LMFDB - Embedded newform 8023.2.a.c.1.16

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:	$158$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q-2.47274 q^{2} -2.32483 q^{3} +4.11444 q^{4} -0.448444 q^{5} +5.74869 q^{6} +4.71625 q^{7} -5.22846 q^{8} +2.40481 q^{9} +O(q^{10})$	\(q-2.47274 q^{2} -2.32483 q^{3} +4.11444 q^{4} -0.448444 q^{5} +5.74869 q^{6} +4.71625 q^{7} -5.22846 q^{8} +2.40481 q^{9} +1.10889 q^{10} -3.11738 q^{11} -9.56535 q^{12} +1.13805 q^{13} -11.6621 q^{14} +1.04255 q^{15} +4.69974 q^{16} -5.01853 q^{17} -5.94648 q^{18} -7.46652 q^{19} -1.84510 q^{20} -10.9645 q^{21} +7.70847 q^{22} -4.64694 q^{23} +12.1553 q^{24} -4.79890 q^{25} -2.81410 q^{26} +1.38371 q^{27} +19.4047 q^{28} -5.28273 q^{29} -2.57797 q^{30} +9.31388 q^{31} -1.16430 q^{32} +7.24737 q^{33} +12.4095 q^{34} -2.11498 q^{35} +9.89446 q^{36} +1.67683 q^{37} +18.4628 q^{38} -2.64577 q^{39} +2.34467 q^{40} +11.3768 q^{41} +27.1123 q^{42} +11.6479 q^{43} -12.8263 q^{44} -1.07842 q^{45} +11.4907 q^{46} -10.6614 q^{47} -10.9261 q^{48} +15.2430 q^{49} +11.8664 q^{50} +11.6672 q^{51} +4.68244 q^{52} +9.13629 q^{53} -3.42154 q^{54} +1.39797 q^{55} -24.6587 q^{56} +17.3584 q^{57} +13.0628 q^{58} -5.36263 q^{59} +4.28953 q^{60} -2.46830 q^{61} -23.0308 q^{62} +11.3417 q^{63} -6.52045 q^{64} -0.510352 q^{65} -17.9209 q^{66} +2.51918 q^{67} -20.6484 q^{68} +10.8033 q^{69} +5.22978 q^{70} -1.00000 q^{71} -12.5735 q^{72} -0.446884 q^{73} -4.14635 q^{74} +11.1566 q^{75} -30.7205 q^{76} -14.7024 q^{77} +6.54230 q^{78} -0.650824 q^{79} -2.10757 q^{80} -10.4313 q^{81} -28.1319 q^{82} +11.8608 q^{83} -45.1126 q^{84} +2.25053 q^{85} -28.8023 q^{86} +12.2814 q^{87} +16.2991 q^{88} -14.4211 q^{89} +2.66666 q^{90} +5.36734 q^{91} -19.1196 q^{92} -21.6531 q^{93} +26.3629 q^{94} +3.34832 q^{95} +2.70680 q^{96} +8.52789 q^{97} -37.6921 q^{98} -7.49672 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9}+O(q^{10}) $ 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9} - 10 q^{10} - 10 q^{11} - 46 q^{12} - 28 q^{13} - 27 q^{14} - 41 q^{15} + 150 q^{16} - 137 q^{17} - 67 q^{18} - 42 q^{19} - 66 q^{20} - 46 q^{21} - 8 q^{22} - 26 q^{23} - 48 q^{24} + 129 q^{25} - 67 q^{26} - 89 q^{27} - 21 q^{28} - 79 q^{29} - 11 q^{30} + 7 q^{31} - 147 q^{32} - 112 q^{33} - 28 q^{34} - 53 q^{35} + 141 q^{36} - 60 q^{37} - 53 q^{38} - 3 q^{39} - 48 q^{40} - 128 q^{41} + 32 q^{42} - 63 q^{43} - 88 q^{45} - 2 q^{46} - 92 q^{47} - 131 q^{48} + 122 q^{49} - 116 q^{50} - 12 q^{51} - 89 q^{52} - 94 q^{53} - 71 q^{54} - 12 q^{55} - 104 q^{56} - 93 q^{57} - 65 q^{58} - 54 q^{59} - 12 q^{60} + 17 q^{61} - 97 q^{62} - 28 q^{63} + 163 q^{64} - 163 q^{65} - 65 q^{66} - 35 q^{67} - 217 q^{68} - 46 q^{69} - 79 q^{70} - 158 q^{71} - 99 q^{72} - 165 q^{73} - 94 q^{75} - 93 q^{76} - 140 q^{77} + 25 q^{78} - 61 q^{79} - 134 q^{80} + 114 q^{81} + 10 q^{82} - 158 q^{83} - 160 q^{84} + 23 q^{85} - 122 q^{86} - 71 q^{87} - 14 q^{88} - 251 q^{89} - 6 q^{90} - 57 q^{91} - 58 q^{92} - 52 q^{93} - 64 q^{94} - 84 q^{95} - 98 q^{96} - 48 q^{97} - 84 q^{98} + 85 q^{99}+O(q^{100}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9 - 10 * q^10 - 10 * q^11 - 46 * q^12 - 28 * q^13 - 27 * q^14 - 41 * q^15 + 150 * q^16 - 137 * q^17 - 67 * q^18 - 42 * q^19 - 66 * q^20 - 46 * q^21 - 8 * q^22 - 26 * q^23 - 48 * q^24 + 129 * q^25 - 67 * q^26 - 89 * q^27 - 21 * q^28 - 79 * q^29 - 11 * q^30 + 7 * q^31 - 147 * q^32 - 112 * q^33 - 28 * q^34 - 53 * q^35 + 141 * q^36 - 60 * q^37 - 53 * q^38 - 3 * q^39 - 48 * q^40 - 128 * q^41 + 32 * q^42 - 63 * q^43 - 88 * q^45 - 2 * q^46 - 92 * q^47 - 131 * q^48 + 122 * q^49 - 116 * q^50 - 12 * q^51 - 89 * q^52 - 94 * q^53 - 71 * q^54 - 12 * q^55 - 104 * q^56 - 93 * q^57 - 65 * q^58 - 54 * q^59 - 12 * q^60 + 17 * q^61 - 97 * q^62 - 28 * q^63 + 163 * q^64 - 163 * q^65 - 65 * q^66 - 35 * q^67 - 217 * q^68 - 46 * q^69 - 79 * q^70 - 158 * q^71 - 99 * q^72 - 165 * q^73 - 94 * q^75 - 93 * q^76 - 140 * q^77 + 25 * q^78 - 61 * q^79 - 134 * q^80 + 114 * q^81 + 10 * q^82 - 158 * q^83 - 160 * q^84 + 23 * q^85 - 122 * q^86 - 71 * q^87 - 14 * q^88 - 251 * q^89 - 6 * q^90 - 57 * q^91 - 58 * q^92 - 52 * q^93 - 64 * q^94 - 84 * q^95 - 98 * q^96 - 48 * q^97 - 84 * q^98 + 85 * 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 $

$2$	−2.47274	−1.74849	−0.874245	−	0.485484i	$-0.838643\pi$
$2$	−2.47274	−1.74849	−0.874245	+	0.485484i	$0.838643\pi$
$3$	−2.32483	−1.34224	−0.671119	−	0.741349i	$-0.734186\pi$
$3$	−2.32483	−1.34224	−0.671119	+	0.741349i	$0.734186\pi$
$4$	4.11444	2.05722
$5$	−0.448444	−0.200550	−0.100275	−	0.994960i	$-0.531972\pi$
$5$	−0.448444	−0.200550	−0.100275	+	0.994960i	$0.531972\pi$
$6$	5.74869	2.34689
$7$	4.71625	1.78258	0.891288	−	0.453437i	$-0.149802\pi$
$7$	4.71625	1.78258	0.891288	+	0.453437i	$0.149802\pi$
$8$	−5.22846	−1.84854
$9$	2.40481	0.801604
$10$	1.10889	0.350660
$11$	−3.11738	−0.939926	−0.469963	−	0.882686i	$-0.655733\pi$
$11$	−3.11738	−0.939926	−0.469963	+	0.882686i	$0.655733\pi$
$12$	−9.56535	−2.76128
$13$	1.13805	0.315638	0.157819	−	0.987468i	$-0.449554\pi$
$13$	1.13805	0.315638	0.157819	+	0.987468i	$0.449554\pi$
$14$	−11.6621	−3.11682
$15$	1.04255	0.269186
$16$	4.69974	1.17493
$17$	−5.01853	−1.21717	−0.608586	−	0.793488i	$-0.708263\pi$
$17$	−5.01853	−1.21717	−0.608586	+	0.793488i	$0.708263\pi$
$18$	−5.94648	−1.40160
$19$	−7.46652	−1.71294	−0.856468	−	0.516199i	$-0.827346\pi$
$19$	−7.46652	−1.71294	−0.856468	+	0.516199i	$0.827346\pi$
$20$	−1.84510	−0.412576
$21$	−10.9645	−2.39264
$22$	7.70847	1.64345
$23$	−4.64694	−0.968954	−0.484477	−	0.874804i	$-0.660990\pi$
$23$	−4.64694	−0.968954	−0.484477	+	0.874804i	$0.660990\pi$
$24$	12.1553	2.48118
$25$	−4.79890	−0.959780
$26$	−2.81410	−0.551891
$27$	1.38371	0.266294
$28$	19.4047	3.66715
$29$	−5.28273	−0.980979	−0.490489	−	0.871447i	$-0.663182\pi$
$29$	−5.28273	−0.980979	−0.490489	+	0.871447i	$0.663182\pi$
$30$	−2.57797	−0.470670
$31$	9.31388	1.67282	0.836411	−	0.548103i	$-0.184650\pi$
$31$	9.31388	1.67282	0.836411	+	0.548103i	$0.184650\pi$
$32$	−1.16430	−0.205822
$33$	7.24737	1.26161
$34$	12.4095	2.12821
$35$	−2.11498	−0.357496
$36$	9.89446	1.64908
$37$	1.67683	0.275669	0.137834	−	0.990455i	$-0.455986\pi$
$37$	1.67683	0.275669	0.137834	+	0.990455i	$0.455986\pi$
$38$	18.4628	2.99505
$39$	−2.64577	−0.423662
$40$	2.34467	0.370725
$41$	11.3768	1.77676	0.888381	−	0.459107i	$-0.151831\pi$
$41$	11.3768	1.77676	0.888381	+	0.459107i	$0.151831\pi$
$42$	27.1123	4.18351
$43$	11.6479	1.77629	0.888146	−	0.459562i	$-0.151994\pi$
$43$	11.6479	1.77629	0.888146	+	0.459562i	$0.151994\pi$
$44$	−12.8263	−1.93363
$45$	−1.07842	−0.160762
$46$	11.4907	1.69421
$47$	−10.6614	−1.55513	−0.777564	−	0.628804i	$-0.783545\pi$
$47$	−10.6614	−1.55513	−0.777564	+	0.628804i	$0.783545\pi$
$48$	−10.9261	−1.57704
$49$	15.2430	2.17758
$50$	11.8664	1.67817
$51$	11.6672	1.63373
$52$	4.68244	0.649338
$53$	9.13629	1.25497	0.627483	−	0.778630i	$-0.284085\pi$
$53$	9.13629	1.25497	0.627483	+	0.778630i	$0.284085\pi$
$54$	−3.42154	−0.465613
$55$	1.39797	0.188502
$56$	−24.6587	−3.29516
$57$	17.3584	2.29917
$58$	13.0628	1.71523
$59$	−5.36263	−0.698155	−0.349078	−	0.937094i	$-0.613505\pi$
$59$	−5.36263	−0.698155	−0.349078	+	0.937094i	$0.613505\pi$
$60$	4.28953	0.553776
$61$	−2.46830	−0.316033	−0.158016	−	0.987436i	$-0.550510\pi$
$61$	−2.46830	−0.316033	−0.158016	+	0.987436i	$0.550510\pi$
$62$	−23.0308	−2.92491
$63$	11.3417	1.42892
$64$	−6.52045	−0.815056
$65$	−0.510352	−0.0633014
$66$	−17.9209	−2.20590
$67$	2.51918	0.307767	0.153883	−	0.988089i	$-0.450822\pi$
$67$	2.51918	0.307767	0.153883	+	0.988089i	$0.450822\pi$
$68$	−20.6484	−2.50399
$69$	10.8033	1.30057
$70$	5.22978	0.625079
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	−12.5735	−1.48180
$73$	−0.446884	−0.0523038	−0.0261519	−	0.999658i	$-0.508325\pi$
$73$	−0.446884	−0.0523038	−0.0261519	+	0.999658i	$0.508325\pi$
$74$	−4.14635	−0.482004
$75$	11.1566	1.28825
$76$	−30.7205	−3.52389
$77$	−14.7024	−1.67549
$78$	6.54230	0.740769
$79$	−0.650824	−0.0732235	−0.0366117	−	0.999330i	$-0.511656\pi$
$79$	−0.650824	−0.0732235	−0.0366117	+	0.999330i	$0.511656\pi$
$80$	−2.10757	−0.235633
$81$	−10.4313	−1.15903
$82$	−28.1319	−3.10665
$83$	11.8608	1.30189	0.650945	−	0.759125i	$-0.274373\pi$
$83$	11.8608	1.30189	0.650945	+	0.759125i	$0.274373\pi$
$84$	−45.1126	−4.92219
$85$	2.25053	0.244104
$86$	−28.8023	−3.10583
$87$	12.2814	1.31671
$88$	16.2991	1.73749
$89$	−14.4211	−1.52863	−0.764317	−	0.644840i	$-0.776924\pi$
$89$	−14.4211	−1.52863	−0.764317	+	0.644840i	$0.776924\pi$
$90$	2.66666	0.281091
$91$	5.36734	0.562650
$92$	−19.1196	−1.99335
$93$	−21.6531	−2.24533
$94$	26.3629	2.71913
$95$	3.34832	0.343530
$96$	2.70680	0.276262
$97$	8.52789	0.865876	0.432938	−	0.901424i	$-0.357477\pi$
$97$	8.52789	0.865876	0.432938	+	0.901424i	$0.357477\pi$
$98$	−37.6921	−3.80747
$99$	−7.49672	−0.753449
$100$	−19.7448	−1.97448
$101$	12.5797	1.25172	0.625862	−	0.779933i	$-0.284747\pi$
$101$	12.5797	1.25172	0.625862	+	0.779933i	$0.284747\pi$
$102$	−28.8499	−2.85657
$103$	−17.2770	−1.70236	−0.851179	−	0.524876i	$-0.824112\pi$
$103$	−17.2770	−1.70236	−0.851179	+	0.524876i	$0.824112\pi$
$104$	−5.95025	−0.583470
$105$	4.91695	0.479845
$106$	−22.5917	−2.19430
$107$	13.5058	1.30566	0.652829	−	0.757505i	$-0.273582\pi$
$107$	13.5058	1.30566	0.652829	+	0.757505i	$0.273582\pi$
$108$	5.69317	0.547826
$109$	10.8420	1.03848	0.519238	−	0.854630i	$-0.326216\pi$
$109$	10.8420	1.03848	0.519238	+	0.854630i	$0.326216\pi$
$110$	−3.45682	−0.329595
$111$	−3.89833	−0.370013
$112$	22.1651	2.09441
$113$	−1.00000	−0.0940721
$113$	−1.00000	−0.0940721
$114$	−42.9227	−4.02008
$115$	2.08389	0.194324
$116$	−21.7355	−2.01809
$117$	2.73680	0.253017
$118$	13.2604	1.22072
$119$	−23.6686	−2.16970
$120$	−5.45095	−0.497602
$121$	−1.28193	−0.116539
$122$	6.10345	0.552581
$123$	−26.4491	−2.38484
$124$	38.3214	3.44136
$125$	4.39426	0.393034
$126$	−28.0451	−2.49846
$127$	10.3746	0.920600	0.460300	−	0.887764i	$-0.347742\pi$
$127$	10.3746	0.920600	0.460300	+	0.887764i	$0.347742\pi$
$128$	18.4520	1.63094
$129$	−27.0794	−2.38421
$130$	1.26197	0.110682
$131$	6.13464	0.535986	0.267993	−	0.963421i	$-0.413640\pi$
$131$	6.13464	0.535986	0.267993	+	0.963421i	$0.413640\pi$
$132$	29.8189	2.59540
$133$	−35.2140	−3.05344
$134$	−6.22928	−0.538127
$135$	−0.620514	−0.0534054
$136$	26.2392	2.24999
$137$	−0.215788	−0.0184360	−0.00921800	−	0.999958i	$-0.502934\pi$
$137$	−0.215788	−0.0184360	−0.00921800	+	0.999958i	$0.502934\pi$
$138$	−26.7138	−2.27403
$139$	17.6972	1.50106	0.750530	−	0.660836i	$-0.229798\pi$
$139$	17.6972	1.50106	0.750530	+	0.660836i	$0.229798\pi$
$140$	−8.70194	−0.735448
$141$	24.7859	2.08735
$142$	2.47274	0.207508
$143$	−3.54774	−0.296677
$144$	11.3020	0.941832
$145$	2.36901	0.196736
$146$	1.10503	0.0914528
$147$	−35.4374	−2.92283
$148$	6.89920	0.567111
$149$	23.2012	1.90072	0.950358	−	0.311157i	$-0.100717\pi$
$149$	23.2012	1.90072	0.950358	+	0.311157i	$0.100717\pi$
$150$	−27.5874	−2.25250
$151$	18.2579	1.48581	0.742904	−	0.669397i	$-0.233448\pi$
$151$	18.2579	1.48581	0.742904	+	0.669397i	$0.233448\pi$
$152$	39.0384	3.16643
$153$	−12.0686	−0.975690
$154$	36.3551	2.92958
$155$	−4.17675	−0.335485
$156$	−10.8859	−0.871566
$157$	−18.9435	−1.51186	−0.755928	−	0.654654i	$-0.772814\pi$
$157$	−18.9435	−1.51186	−0.755928	+	0.654654i	$0.772814\pi$
$158$	1.60932	0.128031
$159$	−21.2403	−1.68446
$160$	0.522125	0.0412776
$161$	−21.9162	−1.72723
$162$	25.7939	2.02656
$163$	−10.2360	−0.801745	−0.400872	−	0.916134i	$-0.631293\pi$
$163$	−10.2360	−0.801745	−0.400872	+	0.916134i	$0.631293\pi$
$164$	46.8093	3.65519
$165$	−3.25004	−0.253015
$166$	−29.3286	−2.27634
$167$	15.1748	1.17426	0.587132	−	0.809491i	$-0.300257\pi$
$167$	15.1748	1.17426	0.587132	+	0.809491i	$0.300257\pi$
$168$	57.3273	4.42289
$169$	−11.7048	−0.900372
$170$	−5.56497	−0.426814
$171$	−17.9556	−1.37310
$172$	47.9247	3.65422
$173$	−3.34857	−0.254587	−0.127294	−	0.991865i	$-0.540629\pi$
$173$	−3.34857	−0.254587	−0.127294	+	0.991865i	$0.540629\pi$
$174$	−30.3688	−2.30225
$175$	−22.6328	−1.71088
$176$	−14.6509	−1.10435
$177$	12.4672	0.937091
$178$	35.6597	2.67280
$179$	1.64435	0.122904	0.0614522	−	0.998110i	$-0.480427\pi$
$179$	1.64435	0.122904	0.0614522	+	0.998110i	$0.480427\pi$
$180$	−4.43711	−0.330723
$181$	23.9239	1.77825	0.889124	−	0.457666i	$-0.151314\pi$
$181$	23.9239	1.77825	0.889124	+	0.457666i	$0.151314\pi$
$182$	−13.2720	−0.983788
$183$	5.73836	0.424192
$184$	24.2963	1.79115
$185$	−0.751963	−0.0552854
$186$	53.5426	3.92593
$187$	15.6447	1.14405
$188$	−43.8658	−3.19924
$189$	6.52590	0.474690
$190$	−8.27951	−0.600659
$191$	−12.8964	−0.933154	−0.466577	−	0.884481i	$-0.654513\pi$
$191$	−12.8964	−0.933154	−0.466577	+	0.884481i	$0.654513\pi$
$192$	15.1589	1.09400
$193$	−6.77538	−0.487702	−0.243851	−	0.969813i	$-0.578411\pi$
$193$	−6.77538	−0.487702	−0.243851	+	0.969813i	$0.578411\pi$
$194$	−21.0873	−1.51398
$195$	1.18648	0.0849656
$196$	62.7166	4.47976
$197$	3.03452	0.216200	0.108100	−	0.994140i	$-0.465523\pi$
$197$	3.03452	0.216200	0.108100	+	0.994140i	$0.465523\pi$
$198$	18.5374	1.31740
$199$	−11.9810	−0.849314	−0.424657	−	0.905354i	$-0.639605\pi$
$199$	−11.9810	−0.849314	−0.424657	+	0.905354i	$0.639605\pi$
$200$	25.0908	1.77419
$201$	−5.85665	−0.413097
$202$	−31.1063	−2.18863
$203$	−24.9147	−1.74867
$204$	48.0040	3.36095
$205$	−5.10187	−0.356330
$206$	42.7216	2.97656
$207$	−11.1750	−0.776718
$208$	5.34854	0.370854
$209$	23.2760	1.61003
$210$	−12.1583	−0.839005
$211$	−20.2056	−1.39101	−0.695504	−	0.718522i	$-0.744819\pi$
$211$	−20.2056	−1.39101	−0.695504	+	0.718522i	$0.744819\pi$
$212$	37.5907	2.58174
$213$	2.32483	0.159294
$214$	−33.3964	−2.28293
$215$	−5.22344	−0.356236
$216$	−7.23464	−0.492255
$217$	43.9266	2.98193
$218$	−26.8095	−1.81577
$219$	1.03893	0.0702042
$220$	5.75187	0.387791
$221$	−5.71134	−0.384186
$222$	9.63955	0.646964
$223$	−20.6600	−1.38349	−0.691747	−	0.722140i	$-0.743159\pi$
$223$	−20.6600	−1.38349	−0.691747	+	0.722140i	$0.743159\pi$
$224$	−5.49115	−0.366893
$225$	−11.5405	−0.769364
$226$	2.47274	0.164484
$227$	−29.7519	−1.97471	−0.987353	−	0.158538i	$-0.949322\pi$
$227$	−29.7519	−1.97471	−0.987353	+	0.158538i	$0.949322\pi$
$228$	71.4199	4.72990
$229$	−15.5414	−1.02700	−0.513502	−	0.858088i	$-0.671652\pi$
$229$	−15.5414	−1.02700	−0.513502	+	0.858088i	$0.671652\pi$
$230$	−5.15293	−0.339774
$231$	34.1804	2.24891
$232$	27.6205	1.81338
$233$	−4.66988	−0.305934	−0.152967	−	0.988231i	$-0.548883\pi$
$233$	−4.66988	−0.305934	−0.152967	+	0.988231i	$0.548883\pi$
$234$	−6.76739	−0.442398
$235$	4.78105	0.311881
$236$	−22.0642	−1.43626
$237$	1.51305	0.0982834
$238$	58.5264	3.79370
$239$	10.1608	0.657246	0.328623	−	0.944461i	$-0.393415\pi$
$239$	10.1608	0.657246	0.328623	+	0.944461i	$0.393415\pi$
$240$	4.89973	0.316276
$241$	10.3195	0.664735	0.332367	−	0.943150i	$-0.392153\pi$
$241$	10.3195	0.664735	0.332367	+	0.943150i	$0.392153\pi$
$242$	3.16987	0.203767
$243$	20.0999	1.28941
$244$	−10.1557	−0.650149
$245$	−6.83565	−0.436714
$246$	65.4018	4.16987
$247$	−8.49728	−0.540669
$248$	−48.6972	−3.09228
$249$	−27.5743	−1.74745
$250$	−10.8659	−0.687217
$251$	−7.99047	−0.504354	−0.252177	−	0.967681i	$-0.581147\pi$
$251$	−7.99047	−0.504354	−0.252177	+	0.967681i	$0.581147\pi$
$252$	46.6648	2.93960
$253$	14.4863	0.910745
$254$	−25.6538	−1.60966
$255$	−5.23209	−0.327646
$256$	−32.5860	−2.03663
$257$	−12.8385	−0.800846	−0.400423	−	0.916330i	$-0.631137\pi$
$257$	−12.8385	−0.800846	−0.400423	+	0.916330i	$0.631137\pi$
$258$	66.9602	4.16876
$259$	7.90834	0.491400
$260$	−2.09981	−0.130225
$261$	−12.7040	−0.786357
$262$	−15.1694	−0.937166
$263$	−16.3684	−1.00932	−0.504659	−	0.863318i	$-0.668382\pi$
$263$	−16.3684	−1.00932	−0.504659	+	0.863318i	$0.668382\pi$
$264$	−37.8926	−2.33213
$265$	−4.09712	−0.251684
$266$	87.0750	5.33891
$267$	33.5266	2.05179
$268$	10.3650	0.633144
$269$	14.7533	0.899523	0.449762	−	0.893149i	$-0.351509\pi$
$269$	14.7533	0.899523	0.449762	+	0.893149i	$0.351509\pi$
$270$	1.53437	0.0933788
$271$	11.6153	0.705582	0.352791	−	0.935702i	$-0.385233\pi$
$271$	11.6153	0.705582	0.352791	+	0.935702i	$0.385233\pi$
$272$	−23.5858	−1.43010
$273$	−12.4781	−0.755210
$274$	0.533587	0.0322352
$275$	14.9600	0.902122
$276$	44.4496	2.67555
$277$	−18.2270	−1.09515	−0.547576	−	0.836756i	$-0.684449\pi$
$277$	−18.2270	−1.09515	−0.547576	+	0.836756i	$0.684449\pi$
$278$	−43.7607	−2.62459
$279$	22.3981	1.34094
$280$	11.0581	0.660846
$281$	−15.1613	−0.904450	−0.452225	−	0.891904i	$-0.649370\pi$
$281$	−15.1613	−0.904450	−0.452225	+	0.891904i	$0.649370\pi$
$282$	−61.2892	−3.64972
$283$	−9.99210	−0.593969	−0.296984	−	0.954882i	$-0.595981\pi$
$283$	−9.99210	−0.593969	−0.296984	+	0.954882i	$0.595981\pi$
$284$	−4.11444	−0.244147
$285$	−7.78425	−0.461099
$286$	8.77263	0.518737
$287$	53.6560	3.16721
$288$	−2.79993	−0.164988
$289$	8.18562	0.481507
$290$	−5.85795	−0.343990
$291$	−19.8259	−1.16221
$292$	−1.83868	−0.107600
$293$	8.74560	0.510923	0.255462	−	0.966819i	$-0.417773\pi$
$293$	8.74560	0.510923	0.255462	+	0.966819i	$0.417773\pi$
$294$	87.6275	5.11054
$295$	2.40484	0.140015
$296$	−8.76722	−0.509584
$297$	−4.31354	−0.250297
$298$	−57.3705	−3.32339
$299$	−5.28845	−0.305839
$300$	45.9032	2.65022
$301$	54.9345	3.16637
$302$	−45.1471	−2.59792
$303$	−29.2456	−1.68011
$304$	−35.0907	−2.01259
$305$	1.10689	0.0633805
$306$	29.8426	1.70599
$307$	12.1528	0.693600	0.346800	−	0.937939i	$-0.387268\pi$
$307$	12.1528	0.693600	0.346800	+	0.937939i	$0.387268\pi$
$308$	−60.4920	−3.44685
$309$	40.1661	2.28497
$310$	10.3280	0.586592
$311$	12.5209	0.709997	0.354999	−	0.934867i	$-0.384481\pi$
$311$	12.5209	0.709997	0.354999	+	0.934867i	$0.384481\pi$
$312$	13.8333	0.783156
$313$	−2.53594	−0.143340	−0.0716700	−	0.997428i	$-0.522833\pi$
$313$	−2.53594	−0.143340	−0.0716700	+	0.997428i	$0.522833\pi$
$314$	46.8424	2.64347
$315$	−5.08612	−0.286571
$316$	−2.67778	−0.150637
$317$	−13.7755	−0.773709	−0.386854	−	0.922141i	$-0.626438\pi$
$317$	−13.7755	−0.773709	−0.386854	+	0.922141i	$0.626438\pi$
$318$	52.5217	2.94527
$319$	16.4683	0.922048
$320$	2.92406	0.163460
$321$	−31.3987	−1.75250
$322$	54.1929	3.02005
$323$	37.4709	2.08494
$324$	−42.9190	−2.38439
$325$	−5.46139	−0.302943
$326$	25.3109	1.40184
$327$	−25.2058	−1.39388
$328$	−59.4833	−3.28441
$329$	−50.2820	−2.77213
$330$	8.03650	0.442395
$331$	−17.7862	−0.977620	−0.488810	−	0.872390i	$-0.662569\pi$
$331$	−17.7862	−0.977620	−0.488810	+	0.872390i	$0.662569\pi$
$332$	48.8005	2.67827
$333$	4.03245	0.220977
$334$	−37.5234	−2.05319
$335$	−1.12971	−0.0617227
$336$	−51.5301	−2.81120
$337$	−25.2938	−1.37784	−0.688921	−	0.724837i	$-0.741915\pi$
$337$	−25.2938	−1.37784	−0.688921	+	0.724837i	$0.741915\pi$
$338$	28.9430	1.57429
$339$	2.32483	0.126267
$340$	9.25967	0.502176
$341$	−29.0349	−1.57233
$342$	44.3995	2.40085
$343$	38.8763	2.09912
$344$	−60.9007	−3.28354
$345$	−4.84469	−0.260829
$346$	8.28014	0.445143
$347$	3.98979	0.214183	0.107092	−	0.994249i	$-0.465846\pi$
$347$	3.98979	0.214183	0.107092	+	0.994249i	$0.465846\pi$
$348$	50.5312	2.70876
$349$	−8.14040	−0.435745	−0.217873	−	0.975977i	$-0.569912\pi$
$349$	−8.14040	−0.435745	−0.217873	+	0.975977i	$0.569912\pi$
$350$	55.9651	2.99146
$351$	1.57473	0.0840527
$352$	3.62958	0.193457
$353$	15.1185	0.804676	0.402338	−	0.915491i	$-0.368198\pi$
$353$	15.1185	0.804676	0.402338	+	0.915491i	$0.368198\pi$
$354$	−30.8281	−1.63849
$355$	0.448444	0.0238009
$356$	−59.3348	−3.14474
$357$	55.0255	2.91226
$358$	−4.06605	−0.214897
$359$	21.7516	1.14800	0.574001	−	0.818854i	$-0.305390\pi$
$359$	21.7516	1.14800	0.574001	+	0.818854i	$0.305390\pi$
$360$	5.63850	0.297175
$361$	36.7489	1.93415
$362$	−59.1575	−3.10925
$363$	2.98026	0.156423
$364$	22.0836	1.15749
$365$	0.200403	0.0104895
$366$	−14.1895	−0.741695
$367$	27.5662	1.43894	0.719471	−	0.694523i	$-0.244384\pi$
$367$	27.5662	1.43894	0.719471	+	0.694523i	$0.244384\pi$
$368$	−21.8394	−1.13846
$369$	27.3591	1.42426
$370$	1.85941	0.0966660
$371$	43.0891	2.23707
$372$	−89.0905	−4.61913
$373$	8.10130	0.419469	0.209735	−	0.977758i	$-0.432740\pi$
$373$	8.10130	0.419469	0.209735	+	0.977758i	$0.432740\pi$
$374$	−38.6852	−2.00036
$375$	−10.2159	−0.527546
$376$	55.7428	2.87472
$377$	−6.01202	−0.309635
$378$	−16.1369	−0.829990
$379$	−32.6199	−1.67557	−0.837787	−	0.545998i	$-0.816151\pi$
$379$	−32.6199	−1.67557	−0.837787	+	0.545998i	$0.816151\pi$
$380$	13.7764	0.706717
$381$	−24.1192	−1.23566
$382$	31.8896	1.63161
$383$	−19.9370	−1.01873	−0.509367	−	0.860549i	$-0.670121\pi$
$383$	−19.9370	−1.01873	−0.509367	+	0.860549i	$0.670121\pi$
$384$	−42.8976	−2.18911
$385$	6.59319	0.336020
$386$	16.7537	0.852743
$387$	28.0111	1.42388
$388$	35.0875	1.78130
$389$	−15.0917	−0.765178	−0.382589	−	0.923919i	$-0.624967\pi$
$389$	−15.0917	−0.765178	−0.382589	+	0.923919i	$0.624967\pi$
$390$	−2.93386	−0.148562
$391$	23.3208	1.17938
$392$	−79.6976	−4.02534
$393$	−14.2620	−0.719421
$394$	−7.50356	−0.378024
$395$	0.291858	0.0146850
$396$	−30.8448	−1.55001
$397$	8.86894	0.445120	0.222560	−	0.974919i	$-0.428559\pi$
$397$	8.86894	0.445120	0.222560	+	0.974919i	$0.428559\pi$
$398$	29.6260	1.48502
$399$	81.8664	4.09845
$400$	−22.5536	−1.12768
$401$	−16.9797	−0.847926	−0.423963	−	0.905679i	$-0.639361\pi$
$401$	−16.9797	−0.847926	−0.423963	+	0.905679i	$0.639361\pi$
$402$	14.4820	0.722295
$403$	10.5997	0.528007
$404$	51.7583	2.57507
$405$	4.67786	0.232445
$406$	61.6076	3.05753
$407$	−5.22731	−0.259108
$408$	−61.0015	−3.02002
$409$	−11.7547	−0.581231	−0.290616	−	0.956840i	$-0.593860\pi$
$409$	−11.7547	−0.581231	−0.290616	+	0.956840i	$0.593860\pi$
$410$	12.6156	0.623040
$411$	0.501669	0.0247455
$412$	−71.0853	−3.50212
$413$	−25.2915	−1.24452
$414$	27.6329	1.35808
$415$	−5.31890	−0.261095
$416$	−1.32504	−0.0649653
$417$	−41.1430	−2.01478
$418$	−57.5555	−2.81513
$419$	−6.78611	−0.331523	−0.165762	−	0.986166i	$-0.553008\pi$
$419$	−6.78611	−0.331523	−0.165762	+	0.986166i	$0.553008\pi$
$420$	20.2305	0.987147
$421$	−2.79379	−0.136161	−0.0680806	−	0.997680i	$-0.521688\pi$
$421$	−2.79379	−0.136161	−0.0680806	+	0.997680i	$0.521688\pi$
$422$	49.9631	2.43217
$423$	−25.6387	−1.24660
$424$	−47.7687	−2.31985
$425$	24.0834	1.16822
$426$	−5.74869	−0.278525
$427$	−11.6411	−0.563353
$428$	55.5689	2.68603
$429$	8.24787	0.398211
$430$	12.9162	0.622875
$431$	9.36821	0.451251	0.225625	−	0.974214i	$-0.427557\pi$
$431$	9.36821	0.451251	0.225625	+	0.974214i	$0.427557\pi$
$432$	6.50305	0.312878
$433$	−15.7728	−0.757993	−0.378996	−	0.925398i	$-0.623731\pi$
$433$	−15.7728	−0.757993	−0.378996	+	0.925398i	$0.623731\pi$
$434$	−108.619	−5.21388
$435$	−5.50754	−0.264066
$436$	44.6088	2.13637
$437$	34.6965	1.65976
$438$	−2.56900	−0.122751
$439$	−18.1870	−0.868017	−0.434008	−	0.900909i	$-0.642901\pi$
$439$	−18.1870	−0.868017	−0.434008	+	0.900909i	$0.642901\pi$
$440$	−7.30924	−0.348454
$441$	36.6567	1.74556
$442$	14.1227	0.671746
$443$	8.37092	0.397714	0.198857	−	0.980028i	$-0.436277\pi$
$443$	8.37092	0.397714	0.198857	+	0.980028i	$0.436277\pi$
$444$	−16.0394	−0.761198
$445$	6.46706	0.306568
$446$	51.0867	2.41903
$447$	−53.9388	−2.55122
$448$	−30.7521	−1.45290
$449$	12.9745	0.612306	0.306153	−	0.951982i	$-0.400958\pi$
$449$	12.9745	0.612306	0.306153	+	0.951982i	$0.400958\pi$
$450$	28.5365	1.34523
$451$	−35.4659	−1.67003
$452$	−4.11444	−0.193527
$453$	−42.4465	−1.99431
$454$	73.5688	3.45275
$455$	−2.40695	−0.112840
$456$	−90.7574	−4.25011
$457$	5.55422	0.259815	0.129908	−	0.991526i	$-0.458532\pi$
$457$	5.55422	0.259815	0.129908	+	0.991526i	$0.458532\pi$
$458$	38.4298	1.79571
$459$	−6.94416	−0.324126
$460$	8.57405	0.399767
$461$	4.06514	0.189333	0.0946663	−	0.995509i	$-0.469822\pi$
$461$	4.06514	0.189333	0.0946663	+	0.995509i	$0.469822\pi$
$462$	−84.5193	−3.93219
$463$	1.41528	0.0657737	0.0328868	−	0.999459i	$-0.489530\pi$
$463$	1.41528	0.0657737	0.0328868	+	0.999459i	$0.489530\pi$
$464$	−24.8274	−1.15259
$465$	9.71022	0.450301
$466$	11.5474	0.534923
$467$	−39.1503	−1.81166	−0.905830	−	0.423640i	$-0.860752\pi$
$467$	−39.1503	−1.81166	−0.905830	+	0.423640i	$0.860752\pi$
$468$	11.2604	0.520512
$469$	11.8811	0.548618
$470$	−11.8223	−0.545322
$471$	44.0404	2.02927
$472$	28.0383	1.29057
$473$	−36.3110	−1.66958
$474$	−3.74139	−0.171848
$475$	35.8311	1.64404
$476$	−97.3832	−4.46355
$477$	21.9711	1.00599
$478$	−25.1250	−1.14919
$479$	−13.0730	−0.597322	−0.298661	−	0.954359i	$-0.596540\pi$
$479$	−13.0730	−0.597322	−0.298661	+	0.954359i	$0.596540\pi$
$480$	−1.21385	−0.0554044
$481$	1.90831	0.0870116
$482$	−25.5173	−1.16228
$483$	50.9512	2.31836
$484$	−5.27442	−0.239746
$485$	−3.82428	−0.173652
$486$	−49.7017	−2.25452
$487$	−2.76391	−0.125245	−0.0626223	−	0.998037i	$-0.519946\pi$
$487$	−2.76391	−0.125245	−0.0626223	+	0.998037i	$0.519946\pi$
$488$	12.9054	0.584199
$489$	23.7969	1.07613
$490$	16.9028	0.763590
$491$	−1.93759	−0.0874423	−0.0437212	−	0.999044i	$-0.513921\pi$
$491$	−1.93759	−0.0874423	−0.0437212	+	0.999044i	$0.513921\pi$
$492$	−108.823	−4.90614
$493$	26.5115	1.19402
$494$	21.0116	0.945354
$495$	3.36186	0.151104
$496$	43.7728	1.96546
$497$	−4.71625	−0.211553
$498$	68.1839	3.05540
$499$	15.2449	0.682457	0.341228	−	0.939980i	$-0.389157\pi$
$499$	15.2449	0.682457	0.341228	+	0.939980i	$0.389157\pi$
$500$	18.0799	0.808558
$501$	−35.2789	−1.57614
$502$	19.7584	0.881859
$503$	−10.9172	−0.486775	−0.243388	−	0.969929i	$-0.578259\pi$
$503$	−10.9172	−0.486775	−0.243388	+	0.969929i	$0.578259\pi$
$504$	−59.2997	−2.64142
$505$	−5.64128	−0.251034
$506$	−35.8208	−1.59243
$507$	27.2117	1.20851
$508$	42.6858	1.89388
$509$	15.9153	0.705435	0.352717	−	0.935730i	$-0.385258\pi$
$509$	15.9153	0.705435	0.352717	+	0.935730i	$0.385258\pi$
$510$	12.9376	0.572886
$511$	−2.10762	−0.0932356
$512$	43.6728	1.93008
$513$	−10.3315	−0.456145
$514$	31.7464	1.40027
$515$	7.74779	0.341408
$516$	−111.416	−4.90484
$517$	33.2357	1.46171
$518$	−19.5553	−0.859209
$519$	7.78484	0.341717
$520$	2.66836	0.117015
$521$	2.98286	0.130681	0.0653407	−	0.997863i	$-0.479187\pi$
$521$	2.98286	0.130681	0.0653407	+	0.997863i	$0.479187\pi$
$522$	31.4136	1.37494
$523$	21.4568	0.938242	0.469121	−	0.883134i	$-0.344571\pi$
$523$	21.4568	0.938242	0.469121	+	0.883134i	$0.344571\pi$
$524$	25.2406	1.10264
$525$	52.6174	2.29641
$526$	40.4748	1.76478
$527$	−46.7420	−2.03611
$528$	34.0607	1.48230
$529$	−1.40594	−0.0611277
$530$	10.1311	0.440067
$531$	−12.8961	−0.559644
$532$	−144.886	−6.28160
$533$	12.9474	0.560814
$534$	−82.9025	−3.58754
$535$	−6.05661	−0.261850
$536$	−13.1714	−0.568919
$537$	−3.82283	−0.164967
$538$	−36.4810	−1.57281
$539$	−47.5184	−2.04676
$540$	−2.55307	−0.109867
$541$	27.0603	1.16341	0.581706	−	0.813399i	$-0.302386\pi$
$541$	27.0603	1.16341	0.581706	+	0.813399i	$0.302386\pi$
$542$	−28.7217	−1.23370
$543$	−55.6189	−2.38683
$544$	5.84309	0.250520
$545$	−4.86204	−0.208267
$546$	30.8551	1.32048
$547$	0.931059	0.0398092	0.0199046	−	0.999802i	$-0.493664\pi$
$547$	0.931059	0.0398092	0.0199046	+	0.999802i	$0.493664\pi$
$548$	−0.887846	−0.0379269
$549$	−5.93579	−0.253333
$550$	−36.9922	−1.57735
$551$	39.4436	1.68035
$552$	−56.4847	−2.40415
$553$	−3.06945	−0.130526
$554$	45.0705	1.91486
$555$	1.74818	0.0742062
$556$	72.8142	3.08801
$557$	−25.9303	−1.09870	−0.549351	−	0.835591i	$-0.685125\pi$
$557$	−25.9303	−1.09870	−0.549351	+	0.835591i	$0.685125\pi$
$558$	−55.3848	−2.34462
$559$	13.2559	0.560666
$560$	−9.93983	−0.420034
$561$	−36.3711	−1.53559
$562$	37.4900	1.58142
$563$	−16.6768	−0.702845	−0.351423	−	0.936217i	$-0.614302\pi$
$563$	−16.6768	−0.702845	−0.351423	+	0.936217i	$0.614302\pi$
$564$	101.980	4.29414
$565$	0.448444	0.0188662
$566$	24.7079	1.03855
$567$	−49.1967	−2.06607
$568$	5.22846	0.219381
$569$	18.4139	0.771952	0.385976	−	0.922509i	$-0.373865\pi$
$569$	18.4139	0.771952	0.385976	+	0.922509i	$0.373865\pi$
$570$	19.2484	0.806228
$571$	39.1999	1.64046	0.820232	−	0.572032i	$-0.193845\pi$
$571$	39.1999	1.64046	0.820232	+	0.572032i	$0.193845\pi$
$572$	−14.5970	−0.610329
$573$	29.9820	1.25252
$574$	−132.677	−5.53784
$575$	22.3002	0.929982
$576$	−15.6805	−0.653353
$577$	−10.1310	−0.421759	−0.210879	−	0.977512i	$-0.567633\pi$
$577$	−10.1310	−0.421759	−0.210879	+	0.977512i	$0.567633\pi$
$578$	−20.2409	−0.841910
$579$	15.7516	0.654613
$580$	9.74715	0.404728
$581$	55.9385	2.32072
$582$	49.0242	2.03212
$583$	−28.4813	−1.17958
$584$	2.33652	0.0966857
$585$	−1.22730	−0.0507427
$586$	−21.6256	−0.893345
$587$	−39.3123	−1.62259	−0.811296	−	0.584636i	$-0.801237\pi$
$587$	−39.3123	−1.62259	−0.811296	+	0.584636i	$0.801237\pi$
$588$	−145.805	−6.01290
$589$	−69.5422	−2.86544
$590$	−5.94655	−0.244815
$591$	−7.05472	−0.290192
$592$	7.88064	0.323892
$593$	16.8202	0.690723	0.345361	−	0.938470i	$-0.387756\pi$
$593$	16.8202	0.690723	0.345361	+	0.938470i	$0.387756\pi$
$594$	10.6663	0.437642
$595$	10.6141	0.435134
$596$	95.4600	3.91019
$597$	27.8538	1.13998
$598$	13.0770	0.534757
$599$	27.5468	1.12553	0.562766	−	0.826616i	$-0.309737\pi$
$599$	27.5468	1.12553	0.562766	+	0.826616i	$0.309737\pi$
$600$	−58.3318	−2.38139
$601$	−30.8954	−1.26025	−0.630124	−	0.776495i	$-0.716996\pi$
$601$	−30.8954	−1.26025	−0.630124	+	0.776495i	$0.716996\pi$
$602$	−135.839	−5.53638
$603$	6.05816	0.246707
$604$	75.1211	3.05664
$605$	0.574873	0.0233719
$606$	72.3166	2.93766
$607$	−17.5847	−0.713742	−0.356871	−	0.934154i	$-0.616156\pi$
$607$	−17.5847	−0.713742	−0.356871	+	0.934154i	$0.616156\pi$
$608$	8.69330	0.352560
$609$	57.9223	2.34713
$610$	−2.73706	−0.110820
$611$	−12.1332	−0.490858
$612$	−49.6556	−2.00721
$613$	−25.2380	−1.01935	−0.509676	−	0.860366i	$-0.670235\pi$
$613$	−25.2380	−1.01935	−0.509676	+	0.860366i	$0.670235\pi$
$614$	−30.0508	−1.21275
$615$	11.8610	0.478280
$616$	76.8707	3.09721
$617$	−42.2751	−1.70193	−0.850966	−	0.525220i	$-0.823983\pi$
$617$	−42.2751	−1.70193	−0.850966	+	0.525220i	$0.823983\pi$
$618$	−99.3203	−3.99525
$619$	18.8517	0.757713	0.378856	−	0.925455i	$-0.376317\pi$
$619$	18.8517	0.757713	0.378856	+	0.925455i	$0.376317\pi$
$620$	−17.1850	−0.690166
$621$	−6.43000	−0.258027
$622$	−30.9610	−1.24142
$623$	−68.0136	−2.72491
$624$	−12.4344	−0.497775
$625$	22.0239	0.880956
$626$	6.27073	0.250629
$627$	−54.1126	−2.16105
$628$	−77.9419	−3.11022
$629$	−8.41520	−0.335536
$630$	12.5767	0.501066
$631$	−5.31278	−0.211498	−0.105749	−	0.994393i	$-0.533724\pi$
$631$	−5.31278	−0.211498	−0.105749	+	0.994393i	$0.533724\pi$
$632$	3.40281	0.135356
$633$	46.9744	1.86707
$634$	34.0632	1.35282
$635$	−4.65244	−0.184627
$636$	−87.3919	−3.46531
$637$	17.3474	0.687327
$638$	−40.7218	−1.61219
$639$	−2.40481	−0.0951329
$640$	−8.27468	−0.327086
$641$	−21.3290	−0.842447	−0.421223	−	0.906957i	$-0.638399\pi$
$641$	−21.3290	−0.842447	−0.421223	+	0.906957i	$0.638399\pi$
$642$	77.6408	3.06424
$643$	−10.5159	−0.414706	−0.207353	−	0.978266i	$-0.566485\pi$
$643$	−10.5159	−0.414706	−0.207353	+	0.978266i	$0.566485\pi$
$644$	−90.1727	−3.55330
$645$	12.1436	0.478153
$646$	−92.6558	−3.64550
$647$	20.2878	0.797595	0.398798	−	0.917039i	$-0.369428\pi$
$647$	20.2878	0.797595	0.398798	+	0.917039i	$0.369428\pi$
$648$	54.5397	2.14252
$649$	16.7174	0.656214
$650$	13.5046	0.529694
$651$	−102.122	−4.00247
$652$	−42.1154	−1.64937
$653$	0.520755	0.0203787	0.0101894	−	0.999948i	$-0.496757\pi$
$653$	0.520755	0.0203787	0.0101894	+	0.999948i	$0.496757\pi$
$654$	62.3273	2.43719
$655$	−2.75104	−0.107492
$656$	53.4681	2.08758
$657$	−1.07467	−0.0419270
$658$	124.334	4.84705
$659$	−8.45241	−0.329259	−0.164630	−	0.986355i	$-0.552643\pi$
$659$	−8.45241	−0.329259	−0.164630	+	0.986355i	$0.552643\pi$
$660$	−13.3721	−0.520508
$661$	−4.42208	−0.171999	−0.0859994	−	0.996295i	$-0.527408\pi$
$661$	−4.42208	−0.171999	−0.0859994	+	0.996295i	$0.527408\pi$
$662$	43.9807	1.70936
$663$	13.2779	0.515670
$664$	−62.0136	−2.40660
$665$	15.7915	0.612368
$666$	−9.97121	−0.386376
$667$	24.5485	0.950523
$668$	62.4360	2.41572
$669$	48.0308	1.85698
$670$	2.79348	0.107922
$671$	7.69462	0.297048
$672$	12.7660	0.492458
$673$	−39.6119	−1.52693	−0.763464	−	0.645851i	$-0.776503\pi$
$673$	−39.6119	−1.52693	−0.763464	+	0.645851i	$0.776503\pi$
$674$	62.5450	2.40914
$675$	−6.64026	−0.255584
$676$	−48.1589	−1.85226
$677$	−5.69647	−0.218933	−0.109467	−	0.993990i	$-0.534914\pi$
$677$	−5.69647	−0.218933	−0.109467	+	0.993990i	$0.534914\pi$
$678$	−5.74869	−0.220777
$679$	40.2197	1.54349
$680$	−11.7668	−0.451236
$681$	69.1681	2.65053
$682$	71.7958	2.74920
$683$	15.2851	0.584869	0.292434	−	0.956286i	$-0.405535\pi$
$683$	15.2851	0.584869	0.292434	+	0.956286i	$0.405535\pi$
$684$	−73.8772	−2.82476
$685$	0.0967688	0.00369735
$686$	−96.1309	−3.67030
$687$	36.1310	1.37848
$688$	54.7421	2.08702
$689$	10.3976	0.396116
$690$	11.9797	0.456058
$691$	−1.50943	−0.0574215	−0.0287107	−	0.999588i	$-0.509140\pi$
$691$	−1.50943	−0.0574215	−0.0287107	+	0.999588i	$0.509140\pi$
$692$	−13.7775	−0.523742
$693$	−35.3564	−1.34308
$694$	−9.86572	−0.374498
$695$	−7.93623	−0.301038
$696$	−64.2129	−2.43399
$697$	−57.0949	−2.16262
$698$	20.1291	0.761897
$699$	10.8567	0.410636
$700$	−93.1214	−3.51966
$701$	−4.31140	−0.162839	−0.0814197	−	0.996680i	$-0.525945\pi$
$701$	−4.31140	−0.162839	−0.0814197	+	0.996680i	$0.525945\pi$
$702$	−3.89389	−0.146965
$703$	−12.5201	−0.472203
$704$	20.3267	0.766093
$705$	−11.1151	−0.418619
$706$	−37.3841	−1.40697
$707$	59.3290	2.23129
$708$	51.2955	1.92780
$709$	−23.9421	−0.899165	−0.449582	−	0.893239i	$-0.648427\pi$
$709$	−23.9421	−0.899165	−0.449582	+	0.893239i	$0.648427\pi$
$710$	−1.10889	−0.0416157
$711$	−1.56511	−0.0586963
$712$	75.4002	2.82574
$713$	−43.2810	−1.62089
$714$	−136.064	−5.09205
$715$	1.59096	0.0594986
$716$	6.76558	0.252842
$717$	−23.6220	−0.882181
$718$	−53.7859	−2.00727
$719$	−44.0363	−1.64228	−0.821138	−	0.570730i	$-0.806660\pi$
$719$	−44.0363	−1.64228	−0.821138	+	0.570730i	$0.806660\pi$
$720$	−5.06831	−0.188885
$721$	−81.4829	−3.03458
$722$	−90.8705	−3.38185
$723$	−23.9909	−0.892233
$724$	98.4334	3.65825
$725$	25.3513	0.941523
$726$	−7.36940	−0.273504
$727$	8.40336	0.311663	0.155832	−	0.987784i	$-0.450194\pi$
$727$	8.40336	0.311663	0.155832	+	0.987784i	$0.450194\pi$
$728$	−28.0629	−1.04008
$729$	−15.4347	−0.571657
$730$	−0.495543	−0.0183409
$731$	−58.4554	−2.16205
$732$	23.6101	0.872655
$733$	26.5469	0.980532	0.490266	−	0.871573i	$-0.336900\pi$
$733$	26.5469	0.980532	0.490266	+	0.871573i	$0.336900\pi$
$734$	−68.1639	−2.51598
$735$	15.8917	0.586174
$736$	5.41045	0.199432
$737$	−7.85325	−0.289278
$738$	−67.6520	−2.49031
$739$	10.8180	0.397947	0.198974	−	0.980005i	$-0.436239\pi$
$739$	10.8180	0.397947	0.198974	+	0.980005i	$0.436239\pi$
$740$	−3.09391	−0.113734
$741$	19.7547	0.725706
$742$	−106.548	−3.91150
$743$	−7.84366	−0.287756	−0.143878	−	0.989595i	$-0.545957\pi$
$743$	−7.84366	−0.287756	−0.143878	+	0.989595i	$0.545957\pi$
$744$	113.213	4.15057
$745$	−10.4044	−0.381189
$746$	−20.0324	−0.733438
$747$	28.5230	1.04360
$748$	64.3690	2.35357
$749$	63.6969	2.32744
$750$	25.2612	0.922409
$751$	20.7755	0.758110	0.379055	−	0.925374i	$-0.376249\pi$
$751$	20.7755	0.758110	0.379055	+	0.925374i	$0.376249\pi$
$752$	−50.1059	−1.82717
$753$	18.5765	0.676964
$754$	14.8662	0.541393
$755$	−8.18766	−0.297979
$756$	26.8504	0.976541
$757$	−26.3390	−0.957305	−0.478653	−	0.878004i	$-0.658875\pi$
$757$	−26.3390	−0.957305	−0.478653	+	0.878004i	$0.658875\pi$
$758$	80.6606	2.92972
$759$	−33.6781	−1.22244
$760$	−17.5065	−0.635029
$761$	27.3512	0.991482	0.495741	−	0.868470i	$-0.334897\pi$
$761$	27.3512	0.991482	0.495741	+	0.868470i	$0.334897\pi$
$762$	59.6405	2.16055
$763$	51.1337	1.85116
$764$	−53.0617	−1.91970
$765$	5.41210	0.195675
$766$	49.2991	1.78125
$767$	−6.10295	−0.220365
$768$	75.7569	2.73364
$769$	−6.35042	−0.229002	−0.114501	−	0.993423i	$-0.536527\pi$
$769$	−6.35042	−0.229002	−0.114501	+	0.993423i	$0.536527\pi$
$770$	−16.3032	−0.587528
$771$	29.8474	1.07493
$772$	−27.8769	−1.00331
$773$	41.9948	1.51045	0.755223	−	0.655468i	$-0.227528\pi$
$773$	41.9948	1.51045	0.755223	+	0.655468i	$0.227528\pi$
$774$	−69.2641	−2.48965
$775$	−44.6964	−1.60554
$776$	−44.5877	−1.60061
$777$	−18.3855	−0.659576
$778$	37.3177	1.33791
$779$	−84.9453	−3.04348
$780$	4.88170	0.174793
$781$	3.11738	0.111549
$782$	−57.6663	−2.06214
$783$	−7.30974	−0.261229
$784$	71.6383	2.55851
$785$	8.49511	0.303203
$786$	35.2661	1.25790
$787$	14.1240	0.503467	0.251734	−	0.967797i	$-0.418999\pi$
$787$	14.1240	0.503467	0.251734	+	0.967797i	$0.418999\pi$
$788$	12.4853	0.444771
$789$	38.0537	1.35475
$790$	−0.721690	−0.0256766
$791$	−4.71625	−0.167691
$792$	39.1963	1.39278
$793$	−2.80905	−0.0997521
$794$	−21.9306	−0.778287
$795$	9.52508	0.337820
$796$	−49.2953	−1.74723
$797$	−15.9738	−0.565821	−0.282910	−	0.959146i	$-0.591300\pi$
$797$	−15.9738	−0.565821	−0.282910	+	0.959146i	$0.591300\pi$
$798$	−202.434	−7.16609
$799$	53.5046	1.89286
$800$	5.58738	0.197544
$801$	−34.6801	−1.22536
$802$	41.9864	1.48259
$803$	1.39311	0.0491617
$804$	−24.0969	−0.849830
$805$	9.82817	0.346397
$806$	−26.2102	−0.923215
$807$	−34.2988	−1.20738
$808$	−65.7723	−2.31386
$809$	32.8254	1.15408	0.577040	−	0.816716i	$-0.304208\pi$
$809$	32.8254	1.15408	0.577040	+	0.816716i	$0.304208\pi$
$810$	−11.5671	−0.406428
$811$	−2.95930	−0.103915	−0.0519576	−	0.998649i	$-0.516546\pi$
$811$	−2.95930	−0.103915	−0.0519576	+	0.998649i	$0.516546\pi$
$812$	−102.510	−3.59740
$813$	−27.0037	−0.947060
$814$	12.9258	0.453048
$815$	4.59027	0.160790
$816$	54.8328	1.91953
$817$	−86.9694	−3.04267
$818$	29.0663	1.01628
$819$	12.9074	0.451022
$820$	−20.9913	−0.733050
$821$	37.0895	1.29443	0.647217	−	0.762306i	$-0.275933\pi$
$821$	37.0895	1.29443	0.647217	+	0.762306i	$0.275933\pi$
$822$	−1.24050	−0.0432673
$823$	−17.2461	−0.601160	−0.300580	−	0.953757i	$-0.597180\pi$
$823$	−17.2461	−0.601160	−0.300580	+	0.953757i	$0.597180\pi$
$824$	90.3323	3.14687
$825$	−34.7794	−1.21086
$826$	62.5394	2.17602
$827$	−36.7882	−1.27925	−0.639626	−	0.768686i	$-0.720911\pi$
$827$	−36.7882	−1.27925	−0.639626	+	0.768686i	$0.720911\pi$
$828$	−45.9790	−1.59788
$829$	4.40770	0.153086	0.0765429	−	0.997066i	$-0.475612\pi$
$829$	4.40770	0.153086	0.0765429	+	0.997066i	$0.475612\pi$
$830$	13.1523	0.456521
$831$	42.3745	1.46996
$832$	−7.42060	−0.257263
$833$	−76.4976	−2.65049
$834$	101.736	3.52283
$835$	−6.80507	−0.235499
$836$	95.7677	3.31219
$837$	12.8877	0.445463
$838$	16.7803	0.579665
$839$	−51.6154	−1.78196	−0.890981	−	0.454040i	$-0.849982\pi$
$839$	−51.6154	−1.78196	−0.890981	+	0.454040i	$0.849982\pi$
$840$	−25.7081	−0.887013
$841$	−1.09274	−0.0376807
$842$	6.90833	0.238077
$843$	35.2475	1.21399
$844$	−83.1346	−2.86161
$845$	5.24897	0.180570
$846$	63.3979	2.17966
$847$	−6.04590	−0.207739
$848$	42.9382	1.47450
$849$	23.2299	0.797247
$850$	−59.5520	−2.04262
$851$	−7.79211	−0.267110
$852$	9.56535	0.327704
$853$	−27.8865	−0.954817	−0.477408	−	0.878682i	$-0.658424\pi$
$853$	−27.8865	−0.954817	−0.477408	+	0.878682i	$0.658424\pi$
$854$	28.7854	0.985017
$855$	8.05208	0.275375
$856$	−70.6147	−2.41356
$857$	6.93319	0.236833	0.118417	−	0.992964i	$-0.462218\pi$
$857$	6.93319	0.236833	0.118417	+	0.992964i	$0.462218\pi$
$858$	−20.3948	−0.696268
$859$	26.3868	0.900305	0.450152	−	0.892952i	$-0.351370\pi$
$859$	26.3868	0.900305	0.450152	+	0.892952i	$0.351370\pi$
$860$	−21.4915	−0.732855
$861$	−124.741	−4.25116
$862$	−23.1651	−0.789007
$863$	35.6393	1.21318	0.606588	−	0.795017i	$-0.292538\pi$
$863$	35.6393	1.21318	0.606588	+	0.795017i	$0.292538\pi$
$864$	−1.61105	−0.0548091
$865$	1.50165	0.0510575
$866$	39.0020	1.32534
$867$	−19.0301	−0.646297
$868$	180.733	6.13449
$869$	2.02887	0.0688246
$870$	13.6187	0.461717
$871$	2.86695	0.0971430
$872$	−56.6870	−1.91966
$873$	20.5080	0.694090
$874$	−85.7953	−2.90207
$875$	20.7244	0.700614
$876$	4.27460	0.144426
$877$	−26.9121	−0.908756	−0.454378	−	0.890809i	$-0.650138\pi$
$877$	−26.9121	−0.908756	−0.454378	+	0.890809i	$0.650138\pi$
$878$	44.9716	1.51772
$879$	−20.3320	−0.685781
$880$	6.57010	0.221478
$881$	−41.5155	−1.39869	−0.699347	−	0.714782i	$-0.746526\pi$
$881$	−41.5155	−1.39869	−0.699347	+	0.714782i	$0.746526\pi$
$882$	−90.6424	−3.05209
$883$	45.6593	1.53656	0.768278	−	0.640116i	$-0.221114\pi$
$883$	45.6593	1.53656	0.768278	+	0.640116i	$0.221114\pi$
$884$	−23.4990	−0.790355
$885$	−5.59084	−0.187934
$886$	−20.6991	−0.695400
$887$	−58.9336	−1.97880	−0.989399	−	0.145226i	$-0.953609\pi$
$887$	−58.9336	−1.97880	−0.989399	+	0.145226i	$0.953609\pi$
$888$	20.3822	0.683983
$889$	48.9294	1.64104
$890$	−15.9914	−0.536032
$891$	32.5184	1.08941
$892$	−85.0042	−2.84615
$893$	79.6037	2.66384
$894$	133.376	4.46078
$895$	−0.737399	−0.0246485
$896$	87.0242	2.90728
$897$	12.2947	0.410509
$898$	−32.0826	−1.07061
$899$	−49.2027	−1.64100
$900$	−47.4825	−1.58275
$901$	−45.8507	−1.52751
$902$	87.6980	2.92002
$903$	−127.713	−4.25003
$904$	5.22846	0.173896
$905$	−10.7285	−0.356628
$906$	104.959	3.48703
$907$	−55.5112	−1.84322	−0.921609	−	0.388120i	$-0.873125\pi$
$907$	−55.5112	−1.84322	−0.921609	+	0.388120i	$0.873125\pi$
$908$	−122.413	−4.06240
$909$	30.2518	1.00339
$910$	5.95176	0.197299
$911$	−12.8600	−0.426069	−0.213035	−	0.977045i	$-0.568335\pi$
$911$	−12.8600	−0.426069	−0.213035	+	0.977045i	$0.568335\pi$
$912$	81.5797	2.70137
$913$	−36.9746	−1.22368
$914$	−13.7341	−0.454285
$915$	−2.57333	−0.0850717
$916$	−63.9441	−2.11277
$917$	28.9325	0.955436
$918$	17.1711	0.566731
$919$	45.9234	1.51487	0.757437	−	0.652908i	$-0.226451\pi$
$919$	45.9234	1.51487	0.757437	+	0.652908i	$0.226451\pi$
$920$	−10.8956	−0.359216
$921$	−28.2533	−0.930976
$922$	−10.0520	−0.331046
$923$	−1.13805	−0.0374594
$924$	140.633	4.62650
$925$	−8.04692	−0.264581
$926$	−3.49962	−0.115005
$927$	−41.5481	−1.36462
$928$	6.15071	0.201907
$929$	12.4602	0.408805	0.204403	−	0.978887i	$-0.434475\pi$
$929$	12.4602	0.408805	0.204403	+	0.978887i	$0.434475\pi$
$930$	−24.0109	−0.787347
$931$	−113.812	−3.73005
$932$	−19.2139	−0.629373
$933$	−29.1090	−0.952986
$934$	96.8085	3.16767
$935$	−7.01576	−0.229440
$936$	−14.3092	−0.467712
$937$	−0.216022	−0.00705713	−0.00352857	−	0.999994i	$-0.501123\pi$
$937$	−0.216022	−0.00705713	−0.00352857	+	0.999994i	$0.501123\pi$
$938$	−29.3788	−0.959253
$939$	5.89562	0.192396
$940$	19.6714	0.641609
$941$	−19.2443	−0.627347	−0.313674	−	0.949531i	$-0.601560\pi$
$941$	−19.2443	−0.627347	−0.313674	+	0.949531i	$0.601560\pi$
$942$	−108.900	−3.54816
$943$	−52.8675	−1.72160
$944$	−25.2030	−0.820286
$945$	−2.92650	−0.0951992
$946$	89.7877	2.91925
$947$	24.3233	0.790402	0.395201	−	0.918595i	$-0.370675\pi$
$947$	24.3233	0.790402	0.395201	+	0.918595i	$0.370675\pi$
$948$	6.22537	0.202190
$949$	−0.508577	−0.0165091
$950$	−88.6009	−2.87459
$951$	32.0256	1.03850
$952$	123.751	4.01078
$953$	−4.24632	−0.137552	−0.0687759	−	0.997632i	$-0.521909\pi$
$953$	−4.24632	−0.137552	−0.0687759	+	0.997632i	$0.521909\pi$
$954$	−54.3288	−1.75896
$955$	5.78334	0.187144
$956$	41.8059	1.35210
$957$	−38.2859	−1.23761
$958$	32.3262	1.04441
$959$	−1.01771	−0.0328636
$960$	−6.79792	−0.219402
$961$	55.7483	1.79833
$962$	−4.71876	−0.152139
$963$	32.4790	1.04662
$964$	42.4588	1.36751
$965$	3.03838	0.0978089
$966$	−125.989	−4.05363
$967$	−9.02839	−0.290333	−0.145167	−	0.989407i	$-0.546372\pi$
$967$	−9.02839	−0.290333	−0.145167	+	0.989407i	$0.546372\pi$
$968$	6.70251	0.215427
$969$	−87.1134	−2.79848
$970$	9.45646	0.303629
$971$	45.7744	1.46897	0.734485	−	0.678625i	$-0.237424\pi$
$971$	45.7744	1.46897	0.734485	+	0.678625i	$0.237424\pi$
$972$	82.6997	2.65259
$973$	83.4647	2.67575
$974$	6.83442	0.218989
$975$	12.6968	0.406622
$976$	−11.6003	−0.371318
$977$	−24.5663	−0.785945	−0.392973	−	0.919550i	$-0.628553\pi$
$977$	−24.5663	−0.785945	−0.392973	+	0.919550i	$0.628553\pi$
$978$	−58.8435	−1.88161
$979$	44.9561	1.43680
$980$	−28.1249	−0.898417
$981$	26.0730	0.832447
$982$	4.79116	0.152892
$983$	0.806857	0.0257347	0.0128674	−	0.999917i	$-0.495904\pi$
$983$	0.806857	0.0257347	0.0128674	+	0.999917i	$0.495904\pi$
$984$	138.288	4.40847
$985$	−1.36081	−0.0433590
$986$	−65.5561	−2.08773
$987$	116.897	3.72087
$988$	−34.9615	−1.11227
$989$	−54.1272	−1.72114
$990$	−8.31301	−0.264205
$991$	13.9277	0.442428	0.221214	−	0.975225i	$-0.428998\pi$
$991$	13.9277	0.442428	0.221214	+	0.975225i	$0.428998\pi$
$992$	−10.8442	−0.344303
$993$	41.3499	1.31220
$994$	11.6621	0.369898
$995$	5.37283	0.170330
$996$	−113.453	−3.59488
$997$	−48.7826	−1.54496	−0.772480	−	0.635039i	$-0.780984\pi$
$997$	−48.7826	−1.54496	−0.772480	+	0.635039i	$0.780984\pi$
$998$	−37.6967	−1.19327
$999$	2.32023	0.0734089

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.c.1.16	✓	158

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.c.1.16	✓	158	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)

\(f(q)\)	\(=\)	\(q-2.47274 q^{2} -2.32483 q^{3} +4.11444 q^{4} -0.448444 q^{5} +5.74869 q^{6} +4.71625 q^{7} -5.22846 q^{8} +2.40481 q^{9} +O(q^{10})\)	\(q-2.47274 q^{2} -2.32483 q^{3} +4.11444 q^{4} -0.448444 q^{5} +5.74869 q^{6} +4.71625 q^{7} -5.22846 q^{8} +2.40481 q^{9} +1.10889 q^{10} -3.11738 q^{11} -9.56535 q^{12} +1.13805 q^{13} -11.6621 q^{14} +1.04255 q^{15} +4.69974 q^{16} -5.01853 q^{17} -5.94648 q^{18} -7.46652 q^{19} -1.84510 q^{20} -10.9645 q^{21} +7.70847 q^{22} -4.64694 q^{23} +12.1553 q^{24} -4.79890 q^{25} -2.81410 q^{26} +1.38371 q^{27} +19.4047 q^{28} -5.28273 q^{29} -2.57797 q^{30} +9.31388 q^{31} -1.16430 q^{32} +7.24737 q^{33} +12.4095 q^{34} -2.11498 q^{35} +9.89446 q^{36} +1.67683 q^{37} +18.4628 q^{38} -2.64577 q^{39} +2.34467 q^{40} +11.3768 q^{41} +27.1123 q^{42} +11.6479 q^{43} -12.8263 q^{44} -1.07842 q^{45} +11.4907 q^{46} -10.6614 q^{47} -10.9261 q^{48} +15.2430 q^{49} +11.8664 q^{50} +11.6672 q^{51} +4.68244 q^{52} +9.13629 q^{53} -3.42154 q^{54} +1.39797 q^{55} -24.6587 q^{56} +17.3584 q^{57} +13.0628 q^{58} -5.36263 q^{59} +4.28953 q^{60} -2.46830 q^{61} -23.0308 q^{62} +11.3417 q^{63} -6.52045 q^{64} -0.510352 q^{65} -17.9209 q^{66} +2.51918 q^{67} -20.6484 q^{68} +10.8033 q^{69} +5.22978 q^{70} -1.00000 q^{71} -12.5735 q^{72} -0.446884 q^{73} -4.14635 q^{74} +11.1566 q^{75} -30.7205 q^{76} -14.7024 q^{77} +6.54230 q^{78} -0.650824 q^{79} -2.10757 q^{80} -10.4313 q^{81} -28.1319 q^{82} +11.8608 q^{83} -45.1126 q^{84} +2.25053 q^{85} -28.8023 q^{86} +12.2814 q^{87} +16.2991 q^{88} -14.4211 q^{89} +2.66666 q^{90} +5.36734 q^{91} -19.1196 q^{92} -21.6531 q^{93} +26.3629 q^{94} +3.34832 q^{95} +2.70680 q^{96} +8.52789 q^{97} -37.6921 q^{98} -7.49672 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9}+O(q^{10}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9} - 10 q^{10} - 10 q^{11} - 46 q^{12} - 28 q^{13} - 27 q^{14} - 41 q^{15} + 150 q^{16} - 137 q^{17} - 67 q^{18} - 42 q^{19} - 66 q^{20} - 46 q^{21} - 8 q^{22} - 26 q^{23} - 48 q^{24} + 129 q^{25} - 67 q^{26} - 89 q^{27} - 21 q^{28} - 79 q^{29} - 11 q^{30} + 7 q^{31} - 147 q^{32} - 112 q^{33} - 28 q^{34} - 53 q^{35} + 141 q^{36} - 60 q^{37} - 53 q^{38} - 3 q^{39} - 48 q^{40} - 128 q^{41} + 32 q^{42} - 63 q^{43} - 88 q^{45} - 2 q^{46} - 92 q^{47} - 131 q^{48} + 122 q^{49} - 116 q^{50} - 12 q^{51} - 89 q^{52} - 94 q^{53} - 71 q^{54} - 12 q^{55} - 104 q^{56} - 93 q^{57} - 65 q^{58} - 54 q^{59} - 12 q^{60} + 17 q^{61} - 97 q^{62} - 28 q^{63} + 163 q^{64} - 163 q^{65} - 65 q^{66} - 35 q^{67} - 217 q^{68} - 46 q^{69} - 79 q^{70} - 158 q^{71} - 99 q^{72} - 165 q^{73} - 94 q^{75} - 93 q^{76} - 140 q^{77} + 25 q^{78} - 61 q^{79} - 134 q^{80} + 114 q^{81} + 10 q^{82} - 158 q^{83} - 160 q^{84} + 23 q^{85} - 122 q^{86} - 71 q^{87} - 14 q^{88} - 251 q^{89} - 6 q^{90} - 57 q^{91} - 58 q^{92} - 52 q^{93} - 64 q^{94} - 84 q^{95} - 98 q^{96} - 48 q^{97} - 84 q^{98} + 85 q^{99}+O(q^{100}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9 - 10 * q^10 - 10 * q^11 - 46 * q^12 - 28 * q^13 - 27 * q^14 - 41 * q^15 + 150 * q^16 - 137 * q^17 - 67 * q^18 - 42 * q^19 - 66 * q^20 - 46 * q^21 - 8 * q^22 - 26 * q^23 - 48 * q^24 + 129 * q^25 - 67 * q^26 - 89 * q^27 - 21 * q^28 - 79 * q^29 - 11 * q^30 + 7 * q^31 - 147 * q^32 - 112 * q^33 - 28 * q^34 - 53 * q^35 + 141 * q^36 - 60 * q^37 - 53 * q^38 - 3 * q^39 - 48 * q^40 - 128 * q^41 + 32 * q^42 - 63 * q^43 - 88 * q^45 - 2 * q^46 - 92 * q^47 - 131 * q^48 + 122 * q^49 - 116 * q^50 - 12 * q^51 - 89 * q^52 - 94 * q^53 - 71 * q^54 - 12 * q^55 - 104 * q^56 - 93 * q^57 - 65 * q^58 - 54 * q^59 - 12 * q^60 + 17 * q^61 - 97 * q^62 - 28 * q^63 + 163 * q^64 - 163 * q^65 - 65 * q^66 - 35 * q^67 - 217 * q^68 - 46 * q^69 - 79 * q^70 - 158 * q^71 - 99 * q^72 - 165 * q^73 - 94 * q^75 - 93 * q^76 - 140 * q^77 + 25 * q^78 - 61 * q^79 - 134 * q^80 + 114 * q^81 + 10 * q^82 - 158 * q^83 - 160 * q^84 + 23 * q^85 - 122 * q^86 - 71 * q^87 - 14 * q^88 - 251 * q^89 - 6 * q^90 - 57 * q^91 - 58 * q^92 - 52 * q^93 - 64 * q^94 - 84 * q^95 - 98 * q^96 - 48 * q^97 - 84 * q^98 + 85 * q^99

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