LMFDB - Embedded newform 8033.2.a.c.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8033,2,Mod(1,8033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8033, 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("8033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8033 = 29 \cdot 277 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8033.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:	$64.1438279437$
Analytic rank:	$1$
Dimension:	$154$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.25887 q^{2} +1.60047 q^{3} +3.10247 q^{4} -3.14219 q^{5} -3.61525 q^{6} -0.353570 q^{7} -2.49034 q^{8} -0.438494 q^{9} +O(q^{10})$	\(q-2.25887 q^{2} +1.60047 q^{3} +3.10247 q^{4} -3.14219 q^{5} -3.61525 q^{6} -0.353570 q^{7} -2.49034 q^{8} -0.438494 q^{9} +7.09779 q^{10} -2.00621 q^{11} +4.96542 q^{12} -3.41743 q^{13} +0.798666 q^{14} -5.02898 q^{15} -0.579606 q^{16} -2.39912 q^{17} +0.990500 q^{18} -0.280294 q^{19} -9.74856 q^{20} -0.565878 q^{21} +4.53175 q^{22} +7.17614 q^{23} -3.98571 q^{24} +4.87336 q^{25} +7.71951 q^{26} -5.50321 q^{27} -1.09694 q^{28} +1.00000 q^{29} +11.3598 q^{30} -5.00569 q^{31} +6.28993 q^{32} -3.21087 q^{33} +5.41930 q^{34} +1.11098 q^{35} -1.36042 q^{36} +10.5391 q^{37} +0.633145 q^{38} -5.46949 q^{39} +7.82512 q^{40} +5.35288 q^{41} +1.27824 q^{42} +7.13341 q^{43} -6.22420 q^{44} +1.37783 q^{45} -16.2099 q^{46} +1.46250 q^{47} -0.927643 q^{48} -6.87499 q^{49} -11.0083 q^{50} -3.83973 q^{51} -10.6025 q^{52} +10.4032 q^{53} +12.4310 q^{54} +6.30388 q^{55} +0.880508 q^{56} -0.448602 q^{57} -2.25887 q^{58} +0.880800 q^{59} -15.6023 q^{60} -1.21490 q^{61} +11.3072 q^{62} +0.155038 q^{63} -13.0489 q^{64} +10.7382 q^{65} +7.25293 q^{66} +14.6268 q^{67} -7.44322 q^{68} +11.4852 q^{69} -2.50956 q^{70} +15.0722 q^{71} +1.09200 q^{72} +0.540235 q^{73} -23.8064 q^{74} +7.79967 q^{75} -0.869603 q^{76} +0.709334 q^{77} +12.3549 q^{78} +5.63957 q^{79} +1.82123 q^{80} -7.49224 q^{81} -12.0914 q^{82} -8.31347 q^{83} -1.75562 q^{84} +7.53850 q^{85} -16.1134 q^{86} +1.60047 q^{87} +4.99613 q^{88} -2.88182 q^{89} -3.11234 q^{90} +1.20830 q^{91} +22.2638 q^{92} -8.01145 q^{93} -3.30359 q^{94} +0.880736 q^{95} +10.0668 q^{96} -14.7259 q^{97} +15.5297 q^{98} +0.879710 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9}+O(q^{10}) $ 154 * q - 12 * q^2 - 36 * q^3 + 142 * q^4 - 9 * q^5 - 11 * q^6 - 68 * q^7 - 33 * q^8 + 146 * q^9	\( 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9} - 40 q^{10} - 36 q^{11} - 67 q^{12} - 51 q^{13} - 19 q^{14} - 48 q^{15} + 122 q^{16} - 54 q^{17} - 46 q^{18} - 73 q^{19} - 21 q^{20} - 8 q^{21} - 23 q^{22} - 38 q^{23} - 17 q^{24} + 133 q^{25} - 20 q^{26} - 129 q^{27} - 99 q^{28} + 154 q^{29} - 10 q^{30} - 91 q^{31} - 88 q^{32} - 39 q^{33} - 42 q^{34} - 36 q^{35} + 101 q^{36} - 50 q^{37} - 17 q^{38} - 33 q^{39} - 92 q^{40} - 31 q^{41} - 62 q^{42} - 154 q^{43} - 42 q^{44} - 14 q^{45} - 24 q^{46} - 140 q^{47} - 118 q^{48} + 126 q^{49} - 5 q^{50} - 16 q^{51} - 133 q^{52} - 40 q^{53} + 14 q^{54} - 203 q^{55} - 44 q^{56} - 16 q^{57} - 12 q^{58} + 5 q^{59} - 28 q^{60} - 106 q^{61} - 30 q^{62} - 145 q^{63} + 111 q^{64} - 15 q^{65} - 49 q^{66} - 78 q^{67} - 118 q^{68} - 32 q^{69} - 43 q^{70} - 4 q^{71} - 152 q^{72} - 137 q^{73} + 9 q^{74} - 129 q^{75} - 204 q^{76} - 76 q^{77} + 15 q^{78} - 141 q^{79} - 44 q^{80} + 122 q^{81} - 71 q^{82} - 90 q^{83} + 92 q^{84} - 41 q^{85} + 9 q^{86} - 36 q^{87} - 109 q^{88} - 51 q^{89} - 82 q^{90} - 22 q^{91} - 8 q^{92} - 10 q^{93} - 106 q^{94} - 55 q^{95} - 49 q^{96} - 140 q^{97} - 4 q^{98} - 101 q^{99}+O(q^{100}) \) 154 * q - 12 * q^2 - 36 * q^3 + 142 * q^4 - 9 * q^5 - 11 * q^6 - 68 * q^7 - 33 * q^8 + 146 * q^9 - 40 * q^10 - 36 * q^11 - 67 * q^12 - 51 * q^13 - 19 * q^14 - 48 * q^15 + 122 * q^16 - 54 * q^17 - 46 * q^18 - 73 * q^19 - 21 * q^20 - 8 * q^21 - 23 * q^22 - 38 * q^23 - 17 * q^24 + 133 * q^25 - 20 * q^26 - 129 * q^27 - 99 * q^28 + 154 * q^29 - 10 * q^30 - 91 * q^31 - 88 * q^32 - 39 * q^33 - 42 * q^34 - 36 * q^35 + 101 * q^36 - 50 * q^37 - 17 * q^38 - 33 * q^39 - 92 * q^40 - 31 * q^41 - 62 * q^42 - 154 * q^43 - 42 * q^44 - 14 * q^45 - 24 * q^46 - 140 * q^47 - 118 * q^48 + 126 * q^49 - 5 * q^50 - 16 * q^51 - 133 * q^52 - 40 * q^53 + 14 * q^54 - 203 * q^55 - 44 * q^56 - 16 * q^57 - 12 * q^58 + 5 * q^59 - 28 * q^60 - 106 * q^61 - 30 * q^62 - 145 * q^63 + 111 * q^64 - 15 * q^65 - 49 * q^66 - 78 * q^67 - 118 * q^68 - 32 * q^69 - 43 * q^70 - 4 * q^71 - 152 * q^72 - 137 * q^73 + 9 * q^74 - 129 * q^75 - 204 * q^76 - 76 * q^77 + 15 * q^78 - 141 * q^79 - 44 * q^80 + 122 * q^81 - 71 * q^82 - 90 * q^83 + 92 * q^84 - 41 * q^85 + 9 * q^86 - 36 * q^87 - 109 * q^88 - 51 * q^89 - 82 * q^90 - 22 * q^91 - 8 * q^92 - 10 * q^93 - 106 * q^94 - 55 * q^95 - 49 * q^96 - 140 * q^97 - 4 * q^98 - 101 * 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 $

$2$	−2.25887	−1.59726	−0.798630	−	0.601823i	$-0.794441\pi$
$2$	−2.25887	−1.59726	−0.798630	+	0.601823i	$0.794441\pi$
$3$	1.60047	0.924032	0.462016	−	0.886872i	$-0.347126\pi$
$3$	1.60047	0.924032	0.462016	+	0.886872i	$0.347126\pi$
$4$	3.10247	1.55124
$5$	−3.14219	−1.40523	−0.702615	−	0.711570i	$-0.747984\pi$
$5$	−3.14219	−1.40523	−0.702615	+	0.711570i	$0.747984\pi$
$6$	−3.61525	−1.47592
$7$	−0.353570	−0.133637	−0.0668184	−	0.997765i	$-0.521285\pi$
$7$	−0.353570	−0.133637	−0.0668184	+	0.997765i	$0.521285\pi$
$8$	−2.49034	−0.880468
$9$	−0.438494	−0.146165
$10$	7.09779	2.24452
$11$	−2.00621	−0.604894	−0.302447	−	0.953166i	$-0.597804\pi$
$11$	−2.00621	−0.604894	−0.302447	+	0.953166i	$0.597804\pi$
$12$	4.96542	1.43339
$13$	−3.41743	−0.947824	−0.473912	−	0.880572i	$-0.657159\pi$
$13$	−3.41743	−0.947824	−0.473912	+	0.880572i	$0.657159\pi$
$14$	0.798666	0.213452
$15$	−5.02898	−1.29848
$16$	−0.579606	−0.144902
$17$	−2.39912	−0.581873	−0.290937	−	0.956742i	$-0.593967\pi$
$17$	−2.39912	−0.581873	−0.290937	+	0.956742i	$0.593967\pi$
$18$	0.990500	0.233463
$19$	−0.280294	−0.0643038	−0.0321519	−	0.999483i	$-0.510236\pi$
$19$	−0.280294	−0.0643038	−0.0321519	+	0.999483i	$0.510236\pi$
$20$	−9.74856	−2.17984
$21$	−0.565878	−0.123485
$22$	4.53175	0.966173
$23$	7.17614	1.49633	0.748164	−	0.663514i	$-0.230936\pi$
$23$	7.17614	1.49633	0.748164	+	0.663514i	$0.230936\pi$
$24$	−3.98571	−0.813580
$25$	4.87336	0.974672
$26$	7.71951	1.51392
$27$	−5.50321	−1.05909
$28$	−1.09694	−0.207302
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	11.3598	2.07401
$31$	−5.00569	−0.899048	−0.449524	−	0.893268i	$-0.648406\pi$
$31$	−5.00569	−0.899048	−0.449524	+	0.893268i	$0.648406\pi$
$32$	6.28993	1.11191
$33$	−3.21087	−0.558942
$34$	5.41930	0.929402
$35$	1.11098	0.187790
$36$	−1.36042	−0.226736
$37$	10.5391	1.73262	0.866308	−	0.499510i	$-0.166487\pi$
$37$	10.5391	1.73262	0.866308	+	0.499510i	$0.166487\pi$
$38$	0.633145	0.102710
$39$	−5.46949	−0.875820
$40$	7.82512	1.23726
$41$	5.35288	0.835980	0.417990	−	0.908452i	$-0.362735\pi$
$41$	5.35288	0.835980	0.417990	+	0.908452i	$0.362735\pi$
$42$	1.27824	0.197237
$43$	7.13341	1.08783	0.543917	−	0.839139i	$-0.316941\pi$
$43$	7.13341	1.08783	0.543917	+	0.839139i	$0.316941\pi$
$44$	−6.22420	−0.938334
$45$	1.37783	0.205395
$46$	−16.2099	−2.39002
$47$	1.46250	0.213328	0.106664	−	0.994295i	$-0.465983\pi$
$47$	1.46250	0.213328	0.106664	+	0.994295i	$0.465983\pi$
$48$	−0.927643	−0.133894
$49$	−6.87499	−0.982141
$50$	−11.0083	−1.55680
$51$	−3.83973	−0.537669
$52$	−10.6025	−1.47030
$53$	10.4032	1.42899	0.714493	−	0.699643i	$-0.246657\pi$
$53$	10.4032	1.42899	0.714493	+	0.699643i	$0.246657\pi$
$54$	12.4310	1.69165
$55$	6.30388	0.850016
$56$	0.880508	0.117663
$57$	−0.448602	−0.0594187
$58$	−2.25887	−0.296604
$59$	0.880800	0.114670	0.0573352	−	0.998355i	$-0.481740\pi$
$59$	0.880800	0.114670	0.0573352	+	0.998355i	$0.481740\pi$
$60$	−15.6023	−2.01425
$61$	−1.21490	−0.155551	−0.0777757	−	0.996971i	$-0.524782\pi$
$61$	−1.21490	−0.155551	−0.0777757	+	0.996971i	$0.524782\pi$
$62$	11.3072	1.43601
$63$	0.155038	0.0195330
$64$	−13.0489	−1.63111
$65$	10.7382	1.33191
$66$	7.25293	0.892775
$67$	14.6268	1.78695	0.893477	−	0.449110i	$-0.148259\pi$
$67$	14.6268	1.78695	0.893477	+	0.449110i	$0.148259\pi$
$68$	−7.44322	−0.902623
$69$	11.4852	1.38265
$70$	−2.50956	−0.299950
$71$	15.0722	1.78875	0.894373	−	0.447323i	$-0.147622\pi$
$71$	15.0722	1.78875	0.894373	+	0.447323i	$0.147622\pi$
$72$	1.09200	0.128693
$73$	0.540235	0.0632297	0.0316149	−	0.999500i	$-0.489935\pi$
$73$	0.540235	0.0632297	0.0316149	+	0.999500i	$0.489935\pi$
$74$	−23.8064	−2.76744
$75$	7.79967	0.900628
$76$	−0.869603	−0.0997503
$77$	0.709334	0.0808361
$78$	12.3549	1.39891
$79$	5.63957	0.634501	0.317251	−	0.948342i	$-0.397240\pi$
$79$	5.63957	0.634501	0.317251	+	0.948342i	$0.397240\pi$
$80$	1.82123	0.203620
$81$	−7.49224	−0.832471
$82$	−12.0914	−1.33528
$83$	−8.31347	−0.912522	−0.456261	−	0.889846i	$-0.650812\pi$
$83$	−8.31347	−0.912522	−0.456261	+	0.889846i	$0.650812\pi$
$84$	−1.75562	−0.191554
$85$	7.53850	0.817666
$86$	−16.1134	−1.73755
$87$	1.60047	0.171588
$88$	4.99613	0.532590
$89$	−2.88182	−0.305472	−0.152736	−	0.988267i	$-0.548808\pi$
$89$	−2.88182	−0.305472	−0.152736	+	0.988267i	$0.548808\pi$
$90$	−3.11234	−0.328069
$91$	1.20830	0.126664
$92$	22.2638	2.32116
$93$	−8.01145	−0.830749
$94$	−3.30359	−0.340740
$95$	0.880736	0.0903616
$96$	10.0668	1.02744
$97$	−14.7259	−1.49519	−0.747595	−	0.664154i	$-0.768792\pi$
$97$	−14.7259	−1.49519	−0.747595	+	0.664154i	$0.768792\pi$
$98$	15.5297	1.56873
$99$	0.879710	0.0884142
$100$	15.1195	1.51195
$101$	−4.16653	−0.414585	−0.207293	−	0.978279i	$-0.566465\pi$
$101$	−4.16653	−0.414585	−0.207293	+	0.978279i	$0.566465\pi$
$102$	8.67343	0.858797
$103$	0.372855	0.0367385	0.0183692	−	0.999831i	$-0.494153\pi$
$103$	0.372855	0.0367385	0.0183692	+	0.999831i	$0.494153\pi$
$104$	8.51056	0.834529
$105$	1.77810	0.173524
$106$	−23.4994	−2.28246
$107$	8.50345	0.822059	0.411030	−	0.911622i	$-0.365169\pi$
$107$	8.50345	0.822059	0.411030	+	0.911622i	$0.365169\pi$
$108$	−17.0736	−1.64290
$109$	−15.2675	−1.46236	−0.731179	−	0.682185i	$-0.761030\pi$
$109$	−15.2675	−1.46236	−0.731179	+	0.682185i	$0.761030\pi$
$110$	−14.2396	−1.35770
$111$	16.8675	1.60099
$112$	0.204931	0.0193642
$113$	5.04892	0.474963	0.237481	−	0.971392i	$-0.423678\pi$
$113$	5.04892	0.474963	0.237481	+	0.971392i	$0.423678\pi$
$114$	1.01333	0.0949071
$115$	−22.5488	−2.10269
$116$	3.10247	0.288057
$117$	1.49852	0.138539
$118$	−1.98961	−0.183158
$119$	0.848257	0.0777596
$120$	12.5239	1.14327
$121$	−6.97513	−0.634103
$122$	2.74429	0.248456
$123$	8.56713	0.772472
$124$	−15.5300	−1.39464
$125$	0.397926	0.0355916
$126$	−0.350211	−0.0311992
$127$	−18.7610	−1.66477	−0.832383	−	0.554201i	$-0.813024\pi$
$127$	−18.7610	−1.66477	−0.832383	+	0.554201i	$0.813024\pi$
$128$	16.8958	1.49339
$129$	11.4168	1.00519
$130$	−24.2562	−2.12741
$131$	−0.809410	−0.0707185	−0.0353592	−	0.999375i	$-0.511258\pi$
$131$	−0.809410	−0.0707185	−0.0353592	+	0.999375i	$0.511258\pi$
$132$	−9.96165	−0.867051
$133$	0.0991033	0.00859334
$134$	−33.0401	−2.85423
$135$	17.2921	1.48827
$136$	5.97463	0.512320
$137$	10.3018	0.880140	0.440070	−	0.897964i	$-0.354954\pi$
$137$	10.3018	0.880140	0.440070	+	0.897964i	$0.354954\pi$
$138$	−25.9435	−2.20846
$139$	−4.39601	−0.372864	−0.186432	−	0.982468i	$-0.559692\pi$
$139$	−4.39601	−0.372864	−0.186432	+	0.982468i	$0.559692\pi$
$140$	3.44679	0.291307
$141$	2.34069	0.197122
$142$	−34.0462	−2.85709
$143$	6.85607	0.573333
$144$	0.254154	0.0211795
$145$	−3.14219	−0.260945
$146$	−1.22032	−0.100994
$147$	−11.0032	−0.907530
$148$	32.6973	2.68770
$149$	17.4422	1.42892	0.714459	−	0.699678i	$-0.246673\pi$
$149$	17.4422	1.42892	0.714459	+	0.699678i	$0.246673\pi$
$150$	−17.6184	−1.43854
$151$	−16.7156	−1.36030	−0.680149	−	0.733074i	$-0.738085\pi$
$151$	−16.7156	−1.36030	−0.680149	+	0.733074i	$0.738085\pi$
$152$	0.698026	0.0566174
$153$	1.05200	0.0850494
$154$	−1.60229	−0.129116
$155$	15.7288	1.26337
$156$	−16.9690	−1.35860
$157$	3.37057	0.269001	0.134501	−	0.990914i	$-0.457057\pi$
$157$	3.37057	0.269001	0.134501	+	0.990914i	$0.457057\pi$
$158$	−12.7390	−1.01346
$159$	16.6500	1.32043
$160$	−19.7642	−1.56249
$161$	−2.53726	−0.199964
$162$	16.9240	1.32967
$163$	−16.3451	−1.28025	−0.640125	−	0.768271i	$-0.721118\pi$
$163$	−16.3451	−1.28025	−0.640125	+	0.768271i	$0.721118\pi$
$164$	16.6072	1.29680
$165$	10.0892	0.785442
$166$	18.7790	1.45753
$167$	−4.16953	−0.322648	−0.161324	−	0.986902i	$-0.551576\pi$
$167$	−4.16953	−0.322648	−0.161324	+	0.986902i	$0.551576\pi$
$168$	1.40923	0.108724
$169$	−1.32118	−0.101629
$170$	−17.0285	−1.30602
$171$	0.122907	0.00939895
$172$	22.1312	1.68749
$173$	2.00360	0.152331	0.0761656	−	0.997095i	$-0.475732\pi$
$173$	2.00360	0.152331	0.0761656	+	0.997095i	$0.475732\pi$
$174$	−3.61525	−0.274071
$175$	−1.72307	−0.130252
$176$	1.16281	0.0876501
$177$	1.40969	0.105959
$178$	6.50964	0.487918
$179$	−21.3800	−1.59801	−0.799007	−	0.601322i	$-0.794641\pi$
$179$	−21.3800	−1.59801	−0.799007	+	0.601322i	$0.794641\pi$
$180$	4.27469	0.318617
$181$	−3.84141	−0.285530	−0.142765	−	0.989757i	$-0.545599\pi$
$181$	−3.84141	−0.285530	−0.142765	+	0.989757i	$0.545599\pi$
$182$	−2.72939	−0.202315
$183$	−1.94440	−0.143735
$184$	−17.8710	−1.31747
$185$	−33.1158	−2.43473
$186$	18.0968	1.32692
$187$	4.81314	0.351972
$188$	4.53737	0.330922
$189$	1.94577	0.141534
$190$	−1.98946	−0.144331
$191$	−15.5697	−1.12658	−0.563291	−	0.826259i	$-0.690465\pi$
$191$	−15.5697	−1.12658	−0.563291	+	0.826259i	$0.690465\pi$
$192$	−20.8844	−1.50720
$193$	20.0100	1.44035	0.720176	−	0.693792i	$-0.244061\pi$
$193$	20.0100	1.44035	0.720176	+	0.693792i	$0.244061\pi$
$194$	33.2639	2.38821
$195$	17.1862	1.23073
$196$	−21.3295	−1.52353
$197$	−9.05009	−0.644792	−0.322396	−	0.946605i	$-0.604488\pi$
$197$	−9.05009	−0.644792	−0.322396	+	0.946605i	$0.604488\pi$
$198$	−1.98715	−0.141220
$199$	20.6141	1.46130	0.730648	−	0.682754i	$-0.239218\pi$
$199$	20.6141	1.46130	0.730648	+	0.682754i	$0.239218\pi$
$200$	−12.1363	−0.858167
$201$	23.4098	1.65120
$202$	9.41164	0.662200
$203$	−0.353570	−0.0248157
$204$	−11.9126	−0.834052
$205$	−16.8198	−1.17474
$206$	−0.842229	−0.0586809
$207$	−3.14670	−0.218710
$208$	1.98076	0.137341
$209$	0.562327	0.0388970
$210$	−4.01648	−0.277163
$211$	−1.35698	−0.0934183	−0.0467091	−	0.998909i	$-0.514873\pi$
$211$	−1.35698	−0.0934183	−0.0467091	+	0.998909i	$0.514873\pi$
$212$	32.2756	2.21670
$213$	24.1227	1.65286
$214$	−19.2081	−1.31304
$215$	−22.4145	−1.52866
$216$	13.7049	0.932497
$217$	1.76986	0.120146
$218$	34.4872	2.33577
$219$	0.864630	0.0584263
$220$	19.5576	1.31858
$221$	8.19884	0.551513
$222$	−38.1014	−2.55720
$223$	23.6983	1.58695	0.793477	−	0.608600i	$-0.208269\pi$
$223$	23.6983	1.58695	0.793477	+	0.608600i	$0.208269\pi$
$224$	−2.22393	−0.148592
$225$	−2.13694	−0.142463
$226$	−11.4048	−0.758639
$227$	−18.4261	−1.22298	−0.611492	−	0.791250i	$-0.709431\pi$
$227$	−18.4261	−1.22298	−0.611492	+	0.791250i	$0.709431\pi$
$228$	−1.39177	−0.0921725
$229$	−5.57204	−0.368211	−0.184105	−	0.982906i	$-0.558939\pi$
$229$	−5.57204	−0.368211	−0.184105	+	0.982906i	$0.558939\pi$
$230$	50.9347	3.35853
$231$	1.13527	0.0746951
$232$	−2.49034	−0.163499
$233$	−26.6055	−1.74298	−0.871491	−	0.490411i	$-0.836847\pi$
$233$	−26.6055	−1.74298	−0.871491	+	0.490411i	$0.836847\pi$
$234$	−3.38496	−0.221282
$235$	−4.59546	−0.299775
$236$	2.73266	0.177881
$237$	9.02597	0.586300
$238$	−1.91610	−0.124202
$239$	21.1850	1.37035	0.685173	−	0.728380i	$-0.259726\pi$
$239$	21.1850	1.37035	0.685173	+	0.728380i	$0.259726\pi$
$240$	2.91483	0.188151
$241$	−17.4754	−1.12569	−0.562844	−	0.826563i	$-0.690293\pi$
$241$	−17.4754	−1.12569	−0.562844	+	0.826563i	$0.690293\pi$
$242$	15.7559	1.01283
$243$	4.51852	0.289863
$244$	−3.76918	−0.241297
$245$	21.6025	1.38013
$246$	−19.3520	−1.23384
$247$	0.957884	0.0609487
$248$	12.4659	0.791583
$249$	−13.3055	−0.843200
$250$	−0.898862	−0.0568490
$251$	−27.8057	−1.75508	−0.877539	−	0.479505i	$-0.840816\pi$
$251$	−27.8057	−1.75508	−0.877539	+	0.479505i	$0.840816\pi$
$252$	0.481002	0.0303003
$253$	−14.3968	−0.905120
$254$	42.3785	2.65906
$255$	12.0652	0.755549
$256$	−12.0676	−0.754227
$257$	10.8725	0.678209	0.339104	−	0.940749i	$-0.389876\pi$
$257$	10.8725	0.678209	0.339104	+	0.940749i	$0.389876\pi$
$258$	−25.7890	−1.60556
$259$	−3.72630	−0.231541
$260$	33.3150	2.06611
$261$	−0.438494	−0.0271421
$262$	1.82835	0.112956
$263$	−8.72504	−0.538009	−0.269004	−	0.963139i	$-0.586695\pi$
$263$	−8.72504	−0.538009	−0.269004	+	0.963139i	$0.586695\pi$
$264$	7.99617	0.492130
$265$	−32.6888	−2.00805
$266$	−0.223861	−0.0137258
$267$	−4.61227	−0.282266
$268$	45.3794	2.77199
$269$	−3.06556	−0.186911	−0.0934553	−	0.995623i	$-0.529791\pi$
$269$	−3.06556	−0.186911	−0.0934553	+	0.995623i	$0.529791\pi$
$270$	−39.0606	−2.37715
$271$	−20.5854	−1.25048	−0.625238	−	0.780434i	$-0.714998\pi$
$271$	−20.5854	−1.25048	−0.625238	+	0.780434i	$0.714998\pi$
$272$	1.39055	0.0843143
$273$	1.93385	0.117042
$274$	−23.2703	−1.40581
$275$	−9.77697	−0.589573
$276$	35.6325	2.14482
$277$	1.00000	0.0600842
$277$	1.00000	0.0600842
$278$	9.92999	0.595561
$279$	2.19497	0.131409
$280$	−2.76672	−0.165343
$281$	24.4214	1.45686	0.728430	−	0.685121i	$-0.240250\pi$
$281$	24.4214	1.45686	0.728430	+	0.685121i	$0.240250\pi$
$282$	−5.28730	−0.314854
$283$	3.01350	0.179134	0.0895669	−	0.995981i	$-0.471452\pi$
$283$	3.01350	0.179134	0.0895669	+	0.995981i	$0.471452\pi$
$284$	46.7612	2.77477
$285$	1.40959	0.0834970
$286$	−15.4869	−0.915762
$287$	−1.89262	−0.111718
$288$	−2.75810	−0.162523
$289$	−11.2442	−0.661424
$290$	7.09779	0.416796
$291$	−23.5684	−1.38160
$292$	1.67606	0.0980843
$293$	6.90374	0.403321	0.201661	−	0.979455i	$-0.435366\pi$
$293$	6.90374	0.403321	0.201661	+	0.979455i	$0.435366\pi$
$294$	24.8548	1.44956
$295$	−2.76764	−0.161138
$296$	−26.2459	−1.52551
$297$	11.0406	0.640639
$298$	−39.3995	−2.28235
$299$	−24.5239	−1.41826
$300$	24.1983	1.39709
$301$	−2.52216	−0.145375
$302$	37.7583	2.17275
$303$	−6.66841	−0.383090
$304$	0.162460	0.00931772
$305$	3.81743	0.218586
$306$	−2.37633	−0.135846
$307$	9.07750	0.518080	0.259040	−	0.965867i	$-0.416594\pi$
$307$	9.07750	0.518080	0.259040	+	0.965867i	$0.416594\pi$
$308$	2.20069	0.125396
$309$	0.596743	0.0339475
$310$	−35.5293	−2.01793
$311$	−0.460783	−0.0261286	−0.0130643	−	0.999915i	$-0.504159\pi$
$311$	−0.460783	−0.0261286	−0.0130643	+	0.999915i	$0.504159\pi$
$312$	13.6209	0.771131
$313$	13.1912	0.745609	0.372804	−	0.927910i	$-0.378396\pi$
$313$	13.1912	0.745609	0.372804	+	0.927910i	$0.378396\pi$
$314$	−7.61367	−0.429665
$315$	−0.487160	−0.0274483
$316$	17.4966	0.984262
$317$	−12.4099	−0.697007	−0.348503	−	0.937307i	$-0.613310\pi$
$317$	−12.4099	−0.697007	−0.348503	+	0.937307i	$0.613310\pi$
$318$	−37.6100	−2.10907
$319$	−2.00621	−0.112326
$320$	41.0021	2.29209
$321$	13.6095	0.759609
$322$	5.73134	0.319395
$323$	0.672459	0.0374166
$324$	−23.2445	−1.29136
$325$	−16.6544	−0.923818
$326$	36.9215	2.04489
$327$	−24.4351	−1.35127
$328$	−13.3305	−0.736053
$329$	−0.517096	−0.0285084
$330$	−22.7901	−1.25455
$331$	20.4025	1.12142	0.560712	−	0.828011i	$-0.310528\pi$
$331$	20.4025	1.12142	0.560712	+	0.828011i	$0.310528\pi$
$332$	−25.7923	−1.41554
$333$	−4.62133	−0.253248
$334$	9.41840	0.515352
$335$	−45.9603	−2.51108
$336$	0.327986	0.0178931
$337$	−17.3213	−0.943554	−0.471777	−	0.881718i	$-0.656387\pi$
$337$	−17.3213	−0.943554	−0.471777	+	0.881718i	$0.656387\pi$
$338$	2.98436	0.162328
$339$	8.08065	0.438881
$340$	23.3880	1.26839
$341$	10.0424	0.543829
$342$	−0.277631	−0.0150126
$343$	4.90577	0.264887
$344$	−17.7646	−0.957803
$345$	−36.0887	−1.94295
$346$	−4.52587	−0.243312
$347$	−9.27739	−0.498036	−0.249018	−	0.968499i	$-0.580108\pi$
$347$	−9.27739	−0.498036	−0.249018	+	0.968499i	$0.580108\pi$
$348$	4.96542	0.266174
$349$	−10.9889	−0.588222	−0.294111	−	0.955771i	$-0.595024\pi$
$349$	−10.9889	−0.588222	−0.294111	+	0.955771i	$0.595024\pi$
$350$	3.89219	0.208046
$351$	18.8068	1.00383
$352$	−12.6189	−0.672590
$353$	−24.9764	−1.32936	−0.664681	−	0.747128i	$-0.731432\pi$
$353$	−24.9764	−1.32936	−0.664681	+	0.747128i	$0.731432\pi$
$354$	−3.18431	−0.169244
$355$	−47.3598	−2.51360
$356$	−8.94077	−0.473860
$357$	1.35761	0.0718524
$358$	48.2945	2.55244
$359$	−12.7875	−0.674899	−0.337449	−	0.941344i	$-0.609564\pi$
$359$	−12.7875	−0.674899	−0.337449	+	0.941344i	$0.609564\pi$
$360$	−3.43127	−0.180844
$361$	−18.9214	−0.995865
$362$	8.67723	0.456065
$363$	−11.1635	−0.585932
$364$	3.74872	0.196486
$365$	−1.69752	−0.0888523
$366$	4.39215	0.229581
$367$	−23.9189	−1.24856	−0.624279	−	0.781201i	$-0.714607\pi$
$367$	−23.9189	−1.24856	−0.624279	+	0.781201i	$0.714607\pi$
$368$	−4.15933	−0.216820
$369$	−2.34721	−0.122191
$370$	74.8042	3.88889
$371$	−3.67825	−0.190965
$372$	−24.8553	−1.28869
$373$	−17.6795	−0.915412	−0.457706	−	0.889104i	$-0.651329\pi$
$373$	−17.6795	−0.915412	−0.457706	+	0.889104i	$0.651329\pi$
$374$	−10.8722	−0.562190
$375$	0.636869	0.0328878
$376$	−3.64212	−0.187828
$377$	−3.41743	−0.176007
$378$	−4.39523	−0.226066
$379$	−2.91658	−0.149815	−0.0749073	−	0.997190i	$-0.523866\pi$
$379$	−2.91658	−0.149815	−0.0749073	+	0.997190i	$0.523866\pi$
$380$	2.73246	0.140172
$381$	−30.0263	−1.53830
$382$	35.1698	1.79944
$383$	−23.5240	−1.20202	−0.601011	−	0.799241i	$-0.705235\pi$
$383$	−23.5240	−1.20202	−0.601011	+	0.799241i	$0.705235\pi$
$384$	27.0413	1.37994
$385$	−2.22886	−0.113593
$386$	−45.1999	−2.30061
$387$	−3.12796	−0.159003
$388$	−45.6868	−2.31939
$389$	−14.7868	−0.749721	−0.374861	−	0.927081i	$-0.622309\pi$
$389$	−14.7868	−0.749721	−0.374861	+	0.927081i	$0.622309\pi$
$390$	−38.8213	−1.96579
$391$	−17.2164	−0.870673
$392$	17.1211	0.864744
$393$	−1.29544	−0.0653461
$394$	20.4429	1.02990
$395$	−17.7206	−0.891621
$396$	2.72928	0.137151
$397$	−22.4609	−1.12728	−0.563640	−	0.826021i	$-0.690599\pi$
$397$	−22.4609	−1.12728	−0.563640	+	0.826021i	$0.690599\pi$
$398$	−46.5645	−2.33407
$399$	0.158612	0.00794053
$400$	−2.82463	−0.141232
$401$	36.3427	1.81487	0.907433	−	0.420196i	$-0.138039\pi$
$401$	36.3427	1.81487	0.907433	+	0.420196i	$0.138039\pi$
$402$	−52.8797	−2.63740
$403$	17.1066	0.852140
$404$	−12.9266	−0.643120
$405$	23.5420	1.16981
$406$	0.798666	0.0396371
$407$	−21.1436	−1.04805
$408$	9.56222	0.473400
$409$	18.3350	0.906607	0.453303	−	0.891356i	$-0.350245\pi$
$409$	18.3350	0.906607	0.453303	+	0.891356i	$0.350245\pi$
$410$	37.9936	1.87637
$411$	16.4877	0.813277
$412$	1.15677	0.0569901
$413$	−0.311424	−0.0153242
$414$	7.10796	0.349337
$415$	26.1225	1.28230
$416$	−21.4954	−1.05390
$417$	−7.03568	−0.344539
$418$	−1.27022	−0.0621285
$419$	10.9910	0.536948	0.268474	−	0.963287i	$-0.413481\pi$
$419$	10.9910	0.536948	0.268474	+	0.963287i	$0.413481\pi$
$420$	5.51649	0.269177
$421$	−2.38773	−0.116371	−0.0581853	−	0.998306i	$-0.518531\pi$
$421$	−2.38773	−0.116371	−0.0581853	+	0.998306i	$0.518531\pi$
$422$	3.06523	0.149213
$423$	−0.641298	−0.0311810
$424$	−25.9074	−1.25818
$425$	−11.6918	−0.567135
$426$	−54.4899	−2.64004
$427$	0.429550	0.0207874
$428$	26.3817	1.27521
$429$	10.9729	0.529778
$430$	50.6314	2.44166
$431$	9.75486	0.469875	0.234937	−	0.972010i	$-0.424511\pi$
$431$	9.75486	0.469875	0.234937	+	0.972010i	$0.424511\pi$
$432$	3.18969	0.153464
$433$	24.5836	1.18141	0.590705	−	0.806887i	$-0.298850\pi$
$433$	24.5836	1.18141	0.590705	+	0.806887i	$0.298850\pi$
$434$	−3.99787	−0.191904
$435$	−5.02898	−0.241121
$436$	−47.3669	−2.26846
$437$	−2.01143	−0.0962195
$438$	−1.95308	−0.0933219
$439$	−1.30653	−0.0623573	−0.0311787	−	0.999514i	$-0.509926\pi$
$439$	−1.30653	−0.0623573	−0.0311787	+	0.999514i	$0.509926\pi$
$440$	−15.6988	−0.748411
$441$	3.01464	0.143554
$442$	−18.5201	−0.880910
$443$	30.1663	1.43324	0.716621	−	0.697463i	$-0.245688\pi$
$443$	30.1663	1.43324	0.716621	+	0.697463i	$0.245688\pi$
$444$	52.3310	2.48352
$445$	9.05523	0.429259
$446$	−53.5312	−2.53478
$447$	27.9157	1.32037
$448$	4.61369	0.217976
$449$	5.11293	0.241294	0.120647	−	0.992695i	$-0.461503\pi$
$449$	5.11293	0.241294	0.120647	+	0.992695i	$0.461503\pi$
$450$	4.82706	0.227550
$451$	−10.7390	−0.505679
$452$	15.6642	0.736780
$453$	−26.7528	−1.25696
$454$	41.6221	1.95342
$455$	−3.79671	−0.177992
$456$	1.11717	0.0523163
$457$	6.36969	0.297962	0.148981	−	0.988840i	$-0.452401\pi$
$457$	6.36969	0.297962	0.148981	+	0.988840i	$0.452401\pi$
$458$	12.5865	0.588128
$459$	13.2029	0.616258
$460$	−69.9570	−3.26176
$461$	26.2538	1.22276	0.611381	−	0.791336i	$-0.290614\pi$
$461$	26.2538	1.22276	0.611381	+	0.791336i	$0.290614\pi$
$462$	−2.56442	−0.119307
$463$	15.1142	0.702415	0.351207	−	0.936298i	$-0.385771\pi$
$463$	15.1142	0.702415	0.351207	+	0.936298i	$0.385771\pi$
$464$	−0.579606	−0.0269075
$465$	25.1735	1.16739
$466$	60.0982	2.78399
$467$	35.6853	1.65132	0.825659	−	0.564169i	$-0.190804\pi$
$467$	35.6853	1.65132	0.825659	+	0.564169i	$0.190804\pi$
$468$	4.64913	0.214906
$469$	−5.17161	−0.238803
$470$	10.3805	0.478818
$471$	5.39451	0.248566
$472$	−2.19349	−0.100964
$473$	−14.3111	−0.658025
$474$	−20.3884	−0.936472
$475$	−1.36597	−0.0626751
$476$	2.63170	0.120624
$477$	−4.56173	−0.208867
$478$	−47.8542	−2.18880
$479$	40.9501	1.87106	0.935529	−	0.353250i	$-0.114923\pi$
$479$	40.9501	1.87106	0.935529	+	0.353250i	$0.114923\pi$
$480$	−31.6319	−1.44379
$481$	−36.0166	−1.64222
$482$	39.4745	1.79801
$483$	−4.06082	−0.184773
$484$	−21.6402	−0.983644
$485$	46.2716	2.10109
$486$	−10.2067	−0.462986
$487$	−28.5564	−1.29402	−0.647008	−	0.762484i	$-0.723980\pi$
$487$	−28.5564	−1.29402	−0.647008	+	0.762484i	$0.723980\pi$
$488$	3.02550	0.136958
$489$	−26.1599	−1.18299
$490$	−48.7972	−2.20443
$491$	36.2089	1.63409	0.817043	−	0.576577i	$-0.195612\pi$
$491$	36.2089	1.63409	0.817043	+	0.576577i	$0.195612\pi$
$492$	26.5793	1.19829
$493$	−2.39912	−0.108051
$494$	−2.16373	−0.0973508
$495$	−2.76422	−0.124242
$496$	2.90133	0.130273
$497$	−5.32908	−0.239042
$498$	30.0553	1.34681
$499$	−8.30600	−0.371828	−0.185914	−	0.982566i	$-0.559525\pi$
$499$	−8.30600	−0.371828	−0.185914	+	0.982566i	$0.559525\pi$
$500$	1.23456	0.0552110
$501$	−6.67321	−0.298137
$502$	62.8093	2.80331
$503$	24.1758	1.07794	0.538972	−	0.842323i	$-0.318813\pi$
$503$	24.1758	1.07794	0.538972	+	0.842323i	$0.318813\pi$
$504$	−0.386098	−0.0171982
$505$	13.0920	0.582588
$506$	32.5205	1.44571
$507$	−2.11450	−0.0939084
$508$	−58.2053	−2.58244
$509$	−33.7917	−1.49779	−0.748896	−	0.662687i	$-0.769416\pi$
$509$	−33.7917	−1.49779	−0.748896	+	0.662687i	$0.769416\pi$
$510$	−27.2536	−1.20681
$511$	−0.191011	−0.00844981
$512$	−6.53252	−0.288699
$513$	1.54251	0.0681037
$514$	−24.5595	−1.08327
$515$	−1.17158	−0.0516260
$516$	35.4203	1.55929
$517$	−2.93408	−0.129041
$518$	8.41722	0.369831
$519$	3.20671	0.140759
$520$	−26.7418	−1.17271
$521$	−11.4590	−0.502026	−0.251013	−	0.967984i	$-0.580764\pi$
$521$	−11.4590	−0.502026	−0.251013	+	0.967984i	$0.580764\pi$
$522$	0.990500	0.0433530
$523$	−0.0712310	−0.00311472	−0.00155736	−	0.999999i	$-0.500496\pi$
$523$	−0.0712310	−0.00311472	−0.00155736	+	0.999999i	$0.500496\pi$
$524$	−2.51117	−0.109701
$525$	−2.75773	−0.120357
$526$	19.7087	0.859339
$527$	12.0093	0.523132
$528$	1.86104	0.0809915
$529$	28.4969	1.23900
$530$	73.8395	3.20738
$531$	−0.386226	−0.0167608
$532$	0.307465	0.0133303
$533$	−18.2931	−0.792362
$534$	10.4185	0.450852
$535$	−26.7194	−1.15518
$536$	−36.4258	−1.57335
$537$	−34.2180	−1.47662
$538$	6.92469	0.298545
$539$	13.7926	0.594091
$540$	53.6484	2.30866
$541$	−32.1698	−1.38309	−0.691544	−	0.722335i	$-0.743069\pi$
$541$	−32.1698	−1.38309	−0.691544	+	0.722335i	$0.743069\pi$
$542$	46.4997	1.99733
$543$	−6.14806	−0.263839
$544$	−15.0903	−0.646992
$545$	47.9733	2.05495
$546$	−4.36830	−0.186946
$547$	−2.46429	−0.105366	−0.0526828	−	0.998611i	$-0.516777\pi$
$547$	−2.46429	−0.105366	−0.0526828	+	0.998611i	$0.516777\pi$
$548$	31.9610	1.36531
$549$	0.532725	0.0227361
$550$	22.0849	0.941701
$551$	−0.280294	−0.0119409
$552$	−28.6020	−1.21738
$553$	−1.99398	−0.0847927
$554$	−2.25887	−0.0959700
$555$	−53.0009	−2.24976
$556$	−13.6385	−0.578401
$557$	18.2663	0.773967	0.386984	−	0.922087i	$-0.373517\pi$
$557$	18.2663	0.773967	0.386984	+	0.922087i	$0.373517\pi$
$558$	−4.95813	−0.209894
$559$	−24.3779	−1.03108
$560$	−0.643933	−0.0272111
$561$	7.70329	0.325233
$562$	−55.1647	−2.32698
$563$	−5.29994	−0.223366	−0.111683	−	0.993744i	$-0.535624\pi$
$563$	−5.29994	−0.223366	−0.111683	+	0.993744i	$0.535624\pi$
$564$	7.26193	0.305782
$565$	−15.8647	−0.667432
$566$	−6.80708	−0.286123
$567$	2.64903	0.111249
$568$	−37.5350	−1.57493
$569$	23.0913	0.968036	0.484018	−	0.875058i	$-0.339177\pi$
$569$	23.0913	0.968036	0.484018	+	0.875058i	$0.339177\pi$
$570$	−3.18408	−0.133366
$571$	21.2764	0.890388	0.445194	−	0.895434i	$-0.353135\pi$
$571$	21.2764	0.890388	0.445194	+	0.895434i	$0.353135\pi$
$572$	21.2708	0.889376
$573$	−24.9188	−1.04100
$574$	4.27517	0.178442
$575$	34.9719	1.45843
$576$	5.72187	0.238411
$577$	38.9123	1.61994	0.809969	−	0.586472i	$-0.199484\pi$
$577$	38.9123	1.61994	0.809969	+	0.586472i	$0.199484\pi$
$578$	25.3991	1.05647
$579$	32.0254	1.33093
$580$	−9.74856	−0.404787
$581$	2.93939	0.121947
$582$	53.2378	2.20678
$583$	−20.8709	−0.864385
$584$	−1.34537	−0.0556717
$585$	−4.70865	−0.194679
$586$	−15.5946	−0.644208
$587$	−3.16546	−0.130653	−0.0653263	−	0.997864i	$-0.520809\pi$
$587$	−3.16546	−0.130653	−0.0653263	+	0.997864i	$0.520809\pi$
$588$	−34.1372	−1.40779
$589$	1.40306	0.0578122
$590$	6.25173	0.257380
$591$	−14.4844	−0.595809
$592$	−6.10853	−0.251059
$593$	12.7689	0.524354	0.262177	−	0.965020i	$-0.415560\pi$
$593$	12.7689	0.524354	0.262177	+	0.965020i	$0.415560\pi$
$594$	−24.9392	−1.02327
$595$	−2.66539	−0.109270
$596$	54.1138	2.21659
$597$	32.9923	1.35028
$598$	55.3963	2.26532
$599$	−21.0552	−0.860290	−0.430145	−	0.902760i	$-0.641538\pi$
$599$	−21.0552	−0.860290	−0.430145	+	0.902760i	$0.641538\pi$
$600$	−19.4238	−0.792974
$601$	−19.8572	−0.809992	−0.404996	−	0.914318i	$-0.632727\pi$
$601$	−19.8572	−0.809992	−0.404996	+	0.914318i	$0.632727\pi$
$602$	5.69721	0.232201
$603$	−6.41379	−0.261190
$604$	−51.8597	−2.11014
$605$	21.9172	0.891061
$606$	15.0630	0.611894
$607$	−13.8429	−0.561866	−0.280933	−	0.959727i	$-0.590644\pi$
$607$	−13.8429	−0.561866	−0.280933	+	0.959727i	$0.590644\pi$
$608$	−1.76303	−0.0715002
$609$	−0.565878	−0.0229305
$610$	−8.62307	−0.349138
$611$	−4.99799	−0.202197
$612$	3.26381	0.131932
$613$	−17.7944	−0.718711	−0.359356	−	0.933201i	$-0.617003\pi$
$613$	−17.7944	−0.718711	−0.359356	+	0.933201i	$0.617003\pi$
$614$	−20.5049	−0.827508
$615$	−26.9196	−1.08550
$616$	−1.76648	−0.0711736
$617$	32.3005	1.30037	0.650184	−	0.759777i	$-0.274692\pi$
$617$	32.3005	1.30037	0.650184	+	0.759777i	$0.274692\pi$
$618$	−1.34796	−0.0542230
$619$	−5.60691	−0.225361	−0.112680	−	0.993631i	$-0.535944\pi$
$619$	−5.60691	−0.225361	−0.112680	+	0.993631i	$0.535944\pi$
$620$	48.7982	1.95978
$621$	−39.4918	−1.58475
$622$	1.04085	0.0417341
$623$	1.01892	0.0408223
$624$	3.17015	0.126908
$625$	−25.6172	−1.02469
$626$	−29.7971	−1.19093
$627$	0.899988	0.0359420
$628$	10.4571	0.417284
$629$	−25.2846	−1.00816
$630$	1.10043	0.0438421
$631$	−2.73916	−0.109044	−0.0545222	−	0.998513i	$-0.517364\pi$
$631$	−2.73916	−0.109044	−0.0545222	+	0.998513i	$0.517364\pi$
$632$	−14.0444	−0.558658
$633$	−2.17180	−0.0863215
$634$	28.0322	1.11330
$635$	58.9505	2.33938
$636$	51.6561	2.04830
$637$	23.4948	0.930897
$638$	4.53175	0.179414
$639$	−6.60909	−0.261452
$640$	−53.0899	−2.09856
$641$	17.6785	0.698260	0.349130	−	0.937074i	$-0.386477\pi$
$641$	17.6785	0.698260	0.349130	+	0.937074i	$0.386477\pi$
$642$	−30.7421	−1.21329
$643$	13.6293	0.537486	0.268743	−	0.963212i	$-0.413392\pi$
$643$	13.6293	0.537486	0.268743	+	0.963212i	$0.413392\pi$
$644$	−7.87179	−0.310192
$645$	−35.8738	−1.41253
$646$	−1.51899	−0.0597640
$647$	21.4671	0.843960	0.421980	−	0.906605i	$-0.361335\pi$
$647$	21.4671	0.843960	0.421980	+	0.906605i	$0.361335\pi$
$648$	18.6582	0.732964
$649$	−1.76707	−0.0693634
$650$	37.6200	1.47558
$651$	2.83261	0.111019
$652$	−50.7104	−1.98597
$653$	−45.1844	−1.76820	−0.884100	−	0.467297i	$-0.845228\pi$
$653$	−45.1844	−1.76820	−0.884100	+	0.467297i	$0.845228\pi$
$654$	55.1957	2.15832
$655$	2.54332	0.0993757
$656$	−3.10256	−0.121135
$657$	−0.236890	−0.00924196
$658$	1.16805	0.0455353
$659$	6.07166	0.236518	0.118259	−	0.992983i	$-0.462269\pi$
$659$	6.07166	0.236518	0.118259	+	0.992983i	$0.462269\pi$
$660$	31.3014	1.21841
$661$	−4.68651	−0.182284	−0.0911420	−	0.995838i	$-0.529052\pi$
$661$	−4.68651	−0.182284	−0.0911420	+	0.995838i	$0.529052\pi$
$662$	−46.0865	−1.79120
$663$	13.1220	0.509616
$664$	20.7034	0.803446
$665$	−0.311401	−0.0120756
$666$	10.4390	0.404502
$667$	7.17614	0.277861
$668$	−12.9359	−0.500503
$669$	37.9284	1.46640
$670$	103.818	4.01085
$671$	2.43733	0.0940922
$672$	−3.55933	−0.137304
$673$	12.0193	0.463309	0.231654	−	0.972798i	$-0.425586\pi$
$673$	12.0193	0.463309	0.231654	+	0.972798i	$0.425586\pi$
$674$	39.1266	1.50710
$675$	−26.8191	−1.03227
$676$	−4.09891	−0.157651
$677$	−46.2075	−1.77590	−0.887949	−	0.459941i	$-0.847870\pi$
$677$	−46.2075	−1.77590	−0.887949	+	0.459941i	$0.847870\pi$
$678$	−18.2531	−0.701006
$679$	5.20664	0.199812
$680$	−18.7734	−0.719928
$681$	−29.4905	−1.13008
$682$	−22.6845	−0.868636
$683$	3.55365	0.135977	0.0679883	−	0.997686i	$-0.478342\pi$
$683$	3.55365	0.135977	0.0679883	+	0.997686i	$0.478342\pi$
$684$	0.381316	0.0145800
$685$	−32.3701	−1.23680
$686$	−11.0815	−0.423093
$687$	−8.91789	−0.340239
$688$	−4.13457	−0.157629
$689$	−35.5521	−1.35443
$690$	81.5194	3.10339
$691$	7.68336	0.292289	0.146144	−	0.989263i	$-0.453314\pi$
$691$	7.68336	0.292289	0.146144	+	0.989263i	$0.453314\pi$
$692$	6.21613	0.236302
$693$	−0.311039	−0.0118154
$694$	20.9564	0.795493
$695$	13.8131	0.523960
$696$	−3.98571	−0.151078
$697$	−12.8422	−0.486434
$698$	24.8224	0.939543
$699$	−42.5813	−1.61057
$700$	−5.34578	−0.202052
$701$	−37.4458	−1.41431	−0.707154	−	0.707059i	$-0.750021\pi$
$701$	−37.4458	−1.41431	−0.707154	+	0.707059i	$0.750021\pi$
$702$	−42.4821	−1.60338
$703$	−2.95404	−0.111414
$704$	26.1788	0.986650
$705$	−7.35489	−0.277001
$706$	56.4184	2.12333
$707$	1.47316	0.0554039
$708$	4.37354	0.164368
$709$	35.9074	1.34853	0.674265	−	0.738489i	$-0.264460\pi$
$709$	35.9074	1.34853	0.674265	+	0.738489i	$0.264460\pi$
$710$	106.979	4.01487
$711$	−2.47292	−0.0927418
$712$	7.17671	0.268959
$713$	−35.9215	−1.34527
$714$	−3.06666	−0.114767
$715$	−21.5431	−0.805665
$716$	−66.3308	−2.47890
$717$	33.9060	1.26624
$718$	28.8853	1.07799
$719$	27.5941	1.02908	0.514542	−	0.857465i	$-0.327962\pi$
$719$	27.5941	1.02908	0.514542	+	0.857465i	$0.327962\pi$
$720$	−0.798601	−0.0297621
$721$	−0.131830	−0.00490961
$722$	42.7410	1.59065
$723$	−27.9688	−1.04017
$724$	−11.9179	−0.442924
$725$	4.87336	0.180992
$726$	25.2168	0.935884
$727$	−2.66236	−0.0987416	−0.0493708	−	0.998781i	$-0.515722\pi$
$727$	−2.66236	−0.0987416	−0.0493708	+	0.998781i	$0.515722\pi$
$728$	−3.00907	−0.111524
$729$	29.7085	1.10031
$730$	3.83447	0.141920
$731$	−17.1139	−0.632982
$732$	−6.03246	−0.222966
$733$	−28.4276	−1.05000	−0.524999	−	0.851103i	$-0.675934\pi$
$733$	−28.4276	−1.05000	−0.524999	+	0.851103i	$0.675934\pi$
$734$	54.0297	1.99427
$735$	34.5742	1.27529
$736$	45.1374	1.66379
$737$	−29.3445	−1.08092
$738$	5.30203	0.195170
$739$	2.21859	0.0816120	0.0408060	−	0.999167i	$-0.487007\pi$
$739$	2.21859	0.0816120	0.0408060	+	0.999167i	$0.487007\pi$
$740$	−102.741	−3.77683
$741$	1.53306	0.0563185
$742$	8.30866	0.305021
$743$	10.1934	0.373958	0.186979	−	0.982364i	$-0.440130\pi$
$743$	10.1934	0.373958	0.186979	+	0.982364i	$0.440130\pi$
$744$	19.9512	0.731448
$745$	−54.8066	−2.00796
$746$	39.9357	1.46215
$747$	3.64541	0.133379
$748$	14.9326	0.545991
$749$	−3.00656	−0.109857
$750$	−1.43860	−0.0525303
$751$	−7.07959	−0.258338	−0.129169	−	0.991623i	$-0.541231\pi$
$751$	−7.07959	−0.258338	−0.129169	+	0.991623i	$0.541231\pi$
$752$	−0.847675	−0.0309115
$753$	−44.5022	−1.62175
$754$	7.71951	0.281128
$755$	52.5236	1.91153
$756$	6.03669	0.219552
$757$	16.6890	0.606573	0.303286	−	0.952899i	$-0.401916\pi$
$757$	16.6890	0.606573	0.303286	+	0.952899i	$0.401916\pi$
$758$	6.58816	0.239293
$759$	−23.0417	−0.836360
$760$	−2.19333	−0.0795605
$761$	7.19340	0.260760	0.130380	−	0.991464i	$-0.458380\pi$
$761$	7.19340	0.260760	0.130380	+	0.991464i	$0.458380\pi$
$762$	67.8255	2.45706
$763$	5.39811	0.195425
$764$	−48.3045	−1.74759
$765$	−3.30559	−0.119514
$766$	53.1376	1.91994
$767$	−3.01007	−0.108687
$768$	−19.3139	−0.696930
$769$	19.1401	0.690209	0.345105	−	0.938564i	$-0.387843\pi$
$769$	19.1401	0.690209	0.345105	+	0.938564i	$0.387843\pi$
$770$	5.03470	0.181438
$771$	17.4011	0.626686
$772$	62.0805	2.23433
$773$	3.07113	0.110461	0.0552304	−	0.998474i	$-0.482411\pi$
$773$	3.07113	0.110461	0.0552304	+	0.998474i	$0.482411\pi$
$774$	7.06564	0.253969
$775$	−24.3945	−0.876277
$776$	36.6725	1.31647
$777$	−5.96384	−0.213951
$778$	33.4014	1.19750
$779$	−1.50038	−0.0537566
$780$	53.3197	1.90915
$781$	−30.2380	−1.08200
$782$	38.8896	1.39069
$783$	−5.50321	−0.196669
$784$	3.98479	0.142314
$785$	−10.5910	−0.378009
$786$	2.92622	0.104375
$787$	2.28812	0.0815625	0.0407812	−	0.999168i	$-0.487015\pi$
$787$	2.28812	0.0815625	0.0407812	+	0.999168i	$0.487015\pi$
$788$	−28.0777	−1.00023
$789$	−13.9642	−0.497137
$790$	40.0285	1.42415
$791$	−1.78515	−0.0634725
$792$	−2.19078	−0.0778459
$793$	4.15182	0.147435
$794$	50.7361	1.80056
$795$	−52.3174	−1.85551
$796$	63.9548	2.26682
$797$	−47.4083	−1.67929	−0.839643	−	0.543138i	$-0.817236\pi$
$797$	−47.4083	−1.67929	−0.839643	+	0.543138i	$0.817236\pi$
$798$	−0.358283	−0.0126831
$799$	−3.50872	−0.124130
$800$	30.6531	1.08375
$801$	1.26366	0.0446493
$802$	−82.0932	−2.89881
$803$	−1.08382	−0.0382473
$804$	72.6284	2.56141
$805$	7.97256	0.280996
$806$	−38.6415	−1.36109
$807$	−4.90634	−0.172711
$808$	10.3761	0.365029
$809$	−16.9051	−0.594351	−0.297175	−	0.954823i	$-0.596045\pi$
$809$	−16.9051	−0.594351	−0.297175	+	0.954823i	$0.596045\pi$
$810$	−53.1783	−1.86850
$811$	−11.7746	−0.413462	−0.206731	−	0.978398i	$-0.566282\pi$
$811$	−11.7746	−0.413462	−0.206731	+	0.978398i	$0.566282\pi$
$812$	−1.09694	−0.0384951
$813$	−32.9464	−1.15548
$814$	47.7606	1.67401
$815$	51.3596	1.79905
$816$	2.22553	0.0779091
$817$	−1.99945	−0.0699518
$818$	−41.4163	−1.44809
$819$	−0.529832	−0.0185138
$820$	−52.1829	−1.82231
$821$	−14.8630	−0.518723	−0.259361	−	0.965780i	$-0.583512\pi$
$821$	−14.8630	−0.518723	−0.259361	+	0.965780i	$0.583512\pi$
$822$	−37.2435	−1.29901
$823$	30.2863	1.05571	0.527857	−	0.849333i	$-0.322996\pi$
$823$	30.2863	1.05571	0.527857	+	0.849333i	$0.322996\pi$
$824$	−0.928535	−0.0323470
$825$	−15.6477	−0.544785
$826$	0.703465	0.0244767
$827$	−9.96894	−0.346654	−0.173327	−	0.984864i	$-0.555452\pi$
$827$	−9.96894	−0.346654	−0.173327	+	0.984864i	$0.555452\pi$
$828$	−9.76254	−0.339272
$829$	−13.8695	−0.481709	−0.240854	−	0.970561i	$-0.577428\pi$
$829$	−13.8695	−0.481709	−0.240854	+	0.970561i	$0.577428\pi$
$830$	−59.0073	−2.04817
$831$	1.60047	0.0555197
$832$	44.5937	1.54601
$833$	16.4939	0.571481
$834$	15.8927	0.550318
$835$	13.1015	0.453394
$836$	1.74460	0.0603384
$837$	27.5473	0.952175
$838$	−24.8273	−0.857645
$839$	45.9752	1.58724	0.793620	−	0.608413i	$-0.208194\pi$
$839$	45.9752	1.58724	0.793620	+	0.608413i	$0.208194\pi$
$840$	−4.42806	−0.152783
$841$	1.00000	0.0344828
$842$	5.39355	0.185874
$843$	39.0858	1.34618
$844$	−4.20999	−0.144914
$845$	4.15139	0.142812
$846$	1.44861	0.0498041
$847$	2.46620	0.0847395
$848$	−6.02974	−0.207062
$849$	4.82301	0.165525
$850$	26.4102	0.905862
$851$	75.6300	2.59256
$852$	74.8399	2.56397
$853$	−27.9033	−0.955392	−0.477696	−	0.878525i	$-0.658528\pi$
$853$	−27.9033	−0.955392	−0.477696	+	0.878525i	$0.658528\pi$
$854$	−0.970296	−0.0332028
$855$	−0.386198	−0.0132077
$856$	−21.1765	−0.723796
$857$	−46.4967	−1.58830	−0.794149	−	0.607724i	$-0.792083\pi$
$857$	−46.4967	−1.58830	−0.794149	+	0.607724i	$0.792083\pi$
$858$	−24.7864	−0.846193
$859$	−41.2104	−1.40608	−0.703040	−	0.711150i	$-0.748174\pi$
$859$	−41.2104	−1.40608	−0.703040	+	0.711150i	$0.748174\pi$
$860$	−69.5405	−2.37131
$861$	−3.02908	−0.103231
$862$	−22.0349	−0.750512
$863$	−52.3210	−1.78103	−0.890514	−	0.454956i	$-0.849655\pi$
$863$	−52.3210	−1.78103	−0.890514	+	0.454956i	$0.849655\pi$
$864$	−34.6148	−1.17762
$865$	−6.29570	−0.214060
$866$	−55.5310	−1.88702
$867$	−17.9960	−0.611177
$868$	5.49094	0.186375
$869$	−11.3141	−0.383806
$870$	11.3598	0.385133
$871$	−49.9862	−1.69372
$872$	38.0212	1.28756
$873$	6.45723	0.218544
$874$	4.54354	0.153687
$875$	−0.140695	−0.00475635
$876$	2.68249	0.0906330
$877$	−14.4338	−0.487395	−0.243697	−	0.969851i	$-0.578360\pi$
$877$	−14.4338	−0.487395	−0.243697	+	0.969851i	$0.578360\pi$
$878$	2.95128	0.0996008
$879$	11.0492	0.372682
$880$	−3.65377	−0.123169
$881$	3.93080	0.132432	0.0662160	−	0.997805i	$-0.478907\pi$
$881$	3.93080	0.132432	0.0662160	+	0.997805i	$0.478907\pi$
$882$	−6.80968	−0.229294
$883$	4.92723	0.165814	0.0829072	−	0.996557i	$-0.473579\pi$
$883$	4.92723	0.165814	0.0829072	+	0.996557i	$0.473579\pi$
$884$	25.4367	0.855528
$885$	−4.42953	−0.148897
$886$	−68.1415	−2.28926
$887$	−56.1141	−1.88413	−0.942064	−	0.335434i	$-0.891117\pi$
$887$	−56.1141	−1.88413	−0.942064	+	0.335434i	$0.891117\pi$
$888$	−42.0058	−1.40962
$889$	6.63330	0.222474
$890$	−20.4545	−0.685638
$891$	15.0310	0.503557
$892$	73.5233	2.46174
$893$	−0.409930	−0.0137178
$894$	−63.0577	−2.10897
$895$	67.1799	2.24558
$896$	−5.97385	−0.199572
$897$	−39.2498	−1.31051
$898$	−11.5494	−0.385409
$899$	−5.00569	−0.166949
$900$	−6.62980	−0.220993
$901$	−24.9585	−0.831488
$902$	24.2579	0.807701
$903$	−4.03664	−0.134331
$904$	−12.5735	−0.418189
$905$	12.0704	0.401235
$906$	60.4311	2.00769
$907$	45.4169	1.50804	0.754022	−	0.656849i	$-0.228111\pi$
$907$	45.4169	1.50804	0.754022	+	0.656849i	$0.228111\pi$
$908$	−57.1666	−1.89714
$909$	1.82700	0.0605978
$910$	8.57625	0.284300
$911$	59.4352	1.96918	0.984588	−	0.174888i	$-0.0559564\pi$
$911$	59.4352	1.96918	0.984588	+	0.174888i	$0.0559564\pi$
$912$	0.260012	0.00860987
$913$	16.6785	0.551979
$914$	−14.3883	−0.475922
$915$	6.10969	0.201980
$916$	−17.2871	−0.571182
$917$	0.286183	0.00945059
$918$	−29.8235	−0.984323
$919$	−42.7595	−1.41050	−0.705252	−	0.708956i	$-0.749166\pi$
$919$	−42.7595	−1.41050	−0.705252	+	0.708956i	$0.749166\pi$
$920$	56.1541	1.85135
$921$	14.5283	0.478723
$922$	−59.3039	−1.95307
$923$	−51.5083	−1.69542
$924$	3.52214	0.115870
$925$	51.3608	1.68873
$926$	−34.1409	−1.12194
$927$	−0.163495	−0.00536987
$928$	6.28993	0.206477
$929$	−10.7441	−0.352501	−0.176251	−	0.984345i	$-0.556397\pi$
$929$	−10.7441	−0.352501	−0.176251	+	0.984345i	$0.556397\pi$
$930$	−56.8636	−1.86463
$931$	1.92702	0.0631554
$932$	−82.5428	−2.70378
$933$	−0.737469	−0.0241437
$934$	−80.6083	−2.63758
$935$	−15.1238	−0.494601
$936$	−3.73183	−0.121979
$937$	−29.1116	−0.951035	−0.475518	−	0.879706i	$-0.657739\pi$
$937$	−29.1116	−0.951035	−0.475518	+	0.879706i	$0.657739\pi$
$938$	11.6820	0.381430
$939$	21.1121	0.688966
$940$	−14.2573	−0.465021
$941$	19.0197	0.620025	0.310013	−	0.950732i	$-0.399667\pi$
$941$	19.0197	0.620025	0.310013	+	0.950732i	$0.399667\pi$
$942$	−12.1855	−0.397024
$943$	38.4130	1.25090
$944$	−0.510517	−0.0166159
$945$	−6.11397	−0.198887
$946$	32.3268	1.05104
$947$	−24.1649	−0.785253	−0.392626	−	0.919698i	$-0.628433\pi$
$947$	−24.1649	−0.785253	−0.392626	+	0.919698i	$0.628433\pi$
$948$	28.0028	0.909489
$949$	−1.84621	−0.0599307
$950$	3.08555	0.100108
$951$	−19.8616	−0.644057
$952$	−2.11245	−0.0684648
$953$	−21.4483	−0.694778	−0.347389	−	0.937721i	$-0.612932\pi$
$953$	−21.4483	−0.694778	−0.347389	+	0.937721i	$0.612932\pi$
$954$	10.3043	0.333615
$955$	48.9228	1.58311
$956$	65.7260	2.12573
$957$	−3.21087	−0.103793
$958$	−92.5008	−2.98856
$959$	−3.64239	−0.117619
$960$	65.6227	2.11796
$961$	−5.94310	−0.191713
$962$	81.3567	2.62304
$963$	−3.72871	−0.120156
$964$	−54.2169	−1.74621
$965$	−62.8752	−2.02403
$966$	9.17284	0.295131
$967$	57.0486	1.83456	0.917280	−	0.398243i	$-0.130380\pi$
$967$	57.0486	1.83456	0.917280	+	0.398243i	$0.130380\pi$
$968$	17.3704	0.558307
$969$	1.07625	0.0345742
$970$	−104.521	−3.35598
$971$	−9.18868	−0.294879	−0.147439	−	0.989071i	$-0.547103\pi$
$971$	−9.18868	−0.294879	−0.147439	+	0.989071i	$0.547103\pi$
$972$	14.0186	0.449646
$973$	1.55429	0.0498284
$974$	64.5051	2.06688
$975$	−26.6548	−0.853637
$976$	0.704161	0.0225397
$977$	−60.2178	−1.92654	−0.963270	−	0.268536i	$-0.913460\pi$
$977$	−60.2178	−1.92654	−0.963270	+	0.268536i	$0.913460\pi$
$978$	59.0917	1.88955
$979$	5.78153	0.184778
$980$	67.0212	2.14092
$981$	6.69470	0.213745
$982$	−81.7911	−2.61006
$983$	44.8793	1.43143	0.715714	−	0.698393i	$-0.246101\pi$
$983$	44.8793	1.43143	0.715714	+	0.698393i	$0.246101\pi$
$984$	−21.3351	−0.680137
$985$	28.4371	0.906082
$986$	5.41930	0.172586
$987$	−0.827597	−0.0263427
$988$	2.97181	0.0945458
$989$	51.1903	1.62776
$990$	6.24400	0.198447
$991$	−23.0856	−0.733339	−0.366670	−	0.930351i	$-0.619502\pi$
$991$	−23.0856	−0.733339	−0.366670	+	0.930351i	$0.619502\pi$
$992$	−31.4854	−0.999663
$993$	32.6536	1.03623
$994$	12.0377	0.381812
$995$	−64.7735	−2.05346
$996$	−41.2799	−1.30800
$997$	−8.22901	−0.260616	−0.130308	−	0.991474i	$-0.541597\pi$
$997$	−8.22901	−0.260616	−0.130308	+	0.991474i	$0.541597\pi$
$998$	18.7621	0.593905
$999$	−57.9988	−1.83500

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.c.1.20	✓	154

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.c.1.20	✓	154	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:	\( N \)	\(=\)	\( 8033 = 29 \cdot 277 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.25887 q^{2} +1.60047 q^{3} +3.10247 q^{4} -3.14219 q^{5} -3.61525 q^{6} -0.353570 q^{7} -2.49034 q^{8} -0.438494 q^{9} +O(q^{10})\)	\(q-2.25887 q^{2} +1.60047 q^{3} +3.10247 q^{4} -3.14219 q^{5} -3.61525 q^{6} -0.353570 q^{7} -2.49034 q^{8} -0.438494 q^{9} +7.09779 q^{10} -2.00621 q^{11} +4.96542 q^{12} -3.41743 q^{13} +0.798666 q^{14} -5.02898 q^{15} -0.579606 q^{16} -2.39912 q^{17} +0.990500 q^{18} -0.280294 q^{19} -9.74856 q^{20} -0.565878 q^{21} +4.53175 q^{22} +7.17614 q^{23} -3.98571 q^{24} +4.87336 q^{25} +7.71951 q^{26} -5.50321 q^{27} -1.09694 q^{28} +1.00000 q^{29} +11.3598 q^{30} -5.00569 q^{31} +6.28993 q^{32} -3.21087 q^{33} +5.41930 q^{34} +1.11098 q^{35} -1.36042 q^{36} +10.5391 q^{37} +0.633145 q^{38} -5.46949 q^{39} +7.82512 q^{40} +5.35288 q^{41} +1.27824 q^{42} +7.13341 q^{43} -6.22420 q^{44} +1.37783 q^{45} -16.2099 q^{46} +1.46250 q^{47} -0.927643 q^{48} -6.87499 q^{49} -11.0083 q^{50} -3.83973 q^{51} -10.6025 q^{52} +10.4032 q^{53} +12.4310 q^{54} +6.30388 q^{55} +0.880508 q^{56} -0.448602 q^{57} -2.25887 q^{58} +0.880800 q^{59} -15.6023 q^{60} -1.21490 q^{61} +11.3072 q^{62} +0.155038 q^{63} -13.0489 q^{64} +10.7382 q^{65} +7.25293 q^{66} +14.6268 q^{67} -7.44322 q^{68} +11.4852 q^{69} -2.50956 q^{70} +15.0722 q^{71} +1.09200 q^{72} +0.540235 q^{73} -23.8064 q^{74} +7.79967 q^{75} -0.869603 q^{76} +0.709334 q^{77} +12.3549 q^{78} +5.63957 q^{79} +1.82123 q^{80} -7.49224 q^{81} -12.0914 q^{82} -8.31347 q^{83} -1.75562 q^{84} +7.53850 q^{85} -16.1134 q^{86} +1.60047 q^{87} +4.99613 q^{88} -2.88182 q^{89} -3.11234 q^{90} +1.20830 q^{91} +22.2638 q^{92} -8.01145 q^{93} -3.30359 q^{94} +0.880736 q^{95} +10.0668 q^{96} -14.7259 q^{97} +15.5297 q^{98} +0.879710 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9}+O(q^{10}) \) 154 * q - 12 * q^2 - 36 * q^3 + 142 * q^4 - 9 * q^5 - 11 * q^6 - 68 * q^7 - 33 * q^8 + 146 * q^9	\( 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9} - 40 q^{10} - 36 q^{11} - 67 q^{12} - 51 q^{13} - 19 q^{14} - 48 q^{15} + 122 q^{16} - 54 q^{17} - 46 q^{18} - 73 q^{19} - 21 q^{20} - 8 q^{21} - 23 q^{22} - 38 q^{23} - 17 q^{24} + 133 q^{25} - 20 q^{26} - 129 q^{27} - 99 q^{28} + 154 q^{29} - 10 q^{30} - 91 q^{31} - 88 q^{32} - 39 q^{33} - 42 q^{34} - 36 q^{35} + 101 q^{36} - 50 q^{37} - 17 q^{38} - 33 q^{39} - 92 q^{40} - 31 q^{41} - 62 q^{42} - 154 q^{43} - 42 q^{44} - 14 q^{45} - 24 q^{46} - 140 q^{47} - 118 q^{48} + 126 q^{49} - 5 q^{50} - 16 q^{51} - 133 q^{52} - 40 q^{53} + 14 q^{54} - 203 q^{55} - 44 q^{56} - 16 q^{57} - 12 q^{58} + 5 q^{59} - 28 q^{60} - 106 q^{61} - 30 q^{62} - 145 q^{63} + 111 q^{64} - 15 q^{65} - 49 q^{66} - 78 q^{67} - 118 q^{68} - 32 q^{69} - 43 q^{70} - 4 q^{71} - 152 q^{72} - 137 q^{73} + 9 q^{74} - 129 q^{75} - 204 q^{76} - 76 q^{77} + 15 q^{78} - 141 q^{79} - 44 q^{80} + 122 q^{81} - 71 q^{82} - 90 q^{83} + 92 q^{84} - 41 q^{85} + 9 q^{86} - 36 q^{87} - 109 q^{88} - 51 q^{89} - 82 q^{90} - 22 q^{91} - 8 q^{92} - 10 q^{93} - 106 q^{94} - 55 q^{95} - 49 q^{96} - 140 q^{97} - 4 q^{98} - 101 q^{99}+O(q^{100}) \) 154 * q - 12 * q^2 - 36 * q^3 + 142 * q^4 - 9 * q^5 - 11 * q^6 - 68 * q^7 - 33 * q^8 + 146 * q^9 - 40 * q^10 - 36 * q^11 - 67 * q^12 - 51 * q^13 - 19 * q^14 - 48 * q^15 + 122 * q^16 - 54 * q^17 - 46 * q^18 - 73 * q^19 - 21 * q^20 - 8 * q^21 - 23 * q^22 - 38 * q^23 - 17 * q^24 + 133 * q^25 - 20 * q^26 - 129 * q^27 - 99 * q^28 + 154 * q^29 - 10 * q^30 - 91 * q^31 - 88 * q^32 - 39 * q^33 - 42 * q^34 - 36 * q^35 + 101 * q^36 - 50 * q^37 - 17 * q^38 - 33 * q^39 - 92 * q^40 - 31 * q^41 - 62 * q^42 - 154 * q^43 - 42 * q^44 - 14 * q^45 - 24 * q^46 - 140 * q^47 - 118 * q^48 + 126 * q^49 - 5 * q^50 - 16 * q^51 - 133 * q^52 - 40 * q^53 + 14 * q^54 - 203 * q^55 - 44 * q^56 - 16 * q^57 - 12 * q^58 + 5 * q^59 - 28 * q^60 - 106 * q^61 - 30 * q^62 - 145 * q^63 + 111 * q^64 - 15 * q^65 - 49 * q^66 - 78 * q^67 - 118 * q^68 - 32 * q^69 - 43 * q^70 - 4 * q^71 - 152 * q^72 - 137 * q^73 + 9 * q^74 - 129 * q^75 - 204 * q^76 - 76 * q^77 + 15 * q^78 - 141 * q^79 - 44 * q^80 + 122 * q^81 - 71 * q^82 - 90 * q^83 + 92 * q^84 - 41 * q^85 + 9 * q^86 - 36 * q^87 - 109 * q^88 - 51 * q^89 - 82 * q^90 - 22 * q^91 - 8 * q^92 - 10 * q^93 - 106 * q^94 - 55 * q^95 - 49 * q^96 - 140 * q^97 - 4 * q^98 - 101 * q^99

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