LMFDB - Embedded newform 2001.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,2,Mod(1,2001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2001.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:	$15.9780654445$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 5x^{5} + 18x^{4} + 4x^{3} - 26x^{2} + x + 8 $ x^7 - 3x^6 - 5x^5 + 18x^4 + 4x^3 - 26*x^2 + x + 8
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.37349$ of defining polynomial
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.37349 q^{2} +1.00000 q^{3} +3.63344 q^{4} -1.31800 q^{5} -2.37349 q^{6} -0.859291 q^{7} -3.87694 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.37349 q^{2} +1.00000 q^{3} +3.63344 q^{4} -1.31800 q^{5} -2.37349 q^{6} -0.859291 q^{7} -3.87694 q^{8} +1.00000 q^{9} +3.12824 q^{10} +4.30847 q^{11} +3.63344 q^{12} -4.15542 q^{13} +2.03951 q^{14} -1.31800 q^{15} +1.93498 q^{16} +2.08920 q^{17} -2.37349 q^{18} -2.45615 q^{19} -4.78885 q^{20} -0.859291 q^{21} -10.2261 q^{22} +1.00000 q^{23} -3.87694 q^{24} -3.26289 q^{25} +9.86283 q^{26} +1.00000 q^{27} -3.12218 q^{28} -1.00000 q^{29} +3.12824 q^{30} -4.70746 q^{31} +3.16122 q^{32} +4.30847 q^{33} -4.95870 q^{34} +1.13254 q^{35} +3.63344 q^{36} -3.94232 q^{37} +5.82963 q^{38} -4.15542 q^{39} +5.10979 q^{40} -3.17442 q^{41} +2.03951 q^{42} +11.0153 q^{43} +15.6545 q^{44} -1.31800 q^{45} -2.37349 q^{46} +11.1103 q^{47} +1.93498 q^{48} -6.26162 q^{49} +7.74442 q^{50} +2.08920 q^{51} -15.0984 q^{52} -14.0165 q^{53} -2.37349 q^{54} -5.67854 q^{55} +3.33142 q^{56} -2.45615 q^{57} +2.37349 q^{58} +8.47222 q^{59} -4.78885 q^{60} -6.39249 q^{61} +11.1731 q^{62} -0.859291 q^{63} -11.3731 q^{64} +5.47682 q^{65} -10.2261 q^{66} +4.74715 q^{67} +7.59099 q^{68} +1.00000 q^{69} -2.68807 q^{70} -12.4909 q^{71} -3.87694 q^{72} +8.54106 q^{73} +9.35703 q^{74} -3.26289 q^{75} -8.92426 q^{76} -3.70223 q^{77} +9.86283 q^{78} -13.0092 q^{79} -2.55030 q^{80} +1.00000 q^{81} +7.53445 q^{82} -14.2415 q^{83} -3.12218 q^{84} -2.75356 q^{85} -26.1447 q^{86} -1.00000 q^{87} -16.7037 q^{88} +0.795808 q^{89} +3.12824 q^{90} +3.57071 q^{91} +3.63344 q^{92} -4.70746 q^{93} -26.3702 q^{94} +3.23719 q^{95} +3.16122 q^{96} +3.92369 q^{97} +14.8619 q^{98} +4.30847 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 3 q^{2} + 7 q^{3} + 5 q^{4} - 3 q^{5} - 3 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 3 * q^2 + 7 * q^3 + 5 * q^4 - 3 * q^5 - 3 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9	\( 7 q - 3 q^{2} + 7 q^{3} + 5 q^{4} - 3 q^{5} - 3 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9} + 3 q^{10} - 4 q^{11} + 5 q^{12} - 18 q^{13} - 2 q^{14} - 3 q^{15} - 7 q^{16} - 3 q^{17} - 3 q^{18} - 4 q^{19} - 2 q^{20} - 5 q^{21} - 26 q^{22} + 7 q^{23} - 6 q^{24} - 8 q^{25} - 7 q^{26} + 7 q^{27} - 6 q^{28} - 7 q^{29} + 3 q^{30} - 22 q^{31} + 5 q^{32} - 4 q^{33} + 9 q^{34} + 3 q^{35} + 5 q^{36} - 25 q^{37} + 14 q^{38} - 18 q^{39} - 10 q^{40} - 13 q^{41} - 2 q^{42} - 2 q^{43} + 4 q^{44} - 3 q^{45} - 3 q^{46} - 25 q^{47} - 7 q^{48} - 8 q^{49} + 19 q^{50} - 3 q^{51} - 12 q^{52} - 5 q^{53} - 3 q^{54} - 15 q^{55} + 18 q^{56} - 4 q^{57} + 3 q^{58} + 11 q^{59} - 2 q^{60} - 33 q^{61} + 28 q^{62} - 5 q^{63} - 14 q^{64} - 2 q^{65} - 26 q^{66} + 8 q^{67} + 12 q^{68} + 7 q^{69} - 22 q^{70} - 6 q^{71} - 6 q^{72} + 15 q^{73} + 34 q^{74} - 8 q^{75} - 28 q^{76} - q^{77} - 7 q^{78} - 15 q^{79} - 12 q^{80} + 7 q^{81} - 14 q^{82} + 21 q^{83} - 6 q^{84} - 28 q^{85} - 12 q^{86} - 7 q^{87} - 13 q^{88} + 8 q^{89} + 3 q^{90} + 6 q^{91} + 5 q^{92} - 22 q^{93} - 35 q^{94} - 25 q^{95} + 5 q^{96} + 13 q^{97} + q^{98} - 4 q^{99}+O(q^{100}) \) 7 * q - 3 * q^2 + 7 * q^3 + 5 * q^4 - 3 * q^5 - 3 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9 + 3 * q^10 - 4 * q^11 + 5 * q^12 - 18 * q^13 - 2 * q^14 - 3 * q^15 - 7 * q^16 - 3 * q^17 - 3 * q^18 - 4 * q^19 - 2 * q^20 - 5 * q^21 - 26 * q^22 + 7 * q^23 - 6 * q^24 - 8 * q^25 - 7 * q^26 + 7 * q^27 - 6 * q^28 - 7 * q^29 + 3 * q^30 - 22 * q^31 + 5 * q^32 - 4 * q^33 + 9 * q^34 + 3 * q^35 + 5 * q^36 - 25 * q^37 + 14 * q^38 - 18 * q^39 - 10 * q^40 - 13 * q^41 - 2 * q^42 - 2 * q^43 + 4 * q^44 - 3 * q^45 - 3 * q^46 - 25 * q^47 - 7 * q^48 - 8 * q^49 + 19 * q^50 - 3 * q^51 - 12 * q^52 - 5 * q^53 - 3 * q^54 - 15 * q^55 + 18 * q^56 - 4 * q^57 + 3 * q^58 + 11 * q^59 - 2 * q^60 - 33 * q^61 + 28 * q^62 - 5 * q^63 - 14 * q^64 - 2 * q^65 - 26 * q^66 + 8 * q^67 + 12 * q^68 + 7 * q^69 - 22 * q^70 - 6 * q^71 - 6 * q^72 + 15 * q^73 + 34 * q^74 - 8 * q^75 - 28 * q^76 - q^77 - 7 * q^78 - 15 * q^79 - 12 * q^80 + 7 * q^81 - 14 * q^82 + 21 * q^83 - 6 * q^84 - 28 * q^85 - 12 * q^86 - 7 * q^87 - 13 * q^88 + 8 * q^89 + 3 * q^90 + 6 * q^91 + 5 * q^92 - 22 * q^93 - 35 * q^94 - 25 * q^95 + 5 * q^96 + 13 * q^97 + q^98 - 4 * 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 $

$2$	−2.37349	−1.67831	−0.839154	−	0.543894i	$-0.816949\pi$
$2$	−2.37349	−1.67831	−0.839154	+	0.543894i	$0.816949\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.63344	1.81672
$5$	−1.31800	−0.589426	−0.294713	−	0.955586i	$-0.595224\pi$
$5$	−1.31800	−0.589426	−0.294713	+	0.955586i	$0.595224\pi$
$6$	−2.37349	−0.968972
$7$	−0.859291	−0.324781	−0.162391	−	0.986727i	$-0.551920\pi$
$7$	−0.859291	−0.324781	−0.162391	+	0.986727i	$0.551920\pi$
$8$	−3.87694	−1.37070
$9$	1.00000	0.333333
$10$	3.12824	0.989238
$11$	4.30847	1.29905	0.649526	−	0.760339i	$-0.274967\pi$
$11$	4.30847	1.29905	0.649526	+	0.760339i	$0.274967\pi$
$12$	3.63344	1.04888
$13$	−4.15542	−1.15251	−0.576253	−	0.817272i	$-0.695486\pi$
$13$	−4.15542	−1.15251	−0.576253	+	0.817272i	$0.695486\pi$
$14$	2.03951	0.545083
$15$	−1.31800	−0.340305
$16$	1.93498	0.483746
$17$	2.08920	0.506706	0.253353	−	0.967374i	$-0.418467\pi$
$17$	2.08920	0.506706	0.253353	+	0.967374i	$0.418467\pi$
$18$	−2.37349	−0.559436
$19$	−2.45615	−0.563479	−0.281740	−	0.959491i	$-0.590911\pi$
$19$	−2.45615	−0.563479	−0.281740	+	0.959491i	$0.590911\pi$
$20$	−4.78885	−1.07082
$21$	−0.859291	−0.187513
$22$	−10.2261	−2.18021
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−3.87694	−0.791376
$25$	−3.26289	−0.652577
$26$	9.86283	1.93426
$27$	1.00000	0.192450
$28$	−3.12218	−0.590036
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	3.12824	0.571137
$31$	−4.70746	−0.845484	−0.422742	−	0.906250i	$-0.638932\pi$
$31$	−4.70746	−0.845484	−0.422742	+	0.906250i	$0.638932\pi$
$32$	3.16122	0.558830
$33$	4.30847	0.750008
$34$	−4.95870	−0.850409
$35$	1.13254	0.191434
$36$	3.63344	0.605573
$37$	−3.94232	−0.648113	−0.324056	−	0.946038i	$-0.605047\pi$
$37$	−3.94232	−0.648113	−0.324056	+	0.946038i	$0.605047\pi$
$38$	5.82963	0.945692
$39$	−4.15542	−0.665399
$40$	5.10979	0.807928
$41$	−3.17442	−0.495762	−0.247881	−	0.968791i	$-0.579734\pi$
$41$	−3.17442	−0.495762	−0.247881	+	0.968791i	$0.579734\pi$
$42$	2.03951	0.314704
$43$	11.0153	1.67982	0.839909	−	0.542727i	$-0.182608\pi$
$43$	11.0153	1.67982	0.839909	+	0.542727i	$0.182608\pi$
$44$	15.6545	2.36001
$45$	−1.31800	−0.196475
$46$	−2.37349	−0.349951
$47$	11.1103	1.62061	0.810303	−	0.586012i	$-0.199303\pi$
$47$	11.1103	1.62061	0.810303	+	0.586012i	$0.199303\pi$
$48$	1.93498	0.279291
$49$	−6.26162	−0.894517
$50$	7.74442	1.09523
$51$	2.08920	0.292547
$52$	−15.0984	−2.09378
$53$	−14.0165	−1.92531	−0.962657	−	0.270723i	$-0.912737\pi$
$53$	−14.0165	−1.92531	−0.962657	+	0.270723i	$0.912737\pi$
$54$	−2.37349	−0.322991
$55$	−5.67854	−0.765695
$56$	3.33142	0.445179
$57$	−2.45615	−0.325325
$58$	2.37349	0.311654
$59$	8.47222	1.10299	0.551495	−	0.834178i	$-0.314058\pi$
$59$	8.47222	1.10299	0.551495	+	0.834178i	$0.314058\pi$
$60$	−4.78885	−0.618238
$61$	−6.39249	−0.818475	−0.409237	−	0.912428i	$-0.634205\pi$
$61$	−6.39249	−0.818475	−0.409237	+	0.912428i	$0.634205\pi$
$62$	11.1731	1.41898
$63$	−0.859291	−0.108260
$64$	−11.3731	−1.42163
$65$	5.47682	0.679316
$66$	−10.2261	−1.25874
$67$	4.74715	0.579956	0.289978	−	0.957033i	$-0.406352\pi$
$67$	4.74715	0.579956	0.289978	+	0.957033i	$0.406352\pi$
$68$	7.59099	0.920542
$69$	1.00000	0.120386
$70$	−2.68807	−0.321286
$71$	−12.4909	−1.48240	−0.741201	−	0.671283i	$-0.765743\pi$
$71$	−12.4909	−1.48240	−0.741201	+	0.671283i	$0.765743\pi$
$72$	−3.87694	−0.456901
$73$	8.54106	0.999655	0.499827	−	0.866125i	$-0.333397\pi$
$73$	8.54106	0.999655	0.499827	+	0.866125i	$0.333397\pi$
$74$	9.35703	1.08773
$75$	−3.26289	−0.376766
$76$	−8.92426	−1.02368
$77$	−3.70223	−0.421908
$78$	9.86283	1.11675
$79$	−13.0092	−1.46365	−0.731827	−	0.681491i	$-0.761332\pi$
$79$	−13.0092	−1.46365	−0.731827	+	0.681491i	$0.761332\pi$
$80$	−2.55030	−0.285132
$81$	1.00000	0.111111
$82$	7.53445	0.832041
$83$	−14.2415	−1.56321	−0.781606	−	0.623772i	$-0.785599\pi$
$83$	−14.2415	−1.56321	−0.781606	+	0.623772i	$0.785599\pi$
$84$	−3.12218	−0.340657
$85$	−2.75356	−0.298666
$86$	−26.1447	−2.81925
$87$	−1.00000	−0.107211
$88$	−16.7037	−1.78062
$89$	0.795808	0.0843554	0.0421777	−	0.999110i	$-0.486570\pi$
$89$	0.795808	0.0843554	0.0421777	+	0.999110i	$0.486570\pi$
$90$	3.12824	0.329746
$91$	3.57071	0.374312
$92$	3.63344	0.378812
$93$	−4.70746	−0.488141
$94$	−26.3702	−2.71988
$95$	3.23719	0.332129
$96$	3.16122	0.322640
$97$	3.92369	0.398390	0.199195	−	0.979960i	$-0.436167\pi$
$97$	3.92369	0.398390	0.199195	+	0.979960i	$0.436167\pi$
$98$	14.8619	1.50128
$99$	4.30847	0.433017
$100$	−11.8555	−1.18555
$101$	3.90652	0.388713	0.194357	−	0.980931i	$-0.437738\pi$
$101$	3.90652	0.388713	0.194357	+	0.980931i	$0.437738\pi$
$102$	−4.95870	−0.490984
$103$	1.68054	0.165589	0.0827944	−	0.996567i	$-0.473616\pi$
$103$	1.68054	0.165589	0.0827944	+	0.996567i	$0.473616\pi$
$104$	16.1103	1.57974
$105$	1.13254	0.110525
$106$	33.2680	3.23127
$107$	11.2977	1.09219	0.546096	−	0.837722i	$-0.316113\pi$
$107$	11.2977	1.09219	0.546096	+	0.837722i	$0.316113\pi$
$108$	3.63344	0.349627
$109$	−17.5897	−1.68479	−0.842394	−	0.538863i	$-0.818854\pi$
$109$	−17.5897	−1.68479	−0.842394	+	0.538863i	$0.818854\pi$
$110$	13.4779	1.28507
$111$	−3.94232	−0.374188
$112$	−1.66271	−0.157112
$113$	−3.98253	−0.374645	−0.187323	−	0.982298i	$-0.559981\pi$
$113$	−3.98253	−0.374645	−0.187323	+	0.982298i	$0.559981\pi$
$114$	5.82963	0.545995
$115$	−1.31800	−0.122904
$116$	−3.63344	−0.337356
$117$	−4.15542	−0.384169
$118$	−20.1087	−1.85116
$119$	−1.79523	−0.164569
$120$	5.10979	0.466458
$121$	7.56290	0.687537
$122$	15.1725	1.37365
$123$	−3.17442	−0.286228
$124$	−17.1042	−1.53601
$125$	10.8905	0.974072
$126$	2.03951	0.181694
$127$	16.7386	1.48531	0.742654	−	0.669675i	$-0.233567\pi$
$127$	16.7386	1.48531	0.742654	+	0.669675i	$0.233567\pi$
$128$	20.6714	1.82711
$129$	11.0153	0.969844
$130$	−12.9992	−1.14010
$131$	−22.3630	−1.95386	−0.976930	−	0.213559i	$-0.931494\pi$
$131$	−22.3630	−1.95386	−0.976930	+	0.213559i	$0.931494\pi$
$132$	15.6545	1.36255
$133$	2.11055	0.183008
$134$	−11.2673	−0.973345
$135$	−1.31800	−0.113435
$136$	−8.09971	−0.694544
$137$	−12.8745	−1.09995	−0.549973	−	0.835182i	$-0.685362\pi$
$137$	−12.8745	−1.09995	−0.549973	+	0.835182i	$0.685362\pi$
$138$	−2.37349	−0.202045
$139$	12.8067	1.08625	0.543123	−	0.839653i	$-0.317242\pi$
$139$	12.8067	1.08625	0.543123	+	0.839653i	$0.317242\pi$
$140$	4.11502	0.347782
$141$	11.1103	0.935657
$142$	29.6471	2.48793
$143$	−17.9035	−1.49716
$144$	1.93498	0.161249
$145$	1.31800	0.109454
$146$	−20.2721	−1.67773
$147$	−6.26162	−0.516450
$148$	−14.3242	−1.17744
$149$	11.7517	0.962740	0.481370	−	0.876518i	$-0.340139\pi$
$149$	11.7517	0.962740	0.481370	+	0.876518i	$0.340139\pi$
$150$	7.74442	0.632329
$151$	−11.1096	−0.904086	−0.452043	−	0.891996i	$-0.649305\pi$
$151$	−11.1096	−0.904086	−0.452043	+	0.891996i	$0.649305\pi$
$152$	9.52233	0.772363
$153$	2.08920	0.168902
$154$	8.78718	0.708091
$155$	6.20441	0.498350
$156$	−15.0984	−1.20884
$157$	−19.4984	−1.55614	−0.778072	−	0.628175i	$-0.783802\pi$
$157$	−19.4984	−1.55614	−0.778072	+	0.628175i	$0.783802\pi$
$158$	30.8772	2.45646
$159$	−14.0165	−1.11158
$160$	−4.16647	−0.329389
$161$	−0.859291	−0.0677216
$162$	−2.37349	−0.186479
$163$	21.4125	1.67716	0.838579	−	0.544779i	$-0.183387\pi$
$163$	21.4125	1.67716	0.838579	+	0.544779i	$0.183387\pi$
$164$	−11.5341	−0.900659
$165$	−5.67854	−0.442074
$166$	33.8021	2.62355
$167$	−3.76831	−0.291600	−0.145800	−	0.989314i	$-0.546576\pi$
$167$	−3.76831	−0.291600	−0.145800	+	0.989314i	$0.546576\pi$
$168$	3.33142	0.257024
$169$	4.26750	0.328269
$170$	6.53554	0.501253
$171$	−2.45615	−0.187826
$172$	40.0234	3.05176
$173$	18.5637	1.41137	0.705686	−	0.708525i	$-0.250639\pi$
$173$	18.5637	1.41137	0.705686	+	0.708525i	$0.250639\pi$
$174$	2.37349	0.179934
$175$	2.80377	0.211945
$176$	8.33681	0.628411
$177$	8.47222	0.636811
$178$	−1.88884	−0.141574
$179$	−21.5082	−1.60760	−0.803798	−	0.594902i	$-0.797191\pi$
$179$	−21.5082	−1.60760	−0.803798	+	0.594902i	$0.797191\pi$
$180$	−4.78885	−0.356940
$181$	−12.8583	−0.955754	−0.477877	−	0.878427i	$-0.658593\pi$
$181$	−12.8583	−0.955754	−0.477877	+	0.878427i	$0.658593\pi$
$182$	−8.47503	−0.628211
$183$	−6.39249	−0.472547
$184$	−3.87694	−0.285812
$185$	5.19596	0.382014
$186$	11.1731	0.819250
$187$	9.00127	0.658238
$188$	40.3686	2.94418
$189$	−0.859291	−0.0625042
$190$	−7.68344	−0.557415
$191$	1.67695	0.121340	0.0606700	−	0.998158i	$-0.480676\pi$
$191$	1.67695	0.121340	0.0606700	+	0.998158i	$0.480676\pi$
$192$	−11.3731	−0.820781
$193$	−13.8369	−0.996002	−0.498001	−	0.867177i	$-0.665932\pi$
$193$	−13.8369	−0.996002	−0.498001	+	0.867177i	$0.665932\pi$
$194$	−9.31282	−0.668622
$195$	5.47682	0.392204
$196$	−22.7512	−1.62509
$197$	−27.8816	−1.98648	−0.993241	−	0.116074i	$-0.962969\pi$
$197$	−27.8816	−1.98648	−0.993241	+	0.116074i	$0.962969\pi$
$198$	−10.2261	−0.726737
$199$	−17.7635	−1.25922	−0.629609	−	0.776912i	$-0.716785\pi$
$199$	−17.7635	−1.25922	−0.629609	+	0.776912i	$0.716785\pi$
$200$	12.6500	0.894490
$201$	4.74715	0.334838
$202$	−9.27207	−0.652380
$203$	0.859291	0.0603104
$204$	7.59099	0.531475
$205$	4.18388	0.292215
$206$	−3.98875	−0.277909
$207$	1.00000	0.0695048
$208$	−8.04066	−0.557520
$209$	−10.5822	−0.731989
$210$	−2.68807	−0.185495
$211$	−21.7285	−1.49585	−0.747926	−	0.663783i	$-0.768950\pi$
$211$	−21.7285	−1.49585	−0.747926	+	0.663783i	$0.768950\pi$
$212$	−50.9281	−3.49775
$213$	−12.4909	−0.855865
$214$	−26.8150	−1.83304
$215$	−14.5181	−0.990128
$216$	−3.87694	−0.263792
$217$	4.04507	0.274598
$218$	41.7489	2.82759
$219$	8.54106	0.577151
$220$	−20.6326	−1.39105
$221$	−8.68152	−0.583982
$222$	9.35703	0.628003
$223$	−0.162927	−0.0109104	−0.00545520	−	0.999985i	$-0.501736\pi$
$223$	−0.162927	−0.0109104	−0.00545520	+	0.999985i	$0.501736\pi$
$224$	−2.71641	−0.181497
$225$	−3.26289	−0.217526
$226$	9.45248	0.628770
$227$	−14.9422	−0.991752	−0.495876	−	0.868393i	$-0.665153\pi$
$227$	−14.9422	−0.991752	−0.495876	+	0.868393i	$0.665153\pi$
$228$	−8.92426	−0.591023
$229$	−9.10145	−0.601441	−0.300720	−	0.953712i	$-0.597227\pi$
$229$	−9.10145	−0.601441	−0.300720	+	0.953712i	$0.597227\pi$
$230$	3.12824	0.206270
$231$	−3.70223	−0.243589
$232$	3.87694	0.254533
$233$	−12.6237	−0.827007	−0.413504	−	0.910502i	$-0.635695\pi$
$233$	−12.6237	−0.827007	−0.413504	+	0.910502i	$0.635695\pi$
$234$	9.86283	0.644753
$235$	−14.6433	−0.955227
$236$	30.7833	2.00382
$237$	−13.0092	−0.845041
$238$	4.26096	0.276197
$239$	16.8514	1.09003	0.545013	−	0.838428i	$-0.316525\pi$
$239$	16.8514	1.09003	0.545013	+	0.838428i	$0.316525\pi$
$240$	−2.55030	−0.164621
$241$	−17.4282	−1.12265	−0.561323	−	0.827597i	$-0.689708\pi$
$241$	−17.4282	−1.12265	−0.561323	+	0.827597i	$0.689708\pi$
$242$	−17.9504	−1.15390
$243$	1.00000	0.0641500
$244$	−23.2267	−1.48694
$245$	8.25279	0.527251
$246$	7.53445	0.480379
$247$	10.2063	0.649413
$248$	18.2505	1.15891
$249$	−14.2415	−0.902521
$250$	−25.8483	−1.63479
$251$	10.2885	0.649407	0.324703	−	0.945816i	$-0.394736\pi$
$251$	10.2885	0.649407	0.324703	+	0.945816i	$0.394736\pi$
$252$	−3.12218	−0.196679
$253$	4.30847	0.270871
$254$	−39.7288	−2.49280
$255$	−2.75356	−0.172435
$256$	−26.3171	−1.64482
$257$	−5.27151	−0.328827	−0.164414	−	0.986391i	$-0.552573\pi$
$257$	−5.27151	−0.328827	−0.164414	+	0.986391i	$0.552573\pi$
$258$	−26.1447	−1.62770
$259$	3.38760	0.210495
$260$	19.8997	1.23413
$261$	−1.00000	−0.0618984
$262$	53.0782	3.27918
$263$	−4.72941	−0.291628	−0.145814	−	0.989312i	$-0.546580\pi$
$263$	−4.72941	−0.291628	−0.145814	+	0.989312i	$0.546580\pi$
$264$	−16.7037	−1.02804
$265$	18.4737	1.13483
$266$	−5.00935	−0.307143
$267$	0.795808	0.0487026
$268$	17.2485	1.05362
$269$	−21.2129	−1.29338	−0.646688	−	0.762754i	$-0.723846\pi$
$269$	−21.2129	−1.29338	−0.646688	+	0.762754i	$0.723846\pi$
$270$	3.12824	0.190379
$271$	−11.0667	−0.672253	−0.336127	−	0.941817i	$-0.609117\pi$
$271$	−11.0667	−0.672253	−0.336127	+	0.941817i	$0.609117\pi$
$272$	4.04257	0.245117
$273$	3.57071	0.216109
$274$	30.5575	1.84605
$275$	−14.0580	−0.847732
$276$	3.63344	0.218707
$277$	−7.98577	−0.479818	−0.239909	−	0.970795i	$-0.577118\pi$
$277$	−7.98577	−0.479818	−0.239909	+	0.970795i	$0.577118\pi$
$278$	−30.3964	−1.82306
$279$	−4.70746	−0.281828
$280$	−4.39079	−0.262400
$281$	6.63114	0.395581	0.197790	−	0.980244i	$-0.436623\pi$
$281$	6.63114	0.395581	0.197790	+	0.980244i	$0.436623\pi$
$282$	−26.3702	−1.57032
$283$	2.98274	0.177306	0.0886528	−	0.996063i	$-0.471744\pi$
$283$	2.98274	0.177306	0.0886528	+	0.996063i	$0.471744\pi$
$284$	−45.3850	−2.69311
$285$	3.23719	0.191755
$286$	42.4937	2.51270
$287$	2.72775	0.161014
$288$	3.16122	0.186277
$289$	−12.6352	−0.743249
$290$	−3.12824	−0.183697
$291$	3.92369	0.230011
$292$	31.0334	1.81609
$293$	13.4117	0.783521	0.391760	−	0.920067i	$-0.371866\pi$
$293$	13.4117	0.783521	0.391760	+	0.920067i	$0.371866\pi$
$294$	14.8619	0.866762
$295$	−11.1664	−0.650130
$296$	15.2841	0.888371
$297$	4.30847	0.250003
$298$	−27.8926	−1.61577
$299$	−4.15542	−0.240314
$300$	−11.8555	−0.684477
$301$	−9.46535	−0.545574
$302$	26.3685	1.51734
$303$	3.90652	0.224424
$304$	−4.75261	−0.272581
$305$	8.42528	0.482430
$306$	−4.95870	−0.283470
$307$	−7.23125	−0.412709	−0.206355	−	0.978477i	$-0.566160\pi$
$307$	−7.23125	−0.412709	−0.206355	+	0.978477i	$0.566160\pi$
$308$	−13.4518	−0.766488
$309$	1.68054	0.0956028
$310$	−14.7261	−0.836385
$311$	0.648787	0.0367894	0.0183947	−	0.999831i	$-0.494144\pi$
$311$	0.648787	0.0367894	0.0183947	+	0.999831i	$0.494144\pi$
$312$	16.1103	0.912066
$313$	18.3081	1.03483	0.517416	−	0.855734i	$-0.326894\pi$
$313$	18.3081	1.03483	0.517416	+	0.855734i	$0.326894\pi$
$314$	46.2793	2.61169
$315$	1.13254	0.0638115
$316$	−47.2682	−2.65905
$317$	−21.4173	−1.20292	−0.601458	−	0.798904i	$-0.705413\pi$
$317$	−21.4173	−1.20292	−0.601458	+	0.798904i	$0.705413\pi$
$318$	33.2680	1.86558
$319$	−4.30847	−0.241228
$320$	14.9897	0.837948
$321$	11.2977	0.630578
$322$	2.03951	0.113658
$323$	−5.13140	−0.285518
$324$	3.63344	0.201858
$325$	13.5587	0.752099
$326$	−50.8223	−2.81479
$327$	−17.5897	−0.972712
$328$	12.3070	0.679542
$329$	−9.54699	−0.526342
$330$	13.4779	0.741936
$331$	2.79629	0.153698	0.0768490	−	0.997043i	$-0.475514\pi$
$331$	2.79629	0.153698	0.0768490	+	0.997043i	$0.475514\pi$
$332$	−51.7457	−2.83992
$333$	−3.94232	−0.216038
$334$	8.94403	0.489395
$335$	−6.25672	−0.341841
$336$	−1.66271	−0.0907084
$337$	−31.0998	−1.69411	−0.847057	−	0.531501i	$-0.821628\pi$
$337$	−31.0998	−1.69411	−0.847057	+	0.531501i	$0.821628\pi$
$338$	−10.1288	−0.550937
$339$	−3.98253	−0.216301
$340$	−10.0049	−0.542591
$341$	−20.2819	−1.09833
$342$	5.82963	0.315231
$343$	11.3956	0.615304
$344$	−42.7056	−2.30253
$345$	−1.31800	−0.0709585
$346$	−44.0607	−2.36872
$347$	34.9752	1.87757	0.938785	−	0.344504i	$-0.111953\pi$
$347$	34.9752	1.87757	0.938785	+	0.344504i	$0.111953\pi$
$348$	−3.63344	−0.194773
$349$	28.8052	1.54191	0.770953	−	0.636892i	$-0.219780\pi$
$349$	28.8052	1.54191	0.770953	+	0.636892i	$0.219780\pi$
$350$	−6.65470	−0.355709
$351$	−4.15542	−0.221800
$352$	13.6200	0.725949
$353$	−11.5890	−0.616819	−0.308409	−	0.951254i	$-0.599797\pi$
$353$	−11.5890	−0.616819	−0.308409	+	0.951254i	$0.599797\pi$
$354$	−20.1087	−1.06877
$355$	16.4630	0.873766
$356$	2.89152	0.153250
$357$	−1.79523	−0.0950138
$358$	51.0493	2.69804
$359$	35.7439	1.88649	0.943246	−	0.332095i	$-0.107755\pi$
$359$	35.7439	1.88649	0.943246	+	0.332095i	$0.107755\pi$
$360$	5.10979	0.269309
$361$	−12.9673	−0.682491
$362$	30.5191	1.60405
$363$	7.56290	0.396949
$364$	12.9740	0.680020
$365$	−11.2571	−0.589222
$366$	15.1725	0.793079
$367$	−27.4350	−1.43209	−0.716046	−	0.698053i	$-0.754050\pi$
$367$	−27.4350	−1.43209	−0.716046	+	0.698053i	$0.754050\pi$
$368$	1.93498	0.100868
$369$	−3.17442	−0.165254
$370$	−12.3325	−0.641138
$371$	12.0443	0.625306
$372$	−17.1042	−0.886814
$373$	13.3266	0.690027	0.345013	−	0.938598i	$-0.387874\pi$
$373$	13.3266	0.690027	0.345013	+	0.938598i	$0.387874\pi$
$374$	−21.3644	−1.10473
$375$	10.8905	0.562380
$376$	−43.0740	−2.22137
$377$	4.15542	0.214015
$378$	2.03951	0.104901
$379$	−5.84883	−0.300434	−0.150217	−	0.988653i	$-0.547997\pi$
$379$	−5.84883	−0.300434	−0.150217	+	0.988653i	$0.547997\pi$
$380$	11.7621	0.603385
$381$	16.7386	0.857543
$382$	−3.98022	−0.203646
$383$	13.9417	0.712388	0.356194	−	0.934412i	$-0.384074\pi$
$383$	13.9417	0.712388	0.356194	+	0.934412i	$0.384074\pi$
$384$	20.6714	1.05488
$385$	4.87952	0.248683
$386$	32.8417	1.67160
$387$	11.0153	0.559940
$388$	14.2565	0.723763
$389$	24.2834	1.23122	0.615608	−	0.788052i	$-0.288910\pi$
$389$	24.2834	1.23122	0.615608	+	0.788052i	$0.288910\pi$
$390$	−12.9992	−0.658238
$391$	2.08920	0.105656
$392$	24.2759	1.22612
$393$	−22.3630	−1.12806
$394$	66.1766	3.33393
$395$	17.1461	0.862715
$396$	15.6545	0.786670
$397$	−33.5680	−1.68473	−0.842364	−	0.538909i	$-0.818837\pi$
$397$	−33.5680	−1.68473	−0.842364	+	0.538909i	$0.818837\pi$
$398$	42.1613	2.11336
$399$	2.11055	0.105659
$400$	−6.31363	−0.315681
$401$	16.7895	0.838426	0.419213	−	0.907888i	$-0.362306\pi$
$401$	16.7895	0.838426	0.419213	+	0.907888i	$0.362306\pi$
$402$	−11.2673	−0.561961
$403$	19.5615	0.974425
$404$	14.1941	0.706182
$405$	−1.31800	−0.0654917
$406$	−2.03951	−0.101219
$407$	−16.9854	−0.841933
$408$	−8.09971	−0.400995
$409$	33.9540	1.67892	0.839458	−	0.543424i	$-0.182872\pi$
$409$	33.9540	1.67892	0.839458	+	0.543424i	$0.182872\pi$
$410$	−9.93037	−0.490426
$411$	−12.8745	−0.635054
$412$	6.10615	0.300828
$413$	−7.28010	−0.358230
$414$	−2.37349	−0.116650
$415$	18.7703	0.921398
$416$	−13.1362	−0.644054
$417$	12.8067	0.627145
$418$	25.1168	1.22850
$419$	1.25305	0.0612157	0.0306079	−	0.999531i	$-0.490256\pi$
$419$	1.25305	0.0612157	0.0306079	+	0.999531i	$0.490256\pi$
$420$	4.11502	0.200792
$421$	19.7566	0.962880	0.481440	−	0.876479i	$-0.340114\pi$
$421$	19.7566	0.962880	0.481440	+	0.876479i	$0.340114\pi$
$422$	51.5723	2.51050
$423$	11.1103	0.540202
$424$	54.3411	2.63904
$425$	−6.81684	−0.330665
$426$	29.6471	1.43640
$427$	5.49301	0.265825
$428$	41.0496	1.98421
$429$	−17.9035	−0.864389
$430$	34.4586	1.66174
$431$	−28.0855	−1.35283	−0.676416	−	0.736520i	$-0.736468\pi$
$431$	−28.0855	−1.35283	−0.676416	+	0.736520i	$0.736468\pi$
$432$	1.93498	0.0930969
$433$	−37.9606	−1.82427	−0.912135	−	0.409890i	$-0.865567\pi$
$433$	−37.9606	−1.82427	−0.912135	+	0.409890i	$0.865567\pi$
$434$	−9.60093	−0.460859
$435$	1.31800	0.0631931
$436$	−63.9110	−3.06078
$437$	−2.45615	−0.117494
$438$	−20.2721	−0.968637
$439$	33.0666	1.57818	0.789091	−	0.614277i	$-0.210552\pi$
$439$	33.0666	1.57818	0.789091	+	0.614277i	$0.210552\pi$
$440$	22.0154	1.04954
$441$	−6.26162	−0.298172
$442$	20.6055	0.980101
$443$	−4.67818	−0.222267	−0.111134	−	0.993805i	$-0.535448\pi$
$443$	−4.67818	−0.222267	−0.111134	+	0.993805i	$0.535448\pi$
$444$	−14.3242	−0.679794
$445$	−1.04887	−0.0497213
$446$	0.386705	0.0183110
$447$	11.7517	0.555838
$448$	9.77278	0.461720
$449$	0.0578209	0.00272873	0.00136437	−	0.999999i	$-0.499566\pi$
$449$	0.0578209	0.00272873	0.00136437	+	0.999999i	$0.499566\pi$
$450$	7.74442	0.365075
$451$	−13.6769	−0.644020
$452$	−14.4703	−0.680624
$453$	−11.1096	−0.521974
$454$	35.4652	1.66446
$455$	−4.70618	−0.220629
$456$	9.52233	0.445924
$457$	−9.68884	−0.453225	−0.226612	−	0.973985i	$-0.572765\pi$
$457$	−9.68884	−0.453225	−0.226612	+	0.973985i	$0.572765\pi$
$458$	21.6022	1.00940
$459$	2.08920	0.0975157
$460$	−4.78885	−0.223281
$461$	13.9639	0.650365	0.325182	−	0.945651i	$-0.394574\pi$
$461$	13.9639	0.650365	0.325182	+	0.945651i	$0.394574\pi$
$462$	8.78718	0.408817
$463$	31.3995	1.45926	0.729629	−	0.683844i	$-0.239693\pi$
$463$	31.3995	1.45926	0.729629	+	0.683844i	$0.239693\pi$
$464$	−1.93498	−0.0898293
$465$	6.20441	0.287723
$466$	29.9622	1.38797
$467$	−20.9278	−0.968422	−0.484211	−	0.874951i	$-0.660893\pi$
$467$	−20.9278	−0.968422	−0.484211	+	0.874951i	$0.660893\pi$
$468$	−15.0984	−0.697926
$469$	−4.07918	−0.188359
$470$	34.7558	1.60316
$471$	−19.4984	−0.898440
$472$	−32.8463	−1.51187
$473$	47.4591	2.18217
$474$	30.8772	1.41824
$475$	8.01414	0.367714
$476$	−6.52286	−0.298975
$477$	−14.0165	−0.641772
$478$	−39.9965	−1.82940
$479$	41.1688	1.88105	0.940525	−	0.339724i	$-0.110334\pi$
$479$	41.1688	1.88105	0.940525	+	0.339724i	$0.110334\pi$
$480$	−4.16647	−0.190173
$481$	16.3820	0.746954
$482$	41.3655	1.88415
$483$	−0.859291	−0.0390991
$484$	27.4793	1.24906
$485$	−5.17141	−0.234821
$486$	−2.37349	−0.107664
$487$	−16.7097	−0.757190	−0.378595	−	0.925562i	$-0.623593\pi$
$487$	−16.7097	−0.757190	−0.378595	+	0.925562i	$0.623593\pi$
$488$	24.7833	1.12189
$489$	21.4125	0.968308
$490$	−19.5879	−0.884890
$491$	18.7578	0.846526	0.423263	−	0.906007i	$-0.360885\pi$
$491$	18.7578	0.846526	0.423263	+	0.906007i	$0.360885\pi$
$492$	−11.5341	−0.519996
$493$	−2.08920	−0.0940930
$494$	−24.2246	−1.08991
$495$	−5.67854	−0.255232
$496$	−9.10885	−0.408999
$497$	10.7333	0.481456
$498$	33.8021	1.51471
$499$	4.60344	0.206078	0.103039	−	0.994677i	$-0.467143\pi$
$499$	4.60344	0.206078	0.103039	+	0.994677i	$0.467143\pi$
$500$	39.5698	1.76961
$501$	−3.76831	−0.168356
$502$	−24.4197	−1.08990
$503$	−10.6369	−0.474276	−0.237138	−	0.971476i	$-0.576209\pi$
$503$	−10.6369	−0.474276	−0.237138	+	0.971476i	$0.576209\pi$
$504$	3.33142	0.148393
$505$	−5.14878	−0.229117
$506$	−10.2261	−0.454605
$507$	4.26750	0.189526
$508$	60.8185	2.69839
$509$	12.0067	0.532186	0.266093	−	0.963947i	$-0.414267\pi$
$509$	12.0067	0.532186	0.266093	+	0.963947i	$0.414267\pi$
$510$	6.53554	0.289399
$511$	−7.33925	−0.324669
$512$	21.1205	0.933404
$513$	−2.45615	−0.108442
$514$	12.5118	0.551874
$515$	−2.21495	−0.0976023
$516$	40.0234	1.76193
$517$	47.8684	2.10525
$518$	−8.04041	−0.353275
$519$	18.5637	0.814856
$520$	−21.2333	−0.931142
$521$	11.2329	0.492123	0.246061	−	0.969254i	$-0.420864\pi$
$521$	11.2329	0.492123	0.246061	+	0.969254i	$0.420864\pi$
$522$	2.37349	0.103885
$523$	−30.6342	−1.33954	−0.669770	−	0.742569i	$-0.733607\pi$
$523$	−30.6342	−1.33954	−0.669770	+	0.742569i	$0.733607\pi$
$524$	−81.2544	−3.54961
$525$	2.80377	0.122366
$526$	11.2252	0.489442
$527$	−9.83484	−0.428412
$528$	8.33681	0.362813
$529$	1.00000	0.0434783
$530$	−43.8471	−1.90459
$531$	8.47222	0.367663
$532$	7.66853	0.332473
$533$	13.1911	0.571368
$534$	−1.88884	−0.0817380
$535$	−14.8904	−0.643766
$536$	−18.4044	−0.794948
$537$	−21.5082	−0.928146
$538$	50.3486	2.17068
$539$	−26.9780	−1.16202
$540$	−4.78885	−0.206079
$541$	−24.1023	−1.03624	−0.518119	−	0.855308i	$-0.673368\pi$
$541$	−24.1023	−1.03624	−0.518119	+	0.855308i	$0.673368\pi$
$542$	26.2666	1.12825
$543$	−12.8583	−0.551805
$544$	6.60443	0.283163
$545$	23.1831	0.993057
$546$	−8.47503	−0.362698
$547$	13.8709	0.593075	0.296538	−	0.955021i	$-0.404168\pi$
$547$	13.8709	0.593075	0.296538	+	0.955021i	$0.404168\pi$
$548$	−46.7788	−1.99829
$549$	−6.39249	−0.272825
$550$	33.3666	1.42276
$551$	2.45615	0.104635
$552$	−3.87694	−0.165013
$553$	11.1787	0.475367
$554$	18.9541	0.805283
$555$	5.19596	0.220556
$556$	46.5322	1.97340
$557$	33.6906	1.42752	0.713758	−	0.700392i	$-0.246991\pi$
$557$	33.6906	1.42752	0.713758	+	0.700392i	$0.246991\pi$
$558$	11.1731	0.472994
$559$	−45.7732	−1.93600
$560$	2.19145	0.0926056
$561$	9.00127	0.380034
$562$	−15.7389	−0.663906
$563$	41.3582	1.74304	0.871520	−	0.490360i	$-0.163135\pi$
$563$	41.3582	1.74304	0.871520	+	0.490360i	$0.163135\pi$
$564$	40.3686	1.69982
$565$	5.24896	0.220825
$566$	−7.07949	−0.297573
$567$	−0.859291	−0.0360868
$568$	48.4266	2.03193
$569$	14.0644	0.589612	0.294806	−	0.955557i	$-0.404745\pi$
$569$	14.0644	0.589612	0.294806	+	0.955557i	$0.404745\pi$
$570$	−7.68344	−0.321824
$571$	−5.85298	−0.244940	−0.122470	−	0.992472i	$-0.539081\pi$
$571$	−5.85298	−0.244940	−0.122470	+	0.992472i	$0.539081\pi$
$572$	−65.0512	−2.71993
$573$	1.67695	0.0700556
$574$	−6.47428	−0.270231
$575$	−3.26289	−0.136072
$576$	−11.3731	−0.473878
$577$	−27.3870	−1.14014	−0.570069	−	0.821597i	$-0.693083\pi$
$577$	−27.3870	−1.14014	−0.570069	+	0.821597i	$0.693083\pi$
$578$	29.9895	1.24740
$579$	−13.8369	−0.575042
$580$	4.78885	0.198846
$581$	12.2376	0.507702
$582$	−9.31282	−0.386029
$583$	−60.3897	−2.50108
$584$	−33.1131	−1.37023
$585$	5.47682	0.226439
$586$	−31.8325	−1.31499
$587$	−45.3687	−1.87257	−0.936284	−	0.351245i	$-0.885758\pi$
$587$	−45.3687	−1.87257	−0.936284	+	0.351245i	$0.885758\pi$
$588$	−22.7512	−0.938243
$589$	11.5622	0.476413
$590$	26.5032	1.09112
$591$	−27.8816	−1.14690
$592$	−7.62832	−0.313522
$593$	17.9412	0.736756	0.368378	−	0.929676i	$-0.379913\pi$
$593$	17.9412	0.736756	0.368378	+	0.929676i	$0.379913\pi$
$594$	−10.2261	−0.419582
$595$	2.36611	0.0970011
$596$	42.6992	1.74903
$597$	−17.7635	−0.727010
$598$	9.86283	0.403321
$599$	−38.0747	−1.55569	−0.777845	−	0.628456i	$-0.783687\pi$
$599$	−38.0747	−1.55569	−0.777845	+	0.628456i	$0.783687\pi$
$600$	12.6500	0.516434
$601$	−25.1262	−1.02492	−0.512461	−	0.858711i	$-0.671266\pi$
$601$	−25.1262	−1.02492	−0.512461	+	0.858711i	$0.671266\pi$
$602$	22.4659	0.915641
$603$	4.74715	0.193319
$604$	−40.3660	−1.64247
$605$	−9.96787	−0.405252
$606$	−9.27207	−0.376652
$607$	19.6470	0.797447	0.398723	−	0.917071i	$-0.369453\pi$
$607$	19.6470	0.797447	0.398723	+	0.917071i	$0.369453\pi$
$608$	−7.76442	−0.314889
$609$	0.859291	0.0348202
$610$	−19.9973	−0.809666
$611$	−46.1680	−1.86776
$612$	7.59099	0.306847
$613$	17.5314	0.708086	0.354043	−	0.935229i	$-0.384807\pi$
$613$	17.5314	0.708086	0.354043	+	0.935229i	$0.384807\pi$
$614$	17.1633	0.692653
$615$	4.18388	0.168710
$616$	14.3533	0.578311
$617$	28.1894	1.13486	0.567430	−	0.823421i	$-0.307938\pi$
$617$	28.1894	1.13486	0.567430	+	0.823421i	$0.307938\pi$
$618$	−3.98875	−0.160451
$619$	12.6807	0.509680	0.254840	−	0.966983i	$-0.417977\pi$
$619$	12.6807	0.509680	0.254840	+	0.966983i	$0.417977\pi$
$620$	22.5433	0.905362
$621$	1.00000	0.0401286
$622$	−1.53989	−0.0617439
$623$	−0.683830	−0.0273971
$624$	−8.04066	−0.321884
$625$	1.96086	0.0784345
$626$	−43.4539	−1.73677
$627$	−10.5822	−0.422614
$628$	−70.8463	−2.82708
$629$	−8.23630	−0.328403
$630$	−2.68807	−0.107095
$631$	24.4176	0.972050	0.486025	−	0.873945i	$-0.338446\pi$
$631$	24.4176	0.972050	0.486025	+	0.873945i	$0.338446\pi$
$632$	50.4360	2.00624
$633$	−21.7285	−0.863630
$634$	50.8337	2.01886
$635$	−22.0614	−0.875479
$636$	−50.9281	−2.01943
$637$	26.0196	1.03094
$638$	10.2261	0.404855
$639$	−12.4909	−0.494134
$640$	−27.2448	−1.07695
$641$	−39.9966	−1.57977	−0.789886	−	0.613254i	$-0.789860\pi$
$641$	−39.9966	−1.57977	−0.789886	+	0.613254i	$0.789860\pi$
$642$	−26.8150	−1.05830
$643$	−21.9596	−0.866002	−0.433001	−	0.901393i	$-0.642545\pi$
$643$	−21.9596	−0.866002	−0.433001	+	0.901393i	$0.642545\pi$
$644$	−3.12218	−0.123031
$645$	−14.5181	−0.571651
$646$	12.1793	0.479188
$647$	5.75236	0.226149	0.113074	−	0.993587i	$-0.463930\pi$
$647$	5.75236	0.226149	0.113074	+	0.993587i	$0.463930\pi$
$648$	−3.87694	−0.152300
$649$	36.5023	1.43284
$650$	−32.1813	−1.26225
$651$	4.04507	0.158539
$652$	77.8010	3.04692
$653$	−16.3800	−0.640998	−0.320499	−	0.947249i	$-0.603851\pi$
$653$	−16.3800	−0.640998	−0.320499	+	0.947249i	$0.603851\pi$
$654$	41.7489	1.63251
$655$	29.4743	1.15166
$656$	−6.14245	−0.239823
$657$	8.54106	0.333218
$658$	22.6596	0.883365
$659$	−7.33501	−0.285731	−0.142866	−	0.989742i	$-0.545632\pi$
$659$	−7.33501	−0.285731	−0.142866	+	0.989742i	$0.545632\pi$
$660$	−20.6326	−0.803124
$661$	23.2593	0.904681	0.452340	−	0.891845i	$-0.350589\pi$
$661$	23.2593	0.904681	0.452340	+	0.891845i	$0.350589\pi$
$662$	−6.63695	−0.257953
$663$	−8.68152	−0.337162
$664$	55.2136	2.14270
$665$	−2.78169	−0.107869
$666$	9.35703	0.362578
$667$	−1.00000	−0.0387202
$668$	−13.6919	−0.529756
$669$	−0.162927	−0.00629913
$670$	14.8502	0.573715
$671$	−27.5418	−1.06324
$672$	−2.71641	−0.104788
$673$	28.8875	1.11353	0.556766	−	0.830670i	$-0.312042\pi$
$673$	28.8875	1.11353	0.556766	+	0.830670i	$0.312042\pi$
$674$	73.8150	2.84325
$675$	−3.26289	−0.125589
$676$	15.5057	0.596372
$677$	27.0586	1.03995	0.519974	−	0.854182i	$-0.325942\pi$
$677$	27.0586	1.03995	0.519974	+	0.854182i	$0.325942\pi$
$678$	9.45248	0.363020
$679$	−3.37159	−0.129390
$680$	10.6754	0.409382
$681$	−14.9422	−0.572588
$682$	48.1389	1.84333
$683$	33.2775	1.27333	0.636664	−	0.771141i	$-0.280314\pi$
$683$	33.2775	1.27333	0.636664	+	0.771141i	$0.280314\pi$
$684$	−8.92426	−0.341228
$685$	16.9686	0.648337
$686$	−27.0473	−1.03267
$687$	−9.10145	−0.347242
$688$	21.3144	0.812605
$689$	58.2444	2.21894
$690$	3.12824	0.119090
$691$	13.0933	0.498093	0.249046	−	0.968492i	$-0.419883\pi$
$691$	13.0933	0.498093	0.249046	+	0.968492i	$0.419883\pi$
$692$	67.4500	2.56406
$693$	−3.70223	−0.140636
$694$	−83.0133	−3.15114
$695$	−16.8791	−0.640262
$696$	3.87694	0.146955
$697$	−6.63202	−0.251206
$698$	−68.3687	−2.58779
$699$	−12.6237	−0.477473
$700$	10.1873	0.385044
$701$	−5.48506	−0.207168	−0.103584	−	0.994621i	$-0.533031\pi$
$701$	−5.48506	−0.207168	−0.103584	+	0.994621i	$0.533031\pi$
$702$	9.86283	0.372248
$703$	9.68292	0.365198
$704$	−49.0005	−1.84678
$705$	−14.6433	−0.551500
$706$	27.5063	1.03521
$707$	−3.35683	−0.126247
$708$	30.7833	1.15691
$709$	9.81311	0.368539	0.184270	−	0.982876i	$-0.441008\pi$
$709$	9.81311	0.368539	0.184270	+	0.982876i	$0.441008\pi$
$710$	−39.0747	−1.46645
$711$	−13.0092	−0.487885
$712$	−3.08530	−0.115626
$713$	−4.70746	−0.176296
$714$	4.26096	0.159462
$715$	23.5967	0.882467
$716$	−78.1485	−2.92055
$717$	16.8514	0.629327
$718$	−84.8377	−3.16611
$719$	−24.9155	−0.929193	−0.464596	−	0.885522i	$-0.653801\pi$
$719$	−24.9155	−0.929193	−0.464596	+	0.885522i	$0.653801\pi$
$720$	−2.55030	−0.0950440
$721$	−1.44408	−0.0537802
$722$	30.7778	1.14543
$723$	−17.4282	−0.648160
$724$	−46.7200	−1.73633
$725$	3.26289	0.121181
$726$	−17.9504	−0.666203
$727$	36.6602	1.35965	0.679825	−	0.733374i	$-0.262056\pi$
$727$	36.6602	1.35965	0.679825	+	0.733374i	$0.262056\pi$
$728$	−13.8434	−0.513071
$729$	1.00000	0.0370370
$730$	26.7185	0.988897
$731$	23.0132	0.851175
$732$	−23.2267	−0.858484
$733$	18.9303	0.699206	0.349603	−	0.936898i	$-0.386317\pi$
$733$	18.9303	0.699206	0.349603	+	0.936898i	$0.386317\pi$
$734$	65.1165	2.40349
$735$	8.25279	0.304409
$736$	3.16122	0.116524
$737$	20.4529	0.753393
$738$	7.53445	0.277347
$739$	8.84818	0.325485	0.162743	−	0.986669i	$-0.447966\pi$
$739$	8.84818	0.325485	0.162743	+	0.986669i	$0.447966\pi$
$740$	18.8792	0.694012
$741$	10.2063	0.374939
$742$	−28.5869	−1.04946
$743$	4.67217	0.171405	0.0857026	−	0.996321i	$-0.472687\pi$
$743$	4.67217	0.171405	0.0857026	+	0.996321i	$0.472687\pi$
$744$	18.2505	0.669096
$745$	−15.4887	−0.567464
$746$	−31.6306	−1.15808
$747$	−14.2415	−0.521071
$748$	32.7055	1.19583
$749$	−9.70803	−0.354724
$750$	−25.8483	−0.943848
$751$	−23.8022	−0.868555	−0.434277	−	0.900779i	$-0.642996\pi$
$751$	−23.8022	−0.868555	−0.434277	+	0.900779i	$0.642996\pi$
$752$	21.4983	0.783961
$753$	10.2885	0.374935
$754$	−9.86283	−0.359183
$755$	14.6424	0.532892
$756$	−3.12218	−0.113552
$757$	−0.980413	−0.0356337	−0.0178169	−	0.999841i	$-0.505672\pi$
$757$	−0.980413	−0.0356337	−0.0178169	+	0.999841i	$0.505672\pi$
$758$	13.8821	0.504221
$759$	4.30847	0.156388
$760$	−12.5504	−0.455251
$761$	28.6974	1.04028	0.520140	−	0.854081i	$-0.325880\pi$
$761$	28.6974	1.04028	0.520140	+	0.854081i	$0.325880\pi$
$762$	−39.7288	−1.43922
$763$	15.1147	0.547187
$764$	6.09309	0.220440
$765$	−2.75356	−0.0995553
$766$	−33.0904	−1.19561
$767$	−35.2056	−1.27120
$768$	−26.3171	−0.949637
$769$	34.6389	1.24911	0.624556	−	0.780980i	$-0.285280\pi$
$769$	34.6389	1.24911	0.624556	+	0.780980i	$0.285280\pi$
$770$	−11.5815	−0.417367
$771$	−5.27151	−0.189849
$772$	−50.2755	−1.80945
$773$	3.18514	0.114561	0.0572807	−	0.998358i	$-0.481757\pi$
$773$	3.18514	0.114561	0.0572807	+	0.998358i	$0.481757\pi$
$774$	−26.1447	−0.939751
$775$	15.3599	0.551744
$776$	−15.2119	−0.546075
$777$	3.38760	0.121529
$778$	−57.6363	−2.06636
$779$	7.79686	0.279351
$780$	19.8997	0.712523
$781$	−53.8168	−1.92572
$782$	−4.95870	−0.177323
$783$	−1.00000	−0.0357371
$784$	−12.1161	−0.432719
$785$	25.6989	0.917232
$786$	53.0782	1.89324
$787$	47.6246	1.69764	0.848818	−	0.528686i	$-0.177315\pi$
$787$	47.6246	1.69764	0.848818	+	0.528686i	$0.177315\pi$
$788$	−101.306	−3.60888
$789$	−4.72941	−0.168371
$790$	−40.6961	−1.44790
$791$	3.42215	0.121678
$792$	−16.7037	−0.593539
$793$	26.5635	0.943297
$794$	79.6731	2.82749
$795$	18.4737	0.655194
$796$	−64.5424	−2.28764
$797$	44.5050	1.57645	0.788223	−	0.615389i	$-0.211001\pi$
$797$	44.5050	1.57645	0.788223	+	0.615389i	$0.211001\pi$
$798$	−5.00935	−0.177329
$799$	23.2117	0.821171
$800$	−10.3147	−0.364680
$801$	0.795808	0.0281185
$802$	−39.8496	−1.40714
$803$	36.7989	1.29860
$804$	17.2485	0.608306
$805$	1.13254	0.0399168
$806$	−46.4288	−1.63539
$807$	−21.2129	−0.746731
$808$	−15.1453	−0.532811
$809$	−34.0983	−1.19883	−0.599416	−	0.800438i	$-0.704600\pi$
$809$	−34.0983	−1.19883	−0.599416	+	0.800438i	$0.704600\pi$
$810$	3.12824	0.109915
$811$	−10.5525	−0.370550	−0.185275	−	0.982687i	$-0.559318\pi$
$811$	−10.5525	−0.370550	−0.185275	+	0.982687i	$0.559318\pi$
$812$	3.12218	0.109567
$813$	−11.0667	−0.388126
$814$	40.3145	1.41302
$815$	−28.2216	−0.988561
$816$	4.04257	0.141518
$817$	−27.0552	−0.946543
$818$	−80.5893	−2.81774
$819$	3.57071	0.124771
$820$	15.2018	0.530872
$821$	30.2775	1.05669	0.528345	−	0.849030i	$-0.322813\pi$
$821$	30.2775	1.05669	0.528345	+	0.849030i	$0.322813\pi$
$822$	30.5575	1.06582
$823$	−40.7346	−1.41992	−0.709960	−	0.704242i	$-0.751287\pi$
$823$	−40.7346	−1.41992	−0.709960	+	0.704242i	$0.751287\pi$
$824$	−6.51536	−0.226973
$825$	−14.0580	−0.489438
$826$	17.2792	0.601221
$827$	7.88557	0.274208	0.137104	−	0.990557i	$-0.456221\pi$
$827$	7.88557	0.274208	0.137104	+	0.990557i	$0.456221\pi$
$828$	3.63344	0.126271
$829$	8.87941	0.308395	0.154197	−	0.988040i	$-0.450721\pi$
$829$	8.87941	0.308395	0.154197	+	0.988040i	$0.450721\pi$
$830$	−44.5510	−1.54639
$831$	−7.98577	−0.277023
$832$	47.2599	1.63844
$833$	−13.0818	−0.453257
$834$	−30.3964	−1.05254
$835$	4.96662	0.171877
$836$	−38.4499	−1.32982
$837$	−4.70746	−0.162714
$838$	−2.97411	−0.102739
$839$	−0.405359	−0.0139946	−0.00699728	−	0.999976i	$-0.502227\pi$
$839$	−0.405359	−0.0139946	−0.00699728	+	0.999976i	$0.502227\pi$
$840$	−4.39079	−0.151497
$841$	1.00000	0.0344828
$842$	−46.8921	−1.61601
$843$	6.63114	0.228389
$844$	−78.9491	−2.71754
$845$	−5.62455	−0.193490
$846$	−26.3702	−0.906625
$847$	−6.49873	−0.223299
$848$	−27.1217	−0.931363
$849$	2.98274	0.102367
$850$	16.1797	0.554958
$851$	−3.94232	−0.135141
$852$	−45.3850	−1.55486
$853$	38.4556	1.31669	0.658347	−	0.752715i	$-0.271256\pi$
$853$	38.4556	1.31669	0.658347	+	0.752715i	$0.271256\pi$
$854$	−13.0376	−0.446137
$855$	3.23719	0.110710
$856$	−43.8006	−1.49707
$857$	−4.08648	−0.139592	−0.0697958	−	0.997561i	$-0.522235\pi$
$857$	−4.08648	−0.139592	−0.0697958	+	0.997561i	$0.522235\pi$
$858$	42.4937	1.45071
$859$	−26.7695	−0.913362	−0.456681	−	0.889631i	$-0.650962\pi$
$859$	−26.7695	−0.913362	−0.456681	+	0.889631i	$0.650962\pi$
$860$	−52.7507	−1.79878
$861$	2.72775	0.0929615
$862$	66.6606	2.27047
$863$	26.1278	0.889402	0.444701	−	0.895679i	$-0.353310\pi$
$863$	26.1278	0.889402	0.444701	+	0.895679i	$0.353310\pi$
$864$	3.16122	0.107547
$865$	−24.4669	−0.831899
$866$	90.0989	3.06169
$867$	−12.6352	−0.429115
$868$	14.6975	0.498866
$869$	−56.0499	−1.90136
$870$	−3.12824	−0.106057
$871$	−19.7264	−0.668403
$872$	68.1941	2.30934
$873$	3.92369	0.132797
$874$	5.82963	0.197190
$875$	−9.35806	−0.316360
$876$	31.0334	1.04852
$877$	−4.82414	−0.162900	−0.0814498	−	0.996677i	$-0.525955\pi$
$877$	−4.82414	−0.162900	−0.0814498	+	0.996677i	$0.525955\pi$
$878$	−78.4831	−2.64867
$879$	13.4117	0.452366
$880$	−10.9879	−0.370402
$881$	−24.2045	−0.815469	−0.407734	−	0.913101i	$-0.633681\pi$
$881$	−24.2045	−0.815469	−0.407734	+	0.913101i	$0.633681\pi$
$882$	14.8619	0.500425
$883$	18.1602	0.611139	0.305570	−	0.952170i	$-0.401153\pi$
$883$	18.1602	0.611139	0.305570	+	0.952170i	$0.401153\pi$
$884$	−31.5437	−1.06093
$885$	−11.1664	−0.375353
$886$	11.1036	0.373033
$887$	−40.7965	−1.36981	−0.684907	−	0.728630i	$-0.740157\pi$
$887$	−40.7965	−1.36981	−0.684907	+	0.728630i	$0.740157\pi$
$888$	15.2841	0.512901
$889$	−14.3833	−0.482400
$890$	2.48948	0.0834476
$891$	4.30847	0.144339
$892$	−0.591985	−0.0198211
$893$	−27.2886	−0.913177
$894$	−27.8926	−0.932867
$895$	28.3477	0.947558
$896$	−17.7627	−0.593411
$897$	−4.15542	−0.138745
$898$	−0.137237	−0.00457966
$899$	4.70746	0.157002
$900$	−11.8555	−0.395183
$901$	−29.2833	−0.975569
$902$	32.4619	1.08086
$903$	−9.46535	−0.314987
$904$	15.4400	0.513528
$905$	16.9473	0.563346
$906$	26.3685	0.876034
$907$	20.5919	0.683744	0.341872	−	0.939747i	$-0.388939\pi$
$907$	20.5919	0.683744	0.341872	+	0.939747i	$0.388939\pi$
$908$	−54.2917	−1.80173
$909$	3.90652	0.129571
$910$	11.1701	0.370284
$911$	0.555205	0.0183948	0.00919738	−	0.999958i	$-0.497072\pi$
$911$	0.555205	0.0183948	0.00919738	+	0.999958i	$0.497072\pi$
$912$	−4.75261	−0.157374
$913$	−61.3593	−2.03069
$914$	22.9963	0.760651
$915$	8.42528	0.278531
$916$	−33.0695	−1.09265
$917$	19.2163	0.634577
$918$	−4.95870	−0.163661
$919$	51.8269	1.70961	0.854805	−	0.518949i	$-0.173676\pi$
$919$	51.8269	1.70961	0.854805	+	0.518949i	$0.173676\pi$
$920$	5.10979	0.168465
$921$	−7.23125	−0.238278
$922$	−33.1432	−1.09151
$923$	51.9051	1.70848
$924$	−13.4518	−0.442532
$925$	12.8633	0.422944
$926$	−74.5262	−2.44908
$927$	1.68054	0.0551963
$928$	−3.16122	−0.103772
$929$	24.3448	0.798727	0.399364	−	0.916793i	$-0.369231\pi$
$929$	24.3448	0.798727	0.399364	+	0.916793i	$0.369231\pi$
$930$	−14.7261	−0.482887
$931$	15.3795	0.504042
$932$	−45.8675	−1.50244
$933$	0.648787	0.0212403
$934$	49.6718	1.62531
$935$	−11.8636	−0.387982
$936$	16.1103	0.526581
$937$	2.62171	0.0856475	0.0428237	−	0.999083i	$-0.486365\pi$
$937$	2.62171	0.0856475	0.0428237	+	0.999083i	$0.486365\pi$
$938$	9.68187	0.316124
$939$	18.3081	0.597461
$940$	−53.2057	−1.73538
$941$	−27.1040	−0.883566	−0.441783	−	0.897122i	$-0.645654\pi$
$941$	−27.1040	−0.883566	−0.441783	+	0.897122i	$0.645654\pi$
$942$	46.2793	1.50786
$943$	−3.17442	−0.103373
$944$	16.3936	0.533566
$945$	1.13254	0.0368416
$946$	−112.644	−3.66236
$947$	1.67384	0.0543924	0.0271962	−	0.999630i	$-0.491342\pi$
$947$	1.67384	0.0543924	0.0271962	+	0.999630i	$0.491342\pi$
$948$	−47.2682	−1.53520
$949$	−35.4917	−1.15211
$950$	−19.0214	−0.617137
$951$	−21.4173	−0.694504
$952$	6.96001	0.225575
$953$	−39.1266	−1.26743	−0.633717	−	0.773565i	$-0.718472\pi$
$953$	−39.1266	−1.26743	−0.633717	+	0.773565i	$0.718472\pi$
$954$	33.2680	1.07709
$955$	−2.21021	−0.0715209
$956$	61.2284	1.98027
$957$	−4.30847	−0.139273
$958$	−97.7136	−3.15698
$959$	11.0630	0.357242
$960$	14.9897	0.483789
$961$	−8.83984	−0.285156
$962$	−38.8824	−1.25362
$963$	11.2977	0.364064
$964$	−63.3241	−2.03953
$965$	18.2370	0.587069
$966$	2.03951	0.0656203
$967$	−46.2331	−1.48676	−0.743378	−	0.668872i	$-0.766777\pi$
$967$	−46.2331	−1.48676	−0.743378	+	0.668872i	$0.766777\pi$
$968$	−29.3209	−0.942409
$969$	−5.13140	−0.164844
$970$	12.2743	0.394103
$971$	39.1168	1.25532	0.627660	−	0.778488i	$-0.284013\pi$
$971$	39.1168	1.25532	0.627660	+	0.778488i	$0.284013\pi$
$972$	3.63344	0.116542
$973$	−11.0046	−0.352793
$974$	39.6603	1.27080
$975$	13.5587	0.434225
$976$	−12.3694	−0.395934
$977$	−11.4002	−0.364725	−0.182363	−	0.983231i	$-0.558374\pi$
$977$	−11.4002	−0.364725	−0.182363	+	0.983231i	$0.558374\pi$
$978$	−50.8223	−1.62512
$979$	3.42871	0.109582
$980$	29.9860	0.957867
$981$	−17.5897	−0.561596
$982$	−44.5213	−1.42073
$983$	47.4586	1.51369	0.756846	−	0.653593i	$-0.226739\pi$
$983$	47.4586	1.51369	0.756846	+	0.653593i	$0.226739\pi$
$984$	12.3070	0.392334
$985$	36.7478	1.17088
$986$	4.95870	0.157917
$987$	−9.54699	−0.303884
$988$	37.0840	1.17980
$989$	11.0153	0.350266
$990$	13.4779	0.428357
$991$	52.3146	1.66183	0.830914	−	0.556401i	$-0.187818\pi$
$991$	52.3146	1.66183	0.830914	+	0.556401i	$0.187818\pi$
$992$	−14.8813	−0.472482
$993$	2.79629	0.0887376
$994$	−25.4754	−0.808032
$995$	23.4122	0.742215
$996$	−51.7457	−1.63963
$997$	−46.9541	−1.48705	−0.743525	−	0.668708i	$-0.766848\pi$
$997$	−46.9541	−1.48705	−0.743525	+	0.668708i	$0.766848\pi$
$998$	−10.9262	−0.345863
$999$	−3.94232	−0.124729

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.i.1.1	✓	7
3.2	odd	2		6003.2.a.j.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.i.1.1	✓	7	1.1	even	1	trivial
6003.2.a.j.1.7		7	3.2	odd	2

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:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.37349 q^{2} +1.00000 q^{3} +3.63344 q^{4} -1.31800 q^{5} -2.37349 q^{6} -0.859291 q^{7} -3.87694 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.37349 q^{2} +1.00000 q^{3} +3.63344 q^{4} -1.31800 q^{5} -2.37349 q^{6} -0.859291 q^{7} -3.87694 q^{8} +1.00000 q^{9} +3.12824 q^{10} +4.30847 q^{11} +3.63344 q^{12} -4.15542 q^{13} +2.03951 q^{14} -1.31800 q^{15} +1.93498 q^{16} +2.08920 q^{17} -2.37349 q^{18} -2.45615 q^{19} -4.78885 q^{20} -0.859291 q^{21} -10.2261 q^{22} +1.00000 q^{23} -3.87694 q^{24} -3.26289 q^{25} +9.86283 q^{26} +1.00000 q^{27} -3.12218 q^{28} -1.00000 q^{29} +3.12824 q^{30} -4.70746 q^{31} +3.16122 q^{32} +4.30847 q^{33} -4.95870 q^{34} +1.13254 q^{35} +3.63344 q^{36} -3.94232 q^{37} +5.82963 q^{38} -4.15542 q^{39} +5.10979 q^{40} -3.17442 q^{41} +2.03951 q^{42} +11.0153 q^{43} +15.6545 q^{44} -1.31800 q^{45} -2.37349 q^{46} +11.1103 q^{47} +1.93498 q^{48} -6.26162 q^{49} +7.74442 q^{50} +2.08920 q^{51} -15.0984 q^{52} -14.0165 q^{53} -2.37349 q^{54} -5.67854 q^{55} +3.33142 q^{56} -2.45615 q^{57} +2.37349 q^{58} +8.47222 q^{59} -4.78885 q^{60} -6.39249 q^{61} +11.1731 q^{62} -0.859291 q^{63} -11.3731 q^{64} +5.47682 q^{65} -10.2261 q^{66} +4.74715 q^{67} +7.59099 q^{68} +1.00000 q^{69} -2.68807 q^{70} -12.4909 q^{71} -3.87694 q^{72} +8.54106 q^{73} +9.35703 q^{74} -3.26289 q^{75} -8.92426 q^{76} -3.70223 q^{77} +9.86283 q^{78} -13.0092 q^{79} -2.55030 q^{80} +1.00000 q^{81} +7.53445 q^{82} -14.2415 q^{83} -3.12218 q^{84} -2.75356 q^{85} -26.1447 q^{86} -1.00000 q^{87} -16.7037 q^{88} +0.795808 q^{89} +3.12824 q^{90} +3.57071 q^{91} +3.63344 q^{92} -4.70746 q^{93} -26.3702 q^{94} +3.23719 q^{95} +3.16122 q^{96} +3.92369 q^{97} +14.8619 q^{98} +4.30847 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 3 q^{2} + 7 q^{3} + 5 q^{4} - 3 q^{5} - 3 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 3 * q^2 + 7 * q^3 + 5 * q^4 - 3 * q^5 - 3 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9	\( 7 q - 3 q^{2} + 7 q^{3} + 5 q^{4} - 3 q^{5} - 3 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9} + 3 q^{10} - 4 q^{11} + 5 q^{12} - 18 q^{13} - 2 q^{14} - 3 q^{15} - 7 q^{16} - 3 q^{17} - 3 q^{18} - 4 q^{19} - 2 q^{20} - 5 q^{21} - 26 q^{22} + 7 q^{23} - 6 q^{24} - 8 q^{25} - 7 q^{26} + 7 q^{27} - 6 q^{28} - 7 q^{29} + 3 q^{30} - 22 q^{31} + 5 q^{32} - 4 q^{33} + 9 q^{34} + 3 q^{35} + 5 q^{36} - 25 q^{37} + 14 q^{38} - 18 q^{39} - 10 q^{40} - 13 q^{41} - 2 q^{42} - 2 q^{43} + 4 q^{44} - 3 q^{45} - 3 q^{46} - 25 q^{47} - 7 q^{48} - 8 q^{49} + 19 q^{50} - 3 q^{51} - 12 q^{52} - 5 q^{53} - 3 q^{54} - 15 q^{55} + 18 q^{56} - 4 q^{57} + 3 q^{58} + 11 q^{59} - 2 q^{60} - 33 q^{61} + 28 q^{62} - 5 q^{63} - 14 q^{64} - 2 q^{65} - 26 q^{66} + 8 q^{67} + 12 q^{68} + 7 q^{69} - 22 q^{70} - 6 q^{71} - 6 q^{72} + 15 q^{73} + 34 q^{74} - 8 q^{75} - 28 q^{76} - q^{77} - 7 q^{78} - 15 q^{79} - 12 q^{80} + 7 q^{81} - 14 q^{82} + 21 q^{83} - 6 q^{84} - 28 q^{85} - 12 q^{86} - 7 q^{87} - 13 q^{88} + 8 q^{89} + 3 q^{90} + 6 q^{91} + 5 q^{92} - 22 q^{93} - 35 q^{94} - 25 q^{95} + 5 q^{96} + 13 q^{97} + q^{98} - 4 q^{99}+O(q^{100}) \) 7 * q - 3 * q^2 + 7 * q^3 + 5 * q^4 - 3 * q^5 - 3 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9 + 3 * q^10 - 4 * q^11 + 5 * q^12 - 18 * q^13 - 2 * q^14 - 3 * q^15 - 7 * q^16 - 3 * q^17 - 3 * q^18 - 4 * q^19 - 2 * q^20 - 5 * q^21 - 26 * q^22 + 7 * q^23 - 6 * q^24 - 8 * q^25 - 7 * q^26 + 7 * q^27 - 6 * q^28 - 7 * q^29 + 3 * q^30 - 22 * q^31 + 5 * q^32 - 4 * q^33 + 9 * q^34 + 3 * q^35 + 5 * q^36 - 25 * q^37 + 14 * q^38 - 18 * q^39 - 10 * q^40 - 13 * q^41 - 2 * q^42 - 2 * q^43 + 4 * q^44 - 3 * q^45 - 3 * q^46 - 25 * q^47 - 7 * q^48 - 8 * q^49 + 19 * q^50 - 3 * q^51 - 12 * q^52 - 5 * q^53 - 3 * q^54 - 15 * q^55 + 18 * q^56 - 4 * q^57 + 3 * q^58 + 11 * q^59 - 2 * q^60 - 33 * q^61 + 28 * q^62 - 5 * q^63 - 14 * q^64 - 2 * q^65 - 26 * q^66 + 8 * q^67 + 12 * q^68 + 7 * q^69 - 22 * q^70 - 6 * q^71 - 6 * q^72 + 15 * q^73 + 34 * q^74 - 8 * q^75 - 28 * q^76 - q^77 - 7 * q^78 - 15 * q^79 - 12 * q^80 + 7 * q^81 - 14 * q^82 + 21 * q^83 - 6 * q^84 - 28 * q^85 - 12 * q^86 - 7 * q^87 - 13 * q^88 + 8 * q^89 + 3 * q^90 + 6 * q^91 + 5 * q^92 - 22 * q^93 - 35 * q^94 - 25 * q^95 + 5 * q^96 + 13 * q^97 + q^98 - 4 * q^99

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