LMFDB - Embedded newform 4334.2.a.a.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - x^{14} - 23 x^{13} + 19 x^{12} + 194 x^{11} - 124 x^{10} - 761 x^{9} + 353 x^{8} + 1417 x^{7} + \cdots + 4 $ x^15 - x^14 - 23x^13 + 19x^12 + 194x^11 - 124x^10 - 761x^9 + 353x^8 + 1417x^7 - 465x^6 - 1128x^5 + 288x^4 + 316x^3 - 79x^2 - 20*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.516772$ of defining polynomial
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.516772 q^{3} +1.00000 q^{4} -1.53195 q^{5} +0.516772 q^{6} -0.576902 q^{7} -1.00000 q^{8} -2.73295 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.516772 q^{3} +1.00000 q^{4} -1.53195 q^{5} +0.516772 q^{6} -0.576902 q^{7} -1.00000 q^{8} -2.73295 q^{9} +1.53195 q^{10} +1.00000 q^{11} -0.516772 q^{12} +6.31699 q^{13} +0.576902 q^{14} +0.791670 q^{15} +1.00000 q^{16} -0.519591 q^{17} +2.73295 q^{18} -0.276328 q^{19} -1.53195 q^{20} +0.298127 q^{21} -1.00000 q^{22} -1.50740 q^{23} +0.516772 q^{24} -2.65312 q^{25} -6.31699 q^{26} +2.96263 q^{27} -0.576902 q^{28} -2.50711 q^{29} -0.791670 q^{30} -0.621065 q^{31} -1.00000 q^{32} -0.516772 q^{33} +0.519591 q^{34} +0.883787 q^{35} -2.73295 q^{36} -4.65628 q^{37} +0.276328 q^{38} -3.26444 q^{39} +1.53195 q^{40} +6.59498 q^{41} -0.298127 q^{42} -8.04854 q^{43} +1.00000 q^{44} +4.18674 q^{45} +1.50740 q^{46} +1.94410 q^{47} -0.516772 q^{48} -6.66718 q^{49} +2.65312 q^{50} +0.268510 q^{51} +6.31699 q^{52} +11.6545 q^{53} -2.96263 q^{54} -1.53195 q^{55} +0.576902 q^{56} +0.142799 q^{57} +2.50711 q^{58} +8.08984 q^{59} +0.791670 q^{60} +2.60152 q^{61} +0.621065 q^{62} +1.57664 q^{63} +1.00000 q^{64} -9.67733 q^{65} +0.516772 q^{66} +5.29122 q^{67} -0.519591 q^{68} +0.778984 q^{69} -0.883787 q^{70} +14.1174 q^{71} +2.73295 q^{72} -2.91021 q^{73} +4.65628 q^{74} +1.37106 q^{75} -0.276328 q^{76} -0.576902 q^{77} +3.26444 q^{78} -5.82588 q^{79} -1.53195 q^{80} +6.66784 q^{81} -6.59498 q^{82} -0.321166 q^{83} +0.298127 q^{84} +0.795989 q^{85} +8.04854 q^{86} +1.29560 q^{87} -1.00000 q^{88} +7.65030 q^{89} -4.18674 q^{90} -3.64429 q^{91} -1.50740 q^{92} +0.320949 q^{93} -1.94410 q^{94} +0.423321 q^{95} +0.516772 q^{96} -6.38659 q^{97} +6.66718 q^{98} -2.73295 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9}+O(q^{10}) $ 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9} + 7 q^{10} + 15 q^{11} - q^{12} - q^{13} - q^{14} - 6 q^{15} + 15 q^{16} - 6 q^{17} - 2 q^{18} - 14 q^{19} - 7 q^{20} - 3 q^{21} - 15 q^{22} + 2 q^{23} + q^{24} - 10 q^{25} + q^{26} - 7 q^{27} + q^{28} + 8 q^{29} + 6 q^{30} - 33 q^{31} - 15 q^{32} - q^{33} + 6 q^{34} - 8 q^{35} + 2 q^{36} - 9 q^{37} + 14 q^{38} - 9 q^{39} + 7 q^{40} - 10 q^{41} + 3 q^{42} - 6 q^{43} + 15 q^{44} - 20 q^{45} - 2 q^{46} - q^{47} - q^{48} - 30 q^{49} + 10 q^{50} + 12 q^{51} - q^{52} + 6 q^{53} + 7 q^{54} - 7 q^{55} - q^{56} - 24 q^{57} - 8 q^{58} - 15 q^{59} - 6 q^{60} - 25 q^{61} + 33 q^{62} + 12 q^{63} + 15 q^{64} + 31 q^{65} + q^{66} - 13 q^{67} - 6 q^{68} - 43 q^{69} + 8 q^{70} - 4 q^{71} - 2 q^{72} - 4 q^{73} + 9 q^{74} - 5 q^{75} - 14 q^{76} + q^{77} + 9 q^{78} - 20 q^{79} - 7 q^{80} + 11 q^{81} + 10 q^{82} + q^{83} - 3 q^{84} - q^{85} + 6 q^{86} + 22 q^{87} - 15 q^{88} - 41 q^{89} + 20 q^{90} - 31 q^{91} + 2 q^{92} + 14 q^{93} + q^{94} + 41 q^{95} + q^{96} - 57 q^{97} + 30 q^{98} + 2 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9 + 7 * q^10 + 15 * q^11 - q^12 - q^13 - q^14 - 6 * q^15 + 15 * q^16 - 6 * q^17 - 2 * q^18 - 14 * q^19 - 7 * q^20 - 3 * q^21 - 15 * q^22 + 2 * q^23 + q^24 - 10 * q^25 + q^26 - 7 * q^27 + q^28 + 8 * q^29 + 6 * q^30 - 33 * q^31 - 15 * q^32 - q^33 + 6 * q^34 - 8 * q^35 + 2 * q^36 - 9 * q^37 + 14 * q^38 - 9 * q^39 + 7 * q^40 - 10 * q^41 + 3 * q^42 - 6 * q^43 + 15 * q^44 - 20 * q^45 - 2 * q^46 - q^47 - q^48 - 30 * q^49 + 10 * q^50 + 12 * q^51 - q^52 + 6 * q^53 + 7 * q^54 - 7 * q^55 - q^56 - 24 * q^57 - 8 * q^58 - 15 * q^59 - 6 * q^60 - 25 * q^61 + 33 * q^62 + 12 * q^63 + 15 * q^64 + 31 * q^65 + q^66 - 13 * q^67 - 6 * q^68 - 43 * q^69 + 8 * q^70 - 4 * q^71 - 2 * q^72 - 4 * q^73 + 9 * q^74 - 5 * q^75 - 14 * q^76 + q^77 + 9 * q^78 - 20 * q^79 - 7 * q^80 + 11 * q^81 + 10 * q^82 + q^83 - 3 * q^84 - q^85 + 6 * q^86 + 22 * q^87 - 15 * q^88 - 41 * q^89 + 20 * q^90 - 31 * q^91 + 2 * q^92 + 14 * q^93 + q^94 + 41 * q^95 + q^96 - 57 * q^97 + 30 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.516772	−0.298358	−0.149179	−	0.988810i	$-0.547663\pi$
$3$	−0.516772	−0.298358	−0.149179	+	0.988810i	$0.547663\pi$
$4$	1.00000	0.500000
$5$	−1.53195	−0.685110	−0.342555	−	0.939498i	$-0.611292\pi$
$5$	−1.53195	−0.685110	−0.342555	+	0.939498i	$0.611292\pi$
$6$	0.516772	0.210971
$7$	−0.576902	−0.218049	−0.109024	−	0.994039i	$-0.534773\pi$
$7$	−0.576902	−0.218049	−0.109024	+	0.994039i	$0.534773\pi$
$8$	−1.00000	−0.353553
$9$	−2.73295	−0.910982
$10$	1.53195	0.484446
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.516772	−0.149179
$13$	6.31699	1.75202	0.876009	−	0.482295i	$-0.160197\pi$
$13$	6.31699	1.75202	0.876009	+	0.482295i	$0.160197\pi$
$14$	0.576902	0.154184
$15$	0.791670	0.204408
$16$	1.00000	0.250000
$17$	−0.519591	−0.126019	−0.0630097	−	0.998013i	$-0.520070\pi$
$17$	−0.519591	−0.126019	−0.0630097	+	0.998013i	$0.520070\pi$
$18$	2.73295	0.644162
$19$	−0.276328	−0.0633940	−0.0316970	−	0.999498i	$-0.510091\pi$
$19$	−0.276328	−0.0633940	−0.0316970	+	0.999498i	$0.510091\pi$
$20$	−1.53195	−0.342555
$21$	0.298127	0.0650566
$22$	−1.00000	−0.213201
$23$	−1.50740	−0.314316	−0.157158	−	0.987574i	$-0.550233\pi$
$23$	−1.50740	−0.314316	−0.157158	+	0.987574i	$0.550233\pi$
$24$	0.516772	0.105486
$25$	−2.65312	−0.530624
$26$	−6.31699	−1.23886
$27$	2.96263	0.570158
$28$	−0.576902	−0.109024
$29$	−2.50711	−0.465558	−0.232779	−	0.972530i	$-0.574782\pi$
$29$	−2.50711	−0.465558	−0.232779	+	0.972530i	$0.574782\pi$
$30$	−0.791670	−0.144539
$31$	−0.621065	−0.111546	−0.0557732	−	0.998443i	$-0.517762\pi$
$31$	−0.621065	−0.111546	−0.0557732	+	0.998443i	$0.517762\pi$
$32$	−1.00000	−0.176777
$33$	−0.516772	−0.0899585
$34$	0.519591	0.0891092
$35$	0.883787	0.149387
$36$	−2.73295	−0.455491
$37$	−4.65628	−0.765488	−0.382744	−	0.923854i	$-0.625021\pi$
$37$	−4.65628	−0.765488	−0.382744	+	0.923854i	$0.625021\pi$
$38$	0.276328	0.0448263
$39$	−3.26444	−0.522729
$40$	1.53195	0.242223
$41$	6.59498	1.02996	0.514981	−	0.857201i	$-0.327799\pi$
$41$	6.59498	1.02996	0.514981	+	0.857201i	$0.327799\pi$
$42$	−0.298127	−0.0460020
$43$	−8.04854	−1.22739	−0.613695	−	0.789543i	$-0.710318\pi$
$43$	−8.04854	−1.22739	−0.613695	+	0.789543i	$0.710318\pi$
$44$	1.00000	0.150756
$45$	4.18674	0.624123
$46$	1.50740	0.222255
$47$	1.94410	0.283577	0.141788	−	0.989897i	$-0.454715\pi$
$47$	1.94410	0.283577	0.141788	+	0.989897i	$0.454715\pi$
$48$	−0.516772	−0.0745896
$49$	−6.66718	−0.952455
$50$	2.65312	0.375208
$51$	0.268510	0.0375990
$52$	6.31699	0.876009
$53$	11.6545	1.60087	0.800435	−	0.599419i	$-0.204602\pi$
$53$	11.6545	1.60087	0.800435	+	0.599419i	$0.204602\pi$
$54$	−2.96263	−0.403162
$55$	−1.53195	−0.206568
$56$	0.576902	0.0770918
$57$	0.142799	0.0189141
$58$	2.50711	0.329199
$59$	8.08984	1.05321	0.526604	−	0.850111i	$-0.323465\pi$
$59$	8.08984	1.05321	0.526604	+	0.850111i	$0.323465\pi$
$60$	0.791670	0.102204
$61$	2.60152	0.333090	0.166545	−	0.986034i	$-0.446739\pi$
$61$	2.60152	0.333090	0.166545	+	0.986034i	$0.446739\pi$
$62$	0.621065	0.0788753
$63$	1.57664	0.198638
$64$	1.00000	0.125000
$65$	−9.67733	−1.20033
$66$	0.516772	0.0636102
$67$	5.29122	0.646425	0.323212	−	0.946326i	$-0.395237\pi$
$67$	5.29122	0.646425	0.323212	+	0.946326i	$0.395237\pi$
$68$	−0.519591	−0.0630097
$69$	0.778984	0.0937787
$70$	−0.883787	−0.105633
$71$	14.1174	1.67542	0.837711	−	0.546114i	$-0.183893\pi$
$71$	14.1174	1.67542	0.837711	+	0.546114i	$0.183893\pi$
$72$	2.73295	0.322081
$73$	−2.91021	−0.340615	−0.170307	−	0.985391i	$-0.554476\pi$
$73$	−2.91021	−0.340615	−0.170307	+	0.985391i	$0.554476\pi$
$74$	4.65628	0.541282
$75$	1.37106	0.158316
$76$	−0.276328	−0.0316970
$77$	−0.576902	−0.0657441
$78$	3.26444	0.369626
$79$	−5.82588	−0.655463	−0.327732	−	0.944771i	$-0.606284\pi$
$79$	−5.82588	−0.655463	−0.327732	+	0.944771i	$0.606284\pi$
$80$	−1.53195	−0.171277
$81$	6.66784	0.740871
$82$	−6.59498	−0.728294
$83$	−0.321166	−0.0352525	−0.0176263	−	0.999845i	$-0.505611\pi$
$83$	−0.321166	−0.0352525	−0.0176263	+	0.999845i	$0.505611\pi$
$84$	0.298127	0.0325283
$85$	0.795989	0.0863371
$86$	8.04854	0.867896
$87$	1.29560	0.138903
$88$	−1.00000	−0.106600
$89$	7.65030	0.810930	0.405465	−	0.914111i	$-0.367110\pi$
$89$	7.65030	0.810930	0.405465	+	0.914111i	$0.367110\pi$
$90$	−4.18674	−0.441322
$91$	−3.64429	−0.382025
$92$	−1.50740	−0.157158
$93$	0.320949	0.0332808
$94$	−1.94410	−0.200519
$95$	0.423321	0.0434319
$96$	0.516772	0.0527428
$97$	−6.38659	−0.648460	−0.324230	−	0.945978i	$-0.605105\pi$
$97$	−6.38659	−0.648460	−0.324230	+	0.945978i	$0.605105\pi$
$98$	6.66718	0.673487
$99$	−2.73295	−0.274671
$100$	−2.65312	−0.265312
$101$	−11.6653	−1.16074	−0.580369	−	0.814353i	$-0.697092\pi$
$101$	−11.6653	−1.16074	−0.580369	+	0.814353i	$0.697092\pi$
$102$	−0.268510	−0.0265865
$103$	0.865809	0.0853107	0.0426554	−	0.999090i	$-0.486418\pi$
$103$	0.865809	0.0853107	0.0426554	+	0.999090i	$0.486418\pi$
$104$	−6.31699	−0.619432
$105$	−0.456716	−0.0445709
$106$	−11.6545	−1.13199
$107$	−9.28437	−0.897554	−0.448777	−	0.893644i	$-0.648140\pi$
$107$	−9.28437	−0.897554	−0.448777	+	0.893644i	$0.648140\pi$
$108$	2.96263	0.285079
$109$	−5.26206	−0.504013	−0.252007	−	0.967725i	$-0.581091\pi$
$109$	−5.26206	−0.504013	−0.252007	+	0.967725i	$0.581091\pi$
$110$	1.53195	0.146066
$111$	2.40624	0.228390
$112$	−0.576902	−0.0545121
$113$	16.7854	1.57904	0.789519	−	0.613726i	$-0.210330\pi$
$113$	16.7854	1.57904	0.789519	+	0.613726i	$0.210330\pi$
$114$	−0.142799	−0.0133743
$115$	2.30927	0.215341
$116$	−2.50711	−0.232779
$117$	−17.2640	−1.59606
$118$	−8.08984	−0.744730
$119$	0.299753	0.0274783
$120$	−0.791670	−0.0722693
$121$	1.00000	0.0909091
$122$	−2.60152	−0.235530
$123$	−3.40810	−0.307298
$124$	−0.621065	−0.0557732
$125$	11.7242	1.04865
$126$	−1.57664	−0.140459
$127$	−8.14472	−0.722727	−0.361363	−	0.932425i	$-0.617689\pi$
$127$	−8.14472	−0.722727	−0.361363	+	0.932425i	$0.617689\pi$
$128$	−1.00000	−0.0883883
$129$	4.15926	0.366202
$130$	9.67733	0.848758
$131$	3.53403	0.308770	0.154385	−	0.988011i	$-0.450660\pi$
$131$	3.53403	0.308770	0.154385	+	0.988011i	$0.450660\pi$
$132$	−0.516772	−0.0449792
$133$	0.159414	0.0138230
$134$	−5.29122	−0.457091
$135$	−4.53860	−0.390621
$136$	0.519591	0.0445546
$137$	−15.4462	−1.31965	−0.659827	−	0.751418i	$-0.729370\pi$
$137$	−15.4462	−1.31965	−0.659827	+	0.751418i	$0.729370\pi$
$138$	−0.778984	−0.0663116
$139$	6.61303	0.560910	0.280455	−	0.959867i	$-0.409515\pi$
$139$	6.61303	0.560910	0.280455	+	0.959867i	$0.409515\pi$
$140$	0.883787	0.0746936
$141$	−1.00466	−0.0846075
$142$	−14.1174	−1.18470
$143$	6.31699	0.528253
$144$	−2.73295	−0.227746
$145$	3.84077	0.318958
$146$	2.91021	0.240851
$147$	3.44541	0.284173
$148$	−4.65628	−0.382744
$149$	−12.3628	−1.01280	−0.506398	−	0.862300i	$-0.669023\pi$
$149$	−12.3628	−1.01280	−0.506398	+	0.862300i	$0.669023\pi$
$150$	−1.37106	−0.111947
$151$	−20.4592	−1.66495	−0.832474	−	0.554063i	$-0.813076\pi$
$151$	−20.4592	−1.66495	−0.832474	+	0.554063i	$0.813076\pi$
$152$	0.276328	0.0224132
$153$	1.42002	0.114801
$154$	0.576902	0.0464881
$155$	0.951441	0.0764216
$156$	−3.26444	−0.261365
$157$	−21.3362	−1.70282	−0.851408	−	0.524505i	$-0.824251\pi$
$157$	−21.3362	−1.70282	−0.851408	+	0.524505i	$0.824251\pi$
$158$	5.82588	0.463482
$159$	−6.02273	−0.477633
$160$	1.53195	0.121111
$161$	0.869625	0.0685360
$162$	−6.66784	−0.523875
$163$	−24.0912	−1.88697	−0.943483	−	0.331421i	$-0.892472\pi$
$163$	−24.0912	−1.88697	−0.943483	+	0.331421i	$0.892472\pi$
$164$	6.59498	0.514981
$165$	0.791670	0.0616314
$166$	0.321166	0.0249273
$167$	21.8326	1.68946	0.844729	−	0.535195i	$-0.179762\pi$
$167$	21.8326	1.68946	0.844729	+	0.535195i	$0.179762\pi$
$168$	−0.298127	−0.0230010
$169$	26.9044	2.06957
$170$	−0.795989	−0.0610496
$171$	0.755190	0.0577508
$172$	−8.04854	−0.613695
$173$	−19.7187	−1.49919	−0.749594	−	0.661898i	$-0.769751\pi$
$173$	−19.7187	−1.49919	−0.749594	+	0.661898i	$0.769751\pi$
$174$	−1.29560	−0.0982194
$175$	1.53059	0.115702
$176$	1.00000	0.0753778
$177$	−4.18060	−0.314233
$178$	−7.65030	−0.573414
$179$	−17.8912	−1.33725	−0.668625	−	0.743600i	$-0.733117\pi$
$179$	−17.8912	−1.33725	−0.668625	+	0.743600i	$0.733117\pi$
$180$	4.18674	0.312061
$181$	−21.6524	−1.60941	−0.804703	−	0.593677i	$-0.797676\pi$
$181$	−21.6524	−1.60941	−0.804703	+	0.593677i	$0.797676\pi$
$182$	3.64429	0.270132
$183$	−1.34439	−0.0993803
$184$	1.50740	0.111127
$185$	7.13321	0.524444
$186$	−0.320949	−0.0235331
$187$	−0.519591	−0.0379963
$188$	1.94410	0.141788
$189$	−1.70915	−0.124322
$190$	−0.423321	−0.0307110
$191$	6.58409	0.476408	0.238204	−	0.971215i	$-0.423441\pi$
$191$	6.58409	0.476408	0.238204	+	0.971215i	$0.423441\pi$
$192$	−0.516772	−0.0372948
$193$	14.5978	1.05077	0.525386	−	0.850864i	$-0.323921\pi$
$193$	14.5978	1.05077	0.525386	+	0.850864i	$0.323921\pi$
$194$	6.38659	0.458531
$195$	5.00097	0.358127
$196$	−6.66718	−0.476227
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	2.73295	0.194222
$199$	−22.2655	−1.57836	−0.789178	−	0.614164i	$-0.789493\pi$
$199$	−22.2655	−1.57836	−0.789178	+	0.614164i	$0.789493\pi$
$200$	2.65312	0.187604
$201$	−2.73435	−0.192866
$202$	11.6653	0.820766
$203$	1.44636	0.101514
$204$	0.268510	0.0187995
$205$	−10.1032	−0.705638
$206$	−0.865809	−0.0603238
$207$	4.11966	0.286336
$208$	6.31699	0.438005
$209$	−0.276328	−0.0191140
$210$	0.456716	0.0315164
$211$	−12.5295	−0.862563	−0.431281	−	0.902217i	$-0.641938\pi$
$211$	−12.5295	−0.862563	−0.431281	+	0.902217i	$0.641938\pi$
$212$	11.6545	0.800435
$213$	−7.29546	−0.499876
$214$	9.28437	0.634667
$215$	12.3300	0.840897
$216$	−2.96263	−0.201581
$217$	0.358294	0.0243226
$218$	5.26206	0.356391
$219$	1.50392	0.101625
$220$	−1.53195	−0.103284
$221$	−3.28225	−0.220788
$222$	−2.40624	−0.161496
$223$	−13.6319	−0.912860	−0.456430	−	0.889759i	$-0.650872\pi$
$223$	−13.6319	−0.912860	−0.456430	+	0.889759i	$0.650872\pi$
$224$	0.576902	0.0385459
$225$	7.25084	0.483389
$226$	−16.7854	−1.11655
$227$	7.51079	0.498508	0.249254	−	0.968438i	$-0.419815\pi$
$227$	7.51079	0.498508	0.249254	+	0.968438i	$0.419815\pi$
$228$	0.142799	0.00945707
$229$	−13.1694	−0.870258	−0.435129	−	0.900368i	$-0.643297\pi$
$229$	−13.1694	−0.870258	−0.435129	+	0.900368i	$0.643297\pi$
$230$	−2.30927	−0.152269
$231$	0.298127	0.0196153
$232$	2.50711	0.164600
$233$	−8.17542	−0.535590	−0.267795	−	0.963476i	$-0.586295\pi$
$233$	−8.17542	−0.535590	−0.267795	+	0.963476i	$0.586295\pi$
$234$	17.2640	1.12858
$235$	−2.97827	−0.194281
$236$	8.08984	0.526604
$237$	3.01065	0.195563
$238$	−0.299753	−0.0194301
$239$	2.81584	0.182141	0.0910707	−	0.995844i	$-0.470971\pi$
$239$	2.81584	0.182141	0.0910707	+	0.995844i	$0.470971\pi$
$240$	0.791670	0.0511021
$241$	8.59567	0.553696	0.276848	−	0.960914i	$-0.410710\pi$
$241$	8.59567	0.553696	0.276848	+	0.960914i	$0.410710\pi$
$242$	−1.00000	−0.0642824
$243$	−12.3336	−0.791203
$244$	2.60152	0.166545
$245$	10.2138	0.652536
$246$	3.40810	0.217293
$247$	−1.74556	−0.111067
$248$	0.621065	0.0394376
$249$	0.165970	0.0105179
$250$	−11.7242	−0.741505
$251$	−7.11696	−0.449218	−0.224609	−	0.974449i	$-0.572111\pi$
$251$	−7.11696	−0.449218	−0.224609	+	0.974449i	$0.572111\pi$
$252$	1.57664	0.0993192
$253$	−1.50740	−0.0947697
$254$	8.14472	0.511045
$255$	−0.411345	−0.0257594
$256$	1.00000	0.0625000
$257$	2.33665	0.145756	0.0728780	−	0.997341i	$-0.476782\pi$
$257$	2.33665	0.145756	0.0728780	+	0.997341i	$0.476782\pi$
$258$	−4.15926	−0.258944
$259$	2.68622	0.166914
$260$	−9.67733	−0.600163
$261$	6.85179	0.424115
$262$	−3.53403	−0.218333
$263$	−28.6230	−1.76497	−0.882485	−	0.470341i	$-0.844131\pi$
$263$	−28.6230	−1.76497	−0.882485	+	0.470341i	$0.844131\pi$
$264$	0.516772	0.0318051
$265$	−17.8542	−1.09677
$266$	−0.159414	−0.00977432
$267$	−3.95346	−0.241948
$268$	5.29122	0.323212
$269$	−14.6174	−0.891240	−0.445620	−	0.895222i	$-0.647017\pi$
$269$	−14.6174	−0.891240	−0.445620	+	0.895222i	$0.647017\pi$
$270$	4.53860	0.276211
$271$	32.6618	1.98406	0.992031	−	0.125993i	$-0.0402117\pi$
$271$	32.6618	1.98406	0.992031	+	0.125993i	$0.0402117\pi$
$272$	−0.519591	−0.0315048
$273$	1.88327	0.113980
$274$	15.4462	0.933136
$275$	−2.65312	−0.159989
$276$	0.778984	0.0468894
$277$	13.4119	0.805841	0.402921	−	0.915235i	$-0.367995\pi$
$277$	13.4119	0.805841	0.402921	+	0.915235i	$0.367995\pi$
$278$	−6.61303	−0.396623
$279$	1.69734	0.101617
$280$	−0.883787	−0.0528164
$281$	−2.23914	−0.133576	−0.0667879	−	0.997767i	$-0.521275\pi$
$281$	−2.23914	−0.133576	−0.0667879	+	0.997767i	$0.521275\pi$
$282$	1.00466	0.0598265
$283$	20.1113	1.19549	0.597747	−	0.801685i	$-0.296063\pi$
$283$	20.1113	1.19549	0.597747	+	0.801685i	$0.296063\pi$
$284$	14.1174	0.837711
$285$	−0.218761	−0.0129583
$286$	−6.31699	−0.373532
$287$	−3.80466	−0.224582
$288$	2.73295	0.161040
$289$	−16.7300	−0.984119
$290$	−3.84077	−0.225538
$291$	3.30041	0.193474
$292$	−2.91021	−0.170307
$293$	12.4760	0.728853	0.364427	−	0.931232i	$-0.381265\pi$
$293$	12.4760	0.728853	0.364427	+	0.931232i	$0.381265\pi$
$294$	−3.44541	−0.200941
$295$	−12.3933	−0.721563
$296$	4.65628	0.270641
$297$	2.96263	0.171909
$298$	12.3628	0.716155
$299$	−9.52226	−0.550687
$300$	1.37106	0.0791581
$301$	4.64322	0.267631
$302$	20.4592	1.17730
$303$	6.02829	0.346316
$304$	−0.276328	−0.0158485
$305$	−3.98540	−0.228203
$306$	−1.42002	−0.0811769
$307$	−1.25071	−0.0713820	−0.0356910	−	0.999363i	$-0.511363\pi$
$307$	−1.25071	−0.0713820	−0.0356910	+	0.999363i	$0.511363\pi$
$308$	−0.576902	−0.0328721
$309$	−0.447426	−0.0254532
$310$	−0.951441	−0.0540382
$311$	8.37779	0.475061	0.237531	−	0.971380i	$-0.423662\pi$
$311$	8.37779	0.475061	0.237531	+	0.971380i	$0.423662\pi$
$312$	3.26444	0.184813
$313$	15.4365	0.872525	0.436263	−	0.899819i	$-0.356302\pi$
$313$	15.4365	0.872525	0.436263	+	0.899819i	$0.356302\pi$
$314$	21.3362	1.20407
$315$	−2.41534	−0.136089
$316$	−5.82588	−0.327732
$317$	−31.9865	−1.79654	−0.898271	−	0.439441i	$-0.855177\pi$
$317$	−31.9865	−1.79654	−0.898271	+	0.439441i	$0.855177\pi$
$318$	6.02273	0.337738
$319$	−2.50711	−0.140371
$320$	−1.53195	−0.0856387
$321$	4.79791	0.267793
$322$	−0.869625	−0.0484623
$323$	0.143578	0.00798887
$324$	6.66784	0.370435
$325$	−16.7597	−0.929663
$326$	24.0912	1.33429
$327$	2.71928	0.150377
$328$	−6.59498	−0.364147
$329$	−1.12156	−0.0618335
$330$	−0.791670	−0.0435800
$331$	8.82597	0.485119	0.242560	−	0.970137i	$-0.422013\pi$
$331$	8.82597	0.485119	0.242560	+	0.970137i	$0.422013\pi$
$332$	−0.321166	−0.0176263
$333$	12.7254	0.697346
$334$	−21.8326	−1.19463
$335$	−8.10589	−0.442872
$336$	0.298127	0.0162642
$337$	−15.7719	−0.859149	−0.429575	−	0.903031i	$-0.641336\pi$
$337$	−15.7719	−0.859149	−0.429575	+	0.903031i	$0.641336\pi$
$338$	−26.9044	−1.46341
$339$	−8.67423	−0.471120
$340$	0.795989	0.0431686
$341$	−0.621065	−0.0336325
$342$	−0.755190	−0.0408360
$343$	7.88463	0.425730
$344$	8.04854	0.433948
$345$	−1.19337	−0.0642487
$346$	19.7187	1.06009
$347$	−15.0085	−0.805701	−0.402851	−	0.915266i	$-0.631981\pi$
$347$	−15.0085	−0.805701	−0.402851	+	0.915266i	$0.631981\pi$
$348$	1.29560	0.0694516
$349$	10.9213	0.584604	0.292302	−	0.956326i	$-0.405579\pi$
$349$	10.9213	0.584604	0.292302	+	0.956326i	$0.405579\pi$
$350$	−1.53059	−0.0818136
$351$	18.7149	0.998927
$352$	−1.00000	−0.0533002
$353$	11.9233	0.634615	0.317307	−	0.948323i	$-0.397221\pi$
$353$	11.9233	0.634615	0.317307	+	0.948323i	$0.397221\pi$
$354$	4.18060	0.222197
$355$	−21.6271	−1.14785
$356$	7.65030	0.405465
$357$	−0.154904	−0.00819840
$358$	17.8912	0.945578
$359$	−20.8521	−1.10053	−0.550265	−	0.834990i	$-0.685473\pi$
$359$	−20.8521	−1.10053	−0.550265	+	0.834990i	$0.685473\pi$
$360$	−4.18674	−0.220661
$361$	−18.9236	−0.995981
$362$	21.6524	1.13802
$363$	−0.516772	−0.0271235
$364$	−3.64429	−0.191013
$365$	4.45831	0.233359
$366$	1.34439	0.0702725
$367$	−11.8600	−0.619086	−0.309543	−	0.950885i	$-0.600176\pi$
$367$	−11.8600	−0.619086	−0.309543	+	0.950885i	$0.600176\pi$
$368$	−1.50740	−0.0785789
$369$	−18.0237	−0.938278
$370$	−7.13321	−0.370838
$371$	−6.72352	−0.349068
$372$	0.320949	0.0166404
$373$	−29.1370	−1.50866	−0.754329	−	0.656497i	$-0.772037\pi$
$373$	−29.1370	−1.50866	−0.754329	+	0.656497i	$0.772037\pi$
$374$	0.519591	0.0268674
$375$	−6.05875	−0.312872
$376$	−1.94410	−0.100259
$377$	−15.8374	−0.815666
$378$	1.70915	0.0879090
$379$	8.69451	0.446607	0.223303	−	0.974749i	$-0.428316\pi$
$379$	8.69451	0.446607	0.223303	+	0.974749i	$0.428316\pi$
$380$	0.423321	0.0217159
$381$	4.20896	0.215632
$382$	−6.58409	−0.336871
$383$	−17.0555	−0.871496	−0.435748	−	0.900069i	$-0.643516\pi$
$383$	−17.0555	−0.871496	−0.435748	+	0.900069i	$0.643516\pi$
$384$	0.516772	0.0263714
$385$	0.883787	0.0450419
$386$	−14.5978	−0.743008
$387$	21.9962	1.11813
$388$	−6.38659	−0.324230
$389$	23.0914	1.17078	0.585389	−	0.810752i	$-0.300942\pi$
$389$	23.0914	1.17078	0.585389	+	0.810752i	$0.300942\pi$
$390$	−5.00097	−0.253234
$391$	0.783234	0.0396099
$392$	6.66718	0.336744
$393$	−1.82629	−0.0921241
$394$	−1.00000	−0.0503793
$395$	8.92498	0.449064
$396$	−2.73295	−0.137336
$397$	14.3188	0.718640	0.359320	−	0.933214i	$-0.383009\pi$
$397$	14.3188	0.718640	0.359320	+	0.933214i	$0.383009\pi$
$398$	22.2655	1.11607
$399$	−0.0823808	−0.00412420
$400$	−2.65312	−0.132656
$401$	−33.6253	−1.67917	−0.839584	−	0.543230i	$-0.817201\pi$
$401$	−33.6253	−1.67917	−0.839584	+	0.543230i	$0.817201\pi$
$402$	2.73435	0.136377
$403$	−3.92326	−0.195431
$404$	−11.6653	−0.580369
$405$	−10.2148	−0.507578
$406$	−1.44636	−0.0717814
$407$	−4.65628	−0.230803
$408$	−0.268510	−0.0132932
$409$	−14.1008	−0.697239	−0.348620	−	0.937264i	$-0.613350\pi$
$409$	−14.1008	−0.697239	−0.348620	+	0.937264i	$0.613350\pi$
$410$	10.1032	0.498961
$411$	7.98214	0.393730
$412$	0.865809	0.0426554
$413$	−4.66705	−0.229650
$414$	−4.11966	−0.202470
$415$	0.492011	0.0241519
$416$	−6.31699	−0.309716
$417$	−3.41743	−0.167352
$418$	0.276328	0.0135156
$419$	−11.0166	−0.538196	−0.269098	−	0.963113i	$-0.586726\pi$
$419$	−11.0166	−0.538196	−0.269098	+	0.963113i	$0.586726\pi$
$420$	−0.456716	−0.0222855
$421$	9.64998	0.470311	0.235156	−	0.971958i	$-0.424440\pi$
$421$	9.64998	0.470311	0.235156	+	0.971958i	$0.424440\pi$
$422$	12.5295	0.609924
$423$	−5.31313	−0.258333
$424$	−11.6545	−0.565993
$425$	1.37854	0.0668690
$426$	7.29546	0.353466
$427$	−1.50082	−0.0726298
$428$	−9.28437	−0.448777
$429$	−3.26444	−0.157609
$430$	−12.3300	−0.594604
$431$	−12.9828	−0.625359	−0.312680	−	0.949859i	$-0.601227\pi$
$431$	−12.9828	−0.625359	−0.312680	+	0.949859i	$0.601227\pi$
$432$	2.96263	0.142539
$433$	10.5182	0.505475	0.252737	−	0.967535i	$-0.418669\pi$
$433$	10.5182	0.505475	0.252737	+	0.967535i	$0.418669\pi$
$434$	−0.358294	−0.0171986
$435$	−1.98480	−0.0951639
$436$	−5.26206	−0.252007
$437$	0.416538	0.0199257
$438$	−1.50392	−0.0718600
$439$	−7.20297	−0.343779	−0.171889	−	0.985116i	$-0.554987\pi$
$439$	−7.20297	−0.343779	−0.171889	+	0.985116i	$0.554987\pi$
$440$	1.53195	0.0730330
$441$	18.2211	0.867669
$442$	3.28225	0.156121
$443$	−20.2810	−0.963580	−0.481790	−	0.876287i	$-0.660013\pi$
$443$	−20.2810	−0.963580	−0.481790	+	0.876287i	$0.660013\pi$
$444$	2.40624	0.114195
$445$	−11.7199	−0.555576
$446$	13.6319	0.645490
$447$	6.38872	0.302176
$448$	−0.576902	−0.0272561
$449$	−31.5168	−1.48737	−0.743685	−	0.668531i	$-0.766924\pi$
$449$	−31.5168	−1.48737	−0.743685	+	0.668531i	$0.766924\pi$
$450$	−7.25084	−0.341808
$451$	6.59498	0.310545
$452$	16.7854	0.789519
$453$	10.5728	0.496752
$454$	−7.51079	−0.352499
$455$	5.58287	0.261729
$456$	−0.142799	−0.00668716
$457$	−31.8248	−1.48870	−0.744351	−	0.667788i	$-0.767241\pi$
$457$	−31.8248	−1.48870	−0.744351	+	0.667788i	$0.767241\pi$
$458$	13.1694	0.615366
$459$	−1.53935	−0.0718509
$460$	2.30927	0.107670
$461$	−15.4987	−0.721847	−0.360923	−	0.932595i	$-0.617538\pi$
$461$	−15.4987	−0.721847	−0.360923	+	0.932595i	$0.617538\pi$
$462$	−0.298127	−0.0138701
$463$	39.0742	1.81593	0.907965	−	0.419045i	$-0.137635\pi$
$463$	39.0742	1.81593	0.907965	+	0.419045i	$0.137635\pi$
$464$	−2.50711	−0.116389
$465$	−0.491678	−0.0228010
$466$	8.17542	0.378719
$467$	30.6437	1.41802	0.709010	−	0.705199i	$-0.249142\pi$
$467$	30.6437	1.41802	0.709010	+	0.705199i	$0.249142\pi$
$468$	−17.2640	−0.798029
$469$	−3.05251	−0.140952
$470$	2.97827	0.137378
$471$	11.0260	0.508049
$472$	−8.08984	−0.372365
$473$	−8.04854	−0.370072
$474$	−3.01065	−0.138284
$475$	0.733132	0.0336384
$476$	0.299753	0.0137392
$477$	−31.8512	−1.45836
$478$	−2.81584	−0.128793
$479$	−12.4403	−0.568412	−0.284206	−	0.958763i	$-0.591730\pi$
$479$	−12.4403	−0.568412	−0.284206	+	0.958763i	$0.591730\pi$
$480$	−0.791670	−0.0361346
$481$	−29.4137	−1.34115
$482$	−8.59567	−0.391522
$483$	−0.449398	−0.0204483
$484$	1.00000	0.0454545
$485$	9.78396	0.444267
$486$	12.3336	0.559465
$487$	−40.5024	−1.83534	−0.917670	−	0.397344i	$-0.869932\pi$
$487$	−40.5024	−1.83534	−0.917670	+	0.397344i	$0.869932\pi$
$488$	−2.60152	−0.117765
$489$	12.4496	0.562992
$490$	−10.2138	−0.461413
$491$	13.4456	0.606792	0.303396	−	0.952865i	$-0.401880\pi$
$491$	13.4456	0.606792	0.303396	+	0.952865i	$0.401880\pi$
$492$	−3.40810	−0.153649
$493$	1.30267	0.0586693
$494$	1.74556	0.0785365
$495$	4.18674	0.188180
$496$	−0.621065	−0.0278866
$497$	−8.14433	−0.365323
$498$	−0.165970	−0.00743727
$499$	−42.6557	−1.90953	−0.954765	−	0.297361i	$-0.903893\pi$
$499$	−42.6557	−1.90953	−0.954765	+	0.297361i	$0.903893\pi$
$500$	11.7242	0.524323
$501$	−11.2825	−0.504064
$502$	7.11696	0.317645
$503$	30.9713	1.38094	0.690471	−	0.723360i	$-0.257404\pi$
$503$	30.9713	1.38094	0.690471	+	0.723360i	$0.257404\pi$
$504$	−1.57664	−0.0702293
$505$	17.8706	0.795233
$506$	1.50740	0.0670123
$507$	−13.9034	−0.617473
$508$	−8.14472	−0.361363
$509$	−26.5455	−1.17661	−0.588305	−	0.808639i	$-0.700205\pi$
$509$	−26.5455	−1.17661	−0.588305	+	0.808639i	$0.700205\pi$
$510$	0.411345	0.0182147
$511$	1.67891	0.0742706
$512$	−1.00000	−0.0441942
$513$	−0.818657	−0.0361446
$514$	−2.33665	−0.103065
$515$	−1.32638	−0.0584472
$516$	4.15926	0.183101
$517$	1.94410	0.0855016
$518$	−2.68622	−0.118026
$519$	10.1901	0.447295
$520$	9.67733	0.424379
$521$	−8.49955	−0.372372	−0.186186	−	0.982515i	$-0.559613\pi$
$521$	−8.49955	−0.372372	−0.186186	+	0.982515i	$0.559613\pi$
$522$	−6.85179	−0.299895
$523$	36.7026	1.60489	0.802445	−	0.596726i	$-0.203532\pi$
$523$	36.7026	1.60489	0.802445	+	0.596726i	$0.203532\pi$
$524$	3.53403	0.154385
$525$	−0.790967	−0.0345206
$526$	28.6230	1.24802
$527$	0.322700	0.0140570
$528$	−0.516772	−0.0224896
$529$	−20.7277	−0.901206
$530$	17.8542	0.775535
$531$	−22.1091	−0.959453
$532$	0.159414	0.00691148
$533$	41.6604	1.80451
$534$	3.95346	0.171083
$535$	14.2232	0.614923
$536$	−5.29122	−0.228546
$537$	9.24566	0.398980
$538$	14.6174	0.630202
$539$	−6.66718	−0.287176
$540$	−4.53860	−0.195310
$541$	38.4107	1.65140	0.825701	−	0.564107i	$-0.190780\pi$
$541$	38.4107	1.65140	0.825701	+	0.564107i	$0.190780\pi$
$542$	−32.6618	−1.40294
$543$	11.1893	0.480180
$544$	0.519591	0.0222773
$545$	8.06122	0.345305
$546$	−1.88327	−0.0805963
$547$	−16.5291	−0.706732	−0.353366	−	0.935485i	$-0.614963\pi$
$547$	−16.5291	−0.706732	−0.353366	+	0.935485i	$0.614963\pi$
$548$	−15.4462	−0.659827
$549$	−7.10981	−0.303439
$550$	2.65312	0.113129
$551$	0.692784	0.0295136
$552$	−0.778984	−0.0331558
$553$	3.36097	0.142923
$554$	−13.4119	−0.569816
$555$	−3.68624	−0.156472
$556$	6.61303	0.280455
$557$	−0.664297	−0.0281472	−0.0140736	−	0.999901i	$-0.504480\pi$
$557$	−0.664297	−0.0281472	−0.0140736	+	0.999901i	$0.504480\pi$
$558$	−1.69734	−0.0718540
$559$	−50.8425	−2.15041
$560$	0.883787	0.0373468
$561$	0.268510	0.0113365
$562$	2.23914	0.0944524
$563$	−9.28117	−0.391155	−0.195577	−	0.980688i	$-0.562658\pi$
$563$	−9.28117	−0.391155	−0.195577	+	0.980688i	$0.562658\pi$
$564$	−1.00466	−0.0423037
$565$	−25.7145	−1.08182
$566$	−20.1113	−0.845342
$567$	−3.84669	−0.161546
$568$	−14.1174	−0.592351
$569$	−11.2214	−0.470424	−0.235212	−	0.971944i	$-0.575578\pi$
$569$	−11.2214	−0.470424	−0.235212	+	0.971944i	$0.575578\pi$
$570$	0.218761	0.00916288
$571$	27.4537	1.14890	0.574451	−	0.818539i	$-0.305215\pi$
$571$	27.4537	1.14890	0.574451	+	0.818539i	$0.305215\pi$
$572$	6.31699	0.264127
$573$	−3.40247	−0.142140
$574$	3.80466	0.158803
$575$	3.99933	0.166783
$576$	−2.73295	−0.113873
$577$	46.9132	1.95302	0.976511	−	0.215468i	$-0.0691277\pi$
$577$	46.9132	1.95302	0.976511	+	0.215468i	$0.0691277\pi$
$578$	16.7300	0.695877
$579$	−7.54373	−0.313507
$580$	3.84077	0.159479
$581$	0.185281	0.00768676
$582$	−3.30041	−0.136807
$583$	11.6545	0.482681
$584$	2.91021	0.120426
$585$	26.4476	1.09347
$586$	−12.4760	−0.515377
$587$	−16.4191	−0.677688	−0.338844	−	0.940843i	$-0.610036\pi$
$587$	−16.4191	−0.677688	−0.338844	+	0.940843i	$0.610036\pi$
$588$	3.44541	0.142086
$589$	0.171618	0.00707138
$590$	12.3933	0.510222
$591$	−0.516772	−0.0212572
$592$	−4.65628	−0.191372
$593$	−9.46890	−0.388841	−0.194421	−	0.980918i	$-0.562283\pi$
$593$	−9.46890	−0.388841	−0.194421	+	0.980918i	$0.562283\pi$
$594$	−2.96263	−0.121558
$595$	−0.459208	−0.0188257
$596$	−12.3628	−0.506398
$597$	11.5062	0.470916
$598$	9.52226	0.389394
$599$	3.39030	0.138524	0.0692619	−	0.997599i	$-0.477936\pi$
$599$	3.39030	0.138524	0.0692619	+	0.997599i	$0.477936\pi$
$600$	−1.37106	−0.0559733
$601$	−21.3548	−0.871082	−0.435541	−	0.900169i	$-0.643443\pi$
$601$	−21.3548	−0.871082	−0.435541	+	0.900169i	$0.643443\pi$
$602$	−4.64322	−0.189243
$603$	−14.4606	−0.588882
$604$	−20.4592	−0.832474
$605$	−1.53195	−0.0622827
$606$	−6.02829	−0.244882
$607$	28.0450	1.13831	0.569156	−	0.822229i	$-0.307270\pi$
$607$	28.0450	1.13831	0.569156	+	0.822229i	$0.307270\pi$
$608$	0.276328	0.0112066
$609$	−0.747436	−0.0302876
$610$	3.98540	0.161364
$611$	12.2809	0.496831
$612$	1.42002	0.0574007
$613$	35.1970	1.42160	0.710798	−	0.703397i	$-0.248334\pi$
$613$	35.1970	1.42160	0.710798	+	0.703397i	$0.248334\pi$
$614$	1.25071	0.0504747
$615$	5.22105	0.210533
$616$	0.576902	0.0232441
$617$	−25.6256	−1.03165	−0.515823	−	0.856695i	$-0.672514\pi$
$617$	−25.6256	−1.03165	−0.515823	+	0.856695i	$0.672514\pi$
$618$	0.447426	0.0179981
$619$	32.1193	1.29099	0.645493	−	0.763767i	$-0.276652\pi$
$619$	32.1193	1.29099	0.645493	+	0.763767i	$0.276652\pi$
$620$	0.951441	0.0382108
$621$	−4.46588	−0.179209
$622$	−8.37779	−0.335919
$623$	−4.41347	−0.176822
$624$	−3.26444	−0.130682
$625$	−4.69534	−0.187813
$626$	−15.4365	−0.616968
$627$	0.142799	0.00570283
$628$	−21.3362	−0.851408
$629$	2.41936	0.0964664
$630$	2.41534	0.0962295
$631$	3.17376	0.126345	0.0631726	−	0.998003i	$-0.479878\pi$
$631$	3.17376	0.126345	0.0631726	+	0.998003i	$0.479878\pi$
$632$	5.82588	0.231741
$633$	6.47487	0.257353
$634$	31.9865	1.27035
$635$	12.4773	0.495147
$636$	−6.02273	−0.238817
$637$	−42.1165	−1.66872
$638$	2.50711	0.0992573
$639$	−38.5820	−1.52628
$640$	1.53195	0.0605557
$641$	25.0824	0.990696	0.495348	−	0.868695i	$-0.335041\pi$
$641$	25.0824	0.990696	0.495348	+	0.868695i	$0.335041\pi$
$642$	−4.79791	−0.189358
$643$	9.69035	0.382150	0.191075	−	0.981575i	$-0.438803\pi$
$643$	9.69035	0.382150	0.191075	+	0.981575i	$0.438803\pi$
$644$	0.869625	0.0342680
$645$	−6.37179	−0.250889
$646$	−0.143578	−0.00564899
$647$	42.4143	1.66748	0.833739	−	0.552159i	$-0.186196\pi$
$647$	42.4143	1.66748	0.833739	+	0.552159i	$0.186196\pi$
$648$	−6.66784	−0.261937
$649$	8.08984	0.317554
$650$	16.7597	0.657371
$651$	−0.185156	−0.00725684
$652$	−24.0912	−0.943483
$653$	38.4602	1.50506	0.752531	−	0.658557i	$-0.228833\pi$
$653$	38.4602	1.50506	0.752531	+	0.658557i	$0.228833\pi$
$654$	−2.71928	−0.106332
$655$	−5.41397	−0.211541
$656$	6.59498	0.257491
$657$	7.95346	0.310294
$658$	1.12156	0.0437229
$659$	30.3041	1.18048	0.590239	−	0.807228i	$-0.299033\pi$
$659$	30.3041	1.18048	0.590239	+	0.807228i	$0.299033\pi$
$660$	0.791670	0.0308157
$661$	−13.8645	−0.539265	−0.269633	−	0.962963i	$-0.586902\pi$
$661$	−13.8645	−0.539265	−0.269633	+	0.962963i	$0.586902\pi$
$662$	−8.82597	−0.343031
$663$	1.69618	0.0658740
$664$	0.321166	0.0124637
$665$	−0.244215	−0.00947025
$666$	−12.7254	−0.493098
$667$	3.77922	0.146332
$668$	21.8326	0.844729
$669$	7.04459	0.272360
$670$	8.10589	0.313158
$671$	2.60152	0.100430
$672$	−0.298127	−0.0115005
$673$	−39.5240	−1.52354	−0.761770	−	0.647848i	$-0.775669\pi$
$673$	−39.5240	−1.52354	−0.761770	+	0.647848i	$0.775669\pi$
$674$	15.7719	0.607510
$675$	−7.86021	−0.302540
$676$	26.9044	1.03478
$677$	−13.6994	−0.526509	−0.263255	−	0.964726i	$-0.584796\pi$
$677$	−13.6994	−0.526509	−0.263255	+	0.964726i	$0.584796\pi$
$678$	8.67423	0.333132
$679$	3.68444	0.141396
$680$	−0.795989	−0.0305248
$681$	−3.88136	−0.148734
$682$	0.621065	0.0237818
$683$	−15.0292	−0.575076	−0.287538	−	0.957769i	$-0.592837\pi$
$683$	−15.0292	−0.575076	−0.287538	+	0.957769i	$0.592837\pi$
$684$	0.755190	0.0288754
$685$	23.6628	0.904108
$686$	−7.88463	−0.301037
$687$	6.80558	0.259649
$688$	−8.04854	−0.306848
$689$	73.6215	2.80475
$690$	1.19337	0.0454307
$691$	−10.5598	−0.401714	−0.200857	−	0.979621i	$-0.564373\pi$
$691$	−10.5598	−0.401714	−0.200857	+	0.979621i	$0.564373\pi$
$692$	−19.7187	−0.749594
$693$	1.57664	0.0598917
$694$	15.0085	0.569717
$695$	−10.1308	−0.384285
$696$	−1.29560	−0.0491097
$697$	−3.42669	−0.129795
$698$	−10.9213	−0.413377
$699$	4.22483	0.159798
$700$	1.53059	0.0578509
$701$	−37.1615	−1.40357	−0.701785	−	0.712389i	$-0.747613\pi$
$701$	−37.1615	−1.40357	−0.701785	+	0.712389i	$0.747613\pi$
$702$	−18.7149	−0.706348
$703$	1.28666	0.0485274
$704$	1.00000	0.0376889
$705$	1.53909	0.0579654
$706$	−11.9233	−0.448740
$707$	6.72972	0.253097
$708$	−4.18060	−0.157117
$709$	−1.26847	−0.0476384	−0.0238192	−	0.999716i	$-0.507583\pi$
$709$	−1.26847	−0.0476384	−0.0238192	+	0.999716i	$0.507583\pi$
$710$	21.6271	0.811651
$711$	15.9218	0.597115
$712$	−7.65030	−0.286707
$713$	0.936196	0.0350608
$714$	0.154904	0.00579714
$715$	−9.67733	−0.361912
$716$	−17.8912	−0.668625
$717$	−1.45515	−0.0543434
$718$	20.8521	0.778193
$719$	17.0687	0.636555	0.318278	−	0.947998i	$-0.396896\pi$
$719$	17.0687	0.636555	0.318278	+	0.947998i	$0.396896\pi$
$720$	4.18674	0.156031
$721$	−0.499487	−0.0186019
$722$	18.9236	0.704265
$723$	−4.44200	−0.165200
$724$	−21.6524	−0.804703
$725$	6.65166	0.247036
$726$	0.516772	0.0191792
$727$	−20.0266	−0.742747	−0.371373	−	0.928484i	$-0.621113\pi$
$727$	−20.0266	−0.742747	−0.371373	+	0.928484i	$0.621113\pi$
$728$	3.64429	0.135066
$729$	−13.6298	−0.504809
$730$	−4.45831	−0.165009
$731$	4.18195	0.154675
$732$	−1.34439	−0.0496901
$733$	46.0965	1.70261	0.851306	−	0.524669i	$-0.175811\pi$
$733$	46.0965	1.70261	0.851306	+	0.524669i	$0.175811\pi$
$734$	11.8600	0.437760
$735$	−5.27821	−0.194690
$736$	1.50740	0.0555637
$737$	5.29122	0.194904
$738$	18.0237	0.663463
$739$	−13.0612	−0.480462	−0.240231	−	0.970716i	$-0.577223\pi$
$739$	−13.0612	−0.480462	−0.240231	+	0.970716i	$0.577223\pi$
$740$	7.13321	0.262222
$741$	0.902058	0.0331379
$742$	6.72352	0.246828
$743$	−15.6807	−0.575269	−0.287635	−	0.957740i	$-0.592869\pi$
$743$	−15.6807	−0.575269	−0.287635	+	0.957740i	$0.592869\pi$
$744$	−0.320949	−0.0117666
$745$	18.9391	0.693877
$746$	29.1370	1.06678
$747$	0.877729	0.0321144
$748$	−0.519591	−0.0189981
$749$	5.35618	0.195710
$750$	6.05875	0.221234
$751$	−45.7780	−1.67046	−0.835231	−	0.549899i	$-0.814666\pi$
$751$	−45.7780	−1.67046	−0.835231	+	0.549899i	$0.814666\pi$
$752$	1.94410	0.0708941
$753$	3.67784	0.134028
$754$	15.8374	0.576763
$755$	31.3426	1.14067
$756$	−1.70915	−0.0621610
$757$	10.3839	0.377409	0.188705	−	0.982034i	$-0.439571\pi$
$757$	10.3839	0.377409	0.188705	+	0.982034i	$0.439571\pi$
$758$	−8.69451	−0.315799
$759$	0.778984	0.0282753
$760$	−0.423321	−0.0153555
$761$	27.5237	0.997735	0.498867	−	0.866678i	$-0.333749\pi$
$761$	27.5237	0.997735	0.498867	+	0.866678i	$0.333749\pi$
$762$	−4.20896	−0.152475
$763$	3.03569	0.109899
$764$	6.58409	0.238204
$765$	−2.17540	−0.0786516
$766$	17.0555	0.616240
$767$	51.1035	1.84524
$768$	−0.516772	−0.0186474
$769$	1.39711	0.0503811	0.0251905	−	0.999683i	$-0.491981\pi$
$769$	1.39711	0.0503811	0.0251905	+	0.999683i	$0.491981\pi$
$770$	−0.883787	−0.0318495
$771$	−1.20751	−0.0434875
$772$	14.5978	0.525386
$773$	−8.08782	−0.290899	−0.145449	−	0.989366i	$-0.546463\pi$
$773$	−8.08782	−0.290899	−0.145449	+	0.989366i	$0.546463\pi$
$774$	−21.9962	−0.790638
$775$	1.64776	0.0591893
$776$	6.38659	0.229265
$777$	−1.38816	−0.0498001
$778$	−23.0914	−0.827865
$779$	−1.82238	−0.0652935
$780$	5.00097	0.179064
$781$	14.1174	0.505159
$782$	−0.783234	−0.0280084
$783$	−7.42762	−0.265441
$784$	−6.66718	−0.238114
$785$	32.6861	1.16662
$786$	1.82629	0.0651416
$787$	46.0364	1.64102	0.820510	−	0.571632i	$-0.193689\pi$
$787$	46.0364	1.64102	0.820510	+	0.571632i	$0.193689\pi$
$788$	1.00000	0.0356235
$789$	14.7916	0.526594
$790$	−8.92498	−0.317536
$791$	−9.68354	−0.344307
$792$	2.73295	0.0971110
$793$	16.4338	0.583580
$794$	−14.3188	−0.508155
$795$	9.22653	0.327231
$796$	−22.2655	−0.789178
$797$	26.9455	0.954459	0.477229	−	0.878779i	$-0.341641\pi$
$797$	26.9455	0.954459	0.477229	+	0.878779i	$0.341641\pi$
$798$	0.0823808	0.00291625
$799$	−1.01014	−0.0357361
$800$	2.65312	0.0938020
$801$	−20.9079	−0.738743
$802$	33.6253	1.18735
$803$	−2.91021	−0.102699
$804$	−2.73435	−0.0964332
$805$	−1.33222	−0.0469547
$806$	3.92326	0.138191
$807$	7.55388	0.265909
$808$	11.6653	0.410383
$809$	−19.8717	−0.698651	−0.349325	−	0.937001i	$-0.613589\pi$
$809$	−19.8717	−0.698651	−0.349325	+	0.937001i	$0.613589\pi$
$810$	10.2148	0.358912
$811$	−24.2933	−0.853054	−0.426527	−	0.904475i	$-0.640263\pi$
$811$	−24.2933	−0.853054	−0.426527	+	0.904475i	$0.640263\pi$
$812$	1.44636	0.0507571
$813$	−16.8787	−0.591962
$814$	4.65628	0.163203
$815$	36.9065	1.29278
$816$	0.268510	0.00939974
$817$	2.22404	0.0778092
$818$	14.1008	0.493023
$819$	9.95964	0.348018
$820$	−10.1032	−0.352819
$821$	−23.7798	−0.829921	−0.414961	−	0.909839i	$-0.636205\pi$
$821$	−23.7798	−0.829921	−0.414961	+	0.909839i	$0.636205\pi$
$822$	−7.98214	−0.278409
$823$	−55.4091	−1.93144	−0.965721	−	0.259584i	$-0.916415\pi$
$823$	−55.4091	−1.93144	−0.965721	+	0.259584i	$0.916415\pi$
$824$	−0.865809	−0.0301619
$825$	1.37106	0.0477342
$826$	4.66705	0.162387
$827$	10.1210	0.351941	0.175971	−	0.984395i	$-0.443694\pi$
$827$	10.1210	0.351941	0.175971	+	0.984395i	$0.443694\pi$
$828$	4.11966	0.143168
$829$	27.9017	0.969066	0.484533	−	0.874773i	$-0.338990\pi$
$829$	27.9017	0.969066	0.484533	+	0.874773i	$0.338990\pi$
$830$	−0.492011	−0.0170779
$831$	−6.93088	−0.240430
$832$	6.31699	0.219002
$833$	3.46421	0.120028
$834$	3.41743	0.118336
$835$	−33.4465	−1.15746
$836$	−0.276328	−0.00955701
$837$	−1.83998	−0.0635991
$838$	11.0166	0.380562
$839$	11.6786	0.403190	0.201595	−	0.979469i	$-0.435388\pi$
$839$	11.6786	0.403190	0.201595	+	0.979469i	$0.435388\pi$
$840$	0.456716	0.0157582
$841$	−22.7144	−0.783256
$842$	−9.64998	−0.332560
$843$	1.15712	0.0398535
$844$	−12.5295	−0.431281
$845$	−41.2162	−1.41788
$846$	5.31313	0.182669
$847$	−0.576902	−0.0198226
$848$	11.6545	0.400218
$849$	−10.3930	−0.356686
$850$	−1.37854	−0.0472835
$851$	7.01890	0.240605
$852$	−7.29546	−0.249938
$853$	−41.6239	−1.42518	−0.712588	−	0.701583i	$-0.752477\pi$
$853$	−41.6239	−1.42518	−0.712588	+	0.701583i	$0.752477\pi$
$854$	1.50082	0.0513570
$855$	−1.15691	−0.0395657
$856$	9.28437	0.317333
$857$	−16.7955	−0.573724	−0.286862	−	0.957972i	$-0.592612\pi$
$857$	−16.7955	−0.573724	−0.286862	+	0.957972i	$0.592612\pi$
$858$	3.26444	0.111446
$859$	50.5448	1.72457	0.862283	−	0.506427i	$-0.169034\pi$
$859$	50.5448	1.72457	0.862283	+	0.506427i	$0.169034\pi$
$860$	12.3300	0.420449
$861$	1.96614	0.0670059
$862$	12.9828	0.442196
$863$	6.29987	0.214450	0.107225	−	0.994235i	$-0.465803\pi$
$863$	6.29987	0.214450	0.107225	+	0.994235i	$0.465803\pi$
$864$	−2.96263	−0.100791
$865$	30.2082	1.02711
$866$	−10.5182	−0.357424
$867$	8.64561	0.293620
$868$	0.358294	0.0121613
$869$	−5.82588	−0.197630
$870$	1.98480	0.0672911
$871$	33.4246	1.13255
$872$	5.26206	0.178196
$873$	17.4542	0.590736
$874$	−0.416538	−0.0140896
$875$	−6.76373	−0.228656
$876$	1.50392	0.0508127
$877$	25.5113	0.861456	0.430728	−	0.902482i	$-0.358257\pi$
$877$	25.5113	0.861456	0.430728	+	0.902482i	$0.358257\pi$
$878$	7.20297	0.243088
$879$	−6.44722	−0.217459
$880$	−1.53195	−0.0516421
$881$	−27.9488	−0.941620	−0.470810	−	0.882235i	$-0.656038\pi$
$881$	−27.9488	−0.941620	−0.470810	+	0.882235i	$0.656038\pi$
$882$	−18.2211	−0.613535
$883$	−22.1577	−0.745665	−0.372833	−	0.927899i	$-0.621613\pi$
$883$	−22.1577	−0.745665	−0.372833	+	0.927899i	$0.621613\pi$
$884$	−3.28225	−0.110394
$885$	6.40449	0.215284
$886$	20.2810	0.681354
$887$	8.67845	0.291394	0.145697	−	0.989329i	$-0.453458\pi$
$887$	8.67845	0.291394	0.145697	+	0.989329i	$0.453458\pi$
$888$	−2.40624	−0.0807480
$889$	4.69871	0.157590
$890$	11.7199	0.392852
$891$	6.66784	0.223381
$892$	−13.6319	−0.456430
$893$	−0.537210	−0.0179771
$894$	−6.38872	−0.213671
$895$	27.4084	0.916163
$896$	0.576902	0.0192730
$897$	4.92084	0.164302
$898$	31.5168	1.05173
$899$	1.55707	0.0519314
$900$	7.25084	0.241695
$901$	−6.05558	−0.201741
$902$	−6.59498	−0.219589
$903$	−2.39949	−0.0798499
$904$	−16.7854	−0.558274
$905$	33.1704	1.10262
$906$	−10.5728	−0.351256
$907$	−22.6484	−0.752027	−0.376013	−	0.926614i	$-0.622705\pi$
$907$	−22.6484	−0.752027	−0.376013	+	0.926614i	$0.622705\pi$
$908$	7.51079	0.249254
$909$	31.8806	1.05741
$910$	−5.58287	−0.185070
$911$	30.7384	1.01841	0.509204	−	0.860646i	$-0.329940\pi$
$911$	30.7384	1.01841	0.509204	+	0.860646i	$0.329940\pi$
$912$	0.142799	0.00472853
$913$	−0.321166	−0.0106290
$914$	31.8248	1.05267
$915$	2.05954	0.0680864
$916$	−13.1694	−0.435129
$917$	−2.03879	−0.0673268
$918$	1.53935	0.0508063
$919$	−22.1039	−0.729141	−0.364570	−	0.931176i	$-0.618784\pi$
$919$	−22.1039	−0.729141	−0.364570	+	0.931176i	$0.618784\pi$
$920$	−2.30927	−0.0761344
$921$	0.646334	0.0212974
$922$	15.4987	0.510423
$923$	89.1792	2.93537
$924$	0.298127	0.00980766
$925$	12.3537	0.406187
$926$	−39.0742	−1.28406
$927$	−2.36621	−0.0777166
$928$	2.50711	0.0822998
$929$	−5.23732	−0.171831	−0.0859154	−	0.996302i	$-0.527381\pi$
$929$	−5.23732	−0.171831	−0.0859154	+	0.996302i	$0.527381\pi$
$930$	0.491678	0.0161228
$931$	1.84233	0.0603799
$932$	−8.17542	−0.267795
$933$	−4.32941	−0.141739
$934$	−30.6437	−1.00269
$935$	0.795989	0.0260316
$936$	17.2640	0.564291
$937$	−8.29459	−0.270973	−0.135486	−	0.990779i	$-0.543260\pi$
$937$	−8.29459	−0.270973	−0.135486	+	0.990779i	$0.543260\pi$
$938$	3.05251	0.0996681
$939$	−7.97718	−0.260325
$940$	−2.97827	−0.0971406
$941$	−50.7882	−1.65565	−0.827825	−	0.560987i	$-0.810422\pi$
$941$	−50.7882	−1.65565	−0.827825	+	0.560987i	$0.810422\pi$
$942$	−11.0260	−0.359245
$943$	−9.94130	−0.323733
$944$	8.08984	0.263302
$945$	2.61833	0.0851743
$946$	8.04854	0.261681
$947$	−26.3951	−0.857724	−0.428862	−	0.903370i	$-0.641085\pi$
$947$	−26.3951	−0.857724	−0.428862	+	0.903370i	$0.641085\pi$
$948$	3.01065	0.0977815
$949$	−18.3838	−0.596763
$950$	−0.733132	−0.0237859
$951$	16.5297	0.536014
$952$	−0.299753	−0.00971506
$953$	49.6464	1.60820	0.804102	−	0.594492i	$-0.202647\pi$
$953$	49.6464	1.60820	0.804102	+	0.594492i	$0.202647\pi$
$954$	31.8512	1.03122
$955$	−10.0865	−0.326392
$956$	2.81584	0.0910707
$957$	1.29560	0.0418809
$958$	12.4403	0.401928
$959$	8.91092	0.287749
$960$	0.791670	0.0255510
$961$	−30.6143	−0.987557
$962$	29.4137	0.948336
$963$	25.3737	0.817656
$964$	8.59567	0.276848
$965$	−22.3631	−0.719895
$966$	0.449398	0.0144591
$967$	−8.50184	−0.273401	−0.136700	−	0.990612i	$-0.543650\pi$
$967$	−8.50184	−0.273401	−0.136700	+	0.990612i	$0.543650\pi$
$968$	−1.00000	−0.0321412
$969$	−0.0741969	−0.00238355
$970$	−9.78396	−0.314144
$971$	10.7205	0.344037	0.172018	−	0.985094i	$-0.444971\pi$
$971$	10.7205	0.344037	0.172018	+	0.985094i	$0.444971\pi$
$972$	−12.3336	−0.395601
$973$	−3.81507	−0.122306
$974$	40.5024	1.29778
$975$	8.66097	0.277373
$976$	2.60152	0.0832725
$977$	36.3637	1.16338	0.581690	−	0.813411i	$-0.302392\pi$
$977$	36.3637	1.16338	0.581690	+	0.813411i	$0.302392\pi$
$978$	−12.4496	−0.398096
$979$	7.65030	0.244505
$980$	10.2138	0.326268
$981$	14.3809	0.459147
$982$	−13.4456	−0.429067
$983$	16.5642	0.528315	0.264157	−	0.964480i	$-0.414906\pi$
$983$	16.5642	0.528315	0.264157	+	0.964480i	$0.414906\pi$
$984$	3.40810	0.108646
$985$	−1.53195	−0.0488121
$986$	−1.30267	−0.0414855
$987$	0.579589	0.0184485
$988$	−1.74556	−0.0555337
$989$	12.1324	0.385788
$990$	−4.18674	−0.133063
$991$	6.84666	0.217491	0.108746	−	0.994070i	$-0.465317\pi$
$991$	6.84666	0.217491	0.108746	+	0.994070i	$0.465317\pi$
$992$	0.621065	0.0197188
$993$	−4.56101	−0.144739
$994$	8.14433	0.258323
$995$	34.1096	1.08135
$996$	0.165970	0.00525895
$997$	27.3637	0.866616	0.433308	−	0.901246i	$-0.357346\pi$
$997$	27.3637	0.866616	0.433308	+	0.901246i	$0.357346\pi$
$998$	42.6557	1.35024
$999$	−13.7948	−0.436449

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.a.1.6	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.a.1.6	✓	15	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.516772 q^{3} +1.00000 q^{4} -1.53195 q^{5} +0.516772 q^{6} -0.576902 q^{7} -1.00000 q^{8} -2.73295 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.516772 q^{3} +1.00000 q^{4} -1.53195 q^{5} +0.516772 q^{6} -0.576902 q^{7} -1.00000 q^{8} -2.73295 q^{9} +1.53195 q^{10} +1.00000 q^{11} -0.516772 q^{12} +6.31699 q^{13} +0.576902 q^{14} +0.791670 q^{15} +1.00000 q^{16} -0.519591 q^{17} +2.73295 q^{18} -0.276328 q^{19} -1.53195 q^{20} +0.298127 q^{21} -1.00000 q^{22} -1.50740 q^{23} +0.516772 q^{24} -2.65312 q^{25} -6.31699 q^{26} +2.96263 q^{27} -0.576902 q^{28} -2.50711 q^{29} -0.791670 q^{30} -0.621065 q^{31} -1.00000 q^{32} -0.516772 q^{33} +0.519591 q^{34} +0.883787 q^{35} -2.73295 q^{36} -4.65628 q^{37} +0.276328 q^{38} -3.26444 q^{39} +1.53195 q^{40} +6.59498 q^{41} -0.298127 q^{42} -8.04854 q^{43} +1.00000 q^{44} +4.18674 q^{45} +1.50740 q^{46} +1.94410 q^{47} -0.516772 q^{48} -6.66718 q^{49} +2.65312 q^{50} +0.268510 q^{51} +6.31699 q^{52} +11.6545 q^{53} -2.96263 q^{54} -1.53195 q^{55} +0.576902 q^{56} +0.142799 q^{57} +2.50711 q^{58} +8.08984 q^{59} +0.791670 q^{60} +2.60152 q^{61} +0.621065 q^{62} +1.57664 q^{63} +1.00000 q^{64} -9.67733 q^{65} +0.516772 q^{66} +5.29122 q^{67} -0.519591 q^{68} +0.778984 q^{69} -0.883787 q^{70} +14.1174 q^{71} +2.73295 q^{72} -2.91021 q^{73} +4.65628 q^{74} +1.37106 q^{75} -0.276328 q^{76} -0.576902 q^{77} +3.26444 q^{78} -5.82588 q^{79} -1.53195 q^{80} +6.66784 q^{81} -6.59498 q^{82} -0.321166 q^{83} +0.298127 q^{84} +0.795989 q^{85} +8.04854 q^{86} +1.29560 q^{87} -1.00000 q^{88} +7.65030 q^{89} -4.18674 q^{90} -3.64429 q^{91} -1.50740 q^{92} +0.320949 q^{93} -1.94410 q^{94} +0.423321 q^{95} +0.516772 q^{96} -6.38659 q^{97} +6.66718 q^{98} -2.73295 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9}+O(q^{10}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9} + 7 q^{10} + 15 q^{11} - q^{12} - q^{13} - q^{14} - 6 q^{15} + 15 q^{16} - 6 q^{17} - 2 q^{18} - 14 q^{19} - 7 q^{20} - 3 q^{21} - 15 q^{22} + 2 q^{23} + q^{24} - 10 q^{25} + q^{26} - 7 q^{27} + q^{28} + 8 q^{29} + 6 q^{30} - 33 q^{31} - 15 q^{32} - q^{33} + 6 q^{34} - 8 q^{35} + 2 q^{36} - 9 q^{37} + 14 q^{38} - 9 q^{39} + 7 q^{40} - 10 q^{41} + 3 q^{42} - 6 q^{43} + 15 q^{44} - 20 q^{45} - 2 q^{46} - q^{47} - q^{48} - 30 q^{49} + 10 q^{50} + 12 q^{51} - q^{52} + 6 q^{53} + 7 q^{54} - 7 q^{55} - q^{56} - 24 q^{57} - 8 q^{58} - 15 q^{59} - 6 q^{60} - 25 q^{61} + 33 q^{62} + 12 q^{63} + 15 q^{64} + 31 q^{65} + q^{66} - 13 q^{67} - 6 q^{68} - 43 q^{69} + 8 q^{70} - 4 q^{71} - 2 q^{72} - 4 q^{73} + 9 q^{74} - 5 q^{75} - 14 q^{76} + q^{77} + 9 q^{78} - 20 q^{79} - 7 q^{80} + 11 q^{81} + 10 q^{82} + q^{83} - 3 q^{84} - q^{85} + 6 q^{86} + 22 q^{87} - 15 q^{88} - 41 q^{89} + 20 q^{90} - 31 q^{91} + 2 q^{92} + 14 q^{93} + q^{94} + 41 q^{95} + q^{96} - 57 q^{97} + 30 q^{98} + 2 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9 + 7 * q^10 + 15 * q^11 - q^12 - q^13 - q^14 - 6 * q^15 + 15 * q^16 - 6 * q^17 - 2 * q^18 - 14 * q^19 - 7 * q^20 - 3 * q^21 - 15 * q^22 + 2 * q^23 + q^24 - 10 * q^25 + q^26 - 7 * q^27 + q^28 + 8 * q^29 + 6 * q^30 - 33 * q^31 - 15 * q^32 - q^33 + 6 * q^34 - 8 * q^35 + 2 * q^36 - 9 * q^37 + 14 * q^38 - 9 * q^39 + 7 * q^40 - 10 * q^41 + 3 * q^42 - 6 * q^43 + 15 * q^44 - 20 * q^45 - 2 * q^46 - q^47 - q^48 - 30 * q^49 + 10 * q^50 + 12 * q^51 - q^52 + 6 * q^53 + 7 * q^54 - 7 * q^55 - q^56 - 24 * q^57 - 8 * q^58 - 15 * q^59 - 6 * q^60 - 25 * q^61 + 33 * q^62 + 12 * q^63 + 15 * q^64 + 31 * q^65 + q^66 - 13 * q^67 - 6 * q^68 - 43 * q^69 + 8 * q^70 - 4 * q^71 - 2 * q^72 - 4 * q^73 + 9 * q^74 - 5 * q^75 - 14 * q^76 + q^77 + 9 * q^78 - 20 * q^79 - 7 * q^80 + 11 * q^81 + 10 * q^82 + q^83 - 3 * q^84 - q^85 + 6 * q^86 + 22 * q^87 - 15 * q^88 - 41 * q^89 + 20 * q^90 - 31 * q^91 + 2 * q^92 + 14 * q^93 + q^94 + 41 * q^95 + q^96 - 57 * q^97 + 30 * q^98 + 2 * q^99

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