LMFDB - Embedded newform 8027.2.a.f.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$0$
Dimension:	$176$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.59269 q^{2} +0.175910 q^{3} +4.72203 q^{4} +3.23280 q^{5} -0.456079 q^{6} +2.53654 q^{7} -7.05738 q^{8} -2.96906 q^{9} +O(q^{10})$	\(q-2.59269 q^{2} +0.175910 q^{3} +4.72203 q^{4} +3.23280 q^{5} -0.456079 q^{6} +2.53654 q^{7} -7.05738 q^{8} -2.96906 q^{9} -8.38164 q^{10} +5.30695 q^{11} +0.830651 q^{12} -5.29312 q^{13} -6.57644 q^{14} +0.568680 q^{15} +8.85352 q^{16} +2.29833 q^{17} +7.69784 q^{18} -3.46792 q^{19} +15.2654 q^{20} +0.446201 q^{21} -13.7593 q^{22} +1.00000 q^{23} -1.24146 q^{24} +5.45098 q^{25} +13.7234 q^{26} -1.05001 q^{27} +11.9776 q^{28} -8.54620 q^{29} -1.47441 q^{30} +5.22128 q^{31} -8.83965 q^{32} +0.933545 q^{33} -5.95884 q^{34} +8.20011 q^{35} -14.0200 q^{36} +9.38807 q^{37} +8.99124 q^{38} -0.931112 q^{39} -22.8151 q^{40} +12.6328 q^{41} -1.15686 q^{42} -3.98512 q^{43} +25.0596 q^{44} -9.59836 q^{45} -2.59269 q^{46} -2.42572 q^{47} +1.55742 q^{48} -0.565990 q^{49} -14.1327 q^{50} +0.404298 q^{51} -24.9943 q^{52} +7.85499 q^{53} +2.72236 q^{54} +17.1563 q^{55} -17.9013 q^{56} -0.610041 q^{57} +22.1576 q^{58} +2.47534 q^{59} +2.68533 q^{60} -13.0307 q^{61} -13.5371 q^{62} -7.53111 q^{63} +5.21143 q^{64} -17.1116 q^{65} -2.42039 q^{66} +7.45338 q^{67} +10.8528 q^{68} +0.175910 q^{69} -21.2603 q^{70} -3.92447 q^{71} +20.9537 q^{72} -13.8239 q^{73} -24.3403 q^{74} +0.958881 q^{75} -16.3756 q^{76} +13.4613 q^{77} +2.41408 q^{78} +1.45457 q^{79} +28.6216 q^{80} +8.72246 q^{81} -32.7528 q^{82} +6.69824 q^{83} +2.10698 q^{84} +7.43002 q^{85} +10.3322 q^{86} -1.50336 q^{87} -37.4532 q^{88} +15.8078 q^{89} +24.8855 q^{90} -13.4262 q^{91} +4.72203 q^{92} +0.918474 q^{93} +6.28913 q^{94} -11.2111 q^{95} -1.55498 q^{96} +11.9373 q^{97} +1.46743 q^{98} -15.7566 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9}+O(q^{10}) $ 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9} + 18 q^{10} + 11 q^{11} + 46 q^{12} + 87 q^{13} - 6 q^{14} + 29 q^{15} + 257 q^{16} + 14 q^{17} + 72 q^{18} + 34 q^{19} + 45 q^{20} + 23 q^{21} + 62 q^{22} + 176 q^{23} + 33 q^{24} + 272 q^{25} + 31 q^{26} + 82 q^{27} + 80 q^{28} + 75 q^{29} - 30 q^{30} + 73 q^{31} + 71 q^{32} + 30 q^{33} + 23 q^{34} + 44 q^{35} + 264 q^{36} + 236 q^{37} - 21 q^{38} + 17 q^{39} + 43 q^{40} + 51 q^{41} + 38 q^{42} + 51 q^{43} + 12 q^{44} + 127 q^{45} + 19 q^{46} + 45 q^{47} + 61 q^{48} + 268 q^{49} + 55 q^{50} - 3 q^{51} + 166 q^{52} + 63 q^{53} - 32 q^{54} + 11 q^{55} - 9 q^{56} + 72 q^{57} + 98 q^{58} + 95 q^{59} - 7 q^{60} + 73 q^{61} + 12 q^{62} + 19 q^{63} + 365 q^{64} + 19 q^{65} - 28 q^{66} + 138 q^{67} + 16 q^{68} + 22 q^{69} + 100 q^{70} + 85 q^{71} + 129 q^{72} + 118 q^{73} - 21 q^{74} - 12 q^{75} + 52 q^{76} + 75 q^{77} + 97 q^{78} + 74 q^{79} + 8 q^{80} + 280 q^{81} + 67 q^{82} + 10 q^{83} - 51 q^{84} + 169 q^{85} - 39 q^{86} - 6 q^{87} + 159 q^{88} + 38 q^{89} + 22 q^{90} + 90 q^{91} + 203 q^{92} + 230 q^{93} + 63 q^{94} + 30 q^{95} + 107 q^{96} + 161 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9 + 18 * q^10 + 11 * q^11 + 46 * q^12 + 87 * q^13 - 6 * q^14 + 29 * q^15 + 257 * q^16 + 14 * q^17 + 72 * q^18 + 34 * q^19 + 45 * q^20 + 23 * q^21 + 62 * q^22 + 176 * q^23 + 33 * q^24 + 272 * q^25 + 31 * q^26 + 82 * q^27 + 80 * q^28 + 75 * q^29 - 30 * q^30 + 73 * q^31 + 71 * q^32 + 30 * q^33 + 23 * q^34 + 44 * q^35 + 264 * q^36 + 236 * q^37 - 21 * q^38 + 17 * q^39 + 43 * q^40 + 51 * q^41 + 38 * q^42 + 51 * q^43 + 12 * q^44 + 127 * q^45 + 19 * q^46 + 45 * q^47 + 61 * q^48 + 268 * q^49 + 55 * q^50 - 3 * q^51 + 166 * q^52 + 63 * q^53 - 32 * q^54 + 11 * q^55 - 9 * q^56 + 72 * q^57 + 98 * q^58 + 95 * q^59 - 7 * q^60 + 73 * q^61 + 12 * q^62 + 19 * q^63 + 365 * q^64 + 19 * q^65 - 28 * q^66 + 138 * q^67 + 16 * q^68 + 22 * q^69 + 100 * q^70 + 85 * q^71 + 129 * q^72 + 118 * q^73 - 21 * q^74 - 12 * q^75 + 52 * q^76 + 75 * q^77 + 97 * q^78 + 74 * q^79 + 8 * q^80 + 280 * q^81 + 67 * q^82 + 10 * q^83 - 51 * q^84 + 169 * q^85 - 39 * q^86 - 6 * q^87 + 159 * q^88 + 38 * q^89 + 22 * q^90 + 90 * q^91 + 203 * q^92 + 230 * q^93 + 63 * q^94 + 30 * q^95 + 107 * q^96 + 161 * q^97 + 58 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.59269	−1.83331	−0.916654	−	0.399682i	$-0.869120\pi$
$2$	−2.59269	−1.83331	−0.916654	+	0.399682i	$0.869120\pi$
$3$	0.175910	0.101562	0.0507808	−	0.998710i	$-0.483829\pi$
$3$	0.175910	0.101562	0.0507808	+	0.998710i	$0.483829\pi$
$4$	4.72203	2.36102
$5$	3.23280	1.44575	0.722876	−	0.690978i	$-0.242820\pi$
$5$	3.23280	1.44575	0.722876	+	0.690978i	$0.242820\pi$
$6$	−0.456079	−0.186193
$7$	2.53654	0.958720	0.479360	−	0.877618i	$-0.340869\pi$
$7$	2.53654	0.958720	0.479360	+	0.877618i	$0.340869\pi$
$8$	−7.05738	−2.49516
$9$	−2.96906	−0.989685
$10$	−8.38164	−2.65051
$11$	5.30695	1.60011	0.800053	−	0.599929i	$-0.204804\pi$
$11$	5.30695	1.60011	0.800053	+	0.599929i	$0.204804\pi$
$12$	0.830651	0.239788
$13$	−5.29312	−1.46805	−0.734024	−	0.679123i	$-0.762360\pi$
$13$	−5.29312	−1.46805	−0.734024	+	0.679123i	$0.762360\pi$
$14$	−6.57644	−1.75763
$15$	0.568680	0.146833
$16$	8.85352	2.21338
$17$	2.29833	0.557426	0.278713	−	0.960374i	$-0.410092\pi$
$17$	2.29833	0.557426	0.278713	+	0.960374i	$0.410092\pi$
$18$	7.69784	1.81440
$19$	−3.46792	−0.795596	−0.397798	−	0.917473i	$-0.630225\pi$
$19$	−3.46792	−0.795596	−0.397798	+	0.917473i	$0.630225\pi$
$20$	15.2654	3.41344
$21$	0.446201	0.0973691
$22$	−13.7593	−2.93349
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.24146	−0.253412
$25$	5.45098	1.09020
$26$	13.7234	2.69138
$27$	−1.05001	−0.202075
$28$	11.9776	2.26355
$29$	−8.54620	−1.58699	−0.793495	−	0.608577i	$-0.791741\pi$
$29$	−8.54620	−1.58699	−0.793495	+	0.608577i	$0.791741\pi$
$30$	−1.47441	−0.269189
$31$	5.22128	0.937769	0.468885	−	0.883259i	$-0.344656\pi$
$31$	5.22128	0.937769	0.468885	+	0.883259i	$0.344656\pi$
$32$	−8.83965	−1.56264
$33$	0.933545	0.162509
$34$	−5.95884	−1.02193
$35$	8.20011	1.38607
$36$	−14.0200	−2.33666
$37$	9.38807	1.54339	0.771694	−	0.635994i	$-0.219410\pi$
$37$	9.38807	1.54339	0.771694	+	0.635994i	$0.219410\pi$
$38$	8.99124	1.45857
$39$	−0.931112	−0.149097
$40$	−22.8151	−3.60738
$41$	12.6328	1.97291	0.986454	−	0.164040i	$-0.0524527\pi$
$41$	12.6328	1.97291	0.986454	+	0.164040i	$0.0524527\pi$
$42$	−1.15686	−0.178507
$43$	−3.98512	−0.607725	−0.303862	−	0.952716i	$-0.598276\pi$
$43$	−3.98512	−0.607725	−0.303862	+	0.952716i	$0.598276\pi$
$44$	25.0596	3.77788
$45$	−9.59836	−1.43084
$46$	−2.59269	−0.382271
$47$	−2.42572	−0.353827	−0.176914	−	0.984226i	$-0.556611\pi$
$47$	−2.42572	−0.353827	−0.176914	+	0.984226i	$0.556611\pi$
$48$	1.55742	0.224794
$49$	−0.565990	−0.0808557
$50$	−14.1327	−1.99867
$51$	0.404298	0.0566130
$52$	−24.9943	−3.46609
$53$	7.85499	1.07897	0.539483	−	0.841996i	$-0.318620\pi$
$53$	7.85499	1.07897	0.539483	+	0.841996i	$0.318620\pi$
$54$	2.72236	0.370466
$55$	17.1563	2.31336
$56$	−17.9013	−2.39216
$57$	−0.610041	−0.0808019
$58$	22.1576	2.90944
$59$	2.47534	0.322262	0.161131	−	0.986933i	$-0.448486\pi$
$59$	2.47534	0.322262	0.161131	+	0.986933i	$0.448486\pi$
$60$	2.68533	0.346674
$61$	−13.0307	−1.66841	−0.834206	−	0.551453i	$-0.814074\pi$
$61$	−13.0307	−1.66841	−0.834206	+	0.551453i	$0.814074\pi$
$62$	−13.5371	−1.71922
$63$	−7.53111	−0.948831
$64$	5.21143	0.651428
$65$	−17.1116	−2.12243
$66$	−2.42039	−0.297929
$67$	7.45338	0.910576	0.455288	−	0.890344i	$-0.349536\pi$
$67$	7.45338	0.910576	0.455288	+	0.890344i	$0.349536\pi$
$68$	10.8528	1.31609
$69$	0.175910	0.0211770
$70$	−21.2603	−2.54109
$71$	−3.92447	−0.465749	−0.232874	−	0.972507i	$-0.574813\pi$
$71$	−3.92447	−0.465749	−0.232874	+	0.972507i	$0.574813\pi$
$72$	20.9537	2.46942
$73$	−13.8239	−1.61797	−0.808985	−	0.587830i	$-0.799982\pi$
$73$	−13.8239	−1.61797	−0.808985	+	0.587830i	$0.799982\pi$
$74$	−24.3403	−2.82951
$75$	0.958881	0.110722
$76$	−16.3756	−1.87841
$77$	13.4613	1.53405
$78$	2.41408	0.273341
$79$	1.45457	0.163652	0.0818262	−	0.996647i	$-0.473925\pi$
$79$	1.45457	0.163652	0.0818262	+	0.996647i	$0.473925\pi$
$80$	28.6216	3.20000
$81$	8.72246	0.969162
$82$	−32.7528	−3.61695
$83$	6.69824	0.735228	0.367614	−	0.929979i	$-0.380175\pi$
$83$	6.69824	0.735228	0.367614	+	0.929979i	$0.380175\pi$
$84$	2.10698	0.229890
$85$	7.43002	0.805899
$86$	10.3322	1.11415
$87$	−1.50336	−0.161177
$88$	−37.4532	−3.99252
$89$	15.8078	1.67562	0.837810	−	0.545962i	$-0.183836\pi$
$89$	15.8078	1.67562	0.837810	+	0.545962i	$0.183836\pi$
$90$	24.8855	2.62317
$91$	−13.4262	−1.40745
$92$	4.72203	0.492306
$93$	0.918474	0.0952413
$94$	6.28913	0.648674
$95$	−11.2111	−1.15023
$96$	−1.55498	−0.158705
$97$	11.9373	1.21205	0.606023	−	0.795447i	$-0.292764\pi$
$97$	11.9373	1.21205	0.606023	+	0.795447i	$0.292764\pi$
$98$	1.46743	0.148233
$99$	−15.7566	−1.58360
$100$	25.7397	2.57397
$101$	−4.49752	−0.447520	−0.223760	−	0.974644i	$-0.571833\pi$
$101$	−4.49752	−0.447520	−0.223760	+	0.974644i	$0.571833\pi$
$102$	−1.04822	−0.103789
$103$	6.36534	0.627195	0.313598	−	0.949556i	$-0.398466\pi$
$103$	6.36534	0.627195	0.313598	+	0.949556i	$0.398466\pi$
$104$	37.3556	3.66302
$105$	1.44248	0.140771
$106$	−20.3656	−1.97808
$107$	−11.3893	−1.10105	−0.550525	−	0.834819i	$-0.685572\pi$
$107$	−11.3893	−1.10105	−0.550525	+	0.834819i	$0.685572\pi$
$108$	−4.95820	−0.477103
$109$	9.00556	0.862576	0.431288	−	0.902214i	$-0.358059\pi$
$109$	9.00556	0.862576	0.431288	+	0.902214i	$0.358059\pi$
$110$	−44.4810	−4.24109
$111$	1.65145	0.156749
$112$	22.4573	2.12201
$113$	−12.8681	−1.21053	−0.605263	−	0.796025i	$-0.706932\pi$
$113$	−12.8681	−1.21053	−0.605263	+	0.796025i	$0.706932\pi$
$114$	1.58165	0.148135
$115$	3.23280	0.301460
$116$	−40.3554	−3.74691
$117$	15.7156	1.45291
$118$	−6.41779	−0.590805
$119$	5.82978	0.534415
$120$	−4.01339	−0.366371
$121$	17.1638	1.56034
$122$	33.7846	3.05871
$123$	2.22223	0.200371
$124$	24.6550	2.21409
$125$	1.45794	0.130402
$126$	19.5258	1.73950
$127$	11.0793	0.983133	0.491566	−	0.870840i	$-0.336424\pi$
$127$	11.0793	0.983133	0.491566	+	0.870840i	$0.336424\pi$
$128$	4.16770	0.368376
$129$	−0.701021	−0.0617214
$130$	44.3650	3.89107
$131$	17.7650	1.55214	0.776068	−	0.630649i	$-0.217211\pi$
$131$	17.7650	1.55214	0.776068	+	0.630649i	$0.217211\pi$
$132$	4.40823	0.383687
$133$	−8.79650	−0.762754
$134$	−19.3243	−1.66937
$135$	−3.39449	−0.292151
$136$	−16.2202	−1.39087
$137$	−14.4118	−1.23129	−0.615644	−	0.788025i	$-0.711104\pi$
$137$	−14.4118	−1.23129	−0.615644	+	0.788025i	$0.711104\pi$
$138$	−0.456079	−0.0388240
$139$	−4.54714	−0.385683	−0.192842	−	0.981230i	$-0.561770\pi$
$139$	−4.54714	−0.385683	−0.192842	+	0.981230i	$0.561770\pi$
$140$	38.7212	3.27254
$141$	−0.426707	−0.0359352
$142$	10.1749	0.853860
$143$	−28.0904	−2.34903
$144$	−26.2866	−2.19055
$145$	−27.6281	−2.29439
$146$	35.8411	2.96623
$147$	−0.0995631	−0.00821182
$148$	44.3307	3.64396
$149$	−23.0896	−1.89158	−0.945789	−	0.324783i	$-0.894709\pi$
$149$	−23.0896	−1.89158	−0.945789	+	0.324783i	$0.894709\pi$
$150$	−2.48608	−0.202987
$151$	−7.98078	−0.649467	−0.324733	−	0.945806i	$-0.605275\pi$
$151$	−7.98078	−0.649467	−0.324733	+	0.945806i	$0.605275\pi$
$152$	24.4744	1.98514
$153$	−6.82386	−0.551676
$154$	−34.9009	−2.81239
$155$	16.8793	1.35578
$156$	−4.39674	−0.352021
$157$	20.5567	1.64061	0.820303	−	0.571929i	$-0.193805\pi$
$157$	20.5567	1.64061	0.820303	+	0.571929i	$0.193805\pi$
$158$	−3.77126	−0.300025
$159$	1.38177	0.109581
$160$	−28.5768	−2.25920
$161$	2.53654	0.199907
$162$	−22.6146	−1.77677
$163$	12.3571	0.967883	0.483942	−	0.875100i	$-0.339205\pi$
$163$	12.3571	0.967883	0.483942	+	0.875100i	$0.339205\pi$
$164$	59.6523	4.65807
$165$	3.01796	0.234948
$166$	−17.3665	−1.34790
$167$	14.0043	1.08368	0.541841	−	0.840481i	$-0.317727\pi$
$167$	14.0043	1.08368	0.541841	+	0.840481i	$0.317727\pi$
$168$	−3.14901	−0.242951
$169$	15.0172	1.15517
$170$	−19.2637	−1.47746
$171$	10.2965	0.787389
$172$	−18.8178	−1.43485
$173$	−3.15493	−0.239865	−0.119933	−	0.992782i	$-0.538268\pi$
$173$	−3.15493	−0.239865	−0.119933	+	0.992782i	$0.538268\pi$
$174$	3.89774	0.295487
$175$	13.8266	1.04519
$176$	46.9852	3.54164
$177$	0.435436	0.0327294
$178$	−40.9846	−3.07193
$179$	15.3675	1.14862	0.574312	−	0.818637i	$-0.305270\pi$
$179$	15.3675	1.14862	0.574312	+	0.818637i	$0.305270\pi$
$180$	−45.3237	−3.37823
$181$	−1.71861	−0.127743	−0.0638717	−	0.997958i	$-0.520345\pi$
$181$	−1.71861	−0.127743	−0.0638717	+	0.997958i	$0.520345\pi$
$182$	34.8099	2.58028
$183$	−2.29223	−0.169446
$184$	−7.05738	−0.520277
$185$	30.3497	2.23136
$186$	−2.38132	−0.174607
$187$	12.1971	0.891941
$188$	−11.4543	−0.835392
$189$	−2.66340	−0.193734
$190$	29.0669	2.10873
$191$	20.4084	1.47670	0.738351	−	0.674416i	$-0.235605\pi$
$191$	20.4084	1.47670	0.738351	+	0.674416i	$0.235605\pi$
$192$	0.916741	0.0661600
$193$	8.25880	0.594481	0.297241	−	0.954803i	$-0.403934\pi$
$193$	8.25880	0.594481	0.297241	+	0.954803i	$0.403934\pi$
$194$	−30.9496	−2.22205
$195$	−3.01010	−0.215558
$196$	−2.67262	−0.190902
$197$	−1.27985	−0.0911852	−0.0455926	−	0.998960i	$-0.514518\pi$
$197$	−1.27985	−0.0911852	−0.0455926	+	0.998960i	$0.514518\pi$
$198$	40.8521	2.90323
$199$	26.9308	1.90908	0.954539	−	0.298088i	$-0.0963487\pi$
$199$	26.9308	1.90908	0.954539	+	0.298088i	$0.0963487\pi$
$200$	−38.4697	−2.72022
$201$	1.31112	0.0924794
$202$	11.6607	0.820442
$203$	−21.6777	−1.52148
$204$	1.90911	0.133664
$205$	40.8392	2.85233
$206$	−16.5033	−1.14984
$207$	−2.96906	−0.206364
$208$	−46.8628	−3.24935
$209$	−18.4041	−1.27304
$210$	−3.73990	−0.258077
$211$	18.0657	1.24369	0.621847	−	0.783139i	$-0.286382\pi$
$211$	18.0657	1.24369	0.621847	+	0.783139i	$0.286382\pi$
$212$	37.0915	2.54746
$213$	−0.690352	−0.0473021
$214$	29.5290	2.01856
$215$	−12.8831	−0.878619
$216$	7.41035	0.504211
$217$	13.2440	0.899058
$218$	−23.3486	−1.58137
$219$	−2.43176	−0.164323
$220$	81.0126	5.46187
$221$	−12.1653	−0.818328
$222$	−4.28170	−0.287369
$223$	17.3104	1.15919	0.579595	−	0.814904i	$-0.303211\pi$
$223$	17.3104	1.15919	0.579595	+	0.814904i	$0.303211\pi$
$224$	−22.4221	−1.49814
$225$	−16.1843	−1.07895
$226$	33.3629	2.21927
$227$	−0.257651	−0.0171009	−0.00855045	−	0.999963i	$-0.502722\pi$
$227$	−0.257651	−0.0171009	−0.00855045	+	0.999963i	$0.502722\pi$
$228$	−2.88063	−0.190775
$229$	1.74044	0.115012	0.0575058	−	0.998345i	$-0.481685\pi$
$229$	1.74044	0.115012	0.0575058	+	0.998345i	$0.481685\pi$
$230$	−8.38164	−0.552669
$231$	2.36797	0.155801
$232$	60.3138	3.95979
$233$	7.55104	0.494685	0.247343	−	0.968928i	$-0.420443\pi$
$233$	7.55104	0.494685	0.247343	+	0.968928i	$0.420443\pi$
$234$	−40.7456	−2.66362
$235$	−7.84186	−0.511546
$236$	11.6886	0.760866
$237$	0.255874	0.0166208
$238$	−15.1148	−0.979748
$239$	15.1585	0.980522	0.490261	−	0.871576i	$-0.336901\pi$
$239$	15.1585	0.980522	0.490261	+	0.871576i	$0.336901\pi$
$240$	5.03482	0.324996
$241$	−11.2210	−0.722809	−0.361405	−	0.932409i	$-0.617703\pi$
$241$	−11.2210	−0.722809	−0.361405	+	0.932409i	$0.617703\pi$
$242$	−44.5003	−2.86059
$243$	4.68441	0.300505
$244$	−61.5315	−3.93915
$245$	−1.82973	−0.116897
$246$	−5.76154	−0.367342
$247$	18.3561	1.16797
$248$	−36.8485	−2.33988
$249$	1.17829	0.0746708
$250$	−3.77998	−0.239067
$251$	−23.0807	−1.45684	−0.728422	−	0.685129i	$-0.759746\pi$
$251$	−23.0807	−1.45684	−0.728422	+	0.685129i	$0.759746\pi$
$252$	−35.5622	−2.24021
$253$	5.30695	0.333645
$254$	−28.7253	−1.80238
$255$	1.30701	0.0818483
$256$	−21.2284	−1.32678
$257$	30.9575	1.93108	0.965538	−	0.260264i	$-0.0838095\pi$
$257$	30.9575	1.93108	0.965538	+	0.260264i	$0.0838095\pi$
$258$	1.81753	0.113154
$259$	23.8132	1.47968
$260$	−80.8015	−5.01110
$261$	25.3741	1.57062
$262$	−46.0591	−2.84554
$263$	13.8789	0.855810	0.427905	−	0.903824i	$-0.359252\pi$
$263$	13.8789	0.855810	0.427905	+	0.903824i	$0.359252\pi$
$264$	−6.58838	−0.405487
$265$	25.3936	1.55992
$266$	22.8066	1.39836
$267$	2.78074	0.170178
$268$	35.1951	2.14988
$269$	−6.99772	−0.426659	−0.213329	−	0.976980i	$-0.568431\pi$
$269$	−6.99772	−0.426659	−0.213329	+	0.976980i	$0.568431\pi$
$270$	8.80084	0.535602
$271$	−3.13129	−0.190212	−0.0951062	−	0.995467i	$-0.530319\pi$
$271$	−3.13129	−0.190212	−0.0951062	+	0.995467i	$0.530319\pi$
$272$	20.3483	1.23379
$273$	−2.36180	−0.142943
$274$	37.3654	2.25733
$275$	28.9281	1.74443
$276$	0.830651	0.0499993
$277$	−19.4257	−1.16718	−0.583590	−	0.812049i	$-0.698352\pi$
$277$	−19.4257	−1.16718	−0.583590	+	0.812049i	$0.698352\pi$
$278$	11.7893	0.707076
$279$	−15.5023	−0.928097
$280$	−57.8712	−3.45847
$281$	11.5559	0.689365	0.344682	−	0.938719i	$-0.387987\pi$
$281$	11.5559	0.689365	0.344682	+	0.938719i	$0.387987\pi$
$282$	1.10632	0.0658804
$283$	15.8417	0.941689	0.470844	−	0.882216i	$-0.343949\pi$
$283$	15.8417	0.941689	0.470844	+	0.882216i	$0.343949\pi$
$284$	−18.5315	−1.09964
$285$	−1.97214	−0.116819
$286$	72.8296	4.30650
$287$	32.0435	1.89147
$288$	26.2454	1.54653
$289$	−11.7177	−0.689276
$290$	71.6312	4.20633
$291$	2.09988	0.123097
$292$	−65.2770	−3.82005
$293$	4.41479	0.257915	0.128957	−	0.991650i	$-0.458837\pi$
$293$	4.41479	0.257915	0.128957	+	0.991650i	$0.458837\pi$
$294$	0.258136	0.0150548
$295$	8.00228	0.465911
$296$	−66.2551	−3.85100
$297$	−5.57238	−0.323342
$298$	59.8642	3.46784
$299$	−5.29312	−0.306109
$300$	4.52787	0.261416
$301$	−10.1084	−0.582638
$302$	20.6917	1.19067
$303$	−0.791157	−0.0454508
$304$	−30.7033	−1.76096
$305$	−42.1257	−2.41211
$306$	17.6921	1.01139
$307$	32.0835	1.83110	0.915550	−	0.402204i	$-0.131756\pi$
$307$	32.0835	1.83110	0.915550	+	0.402204i	$0.131756\pi$
$308$	63.5646	3.62193
$309$	1.11972	0.0636989
$310$	−43.7629	−2.48556
$311$	−4.65407	−0.263908	−0.131954	−	0.991256i	$-0.542125\pi$
$311$	−4.65407	−0.263908	−0.131954	+	0.991256i	$0.542125\pi$
$312$	6.57121	0.372021
$313$	−23.7613	−1.34307	−0.671534	−	0.740974i	$-0.734364\pi$
$313$	−23.7613	−1.34307	−0.671534	+	0.740974i	$0.734364\pi$
$314$	−53.2972	−3.00774
$315$	−24.3466	−1.37177
$316$	6.86854	0.386386
$317$	−7.81222	−0.438778	−0.219389	−	0.975637i	$-0.570406\pi$
$317$	−7.81222	−0.438778	−0.219389	+	0.975637i	$0.570406\pi$
$318$	−3.58250	−0.200896
$319$	−45.3543	−2.53935
$320$	16.8475	0.941803
$321$	−2.00350	−0.111824
$322$	−6.57644	−0.366491
$323$	−7.97041	−0.443486
$324$	41.1877	2.28821
$325$	−28.8527	−1.60046
$326$	−32.0381	−1.77443
$327$	1.58417	0.0876045
$328$	−89.1542	−4.92272
$329$	−6.15292	−0.339222
$330$	−7.82463	−0.430732
$331$	5.44931	0.299521	0.149761	−	0.988722i	$-0.452150\pi$
$331$	5.44931	0.299521	0.149761	+	0.988722i	$0.452150\pi$
$332$	31.6293	1.73588
$333$	−27.8737	−1.52747
$334$	−36.3087	−1.98672
$335$	24.0953	1.31647
$336$	3.95045	0.215515
$337$	−28.3777	−1.54583	−0.772916	−	0.634508i	$-0.781203\pi$
$337$	−28.3777	−1.54583	−0.772916	+	0.634508i	$0.781203\pi$
$338$	−38.9348	−2.11778
$339$	−2.26362	−0.122943
$340$	35.0848	1.90274
$341$	27.7091	1.50053
$342$	−26.6955	−1.44353
$343$	−19.1914	−1.03624
$344$	28.1245	1.51637
$345$	0.568680	0.0306167
$346$	8.17976	0.439747
$347$	17.5063	0.939786	0.469893	−	0.882723i	$-0.344292\pi$
$347$	17.5063	0.939786	0.469893	+	0.882723i	$0.344292\pi$
$348$	−7.09891	−0.380542
$349$	−1.00000	−0.0535288
$349$	−1.00000	−0.0535288
$350$	−35.8481	−1.91616
$351$	5.55786	0.296657
$352$	−46.9116	−2.50040
$353$	−5.20548	−0.277059	−0.138530	−	0.990358i	$-0.544238\pi$
$353$	−5.20548	−0.277059	−0.138530	+	0.990358i	$0.544238\pi$
$354$	−1.12895	−0.0600031
$355$	−12.6870	−0.673357
$356$	74.6448	3.95616
$357$	1.02552	0.0542760
$358$	−39.8432	−2.10578
$359$	−19.8325	−1.04672	−0.523359	−	0.852112i	$-0.675321\pi$
$359$	−19.8325	−1.04672	−0.523359	+	0.852112i	$0.675321\pi$
$360$	67.7392	3.57017
$361$	−6.97352	−0.367027
$362$	4.45582	0.234193
$363$	3.01927	0.158471
$364$	−63.3989	−3.32301
$365$	−44.6900	−2.33918
$366$	5.94304	0.310647
$367$	1.83519	0.0957960	0.0478980	−	0.998852i	$-0.484748\pi$
$367$	1.83519	0.0957960	0.0478980	+	0.998852i	$0.484748\pi$
$368$	8.85352	0.461522
$369$	−37.5074	−1.95256
$370$	−78.6874	−4.09076
$371$	19.9245	1.03443
$372$	4.33706	0.224866
$373$	24.0662	1.24610	0.623050	−	0.782182i	$-0.285893\pi$
$373$	24.0662	1.24610	0.623050	+	0.782182i	$0.285893\pi$
$374$	−31.6233	−1.63520
$375$	0.256466	0.0132438
$376$	17.1192	0.882856
$377$	45.2361	2.32978
$378$	6.90536	0.355174
$379$	−1.26215	−0.0648323	−0.0324161	−	0.999474i	$-0.510320\pi$
$379$	−1.26215	−0.0648323	−0.0324161	+	0.999474i	$0.510320\pi$
$380$	−52.9391	−2.71572
$381$	1.94896	0.0998485
$382$	−52.9127	−2.70725
$383$	−15.1001	−0.771577	−0.385788	−	0.922587i	$-0.626070\pi$
$383$	−15.1001	−0.771577	−0.385788	+	0.922587i	$0.626070\pi$
$384$	0.733139	0.0374128
$385$	43.5176	2.21786
$386$	−21.4125	−1.08987
$387$	11.8320	0.601456
$388$	56.3682	2.86166
$389$	−12.3806	−0.627720	−0.313860	−	0.949469i	$-0.601622\pi$
$389$	−12.3806	−0.627720	−0.313860	+	0.949469i	$0.601622\pi$
$390$	7.80424	0.395183
$391$	2.29833	0.116231
$392$	3.99440	0.201748
$393$	3.12504	0.157637
$394$	3.31824	0.167171
$395$	4.70234	0.236601
$396$	−74.4034	−3.73891
$397$	−5.24230	−0.263103	−0.131552	−	0.991309i	$-0.541996\pi$
$397$	−5.24230	−0.263103	−0.131552	+	0.991309i	$0.541996\pi$
$398$	−69.8233	−3.49992
$399$	−1.54739	−0.0774664
$400$	48.2604	2.41302
$401$	−29.1741	−1.45689	−0.728443	−	0.685106i	$-0.759756\pi$
$401$	−29.1741	−1.45689	−0.728443	+	0.685106i	$0.759756\pi$
$402$	−3.39933	−0.169543
$403$	−27.6369	−1.37669
$404$	−21.2374	−1.05660
$405$	28.1980	1.40117
$406$	56.2036	2.78934
$407$	49.8220	2.46959
$408$	−2.85328	−0.141259
$409$	−16.1404	−0.798090	−0.399045	−	0.916931i	$-0.630658\pi$
$409$	−16.1404	−0.798090	−0.399045	+	0.916931i	$0.630658\pi$
$410$	−105.883	−5.22920
$411$	−2.53518	−0.125051
$412$	30.0573	1.48082
$413$	6.27879	0.308959
$414$	7.69784	0.378328
$415$	21.6541	1.06296
$416$	46.7894	2.29404
$417$	−0.799886	−0.0391706
$418$	47.7161	2.33387
$419$	−29.7775	−1.45473	−0.727364	−	0.686252i	$-0.759255\pi$
$419$	−29.7775	−1.45473	−0.727364	+	0.686252i	$0.759255\pi$
$420$	6.81143	0.332364
$421$	32.4816	1.58306	0.791528	−	0.611133i	$-0.209286\pi$
$421$	32.4816	1.58306	0.791528	+	0.611133i	$0.209286\pi$
$422$	−46.8387	−2.28007
$423$	7.20209	0.350178
$424$	−55.4357	−2.69219
$425$	12.5281	0.607704
$426$	1.78987	0.0867193
$427$	−33.0529	−1.59954
$428$	−53.7808	−2.59960
$429$	−4.94137	−0.238572
$430$	33.4018	1.61078
$431$	−18.6525	−0.898459	−0.449230	−	0.893416i	$-0.648302\pi$
$431$	−18.6525	−0.898459	−0.449230	+	0.893416i	$0.648302\pi$
$432$	−9.29632	−0.447270
$433$	39.5864	1.90240	0.951201	−	0.308572i	$-0.0998512\pi$
$433$	39.5864	1.90240	0.951201	+	0.308572i	$0.0998512\pi$
$434$	−34.3374	−1.64825
$435$	−4.86006	−0.233022
$436$	42.5245	2.03656
$437$	−3.46792	−0.165893
$438$	6.30480	0.301255
$439$	−10.9755	−0.523832	−0.261916	−	0.965091i	$-0.584354\pi$
$439$	−10.9755	−0.523832	−0.261916	+	0.965091i	$0.584354\pi$
$440$	−121.079	−5.77219
$441$	1.68045	0.0800217
$442$	31.5409	1.50025
$443$	−33.5263	−1.59288	−0.796442	−	0.604715i	$-0.793287\pi$
$443$	−33.5263	−1.59288	−0.796442	+	0.604715i	$0.793287\pi$
$444$	7.79821	0.370087
$445$	51.1033	2.42253
$446$	−44.8805	−2.12515
$447$	−4.06169	−0.192111
$448$	13.2190	0.624538
$449$	−9.26977	−0.437468	−0.218734	−	0.975785i	$-0.570193\pi$
$449$	−9.26977	−0.437468	−0.218734	+	0.975785i	$0.570193\pi$
$450$	41.9608	1.97805
$451$	67.0415	3.15686
$452$	−60.7634	−2.85807
$453$	−1.40390	−0.0659608
$454$	0.668009	0.0313512
$455$	−43.4042	−2.03482
$456$	4.30529	0.201614
$457$	−1.67842	−0.0785134	−0.0392567	−	0.999229i	$-0.512499\pi$
$457$	−1.67842	−0.0785134	−0.0392567	+	0.999229i	$0.512499\pi$
$458$	−4.51242	−0.210851
$459$	−2.41328	−0.112642
$460$	15.2654	0.711752
$461$	26.5704	1.23751	0.618753	−	0.785585i	$-0.287638\pi$
$461$	26.5704	1.23751	0.618753	+	0.785585i	$0.287638\pi$
$462$	−6.13940	−0.285631
$463$	−12.6709	−0.588868	−0.294434	−	0.955672i	$-0.595131\pi$
$463$	−12.6709	−0.588868	−0.294434	+	0.955672i	$0.595131\pi$
$464$	−75.6639	−3.51261
$465$	2.96924	0.137695
$466$	−19.5775	−0.906910
$467$	16.2456	0.751756	0.375878	−	0.926669i	$-0.377341\pi$
$467$	16.2456	0.751756	0.375878	+	0.926669i	$0.377341\pi$
$468$	74.2095	3.43033
$469$	18.9058	0.872987
$470$	20.3315	0.937822
$471$	3.61613	0.166623
$472$	−17.4694	−0.804095
$473$	−21.1488	−0.972424
$474$	−0.663400	−0.0304710
$475$	−18.9036	−0.867356
$476$	27.5284	1.26176
$477$	−23.3219	−1.06784
$478$	−39.3013	−1.79760
$479$	−37.6739	−1.72136	−0.860681	−	0.509144i	$-0.829962\pi$
$479$	−37.6739	−1.72136	−0.860681	+	0.509144i	$0.829962\pi$
$480$	−5.02694	−0.229447
$481$	−49.6922	−2.26577
$482$	29.0926	1.32513
$483$	0.446201	0.0203029
$484$	81.0478	3.68399
$485$	38.5908	1.75232
$486$	−12.1452	−0.550918
$487$	7.83577	0.355073	0.177536	−	0.984114i	$-0.443187\pi$
$487$	7.83577	0.355073	0.177536	+	0.984114i	$0.443187\pi$
$488$	91.9627	4.16296
$489$	2.17373	0.0982997
$490$	4.74392	0.214308
$491$	32.9341	1.48630	0.743148	−	0.669127i	$-0.233332\pi$
$491$	32.9341	1.48630	0.743148	+	0.669127i	$0.233332\pi$
$492$	10.4934	0.473080
$493$	−19.6420	−0.884629
$494$	−47.5917	−2.14125
$495$	−50.9380	−2.28949
$496$	46.2267	2.07564
$497$	−9.95455	−0.446523
$498$	−3.05493	−0.136895
$499$	−10.1013	−0.452198	−0.226099	−	0.974104i	$-0.572597\pi$
$499$	−10.1013	−0.452198	−0.226099	+	0.974104i	$0.572597\pi$
$500$	6.88443	0.307881
$501$	2.46349	0.110060
$502$	59.8411	2.67084
$503$	38.1479	1.70093	0.850465	−	0.526031i	$-0.176321\pi$
$503$	38.1479	1.70093	0.850465	+	0.526031i	$0.176321\pi$
$504$	53.1499	2.36749
$505$	−14.5396	−0.647003
$506$	−13.7593	−0.611674
$507$	2.64167	0.117320
$508$	52.3170	2.32119
$509$	17.2125	0.762930	0.381465	−	0.924383i	$-0.375420\pi$
$509$	17.2125	0.762930	0.381465	+	0.924383i	$0.375420\pi$
$510$	−3.38868	−0.150053
$511$	−35.0649	−1.55118
$512$	46.7032	2.06401
$513$	3.64137	0.160770
$514$	−80.2631	−3.54025
$515$	20.5779	0.906768
$516$	−3.31024	−0.145725
$517$	−12.8732	−0.566162
$518$	−61.7401	−2.71270
$519$	−0.554983	−0.0243611
$520$	120.763	5.29581
$521$	−13.1711	−0.577037	−0.288518	−	0.957474i	$-0.593163\pi$
$521$	−13.1711	−0.577037	−0.288518	+	0.957474i	$0.593163\pi$
$522$	−65.7872	−2.87943
$523$	39.3267	1.71964	0.859819	−	0.510599i	$-0.170576\pi$
$523$	39.3267	1.71964	0.859819	+	0.510599i	$0.170576\pi$
$524$	83.8869	3.66462
$525$	2.43223	0.106151
$526$	−35.9837	−1.56896
$527$	12.0002	0.522737
$528$	8.26515	0.359695
$529$	1.00000	0.0434783
$530$	−65.8377	−2.85981
$531$	−7.34943	−0.318938
$532$	−41.5374	−1.80087
$533$	−66.8668	−2.89632
$534$	−7.20959	−0.311989
$535$	−36.8195	−1.59184
$536$	−52.6013	−2.27203
$537$	2.70330	0.116656
$538$	18.1429	0.782196
$539$	−3.00368	−0.129378
$540$	−16.0289	−0.689773
$541$	3.97101	0.170727	0.0853636	−	0.996350i	$-0.472795\pi$
$541$	3.97101	0.170727	0.0853636	+	0.996350i	$0.472795\pi$
$542$	8.11846	0.348718
$543$	−0.302320	−0.0129738
$544$	−20.3164	−0.871059
$545$	29.1132	1.24707
$546$	6.12341	0.262058
$547$	44.0248	1.88236	0.941182	−	0.337900i	$-0.109716\pi$
$547$	44.0248	1.88236	0.941182	+	0.337900i	$0.109716\pi$
$548$	−68.0532	−2.90709
$549$	38.6889	1.65120
$550$	−75.0016	−3.19808
$551$	29.6376	1.26260
$552$	−1.24146	−0.0528401
$553$	3.68958	0.156897
$554$	50.3649	2.13980
$555$	5.33881	0.226620
$556$	−21.4717	−0.910604
$557$	−42.4833	−1.80008	−0.900038	−	0.435812i	$-0.856461\pi$
$557$	−42.4833	−1.80008	−0.900038	+	0.435812i	$0.856461\pi$
$558$	40.1925	1.70149
$559$	21.0937	0.892169
$560$	72.5998	3.06790
$561$	2.14559	0.0905869
$562$	−29.9607	−1.26382
$563$	3.73885	0.157574	0.0787870	−	0.996891i	$-0.474895\pi$
$563$	3.73885	0.157574	0.0787870	+	0.996891i	$0.474895\pi$
$564$	−2.01493	−0.0848437
$565$	−41.5999	−1.75012
$566$	−41.0725	−1.72640
$567$	22.1248	0.929155
$568$	27.6965	1.16212
$569$	−19.7972	−0.829942	−0.414971	−	0.909835i	$-0.636208\pi$
$569$	−19.7972	−0.829942	−0.414971	+	0.909835i	$0.636208\pi$
$570$	5.11314	0.214166
$571$	10.8234	0.452946	0.226473	−	0.974017i	$-0.427281\pi$
$571$	10.8234	0.452946	0.226473	+	0.974017i	$0.427281\pi$
$572$	−132.644	−5.54611
$573$	3.59004	0.149976
$574$	−83.0787	−3.46764
$575$	5.45098	0.227322
$576$	−15.4730	−0.644709
$577$	31.6089	1.31590	0.657948	−	0.753063i	$-0.271424\pi$
$577$	31.6089	1.31590	0.657948	+	0.753063i	$0.271424\pi$
$578$	30.3803	1.26366
$579$	1.45280	0.0603764
$580$	−130.461	−5.41710
$581$	16.9903	0.704878
$582$	−5.44434	−0.225675
$583$	41.6861	1.72646
$584$	97.5607	4.03709
$585$	50.8053	2.10054
$586$	−11.4462	−0.472837
$587$	−43.1552	−1.78121	−0.890604	−	0.454780i	$-0.849718\pi$
$587$	−43.1552	−1.78121	−0.890604	+	0.454780i	$0.849718\pi$
$588$	−0.470140	−0.0193882
$589$	−18.1070	−0.746085
$590$	−20.7474	−0.854157
$591$	−0.225137	−0.00926091
$592$	83.1174	3.41610
$593$	−2.72270	−0.111808	−0.0559040	−	0.998436i	$-0.517804\pi$
$593$	−2.72270	−0.111808	−0.0559040	+	0.998436i	$0.517804\pi$
$594$	14.4474	0.592786
$595$	18.8465	0.772632
$596$	−109.030	−4.46604
$597$	4.73740	0.193889
$598$	13.7234	0.561192
$599$	−17.0076	−0.694912	−0.347456	−	0.937696i	$-0.612954\pi$
$599$	−17.0076	−0.694912	−0.347456	+	0.937696i	$0.612954\pi$
$600$	−6.76718	−0.276269
$601$	−5.13132	−0.209311	−0.104656	−	0.994509i	$-0.533374\pi$
$601$	−5.13132	−0.209311	−0.104656	+	0.994509i	$0.533374\pi$
$602$	26.2079	1.06815
$603$	−22.1295	−0.901183
$604$	−37.6855	−1.53340
$605$	55.4870	2.25587
$606$	2.05122	0.0833253
$607$	−27.1784	−1.10314	−0.551568	−	0.834130i	$-0.685970\pi$
$607$	−27.1784	−1.10314	−0.551568	+	0.834130i	$0.685970\pi$
$608$	30.6552	1.24323
$609$	−3.81332	−0.154524
$610$	109.219	4.42214
$611$	12.8396	0.519436
$612$	−32.2225	−1.30252
$613$	34.6808	1.40075	0.700373	−	0.713777i	$-0.253017\pi$
$613$	34.6808	1.40075	0.700373	+	0.713777i	$0.253017\pi$
$614$	−83.1824	−3.35697
$615$	7.18401	0.289687
$616$	−95.0013	−3.82771
$617$	18.7244	0.753816	0.376908	−	0.926251i	$-0.376987\pi$
$617$	18.7244	0.753816	0.376908	+	0.926251i	$0.376987\pi$
$618$	−2.90310	−0.116780
$619$	−3.41941	−0.137438	−0.0687189	−	0.997636i	$-0.521891\pi$
$619$	−3.41941	−0.137438	−0.0687189	+	0.997636i	$0.521891\pi$
$620$	79.7048	3.20102
$621$	−1.05001	−0.0421356
$622$	12.0666	0.483825
$623$	40.0970	1.60645
$624$	−8.24362	−0.330009
$625$	−22.5417	−0.901668
$626$	61.6056	2.46225
$627$	−3.23746	−0.129292
$628$	97.0696	3.87350
$629$	21.5768	0.860325
$630$	63.1231	2.51488
$631$	7.66016	0.304946	0.152473	−	0.988308i	$-0.451276\pi$
$631$	7.66016	0.304946	0.152473	+	0.988308i	$0.451276\pi$
$632$	−10.2655	−0.408339
$633$	3.17793	0.126311
$634$	20.2546	0.804415
$635$	35.8173	1.42137
$636$	6.52476	0.258724
$637$	2.99585	0.118700
$638$	117.590	4.65541
$639$	11.6520	0.460945
$640$	13.4733	0.532580
$641$	−32.4635	−1.28223	−0.641115	−	0.767445i	$-0.721528\pi$
$641$	−32.4635	−1.28223	−0.641115	+	0.767445i	$0.721528\pi$
$642$	5.19444	0.205008
$643$	−23.6973	−0.934532	−0.467266	−	0.884117i	$-0.654761\pi$
$643$	−23.6973	−0.934532	−0.467266	+	0.884117i	$0.654761\pi$
$644$	11.9776	0.471983
$645$	−2.26626	−0.0892338
$646$	20.6648	0.813045
$647$	8.69439	0.341812	0.170906	−	0.985287i	$-0.445331\pi$
$647$	8.69439	0.341812	0.170906	+	0.985287i	$0.445331\pi$
$648$	−61.5577	−2.41821
$649$	13.1365	0.515654
$650$	74.8061	2.93414
$651$	2.32974	0.0913097
$652$	58.3506	2.28519
$653$	19.3883	0.758724	0.379362	−	0.925248i	$-0.376144\pi$
$653$	19.3883	0.758724	0.379362	+	0.925248i	$0.376144\pi$
$654$	−4.10725	−0.160606
$655$	57.4307	2.24400
$656$	111.844	4.36679
$657$	41.0440	1.60128
$658$	15.9526	0.621897
$659$	−44.0571	−1.71622	−0.858110	−	0.513466i	$-0.828361\pi$
$659$	−44.0571	−1.71622	−0.858110	+	0.513466i	$0.828361\pi$
$660$	14.2509	0.554716
$661$	4.81955	0.187459	0.0937293	−	0.995598i	$-0.470121\pi$
$661$	4.81955	0.187459	0.0937293	+	0.995598i	$0.470121\pi$
$662$	−14.1284	−0.549115
$663$	−2.14000	−0.0831107
$664$	−47.2720	−1.83451
$665$	−28.4373	−1.10275
$666$	72.2678	2.80032
$667$	−8.54620	−0.330910
$668$	66.1286	2.55859
$669$	3.04507	0.117729
$670$	−62.4716	−2.41349
$671$	−69.1534	−2.66964
$672$	−3.94426	−0.152153
$673$	−21.5639	−0.831226	−0.415613	−	0.909542i	$-0.636433\pi$
$673$	−21.5639	−0.831226	−0.415613	+	0.909542i	$0.636433\pi$
$674$	73.5746	2.83399
$675$	−5.72361	−0.220302
$676$	70.9115	2.72737
$677$	−3.86572	−0.148572	−0.0742859	−	0.997237i	$-0.523668\pi$
$677$	−3.86572	−0.148572	−0.0742859	+	0.997237i	$0.523668\pi$
$678$	5.86886	0.225392
$679$	30.2793	1.16201
$680$	−52.4365	−2.01085
$681$	−0.0453233	−0.00173679
$682$	−71.8410	−2.75093
$683$	−40.6051	−1.55371	−0.776855	−	0.629680i	$-0.783186\pi$
$683$	−40.6051	−1.55371	−0.776855	+	0.629680i	$0.783186\pi$
$684$	48.6202	1.85904
$685$	−46.5906	−1.78014
$686$	49.7573	1.89974
$687$	0.306160	0.0116807
$688$	−35.2823	−1.34512
$689$	−41.5775	−1.58398
$690$	−1.47441	−0.0561299
$691$	21.5402	0.819426	0.409713	−	0.912214i	$-0.365629\pi$
$691$	21.5402	0.819426	0.409713	+	0.912214i	$0.365629\pi$
$692$	−14.8977	−0.566325
$693$	−39.9673	−1.51823
$694$	−45.3883	−1.72292
$695$	−14.7000	−0.557602
$696$	10.6098	0.402163
$697$	29.0342	1.09975
$698$	2.59269	0.0981347
$699$	1.32830	0.0502410
$700$	65.2897	2.46772
$701$	45.3565	1.71309	0.856546	−	0.516071i	$-0.172606\pi$
$701$	45.3565	1.71309	0.856546	+	0.516071i	$0.172606\pi$
$702$	−14.4098	−0.543863
$703$	−32.5571	−1.22791
$704$	27.6568	1.04236
$705$	−1.37946	−0.0519534
$706$	13.4962	0.507935
$707$	−11.4081	−0.429046
$708$	2.05614	0.0772747
$709$	−50.5314	−1.89775	−0.948873	−	0.315658i	$-0.897775\pi$
$709$	−50.5314	−1.89775	−0.948873	+	0.315658i	$0.897775\pi$
$710$	32.8935	1.23447
$711$	−4.31871	−0.161964
$712$	−111.561	−4.18094
$713$	5.22128	0.195538
$714$	−2.65884	−0.0995047
$715$	−90.8105	−3.39612
$716$	72.5660	2.71192
$717$	2.66653	0.0995833
$718$	51.4194	1.91896
$719$	7.97915	0.297572	0.148786	−	0.988869i	$-0.452463\pi$
$719$	7.97915	0.297572	0.148786	+	0.988869i	$0.452463\pi$
$720$	−84.9792	−3.16699
$721$	16.1459	0.601305
$722$	18.0802	0.672874
$723$	−1.97389	−0.0734096
$724$	−8.11533	−0.301604
$725$	−46.5852	−1.73013
$726$	−7.82803	−0.290525
$727$	47.7961	1.77266	0.886329	−	0.463056i	$-0.153247\pi$
$727$	47.7961	1.77266	0.886329	+	0.463056i	$0.153247\pi$
$728$	94.7537	3.51181
$729$	−25.3433	−0.938642
$730$	115.867	4.28844
$731$	−9.15910	−0.338761
$732$	−10.8240	−0.400066
$733$	6.50357	0.240215	0.120107	−	0.992761i	$-0.461676\pi$
$733$	6.50357	0.240215	0.120107	+	0.992761i	$0.461676\pi$
$734$	−4.75807	−0.175623
$735$	−0.321867	−0.0118723
$736$	−8.83965	−0.325834
$737$	39.5548	1.45702
$738$	97.2450	3.57964
$739$	15.4770	0.569332	0.284666	−	0.958627i	$-0.408117\pi$
$739$	15.4770	0.569332	0.284666	+	0.958627i	$0.408117\pi$
$740$	143.312	5.26827
$741$	3.22902	0.118621
$742$	−51.6579	−1.89642
$743$	36.3789	1.33461	0.667307	−	0.744783i	$-0.267447\pi$
$743$	36.3789	1.33461	0.667307	+	0.744783i	$0.267447\pi$
$744$	−6.48202	−0.237642
$745$	−74.6442	−2.73475
$746$	−62.3962	−2.28449
$747$	−19.8875	−0.727644
$748$	57.5951	2.10589
$749$	−28.8895	−1.05560
$750$	−0.664935	−0.0242800
$751$	−4.14915	−0.151405	−0.0757024	−	0.997130i	$-0.524120\pi$
$751$	−4.14915	−0.151405	−0.0757024	+	0.997130i	$0.524120\pi$
$752$	−21.4761	−0.783154
$753$	−4.06012	−0.147959
$754$	−117.283	−4.27120
$755$	−25.8002	−0.938967
$756$	−12.5767	−0.457409
$757$	44.8811	1.63123	0.815617	−	0.578593i	$-0.196398\pi$
$757$	44.8811	1.63123	0.815617	+	0.578593i	$0.196398\pi$
$758$	3.27236	0.118857
$759$	0.933545	0.0338855
$760$	79.1209	2.87002
$761$	−22.8383	−0.827887	−0.413944	−	0.910302i	$-0.635849\pi$
$761$	−22.8383	−0.827887	−0.413944	+	0.910302i	$0.635849\pi$
$762$	−5.05306	−0.183053
$763$	22.8429	0.826969
$764$	96.3693	3.48652
$765$	−22.0602	−0.797587
$766$	39.1497	1.41454
$767$	−13.1023	−0.473096
$768$	−3.73428	−0.134749
$769$	45.9753	1.65791	0.828955	−	0.559315i	$-0.188936\pi$
$769$	45.9753	1.65791	0.828955	+	0.559315i	$0.188936\pi$
$770$	−112.828	−4.06602
$771$	5.44572	0.196123
$772$	38.9983	1.40358
$773$	30.3509	1.09164	0.545822	−	0.837901i	$-0.316217\pi$
$773$	30.3509	1.09164	0.545822	+	0.837901i	$0.316217\pi$
$774$	−30.6768	−1.10265
$775$	28.4611	1.02235
$776$	−84.2458	−3.02425
$777$	4.18897	0.150278
$778$	32.0990	1.15080
$779$	−43.8095	−1.56964
$780$	−14.2138	−0.508935
$781$	−20.8270	−0.745248
$782$	−5.95884	−0.213088
$783$	8.97364	0.320692
$784$	−5.01100	−0.178964
$785$	66.4558	2.37191
$786$	−8.10225	−0.288998
$787$	−9.53022	−0.339716	−0.169858	−	0.985469i	$-0.554331\pi$
$787$	−9.53022	−0.339716	−0.169858	+	0.985469i	$0.554331\pi$
$788$	−6.04347	−0.215290
$789$	2.44143	0.0869174
$790$	−12.1917	−0.433762
$791$	−32.6403	−1.16056
$792$	111.201	3.95134
$793$	68.9732	2.44931
$794$	13.5916	0.482349
$795$	4.46698	0.158428
$796$	127.168	4.50736
$797$	−5.71014	−0.202263	−0.101132	−	0.994873i	$-0.532246\pi$
$797$	−5.71014	−0.202263	−0.101132	+	0.994873i	$0.532246\pi$
$798$	4.01190	0.142020
$799$	−5.57509	−0.197233
$800$	−48.1848	−1.70359
$801$	−46.9341	−1.65834
$802$	75.6394	2.67092
$803$	−73.3630	−2.58892
$804$	6.19116	0.218345
$805$	8.20011	0.289016
$806$	71.6538	2.52390
$807$	−1.23097	−0.0433321
$808$	31.7407	1.11663
$809$	−6.76993	−0.238018	−0.119009	−	0.992893i	$-0.537972\pi$
$809$	−6.76993	−0.238018	−0.119009	+	0.992893i	$0.537972\pi$
$810$	−73.1085	−2.56877
$811$	−6.68482	−0.234736	−0.117368	−	0.993088i	$-0.537446\pi$
$811$	−6.68482	−0.234736	−0.117368	+	0.993088i	$0.537446\pi$
$812$	−102.363	−3.59224
$813$	−0.550824	−0.0193183
$814$	−129.173	−4.52751
$815$	39.9480	1.39932
$816$	3.57946	0.125306
$817$	13.8201	0.483503
$818$	41.8470	1.46315
$819$	39.8631	1.39293
$820$	192.844	6.73440
$821$	42.8550	1.49565	0.747825	−	0.663895i	$-0.231098\pi$
$821$	42.8550	1.49565	0.747825	+	0.663895i	$0.231098\pi$
$822$	6.57294	0.229258
$823$	−55.2803	−1.92695	−0.963476	−	0.267795i	$-0.913705\pi$
$823$	−55.2803	−1.92695	−0.963476	+	0.267795i	$0.913705\pi$
$824$	−44.9226	−1.56495
$825$	5.08874	0.177167
$826$	−16.2789	−0.566417
$827$	5.62064	0.195449	0.0977244	−	0.995214i	$-0.468844\pi$
$827$	5.62064	0.195449	0.0977244	+	0.995214i	$0.468844\pi$
$828$	−14.0200	−0.487228
$829$	−7.23925	−0.251430	−0.125715	−	0.992066i	$-0.540122\pi$
$829$	−7.23925	−0.251430	−0.125715	+	0.992066i	$0.540122\pi$
$830$	−56.1422	−1.94873
$831$	−3.41717	−0.118540
$832$	−27.5847	−0.956329
$833$	−1.30083	−0.0450710
$834$	2.07385	0.0718117
$835$	45.2730	1.56674
$836$	−86.9047	−3.00566
$837$	−5.48242	−0.189500
$838$	77.2039	2.66696
$839$	55.5398	1.91745	0.958724	−	0.284339i	$-0.0917740\pi$
$839$	55.5398	1.91745	0.958724	+	0.284339i	$0.0917740\pi$
$840$	−10.1801	−0.351247
$841$	44.0376	1.51854
$842$	−84.2146	−2.90223
$843$	2.03279	0.0700129
$844$	85.3068	2.93638
$845$	48.5475	1.67008
$846$	−18.6728	−0.641984
$847$	43.5365	1.49593
$848$	69.5443	2.38816
$849$	2.78670	0.0956393
$850$	−32.4815	−1.11411
$851$	9.38807	0.321819
$852$	−3.25986	−0.111681
$853$	−5.48135	−0.187678	−0.0938389	−	0.995587i	$-0.529914\pi$
$853$	−5.48135	−0.187678	−0.0938389	+	0.995587i	$0.529914\pi$
$854$	85.6958	2.93245
$855$	33.2863	1.13837
$856$	80.3789	2.74729
$857$	−29.3810	−1.00363	−0.501817	−	0.864974i	$-0.667335\pi$
$857$	−29.3810	−1.00363	−0.501817	+	0.864974i	$0.667335\pi$
$858$	12.8114	0.437375
$859$	−7.37326	−0.251572	−0.125786	−	0.992057i	$-0.540145\pi$
$859$	−7.37326	−0.251572	−0.125786	+	0.992057i	$0.540145\pi$
$860$	−60.8343	−2.07443
$861$	5.63676	0.192100
$862$	48.3601	1.64715
$863$	−37.9220	−1.29088	−0.645440	−	0.763811i	$-0.723326\pi$
$863$	−37.9220	−1.29088	−0.645440	+	0.763811i	$0.723326\pi$
$864$	9.28177	0.315772
$865$	−10.1993	−0.346785
$866$	−102.635	−3.48769
$867$	−2.06126	−0.0700039
$868$	62.5384	2.12269
$869$	7.71936	0.261861
$870$	12.6006	0.427201
$871$	−39.4517	−1.33677
$872$	−63.5557	−2.15227
$873$	−35.4424	−1.19954
$874$	8.99124	0.304133
$875$	3.69811	0.125019
$876$	−11.4829	−0.387970
$877$	58.8995	1.98889	0.994447	−	0.105235i	$-0.0335594\pi$
$877$	58.8995	1.98889	0.994447	+	0.105235i	$0.0335594\pi$
$878$	28.4560	0.960344
$879$	0.776605	0.0261942
$880$	151.894	5.12034
$881$	−14.0544	−0.473504	−0.236752	−	0.971570i	$-0.576083\pi$
$881$	−14.0544	−0.473504	−0.236752	+	0.971570i	$0.576083\pi$
$882$	−4.35690	−0.146704
$883$	50.0721	1.68506	0.842530	−	0.538650i	$-0.181065\pi$
$883$	50.0721	1.68506	0.842530	+	0.538650i	$0.181065\pi$
$884$	−57.4450	−1.93209
$885$	1.40768	0.0473186
$886$	86.9233	2.92024
$887$	−39.1700	−1.31520	−0.657599	−	0.753368i	$-0.728428\pi$
$887$	−39.1700	−1.31520	−0.657599	+	0.753368i	$0.728428\pi$
$888$	−11.6549	−0.391114
$889$	28.1032	0.942549
$890$	−132.495	−4.44124
$891$	46.2897	1.55076
$892$	81.7403	2.73687
$893$	8.41220	0.281504
$894$	10.5307	0.352199
$895$	49.6802	1.66062
$896$	10.5715	0.353170
$897$	−0.931112	−0.0310889
$898$	24.0336	0.802013
$899$	−44.6221	−1.48823
$900$	−76.4226	−2.54742
$901$	18.0533	0.601444
$902$	−173.818	−5.78750
$903$	−1.77816	−0.0591736
$904$	90.8149	3.02046
$905$	−5.55592	−0.184685
$906$	3.63987	0.120926
$907$	−47.9227	−1.59125	−0.795623	−	0.605792i	$-0.792856\pi$
$907$	−47.9227	−1.59125	−0.795623	+	0.605792i	$0.792856\pi$
$908$	−1.21664	−0.0403755
$909$	13.3534	0.442904
$910$	112.534	3.73045
$911$	−46.2741	−1.53313	−0.766565	−	0.642167i	$-0.778036\pi$
$911$	−46.2741	−1.53313	−0.766565	+	0.642167i	$0.778036\pi$
$912$	−5.40101	−0.178845
$913$	35.5473	1.17644
$914$	4.35163	0.143939
$915$	−7.41031	−0.244977
$916$	8.21841	0.271544
$917$	45.0616	1.48806
$918$	6.25687	0.206508
$919$	12.0186	0.396458	0.198229	−	0.980156i	$-0.436481\pi$
$919$	12.0186	0.396458	0.198229	+	0.980156i	$0.436481\pi$
$920$	−22.8151	−0.752191
$921$	5.64379	0.185969
$922$	−68.8887	−2.26873
$923$	20.7727	0.683742
$924$	11.1816	0.367848
$925$	51.1742	1.68260
$926$	32.8517	1.07958
$927$	−18.8990	−0.620726
$928$	75.5455	2.47990
$929$	−3.65244	−0.119833	−0.0599164	−	0.998203i	$-0.519083\pi$
$929$	−3.65244	−0.119833	−0.0599164	+	0.998203i	$0.519083\pi$
$930$	−7.69831	−0.252438
$931$	1.96281	0.0643284
$932$	35.6563	1.16796
$933$	−0.818696	−0.0268029
$934$	−42.1197	−1.37820
$935$	39.4308	1.28952
$936$	−110.911	−3.62523
$937$	−0.787379	−0.0257226	−0.0128613	−	0.999917i	$-0.504094\pi$
$937$	−0.787379	−0.0257226	−0.0128613	+	0.999917i	$0.504094\pi$
$938$	−49.0168	−1.60045
$939$	−4.17984	−0.136404
$940$	−37.0295	−1.20777
$941$	22.5297	0.734447	0.367224	−	0.930133i	$-0.380308\pi$
$941$	22.5297	0.734447	0.367224	+	0.930133i	$0.380308\pi$
$942$	−9.37550	−0.305470
$943$	12.6328	0.411380
$944$	21.9155	0.713288
$945$	−8.61023	−0.280091
$946$	54.8323	1.78275
$947$	33.7184	1.09570	0.547850	−	0.836576i	$-0.315446\pi$
$947$	33.7184	1.09570	0.547850	+	0.836576i	$0.315446\pi$
$948$	1.20824	0.0392419
$949$	73.1718	2.37526
$950$	49.0111	1.59013
$951$	−1.37424	−0.0445629
$952$	−41.1430	−1.33345
$953$	−3.85626	−0.124916	−0.0624582	−	0.998048i	$-0.519894\pi$
$953$	−3.85626	−0.124916	−0.0624582	+	0.998048i	$0.519894\pi$
$954$	60.4665	1.95767
$955$	65.9763	2.13494
$956$	71.5789	2.31503
$957$	−7.97826	−0.257901
$958$	97.6766	3.15579
$959$	−36.5562	−1.18046
$960$	2.96364	0.0956510
$961$	−3.73825	−0.120589
$962$	128.836	4.15385
$963$	33.8156	1.08969
$964$	−52.9860	−1.70656
$965$	26.6990	0.859472
$966$	−1.15686	−0.0372214
$967$	−7.05723	−0.226945	−0.113473	−	0.993541i	$-0.536197\pi$
$967$	−7.05723	−0.226945	−0.113473	+	0.993541i	$0.536197\pi$
$968$	−121.131	−3.89330
$969$	−1.40207	−0.0450411
$970$	−100.054	−3.21254
$971$	−8.62231	−0.276703	−0.138351	−	0.990383i	$-0.544180\pi$
$971$	−8.62231	−0.276703	−0.138351	+	0.990383i	$0.544180\pi$
$972$	22.1199	0.709497
$973$	−11.5340	−0.369762
$974$	−20.3157	−0.650957
$975$	−5.07548	−0.162545
$976$	−115.368	−3.69283
$977$	9.03507	0.289058	0.144529	−	0.989501i	$-0.453833\pi$
$977$	9.03507	0.289058	0.144529	+	0.989501i	$0.453833\pi$
$978$	−5.63581	−0.180213
$979$	83.8911	2.68117
$980$	−8.64004	−0.275996
$981$	−26.7380	−0.853679
$982$	−85.3879	−2.72484
$983$	13.6514	0.435412	0.217706	−	0.976014i	$-0.430143\pi$
$983$	13.6514	0.435412	0.217706	+	0.976014i	$0.430143\pi$
$984$	−15.6831	−0.499959
$985$	−4.13748	−0.131831
$986$	50.9255	1.62180
$987$	−1.08236	−0.0344518
$988$	86.6783	2.75760
$989$	−3.98512	−0.126719
$990$	132.066	4.19735
$991$	−31.4355	−0.998581	−0.499291	−	0.866435i	$-0.666406\pi$
$991$	−31.4355	−0.998581	−0.499291	+	0.866435i	$0.666406\pi$
$992$	−46.1543	−1.46540
$993$	0.958587	0.0304198
$994$	25.8090	0.818613
$995$	87.0620	2.76005
$996$	5.56390	0.176299
$997$	12.7209	0.402875	0.201437	−	0.979501i	$-0.435439\pi$
$997$	12.7209	0.402875	0.201437	+	0.979501i	$0.435439\pi$
$998$	26.1896	0.829017
$999$	−9.85761	−0.311881

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.f.1.10	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.f.1.10	✓	176	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.59269 q^{2} +0.175910 q^{3} +4.72203 q^{4} +3.23280 q^{5} -0.456079 q^{6} +2.53654 q^{7} -7.05738 q^{8} -2.96906 q^{9} +O(q^{10})\)	\(q-2.59269 q^{2} +0.175910 q^{3} +4.72203 q^{4} +3.23280 q^{5} -0.456079 q^{6} +2.53654 q^{7} -7.05738 q^{8} -2.96906 q^{9} -8.38164 q^{10} +5.30695 q^{11} +0.830651 q^{12} -5.29312 q^{13} -6.57644 q^{14} +0.568680 q^{15} +8.85352 q^{16} +2.29833 q^{17} +7.69784 q^{18} -3.46792 q^{19} +15.2654 q^{20} +0.446201 q^{21} -13.7593 q^{22} +1.00000 q^{23} -1.24146 q^{24} +5.45098 q^{25} +13.7234 q^{26} -1.05001 q^{27} +11.9776 q^{28} -8.54620 q^{29} -1.47441 q^{30} +5.22128 q^{31} -8.83965 q^{32} +0.933545 q^{33} -5.95884 q^{34} +8.20011 q^{35} -14.0200 q^{36} +9.38807 q^{37} +8.99124 q^{38} -0.931112 q^{39} -22.8151 q^{40} +12.6328 q^{41} -1.15686 q^{42} -3.98512 q^{43} +25.0596 q^{44} -9.59836 q^{45} -2.59269 q^{46} -2.42572 q^{47} +1.55742 q^{48} -0.565990 q^{49} -14.1327 q^{50} +0.404298 q^{51} -24.9943 q^{52} +7.85499 q^{53} +2.72236 q^{54} +17.1563 q^{55} -17.9013 q^{56} -0.610041 q^{57} +22.1576 q^{58} +2.47534 q^{59} +2.68533 q^{60} -13.0307 q^{61} -13.5371 q^{62} -7.53111 q^{63} +5.21143 q^{64} -17.1116 q^{65} -2.42039 q^{66} +7.45338 q^{67} +10.8528 q^{68} +0.175910 q^{69} -21.2603 q^{70} -3.92447 q^{71} +20.9537 q^{72} -13.8239 q^{73} -24.3403 q^{74} +0.958881 q^{75} -16.3756 q^{76} +13.4613 q^{77} +2.41408 q^{78} +1.45457 q^{79} +28.6216 q^{80} +8.72246 q^{81} -32.7528 q^{82} +6.69824 q^{83} +2.10698 q^{84} +7.43002 q^{85} +10.3322 q^{86} -1.50336 q^{87} -37.4532 q^{88} +15.8078 q^{89} +24.8855 q^{90} -13.4262 q^{91} +4.72203 q^{92} +0.918474 q^{93} +6.28913 q^{94} -11.2111 q^{95} -1.55498 q^{96} +11.9373 q^{97} +1.46743 q^{98} -15.7566 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9}+O(q^{10}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9} + 18 q^{10} + 11 q^{11} + 46 q^{12} + 87 q^{13} - 6 q^{14} + 29 q^{15} + 257 q^{16} + 14 q^{17} + 72 q^{18} + 34 q^{19} + 45 q^{20} + 23 q^{21} + 62 q^{22} + 176 q^{23} + 33 q^{24} + 272 q^{25} + 31 q^{26} + 82 q^{27} + 80 q^{28} + 75 q^{29} - 30 q^{30} + 73 q^{31} + 71 q^{32} + 30 q^{33} + 23 q^{34} + 44 q^{35} + 264 q^{36} + 236 q^{37} - 21 q^{38} + 17 q^{39} + 43 q^{40} + 51 q^{41} + 38 q^{42} + 51 q^{43} + 12 q^{44} + 127 q^{45} + 19 q^{46} + 45 q^{47} + 61 q^{48} + 268 q^{49} + 55 q^{50} - 3 q^{51} + 166 q^{52} + 63 q^{53} - 32 q^{54} + 11 q^{55} - 9 q^{56} + 72 q^{57} + 98 q^{58} + 95 q^{59} - 7 q^{60} + 73 q^{61} + 12 q^{62} + 19 q^{63} + 365 q^{64} + 19 q^{65} - 28 q^{66} + 138 q^{67} + 16 q^{68} + 22 q^{69} + 100 q^{70} + 85 q^{71} + 129 q^{72} + 118 q^{73} - 21 q^{74} - 12 q^{75} + 52 q^{76} + 75 q^{77} + 97 q^{78} + 74 q^{79} + 8 q^{80} + 280 q^{81} + 67 q^{82} + 10 q^{83} - 51 q^{84} + 169 q^{85} - 39 q^{86} - 6 q^{87} + 159 q^{88} + 38 q^{89} + 22 q^{90} + 90 q^{91} + 203 q^{92} + 230 q^{93} + 63 q^{94} + 30 q^{95} + 107 q^{96} + 161 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9 + 18 * q^10 + 11 * q^11 + 46 * q^12 + 87 * q^13 - 6 * q^14 + 29 * q^15 + 257 * q^16 + 14 * q^17 + 72 * q^18 + 34 * q^19 + 45 * q^20 + 23 * q^21 + 62 * q^22 + 176 * q^23 + 33 * q^24 + 272 * q^25 + 31 * q^26 + 82 * q^27 + 80 * q^28 + 75 * q^29 - 30 * q^30 + 73 * q^31 + 71 * q^32 + 30 * q^33 + 23 * q^34 + 44 * q^35 + 264 * q^36 + 236 * q^37 - 21 * q^38 + 17 * q^39 + 43 * q^40 + 51 * q^41 + 38 * q^42 + 51 * q^43 + 12 * q^44 + 127 * q^45 + 19 * q^46 + 45 * q^47 + 61 * q^48 + 268 * q^49 + 55 * q^50 - 3 * q^51 + 166 * q^52 + 63 * q^53 - 32 * q^54 + 11 * q^55 - 9 * q^56 + 72 * q^57 + 98 * q^58 + 95 * q^59 - 7 * q^60 + 73 * q^61 + 12 * q^62 + 19 * q^63 + 365 * q^64 + 19 * q^65 - 28 * q^66 + 138 * q^67 + 16 * q^68 + 22 * q^69 + 100 * q^70 + 85 * q^71 + 129 * q^72 + 118 * q^73 - 21 * q^74 - 12 * q^75 + 52 * q^76 + 75 * q^77 + 97 * q^78 + 74 * q^79 + 8 * q^80 + 280 * q^81 + 67 * q^82 + 10 * q^83 - 51 * q^84 + 169 * q^85 - 39 * q^86 - 6 * q^87 + 159 * q^88 + 38 * q^89 + 22 * q^90 + 90 * q^91 + 203 * q^92 + 230 * q^93 + 63 * q^94 + 30 * q^95 + 107 * q^96 + 161 * q^97 + 58 * q^98 + 7 * q^99

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