LMFDB - Embedded newform 145.2.b.c.59.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [145,2,Mod(59,145)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("145.59"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(145, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 145 = 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	145.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,-14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.15783082931$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.84345856.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 13x^{4} + 41x^{2} + 1 $ x^6 + 13x^4 + 41x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			59.5
Root			$2.30229i$ of defining polynomial
Character	$\chi$	$=$	145.59
Dual form			145.2.b.c.59.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.30229i q^{2} -2.89028i q^{3} -3.30056 q^{4} +(2.17686 - 0.511167i) q^{5} +6.65427 q^{6} -3.91261i q^{7} -2.99427i q^{8} -5.35371 q^{9} +(1.17686 + 5.01177i) q^{10} +2.65427 q^{11} +9.53954i q^{12} +5.62692i q^{13} +9.00799 q^{14} +(-1.47742 - 6.29173i) q^{15} +0.292570 q^{16} +1.86794i q^{17} -12.3258i q^{18} -1.69944 q^{19} +(-7.18485 + 1.68714i) q^{20} -11.3085 q^{21} +6.11092i q^{22} +0.691975i q^{23} -8.65427 q^{24} +(4.47742 - 2.22548i) q^{25} -12.9548 q^{26} +6.80289i q^{27} +12.9138i q^{28} +1.00000 q^{29} +(14.4854 - 3.40145i) q^{30} -0.654273 q^{31} -5.31495i q^{32} -7.67159i q^{33} -4.30056 q^{34} +(-2.00000 - 8.51720i) q^{35} +17.6703 q^{36} +3.91261i q^{37} -3.91261i q^{38} +16.2634 q^{39} +(-1.53057 - 6.51810i) q^{40} -26.0356i q^{42} +10.7155i q^{43} -8.76059 q^{44} +(-11.6543 + 2.73664i) q^{45} -1.59313 q^{46} +4.93495i q^{47} -0.845610i q^{48} -8.30855 q^{49} +(5.12370 + 10.3083i) q^{50} +5.39888 q^{51} -18.5720i q^{52} -7.67159i q^{53} -15.6623 q^{54} +(5.77797 - 1.35678i) q^{55} -11.7154 q^{56} +4.91186i q^{57} +2.30229i q^{58} -10.0000 q^{59} +(4.87630 + 20.7662i) q^{60} -4.70743 q^{61} -1.50633i q^{62} +20.9470i q^{63} +12.8217 q^{64} +(2.87630 + 12.2490i) q^{65} +17.6623 q^{66} -6.47253i q^{67} -6.16526i q^{68} +2.00000 q^{69} +(19.6091 - 4.60459i) q^{70} +2.00000 q^{71} +16.0305i q^{72} +10.5619i q^{73} -9.00799 q^{74} +(-6.43225 - 12.9410i) q^{75} +5.60911 q^{76} -10.3851i q^{77} +37.4431i q^{78} +2.05316 q^{79} +(0.636884 - 0.149552i) q^{80} +3.60112 q^{81} -1.86794i q^{83} +37.3245 q^{84} +(0.954832 + 4.06625i) q^{85} -24.6703 q^{86} -2.89028i q^{87} -7.94761i q^{88} -3.30855 q^{89} +(-6.30056 - 26.8316i) q^{90} +22.0160 q^{91} -2.28390i q^{92} +1.89103i q^{93} -11.3617 q^{94} +(-3.69944 + 0.868699i) q^{95} -15.3617 q^{96} +0.384703i q^{97} -19.1287i q^{98} -14.2102 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 14 q^{4} + 3 q^{5} + 14 q^{6} - 12 q^{9} - 3 q^{10} - 10 q^{11} + 8 q^{14} + 7 q^{15} + 42 q^{16} - 16 q^{19} + 13 q^{20} - 16 q^{21} - 26 q^{24} + 11 q^{25} - 46 q^{26} + 6 q^{29} + 25 q^{30} + 22 q^{31}+ \cdots - 16 q^{99}+O(q^{100}) $ 6 * q - 14 * q^4 + 3 * q^5 + 14 * q^6 - 12 * q^9 - 3 * q^10 - 10 * q^11 + 8 * q^14 + 7 * q^15 + 42 * q^16 - 16 * q^19 + 13 * q^20 - 16 * q^21 - 26 * q^24 + 11 * q^25 - 46 * q^26 + 6 * q^29 + 25 * q^30 + 22 * q^31 - 20 * q^34 - 12 * q^35 - 12 * q^36 + 14 * q^39 + 21 * q^40 + 2 * q^44 - 44 * q^45 - 44 * q^46 + 2 * q^49 + 35 * q^50 + 44 * q^51 - 22 * q^54 + 13 * q^55 + 16 * q^56 - 60 * q^59 + 25 * q^60 + 12 * q^61 - 38 * q^64 + 13 * q^65 + 34 * q^66 + 12 * q^69 + 60 * q^70 + 12 * q^71 - 8 * q^74 + 9 * q^75 - 24 * q^76 - 2 * q^79 - 55 * q^80 + 10 * q^81 + 80 * q^84 - 26 * q^85 - 30 * q^86 + 32 * q^89 - 32 * q^90 + 40 * q^91 - 2 * q^94 - 28 * q^95 - 26 * q^96 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/145\mathbb{Z}\right)^\times$.

$n$	$31$	$117$
$\chi(n)$	$1$	$-1$

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 $

$2$			2.30229i			1.62797i	0.580887	+	0.813984i	$0.302706\pi$
$2$			2.30229i			1.62797i	−0.580887	+	0.813984i	$0.697294\pi$
$3$		−	2.89028i		−	1.66870i	−0.551232	−	0.834352i	$-0.685842\pi$
$3$		−	2.89028i		−	1.66870i	0.551232	−	0.834352i	$-0.314158\pi$
$4$	−3.30056			−1.65028
$5$	2.17686	−	0.511167i	0.973520	−	0.228601i
$5$	2.17686	−	0.511167i	0.973520	−	0.228601i
$6$	6.65427			2.71660
$7$		−	3.91261i		−	1.47883i	−0.673250	−	0.739415i	$-0.735102\pi$
$7$		−	3.91261i		−	1.47883i	0.673250	−	0.739415i	$-0.264898\pi$
$8$		−	2.99427i		−	1.05863i
$9$	−5.35371			−1.78457
$10$	1.17686	+	5.01177i	0.372155	+	1.58486i
$11$	2.65427			0.800294			0.400147	−	0.916451i	$-0.368959\pi$
$11$	2.65427			0.800294			0.400147	+	0.916451i	$0.368959\pi$
$12$			9.53954i			2.75383i
$13$			5.62692i			1.56063i	0.625388	+	0.780314i	$0.284941\pi$
$13$			5.62692i			1.56063i	−0.625388	+	0.780314i	$0.715059\pi$
$14$	9.00799			2.40749
$15$	−1.47742	−	6.29173i	−0.381467	−	1.62452i
$16$	0.292570			0.0731426
$17$			1.86794i			0.453043i	0.974006	+	0.226522i	$0.0727354\pi$
$17$			1.86794i			0.453043i	−0.974006	+	0.226522i	$0.927265\pi$
$18$		−	12.3258i		−	2.90523i
$19$	−1.69944			−0.389879			−0.194939	−	0.980815i	$-0.562451\pi$
$19$	−1.69944			−0.389879			−0.194939	+	0.980815i	$0.562451\pi$
$20$	−7.18485	+	1.68714i	−1.60658	+	0.377255i
$21$	−11.3085			−2.46773
$22$			6.11092i			1.30285i
$23$			0.691975i			0.144287i	0.997394	+	0.0721433i	$0.0229839\pi$
$23$			0.691975i			0.144287i	−0.997394	+	0.0721433i	$0.977016\pi$
$24$	−8.65427			−1.76655
$25$	4.47742	−	2.22548i	0.895483	−	0.445095i
$26$	−12.9548			−2.54065
$27$			6.80289i			1.30922i
$28$			12.9138i			2.44048i
$29$	1.00000			0.185695
$29$	1.00000			0.185695
$30$	14.4854	−	3.40145i	2.64466	−	0.621016i
$31$	−0.654273			−0.117511			−0.0587555	−	0.998272i	$-0.518713\pi$
$31$	−0.654273			−0.117511			−0.0587555	+	0.998272i	$0.518713\pi$
$32$		−	5.31495i		−	0.939560i
$33$		−	7.67159i		−	1.33545i
$34$	−4.30056			−0.737540
$35$	−2.00000	−	8.51720i	−0.338062	−	1.43967i
$36$	17.6703			2.94504
$37$			3.91261i			0.643230i	0.946871	+	0.321615i	$0.104226\pi$
$37$			3.91261i			0.643230i	−0.946871	+	0.321615i	$0.895774\pi$
$38$		−	3.91261i		−	0.634710i
$39$	16.2634			2.60422
$40$	−1.53057	−	6.51810i	−0.242005	−	1.03060i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		−	26.0356i		−	4.01738i
$43$			10.7155i			1.63410i	0.576567	+	0.817050i	$0.304392\pi$
$43$			10.7155i			1.63410i	−0.576567	+	0.817050i	$0.695608\pi$
$44$	−8.76059			−1.32071
$45$	−11.6543	+	2.73664i	−1.73732	+	0.407955i
$46$	−1.59313			−0.234894
$47$			4.93495i			0.719836i	0.932984	+	0.359918i	$0.117195\pi$
$47$			4.93495i			0.719836i	−0.932984	+	0.359918i	$0.882805\pi$
$48$		−	0.845610i		−	0.122053i
$49$	−8.30855			−1.18694
$50$	5.12370	+	10.3083i	0.724601	+	1.45782i
$51$	5.39888			0.755995
$52$		−	18.5720i		−	2.57547i
$53$		−	7.67159i		−	1.05377i	−0.849935	−	0.526887i	$-0.823359\pi$
$53$		−	7.67159i		−	1.05377i	0.849935	−	0.526887i	$-0.176641\pi$
$54$	−15.6623			−2.13136
$55$	5.77797	−	1.35678i	0.779102	−	0.182948i
$56$	−11.7154			−1.56554
$57$			4.91186i			0.650592i
$58$			2.30229i			0.302306i
$59$	−10.0000			−1.30189			−0.650945	−	0.759125i	$-0.725627\pi$
$59$	−10.0000			−1.30189			−0.650945	+	0.759125i	$0.725627\pi$
$60$	4.87630	+	20.7662i	0.629527	+	2.68091i
$61$	−4.70743			−0.602725			−0.301362	−	0.953510i	$-0.597441\pi$
$61$	−4.70743			−0.602725			−0.301362	+	0.953510i	$0.597441\pi$
$62$		−	1.50633i		−	0.191304i
$63$			20.9470i			2.63908i
$64$	12.8217			1.60272
$65$	2.87630	+	12.2490i	0.356761	+	1.51930i
$66$	17.6623			2.17407
$67$		−	6.47253i		−	0.790746i	−0.918521	−	0.395373i	$-0.870615\pi$
$67$		−	6.47253i		−	0.790746i	0.918521	−	0.395373i	$-0.129385\pi$
$68$		−	6.16526i		−	0.747648i
$69$	2.00000			0.240772
$70$	19.6091	−	4.60459i	2.34374	−	0.550354i
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$			16.0305i			1.88921i
$73$			10.5619i			1.23617i	0.786110	+	0.618087i	$0.212092\pi$
$73$			10.5619i			1.23617i	−0.786110	+	0.618087i	$0.787908\pi$
$74$	−9.00799			−1.04716
$75$	−6.43225	−	12.9410i	−0.742732	−	1.49430i
$76$	5.60911			0.643409
$77$		−	10.3851i		−	1.18350i
$78$			37.4431i			4.23959i
$79$	2.05316			0.230998			0.115499	−	0.993308i	$-0.463153\pi$
$79$	2.05316			0.230998			0.115499	+	0.993308i	$0.463153\pi$
$80$	0.636884	−	0.149552i	0.0712058	−	0.0167205i
$81$	3.60112			0.400124
$82$		0			0
$83$		−	1.86794i		−	0.205034i	−0.994731	−	0.102517i	$-0.967310\pi$
$83$		−	1.86794i		−	0.205034i	0.994731	−	0.102517i	$-0.0326895\pi$
$84$	37.3245			4.07244
$85$	0.954832	+	4.06625i	0.103566	+	0.441047i
$86$	−24.6703			−2.66026
$87$		−	2.89028i		−	0.309870i
$88$		−	7.94761i		−	0.847218i
$89$	−3.30855			−0.350705			−0.175353	−	0.984506i	$-0.556107\pi$
$89$	−3.30855			−0.350705			−0.175353	+	0.984506i	$0.556107\pi$
$90$	−6.30056	−	26.8316i	−0.664137	−	2.82830i
$91$	22.0160			2.30790
$92$		−	2.28390i		−	0.238113i
$93$			1.89103i			0.196091i
$94$	−11.3617			−1.17187
$95$	−3.69944	+	0.868699i	−0.379555	+	0.0891266i
$96$	−15.3617			−1.56785
$97$			0.384703i			0.0390607i	0.999809	+	0.0195303i	$0.00621710\pi$
$97$			0.384703i			0.0390607i	−0.999809	+	0.0195303i	$0.993783\pi$
$98$		−	19.1287i		−	1.93229i
$99$	−14.2102			−1.42818
$100$	−14.7780	+	7.34532i	−1.47780	+	0.734532i
$101$	11.9097			1.18506			0.592528	−	0.805550i	$-0.298130\pi$
$101$	11.9097			1.18506			0.592528	+	0.805550i	$0.298130\pi$
$102$			12.4298i			1.23074i
$103$		−	14.9585i		−	1.47390i	−0.675946	−	0.736951i	$-0.736265\pi$
$103$		−	14.9585i		−	1.47390i	0.675946	−	0.736951i	$-0.263735\pi$
$104$	16.8485			1.65213
$105$	−24.6171	+	5.78056i	−2.40238	+	0.564125i
$106$	17.6623			1.71551
$107$			3.91261i			0.378247i	0.981953	+	0.189123i	$0.0605646\pi$
$107$			3.91261i			0.378247i	−0.981953	+	0.189123i	$0.939435\pi$
$108$		−	22.4533i		−	2.16057i
$109$	7.55595			0.723729			0.361864	−	0.932231i	$-0.382140\pi$
$109$	7.55595			0.723729			0.361864	+	0.932231i	$0.382140\pi$
$110$	3.12370	+	13.3026i	0.297833	+	1.26835i
$111$	11.3085			1.07336
$112$		−	1.14472i		−	0.108165i
$113$		−	18.6944i		−	1.75862i	−0.476251	−	0.879309i	$-0.658005\pi$
$113$		−	18.6944i		−	1.75862i	0.476251	−	0.879309i	$-0.341995\pi$
$114$	−11.3085			−1.05914
$115$	0.353715	+	1.50633i	0.0329841	+	0.140466i
$116$	−3.30056			−0.306449
$117$		−	30.1249i		−	2.78505i
$118$		−	23.0229i		−	2.11943i
$119$	7.30855			0.669973
$120$	−18.8391	+	4.42378i	−1.71977	+	0.403834i
$121$	−3.95483			−0.359530
$122$		−	10.8379i		−	0.981216i
$123$		0			0
$124$	2.15947			0.193926
$125$	8.60911	−	7.13325i	0.770022	−	0.638018i
$126$	−48.2262			−4.29633
$127$		−	4.98929i		−	0.442728i	−0.975191	−	0.221364i	$-0.928949\pi$
$127$		−	4.98929i		−	0.442728i	0.975191	−	0.221364i	$-0.0710509\pi$
$128$			18.8895i			1.66961i
$129$	30.9708			2.72683
$130$	−28.2008	+	6.62209i	−2.47338	+	0.580795i
$131$	19.7154			1.72254			0.861272	−	0.508144i	$-0.169668\pi$
$131$	19.7154			1.72254			0.861272	+	0.508144i	$0.169668\pi$
$132$			25.3205i			2.20387i
$133$			6.64926i			0.576564i
$134$	14.9017			1.28731
$135$	3.47742	+	14.8089i	0.299288	+	1.27455i
$136$	5.59313			0.479607
$137$			6.26455i			0.535217i	0.963528	+	0.267608i	$0.0862334\pi$
$137$			6.26455i			0.535217i	−0.963528	+	0.267608i	$0.913767\pi$
$138$			4.60459i			0.391969i
$139$	−21.9097			−1.85835			−0.929177	−	0.369636i	$-0.879482\pi$
$139$	−21.9097			−1.85835			−0.929177	+	0.369636i	$0.879482\pi$
$140$	6.60112	+	28.1115i	0.557896	+	2.37586i
$141$	14.2634			1.20119
$142$			4.60459i			0.386408i
$143$			14.9354i			1.24896i
$144$	−1.56634			−0.130528
$145$	2.17686	−	0.511167i	0.180778	−	0.0424501i
$146$	−24.3165			−2.01245
$147$			24.0140i			1.98064i
$148$		−	12.9138i		−	1.06151i
$149$	−4.24740			−0.347961			−0.173980	−	0.984749i	$-0.555663\pi$
$149$	−4.24740			−0.347961			−0.173980	+	0.984749i	$0.555663\pi$
$150$	29.7940	−	14.8089i	2.43267	−	1.20914i
$151$	−11.3085			−0.920277			−0.460138	−	0.887847i	$-0.652200\pi$
$151$	−11.3085			−0.920277			−0.460138	+	0.887847i	$0.652200\pi$
$152$			5.08858i			0.412739i
$153$		−	10.0004i		−	0.808488i
$154$	23.9097			1.92670
$155$	−1.42426	+	0.334443i	−0.114399	+	0.0268631i
$156$	−53.6782			−4.29770
$157$			4.12059i			0.328859i	0.986389	+	0.164430i	$0.0525783\pi$
$157$			4.12059i			0.328859i	−0.986389	+	0.164430i	$0.947422\pi$
$158$			4.72697i			0.376057i
$159$	−22.1730			−1.75844
$160$	−2.71683	−	11.5699i	−0.214784	−	0.914681i
$161$	2.70743			0.213375
$162$			8.29083i			0.651389i
$163$			3.19755i			0.250452i	0.992128	+	0.125226i	$0.0399655\pi$
$163$			3.19755i			0.250452i	−0.992128	+	0.125226i	$0.960034\pi$
$164$		0			0
$165$	−3.92147	−	16.7000i	−0.305286	−	1.30009i
$166$	4.30056			0.333788
$167$		−	14.6050i		−	1.13017i	−0.825032	−	0.565086i	$-0.808843\pi$
$167$		−	14.6050i		−	1.13017i	0.825032	−	0.565086i	$-0.191157\pi$
$168$			33.8608i			2.61242i
$169$	−18.6623			−1.43556
$170$	−9.36170	+	2.19830i	−0.718010	+	0.168602i
$171$	9.09832			0.695766
$172$		−	35.3672i		−	2.69672i
$173$		−	9.00120i		−	0.684348i	−0.939637	−	0.342174i	$-0.888837\pi$
$173$		−	9.00120i		−	0.684348i	0.939637	−	0.342174i	$-0.111163\pi$
$174$	6.65427			0.504459
$175$	−8.70743	−	17.5184i	−0.658220	−	1.32427i
$176$	0.776562			0.0585356
$177$			28.9028i			2.17247i
$178$		−	7.61725i		−	0.570937i
$179$	21.3085			1.59268			0.796338	−	0.604852i	$-0.206768\pi$
$179$	21.3085			1.59268			0.796338	+	0.604852i	$0.206768\pi$
$180$	38.4656	−	9.03245i	2.86706	−	0.673239i
$181$	−16.9708			−1.26143			−0.630715	−	0.776014i	$-0.717238\pi$
$181$	−16.9708			−1.26143			−0.630715	+	0.776014i	$0.717238\pi$
$182$			50.6873i			3.75719i
$183$			13.6058i			1.00577i
$184$	2.07196			0.152747
$185$	2.00000	+	8.51720i	0.147043	+	0.626197i
$186$	−4.35371			−0.319230
$187$			4.95804i			0.362568i
$188$		−	16.2881i		−	1.18793i
$189$	26.6171			1.93611
$190$	−2.00000	−	8.51720i	−0.145095	−	0.617903i
$191$	−8.40687			−0.608300			−0.304150	−	0.952624i	$-0.598372\pi$
$191$	−8.40687			−0.608300			−0.304150	+	0.952624i	$0.598372\pi$
$192$		−	37.0584i		−	2.67446i
$193$			0.791267i			0.0569567i	0.999594	+	0.0284783i	$0.00906616\pi$
$193$			0.791267i			0.0569567i	−0.999594	+	0.0284783i	$0.990934\pi$
$194$	−0.885700			−0.0635895
$195$	35.4031	−	8.31331i	2.53527	−	0.595328i
$196$	27.4228			1.95877
$197$		−	24.5062i		−	1.74599i	−0.487726	−	0.872997i	$-0.662174\pi$
$197$		−	24.5062i		−	1.74599i	0.487726	−	0.872997i	$-0.337826\pi$
$198$		−	32.7161i		−	2.32503i
$199$	−19.3085			−1.36875			−0.684373	−	0.729132i	$-0.739924\pi$
$199$	−19.3085			−1.36875			−0.684373	+	0.729132i	$0.739924\pi$
$200$	−6.66367	−	13.4066i	−0.471193	−	0.947989i
$201$	−18.7074			−1.31952
$202$			27.4196i			1.92923i
$203$		−	3.91261i		−	0.274612i
$204$	−17.8193			−1.24760
$205$		0			0
$206$	34.4388			2.39947
$207$		−	3.70463i		−	0.257490i
$208$			1.64627i			0.114148i
$209$	−4.51078			−0.312017
$210$	−13.3085	−	56.6758i	−0.918377	−	3.91100i
$211$	19.2554			1.32560			0.662798	−	0.748798i	$-0.269369\pi$
$211$	19.2554			1.32560			0.662798	+	0.748798i	$0.269369\pi$
$212$			25.3205i			1.73902i
$213$		−	5.78056i		−	0.396077i
$214$	−9.00799			−0.615773
$215$	5.47742	+	23.3261i	0.373557	+	1.59083i
$216$	20.3697			1.38598
$217$			2.55992i			0.173779i
$218$			17.3960i			1.17821i
$219$	30.5268			2.06281
$220$	−19.0705	+	4.47812i	−1.28574	+	0.301915i
$221$	−10.5108			−0.707032
$222$			26.0356i			1.74740i
$223$			10.8691i			0.727852i	0.931428	+	0.363926i	$0.118564\pi$
$223$			10.8691i			0.727852i	−0.931428	+	0.363926i	$0.881436\pi$
$224$	−20.7954			−1.38945
$225$	−23.9708	+	11.9146i	−1.59805	+	0.794304i
$226$	43.0399			2.86297
$227$		−	17.3104i		−	1.14893i	−0.818528	−	0.574467i	$-0.805210\pi$
$227$		−	17.3104i		−	1.14893i	0.818528	−	0.574467i	$-0.194790\pi$
$228$		−	16.2119i		−	1.07366i
$229$	−18.7074			−1.23622			−0.618111	−	0.786091i	$-0.712102\pi$
$229$	−18.7074			−1.23622			−0.618111	+	0.786091i	$0.712102\pi$
$230$	−3.46802	+	0.814355i	−0.228674	+	0.0536970i
$231$	−30.0160			−1.97491
$232$		−	2.99427i		−	0.196583i
$233$			14.6281i			0.958320i	0.877728	+	0.479160i	$0.159059\pi$
$233$			14.6281i			0.958320i	−0.877728	+	0.479160i	$0.840941\pi$
$234$	69.3565			4.53397
$235$	2.52258	+	10.7427i	0.164555	+	0.700775i
$236$	33.0056			2.14848
$237$		−	5.93419i		−	0.385467i
$238$			16.8264i			1.09070i
$239$	2.00000			0.129369			0.0646846	−	0.997906i	$-0.479396\pi$
$239$	2.00000			0.129369			0.0646846	+	0.997906i	$0.479396\pi$
$240$	−0.432248	−	1.84077i	−0.0279015	−	0.118821i
$241$	−5.55595			−0.357890			−0.178945	−	0.983859i	$-0.557268\pi$
$241$	−5.55595			−0.357890			−0.178945	+	0.983859i	$0.557268\pi$
$242$		−	9.10519i		−	0.585304i
$243$			10.0004i			0.641529i
$244$	15.5371			0.994664
$245$	−18.0865	+	4.24706i	−1.15551	+	0.271335i
$246$		0			0
$247$		−	9.56263i		−	0.608455i
$248$			1.95907i			0.124401i
$249$	−5.39888			−0.342140
$250$	16.4228	+	19.8207i	1.03867	+	1.25357i
$251$	−9.27137			−0.585204			−0.292602	−	0.956234i	$-0.594521\pi$
$251$	−9.27137			−0.585204			−0.292602	+	0.956234i	$0.594521\pi$
$252$		−	69.1369i		−	4.35521i
$253$			1.83669i			0.115472i
$254$	11.4868			0.720747
$255$	11.7526	−	2.75973i	0.735976	−	0.172821i
$256$	−17.8457			−1.11536
$257$			14.1129i			0.880337i	0.897915	+	0.440168i	$0.145081\pi$
$257$			14.1129i			0.880337i	−0.897915	+	0.440168i	$0.854919\pi$
$258$			71.3039i			4.43919i
$259$	15.3085			0.951227
$260$	−9.49339	−	40.4286i	−0.588755	−	2.50727i
$261$	−5.35371			−0.331387
$262$			45.3907i			2.80425i
$263$			6.97962i			0.430382i	0.976572	+	0.215191i	$0.0690373\pi$
$263$			6.97962i			0.430382i	−0.976572	+	0.215191i	$0.930963\pi$
$264$	−22.9708			−1.41376
$265$	−3.92147	−	16.7000i	−0.240894	−	1.02587i
$266$	−15.3085			−0.938627
$267$			9.56263i			0.585223i
$268$			21.3630i			1.30495i
$269$	7.29257			0.444636			0.222318	−	0.974974i	$-0.428638\pi$
$269$	7.29257			0.444636			0.222318	+	0.974974i	$0.428638\pi$
$270$	−34.0945	+	8.00604i	−2.07493	+	0.487232i
$271$	−23.3617			−1.41912			−0.709561	−	0.704644i	$-0.751107\pi$
$271$	−23.3617			−1.41912			−0.709561	+	0.704644i	$0.751107\pi$
$272$			0.546506i			0.0331368i
$273$		−	63.6323i		−	3.85120i
$274$	−14.4228			−0.871316
$275$	11.8843	−	5.90702i	0.716649	−	0.356207i
$276$	−6.60112			−0.397341
$277$		−	2.91337i		−	0.175047i	−0.996162	−	0.0875236i	$-0.972105\pi$
$277$		−	2.91337i		−	0.175047i	0.996162	−	0.0875236i	$-0.0278953\pi$
$278$		−	50.4425i		−	3.02534i
$279$	3.50279			0.209707
$280$	−25.5028	+	5.98854i	−1.52408	+	0.357884i
$281$	30.1730			1.79997			0.899986	−	0.435918i	$-0.143576\pi$
$281$	30.1730			1.79997			0.899986	+	0.435918i	$0.143576\pi$
$282$			32.8385i			1.95550i
$283$			2.01341i			0.119685i	0.998208	+	0.0598425i	$0.0190599\pi$
$283$			2.01341i			0.119685i	−0.998208	+	0.0598425i	$0.980940\pi$
$284$	−6.60112			−0.391704
$285$	2.51078	+	10.6924i	0.148726	+	0.633364i
$286$	−34.3857			−2.03327
$287$		0			0
$288$			28.4547i			1.67671i
$289$	13.5108			0.794752
$290$	1.17686	+	5.01177i	0.0691074	+	0.294301i
$291$	1.11190			0.0651807
$292$		−	34.8601i		−	2.04003i
$293$			10.8691i			0.634982i	0.948261	+	0.317491i	$0.102840\pi$
$293$			10.8691i			0.634982i	−0.948261	+	0.317491i	$0.897160\pi$
$294$	−55.2873			−3.22442
$295$	−21.7686	+	5.11167i	−1.26742	+	0.297613i
$296$	11.7154			0.680945
$297$			18.0567i			1.04776i
$298$		−	9.77877i		−	0.566469i
$299$	−3.89369			−0.225178
$300$	21.2300	+	42.7125i	1.22572	+	2.46601i
$301$	41.9256			2.41655
$302$		−	26.0356i		−	1.49818i
$303$		−	34.4223i		−	1.97751i
$304$	−0.497206			−0.0285167
$305$	−10.2474	+	2.40628i	−0.586765	+	0.137783i
$306$	23.0240			1.31619
$307$		−	9.02429i		−	0.515043i	−0.966273	−	0.257522i	$-0.917094\pi$
$307$		−	9.02429i		−	0.515043i	0.966273	−	0.257522i	$-0.0829059\pi$
$308$			34.2768i			1.95310i
$309$	−43.2342			−2.45951
$310$	−0.769987	−	3.27907i	−0.0437323	−	0.186238i
$311$	−11.1143			−0.630234			−0.315117	−	0.949053i	$-0.602044\pi$
$311$	−11.1143			−0.630234			−0.315117	+	0.949053i	$0.602044\pi$
$312$		−	48.6969i		−	2.75692i
$313$			25.7365i			1.45471i	0.686260	+	0.727356i	$0.259251\pi$
$313$			25.7365i			1.45471i	−0.686260	+	0.727356i	$0.740749\pi$
$314$	−9.48682			−0.535372
$315$	10.7074	+	45.5987i	0.603295	+	2.56919i
$316$	−6.77656			−0.381211
$317$			0.837444i			0.0470355i	0.999723	+	0.0235178i	$0.00748663\pi$
$317$			0.837444i			0.0470355i	−0.999723	+	0.0235178i	$0.992513\pi$
$318$		−	51.0489i		−	2.86268i
$319$	2.65427			0.148611
$320$	27.9111	−	6.55405i	1.56028	−	0.366382i
$321$	11.3085			0.631182
$322$			6.23330i			0.347368i
$323$		−	3.17446i		−	0.176632i
$324$	−11.8857			−0.660317
$325$	12.5226	+	25.1941i	0.694628	+	1.39752i
$326$	−7.36170			−0.407727
$327$		−	21.8388i		−	1.20769i
$328$		0			0
$329$	19.3085			1.06451
$330$	38.4482	−	9.02837i	2.11651	−	0.496995i
$331$	22.0691			1.21303			0.606515	−	0.795072i	$-0.292567\pi$
$331$	22.0691			1.21303			0.606515	+	0.795072i	$0.292567\pi$
$332$			6.16526i			0.338363i
$333$		−	20.9470i		−	1.14789i
$334$	33.6251			1.83988
$335$	−3.30855	−	14.0898i	−0.180765	−	0.769807i
$336$	−3.30855			−0.180496
$337$			7.74780i			0.422049i	0.977481	+	0.211025i	$0.0676800\pi$
$337$			7.74780i			0.422049i	−0.977481	+	0.211025i	$0.932320\pi$
$338$		−	42.9660i		−	2.33704i
$339$	−54.0320			−2.93461
$340$	−3.15148	−	13.4209i	−0.170913	−	0.727850i
$341$	−1.73662			−0.0940433
$342$			20.9470i			1.13269i
$343$			5.11984i			0.276445i
$344$	32.0851			1.72991
$345$	4.35371	−	1.02233i	0.234396	−	0.0550406i
$346$	20.7234			1.11410
$347$			9.33972i			0.501383i	0.968067	+	0.250691i	$0.0806579\pi$
$347$			9.33972i			0.501383i	−0.968067	+	0.250691i	$0.919342\pi$
$348$			9.53954i			0.511373i
$349$	21.6623			1.15955			0.579777	−	0.814775i	$-0.303140\pi$
$349$	21.6623			1.15955			0.579777	+	0.814775i	$0.303140\pi$
$350$	40.3325	−	20.0471i	2.15586	−	1.07156i
$351$	−38.2794			−2.04320
$352$		−	14.1073i		−	0.751924i
$353$			20.5623i			1.09442i	0.836995	+	0.547211i	$0.184310\pi$
$353$			20.5623i			1.09442i	−0.836995	+	0.547211i	$0.815690\pi$
$354$	−66.5427			−3.53671
$355$	4.35371	−	1.02233i	0.231071	−	0.0542599i
$356$	10.9201			0.578762
$357$		−	21.1237i		−	1.11799i
$358$			49.0585i			2.59282i
$359$	−30.5639			−1.61310			−0.806551	−	0.591164i	$-0.798669\pi$
$359$	−30.5639			−1.61310			−0.806551	+	0.591164i	$0.798669\pi$
$360$	8.19425	+	34.8960i	0.431875	+	1.83918i
$361$	−16.1119			−0.847995
$362$		−	39.0718i		−	2.05357i
$363$			11.4306i			0.599949i
$364$	−72.6650			−3.80868
$365$	5.39888	+	22.9917i	0.282590	+	1.20344i
$366$	−31.3245			−1.63736
$367$			13.7825i			0.719441i	0.933060	+	0.359721i	$0.117128\pi$
$367$			13.7825i			0.719441i	−0.933060	+	0.359721i	$0.882872\pi$
$368$			0.202451i			0.0105535i
$369$		0			0
$370$	−19.6091	+	4.60459i	−1.01943	+	0.239381i
$371$	−30.0160			−1.55835
$372$		−	6.24147i		−	0.323605i
$373$		−	27.2659i		−	1.41178i	−0.708324	−	0.705888i	$-0.750548\pi$
$373$		−	27.2659i		−	1.41178i	0.708324	−	0.705888i	$-0.249452\pi$
$374$	−11.4149			−0.590248
$375$	−20.6171	−	24.8827i	−1.06466	−	1.28494i
$376$	14.7766			0.762043
$377$			5.62692i			0.289801i
$378$			61.2804i			3.15192i
$379$	−16.4069			−0.842764			−0.421382	−	0.906883i	$-0.638455\pi$
$379$	−16.4069			−0.842764			−0.421382	+	0.906883i	$0.638455\pi$
$380$	12.2102	−	2.86719i	0.626371	−	0.147084i
$381$	−14.4204			−0.738782
$382$		−	19.3551i		−	0.990293i
$383$		−	11.7378i		−	0.599776i	−0.953974	−	0.299888i	$-0.903051\pi$
$383$		−	11.7378i		−	0.599776i	0.953974	−	0.299888i	$-0.0969493\pi$
$384$	54.5959			2.78608
$385$	−5.30855	−	22.6070i	−0.270549	−	1.15216i
$386$	−1.82173			−0.0927236
$387$		−	57.3678i		−	2.91617i
$388$		−	1.26974i		−	0.0644610i
$389$	12.0000			0.608424			0.304212	−	0.952604i	$-0.401607\pi$
$389$	12.0000			0.608424			0.304212	+	0.952604i	$0.401607\pi$
$390$	19.1397	+	81.5083i	0.969175	+	4.12733i
$391$	−1.29257			−0.0653681
$392$			24.8780i			1.25653i
$393$		−	56.9831i		−	2.87442i
$394$	56.4204			2.84242
$395$	4.46943	−	1.04951i	0.224881	−	0.0528064i
$396$	46.9017			2.35690
$397$		−	6.03349i		−	0.302812i	−0.988472	−	0.151406i	$-0.951620\pi$
$397$		−	6.03349i		−	0.302812i	0.988472	−	0.151406i	$-0.0483801\pi$
$398$		−	44.4540i		−	2.22828i
$399$	19.2182			0.962114
$400$	1.30996	−	0.651109i	0.0654980	−	0.0325554i
$401$	−21.4656			−1.07194			−0.535971	−	0.844237i	$-0.680054\pi$
$401$	−21.4656			−1.07194			−0.535971	+	0.844237i	$0.680054\pi$
$402$		−	43.0700i		−	2.14814i
$403$		−	3.68155i		−	0.183391i
$404$	−39.3085			−1.95567
$405$	7.83912	−	1.84077i	0.389529	−	0.0914688i
$406$	9.00799			0.447059
$407$			10.3851i			0.514773i
$408$		−	16.1657i		−	0.800322i
$409$	4.49481			0.222254			0.111127	−	0.993806i	$-0.464554\pi$
$409$	4.49481			0.222254			0.111127	+	0.993806i	$0.464554\pi$
$410$		0			0
$411$	18.1063			0.893119
$412$			49.3713i			2.43235i
$413$			39.1261i			1.92527i
$414$	8.52916			0.419185
$415$	−0.954832	−	4.06625i	−0.0468709	−	0.199604i
$416$	29.9068			1.46630
$417$			63.3251i			3.10104i
$418$		−	10.3851i		−	0.507954i
$419$	−4.19665			−0.205020			−0.102510	−	0.994732i	$-0.532687\pi$
$419$	−4.19665			−0.205020			−0.102510	+	0.994732i	$0.532687\pi$
$420$	81.2502	−	19.0791i	3.96460	−	0.930963i
$421$	−18.5108			−0.902160			−0.451080	−	0.892483i	$-0.648961\pi$
$421$	−18.5108			−0.902160			−0.451080	+	0.892483i	$0.648961\pi$
$422$			44.3316i			2.15803i
$423$		−	26.4203i		−	1.28460i
$424$	−22.9708			−1.11556
$425$	4.15707	+	8.36357i	0.201647	+	0.405693i
$426$	13.3085			0.644801
$427$			18.4184i			0.891327i
$428$		−	12.9138i		−	0.624213i
$429$	43.1675			2.08414
$430$	−53.7036	+	12.6106i	−2.58982	+	0.608138i
$431$	37.1279			1.78839			0.894193	−	0.447681i	$-0.147750\pi$
$431$	37.1279			1.78839			0.894193	+	0.447681i	$0.147750\pi$
$432$			1.99033i			0.0957596i
$433$		−	16.8577i		−	0.810128i	−0.914288	−	0.405064i	$-0.867249\pi$
$433$		−	16.8577i		−	0.810128i	0.914288	−	0.405064i	$-0.132751\pi$
$434$	−5.89369			−0.282906
$435$	−1.47742	−	6.29173i	−0.0708367	−	0.301665i
$436$	−24.9389			−1.19435
$437$		−	1.17597i		−	0.0562543i
$438$			70.2816i			3.35818i
$439$	9.21821			0.439961			0.219981	−	0.975504i	$-0.429401\pi$
$439$	9.21821			0.439961			0.219981	+	0.975504i	$0.429401\pi$
$440$	−4.06256	−	17.3008i	−0.193675	−	0.824784i
$441$	44.4816			2.11817
$442$		−	24.1989i		−	1.15102i
$443$			18.9023i			0.898078i	0.893512	+	0.449039i	$0.148234\pi$
$443$			18.9023i			0.898078i	−0.893512	+	0.449039i	$0.851766\pi$
$444$	−37.3245			−1.77134
$445$	−7.20223	+	1.69122i	−0.341419	+	0.0801716i
$446$	−25.0240			−1.18492
$447$			12.2762i			0.580643i
$448$		−	50.1665i		−	2.37014i
$449$	31.3245			1.47830			0.739148	−	0.673543i	$-0.235228\pi$
$449$	31.3245			1.47830			0.739148	+	0.673543i	$0.235228\pi$
$450$	−27.4308	−	55.1879i	−1.29310	−	2.60158i
$451$		0			0
$452$			61.7019i			2.90221i
$453$			32.6849i			1.53567i
$454$	39.8537			1.87043
$455$	47.9256	−	11.2538i	2.24679	−	0.527588i
$456$	14.7074			0.688738
$457$			36.6287i			1.71342i	0.515799	+	0.856710i	$0.327495\pi$
$457$			36.6287i			1.71342i	−0.515799	+	0.856710i	$0.672505\pi$
$458$		−	43.0700i		−	2.01253i
$459$	−12.7074			−0.593132
$460$	−1.16746	−	4.97173i	−0.0544329	−	0.231808i
$461$	28.8297			1.34273			0.671367	−	0.741125i	$-0.265707\pi$
$461$	28.8297			1.34273			0.671367	+	0.741125i	$0.265707\pi$
$462$		−	69.1056i		−	3.21508i
$463$		−	29.6409i		−	1.37753i	−0.724984	−	0.688766i	$-0.758153\pi$
$463$		−	29.6409i		−	1.37753i	0.724984	−	0.688766i	$-0.241847\pi$
$464$	0.292570			0.0135822
$465$	0.966634	+	4.11651i	0.0448266	+	0.190899i
$466$	−33.6782			−1.56011
$467$		−	26.4746i		−	1.22510i	−0.790432	−	0.612550i	$-0.790144\pi$
$467$		−	26.4746i		−	1.22510i	0.790432	−	0.612550i	$-0.209856\pi$
$468$			99.4291i			4.59611i
$469$	−25.3245			−1.16938
$470$	−24.7328	+	5.80773i	−1.14084	+	0.267891i
$471$	11.9097			0.548768
$472$			29.9427i			1.37822i
$473$			28.4419i			1.30776i
$474$	13.6623			0.627528
$475$	−7.60911	+	3.78207i	−0.349130	+	0.173533i
$476$	−24.1223			−1.10564
$477$			41.0715i			1.88054i
$478$			4.60459i			0.210609i
$479$	−27.1810			−1.24193			−0.620967	−	0.783837i	$-0.713260\pi$
$479$	−27.1810			−1.24193			−0.620967	+	0.783837i	$0.713260\pi$
$480$	−33.4402	+	7.85240i	−1.52633	+	0.358411i
$481$	−22.0160			−1.00384
$482$		−	12.7914i		−	0.582634i
$483$		−	7.82523i		−	0.356060i
$484$	13.0532			0.593325
$485$	0.196648	+	0.837444i	0.00892931	+	0.0380264i
$486$	−23.0240			−1.04439
$487$		−	32.0922i		−	1.45424i	−0.686513	−	0.727118i	$-0.740859\pi$
$487$		−	32.0922i		−	1.45424i	0.686513	−	0.727118i	$-0.259141\pi$
$488$			14.0953i			0.638065i
$489$	9.24182			0.417929
$490$	−9.77797	−	41.6405i	−0.441724	−	1.88113i
$491$	−10.0691			−0.454414			−0.227207	−	0.973847i	$-0.572959\pi$
$491$	−10.0691			−0.454414			−0.227207	+	0.973847i	$0.572959\pi$
$492$		0			0
$493$			1.86794i			0.0841280i
$494$	22.0160			0.990546
$495$	−30.9336	+	7.26380i	−1.39036	+	0.326484i
$496$	−0.191421			−0.00859506
$497$		−	7.82523i		−	0.351009i
$498$		−	12.4298i		−	0.556993i
$499$	29.9416			1.34037			0.670185	−	0.742194i	$-0.266215\pi$
$499$	29.9416			1.34037			0.670185	+	0.742194i	$0.266215\pi$
$500$	−28.4149	+	23.5437i	−1.27075	+	1.05291i
$501$	−42.2126			−1.88592
$502$		−	21.3454i		−	0.952693i
$503$		−	24.0140i		−	1.07073i	−0.844620	−	0.535366i	$-0.820174\pi$
$503$		−	24.0140i		−	1.07073i	0.844620	−	0.535366i	$-0.179826\pi$
$504$	62.7210			2.79382
$505$	25.9256	−	6.08783i	1.15368	−	0.270905i
$506$	−4.22860			−0.187984
$507$			53.9391i			2.39552i
$508$			16.4674i			0.730625i
$509$	21.0771			0.934227			0.467113	−	0.884197i	$-0.345294\pi$
$509$	21.0771			0.934227			0.467113	+	0.884197i	$0.345294\pi$
$510$	6.35371	+	27.0579i	0.281347	+	1.19815i
$511$	41.3245			1.82809
$512$		−	3.30707i		−	0.146153i
$513$		−	11.5611i		−	0.510436i
$514$	−32.4920			−1.43316
$515$	−7.64629	−	32.5625i	−0.336936	−	1.43487i
$516$	−102.221			−4.50003
$517$			13.0987i			0.576080i
$518$			35.2448i			1.54857i
$519$	−26.0160			−1.14197
$520$	36.6768	−	8.61241i	1.60839	−	0.377679i
$521$	11.6623			0.510933			0.255466	−	0.966818i	$-0.417771\pi$
$521$	11.6623			0.510933			0.255466	+	0.966818i	$0.417771\pi$
$522$		−	12.3258i		−	0.539487i
$523$		−	36.3895i		−	1.59120i	−0.605821	−	0.795601i	$-0.707155\pi$
$523$		−	36.3895i		−	1.59120i	0.605821	−	0.795601i	$-0.292845\pi$
$524$	−65.0719			−2.84268
$525$	−50.6331	+	25.1669i	−2.20981	+	1.09837i
$526$	−16.0691			−0.700647
$527$		−	1.22215i		−	0.0532376i
$528$		−	2.24448i		−	0.0976785i
$529$	22.5212			0.979181
$530$	38.4482	−	9.02837i	1.67008	−	0.392167i
$531$	53.5371			2.32331
$532$		−	21.9463i		−	0.951491i
$533$		0			0
$534$	−22.0160			−0.952724
$535$	2.00000	+	8.51720i	0.0864675	+	0.368231i
$536$	−19.3805			−0.837110
$537$		−	61.5877i		−	2.65770i
$538$			16.7896i			0.723853i
$539$	−22.0532			−0.949897
$540$	−11.4774	−	48.8777i	−0.493909	−	2.10336i
$541$	9.92564			0.426737			0.213368	−	0.976972i	$-0.431557\pi$
$541$	9.92564			0.426737			0.213368	+	0.976972i	$0.431557\pi$
$542$		−	53.7855i		−	2.31029i
$543$			49.0504i			2.10495i
$544$	9.92804			0.425661
$545$	16.4482	−	3.86235i	0.704565	−	0.165445i
$546$	146.500			6.26964
$547$		−	9.03245i		−	0.386200i	−0.981179	−	0.193100i	$-0.938146\pi$
$547$		−	9.03245i		−	0.386200i	0.981179	−	0.193100i	$-0.0618541\pi$
$548$		−	20.6765i		−	0.883258i
$549$	25.2022			1.07561
$550$	13.5997	+	27.3611i	0.579893	+	1.16668i
$551$	−1.69944			−0.0723986
$552$		−	5.98854i		−	0.254889i
$553$		−	8.03321i		−	0.341607i
$554$	6.70743			0.284971
$555$	24.6171	−	5.78056i	1.04494	−	0.245371i
$556$	72.3141			3.06680
$557$		−	13.7145i		−	0.581101i	−0.956860	−	0.290550i	$-0.906162\pi$
$557$		−	13.7145i		−	0.581101i	0.956860	−	0.290550i	$-0.0938384\pi$
$558$			8.06446i			0.341396i
$559$	−60.2953			−2.55022
$560$	−0.585141	−	2.49188i	−0.0247267	−	0.105301i
$561$	14.3301			0.605018
$562$			69.4672i			2.93030i
$563$		−	20.2781i		−	0.854621i	−0.904105	−	0.427311i	$-0.859461\pi$
$563$		−	20.2781i		−	0.854621i	0.904105	−	0.427311i	$-0.140539\pi$
$564$	−47.0771			−1.98230
$565$	−9.55595	−	40.6950i	−0.402022	−	1.71205i
$566$	−4.63547			−0.194843
$567$		−	14.0898i		−	0.591715i
$568$		−	5.98854i		−	0.251273i
$569$	−13.3085			−0.557923			−0.278962	−	0.960302i	$-0.589990\pi$
$569$	−13.3085			−0.557923			−0.278962	+	0.960302i	$0.589990\pi$
$570$	−24.6171	+	5.78056i	−1.03110	+	0.242121i
$571$	−16.4204			−0.687174			−0.343587	−	0.939121i	$-0.611642\pi$
$571$	−16.4204			−0.687174			−0.343587	+	0.939121i	$0.611642\pi$
$572$		−	49.2951i		−	2.06113i
$573$			24.2982i			1.01507i
$574$		0			0
$575$	1.53997	+	3.09826i	0.0642213	+	0.129206i
$576$	−68.6439			−2.86016
$577$			14.7505i			0.614071i	0.951698	+	0.307036i	$0.0993371\pi$
$577$			14.7505i			0.614071i	−0.951698	+	0.307036i	$0.900663\pi$
$578$			31.1058i			1.29383i
$579$	2.28698			0.0950438
$580$	−7.18485	+	1.68714i	−0.298334	+	0.0700546i
$581$	−7.30855			−0.303210
$582$			2.55992i			0.106112i
$583$		−	20.3625i		−	0.843329i
$584$	31.6251			1.30866
$585$	−15.3989	−	65.5777i	−0.636665	−	2.71130i
$586$	−25.0240			−1.03373
$587$			6.36385i			0.262664i	0.991338	+	0.131332i	$0.0419254\pi$
$587$			6.36385i			0.262664i	−0.991338	+	0.131332i	$0.958075\pi$
$588$		−	79.2597i		−	3.26861i
$589$	1.11190			0.0458150
$590$	−11.7686	−	50.1177i	−0.484505	−	2.06331i
$591$	−70.8297			−2.91355
$592$			1.14472i			0.0470475i
$593$			30.0706i			1.23485i	0.786629	+	0.617426i	$0.211824\pi$
$593$			30.0706i			1.23485i	−0.786629	+	0.617426i	$0.788176\pi$
$594$	−41.5719			−1.70572
$595$	15.9097	−	3.73589i	0.652233	−	0.153157i
$596$	14.0188			0.574233
$597$			55.8071i			2.28403i
$598$		−	8.96442i		−	0.366582i
$599$	25.0587			1.02387			0.511936	−	0.859023i	$-0.328928\pi$
$599$	25.0587			1.02387			0.511936	+	0.859023i	$0.328928\pi$
$600$	−38.7488	+	19.2599i	−1.58191	+	0.786281i
$601$	40.0320			1.63294			0.816469	−	0.577390i	$-0.195929\pi$
$601$	40.0320			1.63294			0.816469	+	0.577390i	$0.195929\pi$
$602$			96.5252i			3.93407i
$603$			34.6521i			1.41114i
$604$	37.3245			1.51871
$605$	−8.60911	+	2.02158i	−0.350010	+	0.0821889i
$606$	79.2502			3.21932
$607$			41.3557i			1.67858i	0.543687	+	0.839288i	$0.317028\pi$
$607$			41.3557i			1.67858i	−0.543687	+	0.839288i	$0.682972\pi$
$608$			9.03245i			0.366314i
$609$	−11.3085			−0.458245
$610$	−5.53997	−	23.5925i	−0.224307	−	0.955234i
$611$	−27.7686			−1.12340
$612$			33.0071i			1.33423i
$613$			40.5183i			1.63652i	0.574851	+	0.818258i	$0.305060\pi$
$613$			40.5183i			1.63652i	−0.574851	+	0.818258i	$0.694940\pi$
$614$	20.7766			0.838474
$615$		0			0
$616$	−31.0959			−1.25289
$617$		−	1.76865i		−	0.0712033i	−0.999366	−	0.0356016i	$-0.988665\pi$
$617$		−	1.76865i		−	0.0712033i	0.999366	−	0.0356016i	$-0.0113347\pi$
$618$		−	99.5378i		−	4.00400i
$619$	0.249804			0.0100405			0.00502023	−	0.999987i	$-0.498402\pi$
$619$	0.249804			0.0100405			0.00502023	+	0.999987i	$0.498402\pi$
$620$	4.70085	−	1.10385i	0.188791	−	0.0443317i
$621$	−4.70743			−0.188903
$622$		−	25.5884i		−	1.02600i
$623$			12.9451i			0.518633i
$624$	4.75818			0.190480
$625$	15.0945	−	19.9288i	0.603780	−	0.797151i
$626$	−59.2530			−2.36823
$627$			13.0374i			0.520664i
$628$		−	13.6003i		−	0.542709i
$629$	−7.30855			−0.291411
$630$	−104.982	+	24.6517i	−4.18257	+	0.982145i
$631$	9.48922			0.377760			0.188880	−	0.982000i	$-0.439514\pi$
$631$	9.48922			0.377760			0.188880	+	0.982000i	$0.439514\pi$
$632$		−	6.14770i		−	0.244542i
$633$		−	55.6535i		−	2.21203i
$634$	−1.92804			−0.0765723
$635$	−2.55036	−	10.8610i	−0.101208	−	0.431005i
$636$	73.1834			2.90191
$637$		−	46.7516i		−	1.85236i
$638$			6.11092i			0.241934i
$639$	−10.7074			−0.423579
$640$	9.65569	+	41.1197i	0.381675	+	1.62540i
$641$	−49.9416			−1.97258			−0.986288	−	0.165035i	$-0.947226\pi$
$641$	−49.9416			−1.97258			−0.986288	+	0.165035i	$0.947226\pi$
$642$			26.0356i			1.02754i
$643$			25.8589i			1.01977i	0.860241	+	0.509887i	$0.170313\pi$
$643$			25.8589i			1.01977i	−0.860241	+	0.509887i	$0.829687\pi$
$644$	−8.93603			−0.352129
$645$	67.4190	−	15.8313i	2.65462	−	0.623355i
$646$	7.30855			0.287551
$647$			32.1384i			1.26349i	0.775177	+	0.631745i	$0.217661\pi$
$647$			32.1384i			1.26349i	−0.775177	+	0.631745i	$0.782339\pi$
$648$		−	10.7827i		−	0.423585i
$649$	−26.5427			−1.04189
$650$	−58.0042	+	28.8307i	−2.27511	+	1.13083i
$651$	7.39888			0.289985
$652$		−	10.5537i		−	0.413315i
$653$		−	9.79247i		−	0.383209i	−0.981472	−	0.191604i	$-0.938631\pi$
$653$		−	9.79247i		−	0.383209i	0.981472	−	0.191604i	$-0.0613691\pi$
$654$	50.2794			1.96608
$655$	42.9177	−	10.0779i	1.67693	−	0.393775i
$656$		0			0
$657$		−	56.5452i		−	2.20604i
$658$			44.4540i			1.73300i
$659$	7.55835			0.294432			0.147216	−	0.989104i	$-0.452969\pi$
$659$	7.55835			0.294432			0.147216	+	0.989104i	$0.452969\pi$
$660$	12.9430	+	55.1192i	0.503807	+	2.14551i
$661$	−10.9041			−0.424119			−0.212060	−	0.977257i	$-0.568017\pi$
$661$	−10.9041			−0.424119			−0.212060	+	0.977257i	$0.568017\pi$
$662$			50.8096i			1.97477i
$663$			30.3791i			1.17983i
$664$	−5.59313			−0.217056
$665$	3.39888	+	14.4745i	0.131803	+	0.561296i
$666$	48.2262			1.86873
$667$			0.691975i			0.0267934i
$668$			48.2048i			1.86510i
$669$	31.4149			1.21457
$670$	32.4388	−	7.61725i	1.25322	−	0.294280i
$671$	−12.4948			−0.482357
$672$			60.1044i			2.31858i
$673$			12.6296i			0.486836i	0.969921	+	0.243418i	$0.0782687\pi$
$673$			12.6296i			0.486836i	−0.969921	+	0.243418i	$0.921731\pi$
$674$	−17.8377			−0.687083
$675$	15.1397	+	30.4594i	0.582726	+	1.17238i
$676$	61.5959			2.36907
$677$			8.87065i			0.340927i	0.985364	+	0.170463i	$0.0545265\pi$
$677$			8.87065i			0.340927i	−0.985364	+	0.170463i	$0.945474\pi$
$678$		−	124.397i		−	4.77746i
$679$	1.50519			0.0577641
$680$	12.1754	−	2.85902i	0.466907	−	0.109639i
$681$	−50.0320			−1.91723
$682$		−	3.99821i		−	0.153099i
$683$			24.4749i			0.936507i	0.883594	+	0.468254i	$0.155117\pi$
$683$			24.4749i			0.936507i	−0.883594	+	0.468254i	$0.844883\pi$
$684$	−30.0296			−1.14821
$685$	3.20223	+	13.6370i	0.122351	+	0.521045i
$686$	−11.7874			−0.450044
$687$			54.0697i			2.06289i
$688$			3.13504i			0.119522i
$689$	43.1675			1.64455
$690$	2.35371	+	10.0235i	0.0896044	+	0.381589i
$691$	−3.30855			−0.125863			−0.0629315	−	0.998018i	$-0.520045\pi$
$691$	−3.30855			−0.125863			−0.0629315	+	0.998018i	$0.520045\pi$
$692$			29.7090i			1.12937i
$693$			55.5991i			2.11204i
$694$	−21.5028			−0.816235
$695$	−47.6942	+	11.1995i	−1.80914	+	0.424821i
$696$	−8.65427			−0.328039
$697$		0			0
$698$			49.8729i			1.88772i
$699$	42.2794			1.59915
$700$	28.7394	+	57.8205i	1.08625	+	2.18541i
$701$	−10.8485			−0.409743			−0.204871	−	0.978789i	$-0.565678\pi$
$701$	−10.8485			−0.409743			−0.204871	+	0.978789i	$0.565678\pi$
$702$		−	88.1303i		−	3.32627i
$703$		−	6.64926i		−	0.250781i
$704$	34.0324			1.28264
$705$	31.0493	−	7.29097i	1.16939	−	0.274594i
$706$	−47.3405			−1.78168
$707$		−	46.5979i		−	1.75250i
$708$		−	95.3954i		−	3.58518i
$709$	31.1675			1.17052			0.585259	−	0.810846i	$-0.300993\pi$
$709$	31.1675			1.17052			0.585259	+	0.810846i	$0.300993\pi$
$710$	2.35371	+	10.0235i	0.0883333	+	0.376176i
$711$	−10.9920			−0.412233
$712$			9.90668i			0.371269i
$713$		−	0.452741i		−	0.0169553i
$714$	48.6331			1.82005
$715$	7.63448	+	32.5122i	0.285513	+	1.21589i
$716$	−70.3301			−2.62836
$717$		−	5.78056i		−	0.215879i
$718$		−	70.3672i		−	2.62608i
$719$	13.0056			0.485027			0.242513	−	0.970148i	$-0.422028\pi$
$719$	13.0056			0.485027			0.242513	+	0.970148i	$0.422028\pi$
$720$	−3.40970	+	0.800661i	−0.127072	+	0.0298389i
$721$	−58.5268			−2.17965
$722$		−	37.0943i		−	1.38051i
$723$			16.0582i			0.597213i
$724$	56.0132			2.08171
$725$	4.47742	−	2.22548i	0.166287	−	0.0826521i
$726$	−26.3165			−0.976698
$727$		−	1.19089i		−	0.0441677i	−0.999756	−	0.0220839i	$-0.992970\pi$
$727$		−	1.19089i		−	0.0441677i	0.999756	−	0.0220839i	$-0.00703008\pi$
$728$		−	65.9218i		−	2.44322i
$729$	39.7074			1.47065
$730$	−52.9336	+	12.4298i	−1.95916	+	0.460048i
$731$	−20.0160			−0.740318
$732$		−	44.9067i		−	1.65980i
$733$		−	34.5990i		−	1.27794i	−0.769231	−	0.638971i	$-0.779360\pi$
$733$		−	34.5990i		−	1.27794i	0.769231	−	0.638971i	$-0.220640\pi$
$734$	−31.7314			−1.17123
$735$	12.2752	+	52.2751i	0.452777	+	1.92820i
$736$	3.67781			0.135566
$737$		−	17.1799i		−	0.632829i
$738$		0			0
$739$	41.7821			1.53698			0.768491	−	0.639861i	$-0.221008\pi$
$739$	41.7821			1.53698			0.768491	+	0.639861i	$0.221008\pi$
$740$	−6.60112	−	28.1115i	−0.242662	−	1.03340i
$741$	−27.6387			−1.01533
$742$		−	69.1056i		−	2.53695i
$743$			4.02130i			0.147527i	0.997276	+	0.0737636i	$0.0235010\pi$
$743$			4.02130i			0.147527i	−0.997276	+	0.0737636i	$0.976499\pi$
$744$	5.66226			0.207589
$745$	−9.24599	+	2.17113i	−0.338747	+	0.0795442i
$746$	62.7742			2.29833
$747$			10.0004i			0.365897i
$748$		−	16.3643i		−	0.598338i
$749$	15.3085			0.559362
$750$	57.2873	−	47.4666i	2.09184	−	1.73324i
$751$	−0.497206			−0.0181433			−0.00907166	−	0.999959i	$-0.502888\pi$
$751$	−0.497206			−0.0181433			−0.00907166	+	0.999959i	$0.502888\pi$
$752$			1.44382i			0.0526507i
$753$			26.7968i			0.976531i
$754$	−12.9548			−0.471787
$755$	−24.6171	+	5.78056i	−0.895908	+	0.210376i
$756$	−87.8513			−3.19512
$757$		−	18.6944i		−	0.679458i	−0.940523	−	0.339729i	$-0.889665\pi$
$757$		−	18.6944i		−	0.679458i	0.940523	−	0.339729i	$-0.110335\pi$
$758$		−	37.7734i		−	1.37199i
$759$	5.30855			0.192688
$760$	2.60112	+	11.0771i	0.0943524	+	0.401809i
$761$	−3.38291			−0.122630			−0.0613151	−	0.998118i	$-0.519529\pi$
$761$	−3.38291			−0.122630			−0.0613151	+	0.998118i	$0.519529\pi$
$762$		−	33.2001i		−	1.20271i
$763$		−	29.5635i		−	1.07027i
$764$	27.7474			1.00386
$765$	−5.11190	−	21.7695i	−0.184821	−	0.787079i
$766$	27.0240			0.976416
$767$		−	56.2692i		−	2.03176i
$768$			51.5790i			1.86120i
$769$	7.41486			0.267387			0.133693	−	0.991023i	$-0.457316\pi$
$769$	7.41486			0.267387			0.133693	+	0.991023i	$0.457316\pi$
$770$	52.0479	−	12.2218i	1.87568	−	0.440444i
$771$	40.7901			1.46902
$772$		−	2.61162i		−	0.0939944i
$773$			33.2775i			1.19691i	0.801156	+	0.598455i	$0.204218\pi$
$773$			33.2775i			1.19691i	−0.801156	+	0.598455i	$0.795782\pi$
$774$	132.077			4.74743
$775$	−2.92945	+	1.45607i	−0.105229	+	0.0523036i
$776$	1.15190			0.0413510
$777$		−	44.2460i		−	1.58732i
$778$			27.6275i			0.990495i
$779$		0			0
$780$	−116.850	+	27.4386i	−4.18390	+	0.982458i
$781$	5.30855			0.189955
$782$		−	2.97588i		−	0.106417i
$783$			6.80289i			0.243116i
$784$	−2.43084			−0.0868156
$785$	2.10631	+	8.96994i	0.0751775	+	0.320151i
$786$	131.192			4.67946
$787$			18.2878i			0.651890i	0.945389	+	0.325945i	$0.105682\pi$
$787$			18.2878i			0.651890i	−0.945389	+	0.325945i	$0.894318\pi$
$788$			80.8841i			2.88138i
$789$	20.1730			0.718179
$790$	2.41627	+	10.2899i	0.0859671	+	0.366100i
$791$	−73.1439			−2.60070
$792$			42.5492i			1.51192i
$793$		−	26.4883i		−	0.940629i
$794$	13.8909			0.492968
$795$	−48.2676	+	11.3341i	−1.71187	+	0.401980i
$796$	63.7290			2.25881
$797$		−	44.5845i		−	1.57926i	−0.613581	−	0.789632i	$-0.710271\pi$
$797$		−	44.5845i		−	1.57926i	0.613581	−	0.789632i	$-0.289729\pi$
$798$			44.2460i			1.56629i
$799$	−9.21821			−0.326117
$800$	−11.8283	−	23.7973i	−0.418194	−	0.841360i
$801$	17.7130			0.625859
$802$		−	49.4202i		−	1.74509i
$803$			28.0341i			0.989302i
$804$	61.7450			2.17758
$805$	5.89369	−	1.38395i	0.207725	−	0.0487778i
$806$	8.47600			0.298554
$807$		−	21.0776i		−	0.741965i
$808$		−	35.6607i		−	1.25454i
$809$	−14.1063			−0.495952			−0.247976	−	0.968766i	$-0.579765\pi$
$809$	−14.1063			−0.495952			−0.247976	+	0.968766i	$0.579765\pi$
$810$	4.23800	+	18.0480i	0.148908	+	0.634141i
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$			12.9138i			0.453186i
$813$			67.5218i			2.36809i
$814$	−23.9097			−0.838033
$815$	1.63448	+	6.96061i	0.0572535	+	0.243820i
$816$	1.57955			0.0552954
$817$		−	18.2104i		−	0.637100i
$818$			10.3484i			0.361822i
$819$	−117.867			−4.11862
$820$		0			0
$821$	18.1571			0.633686			0.316843	−	0.948478i	$-0.397377\pi$
$821$	18.1571			0.633686			0.316843	+	0.948478i	$0.397377\pi$
$822$			41.6861i			1.45397i
$823$		−	3.25189i		−	0.113354i	−0.998393	−	0.0566770i	$-0.981949\pi$
$823$		−	3.25189i		−	0.113354i	0.998393	−	0.0566770i	$-0.0180505\pi$
$824$	−44.7897			−1.56032
$825$	−17.0729	−	34.3489i	−0.594404	−	1.19588i
$826$	−90.0799			−3.13428
$827$			10.7155i			0.372615i	0.982492	+	0.186307i	$0.0596520\pi$
$827$			10.7155i			0.372615i	−0.982492	+	0.186307i	$0.940348\pi$
$828$			12.2274i			0.424930i
$829$	−52.3461			−1.81805			−0.909027	−	0.416736i	$-0.863174\pi$
$829$	−52.3461			−1.81805			−0.909027	+	0.416736i	$0.863174\pi$
$830$	9.36170	−	2.19830i	0.324949	−	0.0763043i
$831$	−8.42045			−0.292102
$832$			72.1469i			2.50124i
$833$		−	15.5199i		−	0.537733i
$834$	−145.793			−5.04840
$835$	−7.46561	−	31.7931i	−0.258358	−	1.10024i
$836$	14.8881			0.514916
$837$		−	4.45095i		−	0.153847i
$838$		−	9.66192i		−	0.333765i
$839$	−24.6703			−0.851712			−0.425856	−	0.904791i	$-0.640027\pi$
$839$	−24.6703			−0.851712			−0.425856	+	0.904791i	$0.640027\pi$
$840$	17.3085	+	73.7102i	0.597202	+	2.54324i
$841$	1.00000			0.0344828
$842$		−	42.6173i		−	1.46869i
$843$		−	87.2085i		−	3.00362i
$844$	−63.5535			−2.18760
$845$	−40.6251	+	9.53954i	−1.39755	+	0.328170i
$846$	60.8273			2.09129
$847$			15.4737i			0.531684i
$848$		−	2.24448i		−	0.0770758i
$849$	5.81933			0.199719
$850$	−19.2554	+	9.57079i	−0.660454	+	0.328275i
$851$	−2.70743			−0.0928095
$852$			19.0791i			0.653638i
$853$			28.1115i			0.962520i	0.876578	+	0.481260i	$0.159821\pi$
$853$			28.1115i			0.962520i	−0.876578	+	0.481260i	$0.840179\pi$
$854$	−42.4045			−1.45105
$855$	19.8058	−	4.65077i	0.677342	−	0.159053i
$856$	11.7154			0.400425
$857$			8.39482i			0.286762i	0.989668	+	0.143381i	$0.0457974\pi$
$857$			8.39482i			0.286762i	−0.989668	+	0.143381i	$0.954203\pi$
$858$			99.3842i			3.39292i
$859$	−17.8405			−0.608711			−0.304356	−	0.952559i	$-0.598441\pi$
$859$	−17.8405			−0.608711			−0.304356	+	0.952559i	$0.598441\pi$
$860$	−18.0785	−	76.9893i	−0.616473	−	2.62531i
$861$		0			0
$862$			85.4793i			2.91144i
$863$			2.48249i			0.0845049i	0.999107	+	0.0422524i	$0.0134534\pi$
$863$			2.48249i			0.0845049i	−0.999107	+	0.0422524i	$0.986547\pi$
$864$	36.1571			1.23009
$865$	−4.60112	−	19.5943i	−0.156443	−	0.666227i
$866$	38.8113			1.31886
$867$		−	39.0499i		−	1.32621i
$868$		−	8.44916i		−	0.286783i
$869$	5.44964			0.184866
$870$	14.4854	−	3.40145i	0.491101	−	0.115320i
$871$	36.4204			1.23406
$872$		−	22.6245i		−	0.766164i
$873$		−	2.05959i		−	0.0697066i
$874$	2.70743			0.0915802
$875$	−27.9097	−	33.6841i	−0.943519	−	1.13873i
$876$	−100.755			−3.40421
$877$		−	25.9813i		−	0.877325i	−0.898652	−	0.438662i	$-0.855452\pi$
$877$		−	25.9813i		−	0.877325i	0.898652	−	0.438662i	$-0.144548\pi$
$878$			21.2230i			0.716243i
$879$	31.4149			1.05960
$880$	1.69046	−	0.396953i	0.0569856	−	0.0133813i
$881$	25.1279			0.846580			0.423290	−	0.905994i	$-0.360875\pi$
$881$	25.1279			0.846580			0.423290	+	0.905994i	$0.360875\pi$
$882$			102.410i			3.44831i
$883$		−	10.9684i		−	0.369117i	−0.982822	−	0.184559i	$-0.940914\pi$
$883$		−	10.9684i		−	0.369117i	0.982822	−	0.184559i	$-0.0590856\pi$
$884$	34.6915			1.16680
$885$	14.7742	+	62.9173i	0.496628	+	2.11494i
$886$	−43.5188			−1.46204
$887$			2.99897i			0.100695i	0.998732	+	0.0503477i	$0.0160330\pi$
$887$			2.99897i			0.100695i	−0.998732	+	0.0503477i	$0.983967\pi$
$888$		−	33.8608i		−	1.13630i
$889$	−19.5212			−0.654719
$890$	−3.89369	−	16.5817i	−0.130517	−	0.555819i
$891$	9.55835			0.320217
$892$		−	35.8742i		−	1.20116i
$893$		−	8.38665i		−	0.280649i
$894$	−28.2634			−0.945269
$895$	46.3857	−	10.8922i	1.55050	−	0.364087i
$896$	73.9073			2.46907
$897$			11.2538i			0.375755i
$898$			72.1183i			2.40662i
$899$	−0.654273			−0.0218212
$900$	79.1171	−	39.3247i	2.63724	−	1.31082i
$901$	14.3301			0.477405
$902$		0			0
$903$		−	121.177i		−	4.03251i
$904$	−55.9760			−1.86173
$905$	−36.9430	+	8.67492i	−1.22803	+	0.288364i
$906$	−75.2502			−2.50002
$907$			50.5567i			1.67871i	0.543585	+	0.839354i	$0.317066\pi$
$907$			50.5567i			1.67871i	−0.543585	+	0.839354i	$0.682934\pi$
$908$			57.1341i			1.89606i
$909$	−63.7609			−2.11482
$910$	25.9097	+	110.339i	0.858897	+	3.65770i
$911$	35.9044			1.18957			0.594784	−	0.803886i	$-0.297238\pi$
$911$	35.9044			1.18957			0.594784	+	0.803886i	$0.297238\pi$
$912$			1.43707i			0.0475860i
$913$		−	4.95804i		−	0.164087i
$914$	−84.3301			−2.78939
$915$	6.95483	+	29.6179i	0.229920	+	0.979136i
$916$	61.7450			2.04011
$917$		−	77.1388i		−	2.54735i
$918$		−	29.2562i		−	0.965600i
$919$	−15.2022			−0.501475			−0.250738	−	0.968055i	$-0.580673\pi$
$919$	−15.2022			−0.501475			−0.250738	+	0.968055i	$0.580673\pi$
$920$	4.51036	−	1.05912i	0.148702	−	0.0349181i
$921$	−26.0827			−0.859454
$922$			66.3745i			2.18593i
$923$			11.2538i			0.370425i
$924$	99.0695			3.25915
$925$	8.70743	+	17.5184i	0.286299	+	0.576001i
$926$	68.2422			2.24258
$927$			80.0834i			2.63029i
$928$		−	5.31495i		−	0.174472i
$929$	6.00000			0.196854			0.0984268	−	0.995144i	$-0.468619\pi$
$929$	6.00000			0.196854			0.0984268	+	0.995144i	$0.468619\pi$
$930$	−9.47742	+	2.22548i	−0.310777	+	0.0729762i
$931$	14.1199			0.462761
$932$		−	48.2810i		−	1.58150i
$933$			32.1234i			1.05167i
$934$	60.9524			1.99442
$935$	2.53439	+	10.7929i	0.0828833	+	0.352967i
$936$	−90.2022			−2.94835
$937$		−	32.1859i		−	1.05147i	−0.850649	−	0.525734i	$-0.823791\pi$
$937$		−	32.1859i		−	1.05147i	0.850649	−	0.525734i	$-0.176209\pi$
$938$		−	58.3045i		−	1.90371i
$939$	74.3857			2.42748
$940$	−8.32594	−	35.4568i	−0.271562	−	1.15647i
$941$	22.3697			0.729231			0.364616	−	0.931158i	$-0.381200\pi$
$941$	22.3697			0.729231			0.364616	+	0.931158i	$0.381200\pi$
$942$			27.4196i			0.893377i
$943$		0			0
$944$	−2.92570			−0.0952236
$945$	57.9416	−	13.6058i	1.88484	−	0.442596i
$946$	−65.4816			−2.12899
$947$			0.122381i			0.00397684i	0.999998	+	0.00198842i	$0.000632935\pi$
$947$			0.122381i			0.00397684i	−0.999998	+	0.00198842i	$0.999367\pi$
$948$			19.5862i			0.636129i
$949$	−59.4308			−1.92921
$950$	−8.70743	−	17.5184i	−0.282506	−	0.568372i
$951$	2.42045			0.0784884
$952$		−	21.8838i		−	0.709257i
$953$			55.4917i			1.79755i	0.438409	+	0.898776i	$0.355542\pi$
$953$			55.4917i			1.79755i	−0.438409	+	0.898776i	$0.644458\pi$
$954$	−94.5587			−3.06145
$955$	−18.3006	+	4.29732i	−0.592192	+	0.139058i
$956$	−6.60112			−0.213495
$957$		−	7.67159i		−	0.247987i
$958$		−	62.5787i		−	2.02183i
$959$	24.5108			0.791494
$960$	−18.9430	−	80.6708i	−0.611384	−	2.60364i
$961$	−30.5719			−0.986191
$962$		−	50.6873i		−	1.63422i
$963$		−	20.9470i		−	0.675008i
$964$	18.3377			0.590619
$965$	0.404470	+	1.72248i	0.0130203	+	0.0554485i
$966$	18.0160			0.579655
$967$			49.0722i			1.57806i	0.614357	+	0.789028i	$0.289416\pi$
$967$			49.0722i			1.57806i	−0.614357	+	0.789028i	$0.710584\pi$
$968$			11.8418i			0.380611i
$969$	−9.17508			−0.294746
$970$	−1.92804	+	0.452741i	−0.0619057	+	0.0145366i
$971$	2.08793			0.0670050			0.0335025	−	0.999439i	$-0.489334\pi$
$971$	2.08793			0.0670050			0.0335025	+	0.999439i	$0.489334\pi$
$972$		−	33.0071i		−	1.05870i
$973$			85.7241i			2.74819i
$974$	73.8856			2.36745
$975$	72.8179	−	36.1938i	2.33204	−	1.15913i
$976$	−1.37725			−0.0440849
$977$		−	36.5119i		−	1.16812i	−0.811711	−	0.584059i	$-0.801464\pi$
$977$		−	36.5119i		−	1.16812i	0.811711	−	0.584059i	$-0.198536\pi$
$978$			21.2774i			0.680376i
$979$	−8.78179			−0.280667
$980$	59.6956	−	14.0177i	1.90691	−	0.447778i
$981$	−40.4524			−1.29155
$982$		−	23.1821i		−	0.739771i
$983$		−	32.8698i		−	1.04838i	−0.851601	−	0.524191i	$-0.824368\pi$
$983$		−	32.8698i		−	1.04838i	0.851601	−	0.524191i	$-0.175632\pi$
$984$		0			0
$985$	−12.5268	−	53.3465i	−0.399136	−	1.69976i
$986$	−4.30056			−0.136958
$987$		−	55.8071i		−	1.77636i
$988$			31.5620i			1.00412i
$989$	−7.41486			−0.235779
$990$	−16.7234	−	71.2183i	−0.531505	−	2.26347i
$991$	−36.0160			−1.14409			−0.572043	−	0.820224i	$-0.693849\pi$
$991$	−36.0160			−1.14409			−0.572043	+	0.820224i	$0.693849\pi$
$992$			3.47743i			0.110409i
$993$		−	63.7860i		−	2.02419i
$994$	18.0160			0.571432
$995$	−42.0320	+	9.86990i	−1.33250	+	0.312897i
$996$	17.8193			0.564627
$997$		−	56.8063i		−	1.79907i	−0.436844	−	0.899537i	$-0.643904\pi$
$997$		−	56.8063i		−	1.79907i	0.436844	−	0.899537i	$-0.356096\pi$
$998$			68.9344i			2.18208i
$999$	−26.6171			−0.842128

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	145.2.b.c.59.5	yes	6
3.2	odd	2		1305.2.c.h.784.2		6
4.3	odd	2		2320.2.d.g.929.6		6
5.2	odd	4		725.2.a.l.1.2		6
5.3	odd	4		725.2.a.l.1.5		6
5.4	even	2	inner	145.2.b.c.59.2	✓	6
15.2	even	4		6525.2.a.bt.1.5		6
15.8	even	4		6525.2.a.bt.1.2		6
15.14	odd	2		1305.2.c.h.784.5		6
20.19	odd	2		2320.2.d.g.929.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.b.c.59.2	✓	6	5.4	even	2	inner
145.2.b.c.59.5	yes	6	1.1	even	1	trivial
725.2.a.l.1.2		6	5.2	odd	4
725.2.a.l.1.5		6	5.3	odd	4
1305.2.c.h.784.2		6	3.2	odd	2
1305.2.c.h.784.5		6	15.14	odd	2
2320.2.d.g.929.1		6	20.19	odd	2
2320.2.d.g.929.6		6	4.3	odd	2
6525.2.a.bt.1.2		6	15.8	even	4
6525.2.a.bt.1.5		6	15.2	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	145.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.30229i q^{2} -2.89028i q^{3} -3.30056 q^{4} +(2.17686 - 0.511167i) q^{5} +6.65427 q^{6} -3.91261i q^{7} -2.99427i q^{8} -5.35371 q^{9} +(1.17686 + 5.01177i) q^{10} +2.65427 q^{11} +9.53954i q^{12} +5.62692i q^{13} +9.00799 q^{14} +(-1.47742 - 6.29173i) q^{15} +0.292570 q^{16} +1.86794i q^{17} -12.3258i q^{18} -1.69944 q^{19} +(-7.18485 + 1.68714i) q^{20} -11.3085 q^{21} +6.11092i q^{22} +0.691975i q^{23} -8.65427 q^{24} +(4.47742 - 2.22548i) q^{25} -12.9548 q^{26} +6.80289i q^{27} +12.9138i q^{28} +1.00000 q^{29} +(14.4854 - 3.40145i) q^{30} -0.654273 q^{31} -5.31495i q^{32} -7.67159i q^{33} -4.30056 q^{34} +(-2.00000 - 8.51720i) q^{35} +17.6703 q^{36} +3.91261i q^{37} -3.91261i q^{38} +16.2634 q^{39} +(-1.53057 - 6.51810i) q^{40} -26.0356i q^{42} +10.7155i q^{43} -8.76059 q^{44} +(-11.6543 + 2.73664i) q^{45} -1.59313 q^{46} +4.93495i q^{47} -0.845610i q^{48} -8.30855 q^{49} +(5.12370 + 10.3083i) q^{50} +5.39888 q^{51} -18.5720i q^{52} -7.67159i q^{53} -15.6623 q^{54} +(5.77797 - 1.35678i) q^{55} -11.7154 q^{56} +4.91186i q^{57} +2.30229i q^{58} -10.0000 q^{59} +(4.87630 + 20.7662i) q^{60} -4.70743 q^{61} -1.50633i q^{62} +20.9470i q^{63} +12.8217 q^{64} +(2.87630 + 12.2490i) q^{65} +17.6623 q^{66} -6.47253i q^{67} -6.16526i q^{68} +2.00000 q^{69} +(19.6091 - 4.60459i) q^{70} +2.00000 q^{71} +16.0305i q^{72} +10.5619i q^{73} -9.00799 q^{74} +(-6.43225 - 12.9410i) q^{75} +5.60911 q^{76} -10.3851i q^{77} +37.4431i q^{78} +2.05316 q^{79} +(0.636884 - 0.149552i) q^{80} +3.60112 q^{81} -1.86794i q^{83} +37.3245 q^{84} +(0.954832 + 4.06625i) q^{85} -24.6703 q^{86} -2.89028i q^{87} -7.94761i q^{88} -3.30855 q^{89} +(-6.30056 - 26.8316i) q^{90} +22.0160 q^{91} -2.28390i q^{92} +1.89103i q^{93} -11.3617 q^{94} +(-3.69944 + 0.868699i) q^{95} -15.3617 q^{96} +0.384703i q^{97} -19.1287i q^{98} -14.2102 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 14 q^{4} + 3 q^{5} + 14 q^{6} - 12 q^{9} - 3 q^{10} - 10 q^{11} + 8 q^{14} + 7 q^{15} + 42 q^{16} - 16 q^{19} + 13 q^{20} - 16 q^{21} - 26 q^{24} + 11 q^{25} - 46 q^{26} + 6 q^{29} + 25 q^{30} + 22 q^{31}+ \cdots - 16 q^{99}+O(q^{100}) \) 6 * q - 14 * q^4 + 3 * q^5 + 14 * q^6 - 12 * q^9 - 3 * q^10 - 10 * q^11 + 8 * q^14 + 7 * q^15 + 42 * q^16 - 16 * q^19 + 13 * q^20 - 16 * q^21 - 26 * q^24 + 11 * q^25 - 46 * q^26 + 6 * q^29 + 25 * q^30 + 22 * q^31 - 20 * q^34 - 12 * q^35 - 12 * q^36 + 14 * q^39 + 21 * q^40 + 2 * q^44 - 44 * q^45 - 44 * q^46 + 2 * q^49 + 35 * q^50 + 44 * q^51 - 22 * q^54 + 13 * q^55 + 16 * q^56 - 60 * q^59 + 25 * q^60 + 12 * q^61 - 38 * q^64 + 13 * q^65 + 34 * q^66 + 12 * q^69 + 60 * q^70 + 12 * q^71 - 8 * q^74 + 9 * q^75 - 24 * q^76 - 2 * q^79 - 55 * q^80 + 10 * q^81 + 80 * q^84 - 26 * q^85 - 30 * q^86 + 32 * q^89 - 32 * q^90 + 40 * q^91 - 2 * q^94 - 28 * q^95 - 26 * q^96 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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