LMFDB - Embedded newform 8022.2.a.r.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8022,2,Mod(1,8022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8022, 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("8022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8022 = 2 \cdot 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8022.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:	$64.0559925015$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 19x^{8} + 28x^{7} + 114x^{6} - 110x^{5} - 282x^{4} + 149x^{3} + 285x^{2} - 49x - 79 $ x^10 - 2x^9 - 19x^8 + 28x^7 + 114x^6 - 110x^5 - 282x^4 + 149x^3 + 285x^2 - 49*x - 79
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-1.81749$ of defining polynomial
Character	$\chi$	$=$	8022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.81749 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.81749 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.81749 q^{10} -5.79788 q^{11} -1.00000 q^{12} -1.03194 q^{13} +1.00000 q^{14} -2.81749 q^{15} +1.00000 q^{16} -1.72802 q^{17} +1.00000 q^{18} +3.05233 q^{19} +2.81749 q^{20} -1.00000 q^{21} -5.79788 q^{22} +5.25355 q^{23} -1.00000 q^{24} +2.93824 q^{25} -1.03194 q^{26} -1.00000 q^{27} +1.00000 q^{28} +3.06331 q^{29} -2.81749 q^{30} +1.18800 q^{31} +1.00000 q^{32} +5.79788 q^{33} -1.72802 q^{34} +2.81749 q^{35} +1.00000 q^{36} +2.53861 q^{37} +3.05233 q^{38} +1.03194 q^{39} +2.81749 q^{40} -7.36786 q^{41} -1.00000 q^{42} +2.13850 q^{43} -5.79788 q^{44} +2.81749 q^{45} +5.25355 q^{46} +6.58087 q^{47} -1.00000 q^{48} +1.00000 q^{49} +2.93824 q^{50} +1.72802 q^{51} -1.03194 q^{52} -8.28137 q^{53} -1.00000 q^{54} -16.3354 q^{55} +1.00000 q^{56} -3.05233 q^{57} +3.06331 q^{58} +9.62868 q^{59} -2.81749 q^{60} -4.92205 q^{61} +1.18800 q^{62} +1.00000 q^{63} +1.00000 q^{64} -2.90748 q^{65} +5.79788 q^{66} +1.66457 q^{67} -1.72802 q^{68} -5.25355 q^{69} +2.81749 q^{70} +13.9102 q^{71} +1.00000 q^{72} +10.8583 q^{73} +2.53861 q^{74} -2.93824 q^{75} +3.05233 q^{76} -5.79788 q^{77} +1.03194 q^{78} -1.51871 q^{79} +2.81749 q^{80} +1.00000 q^{81} -7.36786 q^{82} +10.0679 q^{83} -1.00000 q^{84} -4.86866 q^{85} +2.13850 q^{86} -3.06331 q^{87} -5.79788 q^{88} +8.25577 q^{89} +2.81749 q^{90} -1.03194 q^{91} +5.25355 q^{92} -1.18800 q^{93} +6.58087 q^{94} +8.59990 q^{95} -1.00000 q^{96} +12.6657 q^{97} +1.00000 q^{98} -5.79788 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} - 10 q^{3} + 10 q^{4} + 8 q^{5} - 10 q^{6} + 10 q^{7} + 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 - 10 * q^3 + 10 * q^4 + 8 * q^5 - 10 * q^6 + 10 * q^7 + 10 * q^8 + 10 * q^9	\( 10 q + 10 q^{2} - 10 q^{3} + 10 q^{4} + 8 q^{5} - 10 q^{6} + 10 q^{7} + 10 q^{8} + 10 q^{9} + 8 q^{10} + 4 q^{11} - 10 q^{12} + 6 q^{13} + 10 q^{14} - 8 q^{15} + 10 q^{16} + 5 q^{17} + 10 q^{18} + 15 q^{19} + 8 q^{20} - 10 q^{21} + 4 q^{22} + 12 q^{23} - 10 q^{24} - 2 q^{25} + 6 q^{26} - 10 q^{27} + 10 q^{28} + 7 q^{29} - 8 q^{30} + 28 q^{31} + 10 q^{32} - 4 q^{33} + 5 q^{34} + 8 q^{35} + 10 q^{36} - 3 q^{37} + 15 q^{38} - 6 q^{39} + 8 q^{40} + 24 q^{41} - 10 q^{42} + 4 q^{43} + 4 q^{44} + 8 q^{45} + 12 q^{46} + 16 q^{47} - 10 q^{48} + 10 q^{49} - 2 q^{50} - 5 q^{51} + 6 q^{52} + 5 q^{53} - 10 q^{54} - q^{55} + 10 q^{56} - 15 q^{57} + 7 q^{58} + 17 q^{59} - 8 q^{60} + 15 q^{61} + 28 q^{62} + 10 q^{63} + 10 q^{64} + 14 q^{65} - 4 q^{66} + 6 q^{67} + 5 q^{68} - 12 q^{69} + 8 q^{70} + 5 q^{71} + 10 q^{72} + 16 q^{73} - 3 q^{74} + 2 q^{75} + 15 q^{76} + 4 q^{77} - 6 q^{78} - 5 q^{79} + 8 q^{80} + 10 q^{81} + 24 q^{82} + 24 q^{83} - 10 q^{84} - 19 q^{85} + 4 q^{86} - 7 q^{87} + 4 q^{88} + 17 q^{89} + 8 q^{90} + 6 q^{91} + 12 q^{92} - 28 q^{93} + 16 q^{94} + 15 q^{95} - 10 q^{96} + 20 q^{97} + 10 q^{98} + 4 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - 10 * q^3 + 10 * q^4 + 8 * q^5 - 10 * q^6 + 10 * q^7 + 10 * q^8 + 10 * q^9 + 8 * q^10 + 4 * q^11 - 10 * q^12 + 6 * q^13 + 10 * q^14 - 8 * q^15 + 10 * q^16 + 5 * q^17 + 10 * q^18 + 15 * q^19 + 8 * q^20 - 10 * q^21 + 4 * q^22 + 12 * q^23 - 10 * q^24 - 2 * q^25 + 6 * q^26 - 10 * q^27 + 10 * q^28 + 7 * q^29 - 8 * q^30 + 28 * q^31 + 10 * q^32 - 4 * q^33 + 5 * q^34 + 8 * q^35 + 10 * q^36 - 3 * q^37 + 15 * q^38 - 6 * q^39 + 8 * q^40 + 24 * q^41 - 10 * q^42 + 4 * q^43 + 4 * q^44 + 8 * q^45 + 12 * q^46 + 16 * q^47 - 10 * q^48 + 10 * q^49 - 2 * q^50 - 5 * q^51 + 6 * q^52 + 5 * q^53 - 10 * q^54 - q^55 + 10 * q^56 - 15 * q^57 + 7 * q^58 + 17 * q^59 - 8 * q^60 + 15 * q^61 + 28 * q^62 + 10 * q^63 + 10 * q^64 + 14 * q^65 - 4 * q^66 + 6 * q^67 + 5 * q^68 - 12 * q^69 + 8 * q^70 + 5 * q^71 + 10 * q^72 + 16 * q^73 - 3 * q^74 + 2 * q^75 + 15 * q^76 + 4 * q^77 - 6 * q^78 - 5 * q^79 + 8 * q^80 + 10 * q^81 + 24 * q^82 + 24 * q^83 - 10 * q^84 - 19 * q^85 + 4 * q^86 - 7 * q^87 + 4 * q^88 + 17 * q^89 + 8 * q^90 + 6 * q^91 + 12 * q^92 - 28 * q^93 + 16 * q^94 + 15 * q^95 - 10 * q^96 + 20 * q^97 + 10 * q^98 + 4 * 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
$5$	2.81749	1.26002	0.630009	−	0.776588i	$-0.283051\pi$
$5$	2.81749	1.26002	0.630009	+	0.776588i	$0.283051\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.81749	0.890968
$11$	−5.79788	−1.74813	−0.874063	−	0.485813i	$-0.838524\pi$
$11$	−5.79788	−1.74813	−0.874063	+	0.485813i	$0.838524\pi$
$12$	−1.00000	−0.288675
$13$	−1.03194	−0.286209	−0.143105	−	0.989708i	$-0.545709\pi$
$13$	−1.03194	−0.286209	−0.143105	+	0.989708i	$0.545709\pi$
$14$	1.00000	0.267261
$15$	−2.81749	−0.727472
$16$	1.00000	0.250000
$17$	−1.72802	−0.419105	−0.209553	−	0.977797i	$-0.567201\pi$
$17$	−1.72802	−0.419105	−0.209553	+	0.977797i	$0.567201\pi$
$18$	1.00000	0.235702
$19$	3.05233	0.700252	0.350126	−	0.936703i	$-0.386139\pi$
$19$	3.05233	0.700252	0.350126	+	0.936703i	$0.386139\pi$
$20$	2.81749	0.630009
$21$	−1.00000	−0.218218
$22$	−5.79788	−1.23611
$23$	5.25355	1.09544	0.547721	−	0.836661i	$-0.315496\pi$
$23$	5.25355	1.09544	0.547721	+	0.836661i	$0.315496\pi$
$24$	−1.00000	−0.204124
$25$	2.93824	0.587647
$26$	−1.03194	−0.202380
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	3.06331	0.568842	0.284421	−	0.958699i	$-0.408199\pi$
$29$	3.06331	0.568842	0.284421	+	0.958699i	$0.408199\pi$
$30$	−2.81749	−0.514400
$31$	1.18800	0.213372	0.106686	−	0.994293i	$-0.465976\pi$
$31$	1.18800	0.213372	0.106686	+	0.994293i	$0.465976\pi$
$32$	1.00000	0.176777
$33$	5.79788	1.00928
$34$	−1.72802	−0.296352
$35$	2.81749	0.476242
$36$	1.00000	0.166667
$37$	2.53861	0.417345	0.208673	−	0.977986i	$-0.433086\pi$
$37$	2.53861	0.417345	0.208673	+	0.977986i	$0.433086\pi$
$38$	3.05233	0.495153
$39$	1.03194	0.165243
$40$	2.81749	0.445484
$41$	−7.36786	−1.15067	−0.575333	−	0.817919i	$-0.695127\pi$
$41$	−7.36786	−1.15067	−0.575333	+	0.817919i	$0.695127\pi$
$42$	−1.00000	−0.154303
$43$	2.13850	0.326119	0.163059	−	0.986616i	$-0.447864\pi$
$43$	2.13850	0.326119	0.163059	+	0.986616i	$0.447864\pi$
$44$	−5.79788	−0.874063
$45$	2.81749	0.420006
$46$	5.25355	0.774594
$47$	6.58087	0.959918	0.479959	−	0.877291i	$-0.340651\pi$
$47$	6.58087	0.959918	0.479959	+	0.877291i	$0.340651\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	2.93824	0.415529
$51$	1.72802	0.241971
$52$	−1.03194	−0.143105
$53$	−8.28137	−1.13753	−0.568767	−	0.822499i	$-0.692579\pi$
$53$	−8.28137	−1.13753	−0.568767	+	0.822499i	$0.692579\pi$
$54$	−1.00000	−0.136083
$55$	−16.3354	−2.20267
$56$	1.00000	0.133631
$57$	−3.05233	−0.404291
$58$	3.06331	0.402232
$59$	9.62868	1.25355	0.626773	−	0.779202i	$-0.284375\pi$
$59$	9.62868	1.25355	0.626773	+	0.779202i	$0.284375\pi$
$60$	−2.81749	−0.363736
$61$	−4.92205	−0.630204	−0.315102	−	0.949058i	$-0.602039\pi$
$61$	−4.92205	−0.630204	−0.315102	+	0.949058i	$0.602039\pi$
$62$	1.18800	0.150876
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	−2.90748	−0.360629
$66$	5.79788	0.713669
$67$	1.66457	0.203360	0.101680	−	0.994817i	$-0.467578\pi$
$67$	1.66457	0.203360	0.101680	+	0.994817i	$0.467578\pi$
$68$	−1.72802	−0.209553
$69$	−5.25355	−0.632453
$70$	2.81749	0.336754
$71$	13.9102	1.65084	0.825421	−	0.564518i	$-0.190938\pi$
$71$	13.9102	1.65084	0.825421	+	0.564518i	$0.190938\pi$
$72$	1.00000	0.117851
$73$	10.8583	1.27086	0.635432	−	0.772157i	$-0.280822\pi$
$73$	10.8583	1.27086	0.635432	+	0.772157i	$0.280822\pi$
$74$	2.53861	0.295108
$75$	−2.93824	−0.339278
$76$	3.05233	0.350126
$77$	−5.79788	−0.660729
$78$	1.03194	0.116844
$79$	−1.51871	−0.170869	−0.0854343	−	0.996344i	$-0.527228\pi$
$79$	−1.51871	−0.170869	−0.0854343	+	0.996344i	$0.527228\pi$
$80$	2.81749	0.315005
$81$	1.00000	0.111111
$82$	−7.36786	−0.813644
$83$	10.0679	1.10510	0.552548	−	0.833481i	$-0.313655\pi$
$83$	10.0679	1.10510	0.552548	+	0.833481i	$0.313655\pi$
$84$	−1.00000	−0.109109
$85$	−4.86866	−0.528080
$86$	2.13850	0.230601
$87$	−3.06331	−0.328421
$88$	−5.79788	−0.618056
$89$	8.25577	0.875110	0.437555	−	0.899192i	$-0.355845\pi$
$89$	8.25577	0.875110	0.437555	+	0.899192i	$0.355845\pi$
$90$	2.81749	0.296989
$91$	−1.03194	−0.108177
$92$	5.25355	0.547721
$93$	−1.18800	−0.123190
$94$	6.58087	0.678765
$95$	8.59990	0.882331
$96$	−1.00000	−0.102062
$97$	12.6657	1.28600	0.643001	−	0.765865i	$-0.277689\pi$
$97$	12.6657	1.28600	0.643001	+	0.765865i	$0.277689\pi$
$98$	1.00000	0.101015
$99$	−5.79788	−0.582708
$100$	2.93824	0.293824
$101$	5.75781	0.572923	0.286462	−	0.958092i	$-0.407521\pi$
$101$	5.75781	0.572923	0.286462	+	0.958092i	$0.407521\pi$
$102$	1.72802	0.171099
$103$	−16.4240	−1.61831	−0.809153	−	0.587598i	$-0.800074\pi$
$103$	−16.4240	−1.61831	−0.809153	+	0.587598i	$0.800074\pi$
$104$	−1.03194	−0.101190
$105$	−2.81749	−0.274959
$106$	−8.28137	−0.804358
$107$	16.3272	1.57841	0.789203	−	0.614133i	$-0.210494\pi$
$107$	16.3272	1.57841	0.789203	+	0.614133i	$0.210494\pi$
$108$	−1.00000	−0.0962250
$109$	12.7711	1.22325	0.611626	−	0.791147i	$-0.290516\pi$
$109$	12.7711	1.22325	0.611626	+	0.791147i	$0.290516\pi$
$110$	−16.3354	−1.55752
$111$	−2.53861	−0.240955
$112$	1.00000	0.0944911
$113$	2.54342	0.239265	0.119632	−	0.992818i	$-0.461828\pi$
$113$	2.54342	0.239265	0.119632	+	0.992818i	$0.461828\pi$
$114$	−3.05233	−0.285877
$115$	14.8018	1.38028
$116$	3.06331	0.284421
$117$	−1.03194	−0.0954030
$118$	9.62868	0.886392
$119$	−1.72802	−0.158407
$120$	−2.81749	−0.257200
$121$	22.6154	2.05594
$122$	−4.92205	−0.445621
$123$	7.36786	0.664337
$124$	1.18800	0.106686
$125$	−5.80900	−0.519572
$126$	1.00000	0.0890871
$127$	−3.80895	−0.337990	−0.168995	−	0.985617i	$-0.554052\pi$
$127$	−3.80895	−0.337990	−0.168995	+	0.985617i	$0.554052\pi$
$128$	1.00000	0.0883883
$129$	−2.13850	−0.188285
$130$	−2.90748	−0.255003
$131$	2.10773	0.184154	0.0920768	−	0.995752i	$-0.470649\pi$
$131$	2.10773	0.184154	0.0920768	+	0.995752i	$0.470649\pi$
$132$	5.79788	0.504640
$133$	3.05233	0.264670
$134$	1.66457	0.143797
$135$	−2.81749	−0.242491
$136$	−1.72802	−0.148176
$137$	13.7233	1.17246	0.586230	−	0.810145i	$-0.300612\pi$
$137$	13.7233	1.17246	0.586230	+	0.810145i	$0.300612\pi$
$138$	−5.25355	−0.447212
$139$	−5.56193	−0.471757	−0.235878	−	0.971783i	$-0.575797\pi$
$139$	−5.56193	−0.471757	−0.235878	+	0.971783i	$0.575797\pi$
$140$	2.81749	0.238121
$141$	−6.58087	−0.554209
$142$	13.9102	1.16732
$143$	5.98307	0.500329
$144$	1.00000	0.0833333
$145$	8.63083	0.716752
$146$	10.8583	0.898637
$147$	−1.00000	−0.0824786
$148$	2.53861	0.208673
$149$	7.30653	0.598574	0.299287	−	0.954163i	$-0.403251\pi$
$149$	7.30653	0.598574	0.299287	+	0.954163i	$0.403251\pi$
$150$	−2.93824	−0.239906
$151$	−0.838304	−0.0682202	−0.0341101	−	0.999418i	$-0.510860\pi$
$151$	−0.838304	−0.0682202	−0.0341101	+	0.999418i	$0.510860\pi$
$152$	3.05233	0.247577
$153$	−1.72802	−0.139702
$154$	−5.79788	−0.467206
$155$	3.34718	0.268852
$156$	1.03194	0.0826214
$157$	16.1028	1.28515	0.642573	−	0.766225i	$-0.277867\pi$
$157$	16.1028	1.28515	0.642573	+	0.766225i	$0.277867\pi$
$158$	−1.51871	−0.120822
$159$	8.28137	0.656755
$160$	2.81749	0.222742
$161$	5.25355	0.414038
$162$	1.00000	0.0785674
$163$	−10.5084	−0.823078	−0.411539	−	0.911392i	$-0.635009\pi$
$163$	−10.5084	−0.823078	−0.411539	+	0.911392i	$0.635009\pi$
$164$	−7.36786	−0.575333
$165$	16.3354	1.27171
$166$	10.0679	0.781421
$167$	−2.62206	−0.202901	−0.101450	−	0.994841i	$-0.532348\pi$
$167$	−2.62206	−0.202901	−0.101450	+	0.994841i	$0.532348\pi$
$168$	−1.00000	−0.0771517
$169$	−11.9351	−0.918084
$170$	−4.86866	−0.373409
$171$	3.05233	0.233417
$172$	2.13850	0.163059
$173$	−21.4767	−1.63284	−0.816420	−	0.577458i	$-0.804045\pi$
$173$	−21.4767	−1.63284	−0.816420	+	0.577458i	$0.804045\pi$
$174$	−3.06331	−0.232229
$175$	2.93824	0.222110
$176$	−5.79788	−0.437031
$177$	−9.62868	−0.723736
$178$	8.25577	0.618796
$179$	7.24003	0.541145	0.270573	−	0.962700i	$-0.412787\pi$
$179$	7.24003	0.541145	0.270573	+	0.962700i	$0.412787\pi$
$180$	2.81749	0.210003
$181$	−13.9468	−1.03666	−0.518328	−	0.855182i	$-0.673445\pi$
$181$	−13.9468	−1.03666	−0.518328	+	0.855182i	$0.673445\pi$
$182$	−1.03194	−0.0764926
$183$	4.92205	0.363848
$184$	5.25355	0.387297
$185$	7.15251	0.525863
$186$	−1.18800	−0.0871086
$187$	10.0188	0.732649
$188$	6.58087	0.479959
$189$	−1.00000	−0.0727393
$190$	8.59990	0.623902
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	−1.00000	−0.0721688
$193$	−6.83432	−0.491945	−0.245972	−	0.969277i	$-0.579107\pi$
$193$	−6.83432	−0.491945	−0.245972	+	0.969277i	$0.579107\pi$
$194$	12.6657	0.909341
$195$	2.90748	0.208209
$196$	1.00000	0.0714286
$197$	−8.28110	−0.590004	−0.295002	−	0.955497i	$-0.595320\pi$
$197$	−8.28110	−0.590004	−0.295002	+	0.955497i	$0.595320\pi$
$198$	−5.79788	−0.412037
$199$	20.6243	1.46202	0.731011	−	0.682366i	$-0.239049\pi$
$199$	20.6243	1.46202	0.731011	+	0.682366i	$0.239049\pi$
$200$	2.93824	0.207765
$201$	−1.66457	−0.117410
$202$	5.75781	0.405118
$203$	3.06331	0.215002
$204$	1.72802	0.120985
$205$	−20.7588	−1.44986
$206$	−16.4240	−1.14432
$207$	5.25355	0.365147
$208$	−1.03194	−0.0715523
$209$	−17.6970	−1.22413
$210$	−2.81749	−0.194425
$211$	−15.0461	−1.03582	−0.517909	−	0.855435i	$-0.673290\pi$
$211$	−15.0461	−1.03582	−0.517909	+	0.855435i	$0.673290\pi$
$212$	−8.28137	−0.568767
$213$	−13.9102	−0.953114
$214$	16.3272	1.11610
$215$	6.02521	0.410916
$216$	−1.00000	−0.0680414
$217$	1.18800	0.0806469
$218$	12.7711	0.864969
$219$	−10.8583	−0.733734
$220$	−16.3354	−1.10134
$221$	1.78321	0.119952
$222$	−2.53861	−0.170381
$223$	−16.2621	−1.08899	−0.544496	−	0.838763i	$-0.683279\pi$
$223$	−16.2621	−1.08899	−0.544496	+	0.838763i	$0.683279\pi$
$224$	1.00000	0.0668153
$225$	2.93824	0.195882
$226$	2.54342	0.169186
$227$	−1.69347	−0.112400	−0.0561998	−	0.998420i	$-0.517898\pi$
$227$	−1.69347	−0.112400	−0.0561998	+	0.998420i	$0.517898\pi$
$228$	−3.05233	−0.202145
$229$	−17.5242	−1.15803	−0.579016	−	0.815316i	$-0.696563\pi$
$229$	−17.5242	−1.15803	−0.579016	+	0.815316i	$0.696563\pi$
$230$	14.8018	0.976003
$231$	5.79788	0.381472
$232$	3.06331	0.201116
$233$	−28.4880	−1.86631	−0.933157	−	0.359470i	$-0.882957\pi$
$233$	−28.4880	−1.86631	−0.933157	+	0.359470i	$0.882957\pi$
$234$	−1.03194	−0.0674601
$235$	18.5415	1.20952
$236$	9.62868	0.626773
$237$	1.51871	0.0986510
$238$	−1.72802	−0.112011
$239$	14.5321	0.940006	0.470003	−	0.882665i	$-0.344253\pi$
$239$	14.5321	0.940006	0.470003	+	0.882665i	$0.344253\pi$
$240$	−2.81749	−0.181868
$241$	2.61972	0.168751	0.0843756	−	0.996434i	$-0.473110\pi$
$241$	2.61972	0.168751	0.0843756	+	0.996434i	$0.473110\pi$
$242$	22.6154	1.45377
$243$	−1.00000	−0.0641500
$244$	−4.92205	−0.315102
$245$	2.81749	0.180003
$246$	7.36786	0.469757
$247$	−3.14982	−0.200418
$248$	1.18800	0.0754382
$249$	−10.0679	−0.638028
$250$	−5.80900	−0.367393
$251$	18.0544	1.13958	0.569790	−	0.821790i	$-0.307024\pi$
$251$	18.0544	1.13958	0.569790	+	0.821790i	$0.307024\pi$
$252$	1.00000	0.0629941
$253$	−30.4594	−1.91497
$254$	−3.80895	−0.238995
$255$	4.86866	0.304887
$256$	1.00000	0.0625000
$257$	12.0039	0.748783	0.374392	−	0.927271i	$-0.377852\pi$
$257$	12.0039	0.748783	0.374392	+	0.927271i	$0.377852\pi$
$258$	−2.13850	−0.133137
$259$	2.53861	0.157742
$260$	−2.90748	−0.180314
$261$	3.06331	0.189614
$262$	2.10773	0.130216
$263$	2.32417	0.143315	0.0716573	−	0.997429i	$-0.477171\pi$
$263$	2.32417	0.143315	0.0716573	+	0.997429i	$0.477171\pi$
$264$	5.79788	0.356835
$265$	−23.3327	−1.43331
$266$	3.05233	0.187150
$267$	−8.25577	−0.505245
$268$	1.66457	0.101680
$269$	−14.0405	−0.856067	−0.428033	−	0.903763i	$-0.640793\pi$
$269$	−14.0405	−0.856067	−0.428033	+	0.903763i	$0.640793\pi$
$270$	−2.81749	−0.171467
$271$	9.71550	0.590175	0.295087	−	0.955470i	$-0.404651\pi$
$271$	9.71550	0.590175	0.295087	+	0.955470i	$0.404651\pi$
$272$	−1.72802	−0.104776
$273$	1.03194	0.0624559
$274$	13.7233	0.829054
$275$	−17.0355	−1.02728
$276$	−5.25355	−0.316227
$277$	−9.51456	−0.571674	−0.285837	−	0.958278i	$-0.592272\pi$
$277$	−9.51456	−0.571674	−0.285837	+	0.958278i	$0.592272\pi$
$278$	−5.56193	−0.333582
$279$	1.18800	0.0711238
$280$	2.81749	0.168377
$281$	3.41274	0.203587	0.101793	−	0.994806i	$-0.467542\pi$
$281$	3.41274	0.203587	0.101793	+	0.994806i	$0.467542\pi$
$282$	−6.58087	−0.391885
$283$	5.11997	0.304351	0.152175	−	0.988354i	$-0.451372\pi$
$283$	5.11997	0.304351	0.152175	+	0.988354i	$0.451372\pi$
$284$	13.9102	0.825421
$285$	−8.59990	−0.509414
$286$	5.98307	0.353786
$287$	−7.36786	−0.434911
$288$	1.00000	0.0589256
$289$	−14.0140	−0.824351
$290$	8.63083	0.506820
$291$	−12.6657	−0.742474
$292$	10.8583	0.635432
$293$	−4.41006	−0.257638	−0.128819	−	0.991668i	$-0.541119\pi$
$293$	−4.41006	−0.257638	−0.128819	+	0.991668i	$0.541119\pi$
$294$	−1.00000	−0.0583212
$295$	27.1287	1.57949
$296$	2.53861	0.147554
$297$	5.79788	0.336427
$298$	7.30653	0.423256
$299$	−5.42136	−0.313525
$300$	−2.93824	−0.169639
$301$	2.13850	0.123261
$302$	−0.838304	−0.0482390
$303$	−5.75781	−0.330777
$304$	3.05233	0.175063
$305$	−13.8678	−0.794068
$306$	−1.72802	−0.0987841
$307$	32.2713	1.84182	0.920910	−	0.389775i	$-0.127447\pi$
$307$	32.2713	1.84182	0.920910	+	0.389775i	$0.127447\pi$
$308$	−5.79788	−0.330365
$309$	16.4240	0.934329
$310$	3.34718	0.190107
$311$	−4.40849	−0.249982	−0.124991	−	0.992158i	$-0.539890\pi$
$311$	−4.40849	−0.249982	−0.124991	+	0.992158i	$0.539890\pi$
$312$	1.03194	0.0584222
$313$	7.90886	0.447035	0.223518	−	0.974700i	$-0.428246\pi$
$313$	7.90886	0.447035	0.223518	+	0.974700i	$0.428246\pi$
$314$	16.1028	0.908735
$315$	2.81749	0.158747
$316$	−1.51871	−0.0854343
$317$	20.3641	1.14376	0.571880	−	0.820337i	$-0.306214\pi$
$317$	20.3641	1.14376	0.571880	+	0.820337i	$0.306214\pi$
$318$	8.28137	0.464396
$319$	−17.7607	−0.994407
$320$	2.81749	0.157502
$321$	−16.3272	−0.911293
$322$	5.25355	0.292769
$323$	−5.27447	−0.293479
$324$	1.00000	0.0555556
$325$	−3.03209	−0.168190
$326$	−10.5084	−0.582004
$327$	−12.7711	−0.706244
$328$	−7.36786	−0.406822
$329$	6.58087	0.362815
$330$	16.3354	0.899237
$331$	−4.92800	−0.270868	−0.135434	−	0.990786i	$-0.543243\pi$
$331$	−4.92800	−0.270868	−0.135434	+	0.990786i	$0.543243\pi$
$332$	10.0679	0.552548
$333$	2.53861	0.139115
$334$	−2.62206	−0.143473
$335$	4.68992	0.256238
$336$	−1.00000	−0.0545545
$337$	−13.6337	−0.742675	−0.371337	−	0.928498i	$-0.621101\pi$
$337$	−13.6337	−0.742675	−0.371337	+	0.928498i	$0.621101\pi$
$338$	−11.9351	−0.649184
$339$	−2.54342	−0.138139
$340$	−4.86866	−0.264040
$341$	−6.88789	−0.373000
$342$	3.05233	0.165051
$343$	1.00000	0.0539949
$344$	2.13850	0.115300
$345$	−14.8018	−0.796903
$346$	−21.4767	−1.15459
$347$	19.5526	1.04964	0.524818	−	0.851214i	$-0.324133\pi$
$347$	19.5526	1.04964	0.524818	+	0.851214i	$0.324133\pi$
$348$	−3.06331	−0.164211
$349$	8.04594	0.430689	0.215345	−	0.976538i	$-0.430912\pi$
$349$	8.04594	0.430689	0.215345	+	0.976538i	$0.430912\pi$
$350$	2.93824	0.157055
$351$	1.03194	0.0550809
$352$	−5.79788	−0.309028
$353$	−33.8228	−1.80020	−0.900102	−	0.435679i	$-0.856508\pi$
$353$	−33.8228	−1.80020	−0.900102	+	0.435679i	$0.856508\pi$
$354$	−9.62868	−0.511758
$355$	39.1919	2.08009
$356$	8.25577	0.437555
$357$	1.72802	0.0914563
$358$	7.24003	0.382647
$359$	17.4934	0.923266	0.461633	−	0.887071i	$-0.347264\pi$
$359$	17.4934	0.923266	0.461633	+	0.887071i	$0.347264\pi$
$360$	2.81749	0.148495
$361$	−9.68329	−0.509647
$362$	−13.9468	−0.733026
$363$	−22.6154	−1.18700
$364$	−1.03194	−0.0540884
$365$	30.5930	1.60131
$366$	4.92205	0.257280
$367$	17.0608	0.890565	0.445282	−	0.895390i	$-0.353103\pi$
$367$	17.0608	0.890565	0.445282	+	0.895390i	$0.353103\pi$
$368$	5.25355	0.273860
$369$	−7.36786	−0.383555
$370$	7.15251	0.371841
$371$	−8.28137	−0.429947
$372$	−1.18800	−0.0615951
$373$	3.66543	0.189789	0.0948944	−	0.995487i	$-0.469749\pi$
$373$	3.66543	0.189789	0.0948944	+	0.995487i	$0.469749\pi$
$374$	10.0188	0.518061
$375$	5.80900	0.299975
$376$	6.58087	0.339382
$377$	−3.16115	−0.162808
$378$	−1.00000	−0.0514344
$379$	2.74953	0.141234	0.0706169	−	0.997504i	$-0.477503\pi$
$379$	2.74953	0.141234	0.0706169	+	0.997504i	$0.477503\pi$
$380$	8.59990	0.441165
$381$	3.80895	0.195138
$382$	1.00000	0.0511645
$383$	4.01084	0.204944	0.102472	−	0.994736i	$-0.467325\pi$
$383$	4.01084	0.204944	0.102472	+	0.994736i	$0.467325\pi$
$384$	−1.00000	−0.0510310
$385$	−16.3354	−0.832531
$386$	−6.83432	−0.347858
$387$	2.13850	0.108706
$388$	12.6657	0.643001
$389$	−11.7522	−0.595861	−0.297931	−	0.954588i	$-0.596296\pi$
$389$	−11.7522	−0.595861	−0.297931	+	0.954588i	$0.596296\pi$
$390$	2.90748	0.147226
$391$	−9.07822	−0.459105
$392$	1.00000	0.0505076
$393$	−2.10773	−0.106321
$394$	−8.28110	−0.417196
$395$	−4.27896	−0.215298
$396$	−5.79788	−0.291354
$397$	−30.3832	−1.52489	−0.762445	−	0.647054i	$-0.776001\pi$
$397$	−30.3832	−1.52489	−0.762445	+	0.647054i	$0.776001\pi$
$398$	20.6243	1.03380
$399$	−3.05233	−0.152808
$400$	2.93824	0.146912
$401$	−2.00616	−0.100183	−0.0500914	−	0.998745i	$-0.515951\pi$
$401$	−2.00616	−0.100183	−0.0500914	+	0.998745i	$0.515951\pi$
$402$	−1.66457	−0.0830215
$403$	−1.22595	−0.0610689
$404$	5.75781	0.286462
$405$	2.81749	0.140002
$406$	3.06331	0.152029
$407$	−14.7186	−0.729572
$408$	1.72802	0.0855495
$409$	14.8740	0.735472	0.367736	−	0.929930i	$-0.380133\pi$
$409$	14.8740	0.735472	0.367736	+	0.929930i	$0.380133\pi$
$410$	−20.7588	−1.02521
$411$	−13.7233	−0.676920
$412$	−16.4240	−0.809153
$413$	9.62868	0.473796
$414$	5.25355	0.258198
$415$	28.3662	1.39244
$416$	−1.03194	−0.0505951
$417$	5.56193	0.272369
$418$	−17.6970	−0.865590
$419$	−5.38155	−0.262906	−0.131453	−	0.991322i	$-0.541964\pi$
$419$	−5.38155	−0.262906	−0.131453	+	0.991322i	$0.541964\pi$
$420$	−2.81749	−0.137479
$421$	−18.0717	−0.880762	−0.440381	−	0.897811i	$-0.645157\pi$
$421$	−18.0717	−0.880762	−0.440381	+	0.897811i	$0.645157\pi$
$422$	−15.0461	−0.732435
$423$	6.58087	0.319973
$424$	−8.28137	−0.402179
$425$	−5.07732	−0.246286
$426$	−13.9102	−0.673953
$427$	−4.92205	−0.238195
$428$	16.3272	0.789203
$429$	−5.98307	−0.288865
$430$	6.02521	0.290561
$431$	−15.1968	−0.732003	−0.366002	−	0.930614i	$-0.619274\pi$
$431$	−15.1968	−0.732003	−0.366002	+	0.930614i	$0.619274\pi$
$432$	−1.00000	−0.0481125
$433$	23.0032	1.10546	0.552732	−	0.833359i	$-0.313585\pi$
$433$	23.0032	1.10546	0.552732	+	0.833359i	$0.313585\pi$
$434$	1.18800	0.0570259
$435$	−8.63083	−0.413817
$436$	12.7711	0.611626
$437$	16.0356	0.767085
$438$	−10.8583	−0.518828
$439$	25.6597	1.22467	0.612335	−	0.790598i	$-0.290230\pi$
$439$	25.6597	1.22467	0.612335	+	0.790598i	$0.290230\pi$
$440$	−16.3354	−0.778762
$441$	1.00000	0.0476190
$442$	1.78321	0.0848187
$443$	13.7867	0.655025	0.327513	−	0.944847i	$-0.393790\pi$
$443$	13.7867	0.655025	0.327513	+	0.944847i	$0.393790\pi$
$444$	−2.53861	−0.120477
$445$	23.2605	1.10266
$446$	−16.2621	−0.770034
$447$	−7.30653	−0.345587
$448$	1.00000	0.0472456
$449$	−15.0616	−0.710800	−0.355400	−	0.934714i	$-0.615655\pi$
$449$	−15.0616	−0.710800	−0.355400	+	0.934714i	$0.615655\pi$
$450$	2.93824	0.138510
$451$	42.7179	2.01151
$452$	2.54342	0.119632
$453$	0.838304	0.0393869
$454$	−1.69347	−0.0794785
$455$	−2.90748	−0.136305
$456$	−3.05233	−0.142938
$457$	19.4571	0.910167	0.455083	−	0.890449i	$-0.349609\pi$
$457$	19.4571	0.910167	0.455083	+	0.890449i	$0.349609\pi$
$458$	−17.5242	−0.818852
$459$	1.72802	0.0806569
$460$	14.8018	0.690138
$461$	24.4911	1.14067	0.570333	−	0.821414i	$-0.306814\pi$
$461$	24.4911	1.14067	0.570333	+	0.821414i	$0.306814\pi$
$462$	5.79788	0.269742
$463$	−12.1543	−0.564860	−0.282430	−	0.959288i	$-0.591140\pi$
$463$	−12.1543	−0.564860	−0.282430	+	0.959288i	$0.591140\pi$
$464$	3.06331	0.142210
$465$	−3.34718	−0.155222
$466$	−28.4880	−1.31968
$467$	−40.7035	−1.88353	−0.941766	−	0.336268i	$-0.890835\pi$
$467$	−40.7035	−1.88353	−0.941766	+	0.336268i	$0.890835\pi$
$468$	−1.03194	−0.0477015
$469$	1.66457	0.0768629
$470$	18.5415	0.855256
$471$	−16.1028	−0.741979
$472$	9.62868	0.443196
$473$	−12.3988	−0.570097
$474$	1.51871	0.0697568
$475$	8.96846	0.411501
$476$	−1.72802	−0.0792035
$477$	−8.28137	−0.379178
$478$	14.5321	0.664684
$479$	12.7956	0.584645	0.292323	−	0.956320i	$-0.405572\pi$
$479$	12.7956	0.584645	0.292323	+	0.956320i	$0.405572\pi$
$480$	−2.81749	−0.128600
$481$	−2.61970	−0.119448
$482$	2.61972	0.119325
$483$	−5.25355	−0.239045
$484$	22.6154	1.02797
$485$	35.6853	1.62039
$486$	−1.00000	−0.0453609
$487$	19.9105	0.902231	0.451115	−	0.892466i	$-0.351026\pi$
$487$	19.9105	0.902231	0.451115	+	0.892466i	$0.351026\pi$
$488$	−4.92205	−0.222811
$489$	10.5084	0.475204
$490$	2.81749	0.127281
$491$	3.16409	0.142793	0.0713966	−	0.997448i	$-0.477254\pi$
$491$	3.16409	0.142793	0.0713966	+	0.997448i	$0.477254\pi$
$492$	7.36786	0.332169
$493$	−5.29344	−0.238405
$494$	−3.14982	−0.141717
$495$	−16.3354	−0.734224
$496$	1.18800	0.0533429
$497$	13.9102	0.623959
$498$	−10.0679	−0.451154
$499$	−19.8970	−0.890714	−0.445357	−	0.895353i	$-0.646923\pi$
$499$	−19.8970	−0.890714	−0.445357	+	0.895353i	$0.646923\pi$
$500$	−5.80900	−0.259786
$501$	2.62206	0.117145
$502$	18.0544	0.805805
$503$	−29.1354	−1.29908	−0.649542	−	0.760326i	$-0.725039\pi$
$503$	−29.1354	−1.29908	−0.649542	+	0.760326i	$0.725039\pi$
$504$	1.00000	0.0445435
$505$	16.2226	0.721894
$506$	−30.4594	−1.35409
$507$	11.9351	0.530056
$508$	−3.80895	−0.168995
$509$	2.83340	0.125588	0.0627942	−	0.998026i	$-0.479999\pi$
$509$	2.83340	0.125588	0.0627942	+	0.998026i	$0.479999\pi$
$510$	4.86866	0.215588
$511$	10.8583	0.480342
$512$	1.00000	0.0441942
$513$	−3.05233	−0.134764
$514$	12.0039	0.529470
$515$	−46.2744	−2.03910
$516$	−2.13850	−0.0941424
$517$	−38.1551	−1.67806
$518$	2.53861	0.111540
$519$	21.4767	0.942721
$520$	−2.90748	−0.127501
$521$	11.8477	0.519059	0.259529	−	0.965735i	$-0.416433\pi$
$521$	11.8477	0.519059	0.259529	+	0.965735i	$0.416433\pi$
$522$	3.06331	0.134077
$523$	−39.4642	−1.72565	−0.862824	−	0.505505i	$-0.831306\pi$
$523$	−39.4642	−1.72565	−0.862824	+	0.505505i	$0.831306\pi$
$524$	2.10773	0.0920768
$525$	−2.93824	−0.128235
$526$	2.32417	0.101339
$527$	−2.05289	−0.0894251
$528$	5.79788	0.252320
$529$	4.59980	0.199991
$530$	−23.3327	−1.01351
$531$	9.62868	0.417849
$532$	3.05233	0.132335
$533$	7.60319	0.329331
$534$	−8.25577	−0.357262
$535$	46.0015	1.98882
$536$	1.66457	0.0718987
$537$	−7.24003	−0.312430
$538$	−14.0405	−0.605331
$539$	−5.79788	−0.249732
$540$	−2.81749	−0.121245
$541$	45.3635	1.95033	0.975164	−	0.221482i	$-0.0710895\pi$
$541$	45.3635	1.95033	0.975164	+	0.221482i	$0.0710895\pi$
$542$	9.71550	0.417317
$543$	13.9468	0.598513
$544$	−1.72802	−0.0740880
$545$	35.9825	1.54132
$546$	1.03194	0.0441630
$547$	18.4314	0.788071	0.394035	−	0.919095i	$-0.371079\pi$
$547$	18.4314	0.788071	0.394035	+	0.919095i	$0.371079\pi$
$548$	13.7233	0.586230
$549$	−4.92205	−0.210068
$550$	−17.0355	−0.726397
$551$	9.35022	0.398333
$552$	−5.25355	−0.223606
$553$	−1.51871	−0.0645823
$554$	−9.51456	−0.404235
$555$	−7.15251	−0.303607
$556$	−5.56193	−0.235878
$557$	−1.18208	−0.0500861	−0.0250431	−	0.999686i	$-0.507972\pi$
$557$	−1.18208	−0.0500861	−0.0250431	+	0.999686i	$0.507972\pi$
$558$	1.18800	0.0502922
$559$	−2.20681	−0.0933381
$560$	2.81749	0.119061
$561$	−10.0188	−0.422995
$562$	3.41274	0.143958
$563$	37.1953	1.56760	0.783798	−	0.621016i	$-0.213280\pi$
$563$	37.1953	1.56760	0.783798	+	0.621016i	$0.213280\pi$
$564$	−6.58087	−0.277105
$565$	7.16605	0.301478
$566$	5.11997	0.215208
$567$	1.00000	0.0419961
$568$	13.9102	0.583660
$569$	−23.2225	−0.973537	−0.486769	−	0.873531i	$-0.661824\pi$
$569$	−23.2225	−0.973537	−0.486769	+	0.873531i	$0.661824\pi$
$570$	−8.59990	−0.360210
$571$	5.04949	0.211315	0.105657	−	0.994403i	$-0.466305\pi$
$571$	5.04949	0.211315	0.105657	+	0.994403i	$0.466305\pi$
$572$	5.98307	0.250165
$573$	−1.00000	−0.0417756
$574$	−7.36786	−0.307528
$575$	15.4362	0.643733
$576$	1.00000	0.0416667
$577$	40.3135	1.67827	0.839137	−	0.543920i	$-0.183061\pi$
$577$	40.3135	1.67827	0.839137	+	0.543920i	$0.183061\pi$
$578$	−14.0140	−0.582904
$579$	6.83432	0.284025
$580$	8.63083	0.358376
$581$	10.0679	0.417687
$582$	−12.6657	−0.525009
$583$	48.0144	1.98855
$584$	10.8583	0.449319
$585$	−2.90748	−0.120210
$586$	−4.41006	−0.182178
$587$	18.0253	0.743984	0.371992	−	0.928236i	$-0.378675\pi$
$587$	18.0253	0.743984	0.371992	+	0.928236i	$0.378675\pi$
$588$	−1.00000	−0.0412393
$589$	3.62617	0.149414
$590$	27.1287	1.11687
$591$	8.28110	0.340639
$592$	2.53861	0.104336
$593$	12.4239	0.510190	0.255095	−	0.966916i	$-0.417893\pi$
$593$	12.4239	0.510190	0.255095	+	0.966916i	$0.417893\pi$
$594$	5.79788	0.237890
$595$	−4.86866	−0.199596
$596$	7.30653	0.299287
$597$	−20.6243	−0.844098
$598$	−5.42136	−0.221696
$599$	32.9805	1.34755	0.673773	−	0.738939i	$-0.264673\pi$
$599$	32.9805	1.34755	0.673773	+	0.738939i	$0.264673\pi$
$600$	−2.93824	−0.119953
$601$	−9.27138	−0.378188	−0.189094	−	0.981959i	$-0.560555\pi$
$601$	−9.27138	−0.378188	−0.189094	+	0.981959i	$0.560555\pi$
$602$	2.13850	0.0871589
$603$	1.66457	0.0677867
$604$	−0.838304	−0.0341101
$605$	63.7185	2.59053
$606$	−5.75781	−0.233895
$607$	35.4410	1.43850	0.719252	−	0.694749i	$-0.244484\pi$
$607$	35.4410	1.43850	0.719252	+	0.694749i	$0.244484\pi$
$608$	3.05233	0.123788
$609$	−3.06331	−0.124131
$610$	−13.8678	−0.561491
$611$	−6.79107	−0.274737
$612$	−1.72802	−0.0698509
$613$	−24.6629	−0.996126	−0.498063	−	0.867141i	$-0.665955\pi$
$613$	−24.6629	−0.996126	−0.498063	+	0.867141i	$0.665955\pi$
$614$	32.2713	1.30236
$615$	20.7588	0.837077
$616$	−5.79788	−0.233603
$617$	−33.9718	−1.36765	−0.683826	−	0.729645i	$-0.739685\pi$
$617$	−33.9718	−1.36765	−0.683826	+	0.729645i	$0.739685\pi$
$618$	16.4240	0.660671
$619$	−20.9652	−0.842662	−0.421331	−	0.906907i	$-0.638437\pi$
$619$	−20.9652	−0.842662	−0.421331	+	0.906907i	$0.638437\pi$
$620$	3.34718	0.134426
$621$	−5.25355	−0.210818
$622$	−4.40849	−0.176764
$623$	8.25577	0.330761
$624$	1.03194	0.0413107
$625$	−31.0580	−1.24232
$626$	7.90886	0.316102
$627$	17.6970	0.706751
$628$	16.1028	0.642573
$629$	−4.38676	−0.174912
$630$	2.81749	0.112251
$631$	−34.1657	−1.36011	−0.680057	−	0.733159i	$-0.738045\pi$
$631$	−34.1657	−1.36011	−0.680057	+	0.733159i	$0.738045\pi$
$632$	−1.51871	−0.0604112
$633$	15.0461	0.598030
$634$	20.3641	0.808761
$635$	−10.7317	−0.425873
$636$	8.28137	0.328378
$637$	−1.03194	−0.0408870
$638$	−17.7607	−0.703152
$639$	13.9102	0.550280
$640$	2.81749	0.111371
$641$	−1.68139	−0.0664111	−0.0332055	−	0.999449i	$-0.510572\pi$
$641$	−1.68139	−0.0664111	−0.0332055	+	0.999449i	$0.510572\pi$
$642$	−16.3272	−0.644381
$643$	−44.4638	−1.75348	−0.876741	−	0.480963i	$-0.840287\pi$
$643$	−44.4638	−1.75348	−0.876741	+	0.480963i	$0.840287\pi$
$644$	5.25355	0.207019
$645$	−6.02521	−0.237242
$646$	−5.27447	−0.207521
$647$	−14.1160	−0.554957	−0.277479	−	0.960732i	$-0.589499\pi$
$647$	−14.1160	−0.554957	−0.277479	+	0.960732i	$0.589499\pi$
$648$	1.00000	0.0392837
$649$	−55.8259	−2.19136
$650$	−3.03209	−0.118928
$651$	−1.18800	−0.0465615
$652$	−10.5084	−0.411539
$653$	−16.8908	−0.660990	−0.330495	−	0.943808i	$-0.607216\pi$
$653$	−16.8908	−0.660990	−0.330495	+	0.943808i	$0.607216\pi$
$654$	−12.7711	−0.499390
$655$	5.93852	0.232037
$656$	−7.36786	−0.287666
$657$	10.8583	0.423622
$658$	6.58087	0.256549
$659$	−13.7756	−0.536622	−0.268311	−	0.963332i	$-0.586466\pi$
$659$	−13.7756	−0.536622	−0.268311	+	0.963332i	$0.586466\pi$
$660$	16.3354	0.635856
$661$	−17.8742	−0.695225	−0.347612	−	0.937638i	$-0.613008\pi$
$661$	−17.8742	−0.695225	−0.347612	+	0.937638i	$0.613008\pi$
$662$	−4.92800	−0.191532
$663$	−1.78321	−0.0692542
$664$	10.0679	0.390711
$665$	8.59990	0.333490
$666$	2.53861	0.0983693
$667$	16.0932	0.623133
$668$	−2.62206	−0.101450
$669$	16.2621	0.628730
$670$	4.68992	0.181187
$671$	28.5374	1.10168
$672$	−1.00000	−0.0385758
$673$	−24.2626	−0.935253	−0.467626	−	0.883926i	$-0.654891\pi$
$673$	−24.2626	−0.935253	−0.467626	+	0.883926i	$0.654891\pi$
$674$	−13.6337	−0.525150
$675$	−2.93824	−0.113093
$676$	−11.9351	−0.459042
$677$	−17.3334	−0.666176	−0.333088	−	0.942896i	$-0.608091\pi$
$677$	−17.3334	−0.666176	−0.333088	+	0.942896i	$0.608091\pi$
$678$	−2.54342	−0.0976794
$679$	12.6657	0.486063
$680$	−4.86866	−0.186705
$681$	1.69347	0.0648939
$682$	−6.88789	−0.263751
$683$	−25.7896	−0.986811	−0.493405	−	0.869799i	$-0.664248\pi$
$683$	−25.7896	−0.986811	−0.493405	+	0.869799i	$0.664248\pi$
$684$	3.05233	0.116709
$685$	38.6652	1.47732
$686$	1.00000	0.0381802
$687$	17.5242	0.668590
$688$	2.13850	0.0815297
$689$	8.54589	0.325572
$690$	−14.8018	−0.563495
$691$	48.4933	1.84477	0.922386	−	0.386270i	$-0.126237\pi$
$691$	48.4933	1.84477	0.922386	+	0.386270i	$0.126237\pi$
$692$	−21.4767	−0.816420
$693$	−5.79788	−0.220243
$694$	19.5526	0.742205
$695$	−15.6707	−0.594422
$696$	−3.06331	−0.116114
$697$	12.7318	0.482250
$698$	8.04594	0.304543
$699$	28.4880	1.07752
$700$	2.93824	0.111055
$701$	−35.0035	−1.32206	−0.661032	−	0.750358i	$-0.729881\pi$
$701$	−35.0035	−1.32206	−0.661032	+	0.750358i	$0.729881\pi$
$702$	1.03194	0.0389481
$703$	7.74868	0.292247
$704$	−5.79788	−0.218516
$705$	−18.5415	−0.698314
$706$	−33.8228	−1.27294
$707$	5.75781	0.216545
$708$	−9.62868	−0.361868
$709$	9.80593	0.368270	0.184135	−	0.982901i	$-0.441052\pi$
$709$	9.80593	0.368270	0.184135	+	0.982901i	$0.441052\pi$
$710$	39.1919	1.47085
$711$	−1.51871	−0.0569562
$712$	8.25577	0.309398
$713$	6.24123	0.233736
$714$	1.72802	0.0646693
$715$	16.8572	0.630424
$716$	7.24003	0.270573
$717$	−14.5321	−0.542713
$718$	17.4934	0.652848
$719$	45.1866	1.68518	0.842589	−	0.538558i	$-0.181031\pi$
$719$	45.1866	1.68518	0.842589	+	0.538558i	$0.181031\pi$
$720$	2.81749	0.105002
$721$	−16.4240	−0.611662
$722$	−9.68329	−0.360375
$723$	−2.61972	−0.0974285
$724$	−13.9468	−0.518328
$725$	9.00072	0.334278
$726$	−22.6154	−0.839335
$727$	12.5805	0.466584	0.233292	−	0.972407i	$-0.425050\pi$
$727$	12.5805	0.466584	0.233292	+	0.972407i	$0.425050\pi$
$728$	−1.03194	−0.0382463
$729$	1.00000	0.0370370
$730$	30.5930	1.13230
$731$	−3.69537	−0.136678
$732$	4.92205	0.181924
$733$	−11.1446	−0.411634	−0.205817	−	0.978590i	$-0.565985\pi$
$733$	−11.1446	−0.411634	−0.205817	+	0.978590i	$0.565985\pi$
$734$	17.0608	0.629724
$735$	−2.81749	−0.103925
$736$	5.25355	0.193648
$737$	−9.65100	−0.355499
$738$	−7.36786	−0.271215
$739$	9.87038	0.363088	0.181544	−	0.983383i	$-0.441891\pi$
$739$	9.87038	0.363088	0.181544	+	0.983383i	$0.441891\pi$
$740$	7.15251	0.262932
$741$	3.14982	0.115712
$742$	−8.28137	−0.304019
$743$	−27.8744	−1.02261	−0.511305	−	0.859399i	$-0.670838\pi$
$743$	−27.8744	−1.02261	−0.511305	+	0.859399i	$0.670838\pi$
$744$	−1.18800	−0.0435543
$745$	20.5861	0.754215
$746$	3.66543	0.134201
$747$	10.0679	0.368366
$748$	10.0188	0.366324
$749$	16.3272	0.596581
$750$	5.80900	0.212115
$751$	−36.6760	−1.33832	−0.669162	−	0.743116i	$-0.733347\pi$
$751$	−36.6760	−1.33832	−0.669162	+	0.743116i	$0.733347\pi$
$752$	6.58087	0.239980
$753$	−18.0544	−0.657937
$754$	−3.16115	−0.115122
$755$	−2.36191	−0.0859587
$756$	−1.00000	−0.0363696
$757$	−30.0288	−1.09142	−0.545708	−	0.837975i	$-0.683739\pi$
$757$	−30.0288	−1.09142	−0.545708	+	0.837975i	$0.683739\pi$
$758$	2.74953	0.0998673
$759$	30.4594	1.10561
$760$	8.59990	0.311951
$761$	16.4545	0.596476	0.298238	−	0.954492i	$-0.403601\pi$
$761$	16.4545	0.596476	0.298238	+	0.954492i	$0.403601\pi$
$762$	3.80895	0.137984
$763$	12.7711	0.462345
$764$	1.00000	0.0361787
$765$	−4.86866	−0.176027
$766$	4.01084	0.144917
$767$	−9.93623	−0.358776
$768$	−1.00000	−0.0360844
$769$	17.7379	0.639644	0.319822	−	0.947478i	$-0.396377\pi$
$769$	17.7379	0.639644	0.319822	+	0.947478i	$0.396377\pi$
$770$	−16.3354	−0.588689
$771$	−12.0039	−0.432310
$772$	−6.83432	−0.245972
$773$	25.0307	0.900291	0.450145	−	0.892955i	$-0.351372\pi$
$773$	25.0307	0.900291	0.450145	+	0.892955i	$0.351372\pi$
$774$	2.13850	0.0768669
$775$	3.49063	0.125387
$776$	12.6657	0.454671
$777$	−2.53861	−0.0910722
$778$	−11.7522	−0.421337
$779$	−22.4891	−0.805756
$780$	2.90748	0.104105
$781$	−80.6498	−2.88588
$782$	−9.07822	−0.324636
$783$	−3.06331	−0.109474
$784$	1.00000	0.0357143
$785$	45.3695	1.61931
$786$	−2.10773	−0.0751804
$787$	4.04952	0.144350	0.0721749	−	0.997392i	$-0.477006\pi$
$787$	4.04952	0.144350	0.0721749	+	0.997392i	$0.477006\pi$
$788$	−8.28110	−0.295002
$789$	−2.32417	−0.0827428
$790$	−4.27896	−0.152238
$791$	2.54342	0.0904335
$792$	−5.79788	−0.206019
$793$	5.07927	0.180370
$794$	−30.3832	−1.07826
$795$	23.3327	0.827524
$796$	20.6243	0.731011
$797$	0.225031	0.00797101	0.00398550	−	0.999992i	$-0.498731\pi$
$797$	0.225031	0.00797101	0.00398550	+	0.999992i	$0.498731\pi$
$798$	−3.05233	−0.108051
$799$	−11.3718	−0.402307
$800$	2.93824	0.103882
$801$	8.25577	0.291703
$802$	−2.00616	−0.0708400
$803$	−62.9549	−2.22163
$804$	−1.66457	−0.0587050
$805$	14.8018	0.521695
$806$	−1.22595	−0.0431822
$807$	14.0405	0.494250
$808$	5.75781	0.202559
$809$	−8.60089	−0.302391	−0.151196	−	0.988504i	$-0.548312\pi$
$809$	−8.60089	−0.302391	−0.151196	+	0.988504i	$0.548312\pi$
$810$	2.81749	0.0989964
$811$	−5.84270	−0.205165	−0.102583	−	0.994724i	$-0.532711\pi$
$811$	−5.84270	−0.205165	−0.102583	+	0.994724i	$0.532711\pi$
$812$	3.06331	0.107501
$813$	−9.71550	−0.340738
$814$	−14.7186	−0.515885
$815$	−29.6072	−1.03709
$816$	1.72802	0.0604926
$817$	6.52742	0.228365
$818$	14.8740	0.520057
$819$	−1.03194	−0.0360589
$820$	−20.7588	−0.724930
$821$	18.3399	0.640069	0.320034	−	0.947406i	$-0.396306\pi$
$821$	18.3399	0.640069	0.320034	+	0.947406i	$0.396306\pi$
$822$	−13.7233	−0.478655
$823$	−21.7777	−0.759122	−0.379561	−	0.925167i	$-0.623925\pi$
$823$	−21.7777	−0.759122	−0.379561	+	0.925167i	$0.623925\pi$
$824$	−16.4240	−0.572158
$825$	17.0355	0.593101
$826$	9.62868	0.335024
$827$	−18.7514	−0.652050	−0.326025	−	0.945361i	$-0.605709\pi$
$827$	−18.7514	−0.652050	−0.326025	+	0.945361i	$0.605709\pi$
$828$	5.25355	0.182574
$829$	−2.28809	−0.0794687	−0.0397343	−	0.999210i	$-0.512651\pi$
$829$	−2.28809	−0.0794687	−0.0397343	+	0.999210i	$0.512651\pi$
$830$	28.3662	0.984606
$831$	9.51456	0.330056
$832$	−1.03194	−0.0357761
$833$	−1.72802	−0.0598722
$834$	5.56193	0.192594
$835$	−7.38761	−0.255659
$836$	−17.6970	−0.612064
$837$	−1.18800	−0.0410634
$838$	−5.38155	−0.185903
$839$	55.8306	1.92749	0.963744	−	0.266829i	$-0.0859758\pi$
$839$	55.8306	1.92749	0.963744	+	0.266829i	$0.0859758\pi$
$840$	−2.81749	−0.0972125
$841$	−19.6161	−0.676419
$842$	−18.0717	−0.622793
$843$	−3.41274	−0.117541
$844$	−15.0461	−0.517909
$845$	−33.6270	−1.15680
$846$	6.58087	0.226255
$847$	22.6154	0.777073
$848$	−8.28137	−0.284383
$849$	−5.11997	−0.175717
$850$	−5.07732	−0.174150
$851$	13.3367	0.457177
$852$	−13.9102	−0.476557
$853$	16.9195	0.579314	0.289657	−	0.957130i	$-0.406459\pi$
$853$	16.9195	0.579314	0.289657	+	0.957130i	$0.406459\pi$
$854$	−4.92205	−0.168429
$855$	8.59990	0.294110
$856$	16.3272	0.558051
$857$	24.4690	0.835845	0.417923	−	0.908483i	$-0.362758\pi$
$857$	24.4690	0.835845	0.417923	+	0.908483i	$0.362758\pi$
$858$	−5.98307	−0.204259
$859$	−35.5988	−1.21461	−0.607307	−	0.794467i	$-0.707750\pi$
$859$	−35.5988	−1.21461	−0.607307	+	0.794467i	$0.707750\pi$
$860$	6.02521	0.205458
$861$	7.36786	0.251096
$862$	−15.1968	−0.517605
$863$	32.8838	1.11938	0.559689	−	0.828703i	$-0.310921\pi$
$863$	32.8838	1.11938	0.559689	+	0.828703i	$0.310921\pi$
$864$	−1.00000	−0.0340207
$865$	−60.5102	−2.05741
$866$	23.0032	0.781681
$867$	14.0140	0.475939
$868$	1.18800	0.0403234
$869$	8.80531	0.298700
$870$	−8.63083	−0.292613
$871$	−1.71774	−0.0582035
$872$	12.7711	0.432485
$873$	12.6657	0.428668
$874$	16.0356	0.542411
$875$	−5.80900	−0.196380
$876$	−10.8583	−0.366867
$877$	12.7042	0.428991	0.214496	−	0.976725i	$-0.431189\pi$
$877$	12.7042	0.428991	0.214496	+	0.976725i	$0.431189\pi$
$878$	25.6597	0.865973
$879$	4.41006	0.148748
$880$	−16.3354	−0.550668
$881$	−32.3869	−1.09114	−0.545572	−	0.838064i	$-0.683687\pi$
$881$	−32.3869	−1.09114	−0.545572	+	0.838064i	$0.683687\pi$
$882$	1.00000	0.0336718
$883$	−18.0915	−0.608828	−0.304414	−	0.952540i	$-0.598461\pi$
$883$	−18.0915	−0.608828	−0.304414	+	0.952540i	$0.598461\pi$
$884$	1.78321	0.0599759
$885$	−27.1287	−0.911920
$886$	13.7867	0.463173
$887$	−1.81618	−0.0609813	−0.0304907	−	0.999535i	$-0.509707\pi$
$887$	−1.81618	−0.0609813	−0.0304907	+	0.999535i	$0.509707\pi$
$888$	−2.53861	−0.0851903
$889$	−3.80895	−0.127748
$890$	23.2605	0.779695
$891$	−5.79788	−0.194236
$892$	−16.2621	−0.544496
$893$	20.0870	0.672185
$894$	−7.30653	−0.244367
$895$	20.3987	0.681853
$896$	1.00000	0.0334077
$897$	5.42136	0.181014
$898$	−15.0616	−0.502612
$899$	3.63922	0.121375
$900$	2.93824	0.0979412
$901$	14.3103	0.476746
$902$	42.7179	1.42235
$903$	−2.13850	−0.0711650
$904$	2.54342	0.0845928
$905$	−39.2949	−1.30621
$906$	0.838304	0.0278508
$907$	56.2597	1.86807	0.934036	−	0.357180i	$-0.116262\pi$
$907$	56.2597	1.86807	0.934036	+	0.357180i	$0.116262\pi$
$908$	−1.69347	−0.0561998
$909$	5.75781	0.190974
$910$	−2.90748	−0.0963821
$911$	47.6999	1.58037	0.790184	−	0.612870i	$-0.209985\pi$
$911$	47.6999	1.58037	0.790184	+	0.612870i	$0.209985\pi$
$912$	−3.05233	−0.101073
$913$	−58.3725	−1.93185
$914$	19.4571	0.643585
$915$	13.8678	0.458456
$916$	−17.5242	−0.579016
$917$	2.10773	0.0696035
$918$	1.72802	0.0570330
$919$	−9.96186	−0.328611	−0.164306	−	0.986409i	$-0.552538\pi$
$919$	−9.96186	−0.328611	−0.164306	+	0.986409i	$0.552538\pi$
$920$	14.8018	0.488001
$921$	−32.2713	−1.06338
$922$	24.4911	0.806573
$923$	−14.3545	−0.472486
$924$	5.79788	0.190736
$925$	7.45904	0.245252
$926$	−12.1543	−0.399416
$927$	−16.4240	−0.539435
$928$	3.06331	0.100558
$929$	39.6261	1.30009	0.650045	−	0.759896i	$-0.274750\pi$
$929$	39.6261	1.30009	0.650045	+	0.759896i	$0.274750\pi$
$930$	−3.34718	−0.109758
$931$	3.05233	0.100036
$932$	−28.4880	−0.933157
$933$	4.40849	0.144327
$934$	−40.7035	−1.33186
$935$	28.2279	0.923151
$936$	−1.03194	−0.0337301
$937$	8.50282	0.277775	0.138888	−	0.990308i	$-0.455647\pi$
$937$	8.50282	0.277775	0.138888	+	0.990308i	$0.455647\pi$
$938$	1.66457	0.0543503
$939$	−7.90886	−0.258096
$940$	18.5415	0.604758
$941$	26.9157	0.877427	0.438714	−	0.898627i	$-0.355434\pi$
$941$	26.9157	0.877427	0.438714	+	0.898627i	$0.355434\pi$
$942$	−16.1028	−0.524659
$943$	−38.7074	−1.26049
$944$	9.62868	0.313387
$945$	−2.81749	−0.0916529
$946$	−12.3988	−0.403119
$947$	−32.8534	−1.06759	−0.533795	−	0.845614i	$-0.679235\pi$
$947$	−32.8534	−1.06759	−0.533795	+	0.845614i	$0.679235\pi$
$948$	1.51871	0.0493255
$949$	−11.2051	−0.363733
$950$	8.96846	0.290975
$951$	−20.3641	−0.660350
$952$	−1.72802	−0.0560053
$953$	−13.2645	−0.429681	−0.214840	−	0.976649i	$-0.568923\pi$
$953$	−13.2645	−0.429681	−0.214840	+	0.976649i	$0.568923\pi$
$954$	−8.28137	−0.268119
$955$	2.81749	0.0911718
$956$	14.5321	0.470003
$957$	17.7607	0.574121
$958$	12.7956	0.413407
$959$	13.7233	0.443148
$960$	−2.81749	−0.0909340
$961$	−29.5887	−0.954473
$962$	−2.61970	−0.0844625
$963$	16.3272	0.526135
$964$	2.61972	0.0843756
$965$	−19.2556	−0.619860
$966$	−5.25355	−0.169030
$967$	−57.8916	−1.86167	−0.930835	−	0.365440i	$-0.880918\pi$
$967$	−57.8916	−1.86167	−0.930835	+	0.365440i	$0.880918\pi$
$968$	22.6154	0.726885
$969$	5.27447	0.169440
$970$	35.6853	1.14579
$971$	−19.6926	−0.631965	−0.315983	−	0.948765i	$-0.602334\pi$
$971$	−19.6926	−0.631965	−0.315983	+	0.948765i	$0.602334\pi$
$972$	−1.00000	−0.0320750
$973$	−5.56193	−0.178307
$974$	19.9105	0.637974
$975$	3.03209	0.0971045
$976$	−4.92205	−0.157551
$977$	−18.7957	−0.601328	−0.300664	−	0.953730i	$-0.597208\pi$
$977$	−18.7957	−0.601328	−0.300664	+	0.953730i	$0.597208\pi$
$978$	10.5084	0.336020
$979$	−47.8659	−1.52980
$980$	2.81749	0.0900013
$981$	12.7711	0.407750
$982$	3.16409	0.100970
$983$	43.7691	1.39602	0.698008	−	0.716090i	$-0.254070\pi$
$983$	43.7691	1.39602	0.698008	+	0.716090i	$0.254070\pi$
$984$	7.36786	0.234879
$985$	−23.3319	−0.743416
$986$	−5.29344	−0.168578
$987$	−6.58087	−0.209471
$988$	−3.14982	−0.100209
$989$	11.2347	0.357244
$990$	−16.3354	−0.519174
$991$	−48.7957	−1.55005	−0.775023	−	0.631933i	$-0.782262\pi$
$991$	−48.7957	−1.55005	−0.775023	+	0.631933i	$0.782262\pi$
$992$	1.18800	0.0377191
$993$	4.92800	0.156386
$994$	13.9102	0.441206
$995$	58.1088	1.84217
$996$	−10.0679	−0.319014
$997$	−37.0578	−1.17363	−0.586816	−	0.809720i	$-0.699619\pi$
$997$	−37.0578	−1.17363	−0.586816	+	0.809720i	$0.699619\pi$
$998$	−19.8970	−0.629830
$999$	−2.53861	−0.0803182

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8022.2.a.r.1.9	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8022.2.a.r.1.9	✓	10	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:	\( N \)	\(=\)	\( 8022 = 2 \cdot 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.81749 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.81749 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.81749 q^{10} -5.79788 q^{11} -1.00000 q^{12} -1.03194 q^{13} +1.00000 q^{14} -2.81749 q^{15} +1.00000 q^{16} -1.72802 q^{17} +1.00000 q^{18} +3.05233 q^{19} +2.81749 q^{20} -1.00000 q^{21} -5.79788 q^{22} +5.25355 q^{23} -1.00000 q^{24} +2.93824 q^{25} -1.03194 q^{26} -1.00000 q^{27} +1.00000 q^{28} +3.06331 q^{29} -2.81749 q^{30} +1.18800 q^{31} +1.00000 q^{32} +5.79788 q^{33} -1.72802 q^{34} +2.81749 q^{35} +1.00000 q^{36} +2.53861 q^{37} +3.05233 q^{38} +1.03194 q^{39} +2.81749 q^{40} -7.36786 q^{41} -1.00000 q^{42} +2.13850 q^{43} -5.79788 q^{44} +2.81749 q^{45} +5.25355 q^{46} +6.58087 q^{47} -1.00000 q^{48} +1.00000 q^{49} +2.93824 q^{50} +1.72802 q^{51} -1.03194 q^{52} -8.28137 q^{53} -1.00000 q^{54} -16.3354 q^{55} +1.00000 q^{56} -3.05233 q^{57} +3.06331 q^{58} +9.62868 q^{59} -2.81749 q^{60} -4.92205 q^{61} +1.18800 q^{62} +1.00000 q^{63} +1.00000 q^{64} -2.90748 q^{65} +5.79788 q^{66} +1.66457 q^{67} -1.72802 q^{68} -5.25355 q^{69} +2.81749 q^{70} +13.9102 q^{71} +1.00000 q^{72} +10.8583 q^{73} +2.53861 q^{74} -2.93824 q^{75} +3.05233 q^{76} -5.79788 q^{77} +1.03194 q^{78} -1.51871 q^{79} +2.81749 q^{80} +1.00000 q^{81} -7.36786 q^{82} +10.0679 q^{83} -1.00000 q^{84} -4.86866 q^{85} +2.13850 q^{86} -3.06331 q^{87} -5.79788 q^{88} +8.25577 q^{89} +2.81749 q^{90} -1.03194 q^{91} +5.25355 q^{92} -1.18800 q^{93} +6.58087 q^{94} +8.59990 q^{95} -1.00000 q^{96} +12.6657 q^{97} +1.00000 q^{98} -5.79788 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} - 10 q^{3} + 10 q^{4} + 8 q^{5} - 10 q^{6} + 10 q^{7} + 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 - 10 * q^3 + 10 * q^4 + 8 * q^5 - 10 * q^6 + 10 * q^7 + 10 * q^8 + 10 * q^9	\( 10 q + 10 q^{2} - 10 q^{3} + 10 q^{4} + 8 q^{5} - 10 q^{6} + 10 q^{7} + 10 q^{8} + 10 q^{9} + 8 q^{10} + 4 q^{11} - 10 q^{12} + 6 q^{13} + 10 q^{14} - 8 q^{15} + 10 q^{16} + 5 q^{17} + 10 q^{18} + 15 q^{19} + 8 q^{20} - 10 q^{21} + 4 q^{22} + 12 q^{23} - 10 q^{24} - 2 q^{25} + 6 q^{26} - 10 q^{27} + 10 q^{28} + 7 q^{29} - 8 q^{30} + 28 q^{31} + 10 q^{32} - 4 q^{33} + 5 q^{34} + 8 q^{35} + 10 q^{36} - 3 q^{37} + 15 q^{38} - 6 q^{39} + 8 q^{40} + 24 q^{41} - 10 q^{42} + 4 q^{43} + 4 q^{44} + 8 q^{45} + 12 q^{46} + 16 q^{47} - 10 q^{48} + 10 q^{49} - 2 q^{50} - 5 q^{51} + 6 q^{52} + 5 q^{53} - 10 q^{54} - q^{55} + 10 q^{56} - 15 q^{57} + 7 q^{58} + 17 q^{59} - 8 q^{60} + 15 q^{61} + 28 q^{62} + 10 q^{63} + 10 q^{64} + 14 q^{65} - 4 q^{66} + 6 q^{67} + 5 q^{68} - 12 q^{69} + 8 q^{70} + 5 q^{71} + 10 q^{72} + 16 q^{73} - 3 q^{74} + 2 q^{75} + 15 q^{76} + 4 q^{77} - 6 q^{78} - 5 q^{79} + 8 q^{80} + 10 q^{81} + 24 q^{82} + 24 q^{83} - 10 q^{84} - 19 q^{85} + 4 q^{86} - 7 q^{87} + 4 q^{88} + 17 q^{89} + 8 q^{90} + 6 q^{91} + 12 q^{92} - 28 q^{93} + 16 q^{94} + 15 q^{95} - 10 q^{96} + 20 q^{97} + 10 q^{98} + 4 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - 10 * q^3 + 10 * q^4 + 8 * q^5 - 10 * q^6 + 10 * q^7 + 10 * q^8 + 10 * q^9 + 8 * q^10 + 4 * q^11 - 10 * q^12 + 6 * q^13 + 10 * q^14 - 8 * q^15 + 10 * q^16 + 5 * q^17 + 10 * q^18 + 15 * q^19 + 8 * q^20 - 10 * q^21 + 4 * q^22 + 12 * q^23 - 10 * q^24 - 2 * q^25 + 6 * q^26 - 10 * q^27 + 10 * q^28 + 7 * q^29 - 8 * q^30 + 28 * q^31 + 10 * q^32 - 4 * q^33 + 5 * q^34 + 8 * q^35 + 10 * q^36 - 3 * q^37 + 15 * q^38 - 6 * q^39 + 8 * q^40 + 24 * q^41 - 10 * q^42 + 4 * q^43 + 4 * q^44 + 8 * q^45 + 12 * q^46 + 16 * q^47 - 10 * q^48 + 10 * q^49 - 2 * q^50 - 5 * q^51 + 6 * q^52 + 5 * q^53 - 10 * q^54 - q^55 + 10 * q^56 - 15 * q^57 + 7 * q^58 + 17 * q^59 - 8 * q^60 + 15 * q^61 + 28 * q^62 + 10 * q^63 + 10 * q^64 + 14 * q^65 - 4 * q^66 + 6 * q^67 + 5 * q^68 - 12 * q^69 + 8 * q^70 + 5 * q^71 + 10 * q^72 + 16 * q^73 - 3 * q^74 + 2 * q^75 + 15 * q^76 + 4 * q^77 - 6 * q^78 - 5 * q^79 + 8 * q^80 + 10 * q^81 + 24 * q^82 + 24 * q^83 - 10 * q^84 - 19 * q^85 + 4 * q^86 - 7 * q^87 + 4 * q^88 + 17 * q^89 + 8 * q^90 + 6 * q^91 + 12 * q^92 - 28 * q^93 + 16 * q^94 + 15 * q^95 - 10 * q^96 + 20 * q^97 + 10 * q^98 + 4 * q^99

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