LMFDB - Embedded newform 8007.2.a.j.1.50

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.50
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.95842 q^{2} -1.00000 q^{3} +1.83542 q^{4} -2.19003 q^{5} -1.95842 q^{6} -4.29364 q^{7} -0.322309 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.95842 q^{2} -1.00000 q^{3} +1.83542 q^{4} -2.19003 q^{5} -1.95842 q^{6} -4.29364 q^{7} -0.322309 q^{8} +1.00000 q^{9} -4.28901 q^{10} -6.41477 q^{11} -1.83542 q^{12} +0.303878 q^{13} -8.40876 q^{14} +2.19003 q^{15} -4.30207 q^{16} +1.00000 q^{17} +1.95842 q^{18} +2.54157 q^{19} -4.01963 q^{20} +4.29364 q^{21} -12.5628 q^{22} -4.18200 q^{23} +0.322309 q^{24} -0.203772 q^{25} +0.595123 q^{26} -1.00000 q^{27} -7.88064 q^{28} -7.59690 q^{29} +4.28901 q^{30} -5.54840 q^{31} -7.78065 q^{32} +6.41477 q^{33} +1.95842 q^{34} +9.40319 q^{35} +1.83542 q^{36} -10.8247 q^{37} +4.97746 q^{38} -0.303878 q^{39} +0.705866 q^{40} +7.35158 q^{41} +8.40876 q^{42} -6.10712 q^{43} -11.7738 q^{44} -2.19003 q^{45} -8.19013 q^{46} -1.82760 q^{47} +4.30207 q^{48} +11.4353 q^{49} -0.399072 q^{50} -1.00000 q^{51} +0.557746 q^{52} +7.60145 q^{53} -1.95842 q^{54} +14.0485 q^{55} +1.38388 q^{56} -2.54157 q^{57} -14.8779 q^{58} +4.28415 q^{59} +4.01963 q^{60} -3.97763 q^{61} -10.8661 q^{62} -4.29364 q^{63} -6.63368 q^{64} -0.665503 q^{65} +12.5628 q^{66} -7.16659 q^{67} +1.83542 q^{68} +4.18200 q^{69} +18.4154 q^{70} -2.01765 q^{71} -0.322309 q^{72} +0.629025 q^{73} -21.1993 q^{74} +0.203772 q^{75} +4.66485 q^{76} +27.5427 q^{77} -0.595123 q^{78} +3.27001 q^{79} +9.42165 q^{80} +1.00000 q^{81} +14.3975 q^{82} +7.09295 q^{83} +7.88064 q^{84} -2.19003 q^{85} -11.9603 q^{86} +7.59690 q^{87} +2.06754 q^{88} -2.28542 q^{89} -4.28901 q^{90} -1.30474 q^{91} -7.67574 q^{92} +5.54840 q^{93} -3.57922 q^{94} -5.56610 q^{95} +7.78065 q^{96} +9.74234 q^{97} +22.3952 q^{98} -6.41477 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * 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 $

$2$	1.95842	1.38481	0.692407	−	0.721507i	$-0.256550\pi$
$2$	1.95842	1.38481	0.692407	+	0.721507i	$0.256550\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.83542	0.917712
$5$	−2.19003	−0.979411	−0.489705	−	0.871888i	$-0.662896\pi$
$5$	−2.19003	−0.979411	−0.489705	+	0.871888i	$0.662896\pi$
$6$	−1.95842	−0.799523
$7$	−4.29364	−1.62284	−0.811421	−	0.584462i	$-0.801306\pi$
$7$	−4.29364	−1.62284	−0.811421	+	0.584462i	$0.801306\pi$
$8$	−0.322309	−0.113953
$9$	1.00000	0.333333
$10$	−4.28901	−1.35630
$11$	−6.41477	−1.93413	−0.967063	−	0.254538i	$-0.918076\pi$
$11$	−6.41477	−1.93413	−0.967063	+	0.254538i	$0.918076\pi$
$12$	−1.83542	−0.529841
$13$	0.303878	0.0842807	0.0421404	−	0.999112i	$-0.486582\pi$
$13$	0.303878	0.0842807	0.0421404	+	0.999112i	$0.486582\pi$
$14$	−8.40876	−2.24734
$15$	2.19003	0.565463
$16$	−4.30207	−1.07552
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.95842	0.461605
$19$	2.54157	0.583075	0.291538	−	0.956559i	$-0.405833\pi$
$19$	2.54157	0.583075	0.291538	+	0.956559i	$0.405833\pi$
$20$	−4.01963	−0.898817
$21$	4.29364	0.936948
$22$	−12.5628	−2.67841
$23$	−4.18200	−0.872007	−0.436004	−	0.899945i	$-0.643607\pi$
$23$	−4.18200	−0.872007	−0.436004	+	0.899945i	$0.643607\pi$
$24$	0.322309	0.0657910
$25$	−0.203772	−0.0407544
$26$	0.595123	0.116713
$27$	−1.00000	−0.192450
$28$	−7.88064	−1.48930
$29$	−7.59690	−1.41071	−0.705354	−	0.708855i	$-0.749212\pi$
$29$	−7.59690	−1.41071	−0.705354	+	0.708855i	$0.749212\pi$
$30$	4.28901	0.783062
$31$	−5.54840	−0.996522	−0.498261	−	0.867027i	$-0.666028\pi$
$31$	−5.54840	−0.996522	−0.498261	+	0.867027i	$0.666028\pi$
$32$	−7.78065	−1.37544
$33$	6.41477	1.11667
$34$	1.95842	0.335867
$35$	9.40319	1.58943
$36$	1.83542	0.305904
$37$	−10.8247	−1.77957	−0.889783	−	0.456383i	$-0.849145\pi$
$37$	−10.8247	−1.77957	−0.889783	+	0.456383i	$0.849145\pi$
$38$	4.97746	0.807451
$39$	−0.303878	−0.0486595
$40$	0.705866	0.111607
$41$	7.35158	1.14812	0.574062	−	0.818812i	$-0.305367\pi$
$41$	7.35158	1.14812	0.574062	+	0.818812i	$0.305367\pi$
$42$	8.40876	1.29750
$43$	−6.10712	−0.931326	−0.465663	−	0.884962i	$-0.654184\pi$
$43$	−6.10712	−0.931326	−0.465663	+	0.884962i	$0.654184\pi$
$44$	−11.7738	−1.77497
$45$	−2.19003	−0.326470
$46$	−8.19013	−1.20757
$47$	−1.82760	−0.266584	−0.133292	−	0.991077i	$-0.542555\pi$
$47$	−1.82760	−0.266584	−0.133292	+	0.991077i	$0.542555\pi$
$48$	4.30207	0.620950
$49$	11.4353	1.63362
$50$	−0.399072	−0.0564373
$51$	−1.00000	−0.140028
$52$	0.557746	0.0773454
$53$	7.60145	1.04414	0.522069	−	0.852903i	$-0.325160\pi$
$53$	7.60145	1.04414	0.522069	+	0.852903i	$0.325160\pi$
$54$	−1.95842	−0.266508
$55$	14.0485	1.89430
$56$	1.38388	0.184928
$57$	−2.54157	−0.336639
$58$	−14.8779	−1.95357
$59$	4.28415	0.557749	0.278875	−	0.960327i	$-0.410039\pi$
$59$	4.28415	0.557749	0.278875	+	0.960327i	$0.410039\pi$
$60$	4.01963	0.518932
$61$	−3.97763	−0.509284	−0.254642	−	0.967035i	$-0.581958\pi$
$61$	−3.97763	−0.509284	−0.254642	+	0.967035i	$0.581958\pi$
$62$	−10.8661	−1.38000
$63$	−4.29364	−0.540947
$64$	−6.63368	−0.829210
$65$	−0.665503	−0.0825454
$66$	12.5628	1.54638
$67$	−7.16659	−0.875538	−0.437769	−	0.899087i	$-0.644231\pi$
$67$	−7.16659	−0.875538	−0.437769	+	0.899087i	$0.644231\pi$
$68$	1.83542	0.222578
$69$	4.18200	0.503454
$70$	18.4154	2.20106
$71$	−2.01765	−0.239451	−0.119725	−	0.992807i	$-0.538201\pi$
$71$	−2.01765	−0.239451	−0.119725	+	0.992807i	$0.538201\pi$
$72$	−0.322309	−0.0379845
$73$	0.629025	0.0736218	0.0368109	−	0.999322i	$-0.488280\pi$
$73$	0.629025	0.0736218	0.0368109	+	0.999322i	$0.488280\pi$
$74$	−21.1993	−2.46437
$75$	0.203772	0.0235295
$76$	4.66485	0.535095
$77$	27.5427	3.13878
$78$	−0.595123	−0.0673844
$79$	3.27001	0.367905	0.183952	−	0.982935i	$-0.441111\pi$
$79$	3.27001	0.367905	0.183952	+	0.982935i	$0.441111\pi$
$80$	9.42165	1.05337
$81$	1.00000	0.111111
$82$	14.3975	1.58994
$83$	7.09295	0.778552	0.389276	−	0.921121i	$-0.372725\pi$
$83$	7.09295	0.778552	0.389276	+	0.921121i	$0.372725\pi$
$84$	7.88064	0.859849
$85$	−2.19003	−0.237542
$86$	−11.9603	−1.28971
$87$	7.59690	0.814473
$88$	2.06754	0.220400
$89$	−2.28542	−0.242254	−0.121127	−	0.992637i	$-0.538651\pi$
$89$	−2.28542	−0.242254	−0.121127	+	0.992637i	$0.538651\pi$
$90$	−4.28901	−0.452101
$91$	−1.30474	−0.136774
$92$	−7.67574	−0.800252
$93$	5.54840	0.575342
$94$	−3.57922	−0.369169
$95$	−5.56610	−0.571070
$96$	7.78065	0.794109
$97$	9.74234	0.989185	0.494592	−	0.869125i	$-0.335317\pi$
$97$	9.74234	0.989185	0.494592	+	0.869125i	$0.335317\pi$
$98$	22.3952	2.26226
$99$	−6.41477	−0.644708
$100$	−0.374008	−0.0374008
$101$	−11.9423	−1.18830	−0.594150	−	0.804354i	$-0.702512\pi$
$101$	−11.9423	−1.18830	−0.594150	+	0.804354i	$0.702512\pi$
$102$	−1.95842	−0.193913
$103$	−17.0347	−1.67848	−0.839241	−	0.543759i	$-0.817000\pi$
$103$	−17.0347	−1.67848	−0.839241	+	0.543759i	$0.817000\pi$
$104$	−0.0979427	−0.00960408
$105$	−9.40319	−0.917657
$106$	14.8869	1.44594
$107$	−12.3214	−1.19115	−0.595577	−	0.803298i	$-0.703077\pi$
$107$	−12.3214	−1.19115	−0.595577	+	0.803298i	$0.703077\pi$
$108$	−1.83542	−0.176614
$109$	0.129789	0.0124315	0.00621576	−	0.999981i	$-0.498021\pi$
$109$	0.129789	0.0124315	0.00621576	+	0.999981i	$0.498021\pi$
$110$	27.5130	2.62326
$111$	10.8247	1.02743
$112$	18.4715	1.74539
$113$	−8.67829	−0.816385	−0.408192	−	0.912896i	$-0.633841\pi$
$113$	−8.67829	−0.816385	−0.408192	+	0.912896i	$0.633841\pi$
$114$	−4.97746	−0.466182
$115$	9.15870	0.854053
$116$	−13.9435	−1.29462
$117$	0.303878	0.0280936
$118$	8.39019	0.772380
$119$	−4.29364	−0.393597
$120$	−0.705866	−0.0644365
$121$	30.1492	2.74084
$122$	−7.78989	−0.705264
$123$	−7.35158	−0.662869
$124$	−10.1837	−0.914520
$125$	11.3964	1.01933
$126$	−8.40876	−0.749112
$127$	20.5353	1.82222	0.911108	−	0.412168i	$-0.135228\pi$
$127$	20.5353	1.82222	0.911108	+	0.412168i	$0.135228\pi$
$128$	2.56974	0.227135
$129$	6.10712	0.537701
$130$	−1.30334	−0.114310
$131$	8.57955	0.749599	0.374800	−	0.927106i	$-0.377712\pi$
$131$	8.57955	0.749599	0.374800	+	0.927106i	$0.377712\pi$
$132$	11.7738	1.02478
$133$	−10.9126	−0.946239
$134$	−14.0352	−1.21246
$135$	2.19003	0.188488
$136$	−0.322309	−0.0276378
$137$	8.39400	0.717147	0.358574	−	0.933501i	$-0.383263\pi$
$137$	8.39400	0.717147	0.358574	+	0.933501i	$0.383263\pi$
$138$	8.19013	0.697190
$139$	9.68396	0.821383	0.410691	−	0.911774i	$-0.365287\pi$
$139$	9.68396	0.821383	0.410691	+	0.911774i	$0.365287\pi$
$140$	17.2588	1.45864
$141$	1.82760	0.153912
$142$	−3.95141	−0.331595
$143$	−1.94931	−0.163009
$144$	−4.30207	−0.358506
$145$	16.6374	1.38166
$146$	1.23190	0.101953
$147$	−11.4353	−0.943168
$148$	−19.8679	−1.63313
$149$	−17.2958	−1.41693	−0.708463	−	0.705748i	$-0.750611\pi$
$149$	−17.2958	−1.41693	−0.708463	+	0.705748i	$0.750611\pi$
$150$	0.399072	0.0325841
$151$	−15.8280	−1.28806	−0.644032	−	0.764998i	$-0.722740\pi$
$151$	−15.8280	−1.28806	−0.644032	+	0.764998i	$0.722740\pi$
$152$	−0.819169	−0.0664434
$153$	1.00000	0.0808452
$154$	53.9402	4.34663
$155$	12.1512	0.976005
$156$	−0.557746	−0.0446554
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	6.40406	0.509480
$159$	−7.60145	−0.602834
$160$	17.0399	1.34712
$161$	17.9560	1.41513
$162$	1.95842	0.153868
$163$	2.64691	0.207322	0.103661	−	0.994613i	$-0.466944\pi$
$163$	2.64691	0.207322	0.103661	+	0.994613i	$0.466944\pi$
$164$	13.4933	1.05365
$165$	−14.0485	−1.09368
$166$	13.8910	1.07815
$167$	2.83634	0.219482	0.109741	−	0.993960i	$-0.464998\pi$
$167$	2.83634	0.219482	0.109741	+	0.993960i	$0.464998\pi$
$168$	−1.38388	−0.106768
$169$	−12.9077	−0.992897
$170$	−4.28901	−0.328952
$171$	2.54157	0.194358
$172$	−11.2091	−0.854689
$173$	−0.319446	−0.0242870	−0.0121435	−	0.999926i	$-0.503865\pi$
$173$	−0.319446	−0.0242870	−0.0121435	+	0.999926i	$0.503865\pi$
$174$	14.8779	1.12789
$175$	0.874922	0.0661379
$176$	27.5968	2.08018
$177$	−4.28415	−0.322017
$178$	−4.47582	−0.335477
$179$	−18.6293	−1.39242	−0.696209	−	0.717839i	$-0.745131\pi$
$179$	−18.6293	−1.39242	−0.696209	+	0.717839i	$0.745131\pi$
$180$	−4.01963	−0.299606
$181$	20.9268	1.55548	0.777738	−	0.628588i	$-0.216367\pi$
$181$	20.9268	1.55548	0.777738	+	0.628588i	$0.216367\pi$
$182$	−2.55524	−0.189407
$183$	3.97763	0.294035
$184$	1.34790	0.0993682
$185$	23.7064	1.74293
$186$	10.8661	0.796743
$187$	−6.41477	−0.469094
$188$	−3.35443	−0.244647
$189$	4.29364	0.312316
$190$	−10.9008	−0.790826
$191$	−21.5347	−1.55820	−0.779099	−	0.626901i	$-0.784323\pi$
$191$	−21.5347	−1.55820	−0.779099	+	0.626901i	$0.784323\pi$
$192$	6.63368	0.478745
$193$	5.59292	0.402587	0.201293	−	0.979531i	$-0.435486\pi$
$193$	5.59292	0.402587	0.201293	+	0.979531i	$0.435486\pi$
$194$	19.0796	1.36984
$195$	0.665503	0.0476576
$196$	20.9886	1.49919
$197$	−18.0328	−1.28478	−0.642392	−	0.766376i	$-0.722058\pi$
$197$	−18.0328	−1.28478	−0.642392	+	0.766376i	$0.722058\pi$
$198$	−12.5628	−0.892802
$199$	6.13999	0.435252	0.217626	−	0.976032i	$-0.430169\pi$
$199$	6.13999	0.435252	0.217626	+	0.976032i	$0.430169\pi$
$200$	0.0656775	0.00464410
$201$	7.16659	0.505492
$202$	−23.3880	−1.64558
$203$	32.6183	2.28936
$204$	−1.83542	−0.128505
$205$	−16.1002	−1.12448
$206$	−33.3612	−2.32439
$207$	−4.18200	−0.290669
$208$	−1.30731	−0.0906453
$209$	−16.3036	−1.12774
$210$	−18.4154	−1.27079
$211$	15.9366	1.09712	0.548560	−	0.836111i	$-0.315176\pi$
$211$	15.9366	1.09712	0.548560	+	0.836111i	$0.315176\pi$
$212$	13.9519	0.958219
$213$	2.01765	0.138247
$214$	−24.1305	−1.64953
$215$	13.3748	0.912151
$216$	0.322309	0.0219303
$217$	23.8228	1.61720
$218$	0.254182	0.0172154
$219$	−0.629025	−0.0425055
$220$	25.7850	1.73843
$221$	0.303878	0.0204411
$222$	21.1993	1.42281
$223$	1.84624	0.123633	0.0618167	−	0.998088i	$-0.480311\pi$
$223$	1.84624	0.123633	0.0618167	+	0.998088i	$0.480311\pi$
$224$	33.4073	2.23212
$225$	−0.203772	−0.0135848
$226$	−16.9958	−1.13054
$227$	7.20570	0.478259	0.239129	−	0.970988i	$-0.423138\pi$
$227$	7.20570	0.478259	0.239129	+	0.970988i	$0.423138\pi$
$228$	−4.66485	−0.308937
$229$	4.11164	0.271705	0.135852	−	0.990729i	$-0.456623\pi$
$229$	4.11164	0.271705	0.135852	+	0.990729i	$0.456623\pi$
$230$	17.9366	1.18271
$231$	−27.5427	−1.81218
$232$	2.44855	0.160755
$233$	−8.88317	−0.581956	−0.290978	−	0.956730i	$-0.593981\pi$
$233$	−8.88317	−0.581956	−0.290978	+	0.956730i	$0.593981\pi$
$234$	0.595123	0.0389044
$235$	4.00251	0.261095
$236$	7.86324	0.511853
$237$	−3.27001	−0.212410
$238$	−8.40876	−0.545059
$239$	−24.7988	−1.60410	−0.802049	−	0.597258i	$-0.796257\pi$
$239$	−24.7988	−1.60410	−0.802049	+	0.597258i	$0.796257\pi$
$240$	−9.42165	−0.608165
$241$	4.22606	0.272224	0.136112	−	0.990693i	$-0.456539\pi$
$241$	4.22606	0.272224	0.136112	+	0.990693i	$0.456539\pi$
$242$	59.0450	3.79556
$243$	−1.00000	−0.0641500
$244$	−7.30065	−0.467376
$245$	−25.0437	−1.59998
$246$	−14.3975	−0.917951
$247$	0.772327	0.0491420
$248$	1.78830	0.113557
$249$	−7.09295	−0.449497
$250$	22.3190	1.41158
$251$	7.19708	0.454276	0.227138	−	0.973863i	$-0.427063\pi$
$251$	7.19708	0.454276	0.227138	+	0.973863i	$0.427063\pi$
$252$	−7.88064	−0.496434
$253$	26.8266	1.68657
$254$	40.2169	2.52343
$255$	2.19003	0.137145
$256$	18.3000	1.14375
$257$	10.9722	0.684424	0.342212	−	0.939623i	$-0.388824\pi$
$257$	10.9722	0.684424	0.342212	+	0.939623i	$0.388824\pi$
$258$	11.9603	0.744617
$259$	46.4772	2.88796
$260$	−1.22148	−0.0757530
$261$	−7.59690	−0.470236
$262$	16.8024	1.03806
$263$	3.42840	0.211404	0.105702	−	0.994398i	$-0.466291\pi$
$263$	3.42840	0.211404	0.105702	+	0.994398i	$0.466291\pi$
$264$	−2.06754	−0.127248
$265$	−16.6474	−1.02264
$266$	−21.3714	−1.31037
$267$	2.28542	0.139865
$268$	−13.1537	−0.803492
$269$	−27.3826	−1.66955	−0.834773	−	0.550594i	$-0.814401\pi$
$269$	−27.3826	−1.66955	−0.834773	+	0.550594i	$0.814401\pi$
$270$	4.28901	0.261021
$271$	−23.3262	−1.41697	−0.708484	−	0.705727i	$-0.750621\pi$
$271$	−23.3262	−1.41697	−0.708484	+	0.705727i	$0.750621\pi$
$272$	−4.30207	−0.260851
$273$	1.30474	0.0789667
$274$	16.4390	0.993116
$275$	1.30715	0.0788241
$276$	7.67574	0.462026
$277$	3.97030	0.238552	0.119276	−	0.992861i	$-0.461943\pi$
$277$	3.97030	0.238552	0.119276	+	0.992861i	$0.461943\pi$
$278$	18.9653	1.13746
$279$	−5.54840	−0.332174
$280$	−3.03073	−0.181121
$281$	25.9367	1.54726	0.773628	−	0.633640i	$-0.218440\pi$
$281$	25.9367	1.54726	0.773628	+	0.633640i	$0.218440\pi$
$282$	3.57922	0.213140
$283$	14.5519	0.865020	0.432510	−	0.901629i	$-0.357628\pi$
$283$	14.5519	0.865020	0.432510	+	0.901629i	$0.357628\pi$
$284$	−3.70324	−0.219747
$285$	5.56610	0.329708
$286$	−3.81757	−0.225738
$287$	−31.5650	−1.86322
$288$	−7.78065	−0.458479
$289$	1.00000	0.0588235
$290$	32.5831	1.91335
$291$	−9.74234	−0.571106
$292$	1.15453	0.0675636
$293$	24.9692	1.45871	0.729357	−	0.684133i	$-0.239819\pi$
$293$	24.9692	1.45871	0.729357	+	0.684133i	$0.239819\pi$
$294$	−22.3952	−1.30611
$295$	−9.38242	−0.546266
$296$	3.48889	0.202788
$297$	6.41477	0.372223
$298$	−33.8725	−1.96218
$299$	−1.27082	−0.0734934
$300$	0.374008	0.0215934
$301$	26.2217	1.51140
$302$	−30.9979	−1.78373
$303$	11.9423	0.686066
$304$	−10.9340	−0.627107
$305$	8.71113	0.498798
$306$	1.95842	0.111956
$307$	−22.6609	−1.29333	−0.646663	−	0.762776i	$-0.723836\pi$
$307$	−22.6609	−1.29333	−0.646663	+	0.762776i	$0.723836\pi$
$308$	50.5525	2.88050
$309$	17.0347	0.969072
$310$	23.7971	1.35159
$311$	−18.6754	−1.05898	−0.529492	−	0.848315i	$-0.677617\pi$
$311$	−18.6754	−1.05898	−0.529492	+	0.848315i	$0.677617\pi$
$312$	0.0979427	0.00554492
$313$	−16.6168	−0.939236	−0.469618	−	0.882870i	$-0.655608\pi$
$313$	−16.6168	−0.939236	−0.469618	+	0.882870i	$0.655608\pi$
$314$	−1.95842	−0.110520
$315$	9.40319	0.529810
$316$	6.00185	0.337631
$317$	−14.4688	−0.812650	−0.406325	−	0.913729i	$-0.633190\pi$
$317$	−14.4688	−0.812650	−0.406325	+	0.913729i	$0.633190\pi$
$318$	−14.8869	−0.834813
$319$	48.7323	2.72849
$320$	14.5280	0.812137
$321$	12.3214	0.687714
$322$	35.1654	1.95969
$323$	2.54157	0.141417
$324$	1.83542	0.101968
$325$	−0.0619219	−0.00343481
$326$	5.18378	0.287103
$327$	−0.129789	−0.00717734
$328$	−2.36948	−0.130833
$329$	7.84707	0.432623
$330$	−27.5130	−1.51454
$331$	−28.1638	−1.54802	−0.774010	−	0.633173i	$-0.781752\pi$
$331$	−28.1638	−1.54802	−0.774010	+	0.633173i	$0.781752\pi$
$332$	13.0186	0.714487
$333$	−10.8247	−0.593189
$334$	5.55475	0.303942
$335$	15.6950	0.857512
$336$	−18.4715	−1.00770
$337$	29.6503	1.61515	0.807577	−	0.589762i	$-0.200778\pi$
$337$	29.6503	1.61515	0.807577	+	0.589762i	$0.200778\pi$
$338$	−25.2787	−1.37498
$339$	8.67829	0.471340
$340$	−4.01963	−0.217995
$341$	35.5917	1.92740
$342$	4.97746	0.269150
$343$	−19.0436	−1.02826
$344$	1.96838	0.106128
$345$	−9.15870	−0.493088
$346$	−0.625610	−0.0336330
$347$	19.2910	1.03559	0.517797	−	0.855503i	$-0.326752\pi$
$347$	19.2910	1.03559	0.517797	+	0.855503i	$0.326752\pi$
$348$	13.9435	0.747452
$349$	−21.5713	−1.15469	−0.577343	−	0.816502i	$-0.695910\pi$
$349$	−21.5713	−1.15469	−0.577343	+	0.816502i	$0.695910\pi$
$350$	1.71347	0.0915888
$351$	−0.303878	−0.0162198
$352$	49.9111	2.66027
$353$	−32.1755	−1.71253	−0.856264	−	0.516539i	$-0.827220\pi$
$353$	−32.1755	−1.71253	−0.856264	+	0.516539i	$0.827220\pi$
$354$	−8.39019	−0.445934
$355$	4.41871	0.234521
$356$	−4.19472	−0.222320
$357$	4.29364	0.227243
$358$	−36.4840	−1.92824
$359$	11.9068	0.628418	0.314209	−	0.949354i	$-0.398261\pi$
$359$	11.9068	0.628418	0.314209	+	0.949354i	$0.398261\pi$
$360$	0.705866	0.0372024
$361$	−12.5404	−0.660023
$362$	40.9835	2.15405
$363$	−30.1492	−1.58243
$364$	−2.39476	−0.125519
$365$	−1.37758	−0.0721060
$366$	7.78989	0.407184
$367$	−2.01956	−0.105420	−0.0527102	−	0.998610i	$-0.516786\pi$
$367$	−2.01956	−0.105420	−0.0527102	+	0.998610i	$0.516786\pi$
$368$	17.9912	0.937858
$369$	7.35158	0.382708
$370$	46.4271	2.41363
$371$	−32.6378	−1.69447
$372$	10.1837	0.527999
$373$	0.713674	0.0369526	0.0184763	−	0.999829i	$-0.494118\pi$
$373$	0.713674	0.0369526	0.0184763	+	0.999829i	$0.494118\pi$
$374$	−12.5628	−0.649609
$375$	−11.3964	−0.588508
$376$	0.589053	0.0303781
$377$	−2.30853	−0.118896
$378$	8.40876	0.432500
$379$	−22.4230	−1.15179	−0.575897	−	0.817522i	$-0.695347\pi$
$379$	−22.4230	−1.15179	−0.575897	+	0.817522i	$0.695347\pi$
$380$	−10.2162	−0.524078
$381$	−20.5353	−1.05206
$382$	−42.1741	−2.15781
$383$	−34.1160	−1.74324	−0.871622	−	0.490178i	$-0.836932\pi$
$383$	−34.1160	−1.74324	−0.871622	+	0.490178i	$0.836932\pi$
$384$	−2.56974	−0.131137
$385$	−60.3193	−3.07415
$386$	10.9533	0.557508
$387$	−6.10712	−0.310442
$388$	17.8813	0.907787
$389$	−21.3123	−1.08058	−0.540288	−	0.841480i	$-0.681685\pi$
$389$	−21.3123	−1.08058	−0.540288	+	0.841480i	$0.681685\pi$
$390$	1.30334	0.0659970
$391$	−4.18200	−0.211493
$392$	−3.68570	−0.186156
$393$	−8.57955	−0.432781
$394$	−35.3159	−1.77919
$395$	−7.16142	−0.360330
$396$	−11.7738	−0.591657
$397$	−18.5594	−0.931468	−0.465734	−	0.884925i	$-0.654210\pi$
$397$	−18.5594	−0.931468	−0.465734	+	0.884925i	$0.654210\pi$
$398$	12.0247	0.602744
$399$	10.9126	0.546311
$400$	0.876640	0.0438320
$401$	26.3986	1.31829	0.659143	−	0.752018i	$-0.270919\pi$
$401$	26.3986	1.31829	0.659143	+	0.752018i	$0.270919\pi$
$402$	14.0352	0.700013
$403$	−1.68604	−0.0839876
$404$	−21.9191	−1.09052
$405$	−2.19003	−0.108823
$406$	63.8805	3.17034
$407$	69.4378	3.44191
$408$	0.322309	0.0159567
$409$	5.15886	0.255089	0.127545	−	0.991833i	$-0.459290\pi$
$409$	5.15886	0.255089	0.127545	+	0.991833i	$0.459290\pi$
$410$	−31.5310	−1.55720
$411$	−8.39400	−0.414045
$412$	−31.2660	−1.54036
$413$	−18.3946	−0.905139
$414$	−8.19013	−0.402523
$415$	−15.5338	−0.762522
$416$	−2.36437	−0.115923
$417$	−9.68396	−0.474226
$418$	−31.9293	−1.56171
$419$	−19.8507	−0.969771	−0.484885	−	0.874578i	$-0.661139\pi$
$419$	−19.8507	−0.969771	−0.484885	+	0.874578i	$0.661139\pi$
$420$	−17.2588	−0.842145
$421$	−6.81061	−0.331929	−0.165965	−	0.986132i	$-0.553074\pi$
$421$	−6.81061	−0.331929	−0.165965	+	0.986132i	$0.553074\pi$
$422$	31.2106	1.51931
$423$	−1.82760	−0.0888612
$424$	−2.45001	−0.118983
$425$	−0.203772	−0.00988439
$426$	3.95141	0.191446
$427$	17.0785	0.826487
$428$	−22.6150	−1.09314
$429$	1.94931	0.0941136
$430$	26.1935	1.26316
$431$	−19.3340	−0.931285	−0.465643	−	0.884973i	$-0.654177\pi$
$431$	−19.3340	−0.931285	−0.465643	+	0.884973i	$0.654177\pi$
$432$	4.30207	0.206983
$433$	7.60353	0.365403	0.182701	−	0.983168i	$-0.441516\pi$
$433$	7.60353	0.365403	0.182701	+	0.983168i	$0.441516\pi$
$434$	46.6552	2.23952
$435$	−16.6374	−0.797704
$436$	0.238218	0.0114086
$437$	−10.6288	−0.508446
$438$	−1.23190	−0.0588623
$439$	13.6313	0.650586	0.325293	−	0.945613i	$-0.394537\pi$
$439$	13.6313	0.650586	0.325293	+	0.945613i	$0.394537\pi$
$440$	−4.52797	−0.215862
$441$	11.4353	0.544539
$442$	0.595123	0.0283071
$443$	−2.07073	−0.0983833	−0.0491917	−	0.998789i	$-0.515665\pi$
$443$	−2.07073	−0.0983833	−0.0491917	+	0.998789i	$0.515665\pi$
$444$	19.8679	0.942888
$445$	5.00514	0.237266
$446$	3.61572	0.171209
$447$	17.2958	0.818062
$448$	28.4826	1.34568
$449$	−22.3414	−1.05435	−0.527177	−	0.849756i	$-0.676749\pi$
$449$	−22.3414	−1.05435	−0.527177	+	0.849756i	$0.676749\pi$
$450$	−0.399072	−0.0188124
$451$	−47.1587	−2.22061
$452$	−15.9283	−0.749206
$453$	15.8280	0.743664
$454$	14.1118	0.662300
$455$	2.85743	0.133958
$456$	0.819169	0.0383611
$457$	−1.57026	−0.0734538	−0.0367269	−	0.999325i	$-0.511693\pi$
$457$	−1.57026	−0.0734538	−0.0367269	+	0.999325i	$0.511693\pi$
$458$	8.05233	0.376260
$459$	−1.00000	−0.0466760
$460$	16.8101	0.783775
$461$	−23.8989	−1.11308	−0.556541	−	0.830820i	$-0.687872\pi$
$461$	−23.8989	−1.11308	−0.556541	+	0.830820i	$0.687872\pi$
$462$	−53.9402	−2.50953
$463$	−29.6942	−1.38001	−0.690004	−	0.723805i	$-0.742391\pi$
$463$	−29.6942	−1.38001	−0.690004	+	0.723805i	$0.742391\pi$
$464$	32.6824	1.51724
$465$	−12.1512	−0.563497
$466$	−17.3970	−0.805901
$467$	−32.8333	−1.51935	−0.759673	−	0.650305i	$-0.774641\pi$
$467$	−32.8333	−1.51935	−0.759673	+	0.650305i	$0.774641\pi$
$468$	0.557746	0.0257818
$469$	30.7707	1.42086
$470$	7.83861	0.361568
$471$	1.00000	0.0460776
$472$	−1.38082	−0.0635575
$473$	39.1757	1.80130
$474$	−6.40406	−0.294148
$475$	−0.517900	−0.0237629
$476$	−7.88064	−0.361209
$477$	7.60145	0.348046
$478$	−48.5665	−2.22138
$479$	34.0265	1.55471	0.777355	−	0.629062i	$-0.216561\pi$
$479$	34.0265	1.55471	0.777355	+	0.629062i	$0.216561\pi$
$480$	−17.0399	−0.777759
$481$	−3.28939	−0.149983
$482$	8.27642	0.376980
$483$	−17.9560	−0.817026
$484$	55.3367	2.51530
$485$	−21.3360	−0.968818
$486$	−1.95842	−0.0888359
$487$	24.1286	1.09337	0.546685	−	0.837339i	$-0.315890\pi$
$487$	24.1286	1.09337	0.546685	+	0.837339i	$0.315890\pi$
$488$	1.28203	0.0580346
$489$	−2.64691	−0.119697
$490$	−49.0461	−2.21568
$491$	−30.0780	−1.35740	−0.678701	−	0.734415i	$-0.737457\pi$
$491$	−30.0780	−1.35740	−0.678701	+	0.734415i	$0.737457\pi$
$492$	−13.4933	−0.608323
$493$	−7.59690	−0.342147
$494$	1.51254	0.0680526
$495$	14.0485	0.631434
$496$	23.8696	1.07178
$497$	8.66305	0.388591
$498$	−13.8910	−0.622471
$499$	−37.6935	−1.68739	−0.843697	−	0.536819i	$-0.819626\pi$
$499$	−37.6935	−1.68739	−0.843697	+	0.536819i	$0.819626\pi$
$500$	20.9173	0.935448
$501$	−2.83634	−0.126718
$502$	14.0949	0.629088
$503$	−13.0336	−0.581141	−0.290571	−	0.956854i	$-0.593845\pi$
$503$	−13.0336	−0.581141	−0.290571	+	0.956854i	$0.593845\pi$
$504$	1.38388	0.0616428
$505$	26.1539	1.16383
$506$	52.5378	2.33559
$507$	12.9077	0.573249
$508$	37.6910	1.67227
$509$	−37.6760	−1.66996	−0.834979	−	0.550281i	$-0.814521\pi$
$509$	−37.6760	−1.66996	−0.834979	+	0.550281i	$0.814521\pi$
$510$	4.28901	0.189920
$511$	−2.70080	−0.119476
$512$	30.6997	1.35675
$513$	−2.54157	−0.112213
$514$	21.4881	0.947801
$515$	37.3066	1.64392
$516$	11.2091	0.493455
$517$	11.7237	0.515606
$518$	91.0222	3.99928
$519$	0.319446	0.0140221
$520$	0.214497	0.00940634
$521$	−11.6753	−0.511502	−0.255751	−	0.966743i	$-0.582323\pi$
$521$	−11.6753	−0.511502	−0.255751	+	0.966743i	$0.582323\pi$
$522$	−14.8779	−0.651190
$523$	−5.15069	−0.225224	−0.112612	−	0.993639i	$-0.535922\pi$
$523$	−5.15069	−0.225224	−0.112612	+	0.993639i	$0.535922\pi$
$524$	15.7471	0.687916
$525$	−0.874922	−0.0381847
$526$	6.71426	0.292755
$527$	−5.54840	−0.241692
$528$	−27.5968	−1.20099
$529$	−5.51088	−0.239603
$530$	−32.6026	−1.41617
$531$	4.28415	0.185916
$532$	−20.0292	−0.868375
$533$	2.23399	0.0967647
$534$	4.47582	0.193688
$535$	26.9842	1.16663
$536$	2.30986	0.0997706
$537$	18.6293	0.803913
$538$	−53.6267	−2.31201
$539$	−73.3549	−3.15962
$540$	4.01963	0.172977
$541$	12.0868	0.519651	0.259825	−	0.965656i	$-0.416335\pi$
$541$	12.0868	0.519651	0.259825	+	0.965656i	$0.416335\pi$
$542$	−45.6827	−1.96224
$543$	−20.9268	−0.898055
$544$	−7.78065	−0.333593
$545$	−0.284241	−0.0121756
$546$	2.55524	0.109354
$547$	−5.26910	−0.225290	−0.112645	−	0.993635i	$-0.535932\pi$
$547$	−5.26910	−0.225290	−0.112645	+	0.993635i	$0.535932\pi$
$548$	15.4065	0.658135
$549$	−3.97763	−0.169761
$550$	2.55995	0.109157
$551$	−19.3080	−0.822549
$552$	−1.34790	−0.0573703
$553$	−14.0402	−0.597051
$554$	7.77553	0.330351
$555$	−23.7064	−1.00628
$556$	17.7742	0.753793
$557$	38.5461	1.63325	0.816625	−	0.577169i	$-0.195843\pi$
$557$	38.5461	1.63325	0.816625	+	0.577169i	$0.195843\pi$
$558$	−10.8661	−0.460000
$559$	−1.85582	−0.0784928
$560$	−40.4531	−1.70946
$561$	6.41477	0.270832
$562$	50.7951	2.14266
$563$	−36.2615	−1.52824	−0.764120	−	0.645074i	$-0.776827\pi$
$563$	−36.2615	−1.52824	−0.764120	+	0.645074i	$0.776827\pi$
$564$	3.35443	0.141247
$565$	19.0057	0.799576
$566$	28.4988	1.19789
$567$	−4.29364	−0.180316
$568$	0.650306	0.0272862
$569$	4.94934	0.207487	0.103744	−	0.994604i	$-0.466918\pi$
$569$	4.94934	0.207487	0.103744	+	0.994604i	$0.466918\pi$
$570$	10.9008	0.456584
$571$	5.65712	0.236743	0.118371	−	0.992969i	$-0.462233\pi$
$571$	5.65712	0.236743	0.118371	+	0.992969i	$0.462233\pi$
$572$	−3.57781	−0.149596
$573$	21.5347	0.899626
$574$	−61.8176	−2.58022
$575$	0.852174	0.0355381
$576$	−6.63368	−0.276403
$577$	1.28804	0.0536218	0.0268109	−	0.999641i	$-0.491465\pi$
$577$	1.28804	0.0536218	0.0268109	+	0.999641i	$0.491465\pi$
$578$	1.95842	0.0814597
$579$	−5.59292	−0.232434
$580$	30.5367	1.26797
$581$	−30.4545	−1.26347
$582$	−19.0796	−0.790876
$583$	−48.7615	−2.01950
$584$	−0.202740	−0.00838945
$585$	−0.665503	−0.0275151
$586$	48.9002	2.02005
$587$	−37.2870	−1.53900	−0.769499	−	0.638648i	$-0.779494\pi$
$587$	−37.2870	−1.53900	−0.769499	+	0.638648i	$0.779494\pi$
$588$	−20.9886	−0.865557
$589$	−14.1016	−0.581047
$590$	−18.3748	−0.756477
$591$	18.0328	0.741771
$592$	46.5685	1.91395
$593$	28.6571	1.17680	0.588402	−	0.808568i	$-0.299757\pi$
$593$	28.6571	1.17680	0.588402	+	0.808568i	$0.299757\pi$
$594$	12.5628	0.515459
$595$	9.40319	0.385493
$596$	−31.7451	−1.30033
$597$	−6.13999	−0.251293
$598$	−2.48880	−0.101775
$599$	36.2287	1.48026	0.740132	−	0.672461i	$-0.234763\pi$
$599$	36.2287	1.48026	0.740132	+	0.672461i	$0.234763\pi$
$600$	−0.0656775	−0.00268127
$601$	−1.69355	−0.0690813	−0.0345407	−	0.999403i	$-0.510997\pi$
$601$	−1.69355	−0.0690813	−0.0345407	+	0.999403i	$0.510997\pi$
$602$	51.3533	2.09300
$603$	−7.16659	−0.291846
$604$	−29.0511	−1.18207
$605$	−66.0277	−2.68441
$606$	23.3880	0.950074
$607$	20.3584	0.826320	0.413160	−	0.910658i	$-0.364425\pi$
$607$	20.3584	0.826320	0.413160	+	0.910658i	$0.364425\pi$
$608$	−19.7750	−0.801984
$609$	−32.6183	−1.32176
$610$	17.0601	0.690743
$611$	−0.555370	−0.0224679
$612$	1.83542	0.0741926
$613$	26.0602	1.05256	0.526280	−	0.850311i	$-0.323586\pi$
$613$	26.0602	1.05256	0.526280	+	0.850311i	$0.323586\pi$
$614$	−44.3796	−1.79102
$615$	16.1002	0.649221
$616$	−8.87725	−0.357675
$617$	1.47540	0.0593973	0.0296986	−	0.999559i	$-0.490545\pi$
$617$	1.47540	0.0593973	0.0296986	+	0.999559i	$0.490545\pi$
$618$	33.3612	1.34199
$619$	24.7097	0.993168	0.496584	−	0.867989i	$-0.334587\pi$
$619$	24.7097	0.993168	0.496584	+	0.867989i	$0.334587\pi$
$620$	22.3025	0.895691
$621$	4.18200	0.167818
$622$	−36.5743	−1.46650
$623$	9.81277	0.393140
$624$	1.30731	0.0523341
$625$	−23.9396	−0.957585
$626$	−32.5427	−1.30067
$627$	16.3036	0.651101
$628$	−1.83542	−0.0732414
$629$	−10.8247	−0.431608
$630$	18.4154	0.733688
$631$	−19.3190	−0.769076	−0.384538	−	0.923109i	$-0.625639\pi$
$631$	−19.3190	−0.769076	−0.384538	+	0.923109i	$0.625639\pi$
$632$	−1.05395	−0.0419240
$633$	−15.9366	−0.633423
$634$	−28.3361	−1.12537
$635$	−44.9730	−1.78470
$636$	−13.9519	−0.553228
$637$	3.47494	0.137682
$638$	95.4386	3.77845
$639$	−2.01765	−0.0798169
$640$	−5.62781	−0.222459
$641$	7.08009	0.279647	0.139823	−	0.990176i	$-0.455347\pi$
$641$	7.08009	0.279647	0.139823	+	0.990176i	$0.455347\pi$
$642$	24.1305	0.952356
$643$	12.9008	0.508758	0.254379	−	0.967105i	$-0.418129\pi$
$643$	12.9008	0.508758	0.254379	+	0.967105i	$0.418129\pi$
$644$	32.9569	1.29868
$645$	−13.3748	−0.526631
$646$	4.97746	0.195836
$647$	37.8154	1.48668	0.743339	−	0.668915i	$-0.233241\pi$
$647$	37.8154	1.48668	0.743339	+	0.668915i	$0.233241\pi$
$648$	−0.322309	−0.0126615
$649$	−27.4819	−1.07876
$650$	−0.121269	−0.00475657
$651$	−23.8228	−0.933690
$652$	4.85821	0.190262
$653$	12.9542	0.506937	0.253469	−	0.967344i	$-0.418429\pi$
$653$	12.9542	0.506937	0.253469	+	0.967344i	$0.418429\pi$
$654$	−0.254182	−0.00993929
$655$	−18.7895	−0.734166
$656$	−31.6270	−1.23483
$657$	0.629025	0.0245406
$658$	15.3679	0.599103
$659$	−41.3413	−1.61043	−0.805213	−	0.592985i	$-0.797949\pi$
$659$	−41.3413	−1.61043	−0.805213	+	0.592985i	$0.797949\pi$
$660$	−25.7850	−1.00368
$661$	23.6095	0.918301	0.459151	−	0.888358i	$-0.348154\pi$
$661$	23.6095	0.918301	0.459151	+	0.888358i	$0.348154\pi$
$662$	−55.1566	−2.14372
$663$	−0.303878	−0.0118017
$664$	−2.28612	−0.0887187
$665$	23.8988	0.926757
$666$	−21.1993	−0.821457
$667$	31.7702	1.23015
$668$	5.20588	0.201421
$669$	−1.84624	−0.0713797
$670$	30.7375	1.18749
$671$	25.5156	0.985019
$672$	−33.4073	−1.28871
$673$	32.0614	1.23588	0.617939	−	0.786226i	$-0.287968\pi$
$673$	32.0614	1.23588	0.617939	+	0.786226i	$0.287968\pi$
$674$	58.0679	2.23669
$675$	0.203772	0.00784318
$676$	−23.6910	−0.911193
$677$	21.0515	0.809073	0.404537	−	0.914522i	$-0.367433\pi$
$677$	21.0515	0.809073	0.404537	+	0.914522i	$0.367433\pi$
$678$	16.9958	0.652719
$679$	−41.8301	−1.60529
$680$	0.705866	0.0270687
$681$	−7.20570	−0.276123
$682$	69.7036	2.66909
$683$	4.04157	0.154646	0.0773232	−	0.997006i	$-0.475363\pi$
$683$	4.04157	0.154646	0.0773232	+	0.997006i	$0.475363\pi$
$684$	4.66485	0.178365
$685$	−18.3831	−0.702382
$686$	−37.2954	−1.42395
$687$	−4.11164	−0.156869
$688$	26.2732	1.00166
$689$	2.30992	0.0880008
$690$	−17.9366	−0.682836
$691$	38.8919	1.47952	0.739759	−	0.672872i	$-0.234940\pi$
$691$	38.8919	1.47952	0.739759	+	0.672872i	$0.234940\pi$
$692$	−0.586318	−0.0222885
$693$	27.5427	1.04626
$694$	37.7799	1.43411
$695$	−21.2082	−0.804471
$696$	−2.44855	−0.0928120
$697$	7.35158	0.278461
$698$	−42.2458	−1.59903
$699$	8.88317	0.335992
$700$	1.60585	0.0606956
$701$	−17.1218	−0.646682	−0.323341	−	0.946282i	$-0.604806\pi$
$701$	−17.1218	−0.646682	−0.323341	+	0.946282i	$0.604806\pi$
$702$	−0.595123	−0.0224615
$703$	−27.5116	−1.03762
$704$	42.5535	1.60380
$705$	−4.00251	−0.150743
$706$	−63.0132	−2.37153
$707$	51.2758	1.92842
$708$	−7.86324	−0.295519
$709$	−34.8214	−1.30775	−0.653873	−	0.756604i	$-0.726857\pi$
$709$	−34.8214	−1.30775	−0.653873	+	0.756604i	$0.726857\pi$
$710$	8.65371	0.324768
$711$	3.27001	0.122635
$712$	0.736612	0.0276057
$713$	23.2034	0.868975
$714$	8.40876	0.314690
$715$	4.26905	0.159653
$716$	−34.1926	−1.27784
$717$	24.7988	0.926127
$718$	23.3186	0.870243
$719$	−39.7172	−1.48120	−0.740602	−	0.671944i	$-0.765459\pi$
$719$	−39.7172	−1.48120	−0.740602	+	0.671944i	$0.765459\pi$
$720$	9.42165	0.351124
$721$	73.1409	2.72391
$722$	−24.5595	−0.914010
$723$	−4.22606	−0.157169
$724$	38.4096	1.42748
$725$	1.54803	0.0574925
$726$	−59.0450	−2.19137
$727$	5.18461	0.192287	0.0961433	−	0.995368i	$-0.469349\pi$
$727$	5.18461	0.192287	0.0961433	+	0.995368i	$0.469349\pi$
$728$	0.420530	0.0155859
$729$	1.00000	0.0370370
$730$	−2.69789	−0.0998534
$731$	−6.10712	−0.225880
$732$	7.30065	0.269840
$733$	42.4444	1.56772	0.783860	−	0.620937i	$-0.213248\pi$
$733$	42.4444	1.56772	0.783860	+	0.620937i	$0.213248\pi$
$734$	−3.95516	−0.145988
$735$	25.0437	0.923749
$736$	32.5387	1.19939
$737$	45.9720	1.69340
$738$	14.3975	0.529979
$739$	7.04465	0.259142	0.129571	−	0.991570i	$-0.458640\pi$
$739$	7.04465	0.259142	0.129571	+	0.991570i	$0.458640\pi$
$740$	43.5113	1.59951
$741$	−0.772327	−0.0283721
$742$	−63.9187	−2.34653
$743$	11.2453	0.412549	0.206275	−	0.978494i	$-0.433866\pi$
$743$	11.2453	0.412549	0.206275	+	0.978494i	$0.433866\pi$
$744$	−1.78830	−0.0655622
$745$	37.8783	1.38775
$746$	1.39768	0.0511726
$747$	7.09295	0.259517
$748$	−11.7738	−0.430494
$749$	52.9036	1.93306
$750$	−22.3190	−0.814975
$751$	7.95707	0.290358	0.145179	−	0.989405i	$-0.453624\pi$
$751$	7.95707	0.290358	0.145179	+	0.989405i	$0.453624\pi$
$752$	7.86248	0.286715
$753$	−7.19708	−0.262276
$754$	−4.52109	−0.164648
$755$	34.6638	1.26154
$756$	7.88064	0.286616
$757$	−6.31722	−0.229603	−0.114802	−	0.993388i	$-0.536623\pi$
$757$	−6.31722	−0.229603	−0.114802	+	0.993388i	$0.536623\pi$
$758$	−43.9138	−1.59502
$759$	−26.8266	−0.973742
$760$	1.79401	0.0650754
$761$	26.4046	0.957164	0.478582	−	0.878043i	$-0.341151\pi$
$761$	26.4046	0.957164	0.478582	+	0.878043i	$0.341151\pi$
$762$	−40.2169	−1.45690
$763$	−0.557266	−0.0201744
$764$	−39.5253	−1.42998
$765$	−2.19003	−0.0791807
$766$	−66.8135	−2.41407
$767$	1.30186	0.0470075
$768$	−18.3000	−0.660345
$769$	27.9547	1.00807	0.504035	−	0.863683i	$-0.331848\pi$
$769$	27.9547	1.00807	0.504035	+	0.863683i	$0.331848\pi$
$770$	−118.131	−4.25714
$771$	−10.9722	−0.395153
$772$	10.2654	0.369459
$773$	45.0823	1.62150	0.810748	−	0.585395i	$-0.199061\pi$
$773$	45.0823	1.62150	0.810748	+	0.585395i	$0.199061\pi$
$774$	−11.9603	−0.429905
$775$	1.13061	0.0406126
$776$	−3.14004	−0.112721
$777$	−46.4772	−1.66736
$778$	−41.7385	−1.49640
$779$	18.6845	0.669442
$780$	1.22148	0.0437360
$781$	12.9427	0.463128
$782$	−8.19013	−0.292878
$783$	7.59690	0.271491
$784$	−49.1955	−1.75698
$785$	2.19003	0.0781655
$786$	−16.8024	−0.599322
$787$	24.8141	0.884527	0.442263	−	0.896885i	$-0.354176\pi$
$787$	24.8141	0.884527	0.442263	+	0.896885i	$0.354176\pi$
$788$	−33.0979	−1.17906
$789$	−3.42840	−0.122054
$790$	−14.0251	−0.498990
$791$	37.2614	1.32486
$792$	2.06754	0.0734667
$793$	−1.20872	−0.0429228
$794$	−36.3471	−1.28991
$795$	16.6474	0.590422
$796$	11.2695	0.399436
$797$	−15.9846	−0.566204	−0.283102	−	0.959090i	$-0.591364\pi$
$797$	−15.9846	−0.566204	−0.283102	+	0.959090i	$0.591364\pi$
$798$	21.3714	0.756540
$799$	−1.82760	−0.0646560
$800$	1.58548	0.0560551
$801$	−2.28542	−0.0807514
$802$	51.6997	1.82558
$803$	−4.03505	−0.142394
$804$	13.1537	0.463896
$805$	−39.3241	−1.38599
$806$	−3.30198	−0.116307
$807$	27.3826	0.963913
$808$	3.84910	0.135411
$809$	42.1509	1.48195	0.740973	−	0.671535i	$-0.234365\pi$
$809$	42.1509	1.48195	0.740973	+	0.671535i	$0.234365\pi$
$810$	−4.28901	−0.150700
$811$	−28.9104	−1.01518	−0.507590	−	0.861598i	$-0.669464\pi$
$811$	−28.9104	−1.01518	−0.507590	+	0.861598i	$0.669464\pi$
$812$	59.8684	2.10097
$813$	23.3262	0.818087
$814$	135.989	4.76640
$815$	−5.79681	−0.203054
$816$	4.30207	0.150602
$817$	−15.5216	−0.543033
$818$	10.1032	0.353251
$819$	−1.30474	−0.0455914
$820$	−29.5506	−1.03195
$821$	10.0121	0.349426	0.174713	−	0.984619i	$-0.444100\pi$
$821$	10.0121	0.349426	0.174713	+	0.984619i	$0.444100\pi$
$822$	−16.4390	−0.573376
$823$	−1.54596	−0.0538889	−0.0269445	−	0.999637i	$-0.508578\pi$
$823$	−1.54596	−0.0538889	−0.0269445	+	0.999637i	$0.508578\pi$
$824$	5.49045	0.191269
$825$	−1.30715	−0.0455091
$826$	−36.0244	−1.25345
$827$	−56.8768	−1.97780	−0.988900	−	0.148579i	$-0.952530\pi$
$827$	−56.8768	−1.97780	−0.988900	+	0.148579i	$0.952530\pi$
$828$	−7.67574	−0.266751
$829$	36.3644	1.26299	0.631494	−	0.775381i	$-0.282442\pi$
$829$	36.3644	1.26299	0.631494	+	0.775381i	$0.282442\pi$
$830$	−30.4217	−1.05595
$831$	−3.97030	−0.137728
$832$	−2.01583	−0.0698864
$833$	11.4353	0.396210
$834$	−18.9653	−0.656715
$835$	−6.21166	−0.214963
$836$	−29.9239	−1.03494
$837$	5.54840	0.191781
$838$	−38.8761	−1.34295
$839$	11.6323	0.401593	0.200797	−	0.979633i	$-0.435647\pi$
$839$	11.6323	0.401593	0.200797	+	0.979633i	$0.435647\pi$
$840$	3.03073	0.104570
$841$	28.7129	0.990099
$842$	−13.3381	−0.459660
$843$	−25.9367	−0.893309
$844$	29.2504	1.00684
$845$	28.2681	0.972454
$846$	−3.57922	−0.123056
$847$	−129.450	−4.44795
$848$	−32.7019	−1.12299
$849$	−14.5519	−0.499420
$850$	−0.399072	−0.0136880
$851$	45.2688	1.55180
$852$	3.70324	0.126871
$853$	−46.8967	−1.60571	−0.802855	−	0.596174i	$-0.796687\pi$
$853$	−46.8967	−1.60571	−0.802855	+	0.596174i	$0.796687\pi$
$854$	33.4470	1.14453
$855$	−5.56610	−0.190357
$856$	3.97130	0.135736
$857$	−51.0785	−1.74481	−0.872404	−	0.488785i	$-0.837440\pi$
$857$	−51.0785	−1.74481	−0.872404	+	0.488785i	$0.837440\pi$
$858$	3.81757	0.130330
$859$	40.5643	1.38404	0.692018	−	0.721881i	$-0.256722\pi$
$859$	40.5643	1.38404	0.692018	+	0.721881i	$0.256722\pi$
$860$	24.5484	0.837092
$861$	31.5650	1.07573
$862$	−37.8641	−1.28966
$863$	1.51292	0.0515005	0.0257502	−	0.999668i	$-0.491803\pi$
$863$	1.51292	0.0515005	0.0257502	+	0.999668i	$0.491803\pi$
$864$	7.78065	0.264703
$865$	0.699595	0.0237869
$866$	14.8909	0.506015
$867$	−1.00000	−0.0339618
$868$	43.7250	1.48412
$869$	−20.9764	−0.711574
$870$	−32.5831	−1.10467
$871$	−2.17777	−0.0737910
$872$	−0.0418321	−0.00141661
$873$	9.74234	0.329728
$874$	−20.8158	−0.704103
$875$	−48.9320	−1.65421
$876$	−1.15453	−0.0390079
$877$	−23.8084	−0.803951	−0.401976	−	0.915650i	$-0.631676\pi$
$877$	−23.8084	−0.803951	−0.401976	+	0.915650i	$0.631676\pi$
$878$	26.6958	0.900941
$879$	−24.9692	−0.842189
$880$	−60.4377	−2.03735
$881$	−47.8765	−1.61300	−0.806500	−	0.591234i	$-0.798641\pi$
$881$	−47.8765	−1.61300	−0.806500	+	0.591234i	$0.798641\pi$
$882$	22.3952	0.754085
$883$	−19.1575	−0.644702	−0.322351	−	0.946620i	$-0.604473\pi$
$883$	−19.1575	−0.644702	−0.322351	+	0.946620i	$0.604473\pi$
$884$	0.557746	0.0187590
$885$	9.38242	0.315387
$886$	−4.05537	−0.136243
$887$	−12.9534	−0.434934	−0.217467	−	0.976068i	$-0.569779\pi$
$887$	−12.9534	−0.434934	−0.217467	+	0.976068i	$0.569779\pi$
$888$	−3.48889	−0.117080
$889$	−88.1712	−2.95717
$890$	9.80218	0.328570
$891$	−6.41477	−0.214903
$892$	3.38863	0.113460
$893$	−4.64498	−0.155438
$894$	33.8725	1.13287
$895$	40.7987	1.36375
$896$	−11.0335	−0.368605
$897$	1.27082	0.0424314
$898$	−43.7538	−1.46008
$899$	42.1506	1.40580
$900$	−0.374008	−0.0124669
$901$	7.60145	0.253241
$902$	−92.3566	−3.07514
$903$	−26.2217	−0.872604
$904$	2.79709	0.0930299
$905$	−45.8303	−1.52345
$906$	30.9979	1.02984
$907$	34.9001	1.15884	0.579419	−	0.815030i	$-0.303280\pi$
$907$	34.9001	1.15884	0.579419	+	0.815030i	$0.303280\pi$
$908$	13.2255	0.438904
$909$	−11.9423	−0.396100
$910$	5.59605	0.185507
$911$	−34.9799	−1.15894	−0.579468	−	0.814995i	$-0.696740\pi$
$911$	−34.9799	−1.15894	−0.579468	+	0.814995i	$0.696740\pi$
$912$	10.9340	0.362060
$913$	−45.4996	−1.50582
$914$	−3.07524	−0.101720
$915$	−8.71113	−0.287981
$916$	7.54660	0.249347
$917$	−36.8375	−1.21648
$918$	−1.95842	−0.0646376
$919$	7.10294	0.234304	0.117152	−	0.993114i	$-0.462623\pi$
$919$	7.10294	0.234304	0.117152	+	0.993114i	$0.462623\pi$
$920$	−2.95193	−0.0973223
$921$	22.6609	0.746702
$922$	−46.8041	−1.54141
$923$	−0.613120	−0.0201811
$924$	−50.5525	−1.66306
$925$	2.20577	0.0725251
$926$	−58.1539	−1.91106
$927$	−17.0347	−0.559494
$928$	59.1088	1.94034
$929$	−14.9853	−0.491652	−0.245826	−	0.969314i	$-0.579059\pi$
$929$	−14.9853	−0.491652	−0.245826	+	0.969314i	$0.579059\pi$
$930$	−23.7971	−0.780338
$931$	29.0636	0.952521
$932$	−16.3044	−0.534068
$933$	18.6754	0.611405
$934$	−64.3016	−2.10401
$935$	14.0485	0.459436
$936$	−0.0979427	−0.00320136
$937$	33.3650	1.08999	0.544994	−	0.838440i	$-0.316532\pi$
$937$	33.3650	1.08999	0.544994	+	0.838440i	$0.316532\pi$
$938$	60.2621	1.96763
$939$	16.6168	0.542268
$940$	7.34630	0.239610
$941$	26.4741	0.863030	0.431515	−	0.902106i	$-0.357979\pi$
$941$	26.4741	0.863030	0.431515	+	0.902106i	$0.357979\pi$
$942$	1.95842	0.0638089
$943$	−30.7443	−1.00117
$944$	−18.4307	−0.599869
$945$	−9.40319	−0.305886
$946$	76.7227	2.49447
$947$	0.968495	0.0314719	0.0157359	−	0.999876i	$-0.494991\pi$
$947$	0.968495	0.0314719	0.0157359	+	0.999876i	$0.494991\pi$
$948$	−6.00185	−0.194931
$949$	0.191147	0.00620490
$950$	−1.01427	−0.0329072
$951$	14.4688	0.469184
$952$	1.38388	0.0448517
$953$	8.02056	0.259811	0.129906	−	0.991526i	$-0.458533\pi$
$953$	8.02056	0.259811	0.129906	+	0.991526i	$0.458533\pi$
$954$	14.8869	0.481980
$955$	47.1617	1.52612
$956$	−45.5162	−1.47210
$957$	−48.7323	−1.57529
$958$	66.6383	2.15299
$959$	−36.0408	−1.16382
$960$	−14.5280	−0.468888
$961$	−0.215253	−0.00694365
$962$	−6.44202	−0.207699
$963$	−12.3214	−0.397052
$964$	7.75661	0.249824
$965$	−12.2487	−0.394298
$966$	−35.1654	−1.13143
$967$	−32.0607	−1.03100	−0.515501	−	0.856889i	$-0.672394\pi$
$967$	−32.0607	−1.03100	−0.515501	+	0.856889i	$0.672394\pi$
$968$	−9.71737	−0.312328
$969$	−2.54157	−0.0816469
$970$	−41.7850	−1.34163
$971$	−18.0292	−0.578584	−0.289292	−	0.957241i	$-0.593420\pi$
$971$	−18.0292	−0.578584	−0.289292	+	0.957241i	$0.593420\pi$
$972$	−1.83542	−0.0588713
$973$	−41.5794	−1.33297
$974$	47.2539	1.51411
$975$	0.0619219	0.00198309
$976$	17.1120	0.547743
$977$	−17.5141	−0.560325	−0.280162	−	0.959953i	$-0.590388\pi$
$977$	−17.5141	−0.560325	−0.280162	+	0.959953i	$0.590388\pi$
$978$	−5.18378	−0.165759
$979$	14.6604	0.468550
$980$	−45.9657	−1.46832
$981$	0.129789	0.00414384
$982$	−58.9055	−1.87975
$983$	−16.6709	−0.531721	−0.265860	−	0.964012i	$-0.585656\pi$
$983$	−16.6709	−0.531721	−0.265860	+	0.964012i	$0.585656\pi$
$984$	2.36948	0.0755362
$985$	39.4924	1.25833
$986$	−14.8779	−0.473810
$987$	−7.84707	−0.249775
$988$	1.41755	0.0450982
$989$	25.5400	0.812123
$990$	27.5130	0.874420
$991$	58.5166	1.85884	0.929420	−	0.369023i	$-0.120307\pi$
$991$	58.5166	1.85884	0.929420	+	0.369023i	$0.120307\pi$
$992$	43.1702	1.37065
$993$	28.1638	0.893750
$994$	16.9659	0.538126
$995$	−13.4468	−0.426291
$996$	−13.0186	−0.412509
$997$	−31.7843	−1.00662	−0.503309	−	0.864106i	$-0.667884\pi$
$997$	−31.7843	−1.00662	−0.503309	+	0.864106i	$0.667884\pi$
$998$	−73.8199	−2.33673
$999$	10.8247	0.342478

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.50	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.50	✓	64	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q+1.95842 q^{2} -1.00000 q^{3} +1.83542 q^{4} -2.19003 q^{5} -1.95842 q^{6} -4.29364 q^{7} -0.322309 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.95842 q^{2} -1.00000 q^{3} +1.83542 q^{4} -2.19003 q^{5} -1.95842 q^{6} -4.29364 q^{7} -0.322309 q^{8} +1.00000 q^{9} -4.28901 q^{10} -6.41477 q^{11} -1.83542 q^{12} +0.303878 q^{13} -8.40876 q^{14} +2.19003 q^{15} -4.30207 q^{16} +1.00000 q^{17} +1.95842 q^{18} +2.54157 q^{19} -4.01963 q^{20} +4.29364 q^{21} -12.5628 q^{22} -4.18200 q^{23} +0.322309 q^{24} -0.203772 q^{25} +0.595123 q^{26} -1.00000 q^{27} -7.88064 q^{28} -7.59690 q^{29} +4.28901 q^{30} -5.54840 q^{31} -7.78065 q^{32} +6.41477 q^{33} +1.95842 q^{34} +9.40319 q^{35} +1.83542 q^{36} -10.8247 q^{37} +4.97746 q^{38} -0.303878 q^{39} +0.705866 q^{40} +7.35158 q^{41} +8.40876 q^{42} -6.10712 q^{43} -11.7738 q^{44} -2.19003 q^{45} -8.19013 q^{46} -1.82760 q^{47} +4.30207 q^{48} +11.4353 q^{49} -0.399072 q^{50} -1.00000 q^{51} +0.557746 q^{52} +7.60145 q^{53} -1.95842 q^{54} +14.0485 q^{55} +1.38388 q^{56} -2.54157 q^{57} -14.8779 q^{58} +4.28415 q^{59} +4.01963 q^{60} -3.97763 q^{61} -10.8661 q^{62} -4.29364 q^{63} -6.63368 q^{64} -0.665503 q^{65} +12.5628 q^{66} -7.16659 q^{67} +1.83542 q^{68} +4.18200 q^{69} +18.4154 q^{70} -2.01765 q^{71} -0.322309 q^{72} +0.629025 q^{73} -21.1993 q^{74} +0.203772 q^{75} +4.66485 q^{76} +27.5427 q^{77} -0.595123 q^{78} +3.27001 q^{79} +9.42165 q^{80} +1.00000 q^{81} +14.3975 q^{82} +7.09295 q^{83} +7.88064 q^{84} -2.19003 q^{85} -11.9603 q^{86} +7.59690 q^{87} +2.06754 q^{88} -2.28542 q^{89} -4.28901 q^{90} -1.30474 q^{91} -7.67574 q^{92} +5.54840 q^{93} -3.57922 q^{94} -5.56610 q^{95} +7.78065 q^{96} +9.74234 q^{97} +22.3952 q^{98} -6.41477 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

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