LMFDB - Embedded newform 8039.2.a.b.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8039,2,Mod(1,8039)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8039, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8039.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8039 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8039.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:	$64.1917381849$
Analytic rank:	$0$
Dimension:	$391$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8039.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.67673 q^{2} -3.14138 q^{3} +5.16489 q^{4} -3.87922 q^{5} +8.40863 q^{6} +4.00887 q^{7} -8.47155 q^{8} +6.86827 q^{9} +O(q^{10})$	\(q-2.67673 q^{2} -3.14138 q^{3} +5.16489 q^{4} -3.87922 q^{5} +8.40863 q^{6} +4.00887 q^{7} -8.47155 q^{8} +6.86827 q^{9} +10.3836 q^{10} +4.64474 q^{11} -16.2249 q^{12} -0.215731 q^{13} -10.7307 q^{14} +12.1861 q^{15} +12.3463 q^{16} -5.29246 q^{17} -18.3845 q^{18} -4.20056 q^{19} -20.0358 q^{20} -12.5934 q^{21} -12.4327 q^{22} -3.43454 q^{23} +26.6124 q^{24} +10.0484 q^{25} +0.577455 q^{26} -12.1517 q^{27} +20.7054 q^{28} -9.35621 q^{29} -32.6190 q^{30} -4.22018 q^{31} -16.1046 q^{32} -14.5909 q^{33} +14.1665 q^{34} -15.5513 q^{35} +35.4738 q^{36} -3.74928 q^{37} +11.2438 q^{38} +0.677694 q^{39} +32.8631 q^{40} -8.79191 q^{41} +33.7091 q^{42} -8.07285 q^{43} +23.9896 q^{44} -26.6436 q^{45} +9.19335 q^{46} -2.64725 q^{47} -38.7844 q^{48} +9.07106 q^{49} -26.8968 q^{50} +16.6256 q^{51} -1.11423 q^{52} -8.11709 q^{53} +32.5268 q^{54} -18.0180 q^{55} -33.9614 q^{56} +13.1955 q^{57} +25.0441 q^{58} -5.93570 q^{59} +62.9399 q^{60} +1.74502 q^{61} +11.2963 q^{62} +27.5340 q^{63} +18.4151 q^{64} +0.836870 q^{65} +39.0559 q^{66} -9.55753 q^{67} -27.3350 q^{68} +10.7892 q^{69} +41.6267 q^{70} +13.3288 q^{71} -58.1849 q^{72} -12.5134 q^{73} +10.0358 q^{74} -31.5658 q^{75} -21.6954 q^{76} +18.6202 q^{77} -1.81400 q^{78} -11.1434 q^{79} -47.8940 q^{80} +17.5683 q^{81} +23.5336 q^{82} -1.13411 q^{83} -65.0435 q^{84} +20.5306 q^{85} +21.6088 q^{86} +29.3914 q^{87} -39.3482 q^{88} -3.97359 q^{89} +71.3176 q^{90} -0.864839 q^{91} -17.7390 q^{92} +13.2572 q^{93} +7.08597 q^{94} +16.2949 q^{95} +50.5907 q^{96} +13.8521 q^{97} -24.2808 q^{98} +31.9013 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 391 q + 14 q^{2} + 12 q^{3} + 446 q^{4} + 22 q^{5} + 40 q^{6} + 63 q^{7} + 36 q^{8} + 501 q^{9}+O(q^{10}) $ 391 * q + 14 * q^2 + 12 * q^3 + 446 * q^4 + 22 * q^5 + 40 * q^6 + 63 * q^7 + 36 * q^8 + 501 * q^9	\( 391 q + 14 q^{2} + 12 q^{3} + 446 q^{4} + 22 q^{5} + 40 q^{6} + 63 q^{7} + 36 q^{8} + 501 q^{9} + 40 q^{10} + 57 q^{11} + 20 q^{12} + 83 q^{13} + 21 q^{14} + 60 q^{15} + 548 q^{16} + 59 q^{17} + 54 q^{18} + 131 q^{19} + 35 q^{20} + 121 q^{21} + 89 q^{22} + 34 q^{23} + 110 q^{24} + 609 q^{25} + 54 q^{26} + 27 q^{27} + 182 q^{28} + 102 q^{29} + 92 q^{30} + 88 q^{31} + 76 q^{32} + 131 q^{33} + 128 q^{34} + 31 q^{35} + 654 q^{36} + 135 q^{37} + 23 q^{38} + 96 q^{39} + 113 q^{40} + 128 q^{41} + 45 q^{42} + 140 q^{43} + 151 q^{44} + 77 q^{45} + 245 q^{46} + 22 q^{47} + 25 q^{48} + 712 q^{49} + 53 q^{50} + 102 q^{51} + 174 q^{52} + 54 q^{53} + 131 q^{54} + 101 q^{55} + 43 q^{56} + 226 q^{57} + 109 q^{58} + 40 q^{59} + 123 q^{60} + 249 q^{61} + 28 q^{62} + 139 q^{63} + 730 q^{64} + 227 q^{65} + 55 q^{66} + 169 q^{67} + 48 q^{68} + 89 q^{69} + 98 q^{70} + 66 q^{71} + 120 q^{72} + 324 q^{73} + 60 q^{74} + 19 q^{75} + 356 q^{76} + 83 q^{77} - 11 q^{78} + 195 q^{79} + 26 q^{80} + 807 q^{81} + 49 q^{82} + 74 q^{83} + 252 q^{84} + 373 q^{85} + 100 q^{86} + 43 q^{87} + 211 q^{88} + 207 q^{89} + 10 q^{90} + 189 q^{91} + 30 q^{92} + 172 q^{93} + 130 q^{94} + 43 q^{95} + 203 q^{96} + 254 q^{97} + 26 q^{98} + 273 q^{99}+O(q^{100}) \) 391 * q + 14 * q^2 + 12 * q^3 + 446 * q^4 + 22 * q^5 + 40 * q^6 + 63 * q^7 + 36 * q^8 + 501 * q^9 + 40 * q^10 + 57 * q^11 + 20 * q^12 + 83 * q^13 + 21 * q^14 + 60 * q^15 + 548 * q^16 + 59 * q^17 + 54 * q^18 + 131 * q^19 + 35 * q^20 + 121 * q^21 + 89 * q^22 + 34 * q^23 + 110 * q^24 + 609 * q^25 + 54 * q^26 + 27 * q^27 + 182 * q^28 + 102 * q^29 + 92 * q^30 + 88 * q^31 + 76 * q^32 + 131 * q^33 + 128 * q^34 + 31 * q^35 + 654 * q^36 + 135 * q^37 + 23 * q^38 + 96 * q^39 + 113 * q^40 + 128 * q^41 + 45 * q^42 + 140 * q^43 + 151 * q^44 + 77 * q^45 + 245 * q^46 + 22 * q^47 + 25 * q^48 + 712 * q^49 + 53 * q^50 + 102 * q^51 + 174 * q^52 + 54 * q^53 + 131 * q^54 + 101 * q^55 + 43 * q^56 + 226 * q^57 + 109 * q^58 + 40 * q^59 + 123 * q^60 + 249 * q^61 + 28 * q^62 + 139 * q^63 + 730 * q^64 + 227 * q^65 + 55 * q^66 + 169 * q^67 + 48 * q^68 + 89 * q^69 + 98 * q^70 + 66 * q^71 + 120 * q^72 + 324 * q^73 + 60 * q^74 + 19 * q^75 + 356 * q^76 + 83 * q^77 - 11 * q^78 + 195 * q^79 + 26 * q^80 + 807 * q^81 + 49 * q^82 + 74 * q^83 + 252 * q^84 + 373 * q^85 + 100 * q^86 + 43 * q^87 + 211 * q^88 + 207 * q^89 + 10 * q^90 + 189 * q^91 + 30 * q^92 + 172 * q^93 + 130 * q^94 + 43 * q^95 + 203 * q^96 + 254 * q^97 + 26 * q^98 + 273 * 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 $

$2$	−2.67673	−1.89273	−0.946367	−	0.323093i	$-0.895277\pi$
$2$	−2.67673	−1.89273	−0.946367	+	0.323093i	$0.895277\pi$
$3$	−3.14138	−1.81368	−0.906838	−	0.421479i	$-0.861511\pi$
$3$	−3.14138	−1.81368	−0.906838	+	0.421479i	$0.861511\pi$
$4$	5.16489	2.58244
$5$	−3.87922	−1.73484	−0.867421	−	0.497575i	$-0.834224\pi$
$5$	−3.87922	−1.73484	−0.867421	+	0.497575i	$0.834224\pi$
$6$	8.40863	3.43281
$7$	4.00887	1.51521	0.757606	−	0.652713i	$-0.226369\pi$
$7$	4.00887	1.51521	0.757606	+	0.652713i	$0.226369\pi$
$8$	−8.47155	−2.99515
$9$	6.86827	2.28942
$10$	10.3836	3.28360
$11$	4.64474	1.40044	0.700221	−	0.713926i	$-0.253085\pi$
$11$	4.64474	1.40044	0.700221	+	0.713926i	$0.253085\pi$
$12$	−16.2249	−4.68372
$13$	−0.215731	−0.0598331	−0.0299165	−	0.999552i	$-0.509524\pi$
$13$	−0.215731	−0.0598331	−0.0299165	+	0.999552i	$0.509524\pi$
$14$	−10.7307	−2.86789
$15$	12.1861	3.14644
$16$	12.3463	3.08657
$17$	−5.29246	−1.28361	−0.641805	−	0.766868i	$-0.721814\pi$
$17$	−5.29246	−1.28361	−0.641805	+	0.766868i	$0.721814\pi$
$18$	−18.3845	−4.33327
$19$	−4.20056	−0.963674	−0.481837	−	0.876261i	$-0.660030\pi$
$19$	−4.20056	−0.963674	−0.481837	+	0.876261i	$0.660030\pi$
$20$	−20.0358	−4.48013
$21$	−12.5934	−2.74810
$22$	−12.4327	−2.65066
$23$	−3.43454	−0.716152	−0.358076	−	0.933693i	$-0.616567\pi$
$23$	−3.43454	−0.716152	−0.358076	+	0.933693i	$0.616567\pi$
$24$	26.6124	5.43223
$25$	10.0484	2.00968
$26$	0.577455	0.113248
$27$	−12.1517	−2.33860
$28$	20.7054	3.91295
$29$	−9.35621	−1.73740	−0.868702	−	0.495335i	$-0.835045\pi$
$29$	−9.35621	−1.73740	−0.868702	+	0.495335i	$0.835045\pi$
$30$	−32.6190	−5.95538
$31$	−4.22018	−0.757966	−0.378983	−	0.925404i	$-0.623726\pi$
$31$	−4.22018	−0.757966	−0.378983	+	0.925404i	$0.623726\pi$
$32$	−16.1046	−2.84692
$33$	−14.5909	−2.53995
$34$	14.1665	2.42953
$35$	−15.5513	−2.62865
$36$	35.4738	5.91231
$37$	−3.74928	−0.616377	−0.308189	−	0.951325i	$-0.599723\pi$
$37$	−3.74928	−0.616377	−0.308189	+	0.951325i	$0.599723\pi$
$38$	11.2438	1.82398
$39$	0.677694	0.108518
$40$	32.8631	5.19611
$41$	−8.79191	−1.37307	−0.686533	−	0.727099i	$-0.740868\pi$
$41$	−8.79191	−1.37307	−0.686533	+	0.727099i	$0.740868\pi$
$42$	33.7091	5.20143
$43$	−8.07285	−1.23110	−0.615549	−	0.788099i	$-0.711066\pi$
$43$	−8.07285	−1.23110	−0.615549	+	0.788099i	$0.711066\pi$
$44$	23.9896	3.61656
$45$	−26.6436	−3.97179
$46$	9.19335	1.35548
$47$	−2.64725	−0.386141	−0.193070	−	0.981185i	$-0.561845\pi$
$47$	−2.64725	−0.386141	−0.193070	+	0.981185i	$0.561845\pi$
$48$	−38.7844	−5.59805
$49$	9.07106	1.29587
$50$	−26.8968	−3.80378
$51$	16.6256	2.32805
$52$	−1.11423	−0.154516
$53$	−8.11709	−1.11497	−0.557484	−	0.830188i	$-0.688233\pi$
$53$	−8.11709	−1.11497	−0.557484	+	0.830188i	$0.688233\pi$
$54$	32.5268	4.42634
$55$	−18.0180	−2.42955
$56$	−33.9614	−4.53828
$57$	13.1955	1.74779
$58$	25.0441	3.28845
$59$	−5.93570	−0.772763	−0.386381	−	0.922339i	$-0.626275\pi$
$59$	−5.93570	−0.772763	−0.386381	+	0.922339i	$0.626275\pi$
$60$	62.9399	8.12551
$61$	1.74502	0.223427	0.111714	−	0.993740i	$-0.464366\pi$
$61$	1.74502	0.223427	0.111714	+	0.993740i	$0.464366\pi$
$62$	11.2963	1.43463
$63$	27.5340	3.46896
$64$	18.4151	2.30189
$65$	0.836870	0.103801
$66$	39.0559	4.80745
$67$	−9.55753	−1.16764	−0.583819	−	0.811884i	$-0.698442\pi$
$67$	−9.55753	−1.16764	−0.583819	+	0.811884i	$0.698442\pi$
$68$	−27.3350	−3.31485
$69$	10.7892	1.29887
$70$	41.6267	4.97534
$71$	13.3288	1.58183	0.790917	−	0.611923i	$-0.209604\pi$
$71$	13.3288	1.58183	0.790917	+	0.611923i	$0.209604\pi$
$72$	−58.1849	−6.85716
$73$	−12.5134	−1.46459	−0.732294	−	0.680989i	$-0.761550\pi$
$73$	−12.5134	−1.46459	−0.732294	+	0.680989i	$0.761550\pi$
$74$	10.0358	1.16664
$75$	−31.5658	−3.64490
$76$	−21.6954	−2.48863
$77$	18.6202	2.12197
$78$	−1.81400	−0.205396
$79$	−11.1434	−1.25373	−0.626864	−	0.779129i	$-0.715662\pi$
$79$	−11.1434	−1.25373	−0.626864	+	0.779129i	$0.715662\pi$
$80$	−47.8940	−5.35472
$81$	17.5683	1.95203
$82$	23.5336	2.59885
$83$	−1.13411	−0.124485	−0.0622425	−	0.998061i	$-0.519825\pi$
$83$	−1.13411	−0.124485	−0.0622425	+	0.998061i	$0.519825\pi$
$84$	−65.0435	−7.09682
$85$	20.5306	2.22686
$86$	21.6088	2.33014
$87$	29.3914	3.15109
$88$	−39.3482	−4.19453
$89$	−3.97359	−0.421199	−0.210600	−	0.977572i	$-0.567542\pi$
$89$	−3.97359	−0.421199	−0.210600	+	0.977572i	$0.567542\pi$
$90$	71.3176	7.51754
$91$	−0.864839	−0.0906598
$92$	−17.7390	−1.84942
$93$	13.2572	1.37471
$94$	7.08597	0.730862
$95$	16.2949	1.67182
$96$	50.5907	5.16339
$97$	13.8521	1.40647	0.703235	−	0.710958i	$-0.251738\pi$
$97$	13.8521	1.40647	0.703235	+	0.710958i	$0.251738\pi$
$98$	−24.2808	−2.45273
$99$	31.9013	3.20620
$100$	51.8988	5.18988
$101$	0.446970	0.0444752	0.0222376	−	0.999753i	$-0.492921\pi$
$101$	0.446970	0.0444752	0.0222376	+	0.999753i	$0.492921\pi$
$102$	−44.5023	−4.40639
$103$	0.0121959	0.00120170	0.000600849	−	1.00000i	$-0.499809\pi$
$103$	0.0121959	0.00120170	0.000600849		1.00000i	$0.499809\pi$
$104$	1.82758	0.179209
$105$	48.8526	4.76753
$106$	21.7273	2.11034
$107$	9.52486	0.920803	0.460401	−	0.887711i	$-0.347705\pi$
$107$	9.52486	0.920803	0.460401	+	0.887711i	$0.347705\pi$
$108$	−62.7622	−6.03929
$109$	−12.9916	−1.24437	−0.622183	−	0.782872i	$-0.713754\pi$
$109$	−12.9916	−1.24437	−0.622183	+	0.782872i	$0.713754\pi$
$110$	48.2293	4.59848
$111$	11.7779	1.11791
$112$	49.4947	4.67681
$113$	−19.8252	−1.86500	−0.932499	−	0.361173i	$-0.882377\pi$
$113$	−19.8252	−1.86500	−0.932499	+	0.361173i	$0.882377\pi$
$114$	−35.3209	−3.30811
$115$	13.3234	1.24241
$116$	−48.3238	−4.48675
$117$	−1.48170	−0.136983
$118$	15.8883	1.46263
$119$	−21.2168	−1.94494
$120$	−103.235	−9.42406
$121$	10.5736	0.961237
$122$	−4.67096	−0.422888
$123$	27.6187	2.49030
$124$	−21.7967	−1.95740
$125$	−19.5838	−1.75163
$126$	−73.7011	−6.56582
$127$	−2.26262	−0.200775	−0.100388	−	0.994948i	$-0.532008\pi$
$127$	−2.26262	−0.200775	−0.100388	+	0.994948i	$0.532008\pi$
$128$	−17.0830	−1.50994
$129$	25.3599	2.23281
$130$	−2.24008	−0.196468
$131$	−6.72698	−0.587739	−0.293870	−	0.955846i	$-0.594943\pi$
$131$	−6.72698	−0.587739	−0.293870	+	0.955846i	$0.594943\pi$
$132$	−75.3603	−6.55928
$133$	−16.8395	−1.46017
$134$	25.5829	2.21003
$135$	47.1392	4.05709
$136$	44.8354	3.84460
$137$	5.50886	0.470653	0.235327	−	0.971916i	$-0.424384\pi$
$137$	5.50886	0.470653	0.235327	+	0.971916i	$0.424384\pi$
$138$	−28.8798	−2.45841
$139$	2.39140	0.202836	0.101418	−	0.994844i	$-0.467662\pi$
$139$	2.39140	0.202836	0.101418	+	0.994844i	$0.467662\pi$
$140$	−80.3208	−6.78835
$141$	8.31601	0.700334
$142$	−35.6775	−2.99399
$143$	−1.00202	−0.0837928
$144$	84.7977	7.06647
$145$	36.2948	3.01412
$146$	33.4951	2.77207
$147$	−28.4956	−2.35028
$148$	−19.3646	−1.59176
$149$	−4.10991	−0.336697	−0.168349	−	0.985728i	$-0.553843\pi$
$149$	−4.10991	−0.336697	−0.168349	+	0.985728i	$0.553843\pi$
$150$	84.4931	6.89884
$151$	13.0713	1.06373	0.531863	−	0.846830i	$-0.321492\pi$
$151$	13.0713	1.06373	0.531863	+	0.846830i	$0.321492\pi$
$152$	35.5852	2.88634
$153$	−36.3500	−2.93873
$154$	−49.8412	−4.01632
$155$	16.3710	1.31495
$156$	3.50021	0.280241
$157$	−16.3133	−1.30194	−0.650972	−	0.759102i	$-0.725638\pi$
$157$	−16.3133	−1.30194	−0.650972	+	0.759102i	$0.725638\pi$
$158$	29.8278	2.37297
$159$	25.4989	2.02219
$160$	62.4734	4.93895
$161$	−13.7686	−1.08512
$162$	−47.0256	−3.69468
$163$	−1.67220	−0.130977	−0.0654884	−	0.997853i	$-0.520861\pi$
$163$	−1.67220	−0.130977	−0.0654884	+	0.997853i	$0.520861\pi$
$164$	−45.4092	−3.54586
$165$	56.6014	4.40641
$166$	3.03571	0.235617
$167$	−24.0282	−1.85936	−0.929681	−	0.368367i	$-0.879917\pi$
$167$	−24.0282	−1.85936	−0.929681	+	0.368367i	$0.879917\pi$
$168$	106.686	8.23097
$169$	−12.9535	−0.996420
$170$	−54.9550	−4.21486
$171$	−28.8506	−2.20626
$172$	−41.6954	−3.17924
$173$	−7.28584	−0.553932	−0.276966	−	0.960880i	$-0.589329\pi$
$173$	−7.28584	−0.553932	−0.276966	+	0.960880i	$0.589329\pi$
$174$	−78.6729	−5.96418
$175$	40.2827	3.04509
$176$	57.3453	4.32257
$177$	18.6463	1.40154
$178$	10.6362	0.797218
$179$	14.4862	1.08275	0.541374	−	0.840782i	$-0.317904\pi$
$179$	14.4862	1.08275	0.541374	+	0.840782i	$0.317904\pi$
$180$	−137.611	−10.2569
$181$	−20.9132	−1.55447	−0.777233	−	0.629213i	$-0.783377\pi$
$181$	−20.9132	−1.55447	−0.777233	+	0.629213i	$0.783377\pi$
$182$	2.31494	0.171595
$183$	−5.48178	−0.405225
$184$	29.0959	2.14498
$185$	14.5443	1.06932
$186$	−35.4859	−2.60195
$187$	−24.5821	−1.79762
$188$	−13.6727	−0.997187
$189$	−48.7146	−3.54347
$190$	−43.6171	−3.16432
$191$	17.1896	1.24380	0.621899	−	0.783097i	$-0.286361\pi$
$191$	17.1896	1.24380	0.621899	+	0.783097i	$0.286361\pi$
$192$	−57.8488	−4.17488
$193$	−25.4430	−1.83143	−0.915713	−	0.401832i	$-0.868374\pi$
$193$	−25.4430	−1.83143	−0.915713	+	0.401832i	$0.868374\pi$
$194$	−37.0784	−2.66207
$195$	−2.62893	−0.188261
$196$	46.8510	3.34650
$197$	−15.7417	−1.12155	−0.560774	−	0.827969i	$-0.689496\pi$
$197$	−15.7417	−1.12155	−0.560774	+	0.827969i	$0.689496\pi$
$198$	−85.3912	−6.06849
$199$	24.9006	1.76515	0.882577	−	0.470167i	$-0.155806\pi$
$199$	24.9006	1.76515	0.882577	+	0.470167i	$0.155806\pi$
$200$	−85.1254	−6.01928
$201$	30.0238	2.11772
$202$	−1.19642	−0.0841798
$203$	−37.5078	−2.63253
$204$	85.8695	6.01207
$205$	34.1058	2.38205
$206$	−0.0326451	−0.00227449
$207$	−23.5894	−1.63957
$208$	−2.66348	−0.184679
$209$	−19.5105	−1.34957
$210$	−130.765	−9.02366
$211$	8.72035	0.600334	0.300167	−	0.953887i	$-0.402958\pi$
$211$	8.72035	0.600334	0.300167	+	0.953887i	$0.402958\pi$
$212$	−41.9239	−2.87934
$213$	−41.8707	−2.86894
$214$	−25.4955	−1.74284
$215$	31.3164	2.13576
$216$	102.944	7.00444
$217$	−16.9181	−1.14848
$218$	34.7749	2.35525
$219$	39.3095	2.65629
$220$	−93.0609	−6.27417
$221$	1.14175	0.0768024
$222$	−31.5263	−2.11591
$223$	21.3121	1.42717	0.713583	−	0.700571i	$-0.247071\pi$
$223$	21.3121	1.42717	0.713583	+	0.700571i	$0.247071\pi$
$224$	−64.5613	−4.31368
$225$	69.0150	4.60100
$226$	53.0667	3.52995
$227$	−15.1364	−1.00464	−0.502320	−	0.864682i	$-0.667520\pi$
$227$	−15.1364	−1.00464	−0.502320	+	0.864682i	$0.667520\pi$
$228$	68.1535	4.51358
$229$	6.91088	0.456684	0.228342	−	0.973581i	$-0.426670\pi$
$229$	6.91088	0.456684	0.228342	+	0.973581i	$0.426670\pi$
$230$	−35.6631	−2.35155
$231$	−58.4930	−3.84856
$232$	79.2616	5.20378
$233$	6.45414	0.422825	0.211412	−	0.977397i	$-0.432194\pi$
$233$	6.45414	0.422825	0.211412	+	0.977397i	$0.432194\pi$
$234$	3.96611	0.259273
$235$	10.2693	0.669893
$236$	−30.6572	−1.99562
$237$	35.0056	2.27386
$238$	56.7917	3.68126
$239$	26.1588	1.69207	0.846037	−	0.533124i	$-0.178982\pi$
$239$	26.1588	1.69207	0.846037	+	0.533124i	$0.178982\pi$
$240$	150.453	9.71173
$241$	15.0718	0.970857	0.485428	−	0.874276i	$-0.338664\pi$
$241$	15.0718	0.970857	0.485428	+	0.874276i	$0.338664\pi$
$242$	−28.3027	−1.81937
$243$	−18.7336	−1.20176
$244$	9.01285	0.576988
$245$	−35.1887	−2.24812
$246$	−73.9279	−4.71347
$247$	0.906192	0.0576596
$248$	35.7515	2.27022
$249$	3.56268	0.225776
$250$	52.4206	3.31537
$251$	11.6106	0.732858	0.366429	−	0.930446i	$-0.380580\pi$
$251$	11.6106	0.732858	0.366429	+	0.930446i	$0.380580\pi$
$252$	142.210	8.95839
$253$	−15.9526	−1.00293
$254$	6.05642	0.380014
$255$	−64.4946	−4.03881
$256$	8.89652	0.556032
$257$	4.29021	0.267616	0.133808	−	0.991007i	$-0.457279\pi$
$257$	4.29021	0.267616	0.133808	+	0.991007i	$0.457279\pi$
$258$	−67.8816	−4.22612
$259$	−15.0304	−0.933942
$260$	4.32234	0.268060
$261$	−64.2610	−3.97765
$262$	18.0063	1.11243
$263$	0.649999	0.0400807	0.0200403	−	0.999799i	$-0.493621\pi$
$263$	0.649999	0.0400807	0.0200403	+	0.999799i	$0.493621\pi$
$264$	123.608	7.60752
$265$	31.4880	1.93429
$266$	45.0748	2.76371
$267$	12.4825	0.763919
$268$	−49.3636	−3.01536
$269$	−18.4845	−1.12702	−0.563510	−	0.826109i	$-0.690550\pi$
$269$	−18.4845	−1.12702	−0.563510	+	0.826109i	$0.690550\pi$
$270$	−126.179	−7.67900
$271$	−15.2214	−0.924635	−0.462317	−	0.886715i	$-0.652982\pi$
$271$	−15.2214	−0.924635	−0.462317	+	0.886715i	$0.652982\pi$
$272$	−65.3423	−3.96196
$273$	2.71679	0.164428
$274$	−14.7457	−0.890822
$275$	46.6721	2.81444
$276$	55.7250	3.35425
$277$	−0.778121	−0.0467528	−0.0233764	−	0.999727i	$-0.507442\pi$
$277$	−0.778121	−0.0467528	−0.0233764	+	0.999727i	$0.507442\pi$
$278$	−6.40113	−0.383914
$279$	−28.9853	−1.73530
$280$	131.744	7.87320
$281$	16.8231	1.00358	0.501791	−	0.864989i	$-0.332675\pi$
$281$	16.8231	1.00358	0.501791	+	0.864989i	$0.332675\pi$
$282$	−22.2597	−1.32555
$283$	−7.17480	−0.426498	−0.213249	−	0.976998i	$-0.568405\pi$
$283$	−7.17480	−0.426498	−0.213249	+	0.976998i	$0.568405\pi$
$284$	68.8416	4.08500
$285$	−51.1885	−3.03214
$286$	2.68213	0.158597
$287$	−35.2456	−2.08048
$288$	−110.611	−6.51780
$289$	11.0101	0.647656
$290$	−97.1515	−5.70493
$291$	−43.5148	−2.55088
$292$	−64.6305	−3.78221
$293$	2.58122	0.150796	0.0753981	−	0.997154i	$-0.475977\pi$
$293$	2.58122	0.150796	0.0753981	+	0.997154i	$0.475977\pi$
$294$	76.2752	4.44846
$295$	23.0259	1.34062
$296$	31.7622	1.84614
$297$	−56.4415	−3.27507
$298$	11.0011	0.637279
$299$	0.740938	0.0428496
$300$	−163.034	−9.41276
$301$	−32.3630	−1.86537
$302$	−34.9883	−2.01335
$303$	−1.40410	−0.0806636
$304$	−51.8613	−2.97445
$305$	−6.76933	−0.387611
$306$	97.2993	5.56223
$307$	−26.4602	−1.51016	−0.755081	−	0.655632i	$-0.772402\pi$
$307$	−26.4602	−1.51016	−0.755081	+	0.655632i	$0.772402\pi$
$308$	96.1711	5.47986
$309$	−0.0383119	−0.00217949
$310$	−43.8208	−2.48885
$311$	3.33508	0.189115	0.0945576	−	0.995519i	$-0.469856\pi$
$311$	3.33508	0.189115	0.0945576	+	0.995519i	$0.469856\pi$
$312$	−5.74112	−0.325027
$313$	−5.26678	−0.297696	−0.148848	−	0.988860i	$-0.547557\pi$
$313$	−5.26678	−0.297696	−0.148848	+	0.988860i	$0.547557\pi$
$314$	43.6663	2.46423
$315$	−106.811	−6.01810
$316$	−57.5543	−3.23768
$317$	20.6890	1.16201	0.581004	−	0.813901i	$-0.302660\pi$
$317$	20.6890	1.16201	0.581004	+	0.813901i	$0.302660\pi$
$318$	−68.2536	−3.82747
$319$	−43.4572	−2.43313
$320$	−71.4363	−3.99341
$321$	−29.9212	−1.67004
$322$	36.8549	2.05385
$323$	22.2313	1.23698
$324$	90.7383	5.04102
$325$	−2.16775	−0.120245
$326$	4.47603	0.247904
$327$	40.8114	2.25688
$328$	74.4811	4.11253
$329$	−10.6125	−0.585085
$330$	−151.507	−8.34016
$331$	−9.51923	−0.523224	−0.261612	−	0.965173i	$-0.584254\pi$
$331$	−9.51923	−0.523224	−0.261612	+	0.965173i	$0.584254\pi$
$332$	−5.85756	−0.321476
$333$	−25.7510	−1.41115
$334$	64.3171	3.51928
$335$	37.0758	2.02567
$336$	−155.482	−8.48222
$337$	−18.4836	−1.00687	−0.503434	−	0.864034i	$-0.667930\pi$
$337$	−18.4836	−1.00687	−0.503434	+	0.864034i	$0.667930\pi$
$338$	34.6729	1.88596
$339$	62.2785	3.38250
$340$	106.039	5.75075
$341$	−19.6016	−1.06149
$342$	77.2252	4.17586
$343$	8.30261	0.448299
$344$	68.3896	3.68732
$345$	−41.8537	−2.25333
$346$	19.5022	1.04845
$347$	30.7900	1.65290	0.826448	−	0.563013i	$-0.190358\pi$
$347$	30.7900	1.65290	0.826448	+	0.563013i	$0.190358\pi$
$348$	151.803	8.13751
$349$	−18.0013	−0.963588	−0.481794	−	0.876284i	$-0.660015\pi$
$349$	−18.0013	−0.963588	−0.481794	+	0.876284i	$0.660015\pi$
$350$	−107.826	−5.76354
$351$	2.62150	0.139925
$352$	−74.8017	−3.98694
$353$	−4.53288	−0.241261	−0.120630	−	0.992697i	$-0.538492\pi$
$353$	−4.53288	−0.241261	−0.120630	+	0.992697i	$0.538492\pi$
$354$	−49.9111	−2.65275
$355$	−51.7053	−2.74423
$356$	−20.5231	−1.08772
$357$	66.6500	3.52749
$358$	−38.7756	−2.04935
$359$	−2.43428	−0.128476	−0.0642381	−	0.997935i	$-0.520462\pi$
$359$	−2.43428	−0.128476	−0.0642381	+	0.997935i	$0.520462\pi$
$360$	225.712	11.8961
$361$	−1.35532	−0.0713328
$362$	55.9790	2.94219
$363$	−33.2157	−1.74337
$364$	−4.46680	−0.234124
$365$	48.5424	2.54083
$366$	14.6732	0.766983
$367$	5.59324	0.291965	0.145982	−	0.989287i	$-0.453366\pi$
$367$	5.59324	0.291965	0.145982	+	0.989287i	$0.453366\pi$
$368$	−42.4039	−2.21045
$369$	−60.3852	−3.14353
$370$	−38.9311	−2.02393
$371$	−32.5404	−1.68941
$372$	68.4718	3.55010
$373$	29.9613	1.55134	0.775668	−	0.631142i	$-0.217413\pi$
$373$	29.9613	1.55134	0.775668	+	0.631142i	$0.217413\pi$
$374$	65.7997	3.40242
$375$	61.5202	3.17689
$376$	22.4263	1.15655
$377$	2.01843	0.103954
$378$	130.396	6.70684
$379$	5.85489	0.300746	0.150373	−	0.988629i	$-0.451953\pi$
$379$	5.85489	0.300746	0.150373	+	0.988629i	$0.451953\pi$
$380$	84.1614	4.31739
$381$	7.10775	0.364141
$382$	−46.0120	−2.35418
$383$	11.6215	0.593831	0.296916	−	0.954904i	$-0.404042\pi$
$383$	11.6215	0.593831	0.296916	+	0.954904i	$0.404042\pi$
$384$	53.6643	2.73855
$385$	−72.2318	−3.68127
$386$	68.1041	3.46640
$387$	−55.4465	−2.81850
$388$	71.5446	3.63213
$389$	−24.7835	−1.25657	−0.628287	−	0.777981i	$-0.716244\pi$
$389$	−24.7835	−1.25657	−0.628287	+	0.777981i	$0.716244\pi$
$390$	7.03693	0.356329
$391$	18.1772	0.919260
$392$	−76.8460	−3.88131
$393$	21.1320	1.06597
$394$	42.1362	2.12279
$395$	43.2277	2.17502
$396$	164.767	8.27984
$397$	1.76395	0.0885301	0.0442650	−	0.999020i	$-0.485905\pi$
$397$	1.76395	0.0885301	0.0442650	+	0.999020i	$0.485905\pi$
$398$	−66.6521	−3.34097
$399$	52.8993	2.64828
$400$	124.060	6.20302
$401$	−26.8905	−1.34285	−0.671424	−	0.741074i	$-0.734317\pi$
$401$	−26.8905	−1.34285	−0.671424	+	0.741074i	$0.734317\pi$
$402$	−80.3657	−4.00828
$403$	0.910424	0.0453515
$404$	2.30855	0.114855
$405$	−68.1514	−3.38647
$406$	100.398	4.98269
$407$	−17.4144	−0.863201
$408$	−140.845	−6.97286
$409$	24.0941	1.19138	0.595688	−	0.803216i	$-0.296879\pi$
$409$	24.0941	1.19138	0.595688	+	0.803216i	$0.296879\pi$
$410$	−91.2920	−4.50859
$411$	−17.3054	−0.853613
$412$	0.0629904	0.00310332
$413$	−23.7955	−1.17090
$414$	63.1424	3.10328
$415$	4.39948	0.215962
$416$	3.47427	0.170340
$417$	−7.51230	−0.367879
$418$	52.2243	2.55438
$419$	−1.45646	−0.0711525	−0.0355763	−	0.999367i	$-0.511327\pi$
$419$	−1.45646	−0.0711525	−0.0355763	+	0.999367i	$0.511327\pi$
$420$	252.318	12.3119
$421$	−17.8917	−0.871987	−0.435994	−	0.899950i	$-0.643603\pi$
$421$	−17.8917	−0.871987	−0.435994	+	0.899950i	$0.643603\pi$
$422$	−23.3420	−1.13627
$423$	−18.1820	−0.884039
$424$	68.7644	3.33949
$425$	−53.1807	−2.57964
$426$	112.077	5.43013
$427$	6.99557	0.338539
$428$	49.1948	2.37792
$429$	3.14771	0.151973
$430$	−83.8255	−4.04243
$431$	17.3200	0.834276	0.417138	−	0.908843i	$-0.363033\pi$
$431$	17.3200	0.834276	0.417138	+	0.908843i	$0.363033\pi$
$432$	−150.028	−7.21825
$433$	9.60897	0.461778	0.230889	−	0.972980i	$-0.425837\pi$
$433$	9.60897	0.461778	0.230889	+	0.972980i	$0.425837\pi$
$434$	45.2853	2.17377
$435$	−114.016	−5.46664
$436$	−67.0999	−3.21350
$437$	14.4270	0.690137
$438$	−105.221	−5.02765
$439$	31.9919	1.52689	0.763444	−	0.645874i	$-0.223507\pi$
$439$	31.9919	1.52689	0.763444	+	0.645874i	$0.223507\pi$
$440$	152.640	7.27684
$441$	62.3025	2.96678
$442$	−3.05616	−0.145367
$443$	14.5968	0.693513	0.346756	−	0.937955i	$-0.387283\pi$
$443$	14.5968	0.693513	0.346756	+	0.937955i	$0.387283\pi$
$444$	60.8316	2.88694
$445$	15.4144	0.730714
$446$	−57.0469	−2.70125
$447$	12.9108	0.610660
$448$	73.8237	3.48784
$449$	−11.6984	−0.552084	−0.276042	−	0.961146i	$-0.589023\pi$
$449$	−11.6984	−0.552084	−0.276042	+	0.961146i	$0.589023\pi$
$450$	−184.735	−8.70847
$451$	−40.8361	−1.92290
$452$	−102.395	−4.81625
$453$	−41.0619	−1.92926
$454$	40.5162	1.90152
$455$	3.35491	0.157280
$456$	−111.787	−5.23490
$457$	29.3355	1.37226	0.686128	−	0.727481i	$-0.259309\pi$
$457$	29.3355	1.37226	0.686128	+	0.727481i	$0.259309\pi$
$458$	−18.4986	−0.864381
$459$	64.3124	3.00185
$460$	68.8137	3.20845
$461$	37.3844	1.74116	0.870582	−	0.492023i	$-0.163742\pi$
$461$	37.3844	1.74116	0.870582	+	0.492023i	$0.163742\pi$
$462$	156.570	7.28430
$463$	12.8515	0.597260	0.298630	−	0.954369i	$-0.403470\pi$
$463$	12.8515	0.597260	0.298630	+	0.954369i	$0.403470\pi$
$464$	−115.515	−5.36263
$465$	−51.4276	−2.38490
$466$	−17.2760	−0.800295
$467$	5.98544	0.276973	0.138487	−	0.990364i	$-0.455776\pi$
$467$	5.98544	0.276973	0.138487	+	0.990364i	$0.455776\pi$
$468$	−7.65282	−0.353752
$469$	−38.3149	−1.76922
$470$	−27.4881	−1.26793
$471$	51.2463	2.36131
$472$	50.2846	2.31454
$473$	−37.4963	−1.72408
$474$	−93.7005	−4.30381
$475$	−42.2088	−1.93667
$476$	−109.582	−5.02270
$477$	−55.7504	−2.55263
$478$	−70.0201	−3.20265
$479$	−30.7666	−1.40576	−0.702880	−	0.711308i	$-0.748103\pi$
$479$	−30.7666	−1.40576	−0.702880	+	0.711308i	$0.748103\pi$
$480$	−196.253	−8.95766
$481$	0.808836	0.0368798
$482$	−40.3430	−1.83757
$483$	43.2525	1.96806
$484$	54.6115	2.48234
$485$	−53.7355	−2.44000
$486$	50.1448	2.27462
$487$	−18.2354	−0.826325	−0.413163	−	0.910657i	$-0.635576\pi$
$487$	−18.2354	−0.826325	−0.413163	+	0.910657i	$0.635576\pi$
$488$	−14.7831	−0.669197
$489$	5.25301	0.237549
$490$	94.1906	4.25510
$491$	43.5812	1.96679	0.983395	−	0.181476i	$-0.0580874\pi$
$491$	43.5812	1.96679	0.983395	+	0.181476i	$0.0580874\pi$
$492$	142.648	6.43105
$493$	49.5174	2.23015
$494$	−2.42563	−0.109134
$495$	−123.752	−5.56226
$496$	−52.1035	−2.33952
$497$	53.4334	2.39681
$498$	−9.53633	−0.427333
$499$	−4.07550	−0.182444	−0.0912222	−	0.995831i	$-0.529077\pi$
$499$	−4.07550	−0.182444	−0.0912222	+	0.995831i	$0.529077\pi$
$500$	−101.148	−4.52349
$501$	75.4818	3.37228
$502$	−31.0786	−1.38710
$503$	−37.1942	−1.65841	−0.829204	−	0.558946i	$-0.811206\pi$
$503$	−37.1942	−1.65841	−0.829204	+	0.558946i	$0.811206\pi$
$504$	−233.256	−10.3900
$505$	−1.73390	−0.0771575
$506$	42.7007	1.89828
$507$	40.6917	1.80718
$508$	−11.6862	−0.518490
$509$	−3.95832	−0.175449	−0.0877246	−	0.996145i	$-0.527960\pi$
$509$	−3.95832	−0.175449	−0.0877246	+	0.996145i	$0.527960\pi$
$510$	172.635	7.64439
$511$	−50.1648	−2.21916
$512$	10.3525	0.457520
$513$	51.0439	2.25364
$514$	−11.4837	−0.506526
$515$	−0.0473106	−0.00208475
$516$	130.981	5.76611
$517$	−12.2958	−0.540767
$518$	40.2323	1.76770
$519$	22.8876	1.00465
$520$	−7.08959	−0.310899
$521$	−25.1242	−1.10071	−0.550356	−	0.834930i	$-0.685508\pi$
$521$	−25.1242	−1.10071	−0.550356	+	0.834930i	$0.685508\pi$
$522$	172.009	7.52864
$523$	−17.8978	−0.782617	−0.391308	−	0.920260i	$-0.627977\pi$
$523$	−17.8978	−0.782617	−0.391308	+	0.920260i	$0.627977\pi$
$524$	−34.7441	−1.51780
$525$	−126.543	−5.52280
$526$	−1.73987	−0.0758621
$527$	22.3351	0.972933
$528$	−180.143	−7.83974
$529$	−11.2039	−0.487127
$530$	−84.2850	−3.66111
$531$	−40.7680	−1.76918
$532$	−86.9741	−3.77081
$533$	1.89669	0.0821548
$534$	−33.4124	−1.44590
$535$	−36.9491	−1.59745
$536$	80.9671	3.49725
$537$	−45.5066	−1.96376
$538$	49.4781	2.13315
$539$	42.1327	1.81478
$540$	243.469	10.4772
$541$	−36.2848	−1.56000	−0.780002	−	0.625777i	$-0.784782\pi$
$541$	−36.2848	−1.56000	−0.780002	+	0.625777i	$0.784782\pi$
$542$	40.7436	1.75009
$543$	65.6963	2.81930
$544$	85.2330	3.65433
$545$	50.3972	2.15878
$546$	−7.27211	−0.311218
$547$	29.9701	1.28143	0.640714	−	0.767780i	$-0.278639\pi$
$547$	29.9701	1.28143	0.640714	+	0.767780i	$0.278639\pi$
$548$	28.4526	1.21544
$549$	11.9853	0.511519
$550$	−124.929	−5.32698
$551$	39.3013	1.67429
$552$	−91.4013	−3.89030
$553$	−44.6724	−1.89966
$554$	2.08282	0.0884906
$555$	−45.6891	−1.93940
$556$	12.3513	0.523812
$557$	6.93255	0.293741	0.146871	−	0.989156i	$-0.453080\pi$
$557$	6.93255	0.293741	0.146871	+	0.989156i	$0.453080\pi$
$558$	77.5859	3.28447
$559$	1.74157	0.0736604
$560$	−192.001	−8.11353
$561$	77.2217	3.26030
$562$	−45.0309	−1.89951
$563$	−13.8644	−0.584313	−0.292156	−	0.956371i	$-0.594373\pi$
$563$	−13.8644	−0.584313	−0.292156	+	0.956371i	$0.594373\pi$
$564$	42.9512	1.80857
$565$	76.9064	3.23548
$566$	19.2050	0.807247
$567$	70.4291	2.95774
$568$	−112.915	−4.73783
$569$	−15.1920	−0.636881	−0.318441	−	0.947943i	$-0.603159\pi$
$569$	−15.1920	−0.636881	−0.318441	+	0.947943i	$0.603159\pi$
$570$	137.018	5.73904
$571$	−0.224621	−0.00940008	−0.00470004	−	0.999989i	$-0.501496\pi$
$571$	−0.224621	−0.00940008	−0.00470004	+	0.999989i	$0.501496\pi$
$572$	−5.17530	−0.216390
$573$	−53.9992	−2.25585
$574$	94.3431	3.93780
$575$	−34.5116	−1.43923
$576$	126.480	5.26999
$577$	−32.6287	−1.35835	−0.679176	−	0.733976i	$-0.737663\pi$
$577$	−32.6287	−1.35835	−0.679176	+	0.733976i	$0.737663\pi$
$578$	−29.4712	−1.22584
$579$	79.9261	3.32162
$580$	187.459	7.78380
$581$	−4.54651	−0.188621
$582$	116.477	4.82814
$583$	−37.7018	−1.56145
$584$	106.008	4.38665
$585$	5.74785	0.237644
$586$	−6.90922	−0.285417
$587$	−26.0518	−1.07527	−0.537636	−	0.843177i	$-0.680682\pi$
$587$	−26.0518	−1.07527	−0.537636	+	0.843177i	$0.680682\pi$
$588$	−147.177	−6.06947
$589$	17.7271	0.730432
$590$	−61.6342	−2.53744
$591$	49.4506	2.03413
$592$	−46.2897	−1.90249
$593$	1.60363	0.0658530	0.0329265	−	0.999458i	$-0.489517\pi$
$593$	1.60363	0.0658530	0.0329265	+	0.999458i	$0.489517\pi$
$594$	151.079	6.19883
$595$	82.3047	3.37417
$596$	−21.2272	−0.869502
$597$	−78.2222	−3.20142
$598$	−1.98329	−0.0811029
$599$	−32.5089	−1.32828	−0.664139	−	0.747609i	$-0.731202\pi$
$599$	−32.5089	−1.32828	−0.664139	+	0.747609i	$0.731202\pi$
$600$	267.411	10.9170
$601$	38.8844	1.58613	0.793063	−	0.609139i	$-0.208485\pi$
$601$	38.8844	1.58613	0.793063	+	0.609139i	$0.208485\pi$
$602$	86.6271	3.53066
$603$	−65.6437	−2.67322
$604$	67.5117	2.74701
$605$	−41.0174	−1.66759
$606$	3.75841	0.152675
$607$	25.9068	1.05153	0.525763	−	0.850631i	$-0.323780\pi$
$607$	25.9068	1.05153	0.525763	+	0.850631i	$0.323780\pi$
$608$	67.6483	2.74350
$609$	117.826	4.77457
$610$	18.1197	0.733645
$611$	0.571094	0.0231040
$612$	−187.744	−7.58910
$613$	0.944598	0.0381520	0.0190760	−	0.999818i	$-0.493928\pi$
$613$	0.944598	0.0381520	0.0190760	+	0.999818i	$0.493928\pi$
$614$	70.8267	2.85833
$615$	−107.139	−4.32027
$616$	−157.742	−6.35560
$617$	26.2995	1.05878	0.529389	−	0.848379i	$-0.322421\pi$
$617$	26.2995	1.05878	0.529389	+	0.848379i	$0.322421\pi$
$618$	0.102551	0.00412520
$619$	−27.1174	−1.08994	−0.544970	−	0.838455i	$-0.683459\pi$
$619$	−27.1174	−1.08994	−0.544970	+	0.838455i	$0.683459\pi$
$620$	84.5544	3.39579
$621$	41.7355	1.67479
$622$	−8.92712	−0.357945
$623$	−15.9296	−0.638206
$624$	8.36701	0.334948
$625$	25.7281	1.02912
$626$	14.0977	0.563459
$627$	61.2899	2.44768
$628$	−84.2564	−3.36220
$629$	19.8429	0.791188
$630$	285.903	11.3907
$631$	−17.6645	−0.703212	−0.351606	−	0.936148i	$-0.614364\pi$
$631$	−17.6645	−0.703212	−0.351606	+	0.936148i	$0.614364\pi$
$632$	94.4017	3.75510
$633$	−27.3939	−1.08881
$634$	−55.3788	−2.19937
$635$	8.77721	0.348313
$636$	131.699	5.22220
$637$	−1.95691	−0.0775356
$638$	116.323	4.60528
$639$	91.5456	3.62149
$640$	66.2689	2.61951
$641$	−36.0139	−1.42246	−0.711232	−	0.702957i	$-0.751862\pi$
$641$	−36.0139	−1.42246	−0.711232	+	0.702957i	$0.751862\pi$
$642$	80.0910	3.16094
$643$	−31.6533	−1.24829	−0.624143	−	0.781310i	$-0.714552\pi$
$643$	−31.6533	−1.24829	−0.624143	+	0.781310i	$0.714552\pi$
$644$	−71.1135	−2.80226
$645$	−98.3767	−3.87358
$646$	−59.5072	−2.34128
$647$	−33.9807	−1.33592	−0.667959	−	0.744198i	$-0.732832\pi$
$647$	−33.9807	−1.33592	−0.667959	+	0.744198i	$0.732832\pi$
$648$	−148.831	−5.84663
$649$	−27.5698	−1.08221
$650$	5.80249	0.227592
$651$	53.1463	2.08297
$652$	−8.63672	−0.338240
$653$	4.30292	0.168386	0.0841931	−	0.996449i	$-0.473169\pi$
$653$	4.30292	0.168386	0.0841931	+	0.996449i	$0.473169\pi$
$654$	−109.241	−4.27167
$655$	26.0955	1.01963
$656$	−108.547	−4.23807
$657$	−85.9457	−3.35306
$658$	28.4067	1.10741
$659$	15.9627	0.621820	0.310910	−	0.950439i	$-0.399366\pi$
$659$	15.9627	0.621820	0.310910	+	0.950439i	$0.399366\pi$
$660$	292.340	11.3793
$661$	7.84922	0.305299	0.152650	−	0.988280i	$-0.451219\pi$
$661$	7.84922	0.305299	0.152650	+	0.988280i	$0.451219\pi$
$662$	25.4804	0.990324
$663$	−3.58667	−0.139295
$664$	9.60769	0.372851
$665$	65.3242	2.53316
$666$	68.9286	2.67093
$667$	32.1343	1.24424
$668$	−124.103	−4.80170
$669$	−66.9495	−2.58842
$670$	−99.2419	−3.83405
$671$	8.10518	0.312897
$672$	202.812	7.82362
$673$	42.7628	1.64839	0.824193	−	0.566310i	$-0.191629\pi$
$673$	42.7628	1.64839	0.824193	+	0.566310i	$0.191629\pi$
$674$	49.4757	1.90573
$675$	−122.105	−4.69982
$676$	−66.9032	−2.57320
$677$	42.1913	1.62154	0.810771	−	0.585363i	$-0.199048\pi$
$677$	42.1913	1.62154	0.810771	+	0.585363i	$0.199048\pi$
$678$	−166.703	−6.40218
$679$	55.5314	2.13110
$680$	−173.926	−6.66978
$681$	47.5493	1.82209
$682$	52.4683	2.00911
$683$	−3.64418	−0.139441	−0.0697203	−	0.997567i	$-0.522211\pi$
$683$	−3.64418	−0.139441	−0.0697203	+	0.997567i	$0.522211\pi$
$684$	−149.010	−5.69753
$685$	−21.3701	−0.816509
$686$	−22.2238	−0.848510
$687$	−21.7097	−0.828277
$688$	−99.6697	−3.79987
$689$	1.75111	0.0667120
$690$	112.031	4.26495
$691$	31.9477	1.21535	0.607673	−	0.794187i	$-0.292103\pi$
$691$	31.9477	1.21535	0.607673	+	0.794187i	$0.292103\pi$
$692$	−37.6305	−1.43050
$693$	127.888	4.85808
$694$	−82.4167	−3.12849
$695$	−9.27678	−0.351888
$696$	−248.991	−9.43798
$697$	46.5308	1.76248
$698$	48.1847	1.82382
$699$	−20.2749	−0.766867
$700$	208.056	7.86376
$701$	23.2800	0.879272	0.439636	−	0.898176i	$-0.355107\pi$
$701$	23.2800	0.879272	0.439636	+	0.898176i	$0.355107\pi$
$702$	−7.01706	−0.264842
$703$	15.7490	0.593987
$704$	85.5333	3.22366
$705$	−32.2597	−1.21497
$706$	12.1333	0.456642
$707$	1.79185	0.0673893
$708$	96.3061	3.61940
$709$	27.3039	1.02542	0.512710	−	0.858562i	$-0.328642\pi$
$709$	27.3039	1.02542	0.512710	+	0.858562i	$0.328642\pi$
$710$	138.401	5.19410
$711$	−76.5357	−2.87031
$712$	33.6624	1.26155
$713$	14.4944	0.542819
$714$	−178.404	−6.67661
$715$	3.88704	0.145367
$716$	74.8195	2.79614
$717$	−82.1748	−3.06887
$718$	6.51590	0.243171
$719$	−14.8908	−0.555333	−0.277666	−	0.960678i	$-0.589561\pi$
$719$	−14.8908	−0.555333	−0.277666	+	0.960678i	$0.589561\pi$
$720$	−328.949	−12.2592
$721$	0.0488918	0.00182083
$722$	3.62783	0.135014
$723$	−47.3461	−1.76082
$724$	−108.014	−4.01432
$725$	−94.0148	−3.49162
$726$	88.9096	3.29974
$727$	−27.7220	−1.02815	−0.514076	−	0.857745i	$-0.671865\pi$
$727$	−27.7220	−1.02815	−0.514076	+	0.857745i	$0.671865\pi$
$728$	7.32653	0.271539
$729$	6.14449	0.227574
$730$	−129.935	−4.80911
$731$	42.7252	1.58025
$732$	−28.3128	−1.04647
$733$	44.7700	1.65362	0.826808	−	0.562484i	$-0.190154\pi$
$733$	44.7700	1.65362	0.826808	+	0.562484i	$0.190154\pi$
$734$	−14.9716	−0.552612
$735$	110.541	4.07737
$736$	55.3119	2.03882
$737$	−44.3922	−1.63521
$738$	161.635	5.94986
$739$	29.4762	1.08430	0.542151	−	0.840281i	$-0.317610\pi$
$739$	29.4762	1.08430	0.542151	+	0.840281i	$0.317610\pi$
$740$	75.1196	2.76145
$741$	−2.84669	−0.104576
$742$	87.1019	3.19761
$743$	1.95620	0.0717660	0.0358830	−	0.999356i	$-0.488576\pi$
$743$	1.95620	0.0717660	0.0358830	+	0.999356i	$0.488576\pi$
$744$	−112.309	−4.11744
$745$	15.9433	0.584117
$746$	−80.1982	−2.93627
$747$	−7.78939	−0.284999
$748$	−126.964	−4.64226
$749$	38.1839	1.39521
$750$	−164.673	−6.01301
$751$	−6.08371	−0.221998	−0.110999	−	0.993821i	$-0.535405\pi$
$751$	−6.08371	−0.221998	−0.110999	+	0.993821i	$0.535405\pi$
$752$	−32.6837	−1.19185
$753$	−36.4735	−1.32917
$754$	−5.40279	−0.196758
$755$	−50.7065	−1.84540
$756$	−251.606	−9.15080
$757$	19.1023	0.694286	0.347143	−	0.937812i	$-0.387152\pi$
$757$	19.1023	0.694286	0.347143	+	0.937812i	$0.387152\pi$
$758$	−15.6720	−0.569231
$759$	50.1130	1.81899
$760$	−138.043	−5.00735
$761$	19.8580	0.719852	0.359926	−	0.932981i	$-0.382802\pi$
$761$	19.8580	0.719852	0.359926	+	0.932981i	$0.382802\pi$
$762$	−19.0255	−0.689222
$763$	−52.0815	−1.88548
$764$	88.7825	3.21204
$765$	141.010	5.09823
$766$	−31.1076	−1.12396
$767$	1.28052	0.0462368
$768$	−27.9473	−1.00846
$769$	−28.6236	−1.03219	−0.516097	−	0.856530i	$-0.672616\pi$
$769$	−28.6236	−1.03219	−0.516097	+	0.856530i	$0.672616\pi$
$770$	193.345	6.96768
$771$	−13.4772	−0.485369
$772$	−131.410	−4.72956
$773$	33.5122	1.20535	0.602675	−	0.797987i	$-0.294102\pi$
$773$	33.5122	1.20535	0.602675	+	0.797987i	$0.294102\pi$
$774$	148.415	5.33468
$775$	−42.4060	−1.52327
$776$	−117.349	−4.21258
$777$	47.2161	1.69387
$778$	66.3388	2.37836
$779$	36.9309	1.32319
$780$	−13.5781	−0.486175
$781$	61.9087	2.21527
$782$	−48.6554	−1.73991
$783$	113.694	4.06309
$784$	111.994	3.99978
$785$	63.2830	2.25867
$786$	−56.5647	−2.01760
$787$	−32.1502	−1.14603	−0.573015	−	0.819545i	$-0.694226\pi$
$787$	−32.1502	−1.14603	−0.573015	+	0.819545i	$0.694226\pi$
$788$	−81.3040	−2.89634
$789$	−2.04190	−0.0726934
$790$	−115.709	−4.11674
$791$	−79.4767	−2.82587
$792$	−270.254	−9.60305
$793$	−0.376456	−0.0133683
$794$	−4.72162	−0.167564
$795$	−98.9159	−3.50818
$796$	128.609	4.55841
$797$	34.9403	1.23765	0.618824	−	0.785530i	$-0.287609\pi$
$797$	34.9403	1.23765	0.618824	+	0.785530i	$0.287609\pi$
$798$	−141.597	−5.01248
$799$	14.0105	0.495654
$800$	−161.825	−5.72138
$801$	−27.2917	−0.964303
$802$	71.9786	2.54165
$803$	−58.1217	−2.05107
$804$	155.070	5.46889
$805$	53.4117	1.88251
$806$	−2.43696	−0.0858383
$807$	58.0669	2.04405
$808$	−3.78653	−0.133210
$809$	11.3331	0.398451	0.199225	−	0.979954i	$-0.436157\pi$
$809$	11.3331	0.398451	0.199225	+	0.979954i	$0.436157\pi$
$810$	182.423	6.40969
$811$	−35.5728	−1.24913	−0.624565	−	0.780973i	$-0.714724\pi$
$811$	−35.5728	−1.24913	−0.624565	+	0.780973i	$0.714724\pi$
$812$	−193.724	−6.79837
$813$	47.8162	1.67699
$814$	46.6137	1.63381
$815$	6.48683	0.227224
$816$	205.265	7.18571
$817$	33.9105	1.18638
$818$	−64.4934	−2.25496
$819$	−5.93995	−0.207559
$820$	176.153	6.15151
$821$	−8.30651	−0.289899	−0.144950	−	0.989439i	$-0.546302\pi$
$821$	−8.30651	−0.289899	−0.144950	+	0.989439i	$0.546302\pi$
$822$	46.3219	1.61566
$823$	18.4977	0.644789	0.322394	−	0.946605i	$-0.395512\pi$
$823$	18.4977	0.644789	0.322394	+	0.946605i	$0.395512\pi$
$824$	−0.103318	−0.00359926
$825$	−146.615	−5.10448
$826$	63.6941	2.21620
$827$	−11.5059	−0.400098	−0.200049	−	0.979786i	$-0.564110\pi$
$827$	−11.5059	−0.400098	−0.200049	+	0.979786i	$0.564110\pi$
$828$	−121.836	−4.23411
$829$	−48.3567	−1.67950	−0.839748	−	0.542976i	$-0.817297\pi$
$829$	−48.3567	−1.67950	−0.839748	+	0.542976i	$0.817297\pi$
$830$	−11.7762	−0.408758
$831$	2.44438	0.0847944
$832$	−3.97271	−0.137729
$833$	−48.0082	−1.66339
$834$	20.1084	0.696297
$835$	93.2110	3.22570
$836$	−100.770	−3.48519
$837$	51.2823	1.77258
$838$	3.89854	0.134673
$839$	−8.39900	−0.289966	−0.144983	−	0.989434i	$-0.546313\pi$
$839$	−8.39900	−0.289966	−0.144983	+	0.989434i	$0.546313\pi$
$840$	−413.857	−14.2794
$841$	58.5386	2.01857
$842$	47.8912	1.65044
$843$	−52.8477	−1.82017
$844$	45.0396	1.55033
$845$	50.2494	1.72863
$846$	48.6683	1.67325
$847$	42.3883	1.45648
$848$	−100.216	−3.44143
$849$	22.5388	0.773529
$850$	142.350	4.88258
$851$	12.8770	0.441420
$852$	−216.258	−7.40887
$853$	44.5676	1.52596	0.762982	−	0.646419i	$-0.223734\pi$
$853$	44.5676	1.52596	0.762982	+	0.646419i	$0.223734\pi$
$854$	−18.7253	−0.640765
$855$	111.918	3.82751
$856$	−80.6904	−2.75794
$857$	−28.7366	−0.981623	−0.490812	−	0.871266i	$-0.663300\pi$
$857$	−28.7366	−0.981623	−0.490812	+	0.871266i	$0.663300\pi$
$858$	−8.42558	−0.287645
$859$	−21.2729	−0.725823	−0.362911	−	0.931824i	$-0.618217\pi$
$859$	−21.2729	−0.725823	−0.362911	+	0.931824i	$0.618217\pi$
$860$	161.746	5.51548
$861$	110.720	3.77333
$862$	−46.3610	−1.57906
$863$	−19.5383	−0.665091	−0.332546	−	0.943087i	$-0.607908\pi$
$863$	−19.5383	−0.665091	−0.332546	+	0.943087i	$0.607908\pi$
$864$	195.698	6.65779
$865$	28.2634	0.960984
$866$	−25.7206	−0.874023
$867$	−34.5871	−1.17464
$868$	−87.3803	−2.96588
$869$	−51.7581	−1.75577
$870$	305.190	10.3469
$871$	2.06186	0.0698634
$872$	110.059	3.72706
$873$	95.1400	3.22000
$874$	−38.6172	−1.30625
$875$	−78.5090	−2.65409
$876$	203.029	6.85971
$877$	−39.2057	−1.32388	−0.661941	−	0.749556i	$-0.730267\pi$
$877$	−39.2057	−1.32388	−0.661941	+	0.749556i	$0.730267\pi$
$878$	−85.6336	−2.88999
$879$	−8.10858	−0.273496
$880$	−222.455	−7.49897
$881$	−26.6238	−0.896977	−0.448489	−	0.893789i	$-0.648038\pi$
$881$	−26.6238	−0.896977	−0.448489	+	0.893789i	$0.648038\pi$
$882$	−166.767	−5.61533
$883$	−18.7567	−0.631214	−0.315607	−	0.948890i	$-0.602208\pi$
$883$	−18.7567	−0.631214	−0.315607	+	0.948890i	$0.602208\pi$
$884$	5.89701	0.198338
$885$	−72.3332	−2.43145
$886$	−39.0716	−1.31264
$887$	38.7867	1.30233	0.651165	−	0.758936i	$-0.274280\pi$
$887$	38.7867	1.30233	0.651165	+	0.758936i	$0.274280\pi$
$888$	−99.7771	−3.34830
$889$	−9.07055	−0.304217
$890$	−41.2603	−1.38305
$891$	81.6002	2.73371
$892$	110.075	3.68558
$893$	11.1199	0.372114
$894$	−34.5587	−1.15582
$895$	−56.1952	−1.87840
$896$	−68.4837	−2.28788
$897$	−2.32757	−0.0777153
$898$	31.3136	1.04495
$899$	39.4849	1.31689
$900$	356.455	11.8818
$901$	42.9594	1.43119
$902$	109.307	3.63954
$903$	101.665	3.38318
$904$	167.950	5.58594
$905$	81.1270	2.69675
$906$	109.912	3.65157
$907$	48.6123	1.61415	0.807073	−	0.590452i	$-0.201051\pi$
$907$	48.6123	1.61415	0.807073	+	0.590452i	$0.201051\pi$
$908$	−78.1780	−2.59443
$909$	3.06991	0.101823
$910$	−8.98018	−0.297690
$911$	−1.65805	−0.0549336	−0.0274668	−	0.999623i	$-0.508744\pi$
$911$	−1.65805	−0.0549336	−0.0274668	+	0.999623i	$0.508744\pi$
$912$	162.916	5.39469
$913$	−5.26766	−0.174334
$914$	−78.5231	−2.59731
$915$	21.2651	0.703001
$916$	35.6939	1.17936
$917$	−26.9676	−0.890549
$918$	−172.147	−5.68170
$919$	−16.2790	−0.536995	−0.268497	−	0.963280i	$-0.586527\pi$
$919$	−16.2790	−0.536995	−0.268497	+	0.963280i	$0.586527\pi$
$920$	−112.870	−3.72120
$921$	83.1214	2.73894
$922$	−100.068	−3.29556
$923$	−2.87543	−0.0946461
$924$	−302.110	−9.93869
$925$	−37.6742	−1.23872
$926$	−34.4000	−1.13046
$927$	0.0837647	0.00275119
$928$	150.678	4.94625
$929$	−44.0875	−1.44646	−0.723232	−	0.690605i	$-0.757344\pi$
$929$	−44.0875	−1.44646	−0.723232	+	0.690605i	$0.757344\pi$
$930$	137.658	4.51398
$931$	−38.1035	−1.24879
$932$	33.3349	1.09192
$933$	−10.4768	−0.342994
$934$	−16.0214	−0.524236
$935$	95.3595	3.11859
$936$	12.5523	0.410285
$937$	−10.4882	−0.342635	−0.171317	−	0.985216i	$-0.554802\pi$
$937$	−10.4882	−0.342635	−0.171317	+	0.985216i	$0.554802\pi$
$938$	102.559	3.34866
$939$	16.5450	0.539924
$940$	53.0396	1.72996
$941$	−18.3174	−0.597131	−0.298565	−	0.954389i	$-0.596508\pi$
$941$	−18.3174	−0.597131	−0.298565	+	0.954389i	$0.596508\pi$
$942$	−137.173	−4.46932
$943$	30.1962	0.983323
$944$	−73.2839	−2.38519
$945$	188.975	6.14736
$946$	100.367	3.26323
$947$	13.8470	0.449966	0.224983	−	0.974363i	$-0.427767\pi$
$947$	13.8470	0.449966	0.224983	+	0.974363i	$0.427767\pi$
$948$	180.800	5.87211
$949$	2.69954	0.0876308
$950$	112.982	3.66561
$951$	−64.9919	−2.10751
$952$	179.739	5.82538
$953$	45.0955	1.46079	0.730393	−	0.683027i	$-0.239337\pi$
$953$	45.0955	1.46079	0.730393	+	0.683027i	$0.239337\pi$
$954$	149.229	4.83146
$955$	−66.6824	−2.15779
$956$	135.107	4.36969
$957$	136.515	4.41292
$958$	82.3538	2.66073
$959$	22.0843	0.713139
$960$	224.408	7.24275
$961$	−13.1901	−0.425487
$962$	−2.16504	−0.0698036
$963$	65.4193	2.10811
$964$	77.8439	2.50718
$965$	98.6991	3.17724
$966$	−115.775	−3.72501
$967$	46.8871	1.50779	0.753894	−	0.656996i	$-0.228173\pi$
$967$	46.8871	1.50779	0.753894	+	0.656996i	$0.228173\pi$
$968$	−89.5749	−2.87905
$969$	−69.8369	−2.24348
$970$	143.835	4.61828
$971$	13.4294	0.430970	0.215485	−	0.976507i	$-0.430867\pi$
$971$	13.4294	0.430970	0.215485	+	0.976507i	$0.430867\pi$
$972$	−96.7570	−3.10348
$973$	9.58682	0.307339
$974$	48.8113	1.56401
$975$	6.80973	0.218086
$976$	21.5446	0.689625
$977$	49.1014	1.57089	0.785447	−	0.618929i	$-0.212433\pi$
$977$	49.1014	1.57089	0.785447	+	0.618929i	$0.212433\pi$
$978$	−14.0609	−0.449618
$979$	−18.4563	−0.589865
$980$	−181.746	−5.80565
$981$	−89.2295	−2.84888
$982$	−116.655	−3.72261
$983$	0.216097	0.00689243	0.00344622	−	0.999994i	$-0.498903\pi$
$983$	0.216097	0.00689243	0.00344622	+	0.999994i	$0.498903\pi$
$984$	−233.974	−7.45880
$985$	61.0655	1.94571
$986$	−132.545	−4.22108
$987$	33.3378	1.06115
$988$	4.68038	0.148903
$989$	27.7265	0.881653
$990$	331.252	10.5279
$991$	11.2603	0.357694	0.178847	−	0.983877i	$-0.442763\pi$
$991$	11.2603	0.357694	0.178847	+	0.983877i	$0.442763\pi$
$992$	67.9642	2.15787
$993$	29.9035	0.948959
$994$	−143.027	−4.53653
$995$	−96.5949	−3.06227
$996$	18.4008	0.583053
$997$	−9.54583	−0.302320	−0.151160	−	0.988509i	$-0.548301\pi$
$997$	−9.54583	−0.302320	−0.151160	+	0.988509i	$0.548301\pi$
$998$	10.9090	0.345319
$999$	45.5601	1.44146

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8039.2.a.b.1.14	✓	391

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8039.2.a.b.1.14	✓	391	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:	\( N \)	\(=\)	\( 8039 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8039.a (trivial)

\(f(q)\)	\(=\)	\(q-2.67673 q^{2} -3.14138 q^{3} +5.16489 q^{4} -3.87922 q^{5} +8.40863 q^{6} +4.00887 q^{7} -8.47155 q^{8} +6.86827 q^{9} +O(q^{10})\)	\(q-2.67673 q^{2} -3.14138 q^{3} +5.16489 q^{4} -3.87922 q^{5} +8.40863 q^{6} +4.00887 q^{7} -8.47155 q^{8} +6.86827 q^{9} +10.3836 q^{10} +4.64474 q^{11} -16.2249 q^{12} -0.215731 q^{13} -10.7307 q^{14} +12.1861 q^{15} +12.3463 q^{16} -5.29246 q^{17} -18.3845 q^{18} -4.20056 q^{19} -20.0358 q^{20} -12.5934 q^{21} -12.4327 q^{22} -3.43454 q^{23} +26.6124 q^{24} +10.0484 q^{25} +0.577455 q^{26} -12.1517 q^{27} +20.7054 q^{28} -9.35621 q^{29} -32.6190 q^{30} -4.22018 q^{31} -16.1046 q^{32} -14.5909 q^{33} +14.1665 q^{34} -15.5513 q^{35} +35.4738 q^{36} -3.74928 q^{37} +11.2438 q^{38} +0.677694 q^{39} +32.8631 q^{40} -8.79191 q^{41} +33.7091 q^{42} -8.07285 q^{43} +23.9896 q^{44} -26.6436 q^{45} +9.19335 q^{46} -2.64725 q^{47} -38.7844 q^{48} +9.07106 q^{49} -26.8968 q^{50} +16.6256 q^{51} -1.11423 q^{52} -8.11709 q^{53} +32.5268 q^{54} -18.0180 q^{55} -33.9614 q^{56} +13.1955 q^{57} +25.0441 q^{58} -5.93570 q^{59} +62.9399 q^{60} +1.74502 q^{61} +11.2963 q^{62} +27.5340 q^{63} +18.4151 q^{64} +0.836870 q^{65} +39.0559 q^{66} -9.55753 q^{67} -27.3350 q^{68} +10.7892 q^{69} +41.6267 q^{70} +13.3288 q^{71} -58.1849 q^{72} -12.5134 q^{73} +10.0358 q^{74} -31.5658 q^{75} -21.6954 q^{76} +18.6202 q^{77} -1.81400 q^{78} -11.1434 q^{79} -47.8940 q^{80} +17.5683 q^{81} +23.5336 q^{82} -1.13411 q^{83} -65.0435 q^{84} +20.5306 q^{85} +21.6088 q^{86} +29.3914 q^{87} -39.3482 q^{88} -3.97359 q^{89} +71.3176 q^{90} -0.864839 q^{91} -17.7390 q^{92} +13.2572 q^{93} +7.08597 q^{94} +16.2949 q^{95} +50.5907 q^{96} +13.8521 q^{97} -24.2808 q^{98} +31.9013 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 391 q + 14 q^{2} + 12 q^{3} + 446 q^{4} + 22 q^{5} + 40 q^{6} + 63 q^{7} + 36 q^{8} + 501 q^{9}+O(q^{10}) \) 391 * q + 14 * q^2 + 12 * q^3 + 446 * q^4 + 22 * q^5 + 40 * q^6 + 63 * q^7 + 36 * q^8 + 501 * q^9	\( 391 q + 14 q^{2} + 12 q^{3} + 446 q^{4} + 22 q^{5} + 40 q^{6} + 63 q^{7} + 36 q^{8} + 501 q^{9} + 40 q^{10} + 57 q^{11} + 20 q^{12} + 83 q^{13} + 21 q^{14} + 60 q^{15} + 548 q^{16} + 59 q^{17} + 54 q^{18} + 131 q^{19} + 35 q^{20} + 121 q^{21} + 89 q^{22} + 34 q^{23} + 110 q^{24} + 609 q^{25} + 54 q^{26} + 27 q^{27} + 182 q^{28} + 102 q^{29} + 92 q^{30} + 88 q^{31} + 76 q^{32} + 131 q^{33} + 128 q^{34} + 31 q^{35} + 654 q^{36} + 135 q^{37} + 23 q^{38} + 96 q^{39} + 113 q^{40} + 128 q^{41} + 45 q^{42} + 140 q^{43} + 151 q^{44} + 77 q^{45} + 245 q^{46} + 22 q^{47} + 25 q^{48} + 712 q^{49} + 53 q^{50} + 102 q^{51} + 174 q^{52} + 54 q^{53} + 131 q^{54} + 101 q^{55} + 43 q^{56} + 226 q^{57} + 109 q^{58} + 40 q^{59} + 123 q^{60} + 249 q^{61} + 28 q^{62} + 139 q^{63} + 730 q^{64} + 227 q^{65} + 55 q^{66} + 169 q^{67} + 48 q^{68} + 89 q^{69} + 98 q^{70} + 66 q^{71} + 120 q^{72} + 324 q^{73} + 60 q^{74} + 19 q^{75} + 356 q^{76} + 83 q^{77} - 11 q^{78} + 195 q^{79} + 26 q^{80} + 807 q^{81} + 49 q^{82} + 74 q^{83} + 252 q^{84} + 373 q^{85} + 100 q^{86} + 43 q^{87} + 211 q^{88} + 207 q^{89} + 10 q^{90} + 189 q^{91} + 30 q^{92} + 172 q^{93} + 130 q^{94} + 43 q^{95} + 203 q^{96} + 254 q^{97} + 26 q^{98} + 273 q^{99}+O(q^{100}) \) 391 * q + 14 * q^2 + 12 * q^3 + 446 * q^4 + 22 * q^5 + 40 * q^6 + 63 * q^7 + 36 * q^8 + 501 * q^9 + 40 * q^10 + 57 * q^11 + 20 * q^12 + 83 * q^13 + 21 * q^14 + 60 * q^15 + 548 * q^16 + 59 * q^17 + 54 * q^18 + 131 * q^19 + 35 * q^20 + 121 * q^21 + 89 * q^22 + 34 * q^23 + 110 * q^24 + 609 * q^25 + 54 * q^26 + 27 * q^27 + 182 * q^28 + 102 * q^29 + 92 * q^30 + 88 * q^31 + 76 * q^32 + 131 * q^33 + 128 * q^34 + 31 * q^35 + 654 * q^36 + 135 * q^37 + 23 * q^38 + 96 * q^39 + 113 * q^40 + 128 * q^41 + 45 * q^42 + 140 * q^43 + 151 * q^44 + 77 * q^45 + 245 * q^46 + 22 * q^47 + 25 * q^48 + 712 * q^49 + 53 * q^50 + 102 * q^51 + 174 * q^52 + 54 * q^53 + 131 * q^54 + 101 * q^55 + 43 * q^56 + 226 * q^57 + 109 * q^58 + 40 * q^59 + 123 * q^60 + 249 * q^61 + 28 * q^62 + 139 * q^63 + 730 * q^64 + 227 * q^65 + 55 * q^66 + 169 * q^67 + 48 * q^68 + 89 * q^69 + 98 * q^70 + 66 * q^71 + 120 * q^72 + 324 * q^73 + 60 * q^74 + 19 * q^75 + 356 * q^76 + 83 * q^77 - 11 * q^78 + 195 * q^79 + 26 * q^80 + 807 * q^81 + 49 * q^82 + 74 * q^83 + 252 * q^84 + 373 * q^85 + 100 * q^86 + 43 * q^87 + 211 * q^88 + 207 * q^89 + 10 * q^90 + 189 * q^91 + 30 * q^92 + 172 * q^93 + 130 * q^94 + 43 * q^95 + 203 * q^96 + 254 * q^97 + 26 * q^98 + 273 * q^99

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