LMFDB - Embedded newform 8007.2.a.j.1.5

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			1.5
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)

$f(q)$	$=$	$q-2.53596 q^{2} -1.00000 q^{3} +4.43108 q^{4} -0.923448 q^{5} +2.53596 q^{6} -0.313569 q^{7} -6.16510 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.53596 q^{2} -1.00000 q^{3} +4.43108 q^{4} -0.923448 q^{5} +2.53596 q^{6} -0.313569 q^{7} -6.16510 q^{8} +1.00000 q^{9} +2.34182 q^{10} +0.332092 q^{11} -4.43108 q^{12} -0.593045 q^{13} +0.795197 q^{14} +0.923448 q^{15} +6.77228 q^{16} +1.00000 q^{17} -2.53596 q^{18} -1.79756 q^{19} -4.09187 q^{20} +0.313569 q^{21} -0.842170 q^{22} -4.20574 q^{23} +6.16510 q^{24} -4.14724 q^{25} +1.50394 q^{26} -1.00000 q^{27} -1.38945 q^{28} -6.93910 q^{29} -2.34182 q^{30} +6.67131 q^{31} -4.84401 q^{32} -0.332092 q^{33} -2.53596 q^{34} +0.289564 q^{35} +4.43108 q^{36} -0.302087 q^{37} +4.55853 q^{38} +0.593045 q^{39} +5.69315 q^{40} -1.56912 q^{41} -0.795197 q^{42} -0.0472238 q^{43} +1.47152 q^{44} -0.923448 q^{45} +10.6656 q^{46} +0.813814 q^{47} -6.77228 q^{48} -6.90167 q^{49} +10.5172 q^{50} -1.00000 q^{51} -2.62783 q^{52} -10.6564 q^{53} +2.53596 q^{54} -0.306669 q^{55} +1.93318 q^{56} +1.79756 q^{57} +17.5972 q^{58} -8.10918 q^{59} +4.09187 q^{60} -5.49161 q^{61} -16.9181 q^{62} -0.313569 q^{63} -1.26037 q^{64} +0.547646 q^{65} +0.842170 q^{66} +9.35947 q^{67} +4.43108 q^{68} +4.20574 q^{69} -0.734323 q^{70} +1.59550 q^{71} -6.16510 q^{72} +14.0654 q^{73} +0.766079 q^{74} +4.14724 q^{75} -7.96511 q^{76} -0.104134 q^{77} -1.50394 q^{78} +2.58926 q^{79} -6.25385 q^{80} +1.00000 q^{81} +3.97922 q^{82} +7.39223 q^{83} +1.38945 q^{84} -0.923448 q^{85} +0.119757 q^{86} +6.93910 q^{87} -2.04738 q^{88} -9.87173 q^{89} +2.34182 q^{90} +0.185960 q^{91} -18.6360 q^{92} -6.67131 q^{93} -2.06380 q^{94} +1.65995 q^{95} +4.84401 q^{96} +11.2692 q^{97} +17.5023 q^{98} +0.332092 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.53596	−1.79319	−0.896596	−	0.442849i	$-0.853968\pi$
$2$	−2.53596	−1.79319	−0.896596	+	0.442849i	$0.853968\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.43108	2.21554
$5$	−0.923448	−0.412978	−0.206489	−	0.978449i	$-0.566204\pi$
$5$	−0.923448	−0.412978	−0.206489	+	0.978449i	$0.566204\pi$
$6$	2.53596	1.03530
$7$	−0.313569	−0.118518	−0.0592590	−	0.998243i	$-0.518874\pi$
$7$	−0.313569	−0.118518	−0.0592590	+	0.998243i	$0.518874\pi$
$8$	−6.16510	−2.17969
$9$	1.00000	0.333333
$10$	2.34182	0.740550
$11$	0.332092	0.100129	0.0500647	−	0.998746i	$-0.484057\pi$
$11$	0.332092	0.100129	0.0500647	+	0.998746i	$0.484057\pi$
$12$	−4.43108	−1.27914
$13$	−0.593045	−0.164481	−0.0822405	−	0.996613i	$-0.526208\pi$
$13$	−0.593045	−0.164481	−0.0822405	+	0.996613i	$0.526208\pi$
$14$	0.795197	0.212525
$15$	0.923448	0.238433
$16$	6.77228	1.69307
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.53596	−0.597731
$19$	−1.79756	−0.412388	−0.206194	−	0.978511i	$-0.566108\pi$
$19$	−1.79756	−0.412388	−0.206194	+	0.978511i	$0.566108\pi$
$20$	−4.09187	−0.914969
$21$	0.313569	0.0684263
$22$	−0.842170	−0.179551
$23$	−4.20574	−0.876958	−0.438479	−	0.898741i	$-0.644483\pi$
$23$	−4.20574	−0.876958	−0.438479	+	0.898741i	$0.644483\pi$
$24$	6.16510	1.25845
$25$	−4.14724	−0.829449
$26$	1.50394	0.294946
$27$	−1.00000	−0.192450
$28$	−1.38945	−0.262581
$29$	−6.93910	−1.28856	−0.644279	−	0.764791i	$-0.722842\pi$
$29$	−6.93910	−1.28856	−0.644279	+	0.764791i	$0.722842\pi$
$30$	−2.34182	−0.427556
$31$	6.67131	1.19820	0.599101	−	0.800673i	$-0.295525\pi$
$31$	6.67131	1.19820	0.599101	+	0.800673i	$0.295525\pi$
$32$	−4.84401	−0.856307
$33$	−0.332092	−0.0578097
$34$	−2.53596	−0.434913
$35$	0.289564	0.0489453
$36$	4.43108	0.738513
$37$	−0.302087	−0.0496628	−0.0248314	−	0.999692i	$-0.507905\pi$
$37$	−0.302087	−0.0496628	−0.0248314	+	0.999692i	$0.507905\pi$
$38$	4.55853	0.739490
$39$	0.593045	0.0949632
$40$	5.69315	0.900166
$41$	−1.56912	−0.245055	−0.122528	−	0.992465i	$-0.539100\pi$
$41$	−1.56912	−0.245055	−0.122528	+	0.992465i	$0.539100\pi$
$42$	−0.795197	−0.122702
$43$	−0.0472238	−0.00720156	−0.00360078	−	0.999994i	$-0.501146\pi$
$43$	−0.0472238	−0.00720156	−0.00360078	+	0.999994i	$0.501146\pi$
$44$	1.47152	0.221840
$45$	−0.923448	−0.137659
$46$	10.6656	1.57255
$47$	0.813814	0.118707	0.0593535	−	0.998237i	$-0.481096\pi$
$47$	0.813814	0.118707	0.0593535	+	0.998237i	$0.481096\pi$
$48$	−6.77228	−0.977495
$49$	−6.90167	−0.985954
$50$	10.5172	1.48736
$51$	−1.00000	−0.140028
$52$	−2.62783	−0.364414
$53$	−10.6564	−1.46377	−0.731887	−	0.681426i	$-0.761360\pi$
$53$	−10.6564	−1.46377	−0.731887	+	0.681426i	$0.761360\pi$
$54$	2.53596	0.345100
$55$	−0.306669	−0.0413513
$56$	1.93318	0.258333
$57$	1.79756	0.238092
$58$	17.5972	2.31063
$59$	−8.10918	−1.05573	−0.527863	−	0.849330i	$-0.677006\pi$
$59$	−8.10918	−1.05573	−0.527863	+	0.849330i	$0.677006\pi$
$60$	4.09187	0.528258
$61$	−5.49161	−0.703129	−0.351565	−	0.936164i	$-0.614350\pi$
$61$	−5.49161	−0.703129	−0.351565	+	0.936164i	$0.614350\pi$
$62$	−16.9181	−2.14861
$63$	−0.313569	−0.0395060
$64$	−1.26037	−0.157547
$65$	0.547646	0.0679271
$66$	0.842170	0.103664
$67$	9.35947	1.14344	0.571721	−	0.820448i	$-0.306276\pi$
$67$	9.35947	1.14344	0.571721	+	0.820448i	$0.306276\pi$
$68$	4.43108	0.537347
$69$	4.20574	0.506312
$70$	−0.734323	−0.0877684
$71$	1.59550	0.189351	0.0946756	−	0.995508i	$-0.469819\pi$
$71$	1.59550	0.189351	0.0946756	+	0.995508i	$0.469819\pi$
$72$	−6.16510	−0.726564
$73$	14.0654	1.64623	0.823113	−	0.567878i	$-0.192235\pi$
$73$	14.0654	1.64623	0.823113	+	0.567878i	$0.192235\pi$
$74$	0.766079	0.0890549
$75$	4.14724	0.478883
$76$	−7.96511	−0.913661
$77$	−0.104134	−0.0118671
$78$	−1.50394	−0.170287
$79$	2.58926	0.291314	0.145657	−	0.989335i	$-0.453470\pi$
$79$	2.58926	0.291314	0.145657	+	0.989335i	$0.453470\pi$
$80$	−6.25385	−0.699201
$81$	1.00000	0.111111
$82$	3.97922	0.439432
$83$	7.39223	0.811402	0.405701	−	0.914006i	$-0.367027\pi$
$83$	7.39223	0.811402	0.405701	+	0.914006i	$0.367027\pi$
$84$	1.38945	0.151601
$85$	−0.923448	−0.100162
$86$	0.119757	0.0129138
$87$	6.93910	0.743949
$88$	−2.04738	−0.218251
$89$	−9.87173	−1.04640	−0.523201	−	0.852210i	$-0.675262\pi$
$89$	−9.87173	−1.04640	−0.523201	+	0.852210i	$0.675262\pi$
$90$	2.34182	0.246850
$91$	0.185960	0.0194939
$92$	−18.6360	−1.94293
$93$	−6.67131	−0.691782
$94$	−2.06380	−0.212865
$95$	1.65995	0.170307
$96$	4.84401	0.494389
$97$	11.2692	1.14421	0.572105	−	0.820181i	$-0.306127\pi$
$97$	11.2692	1.14421	0.572105	+	0.820181i	$0.306127\pi$
$98$	17.5023	1.76800
$99$	0.332092	0.0333765
$100$	−18.3768	−1.83768
$101$	−10.0976	−1.00475	−0.502374	−	0.864651i	$-0.667540\pi$
$101$	−10.0976	−1.00475	−0.502374	+	0.864651i	$0.667540\pi$
$102$	2.53596	0.251097
$103$	−0.586459	−0.0577855	−0.0288928	−	0.999583i	$-0.509198\pi$
$103$	−0.586459	−0.0577855	−0.0288928	+	0.999583i	$0.509198\pi$
$104$	3.65618	0.358518
$105$	−0.289564	−0.0282586
$106$	27.0243	2.62483
$107$	8.33650	0.805920	0.402960	−	0.915218i	$-0.367981\pi$
$107$	8.33650	0.805920	0.402960	+	0.915218i	$0.367981\pi$
$108$	−4.43108	−0.426380
$109$	−2.22413	−0.213033	−0.106516	−	0.994311i	$-0.533970\pi$
$109$	−2.22413	−0.213033	−0.106516	+	0.994311i	$0.533970\pi$
$110$	0.777700	0.0741508
$111$	0.302087	0.0286728
$112$	−2.12358	−0.200659
$113$	−16.6199	−1.56347	−0.781734	−	0.623611i	$-0.785665\pi$
$113$	−16.6199	−1.56347	−0.781734	+	0.623611i	$0.785665\pi$
$114$	−4.55853	−0.426945
$115$	3.88378	0.362165
$116$	−30.7477	−2.85485
$117$	−0.593045	−0.0548270
$118$	20.5645	1.89312
$119$	−0.313569	−0.0287448
$120$	−5.69315	−0.519711
$121$	−10.8897	−0.989974
$122$	13.9265	1.26085
$123$	1.56912	0.141483
$124$	29.5611	2.65466
$125$	8.44700	0.755523
$126$	0.795197	0.0708418
$127$	15.3714	1.36399	0.681997	−	0.731355i	$-0.261112\pi$
$127$	15.3714	1.36399	0.681997	+	0.731355i	$0.261112\pi$
$128$	12.8843	1.13882
$129$	0.0472238	0.00415782
$130$	−1.38881	−0.121806
$131$	−8.97750	−0.784368	−0.392184	−	0.919887i	$-0.628280\pi$
$131$	−8.97750	−0.784368	−0.392184	+	0.919887i	$0.628280\pi$
$132$	−1.47152	−0.128080
$133$	0.563658	0.0488753
$134$	−23.7352	−2.05041
$135$	0.923448	0.0794777
$136$	−6.16510	−0.528653
$137$	2.58144	0.220547	0.110274	−	0.993901i	$-0.464827\pi$
$137$	2.58144	0.220547	0.110274	+	0.993901i	$0.464827\pi$
$138$	−10.6656	−0.907915
$139$	1.26738	0.107498	0.0537490	−	0.998554i	$-0.482883\pi$
$139$	1.26738	0.107498	0.0537490	+	0.998554i	$0.482883\pi$
$140$	1.28308	0.108440
$141$	−0.813814	−0.0685355
$142$	−4.04612	−0.339543
$143$	−0.196945	−0.0164694
$144$	6.77228	0.564357
$145$	6.40789	0.532146
$146$	−35.6691	−2.95200
$147$	6.90167	0.569241
$148$	−1.33857	−0.110030
$149$	−8.85684	−0.725580	−0.362790	−	0.931871i	$-0.618176\pi$
$149$	−8.85684	−0.725580	−0.362790	+	0.931871i	$0.618176\pi$
$150$	−10.5172	−0.858728
$151$	18.6267	1.51582	0.757908	−	0.652361i	$-0.226221\pi$
$151$	18.6267	1.51582	0.757908	+	0.652361i	$0.226221\pi$
$152$	11.0821	0.898879
$153$	1.00000	0.0808452
$154$	0.264078	0.0212800
$155$	−6.16060	−0.494832
$156$	2.62783	0.210394
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−6.56624	−0.522382
$159$	10.6564	0.845110
$160$	4.47319	0.353636
$161$	1.31879	0.103935
$162$	−2.53596	−0.199244
$163$	−21.9720	−1.72098	−0.860491	−	0.509465i	$-0.829843\pi$
$163$	−21.9720	−1.72098	−0.860491	+	0.509465i	$0.829843\pi$
$164$	−6.95289	−0.542930
$165$	0.306669	0.0238742
$166$	−18.7464	−1.45500
$167$	−5.88828	−0.455649	−0.227824	−	0.973702i	$-0.573161\pi$
$167$	−5.88828	−0.455649	−0.227824	+	0.973702i	$0.573161\pi$
$168$	−1.93318	−0.149148
$169$	−12.6483	−0.972946
$170$	2.34182	0.179610
$171$	−1.79756	−0.137463
$172$	−0.209252	−0.0159553
$173$	4.36048	0.331521	0.165761	−	0.986166i	$-0.446992\pi$
$173$	4.36048	0.331521	0.165761	+	0.986166i	$0.446992\pi$
$174$	−17.5972	−1.33404
$175$	1.30045	0.0983045
$176$	2.24902	0.169526
$177$	8.10918	0.609523
$178$	25.0343	1.87640
$179$	−17.4253	−1.30243	−0.651216	−	0.758893i	$-0.725741\pi$
$179$	−17.4253	−1.30243	−0.651216	+	0.758893i	$0.725741\pi$
$180$	−4.09187	−0.304990
$181$	2.09162	0.155469	0.0777346	−	0.996974i	$-0.475231\pi$
$181$	2.09162	0.155469	0.0777346	+	0.996974i	$0.475231\pi$
$182$	−0.471587	−0.0349564
$183$	5.49161	0.405952
$184$	25.9288	1.91150
$185$	0.278961	0.0205096
$186$	16.9181	1.24050
$187$	0.332092	0.0242849
$188$	3.60607	0.263000
$189$	0.313569	0.0228088
$190$	−4.20956	−0.305394
$191$	20.6202	1.49203	0.746014	−	0.665930i	$-0.231965\pi$
$191$	20.6202	1.49203	0.746014	+	0.665930i	$0.231965\pi$
$192$	1.26037	0.0909596
$193$	15.8887	1.14370	0.571848	−	0.820360i	$-0.306227\pi$
$193$	15.8887	1.14370	0.571848	+	0.820360i	$0.306227\pi$
$194$	−28.5781	−2.05179
$195$	−0.547646	−0.0392177
$196$	−30.5818	−2.18442
$197$	25.7860	1.83718	0.918590	−	0.395212i	$-0.129329\pi$
$197$	25.7860	1.83718	0.918590	+	0.395212i	$0.129329\pi$
$198$	−0.842170	−0.0598504
$199$	−0.109309	−0.00774871	−0.00387436	−	0.999992i	$-0.501233\pi$
$199$	−0.109309	−0.00774871	−0.00387436	+	0.999992i	$0.501233\pi$
$200$	25.5682	1.80794
$201$	−9.35947	−0.660166
$202$	25.6070	1.80170
$203$	2.17588	0.152717
$204$	−4.43108	−0.310237
$205$	1.44900	0.101203
$206$	1.48723	0.103621
$207$	−4.20574	−0.292319
$208$	−4.01627	−0.278478
$209$	−0.596953	−0.0412921
$210$	0.734323	0.0506731
$211$	−8.52744	−0.587053	−0.293526	−	0.955951i	$-0.594829\pi$
$211$	−8.52744	−0.587053	−0.293526	+	0.955951i	$0.594829\pi$
$212$	−47.2195	−3.24305
$213$	−1.59550	−0.109322
$214$	−21.1410	−1.44517
$215$	0.0436087	0.00297409
$216$	6.16510	0.419482
$217$	−2.09191	−0.142008
$218$	5.64030	0.382009
$219$	−14.0654	−0.950449
$220$	−1.35887	−0.0916153
$221$	−0.593045	−0.0398925
$222$	−0.766079	−0.0514159
$223$	8.31849	0.557048	0.278524	−	0.960429i	$-0.410155\pi$
$223$	8.31849	0.557048	0.278524	+	0.960429i	$0.410155\pi$
$224$	1.51893	0.101488
$225$	−4.14724	−0.276483
$226$	42.1474	2.80360
$227$	−9.17819	−0.609178	−0.304589	−	0.952484i	$-0.598519\pi$
$227$	−9.17819	−0.609178	−0.304589	+	0.952484i	$0.598519\pi$
$228$	7.96511	0.527502
$229$	−5.27359	−0.348489	−0.174244	−	0.984702i	$-0.555748\pi$
$229$	−5.27359	−0.348489	−0.174244	+	0.984702i	$0.555748\pi$
$230$	−9.84911	−0.649431
$231$	0.104134	0.00685149
$232$	42.7802	2.80866
$233$	17.6227	1.15450	0.577250	−	0.816567i	$-0.304126\pi$
$233$	17.6227	1.15450	0.577250	+	0.816567i	$0.304126\pi$
$234$	1.50394	0.0983153
$235$	−0.751515	−0.0490234
$236$	−35.9324	−2.33900
$237$	−2.58926	−0.168190
$238$	0.795197	0.0515450
$239$	−13.2303	−0.855794	−0.427897	−	0.903827i	$-0.640745\pi$
$239$	−13.2303	−0.855794	−0.427897	+	0.903827i	$0.640745\pi$
$240$	6.25385	0.403684
$241$	28.2183	1.81770	0.908850	−	0.417122i	$-0.136961\pi$
$241$	28.2183	1.81770	0.908850	+	0.417122i	$0.136961\pi$
$242$	27.6158	1.77521
$243$	−1.00000	−0.0641500
$244$	−24.3338	−1.55781
$245$	6.37334	0.407177
$246$	−3.97922	−0.253706
$247$	1.06603	0.0678300
$248$	−41.1293	−2.61171
$249$	−7.39223	−0.468463
$250$	−21.4212	−1.35480
$251$	8.95764	0.565401	0.282701	−	0.959208i	$-0.408770\pi$
$251$	8.95764	0.565401	0.282701	+	0.959208i	$0.408770\pi$
$252$	−1.38945	−0.0875270
$253$	−1.39669	−0.0878093
$254$	−38.9813	−2.44590
$255$	0.923448	0.0578285
$256$	−30.1532	−1.88457
$257$	24.0068	1.49750	0.748751	−	0.662852i	$-0.230654\pi$
$257$	24.0068	1.49750	0.748751	+	0.662852i	$0.230654\pi$
$258$	−0.119757	−0.00745577
$259$	0.0947250	0.00588593
$260$	2.42666	0.150495
$261$	−6.93910	−0.429519
$262$	22.7666	1.40652
$263$	−15.3395	−0.945872	−0.472936	−	0.881097i	$-0.656806\pi$
$263$	−15.3395	−0.945872	−0.472936	+	0.881097i	$0.656806\pi$
$264$	2.04738	0.126007
$265$	9.84066	0.604507
$266$	−1.42941	−0.0876429
$267$	9.87173	0.604140
$268$	41.4725	2.53334
$269$	−15.7646	−0.961185	−0.480593	−	0.876944i	$-0.659578\pi$
$269$	−15.7646	−0.961185	−0.480593	+	0.876944i	$0.659578\pi$
$270$	−2.34182	−0.142519
$271$	−13.5474	−0.822945	−0.411473	−	0.911422i	$-0.634985\pi$
$271$	−13.5474	−0.822945	−0.411473	+	0.911422i	$0.634985\pi$
$272$	6.77228	0.410630
$273$	−0.185960	−0.0112548
$274$	−6.54642	−0.395484
$275$	−1.37726	−0.0830522
$276$	18.6360	1.12175
$277$	29.4054	1.76680	0.883401	−	0.468619i	$-0.155248\pi$
$277$	29.4054	1.76680	0.883401	+	0.468619i	$0.155248\pi$
$278$	−3.21403	−0.192765
$279$	6.67131	0.399401
$280$	−1.78519	−0.106686
$281$	8.19382	0.488802	0.244401	−	0.969674i	$-0.421409\pi$
$281$	8.19382	0.488802	0.244401	+	0.969674i	$0.421409\pi$
$282$	2.06380	0.122897
$283$	−16.3506	−0.971944	−0.485972	−	0.873974i	$-0.661534\pi$
$283$	−16.3506	−0.971944	−0.485972	+	0.873974i	$0.661534\pi$
$284$	7.06979	0.419515
$285$	−1.65995	−0.0983269
$286$	0.499444	0.0295328
$287$	0.492027	0.0290435
$288$	−4.84401	−0.285436
$289$	1.00000	0.0588235
$290$	−16.2501	−0.954241
$291$	−11.2692	−0.660610
$292$	62.3247	3.64727
$293$	2.33032	0.136139	0.0680693	−	0.997681i	$-0.478316\pi$
$293$	2.33032	0.136139	0.0680693	+	0.997681i	$0.478316\pi$
$294$	−17.5023	−1.02076
$295$	7.48840	0.435992
$296$	1.86240	0.108250
$297$	−0.332092	−0.0192699
$298$	22.4606	1.30111
$299$	2.49419	0.144243
$300$	18.3768	1.06098
$301$	0.0148079	0.000853514 0
$302$	−47.2364	−2.71815
$303$	10.0976	0.580091
$304$	−12.1736	−0.698201
$305$	5.07122	0.290377
$306$	−2.53596	−0.144971
$307$	−31.7382	−1.81139	−0.905696	−	0.423928i	$-0.860651\pi$
$307$	−31.7382	−1.81139	−0.905696	+	0.423928i	$0.860651\pi$
$308$	−0.461424	−0.0262921
$309$	0.586459	0.0333625
$310$	15.6230	0.887328
$311$	15.1662	0.859997	0.429999	−	0.902830i	$-0.358514\pi$
$311$	15.1662	0.859997	0.429999	+	0.902830i	$0.358514\pi$
$312$	−3.65618	−0.206991
$313$	−11.2491	−0.635834	−0.317917	−	0.948118i	$-0.602983\pi$
$313$	−11.2491	−0.635834	−0.317917	+	0.948118i	$0.602983\pi$
$314$	2.53596	0.143112
$315$	0.289564	0.0163151
$316$	11.4732	0.645417
$317$	−31.3618	−1.76146	−0.880728	−	0.473622i	$-0.842946\pi$
$317$	−31.3618	−1.76146	−0.880728	+	0.473622i	$0.842946\pi$
$318$	−27.0243	−1.51545
$319$	−2.30441	−0.129022
$320$	1.16389	0.0650634
$321$	−8.33650	−0.465298
$322$	−3.34439	−0.186376
$323$	−1.79756	−0.100019
$324$	4.43108	0.246171
$325$	2.45950	0.136429
$326$	55.7201	3.08605
$327$	2.22413	0.122995
$328$	9.67379	0.534146
$329$	−0.255187	−0.0140689
$330$	−0.777700	−0.0428110
$331$	24.2806	1.33458	0.667292	−	0.744796i	$-0.267453\pi$
$331$	24.2806	1.33458	0.667292	+	0.744796i	$0.267453\pi$
$332$	32.7555	1.79769
$333$	−0.302087	−0.0165543
$334$	14.9324	0.817066
$335$	−8.64298	−0.472217
$336$	2.12358	0.115851
$337$	−21.3301	−1.16192	−0.580962	−	0.813931i	$-0.697324\pi$
$337$	−21.3301	−1.16192	−0.580962	+	0.813931i	$0.697324\pi$
$338$	32.0755	1.74468
$339$	16.6199	0.902669
$340$	−4.09187	−0.221913
$341$	2.21548	0.119975
$342$	4.55853	0.246497
$343$	4.35913	0.235371
$344$	0.291139	0.0156972
$345$	−3.88378	−0.209096
$346$	−11.0580	−0.594481
$347$	−11.9899	−0.643652	−0.321826	−	0.946799i	$-0.604297\pi$
$347$	−11.9899	−0.643652	−0.321826	+	0.946799i	$0.604297\pi$
$348$	30.7477	1.64825
$349$	19.2235	1.02901	0.514504	−	0.857488i	$-0.327976\pi$
$349$	19.2235	1.02901	0.514504	+	0.857488i	$0.327976\pi$
$350$	−3.29788	−0.176279
$351$	0.593045	0.0316544
$352$	−1.60865	−0.0857415
$353$	16.8133	0.894880	0.447440	−	0.894314i	$-0.352336\pi$
$353$	16.8133	0.894880	0.447440	+	0.894314i	$0.352336\pi$
$354$	−20.5645	−1.09299
$355$	−1.47336	−0.0781980
$356$	−43.7424	−2.31834
$357$	0.313569	0.0165958
$358$	44.1899	2.33551
$359$	−17.5793	−0.927801	−0.463901	−	0.885887i	$-0.653551\pi$
$359$	−17.5793	−0.927801	−0.463901	+	0.885887i	$0.653551\pi$
$360$	5.69315	0.300055
$361$	−15.7688	−0.829936
$362$	−5.30427	−0.278786
$363$	10.8897	0.571562
$364$	0.824005	0.0431896
$365$	−12.9886	−0.679855
$366$	−13.9265	−0.727950
$367$	−6.31057	−0.329409	−0.164705	−	0.986343i	$-0.552667\pi$
$367$	−6.31057	−0.329409	−0.164705	+	0.986343i	$0.552667\pi$
$368$	−28.4825	−1.48475
$369$	−1.56912	−0.0816852
$370$	−0.707434	−0.0367777
$371$	3.34153	0.173483
$372$	−29.5611	−1.53267
$373$	−1.26394	−0.0654443	−0.0327221	−	0.999464i	$-0.510418\pi$
$373$	−1.26394	−0.0654443	−0.0327221	+	0.999464i	$0.510418\pi$
$374$	−0.842170	−0.0435476
$375$	−8.44700	−0.436201
$376$	−5.01725	−0.258745
$377$	4.11519	0.211943
$378$	−0.795197	−0.0409005
$379$	−36.8623	−1.89349	−0.946744	−	0.321986i	$-0.895649\pi$
$379$	−36.8623	−1.89349	−0.946744	+	0.321986i	$0.895649\pi$
$380$	7.35536	0.377322
$381$	−15.3714	−0.787503
$382$	−52.2920	−2.67549
$383$	−17.0762	−0.872553	−0.436277	−	0.899813i	$-0.643703\pi$
$383$	−17.0762	−0.872553	−0.436277	+	0.899813i	$0.643703\pi$
$384$	−12.8843	−0.657497
$385$	0.0961619	0.00490087
$386$	−40.2931	−2.05087
$387$	−0.0472238	−0.00240052
$388$	49.9345	2.53504
$389$	5.23543	0.265447	0.132723	−	0.991153i	$-0.457628\pi$
$389$	5.23543	0.265447	0.132723	+	0.991153i	$0.457628\pi$
$390$	1.38881	0.0703249
$391$	−4.20574	−0.212694
$392$	42.5495	2.14908
$393$	8.97750	0.452855
$394$	−65.3923	−3.29442
$395$	−2.39104	−0.120306
$396$	1.47152	0.0739468
$397$	9.37319	0.470427	0.235214	−	0.971944i	$-0.424421\pi$
$397$	9.37319	0.470427	0.235214	+	0.971944i	$0.424421\pi$
$398$	0.277203	0.0138949
$399$	−0.563658	−0.0282182
$400$	−28.0863	−1.40432
$401$	11.9830	0.598404	0.299202	−	0.954190i	$-0.403280\pi$
$401$	11.9830	0.598404	0.299202	+	0.954190i	$0.403280\pi$
$402$	23.7352	1.18380
$403$	−3.95638	−0.197081
$404$	−44.7432	−2.22606
$405$	−0.923448	−0.0458865
$406$	−5.51795	−0.273851
$407$	−0.100320	−0.00497270
$408$	6.16510	0.305218
$409$	25.9635	1.28381	0.641907	−	0.766783i	$-0.278144\pi$
$409$	25.9635	1.28381	0.641907	+	0.766783i	$0.278144\pi$
$410$	−3.67460	−0.181476
$411$	−2.58144	−0.127333
$412$	−2.59864	−0.128026
$413$	2.54279	0.125122
$414$	10.6656	0.524185
$415$	−6.82633	−0.335092
$416$	2.87271	0.140846
$417$	−1.26738	−0.0620640
$418$	1.51385	0.0740447
$419$	−10.0075	−0.488899	−0.244450	−	0.969662i	$-0.578607\pi$
$419$	−10.0075	−0.488899	−0.244450	+	0.969662i	$0.578607\pi$
$420$	−1.28308	−0.0626080
$421$	6.16395	0.300412	0.150206	−	0.988655i	$-0.452006\pi$
$421$	6.16395	0.300412	0.150206	+	0.988655i	$0.452006\pi$
$422$	21.6252	1.05270
$423$	0.813814	0.0395690
$424$	65.6980	3.19058
$425$	−4.14724	−0.201171
$426$	4.04612	0.196035
$427$	1.72200	0.0833334
$428$	36.9397	1.78555
$429$	0.196945	0.00950860
$430$	−0.110590	−0.00533311
$431$	−28.0146	−1.34942	−0.674709	−	0.738084i	$-0.735731\pi$
$431$	−28.0146	−1.34942	−0.674709	+	0.738084i	$0.735731\pi$
$432$	−6.77228	−0.325832
$433$	−21.2919	−1.02323	−0.511613	−	0.859216i	$-0.670952\pi$
$433$	−21.2919	−1.02323	−0.511613	+	0.859216i	$0.670952\pi$
$434$	5.30500	0.254648
$435$	−6.40789	−0.307235
$436$	−9.85529	−0.471983
$437$	7.56006	0.361647
$438$	35.6691	1.70434
$439$	−26.2587	−1.25326	−0.626630	−	0.779317i	$-0.715566\pi$
$439$	−26.2587	−1.25326	−0.626630	+	0.779317i	$0.715566\pi$
$440$	1.89065	0.0901331
$441$	−6.90167	−0.328651
$442$	1.50394	0.0715349
$443$	25.5260	1.21278	0.606388	−	0.795169i	$-0.292618\pi$
$443$	25.5260	1.21278	0.606388	+	0.795169i	$0.292618\pi$
$444$	1.33857	0.0635257
$445$	9.11603	0.432141
$446$	−21.0953	−0.998893
$447$	8.85684	0.418914
$448$	0.395214	0.0186721
$449$	−18.6871	−0.881899	−0.440950	−	0.897532i	$-0.645358\pi$
$449$	−18.6871	−0.881899	−0.440950	+	0.897532i	$0.645358\pi$
$450$	10.5172	0.495787
$451$	−0.521092	−0.0245372
$452$	−73.6441	−3.46392
$453$	−18.6267	−0.875157
$454$	23.2755	1.09237
$455$	−0.171725	−0.00805058
$456$	−11.0821	−0.518968
$457$	−38.9868	−1.82373	−0.911863	−	0.410495i	$-0.865356\pi$
$457$	−38.9868	−1.82373	−0.911863	+	0.410495i	$0.865356\pi$
$458$	13.3736	0.624908
$459$	−1.00000	−0.0466760
$460$	17.2093	0.802390
$461$	−33.4769	−1.55918	−0.779588	−	0.626293i	$-0.784571\pi$
$461$	−33.4769	−1.55918	−0.779588	+	0.626293i	$0.784571\pi$
$462$	−0.264078	−0.0122860
$463$	−9.04105	−0.420173	−0.210087	−	0.977683i	$-0.567375\pi$
$463$	−9.04105	−0.420173	−0.210087	+	0.977683i	$0.567375\pi$
$464$	−46.9935	−2.18162
$465$	6.16060	0.285691
$466$	−44.6904	−2.07024
$467$	16.9066	0.782346	0.391173	−	0.920317i	$-0.372069\pi$
$467$	16.9066	0.782346	0.391173	+	0.920317i	$0.372069\pi$
$468$	−2.62783	−0.121471
$469$	−2.93484	−0.135518
$470$	1.90581	0.0879084
$471$	1.00000	0.0460776
$472$	49.9939	2.30116
$473$	−0.0156826	−0.000721088 0
$474$	6.56624	0.301597
$475$	7.45491	0.342055
$476$	−1.38945	−0.0636852
$477$	−10.6564	−0.487925
$478$	33.5514	1.53460
$479$	7.14652	0.326533	0.163266	−	0.986582i	$-0.447797\pi$
$479$	7.14652	0.326533	0.163266	+	0.986582i	$0.447797\pi$
$480$	−4.47319	−0.204172
$481$	0.179151	0.00816858
$482$	−71.5604	−3.25949
$483$	−1.31879	−0.0600070
$484$	−48.2532	−2.19333
$485$	−10.4065	−0.472534
$486$	2.53596	0.115033
$487$	−9.59834	−0.434942	−0.217471	−	0.976067i	$-0.569781\pi$
$487$	−9.59834	−0.434942	−0.217471	+	0.976067i	$0.569781\pi$
$488$	33.8564	1.53261
$489$	21.9720	0.993610
$490$	−16.1625	−0.730147
$491$	−24.3039	−1.09682	−0.548410	−	0.836210i	$-0.684766\pi$
$491$	−24.3039	−1.09682	−0.548410	+	0.836210i	$0.684766\pi$
$492$	6.95289	0.313461
$493$	−6.93910	−0.312521
$494$	−2.70341	−0.121632
$495$	−0.306669	−0.0137838
$496$	45.1800	2.02864
$497$	−0.500300	−0.0224415
$498$	18.7464	0.840045
$499$	9.78357	0.437973	0.218986	−	0.975728i	$-0.429725\pi$
$499$	9.78357	0.437973	0.218986	+	0.975728i	$0.429725\pi$
$500$	37.4293	1.67389
$501$	5.88828	0.263069
$502$	−22.7162	−1.01387
$503$	−38.0479	−1.69647	−0.848237	−	0.529617i	$-0.822336\pi$
$503$	−38.0479	−1.69647	−0.848237	+	0.529617i	$0.822336\pi$
$504$	1.93318	0.0861109
$505$	9.32459	0.414939
$506$	3.54195	0.157459
$507$	12.6483	0.561731
$508$	68.1120	3.02198
$509$	34.8691	1.54554	0.772772	−	0.634683i	$-0.218869\pi$
$509$	34.8691	1.54554	0.772772	+	0.634683i	$0.218869\pi$
$510$	−2.34182	−0.103698
$511$	−4.41046	−0.195107
$512$	50.6986	2.24058
$513$	1.79756	0.0793641
$514$	−60.8801	−2.68531
$515$	0.541564	0.0238642
$516$	0.209252	0.00921181
$517$	0.270261	0.0118861
$518$	−0.240219	−0.0105546
$519$	−4.36048	−0.191404
$520$	−3.37629	−0.148060
$521$	33.2457	1.45652	0.728260	−	0.685301i	$-0.240329\pi$
$521$	33.2457	1.45652	0.728260	+	0.685301i	$0.240329\pi$
$522$	17.5972	0.770210
$523$	21.3107	0.931852	0.465926	−	0.884824i	$-0.345721\pi$
$523$	21.3107	0.931852	0.465926	+	0.884824i	$0.345721\pi$
$524$	−39.7800	−1.73780
$525$	−1.30045	−0.0567562
$526$	38.9002	1.69613
$527$	6.67131	0.290607
$528$	−2.24902	−0.0978759
$529$	−5.31172	−0.230944
$530$	−24.9555	−1.08400
$531$	−8.10918	−0.351908
$532$	2.49761	0.108285
$533$	0.930559	0.0403070
$534$	−25.0343	−1.08334
$535$	−7.69832	−0.332827
$536$	−57.7021	−2.49235
$537$	17.4253	0.751959
$538$	39.9784	1.72359
$539$	−2.29199	−0.0987229
$540$	4.09187	0.176086
$541$	−11.7978	−0.507228	−0.253614	−	0.967305i	$-0.581619\pi$
$541$	−11.7978	−0.507228	−0.253614	+	0.967305i	$0.581619\pi$
$542$	34.3556	1.47570
$543$	−2.09162	−0.0897602
$544$	−4.84401	−0.207685
$545$	2.05387	0.0879780
$546$	0.471587	0.0201821
$547$	18.7172	0.800289	0.400144	−	0.916452i	$-0.368960\pi$
$547$	18.7172	0.800289	0.400144	+	0.916452i	$0.368960\pi$
$548$	11.4386	0.488631
$549$	−5.49161	−0.234376
$550$	3.49268	0.148929
$551$	12.4734	0.531385
$552$	−25.9288	−1.10360
$553$	−0.811910	−0.0345259
$554$	−74.5709	−3.16821
$555$	−0.278961	−0.0118413
$556$	5.61587	0.238166
$557$	−10.5176	−0.445646	−0.222823	−	0.974859i	$-0.571527\pi$
$557$	−10.5176	−0.445646	−0.222823	+	0.974859i	$0.571527\pi$
$558$	−16.9181	−0.716202
$559$	0.0280058	0.00118452
$560$	1.96101	0.0828679
$561$	−0.332092	−0.0140209
$562$	−20.7792	−0.876516
$563$	12.9143	0.544275	0.272137	−	0.962258i	$-0.412269\pi$
$563$	12.9143	0.544275	0.272137	+	0.962258i	$0.412269\pi$
$564$	−3.60607	−0.151843
$565$	15.3476	0.645679
$566$	41.4645	1.74288
$567$	−0.313569	−0.0131687
$568$	−9.83644	−0.412728
$569$	10.0914	0.423053	0.211526	−	0.977372i	$-0.432157\pi$
$569$	10.0914	0.423053	0.211526	+	0.977372i	$0.432157\pi$
$570$	4.20956	0.176319
$571$	45.8348	1.91813	0.959063	−	0.283194i	$-0.0913942\pi$
$571$	45.8348	1.91813	0.959063	+	0.283194i	$0.0913942\pi$
$572$	−0.872679	−0.0364885
$573$	−20.6202	−0.861423
$574$	−1.24776	−0.0520805
$575$	17.4422	0.727392
$576$	−1.26037	−0.0525156
$577$	14.5344	0.605076	0.302538	−	0.953137i	$-0.402166\pi$
$577$	14.5344	0.605076	0.302538	+	0.953137i	$0.402166\pi$
$578$	−2.53596	−0.105482
$579$	−15.8887	−0.660313
$580$	28.3939	1.17899
$581$	−2.31797	−0.0961657
$582$	28.5781	1.18460
$583$	−3.53891	−0.146567
$584$	−86.7144	−3.58827
$585$	0.547646	0.0226424
$586$	−5.90958	−0.244123
$587$	36.9283	1.52420	0.762098	−	0.647462i	$-0.224169\pi$
$587$	36.9283	1.52420	0.762098	+	0.647462i	$0.224169\pi$
$588$	30.5818	1.26117
$589$	−11.9921	−0.494124
$590$	−18.9903	−0.781817
$591$	−25.7860	−1.06070
$592$	−2.04582	−0.0840826
$593$	−21.7314	−0.892401	−0.446200	−	0.894933i	$-0.647223\pi$
$593$	−21.7314	−0.892401	−0.446200	+	0.894933i	$0.647223\pi$
$594$	0.842170	0.0345546
$595$	0.289564	0.0118710
$596$	−39.2453	−1.60755
$597$	0.109309	0.00447372
$598$	−6.32517	−0.258655
$599$	46.0633	1.88209	0.941047	−	0.338276i	$-0.109844\pi$
$599$	46.0633	1.88209	0.941047	+	0.338276i	$0.109844\pi$
$600$	−25.5682	−1.04382
$601$	21.7684	0.887953	0.443977	−	0.896038i	$-0.353567\pi$
$601$	21.7684	0.887953	0.443977	+	0.896038i	$0.353567\pi$
$602$	−0.0375522	−0.00153051
$603$	9.35947	0.381147
$604$	82.5362	3.35835
$605$	10.0561	0.408838
$606$	−25.6070	−1.04021
$607$	−23.8993	−0.970043	−0.485022	−	0.874502i	$-0.661188\pi$
$607$	−23.8993	−0.970043	−0.485022	+	0.874502i	$0.661188\pi$
$608$	8.70737	0.353131
$609$	−2.17588	−0.0881713
$610$	−12.8604	−0.520702
$611$	−0.482628	−0.0195251
$612$	4.43108	0.179116
$613$	8.52372	0.344270	0.172135	−	0.985073i	$-0.444934\pi$
$613$	8.52372	0.344270	0.172135	+	0.985073i	$0.444934\pi$
$614$	80.4866	3.24817
$615$	−1.44900	−0.0584294
$616$	0.641994	0.0258667
$617$	39.1477	1.57603	0.788014	−	0.615657i	$-0.211109\pi$
$617$	39.1477	1.57603	0.788014	+	0.615657i	$0.211109\pi$
$618$	−1.48723	−0.0598254
$619$	47.1167	1.89378	0.946890	−	0.321558i	$-0.104206\pi$
$619$	47.1167	1.89378	0.946890	+	0.321558i	$0.104206\pi$
$620$	−27.2981	−1.09632
$621$	4.20574	0.168771
$622$	−38.4609	−1.54214
$623$	3.09547	0.124017
$624$	4.01627	0.160779
$625$	12.9359	0.517434
$626$	28.5271	1.14017
$627$	0.596953	0.0238400
$628$	−4.43108	−0.176819
$629$	−0.302087	−0.0120450
$630$	−0.734323	−0.0292561
$631$	9.73238	0.387440	0.193720	−	0.981057i	$-0.437945\pi$
$631$	9.73238	0.387440	0.193720	+	0.981057i	$0.437945\pi$
$632$	−15.9630	−0.634975
$633$	8.52744	0.338935
$634$	79.5322	3.15863
$635$	−14.1947	−0.563300
$636$	47.2195	1.87237
$637$	4.09300	0.162171
$638$	5.84390	0.231362
$639$	1.59550	0.0631171
$640$	−11.8979	−0.470308
$641$	34.7684	1.37327	0.686634	−	0.727003i	$-0.259087\pi$
$641$	34.7684	1.37327	0.686634	+	0.727003i	$0.259087\pi$
$642$	21.1410	0.834369
$643$	23.8071	0.938859	0.469430	−	0.882970i	$-0.344460\pi$
$643$	23.8071	0.938859	0.469430	+	0.882970i	$0.344460\pi$
$644$	5.84366	0.230272
$645$	−0.0436087	−0.00171709
$646$	4.55853	0.179353
$647$	30.8358	1.21228	0.606141	−	0.795357i	$-0.292717\pi$
$647$	30.8358	1.21228	0.606141	+	0.795357i	$0.292717\pi$
$648$	−6.16510	−0.242188
$649$	−2.69299	−0.105709
$650$	−6.23719	−0.244643
$651$	2.09191	0.0819886
$652$	−97.3597	−3.81290
$653$	31.1426	1.21870	0.609352	−	0.792900i	$-0.291430\pi$
$653$	31.1426	1.21870	0.609352	+	0.792900i	$0.291430\pi$
$654$	−5.64030	−0.220553
$655$	8.29025	0.323927
$656$	−10.6265	−0.414896
$657$	14.0654	0.548742
$658$	0.647143	0.0252283
$659$	11.1909	0.435935	0.217968	−	0.975956i	$-0.430057\pi$
$659$	11.1909	0.435935	0.217968	+	0.975956i	$0.430057\pi$
$660$	1.35887	0.0528941
$661$	28.3192	1.10149	0.550744	−	0.834674i	$-0.314344\pi$
$661$	28.3192	1.10149	0.550744	+	0.834674i	$0.314344\pi$
$662$	−61.5746	−2.39317
$663$	0.593045	0.0230319
$664$	−45.5738	−1.76861
$665$	−0.520509	−0.0201845
$666$	0.766079	0.0296850
$667$	29.1841	1.13001
$668$	−26.0914	−1.00951
$669$	−8.31849	−0.321612
$670$	21.9182	0.846775
$671$	−1.82372	−0.0704039
$672$	−1.51893	−0.0585940
$673$	−27.3602	−1.05466	−0.527328	−	0.849662i	$-0.676806\pi$
$673$	−27.3602	−1.05466	−0.527328	+	0.849662i	$0.676806\pi$
$674$	54.0922	2.08355
$675$	4.14724	0.159628
$676$	−56.0456	−2.15560
$677$	−31.3378	−1.20441	−0.602204	−	0.798342i	$-0.705711\pi$
$677$	−31.3378	−1.20441	−0.602204	+	0.798342i	$0.705711\pi$
$678$	−42.1474	−1.61866
$679$	−3.53366	−0.135609
$680$	5.69315	0.218322
$681$	9.17819	0.351709
$682$	−5.61837	−0.215139
$683$	47.1546	1.80432	0.902159	−	0.431403i	$-0.141981\pi$
$683$	47.1546	1.80432	0.902159	+	0.431403i	$0.141981\pi$
$684$	−7.96511	−0.304554
$685$	−2.38382	−0.0910812
$686$	−11.0546	−0.422065
$687$	5.27359	0.201200
$688$	−0.319813	−0.0121927
$689$	6.31974	0.240763
$690$	9.84911	0.374949
$691$	−0.589097	−0.0224103	−0.0112052	−	0.999937i	$-0.503567\pi$
$691$	−0.589097	−0.0224103	−0.0112052	+	0.999937i	$0.503567\pi$
$692$	19.3216	0.734498
$693$	−0.104134	−0.00395571
$694$	30.4059	1.15419
$695$	−1.17036	−0.0443944
$696$	−42.7802	−1.62158
$697$	−1.56912	−0.0594347
$698$	−48.7499	−1.84521
$699$	−17.6227	−0.666551
$700$	5.76238	0.217797
$701$	22.9695	0.867547	0.433773	−	0.901022i	$-0.357182\pi$
$701$	22.9695	0.867547	0.433773	+	0.901022i	$0.357182\pi$
$702$	−1.50394	−0.0567624
$703$	0.543018	0.0204803
$704$	−0.418559	−0.0157751
$705$	0.751515	0.0283037
$706$	−42.6377	−1.60469
$707$	3.16629	0.119081
$708$	35.9324	1.35042
$709$	−36.0984	−1.35570	−0.677852	−	0.735199i	$-0.737089\pi$
$709$	−36.0984	−1.35570	−0.677852	+	0.735199i	$0.737089\pi$
$710$	3.73638	0.140224
$711$	2.58926	0.0971047
$712$	60.8602	2.28083
$713$	−28.0578	−1.05077
$714$	−0.795197	−0.0297595
$715$	0.181869	0.00680150
$716$	−77.2130	−2.88559
$717$	13.2303	0.494093
$718$	44.5804	1.66373
$719$	−1.28684	−0.0479910	−0.0239955	−	0.999712i	$-0.507639\pi$
$719$	−1.28684	−0.0479910	−0.0239955	+	0.999712i	$0.507639\pi$
$720$	−6.25385	−0.233067
$721$	0.183895	0.00684862
$722$	39.9890	1.48824
$723$	−28.2183	−1.04945
$724$	9.26814	0.344448
$725$	28.7781	1.06879
$726$	−27.6158	−1.02492
$727$	39.7396	1.47386	0.736930	−	0.675969i	$-0.236275\pi$
$727$	39.7396	1.47386	0.736930	+	0.675969i	$0.236275\pi$
$728$	−1.14646	−0.0424908
$729$	1.00000	0.0370370
$730$	32.9386	1.21911
$731$	−0.0472238	−0.00174663
$732$	24.3338	0.899402
$733$	−15.5985	−0.576145	−0.288072	−	0.957609i	$-0.593014\pi$
$733$	−15.5985	−0.576145	−0.288072	+	0.957609i	$0.593014\pi$
$734$	16.0033	0.590694
$735$	−6.37334	−0.235084
$736$	20.3726	0.750946
$737$	3.10820	0.114492
$738$	3.97922	0.146477
$739$	−5.42021	−0.199386	−0.0996928	−	0.995018i	$-0.531786\pi$
$739$	−5.42021	−0.199386	−0.0996928	+	0.995018i	$0.531786\pi$
$740$	1.23610	0.0454399
$741$	−1.06603	−0.0391616
$742$	−8.47397	−0.311089
$743$	−19.5038	−0.715523	−0.357762	−	0.933813i	$-0.616460\pi$
$743$	−19.5038	−0.715523	−0.357762	+	0.933813i	$0.616460\pi$
$744$	41.1293	1.50787
$745$	8.17883	0.299649
$746$	3.20529	0.117354
$747$	7.39223	0.270467
$748$	1.47152	0.0538042
$749$	−2.61407	−0.0955159
$750$	21.4212	0.782193
$751$	−30.3153	−1.10622	−0.553111	−	0.833107i	$-0.686560\pi$
$751$	−30.3153	−1.10622	−0.553111	+	0.833107i	$0.686560\pi$
$752$	5.51138	0.200979
$753$	−8.95764	−0.326434
$754$	−10.4360	−0.380055
$755$	−17.2008	−0.625999
$756$	1.38945	0.0505337
$757$	34.4270	1.25127	0.625634	−	0.780116i	$-0.284840\pi$
$757$	34.4270	1.25127	0.625634	+	0.780116i	$0.284840\pi$
$758$	93.4812	3.39539
$759$	1.39669	0.0506967
$760$	−10.2338	−0.371217
$761$	10.4328	0.378188	0.189094	−	0.981959i	$-0.439445\pi$
$761$	10.4328	0.378188	0.189094	+	0.981959i	$0.439445\pi$
$762$	38.9813	1.41214
$763$	0.697418	0.0252482
$764$	91.3699	3.30565
$765$	−0.923448	−0.0333873
$766$	43.3045	1.56466
$767$	4.80911	0.173647
$768$	30.1532	1.08806
$769$	49.5981	1.78855	0.894276	−	0.447516i	$-0.147691\pi$
$769$	49.5981	1.78855	0.894276	+	0.447516i	$0.147691\pi$
$770$	−0.243862	−0.00878819
$771$	−24.0068	−0.864583
$772$	70.4041	2.53390
$773$	−44.8291	−1.61239	−0.806195	−	0.591649i	$-0.798477\pi$
$773$	−44.8291	−1.61239	−0.806195	+	0.591649i	$0.798477\pi$
$774$	0.119757	0.00430459
$775$	−27.6675	−0.993847
$776$	−69.4755	−2.49403
$777$	−0.0947250	−0.00339824
$778$	−13.2768	−0.475997
$779$	2.82058	0.101058
$780$	−2.42666	−0.0868884
$781$	0.529853	0.0189596
$782$	10.6656	0.381400
$783$	6.93910	0.247983
$784$	−46.7401	−1.66929
$785$	0.923448	0.0329593
$786$	−22.7666	−0.812056
$787$	−34.6405	−1.23480	−0.617400	−	0.786649i	$-0.711814\pi$
$787$	−34.6405	−1.23480	−0.617400	+	0.786649i	$0.711814\pi$
$788$	114.260	4.07034
$789$	15.3395	0.546100
$790$	6.06358	0.215733
$791$	5.21148	0.185299
$792$	−2.04738	−0.0727504
$793$	3.25677	0.115651
$794$	−23.7700	−0.843566
$795$	−9.84066	−0.349012
$796$	−0.484357	−0.0171676
$797$	45.9079	1.62614	0.813070	−	0.582166i	$-0.197795\pi$
$797$	45.9079	1.62614	0.813070	+	0.582166i	$0.197795\pi$
$798$	1.42941	0.0506006
$799$	0.813814	0.0287907
$800$	20.0893	0.710263
$801$	−9.87173	−0.348800
$802$	−30.3885	−1.07305
$803$	4.67099	0.164836
$804$	−41.4725	−1.46262
$805$	−1.21783	−0.0429230
$806$	10.0332	0.353405
$807$	15.7646	0.554941
$808$	62.2526	2.19004
$809$	30.1172	1.05887	0.529433	−	0.848352i	$-0.322405\pi$
$809$	30.1172	1.05887	0.529433	+	0.848352i	$0.322405\pi$
$810$	2.34182	0.0822833
$811$	−51.6411	−1.81336	−0.906682	−	0.421814i	$-0.861393\pi$
$811$	−51.6411	−1.81336	−0.906682	+	0.421814i	$0.861393\pi$
$812$	9.64151	0.338351
$813$	13.5474	0.475128
$814$	0.254408	0.00891701
$815$	20.2900	0.710728
$816$	−6.77228	−0.237077
$817$	0.0848874	0.00296984
$818$	−65.8423	−2.30212
$819$	0.185960	0.00649798
$820$	6.42063	0.224218
$821$	53.1082	1.85349	0.926744	−	0.375693i	$-0.122595\pi$
$821$	53.1082	1.85349	0.926744	+	0.375693i	$0.122595\pi$
$822$	6.54642	0.228333
$823$	−5.03817	−0.175619	−0.0878097	−	0.996137i	$-0.527987\pi$
$823$	−5.03817	−0.175619	−0.0878097	+	0.996137i	$0.527987\pi$
$824$	3.61558	0.125955
$825$	1.37726	0.0479502
$826$	−6.44840	−0.224368
$827$	−26.6843	−0.927902	−0.463951	−	0.885861i	$-0.653569\pi$
$827$	−26.6843	−0.927902	−0.463951	+	0.885861i	$0.653569\pi$
$828$	−18.6360	−0.647645
$829$	34.6830	1.20459	0.602296	−	0.798273i	$-0.294253\pi$
$829$	34.6830	1.20459	0.602296	+	0.798273i	$0.294253\pi$
$830$	17.3113	0.600884
$831$	−29.4054	−1.02006
$832$	0.747458	0.0259134
$833$	−6.90167	−0.239129
$834$	3.21403	0.111293
$835$	5.43752	0.188173
$836$	−2.64515	−0.0914843
$837$	−6.67131	−0.230594
$838$	25.3786	0.876690
$839$	7.94707	0.274363	0.137182	−	0.990546i	$-0.456196\pi$
$839$	7.94707	0.274363	0.137182	+	0.990546i	$0.456196\pi$
$840$	1.78519	0.0615951
$841$	19.1510	0.660381
$842$	−15.6315	−0.538697
$843$	−8.19382	−0.282210
$844$	−37.7857	−1.30064
$845$	11.6800	0.401806
$846$	−2.06380	−0.0709548
$847$	3.41468	0.117330
$848$	−72.1684	−2.47827
$849$	16.3506	0.561152
$850$	10.5172	0.360738
$851$	1.27050	0.0435522
$852$	−7.06979	−0.242207
$853$	40.3597	1.38189	0.690945	−	0.722907i	$-0.257195\pi$
$853$	40.3597	1.38189	0.690945	+	0.722907i	$0.257195\pi$
$854$	−4.36692	−0.149433
$855$	1.65995	0.0567691
$856$	−51.3954	−1.75666
$857$	25.9641	0.886916	0.443458	−	0.896295i	$-0.353751\pi$
$857$	25.9641	0.886916	0.443458	+	0.896295i	$0.353751\pi$
$858$	−0.499444	−0.0170507
$859$	−26.0911	−0.890217	−0.445109	−	0.895477i	$-0.646835\pi$
$859$	−26.0911	−0.890217	−0.445109	+	0.895477i	$0.646835\pi$
$860$	0.193233	0.00658921
$861$	−0.492027	−0.0167682
$862$	71.0439	2.41976
$863$	22.7478	0.774344	0.387172	−	0.922007i	$-0.373452\pi$
$863$	22.7478	0.774344	0.387172	+	0.922007i	$0.373452\pi$
$864$	4.84401	0.164796
$865$	−4.02668	−0.136911
$866$	53.9954	1.83484
$867$	−1.00000	−0.0339618
$868$	−9.26943	−0.314625
$869$	0.859870	0.0291691
$870$	16.2501	0.550931
$871$	−5.55059	−0.188074
$872$	13.7120	0.464347
$873$	11.2692	0.381403
$874$	−19.1720	−0.648502
$875$	−2.64872	−0.0895430
$876$	−62.3247	−2.10576
$877$	−27.3883	−0.924838	−0.462419	−	0.886661i	$-0.653018\pi$
$877$	−27.3883	−0.924838	−0.462419	+	0.886661i	$0.653018\pi$
$878$	66.5910	2.24734
$879$	−2.33032	−0.0785997
$880$	−2.07685	−0.0700106
$881$	−48.2041	−1.62404	−0.812018	−	0.583632i	$-0.801631\pi$
$881$	−48.2041	−1.62404	−0.812018	+	0.583632i	$0.801631\pi$
$882$	17.5023	0.589335
$883$	48.7104	1.63923	0.819617	−	0.572912i	$-0.194186\pi$
$883$	48.7104	1.63923	0.819617	+	0.572912i	$0.194186\pi$
$884$	−2.62783	−0.0883834
$885$	−7.48840	−0.251720
$886$	−64.7328	−2.17474
$887$	36.4043	1.22234	0.611169	−	0.791500i	$-0.290699\pi$
$887$	36.4043	1.22234	0.611169	+	0.791500i	$0.290699\pi$
$888$	−1.86240	−0.0624979
$889$	−4.82001	−0.161658
$890$	−23.1178	−0.774912
$891$	0.332092	0.0111255
$892$	36.8599	1.23416
$893$	−1.46288	−0.0489533
$894$	−22.4606	−0.751193
$895$	16.0914	0.537876
$896$	−4.04010	−0.134970
$897$	−2.49419	−0.0832787
$898$	47.3897	1.58142
$899$	−46.2928	−1.54395
$900$	−18.3768	−0.612558
$901$	−10.6564	−0.355017
$902$	1.32147	0.0440000
$903$	−0.0148079	−0.000492776 0
$904$	102.463	3.40788
$905$	−1.93151	−0.0642054
$906$	47.2364	1.56932
$907$	−6.05898	−0.201185	−0.100592	−	0.994928i	$-0.532074\pi$
$907$	−6.05898	−0.201185	−0.100592	+	0.994928i	$0.532074\pi$
$908$	−40.6692	−1.34966
$909$	−10.0976	−0.334916
$910$	0.435486	0.0144362
$911$	13.0017	0.430765	0.215382	−	0.976530i	$-0.430900\pi$
$911$	13.0017	0.430765	0.215382	+	0.976530i	$0.430900\pi$
$912$	12.1736	0.403107
$913$	2.45490	0.0812452
$914$	98.8689	3.27029
$915$	−5.07122	−0.167649
$916$	−23.3677	−0.772090
$917$	2.81506	0.0929616
$918$	2.53596	0.0836990
$919$	−36.1559	−1.19267	−0.596337	−	0.802734i	$-0.703378\pi$
$919$	−36.1559	−1.19267	−0.596337	+	0.802734i	$0.703378\pi$
$920$	−23.9439	−0.789408
$921$	31.7382	1.04581
$922$	84.8960	2.79590
$923$	−0.946204	−0.0311447
$924$	0.461424	0.0151797
$925$	1.25283	0.0411927
$926$	22.9277	0.753452
$927$	−0.586459	−0.0192618
$928$	33.6130	1.10340
$929$	35.2188	1.15549	0.577746	−	0.816217i	$-0.303932\pi$
$929$	35.2188	1.15549	0.577746	+	0.816217i	$0.303932\pi$
$930$	−15.6230	−0.512299
$931$	12.4061	0.406595
$932$	78.0875	2.55784
$933$	−15.1662	−0.496520
$934$	−42.8745	−1.40290
$935$	−0.306669	−0.0100292
$936$	3.65618	0.119506
$937$	29.2136	0.954367	0.477184	−	0.878804i	$-0.341658\pi$
$937$	29.2136	0.954367	0.477184	+	0.878804i	$0.341658\pi$
$938$	7.44263	0.243010
$939$	11.2491	0.367099
$940$	−3.33002	−0.108613
$941$	31.4811	1.02625	0.513127	−	0.858313i	$-0.328487\pi$
$941$	31.4811	1.02625	0.513127	+	0.858313i	$0.328487\pi$
$942$	−2.53596	−0.0826259
$943$	6.59932	0.214903
$944$	−54.9176	−1.78742
$945$	−0.289564	−0.00941953
$946$	0.0397704	0.00129305
$947$	−25.0363	−0.813569	−0.406785	−	0.913524i	$-0.633350\pi$
$947$	−25.0363	−0.813569	−0.406785	+	0.913524i	$0.633350\pi$
$948$	−11.4732	−0.372632
$949$	−8.34138	−0.270773
$950$	−18.9053	−0.613370
$951$	31.3618	1.01698
$952$	1.93318	0.0626549
$953$	19.6534	0.636635	0.318317	−	0.947984i	$-0.396882\pi$
$953$	19.6534	0.636635	0.318317	+	0.947984i	$0.396882\pi$
$954$	27.0243	0.874943
$955$	−19.0417	−0.616176
$956$	−58.6243	−1.89604
$957$	2.30441	0.0744912
$958$	−18.1233	−0.585536
$959$	−0.809459	−0.0261388
$960$	−1.16389	−0.0375644
$961$	13.5063	0.435688
$962$	−0.454319	−0.0146478
$963$	8.33650	0.268640
$964$	125.037	4.02719
$965$	−14.6724	−0.472321
$966$	3.34439	0.107604
$967$	30.2418	0.972511	0.486256	−	0.873817i	$-0.338362\pi$
$967$	30.2418	0.972511	0.486256	+	0.873817i	$0.338362\pi$
$968$	67.1362	2.15784
$969$	1.79756	0.0577458
$970$	26.3904	0.847344
$971$	43.6795	1.40174	0.700871	−	0.713288i	$-0.252795\pi$
$971$	43.6795	1.40174	0.700871	+	0.713288i	$0.252795\pi$
$972$	−4.43108	−0.142127
$973$	−0.397412	−0.0127404
$974$	24.3410	0.779935
$975$	−2.45950	−0.0787671
$976$	−37.1908	−1.19045
$977$	−35.1447	−1.12438	−0.562189	−	0.827009i	$-0.690041\pi$
$977$	−35.1447	−1.12438	−0.562189	+	0.827009i	$0.690041\pi$
$978$	−55.7201	−1.78173
$979$	−3.27832	−0.104776
$980$	28.2407	0.902117
$981$	−2.22413	−0.0710110
$982$	61.6336	1.96681
$983$	−17.9334	−0.571986	−0.285993	−	0.958232i	$-0.592323\pi$
$983$	−17.9334	−0.571986	−0.285993	+	0.958232i	$0.592323\pi$
$984$	−9.67379	−0.308389
$985$	−23.8121	−0.758715
$986$	17.5972	0.560410
$987$	0.255187	0.00812269
$988$	4.72367	0.150280
$989$	0.198611	0.00631547
$990$	0.777700	0.0247169
$991$	−29.8720	−0.948916	−0.474458	−	0.880278i	$-0.657356\pi$
$991$	−29.8720	−0.948916	−0.474458	+	0.880278i	$0.657356\pi$
$992$	−32.3159	−1.02603
$993$	−24.2806	−0.770522
$994$	1.26874	0.0402419
$995$	0.100941	0.00320005
$996$	−32.7555	−1.03790
$997$	−13.0881	−0.414505	−0.207253	−	0.978287i	$-0.566452\pi$
$997$	−13.0881	−0.414505	−0.207253	+	0.978287i	$0.566452\pi$
$998$	−24.8107	−0.785370
$999$	0.302087	0.00955760

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.5	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-2.53596 q^{2} -1.00000 q^{3} +4.43108 q^{4} -0.923448 q^{5} +2.53596 q^{6} -0.313569 q^{7} -6.16510 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.53596 q^{2} -1.00000 q^{3} +4.43108 q^{4} -0.923448 q^{5} +2.53596 q^{6} -0.313569 q^{7} -6.16510 q^{8} +1.00000 q^{9} +2.34182 q^{10} +0.332092 q^{11} -4.43108 q^{12} -0.593045 q^{13} +0.795197 q^{14} +0.923448 q^{15} +6.77228 q^{16} +1.00000 q^{17} -2.53596 q^{18} -1.79756 q^{19} -4.09187 q^{20} +0.313569 q^{21} -0.842170 q^{22} -4.20574 q^{23} +6.16510 q^{24} -4.14724 q^{25} +1.50394 q^{26} -1.00000 q^{27} -1.38945 q^{28} -6.93910 q^{29} -2.34182 q^{30} +6.67131 q^{31} -4.84401 q^{32} -0.332092 q^{33} -2.53596 q^{34} +0.289564 q^{35} +4.43108 q^{36} -0.302087 q^{37} +4.55853 q^{38} +0.593045 q^{39} +5.69315 q^{40} -1.56912 q^{41} -0.795197 q^{42} -0.0472238 q^{43} +1.47152 q^{44} -0.923448 q^{45} +10.6656 q^{46} +0.813814 q^{47} -6.77228 q^{48} -6.90167 q^{49} +10.5172 q^{50} -1.00000 q^{51} -2.62783 q^{52} -10.6564 q^{53} +2.53596 q^{54} -0.306669 q^{55} +1.93318 q^{56} +1.79756 q^{57} +17.5972 q^{58} -8.10918 q^{59} +4.09187 q^{60} -5.49161 q^{61} -16.9181 q^{62} -0.313569 q^{63} -1.26037 q^{64} +0.547646 q^{65} +0.842170 q^{66} +9.35947 q^{67} +4.43108 q^{68} +4.20574 q^{69} -0.734323 q^{70} +1.59550 q^{71} -6.16510 q^{72} +14.0654 q^{73} +0.766079 q^{74} +4.14724 q^{75} -7.96511 q^{76} -0.104134 q^{77} -1.50394 q^{78} +2.58926 q^{79} -6.25385 q^{80} +1.00000 q^{81} +3.97922 q^{82} +7.39223 q^{83} +1.38945 q^{84} -0.923448 q^{85} +0.119757 q^{86} +6.93910 q^{87} -2.04738 q^{88} -9.87173 q^{89} +2.34182 q^{90} +0.185960 q^{91} -18.6360 q^{92} -6.67131 q^{93} -2.06380 q^{94} +1.65995 q^{95} +4.84401 q^{96} +11.2692 q^{97} +17.5023 q^{98} +0.332092 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 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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