LMFDB - Embedded newform 8027.2.a.c.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0959177025$
Analytic rank:	$1$
Dimension:	$143$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.32772 q^{2} -2.91674 q^{3} +3.41827 q^{4} +2.71745 q^{5} +6.78934 q^{6} +4.37081 q^{7} -3.30132 q^{8} +5.50736 q^{9} +O(q^{10})$	\(q-2.32772 q^{2} -2.91674 q^{3} +3.41827 q^{4} +2.71745 q^{5} +6.78934 q^{6} +4.37081 q^{7} -3.30132 q^{8} +5.50736 q^{9} -6.32547 q^{10} -0.0600616 q^{11} -9.97018 q^{12} -1.97070 q^{13} -10.1740 q^{14} -7.92610 q^{15} +0.848008 q^{16} +2.62750 q^{17} -12.8196 q^{18} +0.106966 q^{19} +9.28898 q^{20} -12.7485 q^{21} +0.139807 q^{22} +1.00000 q^{23} +9.62909 q^{24} +2.38456 q^{25} +4.58722 q^{26} -7.31331 q^{27} +14.9406 q^{28} -8.98929 q^{29} +18.4497 q^{30} -4.17617 q^{31} +4.62872 q^{32} +0.175184 q^{33} -6.11609 q^{34} +11.8775 q^{35} +18.8256 q^{36} -1.23336 q^{37} -0.248987 q^{38} +5.74800 q^{39} -8.97119 q^{40} +8.97205 q^{41} +29.6749 q^{42} +2.90972 q^{43} -0.205307 q^{44} +14.9660 q^{45} -2.32772 q^{46} -2.43858 q^{47} -2.47342 q^{48} +12.1040 q^{49} -5.55058 q^{50} -7.66374 q^{51} -6.73636 q^{52} -11.1113 q^{53} +17.0233 q^{54} -0.163215 q^{55} -14.4294 q^{56} -0.311993 q^{57} +20.9245 q^{58} -2.96009 q^{59} -27.0935 q^{60} +3.40460 q^{61} +9.72094 q^{62} +24.0716 q^{63} -12.4704 q^{64} -5.35528 q^{65} -0.407779 q^{66} -3.67301 q^{67} +8.98151 q^{68} -2.91674 q^{69} -27.6474 q^{70} +7.37634 q^{71} -18.1816 q^{72} +6.10555 q^{73} +2.87092 q^{74} -6.95514 q^{75} +0.365639 q^{76} -0.262518 q^{77} -13.3797 q^{78} -7.83603 q^{79} +2.30442 q^{80} +4.80894 q^{81} -20.8844 q^{82} -8.56211 q^{83} -43.5778 q^{84} +7.14012 q^{85} -6.77300 q^{86} +26.2194 q^{87} +0.198283 q^{88} +2.03574 q^{89} -34.8366 q^{90} -8.61353 q^{91} +3.41827 q^{92} +12.1808 q^{93} +5.67631 q^{94} +0.290676 q^{95} -13.5008 q^{96} -14.3612 q^{97} -28.1746 q^{98} -0.330781 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) $ 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9 - 22 * q^10 - 14 * q^11 - 36 * q^12 - 87 * q^13 - 18 * q^14 - 19 * q^15 + 81 * q^16 - 14 * q^17 - 60 * q^18 - 18 * q^19 - 25 * q^20 - 26 * q^21 - 62 * q^22 + 143 * q^23 - 21 * q^24 + 67 * q^25 - 5 * q^26 - 47 * q^27 - 76 * q^28 - 54 * q^29 - 22 * q^30 - 62 * q^31 - 117 * q^32 - 59 * q^33 - 35 * q^34 - 52 * q^35 + 52 * q^36 - 190 * q^37 - 19 * q^38 - 43 * q^39 - 41 * q^40 - 50 * q^41 + 8 * q^42 - 50 * q^43 - 18 * q^44 - 75 * q^45 - 17 * q^46 - 63 * q^47 - 35 * q^48 + 74 * q^49 - 53 * q^50 - 33 * q^51 - 124 * q^52 - 100 * q^53 - 46 * q^54 - 61 * q^55 - 3 * q^56 - 80 * q^57 - 112 * q^58 - 109 * q^59 - 55 * q^60 - 76 * q^61 - 6 * q^62 - 93 * q^63 + 57 * q^64 - 17 * q^65 + 50 * q^66 - 120 * q^67 + 26 * q^68 - 17 * q^69 - 109 * q^71 - 153 * q^72 - 94 * q^73 + 35 * q^74 - 105 * q^75 - 16 * q^76 - 52 * q^77 - 59 * q^78 - 29 * q^79 - 30 * q^80 + 39 * q^81 - 65 * q^82 + 8 * q^83 + 11 * q^84 - 155 * q^85 - 15 * q^86 - 25 * q^87 - 139 * q^88 + 6 * q^89 + 82 * q^90 - 34 * q^91 + 121 * q^92 - 151 * q^93 - 3 * q^94 - 70 * q^95 - 23 * q^96 - 203 * q^97 - 18 * q^98 - 49 * 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 $

$2$	−2.32772	−1.64594	−0.822972	−	0.568082i	$-0.807686\pi$
$2$	−2.32772	−1.64594	−0.822972	+	0.568082i	$0.807686\pi$
$3$	−2.91674	−1.68398	−0.841990	−	0.539494i	$-0.818616\pi$
$3$	−2.91674	−1.68398	−0.841990	+	0.539494i	$0.818616\pi$
$4$	3.41827	1.70913
$5$	2.71745	1.21528	0.607641	−	0.794212i	$-0.292116\pi$
$5$	2.71745	1.21528	0.607641	+	0.794212i	$0.292116\pi$
$6$	6.78934	2.77174
$7$	4.37081	1.65201	0.826005	−	0.563662i	$-0.190608\pi$
$7$	4.37081	1.65201	0.826005	+	0.563662i	$0.190608\pi$
$8$	−3.30132	−1.16719
$9$	5.50736	1.83579
$10$	−6.32547	−2.00029
$11$	−0.0600616	−0.0181093	−0.00905463	−	0.999959i	$-0.502882\pi$
$11$	−0.0600616	−0.0181093	−0.00905463	+	0.999959i	$0.502882\pi$
$12$	−9.97018	−2.87814
$13$	−1.97070	−0.546573	−0.273286	−	0.961933i	$-0.588111\pi$
$13$	−1.97070	−0.546573	−0.273286	+	0.961933i	$0.588111\pi$
$14$	−10.1740	−2.71912
$15$	−7.92610	−2.04651
$16$	0.848008	0.212002
$17$	2.62750	0.637263	0.318632	−	0.947879i	$-0.396777\pi$
$17$	2.62750	0.637263	0.318632	+	0.947879i	$0.396777\pi$
$18$	−12.8196	−3.02160
$19$	0.106966	0.0245398	0.0122699	−	0.999925i	$-0.496094\pi$
$19$	0.106966	0.0245398	0.0122699	+	0.999925i	$0.496094\pi$
$20$	9.28898	2.07708
$21$	−12.7485	−2.78195
$22$	0.139807	0.0298068
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	9.62909	1.96553
$25$	2.38456	0.476912
$26$	4.58722	0.899628
$27$	−7.31331	−1.40745
$28$	14.9406	2.82351
$29$	−8.98929	−1.66927	−0.834635	−	0.550803i	$-0.814321\pi$
$29$	−8.98929	−1.66927	−0.834635	+	0.550803i	$0.814321\pi$
$30$	18.4497	3.36844
$31$	−4.17617	−0.750062	−0.375031	−	0.927012i	$-0.622368\pi$
$31$	−4.17617	−0.750062	−0.375031	+	0.927012i	$0.622368\pi$
$32$	4.62872	0.818250
$33$	0.175184	0.0304956
$34$	−6.11609	−1.04890
$35$	11.8775	2.00766
$36$	18.8256	3.13760
$37$	−1.23336	−0.202764	−0.101382	−	0.994848i	$-0.532326\pi$
$37$	−1.23336	−0.202764	−0.101382	+	0.994848i	$0.532326\pi$
$38$	−0.248987	−0.0403911
$39$	5.74800	0.920417
$40$	−8.97119	−1.41847
$41$	8.97205	1.40120	0.700599	−	0.713555i	$-0.252916\pi$
$41$	8.97205	1.40120	0.700599	+	0.713555i	$0.252916\pi$
$42$	29.6749	4.57894
$43$	2.90972	0.443728	0.221864	−	0.975078i	$-0.428786\pi$
$43$	2.90972	0.443728	0.221864	+	0.975078i	$0.428786\pi$
$44$	−0.205307	−0.0309511
$45$	14.9660	2.23100
$46$	−2.32772	−0.343203
$47$	−2.43858	−0.355703	−0.177851	−	0.984057i	$-0.556915\pi$
$47$	−2.43858	−0.355703	−0.177851	+	0.984057i	$0.556915\pi$
$48$	−2.47342	−0.357007
$49$	12.1040	1.72914
$50$	−5.55058	−0.784971
$51$	−7.66374	−1.07314
$52$	−6.73636	−0.934165
$53$	−11.1113	−1.52626	−0.763129	−	0.646246i	$-0.776338\pi$
$53$	−11.1113	−1.52626	−0.763129	+	0.646246i	$0.776338\pi$
$54$	17.0233	2.31658
$55$	−0.163215	−0.0220079
$56$	−14.4294	−1.92822
$57$	−0.311993	−0.0413245
$58$	20.9245	2.74753
$59$	−2.96009	−0.385371	−0.192686	−	0.981261i	$-0.561720\pi$
$59$	−2.96009	−0.385371	−0.192686	+	0.981261i	$0.561720\pi$
$60$	−27.0935	−3.49776
$61$	3.40460	0.435914	0.217957	−	0.975958i	$-0.430061\pi$
$61$	3.40460	0.435914	0.217957	+	0.975958i	$0.430061\pi$
$62$	9.72094	1.23456
$63$	24.0716	3.03274
$64$	−12.4704	−1.55880
$65$	−5.35528	−0.664240
$66$	−0.407779	−0.0501941
$67$	−3.67301	−0.448730	−0.224365	−	0.974505i	$-0.572031\pi$
$67$	−3.67301	−0.448730	−0.224365	+	0.974505i	$0.572031\pi$
$68$	8.98151	1.08917
$69$	−2.91674	−0.351134
$70$	−27.6474	−3.30450
$71$	7.37634	0.875411	0.437705	−	0.899118i	$-0.355791\pi$
$71$	7.37634	0.875411	0.437705	+	0.899118i	$0.355791\pi$
$72$	−18.1816	−2.14272
$73$	6.10555	0.714601	0.357300	−	0.933989i	$-0.383697\pi$
$73$	6.10555	0.714601	0.357300	+	0.933989i	$0.383697\pi$
$74$	2.87092	0.333738
$75$	−6.95514	−0.803111
$76$	0.365639	0.0419417
$77$	−0.262518	−0.0299167
$78$	−13.3797	−1.51496
$79$	−7.83603	−0.881622	−0.440811	−	0.897600i	$-0.645309\pi$
$79$	−7.83603	−0.881622	−0.440811	+	0.897600i	$0.645309\pi$
$80$	2.30442	0.257642
$81$	4.80894	0.534326
$82$	−20.8844	−2.30630
$83$	−8.56211	−0.939814	−0.469907	−	0.882716i	$-0.655712\pi$
$83$	−8.56211	−0.939814	−0.469907	+	0.882716i	$0.655712\pi$
$84$	−43.5778	−4.75473
$85$	7.14012	0.774455
$86$	−6.77300	−0.730352
$87$	26.2194	2.81102
$88$	0.198283	0.0211370
$89$	2.03574	0.215788	0.107894	−	0.994162i	$-0.465589\pi$
$89$	2.03574	0.215788	0.107894	+	0.994162i	$0.465589\pi$
$90$	−34.8366	−3.67210
$91$	−8.61353	−0.902944
$92$	3.41827	0.356379
$93$	12.1808	1.26309
$94$	5.67631	0.585467
$95$	0.290676	0.0298227
$96$	−13.5008	−1.37792
$97$	−14.3612	−1.45816	−0.729078	−	0.684430i	$-0.760051\pi$
$97$	−14.3612	−1.45816	−0.729078	+	0.684430i	$0.760051\pi$
$98$	−28.1746	−2.84607
$99$	−0.330781	−0.0332448
$100$	8.15106	0.815106
$101$	−9.32843	−0.928213	−0.464107	−	0.885779i	$-0.653625\pi$
$101$	−9.32843	−0.928213	−0.464107	+	0.885779i	$0.653625\pi$
$102$	17.8390	1.76633
$103$	−14.5472	−1.43338	−0.716689	−	0.697393i	$-0.754343\pi$
$103$	−14.5472	−1.43338	−0.716689	+	0.697393i	$0.754343\pi$
$104$	6.50590	0.637956
$105$	−34.6435	−3.38086
$106$	25.8640	2.51214
$107$	6.65475	0.643339	0.321670	−	0.946852i	$-0.395756\pi$
$107$	6.65475	0.643339	0.321670	+	0.946852i	$0.395756\pi$
$108$	−24.9988	−2.40552
$109$	−3.47798	−0.333130	−0.166565	−	0.986030i	$-0.553268\pi$
$109$	−3.47798	−0.333130	−0.166565	+	0.986030i	$0.553268\pi$
$110$	0.379918	0.0362237
$111$	3.59740	0.341450
$112$	3.70648	0.350230
$113$	0.0241199	0.00226901	0.00113451	−	0.999999i	$-0.499639\pi$
$113$	0.0241199	0.00226901	0.00113451	+	0.999999i	$0.499639\pi$
$114$	0.726231	0.0680177
$115$	2.71745	0.253404
$116$	−30.7278	−2.85300
$117$	−10.8533	−1.00339
$118$	6.89026	0.634300
$119$	11.4843	1.05277
$120$	26.1666	2.38867
$121$	−10.9964	−0.999672
$122$	−7.92495	−0.717491
$123$	−26.1691	−2.35959
$124$	−14.2753	−1.28196
$125$	−7.10734	−0.635699
$126$	−56.0319	−4.99172
$127$	−6.75766	−0.599646	−0.299823	−	0.953995i	$-0.596928\pi$
$127$	−6.75766	−0.599646	−0.299823	+	0.953995i	$0.596928\pi$
$128$	19.7700	1.74744
$129$	−8.48689	−0.747229
$130$	12.4656	1.09330
$131$	−2.54643	−0.222483	−0.111242	−	0.993793i	$-0.535483\pi$
$131$	−2.54643	−0.222483	−0.111242	+	0.993793i	$0.535483\pi$
$132$	0.598826	0.0521211
$133$	0.467529	0.0405399
$134$	8.54974	0.738585
$135$	−19.8736	−1.71045
$136$	−8.67423	−0.743809
$137$	−11.6360	−0.994131	−0.497066	−	0.867713i	$-0.665589\pi$
$137$	−11.6360	−0.994131	−0.497066	+	0.867713i	$0.665589\pi$
$138$	6.78934	0.577947
$139$	−8.29601	−0.703658	−0.351829	−	0.936064i	$-0.614440\pi$
$139$	−8.29601	−0.703658	−0.351829	+	0.936064i	$0.614440\pi$
$140$	40.6004	3.43136
$141$	7.11269	0.598996
$142$	−17.1700	−1.44088
$143$	0.118363	0.00989803
$144$	4.67029	0.389190
$145$	−24.4280	−2.02864
$146$	−14.2120	−1.17619
$147$	−35.3041	−2.91183
$148$	−4.21596	−0.346550
$149$	−12.4305	−1.01835	−0.509174	−	0.860663i	$-0.670049\pi$
$149$	−12.4305	−1.01835	−0.509174	+	0.860663i	$0.670049\pi$
$150$	16.1896	1.32188
$151$	9.30022	0.756842	0.378421	−	0.925634i	$-0.376467\pi$
$151$	9.30022	0.756842	0.378421	+	0.925634i	$0.376467\pi$
$152$	−0.353130	−0.0286426
$153$	14.4706	1.16988
$154$	0.611068	0.0492412
$155$	−11.3485	−0.911537
$156$	19.6482	1.57311
$157$	−8.95987	−0.715076	−0.357538	−	0.933899i	$-0.616384\pi$
$157$	−8.95987	−0.715076	−0.357538	+	0.933899i	$0.616384\pi$
$158$	18.2401	1.45110
$159$	32.4088	2.57019
$160$	12.5783	0.994405
$161$	4.37081	0.344468
$162$	−11.1938	−0.879471
$163$	4.64558	0.363870	0.181935	−	0.983311i	$-0.441764\pi$
$163$	4.64558	0.363870	0.181935	+	0.983311i	$0.441764\pi$
$164$	30.6688	2.39483
$165$	0.476055	0.0370608
$166$	19.9302	1.54688
$167$	−19.8734	−1.53785	−0.768925	−	0.639339i	$-0.779208\pi$
$167$	−19.8734	−1.53785	−0.768925	+	0.639339i	$0.779208\pi$
$168$	42.0869	3.24707
$169$	−9.11636	−0.701258
$170$	−16.6202	−1.27471
$171$	0.589102	0.0450498
$172$	9.94619	0.758390
$173$	−13.2922	−1.01059	−0.505295	−	0.862947i	$-0.668616\pi$
$173$	−13.2922	−1.01059	−0.505295	+	0.862947i	$0.668616\pi$
$174$	−61.0314	−4.62678
$175$	10.4225	0.787864
$176$	−0.0509328	−0.00383920
$177$	8.63382	0.648958
$178$	−4.73863	−0.355176
$179$	21.0586	1.57399	0.786997	−	0.616957i	$-0.211635\pi$
$179$	21.0586	1.57399	0.786997	+	0.616957i	$0.211635\pi$
$180$	51.1578	3.81308
$181$	20.1539	1.49803	0.749015	−	0.662554i	$-0.230527\pi$
$181$	20.1539	1.49803	0.749015	+	0.662554i	$0.230527\pi$
$182$	20.0499	1.48620
$183$	−9.93033	−0.734071
$184$	−3.30132	−0.243377
$185$	−3.35161	−0.246415
$186$	−28.3534	−2.07897
$187$	−0.157812	−0.0115404
$188$	−8.33570	−0.607943
$189$	−31.9651	−2.32512
$190$	−0.676612	−0.0490866
$191$	7.46425	0.540094	0.270047	−	0.962847i	$-0.412961\pi$
$191$	7.46425	0.540094	0.270047	+	0.962847i	$0.412961\pi$
$192$	36.3728	2.62498
$193$	−3.57801	−0.257550	−0.128775	−	0.991674i	$-0.541105\pi$
$193$	−3.57801	−0.257550	−0.128775	+	0.991674i	$0.541105\pi$
$194$	33.4287	2.40004
$195$	15.6199	1.11857
$196$	41.3746	2.95533
$197$	17.7144	1.26210	0.631051	−	0.775742i	$-0.282624\pi$
$197$	17.7144	1.26210	0.631051	+	0.775742i	$0.282624\pi$
$198$	0.769965	0.0547190
$199$	0.365993	0.0259445	0.0129723	−	0.999916i	$-0.495871\pi$
$199$	0.365993	0.0259445	0.0129723	+	0.999916i	$0.495871\pi$
$200$	−7.87220	−0.556649
$201$	10.7132	0.755652
$202$	21.7139	1.52779
$203$	−39.2905	−2.75765
$204$	−26.1967	−1.83414
$205$	24.3811	1.70285
$206$	33.8618	2.35926
$207$	5.50736	0.382788
$208$	−1.67117	−0.115874
$209$	−0.00642457	−0.000444397 0
$210$	80.6402	5.56470
$211$	−13.9127	−0.957787	−0.478894	−	0.877873i	$-0.658962\pi$
$211$	−13.9127	−0.957787	−0.478894	+	0.877873i	$0.658962\pi$
$212$	−37.9815	−2.60858
$213$	−21.5149	−1.47417
$214$	−15.4904	−1.05890
$215$	7.90703	0.539255
$216$	24.1436	1.64276
$217$	−18.2532	−1.23911
$218$	8.09575	0.548314
$219$	−17.8083	−1.20337
$220$	−0.557912	−0.0376144
$221$	−5.17801	−0.348311
$222$	−8.37372	−0.562007
$223$	−1.01412	−0.0679104	−0.0339552	−	0.999423i	$-0.510810\pi$
$223$	−1.01412	−0.0679104	−0.0339552	+	0.999423i	$0.510810\pi$
$224$	20.2312	1.35176
$225$	13.1326	0.875509
$226$	−0.0561444	−0.00373467
$227$	4.10996	0.272787	0.136394	−	0.990655i	$-0.456449\pi$
$227$	4.10996	0.272787	0.136394	+	0.990655i	$0.456449\pi$
$228$	−1.06647	−0.0706290
$229$	−5.47045	−0.361498	−0.180749	−	0.983529i	$-0.557852\pi$
$229$	−5.47045	−0.361498	−0.180749	+	0.983529i	$0.557852\pi$
$230$	−6.32547	−0.417089
$231$	0.765696	0.0503791
$232$	29.6765	1.94836
$233$	−19.8166	−1.29823	−0.649113	−	0.760692i	$-0.724860\pi$
$233$	−19.8166	−1.29823	−0.649113	+	0.760692i	$0.724860\pi$
$234$	25.2635	1.65153
$235$	−6.62672	−0.432280
$236$	−10.1184	−0.658651
$237$	22.8556	1.48463
$238$	−26.7322	−1.73279
$239$	5.44965	0.352509	0.176254	−	0.984345i	$-0.443602\pi$
$239$	5.44965	0.352509	0.176254	+	0.984345i	$0.443602\pi$
$240$	−6.72140	−0.433864
$241$	−16.6535	−1.07275	−0.536373	−	0.843981i	$-0.680206\pi$
$241$	−16.6535	−1.07275	−0.536373	+	0.843981i	$0.680206\pi$
$242$	25.5965	1.64540
$243$	7.91353	0.507653
$244$	11.6378	0.745036
$245$	32.8920	2.10139
$246$	60.9143	3.88375
$247$	−0.210798	−0.0134128
$248$	13.7869	0.875467
$249$	24.9734	1.58263
$250$	16.5439	1.04633
$251$	1.94039	0.122476	0.0612381	−	0.998123i	$-0.480495\pi$
$251$	1.94039	0.122476	0.0612381	+	0.998123i	$0.480495\pi$
$252$	82.2832	5.18335
$253$	−0.0600616	−0.00377604
$254$	15.7299	0.986983
$255$	−20.8259	−1.30417
$256$	−21.0783	−1.31739
$257$	−22.9532	−1.43178	−0.715892	−	0.698212i	$-0.753979\pi$
$257$	−22.9532	−1.43178	−0.715892	+	0.698212i	$0.753979\pi$
$258$	19.7551	1.22990
$259$	−5.39079	−0.334968
$260$	−18.3058	−1.13527
$261$	−49.5073	−3.06442
$262$	5.92738	0.366195
$263$	12.0580	0.743525	0.371763	−	0.928328i	$-0.378754\pi$
$263$	12.0580	0.743525	0.371763	+	0.928328i	$0.378754\pi$
$264$	−0.578339	−0.0355943
$265$	−30.1945	−1.85484
$266$	−1.08828	−0.0667265
$267$	−5.93773	−0.363383
$268$	−12.5553	−0.766939
$269$	15.3659	0.936876	0.468438	−	0.883496i	$-0.344817\pi$
$269$	15.3659	0.936876	0.468438	+	0.883496i	$0.344817\pi$
$270$	46.2601	2.81530
$271$	2.86678	0.174145	0.0870723	−	0.996202i	$-0.472249\pi$
$271$	2.86678	0.174145	0.0870723	+	0.996202i	$0.472249\pi$
$272$	2.22814	0.135101
$273$	25.1234	1.52054
$274$	27.0853	1.63629
$275$	−0.143221	−0.00863653
$276$	−9.97018	−0.600135
$277$	−22.6157	−1.35884	−0.679422	−	0.733748i	$-0.737769\pi$
$277$	−22.6157	−1.35884	−0.679422	+	0.733748i	$0.737769\pi$
$278$	19.3108	1.15818
$279$	−22.9997	−1.37695
$280$	−39.2114	−2.34333
$281$	24.9226	1.48676	0.743378	−	0.668871i	$-0.233222\pi$
$281$	24.9226	1.48676	0.743378	+	0.668871i	$0.233222\pi$
$282$	−16.5563	−0.985914
$283$	−19.9526	−1.18606	−0.593028	−	0.805182i	$-0.702068\pi$
$283$	−19.9526	−1.18606	−0.593028	+	0.805182i	$0.702068\pi$
$284$	25.2143	1.49619
$285$	−0.847826	−0.0502209
$286$	−0.275516	−0.0162916
$287$	39.2151	2.31480
$288$	25.4920	1.50213
$289$	−10.0962	−0.593895
$290$	56.8615	3.33902
$291$	41.8878	2.45551
$292$	20.8704	1.22135
$293$	−15.4969	−0.905341	−0.452670	−	0.891678i	$-0.649529\pi$
$293$	−15.4969	−0.905341	−0.452670	+	0.891678i	$0.649529\pi$
$294$	82.1780	4.79272
$295$	−8.04392	−0.468335
$296$	4.07173	0.236664
$297$	0.439250	0.0254878
$298$	28.9347	1.67614
$299$	−1.97070	−0.113968
$300$	−23.7745	−1.37262
$301$	12.7178	0.733043
$302$	−21.6483	−1.24572
$303$	27.2086	1.56309
$304$	0.0907083	0.00520248
$305$	9.25185	0.529759
$306$	−33.6835	−1.92556
$307$	2.73083	0.155857	0.0779285	−	0.996959i	$-0.475169\pi$
$307$	2.73083	0.155857	0.0779285	+	0.996959i	$0.475169\pi$
$308$	−0.897356	−0.0511316
$309$	42.4304	2.41378
$310$	26.4162	1.50034
$311$	29.2034	1.65597	0.827985	−	0.560750i	$-0.189487\pi$
$311$	29.2034	1.65597	0.827985	+	0.560750i	$0.189487\pi$
$312$	−18.9760	−1.07430
$313$	12.0707	0.682277	0.341139	−	0.940013i	$-0.389187\pi$
$313$	12.0707	0.682277	0.341139	+	0.940013i	$0.389187\pi$
$314$	20.8560	1.17697
$315$	65.4136	3.68564
$316$	−26.7856	−1.50681
$317$	1.89683	0.106536	0.0532682	−	0.998580i	$-0.483036\pi$
$317$	1.89683	0.106536	0.0532682	+	0.998580i	$0.483036\pi$
$318$	−75.4386	−4.23039
$319$	0.539912	0.0302293
$320$	−33.8876	−1.89438
$321$	−19.4102	−1.08337
$322$	−10.1740	−0.566975
$323$	0.281055	0.0156383
$324$	16.4382	0.913235
$325$	−4.69924	−0.260667
$326$	−10.8136	−0.598910
$327$	10.1444	0.560984
$328$	−29.6196	−1.63547
$329$	−10.6585	−0.587625
$330$	−1.10812	−0.0610001
$331$	−25.2015	−1.38520	−0.692600	−	0.721322i	$-0.743535\pi$
$331$	−25.2015	−1.38520	−0.692600	+	0.721322i	$0.743535\pi$
$332$	−29.2676	−1.60627
$333$	−6.79257	−0.372231
$334$	46.2596	2.53121
$335$	−9.98125	−0.545334
$336$	−10.8108	−0.589779
$337$	−13.9001	−0.757184	−0.378592	−	0.925564i	$-0.623592\pi$
$337$	−13.9001	−0.757184	−0.378592	+	0.925564i	$0.623592\pi$
$338$	21.2203	1.15423
$339$	−0.0703515	−0.00382097
$340$	24.4068	1.32365
$341$	0.250828	0.0135831
$342$	−1.37126	−0.0741494
$343$	22.3085	1.20455
$344$	−9.60592	−0.517916
$345$	−7.92610	−0.426727
$346$	30.9405	1.66337
$347$	17.0519	0.915395	0.457698	−	0.889108i	$-0.348674\pi$
$347$	17.0519	0.915395	0.457698	+	0.889108i	$0.348674\pi$
$348$	89.6249	4.80440
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	−24.2605	−1.29678
$351$	14.4123	0.769272
$352$	−0.278008	−0.0148179
$353$	19.0180	1.01223	0.506114	−	0.862467i	$-0.331082\pi$
$353$	19.0180	1.01223	0.506114	+	0.862467i	$0.331082\pi$
$354$	−20.0971	−1.06815
$355$	20.0449	1.06387
$356$	6.95871	0.368811
$357$	−33.4968	−1.77284
$358$	−49.0184	−2.59071
$359$	17.2128	0.908457	0.454229	−	0.890885i	$-0.349915\pi$
$359$	17.2128	0.908457	0.454229	+	0.890885i	$0.349915\pi$
$360$	−49.4076	−2.60401
$361$	−18.9886	−0.999398
$362$	−46.9126	−2.46567
$363$	32.0736	1.68343
$364$	−29.4433	−1.54325
$365$	16.5916	0.868442
$366$	23.1150	1.20824
$367$	29.5259	1.54124	0.770619	−	0.637296i	$-0.219947\pi$
$367$	29.5259	1.54124	0.770619	+	0.637296i	$0.219947\pi$
$368$	0.848008	0.0442055
$369$	49.4123	2.57230
$370$	7.80160	0.405586
$371$	−48.5655	−2.52140
$372$	41.6372	2.15879
$373$	−29.1893	−1.51137	−0.755683	−	0.654938i	$-0.772695\pi$
$373$	−29.1893	−1.51137	−0.755683	+	0.654938i	$0.772695\pi$
$374$	0.367342	0.0189948
$375$	20.7302	1.07050
$376$	8.05052	0.415174
$377$	17.7152	0.912377
$378$	74.4057	3.82702
$379$	13.7023	0.703842	0.351921	−	0.936030i	$-0.385529\pi$
$379$	13.7023	0.703842	0.351921	+	0.936030i	$0.385529\pi$
$380$	0.993608	0.0509710
$381$	19.7103	1.00979
$382$	−17.3747	−0.888965
$383$	−22.8644	−1.16832	−0.584158	−	0.811640i	$-0.698575\pi$
$383$	−22.8644	−1.16832	−0.584158	+	0.811640i	$0.698575\pi$
$384$	−57.6640	−2.94265
$385$	−0.713381	−0.0363573
$386$	8.32858	0.423914
$387$	16.0249	0.814590
$388$	−49.0903	−2.49218
$389$	−18.3965	−0.932741	−0.466371	−	0.884589i	$-0.654439\pi$
$389$	−18.3965	−0.932741	−0.466371	+	0.884589i	$0.654439\pi$
$390$	−36.3588	−1.84110
$391$	2.62750	0.132879
$392$	−39.9591	−2.01824
$393$	7.42728	0.374657
$394$	−41.2342	−2.07735
$395$	−21.2941	−1.07142
$396$	−1.13070	−0.0568197
$397$	2.41271	0.121090	0.0605452	−	0.998165i	$-0.480716\pi$
$397$	2.41271	0.121090	0.0605452	+	0.998165i	$0.480716\pi$
$398$	−0.851928	−0.0427033
$399$	−1.36366	−0.0682684
$400$	2.02213	0.101106
$401$	18.4063	0.919167	0.459584	−	0.888135i	$-0.347999\pi$
$401$	18.4063	0.919167	0.459584	+	0.888135i	$0.347999\pi$
$402$	−24.9373	−1.24376
$403$	8.22996	0.409963
$404$	−31.8870	−1.58644
$405$	13.0681	0.649358
$406$	91.4571	4.53894
$407$	0.0740778	0.00367190
$408$	25.3005	1.25256
$409$	16.1084	0.796509	0.398254	−	0.917275i	$-0.369616\pi$
$409$	16.1084	0.796509	0.398254	+	0.917275i	$0.369616\pi$
$410$	−56.7524	−2.80280
$411$	33.9392	1.67410
$412$	−49.7262	−2.44983
$413$	−12.9380	−0.636638
$414$	−12.8196	−0.630048
$415$	−23.2671	−1.14214
$416$	−9.12179	−0.447233
$417$	24.1973	1.18495
$418$	0.0149546	0.000731453 0
$419$	−10.4362	−0.509841	−0.254920	−	0.966962i	$-0.582049\pi$
$419$	−10.4362	−0.509841	−0.254920	+	0.966962i	$0.582049\pi$
$420$	−118.421	−5.77834
$421$	−7.36978	−0.359181	−0.179590	−	0.983741i	$-0.557477\pi$
$421$	−7.36978	−0.359181	−0.179590	+	0.983741i	$0.557477\pi$
$422$	32.3847	1.57646
$423$	−13.4301	−0.652995
$424$	36.6821	1.78144
$425$	6.26545	0.303919
$426$	50.0805	2.42641
$427$	14.8809	0.720135
$428$	22.7477	1.09955
$429$	−0.345234	−0.0166681
$430$	−18.4053	−0.887584
$431$	−23.9233	−1.15235	−0.576173	−	0.817328i	$-0.695455\pi$
$431$	−23.9233	−1.15235	−0.576173	+	0.817328i	$0.695455\pi$
$432$	−6.20175	−0.298382
$433$	−15.5706	−0.748276	−0.374138	−	0.927373i	$-0.622061\pi$
$433$	−15.5706	−0.748276	−0.374138	+	0.927373i	$0.622061\pi$
$434$	42.4884	2.03951
$435$	71.2501	3.41618
$436$	−11.8887	−0.569364
$437$	0.106966	0.00511689
$438$	41.4527	1.98069
$439$	−28.1077	−1.34151	−0.670753	−	0.741681i	$-0.734029\pi$
$439$	−28.1077	−1.34151	−0.670753	+	0.741681i	$0.734029\pi$
$440$	0.538824	0.0256874
$441$	66.6610	3.17433
$442$	12.0529	0.573300
$443$	−25.5766	−1.21518	−0.607590	−	0.794251i	$-0.707863\pi$
$443$	−25.5766	−1.21518	−0.607590	+	0.794251i	$0.707863\pi$
$444$	12.2969	0.583583
$445$	5.53204	0.262244
$446$	2.36058	0.111777
$447$	36.2566	1.71488
$448$	−54.5056	−2.57515
$449$	28.1416	1.32808	0.664041	−	0.747696i	$-0.268840\pi$
$449$	28.1416	1.32808	0.664041	+	0.747696i	$0.268840\pi$
$450$	−30.5691	−1.44104
$451$	−0.538876	−0.0253747
$452$	0.0824484	0.00387804
$453$	−27.1263	−1.27451
$454$	−9.56682	−0.448993
$455$	−23.4069	−1.09733
$456$	1.02999	0.0482336
$457$	−4.52354	−0.211602	−0.105801	−	0.994387i	$-0.533741\pi$
$457$	−4.52354	−0.211602	−0.105801	+	0.994387i	$0.533741\pi$
$458$	12.7337	0.595005
$459$	−19.2158	−0.896915
$460$	9.28898	0.433101
$461$	0.916092	0.0426667	0.0213333	−	0.999772i	$-0.493209\pi$
$461$	0.916092	0.0426667	0.0213333	+	0.999772i	$0.493209\pi$
$462$	−1.78232	−0.0829212
$463$	25.8161	1.19977	0.599887	−	0.800085i	$-0.295212\pi$
$463$	25.8161	1.19977	0.599887	+	0.800085i	$0.295212\pi$
$464$	−7.62299	−0.353889
$465$	33.1007	1.53501
$466$	46.1273	2.13681
$467$	13.1039	0.606375	0.303187	−	0.952931i	$-0.401949\pi$
$467$	13.1039	0.606375	0.303187	+	0.952931i	$0.401949\pi$
$468$	−37.0996	−1.71493
$469$	−16.0540	−0.741307
$470$	15.4251	0.711508
$471$	26.1336	1.20417
$472$	9.77222	0.449803
$473$	−0.174763	−0.00803559
$474$	−53.2015	−2.44362
$475$	0.255068	0.0117033
$476$	39.2565	1.79932
$477$	−61.1941	−2.80189
$478$	−12.6852	−0.580209
$479$	26.4002	1.20626	0.603129	−	0.797644i	$-0.293920\pi$
$479$	26.4002	1.20626	0.603129	+	0.797644i	$0.293920\pi$
$480$	−36.6877	−1.67456
$481$	2.43058	0.110825
$482$	38.7646	1.76568
$483$	−12.7485	−0.580077
$484$	−37.5886	−1.70857
$485$	−39.0258	−1.77207
$486$	−18.4205	−0.835569
$487$	14.7776	0.669635	0.334818	−	0.942283i	$-0.391325\pi$
$487$	14.7776	0.669635	0.334818	+	0.942283i	$0.391325\pi$
$488$	−11.2397	−0.508796
$489$	−13.5500	−0.612750
$490$	−76.5633	−3.45878
$491$	−24.2924	−1.09630	−0.548150	−	0.836380i	$-0.684668\pi$
$491$	−24.2924	−1.09630	−0.548150	+	0.836380i	$0.684668\pi$
$492$	−89.4530	−4.03285
$493$	−23.6194	−1.06376
$494$	0.490678	0.0220767
$495$	−0.898883	−0.0404018
$496$	−3.54142	−0.159015
$497$	32.2406	1.44619
$498$	−58.1311	−2.60492
$499$	−33.5458	−1.50172	−0.750859	−	0.660463i	$-0.770360\pi$
$499$	−33.5458	−1.50172	−0.750859	+	0.660463i	$0.770360\pi$
$500$	−24.2948	−1.08649
$501$	57.9655	2.58971
$502$	−4.51667	−0.201589
$503$	−26.4647	−1.18000	−0.590001	−	0.807402i	$-0.700873\pi$
$503$	−26.4647	−1.18000	−0.590001	+	0.807402i	$0.700873\pi$
$504$	−79.4681	−3.53979
$505$	−25.3496	−1.12804
$506$	0.139807	0.00621516
$507$	26.5900	1.18090
$508$	−23.0995	−1.02487
$509$	11.0354	0.489134	0.244567	−	0.969632i	$-0.421354\pi$
$509$	11.0354	0.489134	0.244567	+	0.969632i	$0.421354\pi$
$510$	48.4767	2.14659
$511$	26.6862	1.18053
$512$	9.52428	0.420918
$513$	−0.782278	−0.0345384
$514$	53.4286	2.35664
$515$	−39.5314	−1.74196
$516$	−29.0104	−1.27711
$517$	0.146465	0.00644152
$518$	12.5482	0.551338
$519$	38.7699	1.70181
$520$	17.6795	0.775297
$521$	14.8207	0.649307	0.324653	−	0.945833i	$-0.394752\pi$
$521$	14.8207	0.649307	0.324653	+	0.945833i	$0.394752\pi$
$522$	115.239	5.04387
$523$	−31.7768	−1.38950	−0.694751	−	0.719251i	$-0.744485\pi$
$523$	−31.7768	−1.38950	−0.694751	+	0.719251i	$0.744485\pi$
$524$	−8.70439	−0.380253
$525$	−30.3996	−1.32675
$526$	−28.0675	−1.22380
$527$	−10.9729	−0.477987
$528$	0.148558	0.00646514
$529$	1.00000	0.0434783
$530$	70.2843	3.05296
$531$	−16.3023	−0.707460
$532$	1.59814	0.0692882
$533$	−17.6812	−0.765857
$534$	13.8214	0.598108
$535$	18.0840	0.781839
$536$	12.1258	0.523755
$537$	−61.4224	−2.65057
$538$	−35.7675	−1.54205
$539$	−0.726985	−0.0313134
$540$	−67.9332	−2.92338
$541$	−16.6719	−0.716781	−0.358391	−	0.933572i	$-0.616674\pi$
$541$	−16.6719	−0.716781	−0.358391	+	0.933572i	$0.616674\pi$
$542$	−6.67306	−0.286632
$543$	−58.7837	−2.52265
$544$	12.1620	0.521440
$545$	−9.45125	−0.404847
$546$	−58.4802	−2.50272
$547$	12.1565	0.519776	0.259888	−	0.965639i	$-0.416314\pi$
$547$	12.1565	0.519776	0.259888	+	0.965639i	$0.416314\pi$
$548$	−39.7750	−1.69910
$549$	18.7504	0.800246
$550$	0.333377	0.0142153
$551$	−0.961552	−0.0409635
$552$	9.62909	0.409841
$553$	−34.2498	−1.45645
$554$	52.6429	2.23658
$555$	9.77576	0.414958
$556$	−28.3580	−1.20265
$557$	−10.1546	−0.430266	−0.215133	−	0.976585i	$-0.569018\pi$
$557$	−10.1546	−0.430266	−0.215133	+	0.976585i	$0.569018\pi$
$558$	53.5367	2.26639
$559$	−5.73417	−0.242530
$560$	10.0722	0.425628
$561$	0.460297	0.0194338
$562$	−58.0127	−2.44712
$563$	−2.01872	−0.0850791	−0.0425395	−	0.999095i	$-0.513545\pi$
$563$	−2.01872	−0.0850791	−0.0425395	+	0.999095i	$0.513545\pi$
$564$	24.3131	1.02376
$565$	0.0655449	0.00275749
$566$	46.4439	1.95218
$567$	21.0189	0.882713
$568$	−24.3517	−1.02177
$569$	34.8395	1.46055	0.730273	−	0.683155i	$-0.239393\pi$
$569$	34.8395	1.46055	0.730273	+	0.683155i	$0.239393\pi$
$570$	1.97350	0.0826608
$571$	−23.5742	−0.986550	−0.493275	−	0.869873i	$-0.664200\pi$
$571$	−23.5742	−0.986550	−0.493275	+	0.869873i	$0.664200\pi$
$572$	0.404597	0.0169170
$573$	−21.7713	−0.909507
$574$	−91.2817	−3.81002
$575$	2.38456	0.0994431
$576$	−68.6788	−2.86162
$577$	−39.3911	−1.63987	−0.819936	−	0.572455i	$-0.805991\pi$
$577$	−39.3911	−1.63987	−0.819936	+	0.572455i	$0.805991\pi$
$578$	23.5011	0.977519
$579$	10.4361	0.433710
$580$	−83.5014	−3.46721
$581$	−37.4233	−1.55258
$582$	−97.5029	−4.04162
$583$	0.667365	0.0276394
$584$	−20.1564	−0.834077
$585$	−29.4934	−1.21940
$586$	36.0725	1.49014
$587$	−15.2338	−0.628768	−0.314384	−	0.949296i	$-0.601798\pi$
$587$	−15.2338	−0.628768	−0.314384	+	0.949296i	$0.601798\pi$
$588$	−120.679	−4.97671
$589$	−0.446709	−0.0184063
$590$	18.7240	0.770854
$591$	−51.6684	−2.12535
$592$	−1.04590	−0.0429863
$593$	16.4355	0.674924	0.337462	−	0.941339i	$-0.390432\pi$
$593$	16.4355	0.674924	0.337462	+	0.941339i	$0.390432\pi$
$594$	−1.02245	−0.0419516
$595$	31.2081	1.27941
$596$	−42.4908	−1.74049
$597$	−1.06751	−0.0436901
$598$	4.58722	0.187585
$599$	6.14373	0.251026	0.125513	−	0.992092i	$-0.459942\pi$
$599$	6.14373	0.251026	0.125513	+	0.992092i	$0.459942\pi$
$600$	22.9611	0.937385
$601$	36.4852	1.48826	0.744131	−	0.668033i	$-0.232864\pi$
$601$	36.4852	1.48826	0.744131	+	0.668033i	$0.232864\pi$
$602$	−29.6035	−1.20655
$603$	−20.2286	−0.823773
$604$	31.7906	1.29354
$605$	−29.8822	−1.21488
$606$	−63.3339	−2.57276
$607$	−8.10620	−0.329021	−0.164510	−	0.986375i	$-0.552604\pi$
$607$	−8.10620	−0.329021	−0.164510	+	0.986375i	$0.552604\pi$
$608$	0.495117	0.0200796
$609$	114.600	4.64383
$610$	−21.5357	−0.871954
$611$	4.80569	0.194417
$612$	49.4644	1.99948
$613$	−10.4265	−0.421124	−0.210562	−	0.977581i	$-0.567529\pi$
$613$	−10.4265	−0.421124	−0.210562	+	0.977581i	$0.567529\pi$
$614$	−6.35661	−0.256532
$615$	−71.1134	−2.86757
$616$	0.866656	0.0349186
$617$	22.7424	0.915574	0.457787	−	0.889062i	$-0.348642\pi$
$617$	22.7424	0.915574	0.457787	+	0.889062i	$0.348642\pi$
$618$	−98.7659	−3.97295
$619$	14.0403	0.564327	0.282163	−	0.959366i	$-0.408948\pi$
$619$	14.0403	0.564327	0.282163	+	0.959366i	$0.408948\pi$
$620$	−38.7924	−1.55794
$621$	−7.31331	−0.293473
$622$	−67.9772	−2.72564
$623$	8.89785	0.356485
$624$	4.87435	0.195130
$625$	−31.2367	−1.24947
$626$	−28.0972	−1.12299
$627$	0.0187388	0.000748356 0
$628$	−30.6272	−1.22216
$629$	−3.24067	−0.129214
$630$	−152.264	−6.06635
$631$	37.4268	1.48994	0.744969	−	0.667099i	$-0.232464\pi$
$631$	37.4268	1.48994	0.744969	+	0.667099i	$0.232464\pi$
$632$	25.8692	1.02902
$633$	40.5796	1.61289
$634$	−4.41528	−0.175353
$635$	−18.3636	−0.728739
$636$	110.782	4.39279
$637$	−23.8532	−0.945100
$638$	−1.25676	−0.0497557
$639$	40.6242	1.60707
$640$	53.7242	2.12363
$641$	39.9701	1.57872	0.789362	−	0.613928i	$-0.210411\pi$
$641$	39.9701	1.57872	0.789362	+	0.613928i	$0.210411\pi$
$642$	45.1814	1.78317
$643$	−4.13956	−0.163248	−0.0816241	−	0.996663i	$-0.526011\pi$
$643$	−4.13956	−0.163248	−0.0816241	+	0.996663i	$0.526011\pi$
$644$	14.9406	0.588742
$645$	−23.0627	−0.908094
$646$	−0.654215	−0.0257398
$647$	−2.93387	−0.115342	−0.0576712	−	0.998336i	$-0.518367\pi$
$647$	−2.93387	−0.115342	−0.0576712	+	0.998336i	$0.518367\pi$
$648$	−15.8758	−0.623662
$649$	0.177788	0.00697879
$650$	10.9385	0.429044
$651$	53.2399	2.08664
$652$	15.8798	0.621903
$653$	−3.26616	−0.127815	−0.0639074	−	0.997956i	$-0.520356\pi$
$653$	−3.26616	−0.127815	−0.0639074	+	0.997956i	$0.520356\pi$
$654$	−23.6132	−0.923349
$655$	−6.91982	−0.270380
$656$	7.60837	0.297057
$657$	33.6255	1.31185
$658$	24.8101	0.967198
$659$	−6.40899	−0.249659	−0.124829	−	0.992178i	$-0.539838\pi$
$659$	−6.40899	−0.249659	−0.124829	+	0.992178i	$0.539838\pi$
$660$	1.62728	0.0633419
$661$	−5.26334	−0.204720	−0.102360	−	0.994747i	$-0.532639\pi$
$661$	−5.26334	−0.204720	−0.102360	+	0.994747i	$0.532639\pi$
$662$	58.6619	2.27996
$663$	15.1029	0.586548
$664$	28.2663	1.09694
$665$	1.27049	0.0492675
$666$	15.8112	0.612671
$667$	−8.98929	−0.348067
$668$	−67.9325	−2.62839
$669$	2.95792	0.114360
$670$	23.2335	0.897589
$671$	−0.204486	−0.00789409
$672$	−59.0092	−2.27633
$673$	−8.25517	−0.318213	−0.159107	−	0.987261i	$-0.550861\pi$
$673$	−8.25517	−0.318213	−0.159107	+	0.987261i	$0.550861\pi$
$674$	32.3554	1.24628
$675$	−17.4390	−0.671229
$676$	−31.1621	−1.19854
$677$	−4.28920	−0.164847	−0.0824236	−	0.996597i	$-0.526266\pi$
$677$	−4.28920	−0.164847	−0.0824236	+	0.996597i	$0.526266\pi$
$678$	0.163758	0.00628911
$679$	−62.7700	−2.40889
$680$	−23.5718	−0.903939
$681$	−11.9877	−0.459368
$682$	−0.583855	−0.0223570
$683$	−2.18400	−0.0835685	−0.0417842	−	0.999127i	$-0.513304\pi$
$683$	−2.18400	−0.0835685	−0.0417842	+	0.999127i	$0.513304\pi$
$684$	2.01371	0.0769960
$685$	−31.6203	−1.20815
$686$	−51.9279	−1.98262
$687$	15.9559	0.608755
$688$	2.46747	0.0940712
$689$	21.8971	0.834211
$690$	18.4497	0.702369
$691$	−14.4173	−0.548462	−0.274231	−	0.961664i	$-0.588423\pi$
$691$	−14.4173	−0.548462	−0.274231	+	0.961664i	$0.588423\pi$
$692$	−45.4364	−1.72723
$693$	−1.44578	−0.0549207
$694$	−39.6921	−1.50669
$695$	−22.5440	−0.855144
$696$	−86.5587	−3.28100
$697$	23.5741	0.892933
$698$	−2.32772	−0.0881054
$699$	57.7997	2.18619
$700$	35.6267	1.34656
$701$	−0.573012	−0.0216424	−0.0108212	−	0.999941i	$-0.503445\pi$
$701$	−0.573012	−0.0216424	−0.0108212	+	0.999941i	$0.503445\pi$
$702$	−33.5478	−1.26618
$703$	−0.131928	−0.00497577
$704$	0.748990	0.0282286
$705$	19.3284	0.727950
$706$	−44.2686	−1.66607
$707$	−40.7728	−1.53342
$708$	29.5127	1.10915
$709$	26.9979	1.01393	0.506964	−	0.861967i	$-0.330768\pi$
$709$	26.9979	1.01393	0.506964	+	0.861967i	$0.330768\pi$
$710$	−46.6588	−1.75107
$711$	−43.1558	−1.61847
$712$	−6.72064	−0.251867
$713$	−4.17617	−0.156399
$714$	77.9710	2.91799
$715$	0.321647	0.0120289
$716$	71.9839	2.69016
$717$	−15.8952	−0.593617
$718$	−40.0665	−1.49527
$719$	43.2582	1.61326	0.806630	−	0.591057i	$-0.201289\pi$
$719$	43.2582	1.61326	0.806630	+	0.591057i	$0.201289\pi$
$720$	12.6913	0.472976
$721$	−63.5831	−2.36796
$722$	44.2000	1.64495
$723$	48.5739	1.80648
$724$	68.8914	2.56033
$725$	−21.4355	−0.796095
$726$	−74.6582	−2.77083
$727$	43.9356	1.62948	0.814741	−	0.579825i	$-0.196879\pi$
$727$	43.9356	1.62948	0.814741	+	0.579825i	$0.196879\pi$
$728$	28.4360	1.05391
$729$	−37.5085	−1.38920
$730$	−38.6205	−1.42941
$731$	7.64530	0.282772
$732$	−33.9445	−1.25462
$733$	23.9851	0.885909	0.442954	−	0.896544i	$-0.353930\pi$
$733$	23.9851	0.885909	0.442954	+	0.896544i	$0.353930\pi$
$734$	−68.7279	−2.53679
$735$	−95.9374	−3.53870
$736$	4.62872	0.170617
$737$	0.220607	0.00812617
$738$	−115.018	−4.23387
$739$	30.1479	1.10901	0.554504	−	0.832181i	$-0.312908\pi$
$739$	30.1479	1.10901	0.554504	+	0.832181i	$0.312908\pi$
$740$	−11.4567	−0.421156
$741$	0.614843	0.0225868
$742$	113.047	4.15008
$743$	12.4708	0.457509	0.228755	−	0.973484i	$-0.426535\pi$
$743$	12.4708	0.457509	0.228755	+	0.973484i	$0.426535\pi$
$744$	−40.2127	−1.47427
$745$	−33.7794	−1.23758
$746$	67.9445	2.48762
$747$	−47.1546	−1.72530
$748$	−0.539444	−0.0197240
$749$	29.0866	1.06280
$750$	−48.2541	−1.76199
$751$	−4.19285	−0.152999	−0.0764997	−	0.997070i	$-0.524374\pi$
$751$	−4.19285	−0.152999	−0.0764997	+	0.997070i	$0.524374\pi$
$752$	−2.06793	−0.0754097
$753$	−5.65960	−0.206247
$754$	−41.2359	−1.50172
$755$	25.2729	0.919776
$756$	−109.265	−3.97394
$757$	−20.2686	−0.736674	−0.368337	−	0.929692i	$-0.620073\pi$
$757$	−20.2686	−0.736674	−0.368337	+	0.929692i	$0.620073\pi$
$758$	−31.8952	−1.15848
$759$	0.175184	0.00635878
$760$	−0.959615	−0.0348089
$761$	−19.7806	−0.717045	−0.358522	−	0.933521i	$-0.616719\pi$
$761$	−19.7806	−0.717045	−0.358522	+	0.933521i	$0.616719\pi$
$762$	−45.8801	−1.66206
$763$	−15.2016	−0.550334
$764$	25.5148	0.923092
$765$	39.3232	1.42173
$766$	53.2218	1.92298
$767$	5.83344	0.210633
$768$	61.4799	2.21847
$769$	−5.76355	−0.207839	−0.103919	−	0.994586i	$-0.533138\pi$
$769$	−5.76355	−0.207839	−0.103919	+	0.994586i	$0.533138\pi$
$770$	1.66055	0.0598420
$771$	66.9486	2.41109
$772$	−12.2306	−0.440188
$773$	−38.2974	−1.37746	−0.688730	−	0.725018i	$-0.741832\pi$
$773$	−38.2974	−1.37746	−0.688730	+	0.725018i	$0.741832\pi$
$774$	−37.3014	−1.34077
$775$	−9.95833	−0.357714
$776$	47.4108	1.70195
$777$	15.7235	0.564079
$778$	42.8219	1.53524
$779$	0.959707	0.0343851
$780$	53.3931	1.91178
$781$	−0.443035	−0.0158530
$782$	−6.11609	−0.218711
$783$	65.7415	2.34941
$784$	10.2643	0.366581
$785$	−24.3480	−0.869019
$786$	−17.2886	−0.616664
$787$	7.40823	0.264075	0.132038	−	0.991245i	$-0.457848\pi$
$787$	7.40823	0.264075	0.132038	+	0.991245i	$0.457848\pi$
$788$	60.5526	2.15710
$789$	−35.1699	−1.25208
$790$	49.5665	1.76350
$791$	0.105424	0.00374843
$792$	1.09201	0.0388030
$793$	−6.70943	−0.238259
$794$	−5.61611	−0.199308
$795$	88.0696	3.12351
$796$	1.25106	0.0443427
$797$	14.2481	0.504693	0.252347	−	0.967637i	$-0.418798\pi$
$797$	14.2481	0.504693	0.252347	+	0.967637i	$0.418798\pi$
$798$	3.17422	0.112366
$799$	−6.40737	−0.226676
$800$	11.0375	0.390233
$801$	11.2116	0.396141
$802$	−42.8447	−1.51290
$803$	−0.366710	−0.0129409
$804$	36.6206	1.29151
$805$	11.8775	0.418626
$806$	−19.1570	−0.674777
$807$	−44.8183	−1.57768
$808$	30.7961	1.08340
$809$	53.9350	1.89626	0.948128	−	0.317890i	$-0.102974\pi$
$809$	53.9350	1.89626	0.948128	+	0.317890i	$0.102974\pi$
$810$	−30.4188	−1.06881
$811$	32.5480	1.14291	0.571457	−	0.820632i	$-0.306378\pi$
$811$	32.5480	1.14291	0.571457	+	0.820632i	$0.306378\pi$
$812$	−134.305	−4.71319
$813$	−8.36166	−0.293256
$814$	−0.172432	−0.00604374
$815$	12.6242	0.442205
$816$	−6.49891	−0.227508
$817$	0.311242	0.0108890
$818$	−37.4958	−1.31101
$819$	−47.4378	−1.65761
$820$	83.3412	2.91040
$821$	15.3063	0.534192	0.267096	−	0.963670i	$-0.413936\pi$
$821$	15.3063	0.534192	0.267096	+	0.963670i	$0.413936\pi$
$822$	−79.0008	−2.75547
$823$	28.5176	0.994063	0.497031	−	0.867733i	$-0.334423\pi$
$823$	28.5176	0.994063	0.497031	+	0.867733i	$0.334423\pi$
$824$	48.0250	1.67303
$825$	0.417737	0.0145437
$826$	30.1160	1.04787
$827$	24.8625	0.864554	0.432277	−	0.901741i	$-0.357710\pi$
$827$	24.8625	0.864554	0.432277	+	0.901741i	$0.357710\pi$
$828$	18.8256	0.654236
$829$	−24.8579	−0.863351	−0.431676	−	0.902029i	$-0.642077\pi$
$829$	−24.8579	−0.863351	−0.431676	+	0.902029i	$0.642077\pi$
$830$	54.1593	1.87990
$831$	65.9640	2.28827
$832$	24.5753	0.851995
$833$	31.8032	1.10192
$834$	−56.3244	−1.95036
$835$	−54.0051	−1.86892
$836$	−0.0219609	−0.000759534 0
$837$	30.5416	1.05567
$838$	24.2925	0.839170
$839$	9.91879	0.342435	0.171217	−	0.985233i	$-0.445230\pi$
$839$	9.91879	0.342435	0.171217	+	0.985233i	$0.445230\pi$
$840$	114.369	3.94611
$841$	51.8074	1.78646
$842$	17.1548	0.591192
$843$	−72.6927	−2.50367
$844$	−47.5572	−1.63699
$845$	−24.7733	−0.852227
$846$	31.2615	1.07479
$847$	−48.0631	−1.65147
$848$	−9.42250	−0.323570
$849$	58.1964	1.99729
$850$	−14.5842	−0.500233
$851$	−1.23336	−0.0422791
$852$	−73.5435	−2.51956
$853$	−31.1308	−1.06590	−0.532950	−	0.846147i	$-0.678916\pi$
$853$	−31.1308	−1.06590	−0.532950	+	0.846147i	$0.678916\pi$
$854$	−34.6384	−1.18530
$855$	1.60086	0.0547482
$856$	−21.9695	−0.750901
$857$	−18.2144	−0.622190	−0.311095	−	0.950379i	$-0.600696\pi$
$857$	−18.2144	−0.622190	−0.311095	+	0.950379i	$0.600696\pi$
$858$	0.803608	0.0274347
$859$	−15.1722	−0.517669	−0.258834	−	0.965922i	$-0.583338\pi$
$859$	−15.1722	−0.517669	−0.258834	+	0.965922i	$0.583338\pi$
$860$	27.0283	0.921658
$861$	−114.380	−3.89807
$862$	55.6868	1.89670
$863$	32.7017	1.11318	0.556590	−	0.830787i	$-0.312109\pi$
$863$	32.7017	1.11318	0.556590	+	0.830787i	$0.312109\pi$
$864$	−33.8513	−1.15164
$865$	−36.1210	−1.22815
$866$	36.2440	1.23162
$867$	29.4480	1.00011
$868$	−62.3944	−2.11780
$869$	0.470645	0.0159655
$870$	−165.850	−5.62284
$871$	7.23839	0.245264
$872$	11.4819	0.388827
$873$	−79.0922	−2.67686
$874$	−0.248987	−0.00842212
$875$	−31.0648	−1.05018
$876$	−60.8735	−2.05672
$877$	29.4355	0.993965	0.496983	−	0.867761i	$-0.334441\pi$
$877$	29.4355	0.993965	0.496983	+	0.867761i	$0.334441\pi$
$878$	65.4267	2.20804
$879$	45.2005	1.52458
$880$	−0.138407	−0.00466572
$881$	−40.5443	−1.36597	−0.682987	−	0.730431i	$-0.739319\pi$
$881$	−40.5443	−1.36597	−0.682987	+	0.730431i	$0.739319\pi$
$882$	−155.168	−5.22477
$883$	40.6517	1.36804	0.684019	−	0.729464i	$-0.260230\pi$
$883$	40.6517	1.36804	0.684019	+	0.729464i	$0.260230\pi$
$884$	−17.6998	−0.595309
$885$	23.4620	0.788667
$886$	59.5350	2.00012
$887$	2.45785	0.0825264	0.0412632	−	0.999148i	$-0.486862\pi$
$887$	2.45785	0.0825264	0.0412632	+	0.999148i	$0.486862\pi$
$888$	−11.8762	−0.398538
$889$	−29.5365	−0.990621
$890$	−12.8770	−0.431639
$891$	−0.288833	−0.00967626
$892$	−3.46652	−0.116068
$893$	−0.260846	−0.00872886
$894$	−84.3951	−2.82259
$895$	57.2258	1.91285
$896$	86.4110	2.88679
$897$	5.74800	0.191920
$898$	−65.5056	−2.18595
$899$	37.5408	1.25206
$900$	44.8908	1.49636
$901$	−29.1951	−0.972629
$902$	1.25435	0.0417653
$903$	−37.0946	−1.23443
$904$	−0.0796277	−0.00264838
$905$	54.7674	1.82053
$906$	63.1424	2.09777
$907$	11.1645	0.370711	0.185356	−	0.982672i	$-0.440656\pi$
$907$	11.1645	0.370711	0.185356	+	0.982672i	$0.440656\pi$
$908$	14.0489	0.466230
$909$	−51.3750	−1.70400
$910$	54.4846	1.80615
$911$	20.2189	0.669881	0.334941	−	0.942239i	$-0.391284\pi$
$911$	20.2189	0.669881	0.334941	+	0.942239i	$0.391284\pi$
$912$	−0.264572	−0.00876087
$913$	0.514254	0.0170193
$914$	10.5295	0.348285
$915$	−26.9852	−0.892104
$916$	−18.6995	−0.617848
$917$	−11.1300	−0.367544
$918$	44.7289	1.47627
$919$	1.99264	0.0657311	0.0328656	−	0.999460i	$-0.489537\pi$
$919$	1.99264	0.0657311	0.0328656	+	0.999460i	$0.489537\pi$
$920$	−8.97119	−0.295771
$921$	−7.96513	−0.262460
$922$	−2.13240	−0.0702269
$923$	−14.5365	−0.478476
$924$	2.61735	0.0861046
$925$	−2.94103	−0.0967005
$926$	−60.0925	−1.97476
$927$	−80.1167	−2.63138
$928$	−41.6089	−1.36588
$929$	15.1112	0.495784	0.247892	−	0.968788i	$-0.420262\pi$
$929$	15.1112	0.495784	0.247892	+	0.968788i	$0.420262\pi$
$930$	−77.0492	−2.52654
$931$	1.29472	0.0424327
$932$	−67.7382	−2.21884
$933$	−85.1786	−2.78862
$934$	−30.5021	−0.998059
$935$	−0.428848	−0.0140248
$936$	35.8303	1.17115
$937$	−11.8192	−0.386116	−0.193058	−	0.981187i	$-0.561841\pi$
$937$	−11.8192	−0.386116	−0.193058	+	0.981187i	$0.561841\pi$
$938$	37.3693	1.22015
$939$	−35.2071	−1.14894
$940$	−22.6519	−0.738823
$941$	−6.59967	−0.215143	−0.107572	−	0.994197i	$-0.534307\pi$
$941$	−6.59967	−0.215143	−0.107572	+	0.994197i	$0.534307\pi$
$942$	−60.8316	−1.98200
$943$	8.97205	0.292170
$944$	−2.51018	−0.0816995
$945$	−86.8637	−2.82568
$946$	0.406798	0.0132261
$947$	58.1710	1.89031	0.945153	−	0.326629i	$-0.105913\pi$
$947$	58.1710	1.89031	0.945153	+	0.326629i	$0.105913\pi$
$948$	78.1267	2.53744
$949$	−12.0322	−0.390581
$950$	−0.593726	−0.0192630
$951$	−5.53255	−0.179405
$952$	−37.9134	−1.22878
$953$	−11.5887	−0.375396	−0.187698	−	0.982227i	$-0.560103\pi$
$953$	−11.5887	−0.375396	−0.187698	+	0.982227i	$0.560103\pi$
$954$	142.443	4.61175
$955$	20.2838	0.656367
$956$	18.6283	0.602484
$957$	−1.57478	−0.0509054
$958$	−61.4523	−1.98543
$959$	−50.8588	−1.64232
$960$	98.8414	3.19009
$961$	−13.5596	−0.437407
$962$	−5.65771	−0.182412
$963$	36.6501	1.18103
$964$	−56.9261	−1.83346
$965$	−9.72307	−0.312997
$966$	29.6749	0.954775
$967$	−28.4341	−0.914380	−0.457190	−	0.889369i	$-0.651144\pi$
$967$	−28.4341	−0.914380	−0.457190	+	0.889369i	$0.651144\pi$
$968$	36.3026	1.16681
$969$	−0.819762	−0.0263346
$970$	90.8411	2.91673
$971$	39.0110	1.25192	0.625961	−	0.779855i	$-0.284707\pi$
$971$	39.0110	1.25192	0.625961	+	0.779855i	$0.284707\pi$
$972$	27.0505	0.867647
$973$	−36.2603	−1.16245
$974$	−34.3980	−1.10218
$975$	13.7065	0.438958
$976$	2.88713	0.0924147
$977$	19.7699	0.632496	0.316248	−	0.948677i	$-0.397577\pi$
$977$	19.7699	0.632496	0.316248	+	0.948677i	$0.397577\pi$
$978$	31.5405	1.00855
$979$	−0.122270	−0.00390777
$980$	112.434	3.59156
$981$	−19.1545	−0.611556
$982$	56.5458	1.80445
$983$	−49.1976	−1.56916	−0.784580	−	0.620028i	$-0.787121\pi$
$983$	−49.1976	−1.56916	−0.784580	+	0.620028i	$0.787121\pi$
$984$	86.3926	2.75410
$985$	48.1382	1.53381
$986$	54.9793	1.75090
$987$	31.0882	0.989548
$988$	−0.720564	−0.0229242
$989$	2.90972	0.0925237
$990$	2.09234	0.0664991
$991$	14.8519	0.471786	0.235893	−	0.971779i	$-0.424199\pi$
$991$	14.8519	0.471786	0.235893	+	0.971779i	$0.424199\pi$
$992$	−19.3303	−0.613738
$993$	73.5062	2.33265
$994$	−75.0470	−2.38035
$995$	0.994569	0.0315300
$996$	85.3658	2.70492
$997$	8.65743	0.274184	0.137092	−	0.990558i	$-0.456224\pi$
$997$	8.65743	0.274184	0.137092	+	0.990558i	$0.456224\pi$
$998$	78.0852	2.47174
$999$	9.01997	0.285379

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.c.1.17	✓	143

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.c.1.17	✓	143	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.32772 q^{2} -2.91674 q^{3} +3.41827 q^{4} +2.71745 q^{5} +6.78934 q^{6} +4.37081 q^{7} -3.30132 q^{8} +5.50736 q^{9} +O(q^{10})\)	\(q-2.32772 q^{2} -2.91674 q^{3} +3.41827 q^{4} +2.71745 q^{5} +6.78934 q^{6} +4.37081 q^{7} -3.30132 q^{8} +5.50736 q^{9} -6.32547 q^{10} -0.0600616 q^{11} -9.97018 q^{12} -1.97070 q^{13} -10.1740 q^{14} -7.92610 q^{15} +0.848008 q^{16} +2.62750 q^{17} -12.8196 q^{18} +0.106966 q^{19} +9.28898 q^{20} -12.7485 q^{21} +0.139807 q^{22} +1.00000 q^{23} +9.62909 q^{24} +2.38456 q^{25} +4.58722 q^{26} -7.31331 q^{27} +14.9406 q^{28} -8.98929 q^{29} +18.4497 q^{30} -4.17617 q^{31} +4.62872 q^{32} +0.175184 q^{33} -6.11609 q^{34} +11.8775 q^{35} +18.8256 q^{36} -1.23336 q^{37} -0.248987 q^{38} +5.74800 q^{39} -8.97119 q^{40} +8.97205 q^{41} +29.6749 q^{42} +2.90972 q^{43} -0.205307 q^{44} +14.9660 q^{45} -2.32772 q^{46} -2.43858 q^{47} -2.47342 q^{48} +12.1040 q^{49} -5.55058 q^{50} -7.66374 q^{51} -6.73636 q^{52} -11.1113 q^{53} +17.0233 q^{54} -0.163215 q^{55} -14.4294 q^{56} -0.311993 q^{57} +20.9245 q^{58} -2.96009 q^{59} -27.0935 q^{60} +3.40460 q^{61} +9.72094 q^{62} +24.0716 q^{63} -12.4704 q^{64} -5.35528 q^{65} -0.407779 q^{66} -3.67301 q^{67} +8.98151 q^{68} -2.91674 q^{69} -27.6474 q^{70} +7.37634 q^{71} -18.1816 q^{72} +6.10555 q^{73} +2.87092 q^{74} -6.95514 q^{75} +0.365639 q^{76} -0.262518 q^{77} -13.3797 q^{78} -7.83603 q^{79} +2.30442 q^{80} +4.80894 q^{81} -20.8844 q^{82} -8.56211 q^{83} -43.5778 q^{84} +7.14012 q^{85} -6.77300 q^{86} +26.2194 q^{87} +0.198283 q^{88} +2.03574 q^{89} -34.8366 q^{90} -8.61353 q^{91} +3.41827 q^{92} +12.1808 q^{93} +5.67631 q^{94} +0.290676 q^{95} -13.5008 q^{96} -14.3612 q^{97} -28.1746 q^{98} -0.330781 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9 - 22 * q^10 - 14 * q^11 - 36 * q^12 - 87 * q^13 - 18 * q^14 - 19 * q^15 + 81 * q^16 - 14 * q^17 - 60 * q^18 - 18 * q^19 - 25 * q^20 - 26 * q^21 - 62 * q^22 + 143 * q^23 - 21 * q^24 + 67 * q^25 - 5 * q^26 - 47 * q^27 - 76 * q^28 - 54 * q^29 - 22 * q^30 - 62 * q^31 - 117 * q^32 - 59 * q^33 - 35 * q^34 - 52 * q^35 + 52 * q^36 - 190 * q^37 - 19 * q^38 - 43 * q^39 - 41 * q^40 - 50 * q^41 + 8 * q^42 - 50 * q^43 - 18 * q^44 - 75 * q^45 - 17 * q^46 - 63 * q^47 - 35 * q^48 + 74 * q^49 - 53 * q^50 - 33 * q^51 - 124 * q^52 - 100 * q^53 - 46 * q^54 - 61 * q^55 - 3 * q^56 - 80 * q^57 - 112 * q^58 - 109 * q^59 - 55 * q^60 - 76 * q^61 - 6 * q^62 - 93 * q^63 + 57 * q^64 - 17 * q^65 + 50 * q^66 - 120 * q^67 + 26 * q^68 - 17 * q^69 - 109 * q^71 - 153 * q^72 - 94 * q^73 + 35 * q^74 - 105 * q^75 - 16 * q^76 - 52 * q^77 - 59 * q^78 - 29 * q^79 - 30 * q^80 + 39 * q^81 - 65 * q^82 + 8 * q^83 + 11 * q^84 - 155 * q^85 - 15 * q^86 - 25 * q^87 - 139 * q^88 + 6 * q^89 + 82 * q^90 - 34 * q^91 + 121 * q^92 - 151 * q^93 - 3 * q^94 - 70 * q^95 - 23 * q^96 - 203 * q^97 - 18 * q^98 - 49 * q^99

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