LMFDB - Embedded newform 8007.2.a.j.1.19

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			1.19
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.43835 q^{2} -1.00000 q^{3} +0.0688642 q^{4} -3.82222 q^{5} +1.43835 q^{6} +1.52533 q^{7} +2.77766 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.43835 q^{2} -1.00000 q^{3} +0.0688642 q^{4} -3.82222 q^{5} +1.43835 q^{6} +1.52533 q^{7} +2.77766 q^{8} +1.00000 q^{9} +5.49771 q^{10} -6.21763 q^{11} -0.0688642 q^{12} +0.752284 q^{13} -2.19396 q^{14} +3.82222 q^{15} -4.13299 q^{16} +1.00000 q^{17} -1.43835 q^{18} -0.430910 q^{19} -0.263214 q^{20} -1.52533 q^{21} +8.94315 q^{22} +2.71393 q^{23} -2.77766 q^{24} +9.60936 q^{25} -1.08205 q^{26} -1.00000 q^{27} +0.105040 q^{28} -6.66763 q^{29} -5.49771 q^{30} +2.38194 q^{31} +0.389384 q^{32} +6.21763 q^{33} -1.43835 q^{34} -5.83013 q^{35} +0.0688642 q^{36} -5.35717 q^{37} +0.619801 q^{38} -0.752284 q^{39} -10.6168 q^{40} -3.02822 q^{41} +2.19396 q^{42} +5.74718 q^{43} -0.428172 q^{44} -3.82222 q^{45} -3.90359 q^{46} +5.51028 q^{47} +4.13299 q^{48} -4.67338 q^{49} -13.8217 q^{50} -1.00000 q^{51} +0.0518055 q^{52} +2.44838 q^{53} +1.43835 q^{54} +23.7651 q^{55} +4.23683 q^{56} +0.430910 q^{57} +9.59042 q^{58} -0.432944 q^{59} +0.263214 q^{60} -0.540135 q^{61} -3.42608 q^{62} +1.52533 q^{63} +7.70590 q^{64} -2.87540 q^{65} -8.94315 q^{66} -1.20411 q^{67} +0.0688642 q^{68} -2.71393 q^{69} +8.38579 q^{70} +7.20238 q^{71} +2.77766 q^{72} -8.32312 q^{73} +7.70550 q^{74} -9.60936 q^{75} -0.0296743 q^{76} -9.48390 q^{77} +1.08205 q^{78} +13.1773 q^{79} +15.7972 q^{80} +1.00000 q^{81} +4.35566 q^{82} -12.0488 q^{83} -0.105040 q^{84} -3.82222 q^{85} -8.26649 q^{86} +6.66763 q^{87} -17.2704 q^{88} -13.6432 q^{89} +5.49771 q^{90} +1.14748 q^{91} +0.186893 q^{92} -2.38194 q^{93} -7.92574 q^{94} +1.64703 q^{95} -0.389384 q^{96} -13.3215 q^{97} +6.72198 q^{98} -6.21763 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.43835	−1.01707	−0.508535	−	0.861041i	$-0.669813\pi$
$2$	−1.43835	−1.01707	−0.508535	+	0.861041i	$0.669813\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.0688642	0.0344321
$5$	−3.82222	−1.70935	−0.854674	−	0.519165i	$-0.826243\pi$
$5$	−3.82222	−1.70935	−0.854674	+	0.519165i	$0.826243\pi$
$6$	1.43835	0.587206
$7$	1.52533	0.576519	0.288259	−	0.957552i	$-0.406923\pi$
$7$	1.52533	0.576519	0.288259	+	0.957552i	$0.406923\pi$
$8$	2.77766	0.982050
$9$	1.00000	0.333333
$10$	5.49771	1.73853
$11$	−6.21763	−1.87468	−0.937342	−	0.348410i	$-0.886722\pi$
$11$	−6.21763	−1.87468	−0.937342	+	0.348410i	$0.886722\pi$
$12$	−0.0688642	−0.0198794
$13$	0.752284	0.208646	0.104323	−	0.994543i	$-0.466732\pi$
$13$	0.752284	0.208646	0.104323	+	0.994543i	$0.466732\pi$
$14$	−2.19396	−0.586360
$15$	3.82222	0.986893
$16$	−4.13299	−1.03325
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.43835	−0.339023
$19$	−0.430910	−0.0988575	−0.0494287	−	0.998778i	$-0.515740\pi$
$19$	−0.430910	−0.0988575	−0.0494287	+	0.998778i	$0.515740\pi$
$20$	−0.263214	−0.0588565
$21$	−1.52533	−0.332853
$22$	8.94315	1.90669
$23$	2.71393	0.565893	0.282947	−	0.959136i	$-0.408688\pi$
$23$	2.71393	0.565893	0.282947	+	0.959136i	$0.408688\pi$
$24$	−2.77766	−0.566987
$25$	9.60936	1.92187
$26$	−1.08205	−0.212208
$27$	−1.00000	−0.192450
$28$	0.105040	0.0198508
$29$	−6.66763	−1.23815	−0.619074	−	0.785333i	$-0.712492\pi$
$29$	−6.66763	−1.23815	−0.619074	+	0.785333i	$0.712492\pi$
$30$	−5.49771	−1.00374
$31$	2.38194	0.427810	0.213905	−	0.976854i	$-0.431382\pi$
$31$	2.38194	0.427810	0.213905	+	0.976854i	$0.431382\pi$
$32$	0.389384	0.0688340
$33$	6.21763	1.08235
$34$	−1.43835	−0.246676
$35$	−5.83013	−0.985471
$36$	0.0688642	0.0114774
$37$	−5.35717	−0.880713	−0.440356	−	0.897823i	$-0.645148\pi$
$37$	−5.35717	−0.880713	−0.440356	+	0.897823i	$0.645148\pi$
$38$	0.619801	0.100545
$39$	−0.752284	−0.120462
$40$	−10.6168	−1.67867
$41$	−3.02822	−0.472929	−0.236465	−	0.971640i	$-0.575989\pi$
$41$	−3.02822	−0.472929	−0.236465	+	0.971640i	$0.575989\pi$
$42$	2.19396	0.338535
$43$	5.74718	0.876437	0.438219	−	0.898868i	$-0.355610\pi$
$43$	5.74718	0.876437	0.438219	+	0.898868i	$0.355610\pi$
$44$	−0.428172	−0.0645494
$45$	−3.82222	−0.569783
$46$	−3.90359	−0.575553
$47$	5.51028	0.803757	0.401879	−	0.915693i	$-0.368357\pi$
$47$	5.51028	0.803757	0.401879	+	0.915693i	$0.368357\pi$
$48$	4.13299	0.596545
$49$	−4.67338	−0.667626
$50$	−13.8217	−1.95468
$51$	−1.00000	−0.140028
$52$	0.0518055	0.00718413
$53$	2.44838	0.336311	0.168155	−	0.985761i	$-0.446219\pi$
$53$	2.44838	0.336311	0.168155	+	0.985761i	$0.446219\pi$
$54$	1.43835	0.195735
$55$	23.7651	3.20449
$56$	4.23683	0.566170
$57$	0.430910	0.0570754
$58$	9.59042	1.25928
$59$	−0.432944	−0.0563645	−0.0281822	−	0.999603i	$-0.508972\pi$
$59$	−0.432944	−0.0563645	−0.0281822	+	0.999603i	$0.508972\pi$
$60$	0.263214	0.0339808
$61$	−0.540135	−0.0691573	−0.0345786	−	0.999402i	$-0.511009\pi$
$61$	−0.540135	−0.0691573	−0.0345786	+	0.999402i	$0.511009\pi$
$62$	−3.42608	−0.435113
$63$	1.52533	0.192173
$64$	7.70590	0.963238
$65$	−2.87540	−0.356649
$66$	−8.94315	−1.10083
$67$	−1.20411	−0.147105	−0.0735527	−	0.997291i	$-0.523434\pi$
$67$	−1.20411	−0.147105	−0.0735527	+	0.997291i	$0.523434\pi$
$68$	0.0688642	0.00835102
$69$	−2.71393	−0.326719
$70$	8.38579	1.00229
$71$	7.20238	0.854765	0.427383	−	0.904071i	$-0.359436\pi$
$71$	7.20238	0.854765	0.427383	+	0.904071i	$0.359436\pi$
$72$	2.77766	0.327350
$73$	−8.32312	−0.974148	−0.487074	−	0.873361i	$-0.661936\pi$
$73$	−8.32312	−0.974148	−0.487074	+	0.873361i	$0.661936\pi$
$74$	7.70550	0.895747
$75$	−9.60936	−1.10959
$76$	−0.0296743	−0.00340387
$77$	−9.48390	−1.08079
$78$	1.08205	0.122518
$79$	13.1773	1.48256	0.741281	−	0.671195i	$-0.234219\pi$
$79$	13.1773	1.48256	0.741281	+	0.671195i	$0.234219\pi$
$80$	15.7972	1.76618
$81$	1.00000	0.111111
$82$	4.35566	0.481002
$83$	−12.0488	−1.32253	−0.661266	−	0.750151i	$-0.729981\pi$
$83$	−12.0488	−1.32253	−0.661266	+	0.750151i	$0.729981\pi$
$84$	−0.105040	−0.0114608
$85$	−3.82222	−0.414578
$86$	−8.26649	−0.891398
$87$	6.66763	0.714845
$88$	−17.2704	−1.84103
$89$	−13.6432	−1.44617	−0.723087	−	0.690757i	$-0.757277\pi$
$89$	−13.6432	−1.44617	−0.723087	+	0.690757i	$0.757277\pi$
$90$	5.49771	0.579509
$91$	1.14748	0.120288
$92$	0.186893	0.0194849
$93$	−2.38194	−0.246996
$94$	−7.92574	−0.817478
$95$	1.64703	0.168982
$96$	−0.389384	−0.0397413
$97$	−13.3215	−1.35259	−0.676295	−	0.736631i	$-0.736416\pi$
$97$	−13.3215	−1.35259	−0.676295	+	0.736631i	$0.736416\pi$
$98$	6.72198	0.679023
$99$	−6.21763	−0.624895
$100$	0.661742	0.0661742
$101$	−10.4000	−1.03484	−0.517418	−	0.855733i	$-0.673107\pi$
$101$	−10.4000	−1.03484	−0.517418	+	0.855733i	$0.673107\pi$
$102$	1.43835	0.142418
$103$	2.07038	0.204000	0.102000	−	0.994784i	$-0.467476\pi$
$103$	2.07038	0.204000	0.102000	+	0.994784i	$0.467476\pi$
$104$	2.08959	0.204901
$105$	5.83013	0.568962
$106$	−3.52164	−0.342051
$107$	−7.33432	−0.709036	−0.354518	−	0.935049i	$-0.615355\pi$
$107$	−7.33432	−0.709036	−0.354518	+	0.935049i	$0.615355\pi$
$108$	−0.0688642	−0.00662646
$109$	16.4064	1.57145	0.785724	−	0.618577i	$-0.212291\pi$
$109$	16.4064	1.57145	0.785724	+	0.618577i	$0.212291\pi$
$110$	−34.1827	−3.25919
$111$	5.35717	0.508480
$112$	−6.30415	−0.595686
$113$	−17.5365	−1.64969	−0.824847	−	0.565356i	$-0.808739\pi$
$113$	−17.5365	−1.64969	−0.824847	+	0.565356i	$0.808739\pi$
$114$	−0.619801	−0.0580497
$115$	−10.3732	−0.967309
$116$	−0.459161	−0.0426321
$117$	0.752284	0.0695487
$118$	0.622727	0.0573266
$119$	1.52533	0.139826
$120$	10.6168	0.969179
$121$	27.6589	2.51444
$122$	0.776906	0.0703378
$123$	3.02822	0.273046
$124$	0.164031	0.0147304
$125$	−17.6180	−1.57580
$126$	−2.19396	−0.195453
$127$	2.03917	0.180947	0.0904735	−	0.995899i	$-0.471162\pi$
$127$	2.03917	0.180947	0.0904735	+	0.995899i	$0.471162\pi$
$128$	−11.8626	−1.04851
$129$	−5.74718	−0.506011
$130$	4.13584	0.362737
$131$	3.84201	0.335678	0.167839	−	0.985814i	$-0.446321\pi$
$131$	3.84201	0.335678	0.167839	+	0.985814i	$0.446321\pi$
$132$	0.428172	0.0372676
$133$	−0.657277	−0.0569932
$134$	1.73194	0.149617
$135$	3.82222	0.328964
$136$	2.77766	0.238182
$137$	−17.9908	−1.53706	−0.768529	−	0.639815i	$-0.779011\pi$
$137$	−17.9908	−1.53706	−0.768529	+	0.639815i	$0.779011\pi$
$138$	3.90359	0.332296
$139$	−13.9294	−1.18148	−0.590739	−	0.806863i	$-0.701164\pi$
$139$	−13.9294	−1.18148	−0.590739	+	0.806863i	$0.701164\pi$
$140$	−0.401487	−0.0339319
$141$	−5.51028	−0.464049
$142$	−10.3596	−0.869356
$143$	−4.67742	−0.391146
$144$	−4.13299	−0.344416
$145$	25.4852	2.11643
$146$	11.9716	0.990777
$147$	4.67338	0.385454
$148$	−0.368917	−0.0303248
$149$	−0.887102	−0.0726742	−0.0363371	−	0.999340i	$-0.511569\pi$
$149$	−0.887102	−0.0726742	−0.0363371	+	0.999340i	$0.511569\pi$
$150$	13.8217	1.12853
$151$	−10.6702	−0.868327	−0.434163	−	0.900834i	$-0.642956\pi$
$151$	−10.6702	−0.868327	−0.434163	+	0.900834i	$0.642956\pi$
$152$	−1.19692	−0.0970830
$153$	1.00000	0.0808452
$154$	13.6412	1.09924
$155$	−9.10431	−0.731276
$156$	−0.0518055	−0.00414776
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−18.9536	−1.50787
$159$	−2.44838	−0.194169
$160$	−1.48831	−0.117661
$161$	4.13962	0.326248
$162$	−1.43835	−0.113008
$163$	−23.5485	−1.84446	−0.922230	−	0.386643i	$-0.873635\pi$
$163$	−23.5485	−1.84446	−0.922230	+	0.386643i	$0.873635\pi$
$164$	−0.208536	−0.0162840
$165$	−23.7651	−1.85011
$166$	17.3305	1.34511
$167$	11.6666	0.902787	0.451394	−	0.892325i	$-0.350927\pi$
$167$	11.6666	0.902787	0.451394	+	0.892325i	$0.350927\pi$
$168$	−4.23683	−0.326879
$169$	−12.4341	−0.956467
$170$	5.49771	0.421655
$171$	−0.430910	−0.0329525
$172$	0.395775	0.0301776
$173$	1.44556	0.109904	0.0549521	−	0.998489i	$-0.482499\pi$
$173$	1.44556	0.109904	0.0549521	+	0.998489i	$0.482499\pi$
$174$	−9.59042	−0.727048
$175$	14.6574	1.10800
$176$	25.6974	1.93701
$177$	0.432944	0.0325420
$178$	19.6237	1.47086
$179$	16.9096	1.26388	0.631941	−	0.775017i	$-0.282259\pi$
$179$	16.9096	1.26388	0.631941	+	0.775017i	$0.282259\pi$
$180$	−0.263214	−0.0196188
$181$	−4.83726	−0.359551	−0.179775	−	0.983708i	$-0.557537\pi$
$181$	−4.83726	−0.359551	−0.179775	+	0.983708i	$0.557537\pi$
$182$	−1.65048	−0.122342
$183$	0.540135	0.0399280
$184$	7.53837	0.555736
$185$	20.4763	1.50544
$186$	3.42608	0.251212
$187$	−6.21763	−0.454678
$188$	0.379461	0.0276751
$189$	−1.52533	−0.110951
$190$	−2.36902	−0.171866
$191$	−8.80081	−0.636804	−0.318402	−	0.947956i	$-0.603146\pi$
$191$	−8.80081	−0.636804	−0.318402	+	0.947956i	$0.603146\pi$
$192$	−7.70590	−0.556125
$193$	−27.0924	−1.95015	−0.975075	−	0.221875i	$-0.928782\pi$
$193$	−27.0924	−1.95015	−0.975075	+	0.221875i	$0.928782\pi$
$194$	19.1610	1.37568
$195$	2.87540	0.205911
$196$	−0.321829	−0.0229878
$197$	3.57134	0.254447	0.127224	−	0.991874i	$-0.459393\pi$
$197$	3.57134	0.254447	0.127224	+	0.991874i	$0.459393\pi$
$198$	8.94315	0.635562
$199$	22.2088	1.57434	0.787170	−	0.616736i	$-0.211545\pi$
$199$	22.2088	1.57434	0.787170	+	0.616736i	$0.211545\pi$
$200$	26.6915	1.88738
$201$	1.20411	0.0849314
$202$	14.9589	1.05250
$203$	−10.1703	−0.713816
$204$	−0.0688642	−0.00482146
$205$	11.5745	0.808401
$206$	−2.97793	−0.207483
$207$	2.71393	0.188631
$208$	−3.10918	−0.215583
$209$	2.67924	0.185327
$210$	−8.38579	−0.578675
$211$	5.44530	0.374870	0.187435	−	0.982277i	$-0.439983\pi$
$211$	5.44530	0.374870	0.187435	+	0.982277i	$0.439983\pi$
$212$	0.168606	0.0115799
$213$	−7.20238	−0.493499
$214$	10.5494	0.721139
$215$	−21.9670	−1.49814
$216$	−2.77766	−0.188996
$217$	3.63324	0.246640
$218$	−23.5982	−1.59827
$219$	8.32312	0.562424
$220$	1.63657	0.110337
$221$	0.752284	0.0506041
$222$	−7.70550	−0.517160
$223$	−12.4484	−0.833609	−0.416804	−	0.908996i	$-0.636850\pi$
$223$	−12.4484	−0.833609	−0.416804	+	0.908996i	$0.636850\pi$
$224$	0.593937	0.0396841
$225$	9.60936	0.640624
$226$	25.2237	1.67785
$227$	−16.5389	−1.09772	−0.548862	−	0.835913i	$-0.684939\pi$
$227$	−16.5389	−1.09772	−0.548862	+	0.835913i	$0.684939\pi$
$228$	0.0296743	0.00196523
$229$	13.5732	0.896941	0.448470	−	0.893798i	$-0.351969\pi$
$229$	13.5732	0.896941	0.448470	+	0.893798i	$0.351969\pi$
$230$	14.9204	0.983821
$231$	9.48390	0.623995
$232$	−18.5204	−1.21592
$233$	21.9632	1.43886	0.719430	−	0.694565i	$-0.244403\pi$
$233$	21.9632	1.43886	0.719430	+	0.694565i	$0.244403\pi$
$234$	−1.08205	−0.0707359
$235$	−21.0615	−1.37390
$236$	−0.0298143	−0.00194075
$237$	−13.1773	−0.855958
$238$	−2.19396	−0.142213
$239$	−16.2697	−1.05240	−0.526199	−	0.850361i	$-0.676383\pi$
$239$	−16.2697	−1.05240	−0.526199	+	0.850361i	$0.676383\pi$
$240$	−15.7972	−1.01970
$241$	−14.2950	−0.920820	−0.460410	−	0.887707i	$-0.652298\pi$
$241$	−14.2950	−0.920820	−0.460410	+	0.887707i	$0.652298\pi$
$242$	−39.7833	−2.55736
$243$	−1.00000	−0.0641500
$244$	−0.0371960	−0.00238123
$245$	17.8627	1.14121
$246$	−4.35566	−0.277707
$247$	−0.324167	−0.0206262
$248$	6.61623	0.420131
$249$	12.0488	0.763564
$250$	25.3409	1.60270
$251$	−9.95840	−0.628568	−0.314284	−	0.949329i	$-0.601764\pi$
$251$	−9.95840	−0.628568	−0.314284	+	0.949329i	$0.601764\pi$
$252$	0.105040	0.00661692
$253$	−16.8742	−1.06087
$254$	−2.93305	−0.184036
$255$	3.82222	0.239357
$256$	1.65080	0.103175
$257$	22.4003	1.39729	0.698647	−	0.715467i	$-0.253786\pi$
$257$	22.4003	1.39729	0.698647	+	0.715467i	$0.253786\pi$
$258$	8.26649	0.514649
$259$	−8.17142	−0.507747
$260$	−0.198012	−0.0122802
$261$	−6.66763	−0.412716
$262$	−5.52617	−0.341408
$263$	−19.9317	−1.22904	−0.614521	−	0.788901i	$-0.710651\pi$
$263$	−19.9317	−1.22904	−0.614521	+	0.788901i	$0.710651\pi$
$264$	17.2704	1.06292
$265$	−9.35824	−0.574872
$266$	0.945398	0.0579661
$267$	13.6432	0.834948
$268$	−0.0829201	−0.00506515
$269$	−28.6672	−1.74787	−0.873935	−	0.486042i	$-0.838440\pi$
$269$	−28.6672	−1.74787	−0.873935	+	0.486042i	$0.838440\pi$
$270$	−5.49771	−0.334580
$271$	25.0172	1.51969	0.759844	−	0.650105i	$-0.225275\pi$
$271$	25.0172	1.51969	0.759844	+	0.650105i	$0.225275\pi$
$272$	−4.13299	−0.250599
$273$	−1.14748	−0.0694485
$274$	25.8772	1.56330
$275$	−59.7474	−3.60291
$276$	−0.186893	−0.0112496
$277$	−5.46635	−0.328441	−0.164221	−	0.986424i	$-0.552511\pi$
$277$	−5.46635	−0.328441	−0.164221	+	0.986424i	$0.552511\pi$
$278$	20.0354	1.20165
$279$	2.38194	0.142603
$280$	−16.1941	−0.967783
$281$	−3.24236	−0.193423	−0.0967114	−	0.995312i	$-0.530832\pi$
$281$	−3.24236	−0.193423	−0.0967114	+	0.995312i	$0.530832\pi$
$282$	7.92574	0.471971
$283$	−4.98257	−0.296183	−0.148091	−	0.988974i	$-0.547313\pi$
$283$	−4.98257	−0.296183	−0.148091	+	0.988974i	$0.547313\pi$
$284$	0.495986	0.0294314
$285$	−1.64703	−0.0975617
$286$	6.72779	0.397823
$287$	−4.61903	−0.272653
$288$	0.389384	0.0229447
$289$	1.00000	0.0588235
$290$	−36.6567	−2.15256
$291$	13.3215	0.780918
$292$	−0.573165	−0.0335420
$293$	−20.5351	−1.19967	−0.599837	−	0.800122i	$-0.704768\pi$
$293$	−20.5351	−1.19967	−0.599837	+	0.800122i	$0.704768\pi$
$294$	−6.72198	−0.392034
$295$	1.65481	0.0963465
$296$	−14.8804	−0.864904
$297$	6.21763	0.360783
$298$	1.27597	0.0739148
$299$	2.04165	0.118071
$300$	−0.661742	−0.0382057
$301$	8.76632	0.505282
$302$	15.3475	0.883149
$303$	10.4000	0.597463
$304$	1.78094	0.102144
$305$	2.06452	0.118214
$306$	−1.43835	−0.0822253
$307$	1.02037	0.0582354	0.0291177	−	0.999576i	$-0.490730\pi$
$307$	1.02037	0.0582354	0.0291177	+	0.999576i	$0.490730\pi$
$308$	−0.653101	−0.0372139
$309$	−2.07038	−0.117780
$310$	13.0952	0.743759
$311$	−8.34372	−0.473129	−0.236564	−	0.971616i	$-0.576021\pi$
$311$	−8.34372	−0.473129	−0.236564	+	0.971616i	$0.576021\pi$
$312$	−2.08959	−0.118300
$313$	−15.1766	−0.857833	−0.428917	−	0.903344i	$-0.641105\pi$
$313$	−15.1766	−0.857833	−0.428917	+	0.903344i	$0.641105\pi$
$314$	1.43835	0.0811711
$315$	−5.83013	−0.328490
$316$	0.907445	0.0510478
$317$	6.18538	0.347405	0.173703	−	0.984798i	$-0.444427\pi$
$317$	6.18538	0.347405	0.173703	+	0.984798i	$0.444427\pi$
$318$	3.52164	0.197484
$319$	41.4568	2.32114
$320$	−29.4536	−1.64651
$321$	7.33432	0.409362
$322$	−5.95425	−0.331817
$323$	−0.430910	−0.0239765
$324$	0.0688642	0.00382579
$325$	7.22897	0.400991
$326$	33.8711	1.87594
$327$	−16.4064	−0.907276
$328$	−8.41137	−0.464440
$329$	8.40497	0.463381
$330$	34.1827	1.88170
$331$	−4.63627	−0.254832	−0.127416	−	0.991849i	$-0.540668\pi$
$331$	−4.63627	−0.254832	−0.127416	+	0.991849i	$0.540668\pi$
$332$	−0.829734	−0.0455376
$333$	−5.35717	−0.293571
$334$	−16.7807	−0.918198
$335$	4.60237	0.251454
$336$	6.30415	0.343919
$337$	9.56869	0.521240	0.260620	−	0.965441i	$-0.416073\pi$
$337$	9.56869	0.521240	0.260620	+	0.965441i	$0.416073\pi$
$338$	17.8846	0.972794
$339$	17.5365	0.952451
$340$	−0.263214	−0.0142748
$341$	−14.8100	−0.802008
$342$	0.619801	0.0335150
$343$	−17.8057	−0.961418
$344$	15.9637	0.860706
$345$	10.3732	0.558476
$346$	−2.07923	−0.111780
$347$	−17.9573	−0.963999	−0.482000	−	0.876171i	$-0.660089\pi$
$347$	−17.9573	−0.963999	−0.482000	+	0.876171i	$0.660089\pi$
$348$	0.459161	0.0246136
$349$	1.40644	0.0752850	0.0376425	−	0.999291i	$-0.488015\pi$
$349$	1.40644	0.0752850	0.0376425	+	0.999291i	$0.488015\pi$
$350$	−21.0825	−1.12691
$351$	−0.752284	−0.0401540
$352$	−2.42104	−0.129042
$353$	25.1640	1.33934	0.669671	−	0.742657i	$-0.266435\pi$
$353$	25.1640	1.33934	0.669671	+	0.742657i	$0.266435\pi$
$354$	−0.622727	−0.0330975
$355$	−27.5291	−1.46109
$356$	−0.939526	−0.0497948
$357$	−1.52533	−0.0807288
$358$	−24.3220	−1.28546
$359$	10.9395	0.577364	0.288682	−	0.957425i	$-0.406783\pi$
$359$	10.9395	0.577364	0.288682	+	0.957425i	$0.406783\pi$
$360$	−10.6168	−0.559556
$361$	−18.8143	−0.990227
$362$	6.95770	0.365688
$363$	−27.6589	−1.45171
$364$	0.0790202	0.00414178
$365$	31.8128	1.66516
$366$	−0.776906	−0.0406095
$367$	11.8429	0.618193	0.309096	−	0.951031i	$-0.399973\pi$
$367$	11.8429	0.618193	0.309096	+	0.951031i	$0.399973\pi$
$368$	−11.2166	−0.584707
$369$	−3.02822	−0.157643
$370$	−29.4521	−1.53114
$371$	3.73457	0.193889
$372$	−0.164031	−0.00850460
$373$	13.1676	0.681792	0.340896	−	0.940101i	$-0.389270\pi$
$373$	13.1676	0.681792	0.340896	+	0.940101i	$0.389270\pi$
$374$	8.94315	0.462439
$375$	17.6180	0.909790
$376$	15.3057	0.789330
$377$	−5.01596	−0.258335
$378$	2.19396	0.112845
$379$	−7.35145	−0.377619	−0.188809	−	0.982014i	$-0.560463\pi$
$379$	−7.35145	−0.377619	−0.188809	+	0.982014i	$0.560463\pi$
$380$	0.113422	0.00581840
$381$	−2.03917	−0.104470
$382$	12.6587	0.647675
$383$	27.5449	1.40748	0.703740	−	0.710457i	$-0.251512\pi$
$383$	27.5449	1.40748	0.703740	+	0.710457i	$0.251512\pi$
$384$	11.8626	0.605360
$385$	36.2495	1.84745
$386$	38.9684	1.98344
$387$	5.74718	0.292146
$388$	−0.917373	−0.0465725
$389$	22.1334	1.12221	0.561105	−	0.827745i	$-0.310376\pi$
$389$	22.1334	1.12221	0.561105	+	0.827745i	$0.310376\pi$
$390$	−4.13584	−0.209426
$391$	2.71393	0.137249
$392$	−12.9811	−0.655643
$393$	−3.84201	−0.193804
$394$	−5.13685	−0.258791
$395$	−50.3665	−2.53422
$396$	−0.428172	−0.0215165
$397$	−1.32029	−0.0662636	−0.0331318	−	0.999451i	$-0.510548\pi$
$397$	−1.32029	−0.0662636	−0.0331318	+	0.999451i	$0.510548\pi$
$398$	−31.9441	−1.60121
$399$	0.657277	0.0329050
$400$	−39.7154	−1.98577
$401$	13.4317	0.670747	0.335374	−	0.942085i	$-0.391137\pi$
$401$	13.4317	0.670747	0.335374	+	0.942085i	$0.391137\pi$
$402$	−1.73194	−0.0863812
$403$	1.79190	0.0892608
$404$	−0.716187	−0.0356316
$405$	−3.82222	−0.189928
$406$	14.6285	0.726001
$407$	33.3088	1.65106
$408$	−2.77766	−0.137515
$409$	4.94784	0.244655	0.122327	−	0.992490i	$-0.460964\pi$
$409$	4.94784	0.244655	0.122327	+	0.992490i	$0.460964\pi$
$410$	−16.6483	−0.822201
$411$	17.9908	0.887421
$412$	0.142575	0.00702416
$413$	−0.660380	−0.0324952
$414$	−3.90359	−0.191851
$415$	46.0533	2.26067
$416$	0.292927	0.0143619
$417$	13.9294	0.682127
$418$	−3.85369	−0.188490
$419$	21.6961	1.05992	0.529961	−	0.848022i	$-0.322206\pi$
$419$	21.6961	1.05992	0.529961	+	0.848022i	$0.322206\pi$
$420$	0.401487	0.0195906
$421$	22.6335	1.10309	0.551544	−	0.834146i	$-0.314039\pi$
$421$	22.6335	1.10309	0.551544	+	0.834146i	$0.314039\pi$
$422$	−7.83227	−0.381269
$423$	5.51028	0.267919
$424$	6.80076	0.330274
$425$	9.60936	0.466123
$426$	10.3596	0.501923
$427$	−0.823882	−0.0398705
$428$	−0.505073	−0.0244136
$429$	4.67742	0.225828
$430$	31.5963	1.52371
$431$	−38.5731	−1.85800	−0.929001	−	0.370076i	$-0.879332\pi$
$431$	−38.5731	−1.85800	−0.929001	+	0.370076i	$0.879332\pi$
$432$	4.13299	0.198848
$433$	30.2645	1.45442	0.727210	−	0.686416i	$-0.240817\pi$
$433$	30.2645	1.45442	0.727210	+	0.686416i	$0.240817\pi$
$434$	−5.22589	−0.250851
$435$	−25.4852	−1.22192
$436$	1.12981	0.0541083
$437$	−1.16946	−0.0559428
$438$	−11.9716	−0.572025
$439$	−22.9509	−1.09538	−0.547692	−	0.836680i	$-0.684494\pi$
$439$	−22.9509	−1.09538	−0.547692	+	0.836680i	$0.684494\pi$
$440$	66.0114	3.14697
$441$	−4.67338	−0.222542
$442$	−1.08205	−0.0514680
$443$	24.5386	1.16586	0.582931	−	0.812522i	$-0.301906\pi$
$443$	24.5386	1.16586	0.582931	+	0.812522i	$0.301906\pi$
$444$	0.368917	0.0175080
$445$	52.1472	2.47201
$446$	17.9053	0.847839
$447$	0.887102	0.0419585
$448$	11.7540	0.555324
$449$	−5.93024	−0.279865	−0.139933	−	0.990161i	$-0.544689\pi$
$449$	−5.93024	−0.279865	−0.139933	+	0.990161i	$0.544689\pi$
$450$	−13.8217	−0.651560
$451$	18.8284	0.886593
$452$	−1.20764	−0.0568024
$453$	10.6702	0.501329
$454$	23.7888	1.11646
$455$	−4.38591	−0.205615
$456$	1.19692	0.0560509
$457$	24.6957	1.15522	0.577609	−	0.816314i	$-0.303986\pi$
$457$	24.6957	1.15522	0.577609	+	0.816314i	$0.303986\pi$
$458$	−19.5230	−0.912252
$459$	−1.00000	−0.0466760
$460$	−0.714345	−0.0333065
$461$	23.8315	1.10994	0.554972	−	0.831869i	$-0.312729\pi$
$461$	23.8315	1.10994	0.554972	+	0.831869i	$0.312729\pi$
$462$	−13.6412	−0.634647
$463$	−4.56006	−0.211924	−0.105962	−	0.994370i	$-0.533792\pi$
$463$	−4.56006	−0.211924	−0.105962	+	0.994370i	$0.533792\pi$
$464$	27.5572	1.27931
$465$	9.10431	0.422202
$466$	−31.5909	−1.46342
$467$	4.46006	0.206387	0.103194	−	0.994661i	$-0.467094\pi$
$467$	4.46006	0.206387	0.103194	+	0.994661i	$0.467094\pi$
$468$	0.0518055	0.00239471
$469$	−1.83666	−0.0848090
$470$	30.2939	1.39735
$471$	1.00000	0.0460776
$472$	−1.20257	−0.0553527
$473$	−35.7338	−1.64304
$474$	18.9536	0.870569
$475$	−4.14077	−0.189992
$476$	0.105040	0.00481452
$477$	2.44838	0.112104
$478$	23.4016	1.07036
$479$	−22.3970	−1.02334	−0.511672	−	0.859181i	$-0.670974\pi$
$479$	−22.3970	−1.02334	−0.511672	+	0.859181i	$0.670974\pi$
$480$	1.48831	0.0679318
$481$	−4.03011	−0.183757
$482$	20.5612	0.936538
$483$	−4.13962	−0.188359
$484$	1.90471	0.0865776
$485$	50.9176	2.31205
$486$	1.43835	0.0652451
$487$	15.0572	0.682305	0.341152	−	0.940008i	$-0.389183\pi$
$487$	15.0572	0.682305	0.341152	+	0.940008i	$0.389183\pi$
$488$	−1.50031	−0.0679159
$489$	23.5485	1.06490
$490$	−25.6929	−1.16069
$491$	−18.0724	−0.815595	−0.407797	−	0.913072i	$-0.633703\pi$
$491$	−18.0724	−0.815595	−0.407797	+	0.913072i	$0.633703\pi$
$492$	0.208536	0.00940155
$493$	−6.66763	−0.300295
$494$	0.466267	0.0209783
$495$	23.7651	1.06816
$496$	−9.84454	−0.442033
$497$	10.9860	0.492788
$498$	−17.3305	−0.776599
$499$	−17.9654	−0.804240	−0.402120	−	0.915587i	$-0.631726\pi$
$499$	−17.9654	−0.804240	−0.402120	+	0.915587i	$0.631726\pi$
$500$	−1.21325	−0.0542582
$501$	−11.6666	−0.521225
$502$	14.3237	0.639298
$503$	32.6699	1.45668	0.728339	−	0.685217i	$-0.240292\pi$
$503$	32.6699	1.45668	0.728339	+	0.685217i	$0.240292\pi$
$504$	4.23683	0.188723
$505$	39.7510	1.76890
$506$	24.2711	1.07898
$507$	12.4341	0.552216
$508$	0.140426	0.00623039
$509$	−3.30044	−0.146289	−0.0731447	−	0.997321i	$-0.523303\pi$
$509$	−3.30044	−0.146289	−0.0731447	+	0.997321i	$0.523303\pi$
$510$	−5.49771	−0.243443
$511$	−12.6955	−0.561614
$512$	21.3507	0.943578
$513$	0.430910	0.0190251
$514$	−32.2196	−1.42115
$515$	−7.91343	−0.348707
$516$	−0.395775	−0.0174230
$517$	−34.2609	−1.50679
$518$	11.7534	0.516415
$519$	−1.44556	−0.0634532
$520$	−7.98687	−0.350247
$521$	−16.3043	−0.714305	−0.357152	−	0.934046i	$-0.616252\pi$
$521$	−16.3043	−0.714305	−0.357152	+	0.934046i	$0.616252\pi$
$522$	9.59042	0.419761
$523$	20.3052	0.887885	0.443943	−	0.896055i	$-0.353579\pi$
$523$	20.3052	0.887885	0.443943	+	0.896055i	$0.353579\pi$
$524$	0.264577	0.0115581
$525$	−14.6574	−0.639702
$526$	28.6689	1.25002
$527$	2.38194	0.103759
$528$	−25.6974	−1.11833
$529$	−15.6346	−0.679765
$530$	13.4605	0.584685
$531$	−0.432944	−0.0187882
$532$	−0.0452629	−0.00196240
$533$	−2.27809	−0.0986749
$534$	−19.6237	−0.849201
$535$	28.0334	1.21199
$536$	−3.34461	−0.144465
$537$	−16.9096	−0.729702
$538$	41.2336	1.77771
$539$	29.0573	1.25159
$540$	0.263214	0.0113269
$541$	22.4265	0.964190	0.482095	−	0.876119i	$-0.339876\pi$
$541$	22.4265	0.964190	0.482095	+	0.876119i	$0.339876\pi$
$542$	−35.9837	−1.54563
$543$	4.83726	0.207587
$544$	0.389384	0.0166947
$545$	−62.7089	−2.68615
$546$	1.65048	0.0706341
$547$	4.64730	0.198704	0.0993521	−	0.995052i	$-0.468323\pi$
$547$	4.64730	0.198704	0.0993521	+	0.995052i	$0.468323\pi$
$548$	−1.23892	−0.0529242
$549$	−0.540135	−0.0230524
$550$	85.9380	3.66441
$551$	2.87315	0.122400
$552$	−7.53837	−0.320854
$553$	20.0997	0.854725
$554$	7.86255	0.334048
$555$	−20.4763	−0.869169
$556$	−0.959239	−0.0406808
$557$	−26.6556	−1.12943	−0.564717	−	0.825284i	$-0.691015\pi$
$557$	−26.6556	−1.12943	−0.564717	+	0.825284i	$0.691015\pi$
$558$	−3.42608	−0.145038
$559$	4.32352	0.182865
$560$	24.0958	1.01823
$561$	6.21763	0.262508
$562$	4.66366	0.196725
$563$	−1.29370	−0.0545230	−0.0272615	−	0.999628i	$-0.508679\pi$
$563$	−1.29370	−0.0545230	−0.0272615	+	0.999628i	$0.508679\pi$
$564$	−0.379461	−0.0159782
$565$	67.0283	2.81990
$566$	7.16670	0.301239
$567$	1.52533	0.0640576
$568$	20.0057	0.839423
$569$	27.8421	1.16720	0.583600	−	0.812041i	$-0.301644\pi$
$569$	27.8421	1.16720	0.583600	+	0.812041i	$0.301644\pi$
$570$	2.36902	0.0992272
$571$	1.12877	0.0472376	0.0236188	−	0.999721i	$-0.492481\pi$
$571$	1.12877	0.0472376	0.0236188	+	0.999721i	$0.492481\pi$
$572$	−0.322107	−0.0134680
$573$	8.80081	0.367659
$574$	6.64380	0.277307
$575$	26.0791	1.08757
$576$	7.70590	0.321079
$577$	12.6322	0.525887	0.262944	−	0.964811i	$-0.415307\pi$
$577$	12.6322	0.525887	0.262944	+	0.964811i	$0.415307\pi$
$578$	−1.43835	−0.0598277
$579$	27.0924	1.12592
$580$	1.75502	0.0728731
$581$	−18.3784	−0.762465
$582$	−19.1610	−0.794249
$583$	−15.2231	−0.630476
$584$	−23.1188	−0.956662
$585$	−2.87540	−0.118883
$586$	29.5368	1.22015
$587$	−39.4026	−1.62632	−0.813159	−	0.582042i	$-0.802254\pi$
$587$	−39.4026	−1.62632	−0.813159	+	0.582042i	$0.802254\pi$
$588$	0.321829	0.0132720
$589$	−1.02640	−0.0422922
$590$	−2.38020	−0.0979912
$591$	−3.57134	−0.146905
$592$	22.1411	0.909993
$593$	−0.206735	−0.00848960	−0.00424480	−	0.999991i	$-0.501351\pi$
$593$	−0.206735	−0.00848960	−0.00424480	+	0.999991i	$0.501351\pi$
$594$	−8.94315	−0.366942
$595$	−5.83013	−0.239012
$596$	−0.0610896	−0.00250233
$597$	−22.2088	−0.908946
$598$	−2.93661	−0.120087
$599$	11.7651	0.480711	0.240355	−	0.970685i	$-0.422736\pi$
$599$	11.7651	0.480711	0.240355	+	0.970685i	$0.422736\pi$
$600$	−26.6915	−1.08968
$601$	33.4307	1.36367	0.681833	−	0.731507i	$-0.261183\pi$
$601$	33.4307	1.36367	0.681833	+	0.731507i	$0.261183\pi$
$602$	−12.6091	−0.513908
$603$	−1.20411	−0.0490351
$604$	−0.734794	−0.0298983
$605$	−105.718	−4.29806
$606$	−14.9589	−0.607662
$607$	−10.8257	−0.439402	−0.219701	−	0.975567i	$-0.570508\pi$
$607$	−10.8257	−0.439402	−0.219701	+	0.975567i	$0.570508\pi$
$608$	−0.167789	−0.00680475
$609$	10.1703	0.412122
$610$	−2.96951	−0.120232
$611$	4.14530	0.167701
$612$	0.0688642	0.00278367
$613$	28.6449	1.15696	0.578479	−	0.815697i	$-0.303646\pi$
$613$	28.6449	1.15696	0.578479	+	0.815697i	$0.303646\pi$
$614$	−1.46765	−0.0592295
$615$	−11.5745	−0.466731
$616$	−26.3430	−1.06139
$617$	36.4882	1.46896	0.734480	−	0.678630i	$-0.237426\pi$
$617$	36.4882	1.46896	0.734480	+	0.678630i	$0.237426\pi$
$618$	2.97793	0.119790
$619$	3.28412	0.132000	0.0659999	−	0.997820i	$-0.478976\pi$
$619$	3.28412	0.132000	0.0659999	+	0.997820i	$0.478976\pi$
$620$	−0.626961	−0.0251794
$621$	−2.71393	−0.108906
$622$	12.0012	0.481205
$623$	−20.8103	−0.833746
$624$	3.10918	0.124467
$625$	19.2931	0.771722
$626$	21.8294	0.872477
$627$	−2.67924	−0.106998
$628$	−0.0688642	−0.00274798
$629$	−5.35717	−0.213604
$630$	8.38579	0.334098
$631$	−38.7077	−1.54093	−0.770465	−	0.637482i	$-0.779976\pi$
$631$	−38.7077	−1.54093	−0.770465	+	0.637482i	$0.779976\pi$
$632$	36.6020	1.45595
$633$	−5.44530	−0.216431
$634$	−8.89677	−0.353336
$635$	−7.79415	−0.309302
$636$	−0.168606	−0.00668565
$637$	−3.51571	−0.139298
$638$	−59.6296	−2.36076
$639$	7.20238	0.284922
$640$	45.3414	1.79228
$641$	17.4010	0.687297	0.343649	−	0.939098i	$-0.388337\pi$
$641$	17.4010	0.687297	0.343649	+	0.939098i	$0.388337\pi$
$642$	−10.5494	−0.416350
$643$	39.6465	1.56350	0.781752	−	0.623589i	$-0.214326\pi$
$643$	39.6465	1.56350	0.781752	+	0.623589i	$0.214326\pi$
$644$	0.285072	0.0112334
$645$	21.9670	0.864950
$646$	0.619801	0.0243857
$647$	38.8783	1.52846	0.764232	−	0.644941i	$-0.223118\pi$
$647$	38.8783	1.52846	0.764232	+	0.644941i	$0.223118\pi$
$648$	2.77766	0.109117
$649$	2.69188	0.105666
$650$	−10.3978	−0.407836
$651$	−3.63324	−0.142398
$652$	−1.62165	−0.0635086
$653$	44.5681	1.74409	0.872043	−	0.489430i	$-0.162795\pi$
$653$	44.5681	1.74409	0.872043	+	0.489430i	$0.162795\pi$
$654$	23.5982	0.922763
$655$	−14.6850	−0.573790
$656$	12.5156	0.488653
$657$	−8.32312	−0.324716
$658$	−12.0893	−0.471291
$659$	10.9948	0.428298	0.214149	−	0.976801i	$-0.431302\pi$
$659$	10.9948	0.428298	0.214149	+	0.976801i	$0.431302\pi$
$660$	−1.63657	−0.0637033
$661$	−21.5533	−0.838325	−0.419162	−	0.907911i	$-0.637676\pi$
$661$	−21.5533	−0.838325	−0.419162	+	0.907911i	$0.637676\pi$
$662$	6.66860	0.259183
$663$	−0.752284	−0.0292163
$664$	−33.4676	−1.29879
$665$	2.51226	0.0974212
$666$	7.70550	0.298582
$667$	−18.0955	−0.700660
$668$	0.803410	0.0310849
$669$	12.4484	0.481284
$670$	−6.61984	−0.255747
$671$	3.35836	0.129648
$672$	−0.593937	−0.0229116
$673$	−45.3412	−1.74778	−0.873888	−	0.486127i	$-0.838409\pi$
$673$	−45.3412	−1.74778	−0.873888	+	0.486127i	$0.838409\pi$
$674$	−13.7632	−0.530138
$675$	−9.60936	−0.369865
$676$	−0.856263	−0.0329332
$677$	−34.9181	−1.34201	−0.671005	−	0.741453i	$-0.734137\pi$
$677$	−34.9181	−1.34201	−0.671005	+	0.741453i	$0.734137\pi$
$678$	−25.2237	−0.968710
$679$	−20.3196	−0.779794
$680$	−10.6168	−0.407136
$681$	16.5389	0.633772
$682$	21.3021	0.815699
$683$	24.2071	0.926259	0.463129	−	0.886291i	$-0.346727\pi$
$683$	24.2071	0.926259	0.463129	+	0.886291i	$0.346727\pi$
$684$	−0.0296743	−0.00113462
$685$	68.7648	2.62737
$686$	25.6109	0.977829
$687$	−13.5732	−0.517849
$688$	−23.7530	−0.905576
$689$	1.84188	0.0701699
$690$	−14.9204	−0.568009
$691$	−30.5579	−1.16248	−0.581239	−	0.813733i	$-0.697432\pi$
$691$	−30.5579	−1.16248	−0.581239	+	0.813733i	$0.697432\pi$
$692$	0.0995477	0.00378423
$693$	−9.48390	−0.360264
$694$	25.8290	0.980455
$695$	53.2413	2.01956
$696$	18.5204	0.702014
$697$	−3.02822	−0.114702
$698$	−2.02296	−0.0765702
$699$	−21.9632	−0.830726
$700$	1.00937	0.0381506
$701$	30.6330	1.15699	0.578497	−	0.815685i	$-0.303640\pi$
$701$	30.6330	1.15699	0.578497	+	0.815685i	$0.303640\pi$
$702$	1.08205	0.0408394
$703$	2.30845	0.0870650
$704$	−47.9124	−1.80577
$705$	21.0615	0.793222
$706$	−36.1947	−1.36221
$707$	−15.8634	−0.596603
$708$	0.0298143	0.00112049
$709$	17.2995	0.649697	0.324849	−	0.945766i	$-0.394687\pi$
$709$	17.2995	0.649697	0.324849	+	0.945766i	$0.394687\pi$
$710$	39.5966	1.48603
$711$	13.1773	0.494187
$712$	−37.8961	−1.42021
$713$	6.46443	0.242095
$714$	2.19396	0.0821068
$715$	17.8781	0.668604
$716$	1.16447	0.0435181
$717$	16.2697	0.607602
$718$	−15.7349	−0.587220
$719$	24.7255	0.922104	0.461052	−	0.887373i	$-0.347472\pi$
$719$	24.7255	0.922104	0.461052	+	0.887373i	$0.347472\pi$
$720$	15.7972	0.588726
$721$	3.15800	0.117610
$722$	27.0617	1.00713
$723$	14.2950	0.531635
$724$	−0.333114	−0.0123801
$725$	−64.0717	−2.37956
$726$	39.7833	1.47650
$727$	−31.4252	−1.16550	−0.582749	−	0.812652i	$-0.698023\pi$
$727$	−31.4252	−1.16550	−0.582749	+	0.812652i	$0.698023\pi$
$728$	3.18730	0.118129
$729$	1.00000	0.0370370
$730$	−45.7581	−1.69358
$731$	5.74718	0.212567
$732$	0.0371960	0.00137480
$733$	1.65325	0.0610643	0.0305321	−	0.999534i	$-0.490280\pi$
$733$	1.65325	0.0610643	0.0305321	+	0.999534i	$0.490280\pi$
$734$	−17.0342	−0.628745
$735$	−17.8627	−0.658876
$736$	1.05676	0.0389527
$737$	7.48670	0.275776
$738$	4.35566	0.160334
$739$	13.4396	0.494382	0.247191	−	0.968967i	$-0.420492\pi$
$739$	13.4396	0.494382	0.247191	+	0.968967i	$0.420492\pi$
$740$	1.41008	0.0518357
$741$	0.324167	0.0119086
$742$	−5.37164	−0.197199
$743$	14.0910	0.516949	0.258474	−	0.966018i	$-0.416780\pi$
$743$	14.0910	0.516949	0.258474	+	0.966018i	$0.416780\pi$
$744$	−6.61623	−0.242563
$745$	3.39070	0.124226
$746$	−18.9397	−0.693430
$747$	−12.0488	−0.440844
$748$	−0.428172	−0.0156555
$749$	−11.1872	−0.408772
$750$	−25.3409	−0.925320
$751$	37.1478	1.35554	0.677770	−	0.735274i	$-0.262946\pi$
$751$	37.1478	1.35554	0.677770	+	0.735274i	$0.262946\pi$
$752$	−22.7739	−0.830479
$753$	9.95840	0.362904
$754$	7.21472	0.262745
$755$	40.7838	1.48427
$756$	−0.105040	−0.00382028
$757$	−3.17696	−0.115469	−0.0577343	−	0.998332i	$-0.518388\pi$
$757$	−3.17696	−0.115469	−0.0577343	+	0.998332i	$0.518388\pi$
$758$	10.5740	0.384065
$759$	16.8742	0.612494
$760$	4.57489	0.165949
$761$	1.30286	0.0472287	0.0236144	−	0.999721i	$-0.492483\pi$
$761$	1.30286	0.0472287	0.0236144	+	0.999721i	$0.492483\pi$
$762$	2.93305	0.106253
$763$	25.0251	0.905969
$764$	−0.606061	−0.0219265
$765$	−3.82222	−0.138193
$766$	−39.6194	−1.43151
$767$	−0.325697	−0.0117602
$768$	−1.65080	−0.0595683
$769$	−10.5979	−0.382170	−0.191085	−	0.981574i	$-0.561201\pi$
$769$	−10.5979	−0.382170	−0.191085	+	0.981574i	$0.561201\pi$
$770$	−52.1397	−1.87898
$771$	−22.4003	−0.806728
$772$	−1.86569	−0.0671478
$773$	0.433004	0.0155741	0.00778703	−	0.999970i	$-0.497521\pi$
$773$	0.433004	0.0155741	0.00778703	+	0.999970i	$0.497521\pi$
$774$	−8.26649	−0.297133
$775$	22.8890	0.822196
$776$	−37.0025	−1.32831
$777$	8.17142	0.293148
$778$	−31.8357	−1.14137
$779$	1.30489	0.0467526
$780$	0.198012	0.00708997
$781$	−44.7817	−1.60242
$782$	−3.90359	−0.139592
$783$	6.66763	0.238282
$784$	19.3150	0.689822
$785$	3.82222	0.136421
$786$	5.52617	0.197112
$787$	−38.2522	−1.36354	−0.681772	−	0.731565i	$-0.738790\pi$
$787$	−38.2522	−1.36354	−0.681772	+	0.731565i	$0.738790\pi$
$788$	0.245937	0.00876116
$789$	19.9317	0.709587
$790$	72.4450	2.57748
$791$	−26.7488	−0.951079
$792$	−17.2704	−0.613678
$793$	−0.406336	−0.0144294
$794$	1.89905	0.0673947
$795$	9.35824	0.331903
$796$	1.52939	0.0542079
$797$	19.2828	0.683032	0.341516	−	0.939876i	$-0.389060\pi$
$797$	19.2828	0.683032	0.341516	+	0.939876i	$0.389060\pi$
$798$	−0.945398	−0.0334667
$799$	5.51028	0.194940
$800$	3.74173	0.132290
$801$	−13.6432	−0.482058
$802$	−19.3196	−0.682197
$803$	51.7500	1.82622
$804$	0.0829201	0.00292437
$805$	−15.8226	−0.557672
$806$	−2.57739	−0.0907846
$807$	28.6672	1.00913
$808$	−28.8876	−1.01626
$809$	−52.6404	−1.85074	−0.925368	−	0.379069i	$-0.876244\pi$
$809$	−52.6404	−1.85074	−0.925368	+	0.379069i	$0.876244\pi$
$810$	5.49771	0.193170
$811$	−17.7049	−0.621705	−0.310852	−	0.950458i	$-0.600614\pi$
$811$	−17.7049	−0.621705	−0.310852	+	0.950458i	$0.600614\pi$
$812$	−0.700370	−0.0245782
$813$	−25.0172	−0.877393
$814$	−47.9099	−1.67924
$815$	90.0075	3.15282
$816$	4.13299	0.144683
$817$	−2.47652	−0.0866424
$818$	−7.11674	−0.248831
$819$	1.14748	0.0400961
$820$	0.797072	0.0278350
$821$	6.77416	0.236420	0.118210	−	0.992989i	$-0.462284\pi$
$821$	6.77416	0.236420	0.118210	+	0.992989i	$0.462284\pi$
$822$	−25.8772	−0.902570
$823$	51.2795	1.78749	0.893745	−	0.448576i	$-0.148069\pi$
$823$	51.2795	1.78749	0.893745	+	0.448576i	$0.148069\pi$
$824$	5.75080	0.200338
$825$	59.7474	2.08014
$826$	0.949860	0.0330499
$827$	−36.6917	−1.27590	−0.637948	−	0.770079i	$-0.720217\pi$
$827$	−36.6917	−1.27590	−0.637948	+	0.770079i	$0.720217\pi$
$828$	0.186893	0.00649497
$829$	−6.20366	−0.215462	−0.107731	−	0.994180i	$-0.534359\pi$
$829$	−6.20366	−0.215462	−0.107731	+	0.994180i	$0.534359\pi$
$830$	−66.2410	−2.29926
$831$	5.46635	0.189626
$832$	5.79703	0.200976
$833$	−4.67338	−0.161923
$834$	−20.0354	−0.693771
$835$	−44.5923	−1.54318
$836$	0.184504	0.00638119
$837$	−2.38194	−0.0823320
$838$	−31.2067	−1.07802
$839$	5.91264	0.204127	0.102063	−	0.994778i	$-0.467456\pi$
$839$	5.91264	0.204127	0.102063	+	0.994778i	$0.467456\pi$
$840$	16.1941	0.558750
$841$	15.4573	0.533011
$842$	−32.5550	−1.12192
$843$	3.24236	0.111673
$844$	0.374986	0.0129076
$845$	47.5257	1.63494
$846$	−7.92574	−0.272493
$847$	42.1888	1.44962
$848$	−10.1191	−0.347492
$849$	4.98257	0.171001
$850$	−13.8217	−0.474080
$851$	−14.5390	−0.498389
$852$	−0.495986	−0.0169922
$853$	8.11731	0.277931	0.138966	−	0.990297i	$-0.455622\pi$
$853$	8.11731	0.277931	0.138966	+	0.990297i	$0.455622\pi$
$854$	1.18503	0.0405511
$855$	1.64703	0.0563273
$856$	−20.3722	−0.696309
$857$	28.1373	0.961152	0.480576	−	0.876953i	$-0.340428\pi$
$857$	28.1373	0.961152	0.480576	+	0.876953i	$0.340428\pi$
$858$	−6.72779	−0.229683
$859$	3.70191	0.126308	0.0631538	−	0.998004i	$-0.479884\pi$
$859$	3.70191	0.126308	0.0631538	+	0.998004i	$0.479884\pi$
$860$	−1.51274	−0.0515840
$861$	4.61903	0.157416
$862$	55.4819	1.88972
$863$	21.3274	0.725994	0.362997	−	0.931790i	$-0.381753\pi$
$863$	21.3274	0.725994	0.362997	+	0.931790i	$0.381753\pi$
$864$	−0.389384	−0.0132471
$865$	−5.52526	−0.187865
$866$	−43.5311	−1.47925
$867$	−1.00000	−0.0339618
$868$	0.250200	0.00849235
$869$	−81.9315	−2.77934
$870$	36.6567	1.24278
$871$	−0.905833	−0.0306930
$872$	45.5714	1.54324
$873$	−13.3215	−0.450863
$874$	1.68210	0.0568977
$875$	−26.8732	−0.908479
$876$	0.573165	0.0193655
$877$	−45.0430	−1.52099	−0.760497	−	0.649342i	$-0.775045\pi$
$877$	−45.0430	−1.52099	−0.760497	+	0.649342i	$0.775045\pi$
$878$	33.0115	1.11408
$879$	20.5351	0.692632
$880$	−98.2210	−3.31103
$881$	48.7808	1.64347	0.821733	−	0.569873i	$-0.193008\pi$
$881$	48.7808	1.64347	0.821733	+	0.569873i	$0.193008\pi$
$882$	6.72198	0.226341
$883$	−38.6289	−1.29997	−0.649983	−	0.759949i	$-0.725224\pi$
$883$	−38.6289	−1.29997	−0.649983	+	0.759949i	$0.725224\pi$
$884$	0.0518055	0.00174241
$885$	−1.65481	−0.0556257
$886$	−35.2951	−1.18576
$887$	−32.8324	−1.10240	−0.551202	−	0.834372i	$-0.685831\pi$
$887$	−32.8324	−1.10240	−0.551202	+	0.834372i	$0.685831\pi$
$888$	14.8804	0.499353
$889$	3.11040	0.104319
$890$	−75.0062	−2.51421
$891$	−6.21763	−0.208298
$892$	−0.857252	−0.0287029
$893$	−2.37443	−0.0794574
$894$	−1.27597	−0.0426747
$895$	−64.6321	−2.16041
$896$	−18.0943	−0.604488
$897$	−2.04165	−0.0681686
$898$	8.52979	0.284643
$899$	−15.8819	−0.529692
$900$	0.661742	0.0220581
$901$	2.44838	0.0815673
$902$	−27.0819	−0.901728
$903$	−8.76632	−0.291725
$904$	−48.7104	−1.62008
$905$	18.4891	0.614598
$906$	−15.3475	−0.509887
$907$	−33.9394	−1.12694	−0.563469	−	0.826137i	$-0.690534\pi$
$907$	−33.9394	−1.12694	−0.563469	+	0.826137i	$0.690534\pi$
$908$	−1.13894	−0.0377970
$909$	−10.4000	−0.344946
$910$	6.30850	0.209125
$911$	18.1495	0.601320	0.300660	−	0.953731i	$-0.402793\pi$
$911$	18.1495	0.601320	0.300660	+	0.953731i	$0.402793\pi$
$912$	−1.78094	−0.0589730
$913$	74.9152	2.47933
$914$	−35.5212	−1.17494
$915$	−2.06452	−0.0682508
$916$	0.934707	0.0308836
$917$	5.86031	0.193524
$918$	1.43835	0.0474728
$919$	42.6785	1.40783	0.703917	−	0.710282i	$-0.251433\pi$
$919$	42.6785	1.40783	0.703917	+	0.710282i	$0.251433\pi$
$920$	−28.8133	−0.949946
$921$	−1.02037	−0.0336222
$922$	−34.2781	−1.12889
$923$	5.41824	0.178343
$924$	0.653101	0.0214855
$925$	−51.4790	−1.69262
$926$	6.55898	0.215542
$927$	2.07038	0.0680001
$928$	−2.59627	−0.0852267
$929$	35.1992	1.15485	0.577423	−	0.816445i	$-0.304058\pi$
$929$	35.1992	1.15485	0.577423	+	0.816445i	$0.304058\pi$
$930$	−13.0952	−0.429410
$931$	2.01381	0.0659998
$932$	1.51248	0.0495430
$933$	8.34372	0.273161
$934$	−6.41516	−0.209910
$935$	23.7651	0.777203
$936$	2.08959	0.0683003
$937$	41.2389	1.34721	0.673607	−	0.739089i	$-0.264744\pi$
$937$	41.2389	1.34721	0.673607	+	0.739089i	$0.264744\pi$
$938$	2.64177	0.0862568
$939$	15.1766	0.495270
$940$	−1.45038	−0.0473063
$941$	−41.2104	−1.34342	−0.671711	−	0.740813i	$-0.734440\pi$
$941$	−41.2104	−1.34342	−0.671711	+	0.740813i	$0.734440\pi$
$942$	−1.43835	−0.0468641
$943$	−8.21839	−0.267627
$944$	1.78935	0.0582384
$945$	5.83013	0.189654
$946$	51.3979	1.67109
$947$	19.3450	0.628628	0.314314	−	0.949319i	$-0.398225\pi$
$947$	19.3450	0.628628	0.314314	+	0.949319i	$0.398225\pi$
$948$	−0.907445	−0.0294724
$949$	−6.26135	−0.203252
$950$	5.95589	0.193235
$951$	−6.18538	−0.200575
$952$	4.23683	0.137317
$953$	−14.8511	−0.481075	−0.240537	−	0.970640i	$-0.577324\pi$
$953$	−14.8511	−0.481075	−0.240537	+	0.970640i	$0.577324\pi$
$954$	−3.52164	−0.114017
$955$	33.6386	1.08852
$956$	−1.12040	−0.0362363
$957$	−41.4568	−1.34011
$958$	32.2148	1.04081
$959$	−27.4418	−0.886143
$960$	29.4536	0.950612
$961$	−25.3263	−0.816979
$962$	5.79673	0.186894
$963$	−7.33432	−0.236345
$964$	−0.984412	−0.0317058
$965$	103.553	3.33349
$966$	5.95425	0.191575
$967$	17.2977	0.556258	0.278129	−	0.960544i	$-0.410286\pi$
$967$	17.2977	0.556258	0.278129	+	0.960544i	$0.410286\pi$
$968$	76.8269	2.46931
$969$	0.430910	0.0138428
$970$	−73.2375	−2.35152
$971$	1.61175	0.0517236	0.0258618	−	0.999666i	$-0.491767\pi$
$971$	1.61175	0.0517236	0.0258618	+	0.999666i	$0.491767\pi$
$972$	−0.0688642	−0.00220882
$973$	−21.2469	−0.681144
$974$	−21.6575	−0.693952
$975$	−7.22897	−0.231512
$976$	2.23237	0.0714565
$977$	55.4200	1.77304	0.886521	−	0.462688i	$-0.153115\pi$
$977$	55.4200	1.77304	0.886521	+	0.462688i	$0.153115\pi$
$978$	−33.8711	−1.08308
$979$	84.8281	2.71112
$980$	1.23010	0.0392941
$981$	16.4064	0.523816
$982$	25.9945	0.829517
$983$	18.4063	0.587070	0.293535	−	0.955948i	$-0.405168\pi$
$983$	18.4063	0.587070	0.293535	+	0.955948i	$0.405168\pi$
$984$	8.41137	0.268145
$985$	−13.6504	−0.434939
$986$	9.59042	0.305421
$987$	−8.40497	−0.267533
$988$	−0.0223235	−0.000710205 0
$989$	15.5974	0.495970
$990$	−34.1827	−1.08640
$991$	−1.33640	−0.0424523	−0.0212261	−	0.999775i	$-0.506757\pi$
$991$	−1.33640	−0.0424523	−0.0212261	+	0.999775i	$0.506757\pi$
$992$	0.927490	0.0294478
$993$	4.63627	0.147128
$994$	−15.8017	−0.501200
$995$	−84.8869	−2.69110
$996$	0.829734	0.0262911
$997$	12.4321	0.393728	0.196864	−	0.980431i	$-0.436924\pi$
$997$	12.4321	0.393728	0.196864	+	0.980431i	$0.436924\pi$
$998$	25.8405	0.817968
$999$	5.35717	0.169493

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.19	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.19	✓	64	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-1.43835 q^{2} -1.00000 q^{3} +0.0688642 q^{4} -3.82222 q^{5} +1.43835 q^{6} +1.52533 q^{7} +2.77766 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.43835 q^{2} -1.00000 q^{3} +0.0688642 q^{4} -3.82222 q^{5} +1.43835 q^{6} +1.52533 q^{7} +2.77766 q^{8} +1.00000 q^{9} +5.49771 q^{10} -6.21763 q^{11} -0.0688642 q^{12} +0.752284 q^{13} -2.19396 q^{14} +3.82222 q^{15} -4.13299 q^{16} +1.00000 q^{17} -1.43835 q^{18} -0.430910 q^{19} -0.263214 q^{20} -1.52533 q^{21} +8.94315 q^{22} +2.71393 q^{23} -2.77766 q^{24} +9.60936 q^{25} -1.08205 q^{26} -1.00000 q^{27} +0.105040 q^{28} -6.66763 q^{29} -5.49771 q^{30} +2.38194 q^{31} +0.389384 q^{32} +6.21763 q^{33} -1.43835 q^{34} -5.83013 q^{35} +0.0688642 q^{36} -5.35717 q^{37} +0.619801 q^{38} -0.752284 q^{39} -10.6168 q^{40} -3.02822 q^{41} +2.19396 q^{42} +5.74718 q^{43} -0.428172 q^{44} -3.82222 q^{45} -3.90359 q^{46} +5.51028 q^{47} +4.13299 q^{48} -4.67338 q^{49} -13.8217 q^{50} -1.00000 q^{51} +0.0518055 q^{52} +2.44838 q^{53} +1.43835 q^{54} +23.7651 q^{55} +4.23683 q^{56} +0.430910 q^{57} +9.59042 q^{58} -0.432944 q^{59} +0.263214 q^{60} -0.540135 q^{61} -3.42608 q^{62} +1.52533 q^{63} +7.70590 q^{64} -2.87540 q^{65} -8.94315 q^{66} -1.20411 q^{67} +0.0688642 q^{68} -2.71393 q^{69} +8.38579 q^{70} +7.20238 q^{71} +2.77766 q^{72} -8.32312 q^{73} +7.70550 q^{74} -9.60936 q^{75} -0.0296743 q^{76} -9.48390 q^{77} +1.08205 q^{78} +13.1773 q^{79} +15.7972 q^{80} +1.00000 q^{81} +4.35566 q^{82} -12.0488 q^{83} -0.105040 q^{84} -3.82222 q^{85} -8.26649 q^{86} +6.66763 q^{87} -17.2704 q^{88} -13.6432 q^{89} +5.49771 q^{90} +1.14748 q^{91} +0.186893 q^{92} -2.38194 q^{93} -7.92574 q^{94} +1.64703 q^{95} -0.389384 q^{96} -13.3215 q^{97} +6.72198 q^{98} -6.21763 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 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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