LMFDB - Embedded newform 8027.2.a.e.1.1

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:	$0$
Dimension:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q-2.75446 q^{2} +1.69224 q^{3} +5.58704 q^{4} +1.99190 q^{5} -4.66119 q^{6} -2.92850 q^{7} -9.88036 q^{8} -0.136337 q^{9} +O(q^{10})$	\(q-2.75446 q^{2} +1.69224 q^{3} +5.58704 q^{4} +1.99190 q^{5} -4.66119 q^{6} -2.92850 q^{7} -9.88036 q^{8} -0.136337 q^{9} -5.48661 q^{10} +3.01067 q^{11} +9.45460 q^{12} +0.662787 q^{13} +8.06642 q^{14} +3.37077 q^{15} +16.0410 q^{16} +7.11036 q^{17} +0.375536 q^{18} +1.74382 q^{19} +11.1288 q^{20} -4.95571 q^{21} -8.29277 q^{22} -1.00000 q^{23} -16.7199 q^{24} -1.03233 q^{25} -1.82562 q^{26} -5.30742 q^{27} -16.3616 q^{28} -2.45646 q^{29} -9.28463 q^{30} +7.27196 q^{31} -24.4234 q^{32} +5.09477 q^{33} -19.5852 q^{34} -5.83327 q^{35} -0.761723 q^{36} -5.04952 q^{37} -4.80328 q^{38} +1.12159 q^{39} -19.6807 q^{40} -7.44461 q^{41} +13.6503 q^{42} +5.66679 q^{43} +16.8208 q^{44} -0.271571 q^{45} +2.75446 q^{46} +8.30456 q^{47} +27.1451 q^{48} +1.57609 q^{49} +2.84352 q^{50} +12.0324 q^{51} +3.70302 q^{52} +8.43150 q^{53} +14.6191 q^{54} +5.99696 q^{55} +28.9346 q^{56} +2.95095 q^{57} +6.76623 q^{58} +5.23626 q^{59} +18.8326 q^{60} -12.9899 q^{61} -20.0303 q^{62} +0.399264 q^{63} +35.1915 q^{64} +1.32021 q^{65} -14.0333 q^{66} +6.00025 q^{67} +39.7259 q^{68} -1.69224 q^{69} +16.0675 q^{70} +0.594985 q^{71} +1.34706 q^{72} +5.64916 q^{73} +13.9087 q^{74} -1.74695 q^{75} +9.74279 q^{76} -8.81674 q^{77} -3.08938 q^{78} +5.36976 q^{79} +31.9520 q^{80} -8.57240 q^{81} +20.5059 q^{82} -9.13825 q^{83} -27.6877 q^{84} +14.1631 q^{85} -15.6089 q^{86} -4.15692 q^{87} -29.7465 q^{88} -2.35575 q^{89} +0.748030 q^{90} -1.94097 q^{91} -5.58704 q^{92} +12.3059 q^{93} -22.8746 q^{94} +3.47351 q^{95} -41.3302 q^{96} +9.88017 q^{97} -4.34128 q^{98} -0.410467 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) $ 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9} + 28 q^{10} + 17 q^{11} + 10 q^{12} + 91 q^{13} + 20 q^{14} + 29 q^{15} + 200 q^{16} + 16 q^{17} + 31 q^{18} + 30 q^{19} + 45 q^{20} + 49 q^{21} + 76 q^{22} - 169 q^{23} + 3 q^{24} + 241 q^{25} - 15 q^{26} + 14 q^{27} + 118 q^{28} + 23 q^{29} + 52 q^{30} + 45 q^{31} + 42 q^{32} + 62 q^{33} + 65 q^{34} - 16 q^{35} + 199 q^{36} + 226 q^{37} + 49 q^{38} + 17 q^{39} + 95 q^{40} + 19 q^{41} + 32 q^{42} + 71 q^{43} + 46 q^{44} + 127 q^{45} - 6 q^{46} + 27 q^{47} + 5 q^{48} + 239 q^{49} + 24 q^{50} + 39 q^{51} + 154 q^{52} + 111 q^{53} + 22 q^{54} + 47 q^{55} + 39 q^{56} + 122 q^{57} + 146 q^{58} - 73 q^{59} + 109 q^{60} + 125 q^{61} + 14 q^{62} + 109 q^{63} + 260 q^{64} + 73 q^{65} + 26 q^{66} + 152 q^{67} + 40 q^{68} - 2 q^{69} + 76 q^{70} - 79 q^{71} + 126 q^{72} + 106 q^{73} + 23 q^{74} + 12 q^{75} + 122 q^{76} + 63 q^{77} + 101 q^{78} + 82 q^{79} + 134 q^{80} + 225 q^{81} + 125 q^{82} + 28 q^{83} + 73 q^{84} + 197 q^{85} + 97 q^{86} + 18 q^{87} + 183 q^{88} + 54 q^{89} + 52 q^{90} + 106 q^{91} - 186 q^{92} + 194 q^{93} + q^{94} + 18 q^{95} - 39 q^{96} + 239 q^{97} + 5 q^{98} + 85 q^{99}+O(q^{100}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9 + 28 * q^10 + 17 * q^11 + 10 * q^12 + 91 * q^13 + 20 * q^14 + 29 * q^15 + 200 * q^16 + 16 * q^17 + 31 * q^18 + 30 * q^19 + 45 * q^20 + 49 * q^21 + 76 * q^22 - 169 * q^23 + 3 * q^24 + 241 * q^25 - 15 * q^26 + 14 * q^27 + 118 * q^28 + 23 * q^29 + 52 * q^30 + 45 * q^31 + 42 * q^32 + 62 * q^33 + 65 * q^34 - 16 * q^35 + 199 * q^36 + 226 * q^37 + 49 * q^38 + 17 * q^39 + 95 * q^40 + 19 * q^41 + 32 * q^42 + 71 * q^43 + 46 * q^44 + 127 * q^45 - 6 * q^46 + 27 * q^47 + 5 * q^48 + 239 * q^49 + 24 * q^50 + 39 * q^51 + 154 * q^52 + 111 * q^53 + 22 * q^54 + 47 * q^55 + 39 * q^56 + 122 * q^57 + 146 * q^58 - 73 * q^59 + 109 * q^60 + 125 * q^61 + 14 * q^62 + 109 * q^63 + 260 * q^64 + 73 * q^65 + 26 * q^66 + 152 * q^67 + 40 * q^68 - 2 * q^69 + 76 * q^70 - 79 * q^71 + 126 * q^72 + 106 * q^73 + 23 * q^74 + 12 * q^75 + 122 * q^76 + 63 * q^77 + 101 * q^78 + 82 * q^79 + 134 * q^80 + 225 * q^81 + 125 * q^82 + 28 * q^83 + 73 * q^84 + 197 * q^85 + 97 * q^86 + 18 * q^87 + 183 * q^88 + 54 * q^89 + 52 * q^90 + 106 * q^91 - 186 * q^92 + 194 * q^93 + q^94 + 18 * q^95 - 39 * q^96 + 239 * q^97 + 5 * q^98 + 85 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.75446	−1.94770	−0.973848	−	0.227200i	$-0.927043\pi$
$2$	−2.75446	−1.94770	−0.973848	+	0.227200i	$0.927043\pi$
$3$	1.69224	0.977013	0.488506	−	0.872560i	$-0.337542\pi$
$3$	1.69224	0.977013	0.488506	+	0.872560i	$0.337542\pi$
$4$	5.58704	2.79352
$5$	1.99190	0.890805	0.445402	−	0.895330i	$-0.353061\pi$
$5$	1.99190	0.890805	0.445402	+	0.895330i	$0.353061\pi$
$6$	−4.66119	−1.90292
$7$	−2.92850	−1.10687	−0.553434	−	0.832893i	$-0.686683\pi$
$7$	−2.92850	−1.10687	−0.553434	+	0.832893i	$0.686683\pi$
$8$	−9.88036	−3.49324
$9$	−0.136337	−0.0454458
$10$	−5.48661	−1.73502
$11$	3.01067	0.907752	0.453876	−	0.891065i	$-0.350041\pi$
$11$	3.01067	0.907752	0.453876	+	0.891065i	$0.350041\pi$
$12$	9.45460	2.72931
$13$	0.662787	0.183824	0.0919120	−	0.995767i	$-0.470702\pi$
$13$	0.662787	0.183824	0.0919120	+	0.995767i	$0.470702\pi$
$14$	8.06642	2.15584
$15$	3.37077	0.870328
$16$	16.0410	4.01024
$17$	7.11036	1.72451	0.862257	−	0.506471i	$-0.169050\pi$
$17$	7.11036	1.72451	0.862257	+	0.506471i	$0.169050\pi$
$18$	0.375536	0.0885147
$19$	1.74382	0.400059	0.200030	−	0.979790i	$-0.435896\pi$
$19$	1.74382	0.400059	0.200030	+	0.979790i	$0.435896\pi$
$20$	11.1288	2.48848
$21$	−4.95571	−1.08142
$22$	−8.29277	−1.76803
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−16.7199	−3.41294
$25$	−1.03233	−0.206467
$26$	−1.82562	−0.358033
$27$	−5.30742	−1.02141
$28$	−16.3616	−3.09206
$29$	−2.45646	−0.456154	−0.228077	−	0.973643i	$-0.573244\pi$
$29$	−2.45646	−0.456154	−0.228077	+	0.973643i	$0.573244\pi$
$30$	−9.28463	−1.69513
$31$	7.27196	1.30608	0.653041	−	0.757322i	$-0.273493\pi$
$31$	7.27196	1.30608	0.653041	+	0.757322i	$0.273493\pi$
$32$	−24.4234	−4.31750
$33$	5.09477	0.886885
$34$	−19.5852	−3.35883
$35$	−5.83327	−0.986003
$36$	−0.761723	−0.126954
$37$	−5.04952	−0.830136	−0.415068	−	0.909790i	$-0.636242\pi$
$37$	−5.04952	−0.830136	−0.415068	+	0.909790i	$0.636242\pi$
$38$	−4.80328	−0.779194
$39$	1.12159	0.179598
$40$	−19.6807	−3.11179
$41$	−7.44461	−1.16265	−0.581327	−	0.813670i	$-0.697466\pi$
$41$	−7.44461	−1.16265	−0.581327	+	0.813670i	$0.697466\pi$
$42$	13.6503	2.10629
$43$	5.66679	0.864177	0.432089	−	0.901831i	$-0.357777\pi$
$43$	5.66679	0.864177	0.432089	+	0.901831i	$0.357777\pi$
$44$	16.8208	2.53582
$45$	−0.271571	−0.0404834
$46$	2.75446	0.406123
$47$	8.30456	1.21134	0.605672	−	0.795714i	$-0.292904\pi$
$47$	8.30456	1.21134	0.605672	+	0.795714i	$0.292904\pi$
$48$	27.1451	3.91806
$49$	1.57609	0.225156
$50$	2.84352	0.402135
$51$	12.0324	1.68487
$52$	3.70302	0.513516
$53$	8.43150	1.15816	0.579078	−	0.815272i	$-0.303413\pi$
$53$	8.43150	1.15816	0.579078	+	0.815272i	$0.303413\pi$
$54$	14.6191	1.98940
$55$	5.99696	0.808630
$56$	28.9346	3.86655
$57$	2.95095	0.390863
$58$	6.76623	0.888449
$59$	5.23626	0.681703	0.340851	−	0.940117i	$-0.389285\pi$
$59$	5.23626	0.681703	0.340851	+	0.940117i	$0.389285\pi$
$60$	18.8326	2.43128
$61$	−12.9899	−1.66318	−0.831591	−	0.555388i	$-0.812570\pi$
$61$	−12.9899	−1.66318	−0.831591	+	0.555388i	$0.812570\pi$
$62$	−20.0303	−2.54385
$63$	0.399264	0.0503025
$64$	35.1915	4.39893
$65$	1.32021	0.163751
$66$	−14.0333	−1.72738
$67$	6.00025	0.733048	0.366524	−	0.930409i	$-0.380548\pi$
$67$	6.00025	0.733048	0.366524	+	0.930409i	$0.380548\pi$
$68$	39.7259	4.81747
$69$	−1.69224	−0.203721
$70$	16.0675	1.92043
$71$	0.594985	0.0706118	0.0353059	−	0.999377i	$-0.488759\pi$
$71$	0.594985	0.0706118	0.0353059	+	0.999377i	$0.488759\pi$
$72$	1.34706	0.158753
$73$	5.64916	0.661185	0.330592	−	0.943774i	$-0.392751\pi$
$73$	5.64916	0.661185	0.330592	+	0.943774i	$0.392751\pi$
$74$	13.9087	1.61685
$75$	−1.74695	−0.201721
$76$	9.74279	1.11757
$77$	−8.81674	−1.00476
$78$	−3.08938	−0.349803
$79$	5.36976	0.604145	0.302073	−	0.953285i	$-0.402321\pi$
$79$	5.36976	0.604145	0.302073	+	0.953285i	$0.402321\pi$
$80$	31.9520	3.57234
$81$	−8.57240	−0.952489
$82$	20.5059	2.26450
$83$	−9.13825	−1.00305	−0.501526	−	0.865142i	$-0.667228\pi$
$83$	−9.13825	−1.00305	−0.501526	+	0.865142i	$0.667228\pi$
$84$	−27.6877	−3.02098
$85$	14.1631	1.53621
$86$	−15.6089	−1.68315
$87$	−4.15692	−0.445668
$88$	−29.7465	−3.17099
$89$	−2.35575	−0.249709	−0.124855	−	0.992175i	$-0.539846\pi$
$89$	−2.35575	−0.249709	−0.124855	+	0.992175i	$0.539846\pi$
$90$	0.748030	0.0788493
$91$	−1.94097	−0.203469
$92$	−5.58704	−0.582490
$93$	12.3059	1.27606
$94$	−22.8746	−2.35933
$95$	3.47351	0.356375
$96$	−41.3302	−4.21825
$97$	9.88017	1.00318	0.501590	−	0.865106i	$-0.332749\pi$
$97$	9.88017	1.00318	0.501590	+	0.865106i	$0.332749\pi$
$98$	−4.34128	−0.438535
$99$	−0.410467	−0.0412535
$100$	−5.76769	−0.576769
$101$	13.1296	1.30645	0.653224	−	0.757165i	$-0.273416\pi$
$101$	13.1296	1.30645	0.653224	+	0.757165i	$0.273416\pi$
$102$	−33.1427	−3.28162
$103$	3.67002	0.361618	0.180809	−	0.983518i	$-0.442128\pi$
$103$	3.67002	0.361618	0.180809	+	0.983518i	$0.442128\pi$
$104$	−6.54857	−0.642141
$105$	−9.87127	−0.963338
$106$	−23.2242	−2.25574
$107$	1.41043	0.136351	0.0681756	−	0.997673i	$-0.478282\pi$
$107$	1.41043	0.136351	0.0681756	+	0.997673i	$0.478282\pi$
$108$	−29.6528	−2.85334
$109$	−0.999667	−0.0957507	−0.0478754	−	0.998853i	$-0.515245\pi$
$109$	−0.999667	−0.0957507	−0.0478754	+	0.998853i	$0.515245\pi$
$110$	−16.5184	−1.57497
$111$	−8.54498	−0.811054
$112$	−46.9759	−4.43881
$113$	7.41331	0.697386	0.348693	−	0.937237i	$-0.386626\pi$
$113$	7.41331	0.697386	0.348693	+	0.937237i	$0.386626\pi$
$114$	−8.12828	−0.761283
$115$	−1.99190	−0.185746
$116$	−13.7244	−1.27428
$117$	−0.0903627	−0.00835403
$118$	−14.4231	−1.32775
$119$	−20.8226	−1.90881
$120$	−33.3044	−3.04026
$121$	−1.93585	−0.175986
$122$	35.7801	3.23937
$123$	−12.5980	−1.13593
$124$	40.6287	3.64857
$125$	−12.0158	−1.07473
$126$	−1.09976	−0.0979740
$127$	2.93017	0.260011	0.130005	−	0.991513i	$-0.458501\pi$
$127$	2.93017	0.260011	0.130005	+	0.991513i	$0.458501\pi$
$128$	−48.0865	−4.25029
$129$	9.58954	0.844312
$130$	−3.63645	−0.318938
$131$	−2.27864	−0.199086	−0.0995429	−	0.995033i	$-0.531738\pi$
$131$	−2.27864	−0.199086	−0.0995429	+	0.995033i	$0.531738\pi$
$132$	28.4647	2.47753
$133$	−5.10677	−0.442813
$134$	−16.5275	−1.42775
$135$	−10.5719	−0.909881
$136$	−70.2529	−6.02414
$137$	17.4947	1.49467	0.747337	−	0.664445i	$-0.231332\pi$
$137$	17.4947	1.49467	0.747337	+	0.664445i	$0.231332\pi$
$138$	4.66119	0.396787
$139$	2.70309	0.229273	0.114636	−	0.993408i	$-0.463430\pi$
$139$	2.70309	0.229273	0.114636	+	0.993408i	$0.463430\pi$
$140$	−32.5907	−2.75442
$141$	14.0533	1.18350
$142$	−1.63886	−0.137530
$143$	1.99543	0.166867
$144$	−2.18698	−0.182249
$145$	−4.89303	−0.406344
$146$	−15.5604	−1.28779
$147$	2.66712	0.219980
$148$	−28.2119	−2.31900
$149$	−15.6238	−1.27995	−0.639977	−	0.768394i	$-0.721056\pi$
$149$	−15.6238	−1.27995	−0.639977	+	0.768394i	$0.721056\pi$
$150$	4.81191	0.392891
$151$	11.5861	0.942865	0.471433	−	0.881902i	$-0.343737\pi$
$151$	11.5861	0.942865	0.471433	+	0.881902i	$0.343737\pi$
$152$	−17.2296	−1.39750
$153$	−0.969408	−0.0783720
$154$	24.2854	1.95697
$155$	14.4850	1.16346
$156$	6.26638	0.501712
$157$	−4.03656	−0.322153	−0.161076	−	0.986942i	$-0.551497\pi$
$157$	−4.03656	−0.322153	−0.161076	+	0.986942i	$0.551497\pi$
$158$	−14.7908	−1.17669
$159$	14.2681	1.13153
$160$	−48.6491	−3.84605
$161$	2.92850	0.230798
$162$	23.6123	1.85516
$163$	17.9244	1.40395	0.701974	−	0.712203i	$-0.252302\pi$
$163$	17.9244	1.40395	0.701974	+	0.712203i	$0.252302\pi$
$164$	−41.5934	−3.24790
$165$	10.1483	0.790042
$166$	25.1709	1.95364
$167$	24.1527	1.86899	0.934497	−	0.355971i	$-0.115850\pi$
$167$	24.1527	1.86899	0.934497	+	0.355971i	$0.115850\pi$
$168$	48.9642	3.77767
$169$	−12.5607	−0.966209
$170$	−39.0117	−2.99206
$171$	−0.237748	−0.0181810
$172$	31.6606	2.41410
$173$	−12.3110	−0.935986	−0.467993	−	0.883732i	$-0.655023\pi$
$173$	−12.3110	−0.935986	−0.467993	+	0.883732i	$0.655023\pi$
$174$	11.4501	0.868026
$175$	3.02319	0.228531
$176$	48.2941	3.64030
$177$	8.86098	0.666032
$178$	6.48882	0.486357
$179$	−18.2681	−1.36542	−0.682709	−	0.730690i	$-0.739199\pi$
$179$	−18.2681	−1.36542	−0.682709	+	0.730690i	$0.739199\pi$
$180$	−1.51728	−0.113091
$181$	3.14904	0.234066	0.117033	−	0.993128i	$-0.462662\pi$
$181$	3.14904	0.234066	0.117033	+	0.993128i	$0.462662\pi$
$182$	5.34632	0.396296
$183$	−21.9819	−1.62495
$184$	9.88036	0.728390
$185$	−10.0581	−0.739489
$186$	−33.8960	−2.48538
$187$	21.4070	1.56543
$188$	46.3979	3.38392
$189$	15.5428	1.13057
$190$	−9.56765	−0.694110
$191$	16.7902	1.21489	0.607447	−	0.794360i	$-0.292194\pi$
$191$	16.7902	1.21489	0.607447	+	0.794360i	$0.292194\pi$
$192$	59.5522	4.29781
$193$	−2.24479	−0.161584	−0.0807918	−	0.996731i	$-0.525745\pi$
$193$	−2.24479	−0.161584	−0.0807918	+	0.996731i	$0.525745\pi$
$194$	−27.2145	−1.95389
$195$	2.23410	0.159987
$196$	8.80569	0.628978
$197$	13.6410	0.971879	0.485940	−	0.873992i	$-0.338478\pi$
$197$	13.6410	0.971879	0.485940	+	0.873992i	$0.338478\pi$
$198$	1.13062	0.0803493
$199$	9.29745	0.659079	0.329539	−	0.944142i	$-0.393107\pi$
$199$	9.29745	0.659079	0.329539	+	0.944142i	$0.393107\pi$
$200$	10.1998	0.721237
$201$	10.1538	0.716197
$202$	−36.1651	−2.54456
$203$	7.19374	0.504902
$204$	67.2255	4.70673
$205$	−14.8289	−1.03570
$206$	−10.1089	−0.704322
$207$	0.136337	0.00947611
$208$	10.6317	0.737179
$209$	5.25007	0.363155
$210$	27.1900	1.87629
$211$	−4.24913	−0.292522	−0.146261	−	0.989246i	$-0.546724\pi$
$211$	−4.24913	−0.292522	−0.146261	+	0.989246i	$0.546724\pi$
$212$	47.1071	3.23533
$213$	1.00686	0.0689886
$214$	−3.88497	−0.265571
$215$	11.2877	0.769813
$216$	52.4393	3.56804
$217$	−21.2959	−1.44566
$218$	2.75354	0.186493
$219$	9.55972	0.645986
$220$	33.5053	2.25892
$221$	4.71265	0.317007
$222$	23.5368	1.57969
$223$	8.43421	0.564797	0.282398	−	0.959297i	$-0.408870\pi$
$223$	8.43421	0.564797	0.282398	+	0.959297i	$0.408870\pi$
$224$	71.5240	4.77890
$225$	0.140746	0.00938305
$226$	−20.4197	−1.35830
$227$	−17.6503	−1.17149	−0.585746	−	0.810495i	$-0.699198\pi$
$227$	−17.6503	−1.17149	−0.585746	+	0.810495i	$0.699198\pi$
$228$	16.4871	1.09188
$229$	−5.92644	−0.391630	−0.195815	−	0.980641i	$-0.562735\pi$
$229$	−5.92644	−0.391630	−0.195815	+	0.980641i	$0.562735\pi$
$230$	5.48661	0.361776
$231$	−14.9200	−0.981665
$232$	24.2707	1.59345
$233$	−9.96764	−0.653002	−0.326501	−	0.945197i	$-0.605870\pi$
$233$	−9.96764	−0.653002	−0.326501	+	0.945197i	$0.605870\pi$
$234$	0.248900	0.0162711
$235$	16.5419	1.07907
$236$	29.2552	1.90435
$237$	9.08690	0.590258
$238$	57.3551	3.71778
$239$	−19.8163	−1.28181	−0.640906	−	0.767620i	$-0.721441\pi$
$239$	−19.8163	−1.28181	−0.640906	+	0.767620i	$0.721441\pi$
$240$	54.0703	3.49022
$241$	−13.7961	−0.888688	−0.444344	−	0.895856i	$-0.646563\pi$
$241$	−13.7961	−0.888688	−0.444344	+	0.895856i	$0.646563\pi$
$242$	5.33222	0.342768
$243$	1.41575	0.0908201
$244$	−72.5750	−4.64614
$245$	3.13942	0.200570
$246$	34.7008	2.21244
$247$	1.15578	0.0735405
$248$	−71.8496	−4.56245
$249$	−15.4641	−0.979996
$250$	33.0970	2.09324
$251$	7.83597	0.494602	0.247301	−	0.968939i	$-0.420456\pi$
$251$	7.83597	0.494602	0.247301	+	0.968939i	$0.420456\pi$
$252$	2.23070	0.140521
$253$	−3.01067	−0.189279
$254$	−8.07105	−0.506422
$255$	23.9673	1.50089
$256$	62.0694	3.87934
$257$	−6.03368	−0.376371	−0.188185	−	0.982134i	$-0.560261\pi$
$257$	−6.03368	−0.376371	−0.188185	+	0.982134i	$0.560261\pi$
$258$	−26.4140	−1.64446
$259$	14.7875	0.918851
$260$	7.37604	0.457443
$261$	0.334908	0.0207303
$262$	6.27642	0.387759
$263$	−18.9124	−1.16619	−0.583094	−	0.812405i	$-0.698158\pi$
$263$	−18.9124	−1.16619	−0.583094	+	0.812405i	$0.698158\pi$
$264$	−50.3382	−3.09810
$265$	16.7947	1.03169
$266$	14.0664	0.862465
$267$	−3.98649	−0.243969
$268$	33.5237	2.04778
$269$	16.6090	1.01267	0.506334	−	0.862337i	$-0.331000\pi$
$269$	16.6090	1.01267	0.506334	+	0.862337i	$0.331000\pi$
$270$	29.1197	1.77217
$271$	3.85875	0.234402	0.117201	−	0.993108i	$-0.462608\pi$
$271$	3.85875	0.234402	0.117201	+	0.993108i	$0.462608\pi$
$272$	114.057	6.91572
$273$	−3.28458	−0.198792
$274$	−48.1885	−2.91117
$275$	−3.10802	−0.187421
$276$	−9.45460	−0.569100
$277$	24.9909	1.50156	0.750778	−	0.660555i	$-0.229679\pi$
$277$	24.9909	1.50156	0.750778	+	0.660555i	$0.229679\pi$
$278$	−7.44554	−0.446554
$279$	−0.991440	−0.0593560
$280$	57.6348	3.44434
$281$	−8.15876	−0.486711	−0.243355	−	0.969937i	$-0.578248\pi$
$281$	−8.15876	−0.486711	−0.243355	+	0.969937i	$0.578248\pi$
$282$	−38.7092	−2.30510
$283$	10.8115	0.642675	0.321338	−	0.946965i	$-0.395868\pi$
$283$	10.8115	0.642675	0.321338	+	0.946965i	$0.395868\pi$
$284$	3.32421	0.197255
$285$	5.87800	0.348183
$286$	−5.49634	−0.325005
$287$	21.8015	1.28690
$288$	3.32983	0.196212
$289$	33.5572	1.97395
$290$	13.4776	0.791435
$291$	16.7196	0.980119
$292$	31.5621	1.84703
$293$	18.9705	1.10827	0.554136	−	0.832426i	$-0.313049\pi$
$293$	18.9705	1.10827	0.554136	+	0.832426i	$0.313049\pi$
$294$	−7.34646	−0.428454
$295$	10.4301	0.607264
$296$	49.8911	2.89986
$297$	−15.9789	−0.927191
$298$	43.0352	2.49296
$299$	−0.662787	−0.0383300
$300$	−9.76030	−0.563511
$301$	−16.5952	−0.956530
$302$	−31.9135	−1.83642
$303$	22.2185	1.27642
$304$	27.9725	1.60433
$305$	−25.8745	−1.48157
$306$	2.67019	0.152645
$307$	−13.4972	−0.770323	−0.385162	−	0.922849i	$-0.625854\pi$
$307$	−13.4972	−0.770323	−0.385162	+	0.922849i	$0.625854\pi$
$308$	−49.2595	−2.80682
$309$	6.21054	0.353305
$310$	−39.8984	−2.26608
$311$	−11.6059	−0.658109	−0.329055	−	0.944311i	$-0.606730\pi$
$311$	−11.6059	−0.658109	−0.329055	+	0.944311i	$0.606730\pi$
$312$	−11.0817	−0.627380
$313$	−14.0758	−0.795610	−0.397805	−	0.917470i	$-0.630228\pi$
$313$	−14.0758	−0.795610	−0.397805	+	0.917470i	$0.630228\pi$
$314$	11.1186	0.627456
$315$	0.795293	0.0448097
$316$	30.0011	1.68769
$317$	11.8751	0.666975	0.333487	−	0.942755i	$-0.391775\pi$
$317$	11.8751	0.666975	0.333487	+	0.942755i	$0.391775\pi$
$318$	−39.3009	−2.20388
$319$	−7.39561	−0.414074
$320$	70.0979	3.91859
$321$	2.38678	0.133217
$322$	−8.06642	−0.449524
$323$	12.3992	0.689908
$324$	−47.8944	−2.66080
$325$	−0.684217	−0.0379535
$326$	−49.3720	−2.73446
$327$	−1.69167	−0.0935497
$328$	73.5555	4.06142
$329$	−24.3199	−1.34080
$330$	−27.9530	−1.53876
$331$	3.35791	0.184568	0.0922838	−	0.995733i	$-0.470583\pi$
$331$	3.35791	0.184568	0.0922838	+	0.995733i	$0.470583\pi$
$332$	−51.0558	−2.80205
$333$	0.688439	0.0377262
$334$	−66.5277	−3.64023
$335$	11.9519	0.653002
$336$	−79.4943	−4.33677
$337$	35.9005	1.95563	0.977813	−	0.209478i	$-0.0671763\pi$
$337$	35.9005	1.95563	0.977813	+	0.209478i	$0.0671763\pi$
$338$	34.5980	1.88188
$339$	12.5451	0.681355
$340$	79.1300	4.29142
$341$	21.8935	1.18560
$342$	0.654866	0.0354111
$343$	15.8839	0.857650
$344$	−55.9899	−3.01877
$345$	−3.37077	−0.181476
$346$	33.9101	1.82302
$347$	−36.3332	−1.95047	−0.975234	−	0.221175i	$-0.929011\pi$
$347$	−36.3332	−1.95047	−0.975234	+	0.221175i	$0.929011\pi$
$348$	−23.2249	−1.24498
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	−8.32724	−0.445110
$351$	−3.51769	−0.187760
$352$	−73.5310	−3.91922
$353$	10.6671	0.567751	0.283875	−	0.958861i	$-0.408380\pi$
$353$	10.6671	0.567751	0.283875	+	0.958861i	$0.408380\pi$
$354$	−24.4072	−1.29723
$355$	1.18515	0.0629013
$356$	−13.1617	−0.697568
$357$	−35.2368	−1.86493
$358$	50.3186	2.65942
$359$	−24.4114	−1.28839	−0.644193	−	0.764863i	$-0.722806\pi$
$359$	−24.4114	−1.28839	−0.644193	+	0.764863i	$0.722806\pi$
$360$	2.68322	0.141418
$361$	−15.9591	−0.839952
$362$	−8.67390	−0.455890
$363$	−3.27592	−0.171941
$364$	−10.8443	−0.568395
$365$	11.2526	0.588986
$366$	60.5483	3.16491
$367$	−4.12815	−0.215488	−0.107744	−	0.994179i	$-0.534363\pi$
$367$	−4.12815	−0.215488	−0.107744	+	0.994179i	$0.534363\pi$
$368$	−16.0410	−0.836193
$369$	1.01498	0.0528377
$370$	27.7047	1.44030
$371$	−24.6916	−1.28192
$372$	68.7534	3.56470
$373$	26.2793	1.36069	0.680345	−	0.732892i	$-0.261830\pi$
$373$	26.2793	1.36069	0.680345	+	0.732892i	$0.261830\pi$
$374$	−58.9646	−3.04899
$375$	−20.3336	−1.05002
$376$	−82.0521	−4.23151
$377$	−1.62811	−0.0838520
$378$	−42.8119	−2.20201
$379$	35.9230	1.84524	0.922621	−	0.385708i	$-0.126043\pi$
$379$	35.9230	1.84524	0.922621	+	0.385708i	$0.126043\pi$
$380$	19.4067	0.995541
$381$	4.95855	0.254034
$382$	−46.2478	−2.36624
$383$	−34.6562	−1.77085	−0.885425	−	0.464782i	$-0.846133\pi$
$383$	−34.6562	−1.77085	−0.885425	+	0.464782i	$0.846133\pi$
$384$	−81.3737	−4.15259
$385$	−17.5621	−0.895046
$386$	6.18319	0.314716
$387$	−0.772595	−0.0392732
$388$	55.2009	2.80240
$389$	−17.2323	−0.873711	−0.436855	−	0.899532i	$-0.643908\pi$
$389$	−17.2323	−0.873711	−0.436855	+	0.899532i	$0.643908\pi$
$390$	−6.15373	−0.311606
$391$	−7.11036	−0.359586
$392$	−15.5723	−0.786522
$393$	−3.85600	−0.194509
$394$	−37.5735	−1.89293
$395$	10.6960	0.538176
$396$	−2.29330	−0.115243
$397$	15.4750	0.776667	0.388333	−	0.921519i	$-0.373051\pi$
$397$	15.4750	0.776667	0.388333	+	0.921519i	$0.373051\pi$
$398$	−25.6094	−1.28369
$399$	−8.64185	−0.432634
$400$	−16.5596	−0.827981
$401$	−0.882288	−0.0440594	−0.0220297	−	0.999757i	$-0.507013\pi$
$401$	−0.882288	−0.0440594	−0.0220297	+	0.999757i	$0.507013\pi$
$402$	−27.9684	−1.39493
$403$	4.81976	0.240089
$404$	73.3559	3.64959
$405$	−17.0754	−0.848482
$406$	−19.8149	−0.983395
$407$	−15.2025	−0.753558
$408$	−118.884	−5.88566
$409$	28.3215	1.40041	0.700204	−	0.713943i	$-0.253092\pi$
$409$	28.3215	1.40041	0.700204	+	0.713943i	$0.253092\pi$
$410$	40.8457	2.01722
$411$	29.6052	1.46032
$412$	20.5046	1.01019
$413$	−15.3344	−0.754555
$414$	−0.375536	−0.0184566
$415$	−18.2025	−0.893524
$416$	−16.1875	−0.793659
$417$	4.57426	0.224002
$418$	−14.4611	−0.707315
$419$	−1.05899	−0.0517351	−0.0258675	−	0.999665i	$-0.508235\pi$
$419$	−1.05899	−0.0517351	−0.0258675	+	0.999665i	$0.508235\pi$
$420$	−55.1512	−2.69110
$421$	−6.38994	−0.311427	−0.155713	−	0.987802i	$-0.549768\pi$
$421$	−6.38994	−0.311427	−0.155713	+	0.987802i	$0.549768\pi$
$422$	11.7041	0.569745
$423$	−1.13222	−0.0550506
$424$	−83.3063	−4.04571
$425$	−7.34026	−0.356055
$426$	−2.77334	−0.134369
$427$	38.0408	1.84092
$428$	7.88012	0.380900
$429$	3.37675	0.163031
$430$	−31.0914	−1.49936
$431$	−8.30207	−0.399897	−0.199948	−	0.979806i	$-0.564077\pi$
$431$	−8.30207	−0.399897	−0.199948	+	0.979806i	$0.564077\pi$
$432$	−85.1362	−4.09612
$433$	16.1122	0.774301	0.387150	−	0.922017i	$-0.373459\pi$
$433$	16.1122	0.774301	0.387150	+	0.922017i	$0.373459\pi$
$434$	58.6587	2.81571
$435$	−8.28016	−0.397003
$436$	−5.58518	−0.267482
$437$	−1.74382	−0.0834182
$438$	−26.3319	−1.25818
$439$	21.8253	1.04167	0.520833	−	0.853659i	$-0.325622\pi$
$439$	21.8253	1.04167	0.520833	+	0.853659i	$0.325622\pi$
$440$	−59.2521	−2.82473
$441$	−0.214880	−0.0102324
$442$	−12.9808	−0.617434
$443$	21.5180	1.02235	0.511175	−	0.859477i	$-0.329210\pi$
$443$	21.5180	1.02235	0.511175	+	0.859477i	$0.329210\pi$
$444$	−47.7412	−2.26570
$445$	−4.69242	−0.222442
$446$	−23.2317	−1.10005
$447$	−26.4392	−1.25053
$448$	−103.058	−4.86903
$449$	13.1429	0.620251	0.310126	−	0.950696i	$-0.399629\pi$
$449$	13.1429	0.620251	0.310126	+	0.950696i	$0.399629\pi$
$450$	−0.387678	−0.0182753
$451$	−22.4133	−1.05540
$452$	41.4185	1.94816
$453$	19.6065	0.921191
$454$	48.6170	2.28171
$455$	−3.86622	−0.181251
$456$	−29.1565	−1.36538
$457$	−2.70674	−0.126616	−0.0633079	−	0.997994i	$-0.520165\pi$
$457$	−2.70674	−0.126616	−0.0633079	+	0.997994i	$0.520165\pi$
$458$	16.3241	0.762777
$459$	−37.7377	−1.76144
$460$	−11.1288	−0.518884
$461$	−10.2054	−0.475313	−0.237657	−	0.971349i	$-0.576379\pi$
$461$	−10.2054	−0.475313	−0.237657	+	0.971349i	$0.576379\pi$
$462$	41.0966	1.91198
$463$	27.8926	1.29628	0.648139	−	0.761522i	$-0.275548\pi$
$463$	27.8926	1.29628	0.648139	+	0.761522i	$0.275548\pi$
$464$	−39.4040	−1.82929
$465$	24.5121	1.13672
$466$	27.4555	1.27185
$467$	13.0019	0.601656	0.300828	−	0.953678i	$-0.402737\pi$
$467$	13.0019	0.601656	0.300828	+	0.953678i	$0.402737\pi$
$468$	−0.504860	−0.0233372
$469$	−17.5717	−0.811387
$470$	−45.5639	−2.10170
$471$	−6.83082	−0.314748
$472$	−51.7361	−2.38135
$473$	17.0608	0.784459
$474$	−25.0295	−1.14964
$475$	−1.80020	−0.0825990
$476$	−116.337	−5.33230
$477$	−1.14953	−0.0526333
$478$	54.5832	2.49658
$479$	28.3698	1.29625	0.648124	−	0.761535i	$-0.275554\pi$
$479$	28.3698	1.29625	0.648124	+	0.761535i	$0.275554\pi$
$480$	−82.3257	−3.75764
$481$	−3.34676	−0.152599
$482$	38.0009	1.73089
$483$	4.95571	0.225492
$484$	−10.8157	−0.491622
$485$	19.6803	0.893637
$486$	−3.89961	−0.176890
$487$	3.58400	0.162407	0.0812034	−	0.996698i	$-0.474124\pi$
$487$	3.58400	0.162407	0.0812034	+	0.996698i	$0.474124\pi$
$488$	128.345	5.80989
$489$	30.3323	1.37167
$490$	−8.64739	−0.390649
$491$	−19.5832	−0.883779	−0.441890	−	0.897069i	$-0.645692\pi$
$491$	−19.5832	−0.883779	−0.441890	+	0.897069i	$0.645692\pi$
$492$	−70.3858	−3.17324
$493$	−17.4663	−0.786644
$494$	−3.18355	−0.143235
$495$	−0.817610	−0.0367488
$496$	116.649	5.23770
$497$	−1.74241	−0.0781579
$498$	42.5951	1.90873
$499$	32.1233	1.43804	0.719019	−	0.694990i	$-0.244591\pi$
$499$	32.1233	1.43804	0.719019	+	0.694990i	$0.244591\pi$
$500$	−67.1328	−3.00227
$501$	40.8721	1.82603
$502$	−21.5839	−0.963334
$503$	−4.42630	−0.197359	−0.0986796	−	0.995119i	$-0.531462\pi$
$503$	−4.42630	−0.197359	−0.0986796	+	0.995119i	$0.531462\pi$
$504$	−3.94487	−0.175718
$505$	26.1529	1.16379
$506$	8.29277	0.368659
$507$	−21.2557	−0.943998
$508$	16.3710	0.726346
$509$	33.0552	1.46514	0.732572	−	0.680690i	$-0.238320\pi$
$509$	33.0552	1.46514	0.732572	+	0.680690i	$0.238320\pi$
$510$	−66.0170	−2.92328
$511$	−16.5436	−0.731844
$512$	−74.7946	−3.30549
$513$	−9.25518	−0.408626
$514$	16.6195	0.733056
$515$	7.31032	0.322131
$516$	53.5772	2.35860
$517$	25.0023	1.09960
$518$	−40.7316	−1.78964
$519$	−20.8331	−0.914470
$520$	−13.0441	−0.572022
$521$	−29.9822	−1.31354	−0.656772	−	0.754089i	$-0.728079\pi$
$521$	−29.9822	−1.31354	−0.656772	+	0.754089i	$0.728079\pi$
$522$	−0.922490	−0.0403763
$523$	41.4675	1.81325	0.906623	−	0.421941i	$-0.138651\pi$
$523$	41.4675	1.81325	0.906623	+	0.421941i	$0.138651\pi$
$524$	−12.7309	−0.556150
$525$	5.11594	0.223278
$526$	52.0934	2.27138
$527$	51.7062	2.25236
$528$	81.7250	3.55662
$529$	1.00000	0.0434783
$530$	−46.2603	−2.00942
$531$	−0.713898	−0.0309805
$532$	−28.5317	−1.23701
$533$	−4.93419	−0.213724
$534$	10.9806	0.475177
$535$	2.80943	0.121462
$536$	−59.2847	−2.56071
$537$	−30.9139	−1.33403
$538$	−45.7488	−1.97237
$539$	4.74509	0.204386
$540$	−59.0654	−2.54177
$541$	27.7681	1.19385	0.596923	−	0.802299i	$-0.296390\pi$
$541$	27.7681	1.19385	0.596923	+	0.802299i	$0.296390\pi$
$542$	−10.6288	−0.456544
$543$	5.32892	0.228686
$544$	−173.659	−7.44559
$545$	−1.99124	−0.0852952
$546$	9.04723	0.387186
$547$	−15.1203	−0.646496	−0.323248	−	0.946314i	$-0.604775\pi$
$547$	−15.1203	−0.646496	−0.323248	+	0.946314i	$0.604775\pi$
$548$	97.7437	4.17541
$549$	1.77101	0.0755847
$550$	8.56091	0.365038
$551$	−4.28363	−0.182489
$552$	16.7199	0.711646
$553$	−15.7253	−0.668709
$554$	−68.8363	−2.92458
$555$	−17.0207	−0.722490
$556$	15.1023	0.640478
$557$	18.4809	0.783060	0.391530	−	0.920165i	$-0.371946\pi$
$557$	18.4809	0.783060	0.391530	+	0.920165i	$0.371946\pi$
$558$	2.73088	0.115607
$559$	3.75587	0.158856
$560$	−93.5713	−3.95411
$561$	36.2256	1.52945
$562$	22.4730	0.947965
$563$	−30.4292	−1.28244	−0.641220	−	0.767357i	$-0.721571\pi$
$563$	−30.4292	−1.28244	−0.641220	+	0.767357i	$0.721571\pi$
$564$	78.5163	3.30613
$565$	14.7666	0.621234
$566$	−29.7798	−1.25174
$567$	25.1042	1.05428
$568$	−5.87867	−0.246664
$569$	38.1568	1.59962	0.799809	−	0.600255i	$-0.204934\pi$
$569$	38.1568	1.59962	0.799809	+	0.600255i	$0.204934\pi$
$570$	−16.1907	−0.678155
$571$	−43.7925	−1.83266	−0.916330	−	0.400423i	$-0.868863\pi$
$571$	−43.7925	−1.83266	−0.916330	+	0.400423i	$0.868863\pi$
$572$	11.1486	0.466145
$573$	28.4129	1.18697
$574$	−60.0514	−2.50650
$575$	1.03233	0.0430513
$576$	−4.79791	−0.199913
$577$	7.58849	0.315913	0.157956	−	0.987446i	$-0.449509\pi$
$577$	7.58849	0.315913	0.157956	+	0.987446i	$0.449509\pi$
$578$	−92.4318	−3.84466
$579$	−3.79872	−0.157869
$580$	−27.3376	−1.13513
$581$	26.7613	1.11025
$582$	−46.0534	−1.90897
$583$	25.3845	1.05132
$584$	−55.8158	−2.30967
$585$	−0.179993	−0.00744181
$586$	−52.2536	−2.15858
$587$	−14.7286	−0.607914	−0.303957	−	0.952686i	$-0.598308\pi$
$587$	−14.7286	−0.607914	−0.303957	+	0.952686i	$0.598308\pi$
$588$	14.9013	0.614519
$589$	12.6810	0.522511
$590$	−28.7293	−1.18277
$591$	23.0837	0.949538
$592$	−80.9992	−3.32905
$593$	3.35565	0.137800	0.0688999	−	0.997624i	$-0.478051\pi$
$593$	3.35565	0.137800	0.0688999	+	0.997624i	$0.478051\pi$
$594$	44.0133	1.80589
$595$	−41.4766	−1.70038
$596$	−87.2911	−3.57558
$597$	15.7335	0.643928
$598$	1.82562	0.0746551
$599$	−39.5177	−1.61465	−0.807325	−	0.590107i	$-0.799086\pi$
$599$	−39.5177	−1.61465	−0.807325	+	0.590107i	$0.799086\pi$
$600$	17.2605	0.704658
$601$	−13.5762	−0.553784	−0.276892	−	0.960901i	$-0.589304\pi$
$601$	−13.5762	−0.553784	−0.276892	+	0.960901i	$0.589304\pi$
$602$	45.7107	1.86303
$603$	−0.818059	−0.0333140
$604$	64.7322	2.63391
$605$	−3.85602	−0.156770
$606$	−61.1998	−2.48607
$607$	−2.11021	−0.0856507	−0.0428253	−	0.999083i	$-0.513636\pi$
$607$	−2.11021	−0.0856507	−0.0428253	+	0.999083i	$0.513636\pi$
$608$	−42.5901	−1.72726
$609$	12.1735	0.493296
$610$	71.2703	2.88565
$611$	5.50415	0.222674
$612$	−5.41612	−0.218934
$613$	−12.0098	−0.485072	−0.242536	−	0.970142i	$-0.577979\pi$
$613$	−12.0098	−0.485072	−0.242536	+	0.970142i	$0.577979\pi$
$614$	37.1774	1.50036
$615$	−25.0940	−1.01189
$616$	87.1126	3.50987
$617$	29.9293	1.20491	0.602454	−	0.798154i	$-0.294190\pi$
$617$	29.9293	1.20491	0.602454	+	0.798154i	$0.294190\pi$
$618$	−17.1067	−0.688132
$619$	−11.7970	−0.474160	−0.237080	−	0.971490i	$-0.576190\pi$
$619$	−11.7970	−0.474160	−0.237080	+	0.971490i	$0.576190\pi$
$620$	80.9284	3.25016
$621$	5.30742	0.212980
$622$	31.9679	1.28180
$623$	6.89881	0.276395
$624$	17.9914	0.720233
$625$	−18.7726	−0.750905
$626$	38.7711	1.54961
$627$	8.88435	0.354807
$628$	−22.5525	−0.899941
$629$	−35.9039	−1.43158
$630$	−2.19060	−0.0872757
$631$	1.46408	0.0582842	0.0291421	−	0.999575i	$-0.490722\pi$
$631$	1.46408	0.0582842	0.0291421	+	0.999575i	$0.490722\pi$
$632$	−53.0552	−2.11042
$633$	−7.19054	−0.285798
$634$	−32.7096	−1.29906
$635$	5.83662	0.231619
$636$	79.7164	3.16096
$637$	1.04461	0.0413890
$638$	20.3709	0.806491
$639$	−0.0811188	−0.00320901
$640$	−95.7835	−3.78618
$641$	−27.6769	−1.09317	−0.546587	−	0.837403i	$-0.684073\pi$
$641$	−27.6769	−1.09317	−0.546587	+	0.837403i	$0.684073\pi$
$642$	−6.57428	−0.259466
$643$	−41.8942	−1.65215	−0.826073	−	0.563563i	$-0.809430\pi$
$643$	−41.8942	−1.65215	−0.826073	+	0.563563i	$0.809430\pi$
$644$	16.3616	0.644739
$645$	19.1014	0.752117
$646$	−34.1530	−1.34373
$647$	−21.7454	−0.854901	−0.427450	−	0.904039i	$-0.640588\pi$
$647$	−21.7454	−0.854901	−0.427450	+	0.904039i	$0.640588\pi$
$648$	84.6984	3.32727
$649$	15.7647	0.618817
$650$	1.88465	0.0739220
$651$	−36.0377	−1.41243
$652$	100.144	3.92196
$653$	33.0122	1.29187	0.645933	−	0.763394i	$-0.276469\pi$
$653$	33.0122	1.29187	0.645933	+	0.763394i	$0.276469\pi$
$654$	4.65964	0.182206
$655$	−4.53882	−0.177347
$656$	−119.419	−4.66252
$657$	−0.770193	−0.0300481
$658$	66.9881	2.61147
$659$	28.1489	1.09653	0.548263	−	0.836306i	$-0.315289\pi$
$659$	28.1489	1.09653	0.548263	+	0.836306i	$0.315289\pi$
$660$	56.6988	2.20700
$661$	35.4790	1.37997	0.689986	−	0.723823i	$-0.257617\pi$
$661$	35.4790	1.37997	0.689986	+	0.723823i	$0.257617\pi$
$662$	−9.24924	−0.359482
$663$	7.97492	0.309720
$664$	90.2892	3.50390
$665$	−10.1722	−0.394460
$666$	−1.89628	−0.0734792
$667$	2.45646	0.0951146
$668$	134.942	5.22107
$669$	14.2727	0.551814
$670$	−32.9210	−1.27185
$671$	−39.1082	−1.50976
$672$	121.035	4.66904
$673$	14.0508	0.541619	0.270810	−	0.962633i	$-0.412709\pi$
$673$	14.0508	0.541619	0.270810	+	0.962633i	$0.412709\pi$
$674$	−98.8866	−3.80897
$675$	5.47903	0.210888
$676$	−70.1772	−2.69912
$677$	−39.3681	−1.51304	−0.756519	−	0.653971i	$-0.773102\pi$
$677$	−39.3681	−1.51304	−0.756519	+	0.653971i	$0.773102\pi$
$678$	−34.5549	−1.32707
$679$	−28.9340	−1.11039
$680$	−139.937	−5.36633
$681$	−29.8685	−1.14456
$682$	−60.3047	−2.30919
$683$	−5.57295	−0.213243	−0.106621	−	0.994300i	$-0.534003\pi$
$683$	−5.57295	−0.213243	−0.106621	+	0.994300i	$0.534003\pi$
$684$	−1.32831	−0.0507891
$685$	34.8477	1.33146
$686$	−43.7515	−1.67044
$687$	−10.0289	−0.382628
$688$	90.9007	3.46556
$689$	5.58829	0.212897
$690$	9.28463	0.353460
$691$	3.73975	0.142267	0.0711333	−	0.997467i	$-0.477338\pi$
$691$	3.73975	0.142267	0.0711333	+	0.997467i	$0.477338\pi$
$692$	−68.7819	−2.61470
$693$	1.20205	0.0456622
$694$	100.078	3.79892
$695$	5.38428	0.204237
$696$	41.0718	1.55682
$697$	−52.9338	−2.00501
$698$	−2.75446	−0.104258
$699$	−16.8676	−0.637991
$700$	16.8907	0.638407
$701$	25.8162	0.975065	0.487533	−	0.873105i	$-0.337897\pi$
$701$	25.8162	0.975065	0.487533	+	0.873105i	$0.337897\pi$
$702$	9.68933	0.365700
$703$	−8.80545	−0.332104
$704$	105.950	3.99314
$705$	27.9927	1.05427
$706$	−29.3820	−1.10581
$707$	−38.4501	−1.44607
$708$	49.5067	1.86058
$709$	30.6608	1.15149	0.575745	−	0.817630i	$-0.304712\pi$
$709$	30.6608	1.15149	0.575745	+	0.817630i	$0.304712\pi$
$710$	−3.26445	−0.122513
$711$	−0.732100	−0.0274559
$712$	23.2757	0.872292
$713$	−7.27196	−0.272337
$714$	97.0584	3.63232
$715$	3.97471	0.148646
$716$	−102.064	−3.81433
$717$	−33.5339	−1.25235
$718$	67.2402	2.50938
$719$	−11.6424	−0.434187	−0.217094	−	0.976151i	$-0.569658\pi$
$719$	−11.6424	−0.434187	−0.217094	+	0.976151i	$0.569658\pi$
$720$	−4.35625	−0.162348
$721$	−10.7476	−0.400263
$722$	43.9587	1.63597
$723$	−23.3463	−0.868260
$724$	17.5938	0.653869
$725$	2.53589	0.0941806
$726$	9.02337	0.334889
$727$	−44.2163	−1.63989	−0.819946	−	0.572441i	$-0.805997\pi$
$727$	−44.2163	−1.63989	−0.819946	+	0.572441i	$0.805997\pi$
$728$	19.1775	0.710765
$729$	28.1130	1.04122
$730$	−30.9947	−1.14717
$731$	40.2929	1.49029
$732$	−122.814	−4.53934
$733$	25.2587	0.932950	0.466475	−	0.884534i	$-0.345524\pi$
$733$	25.2587	0.932950	0.466475	+	0.884534i	$0.345524\pi$
$734$	11.3708	0.419705
$735$	5.31263	0.195959
$736$	24.4234	0.900260
$737$	18.0648	0.665426
$738$	−2.79572	−0.102912
$739$	22.4562	0.826065	0.413032	−	0.910716i	$-0.364470\pi$
$739$	22.4562	0.826065	0.413032	+	0.910716i	$0.364470\pi$
$740$	−56.1953	−2.06578
$741$	1.95585	0.0718500
$742$	68.0120	2.49680
$743$	−34.3020	−1.25842	−0.629209	−	0.777236i	$-0.716621\pi$
$743$	−34.3020	−1.25842	−0.629209	+	0.777236i	$0.716621\pi$
$744$	−121.586	−4.45758
$745$	−31.1211	−1.14019
$746$	−72.3852	−2.65021
$747$	1.24589	0.0455846
$748$	119.602	4.37307
$749$	−4.13043	−0.150923
$750$	56.0080	2.04512
$751$	20.5665	0.750483	0.375241	−	0.926927i	$-0.377560\pi$
$751$	20.5665	0.750483	0.375241	+	0.926927i	$0.377560\pi$
$752$	133.213	4.85779
$753$	13.2603	0.483232
$754$	4.48457	0.163318
$755$	23.0784	0.839909
$756$	86.8381	3.15827
$757$	16.8262	0.611559	0.305779	−	0.952102i	$-0.401083\pi$
$757$	16.8262	0.611559	0.305779	+	0.952102i	$0.401083\pi$
$758$	−98.9485	−3.59397
$759$	−5.09477	−0.184928
$760$	−34.3196	−1.24490
$761$	−12.0523	−0.436897	−0.218448	−	0.975849i	$-0.570099\pi$
$761$	−12.0523	−0.436897	−0.218448	+	0.975849i	$0.570099\pi$
$762$	−13.6581	−0.494781
$763$	2.92752	0.105983
$764$	93.8074	3.39383
$765$	−1.93096	−0.0698141
$766$	95.4592	3.44908
$767$	3.47052	0.125313
$768$	105.036	3.79016
$769$	1.95863	0.0706300	0.0353150	−	0.999376i	$-0.488757\pi$
$769$	1.95863	0.0706300	0.0353150	+	0.999376i	$0.488757\pi$
$770$	48.3740	1.74328
$771$	−10.2104	−0.367719
$772$	−12.5418	−0.451387
$773$	17.0256	0.612369	0.306184	−	0.951972i	$-0.400948\pi$
$773$	17.0256	0.612369	0.306184	+	0.951972i	$0.400948\pi$
$774$	2.12808	0.0764923
$775$	−7.50709	−0.269663
$776$	−97.6197	−3.50434
$777$	25.0239	0.897729
$778$	47.4656	1.70172
$779$	−12.9821	−0.465130
$780$	12.4820	0.446928
$781$	1.79131	0.0640980
$782$	19.5852	0.700365
$783$	13.0375	0.465922
$784$	25.2820	0.902929
$785$	−8.04043	−0.286975
$786$	10.6212	0.378845
$787$	27.0778	0.965219	0.482610	−	0.875836i	$-0.339689\pi$
$787$	27.0778	0.965219	0.482610	+	0.875836i	$0.339689\pi$
$788$	76.2127	2.71497
$789$	−32.0042	−1.13938
$790$	−29.4618	−1.04820
$791$	−21.7099	−0.771913
$792$	4.05557	0.144108
$793$	−8.60952	−0.305733
$794$	−42.6252	−1.51271
$795$	28.4206	1.00797
$796$	51.9453	1.84115
$797$	−11.3484	−0.401982	−0.200991	−	0.979593i	$-0.564416\pi$
$797$	−11.3484	−0.401982	−0.200991	+	0.979593i	$0.564416\pi$
$798$	23.8036	0.842639
$799$	59.0484	2.08898
$800$	25.2131	0.891419
$801$	0.321177	0.0113482
$802$	2.43023	0.0858143
$803$	17.0078	0.600192
$804$	56.7300	2.00071
$805$	5.83327	0.205596
$806$	−13.2758	−0.467621
$807$	28.1063	0.989390
$808$	−129.726	−4.56373
$809$	40.7902	1.43411	0.717054	−	0.697017i	$-0.245490\pi$
$809$	40.7902	1.43411	0.717054	+	0.697017i	$0.245490\pi$
$810$	47.0334	1.65258
$811$	−49.1167	−1.72472	−0.862360	−	0.506296i	$-0.831014\pi$
$811$	−49.1167	−1.72472	−0.862360	+	0.506296i	$0.831014\pi$
$812$	40.1918	1.41045
$813$	6.52991	0.229014
$814$	41.8745	1.46770
$815$	35.7036	1.25064
$816$	193.011	6.75675
$817$	9.88185	0.345722
$818$	−78.0104	−2.72757
$819$	0.264627	0.00924681
$820$	−82.8499	−2.89324
$821$	−6.26021	−0.218483	−0.109241	−	0.994015i	$-0.534842\pi$
$821$	−6.26021	−0.218483	−0.109241	+	0.994015i	$0.534842\pi$
$822$	−81.5463	−2.84425
$823$	55.6085	1.93839	0.969196	−	0.246291i	$-0.0792120\pi$
$823$	55.6085	1.93839	0.969196	+	0.246291i	$0.0792120\pi$
$824$	−36.2611	−1.26322
$825$	−5.25950	−0.183112
$826$	42.2379	1.46964
$827$	−2.94902	−0.102547	−0.0512737	−	0.998685i	$-0.516328\pi$
$827$	−2.94902	−0.102547	−0.0512737	+	0.998685i	$0.516328\pi$
$828$	0.761723	0.0264717
$829$	−0.900774	−0.0312852	−0.0156426	−	0.999878i	$-0.504979\pi$
$829$	−0.900774	−0.0312852	−0.0156426	+	0.999878i	$0.504979\pi$
$830$	50.1380	1.74031
$831$	42.2905	1.46704
$832$	23.3244	0.808629
$833$	11.2066	0.388284
$834$	−12.5996	−0.436289
$835$	48.1098	1.66491
$836$	29.3324	1.01448
$837$	−38.5954	−1.33405
$838$	2.91694	0.100764
$839$	37.0158	1.27793	0.638964	−	0.769237i	$-0.279363\pi$
$839$	37.0158	1.27793	0.638964	+	0.769237i	$0.279363\pi$
$840$	97.5318	3.36517
$841$	−22.9658	−0.791924
$842$	17.6008	0.606564
$843$	−13.8065	−0.475523
$844$	−23.7401	−0.817168
$845$	−25.0197	−0.860703
$846$	3.11866	0.107222
$847$	5.66913	0.194794
$848$	135.249	4.64448
$849$	18.2956	0.627902
$850$	20.2184	0.693487
$851$	5.04952	0.173095
$852$	5.62535	0.192721
$853$	−34.8356	−1.19275	−0.596374	−	0.802706i	$-0.703393\pi$
$853$	−34.8356	−1.19275	−0.596374	+	0.802706i	$0.703393\pi$
$854$	−104.782	−3.58556
$855$	−0.473570	−0.0161957
$856$	−13.9355	−0.476307
$857$	18.7005	0.638797	0.319399	−	0.947620i	$-0.396519\pi$
$857$	18.7005	0.638797	0.319399	+	0.947620i	$0.396519\pi$
$858$	−9.30111	−0.317535
$859$	−2.70919	−0.0924362	−0.0462181	−	0.998931i	$-0.514717\pi$
$859$	−2.70919	−0.0924362	−0.0462181	+	0.998931i	$0.514717\pi$
$860$	63.0647	2.15049
$861$	36.8933	1.25732
$862$	22.8677	0.778878
$863$	42.9702	1.46272	0.731361	−	0.681990i	$-0.238885\pi$
$863$	42.9702	1.46272	0.731361	+	0.681990i	$0.238885\pi$
$864$	129.626	4.40995
$865$	−24.5222	−0.833781
$866$	−44.3803	−1.50810
$867$	56.7866	1.92857
$868$	−118.981	−4.03848
$869$	16.1666	0.548414
$870$	22.8074	0.773242
$871$	3.97689	0.134752
$872$	9.87707	0.334480
$873$	−1.34704	−0.0455903
$874$	4.80328	0.162473
$875$	35.1882	1.18958
$876$	53.4106	1.80458
$877$	39.3560	1.32896	0.664478	−	0.747308i	$-0.268654\pi$
$877$	39.3560	1.32896	0.664478	+	0.747308i	$0.268654\pi$
$878$	−60.1169	−2.02885
$879$	32.1026	1.08280
$880$	96.1970	3.24280
$881$	−6.70958	−0.226052	−0.113026	−	0.993592i	$-0.536054\pi$
$881$	−6.70958	−0.226052	−0.113026	+	0.993592i	$0.536054\pi$
$882$	0.591879	0.0199296
$883$	−8.31011	−0.279658	−0.139829	−	0.990176i	$-0.544655\pi$
$883$	−8.31011	−0.279658	−0.139829	+	0.990176i	$0.544655\pi$
$884$	26.3298	0.885566
$885$	17.6502	0.593305
$886$	−59.2704	−1.99123
$887$	−29.2414	−0.981829	−0.490914	−	0.871208i	$-0.663337\pi$
$887$	−29.2414	−0.981829	−0.490914	+	0.871208i	$0.663337\pi$
$888$	84.4275	2.83320
$889$	−8.58101	−0.287798
$890$	12.9251	0.433249
$891$	−25.8087	−0.864624
$892$	47.1223	1.57777
$893$	14.4817	0.484610
$894$	72.8258	2.43566
$895$	−36.3882	−1.21632
$896$	140.821	4.70451
$897$	−1.12159	−0.0374489
$898$	−36.2016	−1.20806
$899$	−17.8633	−0.595774
$900$	0.786352	0.0262117
$901$	59.9510	1.99726
$902$	61.7365	2.05560
$903$	−28.0829	−0.934542
$904$	−73.2462	−2.43613
$905$	6.27257	0.208507
$906$	−54.0052	−1.79420
$907$	−52.3384	−1.73787	−0.868933	−	0.494929i	$-0.835194\pi$
$907$	−52.3384	−1.73787	−0.868933	+	0.494929i	$0.835194\pi$
$908$	−98.6130	−3.27259
$909$	−1.79006	−0.0593726
$910$	10.6493	0.353022
$911$	−13.0601	−0.432702	−0.216351	−	0.976316i	$-0.569416\pi$
$911$	−13.0601	−0.432702	−0.216351	+	0.976316i	$0.569416\pi$
$912$	47.3361	1.56746
$913$	−27.5123	−0.910523
$914$	7.45559	0.246609
$915$	−43.7858	−1.44751
$916$	−33.1113	−1.09403
$917$	6.67299	0.220362
$918$	103.947	3.43076
$919$	−38.8454	−1.28139	−0.640695	−	0.767795i	$-0.721354\pi$
$919$	−38.8454	−1.28139	−0.640695	+	0.767795i	$0.721354\pi$
$920$	19.6807	0.648853
$921$	−22.8404	−0.752616
$922$	28.1104	0.925766
$923$	0.394348	0.0129801
$924$	−83.3587	−2.74230
$925$	5.21279	0.171395
$926$	−76.8289	−2.52476
$927$	−0.500361	−0.0164340
$928$	59.9953	1.96944
$929$	33.3050	1.09270	0.546351	−	0.837556i	$-0.316016\pi$
$929$	33.3050	1.09270	0.546351	+	0.837556i	$0.316016\pi$
$930$	−67.5175	−2.21398
$931$	2.74842	0.0900757
$932$	−55.6897	−1.82418
$933$	−19.6399	−0.642981
$934$	−35.8132	−1.17184
$935$	42.6405	1.39449
$936$	0.892816	0.0291826
$937$	1.20097	0.0392340	0.0196170	−	0.999808i	$-0.493755\pi$
$937$	1.20097	0.0392340	0.0196170	+	0.999808i	$0.493755\pi$
$938$	48.4006	1.58034
$939$	−23.8195	−0.777321
$940$	92.4201	3.01441
$941$	−10.8688	−0.354314	−0.177157	−	0.984183i	$-0.556690\pi$
$941$	−10.8688	−0.354314	−0.177157	+	0.984183i	$0.556690\pi$
$942$	18.8152	0.613033
$943$	7.44461	0.242430
$944$	83.9946	2.73379
$945$	30.9596	1.00712
$946$	−46.9934	−1.52789
$947$	−8.71683	−0.283259	−0.141629	−	0.989920i	$-0.545234\pi$
$947$	−8.71683	−0.283259	−0.141629	+	0.989920i	$0.545234\pi$
$948$	50.7689	1.64890
$949$	3.74419	0.121542
$950$	4.95858	0.160878
$951$	20.0956	0.651643
$952$	205.735	6.66792
$953$	34.1993	1.10782	0.553911	−	0.832576i	$-0.313135\pi$
$953$	34.1993	1.10782	0.553911	+	0.832576i	$0.313135\pi$
$954$	3.16633	0.102514
$955$	33.4443	1.08223
$956$	−110.715	−3.58077
$957$	−12.5151	−0.404556
$958$	−78.1433	−2.52470
$959$	−51.2332	−1.65441
$960$	118.622	3.82851
$961$	21.8814	0.705851
$962$	9.21850	0.297216
$963$	−0.192294	−0.00619659
$964$	−77.0797	−2.48257
$965$	−4.47140	−0.143940
$966$	−13.6503	−0.439191
$967$	−10.9919	−0.353476	−0.176738	−	0.984258i	$-0.556555\pi$
$967$	−10.9919	−0.353476	−0.176738	+	0.984258i	$0.556555\pi$
$968$	19.1269	0.614762
$969$	20.9823	0.674049
$970$	−54.2086	−1.74053
$971$	26.4643	0.849279	0.424639	−	0.905363i	$-0.360401\pi$
$971$	26.4643	0.849279	0.424639	+	0.905363i	$0.360401\pi$
$972$	7.90983	0.253708
$973$	−7.91598	−0.253775
$974$	−9.87199	−0.316319
$975$	−1.15786	−0.0370811
$976$	−208.370	−6.66976
$977$	−39.3324	−1.25836	−0.629178	−	0.777262i	$-0.716608\pi$
$977$	−39.3324	−1.25836	−0.629178	+	0.777262i	$0.716608\pi$
$978$	−83.5491	−2.67161
$979$	−7.09239	−0.226674
$980$	17.5400	0.560296
$981$	0.136292	0.00435147
$982$	53.9412	1.72133
$983$	−24.7592	−0.789697	−0.394849	−	0.918746i	$-0.629203\pi$
$983$	−24.7592	−0.789697	−0.394849	+	0.918746i	$0.629203\pi$
$984$	124.473	3.96806
$985$	27.1715	0.865755
$986$	48.1103	1.53214
$987$	−41.1550	−1.30998
$988$	6.45739	0.205437
$989$	−5.66679	−0.180193
$990$	2.25207	0.0715756
$991$	−1.67620	−0.0532462	−0.0266231	−	0.999646i	$-0.508475\pi$
$991$	−1.67620	−0.0532462	−0.0266231	+	0.999646i	$0.508475\pi$
$992$	−177.606	−5.63901
$993$	5.68238	0.180325
$994$	4.79940	0.152228
$995$	18.5196	0.587111
$996$	−86.3984	−2.73764
$997$	34.2325	1.08416	0.542078	−	0.840328i	$-0.317638\pi$
$997$	34.2325	1.08416	0.542078	+	0.840328i	$0.317638\pi$
$998$	−88.4824	−2.80086
$999$	26.7999	0.847913

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.e.1.1	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.e.1.1	✓	169	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)

\(f(q)\)	\(=\)	\(q-2.75446 q^{2} +1.69224 q^{3} +5.58704 q^{4} +1.99190 q^{5} -4.66119 q^{6} -2.92850 q^{7} -9.88036 q^{8} -0.136337 q^{9} +O(q^{10})\)	\(q-2.75446 q^{2} +1.69224 q^{3} +5.58704 q^{4} +1.99190 q^{5} -4.66119 q^{6} -2.92850 q^{7} -9.88036 q^{8} -0.136337 q^{9} -5.48661 q^{10} +3.01067 q^{11} +9.45460 q^{12} +0.662787 q^{13} +8.06642 q^{14} +3.37077 q^{15} +16.0410 q^{16} +7.11036 q^{17} +0.375536 q^{18} +1.74382 q^{19} +11.1288 q^{20} -4.95571 q^{21} -8.29277 q^{22} -1.00000 q^{23} -16.7199 q^{24} -1.03233 q^{25} -1.82562 q^{26} -5.30742 q^{27} -16.3616 q^{28} -2.45646 q^{29} -9.28463 q^{30} +7.27196 q^{31} -24.4234 q^{32} +5.09477 q^{33} -19.5852 q^{34} -5.83327 q^{35} -0.761723 q^{36} -5.04952 q^{37} -4.80328 q^{38} +1.12159 q^{39} -19.6807 q^{40} -7.44461 q^{41} +13.6503 q^{42} +5.66679 q^{43} +16.8208 q^{44} -0.271571 q^{45} +2.75446 q^{46} +8.30456 q^{47} +27.1451 q^{48} +1.57609 q^{49} +2.84352 q^{50} +12.0324 q^{51} +3.70302 q^{52} +8.43150 q^{53} +14.6191 q^{54} +5.99696 q^{55} +28.9346 q^{56} +2.95095 q^{57} +6.76623 q^{58} +5.23626 q^{59} +18.8326 q^{60} -12.9899 q^{61} -20.0303 q^{62} +0.399264 q^{63} +35.1915 q^{64} +1.32021 q^{65} -14.0333 q^{66} +6.00025 q^{67} +39.7259 q^{68} -1.69224 q^{69} +16.0675 q^{70} +0.594985 q^{71} +1.34706 q^{72} +5.64916 q^{73} +13.9087 q^{74} -1.74695 q^{75} +9.74279 q^{76} -8.81674 q^{77} -3.08938 q^{78} +5.36976 q^{79} +31.9520 q^{80} -8.57240 q^{81} +20.5059 q^{82} -9.13825 q^{83} -27.6877 q^{84} +14.1631 q^{85} -15.6089 q^{86} -4.15692 q^{87} -29.7465 q^{88} -2.35575 q^{89} +0.748030 q^{90} -1.94097 q^{91} -5.58704 q^{92} +12.3059 q^{93} -22.8746 q^{94} +3.47351 q^{95} -41.3302 q^{96} +9.88017 q^{97} -4.34128 q^{98} -0.410467 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9} + 28 q^{10} + 17 q^{11} + 10 q^{12} + 91 q^{13} + 20 q^{14} + 29 q^{15} + 200 q^{16} + 16 q^{17} + 31 q^{18} + 30 q^{19} + 45 q^{20} + 49 q^{21} + 76 q^{22} - 169 q^{23} + 3 q^{24} + 241 q^{25} - 15 q^{26} + 14 q^{27} + 118 q^{28} + 23 q^{29} + 52 q^{30} + 45 q^{31} + 42 q^{32} + 62 q^{33} + 65 q^{34} - 16 q^{35} + 199 q^{36} + 226 q^{37} + 49 q^{38} + 17 q^{39} + 95 q^{40} + 19 q^{41} + 32 q^{42} + 71 q^{43} + 46 q^{44} + 127 q^{45} - 6 q^{46} + 27 q^{47} + 5 q^{48} + 239 q^{49} + 24 q^{50} + 39 q^{51} + 154 q^{52} + 111 q^{53} + 22 q^{54} + 47 q^{55} + 39 q^{56} + 122 q^{57} + 146 q^{58} - 73 q^{59} + 109 q^{60} + 125 q^{61} + 14 q^{62} + 109 q^{63} + 260 q^{64} + 73 q^{65} + 26 q^{66} + 152 q^{67} + 40 q^{68} - 2 q^{69} + 76 q^{70} - 79 q^{71} + 126 q^{72} + 106 q^{73} + 23 q^{74} + 12 q^{75} + 122 q^{76} + 63 q^{77} + 101 q^{78} + 82 q^{79} + 134 q^{80} + 225 q^{81} + 125 q^{82} + 28 q^{83} + 73 q^{84} + 197 q^{85} + 97 q^{86} + 18 q^{87} + 183 q^{88} + 54 q^{89} + 52 q^{90} + 106 q^{91} - 186 q^{92} + 194 q^{93} + q^{94} + 18 q^{95} - 39 q^{96} + 239 q^{97} + 5 q^{98} + 85 q^{99}+O(q^{100}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9 + 28 * q^10 + 17 * q^11 + 10 * q^12 + 91 * q^13 + 20 * q^14 + 29 * q^15 + 200 * q^16 + 16 * q^17 + 31 * q^18 + 30 * q^19 + 45 * q^20 + 49 * q^21 + 76 * q^22 - 169 * q^23 + 3 * q^24 + 241 * q^25 - 15 * q^26 + 14 * q^27 + 118 * q^28 + 23 * q^29 + 52 * q^30 + 45 * q^31 + 42 * q^32 + 62 * q^33 + 65 * q^34 - 16 * q^35 + 199 * q^36 + 226 * q^37 + 49 * q^38 + 17 * q^39 + 95 * q^40 + 19 * q^41 + 32 * q^42 + 71 * q^43 + 46 * q^44 + 127 * q^45 - 6 * q^46 + 27 * q^47 + 5 * q^48 + 239 * q^49 + 24 * q^50 + 39 * q^51 + 154 * q^52 + 111 * q^53 + 22 * q^54 + 47 * q^55 + 39 * q^56 + 122 * q^57 + 146 * q^58 - 73 * q^59 + 109 * q^60 + 125 * q^61 + 14 * q^62 + 109 * q^63 + 260 * q^64 + 73 * q^65 + 26 * q^66 + 152 * q^67 + 40 * q^68 - 2 * q^69 + 76 * q^70 - 79 * q^71 + 126 * q^72 + 106 * q^73 + 23 * q^74 + 12 * q^75 + 122 * q^76 + 63 * q^77 + 101 * q^78 + 82 * q^79 + 134 * q^80 + 225 * q^81 + 125 * q^82 + 28 * q^83 + 73 * q^84 + 197 * q^85 + 97 * q^86 + 18 * q^87 + 183 * q^88 + 54 * q^89 + 52 * q^90 + 106 * q^91 - 186 * q^92 + 194 * q^93 + q^94 + 18 * q^95 - 39 * q^96 + 239 * q^97 + 5 * q^98 + 85 * q^99

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