LMFDB - Embedded newform 644.2.c.a.183.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,2,Mod(183,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("644.183");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	644.c (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$5.14236589017$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			183.22
Character	$\chi$	$=$	644.183
Dual form			644.2.c.a.183.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.425020 + 1.34884i) q^{2} -1.30946i q^{3} +(-1.63872 + 1.14656i) q^{4} -0.616901i q^{5} +(1.76625 - 0.556549i) q^{6} -1.00000 q^{7} +(-2.24301 - 1.72305i) q^{8} +1.28530 q^{9} +O(q^{10})$	\(q+(0.425020 + 1.34884i) q^{2} -1.30946i q^{3} +(-1.63872 + 1.14656i) q^{4} -0.616901i q^{5} +(1.76625 - 0.556549i) q^{6} -1.00000 q^{7} +(-2.24301 - 1.72305i) q^{8} +1.28530 q^{9} +(0.832098 - 0.262195i) q^{10} +1.66304 q^{11} +(1.50139 + 2.14584i) q^{12} +3.32836 q^{13} +(-0.425020 - 1.34884i) q^{14} -0.807810 q^{15} +(1.37078 - 3.75779i) q^{16} -7.61798i q^{17} +(0.546279 + 1.73366i) q^{18} -5.00998 q^{19} +(0.707317 + 1.01093i) q^{20} +1.30946i q^{21} +(0.706827 + 2.24317i) q^{22} +(3.94135 + 2.73236i) q^{23} +(-2.25627 + 2.93715i) q^{24} +4.61943 q^{25} +(1.41462 + 4.48941i) q^{26} -5.61145i q^{27} +(1.63872 - 1.14656i) q^{28} +8.34573 q^{29} +(-0.343336 - 1.08960i) q^{30} +1.61791i q^{31} +(5.65125 + 0.251819i) q^{32} -2.17770i q^{33} +(10.2754 - 3.23779i) q^{34} +0.616901i q^{35} +(-2.10624 + 1.47368i) q^{36} -1.52327i q^{37} +(-2.12934 - 6.75764i) q^{38} -4.35837i q^{39} +(-1.06295 + 1.38372i) q^{40} -5.75587 q^{41} +(-1.76625 + 0.556549i) q^{42} +6.32746 q^{43} +(-2.72526 + 1.90679i) q^{44} -0.792904i q^{45} +(-2.01035 + 6.47754i) q^{46} +0.313665i q^{47} +(-4.92069 - 1.79499i) q^{48} +1.00000 q^{49} +(1.96335 + 6.23086i) q^{50} -9.97548 q^{51} +(-5.45424 + 3.81618i) q^{52} -1.93276i q^{53} +(7.56893 - 2.38498i) q^{54} -1.02593i q^{55} +(2.24301 + 1.72305i) q^{56} +6.56039i q^{57} +(3.54711 + 11.2570i) q^{58} +0.633620i q^{59} +(1.32377 - 0.926207i) q^{60} -2.00565i q^{61} +(-2.18230 + 0.687645i) q^{62} -1.28530 q^{63} +(2.06223 + 7.72963i) q^{64} -2.05327i q^{65} +(2.93736 - 0.925565i) q^{66} -12.5929 q^{67} +(8.73451 + 12.4837i) q^{68} +(3.57792 - 5.16106i) q^{69} +(-0.832098 + 0.262195i) q^{70} -5.31276i q^{71} +(-2.88295 - 2.21463i) q^{72} -5.29417 q^{73} +(2.05465 - 0.647423i) q^{74} -6.04899i q^{75} +(8.20993 - 5.74426i) q^{76} -1.66304 q^{77} +(5.87873 - 1.85240i) q^{78} -7.12582 q^{79} +(-2.31818 - 0.845634i) q^{80} -3.49209 q^{81} +(-2.44636 - 7.76372i) q^{82} +8.64045 q^{83} +(-1.50139 - 2.14584i) q^{84} -4.69954 q^{85} +(2.68930 + 8.53471i) q^{86} -10.9284i q^{87} +(-3.73023 - 2.86550i) q^{88} +15.3479i q^{89} +(1.06950 - 0.337000i) q^{90} -3.32836 q^{91} +(-9.59157 + 0.0414594i) q^{92} +2.11860 q^{93} +(-0.423082 + 0.133314i) q^{94} +3.09066i q^{95} +(0.329748 - 7.40011i) q^{96} +2.19515i q^{97} +(0.425020 + 1.34884i) q^{98} +2.13751 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + q^{2} - 3 q^{4} + q^{6} - 36 q^{7} - 2 q^{8} - 36 q^{9}+O(q^{10}) $ 36 * q + q^2 - 3 * q^4 + q^6 - 36 * q^7 - 2 * q^8 - 36 * q^9	$ 36 q + q^{2} - 3 q^{4} + q^{6} - 36 q^{7} - 2 q^{8} - 36 q^{9} + 8 q^{11} - 3 q^{12} - q^{14} + 8 q^{15} + 9 q^{16} - 8 q^{18} + 8 q^{19} - 14 q^{20} + 24 q^{22} - 8 q^{23} - 4 q^{24} - 36 q^{25} + 7 q^{26} + 3 q^{28} - 8 q^{29} - 9 q^{32} + 14 q^{34} + 14 q^{36} - q^{42} - 40 q^{43} + 16 q^{44} - 9 q^{46} - 39 q^{48} + 36 q^{49} - 43 q^{50} + 25 q^{52} - 33 q^{54} + 2 q^{56} + 19 q^{58} + 76 q^{60} - 5 q^{62} + 36 q^{63} + 12 q^{64} + 50 q^{66} + 8 q^{67} - 60 q^{68} + 28 q^{69} - 36 q^{72} + 36 q^{74} - 8 q^{77} + 17 q^{78} + 40 q^{79} - 50 q^{80} + 28 q^{81} - 17 q^{82} + 3 q^{84} - 24 q^{85} - 16 q^{86} - 28 q^{88} - 98 q^{90} + 19 q^{92} + 8 q^{93} + 35 q^{94} + 91 q^{96} + q^{98} - 24 q^{99}+O(q^{100}) $ 36 * q + q^2 - 3 * q^4 + q^6 - 36 * q^7 - 2 * q^8 - 36 * q^9 + 8 * q^11 - 3 * q^12 - q^14 + 8 * q^15 + 9 * q^16 - 8 * q^18 + 8 * q^19 - 14 * q^20 + 24 * q^22 - 8 * q^23 - 4 * q^24 - 36 * q^25 + 7 * q^26 + 3 * q^28 - 8 * q^29 - 9 * q^32 + 14 * q^34 + 14 * q^36 - q^42 - 40 * q^43 + 16 * q^44 - 9 * q^46 - 39 * q^48 + 36 * q^49 - 43 * q^50 + 25 * q^52 - 33 * q^54 + 2 * q^56 + 19 * q^58 + 76 * q^60 - 5 * q^62 + 36 * q^63 + 12 * q^64 + 50 * q^66 + 8 * q^67 - 60 * q^68 + 28 * q^69 - 36 * q^72 + 36 * q^74 - 8 * q^77 + 17 * q^78 + 40 * q^79 - 50 * q^80 + 28 * q^81 - 17 * q^82 + 3 * q^84 - 24 * q^85 - 16 * q^86 - 28 * q^88 - 98 * q^90 + 19 * q^92 + 8 * q^93 + 35 * q^94 + 91 * q^96 + q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	0.425020	+	1.34884i	0.300535	+	0.953771i
$2$	0.425020	+	1.34884i	0.300535	+	0.953771i
$3$		−	1.30946i		−	0.756020i	−0.925802	−	0.378010i	$-0.876609\pi$
$3$		−	1.30946i		−	0.756020i	0.925802	−	0.378010i	$-0.123391\pi$
$4$	−1.63872	+	1.14656i	−0.819358	+	0.573282i
$5$		−	0.616901i		−	0.275887i	−0.990440	−	0.137943i	$-0.955951\pi$
$5$		−	0.616901i		−	0.275887i	0.990440	−	0.137943i	$-0.0440492\pi$
$6$	1.76625	−	0.556549i	0.721070	−	0.227210i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−2.24301	−	1.72305i	−0.793025	−	0.609188i
$9$	1.28530			0.428434
$10$	0.832098	−	0.262195i	0.263133	−	0.0829135i
$11$	1.66304			0.501426			0.250713	−	0.968061i	$-0.419335\pi$
$11$	1.66304			0.501426			0.250713	+	0.968061i	$0.419335\pi$
$12$	1.50139	+	2.14584i	0.433413	+	0.619451i
$13$	3.32836			0.923121			0.461561	−	0.887109i	$-0.347290\pi$
$13$	3.32836			0.923121			0.461561	+	0.887109i	$0.347290\pi$
$14$	−0.425020	−	1.34884i	−0.113591	−	0.360492i
$15$	−0.807810			−0.208576
$16$	1.37078	−	3.75779i	0.342695	−	0.939447i
$17$		−	7.61798i		−	1.84763i	−0.382838	−	0.923816i	$-0.625053\pi$
$17$		−	7.61798i		−	1.84763i	0.382838	−	0.923816i	$-0.374947\pi$
$18$	0.546279	+	1.73366i	0.128759	+	0.408628i
$19$	−5.00998			−1.14937			−0.574684	−	0.818376i	$-0.694875\pi$
$19$	−5.00998			−1.14937			−0.574684	+	0.818376i	$0.694875\pi$
$20$	0.707317	+	1.01093i	0.158161	+	0.226050i
$21$			1.30946i			0.285749i
$22$	0.706827	+	2.24317i	0.150696	+	0.478246i
$23$	3.94135	+	2.73236i	0.821828	+	0.569735i
$23$	3.94135	+	2.73236i	0.821828	+	0.569735i
$24$	−2.25627	+	2.93715i	−0.460559	+	0.599543i
$25$	4.61943			0.923887
$26$	1.41462	+	4.48941i	0.277430	+	0.880446i
$27$		−	5.61145i		−	1.07992i
$28$	1.63872	−	1.14656i	0.309688	−	0.216680i
$29$	8.34573			1.54976			0.774882	−	0.632106i	$-0.217809\pi$
$29$	8.34573			1.54976			0.774882	+	0.632106i	$0.217809\pi$
$30$	−0.343336	−	1.08960i	−0.0626842	−	0.198933i
$31$			1.61791i			0.290585i	0.989389	+	0.145293i	$0.0464124\pi$
$31$			1.61791i			0.290585i	−0.989389	+	0.145293i	$0.953588\pi$
$32$	5.65125	+	0.251819i	0.999009	+	0.0445158i
$33$		−	2.17770i		−	0.379088i
$34$	10.2754	−	3.23779i	1.76222	−	0.555277i
$35$			0.616901i			0.104275i
$36$	−2.10624	+	1.47368i	−0.351041	+	0.245614i
$37$		−	1.52327i		−	0.250425i	−0.992130	−	0.125212i	$-0.960039\pi$
$37$		−	1.52327i		−	0.250425i	0.992130	−	0.125212i	$-0.0399612\pi$
$38$	−2.12934	−	6.75764i	−0.345425	−	1.09623i
$39$		−	4.35837i		−	0.697898i
$40$	−1.06295	+	1.38372i	−0.168067	+	0.218785i
$41$	−5.75587			−0.898915			−0.449458	−	0.893302i	$-0.648383\pi$
$41$	−5.75587			−0.898915			−0.449458	+	0.893302i	$0.648383\pi$
$42$	−1.76625	+	0.556549i	−0.272539	+	0.0858774i
$43$	6.32746			0.964929			0.482465	−	0.875916i	$-0.339742\pi$
$43$	6.32746			0.964929			0.482465	+	0.875916i	$0.339742\pi$
$44$	−2.72526	+	1.90679i	−0.410848	+	0.287459i
$45$		−	0.792904i		−	0.118199i
$46$	−2.01035	+	6.47754i	−0.296409	+	0.955061i
$47$			0.313665i			0.0457527i	0.999738	+	0.0228764i	$0.00728241\pi$
$47$			0.313665i			0.0457527i	−0.999738	+	0.0228764i	$0.992718\pi$
$48$	−4.92069	−	1.79499i	−0.710241	−	0.259084i
$49$	1.00000			0.142857
$50$	1.96335	+	6.23086i	0.277660	+	0.881176i
$51$	−9.97548			−1.39685
$52$	−5.45424	+	3.81618i	−0.756367	+	0.529209i
$53$		−	1.93276i		−	0.265485i	−0.991151	−	0.132742i	$-0.957622\pi$
$53$		−	1.93276i		−	0.265485i	0.991151	−	0.132742i	$-0.0423783\pi$
$54$	7.56893	−	2.38498i	1.03000	−	0.324555i
$55$		−	1.02593i		−	0.138337i
$56$	2.24301	+	1.72305i	0.299735	+	0.230252i
$57$			6.56039i			0.868945i
$58$	3.54711	+	11.2570i	0.465758	+	1.47812i
$59$			0.633620i			0.0824903i	0.999149	+	0.0412452i	$0.0131325\pi$
$59$			0.633620i			0.0824903i	−0.999149	+	0.0412452i	$0.986868\pi$
$60$	1.32377	−	0.926207i	0.170898	−	0.119573i
$61$		−	2.00565i		−	0.256797i	−0.991723	−	0.128399i	$-0.959016\pi$
$61$		−	2.00565i		−	0.256797i	0.991723	−	0.128399i	$-0.0409837\pi$
$62$	−2.18230	+	0.687645i	−0.277152	+	0.0873310i
$63$	−1.28530			−0.161933
$64$	2.06223	+	7.72963i	0.257779	+	0.966204i
$65$		−	2.05327i		−	0.254677i
$66$	2.93736	−	0.925565i	0.361563	−	0.113929i
$67$	−12.5929			−1.53847			−0.769234	−	0.638967i	$-0.779362\pi$
$67$	−12.5929			−1.53847			−0.769234	+	0.638967i	$0.779362\pi$
$68$	8.73451	+	12.4837i	1.05921	+	1.51387i
$69$	3.57792	−	5.16106i	0.430731	−	0.621318i
$70$	−0.832098	+	0.262195i	−0.0994547	+	0.0313383i
$71$		−	5.31276i		−	0.630509i	−0.949007	−	0.315254i	$-0.897910\pi$
$71$		−	5.31276i		−	0.630509i	0.949007	−	0.315254i	$-0.102090\pi$
$72$	−2.88295	−	2.21463i	−0.339759	−	0.260997i
$73$	−5.29417			−0.619635			−0.309818	−	0.950796i	$-0.600268\pi$
$73$	−5.29417			−0.619635			−0.309818	+	0.950796i	$0.600268\pi$
$74$	2.05465	−	0.647423i	0.238848	−	0.0752613i
$75$		−	6.04899i		−	0.698477i
$76$	8.20993	−	5.74426i	0.941743	−	0.658912i
$77$	−1.66304			−0.189521
$78$	5.87873	−	1.85240i	0.665635	−	0.209743i
$79$	−7.12582			−0.801718			−0.400859	−	0.916140i	$-0.631288\pi$
$79$	−7.12582			−0.801718			−0.400859	+	0.916140i	$0.631288\pi$
$80$	−2.31818	−	0.845634i	−0.259181	−	0.0945448i
$81$	−3.49209			−0.388011
$82$	−2.44636	−	7.76372i	−0.270155	−	0.857359i
$83$	8.64045			0.948413			0.474206	−	0.880414i	$-0.342735\pi$
$83$	8.64045			0.948413			0.474206	+	0.880414i	$0.342735\pi$
$84$	−1.50139	−	2.14584i	−0.163815	−	0.234130i
$85$	−4.69954			−0.509736
$86$	2.68930	+	8.53471i	0.289995	+	0.920321i
$87$		−	10.9284i		−	1.17165i
$88$	−3.73023	−	2.86550i	−0.397644	−	0.305463i
$89$			15.3479i			1.62687i	0.581654	+	0.813436i	$0.302406\pi$
$89$			15.3479i			1.62687i	−0.581654	+	0.813436i	$0.697594\pi$
$90$	1.06950	−	0.337000i	0.112735	−	0.0355229i
$91$	−3.32836			−0.348907
$92$	−9.59157	+	0.0414594i	−0.999991	+	0.00432245i
$93$	2.11860			0.219688
$94$	−0.423082	+	0.133314i	−0.0436376	+	0.0137503i
$95$			3.09066i			0.317095i
$96$	0.329748	−	7.40011i	0.0336548	−	0.755270i
$97$			2.19515i			0.222883i	0.993771	+	0.111442i	$0.0355468\pi$
$97$			2.19515i			0.222883i	−0.993771	+	0.111442i	$0.964453\pi$
$98$	0.425020	+	1.34884i	0.0429335	+	0.136253i
$99$	2.13751			0.214828
$100$	−7.56994	+	5.29648i	−0.756994	+	0.529648i
$101$	−18.6063			−1.85140			−0.925698	−	0.378263i	$-0.876521\pi$
$101$	−18.6063			−1.85140			−0.925698	+	0.378263i	$0.876521\pi$
$102$	−4.23978	−	13.4553i	−0.419801	−	1.33227i
$103$	14.1583			1.39506			0.697532	−	0.716554i	$-0.254282\pi$
$103$	14.1583			1.39506			0.697532	+	0.716554i	$0.254282\pi$
$104$	−7.46556	−	5.73492i	−0.732059	−	0.562355i
$105$	0.807810			0.0788342
$106$	2.60697	−	0.821461i	0.253212	−	0.0797873i
$107$	−12.0171			−1.16174			−0.580870	−	0.813996i	$-0.697287\pi$
$107$	−12.0171			−1.16174			−0.580870	+	0.813996i	$0.697287\pi$
$108$	6.43389	+	9.19557i	0.619102	+	0.884845i
$109$			11.1834i			1.07117i	0.844480	+	0.535587i	$0.179910\pi$
$109$			11.1834i			1.07117i	−0.844480	+	0.535587i	$0.820090\pi$
$110$	1.38382	−	0.436042i	0.131942	−	0.0415750i
$111$	−1.99467			−0.189326
$112$	−1.37078	+	3.75779i	−0.129526	+	0.355078i
$113$			20.8589i			1.96224i	0.193394	+	0.981121i	$0.438051\pi$
$113$			20.8589i			1.96224i	−0.193394	+	0.981121i	$0.561949\pi$
$114$	−8.84889	+	2.78830i	−0.828774	+	0.261148i
$115$	1.68559	−	2.43142i	0.157182	−	0.226731i
$116$	−13.6763	+	9.56893i	−1.26981	+	0.888452i
$117$	4.27795			0.395496
$118$	−0.854649	+	0.269301i	−0.0786769	+	0.0247912i
$119$			7.61798i			0.698339i
$120$	1.81193	+	1.39189i	0.165406	+	0.127062i
$121$	−8.23429			−0.748571
$122$	2.70529	−	0.852441i	0.244926	−	0.0771764i
$123$			7.53710i			0.679598i
$124$	−1.85504	−	2.65130i	−0.166587	−	0.238093i
$125$		−	5.93424i		−	0.530774i
$126$	−0.546279	−	1.73366i	−0.0486664	−	0.154447i
$127$		−	13.5053i		−	1.19840i	−0.800599	−	0.599200i	$-0.795485\pi$
$127$		−	13.5053i		−	1.19840i	0.800599	−	0.599200i	$-0.204515\pi$
$128$	−9.54951	+	6.06686i	−0.844066	+	0.536240i
$129$		−	8.28559i		−	0.729506i
$130$	2.76952	−	0.872681i	0.242903	−	0.0765392i
$131$			3.41155i			0.298069i	0.988832	+	0.149034i	$0.0476165\pi$
$131$			3.41155i			0.298069i	−0.988832	+	0.149034i	$0.952384\pi$
$132$	2.49687	+	3.56863i	0.217325	+	0.310609i
$133$	5.00998			0.434420
$134$	−5.35224	−	16.9858i	−0.462363	−	1.46735i
$135$	−3.46171			−0.297937
$136$	−13.1261	+	17.0872i	−1.12556	+	1.46522i
$137$			14.0285i			1.19853i	0.800550	+	0.599267i	$0.204541\pi$
$137$			14.0285i			1.19853i	−0.800550	+	0.599267i	$0.795459\pi$
$138$	8.48211	+	2.63248i	0.722045	+	0.224091i
$139$		−	18.8883i		−	1.60208i	−0.598608	−	0.801042i	$-0.704279\pi$
$139$		−	18.8883i		−	1.60208i	0.598608	−	0.801042i	$-0.295721\pi$
$140$	−0.707317	−	1.01093i	−0.0597792	−	0.0854388i
$141$	0.410733			0.0345900
$142$	7.16604	−	2.25803i	0.601361	−	0.189490i
$143$	5.53521			0.462877
$144$	1.76186	−	4.82989i	0.146822	−	0.402491i
$145$		−	5.14849i		−	0.427559i
$146$	−2.25013	−	7.14096i	−0.186222	−	0.590990i
$147$		−	1.30946i		−	0.108003i
$148$	1.74653	+	2.49621i	0.143564	+	0.205188i
$149$		−	19.3226i		−	1.58297i	−0.611188	−	0.791485i	$-0.709308\pi$
$149$		−	19.3226i		−	1.58297i	0.611188	−	0.791485i	$-0.290692\pi$
$150$	8.15909	−	2.57094i	0.666187	−	0.209916i
$151$		−	0.737203i		−	0.0599927i	−0.999550	−	0.0299964i	$-0.990450\pi$
$151$		−	0.737203i		−	0.0599927i	0.999550	−	0.0299964i	$-0.00954957\pi$
$152$	11.2375	+	8.63242i	0.911478	+	0.700181i
$153$		−	9.79140i		−	0.791588i
$154$	−0.706827	−	2.24317i	−0.0569577	−	0.180760i
$155$	0.998091			0.0801686
$156$	4.99716	+	7.14213i	0.400093	+	0.571828i
$157$		−	17.5308i		−	1.39911i	−0.714580	−	0.699554i	$-0.753382\pi$
$157$		−	17.5308i		−	1.39911i	0.714580	−	0.699554i	$-0.246618\pi$
$158$	−3.02862	−	9.61156i	−0.240944	−	0.764655i
$159$	−2.53088			−0.200712
$160$	0.155348	−	3.48626i	0.0122813	−	0.275613i
$161$	−3.94135	−	2.73236i	−0.310622	−	0.215340i
$162$	−1.48421	−	4.71026i	−0.116611	−	0.370073i
$163$			8.51837i			0.667210i	0.942713	+	0.333605i	$0.108265\pi$
$163$			8.51837i			0.667210i	−0.942713	+	0.333605i	$0.891735\pi$
$164$	9.43223	−	6.59947i	0.736533	−	0.515332i
$165$	−1.34342			−0.104585
$166$	3.67237	+	11.6545i	0.285031	+	0.904568i
$167$			22.4393i			1.73641i	0.496210	+	0.868203i	$0.334725\pi$
$167$			22.4393i			1.73641i	−0.496210	+	0.868203i	$0.665275\pi$
$168$	2.25627	−	2.93715i	0.174075	−	0.226606i
$169$	−1.92201			−0.147847
$170$	−1.99740	−	6.33890i	−0.153193	−	0.486172i
$171$	−6.43933			−0.492428
$172$	−10.3689	+	7.25485i	−0.790622	+	0.553177i
$173$	9.14923			0.695603			0.347801	−	0.937568i	$-0.386928\pi$
$173$	9.14923			0.695603			0.347801	+	0.937568i	$0.386928\pi$
$174$	14.7407	−	4.64481i	1.11749	−	0.352122i
$175$	−4.61943			−0.349196
$176$	2.27966	−	6.24936i	0.171836	−	0.471064i
$177$	0.829703			0.0623643
$178$	−20.7018	+	6.52316i	−1.55166	+	0.488931i
$179$		−	1.33240i		−	0.0995879i	−0.998760	−	0.0497939i	$-0.984144\pi$
$179$		−	1.33240i		−	0.0995879i	0.998760	−	0.0497939i	$-0.0158565\pi$
$180$	0.909116	+	1.29934i	0.0677615	+	0.0968474i
$181$			13.7083i			1.01893i	0.860492	+	0.509464i	$0.170156\pi$
$181$			13.7083i			1.01893i	−0.860492	+	0.509464i	$0.829844\pi$
$182$	−1.41462	−	4.48941i	−0.104859	−	0.332777i
$183$	−2.62633			−0.194144
$184$	−4.13253	−	12.9198i	−0.304654	−	0.952463i
$185$	−0.939710			−0.0690888
$186$	0.900447	+	2.85764i	0.0660239	+	0.209532i
$187$		−	12.6690i		−	0.926451i
$188$	−0.359637	−	0.514007i	−0.0262292	−	0.0374878i
$189$			5.61145i			0.408173i
$190$	−4.16879	+	1.31359i	−0.302436	+	0.0952980i
$191$	18.3555			1.32816			0.664078	−	0.747664i	$-0.268824\pi$
$191$	18.3555			1.32816			0.664078	+	0.747664i	$0.268824\pi$
$192$	10.1217	−	2.70042i	0.730469	−	0.194886i
$193$	4.91177			0.353557			0.176779	−	0.984251i	$-0.443432\pi$
$193$	4.91177			0.353557			0.176779	+	0.984251i	$0.443432\pi$
$194$	−2.96089	+	0.932982i	−0.212580	+	0.0669842i
$195$	−2.68868			−0.192541
$196$	−1.63872	+	1.14656i	−0.117051	+	0.0818975i
$197$	21.1682			1.50817			0.754086	−	0.656776i	$-0.228080\pi$
$197$	21.1682			1.50817			0.754086	+	0.656776i	$0.228080\pi$
$198$	0.908486	+	2.88315i	0.0645633	+	0.204897i
$199$	0.115462			0.00818487			0.00409243	−	0.999992i	$-0.498697\pi$
$199$	0.115462			0.00818487			0.00409243	+	0.999992i	$0.498697\pi$
$200$	−10.3615	−	7.95949i	−0.732666	−	0.562821i
$201$			16.4900i			1.16311i
$202$	−7.90805	−	25.0968i	−0.556409	−	1.76581i
$203$	−8.34573			−0.585756
$204$	16.3470	−	11.4375i	1.14452	−	0.800787i
$205$			3.55080i			0.247999i
$206$	6.01758	+	19.0973i	0.419265	+	1.33057i
$207$	5.06582	+	3.51190i	0.352099	+	0.244094i
$208$	4.56244	−	12.5073i	0.316349	−	0.867223i
$209$	−8.33181			−0.576323
$210$	0.343336	+	1.08960i	0.0236924	+	0.0751898i
$211$		−	9.77425i		−	0.672887i	−0.941704	−	0.336443i	$-0.890776\pi$
$211$		−	9.77425i		−	0.672887i	0.941704	−	0.336443i	$-0.109224\pi$
$212$	2.21603	+	3.16724i	0.152198	+	0.217527i
$213$	−6.95688			−0.476677
$214$	−5.10752	−	16.2091i	−0.349143	−	1.10803i
$215$		−	3.90342i		−	0.266211i
$216$	−9.66879	+	12.5866i	−0.657878	+	0.856408i
$217$		−	1.61791i		−	0.109831i
$218$	−15.0845	+	4.75316i	−1.02165	+	0.321925i
$219$			6.93252i			0.468457i
$220$	1.17630	+	1.68121i	0.0793061	+	0.113347i
$221$		−	25.3554i		−	1.70559i
$222$	−0.847777	−	2.69049i	−0.0568991	−	0.180574i
$223$			8.54931i			0.572504i	0.958154	+	0.286252i	$0.0924095\pi$
$223$			8.54931i			0.572504i	−0.958154	+	0.286252i	$0.907591\pi$
$224$	−5.65125	−	0.251819i	−0.377590	−	0.0168254i
$225$	5.93737			0.395824
$226$	−28.1353	+	8.86546i	−1.87153	+	0.589722i
$227$	26.3417			1.74836			0.874179	−	0.485604i	$-0.161400\pi$
$227$	26.3417			1.74836			0.874179	+	0.485604i	$0.161400\pi$
$228$	−7.52191	−	10.7506i	−0.498151	−	0.711977i
$229$			1.84935i			0.122209i	0.998131	+	0.0611044i	$0.0194623\pi$
$229$			1.84935i			0.122209i	−0.998131	+	0.0611044i	$0.980538\pi$
$230$	3.99600	+	1.24018i	0.263488	+	0.0817753i
$231$			2.17770i			0.143282i
$232$	−18.7196	−	14.3801i	−1.22900	−	0.944098i
$233$	−8.46427			−0.554513			−0.277256	−	0.960796i	$-0.589425\pi$
$233$	−8.46427			−0.554513			−0.277256	+	0.960796i	$0.589425\pi$
$234$	1.81821	+	5.77025i	0.118860	+	0.377213i
$235$	0.193500			0.0126226
$236$	−0.726486	−	1.03832i	−0.0472902	−	0.0675891i
$237$			9.33101i			0.606114i
$238$	−10.2754	+	3.23779i	−0.666055	+	0.209875i
$239$			21.9654i			1.42082i	0.703788	+	0.710410i	$0.251491\pi$
$239$			21.9654i			1.42082i	−0.703788	+	0.710410i	$0.748509\pi$
$240$	−1.10733	+	3.03558i	−0.0714778	+	0.195946i
$241$		−	1.36229i		−	0.0877527i	−0.999037	−	0.0438764i	$-0.986029\pi$
$241$		−	1.36229i		−	0.0877527i	0.999037	−	0.0438764i	$-0.0139708\pi$
$242$	−3.49974	−	11.1067i	−0.224972	−	0.713966i
$243$		−	12.2616i		−	0.786581i
$244$	2.29961	+	3.28669i	0.147217	+	0.210409i
$245$		−	0.616901i		−	0.0394124i
$246$	−10.1663	+	3.20342i	−0.648181	+	0.204243i
$247$	−16.6750			−1.06101
$248$	2.78773	−	3.62900i	0.177021	−	0.230442i
$249$		−	11.3144i		−	0.717019i
$250$	8.00431	−	2.52217i	0.506237	−	0.159516i
$251$	1.72306			0.108758			0.0543792	−	0.998520i	$-0.482682\pi$
$251$	1.72306			0.108758			0.0543792	+	0.998520i	$0.482682\pi$
$252$	2.10624	−	1.47368i	0.132681	−	0.0928332i
$253$	6.55464	+	4.54403i	0.412086	+	0.285680i
$254$	18.2164	−	5.74002i	1.14300	−	0.360161i
$255$			6.15388i			0.385371i
$256$	−12.2419	−	10.3022i	−0.765121	−	0.643887i
$257$	−7.70084			−0.480365			−0.240183	−	0.970728i	$-0.577207\pi$
$257$	−7.70084			−0.480365			−0.240183	+	0.970728i	$0.577207\pi$
$258$	11.1759	−	3.52154i	0.695781	−	0.219242i
$259$			1.52327i			0.0946517i
$260$	2.35421	+	3.36472i	0.146002	+	0.208671i
$261$	10.7268			0.663971
$262$	−4.60162	+	1.44998i	−0.284289	+	0.0895799i
$263$	−12.2883			−0.757726			−0.378863	−	0.925453i	$-0.623685\pi$
$263$	−12.2883			−0.757726			−0.378863	+	0.925453i	$0.623685\pi$
$264$	−3.75227	+	4.88461i	−0.230936	+	0.300627i
$265$	−1.19232			−0.0732436
$266$	2.12934	+	6.75764i	0.130558	+	0.414337i
$267$	20.0975			1.22995
$268$	20.6362	−	14.4386i	1.26056	−	0.881977i
$269$	14.3522			0.875067			0.437533	−	0.899202i	$-0.355852\pi$
$269$	14.3522			0.875067			0.437533	+	0.899202i	$0.355852\pi$
$270$	−1.47130	−	4.66928i	−0.0895403	−	0.284163i
$271$			24.6338i			1.49639i	0.663477	+	0.748197i	$0.269080\pi$
$271$			24.6338i			1.49639i	−0.663477	+	0.748197i	$0.730920\pi$
$272$	−28.6267	−	10.4426i	−1.73575	−	0.633173i
$273$			4.35837i			0.263781i
$274$	−18.9221	+	5.96238i	−1.14313	+	0.360201i
$275$	7.68232			0.463261
$276$	0.0542897	+	12.5598i	0.00326786	+	0.756013i
$277$	−4.62562			−0.277926			−0.138963	−	0.990298i	$-0.544377\pi$
$277$	−4.62562			−0.277926			−0.138963	+	0.990298i	$0.544377\pi$
$278$	25.4772	−	8.02790i	1.52802	−	0.481482i
$279$			2.07950i			0.124497i
$280$	1.06295	−	1.38372i	0.0635233	−	0.0826930i
$281$			14.3304i			0.854881i	0.904043	+	0.427440i	$0.140585\pi$
$281$			14.3304i			0.854881i	−0.904043	+	0.427440i	$0.859415\pi$
$282$	0.174570	+	0.554011i	0.0103955	+	0.0329909i
$283$	−6.93304			−0.412127			−0.206063	−	0.978539i	$-0.566065\pi$
$283$	−6.93304			−0.412127			−0.206063	+	0.978539i	$0.566065\pi$
$284$	6.09143	+	8.70611i	0.361460	+	0.516612i
$285$	4.04711			0.239730
$286$	2.35258	+	7.46609i	0.139111	+	0.441479i
$287$	5.75587			0.339758
$288$	7.26356	+	0.323664i	0.428009	+	0.0190721i
$289$	−41.0336			−2.41374
$290$	6.94447	−	2.18821i	0.407793	−	0.128496i
$291$	2.87447			0.168504
$292$	8.67563	−	6.07010i	0.507703	−	0.355226i
$293$			13.4803i			0.787528i	0.919212	+	0.393764i	$0.128827\pi$
$293$			13.4803i			0.787528i	−0.919212	+	0.393764i	$0.871173\pi$
$294$	1.76625	−	0.556549i	0.103010	−	0.0324586i
$295$	0.390881			0.0227580
$296$	−2.62467	+	3.41673i	−0.152556	+	0.198593i
$297$		−	9.33209i		−	0.541503i
$298$	26.0630	−	8.21250i	1.50979	−	0.475737i
$299$	13.1182	+	9.09426i	0.758647	+	0.525935i
$300$	6.93555	+	9.91257i	0.400424	+	0.572302i
$301$	−6.32746			−0.364709
$302$	0.994366	−	0.313326i	0.0572193	−	0.0180299i
$303$			24.3643i			1.39969i
$304$	−6.86757	+	18.8264i	−0.393882	+	1.07977i
$305$	−1.23729			−0.0708468
$306$	13.2070	−	4.16154i	0.754993	−	0.237900i
$307$			13.2540i			0.756448i	0.925714	+	0.378224i	$0.123465\pi$
$307$			13.2540i			0.756448i	−0.925714	+	0.378224i	$0.876535\pi$
$308$	2.72526	−	1.90679i	0.155286	−	0.108649i
$309$		−	18.5399i		−	1.05470i
$310$	0.424209	+	1.34626i	0.0240934	+	0.0764625i
$311$			7.87094i			0.446320i	0.974782	+	0.223160i	$0.0716372\pi$
$311$			7.87094i			0.446320i	−0.974782	+	0.223160i	$0.928363\pi$
$312$	−7.50967	+	9.77589i	−0.425151	+	0.553451i
$313$		−	12.6072i		−	0.712599i	−0.934372	−	0.356300i	$-0.884038\pi$
$313$		−	12.6072i		−	0.712599i	0.934372	−	0.356300i	$-0.115962\pi$
$314$	23.6461	−	7.45093i	1.33443	−	0.420480i
$315$			0.792904i			0.0446751i
$316$	11.6772	−	8.17022i	0.656894	−	0.459611i
$317$	4.92885			0.276832			0.138416	−	0.990374i	$-0.455799\pi$
$317$	4.92885			0.276832			0.138416	+	0.990374i	$0.455799\pi$
$318$	−1.07567	−	3.41374i	−0.0603208	−	0.191433i
$319$	13.8793			0.777093
$320$	4.76842	−	1.27219i	0.266563	−	0.0711177i
$321$			15.7360i			0.878298i
$322$	2.01035	−	6.47754i	0.112032	−	0.360979i
$323$			38.1659i			2.12361i
$324$	5.72255	−	4.00391i	0.317919	−	0.222440i
$325$	15.3751			0.852859
$326$	−11.4899	+	3.62048i	−0.636366	+	0.200520i
$327$	14.6443			0.809829
$328$	12.9105	+	9.91762i	0.712863	+	0.547609i
$329$		−	0.313665i		−	0.0172929i
$330$	−0.570982	−	1.81206i	−0.0314315	−	0.0997505i
$331$		−	18.8054i		−	1.03364i	−0.856094	−	0.516820i	$-0.827116\pi$
$331$		−	18.8054i		−	1.03364i	0.856094	−	0.516820i	$-0.172884\pi$
$332$	−14.1592	+	9.90684i	−0.777089	+	0.543708i
$333$		−	1.95787i		−	0.107290i
$334$	−30.2669	+	9.53715i	−1.65613	+	0.521850i
$335$			7.76858i			0.424443i
$336$	4.92069	+	1.79499i	0.268446	+	0.0979245i
$337$			7.94751i			0.432928i	0.976291	+	0.216464i	$0.0694525\pi$
$337$			7.94751i			0.432928i	−0.976291	+	0.216464i	$0.930548\pi$
$338$	−0.816895	−	2.59248i	−0.0444332	−	0.141012i
$339$	27.3140			1.48349
$340$	7.70121	−	5.38833i	0.417657	−	0.292223i
$341$			2.69066i			0.145707i
$342$	−2.73685	−	8.68560i	−0.147992	−	0.469664i
$343$	−1.00000			−0.0539949
$344$	−14.1926	−	10.9025i	−0.765213	−	0.587824i
$345$	−3.18386	−	2.20722i	−0.171413	−	0.118833i
$346$	3.88861	+	12.3408i	0.209053	+	0.663446i
$347$			30.1613i			1.61914i	0.587022	+	0.809571i	$0.300300\pi$
$347$			30.1613i			1.61914i	−0.587022	+	0.809571i	$0.699700\pi$
$348$	12.5302	+	17.9086i	0.671688	+	0.960003i
$349$	16.7841			0.898432			0.449216	−	0.893423i	$-0.351703\pi$
$349$	16.7841			0.898432			0.449216	+	0.893423i	$0.351703\pi$
$350$	−1.96335	−	6.23086i	−0.104946	−	0.333053i
$351$		−	18.6769i		−	0.996901i
$352$	9.39827	+	0.418786i	0.500929	+	0.0223214i
$353$	−7.76744			−0.413419			−0.206709	−	0.978402i	$-0.566275\pi$
$353$	−7.76744			−0.413419			−0.206709	+	0.978402i	$0.566275\pi$
$354$	0.352641	+	1.11913i	0.0187426	+	0.0594813i
$355$	−3.27745			−0.173949
$356$	−17.5973	−	25.1508i	−0.932657	−	1.33299i
$357$	9.97548			0.527958
$358$	1.79718	−	0.566295i	0.0949840	−	0.0299296i
$359$	34.3860			1.81482			0.907412	−	0.420243i	$-0.138055\pi$
$359$	34.3860			1.81482			0.907412	+	0.420243i	$0.138055\pi$
$360$	−1.36621	+	1.77850i	−0.0720055	+	0.0937349i
$361$	6.09987			0.321046
$362$	−18.4902	+	5.82629i	−0.971824	+	0.306223i
$363$			10.7825i			0.565935i
$364$	5.45424	−	3.81618i	0.285880	−	0.200022i
$365$			3.26598i			0.170949i
$366$	−1.11624	−	3.54248i	−0.0583469	−	0.185169i
$367$	−25.8428			−1.34898			−0.674491	−	0.738283i	$-0.735637\pi$
$367$	−25.8428			−1.34898			−0.674491	+	0.738283i	$0.735637\pi$
$368$	15.6703	−	11.0653i	0.816872	−	0.576819i
$369$	−7.39802			−0.385126
$370$	−0.399396	−	1.26751i	−0.0207636	−	0.0658949i
$371$			1.93276i			0.100344i
$372$	−3.47178	+	2.42911i	−0.180003	+	0.125943i
$373$		−	17.6499i		−	0.913876i	−0.889498	−	0.456938i	$-0.848946\pi$
$373$		−	17.6499i		−	0.913876i	0.889498	−	0.456938i	$-0.151054\pi$
$374$	17.0884	−	5.38459i	0.883622	−	0.278431i
$375$	−7.77068			−0.401276
$376$	0.540459	−	0.703555i	0.0278720	−	0.0362831i
$377$	27.7776			1.43062
$378$	−7.56893	+	2.38498i	−0.389304	+	0.122670i
$379$	−12.5394			−0.644106			−0.322053	−	0.946722i	$-0.604373\pi$
$379$	−12.5394			−0.644106			−0.322053	+	0.946722i	$0.604373\pi$
$380$	−3.54364	−	5.06471i	−0.181785	−	0.259814i
$381$	−17.6847			−0.906014
$382$	7.80145	+	24.7585i	0.399157	+	1.26676i
$383$	11.7348			0.599620			0.299810	−	0.953999i	$-0.403077\pi$
$383$	11.7348			0.599620			0.299810	+	0.953999i	$0.403077\pi$
$384$	7.94434	+	12.5048i	0.405408	+	0.638130i
$385$			1.02593i			0.0522864i
$386$	2.08760	+	6.62518i	0.106256	+	0.337213i
$387$	8.13270			0.413408
$388$	−2.51688	−	3.59722i	−0.127775	−	0.182621i
$389$			28.8792i			1.46423i	0.681179	+	0.732117i	$0.261468\pi$
$389$			28.8792i			1.46423i	−0.681179	+	0.732117i	$0.738532\pi$
$390$	−1.14274	−	3.62659i	−0.0578651	−	0.183640i
$391$	20.8150	−	30.0251i	1.05266	−	1.51844i
$392$	−2.24301	−	1.72305i	−0.113289	−	0.0870269i
$393$	4.46731			0.225346
$394$	8.99691	+	28.5524i	0.453258	+	1.43845i
$395$			4.39593i			0.221183i
$396$	−3.50278	+	2.45080i	−0.176021	+	0.123157i
$397$	−19.9901			−1.00328			−0.501638	−	0.865078i	$-0.667269\pi$
$397$	−19.9901			−1.00328			−0.501638	+	0.865078i	$0.667269\pi$
$398$	0.0490736	+	0.155739i	0.00245984	+	0.00780649i
$399$		−	6.56039i		−	0.328430i
$400$	6.33222	−	17.3588i	0.316611	−	0.867942i
$401$		−	20.4825i		−	1.02285i	−0.859329	−	0.511424i	$-0.829118\pi$
$401$		−	20.4825i		−	1.02285i	0.859329	−	0.511424i	$-0.170882\pi$
$402$	−22.2423	+	7.00857i	−1.10934	+	0.349556i
$403$			5.38499i			0.268245i
$404$	30.4904	−	21.3333i	1.51696	−	1.06137i
$405$			2.15428i			0.107047i
$406$	−3.54711	−	11.2570i	−0.176040	−	0.558677i
$407$		−	2.53327i		−	0.125570i
$408$	22.3751	+	17.1882i	1.10773	+	0.850942i
$409$	−20.3169			−1.00461			−0.502303	−	0.864692i	$-0.667514\pi$
$409$	−20.3169			−1.00461			−0.502303	+	0.864692i	$0.667514\pi$
$410$	−4.78945	+	1.50916i	−0.236534	+	0.0745322i
$411$	18.3698			0.906115
$412$	−23.2015	+	16.2335i	−1.14306	+	0.799765i
$413$		−	0.633620i		−	0.0311784i
$414$	−2.58390	+	8.32559i	−0.126992	+	0.409181i
$415$		−	5.33030i		−	0.261654i
$416$	18.8094	+	0.838145i	0.922206	+	0.0410935i
$417$	−24.7336			−1.21121
$418$	−3.54119	−	11.2382i	−0.173205	−	0.549680i
$419$	−26.8033			−1.30942			−0.654712	−	0.755878i	$-0.727210\pi$
$419$	−26.8033			−1.30942			−0.654712	+	0.755878i	$0.727210\pi$
$420$	−1.32377	+	0.926207i	−0.0645934	+	0.0451943i
$421$			31.8955i			1.55449i	0.629197	+	0.777245i	$0.283384\pi$
$421$			31.8955i			1.55449i	−0.629197	+	0.777245i	$0.716616\pi$
$422$	13.1839	−	4.15425i	0.641780	−	0.202226i
$423$			0.403154i			0.0196020i
$424$	−3.33023	+	4.33520i	−0.161730	+	0.210536i
$425$		−	35.1907i		−	1.70700i
$426$	−2.95681	−	9.38368i	−0.143258	−	0.454641i
$427$			2.00565i			0.0970602i
$428$	19.6927	−	13.7784i	0.951880	−	0.666005i
$429$		−	7.24816i		−	0.349945i
$430$	5.26507	−	1.65903i	0.253904	−	0.0800056i
$431$	4.72873			0.227775			0.113888	−	0.993494i	$-0.463670\pi$
$431$	4.72873			0.227775			0.113888	+	0.993494i	$0.463670\pi$
$432$	−21.0866	−	7.69206i	−1.01453	−	0.370084i
$433$			36.6590i			1.76172i	0.473378	+	0.880859i	$0.343034\pi$
$433$			36.6590i			1.76172i	−0.473378	+	0.880859i	$0.656966\pi$
$434$	2.18230	−	0.687645i	0.104754	−	0.0330080i
$435$	−6.74177			−0.323243
$436$	−12.8225	−	18.3264i	−0.614085	−	0.877675i
$437$	−19.7461	−	13.6890i	−0.944583	−	0.654835i
$438$	−9.35084	+	2.94646i	−0.446800	+	0.140787i
$439$		−	34.7822i		−	1.66006i	−0.557717	−	0.830031i	$-0.688323\pi$
$439$		−	34.7822i		−	1.66006i	0.557717	−	0.830031i	$-0.311677\pi$
$440$	−1.76773	+	2.30118i	−0.0842732	+	0.109705i
$441$	1.28530			0.0612048
$442$	34.2002	−	10.7765i	1.62674	−	0.512588i
$443$		−	24.8716i		−	1.18168i	−0.806787	−	0.590842i	$-0.798796\pi$
$443$		−	24.8716i		−	1.18168i	0.806787	−	0.590842i	$-0.201204\pi$
$444$	3.26871	−	2.28702i	0.155126	−	0.108537i
$445$	9.46812			0.448832
$446$	−11.5316	+	3.63363i	−0.546038	+	0.172057i
$447$	−25.3023			−1.19676
$448$	−2.06223	−	7.72963i	−0.0974313	−	0.365191i
$449$	6.64822			0.313749			0.156874	−	0.987619i	$-0.449858\pi$
$449$	6.64822			0.313749			0.156874	+	0.987619i	$0.449858\pi$
$450$	2.52350	+	8.00853i	0.118959	+	0.377526i
$451$	−9.57226			−0.450740
$452$	−23.9161	−	34.1818i	−1.12492	−	1.60778i
$453$	−0.965341			−0.0453557
$454$	11.1957	+	35.5306i	0.525442	+	1.66753i
$455$			2.05327i			0.0962587i
$456$	11.3038	−	14.7151i	0.529351	−	0.689095i
$457$		−	3.31041i		−	0.154854i	−0.996998	−	0.0774271i	$-0.975329\pi$
$457$		−	3.31041i		−	0.154854i	0.996998	−	0.0774271i	$-0.0246705\pi$
$458$	−2.49448	+	0.786013i	−0.116559	+	0.0367280i
$459$	−42.7479			−1.99530
$460$	0.0255764	+	5.91705i	0.00119250	+	0.275884i
$461$	16.1209			0.750827			0.375413	−	0.926858i	$-0.377501\pi$
$461$	16.1209			0.750827			0.375413	+	0.926858i	$0.377501\pi$
$462$	−2.93736	+	0.925565i	−0.136658	+	0.0430612i
$463$			6.25458i			0.290675i	0.989382	+	0.145337i	$0.0464268\pi$
$463$			6.25458i			0.290675i	−0.989382	+	0.145337i	$0.953573\pi$
$464$	11.4402	−	31.3615i	0.531096	−	1.45592i
$465$		−	1.30696i		−	0.0606090i
$466$	−3.59748	−	11.4169i	−0.166650	−	0.528878i
$467$	20.5390			0.950431			0.475215	−	0.879869i	$-0.342370\pi$
$467$	20.5390			0.950431			0.475215	+	0.879869i	$0.342370\pi$
$468$	−7.01034	+	4.90494i	−0.324053	+	0.226731i
$469$	12.5929			0.581486
$470$	0.0822414	+	0.261000i	0.00379352	+	0.0120390i
$471$	−22.9559			−1.05775
$472$	1.09176	−	1.42122i	0.0502521	−	0.0654169i
$473$	10.5228			0.483841
$474$	−12.5860	+	3.96587i	−0.578094	+	0.182158i
$475$	−23.1433			−1.06189
$476$	−8.73451	−	12.4837i	−0.400345	−	0.572189i
$477$		−	2.48418i		−	0.113743i
$478$	−29.6277	+	9.33572i	−1.35514	+	0.427006i
$479$	−25.1957			−1.15122			−0.575610	−	0.817724i	$-0.695235\pi$
$479$	−25.1957			−1.15122			−0.575610	+	0.817724i	$0.695235\pi$
$480$	−4.56513	−	0.203422i	−0.208369	−	0.00928491i
$481$		−	5.07001i		−	0.231172i
$482$	1.83750	−	0.579000i	0.0836960	−	0.0263727i
$483$	−3.57792	+	5.16106i	−0.162801	+	0.234836i
$484$	13.4937	−	9.44114i	0.613348	−	0.429143i
$485$	1.35419			0.0614905
$486$	16.5389	−	5.21142i	0.750218	−	0.236395i
$487$		−	19.3730i		−	0.877874i	−0.898518	−	0.438937i	$-0.855355\pi$
$487$		−	19.3730i		−	0.877874i	0.898518	−	0.438937i	$-0.144645\pi$
$488$	−3.45582	+	4.49870i	−0.156438	+	0.203647i
$489$	11.1545			0.504424
$490$	0.832098	−	0.262195i	0.0375904	−	0.0118448i
$491$		−	21.7646i		−	0.982222i	−0.871097	−	0.491111i	$-0.836591\pi$
$491$		−	21.7646i		−	0.982222i	0.871097	−	0.491111i	$-0.163409\pi$
$492$	−8.64178	−	12.3512i	−0.389601	−	0.556834i
$493$		−	63.5776i		−	2.86339i
$494$	−7.08722	−	22.4919i	−0.318869	−	1.01196i
$495$		−	1.31863i		−	0.0592682i
$496$	6.07976	+	2.21780i	0.272989	+	0.0995820i
$497$			5.31276i			0.238310i
$498$	15.2612	−	4.80883i	0.683872	−	0.215489i
$499$		−	23.7180i		−	1.06176i	−0.847447	−	0.530881i	$-0.821861\pi$
$499$		−	23.7180i		−	1.06176i	0.847447	−	0.530881i	$-0.178139\pi$
$500$	6.80399	+	9.72453i	0.304284	+	0.434894i
$501$	29.3835			1.31276
$502$	0.732334	+	2.32412i	0.0326857	+	0.103731i
$503$	−8.57085			−0.382155			−0.191078	−	0.981575i	$-0.561198\pi$
$503$	−8.57085			−0.382155			−0.191078	+	0.981575i	$0.561198\pi$
$504$	2.88295	+	2.21463i	0.128417	+	0.0986476i
$505$			11.4782i			0.510775i
$506$	−3.34329	+	10.7724i	−0.148627	+	0.478893i
$507$			2.51681i			0.111775i
$508$	15.4847	+	22.1313i	0.687022	+	0.981918i
$509$	18.8353			0.834861			0.417431	−	0.908709i	$-0.362931\pi$
$509$	18.8353			0.834861			0.417431	+	0.908709i	$0.362931\pi$
$510$	−8.30057	+	2.61552i	−0.367556	+	0.115817i
$511$	5.29417			0.234200
$512$	8.69289	−	20.8910i	0.384175	−	0.923260i
$513$			28.1132i			1.24123i
$514$	−3.27301	−	10.3872i	−0.144366	−	0.458158i
$515$		−	8.73430i		−	0.384879i
$516$	9.49997	+	13.5777i	0.418213	+	0.597726i
$517$			0.521638i			0.0229416i
$518$	−2.05465	+	0.647423i	−0.0902760	+	0.0284461i
$519$		−	11.9806i		−	0.525890i
$520$	−3.53788	+	4.60551i	−0.155146	+	0.201965i
$521$			3.63886i			0.159422i	0.996818	+	0.0797108i	$0.0253997\pi$
$521$			3.63886i			0.159422i	−0.996818	+	0.0797108i	$0.974600\pi$
$522$	4.55910	+	14.4687i	0.199546	+	0.633277i
$523$	10.1985			0.445949			0.222974	−	0.974824i	$-0.428423\pi$
$523$	10.1985			0.445949			0.222974	+	0.974824i	$0.428423\pi$
$524$	−3.91156	−	5.59056i	−0.170877	−	0.244225i
$525$			6.04899i			0.263999i
$526$	−5.22276	−	16.5748i	−0.227723	−	0.722697i
$527$	12.3252			0.536895
$528$	−8.18332	−	2.98514i	−0.356133	−	0.129912i
$529$	8.06847	+	21.5383i	0.350803	+	0.936449i
$530$	−0.506760	−	1.60824i	−0.0220122	−	0.0698576i
$531$			0.814393i			0.0353416i
$532$	−8.20993	+	5.74426i	−0.355946	+	0.249045i
$533$	−19.1576			−0.829808
$534$	8.54185	+	27.1082i	0.369642	+	1.17309i
$535$			7.41338i			0.320508i
$536$	28.2461	+	21.6981i	1.22004	+	0.937217i
$537$	−1.74472			−0.0752904
$538$	6.09996	+	19.3587i	0.262988	+	0.834613i
$539$	1.66304			0.0716324
$540$	5.67276	−	3.96908i	0.244117	−	0.170802i
$541$	−8.95405			−0.384965			−0.192482	−	0.981300i	$-0.561654\pi$
$541$	−8.95405			−0.384965			−0.192482	+	0.981300i	$0.561654\pi$
$542$	−33.2269	+	10.4698i	−1.42722	+	0.449718i
$543$	17.9505			0.770330
$544$	1.91835	−	43.0511i	0.0822487	−	1.84580i
$545$	6.89904			0.295522
$546$	−5.87873	+	1.85240i	−0.251586	+	0.0792752i
$547$			4.41474i			0.188761i	0.995536	+	0.0943804i	$0.0300870\pi$
$547$			4.41474i			0.188761i	−0.995536	+	0.0943804i	$0.969913\pi$
$548$	−16.0846	−	22.9887i	−0.687098	−	0.982028i
$549$		−	2.57786i		−	0.110021i
$550$	3.26514	+	10.3622i	0.139226	+	0.441845i
$551$	−41.8119			−1.78125
$552$	−16.9181	+	5.41141i	−0.720081	+	0.230325i
$553$	7.12582			0.303021
$554$	−1.96598	−	6.23920i	−0.0835265	−	0.265078i
$555$			1.23052i			0.0522325i
$556$	21.6566	+	30.9525i	0.918447	+	1.31268i
$557$		−	3.94573i		−	0.167186i	−0.996500	−	0.0835930i	$-0.973360\pi$
$557$		−	3.94573i		−	0.167186i	0.996500	−	0.0835930i	$-0.0266396\pi$
$558$	−2.80491	+	0.883831i	−0.118741	+	0.0374155i
$559$	21.0601			0.890746
$560$	2.31818	+	0.845634i	0.0979611	+	0.0357346i
$561$	−16.5896			−0.700416
$562$	−19.3294	+	6.09072i	−0.815361	+	0.256921i
$563$	26.4156			1.11329			0.556643	−	0.830752i	$-0.312089\pi$
$563$	26.4156			1.11329			0.556643	+	0.830752i	$0.312089\pi$
$564$	−0.673075	+	0.470932i	−0.0283416	+	0.0198298i
$565$	12.8679			0.541356
$566$	−2.94668	−	9.35154i	−0.123858	−	0.393074i
$567$	3.49209			0.146654
$568$	−9.15413	+	11.9166i	−0.384099	+	0.500010i
$569$		−	6.99492i		−	0.293242i	−0.989193	−	0.146621i	$-0.953160\pi$
$569$		−	6.99492i		−	0.293242i	0.989193	−	0.146621i	$-0.0468398\pi$
$570$	1.72010	+	5.45889i	0.0720472	+	0.228648i
$571$	−22.2464			−0.930982			−0.465491	−	0.885053i	$-0.654122\pi$
$571$	−22.2464			−0.930982			−0.465491	+	0.885053i	$0.654122\pi$
$572$	−9.07063	+	6.34648i	−0.379262	+	0.265359i
$573$		−	24.0358i		−	1.00411i
$574$	2.44636	+	7.76372i	0.102109	+	0.324051i
$575$	18.2068	+	12.6219i	0.759276	+	0.526371i
$576$	2.65059	+	9.93491i	0.110441	+	0.413955i
$577$	−20.8729			−0.868952			−0.434476	−	0.900683i	$-0.643066\pi$
$577$	−20.8729			−0.868952			−0.434476	+	0.900683i	$0.643066\pi$
$578$	−17.4401	−	55.3476i	−0.725413	−	2.30216i
$579$		−	6.43180i		−	0.267296i
$580$	5.90308	+	8.43691i	0.245112	+	0.350324i
$581$	−8.64045			−0.358466
$582$	1.22171	+	3.87719i	0.0506414	+	0.160715i
$583$		−	3.21426i		−	0.133121i
$584$	11.8749	+	9.12209i	0.491387	+	0.377475i
$585$		−	2.63907i		−	0.109112i
$586$	−18.1827	+	5.72940i	−0.751121	+	0.236679i
$587$		−	3.18875i		−	0.131614i	−0.997832	−	0.0658068i	$-0.979038\pi$
$587$		−	3.18875i		−	0.131614i	0.997832	−	0.0658068i	$-0.0209621\pi$
$588$	1.50139	+	2.14584i	0.0619161	+	0.0884930i
$589$		−	8.10570i		−	0.333989i
$590$	0.166132	+	0.527234i	0.00683956	+	0.0217059i
$591$		−	27.7190i		−	1.14021i
$592$	−5.72414	−	2.08807i	−0.235261	−	0.0858192i
$593$	−31.5631			−1.29614			−0.648071	−	0.761580i	$-0.724424\pi$
$593$	−31.5631			−1.29614			−0.648071	+	0.761580i	$0.724424\pi$
$594$	12.5875	−	3.96633i	0.516470	−	0.162740i
$595$	4.69954			0.192662
$596$	22.1546	+	31.6643i	0.907489	+	1.29702i
$597$		−	0.151193i		−	0.00618792i
$598$	−6.69115	+	21.5596i	−0.273622	+	0.881637i
$599$		−	8.41847i		−	0.343969i	−0.985100	−	0.171985i	$-0.944982\pi$
$599$		−	8.41847i		−	0.343969i	0.985100	−	0.171985i	$-0.0550180\pi$
$600$	−10.4227	+	13.5680i	−0.425504	+	0.553910i
$601$	−29.8381			−1.21712			−0.608561	−	0.793507i	$-0.708253\pi$
$601$	−29.8381			−1.21712			−0.608561	+	0.793507i	$0.708253\pi$
$602$	−2.68930	−	8.53471i	−0.109608	−	0.347849i
$603$	−16.1857			−0.659132
$604$	0.845251	+	1.20807i	0.0343928	+	0.0491555i
$605$			5.07974i			0.206521i
$606$	−32.8634	+	10.3553i	−1.33499	+	0.420656i
$607$		−	1.39387i		−	0.0565753i	−0.999600	−	0.0282876i	$-0.990995\pi$
$607$		−	1.39387i		−	0.0565753i	0.999600	−	0.0282876i	$-0.00900543\pi$
$608$	−28.3126	−	1.26161i	−1.14823	−	0.0511650i
$609$			10.9284i			0.442843i
$610$	−0.525872	−	1.66890i	−0.0212919	−	0.0675717i
$611$			1.04399i			0.0422353i
$612$	11.2265	+	16.0453i	0.453803	+	0.648594i
$613$			18.6476i			0.753169i	0.926382	+	0.376584i	$0.122902\pi$
$613$			18.6476i			0.753169i	−0.926382	+	0.376584i	$0.877098\pi$
$614$	−17.8775	+	5.63323i	−0.721478	+	0.227339i
$615$	4.64965			0.187492
$616$	3.73023	+	2.86550i	0.150295	+	0.115454i
$617$			17.9429i			0.722354i	0.932497	+	0.361177i	$0.117625\pi$
$617$			17.9429i			0.722354i	−0.932497	+	0.361177i	$0.882375\pi$
$618$	25.0072	−	7.87982i	1.00594	−	0.316973i
$619$	−19.7476			−0.793724			−0.396862	−	0.917878i	$-0.629901\pi$
$619$	−19.7476			−0.793724			−0.396862	+	0.917878i	$0.629901\pi$
$620$	−1.63559	+	1.14438i	−0.0656867	+	0.0459592i
$621$	15.3325	−	22.1167i	0.615271	−	0.887512i
$622$	−10.6166	+	3.34531i	−0.425687	+	0.134135i
$623$		−	15.3479i		−	0.614900i
$624$	−16.3778	−	5.97436i	−0.655638	−	0.239166i
$625$	19.4363			0.777453
$626$	17.0050	−	5.35830i	0.679656	−	0.214161i
$627$			10.9102i			0.435712i
$628$	20.1002	+	28.7280i	0.802084	+	1.14637i
$629$	−11.6043			−0.462693
$630$	−1.06950	+	0.337000i	−0.0426098	+	0.0134264i
$631$	−5.30461			−0.211173			−0.105587	−	0.994410i	$-0.533672\pi$
$631$	−5.30461			−0.211173			−0.105587	+	0.994410i	$0.533672\pi$
$632$	15.9833	+	12.2781i	0.635782	+	0.488397i
$633$	−12.7990			−0.508716
$634$	2.09486	+	6.64822i	0.0831976	+	0.264034i
$635$	−8.33142			−0.330622
$636$	4.14739	−	2.90182i	0.164455	−	0.115064i
$637$	3.32836			0.131874
$638$	5.89899	+	18.7209i	0.233543	+	0.741168i
$639$		−	6.82850i		−	0.270131i
$640$	3.74265	+	5.89110i	0.147941	+	0.232866i
$641$			36.0710i			1.42472i	0.701815	+	0.712360i	$0.252374\pi$
$641$			36.0710i			1.42472i	−0.701815	+	0.712360i	$0.747626\pi$
$642$	−21.2253	+	6.68812i	−0.837695	+	0.263959i
$643$	18.1076			0.714094			0.357047	−	0.934086i	$-0.383784\pi$
$643$	18.1076			0.714094			0.357047	+	0.934086i	$0.383784\pi$
$644$	9.59157	−	0.0414594i	0.377961	−	0.00163373i
$645$	−5.11139			−0.201261
$646$	−51.4795	+	16.2213i	−2.02543	+	0.638218i
$647$			28.5841i			1.12376i	0.827220	+	0.561879i	$0.189921\pi$
$647$			28.5841i			1.12376i	−0.827220	+	0.561879i	$0.810079\pi$
$648$	7.83282	+	6.01704i	0.307702	+	0.236372i
$649$			1.05374i			0.0413628i
$650$	6.53474	+	20.7385i	0.256314	+	0.813432i
$651$	−2.11860			−0.0830344
$652$	−9.76687	−	13.9592i	−0.382500	−	0.546684i
$653$	−5.27973			−0.206612			−0.103306	−	0.994650i	$-0.532942\pi$
$653$	−5.27973			−0.206612			−0.103306	+	0.994650i	$0.532942\pi$
$654$	6.22410	+	19.7527i	0.243382	+	0.772391i
$655$	2.10459			0.0822331
$656$	−7.89002	+	21.6293i	−0.308053	+	0.844483i
$657$	−6.80460			−0.265473
$658$	0.423082	−	0.133314i	0.0164935	−	0.00519712i
$659$	−48.8617			−1.90338			−0.951691	−	0.307057i	$-0.900656\pi$
$659$	−48.8617			−1.90338			−0.951691	+	0.307057i	$0.900656\pi$
$660$	2.20149	−	1.54032i	0.0856928	−	0.0599570i
$661$		−	2.91649i		−	0.113438i	−0.998390	−	0.0567192i	$-0.981936\pi$
$661$		−	2.91649i		−	0.113438i	0.998390	−	0.0567192i	$-0.0180640\pi$
$662$	25.3654	−	7.99269i	0.985856	−	0.310645i
$663$	−33.2020			−1.28946
$664$	−19.3807	−	14.8879i	−0.752115	−	0.577762i
$665$		−	3.09066i		−	0.119851i
$666$	2.64084	−	0.832133i	0.102331	−	0.0322445i
$667$	32.8935	+	22.8035i	1.27364	+	0.882955i
$668$	−25.7281	−	36.7716i	−0.995450	−	1.42274i
$669$	11.1950			0.432825
$670$	−10.4785	+	3.30180i	−0.404821	+	0.127560i
$671$		−	3.33548i		−	0.128765i
$672$	−0.329748	+	7.40011i	−0.0127203	+	0.285465i
$673$	32.6008			1.25667			0.628335	−	0.777943i	$-0.283737\pi$
$673$	32.6008			1.25667			0.628335	+	0.777943i	$0.283737\pi$
$674$	−10.7199	+	3.37785i	−0.412915	+	0.130110i
$675$		−	25.9217i		−	0.997728i
$676$	3.14964	−	2.20371i	0.121140	−	0.0847582i
$677$			1.91684i			0.0736702i	0.999321	+	0.0368351i	$0.0117276\pi$
$677$			1.91684i			0.0736702i	−0.999321	+	0.0368351i	$0.988272\pi$
$678$	11.6090	+	36.8421i	0.445841	+	1.41491i
$679$		−	2.19515i		−	0.0842420i
$680$	10.5411	+	8.09752i	0.404234	+	0.310526i
$681$		−	34.4935i		−	1.32179i
$682$	−3.62925	+	1.14358i	−0.138971	+	0.0437901i
$683$			32.9939i			1.26248i	0.775589	+	0.631238i	$0.217453\pi$
$683$			32.9939i			1.26248i	−0.775589	+	0.631238i	$0.782547\pi$
$684$	10.5522	−	7.38311i	0.403475	−	0.282300i
$685$	8.65418			0.330659
$686$	−0.425020	−	1.34884i	−0.0162273	−	0.0514988i
$687$	2.42166			0.0923923
$688$	8.67355	−	23.7773i	0.330676	−	0.906500i
$689$		−	6.43291i		−	0.245075i
$690$	1.62398	−	5.23262i	0.0618238	−	0.199203i
$691$		−	13.2275i		−	0.503200i	−0.967831	−	0.251600i	$-0.919043\pi$
$691$		−	13.2275i		−	0.503200i	0.967831	−	0.251600i	$-0.0809567\pi$
$692$	−14.9930	+	10.4902i	−0.569948	+	0.398777i
$693$	−2.13751			−0.0811974
$694$	−40.6826	+	12.8192i	−1.54429	+	0.486608i
$695$	−11.6522			−0.441993
$696$	−18.8302	+	24.5127i	−0.713757	+	0.929150i
$697$			43.8481i			1.66086i
$698$	7.13358	+	22.6390i	0.270010	+	0.856899i
$699$			11.0837i			0.419223i
$700$	7.56994	−	5.29648i	0.286117	−	0.200188i
$701$		−	35.7649i		−	1.35082i	−0.737441	−	0.675411i	$-0.763966\pi$
$701$		−	35.7649i		−	1.35082i	0.737441	−	0.675411i	$-0.236034\pi$
$702$	25.1921	−	7.93808i	0.950815	−	0.299603i
$703$			7.63157i			0.287830i
$704$	3.42958	+	12.8547i	0.129257	+	0.484480i
$705$		−	0.253382i		−	0.00954290i
$706$	−3.30132	−	10.4770i	−0.124247	−	0.394307i
$707$	18.6063			0.699762
$708$	−1.35965	+	0.951309i	−0.0510987	+	0.0357524i
$709$			12.9817i			0.487537i	0.969834	+	0.243768i	$0.0783836\pi$
$709$			12.9817i			0.487537i	−0.969834	+	0.243768i	$0.921616\pi$
$710$	−1.39298	−	4.42074i	−0.0522777	−	0.165907i
$711$	−9.15883			−0.343483
$712$	26.4451	−	34.4255i	0.991072	−	1.29015i
$713$	−4.42071	+	6.37675i	−0.165557	+	0.238811i
$714$	4.23978	+	13.4553i	0.158670	+	0.503551i
$715$		−	3.41468i		−	0.127702i
$716$	1.52768	+	2.18342i	0.0570920	+	0.0815981i
$717$	28.7629			1.07417
$718$	14.6147	+	46.3811i	0.545417	+	1.73093i
$719$		−	13.3281i		−	0.497055i	−0.968625	−	0.248528i	$-0.920053\pi$
$719$		−	13.3281i		−	0.497055i	0.968625	−	0.248528i	$-0.0799467\pi$
$720$	−2.97956	−	1.08690i	−0.111042	−	0.0405062i
$721$	−14.1583			−0.527284
$722$	2.59257	+	8.22773i	0.0964854	+	0.306204i
$723$	−1.78387			−0.0663428
$724$	−15.7174	−	22.4640i	−0.584134	−	0.834867i
$725$	38.5526			1.43181
$726$	−14.5438	+	4.58278i	−0.539772	+	0.170083i
$727$	−3.26208			−0.120984			−0.0604919	−	0.998169i	$-0.519267\pi$
$727$	−3.26208			−0.120984			−0.0604919	+	0.998169i	$0.519267\pi$
$728$	7.46556	+	5.73492i	0.276692	+	0.212550i
$729$	−26.5324			−0.982681
$730$	−4.40527	+	1.38811i	−0.163046	+	0.0513761i
$731$		−	48.2025i		−	1.78283i
$732$	4.30380	−	3.01125i	0.159073	−	0.111299i
$733$			15.8147i			0.584131i	0.956398	+	0.292065i	$0.0943424\pi$
$733$			15.8147i			0.584131i	−0.956398	+	0.292065i	$0.905658\pi$
$734$	−10.9837	−	34.8576i	−0.405416	−	1.28662i
$735$	−0.807810			−0.0297965
$736$	21.5855	+	16.4337i	0.795651	+	0.605755i
$737$	−20.9426			−0.771429
$738$	−3.14431	−	9.97872i	−0.115744	−	0.367322i
$739$		−	31.7215i		−	1.16689i	−0.812151	−	0.583447i	$-0.801703\pi$
$739$		−	31.7215i		−	1.16689i	0.812151	−	0.583447i	$-0.198297\pi$
$740$	1.53992	−	1.07744i	0.0566085	−	0.0396074i
$741$			21.8353i			0.802141i
$742$	−2.60697	+	0.821461i	−0.0957050	+	0.0301568i
$743$	−7.03275			−0.258007			−0.129003	−	0.991644i	$-0.541178\pi$
$743$	−7.03275			−0.258007			−0.129003	+	0.991644i	$0.541178\pi$
$744$	−4.75205	−	3.65044i	−0.174218	−	0.133832i
$745$	−11.9201			−0.436720
$746$	23.8068	−	7.50156i	0.871629	−	0.274651i
$747$	11.1056			0.406332
$748$	14.5259	+	20.7609i	0.531118	+	0.759095i
$749$	12.0171			0.439096
$750$	−3.30269	−	10.4814i	−0.120597	−	0.382725i
$751$	−45.1648			−1.64809			−0.824044	−	0.566526i	$-0.808287\pi$
$751$	−45.1648			−1.64809			−0.824044	+	0.566526i	$0.808287\pi$
$752$	1.17869	+	0.429965i	0.0429822	+	0.0156792i
$753$		−	2.25628i		−	0.0822235i
$754$	11.8060	+	37.4674i	0.429951	+	1.36448i
$755$	−0.454781			−0.0165512
$756$	−6.43389	−	9.19557i	−0.233998	−	0.334440i
$757$		−	39.0402i		−	1.41894i	−0.704735	−	0.709470i	$-0.748934\pi$
$757$		−	39.0402i		−	1.41894i	0.704735	−	0.709470i	$-0.251066\pi$
$758$	−5.32950	−	16.9136i	−0.193576	−	0.614329i
$759$	5.95024	−	8.58307i	0.215980	−	0.311546i
$760$	5.32535	−	6.93240i	0.193171	−	0.251464i
$761$	7.60952			0.275845			0.137922	−	0.990443i	$-0.455958\pi$
$761$	7.60952			0.275845			0.137922	+	0.990443i	$0.455958\pi$
$762$	−7.51635	−	23.8537i	−0.272289	−	0.864130i
$763$		−	11.1834i		−	0.404866i
$764$	−30.0794	+	21.0457i	−1.08823	+	0.761408i
$765$	−6.04032			−0.218388
$766$	4.98752	+	15.8283i	0.180207	+	0.571900i
$767$			2.10892i			0.0761485i
$768$	−13.4904	+	16.0304i	−0.486791	+	0.578447i
$769$		−	35.9590i		−	1.29671i	−0.761336	−	0.648357i	$-0.775456\pi$
$769$		−	35.9590i		−	1.29671i	0.761336	−	0.648357i	$-0.224544\pi$
$770$	−1.38382	+	0.436042i	−0.0498692	+	0.0157139i
$771$			10.0840i			0.363166i
$772$	−8.04900	+	5.63167i	−0.289690	+	0.202688i
$773$		−	34.1435i		−	1.22806i	−0.789283	−	0.614029i	$-0.789548\pi$
$773$		−	34.1435i		−	1.22806i	0.789283	−	0.614029i	$-0.210452\pi$
$774$	3.45656	+	10.9697i	0.124244	+	0.394297i
$775$			7.47383i			0.268468i
$776$	3.78234	−	4.92375i	0.135778	−	0.176752i
$777$	1.99467			0.0715586
$778$	−38.9533	+	12.2743i	−1.39654	+	0.440053i
$779$	28.8368			1.03318
$780$	4.40599	−	3.08275i	0.157760	−	0.110380i
$781$		−	8.83535i		−	0.316154i
$782$	49.3458	+	15.3148i	1.76460	+	0.547655i
$783$		−	46.8317i		−	1.67363i
$784$	1.37078	−	3.75779i	0.0489564	−	0.134207i
$785$	−10.8148			−0.385995
$786$	1.89870	+	6.02566i	0.0677242	+	0.214928i
$787$	20.8800			0.744292			0.372146	−	0.928174i	$-0.378622\pi$
$787$	20.8800			0.744292			0.372146	+	0.928174i	$0.378622\pi$
$788$	−34.6887	+	24.2707i	−1.23573	+	0.864608i
$789$			16.0910i			0.572856i
$790$	−5.92938	+	1.86836i	−0.210958	+	0.0664732i
$791$		−	20.8589i		−	0.741658i
$792$	−4.79447	−	3.68303i	−0.170364	−	0.130871i
$793$		−	6.67552i		−	0.237055i
$794$	−8.49620	−	26.9634i	−0.301519	−	0.956895i
$795$			1.56130i			0.0553736i
$796$	−0.189209	+	0.132384i	−0.00670633	+	0.00469224i
$797$			34.4641i			1.22078i	0.792101	+	0.610390i	$0.208987\pi$
$797$			34.4641i			1.22078i	−0.792101	+	0.610390i	$0.791013\pi$
$798$	8.84889	−	2.78830i	0.313247	−	0.0987047i
$799$	2.38949			0.0845341
$800$	26.1056	+	1.16326i	0.922971	+	0.0411275i
$801$			19.7267i			0.697007i
$802$	27.6275	−	8.70548i	0.975562	−	0.307401i
$803$	−8.80443			−0.310702
$804$	−18.9068	−	27.0224i	−0.666792	−	0.953006i
$805$	−1.68559	+	2.43142i	−0.0594093	+	0.0856964i
$806$	−7.26347	+	2.28873i	−0.255845	+	0.0806171i
$807$		−	18.7936i		−	0.661568i
$808$	41.7342	+	32.0595i	1.46820	+	1.12785i
$809$	−12.7210			−0.447248			−0.223624	−	0.974675i	$-0.571789\pi$
$809$	−12.7210			−0.447248			−0.223624	+	0.974675i	$0.571789\pi$
$810$	−2.90577	+	0.915611i	−0.102098	+	0.0321713i
$811$		−	10.3114i		−	0.362082i	−0.983476	−	0.181041i	$-0.942053\pi$
$811$		−	10.3114i		−	0.362082i	0.983476	−	0.181041i	$-0.0579467\pi$
$812$	13.6763	−	9.56893i	0.479944	−	0.335803i
$813$	32.2570			1.13130
$814$	3.41697	−	1.07669i	0.119765	−	0.0377380i
$815$	5.25499			0.184074
$816$	−13.6742	+	37.4857i	−0.478692	+	1.31226i
$817$	−31.7004			−1.10906
$818$	−8.63509	−	27.4041i	−0.301919	−	0.958163i
$819$	−4.27795			−0.149484
$820$	−4.07122	−	5.81875i	−0.142173	−	0.203200i
$821$	−34.6141			−1.20804			−0.604020	−	0.796969i	$-0.706435\pi$
$821$	−34.6141			−1.20804			−0.604020	+	0.796969i	$0.706435\pi$
$822$	7.80753	+	24.7778i	0.272319	+	0.864226i
$823$		−	22.7285i		−	0.792266i	−0.918193	−	0.396133i	$-0.870352\pi$
$823$		−	22.7285i		−	0.792266i	0.918193	−	0.396133i	$-0.129648\pi$
$824$	−31.7574	−	24.3955i	−1.10632	−	0.849857i
$825$		−	10.0597i		−	0.350235i
$826$	0.854649	−	0.269301i	0.0297371	−	0.00937019i
$827$	−18.7081			−0.650545			−0.325272	−	0.945620i	$-0.605456\pi$
$827$	−18.7081			−0.650545			−0.325272	+	0.945620i	$0.605456\pi$
$828$	−12.3281	+	0.0532879i	−0.428430	+	0.00185188i
$829$	−18.2680			−0.634475			−0.317238	−	0.948346i	$-0.602755\pi$
$829$	−18.2680			−0.634475			−0.317238	+	0.948346i	$0.602755\pi$
$830$	7.18970	−	2.26549i	0.249558	−	0.0786362i
$831$			6.05708i			0.210118i
$832$	6.86385	+	25.7270i	0.237961	+	0.891923i
$833$		−	7.61798i		−	0.263947i
$834$	−10.5123	−	33.3615i	−0.364010	−	1.15521i
$835$	13.8428			0.479051
$836$	13.6535	−	9.55296i	0.472215	−	0.330396i
$837$	9.07883			0.313810
$838$	−11.3919	−	36.1532i	−0.393528	−	1.24889i
$839$	−1.42065			−0.0490463			−0.0245232	−	0.999699i	$-0.507807\pi$
$839$	−1.42065			−0.0490463			−0.0245232	+	0.999699i	$0.507807\pi$
$840$	−1.81193	−	1.39189i	−0.0625175	−	0.0480249i
$841$	40.6513			1.40177
$842$	−43.0218	+	13.5562i	−1.48263	+	0.467178i
$843$	18.7652			0.646307
$844$	11.2068	+	16.0172i	0.385754	+	0.551335i
$845$			1.18569i			0.0407891i
$846$	−0.543788	+	0.171349i	−0.0186958	+	0.00589108i
$847$	8.23429			0.282933
$848$	−7.26289	−	2.64938i	−0.249409	−	0.0909801i
$849$			9.07858i			0.311576i
$850$	47.4665	−	14.9568i	1.62809	−	0.513013i
$851$	4.16213	−	6.00376i	0.142676	−	0.205806i
$852$	11.4003	−	7.97651i	0.390569	−	0.273271i
$853$	31.2790			1.07097			0.535487	−	0.844544i	$-0.320128\pi$
$853$	31.2790			1.07097			0.535487	+	0.844544i	$0.320128\pi$
$854$	−2.70529	+	0.852441i	−0.0925732	+	0.0291699i
$855$			3.97243i			0.135854i
$856$	26.9546	+	20.7061i	0.921289	+	0.707718i
$857$	16.9004			0.577308			0.288654	−	0.957433i	$-0.406792\pi$
$857$	16.9004			0.577308			0.288654	+	0.957433i	$0.406792\pi$
$858$	9.77658	−	3.08061i	0.333767	−	0.105170i
$859$			49.5625i			1.69105i	0.533935	+	0.845526i	$0.320713\pi$
$859$			49.5625i			1.69105i	−0.533935	+	0.845526i	$0.679287\pi$
$860$	4.47552	+	6.39659i	0.152614	+	0.218122i
$861$		−	7.53710i		−	0.256864i
$862$	2.00981	+	6.37828i	0.0684543	+	0.217245i
$863$		−	9.77024i		−	0.332583i	−0.986077	−	0.166291i	$-0.946821\pi$
$863$		−	9.77024i		−	0.332583i	0.986077	−	0.166291i	$-0.0531792\pi$
$864$	1.41307	−	31.7117i	0.0480737	−	1.07885i
$865$		−	5.64417i		−	0.191907i
$866$	−49.4470	+	15.5808i	−1.68028	+	0.529457i
$867$			53.7320i			1.82484i
$868$	1.85504	+	2.65130i	0.0629641	+	0.0899908i
$869$	−11.8506			−0.402002
$870$	−2.86539	−	9.09354i	−0.0971458	−	0.308300i
$871$	−41.9137			−1.42019
$872$	19.2695	−	25.0845i	0.652547	−	0.849468i
$873$			2.82143i			0.0954908i
$874$	10.0718	−	32.4523i	0.340683	−	1.09772i
$875$			5.93424i			0.200614i
$876$	−7.94859	−	11.3604i	−0.268558	−	0.383834i
$877$	40.2236			1.35825			0.679127	−	0.734021i	$-0.262358\pi$
$877$	40.2236			1.35825			0.679127	+	0.734021i	$0.262358\pi$
$878$	46.9154	−	14.7831i	1.58332	−	0.498906i
$879$	17.6520			0.595387
$880$	−3.85524	−	1.40633i	−0.129960	−	0.0474073i
$881$			29.3527i			0.988919i	0.869201	+	0.494459i	$0.164634\pi$
$881$			29.3527i			0.988919i	−0.869201	+	0.494459i	$0.835366\pi$
$882$	0.546279	+	1.73366i	0.0183942	+	0.0583754i
$883$			24.9882i			0.840921i	0.907311	+	0.420460i	$0.138131\pi$
$883$			24.9882i			0.840921i	−0.907311	+	0.420460i	$0.861869\pi$
$884$	29.0716	+	41.5503i	0.977783	+	1.39749i
$885$		−	0.511845i		−	0.0172055i
$886$	33.5477	−	10.5709i	1.12706	−	0.355137i
$887$			25.3732i			0.851948i	0.904735	+	0.425974i	$0.140069\pi$
$887$			25.3732i			0.851948i	−0.904735	+	0.425974i	$0.859931\pi$
$888$	4.47409	+	3.43691i	0.150140	+	0.115335i
$889$			13.5053i			0.452953i
$890$	4.02414	+	12.7709i	0.134890	+	0.428083i
$891$	−5.80751			−0.194559
$892$	−9.80234	−	14.0099i	−0.328207	−	0.469086i
$893$		−	1.57145i		−	0.0525867i
$894$	−10.7540	−	34.1286i	−0.359667	−	1.14143i
$895$	−0.821956			−0.0274750
$896$	9.54951	−	6.06686i	0.319027	−	0.202680i
$897$	11.9086	−	17.1779i	0.397617	−	0.573552i
$898$	2.82563	+	8.96736i	0.0942924	+	0.299245i
$899$			13.5027i			0.450339i
$900$	−9.72965	+	6.80757i	−0.324322	+	0.226919i
$901$	−14.7237			−0.490518
$902$	−4.06840	−	12.9114i	−0.135463	−	0.429903i
$903$			8.28559i			0.275727i
$904$	35.9409	−	46.7869i	1.19538	−	1.55611i
$905$	8.45665			0.281109
$906$	−0.410290	−	1.30209i	−0.0136310	−	0.0432589i
$907$	15.1566			0.503266			0.251633	−	0.967823i	$-0.419032\pi$
$907$	15.1566			0.503266			0.251633	+	0.967823i	$0.419032\pi$
$908$	−43.1665	+	30.2024i	−1.43253	+	1.00230i
$909$	−23.9147			−0.793201
$910$	−2.76952	+	0.872681i	−0.0918088	+	0.0289291i
$911$	−34.8863			−1.15583			−0.577917	−	0.816096i	$-0.696134\pi$
$911$	−34.8863			−1.15583			−0.577917	+	0.816096i	$0.696134\pi$
$912$	24.6525	+	8.99284i	0.816327	+	0.297783i
$913$	14.3694			0.475559
$914$	4.46519	−	1.40699i	0.147695	−	0.0465391i
$915$			1.62018i			0.0535616i
$916$	−2.12040	−	3.03057i	−0.0700601	−	0.100133i
$917$		−	3.41155i		−	0.112659i
$918$	−18.1687	−	57.6599i	−0.599657	−	1.90306i
$919$	25.3371			0.835794			0.417897	−	0.908494i	$-0.362767\pi$
$919$	25.3371			0.835794			0.417897	+	0.908494i	$0.362767\pi$
$920$	−7.97026	+	2.54936i	−0.262772	+	0.0840501i
$921$	17.3557			0.571890
$922$	6.85172	+	21.7445i	0.225649	+	0.716117i
$923$		−	17.6828i		−	0.582036i
$924$	−2.49687	−	3.56863i	−0.0821410	−	0.117399i
$925$		−	7.03667i		−	0.231364i
$926$	−8.43640	+	2.65832i	−0.277237	+	0.0873579i
$927$	18.1977			0.597693
$928$	47.1638	+	2.10162i	1.54823	+	0.0689890i
$929$	−57.6692			−1.89207			−0.946033	−	0.324070i	$-0.894949\pi$
$929$	−57.6692			−1.89207			−0.946033	+	0.324070i	$0.894949\pi$
$930$	1.76288	−	0.555486i	0.0578071	−	0.0182151i
$931$	−5.00998			−0.164195
$932$	13.8705	−	9.70483i	0.454344	−	0.317892i
$933$	10.3067			0.337427
$934$	8.72948	+	27.7037i	0.285637	+	0.906493i
$935$	−7.81554			−0.255595
$936$	−9.59550	−	7.37110i	−0.313639	−	0.240932i
$937$		−	52.8048i		−	1.72506i	−0.506007	−	0.862529i	$-0.668879\pi$
$937$		−	52.8048i		−	1.72506i	0.506007	−	0.862529i	$-0.331121\pi$
$938$	5.35224	+	16.9858i	0.174757	+	0.554605i
$939$	−16.5086			−0.538739
$940$	−0.317092	+	0.221860i	−0.0103424	+	0.00723629i
$941$			19.5588i			0.637598i	0.947822	+	0.318799i	$0.103280\pi$
$941$			19.5588i			0.637598i	−0.947822	+	0.318799i	$0.896720\pi$
$942$	−9.75673	−	30.9638i	−0.317892	−	1.00885i
$943$	−22.6859	−	15.7271i	−0.738754	−	0.512144i
$944$	2.38101	+	0.868553i	0.0774953	+	0.0282690i
$945$	3.46171			0.112609
$946$	4.47242	+	14.1936i	0.145411	+	0.461473i
$947$		−	30.1195i		−	0.978753i	−0.872073	−	0.489377i	$-0.837224\pi$
$947$		−	30.1195i		−	0.978753i	0.872073	−	0.489377i	$-0.162776\pi$
$948$	−10.6986	−	15.2909i	−0.347475	−	0.496625i
$949$	−17.6209			−0.571998
$950$	−9.83635	−	31.2165i	−0.319133	−	1.01280i
$951$		−	6.45416i		−	0.209291i
$952$	13.1261	−	17.0872i	0.425420	−	0.553801i
$953$		−	10.7801i		−	0.349203i	−0.984639	−	0.174601i	$-0.944136\pi$
$953$		−	10.7801i		−	0.349203i	0.984639	−	0.174601i	$-0.0558637\pi$
$954$	3.35075	−	1.05583i	0.108484	−	0.0341836i
$955$		−	11.3235i		−	0.366420i
$956$	−25.1847	−	35.9950i	−0.814531	−	1.16416i
$957$		−	18.1745i		−	0.587498i
$958$	−10.7087	−	33.9848i	−0.345982	−	1.09800i
$959$		−	14.0285i		−	0.453003i
$960$	−1.66589	−	6.24408i	−0.0537664	−	0.201527i
$961$	28.3824			0.915560
$962$	6.83861	−	2.15486i	0.220486	−	0.0694753i
$963$	−15.4456			−0.497729
$964$	1.56195	+	2.23240i	0.0503071	+	0.0719009i
$965$		−	3.03008i		−	0.0975417i
$966$	−8.48211	−	2.63248i	−0.272907	−	0.0846985i
$967$			54.3765i			1.74863i	0.485357	+	0.874316i	$0.338689\pi$
$967$			54.3765i			1.74863i	−0.485357	+	0.874316i	$0.661311\pi$
$968$	18.4696	+	14.1880i	0.593636	+	0.456021i
$969$	49.9769			1.60549
$970$	0.575557	+	1.82658i	0.0184800	+	0.0586479i
$971$	−18.5459			−0.595166			−0.297583	−	0.954696i	$-0.596181\pi$
$971$	−18.5459			−0.595166			−0.297583	+	0.954696i	$0.596181\pi$
$972$	14.0587	+	20.0932i	0.450933	+	0.644491i
$973$			18.8883i			0.605531i
$974$	26.1310	−	8.23391i	0.837291	−	0.263832i
$975$		−	20.1332i		−	0.644779i
$976$	−7.53680	−	2.74930i	−0.241247	−	0.0880030i
$977$		−	39.2526i		−	1.25580i	−0.778293	−	0.627901i	$-0.783914\pi$
$977$		−	39.2526i		−	1.25580i	0.778293	−	0.627901i	$-0.216086\pi$
$978$	4.74089	+	15.0456i	0.151597	+	0.481105i
$979$			25.5242i			0.815757i
$980$	0.707317	+	1.01093i	0.0225944	+	0.0322928i
$981$			14.3740i			0.458927i
$982$	29.3569	−	9.25039i	0.936815	−	0.295192i
$983$	26.3835			0.841504			0.420752	−	0.907176i	$-0.361766\pi$
$983$	26.3835			0.841504			0.420752	+	0.907176i	$0.361766\pi$
$984$	12.9868	−	16.9058i	0.414003	−	0.538938i
$985$		−	13.0587i		−	0.416084i
$986$	85.7558	−	27.0218i	2.73102	−	0.860549i
$987$	−0.410733			−0.0130738
$988$	27.3256	−	19.1190i	0.869343	−	0.608256i
$989$	24.9387	+	17.2889i	0.793006	+	0.549754i
$990$	1.77862	−	0.560446i	0.0565283	−	0.0178121i
$991$			20.4638i			0.650054i	0.945705	+	0.325027i	$0.105373\pi$
$991$			20.4638i			0.650054i	−0.945705	+	0.325027i	$0.894627\pi$
$992$	−0.407421	+	9.14321i	−0.0129356	+	0.290297i
$993$	−24.6251			−0.781453
$994$	−7.16604	+	2.25803i	−0.227293	+	0.0716204i
$995$		−	0.0712285i		−	0.00225809i
$996$	12.9727	+	18.5410i	0.411054	+	0.587495i
$997$	−16.2728			−0.515366			−0.257683	−	0.966230i	$-0.582959\pi$
$997$	−16.2728			−0.515366			−0.257683	+	0.966230i	$0.582959\pi$
$998$	31.9916	−	10.0806i	1.01268	−	0.319096i
$999$	−8.54778			−0.270440

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.2.c.a.183.22	yes	36
4.3	odd	2		644.2.c.b.183.21	yes	36
23.22	odd	2		644.2.c.b.183.22	yes	36
92.91	even	2	inner	644.2.c.a.183.21	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.2.c.a.183.21	✓	36	92.91	even	2	inner
644.2.c.a.183.22	yes	36	1.1	even	1	trivial
644.2.c.b.183.21	yes	36	4.3	odd	2
644.2.c.b.183.22	yes	36	23.22	odd	2

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:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	644.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.425020 + 1.34884i) q^{2} -1.30946i q^{3} +(-1.63872 + 1.14656i) q^{4} -0.616901i q^{5} +(1.76625 - 0.556549i) q^{6} -1.00000 q^{7} +(-2.24301 - 1.72305i) q^{8} +1.28530 q^{9} +O(q^{10})\)	\(q+(0.425020 + 1.34884i) q^{2} -1.30946i q^{3} +(-1.63872 + 1.14656i) q^{4} -0.616901i q^{5} +(1.76625 - 0.556549i) q^{6} -1.00000 q^{7} +(-2.24301 - 1.72305i) q^{8} +1.28530 q^{9} +(0.832098 - 0.262195i) q^{10} +1.66304 q^{11} +(1.50139 + 2.14584i) q^{12} +3.32836 q^{13} +(-0.425020 - 1.34884i) q^{14} -0.807810 q^{15} +(1.37078 - 3.75779i) q^{16} -7.61798i q^{17} +(0.546279 + 1.73366i) q^{18} -5.00998 q^{19} +(0.707317 + 1.01093i) q^{20} +1.30946i q^{21} +(0.706827 + 2.24317i) q^{22} +(3.94135 + 2.73236i) q^{23} +(-2.25627 + 2.93715i) q^{24} +4.61943 q^{25} +(1.41462 + 4.48941i) q^{26} -5.61145i q^{27} +(1.63872 - 1.14656i) q^{28} +8.34573 q^{29} +(-0.343336 - 1.08960i) q^{30} +1.61791i q^{31} +(5.65125 + 0.251819i) q^{32} -2.17770i q^{33} +(10.2754 - 3.23779i) q^{34} +0.616901i q^{35} +(-2.10624 + 1.47368i) q^{36} -1.52327i q^{37} +(-2.12934 - 6.75764i) q^{38} -4.35837i q^{39} +(-1.06295 + 1.38372i) q^{40} -5.75587 q^{41} +(-1.76625 + 0.556549i) q^{42} +6.32746 q^{43} +(-2.72526 + 1.90679i) q^{44} -0.792904i q^{45} +(-2.01035 + 6.47754i) q^{46} +0.313665i q^{47} +(-4.92069 - 1.79499i) q^{48} +1.00000 q^{49} +(1.96335 + 6.23086i) q^{50} -9.97548 q^{51} +(-5.45424 + 3.81618i) q^{52} -1.93276i q^{53} +(7.56893 - 2.38498i) q^{54} -1.02593i q^{55} +(2.24301 + 1.72305i) q^{56} +6.56039i q^{57} +(3.54711 + 11.2570i) q^{58} +0.633620i q^{59} +(1.32377 - 0.926207i) q^{60} -2.00565i q^{61} +(-2.18230 + 0.687645i) q^{62} -1.28530 q^{63} +(2.06223 + 7.72963i) q^{64} -2.05327i q^{65} +(2.93736 - 0.925565i) q^{66} -12.5929 q^{67} +(8.73451 + 12.4837i) q^{68} +(3.57792 - 5.16106i) q^{69} +(-0.832098 + 0.262195i) q^{70} -5.31276i q^{71} +(-2.88295 - 2.21463i) q^{72} -5.29417 q^{73} +(2.05465 - 0.647423i) q^{74} -6.04899i q^{75} +(8.20993 - 5.74426i) q^{76} -1.66304 q^{77} +(5.87873 - 1.85240i) q^{78} -7.12582 q^{79} +(-2.31818 - 0.845634i) q^{80} -3.49209 q^{81} +(-2.44636 - 7.76372i) q^{82} +8.64045 q^{83} +(-1.50139 - 2.14584i) q^{84} -4.69954 q^{85} +(2.68930 + 8.53471i) q^{86} -10.9284i q^{87} +(-3.73023 - 2.86550i) q^{88} +15.3479i q^{89} +(1.06950 - 0.337000i) q^{90} -3.32836 q^{91} +(-9.59157 + 0.0414594i) q^{92} +2.11860 q^{93} +(-0.423082 + 0.133314i) q^{94} +3.09066i q^{95} +(0.329748 - 7.40011i) q^{96} +2.19515i q^{97} +(0.425020 + 1.34884i) q^{98} +2.13751 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + q^{2} - 3 q^{4} + q^{6} - 36 q^{7} - 2 q^{8} - 36 q^{9}+O(q^{10}) \) 36 * q + q^2 - 3 * q^4 + q^6 - 36 * q^7 - 2 * q^8 - 36 * q^9	\( 36 q + q^{2} - 3 q^{4} + q^{6} - 36 q^{7} - 2 q^{8} - 36 q^{9} + 8 q^{11} - 3 q^{12} - q^{14} + 8 q^{15} + 9 q^{16} - 8 q^{18} + 8 q^{19} - 14 q^{20} + 24 q^{22} - 8 q^{23} - 4 q^{24} - 36 q^{25} + 7 q^{26} + 3 q^{28} - 8 q^{29} - 9 q^{32} + 14 q^{34} + 14 q^{36} - q^{42} - 40 q^{43} + 16 q^{44} - 9 q^{46} - 39 q^{48} + 36 q^{49} - 43 q^{50} + 25 q^{52} - 33 q^{54} + 2 q^{56} + 19 q^{58} + 76 q^{60} - 5 q^{62} + 36 q^{63} + 12 q^{64} + 50 q^{66} + 8 q^{67} - 60 q^{68} + 28 q^{69} - 36 q^{72} + 36 q^{74} - 8 q^{77} + 17 q^{78} + 40 q^{79} - 50 q^{80} + 28 q^{81} - 17 q^{82} + 3 q^{84} - 24 q^{85} - 16 q^{86} - 28 q^{88} - 98 q^{90} + 19 q^{92} + 8 q^{93} + 35 q^{94} + 91 q^{96} + q^{98} - 24 q^{99}+O(q^{100}) \) 36 * q + q^2 - 3 * q^4 + q^6 - 36 * q^7 - 2 * q^8 - 36 * q^9 + 8 * q^11 - 3 * q^12 - q^14 + 8 * q^15 + 9 * q^16 - 8 * q^18 + 8 * q^19 - 14 * q^20 + 24 * q^22 - 8 * q^23 - 4 * q^24 - 36 * q^25 + 7 * q^26 + 3 * q^28 - 8 * q^29 - 9 * q^32 + 14 * q^34 + 14 * q^36 - q^42 - 40 * q^43 + 16 * q^44 - 9 * q^46 - 39 * q^48 + 36 * q^49 - 43 * q^50 + 25 * q^52 - 33 * q^54 + 2 * q^56 + 19 * q^58 + 76 * q^60 - 5 * q^62 + 36 * q^63 + 12 * q^64 + 50 * q^66 + 8 * q^67 - 60 * q^68 + 28 * q^69 - 36 * q^72 + 36 * q^74 - 8 * q^77 + 17 * q^78 + 40 * q^79 - 50 * q^80 + 28 * q^81 - 17 * q^82 + 3 * q^84 - 24 * q^85 - 16 * q^86 - 28 * q^88 - 98 * q^90 + 19 * q^92 + 8 * q^93 + 35 * q^94 + 91 * q^96 + q^98 - 24 * q^99

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