LMFDB - Embedded newform 4034.2.a.a.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:	$1$
Dimension:	$33$
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.366256 q^{3} +1.00000 q^{4} +0.145528 q^{5} -0.366256 q^{6} +3.13381 q^{7} +1.00000 q^{8} -2.86586 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.366256 q^{3} +1.00000 q^{4} +0.145528 q^{5} -0.366256 q^{6} +3.13381 q^{7} +1.00000 q^{8} -2.86586 q^{9} +0.145528 q^{10} -2.53978 q^{11} -0.366256 q^{12} -2.06766 q^{13} +3.13381 q^{14} -0.0533003 q^{15} +1.00000 q^{16} +4.60540 q^{17} -2.86586 q^{18} -6.21209 q^{19} +0.145528 q^{20} -1.14778 q^{21} -2.53978 q^{22} -6.81602 q^{23} -0.366256 q^{24} -4.97882 q^{25} -2.06766 q^{26} +2.14840 q^{27} +3.13381 q^{28} -4.38115 q^{29} -0.0533003 q^{30} +1.20348 q^{31} +1.00000 q^{32} +0.930208 q^{33} +4.60540 q^{34} +0.456055 q^{35} -2.86586 q^{36} -2.43469 q^{37} -6.21209 q^{38} +0.757294 q^{39} +0.145528 q^{40} +3.27639 q^{41} -1.14778 q^{42} -4.27587 q^{43} -2.53978 q^{44} -0.417061 q^{45} -6.81602 q^{46} +9.97631 q^{47} -0.366256 q^{48} +2.82076 q^{49} -4.97882 q^{50} -1.68675 q^{51} -2.06766 q^{52} -12.2965 q^{53} +2.14840 q^{54} -0.369607 q^{55} +3.13381 q^{56} +2.27521 q^{57} -4.38115 q^{58} -9.09481 q^{59} -0.0533003 q^{60} -12.0357 q^{61} +1.20348 q^{62} -8.98105 q^{63} +1.00000 q^{64} -0.300902 q^{65} +0.930208 q^{66} -2.84168 q^{67} +4.60540 q^{68} +2.49641 q^{69} +0.456055 q^{70} +10.2637 q^{71} -2.86586 q^{72} +6.04280 q^{73} -2.43469 q^{74} +1.82352 q^{75} -6.21209 q^{76} -7.95917 q^{77} +0.757294 q^{78} -2.04976 q^{79} +0.145528 q^{80} +7.81071 q^{81} +3.27639 q^{82} -4.46848 q^{83} -1.14778 q^{84} +0.670212 q^{85} -4.27587 q^{86} +1.60462 q^{87} -2.53978 q^{88} -2.54236 q^{89} -0.417061 q^{90} -6.47966 q^{91} -6.81602 q^{92} -0.440782 q^{93} +9.97631 q^{94} -0.904029 q^{95} -0.366256 q^{96} +16.3159 q^{97} +2.82076 q^{98} +7.27863 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9}+O(q^{10}) $ 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9} - 22 q^{10} - 19 q^{11} - 14 q^{12} - 29 q^{13} - 12 q^{14} - 5 q^{15} + 33 q^{16} - 47 q^{17} + 17 q^{18} - 35 q^{19} - 22 q^{20} - 31 q^{21} - 19 q^{22} - 2 q^{23} - 14 q^{24} + 13 q^{25} - 29 q^{26} - 47 q^{27} - 12 q^{28} - 29 q^{29} - 5 q^{30} - 53 q^{31} + 33 q^{32} - 23 q^{33} - 47 q^{34} - 14 q^{35} + 17 q^{36} - 42 q^{37} - 35 q^{38} - 22 q^{40} - 42 q^{41} - 31 q^{42} - 26 q^{43} - 19 q^{44} - 55 q^{45} - 2 q^{46} - 14 q^{48} - 21 q^{49} + 13 q^{50} - 13 q^{51} - 29 q^{52} - 40 q^{53} - 47 q^{54} - 34 q^{55} - 12 q^{56} - 30 q^{57} - 29 q^{58} - 45 q^{59} - 5 q^{60} - 93 q^{61} - 53 q^{62} + 4 q^{63} + 33 q^{64} - 26 q^{65} - 23 q^{66} - 28 q^{67} - 47 q^{68} - 60 q^{69} - 14 q^{70} + 4 q^{71} + 17 q^{72} - 52 q^{73} - 42 q^{74} - 41 q^{75} - 35 q^{76} - 38 q^{77} - 38 q^{79} - 22 q^{80} + 25 q^{81} - 42 q^{82} - 42 q^{83} - 31 q^{84} - 21 q^{85} - 26 q^{86} + 12 q^{87} - 19 q^{88} - 58 q^{89} - 55 q^{90} - 79 q^{91} - 2 q^{92} + 25 q^{93} + 16 q^{95} - 14 q^{96} - 64 q^{97} - 21 q^{98} - 38 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9 - 22 * q^10 - 19 * q^11 - 14 * q^12 - 29 * q^13 - 12 * q^14 - 5 * q^15 + 33 * q^16 - 47 * q^17 + 17 * q^18 - 35 * q^19 - 22 * q^20 - 31 * q^21 - 19 * q^22 - 2 * q^23 - 14 * q^24 + 13 * q^25 - 29 * q^26 - 47 * q^27 - 12 * q^28 - 29 * q^29 - 5 * q^30 - 53 * q^31 + 33 * q^32 - 23 * q^33 - 47 * q^34 - 14 * q^35 + 17 * q^36 - 42 * q^37 - 35 * q^38 - 22 * q^40 - 42 * q^41 - 31 * q^42 - 26 * q^43 - 19 * q^44 - 55 * q^45 - 2 * q^46 - 14 * q^48 - 21 * q^49 + 13 * q^50 - 13 * q^51 - 29 * q^52 - 40 * q^53 - 47 * q^54 - 34 * q^55 - 12 * q^56 - 30 * q^57 - 29 * q^58 - 45 * q^59 - 5 * q^60 - 93 * q^61 - 53 * q^62 + 4 * q^63 + 33 * q^64 - 26 * q^65 - 23 * q^66 - 28 * q^67 - 47 * q^68 - 60 * q^69 - 14 * q^70 + 4 * q^71 + 17 * q^72 - 52 * q^73 - 42 * q^74 - 41 * q^75 - 35 * q^76 - 38 * q^77 - 38 * q^79 - 22 * q^80 + 25 * q^81 - 42 * q^82 - 42 * q^83 - 31 * q^84 - 21 * q^85 - 26 * q^86 + 12 * q^87 - 19 * q^88 - 58 * q^89 - 55 * q^90 - 79 * q^91 - 2 * q^92 + 25 * q^93 + 16 * q^95 - 14 * q^96 - 64 * q^97 - 21 * q^98 - 38 * 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
$3$	−0.366256	−0.211458	−0.105729	−	0.994395i	$-0.533718\pi$
$3$	−0.366256	−0.211458	−0.105729	+	0.994395i	$0.533718\pi$
$4$	1.00000	0.500000
$5$	0.145528	0.0650819	0.0325409	−	0.999470i	$-0.489640\pi$
$5$	0.145528	0.0650819	0.0325409	+	0.999470i	$0.489640\pi$
$6$	−0.366256	−0.149523
$7$	3.13381	1.18447	0.592234	−	0.805766i	$-0.298246\pi$
$7$	3.13381	1.18447	0.592234	+	0.805766i	$0.298246\pi$
$8$	1.00000	0.353553
$9$	−2.86586	−0.955286
$10$	0.145528	0.0460198
$11$	−2.53978	−0.765771	−0.382886	−	0.923796i	$-0.625070\pi$
$11$	−2.53978	−0.765771	−0.382886	+	0.923796i	$0.625070\pi$
$12$	−0.366256	−0.105729
$13$	−2.06766	−0.573467	−0.286733	−	0.958010i	$-0.592569\pi$
$13$	−2.06766	−0.573467	−0.286733	+	0.958010i	$0.592569\pi$
$14$	3.13381	0.837546
$15$	−0.0533003	−0.0137621
$16$	1.00000	0.250000
$17$	4.60540	1.11697	0.558487	−	0.829514i	$-0.311382\pi$
$17$	4.60540	1.11697	0.558487	+	0.829514i	$0.311382\pi$
$18$	−2.86586	−0.675489
$19$	−6.21209	−1.42515	−0.712575	−	0.701596i	$-0.752471\pi$
$19$	−6.21209	−1.42515	−0.712575	+	0.701596i	$0.752471\pi$
$20$	0.145528	0.0325409
$21$	−1.14778	−0.250465
$22$	−2.53978	−0.541482
$23$	−6.81602	−1.42124	−0.710619	−	0.703577i	$-0.751585\pi$
$23$	−6.81602	−1.42124	−0.710619	+	0.703577i	$0.751585\pi$
$24$	−0.366256	−0.0747616
$25$	−4.97882	−0.995764
$26$	−2.06766	−0.405502
$27$	2.14840	0.413460
$28$	3.13381	0.592234
$29$	−4.38115	−0.813560	−0.406780	−	0.913526i	$-0.633348\pi$
$29$	−4.38115	−0.813560	−0.406780	+	0.913526i	$0.633348\pi$
$30$	−0.0533003	−0.00973126
$31$	1.20348	0.216152	0.108076	−	0.994143i	$-0.465531\pi$
$31$	1.20348	0.216152	0.108076	+	0.994143i	$0.465531\pi$
$32$	1.00000	0.176777
$33$	0.930208	0.161928
$34$	4.60540	0.789819
$35$	0.456055	0.0770874
$36$	−2.86586	−0.477643
$37$	−2.43469	−0.400261	−0.200131	−	0.979769i	$-0.564137\pi$
$37$	−2.43469	−0.400261	−0.200131	+	0.979769i	$0.564137\pi$
$38$	−6.21209	−1.00773
$39$	0.757294	0.121264
$40$	0.145528	0.0230099
$41$	3.27639	0.511686	0.255843	−	0.966718i	$-0.417647\pi$
$41$	3.27639	0.511686	0.255843	+	0.966718i	$0.417647\pi$
$42$	−1.14778	−0.177106
$43$	−4.27587	−0.652064	−0.326032	−	0.945359i	$-0.605712\pi$
$43$	−4.27587	−0.652064	−0.326032	+	0.945359i	$0.605712\pi$
$44$	−2.53978	−0.382886
$45$	−0.417061	−0.0621718
$46$	−6.81602	−1.00497
$47$	9.97631	1.45519	0.727597	−	0.686004i	$-0.240637\pi$
$47$	9.97631	1.45519	0.727597	+	0.686004i	$0.240637\pi$
$48$	−0.366256	−0.0528645
$49$	2.82076	0.402965
$50$	−4.97882	−0.704112
$51$	−1.68675	−0.236193
$52$	−2.06766	−0.286733
$53$	−12.2965	−1.68905	−0.844527	−	0.535513i	$-0.820118\pi$
$53$	−12.2965	−1.68905	−0.844527	+	0.535513i	$0.820118\pi$
$54$	2.14840	0.292361
$55$	−0.369607	−0.0498378
$56$	3.13381	0.418773
$57$	2.27521	0.301359
$58$	−4.38115	−0.575273
$59$	−9.09481	−1.18404	−0.592022	−	0.805922i	$-0.701670\pi$
$59$	−9.09481	−1.18404	−0.592022	+	0.805922i	$0.701670\pi$
$60$	−0.0533003	−0.00688104
$61$	−12.0357	−1.54102	−0.770510	−	0.637428i	$-0.779998\pi$
$61$	−12.0357	−1.54102	−0.770510	+	0.637428i	$0.779998\pi$
$62$	1.20348	0.152842
$63$	−8.98105	−1.13151
$64$	1.00000	0.125000
$65$	−0.300902	−0.0373223
$66$	0.930208	0.114501
$67$	−2.84168	−0.347167	−0.173583	−	0.984819i	$-0.555535\pi$
$67$	−2.84168	−0.347167	−0.173583	+	0.984819i	$0.555535\pi$
$68$	4.60540	0.558487
$69$	2.49641	0.300532
$70$	0.456055	0.0545091
$71$	10.2637	1.21808	0.609040	−	0.793139i	$-0.291555\pi$
$71$	10.2637	1.21808	0.609040	+	0.793139i	$0.291555\pi$
$72$	−2.86586	−0.337744
$73$	6.04280	0.707257	0.353628	−	0.935386i	$-0.384948\pi$
$73$	6.04280	0.707257	0.353628	+	0.935386i	$0.384948\pi$
$74$	−2.43469	−0.283027
$75$	1.82352	0.210562
$76$	−6.21209	−0.712575
$77$	−7.95917	−0.907032
$78$	0.757294	0.0857466
$79$	−2.04976	−0.230616	−0.115308	−	0.993330i	$-0.536786\pi$
$79$	−2.04976	−0.230616	−0.115308	+	0.993330i	$0.536786\pi$
$80$	0.145528	0.0162705
$81$	7.81071	0.867856
$82$	3.27639	0.361817
$83$	−4.46848	−0.490479	−0.245240	−	0.969462i	$-0.578867\pi$
$83$	−4.46848	−0.490479	−0.245240	+	0.969462i	$0.578867\pi$
$84$	−1.14778	−0.125233
$85$	0.670212	0.0726947
$86$	−4.27587	−0.461079
$87$	1.60462	0.172034
$88$	−2.53978	−0.270741
$89$	−2.54236	−0.269489	−0.134745	−	0.990880i	$-0.543021\pi$
$89$	−2.54236	−0.269489	−0.134745	+	0.990880i	$0.543021\pi$
$90$	−0.417061	−0.0439621
$91$	−6.47966	−0.679253
$92$	−6.81602	−0.710619
$93$	−0.440782	−0.0457070
$94$	9.97631	1.02898
$95$	−0.904029	−0.0927515
$96$	−0.366256	−0.0373808
$97$	16.3159	1.65663	0.828315	−	0.560262i	$-0.189300\pi$
$97$	16.3159	1.65663	0.828315	+	0.560262i	$0.189300\pi$
$98$	2.82076	0.284940
$99$	7.27863	0.731530
$100$	−4.97882	−0.497882
$101$	−8.64376	−0.860086	−0.430043	−	0.902808i	$-0.641502\pi$
$101$	−8.64376	−0.860086	−0.430043	+	0.902808i	$0.641502\pi$
$102$	−1.68675	−0.167013
$103$	14.8501	1.46323	0.731613	−	0.681720i	$-0.238768\pi$
$103$	14.8501	1.46323	0.731613	+	0.681720i	$0.238768\pi$
$104$	−2.06766	−0.202751
$105$	−0.167033	−0.0163007
$106$	−12.2965	−1.19434
$107$	−14.4849	−1.40031	−0.700154	−	0.713992i	$-0.746885\pi$
$107$	−14.4849	−1.40031	−0.700154	+	0.713992i	$0.746885\pi$
$108$	2.14840	0.206730
$109$	19.2878	1.84744	0.923720	−	0.383068i	$-0.125132\pi$
$109$	19.2878	1.84744	0.923720	+	0.383068i	$0.125132\pi$
$110$	−0.369607	−0.0352407
$111$	0.891721	0.0846384
$112$	3.13381	0.296117
$113$	2.43644	0.229201	0.114600	−	0.993412i	$-0.463441\pi$
$113$	2.43644	0.229201	0.114600	+	0.993412i	$0.463441\pi$
$114$	2.27521	0.213093
$115$	−0.991919	−0.0924969
$116$	−4.38115	−0.406780
$117$	5.92563	0.547824
$118$	−9.09481	−0.837245
$119$	14.4324	1.32302
$120$	−0.0533003	−0.00486563
$121$	−4.54954	−0.413594
$122$	−12.0357	−1.08967
$123$	−1.20000	−0.108200
$124$	1.20348	0.108076
$125$	−1.45219	−0.129888
$126$	−8.98105	−0.800095
$127$	1.39622	0.123894	0.0619471	−	0.998079i	$-0.480269\pi$
$127$	1.39622	0.123894	0.0619471	+	0.998079i	$0.480269\pi$
$128$	1.00000	0.0883883
$129$	1.56606	0.137884
$130$	−0.300902	−0.0263908
$131$	−8.88147	−0.775978	−0.387989	−	0.921664i	$-0.626830\pi$
$131$	−8.88147	−0.775978	−0.387989	+	0.921664i	$0.626830\pi$
$132$	0.930208	0.0809642
$133$	−19.4675	−1.68805
$134$	−2.84168	−0.245484
$135$	0.312652	0.0269088
$136$	4.60540	0.394910
$137$	0.731194	0.0624701	0.0312351	−	0.999512i	$-0.490056\pi$
$137$	0.731194	0.0624701	0.0312351	+	0.999512i	$0.490056\pi$
$138$	2.49641	0.212508
$139$	9.69652	0.822448	0.411224	−	0.911534i	$-0.365101\pi$
$139$	9.69652	0.822448	0.411224	+	0.911534i	$0.365101\pi$
$140$	0.456055	0.0385437
$141$	−3.65388	−0.307712
$142$	10.2637	0.861313
$143$	5.25140	0.439144
$144$	−2.86586	−0.238821
$145$	−0.637578	−0.0529480
$146$	6.04280	0.500106
$147$	−1.03312	−0.0852102
$148$	−2.43469	−0.200131
$149$	10.3327	0.846486	0.423243	−	0.906016i	$-0.360892\pi$
$149$	10.3327	0.846486	0.423243	+	0.906016i	$0.360892\pi$
$150$	1.82352	0.148890
$151$	−10.8539	−0.883281	−0.441640	−	0.897192i	$-0.645603\pi$
$151$	−10.8539	−0.883281	−0.441640	+	0.897192i	$0.645603\pi$
$152$	−6.21209	−0.503867
$153$	−13.1984	−1.06703
$154$	−7.95917	−0.641368
$155$	0.175140	0.0140676
$156$	0.757294	0.0606320
$157$	−17.7596	−1.41737	−0.708685	−	0.705525i	$-0.750711\pi$
$157$	−17.7596	−1.41737	−0.708685	+	0.705525i	$0.750711\pi$
$158$	−2.04976	−0.163070
$159$	4.50366	0.357164
$160$	0.145528	0.0115050
$161$	−21.3601	−1.68341
$162$	7.81071	0.613667
$163$	−24.9541	−1.95456	−0.977280	−	0.211954i	$-0.932017\pi$
$163$	−24.9541	−1.95456	−0.977280	+	0.211954i	$0.932017\pi$
$164$	3.27639	0.255843
$165$	0.135371	0.0105386
$166$	−4.46848	−0.346821
$167$	8.04828	0.622795	0.311397	−	0.950280i	$-0.399203\pi$
$167$	8.04828	0.622795	0.311397	+	0.950280i	$0.399203\pi$
$168$	−1.14778	−0.0885528
$169$	−8.72477	−0.671136
$170$	0.670212	0.0514029
$171$	17.8029	1.36143
$172$	−4.27587	−0.326032
$173$	24.5022	1.86287	0.931433	−	0.363914i	$-0.118560\pi$
$173$	24.5022	1.86287	0.931433	+	0.363914i	$0.118560\pi$
$174$	1.60462	0.121646
$175$	−15.6027	−1.17945
$176$	−2.53978	−0.191443
$177$	3.33103	0.250375
$178$	−2.54236	−0.190558
$179$	9.70775	0.725591	0.362795	−	0.931869i	$-0.381822\pi$
$179$	9.70775	0.725591	0.362795	+	0.931869i	$0.381822\pi$
$180$	−0.417061	−0.0310859
$181$	−0.414124	−0.0307816	−0.0153908	−	0.999882i	$-0.504899\pi$
$181$	−0.414124	−0.0307816	−0.0153908	+	0.999882i	$0.504899\pi$
$182$	−6.47966	−0.480304
$183$	4.40816	0.325861
$184$	−6.81602	−0.502484
$185$	−0.354315	−0.0260498
$186$	−0.440782	−0.0323197
$187$	−11.6967	−0.855346
$188$	9.97631	0.727597
$189$	6.73269	0.489731
$190$	−0.904029	−0.0655852
$191$	−23.9950	−1.73622	−0.868110	−	0.496372i	$-0.834665\pi$
$191$	−23.9950	−1.73622	−0.868110	+	0.496372i	$0.834665\pi$
$192$	−0.366256	−0.0264322
$193$	−10.9892	−0.791021	−0.395510	−	0.918461i	$-0.629432\pi$
$193$	−10.9892	−0.791021	−0.395510	+	0.918461i	$0.629432\pi$
$194$	16.3159	1.17141
$195$	0.110207	0.00789209
$196$	2.82076	0.201483
$197$	−22.9589	−1.63576	−0.817878	−	0.575392i	$-0.804850\pi$
$197$	−22.9589	−1.63576	−0.817878	+	0.575392i	$0.804850\pi$
$198$	7.27863	0.517270
$199$	8.57194	0.607649	0.303824	−	0.952728i	$-0.401736\pi$
$199$	8.57194	0.607649	0.303824	+	0.952728i	$0.401736\pi$
$200$	−4.97882	−0.352056
$201$	1.04078	0.0734111
$202$	−8.64376	−0.608173
$203$	−13.7297	−0.963636
$204$	−1.68675	−0.118096
$205$	0.476805	0.0333015
$206$	14.8501	1.03466
$207$	19.5337	1.35769
$208$	−2.06766	−0.143367
$209$	15.7773	1.09134
$210$	−0.167033	−0.0115264
$211$	9.10006	0.626474	0.313237	−	0.949675i	$-0.398587\pi$
$211$	9.10006	0.626474	0.313237	+	0.949675i	$0.398587\pi$
$212$	−12.2965	−0.844527
$213$	−3.75915	−0.257573
$214$	−14.4849	−0.990167
$215$	−0.622256	−0.0424375
$216$	2.14840	0.146180
$217$	3.77148	0.256025
$218$	19.2878	1.30634
$219$	−2.21321	−0.149555
$220$	−0.369607	−0.0249189
$221$	−9.52241	−0.640547
$222$	0.891721	0.0598484
$223$	7.41982	0.496868	0.248434	−	0.968649i	$-0.420084\pi$
$223$	7.41982	0.496868	0.248434	+	0.968649i	$0.420084\pi$
$224$	3.13381	0.209386
$225$	14.2686	0.951239
$226$	2.43644	0.162069
$227$	−1.27244	−0.0844550	−0.0422275	−	0.999108i	$-0.513445\pi$
$227$	−1.27244	−0.0844550	−0.0422275	+	0.999108i	$0.513445\pi$
$228$	2.27521	0.150680
$229$	−11.0765	−0.731957	−0.365978	−	0.930623i	$-0.619266\pi$
$229$	−11.0765	−0.731957	−0.365978	+	0.930623i	$0.619266\pi$
$230$	−0.991919	−0.0654052
$231$	2.91509	0.191799
$232$	−4.38115	−0.287637
$233$	4.85323	0.317946	0.158973	−	0.987283i	$-0.449182\pi$
$233$	4.85323	0.317946	0.158973	+	0.987283i	$0.449182\pi$
$234$	5.92563	0.387370
$235$	1.45183	0.0947068
$236$	−9.09481	−0.592022
$237$	0.750737	0.0487656
$238$	14.4324	0.935516
$239$	7.33698	0.474590	0.237295	−	0.971438i	$-0.423739\pi$
$239$	7.33698	0.474590	0.237295	+	0.971438i	$0.423739\pi$
$240$	−0.0533003	−0.00344052
$241$	8.26943	0.532681	0.266340	−	0.963879i	$-0.414185\pi$
$241$	8.26943	0.532681	0.266340	+	0.963879i	$0.414185\pi$
$242$	−4.54954	−0.292455
$243$	−9.30593	−0.596975
$244$	−12.0357	−0.770510
$245$	0.410498	0.0262258
$246$	−1.20000	−0.0765090
$247$	12.8445	0.817276
$248$	1.20348	0.0764212
$249$	1.63661	0.103716
$250$	−1.45219	−0.0918448
$251$	17.8436	1.12628	0.563138	−	0.826363i	$-0.309594\pi$
$251$	17.8436	1.12628	0.563138	+	0.826363i	$0.309594\pi$
$252$	−8.98105	−0.565753
$253$	17.3112	1.08834
$254$	1.39622	0.0876065
$255$	−0.245469	−0.0153719
$256$	1.00000	0.0625000
$257$	−1.53187	−0.0955552	−0.0477776	−	0.998858i	$-0.515214\pi$
$257$	−1.53187	−0.0955552	−0.0477776	+	0.998858i	$0.515214\pi$
$258$	1.56606	0.0974987
$259$	−7.62987	−0.474097
$260$	−0.300902	−0.0186611
$261$	12.5558	0.777182
$262$	−8.88147	−0.548699
$263$	−26.3877	−1.62714	−0.813568	−	0.581470i	$-0.802478\pi$
$263$	−26.3877	−1.62714	−0.813568	+	0.581470i	$0.802478\pi$
$264$	0.930208	0.0572503
$265$	−1.78948	−0.109927
$266$	−19.4675	−1.19363
$267$	0.931153	0.0569857
$268$	−2.84168	−0.173583
$269$	−7.79866	−0.475493	−0.237746	−	0.971327i	$-0.576409\pi$
$269$	−7.79866	−0.475493	−0.237746	+	0.971327i	$0.576409\pi$
$270$	0.312652	0.0190274
$271$	−3.63476	−0.220796	−0.110398	−	0.993887i	$-0.535213\pi$
$271$	−3.63476	−0.220796	−0.110398	+	0.993887i	$0.535213\pi$
$272$	4.60540	0.279243
$273$	2.37321	0.143633
$274$	0.731194	0.0441730
$275$	12.6451	0.762528
$276$	2.49641	0.150266
$277$	12.5130	0.751832	0.375916	−	0.926654i	$-0.377328\pi$
$277$	12.5130	0.751832	0.375916	+	0.926654i	$0.377328\pi$
$278$	9.69652	0.581559
$279$	−3.44901	−0.206487
$280$	0.456055	0.0272545
$281$	−5.90991	−0.352556	−0.176278	−	0.984340i	$-0.556406\pi$
$281$	−5.90991	−0.352556	−0.176278	+	0.984340i	$0.556406\pi$
$282$	−3.65388	−0.217585
$283$	−7.92713	−0.471219	−0.235610	−	0.971848i	$-0.575709\pi$
$283$	−7.92713	−0.471219	−0.235610	+	0.971848i	$0.575709\pi$
$284$	10.2637	0.609040
$285$	0.331106	0.0196130
$286$	5.25140	0.310522
$287$	10.2676	0.606076
$288$	−2.86586	−0.168872
$289$	4.20969	0.247629
$290$	−0.637578	−0.0374399
$291$	−5.97580	−0.350308
$292$	6.04280	0.353628
$293$	3.87756	0.226529	0.113265	−	0.993565i	$-0.463869\pi$
$293$	3.87756	0.226529	0.113265	+	0.993565i	$0.463869\pi$
$294$	−1.03312	−0.0602527
$295$	−1.32354	−0.0770598
$296$	−2.43469	−0.141514
$297$	−5.45646	−0.316616
$298$	10.3327	0.598556
$299$	14.0932	0.815033
$300$	1.82352	0.105281
$301$	−13.3998	−0.772349
$302$	−10.8539	−0.624574
$303$	3.16583	0.181872
$304$	−6.21209	−0.356288
$305$	−1.75153	−0.100292
$306$	−13.1984	−0.754503
$307$	0.0374509	0.00213744	0.00106872	−	0.999999i	$-0.499660\pi$
$307$	0.0374509	0.00213744	0.00106872	+	0.999999i	$0.499660\pi$
$308$	−7.95917	−0.453516
$309$	−5.43894	−0.309411
$310$	0.175140	0.00994727
$311$	−6.10882	−0.346399	−0.173200	−	0.984887i	$-0.555411\pi$
$311$	−6.10882	−0.346399	−0.173200	+	0.984887i	$0.555411\pi$
$312$	0.757294	0.0428733
$313$	−22.3535	−1.26349	−0.631747	−	0.775174i	$-0.717662\pi$
$313$	−22.3535	−1.26349	−0.631747	+	0.775174i	$0.717662\pi$
$314$	−17.7596	−1.00223
$315$	−1.30699	−0.0736405
$316$	−2.04976	−0.115308
$317$	18.5695	1.04297	0.521484	−	0.853261i	$-0.325379\pi$
$317$	18.5695	1.04297	0.521484	+	0.853261i	$0.325379\pi$
$318$	4.50366	0.252553
$319$	11.1271	0.623001
$320$	0.145528	0.00813524
$321$	5.30517	0.296106
$322$	−21.3601	−1.19035
$323$	−28.6091	−1.59185
$324$	7.81071	0.433928
$325$	10.2945	0.571038
$326$	−24.9541	−1.38208
$327$	−7.06428	−0.390656
$328$	3.27639	0.180908
$329$	31.2639	1.72363
$330$	0.135371	0.00745192
$331$	10.4416	0.573923	0.286961	−	0.957942i	$-0.407355\pi$
$331$	10.4416	0.573923	0.286961	+	0.957942i	$0.407355\pi$
$332$	−4.46848	−0.245240
$333$	6.97748	0.382364
$334$	8.04828	0.440382
$335$	−0.413543	−0.0225943
$336$	−1.14778	−0.0626163
$337$	0.466859	0.0254314	0.0127157	−	0.999919i	$-0.495952\pi$
$337$	0.466859	0.0254314	0.0127157	+	0.999919i	$0.495952\pi$
$338$	−8.72477	−0.474565
$339$	−0.892358	−0.0484663
$340$	0.670212	0.0363474
$341$	−3.05657	−0.165523
$342$	17.8029	0.962673
$343$	−13.0969	−0.707169
$344$	−4.27587	−0.230539
$345$	0.363296	0.0195592
$346$	24.5022	1.31724
$347$	22.9790	1.23358	0.616790	−	0.787128i	$-0.288433\pi$
$347$	22.9790	1.23358	0.616790	+	0.787128i	$0.288433\pi$
$348$	1.60462	0.0860168
$349$	13.9854	0.748619	0.374310	−	0.927304i	$-0.377880\pi$
$349$	13.9854	0.748619	0.374310	+	0.927304i	$0.377880\pi$
$350$	−15.6027	−0.833998
$351$	−4.44218	−0.237106
$352$	−2.53978	−0.135371
$353$	7.83916	0.417237	0.208618	−	0.977997i	$-0.433103\pi$
$353$	7.83916	0.417237	0.208618	+	0.977997i	$0.433103\pi$
$354$	3.33103	0.177042
$355$	1.49365	0.0792750
$356$	−2.54236	−0.134745
$357$	−5.28596	−0.279763
$358$	9.70775	0.513070
$359$	0.0947581	0.00500114	0.00250057	−	0.999997i	$-0.499204\pi$
$359$	0.0947581	0.00500114	0.00250057	+	0.999997i	$0.499204\pi$
$360$	−0.417061	−0.0219810
$361$	19.5900	1.03105
$362$	−0.414124	−0.0217659
$363$	1.66629	0.0874578
$364$	−6.47966	−0.339627
$365$	0.879394	0.0460296
$366$	4.40816	0.230418
$367$	−17.6038	−0.918911	−0.459456	−	0.888201i	$-0.651955\pi$
$367$	−17.6038	−0.918911	−0.459456	+	0.888201i	$0.651955\pi$
$368$	−6.81602	−0.355310
$369$	−9.38966	−0.488806
$370$	−0.354315	−0.0184200
$371$	−38.5349	−2.00063
$372$	−0.440782	−0.0228535
$373$	−20.5251	−1.06275	−0.531376	−	0.847136i	$-0.678325\pi$
$373$	−20.5251	−1.06275	−0.531376	+	0.847136i	$0.678325\pi$
$374$	−11.6967	−0.604821
$375$	0.531874	0.0274659
$376$	9.97631	0.514489
$377$	9.05875	0.466549
$378$	6.73269	0.346292
$379$	−0.641769	−0.0329655	−0.0164827	−	0.999864i	$-0.505247\pi$
$379$	−0.641769	−0.0329655	−0.0164827	+	0.999864i	$0.505247\pi$
$380$	−0.904029	−0.0463757
$381$	−0.511373	−0.0261984
$382$	−23.9950	−1.22769
$383$	−35.4842	−1.81316	−0.906580	−	0.422034i	$-0.861316\pi$
$383$	−35.4842	−1.81316	−0.906580	+	0.422034i	$0.861316\pi$
$384$	−0.366256	−0.0186904
$385$	−1.15828	−0.0590314
$386$	−10.9892	−0.559336
$387$	12.2540	0.622907
$388$	16.3159	0.828315
$389$	−28.2847	−1.43409	−0.717046	−	0.697025i	$-0.754506\pi$
$389$	−28.2847	−1.43409	−0.717046	+	0.697025i	$0.754506\pi$
$390$	0.110207	0.00558055
$391$	−31.3905	−1.58749
$392$	2.82076	0.142470
$393$	3.25289	0.164087
$394$	−22.9589	−1.15665
$395$	−0.298297	−0.0150089
$396$	7.27863	0.365765
$397$	−14.8003	−0.742808	−0.371404	−	0.928471i	$-0.621124\pi$
$397$	−14.8003	−0.742808	−0.371404	+	0.928471i	$0.621124\pi$
$398$	8.57194	0.429673
$399$	7.13008	0.356950
$400$	−4.97882	−0.248941
$401$	3.97515	0.198509	0.0992547	−	0.995062i	$-0.468354\pi$
$401$	3.97515	0.198509	0.0992547	+	0.995062i	$0.468354\pi$
$402$	1.04078	0.0519095
$403$	−2.48839	−0.123956
$404$	−8.64376	−0.430043
$405$	1.13667	0.0564817
$406$	−13.7297	−0.681393
$407$	6.18358	0.306509
$408$	−1.68675	−0.0835067
$409$	−13.7296	−0.678883	−0.339442	−	0.940627i	$-0.610238\pi$
$409$	−13.7296	−0.678883	−0.339442	+	0.940627i	$0.610238\pi$
$410$	0.476805	0.0235477
$411$	−0.267804	−0.0132098
$412$	14.8501	0.731613
$413$	−28.5014	−1.40246
$414$	19.5337	0.960031
$415$	−0.650287	−0.0319213
$416$	−2.06766	−0.101376
$417$	−3.55141	−0.173913
$418$	15.7773	0.771693
$419$	30.7099	1.50028	0.750138	−	0.661281i	$-0.229987\pi$
$419$	30.7099	1.50028	0.750138	+	0.661281i	$0.229987\pi$
$420$	−0.167033	−0.00815037
$421$	−7.56377	−0.368635	−0.184318	−	0.982867i	$-0.559008\pi$
$421$	−7.56377	−0.368635	−0.184318	+	0.982867i	$0.559008\pi$
$422$	9.10006	0.442984
$423$	−28.5907	−1.39013
$424$	−12.2965	−0.597171
$425$	−22.9295	−1.11224
$426$	−3.75915	−0.182131
$427$	−37.7177	−1.82529
$428$	−14.4849	−0.700154
$429$	−1.92336	−0.0928605
$430$	−0.622256	−0.0300079
$431$	17.9161	0.862989	0.431495	−	0.902115i	$-0.357986\pi$
$431$	17.9161	0.862989	0.431495	+	0.902115i	$0.357986\pi$
$432$	2.14840	0.103365
$433$	−10.3180	−0.495853	−0.247927	−	0.968779i	$-0.579749\pi$
$433$	−10.3180	−0.495853	−0.247927	+	0.968779i	$0.579749\pi$
$434$	3.77148	0.181037
$435$	0.233517	0.0111963
$436$	19.2878	0.923720
$437$	42.3417	2.02548
$438$	−2.21321	−0.105751
$439$	21.4870	1.02552	0.512760	−	0.858532i	$-0.328623\pi$
$439$	21.4870	1.02552	0.512760	+	0.858532i	$0.328623\pi$
$440$	−0.369607	−0.0176203
$441$	−8.08389	−0.384947
$442$	−9.52241	−0.452935
$443$	19.8834	0.944691	0.472345	−	0.881414i	$-0.343407\pi$
$443$	19.8834	0.944691	0.472345	+	0.881414i	$0.343407\pi$
$444$	0.891721	0.0423192
$445$	−0.369983	−0.0175389
$446$	7.41982	0.351339
$447$	−3.78440	−0.178996
$448$	3.13381	0.148059
$449$	8.72808	0.411903	0.205952	−	0.978562i	$-0.433971\pi$
$449$	8.72808	0.411903	0.205952	+	0.978562i	$0.433971\pi$
$450$	14.2686	0.672628
$451$	−8.32130	−0.391835
$452$	2.43644	0.114600
$453$	3.97532	0.186777
$454$	−1.27244	−0.0597187
$455$	−0.942969	−0.0442071
$456$	2.27521	0.106547
$457$	−34.1222	−1.59617	−0.798084	−	0.602547i	$-0.794153\pi$
$457$	−34.1222	−1.59617	−0.798084	+	0.602547i	$0.794153\pi$
$458$	−11.0765	−0.517572
$459$	9.89425	0.461824
$460$	−0.991919	−0.0462485
$461$	31.1089	1.44888	0.724442	−	0.689335i	$-0.242097\pi$
$461$	31.1089	1.44888	0.724442	+	0.689335i	$0.242097\pi$
$462$	2.91509	0.135622
$463$	−21.6416	−1.00577	−0.502885	−	0.864353i	$-0.667728\pi$
$463$	−21.6416	−1.00577	−0.502885	+	0.864353i	$0.667728\pi$
$464$	−4.38115	−0.203390
$465$	−0.0641459	−0.00297470
$466$	4.85323	0.224821
$467$	36.4205	1.68534	0.842671	−	0.538429i	$-0.180982\pi$
$467$	36.4205	1.68534	0.842671	+	0.538429i	$0.180982\pi$
$468$	5.92563	0.273912
$469$	−8.90529	−0.411208
$470$	1.45183	0.0669678
$471$	6.50455	0.299714
$472$	−9.09481	−0.418622
$473$	10.8597	0.499332
$474$	0.750737	0.0344825
$475$	30.9289	1.41911
$476$	14.4324	0.661510
$477$	35.2400	1.61353
$478$	7.33698	0.335586
$479$	−15.4475	−0.705814	−0.352907	−	0.935658i	$-0.614807\pi$
$479$	−15.4475	−0.705814	−0.352907	+	0.935658i	$0.614807\pi$
$480$	−0.0533003	−0.00243281
$481$	5.03413	0.229536
$482$	8.26943	0.376662
$483$	7.82326	0.355971
$484$	−4.54954	−0.206797
$485$	2.37441	0.107817
$486$	−9.30593	−0.422125
$487$	−2.56916	−0.116420	−0.0582098	−	0.998304i	$-0.518539\pi$
$487$	−2.56916	−0.116420	−0.0582098	+	0.998304i	$0.518539\pi$
$488$	−12.0357	−0.544833
$489$	9.13960	0.413307
$490$	0.410498	0.0185444
$491$	29.1338	1.31479	0.657394	−	0.753547i	$-0.271659\pi$
$491$	29.1338	1.31479	0.657394	+	0.753547i	$0.271659\pi$
$492$	−1.20000	−0.0541000
$493$	−20.1769	−0.908724
$494$	12.8445	0.577901
$495$	1.05924	0.0476094
$496$	1.20348	0.0540379
$497$	32.1646	1.44278
$498$	1.63661	0.0733381
$499$	3.87695	0.173556	0.0867781	−	0.996228i	$-0.472343\pi$
$499$	3.87695	0.173556	0.0867781	+	0.996228i	$0.472343\pi$
$500$	−1.45219	−0.0649441
$501$	−2.94773	−0.131695
$502$	17.8436	0.796397
$503$	26.0304	1.16064	0.580318	−	0.814390i	$-0.302928\pi$
$503$	26.0304	1.16064	0.580318	+	0.814390i	$0.302928\pi$
$504$	−8.98105	−0.400048
$505$	−1.25790	−0.0559760
$506$	17.3112	0.769575
$507$	3.19550	0.141917
$508$	1.39622	0.0619471
$509$	6.19562	0.274616	0.137308	−	0.990528i	$-0.456155\pi$
$509$	6.19562	0.274616	0.137308	+	0.990528i	$0.456155\pi$
$510$	−0.245469	−0.0108696
$511$	18.9370	0.837723
$512$	1.00000	0.0441942
$513$	−13.3461	−0.589243
$514$	−1.53187	−0.0675677
$515$	2.16110	0.0952295
$516$	1.56606	0.0689420
$517$	−25.3376	−1.11435
$518$	−7.62987	−0.335237
$519$	−8.97406	−0.393917
$520$	−0.300902	−0.0131954
$521$	43.1143	1.88887	0.944435	−	0.328698i	$-0.106610\pi$
$521$	43.1143	1.88887	0.944435	+	0.328698i	$0.106610\pi$
$522$	12.5558	0.549550
$523$	9.19146	0.401914	0.200957	−	0.979600i	$-0.435595\pi$
$523$	9.19146	0.401914	0.200957	+	0.979600i	$0.435595\pi$
$524$	−8.88147	−0.387989
$525$	5.71457	0.249404
$526$	−26.3877	−1.15056
$527$	5.54251	0.241436
$528$	0.930208	0.0404821
$529$	23.4582	1.01992
$530$	−1.78948	−0.0777300
$531$	26.0644	1.13110
$532$	−19.4675	−0.844023
$533$	−6.77447	−0.293435
$534$	0.931153	0.0402950
$535$	−2.10795	−0.0911346
$536$	−2.84168	−0.122742
$537$	−3.55552	−0.153432
$538$	−7.79866	−0.336224
$539$	−7.16410	−0.308579
$540$	0.312652	0.0134544
$541$	1.26912	0.0545639	0.0272819	−	0.999628i	$-0.491315\pi$
$541$	1.26912	0.0545639	0.0272819	+	0.999628i	$0.491315\pi$
$542$	−3.63476	−0.156126
$543$	0.151675	0.00650901
$544$	4.60540	0.197455
$545$	2.80691	0.120235
$546$	2.37321	0.101564
$547$	3.13477	0.134033	0.0670166	−	0.997752i	$-0.478652\pi$
$547$	3.13477	0.134033	0.0670166	+	0.997752i	$0.478652\pi$
$548$	0.731194	0.0312351
$549$	34.4927	1.47211
$550$	12.6451	0.539189
$551$	27.2161	1.15944
$552$	2.49641	0.106254
$553$	−6.42356	−0.273158
$554$	12.5130	0.531625
$555$	0.129770	0.00550843
$556$	9.69652	0.411224
$557$	6.03607	0.255756	0.127878	−	0.991790i	$-0.459183\pi$
$557$	6.03607	0.255756	0.127878	+	0.991790i	$0.459183\pi$
$558$	−3.44901	−0.146008
$559$	8.84106	0.373937
$560$	0.456055	0.0192719
$561$	4.28398	0.180870
$562$	−5.90991	−0.249295
$563$	25.1785	1.06115	0.530575	−	0.847638i	$-0.321976\pi$
$563$	25.1785	1.06115	0.530575	+	0.847638i	$0.321976\pi$
$564$	−3.65388	−0.153856
$565$	0.354568	0.0149168
$566$	−7.92713	−0.333202
$567$	24.4773	1.02795
$568$	10.2637	0.430656
$569$	31.3964	1.31620	0.658102	−	0.752929i	$-0.271360\pi$
$569$	31.3964	1.31620	0.658102	+	0.752929i	$0.271360\pi$
$570$	0.331106	0.0138685
$571$	−23.3479	−0.977081	−0.488540	−	0.872541i	$-0.662471\pi$
$571$	−23.3479	−0.977081	−0.488540	+	0.872541i	$0.662471\pi$
$572$	5.25140	0.219572
$573$	8.78832	0.367137
$574$	10.2676	0.428561
$575$	33.9358	1.41522
$576$	−2.86586	−0.119411
$577$	−16.1065	−0.670523	−0.335262	−	0.942125i	$-0.608825\pi$
$577$	−16.1065	−0.670523	−0.335262	+	0.942125i	$0.608825\pi$
$578$	4.20969	0.175100
$579$	4.02486	0.167268
$580$	−0.637578	−0.0264740
$581$	−14.0034	−0.580957
$582$	−5.97580	−0.247705
$583$	31.2303	1.29343
$584$	6.04280	0.250053
$585$	0.862342	0.0356534
$586$	3.87756	0.160180
$587$	−4.63216	−0.191190	−0.0955948	−	0.995420i	$-0.530475\pi$
$587$	−4.63216	−0.191190	−0.0955948	+	0.995420i	$0.530475\pi$
$588$	−1.03312	−0.0426051
$589$	−7.47613	−0.308049
$590$	−1.32354	−0.0544895
$591$	8.40884	0.345893
$592$	−2.43469	−0.100065
$593$	−5.43873	−0.223342	−0.111671	−	0.993745i	$-0.535620\pi$
$593$	−5.43873	−0.223342	−0.111671	+	0.993745i	$0.535620\pi$
$594$	−5.45646	−0.223881
$595$	2.10032	0.0861046
$596$	10.3327	0.423243
$597$	−3.13952	−0.128492
$598$	14.0932	0.576315
$599$	−24.6352	−1.00657	−0.503284	−	0.864121i	$-0.667875\pi$
$599$	−24.6352	−1.00657	−0.503284	+	0.864121i	$0.667875\pi$
$600$	1.82352	0.0744450
$601$	25.1987	1.02788	0.513939	−	0.857827i	$-0.328186\pi$
$601$	25.1987	1.02788	0.513939	+	0.857827i	$0.328186\pi$
$602$	−13.3998	−0.546133
$603$	8.14385	0.331643
$604$	−10.8539	−0.441640
$605$	−0.662083	−0.0269175
$606$	3.16583	0.128603
$607$	12.1295	0.492321	0.246161	−	0.969229i	$-0.420831\pi$
$607$	12.1295	0.492321	0.246161	+	0.969229i	$0.420831\pi$
$608$	−6.21209	−0.251933
$609$	5.02858	0.203768
$610$	−1.75153	−0.0709175
$611$	−20.6277	−0.834506
$612$	−13.1984	−0.533514
$613$	−13.9487	−0.563382	−0.281691	−	0.959505i	$-0.590895\pi$
$613$	−13.9487	−0.563382	−0.281691	+	0.959505i	$0.590895\pi$
$614$	0.0374509	0.00151140
$615$	−0.174633	−0.00704186
$616$	−7.95917	−0.320684
$617$	−14.1094	−0.568022	−0.284011	−	0.958821i	$-0.591665\pi$
$617$	−14.1094	−0.568022	−0.284011	+	0.958821i	$0.591665\pi$
$618$	−5.43894	−0.218786
$619$	5.42921	0.218218	0.109109	−	0.994030i	$-0.465200\pi$
$619$	5.42921	0.218218	0.109109	+	0.994030i	$0.465200\pi$
$620$	0.175140	0.00703378
$621$	−14.6436	−0.587626
$622$	−6.10882	−0.244941
$623$	−7.96727	−0.319202
$624$	0.757294	0.0303160
$625$	24.6828	0.987311
$626$	−22.3535	−0.893426
$627$	−5.77853	−0.230772
$628$	−17.7596	−0.708685
$629$	−11.2127	−0.447081
$630$	−1.30699	−0.0520717
$631$	−35.2104	−1.40171	−0.700853	−	0.713306i	$-0.747197\pi$
$631$	−35.2104	−1.40171	−0.700853	+	0.713306i	$0.747197\pi$
$632$	−2.04976	−0.0815351
$633$	−3.33295	−0.132473
$634$	18.5695	0.737490
$635$	0.203188	0.00806327
$636$	4.50366	0.178582
$637$	−5.83238	−0.231087
$638$	11.1271	0.440528
$639$	−29.4144	−1.16361
$640$	0.145528	0.00575248
$641$	−0.729928	−0.0288304	−0.0144152	−	0.999896i	$-0.504589\pi$
$641$	−0.729928	−0.0288304	−0.0144152	+	0.999896i	$0.504589\pi$
$642$	5.30517	0.209379
$643$	43.7932	1.72703	0.863517	−	0.504320i	$-0.168257\pi$
$643$	43.7932	1.72703	0.863517	+	0.504320i	$0.168257\pi$
$644$	−21.3601	−0.841706
$645$	0.227905	0.00897375
$646$	−28.6091	−1.12561
$647$	−7.02332	−0.276115	−0.138058	−	0.990424i	$-0.544086\pi$
$647$	−7.02332	−0.276115	−0.138058	+	0.990424i	$0.544086\pi$
$648$	7.81071	0.306833
$649$	23.0988	0.906706
$650$	10.2945	0.403785
$651$	−1.38133	−0.0541385
$652$	−24.9541	−0.977280
$653$	46.5540	1.82180	0.910898	−	0.412631i	$-0.135390\pi$
$653$	46.5540	1.82180	0.910898	+	0.412631i	$0.135390\pi$
$654$	−7.06428	−0.276235
$655$	−1.29250	−0.0505021
$656$	3.27639	0.127922
$657$	−17.3178	−0.675632
$658$	31.2639	1.21879
$659$	35.1288	1.36842	0.684212	−	0.729283i	$-0.260146\pi$
$659$	35.1288	1.36842	0.684212	+	0.729283i	$0.260146\pi$
$660$	0.135371	0.00526930
$661$	−41.8079	−1.62614	−0.813070	−	0.582166i	$-0.802205\pi$
$661$	−41.8079	−1.62614	−0.813070	+	0.582166i	$0.802205\pi$
$662$	10.4416	0.405825
$663$	3.48764	0.135449
$664$	−4.46848	−0.173411
$665$	−2.83306	−0.109861
$666$	6.97748	0.270372
$667$	29.8620	1.15626
$668$	8.04828	0.311397
$669$	−2.71755	−0.105067
$670$	−0.413543	−0.0159766
$671$	30.5681	1.18007
$672$	−1.14778	−0.0442764
$673$	−29.6673	−1.14359	−0.571794	−	0.820397i	$-0.693752\pi$
$673$	−29.6673	−1.14359	−0.571794	+	0.820397i	$0.693752\pi$
$674$	0.466859	0.0179827
$675$	−10.6965	−0.411709
$676$	−8.72477	−0.335568
$677$	−46.9476	−1.80434	−0.902171	−	0.431378i	$-0.858027\pi$
$677$	−46.9476	−1.80434	−0.902171	+	0.431378i	$0.858027\pi$
$678$	−0.892358	−0.0342708
$679$	51.1310	1.96223
$680$	0.670212	0.0257015
$681$	0.466039	0.0178587
$682$	−3.05657	−0.117042
$683$	−15.2140	−0.582149	−0.291074	−	0.956700i	$-0.594013\pi$
$683$	−15.2140	−0.582149	−0.291074	+	0.956700i	$0.594013\pi$
$684$	17.8029	0.680713
$685$	0.106409	0.00406567
$686$	−13.0969	−0.500044
$687$	4.05684	0.154778
$688$	−4.27587	−0.163016
$689$	25.4250	0.968616
$690$	0.363296	0.0138304
$691$	21.7467	0.827283	0.413642	−	0.910440i	$-0.364257\pi$
$691$	21.7467	0.827283	0.413642	+	0.910440i	$0.364257\pi$
$692$	24.5022	0.931433
$693$	22.8099	0.866475
$694$	22.9790	0.872272
$695$	1.41111	0.0535265
$696$	1.60462	0.0608230
$697$	15.0891	0.571540
$698$	13.9854	0.529354
$699$	−1.77752	−0.0672321
$700$	−15.6027	−0.589726
$701$	29.1399	1.10060	0.550299	−	0.834968i	$-0.314514\pi$
$701$	29.1399	1.10060	0.550299	+	0.834968i	$0.314514\pi$
$702$	−4.44218	−0.167659
$703$	15.1245	0.570432
$704$	−2.53978	−0.0957214
$705$	−0.531740	−0.0200265
$706$	7.83916	0.295031
$707$	−27.0879	−1.01874
$708$	3.33103	0.125188
$709$	−38.6116	−1.45009	−0.725044	−	0.688702i	$-0.758181\pi$
$709$	−38.6116	−1.45009	−0.725044	+	0.688702i	$0.758181\pi$
$710$	1.49365	0.0560559
$711$	5.87432	0.220304
$712$	−2.54236	−0.0952789
$713$	−8.20296	−0.307203
$714$	−5.28596	−0.197822
$715$	0.764223	0.0285803
$716$	9.70775	0.362795
$717$	−2.68721	−0.100356
$718$	0.0947581	0.00353634
$719$	10.6266	0.396305	0.198152	−	0.980171i	$-0.436506\pi$
$719$	10.6266	0.396305	0.198152	+	0.980171i	$0.436506\pi$
$720$	−0.417061	−0.0155429
$721$	46.5375	1.73315
$722$	19.5900	0.729065
$723$	−3.02873	−0.112640
$724$	−0.414124	−0.0153908
$725$	21.8130	0.810114
$726$	1.66629	0.0618420
$727$	−31.1513	−1.15534	−0.577669	−	0.816271i	$-0.696037\pi$
$727$	−31.1513	−1.15534	−0.577669	+	0.816271i	$0.696037\pi$
$728$	−6.47966	−0.240152
$729$	−20.0238	−0.741621
$730$	0.879394	0.0325478
$731$	−19.6921	−0.728338
$732$	4.40816	0.162930
$733$	−16.0978	−0.594588	−0.297294	−	0.954786i	$-0.596084\pi$
$733$	−16.0978	−0.594588	−0.297294	+	0.954786i	$0.596084\pi$
$734$	−17.6038	−0.649768
$735$	−0.150347	−0.00554564
$736$	−6.81602	−0.251242
$737$	7.21723	0.265850
$738$	−9.38966	−0.345638
$739$	10.8504	0.399138	0.199569	−	0.979884i	$-0.436046\pi$
$739$	10.8504	0.399138	0.199569	+	0.979884i	$0.436046\pi$
$740$	−0.354315	−0.0130249
$741$	−4.70437	−0.172819
$742$	−38.5349	−1.41466
$743$	−37.8758	−1.38953	−0.694763	−	0.719238i	$-0.744491\pi$
$743$	−37.8758	−1.38953	−0.694763	+	0.719238i	$0.744491\pi$
$744$	−0.440782	−0.0161599
$745$	1.50369	0.0550909
$746$	−20.5251	−0.751479
$747$	12.8060	0.468548
$748$	−11.6967	−0.427673
$749$	−45.3929	−1.65862
$750$	0.531874	0.0194213
$751$	43.2804	1.57933	0.789663	−	0.613541i	$-0.210255\pi$
$751$	43.2804	1.57933	0.789663	+	0.613541i	$0.210255\pi$
$752$	9.97631	0.363799
$753$	−6.53530	−0.238160
$754$	9.05875	0.329900
$755$	−1.57955	−0.0574856
$756$	6.73269	0.244865
$757$	−14.0400	−0.510292	−0.255146	−	0.966903i	$-0.582124\pi$
$757$	−14.0400	−0.510292	−0.255146	+	0.966903i	$0.582124\pi$
$758$	−0.641769	−0.0233101
$759$	−6.34032	−0.230139
$760$	−0.904029	−0.0327926
$761$	10.4976	0.380536	0.190268	−	0.981732i	$-0.439064\pi$
$761$	10.4976	0.380536	0.190268	+	0.981732i	$0.439064\pi$
$762$	−0.511373	−0.0185251
$763$	60.4444	2.18824
$764$	−23.9950	−0.868110
$765$	−1.92073	−0.0694442
$766$	−35.4842	−1.28210
$767$	18.8050	0.679009
$768$	−0.366256	−0.0132161
$769$	−45.1401	−1.62779	−0.813897	−	0.581009i	$-0.802658\pi$
$769$	−45.1401	−1.62779	−0.813897	+	0.581009i	$0.802658\pi$
$770$	−1.15828	−0.0417415
$771$	0.561055	0.0202059
$772$	−10.9892	−0.395510
$773$	−1.89270	−0.0680756	−0.0340378	−	0.999421i	$-0.510837\pi$
$773$	−1.89270	−0.0680756	−0.0340378	+	0.999421i	$0.510837\pi$
$774$	12.2540	0.440462
$775$	−5.99192	−0.215236
$776$	16.3159	0.585707
$777$	2.79448	0.100251
$778$	−28.2847	−1.01406
$779$	−20.3532	−0.729230
$780$	0.110207	0.00394605
$781$	−26.0676	−0.932771
$782$	−31.3905	−1.12252
$783$	−9.41248	−0.336375
$784$	2.82076	0.100741
$785$	−2.58451	−0.0922451
$786$	3.25289	0.116027
$787$	−8.00059	−0.285190	−0.142595	−	0.989781i	$-0.545545\pi$
$787$	−8.00059	−0.285190	−0.142595	+	0.989781i	$0.545545\pi$
$788$	−22.9589	−0.817878
$789$	9.66465	0.344071
$790$	−0.298297	−0.0106129
$791$	7.63532	0.271481
$792$	7.27863	0.258635
$793$	24.8859	0.883723
$794$	−14.8003	−0.525245
$795$	0.655407	0.0232449
$796$	8.57194	0.303824
$797$	18.1319	0.642265	0.321133	−	0.947034i	$-0.395936\pi$
$797$	18.1319	0.642265	0.321133	+	0.947034i	$0.395936\pi$
$798$	7.13008	0.252402
$799$	45.9449	1.62541
$800$	−4.97882	−0.176028
$801$	7.28604	0.257439
$802$	3.97515	0.140367
$803$	−15.3474	−0.541597
$804$	1.04078	0.0367055
$805$	−3.10848	−0.109560
$806$	−2.48839	−0.0876500
$807$	2.85630	0.100547
$808$	−8.64376	−0.304086
$809$	−15.6101	−0.548824	−0.274412	−	0.961612i	$-0.588483\pi$
$809$	−15.6101	−0.548824	−0.274412	+	0.961612i	$0.588483\pi$
$810$	1.13667	0.0399386
$811$	−21.2366	−0.745716	−0.372858	−	0.927888i	$-0.621622\pi$
$811$	−21.2366	−0.745716	−0.372858	+	0.927888i	$0.621622\pi$
$812$	−13.7297	−0.481818
$813$	1.33125	0.0466891
$814$	6.18358	0.216734
$815$	−3.63151	−0.127206
$816$	−1.68675	−0.0590482
$817$	26.5621	0.929289
$818$	−13.7296	−0.480043
$819$	18.5698	0.648881
$820$	0.476805	0.0166507
$821$	41.5422	1.44983	0.724916	−	0.688838i	$-0.241879\pi$
$821$	41.5422	1.44983	0.724916	+	0.688838i	$0.241879\pi$
$822$	−0.267804	−0.00934074
$823$	32.6045	1.13652	0.568261	−	0.822848i	$-0.307616\pi$
$823$	32.6045	1.13652	0.568261	+	0.822848i	$0.307616\pi$
$824$	14.8501	0.517329
$825$	−4.63134	−0.161242
$826$	−28.5014	−0.991690
$827$	1.48271	0.0515589	0.0257794	−	0.999668i	$-0.491793\pi$
$827$	1.48271	0.0515589	0.0257794	+	0.999668i	$0.491793\pi$
$828$	19.5337	0.678844
$829$	0.0891552	0.00309649	0.00154824	−	0.999999i	$-0.499507\pi$
$829$	0.0891552	0.00309649	0.00154824	+	0.999999i	$0.499507\pi$
$830$	−0.650287	−0.0225718
$831$	−4.58295	−0.158981
$832$	−2.06766	−0.0716833
$833$	12.9907	0.450102
$834$	−3.55141	−0.122975
$835$	1.17125	0.0405327
$836$	15.7773	0.545670
$837$	2.58556	0.0893702
$838$	30.7099	1.06086
$839$	36.6986	1.26698	0.633488	−	0.773752i	$-0.281622\pi$
$839$	36.6986	1.26698	0.633488	+	0.773752i	$0.281622\pi$
$840$	−0.167033	−0.00576318
$841$	−9.80551	−0.338121
$842$	−7.56377	−0.260665
$843$	2.16454	0.0745507
$844$	9.10006	0.313237
$845$	−1.26969	−0.0436788
$846$	−28.5907	−0.982968
$847$	−14.2574	−0.489889
$848$	−12.2965	−0.422263
$849$	2.90336	0.0996430
$850$	−22.9295	−0.786474
$851$	16.5949	0.568867
$852$	−3.75915	−0.128786
$853$	−48.1940	−1.65013	−0.825066	−	0.565037i	$-0.808862\pi$
$853$	−48.1940	−1.65013	−0.825066	+	0.565037i	$0.808862\pi$
$854$	−37.7177	−1.29067
$855$	2.59082	0.0886041
$856$	−14.4849	−0.495083
$857$	1.44391	0.0493231	0.0246616	−	0.999696i	$-0.492149\pi$
$857$	1.44391	0.0493231	0.0246616	+	0.999696i	$0.492149\pi$
$858$	−1.92336	−0.0656623
$859$	−15.0933	−0.514977	−0.257489	−	0.966281i	$-0.582895\pi$
$859$	−15.0933	−0.514977	−0.257489	+	0.966281i	$0.582895\pi$
$860$	−0.622256	−0.0212188
$861$	−3.76056	−0.128160
$862$	17.9161	0.610226
$863$	35.2529	1.20002	0.600011	−	0.799992i	$-0.295163\pi$
$863$	35.2529	1.20002	0.600011	+	0.799992i	$0.295163\pi$
$864$	2.14840	0.0730902
$865$	3.56574	0.121239
$866$	−10.3180	−0.350621
$867$	−1.54182	−0.0523631
$868$	3.77148	0.128012
$869$	5.20593	0.176599
$870$	0.233517	0.00791696
$871$	5.87564	0.199088
$872$	19.2878	0.653169
$873$	−46.7591	−1.58256
$874$	42.3417	1.43223
$875$	−4.55090	−0.153848
$876$	−2.21321	−0.0747775
$877$	7.74855	0.261650	0.130825	−	0.991405i	$-0.458237\pi$
$877$	7.74855	0.261650	0.130825	+	0.991405i	$0.458237\pi$
$878$	21.4870	0.725152
$879$	−1.42018	−0.0479014
$880$	−0.369607	−0.0124595
$881$	−3.14237	−0.105869	−0.0529346	−	0.998598i	$-0.516857\pi$
$881$	−3.14237	−0.105869	−0.0529346	+	0.998598i	$0.516857\pi$
$882$	−8.08389	−0.272199
$883$	41.1843	1.38596	0.692981	−	0.720956i	$-0.256297\pi$
$883$	41.1843	1.38596	0.692981	+	0.720956i	$0.256297\pi$
$884$	−9.52241	−0.320273
$885$	0.484756	0.0162949
$886$	19.8834	0.667997
$887$	59.2748	1.99025	0.995126	−	0.0986119i	$-0.0314402\pi$
$887$	59.2748	1.99025	0.995126	+	0.0986119i	$0.0314402\pi$
$888$	0.891721	0.0299242
$889$	4.37548	0.146749
$890$	−0.369983	−0.0124019
$891$	−19.8374	−0.664579
$892$	7.41982	0.248434
$893$	−61.9737	−2.07387
$894$	−3.78440	−0.126569
$895$	1.41274	0.0472228
$896$	3.13381	0.104693
$897$	−5.16173	−0.172345
$898$	8.72808	0.291260
$899$	−5.27264	−0.175852
$900$	14.2686	0.475620
$901$	−56.6303	−1.88663
$902$	−8.32130	−0.277069
$903$	4.90774	0.163319
$904$	2.43644	0.0810346
$905$	−0.0602665	−0.00200333
$906$	3.97532	0.132071
$907$	30.9638	1.02814	0.514069	−	0.857749i	$-0.328138\pi$
$907$	30.9638	1.02814	0.514069	+	0.857749i	$0.328138\pi$
$908$	−1.27244	−0.0422275
$909$	24.7718	0.821628
$910$	−0.942969	−0.0312591
$911$	15.4184	0.510836	0.255418	−	0.966831i	$-0.417787\pi$
$911$	15.4184	0.510836	0.255418	+	0.966831i	$0.417787\pi$
$912$	2.27521	0.0753398
$913$	11.3489	0.375595
$914$	−34.1222	−1.12866
$915$	0.641509	0.0212076
$916$	−11.0765	−0.365978
$917$	−27.8328	−0.919121
$918$	9.89425	0.326559
$919$	22.9206	0.756080	0.378040	−	0.925789i	$-0.376598\pi$
$919$	22.9206	0.756080	0.378040	+	0.925789i	$0.376598\pi$
$920$	−0.991919	−0.0327026
$921$	−0.0137166	−0.000451978 0
$922$	31.1089	1.02452
$923$	−21.2219	−0.698528
$924$	2.91509	0.0958995
$925$	12.1219	0.398566
$926$	−21.6416	−0.711186
$927$	−42.5583	−1.39780
$928$	−4.38115	−0.143818
$929$	−42.9821	−1.41020	−0.705098	−	0.709110i	$-0.749097\pi$
$929$	−42.9821	−1.41020	−0.705098	+	0.709110i	$0.749097\pi$
$930$	−0.0641459	−0.00210343
$931$	−17.5228	−0.574286
$932$	4.85323	0.158973
$933$	2.23739	0.0732488
$934$	36.4205	1.19172
$935$	−1.70219	−0.0556675
$936$	5.92563	0.193685
$937$	−30.2550	−0.988387	−0.494194	−	0.869352i	$-0.664537\pi$
$937$	−30.2550	−0.988387	−0.494194	+	0.869352i	$0.664537\pi$
$938$	−8.90529	−0.290768
$939$	8.18710	0.267176
$940$	1.45183	0.0473534
$941$	−23.9151	−0.779611	−0.389806	−	0.920897i	$-0.627458\pi$
$941$	−23.9151	−0.779611	−0.389806	+	0.920897i	$0.627458\pi$
$942$	6.50455	0.211930
$943$	−22.3319	−0.727228
$944$	−9.09481	−0.296011
$945$	0.979791	0.0318726
$946$	10.8597	0.353081
$947$	35.2690	1.14609	0.573044	−	0.819525i	$-0.305763\pi$
$947$	35.2690	1.14609	0.573044	+	0.819525i	$0.305763\pi$
$948$	0.750737	0.0243828
$949$	−12.4945	−0.405588
$950$	30.9289	1.00346
$951$	−6.80119	−0.220544
$952$	14.4324	0.467758
$953$	−23.2328	−0.752584	−0.376292	−	0.926501i	$-0.622801\pi$
$953$	−23.2328	−0.752584	−0.376292	+	0.926501i	$0.622801\pi$
$954$	35.2400	1.14094
$955$	−3.49194	−0.112996
$956$	7.33698	0.237295
$957$	−4.07538	−0.131738
$958$	−15.4475	−0.499086
$959$	2.29142	0.0739939
$960$	−0.0533003	−0.00172026
$961$	−29.5516	−0.953278
$962$	5.03413	0.162307
$963$	41.5116	1.33769
$964$	8.26943	0.266340
$965$	−1.59923	−0.0514811
$966$	7.82326	0.251709
$967$	13.5908	0.437049	0.218525	−	0.975831i	$-0.429876\pi$
$967$	13.5908	0.437049	0.218525	+	0.975831i	$0.429876\pi$
$968$	−4.54954	−0.146228
$969$	10.4783	0.336610
$970$	2.37441	0.0762379
$971$	12.3132	0.395150	0.197575	−	0.980288i	$-0.436693\pi$
$971$	12.3132	0.395150	0.197575	+	0.980288i	$0.436693\pi$
$972$	−9.30593	−0.298488
$973$	30.3870	0.974164
$974$	−2.56916	−0.0823211
$975$	−3.77043	−0.120750
$976$	−12.0357	−0.385255
$977$	−20.0142	−0.640311	−0.320155	−	0.947365i	$-0.603735\pi$
$977$	−20.0142	−0.640311	−0.320155	+	0.947365i	$0.603735\pi$
$978$	9.13960	0.292252
$979$	6.45702	0.206367
$980$	0.410498	0.0131129
$981$	−55.2762	−1.76483
$982$	29.1338	0.929696
$983$	−18.8419	−0.600964	−0.300482	−	0.953787i	$-0.597148\pi$
$983$	−18.8419	−0.600964	−0.300482	+	0.953787i	$0.597148\pi$
$984$	−1.20000	−0.0382545
$985$	−3.34116	−0.106458
$986$	−20.1769	−0.642565
$987$	−11.4506	−0.364476
$988$	12.8445	0.408638
$989$	29.1444	0.926738
$990$	1.05924	0.0336649
$991$	12.7142	0.403880	0.201940	−	0.979398i	$-0.435275\pi$
$991$	12.7142	0.403880	0.201940	+	0.979398i	$0.435275\pi$
$992$	1.20348	0.0382106
$993$	−3.82430	−0.121360
$994$	32.1646	1.02020
$995$	1.24745	0.0395469
$996$	1.63661	0.0518578
$997$	−28.6612	−0.907711	−0.453855	−	0.891075i	$-0.649952\pi$
$997$	−28.6612	−0.907711	−0.453855	+	0.891075i	$0.649952\pi$
$998$	3.87695	0.122723
$999$	−5.23071	−0.165492

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.a.1.17	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.a.1.17	✓	33	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.366256 q^{3} +1.00000 q^{4} +0.145528 q^{5} -0.366256 q^{6} +3.13381 q^{7} +1.00000 q^{8} -2.86586 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.366256 q^{3} +1.00000 q^{4} +0.145528 q^{5} -0.366256 q^{6} +3.13381 q^{7} +1.00000 q^{8} -2.86586 q^{9} +0.145528 q^{10} -2.53978 q^{11} -0.366256 q^{12} -2.06766 q^{13} +3.13381 q^{14} -0.0533003 q^{15} +1.00000 q^{16} +4.60540 q^{17} -2.86586 q^{18} -6.21209 q^{19} +0.145528 q^{20} -1.14778 q^{21} -2.53978 q^{22} -6.81602 q^{23} -0.366256 q^{24} -4.97882 q^{25} -2.06766 q^{26} +2.14840 q^{27} +3.13381 q^{28} -4.38115 q^{29} -0.0533003 q^{30} +1.20348 q^{31} +1.00000 q^{32} +0.930208 q^{33} +4.60540 q^{34} +0.456055 q^{35} -2.86586 q^{36} -2.43469 q^{37} -6.21209 q^{38} +0.757294 q^{39} +0.145528 q^{40} +3.27639 q^{41} -1.14778 q^{42} -4.27587 q^{43} -2.53978 q^{44} -0.417061 q^{45} -6.81602 q^{46} +9.97631 q^{47} -0.366256 q^{48} +2.82076 q^{49} -4.97882 q^{50} -1.68675 q^{51} -2.06766 q^{52} -12.2965 q^{53} +2.14840 q^{54} -0.369607 q^{55} +3.13381 q^{56} +2.27521 q^{57} -4.38115 q^{58} -9.09481 q^{59} -0.0533003 q^{60} -12.0357 q^{61} +1.20348 q^{62} -8.98105 q^{63} +1.00000 q^{64} -0.300902 q^{65} +0.930208 q^{66} -2.84168 q^{67} +4.60540 q^{68} +2.49641 q^{69} +0.456055 q^{70} +10.2637 q^{71} -2.86586 q^{72} +6.04280 q^{73} -2.43469 q^{74} +1.82352 q^{75} -6.21209 q^{76} -7.95917 q^{77} +0.757294 q^{78} -2.04976 q^{79} +0.145528 q^{80} +7.81071 q^{81} +3.27639 q^{82} -4.46848 q^{83} -1.14778 q^{84} +0.670212 q^{85} -4.27587 q^{86} +1.60462 q^{87} -2.53978 q^{88} -2.54236 q^{89} -0.417061 q^{90} -6.47966 q^{91} -6.81602 q^{92} -0.440782 q^{93} +9.97631 q^{94} -0.904029 q^{95} -0.366256 q^{96} +16.3159 q^{97} +2.82076 q^{98} +7.27863 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9}+O(q^{10}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9} - 22 q^{10} - 19 q^{11} - 14 q^{12} - 29 q^{13} - 12 q^{14} - 5 q^{15} + 33 q^{16} - 47 q^{17} + 17 q^{18} - 35 q^{19} - 22 q^{20} - 31 q^{21} - 19 q^{22} - 2 q^{23} - 14 q^{24} + 13 q^{25} - 29 q^{26} - 47 q^{27} - 12 q^{28} - 29 q^{29} - 5 q^{30} - 53 q^{31} + 33 q^{32} - 23 q^{33} - 47 q^{34} - 14 q^{35} + 17 q^{36} - 42 q^{37} - 35 q^{38} - 22 q^{40} - 42 q^{41} - 31 q^{42} - 26 q^{43} - 19 q^{44} - 55 q^{45} - 2 q^{46} - 14 q^{48} - 21 q^{49} + 13 q^{50} - 13 q^{51} - 29 q^{52} - 40 q^{53} - 47 q^{54} - 34 q^{55} - 12 q^{56} - 30 q^{57} - 29 q^{58} - 45 q^{59} - 5 q^{60} - 93 q^{61} - 53 q^{62} + 4 q^{63} + 33 q^{64} - 26 q^{65} - 23 q^{66} - 28 q^{67} - 47 q^{68} - 60 q^{69} - 14 q^{70} + 4 q^{71} + 17 q^{72} - 52 q^{73} - 42 q^{74} - 41 q^{75} - 35 q^{76} - 38 q^{77} - 38 q^{79} - 22 q^{80} + 25 q^{81} - 42 q^{82} - 42 q^{83} - 31 q^{84} - 21 q^{85} - 26 q^{86} + 12 q^{87} - 19 q^{88} - 58 q^{89} - 55 q^{90} - 79 q^{91} - 2 q^{92} + 25 q^{93} + 16 q^{95} - 14 q^{96} - 64 q^{97} - 21 q^{98} - 38 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9 - 22 * q^10 - 19 * q^11 - 14 * q^12 - 29 * q^13 - 12 * q^14 - 5 * q^15 + 33 * q^16 - 47 * q^17 + 17 * q^18 - 35 * q^19 - 22 * q^20 - 31 * q^21 - 19 * q^22 - 2 * q^23 - 14 * q^24 + 13 * q^25 - 29 * q^26 - 47 * q^27 - 12 * q^28 - 29 * q^29 - 5 * q^30 - 53 * q^31 + 33 * q^32 - 23 * q^33 - 47 * q^34 - 14 * q^35 + 17 * q^36 - 42 * q^37 - 35 * q^38 - 22 * q^40 - 42 * q^41 - 31 * q^42 - 26 * q^43 - 19 * q^44 - 55 * q^45 - 2 * q^46 - 14 * q^48 - 21 * q^49 + 13 * q^50 - 13 * q^51 - 29 * q^52 - 40 * q^53 - 47 * q^54 - 34 * q^55 - 12 * q^56 - 30 * q^57 - 29 * q^58 - 45 * q^59 - 5 * q^60 - 93 * q^61 - 53 * q^62 + 4 * q^63 + 33 * q^64 - 26 * q^65 - 23 * q^66 - 28 * q^67 - 47 * q^68 - 60 * q^69 - 14 * q^70 + 4 * q^71 + 17 * q^72 - 52 * q^73 - 42 * q^74 - 41 * q^75 - 35 * q^76 - 38 * q^77 - 38 * q^79 - 22 * q^80 + 25 * q^81 - 42 * q^82 - 42 * q^83 - 31 * q^84 - 21 * q^85 - 26 * q^86 + 12 * q^87 - 19 * q^88 - 58 * q^89 - 55 * q^90 - 79 * q^91 - 2 * q^92 + 25 * q^93 + 16 * q^95 - 14 * q^96 - 64 * q^97 - 21 * q^98 - 38 * q^99

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