LMFDB - Embedded newform 4034.2.a.c.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, 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("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.2116521754$
Analytic rank:	$0$
Dimension:	$49$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.96102 q^{3} +1.00000 q^{4} +1.55397 q^{5} +1.96102 q^{6} -2.12307 q^{7} -1.00000 q^{8} +0.845608 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.96102 q^{3} +1.00000 q^{4} +1.55397 q^{5} +1.96102 q^{6} -2.12307 q^{7} -1.00000 q^{8} +0.845608 q^{9} -1.55397 q^{10} +3.46300 q^{11} -1.96102 q^{12} +3.94806 q^{13} +2.12307 q^{14} -3.04736 q^{15} +1.00000 q^{16} +6.42619 q^{17} -0.845608 q^{18} +2.45290 q^{19} +1.55397 q^{20} +4.16339 q^{21} -3.46300 q^{22} +8.71925 q^{23} +1.96102 q^{24} -2.58519 q^{25} -3.94806 q^{26} +4.22481 q^{27} -2.12307 q^{28} +0.0411628 q^{29} +3.04736 q^{30} +2.72901 q^{31} -1.00000 q^{32} -6.79101 q^{33} -6.42619 q^{34} -3.29918 q^{35} +0.845608 q^{36} -0.677673 q^{37} -2.45290 q^{38} -7.74223 q^{39} -1.55397 q^{40} -1.96279 q^{41} -4.16339 q^{42} +1.87281 q^{43} +3.46300 q^{44} +1.31405 q^{45} -8.71925 q^{46} -3.79326 q^{47} -1.96102 q^{48} -2.49257 q^{49} +2.58519 q^{50} -12.6019 q^{51} +3.94806 q^{52} -4.51482 q^{53} -4.22481 q^{54} +5.38138 q^{55} +2.12307 q^{56} -4.81018 q^{57} -0.0411628 q^{58} +3.27787 q^{59} -3.04736 q^{60} -5.93767 q^{61} -2.72901 q^{62} -1.79528 q^{63} +1.00000 q^{64} +6.13515 q^{65} +6.79101 q^{66} -4.52151 q^{67} +6.42619 q^{68} -17.0986 q^{69} +3.29918 q^{70} +13.5976 q^{71} -0.845608 q^{72} -3.46683 q^{73} +0.677673 q^{74} +5.06961 q^{75} +2.45290 q^{76} -7.35219 q^{77} +7.74223 q^{78} +12.1934 q^{79} +1.55397 q^{80} -10.8218 q^{81} +1.96279 q^{82} +7.79528 q^{83} +4.16339 q^{84} +9.98609 q^{85} -1.87281 q^{86} -0.0807212 q^{87} -3.46300 q^{88} +10.1439 q^{89} -1.31405 q^{90} -8.38201 q^{91} +8.71925 q^{92} -5.35166 q^{93} +3.79326 q^{94} +3.81172 q^{95} +1.96102 q^{96} -2.89886 q^{97} +2.49257 q^{98} +2.92834 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9}+O(q^{10}) $ 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9} + 8 q^{10} + q^{11} + 8 q^{12} + 9 q^{13} - 18 q^{14} + 15 q^{15} + 49 q^{16} - 27 q^{17} - 59 q^{18} + 27 q^{19} - 8 q^{20} + 13 q^{21} - q^{22} + 16 q^{23} - 8 q^{24} + 71 q^{25} - 9 q^{26} + 29 q^{27} + 18 q^{28} - 7 q^{29} - 15 q^{30} + 75 q^{31} - 49 q^{32} - 3 q^{33} + 27 q^{34} - 16 q^{35} + 59 q^{36} + 36 q^{37} - 27 q^{38} + 24 q^{39} + 8 q^{40} - 12 q^{41} - 13 q^{42} + 22 q^{43} + q^{44} + 5 q^{45} - 16 q^{46} + 26 q^{47} + 8 q^{48} + 107 q^{49} - 71 q^{50} + 35 q^{51} + 9 q^{52} - 10 q^{53} - 29 q^{54} + 76 q^{55} - 18 q^{56} - 10 q^{57} + 7 q^{58} + 9 q^{59} + 15 q^{60} + 87 q^{61} - 75 q^{62} + 68 q^{63} + 49 q^{64} - 6 q^{65} + 3 q^{66} + 46 q^{67} - 27 q^{68} + 70 q^{69} + 16 q^{70} + 40 q^{71} - 59 q^{72} + 6 q^{73} - 36 q^{74} + 69 q^{75} + 27 q^{76} - 12 q^{77} - 24 q^{78} + 76 q^{79} - 8 q^{80} + 77 q^{81} + 12 q^{82} - 32 q^{83} + 13 q^{84} + 19 q^{85} - 22 q^{86} + 36 q^{87} - q^{88} + 34 q^{89} - 5 q^{90} + 119 q^{91} + 16 q^{92} - 5 q^{93} - 26 q^{94} - 2 q^{95} - 8 q^{96} + 52 q^{97} - 107 q^{98} + 26 q^{99}+O(q^{100}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9 + 8 * q^10 + q^11 + 8 * q^12 + 9 * q^13 - 18 * q^14 + 15 * q^15 + 49 * q^16 - 27 * q^17 - 59 * q^18 + 27 * q^19 - 8 * q^20 + 13 * q^21 - q^22 + 16 * q^23 - 8 * q^24 + 71 * q^25 - 9 * q^26 + 29 * q^27 + 18 * q^28 - 7 * q^29 - 15 * q^30 + 75 * q^31 - 49 * q^32 - 3 * q^33 + 27 * q^34 - 16 * q^35 + 59 * q^36 + 36 * q^37 - 27 * q^38 + 24 * q^39 + 8 * q^40 - 12 * q^41 - 13 * q^42 + 22 * q^43 + q^44 + 5 * q^45 - 16 * q^46 + 26 * q^47 + 8 * q^48 + 107 * q^49 - 71 * q^50 + 35 * q^51 + 9 * q^52 - 10 * q^53 - 29 * q^54 + 76 * q^55 - 18 * q^56 - 10 * q^57 + 7 * q^58 + 9 * q^59 + 15 * q^60 + 87 * q^61 - 75 * q^62 + 68 * q^63 + 49 * q^64 - 6 * q^65 + 3 * q^66 + 46 * q^67 - 27 * q^68 + 70 * q^69 + 16 * q^70 + 40 * q^71 - 59 * q^72 + 6 * q^73 - 36 * q^74 + 69 * q^75 + 27 * q^76 - 12 * q^77 - 24 * q^78 + 76 * q^79 - 8 * q^80 + 77 * q^81 + 12 * q^82 - 32 * q^83 + 13 * q^84 + 19 * q^85 - 22 * q^86 + 36 * q^87 - q^88 + 34 * q^89 - 5 * q^90 + 119 * q^91 + 16 * q^92 - 5 * q^93 - 26 * q^94 - 2 * q^95 - 8 * q^96 + 52 * q^97 - 107 * q^98 + 26 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.96102	−1.13220	−0.566098	−	0.824338i	$-0.691548\pi$
$3$	−1.96102	−1.13220	−0.566098	+	0.824338i	$0.691548\pi$
$4$	1.00000	0.500000
$5$	1.55397	0.694955	0.347478	−	0.937688i	$-0.387038\pi$
$5$	1.55397	0.694955	0.347478	+	0.937688i	$0.387038\pi$
$6$	1.96102	0.800584
$7$	−2.12307	−0.802445	−0.401223	−	0.915981i	$-0.631415\pi$
$7$	−2.12307	−0.802445	−0.401223	+	0.915981i	$0.631415\pi$
$8$	−1.00000	−0.353553
$9$	0.845608	0.281869
$10$	−1.55397	−0.491407
$11$	3.46300	1.04413	0.522066	−	0.852905i	$-0.325161\pi$
$11$	3.46300	1.04413	0.522066	+	0.852905i	$0.325161\pi$
$12$	−1.96102	−0.566098
$13$	3.94806	1.09499	0.547497	−	0.836807i	$-0.315581\pi$
$13$	3.94806	1.09499	0.547497	+	0.836807i	$0.315581\pi$
$14$	2.12307	0.567414
$15$	−3.04736	−0.786826
$16$	1.00000	0.250000
$17$	6.42619	1.55858	0.779290	−	0.626664i	$-0.215580\pi$
$17$	6.42619	1.55858	0.779290	+	0.626664i	$0.215580\pi$
$18$	−0.845608	−0.199312
$19$	2.45290	0.562733	0.281367	−	0.959600i	$-0.409212\pi$
$19$	2.45290	0.562733	0.281367	+	0.959600i	$0.409212\pi$
$20$	1.55397	0.347478
$21$	4.16339	0.908526
$22$	−3.46300	−0.738314
$23$	8.71925	1.81809	0.909045	−	0.416698i	$-0.136813\pi$
$23$	8.71925	1.81809	0.909045	+	0.416698i	$0.136813\pi$
$24$	1.96102	0.400292
$25$	−2.58519	−0.517037
$26$	−3.94806	−0.774278
$27$	4.22481	0.813065
$28$	−2.12307	−0.401223
$29$	0.0411628	0.00764374	0.00382187	−	0.999993i	$-0.498783\pi$
$29$	0.0411628	0.00764374	0.00382187	+	0.999993i	$0.498783\pi$
$30$	3.04736	0.556370
$31$	2.72901	0.490145	0.245073	−	0.969505i	$-0.421188\pi$
$31$	2.72901	0.490145	0.245073	+	0.969505i	$0.421188\pi$
$32$	−1.00000	−0.176777
$33$	−6.79101	−1.18216
$34$	−6.42619	−1.10208
$35$	−3.29918	−0.557663
$36$	0.845608	0.140935
$37$	−0.677673	−0.111409	−0.0557044	−	0.998447i	$-0.517740\pi$
$37$	−0.677673	−0.111409	−0.0557044	+	0.998447i	$0.517740\pi$
$38$	−2.45290	−0.397912
$39$	−7.74223	−1.23975
$40$	−1.55397	−0.245704
$41$	−1.96279	−0.306537	−0.153268	−	0.988185i	$-0.548980\pi$
$41$	−1.96279	−0.306537	−0.153268	+	0.988185i	$0.548980\pi$
$42$	−4.16339	−0.642425
$43$	1.87281	0.285601	0.142801	−	0.989751i	$-0.454389\pi$
$43$	1.87281	0.285601	0.142801	+	0.989751i	$0.454389\pi$
$44$	3.46300	0.522066
$45$	1.31405	0.195886
$46$	−8.71925	−1.28558
$47$	−3.79326	−0.553303	−0.276652	−	0.960970i	$-0.589225\pi$
$47$	−3.79326	−0.553303	−0.276652	+	0.960970i	$0.589225\pi$
$48$	−1.96102	−0.283049
$49$	−2.49257	−0.356082
$50$	2.58519	0.365601
$51$	−12.6019	−1.76462
$52$	3.94806	0.547497
$53$	−4.51482	−0.620158	−0.310079	−	0.950711i	$-0.600356\pi$
$53$	−4.51482	−0.620158	−0.310079	+	0.950711i	$0.600356\pi$
$54$	−4.22481	−0.574924
$55$	5.38138	0.725626
$56$	2.12307	0.283707
$57$	−4.81018	−0.637125
$58$	−0.0411628	−0.00540494
$59$	3.27787	0.426742	0.213371	−	0.976971i	$-0.431556\pi$
$59$	3.27787	0.426742	0.213371	+	0.976971i	$0.431556\pi$
$60$	−3.04736	−0.393413
$61$	−5.93767	−0.760241	−0.380121	−	0.924937i	$-0.624118\pi$
$61$	−5.93767	−0.760241	−0.380121	+	0.924937i	$0.624118\pi$
$62$	−2.72901	−0.346585
$63$	−1.79528	−0.226185
$64$	1.00000	0.125000
$65$	6.13515	0.760972
$66$	6.79101	0.835916
$67$	−4.52151	−0.552391	−0.276195	−	0.961102i	$-0.589074\pi$
$67$	−4.52151	−0.552391	−0.276195	+	0.961102i	$0.589074\pi$
$68$	6.42619	0.779290
$69$	−17.0986	−2.05844
$70$	3.29918	0.394328
$71$	13.5976	1.61374	0.806868	−	0.590732i	$-0.201161\pi$
$71$	13.5976	1.61374	0.806868	+	0.590732i	$0.201161\pi$
$72$	−0.845608	−0.0996558
$73$	−3.46683	−0.405762	−0.202881	−	0.979203i	$-0.565030\pi$
$73$	−3.46683	−0.405762	−0.202881	+	0.979203i	$0.565030\pi$
$74$	0.677673	0.0787779
$75$	5.06961	0.585388
$76$	2.45290	0.281367
$77$	−7.35219	−0.837859
$78$	7.74223	0.876635
$79$	12.1934	1.37186	0.685932	−	0.727666i	$-0.259395\pi$
$79$	12.1934	1.37186	0.685932	+	0.727666i	$0.259395\pi$
$80$	1.55397	0.173739
$81$	−10.8218	−1.20242
$82$	1.96279	0.216754
$83$	7.79528	0.855643	0.427822	−	0.903863i	$-0.359281\pi$
$83$	7.79528	0.855643	0.427822	+	0.903863i	$0.359281\pi$
$84$	4.16339	0.454263
$85$	9.98609	1.08314
$86$	−1.87281	−0.201950
$87$	−0.0807212	−0.00865422
$88$	−3.46300	−0.369157
$89$	10.1439	1.07526	0.537628	−	0.843182i	$-0.319321\pi$
$89$	10.1439	1.07526	0.537628	+	0.843182i	$0.319321\pi$
$90$	−1.31405	−0.138513
$91$	−8.38201	−0.878673
$92$	8.71925	0.909045
$93$	−5.35166	−0.554941
$94$	3.79326	0.391244
$95$	3.81172	0.391074
$96$	1.96102	0.200146
$97$	−2.89886	−0.294334	−0.147167	−	0.989112i	$-0.547016\pi$
$97$	−2.89886	−0.294334	−0.147167	+	0.989112i	$0.547016\pi$
$98$	2.49257	0.251788
$99$	2.92834	0.294309
$100$	−2.58519	−0.258519
$101$	−7.01462	−0.697981	−0.348991	−	0.937126i	$-0.613475\pi$
$101$	−7.01462	−0.697981	−0.348991	+	0.937126i	$0.613475\pi$
$102$	12.6019	1.24777
$103$	−7.80167	−0.768722	−0.384361	−	0.923183i	$-0.625578\pi$
$103$	−7.80167	−0.768722	−0.384361	+	0.923183i	$0.625578\pi$
$104$	−3.94806	−0.387139
$105$	6.46977	0.631385
$106$	4.51482	0.438518
$107$	2.17657	0.210417	0.105208	−	0.994450i	$-0.466449\pi$
$107$	2.17657	0.210417	0.105208	+	0.994450i	$0.466449\pi$
$108$	4.22481	0.406533
$109$	6.45838	0.618600	0.309300	−	0.950964i	$-0.399905\pi$
$109$	6.45838	0.618600	0.309300	+	0.950964i	$0.399905\pi$
$110$	−5.38138	−0.513095
$111$	1.32893	0.126137
$112$	−2.12307	−0.200611
$113$	−19.8459	−1.86694	−0.933472	−	0.358651i	$-0.883237\pi$
$113$	−19.8459	−1.86694	−0.933472	+	0.358651i	$0.883237\pi$
$114$	4.81018	0.450515
$115$	13.5494	1.26349
$116$	0.0411628	0.00382187
$117$	3.33851	0.308645
$118$	−3.27787	−0.301752
$119$	−13.6433	−1.25067
$120$	3.04736	0.278185
$121$	0.992350	0.0902137
$122$	5.93767	0.537572
$123$	3.84908	0.347060
$124$	2.72901	0.245073
$125$	−11.7871	−1.05427
$126$	1.79528	0.159937
$127$	−6.01152	−0.533436	−0.266718	−	0.963775i	$-0.585939\pi$
$127$	−6.01152	−0.533436	−0.266718	+	0.963775i	$0.585939\pi$
$128$	−1.00000	−0.0883883
$129$	−3.67263	−0.323357
$130$	−6.13515	−0.538089
$131$	10.0782	0.880538	0.440269	−	0.897866i	$-0.354883\pi$
$131$	10.0782	0.880538	0.440269	+	0.897866i	$0.354883\pi$
$132$	−6.79101	−0.591082
$133$	−5.20767	−0.451562
$134$	4.52151	0.390599
$135$	6.56522	0.565044
$136$	−6.42619	−0.551041
$137$	16.7453	1.43065	0.715323	−	0.698794i	$-0.246279\pi$
$137$	16.7453	1.43065	0.715323	+	0.698794i	$0.246279\pi$
$138$	17.0986	1.45553
$139$	−5.81303	−0.493054	−0.246527	−	0.969136i	$-0.579289\pi$
$139$	−5.81303	−0.493054	−0.246527	+	0.969136i	$0.579289\pi$
$140$	−3.29918	−0.278832
$141$	7.43866	0.626448
$142$	−13.5976	−1.14108
$143$	13.6721	1.14332
$144$	0.845608	0.0704673
$145$	0.0639656	0.00531206
$146$	3.46683	0.286917
$147$	4.88799	0.403155
$148$	−0.677673	−0.0557044
$149$	4.52894	0.371025	0.185512	−	0.982642i	$-0.440606\pi$
$149$	4.52894	0.371025	0.185512	+	0.982642i	$0.440606\pi$
$150$	−5.06961	−0.413932
$151$	0.912821	0.0742843	0.0371421	−	0.999310i	$-0.488175\pi$
$151$	0.912821	0.0742843	0.0371421	+	0.999310i	$0.488175\pi$
$152$	−2.45290	−0.198956
$153$	5.43404	0.439316
$154$	7.35219	0.592456
$155$	4.24080	0.340629
$156$	−7.74223	−0.619875
$157$	1.94766	0.155440	0.0777202	−	0.996975i	$-0.475236\pi$
$157$	1.94766	0.155440	0.0777202	+	0.996975i	$0.475236\pi$
$158$	−12.1934	−0.970054
$159$	8.85366	0.702141
$160$	−1.55397	−0.122852
$161$	−18.5116	−1.45892
$162$	10.8218	0.850239
$163$	−6.92925	−0.542741	−0.271370	−	0.962475i	$-0.587477\pi$
$163$	−6.92925	−0.542741	−0.271370	+	0.962475i	$0.587477\pi$
$164$	−1.96279	−0.153268
$165$	−10.5530	−0.821551
$166$	−7.79528	−0.605031
$167$	−9.90821	−0.766720	−0.383360	−	0.923599i	$-0.625233\pi$
$167$	−9.90821	−0.766720	−0.383360	+	0.923599i	$0.625233\pi$
$168$	−4.16339	−0.321212
$169$	2.58717	0.199013
$170$	−9.98609	−0.765898
$171$	2.07419	0.158617
$172$	1.87281	0.142801
$173$	−13.8997	−1.05677	−0.528386	−	0.849004i	$-0.677203\pi$
$173$	−13.8997	−1.05677	−0.528386	+	0.849004i	$0.677203\pi$
$174$	0.0807212	0.00611945
$175$	5.48853	0.414894
$176$	3.46300	0.261033
$177$	−6.42798	−0.483156
$178$	−10.1439	−0.760321
$179$	24.6420	1.84183	0.920915	−	0.389763i	$-0.127443\pi$
$179$	24.6420	1.84183	0.920915	+	0.389763i	$0.127443\pi$
$180$	1.31405	0.0979432
$181$	4.47052	0.332291	0.166146	−	0.986101i	$-0.446868\pi$
$181$	4.47052	0.332291	0.166146	+	0.986101i	$0.446868\pi$
$182$	8.38201	0.621316
$183$	11.6439	0.860743
$184$	−8.71925	−0.642792
$185$	−1.05308	−0.0774241
$186$	5.35166	0.392402
$187$	22.2539	1.62736
$188$	−3.79326	−0.276652
$189$	−8.96957	−0.652440
$190$	−3.81172	−0.276531
$191$	−14.0226	−1.01464	−0.507319	−	0.861758i	$-0.669364\pi$
$191$	−14.0226	−1.01464	−0.507319	+	0.861758i	$0.669364\pi$
$192$	−1.96102	−0.141525
$193$	−15.1309	−1.08915	−0.544574	−	0.838713i	$-0.683308\pi$
$193$	−15.1309	−1.08915	−0.544574	+	0.838713i	$0.683308\pi$
$194$	2.89886	0.208126
$195$	−12.0312	−0.861570
$196$	−2.49257	−0.178041
$197$	8.15034	0.580688	0.290344	−	0.956922i	$-0.406230\pi$
$197$	8.15034	0.580688	0.290344	+	0.956922i	$0.406230\pi$
$198$	−2.92834	−0.208108
$199$	5.50227	0.390045	0.195023	−	0.980799i	$-0.437522\pi$
$199$	5.50227	0.390045	0.195023	+	0.980799i	$0.437522\pi$
$200$	2.58519	0.182800
$201$	8.86679	0.625415
$202$	7.01462	0.493547
$203$	−0.0873915	−0.00613368
$204$	−12.6019	−0.882309
$205$	−3.05012	−0.213029
$206$	7.80167	0.543568
$207$	7.37307	0.512464
$208$	3.94806	0.273749
$209$	8.49437	0.587568
$210$	−6.46977	−0.446456
$211$	12.1345	0.835370	0.417685	−	0.908592i	$-0.362841\pi$
$211$	12.1345	0.835370	0.417685	+	0.908592i	$0.362841\pi$
$212$	−4.51482	−0.310079
$213$	−26.6652	−1.82707
$214$	−2.17657	−0.148787
$215$	2.91029	0.198480
$216$	−4.22481	−0.287462
$217$	−5.79389	−0.393315
$218$	−6.45838	−0.437416
$219$	6.79853	0.459402
$220$	5.38138	0.362813
$221$	25.3710	1.70664
$222$	−1.32893	−0.0891921
$223$	−7.22115	−0.483564	−0.241782	−	0.970331i	$-0.577732\pi$
$223$	−7.22115	−0.483564	−0.241782	+	0.970331i	$0.577732\pi$
$224$	2.12307	0.141854
$225$	−2.18605	−0.145737
$226$	19.8459	1.32013
$227$	9.39590	0.623628	0.311814	−	0.950143i	$-0.399063\pi$
$227$	9.39590	0.623628	0.311814	+	0.950143i	$0.399063\pi$
$228$	−4.81018	−0.318562
$229$	22.5949	1.49311	0.746556	−	0.665323i	$-0.231706\pi$
$229$	22.5949	1.49311	0.746556	+	0.665323i	$0.231706\pi$
$230$	−13.5494	−0.893423
$231$	14.4178	0.948622
$232$	−0.0411628	−0.00270247
$233$	−7.25643	−0.475385	−0.237692	−	0.971340i	$-0.576391\pi$
$233$	−7.25643	−0.475385	−0.237692	+	0.971340i	$0.576391\pi$
$234$	−3.33851	−0.218245
$235$	−5.89459	−0.384521
$236$	3.27787	0.213371
$237$	−23.9115	−1.55322
$238$	13.6433	0.884361
$239$	−10.1843	−0.658767	−0.329383	−	0.944196i	$-0.606841\pi$
$239$	−10.1843	−0.658767	−0.329383	+	0.944196i	$0.606841\pi$
$240$	−3.04736	−0.196706
$241$	20.4590	1.31788	0.658939	−	0.752196i	$-0.271005\pi$
$241$	20.4590	1.31788	0.658939	+	0.752196i	$0.271005\pi$
$242$	−0.992350	−0.0637907
$243$	8.54730	0.548310
$244$	−5.93767	−0.380121
$245$	−3.87338	−0.247461
$246$	−3.84908	−0.245408
$247$	9.68418	0.616190
$248$	−2.72901	−0.173293
$249$	−15.2867	−0.968756
$250$	11.7871	0.745484
$251$	2.68731	0.169621	0.0848107	−	0.996397i	$-0.472971\pi$
$251$	2.68731	0.169621	0.0848107	+	0.996397i	$0.472971\pi$
$252$	−1.79528	−0.113092
$253$	30.1947	1.89833
$254$	6.01152	0.377196
$255$	−19.5829	−1.22633
$256$	1.00000	0.0625000
$257$	6.38204	0.398101	0.199050	−	0.979989i	$-0.436214\pi$
$257$	6.38204	0.398101	0.199050	+	0.979989i	$0.436214\pi$
$258$	3.67263	0.228648
$259$	1.43875	0.0893994
$260$	6.13515	0.380486
$261$	0.0348076	0.00215454
$262$	−10.0782	−0.622634
$263$	−0.117401	−0.00723924	−0.00361962	−	0.999993i	$-0.501152\pi$
$263$	−0.117401	−0.00723924	−0.00361962	+	0.999993i	$0.501152\pi$
$264$	6.79101	0.417958
$265$	−7.01588	−0.430982
$266$	5.20767	0.319303
$267$	−19.8925	−1.21740
$268$	−4.52151	−0.276195
$269$	−7.79121	−0.475038	−0.237519	−	0.971383i	$-0.576334\pi$
$269$	−7.79121	−0.475038	−0.237519	+	0.971383i	$0.576334\pi$
$270$	−6.56522	−0.399546
$271$	19.3862	1.17763	0.588813	−	0.808270i	$-0.299596\pi$
$271$	19.3862	1.17763	0.588813	+	0.808270i	$0.299596\pi$
$272$	6.42619	0.389645
$273$	16.4373	0.994831
$274$	−16.7453	−1.01162
$275$	−8.95250	−0.539856
$276$	−17.0986	−1.02922
$277$	23.8459	1.43276	0.716381	−	0.697709i	$-0.245797\pi$
$277$	23.8459	1.43276	0.716381	+	0.697709i	$0.245797\pi$
$278$	5.81303	0.348642
$279$	2.30768	0.138157
$280$	3.29918	0.197164
$281$	16.6509	0.993309	0.496654	−	0.867948i	$-0.334562\pi$
$281$	16.6509	0.993309	0.496654	+	0.867948i	$0.334562\pi$
$282$	−7.43866	−0.442966
$283$	7.61345	0.452573	0.226286	−	0.974061i	$-0.427341\pi$
$283$	7.61345	0.452573	0.226286	+	0.974061i	$0.427341\pi$
$284$	13.5976	0.806868
$285$	−7.47487	−0.442773
$286$	−13.6721	−0.808449
$287$	4.16715	0.245979
$288$	−0.845608	−0.0498279
$289$	24.2959	1.42917
$290$	−0.0639656	−0.00375619
$291$	5.68472	0.333244
$292$	−3.46683	−0.202881
$293$	9.78310	0.571535	0.285767	−	0.958299i	$-0.407752\pi$
$293$	9.78310	0.571535	0.285767	+	0.958299i	$0.407752\pi$
$294$	−4.88799	−0.285073
$295$	5.09370	0.296567
$296$	0.677673	0.0393890
$297$	14.6305	0.848948
$298$	−4.52894	−0.262354
$299$	34.4241	1.99080
$300$	5.06961	0.292694
$301$	−3.97611	−0.229179
$302$	−0.912821	−0.0525269
$303$	13.7558	0.790252
$304$	2.45290	0.140683
$305$	−9.22695	−0.528334
$306$	−5.43404	−0.310643
$307$	6.69232	0.381951	0.190975	−	0.981595i	$-0.438835\pi$
$307$	6.69232	0.381951	0.190975	+	0.981595i	$0.438835\pi$
$308$	−7.35219	−0.418930
$309$	15.2993	0.870344
$310$	−4.24080	−0.240861
$311$	−5.91699	−0.335522	−0.167761	−	0.985828i	$-0.553654\pi$
$311$	−5.91699	−0.335522	−0.167761	+	0.985828i	$0.553654\pi$
$312$	7.74223	0.438318
$313$	−28.2092	−1.59448	−0.797239	−	0.603664i	$-0.793707\pi$
$313$	−28.2092	−1.59448	−0.797239	+	0.603664i	$0.793707\pi$
$314$	−1.94766	−0.109913
$315$	−2.78981	−0.157188
$316$	12.1934	0.685932
$317$	−16.9584	−0.952481	−0.476241	−	0.879315i	$-0.658001\pi$
$317$	−16.9584	−0.952481	−0.476241	+	0.879315i	$0.658001\pi$
$318$	−8.85366	−0.496489
$319$	0.142547	0.00798108
$320$	1.55397	0.0868694
$321$	−4.26830	−0.238233
$322$	18.5116	1.03161
$323$	15.7628	0.877064
$324$	−10.8218	−0.601209
$325$	−10.2065	−0.566153
$326$	6.92925	0.383776
$327$	−12.6650	−0.700377
$328$	1.96279	0.108377
$329$	8.05335	0.443995
$330$	10.5530	0.580924
$331$	−15.6285	−0.859022	−0.429511	−	0.903062i	$-0.641314\pi$
$331$	−15.6285	−0.859022	−0.429511	+	0.903062i	$0.641314\pi$
$332$	7.79528	0.427822
$333$	−0.573046	−0.0314027
$334$	9.90821	0.542153
$335$	−7.02628	−0.383887
$336$	4.16339	0.227131
$337$	−12.8795	−0.701590	−0.350795	−	0.936452i	$-0.614089\pi$
$337$	−12.8795	−0.701590	−0.350795	+	0.936452i	$0.614089\pi$
$338$	−2.58717	−0.140724
$339$	38.9182	2.11375
$340$	9.98609	0.541572
$341$	9.45057	0.511777
$342$	−2.07419	−0.112159
$343$	20.1534	1.08818
$344$	−1.87281	−0.100975
$345$	−26.5707	−1.43052
$346$	13.8997	0.747251
$347$	−20.0957	−1.07879	−0.539396	−	0.842052i	$-0.681347\pi$
$347$	−20.0957	−1.07879	−0.539396	+	0.842052i	$0.681347\pi$
$348$	−0.0807212	−0.00432711
$349$	−35.2742	−1.88819	−0.944093	−	0.329679i	$-0.893059\pi$
$349$	−35.2742	−1.88819	−0.944093	+	0.329679i	$0.893059\pi$
$350$	−5.48853	−0.293374
$351$	16.6798	0.890302
$352$	−3.46300	−0.184578
$353$	−32.0841	−1.70767	−0.853833	−	0.520548i	$-0.825728\pi$
$353$	−32.0841	−1.70767	−0.853833	+	0.520548i	$0.825728\pi$
$354$	6.42798	0.341643
$355$	21.1302	1.12147
$356$	10.1439	0.537628
$357$	26.7547	1.41601
$358$	−24.6420	−1.30237
$359$	9.10995	0.480805	0.240402	−	0.970673i	$-0.422721\pi$
$359$	9.10995	0.480805	0.240402	+	0.970673i	$0.422721\pi$
$360$	−1.31405	−0.0692563
$361$	−12.9833	−0.683331
$362$	−4.47052	−0.234965
$363$	−1.94602	−0.102140
$364$	−8.38201	−0.439337
$365$	−5.38734	−0.281986
$366$	−11.6439	−0.608637
$367$	−1.99728	−0.104257	−0.0521285	−	0.998640i	$-0.516601\pi$
$367$	−1.99728	−0.104257	−0.0521285	+	0.998640i	$0.516601\pi$
$368$	8.71925	0.454522
$369$	−1.65975	−0.0864033
$370$	1.05308	0.0547471
$371$	9.58528	0.497643
$372$	−5.35166	−0.277470
$373$	30.1942	1.56340	0.781698	−	0.623657i	$-0.214354\pi$
$373$	30.1942	1.56340	0.781698	+	0.623657i	$0.214354\pi$
$374$	−22.2539	−1.15072
$375$	23.1148	1.19364
$376$	3.79326	0.195622
$377$	0.162513	0.00836985
$378$	8.96957	0.461345
$379$	24.1291	1.23943	0.619714	−	0.784828i	$-0.287249\pi$
$379$	24.1291	1.23943	0.619714	+	0.784828i	$0.287249\pi$
$380$	3.81172	0.195537
$381$	11.7887	0.603955
$382$	14.0226	0.717458
$383$	4.18229	0.213705	0.106852	−	0.994275i	$-0.465923\pi$
$383$	4.18229	0.213705	0.106852	+	0.994275i	$0.465923\pi$
$384$	1.96102	0.100073
$385$	−11.4251	−0.582275
$386$	15.1309	0.770143
$387$	1.58366	0.0805022
$388$	−2.89886	−0.147167
$389$	−6.95470	−0.352617	−0.176309	−	0.984335i	$-0.556416\pi$
$389$	−6.95470	−0.352617	−0.176309	+	0.984335i	$0.556416\pi$
$390$	12.0312	0.609222
$391$	56.0316	2.83364
$392$	2.49257	0.125894
$393$	−19.7636	−0.996942
$394$	−8.15034	−0.410608
$395$	18.9481	0.953384
$396$	2.92834	0.147155
$397$	8.61681	0.432465	0.216233	−	0.976342i	$-0.430623\pi$
$397$	8.61681	0.432465	0.216233	+	0.976342i	$0.430623\pi$
$398$	−5.50227	−0.275804
$399$	10.2124	0.511257
$400$	−2.58519	−0.129259
$401$	5.83499	0.291385	0.145693	−	0.989330i	$-0.453459\pi$
$401$	5.83499	0.291385	0.145693	+	0.989330i	$0.453459\pi$
$402$	−8.86679	−0.442235
$403$	10.7743	0.536706
$404$	−7.01462	−0.348991
$405$	−16.8167	−0.835627
$406$	0.0873915	0.00433717
$407$	−2.34678	−0.116326
$408$	12.6019	0.623887
$409$	9.20982	0.455396	0.227698	−	0.973732i	$-0.426880\pi$
$409$	9.20982	0.455396	0.227698	+	0.973732i	$0.426880\pi$
$410$	3.05012	0.150634
$411$	−32.8379	−1.61977
$412$	−7.80167	−0.384361
$413$	−6.95915	−0.342437
$414$	−7.37307	−0.362367
$415$	12.1136	0.594634
$416$	−3.94806	−0.193570
$417$	11.3995	0.558235
$418$	−8.49437	−0.415473
$419$	26.1433	1.27718	0.638592	−	0.769546i	$-0.279517\pi$
$419$	26.1433	1.27718	0.638592	+	0.769546i	$0.279517\pi$
$420$	6.46977	0.315692
$421$	28.2056	1.37466	0.687328	−	0.726347i	$-0.258783\pi$
$421$	28.2056	1.37466	0.687328	+	0.726347i	$0.258783\pi$
$422$	−12.1345	−0.590696
$423$	−3.20761	−0.155959
$424$	4.51482	0.219259
$425$	−16.6129	−0.805844
$426$	26.6652	1.29193
$427$	12.6061	0.610052
$428$	2.17657	0.105208
$429$	−26.8113	−1.29446
$430$	−2.91029	−0.140347
$431$	−33.6868	−1.62264	−0.811319	−	0.584604i	$-0.801250\pi$
$431$	−33.6868	−1.62264	−0.811319	+	0.584604i	$0.801250\pi$
$432$	4.22481	0.203266
$433$	−1.82984	−0.0879365	−0.0439683	−	0.999033i	$-0.514000\pi$
$433$	−1.82984	−0.0879365	−0.0439683	+	0.999033i	$0.514000\pi$
$434$	5.79389	0.278115
$435$	−0.125438	−0.00601429
$436$	6.45838	0.309300
$437$	21.3874	1.02310
$438$	−6.79853	−0.324846
$439$	−12.7105	−0.606641	−0.303320	−	0.952889i	$-0.598095\pi$
$439$	−12.7105	−0.606641	−0.303320	+	0.952889i	$0.598095\pi$
$440$	−5.38138	−0.256547
$441$	−2.10774	−0.100369
$442$	−25.3710	−1.20677
$443$	−15.9955	−0.759970	−0.379985	−	0.924993i	$-0.624071\pi$
$443$	−15.9955	−0.759970	−0.379985	+	0.924993i	$0.624071\pi$
$444$	1.32893	0.0630683
$445$	15.7633	0.747254
$446$	7.22115	0.341931
$447$	−8.88134	−0.420073
$448$	−2.12307	−0.100306
$449$	25.1918	1.18888	0.594438	−	0.804141i	$-0.297374\pi$
$449$	25.1918	1.18888	0.594438	+	0.804141i	$0.297374\pi$
$450$	2.18605	0.103052
$451$	−6.79715	−0.320065
$452$	−19.8459	−0.933472
$453$	−1.79006	−0.0841044
$454$	−9.39590	−0.440971
$455$	−13.0254	−0.610638
$456$	4.81018	0.225258
$457$	40.7140	1.90452	0.952261	−	0.305286i	$-0.0987519\pi$
$457$	40.7140	1.90452	0.952261	+	0.305286i	$0.0987519\pi$
$458$	−22.5949	−1.05579
$459$	27.1494	1.26723
$460$	13.5494	0.631745
$461$	30.7263	1.43106	0.715532	−	0.698580i	$-0.246184\pi$
$461$	30.7263	1.43106	0.715532	+	0.698580i	$0.246184\pi$
$462$	−14.4178	−0.670777
$463$	−9.23026	−0.428967	−0.214483	−	0.976728i	$-0.568807\pi$
$463$	−9.23026	−0.428967	−0.214483	+	0.976728i	$0.568807\pi$
$464$	0.0411628	0.00191093
$465$	−8.31630	−0.385659
$466$	7.25643	0.336148
$467$	8.53279	0.394850	0.197425	−	0.980318i	$-0.436742\pi$
$467$	8.53279	0.394850	0.197425	+	0.980318i	$0.436742\pi$
$468$	3.33851	0.154323
$469$	9.59949	0.443263
$470$	5.89459	0.271897
$471$	−3.81941	−0.175989
$472$	−3.27787	−0.150876
$473$	6.48554	0.298206
$474$	23.9115	1.09829
$475$	−6.34120	−0.290954
$476$	−13.6433	−0.625337
$477$	−3.81777	−0.174804
$478$	10.1843	0.465818
$479$	−32.5010	−1.48501	−0.742505	−	0.669840i	$-0.766363\pi$
$479$	−32.5010	−1.48501	−0.742505	+	0.669840i	$0.766363\pi$
$480$	3.04736	0.139092
$481$	−2.67549	−0.121992
$482$	−20.4590	−0.931881
$483$	36.3016	1.65178
$484$	0.992350	0.0451068
$485$	−4.50473	−0.204549
$486$	−8.54730	−0.387713
$487$	40.3462	1.82826	0.914131	−	0.405418i	$-0.132874\pi$
$487$	40.3462	1.82826	0.914131	+	0.405418i	$0.132874\pi$
$488$	5.93767	0.268786
$489$	13.5884	0.614489
$490$	3.87338	0.174981
$491$	16.3148	0.736277	0.368139	−	0.929771i	$-0.379995\pi$
$491$	16.3148	0.736277	0.368139	+	0.929771i	$0.379995\pi$
$492$	3.84908	0.173530
$493$	0.264520	0.0119134
$494$	−9.68418	−0.435712
$495$	4.55054	0.204532
$496$	2.72901	0.122536
$497$	−28.8686	−1.29493
$498$	15.2867	0.685014
$499$	9.91523	0.443867	0.221933	−	0.975062i	$-0.428763\pi$
$499$	9.91523	0.443867	0.221933	+	0.975062i	$0.428763\pi$
$500$	−11.7871	−0.527136
$501$	19.4302	0.868078
$502$	−2.68731	−0.119940
$503$	−11.7803	−0.525260	−0.262630	−	0.964897i	$-0.584590\pi$
$503$	−11.7803	−0.525260	−0.262630	+	0.964897i	$0.584590\pi$
$504$	1.79528	0.0799683
$505$	−10.9005	−0.485065
$506$	−30.1947	−1.34232
$507$	−5.07350	−0.225322
$508$	−6.01152	−0.266718
$509$	20.5176	0.909429	0.454714	−	0.890637i	$-0.349741\pi$
$509$	20.5176	0.909429	0.454714	+	0.890637i	$0.349741\pi$
$510$	19.5829	0.867147
$511$	7.36032	0.325602
$512$	−1.00000	−0.0441942
$513$	10.3630	0.457539
$514$	−6.38204	−0.281500
$515$	−12.1235	−0.534227
$516$	−3.67263	−0.161678
$517$	−13.1360	−0.577722
$518$	−1.43875	−0.0632150
$519$	27.2576	1.19647
$520$	−6.13515	−0.269044
$521$	−26.8045	−1.17433	−0.587164	−	0.809468i	$-0.699756\pi$
$521$	−26.8045	−1.17433	−0.587164	+	0.809468i	$0.699756\pi$
$522$	−0.0348076	−0.00152349
$523$	−5.48618	−0.239894	−0.119947	−	0.992780i	$-0.538272\pi$
$523$	−5.48618	−0.239894	−0.119947	+	0.992780i	$0.538272\pi$
$524$	10.0782	0.440269
$525$	−10.7631	−0.469742
$526$	0.117401	0.00511892
$527$	17.5372	0.763931
$528$	−6.79101	−0.295541
$529$	53.0254	2.30545
$530$	7.01588	0.304750
$531$	2.77179	0.120286
$532$	−5.20767	−0.225781
$533$	−7.74922	−0.335656
$534$	19.8925	0.860832
$535$	3.38231	0.146230
$536$	4.52151	0.195300
$537$	−48.3235	−2.08531
$538$	7.79121	0.335903
$539$	−8.63177	−0.371797
$540$	6.56522	0.282522
$541$	29.5914	1.27223	0.636117	−	0.771593i	$-0.280540\pi$
$541$	29.5914	1.27223	0.636117	+	0.771593i	$0.280540\pi$
$542$	−19.3862	−0.832707
$543$	−8.76679	−0.376219
$544$	−6.42619	−0.275521
$545$	10.0361	0.429899
$546$	−16.4373	−0.703452
$547$	−16.1028	−0.688504	−0.344252	−	0.938877i	$-0.611867\pi$
$547$	−16.1028	−0.688504	−0.344252	+	0.938877i	$0.611867\pi$
$548$	16.7453	0.715323
$549$	−5.02094	−0.214289
$550$	8.95250	0.381736
$551$	0.100968	0.00430138
$552$	17.0986	0.727767
$553$	−25.8874	−1.10085
$554$	−23.8459	−1.01312
$555$	2.06512	0.0876593
$556$	−5.81303	−0.246527
$557$	5.50877	0.233414	0.116707	−	0.993166i	$-0.462766\pi$
$557$	5.50877	0.233414	0.116707	+	0.993166i	$0.462766\pi$
$558$	−2.30768	−0.0976917
$559$	7.39397	0.312732
$560$	−3.29918	−0.139416
$561$	−43.6403	−1.84250
$562$	−16.6509	−0.702375
$563$	−12.1507	−0.512089	−0.256045	−	0.966665i	$-0.582419\pi$
$563$	−12.1507	−0.512089	−0.256045	+	0.966665i	$0.582419\pi$
$564$	7.43866	0.313224
$565$	−30.8398	−1.29744
$566$	−7.61345	−0.320017
$567$	22.9754	0.964875
$568$	−13.5976	−0.570542
$569$	−23.4439	−0.982821	−0.491411	−	0.870928i	$-0.663519\pi$
$569$	−23.4439	−0.982821	−0.491411	+	0.870928i	$0.663519\pi$
$570$	7.47487	0.313088
$571$	−6.40090	−0.267869	−0.133935	−	0.990990i	$-0.542761\pi$
$571$	−6.40090	−0.267869	−0.133935	+	0.990990i	$0.542761\pi$
$572$	13.6721	0.571660
$573$	27.4986	1.14877
$574$	−4.16715	−0.173933
$575$	−22.5409	−0.940020
$576$	0.845608	0.0352337
$577$	21.6554	0.901528	0.450764	−	0.892643i	$-0.351152\pi$
$577$	21.6554	0.901528	0.450764	+	0.892643i	$0.351152\pi$
$578$	−24.2959	−1.01058
$579$	29.6721	1.23313
$580$	0.0639656	0.00265603
$581$	−16.5499	−0.686607
$582$	−5.68472	−0.235639
$583$	−15.6348	−0.647528
$584$	3.46683	0.143458
$585$	5.18793	0.214495
$586$	−9.78310	−0.404136
$587$	−0.947979	−0.0391273	−0.0195636	−	0.999809i	$-0.506228\pi$
$587$	−0.947979	−0.0391273	−0.0195636	+	0.999809i	$0.506228\pi$
$588$	4.88799	0.201577
$589$	6.69399	0.275821
$590$	−5.09370	−0.209704
$591$	−15.9830	−0.657453
$592$	−0.677673	−0.0278522
$593$	31.7835	1.30519	0.652597	−	0.757706i	$-0.273680\pi$
$593$	31.7835	1.30519	0.652597	+	0.757706i	$0.273680\pi$
$594$	−14.6305	−0.600297
$595$	−21.2012	−0.869163
$596$	4.52894	0.185512
$597$	−10.7901	−0.441608
$598$	−34.4241	−1.40771
$599$	5.68430	0.232254	0.116127	−	0.993234i	$-0.462952\pi$
$599$	5.68430	0.232254	0.116127	+	0.993234i	$0.462952\pi$
$600$	−5.06961	−0.206966
$601$	40.7965	1.66412	0.832061	−	0.554684i	$-0.187161\pi$
$601$	40.7965	1.66412	0.832061	+	0.554684i	$0.187161\pi$
$602$	3.97611	0.162054
$603$	−3.82343	−0.155702
$604$	0.912821	0.0371421
$605$	1.54208	0.0626945
$606$	−13.7558	−0.558792
$607$	−10.3706	−0.420930	−0.210465	−	0.977601i	$-0.567498\pi$
$607$	−10.3706	−0.420930	−0.210465	+	0.977601i	$0.567498\pi$
$608$	−2.45290	−0.0994781
$609$	0.171377	0.00694453
$610$	9.22695	0.373588
$611$	−14.9760	−0.605864
$612$	5.43404	0.219658
$613$	8.21291	0.331716	0.165858	−	0.986150i	$-0.446961\pi$
$613$	8.21291	0.331716	0.165858	+	0.986150i	$0.446961\pi$
$614$	−6.69232	−0.270080
$615$	5.98134	0.241191
$616$	7.35219	0.296228
$617$	2.77979	0.111910	0.0559552	−	0.998433i	$-0.482180\pi$
$617$	2.77979	0.111910	0.0559552	+	0.998433i	$0.482180\pi$
$618$	−15.2993	−0.615426
$619$	3.45001	0.138668	0.0693338	−	0.997594i	$-0.477913\pi$
$619$	3.45001	0.138668	0.0693338	+	0.997594i	$0.477913\pi$
$620$	4.24080	0.170314
$621$	36.8372	1.47823
$622$	5.91699	0.237250
$623$	−21.5363	−0.862834
$624$	−7.74223	−0.309937
$625$	−5.39087	−0.215635
$626$	28.2092	1.12747
$627$	−16.6577	−0.665243
$628$	1.94766	0.0777202
$629$	−4.35486	−0.173640
$630$	2.78981	0.111149
$631$	4.47440	0.178123	0.0890615	−	0.996026i	$-0.471613\pi$
$631$	4.47440	0.178123	0.0890615	+	0.996026i	$0.471613\pi$
$632$	−12.1934	−0.485027
$633$	−23.7959	−0.945804
$634$	16.9584	0.673506
$635$	−9.34170	−0.370714
$636$	8.85366	0.351070
$637$	−9.84082	−0.389908
$638$	−0.142547	−0.00564348
$639$	11.4982	0.454863
$640$	−1.55397	−0.0614259
$641$	9.81012	0.387477	0.193738	−	0.981053i	$-0.437939\pi$
$641$	9.81012	0.387477	0.193738	+	0.981053i	$0.437939\pi$
$642$	4.26830	0.168456
$643$	−29.7881	−1.17473	−0.587363	−	0.809324i	$-0.699834\pi$
$643$	−29.7881	−1.17473	−0.587363	+	0.809324i	$0.699834\pi$
$644$	−18.5116	−0.729459
$645$	−5.70714	−0.224718
$646$	−15.7628	−0.620178
$647$	31.0641	1.22126	0.610628	−	0.791918i	$-0.290917\pi$
$647$	31.0641	1.22126	0.610628	+	0.791918i	$0.290917\pi$
$648$	10.8218	0.425119
$649$	11.3513	0.445576
$650$	10.2065	0.400331
$651$	11.3619	0.445310
$652$	−6.92925	−0.271370
$653$	0.972894	0.0380723	0.0190361	−	0.999819i	$-0.493940\pi$
$653$	0.972894	0.0380723	0.0190361	+	0.999819i	$0.493940\pi$
$654$	12.6650	0.495241
$655$	15.6612	0.611934
$656$	−1.96279	−0.0766342
$657$	−2.93158	−0.114372
$658$	−8.05335	−0.313952
$659$	−37.9400	−1.47793	−0.738966	−	0.673743i	$-0.764685\pi$
$659$	−37.9400	−1.47793	−0.738966	+	0.673743i	$0.764685\pi$
$660$	−10.5530	−0.410775
$661$	−16.2064	−0.630354	−0.315177	−	0.949033i	$-0.602064\pi$
$661$	−16.2064	−0.630354	−0.315177	+	0.949033i	$0.602064\pi$
$662$	15.6285	0.607420
$663$	−49.7530	−1.93225
$664$	−7.79528	−0.302516
$665$	−8.09255	−0.313816
$666$	0.573046	0.0222051
$667$	0.358909	0.0138970
$668$	−9.90821	−0.383360
$669$	14.1608	0.547489
$670$	7.02628	0.271449
$671$	−20.5622	−0.793793
$672$	−4.16339	−0.160606
$673$	−24.5478	−0.946249	−0.473125	−	0.880996i	$-0.656874\pi$
$673$	−24.5478	−0.946249	−0.473125	+	0.880996i	$0.656874\pi$
$674$	12.8795	0.496099
$675$	−10.9219	−0.420385
$676$	2.58717	0.0995066
$677$	−14.9808	−0.575761	−0.287880	−	0.957666i	$-0.592951\pi$
$677$	−14.9808	−0.575761	−0.287880	+	0.957666i	$0.592951\pi$
$678$	−38.9182	−1.49464
$679$	6.15448	0.236187
$680$	−9.98609	−0.382949
$681$	−18.4256	−0.706069
$682$	−9.45057	−0.361881
$683$	−39.2341	−1.50125	−0.750625	−	0.660728i	$-0.770248\pi$
$683$	−39.2341	−1.50125	−0.750625	+	0.660728i	$0.770248\pi$
$684$	2.07419	0.0793086
$685$	26.0216	0.994235
$686$	−20.1534	−0.769460
$687$	−44.3091	−1.69050
$688$	1.87281	0.0714003
$689$	−17.8248	−0.679070
$690$	26.5707	1.01153
$691$	21.0114	0.799310	0.399655	−	0.916666i	$-0.369130\pi$
$691$	21.0114	0.799310	0.399655	+	0.916666i	$0.369130\pi$
$692$	−13.8997	−0.528386
$693$	−6.21707	−0.236167
$694$	20.0957	0.762821
$695$	−9.03325	−0.342651
$696$	0.0807212	0.00305973
$697$	−12.6133	−0.477762
$698$	35.2742	1.33515
$699$	14.2300	0.538229
$700$	5.48853	0.207447
$701$	9.74035	0.367888	0.183944	−	0.982937i	$-0.441114\pi$
$701$	9.74035	0.367888	0.183944	+	0.982937i	$0.441114\pi$
$702$	−16.6798	−0.629539
$703$	−1.66226	−0.0626934
$704$	3.46300	0.130517
$705$	11.5594	0.435353
$706$	32.0841	1.20750
$707$	14.8925	0.560092
$708$	−6.42798	−0.241578
$709$	−51.7143	−1.94217	−0.971086	−	0.238732i	$-0.923268\pi$
$709$	−51.7143	−1.94217	−0.971086	+	0.238732i	$0.923268\pi$
$710$	−21.1302	−0.793002
$711$	10.3108	0.386686
$712$	−10.1439	−0.380160
$713$	23.7950	0.891128
$714$	−26.7547	−1.00127
$715$	21.2460	0.794556
$716$	24.6420	0.920915
$717$	19.9716	0.745854
$718$	−9.10995	−0.339980
$719$	9.34044	0.348340	0.174170	−	0.984716i	$-0.444276\pi$
$719$	9.34044	0.348340	0.174170	+	0.984716i	$0.444276\pi$
$720$	1.31405	0.0489716
$721$	16.5635	0.616857
$722$	12.9833	0.483188
$723$	−40.1205	−1.49210
$724$	4.47052	0.166146
$725$	−0.106414	−0.00395210
$726$	1.94602	0.0722236
$727$	−27.5494	−1.02175	−0.510876	−	0.859655i	$-0.670679\pi$
$727$	−27.5494	−1.02175	−0.510876	+	0.859655i	$0.670679\pi$
$728$	8.38201	0.310658
$729$	15.7039	0.581625
$730$	5.38734	0.199394
$731$	12.0350	0.445132
$732$	11.6439	0.430371
$733$	−47.9648	−1.77162	−0.885810	−	0.464048i	$-0.846396\pi$
$733$	−47.9648	−1.77162	−0.885810	+	0.464048i	$0.846396\pi$
$734$	1.99728	0.0737208
$735$	7.59577	0.280174
$736$	−8.71925	−0.321396
$737$	−15.6580	−0.576769
$738$	1.65975	0.0610964
$739$	−9.28673	−0.341618	−0.170809	−	0.985304i	$-0.554638\pi$
$739$	−9.28673	−0.341618	−0.170809	+	0.985304i	$0.554638\pi$
$740$	−1.05308	−0.0387121
$741$	−18.9909	−0.697648
$742$	−9.58528	−0.351887
$743$	−3.83821	−0.140810	−0.0704051	−	0.997518i	$-0.522429\pi$
$743$	−3.83821	−0.140810	−0.0704051	+	0.997518i	$0.522429\pi$
$744$	5.35166	0.196201
$745$	7.03782	0.257846
$746$	−30.1942	−1.10549
$747$	6.59175	0.241180
$748$	22.2539	0.813682
$749$	−4.62101	−0.168848
$750$	−23.1148	−0.844034
$751$	25.2535	0.921513	0.460756	−	0.887527i	$-0.347578\pi$
$751$	25.2535	0.921513	0.460756	+	0.887527i	$0.347578\pi$
$752$	−3.79326	−0.138326
$753$	−5.26987	−0.192045
$754$	−0.162513	−0.00591838
$755$	1.41849	0.0516242
$756$	−8.96957	−0.326220
$757$	−18.8988	−0.686887	−0.343443	−	0.939173i	$-0.611593\pi$
$757$	−18.8988	−0.686887	−0.343443	+	0.939173i	$0.611593\pi$
$758$	−24.1291	−0.876408
$759$	−59.2126	−2.14928
$760$	−3.81172	−0.138266
$761$	−40.0481	−1.45174	−0.725870	−	0.687831i	$-0.758563\pi$
$761$	−40.0481	−1.45174	−0.725870	+	0.687831i	$0.758563\pi$
$762$	−11.7887	−0.427060
$763$	−13.7116	−0.496393
$764$	−14.0226	−0.507319
$765$	8.44431	0.305305
$766$	−4.18229	−0.151112
$767$	12.9412	0.467281
$768$	−1.96102	−0.0707623
$769$	−1.42156	−0.0512628	−0.0256314	−	0.999671i	$-0.508160\pi$
$769$	−1.42156	−0.0512628	−0.0256314	+	0.999671i	$0.508160\pi$
$770$	11.4251	0.411730
$771$	−12.5153	−0.450729
$772$	−15.1309	−0.544574
$773$	−26.8188	−0.964607	−0.482303	−	0.876004i	$-0.660200\pi$
$773$	−26.8188	−0.964607	−0.482303	+	0.876004i	$0.660200\pi$
$774$	−1.58366	−0.0569236
$775$	−7.05501	−0.253423
$776$	2.89886	0.104063
$777$	−2.82142	−0.101218
$778$	6.95470	0.249338
$779$	−4.81453	−0.172498
$780$	−12.0312	−0.430785
$781$	47.0884	1.68496
$782$	−56.0316	−2.00368
$783$	0.173905	0.00621486
$784$	−2.49257	−0.0890204
$785$	3.02660	0.108024
$786$	19.7636	0.704945
$787$	−15.4101	−0.549311	−0.274655	−	0.961543i	$-0.588564\pi$
$787$	−15.4101	−0.549311	−0.274655	+	0.961543i	$0.588564\pi$
$788$	8.15034	0.290344
$789$	0.230226	0.00819625
$790$	−18.9481	−0.674144
$791$	42.1342	1.49812
$792$	−2.92834	−0.104054
$793$	−23.4423	−0.832460
$794$	−8.61681	−0.305799
$795$	13.7583	0.487956
$796$	5.50227	0.195023
$797$	−27.0053	−0.956578	−0.478289	−	0.878203i	$-0.658743\pi$
$797$	−27.0053	−0.956578	−0.478289	+	0.878203i	$0.658743\pi$
$798$	−10.2124	−0.361514
$799$	−24.3762	−0.862367
$800$	2.58519	0.0914002
$801$	8.57780	0.303082
$802$	−5.83499	−0.206041
$803$	−12.0056	−0.423669
$804$	8.86679	0.312707
$805$	−28.7664	−1.01388
$806$	−10.7743	−0.379509
$807$	15.2787	0.537837
$808$	7.01462	0.246774
$809$	−12.1615	−0.427575	−0.213788	−	0.976880i	$-0.568580\pi$
$809$	−12.1615	−0.427575	−0.213788	+	0.976880i	$0.568580\pi$
$810$	16.8167	0.590878
$811$	−15.3638	−0.539496	−0.269748	−	0.962931i	$-0.586940\pi$
$811$	−15.3638	−0.539496	−0.269748	+	0.962931i	$0.586940\pi$
$812$	−0.0873915	−0.00306684
$813$	−38.0167	−1.33330
$814$	2.34678	0.0822546
$815$	−10.7678	−0.377180
$816$	−12.6019	−0.441155
$817$	4.59381	0.160717
$818$	−9.20982	−0.322014
$819$	−7.08789	−0.247671
$820$	−3.05012	−0.106515
$821$	1.98961	0.0694379	0.0347190	−	0.999397i	$-0.488946\pi$
$821$	1.98961	0.0694379	0.0347190	+	0.999397i	$0.488946\pi$
$822$	32.8379	1.14535
$823$	34.7648	1.21183	0.605913	−	0.795531i	$-0.292808\pi$
$823$	34.7648	1.21183	0.605913	+	0.795531i	$0.292808\pi$
$824$	7.80167	0.271784
$825$	17.5560	0.611223
$826$	6.95915	0.242140
$827$	−26.5282	−0.922475	−0.461237	−	0.887277i	$-0.652594\pi$
$827$	−26.5282	−0.922475	−0.461237	+	0.887277i	$0.652594\pi$
$828$	7.37307	0.256232
$829$	16.5215	0.573816	0.286908	−	0.957958i	$-0.407373\pi$
$829$	16.5215	0.573816	0.286908	+	0.957958i	$0.407373\pi$
$830$	−12.1136	−0.420469
$831$	−46.7624	−1.62217
$832$	3.94806	0.136874
$833$	−16.0177	−0.554982
$834$	−11.3995	−0.394731
$835$	−15.3970	−0.532836
$836$	8.49437	0.293784
$837$	11.5296	0.398520
$838$	−26.1433	−0.903105
$839$	48.1119	1.66101	0.830503	−	0.557014i	$-0.188053\pi$
$839$	48.1119	1.66101	0.830503	+	0.557014i	$0.188053\pi$
$840$	−6.46977	−0.223228
$841$	−28.9983	−0.999942
$842$	−28.2056	−0.972029
$843$	−32.6528	−1.12462
$844$	12.1345	0.417685
$845$	4.02038	0.138305
$846$	3.20761	0.110280
$847$	−2.10683	−0.0723915
$848$	−4.51482	−0.155040
$849$	−14.9301	−0.512401
$850$	16.6129	0.569818
$851$	−5.90880	−0.202551
$852$	−26.6652	−0.913533
$853$	−51.7212	−1.77090	−0.885450	−	0.464735i	$-0.846150\pi$
$853$	−51.7212	−1.77090	−0.885450	+	0.464735i	$0.846150\pi$
$854$	−12.6061	−0.431372
$855$	3.22322	0.110232
$856$	−2.17657	−0.0743935
$857$	24.7099	0.844076	0.422038	−	0.906578i	$-0.361315\pi$
$857$	24.7099	0.844076	0.422038	+	0.906578i	$0.361315\pi$
$858$	26.8113	0.915324
$859$	−45.6979	−1.55919	−0.779596	−	0.626283i	$-0.784576\pi$
$859$	−45.6979	−1.55919	−0.779596	+	0.626283i	$0.784576\pi$
$860$	2.91029	0.0992400
$861$	−8.17187	−0.278497
$862$	33.6868	1.14738
$863$	12.6886	0.431926	0.215963	−	0.976402i	$-0.430711\pi$
$863$	12.6886	0.431926	0.215963	+	0.976402i	$0.430711\pi$
$864$	−4.22481	−0.143731
$865$	−21.5996	−0.734409
$866$	1.82984	0.0621805
$867$	−47.6448	−1.61810
$868$	−5.79389	−0.196657
$869$	42.2257	1.43241
$870$	0.125438	0.00425275
$871$	−17.8512	−0.604865
$872$	−6.45838	−0.218708
$873$	−2.45130	−0.0829638
$874$	−21.3874	−0.723440
$875$	25.0249	0.845996
$876$	6.79853	0.229701
$877$	24.7057	0.834252	0.417126	−	0.908849i	$-0.363037\pi$
$877$	24.7057	0.834252	0.417126	+	0.908849i	$0.363037\pi$
$878$	12.7105	0.428960
$879$	−19.1849	−0.647090
$880$	5.38138	0.181406
$881$	−28.8346	−0.971462	−0.485731	−	0.874108i	$-0.661447\pi$
$881$	−28.8346	−0.971462	−0.485731	+	0.874108i	$0.661447\pi$
$882$	2.10774	0.0709713
$883$	48.1119	1.61909	0.809547	−	0.587055i	$-0.199713\pi$
$883$	48.1119	1.61909	0.809547	+	0.587055i	$0.199713\pi$
$884$	25.3710	0.853318
$885$	−9.98886	−0.335772
$886$	15.9955	0.537380
$887$	−5.44749	−0.182909	−0.0914544	−	0.995809i	$-0.529152\pi$
$887$	−5.44749	−0.182909	−0.0914544	+	0.995809i	$0.529152\pi$
$888$	−1.32893	−0.0445960
$889$	12.7629	0.428053
$890$	−15.7633	−0.528389
$891$	−37.4758	−1.25549
$892$	−7.22115	−0.241782
$893$	−9.30446	−0.311362
$894$	8.88134	0.297037
$895$	38.2929	1.27999
$896$	2.12307	0.0709268
$897$	−67.5065	−2.25398
$898$	−25.1918	−0.840663
$899$	0.112334	0.00374654
$900$	−2.18605	−0.0728685
$901$	−29.0131	−0.966566
$902$	6.79715	0.226320
$903$	7.79724	0.259476
$904$	19.8459	0.660064
$905$	6.94704	0.230927
$906$	1.79006	0.0594708
$907$	−35.7893	−1.18836	−0.594182	−	0.804331i	$-0.702524\pi$
$907$	−35.7893	−1.18836	−0.594182	+	0.804331i	$0.702524\pi$
$908$	9.39590	0.311814
$909$	−5.93162	−0.196739
$910$	13.0254	0.431787
$911$	27.3380	0.905749	0.452875	−	0.891574i	$-0.350399\pi$
$911$	27.3380	0.905749	0.452875	+	0.891574i	$0.350399\pi$
$912$	−4.81018	−0.159281
$913$	26.9950	0.893405
$914$	−40.7140	−1.34670
$915$	18.0943	0.598178
$916$	22.5949	0.746556
$917$	−21.3968	−0.706583
$918$	−27.1494	−0.896065
$919$	32.0541	1.05737	0.528684	−	0.848818i	$-0.322686\pi$
$919$	32.0541	1.05737	0.528684	+	0.848818i	$0.322686\pi$
$920$	−13.5494	−0.446711
$921$	−13.1238	−0.432443
$922$	−30.7263	−1.01192
$923$	53.6841	1.76703
$924$	14.4178	0.474311
$925$	1.75191	0.0576025
$926$	9.23026	0.303325
$927$	−6.59716	−0.216679
$928$	−0.0411628	−0.00135123
$929$	−20.9136	−0.686154	−0.343077	−	0.939307i	$-0.611469\pi$
$929$	−20.9136	−0.686154	−0.343077	+	0.939307i	$0.611469\pi$
$930$	8.31630	0.272702
$931$	−6.11402	−0.200379
$932$	−7.25643	−0.237692
$933$	11.6033	0.379876
$934$	−8.53279	−0.279201
$935$	34.5818	1.13095
$936$	−3.33851	−0.109123
$937$	32.4072	1.05870	0.529349	−	0.848404i	$-0.322436\pi$
$937$	32.4072	1.05870	0.529349	+	0.848404i	$0.322436\pi$
$938$	−9.59949	−0.313434
$939$	55.3189	1.80526
$940$	−5.89459	−0.192260
$941$	−29.2531	−0.953623	−0.476811	−	0.879006i	$-0.658208\pi$
$941$	−29.2531	−0.953623	−0.476811	+	0.879006i	$0.658208\pi$
$942$	3.81941	0.124443
$943$	−17.1141	−0.557311
$944$	3.27787	0.106686
$945$	−13.9384	−0.453417
$946$	−6.48554	−0.210863
$947$	9.69549	0.315061	0.157531	−	0.987514i	$-0.449647\pi$
$947$	9.69549	0.315061	0.157531	+	0.987514i	$0.449647\pi$
$948$	−23.9115	−0.776610
$949$	−13.6872	−0.444307
$950$	6.34120	0.205736
$951$	33.2559	1.07840
$952$	13.6433	0.442180
$953$	−23.3175	−0.755327	−0.377664	−	0.925943i	$-0.623272\pi$
$953$	−23.3175	−0.755327	−0.377664	+	0.925943i	$0.623272\pi$
$954$	3.81777	0.123605
$955$	−21.7906	−0.705128
$956$	−10.1843	−0.329383
$957$	−0.279537	−0.00903615
$958$	32.5010	1.05006
$959$	−35.5514	−1.14802
$960$	−3.04736	−0.0983532
$961$	−23.5525	−0.759758
$962$	2.67549	0.0862614
$963$	1.84052	0.0593100
$964$	20.4590	0.658939
$965$	−23.5129	−0.756908
$966$	−36.3016	−1.16799
$967$	−19.8554	−0.638507	−0.319254	−	0.947669i	$-0.603432\pi$
$967$	−19.8554	−0.638507	−0.319254	+	0.947669i	$0.603432\pi$
$968$	−0.992350	−0.0318953
$969$	−30.9112	−0.993009
$970$	4.50473	0.144638
$971$	26.0014	0.834425	0.417212	−	0.908809i	$-0.363007\pi$
$971$	26.0014	0.834425	0.417212	+	0.908809i	$0.363007\pi$
$972$	8.54730	0.274155
$973$	12.3415	0.395649
$974$	−40.3462	−1.29278
$975$	20.0151	0.640997
$976$	−5.93767	−0.190060
$977$	44.3983	1.42043	0.710214	−	0.703986i	$-0.248598\pi$
$977$	44.3983	1.42043	0.710214	+	0.703986i	$0.248598\pi$
$978$	−13.5884	−0.434509
$979$	35.1284	1.12271
$980$	−3.87338	−0.123730
$981$	5.46125	0.174364
$982$	−16.3148	−0.520627
$983$	−16.6311	−0.530450	−0.265225	−	0.964187i	$-0.585446\pi$
$983$	−16.6311	−0.530450	−0.265225	+	0.964187i	$0.585446\pi$
$984$	−3.84908	−0.122704
$985$	12.6654	0.403552
$986$	−0.264520	−0.00842403
$987$	−15.7928	−0.502690
$988$	9.68418	0.308095
$989$	16.3295	0.519248
$990$	−4.55054	−0.144626
$991$	55.3037	1.75678	0.878389	−	0.477945i	$-0.158618\pi$
$991$	55.3037	1.75678	0.878389	+	0.477945i	$0.158618\pi$
$992$	−2.72901	−0.0866463
$993$	30.6479	0.972582
$994$	28.8686	0.915657
$995$	8.55034	0.271064
$996$	−15.2867	−0.484378
$997$	−15.0722	−0.477341	−0.238671	−	0.971101i	$-0.576712\pi$
$997$	−15.0722	−0.477341	−0.238671	+	0.971101i	$0.576712\pi$
$998$	−9.91523	−0.313861
$999$	−2.86304	−0.0905826

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.c.1.10	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.c.1.10	✓	49	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.96102 q^{3} +1.00000 q^{4} +1.55397 q^{5} +1.96102 q^{6} -2.12307 q^{7} -1.00000 q^{8} +0.845608 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.96102 q^{3} +1.00000 q^{4} +1.55397 q^{5} +1.96102 q^{6} -2.12307 q^{7} -1.00000 q^{8} +0.845608 q^{9} -1.55397 q^{10} +3.46300 q^{11} -1.96102 q^{12} +3.94806 q^{13} +2.12307 q^{14} -3.04736 q^{15} +1.00000 q^{16} +6.42619 q^{17} -0.845608 q^{18} +2.45290 q^{19} +1.55397 q^{20} +4.16339 q^{21} -3.46300 q^{22} +8.71925 q^{23} +1.96102 q^{24} -2.58519 q^{25} -3.94806 q^{26} +4.22481 q^{27} -2.12307 q^{28} +0.0411628 q^{29} +3.04736 q^{30} +2.72901 q^{31} -1.00000 q^{32} -6.79101 q^{33} -6.42619 q^{34} -3.29918 q^{35} +0.845608 q^{36} -0.677673 q^{37} -2.45290 q^{38} -7.74223 q^{39} -1.55397 q^{40} -1.96279 q^{41} -4.16339 q^{42} +1.87281 q^{43} +3.46300 q^{44} +1.31405 q^{45} -8.71925 q^{46} -3.79326 q^{47} -1.96102 q^{48} -2.49257 q^{49} +2.58519 q^{50} -12.6019 q^{51} +3.94806 q^{52} -4.51482 q^{53} -4.22481 q^{54} +5.38138 q^{55} +2.12307 q^{56} -4.81018 q^{57} -0.0411628 q^{58} +3.27787 q^{59} -3.04736 q^{60} -5.93767 q^{61} -2.72901 q^{62} -1.79528 q^{63} +1.00000 q^{64} +6.13515 q^{65} +6.79101 q^{66} -4.52151 q^{67} +6.42619 q^{68} -17.0986 q^{69} +3.29918 q^{70} +13.5976 q^{71} -0.845608 q^{72} -3.46683 q^{73} +0.677673 q^{74} +5.06961 q^{75} +2.45290 q^{76} -7.35219 q^{77} +7.74223 q^{78} +12.1934 q^{79} +1.55397 q^{80} -10.8218 q^{81} +1.96279 q^{82} +7.79528 q^{83} +4.16339 q^{84} +9.98609 q^{85} -1.87281 q^{86} -0.0807212 q^{87} -3.46300 q^{88} +10.1439 q^{89} -1.31405 q^{90} -8.38201 q^{91} +8.71925 q^{92} -5.35166 q^{93} +3.79326 q^{94} +3.81172 q^{95} +1.96102 q^{96} -2.89886 q^{97} +2.49257 q^{98} +2.92834 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9}+O(q^{10}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9} + 8 q^{10} + q^{11} + 8 q^{12} + 9 q^{13} - 18 q^{14} + 15 q^{15} + 49 q^{16} - 27 q^{17} - 59 q^{18} + 27 q^{19} - 8 q^{20} + 13 q^{21} - q^{22} + 16 q^{23} - 8 q^{24} + 71 q^{25} - 9 q^{26} + 29 q^{27} + 18 q^{28} - 7 q^{29} - 15 q^{30} + 75 q^{31} - 49 q^{32} - 3 q^{33} + 27 q^{34} - 16 q^{35} + 59 q^{36} + 36 q^{37} - 27 q^{38} + 24 q^{39} + 8 q^{40} - 12 q^{41} - 13 q^{42} + 22 q^{43} + q^{44} + 5 q^{45} - 16 q^{46} + 26 q^{47} + 8 q^{48} + 107 q^{49} - 71 q^{50} + 35 q^{51} + 9 q^{52} - 10 q^{53} - 29 q^{54} + 76 q^{55} - 18 q^{56} - 10 q^{57} + 7 q^{58} + 9 q^{59} + 15 q^{60} + 87 q^{61} - 75 q^{62} + 68 q^{63} + 49 q^{64} - 6 q^{65} + 3 q^{66} + 46 q^{67} - 27 q^{68} + 70 q^{69} + 16 q^{70} + 40 q^{71} - 59 q^{72} + 6 q^{73} - 36 q^{74} + 69 q^{75} + 27 q^{76} - 12 q^{77} - 24 q^{78} + 76 q^{79} - 8 q^{80} + 77 q^{81} + 12 q^{82} - 32 q^{83} + 13 q^{84} + 19 q^{85} - 22 q^{86} + 36 q^{87} - q^{88} + 34 q^{89} - 5 q^{90} + 119 q^{91} + 16 q^{92} - 5 q^{93} - 26 q^{94} - 2 q^{95} - 8 q^{96} + 52 q^{97} - 107 q^{98} + 26 q^{99}+O(q^{100}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9 + 8 * q^10 + q^11 + 8 * q^12 + 9 * q^13 - 18 * q^14 + 15 * q^15 + 49 * q^16 - 27 * q^17 - 59 * q^18 + 27 * q^19 - 8 * q^20 + 13 * q^21 - q^22 + 16 * q^23 - 8 * q^24 + 71 * q^25 - 9 * q^26 + 29 * q^27 + 18 * q^28 - 7 * q^29 - 15 * q^30 + 75 * q^31 - 49 * q^32 - 3 * q^33 + 27 * q^34 - 16 * q^35 + 59 * q^36 + 36 * q^37 - 27 * q^38 + 24 * q^39 + 8 * q^40 - 12 * q^41 - 13 * q^42 + 22 * q^43 + q^44 + 5 * q^45 - 16 * q^46 + 26 * q^47 + 8 * q^48 + 107 * q^49 - 71 * q^50 + 35 * q^51 + 9 * q^52 - 10 * q^53 - 29 * q^54 + 76 * q^55 - 18 * q^56 - 10 * q^57 + 7 * q^58 + 9 * q^59 + 15 * q^60 + 87 * q^61 - 75 * q^62 + 68 * q^63 + 49 * q^64 - 6 * q^65 + 3 * q^66 + 46 * q^67 - 27 * q^68 + 70 * q^69 + 16 * q^70 + 40 * q^71 - 59 * q^72 + 6 * q^73 - 36 * q^74 + 69 * q^75 + 27 * q^76 - 12 * q^77 - 24 * q^78 + 76 * q^79 - 8 * q^80 + 77 * q^81 + 12 * q^82 - 32 * q^83 + 13 * q^84 + 19 * q^85 - 22 * q^86 + 36 * q^87 - q^88 + 34 * q^89 - 5 * q^90 + 119 * q^91 + 16 * q^92 - 5 * q^93 - 26 * q^94 - 2 * q^95 - 8 * q^96 + 52 * q^97 - 107 * q^98 + 26 * q^99

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