LMFDB - Embedded newform 4034.2.a.c.1.17

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			1.17
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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.796272 q^{3} +1.00000 q^{4} -4.15767 q^{5} +0.796272 q^{6} +2.72658 q^{7} -1.00000 q^{8} -2.36595 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.796272 q^{3} +1.00000 q^{4} -4.15767 q^{5} +0.796272 q^{6} +2.72658 q^{7} -1.00000 q^{8} -2.36595 q^{9} +4.15767 q^{10} +1.04446 q^{11} -0.796272 q^{12} -4.91347 q^{13} -2.72658 q^{14} +3.31063 q^{15} +1.00000 q^{16} -5.30267 q^{17} +2.36595 q^{18} +5.52945 q^{19} -4.15767 q^{20} -2.17110 q^{21} -1.04446 q^{22} -4.24285 q^{23} +0.796272 q^{24} +12.2862 q^{25} +4.91347 q^{26} +4.27276 q^{27} +2.72658 q^{28} +0.0849704 q^{29} -3.31063 q^{30} -4.32000 q^{31} -1.00000 q^{32} -0.831677 q^{33} +5.30267 q^{34} -11.3362 q^{35} -2.36595 q^{36} -7.16359 q^{37} -5.52945 q^{38} +3.91246 q^{39} +4.15767 q^{40} -4.60832 q^{41} +2.17110 q^{42} -9.22942 q^{43} +1.04446 q^{44} +9.83684 q^{45} +4.24285 q^{46} -0.965307 q^{47} -0.796272 q^{48} +0.434261 q^{49} -12.2862 q^{50} +4.22237 q^{51} -4.91347 q^{52} -10.7612 q^{53} -4.27276 q^{54} -4.34254 q^{55} -2.72658 q^{56} -4.40295 q^{57} -0.0849704 q^{58} -4.49308 q^{59} +3.31063 q^{60} +10.2051 q^{61} +4.32000 q^{62} -6.45097 q^{63} +1.00000 q^{64} +20.4286 q^{65} +0.831677 q^{66} -6.24724 q^{67} -5.30267 q^{68} +3.37846 q^{69} +11.3362 q^{70} +15.4704 q^{71} +2.36595 q^{72} +10.2130 q^{73} +7.16359 q^{74} -9.78316 q^{75} +5.52945 q^{76} +2.84782 q^{77} -3.91246 q^{78} -15.4891 q^{79} -4.15767 q^{80} +3.69558 q^{81} +4.60832 q^{82} +1.10141 q^{83} -2.17110 q^{84} +22.0467 q^{85} +9.22942 q^{86} -0.0676595 q^{87} -1.04446 q^{88} -15.3407 q^{89} -9.83684 q^{90} -13.3970 q^{91} -4.24285 q^{92} +3.43990 q^{93} +0.965307 q^{94} -22.9896 q^{95} +0.796272 q^{96} +9.76359 q^{97} -0.434261 q^{98} -2.47115 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.796272	−0.459728	−0.229864	−	0.973223i	$-0.573828\pi$
$3$	−0.796272	−0.459728	−0.229864	+	0.973223i	$0.573828\pi$
$4$	1.00000	0.500000
$5$	−4.15767	−1.85937	−0.929683	−	0.368361i	$-0.879919\pi$
$5$	−4.15767	−1.85937	−0.929683	+	0.368361i	$0.879919\pi$
$6$	0.796272	0.325077
$7$	2.72658	1.03055	0.515276	−	0.857024i	$-0.327689\pi$
$7$	2.72658	1.03055	0.515276	+	0.857024i	$0.327689\pi$
$8$	−1.00000	−0.353553
$9$	−2.36595	−0.788650
$10$	4.15767	1.31477
$11$	1.04446	0.314918	0.157459	−	0.987526i	$-0.449670\pi$
$11$	1.04446	0.314918	0.157459	+	0.987526i	$0.449670\pi$
$12$	−0.796272	−0.229864
$13$	−4.91347	−1.36275	−0.681376	−	0.731934i	$-0.738618\pi$
$13$	−4.91347	−1.36275	−0.681376	+	0.731934i	$0.738618\pi$
$14$	−2.72658	−0.728710
$15$	3.31063	0.854802
$16$	1.00000	0.250000
$17$	−5.30267	−1.28609	−0.643043	−	0.765830i	$-0.722328\pi$
$17$	−5.30267	−1.28609	−0.643043	+	0.765830i	$0.722328\pi$
$18$	2.36595	0.557660
$19$	5.52945	1.26854	0.634272	−	0.773110i	$-0.281300\pi$
$19$	5.52945	1.26854	0.634272	+	0.773110i	$0.281300\pi$
$20$	−4.15767	−0.929683
$21$	−2.17110	−0.473773
$22$	−1.04446	−0.222680
$23$	−4.24285	−0.884696	−0.442348	−	0.896844i	$-0.645854\pi$
$23$	−4.24285	−0.884696	−0.442348	+	0.896844i	$0.645854\pi$
$24$	0.796272	0.162538
$25$	12.2862	2.45724
$26$	4.91347	0.963611
$27$	4.27276	0.822292
$28$	2.72658	0.515276
$29$	0.0849704	0.0157786	0.00788930	−	0.999969i	$-0.497489\pi$
$29$	0.0849704	0.0157786	0.00788930	+	0.999969i	$0.497489\pi$
$30$	−3.31063	−0.604436
$31$	−4.32000	−0.775895	−0.387948	−	0.921681i	$-0.626816\pi$
$31$	−4.32000	−0.775895	−0.387948	+	0.921681i	$0.626816\pi$
$32$	−1.00000	−0.176777
$33$	−0.831677	−0.144776
$34$	5.30267	0.909400
$35$	−11.3362	−1.91617
$36$	−2.36595	−0.394325
$37$	−7.16359	−1.17769	−0.588843	−	0.808247i	$-0.700416\pi$
$37$	−7.16359	−1.17769	−0.588843	+	0.808247i	$0.700416\pi$
$38$	−5.52945	−0.896996
$39$	3.91246	0.626495
$40$	4.15767	0.657385
$41$	−4.60832	−0.719699	−0.359850	−	0.933010i	$-0.617172\pi$
$41$	−4.60832	−0.719699	−0.359850	+	0.933010i	$0.617172\pi$
$42$	2.17110	0.335008
$43$	−9.22942	−1.40747	−0.703737	−	0.710461i	$-0.748487\pi$
$43$	−9.22942	−1.40747	−0.703737	+	0.710461i	$0.748487\pi$
$44$	1.04446	0.157459
$45$	9.83684	1.46639
$46$	4.24285	0.625574
$47$	−0.965307	−0.140804	−0.0704022	−	0.997519i	$-0.522428\pi$
$47$	−0.965307	−0.140804	−0.0704022	+	0.997519i	$0.522428\pi$
$48$	−0.796272	−0.114932
$49$	0.434261	0.0620374
$50$	−12.2862	−1.73753
$51$	4.22237	0.591249
$52$	−4.91347	−0.681376
$53$	−10.7612	−1.47817	−0.739084	−	0.673614i	$-0.764741\pi$
$53$	−10.7612	−1.47817	−0.739084	+	0.673614i	$0.764741\pi$
$54$	−4.27276	−0.581448
$55$	−4.34254	−0.585547
$56$	−2.72658	−0.364355
$57$	−4.40295	−0.583185
$58$	−0.0849704	−0.0111572
$59$	−4.49308	−0.584949	−0.292475	−	0.956273i	$-0.594479\pi$
$59$	−4.49308	−0.584949	−0.292475	+	0.956273i	$0.594479\pi$
$60$	3.31063	0.427401
$61$	10.2051	1.30663	0.653313	−	0.757088i	$-0.273379\pi$
$61$	10.2051	1.30663	0.653313	+	0.757088i	$0.273379\pi$
$62$	4.32000	0.548641
$63$	−6.45097	−0.812745
$64$	1.00000	0.125000
$65$	20.4286	2.53385
$66$	0.831677	0.102372
$67$	−6.24724	−0.763221	−0.381611	−	0.924323i	$-0.624630\pi$
$67$	−6.24724	−0.763221	−0.381611	+	0.924323i	$0.624630\pi$
$68$	−5.30267	−0.643043
$69$	3.37846	0.406719
$70$	11.3362	1.35494
$71$	15.4704	1.83600	0.918000	−	0.396580i	$-0.129803\pi$
$71$	15.4704	1.83600	0.918000	+	0.396580i	$0.129803\pi$
$72$	2.36595	0.278830
$73$	10.2130	1.19535	0.597674	−	0.801740i	$-0.296092\pi$
$73$	10.2130	1.19535	0.597674	+	0.801740i	$0.296092\pi$
$74$	7.16359	0.832750
$75$	−9.78316	−1.12966
$76$	5.52945	0.634272
$77$	2.84782	0.324539
$78$	−3.91246	−0.442999
$79$	−15.4891	−1.74266	−0.871332	−	0.490694i	$-0.836743\pi$
$79$	−15.4891	−1.74266	−0.871332	+	0.490694i	$0.836743\pi$
$80$	−4.15767	−0.464841
$81$	3.69558	0.410620
$82$	4.60832	0.508904
$83$	1.10141	0.120895	0.0604475	−	0.998171i	$-0.480747\pi$
$83$	1.10141	0.120895	0.0604475	+	0.998171i	$0.480747\pi$
$84$	−2.17110	−0.236887
$85$	22.0467	2.39130
$86$	9.22942	0.995234
$87$	−0.0676595	−0.00725386
$88$	−1.04446	−0.111340
$89$	−15.3407	−1.62611	−0.813055	−	0.582187i	$-0.802197\pi$
$89$	−15.3407	−1.62611	−0.813055	+	0.582187i	$0.802197\pi$
$90$	−9.83684	−1.03689
$91$	−13.3970	−1.40439
$92$	−4.24285	−0.442348
$93$	3.43990	0.356701
$94$	0.965307	0.0995638
$95$	−22.9896	−2.35869
$96$	0.796272	0.0812691
$97$	9.76359	0.991342	0.495671	−	0.868510i	$-0.334922\pi$
$97$	9.76359	0.991342	0.495671	+	0.868510i	$0.334922\pi$
$98$	−0.434261	−0.0438670
$99$	−2.47115	−0.248360
$100$	12.2862	1.22862
$101$	16.1462	1.60660	0.803302	−	0.595572i	$-0.203075\pi$
$101$	16.1462	1.60660	0.803302	+	0.595572i	$0.203075\pi$
$102$	−4.22237	−0.418076
$103$	−2.35415	−0.231961	−0.115980	−	0.993251i	$-0.537001\pi$
$103$	−2.35415	−0.231961	−0.115980	+	0.993251i	$0.537001\pi$
$104$	4.91347	0.481806
$105$	9.02672	0.880918
$106$	10.7612	1.04522
$107$	−9.22513	−0.891827	−0.445914	−	0.895076i	$-0.647121\pi$
$107$	−9.22513	−0.891827	−0.445914	+	0.895076i	$0.647121\pi$
$108$	4.27276	0.411146
$109$	12.8795	1.23363	0.616814	−	0.787109i	$-0.288423\pi$
$109$	12.8795	1.23363	0.616814	+	0.787109i	$0.288423\pi$
$110$	4.34254	0.414044
$111$	5.70416	0.541415
$112$	2.72658	0.257638
$113$	−9.12654	−0.858553	−0.429276	−	0.903173i	$-0.641231\pi$
$113$	−9.12654	−0.858553	−0.429276	+	0.903173i	$0.641231\pi$
$114$	4.40295	0.412374
$115$	17.6404	1.64497
$116$	0.0849704	0.00788930
$117$	11.6250	1.07473
$118$	4.49308	0.413622
$119$	−14.4582	−1.32538
$120$	−3.31063	−0.302218
$121$	−9.90909	−0.900827
$122$	−10.2051	−0.923924
$123$	3.66948	0.330866
$124$	−4.32000	−0.387948
$125$	−30.2936	−2.70954
$126$	6.45097	0.574698
$127$	−5.38474	−0.477818	−0.238909	−	0.971042i	$-0.576790\pi$
$127$	−5.38474	−0.477818	−0.238909	+	0.971042i	$0.576790\pi$
$128$	−1.00000	−0.0883883
$129$	7.34913	0.647055
$130$	−20.4286	−1.79171
$131$	−21.3740	−1.86746	−0.933729	−	0.357981i	$-0.883465\pi$
$131$	−21.3740	−1.86746	−0.933729	+	0.357981i	$0.883465\pi$
$132$	−0.831677	−0.0723882
$133$	15.0765	1.30730
$134$	6.24724	0.539679
$135$	−17.7647	−1.52894
$136$	5.30267	0.454700
$137$	2.77780	0.237324	0.118662	−	0.992935i	$-0.462140\pi$
$137$	2.77780	0.237324	0.118662	+	0.992935i	$0.462140\pi$
$138$	−3.37846	−0.287594
$139$	5.92830	0.502832	0.251416	−	0.967879i	$-0.419104\pi$
$139$	5.92830	0.502832	0.251416	+	0.967879i	$0.419104\pi$
$140$	−11.3362	−0.958087
$141$	0.768646	0.0647317
$142$	−15.4704	−1.29825
$143$	−5.13194	−0.429155
$144$	−2.36595	−0.197163
$145$	−0.353279	−0.0293382
$146$	−10.2130	−0.845238
$147$	−0.345790	−0.0285203
$148$	−7.16359	−0.588843
$149$	7.77413	0.636882	0.318441	−	0.947943i	$-0.396841\pi$
$149$	7.77413	0.636882	0.318441	+	0.947943i	$0.396841\pi$
$150$	9.78316	0.798791
$151$	13.7271	1.11710	0.558549	−	0.829471i	$-0.311358\pi$
$151$	13.7271	1.11710	0.558549	+	0.829471i	$0.311358\pi$
$152$	−5.52945	−0.448498
$153$	12.5459	1.01427
$154$	−2.84782	−0.229484
$155$	17.9611	1.44267
$156$	3.91246	0.313247
$157$	−19.9656	−1.59343	−0.796716	−	0.604354i	$-0.793431\pi$
$157$	−19.9656	−1.59343	−0.796716	+	0.604354i	$0.793431\pi$
$158$	15.4891	1.23225
$159$	8.56886	0.679554
$160$	4.15767	0.328693
$161$	−11.5685	−0.911725
$162$	−3.69558	−0.290352
$163$	2.07911	0.162848	0.0814242	−	0.996680i	$-0.474053\pi$
$163$	2.07911	0.162848	0.0814242	+	0.996680i	$0.474053\pi$
$164$	−4.60832	−0.359850
$165$	3.45784	0.269192
$166$	−1.10141	−0.0854857
$167$	20.4530	1.58270	0.791352	−	0.611361i	$-0.209378\pi$
$167$	20.4530	1.58270	0.791352	+	0.611361i	$0.209378\pi$
$168$	2.17110	0.167504
$169$	11.1422	0.857093
$170$	−22.0467	−1.69091
$171$	−13.0824	−1.00044
$172$	−9.22942	−0.703737
$173$	−12.7131	−0.966556	−0.483278	−	0.875467i	$-0.660554\pi$
$173$	−12.7131	−0.966556	−0.483278	+	0.875467i	$0.660554\pi$
$174$	0.0676595	0.00512925
$175$	33.4994	2.53231
$176$	1.04446	0.0787294
$177$	3.57771	0.268917
$178$	15.3407	1.14983
$179$	−11.5912	−0.866368	−0.433184	−	0.901306i	$-0.642610\pi$
$179$	−11.5912	−0.866368	−0.433184	+	0.901306i	$0.642610\pi$
$180$	9.83684	0.733195
$181$	23.0053	1.70997	0.854986	−	0.518651i	$-0.173566\pi$
$181$	23.0053	1.70997	0.854986	+	0.518651i	$0.173566\pi$
$182$	13.3970	0.993051
$183$	−8.12601	−0.600692
$184$	4.24285	0.312787
$185$	29.7838	2.18975
$186$	−3.43990	−0.252225
$187$	−5.53845	−0.405011
$188$	−0.965307	−0.0704022
$189$	11.6500	0.847415
$190$	22.9896	1.66784
$191$	16.8962	1.22256	0.611282	−	0.791413i	$-0.290654\pi$
$191$	16.8962	1.22256	0.611282	+	0.791413i	$0.290654\pi$
$192$	−0.796272	−0.0574660
$193$	3.44369	0.247882	0.123941	−	0.992290i	$-0.460447\pi$
$193$	3.44369	0.247882	0.123941	+	0.992290i	$0.460447\pi$
$194$	−9.76359	−0.700985
$195$	−16.2667	−1.16488
$196$	0.434261	0.0310187
$197$	−19.6027	−1.39664	−0.698318	−	0.715788i	$-0.746068\pi$
$197$	−19.6027	−1.39664	−0.698318	+	0.715788i	$0.746068\pi$
$198$	2.47115	0.175617
$199$	−4.42237	−0.313494	−0.156747	−	0.987639i	$-0.550101\pi$
$199$	−4.42237	−0.313494	−0.156747	+	0.987639i	$0.550101\pi$
$200$	−12.2862	−0.868766
$201$	4.97450	0.350874
$202$	−16.1462	−1.13604
$203$	0.231679	0.0162607
$204$	4.22237	0.295625
$205$	19.1599	1.33818
$206$	2.35415	0.164021
$207$	10.0384	0.697716
$208$	−4.91347	−0.340688
$209$	5.77532	0.399487
$210$	−9.02672	−0.622903
$211$	13.3215	0.917090	0.458545	−	0.888671i	$-0.348371\pi$
$211$	13.3215	0.917090	0.458545	+	0.888671i	$0.348371\pi$
$212$	−10.7612	−0.739084
$213$	−12.3187	−0.844060
$214$	9.22513	0.630617
$215$	38.3729	2.61701
$216$	−4.27276	−0.290724
$217$	−11.7789	−0.799600
$218$	−12.8795	−0.872307
$219$	−8.13236	−0.549534
$220$	−4.34254	−0.292774
$221$	26.0545	1.75262
$222$	−5.70416	−0.382838
$223$	19.1351	1.28138	0.640689	−	0.767800i	$-0.278649\pi$
$223$	19.1351	1.28138	0.640689	+	0.767800i	$0.278649\pi$
$224$	−2.72658	−0.182178
$225$	−29.0686	−1.93790
$226$	9.12654	0.607088
$227$	−4.22551	−0.280457	−0.140229	−	0.990119i	$-0.544784\pi$
$227$	−4.22551	−0.280457	−0.140229	+	0.990119i	$0.544784\pi$
$228$	−4.40295	−0.291592
$229$	−22.1198	−1.46172	−0.730859	−	0.682529i	$-0.760880\pi$
$229$	−22.1198	−1.46172	−0.730859	+	0.682529i	$0.760880\pi$
$230$	−17.6404	−1.16317
$231$	−2.26764	−0.149200
$232$	−0.0849704	−0.00557858
$233$	18.4305	1.20742	0.603711	−	0.797203i	$-0.293688\pi$
$233$	18.4305	1.20742	0.603711	+	0.797203i	$0.293688\pi$
$234$	−11.6250	−0.759952
$235$	4.01342	0.261807
$236$	−4.49308	−0.292475
$237$	12.3336	0.801151
$238$	14.4582	0.937184
$239$	12.8391	0.830495	0.415247	−	0.909709i	$-0.363695\pi$
$239$	12.8391	0.830495	0.415247	+	0.909709i	$0.363695\pi$
$240$	3.31063	0.213700
$241$	4.36970	0.281477	0.140739	−	0.990047i	$-0.455052\pi$
$241$	4.36970	0.281477	0.140739	+	0.990047i	$0.455052\pi$
$242$	9.90909	0.636981
$243$	−15.7610	−1.01107
$244$	10.2051	0.653313
$245$	−1.80552	−0.115350
$246$	−3.66948	−0.233957
$247$	−27.1688	−1.72871
$248$	4.32000	0.274320
$249$	−0.877019	−0.0555788
$250$	30.2936	1.91594
$251$	22.8214	1.44047	0.720236	−	0.693729i	$-0.244033\pi$
$251$	22.8214	1.44047	0.720236	+	0.693729i	$0.244033\pi$
$252$	−6.45097	−0.406373
$253$	−4.43151	−0.278606
$254$	5.38474	0.337869
$255$	−17.5552	−1.09935
$256$	1.00000	0.0625000
$257$	19.2461	1.20054	0.600269	−	0.799798i	$-0.295060\pi$
$257$	19.2461	1.20054	0.600269	+	0.799798i	$0.295060\pi$
$258$	−7.34913	−0.457537
$259$	−19.5321	−1.21367
$260$	20.4286	1.26693
$261$	−0.201036	−0.0124438
$262$	21.3740	1.32049
$263$	14.6674	0.904429	0.452214	−	0.891909i	$-0.350634\pi$
$263$	14.6674	0.904429	0.452214	+	0.891909i	$0.350634\pi$
$264$	0.831677	0.0511862
$265$	44.7416	2.74845
$266$	−15.0765	−0.924401
$267$	12.2154	0.747568
$268$	−6.24724	−0.381611
$269$	11.0432	0.673314	0.336657	−	0.941627i	$-0.390704\pi$
$269$	11.0432	0.673314	0.336657	+	0.941627i	$0.390704\pi$
$270$	17.7647	1.08113
$271$	27.4619	1.66819	0.834095	−	0.551620i	$-0.185990\pi$
$271$	27.4619	1.66819	0.834095	+	0.551620i	$0.185990\pi$
$272$	−5.30267	−0.321522
$273$	10.6676	0.645635
$274$	−2.77780	−0.167813
$275$	12.8325	0.773829
$276$	3.37846	0.203360
$277$	20.7211	1.24501	0.622504	−	0.782617i	$-0.286116\pi$
$277$	20.7211	1.24501	0.622504	+	0.782617i	$0.286116\pi$
$278$	−5.92830	−0.355556
$279$	10.2209	0.611910
$280$	11.3362	0.677469
$281$	−9.09098	−0.542322	−0.271161	−	0.962534i	$-0.587408\pi$
$281$	−9.09098	−0.542322	−0.271161	+	0.962534i	$0.587408\pi$
$282$	−0.768646	−0.0457722
$283$	−17.7388	−1.05446	−0.527232	−	0.849721i	$-0.676770\pi$
$283$	−17.7388	−1.05446	−0.527232	+	0.849721i	$0.676770\pi$
$284$	15.4704	0.918000
$285$	18.3060	1.08435
$286$	5.13194	0.303458
$287$	−12.5650	−0.741688
$288$	2.36595	0.139415
$289$	11.1183	0.654018
$290$	0.353279	0.0207452
$291$	−7.77447	−0.455748
$292$	10.2130	0.597674
$293$	27.6779	1.61696	0.808480	−	0.588524i	$-0.200291\pi$
$293$	27.6779	1.61696	0.808480	+	0.588524i	$0.200291\pi$
$294$	0.345790	0.0201669
$295$	18.6807	1.08763
$296$	7.16359	0.416375
$297$	4.46274	0.258954
$298$	−7.77413	−0.450343
$299$	20.8471	1.20562
$300$	−9.78316	−0.564831
$301$	−25.1648	−1.45048
$302$	−13.7271	−0.789908
$303$	−12.8567	−0.738600
$304$	5.52945	0.317136
$305$	−42.4293	−2.42949
$306$	−12.5459	−0.717199
$307$	13.7627	0.785476	0.392738	−	0.919650i	$-0.371528\pi$
$307$	13.7627	0.785476	0.392738	+	0.919650i	$0.371528\pi$
$308$	2.84782	0.162270
$309$	1.87454	0.106639
$310$	−17.9611	−1.02012
$311$	−24.2480	−1.37498	−0.687489	−	0.726194i	$-0.741287\pi$
$311$	−24.2480	−1.37498	−0.687489	+	0.726194i	$0.741287\pi$
$312$	−3.91246	−0.221499
$313$	−10.6243	−0.600521	−0.300261	−	0.953857i	$-0.597074\pi$
$313$	−10.6243	−0.600521	−0.300261	+	0.953857i	$0.597074\pi$
$314$	19.9656	1.12673
$315$	26.8210	1.51119
$316$	−15.4891	−0.871332
$317$	10.3996	0.584098	0.292049	−	0.956403i	$-0.405663\pi$
$317$	10.3996	0.584098	0.292049	+	0.956403i	$0.405663\pi$
$318$	−8.56886	−0.480518
$319$	0.0887485	0.00496896
$320$	−4.15767	−0.232421
$321$	7.34571	0.409998
$322$	11.5685	0.644687
$323$	−29.3209	−1.63146
$324$	3.69558	0.205310
$325$	−60.3679	−3.34861
$326$	−2.07911	−0.115151
$327$	−10.2555	−0.567133
$328$	4.60832	0.254452
$329$	−2.63199	−0.145106
$330$	−3.45784	−0.190348
$331$	−25.9273	−1.42509	−0.712545	−	0.701626i	$-0.752458\pi$
$331$	−25.9273	−1.42509	−0.712545	+	0.701626i	$0.752458\pi$
$332$	1.10141	0.0604475
$333$	16.9487	0.928783
$334$	−20.4530	−1.11914
$335$	25.9739	1.41911
$336$	−2.17110	−0.118443
$337$	20.6830	1.12667	0.563337	−	0.826227i	$-0.309517\pi$
$337$	20.6830	1.12667	0.563337	+	0.826227i	$0.309517\pi$
$338$	−11.1422	−0.606056
$339$	7.26721	0.394700
$340$	22.0467	1.19565
$341$	−4.51209	−0.244343
$342$	13.0824	0.707416
$343$	−17.9020	−0.966619
$344$	9.22942	0.497617
$345$	−14.0465	−0.756239
$346$	12.7131	0.683458
$347$	−24.2528	−1.30196	−0.650981	−	0.759094i	$-0.725642\pi$
$347$	−24.2528	−1.30196	−0.650981	+	0.759094i	$0.725642\pi$
$348$	−0.0676595	−0.00362693
$349$	−14.1792	−0.758993	−0.379496	−	0.925193i	$-0.623903\pi$
$349$	−14.1792	−0.758993	−0.379496	+	0.925193i	$0.623903\pi$
$350$	−33.4994	−1.79062
$351$	−20.9941	−1.12058
$352$	−1.04446	−0.0556701
$353$	9.45687	0.503338	0.251669	−	0.967813i	$-0.419021\pi$
$353$	9.45687	0.503338	0.251669	+	0.967813i	$0.419021\pi$
$354$	−3.57771	−0.190153
$355$	−64.3209	−3.41380
$356$	−15.3407	−0.813055
$357$	11.5126	0.609313
$358$	11.5912	0.612614
$359$	29.2790	1.54529	0.772643	−	0.634841i	$-0.218934\pi$
$359$	29.2790	1.54529	0.772643	+	0.634841i	$0.218934\pi$
$360$	−9.83684	−0.518447
$361$	11.5749	0.609203
$362$	−23.0053	−1.20913
$363$	7.89033	0.414135
$364$	−13.3970	−0.702193
$365$	−42.4625	−2.22259
$366$	8.12601	0.424753
$367$	33.2286	1.73452	0.867259	−	0.497857i	$-0.165879\pi$
$367$	33.2286	1.73452	0.867259	+	0.497857i	$0.165879\pi$
$368$	−4.24285	−0.221174
$369$	10.9031	0.567591
$370$	−29.7838	−1.54839
$371$	−29.3414	−1.52333
$372$	3.43990	0.178350
$373$	9.39712	0.486564	0.243282	−	0.969956i	$-0.421776\pi$
$373$	9.39712	0.486564	0.243282	+	0.969956i	$0.421776\pi$
$374$	5.53845	0.286386
$375$	24.1220	1.24565
$376$	0.965307	0.0497819
$377$	−0.417500	−0.0215023
$378$	−11.6500	−0.599213
$379$	−5.69297	−0.292428	−0.146214	−	0.989253i	$-0.546709\pi$
$379$	−5.69297	−0.292428	−0.146214	+	0.989253i	$0.546709\pi$
$380$	−22.9896	−1.17934
$381$	4.28771	0.219666
$382$	−16.8962	−0.864484
$383$	14.8890	0.760791	0.380395	−	0.924824i	$-0.375788\pi$
$383$	14.8890	0.760791	0.380395	+	0.924824i	$0.375788\pi$
$384$	0.796272	0.0406346
$385$	−11.8403	−0.603437
$386$	−3.44369	−0.175279
$387$	21.8364	1.11001
$388$	9.76359	0.495671
$389$	19.3846	0.982836	0.491418	−	0.870924i	$-0.336479\pi$
$389$	19.3846	0.982836	0.491418	+	0.870924i	$0.336479\pi$
$390$	16.2667	0.823697
$391$	22.4984	1.13779
$392$	−0.434261	−0.0219335
$393$	17.0195	0.858522
$394$	19.6027	0.987571
$395$	64.3987	3.24025
$396$	−2.47115	−0.124180
$397$	−22.7679	−1.14269	−0.571344	−	0.820710i	$-0.693578\pi$
$397$	−22.7679	−1.14269	−0.571344	+	0.820710i	$0.693578\pi$
$398$	4.42237	0.221673
$399$	−12.0050	−0.601002
$400$	12.2862	0.614310
$401$	37.4048	1.86791	0.933954	−	0.357394i	$-0.116335\pi$
$401$	37.4048	1.86791	0.933954	+	0.357394i	$0.116335\pi$
$402$	−4.97450	−0.248105
$403$	21.2262	1.05735
$404$	16.1462	0.803302
$405$	−15.3650	−0.763493
$406$	−0.231679	−0.0114980
$407$	−7.48211	−0.370874
$408$	−4.22237	−0.209038
$409$	22.0151	1.08858	0.544289	−	0.838898i	$-0.316800\pi$
$409$	22.0151	1.08858	0.544289	+	0.838898i	$0.316800\pi$
$410$	−19.1599	−0.946239
$411$	−2.21189	−0.109104
$412$	−2.35415	−0.115980
$413$	−12.2508	−0.602821
$414$	−10.0384	−0.493359
$415$	−4.57928	−0.224788
$416$	4.91347	0.240903
$417$	−4.72054	−0.231166
$418$	−5.77532	−0.282480
$419$	−19.5914	−0.957102	−0.478551	−	0.878060i	$-0.658838\pi$
$419$	−19.5914	−0.957102	−0.478551	+	0.878060i	$0.658838\pi$
$420$	9.02672	0.440459
$421$	18.4985	0.901562	0.450781	−	0.892634i	$-0.351145\pi$
$421$	18.4985	0.901562	0.450781	+	0.892634i	$0.351145\pi$
$422$	−13.3215	−0.648481
$423$	2.28387	0.111045
$424$	10.7612	0.522611
$425$	−65.1497	−3.16022
$426$	12.3187	0.596841
$427$	27.8250	1.34655
$428$	−9.22513	−0.445914
$429$	4.08642	0.197294
$430$	−38.3729	−1.85050
$431$	−9.19105	−0.442717	−0.221359	−	0.975192i	$-0.571049\pi$
$431$	−9.19105	−0.442717	−0.221359	+	0.975192i	$0.571049\pi$
$432$	4.27276	0.205573
$433$	22.0304	1.05871	0.529356	−	0.848400i	$-0.322433\pi$
$433$	22.0304	1.05871	0.529356	+	0.848400i	$0.322433\pi$
$434$	11.7789	0.565403
$435$	0.281306	0.0134876
$436$	12.8795	0.616814
$437$	−23.4607	−1.12228
$438$	8.13236	0.388579
$439$	−25.6212	−1.22283	−0.611417	−	0.791309i	$-0.709400\pi$
$439$	−25.6212	−1.22283	−0.611417	+	0.791309i	$0.709400\pi$
$440$	4.34254	0.207022
$441$	−1.02744	−0.0489258
$442$	−26.0545	−1.23929
$443$	−0.346277	−0.0164521	−0.00822606	−	0.999966i	$-0.502618\pi$
$443$	−0.346277	−0.0164521	−0.00822606	+	0.999966i	$0.502618\pi$
$444$	5.70416	0.270707
$445$	63.7815	3.02353
$446$	−19.1351	−0.906071
$447$	−6.19032	−0.292792
$448$	2.72658	0.128819
$449$	−39.2209	−1.85095	−0.925475	−	0.378808i	$-0.876334\pi$
$449$	−39.2209	−1.85095	−0.925475	+	0.378808i	$0.876334\pi$
$450$	29.0686	1.37031
$451$	−4.81323	−0.226646
$452$	−9.12654	−0.429276
$453$	−10.9305	−0.513561
$454$	4.22551	0.198313
$455$	55.7003	2.61127
$456$	4.40295	0.206187
$457$	9.86933	0.461668	0.230834	−	0.972993i	$-0.425855\pi$
$457$	9.86933	0.461668	0.230834	+	0.972993i	$0.425855\pi$
$458$	22.1198	1.03359
$459$	−22.6570	−1.05754
$460$	17.6404	0.822486
$461$	16.1340	0.751436	0.375718	−	0.926734i	$-0.377396\pi$
$461$	16.1340	0.751436	0.375718	+	0.926734i	$0.377396\pi$
$462$	2.26764	0.105500
$463$	14.4706	0.672508	0.336254	−	0.941771i	$-0.390840\pi$
$463$	14.4706	0.672508	0.336254	+	0.941771i	$0.390840\pi$
$464$	0.0849704	0.00394465
$465$	−14.3019	−0.663237
$466$	−18.4305	−0.853777
$467$	5.10657	0.236304	0.118152	−	0.992996i	$-0.462303\pi$
$467$	5.10657	0.236304	0.118152	+	0.992996i	$0.462303\pi$
$468$	11.6250	0.537367
$469$	−17.0336	−0.786539
$470$	−4.01342	−0.185125
$471$	15.8981	0.732545
$472$	4.49308	0.206811
$473$	−9.63980	−0.443239
$474$	−12.3336	−0.566499
$475$	67.9360	3.11712
$476$	−14.4582	−0.662689
$477$	25.4605	1.16576
$478$	−12.8391	−0.587248
$479$	−2.57666	−0.117731	−0.0588654	−	0.998266i	$-0.518748\pi$
$479$	−2.57666	−0.117731	−0.0588654	+	0.998266i	$0.518748\pi$
$480$	−3.31063	−0.151109
$481$	35.1981	1.60489
$482$	−4.36970	−0.199034
$483$	9.21166	0.419145
$484$	−9.90909	−0.450413
$485$	−40.5938	−1.84327
$486$	15.7610	0.714931
$487$	16.9642	0.768721	0.384360	−	0.923183i	$-0.374422\pi$
$487$	16.9642	0.768721	0.384360	+	0.923183i	$0.374422\pi$
$488$	−10.2051	−0.461962
$489$	−1.65554	−0.0748659
$490$	1.80552	0.0815649
$491$	−38.1034	−1.71958	−0.859791	−	0.510646i	$-0.829406\pi$
$491$	−38.1034	−1.71958	−0.859791	+	0.510646i	$0.829406\pi$
$492$	3.66948	0.165433
$493$	−0.450570	−0.0202926
$494$	27.1688	1.22238
$495$	10.2742	0.461792
$496$	−4.32000	−0.193974
$497$	42.1814	1.89209
$498$	0.877019	0.0393001
$499$	−36.3912	−1.62909	−0.814546	−	0.580099i	$-0.803014\pi$
$499$	−36.3912	−1.62909	−0.814546	+	0.580099i	$0.803014\pi$
$500$	−30.2936	−1.35477
$501$	−16.2862	−0.727613
$502$	−22.8214	−1.01857
$503$	13.9386	0.621492	0.310746	−	0.950493i	$-0.399421\pi$
$503$	13.9386	0.621492	0.310746	+	0.950493i	$0.399421\pi$
$504$	6.45097	0.287349
$505$	−67.1304	−2.98726
$506$	4.43151	0.197004
$507$	−8.87222	−0.394029
$508$	−5.38474	−0.238909
$509$	27.4044	1.21468	0.607339	−	0.794443i	$-0.292237\pi$
$509$	27.4044	1.21468	0.607339	+	0.794443i	$0.292237\pi$
$510$	17.5552	0.777357
$511$	27.8467	1.23187
$512$	−1.00000	−0.0441942
$513$	23.6260	1.04311
$514$	−19.2461	−0.848909
$515$	9.78776	0.431300
$516$	7.34913	0.323527
$517$	−1.00823	−0.0443418
$518$	19.5321	0.858192
$519$	10.1230	0.444352
$520$	−20.4286	−0.895853
$521$	−17.0823	−0.748387	−0.374194	−	0.927351i	$-0.622080\pi$
$521$	−17.0823	−0.748387	−0.374194	+	0.927351i	$0.622080\pi$
$522$	0.201036	0.00879910
$523$	14.0249	0.613265	0.306633	−	0.951828i	$-0.400798\pi$
$523$	14.0249	0.613265	0.306633	+	0.951828i	$0.400798\pi$
$524$	−21.3740	−0.933729
$525$	−26.6746	−1.16418
$526$	−14.6674	−0.639528
$527$	22.9075	0.997868
$528$	−0.831677	−0.0361941
$529$	−4.99821	−0.217314
$530$	−44.7416	−1.94345
$531$	10.6304	0.461320
$532$	15.0765	0.653650
$533$	22.6429	0.980772
$534$	−12.2154	−0.528610
$535$	38.3550	1.65823
$536$	6.24724	0.269840
$537$	9.22975	0.398293
$538$	−11.0432	−0.476105
$539$	0.453571	0.0195367
$540$	−17.7647	−0.764471
$541$	−2.60009	−0.111786	−0.0558932	−	0.998437i	$-0.517801\pi$
$541$	−2.60009	−0.111786	−0.0558932	+	0.998437i	$0.517801\pi$
$542$	−27.4619	−1.17959
$543$	−18.3185	−0.786122
$544$	5.30267	0.227350
$545$	−53.5485	−2.29377
$546$	−10.6676	−0.456533
$547$	12.3445	0.527813	0.263906	−	0.964548i	$-0.414989\pi$
$547$	12.3445	0.527813	0.263906	+	0.964548i	$0.414989\pi$
$548$	2.77780	0.118662
$549$	−24.1447	−1.03047
$550$	−12.8325	−0.547180
$551$	0.469840	0.0200159
$552$	−3.37846	−0.143797
$553$	−42.2324	−1.79591
$554$	−20.7211	−0.880353
$555$	−23.7160	−1.00669
$556$	5.92830	0.251416
$557$	−39.6356	−1.67942	−0.839708	−	0.543038i	$-0.817274\pi$
$557$	−39.6356	−1.67942	−0.839708	+	0.543038i	$0.817274\pi$
$558$	−10.2209	−0.432686
$559$	45.3485	1.91804
$560$	−11.3362	−0.479043
$561$	4.41011	0.186195
$562$	9.09098	0.383480
$563$	−5.02645	−0.211840	−0.105920	−	0.994375i	$-0.533779\pi$
$563$	−5.02645	−0.211840	−0.105920	+	0.994375i	$0.533779\pi$
$564$	0.768646	0.0323658
$565$	37.9451	1.59636
$566$	17.7388	0.745619
$567$	10.0763	0.423165
$568$	−15.4704	−0.649124
$569$	−26.4742	−1.10986	−0.554928	−	0.831898i	$-0.687254\pi$
$569$	−26.4742	−1.10986	−0.554928	+	0.831898i	$0.687254\pi$
$570$	−18.3060	−0.766754
$571$	26.4826	1.10826	0.554132	−	0.832429i	$-0.313050\pi$
$571$	26.4826	1.10826	0.554132	+	0.832429i	$0.313050\pi$
$572$	−5.13194	−0.214577
$573$	−13.4539	−0.562047
$574$	12.5650	0.524452
$575$	−52.1285	−2.17391
$576$	−2.36595	−0.0985813
$577$	−18.3723	−0.764850	−0.382425	−	0.923986i	$-0.624911\pi$
$577$	−18.3723	−0.764850	−0.382425	+	0.923986i	$0.624911\pi$
$578$	−11.1183	−0.462460
$579$	−2.74211	−0.113958
$580$	−0.353279	−0.0146691
$581$	3.00308	0.124589
$582$	7.77447	0.322262
$583$	−11.2397	−0.465501
$584$	−10.2130	−0.422619
$585$	−48.3330	−1.99833
$586$	−27.6779	−1.14336
$587$	11.2472	0.464224	0.232112	−	0.972689i	$-0.425436\pi$
$587$	11.2472	0.464224	0.232112	+	0.972689i	$0.425436\pi$
$588$	−0.345790	−0.0142601
$589$	−23.8873	−0.984257
$590$	−18.6807	−0.769074
$591$	15.6091	0.642072
$592$	−7.16359	−0.294422
$593$	−27.3277	−1.12221	−0.561107	−	0.827743i	$-0.689624\pi$
$593$	−27.3277	−1.12221	−0.561107	+	0.827743i	$0.689624\pi$
$594$	−4.46274	−0.183108
$595$	60.1123	2.46436
$596$	7.77413	0.318441
$597$	3.52141	0.144122
$598$	−20.8471	−0.852503
$599$	−8.45046	−0.345276	−0.172638	−	0.984985i	$-0.555229\pi$
$599$	−8.45046	−0.345276	−0.172638	+	0.984985i	$0.555229\pi$
$600$	9.78316	0.399396
$601$	−13.6415	−0.556450	−0.278225	−	0.960516i	$-0.589746\pi$
$601$	−13.6415	−0.556450	−0.278225	+	0.960516i	$0.589746\pi$
$602$	25.1648	1.02564
$603$	14.7807	0.601915
$604$	13.7271	0.558549
$605$	41.1987	1.67497
$606$	12.8567	0.522269
$607$	−15.1629	−0.615444	−0.307722	−	0.951476i	$-0.599567\pi$
$607$	−15.1629	−0.615444	−0.307722	+	0.951476i	$0.599567\pi$
$608$	−5.52945	−0.224249
$609$	−0.184479	−0.00747548
$610$	42.4293	1.71791
$611$	4.74301	0.191882
$612$	12.5459	0.507136
$613$	1.00230	0.0404827	0.0202413	−	0.999795i	$-0.493557\pi$
$613$	1.00230	0.0404827	0.0202413	+	0.999795i	$0.493557\pi$
$614$	−13.7627	−0.555416
$615$	−15.2565	−0.615200
$616$	−2.84782	−0.114742
$617$	17.8753	0.719631	0.359815	−	0.933024i	$-0.382840\pi$
$617$	17.8753	0.719631	0.359815	+	0.933024i	$0.382840\pi$
$618$	−1.87454	−0.0754051
$619$	−35.3280	−1.41995	−0.709977	−	0.704225i	$-0.751295\pi$
$619$	−35.3280	−1.41995	−0.709977	+	0.704225i	$0.751295\pi$
$620$	17.9611	0.721337
$621$	−18.1287	−0.727478
$622$	24.2480	0.972257
$623$	−41.8277	−1.67579
$624$	3.91246	0.156624
$625$	64.5198	2.58079
$626$	10.6243	0.424633
$627$	−4.59872	−0.183655
$628$	−19.9656	−0.796716
$629$	37.9861	1.51461
$630$	−26.8210	−1.06857
$631$	12.8517	0.511620	0.255810	−	0.966727i	$-0.417658\pi$
$631$	12.8517	0.511620	0.255810	+	0.966727i	$0.417658\pi$
$632$	15.4891	0.616125
$633$	−10.6075	−0.421612
$634$	−10.3996	−0.413020
$635$	22.3880	0.888439
$636$	8.56886	0.339777
$637$	−2.13373	−0.0845415
$638$	−0.0887485	−0.00351359
$639$	−36.6023	−1.44796
$640$	4.15767	0.164346
$641$	−29.5769	−1.16822	−0.584109	−	0.811675i	$-0.698556\pi$
$641$	−29.5769	−1.16822	−0.584109	+	0.811675i	$0.698556\pi$
$642$	−7.34571	−0.289912
$643$	−47.5889	−1.87672	−0.938361	−	0.345658i	$-0.887656\pi$
$643$	−47.5889	−1.87672	−0.938361	+	0.345658i	$0.887656\pi$
$644$	−11.5685	−0.455862
$645$	−30.5552	−1.20311
$646$	29.3209	1.15361
$647$	25.6676	1.00910	0.504550	−	0.863383i	$-0.331659\pi$
$647$	25.6676	1.00910	0.504550	+	0.863383i	$0.331659\pi$
$648$	−3.69558	−0.145176
$649$	−4.69286	−0.184211
$650$	60.3679	2.36782
$651$	9.37917	0.367598
$652$	2.07911	0.0814242
$653$	−6.42578	−0.251460	−0.125730	−	0.992064i	$-0.540127\pi$
$653$	−6.42578	−0.251460	−0.125730	+	0.992064i	$0.540127\pi$
$654$	10.2555	0.401024
$655$	88.8661	3.47229
$656$	−4.60832	−0.179925
$657$	−24.1636	−0.942711
$658$	2.63199	0.102606
$659$	6.88770	0.268307	0.134153	−	0.990961i	$-0.457168\pi$
$659$	6.88770	0.268307	0.134153	+	0.990961i	$0.457168\pi$
$660$	3.45784	0.134596
$661$	40.2986	1.56743	0.783717	−	0.621119i	$-0.213321\pi$
$661$	40.2986	1.56743	0.783717	+	0.621119i	$0.213321\pi$
$662$	25.9273	1.00769
$663$	−20.7465	−0.805726
$664$	−1.10141	−0.0427429
$665$	−62.6832	−2.43075
$666$	−16.9487	−0.656749
$667$	−0.360517	−0.0139593
$668$	20.4530	0.791352
$669$	−15.2367	−0.589085
$670$	−25.9739	−1.00346
$671$	10.6588	0.411480
$672$	2.17110	0.0837521
$673$	−19.8541	−0.765318	−0.382659	−	0.923890i	$-0.624992\pi$
$673$	−19.8541	−0.765318	−0.382659	+	0.923890i	$0.624992\pi$
$674$	−20.6830	−0.796679
$675$	52.4959	2.02057
$676$	11.1422	0.428546
$677$	36.6163	1.40728	0.703639	−	0.710557i	$-0.251557\pi$
$677$	36.6163	1.40728	0.703639	+	0.710557i	$0.251557\pi$
$678$	−7.26721	−0.279095
$679$	26.6213	1.02163
$680$	−22.0467	−0.845454
$681$	3.36466	0.128934
$682$	4.51209	0.172777
$683$	−9.41671	−0.360320	−0.180160	−	0.983637i	$-0.557662\pi$
$683$	−9.41671	−0.360320	−0.180160	+	0.983637i	$0.557662\pi$
$684$	−13.0824	−0.500219
$685$	−11.5492	−0.441272
$686$	17.9020	0.683503
$687$	17.6134	0.671992
$688$	−9.22942	−0.351868
$689$	52.8750	2.01438
$690$	14.0465	0.534742
$691$	10.3749	0.394681	0.197340	−	0.980335i	$-0.436770\pi$
$691$	10.3749	0.394681	0.197340	+	0.980335i	$0.436770\pi$
$692$	−12.7131	−0.483278
$693$	−6.73780	−0.255948
$694$	24.2528	0.920626
$695$	−24.6479	−0.934948
$696$	0.0676595	0.00256463
$697$	24.4364	0.925595
$698$	14.1792	0.536689
$699$	−14.6757	−0.555086
$700$	33.4994	1.26616
$701$	−37.4291	−1.41368	−0.706839	−	0.707374i	$-0.749879\pi$
$701$	−37.4291	−1.41368	−0.706839	+	0.707374i	$0.749879\pi$
$702$	20.9941	0.792370
$703$	−39.6107	−1.49395
$704$	1.04446	0.0393647
$705$	−3.19578	−0.120360
$706$	−9.45687	−0.355914
$707$	44.0239	1.65569
$708$	3.57771	0.134459
$709$	−35.1268	−1.31921	−0.659606	−	0.751611i	$-0.729277\pi$
$709$	−35.1268	−1.31921	−0.659606	+	0.751611i	$0.729277\pi$
$710$	64.3209	2.41392
$711$	36.6465	1.37435
$712$	15.3407	0.574917
$713$	18.3291	0.686431
$714$	−11.5126	−0.430850
$715$	21.3369	0.797956
$716$	−11.5912	−0.433184
$717$	−10.2234	−0.381801
$718$	−29.2790	−1.09268
$719$	−17.2104	−0.641838	−0.320919	−	0.947107i	$-0.603992\pi$
$719$	−17.2104	−0.641838	−0.320919	+	0.947107i	$0.603992\pi$
$720$	9.83684	0.366597
$721$	−6.41878	−0.239048
$722$	−11.5749	−0.430772
$723$	−3.47947	−0.129403
$724$	23.0053	0.854986
$725$	1.04396	0.0387718
$726$	−7.89033	−0.292838
$727$	−22.6983	−0.841835	−0.420917	−	0.907099i	$-0.638292\pi$
$727$	−22.6983	−0.841835	−0.420917	+	0.907099i	$0.638292\pi$
$728$	13.3970	0.496526
$729$	1.46326	0.0541948
$730$	42.4625	1.57161
$731$	48.9406	1.81013
$732$	−8.12601	−0.300346
$733$	−43.0950	−1.59175	−0.795874	−	0.605462i	$-0.792988\pi$
$733$	−43.0950	−1.59175	−0.795874	+	0.605462i	$0.792988\pi$
$734$	−33.2286	−1.22649
$735$	1.43768	0.0530296
$736$	4.24285	0.156394
$737$	−6.52501	−0.240352
$738$	−10.9031	−0.401348
$739$	−13.8983	−0.511256	−0.255628	−	0.966775i	$-0.582282\pi$
$739$	−13.8983	−0.511256	−0.255628	+	0.966775i	$0.582282\pi$
$740$	29.7838	1.09487
$741$	21.6338	0.794736
$742$	29.3414	1.07716
$743$	−2.33486	−0.0856577	−0.0428288	−	0.999082i	$-0.513637\pi$
$743$	−2.33486	−0.0856577	−0.0428288	+	0.999082i	$0.513637\pi$
$744$	−3.43990	−0.126113
$745$	−32.3223	−1.18420
$746$	−9.39712	−0.344053
$747$	−2.60587	−0.0953439
$748$	−5.53845	−0.202506
$749$	−25.1531	−0.919074
$750$	−24.1220	−0.880809
$751$	−8.39427	−0.306311	−0.153156	−	0.988202i	$-0.548944\pi$
$751$	−8.39427	−0.306311	−0.153156	+	0.988202i	$0.548944\pi$
$752$	−0.965307	−0.0352011
$753$	−18.1720	−0.662225
$754$	0.417500	0.0152044
$755$	−57.0729	−2.07709
$756$	11.6500	0.423707
$757$	8.41764	0.305944	0.152972	−	0.988231i	$-0.451116\pi$
$757$	8.41764	0.305944	0.152972	+	0.988231i	$0.451116\pi$
$758$	5.69297	0.206778
$759$	3.52868	0.128083
$760$	22.9896	0.833922
$761$	28.9217	1.04841	0.524205	−	0.851592i	$-0.324362\pi$
$761$	28.9217	1.04841	0.524205	+	0.851592i	$0.324362\pi$
$762$	−4.28771	−0.155328
$763$	35.1169	1.27132
$764$	16.8962	0.611282
$765$	−52.1615	−1.88590
$766$	−14.8890	−0.537960
$767$	22.0766	0.797141
$768$	−0.796272	−0.0287330
$769$	−27.4388	−0.989469	−0.494734	−	0.869044i	$-0.664735\pi$
$769$	−27.4388	−0.989469	−0.494734	+	0.869044i	$0.664735\pi$
$770$	11.8403	0.426694
$771$	−15.3251	−0.551921
$772$	3.44369	0.123941
$773$	41.5794	1.49551	0.747753	−	0.663977i	$-0.231133\pi$
$773$	41.5794	1.49551	0.747753	+	0.663977i	$0.231133\pi$
$774$	−21.8364	−0.784892
$775$	−53.0764	−1.90656
$776$	−9.76359	−0.350492
$777$	15.5529	0.557956
$778$	−19.3846	−0.694970
$779$	−25.4815	−0.912970
$780$	−16.2667	−0.582441
$781$	16.1583	0.578189
$782$	−22.4984	−0.804542
$783$	0.363058	0.0129746
$784$	0.434261	0.0155093
$785$	83.0105	2.96277
$786$	−17.0195	−0.607067
$787$	28.4574	1.01440	0.507198	−	0.861829i	$-0.330681\pi$
$787$	28.4574	1.01440	0.507198	+	0.861829i	$0.330681\pi$
$788$	−19.6027	−0.698318
$789$	−11.6792	−0.415791
$790$	−64.3987	−2.29120
$791$	−24.8843	−0.884783
$792$	2.47115	0.0878085
$793$	−50.1423	−1.78061
$794$	22.7679	0.808003
$795$	−35.6265	−1.26354
$796$	−4.42237	−0.156747
$797$	−30.9273	−1.09550	−0.547750	−	0.836642i	$-0.684516\pi$
$797$	−30.9273	−1.09550	−0.547750	+	0.836642i	$0.684516\pi$
$798$	12.0050	0.424973
$799$	5.11870	0.181087
$800$	−12.2862	−0.434383
$801$	36.2953	1.28243
$802$	−37.4048	−1.32081
$803$	10.6672	0.376436
$804$	4.97450	0.175437
$805$	48.0979	1.69523
$806$	−21.2262	−0.747661
$807$	−8.79337	−0.309541
$808$	−16.1462	−0.568020
$809$	4.53749	0.159530	0.0797648	−	0.996814i	$-0.474583\pi$
$809$	4.53749	0.159530	0.0797648	+	0.996814i	$0.474583\pi$
$810$	15.3650	0.539871
$811$	42.9281	1.50741	0.753704	−	0.657214i	$-0.228265\pi$
$811$	42.9281	1.50741	0.753704	+	0.657214i	$0.228265\pi$
$812$	0.231679	0.00813034
$813$	−21.8671	−0.766914
$814$	7.48211	0.262248
$815$	−8.64424	−0.302795
$816$	4.22237	0.147812
$817$	−51.0337	−1.78544
$818$	−22.0151	−0.769741
$819$	31.6966	1.10757
$820$	19.1599	0.669092
$821$	28.1013	0.980744	0.490372	−	0.871513i	$-0.336861\pi$
$821$	28.1013	0.980744	0.490372	+	0.871513i	$0.336861\pi$
$822$	2.21189	0.0771484
$823$	10.0035	0.348700	0.174350	−	0.984684i	$-0.444218\pi$
$823$	10.0035	0.348700	0.174350	+	0.984684i	$0.444218\pi$
$824$	2.35415	0.0820106
$825$	−10.2182	−0.355751
$826$	12.2508	0.426259
$827$	37.1052	1.29028	0.645138	−	0.764066i	$-0.276800\pi$
$827$	37.1052	1.29028	0.645138	+	0.764066i	$0.276800\pi$
$828$	10.0384	0.348858
$829$	33.9220	1.17816	0.589080	−	0.808075i	$-0.299490\pi$
$829$	33.9220	1.17816	0.589080	+	0.808075i	$0.299490\pi$
$830$	4.57928	0.158949
$831$	−16.4996	−0.572364
$832$	−4.91347	−0.170344
$833$	−2.30274	−0.0797854
$834$	4.72054	0.163459
$835$	−85.0369	−2.94282
$836$	5.77532	0.199743
$837$	−18.4583	−0.638013
$838$	19.5914	0.676773
$839$	17.6149	0.608135	0.304067	−	0.952651i	$-0.401655\pi$
$839$	17.6149	0.608135	0.304067	+	0.952651i	$0.401655\pi$
$840$	−9.02672	−0.311451
$841$	−28.9928	−0.999751
$842$	−18.4985	−0.637501
$843$	7.23889	0.249321
$844$	13.3215	0.458545
$845$	−46.3256	−1.59365
$846$	−2.28387	−0.0785210
$847$	−27.0180	−0.928349
$848$	−10.7612	−0.369542
$849$	14.1249	0.484766
$850$	65.1497	2.23462
$851$	30.3940	1.04189
$852$	−12.3187	−0.422030
$853$	−19.4572	−0.666202	−0.333101	−	0.942891i	$-0.608095\pi$
$853$	−19.4572	−0.666202	−0.333101	+	0.942891i	$0.608095\pi$
$854$	−27.8250	−0.952151
$855$	54.3924	1.86018
$856$	9.22513	0.315309
$857$	38.3584	1.31030	0.655149	−	0.755500i	$-0.272606\pi$
$857$	38.3584	1.31030	0.655149	+	0.755500i	$0.272606\pi$
$858$	−4.08642	−0.139508
$859$	8.61559	0.293960	0.146980	−	0.989139i	$-0.453045\pi$
$859$	8.61559	0.293960	0.146980	+	0.989139i	$0.453045\pi$
$860$	38.3729	1.30850
$861$	10.0051	0.340974
$862$	9.19105	0.313048
$863$	−19.0566	−0.648693	−0.324347	−	0.945938i	$-0.605144\pi$
$863$	−19.0566	−0.648693	−0.324347	+	0.945938i	$0.605144\pi$
$864$	−4.27276	−0.145362
$865$	52.8567	1.79718
$866$	−22.0304	−0.748623
$867$	−8.85319	−0.300670
$868$	−11.7789	−0.399800
$869$	−16.1778	−0.548796
$870$	−0.281306	−0.00953716
$871$	30.6956	1.04008
$872$	−12.8795	−0.436153
$873$	−23.1002	−0.781823
$874$	23.4607	0.793568
$875$	−82.5981	−2.79233
$876$	−8.13236	−0.274767
$877$	−6.87846	−0.232269	−0.116135	−	0.993233i	$-0.537050\pi$
$877$	−6.87846	−0.232269	−0.116135	+	0.993233i	$0.537050\pi$
$878$	25.6212	0.864674
$879$	−22.0391	−0.743361
$880$	−4.34254	−0.146387
$881$	−2.76066	−0.0930090	−0.0465045	−	0.998918i	$-0.514808\pi$
$881$	−2.76066	−0.0930090	−0.0465045	+	0.998918i	$0.514808\pi$
$882$	1.02744	0.0345958
$883$	−14.4259	−0.485471	−0.242736	−	0.970092i	$-0.578045\pi$
$883$	−14.4259	−0.485471	−0.242736	+	0.970092i	$0.578045\pi$
$884$	26.0545	0.876308
$885$	−14.8749	−0.500016
$886$	0.346277	0.0116334
$887$	−6.19030	−0.207850	−0.103925	−	0.994585i	$-0.533140\pi$
$887$	−6.19030	−0.207850	−0.103925	+	0.994585i	$0.533140\pi$
$888$	−5.70416	−0.191419
$889$	−14.6819	−0.492417
$890$	−63.7815	−2.13796
$891$	3.85990	0.129312
$892$	19.1351	0.640689
$893$	−5.33762	−0.178617
$894$	6.19032	0.207035
$895$	48.1924	1.61089
$896$	−2.72658	−0.0910888
$897$	−16.6000	−0.554257
$898$	39.2209	1.30882
$899$	−0.367072	−0.0122425
$900$	−29.0686	−0.968952
$901$	57.0632	1.90105
$902$	4.81323	0.160263
$903$	20.0380	0.666824
$904$	9.12654	0.303544
$905$	−95.6485	−3.17946
$906$	10.9305	0.363142
$907$	−19.0870	−0.633774	−0.316887	−	0.948463i	$-0.602638\pi$
$907$	−19.0870	−0.633774	−0.316887	+	0.948463i	$0.602638\pi$
$908$	−4.22551	−0.140229
$909$	−38.2010	−1.26705
$910$	−55.7003	−1.84645
$911$	−7.92294	−0.262499	−0.131249	−	0.991349i	$-0.541899\pi$
$911$	−7.92294	−0.262499	−0.131249	+	0.991349i	$0.541899\pi$
$912$	−4.40295	−0.145796
$913$	1.15038	0.0380720
$914$	−9.86933	−0.326448
$915$	33.7852	1.11691
$916$	−22.1198	−0.730859
$917$	−58.2781	−1.92451
$918$	22.6570	0.747793
$919$	15.0820	0.497510	0.248755	−	0.968566i	$-0.419979\pi$
$919$	15.0820	0.497510	0.248755	+	0.968566i	$0.419979\pi$
$920$	−17.6404	−0.581586
$921$	−10.9588	−0.361105
$922$	−16.1340	−0.531346
$923$	−76.0135	−2.50201
$924$	−2.26764	−0.0745998
$925$	−88.0133	−2.89386
$926$	−14.4706	−0.475535
$927$	5.56980	0.182936
$928$	−0.0849704	−0.00278929
$929$	35.6215	1.16870	0.584352	−	0.811500i	$-0.301349\pi$
$929$	35.6215	1.16870	0.584352	+	0.811500i	$0.301349\pi$
$930$	14.3019	0.468979
$931$	2.40123	0.0786971
$932$	18.4305	0.603711
$933$	19.3080	0.632116
$934$	−5.10657	−0.167092
$935$	23.0270	0.753064
$936$	−11.6250	−0.379976
$937$	9.00560	0.294200	0.147100	−	0.989122i	$-0.453006\pi$
$937$	9.00560	0.294200	0.147100	+	0.989122i	$0.453006\pi$
$938$	17.0336	0.556167
$939$	8.45983	0.276076
$940$	4.01342	0.130903
$941$	−15.4085	−0.502303	−0.251152	−	0.967948i	$-0.580809\pi$
$941$	−15.4085	−0.502303	−0.251152	+	0.967948i	$0.580809\pi$
$942$	−15.8981	−0.517987
$943$	19.5524	0.636715
$944$	−4.49308	−0.146237
$945$	−48.4369	−1.57565
$946$	9.63980	0.313417
$947$	−44.0462	−1.43131	−0.715655	−	0.698454i	$-0.753871\pi$
$947$	−44.0462	−1.43131	−0.715655	+	0.698454i	$0.753871\pi$
$948$	12.3336	0.400575
$949$	−50.1815	−1.62896
$950$	−67.9360	−2.20414
$951$	−8.28088	−0.268526
$952$	14.4582	0.468592
$953$	14.4532	0.468185	0.234092	−	0.972214i	$-0.424788\pi$
$953$	14.4532	0.468185	0.234092	+	0.972214i	$0.424788\pi$
$954$	−25.4605	−0.824315
$955$	−70.2487	−2.27319
$956$	12.8391	0.415247
$957$	−0.0706679	−0.00228437
$958$	2.57666	0.0832482
$959$	7.57391	0.244574
$960$	3.31063	0.106850
$961$	−12.3376	−0.397986
$962$	−35.1981	−1.13483
$963$	21.8262	0.703340
$964$	4.36970	0.140739
$965$	−14.3177	−0.460903
$966$	−9.21166	−0.296380
$967$	−43.2475	−1.39075	−0.695373	−	0.718649i	$-0.744761\pi$
$967$	−43.2475	−1.39075	−0.695373	+	0.718649i	$0.744761\pi$
$968$	9.90909	0.318490
$969$	23.3474	0.750026
$970$	40.5938	1.30339
$971$	41.0336	1.31683	0.658416	−	0.752654i	$-0.271227\pi$
$971$	41.0336	1.31683	0.658416	+	0.752654i	$0.271227\pi$
$972$	−15.7610	−0.505533
$973$	16.1640	0.518194
$974$	−16.9642	−0.543567
$975$	48.0693	1.53945
$976$	10.2051	0.326656
$977$	−1.10995	−0.0355106	−0.0177553	−	0.999842i	$-0.505652\pi$
$977$	−1.10995	−0.0355106	−0.0177553	+	0.999842i	$0.505652\pi$
$978$	1.65554	0.0529382
$979$	−16.0228	−0.512091
$980$	−1.80552	−0.0576751
$981$	−30.4722	−0.972901
$982$	38.1034	1.21593
$983$	6.03000	0.192327	0.0961636	−	0.995366i	$-0.469343\pi$
$983$	6.03000	0.192327	0.0961636	+	0.995366i	$0.469343\pi$
$984$	−3.66948	−0.116979
$985$	81.5016	2.59686
$986$	0.450570	0.0143491
$987$	2.09578	0.0667094
$988$	−27.1688	−0.864355
$989$	39.1591	1.24519
$990$	−10.2742	−0.326536
$991$	−32.9203	−1.04575	−0.522874	−	0.852410i	$-0.675140\pi$
$991$	−32.9203	−1.04575	−0.522874	+	0.852410i	$0.675140\pi$
$992$	4.32000	0.137160
$993$	20.6451	0.655154
$994$	−42.1814	−1.33791
$995$	18.3867	0.582899
$996$	−0.877019	−0.0277894
$997$	8.38736	0.265630	0.132815	−	0.991141i	$-0.457598\pi$
$997$	8.38736	0.265630	0.132815	+	0.991141i	$0.457598\pi$
$998$	36.3912	1.15194
$999$	−30.6082	−0.968402

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.c.1.17	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.c.1.17	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.796272 q^{3} +1.00000 q^{4} -4.15767 q^{5} +0.796272 q^{6} +2.72658 q^{7} -1.00000 q^{8} -2.36595 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.796272 q^{3} +1.00000 q^{4} -4.15767 q^{5} +0.796272 q^{6} +2.72658 q^{7} -1.00000 q^{8} -2.36595 q^{9} +4.15767 q^{10} +1.04446 q^{11} -0.796272 q^{12} -4.91347 q^{13} -2.72658 q^{14} +3.31063 q^{15} +1.00000 q^{16} -5.30267 q^{17} +2.36595 q^{18} +5.52945 q^{19} -4.15767 q^{20} -2.17110 q^{21} -1.04446 q^{22} -4.24285 q^{23} +0.796272 q^{24} +12.2862 q^{25} +4.91347 q^{26} +4.27276 q^{27} +2.72658 q^{28} +0.0849704 q^{29} -3.31063 q^{30} -4.32000 q^{31} -1.00000 q^{32} -0.831677 q^{33} +5.30267 q^{34} -11.3362 q^{35} -2.36595 q^{36} -7.16359 q^{37} -5.52945 q^{38} +3.91246 q^{39} +4.15767 q^{40} -4.60832 q^{41} +2.17110 q^{42} -9.22942 q^{43} +1.04446 q^{44} +9.83684 q^{45} +4.24285 q^{46} -0.965307 q^{47} -0.796272 q^{48} +0.434261 q^{49} -12.2862 q^{50} +4.22237 q^{51} -4.91347 q^{52} -10.7612 q^{53} -4.27276 q^{54} -4.34254 q^{55} -2.72658 q^{56} -4.40295 q^{57} -0.0849704 q^{58} -4.49308 q^{59} +3.31063 q^{60} +10.2051 q^{61} +4.32000 q^{62} -6.45097 q^{63} +1.00000 q^{64} +20.4286 q^{65} +0.831677 q^{66} -6.24724 q^{67} -5.30267 q^{68} +3.37846 q^{69} +11.3362 q^{70} +15.4704 q^{71} +2.36595 q^{72} +10.2130 q^{73} +7.16359 q^{74} -9.78316 q^{75} +5.52945 q^{76} +2.84782 q^{77} -3.91246 q^{78} -15.4891 q^{79} -4.15767 q^{80} +3.69558 q^{81} +4.60832 q^{82} +1.10141 q^{83} -2.17110 q^{84} +22.0467 q^{85} +9.22942 q^{86} -0.0676595 q^{87} -1.04446 q^{88} -15.3407 q^{89} -9.83684 q^{90} -13.3970 q^{91} -4.24285 q^{92} +3.43990 q^{93} +0.965307 q^{94} -22.9896 q^{95} +0.796272 q^{96} +9.76359 q^{97} -0.434261 q^{98} -2.47115 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9}+O(q^{10}) \) 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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