LMFDB - Embedded newform 8034.2.a.t.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:	$0$
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} - 4 x^{10} - 24 x^{9} + 88 x^{8} + 220 x^{7} - 637 x^{6} - 977 x^{5} + 1739 x^{4} + 1872 x^{3} + \cdots - 162 $ x^11 - 4x^10 - 24x^9 + 88x^8 + 220x^7 - 637x^6 - 977x^5 + 1739x^4 + 1872x^3 - 1494x^2 - 1161x - 162
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.06747$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.06747 q^{5} -1.00000 q^{6} -2.54251 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.06747 q^{5} -1.00000 q^{6} -2.54251 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.06747 q^{10} -0.325101 q^{11} +1.00000 q^{12} -1.00000 q^{13} +2.54251 q^{14} -2.06747 q^{15} +1.00000 q^{16} -7.70014 q^{17} -1.00000 q^{18} -1.05544 q^{19} -2.06747 q^{20} -2.54251 q^{21} +0.325101 q^{22} -2.56996 q^{23} -1.00000 q^{24} -0.725568 q^{25} +1.00000 q^{26} +1.00000 q^{27} -2.54251 q^{28} +0.0777727 q^{29} +2.06747 q^{30} -5.03097 q^{31} -1.00000 q^{32} -0.325101 q^{33} +7.70014 q^{34} +5.25655 q^{35} +1.00000 q^{36} -10.2755 q^{37} +1.05544 q^{38} -1.00000 q^{39} +2.06747 q^{40} +5.75538 q^{41} +2.54251 q^{42} -7.40377 q^{43} -0.325101 q^{44} -2.06747 q^{45} +2.56996 q^{46} +11.7938 q^{47} +1.00000 q^{48} -0.535664 q^{49} +0.725568 q^{50} -7.70014 q^{51} -1.00000 q^{52} -11.7975 q^{53} -1.00000 q^{54} +0.672136 q^{55} +2.54251 q^{56} -1.05544 q^{57} -0.0777727 q^{58} +5.79963 q^{59} -2.06747 q^{60} +10.5128 q^{61} +5.03097 q^{62} -2.54251 q^{63} +1.00000 q^{64} +2.06747 q^{65} +0.325101 q^{66} -4.95776 q^{67} -7.70014 q^{68} -2.56996 q^{69} -5.25655 q^{70} +10.9990 q^{71} -1.00000 q^{72} +9.54903 q^{73} +10.2755 q^{74} -0.725568 q^{75} -1.05544 q^{76} +0.826571 q^{77} +1.00000 q^{78} -7.67987 q^{79} -2.06747 q^{80} +1.00000 q^{81} -5.75538 q^{82} -13.2806 q^{83} -2.54251 q^{84} +15.9198 q^{85} +7.40377 q^{86} +0.0777727 q^{87} +0.325101 q^{88} +16.6191 q^{89} +2.06747 q^{90} +2.54251 q^{91} -2.56996 q^{92} -5.03097 q^{93} -11.7938 q^{94} +2.18209 q^{95} -1.00000 q^{96} -13.2571 q^{97} +0.535664 q^{98} -0.325101 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} + 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 4 q^{7} - 11 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 + 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 4 * q^7 - 11 * q^8 + 11 * q^9	\( 11 q - 11 q^{2} + 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 4 q^{7} - 11 q^{8} + 11 q^{9} - 4 q^{10} + 5 q^{11} + 11 q^{12} - 11 q^{13} - 4 q^{14} + 4 q^{15} + 11 q^{16} + 8 q^{17} - 11 q^{18} - 2 q^{19} + 4 q^{20} + 4 q^{21} - 5 q^{22} + 3 q^{23} - 11 q^{24} + 9 q^{25} + 11 q^{26} + 11 q^{27} + 4 q^{28} + 7 q^{29} - 4 q^{30} + 20 q^{31} - 11 q^{32} + 5 q^{33} - 8 q^{34} + 9 q^{35} + 11 q^{36} + q^{37} + 2 q^{38} - 11 q^{39} - 4 q^{40} + 37 q^{41} - 4 q^{42} - 16 q^{43} + 5 q^{44} + 4 q^{45} - 3 q^{46} + 28 q^{47} + 11 q^{48} + 17 q^{49} - 9 q^{50} + 8 q^{51} - 11 q^{52} - 5 q^{53} - 11 q^{54} - 28 q^{55} - 4 q^{56} - 2 q^{57} - 7 q^{58} + 31 q^{59} + 4 q^{60} + 8 q^{61} - 20 q^{62} + 4 q^{63} + 11 q^{64} - 4 q^{65} - 5 q^{66} - 22 q^{67} + 8 q^{68} + 3 q^{69} - 9 q^{70} + 42 q^{71} - 11 q^{72} - 4 q^{73} - q^{74} + 9 q^{75} - 2 q^{76} - 21 q^{77} + 11 q^{78} + 33 q^{79} + 4 q^{80} + 11 q^{81} - 37 q^{82} + 18 q^{83} + 4 q^{84} + 17 q^{85} + 16 q^{86} + 7 q^{87} - 5 q^{88} + 67 q^{89} - 4 q^{90} - 4 q^{91} + 3 q^{92} + 20 q^{93} - 28 q^{94} + 32 q^{95} - 11 q^{96} - 15 q^{97} - 17 q^{98} + 5 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 + 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 4 * q^7 - 11 * q^8 + 11 * q^9 - 4 * q^10 + 5 * q^11 + 11 * q^12 - 11 * q^13 - 4 * q^14 + 4 * q^15 + 11 * q^16 + 8 * q^17 - 11 * q^18 - 2 * q^19 + 4 * q^20 + 4 * q^21 - 5 * q^22 + 3 * q^23 - 11 * q^24 + 9 * q^25 + 11 * q^26 + 11 * q^27 + 4 * q^28 + 7 * q^29 - 4 * q^30 + 20 * q^31 - 11 * q^32 + 5 * q^33 - 8 * q^34 + 9 * q^35 + 11 * q^36 + q^37 + 2 * q^38 - 11 * q^39 - 4 * q^40 + 37 * q^41 - 4 * q^42 - 16 * q^43 + 5 * q^44 + 4 * q^45 - 3 * q^46 + 28 * q^47 + 11 * q^48 + 17 * q^49 - 9 * q^50 + 8 * q^51 - 11 * q^52 - 5 * q^53 - 11 * q^54 - 28 * q^55 - 4 * q^56 - 2 * q^57 - 7 * q^58 + 31 * q^59 + 4 * q^60 + 8 * q^61 - 20 * q^62 + 4 * q^63 + 11 * q^64 - 4 * q^65 - 5 * q^66 - 22 * q^67 + 8 * q^68 + 3 * q^69 - 9 * q^70 + 42 * q^71 - 11 * q^72 - 4 * q^73 - q^74 + 9 * q^75 - 2 * q^76 - 21 * q^77 + 11 * q^78 + 33 * q^79 + 4 * q^80 + 11 * q^81 - 37 * q^82 + 18 * q^83 + 4 * q^84 + 17 * q^85 + 16 * q^86 + 7 * q^87 - 5 * q^88 + 67 * q^89 - 4 * q^90 - 4 * q^91 + 3 * q^92 + 20 * q^93 - 28 * q^94 + 32 * q^95 - 11 * q^96 - 15 * q^97 - 17 * q^98 + 5 * 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
$5$	−2.06747	−0.924601	−0.462300	−	0.886723i	$-0.652976\pi$
$5$	−2.06747	−0.924601	−0.462300	+	0.886723i	$0.652976\pi$
$6$	−1.00000	−0.408248
$7$	−2.54251	−0.960977	−0.480488	−	0.877001i	$-0.659541\pi$
$7$	−2.54251	−0.960977	−0.480488	+	0.877001i	$0.659541\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.06747	0.653791
$11$	−0.325101	−0.0980216	−0.0490108	−	0.998798i	$-0.515607\pi$
$11$	−0.325101	−0.0980216	−0.0490108	+	0.998798i	$0.515607\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	2.54251	0.679513
$15$	−2.06747	−0.533818
$16$	1.00000	0.250000
$17$	−7.70014	−1.86756	−0.933779	−	0.357849i	$-0.883510\pi$
$17$	−7.70014	−1.86756	−0.933779	+	0.357849i	$0.883510\pi$
$18$	−1.00000	−0.235702
$19$	−1.05544	−0.242134	−0.121067	−	0.992644i	$-0.538632\pi$
$19$	−1.05544	−0.242134	−0.121067	+	0.992644i	$0.538632\pi$
$20$	−2.06747	−0.462300
$21$	−2.54251	−0.554820
$22$	0.325101	0.0693117
$23$	−2.56996	−0.535873	−0.267937	−	0.963437i	$-0.586342\pi$
$23$	−2.56996	−0.535873	−0.267937	+	0.963437i	$0.586342\pi$
$24$	−1.00000	−0.204124
$25$	−0.725568	−0.145114
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	−2.54251	−0.480488
$29$	0.0777727	0.0144420	0.00722102	−	0.999974i	$-0.497701\pi$
$29$	0.0777727	0.0144420	0.00722102	+	0.999974i	$0.497701\pi$
$30$	2.06747	0.377467
$31$	−5.03097	−0.903588	−0.451794	−	0.892122i	$-0.649216\pi$
$31$	−5.03097	−0.903588	−0.451794	+	0.892122i	$0.649216\pi$
$32$	−1.00000	−0.176777
$33$	−0.325101	−0.0565928
$34$	7.70014	1.32056
$35$	5.25655	0.888520
$36$	1.00000	0.166667
$37$	−10.2755	−1.68928	−0.844642	−	0.535332i	$-0.820186\pi$
$37$	−10.2755	−1.68928	−0.844642	+	0.535332i	$0.820186\pi$
$38$	1.05544	0.171215
$39$	−1.00000	−0.160128
$40$	2.06747	0.326896
$41$	5.75538	0.898840	0.449420	−	0.893321i	$-0.351631\pi$
$41$	5.75538	0.898840	0.449420	+	0.893321i	$0.351631\pi$
$42$	2.54251	0.392317
$43$	−7.40377	−1.12906	−0.564532	−	0.825411i	$-0.690943\pi$
$43$	−7.40377	−1.12906	−0.564532	+	0.825411i	$0.690943\pi$
$44$	−0.325101	−0.0490108
$45$	−2.06747	−0.308200
$46$	2.56996	0.378920
$47$	11.7938	1.72031	0.860153	−	0.510036i	$-0.170368\pi$
$47$	11.7938	1.72031	0.860153	+	0.510036i	$0.170368\pi$
$48$	1.00000	0.144338
$49$	−0.535664	−0.0765234
$50$	0.725568	0.102611
$51$	−7.70014	−1.07824
$52$	−1.00000	−0.138675
$53$	−11.7975	−1.62051	−0.810254	−	0.586080i	$-0.800671\pi$
$53$	−11.7975	−1.62051	−0.810254	+	0.586080i	$0.800671\pi$
$54$	−1.00000	−0.136083
$55$	0.672136	0.0906308
$56$	2.54251	0.339757
$57$	−1.05544	−0.139796
$58$	−0.0777727	−0.0102121
$59$	5.79963	0.755047	0.377524	−	0.926000i	$-0.376776\pi$
$59$	5.79963	0.755047	0.377524	+	0.926000i	$0.376776\pi$
$60$	−2.06747	−0.266909
$61$	10.5128	1.34602	0.673012	−	0.739632i	$-0.265000\pi$
$61$	10.5128	1.34602	0.673012	+	0.739632i	$0.265000\pi$
$62$	5.03097	0.638933
$63$	−2.54251	−0.320326
$64$	1.00000	0.125000
$65$	2.06747	0.256438
$66$	0.325101	0.0400171
$67$	−4.95776	−0.605687	−0.302843	−	0.953040i	$-0.597936\pi$
$67$	−4.95776	−0.605687	−0.302843	+	0.953040i	$0.597936\pi$
$68$	−7.70014	−0.933779
$69$	−2.56996	−0.309387
$70$	−5.25655	−0.628278
$71$	10.9990	1.30535	0.652673	−	0.757640i	$-0.273648\pi$
$71$	10.9990	1.30535	0.652673	+	0.757640i	$0.273648\pi$
$72$	−1.00000	−0.117851
$73$	9.54903	1.11763	0.558815	−	0.829292i	$-0.311256\pi$
$73$	9.54903	1.11763	0.558815	+	0.829292i	$0.311256\pi$
$74$	10.2755	1.19450
$75$	−0.725568	−0.0837813
$76$	−1.05544	−0.121067
$77$	0.826571	0.0941965
$78$	1.00000	0.113228
$79$	−7.67987	−0.864053	−0.432026	−	0.901861i	$-0.642201\pi$
$79$	−7.67987	−0.864053	−0.432026	+	0.901861i	$0.642201\pi$
$80$	−2.06747	−0.231150
$81$	1.00000	0.111111
$82$	−5.75538	−0.635576
$83$	−13.2806	−1.45773	−0.728865	−	0.684657i	$-0.759952\pi$
$83$	−13.2806	−1.45773	−0.728865	+	0.684657i	$0.759952\pi$
$84$	−2.54251	−0.277410
$85$	15.9198	1.72675
$86$	7.40377	0.798369
$87$	0.0777727	0.00833811
$88$	0.325101	0.0346559
$89$	16.6191	1.76162	0.880808	−	0.473473i	$-0.157000\pi$
$89$	16.6191	1.76162	0.880808	+	0.473473i	$0.157000\pi$
$90$	2.06747	0.217930
$91$	2.54251	0.266527
$92$	−2.56996	−0.267937
$93$	−5.03097	−0.521687
$94$	−11.7938	−1.21644
$95$	2.18209	0.223878
$96$	−1.00000	−0.102062
$97$	−13.2571	−1.34605	−0.673026	−	0.739619i	$-0.735006\pi$
$97$	−13.2571	−1.34605	−0.673026	+	0.739619i	$0.735006\pi$
$98$	0.535664	0.0541102
$99$	−0.325101	−0.0326739
$100$	−0.725568	−0.0725568
$101$	10.5464	1.04941	0.524703	−	0.851286i	$-0.324177\pi$
$101$	10.5464	1.04941	0.524703	+	0.851286i	$0.324177\pi$
$102$	7.70014	0.762428
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.00000	0.0980581
$105$	5.25655	0.512987
$106$	11.7975	1.14587
$107$	−1.98677	−0.192069	−0.0960343	−	0.995378i	$-0.530616\pi$
$107$	−1.98677	−0.192069	−0.0960343	+	0.995378i	$0.530616\pi$
$108$	1.00000	0.0962250
$109$	13.7733	1.31924	0.659622	−	0.751597i	$-0.270716\pi$
$109$	13.7733	1.31924	0.659622	+	0.751597i	$0.270716\pi$
$110$	−0.672136	−0.0640857
$111$	−10.2755	−0.975308
$112$	−2.54251	−0.240244
$113$	−3.02600	−0.284662	−0.142331	−	0.989819i	$-0.545460\pi$
$113$	−3.02600	−0.284662	−0.142331	+	0.989819i	$0.545460\pi$
$114$	1.05544	0.0988509
$115$	5.31331	0.495469
$116$	0.0777727	0.00722102
$117$	−1.00000	−0.0924500
$118$	−5.79963	−0.533899
$119$	19.5777	1.79468
$120$	2.06747	0.188733
$121$	−10.8943	−0.990392
$122$	−10.5128	−0.951782
$123$	5.75538	0.518945
$124$	−5.03097	−0.451794
$125$	11.8374	1.05877
$126$	2.54251	0.226504
$127$	−5.38570	−0.477903	−0.238952	−	0.971031i	$-0.576804\pi$
$127$	−5.38570	−0.477903	−0.238952	+	0.971031i	$0.576804\pi$
$128$	−1.00000	−0.0883883
$129$	−7.40377	−0.651866
$130$	−2.06747	−0.181329
$131$	13.5215	1.18138	0.590690	−	0.806898i	$-0.298855\pi$
$131$	13.5215	1.18138	0.590690	+	0.806898i	$0.298855\pi$
$132$	−0.325101	−0.0282964
$133$	2.68346	0.232685
$134$	4.95776	0.428285
$135$	−2.06747	−0.177939
$136$	7.70014	0.660282
$137$	5.70337	0.487272	0.243636	−	0.969867i	$-0.421660\pi$
$137$	5.70337	0.487272	0.243636	+	0.969867i	$0.421660\pi$
$138$	2.56996	0.218769
$139$	−7.96711	−0.675761	−0.337881	−	0.941189i	$-0.609710\pi$
$139$	−7.96711	−0.675761	−0.337881	+	0.941189i	$0.609710\pi$
$140$	5.25655	0.444260
$141$	11.7938	0.993219
$142$	−10.9990	−0.923018
$143$	0.325101	0.0271863
$144$	1.00000	0.0833333
$145$	−0.160793	−0.0133531
$146$	−9.54903	−0.790283
$147$	−0.535664	−0.0441808
$148$	−10.2755	−0.844642
$149$	−16.2383	−1.33029	−0.665147	−	0.746713i	$-0.731631\pi$
$149$	−16.2383	−1.33029	−0.665147	+	0.746713i	$0.731631\pi$
$150$	0.725568	0.0592423
$151$	13.1343	1.06885	0.534427	−	0.845215i	$-0.320528\pi$
$151$	13.1343	1.06885	0.534427	+	0.845215i	$0.320528\pi$
$152$	1.05544	0.0856074
$153$	−7.70014	−0.622520
$154$	−0.826571	−0.0666070
$155$	10.4014	0.835458
$156$	−1.00000	−0.0800641
$157$	−5.30295	−0.423222	−0.211611	−	0.977354i	$-0.567871\pi$
$157$	−5.30295	−0.423222	−0.211611	+	0.977354i	$0.567871\pi$
$158$	7.67987	0.610978
$159$	−11.7975	−0.935600
$160$	2.06747	0.163448
$161$	6.53413	0.514962
$162$	−1.00000	−0.0785674
$163$	−6.97609	−0.546409	−0.273205	−	0.961956i	$-0.588084\pi$
$163$	−6.97609	−0.546409	−0.273205	+	0.961956i	$0.588084\pi$
$164$	5.75538	0.449420
$165$	0.672136	0.0523257
$166$	13.2806	1.03077
$167$	−15.1969	−1.17597	−0.587985	−	0.808872i	$-0.700079\pi$
$167$	−15.1969	−1.17597	−0.587985	+	0.808872i	$0.700079\pi$
$168$	2.54251	0.196159
$169$	1.00000	0.0769231
$170$	−15.9198	−1.22099
$171$	−1.05544	−0.0807114
$172$	−7.40377	−0.564532
$173$	−1.82523	−0.138770	−0.0693848	−	0.997590i	$-0.522104\pi$
$173$	−1.82523	−0.138770	−0.0693848	+	0.997590i	$0.522104\pi$
$174$	−0.0777727	−0.00589594
$175$	1.84476	0.139451
$176$	−0.325101	−0.0245054
$177$	5.79963	0.435927
$178$	−16.6191	−1.24565
$179$	−14.3397	−1.07180	−0.535900	−	0.844282i	$-0.680027\pi$
$179$	−14.3397	−1.07180	−0.535900	+	0.844282i	$0.680027\pi$
$180$	−2.06747	−0.154100
$181$	−9.00560	−0.669381	−0.334691	−	0.942328i	$-0.608632\pi$
$181$	−9.00560	−0.669381	−0.334691	+	0.942328i	$0.608632\pi$
$182$	−2.54251	−0.188463
$183$	10.5128	0.777127
$184$	2.56996	0.189460
$185$	21.2443	1.56191
$186$	5.03097	0.368888
$187$	2.50332	0.183061
$188$	11.7938	0.860153
$189$	−2.54251	−0.184940
$190$	−2.18209	−0.158305
$191$	−7.19831	−0.520851	−0.260426	−	0.965494i	$-0.583863\pi$
$191$	−7.19831	−0.520851	−0.260426	+	0.965494i	$0.583863\pi$
$192$	1.00000	0.0721688
$193$	23.6641	1.70338	0.851691	−	0.524045i	$-0.175578\pi$
$193$	23.6641	1.70338	0.851691	+	0.524045i	$0.175578\pi$
$194$	13.2571	0.951803
$195$	2.06747	0.148055
$196$	−0.535664	−0.0382617
$197$	11.6426	0.829499	0.414749	−	0.909936i	$-0.363869\pi$
$197$	11.6426	0.829499	0.414749	+	0.909936i	$0.363869\pi$
$198$	0.325101	0.0231039
$199$	18.1687	1.28795	0.643974	−	0.765047i	$-0.277284\pi$
$199$	18.1687	1.28795	0.643974	+	0.765047i	$0.277284\pi$
$200$	0.725568	0.0513054
$201$	−4.95776	−0.349693
$202$	−10.5464	−0.742041
$203$	−0.197738	−0.0138785
$204$	−7.70014	−0.539118
$205$	−11.8991	−0.831068
$206$	1.00000	0.0696733
$207$	−2.56996	−0.178624
$208$	−1.00000	−0.0693375
$209$	0.343124	0.0237344
$210$	−5.25655	−0.362737
$211$	−20.4264	−1.40621	−0.703106	−	0.711085i	$-0.748204\pi$
$211$	−20.4264	−1.40621	−0.703106	+	0.711085i	$0.748204\pi$
$212$	−11.7975	−0.810254
$213$	10.9990	0.753641
$214$	1.98677	0.135813
$215$	15.3071	1.04393
$216$	−1.00000	−0.0680414
$217$	12.7913	0.868327
$218$	−13.7733	−0.932847
$219$	9.54903	0.645264
$220$	0.672136	0.0453154
$221$	7.70014	0.517968
$222$	10.2755	0.689647
$223$	−13.8008	−0.924172	−0.462086	−	0.886835i	$-0.652899\pi$
$223$	−13.8008	−0.924172	−0.462086	+	0.886835i	$0.652899\pi$
$224$	2.54251	0.169878
$225$	−0.725568	−0.0483712
$226$	3.02600	0.201287
$227$	2.07777	0.137906	0.0689532	−	0.997620i	$-0.478034\pi$
$227$	2.07777	0.137906	0.0689532	+	0.997620i	$0.478034\pi$
$228$	−1.05544	−0.0698981
$229$	6.47237	0.427706	0.213853	−	0.976866i	$-0.431399\pi$
$229$	6.47237	0.427706	0.213853	+	0.976866i	$0.431399\pi$
$230$	−5.31331	−0.350349
$231$	0.826571	0.0543844
$232$	−0.0777727	−0.00510603
$233$	−11.6404	−0.762585	−0.381292	−	0.924454i	$-0.624521\pi$
$233$	−11.6404	−0.762585	−0.381292	+	0.924454i	$0.624521\pi$
$234$	1.00000	0.0653720
$235$	−24.3834	−1.59060
$236$	5.79963	0.377524
$237$	−7.67987	−0.498861
$238$	−19.5777	−1.26903
$239$	8.98511	0.581199	0.290599	−	0.956845i	$-0.406145\pi$
$239$	8.98511	0.581199	0.290599	+	0.956845i	$0.406145\pi$
$240$	−2.06747	−0.133455
$241$	−13.0816	−0.842662	−0.421331	−	0.906907i	$-0.638437\pi$
$241$	−13.0816	−0.842662	−0.421331	+	0.906907i	$0.638437\pi$
$242$	10.8943	0.700313
$243$	1.00000	0.0641500
$244$	10.5128	0.673012
$245$	1.10747	0.0707536
$246$	−5.75538	−0.366950
$247$	1.05544	0.0671560
$248$	5.03097	0.319467
$249$	−13.2806	−0.841621
$250$	−11.8374	−0.748665
$251$	20.2288	1.27683	0.638416	−	0.769692i	$-0.279590\pi$
$251$	20.2288	1.27683	0.638416	+	0.769692i	$0.279590\pi$
$252$	−2.54251	−0.160163
$253$	0.835495	0.0525271
$254$	5.38570	0.337929
$255$	15.9198	0.996937
$256$	1.00000	0.0625000
$257$	−13.8737	−0.865417	−0.432708	−	0.901534i	$-0.642442\pi$
$257$	−13.8737	−0.865417	−0.432708	+	0.901534i	$0.642442\pi$
$258$	7.40377	0.460939
$259$	26.1255	1.62336
$260$	2.06747	0.128219
$261$	0.0777727	0.00481401
$262$	−13.5215	−0.835362
$263$	−3.98045	−0.245445	−0.122723	−	0.992441i	$-0.539163\pi$
$263$	−3.98045	−0.245445	−0.122723	+	0.992441i	$0.539163\pi$
$264$	0.325101	0.0200086
$265$	24.3909	1.49832
$266$	−2.68346	−0.164533
$267$	16.6191	1.01707
$268$	−4.95776	−0.302843
$269$	−17.3408	−1.05728	−0.528642	−	0.848845i	$-0.677299\pi$
$269$	−17.3408	−1.05728	−0.528642	+	0.848845i	$0.677299\pi$
$270$	2.06747	0.125822
$271$	−0.980838	−0.0595816	−0.0297908	−	0.999556i	$-0.509484\pi$
$271$	−0.980838	−0.0595816	−0.0297908	+	0.999556i	$0.509484\pi$
$272$	−7.70014	−0.466890
$273$	2.54251	0.153879
$274$	−5.70337	−0.344553
$275$	0.235883	0.0142243
$276$	−2.56996	−0.154693
$277$	21.1222	1.26911	0.634555	−	0.772878i	$-0.281183\pi$
$277$	21.1222	1.26911	0.634555	+	0.772878i	$0.281183\pi$
$278$	7.96711	0.477835
$279$	−5.03097	−0.301196
$280$	−5.25655	−0.314139
$281$	−18.6821	−1.11448	−0.557240	−	0.830351i	$-0.688140\pi$
$281$	−18.6821	−1.11448	−0.557240	+	0.830351i	$0.688140\pi$
$282$	−11.7938	−0.702312
$283$	−14.0679	−0.836253	−0.418126	−	0.908389i	$-0.637313\pi$
$283$	−14.0679	−0.836253	−0.418126	+	0.908389i	$0.637313\pi$
$284$	10.9990	0.652673
$285$	2.18209	0.129256
$286$	−0.325101	−0.0192236
$287$	−14.6331	−0.863764
$288$	−1.00000	−0.0589256
$289$	42.2922	2.48778
$290$	0.160793	0.00944208
$291$	−13.2571	−0.777144
$292$	9.54903	0.558815
$293$	32.6983	1.91025	0.955126	−	0.296199i	$-0.0957192\pi$
$293$	32.6983	1.91025	0.955126	+	0.296199i	$0.0957192\pi$
$294$	0.535664	0.0312405
$295$	−11.9906	−0.698117
$296$	10.2755	0.597252
$297$	−0.325101	−0.0188643
$298$	16.2383	0.940660
$299$	2.56996	0.148624
$300$	−0.725568	−0.0418907
$301$	18.8241	1.08500
$302$	−13.1343	−0.755793
$303$	10.5464	0.605874
$304$	−1.05544	−0.0605336
$305$	−21.7349	−1.24453
$306$	7.70014	0.440188
$307$	13.9788	0.797813	0.398906	−	0.916992i	$-0.369390\pi$
$307$	13.9788	0.797813	0.398906	+	0.916992i	$0.369390\pi$
$308$	0.826571	0.0470982
$309$	−1.00000	−0.0568880
$310$	−10.4014	−0.590758
$311$	35.0655	1.98838	0.994190	−	0.107639i	$-0.0343290\pi$
$311$	35.0655	1.98838	0.994190	+	0.107639i	$0.0343290\pi$
$312$	1.00000	0.0566139
$313$	7.76646	0.438986	0.219493	−	0.975614i	$-0.429560\pi$
$313$	7.76646	0.438986	0.219493	+	0.975614i	$0.429560\pi$
$314$	5.30295	0.299263
$315$	5.25655	0.296173
$316$	−7.67987	−0.432026
$317$	7.12334	0.400087	0.200043	−	0.979787i	$-0.435892\pi$
$317$	7.12334	0.400087	0.200043	+	0.979787i	$0.435892\pi$
$318$	11.7975	0.661569
$319$	−0.0252840	−0.00141563
$320$	−2.06747	−0.115575
$321$	−1.98677	−0.110891
$322$	−6.53413	−0.364133
$323$	8.12703	0.452200
$324$	1.00000	0.0555556
$325$	0.725568	0.0402472
$326$	6.97609	0.386370
$327$	13.7733	0.761666
$328$	−5.75538	−0.317788
$329$	−29.9859	−1.65317
$330$	−0.672136	−0.0369999
$331$	4.99331	0.274457	0.137228	−	0.990539i	$-0.456181\pi$
$331$	4.99331	0.274457	0.137228	+	0.990539i	$0.456181\pi$
$332$	−13.2806	−0.728865
$333$	−10.2755	−0.563094
$334$	15.1969	0.831536
$335$	10.2500	0.560018
$336$	−2.54251	−0.138705
$337$	33.2728	1.81248	0.906241	−	0.422761i	$-0.138939\pi$
$337$	33.2728	1.81248	0.906241	+	0.422761i	$0.138939\pi$
$338$	−1.00000	−0.0543928
$339$	−3.02600	−0.164350
$340$	15.9198	0.863373
$341$	1.63557	0.0885712
$342$	1.05544	0.0570716
$343$	19.1595	1.03451
$344$	7.40377	0.399185
$345$	5.31331	0.286059
$346$	1.82523	0.0981249
$347$	6.18401	0.331975	0.165988	−	0.986128i	$-0.446919\pi$
$347$	6.18401	0.331975	0.165988	+	0.986128i	$0.446919\pi$
$348$	0.0777727	0.00416906
$349$	−9.15281	−0.489939	−0.244969	−	0.969531i	$-0.578778\pi$
$349$	−9.15281	−0.489939	−0.244969	+	0.969531i	$0.578778\pi$
$350$	−1.84476	−0.0986066
$351$	−1.00000	−0.0533761
$352$	0.325101	0.0173279
$353$	−4.00474	−0.213151	−0.106575	−	0.994305i	$-0.533989\pi$
$353$	−4.00474	−0.213151	−0.106575	+	0.994305i	$0.533989\pi$
$354$	−5.79963	−0.308247
$355$	−22.7402	−1.20692
$356$	16.6191	0.880808
$357$	19.5777	1.03616
$358$	14.3397	0.757876
$359$	17.4058	0.918641	0.459321	−	0.888270i	$-0.348093\pi$
$359$	17.4058	0.918641	0.459321	+	0.888270i	$0.348093\pi$
$360$	2.06747	0.108965
$361$	−17.8860	−0.941371
$362$	9.00560	0.473324
$363$	−10.8943	−0.571803
$364$	2.54251	0.133264
$365$	−19.7423	−1.03336
$366$	−10.5128	−0.549512
$367$	−10.4353	−0.544719	−0.272360	−	0.962196i	$-0.587804\pi$
$367$	−10.4353	−0.544719	−0.272360	+	0.962196i	$0.587804\pi$
$368$	−2.56996	−0.133968
$369$	5.75538	0.299613
$370$	−21.2443	−1.10444
$371$	29.9951	1.55727
$372$	−5.03097	−0.260843
$373$	14.6744	0.759814	0.379907	−	0.925025i	$-0.375956\pi$
$373$	14.6744	0.759814	0.379907	+	0.925025i	$0.375956\pi$
$374$	−2.50332	−0.129444
$375$	11.8374	0.611283
$376$	−11.7938	−0.608220
$377$	−0.0777727	−0.00400550
$378$	2.54251	0.130772
$379$	3.19215	0.163970	0.0819848	−	0.996634i	$-0.473874\pi$
$379$	3.19215	0.163970	0.0819848	+	0.996634i	$0.473874\pi$
$380$	2.18209	0.111939
$381$	−5.38570	−0.275918
$382$	7.19831	0.368298
$383$	24.6706	1.26061	0.630305	−	0.776348i	$-0.282930\pi$
$383$	24.6706	1.26061	0.630305	+	0.776348i	$0.282930\pi$
$384$	−1.00000	−0.0510310
$385$	−1.70891	−0.0870941
$386$	−23.6641	−1.20447
$387$	−7.40377	−0.376355
$388$	−13.2571	−0.673026
$389$	23.4472	1.18882	0.594411	−	0.804162i	$-0.297385\pi$
$389$	23.4472	1.18882	0.594411	+	0.804162i	$0.297385\pi$
$390$	−2.06747	−0.104690
$391$	19.7890	1.00077
$392$	0.535664	0.0270551
$393$	13.5215	0.682071
$394$	−11.6426	−0.586544
$395$	15.8779	0.798904
$396$	−0.325101	−0.0163369
$397$	−11.3002	−0.567141	−0.283571	−	0.958951i	$-0.591519\pi$
$397$	−11.3002	−0.567141	−0.283571	+	0.958951i	$0.591519\pi$
$398$	−18.1687	−0.910717
$399$	2.68346	0.134341
$400$	−0.725568	−0.0362784
$401$	10.0453	0.501636	0.250818	−	0.968034i	$-0.419300\pi$
$401$	10.0453	0.501636	0.250818	+	0.968034i	$0.419300\pi$
$402$	4.95776	0.247271
$403$	5.03097	0.250610
$404$	10.5464	0.524703
$405$	−2.06747	−0.102733
$406$	0.197738	0.00981356
$407$	3.34058	0.165586
$408$	7.70014	0.381214
$409$	12.1637	0.601456	0.300728	−	0.953710i	$-0.402770\pi$
$409$	12.1637	0.601456	0.300728	+	0.953710i	$0.402770\pi$
$410$	11.8991	0.587654
$411$	5.70337	0.281327
$412$	−1.00000	−0.0492665
$413$	−14.7456	−0.725583
$414$	2.56996	0.126307
$415$	27.4571	1.34782
$416$	1.00000	0.0490290
$417$	−7.96711	−0.390151
$418$	−0.343124	−0.0167827
$419$	−16.9888	−0.829957	−0.414978	−	0.909831i	$-0.636211\pi$
$419$	−16.9888	−0.829957	−0.414978	+	0.909831i	$0.636211\pi$
$420$	5.25655	0.256494
$421$	−18.5643	−0.904768	−0.452384	−	0.891823i	$-0.649426\pi$
$421$	−18.5643	−0.904768	−0.452384	+	0.891823i	$0.649426\pi$
$422$	20.4264	0.994342
$423$	11.7938	0.573435
$424$	11.7975	0.572936
$425$	5.58697	0.271008
$426$	−10.9990	−0.532905
$427$	−26.7288	−1.29350
$428$	−1.98677	−0.0960343
$429$	0.325101	0.0156960
$430$	−15.3071	−0.738173
$431$	16.0679	0.773961	0.386981	−	0.922088i	$-0.373518\pi$
$431$	16.0679	0.773961	0.386981	+	0.922088i	$0.373518\pi$
$432$	1.00000	0.0481125
$433$	28.1447	1.35255	0.676274	−	0.736650i	$-0.263594\pi$
$433$	28.1447	1.35255	0.676274	+	0.736650i	$0.263594\pi$
$434$	−12.7913	−0.614000
$435$	−0.160793	−0.00770943
$436$	13.7733	0.659622
$437$	2.71243	0.129753
$438$	−9.54903	−0.456270
$439$	7.96025	0.379922	0.189961	−	0.981792i	$-0.439164\pi$
$439$	7.96025	0.379922	0.189961	+	0.981792i	$0.439164\pi$
$440$	−0.672136	−0.0320428
$441$	−0.535664	−0.0255078
$442$	−7.70014	−0.366258
$443$	23.6736	1.12477	0.562384	−	0.826876i	$-0.309884\pi$
$443$	23.6736	1.12477	0.562384	+	0.826876i	$0.309884\pi$
$444$	−10.2755	−0.487654
$445$	−34.3594	−1.62879
$446$	13.8008	0.653488
$447$	−16.2383	−0.768046
$448$	−2.54251	−0.120122
$449$	10.8744	0.513195	0.256598	−	0.966518i	$-0.417398\pi$
$449$	10.8744	0.513195	0.256598	+	0.966518i	$0.417398\pi$
$450$	0.725568	0.0342036
$451$	−1.87108	−0.0881057
$452$	−3.02600	−0.142331
$453$	13.1343	0.617103
$454$	−2.07777	−0.0975145
$455$	−5.25655	−0.246431
$456$	1.05544	0.0494254
$457$	−41.2830	−1.93114	−0.965568	−	0.260152i	$-0.916227\pi$
$457$	−41.2830	−1.93114	−0.965568	+	0.260152i	$0.916227\pi$
$458$	−6.47237	−0.302434
$459$	−7.70014	−0.359412
$460$	5.31331	0.247734
$461$	−10.9231	−0.508741	−0.254370	−	0.967107i	$-0.581868\pi$
$461$	−10.9231	−0.508741	−0.254370	+	0.967107i	$0.581868\pi$
$462$	−0.826571	−0.0384556
$463$	40.3828	1.87675	0.938373	−	0.345624i	$-0.112333\pi$
$463$	40.3828	1.87675	0.938373	+	0.345624i	$0.112333\pi$
$464$	0.0777727	0.00361051
$465$	10.4014	0.482352
$466$	11.6404	0.539229
$467$	−4.07854	−0.188732	−0.0943661	−	0.995538i	$-0.530082\pi$
$467$	−4.07854	−0.188732	−0.0943661	+	0.995538i	$0.530082\pi$
$468$	−1.00000	−0.0462250
$469$	12.6051	0.582051
$470$	24.3834	1.12472
$471$	−5.30295	−0.244347
$472$	−5.79963	−0.266949
$473$	2.40697	0.110673
$474$	7.67987	0.352748
$475$	0.765792	0.0351370
$476$	19.5777	0.897340
$477$	−11.7975	−0.540169
$478$	−8.98511	−0.410969
$479$	−6.34535	−0.289926	−0.144963	−	0.989437i	$-0.546306\pi$
$479$	−6.34535	−0.289926	−0.144963	+	0.989437i	$0.546306\pi$
$480$	2.06747	0.0943667
$481$	10.2755	0.468523
$482$	13.0816	0.595852
$483$	6.53413	0.297313
$484$	−10.8943	−0.495196
$485$	27.4086	1.24456
$486$	−1.00000	−0.0453609
$487$	−25.3018	−1.14653	−0.573267	−	0.819368i	$-0.694324\pi$
$487$	−25.3018	−1.14653	−0.573267	+	0.819368i	$0.694324\pi$
$488$	−10.5128	−0.475891
$489$	−6.97609	−0.315470
$490$	−1.10747	−0.0500303
$491$	−34.6281	−1.56275	−0.781373	−	0.624064i	$-0.785480\pi$
$491$	−34.6281	−1.56275	−0.781373	+	0.624064i	$0.785480\pi$
$492$	5.75538	0.259473
$493$	−0.598861	−0.0269714
$494$	−1.05544	−0.0474864
$495$	0.672136	0.0302103
$496$	−5.03097	−0.225897
$497$	−27.9651	−1.25441
$498$	13.2806	0.595116
$499$	−11.3330	−0.507334	−0.253667	−	0.967292i	$-0.581637\pi$
$499$	−11.3330	−0.507334	−0.253667	+	0.967292i	$0.581637\pi$
$500$	11.8374	0.529386
$501$	−15.1969	−0.678947
$502$	−20.2288	−0.902856
$503$	−28.0509	−1.25073	−0.625363	−	0.780334i	$-0.715049\pi$
$503$	−28.0509	−1.25073	−0.625363	+	0.780334i	$0.715049\pi$
$504$	2.54251	0.113252
$505$	−21.8043	−0.970281
$506$	−0.835495	−0.0371423
$507$	1.00000	0.0444116
$508$	−5.38570	−0.238952
$509$	15.4230	0.683612	0.341806	−	0.939770i	$-0.388961\pi$
$509$	15.4230	0.683612	0.341806	+	0.939770i	$0.388961\pi$
$510$	−15.9198	−0.704941
$511$	−24.2785	−1.07402
$512$	−1.00000	−0.0441942
$513$	−1.05544	−0.0465988
$514$	13.8737	0.611942
$515$	2.06747	0.0911036
$516$	−7.40377	−0.325933
$517$	−3.83418	−0.168627
$518$	−26.1255	−1.14789
$519$	−1.82523	−0.0801187
$520$	−2.06747	−0.0906646
$521$	14.2942	0.626242	0.313121	−	0.949713i	$-0.398626\pi$
$521$	14.2942	0.626242	0.313121	+	0.949713i	$0.398626\pi$
$522$	−0.0777727	−0.00340402
$523$	37.8464	1.65491	0.827454	−	0.561533i	$-0.189788\pi$
$523$	37.8464	1.65491	0.827454	+	0.561533i	$0.189788\pi$
$524$	13.5215	0.590690
$525$	1.84476	0.0805119
$526$	3.98045	0.173556
$527$	38.7392	1.68750
$528$	−0.325101	−0.0141482
$529$	−16.3953	−0.712840
$530$	−24.3909	−1.05947
$531$	5.79963	0.251682
$532$	2.68346	0.116343
$533$	−5.75538	−0.249293
$534$	−16.6191	−0.719177
$535$	4.10759	0.177587
$536$	4.95776	0.214143
$537$	−14.3397	−0.618804
$538$	17.3408	0.747613
$539$	0.174145	0.00750094
$540$	−2.06747	−0.0889697
$541$	−45.2386	−1.94496	−0.972479	−	0.232990i	$-0.925149\pi$
$541$	−45.2386	−1.94496	−0.972479	+	0.232990i	$0.925149\pi$
$542$	0.980838	0.0421306
$543$	−9.00560	−0.386467
$544$	7.70014	0.330141
$545$	−28.4759	−1.21977
$546$	−2.54251	−0.108809
$547$	26.2794	1.12363	0.561813	−	0.827264i	$-0.310104\pi$
$547$	26.2794	1.12363	0.561813	+	0.827264i	$0.310104\pi$
$548$	5.70337	0.243636
$549$	10.5128	0.448675
$550$	−0.235883	−0.0100581
$551$	−0.0820844	−0.00349691
$552$	2.56996	0.109385
$553$	19.5261	0.830335
$554$	−21.1222	−0.897396
$555$	21.2443	0.901771
$556$	−7.96711	−0.337881
$557$	24.2072	1.02569	0.512845	−	0.858481i	$-0.328592\pi$
$557$	24.2072	1.02569	0.512845	+	0.858481i	$0.328592\pi$
$558$	5.03097	0.212978
$559$	7.40377	0.313146
$560$	5.25655	0.222130
$561$	2.50332	0.105690
$562$	18.6821	0.788056
$563$	12.3599	0.520906	0.260453	−	0.965487i	$-0.416128\pi$
$563$	12.3599	0.520906	0.260453	+	0.965487i	$0.416128\pi$
$564$	11.7938	0.496610
$565$	6.25617	0.263199
$566$	14.0679	0.591320
$567$	−2.54251	−0.106775
$568$	−10.9990	−0.461509
$569$	12.5085	0.524383	0.262192	−	0.965016i	$-0.415555\pi$
$569$	12.5085	0.524383	0.262192	+	0.965016i	$0.415555\pi$
$570$	−2.18209	−0.0913976
$571$	−37.8918	−1.58572	−0.792860	−	0.609403i	$-0.791409\pi$
$571$	−37.8918	−1.58572	−0.792860	+	0.609403i	$0.791409\pi$
$572$	0.325101	0.0135931
$573$	−7.19831	−0.300714
$574$	14.6331	0.610774
$575$	1.86468	0.0777624
$576$	1.00000	0.0416667
$577$	−43.6088	−1.81546	−0.907729	−	0.419557i	$-0.862185\pi$
$577$	−43.6088	−1.81546	−0.907729	+	0.419557i	$0.862185\pi$
$578$	−42.2922	−1.75912
$579$	23.6641	0.983448
$580$	−0.160793	−0.00667656
$581$	33.7659	1.40085
$582$	13.2571	0.549524
$583$	3.83537	0.158845
$584$	−9.54903	−0.395142
$585$	2.06747	0.0854794
$586$	−32.6983	−1.35075
$587$	28.8699	1.19159	0.595794	−	0.803137i	$-0.296837\pi$
$587$	28.8699	1.19159	0.595794	+	0.803137i	$0.296837\pi$
$588$	−0.535664	−0.0220904
$589$	5.30988	0.218790
$590$	11.9906	0.493643
$591$	11.6426	0.478911
$592$	−10.2755	−0.422321
$593$	3.34321	0.137289	0.0686446	−	0.997641i	$-0.478133\pi$
$593$	3.34321	0.137289	0.0686446	+	0.997641i	$0.478133\pi$
$594$	0.325101	0.0133390
$595$	−40.4762	−1.65936
$596$	−16.2383	−0.665147
$597$	18.1687	0.743597
$598$	−2.56996	−0.105093
$599$	−3.80516	−0.155474	−0.0777372	−	0.996974i	$-0.524770\pi$
$599$	−3.80516	−0.155474	−0.0777372	+	0.996974i	$0.524770\pi$
$600$	0.725568	0.0296212
$601$	1.40160	0.0571724	0.0285862	−	0.999591i	$-0.490899\pi$
$601$	1.40160	0.0571724	0.0285862	+	0.999591i	$0.490899\pi$
$602$	−18.8241	−0.767214
$603$	−4.95776	−0.201896
$604$	13.1343	0.534427
$605$	22.5237	0.915717
$606$	−10.5464	−0.428418
$607$	−15.8113	−0.641759	−0.320880	−	0.947120i	$-0.603978\pi$
$607$	−15.8113	−0.641759	−0.320880	+	0.947120i	$0.603978\pi$
$608$	1.05544	0.0428037
$609$	−0.197738	−0.00801273
$610$	21.7349	0.880019
$611$	−11.7938	−0.477127
$612$	−7.70014	−0.311260
$613$	−30.8319	−1.24529	−0.622645	−	0.782505i	$-0.713942\pi$
$613$	−30.8319	−1.24529	−0.622645	+	0.782505i	$0.713942\pi$
$614$	−13.9788	−0.564139
$615$	−11.8991	−0.479817
$616$	−0.826571	−0.0333035
$617$	27.0953	1.09082	0.545408	−	0.838171i	$-0.316375\pi$
$617$	27.0953	1.09082	0.545408	+	0.838171i	$0.316375\pi$
$618$	1.00000	0.0402259
$619$	−13.4552	−0.540811	−0.270406	−	0.962746i	$-0.587158\pi$
$619$	−13.4552	−0.540811	−0.270406	+	0.962746i	$0.587158\pi$
$620$	10.4014	0.417729
$621$	−2.56996	−0.103129
$622$	−35.0655	−1.40600
$623$	−42.2541	−1.69287
$624$	−1.00000	−0.0400320
$625$	−20.8457	−0.833829
$626$	−7.76646	−0.310410
$627$	0.343124	0.0137031
$628$	−5.30295	−0.211611
$629$	79.1229	3.15484
$630$	−5.25655	−0.209426
$631$	−6.10024	−0.242847	−0.121423	−	0.992601i	$-0.538746\pi$
$631$	−6.10024	−0.242847	−0.121423	+	0.992601i	$0.538746\pi$
$632$	7.67987	0.305489
$633$	−20.4264	−0.811877
$634$	−7.12334	−0.282904
$635$	11.1348	0.441870
$636$	−11.7975	−0.467800
$637$	0.535664	0.0212238
$638$	0.0252840	0.00100100
$639$	10.9990	0.435115
$640$	2.06747	0.0817239
$641$	−30.6376	−1.21011	−0.605056	−	0.796183i	$-0.706849\pi$
$641$	−30.6376	−1.21011	−0.605056	+	0.796183i	$0.706849\pi$
$642$	1.98677	0.0784117
$643$	−23.8904	−0.942145	−0.471072	−	0.882095i	$-0.656133\pi$
$643$	−23.8904	−0.942145	−0.471072	+	0.882095i	$0.656133\pi$
$644$	6.53413	0.257481
$645$	15.3071	0.602716
$646$	−8.12703	−0.319754
$647$	15.2851	0.600921	0.300461	−	0.953794i	$-0.402860\pi$
$647$	15.2851	0.600921	0.300461	+	0.953794i	$0.402860\pi$
$648$	−1.00000	−0.0392837
$649$	−1.88546	−0.0740109
$650$	−0.725568	−0.0284591
$651$	12.7913	0.501329
$652$	−6.97609	−0.273205
$653$	9.80130	0.383555	0.191777	−	0.981438i	$-0.438575\pi$
$653$	9.80130	0.383555	0.191777	+	0.981438i	$0.438575\pi$
$654$	−13.7733	−0.538579
$655$	−27.9553	−1.09231
$656$	5.75538	0.224710
$657$	9.54903	0.372543
$658$	29.9859	1.16897
$659$	15.2342	0.593439	0.296720	−	0.954965i	$-0.404107\pi$
$659$	15.2342	0.593439	0.296720	+	0.954965i	$0.404107\pi$
$660$	0.672136	0.0261629
$661$	18.8487	0.733129	0.366564	−	0.930393i	$-0.380534\pi$
$661$	18.8487	0.733129	0.366564	+	0.930393i	$0.380534\pi$
$662$	−4.99331	−0.194070
$663$	7.70014	0.299049
$664$	13.2806	0.515385
$665$	−5.54797	−0.215141
$666$	10.2755	0.398168
$667$	−0.199873	−0.00773910
$668$	−15.1969	−0.587985
$669$	−13.8008	−0.533571
$670$	−10.2500	−0.395993
$671$	−3.41771	−0.131939
$672$	2.54251	0.0980793
$673$	−29.0838	−1.12110	−0.560549	−	0.828121i	$-0.689410\pi$
$673$	−29.0838	−1.12110	−0.560549	+	0.828121i	$0.689410\pi$
$674$	−33.2728	−1.28162
$675$	−0.725568	−0.0279271
$676$	1.00000	0.0384615
$677$	30.7737	1.18273	0.591364	−	0.806405i	$-0.298590\pi$
$677$	30.7737	1.18273	0.591364	+	0.806405i	$0.298590\pi$
$678$	3.02600	0.116213
$679$	33.7062	1.29353
$680$	−15.9198	−0.610497
$681$	2.07777	0.0796203
$682$	−1.63557	−0.0626293
$683$	−35.3288	−1.35182	−0.675910	−	0.736984i	$-0.736249\pi$
$683$	−35.3288	−1.35182	−0.675910	+	0.736984i	$0.736249\pi$
$684$	−1.05544	−0.0403557
$685$	−11.7916	−0.450532
$686$	−19.1595	−0.731512
$687$	6.47237	0.246936
$688$	−7.40377	−0.282266
$689$	11.7975	0.449448
$690$	−5.31331	−0.202274
$691$	−38.8119	−1.47647	−0.738237	−	0.674541i	$-0.764341\pi$
$691$	−38.8119	−1.47647	−0.738237	+	0.674541i	$0.764341\pi$
$692$	−1.82523	−0.0693848
$693$	0.826571	0.0313988
$694$	−6.18401	−0.234742
$695$	16.4718	0.624809
$696$	−0.0777727	−0.00294797
$697$	−44.3173	−1.67864
$698$	9.15281	0.346439
$699$	−11.6404	−0.440279
$700$	1.84476	0.0697254
$701$	−21.8017	−0.823440	−0.411720	−	0.911310i	$-0.635072\pi$
$701$	−21.8017	−0.823440	−0.411720	+	0.911310i	$0.635072\pi$
$702$	1.00000	0.0377426
$703$	10.8452	0.409033
$704$	−0.325101	−0.0122527
$705$	−24.3834	−0.918331
$706$	4.00474	0.150720
$707$	−26.8143	−1.00845
$708$	5.79963	0.217963
$709$	16.1927	0.608131	0.304065	−	0.952651i	$-0.401656\pi$
$709$	16.1927	0.608131	0.304065	+	0.952651i	$0.401656\pi$
$710$	22.7402	0.853423
$711$	−7.67987	−0.288018
$712$	−16.6191	−0.622826
$713$	12.9294	0.484209
$714$	−19.5777	−0.732675
$715$	−0.672136	−0.0251365
$716$	−14.3397	−0.535900
$717$	8.98511	0.335555
$718$	−17.4058	−0.649578
$719$	−1.68185	−0.0627223	−0.0313612	−	0.999508i	$-0.509984\pi$
$719$	−1.68185	−0.0627223	−0.0313612	+	0.999508i	$0.509984\pi$
$720$	−2.06747	−0.0770501
$721$	2.54251	0.0946879
$722$	17.8860	0.665650
$723$	−13.0816	−0.486511
$724$	−9.00560	−0.334691
$725$	−0.0564294	−0.00209573
$726$	10.8943	0.404326
$727$	21.6799	0.804063	0.402031	−	0.915626i	$-0.368304\pi$
$727$	21.6799	0.804063	0.402031	+	0.915626i	$0.368304\pi$
$728$	−2.54251	−0.0942315
$729$	1.00000	0.0370370
$730$	19.7423	0.730697
$731$	57.0101	2.10859
$732$	10.5128	0.388564
$733$	−30.1133	−1.11226	−0.556131	−	0.831095i	$-0.687715\pi$
$733$	−30.1133	−1.11226	−0.556131	+	0.831095i	$0.687715\pi$
$734$	10.4353	0.385175
$735$	1.10747	0.0408496
$736$	2.56996	0.0947299
$737$	1.61177	0.0593704
$738$	−5.75538	−0.211859
$739$	11.8672	0.436544	0.218272	−	0.975888i	$-0.429958\pi$
$739$	11.8672	0.436544	0.218272	+	0.975888i	$0.429958\pi$
$740$	21.2443	0.780956
$741$	1.05544	0.0387725
$742$	−29.9951	−1.10116
$743$	14.7246	0.540192	0.270096	−	0.962833i	$-0.412945\pi$
$743$	14.7246	0.540192	0.270096	+	0.962833i	$0.412945\pi$
$744$	5.03097	0.184444
$745$	33.5722	1.22999
$746$	−14.6744	−0.537270
$747$	−13.2806	−0.485910
$748$	2.50332	0.0915306
$749$	5.05138	0.184574
$750$	−11.8374	−0.432242
$751$	−32.3583	−1.18077	−0.590385	−	0.807121i	$-0.701024\pi$
$751$	−32.3583	−1.18077	−0.590385	+	0.807121i	$0.701024\pi$
$752$	11.7938	0.430076
$753$	20.2288	0.737179
$754$	0.0777727	0.00283232
$755$	−27.1548	−0.988263
$756$	−2.54251	−0.0924700
$757$	34.4788	1.25315	0.626576	−	0.779360i	$-0.284456\pi$
$757$	34.4788	1.25315	0.626576	+	0.779360i	$0.284456\pi$
$758$	−3.19215	−0.115944
$759$	0.835495	0.0303266
$760$	−2.18209	−0.0791527
$761$	−37.3399	−1.35357	−0.676785	−	0.736181i	$-0.736627\pi$
$761$	−37.3399	−1.35357	−0.676785	+	0.736181i	$0.736627\pi$
$762$	5.38570	0.195103
$763$	−35.0187	−1.26776
$764$	−7.19831	−0.260426
$765$	15.9198	0.575582
$766$	−24.6706	−0.891386
$767$	−5.79963	−0.209412
$768$	1.00000	0.0360844
$769$	44.5051	1.60490	0.802448	−	0.596723i	$-0.203531\pi$
$769$	44.5051	1.60490	0.802448	+	0.596723i	$0.203531\pi$
$770$	1.70891	0.0615849
$771$	−13.8737	−0.499649
$772$	23.6641	0.851691
$773$	−20.5837	−0.740344	−0.370172	−	0.928963i	$-0.620701\pi$
$773$	−20.5837	−0.740344	−0.370172	+	0.928963i	$0.620701\pi$
$774$	7.40377	0.266123
$775$	3.65031	0.131123
$776$	13.2571	0.475901
$777$	26.1255	0.937249
$778$	−23.4472	−0.840624
$779$	−6.07446	−0.217640
$780$	2.06747	0.0740273
$781$	−3.57580	−0.127952
$782$	−19.7890	−0.707655
$783$	0.0777727	0.00277937
$784$	−0.535664	−0.0191308
$785$	10.9637	0.391311
$786$	−13.5215	−0.482297
$787$	51.1180	1.82216	0.911080	−	0.412229i	$-0.135250\pi$
$787$	51.1180	1.82216	0.911080	+	0.412229i	$0.135250\pi$
$788$	11.6426	0.414749
$789$	−3.98045	−0.141708
$790$	−15.8779	−0.564910
$791$	7.69363	0.273554
$792$	0.325101	0.0115520
$793$	−10.5128	−0.373320
$794$	11.3002	0.401029
$795$	24.3909	0.865057
$796$	18.1687	0.643974
$797$	−22.6204	−0.801254	−0.400627	−	0.916241i	$-0.631208\pi$
$797$	−22.6204	−0.801254	−0.400627	+	0.916241i	$0.631208\pi$
$798$	−2.68346	−0.0949934
$799$	−90.8141	−3.21277
$800$	0.725568	0.0256527
$801$	16.6191	0.587206
$802$	−10.0453	−0.354710
$803$	−3.10440	−0.109552
$804$	−4.95776	−0.174847
$805$	−13.5091	−0.476134
$806$	−5.03097	−0.177208
$807$	−17.3408	−0.610424
$808$	−10.5464	−0.371021
$809$	−3.65170	−0.128387	−0.0641935	−	0.997937i	$-0.520447\pi$
$809$	−3.65170	−0.128387	−0.0641935	+	0.997937i	$0.520447\pi$
$810$	2.06747	0.0726435
$811$	−25.9126	−0.909914	−0.454957	−	0.890513i	$-0.650345\pi$
$811$	−25.9126	−0.909914	−0.454957	+	0.890513i	$0.650345\pi$
$812$	−0.197738	−0.00693923
$813$	−0.980838	−0.0343995
$814$	−3.34058	−0.117087
$815$	14.4229	0.505211
$816$	−7.70014	−0.269559
$817$	7.81423	0.273385
$818$	−12.1637	−0.425293
$819$	2.54251	0.0888423
$820$	−11.8991	−0.415534
$821$	55.0626	1.92170	0.960850	−	0.277070i	$-0.0893633\pi$
$821$	55.0626	1.92170	0.960850	+	0.277070i	$0.0893633\pi$
$822$	−5.70337	−0.198928
$823$	26.6142	0.927714	0.463857	−	0.885910i	$-0.346465\pi$
$823$	26.6142	0.927714	0.463857	+	0.885910i	$0.346465\pi$
$824$	1.00000	0.0348367
$825$	0.235883	0.00821238
$826$	14.7456	0.513065
$827$	−14.0781	−0.489542	−0.244771	−	0.969581i	$-0.578713\pi$
$827$	−14.0781	−0.489542	−0.244771	+	0.969581i	$0.578713\pi$
$828$	−2.56996	−0.0893122
$829$	48.6722	1.69046	0.845228	−	0.534406i	$-0.179465\pi$
$829$	48.6722	1.69046	0.845228	+	0.534406i	$0.179465\pi$
$830$	−27.4571	−0.953051
$831$	21.1222	0.732721
$832$	−1.00000	−0.0346688
$833$	4.12469	0.142912
$834$	7.96711	0.275878
$835$	31.4191	1.08730
$836$	0.343124	0.0118672
$837$	−5.03097	−0.173896
$838$	16.9888	0.586868
$839$	−36.5694	−1.26252	−0.631258	−	0.775573i	$-0.717461\pi$
$839$	−36.5694	−1.26252	−0.631258	+	0.775573i	$0.717461\pi$
$840$	−5.25655	−0.181368
$841$	−28.9940	−0.999791
$842$	18.5643	0.639768
$843$	−18.6821	−0.643445
$844$	−20.4264	−0.703106
$845$	−2.06747	−0.0711231
$846$	−11.7938	−0.405480
$847$	27.6988	0.951744
$848$	−11.7975	−0.405127
$849$	−14.0679	−0.482811
$850$	−5.58697	−0.191632
$851$	26.4076	0.905241
$852$	10.9990	0.376821
$853$	35.5851	1.21841	0.609205	−	0.793013i	$-0.291489\pi$
$853$	35.5851	1.21841	0.609205	+	0.793013i	$0.291489\pi$
$854$	26.7288	0.914641
$855$	2.18209	0.0746258
$856$	1.98677	0.0679065
$857$	8.03135	0.274346	0.137173	−	0.990547i	$-0.456198\pi$
$857$	8.03135	0.274346	0.137173	+	0.990547i	$0.456198\pi$
$858$	−0.325101	−0.0110988
$859$	−11.6808	−0.398543	−0.199271	−	0.979944i	$-0.563857\pi$
$859$	−11.6808	−0.398543	−0.199271	+	0.979944i	$0.563857\pi$
$860$	15.3071	0.521967
$861$	−14.6331	−0.498695
$862$	−16.0679	−0.547273
$863$	4.63476	0.157769	0.0788845	−	0.996884i	$-0.474864\pi$
$863$	4.63476	0.157769	0.0788845	+	0.996884i	$0.474864\pi$
$864$	−1.00000	−0.0340207
$865$	3.77361	0.128306
$866$	−28.1447	−0.956396
$867$	42.2922	1.43632
$868$	12.7913	0.434164
$869$	2.49673	0.0846958
$870$	0.160793	0.00545139
$871$	4.95776	0.167987
$872$	−13.7733	−0.466423
$873$	−13.2571	−0.448684
$874$	−2.71243	−0.0917494
$875$	−30.0968	−1.01746
$876$	9.54903	0.322632
$877$	−8.52160	−0.287754	−0.143877	−	0.989596i	$-0.545957\pi$
$877$	−8.52160	−0.287754	−0.143877	+	0.989596i	$0.545957\pi$
$878$	−7.96025	−0.268646
$879$	32.6983	1.10288
$880$	0.672136	0.0226577
$881$	−24.0145	−0.809068	−0.404534	−	0.914523i	$-0.632566\pi$
$881$	−24.0145	−0.809068	−0.404534	+	0.914523i	$0.632566\pi$
$882$	0.535664	0.0180367
$883$	−39.6574	−1.33458	−0.667288	−	0.744800i	$-0.732545\pi$
$883$	−39.6574	−1.33458	−0.667288	+	0.744800i	$0.732545\pi$
$884$	7.70014	0.258984
$885$	−11.9906	−0.403058
$886$	−23.6736	−0.795331
$887$	−19.6477	−0.659704	−0.329852	−	0.944033i	$-0.606999\pi$
$887$	−19.6477	−0.659704	−0.329852	+	0.944033i	$0.606999\pi$
$888$	10.2755	0.344823
$889$	13.6932	0.459254
$890$	34.3594	1.15173
$891$	−0.325101	−0.0108913
$892$	−13.8008	−0.462086
$893$	−12.4477	−0.416545
$894$	16.2383	0.543090
$895$	29.6469	0.990986
$896$	2.54251	0.0849392
$897$	2.56996	0.0858084
$898$	−10.8744	−0.362884
$899$	−0.391272	−0.0130497
$900$	−0.725568	−0.0241856
$901$	90.8422	3.02639
$902$	1.87108	0.0623002
$903$	18.8241	0.626428
$904$	3.02600	0.100643
$905$	18.6188	0.618910
$906$	−13.1343	−0.436358
$907$	30.4073	1.00966	0.504829	−	0.863220i	$-0.331556\pi$
$907$	30.4073	1.00966	0.504829	+	0.863220i	$0.331556\pi$
$908$	2.07777	0.0689532
$909$	10.5464	0.349802
$910$	5.25655	0.174253
$911$	24.4054	0.808588	0.404294	−	0.914629i	$-0.367517\pi$
$911$	24.4054	0.808588	0.404294	+	0.914629i	$0.367517\pi$
$912$	−1.05544	−0.0349491
$913$	4.31752	0.142889
$914$	41.2830	1.36552
$915$	−21.7349	−0.718532
$916$	6.47237	0.213853
$917$	−34.3786	−1.13528
$918$	7.70014	0.254143
$919$	20.7953	0.685973	0.342986	−	0.939340i	$-0.388561\pi$
$919$	20.7953	0.685973	0.342986	+	0.939340i	$0.388561\pi$
$920$	−5.31331	−0.175175
$921$	13.9788	0.460617
$922$	10.9231	0.359734
$923$	−10.9990	−0.362038
$924$	0.826571	0.0271922
$925$	7.45558	0.245138
$926$	−40.3828	−1.32706
$927$	−1.00000	−0.0328443
$928$	−0.0777727	−0.00255302
$929$	35.1368	1.15280	0.576401	−	0.817167i	$-0.304457\pi$
$929$	35.1368	1.15280	0.576401	+	0.817167i	$0.304457\pi$
$930$	−10.4014	−0.341074
$931$	0.565360	0.0185289
$932$	−11.6404	−0.381292
$933$	35.0655	1.14799
$934$	4.07854	0.133454
$935$	−5.17555	−0.169258
$936$	1.00000	0.0326860
$937$	−13.6863	−0.447113	−0.223557	−	0.974691i	$-0.571767\pi$
$937$	−13.6863	−0.447113	−0.223557	+	0.974691i	$0.571767\pi$
$938$	−12.6051	−0.411572
$939$	7.76646	0.253449
$940$	−24.3834	−0.795298
$941$	−22.3737	−0.729362	−0.364681	−	0.931132i	$-0.618822\pi$
$941$	−22.3737	−0.729362	−0.364681	+	0.931132i	$0.618822\pi$
$942$	5.30295	0.172779
$943$	−14.7911	−0.481664
$944$	5.79963	0.188762
$945$	5.25655	0.170996
$946$	−2.40697	−0.0782574
$947$	35.7475	1.16164	0.580818	−	0.814033i	$-0.302733\pi$
$947$	35.7475	1.16164	0.580818	+	0.814033i	$0.302733\pi$
$948$	−7.67987	−0.249431
$949$	−9.54903	−0.309975
$950$	−0.765792	−0.0248456
$951$	7.12334	0.230990
$952$	−19.5777	−0.634516
$953$	−9.86342	−0.319507	−0.159754	−	0.987157i	$-0.551070\pi$
$953$	−9.86342	−0.319507	−0.159754	+	0.987157i	$0.551070\pi$
$954$	11.7975	0.381957
$955$	14.8823	0.481580
$956$	8.98511	0.290599
$957$	−0.0252840	−0.000817315 0
$958$	6.34535	0.205009
$959$	−14.5009	−0.468257
$960$	−2.06747	−0.0667273
$961$	−5.68938	−0.183528
$962$	−10.2755	−0.331296
$963$	−1.98677	−0.0640229
$964$	−13.0816	−0.421331
$965$	−48.9249	−1.57495
$966$	−6.53413	−0.210232
$967$	26.3830	0.848420	0.424210	−	0.905564i	$-0.360552\pi$
$967$	26.3830	0.848420	0.424210	+	0.905564i	$0.360552\pi$
$968$	10.8943	0.350156
$969$	8.12703	0.261078
$970$	−27.4086	−0.880037
$971$	43.4753	1.39519	0.697594	−	0.716493i	$-0.254254\pi$
$971$	43.4753	1.39519	0.697594	+	0.716493i	$0.254254\pi$
$972$	1.00000	0.0320750
$973$	20.2564	0.649391
$974$	25.3018	0.810722
$975$	0.725568	0.0232368
$976$	10.5128	0.336506
$977$	−46.3364	−1.48243	−0.741217	−	0.671265i	$-0.765751\pi$
$977$	−46.3364	−1.48243	−0.741217	+	0.671265i	$0.765751\pi$
$978$	6.97609	0.223071
$979$	−5.40287	−0.172676
$980$	1.10747	0.0353768
$981$	13.7733	0.439748
$982$	34.6281	1.10503
$983$	48.1031	1.53425	0.767126	−	0.641497i	$-0.221686\pi$
$983$	48.1031	1.53425	0.767126	+	0.641497i	$0.221686\pi$
$984$	−5.75538	−0.183475
$985$	−24.0707	−0.766955
$986$	0.598861	0.0190716
$987$	−29.9859	−0.954461
$988$	1.05544	0.0335780
$989$	19.0274	0.605035
$990$	−0.672136	−0.0213619
$991$	2.49557	0.0792745	0.0396372	−	0.999214i	$-0.487380\pi$
$991$	2.49557	0.0792745	0.0396372	+	0.999214i	$0.487380\pi$
$992$	5.03097	0.159733
$993$	4.99331	0.158458
$994$	27.9651	0.886999
$995$	−37.5633	−1.19084
$996$	−13.2806	−0.420810
$997$	16.1684	0.512058	0.256029	−	0.966669i	$-0.417586\pi$
$997$	16.1684	0.512058	0.256029	+	0.966669i	$0.417586\pi$
$998$	11.3330	0.358739
$999$	−10.2755	−0.325103

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.t.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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.06747 q^{5} -1.00000 q^{6} -2.54251 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.06747 q^{5} -1.00000 q^{6} -2.54251 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.06747 q^{10} -0.325101 q^{11} +1.00000 q^{12} -1.00000 q^{13} +2.54251 q^{14} -2.06747 q^{15} +1.00000 q^{16} -7.70014 q^{17} -1.00000 q^{18} -1.05544 q^{19} -2.06747 q^{20} -2.54251 q^{21} +0.325101 q^{22} -2.56996 q^{23} -1.00000 q^{24} -0.725568 q^{25} +1.00000 q^{26} +1.00000 q^{27} -2.54251 q^{28} +0.0777727 q^{29} +2.06747 q^{30} -5.03097 q^{31} -1.00000 q^{32} -0.325101 q^{33} +7.70014 q^{34} +5.25655 q^{35} +1.00000 q^{36} -10.2755 q^{37} +1.05544 q^{38} -1.00000 q^{39} +2.06747 q^{40} +5.75538 q^{41} +2.54251 q^{42} -7.40377 q^{43} -0.325101 q^{44} -2.06747 q^{45} +2.56996 q^{46} +11.7938 q^{47} +1.00000 q^{48} -0.535664 q^{49} +0.725568 q^{50} -7.70014 q^{51} -1.00000 q^{52} -11.7975 q^{53} -1.00000 q^{54} +0.672136 q^{55} +2.54251 q^{56} -1.05544 q^{57} -0.0777727 q^{58} +5.79963 q^{59} -2.06747 q^{60} +10.5128 q^{61} +5.03097 q^{62} -2.54251 q^{63} +1.00000 q^{64} +2.06747 q^{65} +0.325101 q^{66} -4.95776 q^{67} -7.70014 q^{68} -2.56996 q^{69} -5.25655 q^{70} +10.9990 q^{71} -1.00000 q^{72} +9.54903 q^{73} +10.2755 q^{74} -0.725568 q^{75} -1.05544 q^{76} +0.826571 q^{77} +1.00000 q^{78} -7.67987 q^{79} -2.06747 q^{80} +1.00000 q^{81} -5.75538 q^{82} -13.2806 q^{83} -2.54251 q^{84} +15.9198 q^{85} +7.40377 q^{86} +0.0777727 q^{87} +0.325101 q^{88} +16.6191 q^{89} +2.06747 q^{90} +2.54251 q^{91} -2.56996 q^{92} -5.03097 q^{93} -11.7938 q^{94} +2.18209 q^{95} -1.00000 q^{96} -13.2571 q^{97} +0.535664 q^{98} -0.325101 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} + 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 4 q^{7} - 11 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 + 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 4 * q^7 - 11 * q^8 + 11 * q^9	\( 11 q - 11 q^{2} + 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 4 q^{7} - 11 q^{8} + 11 q^{9} - 4 q^{10} + 5 q^{11} + 11 q^{12} - 11 q^{13} - 4 q^{14} + 4 q^{15} + 11 q^{16} + 8 q^{17} - 11 q^{18} - 2 q^{19} + 4 q^{20} + 4 q^{21} - 5 q^{22} + 3 q^{23} - 11 q^{24} + 9 q^{25} + 11 q^{26} + 11 q^{27} + 4 q^{28} + 7 q^{29} - 4 q^{30} + 20 q^{31} - 11 q^{32} + 5 q^{33} - 8 q^{34} + 9 q^{35} + 11 q^{36} + q^{37} + 2 q^{38} - 11 q^{39} - 4 q^{40} + 37 q^{41} - 4 q^{42} - 16 q^{43} + 5 q^{44} + 4 q^{45} - 3 q^{46} + 28 q^{47} + 11 q^{48} + 17 q^{49} - 9 q^{50} + 8 q^{51} - 11 q^{52} - 5 q^{53} - 11 q^{54} - 28 q^{55} - 4 q^{56} - 2 q^{57} - 7 q^{58} + 31 q^{59} + 4 q^{60} + 8 q^{61} - 20 q^{62} + 4 q^{63} + 11 q^{64} - 4 q^{65} - 5 q^{66} - 22 q^{67} + 8 q^{68} + 3 q^{69} - 9 q^{70} + 42 q^{71} - 11 q^{72} - 4 q^{73} - q^{74} + 9 q^{75} - 2 q^{76} - 21 q^{77} + 11 q^{78} + 33 q^{79} + 4 q^{80} + 11 q^{81} - 37 q^{82} + 18 q^{83} + 4 q^{84} + 17 q^{85} + 16 q^{86} + 7 q^{87} - 5 q^{88} + 67 q^{89} - 4 q^{90} - 4 q^{91} + 3 q^{92} + 20 q^{93} - 28 q^{94} + 32 q^{95} - 11 q^{96} - 15 q^{97} - 17 q^{98} + 5 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 + 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 4 * q^7 - 11 * q^8 + 11 * q^9 - 4 * q^10 + 5 * q^11 + 11 * q^12 - 11 * q^13 - 4 * q^14 + 4 * q^15 + 11 * q^16 + 8 * q^17 - 11 * q^18 - 2 * q^19 + 4 * q^20 + 4 * q^21 - 5 * q^22 + 3 * q^23 - 11 * q^24 + 9 * q^25 + 11 * q^26 + 11 * q^27 + 4 * q^28 + 7 * q^29 - 4 * q^30 + 20 * q^31 - 11 * q^32 + 5 * q^33 - 8 * q^34 + 9 * q^35 + 11 * q^36 + q^37 + 2 * q^38 - 11 * q^39 - 4 * q^40 + 37 * q^41 - 4 * q^42 - 16 * q^43 + 5 * q^44 + 4 * q^45 - 3 * q^46 + 28 * q^47 + 11 * q^48 + 17 * q^49 - 9 * q^50 + 8 * q^51 - 11 * q^52 - 5 * q^53 - 11 * q^54 - 28 * q^55 - 4 * q^56 - 2 * q^57 - 7 * q^58 + 31 * q^59 + 4 * q^60 + 8 * q^61 - 20 * q^62 + 4 * q^63 + 11 * q^64 - 4 * q^65 - 5 * q^66 - 22 * q^67 + 8 * q^68 + 3 * q^69 - 9 * q^70 + 42 * q^71 - 11 * q^72 - 4 * q^73 - q^74 + 9 * q^75 - 2 * q^76 - 21 * q^77 + 11 * q^78 + 33 * q^79 + 4 * q^80 + 11 * q^81 - 37 * q^82 + 18 * q^83 + 4 * q^84 + 17 * q^85 + 16 * q^86 + 7 * q^87 - 5 * q^88 + 67 * q^89 - 4 * q^90 - 4 * q^91 + 3 * q^92 + 20 * q^93 - 28 * q^94 + 32 * q^95 - 11 * q^96 - 15 * q^97 - 17 * q^98 + 5 * q^99

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