LMFDB - Embedded newform 8034.2.a.u.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, 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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.1518129839$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 4x^{10} - 18x^{9} + 64x^{8} + 85x^{7} - 249x^{6} - 109x^{5} + 230x^{4} + 97x^{3} - 53x^{2} - 32x - 4 $ x^11 - 4x^10 - 18x^9 + 64x^8 + 85x^7 - 249x^6 - 109x^5 + 230x^4 + 97x^3 - 53x^2 - 32x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.71784$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.58633 q^{5} -1.00000 q^{6} +3.26383 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.58633 q^{5} -1.00000 q^{6} +3.26383 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.58633 q^{10} -5.04950 q^{11} -1.00000 q^{12} -1.00000 q^{13} +3.26383 q^{14} +2.58633 q^{15} +1.00000 q^{16} +3.96813 q^{17} +1.00000 q^{18} -1.09958 q^{19} -2.58633 q^{20} -3.26383 q^{21} -5.04950 q^{22} +6.36847 q^{23} -1.00000 q^{24} +1.68909 q^{25} -1.00000 q^{26} -1.00000 q^{27} +3.26383 q^{28} +1.31929 q^{29} +2.58633 q^{30} -9.20293 q^{31} +1.00000 q^{32} +5.04950 q^{33} +3.96813 q^{34} -8.44134 q^{35} +1.00000 q^{36} -8.79533 q^{37} -1.09958 q^{38} +1.00000 q^{39} -2.58633 q^{40} +5.07728 q^{41} -3.26383 q^{42} +3.38706 q^{43} -5.04950 q^{44} -2.58633 q^{45} +6.36847 q^{46} +2.09076 q^{47} -1.00000 q^{48} +3.65261 q^{49} +1.68909 q^{50} -3.96813 q^{51} -1.00000 q^{52} +1.27373 q^{53} -1.00000 q^{54} +13.0597 q^{55} +3.26383 q^{56} +1.09958 q^{57} +1.31929 q^{58} -0.585224 q^{59} +2.58633 q^{60} -3.12507 q^{61} -9.20293 q^{62} +3.26383 q^{63} +1.00000 q^{64} +2.58633 q^{65} +5.04950 q^{66} -2.90850 q^{67} +3.96813 q^{68} -6.36847 q^{69} -8.44134 q^{70} -1.22777 q^{71} +1.00000 q^{72} +8.28463 q^{73} -8.79533 q^{74} -1.68909 q^{75} -1.09958 q^{76} -16.4807 q^{77} +1.00000 q^{78} -6.38385 q^{79} -2.58633 q^{80} +1.00000 q^{81} +5.07728 q^{82} +11.7908 q^{83} -3.26383 q^{84} -10.2629 q^{85} +3.38706 q^{86} -1.31929 q^{87} -5.04950 q^{88} -2.27017 q^{89} -2.58633 q^{90} -3.26383 q^{91} +6.36847 q^{92} +9.20293 q^{93} +2.09076 q^{94} +2.84387 q^{95} -1.00000 q^{96} -15.4982 q^{97} +3.65261 q^{98} -5.04950 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 2 * q^5 - 11 * q^6 - 2 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 11 q^{8} + 11 q^{9} - 2 q^{10} - 10 q^{11} - 11 q^{12} - 11 q^{13} - 2 q^{14} + 2 q^{15} + 11 q^{16} + 6 q^{17} + 11 q^{18} - 3 q^{19} - 2 q^{20} + 2 q^{21} - 10 q^{22} + 3 q^{23} - 11 q^{24} - q^{25} - 11 q^{26} - 11 q^{27} - 2 q^{28} - 22 q^{29} + 2 q^{30} - 5 q^{31} + 11 q^{32} + 10 q^{33} + 6 q^{34} - 20 q^{35} + 11 q^{36} - 26 q^{37} - 3 q^{38} + 11 q^{39} - 2 q^{40} - 6 q^{41} + 2 q^{42} - 8 q^{43} - 10 q^{44} - 2 q^{45} + 3 q^{46} + 6 q^{47} - 11 q^{48} - 5 q^{49} - q^{50} - 6 q^{51} - 11 q^{52} - 25 q^{53} - 11 q^{54} - 2 q^{56} + 3 q^{57} - 22 q^{58} + 7 q^{59} + 2 q^{60} - 36 q^{61} - 5 q^{62} - 2 q^{63} + 11 q^{64} + 2 q^{65} + 10 q^{66} - 12 q^{67} + 6 q^{68} - 3 q^{69} - 20 q^{70} - 15 q^{71} + 11 q^{72} - 12 q^{73} - 26 q^{74} + q^{75} - 3 q^{76} - q^{77} + 11 q^{78} - 15 q^{79} - 2 q^{80} + 11 q^{81} - 6 q^{82} - 16 q^{83} + 2 q^{84} - 25 q^{85} - 8 q^{86} + 22 q^{87} - 10 q^{88} - 2 q^{89} - 2 q^{90} + 2 q^{91} + 3 q^{92} + 5 q^{93} + 6 q^{94} + 16 q^{95} - 11 q^{96} - 10 q^{97} - 5 q^{98} - 10 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 2 * q^5 - 11 * q^6 - 2 * q^7 + 11 * q^8 + 11 * q^9 - 2 * q^10 - 10 * q^11 - 11 * q^12 - 11 * q^13 - 2 * q^14 + 2 * q^15 + 11 * q^16 + 6 * q^17 + 11 * q^18 - 3 * q^19 - 2 * q^20 + 2 * q^21 - 10 * q^22 + 3 * q^23 - 11 * q^24 - q^25 - 11 * q^26 - 11 * q^27 - 2 * q^28 - 22 * q^29 + 2 * q^30 - 5 * q^31 + 11 * q^32 + 10 * q^33 + 6 * q^34 - 20 * q^35 + 11 * q^36 - 26 * q^37 - 3 * q^38 + 11 * q^39 - 2 * q^40 - 6 * q^41 + 2 * q^42 - 8 * q^43 - 10 * q^44 - 2 * q^45 + 3 * q^46 + 6 * q^47 - 11 * q^48 - 5 * q^49 - q^50 - 6 * q^51 - 11 * q^52 - 25 * q^53 - 11 * q^54 - 2 * q^56 + 3 * q^57 - 22 * q^58 + 7 * q^59 + 2 * q^60 - 36 * q^61 - 5 * q^62 - 2 * q^63 + 11 * q^64 + 2 * q^65 + 10 * q^66 - 12 * q^67 + 6 * q^68 - 3 * q^69 - 20 * q^70 - 15 * q^71 + 11 * q^72 - 12 * q^73 - 26 * q^74 + q^75 - 3 * q^76 - q^77 + 11 * q^78 - 15 * q^79 - 2 * q^80 + 11 * q^81 - 6 * q^82 - 16 * q^83 + 2 * q^84 - 25 * q^85 - 8 * q^86 + 22 * q^87 - 10 * q^88 - 2 * q^89 - 2 * q^90 + 2 * q^91 + 3 * q^92 + 5 * q^93 + 6 * q^94 + 16 * q^95 - 11 * q^96 - 10 * q^97 - 5 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−2.58633	−1.15664	−0.578320	−	0.815810i	$-0.696292\pi$
$5$	−2.58633	−1.15664	−0.578320	+	0.815810i	$0.696292\pi$
$6$	−1.00000	−0.408248
$7$	3.26383	1.23361	0.616807	−	0.787115i	$-0.288426\pi$
$7$	3.26383	1.23361	0.616807	+	0.787115i	$0.288426\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.58633	−0.817868
$11$	−5.04950	−1.52248	−0.761241	−	0.648469i	$-0.775410\pi$
$11$	−5.04950	−1.52248	−0.761241	+	0.648469i	$0.775410\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	3.26383	0.872296
$15$	2.58633	0.667787
$16$	1.00000	0.250000
$17$	3.96813	0.962412	0.481206	−	0.876607i	$-0.340199\pi$
$17$	3.96813	0.962412	0.481206	+	0.876607i	$0.340199\pi$
$18$	1.00000	0.235702
$19$	−1.09958	−0.252261	−0.126130	−	0.992014i	$-0.540256\pi$
$19$	−1.09958	−0.252261	−0.126130	+	0.992014i	$0.540256\pi$
$20$	−2.58633	−0.578320
$21$	−3.26383	−0.712227
$22$	−5.04950	−1.07656
$23$	6.36847	1.32792	0.663959	−	0.747769i	$-0.268875\pi$
$23$	6.36847	1.32792	0.663959	+	0.747769i	$0.268875\pi$
$24$	−1.00000	−0.204124
$25$	1.68909	0.337817
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	3.26383	0.616807
$29$	1.31929	0.244986	0.122493	−	0.992469i	$-0.460911\pi$
$29$	1.31929	0.244986	0.122493	+	0.992469i	$0.460911\pi$
$30$	2.58633	0.472197
$31$	−9.20293	−1.65289	−0.826447	−	0.563014i	$-0.809642\pi$
$31$	−9.20293	−1.65289	−0.826447	+	0.563014i	$0.809642\pi$
$32$	1.00000	0.176777
$33$	5.04950	0.879006
$34$	3.96813	0.680528
$35$	−8.44134	−1.42685
$36$	1.00000	0.166667
$37$	−8.79533	−1.44594	−0.722971	−	0.690878i	$-0.757224\pi$
$37$	−8.79533	−1.44594	−0.722971	+	0.690878i	$0.757224\pi$
$38$	−1.09958	−0.178375
$39$	1.00000	0.160128
$40$	−2.58633	−0.408934
$41$	5.07728	0.792938	0.396469	−	0.918048i	$-0.370235\pi$
$41$	5.07728	0.792938	0.396469	+	0.918048i	$0.370235\pi$
$42$	−3.26383	−0.503620
$43$	3.38706	0.516523	0.258261	−	0.966075i	$-0.416850\pi$
$43$	3.38706	0.516523	0.258261	+	0.966075i	$0.416850\pi$
$44$	−5.04950	−0.761241
$45$	−2.58633	−0.385547
$46$	6.36847	0.938979
$47$	2.09076	0.304968	0.152484	−	0.988306i	$-0.451273\pi$
$47$	2.09076	0.304968	0.152484	+	0.988306i	$0.451273\pi$
$48$	−1.00000	−0.144338
$49$	3.65261	0.521802
$50$	1.68909	0.238873
$51$	−3.96813	−0.555649
$52$	−1.00000	−0.138675
$53$	1.27373	0.174961	0.0874803	−	0.996166i	$-0.472119\pi$
$53$	1.27373	0.174961	0.0874803	+	0.996166i	$0.472119\pi$
$54$	−1.00000	−0.136083
$55$	13.0597	1.76097
$56$	3.26383	0.436148
$57$	1.09958	0.145643
$58$	1.31929	0.173231
$59$	−0.585224	−0.0761897	−0.0380949	−	0.999274i	$-0.512129\pi$
$59$	−0.585224	−0.0761897	−0.0380949	+	0.999274i	$0.512129\pi$
$60$	2.58633	0.333893
$61$	−3.12507	−0.400124	−0.200062	−	0.979783i	$-0.564114\pi$
$61$	−3.12507	−0.400124	−0.200062	+	0.979783i	$0.564114\pi$
$62$	−9.20293	−1.16877
$63$	3.26383	0.411204
$64$	1.00000	0.125000
$65$	2.58633	0.320794
$66$	5.04950	0.621551
$67$	−2.90850	−0.355330	−0.177665	−	0.984091i	$-0.556854\pi$
$67$	−2.90850	−0.355330	−0.177665	+	0.984091i	$0.556854\pi$
$68$	3.96813	0.481206
$69$	−6.36847	−0.766673
$70$	−8.44134	−1.00893
$71$	−1.22777	−0.145710	−0.0728548	−	0.997343i	$-0.523211\pi$
$71$	−1.22777	−0.145710	−0.0728548	+	0.997343i	$0.523211\pi$
$72$	1.00000	0.117851
$73$	8.28463	0.969642	0.484821	−	0.874613i	$-0.338885\pi$
$73$	8.28463	0.969642	0.484821	+	0.874613i	$0.338885\pi$
$74$	−8.79533	−1.02244
$75$	−1.68909	−0.195039
$76$	−1.09958	−0.126130
$77$	−16.4807	−1.87815
$78$	1.00000	0.113228
$79$	−6.38385	−0.718239	−0.359120	−	0.933292i	$-0.616923\pi$
$79$	−6.38385	−0.718239	−0.359120	+	0.933292i	$0.616923\pi$
$80$	−2.58633	−0.289160
$81$	1.00000	0.111111
$82$	5.07728	0.560692
$83$	11.7908	1.29421	0.647106	−	0.762400i	$-0.275979\pi$
$83$	11.7908	1.29421	0.647106	+	0.762400i	$0.275979\pi$
$84$	−3.26383	−0.356113
$85$	−10.2629	−1.11317
$86$	3.38706	0.365237
$87$	−1.31929	−0.141443
$88$	−5.04950	−0.538279
$89$	−2.27017	−0.240638	−0.120319	−	0.992735i	$-0.538392\pi$
$89$	−2.27017	−0.240638	−0.120319	+	0.992735i	$0.538392\pi$
$90$	−2.58633	−0.272623
$91$	−3.26383	−0.342143
$92$	6.36847	0.663959
$93$	9.20293	0.954299
$94$	2.09076	0.215645
$95$	2.84387	0.291775
$96$	−1.00000	−0.102062
$97$	−15.4982	−1.57360	−0.786801	−	0.617206i	$-0.788264\pi$
$97$	−15.4982	−1.57360	−0.786801	+	0.617206i	$0.788264\pi$
$98$	3.65261	0.368969
$99$	−5.04950	−0.507494
$100$	1.68909	0.168909
$101$	−7.67767	−0.763957	−0.381978	−	0.924171i	$-0.624757\pi$
$101$	−7.67767	−0.763957	−0.381978	+	0.924171i	$0.624757\pi$
$102$	−3.96813	−0.392903
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	8.44134	0.823791
$106$	1.27373	0.123716
$107$	−20.5151	−1.98327	−0.991634	−	0.129081i	$-0.958797\pi$
$107$	−20.5151	−1.98327	−0.991634	+	0.129081i	$0.958797\pi$
$108$	−1.00000	−0.0962250
$109$	1.38576	0.132732	0.0663660	−	0.997795i	$-0.478859\pi$
$109$	1.38576	0.132732	0.0663660	+	0.997795i	$0.478859\pi$
$110$	13.0597	1.24519
$111$	8.79533	0.834816
$112$	3.26383	0.308403
$113$	−10.3227	−0.971074	−0.485537	−	0.874216i	$-0.661376\pi$
$113$	−10.3227	−0.971074	−0.485537	+	0.874216i	$0.661376\pi$
$114$	1.09958	0.102985
$115$	−16.4709	−1.53592
$116$	1.31929	0.122493
$117$	−1.00000	−0.0924500
$118$	−0.585224	−0.0538743
$119$	12.9513	1.18724
$120$	2.58633	0.236098
$121$	14.4975	1.31795
$122$	−3.12507	−0.282931
$123$	−5.07728	−0.457803
$124$	−9.20293	−0.826447
$125$	8.56310	0.765907
$126$	3.26383	0.290765
$127$	18.6909	1.65855	0.829273	−	0.558844i	$-0.188755\pi$
$127$	18.6909	1.65855	0.829273	+	0.558844i	$0.188755\pi$
$128$	1.00000	0.0883883
$129$	−3.38706	−0.298214
$130$	2.58633	0.226836
$131$	5.07360	0.443283	0.221641	−	0.975128i	$-0.428859\pi$
$131$	5.07360	0.443283	0.221641	+	0.975128i	$0.428859\pi$
$132$	5.04950	0.439503
$133$	−3.58884	−0.311192
$134$	−2.90850	−0.251256
$135$	2.58633	0.222596
$136$	3.96813	0.340264
$137$	8.93266	0.763168	0.381584	−	0.924334i	$-0.375379\pi$
$137$	8.93266	0.763168	0.381584	+	0.924334i	$0.375379\pi$
$138$	−6.36847	−0.542120
$139$	−7.90112	−0.670164	−0.335082	−	0.942189i	$-0.608764\pi$
$139$	−7.90112	−0.670164	−0.335082	+	0.942189i	$0.608764\pi$
$140$	−8.44134	−0.713424
$141$	−2.09076	−0.176074
$142$	−1.22777	−0.103032
$143$	5.04950	0.422261
$144$	1.00000	0.0833333
$145$	−3.41212	−0.283361
$146$	8.28463	0.685641
$147$	−3.65261	−0.301262
$148$	−8.79533	−0.722971
$149$	−19.9344	−1.63309	−0.816545	−	0.577282i	$-0.804113\pi$
$149$	−19.9344	−1.63309	−0.816545	+	0.577282i	$0.804113\pi$
$150$	−1.68909	−0.137913
$151$	9.91239	0.806659	0.403330	−	0.915055i	$-0.367853\pi$
$151$	9.91239	0.806659	0.403330	+	0.915055i	$0.367853\pi$
$152$	−1.09958	−0.0891877
$153$	3.96813	0.320804
$154$	−16.4807	−1.32806
$155$	23.8018	1.91180
$156$	1.00000	0.0800641
$157$	−11.9341	−0.952443	−0.476222	−	0.879325i	$-0.657994\pi$
$157$	−11.9341	−0.952443	−0.476222	+	0.879325i	$0.657994\pi$
$158$	−6.38385	−0.507872
$159$	−1.27373	−0.101014
$160$	−2.58633	−0.204467
$161$	20.7856	1.63814
$162$	1.00000	0.0785674
$163$	−16.2967	−1.27646	−0.638228	−	0.769847i	$-0.720332\pi$
$163$	−16.2967	−1.27646	−0.638228	+	0.769847i	$0.720332\pi$
$164$	5.07728	0.396469
$165$	−13.0597	−1.01669
$166$	11.7908	0.915146
$167$	−1.14380	−0.0885099	−0.0442549	−	0.999020i	$-0.514091\pi$
$167$	−1.14380	−0.0885099	−0.0442549	+	0.999020i	$0.514091\pi$
$168$	−3.26383	−0.251810
$169$	1.00000	0.0769231
$170$	−10.2629	−0.787127
$171$	−1.09958	−0.0840869
$172$	3.38706	0.258261
$173$	−7.53776	−0.573085	−0.286543	−	0.958067i	$-0.592506\pi$
$173$	−7.53776	−0.573085	−0.286543	+	0.958067i	$0.592506\pi$
$174$	−1.31929	−0.100015
$175$	5.51290	0.416736
$176$	−5.04950	−0.380621
$177$	0.585224	0.0439882
$178$	−2.27017	−0.170157
$179$	−10.9526	−0.818637	−0.409319	−	0.912391i	$-0.634234\pi$
$179$	−10.9526	−0.818637	−0.409319	+	0.912391i	$0.634234\pi$
$180$	−2.58633	−0.192773
$181$	9.46537	0.703555	0.351778	−	0.936084i	$-0.385577\pi$
$181$	9.46537	0.703555	0.351778	+	0.936084i	$0.385577\pi$
$182$	−3.26383	−0.241931
$183$	3.12507	0.231012
$184$	6.36847	0.469490
$185$	22.7476	1.67244
$186$	9.20293	0.674791
$187$	−20.0371	−1.46526
$188$	2.09076	0.152484
$189$	−3.26383	−0.237409
$190$	2.84387	0.206316
$191$	10.3592	0.749566	0.374783	−	0.927113i	$-0.377717\pi$
$191$	10.3592	0.749566	0.374783	+	0.927113i	$0.377717\pi$
$192$	−1.00000	−0.0721688
$193$	−18.0661	−1.30043	−0.650213	−	0.759752i	$-0.725320\pi$
$193$	−18.0661	−1.30043	−0.650213	+	0.759752i	$0.725320\pi$
$194$	−15.4982	−1.11271
$195$	−2.58633	−0.185211
$196$	3.65261	0.260901
$197$	−16.6620	−1.18712	−0.593558	−	0.804791i	$-0.702277\pi$
$197$	−16.6620	−1.18712	−0.593558	+	0.804791i	$0.702277\pi$
$198$	−5.04950	−0.358853
$199$	−8.32966	−0.590474	−0.295237	−	0.955424i	$-0.595399\pi$
$199$	−8.32966	−0.590474	−0.295237	+	0.955424i	$0.595399\pi$
$200$	1.68909	0.119436
$201$	2.90850	0.205150
$202$	−7.67767	−0.540199
$203$	4.30595	0.302218
$204$	−3.96813	−0.277825
$205$	−13.1315	−0.917145
$206$	1.00000	0.0696733
$207$	6.36847	0.442639
$208$	−1.00000	−0.0693375
$209$	5.55233	0.384063
$210$	8.44134	0.582508
$211$	−21.5780	−1.48549	−0.742747	−	0.669573i	$-0.766477\pi$
$211$	−21.5780	−1.48549	−0.742747	+	0.669573i	$0.766477\pi$
$212$	1.27373	0.0874803
$213$	1.22777	0.0841254
$214$	−20.5151	−1.40238
$215$	−8.76006	−0.597431
$216$	−1.00000	−0.0680414
$217$	−30.0368	−2.03903
$218$	1.38576	0.0938558
$219$	−8.28463	−0.559823
$220$	13.0597	0.880483
$221$	−3.96813	−0.266925
$222$	8.79533	0.590304
$223$	−25.7402	−1.72369	−0.861847	−	0.507168i	$-0.830692\pi$
$223$	−25.7402	−1.72369	−0.861847	+	0.507168i	$0.830692\pi$
$224$	3.26383	0.218074
$225$	1.68909	0.112606
$226$	−10.3227	−0.686653
$227$	−4.56547	−0.303021	−0.151510	−	0.988456i	$-0.548414\pi$
$227$	−4.56547	−0.303021	−0.151510	+	0.988456i	$0.548414\pi$
$228$	1.09958	0.0728214
$229$	−4.72707	−0.312374	−0.156187	−	0.987728i	$-0.549920\pi$
$229$	−4.72707	−0.312374	−0.156187	+	0.987728i	$0.549920\pi$
$230$	−16.4709	−1.08606
$231$	16.4807	1.08435
$232$	1.31929	0.0866157
$233$	2.72230	0.178344	0.0891720	−	0.996016i	$-0.471578\pi$
$233$	2.72230	0.178344	0.0891720	+	0.996016i	$0.471578\pi$
$234$	−1.00000	−0.0653720
$235$	−5.40739	−0.352739
$236$	−0.585224	−0.0380949
$237$	6.38385	0.414676
$238$	12.9513	0.839509
$239$	−3.50420	−0.226668	−0.113334	−	0.993557i	$-0.536153\pi$
$239$	−3.50420	−0.226668	−0.113334	+	0.993557i	$0.536153\pi$
$240$	2.58633	0.166947
$241$	5.54442	0.357147	0.178574	−	0.983927i	$-0.442852\pi$
$241$	5.54442	0.357147	0.178574	+	0.983927i	$0.442852\pi$
$242$	14.4975	0.931934
$243$	−1.00000	−0.0641500
$244$	−3.12507	−0.200062
$245$	−9.44685	−0.603537
$246$	−5.07728	−0.323716
$247$	1.09958	0.0699646
$248$	−9.20293	−0.584386
$249$	−11.7908	−0.747214
$250$	8.56310	0.541578
$251$	20.1646	1.27278	0.636389	−	0.771368i	$-0.280427\pi$
$251$	20.1646	1.27278	0.636389	+	0.771368i	$0.280427\pi$
$252$	3.26383	0.205602
$253$	−32.1576	−2.02173
$254$	18.6909	1.17277
$255$	10.2629	0.642686
$256$	1.00000	0.0625000
$257$	−6.76155	−0.421774	−0.210887	−	0.977510i	$-0.567635\pi$
$257$	−6.76155	−0.421774	−0.210887	+	0.977510i	$0.567635\pi$
$258$	−3.38706	−0.210869
$259$	−28.7065	−1.78373
$260$	2.58633	0.160397
$261$	1.31929	0.0816621
$262$	5.07360	0.313448
$263$	−0.821275	−0.0506420	−0.0253210	−	0.999679i	$-0.508061\pi$
$263$	−0.821275	−0.0506420	−0.0253210	+	0.999679i	$0.508061\pi$
$264$	5.04950	0.310775
$265$	−3.29429	−0.202367
$266$	−3.58884	−0.220046
$267$	2.27017	0.138932
$268$	−2.90850	−0.177665
$269$	30.2037	1.84155	0.920776	−	0.390093i	$-0.127557\pi$
$269$	30.2037	1.84155	0.920776	+	0.390093i	$0.127557\pi$
$270$	2.58633	0.157399
$271$	−11.3371	−0.688681	−0.344340	−	0.938845i	$-0.611897\pi$
$271$	−11.3371	−0.688681	−0.344340	+	0.938845i	$0.611897\pi$
$272$	3.96813	0.240603
$273$	3.26383	0.197536
$274$	8.93266	0.539641
$275$	−8.52905	−0.514321
$276$	−6.36847	−0.383337
$277$	21.7770	1.30845	0.654227	−	0.756299i	$-0.272994\pi$
$277$	21.7770	1.30845	0.654227	+	0.756299i	$0.272994\pi$
$278$	−7.90112	−0.473878
$279$	−9.20293	−0.550965
$280$	−8.44134	−0.504467
$281$	−22.7937	−1.35976	−0.679879	−	0.733324i	$-0.737968\pi$
$281$	−22.7937	−1.35976	−0.679879	+	0.733324i	$0.737968\pi$
$282$	−2.09076	−0.124503
$283$	−19.3591	−1.15078	−0.575391	−	0.817879i	$-0.695150\pi$
$283$	−19.3591	−1.15078	−0.575391	+	0.817879i	$0.695150\pi$
$284$	−1.22777	−0.0728548
$285$	−2.84387	−0.168456
$286$	5.04950	0.298583
$287$	16.5714	0.978179
$288$	1.00000	0.0589256
$289$	−1.25396	−0.0737624
$290$	−3.41212	−0.200366
$291$	15.4982	0.908520
$292$	8.28463	0.484821
$293$	14.5669	0.851007	0.425504	−	0.904957i	$-0.360097\pi$
$293$	14.5669	0.851007	0.425504	+	0.904957i	$0.360097\pi$
$294$	−3.65261	−0.213025
$295$	1.51358	0.0881241
$296$	−8.79533	−0.511218
$297$	5.04950	0.293002
$298$	−19.9344	−1.15477
$299$	−6.36847	−0.368298
$300$	−1.68909	−0.0975194
$301$	11.0548	0.637189
$302$	9.91239	0.570394
$303$	7.67767	0.441071
$304$	−1.09958	−0.0630652
$305$	8.08246	0.462800
$306$	3.96813	0.226843
$307$	5.93484	0.338719	0.169360	−	0.985554i	$-0.445830\pi$
$307$	5.93484	0.338719	0.169360	+	0.985554i	$0.445830\pi$
$308$	−16.4807	−0.939077
$309$	−1.00000	−0.0568880
$310$	23.8018	1.35185
$311$	13.6957	0.776610	0.388305	−	0.921531i	$-0.373061\pi$
$311$	13.6957	0.776610	0.388305	+	0.921531i	$0.373061\pi$
$312$	1.00000	0.0566139
$313$	−21.2483	−1.20103	−0.600513	−	0.799615i	$-0.705037\pi$
$313$	−21.2483	−1.20103	−0.600513	+	0.799615i	$0.705037\pi$
$314$	−11.9341	−0.673479
$315$	−8.44134	−0.475616
$316$	−6.38385	−0.359120
$317$	−26.2038	−1.47175	−0.735876	−	0.677116i	$-0.763229\pi$
$317$	−26.2038	−1.47175	−0.735876	+	0.677116i	$0.763229\pi$
$318$	−1.27373	−0.0714274
$319$	−6.66177	−0.372987
$320$	−2.58633	−0.144580
$321$	20.5151	1.14504
$322$	20.7856	1.15834
$323$	−4.36327	−0.242779
$324$	1.00000	0.0555556
$325$	−1.68909	−0.0936936
$326$	−16.2967	−0.902591
$327$	−1.38576	−0.0766329
$328$	5.07728	0.280346
$329$	6.82389	0.376213
$330$	−13.0597	−0.718911
$331$	−8.67449	−0.476793	−0.238397	−	0.971168i	$-0.576622\pi$
$331$	−8.67449	−0.476793	−0.238397	+	0.971168i	$0.576622\pi$
$332$	11.7908	0.647106
$333$	−8.79533	−0.481981
$334$	−1.14380	−0.0625859
$335$	7.52232	0.410989
$336$	−3.26383	−0.178057
$337$	−2.76207	−0.150460	−0.0752299	−	0.997166i	$-0.523969\pi$
$337$	−2.76207	−0.150460	−0.0752299	+	0.997166i	$0.523969\pi$
$338$	1.00000	0.0543928
$339$	10.3227	0.560650
$340$	−10.2629	−0.556583
$341$	46.4702	2.51650
$342$	−1.09958	−0.0594584
$343$	−10.9253	−0.589912
$344$	3.38706	0.182618
$345$	16.4709	0.886766
$346$	−7.53776	−0.405233
$347$	0.174289	0.00935630	0.00467815	−	0.999989i	$-0.498511\pi$
$347$	0.174289	0.00935630	0.00467815	+	0.999989i	$0.498511\pi$
$348$	−1.31929	−0.0707214
$349$	−15.0994	−0.808254	−0.404127	−	0.914703i	$-0.632425\pi$
$349$	−15.0994	−0.808254	−0.404127	+	0.914703i	$0.632425\pi$
$350$	5.51290	0.294677
$351$	1.00000	0.0533761
$352$	−5.04950	−0.269139
$353$	−15.6514	−0.833040	−0.416520	−	0.909127i	$-0.636750\pi$
$353$	−15.6514	−0.833040	−0.416520	+	0.909127i	$0.636750\pi$
$354$	0.585224	0.0311043
$355$	3.17542	0.168534
$356$	−2.27017	−0.120319
$357$	−12.9513	−0.685456
$358$	−10.9526	−0.578864
$359$	−1.43312	−0.0756370	−0.0378185	−	0.999285i	$-0.512041\pi$
$359$	−1.43312	−0.0756370	−0.0378185	+	0.999285i	$0.512041\pi$
$360$	−2.58633	−0.136311
$361$	−17.7909	−0.936364
$362$	9.46537	0.497489
$363$	−14.4975	−0.760921
$364$	−3.26383	−0.171071
$365$	−21.4268	−1.12153
$366$	3.12507	0.163350
$367$	−14.5873	−0.761451	−0.380726	−	0.924688i	$-0.624326\pi$
$367$	−14.5873	−0.761451	−0.380726	+	0.924688i	$0.624326\pi$
$368$	6.36847	0.331979
$369$	5.07728	0.264313
$370$	22.7476	1.18259
$371$	4.15725	0.215834
$372$	9.20293	0.477150
$373$	22.4462	1.16222	0.581110	−	0.813825i	$-0.302619\pi$
$373$	22.4462	1.16222	0.581110	+	0.813825i	$0.302619\pi$
$374$	−20.0371	−1.03609
$375$	−8.56310	−0.442197
$376$	2.09076	0.107823
$377$	−1.31929	−0.0679470
$378$	−3.26383	−0.167873
$379$	22.1475	1.13764	0.568821	−	0.822461i	$-0.307400\pi$
$379$	22.1475	1.13764	0.568821	+	0.822461i	$0.307400\pi$
$380$	2.84387	0.145888
$381$	−18.6909	−0.957561
$382$	10.3592	0.530023
$383$	−25.4503	−1.30045	−0.650224	−	0.759743i	$-0.725325\pi$
$383$	−25.4503	−1.30045	−0.650224	+	0.759743i	$0.725325\pi$
$384$	−1.00000	−0.0510310
$385$	42.6246	2.17235
$386$	−18.0661	−0.919540
$387$	3.38706	0.172174
$388$	−15.4982	−0.786801
$389$	35.4634	1.79807	0.899034	−	0.437879i	$-0.144270\pi$
$389$	35.4634	1.79807	0.899034	+	0.437879i	$0.144270\pi$
$390$	−2.58633	−0.130964
$391$	25.2709	1.27800
$392$	3.65261	0.184485
$393$	−5.07360	−0.255929
$394$	−16.6620	−0.839418
$395$	16.5107	0.830744
$396$	−5.04950	−0.253747
$397$	−22.8936	−1.14900	−0.574498	−	0.818506i	$-0.694803\pi$
$397$	−22.8936	−1.14900	−0.574498	+	0.818506i	$0.694803\pi$
$398$	−8.32966	−0.417528
$399$	3.58884	0.179667
$400$	1.68909	0.0844543
$401$	4.12648	0.206067	0.103033	−	0.994678i	$-0.467145\pi$
$401$	4.12648	0.206067	0.103033	+	0.994678i	$0.467145\pi$
$402$	2.90850	0.145063
$403$	9.20293	0.458430
$404$	−7.67767	−0.381978
$405$	−2.58633	−0.128516
$406$	4.30595	0.213701
$407$	44.4120	2.20142
$408$	−3.96813	−0.196452
$409$	29.2954	1.44856	0.724282	−	0.689504i	$-0.242171\pi$
$409$	29.2954	1.44856	0.724282	+	0.689504i	$0.242171\pi$
$410$	−13.1315	−0.648519
$411$	−8.93266	−0.440615
$412$	1.00000	0.0492665
$413$	−1.91008	−0.0939887
$414$	6.36847	0.312993
$415$	−30.4950	−1.49694
$416$	−1.00000	−0.0490290
$417$	7.90112	0.386920
$418$	5.55233	0.271573
$419$	−0.0991300	−0.00484282	−0.00242141	−	0.999997i	$-0.500771\pi$
$419$	−0.0991300	−0.00484282	−0.00242141	+	0.999997i	$0.500771\pi$
$420$	8.44134	0.411895
$421$	16.8298	0.820235	0.410118	−	0.912033i	$-0.365488\pi$
$421$	16.8298	0.820235	0.410118	+	0.912033i	$0.365488\pi$
$422$	−21.5780	−1.05040
$423$	2.09076	0.101656
$424$	1.27373	0.0618579
$425$	6.70251	0.325120
$426$	1.22777	0.0594857
$427$	−10.1997	−0.493599
$428$	−20.5151	−0.991634
$429$	−5.04950	−0.243792
$430$	−8.76006	−0.422447
$431$	−19.7165	−0.949708	−0.474854	−	0.880065i	$-0.657499\pi$
$431$	−19.7165	−0.949708	−0.474854	+	0.880065i	$0.657499\pi$
$432$	−1.00000	−0.0481125
$433$	1.07818	0.0518142	0.0259071	−	0.999664i	$-0.491753\pi$
$433$	1.07818	0.0518142	0.0259071	+	0.999664i	$0.491753\pi$
$434$	−30.0368	−1.44181
$435$	3.41212	0.163599
$436$	1.38576	0.0663660
$437$	−7.00264	−0.334981
$438$	−8.28463	−0.395855
$439$	−30.2389	−1.44322	−0.721612	−	0.692298i	$-0.756599\pi$
$439$	−30.2389	−1.44322	−0.721612	+	0.692298i	$0.756599\pi$
$440$	13.0597	0.622595
$441$	3.65261	0.173934
$442$	−3.96813	−0.188745
$443$	−8.66943	−0.411897	−0.205948	−	0.978563i	$-0.566028\pi$
$443$	−8.66943	−0.411897	−0.205948	+	0.978563i	$0.566028\pi$
$444$	8.79533	0.417408
$445$	5.87141	0.278332
$446$	−25.7402	−1.21884
$447$	19.9344	0.942864
$448$	3.26383	0.154202
$449$	3.28847	0.155193	0.0775964	−	0.996985i	$-0.475275\pi$
$449$	3.28847	0.155193	0.0775964	+	0.996985i	$0.475275\pi$
$450$	1.68909	0.0796243
$451$	−25.6378	−1.20724
$452$	−10.3227	−0.485537
$453$	−9.91239	−0.465725
$454$	−4.56547	−0.214268
$455$	8.44134	0.395736
$456$	1.09958	0.0514925
$457$	−37.8667	−1.77133	−0.885665	−	0.464325i	$-0.846297\pi$
$457$	−37.8667	−1.77133	−0.885665	+	0.464325i	$0.846297\pi$
$458$	−4.72707	−0.220881
$459$	−3.96813	−0.185216
$460$	−16.4709	−0.767962
$461$	−14.6597	−0.682771	−0.341386	−	0.939923i	$-0.610896\pi$
$461$	−14.6597	−0.682771	−0.341386	+	0.939923i	$0.610896\pi$
$462$	16.4807	0.766753
$463$	−17.1345	−0.796306	−0.398153	−	0.917319i	$-0.630349\pi$
$463$	−17.1345	−0.796306	−0.398153	+	0.917319i	$0.630349\pi$
$464$	1.31929	0.0612466
$465$	−23.8018	−1.10378
$466$	2.72230	0.126108
$467$	10.8737	0.503173	0.251586	−	0.967835i	$-0.419048\pi$
$467$	10.8737	0.503173	0.251586	+	0.967835i	$0.419048\pi$
$468$	−1.00000	−0.0462250
$469$	−9.49285	−0.438339
$470$	−5.40739	−0.249424
$471$	11.9341	0.549893
$472$	−0.585224	−0.0269371
$473$	−17.1030	−0.786397
$474$	6.38385	0.293220
$475$	−1.85728	−0.0852180
$476$	12.9513	0.593622
$477$	1.27373	0.0583202
$478$	−3.50420	−0.160279
$479$	−0.456662	−0.0208654	−0.0104327	−	0.999946i	$-0.503321\pi$
$479$	−0.456662	−0.0208654	−0.0104327	+	0.999946i	$0.503321\pi$
$480$	2.58633	0.118049
$481$	8.79533	0.401032
$482$	5.54442	0.252541
$483$	−20.7856	−0.945779
$484$	14.4975	0.658977
$485$	40.0834	1.82009
$486$	−1.00000	−0.0453609
$487$	−19.4436	−0.881074	−0.440537	−	0.897734i	$-0.645212\pi$
$487$	−19.4436	−0.881074	−0.440537	+	0.897734i	$0.645212\pi$
$488$	−3.12507	−0.141465
$489$	16.2967	0.736962
$490$	−9.44685	−0.426765
$491$	−37.6264	−1.69805	−0.849027	−	0.528350i	$-0.822811\pi$
$491$	−37.6264	−1.69805	−0.849027	+	0.528350i	$0.822811\pi$
$492$	−5.07728	−0.228902
$493$	5.23512	0.235778
$494$	1.09958	0.0494724
$495$	13.0597	0.586988
$496$	−9.20293	−0.413224
$497$	−4.00724	−0.179749
$498$	−11.7908	−0.528360
$499$	22.5980	1.01163	0.505814	−	0.862643i	$-0.331192\pi$
$499$	22.5980	1.01163	0.505814	+	0.862643i	$0.331192\pi$
$500$	8.56310	0.382954
$501$	1.14380	0.0511012
$502$	20.1646	0.899990
$503$	40.1851	1.79177	0.895883	−	0.444290i	$-0.146544\pi$
$503$	40.1851	1.79177	0.895883	+	0.444290i	$0.146544\pi$
$504$	3.26383	0.145383
$505$	19.8570	0.883623
$506$	−32.1576	−1.42958
$507$	−1.00000	−0.0444116
$508$	18.6909	0.829273
$509$	−14.6278	−0.648365	−0.324182	−	0.945995i	$-0.605089\pi$
$509$	−14.6278	−0.648365	−0.324182	+	0.945995i	$0.605089\pi$
$510$	10.2629	0.454448
$511$	27.0397	1.19616
$512$	1.00000	0.0441942
$513$	1.09958	0.0485476
$514$	−6.76155	−0.298239
$515$	−2.58633	−0.113967
$516$	−3.38706	−0.149107
$517$	−10.5573	−0.464309
$518$	−28.7065	−1.26129
$519$	7.53776	0.330871
$520$	2.58633	0.113418
$521$	19.9760	0.875164	0.437582	−	0.899179i	$-0.355835\pi$
$521$	19.9760	0.875164	0.437582	+	0.899179i	$0.355835\pi$
$522$	1.31929	0.0577438
$523$	−1.31871	−0.0576632	−0.0288316	−	0.999584i	$-0.509179\pi$
$523$	−1.31871	−0.0576632	−0.0288316	+	0.999584i	$0.509179\pi$
$524$	5.07360	0.221641
$525$	−5.51290	−0.240603
$526$	−0.821275	−0.0358093
$527$	−36.5184	−1.59077
$528$	5.04950	0.219751
$529$	17.5574	0.763365
$530$	−3.29429	−0.143095
$531$	−0.585224	−0.0253966
$532$	−3.58884	−0.155596
$533$	−5.07728	−0.219922
$534$	2.27017	0.0982400
$535$	53.0587	2.29393
$536$	−2.90850	−0.125628
$537$	10.9526	0.472641
$538$	30.2037	1.30217
$539$	−18.4439	−0.794434
$540$	2.58633	0.111298
$541$	−11.3795	−0.489244	−0.244622	−	0.969618i	$-0.578664\pi$
$541$	−11.3795	−0.489244	−0.244622	+	0.969618i	$0.578664\pi$
$542$	−11.3371	−0.486971
$543$	−9.46537	−0.406198
$544$	3.96813	0.170132
$545$	−3.58404	−0.153523
$546$	3.26383	0.139679
$547$	−26.6627	−1.14001	−0.570007	−	0.821640i	$-0.693060\pi$
$547$	−26.6627	−1.14001	−0.570007	+	0.821640i	$0.693060\pi$
$548$	8.93266	0.381584
$549$	−3.12507	−0.133375
$550$	−8.52905	−0.363680
$551$	−1.45067	−0.0618004
$552$	−6.36847	−0.271060
$553$	−20.8358	−0.886029
$554$	21.7770	0.925216
$555$	−22.7476	−0.965582
$556$	−7.90112	−0.335082
$557$	11.4909	0.486886	0.243443	−	0.969915i	$-0.421723\pi$
$557$	11.4909	0.486886	0.243443	+	0.969915i	$0.421723\pi$
$558$	−9.20293	−0.389591
$559$	−3.38706	−0.143258
$560$	−8.44134	−0.356712
$561$	20.0371	0.845966
$562$	−22.7937	−0.961494
$563$	21.7841	0.918089	0.459044	−	0.888413i	$-0.348192\pi$
$563$	21.7841	0.918089	0.459044	+	0.888413i	$0.348192\pi$
$564$	−2.09076	−0.0880368
$565$	26.6978	1.12318
$566$	−19.3591	−0.813726
$567$	3.26383	0.137068
$568$	−1.22777	−0.0515161
$569$	−8.16236	−0.342184	−0.171092	−	0.985255i	$-0.554730\pi$
$569$	−8.16236	−0.342184	−0.171092	+	0.985255i	$0.554730\pi$
$570$	−2.84387	−0.119117
$571$	25.6290	1.07254	0.536270	−	0.844046i	$-0.319833\pi$
$571$	25.6290	1.07254	0.536270	+	0.844046i	$0.319833\pi$
$572$	5.04950	0.211130
$573$	−10.3592	−0.432762
$574$	16.5714	0.691677
$575$	10.7569	0.448593
$576$	1.00000	0.0416667
$577$	9.16724	0.381637	0.190819	−	0.981625i	$-0.438886\pi$
$577$	9.16724	0.381637	0.190819	+	0.981625i	$0.438886\pi$
$578$	−1.25396	−0.0521579
$579$	18.0661	0.750801
$580$	−3.41212	−0.141681
$581$	38.4833	1.59656
$582$	15.4982	0.642421
$583$	−6.43172	−0.266374
$584$	8.28463	0.342820
$585$	2.58633	0.106931
$586$	14.5669	0.601753
$587$	37.5871	1.55139	0.775693	−	0.631110i	$-0.217400\pi$
$587$	37.5871	1.55139	0.775693	+	0.631110i	$0.217400\pi$
$588$	−3.65261	−0.150631
$589$	10.1193	0.416960
$590$	1.51358	0.0623132
$591$	16.6620	0.685382
$592$	−8.79533	−0.361486
$593$	19.0589	0.782654	0.391327	−	0.920252i	$-0.372016\pi$
$593$	19.0589	0.782654	0.391327	+	0.920252i	$0.372016\pi$
$594$	5.04950	0.207184
$595$	−33.4963	−1.37322
$596$	−19.9344	−0.816545
$597$	8.32966	0.340910
$598$	−6.36847	−0.260426
$599$	−22.5483	−0.921298	−0.460649	−	0.887582i	$-0.652383\pi$
$599$	−22.5483	−0.921298	−0.460649	+	0.887582i	$0.652383\pi$
$600$	−1.68909	−0.0689567
$601$	−38.7686	−1.58141	−0.790703	−	0.612200i	$-0.790285\pi$
$601$	−38.7686	−1.58141	−0.790703	+	0.612200i	$0.790285\pi$
$602$	11.0548	0.450561
$603$	−2.90850	−0.118443
$604$	9.91239	0.403330
$605$	−37.4952	−1.52440
$606$	7.67767	0.311884
$607$	7.15081	0.290242	0.145121	−	0.989414i	$-0.453643\pi$
$607$	7.15081	0.290242	0.145121	+	0.989414i	$0.453643\pi$
$608$	−1.09958	−0.0445938
$609$	−4.30595	−0.174486
$610$	8.08246	0.327249
$611$	−2.09076	−0.0845830
$612$	3.96813	0.160402
$613$	24.1609	0.975848	0.487924	−	0.872886i	$-0.337754\pi$
$613$	24.1609	0.975848	0.487924	+	0.872886i	$0.337754\pi$
$614$	5.93484	0.239511
$615$	13.1315	0.529514
$616$	−16.4807	−0.664028
$617$	13.9374	0.561098	0.280549	−	0.959840i	$-0.409483\pi$
$617$	13.9374	0.561098	0.280549	+	0.959840i	$0.409483\pi$
$618$	−1.00000	−0.0402259
$619$	−44.1988	−1.77650	−0.888250	−	0.459360i	$-0.848079\pi$
$619$	−44.1988	−1.77650	−0.888250	+	0.459360i	$0.848079\pi$
$620$	23.8018	0.955902
$621$	−6.36847	−0.255558
$622$	13.6957	0.549146
$623$	−7.40947	−0.296854
$624$	1.00000	0.0400320
$625$	−30.5924	−1.22370
$626$	−21.2483	−0.849253
$627$	−5.55233	−0.221739
$628$	−11.9341	−0.476222
$629$	−34.9010	−1.39159
$630$	−8.44134	−0.336311
$631$	−34.5081	−1.37375	−0.686873	−	0.726777i	$-0.741017\pi$
$631$	−34.5081	−1.37375	−0.686873	+	0.726777i	$0.741017\pi$
$632$	−6.38385	−0.253936
$633$	21.5780	0.857650
$634$	−26.2038	−1.04069
$635$	−48.3407	−1.91834
$636$	−1.27373	−0.0505068
$637$	−3.65261	−0.144722
$638$	−6.66177	−0.263742
$639$	−1.22777	−0.0485698
$640$	−2.58633	−0.102234
$641$	−6.91448	−0.273106	−0.136553	−	0.990633i	$-0.543602\pi$
$641$	−6.91448	−0.273106	−0.136553	+	0.990633i	$0.543602\pi$
$642$	20.5151	0.809666
$643$	−1.21092	−0.0477541	−0.0238771	−	0.999715i	$-0.507601\pi$
$643$	−1.21092	−0.0477541	−0.0238771	+	0.999715i	$0.507601\pi$
$644$	20.7856	0.819068
$645$	8.76006	0.344927
$646$	−4.36327	−0.171671
$647$	28.9173	1.13686	0.568429	−	0.822733i	$-0.307552\pi$
$647$	28.9173	1.13686	0.568429	+	0.822733i	$0.307552\pi$
$648$	1.00000	0.0392837
$649$	2.95509	0.115998
$650$	−1.68909	−0.0662514
$651$	30.0368	1.17724
$652$	−16.2967	−0.638228
$653$	−9.25548	−0.362195	−0.181097	−	0.983465i	$-0.557965\pi$
$653$	−9.25548	−0.362195	−0.181097	+	0.983465i	$0.557965\pi$
$654$	−1.38576	−0.0541876
$655$	−13.1220	−0.512719
$656$	5.07728	0.198235
$657$	8.28463	0.323214
$658$	6.82389	0.266023
$659$	2.44040	0.0950644	0.0475322	−	0.998870i	$-0.484864\pi$
$659$	2.44040	0.0950644	0.0475322	+	0.998870i	$0.484864\pi$
$660$	−13.0597	−0.508347
$661$	−33.4088	−1.29945	−0.649725	−	0.760169i	$-0.725116\pi$
$661$	−33.4088	−1.29945	−0.649725	+	0.760169i	$0.725116\pi$
$662$	−8.67449	−0.337144
$663$	3.96813	0.154109
$664$	11.7908	0.457573
$665$	9.28192	0.359938
$666$	−8.79533	−0.340812
$667$	8.40186	0.325321
$668$	−1.14380	−0.0442549
$669$	25.7402	0.995175
$670$	7.52232	0.290613
$671$	15.7801	0.609183
$672$	−3.26383	−0.125905
$673$	7.91974	0.305284	0.152642	−	0.988282i	$-0.451222\pi$
$673$	7.91974	0.305284	0.152642	+	0.988282i	$0.451222\pi$
$674$	−2.76207	−0.106391
$675$	−1.68909	−0.0650130
$676$	1.00000	0.0384615
$677$	18.0533	0.693844	0.346922	−	0.937894i	$-0.387227\pi$
$677$	18.0533	0.693844	0.346922	+	0.937894i	$0.387227\pi$
$678$	10.3227	0.396439
$679$	−50.5835	−1.94122
$680$	−10.2629	−0.393563
$681$	4.56547	0.174949
$682$	46.4702	1.77944
$683$	−17.5773	−0.672575	−0.336287	−	0.941759i	$-0.609171\pi$
$683$	−17.5773	−0.672575	−0.336287	+	0.941759i	$0.609171\pi$
$684$	−1.09958	−0.0420435
$685$	−23.1028	−0.882711
$686$	−10.9253	−0.417131
$687$	4.72707	0.180349
$688$	3.38706	0.129131
$689$	−1.27373	−0.0485253
$690$	16.4709	0.627038
$691$	35.8248	1.36284	0.681421	−	0.731892i	$-0.261362\pi$
$691$	35.8248	1.36284	0.681421	+	0.731892i	$0.261362\pi$
$692$	−7.53776	−0.286543
$693$	−16.4807	−0.626052
$694$	0.174289	0.00661591
$695$	20.4349	0.775139
$696$	−1.31929	−0.0500076
$697$	20.1473	0.763134
$698$	−15.0994	−0.571522
$699$	−2.72230	−0.102967
$700$	5.51290	0.208368
$701$	−32.3796	−1.22296	−0.611480	−	0.791260i	$-0.709425\pi$
$701$	−32.3796	−1.22296	−0.611480	+	0.791260i	$0.709425\pi$
$702$	1.00000	0.0377426
$703$	9.67116	0.364755
$704$	−5.04950	−0.190310
$705$	5.40739	0.203654
$706$	−15.6514	−0.589048
$707$	−25.0586	−0.942427
$708$	0.585224	0.0219941
$709$	−15.6976	−0.589536	−0.294768	−	0.955569i	$-0.595242\pi$
$709$	−15.6976	−0.589536	−0.294768	+	0.955569i	$0.595242\pi$
$710$	3.17542	0.119171
$711$	−6.38385	−0.239413
$712$	−2.27017	−0.0850784
$713$	−58.6085	−2.19491
$714$	−12.9513	−0.484691
$715$	−13.0597	−0.488404
$716$	−10.9526	−0.409319
$717$	3.50420	0.130867
$718$	−1.43312	−0.0534834
$719$	−7.74491	−0.288836	−0.144418	−	0.989517i	$-0.546131\pi$
$719$	−7.74491	−0.288836	−0.144418	+	0.989517i	$0.546131\pi$
$720$	−2.58633	−0.0963867
$721$	3.26383	0.121552
$722$	−17.7909	−0.662110
$723$	−5.54442	−0.206199
$724$	9.46537	0.351778
$725$	2.22840	0.0827606
$726$	−14.4975	−0.538052
$727$	5.63394	0.208951	0.104476	−	0.994527i	$-0.466684\pi$
$727$	5.63394	0.208951	0.104476	+	0.994527i	$0.466684\pi$
$728$	−3.26383	−0.120966
$729$	1.00000	0.0370370
$730$	−21.4268	−0.793040
$731$	13.4403	0.497108
$732$	3.12507	0.115506
$733$	−6.82775	−0.252189	−0.126094	−	0.992018i	$-0.540244\pi$
$733$	−6.82775	−0.252189	−0.126094	+	0.992018i	$0.540244\pi$
$734$	−14.5873	−0.538427
$735$	9.44685	0.348452
$736$	6.36847	0.234745
$737$	14.6865	0.540983
$738$	5.07728	0.186897
$739$	42.6127	1.56753	0.783766	−	0.621056i	$-0.213296\pi$
$739$	42.6127	1.56753	0.783766	+	0.621056i	$0.213296\pi$
$740$	22.7476	0.836218
$741$	−1.09958	−0.0403941
$742$	4.15725	0.152617
$743$	−28.8400	−1.05804	−0.529019	−	0.848610i	$-0.677440\pi$
$743$	−28.8400	−1.05804	−0.529019	+	0.848610i	$0.677440\pi$
$744$	9.20293	0.337396
$745$	51.5569	1.88890
$746$	22.4462	0.821814
$747$	11.7908	0.431404
$748$	−20.0371	−0.732628
$749$	−66.9578	−2.44659
$750$	−8.56310	−0.312680
$751$	−5.01222	−0.182899	−0.0914493	−	0.995810i	$-0.529150\pi$
$751$	−5.01222	−0.182899	−0.0914493	+	0.995810i	$0.529150\pi$
$752$	2.09076	0.0762421
$753$	−20.1646	−0.734839
$754$	−1.31929	−0.0480458
$755$	−25.6367	−0.933015
$756$	−3.26383	−0.118704
$757$	−20.1426	−0.732097	−0.366048	−	0.930596i	$-0.619290\pi$
$757$	−20.1426	−0.732097	−0.366048	+	0.930596i	$0.619290\pi$
$758$	22.1475	0.804434
$759$	32.1576	1.16725
$760$	2.84387	0.103158
$761$	31.1012	1.12742	0.563708	−	0.825974i	$-0.309374\pi$
$761$	31.1012	1.12742	0.563708	+	0.825974i	$0.309374\pi$
$762$	−18.6909	−0.677098
$763$	4.52290	0.163740
$764$	10.3592	0.374783
$765$	−10.2629	−0.371055
$766$	−25.4503	−0.919556
$767$	0.585224	0.0211312
$768$	−1.00000	−0.0360844
$769$	15.6768	0.565320	0.282660	−	0.959220i	$-0.408783\pi$
$769$	15.6768	0.565320	0.282660	+	0.959220i	$0.408783\pi$
$770$	42.6246	1.53608
$771$	6.76155	0.243511
$772$	−18.0661	−0.650213
$773$	−17.2048	−0.618814	−0.309407	−	0.950930i	$-0.600131\pi$
$773$	−17.2048	−0.618814	−0.309407	+	0.950930i	$0.600131\pi$
$774$	3.38706	0.121746
$775$	−15.5445	−0.558376
$776$	−15.4982	−0.556353
$777$	28.7065	1.02984
$778$	35.4634	1.27143
$779$	−5.58288	−0.200027
$780$	−2.58633	−0.0926054
$781$	6.19963	0.221840
$782$	25.2709	0.903685
$783$	−1.31929	−0.0471476
$784$	3.65261	0.130450
$785$	30.8654	1.10163
$786$	−5.07360	−0.180969
$787$	−6.53585	−0.232978	−0.116489	−	0.993192i	$-0.537164\pi$
$787$	−6.53585	−0.232978	−0.116489	+	0.993192i	$0.537164\pi$
$788$	−16.6620	−0.593558
$789$	0.821275	0.0292381
$790$	16.5107	0.587425
$791$	−33.6914	−1.19793
$792$	−5.04950	−0.179426
$793$	3.12507	0.110975
$794$	−22.8936	−0.812463
$795$	3.29429	0.116836
$796$	−8.32966	−0.295237
$797$	−38.2429	−1.35463	−0.677317	−	0.735691i	$-0.736857\pi$
$797$	−38.2429	−1.35463	−0.677317	+	0.735691i	$0.736857\pi$
$798$	3.58884	0.127044
$799$	8.29640	0.293505
$800$	1.68909	0.0597182
$801$	−2.27017	−0.0802126
$802$	4.12648	0.145711
$803$	−41.8333	−1.47626
$804$	2.90850	0.102575
$805$	−53.7584	−1.89473
$806$	9.20293	0.324159
$807$	−30.2037	−1.06322
$808$	−7.67767	−0.270099
$809$	−8.21963	−0.288987	−0.144493	−	0.989506i	$-0.546155\pi$
$809$	−8.21963	−0.288987	−0.144493	+	0.989506i	$0.546155\pi$
$810$	−2.58633	−0.0908743
$811$	30.0048	1.05361	0.526805	−	0.849986i	$-0.323390\pi$
$811$	30.0048	1.05361	0.526805	+	0.849986i	$0.323390\pi$
$812$	4.30595	0.151109
$813$	11.3371	0.397610
$814$	44.4120	1.55664
$815$	42.1486	1.47640
$816$	−3.96813	−0.138912
$817$	−3.72435	−0.130298
$818$	29.2954	1.02429
$819$	−3.26383	−0.114048
$820$	−13.1315	−0.458572
$821$	8.96030	0.312717	0.156358	−	0.987700i	$-0.450025\pi$
$821$	8.96030	0.312717	0.156358	+	0.987700i	$0.450025\pi$
$822$	−8.93266	−0.311562
$823$	−1.03466	−0.0360661	−0.0180331	−	0.999837i	$-0.505740\pi$
$823$	−1.03466	−0.0360661	−0.0180331	+	0.999837i	$0.505740\pi$
$824$	1.00000	0.0348367
$825$	8.52905	0.296943
$826$	−1.91008	−0.0664600
$827$	−19.4171	−0.675197	−0.337599	−	0.941290i	$-0.609615\pi$
$827$	−19.4171	−0.675197	−0.337599	+	0.941290i	$0.609615\pi$
$828$	6.36847	0.221320
$829$	32.8890	1.14228	0.571141	−	0.820852i	$-0.306501\pi$
$829$	32.8890	1.14228	0.571141	+	0.820852i	$0.306501\pi$
$830$	−30.4950	−1.05850
$831$	−21.7770	−0.755436
$832$	−1.00000	−0.0346688
$833$	14.4940	0.502188
$834$	7.90112	0.273593
$835$	2.95824	0.102374
$836$	5.55233	0.192031
$837$	9.20293	0.318100
$838$	−0.0991300	−0.00342439
$839$	42.0324	1.45112	0.725560	−	0.688158i	$-0.241581\pi$
$839$	42.0324	1.45112	0.725560	+	0.688158i	$0.241581\pi$
$840$	8.44134	0.291254
$841$	−27.2595	−0.939982
$842$	16.8298	0.579994
$843$	22.7937	0.785057
$844$	−21.5780	−0.742747
$845$	−2.58633	−0.0889723
$846$	2.09076	0.0718818
$847$	47.3174	1.62584
$848$	1.27373	0.0437402
$849$	19.3591	0.664404
$850$	6.70251	0.229894
$851$	−56.0128	−1.92009
$852$	1.22777	0.0420627
$853$	−48.9872	−1.67729	−0.838644	−	0.544679i	$-0.816651\pi$
$853$	−48.9872	−1.67729	−0.838644	+	0.544679i	$0.816651\pi$
$854$	−10.1997	−0.349027
$855$	2.84387	0.0972583
$856$	−20.5151	−0.701191
$857$	3.80196	0.129873	0.0649363	−	0.997889i	$-0.479316\pi$
$857$	3.80196	0.129873	0.0649363	+	0.997889i	$0.479316\pi$
$858$	−5.04950	−0.172387
$859$	37.0815	1.26520	0.632602	−	0.774477i	$-0.281987\pi$
$859$	37.0815	1.26520	0.632602	+	0.774477i	$0.281987\pi$
$860$	−8.76006	−0.298715
$861$	−16.5714	−0.564752
$862$	−19.7165	−0.671545
$863$	38.0451	1.29507	0.647535	−	0.762035i	$-0.275800\pi$
$863$	38.0451	1.29507	0.647535	+	0.762035i	$0.275800\pi$
$864$	−1.00000	−0.0340207
$865$	19.4951	0.662854
$866$	1.07818	0.0366382
$867$	1.25396	0.0425867
$868$	−30.0368	−1.01952
$869$	32.2353	1.09351
$870$	3.41212	0.115682
$871$	2.90850	0.0985507
$872$	1.38576	0.0469279
$873$	−15.4982	−0.524534
$874$	−7.00264	−0.236868
$875$	27.9486	0.944834
$876$	−8.28463	−0.279912
$877$	6.54738	0.221089	0.110545	−	0.993871i	$-0.464740\pi$
$877$	6.54738	0.221089	0.110545	+	0.993871i	$0.464740\pi$
$878$	−30.2389	−1.02051
$879$	−14.5669	−0.491329
$880$	13.0597	0.440241
$881$	−21.9076	−0.738087	−0.369043	−	0.929412i	$-0.620315\pi$
$881$	−21.9076	−0.738087	−0.369043	+	0.929412i	$0.620315\pi$
$882$	3.65261	0.122990
$883$	42.2700	1.42250	0.711249	−	0.702940i	$-0.248130\pi$
$883$	42.2700	1.42250	0.711249	+	0.702940i	$0.248130\pi$
$884$	−3.96813	−0.133463
$885$	−1.51358	−0.0508785
$886$	−8.66943	−0.291255
$887$	43.9327	1.47512	0.737558	−	0.675283i	$-0.235979\pi$
$887$	43.9327	1.47512	0.737558	+	0.675283i	$0.235979\pi$
$888$	8.79533	0.295152
$889$	61.0038	2.04600
$890$	5.87141	0.196810
$891$	−5.04950	−0.169165
$892$	−25.7402	−0.861847
$893$	−2.29895	−0.0769316
$894$	19.9344	0.666706
$895$	28.3271	0.946869
$896$	3.26383	0.109037
$897$	6.36847	0.212637
$898$	3.28847	0.109738
$899$	−12.1413	−0.404936
$900$	1.68909	0.0563029
$901$	5.05433	0.168384
$902$	−25.6378	−0.853644
$903$	−11.0548	−0.367881
$904$	−10.3227	−0.343326
$905$	−24.4805	−0.813761
$906$	−9.91239	−0.329317
$907$	−3.52779	−0.117138	−0.0585691	−	0.998283i	$-0.518654\pi$
$907$	−3.52779	−0.117138	−0.0585691	+	0.998283i	$0.518654\pi$
$908$	−4.56547	−0.151510
$909$	−7.67767	−0.254652
$910$	8.44134	0.279828
$911$	−20.9171	−0.693016	−0.346508	−	0.938047i	$-0.612633\pi$
$911$	−20.9171	−0.693016	−0.346508	+	0.938047i	$0.612633\pi$
$912$	1.09958	0.0364107
$913$	−59.5379	−1.97042
$914$	−37.8667	−1.25252
$915$	−8.08246	−0.267198
$916$	−4.72707	−0.156187
$917$	16.5594	0.546839
$918$	−3.96813	−0.130968
$919$	29.1550	0.961735	0.480868	−	0.876793i	$-0.340322\pi$
$919$	29.1550	0.961735	0.480868	+	0.876793i	$0.340322\pi$
$920$	−16.4709	−0.543031
$921$	−5.93484	−0.195560
$922$	−14.6597	−0.482792
$923$	1.22777	0.0404126
$924$	16.4807	0.542177
$925$	−14.8561	−0.488464
$926$	−17.1345	−0.563073
$927$	1.00000	0.0328443
$928$	1.31929	0.0433079
$929$	32.5406	1.06762	0.533811	−	0.845604i	$-0.320759\pi$
$929$	32.5406	1.06762	0.533811	+	0.845604i	$0.320759\pi$
$930$	−23.8018	−0.780491
$931$	−4.01634	−0.131630
$932$	2.72230	0.0891720
$933$	−13.6957	−0.448376
$934$	10.8737	0.355797
$935$	51.8224	1.69477
$936$	−1.00000	−0.0326860
$937$	18.2879	0.597440	0.298720	−	0.954341i	$-0.403440\pi$
$937$	18.2879	0.597440	0.298720	+	0.954341i	$0.403440\pi$
$938$	−9.49285	−0.309953
$939$	21.2483	0.693413
$940$	−5.40739	−0.176369
$941$	−1.18747	−0.0387103	−0.0193551	−	0.999813i	$-0.506161\pi$
$941$	−1.18747	−0.0387103	−0.0193551	+	0.999813i	$0.506161\pi$
$942$	11.9341	0.388833
$943$	32.3345	1.05296
$944$	−0.585224	−0.0190474
$945$	8.44134	0.274597
$946$	−17.1030	−0.556066
$947$	−34.0318	−1.10589	−0.552943	−	0.833219i	$-0.686495\pi$
$947$	−34.0318	−1.10589	−0.552943	+	0.833219i	$0.686495\pi$
$948$	6.38385	0.207338
$949$	−8.28463	−0.268930
$950$	−1.85728	−0.0602583
$951$	26.2038	0.849716
$952$	12.9513	0.419754
$953$	−20.1190	−0.651718	−0.325859	−	0.945418i	$-0.605654\pi$
$953$	−20.1190	−0.651718	−0.325859	+	0.945418i	$0.605654\pi$
$954$	1.27373	0.0412386
$955$	−26.7923	−0.866978
$956$	−3.50420	−0.113334
$957$	6.66177	0.215344
$958$	−0.456662	−0.0147541
$959$	29.1547	0.941455
$960$	2.58633	0.0834733
$961$	53.6939	1.73206
$962$	8.79533	0.283573
$963$	−20.5151	−0.661089
$964$	5.54442	0.178574
$965$	46.7248	1.50413
$966$	−20.7856	−0.668766
$967$	28.8891	0.929011	0.464505	−	0.885570i	$-0.346232\pi$
$967$	28.8891	0.929011	0.464505	+	0.885570i	$0.346232\pi$
$968$	14.4975	0.465967
$969$	4.36327	0.140168
$970$	40.0834	1.28700
$971$	−9.05129	−0.290470	−0.145235	−	0.989397i	$-0.546394\pi$
$971$	−9.05129	−0.290470	−0.145235	+	0.989397i	$0.546394\pi$
$972$	−1.00000	−0.0320750
$973$	−25.7879	−0.826724
$974$	−19.4436	−0.623013
$975$	1.68909	0.0540941
$976$	−3.12507	−0.100031
$977$	16.1280	0.515980	0.257990	−	0.966148i	$-0.416940\pi$
$977$	16.1280	0.515980	0.257990	+	0.966148i	$0.416940\pi$
$978$	16.2967	0.521111
$979$	11.4633	0.366367
$980$	−9.44685	−0.301768
$981$	1.38576	0.0442440
$982$	−37.6264	−1.20071
$983$	43.7312	1.39481	0.697404	−	0.716678i	$-0.254338\pi$
$983$	43.7312	1.39481	0.697404	+	0.716678i	$0.254338\pi$
$984$	−5.07728	−0.161858
$985$	43.0933	1.37307
$986$	5.23512	0.166720
$987$	−6.82389	−0.217207
$988$	1.09958	0.0349823
$989$	21.5704	0.685899
$990$	13.0597	0.415063
$991$	22.8528	0.725942	0.362971	−	0.931800i	$-0.381762\pi$
$991$	22.8528	0.725942	0.362971	+	0.931800i	$0.381762\pi$
$992$	−9.20293	−0.292193
$993$	8.67449	0.275277
$994$	−4.00724	−0.127102
$995$	21.5432	0.682966
$996$	−11.7908	−0.373607
$997$	21.0694	0.667276	0.333638	−	0.942701i	$-0.391724\pi$
$997$	21.0694	0.667276	0.333638	+	0.942701i	$0.391724\pi$
$998$	22.5980	0.715328
$999$	8.79533	0.278272

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.u.1.3	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.u.1.3	✓	11	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.58633 q^{5} -1.00000 q^{6} +3.26383 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.58633 q^{5} -1.00000 q^{6} +3.26383 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.58633 q^{10} -5.04950 q^{11} -1.00000 q^{12} -1.00000 q^{13} +3.26383 q^{14} +2.58633 q^{15} +1.00000 q^{16} +3.96813 q^{17} +1.00000 q^{18} -1.09958 q^{19} -2.58633 q^{20} -3.26383 q^{21} -5.04950 q^{22} +6.36847 q^{23} -1.00000 q^{24} +1.68909 q^{25} -1.00000 q^{26} -1.00000 q^{27} +3.26383 q^{28} +1.31929 q^{29} +2.58633 q^{30} -9.20293 q^{31} +1.00000 q^{32} +5.04950 q^{33} +3.96813 q^{34} -8.44134 q^{35} +1.00000 q^{36} -8.79533 q^{37} -1.09958 q^{38} +1.00000 q^{39} -2.58633 q^{40} +5.07728 q^{41} -3.26383 q^{42} +3.38706 q^{43} -5.04950 q^{44} -2.58633 q^{45} +6.36847 q^{46} +2.09076 q^{47} -1.00000 q^{48} +3.65261 q^{49} +1.68909 q^{50} -3.96813 q^{51} -1.00000 q^{52} +1.27373 q^{53} -1.00000 q^{54} +13.0597 q^{55} +3.26383 q^{56} +1.09958 q^{57} +1.31929 q^{58} -0.585224 q^{59} +2.58633 q^{60} -3.12507 q^{61} -9.20293 q^{62} +3.26383 q^{63} +1.00000 q^{64} +2.58633 q^{65} +5.04950 q^{66} -2.90850 q^{67} +3.96813 q^{68} -6.36847 q^{69} -8.44134 q^{70} -1.22777 q^{71} +1.00000 q^{72} +8.28463 q^{73} -8.79533 q^{74} -1.68909 q^{75} -1.09958 q^{76} -16.4807 q^{77} +1.00000 q^{78} -6.38385 q^{79} -2.58633 q^{80} +1.00000 q^{81} +5.07728 q^{82} +11.7908 q^{83} -3.26383 q^{84} -10.2629 q^{85} +3.38706 q^{86} -1.31929 q^{87} -5.04950 q^{88} -2.27017 q^{89} -2.58633 q^{90} -3.26383 q^{91} +6.36847 q^{92} +9.20293 q^{93} +2.09076 q^{94} +2.84387 q^{95} -1.00000 q^{96} -15.4982 q^{97} +3.65261 q^{98} -5.04950 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 2 * q^5 - 11 * q^6 - 2 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 11 q^{8} + 11 q^{9} - 2 q^{10} - 10 q^{11} - 11 q^{12} - 11 q^{13} - 2 q^{14} + 2 q^{15} + 11 q^{16} + 6 q^{17} + 11 q^{18} - 3 q^{19} - 2 q^{20} + 2 q^{21} - 10 q^{22} + 3 q^{23} - 11 q^{24} - q^{25} - 11 q^{26} - 11 q^{27} - 2 q^{28} - 22 q^{29} + 2 q^{30} - 5 q^{31} + 11 q^{32} + 10 q^{33} + 6 q^{34} - 20 q^{35} + 11 q^{36} - 26 q^{37} - 3 q^{38} + 11 q^{39} - 2 q^{40} - 6 q^{41} + 2 q^{42} - 8 q^{43} - 10 q^{44} - 2 q^{45} + 3 q^{46} + 6 q^{47} - 11 q^{48} - 5 q^{49} - q^{50} - 6 q^{51} - 11 q^{52} - 25 q^{53} - 11 q^{54} - 2 q^{56} + 3 q^{57} - 22 q^{58} + 7 q^{59} + 2 q^{60} - 36 q^{61} - 5 q^{62} - 2 q^{63} + 11 q^{64} + 2 q^{65} + 10 q^{66} - 12 q^{67} + 6 q^{68} - 3 q^{69} - 20 q^{70} - 15 q^{71} + 11 q^{72} - 12 q^{73} - 26 q^{74} + q^{75} - 3 q^{76} - q^{77} + 11 q^{78} - 15 q^{79} - 2 q^{80} + 11 q^{81} - 6 q^{82} - 16 q^{83} + 2 q^{84} - 25 q^{85} - 8 q^{86} + 22 q^{87} - 10 q^{88} - 2 q^{89} - 2 q^{90} + 2 q^{91} + 3 q^{92} + 5 q^{93} + 6 q^{94} + 16 q^{95} - 11 q^{96} - 10 q^{97} - 5 q^{98} - 10 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 2 * q^5 - 11 * q^6 - 2 * q^7 + 11 * q^8 + 11 * q^9 - 2 * q^10 - 10 * q^11 - 11 * q^12 - 11 * q^13 - 2 * q^14 + 2 * q^15 + 11 * q^16 + 6 * q^17 + 11 * q^18 - 3 * q^19 - 2 * q^20 + 2 * q^21 - 10 * q^22 + 3 * q^23 - 11 * q^24 - q^25 - 11 * q^26 - 11 * q^27 - 2 * q^28 - 22 * q^29 + 2 * q^30 - 5 * q^31 + 11 * q^32 + 10 * q^33 + 6 * q^34 - 20 * q^35 + 11 * q^36 - 26 * q^37 - 3 * q^38 + 11 * q^39 - 2 * q^40 - 6 * q^41 + 2 * q^42 - 8 * q^43 - 10 * q^44 - 2 * q^45 + 3 * q^46 + 6 * q^47 - 11 * q^48 - 5 * q^49 - q^50 - 6 * q^51 - 11 * q^52 - 25 * q^53 - 11 * q^54 - 2 * q^56 + 3 * q^57 - 22 * q^58 + 7 * q^59 + 2 * q^60 - 36 * q^61 - 5 * q^62 - 2 * q^63 + 11 * q^64 + 2 * q^65 + 10 * q^66 - 12 * q^67 + 6 * q^68 - 3 * q^69 - 20 * q^70 - 15 * q^71 + 11 * q^72 - 12 * q^73 - 26 * q^74 + q^75 - 3 * q^76 - q^77 + 11 * q^78 - 15 * q^79 - 2 * q^80 + 11 * q^81 - 6 * q^82 - 16 * q^83 + 2 * q^84 - 25 * q^85 - 8 * q^86 + 22 * q^87 - 10 * q^88 - 2 * q^89 - 2 * q^90 + 2 * q^91 + 3 * q^92 + 5 * q^93 + 6 * q^94 + 16 * q^95 - 11 * q^96 - 10 * q^97 - 5 * q^98 - 10 * q^99

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