LMFDB - Embedded newform 8023.2.a.d.1.60

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:	$0$
Dimension:	$165$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.60
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)

$f(q)$	$=$	$q-0.880927 q^{2} -3.28134 q^{3} -1.22397 q^{4} +3.48829 q^{5} +2.89062 q^{6} -0.855742 q^{7} +2.84008 q^{8} +7.76719 q^{9} +O(q^{10})$	\(q-0.880927 q^{2} -3.28134 q^{3} -1.22397 q^{4} +3.48829 q^{5} +2.89062 q^{6} -0.855742 q^{7} +2.84008 q^{8} +7.76719 q^{9} -3.07293 q^{10} -1.89405 q^{11} +4.01626 q^{12} +2.41919 q^{13} +0.753846 q^{14} -11.4463 q^{15} -0.0539646 q^{16} -1.69200 q^{17} -6.84233 q^{18} +0.284180 q^{19} -4.26956 q^{20} +2.80798 q^{21} +1.66851 q^{22} -6.81499 q^{23} -9.31927 q^{24} +7.16817 q^{25} -2.13113 q^{26} -15.6428 q^{27} +1.04740 q^{28} +0.274863 q^{29} +10.0833 q^{30} +0.799360 q^{31} -5.63262 q^{32} +6.21501 q^{33} +1.49053 q^{34} -2.98508 q^{35} -9.50680 q^{36} +7.39444 q^{37} -0.250342 q^{38} -7.93819 q^{39} +9.90702 q^{40} -1.73331 q^{41} -2.47362 q^{42} -9.62996 q^{43} +2.31825 q^{44} +27.0942 q^{45} +6.00351 q^{46} +5.25933 q^{47} +0.177076 q^{48} -6.26771 q^{49} -6.31463 q^{50} +5.55203 q^{51} -2.96101 q^{52} +8.70512 q^{53} +13.7801 q^{54} -6.60698 q^{55} -2.43037 q^{56} -0.932491 q^{57} -0.242134 q^{58} +3.15311 q^{59} +14.0099 q^{60} -3.49138 q^{61} -0.704178 q^{62} -6.64671 q^{63} +5.06985 q^{64} +8.43884 q^{65} -5.47496 q^{66} +9.32852 q^{67} +2.07096 q^{68} +22.3623 q^{69} +2.62963 q^{70} +1.00000 q^{71} +22.0594 q^{72} +6.15011 q^{73} -6.51396 q^{74} -23.5212 q^{75} -0.347827 q^{76} +1.62081 q^{77} +6.99296 q^{78} -5.42164 q^{79} -0.188244 q^{80} +28.0277 q^{81} +1.52692 q^{82} +11.2468 q^{83} -3.43688 q^{84} -5.90219 q^{85} +8.48329 q^{86} -0.901918 q^{87} -5.37924 q^{88} -6.72757 q^{89} -23.8680 q^{90} -2.07020 q^{91} +8.34133 q^{92} -2.62297 q^{93} -4.63309 q^{94} +0.991302 q^{95} +18.4825 q^{96} -2.55298 q^{97} +5.52139 q^{98} -14.7114 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9}+O(q^{10}) $ 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9} + 14 q^{10} + 18 q^{11} + 54 q^{12} + 44 q^{13} + 26 q^{14} + 24 q^{15} + 168 q^{16} + 143 q^{17} + 57 q^{18} + 20 q^{19} + 49 q^{20} + 39 q^{21} + 25 q^{22} + 52 q^{23} + 27 q^{24} + 175 q^{25} + 48 q^{26} + 69 q^{27} + 28 q^{28} + 58 q^{29} - 11 q^{30} + 28 q^{31} + 114 q^{32} + 110 q^{33} + 55 q^{34} + 67 q^{35} + 202 q^{36} + 44 q^{37} + 35 q^{38} + 27 q^{39} + 53 q^{40} + 141 q^{41} + 40 q^{42} + 29 q^{43} + 52 q^{44} + 54 q^{45} + 29 q^{46} + 87 q^{47} + 53 q^{48} + 143 q^{49} + 16 q^{50} + 37 q^{51} + 105 q^{52} + 101 q^{53} - 36 q^{54} + 72 q^{55} + 57 q^{56} + 82 q^{57} + 4 q^{58} + 103 q^{59} + 53 q^{60} + 16 q^{61} + 54 q^{62} + 126 q^{63} + 136 q^{64} + 159 q^{65} + 53 q^{66} + 60 q^{67} + 220 q^{68} + 81 q^{69} + 16 q^{70} + 165 q^{71} + 176 q^{72} + 124 q^{73} + 29 q^{74} + 44 q^{75} + 18 q^{76} + 127 q^{77} - 91 q^{78} + 14 q^{79} + 158 q^{80} + 213 q^{81} + 20 q^{82} + 116 q^{83} + 67 q^{84} + 59 q^{85} + 30 q^{86} + 28 q^{87} + 79 q^{88} + 195 q^{89} + 16 q^{90} - 26 q^{91} + 173 q^{92} + 116 q^{93} + 53 q^{94} + 26 q^{95} - 36 q^{96} + 88 q^{97} + 150 q^{98} + 12 q^{99}+O(q^{100}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9 + 14 * q^10 + 18 * q^11 + 54 * q^12 + 44 * q^13 + 26 * q^14 + 24 * q^15 + 168 * q^16 + 143 * q^17 + 57 * q^18 + 20 * q^19 + 49 * q^20 + 39 * q^21 + 25 * q^22 + 52 * q^23 + 27 * q^24 + 175 * q^25 + 48 * q^26 + 69 * q^27 + 28 * q^28 + 58 * q^29 - 11 * q^30 + 28 * q^31 + 114 * q^32 + 110 * q^33 + 55 * q^34 + 67 * q^35 + 202 * q^36 + 44 * q^37 + 35 * q^38 + 27 * q^39 + 53 * q^40 + 141 * q^41 + 40 * q^42 + 29 * q^43 + 52 * q^44 + 54 * q^45 + 29 * q^46 + 87 * q^47 + 53 * q^48 + 143 * q^49 + 16 * q^50 + 37 * q^51 + 105 * q^52 + 101 * q^53 - 36 * q^54 + 72 * q^55 + 57 * q^56 + 82 * q^57 + 4 * q^58 + 103 * q^59 + 53 * q^60 + 16 * q^61 + 54 * q^62 + 126 * q^63 + 136 * q^64 + 159 * q^65 + 53 * q^66 + 60 * q^67 + 220 * q^68 + 81 * q^69 + 16 * q^70 + 165 * q^71 + 176 * q^72 + 124 * q^73 + 29 * q^74 + 44 * q^75 + 18 * q^76 + 127 * q^77 - 91 * q^78 + 14 * q^79 + 158 * q^80 + 213 * q^81 + 20 * q^82 + 116 * q^83 + 67 * q^84 + 59 * q^85 + 30 * q^86 + 28 * q^87 + 79 * q^88 + 195 * q^89 + 16 * q^90 - 26 * q^91 + 173 * q^92 + 116 * q^93 + 53 * q^94 + 26 * q^95 - 36 * q^96 + 88 * q^97 + 150 * q^98 + 12 * 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 $

$2$	−0.880927	−0.622909	−0.311455	−	0.950261i	$-0.600816\pi$
$2$	−0.880927	−0.622909	−0.311455	+	0.950261i	$0.600816\pi$
$3$	−3.28134	−1.89448	−0.947241	−	0.320521i	$-0.896142\pi$
$3$	−3.28134	−1.89448	−0.947241	+	0.320521i	$0.896142\pi$
$4$	−1.22397	−0.611984
$5$	3.48829	1.56001	0.780005	−	0.625773i	$-0.215216\pi$
$5$	3.48829	1.56001	0.780005	+	0.625773i	$0.215216\pi$
$6$	2.89062	1.18009
$7$	−0.855742	−0.323440	−0.161720	−	0.986837i	$-0.551704\pi$
$7$	−0.855742	−0.323440	−0.161720	+	0.986837i	$0.551704\pi$
$8$	2.84008	1.00412
$9$	7.76719	2.58906
$10$	−3.07293	−0.971745
$11$	−1.89405	−0.571076	−0.285538	−	0.958367i	$-0.592172\pi$
$11$	−1.89405	−0.571076	−0.285538	+	0.958367i	$0.592172\pi$
$12$	4.01626	1.15939
$13$	2.41919	0.670963	0.335481	−	0.942047i	$-0.391101\pi$
$13$	2.41919	0.670963	0.335481	+	0.942047i	$0.391101\pi$
$14$	0.753846	0.201474
$15$	−11.4463	−2.95541
$16$	−0.0539646	−0.0134911
$17$	−1.69200	−0.410370	−0.205185	−	0.978723i	$-0.565780\pi$
$17$	−1.69200	−0.410370	−0.205185	+	0.978723i	$0.565780\pi$
$18$	−6.84233	−1.61275
$19$	0.284180	0.0651953	0.0325977	−	0.999469i	$-0.489622\pi$
$19$	0.284180	0.0651953	0.0325977	+	0.999469i	$0.489622\pi$
$20$	−4.26956	−0.954702
$21$	2.80798	0.612751
$22$	1.66851	0.355729
$23$	−6.81499	−1.42102	−0.710512	−	0.703685i	$-0.751537\pi$
$23$	−6.81499	−1.42102	−0.710512	+	0.703685i	$0.751537\pi$
$24$	−9.31927	−1.90229
$25$	7.16817	1.43363
$26$	−2.13113	−0.417949
$27$	−15.6428	−3.01045
$28$	1.04740	0.197940
$29$	0.274863	0.0510407	0.0255204	−	0.999674i	$-0.491876\pi$
$29$	0.274863	0.0510407	0.0255204	+	0.999674i	$0.491876\pi$
$30$	10.0833	1.84095
$31$	0.799360	0.143569	0.0717847	−	0.997420i	$-0.477131\pi$
$31$	0.799360	0.143569	0.0717847	+	0.997420i	$0.477131\pi$
$32$	−5.63262	−0.995716
$33$	6.21501	1.08189
$34$	1.49053	0.255624
$35$	−2.98508	−0.504570
$36$	−9.50680	−1.58447
$37$	7.39444	1.21564	0.607819	−	0.794076i	$-0.292045\pi$
$37$	7.39444	1.21564	0.607819	+	0.794076i	$0.292045\pi$
$38$	−0.250342	−0.0406108
$39$	−7.93819	−1.27113
$40$	9.90702	1.56644
$41$	−1.73331	−0.270697	−0.135348	−	0.990798i	$-0.543215\pi$
$41$	−1.73331	−0.270697	−0.135348	+	0.990798i	$0.543215\pi$
$42$	−2.47362	−0.381688
$43$	−9.62996	−1.46856	−0.734278	−	0.678849i	$-0.762479\pi$
$43$	−9.62996	−1.46856	−0.734278	+	0.678849i	$0.762479\pi$
$44$	2.31825	0.349490
$45$	27.0942	4.03897
$46$	6.00351	0.885169
$47$	5.25933	0.767153	0.383576	−	0.923509i	$-0.374692\pi$
$47$	5.25933	0.767153	0.383576	+	0.923509i	$0.374692\pi$
$48$	0.177076	0.0255587
$49$	−6.26771	−0.895387
$50$	−6.31463	−0.893023
$51$	5.55203	0.777440
$52$	−2.96101	−0.410619
$53$	8.70512	1.19574	0.597870	−	0.801593i	$-0.296014\pi$
$53$	8.70512	1.19574	0.597870	+	0.801593i	$0.296014\pi$
$54$	13.7801	1.87524
$55$	−6.60698	−0.890885
$56$	−2.43037	−0.324772
$57$	−0.932491	−0.123511
$58$	−0.242134	−0.0317937
$59$	3.15311	0.410500	0.205250	−	0.978710i	$-0.434199\pi$
$59$	3.15311	0.410500	0.205250	+	0.978710i	$0.434199\pi$
$60$	14.0099	1.80867
$61$	−3.49138	−0.447026	−0.223513	−	0.974701i	$-0.571752\pi$
$61$	−3.49138	−0.447026	−0.223513	+	0.974701i	$0.571752\pi$
$62$	−0.704178	−0.0894306
$63$	−6.64671	−0.837407
$64$	5.06985	0.633732
$65$	8.43884	1.04671
$66$	−5.47496	−0.673922
$67$	9.32852	1.13966	0.569830	−	0.821763i	$-0.307009\pi$
$67$	9.32852	1.13966	0.569830	+	0.821763i	$0.307009\pi$
$68$	2.07096	0.251140
$69$	22.3623	2.69211
$70$	2.62963	0.314301
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	22.0594	2.59973
$73$	6.15011	0.719816	0.359908	−	0.932988i	$-0.382808\pi$
$73$	6.15011	0.719816	0.359908	+	0.932988i	$0.382808\pi$
$74$	−6.51396	−0.757232
$75$	−23.5212	−2.71599
$76$	−0.347827	−0.0398985
$77$	1.62081	0.184709
$78$	6.99296	0.791797
$79$	−5.42164	−0.609982	−0.304991	−	0.952355i	$-0.598653\pi$
$79$	−5.42164	−0.609982	−0.304991	+	0.952355i	$0.598653\pi$
$80$	−0.188244	−0.0210463
$81$	28.0277	3.11419
$82$	1.52692	0.168620
$83$	11.2468	1.23450	0.617249	−	0.786768i	$-0.288247\pi$
$83$	11.2468	1.23450	0.617249	+	0.786768i	$0.288247\pi$
$84$	−3.43688	−0.374994
$85$	−5.90219	−0.640182
$86$	8.48329	0.914777
$87$	−0.901918	−0.0966958
$88$	−5.37924	−0.573429
$89$	−6.72757	−0.713121	−0.356560	−	0.934272i	$-0.616051\pi$
$89$	−6.72757	−0.713121	−0.356560	+	0.934272i	$0.616051\pi$
$90$	−23.8680	−2.51591
$91$	−2.07020	−0.217016
$92$	8.34133	0.869644
$93$	−2.62297	−0.271990
$94$	−4.63309	−0.477866
$95$	0.991302	0.101705
$96$	18.4825	1.88637
$97$	−2.55298	−0.259216	−0.129608	−	0.991565i	$-0.541372\pi$
$97$	−2.55298	−0.259216	−0.129608	+	0.991565i	$0.541372\pi$
$98$	5.52139	0.557744
$99$	−14.7114	−1.47855
$100$	−8.77361	−0.877361
$101$	19.2892	1.91935	0.959673	−	0.281119i	$-0.0907057\pi$
$101$	19.2892	1.91935	0.959673	+	0.281119i	$0.0907057\pi$
$102$	−4.89093	−0.484274
$103$	−7.27985	−0.717305	−0.358652	−	0.933471i	$-0.616764\pi$
$103$	−7.27985	−0.717305	−0.358652	+	0.933471i	$0.616764\pi$
$104$	6.87069	0.673727
$105$	9.79505	0.955899
$106$	−7.66857	−0.744837
$107$	−5.96133	−0.576304	−0.288152	−	0.957585i	$-0.593041\pi$
$107$	−5.96133	−0.576304	−0.288152	+	0.957585i	$0.593041\pi$
$108$	19.1463	1.84235
$109$	4.77471	0.457335	0.228667	−	0.973505i	$-0.426563\pi$
$109$	4.77471	0.457335	0.228667	+	0.973505i	$0.426563\pi$
$110$	5.82026	0.554940
$111$	−24.2637	−2.30301
$112$	0.0461798	0.00436358
$113$	−1.00000	−0.0940721
$113$	−1.00000	−0.0940721
$114$	0.821456	0.0769364
$115$	−23.7727	−2.21681
$116$	−0.336423	−0.0312361
$117$	18.7903	1.73717
$118$	−2.77766	−0.255704
$119$	1.44792	0.132730
$120$	−32.5083	−2.96759
$121$	−7.41259	−0.673872
$122$	3.07565	0.278456
$123$	5.68757	0.512831
$124$	−0.978391	−0.0878621
$125$	7.56319	0.676472
$126$	5.85526	0.521628
$127$	0.886823	0.0786928	0.0393464	−	0.999226i	$-0.487472\pi$
$127$	0.886823	0.0786928	0.0393464	+	0.999226i	$0.487472\pi$
$128$	6.79907	0.600959
$129$	31.5992	2.78215
$130$	−7.43400	−0.652005
$131$	3.06947	0.268181	0.134091	−	0.990969i	$-0.457189\pi$
$131$	3.06947	0.268181	0.134091	+	0.990969i	$0.457189\pi$
$132$	−7.60697	−0.662102
$133$	−0.243185	−0.0210868
$134$	−8.21774	−0.709905
$135$	−54.5666	−4.69634
$136$	−4.80542	−0.412061
$137$	9.97460	0.852188	0.426094	−	0.904679i	$-0.359889\pi$
$137$	9.97460	0.852188	0.426094	+	0.904679i	$0.359889\pi$
$138$	−19.6995	−1.67694
$139$	6.37690	0.540882	0.270441	−	0.962737i	$-0.412831\pi$
$139$	6.37690	0.540882	0.270441	+	0.962737i	$0.412831\pi$
$140$	3.65364	0.308789
$141$	−17.2577	−1.45336
$142$	−0.880927	−0.0739257
$143$	−4.58206	−0.383171
$144$	−0.419153	−0.0349295
$145$	0.958801	0.0796241
$146$	−5.41780	−0.448380
$147$	20.5665	1.69629
$148$	−9.05056	−0.743951
$149$	−8.39050	−0.687376	−0.343688	−	0.939084i	$-0.611676\pi$
$149$	−8.39050	−0.687376	−0.343688	+	0.939084i	$0.611676\pi$
$150$	20.7204	1.69182
$151$	0.442906	0.0360432	0.0180216	−	0.999838i	$-0.494263\pi$
$151$	0.442906	0.0360432	0.0180216	+	0.999838i	$0.494263\pi$
$152$	0.807094	0.0654639
$153$	−13.1421	−1.06248
$154$	−1.42782	−0.115057
$155$	2.78840	0.223970
$156$	9.71609	0.777910
$157$	0.122025	0.00973869	0.00486935	−	0.999988i	$-0.498450\pi$
$157$	0.122025	0.00973869	0.00486935	+	0.999988i	$0.498450\pi$
$158$	4.77607	0.379963
$159$	−28.5645	−2.26531
$160$	−19.6482	−1.55333
$161$	5.83187	0.459616
$162$	−24.6904	−1.93986
$163$	14.2023	1.11241	0.556205	−	0.831045i	$-0.312257\pi$
$163$	14.2023	1.11241	0.556205	+	0.831045i	$0.312257\pi$
$164$	2.12151	0.165662
$165$	21.6797	1.68777
$166$	−9.90761	−0.768980
$167$	−7.61360	−0.589158	−0.294579	−	0.955627i	$-0.595179\pi$
$167$	−7.61360	−0.589158	−0.294579	+	0.955627i	$0.595179\pi$
$168$	7.97489	0.615276
$169$	−7.14752	−0.549809
$170$	5.19940	0.398775
$171$	2.20728	0.168795
$172$	11.7868	0.898733
$173$	−20.2990	−1.54331	−0.771653	−	0.636043i	$-0.780570\pi$
$173$	−20.2990	−1.54331	−0.771653	+	0.636043i	$0.780570\pi$
$174$	0.794524	0.0602327
$175$	−6.13410	−0.463694
$176$	0.102211	0.00770447
$177$	−10.3464	−0.777686
$178$	5.92649	0.444210
$179$	6.87141	0.513593	0.256797	−	0.966465i	$-0.417333\pi$
$179$	6.87141	0.513593	0.256797	+	0.966465i	$0.417333\pi$
$180$	−33.1625	−2.47178
$181$	−10.8569	−0.806984	−0.403492	−	0.914983i	$-0.632204\pi$
$181$	−10.8569	−0.806984	−0.403492	+	0.914983i	$0.632204\pi$
$182$	1.82370	0.135181
$183$	11.4564	0.846882
$184$	−19.3551	−1.42688
$185$	25.7939	1.89641
$186$	2.31065	0.169425
$187$	3.20473	0.234353
$188$	−6.43726	−0.469485
$189$	13.3862	0.973701
$190$	−0.873264	−0.0633532
$191$	−15.6767	−1.13432	−0.567162	−	0.823606i	$-0.691959\pi$
$191$	−15.6767	−1.13432	−0.567162	+	0.823606i	$0.691959\pi$
$192$	−16.6359	−1.20059
$193$	9.91588	0.713760	0.356880	−	0.934150i	$-0.383840\pi$
$193$	9.91588	0.713760	0.356880	+	0.934150i	$0.383840\pi$
$194$	2.24899	0.161468
$195$	−27.6907	−1.98297
$196$	7.67147	0.547962
$197$	16.3615	1.16571	0.582854	−	0.812577i	$-0.301936\pi$
$197$	16.3615	1.16571	0.582854	+	0.812577i	$0.301936\pi$
$198$	12.9597	0.921004
$199$	−10.9189	−0.774023	−0.387012	−	0.922075i	$-0.626493\pi$
$199$	−10.9189	−0.774023	−0.387012	+	0.922075i	$0.626493\pi$
$200$	20.3582	1.43954
$201$	−30.6100	−2.15907
$202$	−16.9924	−1.19558
$203$	−0.235211	−0.0165086
$204$	−6.79551	−0.475781
$205$	−6.04627	−0.422290
$206$	6.41301	0.446816
$207$	−52.9334	−3.67912
$208$	−0.130551	−0.00905206
$209$	−0.538250	−0.0372315
$210$	−8.62872	−0.595438
$211$	−3.53368	−0.243268	−0.121634	−	0.992575i	$-0.538813\pi$
$211$	−3.53368	−0.243268	−0.121634	+	0.992575i	$0.538813\pi$
$212$	−10.6548	−0.731774
$213$	−3.28134	−0.224834
$214$	5.25150	0.358985
$215$	−33.5921	−2.29096
$216$	−44.4267	−3.02286
$217$	−0.684046	−0.0464361
$218$	−4.20617	−0.284878
$219$	−20.1806	−1.36368
$220$	8.08673	0.545207
$221$	−4.09327	−0.275343
$222$	21.3745	1.43456
$223$	23.2954	1.55998	0.779989	−	0.625794i	$-0.215225\pi$
$223$	23.2954	1.55998	0.779989	+	0.625794i	$0.215225\pi$
$224$	4.82007	0.322054
$225$	55.6765	3.71177
$226$	0.880927	0.0585984
$227$	−3.09124	−0.205173	−0.102586	−	0.994724i	$-0.532712\pi$
$227$	−3.09124	−0.205173	−0.102586	+	0.994724i	$0.532712\pi$
$228$	1.14134	0.0755871
$229$	9.80821	0.648144	0.324072	−	0.946032i	$-0.394948\pi$
$229$	9.80821	0.648144	0.324072	+	0.946032i	$0.394948\pi$
$230$	20.9420	1.38087
$231$	−5.31844	−0.349928
$232$	0.780632	0.0512510
$233$	−10.2530	−0.671694	−0.335847	−	0.941916i	$-0.609023\pi$
$233$	−10.2530	−0.671694	−0.335847	+	0.941916i	$0.609023\pi$
$234$	−16.5529	−1.08210
$235$	18.3461	1.19677
$236$	−3.85931	−0.251220
$237$	17.7902	1.15560
$238$	−1.27551	−0.0826789
$239$	23.4327	1.51573	0.757867	−	0.652409i	$-0.226241\pi$
$239$	23.4327	1.51573	0.757867	+	0.652409i	$0.226241\pi$
$240$	0.617693	0.0398719
$241$	−9.05866	−0.583520	−0.291760	−	0.956492i	$-0.594241\pi$
$241$	−9.05866	−0.583520	−0.291760	+	0.956492i	$0.594241\pi$
$242$	6.52995	0.419761
$243$	−45.0401	−2.88932
$244$	4.27334	0.273573
$245$	−21.8636	−1.39681
$246$	−5.01033	−0.319447
$247$	0.687485	0.0437436
$248$	2.27025	0.144161
$249$	−36.9046	−2.33873
$250$	−6.66261	−0.421381
$251$	5.33584	0.336795	0.168398	−	0.985719i	$-0.446141\pi$
$251$	5.33584	0.336795	0.168398	+	0.985719i	$0.446141\pi$
$252$	8.13537	0.512480
$253$	12.9079	0.811513
$254$	−0.781226	−0.0490185
$255$	19.3671	1.21281
$256$	−16.1292	−1.00807
$257$	−21.8286	−1.36163	−0.680816	−	0.732455i	$-0.738375\pi$
$257$	−21.8286	−1.36163	−0.680816	+	0.732455i	$0.738375\pi$
$258$	−27.8366	−1.73303
$259$	−6.32773	−0.393186
$260$	−10.3289	−0.640569
$261$	2.13491	0.132148
$262$	−2.70398	−0.167052
$263$	4.01471	0.247558	0.123779	−	0.992310i	$-0.460499\pi$
$263$	4.01471	0.247558	0.123779	+	0.992310i	$0.460499\pi$
$264$	17.6511	1.08635
$265$	30.3660	1.86537
$266$	0.214228	0.0131351
$267$	22.0754	1.35100
$268$	−11.4178	−0.697454
$269$	−12.0171	−0.732697	−0.366349	−	0.930478i	$-0.619392\pi$
$269$	−12.0171	−0.732697	−0.366349	+	0.930478i	$0.619392\pi$
$270$	48.0691	2.92539
$271$	9.84908	0.598289	0.299144	−	0.954208i	$-0.403299\pi$
$271$	9.84908	0.598289	0.299144	+	0.954208i	$0.403299\pi$
$272$	0.0913081	0.00553637
$273$	6.79304	0.411133
$274$	−8.78689	−0.530836
$275$	−13.5768	−0.818714
$276$	−27.3708	−1.64753
$277$	−5.89830	−0.354394	−0.177197	−	0.984175i	$-0.556703\pi$
$277$	−5.89830	−0.354394	−0.177197	+	0.984175i	$0.556703\pi$
$278$	−5.61758	−0.336920
$279$	6.20878	0.371710
$280$	−8.47785	−0.506649
$281$	−20.7902	−1.24024	−0.620118	−	0.784508i	$-0.712915\pi$
$281$	−20.7902	−1.24024	−0.620118	+	0.784508i	$0.712915\pi$
$282$	15.2027	0.905310
$283$	15.0891	0.896951	0.448475	−	0.893795i	$-0.351967\pi$
$283$	15.0891	0.896951	0.448475	+	0.893795i	$0.351967\pi$
$284$	−1.22397	−0.0726292
$285$	−3.25280	−0.192679
$286$	4.03646	0.238681
$287$	1.48326	0.0875542
$288$	−43.7496	−2.57797
$289$	−14.1371	−0.831596
$290$	−0.844633	−0.0495986
$291$	8.37720	0.491080
$292$	−7.52754	−0.440516
$293$	−30.1968	−1.76412	−0.882059	−	0.471140i	$-0.843843\pi$
$293$	−30.1968	−1.76412	−0.882059	+	0.471140i	$0.843843\pi$
$294$	−18.1176	−1.05664
$295$	10.9990	0.640385
$296$	21.0008	1.22065
$297$	29.6281	1.71920
$298$	7.39141	0.428173
$299$	−16.4868	−0.953454
$300$	28.7892	1.66214
$301$	8.24076	0.474990
$302$	−0.390168	−0.0224516
$303$	−63.2944	−3.63617
$304$	−0.0153357	−0.000879560 0
$305$	−12.1789	−0.697365
$306$	11.5772	0.661826
$307$	8.20159	0.468090	0.234045	−	0.972226i	$-0.424804\pi$
$307$	8.20159	0.468090	0.234045	+	0.972226i	$0.424804\pi$
$308$	−1.98382	−0.113039
$309$	23.8877	1.35892
$310$	−2.45638	−0.139513
$311$	−9.02422	−0.511717	−0.255858	−	0.966714i	$-0.582358\pi$
$311$	−9.02422	−0.511717	−0.255858	+	0.966714i	$0.582358\pi$
$312$	−22.5451	−1.27636
$313$	31.6865	1.79103	0.895513	−	0.445036i	$-0.146809\pi$
$313$	31.6865	1.79103	0.895513	+	0.445036i	$0.146809\pi$
$314$	−0.107495	−0.00606632
$315$	−23.1857	−1.30636
$316$	6.63592	0.373299
$317$	25.6245	1.43921	0.719607	−	0.694381i	$-0.244322\pi$
$317$	25.6245	1.43921	0.719607	+	0.694381i	$0.244322\pi$
$318$	25.1632	1.41108
$319$	−0.520602	−0.0291481
$320$	17.6851	0.988628
$321$	19.5612	1.09180
$322$	−5.13745	−0.286299
$323$	−0.480833	−0.0267542
$324$	−34.3050	−1.90583
$325$	17.3412	0.961914
$326$	−12.5112	−0.692931
$327$	−15.6675	−0.866413
$328$	−4.92273	−0.271812
$329$	−4.50063	−0.248128
$330$	−19.0983	−1.05132
$331$	20.1722	1.10877	0.554383	−	0.832262i	$-0.312954\pi$
$331$	20.1722	1.10877	0.554383	+	0.832262i	$0.312954\pi$
$332$	−13.7657	−0.755493
$333$	57.4340	3.14737
$334$	6.70703	0.366992
$335$	32.5406	1.77788
$336$	−0.151532	−0.00826672
$337$	7.70671	0.419811	0.209906	−	0.977722i	$-0.432684\pi$
$337$	7.70671	0.419811	0.209906	+	0.977722i	$0.432684\pi$
$338$	6.29644	0.342481
$339$	3.28134	0.178218
$340$	7.22409	0.391781
$341$	−1.51402	−0.0819890
$342$	−1.94445	−0.105144
$343$	11.3537	0.613044
$344$	−27.3499	−1.47461
$345$	78.0062	4.19971
$346$	17.8820	0.961340
$347$	−11.9119	−0.639462	−0.319731	−	0.947508i	$-0.603593\pi$
$347$	−11.9119	−0.639462	−0.319731	+	0.947508i	$0.603593\pi$
$348$	1.10392	0.0591763
$349$	0.997579	0.0533992	0.0266996	−	0.999644i	$-0.491500\pi$
$349$	0.997579	0.0533992	0.0266996	+	0.999644i	$0.491500\pi$
$350$	5.40369	0.288839
$351$	−37.8429	−2.01990
$352$	10.6684	0.568630
$353$	10.5115	0.559468	0.279734	−	0.960078i	$-0.409754\pi$
$353$	10.5115	0.559468	0.279734	+	0.960078i	$0.409754\pi$
$354$	9.11445	0.484428
$355$	3.48829	0.185139
$356$	8.23433	0.436419
$357$	−4.75110	−0.251455
$358$	−6.05321	−0.319922
$359$	28.2462	1.49078	0.745390	−	0.666629i	$-0.232263\pi$
$359$	28.2462	1.49078	0.745390	+	0.666629i	$0.232263\pi$
$360$	76.9497	4.05561
$361$	−18.9192	−0.995750
$362$	9.56409	0.502678
$363$	24.3232	1.27664
$364$	2.53386	0.132810
$365$	21.4534	1.12292
$366$	−10.0923	−0.527531
$367$	7.33371	0.382816	0.191408	−	0.981511i	$-0.438695\pi$
$367$	7.33371	0.382816	0.191408	+	0.981511i	$0.438695\pi$
$368$	0.367768	0.0191712
$369$	−13.4629	−0.700852
$370$	−22.7226	−1.18129
$371$	−7.44933	−0.386750
$372$	3.21044	0.166453
$373$	−8.40168	−0.435023	−0.217511	−	0.976058i	$-0.569794\pi$
$373$	−8.40168	−0.435023	−0.217511	+	0.976058i	$0.569794\pi$
$374$	−2.82313	−0.145981
$375$	−24.8174	−1.28156
$376$	14.9369	0.770313
$377$	0.664945	0.0342464
$378$	−11.7922	−0.606528
$379$	−10.2800	−0.528051	−0.264025	−	0.964516i	$-0.585050\pi$
$379$	−10.2800	−0.528051	−0.264025	+	0.964516i	$0.585050\pi$
$380$	−1.21332	−0.0622421
$381$	−2.90997	−0.149082
$382$	13.8100	0.706581
$383$	3.88154	0.198337	0.0991686	−	0.995071i	$-0.468382\pi$
$383$	3.88154	0.198337	0.0991686	+	0.995071i	$0.468382\pi$
$384$	−22.3101	−1.13851
$385$	5.65387	0.288148
$386$	−8.73516	−0.444608
$387$	−74.7978	−3.80219
$388$	3.12477	0.158636
$389$	−39.0528	−1.98006	−0.990028	−	0.140870i	$-0.955010\pi$
$389$	−39.0528	−1.98006	−0.990028	+	0.140870i	$0.955010\pi$
$390$	24.3935	1.23521
$391$	11.5310	0.583146
$392$	−17.8008	−0.899075
$393$	−10.0720	−0.508065
$394$	−14.4133	−0.726130
$395$	−18.9123	−0.951579
$396$	18.0063	0.904851
$397$	−4.76786	−0.239292	−0.119646	−	0.992817i	$-0.538176\pi$
$397$	−4.76786	−0.239292	−0.119646	+	0.992817i	$0.538176\pi$
$398$	9.61879	0.482146
$399$	0.797972	0.0399485
$400$	−0.386827	−0.0193414
$401$	17.0775	0.852811	0.426406	−	0.904532i	$-0.359780\pi$
$401$	17.0775	0.852811	0.426406	+	0.904532i	$0.359780\pi$
$402$	26.9652	1.34490
$403$	1.93380	0.0963296
$404$	−23.6094	−1.17461
$405$	97.7688	4.85817
$406$	0.207204	0.0102834
$407$	−14.0054	−0.694222
$408$	15.7682	0.780643
$409$	17.5055	0.865593	0.432797	−	0.901492i	$-0.357527\pi$
$409$	17.5055	0.865593	0.432797	+	0.901492i	$0.357527\pi$
$410$	5.32632	0.263048
$411$	−32.7301	−1.61446
$412$	8.91030	0.438979
$413$	−2.69825	−0.132772
$414$	46.6304	2.29176
$415$	39.2321	1.92583
$416$	−13.6264	−0.668088
$417$	−20.9248	−1.02469
$418$	0.474158	0.0231918
$419$	24.5629	1.19998	0.599988	−	0.800009i	$-0.295172\pi$
$419$	24.5629	1.19998	0.599988	+	0.800009i	$0.295172\pi$
$420$	−11.9888	−0.584995
$421$	18.0538	0.879887	0.439943	−	0.898026i	$-0.354999\pi$
$421$	18.0538	0.879887	0.439943	+	0.898026i	$0.354999\pi$
$422$	3.11291	0.151534
$423$	40.8503	1.98621
$424$	24.7232	1.20067
$425$	−12.1285	−0.588321
$426$	2.89062	0.140051
$427$	2.98772	0.144586
$428$	7.29648	0.352689
$429$	15.0353	0.725910
$430$	29.5922	1.42706
$431$	1.99407	0.0960510	0.0480255	−	0.998846i	$-0.484707\pi$
$431$	1.99407	0.0960510	0.0480255	+	0.998846i	$0.484707\pi$
$432$	0.844156	0.0406145
$433$	−26.7001	−1.28312	−0.641562	−	0.767072i	$-0.721713\pi$
$433$	−26.7001	−1.28312	−0.641562	+	0.767072i	$0.721713\pi$
$434$	0.602594	0.0289254
$435$	−3.14615	−0.150846
$436$	−5.84410	−0.279882
$437$	−1.93668	−0.0926441
$438$	17.7776	0.849448
$439$	−30.4587	−1.45371	−0.726857	−	0.686789i	$-0.759020\pi$
$439$	−30.4587	−1.45371	−0.726857	+	0.686789i	$0.759020\pi$
$440$	−18.7643	−0.894555
$441$	−48.6825	−2.31821
$442$	3.60587	0.171514
$443$	33.4514	1.58933	0.794663	−	0.607051i	$-0.207648\pi$
$443$	33.4514	1.58933	0.794663	+	0.607051i	$0.207648\pi$
$444$	29.6980	1.40940
$445$	−23.4677	−1.11248
$446$	−20.5216	−0.971724
$447$	27.5321	1.30222
$448$	−4.33849	−0.204974
$449$	−2.65523	−0.125308	−0.0626541	−	0.998035i	$-0.519956\pi$
$449$	−2.65523	−0.125308	−0.0626541	+	0.998035i	$0.519956\pi$
$450$	−49.0469	−2.31209
$451$	3.28296	0.154589
$452$	1.22397	0.0575706
$453$	−1.45333	−0.0682832
$454$	2.72316	0.127804
$455$	−7.22147	−0.338548
$456$	−2.64835	−0.124020
$457$	0.944203	0.0441679	0.0220840	−	0.999756i	$-0.492970\pi$
$457$	0.944203	0.0441679	0.0220840	+	0.999756i	$0.492970\pi$
$458$	−8.64031	−0.403735
$459$	26.4676	1.23540
$460$	29.0970	1.35665
$461$	25.0486	1.16663	0.583315	−	0.812246i	$-0.301755\pi$
$461$	25.0486	1.16663	0.583315	+	0.812246i	$0.301755\pi$
$462$	4.68516	0.217973
$463$	−2.76129	−0.128328	−0.0641641	−	0.997939i	$-0.520438\pi$
$463$	−2.76129	−0.128328	−0.0641641	+	0.997939i	$0.520438\pi$
$464$	−0.0148329	−0.000688598 0
$465$	−9.14969	−0.424307
$466$	9.03211	0.418405
$467$	4.71240	0.218064	0.109032	−	0.994038i	$-0.465225\pi$
$467$	4.71240	0.218064	0.109032	+	0.994038i	$0.465225\pi$
$468$	−22.9988	−1.06312
$469$	−7.98281	−0.368612
$470$	−16.1616	−0.745477
$471$	−0.400407	−0.0184498
$472$	8.95509	0.412192
$473$	18.2396	0.838657
$474$	−15.6719	−0.719834
$475$	2.03705	0.0934662
$476$	−1.77220	−0.0812288
$477$	67.6143	3.09585
$478$	−20.6425	−0.944165
$479$	1.85631	0.0848171	0.0424086	−	0.999100i	$-0.486497\pi$
$479$	1.85631	0.0848171	0.0424086	+	0.999100i	$0.486497\pi$
$480$	64.4725	2.94275
$481$	17.8886	0.815648
$482$	7.98001	0.363480
$483$	−19.1364	−0.870734
$484$	9.07278	0.412399
$485$	−8.90554	−0.404380
$486$	39.6770	1.79979
$487$	26.9012	1.21901	0.609505	−	0.792782i	$-0.291368\pi$
$487$	26.9012	1.21901	0.609505	+	0.792782i	$0.291368\pi$
$488$	−9.91580	−0.448867
$489$	−46.6026	−2.10744
$490$	19.2602	0.870087
$491$	17.9317	0.809246	0.404623	−	0.914484i	$-0.367403\pi$
$491$	17.9317	0.809246	0.404623	+	0.914484i	$0.367403\pi$
$492$	−6.96140	−0.313844
$493$	−0.465068	−0.0209456
$494$	−0.605624	−0.0272483
$495$	−51.3177	−2.30656
$496$	−0.0431371	−0.00193691
$497$	−0.855742	−0.0383853
$498$	32.5102	1.45682
$499$	14.3233	0.641198	0.320599	−	0.947215i	$-0.396116\pi$
$499$	14.3233	0.641198	0.320599	+	0.947215i	$0.396116\pi$
$500$	−9.25710	−0.413990
$501$	24.9828	1.11615
$502$	−4.70048	−0.209793
$503$	30.4682	1.35851	0.679255	−	0.733902i	$-0.262303\pi$
$503$	30.4682	1.35851	0.679255	+	0.733902i	$0.262303\pi$
$504$	−18.8772	−0.840857
$505$	67.2863	2.99420
$506$	−11.3709	−0.505499
$507$	23.4534	1.04160
$508$	−1.08544	−0.0481588
$509$	11.0206	0.488481	0.244241	−	0.969715i	$-0.421461\pi$
$509$	11.0206	0.488481	0.244241	+	0.969715i	$0.421461\pi$
$510$	−17.0610	−0.755473
$511$	−5.26291	−0.232817
$512$	0.610490	0.0269801
$513$	−4.44536	−0.196268
$514$	19.2294	0.848173
$515$	−25.3942	−1.11900
$516$	−38.6764	−1.70263
$517$	−9.96142	−0.438103
$518$	5.57427	0.244919
$519$	66.6080	2.92377
$520$	23.9670	1.05102
$521$	13.7742	0.603458	0.301729	−	0.953394i	$-0.402436\pi$
$521$	13.7742	0.603458	0.301729	+	0.953394i	$0.402436\pi$
$522$	−1.88070	−0.0823160
$523$	30.2433	1.32245	0.661223	−	0.750189i	$-0.270038\pi$
$523$	30.2433	1.32245	0.661223	+	0.750189i	$0.270038\pi$
$524$	−3.75694	−0.164123
$525$	20.1281	0.878461
$526$	−3.53667	−0.154206
$527$	−1.35252	−0.0589166
$528$	−0.335390	−0.0145960
$529$	23.4441	1.01931
$530$	−26.7502	−1.16195
$531$	24.4908	1.06281
$532$	0.297650	0.0129048
$533$	−4.19320	−0.181628
$534$	−19.4468	−0.841547
$535$	−20.7949	−0.899040
$536$	26.4937	1.14436
$537$	−22.5474	−0.972994
$538$	10.5862	0.456404
$539$	11.8713	0.511334
$540$	66.7877	2.87409
$541$	−3.50579	−0.150726	−0.0753628	−	0.997156i	$-0.524011\pi$
$541$	−3.50579	−0.150726	−0.0753628	+	0.997156i	$0.524011\pi$
$542$	−8.67631	−0.372680
$543$	35.6250	1.52882
$544$	9.53040	0.408612
$545$	16.6556	0.713447
$546$	−5.98417	−0.256099
$547$	1.39694	0.0597289	0.0298644	−	0.999554i	$-0.490492\pi$
$547$	1.39694	0.0597289	0.0298644	+	0.999554i	$0.490492\pi$
$548$	−12.2086	−0.521525
$549$	−27.1182	−1.15738
$550$	11.9602	0.509984
$551$	0.0781105	0.00332762
$552$	63.5107	2.70320
$553$	4.63952	0.197293
$554$	5.19597	0.220755
$555$	−84.6387	−3.59271
$556$	−7.80512	−0.331011
$557$	8.76844	0.371531	0.185765	−	0.982594i	$-0.440524\pi$
$557$	8.76844	0.371531	0.185765	+	0.982594i	$0.440524\pi$
$558$	−5.46948	−0.231542
$559$	−23.2967	−0.985346
$560$	0.161088	0.00680723
$561$	−10.5158	−0.443977
$562$	18.3146	0.772555
$563$	−25.3762	−1.06948	−0.534739	−	0.845017i	$-0.679590\pi$
$563$	−25.3762	−1.06948	−0.534739	+	0.845017i	$0.679590\pi$
$564$	21.1228	0.889432
$565$	−3.48829	−0.146753
$566$	−13.2923	−0.558719
$567$	−23.9845	−1.00725
$568$	2.84008	0.119167
$569$	38.6774	1.62144	0.810720	−	0.585434i	$-0.199076\pi$
$569$	38.6774	1.62144	0.810720	+	0.585434i	$0.199076\pi$
$570$	2.86548	0.120022
$571$	−21.7522	−0.910300	−0.455150	−	0.890415i	$-0.650414\pi$
$571$	−21.7522	−0.910300	−0.455150	+	0.890415i	$0.650414\pi$
$572$	5.60829	0.234494
$573$	51.4405	2.14896
$574$	−1.30665	−0.0545383
$575$	−48.8510	−2.03723
$576$	39.3785	1.64077
$577$	45.9456	1.91274	0.956370	−	0.292158i	$-0.0943732\pi$
$577$	45.9456	1.91274	0.956370	+	0.292158i	$0.0943732\pi$
$578$	12.4538	0.518009
$579$	−32.5374	−1.35221
$580$	−1.17354	−0.0487287
$581$	−9.62436	−0.399286
$582$	−7.37970	−0.305898
$583$	−16.4879	−0.682859
$584$	17.4668	0.722781
$585$	65.5461	2.71000
$586$	26.6012	1.09888
$587$	−7.53350	−0.310941	−0.155470	−	0.987841i	$-0.549689\pi$
$587$	−7.53350	−0.310941	−0.155470	+	0.987841i	$0.549689\pi$
$588$	−25.1727	−1.03811
$589$	0.227162	0.00936005
$590$	−9.68929	−0.398902
$591$	−53.6876	−2.20841
$592$	−0.399038	−0.0164004
$593$	−34.9755	−1.43627	−0.718136	−	0.695903i	$-0.755004\pi$
$593$	−34.9755	−1.43627	−0.718136	+	0.695903i	$0.755004\pi$
$594$	−26.1002	−1.07090
$595$	5.05075	0.207061
$596$	10.2697	0.420663
$597$	35.8288	1.46637
$598$	14.5236	0.593915
$599$	6.40445	0.261679	0.130839	−	0.991404i	$-0.458233\pi$
$599$	6.40445	0.261679	0.130839	+	0.991404i	$0.458233\pi$
$600$	−66.8020	−2.72718
$601$	2.94249	0.120027	0.0600133	−	0.998198i	$-0.480886\pi$
$601$	2.94249	0.120027	0.0600133	+	0.998198i	$0.480886\pi$
$602$	−7.25951	−0.295875
$603$	72.4564	2.95065
$604$	−0.542103	−0.0220579
$605$	−25.8573	−1.05125
$606$	55.7577	2.26500
$607$	−22.3284	−0.906283	−0.453141	−	0.891439i	$-0.649697\pi$
$607$	−22.3284	−0.906283	−0.453141	+	0.891439i	$0.649697\pi$
$608$	−1.60068	−0.0649160
$609$	0.771809	0.0312753
$610$	10.7288	0.434395
$611$	12.7233	0.514731
$612$	16.0855	0.650218
$613$	33.2761	1.34401	0.672005	−	0.740547i	$-0.265433\pi$
$613$	33.2761	1.34401	0.672005	+	0.740547i	$0.265433\pi$
$614$	−7.22500	−0.291577
$615$	19.8399	0.800021
$616$	4.60324	0.185470
$617$	−25.2287	−1.01567	−0.507834	−	0.861455i	$-0.669554\pi$
$617$	−25.2287	−1.01567	−0.507834	+	0.861455i	$0.669554\pi$
$618$	−21.0433	−0.846485
$619$	−26.2785	−1.05622	−0.528111	−	0.849175i	$-0.677100\pi$
$619$	−26.2785	−1.05622	−0.528111	+	0.849175i	$0.677100\pi$
$620$	−3.41291	−0.137066
$621$	106.605	4.27793
$622$	7.94968	0.318753
$623$	5.75706	0.230652
$624$	0.428381	0.0171490
$625$	−9.45823	−0.378329
$626$	−27.9135	−1.11565
$627$	1.76618	0.0705344
$628$	−0.149355	−0.00595993
$629$	−12.5114	−0.498862
$630$	20.4249	0.813746
$631$	−22.0042	−0.875974	−0.437987	−	0.898981i	$-0.644308\pi$
$631$	−22.0042	−0.875974	−0.437987	+	0.898981i	$0.644308\pi$
$632$	−15.3979	−0.612495
$633$	11.5952	0.460868
$634$	−22.5733	−0.896500
$635$	3.09350	0.122762
$636$	34.9620	1.38633
$637$	−15.1628	−0.600771
$638$	0.458613	0.0181566
$639$	7.76719	0.307265
$640$	23.7171	0.937502
$641$	39.6920	1.56774	0.783870	−	0.620925i	$-0.213243\pi$
$641$	39.6920	1.56774	0.783870	+	0.620925i	$0.213243\pi$
$642$	−17.2320	−0.680091
$643$	−29.5811	−1.16657	−0.583283	−	0.812269i	$-0.698232\pi$
$643$	−29.5811	−1.16657	−0.583283	+	0.812269i	$0.698232\pi$
$644$	−7.13803	−0.281278
$645$	110.227	4.34019
$646$	0.423578	0.0166655
$647$	12.4665	0.490107	0.245054	−	0.969509i	$-0.421194\pi$
$647$	12.4665	0.490107	0.245054	+	0.969509i	$0.421194\pi$
$648$	79.6009	3.12702
$649$	−5.97214	−0.234427
$650$	−15.2763	−0.599185
$651$	2.24459	0.0879723
$652$	−17.3832	−0.680778
$653$	−3.93309	−0.153914	−0.0769569	−	0.997034i	$-0.524520\pi$
$653$	−3.93309	−0.153914	−0.0769569	+	0.997034i	$0.524520\pi$
$654$	13.8019	0.539696
$655$	10.7072	0.418365
$656$	0.0935372	0.00365201
$657$	47.7691	1.86365
$658$	3.96473	0.154561
$659$	−24.6861	−0.961633	−0.480817	−	0.876821i	$-0.659660\pi$
$659$	−24.6861	−0.961633	−0.480817	+	0.876821i	$0.659660\pi$
$660$	−26.5353	−1.03289
$661$	14.8682	0.578308	0.289154	−	0.957283i	$-0.406626\pi$
$661$	14.8682	0.578308	0.289154	+	0.957283i	$0.406626\pi$
$662$	−17.7703	−0.690661
$663$	13.4314	0.521633
$664$	31.9418	1.23958
$665$	−0.848299	−0.0328956
$666$	−50.5952	−1.96052
$667$	−1.87319	−0.0725301
$668$	9.31881	0.360556
$669$	−76.4402	−2.95535
$670$	−28.6659	−1.10746
$671$	6.61283	0.255286
$672$	−15.8163	−0.610126
$673$	−16.6045	−0.640055	−0.320027	−	0.947408i	$-0.603692\pi$
$673$	−16.6045	−0.640055	−0.320027	+	0.947408i	$0.603692\pi$
$674$	−6.78904	−0.261504
$675$	−112.130	−4.31589
$676$	8.74834	0.336474
$677$	22.5446	0.866460	0.433230	−	0.901283i	$-0.357374\pi$
$677$	22.5446	0.866460	0.433230	+	0.901283i	$0.357374\pi$
$678$	−2.89062	−0.111014
$679$	2.18469	0.0838408
$680$	−16.7627	−0.642820
$681$	10.1434	0.388696
$682$	1.33374	0.0510717
$683$	−10.8091	−0.413598	−0.206799	−	0.978383i	$-0.566305\pi$
$683$	−10.8091	−0.413598	−0.206799	+	0.978383i	$0.566305\pi$
$684$	−2.70164	−0.103300
$685$	34.7943	1.32942
$686$	−10.0018	−0.381871
$687$	−32.1841	−1.22790
$688$	0.519677	0.0198125
$689$	21.0593	0.802297
$690$	−68.7177	−2.61604
$691$	−46.4246	−1.76608	−0.883038	−	0.469301i	$-0.844506\pi$
$691$	−46.4246	−1.76608	−0.883038	+	0.469301i	$0.844506\pi$
$692$	24.8454	0.944479
$693$	12.5892	0.478223
$694$	10.4935	0.398327
$695$	22.2445	0.843781
$696$	−2.56152	−0.0970941
$697$	2.93276	0.111086
$698$	−0.878794	−0.0332629
$699$	33.6435	1.27251
$700$	7.50794	0.283774
$701$	26.2492	0.991419	0.495709	−	0.868488i	$-0.334908\pi$
$701$	26.2492	0.991419	0.495709	+	0.868488i	$0.334908\pi$
$702$	33.3368	1.25822
$703$	2.10135	0.0792540
$704$	−9.60253	−0.361909
$705$	−60.1997	−2.26725
$706$	−9.25982	−0.348498
$707$	−16.5066	−0.620793
$708$	12.6637	0.475932
$709$	−27.0757	−1.01685	−0.508425	−	0.861106i	$-0.669772\pi$
$709$	−27.0757	−1.01685	−0.508425	+	0.861106i	$0.669772\pi$
$710$	−3.07293	−0.115325
$711$	−42.1109	−1.57928
$712$	−19.1068	−0.716059
$713$	−5.44763	−0.204015
$714$	4.18537	0.156634
$715$	−15.9835	−0.597751
$716$	−8.41039	−0.314311
$717$	−76.8906	−2.87153
$718$	−24.8829	−0.928620
$719$	−2.54997	−0.0950978	−0.0475489	−	0.998869i	$-0.515141\pi$
$719$	−2.54997	−0.0950978	−0.0475489	+	0.998869i	$0.515141\pi$
$720$	−1.46213	−0.0544903
$721$	6.22967	0.232005
$722$	16.6665	0.620262
$723$	29.7245	1.10547
$724$	13.2884	0.493861
$725$	1.97026	0.0731737
$726$	−21.4270	−0.795230
$727$	40.2787	1.49385	0.746927	−	0.664906i	$-0.231528\pi$
$727$	40.2787	1.49385	0.746927	+	0.664906i	$0.231528\pi$
$728$	−5.87954	−0.217910
$729$	63.7088	2.35958
$730$	−18.8988	−0.699478
$731$	16.2939	0.602652
$732$	−14.0223	−0.518279
$733$	28.8159	1.06434	0.532170	−	0.846638i	$-0.321377\pi$
$733$	28.8159	1.06434	0.532170	+	0.846638i	$0.321377\pi$
$734$	−6.46046	−0.238460
$735$	71.7418	2.64624
$736$	38.3863	1.41494
$737$	−17.6686	−0.650833
$738$	11.8598	0.436567
$739$	3.01976	0.111084	0.0555418	−	0.998456i	$-0.482311\pi$
$739$	3.01976	0.111084	0.0555418	+	0.998456i	$0.482311\pi$
$740$	−31.5710	−1.16057
$741$	−2.25587	−0.0828716
$742$	6.56232	0.240910
$743$	31.5134	1.15612	0.578058	−	0.815996i	$-0.303811\pi$
$743$	31.5134	1.15612	0.578058	+	0.815996i	$0.303811\pi$
$744$	−7.44945	−0.273110
$745$	−29.2685	−1.07231
$746$	7.40127	0.270980
$747$	87.3561	3.19619
$748$	−3.92248	−0.143420
$749$	5.10136	0.186400
$750$	21.8623	0.798298
$751$	39.7383	1.45007	0.725036	−	0.688711i	$-0.241823\pi$
$751$	39.7383	1.45007	0.725036	+	0.688711i	$0.241823\pi$
$752$	−0.283818	−0.0103498
$753$	−17.5087	−0.638053
$754$	−0.585768	−0.0213324
$755$	1.54499	0.0562278
$756$	−16.3843	−0.595890
$757$	−0.985933	−0.0358344	−0.0179172	−	0.999839i	$-0.505704\pi$
$757$	−0.985933	−0.0358344	−0.0179172	+	0.999839i	$0.505704\pi$
$758$	9.05597	0.328928
$759$	−42.3552	−1.53740
$760$	2.81538	0.102124
$761$	−2.65182	−0.0961286	−0.0480643	−	0.998844i	$-0.515305\pi$
$761$	−2.65182	−0.0961286	−0.0480643	+	0.998844i	$0.515305\pi$
$762$	2.56347	0.0928647
$763$	−4.08592	−0.147920
$764$	19.1878	0.694189
$765$	−45.8434	−1.65747
$766$	−3.41935	−0.123546
$767$	7.62798	0.275430
$768$	52.9254	1.90978
$769$	−23.1708	−0.835559	−0.417780	−	0.908548i	$-0.637192\pi$
$769$	−23.1708	−0.835559	−0.417780	+	0.908548i	$0.637192\pi$
$770$	−4.98064	−0.179490
$771$	71.6271	2.57959
$772$	−12.1367	−0.436810
$773$	9.31706	0.335111	0.167556	−	0.985863i	$-0.446413\pi$
$773$	9.31706	0.335111	0.167556	+	0.985863i	$0.446413\pi$
$774$	65.8914	2.36842
$775$	5.72995	0.205826
$776$	−7.25067	−0.260284
$777$	20.7634	0.744884
$778$	34.4027	1.23340
$779$	−0.492571	−0.0176482
$780$	33.8925	1.21355
$781$	−1.89405	−0.0677743
$782$	−10.1579	−0.363247
$783$	−4.29962	−0.153656
$784$	0.338234	0.0120798
$785$	0.425660	0.0151925
$786$	8.87268	0.316478
$787$	1.97465	0.0703888	0.0351944	−	0.999380i	$-0.488795\pi$
$787$	1.97465	0.0703888	0.0351944	+	0.999380i	$0.488795\pi$
$788$	−20.0260	−0.713395
$789$	−13.1736	−0.468994
$790$	16.6603	0.592747
$791$	0.855742	0.0304267
$792$	−41.7816	−1.48464
$793$	−8.44632	−0.299937
$794$	4.20014	0.149057
$795$	−99.6411	−3.53391
$796$	13.3644	0.473690
$797$	15.0596	0.533438	0.266719	−	0.963774i	$-0.414060\pi$
$797$	15.0596	0.533438	0.266719	+	0.963774i	$0.414060\pi$
$798$	−0.702954	−0.0248843
$799$	−8.89880	−0.314817
$800$	−40.3756	−1.42749
$801$	−52.2543	−1.84632
$802$	−15.0441	−0.531224
$803$	−11.6486	−0.411070
$804$	37.4657	1.32131
$805$	20.3433	0.717006
$806$	−1.70354	−0.0600046
$807$	39.4323	1.38808
$808$	54.7828	1.92725
$809$	39.9114	1.40321	0.701604	−	0.712567i	$-0.252467\pi$
$809$	39.9114	1.40321	0.701604	+	0.712567i	$0.252467\pi$
$810$	−86.1271	−3.02620
$811$	8.04538	0.282512	0.141256	−	0.989973i	$-0.454886\pi$
$811$	8.04538	0.282512	0.141256	+	0.989973i	$0.454886\pi$
$812$	0.287891	0.0101030
$813$	−32.3182	−1.13345
$814$	12.3377	0.432437
$815$	49.5418	1.73537
$816$	−0.299613	−0.0104886
$817$	−2.73664	−0.0957430
$818$	−15.4211	−0.539186
$819$	−16.0797	−0.561869
$820$	7.40045	0.258435
$821$	−43.7321	−1.52626	−0.763131	−	0.646244i	$-0.776339\pi$
$821$	−43.7321	−1.52626	−0.763131	+	0.646244i	$0.776339\pi$
$822$	28.8328	1.00566
$823$	26.0206	0.907022	0.453511	−	0.891251i	$-0.350171\pi$
$823$	26.0206	0.907022	0.453511	+	0.891251i	$0.350171\pi$
$824$	−20.6753	−0.720260
$825$	44.5502	1.55104
$826$	2.37696	0.0827051
$827$	8.17046	0.284115	0.142057	−	0.989858i	$-0.454628\pi$
$827$	8.17046	0.284115	0.142057	+	0.989858i	$0.454628\pi$
$828$	64.7887	2.25156
$829$	−25.1122	−0.872182	−0.436091	−	0.899903i	$-0.643637\pi$
$829$	−25.1122	−0.872182	−0.436091	+	0.899903i	$0.643637\pi$
$830$	−34.5606	−1.19962
$831$	19.3543	0.671394
$832$	12.2649	0.425210
$833$	10.6050	0.367440
$834$	18.4332	0.638289
$835$	−26.5585	−0.919093
$836$	0.658801	0.0227851
$837$	−12.5042	−0.432209
$838$	−21.6381	−0.747477
$839$	−12.0534	−0.416130	−0.208065	−	0.978115i	$-0.566717\pi$
$839$	−12.0534	−0.416130	−0.208065	+	0.978115i	$0.566717\pi$
$840$	27.8187	0.959837
$841$	−28.9245	−0.997395
$842$	−15.9040	−0.548089
$843$	68.2196	2.34961
$844$	4.32511	0.148876
$845$	−24.9326	−0.857708
$846$	−35.9861	−1.23723
$847$	6.34326	0.217957
$848$	−0.469768	−0.0161319
$849$	−49.5123	−1.69926
$850$	10.6844	0.366470
$851$	−50.3930	−1.72745
$852$	4.01626	0.137595
$853$	−10.7221	−0.367118	−0.183559	−	0.983009i	$-0.558762\pi$
$853$	−10.7221	−0.367118	−0.183559	+	0.983009i	$0.558762\pi$
$854$	−2.63196	−0.0900639
$855$	7.69963	0.263322
$856$	−16.9307	−0.578678
$857$	20.9794	0.716644	0.358322	−	0.933598i	$-0.383349\pi$
$857$	20.9794	0.716644	0.358322	+	0.933598i	$0.383349\pi$
$858$	−13.2450	−0.452176
$859$	−18.3777	−0.627038	−0.313519	−	0.949582i	$-0.601508\pi$
$859$	−18.3777	−0.627038	−0.313519	+	0.949582i	$0.601508\pi$
$860$	41.1157	1.40203
$861$	−4.86709	−0.165870
$862$	−1.75663	−0.0598311
$863$	−50.8557	−1.73115	−0.865574	−	0.500782i	$-0.833046\pi$
$863$	−50.8557	−1.73115	−0.865574	+	0.500782i	$0.833046\pi$
$864$	88.1098	2.99756
$865$	−70.8089	−2.40757
$866$	23.5208	0.799269
$867$	46.3887	1.57544
$868$	0.837250	0.0284181
$869$	10.2688	0.348346
$870$	2.77153	0.0939636
$871$	22.5675	0.764669
$872$	13.5606	0.459219
$873$	−19.8295	−0.671127
$874$	1.70608	0.0577089
$875$	−6.47214	−0.218798
$876$	24.7004	0.834550
$877$	−4.93447	−0.166625	−0.0833125	−	0.996523i	$-0.526550\pi$
$877$	−4.93447	−0.166625	−0.0833125	+	0.996523i	$0.526550\pi$
$878$	26.8319	0.905532
$879$	99.0861	3.34209
$880$	0.356543	0.0120191
$881$	9.97705	0.336136	0.168068	−	0.985775i	$-0.446247\pi$
$881$	9.97705	0.336136	0.168068	+	0.985775i	$0.446247\pi$
$882$	42.8857	1.44404
$883$	−28.0185	−0.942897	−0.471449	−	0.881894i	$-0.656269\pi$
$883$	−28.0185	−0.942897	−0.471449	+	0.881894i	$0.656269\pi$
$884$	5.01004	0.168506
$885$	−36.0914	−1.21320
$886$	−29.4683	−0.990005
$887$	−3.63781	−0.122146	−0.0610729	−	0.998133i	$-0.519452\pi$
$887$	−3.63781	−0.122146	−0.0610729	+	0.998133i	$0.519452\pi$
$888$	−68.9107	−2.31249
$889$	−0.758892	−0.0254524
$890$	20.6733	0.692972
$891$	−53.0858	−1.77844
$892$	−28.5129	−0.954681
$893$	1.49460	0.0500148
$894$	−24.2537	−0.811166
$895$	23.9695	0.801211
$896$	−5.81825	−0.194374
$897$	54.0987	1.80630
$898$	2.33906	0.0780556
$899$	0.219714	0.00732788
$900$	−68.1463	−2.27154
$901$	−14.7291	−0.490696
$902$	−2.89205	−0.0962946
$903$	−27.0407	−0.899860
$904$	−2.84008	−0.0944596
$905$	−37.8719	−1.25890
$906$	1.28027	0.0425343
$907$	36.0007	1.19538	0.597691	−	0.801726i	$-0.296085\pi$
$907$	36.0007	1.19538	0.597691	+	0.801726i	$0.296085\pi$
$908$	3.78358	0.125563
$909$	149.823	4.96931
$910$	6.36158	0.210884
$911$	1.92798	0.0638767	0.0319384	−	0.999490i	$-0.489832\pi$
$911$	1.92798	0.0638767	0.0319384	+	0.999490i	$0.489832\pi$
$912$	0.0503215	0.00166631
$913$	−21.3020	−0.704992
$914$	−0.831773	−0.0275126
$915$	39.9633	1.32115
$916$	−12.0049	−0.396654
$917$	−2.62668	−0.0867405
$918$	−23.3160	−0.769543
$919$	30.8812	1.01868	0.509338	−	0.860567i	$-0.329890\pi$
$919$	30.8812	1.01868	0.509338	+	0.860567i	$0.329890\pi$
$920$	−67.5163	−2.22594
$921$	−26.9122	−0.886788
$922$	−22.0660	−0.726705
$923$	2.41919	0.0796286
$924$	6.50960	0.214150
$925$	53.0046	1.74278
$926$	2.43250	0.0799368
$927$	−56.5440	−1.85715
$928$	−1.54820	−0.0508221
$929$	−38.7949	−1.27282	−0.636410	−	0.771351i	$-0.719582\pi$
$929$	−38.7949	−1.27282	−0.636410	+	0.771351i	$0.719582\pi$
$930$	8.06020	0.264304
$931$	−1.78116	−0.0583750
$932$	12.5493	0.411066
$933$	29.6115	0.969438
$934$	−4.15128	−0.135834
$935$	11.1790	0.365593
$936$	53.3660	1.74432
$937$	33.4526	1.09285	0.546424	−	0.837509i	$-0.315989\pi$
$937$	33.4526	1.09285	0.546424	+	0.837509i	$0.315989\pi$
$938$	7.03227	0.229612
$939$	−103.974	−3.39307
$940$	−22.4550	−0.732402
$941$	18.8941	0.615930	0.307965	−	0.951398i	$-0.400352\pi$
$941$	18.8941	0.615930	0.307965	+	0.951398i	$0.400352\pi$
$942$	0.352729	0.0114925
$943$	11.8125	0.384667
$944$	−0.170157	−0.00553812
$945$	46.6949	1.51898
$946$	−16.0677	−0.522407
$947$	25.5006	0.828660	0.414330	−	0.910127i	$-0.364016\pi$
$947$	25.5006	0.828660	0.414330	+	0.910127i	$0.364016\pi$
$948$	−21.7747	−0.707209
$949$	14.8783	0.482970
$950$	−1.79449	−0.0582210
$951$	−84.0827	−2.72657
$952$	4.11220	0.133277
$953$	47.9133	1.55206	0.776032	−	0.630693i	$-0.217229\pi$
$953$	47.9133	1.55206	0.776032	+	0.630693i	$0.217229\pi$
$954$	−59.5633	−1.92843
$955$	−54.6848	−1.76956
$956$	−28.6809	−0.927606
$957$	1.70827	0.0552206
$958$	−1.63528	−0.0528334
$959$	−8.53568	−0.275632
$960$	−58.0309	−1.87294
$961$	−30.3610	−0.979388
$962$	−15.7585	−0.508075
$963$	−46.3028	−1.49209
$964$	11.0875	0.357105
$965$	34.5894	1.11347
$966$	16.8577	0.542388
$967$	44.0122	1.41534	0.707668	−	0.706545i	$-0.249747\pi$
$967$	44.0122	1.41534	0.707668	+	0.706545i	$0.249747\pi$
$968$	−21.0523	−0.676648
$969$	1.57778	0.0506855
$970$	7.84513	0.251892
$971$	51.5006	1.65273	0.826367	−	0.563132i	$-0.190404\pi$
$971$	51.5006	1.65273	0.826367	+	0.563132i	$0.190404\pi$
$972$	55.1277	1.76822
$973$	−5.45698	−0.174943
$974$	−23.6980	−0.759332
$975$	−56.9022	−1.82233
$976$	0.188411	0.00603089
$977$	−2.95205	−0.0944446	−0.0472223	−	0.998884i	$-0.515037\pi$
$977$	−2.95205	−0.0944446	−0.0472223	+	0.998884i	$0.515037\pi$
$978$	41.0535	1.31274
$979$	12.7423	0.407246
$980$	26.7603	0.854827
$981$	37.0861	1.18407
$982$	−15.7965	−0.504086
$983$	42.3862	1.35191	0.675955	−	0.736942i	$-0.263731\pi$
$983$	42.3862	1.35191	0.675955	+	0.736942i	$0.263731\pi$
$984$	16.1531	0.514943
$985$	57.0736	1.81852
$986$	0.409691	0.0130472
$987$	14.7681	0.470074
$988$	−0.841460	−0.0267704
$989$	65.6281	2.08685
$990$	45.2071	1.43678
$991$	31.6598	1.00571	0.502854	−	0.864371i	$-0.332283\pi$
$991$	31.6598	1.00571	0.502854	+	0.864371i	$0.332283\pi$
$992$	−4.50249	−0.142954
$993$	−66.1920	−2.10054
$994$	0.753846	0.0239105
$995$	−38.0884	−1.20748
$996$	45.1701	1.43127
$997$	22.0770	0.699184	0.349592	−	0.936902i	$-0.386320\pi$
$997$	22.0770	0.699184	0.349592	+	0.936902i	$0.386320\pi$
$998$	−12.6178	−0.399408
$999$	−115.670	−3.65962

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.d.1.60	✓	165

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.d.1.60	✓	165	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)

\(f(q)\)	\(=\)	\(q-0.880927 q^{2} -3.28134 q^{3} -1.22397 q^{4} +3.48829 q^{5} +2.89062 q^{6} -0.855742 q^{7} +2.84008 q^{8} +7.76719 q^{9} +O(q^{10})\)	\(q-0.880927 q^{2} -3.28134 q^{3} -1.22397 q^{4} +3.48829 q^{5} +2.89062 q^{6} -0.855742 q^{7} +2.84008 q^{8} +7.76719 q^{9} -3.07293 q^{10} -1.89405 q^{11} +4.01626 q^{12} +2.41919 q^{13} +0.753846 q^{14} -11.4463 q^{15} -0.0539646 q^{16} -1.69200 q^{17} -6.84233 q^{18} +0.284180 q^{19} -4.26956 q^{20} +2.80798 q^{21} +1.66851 q^{22} -6.81499 q^{23} -9.31927 q^{24} +7.16817 q^{25} -2.13113 q^{26} -15.6428 q^{27} +1.04740 q^{28} +0.274863 q^{29} +10.0833 q^{30} +0.799360 q^{31} -5.63262 q^{32} +6.21501 q^{33} +1.49053 q^{34} -2.98508 q^{35} -9.50680 q^{36} +7.39444 q^{37} -0.250342 q^{38} -7.93819 q^{39} +9.90702 q^{40} -1.73331 q^{41} -2.47362 q^{42} -9.62996 q^{43} +2.31825 q^{44} +27.0942 q^{45} +6.00351 q^{46} +5.25933 q^{47} +0.177076 q^{48} -6.26771 q^{49} -6.31463 q^{50} +5.55203 q^{51} -2.96101 q^{52} +8.70512 q^{53} +13.7801 q^{54} -6.60698 q^{55} -2.43037 q^{56} -0.932491 q^{57} -0.242134 q^{58} +3.15311 q^{59} +14.0099 q^{60} -3.49138 q^{61} -0.704178 q^{62} -6.64671 q^{63} +5.06985 q^{64} +8.43884 q^{65} -5.47496 q^{66} +9.32852 q^{67} +2.07096 q^{68} +22.3623 q^{69} +2.62963 q^{70} +1.00000 q^{71} +22.0594 q^{72} +6.15011 q^{73} -6.51396 q^{74} -23.5212 q^{75} -0.347827 q^{76} +1.62081 q^{77} +6.99296 q^{78} -5.42164 q^{79} -0.188244 q^{80} +28.0277 q^{81} +1.52692 q^{82} +11.2468 q^{83} -3.43688 q^{84} -5.90219 q^{85} +8.48329 q^{86} -0.901918 q^{87} -5.37924 q^{88} -6.72757 q^{89} -23.8680 q^{90} -2.07020 q^{91} +8.34133 q^{92} -2.62297 q^{93} -4.63309 q^{94} +0.991302 q^{95} +18.4825 q^{96} -2.55298 q^{97} +5.52139 q^{98} -14.7114 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9}+O(q^{10}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9} + 14 q^{10} + 18 q^{11} + 54 q^{12} + 44 q^{13} + 26 q^{14} + 24 q^{15} + 168 q^{16} + 143 q^{17} + 57 q^{18} + 20 q^{19} + 49 q^{20} + 39 q^{21} + 25 q^{22} + 52 q^{23} + 27 q^{24} + 175 q^{25} + 48 q^{26} + 69 q^{27} + 28 q^{28} + 58 q^{29} - 11 q^{30} + 28 q^{31} + 114 q^{32} + 110 q^{33} + 55 q^{34} + 67 q^{35} + 202 q^{36} + 44 q^{37} + 35 q^{38} + 27 q^{39} + 53 q^{40} + 141 q^{41} + 40 q^{42} + 29 q^{43} + 52 q^{44} + 54 q^{45} + 29 q^{46} + 87 q^{47} + 53 q^{48} + 143 q^{49} + 16 q^{50} + 37 q^{51} + 105 q^{52} + 101 q^{53} - 36 q^{54} + 72 q^{55} + 57 q^{56} + 82 q^{57} + 4 q^{58} + 103 q^{59} + 53 q^{60} + 16 q^{61} + 54 q^{62} + 126 q^{63} + 136 q^{64} + 159 q^{65} + 53 q^{66} + 60 q^{67} + 220 q^{68} + 81 q^{69} + 16 q^{70} + 165 q^{71} + 176 q^{72} + 124 q^{73} + 29 q^{74} + 44 q^{75} + 18 q^{76} + 127 q^{77} - 91 q^{78} + 14 q^{79} + 158 q^{80} + 213 q^{81} + 20 q^{82} + 116 q^{83} + 67 q^{84} + 59 q^{85} + 30 q^{86} + 28 q^{87} + 79 q^{88} + 195 q^{89} + 16 q^{90} - 26 q^{91} + 173 q^{92} + 116 q^{93} + 53 q^{94} + 26 q^{95} - 36 q^{96} + 88 q^{97} + 150 q^{98} + 12 q^{99}+O(q^{100}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9 + 14 * q^10 + 18 * q^11 + 54 * q^12 + 44 * q^13 + 26 * q^14 + 24 * q^15 + 168 * q^16 + 143 * q^17 + 57 * q^18 + 20 * q^19 + 49 * q^20 + 39 * q^21 + 25 * q^22 + 52 * q^23 + 27 * q^24 + 175 * q^25 + 48 * q^26 + 69 * q^27 + 28 * q^28 + 58 * q^29 - 11 * q^30 + 28 * q^31 + 114 * q^32 + 110 * q^33 + 55 * q^34 + 67 * q^35 + 202 * q^36 + 44 * q^37 + 35 * q^38 + 27 * q^39 + 53 * q^40 + 141 * q^41 + 40 * q^42 + 29 * q^43 + 52 * q^44 + 54 * q^45 + 29 * q^46 + 87 * q^47 + 53 * q^48 + 143 * q^49 + 16 * q^50 + 37 * q^51 + 105 * q^52 + 101 * q^53 - 36 * q^54 + 72 * q^55 + 57 * q^56 + 82 * q^57 + 4 * q^58 + 103 * q^59 + 53 * q^60 + 16 * q^61 + 54 * q^62 + 126 * q^63 + 136 * q^64 + 159 * q^65 + 53 * q^66 + 60 * q^67 + 220 * q^68 + 81 * q^69 + 16 * q^70 + 165 * q^71 + 176 * q^72 + 124 * q^73 + 29 * q^74 + 44 * q^75 + 18 * q^76 + 127 * q^77 - 91 * q^78 + 14 * q^79 + 158 * q^80 + 213 * q^81 + 20 * q^82 + 116 * q^83 + 67 * q^84 + 59 * q^85 + 30 * q^86 + 28 * q^87 + 79 * q^88 + 195 * q^89 + 16 * q^90 - 26 * q^91 + 173 * q^92 + 116 * q^93 + 53 * q^94 + 26 * q^95 - 36 * q^96 + 88 * q^97 + 150 * q^98 + 12 * q^99

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