703
$487$	3.52972	0.159947	0.0799735	−	0.996797i	$-0.474516\pi$
$487$	3.52972	0.159947	0.0799735	+	0.996797i	$0.474516\pi$
$488$	−13.7078	−0.620522
$489$	−2.71047	−0.122572
$490$	1.11546	0.0503915
$491$	14.8014	0.667976	0.333988	−	0.942577i	$-0.391605\pi$
$491$	14.8014	0.667976	0.333988	+	0.942577i	$0.391605\pi$
$492$	3.14689	0.141873
$493$	−14.9361	−0.672688
$494$	−19.0381	−0.856564
$495$	−0.383415	−0.0172332
$496$	−8.47839	−0.380691
$497$	−10.7864	−0.483835
$498$	22.0720	0.989071
$499$	1.23371	0.0552284	0.0276142	−	0.999619i	$-0.491209\pi$
$499$	1.23371	0.0552284	0.0276142	+	0.999619i	$0.491209\pi$
$500$	−2.11983	−0.0948017
$501$	23.1319	1.03346
$502$	27.7956	1.24058
$503$	35.4151	1.57908	0.789541	−	0.613698i	$-0.210319\pi$
$503$	35.4151	1.57908	0.789541	+	0.613698i	$0.210319\pi$
$504$	−1.49615	−0.0666438
$505$	−2.55397	−0.113650
$506$	0.750283	0.0333541
$507$	10.4645	0.464743
$508$	21.9647	0.974524
$509$	−0.506715	−0.0224597	−0.0112299	−	0.999937i	$-0.503575\pi$
$509$	−0.506715	−0.0224597	−0.0112299	+	0.999937i	$0.503575\pi$
$510$	−1.41081	−0.0624719
$511$	16.4214	0.726441
$512$	−1.00000	−0.0441942
$513$	−46.4740	−2.05188
$514$	−1.02652	−0.0452777
$515$	−2.32336	−0.102379
$516$	−2.98129	−0.131244
$517$	−11.8477	−0.521061
$518$	−8.69954	−0.382236
$519$	21.9441	0.963241
$520$	0.492708	0.0216067
$521$	−11.9110	−0.521828	−0.260914	−	0.965362i	$-0.584024\pi$
$521$	−11.9110	−0.521828	−0.260914	+	0.965362i	$0.584024\pi$
$522$	3.47763	0.152212
$523$	19.4557	0.850739	0.425370	−	0.905020i	$-0.360144\pi$
$523$	19.4557	0.850739	0.425370	+	0.905020i	$0.360144\pi$
$524$	−0.121567	−0.00531069
$525$	−8.99999	−0.392792
$526$	0.598797	0.0261088
$527$	41.0450	1.78795
$528$	−2.18599	−0.0951329
$529$	−22.7794	−0.990408
$530$	−2.65903	−0.115501
$531$	−0.0601489	−0.00261024
$532$	10.9217	0.473515
$533$	5.32045	0.230454
$534$	−22.5992	−0.977964
$535$	0.622955	0.0269327
$536$	7.30748	0.315635
$537$	−27.8324	−1.20106
$538$	−18.3297	−0.790248
$539$	−8.36720	−0.360401
$540$	1.20275	0.0517582
$541$	−17.0750	−0.734110	−0.367055	−	0.930199i	$-0.619634\pi$
$541$	−17.0750	−0.734110	−0.367055	+	0.930199i	$0.619634\pi$
$542$	−17.5748	−0.754902
$543$	−35.9379	−1.54224
$544$	4.84113	0.207562
$545$	1.54373	0.0661259
$546$	4.20284	0.179865
$547$	24.8608	1.06297	0.531486	−	0.847067i	$-0.321634\pi$
$547$	24.8608	1.06297	0.531486	+	0.847067i	$0.321634\pi$
$548$	23.1207	0.987668
$549$	−15.4512	−0.659440
$550$	7.91431	0.337467
$551$	−25.3863	−1.08149
$552$	−0.642796	−0.0273592
$553$	14.5449	0.618514
$554$	−12.6741	−0.538472
$555$	1.91002	0.0810758
$556$	15.7535	0.668097
$557$	24.8157	1.05148	0.525738	−	0.850647i	$-0.323789\pi$
$557$	24.8157	1.05148	0.525738	+	0.850647i	$0.323789\pi$
$558$	−9.55669	−0.404567
$559$	−5.04047	−0.213189
$560$	−0.282654	−0.0119443
$561$	10.5827	0.446800
$562$	−8.57436	−0.361688
$563$	−30.3439	−1.27884	−0.639421	−	0.768857i	$-0.720826\pi$
$563$	−30.3439	−1.27884	−0.639421	+	0.768857i	$0.720826\pi$
$564$	10.1504	0.427407
$565$	−2.91777	−0.122752
$566$	−30.4095	−1.27821
$567$	5.77114	0.242365
$568$	−8.12634	−0.340974
$569$	19.2409	0.806622	0.403311	−	0.915063i	$-0.367859\pi$
$569$	19.2409	0.806622	0.403311	+	0.915063i	$0.367859\pi$
$570$	−2.39790	−0.100437
$571$	30.6273	1.28171	0.640856	−	0.767661i	$-0.278580\pi$
$571$	30.6273	1.28171	0.640856	+	0.767661i	$0.278580\pi$
$572$	−3.69585	−0.154531
$573$	−16.5743	−0.692401
$574$	−3.05221	−0.127397
$575$	2.32722	0.0970520
$576$	−1.12718	−0.0469659
$577$	−35.5743	−1.48098	−0.740489	−	0.672069i	$-0.765406\pi$
$577$	−35.5743	−1.48098	−0.740489	+	0.672069i	$0.765406\pi$
$578$	−6.43658	−0.267727
$579$	−4.49690	−0.186885
$580$	0.656999	0.0272804
$581$	−21.4080	−0.888152
$582$	26.6587	1.10504
$583$	19.9456	0.826064
$584$	12.3717	0.511945
$585$	0.555372	0.0229618
$586$	−7.72776	−0.319231
$587$	−8.51897	−0.351615	−0.175808	−	0.984425i	$-0.556254\pi$
$587$	−8.51897	−0.351615	−0.175808	+	0.984425i	$0.556254\pi$
$588$	7.16850	0.295624
$589$	69.7625	2.87452
$590$	−0.0113634	−0.000467824 0
$591$	15.1344	0.622544
$592$	−6.55413	−0.269373
$593$	30.1908	1.23979	0.619894	−	0.784686i	$-0.287176\pi$
$593$	30.1908	1.23979	0.619894	+	0.784686i	$0.287176\pi$
$594$	−9.02197	−0.370176
$595$	1.36837	0.0560976
$596$	−22.8646	−0.936571
$597$	1.65390	0.0676898
$598$	−1.08678	−0.0444415
$599$	15.0961	0.616811	0.308406	−	0.951255i	$-0.400205\pi$
$599$	15.0961	0.616811	0.308406	+	0.951255i	$0.400205\pi$
$600$	−6.78049	−0.276812
$601$	28.8593	1.17719	0.588597	−	0.808426i	$-0.299680\pi$
$601$	28.8593	1.17719	0.588597	+	0.808426i	$0.299680\pi$
$602$	2.89159	0.117853
$603$	8.23687	0.335431
$604$	−23.2458	−0.945858
$605$	−1.79909	−0.0731435
$606$	−16.4131	−0.666735
$607$	9.16150	0.371854	0.185927	−	0.982564i	$-0.440471\pi$
$607$	9.16150	0.371854	0.185927	+	0.982564i	$0.440471\pi$
$608$	8.22828	0.333701
$609$	5.60426	0.227096
$610$	−2.91905	−0.118189
$611$	17.1612	0.694269
$612$	5.45684	0.220580
$613$	2.16048	0.0872611	0.0436306	−	0.999048i	$-0.486108\pi$
$613$	2.16048	0.0872611	0.0436306	+	0.999048i	$0.486108\pi$
$614$	2.21630	0.0894427
$615$	0.670126	0.0270221
$616$	2.12022	0.0854261
$617$	−23.7583	−0.956473	−0.478237	−	0.878231i	$-0.658724\pi$
$617$	−23.7583	−0.956473	−0.478237	+	0.878231i	$0.658724\pi$
$618$	−14.9310	−0.600613
$619$	−4.30994	−0.173231	−0.0866156	−	0.996242i	$-0.527605\pi$
$619$	−4.30994	−0.173231	−0.0866156	+	0.996242i	$0.527605\pi$
$620$	−1.80546	−0.0725091
$621$	−2.65293	−0.106459
$622$	6.71998	0.269447
$623$	21.9193	0.878179
$624$	3.16637	0.126756
$625$	24.3218	0.972874
$626$	−17.4062	−0.695692
$627$	17.9869	0.718328
$628$	8.91507	0.355750
$629$	31.7294	1.26514
$630$	−0.318603	−0.0126935
$631$	6.72469	0.267706	0.133853	−	0.991001i	$-0.457265\pi$
$631$	6.72469	0.267706	0.133853	+	0.991001i	$0.457265\pi$
$632$	10.9580	0.435886
$633$	9.34456	0.371413
$634$	−1.59302	−0.0632670
$635$	4.67734	0.185615
$636$	−17.0882	−0.677591
$637$	12.1198	0.480203
$638$	−4.92821	−0.195110
$639$	−9.15987	−0.362359
$640$	−0.212949	−0.00841753
$641$	20.9917	0.829123	0.414562	−	0.910021i	$-0.363935\pi$
$641$	20.9917	0.829123	0.414562	+	0.910021i	$0.363935\pi$
$642$	4.00341	0.158002
$643$	1.97112	0.0777335	0.0388668	−	0.999244i	$-0.487625\pi$
$643$	1.97112	0.0777335	0.0388668	+	0.999244i	$0.487625\pi$
$644$	0.623456	0.0245676
$645$	−0.634861	−0.0249976
$646$	−39.8342	−1.56726
$647$	−14.2023	−0.558351	−0.279175	−	0.960240i	$-0.590061\pi$
$647$	−14.2023	−0.558351	−0.279175	+	0.960240i	$0.590061\pi$
$648$	4.34791	0.170802
$649$	0.0852380	0.00334588
$650$	−11.4638	−0.449646
$651$	−15.4008	−0.603603
$652$	1.98060	0.0775663
$653$	38.4465	1.50453	0.752264	−	0.658862i	$-0.228962\pi$
$653$	38.4465	1.50453	0.752264	+	0.658862i	$0.228962\pi$
$654$	9.92072	0.387931
$655$	−0.0258876	−0.00101151
$656$	−2.29950	−0.0897805
$657$	13.9452	0.544053
$658$	−9.84498	−0.383797
$659$	7.31809	0.285072	0.142536	−	0.989790i	$-0.454474\pi$
$659$	7.31809	0.285072	0.142536	+	0.989790i	$0.454474\pi$
$660$	−0.465503	−0.0181197
$661$	20.9439	0.814623	0.407311	−	0.913289i	$-0.366466\pi$
$661$	20.9439	0.814623	0.407311	+	0.913289i	$0.366466\pi$
$662$	12.6917	0.493275
$663$	−15.3288	−0.595323
$664$	−16.1285	−0.625908
$665$	2.32576	0.0901891
$666$	−7.38770	−0.286268
$667$	−1.44915	−0.0561115
$668$	−16.9030	−0.653996
$669$	22.9340	0.886678
$670$	1.55612	0.0601181
$671$	21.8961	0.845290
$672$	−1.81647	−0.0700719
$673$	−6.93816	−0.267446	−0.133723	−	0.991019i	$-0.542693\pi$
$673$	−6.93816	−0.267446	−0.133723	+	0.991019i	$0.542693\pi$
$674$	−8.43182	−0.324781
$675$	−27.9843	−1.07712
$676$	−7.64661	−0.294100
$677$	1.76497	0.0678334	0.0339167	−	0.999425i	$-0.489202\pi$
$677$	1.76497	0.0678334	0.0339167	+	0.999425i	$0.489202\pi$
$678$	−18.7510	−0.720128
$679$	−25.8567	−0.992288
$680$	1.03091	0.0395337
$681$	4.06304	0.155696
$682$	13.5429	0.518586
$683$	−34.4833	−1.31947	−0.659734	−	0.751499i	$-0.729331\pi$
$683$	−34.4833	−1.31947	−0.659734	+	0.751499i	$0.729331\pi$
$684$	9.27477	0.354630
$685$	4.92353	0.188118
$686$	−16.2442	−0.620206
$687$	24.9533	0.952029
$688$	2.17849	0.0830543
$689$	−28.8910	−1.10066
$690$	−0.136882	−0.00521102
$691$	12.5047	0.475703	0.237851	−	0.971302i	$-0.423557\pi$
$691$	12.5047	0.475703	0.237851	+	0.971302i	$0.423557\pi$
$692$	−16.0351	−0.609562
$693$	2.38987	0.0907838
$694$	−30.1133	−1.14309
$695$	3.35468	0.127250
$696$	4.22219	0.160042
$697$	11.1322	0.421662
$698$	29.5639	1.11901
$699$	18.3683	0.694754
$700$	6.57649	0.248568
$701$	−26.4229	−0.997977	−0.498989	−	0.866609i	$-0.666295\pi$
$701$	−26.4229	−0.997977	−0.498989	+	0.866609i	$0.666295\pi$
$702$	13.0682	0.493228
$703$	53.9292	2.03398
$704$	1.59735	0.0602024
$705$	2.16151	0.0814070
$706$	25.6827	0.966583
$707$	15.9193	0.598705
$708$	−0.0730266	−0.00274451
$709$	17.1012	0.642248	0.321124	−	0.947037i	$-0.395939\pi$
$709$	17.1012	0.642248	0.321124	+	0.947037i	$0.395939\pi$
$710$	−1.73049	−0.0649442
$711$	12.3517	0.463224
$712$	16.5138	0.618879
$713$	3.98234	0.149140
$714$	8.79379	0.329099
$715$	−0.787026	−0.0294331
$716$	20.3378	0.760059
$717$	4.84467	0.180927
$718$	0.830194	0.0309826
$719$	32.6328	1.21700	0.608498	−	0.793555i	$-0.291772\pi$
$719$	32.6328	1.21700	0.608498	+	0.793555i	$0.291772\pi$
$720$	−0.240032	−0.00894546
$721$	14.4818	0.539330
$722$	−48.7046	−1.81260
$723$	−3.98893	−0.148350
$724$	26.2606	0.975969
$725$	−15.2863	−0.567720
$726$	−11.5618	−0.429099
$727$	26.2260	0.972669	0.486334	−	0.873773i	$-0.338334\pi$
$727$	26.2260	0.972669	0.486334	+	0.873773i	$0.338334\pi$
$728$	−3.07111	−0.113823
$729$	28.0893	1.04034
$730$	2.63454	0.0975087
$731$	−10.5464	−0.390072
$732$	−18.7592	−0.693361
$733$	−1.65934	−0.0612890	−0.0306445	−	0.999530i	$-0.509756\pi$
$733$	−1.65934	−0.0612890	−0.0306445	+	0.999530i	$0.509756\pi$
$734$	−8.82226	−0.325635
$735$	1.52652	0.0563066
$736$	0.469705	0.0173136
$737$	−11.6726	−0.429966
$738$	−2.59196	−0.0954113
$739$	17.1940	0.632490	0.316245	−	0.948678i	$-0.397578\pi$
$739$	17.1940	0.632490	0.316245	+	0.948678i	$0.397578\pi$
$740$	−1.39569	−0.0513067
$741$	−26.0538	−0.957111
$742$	16.5741	0.608453
$743$	−42.7200	−1.56725	−0.783623	−	0.621237i	$-0.786630\pi$
$743$	−42.7200	−1.56725	−0.783623	+	0.621237i	$0.786630\pi$
$744$	−11.6028	−0.425378
$745$	−4.86899	−0.178386
$746$	22.0294	0.806553
$747$	−18.1798	−0.665163
$748$	−7.73298	−0.282746
$749$	−3.88296	−0.141880
$750$	−2.90101	−0.105930
$751$	35.6088	1.29938	0.649691	−	0.760198i	$-0.274898\pi$
$751$	35.6088	1.29938	0.649691	+	0.760198i	$0.274898\pi$
$752$	−7.41710	−0.270474
$753$	38.0386	1.38620
$754$	7.13846	0.259967
$755$	−4.95016	−0.180155
$756$	−7.49691	−0.272660
$757$	−19.1034	−0.694325	−0.347163	−	0.937805i	$-0.612855\pi$
$757$	−19.1034	−0.694325	−0.347163	+	0.937805i	$0.612855\pi$
$758$	1.91057	0.0693951
$759$	1.02677	0.0372693
$760$	1.75220	0.0635590
$761$	−16.9544	−0.614595	−0.307297	−	0.951614i	$-0.599425\pi$
$761$	−16.9544	−0.614595	−0.307297	+	0.951614i	$0.599425\pi$
$762$	30.0588	1.08892
$763$	−9.62224	−0.348349
$764$	12.1112	0.438168
$765$	1.16203	0.0420132
$766$	−16.9908	−0.613902
$767$	−0.123466	−0.00445810
$768$	−1.36851	−0.0493818
$769$	34.3046	1.23705	0.618527	−	0.785763i	$-0.287730\pi$
$769$	34.3046	1.23705	0.618527	+	0.785763i	$0.287730\pi$
$770$	0.451498	0.0162708
$771$	−1.40480	−0.0505925
$772$	3.28598	0.118265
$773$	−30.5511	−1.09885	−0.549424	−	0.835544i	$-0.685153\pi$
$773$	−30.5511	−1.09885	−0.549424	+	0.835544i	$0.685153\pi$
$774$	2.45556	0.0882633
$775$	42.0075	1.50895
$776$	−19.4801	−0.699296
$777$	−11.9054	−0.427104
$778$	33.6393	1.20603
$779$	18.9209	0.677913
$780$	0.674275	0.0241429
$781$	12.9806	0.464482
$782$	−2.27390	−0.0813147
$783$	17.4257	0.622745
$784$	−5.23818	−0.187078
$785$	1.89845	0.0677587
$786$	−0.166366	−0.00593407
$787$	−12.3637	−0.440718	−0.220359	−	0.975419i	$-0.570723\pi$
$787$	−12.3637	−0.440718	−0.220359	+	0.975419i	$0.570723\pi$
$788$	−11.0590	−0.393961
$789$	0.819459	0.0291735
$790$	2.33349	0.0830219
$791$	18.1869	0.646651
$792$	1.80050	0.0639781
$793$	−31.7163	−1.12628
$794$	−2.77808	−0.0985905
$795$	−3.63891	−0.129059
$796$	−1.20854	−0.0428357
$797$	−5.47297	−0.193863	−0.0969313	−	0.995291i	$-0.530903\pi$
$797$	−5.47297	−0.193863	−0.0969313	+	0.995291i	$0.530903\pi$
$798$	14.9464	0.529098
$799$	35.9072	1.27030
$800$	4.95465	0.175173
$801$	18.6140	0.657694
$802$	11.8701	0.419148
$803$	−19.7619	−0.697384
$804$	10.0004	0.352685
$805$	0.132764	0.00467932
$806$	−19.6168	−0.690972
$807$	−25.0843	−0.883010
$808$	11.9934	0.421926
$809$	−10.8826	−0.382610	−0.191305	−	0.981531i	$-0.561272\pi$
$809$	−10.8826	−0.382610	−0.191305	+	0.981531i	$0.561272\pi$
$810$	0.925882	0.0325322
$811$	44.8545	1.57505	0.787527	−	0.616280i	$-0.211361\pi$
$811$	44.8545	1.57505	0.787527	+	0.616280i	$0.211361\pi$
$812$	−4.09516	−0.143712
$813$	−24.0513	−0.843515
$814$	10.4692	0.366947
$815$	0.421766	0.0147738
$816$	6.62514	0.231926
$817$	−17.9253	−0.627125
$818$	29.3187	1.02511
$819$	−3.46170	−0.120962
$820$	−0.489676	−0.0171002
$821$	15.4551	0.539386	0.269693	−	0.962946i	$-0.413078\pi$
$821$	15.4551	0.539386	0.269693	+	0.962946i	$0.413078\pi$
$822$	31.6409	1.10360
$823$	−47.4293	−1.65328	−0.826641	−	0.562730i	$-0.809751\pi$
$823$	−47.4293	−1.65328	−0.826641	+	0.562730i	$0.809751\pi$
$824$	10.9104	0.380082
$825$	10.8308	0.377080
$826$	0.0708295	0.00246447
$827$	21.2845	0.740133	0.370067	−	0.929005i	$-0.379335\pi$
$827$	21.2845	0.740133	0.370067	+	0.929005i	$0.379335\pi$
$828$	0.529443	0.0183994
$829$	−33.8913	−1.17709	−0.588547	−	0.808463i	$-0.700300\pi$
$829$	−33.8913	−1.17709	−0.588547	+	0.808463i	$0.700300\pi$
$830$	−3.43454	−0.119215
$831$	−17.3447	−0.601679
$832$	−2.31374	−0.0802145
$833$	25.3587	0.878628
$834$	21.5588	0.746520
$835$	−3.59946	−0.124565
$836$	−13.1434	−0.454575
$837$	−47.8867	−1.65521
$838$	−14.1194	−0.487746
$839$	−49.2777	−1.70126	−0.850628	−	0.525768i	$-0.823778\pi$
$839$	−49.2777	−1.70126	−0.850628	+	0.525768i	$0.823778\pi$
$840$	−0.386815	−0.0133464
$841$	−19.4813	−0.671768
$842$	−27.4877	−0.947288
$843$	−11.7341	−0.404144
$844$	−6.82828	−0.235039
$845$	−1.62833	−0.0560164
$846$	−8.36042	−0.287437
$847$	11.2140	0.385317
$848$	12.4867	0.428796
$849$	−41.6157	−1.42825
$850$	−23.9861	−0.822718
$851$	3.07851	0.105530
$852$	−11.1210	−0.380998
$853$	15.5553	0.532604	0.266302	−	0.963890i	$-0.414198\pi$
$853$	15.5553	0.532604	0.266302	+	0.963890i	$0.414198\pi$
$854$	18.1948	0.622615
$855$	1.97505	0.0675453
$856$	−2.92538	−0.0999874
$857$	−14.3433	−0.489957	−0.244979	−	0.969528i	$-0.578781\pi$
$857$	−14.3433	−0.489957	−0.244979	+	0.969528i	$0.578781\pi$
$858$	−5.05781	−0.172671
$859$	−36.5464	−1.24695	−0.623474	−	0.781844i	$-0.714279\pi$
$859$	−36.5464	−1.24695	−0.623474	+	0.781844i	$0.714279\pi$
$860$	0.463907	0.0158191
$861$	−4.17698	−0.142351
$862$	−12.7215	−0.433295
$863$	45.8815	1.56182	0.780912	−	0.624641i	$-0.214755\pi$
$863$	45.8815	1.56182	0.780912	+	0.624641i	$0.214755\pi$
$864$	−5.64809	−0.192152
$865$	−3.41465	−0.116101
$866$	27.8917	0.947799
$867$	−8.80853	−0.299153
$868$	11.2537	0.381975
$869$	−17.5037	−0.593774
$870$	0.899109	0.0304826
$871$	16.9076	0.572893
$872$	−7.24929	−0.245492
$873$	−21.9577	−0.743154
$874$	−3.86486	−0.130731
$875$	2.81373	0.0951213
$876$	16.9308	0.572039
$877$	−16.6677	−0.562829	−0.281414	−	0.959586i	$-0.590803\pi$
$877$	−16.6677	−0.562829	−0.281414	+	0.959586i	$0.590803\pi$
$878$	3.70196	0.124935
$879$	−10.5755	−0.356703
$880$	0.340153	0.0114666
$881$	−12.5220	−0.421878	−0.210939	−	0.977499i	$-0.567652\pi$
$881$	−12.5220	−0.421878	−0.210939	+	0.977499i	$0.567652\pi$
$882$	−5.90438	−0.198811
$883$	0.226938	0.00763708	0.00381854	−	0.999993i	$-0.498785\pi$
$883$	0.226938	0.00763708	0.00381854	+	0.999993i	$0.498785\pi$
$884$	11.2011	0.376735
$885$	−0.0155509	−0.000522738 0
$886$	−27.9384	−0.938607
$887$	5.86122	0.196801	0.0984003	−	0.995147i	$-0.468627\pi$
$887$	5.86122	0.196801	0.0984003	+	0.995147i	$0.468627\pi$
$888$	−8.96939	−0.300993
$889$	−29.1545	−0.977810
$890$	3.51658	0.117876
$891$	−6.94513	−0.232671
$892$	−16.7584	−0.561111
$893$	61.0299	2.04229
$894$	−31.2904	−1.04651
$895$	4.33090	0.144766
$896$	1.32734	0.0443432
$897$	−1.48726	−0.0496582
$898$	−30.4436	−1.01592
$899$	−26.1579	−0.872415
$900$	5.58480	0.186160
$901$	−60.4499	−2.01388
$902$	3.67311	0.122301
$903$	3.95717	0.131686
$904$	13.7018	0.455714
$905$	5.59217	0.185890
$906$	−31.8121	−1.05689
$907$	4.76302	0.158153	0.0790767	−	0.996869i	$-0.474803\pi$
$907$	4.76302	0.158153	0.0790767	+	0.996869i	$0.474803\pi$
$908$	−2.96896	−0.0985283
$909$	13.5187	0.448388
$910$	−0.653989	−0.0216795
$911$	−22.1431	−0.733633	−0.366816	−	0.930293i	$-0.619552\pi$
$911$	−22.1431	−0.733633	−0.366816	+	0.930293i	$0.619552\pi$
$912$	11.2605	0.372872
$913$	25.7629	0.852626
$914$	−34.7731	−1.15019
$915$	−3.99475	−0.132062
$916$	−18.2340	−0.602467
$917$	0.161361	0.00532860
$918$	27.3432	0.902458
$919$	−37.8376	−1.24815	−0.624073	−	0.781366i	$-0.714523\pi$
$919$	−37.8376	−1.24815	−0.624073	+	0.781366i	$0.714523\pi$
$920$	0.100023	0.00329766
$921$	3.03303	0.0999418
$922$	17.3257	0.570590
$923$	−18.8022	−0.618883
$924$	2.90154	0.0954536
$925$	32.4735	1.06772
$926$	−12.9817	−0.426605
$927$	12.2980	0.403920
$928$	−3.08525	−0.101278
$929$	−6.45709	−0.211850	−0.105925	−	0.994374i	$-0.533780\pi$
$929$	−6.45709	−0.211850	−0.105925	+	0.994374i	$0.533780\pi$
$930$	−2.47079	−0.0810204
$931$	43.1012	1.41258
$932$	−13.4222	−0.439657
$933$	9.19635	0.301075
$934$	−13.0650	−0.427499
$935$	−1.64673	−0.0538537
$936$	−2.60801	−0.0852454
$937$	−31.4042	−1.02593	−0.512965	−	0.858410i	$-0.671453\pi$
$937$	−31.4042	−1.02593	−0.512965	+	0.858410i	$0.671453\pi$
$938$	−9.69949	−0.316699
$939$	−23.8206	−0.777355
$940$	−1.57946	−0.0515163
$941$	−48.6055	−1.58449	−0.792247	−	0.610200i	$-0.791089\pi$
$941$	−48.6055	−1.58449	−0.792247	+	0.610200i	$0.791089\pi$
$942$	12.2004	0.397509
$943$	1.08009	0.0351725
$944$	0.0533622	0.00173679
$945$	−1.59646	−0.0519327
$946$	−3.47981	−0.113139
$947$	14.1094	0.458494	0.229247	−	0.973368i	$-0.426374\pi$
$947$	14.1094	0.458494	0.229247	+	0.973368i	$0.426374\pi$
$948$	14.9961	0.487051
$949$	28.6249	0.929205
$950$	−40.7683	−1.32270
$951$	−2.18007	−0.0706935
$952$	−6.42581	−0.208262
$953$	3.68347	0.119319	0.0596597	−	0.998219i	$-0.480998\pi$
$953$	3.68347	0.119319	0.0596597	+	0.998219i	$0.480998\pi$
$954$	14.0748	0.455689
$955$	2.57906	0.0834565
$956$	−3.54010	−0.114495
$957$	−6.74431	−0.218012
$958$	27.7403	0.896249
$959$	−30.6890	−0.990999
$960$	−0.291422	−0.00940561
$961$	40.8831	1.31881
$962$	−15.1646	−0.488925
$963$	−3.29744	−0.106258
$964$	2.91480	0.0938795
$965$	0.699746	0.0225256
$966$	0.853206	0.0274514
$967$	−14.7374	−0.473924	−0.236962	−	0.971519i	$-0.576152\pi$
$967$	−14.7374	−0.473924	−0.236962	+	0.971519i	$0.576152\pi$
$968$	8.44848	0.271544
$969$	−54.5135	−1.75123
$970$	−4.14827	−0.133193
$971$	10.4158	0.334259	0.167129	−	0.985935i	$-0.446550\pi$
$971$	10.4158	0.334259	0.167129	+	0.985935i	$0.446550\pi$
$972$	−10.9941	−0.352636
$973$	−20.9102	−0.670350
$974$	−3.52972	−0.113100
$975$	−15.6883	−0.502427
$976$	13.7078	0.438776
$977$	25.7260	0.823047	0.411523	−	0.911399i	$-0.364997\pi$
$977$	25.7260	0.823047	0.411523	+	0.911399i	$0.364997\pi$
$978$	2.71047	0.0866712
$979$	−26.3782	−0.843052
$980$	−1.11546	−0.0356322
$981$	−8.17127	−0.260889
$982$	−14.8014	−0.472331
$983$	22.7965	0.727095	0.363548	−	0.931576i	$-0.381565\pi$
$983$	22.7965	0.727095	0.363548	+	0.931576i	$0.381565\pi$
$984$	−3.14689	−0.100319
$985$	−2.35500	−0.0750365
$986$	14.9361	0.475662
$987$	−13.4729	−0.428849
$988$	19.0381	0.605683
$989$	−1.02325	−0.0325374
$990$	0.383415	0.0121857
$991$	56.8458	1.80577	0.902883	−	0.429886i	$-0.141446\pi$
$991$	56.8458	1.80577	0.902883	+	0.429886i	$0.141446\pi$
$992$	8.47839	0.269189
$993$	17.3687	0.551177
$994$	10.7864	0.342123
$995$	−0.257358	−0.00815879
$996$	−22.0720	−0.699379
$997$	16.0566	0.508518	0.254259	−	0.967136i	$-0.418168\pi$
$997$	16.0566	0.508518	0.254259	+	0.967136i	$0.418168\pi$
$998$	−1.23371	−0.0390524
$999$	−37.0183	−1.17121

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.c.1.18	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.c.1.18	✓	69	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:	\( N \)	\(=\)	\( 6002 = 2 \cdot 3001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.36851 q^{3} +1.00000 q^{4} +0.212949 q^{5} +1.36851 q^{6} -1.32734 q^{7} -1.00000 q^{8} -1.12718 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.36851 q^{3} +1.00000 q^{4} +0.212949 q^{5} +1.36851 q^{6} -1.32734 q^{7} -1.00000 q^{8} -1.12718 q^{9} -0.212949 q^{10} +1.59735 q^{11} -1.36851 q^{12} -2.31374 q^{13} +1.32734 q^{14} -0.291422 q^{15} +1.00000 q^{16} -4.84113 q^{17} +1.12718 q^{18} -8.22828 q^{19} +0.212949 q^{20} +1.81647 q^{21} -1.59735 q^{22} -0.469705 q^{23} +1.36851 q^{24} -4.95465 q^{25} +2.31374 q^{26} +5.64809 q^{27} -1.32734 q^{28} +3.08525 q^{29} +0.291422 q^{30} -8.47839 q^{31} -1.00000 q^{32} -2.18599 q^{33} +4.84113 q^{34} -0.282654 q^{35} -1.12718 q^{36} -6.55413 q^{37} +8.22828 q^{38} +3.16637 q^{39} -0.212949 q^{40} -2.29950 q^{41} -1.81647 q^{42} +2.17849 q^{43} +1.59735 q^{44} -0.240032 q^{45} +0.469705 q^{46} -7.41710 q^{47} -1.36851 q^{48} -5.23818 q^{49} +4.95465 q^{50} +6.62514 q^{51} -2.31374 q^{52} +12.4867 q^{53} -5.64809 q^{54} +0.340153 q^{55} +1.32734 q^{56} +11.2605 q^{57} -3.08525 q^{58} +0.0533622 q^{59} -0.291422 q^{60} +13.7078 q^{61} +8.47839 q^{62} +1.49615 q^{63} +1.00000 q^{64} -0.492708 q^{65} +2.18599 q^{66} -7.30748 q^{67} -4.84113 q^{68} +0.642796 q^{69} +0.282654 q^{70} +8.12634 q^{71} +1.12718 q^{72} -12.3717 q^{73} +6.55413 q^{74} +6.78049 q^{75} -8.22828 q^{76} -2.12022 q^{77} -3.16637 q^{78} -10.9580 q^{79} +0.212949 q^{80} -4.34791 q^{81} +2.29950 q^{82} +16.1285 q^{83} +1.81647 q^{84} -1.03091 q^{85} -2.17849 q^{86} -4.22219 q^{87} -1.59735 q^{88} -16.5138 q^{89} +0.240032 q^{90} +3.07111 q^{91} -0.469705 q^{92} +11.6028 q^{93} +7.41710 q^{94} -1.75220 q^{95} +1.36851 q^{96} +19.4801 q^{97} +5.23818 q^{98} -1.80050 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q - 69 q^{2} + 11 q^{3} + 69 q^{4} - 2 q^{5} - 11 q^{6} + 23 q^{7} - 69 q^{8} + 72 q^{9}+O(q^{10}) \) 69 * q - 69 * q^2 + 11 * q^3 + 69 * q^4 - 2 * q^5 - 11 * q^6 + 23 * q^7 - 69 * q^8 + 72 * q^9	\( 69 q - 69 q^{2} + 11 q^{3} + 69 q^{4} - 2 q^{5} - 11 q^{6} + 23 q^{7} - 69 q^{8} + 72 q^{9} + 2 q^{10} - 14 q^{11} + 11 q^{12} + 31 q^{13} - 23 q^{14} + 34 q^{15} + 69 q^{16} - 4 q^{17} - 72 q^{18} + 17 q^{19} - 2 q^{20} - 11 q^{21} + 14 q^{22} + 33 q^{23} - 11 q^{24} + 119 q^{25} - 31 q^{26} + 44 q^{27} + 23 q^{28} - 25 q^{29} - 34 q^{30} + 49 q^{31} - 69 q^{32} + 10 q^{33} + 4 q^{34} - 11 q^{35} + 72 q^{36} + 73 q^{37} - 17 q^{38} + 31 q^{39} + 2 q^{40} - 46 q^{41} + 11 q^{42} + 76 q^{43} - 14 q^{44} + 9 q^{45} - 33 q^{46} + 23 q^{47} + 11 q^{48} + 100 q^{49} - 119 q^{50} + 25 q^{51} + 31 q^{52} + 30 q^{53} - 44 q^{54} + 81 q^{55} - 23 q^{56} + 12 q^{57} + 25 q^{58} - 3 q^{59} + 34 q^{60} + 13 q^{61} - 49 q^{62} + 65 q^{63} + 69 q^{64} - 27 q^{65} - 10 q^{66} + 105 q^{67} - 4 q^{68} + 19 q^{69} + 11 q^{70} + 51 q^{71} - 72 q^{72} + 43 q^{73} - 73 q^{74} + 77 q^{75} + 17 q^{76} - 19 q^{77} - 31 q^{78} + 89 q^{79} - 2 q^{80} + 73 q^{81} + 46 q^{82} - 10 q^{83} - 11 q^{84} + 44 q^{85} - 76 q^{86} + 57 q^{87} + 14 q^{88} - 28 q^{89} - 9 q^{90} + 76 q^{91} + 33 q^{92} + 59 q^{93} - 23 q^{94} + 72 q^{95} - 11 q^{96} + 89 q^{97} - 100 q^{98} - 17 q^{99}+O(q^{100}) \) 69 * q - 69 * q^2 + 11 * q^3 + 69 * q^4 - 2 * q^5 - 11 * q^6 + 23 * q^7 - 69 * q^8 + 72 * q^9 + 2 * q^10 - 14 * q^11 + 11 * q^12 + 31 * q^13 - 23 * q^14 + 34 * q^15 + 69 * q^16 - 4 * q^17 - 72 * q^18 + 17 * q^19 - 2 * q^20 - 11 * q^21 + 14 * q^22 + 33 * q^23 - 11 * q^24 + 119 * q^25 - 31 * q^26 + 44 * q^27 + 23 * q^28 - 25 * q^29 - 34 * q^30 + 49 * q^31 - 69 * q^32 + 10 * q^33 + 4 * q^34 - 11 * q^35 + 72 * q^36 + 73 * q^37 - 17 * q^38 + 31 * q^39 + 2 * q^40 - 46 * q^41 + 11 * q^42 + 76 * q^43 - 14 * q^44 + 9 * q^45 - 33 * q^46 + 23 * q^47 + 11 * q^48 + 100 * q^49 - 119 * q^50 + 25 * q^51 + 31 * q^52 + 30 * q^53 - 44 * q^54 + 81 * q^55 - 23 * q^56 + 12 * q^57 + 25 * q^58 - 3 * q^59 + 34 * q^60 + 13 * q^61 - 49 * q^62 + 65 * q^63 + 69 * q^64 - 27 * q^65 - 10 * q^66 + 105 * q^67 - 4 * q^68 + 19 * q^69 + 11 * q^70 + 51 * q^71 - 72 * q^72 + 43 * q^73 - 73 * q^74 + 77 * q^75 + 17 * q^76 - 19 * q^77 - 31 * q^78 + 89 * q^79 - 2 * q^80 + 73 * q^81 + 46 * q^82 - 10 * q^83 - 11 * q^84 + 44 * q^85 - 76 * q^86 + 57 * q^87 + 14 * q^88 - 28 * q^89 - 9 * q^90 + 76 * q^91 + 33 * q^92 + 59 * q^93 - 23 * q^94 + 72 * q^95 - 11 * q^96 + 89 * q^97 - 100 * q^98 - 17 * q^99

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