LMFDB - Embedded newform 8005.2.a.f.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8005,2,Mod(1,8005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8005, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8005 = 5 \cdot 1601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8005.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:	$63.9202468180$
Analytic rank:	$1$
Dimension:	$127$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	8005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.10003 q^{2} -0.379559 q^{3} +2.41011 q^{4} -1.00000 q^{5} +0.797083 q^{6} -3.17706 q^{7} -0.861245 q^{8} -2.85594 q^{9} +O(q^{10})$	\(q-2.10003 q^{2} -0.379559 q^{3} +2.41011 q^{4} -1.00000 q^{5} +0.797083 q^{6} -3.17706 q^{7} -0.861245 q^{8} -2.85594 q^{9} +2.10003 q^{10} +4.19229 q^{11} -0.914779 q^{12} +3.09874 q^{13} +6.67191 q^{14} +0.379559 q^{15} -3.01159 q^{16} +3.17619 q^{17} +5.99754 q^{18} +1.69714 q^{19} -2.41011 q^{20} +1.20588 q^{21} -8.80393 q^{22} -0.0633445 q^{23} +0.326893 q^{24} +1.00000 q^{25} -6.50743 q^{26} +2.22267 q^{27} -7.65707 q^{28} -1.33902 q^{29} -0.797083 q^{30} -4.41429 q^{31} +8.04690 q^{32} -1.59122 q^{33} -6.67009 q^{34} +3.17706 q^{35} -6.88312 q^{36} -2.21913 q^{37} -3.56403 q^{38} -1.17615 q^{39} +0.861245 q^{40} -7.53145 q^{41} -2.53238 q^{42} +4.52807 q^{43} +10.1039 q^{44} +2.85594 q^{45} +0.133025 q^{46} -6.08171 q^{47} +1.14307 q^{48} +3.09372 q^{49} -2.10003 q^{50} -1.20555 q^{51} +7.46830 q^{52} -7.07597 q^{53} -4.66767 q^{54} -4.19229 q^{55} +2.73623 q^{56} -0.644163 q^{57} +2.81197 q^{58} +2.95803 q^{59} +0.914779 q^{60} -9.19495 q^{61} +9.27014 q^{62} +9.07348 q^{63} -10.8755 q^{64} -3.09874 q^{65} +3.34161 q^{66} -7.68192 q^{67} +7.65498 q^{68} +0.0240429 q^{69} -6.67191 q^{70} +11.2828 q^{71} +2.45966 q^{72} -12.4173 q^{73} +4.66023 q^{74} -0.379559 q^{75} +4.09029 q^{76} -13.3192 q^{77} +2.46995 q^{78} +1.75127 q^{79} +3.01159 q^{80} +7.72417 q^{81} +15.8163 q^{82} +11.9133 q^{83} +2.90631 q^{84} -3.17619 q^{85} -9.50907 q^{86} +0.508236 q^{87} -3.61059 q^{88} +2.21917 q^{89} -5.99754 q^{90} -9.84488 q^{91} -0.152667 q^{92} +1.67548 q^{93} +12.7718 q^{94} -1.69714 q^{95} -3.05427 q^{96} -8.32296 q^{97} -6.49690 q^{98} -11.9729 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 127 q - 6 q^{2} - 18 q^{3} + 114 q^{4} - 127 q^{5} - 20 q^{6} + 28 q^{7} - 18 q^{8} + 101 q^{9}+O(q^{10}) $ 127 * q - 6 * q^2 - 18 * q^3 + 114 * q^4 - 127 * q^5 - 20 * q^6 + 28 * q^7 - 18 * q^8 + 101 * q^9	\( 127 q - 6 q^{2} - 18 q^{3} + 114 q^{4} - 127 q^{5} - 20 q^{6} + 28 q^{7} - 18 q^{8} + 101 q^{9} + 6 q^{10} - 45 q^{11} - 30 q^{12} - 53 q^{14} + 18 q^{15} + 84 q^{16} - 36 q^{17} - 10 q^{18} - 49 q^{19} - 114 q^{20} - 48 q^{21} + 13 q^{22} - 29 q^{23} - 63 q^{24} + 127 q^{25} - 55 q^{26} - 75 q^{27} + 44 q^{28} - 45 q^{29} + 20 q^{30} - 49 q^{31} - 32 q^{32} - 8 q^{33} - 52 q^{34} - 28 q^{35} + 44 q^{36} + 36 q^{37} - 65 q^{38} - 52 q^{39} + 18 q^{40} - 66 q^{41} - 18 q^{42} - 5 q^{43} - 93 q^{44} - 101 q^{45} - 25 q^{46} - 32 q^{47} - 54 q^{48} + 77 q^{49} - 6 q^{50} - 102 q^{51} - 13 q^{52} - 67 q^{53} - 53 q^{54} + 45 q^{55} - 158 q^{56} + 16 q^{57} + 35 q^{58} - 213 q^{59} + 30 q^{60} - 62 q^{61} - 33 q^{62} + 59 q^{63} + 34 q^{64} - 60 q^{66} + 10 q^{67} - 94 q^{68} - 93 q^{69} + 53 q^{70} - 118 q^{71} - 24 q^{72} + 35 q^{73} - 107 q^{74} - 18 q^{75} - 98 q^{76} - 93 q^{77} + 21 q^{78} - 64 q^{79} - 84 q^{80} + 15 q^{81} + 15 q^{82} - 187 q^{83} - 118 q^{84} + 36 q^{85} - 126 q^{86} - 53 q^{87} + 15 q^{88} - 138 q^{89} + 10 q^{90} - 138 q^{91} - 86 q^{92} + 23 q^{93} - 60 q^{94} + 49 q^{95} - 92 q^{96} + 9 q^{97} - 67 q^{98} - 147 q^{99}+O(q^{100}) \) 127 * q - 6 * q^2 - 18 * q^3 + 114 * q^4 - 127 * q^5 - 20 * q^6 + 28 * q^7 - 18 * q^8 + 101 * q^9 + 6 * q^10 - 45 * q^11 - 30 * q^12 - 53 * q^14 + 18 * q^15 + 84 * q^16 - 36 * q^17 - 10 * q^18 - 49 * q^19 - 114 * q^20 - 48 * q^21 + 13 * q^22 - 29 * q^23 - 63 * q^24 + 127 * q^25 - 55 * q^26 - 75 * q^27 + 44 * q^28 - 45 * q^29 + 20 * q^30 - 49 * q^31 - 32 * q^32 - 8 * q^33 - 52 * q^34 - 28 * q^35 + 44 * q^36 + 36 * q^37 - 65 * q^38 - 52 * q^39 + 18 * q^40 - 66 * q^41 - 18 * q^42 - 5 * q^43 - 93 * q^44 - 101 * q^45 - 25 * q^46 - 32 * q^47 - 54 * q^48 + 77 * q^49 - 6 * q^50 - 102 * q^51 - 13 * q^52 - 67 * q^53 - 53 * q^54 + 45 * q^55 - 158 * q^56 + 16 * q^57 + 35 * q^58 - 213 * q^59 + 30 * q^60 - 62 * q^61 - 33 * q^62 + 59 * q^63 + 34 * q^64 - 60 * q^66 + 10 * q^67 - 94 * q^68 - 93 * q^69 + 53 * q^70 - 118 * q^71 - 24 * q^72 + 35 * q^73 - 107 * q^74 - 18 * q^75 - 98 * q^76 - 93 * q^77 + 21 * q^78 - 64 * q^79 - 84 * q^80 + 15 * q^81 + 15 * q^82 - 187 * q^83 - 118 * q^84 + 36 * q^85 - 126 * q^86 - 53 * q^87 + 15 * q^88 - 138 * q^89 + 10 * q^90 - 138 * q^91 - 86 * q^92 + 23 * q^93 - 60 * q^94 + 49 * q^95 - 92 * q^96 + 9 * q^97 - 67 * q^98 - 147 * 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 $

$2$	−2.10003	−1.48494	−0.742472	−	0.669878i	$-0.766347\pi$
$2$	−2.10003	−1.48494	−0.742472	+	0.669878i	$0.766347\pi$
$3$	−0.379559	−0.219138	−0.109569	−	0.993979i	$-0.534947\pi$
$3$	−0.379559	−0.219138	−0.109569	+	0.993979i	$0.534947\pi$
$4$	2.41011	1.20506
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.797083	0.325408
$7$	−3.17706	−1.20082	−0.600408	−	0.799694i	$-0.704995\pi$
$7$	−3.17706	−1.20082	−0.600408	+	0.799694i	$0.704995\pi$
$8$	−0.861245	−0.304496
$9$	−2.85594	−0.951978
$10$	2.10003	0.664087
$11$	4.19229	1.26402	0.632012	−	0.774959i	$-0.282229\pi$
$11$	4.19229	1.26402	0.632012	+	0.774959i	$0.282229\pi$
$12$	−0.914779	−0.264074
$13$	3.09874	0.859435	0.429718	−	0.902963i	$-0.358613\pi$
$13$	3.09874	0.859435	0.429718	+	0.902963i	$0.358613\pi$
$14$	6.67191	1.78314
$15$	0.379559	0.0980016
$16$	−3.01159	−0.752896
$17$	3.17619	0.770340	0.385170	−	0.922846i	$-0.374143\pi$
$17$	3.17619	0.770340	0.385170	+	0.922846i	$0.374143\pi$
$18$	5.99754	1.41363
$19$	1.69714	0.389350	0.194675	−	0.980868i	$-0.437635\pi$
$19$	1.69714	0.389350	0.194675	+	0.980868i	$0.437635\pi$
$20$	−2.41011	−0.538917
$21$	1.20588	0.263145
$22$	−8.80393	−1.87700
$23$	−0.0633445	−0.0132082	−0.00660412	−	0.999978i	$-0.502102\pi$
$23$	−0.0633445	−0.0132082	−0.00660412	+	0.999978i	$0.502102\pi$
$24$	0.326893	0.0667268
$25$	1.00000	0.200000
$26$	−6.50743	−1.27621
$27$	2.22267	0.427753
$28$	−7.65707	−1.44705
$29$	−1.33902	−0.248649	−0.124325	−	0.992242i	$-0.539676\pi$
$29$	−1.33902	−0.248649	−0.124325	+	0.992242i	$0.539676\pi$
$30$	−0.797083	−0.145527
$31$	−4.41429	−0.792831	−0.396415	−	0.918071i	$-0.629746\pi$
$31$	−4.41429	−0.792831	−0.396415	+	0.918071i	$0.629746\pi$
$32$	8.04690	1.42250
$33$	−1.59122	−0.276996
$34$	−6.67009	−1.14391
$35$	3.17706	0.537021
$36$	−6.88312	−1.14719
$37$	−2.21913	−0.364823	−0.182411	−	0.983222i	$-0.558390\pi$
$37$	−2.21913	−0.364823	−0.182411	+	0.983222i	$0.558390\pi$
$38$	−3.56403	−0.578162
$39$	−1.17615	−0.188335
$40$	0.861245	0.136175
$41$	−7.53145	−1.17622	−0.588108	−	0.808783i	$-0.700127\pi$
$41$	−7.53145	−1.17622	−0.588108	+	0.808783i	$0.700127\pi$
$42$	−2.53238	−0.390755
$43$	4.52807	0.690524	0.345262	−	0.938506i	$-0.387790\pi$
$43$	4.52807	0.690524	0.345262	+	0.938506i	$0.387790\pi$
$44$	10.1039	1.52322
$45$	2.85594	0.425738
$46$	0.133025	0.0196135
$47$	−6.08171	−0.887108	−0.443554	−	0.896248i	$-0.646283\pi$
$47$	−6.08171	−0.887108	−0.443554	+	0.896248i	$0.646283\pi$
$48$	1.14307	0.164988
$49$	3.09372	0.441960
$50$	−2.10003	−0.296989
$51$	−1.20555	−0.168811
$52$	7.46830	1.03567
$53$	−7.07597	−0.971959	−0.485979	−	0.873970i	$-0.661537\pi$
$53$	−7.07597	−0.971959	−0.485979	+	0.873970i	$0.661537\pi$
$54$	−4.66767	−0.635189
$55$	−4.19229	−0.565289
$56$	2.73623	0.365644
$57$	−0.644163	−0.0853214
$58$	2.81197	0.369230
$59$	2.95803	0.385102	0.192551	−	0.981287i	$-0.438324\pi$
$59$	2.95803	0.385102	0.192551	+	0.981287i	$0.438324\pi$
$60$	0.914779	0.118097
$61$	−9.19495	−1.17729	−0.588646	−	0.808391i	$-0.700339\pi$
$61$	−9.19495	−1.17729	−0.588646	+	0.808391i	$0.700339\pi$
$62$	9.27014	1.17731
$63$	9.07348	1.14315
$64$	−10.8755	−1.35944
$65$	−3.09874	−0.384351
$66$	3.34161	0.411323
$67$	−7.68192	−0.938496	−0.469248	−	0.883066i	$-0.655475\pi$
$67$	−7.68192	−0.938496	−0.469248	+	0.883066i	$0.655475\pi$
$68$	7.65498	0.928302
$69$	0.0240429	0.00289443
$70$	−6.67191	−0.797446
$71$	11.2828	1.33902	0.669512	−	0.742801i	$-0.266503\pi$
$71$	11.2828	1.33902	0.669512	+	0.742801i	$0.266503\pi$
$72$	2.45966	0.289874
$73$	−12.4173	−1.45333	−0.726666	−	0.686991i	$-0.758931\pi$
$73$	−12.4173	−1.45333	−0.726666	+	0.686991i	$0.758931\pi$
$74$	4.66023	0.541741
$75$	−0.379559	−0.0438277
$76$	4.09029	0.469188
$77$	−13.3192	−1.51786
$78$	2.46995	0.279667
$79$	1.75127	0.197034	0.0985169	−	0.995135i	$-0.468590\pi$
$79$	1.75127	0.197034	0.0985169	+	0.995135i	$0.468590\pi$
$80$	3.01159	0.336705
$81$	7.72417	0.858241
$82$	15.8163	1.74661
$83$	11.9133	1.30765	0.653825	−	0.756646i	$-0.273163\pi$
$83$	11.9133	1.30765	0.653825	+	0.756646i	$0.273163\pi$
$84$	2.90631	0.317104
$85$	−3.17619	−0.344506
$86$	−9.50907	−1.02539
$87$	0.508236	0.0544886
$88$	−3.61059	−0.384891
$89$	2.21917	0.235231	0.117616	−	0.993059i	$-0.462475\pi$
$89$	2.21917	0.235231	0.117616	+	0.993059i	$0.462475\pi$
$90$	−5.99754	−0.632196
$91$	−9.84488	−1.03202
$92$	−0.152667	−0.0159167
$93$	1.67548	0.173740
$94$	12.7718	1.31731
$95$	−1.69714	−0.174123
$96$	−3.05427	−0.311725
$97$	−8.32296	−0.845069	−0.422534	−	0.906347i	$-0.638859\pi$
$97$	−8.32296	−0.845069	−0.422534	+	0.906347i	$0.638859\pi$
$98$	−6.49690	−0.656286
$99$	−11.9729	−1.20332
$100$	2.41011	0.241011
$101$	−8.39994	−0.835825	−0.417913	−	0.908487i	$-0.637238\pi$
$101$	−8.39994	−0.835825	−0.417913	+	0.908487i	$0.637238\pi$
$102$	2.53169	0.250675
$103$	17.9692	1.77056	0.885278	−	0.465062i	$-0.153968\pi$
$103$	17.9692	1.77056	0.885278	+	0.465062i	$0.153968\pi$
$104$	−2.66877	−0.261695
$105$	−1.20588	−0.117682
$106$	14.8597	1.44330
$107$	17.8684	1.72740	0.863701	−	0.504005i	$-0.168141\pi$
$107$	17.8684	1.72740	0.863701	+	0.504005i	$0.168141\pi$
$108$	5.35688	0.515466
$109$	12.8490	1.23071	0.615355	−	0.788250i	$-0.289013\pi$
$109$	12.8490	1.23071	0.615355	+	0.788250i	$0.289013\pi$
$110$	8.80393	0.839422
$111$	0.842290	0.0799467
$112$	9.56799	0.904090
$113$	16.1965	1.52363	0.761817	−	0.647792i	$-0.224307\pi$
$113$	16.1965	1.52363	0.761817	+	0.647792i	$0.224307\pi$
$114$	1.35276	0.126697
$115$	0.0633445	0.00590690
$116$	−3.22718	−0.299636
$117$	−8.84980	−0.818164
$118$	−6.21194	−0.571855
$119$	−10.0910	−0.925036
$120$	−0.326893	−0.0298411
$121$	6.57533	0.597757
$122$	19.3096	1.74821
$123$	2.85863	0.257754
$124$	−10.6389	−0.955405
$125$	−1.00000	−0.0894427
$126$	−19.0546	−1.69751
$127$	3.66416	0.325141	0.162571	−	0.986697i	$-0.448021\pi$
$127$	3.66416	0.325141	0.162571	+	0.986697i	$0.448021\pi$
$128$	6.74511	0.596189
$129$	−1.71867	−0.151320
$130$	6.50743	0.570740
$131$	−10.0229	−0.875703	−0.437852	−	0.899047i	$-0.644260\pi$
$131$	−10.0229	−0.875703	−0.437852	+	0.899047i	$0.644260\pi$
$132$	−3.83502	−0.333796
$133$	−5.39191	−0.467538
$134$	16.1322	1.39361
$135$	−2.22267	−0.191297
$136$	−2.73548	−0.234565
$137$	8.46346	0.723083	0.361541	−	0.932356i	$-0.382251\pi$
$137$	8.46346	0.723083	0.361541	+	0.932356i	$0.382251\pi$
$138$	−0.0504908	−0.00429806
$139$	7.69898	0.653019	0.326509	−	0.945194i	$-0.394128\pi$
$139$	7.69898	0.653019	0.326509	+	0.945194i	$0.394128\pi$
$140$	7.65707	0.647141
$141$	2.30837	0.194399
$142$	−23.6942	−1.98838
$143$	12.9908	1.08635
$144$	8.60089	0.716741
$145$	1.33902	0.111199
$146$	26.0766	2.15812
$147$	−1.17425	−0.0968504
$148$	−5.34835	−0.439632
$149$	8.63028	0.707020	0.353510	−	0.935431i	$-0.384988\pi$
$149$	8.63028	0.707020	0.353510	+	0.935431i	$0.384988\pi$
$150$	0.797083	0.0650816
$151$	7.67796	0.624823	0.312412	−	0.949947i	$-0.398863\pi$
$151$	7.67796	0.624823	0.312412	+	0.949947i	$0.398863\pi$
$152$	−1.46165	−0.118556
$153$	−9.07100	−0.733347
$154$	27.9706	2.25394
$155$	4.41429	0.354565
$156$	−2.83466	−0.226954
$157$	20.4372	1.63107	0.815534	−	0.578709i	$-0.196443\pi$
$157$	20.4372	1.63107	0.815534	+	0.578709i	$0.196443\pi$
$158$	−3.67772	−0.292584
$159$	2.68574	0.212993
$160$	−8.04690	−0.636163
$161$	0.201249	0.0158607
$162$	−16.2210	−1.27444
$163$	10.7625	0.842984	0.421492	−	0.906832i	$-0.361507\pi$
$163$	10.7625	0.842984	0.421492	+	0.906832i	$0.361507\pi$
$164$	−18.1516	−1.41741
$165$	1.59122	0.123876
$166$	−25.0182	−1.94179
$167$	9.36220	0.724469	0.362235	−	0.932087i	$-0.382014\pi$
$167$	9.36220	0.724469	0.362235	+	0.932087i	$0.382014\pi$
$168$	−1.03856	−0.0801266
$169$	−3.39782	−0.261371
$170$	6.67009	0.511572
$171$	−4.84691	−0.370653
$172$	10.9132	0.832120
$173$	−16.1864	−1.23063	−0.615314	−	0.788282i	$-0.710971\pi$
$173$	−16.1864	−1.23063	−0.615314	+	0.788282i	$0.710971\pi$
$174$	−1.06731	−0.0809125
$175$	−3.17706	−0.240163
$176$	−12.6254	−0.951679
$177$	−1.12275	−0.0843907
$178$	−4.66031	−0.349305
$179$	−15.3422	−1.14673	−0.573366	−	0.819299i	$-0.694363\pi$
$179$	−15.3422	−1.14673	−0.573366	+	0.819299i	$0.694363\pi$
$180$	6.88312	0.513038
$181$	−15.2929	−1.13671	−0.568356	−	0.822783i	$-0.692420\pi$
$181$	−15.2929	−1.13671	−0.568356	+	0.822783i	$0.692420\pi$
$182$	20.6745	1.53250
$183$	3.49002	0.257990
$184$	0.0545551	0.00402186
$185$	2.21913	0.163154
$186$	−3.51856	−0.257993
$187$	13.3155	0.973728
$188$	−14.6576	−1.06902
$189$	−7.06156	−0.513653
$190$	3.56403	0.258562
$191$	−13.6292	−0.986176	−0.493088	−	0.869979i	$-0.664132\pi$
$191$	−13.6292	−0.986176	−0.493088	+	0.869979i	$0.664132\pi$
$192$	4.12790	0.297906
$193$	8.06774	0.580728	0.290364	−	0.956916i	$-0.406224\pi$
$193$	8.06774	0.580728	0.290364	+	0.956916i	$0.406224\pi$
$194$	17.4784	1.25488
$195$	1.17615	0.0842260
$196$	7.45621	0.532587
$197$	22.9958	1.63838	0.819191	−	0.573521i	$-0.194423\pi$
$197$	22.9958	1.63838	0.819191	+	0.573521i	$0.194423\pi$
$198$	25.1434	1.78687
$199$	−17.8764	−1.26722	−0.633611	−	0.773652i	$-0.718428\pi$
$199$	−17.8764	−1.26722	−0.633611	+	0.773652i	$0.718428\pi$
$200$	−0.861245	−0.0608992
$201$	2.91574	0.205660
$202$	17.6401	1.24115
$203$	4.25414	0.298582
$204$	−2.90551	−0.203427
$205$	7.53145	0.526020
$206$	−37.7358	−2.62918
$207$	0.180908	0.0125740
$208$	−9.33211	−0.647066
$209$	7.11489	0.492147
$210$	2.53238	0.174751
$211$	7.32968	0.504596	0.252298	−	0.967650i	$-0.418814\pi$
$211$	7.32968	0.504596	0.252298	+	0.967650i	$0.418814\pi$
$212$	−17.0539	−1.17126
$213$	−4.28249	−0.293432
$214$	−37.5241	−2.56509
$215$	−4.52807	−0.308812
$216$	−1.91426	−0.130249
$217$	14.0245	0.952044
$218$	−26.9832	−1.82753
$219$	4.71308	0.318481
$220$	−10.1039	−0.681204
$221$	9.84219	0.662057
$222$	−1.76883	−0.118716
$223$	17.0828	1.14395	0.571975	−	0.820271i	$-0.306177\pi$
$223$	17.0828	1.14395	0.571975	+	0.820271i	$0.306177\pi$
$224$	−25.5655	−1.70817
$225$	−2.85594	−0.190396
$226$	−34.0130	−2.26251
$227$	−20.0045	−1.32775	−0.663873	−	0.747846i	$-0.731088\pi$
$227$	−20.0045	−1.32775	−0.663873	+	0.747846i	$0.731088\pi$
$228$	−1.55250	−0.102817
$229$	15.3543	1.01464	0.507321	−	0.861757i	$-0.330636\pi$
$229$	15.3543	1.01464	0.507321	+	0.861757i	$0.330636\pi$
$230$	−0.133025	−0.00877141
$231$	5.05541	0.332621
$232$	1.15322	0.0757128
$233$	−23.1576	−1.51710	−0.758552	−	0.651613i	$-0.774093\pi$
$233$	−23.1576	−1.51710	−0.758552	+	0.651613i	$0.774093\pi$
$234$	18.5848	1.21493
$235$	6.08171	0.396727
$236$	7.12918	0.464070
$237$	−0.664711	−0.0431776
$238$	21.1913	1.37363
$239$	−22.3487	−1.44562	−0.722808	−	0.691049i	$-0.757149\pi$
$239$	−22.3487	−1.44562	−0.722808	+	0.691049i	$0.757149\pi$
$240$	−1.14307	−0.0737850
$241$	−12.5912	−0.811072	−0.405536	−	0.914079i	$-0.632915\pi$
$241$	−12.5912	−0.811072	−0.405536	+	0.914079i	$0.632915\pi$
$242$	−13.8084	−0.887635
$243$	−9.59979	−0.615827
$244$	−22.1608	−1.41870
$245$	−3.09372	−0.197651
$246$	−6.00320	−0.382750
$247$	5.25898	0.334621
$248$	3.80179	0.241414
$249$	−4.52178	−0.286556
$250$	2.10003	0.132817
$251$	−26.3604	−1.66385	−0.831927	−	0.554886i	$-0.812762\pi$
$251$	−26.3604	−1.66385	−0.831927	+	0.554886i	$0.812762\pi$
$252$	21.8681	1.37756
$253$	−0.265559	−0.0166955
$254$	−7.69483	−0.482816
$255$	1.20555	0.0754945
$256$	7.58616	0.474135
$257$	−13.1171	−0.818224	−0.409112	−	0.912484i	$-0.634161\pi$
$257$	−13.1171	−0.818224	−0.409112	+	0.912484i	$0.634161\pi$
$258$	3.60925	0.224702
$259$	7.05032	0.438085
$260$	−7.46830	−0.463165
$261$	3.82415	0.236709
$262$	21.0483	1.30037
$263$	12.8818	0.794328	0.397164	−	0.917748i	$-0.369994\pi$
$263$	12.8818	0.794328	0.397164	+	0.917748i	$0.369994\pi$
$264$	1.37043	0.0843442
$265$	7.07597	0.434673
$266$	11.3231	0.694267
$267$	−0.842305	−0.0515482
$268$	−18.5143	−1.13094
$269$	25.6751	1.56544	0.782719	−	0.622376i	$-0.213832\pi$
$269$	25.6751	1.56544	0.782719	+	0.622376i	$0.213832\pi$
$270$	4.66767	0.284065
$271$	−24.5280	−1.48997	−0.744986	−	0.667080i	$-0.767544\pi$
$271$	−24.5280	−1.48997	−0.744986	+	0.667080i	$0.767544\pi$
$272$	−9.56537	−0.579986
$273$	3.73671	0.226156
$274$	−17.7735	−1.07374
$275$	4.19229	0.252805
$276$	0.0579462	0.00348795
$277$	27.8754	1.67487	0.837435	−	0.546537i	$-0.184054\pi$
$277$	27.8754	1.67487	0.837435	+	0.546537i	$0.184054\pi$
$278$	−16.1681	−0.969696
$279$	12.6069	0.754758
$280$	−2.73623	−0.163521
$281$	−4.98997	−0.297677	−0.148838	−	0.988862i	$-0.547553\pi$
$281$	−4.98997	−0.297677	−0.148838	+	0.988862i	$0.547553\pi$
$282$	−4.84763	−0.288672
$283$	−14.6401	−0.870263	−0.435131	−	0.900367i	$-0.643298\pi$
$283$	−14.6401	−0.870263	−0.435131	+	0.900367i	$0.643298\pi$
$284$	27.1929	1.61360
$285$	0.644163	0.0381569
$286$	−27.2811	−1.61316
$287$	23.9279	1.41242
$288$	−22.9814	−1.35419
$289$	−6.91181	−0.406577
$290$	−2.81197	−0.165125
$291$	3.15905	0.185187
$292$	−29.9270	−1.75135
$293$	−13.6819	−0.799304	−0.399652	−	0.916667i	$-0.630869\pi$
$293$	−13.6819	−0.799304	−0.399652	+	0.916667i	$0.630869\pi$
$294$	2.46595	0.143817
$295$	−2.95803	−0.172223
$296$	1.91122	0.111087
$297$	9.31809	0.540690
$298$	−18.1238	−1.04988
$299$	−0.196288	−0.0113516
$300$	−0.914779	−0.0528148
$301$	−14.3860	−0.829193
$302$	−16.1239	−0.927827
$303$	3.18827	0.183161
$304$	−5.11107	−0.293140
$305$	9.19495	0.526501
$306$	19.0493	1.08898
$307$	−22.0263	−1.25710	−0.628552	−	0.777767i	$-0.716352\pi$
$307$	−22.0263	−1.25710	−0.628552	+	0.777767i	$0.716352\pi$
$308$	−32.1007	−1.82911
$309$	−6.82036	−0.387997
$310$	−9.27014	−0.526508
$311$	4.76204	0.270030	0.135015	−	0.990844i	$-0.456892\pi$
$311$	4.76204	0.270030	0.135015	+	0.990844i	$0.456892\pi$
$312$	1.01296	0.0573473
$313$	−7.55125	−0.426822	−0.213411	−	0.976963i	$-0.568457\pi$
$313$	−7.55125	−0.426822	−0.213411	+	0.976963i	$0.568457\pi$
$314$	−42.9187	−2.42204
$315$	−9.07348	−0.511233
$316$	4.22077	0.237437
$317$	25.5047	1.43249	0.716244	−	0.697850i	$-0.245860\pi$
$317$	25.5047	1.43249	0.716244	+	0.697850i	$0.245860\pi$
$318$	−5.64013	−0.316283
$319$	−5.61356	−0.314299
$320$	10.8755	0.607961
$321$	−6.78210	−0.378540
$322$	−0.422629	−0.0235522
$323$	5.39043	0.299932
$324$	18.6161	1.03423
$325$	3.09874	0.171887
$326$	−22.6015	−1.25178
$327$	−4.87695	−0.269696
$328$	6.48643	0.358153
$329$	19.3220	1.06525
$330$	−3.34161	−0.183949
$331$	−5.26099	−0.289170	−0.144585	−	0.989492i	$-0.546185\pi$
$331$	−5.26099	−0.289170	−0.144585	+	0.989492i	$0.546185\pi$
$332$	28.7123	1.57579
$333$	6.33770	0.347304
$334$	−19.6609	−1.07580
$335$	7.68192	0.419708
$336$	−3.63161	−0.198121
$337$	−30.2921	−1.65012	−0.825059	−	0.565046i	$-0.808858\pi$
$337$	−30.2921	−1.65012	−0.825059	+	0.565046i	$0.808858\pi$
$338$	7.13552	0.388121
$339$	−6.14751	−0.333887
$340$	−7.65498	−0.415149
$341$	−18.5060	−1.00216
$342$	10.1786	0.550398
$343$	12.4105	0.670103
$344$	−3.89978	−0.210262
$345$	−0.0240429	−0.00129443
$346$	33.9918	1.82741
$347$	−2.79317	−0.149945	−0.0749727	−	0.997186i	$-0.523887\pi$
$347$	−2.79317	−0.149945	−0.0749727	+	0.997186i	$0.523887\pi$
$348$	1.22491	0.0656618
$349$	−15.6845	−0.839574	−0.419787	−	0.907623i	$-0.637895\pi$
$349$	−15.6845	−0.839574	−0.419787	+	0.907623i	$0.637895\pi$
$350$	6.67191	0.356629
$351$	6.88747	0.367626
$352$	33.7350	1.79808
$353$	−4.50623	−0.239842	−0.119921	−	0.992783i	$-0.538264\pi$
$353$	−4.50623	−0.239842	−0.119921	+	0.992783i	$0.538264\pi$
$354$	2.35779	0.125315
$355$	−11.2828	−0.598830
$356$	5.34844	0.283467
$357$	3.83011	0.202711
$358$	32.2191	1.70283
$359$	−25.9441	−1.36928	−0.684638	−	0.728883i	$-0.740040\pi$
$359$	−25.9441	−1.36928	−0.684638	+	0.728883i	$0.740040\pi$
$360$	−2.45966	−0.129636
$361$	−16.1197	−0.848407
$362$	32.1155	1.68795
$363$	−2.49572	−0.130991
$364$	−23.7273	−1.24365
$365$	12.4173	0.649950
$366$	−7.32914	−0.383100
$367$	7.97494	0.416288	0.208144	−	0.978098i	$-0.433258\pi$
$367$	7.97494	0.416288	0.208144	+	0.978098i	$0.433258\pi$
$368$	0.190767	0.00994443
$369$	21.5093	1.11973
$370$	−4.66023	−0.242274
$371$	22.4808	1.16714
$372$	4.03810	0.209366
$373$	36.5885	1.89448	0.947241	−	0.320524i	$-0.103859\pi$
$373$	36.5885	1.89448	0.947241	+	0.320524i	$0.103859\pi$
$374$	−27.9630	−1.44593
$375$	0.379559	0.0196003
$376$	5.23784	0.270121
$377$	−4.14927	−0.213698
$378$	14.8295	0.762745
$379$	−0.644261	−0.0330934	−0.0165467	−	0.999863i	$-0.505267\pi$
$379$	−0.644261	−0.0330934	−0.0165467	+	0.999863i	$0.505267\pi$
$380$	−4.09029	−0.209827
$381$	−1.39076	−0.0712509
$382$	28.6217	1.46442
$383$	−17.7100	−0.904941	−0.452470	−	0.891779i	$-0.649457\pi$
$383$	−17.7100	−0.904941	−0.452470	+	0.891779i	$0.649457\pi$
$384$	−2.56016	−0.130648
$385$	13.3192	0.678808
$386$	−16.9425	−0.862349
$387$	−12.9319	−0.657364
$388$	−20.0593	−1.01835
$389$	27.6450	1.40165	0.700827	−	0.713331i	$-0.252814\pi$
$389$	27.6450	1.40165	0.700827	+	0.713331i	$0.252814\pi$
$390$	−2.46995	−0.125071
$391$	−0.201194	−0.0101748
$392$	−2.66445	−0.134575
$393$	3.80427	0.191900
$394$	−48.2918	−2.43290
$395$	−1.75127	−0.0881162
$396$	−28.8561	−1.45007
$397$	−9.39665	−0.471604	−0.235802	−	0.971801i	$-0.575772\pi$
$397$	−9.39665	−0.471604	−0.235802	+	0.971801i	$0.575772\pi$
$398$	37.5408	1.88175
$399$	2.04654	0.102455
$400$	−3.01159	−0.150579
$401$	−28.2217	−1.40933	−0.704663	−	0.709542i	$-0.748902\pi$
$401$	−28.2217	−1.40933	−0.704663	+	0.709542i	$0.748902\pi$
$402$	−6.12313	−0.305394
$403$	−13.6787	−0.681387
$404$	−20.2448	−1.00722
$405$	−7.72417	−0.383817
$406$	−8.93381	−0.443378
$407$	−9.30325	−0.461145
$408$	1.03827	0.0514023
$409$	20.1005	0.993908	0.496954	−	0.867777i	$-0.334452\pi$
$409$	20.1005	0.993908	0.496954	+	0.867777i	$0.334452\pi$
$410$	−15.8163	−0.781109
$411$	−3.21238	−0.158455
$412$	43.3077	2.13362
$413$	−9.39784	−0.462437
$414$	−0.379911	−0.0186716
$415$	−11.9133	−0.584799
$416$	24.9352	1.22255
$417$	−2.92221	−0.143101
$418$	−14.9415	−0.730811
$419$	10.6754	0.521529	0.260764	−	0.965403i	$-0.416025\pi$
$419$	10.6754	0.521529	0.260764	+	0.965403i	$0.416025\pi$
$420$	−2.90631	−0.141813
$421$	3.85303	0.187785	0.0938926	−	0.995582i	$-0.470069\pi$
$421$	3.85303	0.187785	0.0938926	+	0.995582i	$0.470069\pi$
$422$	−15.3925	−0.749296
$423$	17.3690	0.844508
$424$	6.09414	0.295958
$425$	3.17619	0.154068
$426$	8.99335	0.435729
$427$	29.2129	1.41371
$428$	43.0648	2.08161
$429$	−4.93078	−0.238060
$430$	9.50907	0.458568
$431$	−35.0737	−1.68944	−0.844720	−	0.535209i	$-0.820233\pi$
$431$	−35.0737	−1.68944	−0.844720	+	0.535209i	$0.820233\pi$
$432$	−6.69376	−0.322054
$433$	32.0307	1.53930	0.769649	−	0.638467i	$-0.220431\pi$
$433$	32.0307	1.53930	0.769649	+	0.638467i	$0.220431\pi$
$434$	−29.4518	−1.41373
$435$	−0.508236	−0.0243680
$436$	30.9675	1.48307
$437$	−0.107504	−0.00514262
$438$	−9.89760	−0.472926
$439$	15.3875	0.734403	0.367202	−	0.930141i	$-0.380316\pi$
$439$	15.3875	0.734403	0.367202	+	0.930141i	$0.380316\pi$
$440$	3.61059	0.172128
$441$	−8.83547	−0.420737
$442$	−20.6689	−0.983117
$443$	−9.03577	−0.429302	−0.214651	−	0.976691i	$-0.568861\pi$
$443$	−9.03577	−0.429302	−0.214651	+	0.976691i	$0.568861\pi$
$444$	2.03001	0.0963402
$445$	−2.21917	−0.105199
$446$	−35.8744	−1.69870
$447$	−3.27570	−0.154935
$448$	34.5522	1.63244
$449$	5.61728	0.265096	0.132548	−	0.991177i	$-0.457684\pi$
$449$	5.61728	0.265096	0.132548	+	0.991177i	$0.457684\pi$
$450$	5.99754	0.282727
$451$	−31.5741	−1.48676
$452$	39.0353	1.83607
$453$	−2.91423	−0.136923
$454$	42.0100	1.97163
$455$	9.84488	0.461535
$456$	0.554782	0.0259801
$457$	−19.9671	−0.934023	−0.467012	−	0.884251i	$-0.654669\pi$
$457$	−19.9671	−0.934023	−0.467012	+	0.884251i	$0.654669\pi$
$458$	−32.2445	−1.50669
$459$	7.05963	0.329515
$460$	0.152667	0.00711815
$461$	24.7042	1.15059	0.575295	−	0.817946i	$-0.304887\pi$
$461$	24.7042	1.15059	0.575295	+	0.817946i	$0.304887\pi$
$462$	−10.6165	−0.493924
$463$	15.4265	0.716929	0.358464	−	0.933543i	$-0.383300\pi$
$463$	15.4265	0.716929	0.358464	+	0.933543i	$0.383300\pi$
$464$	4.03257	0.187207
$465$	−1.67548	−0.0776987
$466$	48.6315	2.25281
$467$	12.6272	0.584318	0.292159	−	0.956370i	$-0.405626\pi$
$467$	12.6272	0.584318	0.292159	+	0.956370i	$0.405626\pi$
$468$	−21.3290	−0.985933
$469$	24.4059	1.12696
$470$	−12.7718	−0.589117
$471$	−7.75713	−0.357430
$472$	−2.54759	−0.117262
$473$	18.9830	0.872839
$474$	1.39591	0.0641163
$475$	1.69714	0.0778700
$476$	−24.3203	−1.11472
$477$	20.2085	0.925284
$478$	46.9328	2.14666
$479$	3.83121	0.175052	0.0875261	−	0.996162i	$-0.472104\pi$
$479$	3.83121	0.175052	0.0875261	+	0.996162i	$0.472104\pi$
$480$	3.05427	0.139408
$481$	−6.87651	−0.313542
$482$	26.4419	1.20440
$483$	−0.0763859	−0.00347568
$484$	15.8473	0.720330
$485$	8.32296	0.377926
$486$	20.1598	0.914468
$487$	12.4787	0.565463	0.282731	−	0.959199i	$-0.408759\pi$
$487$	12.4787	0.565463	0.282731	+	0.959199i	$0.408759\pi$
$488$	7.91910	0.358481
$489$	−4.08500	−0.184730
$490$	6.49690	0.293500
$491$	−32.5984	−1.47114	−0.735572	−	0.677447i	$-0.763086\pi$
$491$	−32.5984	−1.47114	−0.735572	+	0.677447i	$0.763086\pi$
$492$	6.88961	0.310608
$493$	−4.25298	−0.191544
$494$	−11.0440	−0.496893
$495$	11.9729	0.538143
$496$	13.2940	0.596919
$497$	−35.8462	−1.60792
$498$	9.49586	0.425520
$499$	−4.58500	−0.205253	−0.102626	−	0.994720i	$-0.532725\pi$
$499$	−4.58500	−0.205253	−0.102626	+	0.994720i	$0.532725\pi$
$500$	−2.41011	−0.107783
$501$	−3.55351	−0.158759
$502$	55.3575	2.47073
$503$	−20.9088	−0.932277	−0.466138	−	0.884712i	$-0.654355\pi$
$503$	−20.9088	−0.932277	−0.466138	+	0.884712i	$0.654355\pi$
$504$	−7.81449	−0.348085
$505$	8.39994	0.373793
$506$	0.557680	0.0247919
$507$	1.28967	0.0572764
$508$	8.83103	0.391814
$509$	−30.1466	−1.33622	−0.668112	−	0.744060i	$-0.732897\pi$
$509$	−30.1466	−1.33622	−0.668112	+	0.744060i	$0.732897\pi$
$510$	−2.53169	−0.112105
$511$	39.4505	1.74519
$512$	−29.4214	−1.30025
$513$	3.77218	0.166546
$514$	27.5463	1.21502
$515$	−17.9692	−0.791817
$516$	−4.14218	−0.182349
$517$	−25.4963	−1.12133
$518$	−14.8059	−0.650532
$519$	6.14368	0.269678
$520$	2.66877	0.117033
$521$	17.7611	0.778126	0.389063	−	0.921211i	$-0.372799\pi$
$521$	17.7611	0.778126	0.389063	+	0.921211i	$0.372799\pi$
$522$	−8.03082	−0.351499
$523$	8.93646	0.390764	0.195382	−	0.980727i	$-0.437405\pi$
$523$	8.93646	0.390764	0.195382	+	0.980727i	$0.437405\pi$
$524$	−24.1563	−1.05527
$525$	1.20588	0.0526290
$526$	−27.0522	−1.17953
$527$	−14.0206	−0.610749
$528$	4.79210	0.208549
$529$	−22.9960	−0.999826
$530$	−14.8597	−0.645465
$531$	−8.44794	−0.366609
$532$	−12.9951	−0.563409
$533$	−23.3380	−1.01088
$534$	1.76886	0.0765461
$535$	−17.8684	−0.772517
$536$	6.61602	0.285769
$537$	5.82327	0.251293
$538$	−53.9183	−2.32458
$539$	12.9698	0.558648
$540$	−5.35688	−0.230524
$541$	−5.58199	−0.239989	−0.119994	−	0.992775i	$-0.538288\pi$
$541$	−5.58199	−0.239989	−0.119994	+	0.992775i	$0.538288\pi$
$542$	51.5095	2.21252
$543$	5.80455	0.249097
$544$	25.5585	1.09581
$545$	−12.8490	−0.550390
$546$	−7.84719	−0.335829
$547$	−17.9416	−0.767126	−0.383563	−	0.923515i	$-0.625303\pi$
$547$	−17.9416	−0.767126	−0.383563	+	0.923515i	$0.625303\pi$
$548$	20.3979	0.871355
$549$	26.2602	1.12076
$550$	−8.80393	−0.375401
$551$	−2.27250	−0.0968116
$552$	−0.0207069	−0.000881343 0
$553$	−5.56391	−0.236601
$554$	−58.5391	−2.48709
$555$	−0.842290	−0.0357532
$556$	18.5554	0.786924
$557$	26.1251	1.10695	0.553477	−	0.832864i	$-0.313301\pi$
$557$	26.1251	1.10695	0.553477	+	0.832864i	$0.313301\pi$
$558$	−26.4749	−1.12077
$559$	14.0313	0.593461
$560$	−9.56799	−0.404321
$561$	−5.05402	−0.213381
$562$	10.4791	0.442033
$563$	−44.1473	−1.86059	−0.930294	−	0.366816i	$-0.880448\pi$
$563$	−44.1473	−1.86059	−0.930294	+	0.366816i	$0.880448\pi$
$564$	5.56342	0.234262
$565$	−16.1965	−0.681390
$566$	30.7446	1.29229
$567$	−24.5402	−1.03059
$568$	−9.71728	−0.407728
$569$	17.6225	0.738772	0.369386	−	0.929276i	$-0.379568\pi$
$569$	17.6225	0.738772	0.369386	+	0.929276i	$0.379568\pi$
$570$	−1.35276	−0.0566608
$571$	27.1878	1.13777	0.568886	−	0.822416i	$-0.307374\pi$
$571$	27.1878	1.13777	0.568886	+	0.822416i	$0.307374\pi$
$572$	31.3093	1.30911
$573$	5.17309	0.216109
$574$	−50.2492	−2.09736
$575$	−0.0633445	−0.00264165
$576$	31.0598	1.29416
$577$	−28.4877	−1.18596	−0.592980	−	0.805217i	$-0.702049\pi$
$577$	−28.4877	−1.18596	−0.592980	+	0.805217i	$0.702049\pi$
$578$	14.5150	0.603744
$579$	−3.06218	−0.127260
$580$	3.22718	0.134001
$581$	−37.8492	−1.57025
$582$	−6.63409	−0.274992
$583$	−29.6645	−1.22858
$584$	10.6943	0.442534
$585$	8.84980	0.365894
$586$	28.7323	1.18692
$587$	−35.8269	−1.47873	−0.739366	−	0.673303i	$-0.764875\pi$
$587$	−35.8269	−1.47873	−0.739366	+	0.673303i	$0.764875\pi$
$588$	−2.83007	−0.116710
$589$	−7.49166	−0.308688
$590$	6.21194	0.255741
$591$	−8.72825	−0.359032
$592$	6.68310	0.274674
$593$	1.91016	0.0784408	0.0392204	−	0.999231i	$-0.487513\pi$
$593$	1.91016	0.0784408	0.0392204	+	0.999231i	$0.487513\pi$
$594$	−19.5682	−0.802894
$595$	10.0910	0.413689
$596$	20.7999	0.851999
$597$	6.78513	0.277697
$598$	0.412210	0.0168565
$599$	40.3792	1.64985	0.824926	−	0.565241i	$-0.191217\pi$
$599$	40.3792	1.64985	0.824926	+	0.565241i	$0.191217\pi$
$600$	0.326893	0.0133454
$601$	−11.9139	−0.485977	−0.242988	−	0.970029i	$-0.578128\pi$
$601$	−11.9139	−0.485977	−0.242988	+	0.970029i	$0.578128\pi$
$602$	30.2109	1.23130
$603$	21.9391	0.893428
$604$	18.5047	0.752947
$605$	−6.57533	−0.267325
$606$	−6.69545	−0.271984
$607$	−44.7931	−1.81809	−0.909047	−	0.416694i	$-0.863189\pi$
$607$	−44.7931	−1.81809	−0.909047	+	0.416694i	$0.863189\pi$
$608$	13.6567	0.553852
$609$	−1.61470	−0.0654308
$610$	−19.3096	−0.781824
$611$	−18.8456	−0.762412
$612$	−21.8621	−0.883724
$613$	44.5204	1.79816	0.899082	−	0.437781i	$-0.144235\pi$
$613$	44.5204	1.79816	0.899082	+	0.437781i	$0.144235\pi$
$614$	46.2557	1.86673
$615$	−2.85863	−0.115271
$616$	11.4711	0.462183
$617$	−31.8193	−1.28100	−0.640499	−	0.767959i	$-0.721273\pi$
$617$	−31.8193	−1.28100	−0.640499	+	0.767959i	$0.721273\pi$
$618$	14.3229	0.576153
$619$	36.2295	1.45619	0.728093	−	0.685478i	$-0.240407\pi$
$619$	36.2295	1.45619	0.728093	+	0.685478i	$0.240407\pi$
$620$	10.6389	0.427270
$621$	−0.140794	−0.00564986
$622$	−10.0004	−0.400980
$623$	−7.05044	−0.282470
$624$	3.54208	0.141797
$625$	1.00000	0.0400000
$626$	15.8578	0.633806
$627$	−2.70052	−0.107848
$628$	49.2560	1.96553
$629$	−7.04839	−0.281038
$630$	19.0546	0.759152
$631$	37.8583	1.50711	0.753557	−	0.657383i	$-0.228337\pi$
$631$	37.8583	1.50711	0.753557	+	0.657383i	$0.228337\pi$
$632$	−1.50828	−0.0599960
$633$	−2.78204	−0.110576
$634$	−53.5606	−2.12716
$635$	−3.66416	−0.145408
$636$	6.47294	0.256669
$637$	9.58663	0.379836
$638$	11.7886	0.466716
$639$	−32.2230	−1.27472
$640$	−6.74511	−0.266624
$641$	25.2613	0.997760	0.498880	−	0.866671i	$-0.333745\pi$
$641$	25.2613	0.997760	0.498880	+	0.866671i	$0.333745\pi$
$642$	14.2426	0.562110
$643$	46.6275	1.83881	0.919405	−	0.393312i	$-0.128671\pi$
$643$	46.6275	1.83881	0.919405	+	0.393312i	$0.128671\pi$
$644$	0.485033	0.0191130
$645$	1.71867	0.0676725
$646$	−11.3200	−0.445381
$647$	−2.71576	−0.106767	−0.0533837	−	0.998574i	$-0.517001\pi$
$647$	−2.71576	−0.106767	−0.0533837	+	0.998574i	$0.517001\pi$
$648$	−6.65241	−0.261331
$649$	12.4009	0.486779
$650$	−6.50743	−0.255242
$651$	−5.32311	−0.208629
$652$	25.9388	1.01584
$653$	4.76083	0.186306	0.0931529	−	0.995652i	$-0.470305\pi$
$653$	4.76083	0.186306	0.0931529	+	0.995652i	$0.470305\pi$
$654$	10.2417	0.400483
$655$	10.0229	0.391626
$656$	22.6816	0.885568
$657$	35.4629	1.38354
$658$	−40.5766	−1.58184
$659$	−24.6899	−0.961784	−0.480892	−	0.876780i	$-0.659687\pi$
$659$	−24.6899	−0.961784	−0.480892	+	0.876780i	$0.659687\pi$
$660$	3.83502	0.149278
$661$	17.9325	0.697492	0.348746	−	0.937217i	$-0.386608\pi$
$661$	17.9325	0.697492	0.348746	+	0.937217i	$0.386608\pi$
$662$	11.0482	0.429402
$663$	−3.73569	−0.145082
$664$	−10.2602	−0.398175
$665$	5.39191	0.209089
$666$	−13.3093	−0.515726
$667$	0.0848194	0.00328422
$668$	22.5640	0.873026
$669$	−6.48393	−0.250683
$670$	−16.1322	−0.623243
$671$	−38.5479	−1.48813
$672$	9.70360	0.374325
$673$	−29.8944	−1.15234	−0.576172	−	0.817329i	$-0.695454\pi$
$673$	−29.8944	−1.15234	−0.576172	+	0.817329i	$0.695454\pi$
$674$	63.6143	2.45033
$675$	2.22267	0.0855506
$676$	−8.18913	−0.314967
$677$	−10.5935	−0.407140	−0.203570	−	0.979060i	$-0.565254\pi$
$677$	−10.5935	−0.407140	−0.203570	+	0.979060i	$0.565254\pi$
$678$	12.9099	0.495803
$679$	26.4426	1.01477
$680$	2.73548	0.104901
$681$	7.59288	0.290960
$682$	38.8631	1.48815
$683$	−1.02906	−0.0393758	−0.0196879	−	0.999806i	$-0.506267\pi$
$683$	−1.02906	−0.0393758	−0.0196879	+	0.999806i	$0.506267\pi$
$684$	−11.6816	−0.446657
$685$	−8.46346	−0.323372
$686$	−26.0624	−0.995065
$687$	−5.82787	−0.222347
$688$	−13.6367	−0.519893
$689$	−21.9266	−0.835336
$690$	0.0504908	0.00192215
$691$	−42.9997	−1.63579	−0.817894	−	0.575370i	$-0.804858\pi$
$691$	−42.9997	−1.63579	−0.817894	+	0.575370i	$0.804858\pi$
$692$	−39.0110	−1.48297
$693$	38.0387	1.44497
$694$	5.86574	0.222660
$695$	−7.69898	−0.292039
$696$	−0.437716	−0.0165916
$697$	−23.9213	−0.906085
$698$	32.9379	1.24672
$699$	8.78966	0.332455
$700$	−7.65707	−0.289410
$701$	−7.69500	−0.290636	−0.145318	−	0.989385i	$-0.546421\pi$
$701$	−7.69500	−0.290636	−0.145318	+	0.989385i	$0.546421\pi$
$702$	−14.4639	−0.545904
$703$	−3.76617	−0.142044
$704$	−45.5934	−1.71837
$705$	−2.30837	−0.0869381
$706$	9.46320	0.356152
$707$	26.6871	1.00367
$708$	−2.70594	−0.101695
$709$	−20.9103	−0.785303	−0.392651	−	0.919687i	$-0.628442\pi$
$709$	−20.9103	−0.785303	−0.392651	+	0.919687i	$0.628442\pi$
$710$	23.6942	0.889228
$711$	−5.00153	−0.187572
$712$	−1.91125	−0.0716271
$713$	0.279621	0.0104719
$714$	−8.04333	−0.301014
$715$	−12.9908	−0.485829
$716$	−36.9765	−1.38188
$717$	8.48263	0.316790
$718$	54.4833	2.03330
$719$	−28.2245	−1.05260	−0.526298	−	0.850300i	$-0.676420\pi$
$719$	−28.2245	−1.05260	−0.526298	+	0.850300i	$0.676420\pi$
$720$	−8.60089	−0.320536
$721$	−57.0892	−2.12611
$722$	33.8519	1.25984
$723$	4.77911	0.177737
$724$	−36.8576	−1.36980
$725$	−1.33902	−0.0497299
$726$	5.24108	0.194515
$727$	−23.4823	−0.870911	−0.435456	−	0.900210i	$-0.643413\pi$
$727$	−23.4823	−0.870911	−0.435456	+	0.900210i	$0.643413\pi$
$728$	8.47886	0.314247
$729$	−19.5288	−0.723290
$730$	−26.0766	−0.965139
$731$	14.3820	0.531938
$732$	8.41134	0.310892
$733$	28.8843	1.06687	0.533434	−	0.845842i	$-0.320901\pi$
$733$	28.8843	1.06687	0.533434	+	0.845842i	$0.320901\pi$
$734$	−16.7476	−0.618165
$735$	1.17425	0.0433128
$736$	−0.509727	−0.0187888
$737$	−32.2049	−1.18628
$738$	−45.1702	−1.66274
$739$	−0.402937	−0.0148223	−0.00741113	−	0.999973i	$-0.502359\pi$
$739$	−0.402937	−0.0148223	−0.00741113	+	0.999973i	$0.502359\pi$
$740$	5.34835	0.196609
$741$	−1.99609	−0.0733283
$742$	−47.2102	−1.73314
$743$	−25.8983	−0.950115	−0.475057	−	0.879955i	$-0.657573\pi$
$743$	−25.8983	−0.950115	−0.475057	+	0.879955i	$0.657573\pi$
$744$	−1.44300	−0.0529030
$745$	−8.63028	−0.316189
$746$	−76.8368	−2.81320
$747$	−34.0235	−1.24485
$748$	32.0919	1.17340
$749$	−56.7689	−2.07429
$750$	−0.797083	−0.0291054
$751$	46.1801	1.68514	0.842569	−	0.538589i	$-0.181042\pi$
$751$	46.1801	1.68514	0.842569	+	0.538589i	$0.181042\pi$
$752$	18.3156	0.667901
$753$	10.0053	0.364614
$754$	8.71357	0.317330
$755$	−7.67796	−0.279429
$756$	−17.0192	−0.618981
$757$	−48.4616	−1.76137	−0.880683	−	0.473706i	$-0.842916\pi$
$757$	−48.4616	−1.76137	−0.880683	+	0.473706i	$0.842916\pi$
$758$	1.35296	0.0491419
$759$	0.100795	0.00365863
$760$	1.46165	0.0530196
$761$	−50.5893	−1.83386	−0.916930	−	0.399049i	$-0.869340\pi$
$761$	−50.5893	−1.83386	−0.916930	+	0.399049i	$0.869340\pi$
$762$	2.92064	0.105804
$763$	−40.8220	−1.47786
$764$	−32.8480	−1.18840
$765$	9.07100	0.327963
$766$	37.1915	1.34379
$767$	9.16615	0.330971
$768$	−2.87939	−0.103901
$769$	5.80863	0.209464	0.104732	−	0.994500i	$-0.466601\pi$
$769$	5.80863	0.209464	0.104732	+	0.994500i	$0.466601\pi$
$770$	−27.9706	−1.00799
$771$	4.97872	0.179304
$772$	19.4441	0.699810
$773$	−43.9872	−1.58211	−0.791056	−	0.611744i	$-0.790468\pi$
$773$	−43.9872	−1.58211	−0.791056	+	0.611744i	$0.790468\pi$
$774$	27.1573	0.976149
$775$	−4.41429	−0.158566
$776$	7.16811	0.257320
$777$	−2.67601	−0.0960013
$778$	−58.0551	−2.08138
$779$	−12.7819	−0.457959
$780$	2.83466	0.101497
$781$	47.3009	1.69256
$782$	0.422513	0.0151090
$783$	−2.97620	−0.106361
$784$	−9.31701	−0.332750
$785$	−20.4372	−0.729436
$786$	−7.98907	−0.284961
$787$	27.0445	0.964034	0.482017	−	0.876162i	$-0.339904\pi$
$787$	27.0445	0.964034	0.482017	+	0.876162i	$0.339904\pi$
$788$	55.4224	1.97434
$789$	−4.88941	−0.174068
$790$	3.67772	0.130848
$791$	−51.4572	−1.82961
$792$	10.3116	0.366407
$793$	−28.4927	−1.01181
$794$	19.7332	0.700305
$795$	−2.68574	−0.0952535
$796$	−43.0840	−1.52707
$797$	0.687533	0.0243537	0.0121768	−	0.999926i	$-0.496124\pi$
$797$	0.687533	0.0243537	0.0121768	+	0.999926i	$0.496124\pi$
$798$	−4.29780	−0.152140
$799$	−19.3167	−0.683375
$800$	8.04690	0.284501
$801$	−6.33780	−0.223935
$802$	59.2664	2.09277
$803$	−52.0569	−1.83705
$804$	7.02726	0.247832
$805$	−0.201249	−0.00709311
$806$	28.7257	1.01182
$807$	−9.74520	−0.343047
$808$	7.23441	0.254506
$809$	−12.7158	−0.447062	−0.223531	−	0.974697i	$-0.571758\pi$
$809$	−12.7158	−0.447062	−0.223531	+	0.974697i	$0.571758\pi$
$810$	16.2210	0.569947
$811$	10.5107	0.369080	0.184540	−	0.982825i	$-0.440921\pi$
$811$	10.5107	0.369080	0.184540	+	0.982825i	$0.440921\pi$
$812$	10.2530	0.359808
$813$	9.30982	0.326510
$814$	19.5371	0.684774
$815$	−10.7625	−0.376994
$816$	3.63062	0.127097
$817$	7.68475	0.268856
$818$	−42.2117	−1.47590
$819$	28.1163	0.982465
$820$	18.1516	0.633883
$821$	−18.9153	−0.660148	−0.330074	−	0.943955i	$-0.607074\pi$
$821$	−18.9153	−0.660148	−0.330074	+	0.943955i	$0.607074\pi$
$822$	6.74608	0.235297
$823$	21.3701	0.744916	0.372458	−	0.928049i	$-0.378515\pi$
$823$	21.3701	0.744916	0.372458	+	0.928049i	$0.378515\pi$
$824$	−15.4759	−0.539128
$825$	−1.59122	−0.0553992
$826$	19.7357	0.686693
$827$	28.1921	0.980336	0.490168	−	0.871628i	$-0.336935\pi$
$827$	28.1921	0.980336	0.490168	+	0.871628i	$0.336935\pi$
$828$	0.436008	0.0151523
$829$	12.4804	0.433461	0.216730	−	0.976231i	$-0.430461\pi$
$829$	12.4804	0.433461	0.216730	+	0.976231i	$0.430461\pi$
$830$	25.0182	0.868393
$831$	−10.5803	−0.367028
$832$	−33.7004	−1.16835
$833$	9.82625	0.340459
$834$	6.13673	0.212497
$835$	−9.36220	−0.323992
$836$	17.1477	0.593065
$837$	−9.81152	−0.339136
$838$	−22.4187	−0.774440
$839$	2.00734	0.0693009	0.0346505	−	0.999399i	$-0.488968\pi$
$839$	2.00734	0.0693009	0.0346505	+	0.999399i	$0.488968\pi$
$840$	1.03856	0.0358337
$841$	−27.2070	−0.938173
$842$	−8.09147	−0.278850
$843$	1.89399	0.0652323
$844$	17.6653	0.608066
$845$	3.39782	0.116889
$846$	−36.4753	−1.25405
$847$	−20.8902	−0.717796
$848$	21.3099	0.731784
$849$	5.55677	0.190708
$850$	−6.67009	−0.228782
$851$	0.140570	0.00481867
$852$	−10.3213	−0.353601
$853$	−37.9319	−1.29876	−0.649381	−	0.760463i	$-0.724972\pi$
$853$	−37.9319	−1.29876	−0.649381	+	0.760463i	$0.724972\pi$
$854$	−61.3479	−2.09928
$855$	4.84691	0.165761
$856$	−15.3891	−0.525987
$857$	5.06292	0.172946	0.0864731	−	0.996254i	$-0.472440\pi$
$857$	5.06292	0.172946	0.0864731	+	0.996254i	$0.472440\pi$
$858$	10.3548	0.353506
$859$	−46.5209	−1.58727	−0.793637	−	0.608392i	$-0.791815\pi$
$859$	−46.5209	−1.58727	−0.793637	+	0.608392i	$0.791815\pi$
$860$	−10.9132	−0.372136
$861$	−9.08204	−0.309515
$862$	73.6557	2.50872
$863$	16.2062	0.551665	0.275832	−	0.961206i	$-0.411047\pi$
$863$	16.2062	0.551665	0.275832	+	0.961206i	$0.411047\pi$
$864$	17.8856	0.608481
$865$	16.1864	0.550353
$866$	−67.2654	−2.28577
$867$	2.62344	0.0890966
$868$	33.8006	1.14727
$869$	7.34186	0.249055
$870$	1.06731	0.0361852
$871$	−23.8043	−0.806577
$872$	−11.0661	−0.374747
$873$	23.7698	0.804487
$874$	0.225762	0.00763650
$875$	3.17706	0.107404
$876$	11.3591	0.383787
$877$	31.0117	1.04719	0.523595	−	0.851967i	$-0.324591\pi$
$877$	31.0117	1.04719	0.523595	+	0.851967i	$0.324591\pi$
$878$	−32.3141	−1.09055
$879$	5.19308	0.175158
$880$	12.6254	0.425604
$881$	−1.90397	−0.0641463	−0.0320732	−	0.999486i	$-0.510211\pi$
$881$	−1.90397	−0.0641463	−0.0320732	+	0.999486i	$0.510211\pi$
$882$	18.5547	0.624770
$883$	−3.80620	−0.128089	−0.0640444	−	0.997947i	$-0.520400\pi$
$883$	−3.80620	−0.128089	−0.0640444	+	0.997947i	$0.520400\pi$
$884$	23.7208	0.797816
$885$	1.12275	0.0377407
$886$	18.9754	0.637489
$887$	−45.2401	−1.51901	−0.759506	−	0.650500i	$-0.774559\pi$
$887$	−45.2401	−1.51901	−0.759506	+	0.650500i	$0.774559\pi$
$888$	−0.725419	−0.0243435
$889$	−11.6413	−0.390435
$890$	4.66031	0.156214
$891$	32.3820	1.08484
$892$	41.1715	1.37852
$893$	−10.3215	−0.345395
$894$	6.87905	0.230070
$895$	15.3422	0.512834
$896$	−21.4296	−0.715914
$897$	0.0745028	0.00248758
$898$	−11.7964	−0.393652
$899$	5.91082	0.197137
$900$	−6.88312	−0.229437
$901$	−22.4746	−0.748738
$902$	66.3064	2.20776
$903$	5.46032	0.181708
$904$	−13.9491	−0.463941
$905$	15.2929	0.508353
$906$	6.11997	0.203322
$907$	−31.1550	−1.03448	−0.517242	−	0.855839i	$-0.673041\pi$
$907$	−31.1550	−1.03448	−0.517242	+	0.855839i	$0.673041\pi$
$908$	−48.2131	−1.60001
$909$	23.9897	0.795688
$910$	−20.6745	−0.685353
$911$	−59.4939	−1.97112	−0.985560	−	0.169324i	$-0.945842\pi$
$911$	−59.4939	−1.97112	−0.985560	+	0.169324i	$0.945842\pi$
$912$	1.93995	0.0642382
$913$	49.9439	1.65290
$914$	41.9315	1.38697
$915$	−3.49002	−0.115377
$916$	37.0056	1.22270
$917$	31.8433	1.05156
$918$	−14.8254	−0.489311
$919$	34.9043	1.15139	0.575694	−	0.817666i	$-0.304732\pi$
$919$	34.9043	1.15139	0.575694	+	0.817666i	$0.304732\pi$
$920$	−0.0545551	−0.00179863
$921$	8.36026	0.275480
$922$	−51.8795	−1.70856
$923$	34.9625	1.15081
$924$	12.1841	0.400827
$925$	−2.21913	−0.0729646
$926$	−32.3960	−1.06460
$927$	−51.3188	−1.68553
$928$	−10.7749	−0.353705
$929$	−44.2121	−1.45055	−0.725276	−	0.688458i	$-0.758288\pi$
$929$	−44.2121	−1.45055	−0.725276	+	0.688458i	$0.758288\pi$
$930$	3.51856	0.115378
$931$	5.25047	0.172077
$932$	−55.8123	−1.82819
$933$	−1.80747	−0.0591740
$934$	−26.5175	−0.867678
$935$	−13.3155	−0.435464
$936$	7.62184	0.249128
$937$	16.5052	0.539202	0.269601	−	0.962972i	$-0.413108\pi$
$937$	16.5052	0.539202	0.269601	+	0.962972i	$0.413108\pi$
$938$	−51.2531	−1.67347
$939$	2.86614	0.0935330
$940$	14.6576	0.478078
$941$	53.4673	1.74299	0.871493	−	0.490408i	$-0.163152\pi$
$941$	53.4673	1.74299	0.871493	+	0.490408i	$0.163152\pi$
$942$	16.2902	0.530763
$943$	0.477076	0.0155357
$944$	−8.90835	−0.289942
$945$	7.06156	0.229713
$946$	−39.8648	−1.29612
$947$	35.4936	1.15339	0.576694	−	0.816960i	$-0.304343\pi$
$947$	35.4936	1.15339	0.576694	+	0.816960i	$0.304343\pi$
$948$	−1.60203	−0.0520315
$949$	−38.4779	−1.24905
$950$	−3.56403	−0.115632
$951$	−9.68053	−0.313913
$952$	8.69079	0.281670
$953$	−58.5612	−1.89698	−0.948491	−	0.316803i	$-0.897391\pi$
$953$	−58.5612	−1.89698	−0.948491	+	0.316803i	$0.897391\pi$
$954$	−42.4384	−1.37399
$955$	13.6292	0.441031
$956$	−53.8628	−1.74205
$957$	2.13067	0.0688749
$958$	−8.04563	−0.259943
$959$	−26.8889	−0.868289
$960$	−4.12790	−0.133227
$961$	−11.5140	−0.371419
$962$	14.4408	0.465592
$963$	−51.0309	−1.64445
$964$	−30.3463	−0.977387
$965$	−8.06774	−0.259710
$966$	0.160412	0.00516119
$967$	17.7176	0.569759	0.284879	−	0.958563i	$-0.408046\pi$
$967$	17.7176	0.569759	0.284879	+	0.958563i	$0.408046\pi$
$968$	−5.66297	−0.182015
$969$	−2.04598	−0.0657265
$970$	−17.4784	−0.561199
$971$	17.2477	0.553506	0.276753	−	0.960941i	$-0.410742\pi$
$971$	17.2477	0.553506	0.276753	+	0.960941i	$0.410742\pi$
$972$	−23.1366	−0.742105
$973$	−24.4601	−0.784156
$974$	−26.2056	−0.839680
$975$	−1.17615	−0.0376670
$976$	27.6914	0.886379
$977$	−11.6562	−0.372916	−0.186458	−	0.982463i	$-0.559701\pi$
$977$	−11.6562	−0.372916	−0.186458	+	0.982463i	$0.559701\pi$
$978$	8.57861	0.274314
$979$	9.30341	0.297338
$980$	−7.45621	−0.238180
$981$	−36.6959	−1.17161
$982$	68.4574	2.18456
$983$	−1.98101	−0.0631844	−0.0315922	−	0.999501i	$-0.510058\pi$
$983$	−1.98101	−0.0631844	−0.0315922	+	0.999501i	$0.510058\pi$
$984$	−2.46198	−0.0784851
$985$	−22.9958	−0.732707
$986$	8.93137	0.284433
$987$	−7.33382	−0.233438
$988$	12.6747	0.403237
$989$	−0.286828	−0.00912061
$990$	−25.1434	−0.799111
$991$	38.7206	1.23000	0.615001	−	0.788526i	$-0.289156\pi$
$991$	38.7206	1.23000	0.615001	+	0.788526i	$0.289156\pi$
$992$	−35.5214	−1.12781
$993$	1.99686	0.0633683
$994$	75.2780	2.38767
$995$	17.8764	0.566719
$996$	−10.8980	−0.345316
$997$	30.9016	0.978664	0.489332	−	0.872098i	$-0.337241\pi$
$997$	30.9016	0.978664	0.489332	+	0.872098i	$0.337241\pi$
$998$	9.62862	0.304789
$999$	−4.93240	−0.156054

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8005.2.a.f.1.19	✓	127

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8005.2.a.f.1.19	✓	127	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:	\( N \)	\(=\)	\( 8005 = 5 \cdot 1601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.10003 q^{2} -0.379559 q^{3} +2.41011 q^{4} -1.00000 q^{5} +0.797083 q^{6} -3.17706 q^{7} -0.861245 q^{8} -2.85594 q^{9} +O(q^{10})\)	\(q-2.10003 q^{2} -0.379559 q^{3} +2.41011 q^{4} -1.00000 q^{5} +0.797083 q^{6} -3.17706 q^{7} -0.861245 q^{8} -2.85594 q^{9} +2.10003 q^{10} +4.19229 q^{11} -0.914779 q^{12} +3.09874 q^{13} +6.67191 q^{14} +0.379559 q^{15} -3.01159 q^{16} +3.17619 q^{17} +5.99754 q^{18} +1.69714 q^{19} -2.41011 q^{20} +1.20588 q^{21} -8.80393 q^{22} -0.0633445 q^{23} +0.326893 q^{24} +1.00000 q^{25} -6.50743 q^{26} +2.22267 q^{27} -7.65707 q^{28} -1.33902 q^{29} -0.797083 q^{30} -4.41429 q^{31} +8.04690 q^{32} -1.59122 q^{33} -6.67009 q^{34} +3.17706 q^{35} -6.88312 q^{36} -2.21913 q^{37} -3.56403 q^{38} -1.17615 q^{39} +0.861245 q^{40} -7.53145 q^{41} -2.53238 q^{42} +4.52807 q^{43} +10.1039 q^{44} +2.85594 q^{45} +0.133025 q^{46} -6.08171 q^{47} +1.14307 q^{48} +3.09372 q^{49} -2.10003 q^{50} -1.20555 q^{51} +7.46830 q^{52} -7.07597 q^{53} -4.66767 q^{54} -4.19229 q^{55} +2.73623 q^{56} -0.644163 q^{57} +2.81197 q^{58} +2.95803 q^{59} +0.914779 q^{60} -9.19495 q^{61} +9.27014 q^{62} +9.07348 q^{63} -10.8755 q^{64} -3.09874 q^{65} +3.34161 q^{66} -7.68192 q^{67} +7.65498 q^{68} +0.0240429 q^{69} -6.67191 q^{70} +11.2828 q^{71} +2.45966 q^{72} -12.4173 q^{73} +4.66023 q^{74} -0.379559 q^{75} +4.09029 q^{76} -13.3192 q^{77} +2.46995 q^{78} +1.75127 q^{79} +3.01159 q^{80} +7.72417 q^{81} +15.8163 q^{82} +11.9133 q^{83} +2.90631 q^{84} -3.17619 q^{85} -9.50907 q^{86} +0.508236 q^{87} -3.61059 q^{88} +2.21917 q^{89} -5.99754 q^{90} -9.84488 q^{91} -0.152667 q^{92} +1.67548 q^{93} +12.7718 q^{94} -1.69714 q^{95} -3.05427 q^{96} -8.32296 q^{97} -6.49690 q^{98} -11.9729 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 127 q - 6 q^{2} - 18 q^{3} + 114 q^{4} - 127 q^{5} - 20 q^{6} + 28 q^{7} - 18 q^{8} + 101 q^{9}+O(q^{10}) \) 127 * q - 6 * q^2 - 18 * q^3 + 114 * q^4 - 127 * q^5 - 20 * q^6 + 28 * q^7 - 18 * q^8 + 101 * q^9	\( 127 q - 6 q^{2} - 18 q^{3} + 114 q^{4} - 127 q^{5} - 20 q^{6} + 28 q^{7} - 18 q^{8} + 101 q^{9} + 6 q^{10} - 45 q^{11} - 30 q^{12} - 53 q^{14} + 18 q^{15} + 84 q^{16} - 36 q^{17} - 10 q^{18} - 49 q^{19} - 114 q^{20} - 48 q^{21} + 13 q^{22} - 29 q^{23} - 63 q^{24} + 127 q^{25} - 55 q^{26} - 75 q^{27} + 44 q^{28} - 45 q^{29} + 20 q^{30} - 49 q^{31} - 32 q^{32} - 8 q^{33} - 52 q^{34} - 28 q^{35} + 44 q^{36} + 36 q^{37} - 65 q^{38} - 52 q^{39} + 18 q^{40} - 66 q^{41} - 18 q^{42} - 5 q^{43} - 93 q^{44} - 101 q^{45} - 25 q^{46} - 32 q^{47} - 54 q^{48} + 77 q^{49} - 6 q^{50} - 102 q^{51} - 13 q^{52} - 67 q^{53} - 53 q^{54} + 45 q^{55} - 158 q^{56} + 16 q^{57} + 35 q^{58} - 213 q^{59} + 30 q^{60} - 62 q^{61} - 33 q^{62} + 59 q^{63} + 34 q^{64} - 60 q^{66} + 10 q^{67} - 94 q^{68} - 93 q^{69} + 53 q^{70} - 118 q^{71} - 24 q^{72} + 35 q^{73} - 107 q^{74} - 18 q^{75} - 98 q^{76} - 93 q^{77} + 21 q^{78} - 64 q^{79} - 84 q^{80} + 15 q^{81} + 15 q^{82} - 187 q^{83} - 118 q^{84} + 36 q^{85} - 126 q^{86} - 53 q^{87} + 15 q^{88} - 138 q^{89} + 10 q^{90} - 138 q^{91} - 86 q^{92} + 23 q^{93} - 60 q^{94} + 49 q^{95} - 92 q^{96} + 9 q^{97} - 67 q^{98} - 147 q^{99}+O(q^{100}) \) 127 * q - 6 * q^2 - 18 * q^3 + 114 * q^4 - 127 * q^5 - 20 * q^6 + 28 * q^7 - 18 * q^8 + 101 * q^9 + 6 * q^10 - 45 * q^11 - 30 * q^12 - 53 * q^14 + 18 * q^15 + 84 * q^16 - 36 * q^17 - 10 * q^18 - 49 * q^19 - 114 * q^20 - 48 * q^21 + 13 * q^22 - 29 * q^23 - 63 * q^24 + 127 * q^25 - 55 * q^26 - 75 * q^27 + 44 * q^28 - 45 * q^29 + 20 * q^30 - 49 * q^31 - 32 * q^32 - 8 * q^33 - 52 * q^34 - 28 * q^35 + 44 * q^36 + 36 * q^37 - 65 * q^38 - 52 * q^39 + 18 * q^40 - 66 * q^41 - 18 * q^42 - 5 * q^43 - 93 * q^44 - 101 * q^45 - 25 * q^46 - 32 * q^47 - 54 * q^48 + 77 * q^49 - 6 * q^50 - 102 * q^51 - 13 * q^52 - 67 * q^53 - 53 * q^54 + 45 * q^55 - 158 * q^56 + 16 * q^57 + 35 * q^58 - 213 * q^59 + 30 * q^60 - 62 * q^61 - 33 * q^62 + 59 * q^63 + 34 * q^64 - 60 * q^66 + 10 * q^67 - 94 * q^68 - 93 * q^69 + 53 * q^70 - 118 * q^71 - 24 * q^72 + 35 * q^73 - 107 * q^74 - 18 * q^75 - 98 * q^76 - 93 * q^77 + 21 * q^78 - 64 * q^79 - 84 * q^80 + 15 * q^81 + 15 * q^82 - 187 * q^83 - 118 * q^84 + 36 * q^85 - 126 * q^86 - 53 * q^87 + 15 * q^88 - 138 * q^89 + 10 * q^90 - 138 * q^91 - 86 * q^92 + 23 * q^93 - 60 * q^94 + 49 * q^95 - 92 * q^96 + 9 * q^97 - 67 * q^98 - 147 * q^99

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