LMFDB - Embedded newform 8007.2.a.f.1.48

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:	$1$
Dimension:	$48$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.48
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.78887 q^{2} -1.00000 q^{3} +5.77777 q^{4} -2.00554 q^{5} -2.78887 q^{6} +0.938230 q^{7} +10.5357 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.78887 q^{2} -1.00000 q^{3} +5.77777 q^{4} -2.00554 q^{5} -2.78887 q^{6} +0.938230 q^{7} +10.5357 q^{8} +1.00000 q^{9} -5.59318 q^{10} -5.68987 q^{11} -5.77777 q^{12} +0.884003 q^{13} +2.61660 q^{14} +2.00554 q^{15} +17.8271 q^{16} -1.00000 q^{17} +2.78887 q^{18} -2.71161 q^{19} -11.5876 q^{20} -0.938230 q^{21} -15.8683 q^{22} -5.54959 q^{23} -10.5357 q^{24} -0.977804 q^{25} +2.46536 q^{26} -1.00000 q^{27} +5.42087 q^{28} -2.01589 q^{29} +5.59318 q^{30} -8.73145 q^{31} +28.6459 q^{32} +5.68987 q^{33} -2.78887 q^{34} -1.88166 q^{35} +5.77777 q^{36} -2.54729 q^{37} -7.56231 q^{38} -0.884003 q^{39} -21.1298 q^{40} -0.0735028 q^{41} -2.61660 q^{42} -9.11491 q^{43} -32.8747 q^{44} -2.00554 q^{45} -15.4771 q^{46} +6.75641 q^{47} -17.8271 q^{48} -6.11973 q^{49} -2.72696 q^{50} +1.00000 q^{51} +5.10756 q^{52} -6.52204 q^{53} -2.78887 q^{54} +11.4113 q^{55} +9.88489 q^{56} +2.71161 q^{57} -5.62204 q^{58} +4.86184 q^{59} +11.5876 q^{60} +5.04917 q^{61} -24.3508 q^{62} +0.938230 q^{63} +44.2355 q^{64} -1.77290 q^{65} +15.8683 q^{66} -4.00085 q^{67} -5.77777 q^{68} +5.54959 q^{69} -5.24769 q^{70} +13.2959 q^{71} +10.5357 q^{72} +11.9510 q^{73} -7.10404 q^{74} +0.977804 q^{75} -15.6670 q^{76} -5.33840 q^{77} -2.46536 q^{78} -8.53302 q^{79} -35.7529 q^{80} +1.00000 q^{81} -0.204989 q^{82} +3.13577 q^{83} -5.42087 q^{84} +2.00554 q^{85} -25.4203 q^{86} +2.01589 q^{87} -59.9467 q^{88} -9.82268 q^{89} -5.59318 q^{90} +0.829398 q^{91} -32.0642 q^{92} +8.73145 q^{93} +18.8427 q^{94} +5.43824 q^{95} -28.6459 q^{96} -8.29213 q^{97} -17.0671 q^{98} -5.68987 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9}+O(q^{10}) $ 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9} - 20 q^{10} + 5 q^{11} - 45 q^{12} - 8 q^{13} + 4 q^{14} - q^{15} + 39 q^{16} - 48 q^{17} - q^{18} - 6 q^{19} + 6 q^{20} + 13 q^{21} - 35 q^{22} - 8 q^{23} + 6 q^{24} + 13 q^{25} + 17 q^{26} - 48 q^{27} - 38 q^{28} + q^{29} + 20 q^{30} - 21 q^{31} - 3 q^{32} - 5 q^{33} + q^{34} + 19 q^{35} + 45 q^{36} - 58 q^{37} - 14 q^{38} + 8 q^{39} - 54 q^{40} - 3 q^{41} - 4 q^{42} - 33 q^{43} + 2 q^{44} + q^{45} - 26 q^{46} + 9 q^{47} - 39 q^{48} + 11 q^{49} + 4 q^{50} + 48 q^{51} - 31 q^{52} - 33 q^{53} + q^{54} - 21 q^{55} + 6 q^{57} - 55 q^{58} + 77 q^{59} - 6 q^{60} - 29 q^{61} - 46 q^{62} - 13 q^{63} + 24 q^{64} - 49 q^{65} + 35 q^{66} - 44 q^{67} - 45 q^{68} + 8 q^{69} + 4 q^{70} + 22 q^{71} - 6 q^{72} - 63 q^{73} - 16 q^{74} - 13 q^{75} - 46 q^{76} - 30 q^{77} - 17 q^{78} - 46 q^{79} - 14 q^{80} + 48 q^{81} - 75 q^{82} + 11 q^{83} + 38 q^{84} - q^{85} + 8 q^{86} - q^{87} - 116 q^{88} + 10 q^{89} - 20 q^{90} - 67 q^{91} - 64 q^{92} + 21 q^{93} - 16 q^{94} - 8 q^{95} + 3 q^{96} - 96 q^{97} - 46 q^{98} + 5 q^{99}+O(q^{100}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9 - 20 * q^10 + 5 * q^11 - 45 * q^12 - 8 * q^13 + 4 * q^14 - q^15 + 39 * q^16 - 48 * q^17 - q^18 - 6 * q^19 + 6 * q^20 + 13 * q^21 - 35 * q^22 - 8 * q^23 + 6 * q^24 + 13 * q^25 + 17 * q^26 - 48 * q^27 - 38 * q^28 + q^29 + 20 * q^30 - 21 * q^31 - 3 * q^32 - 5 * q^33 + q^34 + 19 * q^35 + 45 * q^36 - 58 * q^37 - 14 * q^38 + 8 * q^39 - 54 * q^40 - 3 * q^41 - 4 * q^42 - 33 * q^43 + 2 * q^44 + q^45 - 26 * q^46 + 9 * q^47 - 39 * q^48 + 11 * q^49 + 4 * q^50 + 48 * q^51 - 31 * q^52 - 33 * q^53 + q^54 - 21 * q^55 + 6 * q^57 - 55 * q^58 + 77 * q^59 - 6 * q^60 - 29 * q^61 - 46 * q^62 - 13 * q^63 + 24 * q^64 - 49 * q^65 + 35 * q^66 - 44 * q^67 - 45 * q^68 + 8 * q^69 + 4 * q^70 + 22 * q^71 - 6 * q^72 - 63 * q^73 - 16 * q^74 - 13 * q^75 - 46 * q^76 - 30 * q^77 - 17 * q^78 - 46 * q^79 - 14 * q^80 + 48 * q^81 - 75 * q^82 + 11 * q^83 + 38 * q^84 - q^85 + 8 * q^86 - q^87 - 116 * q^88 + 10 * q^89 - 20 * q^90 - 67 * q^91 - 64 * q^92 + 21 * q^93 - 16 * q^94 - 8 * q^95 + 3 * q^96 - 96 * q^97 - 46 * q^98 + 5 * 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 $

$2$	2.78887	1.97203	0.986013	−	0.166670i	$-0.0533015\pi$
$2$	2.78887	1.97203	0.986013	+	0.166670i	$0.0533015\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.77777	2.88888
$5$	−2.00554	−0.896905	−0.448453	−	0.893807i	$-0.648025\pi$
$5$	−2.00554	−0.896905	−0.448453	+	0.893807i	$0.648025\pi$
$6$	−2.78887	−1.13855
$7$	0.938230	0.354617	0.177309	−	0.984155i	$-0.443261\pi$
$7$	0.938230	0.354617	0.177309	+	0.984155i	$0.443261\pi$
$8$	10.5357	3.72493
$9$	1.00000	0.333333
$10$	−5.59318	−1.76872
$11$	−5.68987	−1.71556	−0.857780	−	0.514018i	$-0.828157\pi$
$11$	−5.68987	−1.71556	−0.857780	+	0.514018i	$0.828157\pi$
$12$	−5.77777	−1.66790
$13$	0.884003	0.245178	0.122589	−	0.992458i	$-0.460880\pi$
$13$	0.884003	0.245178	0.122589	+	0.992458i	$0.460880\pi$
$14$	2.61660	0.699315
$15$	2.00554	0.517829
$16$	17.8271	4.45677
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	2.78887	0.657342
$19$	−2.71161	−0.622086	−0.311043	−	0.950396i	$-0.600678\pi$
$19$	−2.71161	−0.622086	−0.311043	+	0.950396i	$0.600678\pi$
$20$	−11.5876	−2.59106
$21$	−0.938230	−0.204738
$22$	−15.8683	−3.38313
$23$	−5.54959	−1.15717	−0.578585	−	0.815622i	$-0.696395\pi$
$23$	−5.54959	−1.15717	−0.578585	+	0.815622i	$0.696395\pi$
$24$	−10.5357	−2.15059
$25$	−0.977804	−0.195561
$26$	2.46536	0.483498
$27$	−1.00000	−0.192450
$28$	5.42087	1.02445
$29$	−2.01589	−0.374341	−0.187170	−	0.982327i	$-0.559932\pi$
$29$	−2.01589	−0.374341	−0.187170	+	0.982327i	$0.559932\pi$
$30$	5.59318	1.02117
$31$	−8.73145	−1.56821	−0.784107	−	0.620625i	$-0.786879\pi$
$31$	−8.73145	−1.56821	−0.784107	+	0.620625i	$0.786879\pi$
$32$	28.6459	5.06393
$33$	5.68987	0.990479
$34$	−2.78887	−0.478286
$35$	−1.88166	−0.318058
$36$	5.77777	0.962961
$37$	−2.54729	−0.418771	−0.209386	−	0.977833i	$-0.567146\pi$
$37$	−2.54729	−0.418771	−0.209386	+	0.977833i	$0.567146\pi$
$38$	−7.56231	−1.22677
$39$	−0.884003	−0.141554
$40$	−21.1298	−3.34091
$41$	−0.0735028	−0.0114792	−0.00573960	−	0.999984i	$-0.501827\pi$
$41$	−0.0735028	−0.0114792	−0.00573960	+	0.999984i	$0.501827\pi$
$42$	−2.61660	−0.403750
$43$	−9.11491	−1.39001	−0.695005	−	0.719004i	$-0.744598\pi$
$43$	−9.11491	−1.39001	−0.695005	+	0.719004i	$0.744598\pi$
$44$	−32.8747	−4.95605
$45$	−2.00554	−0.298968
$46$	−15.4771	−2.28197
$47$	6.75641	0.985523	0.492762	−	0.870164i	$-0.335987\pi$
$47$	6.75641	0.985523	0.492762	+	0.870164i	$0.335987\pi$
$48$	−17.8271	−2.57312
$49$	−6.11973	−0.874246
$50$	−2.72696	−0.385651
$51$	1.00000	0.140028
$52$	5.10756	0.708292
$53$	−6.52204	−0.895871	−0.447936	−	0.894066i	$-0.647841\pi$
$53$	−6.52204	−0.895871	−0.447936	+	0.894066i	$0.647841\pi$
$54$	−2.78887	−0.379516
$55$	11.4113	1.53869
$56$	9.88489	1.32092
$57$	2.71161	0.359161
$58$	−5.62204	−0.738210
$59$	4.86184	0.632957	0.316479	−	0.948600i	$-0.397499\pi$
$59$	4.86184	0.632957	0.316479	+	0.948600i	$0.397499\pi$
$60$	11.5876	1.49595
$61$	5.04917	0.646480	0.323240	−	0.946317i	$-0.395228\pi$
$61$	5.04917	0.646480	0.323240	+	0.946317i	$0.395228\pi$
$62$	−24.3508	−3.09256
$63$	0.938230	0.118206
$64$	44.2355	5.52943
$65$	−1.77290	−0.219902
$66$	15.8683	1.95325
$67$	−4.00085	−0.488781	−0.244391	−	0.969677i	$-0.578588\pi$
$67$	−4.00085	−0.488781	−0.244391	+	0.969677i	$0.578588\pi$
$68$	−5.77777	−0.700657
$69$	5.54959	0.668092
$70$	−5.24769	−0.627219
$71$	13.2959	1.57793	0.788965	−	0.614438i	$-0.210617\pi$
$71$	13.2959	1.57793	0.788965	+	0.614438i	$0.210617\pi$
$72$	10.5357	1.24164
$73$	11.9510	1.39876	0.699379	−	0.714751i	$-0.253460\pi$
$73$	11.9510	1.39876	0.699379	+	0.714751i	$0.253460\pi$
$74$	−7.10404	−0.825828
$75$	0.977804	0.112907
$76$	−15.6670	−1.79713
$77$	−5.33840	−0.608367
$78$	−2.46536	−0.279148
$79$	−8.53302	−0.960039	−0.480020	−	0.877258i	$-0.659370\pi$
$79$	−8.53302	−0.960039	−0.480020	+	0.877258i	$0.659370\pi$
$80$	−35.7529	−3.99730
$81$	1.00000	0.111111
$82$	−0.204989	−0.0226373
$83$	3.13577	0.344196	0.172098	−	0.985080i	$-0.444945\pi$
$83$	3.13577	0.344196	0.172098	+	0.985080i	$0.444945\pi$
$84$	−5.42087	−0.591466
$85$	2.00554	0.217531
$86$	−25.4203	−2.74114
$87$	2.01589	0.216126
$88$	−59.9467	−6.39033
$89$	−9.82268	−1.04120	−0.520601	−	0.853800i	$-0.674292\pi$
$89$	−9.82268	−1.04120	−0.520601	+	0.853800i	$0.674292\pi$
$90$	−5.59318	−0.589573
$91$	0.829398	0.0869445
$92$	−32.0642	−3.34293
$93$	8.73145	0.905409
$94$	18.8427	1.94348
$95$	5.43824	0.557952
$96$	−28.6459	−2.92366
$97$	−8.29213	−0.841938	−0.420969	−	0.907075i	$-0.638310\pi$
$97$	−8.29213	−0.841938	−0.420969	+	0.907075i	$0.638310\pi$
$98$	−17.0671	−1.72404
$99$	−5.68987	−0.571853
$100$	−5.64953	−0.564953
$101$	6.21399	0.618316	0.309158	−	0.951011i	$-0.399953\pi$
$101$	6.21399	0.618316	0.309158	+	0.951011i	$0.399953\pi$
$102$	2.78887	0.276139
$103$	−0.886060	−0.0873061	−0.0436530	−	0.999047i	$-0.513900\pi$
$103$	−0.886060	−0.0873061	−0.0436530	+	0.999047i	$0.513900\pi$
$104$	9.31358	0.913271
$105$	1.88166	0.183631
$106$	−18.1891	−1.76668
$107$	18.0354	1.74355	0.871775	−	0.489907i	$-0.162969\pi$
$107$	18.0354	1.74355	0.871775	+	0.489907i	$0.162969\pi$
$108$	−5.77777	−0.555966
$109$	−7.83931	−0.750869	−0.375435	−	0.926849i	$-0.622507\pi$
$109$	−7.83931	−0.750869	−0.375435	+	0.926849i	$0.622507\pi$
$110$	31.8245	3.03434
$111$	2.54729	0.241778
$112$	16.7259	1.58045
$113$	−10.4815	−0.986020	−0.493010	−	0.870024i	$-0.664103\pi$
$113$	−10.4815	−0.986020	−0.493010	+	0.870024i	$0.664103\pi$
$114$	7.56231	0.708275
$115$	11.1299	1.03787
$116$	−11.6473	−1.08143
$117$	0.884003	0.0817261
$118$	13.5590	1.24821
$119$	−0.938230	−0.0860074
$120$	21.1298	1.92887
$121$	21.3746	1.94314
$122$	14.0814	1.27487
$123$	0.0735028	0.00662752
$124$	−50.4483	−4.53039
$125$	11.9887	1.07230
$126$	2.61660	0.233105
$127$	−2.15624	−0.191335	−0.0956676	−	0.995413i	$-0.530499\pi$
$127$	−2.15624	−0.191335	−0.0956676	+	0.995413i	$0.530499\pi$
$128$	66.0749	5.84025
$129$	9.11491	0.802523
$130$	−4.94439	−0.433652
$131$	0.296009	0.0258624	0.0129312	−	0.999916i	$-0.495884\pi$
$131$	0.296009	0.0258624	0.0129312	+	0.999916i	$0.495884\pi$
$132$	32.8747	2.86138
$133$	−2.54411	−0.220602
$134$	−11.1578	−0.963889
$135$	2.00554	0.172610
$136$	−10.5357	−0.903428
$137$	−16.2587	−1.38907	−0.694535	−	0.719459i	$-0.744390\pi$
$137$	−16.2587	−1.38907	−0.694535	+	0.719459i	$0.744390\pi$
$138$	15.4771	1.31749
$139$	−4.25297	−0.360732	−0.180366	−	0.983600i	$-0.557728\pi$
$139$	−4.25297	−0.360732	−0.180366	+	0.983600i	$0.557728\pi$
$140$	−10.8718	−0.918834
$141$	−6.75641	−0.568992
$142$	37.0804	3.11172
$143$	−5.02986	−0.420618
$144$	17.8271	1.48559
$145$	4.04295	0.335748
$146$	33.3297	2.75839
$147$	6.11973	0.504746
$148$	−14.7176	−1.20978
$149$	−0.706085	−0.0578447	−0.0289224	−	0.999582i	$-0.509208\pi$
$149$	−0.706085	−0.0578447	−0.0289224	+	0.999582i	$0.509208\pi$
$150$	2.72696	0.222656
$151$	−7.34120	−0.597418	−0.298709	−	0.954344i	$-0.596556\pi$
$151$	−7.34120	−0.597418	−0.298709	+	0.954344i	$0.596556\pi$
$152$	−28.5687	−2.31722
$153$	−1.00000	−0.0808452
$154$	−14.8881	−1.19972
$155$	17.5113	1.40654
$156$	−5.10756	−0.408932
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−23.7974	−1.89322
$159$	6.52204	0.517232
$160$	−57.4506	−4.54187
$161$	−5.20679	−0.410353
$162$	2.78887	0.219114
$163$	−12.9110	−1.01127	−0.505634	−	0.862748i	$-0.668741\pi$
$163$	−12.9110	−1.01127	−0.505634	+	0.862748i	$0.668741\pi$
$164$	−0.424682	−0.0331621
$165$	−11.4113	−0.888366
$166$	8.74524	0.678762
$167$	8.55471	0.661984	0.330992	−	0.943634i	$-0.392617\pi$
$167$	8.55471	0.661984	0.330992	+	0.943634i	$0.392617\pi$
$168$	−9.88489	−0.762636
$169$	−12.2185	−0.939888
$170$	5.59318	0.428978
$171$	−2.71161	−0.207362
$172$	−52.6639	−4.01558
$173$	8.36711	0.636139	0.318070	−	0.948067i	$-0.396965\pi$
$173$	8.36711	0.636139	0.318070	+	0.948067i	$0.396965\pi$
$174$	5.62204	0.426206
$175$	−0.917405	−0.0693493
$176$	−101.434	−7.64585
$177$	−4.86184	−0.365438
$178$	−27.3941	−2.05328
$179$	17.5766	1.31374	0.656868	−	0.754006i	$-0.271881\pi$
$179$	17.5766	1.31374	0.656868	+	0.754006i	$0.271881\pi$
$180$	−11.5876	−0.863685
$181$	−12.0620	−0.896565	−0.448282	−	0.893892i	$-0.647964\pi$
$181$	−12.0620	−0.896565	−0.448282	+	0.893892i	$0.647964\pi$
$182$	2.31308	0.171457
$183$	−5.04917	−0.373245
$184$	−58.4687	−4.31037
$185$	5.10869	0.375598
$186$	24.3508	1.78549
$187$	5.68987	0.416084
$188$	39.0369	2.84706
$189$	−0.938230	−0.0682462
$190$	15.1665	1.10030
$191$	1.26448	0.0914949	0.0457474	−	0.998953i	$-0.485433\pi$
$191$	1.26448	0.0914949	0.0457474	+	0.998953i	$0.485433\pi$
$192$	−44.2355	−3.19242
$193$	12.4851	0.898696	0.449348	−	0.893357i	$-0.351656\pi$
$193$	12.4851	0.898696	0.449348	+	0.893357i	$0.351656\pi$
$194$	−23.1256	−1.66032
$195$	1.77290	0.126960
$196$	−35.3584	−2.52560
$197$	−24.2350	−1.72667	−0.863335	−	0.504632i	$-0.831628\pi$
$197$	−24.2350	−1.72667	−0.863335	+	0.504632i	$0.831628\pi$
$198$	−15.8683	−1.12771
$199$	−19.0665	−1.35159	−0.675794	−	0.737091i	$-0.736199\pi$
$199$	−19.0665	−1.35159	−0.675794	+	0.737091i	$0.736199\pi$
$200$	−10.3018	−0.728450
$201$	4.00085	0.282198
$202$	17.3300	1.21933
$203$	−1.89137	−0.132748
$204$	5.77777	0.404525
$205$	0.147413	0.0102958
$206$	−2.47110	−0.172170
$207$	−5.54959	−0.385723
$208$	15.7592	1.09270
$209$	15.4287	1.06722
$210$	5.24769	0.362125
$211$	−19.2721	−1.32675	−0.663375	−	0.748287i	$-0.730876\pi$
$211$	−19.2721	−1.32675	−0.663375	+	0.748287i	$0.730876\pi$
$212$	−37.6828	−2.58807
$213$	−13.2959	−0.911018
$214$	50.2983	3.43832
$215$	18.2803	1.24671
$216$	−10.5357	−0.716863
$217$	−8.19211	−0.556116
$218$	−21.8628	−1.48073
$219$	−11.9510	−0.807574
$220$	65.9316	4.44511
$221$	−0.884003	−0.0594645
$222$	7.10404	0.476792
$223$	10.6893	0.715811	0.357906	−	0.933758i	$-0.383491\pi$
$223$	10.6893	0.715811	0.357906	+	0.933758i	$0.383491\pi$
$224$	26.8765	1.79576
$225$	−0.977804	−0.0651869
$226$	−29.2316	−1.94446
$227$	22.9635	1.52414	0.762071	−	0.647494i	$-0.224183\pi$
$227$	22.9635	1.52414	0.762071	+	0.647494i	$0.224183\pi$
$228$	15.6670	1.03758
$229$	−14.5969	−0.964587	−0.482294	−	0.876010i	$-0.660196\pi$
$229$	−14.5969	−0.964587	−0.482294	+	0.876010i	$0.660196\pi$
$230$	31.0399	2.04671
$231$	5.33840	0.351241
$232$	−21.2388	−1.39439
$233$	−3.28987	−0.215527	−0.107763	−	0.994177i	$-0.534369\pi$
$233$	−3.28987	−0.215527	−0.107763	+	0.994177i	$0.534369\pi$
$234$	2.46536	0.161166
$235$	−13.5503	−0.883921
$236$	28.0906	1.82854
$237$	8.53302	0.554279
$238$	−2.61660	−0.169609
$239$	25.3732	1.64126	0.820628	−	0.571463i	$-0.193624\pi$
$239$	25.3732	1.64126	0.820628	+	0.571463i	$0.193624\pi$
$240$	35.7529	2.30784
$241$	−20.3604	−1.31153	−0.655765	−	0.754965i	$-0.727654\pi$
$241$	−20.3604	−1.31153	−0.655765	+	0.754965i	$0.727654\pi$
$242$	59.6108	3.83193
$243$	−1.00000	−0.0641500
$244$	29.1729	1.86760
$245$	12.2734	0.784116
$246$	0.204989	0.0130696
$247$	−2.39707	−0.152522
$248$	−91.9918	−5.84149
$249$	−3.13577	−0.198721
$250$	33.4350	2.11461
$251$	22.3281	1.40934	0.704669	−	0.709536i	$-0.251095\pi$
$251$	22.3281	1.40934	0.704669	+	0.709536i	$0.251095\pi$
$252$	5.42087	0.341483
$253$	31.5764	1.98519
$254$	−6.01346	−0.377318
$255$	−2.00554	−0.125592
$256$	95.8031	5.98769
$257$	−22.6630	−1.41368	−0.706839	−	0.707374i	$-0.749879\pi$
$257$	−22.6630	−1.41368	−0.706839	+	0.707374i	$0.749879\pi$
$258$	25.4203	1.58260
$259$	−2.38994	−0.148504
$260$	−10.2434	−0.635271
$261$	−2.01589	−0.124780
$262$	0.825529	0.0510013
$263$	−29.3086	−1.80725	−0.903623	−	0.428328i	$-0.859103\pi$
$263$	−29.3086	−1.80725	−0.903623	+	0.428328i	$0.859103\pi$
$264$	59.9467	3.68946
$265$	13.0802	0.803512
$266$	−7.09518	−0.435034
$267$	9.82268	0.601138
$268$	−23.1160	−1.41203
$269$	6.06184	0.369597	0.184798	−	0.982776i	$-0.440837\pi$
$269$	6.06184	0.369597	0.184798	+	0.982776i	$0.440837\pi$
$270$	5.59318	0.340390
$271$	15.8326	0.961760	0.480880	−	0.876787i	$-0.340317\pi$
$271$	15.8326	0.961760	0.480880	+	0.876787i	$0.340317\pi$
$272$	−17.8271	−1.08093
$273$	−0.829398	−0.0501974
$274$	−45.3432	−2.73928
$275$	5.56357	0.335496
$276$	32.0642	1.93004
$277$	−4.68921	−0.281747	−0.140874	−	0.990028i	$-0.544991\pi$
$277$	−4.68921	−0.281747	−0.140874	+	0.990028i	$0.544991\pi$
$278$	−11.8610	−0.711373
$279$	−8.73145	−0.522738
$280$	−19.8246	−1.18474
$281$	−16.1476	−0.963288	−0.481644	−	0.876367i	$-0.659960\pi$
$281$	−16.1476	−0.963288	−0.481644	+	0.876367i	$0.659960\pi$
$282$	−18.8427	−1.12207
$283$	27.1922	1.61641	0.808205	−	0.588901i	$-0.200439\pi$
$283$	27.1922	1.61641	0.808205	+	0.588901i	$0.200439\pi$
$284$	76.8205	4.55846
$285$	−5.43824	−0.322134
$286$	−14.0276	−0.829469
$287$	−0.0689625	−0.00407073
$288$	28.6459	1.68798
$289$	1.00000	0.0588235
$290$	11.2752	0.662104
$291$	8.29213	0.486093
$292$	69.0501	4.04085
$293$	−4.54065	−0.265268	−0.132634	−	0.991165i	$-0.542343\pi$
$293$	−4.54065	−0.265268	−0.132634	+	0.991165i	$0.542343\pi$
$294$	17.0671	0.995373
$295$	−9.75061	−0.567703
$296$	−26.8374	−1.55989
$297$	5.68987	0.330160
$298$	−1.96918	−0.114071
$299$	−4.90585	−0.283713
$300$	5.64953	0.326175
$301$	−8.55188	−0.492922
$302$	−20.4736	−1.17812
$303$	−6.21399	−0.356985
$304$	−48.3400	−2.77249
$305$	−10.1263	−0.579831
$306$	−2.78887	−0.159429
$307$	5.71063	0.325923	0.162961	−	0.986632i	$-0.447895\pi$
$307$	5.71063	0.325923	0.162961	+	0.986632i	$0.447895\pi$
$308$	−30.8440	−1.75750
$309$	0.886060	0.0504062
$310$	48.8366	2.77373
$311$	−21.9814	−1.24645	−0.623227	−	0.782041i	$-0.714179\pi$
$311$	−21.9814	−1.24645	−0.623227	+	0.782041i	$0.714179\pi$
$312$	−9.31358	−0.527278
$313$	−15.8885	−0.898073	−0.449037	−	0.893513i	$-0.648233\pi$
$313$	−15.8885	−0.898073	−0.449037	+	0.893513i	$0.648233\pi$
$314$	−2.78887	−0.157385
$315$	−1.88166	−0.106019
$316$	−49.3018	−2.77344
$317$	29.9059	1.67968	0.839841	−	0.542833i	$-0.182648\pi$
$317$	29.9059	1.67968	0.839841	+	0.542833i	$0.182648\pi$
$318$	18.1891	1.01999
$319$	11.4701	0.642204
$320$	−88.7161	−4.95938
$321$	−18.0354	−1.00664
$322$	−14.5210	−0.809226
$323$	2.71161	0.150878
$324$	5.77777	0.320987
$325$	−0.864382	−0.0479473
$326$	−36.0070	−1.99425
$327$	7.83931	0.433515
$328$	−0.774403	−0.0427592
$329$	6.33906	0.349484
$330$	−31.8245	−1.75188
$331$	10.0149	0.550469	0.275235	−	0.961377i	$-0.411244\pi$
$331$	10.0149	0.550469	0.275235	+	0.961377i	$0.411244\pi$
$332$	18.1178	0.994341
$333$	−2.54729	−0.139590
$334$	23.8579	1.30545
$335$	8.02386	0.438390
$336$	−16.7259	−0.912472
$337$	5.69196	0.310061	0.155030	−	0.987910i	$-0.450452\pi$
$337$	5.69196	0.310061	0.155030	+	0.987910i	$0.450452\pi$
$338$	−34.0759	−1.85348
$339$	10.4815	0.569279
$340$	11.5876	0.628423
$341$	49.6808	2.69037
$342$	−7.56231	−0.408923
$343$	−12.3093	−0.664641
$344$	−96.0319	−5.17769
$345$	−11.1299	−0.599215
$346$	23.3347	1.25448
$347$	17.8930	0.960549	0.480274	−	0.877118i	$-0.340537\pi$
$347$	17.8930	0.960549	0.480274	+	0.877118i	$0.340537\pi$
$348$	11.6473	0.624363
$349$	6.00639	0.321515	0.160757	−	0.986994i	$-0.448606\pi$
$349$	6.00639	0.321515	0.160757	+	0.986994i	$0.448606\pi$
$350$	−2.55852	−0.136759
$351$	−0.884003	−0.0471846
$352$	−162.991	−8.68748
$353$	1.82292	0.0970241	0.0485121	−	0.998823i	$-0.484552\pi$
$353$	1.82292	0.0970241	0.0485121	+	0.998823i	$0.484552\pi$
$354$	−13.5590	−0.720653
$355$	−26.6654	−1.41525
$356$	−56.7532	−3.00791
$357$	0.938230	0.0496564
$358$	49.0187	2.59072
$359$	−4.99403	−0.263575	−0.131788	−	0.991278i	$-0.542072\pi$
$359$	−4.99403	−0.263575	−0.131788	+	0.991278i	$0.542072\pi$
$360$	−21.1298	−1.11364
$361$	−11.6472	−0.613010
$362$	−33.6394	−1.76805
$363$	−21.3746	−1.12187
$364$	4.79207	0.251173
$365$	−23.9682	−1.25455
$366$	−14.0814	−0.736049
$367$	1.96232	0.102432	0.0512162	−	0.998688i	$-0.483690\pi$
$367$	1.96232	0.102432	0.0512162	+	0.998688i	$0.483690\pi$
$368$	−98.9330	−5.15724
$369$	−0.0735028	−0.00382640
$370$	14.2474	0.740689
$371$	−6.11917	−0.317692
$372$	50.4483	2.61562
$373$	−23.2455	−1.20361	−0.601804	−	0.798644i	$-0.705551\pi$
$373$	−23.2455	−1.20361	−0.601804	+	0.798644i	$0.705551\pi$
$374$	15.8683	0.820529
$375$	−11.9887	−0.619096
$376$	71.1834	3.67100
$377$	−1.78205	−0.0917803
$378$	−2.61660	−0.134583
$379$	18.1998	0.934860	0.467430	−	0.884030i	$-0.345180\pi$
$379$	18.1998	0.934860	0.467430	+	0.884030i	$0.345180\pi$
$380$	31.4209	1.61186
$381$	2.15624	0.110467
$382$	3.52648	0.180430
$383$	−22.7595	−1.16296	−0.581478	−	0.813562i	$-0.697525\pi$
$383$	−22.7595	−1.16296	−0.581478	+	0.813562i	$0.697525\pi$
$384$	−66.0749	−3.37187
$385$	10.7064	0.545648
$386$	34.8192	1.77225
$387$	−9.11491	−0.463337
$388$	−47.9100	−2.43226
$389$	24.9987	1.26748	0.633742	−	0.773545i	$-0.281518\pi$
$389$	24.9987	1.26748	0.633742	+	0.773545i	$0.281518\pi$
$390$	4.94439	0.250369
$391$	5.54959	0.280655
$392$	−64.4755	−3.25650
$393$	−0.296009	−0.0149317
$394$	−67.5880	−3.40504
$395$	17.1133	0.861064
$396$	−32.8747	−1.65202
$397$	22.5186	1.13018	0.565089	−	0.825030i	$-0.308842\pi$
$397$	22.5186	1.13018	0.565089	+	0.825030i	$0.308842\pi$
$398$	−53.1739	−2.66537
$399$	2.54411	0.127365
$400$	−17.4314	−0.871569
$401$	−4.59371	−0.229399	−0.114699	−	0.993400i	$-0.536591\pi$
$401$	−4.59371	−0.229399	−0.114699	+	0.993400i	$0.536591\pi$
$402$	11.1578	0.556501
$403$	−7.71863	−0.384492
$404$	35.9030	1.78624
$405$	−2.00554	−0.0996561
$406$	−5.27476	−0.261782
$407$	14.4937	0.718427
$408$	10.5357	0.521594
$409$	6.36177	0.314569	0.157285	−	0.987553i	$-0.449726\pi$
$409$	6.36177	0.314569	0.157285	+	0.987553i	$0.449726\pi$
$410$	0.411115	0.0203035
$411$	16.2587	0.801980
$412$	−5.11945	−0.252217
$413$	4.56152	0.224458
$414$	−15.4771	−0.760656
$415$	−6.28892	−0.308711
$416$	25.3231	1.24157
$417$	4.25297	0.208269
$418$	43.0285	2.10459
$419$	21.9054	1.07015	0.535074	−	0.844805i	$-0.320284\pi$
$419$	21.9054	1.07015	0.535074	+	0.844805i	$0.320284\pi$
$420$	10.8718	0.530489
$421$	−17.4055	−0.848290	−0.424145	−	0.905594i	$-0.639425\pi$
$421$	−17.4055	−0.848290	−0.424145	+	0.905594i	$0.639425\pi$
$422$	−53.7474	−2.61638
$423$	6.75641	0.328508
$424$	−68.7142	−3.33706
$425$	0.977804	0.0474305
$426$	−37.0804	−1.79655
$427$	4.73728	0.229253
$428$	104.204	5.03691
$429$	5.02986	0.242844
$430$	50.9814	2.45854
$431$	6.62138	0.318940	0.159470	−	0.987203i	$-0.449021\pi$
$431$	6.62138	0.318940	0.159470	+	0.987203i	$0.449021\pi$
$432$	−17.8271	−0.857705
$433$	−13.8039	−0.663373	−0.331686	−	0.943390i	$-0.607618\pi$
$433$	−13.8039	−0.663373	−0.331686	+	0.943390i	$0.607618\pi$
$434$	−22.8467	−1.09668
$435$	−4.04295	−0.193844
$436$	−45.2937	−2.16918
$437$	15.0483	0.719858
$438$	−33.3297	−1.59256
$439$	37.4976	1.78967	0.894833	−	0.446402i	$-0.147295\pi$
$439$	37.4976	1.78967	0.894833	+	0.446402i	$0.147295\pi$
$440$	120.225	5.73153
$441$	−6.11973	−0.291415
$442$	−2.46536	−0.117265
$443$	33.8075	1.60624	0.803121	−	0.595816i	$-0.203171\pi$
$443$	33.8075	1.60624	0.803121	+	0.595816i	$0.203171\pi$
$444$	14.7176	0.698468
$445$	19.6998	0.933860
$446$	29.8111	1.41160
$447$	0.706085	0.0333967
$448$	41.5030	1.96083
$449$	−27.7681	−1.31046	−0.655229	−	0.755430i	$-0.727428\pi$
$449$	−27.7681	−1.31046	−0.655229	+	0.755430i	$0.727428\pi$
$450$	−2.72696	−0.128550
$451$	0.418221	0.0196933
$452$	−60.5599	−2.84850
$453$	7.34120	0.344919
$454$	64.0421	3.00565
$455$	−1.66339	−0.0779810
$456$	28.5687	1.33785
$457$	−10.7153	−0.501241	−0.250620	−	0.968085i	$-0.580635\pi$
$457$	−10.7153	−0.501241	−0.250620	+	0.968085i	$0.580635\pi$
$458$	−40.7087	−1.90219
$459$	1.00000	0.0466760
$460$	64.3062	2.99829
$461$	2.41294	0.112382	0.0561909	−	0.998420i	$-0.482104\pi$
$461$	2.41294	0.112382	0.0561909	+	0.998420i	$0.482104\pi$
$462$	14.8881	0.692656
$463$	−9.50331	−0.441656	−0.220828	−	0.975313i	$-0.570876\pi$
$463$	−9.50331	−0.441656	−0.220828	+	0.975313i	$0.570876\pi$
$464$	−35.9374	−1.66835
$465$	−17.5113	−0.812066
$466$	−9.17501	−0.425024
$467$	13.1964	0.610654	0.305327	−	0.952248i	$-0.401234\pi$
$467$	13.1964	0.610654	0.305327	+	0.952248i	$0.401234\pi$
$468$	5.10756	0.236097
$469$	−3.75371	−0.173330
$470$	−37.7898	−1.74311
$471$	1.00000	0.0460776
$472$	51.2228	2.35772
$473$	51.8626	2.38465
$474$	23.7974	1.09305
$475$	2.65142	0.121656
$476$	−5.42087	−0.248465
$477$	−6.52204	−0.298624
$478$	70.7625	3.23660
$479$	−3.19467	−0.145968	−0.0729842	−	0.997333i	$-0.523252\pi$
$479$	−3.19467	−0.145968	−0.0729842	+	0.997333i	$0.523252\pi$
$480$	57.4506	2.62225
$481$	−2.25181	−0.102674
$482$	−56.7825	−2.58637
$483$	5.20679	0.236917
$484$	123.497	5.61352
$485$	16.6302	0.755139
$486$	−2.78887	−0.126505
$487$	−34.6541	−1.57033	−0.785163	−	0.619289i	$-0.787421\pi$
$487$	−34.6541	−1.57033	−0.785163	+	0.619289i	$0.787421\pi$
$488$	53.1964	2.40809
$489$	12.9110	0.583856
$490$	34.2288	1.54630
$491$	10.6240	0.479455	0.239728	−	0.970840i	$-0.422942\pi$
$491$	10.6240	0.479455	0.239728	+	0.970840i	$0.422942\pi$
$492$	0.424682	0.0191462
$493$	2.01589	0.0907910
$494$	−6.68510	−0.300777
$495$	11.4113	0.512898
$496$	−155.656	−6.98917
$497$	12.4746	0.559562
$498$	−8.74524	−0.391884
$499$	−16.3321	−0.731126	−0.365563	−	0.930787i	$-0.619124\pi$
$499$	−16.3321	−0.731126	−0.365563	+	0.930787i	$0.619124\pi$
$500$	69.2681	3.09776
$501$	−8.55471	−0.382196
$502$	62.2701	2.77925
$503$	38.8392	1.73175	0.865876	−	0.500258i	$-0.166762\pi$
$503$	38.8392	1.73175	0.865876	+	0.500258i	$0.166762\pi$
$504$	9.88489	0.440308
$505$	−12.4624	−0.554570
$506$	88.0624	3.91485
$507$	12.2185	0.542644
$508$	−12.4582	−0.552745
$509$	−6.19319	−0.274508	−0.137254	−	0.990536i	$-0.543828\pi$
$509$	−6.19319	−0.274508	−0.137254	+	0.990536i	$0.543828\pi$
$510$	−5.59318	−0.247670
$511$	11.2128	0.496024
$512$	135.032	5.96763
$513$	2.71161	0.119720
$514$	−63.2040	−2.78781
$515$	1.77703	0.0783053
$516$	52.6639	2.31840
$517$	−38.4430	−1.69072
$518$	−6.66522	−0.292853
$519$	−8.36711	−0.367275
$520$	−18.6788	−0.819118
$521$	42.3152	1.85386	0.926932	−	0.375230i	$-0.122436\pi$
$521$	42.3152	1.85386	0.926932	+	0.375230i	$0.122436\pi$
$522$	−5.62204	−0.246070
$523$	44.6336	1.95169	0.975845	−	0.218464i	$-0.0701047\pi$
$523$	44.6336	1.95169	0.975845	+	0.218464i	$0.0701047\pi$
$524$	1.71027	0.0747135
$525$	0.917405	0.0400388
$526$	−81.7378	−3.56394
$527$	8.73145	0.380348
$528$	101.434	4.41433
$529$	7.79795	0.339041
$530$	36.4790	1.58455
$531$	4.86184	0.210986
$532$	−14.6993	−0.637295
$533$	−0.0649767	−0.00281445
$534$	27.3941	1.18546
$535$	−36.1708	−1.56380
$536$	−42.1517	−1.82067
$537$	−17.5766	−0.758485
$538$	16.9056	0.728854
$539$	34.8204	1.49982
$540$	11.5876	0.498649
$541$	−8.83809	−0.379979	−0.189990	−	0.981786i	$-0.560845\pi$
$541$	−8.83809	−0.379979	−0.189990	+	0.981786i	$0.560845\pi$
$542$	44.1549	1.89661
$543$	12.0620	0.517632
$544$	−28.6459	−1.22818
$545$	15.7221	0.673459
$546$	−2.31308	−0.0989906
$547$	15.5898	0.666571	0.333285	−	0.942826i	$-0.391843\pi$
$547$	15.5898	0.666571	0.333285	+	0.942826i	$0.391843\pi$
$548$	−93.9388	−4.01286
$549$	5.04917	0.215493
$550$	15.5161	0.661607
$551$	5.46630	0.232872
$552$	58.4687	2.48860
$553$	−8.00593	−0.340447
$554$	−13.0776	−0.555612
$555$	−5.10869	−0.216852
$556$	−24.5727	−1.04211
$557$	−26.0451	−1.10357	−0.551784	−	0.833987i	$-0.686053\pi$
$557$	−26.0451	−1.10357	−0.551784	+	0.833987i	$0.686053\pi$
$558$	−24.3508	−1.03085
$559$	−8.05761	−0.340801
$560$	−33.5445	−1.41751
$561$	−5.68987	−0.240226
$562$	−45.0336	−1.89963
$563$	−15.0479	−0.634195	−0.317098	−	0.948393i	$-0.602708\pi$
$563$	−15.0479	−0.634195	−0.317098	+	0.948393i	$0.602708\pi$
$564$	−39.0369	−1.64375
$565$	21.0212	0.884367
$566$	75.8354	3.18760
$567$	0.938230	0.0394019
$568$	140.081	5.87768
$569$	−24.9562	−1.04622	−0.523109	−	0.852266i	$-0.675228\pi$
$569$	−24.9562	−1.04622	−0.523109	+	0.852266i	$0.675228\pi$
$570$	−15.1665	−0.635256
$571$	−12.0208	−0.503056	−0.251528	−	0.967850i	$-0.580933\pi$
$571$	−12.0208	−0.503056	−0.251528	+	0.967850i	$0.580933\pi$
$572$	−29.0614	−1.21512
$573$	−1.26448	−0.0528246
$574$	−0.192327	−0.00802758
$575$	5.42641	0.226297
$576$	44.2355	1.84314
$577$	−10.1479	−0.422464	−0.211232	−	0.977436i	$-0.567748\pi$
$577$	−10.1479	−0.422464	−0.211232	+	0.977436i	$0.567748\pi$
$578$	2.78887	0.116001
$579$	−12.4851	−0.518862
$580$	23.3592	0.969938
$581$	2.94207	0.122058
$582$	23.1256	0.958588
$583$	37.1095	1.53692
$584$	125.912	5.21028
$585$	−1.77290	−0.0733006
$586$	−12.6633	−0.523115
$587$	−4.30570	−0.177715	−0.0888577	−	0.996044i	$-0.528322\pi$
$587$	−4.30570	−0.177715	−0.0888577	+	0.996044i	$0.528322\pi$
$588$	35.3584	1.45815
$589$	23.6763	0.975564
$590$	−27.1931	−1.11952
$591$	24.2350	0.996893
$592$	−45.4107	−1.86637
$593$	1.35234	0.0555340	0.0277670	−	0.999614i	$-0.491160\pi$
$593$	1.35234	0.0555340	0.0277670	+	0.999614i	$0.491160\pi$
$594$	15.8683	0.651083
$595$	1.88166	0.0771405
$596$	−4.07959	−0.167107
$597$	19.0665	0.780340
$598$	−13.6818	−0.559489
$599$	−21.2709	−0.869107	−0.434554	−	0.900646i	$-0.643094\pi$
$599$	−21.2709	−0.869107	−0.434554	+	0.900646i	$0.643094\pi$
$600$	10.3018	0.420571
$601$	−30.1489	−1.22980	−0.614899	−	0.788606i	$-0.710803\pi$
$601$	−30.1489	−1.22980	−0.614899	+	0.788606i	$0.710803\pi$
$602$	−23.8500	−0.972055
$603$	−4.00085	−0.162927
$604$	−42.4157	−1.72587
$605$	−42.8676	−1.74282
$606$	−17.3300	−0.703983
$607$	−40.4498	−1.64181	−0.820904	−	0.571066i	$-0.806530\pi$
$607$	−40.4498	−1.64181	−0.820904	+	0.571066i	$0.806530\pi$
$608$	−77.6765	−3.15020
$609$	1.89137	0.0766420
$610$	−28.2409	−1.14344
$611$	5.97268	0.241629
$612$	−5.77777	−0.233552
$613$	30.4405	1.22948	0.614740	−	0.788730i	$-0.289261\pi$
$613$	30.4405	1.22948	0.614740	+	0.788730i	$0.289261\pi$
$614$	15.9262	0.642728
$615$	−0.147413	−0.00594426
$616$	−56.2437	−2.26612
$617$	16.1377	0.649679	0.324839	−	0.945769i	$-0.394690\pi$
$617$	16.1377	0.649679	0.324839	+	0.945769i	$0.394690\pi$
$618$	2.47110	0.0994023
$619$	8.19642	0.329442	0.164721	−	0.986340i	$-0.447328\pi$
$619$	8.19642	0.329442	0.164721	+	0.986340i	$0.447328\pi$
$620$	101.176	4.06333
$621$	5.54959	0.222697
$622$	−61.3033	−2.45804
$623$	−9.21593	−0.369228
$624$	−15.7592	−0.630872
$625$	−19.1549	−0.766195
$626$	−44.3110	−1.77102
$627$	−15.4287	−0.616162
$628$	−5.77777	−0.230558
$629$	2.54729	0.101567
$630$	−5.24769	−0.209073
$631$	26.5909	1.05857	0.529284	−	0.848445i	$-0.322461\pi$
$631$	26.5909	1.05857	0.529284	+	0.848445i	$0.322461\pi$
$632$	−89.9012	−3.57608
$633$	19.2721	0.765999
$634$	83.4035	3.31238
$635$	4.32442	0.171610
$636$	37.6828	1.49422
$637$	−5.40985	−0.214346
$638$	31.9887	1.26644
$639$	13.2959	0.525977
$640$	−132.516	−5.23816
$641$	45.5788	1.80025	0.900127	−	0.435628i	$-0.143474\pi$
$641$	45.5788	1.80025	0.900127	+	0.435628i	$0.143474\pi$
$642$	−50.2983	−1.98512
$643$	37.0813	1.46234	0.731171	−	0.682194i	$-0.238974\pi$
$643$	37.0813	1.46234	0.731171	+	0.682194i	$0.238974\pi$
$644$	−30.0836	−1.18546
$645$	−18.2803	−0.719787
$646$	7.56231	0.297535
$647$	4.44752	0.174850	0.0874251	−	0.996171i	$-0.472136\pi$
$647$	4.44752	0.174850	0.0874251	+	0.996171i	$0.472136\pi$
$648$	10.5357	0.413881
$649$	−27.6632	−1.08588
$650$	−2.41064	−0.0945532
$651$	8.19211	0.321074
$652$	−74.5968	−2.92144
$653$	17.6054	0.688951	0.344475	−	0.938795i	$-0.388057\pi$
$653$	17.6054	0.688951	0.344475	+	0.938795i	$0.388057\pi$
$654$	21.8628	0.854902
$655$	−0.593658	−0.0231961
$656$	−1.31034	−0.0511602
$657$	11.9510	0.466253
$658$	17.6788	0.689191
$659$	2.98395	0.116238	0.0581192	−	0.998310i	$-0.481490\pi$
$659$	2.98395	0.116238	0.0581192	+	0.998310i	$0.481490\pi$
$660$	−65.9316	−2.56639
$661$	−40.4272	−1.57243	−0.786217	−	0.617951i	$-0.787963\pi$
$661$	−40.4272	−1.57243	−0.786217	+	0.617951i	$0.787963\pi$
$662$	27.9302	1.08554
$663$	0.884003	0.0343318
$664$	33.0375	1.28210
$665$	5.10232	0.197859
$666$	−7.10404	−0.275276
$667$	11.1874	0.433176
$668$	49.4271	1.91239
$669$	−10.6893	−0.413274
$670$	22.3775	0.864517
$671$	−28.7291	−1.10907
$672$	−26.8765	−1.03678
$673$	46.3881	1.78813	0.894066	−	0.447936i	$-0.147841\pi$
$673$	46.3881	1.78813	0.894066	+	0.447936i	$0.147841\pi$
$674$	15.8741	0.611448
$675$	0.977804	0.0376357
$676$	−70.5959	−2.71523
$677$	−6.82054	−0.262135	−0.131067	−	0.991373i	$-0.541840\pi$
$677$	−6.82054	−0.262135	−0.131067	+	0.991373i	$0.541840\pi$
$678$	29.2316	1.12263
$679$	−7.77992	−0.298566
$680$	21.1298	0.810289
$681$	−22.9635	−0.879964
$682$	138.553	5.30547
$683$	−5.98157	−0.228879	−0.114439	−	0.993430i	$-0.536507\pi$
$683$	−5.98157	−0.228879	−0.114439	+	0.993430i	$0.536507\pi$
$684$	−15.6670	−0.599044
$685$	32.6074	1.24587
$686$	−34.3290	−1.31069
$687$	14.5969	0.556905
$688$	−162.492	−6.19496
$689$	−5.76550	−0.219648
$690$	−31.0399	−1.18167
$691$	−20.4733	−0.778842	−0.389421	−	0.921060i	$-0.627325\pi$
$691$	−20.4733	−0.778842	−0.389421	+	0.921060i	$0.627325\pi$
$692$	48.3432	1.83773
$693$	−5.33840	−0.202789
$694$	49.9013	1.89423
$695$	8.52951	0.323543
$696$	21.2388	0.805053
$697$	0.0735028	0.00278412
$698$	16.7510	0.634035
$699$	3.28987	0.124434
$700$	−5.30055	−0.200342
$701$	8.21987	0.310460	0.155230	−	0.987878i	$-0.450388\pi$
$701$	8.21987	0.310460	0.155230	+	0.987878i	$0.450388\pi$
$702$	−2.46536	−0.0930492
$703$	6.90724	0.260512
$704$	−251.694	−9.48607
$705$	13.5503	0.510332
$706$	5.08387	0.191334
$707$	5.83015	0.219265
$708$	−28.0906	−1.05571
$709$	5.10933	0.191885	0.0959424	−	0.995387i	$-0.469414\pi$
$709$	5.10933	0.191885	0.0959424	+	0.995387i	$0.469414\pi$
$710$	−74.3663	−2.79092
$711$	−8.53302	−0.320013
$712$	−103.489	−3.87840
$713$	48.4560	1.81469
$714$	2.61660	0.0979236
$715$	10.0876	0.377254
$716$	101.553	3.79523
$717$	−25.3732	−0.947580
$718$	−13.9277	−0.519777
$719$	−52.6042	−1.96180	−0.980902	−	0.194503i	$-0.937691\pi$
$719$	−52.6042	−1.96180	−0.980902	+	0.194503i	$0.937691\pi$
$720$	−35.7529	−1.33243
$721$	−0.831328	−0.0309603
$722$	−32.4824	−1.20887
$723$	20.3604	0.757212
$724$	−69.6917	−2.59007
$725$	1.97114	0.0732064
$726$	−59.6108	−2.21236
$727$	−1.08047	−0.0400726	−0.0200363	−	0.999799i	$-0.506378\pi$
$727$	−1.08047	−0.0400726	−0.0200363	+	0.999799i	$0.506378\pi$
$728$	8.73828	0.323862
$729$	1.00000	0.0370370
$730$	−66.8442	−2.47401
$731$	9.11491	0.337127
$732$	−29.1729	−1.07826
$733$	15.7632	0.582229	0.291114	−	0.956688i	$-0.405974\pi$
$733$	15.7632	0.582229	0.291114	+	0.956688i	$0.405974\pi$
$734$	5.47265	0.201999
$735$	−12.2734	−0.452710
$736$	−158.973	−5.85983
$737$	22.7643	0.838533
$738$	−0.204989	−0.00754576
$739$	−38.2517	−1.40711	−0.703556	−	0.710640i	$-0.748406\pi$
$739$	−38.2517	−1.40711	−0.703556	+	0.710640i	$0.748406\pi$
$740$	29.5168	1.08506
$741$	2.39707	0.0880585
$742$	−17.0655	−0.626496
$743$	−22.1121	−0.811215	−0.405607	−	0.914047i	$-0.632940\pi$
$743$	−22.1121	−0.811215	−0.405607	+	0.914047i	$0.632940\pi$
$744$	91.9918	3.37258
$745$	1.41608	0.0518812
$746$	−64.8287	−2.37355
$747$	3.13577	0.114732
$748$	32.8747	1.20202
$749$	16.9214	0.618293
$750$	−33.4350	−1.22087
$751$	48.0731	1.75421	0.877106	−	0.480297i	$-0.159471\pi$
$751$	48.0731	1.75421	0.877106	+	0.480297i	$0.159471\pi$
$752$	120.447	4.39225
$753$	−22.3281	−0.813682
$754$	−4.96990	−0.180993
$755$	14.7231	0.535827
$756$	−5.42087	−0.197155
$757$	−16.0190	−0.582219	−0.291109	−	0.956690i	$-0.594024\pi$
$757$	−16.0190	−0.582219	−0.291109	+	0.956690i	$0.594024\pi$
$758$	50.7567	1.84357
$759$	−31.5764	−1.14615
$760$	57.2956	2.07833
$761$	−18.7214	−0.678652	−0.339326	−	0.940669i	$-0.610199\pi$
$761$	−18.7214	−0.678652	−0.339326	+	0.940669i	$0.610199\pi$
$762$	6.01346	0.217845
$763$	−7.35507	−0.266271
$764$	7.30590	0.264318
$765$	2.00554	0.0725105
$766$	−63.4731	−2.29338
$767$	4.29788	0.155187
$768$	−95.8031	−3.45700
$769$	5.48298	0.197721	0.0988607	−	0.995101i	$-0.468480\pi$
$769$	5.48298	0.197721	0.0988607	+	0.995101i	$0.468480\pi$
$770$	29.8587	1.07603
$771$	22.6630	0.816187
$772$	72.1359	2.59623
$773$	28.4559	1.02349	0.511744	−	0.859138i	$-0.329000\pi$
$773$	28.4559	1.02349	0.511744	+	0.859138i	$0.329000\pi$
$774$	−25.4203	−0.913712
$775$	8.53765	0.306681
$776$	−87.3633	−3.13616
$777$	2.38994	0.0857386
$778$	69.7180	2.49951
$779$	0.199311	0.00714105
$780$	10.2434	0.366774
$781$	−75.6518	−2.70703
$782$	15.4771	0.553459
$783$	2.01589	0.0720420
$784$	−109.097	−3.89631
$785$	2.00554	0.0715808
$786$	−0.825529	−0.0294456
$787$	−37.9070	−1.35124	−0.675620	−	0.737250i	$-0.736124\pi$
$787$	−37.9070	−1.35124	−0.675620	+	0.737250i	$0.736124\pi$
$788$	−140.024	−4.98815
$789$	29.3086	1.04341
$790$	47.7267	1.69804
$791$	−9.83409	−0.349660
$792$	−59.9467	−2.13011
$793$	4.46348	0.158503
$794$	62.8014	2.22874
$795$	−13.0802	−0.463908
$796$	−110.162	−3.90458
$797$	−45.2388	−1.60244	−0.801220	−	0.598370i	$-0.795815\pi$
$797$	−45.2388	−1.60244	−0.801220	+	0.598370i	$0.795815\pi$
$798$	7.09518	0.251167
$799$	−6.75641	−0.239024
$800$	−28.0101	−0.990307
$801$	−9.82268	−0.347067
$802$	−12.8112	−0.452380
$803$	−67.9996	−2.39965
$804$	23.1160	0.815237
$805$	10.4424	0.368047
$806$	−21.5262	−0.758228
$807$	−6.06184	−0.213387
$808$	65.4687	2.30318
$809$	−49.3446	−1.73487	−0.867433	−	0.497555i	$-0.834231\pi$
$809$	−49.3446	−1.73487	−0.867433	+	0.497555i	$0.834231\pi$
$810$	−5.59318	−0.196524
$811$	−24.2622	−0.851962	−0.425981	−	0.904732i	$-0.640071\pi$
$811$	−24.2622	−0.851962	−0.425981	+	0.904732i	$0.640071\pi$
$812$	−10.9279	−0.383493
$813$	−15.8326	−0.555272
$814$	40.4210	1.41676
$815$	25.8935	0.907011
$816$	17.8271	0.624072
$817$	24.7161	0.864706
$818$	17.7421	0.620339
$819$	0.829398	0.0289815
$820$	0.851718	0.0297433
$821$	3.36764	0.117531	0.0587657	−	0.998272i	$-0.481284\pi$
$821$	3.36764	0.117531	0.0587657	+	0.998272i	$0.481284\pi$
$822$	45.3432	1.58153
$823$	28.3350	0.987695	0.493848	−	0.869548i	$-0.335590\pi$
$823$	28.3350	0.987695	0.493848	+	0.869548i	$0.335590\pi$
$824$	−9.33525	−0.325209
$825$	−5.56357	−0.193699
$826$	12.7215	0.442636
$827$	33.9009	1.17885	0.589425	−	0.807823i	$-0.299354\pi$
$827$	33.9009	1.17885	0.589425	+	0.807823i	$0.299354\pi$
$828$	−32.0642	−1.11431
$829$	30.0976	1.04533	0.522666	−	0.852537i	$-0.324937\pi$
$829$	30.0976	1.04533	0.522666	+	0.852537i	$0.324937\pi$
$830$	−17.5389	−0.608786
$831$	4.68921	0.162667
$832$	39.1043	1.35570
$833$	6.11973	0.212036
$834$	11.8610	0.410711
$835$	−17.1568	−0.593737
$836$	89.1434	3.08309
$837$	8.73145	0.301803
$838$	61.0912	2.11036
$839$	−22.2183	−0.767062	−0.383531	−	0.923528i	$-0.625292\pi$
$839$	−22.2183	−0.767062	−0.383531	+	0.923528i	$0.625292\pi$
$840$	19.8246	0.684012
$841$	−24.9362	−0.859869
$842$	−48.5415	−1.67285
$843$	16.1476	0.556154
$844$	−111.350	−3.83283
$845$	24.5048	0.842990
$846$	18.8427	0.647826
$847$	20.0543	0.689073
$848$	−116.269	−3.99269
$849$	−27.1922	−0.933235
$850$	2.72696	0.0935341
$851$	14.1364	0.484589
$852$	−76.8205	−2.63183
$853$	21.2252	0.726737	0.363369	−	0.931645i	$-0.381627\pi$
$853$	21.2252	0.726737	0.363369	+	0.931645i	$0.381627\pi$
$854$	13.2116	0.452093
$855$	5.43824	0.185984
$856$	190.015	6.49459
$857$	4.71001	0.160891	0.0804455	−	0.996759i	$-0.474366\pi$
$857$	4.71001	0.160891	0.0804455	+	0.996759i	$0.474366\pi$
$858$	14.0276	0.478894
$859$	−3.67869	−0.125515	−0.0627577	−	0.998029i	$-0.519990\pi$
$859$	−3.67869	−0.125515	−0.0627577	+	0.998029i	$0.519990\pi$
$860$	105.620	3.60160
$861$	0.0689625	0.00235024
$862$	18.4661	0.628959
$863$	9.88978	0.336652	0.168326	−	0.985731i	$-0.446164\pi$
$863$	9.88978	0.336652	0.168326	+	0.985731i	$0.446164\pi$
$864$	−28.6459	−0.974554
$865$	−16.7806	−0.570557
$866$	−38.4972	−1.30819
$867$	−1.00000	−0.0339618
$868$	−47.3321	−1.60656
$869$	48.5517	1.64700
$870$	−11.2752	−0.382266
$871$	−3.53676	−0.119839
$872$	−82.5925	−2.79693
$873$	−8.29213	−0.280646
$874$	41.9677	1.41958
$875$	11.2482	0.380258
$876$	−69.0501	−2.33299
$877$	0.562270	0.0189865	0.00949326	−	0.999955i	$-0.496978\pi$
$877$	0.562270	0.0189865	0.00949326	+	0.999955i	$0.496978\pi$
$878$	104.576	3.52927
$879$	4.54065	0.153152
$880$	203.429	6.85760
$881$	29.9300	1.00837	0.504184	−	0.863596i	$-0.331793\pi$
$881$	29.9300	1.00837	0.504184	+	0.863596i	$0.331793\pi$
$882$	−17.0671	−0.574679
$883$	−13.6135	−0.458130	−0.229065	−	0.973411i	$-0.573567\pi$
$883$	−13.6135	−0.458130	−0.229065	+	0.973411i	$0.573567\pi$
$884$	−5.10756	−0.171786
$885$	9.75061	0.327763
$886$	94.2845	3.16755
$887$	4.32667	0.145275	0.0726377	−	0.997358i	$-0.476858\pi$
$887$	4.32667	0.145275	0.0726377	+	0.997358i	$0.476858\pi$
$888$	26.8374	0.900605
$889$	−2.02305	−0.0678508
$890$	54.9401	1.84160
$891$	−5.68987	−0.190618
$892$	61.7605	2.06790
$893$	−18.3207	−0.613080
$894$	1.96918	0.0658591
$895$	−35.2506	−1.17830
$896$	61.9935	2.07106
$897$	4.90585	0.163802
$898$	−77.4415	−2.58426
$899$	17.6016	0.587047
$900$	−5.64953	−0.188318
$901$	6.52204	0.217281
$902$	1.16636	0.0388356
$903$	8.55188	0.284589
$904$	−110.430	−3.67285
$905$	24.1909	0.804134
$906$	20.4736	0.680190
$907$	−6.02218	−0.199963	−0.0999816	−	0.994989i	$-0.531878\pi$
$907$	−6.02218	−0.199963	−0.0999816	+	0.994989i	$0.531878\pi$
$908$	132.678	4.40307
$909$	6.21399	0.206105
$910$	−4.63897	−0.153781
$911$	−34.2084	−1.13337	−0.566687	−	0.823933i	$-0.691775\pi$
$911$	−34.2084	−1.13337	−0.566687	+	0.823933i	$0.691775\pi$
$912$	48.3400	1.60070
$913$	−17.8421	−0.590488
$914$	−29.8835	−0.988460
$915$	10.1263	0.334766
$916$	−84.3373	−2.78658
$917$	0.277724	0.00917126
$918$	2.78887	0.0920463
$919$	−19.8603	−0.655129	−0.327565	−	0.944829i	$-0.606228\pi$
$919$	−19.8603	−0.655129	−0.327565	+	0.944829i	$0.606228\pi$
$920$	117.261	3.86600
$921$	−5.71063	−0.188172
$922$	6.72936	0.221620
$923$	11.7536	0.386874
$924$	30.8440	1.01469
$925$	2.49075	0.0818953
$926$	−26.5034	−0.870957
$927$	−0.886060	−0.0291020
$928$	−57.7470	−1.89564
$929$	−10.7504	−0.352711	−0.176355	−	0.984327i	$-0.556431\pi$
$929$	−10.7504	−0.352711	−0.176355	+	0.984327i	$0.556431\pi$
$930$	−48.8366	−1.60142
$931$	16.5943	0.543856
$932$	−19.0081	−0.622632
$933$	21.9814	0.719640
$934$	36.8028	1.20423
$935$	−11.4113	−0.373188
$936$	9.31358	0.304424
$937$	6.57146	0.214680	0.107340	−	0.994222i	$-0.465767\pi$
$937$	6.57146	0.214680	0.107340	+	0.994222i	$0.465767\pi$
$938$	−10.4686	−0.341812
$939$	15.8885	0.518503
$940$	−78.2902	−2.55355
$941$	−35.3121	−1.15114	−0.575570	−	0.817752i	$-0.695220\pi$
$941$	−35.3121	−1.15114	−0.575570	+	0.817752i	$0.695220\pi$
$942$	2.78887	0.0908661
$943$	0.407910	0.0132834
$944$	86.6723	2.82094
$945$	1.88166	0.0612103
$946$	144.638	4.70258
$947$	−60.1124	−1.95339	−0.976696	−	0.214628i	$-0.931146\pi$
$947$	−60.1124	−1.95339	−0.976696	+	0.214628i	$0.931146\pi$
$948$	49.3018	1.60125
$949$	10.5647	0.342945
$950$	7.39446	0.239908
$951$	−29.9059	−0.969765
$952$	−9.88489	−0.320371
$953$	8.40854	0.272379	0.136190	−	0.990683i	$-0.456514\pi$
$953$	8.40854	0.272379	0.136190	+	0.990683i	$0.456514\pi$
$954$	−18.1891	−0.588894
$955$	−2.53598	−0.0820622
$956$	146.601	4.74140
$957$	−11.4701	−0.370777
$958$	−8.90951	−0.287853
$959$	−15.2544	−0.492589
$960$	88.7161	2.86330
$961$	45.2382	1.45930
$962$	−6.27999	−0.202475
$963$	18.0354	0.581183
$964$	−117.638	−3.78886
$965$	−25.0394	−0.806045
$966$	14.5210	0.467207
$967$	13.7991	0.443748	0.221874	−	0.975075i	$-0.428783\pi$
$967$	13.7991	0.443748	0.221874	+	0.975075i	$0.428783\pi$
$968$	225.196	7.23807
$969$	−2.71161	−0.0871094
$970$	46.3794	1.48915
$971$	36.4302	1.16910	0.584551	−	0.811357i	$-0.301271\pi$
$971$	36.4302	1.16910	0.584551	+	0.811357i	$0.301271\pi$
$972$	−5.77777	−0.185322
$973$	−3.99026	−0.127922
$974$	−96.6456	−3.09672
$975$	0.864382	0.0276824
$976$	90.0119	2.88121
$977$	−49.0046	−1.56780	−0.783898	−	0.620889i	$-0.786772\pi$
$977$	−49.0046	−1.56780	−0.783898	+	0.620889i	$0.786772\pi$
$978$	36.0070	1.15138
$979$	55.8897	1.78624
$980$	70.9126	2.26522
$981$	−7.83931	−0.250290
$982$	29.6290	0.945498
$983$	41.6683	1.32901	0.664505	−	0.747283i	$-0.268642\pi$
$983$	41.6683	1.32901	0.664505	+	0.747283i	$0.268642\pi$
$984$	0.774403	0.0246871
$985$	48.6042	1.54866
$986$	5.62204	0.179042
$987$	−6.33906	−0.201775
$988$	−13.8497	−0.440618
$989$	50.5840	1.60848
$990$	31.8245	1.01145
$991$	14.3526	0.455924	0.227962	−	0.973670i	$-0.426794\pi$
$991$	14.3526	0.455924	0.227962	+	0.973670i	$0.426794\pi$
$992$	−250.120	−7.94133
$993$	−10.0149	−0.317813
$994$	34.7899	1.10347
$995$	38.2386	1.21225
$996$	−18.1178	−0.574083
$997$	−37.0351	−1.17291	−0.586457	−	0.809981i	$-0.699478\pi$
$997$	−37.0351	−1.17291	−0.586457	+	0.809981i	$0.699478\pi$
$998$	−45.5481	−1.44180
$999$	2.54729	0.0805926

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.f.1.48	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.f.1.48	✓	48	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.78887 q^{2} -1.00000 q^{3} +5.77777 q^{4} -2.00554 q^{5} -2.78887 q^{6} +0.938230 q^{7} +10.5357 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.78887 q^{2} -1.00000 q^{3} +5.77777 q^{4} -2.00554 q^{5} -2.78887 q^{6} +0.938230 q^{7} +10.5357 q^{8} +1.00000 q^{9} -5.59318 q^{10} -5.68987 q^{11} -5.77777 q^{12} +0.884003 q^{13} +2.61660 q^{14} +2.00554 q^{15} +17.8271 q^{16} -1.00000 q^{17} +2.78887 q^{18} -2.71161 q^{19} -11.5876 q^{20} -0.938230 q^{21} -15.8683 q^{22} -5.54959 q^{23} -10.5357 q^{24} -0.977804 q^{25} +2.46536 q^{26} -1.00000 q^{27} +5.42087 q^{28} -2.01589 q^{29} +5.59318 q^{30} -8.73145 q^{31} +28.6459 q^{32} +5.68987 q^{33} -2.78887 q^{34} -1.88166 q^{35} +5.77777 q^{36} -2.54729 q^{37} -7.56231 q^{38} -0.884003 q^{39} -21.1298 q^{40} -0.0735028 q^{41} -2.61660 q^{42} -9.11491 q^{43} -32.8747 q^{44} -2.00554 q^{45} -15.4771 q^{46} +6.75641 q^{47} -17.8271 q^{48} -6.11973 q^{49} -2.72696 q^{50} +1.00000 q^{51} +5.10756 q^{52} -6.52204 q^{53} -2.78887 q^{54} +11.4113 q^{55} +9.88489 q^{56} +2.71161 q^{57} -5.62204 q^{58} +4.86184 q^{59} +11.5876 q^{60} +5.04917 q^{61} -24.3508 q^{62} +0.938230 q^{63} +44.2355 q^{64} -1.77290 q^{65} +15.8683 q^{66} -4.00085 q^{67} -5.77777 q^{68} +5.54959 q^{69} -5.24769 q^{70} +13.2959 q^{71} +10.5357 q^{72} +11.9510 q^{73} -7.10404 q^{74} +0.977804 q^{75} -15.6670 q^{76} -5.33840 q^{77} -2.46536 q^{78} -8.53302 q^{79} -35.7529 q^{80} +1.00000 q^{81} -0.204989 q^{82} +3.13577 q^{83} -5.42087 q^{84} +2.00554 q^{85} -25.4203 q^{86} +2.01589 q^{87} -59.9467 q^{88} -9.82268 q^{89} -5.59318 q^{90} +0.829398 q^{91} -32.0642 q^{92} +8.73145 q^{93} +18.8427 q^{94} +5.43824 q^{95} -28.6459 q^{96} -8.29213 q^{97} -17.0671 q^{98} -5.68987 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9}+O(q^{10}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9} - 20 q^{10} + 5 q^{11} - 45 q^{12} - 8 q^{13} + 4 q^{14} - q^{15} + 39 q^{16} - 48 q^{17} - q^{18} - 6 q^{19} + 6 q^{20} + 13 q^{21} - 35 q^{22} - 8 q^{23} + 6 q^{24} + 13 q^{25} + 17 q^{26} - 48 q^{27} - 38 q^{28} + q^{29} + 20 q^{30} - 21 q^{31} - 3 q^{32} - 5 q^{33} + q^{34} + 19 q^{35} + 45 q^{36} - 58 q^{37} - 14 q^{38} + 8 q^{39} - 54 q^{40} - 3 q^{41} - 4 q^{42} - 33 q^{43} + 2 q^{44} + q^{45} - 26 q^{46} + 9 q^{47} - 39 q^{48} + 11 q^{49} + 4 q^{50} + 48 q^{51} - 31 q^{52} - 33 q^{53} + q^{54} - 21 q^{55} + 6 q^{57} - 55 q^{58} + 77 q^{59} - 6 q^{60} - 29 q^{61} - 46 q^{62} - 13 q^{63} + 24 q^{64} - 49 q^{65} + 35 q^{66} - 44 q^{67} - 45 q^{68} + 8 q^{69} + 4 q^{70} + 22 q^{71} - 6 q^{72} - 63 q^{73} - 16 q^{74} - 13 q^{75} - 46 q^{76} - 30 q^{77} - 17 q^{78} - 46 q^{79} - 14 q^{80} + 48 q^{81} - 75 q^{82} + 11 q^{83} + 38 q^{84} - q^{85} + 8 q^{86} - q^{87} - 116 q^{88} + 10 q^{89} - 20 q^{90} - 67 q^{91} - 64 q^{92} + 21 q^{93} - 16 q^{94} - 8 q^{95} + 3 q^{96} - 96 q^{97} - 46 q^{98} + 5 q^{99}+O(q^{100}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9 - 20 * q^10 + 5 * q^11 - 45 * q^12 - 8 * q^13 + 4 * q^14 - q^15 + 39 * q^16 - 48 * q^17 - q^18 - 6 * q^19 + 6 * q^20 + 13 * q^21 - 35 * q^22 - 8 * q^23 + 6 * q^24 + 13 * q^25 + 17 * q^26 - 48 * q^27 - 38 * q^28 + q^29 + 20 * q^30 - 21 * q^31 - 3 * q^32 - 5 * q^33 + q^34 + 19 * q^35 + 45 * q^36 - 58 * q^37 - 14 * q^38 + 8 * q^39 - 54 * q^40 - 3 * q^41 - 4 * q^42 - 33 * q^43 + 2 * q^44 + q^45 - 26 * q^46 + 9 * q^47 - 39 * q^48 + 11 * q^49 + 4 * q^50 + 48 * q^51 - 31 * q^52 - 33 * q^53 + q^54 - 21 * q^55 + 6 * q^57 - 55 * q^58 + 77 * q^59 - 6 * q^60 - 29 * q^61 - 46 * q^62 - 13 * q^63 + 24 * q^64 - 49 * q^65 + 35 * q^66 - 44 * q^67 - 45 * q^68 + 8 * q^69 + 4 * q^70 + 22 * q^71 - 6 * q^72 - 63 * q^73 - 16 * q^74 - 13 * q^75 - 46 * q^76 - 30 * q^77 - 17 * q^78 - 46 * q^79 - 14 * q^80 + 48 * q^81 - 75 * q^82 + 11 * q^83 + 38 * q^84 - q^85 + 8 * q^86 - q^87 - 116 * q^88 + 10 * q^89 - 20 * q^90 - 67 * q^91 - 64 * q^92 + 21 * q^93 - 16 * q^94 - 8 * q^95 + 3 * q^96 - 96 * q^97 - 46 * q^98 + 5 * q^99

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