LMFDB - Embedded newform 731.2.f.d.259.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(259,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("731.259");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.f (of order $4$, degree $2$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			259.8
Character	$\chi$	$=$	731.259
Dual form			731.2.f.d.302.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.84807i q^{2} +(1.37079 - 1.37079i) q^{3} -1.41535 q^{4} +(2.26460 - 2.26460i) q^{5} +(-2.53331 - 2.53331i) q^{6} +(-1.84433 - 1.84433i) q^{7} -1.08047i q^{8} -0.758116i q^{9} +O(q^{10})$	\(q-1.84807i q^{2} +(1.37079 - 1.37079i) q^{3} -1.41535 q^{4} +(2.26460 - 2.26460i) q^{5} +(-2.53331 - 2.53331i) q^{6} +(-1.84433 - 1.84433i) q^{7} -1.08047i q^{8} -0.758116i q^{9} +(-4.18514 - 4.18514i) q^{10} +(1.92945 + 1.92945i) q^{11} +(-1.94015 + 1.94015i) q^{12} -3.60466 q^{13} +(-3.40845 + 3.40845i) q^{14} -6.20857i q^{15} -4.82748 q^{16} +(3.03341 + 2.79257i) q^{17} -1.40105 q^{18} +2.31416i q^{19} +(-3.20521 + 3.20521i) q^{20} -5.05637 q^{21} +(3.56575 - 3.56575i) q^{22} +(4.55338 + 4.55338i) q^{23} +(-1.48109 - 1.48109i) q^{24} -5.25684i q^{25} +6.66165i q^{26} +(3.07315 + 3.07315i) q^{27} +(2.61038 + 2.61038i) q^{28} +(4.85926 - 4.85926i) q^{29} -11.4739 q^{30} +(0.349269 - 0.349269i) q^{31} +6.76058i q^{32} +5.28972 q^{33} +(5.16085 - 5.60595i) q^{34} -8.35335 q^{35} +1.07300i q^{36} +(-1.54275 + 1.54275i) q^{37} +4.27673 q^{38} +(-4.94122 + 4.94122i) q^{39} +(-2.44682 - 2.44682i) q^{40} +(-3.77650 - 3.77650i) q^{41} +9.34452i q^{42} -1.00000i q^{43} +(-2.73085 - 2.73085i) q^{44} +(-1.71683 - 1.71683i) q^{45} +(8.41496 - 8.41496i) q^{46} -1.29183 q^{47} +(-6.61745 + 6.61745i) q^{48} -0.196879i q^{49} -9.71499 q^{50} +(7.98617 - 0.330145i) q^{51} +5.10186 q^{52} +7.45398i q^{53} +(5.67938 - 5.67938i) q^{54} +8.73886 q^{55} +(-1.99274 + 1.99274i) q^{56} +(3.17222 + 3.17222i) q^{57} +(-8.98025 - 8.98025i) q^{58} -7.93048i q^{59} +8.78733i q^{60} +(4.64527 + 4.64527i) q^{61} +(-0.645473 - 0.645473i) q^{62} +(-1.39822 + 1.39822i) q^{63} +2.83904 q^{64} +(-8.16311 + 8.16311i) q^{65} -9.77577i q^{66} -3.69490 q^{67} +(-4.29335 - 3.95247i) q^{68} +12.4834 q^{69} +15.4376i q^{70} +(7.25338 - 7.25338i) q^{71} -0.819118 q^{72} +(-5.32161 + 5.32161i) q^{73} +(2.85110 + 2.85110i) q^{74} +(-7.20601 - 7.20601i) q^{75} -3.27536i q^{76} -7.11708i q^{77} +(9.13170 + 9.13170i) q^{78} +(-0.764989 - 0.764989i) q^{79} +(-10.9323 + 10.9323i) q^{80} +10.6996 q^{81} +(-6.97922 + 6.97922i) q^{82} +5.22419i q^{83} +7.15656 q^{84} +(13.1935 - 0.545414i) q^{85} -1.84807 q^{86} -13.3220i q^{87} +(2.08470 - 2.08470i) q^{88} -13.7253 q^{89} +(-3.17282 + 3.17282i) q^{90} +(6.64818 + 6.64818i) q^{91} +(-6.44465 - 6.44465i) q^{92} -0.957548i q^{93} +2.38739i q^{94} +(5.24065 + 5.24065i) q^{95} +(9.26732 + 9.26732i) q^{96} +(-9.25995 + 9.25995i) q^{97} -0.363846 q^{98} +(1.46274 - 1.46274i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 76 q^{4} - 4 q^{5} + 4 q^{6}+O(q^{10}) $ 68 * q - 76 * q^4 - 4 * q^5 + 4 * q^6	$ 68 q - 76 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{10} - 6 q^{11} - 10 q^{12} - 24 q^{13} - 22 q^{14} + 84 q^{16} - 2 q^{17} + 28 q^{18} + 10 q^{20} - 36 q^{21} + 8 q^{22} + 14 q^{23} - 62 q^{24} - 12 q^{27} - 58 q^{28} + 2 q^{29} + 160 q^{30} - 26 q^{31} + 44 q^{33} + 16 q^{34} + 56 q^{35} - 6 q^{37} - 56 q^{38} - 24 q^{39} + 70 q^{40} + 6 q^{41} + 14 q^{44} + 10 q^{45} + 2 q^{46} - 68 q^{47} - 58 q^{48} + 40 q^{50} + 16 q^{51} + 4 q^{52} + 26 q^{54} - 16 q^{55} + 50 q^{56} + 18 q^{57} - 94 q^{58} + 22 q^{61} - 48 q^{62} + 16 q^{63} + 60 q^{64} - 22 q^{65} + 24 q^{67} + 20 q^{68} + 8 q^{69} - 14 q^{71} - 84 q^{72} + 34 q^{73} + 26 q^{74} - 102 q^{75} + 40 q^{78} + 4 q^{79} - 30 q^{80} - 92 q^{81} - 76 q^{82} + 108 q^{84} + 8 q^{85} + 8 q^{86} + 16 q^{88} - 72 q^{89} + 132 q^{90} + 12 q^{91} - 174 q^{92} + 50 q^{95} + 10 q^{96} - 16 q^{97} - 28 q^{98} - 86 q^{99}+O(q^{100}) $ 68 * q - 76 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^10 - 6 * q^11 - 10 * q^12 - 24 * q^13 - 22 * q^14 + 84 * q^16 - 2 * q^17 + 28 * q^18 + 10 * q^20 - 36 * q^21 + 8 * q^22 + 14 * q^23 - 62 * q^24 - 12 * q^27 - 58 * q^28 + 2 * q^29 + 160 * q^30 - 26 * q^31 + 44 * q^33 + 16 * q^34 + 56 * q^35 - 6 * q^37 - 56 * q^38 - 24 * q^39 + 70 * q^40 + 6 * q^41 + 14 * q^44 + 10 * q^45 + 2 * q^46 - 68 * q^47 - 58 * q^48 + 40 * q^50 + 16 * q^51 + 4 * q^52 + 26 * q^54 - 16 * q^55 + 50 * q^56 + 18 * q^57 - 94 * q^58 + 22 * q^61 - 48 * q^62 + 16 * q^63 + 60 * q^64 - 22 * q^65 + 24 * q^67 + 20 * q^68 + 8 * q^69 - 14 * q^71 - 84 * q^72 + 34 * q^73 + 26 * q^74 - 102 * q^75 + 40 * q^78 + 4 * q^79 - 30 * q^80 - 92 * q^81 - 76 * q^82 + 108 * q^84 + 8 * q^85 + 8 * q^86 + 16 * q^88 - 72 * q^89 + 132 * q^90 + 12 * q^91 - 174 * q^92 + 50 * q^95 + 10 * q^96 - 16 * q^97 - 28 * q^98 - 86 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$		−	1.84807i		−	1.30678i	−0.757021	−	0.653391i	$-0.773346\pi$
$2$		−	1.84807i		−	1.30678i	0.757021	−	0.653391i	$-0.226654\pi$
$3$	1.37079	−	1.37079i	0.791424	−	0.791424i	−0.190301	−	0.981726i	$-0.560946\pi$
$3$	1.37079	−	1.37079i	0.791424	−	0.791424i	0.981726	+	0.190301i	$0.0609465\pi$
$4$	−1.41535			−0.707677
$5$	2.26460	−	2.26460i	1.01276	−	1.01276i	0.0128429	−	0.999918i	$-0.495912\pi$
$5$	2.26460	−	2.26460i	1.01276	−	1.01276i	0.999918	−	0.0128429i	$-0.00408813\pi$
$6$	−2.53331	−	2.53331i	−1.03422	−	1.03422i
$7$	−1.84433	−	1.84433i	−0.697092	−	0.697092i	0.266690	−	0.963782i	$-0.414070\pi$
$7$	−1.84433	−	1.84433i	−0.697092	−	0.697092i	−0.963782	+	0.266690i	$0.914070\pi$
$8$		−	1.08047i		−	0.382002i
$9$		−	0.758116i		−	0.252705i
$10$	−4.18514	−	4.18514i	−1.32346	−	1.32346i
$11$	1.92945	+	1.92945i	0.581750	+	0.581750i	0.935384	−	0.353634i	$-0.115054\pi$
$11$	1.92945	+	1.92945i	0.581750	+	0.581750i	−0.353634	+	0.935384i	$0.615054\pi$
$12$	−1.94015	+	1.94015i	−0.560073	+	0.560073i
$13$	−3.60466			−0.999752			−0.499876	−	0.866097i	$-0.666621\pi$
$13$	−3.60466			−0.999752			−0.499876	+	0.866097i	$0.666621\pi$
$14$	−3.40845	+	3.40845i	−0.910947	+	0.910947i
$15$		−	6.20857i		−	1.60305i
$16$	−4.82748			−1.20687
$17$	3.03341	+	2.79257i	0.735710	+	0.677297i
$17$	3.03341	+	2.79257i	0.735710	+	0.677297i
$18$	−1.40105			−0.330230
$19$			2.31416i			0.530905i	0.964124	+	0.265453i	$0.0855214\pi$
$19$			2.31416i			0.530905i	−0.964124	+	0.265453i	$0.914479\pi$
$20$	−3.20521	+	3.20521i	−0.716707	+	0.716707i
$21$	−5.05637			−1.10339
$22$	3.56575	−	3.56575i	0.760220	−	0.760220i
$23$	4.55338	+	4.55338i	0.949446	+	0.949446i	0.998782	−	0.0493363i	$-0.0157106\pi$
$23$	4.55338	+	4.55338i	0.949446	+	0.949446i	−0.0493363	+	0.998782i	$0.515711\pi$
$24$	−1.48109	−	1.48109i	−0.302326	−	0.302326i
$25$		−	5.25684i		−	1.05137i
$26$			6.66165i			1.30646i
$27$	3.07315	+	3.07315i	0.591427	+	0.591427i
$28$	2.61038	+	2.61038i	0.493316	+	0.493316i
$29$	4.85926	−	4.85926i	0.902343	−	0.902343i	−0.0932957	−	0.995638i	$-0.529740\pi$
$29$	4.85926	−	4.85926i	0.902343	−	0.902343i	0.995638	+	0.0932957i	$0.0297402\pi$
$30$	−11.4739			−2.09483
$31$	0.349269	−	0.349269i	0.0627306	−	0.0627306i	−0.675045	−	0.737776i	$-0.735876\pi$
$31$	0.349269	−	0.349269i	0.0627306	−	0.0627306i	0.737776	+	0.675045i	$0.235876\pi$
$32$			6.76058i			1.19511i
$33$	5.28972			0.920823
$34$	5.16085	−	5.60595i	0.885079	−	0.961412i
$35$	−8.35335			−1.41197
$36$			1.07300i			0.178834i
$37$	−1.54275	+	1.54275i	−0.253626	+	0.253626i	−0.822456	−	0.568829i	$-0.807396\pi$
$37$	−1.54275	+	1.54275i	−0.253626	+	0.253626i	0.568829	+	0.822456i	$0.307396\pi$
$38$	4.27673			0.693777
$39$	−4.94122	+	4.94122i	−0.791228	+	0.791228i
$40$	−2.44682	−	2.44682i	−0.386877	−	0.386877i
$41$	−3.77650	−	3.77650i	−0.589790	−	0.589790i	0.347785	−	0.937574i	$-0.386934\pi$
$41$	−3.77650	−	3.77650i	−0.589790	−	0.589790i	−0.937574	+	0.347785i	$0.886934\pi$
$42$			9.34452i			1.44189i
$43$		−	1.00000i		−	0.152499i
$43$		−	1.00000i		−	0.152499i
$44$	−2.73085	−	2.73085i	−0.411691	−	0.411691i
$45$	−1.71683	−	1.71683i	−0.255930	−	0.255930i
$46$	8.41496	−	8.41496i	1.24072	−	1.24072i
$47$	−1.29183			−0.188433			−0.0942164	−	0.995552i	$-0.530035\pi$
$47$	−1.29183			−0.188433			−0.0942164	+	0.995552i	$0.530035\pi$
$48$	−6.61745	+	6.61745i	−0.955147	+	0.955147i
$49$		−	0.196879i		−	0.0281256i
$50$	−9.71499			−1.37391
$51$	7.98617	−	0.330145i	1.11829	−	0.0462295i
$52$	5.10186			0.707501
$53$			7.45398i			1.02388i	0.859020	+	0.511942i	$0.171074\pi$
$53$			7.45398i			1.02388i	−0.859020	+	0.511942i	$0.828926\pi$
$54$	5.67938	−	5.67938i	0.772866	−	0.772866i
$55$	8.73886			1.17835
$56$	−1.99274	+	1.99274i	−0.266291	+	0.266291i
$57$	3.17222	+	3.17222i	0.420171	+	0.420171i
$58$	−8.98025	−	8.98025i	−1.17916	−	1.17916i
$59$		−	7.93048i		−	1.03246i	−0.856450	−	0.516230i	$-0.827335\pi$
$59$		−	7.93048i		−	1.03246i	0.856450	−	0.516230i	$-0.172665\pi$
$60$			8.78733i			1.13444i
$61$	4.64527	+	4.64527i	0.594766	+	0.594766i	0.938915	−	0.344149i	$-0.111833\pi$
$61$	4.64527	+	4.64527i	0.594766	+	0.594766i	−0.344149	+	0.938915i	$0.611833\pi$
$62$	−0.645473	−	0.645473i	−0.0819752	−	0.0819752i
$63$	−1.39822	+	1.39822i	−0.176159	+	0.176159i
$64$	2.83904			0.354881
$65$	−8.16311	+	8.16311i	−1.01251	+	1.01251i
$66$		−	9.77577i		−	1.20331i
$67$	−3.69490			−0.451403			−0.225702	−	0.974196i	$-0.572467\pi$
$67$	−3.69490			−0.451403			−0.225702	+	0.974196i	$0.572467\pi$
$68$	−4.29335	−	3.95247i	−0.520645	−	0.479307i
$69$	12.4834			1.50283
$70$			15.4376i			1.84514i
$71$	7.25338	−	7.25338i	0.860817	−	0.860817i	−0.130616	−	0.991433i	$-0.541695\pi$
$71$	7.25338	−	7.25338i	0.860817	−	0.860817i	0.991433	+	0.130616i	$0.0416954\pi$
$72$	−0.819118			−0.0965340
$73$	−5.32161	+	5.32161i	−0.622847	+	0.622847i	−0.946258	−	0.323411i	$-0.895170\pi$
$73$	−5.32161	+	5.32161i	−0.622847	+	0.622847i	0.323411	+	0.946258i	$0.395170\pi$
$74$	2.85110	+	2.85110i	0.331434	+	0.331434i
$75$	−7.20601	−	7.20601i	−0.832078	−	0.832078i
$76$		−	3.27536i		−	0.375709i
$77$		−	7.11708i		−	0.811067i
$78$	9.13170	+	9.13170i	1.03396	+	1.03396i
$79$	−0.764989	−	0.764989i	−0.0860680	−	0.0860680i	0.662762	−	0.748830i	$-0.269384\pi$
$79$	−0.764989	−	0.764989i	−0.0860680	−	0.0860680i	−0.748830	+	0.662762i	$0.769384\pi$
$80$	−10.9323	+	10.9323i	−1.22227	+	1.22227i
$81$	10.6996			1.18885
$82$	−6.97922	+	6.97922i	−0.770726	+	0.770726i
$83$			5.22419i			0.573430i	0.958016	+	0.286715i	$0.0925632\pi$
$83$			5.22419i			0.573430i	−0.958016	+	0.286715i	$0.907437\pi$
$84$	7.15656			0.780844
$85$	13.1935	−	0.545414i	1.43104	−	0.0591584i
$86$	−1.84807			−0.199282
$87$		−	13.3220i		−	1.42827i
$88$	2.08470	−	2.08470i	0.222230	−	0.222230i
$89$	−13.7253			−1.45488			−0.727440	−	0.686171i	$-0.759290\pi$
$89$	−13.7253			−1.45488			−0.727440	+	0.686171i	$0.759290\pi$
$90$	−3.17282	+	3.17282i	−0.334444	+	0.334444i
$91$	6.64818	+	6.64818i	0.696919	+	0.696919i
$92$	−6.44465	−	6.44465i	−0.671901	−	0.671901i
$93$		−	0.957548i		−	0.0992931i
$94$			2.38739i			0.246240i
$95$	5.24065	+	5.24065i	0.537680	+	0.537680i
$96$	9.26732	+	9.26732i	0.945842	+	0.945842i
$97$	−9.25995	+	9.25995i	−0.940206	+	0.940206i	−0.998310	−	0.0581049i	$-0.981494\pi$
$97$	−9.25995	+	9.25995i	−0.940206	+	0.940206i	0.0581049	+	0.998310i	$0.481494\pi$
$98$	−0.363846			−0.0367540
$99$	1.46274	−	1.46274i	0.147011	−	0.147011i
$100$			7.44028i			0.744028i
$101$	−9.49224			−0.944514			−0.472257	−	0.881461i	$-0.656560\pi$
$101$	−9.49224			−0.944514			−0.472257	+	0.881461i	$0.656560\pi$
$102$	−0.610130	−	14.7590i	−0.0604118	−	1.46136i
$103$	−0.138265			−0.0136236			−0.00681182	−	0.999977i	$-0.502168\pi$
$103$	−0.138265			−0.0136236			−0.00681182	+	0.999977i	$0.502168\pi$
$104$			3.89471i			0.381908i
$105$	−11.4507	+	11.4507i	−1.11747	+	1.11747i
$106$	13.7755			1.33799
$107$	−1.13577	+	1.13577i	−0.109799	+	0.109799i	−0.759872	−	0.650073i	$-0.774738\pi$
$107$	−1.13577	+	1.13577i	−0.109799	+	0.109799i	0.650073	+	0.759872i	$0.274738\pi$
$108$	−4.34959	−	4.34959i	−0.418539	−	0.418539i
$109$	2.23217	+	2.23217i	0.213803	+	0.213803i	0.805881	−	0.592078i	$-0.201692\pi$
$109$	2.23217	+	2.23217i	0.213803	+	0.213803i	−0.592078	+	0.805881i	$0.701692\pi$
$110$		−	16.1500i		−	1.53984i
$111$			4.22956i			0.401452i
$112$	8.90348	+	8.90348i	0.841300	+	0.841300i
$113$	−0.337922	−	0.337922i	−0.0317890	−	0.0317890i	0.691034	−	0.722823i	$-0.257156\pi$
$113$	−0.337922	−	0.337922i	−0.0317890	−	0.0317890i	−0.722823	+	0.691034i	$0.757156\pi$
$114$	5.86248	−	5.86248i	0.549072	−	0.549072i
$115$	20.6232			1.92312
$116$	−6.87758	+	6.87758i	−0.638567	+	0.638567i
$117$			2.73275i			0.252642i
$118$	−14.6561			−1.34920
$119$	−0.444195	−	10.7450i	−0.0407193	−	0.984996i
$120$	−6.70815			−0.612368
$121$		−	3.55447i		−	0.323133i
$122$	8.58477	−	8.58477i	0.777229	−	0.777229i
$123$	−10.3535			−0.933548
$124$	−0.494340	+	0.494340i	−0.0443930	+	0.0443930i
$125$	−0.581633	−	0.581633i	−0.0520228	−	0.0520228i
$126$	2.58400	+	2.58400i	0.230201	+	0.230201i
$127$		−	7.17905i		−	0.637037i	−0.947917	−	0.318519i	$-0.896815\pi$
$127$		−	7.17905i		−	0.637037i	0.947917	−	0.318519i	$-0.103185\pi$
$128$			8.27441i			0.731362i
$129$	−1.37079	−	1.37079i	−0.120691	−	0.120691i
$130$	15.0860	+	15.0860i	1.32313	+	1.32313i
$131$	1.85303	−	1.85303i	0.161900	−	0.161900i	−0.621508	−	0.783408i	$-0.713480\pi$
$131$	1.85303	−	1.85303i	0.161900	−	0.161900i	0.783408	+	0.621508i	$0.213480\pi$
$132$	−7.48683			−0.651645
$133$	4.26808	−	4.26808i	0.370090	−	0.370090i
$134$			6.82842i			0.589885i
$135$	13.9189			1.19795
$136$	3.01727	−	3.27750i	0.258729	−	0.281043i
$137$	1.47071			0.125651			0.0628256	−	0.998025i	$-0.479989\pi$
$137$	1.47071			0.125651			0.0628256	+	0.998025i	$0.479989\pi$
$138$		−	23.0702i		−	1.96387i
$139$	−5.85759	+	5.85759i	−0.496834	+	0.496834i	−0.910451	−	0.413617i	$-0.864265\pi$
$139$	−5.85759	+	5.85759i	−0.496834	+	0.496834i	0.413617	+	0.910451i	$0.364265\pi$
$140$	11.8229			0.999221
$141$	−1.77082	+	1.77082i	−0.149130	+	0.149130i
$142$	−13.4047	−	13.4047i	−1.12490	−	1.12490i
$143$	−6.95500	−	6.95500i	−0.581606	−	0.581606i
$144$			3.65979i			0.304982i
$145$		−	22.0086i		−	1.82771i
$146$	9.83469	+	9.83469i	0.813925	+	0.813925i
$147$	−0.269879	−	0.269879i	−0.0222593	−	0.0222593i
$148$	2.18353	−	2.18353i	0.179485	−	0.179485i
$149$	−9.40634			−0.770597			−0.385299	−	0.922792i	$-0.625902\pi$
$149$	−9.40634			−0.770597			−0.385299	+	0.922792i	$0.625902\pi$
$150$	−13.3172	+	13.3172i	−1.08734	+	1.08734i
$151$		−	6.90876i		−	0.562227i	−0.959674	−	0.281114i	$-0.909296\pi$
$151$		−	6.90876i		−	0.562227i	0.959674	−	0.281114i	$-0.0907038\pi$
$152$	2.50037			0.202807
$153$	2.11709	−	2.29967i	0.171156	−	0.185918i
$154$	−13.1529			−1.05989
$155$		−	1.58191i		−	0.127062i
$156$	6.99357	−	6.99357i	0.559934	−	0.559934i
$157$	12.2533			0.977919			0.488959	−	0.872307i	$-0.337377\pi$
$157$	12.2533			0.977919			0.488959	+	0.872307i	$0.337377\pi$
$158$	−1.41375	+	1.41375i	−0.112472	+	0.112472i
$159$	10.2178	+	10.2178i	0.810326	+	0.810326i
$160$	15.3100	+	15.3100i	1.21036	+	1.21036i
$161$		−	16.7959i		−	1.32370i
$162$		−	19.7736i		−	1.55356i
$163$	12.2295	+	12.2295i	0.957890	+	0.957890i	0.999148	−	0.0412588i	$-0.0131368\pi$
$163$	12.2295	+	12.2295i	0.957890	+	0.957890i	−0.0412588	+	0.999148i	$0.513137\pi$
$164$	5.34508	+	5.34508i	0.417380	+	0.417380i
$165$	11.9791	−	11.9791i	0.932573	−	0.932573i
$166$	9.65466			0.749347
$167$	17.4838	−	17.4838i	1.35294	−	1.35294i	0.470587	−	0.882354i	$-0.344042\pi$
$167$	17.4838	−	17.4838i	1.35294	−	1.35294i	0.882354	−	0.470587i	$-0.155958\pi$
$168$			5.46324i			0.421498i
$169$	−0.00644902			−0.000496079
$170$	−1.00796	−	24.3825i	−0.0773071	−	1.87005i
$171$	1.75440			0.134162
$172$			1.41535i			0.107920i
$173$	−9.37820	+	9.37820i	−0.713011	+	0.713011i	−0.967164	−	0.254153i	$-0.918203\pi$
$173$	−9.37820	+	9.37820i	−0.713011	+	0.713011i	0.254153	+	0.967164i	$0.418203\pi$
$174$	−24.6200			−1.86644
$175$	−9.69535	+	9.69535i	−0.732900	+	0.732900i
$176$	−9.31437	−	9.31437i	−0.702097	−	0.702097i
$177$	−10.8710	−	10.8710i	−0.817115	−	0.817115i
$178$			25.3653i			1.90121i
$179$		−	9.60672i		−	0.718040i	−0.933330	−	0.359020i	$-0.883111\pi$
$179$		−	9.60672i		−	0.718040i	0.933330	−	0.359020i	$-0.116889\pi$
$180$	2.42992	+	2.42992i	0.181116	+	0.181116i
$181$	15.3588	+	15.3588i	1.14161	+	1.14161i	0.988156	+	0.153453i	$0.0490395\pi$
$181$	15.3588	+	15.3588i	1.14161	+	1.14161i	0.153453	+	0.988156i	$0.450961\pi$
$182$	12.2863	−	12.2863i	0.910721	−	0.910721i
$183$	12.7354			0.941424
$184$	4.91978	−	4.91978i	0.362691	−	0.362691i
$185$			6.98741i			0.513725i
$186$	−1.76961			−0.129754
$187$	0.464694	+	11.2409i	0.0339818	+	0.822017i
$188$	1.82840			0.133350
$189$		−	11.3358i		−	0.824559i
$190$	9.68508	−	9.68508i	0.702630	−	0.702630i
$191$	−2.04051			−0.147646			−0.0738232	−	0.997271i	$-0.523520\pi$
$191$	−2.04051			−0.147646			−0.0738232	+	0.997271i	$0.523520\pi$
$192$	3.89173	−	3.89173i	0.280861	−	0.280861i
$193$	−12.8801	−	12.8801i	−0.927129	−	0.927129i	0.0703904	−	0.997520i	$-0.477575\pi$
$193$	−12.8801	−	12.8801i	−0.927129	−	0.927129i	−0.997520	+	0.0703904i	$0.977575\pi$
$194$	17.1130	+	17.1130i	1.22864	+	1.22864i
$195$			22.3798i			1.60265i
$196$			0.278654i			0.0199038i
$197$	−8.08687	−	8.08687i	−0.576166	−	0.576166i	0.357679	−	0.933845i	$-0.383568\pi$
$197$	−8.08687	−	8.08687i	−0.576166	−	0.576166i	−0.933845	+	0.357679i	$0.883568\pi$
$198$	−2.70325	−	2.70325i	−0.192112	−	0.192112i
$199$	17.7594	−	17.7594i	1.25893	−	1.25893i	0.307328	−	0.951604i	$-0.400565\pi$
$199$	17.7594	−	17.7594i	1.25893	−	1.25893i	0.951604	−	0.307328i	$-0.0994350\pi$
$200$	−5.67983			−0.401625
$201$	−5.06492	+	5.06492i	−0.357252	+	0.357252i
$202$			17.5423i			1.23427i
$203$	−17.9242			−1.25803
$204$	−11.3033	+	0.467271i	−0.791386	+	0.0327155i
$205$	−17.1045			−1.19463
$206$			0.255523i			0.0178031i
$207$	3.45199	−	3.45199i	0.239930	−	0.239930i
$208$	17.4014			1.20657
$209$	−4.46505	+	4.46505i	−0.308854	+	0.308854i
$210$	21.1616	+	21.1616i	1.46029	+	1.46029i
$211$	−13.8589	−	13.8589i	−0.954088	−	0.954088i	0.0449031	−	0.998991i	$-0.485702\pi$
$211$	−13.8589	−	13.8589i	−0.954088	−	0.954088i	−0.998991	+	0.0449031i	$0.985702\pi$
$212$		−	10.5500i		−	0.724578i
$213$		−	19.8857i		−	1.36254i
$214$	2.09898	+	2.09898i	0.143483	+	0.143483i
$215$	−2.26460	−	2.26460i	−0.154445	−	0.154445i
$216$	3.32043	−	3.32043i	0.225927	−	0.225927i
$217$	−1.28834			−0.0874580
$218$	4.12520	−	4.12520i	0.279394	−	0.279394i
$219$			14.5896i			0.985873i
$220$	−12.3686			−0.833889
$221$	−10.9344	−	10.0662i	−0.735527	−	0.677129i
$222$	7.81651			0.524609
$223$			15.8843i			1.06369i	0.846842	+	0.531845i	$0.178501\pi$
$223$			15.8843i			1.06369i	−0.846842	+	0.531845i	$0.821499\pi$
$224$	12.4688	−	12.4688i	0.833104	−	0.833104i
$225$	−3.98529			−0.265686
$226$	−0.624502	+	0.624502i	−0.0415412	+	0.0415412i
$227$	−8.96922	−	8.96922i	−0.595308	−	0.595308i	0.343752	−	0.939060i	$-0.388302\pi$
$227$	−8.96922	−	8.96922i	−0.595308	−	0.595308i	−0.939060	+	0.343752i	$0.888302\pi$
$228$	−4.48982	−	4.48982i	−0.297345	−	0.297345i
$229$		−	25.1388i		−	1.66122i	−0.556857	−	0.830608i	$-0.687993\pi$
$229$		−	25.1388i		−	1.66122i	0.556857	−	0.830608i	$-0.312007\pi$
$230$		−	38.1130i		−	2.51310i
$231$	−9.75601	−	9.75601i	−0.641898	−	0.641898i
$232$	−5.25027	−	5.25027i	−0.344697	−	0.344697i
$233$	8.00782	−	8.00782i	0.524610	−	0.524610i	−0.394350	−	0.918960i	$-0.629030\pi$
$233$	8.00782	−	8.00782i	0.524610	−	0.524610i	0.918960	+	0.394350i	$0.129030\pi$
$234$	5.05030			0.330148
$235$	−2.92548	+	2.92548i	−0.190837	+	0.190837i
$236$			11.2244i			0.730648i
$237$	−2.09727			−0.136233
$238$	−19.8575	+	0.820902i	−1.28717	+	0.0532111i
$239$	15.4508			0.999432			0.499716	−	0.866189i	$-0.333438\pi$
$239$	15.4508			0.999432			0.499716	+	0.866189i	$0.333438\pi$
$240$			29.9718i			1.93467i
$241$	−14.1913	+	14.1913i	−0.914141	+	0.914141i	−0.996595	−	0.0824537i	$-0.973724\pi$
$241$	−14.1913	+	14.1913i	−0.914141	+	0.914141i	0.0824537	+	0.996595i	$0.473724\pi$
$242$	−6.56889			−0.422264
$243$	5.44745	−	5.44745i	0.349454	−	0.349454i
$244$	−6.57470	−	6.57470i	−0.420902	−	0.420902i
$245$	−0.445853	−	0.445853i	−0.0284845	−	0.0284845i
$246$			19.1341i			1.21994i
$247$		−	8.34176i		−	0.530773i
$248$	−0.377374	−	0.377374i	−0.0239633	−	0.0239633i
$249$	7.16126	+	7.16126i	0.453826	+	0.453826i
$250$	−1.07490	+	1.07490i	−0.0679825	+	0.0679825i
$251$	28.1349			1.77586			0.887930	−	0.459978i	$-0.152143\pi$
$251$	28.1349			1.77586			0.887930	+	0.459978i	$0.152143\pi$
$252$	1.97897	−	1.97897i	0.124663	−	0.124663i
$253$			17.5710i			1.10468i
$254$	−13.2674			−0.832468
$255$	17.3379	−	18.8331i	1.08574	−	1.17938i
$256$	20.9698			1.31061
$257$			26.1744i			1.63272i	0.577546	+	0.816358i	$0.304011\pi$
$257$			26.1744i			1.63272i	−0.577546	+	0.816358i	$0.695989\pi$
$258$	−2.53331	+	2.53331i	−0.157717	+	0.157717i
$259$	5.69068			0.353601
$260$	11.5537	−	11.5537i	0.716529	−	0.716529i
$261$	−3.68388	−	3.68388i	−0.228027	−	0.228027i
$262$	−3.42453	−	3.42453i	−0.211568	−	0.211568i
$263$			31.6151i			1.94947i	0.223366	+	0.974735i	$0.428296\pi$
$263$			31.6151i			1.94947i	−0.223366	+	0.974735i	$0.571704\pi$
$264$		−	5.71537i		−	0.351757i
$265$	16.8803	+	16.8803i	1.03695	+	1.03695i
$266$	−7.88770	−	7.88770i	−0.483626	−	0.483626i
$267$	−18.8145	+	18.8145i	−1.15143	+	1.15143i
$268$	5.22958			0.319448
$269$	−7.83821	+	7.83821i	−0.477904	+	0.477904i	−0.904461	−	0.426557i	$-0.859727\pi$
$269$	−7.83821	+	7.83821i	−0.477904	+	0.477904i	0.426557	+	0.904461i	$0.359727\pi$
$270$		−	25.7231i		−	1.56546i
$271$	13.2848			0.806991			0.403496	−	0.914982i	$-0.367795\pi$
$271$	13.2848			0.806991			0.403496	+	0.914982i	$0.367795\pi$
$272$	−14.6437	−	13.4811i	−0.887906	−	0.817409i
$273$	18.2265			1.10312
$274$		−	2.71797i		−	0.164199i
$275$	10.1428	−	10.1428i	0.611633	−	0.611633i
$276$	−17.6685			−1.06352
$277$	15.8027	−	15.8027i	0.949494	−	0.949494i	−0.0492909	−	0.998784i	$-0.515696\pi$
$277$	15.8027	−	15.8027i	0.949494	−	0.949494i	0.998784	+	0.0492909i	$0.0156962\pi$
$278$	10.8252	+	10.8252i	0.649254	+	0.649254i
$279$	−0.264787	−	0.264787i	−0.0158524	−	0.0158524i
$280$			9.02551i			0.539378i
$281$			25.5399i			1.52358i	0.647824	+	0.761790i	$0.275679\pi$
$281$			25.5399i			1.52358i	−0.647824	+	0.761790i	$0.724321\pi$
$282$	3.27260	+	3.27260i	0.194881	+	0.194881i
$283$	12.1036	+	12.1036i	0.719487	+	0.719487i	0.968500	−	0.249013i	$-0.0801063\pi$
$283$	12.1036	+	12.1036i	0.719487	+	0.719487i	−0.249013	+	0.968500i	$0.580106\pi$
$284$	−10.2661	+	10.2661i	−0.609181	+	0.609181i
$285$	14.3676			0.851066
$286$	−12.8533	+	12.8533i	−0.760032	+	0.760032i
$287$			13.9302i			0.822275i
$288$	5.12530			0.302011
$289$	1.40315	+	16.9420i	0.0825380	+	0.996588i
$290$	−40.6734			−2.38842
$291$			25.3868i			1.48820i
$292$	7.53196	−	7.53196i	0.440774	−	0.440774i
$293$	−20.0462			−1.17111			−0.585555	−	0.810632i	$-0.699123\pi$
$293$	−20.0462			−1.17111			−0.585555	+	0.810632i	$0.699123\pi$
$294$	−0.498755	+	0.498755i	−0.0290880	+	0.0290880i
$295$	−17.9594	−	17.9594i	−1.04564	−	1.04564i
$296$	1.66689	+	1.66689i	0.0968858	+	0.0968858i
$297$			11.8589i			0.688126i
$298$			17.3835i			1.00700i
$299$	−16.4134	−	16.4134i	−0.949210	−	0.949210i
$300$	10.1990	+	10.1990i	0.588842	+	0.588842i
$301$	−1.84433	+	1.84433i	−0.106306	+	0.106306i
$302$	−12.7679			−0.734708
$303$	−13.0118	+	13.0118i	−0.747511	+	0.747511i
$304$		−	11.1716i		−	0.640734i
$305$	21.0394			1.20471
$306$	−4.24995	−	3.91252i	−0.242954	−	0.223664i
$307$	−26.5446			−1.51498			−0.757489	−	0.652848i	$-0.773574\pi$
$307$	−26.5446			−1.51498			−0.757489	+	0.652848i	$0.773574\pi$
$308$			10.0732i			0.573973i
$309$	−0.189532	+	0.189532i	−0.0107821	+	0.0107821i
$310$	−2.92348			−0.166042
$311$	1.95608	−	1.95608i	0.110919	−	0.110919i	−0.649469	−	0.760388i	$-0.725009\pi$
$311$	1.95608	−	1.95608i	0.110919	−	0.110919i	0.760388	+	0.649469i	$0.225009\pi$
$312$	5.33882	+	5.33882i	0.302251	+	0.302251i
$313$	19.9452	+	19.9452i	1.12737	+	1.12737i	0.990603	+	0.136766i	$0.0436710\pi$
$313$	19.9452	+	19.9452i	1.12737	+	1.12737i	0.136766	+	0.990603i	$0.456329\pi$
$314$		−	22.6449i		−	1.27793i
$315$			6.33281i			0.356813i
$316$	1.08273	+	1.08273i	0.0609083	+	0.0609083i
$317$	22.0367	+	22.0367i	1.23771	+	1.23771i	0.960936	+	0.276770i	$0.0892639\pi$
$317$	22.0367	+	22.0367i	1.23771	+	1.23771i	0.276770	+	0.960936i	$0.410736\pi$
$318$	18.8832	−	18.8832i	1.05892	−	1.05892i
$319$	18.7514			1.04988
$320$	6.42930	−	6.42930i	0.359409	−	0.359409i
$321$			3.11380i			0.173795i
$322$	−31.0400			−1.72979
$323$	−6.46245	+	7.01980i	−0.359580	+	0.390592i
$324$	−15.1437			−0.841318
$325$			18.9491i			1.05111i
$326$	22.6010	−	22.6010i	1.25175	−	1.25175i
$327$	6.11966			0.338418
$328$	−4.08038	+	4.08038i	−0.225301	+	0.225301i
$329$	2.38256	+	2.38256i	0.131355	+	0.131355i
$330$	−22.1382	−	22.1382i	−1.21867	−	1.21867i
$331$			12.6882i			0.697409i	0.937233	+	0.348704i	$0.113378\pi$
$331$			12.6882i			0.697409i	−0.937233	+	0.348704i	$0.886622\pi$
$332$		−	7.39408i		−	0.405803i
$333$	1.16958	+	1.16958i	0.0640926	+	0.0640926i
$334$	−32.3113	−	32.3113i	−1.76800	−	1.76800i
$335$	−8.36747	+	8.36747i	−0.457163	+	0.457163i
$336$	24.4095			1.33165
$337$	−16.1338	+	16.1338i	−0.878867	+	0.878867i	−0.993417	−	0.114551i	$-0.963457\pi$
$337$	−16.1338	+	16.1338i	−0.878867	+	0.878867i	0.114551	+	0.993417i	$0.463457\pi$
$338$			0.0119182i			0.000648266i
$339$	−0.926437			−0.0503172
$340$	−18.6735	+	0.771953i	−1.01271	+	0.0418650i
$341$	1.34779			0.0729871
$342$		−	3.24225i		−	0.175321i
$343$	−13.2734	+	13.2734i	−0.716698	+	0.716698i
$344$	−1.08047			−0.0582548
$345$	28.2700	−	28.2700i	1.52201	−	1.52201i
$346$	17.3315	+	17.3315i	0.931749	+	0.931749i
$347$	−19.6529	−	19.6529i	−1.05502	−	1.05502i	−0.998395	−	0.0566277i	$-0.981965\pi$
$347$	−19.6529	−	19.6529i	−1.05502	−	1.05502i	−0.0566277	−	0.998395i	$-0.518035\pi$
$348$			18.8554i			1.01076i
$349$		−	2.80343i		−	0.150064i	−0.997181	−	0.0750320i	$-0.976094\pi$
$349$		−	2.80343i		−	0.150064i	0.997181	−	0.0750320i	$-0.0239059\pi$
$350$	17.9177	+	17.9177i	0.957740	+	0.957740i
$351$	−11.0776	−	11.0776i	−0.591281	−	0.591281i
$352$	−13.0442	+	13.0442i	−0.695257	+	0.695257i
$353$	21.1024			1.12317			0.561583	−	0.827420i	$-0.310192\pi$
$353$	21.1024			1.12317			0.561583	+	0.827420i	$0.310192\pi$
$354$	−20.0903	+	20.0903i	−1.06779	+	1.06779i
$355$		−	32.8520i		−	1.74360i
$356$	19.4262			1.02959
$357$	−15.3381	−	14.1203i	−0.811776	−	0.747323i
$358$	−17.7539			−0.938321
$359$		−	25.5708i		−	1.34958i	−0.738011	−	0.674788i	$-0.764235\pi$
$359$		−	25.5708i		−	1.34958i	0.738011	−	0.674788i	$-0.235765\pi$
$360$	−1.85498	+	1.85498i	−0.0977658	+	0.0977658i
$361$	13.6447			0.718140
$362$	28.3841	−	28.3841i	1.49183	−	1.49183i
$363$	−4.87242	−	4.87242i	−0.255736	−	0.255736i
$364$	−9.40953	−	9.40953i	−0.493193	−	0.493193i
$365$			24.1026i			1.26159i
$366$		−	23.5358i		−	1.23024i
$367$	−9.29738	−	9.29738i	−0.485319	−	0.485319i	0.421506	−	0.906826i	$-0.361502\pi$
$367$	−9.29738	−	9.29738i	−0.485319	−	0.485319i	−0.906826	+	0.421506i	$0.861502\pi$
$368$	−21.9814	−	21.9814i	−1.14586	−	1.14586i
$369$	−2.86302	+	2.86302i	−0.149043	+	0.149043i
$370$	12.9132			0.671326
$371$	13.7476	−	13.7476i	0.713741	−	0.713741i
$372$			1.35527i			0.0702674i
$373$	−8.08895			−0.418830			−0.209415	−	0.977827i	$-0.567156\pi$
$373$	−8.08895			−0.418830			−0.209415	+	0.977827i	$0.567156\pi$
$374$	20.7740	−	0.858786i	1.07420	−	0.0444068i
$375$	−1.59459			−0.0823443
$376$			1.39578i			0.0719818i
$377$	−17.5160	+	17.5160i	−0.902119	+	0.902119i
$378$	−20.9493			−1.07752
$379$	−23.0712	+	23.0712i	−1.18509	+	1.18509i	−0.206678	+	0.978409i	$0.566265\pi$
$379$	−23.0712	+	23.0712i	−1.18509	+	1.18509i	−0.978409	+	0.206678i	$0.933735\pi$
$380$	−7.41738	−	7.41738i	−0.380503	−	0.380503i
$381$	−9.84094	−	9.84094i	−0.504167	−	0.504167i
$382$			3.77101i			0.192941i
$383$			22.5810i			1.15383i	0.816803	+	0.576917i	$0.195744\pi$
$383$			22.5810i			1.15383i	−0.816803	+	0.576917i	$0.804256\pi$
$384$	11.3425	+	11.3425i	0.578818	+	0.578818i
$385$	−16.1174	−	16.1174i	−0.821416	−	0.821416i
$386$	−23.8033	+	23.8033i	−1.21155	+	1.21155i
$387$	−0.758116			−0.0385372
$388$	13.1061	−	13.1061i	0.665362	−	0.665362i
$389$			10.3087i			0.522672i	0.965248	+	0.261336i	$0.0841631\pi$
$389$			10.3087i			0.522672i	−0.965248	+	0.261336i	$0.915837\pi$
$390$	41.3593			2.09431
$391$	1.09665	+	26.5279i	0.0554600	+	1.34157i
$392$	−0.212721			−0.0107440
$393$		−	5.08023i		−	0.256264i
$394$	−14.9451	+	14.9451i	−0.752922	+	0.752922i
$395$	−3.46479			−0.174333
$396$	−2.07030	+	2.07030i	−0.104036	+	0.104036i
$397$	−7.56504	−	7.56504i	−0.379679	−	0.379679i	0.491308	−	0.870986i	$-0.336519\pi$
$397$	−7.56504	−	7.56504i	−0.379679	−	0.379679i	−0.870986	+	0.491308i	$0.836519\pi$
$398$	−32.8206	−	32.8206i	−1.64515	−	1.64515i
$399$		−	11.7013i		−	0.585796i
$400$			25.3773i			1.26886i
$401$	−22.6128	−	22.6128i	−1.12923	−	1.12923i	−0.990303	−	0.138925i	$-0.955635\pi$
$401$	−22.6128	−	22.6128i	−1.12923	−	1.12923i	−0.138925	−	0.990303i	$-0.544365\pi$
$402$	9.36031	+	9.36031i	0.466850	+	0.466850i
$403$	−1.25900	+	1.25900i	−0.0627151	+	0.0627151i
$404$	13.4349			0.668410
$405$	24.2303	−	24.2303i	1.20402	−	1.20402i
$406$			33.1251i			1.64397i
$407$	−5.95330			−0.295094
$408$	−0.356710	−	8.62879i	−0.0176598	−	0.427189i
$409$	−2.43015			−0.120163			−0.0600817	−	0.998193i	$-0.519136\pi$
$409$	−2.43015			−0.120163			−0.0600817	+	0.998193i	$0.519136\pi$
$410$			31.6103i			1.56112i
$411$	2.01603	−	2.01603i	0.0994435	−	0.0994435i
$412$	0.195694			0.00964113
$413$	−14.6264	+	14.6264i	−0.719720	+	0.719720i
$414$	−6.37951	−	6.37951i	−0.313536	−	0.313536i
$415$	11.8307	+	11.8307i	0.580747	+	0.580747i
$416$		−	24.3696i		−	1.19482i
$417$			16.0590i			0.786414i
$418$	8.25172	+	8.25172i	0.403605	+	0.403605i
$419$	22.2751	+	22.2751i	1.08821	+	1.08821i	0.995713	+	0.0924967i	$0.0294847\pi$
$419$	22.2751	+	22.2751i	1.08821	+	1.08821i	0.0924967	+	0.995713i	$0.470515\pi$
$420$	16.2067	−	16.2067i	0.790808	−	0.790808i
$421$	−22.8578			−1.11402			−0.557011	−	0.830505i	$-0.688052\pi$
$421$	−22.8578			−1.11402			−0.557011	+	0.830505i	$0.688052\pi$
$422$	−25.6122	+	25.6122i	−1.24678	+	1.24678i
$423$			0.979356i			0.0476179i
$424$	8.05378			0.391126
$425$	14.6801	−	15.9461i	0.712088	−	0.773501i
$426$	−36.7501			−1.78055
$427$		−	17.1348i		−	0.829213i
$428$	1.60752	−	1.60752i	0.0777023	−	0.0777023i
$429$	−19.0676			−0.920594
$430$	−4.18514	+	4.18514i	−0.201825	+	0.201825i
$431$	−16.5867	−	16.5867i	−0.798955	−	0.798955i	0.183976	−	0.982931i	$-0.441103\pi$
$431$	−16.5867	−	16.5867i	−0.798955	−	0.798955i	−0.982931	+	0.183976i	$0.941103\pi$
$432$	−14.8356	−	14.8356i	−0.713776	−	0.713776i
$433$		−	2.43481i		−	0.117010i	−0.998287	−	0.0585048i	$-0.981367\pi$
$433$		−	2.43481i		−	0.117010i	0.998287	−	0.0585048i	$-0.0186333\pi$
$434$			2.38093i			0.114289i
$435$	−30.1691	−	30.1691i	−1.44650	−	1.44650i
$436$	−3.15931	−	3.15931i	−0.151303	−	0.151303i
$437$	−10.5373	+	10.5373i	−0.504066	+	0.504066i
$438$	26.9625			1.28832
$439$	16.7966	−	16.7966i	0.801658	−	0.801658i	−0.181696	−	0.983355i	$-0.558159\pi$
$439$	16.7966	−	16.7966i	0.801658	−	0.801658i	0.983355	+	0.181696i	$0.0581588\pi$
$440$		−	9.44204i		−	0.450132i
$441$	−0.149257			−0.00710748
$442$	−18.6031	+	20.2075i	−0.884859	+	0.961173i
$443$	16.4136			0.779835			0.389918	−	0.920850i	$-0.372503\pi$
$443$	16.4136			0.779835			0.389918	+	0.920850i	$0.372503\pi$
$444$		−	5.98632i		−	0.284098i
$445$	−31.0824	+	31.0824i	−1.47345	+	1.47345i
$446$	29.3552			1.39001
$447$	−12.8941	+	12.8941i	−0.609869	+	0.609869i
$448$	−5.23614	−	5.23614i	−0.247384	−	0.247384i
$449$	−25.3517	−	25.3517i	−1.19642	−	1.19642i	−0.975231	−	0.221189i	$-0.929006\pi$
$449$	−25.3517	−	25.3517i	−1.19642	−	1.19642i	−0.221189	−	0.975231i	$-0.570994\pi$
$450$			7.36508i			0.347193i
$451$		−	14.5731i		−	0.686221i
$452$	0.478278	+	0.478278i	0.0224963	+	0.0224963i
$453$	−9.47045	−	9.47045i	−0.444960	−	0.444960i
$454$	−16.5757	+	16.5757i	−0.777937	+	0.777937i
$455$	30.1110			1.41162
$456$	3.42748	−	3.42748i	0.160506	−	0.160506i
$457$			27.3947i			1.28147i	0.767763	+	0.640734i	$0.221370\pi$
$457$			27.3947i			1.28147i	−0.767763	+	0.640734i	$0.778630\pi$
$458$	−46.4581			−2.17085
$459$	0.740146	+	17.9041i	0.0345471	+	0.835691i
$460$	−29.1891			−1.36095
$461$			13.0063i			0.605763i	0.953028	+	0.302882i	$0.0979487\pi$
$461$			13.0063i			0.605763i	−0.953028	+	0.302882i	$0.902051\pi$
$462$	−18.0298	+	18.0298i	−0.838820	+	0.838820i
$463$	−0.902635			−0.0419490			−0.0209745	−	0.999780i	$-0.506677\pi$
$463$	−0.902635			−0.0419490			−0.0209745	+	0.999780i	$0.506677\pi$
$464$	−23.4580	+	23.4580i	−1.08901	+	1.08901i
$465$	−2.16846	−	2.16846i	−0.100560	−	0.100560i
$466$	−14.7990	−	14.7990i	−0.685550	−	0.685550i
$467$		−	21.4668i		−	0.993364i	−0.867933	−	0.496682i	$-0.834552\pi$
$467$		−	21.4668i		−	0.993364i	0.867933	−	0.496682i	$-0.165448\pi$
$468$		−	3.86780i		−	0.178789i
$469$	6.81461	+	6.81461i	0.314670	+	0.314670i
$470$	5.40648	+	5.40648i	0.249383	+	0.249383i
$471$	16.7966	−	16.7966i	0.773949	−	0.773949i
$472$	−8.56862			−0.394402
$473$	1.92945	−	1.92945i	0.0887161	−	0.0887161i
$474$			3.87591i			0.178026i
$475$	12.1652			0.558176
$476$	0.628692	+	15.2080i	0.0288161	+	0.697059i
$477$	5.65098			0.258741
$478$		−	28.5542i		−	1.30604i
$479$	−7.65362	+	7.65362i	−0.349703	+	0.349703i	−0.859999	−	0.510296i	$-0.829536\pi$
$479$	−7.65362	+	7.65362i	−0.349703	+	0.349703i	0.510296	+	0.859999i	$0.329536\pi$
$480$	41.9736			1.91582
$481$	5.56107	−	5.56107i	0.253563	−	0.253563i
$482$	26.2265	+	26.2265i	1.19458	+	1.19458i
$483$	−23.0236	−	23.0236i	−1.04761	−	1.04761i
$484$			5.03083i			0.228674i
$485$			41.9402i			1.90441i
$486$	−10.0672	−	10.0672i	−0.456660	−	0.456660i
$487$	6.39247	+	6.39247i	0.289670	+	0.289670i	0.836950	−	0.547280i	$-0.184337\pi$
$487$	6.39247	+	6.39247i	0.289670	+	0.289670i	−0.547280	+	0.836950i	$0.684337\pi$
$488$	5.01906	−	5.01906i	0.227202	−	0.227202i
$489$	33.5281			1.51619
$490$	−0.823966	+	0.823966i	−0.0372230	+	0.0372230i
$491$		−	13.1013i		−	0.591251i	−0.955304	−	0.295626i	$-0.904472\pi$
$491$		−	13.1013i		−	0.591251i	0.955304	−	0.295626i	$-0.0955281\pi$
$492$	14.6539			0.660650
$493$	28.3100	−	1.17032i	1.27502	−	0.0527086i
$494$	−15.4161			−0.693605
$495$		−	6.62506i		−	0.297774i
$496$	−1.68609	+	1.68609i	−0.0757077	+	0.0757077i
$497$	−26.7553			−1.20014
$498$	13.2345	−	13.2345i	0.593052	−	0.593052i
$499$	−4.97031	−	4.97031i	−0.222501	−	0.222501i	0.587050	−	0.809551i	$-0.300289\pi$
$499$	−4.97031	−	4.97031i	−0.222501	−	0.222501i	−0.809551	+	0.587050i	$0.800289\pi$
$500$	0.823216	+	0.823216i	0.0368153	+	0.0368153i
$501$		−	47.9333i		−	2.14150i
$502$		−	51.9952i		−	2.32066i
$503$	23.3592	+	23.3592i	1.04154	+	1.04154i	0.999099	+	0.0424370i	$0.0135122\pi$
$503$	23.3592	+	23.3592i	1.04154	+	1.04154i	0.0424370	+	0.999099i	$0.486488\pi$
$504$	1.51073	+	1.51073i	0.0672931	+	0.0672931i
$505$	−21.4961	+	21.4961i	−0.956566	+	0.956566i
$506$	32.4724			1.44358
$507$	−0.00884024	+	0.00884024i	−0.000392609	+	0.000392609i
$508$			10.1609i			0.450816i
$509$	7.57486			0.335750			0.167875	−	0.985808i	$-0.446310\pi$
$509$	7.57486			0.335750			0.167875	+	0.985808i	$0.446310\pi$
$510$	−34.8049	−	32.0415i	−1.54119	−	1.41882i
$511$	19.6296			0.868363
$512$		−	22.2047i		−	0.981319i
$513$	−7.11176	+	7.11176i	−0.313992	+	0.313992i
$514$	48.3721			2.13360
$515$	−0.313115	+	0.313115i	−0.0137975	+	0.0137975i
$516$	1.94015	+	1.94015i	0.0854103	+	0.0854103i
$517$	−2.49252	−	2.49252i	−0.109621	−	0.109621i
$518$		−	10.5168i		−	0.462080i
$519$			25.7110i			1.12859i
$520$	8.81996	+	8.81996i	0.386781	+	0.386781i
$521$	−20.9981	−	20.9981i	−0.919946	−	0.919946i	0.0770794	−	0.997025i	$-0.475440\pi$
$521$	−20.9981	−	20.9981i	−0.919946	−	0.919946i	−0.997025	+	0.0770794i	$0.975440\pi$
$522$	−6.80807	+	6.80807i	−0.297981	+	0.297981i
$523$	5.31375			0.232354			0.116177	−	0.993229i	$-0.462936\pi$
$523$	5.31375			0.232354			0.116177	+	0.993229i	$0.462936\pi$
$524$	−2.62270	+	2.62270i	−0.114573	+	0.114573i
$525$			26.5805i			1.16007i
$526$	58.4268			2.54753
$527$	2.03484	−	0.0841191i	0.0886388	−	0.00366429i
$528$	−25.5360			−1.11131
$529$			18.4666i			0.802895i
$530$	31.1959	−	31.1959i	1.35506	−	1.35506i
$531$	−6.01222			−0.260908
$532$	−6.04085	+	6.04085i	−0.261904	+	0.261904i
$533$	13.6130	+	13.6130i	0.589643	+	0.589643i
$534$	34.7704	+	34.7704i	1.50466	+	1.50466i
$535$			5.14414i			0.222400i
$536$			3.99221i			0.172437i
$537$	−13.1688	−	13.1688i	−0.568275	−	0.568275i
$538$	14.4855	+	14.4855i	0.624516	+	0.624516i
$539$	0.379868	−	0.379868i	0.0163621	−	0.0163621i
$540$	−19.7002			−0.847760
$541$	20.3897	−	20.3897i	0.876623	−	0.876623i	−0.116561	−	0.993184i	$-0.537187\pi$
$541$	20.3897	−	20.3897i	0.876623	−	0.876623i	0.993184	+	0.116561i	$0.0371870\pi$
$542$		−	24.5511i		−	1.05456i
$543$	42.1072			1.80699
$544$	−18.8794	+	20.5076i	−0.809446	+	0.879256i
$545$	10.1099			0.433062
$546$		−	33.6838i		−	1.44153i
$547$	29.3462	−	29.3462i	1.25475	−	1.25475i	0.301191	−	0.953564i	$-0.402616\pi$
$547$	29.3462	−	29.3462i	1.25475	−	1.25475i	0.953564	−	0.301191i	$-0.0973841\pi$
$548$	−2.08158			−0.0889205
$549$	3.52165	−	3.52165i	0.150300	−	0.150300i
$550$	−18.7446	−	18.7446i	−0.799271	−	0.799271i
$551$	11.2451	+	11.2451i	0.479058	+	0.479058i
$552$		−	13.4879i		−	0.574085i
$553$			2.82179i			0.119995i
$554$	−29.2045	−	29.2045i	−1.24078	−	1.24078i
$555$	9.57826	+	9.57826i	0.406574	+	0.406574i
$556$	8.29056	−	8.29056i	0.351598	−	0.351598i
$557$	−35.9168			−1.52184			−0.760921	−	0.648844i	$-0.775253\pi$
$557$	−35.9168			−1.52184			−0.760921	+	0.648844i	$0.775253\pi$
$558$	−0.489343	+	0.489343i	−0.0207156	+	0.0207156i
$559$			3.60466i			0.152461i
$560$	40.3257			1.70407
$561$	16.0459	+	14.7719i	0.677458	+	0.623670i
$562$	47.1994			1.99099
$563$			41.7148i			1.75807i	0.476757	+	0.879035i	$0.341812\pi$
$563$			41.7148i			1.75807i	−0.476757	+	0.879035i	$0.658188\pi$
$564$	2.50634	−	2.50634i	0.105536	−	0.105536i
$565$	−1.53051			−0.0643892
$566$	22.3683	−	22.3683i	0.940212	−	0.940212i
$567$	−19.7336	−	19.7336i	−0.828734	−	0.828734i
$568$	−7.83703	−	7.83703i	−0.328834	−	0.328834i
$569$		−	22.4336i		−	0.940464i	−0.882543	−	0.470232i	$-0.844170\pi$
$569$		−	22.4336i		−	0.940464i	0.882543	−	0.470232i	$-0.155830\pi$
$570$		−	26.5524i		−	1.11216i
$571$	−12.2070	−	12.2070i	−0.510847	−	0.510847i	0.403939	−	0.914786i	$-0.367641\pi$
$571$	−12.2070	−	12.2070i	−0.510847	−	0.510847i	−0.914786	+	0.403939i	$0.867641\pi$
$572$	9.84378	+	9.84378i	0.411589	+	0.411589i
$573$	−2.79711	+	2.79711i	−0.116851	+	0.116851i
$574$	25.7440			1.07453
$575$	23.9364	−	23.9364i	0.998216	−	0.998216i
$576$		−	2.15232i		−	0.0896801i
$577$	23.2896			0.969559			0.484780	−	0.874636i	$-0.338900\pi$
$577$	23.2896			0.969559			0.484780	+	0.874636i	$0.338900\pi$
$578$	31.3099	−	2.59311i	1.30232	−	0.107859i
$579$	−35.3117			−1.46751
$580$			31.1499i			1.29343i
$581$	9.63515	−	9.63515i	0.399733	−	0.399733i
$582$	46.9166			1.94476
$583$	−14.3821	+	14.3821i	−0.595644	+	0.595644i
$584$	5.74982	+	5.74982i	0.237929	+	0.237929i
$585$	6.18858	+	6.18858i	0.255866	+	0.255866i
$586$			37.0467i			1.53039i
$587$		−	15.9982i		−	0.660316i	−0.943926	−	0.330158i	$-0.892898\pi$
$587$		−	15.9982i		−	0.660316i	0.943926	−	0.330158i	$-0.107102\pi$
$588$	0.381975	+	0.381975i	0.0157524	+	0.0157524i
$589$	0.808266	+	0.808266i	0.0333040	+	0.0333040i
$590$	−33.1901	+	33.1901i	−1.36642	+	1.36642i
$591$	−22.1708			−0.911983
$592$	7.44758	−	7.44758i	0.306094	−	0.306094i
$593$		−	3.32104i		−	0.136379i	−0.997672	−	0.0681894i	$-0.978278\pi$
$593$		−	3.32104i		−	0.136379i	0.997672	−	0.0681894i	$-0.0217222\pi$
$594$	21.9161			0.899230
$595$	−25.3391	−	23.3273i	−1.03880	−	0.956326i
$596$	13.3133			0.545334
$597$		−	48.6888i		−	1.99270i
$598$	−30.3330	+	30.3330i	−1.24041	+	1.24041i
$599$	37.7614			1.54289			0.771443	−	0.636298i	$-0.219535\pi$
$599$	37.7614			1.54289			0.771443	+	0.636298i	$0.219535\pi$
$600$	−7.78584	+	7.78584i	−0.317856	+	0.317856i
$601$	−17.5016	−	17.5016i	−0.713905	−	0.713905i	0.253445	−	0.967350i	$-0.418436\pi$
$601$	−17.5016	−	17.5016i	−0.713905	−	0.713905i	−0.967350	+	0.253445i	$0.918436\pi$
$602$	3.40845	+	3.40845i	0.138918	+	0.138918i
$603$			2.80116i			0.114072i
$604$			9.77834i			0.397875i
$605$	−8.04945	−	8.04945i	−0.327257	−	0.327257i
$606$	24.0468	+	24.0468i	0.976833	+	0.976833i
$607$	−13.7540	+	13.7540i	−0.558257	+	0.558257i	−0.928811	−	0.370554i	$-0.879168\pi$
$607$	−13.7540	+	13.7540i	−0.558257	+	0.558257i	0.370554	+	0.928811i	$0.379168\pi$
$608$	−15.6451			−0.634491
$609$	−24.5703	+	24.5703i	−0.995637	+	0.995637i
$610$		−	38.8822i		−	1.57429i
$611$	4.65660			0.188386
$612$	−2.99643	+	3.25485i	−0.121123	+	0.131570i
$613$	14.3457			0.579419			0.289710	−	0.957115i	$-0.406441\pi$
$613$	14.3457			0.579419			0.289710	+	0.957115i	$0.406441\pi$
$614$			49.0561i			1.97975i
$615$	−23.4467	+	23.4467i	−0.945460	+	0.945460i
$616$	−7.68977			−0.309830
$617$	−5.66156	+	5.66156i	−0.227926	+	0.227926i	−0.811826	−	0.583900i	$-0.801526\pi$
$617$	−5.66156	+	5.66156i	−0.227926	+	0.227926i	0.583900	+	0.811826i	$0.301526\pi$
$618$	0.350267	+	0.350267i	0.0140898	+	0.0140898i
$619$	−17.8400	−	17.8400i	−0.717050	−	0.717050i	0.250950	−	0.968000i	$-0.419257\pi$
$619$	−17.8400	−	17.8400i	−0.717050	−	0.717050i	−0.968000	+	0.250950i	$0.919257\pi$
$620$			2.23896i			0.0899190i
$621$			27.9864i			1.12306i
$622$	−3.61496	−	3.61496i	−0.144947	−	0.144947i
$623$	25.3140	+	25.3140i	1.01419	+	1.01419i
$624$	23.8536	−	23.8536i	0.954910	−	0.954910i
$625$	23.6499			0.945994
$626$	36.8601	−	36.8601i	1.47323	−	1.47323i
$627$			12.2413i			0.488869i
$628$	−17.3427			−0.692050
$629$	−8.98801	+	0.371560i	−0.358375	+	0.0148151i
$630$	11.7035			0.466277
$631$			34.0800i			1.35670i	0.734738	+	0.678351i	$0.237305\pi$
$631$			34.0800i			1.35670i	−0.734738	+	0.678351i	$0.762695\pi$
$632$	−0.826545	+	0.826545i	−0.0328782	+	0.0328782i
$633$	−37.9953			−1.51018
$634$	40.7254	−	40.7254i	1.61741	−	1.61741i
$635$	−16.2577	−	16.2577i	−0.645166	−	0.645166i
$636$	−14.4618	−	14.4618i	−0.573449	−	0.573449i
$637$			0.709682i			0.0281186i
$638$		−	34.6538i		−	1.37196i
$639$	−5.49890	−	5.49890i	−0.217533	−	0.217533i
$640$	18.7382	+	18.7382i	0.740694	+	0.740694i
$641$	−3.44604	+	3.44604i	−0.136111	+	0.136111i	−0.771879	−	0.635769i	$-0.780683\pi$
$641$	−3.44604	+	3.44604i	−0.136111	+	0.136111i	0.635769	+	0.771879i	$0.280683\pi$
$642$	5.75451			0.227113
$643$	−5.83601	+	5.83601i	−0.230150	+	0.230150i	−0.812755	−	0.582605i	$-0.802033\pi$
$643$	−5.83601	+	5.83601i	−0.230150	+	0.230150i	0.582605	+	0.812755i	$0.302033\pi$
$644$			23.7721i			0.936753i
$645$	−6.20857			−0.244462
$646$	12.9731	+	11.9430i	0.510418	+	0.469893i
$647$	−7.45904			−0.293245			−0.146622	−	0.989193i	$-0.546840\pi$
$647$	−7.45904			−0.293245			−0.146622	+	0.989193i	$0.546840\pi$
$648$		−	11.5606i		−	0.454142i
$649$	15.3014	−	15.3014i	0.600634	−	0.600634i
$650$	35.0192			1.37357
$651$	−1.76604	+	1.76604i	−0.0692164	+	0.0692164i
$652$	−17.3091	−	17.3091i	−0.677876	−	0.677876i
$653$	−20.8903	−	20.8903i	−0.817499	−	0.817499i	0.168246	−	0.985745i	$-0.446190\pi$
$653$	−20.8903	−	20.8903i	−0.817499	−	0.817499i	−0.985745	+	0.168246i	$0.946190\pi$
$654$		−	11.3095i		−	0.442238i
$655$		−	8.39276i		−	0.327932i
$656$	18.2310	+	18.2310i	0.711800	+	0.711800i
$657$	4.03439	+	4.03439i	0.157397	+	0.157397i
$658$	4.40314	−	4.40314i	0.171652	−	0.171652i
$659$	−30.7648			−1.19843			−0.599213	−	0.800589i	$-0.704520\pi$
$659$	−30.7648			−1.19843			−0.599213	+	0.800589i	$0.704520\pi$
$660$	−16.9547	+	16.9547i	−0.659960	+	0.659960i
$661$		−	49.3755i		−	1.92049i	−0.279166	−	0.960243i	$-0.590058\pi$
$661$		−	49.3755i		−	1.92049i	0.279166	−	0.960243i	$-0.409942\pi$
$662$	23.4487			0.911361
$663$	−28.7874	+	1.19006i	−1.11801	+	0.0462180i
$664$	5.64456			0.219052
$665$		−	19.3310i		−	0.749624i
$666$	2.16146	−	2.16146i	0.0837550	−	0.0837550i
$667$	44.2522			1.71345
$668$	−24.7458	+	24.7458i	−0.957444	+	0.957444i
$669$	21.7740	+	21.7740i	0.841830	+	0.841830i
$670$	15.4636	+	15.4636i	0.597413	+	0.597413i
$671$			17.9256i			0.692010i
$672$		−	34.1840i		−	1.31868i
$673$	10.5850	+	10.5850i	0.408022	+	0.408022i	0.881048	−	0.473027i	$-0.156839\pi$
$673$	10.5850	+	10.5850i	0.408022	+	0.408022i	−0.473027	+	0.881048i	$0.656839\pi$
$674$	29.8164	+	29.8164i	1.14849	+	1.14849i
$675$	16.1550	−	16.1550i	0.621807	−	0.621807i
$676$	0.00912765			0.000351063
$677$	−9.58079	+	9.58079i	−0.368220	+	0.368220i	−0.866828	−	0.498608i	$-0.833845\pi$
$677$	−9.58079	+	9.58079i	−0.368220	+	0.368220i	0.498608	+	0.866828i	$0.333845\pi$
$678$			1.71212i			0.0657535i
$679$	34.1568			1.31082
$680$	−0.589301	−	14.2551i	−0.0225987	−	0.546660i
$681$	−24.5898			−0.942283
$682$		−	2.49081i		−	0.0953782i
$683$	−16.7290	+	16.7290i	−0.640117	+	0.640117i	−0.950584	−	0.310467i	$-0.899515\pi$
$683$	−16.7290	+	16.7290i	−0.640117	+	0.640117i	0.310467	+	0.950584i	$0.399515\pi$
$684$	−2.48310			−0.0949437
$685$	3.33057	−	3.33057i	0.127255	−	0.127255i
$686$	24.5302	+	24.5302i	0.936567	+	0.936567i
$687$	−34.4599	−	34.4599i	−1.31473	−	1.31473i
$688$			4.82748i			0.184046i
$689$		−	26.8691i		−	1.02363i
$690$	−52.2449	−	52.2449i	−1.98893	−	1.98893i
$691$	2.36872	+	2.36872i	0.0901105	+	0.0901105i	0.750725	−	0.660615i	$-0.229704\pi$
$691$	2.36872	+	2.36872i	0.0901105	+	0.0901105i	−0.660615	+	0.750725i	$0.729704\pi$
$692$	13.2735	−	13.2735i	0.504581	−	0.504581i
$693$	−5.39557			−0.204961
$694$	−36.3199	+	36.3199i	−1.37868	+	1.37868i
$695$			26.5302i			1.00635i
$696$	−14.3940			−0.545604
$697$	−0.909543	−	22.0018i	−0.0344514	−	0.833377i
$698$	−5.18092			−0.196101
$699$		−	21.9540i		−	0.830378i
$700$	13.7224	−	13.7224i	0.518656	−	0.518656i
$701$	−50.1415			−1.89382			−0.946908	−	0.321504i	$-0.895812\pi$
$701$	−50.1415			−1.89382			−0.946908	+	0.321504i	$0.895812\pi$
$702$	−20.4722	+	20.4722i	−0.772674	+	0.772674i
$703$	−3.57017	−	3.57017i	−0.134651	−	0.134651i
$704$	5.47779	+	5.47779i	0.206452	+	0.206452i
$705$			8.02042i			0.302067i
$706$		−	38.9986i		−	1.46773i
$707$	17.5068	+	17.5068i	0.658413	+	0.658413i
$708$	15.3863	+	15.3863i	0.578253	+	0.578253i
$709$	−27.5951	+	27.5951i	−1.03636	+	1.03636i	−0.0370436	+	0.999314i	$0.511794\pi$
$709$	−27.5951	+	27.5951i	−1.03636	+	1.03636i	−0.999314	+	0.0370436i	$0.988206\pi$
$710$	−60.7127			−2.27851
$711$	−0.579950	+	0.579950i	−0.0217498	+	0.0217498i
$712$			14.8297i			0.555768i
$713$	3.18071			0.119119
$714$	−26.0952	+	28.3458i	−0.976588	+	1.06081i
$715$	−31.5006			−1.17806
$716$			13.5969i			0.508140i
$717$	21.1798	−	21.1798i	0.790975	−	0.790975i
$718$	−47.2566			−1.76360
$719$	−16.3576	+	16.3576i	−0.610036	+	0.610036i	−0.942955	−	0.332919i	$-0.891966\pi$
$719$	−16.3576	+	16.3576i	−0.610036	+	0.610036i	0.332919	+	0.942955i	$0.391966\pi$
$720$	8.28796	+	8.28796i	0.308874	+	0.308874i
$721$	0.255006	+	0.255006i	0.00949693	+	0.00949693i
$722$		−	25.2162i		−	0.938451i
$723$			38.9065i			1.44695i
$724$	−21.7381	−	21.7381i	−0.807890	−	0.807890i
$725$	−25.5444	−	25.5444i	−0.948694	−	0.948694i
$726$	−9.00455	+	9.00455i	−0.334190	+	0.334190i
$727$	1.08108			0.0400952			0.0200476	−	0.999799i	$-0.493618\pi$
$727$	1.08108			0.0400952			0.0200476	+	0.999799i	$0.493618\pi$
$728$	7.18314	−	7.18314i	0.266225	−	0.266225i
$729$			17.1642i			0.635713i
$730$	44.5433			1.64862
$731$	2.79257	−	3.03341i	0.103287	−	0.112195i
$732$	−18.0250			−0.666224
$733$		−	23.8860i		−	0.882248i	−0.897446	−	0.441124i	$-0.854580\pi$
$733$		−	23.8860i		−	0.882248i	0.897446	−	0.441124i	$-0.145420\pi$
$734$	−17.1822	+	17.1822i	−0.634206	+	0.634206i
$735$	−1.22234			−0.0450866
$736$	−30.7835	+	30.7835i	−1.13470	+	1.13470i
$737$	−7.12911	−	7.12911i	−0.262604	−	0.262604i
$738$	5.29105	+	5.29105i	0.194766	+	0.194766i
$739$		−	8.97858i		−	0.330282i	−0.986270	−	0.165141i	$-0.947192\pi$
$739$		−	8.97858i		−	0.330282i	0.986270	−	0.165141i	$-0.0528080\pi$
$740$		−	9.88966i		−	0.363551i
$741$	−11.4348	−	11.4348i	−0.420067	−	0.420067i
$742$	−25.4065	−	25.4065i	−0.932703	−	0.932703i
$743$	22.4784	−	22.4784i	0.824652	−	0.824652i	−0.162119	−	0.986771i	$-0.551833\pi$
$743$	22.4784	−	22.4784i	0.824652	−	0.824652i	0.986771	+	0.162119i	$0.0518328\pi$
$744$	−1.03460			−0.0379302
$745$	−21.3016	+	21.3016i	−0.780430	+	0.780430i
$746$			14.9489i			0.547319i
$747$	3.96054			0.144909
$748$	−0.657706	−	15.9099i	−0.0240481	−	0.581722i
$749$	4.18948			0.153080
$750$			2.94691i			0.107606i
$751$	−14.2550	+	14.2550i	−0.520171	+	0.520171i	−0.917623	−	0.397452i	$-0.869894\pi$
$751$	−14.2550	+	14.2550i	−0.520171	+	0.520171i	0.397452	+	0.917623i	$0.369894\pi$
$752$	6.23629			0.227414
$753$	38.5670	−	38.5670i	1.40546	−	1.40546i
$754$	32.3707	+	32.3707i	1.17887	+	1.17887i
$755$	−15.6456	−	15.6456i	−0.569402	−	0.569402i
$756$			16.0442i			0.583521i
$757$		−	34.3578i		−	1.24876i	−0.781122	−	0.624378i	$-0.785353\pi$
$757$		−	34.3578i		−	1.24876i	0.781122	−	0.624378i	$-0.214647\pi$
$758$	42.6371	+	42.6371i	1.54865	+	1.54865i
$759$	24.0861	+	24.0861i	0.874271	+	0.874271i
$760$	5.66235	−	5.66235i	0.205395	−	0.205395i
$761$	−8.81692			−0.319613			−0.159807	−	0.987148i	$-0.551087\pi$
$761$	−8.81692			−0.319613			−0.159807	+	0.987148i	$0.551087\pi$
$762$	−18.1867	+	18.1867i	−0.658836	+	0.658836i
$763$		−	8.23372i		−	0.298081i
$764$	2.88805			0.104486
$765$	−0.413486	−	10.0022i	−0.0149496	−	0.361631i
$766$	41.7312			1.50781
$767$			28.5867i			1.03220i
$768$	28.7451	−	28.7451i	1.03725	−	1.03725i
$769$	−28.1135			−1.01380			−0.506899	−	0.862005i	$-0.669208\pi$
$769$	−28.1135			−1.01380			−0.506899	+	0.862005i	$0.669208\pi$
$770$	−29.7860	+	29.7860i	−1.07341	+	1.07341i
$771$	35.8796	+	35.8796i	1.29217	+	1.29217i
$772$	18.2299	+	18.2299i	0.656108	+	0.656108i
$773$			25.4495i			0.915354i	0.889119	+	0.457677i	$0.151318\pi$
$773$			25.4495i			0.915354i	−0.889119	+	0.457677i	$0.848682\pi$
$774$			1.40105i			0.0503597i
$775$	−1.83605	−	1.83605i	−0.0659529	−	0.0659529i
$776$	10.0051	+	10.0051i	0.359161	+	0.359161i
$777$	7.80071	−	7.80071i	0.279849	−	0.279849i
$778$	19.0512			0.683018
$779$	8.73942	−	8.73942i	0.313122	−	0.313122i
$780$		−	31.6753i		−	1.13416i
$781$	27.9900			1.00156
$782$	49.0253	−	2.02668i	1.75314	−	0.0724741i
$783$	29.8665			1.06734
$784$			0.950430i			0.0339439i
$785$	27.7488	−	27.7488i	0.990397	−	0.990397i
$786$	−9.38860			−0.334880
$787$	33.2494	−	33.2494i	1.18521	−	1.18521i	0.206839	−	0.978375i	$-0.433682\pi$
$787$	33.2494	−	33.2494i	1.18521	−	1.18521i	0.978375	−	0.206839i	$-0.0663178\pi$
$788$	11.4458	+	11.4458i	0.407739	+	0.407739i
$789$	43.3376	+	43.3376i	1.54286	+	1.54286i
$790$			6.40317i			0.227814i
$791$			1.24648i			0.0443197i
$792$	−1.58045	−	1.58045i	−0.0561587	−	0.0561587i
$793$	−16.7446	−	16.7446i	−0.594618	−	0.594618i
$794$	−13.9807	+	13.9807i	−0.496157	+	0.496157i
$795$	46.2786			1.64133
$796$	−25.1359	+	25.1359i	−0.890917	+	0.890917i
$797$		−	22.7800i		−	0.806908i	−0.915000	−	0.403454i	$-0.867810\pi$
$797$		−	22.7800i		−	0.806908i	0.915000	−	0.403454i	$-0.132190\pi$
$798$	−21.6247			−0.765507
$799$	−3.91865	−	3.60752i	−0.138632	−	0.127625i
$800$	35.5393			1.25650
$801$			10.4054i			0.367656i
$802$	−41.7899	+	41.7899i	−1.47565	+	1.47565i
$803$	−20.5355			−0.724683
$804$	7.16865	−	7.16865i	0.252819	−	0.252819i
$805$	−38.0360	−	38.0360i	−1.34059	−	1.34059i
$806$	2.32671	+	2.32671i	0.0819549	+	0.0819549i
$807$			21.4890i			0.756450i
$808$			10.2560i			0.360807i
$809$	−0.452482	−	0.452482i	−0.0159084	−	0.0159084i	0.699108	−	0.715016i	$-0.253581\pi$
$809$	−0.452482	−	0.452482i	−0.0159084	−	0.0159084i	−0.715016	+	0.699108i	$0.753581\pi$
$810$	−44.7793	−	44.7793i	−1.57338	−	1.57338i
$811$	−35.9577	+	35.9577i	−1.26265	+	1.26265i	−0.312842	+	0.949805i	$0.601281\pi$
$811$	−35.9577	+	35.9577i	−1.26265	+	1.26265i	−0.949805	+	0.312842i	$0.898719\pi$
$812$	25.3691			0.890280
$813$	18.2106	−	18.2106i	0.638673	−	0.638673i
$814$			11.0021i			0.385623i
$815$	55.3900			1.94023
$816$	−38.5531	+	1.59377i	−1.34963	+	0.0557930i
$817$	2.31416			0.0809623
$818$			4.49109i			0.157027i
$819$	5.04009	−	5.04009i	0.176115	−	0.176115i
$820$	24.2089			0.845413
$821$	−5.24314	+	5.24314i	−0.182987	+	0.182987i	−0.792656	−	0.609669i	$-0.791302\pi$
$821$	−5.24314	+	5.24314i	−0.182987	+	0.182987i	0.609669	+	0.792656i	$0.291302\pi$
$822$	−3.72576	−	3.72576i	−0.129951	−	0.129951i
$823$	−28.5510	−	28.5510i	−0.995224	−	0.995224i	0.00476460	−	0.999989i	$-0.498483\pi$
$823$	−28.5510	−	28.5510i	−0.995224	−	0.995224i	−0.999989	+	0.00476460i	$0.998483\pi$
$824$			0.149390i			0.00520426i
$825$		−	27.8072i		−	0.968123i
$826$	27.0306	+	27.0306i	0.940516	+	0.940516i
$827$	−27.3958	−	27.3958i	−0.952646	−	0.952646i	0.0462827	−	0.998928i	$-0.485262\pi$
$827$	−27.3958	−	27.3958i	−0.952646	−	0.952646i	−0.998928	+	0.0462827i	$0.985262\pi$
$828$	−4.88579	+	4.88579i	−0.169793	+	0.169793i
$829$	6.65282			0.231062			0.115531	−	0.993304i	$-0.463143\pi$
$829$	6.65282			0.231062			0.115531	+	0.993304i	$0.463143\pi$
$830$	21.8640	−	21.8640i	0.758909	−	0.758909i
$831$		−	43.3243i		−	1.50290i
$832$	−10.2338			−0.354792
$833$	0.549798	−	0.597215i	0.0190494	−	0.0206923i
$834$	29.6782			1.02767
$835$		−	79.1879i		−	2.74041i
$836$	6.31963	−	6.31963i	0.218569	−	0.218569i
$837$	2.14671			0.0742012
$838$	41.1659	−	41.1659i	1.42205	−	1.42205i
$839$	19.8645	+	19.8645i	0.685798	+	0.685798i	0.961300	−	0.275502i	$-0.0888441\pi$
$839$	19.8645	+	19.8645i	0.685798	+	0.685798i	−0.275502	+	0.961300i	$0.588844\pi$
$840$	12.3721	+	12.3721i	0.426877	+	0.426877i
$841$		−	18.2249i		−	0.628445i
$842$			42.2428i			1.45578i
$843$	35.0097	+	35.0097i	1.20580	+	1.20580i
$844$	19.6153	+	19.6153i	0.675186	+	0.675186i
$845$	−0.0146045	+	0.0146045i	−0.000502409	+	0.000502409i
$846$	1.80992			0.0622262
$847$	−6.55561	+	6.55561i	−0.225254	+	0.225254i
$848$		−	35.9840i		−	1.23569i
$849$	33.1830			1.13884
$850$	−29.4695	−	27.1298i	−1.01080	−	0.930543i
$851$	−14.0494			−0.481608
$852$			28.1453i			0.964241i
$853$	−11.8927	+	11.8927i	−0.407200	+	0.407200i	−0.880761	−	0.473561i	$-0.842968\pi$
$853$	−11.8927	+	11.8927i	−0.407200	+	0.407200i	0.473561	+	0.880761i	$0.342968\pi$
$854$	−31.6663			−1.08360
$855$	3.97302	−	3.97302i	0.135874	−	0.135874i
$856$	1.22716	+	1.22716i	0.0419435	+	0.0419435i
$857$	17.4436	+	17.4436i	0.595863	+	0.595863i	0.939209	−	0.343346i	$-0.111560\pi$
$857$	17.4436	+	17.4436i	0.595863	+	0.595863i	−0.343346	+	0.939209i	$0.611560\pi$
$858$			35.2383i			1.20302i
$859$		−	0.383821i		−	0.0130958i	−0.999979	−	0.00654789i	$-0.997916\pi$
$859$		−	0.383821i		−	0.0130958i	0.999979	−	0.00654789i	$-0.00208427\pi$
$860$	3.20521	+	3.20521i	0.109297	+	0.109297i
$861$	19.0954	+	19.0954i	0.650769	+	0.650769i
$862$	−30.6534	+	30.6534i	−1.04406	+	1.04406i
$863$	−47.5471			−1.61852			−0.809261	−	0.587449i	$-0.800132\pi$
$863$	−47.5471			−1.61852			−0.809261	+	0.587449i	$0.800132\pi$
$864$	−20.7763	+	20.7763i	−0.706822	+	0.706822i
$865$			42.4757i			1.44422i
$866$	−4.49970			−0.152906
$867$	25.1473	+	21.3005i	0.854047	+	0.723401i
$868$	1.82345			0.0618920
$869$		−	2.95201i		−	0.100140i
$870$	−55.7545	+	55.7545i	−1.89026	+	1.89026i
$871$	13.3188			0.451291
$872$	2.41178	−	2.41178i	0.0816732	−	0.0816732i
$873$	7.02011	+	7.02011i	0.237595	+	0.237595i
$874$	19.4736	+	19.4736i	0.658703	+	0.658703i
$875$			2.14545i			0.0725294i
$876$		−	20.6494i		−	0.697679i
$877$	−19.0222	−	19.0222i	−0.642334	−	0.642334i	0.308795	−	0.951129i	$-0.400074\pi$
$877$	−19.0222	−	19.0222i	−0.642334	−	0.642334i	−0.951129	+	0.308795i	$0.900074\pi$
$878$	−31.0413	−	31.0413i	−1.04759	−	1.04759i
$879$	−27.4791	+	27.4791i	−0.926846	+	0.926846i
$880$	−42.1867			−1.42211
$881$	−33.1275	+	33.1275i	−1.11609	+	1.11609i	−0.123783	+	0.992309i	$0.539503\pi$
$881$	−33.1275	+	33.1275i	−1.11609	+	1.11609i	−0.992309	+	0.123783i	$0.960497\pi$
$882$			0.275837i			0.00928792i
$883$	35.2535			1.18638			0.593188	−	0.805064i	$-0.297869\pi$
$883$	35.2535			1.18638			0.593188	+	0.805064i	$0.297869\pi$
$884$	15.4760	+	14.2473i	0.520516	+	0.479188i
$885$	−49.2370			−1.65508
$886$		−	30.3335i		−	1.01907i
$887$	14.0292	−	14.0292i	0.471053	−	0.471053i	−0.431202	−	0.902255i	$-0.641910\pi$
$887$	14.0292	−	14.0292i	0.471053	−	0.471053i	0.902255	+	0.431202i	$0.141910\pi$
$888$	4.56989			0.153356
$889$	−13.2405	+	13.2405i	−0.444074	+	0.444074i
$890$	57.4423	+	57.4423i	1.92547	+	1.92547i
$891$	20.6443	+	20.6443i	0.691611	+	0.691611i
$892$		−	22.4819i		−	0.752749i
$893$		−	2.98950i		−	0.100040i
$894$	23.8291	+	23.8291i	0.796966	+	0.796966i
$895$	−21.7554	−	21.7554i	−0.727203	−	0.727203i
$896$	15.2608	−	15.2608i	0.509826	−	0.509826i
$897$	−44.9985			−1.50246
$898$	−46.8516	+	46.8516i	−1.56346	+	1.56346i
$899$		−	3.39438i		−	0.113209i
$900$	5.64059			0.188020
$901$	−20.8157	+	22.6110i	−0.693473	+	0.753281i
$902$	−26.9321			−0.896740
$903$			5.05637i			0.168266i
$904$	−0.365113	+	0.365113i	−0.0121435	+	0.0121435i
$905$	69.5630			2.31235
$906$	−17.5020	+	17.5020i	−0.581466	+	0.581466i
$907$	−8.31774	−	8.31774i	−0.276186	−	0.276186i	0.555398	−	0.831584i	$-0.312566\pi$
$907$	−8.31774	−	8.31774i	−0.276186	−	0.276186i	−0.831584	+	0.555398i	$0.812566\pi$
$908$	12.6946	+	12.6946i	0.421286	+	0.421286i
$909$			7.19622i			0.238683i
$910$		−	55.6471i		−	1.84468i
$911$	23.3864	+	23.3864i	0.774826	+	0.774826i	0.978946	−	0.204120i	$-0.0654331\pi$
$911$	23.3864	+	23.3864i	0.774826	+	0.774826i	−0.204120	+	0.978946i	$0.565433\pi$
$912$	−15.3138	−	15.3138i	−0.507092	−	0.507092i
$913$	−10.0798	+	10.0798i	−0.333593	+	0.333593i
$914$	50.6272			1.67460
$915$	28.8405	−	28.8405i	0.953437	−	0.953437i
$916$			35.5802i			1.17560i
$917$	−6.83521			−0.225719
$918$	33.0879	−	1.36784i	1.09206	−	0.0451454i
$919$	40.0326			1.32055			0.660277	−	0.751022i	$-0.270439\pi$
$919$	40.0326			1.32055			0.660277	+	0.751022i	$0.270439\pi$
$920$		−	22.2827i		−	0.734638i
$921$	−36.3870	+	36.3870i	−1.19899	+	1.19899i
$922$	24.0365			0.791600
$923$	−26.1459	+	26.1459i	−0.860604	+	0.860604i
$924$	13.8082	+	13.8082i	0.454256	+	0.454256i
$925$	8.10997	+	8.10997i	0.266654	+	0.266654i
$926$			1.66813i			0.0548182i
$927$			0.104821i			0.00344276i
$928$	32.8514	+	32.8514i	1.07840	+	1.07840i
$929$	−25.9782	−	25.9782i	−0.852318	−	0.852318i	0.138100	−	0.990418i	$-0.455900\pi$
$929$	−25.9782	−	25.9782i	−0.852318	−	0.852318i	−0.990418	+	0.138100i	$0.955900\pi$
$930$	−4.00747	+	4.00747i	−0.131410	+	0.131410i
$931$	0.455610			0.0149320
$932$	−11.3339	+	11.3339i	−0.371254	+	0.371254i
$933$		−	5.36273i		−	0.175568i
$934$	−39.6720			−1.29811
$935$	26.5085	+	24.4038i	0.866922	+	0.798091i
$936$	2.95264			0.0965101
$937$		−	54.4622i		−	1.77920i	−0.456739	−	0.889601i	$-0.650983\pi$
$937$		−	54.4622i		−	1.77920i	0.456739	−	0.889601i	$-0.349017\pi$
$938$	12.5939	−	12.5939i	0.411204	−	0.411204i
$939$	54.6813			1.78446
$940$	4.14059	−	4.14059i	0.135051	−	0.135051i
$941$	15.8634	+	15.8634i	0.517133	+	0.517133i	0.916703	−	0.399570i	$-0.130841\pi$
$941$	15.8634	+	15.8634i	0.517133	+	0.517133i	−0.399570	+	0.916703i	$0.630841\pi$
$942$	−31.0413	−	31.0413i	−1.01138	−	1.01138i
$943$		−	34.3917i		−	1.11995i
$944$			38.2842i			1.24605i
$945$	−25.6711	−	25.6711i	−0.835080	−	0.835080i
$946$	−3.56575	−	3.56575i	−0.115933	−	0.115933i
$947$	31.7527	−	31.7527i	1.03182	−	1.03182i	0.0323466	−	0.999477i	$-0.489702\pi$
$947$	31.7527	−	31.7527i	1.03182	−	1.03182i	0.999477	−	0.0323466i	$-0.0102980\pi$
$948$	2.96839			0.0964087
$949$	19.1826	−	19.1826i	0.622692	−	0.622692i
$950$		−	22.4821i		−	0.729414i
$951$	60.4153			1.95910
$952$	−11.6096	+	0.479937i	−0.376271	+	0.0155549i
$953$	20.4738			0.663211			0.331606	−	0.943418i	$-0.392410\pi$
$953$	20.4738			0.663211			0.331606	+	0.943418i	$0.392410\pi$
$954$		−	10.4434i		−	0.338117i
$955$	−4.62095	+	4.62095i	−0.149530	+	0.149530i
$956$	−21.8684			−0.707275
$957$	25.7042	−	25.7042i	0.830898	−	0.830898i
$958$	14.1444	+	14.1444i	0.456985	+	0.456985i
$959$	−2.71248	−	2.71248i	−0.0875905	−	0.0875905i
$960$		−	17.6264i		−	0.568890i
$961$			30.7560i			0.992130i
$962$	−10.2772	−	10.2772i	−0.331352	−	0.331352i
$963$	0.861046	+	0.861046i	0.0277468	+	0.0277468i
$964$	20.0857	−	20.0857i	0.646916	−	0.646916i
$965$	−58.3365			−1.87792
$966$	−42.5492	+	42.5492i	−1.36900	+	1.36900i
$967$		−	4.86270i		−	0.156374i	−0.996939	−	0.0781869i	$-0.975087\pi$
$967$		−	4.86270i		−	0.156374i	0.996939	−	0.0781869i	$-0.0249131\pi$
$968$	−3.84048			−0.123438
$969$	0.764008	+	18.4813i	0.0245435	+	0.593705i
$970$	77.5083			2.48864
$971$			11.8092i			0.378976i	0.981883	+	0.189488i	$0.0606828\pi$
$971$			11.8092i			0.378976i	−0.981883	+	0.189488i	$0.939317\pi$
$972$	−7.71006	+	7.71006i	−0.247300	+	0.247300i
$973$	21.6067			0.692679
$974$	11.8137	−	11.8137i	0.378536	−	0.378536i
$975$	25.9752	+	25.9752i	0.831871	+	0.831871i
$976$	−22.4250	−	22.4250i	−0.717805	−	0.717805i
$977$		−	16.6585i		−	0.532951i	−0.963842	−	0.266476i	$-0.914141\pi$
$977$		−	16.6585i		−	0.532951i	0.963842	−	0.266476i	$-0.0858592\pi$
$978$		−	61.9623i		−	1.98133i
$979$	−26.4823	−	26.4823i	−0.846377	−	0.846377i
$980$	0.631039	+	0.631039i	0.0201578	+	0.0201578i
$981$	1.69224	−	1.69224i	0.0540291	−	0.0540291i
$982$	−24.2120			−0.772636
$983$	−7.56143	+	7.56143i	−0.241172	+	0.241172i	−0.817335	−	0.576163i	$-0.804549\pi$
$983$	−7.56143	+	7.56143i	−0.241172	+	0.241172i	0.576163	+	0.817335i	$0.304549\pi$
$984$			11.1867i			0.356618i
$985$	−36.6271			−1.16704
$986$	−2.16283	−	52.3187i	−0.0688786	−	1.66617i
$987$	6.53198			0.207915
$988$			11.8065i			0.375616i
$989$	4.55338	−	4.55338i	0.144789	−	0.144789i
$990$	−12.2436			−0.389126
$991$	4.74956	−	4.74956i	0.150875	−	0.150875i	−0.627634	−	0.778509i	$-0.715976\pi$
$991$	4.74956	−	4.74956i	0.150875	−	0.150875i	0.778509	+	0.627634i	$0.215976\pi$
$992$	2.36126	+	2.36126i	0.0749702	+	0.0749702i
$993$	17.3929	+	17.3929i	0.551946	+	0.551946i
$994$			49.4455i			1.56832i
$995$		−	80.4360i		−	2.54999i
$996$	−10.1357	−	10.1357i	−0.321162	−	0.321162i
$997$	−4.11728	−	4.11728i	−0.130396	−	0.130396i	0.638897	−	0.769292i	$-0.279391\pi$
$997$	−4.11728	−	4.11728i	−0.130396	−	0.130396i	−0.769292	+	0.638897i	$0.779391\pi$
$998$	−9.18546	+	9.18546i	−0.290761	+	0.290761i
$999$	−9.48218			−0.300003

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.f.d.259.8	✓	68
17.13	even	4	inner	731.2.f.d.302.27	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.f.d.259.8	✓	68	1.1	even	1	trivial
731.2.f.d.302.27	yes	68	17.13	even	4	inner

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.84807i q^{2} +(1.37079 - 1.37079i) q^{3} -1.41535 q^{4} +(2.26460 - 2.26460i) q^{5} +(-2.53331 - 2.53331i) q^{6} +(-1.84433 - 1.84433i) q^{7} -1.08047i q^{8} -0.758116i q^{9} +O(q^{10})\)	\(q-1.84807i q^{2} +(1.37079 - 1.37079i) q^{3} -1.41535 q^{4} +(2.26460 - 2.26460i) q^{5} +(-2.53331 - 2.53331i) q^{6} +(-1.84433 - 1.84433i) q^{7} -1.08047i q^{8} -0.758116i q^{9} +(-4.18514 - 4.18514i) q^{10} +(1.92945 + 1.92945i) q^{11} +(-1.94015 + 1.94015i) q^{12} -3.60466 q^{13} +(-3.40845 + 3.40845i) q^{14} -6.20857i q^{15} -4.82748 q^{16} +(3.03341 + 2.79257i) q^{17} -1.40105 q^{18} +2.31416i q^{19} +(-3.20521 + 3.20521i) q^{20} -5.05637 q^{21} +(3.56575 - 3.56575i) q^{22} +(4.55338 + 4.55338i) q^{23} +(-1.48109 - 1.48109i) q^{24} -5.25684i q^{25} +6.66165i q^{26} +(3.07315 + 3.07315i) q^{27} +(2.61038 + 2.61038i) q^{28} +(4.85926 - 4.85926i) q^{29} -11.4739 q^{30} +(0.349269 - 0.349269i) q^{31} +6.76058i q^{32} +5.28972 q^{33} +(5.16085 - 5.60595i) q^{34} -8.35335 q^{35} +1.07300i q^{36} +(-1.54275 + 1.54275i) q^{37} +4.27673 q^{38} +(-4.94122 + 4.94122i) q^{39} +(-2.44682 - 2.44682i) q^{40} +(-3.77650 - 3.77650i) q^{41} +9.34452i q^{42} -1.00000i q^{43} +(-2.73085 - 2.73085i) q^{44} +(-1.71683 - 1.71683i) q^{45} +(8.41496 - 8.41496i) q^{46} -1.29183 q^{47} +(-6.61745 + 6.61745i) q^{48} -0.196879i q^{49} -9.71499 q^{50} +(7.98617 - 0.330145i) q^{51} +5.10186 q^{52} +7.45398i q^{53} +(5.67938 - 5.67938i) q^{54} +8.73886 q^{55} +(-1.99274 + 1.99274i) q^{56} +(3.17222 + 3.17222i) q^{57} +(-8.98025 - 8.98025i) q^{58} -7.93048i q^{59} +8.78733i q^{60} +(4.64527 + 4.64527i) q^{61} +(-0.645473 - 0.645473i) q^{62} +(-1.39822 + 1.39822i) q^{63} +2.83904 q^{64} +(-8.16311 + 8.16311i) q^{65} -9.77577i q^{66} -3.69490 q^{67} +(-4.29335 - 3.95247i) q^{68} +12.4834 q^{69} +15.4376i q^{70} +(7.25338 - 7.25338i) q^{71} -0.819118 q^{72} +(-5.32161 + 5.32161i) q^{73} +(2.85110 + 2.85110i) q^{74} +(-7.20601 - 7.20601i) q^{75} -3.27536i q^{76} -7.11708i q^{77} +(9.13170 + 9.13170i) q^{78} +(-0.764989 - 0.764989i) q^{79} +(-10.9323 + 10.9323i) q^{80} +10.6996 q^{81} +(-6.97922 + 6.97922i) q^{82} +5.22419i q^{83} +7.15656 q^{84} +(13.1935 - 0.545414i) q^{85} -1.84807 q^{86} -13.3220i q^{87} +(2.08470 - 2.08470i) q^{88} -13.7253 q^{89} +(-3.17282 + 3.17282i) q^{90} +(6.64818 + 6.64818i) q^{91} +(-6.44465 - 6.44465i) q^{92} -0.957548i q^{93} +2.38739i q^{94} +(5.24065 + 5.24065i) q^{95} +(9.26732 + 9.26732i) q^{96} +(-9.25995 + 9.25995i) q^{97} -0.363846 q^{98} +(1.46274 - 1.46274i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 76 q^{4} - 4 q^{5} + 4 q^{6}+O(q^{10}) \) 68 * q - 76 * q^4 - 4 * q^5 + 4 * q^6	\( 68 q - 76 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{10} - 6 q^{11} - 10 q^{12} - 24 q^{13} - 22 q^{14} + 84 q^{16} - 2 q^{17} + 28 q^{18} + 10 q^{20} - 36 q^{21} + 8 q^{22} + 14 q^{23} - 62 q^{24} - 12 q^{27} - 58 q^{28} + 2 q^{29} + 160 q^{30} - 26 q^{31} + 44 q^{33} + 16 q^{34} + 56 q^{35} - 6 q^{37} - 56 q^{38} - 24 q^{39} + 70 q^{40} + 6 q^{41} + 14 q^{44} + 10 q^{45} + 2 q^{46} - 68 q^{47} - 58 q^{48} + 40 q^{50} + 16 q^{51} + 4 q^{52} + 26 q^{54} - 16 q^{55} + 50 q^{56} + 18 q^{57} - 94 q^{58} + 22 q^{61} - 48 q^{62} + 16 q^{63} + 60 q^{64} - 22 q^{65} + 24 q^{67} + 20 q^{68} + 8 q^{69} - 14 q^{71} - 84 q^{72} + 34 q^{73} + 26 q^{74} - 102 q^{75} + 40 q^{78} + 4 q^{79} - 30 q^{80} - 92 q^{81} - 76 q^{82} + 108 q^{84} + 8 q^{85} + 8 q^{86} + 16 q^{88} - 72 q^{89} + 132 q^{90} + 12 q^{91} - 174 q^{92} + 50 q^{95} + 10 q^{96} - 16 q^{97} - 28 q^{98} - 86 q^{99}+O(q^{100}) \) 68 * q - 76 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^10 - 6 * q^11 - 10 * q^12 - 24 * q^13 - 22 * q^14 + 84 * q^16 - 2 * q^17 + 28 * q^18 + 10 * q^20 - 36 * q^21 + 8 * q^22 + 14 * q^23 - 62 * q^24 - 12 * q^27 - 58 * q^28 + 2 * q^29 + 160 * q^30 - 26 * q^31 + 44 * q^33 + 16 * q^34 + 56 * q^35 - 6 * q^37 - 56 * q^38 - 24 * q^39 + 70 * q^40 + 6 * q^41 + 14 * q^44 + 10 * q^45 + 2 * q^46 - 68 * q^47 - 58 * q^48 + 40 * q^50 + 16 * q^51 + 4 * q^52 + 26 * q^54 - 16 * q^55 + 50 * q^56 + 18 * q^57 - 94 * q^58 + 22 * q^61 - 48 * q^62 + 16 * q^63 + 60 * q^64 - 22 * q^65 + 24 * q^67 + 20 * q^68 + 8 * q^69 - 14 * q^71 - 84 * q^72 + 34 * q^73 + 26 * q^74 - 102 * q^75 + 40 * q^78 + 4 * q^79 - 30 * q^80 - 92 * q^81 - 76 * q^82 + 108 * q^84 + 8 * q^85 + 8 * q^86 + 16 * q^88 - 72 * q^89 + 132 * q^90 + 12 * q^91 - 174 * q^92 + 50 * q^95 + 10 * q^96 - 16 * q^97 - 28 * q^98 - 86 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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