LMFDB - Embedded newform 4027.2.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4027,2,Mod(1,4027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4027, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4027 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4027.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:	$32.1557568940$
Analytic rank:	$1$
Dimension:	$159$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	4027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.78842 q^{2} -1.28715 q^{3} +5.77530 q^{4} -4.20295 q^{5} +3.58911 q^{6} -2.09011 q^{7} -10.5271 q^{8} -1.34326 q^{9} +O(q^{10})$	\(q-2.78842 q^{2} -1.28715 q^{3} +5.77530 q^{4} -4.20295 q^{5} +3.58911 q^{6} -2.09011 q^{7} -10.5271 q^{8} -1.34326 q^{9} +11.7196 q^{10} -3.51880 q^{11} -7.43365 q^{12} -6.67494 q^{13} +5.82812 q^{14} +5.40981 q^{15} +17.8035 q^{16} -7.84943 q^{17} +3.74557 q^{18} -0.668575 q^{19} -24.2733 q^{20} +2.69028 q^{21} +9.81191 q^{22} -0.593440 q^{23} +13.5500 q^{24} +12.6648 q^{25} +18.6126 q^{26} +5.59040 q^{27} -12.0710 q^{28} -5.66838 q^{29} -15.0848 q^{30} +6.70993 q^{31} -28.5894 q^{32} +4.52921 q^{33} +21.8875 q^{34} +8.78464 q^{35} -7.75771 q^{36} -1.73639 q^{37} +1.86427 q^{38} +8.59162 q^{39} +44.2450 q^{40} +10.4094 q^{41} -7.50164 q^{42} -2.32144 q^{43} -20.3222 q^{44} +5.64564 q^{45} +1.65476 q^{46} +3.51390 q^{47} -22.9157 q^{48} -2.63143 q^{49} -35.3148 q^{50} +10.1034 q^{51} -38.5498 q^{52} +9.58224 q^{53} -15.5884 q^{54} +14.7894 q^{55} +22.0029 q^{56} +0.860553 q^{57} +15.8058 q^{58} +8.18161 q^{59} +31.2433 q^{60} -3.21562 q^{61} -18.7101 q^{62} +2.80756 q^{63} +44.1124 q^{64} +28.0544 q^{65} -12.6294 q^{66} -4.18778 q^{67} -45.3328 q^{68} +0.763843 q^{69} -24.4953 q^{70} -5.21564 q^{71} +14.1406 q^{72} +13.0135 q^{73} +4.84180 q^{74} -16.3014 q^{75} -3.86122 q^{76} +7.35470 q^{77} -23.9571 q^{78} -15.4864 q^{79} -74.8272 q^{80} -3.16589 q^{81} -29.0257 q^{82} -13.8017 q^{83} +15.5372 q^{84} +32.9908 q^{85} +6.47317 q^{86} +7.29603 q^{87} +37.0429 q^{88} +2.61625 q^{89} -15.7424 q^{90} +13.9514 q^{91} -3.42729 q^{92} -8.63666 q^{93} -9.79824 q^{94} +2.80999 q^{95} +36.7987 q^{96} +2.54750 q^{97} +7.33753 q^{98} +4.72666 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9}+O(q^{10}) $ 159 * q - 22 * q^2 - 19 * q^3 + 148 * q^4 - 70 * q^5 - 23 * q^6 - 19 * q^7 - 66 * q^8 + 126 * q^9	\( 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9} - 23 q^{10} - 33 q^{11} - 57 q^{12} - 90 q^{13} - 28 q^{14} - 22 q^{15} + 130 q^{16} - 145 q^{17} - 50 q^{18} - 28 q^{19} - 121 q^{20} - 69 q^{21} - 26 q^{22} - 79 q^{23} - 62 q^{24} + 123 q^{25} - 40 q^{26} - 70 q^{27} - 43 q^{28} - 109 q^{29} - 43 q^{30} - 21 q^{31} - 139 q^{32} - 83 q^{33} - 93 q^{35} + 75 q^{36} - 65 q^{37} - 122 q^{38} - 18 q^{39} - 43 q^{40} - 71 q^{41} - 88 q^{42} - 72 q^{43} - 79 q^{44} - 181 q^{45} - 11 q^{46} - 114 q^{47} - 118 q^{48} + 118 q^{49} - 77 q^{50} - 29 q^{51} - 169 q^{52} - 220 q^{53} - 80 q^{54} - 37 q^{55} - 72 q^{56} - 90 q^{57} - 8 q^{58} - 60 q^{59} - 42 q^{60} - 108 q^{61} - 152 q^{62} - 65 q^{63} + 114 q^{64} - 81 q^{65} - 40 q^{66} - 50 q^{67} - 319 q^{68} - 103 q^{69} + 4 q^{70} - 7 q^{71} - 129 q^{72} - 94 q^{73} - 79 q^{74} - 59 q^{75} - 46 q^{76} - 329 q^{77} + 8 q^{78} - 18 q^{79} - 190 q^{80} + 59 q^{81} - 56 q^{82} - 201 q^{83} - 71 q^{84} - 26 q^{85} - 52 q^{86} - 126 q^{87} - 66 q^{88} - 114 q^{89} - 33 q^{90} - 30 q^{91} - 204 q^{92} - 125 q^{93} + 9 q^{94} - 84 q^{95} - 88 q^{96} - 56 q^{97} - 110 q^{98} - 46 q^{99}+O(q^{100}) \) 159 * q - 22 * q^2 - 19 * q^3 + 148 * q^4 - 70 * q^5 - 23 * q^6 - 19 * q^7 - 66 * q^8 + 126 * q^9 - 23 * q^10 - 33 * q^11 - 57 * q^12 - 90 * q^13 - 28 * q^14 - 22 * q^15 + 130 * q^16 - 145 * q^17 - 50 * q^18 - 28 * q^19 - 121 * q^20 - 69 * q^21 - 26 * q^22 - 79 * q^23 - 62 * q^24 + 123 * q^25 - 40 * q^26 - 70 * q^27 - 43 * q^28 - 109 * q^29 - 43 * q^30 - 21 * q^31 - 139 * q^32 - 83 * q^33 - 93 * q^35 + 75 * q^36 - 65 * q^37 - 122 * q^38 - 18 * q^39 - 43 * q^40 - 71 * q^41 - 88 * q^42 - 72 * q^43 - 79 * q^44 - 181 * q^45 - 11 * q^46 - 114 * q^47 - 118 * q^48 + 118 * q^49 - 77 * q^50 - 29 * q^51 - 169 * q^52 - 220 * q^53 - 80 * q^54 - 37 * q^55 - 72 * q^56 - 90 * q^57 - 8 * q^58 - 60 * q^59 - 42 * q^60 - 108 * q^61 - 152 * q^62 - 65 * q^63 + 114 * q^64 - 81 * q^65 - 40 * q^66 - 50 * q^67 - 319 * q^68 - 103 * q^69 + 4 * q^70 - 7 * q^71 - 129 * q^72 - 94 * q^73 - 79 * q^74 - 59 * q^75 - 46 * q^76 - 329 * q^77 + 8 * q^78 - 18 * q^79 - 190 * q^80 + 59 * q^81 - 56 * q^82 - 201 * q^83 - 71 * q^84 - 26 * q^85 - 52 * q^86 - 126 * q^87 - 66 * q^88 - 114 * q^89 - 33 * q^90 - 30 * q^91 - 204 * q^92 - 125 * q^93 + 9 * q^94 - 84 * q^95 - 88 * q^96 - 56 * q^97 - 110 * q^98 - 46 * 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 $

$2$	−2.78842	−1.97171	−0.985856	−	0.167593i	$-0.946401\pi$
$2$	−2.78842	−1.97171	−0.985856	+	0.167593i	$0.946401\pi$
$3$	−1.28715	−0.743134	−0.371567	−	0.928406i	$-0.621179\pi$
$3$	−1.28715	−0.743134	−0.371567	+	0.928406i	$0.621179\pi$
$4$	5.77530	2.88765
$5$	−4.20295	−1.87962	−0.939808	−	0.341702i	$-0.888997\pi$
$5$	−4.20295	−1.87962	−0.939808	+	0.341702i	$0.888997\pi$
$6$	3.58911	1.46525
$7$	−2.09011	−0.789989	−0.394994	−	0.918684i	$-0.629253\pi$
$7$	−2.09011	−0.789989	−0.394994	+	0.918684i	$0.629253\pi$
$8$	−10.5271	−3.72190
$9$	−1.34326	−0.447752
$10$	11.7196	3.70606
$11$	−3.51880	−1.06096	−0.530480	−	0.847698i	$-0.677988\pi$
$11$	−3.51880	−1.06096	−0.530480	+	0.847698i	$0.677988\pi$
$12$	−7.43365	−2.14591
$13$	−6.67494	−1.85130	−0.925648	−	0.378387i	$-0.876479\pi$
$13$	−6.67494	−1.85130	−0.925648	+	0.378387i	$0.876479\pi$
$14$	5.82812	1.55763
$15$	5.40981	1.39681
$16$	17.8035	4.45087
$17$	−7.84943	−1.90377	−0.951883	−	0.306461i	$-0.900855\pi$
$17$	−7.84943	−1.90377	−0.951883	+	0.306461i	$0.900855\pi$
$18$	3.74557	0.882838
$19$	−0.668575	−0.153382	−0.0766908	−	0.997055i	$-0.524435\pi$
$19$	−0.668575	−0.153382	−0.0766908	+	0.997055i	$0.524435\pi$
$20$	−24.2733	−5.42768
$21$	2.69028	0.587067
$22$	9.81191	2.09191
$23$	−0.593440	−0.123741	−0.0618703	−	0.998084i	$-0.519707\pi$
$23$	−0.593440	−0.123741	−0.0618703	+	0.998084i	$0.519707\pi$
$24$	13.5500	2.76587
$25$	12.6648	2.53296
$26$	18.6126	3.65022
$27$	5.59040	1.07587
$28$	−12.0710	−2.28121
$29$	−5.66838	−1.05259	−0.526295	−	0.850302i	$-0.676419\pi$
$29$	−5.66838	−1.05259	−0.526295	+	0.850302i	$0.676419\pi$
$30$	−15.0848	−2.75410
$31$	6.70993	1.20514	0.602569	−	0.798066i	$-0.294144\pi$
$31$	6.70993	1.20514	0.602569	+	0.798066i	$0.294144\pi$
$32$	−28.5894	−5.05394
$33$	4.52921	0.788435
$34$	21.8875	3.75368
$35$	8.78464	1.48488
$36$	−7.75771	−1.29295
$37$	−1.73639	−0.285461	−0.142731	−	0.989762i	$-0.545588\pi$
$37$	−1.73639	−0.285461	−0.142731	+	0.989762i	$0.545588\pi$
$38$	1.86427	0.302424
$39$	8.59162	1.37576
$40$	44.2450	6.99575
$41$	10.4094	1.62567	0.812835	−	0.582494i	$-0.197923\pi$
$41$	10.4094	1.62567	0.812835	+	0.582494i	$0.197923\pi$
$42$	−7.50164	−1.15753
$43$	−2.32144	−0.354017	−0.177008	−	0.984209i	$-0.556642\pi$
$43$	−2.32144	−0.354017	−0.177008	+	0.984209i	$0.556642\pi$
$44$	−20.3222	−3.06368
$45$	5.64564	0.841602
$46$	1.65476	0.243981
$47$	3.51390	0.512555	0.256278	−	0.966603i	$-0.417504\pi$
$47$	3.51390	0.512555	0.256278	+	0.966603i	$0.417504\pi$
$48$	−22.9157	−3.30760
$49$	−2.63143	−0.375918
$50$	−35.3148	−4.99427
$51$	10.1034	1.41475
$52$	−38.5498	−5.34589
$53$	9.58224	1.31622	0.658111	−	0.752921i	$-0.271356\pi$
$53$	9.58224	1.31622	0.658111	+	0.752921i	$0.271356\pi$
$54$	−15.5884	−2.12131
$55$	14.7894	1.99420
$56$	22.0029	2.94026
$57$	0.860553	0.113983
$58$	15.8058	2.07541
$59$	8.18161	1.06516	0.532578	−	0.846381i	$-0.321223\pi$
$59$	8.18161	1.06516	0.532578	+	0.846381i	$0.321223\pi$
$60$	31.2433	4.03349
$61$	−3.21562	−0.411718	−0.205859	−	0.978582i	$-0.565999\pi$
$61$	−3.21562	−0.411718	−0.205859	+	0.978582i	$0.565999\pi$
$62$	−18.7101	−2.37619
$63$	2.80756	0.353719
$64$	44.1124	5.51404
$65$	28.0544	3.47973
$66$	−12.6294	−1.55457
$67$	−4.18778	−0.511619	−0.255809	−	0.966727i	$-0.582342\pi$
$67$	−4.18778	−0.511619	−0.255809	+	0.966727i	$0.582342\pi$
$68$	−45.3328	−5.49741
$69$	0.763843	0.0919559
$70$	−24.4953	−2.92775
$71$	−5.21564	−0.618983	−0.309492	−	0.950902i	$-0.600159\pi$
$71$	−5.21564	−0.618983	−0.309492	+	0.950902i	$0.600159\pi$
$72$	14.1406	1.66649
$73$	13.0135	1.52312	0.761558	−	0.648097i	$-0.224435\pi$
$73$	13.0135	1.52312	0.761558	+	0.648097i	$0.224435\pi$
$74$	4.84180	0.562848
$75$	−16.3014	−1.88233
$76$	−3.86122	−0.442912
$77$	7.35470	0.838146
$78$	−23.9571	−2.71260
$79$	−15.4864	−1.74236	−0.871178	−	0.490968i	$-0.836643\pi$
$79$	−15.4864	−1.74236	−0.871178	+	0.490968i	$0.836643\pi$
$80$	−74.8272	−8.36594
$81$	−3.16589	−0.351766
$82$	−29.0257	−3.20535
$83$	−13.8017	−1.51493	−0.757466	−	0.652875i	$-0.773563\pi$
$83$	−13.8017	−1.51493	−0.757466	+	0.652875i	$0.773563\pi$
$84$	15.5372	1.69524
$85$	32.9908	3.57835
$86$	6.47317	0.698020
$87$	7.29603	0.782216
$88$	37.0429	3.94879
$89$	2.61625	0.277322	0.138661	−	0.990340i	$-0.455720\pi$
$89$	2.61625	0.277322	0.138661	+	0.990340i	$0.455720\pi$
$90$	−15.7424	−1.65940
$91$	13.9514	1.46250
$92$	−3.42729	−0.357320
$93$	−8.63666	−0.895579
$94$	−9.79824	−1.01061
$95$	2.80999	0.288299
$96$	36.7987	3.75575
$97$	2.54750	0.258660	0.129330	−	0.991602i	$-0.458717\pi$
$97$	2.54750	0.258660	0.129330	+	0.991602i	$0.458717\pi$
$98$	7.33753	0.741203
$99$	4.72666	0.475047
$100$	73.1430	7.31430
$101$	−6.14362	−0.611313	−0.305657	−	0.952142i	$-0.598876\pi$
$101$	−6.14362	−0.611313	−0.305657	+	0.952142i	$0.598876\pi$
$102$	−28.1724	−2.78949
$103$	−10.4503	−1.02970	−0.514851	−	0.857280i	$-0.672153\pi$
$103$	−10.4503	−1.02970	−0.514851	+	0.857280i	$0.672153\pi$
$104$	70.2680	6.89034
$105$	−11.3071	−1.10346
$106$	−26.7193	−2.59521
$107$	−9.47843	−0.916314	−0.458157	−	0.888871i	$-0.651490\pi$
$107$	−9.47843	−0.916314	−0.458157	+	0.888871i	$0.651490\pi$
$108$	32.2863	3.10675
$109$	8.39167	0.803776	0.401888	−	0.915689i	$-0.368354\pi$
$109$	8.39167	0.803776	0.401888	+	0.915689i	$0.368354\pi$
$110$	−41.2390	−3.93198
$111$	2.23499	0.212136
$112$	−37.2113	−3.51614
$113$	3.92596	0.369323	0.184662	−	0.982802i	$-0.440881\pi$
$113$	3.92596	0.369323	0.184662	+	0.982802i	$0.440881\pi$
$114$	−2.39959	−0.224742
$115$	2.49420	0.232585
$116$	−32.7366	−3.03951
$117$	8.96615	0.828921
$118$	−22.8138	−2.10018
$119$	16.4062	1.50395
$120$	−56.9498	−5.19878
$121$	1.38198	0.125635
$122$	8.96650	0.811789
$123$	−13.3984	−1.20809
$124$	38.7519	3.48002
$125$	−32.2148	−2.88138
$126$	−7.82866	−0.697432
$127$	−6.42079	−0.569753	−0.284877	−	0.958564i	$-0.591953\pi$
$127$	−6.42079	−0.569753	−0.284877	+	0.958564i	$0.591953\pi$
$128$	−65.8251	−5.81817
$129$	2.98804	0.263082
$130$	−78.2276	−6.86102
$131$	−12.2415	−1.06955	−0.534773	−	0.844996i	$-0.679603\pi$
$131$	−12.2415	−1.06955	−0.534773	+	0.844996i	$0.679603\pi$
$132$	26.1576	2.27672
$133$	1.39740	0.121170
$134$	11.6773	1.00877
$135$	−23.4962	−2.02223
$136$	82.6320	7.08563
$137$	1.63262	0.139484	0.0697420	−	0.997565i	$-0.477782\pi$
$137$	1.63262	0.139484	0.0697420	+	0.997565i	$0.477782\pi$
$138$	−2.12992	−0.181311
$139$	1.89478	0.160714	0.0803568	−	0.996766i	$-0.474394\pi$
$139$	1.89478	0.160714	0.0803568	+	0.996766i	$0.474394\pi$
$140$	50.7340	4.28780
$141$	−4.52290	−0.380897
$142$	14.5434	1.22046
$143$	23.4878	1.96415
$144$	−23.9147	−1.99289
$145$	23.8239	1.97847
$146$	−36.2871	−3.00315
$147$	3.38703	0.279358
$148$	−10.0282	−0.824313
$149$	2.60762	0.213625	0.106812	−	0.994279i	$-0.465936\pi$
$149$	2.60762	0.213625	0.106812	+	0.994279i	$0.465936\pi$
$150$	45.4553	3.71141
$151$	1.32976	0.108215	0.0541073	−	0.998535i	$-0.482769\pi$
$151$	1.32976	0.108215	0.0541073	+	0.998535i	$0.482769\pi$
$152$	7.03818	0.570871
$153$	10.5438	0.852415
$154$	−20.5080	−1.65258
$155$	−28.2015	−2.26520
$156$	49.6192	3.97271
$157$	−7.62389	−0.608453	−0.304227	−	0.952600i	$-0.598398\pi$
$157$	−7.62389	−0.608453	−0.304227	+	0.952600i	$0.598398\pi$
$158$	43.1826	3.43542
$159$	−12.3337	−0.978130
$160$	120.160	9.49947
$161$	1.24036	0.0977537
$162$	8.82785	0.693581
$163$	12.1172	0.949092	0.474546	−	0.880231i	$-0.342612\pi$
$163$	12.1172	0.949092	0.474546	+	0.880231i	$0.342612\pi$
$164$	60.1172	4.69437
$165$	−19.0361	−1.48196
$166$	38.4849	2.98701
$167$	−6.91912	−0.535418	−0.267709	−	0.963500i	$-0.586267\pi$
$167$	−6.91912	−0.535418	−0.267709	+	0.963500i	$0.586267\pi$
$168$	−28.3209	−2.18501
$169$	31.5548	2.42729
$170$	−91.9922	−7.05548
$171$	0.898067	0.0686769
$172$	−13.4070	−1.02228
$173$	−0.257019	−0.0195408	−0.00977041	−	0.999952i	$-0.503110\pi$
$173$	−0.257019	−0.0195408	−0.00977041	+	0.999952i	$0.503110\pi$
$174$	−20.3444	−1.54231
$175$	−26.4709	−2.00101
$176$	−62.6470	−4.72220
$177$	−10.5309	−0.791553
$178$	−7.29520	−0.546798
$179$	2.84073	0.212326	0.106163	−	0.994349i	$-0.466143\pi$
$179$	2.84073	0.212326	0.106163	+	0.994349i	$0.466143\pi$
$180$	32.6053	2.43025
$181$	−17.6541	−1.31222	−0.656110	−	0.754666i	$-0.727799\pi$
$181$	−17.6541	−1.31222	−0.656110	+	0.754666i	$0.727799\pi$
$182$	−38.9023	−2.88363
$183$	4.13897	0.305961
$184$	6.24722	0.460551
$185$	7.29798	0.536558
$186$	24.0826	1.76583
$187$	27.6206	2.01982
$188$	20.2938	1.48008
$189$	−11.6846	−0.849928
$190$	−7.83543	−0.568442
$191$	5.48457	0.396850	0.198425	−	0.980116i	$-0.436417\pi$
$191$	5.48457	0.396850	0.198425	+	0.980116i	$0.436417\pi$
$192$	−56.7790	−4.09767
$193$	3.21264	0.231251	0.115625	−	0.993293i	$-0.463113\pi$
$193$	3.21264	0.231251	0.115625	+	0.993293i	$0.463113\pi$
$194$	−7.10351	−0.510003
$195$	−36.1102	−2.58590
$196$	−15.1973	−1.08552
$197$	7.10351	0.506104	0.253052	−	0.967453i	$-0.418566\pi$
$197$	7.10351	0.506104	0.253052	+	0.967453i	$0.418566\pi$
$198$	−13.1799	−0.936656
$199$	−2.37637	−0.168457	−0.0842283	−	0.996446i	$-0.526843\pi$
$199$	−2.37637	−0.168457	−0.0842283	+	0.996446i	$0.526843\pi$
$200$	−133.324	−9.42743
$201$	5.39028	0.380201
$202$	17.1310	1.20533
$203$	11.8475	0.831535
$204$	58.3499	4.08531
$205$	−43.7500	−3.05564
$206$	29.1400	2.03028
$207$	0.797141	0.0554052
$208$	−118.837	−8.23988
$209$	2.35258	0.162732
$210$	31.5290	2.17571
$211$	−14.8900	−1.02507	−0.512536	−	0.858666i	$-0.671294\pi$
$211$	−14.8900	−1.02507	−0.512536	+	0.858666i	$0.671294\pi$
$212$	55.3403	3.80079
$213$	6.71329	0.459987
$214$	26.4299	1.80671
$215$	9.75692	0.665416
$216$	−58.8509	−4.00430
$217$	−14.0245	−0.952046
$218$	−23.3995	−1.58482
$219$	−16.7503	−1.13188
$220$	85.4130	5.75854
$221$	52.3945	3.52443
$222$	−6.23210	−0.418271
$223$	11.7892	0.789466	0.394733	−	0.918796i	$-0.370837\pi$
$223$	11.7892	0.789466	0.394733	+	0.918796i	$0.370837\pi$
$224$	59.7551	3.99256
$225$	−17.0121	−1.13414
$226$	−10.9472	−0.728199
$227$	2.12599	0.141107	0.0705535	−	0.997508i	$-0.477523\pi$
$227$	2.12599	0.141107	0.0705535	+	0.997508i	$0.477523\pi$
$228$	4.96995	0.329143
$229$	7.12662	0.470941	0.235470	−	0.971882i	$-0.424337\pi$
$229$	7.12662	0.470941	0.235470	+	0.971882i	$0.424337\pi$
$230$	−6.95488	−0.458591
$231$	−9.46657	−0.622854
$232$	59.6718	3.91764
$233$	16.3829	1.07328	0.536639	−	0.843812i	$-0.319694\pi$
$233$	16.3829	1.07328	0.536639	+	0.843812i	$0.319694\pi$
$234$	−25.0014	−1.63439
$235$	−14.7688	−0.963407
$236$	47.2513	3.07580
$237$	19.9332	1.29480
$238$	−45.7474	−2.96536
$239$	11.2016	0.724574	0.362287	−	0.932066i	$-0.381996\pi$
$239$	11.2016	0.724574	0.362287	+	0.932066i	$0.381996\pi$
$240$	96.3135	6.21701
$241$	−3.65178	−0.235232	−0.117616	−	0.993059i	$-0.537525\pi$
$241$	−3.65178	−0.235232	−0.117616	+	0.993059i	$0.537525\pi$
$242$	−3.85355	−0.247715
$243$	−12.6962	−0.814464
$244$	−18.5712	−1.18890
$245$	11.0598	0.706582
$246$	37.3603	2.38201
$247$	4.46270	0.283955
$248$	−70.6363	−4.48541
$249$	17.7648	1.12580
$250$	89.8284	5.68125
$251$	11.4399	0.722080	0.361040	−	0.932550i	$-0.382422\pi$
$251$	11.4399	0.722080	0.361040	+	0.932550i	$0.382422\pi$
$252$	16.2145	1.02142
$253$	2.08820	0.131284
$254$	17.9039	1.12339
$255$	−42.4639	−2.65919
$256$	95.3234	5.95771
$257$	−4.39563	−0.274192	−0.137096	−	0.990558i	$-0.543777\pi$
$257$	−4.39563	−0.274192	−0.137096	+	0.990558i	$0.543777\pi$
$258$	−8.33191	−0.518722
$259$	3.62926	0.225511
$260$	162.023	10.0482
$261$	7.61408	0.471300
$262$	34.1345	2.10884
$263$	22.6257	1.39516	0.697580	−	0.716507i	$-0.254260\pi$
$263$	22.6257	1.39516	0.697580	+	0.716507i	$0.254260\pi$
$264$	−47.6796	−2.93448
$265$	−40.2737	−2.47399
$266$	−3.89653	−0.238912
$267$	−3.36749	−0.206087
$268$	−24.1857	−1.47738
$269$	−2.87715	−0.175423	−0.0877116	−	0.996146i	$-0.527955\pi$
$269$	−2.87715	−0.175423	−0.0877116	+	0.996146i	$0.527955\pi$
$270$	65.5173	3.98726
$271$	−2.04088	−0.123975	−0.0619873	−	0.998077i	$-0.519744\pi$
$271$	−2.04088	−0.123975	−0.0619873	+	0.998077i	$0.519744\pi$
$272$	−139.747	−8.47342
$273$	−17.9575	−1.08683
$274$	−4.55243	−0.275022
$275$	−44.5649	−2.68737
$276$	4.41142	0.265536
$277$	13.1084	0.787607	0.393804	−	0.919195i	$-0.371159\pi$
$277$	13.1084	0.787607	0.393804	+	0.919195i	$0.371159\pi$
$278$	−5.28346	−0.316881
$279$	−9.01315	−0.539603
$280$	−92.4771	−5.52656
$281$	16.1958	0.966160	0.483080	−	0.875576i	$-0.339518\pi$
$281$	16.1958	0.966160	0.483080	+	0.875576i	$0.339518\pi$
$282$	12.6118	0.751019
$283$	7.42980	0.441656	0.220828	−	0.975313i	$-0.429124\pi$
$283$	7.42980	0.441656	0.220828	+	0.975313i	$0.429124\pi$
$284$	−30.1219	−1.78741
$285$	−3.61686	−0.214244
$286$	−65.4939	−3.87274
$287$	−21.7567	−1.28426
$288$	38.4029	2.26291
$289$	44.6135	2.62433
$290$	−66.4311	−3.90097
$291$	−3.27901	−0.192219
$292$	75.1569	4.39822
$293$	−10.7516	−0.628117	−0.314059	−	0.949404i	$-0.601689\pi$
$293$	−10.7516	−0.628117	−0.314059	+	0.949404i	$0.601689\pi$
$294$	−9.44447	−0.550813
$295$	−34.3869	−2.00208
$296$	18.2793	1.06246
$297$	−19.6715	−1.14146
$298$	−7.27116	−0.421207
$299$	3.96117	0.229081
$300$	−94.1457	−5.43551
$301$	4.85208	0.279669
$302$	−3.70794	−0.213368
$303$	7.90773	0.454287
$304$	−11.9030	−0.682682
$305$	13.5151	0.773872
$306$	−29.4006	−1.68072
$307$	−17.7525	−1.01319	−0.506595	−	0.862184i	$-0.669096\pi$
$307$	−17.7525	−1.01319	−0.506595	+	0.862184i	$0.669096\pi$
$308$	42.4756	2.42027
$309$	13.4511	0.765207
$310$	78.6377	4.46632
$311$	19.6588	1.11475	0.557374	−	0.830261i	$-0.311809\pi$
$311$	19.6588	1.11475	0.557374	+	0.830261i	$0.311809\pi$
$312$	−90.4451	−5.12045
$313$	9.05112	0.511600	0.255800	−	0.966730i	$-0.417661\pi$
$313$	9.05112	0.511600	0.255800	+	0.966730i	$0.417661\pi$
$314$	21.2586	1.19969
$315$	−11.8000	−0.664856
$316$	−89.4386	−5.03131
$317$	21.1816	1.18968	0.594839	−	0.803845i	$-0.297216\pi$
$317$	21.1816	1.18968	0.594839	+	0.803845i	$0.297216\pi$
$318$	34.3917	1.92859
$319$	19.9459	1.11676
$320$	−185.402	−10.3643
$321$	12.2001	0.680944
$322$	−3.45864	−0.192742
$323$	5.24793	0.292003
$324$	−18.2840	−1.01578
$325$	−84.5368	−4.68926
$326$	−33.7879	−1.87134
$327$	−10.8013	−0.597313
$328$	−109.581	−6.05059
$329$	−7.34445	−0.404913
$330$	53.0806	2.92199
$331$	31.0776	1.70818	0.854090	−	0.520125i	$-0.174115\pi$
$331$	31.0776	1.70818	0.854090	+	0.520125i	$0.174115\pi$
$332$	−79.7089	−4.37459
$333$	2.33242	0.127816
$334$	19.2934	1.05569
$335$	17.6010	0.961647
$336$	47.8964	2.61296
$337$	−33.9922	−1.85167	−0.925836	−	0.377925i	$-0.876638\pi$
$337$	−33.9922	−1.85167	−0.925836	+	0.377925i	$0.876638\pi$
$338$	−87.9882	−4.78592
$339$	−5.05328	−0.274456
$340$	190.532	10.3330
$341$	−23.6109	−1.27860
$342$	−2.50419	−0.135411
$343$	20.1308	1.08696
$344$	24.4382	1.31762
$345$	−3.21039	−0.172842
$346$	0.716679	0.0385289
$347$	30.9573	1.66187	0.830937	−	0.556367i	$-0.187805\pi$
$347$	30.9573	1.66187	0.830937	+	0.556367i	$0.187805\pi$
$348$	42.1367	2.25877
$349$	11.8337	0.633443	0.316721	−	0.948519i	$-0.397418\pi$
$349$	11.8337	0.633443	0.316721	+	0.948519i	$0.397418\pi$
$350$	73.8119	3.94541
$351$	−37.3156	−1.99176
$352$	100.601	5.36203
$353$	−20.6498	−1.09908	−0.549538	−	0.835469i	$-0.685196\pi$
$353$	−20.6498	−1.09908	−0.549538	+	0.835469i	$0.685196\pi$
$354$	29.3647	1.56071
$355$	21.9211	1.16345
$356$	15.1096	0.800808
$357$	−21.1172	−1.11764
$358$	−7.92117	−0.418647
$359$	−12.4939	−0.659402	−0.329701	−	0.944085i	$-0.606948\pi$
$359$	−12.4939	−0.659402	−0.329701	+	0.944085i	$0.606948\pi$
$360$	−59.4324	−3.13236
$361$	−18.5530	−0.976474
$362$	49.2271	2.58732
$363$	−1.77881	−0.0933634
$364$	80.5734	4.22319
$365$	−54.6951	−2.86287
$366$	−11.5412	−0.603268
$367$	−16.9247	−0.883462	−0.441731	−	0.897148i	$-0.645635\pi$
$367$	−16.9247	−0.883462	−0.441731	+	0.897148i	$0.645635\pi$
$368$	−10.5653	−0.550754
$369$	−13.9824	−0.727897
$370$	−20.3499	−1.05794
$371$	−20.0280	−1.03980
$372$	−49.8793	−2.58612
$373$	−4.35952	−0.225727	−0.112864	−	0.993610i	$-0.536002\pi$
$373$	−4.35952	−0.225727	−0.112864	+	0.993610i	$0.536002\pi$
$374$	−77.0179	−3.98250
$375$	41.4651	2.14125
$376$	−36.9913	−1.90768
$377$	37.8361	1.94866
$378$	32.5815	1.67581
$379$	−21.8809	−1.12395	−0.561973	−	0.827155i	$-0.689958\pi$
$379$	−21.8809	−1.12395	−0.561973	+	0.827155i	$0.689958\pi$
$380$	16.2285	0.832506
$381$	8.26449	0.423403
$382$	−15.2933	−0.782473
$383$	26.7267	1.36567	0.682836	−	0.730572i	$-0.260746\pi$
$383$	26.7267	1.36567	0.682836	+	0.730572i	$0.260746\pi$
$384$	84.7265	4.32368
$385$	−30.9114	−1.57539
$386$	−8.95819	−0.455960
$387$	3.11829	0.158512
$388$	14.7126	0.746919
$389$	−32.1733	−1.63125	−0.815627	−	0.578578i	$-0.803608\pi$
$389$	−32.1733	−1.63125	−0.815627	+	0.578578i	$0.803608\pi$
$390$	100.690	5.09865
$391$	4.65816	0.235573
$392$	27.7014	1.39913
$393$	15.7566	0.794816
$394$	−19.8076	−0.997892
$395$	65.0885	3.27496
$396$	27.2979	1.37177
$397$	−9.02294	−0.452848	−0.226424	−	0.974029i	$-0.572704\pi$
$397$	−9.02294	−0.452848	−0.226424	+	0.974029i	$0.572704\pi$
$398$	6.62633	0.332148
$399$	−1.79865	−0.0900453
$400$	225.478	11.2739
$401$	−5.41828	−0.270576	−0.135288	−	0.990806i	$-0.543196\pi$
$401$	−5.41828	−0.270576	−0.135288	+	0.990806i	$0.543196\pi$
$402$	−15.0304	−0.749648
$403$	−44.7884	−2.23107
$404$	−35.4813	−1.76526
$405$	13.3061	0.661185
$406$	−33.0360	−1.63955
$407$	6.11003	0.302863
$408$	−106.359	−5.26558
$409$	−28.7787	−1.42301	−0.711507	−	0.702679i	$-0.751987\pi$
$409$	−28.7787	−1.42301	−0.711507	+	0.702679i	$0.751987\pi$
$410$	121.994	6.02484
$411$	−2.10142	−0.103655
$412$	−60.3538	−2.97342
$413$	−17.1005	−0.841460
$414$	−2.22277	−0.109243
$415$	58.0078	2.84749
$416$	190.833	9.35634
$417$	−2.43886	−0.119432
$418$	−6.56000	−0.320860
$419$	12.3053	0.601153	0.300576	−	0.953758i	$-0.402821\pi$
$419$	12.3053	0.601153	0.300576	+	0.953758i	$0.402821\pi$
$420$	−65.3020	−3.18641
$421$	−11.2958	−0.550525	−0.275262	−	0.961369i	$-0.588765\pi$
$421$	−11.2958	−0.550525	−0.275262	+	0.961369i	$0.588765\pi$
$422$	41.5197	2.02115
$423$	−4.72007	−0.229498
$424$	−100.874	−4.89885
$425$	−99.4114	−4.82216
$426$	−18.7195	−0.906963
$427$	6.72101	0.325252
$428$	−54.7408	−2.64599
$429$	−30.2322	−1.45963
$430$	−27.2064	−1.31201
$431$	−17.5893	−0.847249	−0.423624	−	0.905838i	$-0.639242\pi$
$431$	−17.5893	−0.847249	−0.423624	+	0.905838i	$0.639242\pi$
$432$	99.5287	4.78858
$433$	27.5226	1.32265	0.661325	−	0.750100i	$-0.269994\pi$
$433$	27.5226	1.32265	0.661325	+	0.750100i	$0.269994\pi$
$434$	39.1063	1.87716
$435$	−30.6648	−1.47027
$436$	48.4644	2.32103
$437$	0.396759	0.0189795
$438$	46.7068	2.23174
$439$	−19.5613	−0.933609	−0.466804	−	0.884361i	$-0.654595\pi$
$439$	−19.5613	−0.933609	−0.466804	+	0.884361i	$0.654595\pi$
$440$	−155.690	−7.42221
$441$	3.53468	0.168318
$442$	−146.098	−6.94917
$443$	11.0291	0.524006	0.262003	−	0.965067i	$-0.415617\pi$
$443$	11.0291	0.524006	0.262003	+	0.965067i	$0.415617\pi$
$444$	12.9078	0.612575
$445$	−10.9960	−0.521258
$446$	−32.8734	−1.55660
$447$	−3.35639	−0.158752
$448$	−92.1998	−4.35603
$449$	10.5442	0.497609	0.248805	−	0.968554i	$-0.419962\pi$
$449$	10.5442	0.497609	0.248805	+	0.968554i	$0.419962\pi$
$450$	47.4368	2.23619
$451$	−36.6285	−1.72477
$452$	22.6736	1.06648
$453$	−1.71160	−0.0804180
$454$	−5.92816	−0.278222
$455$	−58.6370	−2.74894
$456$	−9.05916	−0.424234
$457$	−9.28270	−0.434226	−0.217113	−	0.976146i	$-0.569664\pi$
$457$	−9.28270	−0.434226	−0.217113	+	0.976146i	$0.569664\pi$
$458$	−19.8720	−0.928560
$459$	−43.8815	−2.04821
$460$	14.4047	0.671624
$461$	−26.2294	−1.22163	−0.610813	−	0.791775i	$-0.709157\pi$
$461$	−26.2294	−1.22163	−0.610813	+	0.791775i	$0.709157\pi$
$462$	26.3968	1.22809
$463$	−13.8284	−0.642663	−0.321331	−	0.946967i	$-0.604130\pi$
$463$	−13.8284	−0.642663	−0.321331	+	0.946967i	$0.604130\pi$
$464$	−100.917	−4.68495
$465$	36.2994	1.68335
$466$	−45.6824	−2.11620
$467$	−26.2755	−1.21589	−0.607944	−	0.793980i	$-0.708005\pi$
$467$	−26.2755	−1.21589	−0.607944	+	0.793980i	$0.708005\pi$
$468$	51.7822	2.39363
$469$	8.75293	0.404173
$470$	41.1815	1.89956
$471$	9.81306	0.452162
$472$	−86.1289	−3.96440
$473$	8.16871	0.375598
$474$	−55.5823	−2.55298
$475$	−8.46736	−0.388509
$476$	94.7507	4.34289
$477$	−12.8714	−0.589341
$478$	−31.2349	−1.42865
$479$	−18.7167	−0.855187	−0.427594	−	0.903971i	$-0.640639\pi$
$479$	−18.7167	−0.855187	−0.427594	+	0.903971i	$0.640639\pi$
$480$	−154.663	−7.05938
$481$	11.5903	0.528473
$482$	10.1827	0.463809
$483$	−1.59652	−0.0726441
$484$	7.98136	0.362789
$485$	−10.7070	−0.486181
$486$	35.4025	1.60589
$487$	42.2539	1.91471	0.957353	−	0.288921i	$-0.0932967\pi$
$487$	42.2539	1.91471	0.957353	+	0.288921i	$0.0932967\pi$
$488$	33.8513	1.53237
$489$	−15.5966	−0.705302
$490$	−30.8393	−1.39318
$491$	36.9724	1.66854	0.834271	−	0.551354i	$-0.185889\pi$
$491$	36.9724	1.66854	0.834271	+	0.551354i	$0.185889\pi$
$492$	−77.3796	−3.48854
$493$	44.4935	2.00389
$494$	−12.4439	−0.559877
$495$	−19.8659	−0.892906
$496$	119.460	5.36392
$497$	10.9013	0.488990
$498$	−49.5357	−2.21975
$499$	14.3812	0.643790	0.321895	−	0.946775i	$-0.395680\pi$
$499$	14.3812	0.643790	0.321895	+	0.946775i	$0.395680\pi$
$500$	−186.050	−8.32041
$501$	8.90592	0.397887
$502$	−31.8993	−1.42373
$503$	−26.5024	−1.18168	−0.590842	−	0.806787i	$-0.701204\pi$
$503$	−26.5024	−1.18168	−0.590842	+	0.806787i	$0.701204\pi$
$504$	−29.5555	−1.31651
$505$	25.8213	1.14903
$506$	−5.82278	−0.258854
$507$	−40.6156	−1.80380
$508$	−37.0820	−1.64525
$509$	6.06565	0.268855	0.134428	−	0.990923i	$-0.457080\pi$
$509$	6.06565	0.268855	0.134428	+	0.990923i	$0.457080\pi$
$510$	118.407	5.24317
$511$	−27.1997	−1.20324
$512$	−134.152	−5.92873
$513$	−3.73760	−0.165019
$514$	12.2569	0.540627
$515$	43.9223	1.93545
$516$	17.2568	0.759689
$517$	−12.3647	−0.543800
$518$	−10.1199	−0.444643
$519$	0.330821	0.0145215
$520$	−295.333	−12.9512
$521$	−29.1162	−1.27561	−0.637803	−	0.770200i	$-0.720157\pi$
$521$	−29.1162	−1.27561	−0.637803	+	0.770200i	$0.720157\pi$
$522$	−21.2313	−0.929268
$523$	2.12037	0.0927172	0.0463586	−	0.998925i	$-0.485238\pi$
$523$	2.12037	0.0927172	0.0463586	+	0.998925i	$0.485238\pi$
$524$	−70.6984	−3.08847
$525$	34.0719	1.48702
$526$	−63.0900	−2.75086
$527$	−52.6691	−2.29430
$528$	80.6358	3.50922
$529$	−22.6478	−0.984688
$530$	112.300	4.87801
$531$	−10.9900	−0.476925
$532$	8.07039	0.349896
$533$	−69.4819	−3.00959
$534$	9.38999	0.406344
$535$	39.8374	1.72232
$536$	44.0853	1.90420
$537$	−3.65644	−0.157787
$538$	8.02272	0.345884
$539$	9.25948	0.398834
$540$	−135.698	−5.83949
$541$	23.1734	0.996303	0.498151	−	0.867090i	$-0.334012\pi$
$541$	23.1734	0.996303	0.498151	+	0.867090i	$0.334012\pi$
$542$	5.69084	0.244442
$543$	22.7234	0.975154
$544$	224.411	9.62152
$545$	−35.2698	−1.51079
$546$	50.0730	2.14293
$547$	−8.78935	−0.375806	−0.187903	−	0.982188i	$-0.560169\pi$
$547$	−8.78935	−0.375806	−0.187903	+	0.982188i	$0.560169\pi$
$548$	9.42886	0.402781
$549$	4.31940	0.184348
$550$	124.266	5.29872
$551$	3.78973	0.161448
$552$	−8.04108	−0.342251
$553$	32.3683	1.37644
$554$	−36.5518	−1.55294
$555$	−9.39356	−0.398734
$556$	10.9429	0.464084
$557$	−37.4796	−1.58806	−0.794032	−	0.607877i	$-0.792022\pi$
$557$	−37.4796	−1.58806	−0.794032	+	0.607877i	$0.792022\pi$
$558$	25.1325	1.06394
$559$	15.4955	0.655390
$560$	156.397	6.60900
$561$	−35.5517	−1.50100
$562$	−45.1607	−1.90499
$563$	1.72799	0.0728261	0.0364130	−	0.999337i	$-0.488407\pi$
$563$	1.72799	0.0728261	0.0364130	+	0.999337i	$0.488407\pi$
$564$	−26.1211	−1.09990
$565$	−16.5006	−0.694186
$566$	−20.7174	−0.870819
$567$	6.61708	0.277891
$568$	54.9058	2.30380
$569$	6.57622	0.275690	0.137845	−	0.990454i	$-0.455982\pi$
$569$	6.57622	0.275690	0.137845	+	0.990454i	$0.455982\pi$
$570$	10.0853	0.422428
$571$	−8.83204	−0.369609	−0.184805	−	0.982775i	$-0.559165\pi$
$571$	−8.83204	−0.369609	−0.184805	+	0.982775i	$0.559165\pi$
$572$	135.649	5.67177
$573$	−7.05944	−0.294912
$574$	60.6670	2.53219
$575$	−7.51579	−0.313430
$576$	−59.2542	−2.46892
$577$	45.2129	1.88224	0.941119	−	0.338076i	$-0.109776\pi$
$577$	45.2129	1.88224	0.941119	+	0.338076i	$0.109776\pi$
$578$	−124.401	−5.17442
$579$	−4.13513	−0.171850
$580$	137.590	5.71312
$581$	28.8471	1.19678
$582$	9.14326	0.379000
$583$	−33.7180	−1.39646
$584$	−136.995	−5.66889
$585$	−37.6843	−1.55805
$586$	29.9801	1.23847
$587$	31.8880	1.31616	0.658080	−	0.752948i	$-0.271369\pi$
$587$	31.8880	1.31616	0.658080	+	0.752948i	$0.271369\pi$
$588$	19.5611	0.806687
$589$	−4.48609	−0.184846
$590$	95.8852	3.94753
$591$	−9.14326	−0.376103
$592$	−30.9139	−1.27055
$593$	27.8300	1.14284	0.571420	−	0.820658i	$-0.306393\pi$
$593$	27.8300	1.14284	0.571420	+	0.820658i	$0.306393\pi$
$594$	54.8525	2.25063
$595$	−68.9544	−2.82686
$596$	15.0598	0.616874
$597$	3.05874	0.125186
$598$	−11.0454	−0.451681
$599$	25.5757	1.04499	0.522497	−	0.852641i	$-0.325001\pi$
$599$	25.5757	1.04499	0.522497	+	0.852641i	$0.325001\pi$
$600$	171.607	7.00584
$601$	23.8245	0.971823	0.485912	−	0.874008i	$-0.338488\pi$
$601$	23.8245	0.971823	0.485912	+	0.874008i	$0.338488\pi$
$602$	−13.5297	−0.551428
$603$	5.62526	0.229078
$604$	7.67979	0.312486
$605$	−5.80840	−0.236145
$606$	−22.0501	−0.895724
$607$	34.2909	1.39183	0.695913	−	0.718126i	$-0.255000\pi$
$607$	34.2909	1.39183	0.695913	+	0.718126i	$0.255000\pi$
$608$	19.1142	0.775181
$609$	−15.2495	−0.617942
$610$	−37.6858	−1.52585
$611$	−23.4551	−0.948891
$612$	60.8936	2.46148
$613$	7.36431	0.297442	0.148721	−	0.988879i	$-0.452484\pi$
$613$	7.36431	0.297442	0.148721	+	0.988879i	$0.452484\pi$
$614$	49.5015	1.99772
$615$	56.3127	2.27075
$616$	−77.4239	−3.11950
$617$	−10.7842	−0.434156	−0.217078	−	0.976154i	$-0.569653\pi$
$617$	−10.7842	−0.434156	−0.217078	+	0.976154i	$0.569653\pi$
$618$	−37.5074	−1.50877
$619$	13.7874	0.554164	0.277082	−	0.960846i	$-0.410633\pi$
$619$	13.7874	0.554164	0.277082	+	0.960846i	$0.410633\pi$
$620$	−162.872	−6.54110
$621$	−3.31757	−0.133129
$622$	−54.8171	−2.19796
$623$	−5.46825	−0.219081
$624$	152.961	6.12333
$625$	72.0731	2.88292
$626$	−25.2384	−1.00873
$627$	−3.02812	−0.120931
$628$	−44.0303	−1.75700
$629$	13.6297	0.543452
$630$	32.9035	1.31091
$631$	22.4135	0.892266	0.446133	−	0.894967i	$-0.352801\pi$
$631$	22.4135	0.892266	0.446133	+	0.894967i	$0.352801\pi$
$632$	163.027	6.48488
$633$	19.1656	0.761765
$634$	−59.0632	−2.34570
$635$	26.9863	1.07092
$636$	−71.2311	−2.82450
$637$	17.5646	0.695935
$638$	−55.6176	−2.20192
$639$	7.00595	0.277151
$640$	276.660	10.9359
$641$	14.7397	0.582181	0.291091	−	0.956695i	$-0.405982\pi$
$641$	14.7397	0.582181	0.291091	+	0.956695i	$0.405982\pi$
$642$	−34.0191	−1.34263
$643$	11.6908	0.461041	0.230520	−	0.973067i	$-0.425957\pi$
$643$	11.6908	0.461041	0.230520	+	0.973067i	$0.425957\pi$
$644$	7.16343	0.282279
$645$	−12.5586	−0.494493
$646$	−14.6334	−0.575745
$647$	−12.5883	−0.494898	−0.247449	−	0.968901i	$-0.579592\pi$
$647$	−12.5883	−0.494898	−0.247449	+	0.968901i	$0.579592\pi$
$648$	33.3278	1.30924
$649$	−28.7895	−1.13009
$650$	235.724	9.24586
$651$	18.0516	0.707497
$652$	69.9804	2.74065
$653$	7.54883	0.295409	0.147704	−	0.989032i	$-0.452812\pi$
$653$	7.54883	0.295409	0.147704	+	0.989032i	$0.452812\pi$
$654$	30.1186	1.17773
$655$	51.4505	2.01034
$656$	185.323	7.23565
$657$	−17.4805	−0.681978
$658$	20.4794	0.798371
$659$	16.6421	0.648284	0.324142	−	0.946008i	$-0.394924\pi$
$659$	16.6421	0.648284	0.324142	+	0.946008i	$0.394924\pi$
$660$	−109.939	−4.27937
$661$	−10.8078	−0.420373	−0.210187	−	0.977661i	$-0.567407\pi$
$661$	−10.8078	−0.420373	−0.210187	+	0.977661i	$0.567407\pi$
$662$	−86.6575	−3.36804
$663$	−67.4393	−2.61913
$664$	145.292	5.63843
$665$	−5.87319	−0.227753
$666$	−6.50378	−0.252016
$667$	3.36384	0.130248
$668$	−39.9600	−1.54610
$669$	−15.1745	−0.586679
$670$	−49.0791	−1.89609
$671$	11.3151	0.436816
$672$	−76.9135	−2.96700
$673$	−18.3694	−0.708088	−0.354044	−	0.935229i	$-0.615194\pi$
$673$	−18.3694	−0.708088	−0.354044	+	0.935229i	$0.615194\pi$
$674$	94.7846	3.65097
$675$	70.8013	2.72514
$676$	182.239	7.00917
$677$	−11.4478	−0.439976	−0.219988	−	0.975503i	$-0.570602\pi$
$677$	−11.4478	−0.439976	−0.219988	+	0.975503i	$0.570602\pi$
$678$	14.0907	0.541149
$679$	−5.32457	−0.204338
$680$	−347.298	−13.3183
$681$	−2.73646	−0.104861
$682$	65.8372	2.52104
$683$	−8.29956	−0.317574	−0.158787	−	0.987313i	$-0.550758\pi$
$683$	−8.29956	−0.317574	−0.158787	+	0.987313i	$0.550758\pi$
$684$	5.18661	0.198315
$685$	−6.86181	−0.262176
$686$	−56.1331	−2.14317
$687$	−9.17300	−0.349972
$688$	−41.3298	−1.57569
$689$	−63.9609	−2.43672
$690$	8.95194	0.340794
$691$	−38.7936	−1.47578	−0.737889	−	0.674922i	$-0.764177\pi$
$691$	−38.7936	−1.47578	−0.737889	+	0.674922i	$0.764177\pi$
$692$	−1.48436	−0.0564271
$693$	−9.87924	−0.375281
$694$	−86.3220	−3.27674
$695$	−7.96369	−0.302080
$696$	−76.8062	−2.91133
$697$	−81.7076	−3.09489
$698$	−32.9973	−1.24897
$699$	−21.0871	−0.797589
$700$	−152.877	−5.77821
$701$	13.8044	0.521384	0.260692	−	0.965422i	$-0.416049\pi$
$701$	13.8044	0.521384	0.260692	+	0.965422i	$0.416049\pi$
$702$	104.052	3.92718
$703$	1.16091	0.0437845
$704$	−155.223	−5.85018
$705$	19.0095	0.715940
$706$	57.5802	2.16706
$707$	12.8409	0.482930
$708$	−60.8193	−2.28573
$709$	−5.06231	−0.190119	−0.0950594	−	0.995472i	$-0.530304\pi$
$709$	−5.06231	−0.190119	−0.0950594	+	0.995472i	$0.530304\pi$
$710$	−61.1253	−2.29399
$711$	20.8022	0.780143
$712$	−27.5416	−1.03216
$713$	−3.98194	−0.149125
$714$	58.8836	2.20366
$715$	−98.7181	−3.69185
$716$	16.4061	0.613124
$717$	−14.4182	−0.538456
$718$	34.8382	1.30015
$719$	3.19794	0.119263	0.0596315	−	0.998220i	$-0.481007\pi$
$719$	3.19794	0.119263	0.0596315	+	0.998220i	$0.481007\pi$
$720$	100.512	3.74587
$721$	21.8424	0.813453
$722$	51.7336	1.92533
$723$	4.70037	0.174809
$724$	−101.958	−3.78923
$725$	−71.7888	−2.66617
$726$	4.96008	0.184086
$727$	−13.8992	−0.515493	−0.257747	−	0.966213i	$-0.582980\pi$
$727$	−13.8992	−0.515493	−0.257747	+	0.966213i	$0.582980\pi$
$728$	−146.868	−5.44329
$729$	25.8396	0.957022
$730$	152.513	5.64476
$731$	18.2220	0.673966
$732$	23.9038	0.883510
$733$	37.2771	1.37686	0.688431	−	0.725302i	$-0.258300\pi$
$733$	37.2771	1.37686	0.688431	+	0.725302i	$0.258300\pi$
$734$	47.1932	1.74193
$735$	−14.2355	−0.525085
$736$	16.9661	0.625378
$737$	14.7360	0.542807
$738$	38.9890	1.43520
$739$	−26.8520	−0.987767	−0.493883	−	0.869528i	$-0.664423\pi$
$739$	−26.8520	−0.987767	−0.493883	+	0.869528i	$0.664423\pi$
$740$	42.1480	1.54939
$741$	−5.74414	−0.211016
$742$	55.8465	2.05019
$743$	1.55999	0.0572306	0.0286153	−	0.999590i	$-0.490890\pi$
$743$	1.55999	0.0572306	0.0286153	+	0.999590i	$0.490890\pi$
$744$	90.9192	3.33326
$745$	−10.9597	−0.401533
$746$	12.1562	0.445070
$747$	18.5392	0.678314
$748$	159.517	5.83253
$749$	19.8110	0.723877
$750$	−115.622	−4.22193
$751$	46.2302	1.68696	0.843482	−	0.537157i	$-0.180502\pi$
$751$	46.2302	1.68696	0.843482	+	0.537157i	$0.180502\pi$
$752$	62.5597	2.28132
$753$	−14.7248	−0.536602
$754$	−105.503	−3.84219
$755$	−5.58893	−0.203402
$756$	−67.4819	−2.45429
$757$	−7.58743	−0.275770	−0.137885	−	0.990448i	$-0.544030\pi$
$757$	−7.58743	−0.275770	−0.137885	+	0.990448i	$0.544030\pi$
$758$	61.0132	2.21610
$759$	−2.68781	−0.0975615
$760$	−29.5811	−1.07302
$761$	11.0108	0.399140	0.199570	−	0.979884i	$-0.436045\pi$
$761$	11.0108	0.399140	0.199570	+	0.979884i	$0.436045\pi$
$762$	−23.0449	−0.834829
$763$	−17.5395	−0.634974
$764$	31.6750	1.14596
$765$	−44.3151	−1.60221
$766$	−74.5254	−2.69271
$767$	−54.6118	−1.97192
$768$	−122.695	−4.42738
$769$	43.6752	1.57497	0.787485	−	0.616334i	$-0.211383\pi$
$769$	43.6752	1.57497	0.787485	+	0.616334i	$0.211383\pi$
$770$	86.1942	3.10622
$771$	5.65781	0.203761
$772$	18.5539	0.667771
$773$	−30.2553	−1.08821	−0.544104	−	0.839018i	$-0.683130\pi$
$773$	−30.2553	−1.08821	−0.544104	+	0.839018i	$0.683130\pi$
$774$	−8.69512	−0.312540
$775$	84.9799	3.05257
$776$	−26.8179	−0.962707
$777$	−4.67139	−0.167585
$778$	89.7129	3.21636
$779$	−6.95944	−0.249348
$780$	−208.547	−7.46718
$781$	18.3528	0.656716
$782$	−12.9889	−0.464483
$783$	−31.6885	−1.13245
$784$	−46.8486	−1.67316
$785$	32.0429	1.14366
$786$	−43.9361	−1.56715
$787$	8.92906	0.318287	0.159143	−	0.987256i	$-0.449127\pi$
$787$	8.92906	0.318287	0.159143	+	0.987256i	$0.449127\pi$
$788$	41.0249	1.46145
$789$	−29.1226	−1.03679
$790$	−181.494	−6.45728
$791$	−8.20570	−0.291761
$792$	−49.7581	−1.76808
$793$	21.4641	0.762211
$794$	25.1598	0.892887
$795$	51.8381	1.83851
$796$	−13.7243	−0.486444
$797$	26.6777	0.944972	0.472486	−	0.881338i	$-0.343357\pi$
$797$	26.6777	0.944972	0.472486	+	0.881338i	$0.343357\pi$
$798$	5.01541	0.177543
$799$	−27.5821	−0.975785
$800$	−362.079	−12.8014
$801$	−3.51429	−0.124171
$802$	15.1085	0.533498
$803$	−45.7920	−1.61596
$804$	31.1305	1.09789
$805$	−5.21315	−0.183740
$806$	124.889	4.39902
$807$	3.70332	0.130363
$808$	64.6747	2.27525
$809$	35.9138	1.26266	0.631330	−	0.775514i	$-0.282509\pi$
$809$	35.9138	1.26266	0.631330	+	0.775514i	$0.282509\pi$
$810$	−37.1030	−1.30367
$811$	30.6297	1.07555	0.537776	−	0.843088i	$-0.319265\pi$
$811$	30.6297	1.07555	0.537776	+	0.843088i	$0.319265\pi$
$812$	68.4231	2.40118
$813$	2.62691	0.0921298
$814$	−17.0373	−0.597159
$815$	−50.9280	−1.78393
$816$	179.875	6.29689
$817$	1.55206	0.0542997
$818$	80.2472	2.80578
$819$	−18.7403	−0.654838
$820$	−252.670	−8.82361
$821$	53.9118	1.88153	0.940767	−	0.339053i	$-0.110107\pi$
$821$	53.9118	1.88153	0.940767	+	0.339053i	$0.110107\pi$
$822$	5.85964	0.204378
$823$	19.0853	0.665272	0.332636	−	0.943055i	$-0.392062\pi$
$823$	19.0853	0.665272	0.332636	+	0.943055i	$0.392062\pi$
$824$	110.012	3.83245
$825$	57.3616	1.99707
$826$	47.6834	1.65912
$827$	33.4615	1.16357	0.581785	−	0.813343i	$-0.302355\pi$
$827$	33.4615	1.16357	0.581785	+	0.813343i	$0.302355\pi$
$828$	4.60373	0.159991
$829$	−3.47643	−0.120741	−0.0603707	−	0.998176i	$-0.519228\pi$
$829$	−3.47643	−0.120741	−0.0603707	+	0.998176i	$0.519228\pi$
$830$	−161.750	−5.61443
$831$	−16.8724	−0.585298
$832$	−294.447	−10.2081
$833$	20.6552	0.715660
$834$	6.80058	0.235485
$835$	29.0807	1.00638
$836$	13.5869	0.469912
$837$	37.5112	1.29658
$838$	−34.3123	−1.18530
$839$	−8.81630	−0.304373	−0.152186	−	0.988352i	$-0.548631\pi$
$839$	−8.81630	−0.304373	−0.152186	+	0.988352i	$0.548631\pi$
$840$	119.032	4.10698
$841$	3.13049	0.107948
$842$	31.4975	1.08548
$843$	−20.8464	−0.717986
$844$	−85.9944	−2.96005
$845$	−132.623	−4.56238
$846$	13.1615	0.452503
$847$	−2.88850	−0.0992499
$848$	170.597	5.85834
$849$	−9.56324	−0.328209
$850$	277.201	9.50792
$851$	1.03044	0.0353232
$852$	38.7713	1.32828
$853$	−44.5341	−1.52482	−0.762409	−	0.647095i	$-0.775984\pi$
$853$	−44.5341	−1.52482	−0.762409	+	0.647095i	$0.775984\pi$
$854$	−18.7410	−0.641304
$855$	−3.77453	−0.129086
$856$	99.7807	3.41043
$857$	33.4987	1.14429	0.572147	−	0.820151i	$-0.306111\pi$
$857$	33.4987	1.14429	0.572147	+	0.820151i	$0.306111\pi$
$858$	84.3002	2.87796
$859$	−23.2516	−0.793334	−0.396667	−	0.917963i	$-0.629833\pi$
$859$	−23.2516	−0.793334	−0.396667	+	0.917963i	$0.629833\pi$
$860$	56.3491	1.92149
$861$	28.0041	0.954377
$862$	49.0465	1.67053
$863$	−0.770147	−0.0262161	−0.0131081	−	0.999914i	$-0.504173\pi$
$863$	−0.770147	−0.0262161	−0.0131081	+	0.999914i	$0.504173\pi$
$864$	−159.826	−5.43740
$865$	1.08024	0.0367293
$866$	−76.7445	−2.60789
$867$	−57.4241	−1.95023
$868$	−80.9958	−2.74918
$869$	54.4936	1.84857
$870$	85.5065	2.89894
$871$	27.9532	0.947157
$872$	−88.3403	−2.99158
$873$	−3.42195	−0.115815
$874$	−1.10633	−0.0374222
$875$	67.3325	2.27625
$876$	−96.7379	−3.26847
$877$	48.0021	1.62092	0.810458	−	0.585796i	$-0.199218\pi$
$877$	48.0021	1.62092	0.810458	+	0.585796i	$0.199218\pi$
$878$	54.5451	1.84081
$879$	13.8389	0.466775
$880$	263.302	8.87592
$881$	−16.9411	−0.570760	−0.285380	−	0.958414i	$-0.592120\pi$
$881$	−16.9411	−0.570760	−0.285380	+	0.958414i	$0.592120\pi$
$882$	−9.85618	−0.331875
$883$	−34.4824	−1.16042	−0.580212	−	0.814465i	$-0.697030\pi$
$883$	−34.4824	−1.16042	−0.580212	+	0.814465i	$0.697030\pi$
$884$	302.594	10.1773
$885$	44.2610	1.48782
$886$	−30.7537	−1.03319
$887$	47.8487	1.60660	0.803301	−	0.595574i	$-0.203075\pi$
$887$	47.8487	1.60660	0.803301	+	0.595574i	$0.203075\pi$
$888$	−23.5281	−0.789550
$889$	13.4202	0.450098
$890$	30.6614	1.02777
$891$	11.1402	0.373209
$892$	68.0864	2.27970
$893$	−2.34931	−0.0786165
$894$	9.35904	0.313013
$895$	−11.9395	−0.399092
$896$	137.582	4.59629
$897$	−5.09861	−0.170237
$898$	−29.4016	−0.981143
$899$	−38.0344	−1.26852
$900$	−98.2498	−3.27499
$901$	−75.2151	−2.50578
$902$	102.136	3.40075
$903$	−6.24534	−0.207832
$904$	−41.3291	−1.37459
$905$	74.1993	2.46647
$906$	4.77266	0.158561
$907$	−21.9622	−0.729245	−0.364622	−	0.931156i	$-0.618802\pi$
$907$	−21.9622	−0.729245	−0.364622	+	0.931156i	$0.618802\pi$
$908$	12.2782	0.407467
$909$	8.25246	0.273717
$910$	163.505	5.42013
$911$	−46.9475	−1.55544	−0.777720	−	0.628611i	$-0.783624\pi$
$911$	−46.9475	−1.55544	−0.777720	+	0.628611i	$0.783624\pi$
$912$	15.3209	0.507324
$913$	48.5654	1.60728
$914$	25.8841	0.856169
$915$	−17.3959	−0.575090
$916$	41.1584	1.35991
$917$	25.5861	0.844929
$918$	122.360	4.03848
$919$	−16.1902	−0.534065	−0.267033	−	0.963687i	$-0.586043\pi$
$919$	−16.1902	−0.534065	−0.267033	+	0.963687i	$0.586043\pi$
$920$	−26.2567	−0.865659
$921$	22.8501	0.752936
$922$	73.1387	2.40869
$923$	34.8141	1.14592
$924$	−54.6723	−1.79859
$925$	−21.9911	−0.723062
$926$	38.5596	1.26715
$927$	14.0375	0.461051
$928$	162.056	5.31973
$929$	−19.3484	−0.634801	−0.317400	−	0.948292i	$-0.602810\pi$
$929$	−19.3484	−0.634801	−0.317400	+	0.948292i	$0.602810\pi$
$930$	−101.218	−3.31907
$931$	1.75931	0.0576589
$932$	94.6160	3.09925
$933$	−25.3038	−0.828408
$934$	73.2673	2.39738
$935$	−116.088	−3.79648
$936$	−94.3879	−3.08517
$937$	−10.8881	−0.355699	−0.177849	−	0.984058i	$-0.556914\pi$
$937$	−10.8881	−0.355699	−0.177849	+	0.984058i	$0.556914\pi$
$938$	−24.4069	−0.796913
$939$	−11.6501	−0.380187
$940$	−85.2940	−2.78198
$941$	−47.3361	−1.54311	−0.771557	−	0.636161i	$-0.780522\pi$
$941$	−47.3361	−1.54311	−0.771557	+	0.636161i	$0.780522\pi$
$942$	−27.3630	−0.891534
$943$	−6.17733	−0.201161
$944$	145.661	4.74087
$945$	49.1097	1.59754
$946$	−22.7778	−0.740571
$947$	−45.5612	−1.48054	−0.740270	−	0.672310i	$-0.765302\pi$
$947$	−45.5612	−1.48054	−0.740270	+	0.672310i	$0.765302\pi$
$948$	115.120	3.73894
$949$	−86.8643	−2.81974
$950$	23.6106	0.766029
$951$	−27.2638	−0.884089
$952$	−172.710	−5.59757
$953$	36.5731	1.18472	0.592359	−	0.805674i	$-0.298197\pi$
$953$	36.5731	1.18472	0.592359	+	0.805674i	$0.298197\pi$
$954$	35.8909	1.16201
$955$	−23.0514	−0.745925
$956$	64.6929	2.09232
$957$	−25.6733	−0.829899
$958$	52.1900	1.68618
$959$	−3.41236	−0.110191
$960$	238.639	7.70206
$961$	14.0231	0.452360
$962$	−32.3187	−1.04200
$963$	12.7320	0.410281
$964$	−21.0901	−0.679267
$965$	−13.5026	−0.434663
$966$	4.45177	0.143233
$967$	−5.58003	−0.179442	−0.0897209	−	0.995967i	$-0.528598\pi$
$967$	−5.58003	−0.179442	−0.0897209	+	0.995967i	$0.528598\pi$
$968$	−14.5483	−0.467600
$969$	−6.75485	−0.216997
$970$	29.8557	0.958609
$971$	17.2716	0.554271	0.277136	−	0.960831i	$-0.410615\pi$
$971$	17.2716	0.554271	0.277136	+	0.960831i	$0.410615\pi$
$972$	−73.3246	−2.35189
$973$	−3.96031	−0.126962
$974$	−117.822	−3.77525
$975$	108.811	3.48474
$976$	−57.2493	−1.83250
$977$	29.3227	0.938115	0.469058	−	0.883168i	$-0.344594\pi$
$977$	29.3227	0.938115	0.469058	+	0.883168i	$0.344594\pi$
$978$	43.4899	1.39065
$979$	−9.20606	−0.294227
$980$	63.8734	2.04036
$981$	−11.2722	−0.359893
$982$	−103.095	−3.28989
$983$	−6.45477	−0.205875	−0.102938	−	0.994688i	$-0.532824\pi$
$983$	−6.45477	−0.205875	−0.102938	+	0.994688i	$0.532824\pi$
$984$	141.046	4.49640
$985$	−29.8557	−0.951282
$986$	−124.067	−3.95109
$987$	9.45338	0.300904
$988$	25.7734	0.819961
$989$	1.37764	0.0438063
$990$	55.3945	1.76055
$991$	29.9182	0.950382	0.475191	−	0.879883i	$-0.342379\pi$
$991$	29.9182	0.950382	0.475191	+	0.879883i	$0.342379\pi$
$992$	−191.833	−6.09070
$993$	−40.0014	−1.26941
$994$	−30.3974	−0.964147
$995$	9.98778	0.316634
$996$	102.597	3.25091
$997$	32.5489	1.03083	0.515417	−	0.856940i	$-0.327637\pi$
$997$	32.5489	1.03083	0.515417	+	0.856940i	$0.327637\pi$
$998$	−40.1008	−1.26937
$999$	−9.70714	−0.307120

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4027.2.a.b.1.2	✓	159

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4027.2.a.b.1.2	✓	159	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:	\( N \)	\(=\)	\( 4027 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.78842 q^{2} -1.28715 q^{3} +5.77530 q^{4} -4.20295 q^{5} +3.58911 q^{6} -2.09011 q^{7} -10.5271 q^{8} -1.34326 q^{9} +O(q^{10})\)	\(q-2.78842 q^{2} -1.28715 q^{3} +5.77530 q^{4} -4.20295 q^{5} +3.58911 q^{6} -2.09011 q^{7} -10.5271 q^{8} -1.34326 q^{9} +11.7196 q^{10} -3.51880 q^{11} -7.43365 q^{12} -6.67494 q^{13} +5.82812 q^{14} +5.40981 q^{15} +17.8035 q^{16} -7.84943 q^{17} +3.74557 q^{18} -0.668575 q^{19} -24.2733 q^{20} +2.69028 q^{21} +9.81191 q^{22} -0.593440 q^{23} +13.5500 q^{24} +12.6648 q^{25} +18.6126 q^{26} +5.59040 q^{27} -12.0710 q^{28} -5.66838 q^{29} -15.0848 q^{30} +6.70993 q^{31} -28.5894 q^{32} +4.52921 q^{33} +21.8875 q^{34} +8.78464 q^{35} -7.75771 q^{36} -1.73639 q^{37} +1.86427 q^{38} +8.59162 q^{39} +44.2450 q^{40} +10.4094 q^{41} -7.50164 q^{42} -2.32144 q^{43} -20.3222 q^{44} +5.64564 q^{45} +1.65476 q^{46} +3.51390 q^{47} -22.9157 q^{48} -2.63143 q^{49} -35.3148 q^{50} +10.1034 q^{51} -38.5498 q^{52} +9.58224 q^{53} -15.5884 q^{54} +14.7894 q^{55} +22.0029 q^{56} +0.860553 q^{57} +15.8058 q^{58} +8.18161 q^{59} +31.2433 q^{60} -3.21562 q^{61} -18.7101 q^{62} +2.80756 q^{63} +44.1124 q^{64} +28.0544 q^{65} -12.6294 q^{66} -4.18778 q^{67} -45.3328 q^{68} +0.763843 q^{69} -24.4953 q^{70} -5.21564 q^{71} +14.1406 q^{72} +13.0135 q^{73} +4.84180 q^{74} -16.3014 q^{75} -3.86122 q^{76} +7.35470 q^{77} -23.9571 q^{78} -15.4864 q^{79} -74.8272 q^{80} -3.16589 q^{81} -29.0257 q^{82} -13.8017 q^{83} +15.5372 q^{84} +32.9908 q^{85} +6.47317 q^{86} +7.29603 q^{87} +37.0429 q^{88} +2.61625 q^{89} -15.7424 q^{90} +13.9514 q^{91} -3.42729 q^{92} -8.63666 q^{93} -9.79824 q^{94} +2.80999 q^{95} +36.7987 q^{96} +2.54750 q^{97} +7.33753 q^{98} +4.72666 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9}+O(q^{10}) \) 159 * q - 22 * q^2 - 19 * q^3 + 148 * q^4 - 70 * q^5 - 23 * q^6 - 19 * q^7 - 66 * q^8 + 126 * q^9	\( 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9} - 23 q^{10} - 33 q^{11} - 57 q^{12} - 90 q^{13} - 28 q^{14} - 22 q^{15} + 130 q^{16} - 145 q^{17} - 50 q^{18} - 28 q^{19} - 121 q^{20} - 69 q^{21} - 26 q^{22} - 79 q^{23} - 62 q^{24} + 123 q^{25} - 40 q^{26} - 70 q^{27} - 43 q^{28} - 109 q^{29} - 43 q^{30} - 21 q^{31} - 139 q^{32} - 83 q^{33} - 93 q^{35} + 75 q^{36} - 65 q^{37} - 122 q^{38} - 18 q^{39} - 43 q^{40} - 71 q^{41} - 88 q^{42} - 72 q^{43} - 79 q^{44} - 181 q^{45} - 11 q^{46} - 114 q^{47} - 118 q^{48} + 118 q^{49} - 77 q^{50} - 29 q^{51} - 169 q^{52} - 220 q^{53} - 80 q^{54} - 37 q^{55} - 72 q^{56} - 90 q^{57} - 8 q^{58} - 60 q^{59} - 42 q^{60} - 108 q^{61} - 152 q^{62} - 65 q^{63} + 114 q^{64} - 81 q^{65} - 40 q^{66} - 50 q^{67} - 319 q^{68} - 103 q^{69} + 4 q^{70} - 7 q^{71} - 129 q^{72} - 94 q^{73} - 79 q^{74} - 59 q^{75} - 46 q^{76} - 329 q^{77} + 8 q^{78} - 18 q^{79} - 190 q^{80} + 59 q^{81} - 56 q^{82} - 201 q^{83} - 71 q^{84} - 26 q^{85} - 52 q^{86} - 126 q^{87} - 66 q^{88} - 114 q^{89} - 33 q^{90} - 30 q^{91} - 204 q^{92} - 125 q^{93} + 9 q^{94} - 84 q^{95} - 88 q^{96} - 56 q^{97} - 110 q^{98} - 46 q^{99}+O(q^{100}) \) 159 * q - 22 * q^2 - 19 * q^3 + 148 * q^4 - 70 * q^5 - 23 * q^6 - 19 * q^7 - 66 * q^8 + 126 * q^9 - 23 * q^10 - 33 * q^11 - 57 * q^12 - 90 * q^13 - 28 * q^14 - 22 * q^15 + 130 * q^16 - 145 * q^17 - 50 * q^18 - 28 * q^19 - 121 * q^20 - 69 * q^21 - 26 * q^22 - 79 * q^23 - 62 * q^24 + 123 * q^25 - 40 * q^26 - 70 * q^27 - 43 * q^28 - 109 * q^29 - 43 * q^30 - 21 * q^31 - 139 * q^32 - 83 * q^33 - 93 * q^35 + 75 * q^36 - 65 * q^37 - 122 * q^38 - 18 * q^39 - 43 * q^40 - 71 * q^41 - 88 * q^42 - 72 * q^43 - 79 * q^44 - 181 * q^45 - 11 * q^46 - 114 * q^47 - 118 * q^48 + 118 * q^49 - 77 * q^50 - 29 * q^51 - 169 * q^52 - 220 * q^53 - 80 * q^54 - 37 * q^55 - 72 * q^56 - 90 * q^57 - 8 * q^58 - 60 * q^59 - 42 * q^60 - 108 * q^61 - 152 * q^62 - 65 * q^63 + 114 * q^64 - 81 * q^65 - 40 * q^66 - 50 * q^67 - 319 * q^68 - 103 * q^69 + 4 * q^70 - 7 * q^71 - 129 * q^72 - 94 * q^73 - 79 * q^74 - 59 * q^75 - 46 * q^76 - 329 * q^77 + 8 * q^78 - 18 * q^79 - 190 * q^80 + 59 * q^81 - 56 * q^82 - 201 * q^83 - 71 * q^84 - 26 * q^85 - 52 * q^86 - 126 * q^87 - 66 * q^88 - 114 * q^89 - 33 * q^90 - 30 * q^91 - 204 * q^92 - 125 * q^93 + 9 * q^94 - 84 * q^95 - 88 * q^96 - 56 * q^97 - 110 * q^98 - 46 * q^99

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