LMFDB - Embedded newform 8027.2.a.c.1.16

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			1.16
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)

$f(q)$	$=$	$q-2.40357 q^{2} +1.04878 q^{3} +3.77713 q^{4} -2.29703 q^{5} -2.52082 q^{6} -0.387376 q^{7} -4.27144 q^{8} -1.90005 q^{9} +O(q^{10})$	\(q-2.40357 q^{2} +1.04878 q^{3} +3.77713 q^{4} -2.29703 q^{5} -2.52082 q^{6} -0.387376 q^{7} -4.27144 q^{8} -1.90005 q^{9} +5.52106 q^{10} +1.64959 q^{11} +3.96139 q^{12} -1.09743 q^{13} +0.931084 q^{14} -2.40909 q^{15} +2.71244 q^{16} -2.69721 q^{17} +4.56690 q^{18} +0.0823446 q^{19} -8.67617 q^{20} -0.406274 q^{21} -3.96489 q^{22} +1.00000 q^{23} -4.47983 q^{24} +0.276337 q^{25} +2.63774 q^{26} -5.13910 q^{27} -1.46317 q^{28} +1.42708 q^{29} +5.79040 q^{30} +3.48130 q^{31} +2.02336 q^{32} +1.73006 q^{33} +6.48292 q^{34} +0.889814 q^{35} -7.17673 q^{36} +1.61963 q^{37} -0.197921 q^{38} -1.15096 q^{39} +9.81163 q^{40} +0.823472 q^{41} +0.976507 q^{42} +4.95785 q^{43} +6.23070 q^{44} +4.36447 q^{45} -2.40357 q^{46} +0.644770 q^{47} +2.84477 q^{48} -6.84994 q^{49} -0.664195 q^{50} -2.82879 q^{51} -4.14512 q^{52} +13.1004 q^{53} +12.3522 q^{54} -3.78915 q^{55} +1.65466 q^{56} +0.0863618 q^{57} -3.43008 q^{58} +4.99826 q^{59} -9.09943 q^{60} -0.219039 q^{61} -8.36754 q^{62} +0.736034 q^{63} -10.2882 q^{64} +2.52082 q^{65} -4.15832 q^{66} +1.85069 q^{67} -10.1877 q^{68} +1.04878 q^{69} -2.13873 q^{70} +13.0713 q^{71} +8.11596 q^{72} -5.52804 q^{73} -3.89289 q^{74} +0.289818 q^{75} +0.311026 q^{76} -0.639011 q^{77} +2.76642 q^{78} -0.390797 q^{79} -6.23055 q^{80} +0.310342 q^{81} -1.97927 q^{82} +8.94397 q^{83} -1.53455 q^{84} +6.19556 q^{85} -11.9165 q^{86} +1.49670 q^{87} -7.04612 q^{88} -10.1117 q^{89} -10.4903 q^{90} +0.425117 q^{91} +3.77713 q^{92} +3.65114 q^{93} -1.54975 q^{94} -0.189148 q^{95} +2.12207 q^{96} -3.97541 q^{97} +16.4643 q^{98} -3.13430 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.40357	−1.69958	−0.849789	−	0.527123i	$-0.823271\pi$
$2$	−2.40357	−1.69958	−0.849789	+	0.527123i	$0.823271\pi$
$3$	1.04878	0.605516	0.302758	−	0.953067i	$-0.402093\pi$
$3$	1.04878	0.605516	0.302758	+	0.953067i	$0.402093\pi$
$4$	3.77713	1.88856
$5$	−2.29703	−1.02726	−0.513631	−	0.858011i	$-0.671700\pi$
$5$	−2.29703	−1.02726	−0.513631	+	0.858011i	$0.671700\pi$
$6$	−2.52082	−1.02912
$7$	−0.387376	−0.146414	−0.0732072	−	0.997317i	$-0.523323\pi$
$7$	−0.387376	−0.146414	−0.0732072	+	0.997317i	$0.523323\pi$
$8$	−4.27144	−1.51018
$9$	−1.90005	−0.633350
$10$	5.52106	1.74591
$11$	1.64959	0.497369	0.248685	−	0.968585i	$-0.420002\pi$
$11$	1.64959	0.497369	0.248685	+	0.968585i	$0.420002\pi$
$12$	3.96139	1.14356
$13$	−1.09743	−0.304371	−0.152186	−	0.988352i	$-0.548631\pi$
$13$	−1.09743	−0.304371	−0.152186	+	0.988352i	$0.548631\pi$
$14$	0.931084	0.248843
$15$	−2.40909	−0.622024
$16$	2.71244	0.678110
$17$	−2.69721	−0.654169	−0.327085	−	0.944995i	$-0.606066\pi$
$17$	−2.69721	−0.654169	−0.327085	+	0.944995i	$0.606066\pi$
$18$	4.56690	1.07643
$19$	0.0823446	0.0188912	0.00944558	−	0.999955i	$-0.496993\pi$
$19$	0.0823446	0.0188912	0.00944558	+	0.999955i	$0.496993\pi$
$20$	−8.67617	−1.94005
$21$	−0.406274	−0.0886563
$22$	−3.96489	−0.845318
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−4.47983	−0.914441
$25$	0.276337	0.0552675
$26$	2.63774	0.517303
$27$	−5.13910	−0.989020
$28$	−1.46317	−0.276513
$29$	1.42708	0.265002	0.132501	−	0.991183i	$-0.457699\pi$
$29$	1.42708	0.265002	0.132501	+	0.991183i	$0.457699\pi$
$30$	5.79040	1.05718
$31$	3.48130	0.625260	0.312630	−	0.949875i	$-0.398790\pi$
$31$	3.48130	0.625260	0.312630	+	0.949875i	$0.398790\pi$
$32$	2.02336	0.357683
$33$	1.73006	0.301165
$34$	6.48292	1.11181
$35$	0.889814	0.150406
$36$	−7.17673	−1.19612
$37$	1.61963	0.266265	0.133133	−	0.991098i	$-0.457496\pi$
$37$	1.61963	0.266265	0.133133	+	0.991098i	$0.457496\pi$
$38$	−0.197921	−0.0321070
$39$	−1.15096	−0.184302
$40$	9.81163	1.55135
$41$	0.823472	0.128605	0.0643024	−	0.997930i	$-0.479518\pi$
$41$	0.823472	0.128605	0.0643024	+	0.997930i	$0.479518\pi$
$42$	0.976507	0.150678
$43$	4.95785	0.756065	0.378033	−	0.925792i	$-0.376601\pi$
$43$	4.95785	0.756065	0.378033	+	0.925792i	$0.376601\pi$
$44$	6.23070	0.939314
$45$	4.36447	0.650617
$46$	−2.40357	−0.354386
$47$	0.644770	0.0940494	0.0470247	−	0.998894i	$-0.485026\pi$
$47$	0.644770	0.0940494	0.0470247	+	0.998894i	$0.485026\pi$
$48$	2.84477	0.410607
$49$	−6.84994	−0.978563
$50$	−0.664195	−0.0939314
$51$	−2.82879	−0.396110
$52$	−4.14512	−0.574825
$53$	13.1004	1.79948	0.899742	−	0.436422i	$-0.143754\pi$
$53$	13.1004	1.79948	0.899742	+	0.436422i	$0.143754\pi$
$54$	12.3522	1.68092
$55$	−3.78915	−0.510929
$56$	1.65466	0.221113
$57$	0.0863618	0.0114389
$58$	−3.43008	−0.450392
$59$	4.99826	0.650717	0.325359	−	0.945591i	$-0.394515\pi$
$59$	4.99826	0.650717	0.325359	+	0.945591i	$0.394515\pi$
$60$	−9.09943	−1.17473
$61$	−0.219039	−0.0280451	−0.0140225	−	0.999902i	$-0.504464\pi$
$61$	−0.219039	−0.0280451	−0.0140225	+	0.999902i	$0.504464\pi$
$62$	−8.36754	−1.06268
$63$	0.736034	0.0927316
$64$	−10.2882	−1.28602
$65$	2.52082	0.312669
$66$	−4.15832	−0.511854
$67$	1.85069	0.226098	0.113049	−	0.993589i	$-0.463938\pi$
$67$	1.85069	0.226098	0.113049	+	0.993589i	$0.463938\pi$
$68$	−10.1877	−1.23544
$69$	1.04878	0.126259
$70$	−2.13873	−0.255627
$71$	13.0713	1.55128	0.775638	−	0.631178i	$-0.217428\pi$
$71$	13.0713	1.55128	0.775638	+	0.631178i	$0.217428\pi$
$72$	8.11596	0.956475
$73$	−5.52804	−0.647009	−0.323504	−	0.946227i	$-0.604861\pi$
$73$	−5.52804	−0.647009	−0.323504	+	0.946227i	$0.604861\pi$
$74$	−3.89289	−0.452539
$75$	0.289818	0.0334654
$76$	0.311026	0.0356772
$77$	−0.639011	−0.0728221
$78$	2.76642	0.313235
$79$	−0.390797	−0.0439681	−0.0219841	−	0.999758i	$-0.506998\pi$
$79$	−0.390797	−0.0439681	−0.0219841	+	0.999758i	$0.506998\pi$
$80$	−6.23055	−0.696597
$81$	0.310342	0.0344825
$82$	−1.97927	−0.218574
$83$	8.94397	0.981728	0.490864	−	0.871236i	$-0.336681\pi$
$83$	8.94397	0.981728	0.490864	+	0.871236i	$0.336681\pi$
$84$	−1.53455	−0.167433
$85$	6.19556	0.672003
$86$	−11.9165	−1.28499
$87$	1.49670	0.160463
$88$	−7.04612	−0.751119
$89$	−10.1117	−1.07184	−0.535920	−	0.844269i	$-0.680035\pi$
$89$	−10.1117	−1.07184	−0.535920	+	0.844269i	$0.680035\pi$
$90$	−10.4903	−1.10577
$91$	0.425117	0.0445644
$92$	3.77713	0.393793
$93$	3.65114	0.378605
$94$	−1.54975	−0.159844
$95$	−0.189148	−0.0194062
$96$	2.12207	0.216583
$97$	−3.97541	−0.403641	−0.201821	−	0.979422i	$-0.564686\pi$
$97$	−3.97541	−0.403641	−0.201821	+	0.979422i	$0.564686\pi$
$98$	16.4643	1.66314
$99$	−3.13430	−0.315009
$100$	1.04376	0.104376
$101$	8.87362	0.882958	0.441479	−	0.897272i	$-0.354454\pi$
$101$	8.87362	0.882958	0.441479	+	0.897272i	$0.354454\pi$
$102$	6.79919	0.673220
$103$	−11.7100	−1.15382	−0.576909	−	0.816808i	$-0.695741\pi$
$103$	−11.7100	−1.15382	−0.576909	+	0.816808i	$0.695741\pi$
$104$	4.68760	0.459657
$105$	0.933224	0.0910733
$106$	−31.4878	−3.05836
$107$	−14.5586	−1.40743	−0.703717	−	0.710480i	$-0.748478\pi$
$107$	−14.5586	−1.40743	−0.703717	+	0.710480i	$0.748478\pi$
$108$	−19.4110	−1.86783
$109$	0.325965	0.0312218	0.0156109	−	0.999878i	$-0.495031\pi$
$109$	0.325965	0.0312218	0.0156109	+	0.999878i	$0.495031\pi$
$110$	9.10747	0.868363
$111$	1.69864	0.161228
$112$	−1.05073	−0.0992851
$113$	−7.35403	−0.691809	−0.345904	−	0.938270i	$-0.612428\pi$
$113$	−7.35403	−0.691809	−0.345904	+	0.938270i	$0.612428\pi$
$114$	−0.207576	−0.0194413
$115$	−2.29703	−0.214199
$116$	5.39026	0.500473
$117$	2.08517	0.192774
$118$	−12.0136	−1.10594
$119$	1.04483	0.0957799
$120$	10.2903	0.939370
$121$	−8.27886	−0.752624
$122$	0.526474	0.0476648
$123$	0.863645	0.0778722
$124$	13.1493	1.18084
$125$	10.8504	0.970488
$126$	−1.76911	−0.157605
$127$	−9.44020	−0.837682	−0.418841	−	0.908060i	$-0.637564\pi$
$127$	−9.44020	−0.837682	−0.418841	+	0.908060i	$0.637564\pi$
$128$	20.6815	1.82801
$129$	5.19972	0.457810
$130$	−6.05895	−0.531405
$131$	20.3906	1.78154	0.890768	−	0.454457i	$-0.150167\pi$
$131$	20.3906	1.78154	0.890768	+	0.454457i	$0.150167\pi$
$132$	6.53467	0.568770
$133$	−0.0318984	−0.00276594
$134$	−4.44826	−0.384271
$135$	11.8047	1.01598
$136$	11.5210	0.987916
$137$	7.82703	0.668708	0.334354	−	0.942448i	$-0.391482\pi$
$137$	7.82703	0.668708	0.334354	+	0.942448i	$0.391482\pi$
$138$	−2.52082	−0.214587
$139$	−3.87267	−0.328475	−0.164238	−	0.986421i	$-0.552516\pi$
$139$	−3.87267	−0.328475	−0.164238	+	0.986421i	$0.552516\pi$
$140$	3.36094	0.284051
$141$	0.676225	0.0569484
$142$	−31.4177	−2.63651
$143$	−1.81030	−0.151385
$144$	−5.15377	−0.429481
$145$	−3.27804	−0.272227
$146$	13.2870	1.09964
$147$	−7.18411	−0.592536
$148$	6.11755	0.502859
$149$	4.65345	0.381225	0.190613	−	0.981665i	$-0.438953\pi$
$149$	4.65345	0.381225	0.190613	+	0.981665i	$0.438953\pi$
$150$	−0.696598	−0.0568770
$151$	−9.77890	−0.795796	−0.397898	−	0.917430i	$-0.630260\pi$
$151$	−9.77890	−0.795796	−0.397898	+	0.917430i	$0.630260\pi$
$152$	−0.351730	−0.0285291
$153$	5.12483	0.414318
$154$	1.53591	0.123767
$155$	−7.99665	−0.642306
$156$	−4.34734	−0.348066
$157$	13.8327	1.10397	0.551983	−	0.833855i	$-0.313871\pi$
$157$	13.8327	1.10397	0.551983	+	0.833855i	$0.313871\pi$
$158$	0.939307	0.0747272
$159$	13.7395	1.08962
$160$	−4.64772	−0.367434
$161$	−0.387376	−0.0305295
$162$	−0.745928	−0.0586057
$163$	9.78585	0.766487	0.383243	−	0.923647i	$-0.374807\pi$
$163$	9.78585	0.766487	0.383243	+	0.923647i	$0.374807\pi$
$164$	3.11036	0.242878
$165$	−3.97400	−0.309376
$166$	−21.4974	−1.66852
$167$	6.27087	0.485255	0.242627	−	0.970120i	$-0.421991\pi$
$167$	6.27087	0.485255	0.242627	+	0.970120i	$0.421991\pi$
$168$	1.73538	0.133887
$169$	−11.7957	−0.907358
$170$	−14.8914	−1.14212
$171$	−0.156459	−0.0119647
$172$	18.7264	1.42788
$173$	−8.59934	−0.653796	−0.326898	−	0.945060i	$-0.606003\pi$
$173$	−8.59934	−0.653796	−0.326898	+	0.945060i	$0.606003\pi$
$174$	−3.59742	−0.272719
$175$	−0.107047	−0.00809196
$176$	4.47441	0.337271
$177$	5.24209	0.394020
$178$	24.3042	1.82167
$179$	11.1804	0.835665	0.417832	−	0.908524i	$-0.362790\pi$
$179$	11.1804	0.835665	0.417832	+	0.908524i	$0.362790\pi$
$180$	16.4852	1.22873
$181$	19.6176	1.45817	0.729084	−	0.684424i	$-0.239946\pi$
$181$	19.6176	1.45817	0.729084	+	0.684424i	$0.239946\pi$
$182$	−1.02180	−0.0757406
$183$	−0.229725	−0.0169817
$184$	−4.27144	−0.314895
$185$	−3.72033	−0.273524
$186$	−8.77575	−0.643469
$187$	−4.44928	−0.325364
$188$	2.43538	0.177618
$189$	1.99076	0.144807
$190$	0.454629	0.0329823
$191$	−19.6632	−1.42278	−0.711391	−	0.702796i	$-0.751935\pi$
$191$	−19.6632	−1.42278	−0.711391	+	0.702796i	$0.751935\pi$
$192$	−10.7901	−0.778706
$193$	5.37040	0.386570	0.193285	−	0.981143i	$-0.438086\pi$
$193$	5.37040	0.386570	0.193285	+	0.981143i	$0.438086\pi$
$194$	9.55515	0.686020
$195$	2.64380	0.189326
$196$	−25.8731	−1.84808
$197$	−5.39946	−0.384696	−0.192348	−	0.981327i	$-0.561610\pi$
$197$	−5.39946	−0.384696	−0.192348	+	0.981327i	$0.561610\pi$
$198$	7.53349	0.535382
$199$	−21.3486	−1.51336	−0.756679	−	0.653786i	$-0.773180\pi$
$199$	−21.3486	−1.51336	−0.756679	+	0.653786i	$0.773180\pi$
$200$	−1.18036	−0.0834640
$201$	1.94098	0.136906
$202$	−21.3283	−1.50066
$203$	−0.552817	−0.0388001
$204$	−10.6847	−0.748079
$205$	−1.89154	−0.132111
$206$	28.1457	1.96100
$207$	−1.90005	−0.132063
$208$	−2.97670	−0.206397
$209$	0.135835	0.00939588
$210$	−2.24306	−0.154786
$211$	5.75824	0.396414	0.198207	−	0.980160i	$-0.436488\pi$
$211$	5.75824	0.396414	0.198207	+	0.980160i	$0.436488\pi$
$212$	49.4821	3.39844
$213$	13.7090	0.939322
$214$	34.9926	2.39204
$215$	−11.3883	−0.776677
$216$	21.9514	1.49360
$217$	−1.34857	−0.0915472
$218$	−0.783478	−0.0530638
$219$	−5.79773	−0.391774
$220$	−14.3121	−0.964921
$221$	2.95999	0.199110
$222$	−4.08280	−0.274020
$223$	−4.98527	−0.333838	−0.166919	−	0.985971i	$-0.553382\pi$
$223$	−4.98527	−0.333838	−0.166919	+	0.985971i	$0.553382\pi$
$224$	−0.783802	−0.0523700
$225$	−0.525055	−0.0350037
$226$	17.6759	1.17578
$227$	−21.7754	−1.44528	−0.722640	−	0.691224i	$-0.757072\pi$
$227$	−21.7754	−1.44528	−0.722640	+	0.691224i	$0.757072\pi$
$228$	0.326200	0.0216031
$229$	−23.1259	−1.52820	−0.764101	−	0.645096i	$-0.776817\pi$
$229$	−23.1259	−1.52820	−0.764101	+	0.645096i	$0.776817\pi$
$230$	5.52106	0.364048
$231$	−0.670185	−0.0440949
$232$	−6.09569	−0.400202
$233$	7.12050	0.466480	0.233240	−	0.972419i	$-0.425067\pi$
$233$	7.12050	0.466480	0.233240	+	0.972419i	$0.425067\pi$
$234$	−5.01183	−0.327634
$235$	−1.48106	−0.0966134
$236$	18.8790	1.22892
$237$	−0.409862	−0.0266234
$238$	−2.51133	−0.162785
$239$	−6.89053	−0.445712	−0.222856	−	0.974851i	$-0.571538\pi$
$239$	−6.89053	−0.445712	−0.222856	+	0.974851i	$0.571538\pi$
$240$	−6.53451	−0.421801
$241$	23.7227	1.52811	0.764057	−	0.645149i	$-0.223205\pi$
$241$	23.7227	1.52811	0.764057	+	0.645149i	$0.223205\pi$
$242$	19.8988	1.27914
$243$	15.7428	1.00990
$244$	−0.827338	−0.0529649
$245$	15.7345	1.00524
$246$	−2.07583	−0.132350
$247$	−0.0903672	−0.00574993
$248$	−14.8702	−0.944258
$249$	9.38030	0.594452
$250$	−26.0796	−1.64942
$251$	8.53419	0.538673	0.269337	−	0.963046i	$-0.413196\pi$
$251$	8.53419	0.538673	0.269337	+	0.963046i	$0.413196\pi$
$252$	2.78010	0.175130
$253$	1.64959	0.103709
$254$	22.6901	1.42371
$255$	6.49781	0.406909
$256$	−29.1331	−1.82082
$257$	−8.86630	−0.553064	−0.276532	−	0.961005i	$-0.589185\pi$
$257$	−8.86630	−0.553064	−0.276532	+	0.961005i	$0.589185\pi$
$258$	−12.4979	−0.778083
$259$	−0.627406	−0.0389851
$260$	9.52146	0.590496
$261$	−2.71152	−0.167839
$262$	−49.0102	−3.02786
$263$	−29.2434	−1.80322	−0.901612	−	0.432546i	$-0.857615\pi$
$263$	−29.2434	−1.80322	−0.901612	+	0.432546i	$0.857615\pi$
$264$	−7.38986	−0.454815
$265$	−30.0921	−1.84854
$266$	0.0766698	0.00470093
$267$	−10.6050	−0.649016
$268$	6.99029	0.427000
$269$	−22.6360	−1.38014	−0.690071	−	0.723741i	$-0.742421\pi$
$269$	−22.6360	−1.38014	−0.690071	+	0.723741i	$0.742421\pi$
$270$	−28.3733	−1.72674
$271$	3.29494	0.200153	0.100077	−	0.994980i	$-0.468091\pi$
$271$	3.29494	0.200153	0.100077	+	0.994980i	$0.468091\pi$
$272$	−7.31602	−0.443599
$273$	0.445856	0.0269844
$274$	−18.8128	−1.13652
$275$	0.455843	0.0274883
$276$	3.96139	0.238448
$277$	−8.89666	−0.534549	−0.267274	−	0.963620i	$-0.586123\pi$
$277$	−8.89666	−0.534549	−0.267274	+	0.963620i	$0.586123\pi$
$278$	9.30821	0.558269
$279$	−6.61465	−0.396009
$280$	−3.80079	−0.227141
$281$	7.51929	0.448563	0.224282	−	0.974524i	$-0.427996\pi$
$281$	7.51929	0.448563	0.224282	+	0.974524i	$0.427996\pi$
$282$	−1.62535	−0.0967883
$283$	15.5559	0.924705	0.462352	−	0.886696i	$-0.347006\pi$
$283$	15.5559	0.924705	0.462352	+	0.886696i	$0.347006\pi$
$284$	49.3719	2.92968
$285$	−0.198375	−0.0117507
$286$	4.35118	0.257291
$287$	−0.318994	−0.0188296
$288$	−3.84449	−0.226539
$289$	−9.72506	−0.572063
$290$	7.87899	0.462670
$291$	−4.16935	−0.244411
$292$	−20.8801	−1.22192
$293$	−18.3870	−1.07418	−0.537090	−	0.843525i	$-0.680476\pi$
$293$	−18.3870	−1.07418	−0.537090	+	0.843525i	$0.680476\pi$
$294$	17.2675	1.00706
$295$	−11.4811	−0.668457
$296$	−6.91815	−0.402110
$297$	−8.47739	−0.491908
$298$	−11.1849	−0.647922
$299$	−1.09743	−0.0634658
$300$	1.09468	0.0632015
$301$	−1.92055	−0.110699
$302$	23.5042	1.35252
$303$	9.30652	0.534646
$304$	0.223355	0.0128103
$305$	0.503139	0.0288096
$306$	−12.3179	−0.704166
$307$	−32.9500	−1.88055	−0.940277	−	0.340409i	$-0.889434\pi$
$307$	−32.9500	−1.88055	−0.940277	+	0.340409i	$0.889434\pi$
$308$	−2.41363	−0.137529
$309$	−12.2812	−0.698656
$310$	19.2205	1.09165
$311$	18.1740	1.03055	0.515275	−	0.857025i	$-0.327690\pi$
$311$	18.1740	1.03055	0.515275	+	0.857025i	$0.327690\pi$
$312$	4.91628	0.278329
$313$	−32.2115	−1.82070	−0.910350	−	0.413839i	$-0.864188\pi$
$313$	−32.2115	−1.82070	−0.910350	+	0.413839i	$0.864188\pi$
$314$	−33.2477	−1.87628
$315$	−1.69069	−0.0952597
$316$	−1.47609	−0.0830366
$317$	−6.00618	−0.337341	−0.168670	−	0.985673i	$-0.553947\pi$
$317$	−6.00618	−0.337341	−0.168670	+	0.985673i	$0.553947\pi$
$318$	−33.0239	−1.85189
$319$	2.35409	0.131804
$320$	23.6322	1.32108
$321$	−15.2689	−0.852225
$322$	0.931084	0.0518873
$323$	−0.222101	−0.0123580
$324$	1.17220	0.0651224
$325$	−0.303260	−0.0168218
$326$	−23.5209	−1.30270
$327$	0.341867	0.0189053
$328$	−3.51741	−0.194217
$329$	−0.249769	−0.0137702
$330$	9.55177	0.525808
$331$	13.9773	0.768261	0.384130	−	0.923279i	$-0.374501\pi$
$331$	13.9773	0.768261	0.384130	+	0.923279i	$0.374501\pi$
$332$	33.7825	1.85406
$333$	−3.07738	−0.168639
$334$	−15.0725	−0.824728
$335$	−4.25109	−0.232262
$336$	−1.10199	−0.0601187
$337$	4.11742	0.224290	0.112145	−	0.993692i	$-0.464228\pi$
$337$	4.11742	0.224290	0.112145	+	0.993692i	$0.464228\pi$
$338$	28.3516	1.54213
$339$	−7.71279	−0.418901
$340$	23.4014	1.26912
$341$	5.74271	0.310985
$342$	0.376059	0.0203350
$343$	5.36514	0.289690
$344$	−21.1772	−1.14180
$345$	−2.40909	−0.129701
$346$	20.6691	1.11118
$347$	−0.596804	−0.0320381	−0.0160191	−	0.999872i	$-0.505099\pi$
$347$	−0.596804	−0.0320381	−0.0160191	+	0.999872i	$0.505099\pi$
$348$	5.65323	0.303045
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	0.257293	0.0137529
$351$	5.63978	0.301029
$352$	3.33771	0.177901
$353$	−17.4775	−0.930236	−0.465118	−	0.885249i	$-0.653988\pi$
$353$	−17.4775	−0.930236	−0.465118	+	0.885249i	$0.653988\pi$
$354$	−12.5997	−0.669667
$355$	−30.0251	−1.59357
$356$	−38.1932	−2.02424
$357$	1.09581	0.0579963
$358$	−26.8729	−1.42028
$359$	−15.2578	−0.805274	−0.402637	−	0.915360i	$-0.631906\pi$
$359$	−15.2578	−0.805274	−0.402637	+	0.915360i	$0.631906\pi$
$360$	−18.6426	−0.982550
$361$	−18.9932	−0.999643
$362$	−47.1523	−2.47827
$363$	−8.68274	−0.455726
$364$	1.60572	0.0841627
$365$	12.6981	0.664648
$366$	0.552158	0.0288618
$367$	34.7530	1.81409	0.907046	−	0.421032i	$-0.138332\pi$
$367$	34.7530	1.81409	0.907046	+	0.421032i	$0.138332\pi$
$368$	2.71244	0.141396
$369$	−1.56464	−0.0814518
$370$	8.94207	0.464876
$371$	−5.07480	−0.263471
$372$	13.7908	0.715020
$373$	19.6263	1.01621	0.508106	−	0.861294i	$-0.330346\pi$
$373$	19.6263	1.01621	0.508106	+	0.861294i	$0.330346\pi$
$374$	10.6941	0.552981
$375$	11.3797	0.587646
$376$	−2.75410	−0.142032
$377$	−1.56611	−0.0806590
$378$	−4.78493	−0.246110
$379$	−8.59488	−0.441489	−0.220745	−	0.975332i	$-0.570849\pi$
$379$	−8.59488	−0.441489	−0.220745	+	0.975332i	$0.570849\pi$
$380$	−0.714436	−0.0366498
$381$	−9.90074	−0.507230
$382$	47.2619	2.41813
$383$	−32.6497	−1.66832	−0.834161	−	0.551521i	$-0.814048\pi$
$383$	−32.6497	−1.66832	−0.834161	+	0.551521i	$0.814048\pi$
$384$	21.6905	1.10689
$385$	1.46783	0.0748074
$386$	−12.9081	−0.657005
$387$	−9.42016	−0.478854
$388$	−15.0156	−0.762303
$389$	26.3021	1.33357	0.666784	−	0.745251i	$-0.267671\pi$
$389$	26.3021	1.33357	0.666784	+	0.745251i	$0.267671\pi$
$390$	−6.35454	−0.321775
$391$	−2.69721	−0.136404
$392$	29.2591	1.47781
$393$	21.3854	1.07875
$394$	12.9780	0.653821
$395$	0.897672	0.0451668
$396$	−11.8386	−0.594915
$397$	37.8448	1.89937	0.949687	−	0.313199i	$-0.101401\pi$
$397$	37.8448	1.89937	0.949687	+	0.313199i	$0.101401\pi$
$398$	51.3126	2.57207
$399$	−0.0334545	−0.00167482
$400$	0.749548	0.0374774
$401$	−23.0175	−1.14944	−0.574719	−	0.818351i	$-0.694889\pi$
$401$	−23.0175	−1.14944	−0.574719	+	0.818351i	$0.694889\pi$
$402$	−4.66526	−0.232682
$403$	−3.82047	−0.190311
$404$	33.5168	1.66752
$405$	−0.712865	−0.0354225
$406$	1.32873	0.0659438
$407$	2.67172	0.132432
$408$	12.0830	0.598199
$409$	−0.133785	−0.00661523	−0.00330762	−	0.999995i	$-0.501053\pi$
$409$	−0.133785	−0.00661523	−0.00330762	+	0.999995i	$0.501053\pi$
$410$	4.54644	0.224532
$411$	8.20887	0.404914
$412$	−44.2301	−2.17906
$413$	−1.93621	−0.0952744
$414$	4.56690	0.224451
$415$	−20.5446	−1.00849
$416$	−2.22049	−0.108868
$417$	−4.06159	−0.198897
$418$	−0.326488	−0.0159690
$419$	32.2937	1.57765	0.788825	−	0.614618i	$-0.210690\pi$
$419$	32.2937	1.57765	0.788825	+	0.614618i	$0.210690\pi$
$420$	3.52490	0.171998
$421$	−16.3994	−0.799258	−0.399629	−	0.916677i	$-0.630861\pi$
$421$	−16.3994	−0.799258	−0.399629	+	0.916677i	$0.630861\pi$
$422$	−13.8403	−0.673736
$423$	−1.22510	−0.0595662
$424$	−55.9578	−2.71755
$425$	−0.745340	−0.0361543
$426$	−32.9504	−1.59645
$427$	0.0848505	0.00410620
$428$	−54.9898	−2.65803
$429$	−1.89862	−0.0916661
$430$	27.3726	1.32002
$431$	3.71172	0.178787	0.0893935	−	0.995996i	$-0.471507\pi$
$431$	3.71172	0.178787	0.0893935	+	0.995996i	$0.471507\pi$
$432$	−13.9395	−0.670664
$433$	−2.96232	−0.142360	−0.0711800	−	0.997463i	$-0.522676\pi$
$433$	−2.96232	−0.142360	−0.0711800	+	0.997463i	$0.522676\pi$
$434$	3.24139	0.155592
$435$	−3.43796	−0.164838
$436$	1.23121	0.0589643
$437$	0.0823446	0.00393908
$438$	13.9352	0.665851
$439$	27.5014	1.31257	0.656285	−	0.754513i	$-0.272127\pi$
$439$	27.5014	1.31257	0.656285	+	0.754513i	$0.272127\pi$
$440$	16.1851	0.771596
$441$	13.0152	0.619773
$442$	−7.11453	−0.338404
$443$	31.2753	1.48593	0.742967	−	0.669329i	$-0.233418\pi$
$443$	31.2753	1.48593	0.742967	+	0.669329i	$0.233418\pi$
$444$	6.41599	0.304489
$445$	23.2269	1.10106
$446$	11.9824	0.567384
$447$	4.88046	0.230838
$448$	3.98539	0.188292
$449$	−5.71734	−0.269818	−0.134909	−	0.990858i	$-0.543074\pi$
$449$	−5.71734	−0.269818	−0.134909	+	0.990858i	$0.543074\pi$
$450$	1.26200	0.0594914
$451$	1.35839	0.0639640
$452$	−27.7771	−1.30652
$453$	−10.2560	−0.481867
$454$	52.3385	2.45637
$455$	−0.976506	−0.0457793
$456$	−0.368890	−0.0172748
$457$	−10.5848	−0.495135	−0.247568	−	0.968871i	$-0.579631\pi$
$457$	−10.5848	−0.495135	−0.247568	+	0.968871i	$0.579631\pi$
$458$	55.5846	2.59730
$459$	13.8612	0.646986
$460$	−8.67617	−0.404528
$461$	17.7486	0.826633	0.413316	−	0.910588i	$-0.364370\pi$
$461$	17.7486	0.826633	0.413316	+	0.910588i	$0.364370\pi$
$462$	1.61083	0.0749428
$463$	−42.5341	−1.97673	−0.988364	−	0.152107i	$-0.951394\pi$
$463$	−42.5341	−1.97673	−0.988364	+	0.152107i	$0.951394\pi$
$464$	3.87087	0.179700
$465$	−8.38677	−0.388927
$466$	−17.1146	−0.792818
$467$	−10.9996	−0.509000	−0.254500	−	0.967073i	$-0.581911\pi$
$467$	−10.9996	−0.509000	−0.254500	+	0.967073i	$0.581911\pi$
$468$	7.87594	0.364065
$469$	−0.716913	−0.0331040
$470$	3.55981	0.164202
$471$	14.5075	0.668470
$472$	−21.3498	−0.982703
$473$	8.17841	0.376044
$474$	0.985130	0.0452485
$475$	0.0227549	0.00104407
$476$	3.94647	0.180886
$477$	−24.8915	−1.13970
$478$	16.5618	0.757521
$479$	−29.4861	−1.34726	−0.673628	−	0.739071i	$-0.735265\pi$
$479$	−29.4861	−1.34726	−0.673628	+	0.739071i	$0.735265\pi$
$480$	−4.87446	−0.222487
$481$	−1.77742	−0.0810436
$482$	−57.0191	−2.59715
$483$	−0.406274	−0.0184861
$484$	−31.2703	−1.42138
$485$	9.13162	0.414646
$486$	−37.8388	−1.71640
$487$	31.6418	1.43383	0.716914	−	0.697162i	$-0.245554\pi$
$487$	31.6418	1.43383	0.716914	+	0.697162i	$0.245554\pi$
$488$	0.935612	0.0423532
$489$	10.2632	0.464120
$490$	−37.8189	−1.70848
$491$	−5.67088	−0.255923	−0.127962	−	0.991779i	$-0.540843\pi$
$491$	−5.67088	−0.255923	−0.127962	+	0.991779i	$0.540843\pi$
$492$	3.26210	0.147067
$493$	−3.84913	−0.173356
$494$	0.217203	0.00977245
$495$	7.19957	0.323597
$496$	9.44282	0.423995
$497$	−5.06350	−0.227129
$498$	−22.5462	−1.01032
$499$	−17.4100	−0.779378	−0.389689	−	0.920946i	$-0.627418\pi$
$499$	−17.4100	−0.779378	−0.389689	+	0.920946i	$0.627418\pi$
$500$	40.9833	1.83283
$501$	6.57680	0.293830
$502$	−20.5125	−0.915517
$503$	8.18885	0.365123	0.182561	−	0.983194i	$-0.441561\pi$
$503$	8.18885	0.365123	0.182561	+	0.983194i	$0.441561\pi$
$504$	−3.14393	−0.140042
$505$	−20.3830	−0.907030
$506$	−3.96489	−0.176261
$507$	−12.3711	−0.549420
$508$	−35.6568	−1.58202
$509$	5.63875	0.249933	0.124967	−	0.992161i	$-0.460118\pi$
$509$	5.63875	0.249933	0.124967	+	0.992161i	$0.460118\pi$
$510$	−15.6179	−0.691573
$511$	2.14143	0.0947314
$512$	28.6603	1.26662
$513$	−0.423177	−0.0186837
$514$	21.3107	0.939976
$515$	26.8981	1.18527
$516$	19.6400	0.864603
$517$	1.06361	0.0467773
$518$	1.50801	0.0662582
$519$	−9.01886	−0.395884
$520$	−10.7675	−0.472188
$521$	40.6396	1.78045	0.890227	−	0.455516i	$-0.150545\pi$
$521$	40.6396	1.78045	0.890227	+	0.455516i	$0.150545\pi$
$522$	6.51732	0.285256
$523$	−44.2511	−1.93496	−0.967482	−	0.252941i	$-0.918602\pi$
$523$	−44.2511	−1.93496	−0.967482	+	0.252941i	$0.918602\pi$
$524$	77.0180	3.36455
$525$	−0.112269	−0.00489981
$526$	70.2884	3.06472
$527$	−9.38980	−0.409026
$528$	4.69269	0.204223
$529$	1.00000	0.0434783
$530$	72.3283	3.14174
$531$	−9.49694	−0.412132
$532$	−0.120484	−0.00522365
$533$	−0.903700	−0.0391436
$534$	25.4898	1.10305
$535$	33.4416	1.44580
$536$	−7.90512	−0.341449
$537$	11.7259	0.506009
$538$	54.4072	2.34566
$539$	−11.2996	−0.486707
$540$	44.5877	1.91875
$541$	4.85468	0.208719	0.104359	−	0.994540i	$-0.466721\pi$
$541$	4.85468	0.208719	0.104359	+	0.994540i	$0.466721\pi$
$542$	−7.91960	−0.340176
$543$	20.5747	0.882944
$544$	−5.45743	−0.233985
$545$	−0.748750	−0.0320729
$546$	−1.07164	−0.0458622
$547$	14.6958	0.628346	0.314173	−	0.949366i	$-0.398273\pi$
$547$	14.6958	0.628346	0.314173	+	0.949366i	$0.398273\pi$
$548$	29.5637	1.26290
$549$	0.416185	0.0177623
$550$	−1.09565	−0.0467186
$551$	0.117512	0.00500619
$552$	−4.47983	−0.190674
$553$	0.151386	0.00643757
$554$	21.3837	0.908507
$555$	−3.90183	−0.165623
$556$	−14.6276	−0.620347
$557$	25.1307	1.06482	0.532411	−	0.846486i	$-0.321286\pi$
$557$	25.1307	1.06482	0.532411	+	0.846486i	$0.321286\pi$
$558$	15.8987	0.673048
$559$	−5.44088	−0.230125
$560$	2.41357	0.101992
$561$	−4.66634	−0.197013
$562$	−18.0731	−0.762368
$563$	−39.5371	−1.66629	−0.833145	−	0.553055i	$-0.813462\pi$
$563$	−39.5371	−1.66629	−0.833145	+	0.553055i	$0.813462\pi$
$564$	2.55419	0.107551
$565$	16.8924	0.710669
$566$	−37.3897	−1.57161
$567$	−0.120219	−0.00504873
$568$	−55.8332	−2.34271
$569$	−0.801826	−0.0336143	−0.0168071	−	0.999859i	$-0.505350\pi$
$569$	−0.801826	−0.0336143	−0.0168071	+	0.999859i	$0.505350\pi$
$570$	0.476809	0.0199713
$571$	−18.8758	−0.789930	−0.394965	−	0.918696i	$-0.629243\pi$
$571$	−18.8758	−0.789930	−0.394965	+	0.918696i	$0.629243\pi$
$572$	−6.83774	−0.285900
$573$	−20.6225	−0.861518
$574$	0.766722	0.0320024
$575$	0.276337	0.0115241
$576$	19.5480	0.814501
$577$	11.2588	0.468708	0.234354	−	0.972151i	$-0.424702\pi$
$577$	11.2588	0.468708	0.234354	+	0.972151i	$0.424702\pi$
$578$	23.3748	0.972265
$579$	5.63239	0.234074
$580$	−12.3816	−0.514117
$581$	−3.46468	−0.143739
$582$	10.0213	0.415396
$583$	21.6103	0.895008
$584$	23.6127	0.977102
$585$	−4.78968	−0.198029
$586$	44.1944	1.82565
$587$	−7.25538	−0.299462	−0.149731	−	0.988727i	$-0.547841\pi$
$587$	−7.25538	−0.299462	−0.149731	+	0.988727i	$0.547841\pi$
$588$	−27.1353	−1.11904
$589$	0.286667	0.0118119
$590$	27.5957	1.13610
$591$	−5.66288	−0.232940
$592$	4.39315	0.180557
$593$	24.9857	1.02604	0.513021	−	0.858376i	$-0.328526\pi$
$593$	24.9857	1.02604	0.513021	+	0.858376i	$0.328526\pi$
$594$	20.3760	0.836036
$595$	−2.40001	−0.0983910
$596$	17.5767	0.719968
$597$	−22.3900	−0.916363
$598$	2.63774	0.107865
$599$	−17.7485	−0.725183	−0.362592	−	0.931948i	$-0.618108\pi$
$599$	−17.7485	−0.725183	−0.362592	+	0.931948i	$0.618108\pi$
$600$	−1.23794	−0.0505388
$601$	−19.7285	−0.804741	−0.402371	−	0.915477i	$-0.631814\pi$
$601$	−19.7285	−0.804741	−0.402371	+	0.915477i	$0.631814\pi$
$602$	4.61618	0.188141
$603$	−3.51640	−0.143199
$604$	−36.9362	−1.50291
$605$	19.0168	0.773142
$606$	−22.3688	−0.908672
$607$	−16.8070	−0.682174	−0.341087	−	0.940032i	$-0.610795\pi$
$607$	−16.8070	−0.682174	−0.341087	+	0.940032i	$0.610795\pi$
$608$	0.166613	0.00675705
$609$	−0.579786	−0.0234941
$610$	−1.20933	−0.0489642
$611$	−0.707588	−0.0286259
$612$	19.3571	0.782466
$613$	−0.919779	−0.0371495	−0.0185748	−	0.999827i	$-0.505913\pi$
$613$	−0.919779	−0.0371495	−0.0185748	+	0.999827i	$0.505913\pi$
$614$	79.1974	3.19615
$615$	−1.98382	−0.0799952
$616$	2.72950	0.109975
$617$	−22.1434	−0.891461	−0.445731	−	0.895167i	$-0.647056\pi$
$617$	−22.1434	−0.891461	−0.445731	+	0.895167i	$0.647056\pi$
$618$	29.5188	1.18742
$619$	14.9296	0.600071	0.300035	−	0.953928i	$-0.403002\pi$
$619$	14.9296	0.600071	0.300035	+	0.953928i	$0.403002\pi$
$620$	−30.2044	−1.21304
$621$	−5.13910	−0.206225
$622$	−43.6823	−1.75150
$623$	3.91704	0.156933
$624$	−3.12192	−0.124977
$625$	−26.3053	−1.05221
$626$	77.4224	3.09442
$627$	0.142461	0.00568936
$628$	52.2477	2.08491
$629$	−4.36848	−0.174183
$630$	4.06369	0.161901
$631$	−29.8467	−1.18818	−0.594089	−	0.804399i	$-0.702487\pi$
$631$	−29.8467	−1.18818	−0.594089	+	0.804399i	$0.702487\pi$
$632$	1.66927	0.0663999
$633$	6.03916	0.240035
$634$	14.4363	0.573337
$635$	21.6844	0.860519
$636$	51.8960	2.05781
$637$	7.51730	0.297846
$638$	−5.65822	−0.224011
$639$	−24.8361	−0.982500
$640$	−47.5061	−1.87784
$641$	34.7593	1.37291	0.686455	−	0.727172i	$-0.259166\pi$
$641$	34.7593	1.37291	0.686455	+	0.727172i	$0.259166\pi$
$642$	36.6997	1.44842
$643$	−45.7299	−1.80341	−0.901705	−	0.432351i	$-0.857684\pi$
$643$	−45.7299	−1.80341	−0.901705	+	0.432351i	$0.857684\pi$
$644$	−1.46317	−0.0576570
$645$	−11.9439	−0.470291
$646$	0.533834	0.0210034
$647$	−43.0720	−1.69333	−0.846667	−	0.532123i	$-0.821394\pi$
$647$	−43.0720	−1.69333	−0.846667	+	0.532123i	$0.821394\pi$
$648$	−1.32561	−0.0520749
$649$	8.24506	0.323647
$650$	0.728905	0.0285900
$651$	−1.41436	−0.0554333
$652$	36.9624	1.44756
$653$	−8.31954	−0.325569	−0.162784	−	0.986662i	$-0.552048\pi$
$653$	−8.31954	−0.325569	−0.162784	+	0.986662i	$0.552048\pi$
$654$	−0.821700	−0.0321310
$655$	−46.8378	−1.83011
$656$	2.23362	0.0872081
$657$	10.5036	0.409783
$658$	0.600336	0.0234035
$659$	−5.92997	−0.230999	−0.115499	−	0.993308i	$-0.536847\pi$
$659$	−5.92997	−0.230999	−0.115499	+	0.993308i	$0.536847\pi$
$660$	−15.0103	−0.584276
$661$	15.8104	0.614954	0.307477	−	0.951556i	$-0.400515\pi$
$661$	15.8104	0.614954	0.307477	+	0.951556i	$0.400515\pi$
$662$	−33.5953	−1.30572
$663$	3.10439	0.120565
$664$	−38.2037	−1.48259
$665$	0.0732714	0.00284134
$666$	7.39668	0.286615
$667$	1.42708	0.0552567
$668$	23.6859	0.916435
$669$	−5.22847	−0.202144
$670$	10.2178	0.394747
$671$	−0.361324	−0.0139488
$672$	−0.822040	−0.0317109
$673$	−40.2791	−1.55265	−0.776323	−	0.630336i	$-0.782917\pi$
$673$	−40.2791	−1.55265	−0.776323	+	0.630336i	$0.782917\pi$
$674$	−9.89650	−0.381199
$675$	−1.42012	−0.0546606
$676$	−44.5537	−1.71360
$677$	19.8180	0.761669	0.380834	−	0.924643i	$-0.375637\pi$
$677$	19.8180	0.761669	0.380834	+	0.924643i	$0.375637\pi$
$678$	18.5382	0.711955
$679$	1.53998	0.0590989
$680$	−26.4640	−1.01485
$681$	−22.8377	−0.875141
$682$	−13.8030	−0.528544
$683$	32.1074	1.22856	0.614278	−	0.789089i	$-0.289447\pi$
$683$	32.1074	1.22856	0.614278	+	0.789089i	$0.289447\pi$
$684$	−0.590966	−0.0225961
$685$	−17.9789	−0.686939
$686$	−12.8955	−0.492351
$687$	−24.2541	−0.925352
$688$	13.4479	0.512695
$689$	−14.3768	−0.547711
$690$	5.79040	0.220437
$691$	−37.8642	−1.44042	−0.720211	−	0.693755i	$-0.755955\pi$
$691$	−37.8642	−1.44042	−0.720211	+	0.693755i	$0.755955\pi$
$692$	−32.4808	−1.23474
$693$	1.21415	0.0461219
$694$	1.43446	0.0544513
$695$	8.89562	0.337430
$696$	−6.39307	−0.242329
$697$	−2.22108	−0.0841293
$698$	−2.40357	−0.0909763
$699$	7.46788	0.282461
$700$	−0.404329	−0.0152822
$701$	17.9732	0.678837	0.339419	−	0.940635i	$-0.389770\pi$
$701$	17.9732	0.678837	0.339419	+	0.940635i	$0.389770\pi$
$702$	−13.5556	−0.511623
$703$	0.133368	0.00503006
$704$	−16.9712	−0.639627
$705$	−1.55331	−0.0585010
$706$	42.0084	1.58101
$707$	−3.43743	−0.129278
$708$	19.8001	0.744132
$709$	−10.4896	−0.393947	−0.196973	−	0.980409i	$-0.563111\pi$
$709$	−10.4896	−0.393947	−0.196973	+	0.980409i	$0.563111\pi$
$710$	72.1673	2.70839
$711$	0.742534	0.0278472
$712$	43.1916	1.61867
$713$	3.48130	0.130376
$714$	−2.63384	−0.0985691
$715$	4.15831	0.155512
$716$	42.2299	1.57821
$717$	−7.22669	−0.269886
$718$	36.6730	1.36863
$719$	20.8298	0.776819	0.388410	−	0.921487i	$-0.373025\pi$
$719$	20.8298	0.776819	0.388410	+	0.921487i	$0.373025\pi$
$720$	11.8384	0.441190
$721$	4.53617	0.168936
$722$	45.6514	1.69897
$723$	24.8800	0.925298
$724$	74.0984	2.75384
$725$	0.394355	0.0146460
$726$	20.8695	0.774541
$727$	−8.18475	−0.303556	−0.151778	−	0.988415i	$-0.548500\pi$
$727$	−8.18475	−0.303556	−0.151778	+	0.988415i	$0.548500\pi$
$728$	−1.81586	−0.0673004
$729$	15.5798	0.577028
$730$	−30.5207	−1.12962
$731$	−13.3724	−0.494595
$732$	−0.867700	−0.0320711
$733$	36.1608	1.33563	0.667814	−	0.744328i	$-0.267230\pi$
$733$	36.1608	1.33563	0.667814	+	0.744328i	$0.267230\pi$
$734$	−83.5311	−3.08319
$735$	16.5021	0.608689
$736$	2.02336	0.0745821
$737$	3.05288	0.112454
$738$	3.76071	0.138434
$739$	−38.8403	−1.42876	−0.714381	−	0.699757i	$-0.753292\pi$
$739$	−38.8403	−1.42876	−0.714381	+	0.699757i	$0.753292\pi$
$740$	−14.0522	−0.516568
$741$	−0.0947757	−0.00348167
$742$	12.1976	0.447789
$743$	−3.95196	−0.144983	−0.0724916	−	0.997369i	$-0.523095\pi$
$743$	−3.95196	−0.144983	−0.0724916	+	0.997369i	$0.523095\pi$
$744$	−15.5956	−0.571764
$745$	−10.6891	−0.391618
$746$	−47.1732	−1.72713
$747$	−16.9940	−0.621778
$748$	−16.8055	−0.614470
$749$	5.63966	0.206069
$750$	−27.3519	−0.998750
$751$	26.3034	0.959823	0.479912	−	0.877317i	$-0.340669\pi$
$751$	26.3034	0.959823	0.479912	+	0.877317i	$0.340669\pi$
$752$	1.74890	0.0637758
$753$	8.95053	0.326175
$754$	3.76426	0.137086
$755$	22.4624	0.817491
$756$	7.51937	0.273477
$757$	−13.3749	−0.486120	−0.243060	−	0.970011i	$-0.578151\pi$
$757$	−13.3749	−0.486120	−0.243060	+	0.970011i	$0.578151\pi$
$758$	20.6584	0.750346
$759$	1.73006	0.0627973
$760$	0.807935	0.0293069
$761$	22.9183	0.830786	0.415393	−	0.909642i	$-0.363644\pi$
$761$	22.9183	0.830786	0.415393	+	0.909642i	$0.363644\pi$
$762$	23.7971	0.862077
$763$	−0.126271	−0.00457132
$764$	−74.2706	−2.68702
$765$	−11.7719	−0.425613
$766$	78.4757	2.83544
$767$	−5.48522	−0.198060
$768$	−30.5544	−1.10254
$769$	−8.11434	−0.292610	−0.146305	−	0.989239i	$-0.546738\pi$
$769$	−8.11434	−0.292610	−0.146305	+	0.989239i	$0.546738\pi$
$770$	−3.52802	−0.127141
$771$	−9.29884	−0.334889
$772$	20.2847	0.730061
$773$	−23.9182	−0.860277	−0.430138	−	0.902763i	$-0.641535\pi$
$773$	−23.9182	−0.860277	−0.430138	+	0.902763i	$0.641535\pi$
$774$	22.6420	0.813849
$775$	0.962014	0.0345566
$776$	16.9807	0.609573
$777$	−0.658014	−0.0236061
$778$	−63.2187	−2.26650
$779$	0.0678085	0.00242949
$780$	9.98596	0.357555
$781$	21.5622	0.771557
$782$	6.48292	0.231829
$783$	−7.33390	−0.262092
$784$	−18.5800	−0.663573
$785$	−31.7740	−1.13406
$786$	−51.4012	−1.83342
$787$	4.15588	0.148141	0.0740706	−	0.997253i	$-0.476401\pi$
$787$	4.15588	0.148141	0.0740706	+	0.997253i	$0.476401\pi$
$788$	−20.3945	−0.726523
$789$	−30.6700	−1.09188
$790$	−2.15761	−0.0767644
$791$	2.84878	0.101291
$792$	13.3880	0.475721
$793$	0.240379	0.00853611
$794$	−90.9624	−3.22813
$795$	−31.5601	−1.11932
$796$	−80.6362	−2.85807
$797$	−14.0679	−0.498311	−0.249155	−	0.968464i	$-0.580153\pi$
$797$	−14.0679	−0.498311	−0.249155	+	0.968464i	$0.580153\pi$
$798$	0.0804101	0.00284649
$799$	−1.73908	−0.0615242
$800$	0.559130	0.0197682
$801$	19.2128	0.678850
$802$	55.3241	1.95356
$803$	−9.11899	−0.321802
$804$	7.33131	0.258555
$805$	0.889814	0.0313618
$806$	9.18276	0.323449
$807$	−23.7403	−0.835699
$808$	−37.9032	−1.33343
$809$	−44.1825	−1.55338	−0.776688	−	0.629886i	$-0.783102\pi$
$809$	−44.1825	−1.55338	−0.776688	+	0.629886i	$0.783102\pi$
$810$	1.71342	0.0602034
$811$	−6.61342	−0.232229	−0.116114	−	0.993236i	$-0.537044\pi$
$811$	−6.61342	−0.232229	−0.116114	+	0.993236i	$0.537044\pi$
$812$	−2.08806	−0.0732765
$813$	3.45568	0.121196
$814$	−6.42165	−0.225079
$815$	−22.4784	−0.787383
$816$	−7.67293	−0.268606
$817$	0.408252	0.0142829
$818$	0.321561	0.0112431
$819$	−0.807744	−0.0282248
$820$	−7.14458	−0.249500
$821$	−50.1375	−1.74981	−0.874906	−	0.484292i	$-0.839077\pi$
$821$	−50.1375	−1.74981	−0.874906	+	0.484292i	$0.839077\pi$
$822$	−19.7306	−0.688182
$823$	8.35835	0.291354	0.145677	−	0.989332i	$-0.453464\pi$
$823$	8.35835	0.291354	0.145677	+	0.989332i	$0.453464\pi$
$824$	50.0185	1.74248
$825$	0.478081	0.0166446
$826$	4.65380	0.161926
$827$	−45.6432	−1.58717	−0.793585	−	0.608459i	$-0.791788\pi$
$827$	−45.6432	−1.58717	−0.793585	+	0.608459i	$0.791788\pi$
$828$	−7.17673	−0.249409
$829$	8.33001	0.289313	0.144657	−	0.989482i	$-0.453792\pi$
$829$	8.33001	0.289313	0.144657	+	0.989482i	$0.453792\pi$
$830$	49.3802	1.71401
$831$	−9.33069	−0.323678
$832$	11.2905	0.391428
$833$	18.4757	0.640146
$834$	9.76231	0.338041
$835$	−14.4044	−0.498484
$836$	0.513065	0.0177447
$837$	−17.8908	−0.618395
$838$	−77.6200	−2.68134
$839$	19.3485	0.667983	0.333991	−	0.942576i	$-0.391604\pi$
$839$	19.3485	0.667983	0.333991	+	0.942576i	$0.391604\pi$
$840$	−3.98621	−0.137537
$841$	−26.9634	−0.929774
$842$	39.4170	1.35840
$843$	7.88612	0.271612
$844$	21.7496	0.748653
$845$	27.0949	0.932095
$846$	2.94460	0.101237
$847$	3.20703	0.110195
$848$	35.5342	1.22025
$849$	16.3148	0.559924
$850$	1.79147	0.0614470
$851$	1.61963	0.0555202
$852$	51.7805	1.77397
$853$	−46.5990	−1.59552	−0.797759	−	0.602976i	$-0.793981\pi$
$853$	−46.5990	−1.59552	−0.797759	+	0.602976i	$0.793981\pi$
$854$	−0.203944	−0.00697881
$855$	0.359391	0.0122909
$856$	62.1863	2.12548
$857$	33.2593	1.13612	0.568058	−	0.822988i	$-0.307695\pi$
$857$	33.2593	1.13612	0.568058	+	0.822988i	$0.307695\pi$
$858$	4.56345	0.155794
$859$	−4.79370	−0.163559	−0.0817795	−	0.996650i	$-0.526060\pi$
$859$	−4.79370	−0.163559	−0.0817795	+	0.996650i	$0.526060\pi$
$860$	−43.0151	−1.46680
$861$	−0.334556	−0.0114016
$862$	−8.92135	−0.303863
$863$	−31.8361	−1.08371	−0.541857	−	0.840471i	$-0.682278\pi$
$863$	−31.8361	−1.08371	−0.541857	+	0.840471i	$0.682278\pi$
$864$	−10.3983	−0.353756
$865$	19.7529	0.671620
$866$	7.12013	0.241952
$867$	−10.1995	−0.346393
$868$	−5.09374	−0.172893
$869$	−0.644654	−0.0218684
$870$	8.26336	0.280154
$871$	−2.03100	−0.0688177
$872$	−1.39234	−0.0471506
$873$	7.55347	0.255646
$874$	−0.197921	−0.00669477
$875$	−4.20318	−0.142093
$876$	−21.8988	−0.739891
$877$	54.7471	1.84868	0.924339	−	0.381573i	$-0.124618\pi$
$877$	54.7471	1.84868	0.924339	+	0.381573i	$0.124618\pi$
$878$	−66.1014	−2.23081
$879$	−19.2840	−0.650433
$880$	−10.2778	−0.346466
$881$	45.3480	1.52781	0.763907	−	0.645327i	$-0.223279\pi$
$881$	45.3480	1.52781	0.763907	+	0.645327i	$0.223279\pi$
$882$	−31.2830	−1.05335
$883$	9.18720	0.309174	0.154587	−	0.987979i	$-0.450595\pi$
$883$	9.18720	0.309174	0.154587	+	0.987979i	$0.450595\pi$
$884$	11.1803	0.376033
$885$	−12.0412	−0.404762
$886$	−75.1722	−2.52546
$887$	−6.92389	−0.232482	−0.116241	−	0.993221i	$-0.537084\pi$
$887$	−6.92389	−0.232482	−0.116241	+	0.993221i	$0.537084\pi$
$888$	−7.25566	−0.243484
$889$	3.65691	0.122649
$890$	−55.8274	−1.87134
$891$	0.511937	0.0171505
$892$	−18.8300	−0.630474
$893$	0.0530934	0.00177670
$894$	−11.7305	−0.392327
$895$	−25.6818	−0.858447
$896$	−8.01154	−0.267647
$897$	−1.15096	−0.0384296
$898$	13.7420	0.458577
$899$	4.96810	0.165695
$900$	−1.98320	−0.0661067
$901$	−35.3346	−1.17717
$902$	−3.26498	−0.108712
$903$	−2.01425	−0.0670300
$904$	31.4123	1.04476
$905$	−45.0623	−1.49792
$906$	24.6509	0.818971
$907$	−9.83107	−0.326435	−0.163218	−	0.986590i	$-0.552187\pi$
$907$	−9.83107	−0.326435	−0.163218	+	0.986590i	$0.552187\pi$
$908$	−82.2483	−2.72951
$909$	−16.8603	−0.559222
$910$	2.34710	0.0778055
$911$	−9.43243	−0.312510	−0.156255	−	0.987717i	$-0.549942\pi$
$911$	−9.43243	−0.312510	−0.156255	+	0.987717i	$0.549942\pi$
$912$	0.234251	0.00775683
$913$	14.7539	0.488282
$914$	25.4412	0.841521
$915$	0.527684	0.0174447
$916$	−87.3495	−2.88611
$917$	−7.89884	−0.260843
$918$	−33.3164	−1.09960
$919$	−10.8949	−0.359390	−0.179695	−	0.983722i	$-0.557511\pi$
$919$	−10.8949	−0.359390	−0.179695	+	0.983722i	$0.557511\pi$
$920$	9.81163	0.323480
$921$	−34.5574	−1.13871
$922$	−42.6598	−1.40493
$923$	−14.3448	−0.472164
$924$	−2.53138	−0.0832761
$925$	0.447564	0.0147158
$926$	102.234	3.35960
$927$	22.2495	0.730771
$928$	2.88750	0.0947867
$929$	−39.7926	−1.30555	−0.652776	−	0.757551i	$-0.726396\pi$
$929$	−39.7926	−1.30555	−0.652776	+	0.757551i	$0.726396\pi$
$930$	20.1581	0.661012
$931$	−0.564056	−0.0184862
$932$	26.8951	0.880977
$933$	19.0606	0.624015
$934$	26.4382	0.865085
$935$	10.2201	0.334234
$936$	−8.90667	−0.291124
$937$	−13.9200	−0.454747	−0.227374	−	0.973808i	$-0.573014\pi$
$937$	−13.9200	−0.454747	−0.227374	+	0.973808i	$0.573014\pi$
$938$	1.72315	0.0562628
$939$	−33.7829	−1.10246
$940$	−5.59414	−0.182461
$941$	−10.6780	−0.348094	−0.174047	−	0.984737i	$-0.555684\pi$
$941$	−10.6780	−0.348094	−0.174047	+	0.984737i	$0.555684\pi$
$942$	−34.8697	−1.13612
$943$	0.823472	0.0268159
$944$	13.5575	0.441258
$945$	−4.57284	−0.148755
$946$	−19.6573	−0.639115
$947$	−51.4681	−1.67249	−0.836244	−	0.548357i	$-0.815253\pi$
$947$	−51.4681	−1.67249	−0.836244	+	0.548357i	$0.815253\pi$
$948$	−1.54810	−0.0502800
$949$	6.06662	0.196931
$950$	−0.0546929	−0.00177447
$951$	−6.29919	−0.204265
$952$	−4.46295	−0.144645
$953$	−1.80826	−0.0585752	−0.0292876	−	0.999571i	$-0.509324\pi$
$953$	−1.80826	−0.0585752	−0.0292876	+	0.999571i	$0.509324\pi$
$954$	59.8284	1.93701
$955$	45.1670	1.46157
$956$	−26.0264	−0.841755
$957$	2.46894	0.0798094
$958$	70.8718	2.28976
$959$	−3.03201	−0.0979086
$960$	24.7851	0.799935
$961$	−18.8805	−0.609049
$962$	4.27216	0.137740
$963$	27.6621	0.891399
$964$	89.6037	2.88594
$965$	−12.3359	−0.397108
$966$	0.976507	0.0314186
$967$	−29.9625	−0.963530	−0.481765	−	0.876300i	$-0.660004\pi$
$967$	−29.9625	−0.963530	−0.481765	+	0.876300i	$0.660004\pi$
$968$	35.3627	1.13660
$969$	−0.232936	−0.00748298
$970$	−21.9484	−0.704722
$971$	3.31900	0.106512	0.0532559	−	0.998581i	$-0.483040\pi$
$971$	3.31900	0.106512	0.0532559	+	0.998581i	$0.483040\pi$
$972$	59.4625	1.90726
$973$	1.50018	0.0480935
$974$	−76.0532	−2.43690
$975$	−0.318054	−0.0101859
$976$	−0.594130	−0.0190176
$977$	−10.6293	−0.340062	−0.170031	−	0.985439i	$-0.554387\pi$
$977$	−10.6293	−0.340062	−0.170031	+	0.985439i	$0.554387\pi$
$978$	−24.6684	−0.788808
$979$	−16.6802	−0.533100
$980$	59.4312	1.89846
$981$	−0.619350	−0.0197743
$982$	13.6303	0.434961
$983$	−28.0979	−0.896185	−0.448092	−	0.893987i	$-0.647896\pi$
$983$	−28.0979	−0.896185	−0.448092	+	0.893987i	$0.647896\pi$
$984$	−3.68901	−0.117601
$985$	12.4027	0.395184
$986$	9.25164	0.294632
$987$	−0.261954	−0.00833808
$988$	−0.341328	−0.0108591
$989$	4.95785	0.157650
$990$	−17.3046	−0.549978
$991$	55.2238	1.75424	0.877120	−	0.480271i	$-0.159462\pi$
$991$	55.2238	1.75424	0.877120	+	0.480271i	$0.159462\pi$
$992$	7.04393	0.223645
$993$	14.6592	0.465194
$994$	12.1705	0.386024
$995$	49.0382	1.55462
$996$	35.4306	1.12266
$997$	−37.9277	−1.20118	−0.600590	−	0.799557i	$-0.705068\pi$
$997$	−37.9277	−1.20118	−0.600590	+	0.799557i	$0.705068\pi$
$998$	41.8461	1.32461
$999$	−8.32343	−0.263342

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.c.1.16	✓	143

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.c.1.16	✓	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)

\(f(q)\)	\(=\)	\(q-2.40357 q^{2} +1.04878 q^{3} +3.77713 q^{4} -2.29703 q^{5} -2.52082 q^{6} -0.387376 q^{7} -4.27144 q^{8} -1.90005 q^{9} +O(q^{10})\)	\(q-2.40357 q^{2} +1.04878 q^{3} +3.77713 q^{4} -2.29703 q^{5} -2.52082 q^{6} -0.387376 q^{7} -4.27144 q^{8} -1.90005 q^{9} +5.52106 q^{10} +1.64959 q^{11} +3.96139 q^{12} -1.09743 q^{13} +0.931084 q^{14} -2.40909 q^{15} +2.71244 q^{16} -2.69721 q^{17} +4.56690 q^{18} +0.0823446 q^{19} -8.67617 q^{20} -0.406274 q^{21} -3.96489 q^{22} +1.00000 q^{23} -4.47983 q^{24} +0.276337 q^{25} +2.63774 q^{26} -5.13910 q^{27} -1.46317 q^{28} +1.42708 q^{29} +5.79040 q^{30} +3.48130 q^{31} +2.02336 q^{32} +1.73006 q^{33} +6.48292 q^{34} +0.889814 q^{35} -7.17673 q^{36} +1.61963 q^{37} -0.197921 q^{38} -1.15096 q^{39} +9.81163 q^{40} +0.823472 q^{41} +0.976507 q^{42} +4.95785 q^{43} +6.23070 q^{44} +4.36447 q^{45} -2.40357 q^{46} +0.644770 q^{47} +2.84477 q^{48} -6.84994 q^{49} -0.664195 q^{50} -2.82879 q^{51} -4.14512 q^{52} +13.1004 q^{53} +12.3522 q^{54} -3.78915 q^{55} +1.65466 q^{56} +0.0863618 q^{57} -3.43008 q^{58} +4.99826 q^{59} -9.09943 q^{60} -0.219039 q^{61} -8.36754 q^{62} +0.736034 q^{63} -10.2882 q^{64} +2.52082 q^{65} -4.15832 q^{66} +1.85069 q^{67} -10.1877 q^{68} +1.04878 q^{69} -2.13873 q^{70} +13.0713 q^{71} +8.11596 q^{72} -5.52804 q^{73} -3.89289 q^{74} +0.289818 q^{75} +0.311026 q^{76} -0.639011 q^{77} +2.76642 q^{78} -0.390797 q^{79} -6.23055 q^{80} +0.310342 q^{81} -1.97927 q^{82} +8.94397 q^{83} -1.53455 q^{84} +6.19556 q^{85} -11.9165 q^{86} +1.49670 q^{87} -7.04612 q^{88} -10.1117 q^{89} -10.4903 q^{90} +0.425117 q^{91} +3.77713 q^{92} +3.65114 q^{93} -1.54975 q^{94} -0.189148 q^{95} +2.12207 q^{96} -3.97541 q^{97} +16.4643 q^{98} -3.13430 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) \) 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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