LMFDB - Embedded newform 272.2.l.b.69.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [272,2,Mod(69,272)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(272, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("272.69"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 272 = 2^{4} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	272.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [30] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.17193093498$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			69.4
Character	$\chi$	$=$	272.69
Dual form			272.2.l.b.205.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.812807 + 1.15730i) q^{2} +(-1.22998 + 1.22998i) q^{3} +(-0.678689 - 1.88132i) q^{4} +(-2.77156 - 2.77156i) q^{5} +(-0.423720 - 2.42319i) q^{6} +0.669690i q^{7} +(2.72890 + 0.743706i) q^{8} -0.0256965i q^{9} +(5.46027 - 0.954783i) q^{10} +(2.63074 + 2.63074i) q^{11} +(3.14876 + 1.47922i) q^{12} +(4.59382 - 4.59382i) q^{13} +(-0.775032 - 0.544329i) q^{14} +6.81792 q^{15} +(-3.07876 + 2.55367i) q^{16} -1.00000 q^{17} +(0.0297385 + 0.0208863i) q^{18} +(4.22302 - 4.22302i) q^{19} +(-3.33317 + 7.09522i) q^{20} +(-0.823704 - 0.823704i) q^{21} +(-5.18283 + 0.906271i) q^{22} -2.17156i q^{23} +(-4.27123 + 2.44175i) q^{24} +10.3631i q^{25} +(1.58254 + 9.05032i) q^{26} +(-3.65833 - 3.65833i) q^{27} +(1.25990 - 0.454511i) q^{28} +(1.35054 - 1.35054i) q^{29} +(-5.54165 + 7.89038i) q^{30} +7.26759 q^{31} +(-0.452922 - 5.63869i) q^{32} -6.47150 q^{33} +(0.812807 - 1.15730i) q^{34} +(1.85608 - 1.85608i) q^{35} +(-0.0483434 + 0.0174399i) q^{36} +(-4.69542 - 4.69542i) q^{37} +(1.45480 + 8.31980i) q^{38} +11.3006i q^{39} +(-5.50208 - 9.62453i) q^{40} -2.91709i q^{41} +(1.62279 - 0.283761i) q^{42} +(0.0731686 + 0.0731686i) q^{43} +(3.16382 - 6.73472i) q^{44} +(-0.0712193 + 0.0712193i) q^{45} +(2.51315 + 1.76506i) q^{46} +4.07818 q^{47} +(0.645854 - 6.92777i) q^{48} +6.55152 q^{49} +(-11.9932 - 8.42317i) q^{50} +(1.22998 - 1.22998i) q^{51} +(-11.7602 - 5.52469i) q^{52} +(-2.97112 - 2.97112i) q^{53} +(7.20731 - 1.26027i) q^{54} -14.5825i q^{55} +(-0.498053 + 1.82752i) q^{56} +10.3884i q^{57} +(0.465252 + 2.66071i) q^{58} +(2.37239 + 2.37239i) q^{59} +(-4.62724 - 12.8267i) q^{60} +(-1.26981 + 1.26981i) q^{61} +(-5.90715 + 8.41079i) q^{62} +0.0172087 q^{63} +(6.89380 + 4.05900i) q^{64} -25.4641 q^{65} +(5.26008 - 7.48947i) q^{66} +(9.07209 - 9.07209i) q^{67} +(0.678689 + 1.88132i) q^{68} +(2.67097 + 2.67097i) q^{69} +(0.639409 + 3.65669i) q^{70} +10.3263i q^{71} +(0.0191106 - 0.0701231i) q^{72} +4.88975i q^{73} +(9.25048 - 1.61754i) q^{74} +(-12.7464 - 12.7464i) q^{75} +(-10.8110 - 5.07875i) q^{76} +(-1.76178 + 1.76178i) q^{77} +(-13.0782 - 9.18521i) q^{78} -7.21372 q^{79} +(15.6106 + 1.45533i) q^{80} +9.07643 q^{81} +(3.37595 + 2.37103i) q^{82} +(-9.30557 + 9.30557i) q^{83} +(-0.990616 + 2.10869i) q^{84} +(2.77156 + 2.77156i) q^{85} +(-0.144150 + 0.0252061i) q^{86} +3.32227i q^{87} +(5.22252 + 9.13552i) q^{88} -16.9209i q^{89} +(-0.0245346 - 0.140310i) q^{90} +(3.07643 + 3.07643i) q^{91} +(-4.08541 + 1.47381i) q^{92} +(-8.93899 + 8.93899i) q^{93} +(-3.31478 + 4.71968i) q^{94} -23.4087 q^{95} +(7.49256 + 6.37839i) q^{96} +5.46761 q^{97} +(-5.32512 + 7.58207i) q^{98} +(0.0676007 - 0.0676007i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} + 8 q^{6} + 2 q^{8} - 6 q^{10} - 10 q^{11} - 2 q^{12} - 6 q^{13} - 22 q^{14} - 28 q^{15} + 2 q^{16} - 30 q^{17} + 8 q^{18} + 10 q^{19} - 10 q^{20} - 4 q^{21}+ \cdots + 54 q^{99}+O(q^{100}) $ 30 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 + 8 * q^6 + 2 * q^8 - 6 * q^10 - 10 * q^11 - 2 * q^12 - 6 * q^13 - 22 * q^14 - 28 * q^15 + 2 * q^16 - 30 * q^17 + 8 * q^18 + 10 * q^19 - 10 * q^20 - 4 * q^21 + 28 * q^22 + 18 * q^24 + 6 * q^26 + 4 * q^27 + 8 * q^28 - 18 * q^29 - 56 * q^30 + 48 * q^31 - 38 * q^32 - 12 * q^33 - 2 * q^34 + 16 * q^35 + 20 * q^36 + 6 * q^37 + 42 * q^38 + 10 * q^40 + 12 * q^42 + 2 * q^43 + 22 * q^44 + 42 * q^45 - 14 * q^46 - 32 * q^47 - 62 * q^48 - 38 * q^49 - 28 * q^50 + 2 * q^51 - 10 * q^52 - 6 * q^53 + 40 * q^54 + 96 * q^56 + 62 * q^58 - 14 * q^59 - 28 * q^60 + 6 * q^61 - 74 * q^62 + 84 * q^63 - 38 * q^64 - 12 * q^65 + 26 * q^67 + 2 * q^68 + 12 * q^69 + 48 * q^70 + 44 * q^72 + 42 * q^74 - 26 * q^75 - 38 * q^76 - 28 * q^77 - 56 * q^78 - 72 * q^79 - 38 * q^80 - 10 * q^81 - 76 * q^82 - 34 * q^83 + 104 * q^84 + 2 * q^85 + 34 * q^86 - 2 * q^88 + 70 * q^90 + 16 * q^91 - 40 * q^92 - 24 * q^93 - 44 * q^94 + 76 * q^95 - 126 * q^96 - 28 * q^97 - 30 * q^98 + 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/272\mathbb{Z}\right)^\times$.

$n$	$69$	$239$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.812807	+	1.15730i	−0.574741	+	0.818335i
$2$	−0.812807	+	1.15730i	−0.574741	+	0.818335i
$3$	−1.22998	+	1.22998i	−0.710129	+	0.710129i	−0.966562	−	0.256433i	$-0.917453\pi$
$3$	−1.22998	+	1.22998i	−0.710129	+	0.710129i	0.256433	+	0.966562i	$0.417453\pi$
$4$	−0.678689	−	1.88132i	−0.339345	−	0.940662i
$5$	−2.77156	−	2.77156i	−1.23948	−	1.23948i	−0.960214	−	0.279264i	$-0.909910\pi$
$5$	−2.77156	−	2.77156i	−1.23948	−	1.23948i	−0.279264	−	0.960214i	$-0.590090\pi$
$6$	−0.423720	−	2.42319i	−0.172983	−	0.989264i
$7$			0.669690i			0.253119i	0.991959	+	0.126559i	$0.0403935\pi$
$7$			0.669690i			0.253119i	−0.991959	+	0.126559i	$0.959607\pi$
$8$	2.72890	+	0.743706i	0.964812	+	0.262940i
$9$		−	0.0256965i		−	0.00856549i
$10$	5.46027	−	0.954783i	1.72669	−	0.301929i
$11$	2.63074	+	2.63074i	0.793197	+	0.793197i	0.982013	−	0.188816i	$-0.0604648\pi$
$11$	2.63074	+	2.63074i	0.793197	+	0.793197i	−0.188816	+	0.982013i	$0.560465\pi$
$12$	3.14876	+	1.47922i	0.908969	+	0.427013i
$13$	4.59382	−	4.59382i	1.27410	−	1.27410i	0.330177	−	0.943919i	$-0.392892\pi$
$13$	4.59382	−	4.59382i	1.27410	−	1.27410i	0.943919	−	0.330177i	$-0.107108\pi$
$14$	−0.775032	−	0.544329i	−0.207136	−	0.145478i
$15$	6.81792			1.76038
$16$	−3.07876	+	2.55367i	−0.769691	+	0.638417i
$17$	−1.00000			−0.242536
$17$	−1.00000			−0.242536
$18$	0.0297385	+	0.0208863i	0.00700944	+	0.00492294i
$19$	4.22302	−	4.22302i	0.968827	−	0.968827i	−0.0307018	−	0.999529i	$-0.509774\pi$
$19$	4.22302	−	4.22302i	0.968827	−	0.968827i	0.999529	+	0.0307018i	$0.00977423\pi$
$20$	−3.33317	+	7.09522i	−0.745320	+	1.58654i
$21$	−0.823704	−	0.823704i	−0.179747	−	0.179747i
$22$	−5.18283	+	0.906271i	−1.10498	+	0.193218i
$23$		−	2.17156i		−	0.452802i	−0.974034	−	0.226401i	$-0.927304\pi$
$23$		−	2.17156i		−	0.452802i	0.974034	−	0.226401i	$-0.0726959\pi$
$24$	−4.27123	+	2.44175i	−0.871862	+	0.498420i
$25$			10.3631i			2.07261i
$26$	1.58254	+	9.05032i	0.310362	+	1.77491i
$27$	−3.65833	−	3.65833i	−0.704046	−	0.704046i
$28$	1.25990	−	0.454511i	0.238099	−	0.0858945i
$29$	1.35054	−	1.35054i	0.250789	−	0.250789i	−0.570505	−	0.821294i	$-0.693253\pi$
$29$	1.35054	−	1.35054i	0.250789	−	0.250789i	0.821294	+	0.570505i	$0.193253\pi$
$30$	−5.54165	+	7.89038i	−1.01176	+	1.44058i
$31$	7.26759			1.30530			0.652649	−	0.757660i	$-0.273658\pi$
$31$	7.26759			1.30530			0.652649	+	0.757660i	$0.273658\pi$
$32$	−0.452922	−	5.63869i	−0.0800661	−	0.996790i
$33$	−6.47150			−1.12654
$34$	0.812807	−	1.15730i	0.139395	−	0.198475i
$35$	1.85608	−	1.85608i	0.313735	−	0.313735i
$36$	−0.0483434	+	0.0174399i	−0.00805723	+	0.00290665i
$37$	−4.69542	−	4.69542i	−0.771922	−	0.771922i	0.206520	−	0.978442i	$-0.433786\pi$
$37$	−4.69542	−	4.69542i	−0.771922	−	0.771922i	−0.978442	+	0.206520i	$0.933786\pi$
$38$	1.45480	+	8.31980i	0.236000	+	1.34965i
$39$			11.3006i			1.80954i
$40$	−5.50208	−	9.62453i	−0.869955	−	1.52177i
$41$		−	2.91709i		−	0.455572i	−0.973711	−	0.227786i	$-0.926851\pi$
$41$		−	2.91709i		−	0.455572i	0.973711	−	0.227786i	$-0.0731487\pi$
$42$	1.62279	−	0.283761i	0.250401	−	0.0437852i
$43$	0.0731686	+	0.0731686i	0.0111581	+	0.0111581i	0.712664	−	0.701506i	$-0.247489\pi$
$43$	0.0731686	+	0.0731686i	0.0111581	+	0.0111581i	−0.701506	+	0.712664i	$0.747489\pi$
$44$	3.16382	−	6.73472i	0.476963	−	1.01530i
$45$	−0.0712193	+	0.0712193i	−0.0106167	+	0.0106167i
$46$	2.51315	+	1.76506i	0.370543	+	0.260244i
$47$	4.07818			0.594864			0.297432	−	0.954743i	$-0.403870\pi$
$47$	4.07818			0.594864			0.297432	+	0.954743i	$0.403870\pi$
$48$	0.645854	−	6.92777i	0.0932210	−	0.999938i
$49$	6.55152			0.935931
$50$	−11.9932	−	8.42317i	−1.69609	−	1.19122i
$51$	1.22998	−	1.22998i	0.172232	−	0.172232i
$52$	−11.7602	−	5.52469i	−1.63085	−	0.766136i
$53$	−2.97112	−	2.97112i	−0.408115	−	0.408115i	0.472966	−	0.881081i	$-0.343183\pi$
$53$	−2.97112	−	2.97112i	−0.408115	−	0.408115i	−0.881081	+	0.472966i	$0.843183\pi$
$54$	7.20731	−	1.26027i	0.980790	−	0.171501i
$55$		−	14.5825i		−	1.96630i
$56$	−0.498053	+	1.82752i	−0.0665551	+	0.244212i
$57$			10.3884i			1.37598i
$58$	0.465252	+	2.66071i	0.0610906	+	0.349368i
$59$	2.37239	+	2.37239i	0.308859	+	0.308859i	0.844467	−	0.535608i	$-0.179917\pi$
$59$	2.37239	+	2.37239i	0.308859	+	0.308859i	−0.535608	+	0.844467i	$0.679917\pi$
$60$	−4.62724	−	12.8267i	−0.597375	−	1.65592i
$61$	−1.26981	+	1.26981i	−0.162582	+	0.162582i	−0.783710	−	0.621127i	$-0.786675\pi$
$61$	−1.26981	+	1.26981i	−0.162582	+	0.162582i	0.621127	+	0.783710i	$0.286675\pi$
$62$	−5.90715	+	8.41079i	−0.750209	+	1.06817i
$63$	0.0172087			0.00216809
$64$	6.89380	+	4.05900i	0.861725	+	0.507375i
$65$	−25.4641			−3.15843
$66$	5.26008	−	7.48947i	0.647471	−	0.921890i
$67$	9.07209	−	9.07209i	1.10833	−	1.10833i	0.114962	−	0.993370i	$-0.463325\pi$
$67$	9.07209	−	9.07209i	1.10833	−	1.10833i	0.993370	−	0.114962i	$-0.0366747\pi$
$68$	0.678689	+	1.88132i	0.0823031	+	0.228144i
$69$	2.67097	+	2.67097i	0.321547	+	0.321547i
$70$	0.639409	+	3.65669i	0.0764240	+	0.437057i
$71$			10.3263i			1.22550i	0.790276	+	0.612751i	$0.209937\pi$
$71$			10.3263i			1.22550i	−0.790276	+	0.612751i	$0.790063\pi$
$72$	0.0191106	−	0.0701231i	0.00225221	−	0.00826409i
$73$			4.88975i			0.572302i	0.958185	+	0.286151i	$0.0923758\pi$
$73$			4.88975i			0.572302i	−0.958185	+	0.286151i	$0.907624\pi$
$74$	9.25048	−	1.61754i	1.07535	−	0.188035i
$75$	−12.7464	−	12.7464i	−1.47182	−	1.47182i
$76$	−10.8110	−	5.07875i	−1.24010	−	0.582573i
$77$	−1.76178	+	1.76178i	−0.200773	+	0.200773i
$78$	−13.0782	−	9.18521i	−1.48081	−	1.04002i
$79$	−7.21372			−0.811606			−0.405803	−	0.913960i	$-0.633008\pi$
$79$	−7.21372			−0.811606			−0.405803	+	0.913960i	$0.633008\pi$
$80$	15.6106	+	1.45533i	1.74532	+	0.162710i
$81$	9.07643			1.00849
$82$	3.37595	+	2.37103i	0.372811	+	0.261836i
$83$	−9.30557	+	9.30557i	−1.02142	+	1.02142i	−0.0216532	+	0.999766i	$0.506893\pi$
$83$	−9.30557	+	9.30557i	−1.02142	+	1.02142i	−0.999766	+	0.0216532i	$0.993107\pi$
$84$	−0.990616	+	2.10869i	−0.108085	+	0.230077i
$85$	2.77156	+	2.77156i	0.300618	+	0.300618i
$86$	−0.144150	+	0.0252061i	−0.0155441	+	0.00271804i
$87$			3.32227i			0.356185i
$88$	5.22252	+	9.13552i	0.556723	+	0.973849i
$89$		−	16.9209i		−	1.79361i	−0.442428	−	0.896804i	$-0.645883\pi$
$89$		−	16.9209i		−	1.79361i	0.442428	−	0.896804i	$-0.354117\pi$
$90$	−0.0245346	−	0.140310i	−0.00258617	−	0.0147899i
$91$	3.07643	+	3.07643i	0.322498	+	0.322498i
$92$	−4.08541	+	1.47381i	−0.425933	+	0.153656i
$93$	−8.93899	+	8.93899i	−0.926930	+	0.926930i
$94$	−3.31478	+	4.71968i	−0.341893	+	0.486798i
$95$	−23.4087			−2.40168
$96$	7.49256	+	6.37839i	0.764706	+	0.650992i
$97$	5.46761			0.555152			0.277576	−	0.960704i	$-0.410469\pi$
$97$	5.46761			0.555152			0.277576	+	0.960704i	$0.410469\pi$
$98$	−5.32512	+	7.58207i	−0.537918	+	0.765905i
$99$	0.0676007	−	0.0676007i	0.00679412	−	0.00679412i
$100$	19.4963	−	7.03330i	1.94963	−	0.703330i
$101$	1.86517	+	1.86517i	0.185592	+	0.185592i	0.793787	−	0.608195i	$-0.208106\pi$
$101$	1.86517	+	1.86517i	0.185592	+	0.185592i	−0.608195	+	0.793787i	$0.708106\pi$
$102$	0.423720	+	2.42319i	0.0419545	+	0.239932i
$103$		−	6.27078i		−	0.617878i	−0.951082	−	0.308939i	$-0.900026\pi$
$103$		−	6.27078i		−	0.617878i	0.951082	−	0.308939i	$-0.0999740\pi$
$104$	15.9525	−	9.11962i	1.56427	−	0.894253i
$105$			4.56589i			0.445585i
$106$	5.85343	−	1.02353i	0.568535	−	0.0994142i
$107$	2.26214	+	2.26214i	0.218689	+	0.218689i	0.807946	−	0.589257i	$-0.200579\pi$
$107$	2.26214	+	2.26214i	0.218689	+	0.218689i	−0.589257	+	0.807946i	$0.700579\pi$
$108$	−4.39964	+	9.36538i	−0.423355	+	0.901184i
$109$	9.79055	−	9.79055i	0.937764	−	0.937764i	−0.0604094	−	0.998174i	$-0.519241\pi$
$109$	9.79055	−	9.79055i	0.937764	−	0.937764i	0.998174	+	0.0604094i	$0.0192406\pi$
$110$	16.8763	+	11.8527i	1.60909	+	1.13011i
$111$	11.5505			1.09633
$112$	−1.71017	−	2.06182i	−0.161595	−	0.194823i
$113$	−11.3675			−1.06936			−0.534680	−	0.845055i	$-0.679568\pi$
$113$	−11.3675			−1.06936			−0.534680	+	0.845055i	$0.679568\pi$
$114$	−12.0226	−	8.44380i	−1.12602	−	0.790835i
$115$	−6.01860	+	6.01860i	−0.561238	+	0.561238i
$116$	−3.45740	−	1.62421i	−0.321011	−	0.150804i
$117$	−0.118045	−	0.118045i	−0.0109133	−	0.0109133i
$118$	−4.67387	+	0.817274i	−0.430265	+	0.0752362i
$119$		−	0.669690i		−	0.0613904i
$120$	18.6054	+	5.07053i	1.69843	+	0.462874i
$121$			2.84155i			0.258323i
$122$	−0.437440	−	2.50166i	−0.0396040	−	0.226489i
$123$	3.58796	+	3.58796i	0.323515	+	0.323515i
$124$	−4.93244	−	13.6727i	−0.442946	−	1.22784i
$125$	14.8640	−	14.8640i	1.32948	−	1.32948i
$126$	−0.0139873	+	0.0199156i	−0.00124609	+	0.00177422i
$127$	4.23601			0.375885			0.187943	−	0.982180i	$-0.439818\pi$
$127$	4.23601			0.375885			0.187943	+	0.982180i	$0.439818\pi$
$128$	−10.3008	+	4.67901i	−0.910472	+	0.413570i
$129$	−0.179992			−0.0158474
$130$	20.6974	−	29.4696i	1.81528	−	2.58465i
$131$	−2.62415	+	2.62415i	−0.229273	+	0.229273i	−0.812389	−	0.583116i	$-0.801833\pi$
$131$	−2.62415	+	2.62415i	−0.229273	+	0.229273i	0.583116	+	0.812389i	$0.301833\pi$
$132$	4.39214	+	12.1750i	0.382287	+	1.05970i
$133$	2.82811	+	2.82811i	0.245228	+	0.245228i
$134$	3.12527	+	17.8730i	0.269983	+	1.54399i
$135$			20.2785i			1.74530i
$136$	−2.72890	−	0.743706i	−0.234001	−	0.0637723i
$137$			3.23307i			0.276220i	0.990417	+	0.138110i	$0.0441027\pi$
$137$			3.23307i			0.276220i	−0.990417	+	0.138110i	$0.955897\pi$
$138$	−5.26210	+	0.920133i	−0.447940	+	0.0783269i
$139$	0.0629711	+	0.0629711i	0.00534114	+	0.00534114i	0.709772	−	0.704431i	$-0.248798\pi$
$139$	0.0629711	+	0.0629711i	0.00534114	+	0.00534114i	−0.704431	+	0.709772i	$0.748798\pi$
$140$	−4.75160	−	2.23219i	−0.401583	−	0.188655i
$141$	−5.01608	+	5.01608i	−0.422430	+	0.422430i
$142$	−11.9506	−	8.39327i	−1.00287	−	0.704347i
$143$	24.1703			2.02122
$144$	0.0656203	+	0.0791133i	0.00546836	+	0.00659278i
$145$	−7.48619			−0.621695
$146$	−5.65891	−	3.97442i	−0.468334	−	0.328925i
$147$	−8.05823	+	8.05823i	−0.664631	+	0.664631i
$148$	−5.64687	+	12.0203i	−0.464170	+	0.988065i
$149$	3.82246	+	3.82246i	0.313148	+	0.313148i	0.846128	−	0.532980i	$-0.178928\pi$
$149$	3.82246	+	3.82246i	0.313148	+	0.313148i	−0.532980	+	0.846128i	$0.678928\pi$
$150$	25.1117	−	4.39103i	2.05036	−	0.358526i
$151$			7.99432i			0.650568i	0.945616	+	0.325284i	$0.105460\pi$
$151$			7.99432i			0.650568i	−0.945616	+	0.325284i	$0.894540\pi$
$152$	14.6649	−	8.38351i	1.18948	−	0.679993i
$153$			0.0256965i			0.00207744i
$154$	−0.606921	−	3.47089i	−0.0489071	−	0.279692i
$155$	−20.1426	−	20.1426i	−1.61789	−	1.61789i
$156$	21.2601	−	7.66959i	1.70217	−	0.614059i
$157$	−12.2408	+	12.2408i	−0.976923	+	0.976923i	−0.999740	−	0.0228169i	$-0.992737\pi$
$157$	−12.2408	+	12.2408i	−0.976923	+	0.976923i	0.0228169	+	0.999740i	$0.492737\pi$
$158$	5.86336	−	8.34844i	0.466464	−	0.664166i
$159$	7.30883			0.579628
$160$	−14.3727	+	16.8833i	−1.13626	+	1.33474i
$161$	1.45427			0.114613
$162$	−7.37739	+	10.5042i	−0.579622	+	0.825284i
$163$	−15.0106	+	15.0106i	−1.17572	+	1.17572i	−0.194901	+	0.980823i	$0.562438\pi$
$163$	−15.0106	+	15.0106i	−1.17572	+	1.17572i	−0.980823	+	0.194901i	$0.937562\pi$
$164$	−5.48799	+	1.97980i	−0.428540	+	0.154596i
$165$	17.9361	+	17.9361i	1.39633	+	1.39633i
$166$	−3.20571	−	18.3330i	−0.248811	−	1.42291i
$167$		−	0.437410i		−	0.0338478i	−0.999857	−	0.0169239i	$-0.994613\pi$
$167$		−	0.437410i		−	0.0338478i	0.999857	−	0.0169239i	$-0.00538730\pi$
$168$	−1.63521	−	2.86040i	−0.126159	−	0.220685i
$169$		−	29.2063i		−	2.24664i
$170$	−5.46027	+	0.954783i	−0.418783	+	0.0732285i
$171$	−0.108517	−	0.108517i	−0.00829848	−	0.00829848i
$172$	0.0879951	−	0.187313i	0.00670957	−	0.0142825i
$173$	13.6346	−	13.6346i	1.03662	−	1.03662i	0.0373183	−	0.999303i	$-0.488118\pi$
$173$	13.6346	−	13.6346i	1.03662	−	1.03662i	0.999303	−	0.0373183i	$-0.0118815\pi$
$174$	−3.84486	−	2.70036i	−0.291478	−	0.204714i
$175$	−6.94004			−0.524618
$176$	−14.8174	−	1.38138i	−1.11691	−	0.104126i
$177$	−5.83599			−0.438660
$178$	19.5825	+	13.7534i	1.46777	+	1.03086i
$179$	−1.88552	+	1.88552i	−0.140931	+	0.140931i	−0.774052	−	0.633122i	$-0.781773\pi$
$179$	−1.88552	+	1.88552i	−0.140931	+	0.140931i	0.633122	+	0.774052i	$0.281773\pi$
$180$	0.182322	+	0.0856508i	0.0135895	+	0.00638403i
$181$	6.71023	+	6.71023i	0.498767	+	0.498767i	0.911054	−	0.412287i	$-0.135270\pi$
$181$	6.71023	+	6.71023i	0.498767	+	0.498767i	−0.412287	+	0.911054i	$0.635270\pi$
$182$	−6.06090	+	1.05981i	−0.449264	+	0.0785584i
$183$		−	3.12367i		−	0.230909i
$184$	1.61500	−	5.92597i	0.119060	−	0.436868i
$185$			26.0272i			1.91356i
$186$	−3.07942	−	17.6108i	−0.225794	−	1.29128i
$187$	−2.63074	−	2.63074i	−0.192379	−	0.192379i
$188$	−2.76782	−	7.67239i	−0.201864	−	0.559566i
$189$	2.44995	−	2.44995i	0.178207	−	0.178207i
$190$	19.0267	−	27.0909i	1.38034	−	1.96538i
$191$	27.2259			1.97000			0.984998	−	0.172565i	$-0.0552054\pi$
$191$	27.2259			1.97000			0.984998	+	0.172565i	$0.0552054\pi$
$192$	−13.4717	+	3.48674i	−0.972238	+	0.251634i
$193$	10.9591			0.788856			0.394428	−	0.918927i	$-0.370943\pi$
$193$	10.9591			0.788856			0.394428	+	0.918927i	$0.370943\pi$
$194$	−4.44411	+	6.32767i	−0.319069	+	0.454300i
$195$	31.3203	−	31.3203i	2.24289	−	2.24289i
$196$	−4.44644	−	12.3255i	−0.317603	−	0.880395i
$197$	−16.0302	−	16.0302i	−1.14210	−	1.14210i	−0.988065	−	0.154040i	$-0.950772\pi$
$197$	−16.0302	−	16.0302i	−1.14210	−	1.14210i	−0.154040	−	0.988065i	$-0.549228\pi$
$198$	0.0232880	+	0.133181i	0.00165500	+	0.00946473i
$199$			4.30078i			0.304874i	0.988313	+	0.152437i	$0.0487121\pi$
$199$			4.30078i			0.304874i	−0.988313	+	0.152437i	$0.951288\pi$
$200$	−7.70708	+	28.2798i	−0.544973	+	1.99968i
$201$			22.3170i			1.57412i
$202$	−3.67459	+	0.642540i	−0.258544	+	0.0452090i
$203$	0.904442	+	0.904442i	0.0634794	+	0.0634794i
$204$	−3.14876	−	1.47922i	−0.220457	−	0.103566i
$205$	−8.08488	+	8.08488i	−0.564672	+	0.564672i
$206$	7.25718	+	5.09694i	0.505632	+	0.355120i
$207$	−0.0558014			−0.00387847
$208$	−2.41218	+	25.8744i	−0.167255	+	1.79406i
$209$	22.2193			1.53694
$210$	−5.28411	−	3.71119i	−0.364638	−	0.256096i
$211$	−16.5176	+	16.5176i	−1.13712	+	1.13712i	−0.148152	+	0.988965i	$0.547333\pi$
$211$	−16.5176	+	16.5176i	−1.13712	+	1.13712i	−0.988965	+	0.148152i	$0.952667\pi$
$212$	−3.57318	+	7.60611i	−0.245407	+	0.522390i
$213$	−12.7011	−	12.7011i	−0.870265	−	0.870265i
$214$	−4.45665	+	0.779291i	−0.304650	+	0.0532712i
$215$		−	0.405582i		−	0.0276605i
$216$	−7.26250	−	12.7039i	−0.494150	−	0.864394i
$217$			4.86703i			0.330396i
$218$	3.37278	+	19.2884i	0.228433	+	1.30638i
$219$	−6.01429	−	6.01429i	−0.406408	−	0.406408i
$220$	−27.4344	+	9.89697i	−1.84962	+	0.667253i
$221$	−4.59382	+	4.59382i	−0.309014	+	0.309014i
$222$	−9.38835	+	13.3674i	−0.630105	+	0.897164i
$223$	−16.0248			−1.07310			−0.536549	−	0.843869i	$-0.680272\pi$
$223$	−16.0248			−1.07310			−0.536549	+	0.843869i	$0.680272\pi$
$224$	3.77618	−	0.303317i	0.252306	−	0.0202663i
$225$	0.266294			0.0177529
$226$	9.23955	−	13.1556i	0.614606	−	0.875095i
$227$	4.97122	−	4.97122i	0.329951	−	0.329951i	−0.522616	−	0.852568i	$-0.675044\pi$
$227$	4.97122	−	4.97122i	0.329951	−	0.329951i	0.852568	+	0.522616i	$0.175044\pi$
$228$	19.5440	−	7.05053i	1.29434	−	0.466932i
$229$	−6.11057	−	6.11057i	−0.403798	−	0.403798i	0.475771	−	0.879569i	$-0.342169\pi$
$229$	−6.11057	−	6.11057i	−0.403798	−	0.403798i	−0.879569	+	0.475771i	$0.842169\pi$
$230$	−2.07337	−	11.8573i	−0.136714	−	0.781847i
$231$		−	4.33390i		−	0.285150i
$232$	4.68989	−	2.68108i	0.307907	−	0.176022i
$233$		−	23.8300i		−	1.56116i	−0.625057	−	0.780579i	$-0.714924\pi$
$233$		−	23.8300i		−	1.56116i	0.625057	−	0.780579i	$-0.285076\pi$
$234$	0.232561	−	0.0406657i	0.0152030	−	0.00265840i
$235$	−11.3029	−	11.3029i	−0.737321	−	0.737321i
$236$	2.85313	−	6.07336i	0.185723	−	0.395342i
$237$	8.87272	−	8.87272i	0.576345	−	0.576345i
$238$	0.775032	+	0.544329i	0.0502379	+	0.0352836i
$239$	1.18840			0.0768713			0.0384356	−	0.999261i	$-0.487763\pi$
$239$	1.18840			0.0768713			0.0384356	+	0.999261i	$0.487763\pi$
$240$	−20.9907	+	17.4107i	−1.35495	+	1.12386i
$241$	−2.76856			−0.178339			−0.0891693	−	0.996016i	$-0.528421\pi$
$241$	−2.76856			−0.178339			−0.0891693	+	0.996016i	$0.528421\pi$
$242$	−3.28853	−	2.30963i	−0.211395	−	0.148469i
$243$	−0.188825	+	0.188825i	−0.0121131	+	0.0121131i
$244$	3.25072	+	1.52711i	0.208106	+	0.0977635i
$245$	−18.1579	−	18.1579i	−1.16007	−	1.16007i
$246$	−7.06866	+	1.23603i	−0.450681	+	0.0788062i
$247$		−	38.7996i		−	2.46876i
$248$	19.8325	+	5.40496i	1.25937	+	0.343215i
$249$		−	22.8913i		−	1.45068i
$250$	5.12056	+	29.2838i	0.323853	+	1.85207i
$251$	−3.82757	−	3.82757i	−0.241594	−	0.241594i	0.575915	−	0.817509i	$-0.304646\pi$
$251$	−3.82757	−	3.82757i	−0.241594	−	0.241594i	−0.817509	+	0.575915i	$0.804646\pi$
$252$	−0.0116793	−	0.0323751i	−0.000735729	−	0.00203944i
$253$	5.71280	−	5.71280i	0.359161	−	0.359161i
$254$	−3.44306	+	4.90234i	−0.216037	+	0.307600i
$255$	−6.81792			−0.426954
$256$	2.95755	−	15.7243i	0.184847	−	0.982767i
$257$	19.4185			1.21129			0.605647	−	0.795733i	$-0.292914\pi$
$257$	19.4185			1.21129			0.605647	+	0.795733i	$0.292914\pi$
$258$	0.146299	−	0.208304i	0.00910815	−	0.0129685i
$259$	3.14447	−	3.14447i	0.195388	−	0.195388i
$260$	17.2822	+	47.9062i	1.07180	+	2.97101i
$261$	−0.0347041	−	0.0347041i	−0.00214813	−	0.00214813i
$262$	−0.904004	−	5.16987i	−0.0558495	−	0.319395i
$263$			3.00537i			0.185319i	0.995698	+	0.0926595i	$0.0295368\pi$
$263$			3.00537i			0.185319i	−0.995698	+	0.0926595i	$0.970463\pi$
$264$	−17.6601	−	4.81290i	−1.08690	−	0.296213i
$265$			16.4693i			1.01170i
$266$	−5.57169	+	0.974266i	−0.341622	+	0.0597361i
$267$	20.8123	+	20.8123i	1.27369	+	1.27369i
$268$	−23.2247	−	10.9104i	−1.41867	−	0.666459i
$269$	−4.32516	+	4.32516i	−0.263709	+	0.263709i	−0.826559	−	0.562850i	$-0.809705\pi$
$269$	−4.32516	+	4.32516i	−0.263709	+	0.263709i	0.562850	+	0.826559i	$0.309705\pi$
$270$	−23.4684	−	16.4825i	−1.42824	−	1.00310i
$271$	−17.2911			−1.05036			−0.525178	−	0.850992i	$-0.676001\pi$
$271$	−17.2911			−1.05036			−0.525178	+	0.850992i	$0.676001\pi$
$272$	3.07876	−	2.55367i	0.186677	−	0.154839i
$273$	−7.56790			−0.458030
$274$	−3.74163	−	2.62786i	−0.226040	−	0.158755i
$275$	−27.2625	+	27.2625i	−1.64399	+	1.64399i
$276$	3.21221	−	6.83773i	0.193352	−	0.411583i
$277$	−11.0214	−	11.0214i	−0.662210	−	0.662210i	0.293690	−	0.955901i	$-0.405117\pi$
$277$	−11.0214	−	11.0214i	−0.662210	−	0.662210i	−0.955901	+	0.293690i	$0.905117\pi$
$278$	−0.124060	+	0.0216931i	−0.00744062	+	0.00130107i
$279$		−	0.186752i		−	0.0111805i
$280$	6.44545	−	3.68469i	0.385189	−	0.220202i
$281$			19.5379i			1.16553i	0.812640	+	0.582765i	$0.198029\pi$
$281$			19.5379i			1.16553i	−0.812640	+	0.582765i	$0.801971\pi$
$282$	−1.72801	−	9.88222i	−0.102901	−	0.588478i
$283$	5.69674	+	5.69674i	0.338636	+	0.338636i	0.855854	−	0.517218i	$-0.173032\pi$
$283$	5.69674	+	5.69674i	0.338636	+	0.338636i	−0.517218	+	0.855854i	$0.673032\pi$
$284$	19.4271	−	7.00833i	1.15278	−	0.415868i
$285$	28.7922	−	28.7922i	1.70550	−	1.70550i
$286$	−19.6458	+	27.9722i	−1.16168	+	1.65403i
$287$	1.95354			0.115314
$288$	−0.144895	+	0.0116385i	−0.00853799	+	0.000685806i
$289$	1.00000			0.0588235
$290$	6.08483	−	8.66378i	0.357314	−	0.508755i
$291$	−6.72504	+	6.72504i	−0.394229	+	0.394229i
$292$	9.19920	−	3.31862i	0.538342	−	0.194207i
$293$	12.4897	+	12.4897i	0.729656	+	0.729656i	0.970551	−	0.240895i	$-0.0774410\pi$
$293$	12.4897	+	12.4897i	0.729656	+	0.729656i	−0.240895	+	0.970551i	$0.577441\pi$
$294$	−2.77601	−	15.8756i	−0.161900	−	0.925882i
$295$		−	13.1505i		−	0.765649i
$296$	−9.32132	−	16.3053i	−0.541791	−	0.947729i
$297$		−	19.2482i		−	1.11689i
$298$	−7.53066	+	1.31681i	−0.436239	+	0.0762809i
$299$	−9.97575	−	9.97575i	−0.576913	−	0.576913i
$300$	−15.3292	+	32.6308i	−0.885032	+	1.88394i
$301$	−0.0490003	+	0.0490003i	−0.00282433	+	0.00282433i
$302$	−9.25183	−	6.49784i	−0.532383	−	0.373909i
$303$	−4.58825			−0.263588
$304$	−2.21748	+	23.7859i	−0.127181	+	1.36421i
$305$	7.03869			0.403034
$306$	−0.0297385	−	0.0208863i	−0.00170004	−	0.00119399i
$307$	−4.54572	+	4.54572i	−0.259438	+	0.259438i	−0.824825	−	0.565388i	$-0.808727\pi$
$307$	−4.54572	+	4.54572i	−0.259438	+	0.259438i	0.565388	+	0.824825i	$0.308727\pi$
$308$	4.51017	+	2.11878i	0.256991	+	0.120728i
$309$	7.71293	+	7.71293i	0.438773	+	0.438773i
$310$	39.6830	−	6.93898i	2.25384	−	0.394107i
$311$		−	10.6997i		−	0.606725i	−0.952875	−	0.303363i	$-0.901891\pi$
$311$		−	10.6997i		−	0.606725i	0.952875	−	0.303363i	$-0.0981094\pi$
$312$	−8.40433	+	30.8382i	−0.475801	+	1.74587i
$313$			15.4415i			0.872803i	0.899752	+	0.436401i	$0.143747\pi$
$313$			15.4415i			0.872803i	−0.899752	+	0.436401i	$0.856253\pi$
$314$	−4.21688	−	24.1157i	−0.237972	−	1.36093i
$315$	−0.0476948	−	0.0476948i	−0.00268730	−	0.00268730i
$316$	4.89587	+	13.5713i	0.275414	+	0.763447i
$317$	−3.41974	+	3.41974i	−0.192071	+	0.192071i	−0.796591	−	0.604519i	$-0.793365\pi$
$317$	−3.41974	+	3.41974i	−0.192071	+	0.192071i	0.604519	+	0.796591i	$0.293365\pi$
$318$	−5.94067	+	8.45852i	−0.333136	+	0.474330i
$319$	7.10583			0.397850
$320$	−7.85681	−	30.3563i	−0.439209	−	1.69697i
$321$	−5.56476			−0.310595
$322$	−1.18204	+	1.68303i	−0.0658726	+	0.0937916i
$323$	−4.22302	+	4.22302i	−0.234975	+	0.234975i
$324$	−6.16007	−	17.0757i	−0.342226	−	0.948650i
$325$	47.6060	+	47.6060i	2.64071	+	2.64071i
$326$	−5.17106	−	29.5726i	−0.286399	−	1.63787i
$327$			24.0843i			1.33187i
$328$	2.16946	−	7.96044i	0.119788	−	0.439542i
$329$			2.73112i			0.150571i
$330$	−35.3361	+	6.17888i	−1.94519	+	0.340136i
$331$	13.9438	+	13.9438i	0.766421	+	0.766421i	0.977474	−	0.211054i	$-0.0676895\pi$
$331$	13.9438	+	13.9438i	0.766421	+	0.766421i	−0.211054	+	0.977474i	$0.567690\pi$
$332$	23.8224	+	11.1912i	1.30742	+	0.614197i
$333$	−0.120656	+	0.120656i	−0.00661189	+	0.00661189i
$334$	0.506215	+	0.355530i	0.0276989	+	0.0194537i
$335$	−50.2876			−2.74751
$336$	4.63946	+	0.432522i	0.253103	+	0.0235960i
$337$	9.02838			0.491807			0.245904	−	0.969294i	$-0.420915\pi$
$337$	9.02838			0.491807			0.245904	+	0.969294i	$0.420915\pi$
$338$	33.8005	+	23.7391i	1.83850	+	1.29124i
$339$	13.9817	−	13.9817i	0.759383	−	0.759383i
$340$	3.33317	−	7.09522i	0.180767	−	0.384793i
$341$	19.1191	+	19.1191i	1.03536	+	1.03536i
$342$	0.213790	−	0.0373833i	0.0115604	−	0.00202146i
$343$			9.07531i			0.490021i
$344$	0.145254	+	0.254086i	0.00783157	+	0.0136994i
$345$		−	14.8055i		−	0.797102i
$346$	4.69704	+	26.8617i	0.252514	+	1.44409i
$347$	5.95998	+	5.95998i	0.319948	+	0.319948i	0.848747	−	0.528799i	$-0.177357\pi$
$347$	5.95998	+	5.95998i	0.319948	+	0.319948i	−0.528799	+	0.848747i	$0.677357\pi$
$348$	6.25027	−	2.25479i	0.335049	−	0.120869i
$349$	−12.7725	+	12.7725i	−0.683694	+	0.683694i	−0.960830	−	0.277137i	$-0.910614\pi$
$349$	−12.7725	+	12.7725i	−0.683694	+	0.683694i	0.277137	+	0.960830i	$0.410614\pi$
$350$	5.64091	−	8.03171i	0.301519	−	0.429313i
$351$	−33.6114			−1.79404
$352$	13.6424	−	16.0254i	0.727142	−	0.854159i
$353$	21.1594			1.12620			0.563100	−	0.826389i	$-0.309609\pi$
$353$	21.1594			1.12620			0.563100	+	0.826389i	$0.309609\pi$
$354$	4.74354	−	6.75400i	0.252116	−	0.358971i
$355$	28.6199	−	28.6199i	1.51898	−	1.51898i
$356$	−31.8336	+	11.4840i	−1.68718	+	0.608651i
$357$	0.823704	+	0.823704i	0.0435951	+	0.0435951i
$358$	−0.649550	−	3.71468i	−0.0343298	−	0.196327i
$359$		−	16.4930i		−	0.870466i	−0.900318	−	0.435233i	$-0.856666\pi$
$359$		−	16.4930i		−	0.870466i	0.900318	−	0.435233i	$-0.143334\pi$
$360$	−0.247317	+	0.141384i	−0.0130347	+	0.00745160i
$361$		−	16.6678i		−	0.877251i
$362$	−13.2199	+	2.31163i	−0.694821	+	0.121497i
$363$	−3.49505	−	3.49505i	−0.183442	−	0.183442i
$364$	3.69983	−	7.87571i	0.193924	−	0.412799i
$365$	13.5522	−	13.5522i	0.709355	−	0.709355i
$366$	3.61503	+	2.53894i	0.188961	+	0.132713i
$367$	−4.65976			−0.243238			−0.121619	−	0.992577i	$-0.538809\pi$
$367$	−4.65976			−0.243238			−0.121619	+	0.992577i	$0.538809\pi$
$368$	5.54544	+	6.68572i	0.289076	+	0.348517i
$369$	−0.0749589			−0.00390220
$370$	−30.1213	−	21.1551i	−1.56593	−	1.09980i
$371$	1.98973	−	1.98973i	0.103302	−	0.103302i
$372$	22.8839	+	10.7503i	1.18648	+	0.557379i
$373$	−2.64020	−	2.64020i	−0.136704	−	0.136704i	0.635443	−	0.772148i	$-0.280817\pi$
$373$	−2.64020	−	2.64020i	−0.136704	−	0.136704i	−0.772148	+	0.635443i	$0.780817\pi$
$374$	5.18283	−	0.906271i	0.267998	−	0.0468622i
$375$			36.5649i			1.88820i
$376$	11.1290	+	3.03297i	0.573932	+	0.156414i
$377$		−	12.4083i		−	0.639058i
$378$	0.843991	+	4.82666i	0.0434102	+	0.248257i
$379$	3.64201	+	3.64201i	0.187078	+	0.187078i	0.794431	−	0.607354i	$-0.207769\pi$
$379$	3.64201	+	3.64201i	0.187078	+	0.187078i	−0.607354	+	0.794431i	$0.707769\pi$
$380$	15.8872	+	44.0393i	0.814997	+	2.25917i
$381$	−5.21020	+	5.21020i	−0.266927	+	0.266927i
$382$	−22.1294	+	31.5085i	−1.13224	+	1.61212i
$383$	9.62246			0.491685			0.245842	−	0.969310i	$-0.420935\pi$
$383$	9.62246			0.491685			0.245842	+	0.969310i	$0.420935\pi$
$384$	6.91470	−	18.4249i	0.352864	−	0.940241i
$385$	9.76574			0.497708
$386$	−8.90767	+	12.6830i	−0.453388	+	0.645549i
$387$	0.00188018	−	0.00188018i	9.55747e−5	−	9.55747e-5i
$388$	−3.71081	−	10.2863i	−0.188388	−	0.522210i
$389$	−21.2069	−	21.2069i	−1.07523	−	1.07523i	−0.996930	−	0.0783019i	$-0.975050\pi$
$389$	−21.2069	−	21.2069i	−1.07523	−	1.07523i	−0.0783019	−	0.996930i	$-0.524950\pi$
$390$	10.7896	+	61.7043i	0.546354	+	3.12452i
$391$			2.17156i			0.109821i
$392$	17.8784	+	4.87240i	0.902997	+	0.246094i
$393$		−	6.45531i		−	0.325627i
$394$	31.5812	−	5.52230i	1.59104	−	0.278209i
$395$	19.9932	+	19.9932i	1.00597	+	1.00597i
$396$	−0.173059	−	0.0812989i	−0.00869652	−	0.00408543i
$397$	2.14109	−	2.14109i	0.107458	−	0.107458i	−0.651333	−	0.758792i	$-0.725790\pi$
$397$	2.14109	−	2.14109i	0.107458	−	0.107458i	0.758792	+	0.651333i	$0.225790\pi$
$398$	−4.97729	−	3.49570i	−0.249489	−	0.175224i
$399$	−6.95704			−0.348287
$400$	−26.4638	−	31.9054i	−1.32319	−	1.59527i
$401$	6.02151			0.300700			0.150350	−	0.988633i	$-0.451960\pi$
$401$	6.02151			0.300700			0.150350	+	0.988633i	$0.451960\pi$
$402$	−25.8274	−	18.1394i	−1.28815	−	0.904710i
$403$	33.3860	−	33.3860i	1.66308	−	1.66308i
$404$	2.24312	−	4.77487i	0.111600	−	0.237559i
$405$	−25.1558	−	25.1558i	−1.25000	−	1.25000i
$406$	−1.78185	+	0.311574i	−0.0884317	+	0.0154632i
$407$		−	24.7048i		−	1.22457i
$408$	4.27123	−	2.44175i	0.211458	−	0.120885i
$409$			1.74901i			0.0864829i	0.999065	+	0.0432415i	$0.0137685\pi$
$409$			1.74901i			0.0864829i	−0.999065	+	0.0432415i	$0.986232\pi$
$410$	−2.78519	−	15.9281i	−0.137551	−	0.786632i
$411$	−3.97661	−	3.97661i	−0.196152	−	0.196152i
$412$	−11.7974	+	4.25591i	−0.581215	+	0.209674i
$413$	−1.58877	+	1.58877i	−0.0781782	+	0.0781782i
$414$	0.0453558	−	0.0645790i	0.00222912	−	0.00317389i
$415$	51.5818			2.53205
$416$	−27.9838	−	23.8225i	−1.37202	−	1.16799i
$417$	−0.154906			−0.00758579
$418$	−18.0600	+	25.7144i	−0.883344	+	1.25773i
$419$	16.0055	−	16.0055i	0.781920	−	0.781920i	−0.198234	−	0.980155i	$-0.563521\pi$
$419$	16.0055	−	16.0055i	0.781920	−	0.781920i	0.980155	+	0.198234i	$0.0635207\pi$
$420$	8.58992	−	3.09882i	0.419145	−	0.151207i
$421$	15.0910	+	15.0910i	0.735488	+	0.735488i	0.971701	−	0.236213i	$-0.0759063\pi$
$421$	15.0910	+	15.0910i	0.735488	+	0.735488i	−0.236213	+	0.971701i	$0.575906\pi$
$422$	−5.69020	−	32.5414i	−0.276994	−	1.58409i
$423$		−	0.104795i		−	0.00509531i
$424$	−5.89825	−	10.3175i	−0.286445	−	0.501064i
$425$		−	10.3631i		−	0.502682i
$426$	25.0225	−	4.37544i	1.21235	−	0.211991i
$427$	−0.850377	−	0.850377i	−0.0411526	−	0.0411526i
$428$	2.72052	−	5.79110i	0.131502	−	0.279923i
$429$	−29.7289	+	29.7289i	−1.43532	+	1.43532i
$430$	0.469380	+	0.329660i	0.0226355	+	0.0158976i
$431$	−27.4039			−1.32000			−0.659999	−	0.751266i	$-0.729443\pi$
$431$	−27.4039			−1.32000			−0.659999	+	0.751266i	$0.729443\pi$
$432$	20.6053	+	1.92097i	0.991373	+	0.0924225i
$433$	−19.4730			−0.935812			−0.467906	−	0.883778i	$-0.654991\pi$
$433$	−19.4730			−0.935812			−0.467906	+	0.883778i	$0.654991\pi$
$434$	−5.63262	−	3.95596i	−0.270374	−	0.189892i
$435$	9.20786	−	9.20786i	0.441483	−	0.441483i
$436$	−25.0639	−	11.7745i	−1.20034	−	0.563894i
$437$	−9.17054	−	9.17054i	−0.438686	−	0.438686i
$438$	11.8488	−	2.07188i	0.566157	−	0.0989983i
$439$			7.39915i			0.353142i	0.984288	+	0.176571i	$0.0565005\pi$
$439$			7.39915i			0.353142i	−0.984288	+	0.176571i	$0.943499\pi$
$440$	10.8451	−	39.7941i	0.517019	−	1.89711i
$441$		−	0.168351i		−	0.00801671i
$442$	−1.58254	−	9.05032i	−0.0752738	−	0.430480i
$443$	4.11531	+	4.11531i	0.195525	+	0.195525i	0.798078	−	0.602554i	$-0.205850\pi$
$443$	4.11531	+	4.11531i	0.195525	+	0.195525i	−0.602554	+	0.798078i	$0.705850\pi$
$444$	−7.83922	−	21.7303i	−0.372033	−	1.03127i
$445$	−46.8972	+	46.8972i	−2.22314	+	2.22314i
$446$	13.0251	−	18.5455i	0.616754	−	0.878154i
$447$	−9.40309			−0.444751
$448$	−2.71827	+	4.61671i	−0.128426	+	0.218119i
$449$	4.43525			0.209312			0.104656	−	0.994508i	$-0.466626\pi$
$449$	4.43525			0.209312			0.104656	+	0.994508i	$0.466626\pi$
$450$	−0.216446	+	0.308182i	−0.0102034	+	0.0145279i
$451$	7.67409	−	7.67409i	0.361359	−	0.361359i
$452$	7.71497	+	21.3859i	0.362882	+	1.00591i
$453$	−9.83284	−	9.83284i	−0.461987	−	0.461987i
$454$	1.71255	+	9.79384i	0.0803741	+	0.459648i
$455$		−	17.0530i		−	0.799458i
$456$	−7.72596	+	28.3490i	−0.361801	+	1.32757i
$457$			29.8052i			1.39423i	0.716961	+	0.697114i	$0.245533\pi$
$457$			29.8052i			1.39423i	−0.716961	+	0.697114i	$0.754467\pi$
$458$	12.0385	−	2.10505i	0.562521	−	0.0983625i
$459$	3.65833	+	3.65833i	0.170756	+	0.170756i
$460$	15.4077	+	7.23818i	0.718388	+	0.337482i
$461$	3.15173	−	3.15173i	0.146791	−	0.146791i	−0.629892	−	0.776683i	$-0.716901\pi$
$461$	3.15173	−	3.15173i	0.146791	−	0.146791i	0.776683	+	0.629892i	$0.216901\pi$
$462$	5.01562	+	3.52262i	0.233348	+	0.163887i
$463$	−37.2282			−1.73014			−0.865071	−	0.501649i	$-0.832727\pi$
$463$	−37.2282			−1.73014			−0.865071	+	0.501649i	$0.832727\pi$
$464$	−0.709159	+	7.60682i	−0.0329219	+	0.353138i
$465$	49.5498			2.29782
$466$	27.5785	+	19.3692i	1.27755	+	0.897262i
$467$	−1.88802	+	1.88802i	−0.0873670	+	0.0873670i	−0.749440	−	0.662073i	$-0.769677\pi$
$467$	−1.88802	+	1.88802i	−0.0873670	+	0.0873670i	0.662073	+	0.749440i	$0.269677\pi$
$468$	−0.141965	+	0.302197i	−0.00656233	+	0.0139690i
$469$	6.07549	+	6.07549i	0.280540	+	0.280540i
$470$	22.2680	−	3.89378i	1.02715	−	0.179607i
$471$		−	30.1119i		−	1.38748i
$472$	4.70966	+	8.23840i	0.216780	+	0.379203i
$473$			0.384975i			0.0177012i
$474$	3.05659	+	17.4802i	0.140394	+	0.802893i
$475$	43.7634	+	43.7634i	2.00800	+	2.00800i
$476$	−1.25990	+	0.454511i	−0.0577476	+	0.0208325i
$477$	−0.0763473	+	0.0763473i	−0.00349571	+	0.00349571i
$478$	−0.965941	+	1.37534i	−0.0441811	+	0.0629064i
$479$	13.4877			0.616270			0.308135	−	0.951343i	$-0.400295\pi$
$479$	13.4877			0.616270			0.308135	+	0.951343i	$0.400295\pi$
$480$	−3.08799	−	38.4441i	−0.140947	−	1.75473i
$481$	−43.1398			−1.96701
$482$	2.25030	−	3.20406i	0.102499	−	0.145941i
$483$	−1.78872	+	1.78872i	−0.0813897	+	0.0813897i
$484$	5.34588	−	1.92853i	0.242995	−	0.0876604i
$485$	−15.1538	−	15.1538i	−0.688098	−	0.688098i
$486$	−0.0650488	−	0.372005i	−0.00295067	−	0.0168745i
$487$			36.1819i			1.63956i	0.572681	+	0.819778i	$0.305903\pi$
$487$			36.1819i			1.63956i	−0.572681	+	0.819778i	$0.694097\pi$
$488$	−4.40954	+	2.52081i	−0.199611	+	0.114112i
$489$		−	36.9255i		−	1.66983i
$490$	35.7730	−	6.25528i	1.61606	−	0.282585i
$491$	1.87278	+	1.87278i	0.0845172	+	0.0845172i	0.748102	−	0.663584i	$-0.230966\pi$
$491$	1.87278	+	1.87278i	0.0845172	+	0.0845172i	−0.663584	+	0.748102i	$0.730966\pi$
$492$	4.31500	−	9.18522i	0.194535	−	0.414101i
$493$	−1.35054	+	1.35054i	−0.0608252	+	0.0608252i
$494$	44.9027	+	31.5366i	2.02027	+	1.41890i
$495$	−0.374718			−0.0168423
$496$	−22.3752	+	18.5590i	−1.00468	+	0.833325i
$497$	−6.91540			−0.310198
$498$	26.4921	+	18.6062i	1.18714	+	0.833764i
$499$	1.86183	−	1.86183i	0.0833470	−	0.0833470i	−0.664204	−	0.747551i	$-0.731229\pi$
$499$	1.86183	−	1.86183i	0.0833470	−	0.0833470i	0.747551	+	0.664204i	$0.231229\pi$
$500$	−38.0521	−	17.8760i	−1.70174	−	0.799440i
$501$	0.538005	+	0.538005i	0.0240363	+	0.0240363i
$502$	7.54073	−	1.31857i	0.336559	−	0.0588509i
$503$		−	17.6969i		−	0.789066i	−0.918882	−	0.394533i	$-0.870906\pi$
$503$		−	17.6969i		−	0.789066i	0.918882	−	0.394533i	$-0.129094\pi$
$504$	0.0469608	+	0.0127982i	0.00209180	+	0.000570077i
$505$		−	10.3389i		−	0.460074i
$506$	1.96802	+	11.2548i	0.0874893	+	0.500338i
$507$	35.9232	+	35.9232i	1.59540	+	1.59540i
$508$	−2.87493	−	7.96931i	−0.127555	−	0.353581i
$509$	−21.8391	+	21.8391i	−0.968003	+	0.968003i	−0.999504	−	0.0315007i	$-0.989971\pi$
$509$	−21.8391	+	21.8391i	−0.968003	+	0.968003i	0.0315007	+	0.999504i	$0.489971\pi$
$510$	5.54165	−	7.89038i	0.245388	−	0.349392i
$511$	−3.27461			−0.144860
$512$	15.7938	+	16.2036i	0.697994	+	0.716104i
$513$	−30.8984			−1.36420
$514$	−15.7835	+	22.4731i	−0.696181	+	0.991245i
$515$	−17.3798	+	17.3798i	−0.765847	+	0.765847i
$516$	0.122158	+	0.338623i	0.00537772	+	0.0149070i
$517$	10.7286	+	10.7286i	0.471845	+	0.471845i
$518$	1.08325	+	6.19495i	0.0475953	+	0.272191i
$519$			33.5406i			1.47227i
$520$	−69.4889	−	18.9378i	−3.04729	−	0.830477i
$521$			25.3819i			1.11200i	0.831182	+	0.556001i	$0.187665\pi$
$521$			25.3819i			1.11200i	−0.831182	+	0.556001i	$0.812335\pi$
$522$	0.0683708	−	0.0119553i	0.00299251	−	0.000523271i
$523$	−32.1058	−	32.1058i	−1.40389	−	1.40389i	−0.787233	−	0.616655i	$-0.788487\pi$
$523$	−32.1058	−	32.1058i	−1.40389	−	1.40389i	−0.616655	−	0.787233i	$-0.711513\pi$
$524$	6.71787	+	3.15590i	0.293471	+	0.137866i
$525$	8.53610	−	8.53610i	0.372546	−	0.372546i
$526$	−3.47811	−	2.44278i	−0.151653	−	0.106510i
$527$	−7.26759			−0.316581
$528$	19.9242	−	16.5261i	0.867090	−	0.719205i
$529$	18.2843			0.794971
$530$	−19.0599	−	13.3863i	−0.827909	−	0.581465i
$531$	0.0609622	−	0.0609622i	0.00264553	−	0.00264553i
$532$	3.40119	−	7.24001i	0.147460	−	0.313894i
$533$	−13.4006	−	13.4006i	−0.580443	−	0.580443i
$534$	−41.0025	+	7.16970i	−1.77435	+	0.310263i
$535$		−	12.5393i		−	0.542121i
$536$	31.5038	−	18.0099i	1.36076	−	0.777907i
$537$		−	4.63830i		−	0.200158i
$538$	−1.48999	−	8.52102i	−0.0642379	−	0.367367i
$539$	17.2353	+	17.2353i	0.742377	+	0.742377i
$540$	38.1505	−	13.7628i	1.64174	−	0.592258i
$541$	−25.0051	+	25.0051i	−1.07505	+	1.07505i	−0.0781100	+	0.996945i	$0.524889\pi$
$541$	−25.0051	+	25.0051i	−1.07505	+	1.07505i	−0.996945	+	0.0781100i	$0.975111\pi$
$542$	14.0543	−	20.0109i	0.603684	−	0.859544i
$543$	−16.5069			−0.708378
$544$	0.452922	+	5.63869i	0.0194189	+	0.241757i
$545$	−54.2701			−2.32468
$546$	6.15124	−	8.75833i	0.263249	−	0.374822i
$547$	−22.4286	+	22.4286i	−0.958979	+	0.958979i	−0.999191	−	0.0402124i	$-0.987197\pi$
$547$	−22.4286	+	22.4286i	−0.958979	+	0.958979i	0.0402124	+	0.999191i	$0.487197\pi$
$548$	6.08245	−	2.19425i	0.259829	−	0.0937337i
$549$	0.0326296	+	0.0326296i	0.00139260	+	0.00139260i
$550$	−9.39175	−	53.7100i	−0.400466	−	2.29020i
$551$		−	11.4067i		−	0.485942i
$552$	5.30240	+	9.27524i	0.225685	+	0.394780i
$553$		−	4.83095i		−	0.205433i
$554$	21.7133	−	3.79679i	0.922510	−	0.161310i
$555$	−32.0130	−	32.0130i	−1.35887	−	1.35887i
$556$	0.0757313	−	0.161207i	0.00321172	−	0.00683670i
$557$	−22.9125	+	22.9125i	−0.970832	+	0.970832i	−0.999587	−	0.0287542i	$-0.990846\pi$
$557$	−22.9125	+	22.9125i	−0.970832	+	0.970832i	0.0287542	+	0.999587i	$0.490846\pi$
$558$	0.216128	+	0.151793i	0.00914941	+	0.00642591i
$559$	0.672246			0.0284330
$560$	−0.974618	+	10.4543i	−0.0411851	+	0.441773i
$561$	6.47150			0.273227
$562$	−22.6112	−	15.8805i	−0.953795	−	0.669879i
$563$	−28.0030	+	28.0030i	−1.18019	+	1.18019i	−0.200490	+	0.979696i	$0.564254\pi$
$563$	−28.0030	+	28.0030i	−1.18019	+	1.18019i	−0.979696	+	0.200490i	$0.935746\pi$
$564$	12.8412	+	6.03251i	0.540713	+	0.254015i
$565$	31.5056	+	31.5056i	1.32545	+	1.32545i
$566$	−11.2232	+	1.96249i	−0.471746	+	0.0824896i
$567$			6.07839i			0.255268i
$568$	−7.67971	+	28.1794i	−0.322234	+	1.18238i
$569$		−	6.74859i		−	0.282916i	−0.989944	−	0.141458i	$-0.954821\pi$
$569$		−	6.74859i		−	0.282916i	0.989944	−	0.141458i	$-0.0451789\pi$
$570$	9.91872	+	56.7237i	0.415449	+	2.37589i
$571$	24.6111	+	24.6111i	1.02994	+	1.02994i	0.999538	+	0.0304058i	$0.00967996\pi$
$571$	24.6111	+	24.6111i	1.02994	+	1.02994i	0.0304058	+	0.999538i	$0.490320\pi$
$572$	−16.4041	−	45.4721i	−0.685889	−	1.90128i
$573$	−33.4873	+	33.4873i	−1.39895	+	1.39895i
$574$	−1.58785	+	2.26084i	−0.0662758	+	0.0943655i
$575$	22.5040			0.938482
$576$	0.104302	−	0.177146i	0.00434592	−	0.00738110i
$577$	−30.4929			−1.26944			−0.634719	−	0.772743i	$-0.718884\pi$
$577$	−30.4929			−1.26944			−0.634719	+	0.772743i	$0.718884\pi$
$578$	−0.812807	+	1.15730i	−0.0338083	+	0.0481374i
$579$	−13.4795	+	13.4795i	−0.560189	+	0.560189i
$580$	5.08080	+	14.0840i	0.210969	+	0.584805i
$581$	−6.23184	−	6.23184i	−0.258540	−	0.258540i
$582$	−2.31673	−	13.2491i	−0.0960317	−	0.549191i
$583$		−	15.6325i		−	0.647431i
$584$	−3.63654	+	13.3436i	−0.150481	+	0.552163i
$585$			0.654337i			0.0270535i
$586$	−24.6061	+	4.30262i	−1.01647	+	0.177740i
$587$	12.5298	+	12.5298i	0.517162	+	0.517162i	0.916712	−	0.399550i	$-0.130833\pi$
$587$	12.5298	+	12.5298i	0.517162	+	0.517162i	−0.399550	+	0.916712i	$0.630833\pi$
$588$	20.6292	+	9.69111i	0.850733	+	0.399654i
$589$	30.6912	−	30.6912i	1.26461	−	1.26461i
$590$	15.2190	+	10.6888i	0.626558	+	0.440050i
$591$	39.4336			1.62208
$592$	26.4466	+	2.46553i	1.08695	+	0.101333i
$593$	−12.0292			−0.493981			−0.246990	−	0.969018i	$-0.579442\pi$
$593$	−12.0292			−0.493981			−0.246990	+	0.969018i	$0.579442\pi$
$594$	22.2760	+	15.6451i	0.913994	+	0.641926i
$595$	−1.85608	+	1.85608i	−0.0760920	+	0.0760920i
$596$	4.59703	−	9.78555i	0.188302	−	0.400832i
$597$	−5.28987	−	5.28987i	−0.216500	−	0.216500i
$598$	19.6533	−	3.43658i	0.803683	−	0.140532i
$599$			14.2803i			0.583477i	0.956498	+	0.291739i	$0.0942338\pi$
$599$			14.2803i			0.583477i	−0.956498	+	0.291739i	$0.905766\pi$
$600$	−25.3040	−	44.2631i	−1.03303	−	1.80703i
$601$		−	6.77326i		−	0.276287i	−0.990412	−	0.138143i	$-0.955887\pi$
$601$		−	6.77326i		−	0.276287i	0.990412	−	0.138143i	$-0.0441135\pi$
$602$	−0.0168803	−	0.0965358i	−0.000687988	−	0.00393451i
$603$	−0.233121	−	0.233121i	−0.00949341	−	0.00949341i
$604$	15.0399	−	5.42566i	0.611965	−	0.220767i
$605$	7.87552	−	7.87552i	0.320186	−	0.320186i
$606$	3.72936	−	5.30999i	0.151495	−	0.215703i
$607$	43.7102			1.77414			0.887070	−	0.461634i	$-0.152737\pi$
$607$	43.7102			1.77414			0.887070	+	0.461634i	$0.152737\pi$
$608$	−25.7250	−	21.8996i	−1.04329	−	0.888146i
$609$	−2.22489			−0.0901571
$610$	−5.72110	+	8.14588i	−0.231640	+	0.329817i
$611$	18.7344	−	18.7344i	0.757914	−	0.757914i
$612$	0.0483434	−	0.0174399i	0.00195417	−	0.000704967i
$613$	−19.2198	−	19.2198i	−0.776280	−	0.776280i	0.202917	−	0.979196i	$-0.434958\pi$
$613$	−19.2198	−	19.2198i	−0.776280	−	0.776280i	−0.979196	+	0.202917i	$0.934958\pi$
$614$	−1.56597	−	8.95555i	−0.0631974	−	0.361417i
$615$		−	19.8885i		−	0.801980i
$616$	−6.11796	+	3.49747i	−0.246500	+	0.140917i
$617$			7.35679i			0.296173i	0.988974	+	0.148087i	$0.0473114\pi$
$617$			7.35679i			0.296173i	−0.988974	+	0.148087i	$0.952689\pi$
$618$	−15.1953	+	2.65705i	−0.611245	+	0.106882i
$619$	−31.7069	−	31.7069i	−1.27441	−	1.27441i	−0.943751	−	0.330658i	$-0.892729\pi$
$619$	−31.7069	−	31.7069i	−1.27441	−	1.27441i	−0.330658	−	0.943751i	$-0.607271\pi$
$620$	−24.2241	+	51.5652i	−0.972865	+	2.07091i
$621$	−7.94428	+	7.94428i	−0.318793	+	0.318793i
$622$	12.3828	+	8.69681i	0.496505	+	0.348710i
$623$	11.3317			0.453996
$624$	−28.8580	−	34.7919i	−1.15524	−	1.39279i
$625$	−30.5778			−1.22311
$626$	−17.8704	−	12.5509i	−0.714245	−	0.501636i
$627$	−27.3293	+	27.3293i	−1.09143	+	1.09143i
$628$	31.3366	+	14.7212i	1.25047	+	0.587441i
$629$	4.69542	+	4.69542i	0.187219	+	0.187219i
$630$	0.0939639	−	0.0164306i	0.00374361	−	0.000654609i
$631$		−	6.28851i		−	0.250341i	−0.992135	−	0.125171i	$-0.960052\pi$
$631$		−	6.28851i		−	0.250341i	0.992135	−	0.125171i	$-0.0399479\pi$
$632$	−19.6855	−	5.36489i	−0.783048	−	0.213404i
$633$		−	40.6325i		−	1.61500i
$634$	−1.17808	−	6.73725i	−0.0467874	−	0.267570i
$635$	−11.7403	−	11.7403i	−0.465902	−	0.465902i
$636$	−4.96043	−	13.7503i	−0.196694	−	0.545234i
$637$	30.0965	−	30.0965i	1.19247	−	1.19247i
$638$	−5.77567	+	8.22358i	−0.228661	+	0.325575i
$639$	0.265349			0.0104970
$640$	41.5175	+	15.5812i	1.64112	+	0.615899i
$641$	38.5848			1.52401			0.762004	−	0.647572i	$-0.224216\pi$
$641$	38.5848			1.52401			0.762004	+	0.647572i	$0.224216\pi$
$642$	4.52308	−	6.44010i	0.178512	−	0.254170i
$643$	3.89161	−	3.89161i	0.153470	−	0.153470i	−0.626196	−	0.779666i	$-0.715389\pi$
$643$	3.89161	−	3.89161i	0.153470	−	0.153470i	0.779666	+	0.626196i	$0.215389\pi$
$644$	−0.986998	−	2.73596i	−0.0388932	−	0.107812i
$645$	0.498857	+	0.498857i	0.0196425	+	0.0196425i
$646$	−1.45480	−	8.31980i	−0.0572384	−	0.327338i
$647$		−	7.12724i		−	0.280201i	−0.990137	−	0.140100i	$-0.955257\pi$
$647$		−	7.12724i		−	0.280201i	0.990137	−	0.140100i	$-0.0447425\pi$
$648$	24.7687	+	6.75020i	0.973006	+	0.265173i
$649$			12.4823i			0.489973i
$650$	−93.7890	+	16.4000i	−3.67871	+	0.643260i
$651$	−5.98635	−	5.98635i	−0.234624	−	0.234624i
$652$	38.4274	+	18.0523i	1.50493	+	0.706983i
$653$	0.279397	−	0.279397i	0.0109336	−	0.0109336i	−0.701619	−	0.712552i	$-0.747539\pi$
$653$	0.279397	−	0.279397i	0.0109336	−	0.0109336i	0.712552	+	0.701619i	$0.247539\pi$
$654$	−27.8728	−	19.5759i	−1.08991	−	0.765479i
$655$	14.5460			0.568359
$656$	7.44927	+	8.98102i	0.290845	+	0.350650i
$657$	0.125649			0.00490204
$658$	−3.16072	−	2.21987i	−0.123218	−	0.0865396i
$659$	−18.3142	+	18.3142i	−0.713418	+	0.713418i	−0.967249	−	0.253830i	$-0.918310\pi$
$659$	−18.3142	+	18.3142i	−0.713418	+	0.713418i	0.253830	+	0.967249i	$0.418310\pi$
$660$	21.5706	−	45.9168i	0.839636	−	1.78731i
$661$	−29.7476	−	29.7476i	−1.15705	−	1.15705i	−0.985107	−	0.171941i	$-0.944996\pi$
$661$	−29.7476	−	29.7476i	−1.15705	−	1.15705i	−0.171941	−	0.985107i	$-0.555004\pi$
$662$	−27.4708	+	4.80355i	−1.06768	+	0.186695i
$663$		−	11.3006i		−	0.438879i
$664$	−32.3146	+	18.4734i	−1.25405	+	0.716905i
$665$		−	15.6766i		−	0.607911i
$666$	−0.0415651	−	0.237705i	−0.00161061	−	0.00921087i
$667$	−2.93278	−	2.93278i	−0.113558	−	0.113558i
$668$	−0.822910	+	0.296866i	−0.0318394	+	0.0114861i
$669$	19.7101	−	19.7101i	0.762038	−	0.762038i
$670$	40.8741	−	58.1979i	1.57911	−	2.24838i
$671$	−6.68106			−0.257919
$672$	−4.27154	+	5.01769i	−0.164778	+	0.193562i
$673$	15.2533			0.587972			0.293986	−	0.955810i	$-0.405018\pi$
$673$	15.2533			0.587972			0.293986	+	0.955810i	$0.405018\pi$
$674$	−7.33834	+	10.4486i	−0.282662	+	0.402463i
$675$	37.9115	−	37.9115i	1.45921	−	1.45921i
$676$	−54.9466	+	19.8220i	−2.11333	+	0.762385i
$677$	−30.6864	−	30.6864i	−1.17937	−	1.17937i	−0.979904	−	0.199471i	$-0.936078\pi$
$677$	−30.6864	−	30.6864i	−1.17937	−	1.17937i	−0.199471	−	0.979904i	$-0.563922\pi$
$678$	4.81661	+	27.5455i	0.184981	+	1.05788i
$679$			3.66160i			0.140519i
$680$	5.50208	+	9.62453i	0.210995	+	0.369084i
$681$			12.2290i			0.468616i
$682$	−37.6667	+	6.58641i	−1.44233	+	0.252207i
$683$	34.6442	+	34.6442i	1.32562	+	1.32562i	0.909147	+	0.416474i	$0.136734\pi$
$683$	34.6442	+	34.6442i	1.32562	+	1.32562i	0.416474	+	0.909147i	$0.363266\pi$
$684$	−0.130506	+	0.277804i	−0.00499002	+	0.0106221i
$685$	8.96064	−	8.96064i	0.342368	−	0.342368i
$686$	−10.5029	−	7.37648i	−0.401001	−	0.281635i
$687$	15.0317			0.573497
$688$	−0.412117	−	0.0384204i	−0.0157118	−	0.00146476i
$689$	−27.2976			−1.03996
$690$	17.1344	+	12.0340i	0.652296	+	0.458128i
$691$	19.2513	−	19.2513i	0.732355	−	0.732355i	−0.238731	−	0.971086i	$-0.576731\pi$
$691$	19.2513	−	19.2513i	0.732355	−	0.732355i	0.971086	+	0.238731i	$0.0767313\pi$
$692$	−34.9048	−	16.3975i	−1.32688	−	0.623339i
$693$	0.0452715	+	0.0452715i	0.00171972	+	0.00171972i
$694$	−11.7418	+	2.05317i	−0.445713	+	0.0779374i
$695$		−	0.349056i		−	0.0132405i
$696$	−2.47079	+	9.06615i	−0.0936552	+	0.343651i
$697$			2.91709i			0.110493i
$698$	−4.40003	−	25.1631i	−0.166543	−	0.952438i
$699$	29.3104	+	29.3104i	1.10862	+	1.10862i
$700$	4.71013	+	13.0565i	0.178026	+	0.493488i
$701$	27.6953	−	27.6953i	1.04604	−	1.04604i	0.0471474	−	0.998888i	$-0.484987\pi$
$701$	27.6953	−	27.6953i	1.04604	−	1.04604i	0.998888	−	0.0471474i	$-0.0150131\pi$
$702$	27.3196	−	38.8985i	1.03111	−	1.46813i
$703$	−39.6577			−1.49572
$704$	7.45761	+	28.8139i	0.281069	+	1.08597i
$705$	27.8047			1.04719
$706$	−17.1985	+	24.4877i	−0.647273	+	0.921608i
$707$	−1.24909	+	1.24909i	−0.0469768	+	0.0469768i
$708$	3.96082	+	10.9794i	0.148857	+	0.412631i
$709$	−20.8677	−	20.8677i	−0.783704	−	0.783704i	0.196750	−	0.980454i	$-0.436961\pi$
$709$	−20.8677	−	20.8677i	−0.783704	−	0.783704i	−0.980454	+	0.196750i	$0.936961\pi$
$710$	9.85935	+	56.3842i	0.370015	+	2.11606i
$711$			0.185367i			0.00695181i
$712$	12.5842	−	46.1754i	0.471611	−	1.73049i
$713$		−	15.7820i		−	0.591041i
$714$	−1.62279	+	0.283761i	−0.0607313	+	0.0106195i
$715$	−66.9892	−	66.9892i	−2.50526	−	2.50526i
$716$	4.82696	+	2.26759i	0.180392	+	0.0847440i
$717$	−1.46171	+	1.46171i	−0.0545885	+	0.0545885i
$718$	19.0873	+	13.4056i	0.712333	+	0.500293i
$719$	−35.5384			−1.32536			−0.662679	−	0.748904i	$-0.730581\pi$
$719$	−35.5384			−1.32536			−0.662679	+	0.748904i	$0.730581\pi$
$720$	0.0373968	−	0.401138i	0.00139370	−	0.0149495i
$721$	4.19948			0.156397
$722$	19.2896	+	13.5477i	0.717885	+	0.504192i
$723$	3.40527	−	3.40527i	0.126643	−	0.126643i
$724$	8.06996	−	17.1783i	0.299918	−	0.638426i
$725$	13.9957	+	13.9957i	0.519788	+	0.519788i
$726$	6.88562	−	1.20402i	0.255549	−	0.0446854i
$727$			11.9097i			0.441706i	0.975307	+	0.220853i	$0.0708841\pi$
$727$			11.9097i			0.441706i	−0.975307	+	0.220853i	$0.929116\pi$
$728$	6.10732	+	10.6832i	0.226352	+	0.395947i
$729$			26.7648i			0.991288i
$730$	4.66865	+	26.6993i	0.172794	+	0.988186i
$731$	−0.0731686	−	0.0731686i	−0.00270624	−	0.00270624i
$732$	−5.87664	+	2.12000i	−0.217207	+	0.0783576i
$733$	−5.33642	+	5.33642i	−0.197105	+	0.197105i	−0.798758	−	0.601653i	$-0.794509\pi$
$733$	−5.33642	+	5.33642i	−0.197105	+	0.197105i	0.601653	+	0.798758i	$0.294509\pi$
$734$	3.78749	−	5.39275i	0.139799	−	0.199050i
$735$	44.6677			1.64759
$736$	−12.2448	+	0.983548i	−0.451348	+	0.0362541i
$737$	47.7326			1.75825
$738$	0.0609271	−	0.0867499i	0.00224276	−	0.00319331i
$739$	−25.0428	+	25.0428i	−0.921214	+	0.921214i	−0.997115	−	0.0759015i	$-0.975817\pi$
$739$	−25.0428	+	25.0428i	−0.921214	+	0.921214i	0.0759015	+	0.997115i	$0.475817\pi$
$740$	48.9657	−	17.6644i	1.80001	−	0.649357i
$741$	47.7226	+	47.7226i	1.75313	+	1.75313i
$742$	0.685449	+	3.91998i	0.0251636	+	0.143907i
$743$		−	24.2530i		−	0.889755i	−0.895592	−	0.444877i	$-0.853247\pi$
$743$		−	24.2530i		−	0.889755i	0.895592	−	0.444877i	$-0.146753\pi$
$744$	−31.0416	+	17.7456i	−1.13804	+	0.650586i
$745$		−	21.1883i		−	0.776281i
$746$	5.20147	−	0.909530i	0.190439	−	0.0333003i
$747$	0.239120	+	0.239120i	0.00874895	+	0.00874895i
$748$	−3.16382	+	6.73472i	−0.115681	+	0.246246i
$749$	−1.51493	+	1.51493i	−0.0553543	+	0.0553543i
$750$	−42.3166	−	29.7202i	−1.54518	−	1.08523i
$751$	−19.4498			−0.709733			−0.354867	−	0.934917i	$-0.615474\pi$
$751$	−19.4498			−0.709733			−0.354867	+	0.934917i	$0.615474\pi$
$752$	−12.5558	+	10.4143i	−0.457861	+	0.379772i
$753$	9.41567			0.343126
$754$	14.3601	+	10.0855i	0.522964	+	0.367293i
$755$	22.1567	−	22.1567i	0.806365	−	0.806365i
$756$	−6.27190	−	2.94639i	−0.228107	−	0.107159i
$757$	33.0393	+	33.0393i	1.20083	+	1.20083i	0.973913	+	0.226921i	$0.0728660\pi$
$757$	33.0393	+	33.0393i	1.20083	+	1.20083i	0.226921	+	0.973913i	$0.427134\pi$
$758$	−7.17516	+	1.25465i	−0.260613	+	0.0455709i
$759$			14.0533i			0.510101i
$760$	−63.8800	−	17.4092i	−2.31717	−	0.631497i
$761$			44.4553i			1.61150i	0.592254	+	0.805751i	$0.298238\pi$
$761$			44.4553i			1.61150i	−0.592254	+	0.805751i	$0.701762\pi$
$762$	−1.79488	−	10.2647i	−0.0650217	−	0.371850i
$763$	6.55663	+	6.55663i	0.237366	+	0.237366i
$764$	−18.4779	−	51.2207i	−0.668508	−	1.85310i
$765$	0.0712193	−	0.0712193i	0.00257494	−	0.00257494i
$766$	−7.82121	+	11.1361i	−0.282592	+	0.402363i
$767$	21.7967			0.787033
$768$	15.7028	+	22.9783i	0.566626	+	0.829156i
$769$	15.0905			0.544177			0.272088	−	0.962272i	$-0.412286\pi$
$769$	15.0905			0.544177			0.272088	+	0.962272i	$0.412286\pi$
$770$	−7.93766	+	11.3019i	−0.286053	+	0.407292i
$771$	−23.8844	+	23.8844i	−0.860175	+	0.860175i
$772$	−7.43785	−	20.6177i	−0.267694	−	0.742047i
$773$	29.2378	+	29.2378i	1.05161	+	1.05161i	0.998594	+	0.0530154i	$0.0168832\pi$
$773$	29.2378	+	29.2378i	1.05161	+	1.05161i	0.0530154	+	0.998594i	$0.483117\pi$
$774$	0.000647708		0.00370415i	2.32814e−5		0.000133143i
$775$			75.3145i			2.70538i
$776$	14.9206	+	4.06630i	0.535617	+	0.145972i
$777$			7.73527i			0.277501i
$778$	41.7798	−	7.30563i	1.49788	−	0.261920i
$779$	−12.3189	−	12.3189i	−0.441371	−	0.441371i
$780$	−80.1803	−	37.6668i	−2.87091	−	1.34869i
$781$	−27.1657	+	27.1657i	−0.972065	+	0.972065i
$782$	−2.51315	−	1.76506i	−0.0898700	−	0.0631184i
$783$	−9.88144			−0.353134
$784$	−20.1706	+	16.7304i	−0.720377	+	0.597514i
$785$	67.8522			2.42175
$786$	7.47073	+	5.24692i	0.266472	+	0.187151i
$787$	37.3319	−	37.3319i	1.33074	−	1.33074i	0.426031	−	0.904709i	$-0.359912\pi$
$787$	37.3319	−	37.3319i	1.33074	−	1.33074i	0.904709	−	0.426031i	$-0.140088\pi$
$788$	−19.2785	+	41.0375i	−0.686768	+	1.46190i
$789$	−3.69654	−	3.69654i	−0.131600	−	0.131600i
$790$	−39.3888	+	6.88754i	−1.40139	+	0.245048i
$791$		−	7.61267i		−	0.270675i
$792$	0.234751	−	0.134200i	0.00834150	−	0.00476861i
$793$			11.6665i			0.414291i
$794$	0.737592	+	4.21818i	0.0261761	+	0.149698i
$795$	−20.2569	−	20.2569i	−0.718437	−	0.718437i
$796$	8.09116	−	2.91889i	0.286784	−	0.103457i
$797$	−9.53831	+	9.53831i	−0.337864	+	0.337864i	−0.855563	−	0.517699i	$-0.826789\pi$
$797$	−9.53831	+	9.53831i	−0.337864	+	0.337864i	0.517699	+	0.855563i	$0.326789\pi$
$798$	5.65473	−	8.05138i	0.200175	−	0.285016i
$799$	−4.07818			−0.144276
$800$	58.4341	−	4.69366i	2.06596	−	0.165946i
$801$	−0.434807			−0.0153631
$802$	−4.89433	+	6.96870i	−0.172825	+	0.246073i
$803$	−12.8636	+	12.8636i	−0.453948	+	0.453948i
$804$	41.9854	−	15.1463i	1.48071	−	0.534168i
$805$	−4.03060	−	4.03060i	−0.142060	−	0.142060i
$806$	11.5013	+	65.7740i	0.405115	+	2.31679i
$807$		−	10.6397i		−	0.374535i
$808$	3.70273	+	6.47702i	0.130262	+	0.227861i
$809$			28.0145i			0.984937i	0.870330	+	0.492469i	$0.163905\pi$
$809$			28.0145i			0.984937i	−0.870330	+	0.492469i	$0.836095\pi$
$810$	49.5597	−	8.66602i	1.74135	−	0.304493i
$811$	5.13450	+	5.13450i	0.180297	+	0.180297i	0.791485	−	0.611188i	$-0.209308\pi$
$811$	5.13450	+	5.13450i	0.180297	+	0.180297i	−0.611188	+	0.791485i	$0.709308\pi$
$812$	1.08771	−	2.31538i	0.0381713	−	0.0812541i
$813$	21.2676	−	21.2676i	0.745889	−	0.745889i
$814$	28.5909	+	20.0803i	1.00211	+	0.703812i
$815$	83.2057			2.91457
$816$	−0.645854	+	6.92777i	−0.0226094	+	0.242521i
$817$	0.617985			0.0216205
$818$	−2.02413	−	1.42161i	−0.0707720	−	0.0497053i
$819$	0.0790535	−	0.0790535i	0.00276235	−	0.00276235i
$820$	20.6974	+	9.72316i	0.722784	+	0.339547i
$821$	17.9984	+	17.9984i	0.628149	+	0.628149i	0.947602	−	0.319453i	$-0.103499\pi$
$821$	17.9984	+	17.9984i	0.628149	+	0.628149i	−0.319453	+	0.947602i	$0.603499\pi$
$822$	7.83434	−	1.36991i	0.273254	−	0.0477813i
$823$		−	27.3678i		−	0.953980i	−0.878909	−	0.476990i	$-0.841728\pi$
$823$		−	27.3678i		−	0.953980i	0.878909	−	0.476990i	$-0.158272\pi$
$824$	4.66362	−	17.1123i	0.162465	−	0.596137i
$825$		−	67.0646i		−	2.33489i
$826$	−0.547320	−	3.13005i	−0.0190437	−	0.108908i
$827$	−1.99775	−	1.99775i	−0.0694686	−	0.0694686i	0.671519	−	0.740987i	$-0.265642\pi$
$827$	−1.99775	−	1.99775i	−0.0694686	−	0.0694686i	−0.740987	+	0.671519i	$0.765642\pi$
$828$	0.0378718	+	0.104981i	0.00131614	+	0.00364833i
$829$	33.6132	−	33.6132i	1.16744	−	1.16744i	0.184627	−	0.982809i	$-0.440892\pi$
$829$	33.6132	−	33.6132i	1.16744	−	1.16744i	0.982809	−	0.184627i	$-0.0591077\pi$
$830$	−41.9261	+	59.6957i	−1.45528	+	2.07207i
$831$	27.1121			0.940509
$832$	50.3152	−	13.0225i	1.74437	−	0.451476i
$833$	−6.55152			−0.226997
$834$	0.125909	−	0.179273i	0.00435987	−	0.00620772i
$835$	−1.21231	+	1.21231i	−0.0419536	+	0.0419536i
$836$	−15.0800	−	41.8017i	−0.521553	−	1.44574i
$837$	−26.5873	−	26.5873i	−0.918990	−	0.918990i
$838$	5.51379	+	31.5326i	0.190471	+	1.08927i
$839$			9.85093i			0.340092i	0.985436	+	0.170046i	$0.0543916\pi$
$839$			9.85093i			0.340092i	−0.985436	+	0.170046i	$0.945608\pi$
$840$	−3.39568	+	12.4599i	−0.117162	+	0.429906i
$841$			25.3521i			0.874210i
$842$	−29.7308	+	5.19874i	−1.02459	+	0.179160i
$843$	−24.0312	−	24.0312i	−0.827677	−	0.827677i
$844$	42.2852	+	19.8646i	1.45552	+	0.683768i
$845$	−80.9470	+	80.9470i	−2.78466	+	2.78466i
$846$	0.121279	+	0.0851781i	0.00416967	+	0.00292848i
$847$	−1.90296			−0.0653864
$848$	16.7346	+	1.56012i	0.574670	+	0.0535746i
$849$	−14.0137			−0.480951
$850$	11.9932	+	8.42317i	0.411363	+	0.288912i
$851$	−10.1964	+	10.1964i	−0.349527	+	0.349527i
$852$	−15.2748	+	32.5150i	−0.523305	+	1.11394i
$853$	22.1305	+	22.1305i	0.757732	+	0.757732i	0.975909	−	0.218177i	$-0.0700110\pi$
$853$	22.1305	+	22.1305i	0.757732	+	0.757732i	−0.218177	+	0.975909i	$0.570011\pi$
$854$	1.67533	−	0.292949i	0.0573288	−	0.0100245i
$855$			0.601520i			0.0205716i
$856$	4.49078	+	7.85551i	0.153492	+	0.268496i
$857$		−	0.176386i		−	0.00602525i	−0.999995	−	0.00301262i	$-0.999041\pi$
$857$		−	0.176386i		−	0.00602525i	0.999995	−	0.00301262i	$-0.000958949\pi$
$858$	−10.2414	−	58.5691i	−0.349636	−	1.99952i
$859$	23.9498	+	23.9498i	0.817158	+	0.817158i	0.985695	−	0.168538i	$-0.0539045\pi$
$859$	23.9498	+	23.9498i	0.817158	+	0.817158i	−0.168538	+	0.985695i	$0.553904\pi$
$860$	−0.763031	+	0.275264i	−0.0260192	+	0.00938643i
$861$	−2.40282	+	2.40282i	−0.0818878	+	0.0818878i
$862$	22.2741	−	31.7145i	0.758658	−	1.08020i
$863$	8.20075			0.279157			0.139578	−	0.990211i	$-0.455425\pi$
$863$	8.20075			0.279157			0.139578	+	0.990211i	$0.455425\pi$
$864$	−18.9713	+	22.2851i	−0.645416	+	0.758156i
$865$	−75.5783			−2.56974
$866$	15.8278	−	22.5361i	0.537850	−	0.765808i
$867$	−1.22998	+	1.22998i	−0.0417723	+	0.0417723i
$868$	9.15647	−	3.30320i	0.310791	−	0.112118i
$869$	−18.9774	−	18.9774i	−0.643764	−	0.643764i
$870$	3.17205	+	18.1405i	0.107542	+	0.615020i
$871$		−	83.3510i		−	2.82424i
$872$	33.9987	−	19.4361i	1.15134	−	0.658191i
$873$		−	0.140498i		−	0.00475515i
$874$	18.0669	−	3.15919i	0.611124	−	0.106861i
$875$	9.95430	+	9.95430i	0.336517	+	0.336517i
$876$	−7.23299	+	15.3967i	−0.244380	+	0.520205i
$877$	1.72557	−	1.72557i	0.0582684	−	0.0582684i	−0.677372	−	0.735641i	$-0.736881\pi$
$877$	1.72557	−	1.72557i	0.0582684	−	0.0582684i	0.735641	+	0.677372i	$0.236881\pi$
$878$	−8.56304	−	6.01408i	−0.288988	−	0.202965i
$879$	−30.7241			−1.03630
$880$	37.2388	+	44.8960i	1.25532	+	1.51344i
$881$	7.77162			0.261832			0.130916	−	0.991393i	$-0.458208\pi$
$881$	7.77162			0.261832			0.130916	+	0.991393i	$0.458208\pi$
$882$	0.194833	+	0.136837i	0.00656035	+	0.00460753i
$883$	10.7383	−	10.7383i	0.361371	−	0.361371i	−0.502947	−	0.864318i	$-0.667751\pi$
$883$	10.7383	−	10.7383i	0.361371	−	0.361371i	0.864318	+	0.502947i	$0.167751\pi$
$884$	11.7602	+	5.52469i	0.395540	+	0.185815i
$885$	16.1748	+	16.1748i	0.543709	+	0.543709i
$886$	−8.10761	+	1.41770i	−0.272381	+	0.0476285i
$887$		−	37.4106i		−	1.25613i	−0.778162	−	0.628063i	$-0.783848\pi$
$887$		−	37.4106i		−	1.25613i	0.778162	−	0.628063i	$-0.216152\pi$
$888$	31.5203	+	8.59020i	1.05775	+	0.288268i
$889$			2.83681i			0.0951437i
$890$	−16.1558	−	92.3924i	−0.541542	−	3.09700i
$891$	23.8777	+	23.8777i	0.799933	+	0.799933i
$892$	10.8758	+	30.1478i	0.364150	+	1.00942i
$893$	17.2222	−	17.2222i	0.576320	−	0.576320i
$894$	7.64290	−	10.8822i	0.255617	−	0.363955i
$895$	10.4517			0.349361
$896$	−3.13349	−	6.89835i	−0.104682	−	0.230458i
$897$	24.5399			0.819364
$898$	−3.60500	+	5.13291i	−0.120300	+	0.171288i
$899$	9.81517	−	9.81517i	0.327354	−	0.327354i
$900$	−0.180731	−	0.500986i	−0.00602437	−	0.0166995i
$901$	2.97112	+	2.97112i	0.0989824	+	0.0989824i
$902$	2.64367	+	15.1188i	0.0880247	+	0.503400i
$903$		−	0.120539i		−	0.00401127i
$904$	−31.0207	−	8.45405i	−1.03173	−	0.281178i
$905$		−	37.1956i		−	1.23642i
$906$	19.3718	−	3.38735i	0.643584	−	0.112537i
$907$	19.9032	+	19.9032i	0.660875	+	0.660875i	0.955586	−	0.294711i	$-0.0952234\pi$
$907$	19.9032	+	19.9032i	0.660875	+	0.660875i	−0.294711	+	0.955586i	$0.595223\pi$
$908$	−12.7264	−	5.97856i	−0.422340	−	0.198406i
$909$	0.0479284	−	0.0479284i	0.00158969	−	0.00158969i
$910$	19.7355	+	13.8608i	0.654225	+	0.459482i
$911$	−21.7379			−0.720208			−0.360104	−	0.932912i	$-0.617259\pi$
$911$	−21.7379			−0.720208			−0.360104	+	0.932912i	$0.617259\pi$
$912$	−26.5287	−	31.9836i	−0.878451	−	1.05908i
$913$	−48.9610			−1.62037
$914$	−34.4935	−	24.2259i	−1.14094	−	0.801320i
$915$	−8.65744	+	8.65744i	−0.286206	+	0.286206i
$916$	−7.34878	+	15.6431i	−0.242811	+	0.516864i
$917$	−1.75737	−	1.75737i	−0.0580334	−	0.0580334i
$918$	−7.20731	+	1.26027i	−0.237877	+	0.0415951i
$919$			26.2923i			0.867302i	0.901081	+	0.433651i	$0.142775\pi$
$919$			26.2923i			0.867302i	−0.901081	+	0.433651i	$0.857225\pi$
$920$	−20.9002	+	11.9481i	−0.689061	+	0.393917i
$921$		−	11.1823i		−	0.368469i
$922$	1.08575	+	6.20925i	0.0357573	+	0.204491i
$923$	47.4370	+	47.4370i	1.56141	+	1.56141i
$924$	−8.15347	+	2.94137i	−0.268229	+	0.0967640i
$925$	48.6589	−	48.6589i	1.59990	−	1.59990i
$926$	30.2594	−	43.0842i	0.994385	−	1.41584i
$927$	−0.161137			−0.00529243
$928$	−8.22697	−	7.00359i	−0.270063	−	0.229904i
$929$	30.8646			1.01263			0.506317	−	0.862348i	$-0.331007\pi$
$929$	30.8646			1.01263			0.506317	+	0.862348i	$0.331007\pi$
$930$	−40.2745	+	57.3441i	−1.32065	+	1.88039i
$931$	27.6672	−	27.6672i	0.906755	−	0.906755i
$932$	−44.8320	+	16.1732i	−1.46852	+	0.529770i
$933$	13.1604	+	13.1604i	0.430853	+	0.430853i
$934$	−0.650409	−	3.71959i	−0.0212820	−	0.121709i
$935$			14.5825i			0.476898i
$936$	−0.234342	−	0.409924i	−0.00765971	−	0.0133988i
$937$		−	34.7688i		−	1.13585i	−0.823081	−	0.567924i	$-0.807747\pi$
$937$		−	34.7688i		−	1.13585i	0.823081	−	0.567924i	$-0.192253\pi$
$938$	−11.9694	+	2.09296i	−0.390813	+	0.0683377i
$939$	−18.9927	−	18.9927i	−0.619802	−	0.619802i
$940$	−13.5933	+	28.9356i	−0.443364	+	0.943776i
$941$	4.42293	−	4.42293i	0.144183	−	0.144183i	−0.631331	−	0.775514i	$-0.717491\pi$
$941$	4.42293	−	4.42293i	0.144183	−	0.144183i	0.775514	+	0.631331i	$0.217491\pi$
$942$	34.8485	+	24.4751i	1.13542	+	0.797443i
$943$	−6.33463			−0.206284
$944$	−13.3623	−	1.24573i	−0.434907	−	0.0405450i
$945$	−13.5803			−0.441768
$946$	−0.445531	−	0.312910i	−0.0144855	−	0.0101736i
$947$	−31.3780	+	31.3780i	−1.01965	+	1.01965i	−0.0198459	+	0.999803i	$0.506318\pi$
$947$	−31.3780	+	31.3780i	−1.01965	+	1.01965i	−0.999803	+	0.0198459i	$0.993682\pi$
$948$	−22.7143	−	10.6706i	−0.737725	−	0.346566i
$949$	22.4626	+	22.4626i	0.729167	+	0.729167i
$950$	−86.2186	+	15.0762i	−2.79730	+	0.489137i
$951$		−	8.41241i		−	0.272791i
$952$	0.498053	−	1.82752i	0.0161420	−	0.0592302i
$953$		−	2.41126i		−	0.0781084i	−0.999237	−	0.0390542i	$-0.987565\pi$
$953$		−	2.41126i		−	0.0781084i	0.999237	−	0.0390542i	$-0.0124345\pi$
$954$	−0.0263012	−	0.150413i	−0.000851531	−	0.00486978i
$955$	−75.4581	−	75.4581i	−2.44177	−	2.44177i
$956$	−0.806555	−	2.23577i	−0.0260858	−	0.0723099i
$957$	−8.74002	+	8.74002i	−0.282525	+	0.282525i
$958$	−10.9629	+	15.6093i	−0.354196	+	0.504315i
$959$	−2.16515			−0.0699165
$960$	47.0014	+	27.6739i	1.51696	+	0.893172i
$961$	21.8179			0.703804
$962$	35.0643	−	49.9257i	1.13052	−	1.60967i
$963$	0.0581289	−	0.0581289i	0.00187318	−	0.00187318i
$964$	1.87899	+	5.20856i	0.0605182	+	0.167756i
$965$	−30.3739	−	30.3739i	−0.977770	−	0.977770i
$966$	−0.616203	−	3.52398i	−0.0198260	−	0.113382i
$967$			14.3228i			0.460589i	0.973121	+	0.230294i	$0.0739689\pi$
$967$			14.3228i			0.460589i	−0.973121	+	0.230294i	$0.926031\pi$
$968$	−2.11328	+	7.75431i	−0.0679234	+	0.249233i
$969$		−	10.3884i		−	0.333725i
$970$	29.8546	−	5.22038i	0.958574	−	0.167616i
$971$	−41.5020	−	41.5020i	−1.33186	−	1.33186i	−0.903703	−	0.428159i	$-0.859162\pi$
$971$	−41.5020	−	41.5020i	−1.33186	−	1.33186i	−0.428159	−	0.903703i	$-0.640838\pi$
$972$	0.483393	+	0.227087i	0.0155049	+	0.00728382i
$973$	−0.0421711	+	0.0421711i	−0.00135194	+	0.00135194i
$974$	−41.8733	−	29.4089i	−1.34171	−	0.942321i
$975$	−117.109			−3.75048
$976$	0.666768	−	7.15210i	0.0213427	−	0.228933i
$977$	−4.56938			−0.146187			−0.0730936	−	0.997325i	$-0.523287\pi$
$977$	−4.56938			−0.146187			−0.0730936	+	0.997325i	$0.523287\pi$
$978$	42.7339	+	30.0133i	1.36648	+	0.959721i
$979$	44.5143	−	44.5143i	1.42268	−	1.42268i
$980$	−21.8373	+	46.4845i	−0.697568	+	1.48489i
$981$	−0.251583	−	0.251583i	−0.00803241	−	0.00803241i
$982$	−3.68957	+	0.645159i	−0.117739	+	0.0205878i
$983$			34.5229i			1.10111i	0.834799	+	0.550554i	$0.185584\pi$
$983$			34.5229i			1.10111i	−0.834799	+	0.550554i	$0.814416\pi$
$984$	7.12279	+	12.4596i	0.227066	+	0.397196i
$985$			88.8573i			2.83123i
$986$	−0.465252	−	2.66071i	−0.0148166	−	0.0847342i
$987$	−3.35922	−	3.35922i	−0.106925	−	0.106925i
$988$	−72.9945	+	26.3328i	−2.32227	+	0.837759i
$989$	0.158890	−	0.158890i	0.00505241	−	0.00505241i
$990$	0.304574	−	0.433662i	0.00967999	−	0.0137827i
$991$	−15.7822			−0.501339			−0.250670	−	0.968073i	$-0.580651\pi$
$991$	−15.7822			−0.501339			−0.250670	+	0.968073i	$0.580651\pi$
$992$	−3.29166	−	40.9797i	−0.104510	−	1.30111i
$993$	−34.3012			−1.08851
$994$	5.62088	−	8.00319i	0.178284	−	0.253846i
$995$	11.9199	−	11.9199i	0.377885	−	0.377885i
$996$	−43.0660	+	15.5361i	−1.36460	+	0.492280i
$997$	21.6308	+	21.6308i	0.685054	+	0.685054i	0.961135	−	0.276080i	$-0.0890356\pi$
$997$	21.6308	+	21.6308i	0.685054	+	0.685054i	−0.276080	+	0.961135i	$0.589036\pi$
$998$	0.641388	+	3.66801i	0.0203028	+	0.116109i
$999$			34.3548i			1.08694i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	272.2.l.b.69.4	✓	30
4.3	odd	2		1088.2.l.b.817.11		30
16.3	odd	4		1088.2.l.b.273.11		30
16.13	even	4	inner	272.2.l.b.205.4	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
272.2.l.b.69.4	✓	30	1.1	even	1	trivial
272.2.l.b.205.4	yes	30	16.13	even	4	inner
1088.2.l.b.273.11		30	16.3	odd	4
1088.2.l.b.817.11		30	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	272.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.812807 + 1.15730i) q^{2} +(-1.22998 + 1.22998i) q^{3} +(-0.678689 - 1.88132i) q^{4} +(-2.77156 - 2.77156i) q^{5} +(-0.423720 - 2.42319i) q^{6} +0.669690i q^{7} +(2.72890 + 0.743706i) q^{8} -0.0256965i q^{9} +(5.46027 - 0.954783i) q^{10} +(2.63074 + 2.63074i) q^{11} +(3.14876 + 1.47922i) q^{12} +(4.59382 - 4.59382i) q^{13} +(-0.775032 - 0.544329i) q^{14} +6.81792 q^{15} +(-3.07876 + 2.55367i) q^{16} -1.00000 q^{17} +(0.0297385 + 0.0208863i) q^{18} +(4.22302 - 4.22302i) q^{19} +(-3.33317 + 7.09522i) q^{20} +(-0.823704 - 0.823704i) q^{21} +(-5.18283 + 0.906271i) q^{22} -2.17156i q^{23} +(-4.27123 + 2.44175i) q^{24} +10.3631i q^{25} +(1.58254 + 9.05032i) q^{26} +(-3.65833 - 3.65833i) q^{27} +(1.25990 - 0.454511i) q^{28} +(1.35054 - 1.35054i) q^{29} +(-5.54165 + 7.89038i) q^{30} +7.26759 q^{31} +(-0.452922 - 5.63869i) q^{32} -6.47150 q^{33} +(0.812807 - 1.15730i) q^{34} +(1.85608 - 1.85608i) q^{35} +(-0.0483434 + 0.0174399i) q^{36} +(-4.69542 - 4.69542i) q^{37} +(1.45480 + 8.31980i) q^{38} +11.3006i q^{39} +(-5.50208 - 9.62453i) q^{40} -2.91709i q^{41} +(1.62279 - 0.283761i) q^{42} +(0.0731686 + 0.0731686i) q^{43} +(3.16382 - 6.73472i) q^{44} +(-0.0712193 + 0.0712193i) q^{45} +(2.51315 + 1.76506i) q^{46} +4.07818 q^{47} +(0.645854 - 6.92777i) q^{48} +6.55152 q^{49} +(-11.9932 - 8.42317i) q^{50} +(1.22998 - 1.22998i) q^{51} +(-11.7602 - 5.52469i) q^{52} +(-2.97112 - 2.97112i) q^{53} +(7.20731 - 1.26027i) q^{54} -14.5825i q^{55} +(-0.498053 + 1.82752i) q^{56} +10.3884i q^{57} +(0.465252 + 2.66071i) q^{58} +(2.37239 + 2.37239i) q^{59} +(-4.62724 - 12.8267i) q^{60} +(-1.26981 + 1.26981i) q^{61} +(-5.90715 + 8.41079i) q^{62} +0.0172087 q^{63} +(6.89380 + 4.05900i) q^{64} -25.4641 q^{65} +(5.26008 - 7.48947i) q^{66} +(9.07209 - 9.07209i) q^{67} +(0.678689 + 1.88132i) q^{68} +(2.67097 + 2.67097i) q^{69} +(0.639409 + 3.65669i) q^{70} +10.3263i q^{71} +(0.0191106 - 0.0701231i) q^{72} +4.88975i q^{73} +(9.25048 - 1.61754i) q^{74} +(-12.7464 - 12.7464i) q^{75} +(-10.8110 - 5.07875i) q^{76} +(-1.76178 + 1.76178i) q^{77} +(-13.0782 - 9.18521i) q^{78} -7.21372 q^{79} +(15.6106 + 1.45533i) q^{80} +9.07643 q^{81} +(3.37595 + 2.37103i) q^{82} +(-9.30557 + 9.30557i) q^{83} +(-0.990616 + 2.10869i) q^{84} +(2.77156 + 2.77156i) q^{85} +(-0.144150 + 0.0252061i) q^{86} +3.32227i q^{87} +(5.22252 + 9.13552i) q^{88} -16.9209i q^{89} +(-0.0245346 - 0.140310i) q^{90} +(3.07643 + 3.07643i) q^{91} +(-4.08541 + 1.47381i) q^{92} +(-8.93899 + 8.93899i) q^{93} +(-3.31478 + 4.71968i) q^{94} -23.4087 q^{95} +(7.49256 + 6.37839i) q^{96} +5.46761 q^{97} +(-5.32512 + 7.58207i) q^{98} +(0.0676007 - 0.0676007i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} + 8 q^{6} + 2 q^{8} - 6 q^{10} - 10 q^{11} - 2 q^{12} - 6 q^{13} - 22 q^{14} - 28 q^{15} + 2 q^{16} - 30 q^{17} + 8 q^{18} + 10 q^{19} - 10 q^{20} - 4 q^{21}+ \cdots + 54 q^{99}+O(q^{100}) \) 30 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 + 8 * q^6 + 2 * q^8 - 6 * q^10 - 10 * q^11 - 2 * q^12 - 6 * q^13 - 22 * q^14 - 28 * q^15 + 2 * q^16 - 30 * q^17 + 8 * q^18 + 10 * q^19 - 10 * q^20 - 4 * q^21 + 28 * q^22 + 18 * q^24 + 6 * q^26 + 4 * q^27 + 8 * q^28 - 18 * q^29 - 56 * q^30 + 48 * q^31 - 38 * q^32 - 12 * q^33 - 2 * q^34 + 16 * q^35 + 20 * q^36 + 6 * q^37 + 42 * q^38 + 10 * q^40 + 12 * q^42 + 2 * q^43 + 22 * q^44 + 42 * q^45 - 14 * q^46 - 32 * q^47 - 62 * q^48 - 38 * q^49 - 28 * q^50 + 2 * q^51 - 10 * q^52 - 6 * q^53 + 40 * q^54 + 96 * q^56 + 62 * q^58 - 14 * q^59 - 28 * q^60 + 6 * q^61 - 74 * q^62 + 84 * q^63 - 38 * q^64 - 12 * q^65 + 26 * q^67 + 2 * q^68 + 12 * q^69 + 48 * q^70 + 44 * q^72 + 42 * q^74 - 26 * q^75 - 38 * q^76 - 28 * q^77 - 56 * q^78 - 72 * q^79 - 38 * q^80 - 10 * q^81 - 76 * q^82 - 34 * q^83 + 104 * q^84 + 2 * q^85 + 34 * q^86 - 2 * q^88 + 70 * q^90 + 16 * q^91 - 40 * q^92 - 24 * q^93 - 44 * q^94 + 76 * q^95 - 126 * q^96 - 28 * q^97 - 30 * q^98 + 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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