LMFDB - Embedded newform 4730.2.a.be.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4730,2,Mod(1,4730)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.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:	$37.7692401561$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 26 x^{10} + 79 x^{9} + 247 x^{8} - 766 x^{7} - 1023 x^{6} + 3281 x^{5} + 1634 x^{4} + \cdots + 392 $ x^12 - 3x^11 - 26x^10 + 79x^9 + 247x^8 - 766x^7 - 1023x^6 + 3281x^5 + 1634x^4 - 5557x^3 - 483x^2 + 1648*x + 392
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.343172$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.343172 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.343172 q^{6} +1.96292 q^{7} +1.00000 q^{8} -2.88223 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.343172 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.343172 q^{6} +1.96292 q^{7} +1.00000 q^{8} -2.88223 q^{9} +1.00000 q^{10} -1.00000 q^{11} -0.343172 q^{12} +1.02610 q^{13} +1.96292 q^{14} -0.343172 q^{15} +1.00000 q^{16} +0.111417 q^{17} -2.88223 q^{18} +5.01168 q^{19} +1.00000 q^{20} -0.673617 q^{21} -1.00000 q^{22} +0.973905 q^{23} -0.343172 q^{24} +1.00000 q^{25} +1.02610 q^{26} +2.01862 q^{27} +1.96292 q^{28} -9.68570 q^{29} -0.343172 q^{30} +4.48766 q^{31} +1.00000 q^{32} +0.343172 q^{33} +0.111417 q^{34} +1.96292 q^{35} -2.88223 q^{36} +7.67715 q^{37} +5.01168 q^{38} -0.352127 q^{39} +1.00000 q^{40} +10.2966 q^{41} -0.673617 q^{42} +1.00000 q^{43} -1.00000 q^{44} -2.88223 q^{45} +0.973905 q^{46} -0.925482 q^{47} -0.343172 q^{48} -3.14696 q^{49} +1.00000 q^{50} -0.0382353 q^{51} +1.02610 q^{52} -2.23401 q^{53} +2.01862 q^{54} -1.00000 q^{55} +1.96292 q^{56} -1.71987 q^{57} -9.68570 q^{58} +5.32880 q^{59} -0.343172 q^{60} +0.397349 q^{61} +4.48766 q^{62} -5.65758 q^{63} +1.00000 q^{64} +1.02610 q^{65} +0.343172 q^{66} -13.1451 q^{67} +0.111417 q^{68} -0.334216 q^{69} +1.96292 q^{70} +12.5445 q^{71} -2.88223 q^{72} +12.9714 q^{73} +7.67715 q^{74} -0.343172 q^{75} +5.01168 q^{76} -1.96292 q^{77} -0.352127 q^{78} +13.2526 q^{79} +1.00000 q^{80} +7.95397 q^{81} +10.2966 q^{82} -0.377731 q^{83} -0.673617 q^{84} +0.111417 q^{85} +1.00000 q^{86} +3.32386 q^{87} -1.00000 q^{88} +7.70612 q^{89} -2.88223 q^{90} +2.01414 q^{91} +0.973905 q^{92} -1.54004 q^{93} -0.925482 q^{94} +5.01168 q^{95} -0.343172 q^{96} -1.20697 q^{97} -3.14696 q^{98} +2.88223 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 12 q^{5} + 3 q^{6} + 8 q^{7} + 12 q^{8} + 25 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 12 * q^5 + 3 * q^6 + 8 * q^7 + 12 * q^8 + 25 * q^9	\( 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 12 q^{5} + 3 q^{6} + 8 q^{7} + 12 q^{8} + 25 q^{9} + 12 q^{10} - 12 q^{11} + 3 q^{12} + 16 q^{13} + 8 q^{14} + 3 q^{15} + 12 q^{16} + 18 q^{17} + 25 q^{18} - 4 q^{19} + 12 q^{20} + 4 q^{21} - 12 q^{22} + 8 q^{23} + 3 q^{24} + 12 q^{25} + 16 q^{26} + 6 q^{27} + 8 q^{28} + 20 q^{29} + 3 q^{30} + 5 q^{31} + 12 q^{32} - 3 q^{33} + 18 q^{34} + 8 q^{35} + 25 q^{36} + 19 q^{37} - 4 q^{38} + 6 q^{39} + 12 q^{40} + 16 q^{41} + 4 q^{42} + 12 q^{43} - 12 q^{44} + 25 q^{45} + 8 q^{46} - q^{47} + 3 q^{48} + 52 q^{49} + 12 q^{50} + q^{51} + 16 q^{52} + 11 q^{53} + 6 q^{54} - 12 q^{55} + 8 q^{56} + 9 q^{57} + 20 q^{58} - 11 q^{59} + 3 q^{60} + 18 q^{61} + 5 q^{62} + 15 q^{63} + 12 q^{64} + 16 q^{65} - 3 q^{66} - 10 q^{67} + 18 q^{68} + 8 q^{70} - 2 q^{71} + 25 q^{72} + 29 q^{73} + 19 q^{74} + 3 q^{75} - 4 q^{76} - 8 q^{77} + 6 q^{78} + 2 q^{79} + 12 q^{80} - 8 q^{81} + 16 q^{82} + 26 q^{83} + 4 q^{84} + 18 q^{85} + 12 q^{86} - 4 q^{87} - 12 q^{88} + 41 q^{89} + 25 q^{90} - 4 q^{91} + 8 q^{92} + 5 q^{93} - q^{94} - 4 q^{95} + 3 q^{96} - 7 q^{97} + 52 q^{98} - 25 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 12 * q^5 + 3 * q^6 + 8 * q^7 + 12 * q^8 + 25 * q^9 + 12 * q^10 - 12 * q^11 + 3 * q^12 + 16 * q^13 + 8 * q^14 + 3 * q^15 + 12 * q^16 + 18 * q^17 + 25 * q^18 - 4 * q^19 + 12 * q^20 + 4 * q^21 - 12 * q^22 + 8 * q^23 + 3 * q^24 + 12 * q^25 + 16 * q^26 + 6 * q^27 + 8 * q^28 + 20 * q^29 + 3 * q^30 + 5 * q^31 + 12 * q^32 - 3 * q^33 + 18 * q^34 + 8 * q^35 + 25 * q^36 + 19 * q^37 - 4 * q^38 + 6 * q^39 + 12 * q^40 + 16 * q^41 + 4 * q^42 + 12 * q^43 - 12 * q^44 + 25 * q^45 + 8 * q^46 - q^47 + 3 * q^48 + 52 * q^49 + 12 * q^50 + q^51 + 16 * q^52 + 11 * q^53 + 6 * q^54 - 12 * q^55 + 8 * q^56 + 9 * q^57 + 20 * q^58 - 11 * q^59 + 3 * q^60 + 18 * q^61 + 5 * q^62 + 15 * q^63 + 12 * q^64 + 16 * q^65 - 3 * q^66 - 10 * q^67 + 18 * q^68 + 8 * q^70 - 2 * q^71 + 25 * q^72 + 29 * q^73 + 19 * q^74 + 3 * q^75 - 4 * q^76 - 8 * q^77 + 6 * q^78 + 2 * q^79 + 12 * q^80 - 8 * q^81 + 16 * q^82 + 26 * q^83 + 4 * q^84 + 18 * q^85 + 12 * q^86 - 4 * q^87 - 12 * q^88 + 41 * q^89 + 25 * q^90 - 4 * q^91 + 8 * q^92 + 5 * q^93 - q^94 - 4 * q^95 + 3 * q^96 - 7 * q^97 + 52 * q^98 - 25 * 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
$3$	−0.343172	−0.198130	−0.0990651	−	0.995081i	$-0.531585\pi$
$3$	−0.343172	−0.198130	−0.0990651	+	0.995081i	$0.531585\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.343172	−0.140099
$7$	1.96292	0.741913	0.370956	−	0.928650i	$-0.379030\pi$
$7$	1.96292	0.741913	0.370956	+	0.928650i	$0.379030\pi$
$8$	1.00000	0.353553
$9$	−2.88223	−0.960744
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.343172	−0.0990651
$13$	1.02610	0.284588	0.142294	−	0.989824i	$-0.454552\pi$
$13$	1.02610	0.284588	0.142294	+	0.989824i	$0.454552\pi$
$14$	1.96292	0.524611
$15$	−0.343172	−0.0886065
$16$	1.00000	0.250000
$17$	0.111417	0.0270227	0.0135114	−	0.999909i	$-0.495699\pi$
$17$	0.111417	0.0270227	0.0135114	+	0.999909i	$0.495699\pi$
$18$	−2.88223	−0.679349
$19$	5.01168	1.14976	0.574879	−	0.818238i	$-0.305049\pi$
$19$	5.01168	1.14976	0.574879	+	0.818238i	$0.305049\pi$
$20$	1.00000	0.223607
$21$	−0.673617	−0.146995
$22$	−1.00000	−0.213201
$23$	0.973905	0.203073	0.101537	−	0.994832i	$-0.467624\pi$
$23$	0.973905	0.203073	0.101537	+	0.994832i	$0.467624\pi$
$24$	−0.343172	−0.0700496
$25$	1.00000	0.200000
$26$	1.02610	0.201234
$27$	2.01862	0.388483
$28$	1.96292	0.370956
$29$	−9.68570	−1.79859	−0.899295	−	0.437343i	$-0.855920\pi$
$29$	−9.68570	−1.79859	−0.899295	+	0.437343i	$0.855920\pi$
$30$	−0.343172	−0.0626543
$31$	4.48766	0.806007	0.403003	−	0.915198i	$-0.367966\pi$
$31$	4.48766	0.806007	0.403003	+	0.915198i	$0.367966\pi$
$32$	1.00000	0.176777
$33$	0.343172	0.0597385
$34$	0.111417	0.0191079
$35$	1.96292	0.331793
$36$	−2.88223	−0.480372
$37$	7.67715	1.26212	0.631058	−	0.775736i	$-0.282621\pi$
$37$	7.67715	1.26212	0.631058	+	0.775736i	$0.282621\pi$
$38$	5.01168	0.813002
$39$	−0.352127	−0.0563854
$40$	1.00000	0.158114
$41$	10.2966	1.60806	0.804028	−	0.594591i	$-0.202686\pi$
$41$	10.2966	1.60806	0.804028	+	0.594591i	$0.202686\pi$
$42$	−0.673617	−0.103941
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.00000	−0.150756
$45$	−2.88223	−0.429658
$46$	0.973905	0.143594
$47$	−0.925482	−0.134995	−0.0674977	−	0.997719i	$-0.521502\pi$
$47$	−0.925482	−0.134995	−0.0674977	+	0.997719i	$0.521502\pi$
$48$	−0.343172	−0.0495326
$49$	−3.14696	−0.449566
$50$	1.00000	0.141421
$51$	−0.0382353	−0.00535401
$52$	1.02610	0.142294
$53$	−2.23401	−0.306865	−0.153433	−	0.988159i	$-0.549033\pi$
$53$	−2.23401	−0.306865	−0.153433	+	0.988159i	$0.549033\pi$
$54$	2.01862	0.274699
$55$	−1.00000	−0.134840
$56$	1.96292	0.262306
$57$	−1.71987	−0.227802
$58$	−9.68570	−1.27180
$59$	5.32880	0.693751	0.346875	−	0.937911i	$-0.387243\pi$
$59$	5.32880	0.693751	0.346875	+	0.937911i	$0.387243\pi$
$60$	−0.343172	−0.0443033
$61$	0.397349	0.0508753	0.0254376	−	0.999676i	$-0.491902\pi$
$61$	0.397349	0.0508753	0.0254376	+	0.999676i	$0.491902\pi$
$62$	4.48766	0.569933
$63$	−5.65758	−0.712788
$64$	1.00000	0.125000
$65$	1.02610	0.127271
$66$	0.343172	0.0422415
$67$	−13.1451	−1.60593	−0.802963	−	0.596028i	$-0.796745\pi$
$67$	−13.1451	−1.60593	−0.802963	+	0.596028i	$0.796745\pi$
$68$	0.111417	0.0135114
$69$	−0.334216	−0.0402349
$70$	1.96292	0.234613
$71$	12.5445	1.48876	0.744378	−	0.667758i	$-0.232746\pi$
$71$	12.5445	1.48876	0.744378	+	0.667758i	$0.232746\pi$
$72$	−2.88223	−0.339674
$73$	12.9714	1.51819	0.759096	−	0.650979i	$-0.225641\pi$
$73$	12.9714	1.51819	0.759096	+	0.650979i	$0.225641\pi$
$74$	7.67715	0.892450
$75$	−0.343172	−0.0396260
$76$	5.01168	0.574879
$77$	−1.96292	−0.223695
$78$	−0.352127	−0.0398705
$79$	13.2526	1.49103	0.745517	−	0.666487i	$-0.232203\pi$
$79$	13.2526	1.49103	0.745517	+	0.666487i	$0.232203\pi$
$80$	1.00000	0.111803
$81$	7.95397	0.883774
$82$	10.2966	1.13707
$83$	−0.377731	−0.0414614	−0.0207307	−	0.999785i	$-0.506599\pi$
$83$	−0.377731	−0.0414614	−0.0207307	+	0.999785i	$0.506599\pi$
$84$	−0.673617	−0.0734977
$85$	0.111417	0.0120849
$86$	1.00000	0.107833
$87$	3.32386	0.356355
$88$	−1.00000	−0.106600
$89$	7.70612	0.816847	0.408423	−	0.912793i	$-0.366079\pi$
$89$	7.70612	0.816847	0.408423	+	0.912793i	$0.366079\pi$
$90$	−2.88223	−0.303814
$91$	2.01414	0.211139
$92$	0.973905	0.101537
$93$	−1.54004	−0.159694
$94$	−0.925482	−0.0954562
$95$	5.01168	0.514188
$96$	−0.343172	−0.0350248
$97$	−1.20697	−0.122549	−0.0612747	−	0.998121i	$-0.519517\pi$
$97$	−1.20697	−0.122549	−0.0612747	+	0.998121i	$0.519517\pi$
$98$	−3.14696	−0.317891
$99$	2.88223	0.289675
$100$	1.00000	0.100000
$101$	−11.1242	−1.10689	−0.553447	−	0.832884i	$-0.686688\pi$
$101$	−11.1242	−1.10689	−0.553447	+	0.832884i	$0.686688\pi$
$102$	−0.0382353	−0.00378586
$103$	9.21177	0.907663	0.453832	−	0.891088i	$-0.350057\pi$
$103$	9.21177	0.907663	0.453832	+	0.891088i	$0.350057\pi$
$104$	1.02610	0.100617
$105$	−0.673617	−0.0657383
$106$	−2.23401	−0.216987
$107$	−9.38489	−0.907272	−0.453636	−	0.891187i	$-0.649873\pi$
$107$	−9.38489	−0.907272	−0.453636	+	0.891187i	$0.649873\pi$
$108$	2.01862	0.194241
$109$	0.143253	0.0137211	0.00686057	−	0.999976i	$-0.497816\pi$
$109$	0.143253	0.0137211	0.00686057	+	0.999976i	$0.497816\pi$
$110$	−1.00000	−0.0953463
$111$	−2.63458	−0.250063
$112$	1.96292	0.185478
$113$	2.94465	0.277009	0.138504	−	0.990362i	$-0.455770\pi$
$113$	2.94465	0.277009	0.138504	+	0.990362i	$0.455770\pi$
$114$	−1.71987	−0.161080
$115$	0.973905	0.0908171
$116$	−9.68570	−0.899295
$117$	−2.95745	−0.273416
$118$	5.32880	0.490556
$119$	0.218703	0.0200485
$120$	−0.343172	−0.0313271
$121$	1.00000	0.0909091
$122$	0.397349	0.0359743
$123$	−3.53349	−0.318604
$124$	4.48766	0.403003
$125$	1.00000	0.0894427
$126$	−5.65758	−0.504018
$127$	−3.00367	−0.266533	−0.133266	−	0.991080i	$-0.542547\pi$
$127$	−3.00367	−0.266533	−0.133266	+	0.991080i	$0.542547\pi$
$128$	1.00000	0.0883883
$129$	−0.343172	−0.0302146
$130$	1.02610	0.0899945
$131$	−0.295344	−0.0258043	−0.0129021	−	0.999917i	$-0.504107\pi$
$131$	−0.295344	−0.0258043	−0.0129021	+	0.999917i	$0.504107\pi$
$132$	0.343172	0.0298693
$133$	9.83751	0.853020
$134$	−13.1451	−1.13556
$135$	2.01862	0.173735
$136$	0.111417	0.00955397
$137$	−21.6844	−1.85262	−0.926311	−	0.376759i	$-0.877038\pi$
$137$	−21.6844	−1.85262	−0.926311	+	0.376759i	$0.877038\pi$
$138$	−0.334216	−0.0284504
$139$	1.97472	0.167494	0.0837468	−	0.996487i	$-0.473311\pi$
$139$	1.97472	0.167494	0.0837468	+	0.996487i	$0.473311\pi$
$140$	1.96292	0.165897
$141$	0.317599	0.0267467
$142$	12.5445	1.05271
$143$	−1.02610	−0.0858064
$144$	−2.88223	−0.240186
$145$	−9.68570	−0.804354
$146$	12.9714	1.07352
$147$	1.07995	0.0890725
$148$	7.67715	0.631058
$149$	−14.3032	−1.17177	−0.585883	−	0.810396i	$-0.699252\pi$
$149$	−14.3032	−1.17177	−0.585883	+	0.810396i	$0.699252\pi$
$150$	−0.343172	−0.0280198
$151$	18.6113	1.51456	0.757282	−	0.653088i	$-0.226527\pi$
$151$	18.6113	1.51456	0.757282	+	0.653088i	$0.226527\pi$
$152$	5.01168	0.406501
$153$	−0.321131	−0.0259619
$154$	−1.96292	−0.158176
$155$	4.48766	0.360457
$156$	−0.352127	−0.0281927
$157$	1.59630	0.127399	0.0636994	−	0.997969i	$-0.479710\pi$
$157$	1.59630	0.127399	0.0636994	+	0.997969i	$0.479710\pi$
$158$	13.2526	1.05432
$159$	0.766650	0.0607993
$160$	1.00000	0.0790569
$161$	1.91169	0.150663
$162$	7.95397	0.624923
$163$	7.78911	0.610090	0.305045	−	0.952338i	$-0.401328\pi$
$163$	7.78911	0.610090	0.305045	+	0.952338i	$0.401328\pi$
$164$	10.2966	0.804028
$165$	0.343172	0.0267159
$166$	−0.377731	−0.0293176
$167$	17.5114	1.35507	0.677537	−	0.735489i	$-0.263047\pi$
$167$	17.5114	1.35507	0.677537	+	0.735489i	$0.263047\pi$
$168$	−0.673617	−0.0519707
$169$	−11.9471	−0.919010
$170$	0.111417	0.00854533
$171$	−14.4448	−1.10462
$172$	1.00000	0.0762493
$173$	5.73942	0.436360	0.218180	−	0.975909i	$-0.429988\pi$
$173$	5.73942	0.436360	0.218180	+	0.975909i	$0.429988\pi$
$174$	3.32386	0.251981
$175$	1.96292	0.148383
$176$	−1.00000	−0.0753778
$177$	−1.82869	−0.137453
$178$	7.70612	0.577598
$179$	2.34829	0.175520	0.0877599	−	0.996142i	$-0.472029\pi$
$179$	2.34829	0.175520	0.0877599	+	0.996142i	$0.472029\pi$
$180$	−2.88223	−0.214829
$181$	6.24247	0.463999	0.232000	−	0.972716i	$-0.425473\pi$
$181$	6.24247	0.463999	0.232000	+	0.972716i	$0.425473\pi$
$182$	2.01414	0.149298
$183$	−0.136359	−0.0100799
$184$	0.973905	0.0717972
$185$	7.67715	0.564435
$186$	−1.54004	−0.112921
$187$	−0.111417	−0.00814765
$188$	−0.925482	−0.0674977
$189$	3.96237	0.288220
$190$	5.01168	0.363585
$191$	−21.8063	−1.57785	−0.788924	−	0.614490i	$-0.789362\pi$
$191$	−21.8063	−1.57785	−0.788924	+	0.614490i	$0.789362\pi$
$192$	−0.343172	−0.0247663
$193$	12.6708	0.912061	0.456031	−	0.889964i	$-0.349271\pi$
$193$	12.6708	0.912061	0.456031	+	0.889964i	$0.349271\pi$
$194$	−1.20697	−0.0866555
$195$	−0.352127	−0.0252163
$196$	−3.14696	−0.224783
$197$	11.7321	0.835877	0.417938	−	0.908475i	$-0.362753\pi$
$197$	11.7321	0.835877	0.417938	+	0.908475i	$0.362753\pi$
$198$	2.88223	0.204831
$199$	13.7446	0.974332	0.487166	−	0.873309i	$-0.338031\pi$
$199$	13.7446	0.974332	0.487166	+	0.873309i	$0.338031\pi$
$200$	1.00000	0.0707107
$201$	4.51102	0.318183
$202$	−11.1242	−0.782693
$203$	−19.0122	−1.33440
$204$	−0.0382353	−0.00267701
$205$	10.2966	0.719145
$206$	9.21177	0.641815
$207$	−2.80702	−0.195101
$208$	1.02610	0.0711469
$209$	−5.01168	−0.346665
$210$	−0.673617	−0.0464840
$211$	13.2387	0.911390	0.455695	−	0.890136i	$-0.349391\pi$
$211$	13.2387	0.911390	0.455695	+	0.890136i	$0.349391\pi$
$212$	−2.23401	−0.153433
$213$	−4.30491	−0.294968
$214$	−9.38489	−0.641538
$215$	1.00000	0.0681994
$216$	2.01862	0.137349
$217$	8.80889	0.597987
$218$	0.143253	0.00970231
$219$	−4.45143	−0.300800
$220$	−1.00000	−0.0674200
$221$	0.114325	0.00769033
$222$	−2.63458	−0.176821
$223$	0.0844328	0.00565404	0.00282702	−	0.999996i	$-0.499100\pi$
$223$	0.0844328	0.00565404	0.00282702	+	0.999996i	$0.499100\pi$
$224$	1.96292	0.131153
$225$	−2.88223	−0.192149
$226$	2.94465	0.195875
$227$	−7.76423	−0.515330	−0.257665	−	0.966234i	$-0.582953\pi$
$227$	−7.76423	−0.515330	−0.257665	+	0.966234i	$0.582953\pi$
$228$	−1.71987	−0.113901
$229$	−14.5242	−0.959787	−0.479894	−	0.877327i	$-0.659325\pi$
$229$	−14.5242	−0.959787	−0.479894	+	0.877327i	$0.659325\pi$
$230$	0.973905	0.0642174
$231$	0.673617	0.0443208
$232$	−9.68570	−0.635898
$233$	−13.5831	−0.889862	−0.444931	−	0.895565i	$-0.646772\pi$
$233$	−13.5831	−0.889862	−0.444931	+	0.895565i	$0.646772\pi$
$234$	−2.95745	−0.193334
$235$	−0.925482	−0.0603718
$236$	5.32880	0.346875
$237$	−4.54792	−0.295419
$238$	0.218703	0.0141764
$239$	−27.7787	−1.79685	−0.898426	−	0.439125i	$-0.855288\pi$
$239$	−27.7787	−1.79685	−0.898426	+	0.439125i	$0.855288\pi$
$240$	−0.343172	−0.0221516
$241$	2.27253	0.146387	0.0731934	−	0.997318i	$-0.476681\pi$
$241$	2.27253	0.146387	0.0731934	+	0.997318i	$0.476681\pi$
$242$	1.00000	0.0642824
$243$	−8.78542	−0.563585
$244$	0.397349	0.0254376
$245$	−3.14696	−0.201052
$246$	−3.53349	−0.225287
$247$	5.14246	0.327207
$248$	4.48766	0.284966
$249$	0.129627	0.00821475
$250$	1.00000	0.0632456
$251$	3.81438	0.240762	0.120381	−	0.992728i	$-0.461588\pi$
$251$	3.81438	0.240762	0.120381	+	0.992728i	$0.461588\pi$
$252$	−5.65758	−0.356394
$253$	−0.973905	−0.0612289
$254$	−3.00367	−0.188467
$255$	−0.0382353	−0.00239439
$256$	1.00000	0.0625000
$257$	12.0793	0.753485	0.376742	−	0.926318i	$-0.377044\pi$
$257$	12.0793	0.753485	0.376742	+	0.926318i	$0.377044\pi$
$258$	−0.343172	−0.0213649
$259$	15.0696	0.936379
$260$	1.02610	0.0636357
$261$	27.9165	1.72799
$262$	−0.295344	−0.0182464
$263$	−31.7516	−1.95789	−0.978944	−	0.204131i	$-0.934563\pi$
$263$	−31.7516	−1.95789	−0.978944	+	0.204131i	$0.934563\pi$
$264$	0.343172	0.0211208
$265$	−2.23401	−0.137234
$266$	9.83751	0.603176
$267$	−2.64452	−0.161842
$268$	−13.1451	−0.802963
$269$	21.4952	1.31058	0.655292	−	0.755376i	$-0.272546\pi$
$269$	21.4952	1.31058	0.655292	+	0.755376i	$0.272546\pi$
$270$	2.01862	0.122849
$271$	−6.78375	−0.412083	−0.206042	−	0.978543i	$-0.566058\pi$
$271$	−6.78375	−0.412083	−0.206042	+	0.978543i	$0.566058\pi$
$272$	0.111417	0.00675568
$273$	−0.691195	−0.0418330
$274$	−21.6844	−1.31000
$275$	−1.00000	−0.0603023
$276$	−0.334216	−0.0201175
$277$	−13.2481	−0.795999	−0.397999	−	0.917386i	$-0.630295\pi$
$277$	−13.2481	−0.795999	−0.397999	+	0.917386i	$0.630295\pi$
$278$	1.97472	0.118436
$279$	−12.9345	−0.774366
$280$	1.96292	0.117307
$281$	−12.2670	−0.731786	−0.365893	−	0.930657i	$-0.619236\pi$
$281$	−12.2670	−0.731786	−0.365893	+	0.930657i	$0.619236\pi$
$282$	0.317599	0.0189128
$283$	−12.3738	−0.735545	−0.367773	−	0.929916i	$-0.619880\pi$
$283$	−12.3738	−0.735545	−0.367773	+	0.929916i	$0.619880\pi$
$284$	12.5445	0.744378
$285$	−1.71987	−0.101876
$286$	−1.02610	−0.0606743
$287$	20.2113	1.19304
$288$	−2.88223	−0.169837
$289$	−16.9876	−0.999270
$290$	−9.68570	−0.568764
$291$	0.414198	0.0242807
$292$	12.9714	0.759096
$293$	29.9259	1.74829	0.874144	−	0.485667i	$-0.161423\pi$
$293$	29.9259	1.74829	0.874144	+	0.485667i	$0.161423\pi$
$294$	1.07995	0.0629838
$295$	5.32880	0.310255
$296$	7.67715	0.446225
$297$	−2.01862	−0.117132
$298$	−14.3032	−0.828563
$299$	0.999319	0.0577921
$300$	−0.343172	−0.0198130
$301$	1.96292	0.113141
$302$	18.6113	1.07096
$303$	3.81749	0.219309
$304$	5.01168	0.287440
$305$	0.397349	0.0227521
$306$	−0.321131	−0.0183578
$307$	−11.9013	−0.679246	−0.339623	−	0.940562i	$-0.610299\pi$
$307$	−11.9013	−0.679246	−0.339623	+	0.940562i	$0.610299\pi$
$308$	−1.96292	−0.111848
$309$	−3.16122	−0.179835
$310$	4.48766	0.254882
$311$	1.78101	0.100992	0.0504960	−	0.998724i	$-0.483920\pi$
$311$	1.78101	0.100992	0.0504960	+	0.998724i	$0.483920\pi$
$312$	−0.352127	−0.0199352
$313$	19.0655	1.07765	0.538824	−	0.842418i	$-0.318869\pi$
$313$	19.0655	1.07765	0.538824	+	0.842418i	$0.318869\pi$
$314$	1.59630	0.0900845
$315$	−5.65758	−0.318769
$316$	13.2526	0.745517
$317$	20.8421	1.17061	0.585305	−	0.810813i	$-0.300975\pi$
$317$	20.8421	1.17061	0.585305	+	0.810813i	$0.300975\pi$
$318$	0.766650	0.0429916
$319$	9.68570	0.542295
$320$	1.00000	0.0559017
$321$	3.22063	0.179758
$322$	1.91169	0.106535
$323$	0.558389	0.0310696
$324$	7.95397	0.441887
$325$	1.02610	0.0569175
$326$	7.78911	0.431399
$327$	−0.0491603	−0.00271857
$328$	10.2966	0.568534
$329$	−1.81664	−0.100155
$330$	0.343172	0.0188910
$331$	5.22670	0.287285	0.143643	−	0.989630i	$-0.454118\pi$
$331$	5.22670	0.287285	0.143643	+	0.989630i	$0.454118\pi$
$332$	−0.377731	−0.0207307
$333$	−22.1273	−1.21257
$334$	17.5114	0.958182
$335$	−13.1451	−0.718192
$336$	−0.673617	−0.0367488
$337$	−10.1257	−0.551582	−0.275791	−	0.961218i	$-0.588940\pi$
$337$	−10.1257	−0.551582	−0.275791	+	0.961218i	$0.588940\pi$
$338$	−11.9471	−0.649838
$339$	−1.01052	−0.0548838
$340$	0.111417	0.00604246
$341$	−4.48766	−0.243020
$342$	−14.4448	−0.781087
$343$	−19.9176	−1.07545
$344$	1.00000	0.0539164
$345$	−0.334216	−0.0179936
$346$	5.73942	0.308553
$347$	8.66305	0.465057	0.232528	−	0.972590i	$-0.425300\pi$
$347$	8.66305	0.465057	0.232528	+	0.972590i	$0.425300\pi$
$348$	3.32386	0.178177
$349$	18.7900	1.00580	0.502902	−	0.864343i	$-0.332266\pi$
$349$	18.7900	1.00580	0.502902	+	0.864343i	$0.332266\pi$
$350$	1.96292	0.104922
$351$	2.07129	0.110557
$352$	−1.00000	−0.0533002
$353$	15.1121	0.804335	0.402167	−	0.915566i	$-0.368257\pi$
$353$	15.1121	0.804335	0.402167	+	0.915566i	$0.368257\pi$
$354$	−1.82869	−0.0971939
$355$	12.5445	0.665792
$356$	7.70612	0.408423
$357$	−0.0750527	−0.00397221
$358$	2.34829	0.124111
$359$	−3.80496	−0.200818	−0.100409	−	0.994946i	$-0.532015\pi$
$359$	−3.80496	−0.200818	−0.100409	+	0.994946i	$0.532015\pi$
$360$	−2.88223	−0.151907
$361$	6.11694	0.321944
$362$	6.24247	0.328097
$363$	−0.343172	−0.0180118
$364$	2.01414	0.105570
$365$	12.9714	0.678956
$366$	−0.136359	−0.00712759
$367$	−34.8167	−1.81742	−0.908709	−	0.417430i	$-0.862931\pi$
$367$	−34.8167	−1.81742	−0.908709	+	0.417430i	$0.862931\pi$
$368$	0.973905	0.0507683
$369$	−29.6772	−1.54493
$370$	7.67715	0.399116
$371$	−4.38518	−0.227667
$372$	−1.54004	−0.0798471
$373$	−28.2729	−1.46392	−0.731958	−	0.681350i	$-0.761393\pi$
$373$	−28.2729	−1.46392	−0.731958	+	0.681350i	$0.761393\pi$
$374$	−0.111417	−0.00576126
$375$	−0.343172	−0.0177213
$376$	−0.925482	−0.0477281
$377$	−9.93845	−0.511856
$378$	3.96237	0.203802
$379$	9.57960	0.492071	0.246036	−	0.969261i	$-0.420872\pi$
$379$	9.57960	0.492071	0.246036	+	0.969261i	$0.420872\pi$
$380$	5.01168	0.257094
$381$	1.03077	0.0528082
$382$	−21.8063	−1.11571
$383$	15.6621	0.800297	0.400149	−	0.916450i	$-0.368959\pi$
$383$	15.6621	0.800297	0.400149	+	0.916450i	$0.368959\pi$
$384$	−0.343172	−0.0175124
$385$	−1.96292	−0.100039
$386$	12.6708	0.644925
$387$	−2.88223	−0.146512
$388$	−1.20697	−0.0612747
$389$	−30.3737	−1.54001	−0.770004	−	0.638039i	$-0.779746\pi$
$389$	−30.3737	−1.54001	−0.770004	+	0.638039i	$0.779746\pi$
$390$	−0.352127	−0.0178306
$391$	0.108510	0.00548759
$392$	−3.14696	−0.158945
$393$	0.101354	0.00511261
$394$	11.7321	0.591054
$395$	13.2526	0.666811
$396$	2.88223	0.144838
$397$	29.6066	1.48591	0.742957	−	0.669339i	$-0.233423\pi$
$397$	29.6066	1.48591	0.742957	+	0.669339i	$0.233423\pi$
$398$	13.7446	0.688957
$399$	−3.37595	−0.169009
$400$	1.00000	0.0500000
$401$	30.6065	1.52841	0.764207	−	0.644971i	$-0.223130\pi$
$401$	30.6065	1.52841	0.764207	+	0.644971i	$0.223130\pi$
$402$	4.51102	0.224989
$403$	4.60476	0.229380
$404$	−11.1242	−0.553447
$405$	7.95397	0.395236
$406$	−19.0122	−0.943561
$407$	−7.67715	−0.380542
$408$	−0.0382353	−0.00189293
$409$	7.09463	0.350807	0.175403	−	0.984497i	$-0.443877\pi$
$409$	7.09463	0.350807	0.175403	+	0.984497i	$0.443877\pi$
$410$	10.2966	0.508512
$411$	7.44147	0.367060
$412$	9.21177	0.453832
$413$	10.4600	0.514702
$414$	−2.80702	−0.137958
$415$	−0.377731	−0.0185421
$416$	1.02610	0.0503085
$417$	−0.677668	−0.0331855
$418$	−5.01168	−0.245129
$419$	22.2850	1.08869	0.544347	−	0.838860i	$-0.316777\pi$
$419$	22.2850	1.08869	0.544347	+	0.838860i	$0.316777\pi$
$420$	−0.673617	−0.0328692
$421$	6.48375	0.315999	0.157999	−	0.987439i	$-0.449496\pi$
$421$	6.48375	0.315999	0.157999	+	0.987439i	$0.449496\pi$
$422$	13.2387	0.644450
$423$	2.66746	0.129696
$424$	−2.23401	−0.108493
$425$	0.111417	0.00540454
$426$	−4.30491	−0.208574
$427$	0.779962	0.0377450
$428$	−9.38489	−0.453636
$429$	0.352127	0.0170008
$430$	1.00000	0.0482243
$431$	−12.9277	−0.622707	−0.311354	−	0.950294i	$-0.600782\pi$
$431$	−12.9277	−0.622707	−0.311354	+	0.950294i	$0.600782\pi$
$432$	2.01862	0.0971207
$433$	2.97786	0.143107	0.0715533	−	0.997437i	$-0.477204\pi$
$433$	2.97786	0.143107	0.0715533	+	0.997437i	$0.477204\pi$
$434$	8.80889	0.422840
$435$	3.32386	0.159367
$436$	0.143253	0.00686057
$437$	4.88090	0.233485
$438$	−4.45143	−0.212697
$439$	−37.1138	−1.77135	−0.885673	−	0.464310i	$-0.846302\pi$
$439$	−37.1138	−1.77135	−0.885673	+	0.464310i	$0.846302\pi$
$440$	−1.00000	−0.0476731
$441$	9.07027	0.431918
$442$	0.114325	0.00543788
$443$	−10.7486	−0.510679	−0.255340	−	0.966851i	$-0.582187\pi$
$443$	−10.7486	−0.510679	−0.255340	+	0.966851i	$0.582187\pi$
$444$	−2.63458	−0.125032
$445$	7.70612	0.365305
$446$	0.0844328	0.00399801
$447$	4.90846	0.232162
$448$	1.96292	0.0927391
$449$	23.0084	1.08583	0.542916	−	0.839787i	$-0.317320\pi$
$449$	23.0084	1.08583	0.542916	+	0.839787i	$0.317320\pi$
$450$	−2.88223	−0.135870
$451$	−10.2966	−0.484847
$452$	2.94465	0.138504
$453$	−6.38686	−0.300081
$454$	−7.76423	−0.364393
$455$	2.01414	0.0944243
$456$	−1.71987	−0.0805401
$457$	−0.101260	−0.00473677	−0.00236838	−	0.999997i	$-0.500754\pi$
$457$	−0.101260	−0.00473677	−0.00236838	+	0.999997i	$0.500754\pi$
$458$	−14.5242	−0.678672
$459$	0.224909	0.0104979
$460$	0.973905	0.0454085
$461$	21.5663	1.00444	0.502222	−	0.864739i	$-0.332516\pi$
$461$	21.5663	1.00444	0.502222	+	0.864739i	$0.332516\pi$
$462$	0.673617	0.0313395
$463$	2.27969	0.105946	0.0529730	−	0.998596i	$-0.483130\pi$
$463$	2.27969	0.105946	0.0529730	+	0.998596i	$0.483130\pi$
$464$	−9.68570	−0.449647
$465$	−1.54004	−0.0714175
$466$	−13.5831	−0.629227
$467$	12.5029	0.578564	0.289282	−	0.957244i	$-0.406583\pi$
$467$	12.5029	0.578564	0.289282	+	0.957244i	$0.406583\pi$
$468$	−2.95745	−0.136708
$469$	−25.8027	−1.19146
$470$	−0.925482	−0.0426893
$471$	−0.547805	−0.0252415
$472$	5.32880	0.245278
$473$	−1.00000	−0.0459800
$474$	−4.54792	−0.208893
$475$	5.01168	0.229952
$476$	0.218703	0.0100242
$477$	6.43895	0.294819
$478$	−27.7787	−1.27057
$479$	−22.1637	−1.01269	−0.506344	−	0.862332i	$-0.669003\pi$
$479$	−22.1637	−1.01269	−0.506344	+	0.862332i	$0.669003\pi$
$480$	−0.343172	−0.0156636
$481$	7.87748	0.359182
$482$	2.27253	0.103511
$483$	−0.656039	−0.0298508
$484$	1.00000	0.0454545
$485$	−1.20697	−0.0548057
$486$	−8.78542	−0.398515
$487$	16.4673	0.746204	0.373102	−	0.927790i	$-0.378294\pi$
$487$	16.4673	0.746204	0.373102	+	0.927790i	$0.378294\pi$
$488$	0.397349	0.0179871
$489$	−2.67300	−0.120877
$490$	−3.14696	−0.142165
$491$	−30.6167	−1.38171	−0.690856	−	0.722992i	$-0.742766\pi$
$491$	−30.6167	−1.38171	−0.690856	+	0.722992i	$0.742766\pi$
$492$	−3.53349	−0.159302
$493$	−1.07916	−0.0486028
$494$	5.14246	0.231370
$495$	2.88223	0.129547
$496$	4.48766	0.201502
$497$	24.6238	1.10453
$498$	0.129627	0.00580871
$499$	−13.1706	−0.589598	−0.294799	−	0.955559i	$-0.595253\pi$
$499$	−13.1706	−0.589598	−0.294799	+	0.955559i	$0.595253\pi$
$500$	1.00000	0.0447214
$501$	−6.00942	−0.268481
$502$	3.81438	0.170244
$503$	14.5640	0.649377	0.324688	−	0.945821i	$-0.394741\pi$
$503$	14.5640	0.649377	0.324688	+	0.945821i	$0.394741\pi$
$504$	−5.65758	−0.252009
$505$	−11.1242	−0.495018
$506$	−0.973905	−0.0432954
$507$	4.09992	0.182084
$508$	−3.00367	−0.133266
$509$	−36.2267	−1.60572	−0.802861	−	0.596167i	$-0.796690\pi$
$509$	−36.2267	−1.60572	−0.802861	+	0.596167i	$0.796690\pi$
$510$	−0.0382353	−0.00169309
$511$	25.4618	1.12637
$512$	1.00000	0.0441942
$513$	10.1167	0.446661
$514$	12.0793	0.532794
$515$	9.21177	0.405919
$516$	−0.343172	−0.0151073
$517$	0.925482	0.0407027
$518$	15.0696	0.662120
$519$	−1.96960	−0.0864561
$520$	1.02610	0.0449972
$521$	−1.76200	−0.0771945	−0.0385972	−	0.999255i	$-0.512289\pi$
$521$	−1.76200	−0.0771945	−0.0385972	+	0.999255i	$0.512289\pi$
$522$	27.9165	1.22187
$523$	−1.47339	−0.0644271	−0.0322135	−	0.999481i	$-0.510256\pi$
$523$	−1.47339	−0.0644271	−0.0322135	+	0.999481i	$0.510256\pi$
$524$	−0.295344	−0.0129021
$525$	−0.673617	−0.0293991
$526$	−31.7516	−1.38444
$527$	0.500003	0.0217805
$528$	0.343172	0.0149346
$529$	−22.0515	−0.958761
$530$	−2.23401	−0.0970393
$531$	−15.3588	−0.666517
$532$	9.83751	0.426510
$533$	10.5653	0.457633
$534$	−2.64452	−0.114440
$535$	−9.38489	−0.405744
$536$	−13.1451	−0.567781
$537$	−0.805868	−0.0347758
$538$	21.4952	0.926723
$539$	3.14696	0.135549
$540$	2.01862	0.0868674
$541$	25.4366	1.09360	0.546802	−	0.837262i	$-0.315845\pi$
$541$	25.4366	1.09360	0.546802	+	0.837262i	$0.315845\pi$
$542$	−6.78375	−0.291387
$543$	−2.14224	−0.0919322
$544$	0.111417	0.00477698
$545$	0.143253	0.00613628
$546$	−0.691195	−0.0295804
$547$	2.43575	0.104145	0.0520726	−	0.998643i	$-0.483417\pi$
$547$	2.43575	0.104145	0.0520726	+	0.998643i	$0.483417\pi$
$548$	−21.6844	−0.926311
$549$	−1.14525	−0.0488782
$550$	−1.00000	−0.0426401
$551$	−48.5416	−2.06794
$552$	−0.334216	−0.0142252
$553$	26.0137	1.10622
$554$	−13.2481	−0.562856
$555$	−2.63458	−0.111832
$556$	1.97472	0.0837468
$557$	−28.8244	−1.22133	−0.610664	−	0.791889i	$-0.709098\pi$
$557$	−28.8244	−1.22133	−0.610664	+	0.791889i	$0.709098\pi$
$558$	−12.9345	−0.547560
$559$	1.02610	0.0433992
$560$	1.96292	0.0829484
$561$	0.0382353	0.00161430
$562$	−12.2670	−0.517451
$563$	13.8736	0.584702	0.292351	−	0.956311i	$-0.405562\pi$
$563$	13.8736	0.584702	0.292351	+	0.956311i	$0.405562\pi$
$564$	0.317599	0.0133733
$565$	2.94465	0.123882
$566$	−12.3738	−0.520109
$567$	15.6130	0.655683
$568$	12.5445	0.526355
$569$	−25.3533	−1.06286	−0.531432	−	0.847101i	$-0.678346\pi$
$569$	−25.3533	−1.06286	−0.531432	+	0.847101i	$0.678346\pi$
$570$	−1.71987	−0.0720373
$571$	−11.0741	−0.463436	−0.231718	−	0.972783i	$-0.574435\pi$
$571$	−11.0741	−0.463436	−0.231718	+	0.972783i	$0.574435\pi$
$572$	−1.02610	−0.0429032
$573$	7.48330	0.312619
$574$	20.2113	0.843605
$575$	0.973905	0.0406146
$576$	−2.88223	−0.120093
$577$	20.1569	0.839144	0.419572	−	0.907722i	$-0.362180\pi$
$577$	20.1569	0.839144	0.419572	+	0.907722i	$0.362180\pi$
$578$	−16.9876	−0.706590
$579$	−4.34824	−0.180707
$580$	−9.68570	−0.402177
$581$	−0.741455	−0.0307607
$582$	0.414198	0.0171691
$583$	2.23401	0.0925234
$584$	12.9714	0.536762
$585$	−2.95745	−0.122275
$586$	29.9259	1.23623
$587$	−25.8882	−1.06852	−0.534260	−	0.845320i	$-0.679410\pi$
$587$	−25.8882	−1.06852	−0.534260	+	0.845320i	$0.679410\pi$
$588$	1.07995	0.0445363
$589$	22.4907	0.926713
$590$	5.32880	0.219383
$591$	−4.02612	−0.165612
$592$	7.67715	0.315529
$593$	−6.42505	−0.263845	−0.131923	−	0.991260i	$-0.542115\pi$
$593$	−6.42505	−0.263845	−0.131923	+	0.991260i	$0.542115\pi$
$594$	−2.01862	−0.0828248
$595$	0.218703	0.00896596
$596$	−14.3032	−0.585883
$597$	−4.71677	−0.193045
$598$	0.999319	0.0408652
$599$	−13.9429	−0.569692	−0.284846	−	0.958573i	$-0.591942\pi$
$599$	−13.9429	−0.569692	−0.284846	+	0.958573i	$0.591942\pi$
$600$	−0.343172	−0.0140099
$601$	0.196244	0.00800494	0.00400247	−	0.999992i	$-0.498726\pi$
$601$	0.196244	0.00800494	0.00400247	+	0.999992i	$0.498726\pi$
$602$	1.96292	0.0800025
$603$	37.8872	1.54289
$604$	18.6113	0.757282
$605$	1.00000	0.0406558
$606$	3.81749	0.155075
$607$	−10.3194	−0.418853	−0.209426	−	0.977824i	$-0.567160\pi$
$607$	−10.3194	−0.418853	−0.209426	+	0.977824i	$0.567160\pi$
$608$	5.01168	0.203250
$609$	6.52446	0.264384
$610$	0.397349	0.0160882
$611$	−0.949633	−0.0384180
$612$	−0.321131	−0.0129810
$613$	42.3780	1.71163	0.855815	−	0.517282i	$-0.173056\pi$
$613$	42.3780	1.71163	0.855815	+	0.517282i	$0.173056\pi$
$614$	−11.9013	−0.480299
$615$	−3.53349	−0.142484
$616$	−1.96292	−0.0790882
$617$	−24.2224	−0.975157	−0.487578	−	0.873079i	$-0.662120\pi$
$617$	−24.2224	−0.975157	−0.487578	+	0.873079i	$0.662120\pi$
$618$	−3.16122	−0.127163
$619$	−7.33881	−0.294972	−0.147486	−	0.989064i	$-0.547118\pi$
$619$	−7.33881	−0.294972	−0.147486	+	0.989064i	$0.547118\pi$
$620$	4.48766	0.180229
$621$	1.96594	0.0788904
$622$	1.78101	0.0714121
$623$	15.1265	0.606029
$624$	−0.352127	−0.0140963
$625$	1.00000	0.0400000
$626$	19.0655	0.762012
$627$	1.71987	0.0686848
$628$	1.59630	0.0636994
$629$	0.855368	0.0341058
$630$	−5.65758	−0.225404
$631$	−31.5130	−1.25451	−0.627257	−	0.778813i	$-0.715822\pi$
$631$	−31.5130	−1.25451	−0.627257	+	0.778813i	$0.715822\pi$
$632$	13.2526	0.527160
$633$	−4.54314	−0.180574
$634$	20.8421	0.827746
$635$	−3.00367	−0.119197
$636$	0.766650	0.0303996
$637$	−3.22908	−0.127941
$638$	9.68570	0.383461
$639$	−36.1561	−1.43031
$640$	1.00000	0.0395285
$641$	2.79158	0.110261	0.0551303	−	0.998479i	$-0.482443\pi$
$641$	2.79158	0.110261	0.0551303	+	0.998479i	$0.482443\pi$
$642$	3.22063	0.127108
$643$	−31.7926	−1.25378	−0.626890	−	0.779108i	$-0.715672\pi$
$643$	−31.7926	−1.25378	−0.626890	+	0.779108i	$0.715672\pi$
$644$	1.91169	0.0753313
$645$	−0.343172	−0.0135124
$646$	0.558389	0.0219695
$647$	1.27271	0.0500356	0.0250178	−	0.999687i	$-0.492036\pi$
$647$	1.27271	0.0500356	0.0250178	+	0.999687i	$0.492036\pi$
$648$	7.95397	0.312461
$649$	−5.32880	−0.209174
$650$	1.02610	0.0402468
$651$	−3.02296	−0.118479
$652$	7.78911	0.305045
$653$	−17.4024	−0.681010	−0.340505	−	0.940243i	$-0.610598\pi$
$653$	−17.4024	−0.681010	−0.340505	+	0.940243i	$0.610598\pi$
$654$	−0.0491603	−0.00192232
$655$	−0.295344	−0.0115400
$656$	10.2966	0.402014
$657$	−37.3867	−1.45859
$658$	−1.81664	−0.0708202
$659$	14.7523	0.574668	0.287334	−	0.957830i	$-0.407231\pi$
$659$	14.7523	0.574668	0.287334	+	0.957830i	$0.407231\pi$
$660$	0.343172	0.0133579
$661$	−24.6197	−0.957594	−0.478797	−	0.877926i	$-0.658927\pi$
$661$	−24.6197	−0.957594	−0.478797	+	0.877926i	$0.658927\pi$
$662$	5.22670	0.203141
$663$	−0.0392331	−0.00152369
$664$	−0.377731	−0.0146588
$665$	9.83751	0.381482
$666$	−22.1273	−0.857416
$667$	−9.43295	−0.365245
$668$	17.5114	0.677537
$669$	−0.0289749	−0.00112024
$670$	−13.1451	−0.507839
$671$	−0.397349	−0.0153395
$672$	−0.673617	−0.0259853
$673$	14.2257	0.548361	0.274180	−	0.961678i	$-0.411593\pi$
$673$	14.2257	0.548361	0.274180	+	0.961678i	$0.411593\pi$
$674$	−10.1257	−0.390027
$675$	2.01862	0.0776965
$676$	−11.9471	−0.459505
$677$	−8.69383	−0.334131	−0.167065	−	0.985946i	$-0.553429\pi$
$677$	−8.69383	−0.334131	−0.167065	+	0.985946i	$0.553429\pi$
$678$	−1.01052	−0.0388087
$679$	−2.36918	−0.0909209
$680$	0.111417	0.00427267
$681$	2.66446	0.102102
$682$	−4.48766	−0.171841
$683$	18.6887	0.715104	0.357552	−	0.933893i	$-0.383612\pi$
$683$	18.6887	0.715104	0.357552	+	0.933893i	$0.383612\pi$
$684$	−14.4448	−0.552312
$685$	−21.6844	−0.828518
$686$	−19.9176	−0.760459
$687$	4.98430	0.190163
$688$	1.00000	0.0381246
$689$	−2.29231	−0.0873301
$690$	−0.334216	−0.0127234
$691$	32.5136	1.23688	0.618438	−	0.785834i	$-0.287766\pi$
$691$	32.5136	1.23688	0.618438	+	0.785834i	$0.287766\pi$
$692$	5.73942	0.218180
$693$	5.65758	0.214914
$694$	8.66305	0.328845
$695$	1.97472	0.0749054
$696$	3.32386	0.125991
$697$	1.14722	0.0434540
$698$	18.7900	0.711211
$699$	4.66135	0.176308
$700$	1.96292	0.0741913
$701$	−4.14350	−0.156498	−0.0782489	−	0.996934i	$-0.524933\pi$
$701$	−4.14350	−0.156498	−0.0782489	+	0.996934i	$0.524933\pi$
$702$	2.07129	0.0781759
$703$	38.4754	1.45113
$704$	−1.00000	−0.0376889
$705$	0.317599	0.0119615
$706$	15.1121	0.568750
$707$	−21.8358	−0.821219
$708$	−1.82869	−0.0687265
$709$	−36.8274	−1.38308	−0.691542	−	0.722337i	$-0.743068\pi$
$709$	−36.8274	−1.38308	−0.691542	+	0.722337i	$0.743068\pi$
$710$	12.5445	0.470786
$711$	−38.1971	−1.43250
$712$	7.70612	0.288799
$713$	4.37055	0.163678
$714$	−0.0750527	−0.00280878
$715$	−1.02610	−0.0383738
$716$	2.34829	0.0877599
$717$	9.53284	0.356011
$718$	−3.80496	−0.142000
$719$	−23.8324	−0.888797	−0.444398	−	0.895829i	$-0.646583\pi$
$719$	−23.8324	−0.888797	−0.444398	+	0.895829i	$0.646583\pi$
$720$	−2.88223	−0.107414
$721$	18.0819	0.673407
$722$	6.11694	0.227649
$723$	−0.779869	−0.0290036
$724$	6.24247	0.232000
$725$	−9.68570	−0.359718
$726$	−0.343172	−0.0127363
$727$	−20.8335	−0.772670	−0.386335	−	0.922358i	$-0.626259\pi$
$727$	−20.8335	−0.772670	−0.386335	+	0.922358i	$0.626259\pi$
$728$	2.01414	0.0746490
$729$	−20.8470	−0.772111
$730$	12.9714	0.480094
$731$	0.111417	0.00412092
$732$	−0.136359	−0.00503997
$733$	−25.8535	−0.954920	−0.477460	−	0.878653i	$-0.658442\pi$
$733$	−25.8535	−0.954920	−0.477460	+	0.878653i	$0.658442\pi$
$734$	−34.8167	−1.28511
$735$	1.07995	0.0398344
$736$	0.973905	0.0358986
$737$	13.1451	0.484205
$738$	−29.6772	−1.09243
$739$	−49.0281	−1.80353	−0.901764	−	0.432229i	$-0.857727\pi$
$739$	−49.0281	−1.80353	−0.901764	+	0.432229i	$0.857727\pi$
$740$	7.67715	0.282218
$741$	−1.76475	−0.0648296
$742$	−4.38518	−0.160985
$743$	−49.1901	−1.80461	−0.902305	−	0.431098i	$-0.858126\pi$
$743$	−49.1901	−1.80461	−0.902305	+	0.431098i	$0.858126\pi$
$744$	−1.54004	−0.0564605
$745$	−14.3032	−0.524029
$746$	−28.2729	−1.03515
$747$	1.08871	0.0398338
$748$	−0.111417	−0.00407383
$749$	−18.4218	−0.673116
$750$	−0.343172	−0.0125309
$751$	−7.51803	−0.274337	−0.137168	−	0.990548i	$-0.543800\pi$
$751$	−7.51803	−0.274337	−0.137168	+	0.990548i	$0.543800\pi$
$752$	−0.925482	−0.0337489
$753$	−1.30899	−0.0477022
$754$	−9.93845	−0.361937
$755$	18.6113	0.677334
$756$	3.96237	0.144110
$757$	−8.19726	−0.297934	−0.148967	−	0.988842i	$-0.547595\pi$
$757$	−8.19726	−0.297934	−0.148967	+	0.988842i	$0.547595\pi$
$758$	9.57960	0.347947
$759$	0.334216	0.0121313
$760$	5.01168	0.181793
$761$	−19.6549	−0.712491	−0.356245	−	0.934392i	$-0.615943\pi$
$761$	−19.6549	−0.712491	−0.356245	+	0.934392i	$0.615943\pi$
$762$	1.03077	0.0373410
$763$	0.281193	0.0101799
$764$	−21.8063	−0.788924
$765$	−0.321131	−0.0116105
$766$	15.6621	0.565895
$767$	5.46786	0.197433
$768$	−0.343172	−0.0123831
$769$	−30.7496	−1.10886	−0.554429	−	0.832231i	$-0.687063\pi$
$769$	−30.7496	−1.10886	−0.554429	+	0.832231i	$0.687063\pi$
$770$	−1.96292	−0.0707386
$771$	−4.14527	−0.149288
$772$	12.6708	0.456031
$773$	−22.9023	−0.823737	−0.411869	−	0.911243i	$-0.635124\pi$
$773$	−22.9023	−0.823737	−0.411869	+	0.911243i	$0.635124\pi$
$774$	−2.88223	−0.103600
$775$	4.48766	0.161201
$776$	−1.20697	−0.0433277
$777$	−5.17146	−0.185525
$778$	−30.3737	−1.08895
$779$	51.6032	1.84888
$780$	−0.352127	−0.0126082
$781$	−12.5445	−0.448877
$782$	0.108510	0.00388031
$783$	−19.5517	−0.698721
$784$	−3.14696	−0.112391
$785$	1.59630	0.0569745
$786$	0.101354	0.00361516
$787$	−31.2694	−1.11463	−0.557317	−	0.830300i	$-0.688169\pi$
$787$	−31.2694	−1.11463	−0.557317	+	0.830300i	$0.688169\pi$
$788$	11.7321	0.417938
$789$	10.8962	0.387917
$790$	13.2526	0.471506
$791$	5.78009	0.205516
$792$	2.88223	0.102416
$793$	0.407718	0.0144785
$794$	29.6066	1.05070
$795$	0.766650	0.0271903
$796$	13.7446	0.487166
$797$	−17.7656	−0.629289	−0.314644	−	0.949210i	$-0.601885\pi$
$797$	−17.7656	−0.629289	−0.314644	+	0.949210i	$0.601885\pi$
$798$	−3.37595	−0.119507
$799$	−0.103115	−0.00364794
$800$	1.00000	0.0353553
$801$	−22.2108	−0.784781
$802$	30.6065	1.08075
$803$	−12.9714	−0.457752
$804$	4.51102	0.159091
$805$	1.91169	0.0673784
$806$	4.60476	0.162196
$807$	−7.37654	−0.259666
$808$	−11.1242	−0.391346
$809$	−20.3331	−0.714874	−0.357437	−	0.933937i	$-0.616349\pi$
$809$	−20.3331	−0.714874	−0.357437	+	0.933937i	$0.616349\pi$
$810$	7.95397	0.279474
$811$	−21.2597	−0.746528	−0.373264	−	0.927725i	$-0.621762\pi$
$811$	−21.2597	−0.746528	−0.373264	+	0.927725i	$0.621762\pi$
$812$	−19.0122	−0.667198
$813$	2.32799	0.0816461
$814$	−7.67715	−0.269084
$815$	7.78911	0.272841
$816$	−0.0382353	−0.00133850
$817$	5.01168	0.175336
$818$	7.09463	0.248058
$819$	−5.80522	−0.202851
$820$	10.2966	0.359572
$821$	−43.8439	−1.53016	−0.765082	−	0.643933i	$-0.777302\pi$
$821$	−43.8439	−1.53016	−0.765082	+	0.643933i	$0.777302\pi$
$822$	7.44147	0.259551
$823$	6.55152	0.228372	0.114186	−	0.993459i	$-0.463574\pi$
$823$	6.55152	0.228372	0.114186	+	0.993459i	$0.463574\pi$
$824$	9.21177	0.320907
$825$	0.343172	0.0119477
$826$	10.4600	0.363950
$827$	23.6083	0.820940	0.410470	−	0.911874i	$-0.365365\pi$
$827$	23.6083	0.820940	0.410470	+	0.911874i	$0.365365\pi$
$828$	−2.80702	−0.0975507
$829$	−6.99960	−0.243106	−0.121553	−	0.992585i	$-0.538787\pi$
$829$	−6.99960	−0.243106	−0.121553	+	0.992585i	$0.538787\pi$
$830$	−0.377731	−0.0131112
$831$	4.54636	0.157711
$832$	1.02610	0.0355734
$833$	−0.350626	−0.0121485
$834$	−0.677668	−0.0234657
$835$	17.5114	0.606007
$836$	−5.01168	−0.173333
$837$	9.05885	0.313120
$838$	22.2850	0.769823
$839$	−39.3566	−1.35874	−0.679370	−	0.733796i	$-0.737747\pi$
$839$	−39.3566	−1.35874	−0.679370	+	0.733796i	$0.737747\pi$
$840$	−0.673617	−0.0232420
$841$	64.8128	2.23493
$842$	6.48375	0.223445
$843$	4.20967	0.144989
$844$	13.2387	0.455695
$845$	−11.9471	−0.410994
$846$	2.66746	0.0917090
$847$	1.96292	0.0674466
$848$	−2.23401	−0.0767163
$849$	4.24633	0.145734
$850$	0.111417	0.00382159
$851$	7.47681	0.256302
$852$	−4.30491	−0.147484
$853$	−38.7813	−1.32785	−0.663923	−	0.747801i	$-0.731110\pi$
$853$	−38.7813	−1.32785	−0.663923	+	0.747801i	$0.731110\pi$
$854$	0.779962	0.0266898
$855$	−14.4448	−0.494003
$856$	−9.38489	−0.320769
$857$	31.7042	1.08299	0.541497	−	0.840703i	$-0.317858\pi$
$857$	31.7042	1.08299	0.541497	+	0.840703i	$0.317858\pi$
$858$	0.352127	0.0120214
$859$	−29.0990	−0.992846	−0.496423	−	0.868081i	$-0.665354\pi$
$859$	−29.0990	−0.992846	−0.496423	+	0.868081i	$0.665354\pi$
$860$	1.00000	0.0340997
$861$	−6.93595	−0.236377
$862$	−12.9277	−0.440321
$863$	8.83357	0.300698	0.150349	−	0.988633i	$-0.451960\pi$
$863$	8.83357	0.300698	0.150349	+	0.988633i	$0.451960\pi$
$864$	2.01862	0.0686747
$865$	5.73942	0.195146
$866$	2.97786	0.101192
$867$	5.82966	0.197986
$868$	8.80889	0.298993
$869$	−13.2526	−0.449564
$870$	3.32386	0.112689
$871$	−13.4881	−0.457027
$872$	0.143253	0.00485115
$873$	3.47877	0.117739
$874$	4.88090	0.165099
$875$	1.96292	0.0663587
$876$	−4.45143	−0.150400
$877$	51.4452	1.73718	0.868591	−	0.495530i	$-0.165026\pi$
$877$	51.4452	1.73718	0.868591	+	0.495530i	$0.165026\pi$
$878$	−37.1138	−1.25253
$879$	−10.2697	−0.346389
$880$	−1.00000	−0.0337100
$881$	40.5489	1.36613	0.683064	−	0.730358i	$-0.260647\pi$
$881$	40.5489	1.36613	0.683064	+	0.730358i	$0.260647\pi$
$882$	9.07027	0.305412
$883$	−22.1177	−0.744320	−0.372160	−	0.928169i	$-0.621383\pi$
$883$	−22.1177	−0.744320	−0.372160	+	0.928169i	$0.621383\pi$
$884$	0.114325	0.00384516
$885$	−1.82869	−0.0614708
$886$	−10.7486	−0.361105
$887$	58.9014	1.97772	0.988858	−	0.148860i	$-0.0475604\pi$
$887$	58.9014	1.97772	0.988858	+	0.148860i	$0.0475604\pi$
$888$	−2.63458	−0.0884107
$889$	−5.89596	−0.197744
$890$	7.70612	0.258310
$891$	−7.95397	−0.266468
$892$	0.0844328	0.00282702
$893$	−4.63822	−0.155212
$894$	4.90846	0.164163
$895$	2.34829	0.0784948
$896$	1.96292	0.0655764
$897$	−0.342938	−0.0114504
$898$	23.0084	0.767800
$899$	−43.4661	−1.44968
$900$	−2.88223	−0.0960744
$901$	−0.248908	−0.00829233
$902$	−10.2966	−0.342839
$903$	−0.673617	−0.0224166
$904$	2.94465	0.0979375
$905$	6.24247	0.207507
$906$	−6.38686	−0.212189
$907$	−41.4615	−1.37671	−0.688354	−	0.725375i	$-0.741666\pi$
$907$	−41.4615	−1.37671	−0.688354	+	0.725375i	$0.741666\pi$
$908$	−7.76423	−0.257665
$909$	32.0624	1.06344
$910$	2.01414	0.0667681
$911$	−8.14102	−0.269724	−0.134862	−	0.990864i	$-0.543059\pi$
$911$	−8.14102	−0.269724	−0.134862	+	0.990864i	$0.543059\pi$
$912$	−1.71987	−0.0569505
$913$	0.377731	0.0125011
$914$	−0.101260	−0.00334940
$915$	−0.136359	−0.00450788
$916$	−14.5242	−0.479894
$917$	−0.579735	−0.0191445
$918$	0.224909	0.00742310
$919$	32.5609	1.07408	0.537042	−	0.843556i	$-0.319542\pi$
$919$	32.5609	1.07408	0.537042	+	0.843556i	$0.319542\pi$
$920$	0.973905	0.0321087
$921$	4.08420	0.134579
$922$	21.5663	0.710249
$923$	12.8718	0.423682
$924$	0.673617	0.0221604
$925$	7.67715	0.252423
$926$	2.27969	0.0749152
$927$	−26.5505	−0.872032
$928$	−9.68570	−0.317949
$929$	3.26716	0.107192	0.0535960	−	0.998563i	$-0.482932\pi$
$929$	3.26716	0.107192	0.0535960	+	0.998563i	$0.482932\pi$
$930$	−1.54004	−0.0504998
$931$	−15.7716	−0.516892
$932$	−13.5831	−0.444931
$933$	−0.611193	−0.0200096
$934$	12.5029	0.409107
$935$	−0.111417	−0.00364374
$936$	−2.95745	−0.0966671
$937$	33.4826	1.09383	0.546914	−	0.837189i	$-0.315802\pi$
$937$	33.4826	1.09383	0.546914	+	0.837189i	$0.315802\pi$
$938$	−25.8027	−0.842488
$939$	−6.54275	−0.213515
$940$	−0.925482	−0.0301859
$941$	−18.3771	−0.599075	−0.299538	−	0.954085i	$-0.596832\pi$
$941$	−18.3771	−0.599075	−0.299538	+	0.954085i	$0.596832\pi$
$942$	−0.547805	−0.0178485
$943$	10.0279	0.326553
$944$	5.32880	0.173438
$945$	3.96237	0.128896
$946$	−1.00000	−0.0325128
$947$	−30.2576	−0.983239	−0.491619	−	0.870810i	$-0.663595\pi$
$947$	−30.2576	−0.983239	−0.491619	+	0.870810i	$0.663595\pi$
$948$	−4.54792	−0.147709
$949$	13.3099	0.432059
$950$	5.01168	0.162600
$951$	−7.15242	−0.231933
$952$	0.218703	0.00708821
$953$	57.6983	1.86903	0.934515	−	0.355924i	$-0.115834\pi$
$953$	57.6983	1.86903	0.934515	+	0.355924i	$0.115834\pi$
$954$	6.43895	0.208469
$955$	−21.8063	−0.705635
$956$	−27.7787	−0.898426
$957$	−3.32386	−0.107445
$958$	−22.1637	−0.716078
$959$	−42.5646	−1.37448
$960$	−0.343172	−0.0110758
$961$	−10.8609	−0.350353
$962$	7.87748	0.253980
$963$	27.0494	0.871656
$964$	2.27253	0.0731934
$965$	12.6708	0.407886
$966$	−0.656039	−0.0211077
$967$	23.7027	0.762226	0.381113	−	0.924528i	$-0.375541\pi$
$967$	23.7027	0.762226	0.381113	+	0.924528i	$0.375541\pi$
$968$	1.00000	0.0321412
$969$	−0.191623	−0.00615582
$970$	−1.20697	−0.0387535
$971$	−33.7868	−1.08427	−0.542135	−	0.840291i	$-0.682384\pi$
$971$	−33.7868	−1.08427	−0.542135	+	0.840291i	$0.682384\pi$
$972$	−8.78542	−0.281793
$973$	3.87621	0.124266
$974$	16.4673	0.527646
$975$	−0.352127	−0.0112771
$976$	0.397349	0.0127188
$977$	5.39425	0.172577	0.0862886	−	0.996270i	$-0.472499\pi$
$977$	5.39425	0.172577	0.0862886	+	0.996270i	$0.472499\pi$
$978$	−2.67300	−0.0854732
$979$	−7.70612	−0.246289
$980$	−3.14696	−0.100526
$981$	−0.412888	−0.0131825
$982$	−30.6167	−0.977018
$983$	20.1642	0.643138	0.321569	−	0.946886i	$-0.395790\pi$
$983$	20.1642	0.643138	0.321569	+	0.946886i	$0.395790\pi$
$984$	−3.53349	−0.112644
$985$	11.7321	0.373815
$986$	−1.07916	−0.0343673
$987$	0.623421	0.0198437
$988$	5.14246	0.163603
$989$	0.973905	0.0309684
$990$	2.88223	0.0916034
$991$	50.4193	1.60162	0.800811	−	0.598917i	$-0.204402\pi$
$991$	50.4193	1.60162	0.800811	+	0.598917i	$0.204402\pi$
$992$	4.48766	0.142483
$993$	−1.79365	−0.0569199
$994$	24.6238	0.781019
$995$	13.7446	0.435735
$996$	0.129627	0.00410738
$997$	15.1520	0.479869	0.239934	−	0.970789i	$-0.422874\pi$
$997$	15.1520	0.479869	0.239934	+	0.970789i	$0.422874\pi$
$998$	−13.1706	−0.416909
$999$	15.4972	0.490310

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.be.1.5	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.be.1.5	✓	12	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:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.343172 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.343172 q^{6} +1.96292 q^{7} +1.00000 q^{8} -2.88223 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.343172 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.343172 q^{6} +1.96292 q^{7} +1.00000 q^{8} -2.88223 q^{9} +1.00000 q^{10} -1.00000 q^{11} -0.343172 q^{12} +1.02610 q^{13} +1.96292 q^{14} -0.343172 q^{15} +1.00000 q^{16} +0.111417 q^{17} -2.88223 q^{18} +5.01168 q^{19} +1.00000 q^{20} -0.673617 q^{21} -1.00000 q^{22} +0.973905 q^{23} -0.343172 q^{24} +1.00000 q^{25} +1.02610 q^{26} +2.01862 q^{27} +1.96292 q^{28} -9.68570 q^{29} -0.343172 q^{30} +4.48766 q^{31} +1.00000 q^{32} +0.343172 q^{33} +0.111417 q^{34} +1.96292 q^{35} -2.88223 q^{36} +7.67715 q^{37} +5.01168 q^{38} -0.352127 q^{39} +1.00000 q^{40} +10.2966 q^{41} -0.673617 q^{42} +1.00000 q^{43} -1.00000 q^{44} -2.88223 q^{45} +0.973905 q^{46} -0.925482 q^{47} -0.343172 q^{48} -3.14696 q^{49} +1.00000 q^{50} -0.0382353 q^{51} +1.02610 q^{52} -2.23401 q^{53} +2.01862 q^{54} -1.00000 q^{55} +1.96292 q^{56} -1.71987 q^{57} -9.68570 q^{58} +5.32880 q^{59} -0.343172 q^{60} +0.397349 q^{61} +4.48766 q^{62} -5.65758 q^{63} +1.00000 q^{64} +1.02610 q^{65} +0.343172 q^{66} -13.1451 q^{67} +0.111417 q^{68} -0.334216 q^{69} +1.96292 q^{70} +12.5445 q^{71} -2.88223 q^{72} +12.9714 q^{73} +7.67715 q^{74} -0.343172 q^{75} +5.01168 q^{76} -1.96292 q^{77} -0.352127 q^{78} +13.2526 q^{79} +1.00000 q^{80} +7.95397 q^{81} +10.2966 q^{82} -0.377731 q^{83} -0.673617 q^{84} +0.111417 q^{85} +1.00000 q^{86} +3.32386 q^{87} -1.00000 q^{88} +7.70612 q^{89} -2.88223 q^{90} +2.01414 q^{91} +0.973905 q^{92} -1.54004 q^{93} -0.925482 q^{94} +5.01168 q^{95} -0.343172 q^{96} -1.20697 q^{97} -3.14696 q^{98} +2.88223 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 12 q^{5} + 3 q^{6} + 8 q^{7} + 12 q^{8} + 25 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 12 * q^5 + 3 * q^6 + 8 * q^7 + 12 * q^8 + 25 * q^9	\( 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 12 q^{5} + 3 q^{6} + 8 q^{7} + 12 q^{8} + 25 q^{9} + 12 q^{10} - 12 q^{11} + 3 q^{12} + 16 q^{13} + 8 q^{14} + 3 q^{15} + 12 q^{16} + 18 q^{17} + 25 q^{18} - 4 q^{19} + 12 q^{20} + 4 q^{21} - 12 q^{22} + 8 q^{23} + 3 q^{24} + 12 q^{25} + 16 q^{26} + 6 q^{27} + 8 q^{28} + 20 q^{29} + 3 q^{30} + 5 q^{31} + 12 q^{32} - 3 q^{33} + 18 q^{34} + 8 q^{35} + 25 q^{36} + 19 q^{37} - 4 q^{38} + 6 q^{39} + 12 q^{40} + 16 q^{41} + 4 q^{42} + 12 q^{43} - 12 q^{44} + 25 q^{45} + 8 q^{46} - q^{47} + 3 q^{48} + 52 q^{49} + 12 q^{50} + q^{51} + 16 q^{52} + 11 q^{53} + 6 q^{54} - 12 q^{55} + 8 q^{56} + 9 q^{57} + 20 q^{58} - 11 q^{59} + 3 q^{60} + 18 q^{61} + 5 q^{62} + 15 q^{63} + 12 q^{64} + 16 q^{65} - 3 q^{66} - 10 q^{67} + 18 q^{68} + 8 q^{70} - 2 q^{71} + 25 q^{72} + 29 q^{73} + 19 q^{74} + 3 q^{75} - 4 q^{76} - 8 q^{77} + 6 q^{78} + 2 q^{79} + 12 q^{80} - 8 q^{81} + 16 q^{82} + 26 q^{83} + 4 q^{84} + 18 q^{85} + 12 q^{86} - 4 q^{87} - 12 q^{88} + 41 q^{89} + 25 q^{90} - 4 q^{91} + 8 q^{92} + 5 q^{93} - q^{94} - 4 q^{95} + 3 q^{96} - 7 q^{97} + 52 q^{98} - 25 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 12 * q^5 + 3 * q^6 + 8 * q^7 + 12 * q^8 + 25 * q^9 + 12 * q^10 - 12 * q^11 + 3 * q^12 + 16 * q^13 + 8 * q^14 + 3 * q^15 + 12 * q^16 + 18 * q^17 + 25 * q^18 - 4 * q^19 + 12 * q^20 + 4 * q^21 - 12 * q^22 + 8 * q^23 + 3 * q^24 + 12 * q^25 + 16 * q^26 + 6 * q^27 + 8 * q^28 + 20 * q^29 + 3 * q^30 + 5 * q^31 + 12 * q^32 - 3 * q^33 + 18 * q^34 + 8 * q^35 + 25 * q^36 + 19 * q^37 - 4 * q^38 + 6 * q^39 + 12 * q^40 + 16 * q^41 + 4 * q^42 + 12 * q^43 - 12 * q^44 + 25 * q^45 + 8 * q^46 - q^47 + 3 * q^48 + 52 * q^49 + 12 * q^50 + q^51 + 16 * q^52 + 11 * q^53 + 6 * q^54 - 12 * q^55 + 8 * q^56 + 9 * q^57 + 20 * q^58 - 11 * q^59 + 3 * q^60 + 18 * q^61 + 5 * q^62 + 15 * q^63 + 12 * q^64 + 16 * q^65 - 3 * q^66 - 10 * q^67 + 18 * q^68 + 8 * q^70 - 2 * q^71 + 25 * q^72 + 29 * q^73 + 19 * q^74 + 3 * q^75 - 4 * q^76 - 8 * q^77 + 6 * q^78 + 2 * q^79 + 12 * q^80 - 8 * q^81 + 16 * q^82 + 26 * q^83 + 4 * q^84 + 18 * q^85 + 12 * q^86 - 4 * q^87 - 12 * q^88 + 41 * q^89 + 25 * q^90 - 4 * q^91 + 8 * q^92 + 5 * q^93 - q^94 - 4 * q^95 + 3 * q^96 - 7 * q^97 + 52 * q^98 - 25 * q^99

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