LMFDB - Embedded newform 8023.2.a.b.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8023,2,Mod(1,8023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8023, 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("8023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8023 = 71 \cdot 113 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8023.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:	$64.0639775417$
Analytic rank:	$1$
Dimension:	$155$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.57631 q^{2} -2.78784 q^{3} +4.63739 q^{4} +0.760791 q^{5} +7.18234 q^{6} -2.92762 q^{7} -6.79473 q^{8} +4.77204 q^{9} +O(q^{10})$	\(q-2.57631 q^{2} -2.78784 q^{3} +4.63739 q^{4} +0.760791 q^{5} +7.18234 q^{6} -2.92762 q^{7} -6.79473 q^{8} +4.77204 q^{9} -1.96004 q^{10} +5.98266 q^{11} -12.9283 q^{12} -3.44832 q^{13} +7.54246 q^{14} -2.12096 q^{15} +8.23058 q^{16} +6.23699 q^{17} -12.2943 q^{18} +4.28132 q^{19} +3.52808 q^{20} +8.16172 q^{21} -15.4132 q^{22} +2.36302 q^{23} +18.9426 q^{24} -4.42120 q^{25} +8.88396 q^{26} -4.94016 q^{27} -13.5765 q^{28} +7.36329 q^{29} +5.46426 q^{30} -4.49583 q^{31} -7.61507 q^{32} -16.6787 q^{33} -16.0684 q^{34} -2.22731 q^{35} +22.1298 q^{36} -6.45544 q^{37} -11.0300 q^{38} +9.61336 q^{39} -5.16937 q^{40} +2.83527 q^{41} -21.0271 q^{42} +1.77408 q^{43} +27.7439 q^{44} +3.63053 q^{45} -6.08787 q^{46} -2.92887 q^{47} -22.9455 q^{48} +1.57094 q^{49} +11.3904 q^{50} -17.3877 q^{51} -15.9912 q^{52} +2.97703 q^{53} +12.7274 q^{54} +4.55156 q^{55} +19.8924 q^{56} -11.9356 q^{57} -18.9701 q^{58} -6.33108 q^{59} -9.83572 q^{60} -7.18208 q^{61} +11.5827 q^{62} -13.9707 q^{63} +3.15766 q^{64} -2.62345 q^{65} +42.9695 q^{66} +7.93165 q^{67} +28.9233 q^{68} -6.58771 q^{69} +5.73823 q^{70} +1.00000 q^{71} -32.4247 q^{72} +5.13937 q^{73} +16.6312 q^{74} +12.3256 q^{75} +19.8542 q^{76} -17.5149 q^{77} -24.7670 q^{78} -2.00273 q^{79} +6.26175 q^{80} -0.543764 q^{81} -7.30455 q^{82} -8.65243 q^{83} +37.8490 q^{84} +4.74505 q^{85} -4.57058 q^{86} -20.5276 q^{87} -40.6506 q^{88} -7.58731 q^{89} -9.35337 q^{90} +10.0954 q^{91} +10.9582 q^{92} +12.5336 q^{93} +7.54567 q^{94} +3.25719 q^{95} +21.2296 q^{96} -11.2053 q^{97} -4.04723 q^{98} +28.5495 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9}+O(q^{10}) $ 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9	\( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9} - 2 q^{10} - 24 q^{11} - 32 q^{12} - 62 q^{13} - 18 q^{14} - 12 q^{15} + 155 q^{16} - 129 q^{17} - 42 q^{18} - 18 q^{19} - 59 q^{20} - 45 q^{21} - 17 q^{22} - 38 q^{23} - 27 q^{24} + 129 q^{25} - 44 q^{26} - 43 q^{27} - 100 q^{28} - 52 q^{29} - 39 q^{30} - 56 q^{31} - 145 q^{32} - 126 q^{33} - q^{34} - 49 q^{35} + 131 q^{36} - 30 q^{37} - 91 q^{38} - 29 q^{39} - 5 q^{40} - 163 q^{41} - 80 q^{42} - 15 q^{43} - 118 q^{44} - 66 q^{45} + 2 q^{46} - 111 q^{47} - 89 q^{48} + 101 q^{49} - 121 q^{50} + 5 q^{51} - 111 q^{52} - 93 q^{53} - 68 q^{54} - 60 q^{55} - 27 q^{56} - 106 q^{57} + 16 q^{58} - 79 q^{59} - 103 q^{60} - 74 q^{61} - 102 q^{62} - 118 q^{63} + 175 q^{64} - 109 q^{65} + 65 q^{66} - 18 q^{67} - 346 q^{68} - 39 q^{69} + 32 q^{70} + 155 q^{71} - 203 q^{72} - 108 q^{73} - 87 q^{74} - 22 q^{75} - 16 q^{76} - 121 q^{77} - 75 q^{78} - 6 q^{79} - 136 q^{80} + 107 q^{81} - 30 q^{82} - 116 q^{83} - 5 q^{84} - 53 q^{85} + 8 q^{86} - 100 q^{87} - 43 q^{88} - 189 q^{89} - 76 q^{90} + 14 q^{91} - 99 q^{92} - 72 q^{93} + 17 q^{94} - 18 q^{95} - 50 q^{96} - 184 q^{97} - 249 q^{98} - 114 q^{99}+O(q^{100}) \) 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9 - 2 * q^10 - 24 * q^11 - 32 * q^12 - 62 * q^13 - 18 * q^14 - 12 * q^15 + 155 * q^16 - 129 * q^17 - 42 * q^18 - 18 * q^19 - 59 * q^20 - 45 * q^21 - 17 * q^22 - 38 * q^23 - 27 * q^24 + 129 * q^25 - 44 * q^26 - 43 * q^27 - 100 * q^28 - 52 * q^29 - 39 * q^30 - 56 * q^31 - 145 * q^32 - 126 * q^33 - q^34 - 49 * q^35 + 131 * q^36 - 30 * q^37 - 91 * q^38 - 29 * q^39 - 5 * q^40 - 163 * q^41 - 80 * q^42 - 15 * q^43 - 118 * q^44 - 66 * q^45 + 2 * q^46 - 111 * q^47 - 89 * q^48 + 101 * q^49 - 121 * q^50 + 5 * q^51 - 111 * q^52 - 93 * q^53 - 68 * q^54 - 60 * q^55 - 27 * q^56 - 106 * q^57 + 16 * q^58 - 79 * q^59 - 103 * q^60 - 74 * q^61 - 102 * q^62 - 118 * q^63 + 175 * q^64 - 109 * q^65 + 65 * q^66 - 18 * q^67 - 346 * q^68 - 39 * q^69 + 32 * q^70 + 155 * q^71 - 203 * q^72 - 108 * q^73 - 87 * q^74 - 22 * q^75 - 16 * q^76 - 121 * q^77 - 75 * q^78 - 6 * q^79 - 136 * q^80 + 107 * q^81 - 30 * q^82 - 116 * q^83 - 5 * q^84 - 53 * q^85 + 8 * q^86 - 100 * q^87 - 43 * q^88 - 189 * q^89 - 76 * q^90 + 14 * q^91 - 99 * q^92 - 72 * q^93 + 17 * q^94 - 18 * q^95 - 50 * q^96 - 184 * q^97 - 249 * q^98 - 114 * 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 $

$2$	−2.57631	−1.82173	−0.910864	−	0.412707i	$-0.864583\pi$
$2$	−2.57631	−1.82173	−0.910864	+	0.412707i	$0.864583\pi$
$3$	−2.78784	−1.60956	−0.804779	−	0.593574i	$-0.797716\pi$
$3$	−2.78784	−1.60956	−0.804779	+	0.593574i	$0.797716\pi$
$4$	4.63739	2.31869
$5$	0.760791	0.340236	0.170118	−	0.985424i	$-0.445585\pi$
$5$	0.760791	0.340236	0.170118	+	0.985424i	$0.445585\pi$
$6$	7.18234	2.93218
$7$	−2.92762	−1.10654	−0.553268	−	0.833004i	$-0.686619\pi$
$7$	−2.92762	−1.10654	−0.553268	+	0.833004i	$0.686619\pi$
$8$	−6.79473	−2.40230
$9$	4.77204	1.59068
$10$	−1.96004	−0.619818
$11$	5.98266	1.80384	0.901920	−	0.431902i	$-0.142158\pi$
$11$	5.98266	1.80384	0.901920	+	0.431902i	$0.142158\pi$
$12$	−12.9283	−3.73207
$13$	−3.44832	−0.956393	−0.478196	−	0.878253i	$-0.658709\pi$
$13$	−3.44832	−0.956393	−0.478196	+	0.878253i	$0.658709\pi$
$14$	7.54246	2.01581
$15$	−2.12096	−0.547630
$16$	8.23058	2.05764
$17$	6.23699	1.51269	0.756346	−	0.654172i	$-0.226983\pi$
$17$	6.23699	1.51269	0.756346	+	0.654172i	$0.226983\pi$
$18$	−12.2943	−2.89779
$19$	4.28132	0.982203	0.491102	−	0.871102i	$-0.336594\pi$
$19$	4.28132	0.982203	0.491102	+	0.871102i	$0.336594\pi$
$20$	3.52808	0.788903
$21$	8.16172	1.78103
$22$	−15.4132	−3.28611
$23$	2.36302	0.492723	0.246362	−	0.969178i	$-0.420765\pi$
$23$	2.36302	0.492723	0.246362	+	0.969178i	$0.420765\pi$
$24$	18.9426	3.86664
$25$	−4.42120	−0.884239
$26$	8.88396	1.74229
$27$	−4.94016	−0.950733
$28$	−13.5765	−2.56572
$29$	7.36329	1.36733	0.683664	−	0.729797i	$-0.260385\pi$
$29$	7.36329	1.36733	0.683664	+	0.729797i	$0.260385\pi$
$30$	5.46426	0.997633
$31$	−4.49583	−0.807475	−0.403737	−	0.914875i	$-0.632289\pi$
$31$	−4.49583	−0.807475	−0.403737	+	0.914875i	$0.632289\pi$
$32$	−7.61507	−1.34617
$33$	−16.6787	−2.90339
$34$	−16.0684	−2.75571
$35$	−2.22731	−0.376483
$36$	22.1298	3.68830
$37$	−6.45544	−1.06127	−0.530634	−	0.847601i	$-0.678046\pi$
$37$	−6.45544	−1.06127	−0.530634	+	0.847601i	$0.678046\pi$
$38$	−11.0300	−1.78931
$39$	9.61336	1.53937
$40$	−5.16937	−0.817349
$41$	2.83527	0.442795	0.221398	−	0.975184i	$-0.428938\pi$
$41$	2.83527	0.442795	0.221398	+	0.975184i	$0.428938\pi$
$42$	−21.0271	−3.24456
$43$	1.77408	0.270544	0.135272	−	0.990808i	$-0.456809\pi$
$43$	1.77408	0.270544	0.135272	+	0.990808i	$0.456809\pi$
$44$	27.7439	4.18255
$45$	3.63053	0.541207
$46$	−6.08787	−0.897608
$47$	−2.92887	−0.427219	−0.213609	−	0.976919i	$-0.568522\pi$
$47$	−2.92887	−0.427219	−0.213609	+	0.976919i	$0.568522\pi$
$48$	−22.9455	−3.31190
$49$	1.57094	0.224420
$50$	11.3904	1.61084
$51$	−17.3877	−2.43477
$52$	−15.9912	−2.21758
$53$	2.97703	0.408927	0.204463	−	0.978874i	$-0.434455\pi$
$53$	2.97703	0.408927	0.204463	+	0.978874i	$0.434455\pi$
$54$	12.7274	1.73198
$55$	4.55156	0.613732
$56$	19.8924	2.65823
$57$	−11.9356	−1.58091
$58$	−18.9701	−2.49090
$59$	−6.33108	−0.824237	−0.412118	−	0.911130i	$-0.635211\pi$
$59$	−6.33108	−0.824237	−0.412118	+	0.911130i	$0.635211\pi$
$60$	−9.83572	−1.26979
$61$	−7.18208	−0.919571	−0.459786	−	0.888030i	$-0.652074\pi$
$61$	−7.18208	−0.919571	−0.459786	+	0.888030i	$0.652074\pi$
$62$	11.5827	1.47100
$63$	−13.9707	−1.76014
$64$	3.15766	0.394707
$65$	−2.62345	−0.325399
$66$	42.9695	5.28918
$67$	7.93165	0.969005	0.484503	−	0.874790i	$-0.339001\pi$
$67$	7.93165	0.969005	0.484503	+	0.874790i	$0.339001\pi$
$68$	28.9233	3.50747
$69$	−6.58771	−0.793067
$70$	5.73823	0.685850
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	−32.4247	−3.82129
$73$	5.13937	0.601518	0.300759	−	0.953700i	$-0.402760\pi$
$73$	5.13937	0.601518	0.300759	+	0.953700i	$0.402760\pi$
$74$	16.6312	1.93334
$75$	12.3256	1.42324
$76$	19.8542	2.27743
$77$	−17.5149	−1.99601
$78$	−24.7670	−2.80431
$79$	−2.00273	−0.225325	−0.112662	−	0.993633i	$-0.535938\pi$
$79$	−2.00273	−0.225325	−0.112662	+	0.993633i	$0.535938\pi$
$80$	6.26175	0.700085
$81$	−0.543764	−0.0604182
$82$	−7.30455	−0.806652
$83$	−8.65243	−0.949728	−0.474864	−	0.880059i	$-0.657503\pi$
$83$	−8.65243	−0.949728	−0.474864	+	0.880059i	$0.657503\pi$
$84$	37.8490	4.12967
$85$	4.74505	0.514673
$86$	−4.57058	−0.492858
$87$	−20.5276	−2.20079
$88$	−40.6506	−4.33337
$89$	−7.58731	−0.804253	−0.402127	−	0.915584i	$-0.631729\pi$
$89$	−7.58731	−0.804253	−0.402127	+	0.915584i	$0.631729\pi$
$90$	−9.35337	−0.985932
$91$	10.0954	1.05828
$92$	10.9582	1.14247
$93$	12.5336	1.29968
$94$	7.54567	0.778277
$95$	3.25719	0.334181
$96$	21.2296	2.16674
$97$	−11.2053	−1.13773	−0.568865	−	0.822431i	$-0.692617\pi$
$97$	−11.2053	−1.13773	−0.568865	+	0.822431i	$0.692617\pi$
$98$	−4.04723	−0.408832
$99$	28.5495	2.86933
$100$	−20.5028	−2.05028
$101$	4.34313	0.432157	0.216079	−	0.976376i	$-0.430673\pi$
$101$	4.34313	0.432157	0.216079	+	0.976376i	$0.430673\pi$
$102$	44.7962	4.43548
$103$	−9.38031	−0.924269	−0.462135	−	0.886810i	$-0.652916\pi$
$103$	−9.38031	−0.924269	−0.462135	+	0.886810i	$0.652916\pi$
$104$	23.4304	2.29754
$105$	6.20937	0.605972
$106$	−7.66976	−0.744953
$107$	−7.19536	−0.695602	−0.347801	−	0.937568i	$-0.613071\pi$
$107$	−7.19536	−0.695602	−0.347801	+	0.937568i	$0.613071\pi$
$108$	−22.9094	−2.20446
$109$	−0.305507	−0.0292622	−0.0146311	−	0.999893i	$-0.504657\pi$
$109$	−0.305507	−0.0292622	−0.0146311	+	0.999893i	$0.504657\pi$
$110$	−11.7262	−1.11805
$111$	17.9967	1.70817
$112$	−24.0960	−2.27686
$113$	1.00000	0.0940721
$113$	1.00000	0.0940721
$114$	30.7499	2.88000
$115$	1.79776	0.167642
$116$	34.1464	3.17041
$117$	−16.4555	−1.52131
$118$	16.3108	1.50153
$119$	−18.2595	−1.67385
$120$	14.4114	1.31557
$121$	24.7923	2.25384
$122$	18.5033	1.67521
$123$	−7.90428	−0.712705
$124$	−20.8489	−1.87229
$125$	−7.16756	−0.641086
$126$	35.9929	3.20650
$127$	12.0868	1.07253	0.536263	−	0.844051i	$-0.319835\pi$
$127$	12.0868	1.07253	0.536263	+	0.844051i	$0.319835\pi$
$128$	7.09503	0.627118
$129$	−4.94584	−0.435457
$130$	6.75884	0.592789
$131$	−2.51824	−0.220020	−0.110010	−	0.993931i	$-0.535088\pi$
$131$	−2.51824	−0.220020	−0.110010	+	0.993931i	$0.535088\pi$
$132$	−77.3455	−6.73206
$133$	−12.5341	−1.08684
$134$	−20.4344	−1.76526
$135$	−3.75843	−0.323474
$136$	−42.3786	−3.63394
$137$	−15.6756	−1.33926	−0.669629	−	0.742696i	$-0.733547\pi$
$137$	−15.6756	−1.33926	−0.669629	+	0.742696i	$0.733547\pi$
$138$	16.9720	1.44475
$139$	−5.10750	−0.433213	−0.216606	−	0.976259i	$-0.569499\pi$
$139$	−5.10750	−0.433213	−0.216606	+	0.976259i	$0.569499\pi$
$140$	−10.3289	−0.872949
$141$	8.16520	0.687634
$142$	−2.57631	−0.216199
$143$	−20.6302	−1.72518
$144$	39.2766	3.27305
$145$	5.60192	0.465214
$146$	−13.2406	−1.09580
$147$	−4.37953	−0.361217
$148$	−29.9364	−2.46075
$149$	7.79402	0.638511	0.319255	−	0.947669i	$-0.396567\pi$
$149$	7.79402	0.638511	0.319255	+	0.947669i	$0.396567\pi$
$150$	−31.7545	−2.59275
$151$	2.93453	0.238808	0.119404	−	0.992846i	$-0.461902\pi$
$151$	2.93453	0.238808	0.119404	+	0.992846i	$0.461902\pi$
$152$	−29.0904	−2.35955
$153$	29.7631	2.40621
$154$	45.1240	3.63619
$155$	−3.42039	−0.274732
$156$	44.5809	3.56933
$157$	−11.4423	−0.913198	−0.456599	−	0.889672i	$-0.650933\pi$
$157$	−11.4423	−0.913198	−0.456599	+	0.889672i	$0.650933\pi$
$158$	5.15965	0.410480
$159$	−8.29948	−0.658191
$160$	−5.79348	−0.458015
$161$	−6.91801	−0.545215
$162$	1.40091	0.110066
$163$	−3.32521	−0.260450	−0.130225	−	0.991484i	$-0.541570\pi$
$163$	−3.32521	−0.260450	−0.130225	+	0.991484i	$0.541570\pi$
$164$	13.1483	1.02671
$165$	−12.6890	−0.987838
$166$	22.2914	1.73015
$167$	21.8780	1.69297	0.846487	−	0.532409i	$-0.178713\pi$
$167$	21.8780	1.69297	0.846487	+	0.532409i	$0.178713\pi$
$168$	−55.4567	−4.27858
$169$	−1.10907	−0.0853131
$170$	−12.2247	−0.937593
$171$	20.4306	1.56237
$172$	8.22708	0.627309
$173$	−10.1631	−0.772689	−0.386344	−	0.922355i	$-0.626262\pi$
$173$	−10.1631	−0.772689	−0.386344	+	0.922355i	$0.626262\pi$
$174$	52.8856	4.00925
$175$	12.9436	0.978442
$176$	49.2408	3.71166
$177$	17.6500	1.32666
$178$	19.5473	1.46513
$179$	−23.5561	−1.76066	−0.880331	−	0.474360i	$-0.842680\pi$
$179$	−23.5561	−1.76066	−0.880331	+	0.474360i	$0.842680\pi$
$180$	16.8361	1.25489
$181$	−22.5920	−1.67925	−0.839625	−	0.543167i	$-0.817225\pi$
$181$	−22.5920	−1.67925	−0.839625	+	0.543167i	$0.817225\pi$
$182$	−26.0088	−1.92790
$183$	20.0225	1.48010
$184$	−16.0561	−1.18367
$185$	−4.91124	−0.361082
$186$	−32.2906	−2.36766
$187$	37.3138	2.72865
$188$	−13.5823	−0.990590
$189$	14.4629	1.05202
$190$	−8.39155	−0.608787
$191$	0.186753	0.0135130	0.00675650	−	0.999977i	$-0.497849\pi$
$191$	0.186753	0.0135130	0.00675650	+	0.999977i	$0.497849\pi$
$192$	−8.80304	−0.635305
$193$	−18.3069	−1.31776	−0.658878	−	0.752249i	$-0.728969\pi$
$193$	−18.3069	−1.31776	−0.658878	+	0.752249i	$0.728969\pi$
$194$	28.8685	2.07263
$195$	7.31376	0.523749
$196$	7.28506	0.520361
$197$	−2.02736	−0.144444	−0.0722218	−	0.997389i	$-0.523009\pi$
$197$	−2.02736	−0.144444	−0.0722218	+	0.997389i	$0.523009\pi$
$198$	−73.5524	−5.22714
$199$	−4.95973	−0.351586	−0.175793	−	0.984427i	$-0.556249\pi$
$199$	−4.95973	−0.351586	−0.175793	+	0.984427i	$0.556249\pi$
$200$	30.0408	2.12421
$201$	−22.1122	−1.55967
$202$	−11.1893	−0.787273
$203$	−21.5569	−1.51300
$204$	−80.6335	−5.64548
$205$	2.15705	0.150655
$206$	24.1666	1.68377
$207$	11.2764	0.783765
$208$	−28.3817	−1.96792
$209$	25.6137	1.77174
$210$	−15.9973	−1.10392
$211$	−17.0099	−1.17101	−0.585505	−	0.810669i	$-0.699104\pi$
$211$	−17.0099	−1.17101	−0.585505	+	0.810669i	$0.699104\pi$
$212$	13.8056	0.948175
$213$	−2.78784	−0.191019
$214$	18.5375	1.26720
$215$	1.34970	0.0920490
$216$	33.5670	2.28395
$217$	13.1621	0.893499
$218$	0.787080	0.0533078
$219$	−14.3277	−0.968179
$220$	21.1073	1.42306
$221$	−21.5071	−1.44673
$222$	−46.3652	−3.11183
$223$	14.5470	0.974142	0.487071	−	0.873362i	$-0.338065\pi$
$223$	14.5470	0.974142	0.487071	+	0.873362i	$0.338065\pi$
$224$	22.2940	1.48958
$225$	−21.0981	−1.40654
$226$	−2.57631	−0.171374
$227$	−15.7477	−1.04521	−0.522605	−	0.852575i	$-0.675040\pi$
$227$	−15.7477	−1.04521	−0.522605	+	0.852575i	$0.675040\pi$
$228$	−55.3502	−3.66565
$229$	5.49174	0.362904	0.181452	−	0.983400i	$-0.441920\pi$
$229$	5.49174	0.362904	0.181452	+	0.983400i	$0.441920\pi$
$230$	−4.63160	−0.305399
$231$	48.8288	3.21270
$232$	−50.0315	−3.28473
$233$	3.23064	0.211646	0.105823	−	0.994385i	$-0.466252\pi$
$233$	3.23064	0.211646	0.105823	+	0.994385i	$0.466252\pi$
$234$	42.3946	2.77142
$235$	−2.22826	−0.145355
$236$	−29.3597	−1.91115
$237$	5.58328	0.362673
$238$	47.0422	3.04929
$239$	1.12231	0.0725960	0.0362980	−	0.999341i	$-0.488443\pi$
$239$	1.12231	0.0725960	0.0362980	+	0.999341i	$0.488443\pi$
$240$	−17.4567	−1.12683
$241$	−25.0986	−1.61674	−0.808370	−	0.588674i	$-0.799650\pi$
$241$	−25.0986	−1.61674	−0.808370	+	0.588674i	$0.799650\pi$
$242$	−63.8726	−4.10589
$243$	16.3364	1.04798
$244$	−33.3061	−2.13220
$245$	1.19516	0.0763558
$246$	20.3639	1.29835
$247$	−14.7634	−0.939372
$248$	30.5479	1.93980
$249$	24.1216	1.52864
$250$	18.4659	1.16789
$251$	7.38086	0.465875	0.232938	−	0.972492i	$-0.425166\pi$
$251$	7.38086	0.465875	0.232938	+	0.972492i	$0.425166\pi$
$252$	−64.7875	−4.08123
$253$	14.1371	0.888794
$254$	−31.1393	−1.95385
$255$	−13.2284	−0.828396
$256$	−24.5943	−1.53715
$257$	2.50072	0.155990	0.0779952	−	0.996954i	$-0.475148\pi$
$257$	2.50072	0.155990	0.0779952	+	0.996954i	$0.475148\pi$
$258$	12.7420	0.793284
$259$	18.8991	1.17433
$260$	−12.1660	−0.754501
$261$	35.1379	2.17498
$262$	6.48777	0.400816
$263$	7.57278	0.466958	0.233479	−	0.972362i	$-0.424989\pi$
$263$	7.57278	0.466958	0.233479	+	0.972362i	$0.424989\pi$
$264$	113.327	6.97481
$265$	2.26490	0.139132
$266$	32.2917	1.97993
$267$	21.1522	1.29449
$268$	36.7821	2.24683
$269$	21.6025	1.31713	0.658564	−	0.752525i	$-0.271164\pi$
$269$	21.6025	1.31713	0.658564	+	0.752525i	$0.271164\pi$
$270$	9.68288	0.589282
$271$	24.5192	1.48944	0.744718	−	0.667379i	$-0.232584\pi$
$271$	24.5192	1.48944	0.744718	+	0.667379i	$0.232584\pi$
$272$	51.3340	3.11258
$273$	−28.1442	−1.70337
$274$	40.3853	2.43976
$275$	−26.4505	−1.59503
$276$	−30.5497	−1.83888
$277$	6.45872	0.388067	0.194033	−	0.980995i	$-0.437843\pi$
$277$	6.45872	0.388067	0.194033	+	0.980995i	$0.437843\pi$
$278$	13.1585	0.789196
$279$	−21.4543	−1.28443
$280$	15.1339	0.904426
$281$	−27.5636	−1.64431	−0.822153	−	0.569266i	$-0.807227\pi$
$281$	−27.5636	−1.64431	−0.822153	+	0.569266i	$0.807227\pi$
$282$	−21.0361	−1.25268
$283$	5.57710	0.331524	0.165762	−	0.986166i	$-0.446992\pi$
$283$	5.57710	0.331524	0.165762	+	0.986166i	$0.446992\pi$
$284$	4.63739	0.275178
$285$	−9.08053	−0.537884
$286$	53.1497	3.14281
$287$	−8.30059	−0.489968
$288$	−36.3394	−2.14132
$289$	21.9000	1.28824
$290$	−14.4323	−0.847494
$291$	31.2387	1.83124
$292$	23.8333	1.39474
$293$	19.9780	1.16712	0.583562	−	0.812068i	$-0.301658\pi$
$293$	19.9780	1.16712	0.583562	+	0.812068i	$0.301658\pi$
$294$	11.2830	0.658040
$295$	−4.81663	−0.280435
$296$	43.8630	2.54948
$297$	−29.5553	−1.71497
$298$	−20.0798	−1.16319
$299$	−8.14845	−0.471237
$300$	57.1585	3.30005
$301$	−5.19382	−0.299367
$302$	−7.56026	−0.435044
$303$	−12.1079	−0.695582
$304$	35.2378	2.02102
$305$	−5.46407	−0.312871
$306$	−76.6792	−4.38346
$307$	−10.8114	−0.617042	−0.308521	−	0.951218i	$-0.599834\pi$
$307$	−10.8114	−0.617042	−0.308521	+	0.951218i	$0.599834\pi$
$308$	−81.2236	−4.62814
$309$	26.1508	1.48767
$310$	8.81198	0.500487
$311$	29.1346	1.65207	0.826035	−	0.563618i	$-0.190591\pi$
$311$	29.1346	1.65207	0.826035	+	0.563618i	$0.190591\pi$
$312$	−65.3202	−3.69803
$313$	19.4741	1.10074	0.550371	−	0.834921i	$-0.314486\pi$
$313$	19.4741	1.10074	0.550371	+	0.834921i	$0.314486\pi$
$314$	29.4791	1.66360
$315$	−10.6288	−0.598864
$316$	−9.28742	−0.522458
$317$	23.3808	1.31319	0.656597	−	0.754241i	$-0.271995\pi$
$317$	23.3808	1.31319	0.656597	+	0.754241i	$0.271995\pi$
$318$	21.3820	1.19905
$319$	44.0521	2.46644
$320$	2.40232	0.134294
$321$	20.0595	1.11961
$322$	17.8230	0.993234
$323$	26.7026	1.48577
$324$	−2.52164	−0.140091
$325$	15.2457	0.845680
$326$	8.56677	0.474470
$327$	0.851703	0.0470993
$328$	−19.2649	−1.06373
$329$	8.57460	0.472733
$330$	32.6908	1.79957
$331$	20.9269	1.15025	0.575123	−	0.818067i	$-0.304954\pi$
$331$	20.9269	1.15025	0.575123	+	0.818067i	$0.304954\pi$
$332$	−40.1247	−2.20213
$333$	−30.8056	−1.68814
$334$	−56.3647	−3.08414
$335$	6.03433	0.329691
$336$	67.1757	3.66473
$337$	29.2419	1.59291	0.796454	−	0.604699i	$-0.206706\pi$
$337$	29.2419	1.59291	0.796454	+	0.604699i	$0.206706\pi$
$338$	2.85731	0.155417
$339$	−2.78784	−0.151415
$340$	22.0046	1.19337
$341$	−26.8970	−1.45656
$342$	−52.6357	−2.84621
$343$	15.8942	0.858206
$344$	−12.0544	−0.649929
$345$	−5.01187	−0.269830
$346$	26.1834	1.40763
$347$	−18.2552	−0.979991	−0.489996	−	0.871725i	$-0.663002\pi$
$347$	−18.2552	−0.979991	−0.489996	+	0.871725i	$0.663002\pi$
$348$	−95.1946	−5.10297
$349$	0.938089	0.0502148	0.0251074	−	0.999685i	$-0.492007\pi$
$349$	0.938089	0.0502148	0.0251074	+	0.999685i	$0.492007\pi$
$350$	−33.3467	−1.78246
$351$	17.0353	0.909274
$352$	−45.5584	−2.42827
$353$	−16.1734	−0.860821	−0.430411	−	0.902633i	$-0.641631\pi$
$353$	−16.1734	−0.860821	−0.430411	+	0.902633i	$0.641631\pi$
$354$	−45.4720	−2.41681
$355$	0.760791	0.0403786
$356$	−35.1853	−1.86482
$357$	50.9046	2.69415
$358$	60.6878	3.20745
$359$	12.1575	0.641651	0.320825	−	0.947138i	$-0.396040\pi$
$359$	12.1575	0.641651	0.320825	+	0.947138i	$0.396040\pi$
$360$	−24.6684	−1.30014
$361$	−0.670258	−0.0352768
$362$	58.2040	3.05914
$363$	−69.1168	−3.62769
$364$	46.8161	2.45383
$365$	3.90999	0.204658
$366$	−51.5842	−2.69635
$367$	32.4197	1.69229	0.846147	−	0.532949i	$-0.178916\pi$
$367$	32.4197	1.69229	0.846147	+	0.532949i	$0.178916\pi$
$368$	19.4490	1.01385
$369$	13.5300	0.704345
$370$	12.6529	0.657793
$371$	−8.71560	−0.452492
$372$	58.1233	3.01355
$373$	2.40546	0.124550	0.0622751	−	0.998059i	$-0.480164\pi$
$373$	2.40546	0.124550	0.0622751	+	0.998059i	$0.480164\pi$
$374$	−96.1320	−4.97087
$375$	19.9820	1.03187
$376$	19.9009	1.02631
$377$	−25.3910	−1.30770
$378$	−37.2609	−1.91649
$379$	21.5193	1.10537	0.552686	−	0.833389i	$-0.313603\pi$
$379$	21.5193	1.10537	0.552686	+	0.833389i	$0.313603\pi$
$380$	15.1049	0.774863
$381$	−33.6959	−1.72629
$382$	−0.481135	−0.0246170
$383$	−18.7236	−0.956731	−0.478366	−	0.878161i	$-0.658771\pi$
$383$	−18.7236	−0.956731	−0.478366	+	0.878161i	$0.658771\pi$
$384$	−19.7798	−1.00938
$385$	−13.3252	−0.679116
$386$	47.1642	2.40059
$387$	8.46597	0.430349
$388$	−51.9635	−2.63805
$389$	−6.11441	−0.310013	−0.155006	−	0.987913i	$-0.549540\pi$
$389$	−6.11441	−0.310013	−0.155006	+	0.987913i	$0.549540\pi$
$390$	−18.8425	−0.954129
$391$	14.7381	0.745338
$392$	−10.6741	−0.539124
$393$	7.02044	0.354134
$394$	5.22312	0.263137
$395$	−1.52366	−0.0766636
$396$	132.395	6.65310
$397$	−24.2447	−1.21681	−0.608404	−	0.793628i	$-0.708190\pi$
$397$	−24.2447	−1.21681	−0.608404	+	0.793628i	$0.708190\pi$
$398$	12.7778	0.640493
$399$	34.9430	1.74934
$400$	−36.3890	−1.81945
$401$	17.6166	0.879732	0.439866	−	0.898064i	$-0.355026\pi$
$401$	17.6166	0.879732	0.439866	+	0.898064i	$0.355026\pi$
$402$	56.9678	2.84130
$403$	15.5031	0.772263
$404$	20.1408	1.00204
$405$	−0.413691	−0.0205565
$406$	55.5373	2.75627
$407$	−38.6207	−1.91436
$408$	118.145	5.84904
$409$	8.74036	0.432183	0.216091	−	0.976373i	$-0.430669\pi$
$409$	8.74036	0.432183	0.216091	+	0.976373i	$0.430669\pi$
$410$	−5.55724	−0.274452
$411$	43.7011	2.15561
$412$	−43.5001	−2.14310
$413$	18.5350	0.912047
$414$	−29.0516	−1.42781
$415$	−6.58269	−0.323132
$416$	26.2592	1.28746
$417$	14.2389	0.697281
$418$	−65.9889	−3.22762
$419$	5.86543	0.286545	0.143273	−	0.989683i	$-0.454237\pi$
$419$	5.86543	0.286545	0.143273	+	0.989683i	$0.454237\pi$
$420$	28.7952	1.40506
$421$	−7.79754	−0.380029	−0.190014	−	0.981781i	$-0.560853\pi$
$421$	−7.79754	−0.380029	−0.190014	+	0.981781i	$0.560853\pi$
$422$	43.8228	2.13326
$423$	−13.9767	−0.679568
$424$	−20.2281	−0.982364
$425$	−27.5749	−1.33758
$426$	7.18234	0.347986
$427$	21.0264	1.01754
$428$	−33.3677	−1.61289
$429$	57.5135	2.77678
$430$	−3.47726	−0.167688
$431$	9.30625	0.448266	0.224133	−	0.974559i	$-0.428045\pi$
$431$	9.30625	0.448266	0.224133	+	0.974559i	$0.428045\pi$
$432$	−40.6603	−1.95627
$433$	−15.9406	−0.766057	−0.383028	−	0.923737i	$-0.625119\pi$
$433$	−15.9406	−0.766057	−0.383028	+	0.923737i	$0.625119\pi$
$434$	−33.9096	−1.62771
$435$	−15.6173	−0.748790
$436$	−1.41675	−0.0678501
$437$	10.1168	0.483954
$438$	36.9127	1.76376
$439$	−15.0413	−0.717880	−0.358940	−	0.933361i	$-0.616862\pi$
$439$	−15.0413	−0.717880	−0.358940	+	0.933361i	$0.616862\pi$
$440$	−30.9266	−1.47437
$441$	7.49659	0.356980
$442$	55.4091	2.63554
$443$	23.8879	1.13495	0.567473	−	0.823392i	$-0.307921\pi$
$443$	23.8879	1.13495	0.567473	+	0.823392i	$0.307921\pi$
$444$	83.4577	3.96073
$445$	−5.77236	−0.273636
$446$	−37.4777	−1.77462
$447$	−21.7285	−1.02772
$448$	−9.24442	−0.436758
$449$	−10.3539	−0.488629	−0.244315	−	0.969696i	$-0.578563\pi$
$449$	−10.3539	−0.488629	−0.244315	+	0.969696i	$0.578563\pi$
$450$	54.3554	2.56234
$451$	16.9625	0.798732
$452$	4.63739	0.218124
$453$	−8.18099	−0.384376
$454$	40.5709	1.90409
$455$	7.68047	0.360066
$456$	81.0994	3.79783
$457$	−40.2291	−1.88184	−0.940918	−	0.338634i	$-0.890035\pi$
$457$	−40.2291	−1.88184	−0.940918	+	0.338634i	$0.890035\pi$
$458$	−14.1484	−0.661113
$459$	−30.8117	−1.43817
$460$	8.33692	0.388711
$461$	−4.51166	−0.210129	−0.105064	−	0.994465i	$-0.533505\pi$
$461$	−4.51166	−0.210129	−0.105064	+	0.994465i	$0.533505\pi$
$462$	−125.798	−5.85267
$463$	16.8840	0.784667	0.392334	−	0.919823i	$-0.371668\pi$
$463$	16.8840	0.784667	0.392334	+	0.919823i	$0.371668\pi$
$464$	60.6041	2.81347
$465$	9.53548	0.442197
$466$	−8.32314	−0.385562
$467$	−36.1679	−1.67365	−0.836825	−	0.547470i	$-0.815591\pi$
$467$	−36.1679	−1.67365	−0.836825	+	0.547470i	$0.815591\pi$
$468$	−76.3106	−3.52746
$469$	−23.2208	−1.07224
$470$	5.74068	0.264798
$471$	31.8994	1.46985
$472$	43.0180	1.98006
$473$	10.6137	0.488019
$474$	−14.3843	−0.660692
$475$	−18.9286	−0.868503
$476$	−84.6764	−3.88114
$477$	14.2065	0.650471
$478$	−2.89141	−0.132250
$479$	−23.2173	−1.06083	−0.530413	−	0.847739i	$-0.677963\pi$
$479$	−23.2173	−1.06083	−0.530413	+	0.847739i	$0.677963\pi$
$480$	16.1513	0.737202
$481$	22.2604	1.01499
$482$	64.6617	2.94526
$483$	19.2863	0.877556
$484$	114.971	5.22597
$485$	−8.52492	−0.387097
$486$	−42.0877	−1.90913
$487$	−10.7789	−0.488438	−0.244219	−	0.969720i	$-0.578532\pi$
$487$	−10.7789	−0.488438	−0.244219	+	0.969720i	$0.578532\pi$
$488$	48.8003	2.20909
$489$	9.27014	0.419210
$490$	−3.07910	−0.139100
$491$	32.6893	1.47525	0.737624	−	0.675211i	$-0.235948\pi$
$491$	32.6893	1.47525	0.737624	+	0.675211i	$0.235948\pi$
$492$	−36.6552	−1.65254
$493$	45.9247	2.06835
$494$	38.0351	1.71128
$495$	21.7202	0.976251
$496$	−37.0033	−1.66150
$497$	−2.92762	−0.131322
$498$	−62.1447	−2.78477
$499$	−23.8217	−1.06640	−0.533202	−	0.845988i	$-0.679012\pi$
$499$	−23.8217	−1.06640	−0.533202	+	0.845988i	$0.679012\pi$
$500$	−33.2388	−1.48648
$501$	−60.9925	−2.72494
$502$	−19.0154	−0.848698
$503$	14.9798	0.667914	0.333957	−	0.942588i	$-0.391616\pi$
$503$	14.9798	0.667914	0.333957	+	0.942588i	$0.391616\pi$
$504$	94.9271	4.22839
$505$	3.30421	0.147036
$506$	−36.4217	−1.61914
$507$	3.09191	0.137316
$508$	56.0510	2.48686
$509$	−33.5549	−1.48730	−0.743648	−	0.668572i	$-0.766906\pi$
$509$	−33.5549	−1.48730	−0.743648	+	0.668572i	$0.766906\pi$
$510$	34.0805	1.50911
$511$	−15.0461	−0.665601
$512$	49.1726	2.17314
$513$	−21.1504	−0.933813
$514$	−6.44263	−0.284172
$515$	−7.13646	−0.314470
$516$	−22.9358	−1.00969
$517$	−17.5224	−0.770635
$518$	−48.6899	−2.13931
$519$	28.3332	1.24369
$520$	17.8257	0.781707
$521$	−41.1039	−1.80079	−0.900397	−	0.435068i	$-0.856724\pi$
$521$	−41.1039	−1.80079	−0.900397	+	0.435068i	$0.856724\pi$
$522$	−90.5262	−3.96222
$523$	−29.4636	−1.28836	−0.644178	−	0.764876i	$-0.722800\pi$
$523$	−29.4636	−1.28836	−0.644178	+	0.764876i	$0.722800\pi$
$524$	−11.6780	−0.510158
$525$	−36.0846	−1.57486
$526$	−19.5098	−0.850670
$527$	−28.0404	−1.22146
$528$	−137.275	−5.97414
$529$	−17.4161	−0.757224
$530$	−5.83509	−0.253460
$531$	−30.2122	−1.31110
$532$	−58.1254	−2.52005
$533$	−9.77693	−0.423486
$534$	−54.4946	−2.35821
$535$	−5.47417	−0.236669
$536$	−53.8934	−2.32784
$537$	65.6705	2.83389
$538$	−55.6548	−2.39945
$539$	9.39841	0.404818
$540$	−17.4293	−0.750037
$541$	5.14948	0.221393	0.110697	−	0.993854i	$-0.464692\pi$
$541$	5.14948	0.221393	0.110697	+	0.993854i	$0.464692\pi$
$542$	−63.1691	−2.71335
$543$	62.9828	2.70285
$544$	−47.4951	−2.03634
$545$	−0.232427	−0.00995607
$546$	72.5084	3.10307
$547$	15.5762	0.665991	0.332995	−	0.942928i	$-0.391941\pi$
$547$	15.5762	0.665991	0.332995	+	0.942928i	$0.391941\pi$
$548$	−72.6939	−3.10533
$549$	−34.2732	−1.46274
$550$	68.1448	2.90571
$551$	31.5246	1.34299
$552$	44.7617	1.90518
$553$	5.86322	0.249330
$554$	−16.6397	−0.706952
$555$	13.6917	0.581182
$556$	−23.6855	−1.00449
$557$	31.3827	1.32973	0.664865	−	0.746964i	$-0.268489\pi$
$557$	31.3827	1.32973	0.664865	+	0.746964i	$0.268489\pi$
$558$	55.2729	2.33989
$559$	−6.11759	−0.258747
$560$	−18.3320	−0.774669
$561$	−104.025	−4.39193
$562$	71.0125	2.99548
$563$	−7.27545	−0.306624	−0.153312	−	0.988178i	$-0.548994\pi$
$563$	−7.27545	−0.306624	−0.153312	+	0.988178i	$0.548994\pi$
$564$	37.8652	1.59441
$565$	0.760791	0.0320067
$566$	−14.3683	−0.603947
$567$	1.59193	0.0668549
$568$	−6.79473	−0.285101
$569$	3.47563	0.145706	0.0728529	−	0.997343i	$-0.476790\pi$
$569$	3.47563	0.145706	0.0728529	+	0.997343i	$0.476790\pi$
$570$	23.3943	0.979879
$571$	−26.0413	−1.08979	−0.544897	−	0.838503i	$-0.683431\pi$
$571$	−26.0413	−1.08979	−0.544897	+	0.838503i	$0.683431\pi$
$572$	−95.6700	−4.00016
$573$	−0.520638	−0.0217500
$574$	21.3849	0.892589
$575$	−10.4474	−0.435685
$576$	15.0685	0.627853
$577$	5.22302	0.217437	0.108719	−	0.994073i	$-0.465325\pi$
$577$	5.22302	0.217437	0.108719	+	0.994073i	$0.465325\pi$
$578$	−56.4213	−2.34682
$579$	51.0366	2.12101
$580$	25.9783	1.07869
$581$	25.3310	1.05091
$582$	−80.4806	−3.33603
$583$	17.8106	0.737638
$584$	−34.9207	−1.44503
$585$	−12.5192	−0.517606
$586$	−51.4694	−2.12618
$587$	1.83918	0.0759109	0.0379554	−	0.999279i	$-0.487916\pi$
$587$	1.83918	0.0759109	0.0379554	+	0.999279i	$0.487916\pi$
$588$	−20.3096	−0.837552
$589$	−19.2481	−0.793104
$590$	12.4091	0.510877
$591$	5.65196	0.232491
$592$	−53.1320	−2.18371
$593$	12.1809	0.500211	0.250105	−	0.968219i	$-0.419535\pi$
$593$	12.1809	0.500211	0.250105	+	0.968219i	$0.419535\pi$
$594$	76.1436	3.12421
$595$	−13.8917	−0.569503
$596$	36.1439	1.48051
$597$	13.8269	0.565898
$598$	20.9929	0.858465
$599$	−7.98954	−0.326444	−0.163222	−	0.986589i	$-0.552189\pi$
$599$	−7.98954	−0.326444	−0.163222	+	0.986589i	$0.552189\pi$
$600$	−83.7490	−3.41904
$601$	−16.6579	−0.679488	−0.339744	−	0.940518i	$-0.610341\pi$
$601$	−16.6579	−0.679488	−0.339744	+	0.940518i	$0.610341\pi$
$602$	13.3809	0.545365
$603$	37.8501	1.54138
$604$	13.6085	0.553724
$605$	18.8617	0.766838
$606$	31.1938	1.26716
$607$	−48.3961	−1.96434	−0.982168	−	0.188005i	$-0.939798\pi$
$607$	−48.3961	−1.96434	−0.982168	+	0.188005i	$0.939798\pi$
$608$	−32.6026	−1.32221
$609$	60.0971	2.43526
$610$	14.0771	0.569967
$611$	10.0997	0.408589
$612$	138.023	5.57926
$613$	−24.7919	−1.00133	−0.500667	−	0.865640i	$-0.666912\pi$
$613$	−24.7919	−1.00133	−0.500667	+	0.865640i	$0.666912\pi$
$614$	27.8537	1.12408
$615$	−6.01351	−0.242488
$616$	119.009	4.79502
$617$	−7.48711	−0.301420	−0.150710	−	0.988578i	$-0.548156\pi$
$617$	−7.48711	−0.301420	−0.150710	+	0.988578i	$0.548156\pi$
$618$	−67.3726	−2.71012
$619$	35.7364	1.43637	0.718183	−	0.695854i	$-0.244974\pi$
$619$	35.7364	1.43637	0.718183	+	0.695854i	$0.244974\pi$
$620$	−15.8617	−0.637019
$621$	−11.6737	−0.468448
$622$	−75.0598	−3.00962
$623$	22.2127	0.889935
$624$	79.1235	3.16748
$625$	16.6530	0.666118
$626$	−50.1714	−2.00525
$627$	−71.4069	−2.85172
$628$	−53.0626	−2.11743
$629$	−40.2625	−1.60537
$630$	27.3831	1.09097
$631$	−40.0608	−1.59479	−0.797397	−	0.603455i	$-0.793790\pi$
$631$	−40.0608	−1.59479	−0.797397	+	0.603455i	$0.793790\pi$
$632$	13.6080	0.541297
$633$	47.4208	1.88481
$634$	−60.2361	−2.39228
$635$	9.19550	0.364912
$636$	−38.4879	−1.52614
$637$	−5.41711	−0.214634
$638$	−113.492	−4.49319
$639$	4.77204	0.188779
$640$	5.39784	0.213368
$641$	17.5140	0.691763	0.345881	−	0.938278i	$-0.387580\pi$
$641$	17.5140	0.691763	0.345881	+	0.938278i	$0.387580\pi$
$642$	−51.6795	−2.03963
$643$	10.5025	0.414178	0.207089	−	0.978322i	$-0.433601\pi$
$643$	10.5025	0.414178	0.207089	+	0.978322i	$0.433601\pi$
$644$	−32.0815	−1.26419
$645$	−3.76275	−0.148158
$646$	−68.7942	−2.70667
$647$	0.773393	0.0304052	0.0152026	−	0.999884i	$-0.495161\pi$
$647$	0.773393	0.0304052	0.0152026	+	0.999884i	$0.495161\pi$
$648$	3.69473	0.145143
$649$	−37.8767	−1.48679
$650$	−39.2777	−1.54060
$651$	−36.6937	−1.43814
$652$	−15.4203	−0.603904
$653$	13.3195	0.521234	0.260617	−	0.965442i	$-0.416074\pi$
$653$	13.3195	0.521234	0.260617	+	0.965442i	$0.416074\pi$
$654$	−2.19425	−0.0858021
$655$	−1.91585	−0.0748586
$656$	23.3359	0.911115
$657$	24.5253	0.956823
$658$	−22.0908	−0.861191
$659$	−16.0193	−0.624023	−0.312011	−	0.950078i	$-0.601003\pi$
$659$	−16.0193	−0.624023	−0.312011	+	0.950078i	$0.601003\pi$
$660$	−58.8438	−2.29049
$661$	−45.6511	−1.77562	−0.887812	−	0.460207i	$-0.847775\pi$
$661$	−45.6511	−1.77562	−0.887812	+	0.460207i	$0.847775\pi$
$662$	−53.9142	−2.09543
$663$	59.9584	2.32859
$664$	58.7909	2.28153
$665$	−9.53582	−0.369783
$666$	79.3649	3.07533
$667$	17.3996	0.673714
$668$	101.457	3.92549
$669$	−40.5548	−1.56794
$670$	−15.5463	−0.600607
$671$	−42.9680	−1.65876
$672$	−62.1521	−2.39757
$673$	−12.3067	−0.474390	−0.237195	−	0.971462i	$-0.576228\pi$
$673$	−12.3067	−0.474390	−0.237195	+	0.971462i	$0.576228\pi$
$674$	−75.3363	−2.90185
$675$	21.8414	0.840676
$676$	−5.14319	−0.197815
$677$	−42.3246	−1.62666	−0.813332	−	0.581799i	$-0.802349\pi$
$677$	−42.3246	−1.62666	−0.813332	+	0.581799i	$0.802349\pi$
$678$	7.18234	0.275836
$679$	32.8049	1.25894
$680$	−32.2413	−1.23640
$681$	43.9019	1.68233
$682$	69.2951	2.65345
$683$	−40.1509	−1.53633	−0.768166	−	0.640250i	$-0.778831\pi$
$683$	−40.1509	−1.53633	−0.768166	+	0.640250i	$0.778831\pi$
$684$	94.7448	3.62266
$685$	−11.9259	−0.455664
$686$	−40.9484	−1.56342
$687$	−15.3101	−0.584115
$688$	14.6017	0.556684
$689$	−10.2658	−0.391094
$690$	12.9121	0.491557
$691$	50.5662	1.92363	0.961815	−	0.273700i	$-0.0882476\pi$
$691$	50.5662	1.92363	0.961815	+	0.273700i	$0.0882476\pi$
$692$	−47.1304	−1.79163
$693$	−83.5820	−3.17502
$694$	47.0311	1.78528
$695$	−3.88574	−0.147395
$696$	139.480	5.28697
$697$	17.6836	0.669813
$698$	−2.41681	−0.0914776
$699$	−9.00650	−0.340657
$700$	60.0243	2.26871
$701$	12.7596	0.481922	0.240961	−	0.970535i	$-0.422537\pi$
$701$	12.7596	0.481922	0.240961	+	0.970535i	$0.422537\pi$
$702$	−43.8881	−1.65645
$703$	−27.6378	−1.04238
$704$	18.8912	0.711989
$705$	6.21201	0.233958
$706$	41.6676	1.56818
$707$	−12.7150	−0.478197
$708$	81.8500	3.07611
$709$	−19.8082	−0.743913	−0.371956	−	0.928250i	$-0.621313\pi$
$709$	−19.8082	−0.743913	−0.371956	+	0.928250i	$0.621313\pi$
$710$	−1.96004	−0.0735588
$711$	−9.55710	−0.358419
$712$	51.5537	1.93206
$713$	−10.6237	−0.397861
$714$	−131.146	−4.90802
$715$	−15.6952	−0.586969
$716$	−109.239	−4.08244
$717$	−3.12881	−0.116847
$718$	−31.3216	−1.16891
$719$	25.5958	0.954564	0.477282	−	0.878750i	$-0.341622\pi$
$719$	25.5958	0.954564	0.477282	+	0.878750i	$0.341622\pi$
$720$	29.8813	1.11361
$721$	27.4619	1.02274
$722$	1.72680	0.0642647
$723$	69.9707	2.60224
$724$	−104.768	−3.89366
$725$	−32.5545	−1.20905
$726$	178.066	6.60866
$727$	29.4554	1.09244	0.546221	−	0.837641i	$-0.316066\pi$
$727$	29.4554	1.09244	0.546221	+	0.837641i	$0.316066\pi$
$728$	−68.5953	−2.54231
$729$	−43.9119	−1.62637
$730$	−10.0734	−0.372832
$731$	11.0649	0.409250
$732$	92.8520	3.43191
$733$	−41.4885	−1.53241	−0.766206	−	0.642594i	$-0.777858\pi$
$733$	−41.4885	−1.53241	−0.766206	+	0.642594i	$0.777858\pi$
$734$	−83.5233	−3.08290
$735$	−3.33191	−0.122899
$736$	−17.9946	−0.663288
$737$	47.4524	1.74793
$738$	−34.8576	−1.28313
$739$	8.46277	0.311308	0.155654	−	0.987812i	$-0.450251\pi$
$739$	8.46277	0.311308	0.155654	+	0.987812i	$0.450251\pi$
$740$	−22.7753	−0.837237
$741$	41.1579	1.51197
$742$	22.4541	0.824317
$743$	17.3307	0.635800	0.317900	−	0.948124i	$-0.397022\pi$
$743$	17.3307	0.635800	0.317900	+	0.948124i	$0.397022\pi$
$744$	−85.1627	−3.12222
$745$	5.92962	0.217245
$746$	−6.19723	−0.226897
$747$	−41.2897	−1.51071
$748$	173.038	6.32691
$749$	21.0653	0.769708
$750$	−51.4799	−1.87978
$751$	42.4036	1.54733	0.773664	−	0.633596i	$-0.218422\pi$
$751$	42.4036	1.54733	0.773664	+	0.633596i	$0.218422\pi$
$752$	−24.1062	−0.879064
$753$	−20.5766	−0.749854
$754$	65.4151	2.38228
$755$	2.23256	0.0812513
$756$	67.0700	2.43931
$757$	37.5402	1.36442	0.682212	−	0.731155i	$-0.261018\pi$
$757$	37.5402	1.36442	0.682212	+	0.731155i	$0.261018\pi$
$758$	−55.4405	−2.01369
$759$	−39.4120	−1.43057
$760$	−22.1318	−0.802803
$761$	17.8443	0.646857	0.323428	−	0.946253i	$-0.395164\pi$
$761$	17.8443	0.646857	0.323428	+	0.946253i	$0.395164\pi$
$762$	86.8113	3.14484
$763$	0.894406	0.0323797
$764$	0.866047	0.0313325
$765$	22.6435	0.818679
$766$	48.2378	1.74290
$767$	21.8316	0.788294
$768$	68.5650	2.47413
$769$	−38.1140	−1.37443	−0.687213	−	0.726456i	$-0.741166\pi$
$769$	−38.1140	−1.37443	−0.687213	+	0.726456i	$0.741166\pi$
$770$	34.3299	1.23716
$771$	−6.97159	−0.251076
$772$	−84.8960	−3.05547
$773$	38.3284	1.37858	0.689289	−	0.724487i	$-0.257923\pi$
$773$	38.3284	1.37858	0.689289	+	0.724487i	$0.257923\pi$
$774$	−21.8110	−0.783979
$775$	19.8769	0.714001
$776$	76.1372	2.73317
$777$	−52.6875	−1.89015
$778$	15.7526	0.564759
$779$	12.1387	0.434915
$780$	33.9167	1.21441
$781$	5.98266	0.214076
$782$	−37.9700	−1.35780
$783$	−36.3758	−1.29996
$784$	12.9297	0.461777
$785$	−8.70524	−0.310703
$786$	−18.0869	−0.645137
$787$	−32.6004	−1.16208	−0.581040	−	0.813875i	$-0.697354\pi$
$787$	−32.6004	−1.16208	−0.581040	+	0.813875i	$0.697354\pi$
$788$	−9.40167	−0.334921
$789$	−21.1117	−0.751596
$790$	3.92542	0.139660
$791$	−2.92762	−0.104094
$792$	−193.986	−6.89300
$793$	24.7661	0.879471
$794$	62.4620	2.21669
$795$	−6.31417	−0.223941
$796$	−23.0002	−0.815219
$797$	−0.749679	−0.0265550	−0.0132775	−	0.999912i	$-0.504226\pi$
$797$	−0.749679	−0.0265550	−0.0132775	+	0.999912i	$0.504226\pi$
$798$	−90.0240	−3.18682
$799$	−18.2673	−0.646251
$800$	33.6677	1.19033
$801$	−36.2069	−1.27931
$802$	−45.3859	−1.60263
$803$	30.7471	1.08504
$804$	−102.543	−3.61640
$805$	−5.26316	−0.185502
$806$	−39.9407	−1.40685
$807$	−60.2242	−2.11999
$808$	−29.5104	−1.03817
$809$	−7.21170	−0.253550	−0.126775	−	0.991932i	$-0.540463\pi$
$809$	−7.21170	−0.253550	−0.126775	+	0.991932i	$0.540463\pi$
$810$	1.06580	0.0374483
$811$	28.2972	0.993649	0.496824	−	0.867851i	$-0.334499\pi$
$811$	28.2972	0.993649	0.496824	+	0.867851i	$0.334499\pi$
$812$	−99.9676	−3.50817
$813$	−68.3556	−2.39733
$814$	99.4990	3.48744
$815$	−2.52979	−0.0886146
$816$	−143.111	−5.00988
$817$	7.59540	0.265730
$818$	−22.5179	−0.787320
$819$	48.1755	1.68339
$820$	10.0031	0.349323
$821$	−5.81152	−0.202824	−0.101412	−	0.994845i	$-0.532336\pi$
$821$	−5.81152	−0.202824	−0.101412	+	0.994845i	$0.532336\pi$
$822$	−112.588	−3.92694
$823$	−6.27179	−0.218621	−0.109310	−	0.994008i	$-0.534864\pi$
$823$	−6.27179	−0.218621	−0.109310	+	0.994008i	$0.534864\pi$
$824$	63.7367	2.22037
$825$	73.7398	2.56729
$826$	−47.7519	−1.66150
$827$	16.7861	0.583710	0.291855	−	0.956463i	$-0.405728\pi$
$827$	16.7861	0.583710	0.291855	+	0.956463i	$0.405728\pi$
$828$	52.2931	1.81731
$829$	30.9566	1.07517	0.537583	−	0.843211i	$-0.319338\pi$
$829$	30.9566	1.07517	0.537583	+	0.843211i	$0.319338\pi$
$830$	16.9591	0.588658
$831$	−18.0058	−0.624616
$832$	−10.8886	−0.377495
$833$	9.79794	0.339478
$834$	−36.6838	−1.27026
$835$	16.6446	0.576011
$836$	118.781	4.10812
$837$	22.2101	0.767693
$838$	−15.1112	−0.522007
$839$	−40.4539	−1.39662	−0.698312	−	0.715794i	$-0.746065\pi$
$839$	−40.4539	−1.39662	−0.698312	+	0.715794i	$0.746065\pi$
$840$	−42.1910	−1.45573
$841$	25.2180	0.869585
$842$	20.0889	0.692309
$843$	76.8429	2.64661
$844$	−78.8814	−2.71521
$845$	−0.843771	−0.0290266
$846$	36.0082	1.23799
$847$	−72.5822	−2.49395
$848$	24.5027	0.841425
$849$	−15.5480	−0.533607
$850$	71.0417	2.43671
$851$	−15.2543	−0.522911
$852$	−12.9283	−0.442916
$853$	−53.3085	−1.82525	−0.912623	−	0.408802i	$-0.865947\pi$
$853$	−53.3085	−1.82525	−0.912623	+	0.408802i	$0.865947\pi$
$854$	−54.1705	−1.85368
$855$	15.5435	0.531575
$856$	48.8905	1.67104
$857$	30.6806	1.04803	0.524015	−	0.851709i	$-0.324433\pi$
$857$	30.6806	1.04803	0.524015	+	0.851709i	$0.324433\pi$
$858$	−148.173	−5.05854
$859$	−35.9655	−1.22713	−0.613564	−	0.789645i	$-0.710265\pi$
$859$	−35.9655	−1.22713	−0.613564	+	0.789645i	$0.710265\pi$
$860$	6.25909	0.213433
$861$	23.1407	0.788633
$862$	−23.9758	−0.816619
$863$	−13.9479	−0.474792	−0.237396	−	0.971413i	$-0.576294\pi$
$863$	−13.9479	−0.474792	−0.237396	+	0.971413i	$0.576294\pi$
$864$	37.6197	1.27985
$865$	−7.73202	−0.262897
$866$	41.0680	1.39555
$867$	−61.0537	−2.07349
$868$	61.0376	2.07175
$869$	−11.9816	−0.406450
$870$	40.2349	1.36409
$871$	−27.3509	−0.926749
$872$	2.07583	0.0702966
$873$	−53.4723	−1.80976
$874$	−26.0642	−0.881633
$875$	20.9839	0.709385
$876$	−66.4432	−2.24491
$877$	−35.3899	−1.19503	−0.597516	−	0.801857i	$-0.703845\pi$
$877$	−35.3899	−1.19503	−0.597516	+	0.801857i	$0.703845\pi$
$878$	38.7510	1.30778
$879$	−55.6953	−1.87856
$880$	37.4619	1.26284
$881$	−50.0242	−1.68536	−0.842679	−	0.538416i	$-0.819023\pi$
$881$	−50.0242	−1.68536	−0.842679	+	0.538416i	$0.819023\pi$
$882$	−19.3136	−0.650321
$883$	43.3557	1.45904	0.729518	−	0.683962i	$-0.239745\pi$
$883$	43.3557	1.45904	0.729518	+	0.683962i	$0.239745\pi$
$884$	−99.7369	−3.35452
$885$	13.4280	0.451377
$886$	−61.5426	−2.06756
$887$	52.2819	1.75545	0.877727	−	0.479161i	$-0.159059\pi$
$887$	52.2819	1.75545	0.877727	+	0.479161i	$0.159059\pi$
$888$	−122.283	−4.10354
$889$	−35.3854	−1.18679
$890$	14.8714	0.498491
$891$	−3.25316	−0.108985
$892$	67.4602	2.25874
$893$	−12.5394	−0.419616
$894$	55.9793	1.87223
$895$	−17.9212	−0.599041
$896$	−20.7715	−0.693928
$897$	22.7165	0.758483
$898$	26.6748	0.890150
$899$	−33.1041	−1.10408
$900$	−97.8401	−3.26134
$901$	18.5677	0.618580
$902$	−43.7006	−1.45507
$903$	14.4795	0.481848
$904$	−6.79473	−0.225989
$905$	−17.1878	−0.571342
$906$	21.0768	0.700229
$907$	−51.5033	−1.71014	−0.855070	−	0.518512i	$-0.826486\pi$
$907$	−51.5033	−1.71014	−0.855070	+	0.518512i	$0.826486\pi$
$908$	−73.0280	−2.42352
$909$	20.7256	0.687424
$910$	−19.7873	−0.655942
$911$	16.5406	0.548015	0.274008	−	0.961728i	$-0.411651\pi$
$911$	16.5406	0.548015	0.274008	+	0.961728i	$0.411651\pi$
$912$	−98.2372	−3.25296
$913$	−51.7646	−1.71316
$914$	103.643	3.42819
$915$	15.2329	0.503585
$916$	25.4673	0.841463
$917$	7.37244	0.243459
$918$	79.3805	2.61995
$919$	15.4866	0.510855	0.255428	−	0.966828i	$-0.417784\pi$
$919$	15.4866	0.510855	0.255428	+	0.966828i	$0.417784\pi$
$920$	−12.2153	−0.402727
$921$	30.1405	0.993165
$922$	11.6234	0.382798
$923$	−3.44832	−0.113503
$924$	226.438	7.44927
$925$	28.5408	0.938415
$926$	−43.4985	−1.42945
$927$	−44.7632	−1.47022
$928$	−56.0720	−1.84065
$929$	24.2758	0.796462	0.398231	−	0.917285i	$-0.369624\pi$
$929$	24.2758	0.796462	0.398231	+	0.917285i	$0.369624\pi$
$930$	−24.5664	−0.805563
$931$	6.72571	0.220426
$932$	14.9817	0.490743
$933$	−81.2225	−2.65911
$934$	93.1798	3.04894
$935$	28.3880	0.928387
$936$	111.811	3.65465
$937$	−39.3571	−1.28574	−0.642870	−	0.765975i	$-0.722256\pi$
$937$	−39.3571	−1.28574	−0.642870	+	0.765975i	$0.722256\pi$
$938$	59.8241	1.95333
$939$	−54.2906	−1.77171
$940$	−10.3333	−0.337034
$941$	−48.3008	−1.57456	−0.787281	−	0.616594i	$-0.788512\pi$
$941$	−48.3008	−1.57456	−0.787281	+	0.616594i	$0.788512\pi$
$942$	−82.1828	−2.67766
$943$	6.69980	0.218175
$944$	−52.1084	−1.69599
$945$	11.0032	0.357935
$946$	−27.3442	−0.889038
$947$	−7.45435	−0.242234	−0.121117	−	0.992638i	$-0.538648\pi$
$947$	−7.45435	−0.242234	−0.121117	+	0.992638i	$0.538648\pi$
$948$	25.8918	0.840927
$949$	−17.7222	−0.575288
$950$	48.7659	1.58218
$951$	−65.1818	−2.11366
$952$	124.068	4.02108
$953$	43.5030	1.40920	0.704601	−	0.709604i	$-0.251126\pi$
$953$	43.5030	1.40920	0.704601	+	0.709604i	$0.251126\pi$
$954$	−36.6004	−1.18498
$955$	0.142080	0.00459761
$956$	5.20457	0.168328
$957$	−122.810	−3.96988
$958$	59.8151	1.93254
$959$	45.8922	1.48194
$960$	−6.69728	−0.216154
$961$	−10.7875	−0.347985
$962$	−57.3498	−1.84903
$963$	−34.3365	−1.10648
$964$	−116.392	−3.74872
$965$	−13.9277	−0.448349
$966$	−49.6875	−1.59867
$967$	58.9533	1.89581	0.947905	−	0.318554i	$-0.103197\pi$
$967$	58.9533	1.89581	0.947905	+	0.318554i	$0.103197\pi$
$968$	−168.457	−5.41440
$969$	−74.4424	−2.39144
$970$	21.9629	0.705185
$971$	41.5644	1.33386	0.666932	−	0.745118i	$-0.267607\pi$
$971$	41.5644	1.33386	0.666932	+	0.745118i	$0.267607\pi$
$972$	75.7582	2.42994
$973$	14.9528	0.479365
$974$	27.7698	0.889801
$975$	−42.5026	−1.36117
$976$	−59.1127	−1.89215
$977$	−20.7744	−0.664633	−0.332317	−	0.943168i	$-0.607830\pi$
$977$	−20.7744	−0.664633	−0.332317	+	0.943168i	$0.607830\pi$
$978$	−23.8828	−0.763687
$979$	−45.3923	−1.45074
$980$	5.54241	0.177046
$981$	−1.45789	−0.0465468
$982$	−84.2179	−2.68750
$983$	3.90550	0.124566	0.0622831	−	0.998059i	$-0.480162\pi$
$983$	3.90550	0.124566	0.0622831	+	0.998059i	$0.480162\pi$
$984$	53.7074	1.71213
$985$	−1.54240	−0.0491450
$986$	−118.316	−3.76796
$987$	−23.9046	−0.760891
$988$	−68.4635	−2.17812
$989$	4.19218	0.133303
$990$	−55.9580	−1.77846
$991$	−8.66335	−0.275201	−0.137600	−	0.990488i	$-0.543939\pi$
$991$	−8.66335	−0.275201	−0.137600	+	0.990488i	$0.543939\pi$
$992$	34.2361	1.08700
$993$	−58.3408	−1.85139
$994$	7.54246	0.239232
$995$	−3.77332	−0.119622
$996$	111.861	3.54445
$997$	4.05790	0.128515	0.0642574	−	0.997933i	$-0.479532\pi$
$997$	4.05790	0.128515	0.0642574	+	0.997933i	$0.479532\pi$
$998$	61.3721	1.94270
$999$	31.8909	1.00898

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.b.1.10	✓	155

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.b.1.10	✓	155	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:	\( N \)	\(=\)	\( 8023 = 71 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.57631 q^{2} -2.78784 q^{3} +4.63739 q^{4} +0.760791 q^{5} +7.18234 q^{6} -2.92762 q^{7} -6.79473 q^{8} +4.77204 q^{9} +O(q^{10})\)	\(q-2.57631 q^{2} -2.78784 q^{3} +4.63739 q^{4} +0.760791 q^{5} +7.18234 q^{6} -2.92762 q^{7} -6.79473 q^{8} +4.77204 q^{9} -1.96004 q^{10} +5.98266 q^{11} -12.9283 q^{12} -3.44832 q^{13} +7.54246 q^{14} -2.12096 q^{15} +8.23058 q^{16} +6.23699 q^{17} -12.2943 q^{18} +4.28132 q^{19} +3.52808 q^{20} +8.16172 q^{21} -15.4132 q^{22} +2.36302 q^{23} +18.9426 q^{24} -4.42120 q^{25} +8.88396 q^{26} -4.94016 q^{27} -13.5765 q^{28} +7.36329 q^{29} +5.46426 q^{30} -4.49583 q^{31} -7.61507 q^{32} -16.6787 q^{33} -16.0684 q^{34} -2.22731 q^{35} +22.1298 q^{36} -6.45544 q^{37} -11.0300 q^{38} +9.61336 q^{39} -5.16937 q^{40} +2.83527 q^{41} -21.0271 q^{42} +1.77408 q^{43} +27.7439 q^{44} +3.63053 q^{45} -6.08787 q^{46} -2.92887 q^{47} -22.9455 q^{48} +1.57094 q^{49} +11.3904 q^{50} -17.3877 q^{51} -15.9912 q^{52} +2.97703 q^{53} +12.7274 q^{54} +4.55156 q^{55} +19.8924 q^{56} -11.9356 q^{57} -18.9701 q^{58} -6.33108 q^{59} -9.83572 q^{60} -7.18208 q^{61} +11.5827 q^{62} -13.9707 q^{63} +3.15766 q^{64} -2.62345 q^{65} +42.9695 q^{66} +7.93165 q^{67} +28.9233 q^{68} -6.58771 q^{69} +5.73823 q^{70} +1.00000 q^{71} -32.4247 q^{72} +5.13937 q^{73} +16.6312 q^{74} +12.3256 q^{75} +19.8542 q^{76} -17.5149 q^{77} -24.7670 q^{78} -2.00273 q^{79} +6.26175 q^{80} -0.543764 q^{81} -7.30455 q^{82} -8.65243 q^{83} +37.8490 q^{84} +4.74505 q^{85} -4.57058 q^{86} -20.5276 q^{87} -40.6506 q^{88} -7.58731 q^{89} -9.35337 q^{90} +10.0954 q^{91} +10.9582 q^{92} +12.5336 q^{93} +7.54567 q^{94} +3.25719 q^{95} +21.2296 q^{96} -11.2053 q^{97} -4.04723 q^{98} +28.5495 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9}+O(q^{10}) \) 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9	\( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9} - 2 q^{10} - 24 q^{11} - 32 q^{12} - 62 q^{13} - 18 q^{14} - 12 q^{15} + 155 q^{16} - 129 q^{17} - 42 q^{18} - 18 q^{19} - 59 q^{20} - 45 q^{21} - 17 q^{22} - 38 q^{23} - 27 q^{24} + 129 q^{25} - 44 q^{26} - 43 q^{27} - 100 q^{28} - 52 q^{29} - 39 q^{30} - 56 q^{31} - 145 q^{32} - 126 q^{33} - q^{34} - 49 q^{35} + 131 q^{36} - 30 q^{37} - 91 q^{38} - 29 q^{39} - 5 q^{40} - 163 q^{41} - 80 q^{42} - 15 q^{43} - 118 q^{44} - 66 q^{45} + 2 q^{46} - 111 q^{47} - 89 q^{48} + 101 q^{49} - 121 q^{50} + 5 q^{51} - 111 q^{52} - 93 q^{53} - 68 q^{54} - 60 q^{55} - 27 q^{56} - 106 q^{57} + 16 q^{58} - 79 q^{59} - 103 q^{60} - 74 q^{61} - 102 q^{62} - 118 q^{63} + 175 q^{64} - 109 q^{65} + 65 q^{66} - 18 q^{67} - 346 q^{68} - 39 q^{69} + 32 q^{70} + 155 q^{71} - 203 q^{72} - 108 q^{73} - 87 q^{74} - 22 q^{75} - 16 q^{76} - 121 q^{77} - 75 q^{78} - 6 q^{79} - 136 q^{80} + 107 q^{81} - 30 q^{82} - 116 q^{83} - 5 q^{84} - 53 q^{85} + 8 q^{86} - 100 q^{87} - 43 q^{88} - 189 q^{89} - 76 q^{90} + 14 q^{91} - 99 q^{92} - 72 q^{93} + 17 q^{94} - 18 q^{95} - 50 q^{96} - 184 q^{97} - 249 q^{98} - 114 q^{99}+O(q^{100}) \) 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9 - 2 * q^10 - 24 * q^11 - 32 * q^12 - 62 * q^13 - 18 * q^14 - 12 * q^15 + 155 * q^16 - 129 * q^17 - 42 * q^18 - 18 * q^19 - 59 * q^20 - 45 * q^21 - 17 * q^22 - 38 * q^23 - 27 * q^24 + 129 * q^25 - 44 * q^26 - 43 * q^27 - 100 * q^28 - 52 * q^29 - 39 * q^30 - 56 * q^31 - 145 * q^32 - 126 * q^33 - q^34 - 49 * q^35 + 131 * q^36 - 30 * q^37 - 91 * q^38 - 29 * q^39 - 5 * q^40 - 163 * q^41 - 80 * q^42 - 15 * q^43 - 118 * q^44 - 66 * q^45 + 2 * q^46 - 111 * q^47 - 89 * q^48 + 101 * q^49 - 121 * q^50 + 5 * q^51 - 111 * q^52 - 93 * q^53 - 68 * q^54 - 60 * q^55 - 27 * q^56 - 106 * q^57 + 16 * q^58 - 79 * q^59 - 103 * q^60 - 74 * q^61 - 102 * q^62 - 118 * q^63 + 175 * q^64 - 109 * q^65 + 65 * q^66 - 18 * q^67 - 346 * q^68 - 39 * q^69 + 32 * q^70 + 155 * q^71 - 203 * q^72 - 108 * q^73 - 87 * q^74 - 22 * q^75 - 16 * q^76 - 121 * q^77 - 75 * q^78 - 6 * q^79 - 136 * q^80 + 107 * q^81 - 30 * q^82 - 116 * q^83 - 5 * q^84 - 53 * q^85 + 8 * q^86 - 100 * q^87 - 43 * q^88 - 189 * q^89 - 76 * q^90 + 14 * q^91 - 99 * q^92 - 72 * q^93 + 17 * q^94 - 18 * q^95 - 50 * q^96 - 184 * q^97 - 249 * q^98 - 114 * q^99

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