LMFDB - Embedded newform 456.2.bk.a.61.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [456,2,Mod(61,456)] 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("456.61"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(456, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bk (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			61.14
Character	$\chi$	$=$	456.61
Dual form			456.2.bk.a.157.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.679191 - 1.24044i) q^{2} +(-0.984808 + 0.173648i) q^{3} +(-1.07740 + 1.68500i) q^{4} +(-0.782380 - 0.932405i) q^{5} +(0.884273 + 1.10366i) q^{6} +(-1.79007 + 3.10050i) q^{7} +(2.82190 + 0.192022i) q^{8} +(0.939693 - 0.342020i) q^{9} +(-0.625210 + 1.60378i) q^{10} +(5.51234 - 3.18255i) q^{11} +(0.768436 - 1.84648i) q^{12} +(-0.0530119 - 0.00934743i) q^{13} +(5.06179 + 0.114656i) q^{14} +(0.932405 + 0.782380i) q^{15} +(-1.67842 - 3.63083i) q^{16} +(-6.68599 - 2.43350i) q^{17} +(-1.06249 - 0.933339i) q^{18} +(-0.0379798 - 4.35873i) q^{19} +(2.41403 - 0.313734i) q^{20} +(1.22448 - 3.36423i) q^{21} +(-7.69170 - 4.67619i) q^{22} +(4.19254 + 3.51795i) q^{23} +(-2.81237 + 0.300914i) q^{24} +(0.610982 - 3.46505i) q^{25} +(0.0244102 + 0.0721070i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(-3.29570 - 6.35674i) q^{28} +(-1.38766 - 3.81257i) q^{29} +(0.337218 - 1.68798i) q^{30} +(2.70891 - 4.69196i) q^{31} +(-3.36387 + 4.54801i) q^{32} +(-4.87595 + 4.09141i) q^{33} +(1.52244 + 9.94640i) q^{34} +(4.29143 - 0.756696i) q^{35} +(-0.436123 + 1.95187i) q^{36} -1.63372i q^{37} +(-5.38097 + 3.00752i) q^{38} +0.0538297 q^{39} +(-2.02876 - 2.78139i) q^{40} +(-0.104577 - 0.593088i) q^{41} +(-5.00480 + 0.766056i) q^{42} +(-1.27465 - 1.51907i) q^{43} +(-0.576415 + 12.7171i) q^{44} +(-1.05410 - 0.608584i) q^{45} +(1.51629 - 7.58997i) q^{46} +(4.54888 - 1.65566i) q^{47} +(2.28340 + 3.28421i) q^{48} +(-2.90872 - 5.03804i) q^{49} +(-4.71317 + 1.59554i) q^{50} +(7.00699 + 1.23552i) q^{51} +(0.0728654 - 0.0792539i) q^{52} +(8.44443 - 10.0637i) q^{53} +(1.20842 + 0.734660i) q^{54} +(-7.28017 - 2.64977i) q^{55} +(-5.64677 + 8.40556i) q^{56} +(0.794289 + 4.28592i) q^{57} +(-3.78680 + 4.31078i) q^{58} +(1.62716 - 4.47058i) q^{59} +(-2.32288 + 0.728160i) q^{60} +(-6.19143 + 7.37866i) q^{61} +(-7.65998 - 0.173508i) q^{62} +(-0.621685 + 3.52575i) q^{63} +(7.92626 + 1.08373i) q^{64} +(0.0327599 + 0.0567418i) q^{65} +(8.38686 + 3.26950i) q^{66} +(-2.64384 - 7.26389i) q^{67} +(11.3039 - 8.64400i) q^{68} +(-4.73973 - 2.73648i) q^{69} +(-3.85334 - 4.80934i) q^{70} +(5.72109 - 4.80057i) q^{71} +(2.71740 - 0.784706i) q^{72} +(1.33009 + 7.54329i) q^{73} +(-2.02654 + 1.10961i) q^{74} +3.51850i q^{75} +(7.38536 + 4.63211i) q^{76} +22.7880i q^{77} +(-0.0365606 - 0.0667727i) q^{78} +(1.03823 + 5.88807i) q^{79} +(-2.07224 + 4.40565i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-0.664665 + 0.532542i) q^{82} +(-6.95877 - 4.01765i) q^{83} +(4.34946 + 5.68787i) q^{84} +(2.96198 + 8.13797i) q^{85} +(-1.01859 + 2.61287i) q^{86} +(2.02863 + 3.51369i) q^{87} +(16.1664 - 7.92236i) q^{88} +(2.02146 - 11.4642i) q^{89} +(-0.0389804 + 1.72089i) q^{90} +(0.123877 - 0.147631i) q^{91} +(-10.4448 + 3.27416i) q^{92} +(-1.85300 + 5.09108i) q^{93} +(-5.14330 - 4.51812i) q^{94} +(-4.03439 + 3.44560i) q^{95} +(2.52302 - 5.06304i) q^{96} +(-6.87450 - 2.50211i) q^{97} +(-4.27384 + 7.02989i) q^{98} +(4.09141 - 4.87595i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.679191	−	1.24044i	−0.480260	−	0.877126i
$2$	−0.679191	−	1.24044i	−0.480260	−	0.877126i
$3$	−0.984808	+	0.173648i	−0.568579	+	0.100256i
$3$	−0.984808	+	0.173648i	−0.568579	+	0.100256i
$4$	−1.07740	+	1.68500i	−0.538700	+	0.842498i
$5$	−0.782380	−	0.932405i	−0.349891	−	0.416984i	0.562181	−	0.827014i	$-0.309963\pi$
$5$	−0.782380	−	0.932405i	−0.349891	−	0.416984i	−0.912072	+	0.410030i	$0.865518\pi$
$6$	0.884273	+	1.10366i	0.361003	+	0.450567i
$7$	−1.79007	+	3.10050i	−0.676584	+	1.17188i	0.299420	+	0.954122i	$0.403207\pi$
$7$	−1.79007	+	3.10050i	−0.676584	+	1.17188i	−0.976003	+	0.217756i	$0.930126\pi$
$8$	2.82190	+	0.192022i	0.997693	+	0.0678899i
$9$	0.939693	−	0.342020i	0.313231	−	0.114007i
$10$	−0.625210	+	1.60378i	−0.197709	+	0.507160i
$11$	5.51234	−	3.18255i	1.66203	−	0.959575i	0.690291	−	0.723532i	$-0.257483\pi$
$11$	5.51234	−	3.18255i	1.66203	−	0.959575i	0.971743	−	0.236043i	$-0.0758507\pi$
$12$	0.768436	−	1.84648i	0.221828	−	0.533034i
$13$	−0.0530119	−	0.00934743i	−0.0147029	−	0.00259251i	0.166292	−	0.986077i	$-0.446821\pi$
$13$	−0.0530119	−	0.00934743i	−0.0147029	−	0.00259251i	−0.180995	+	0.983484i	$0.557932\pi$
$14$	5.06179	+	0.114656i	1.35282	+	0.0306431i
$15$	0.932405	+	0.782380i	0.240746	+	0.202010i
$16$	−1.67842	−	3.63083i	−0.419604	−	0.907707i
$17$	−6.68599	−	2.43350i	−1.62159	−	0.590211i	−0.637906	−	0.770114i	$-0.720199\pi$
$17$	−6.68599	−	2.43350i	−1.62159	−	0.590211i	−0.983684	+	0.179904i	$0.942421\pi$
$18$	−1.06249	−	0.933339i	−0.250431	−	0.219990i
$19$	−0.0379798	−	4.35873i	−0.00871318	−	0.999962i
$19$	−0.0379798	−	4.35873i	−0.00871318	−	0.999962i
$20$	2.41403	−	0.313734i	0.539794	−	0.0701530i
$21$	1.22448	−	3.36423i	0.267204	−	0.734136i
$22$	−7.69170	−	4.67619i	−1.63988	−	0.996967i
$23$	4.19254	+	3.51795i	0.874204	+	0.733544i	0.964979	−	0.262327i	$-0.0844899\pi$
$23$	4.19254	+	3.51795i	0.874204	+	0.733544i	−0.0907749	+	0.995871i	$0.528934\pi$
$24$	−2.81237	+	0.300914i	−0.574074	+	0.0614237i
$25$	0.610982	−	3.46505i	0.122196	−	0.693010i
$26$	0.0244102	+	0.0721070i	0.00478724	+	0.0141413i
$27$	−0.866025	+	0.500000i	−0.166667	+	0.0962250i
$28$	−3.29570	−	6.35674i	−0.622828	−	1.20131i
$29$	−1.38766	−	3.81257i	−0.257683	−	0.707977i	−0.999309	−	0.0371643i	$-0.988168\pi$
$29$	−1.38766	−	3.81257i	−0.257683	−	0.707977i	0.741626	−	0.670813i	$-0.234055\pi$
$30$	0.337218	−	1.68798i	0.0615674	−	0.308182i
$31$	2.70891	−	4.69196i	0.486534	−	0.842701i	−0.513346	−	0.858182i	$-0.671594\pi$
$31$	2.70891	−	4.69196i	0.486534	−	0.842701i	0.999880	+	0.0154802i	$0.00492769\pi$
$32$	−3.36387	+	4.54801i	−0.594654	+	0.803981i
$33$	−4.87595	+	4.09141i	−0.848794	+	0.712223i
$34$	1.52244	+	9.94640i	0.261096	+	1.70579i
$35$	4.29143	−	0.756696i	0.725385	−	0.127905i
$36$	−0.436123	+	1.95187i	−0.0726872	+	0.325312i
$37$		−	1.63372i		−	0.268582i	−0.990942	−	0.134291i	$-0.957124\pi$
$37$		−	1.63372i		−	0.268582i	0.990942	−	0.134291i	$-0.0428757\pi$
$38$	−5.38097	+	3.00752i	−0.872908	+	0.487885i
$39$	0.0538297			0.00861965
$40$	−2.02876	−	2.78139i	−0.320775	−	0.439776i
$41$	−0.104577	−	0.593088i	−0.0163323	−	0.0926248i	0.975552	−	0.219768i	$-0.0705302\pi$
$41$	−0.104577	−	0.593088i	−0.0163323	−	0.0926248i	−0.991884	+	0.127144i	$0.959419\pi$
$42$	−5.00480	+	0.766056i	−0.772257	+	0.118205i
$43$	−1.27465	−	1.51907i	−0.194382	−	0.231656i	0.660046	−	0.751225i	$-0.270537\pi$
$43$	−1.27465	−	1.51907i	−0.194382	−	0.231656i	−0.854428	+	0.519570i	$0.826092\pi$
$44$	−0.576415	+	12.7171i	−0.0868978	+	1.91718i
$45$	−1.05410	−	0.608584i	−0.157136	−	0.0907223i
$46$	1.51629	−	7.58997i	0.223565	−	1.11908i
$47$	4.54888	−	1.65566i	0.663522	−	0.241502i	0.0117659	−	0.999931i	$-0.496255\pi$
$47$	4.54888	−	1.65566i	0.663522	−	0.241502i	0.651756	+	0.758428i	$0.274033\pi$
$48$	2.28340	+	3.28421i	0.329581	+	0.474036i
$49$	−2.90872	−	5.03804i	−0.415531	−	0.719720i
$50$	−4.71317	+	1.59554i	−0.666543	+	0.225643i
$51$	7.00699	+	1.23552i	0.981174	+	0.173007i
$52$	0.0728654	−	0.0792539i	0.0101046	−	0.0109905i
$53$	8.44443	−	10.0637i	1.15993	−	1.38235i	0.249663	−	0.968333i	$-0.419680\pi$
$53$	8.44443	−	10.0637i	1.15993	−	1.38235i	0.910268	−	0.414019i	$-0.135875\pi$
$54$	1.20842	+	0.734660i	0.164445	+	0.0999746i
$55$	−7.28017	−	2.64977i	−0.981658	−	0.357294i
$56$	−5.64677	+	8.40556i	−0.754581	+	1.12324i
$57$	0.794289	+	4.28592i	0.105206	+	0.567684i
$58$	−3.78680	+	4.31078i	−0.497231	+	0.566034i
$59$	1.62716	−	4.47058i	0.211838	−	0.582020i	−0.787577	−	0.616216i	$-0.788665\pi$
$59$	1.62716	−	4.47058i	0.211838	−	0.582020i	0.999415	+	0.0341958i	$0.0108870\pi$
$60$	−2.32288	+	0.728160i	−0.299883	+	0.0940051i
$61$	−6.19143	+	7.37866i	−0.792731	+	0.944741i	−0.999433	−	0.0336634i	$-0.989283\pi$
$61$	−6.19143	+	7.37866i	−0.792731	+	0.944741i	0.206702	+	0.978404i	$0.433727\pi$
$62$	−7.65998	−	0.173508i	−0.972818	−	0.0220356i
$63$	−0.621685	+	3.52575i	−0.0783250	+	0.444203i
$64$	7.92626	+	1.08373i	0.990782	+	0.135467i
$65$	0.0327599	+	0.0567418i	0.00406337	+	0.00703796i
$66$	8.38686	+	3.26950i	1.03235	+	0.402447i
$67$	−2.64384	−	7.26389i	−0.322996	−	0.887425i	−0.989835	−	0.142223i	$-0.954575\pi$
$67$	−2.64384	−	7.26389i	−0.322996	−	0.887425i	0.666838	−	0.745202i	$-0.267647\pi$
$68$	11.3039	−	8.64400i	1.37080	−	1.04824i
$69$	−4.73973	−	2.73648i	−0.570596	−	0.329434i
$70$	−3.85334	−	4.80934i	−0.460562	−	0.574826i
$71$	5.72109	−	4.80057i	0.678969	−	0.569722i	−0.236736	−	0.971574i	$-0.576078\pi$
$71$	5.72109	−	4.80057i	0.678969	−	0.569722i	0.915705	+	0.401852i	$0.131633\pi$
$72$	2.71740	−	0.784706i	0.320248	−	0.0924785i
$73$	1.33009	+	7.54329i	0.155675	+	0.882875i	0.958166	+	0.286212i	$0.0923961\pi$
$73$	1.33009	+	7.54329i	0.155675	+	0.882875i	−0.802492	+	0.596663i	$0.796493\pi$
$74$	−2.02654	+	1.10961i	−0.235580	+	0.128989i
$75$			3.51850i			0.406282i
$76$	7.38536	+	4.63211i	0.847159	+	0.531339i
$77$			22.7880i			2.59693i
$78$	−0.0365606	−	0.0667727i	−0.00413968	−	0.00756052i
$79$	1.03823	+	5.88807i	0.116809	+	0.662459i	0.985838	+	0.167698i	$0.0536334\pi$
$79$	1.03823	+	5.88807i	0.116809	+	0.662459i	−0.869029	+	0.494761i	$0.835255\pi$
$80$	−2.07224	+	4.40565i	−0.231684	+	0.492567i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	−0.664665	+	0.532542i	−0.0733999	+	0.0588095i
$83$	−6.95877	−	4.01765i	−0.763824	−	0.440994i	0.0668431	−	0.997763i	$-0.478707\pi$
$83$	−6.95877	−	4.01765i	−0.763824	−	0.440994i	−0.830667	+	0.556770i	$0.812041\pi$
$84$	4.34946	+	5.68787i	0.474565	+	0.620598i
$85$	2.96198	+	8.13797i	0.321272	+	0.882687i
$86$	−1.01859	+	2.61287i	−0.109837	+	0.281753i
$87$	2.02863	+	3.51369i	0.217492	+	0.376707i
$88$	16.1664	−	7.92236i	1.72334	−	0.844526i
$89$	2.02146	−	11.4642i	0.214274	−	1.21521i	−0.667888	−	0.744262i	$-0.732802\pi$
$89$	2.02146	−	11.4642i	0.214274	−	1.21521i	0.882162	−	0.470946i	$-0.156087\pi$
$90$	−0.0389804	+	1.72089i	−0.00410890	+	0.181398i
$91$	0.123877	−	0.147631i	0.0129858	−	0.0154759i
$92$	−10.4448	+	3.27416i	−1.08894	+	0.341354i
$93$	−1.85300	+	5.09108i	−0.192147	+	0.527920i
$94$	−5.14330	−	4.51812i	−0.530491	−	0.466009i
$95$	−4.03439	+	3.44560i	−0.413920	+	0.353511i
$96$	2.52302	−	5.06304i	0.257504	−	0.516745i
$97$	−6.87450	−	2.50211i	−0.698000	−	0.254051i	−0.0314430	−	0.999506i	$-0.510010\pi$
$97$	−6.87450	−	2.50211i	−0.698000	−	0.254051i	−0.666557	+	0.745454i	$0.732232\pi$
$98$	−4.27384	+	7.02989i	−0.431723	+	0.710126i
$99$	4.09141	−	4.87595i	0.411202	−	0.490052i
$100$	5.18032	+	4.76275i	0.518032	+	0.476275i
$101$	−6.29814	−	1.11053i	−0.626689	−	0.110502i	−0.148721	−	0.988879i	$-0.547515\pi$
$101$	−6.29814	−	1.11053i	−0.626689	−	0.110502i	−0.477968	+	0.878377i	$0.658627\pi$
$102$	−3.22648	−	9.53092i	−0.319470	−	0.943702i
$103$	9.14418	+	15.8382i	0.901003	+	1.56058i	0.826195	+	0.563385i	$0.190501\pi$
$103$	9.14418	+	15.8382i	0.901003	+	1.56058i	0.0748082	+	0.997198i	$0.476166\pi$
$104$	−0.147800	−	0.0365570i	−0.0144929	−	0.00358471i
$105$	−4.09484	+	1.49040i	−0.399615	+	0.145448i
$106$	−18.2188	−	3.63968i	−1.76957	−	0.353517i
$107$	12.5343	+	7.23667i	1.21173	+	0.699595i	0.963137	−	0.269012i	$-0.0866971\pi$
$107$	12.5343	+	7.23667i	1.21173	+	0.699595i	0.248597	+	0.968607i	$0.420030\pi$
$108$	0.0905586	−	1.99795i	0.00871401	−	0.192253i
$109$	−6.40684	−	7.63538i	−0.613664	−	0.731336i	0.366303	−	0.930496i	$-0.380623\pi$
$109$	−6.40684	−	7.63538i	−0.613664	−	0.731336i	−0.979967	+	0.199159i	$0.936179\pi$
$110$	1.65774	+	10.8303i	0.158059	+	1.03263i
$111$	0.283693	+	1.60890i	0.0269269	+	0.152710i
$112$	14.2619	+	1.29552i	1.34762	+	0.122415i
$113$	15.0800			1.41861			0.709304	−	0.704902i	$-0.249009\pi$
$113$	15.0800			1.41861			0.709304	+	0.704902i	$0.249009\pi$
$114$	4.77697	−	3.89623i	0.447404	−	0.364915i
$115$		−	6.66152i		−	0.621190i
$116$	7.91924	+	1.76946i	0.735283	+	0.164291i
$117$	−0.0530119	+	0.00934743i	−0.00490095	+	0.000864170i
$118$	−6.65066	+	1.01798i	−0.612243	+	0.0937125i
$119$	19.5135	−	16.3737i	1.78880	−	1.50098i
$120$	2.48092	+	2.38684i	0.226476	+	0.217888i
$121$	14.7573	−	25.5603i	1.34157	−	2.32367i
$122$	13.3580	+	2.66860i	1.20937	+	0.241604i
$123$	0.205977	+	0.565918i	0.0185724	+	0.0510271i
$124$	4.98736	+	9.61962i	0.447878	+	0.863867i
$125$	−8.97934	+	5.18422i	−0.803136	+	0.463691i
$126$	4.79574	−	1.62349i	0.427239	−	0.144632i
$127$	−2.00380	+	11.3641i	−0.177808	+	1.00840i	0.757044	+	0.653364i	$0.226643\pi$
$127$	−2.00380	+	11.3641i	−0.177808	+	1.00840i	−0.934852	+	0.355037i	$0.884468\pi$
$128$	−4.03913	−	10.5681i	−0.357012	−	0.934100i
$129$	1.51907	+	1.27465i	0.133746	+	0.112227i
$130$	0.0481348	−	0.0791753i	0.00422170	−	0.00694413i
$131$	−5.14262	+	14.1292i	−0.449312	+	1.23448i	0.483891	+	0.875128i	$0.339223\pi$
$131$	−5.14262	+	14.1292i	−0.449312	+	1.23448i	−0.933204	+	0.359348i	$0.882999\pi$
$132$	−1.64065	−	12.6240i	−0.142800	−	1.09878i
$133$	13.5822	+	7.68469i	1.17773	+	0.666347i
$134$	−7.21477	+	8.21310i	−0.623261	+	0.709504i
$135$	1.14376	+	0.416296i	0.0984395	+	0.0358290i
$136$	−18.3999	−	8.15095i	−1.57778	−	0.698938i
$137$	3.09827	+	2.59975i	0.264703	+	0.222112i	0.765473	−	0.643469i	$-0.222505\pi$
$137$	3.09827	+	2.59975i	0.264703	+	0.222112i	−0.500770	+	0.865580i	$0.666950\pi$
$138$	−0.175275	+	7.73796i	−0.0149204	+	0.658699i
$139$	15.8721	+	2.79869i	1.34626	+	0.237381i	0.799881	−	0.600158i	$-0.204896\pi$
$139$	15.8721	+	2.79869i	1.34626	+	0.237381i	0.546376	+	0.837540i	$0.316007\pi$
$140$	−3.34856	+	8.04631i	−0.283005	+	0.680037i
$141$	−4.19227	+	2.42041i	−0.353053	+	0.203835i
$142$	−9.84054	−	3.83619i	−0.825800	−	0.321926i
$143$	−0.321968	+	0.117187i	−0.0269244	+	0.00979966i
$144$	−2.81901	−	2.83781i	−0.234918	−	0.236484i
$145$	−2.46918	+	4.27675i	−0.205054	+	0.355165i
$146$	8.45364	−	6.77323i	0.699629	−	0.560556i
$147$	3.73937	+	4.45641i	0.308418	+	0.367559i
$148$	2.75281	+	1.76017i	0.226280	+	0.144685i
$149$	−6.59194	+	1.16234i	−0.540033	+	0.0952223i	−0.437010	−	0.899457i	$-0.643963\pi$
$149$	−6.59194	+	1.16234i	−0.540033	+	0.0952223i	−0.103023	+	0.994679i	$0.532851\pi$
$150$	4.36450	−	2.38973i	0.356360	−	0.195121i
$151$	−11.1184			−0.904803			−0.452401	−	0.891814i	$-0.649433\pi$
$151$	−11.1184			−0.904803			−0.452401	+	0.891814i	$0.649433\pi$
$152$	0.729796	−	12.3072i	0.0591943	−	0.998246i
$153$	−7.11508			−0.575220
$154$	28.2672	−	15.4774i	2.27784	−	1.24720i
$155$	−6.49420	+	1.14510i	−0.521627	+	0.0919769i
$156$	−0.0579962	+	0.0907028i	−0.00464341	+	0.00726204i
$157$	−1.73586	−	2.06872i	−0.138537	−	0.165102i	0.692315	−	0.721595i	$-0.256591\pi$
$157$	−1.73586	−	2.06872i	−0.138537	−	0.165102i	−0.830852	+	0.556493i	$0.812146\pi$
$158$	6.59866	−	5.28698i	0.524961	−	0.420610i
$159$	−6.56860	+	11.3771i	−0.520924	+	0.902266i
$160$	6.87241	−	0.421779i	0.543312	−	0.0333446i
$161$	−18.4123	+	6.70155i	−1.45110	+	0.528156i
$162$	−1.31763	−	0.513660i	−0.103523	−	0.0403569i
$163$	−5.09870	+	2.94374i	−0.399361	+	0.230571i	−0.686208	−	0.727405i	$-0.740726\pi$
$163$	−5.09870	+	2.94374i	−0.399361	+	0.230571i	0.286847	+	0.957976i	$0.407393\pi$
$164$	1.11202	+	0.462781i	0.0868344	+	0.0361371i
$165$	7.62970	+	1.34532i	0.593971	+	0.104733i
$166$	−0.257334	+	11.3607i	−0.0199730	+	0.881762i
$167$	−13.7982	−	11.5780i	−1.06773	−	0.895935i	−0.0728882	−	0.997340i	$-0.523222\pi$
$167$	−13.7982	−	11.5780i	−1.06773	−	0.895935i	−0.994845	+	0.101405i	$0.967666\pi$
$168$	4.10137	−	9.25841i	0.316428	−	0.714302i
$169$	−12.2133	−	4.44527i	−0.939483	−	0.341944i
$170$	8.08294	−	9.20140i	0.619933	−	0.705715i
$171$	−1.52646	−	4.08288i	−0.116732	−	0.312226i
$172$	3.93293	−	0.511133i	0.299883	−	0.0389735i
$173$	1.44932	−	3.98197i	0.110190	−	0.302743i	−0.872326	−	0.488925i	$-0.837389\pi$
$173$	1.44932	−	3.98197i	0.110190	−	0.302743i	0.982515	+	0.186182i	$0.0596113\pi$
$174$	2.98071	−	4.90286i	0.225967	−	0.371685i
$175$	9.64967	+	8.09703i	0.729446	+	0.612078i
$176$	−20.8073	−	14.6727i	−1.56841	−	1.10600i
$177$	−0.826130	+	4.68522i	−0.0620958	+	0.352163i
$178$	−15.5937	+	5.27891i	−1.16880	+	0.395671i
$179$	−2.07451	+	1.19772i	−0.155056	+	0.0895216i	−0.575520	−	0.817787i	$-0.695200\pi$
$179$	−2.07451	+	1.19772i	−0.155056	+	0.0895216i	0.420465	+	0.907309i	$0.361867\pi$
$180$	2.16115	−	1.12046i	0.161082	−	0.0835143i
$181$	1.18379	+	3.25243i	0.0879903	+	0.241751i	0.975881	−	0.218303i	$-0.0700521\pi$
$181$	1.18379	+	3.25243i	0.0879903	+	0.241751i	−0.887891	+	0.460054i	$0.847830\pi$
$182$	−0.267263	−	0.0533929i	−0.0198109	−	0.00395774i
$183$	4.81608	−	8.34169i	0.356015	−	0.616636i
$184$	11.1554	+	10.7324i	0.822387	+	0.791202i
$185$	−1.52329	+	1.27819i	−0.111994	+	0.0939745i
$186$	7.57374	−	1.15927i	0.555333	−	0.0850017i
$187$	−44.6002	+	7.86422i	−3.26149	+	0.575088i
$188$	−2.11119	+	9.44864i	−0.153974	+	0.689113i
$189$		−	3.58014i		−	0.260417i
$190$	7.01419	+	2.66421i	0.508863	+	0.193282i
$191$	−23.4516			−1.69690			−0.848451	−	0.529274i	$-0.822464\pi$
$191$	−23.4516			−1.69690			−0.848451	+	0.529274i	$0.822464\pi$
$192$	−7.99403	+	0.309111i	−0.576919	+	0.0223082i
$193$	0.0645925	+	0.366322i	0.00464947	+	0.0263685i	0.987044	−	0.160448i	$-0.0512940\pi$
$193$	0.0645925	+	0.366322i	0.00464947	+	0.0263685i	−0.982395	+	0.186817i	$0.940183\pi$
$194$	1.56536	+	10.2268i	0.112387	+	0.734244i
$195$	−0.0421153	−	0.0501911i	−0.00301594	−	0.00359426i
$196$	11.6229	+	0.526819i	0.830209	+	0.0376299i
$197$	−10.3541	−	5.97796i	−0.737701	−	0.425912i	0.0835317	−	0.996505i	$-0.473380\pi$
$197$	−10.3541	−	5.97796i	−0.737701	−	0.425912i	−0.821233	+	0.570593i	$0.806713\pi$
$198$	−8.82719	−	1.76346i	−0.627321	−	0.125324i
$199$	−6.64078	+	2.41705i	−0.470752	+	0.171340i	−0.566493	−	0.824066i	$-0.691700\pi$
$199$	−6.64078	+	2.41705i	−0.470752	+	0.171340i	0.0957408	+	0.995406i	$0.469478\pi$
$200$	2.38949	−	9.66070i	0.168963	−	0.683115i
$201$	3.86503	+	6.69444i	0.272619	+	0.472189i
$202$	2.90009	+	8.56676i	0.204049	+	0.602755i
$203$	14.3049	+	2.52234i	1.00401	+	0.177033i
$204$	−9.63118	+	10.4756i	−0.674317	+	0.733438i
$205$	−0.471179	+	0.561529i	−0.0329086	+	0.0392189i
$206$	13.4357	−	22.1000i	0.936112	−	1.53978i
$207$	5.14291	+	1.87186i	0.357457	+	0.130104i
$208$	0.0550372	+	0.208166i	0.00381614	+	0.0144337i
$209$	−14.0813	−	23.9060i	−0.974021	−	1.65361i
$210$	4.62993	+	4.06715i	0.319496	+	0.280660i
$211$	0.876074	−	2.40699i	0.0603114	−	0.165704i	−0.905877	−	0.423540i	$-0.860787\pi$
$211$	0.876074	−	2.40699i	0.0603114	−	0.165704i	0.966189	+	0.257836i	$0.0830094\pi$
$212$	7.85921	+	25.0714i	0.539773	+	1.72191i
$213$	−4.80057	+	5.72109i	−0.328929	+	0.392003i
$214$	0.463516	−	20.4631i	0.0316853	−	1.39883i
$215$	−0.419125	+	2.37698i	−0.0285841	+	0.162108i
$216$	−2.53985	+	1.24466i	−0.172815	+	0.0846880i
$217$	9.69827	+	16.7979i	0.658362	+	1.14032i
$218$	−5.11979	+	13.1332i	−0.346756	+	0.889493i
$219$	−2.61976	−	7.19772i	−0.177027	−	0.486377i
$220$	12.3085	−	9.41220i	0.829839	−	0.634570i
$221$	0.331690	+	0.191501i	0.0223119	+	0.0128818i
$222$	1.80307	−	1.44466i	0.121014	−	0.0969589i
$223$	−2.26800	+	1.90308i	−0.151876	+	0.127439i	−0.715560	−	0.698552i	$-0.753828\pi$
$223$	−2.26800	+	1.90308i	−0.151876	+	0.127439i	0.563683	+	0.825991i	$0.309384\pi$
$224$	−8.07950	−	18.5709i	−0.539834	−	1.24082i
$225$	−0.610982	−	3.46505i	−0.0407321	−	0.231003i
$226$	−10.2422	−	18.7059i	−0.681301	−	1.24430i
$227$		−	5.25834i		−	0.349008i	−0.984656	−	0.174504i	$-0.944168\pi$
$227$		−	5.25834i		−	0.349008i	0.984656	−	0.174504i	$-0.0558323\pi$
$228$	−8.07752	−	3.27928i	−0.534947	−	0.217176i
$229$			9.57101i			0.632470i	0.948681	+	0.316235i	$0.102419\pi$
$229$			9.57101i			0.632470i	−0.948681	+	0.316235i	$0.897581\pi$
$230$	−8.26324	+	4.52444i	−0.544862	+	0.298333i
$231$	−3.95709	−	22.4418i	−0.260358	−	1.47656i
$232$	−3.18375	−	11.0252i	−0.209024	−	0.723838i
$233$	4.60373	−	3.86299i	0.301601	−	0.253073i	−0.479409	−	0.877591i	$-0.659149\pi$
$233$	4.60373	−	3.86299i	0.301601	−	0.253073i	0.781010	+	0.624518i	$0.214705\pi$
$234$	0.0476002	+	0.0594096i	0.00311172	+	0.00388373i
$235$	−5.10270	−	2.94604i	−0.332863	−	0.192179i
$236$	5.77981	+	7.55836i	0.376233	+	0.492008i
$237$	−2.04490	−	5.61833i	−0.132831	−	0.364950i
$238$	−33.5640	−	13.0845i	−2.17563	−	0.848139i
$239$	12.1784	+	21.0936i	0.787754	+	1.36443i	0.927340	+	0.374220i	$0.122090\pi$
$239$	12.1784	+	21.0936i	0.787754	+	1.36443i	−0.139586	+	0.990210i	$0.544577\pi$
$240$	1.27573	−	4.69856i	0.0823478	−	0.303291i
$241$	−1.23034	+	6.97758i	−0.0792529	+	0.449466i	0.919196	+	0.393799i	$0.128839\pi$
$241$	−1.23034	+	6.97758i	−0.0792529	+	0.449466i	−0.998449	+	0.0556665i	$0.982272\pi$
$242$	−41.7291	−	0.945218i	−2.68245	−	0.0607609i
$243$	−0.642788	+	0.766044i	−0.0412348	+	0.0491418i
$244$	−5.76235	−	18.3823i	−0.368897	−	1.17681i
$245$	−2.42177	+	6.65377i	−0.154721	+	0.425094i
$246$	0.562092	−	0.639870i	0.0358377	−	0.0407966i
$247$	−0.0387296	+	0.231420i	−0.00246430	+	0.0147249i
$248$	8.54522	−	12.7201i	0.542622	−	0.807726i
$249$	7.55070	+	2.74823i	0.478506	+	0.174162i
$250$	12.5294	+	7.61729i	0.792430	+	0.481760i
$251$	−0.492247	+	0.586637i	−0.0310704	+	0.0370282i	−0.781356	−	0.624086i	$-0.785472\pi$
$251$	−0.492247	+	0.586637i	−0.0310704	+	0.0370282i	0.750285	+	0.661114i	$0.229916\pi$
$252$	−5.27107	−	4.84619i	−0.332046	−	0.305281i
$253$	34.3068	+	6.04921i	2.15685	+	0.380310i
$254$	15.4575	−	5.23279i	0.969888	−	0.328334i
$255$	−4.33012	−	7.49999i	−0.271163	−	0.469668i
$256$	−10.3658	+	12.1881i	−0.647865	+	0.761755i
$257$	1.22031	−	0.444156i	0.0761208	−	0.0277057i	−0.303679	−	0.952774i	$-0.598215\pi$
$257$	1.22031	−	0.444156i	0.0761208	−	0.0277057i	0.379800	+	0.925069i	$0.375993\pi$
$258$	0.549394	−	2.75005i	0.0342038	−	0.171210i
$259$	5.06534	+	2.92448i	0.314745	+	0.181718i
$260$	−0.130905	−	0.00593338i	−0.00811840	−	0.000367973i
$261$	−2.60795	−	3.10804i	−0.161428	−	0.192383i
$262$	21.0193	−	3.21731i	1.29858	−	0.198766i
$263$	−4.82009	−	27.3361i	−0.297220	−	1.68562i	−0.658042	−	0.752981i	$-0.728615\pi$
$263$	−4.82009	−	27.3361i	−0.297220	−	1.68562i	0.360823	−	0.932634i	$-0.382496\pi$
$264$	−14.5451	+	10.6093i	−0.895189	+	0.652955i
$265$	−15.9902			−0.982268
$266$	0.307509	−	22.0673i	0.0188546	−	1.35304i
$267$			11.6411i			0.712424i
$268$	15.0881	+	3.37126i	0.921652	+	0.205933i
$269$	10.3763	−	1.82963i	0.632656	−	0.111554i	0.151882	−	0.988399i	$-0.451467\pi$
$269$	10.3763	−	1.82963i	0.632656	−	0.111554i	0.480774	+	0.876844i	$0.340356\pi$
$270$	−0.260442	−	1.70152i	−0.0158500	−	0.103551i
$271$	3.78339	−	3.17464i	0.229825	−	0.192846i	−0.520602	−	0.853799i	$-0.674292\pi$
$271$	3.78339	−	3.17464i	0.229825	−	0.192846i	0.750427	+	0.660954i	$0.229848\pi$
$272$	2.38625	+	28.3601i	0.144688	+	1.71958i
$273$	−0.0963591	+	0.166899i	−0.00583192	+	0.0101012i
$274$	1.12053	−	5.60895i	0.0676940	−	0.338849i
$275$	−7.65976	−	21.0450i	−0.461901	−	1.26906i
$276$	9.71755	−	5.03813i	0.584928	−	0.303260i
$277$	0.567859	−	0.327853i	0.0341193	−	0.0196988i	−0.482843	−	0.875707i	$-0.660396\pi$
$277$	0.567859	−	0.327853i	0.0341193	−	0.0196988i	0.516963	+	0.856008i	$0.327063\pi$
$278$	−7.30859	−	21.5893i	−0.438340	−	1.29484i
$279$	0.940793	−	5.33550i	0.0563238	−	0.319428i
$280$	12.2553	−	1.31127i	0.732395	−	0.0783635i
$281$	7.81713	+	6.55935i	0.466331	+	0.391298i	0.845454	−	0.534048i	$-0.179330\pi$
$281$	7.81713	+	6.55935i	0.466331	+	0.391298i	−0.379123	+	0.925346i	$0.623774\pi$
$282$	5.84973	+	3.55636i	0.348346	+	0.211778i
$283$	−1.94793	+	5.35189i	−0.115792	+	0.318137i	−0.984028	−	0.178016i	$-0.943032\pi$
$283$	−1.94793	+	5.35189i	−0.115792	+	0.318137i	0.868235	+	0.496153i	$0.165254\pi$
$284$	1.92502	+	14.8121i	0.114229	+	0.878939i
$285$	3.37478	−	4.09382i	0.199904	−	0.242497i
$286$	0.364042	+	0.319791i	0.0215262	+	0.0189097i
$287$	2.02607	+	0.737429i	0.119595	+	0.0435290i
$288$	−1.60550	+	5.42424i	−0.0946049	+	0.319626i
$289$	25.7577	+	21.6133i	1.51516	+	1.27137i
$290$	6.98211	+	0.158154i	0.410004	+	0.00928710i
$291$	7.20455	+	1.27036i	0.422338	+	0.0744696i
$292$	−14.1434	−	5.88596i	−0.827682	−	0.344450i
$293$	11.7846	−	6.80384i	0.688464	−	0.397485i	−0.114573	−	0.993415i	$-0.536550\pi$
$293$	11.7846	−	6.80384i	0.688464	−	0.397485i	0.803036	+	0.595930i	$0.203216\pi$
$294$	2.98818	−	7.66523i	0.174274	−	0.447045i
$295$	−5.44145	+	1.98053i	−0.316813	+	0.115311i
$296$	0.313710	−	4.61020i	0.0182340	−	0.267962i
$297$	−3.18255	+	5.51234i	−0.184670	+	0.319858i
$298$	5.91900	+	7.38748i	0.342878	+	0.427945i
$299$	−0.189371	−	0.225683i	−0.0109516	−	0.0130516i
$300$	−5.92866	−	3.79084i	−0.342291	−	0.218864i
$301$	6.99157	−	1.23280i	0.402988	−	0.0710576i
$302$	7.55151	+	13.7918i	0.434541	+	0.793626i
$303$	6.39530			0.367401
$304$	−15.7621	+	7.45367i	−0.904017	+	0.427497i
$305$	11.7240			0.671311
$306$	4.83249	+	8.82585i	0.276255	+	0.504541i
$307$	3.04647	−	0.537175i	0.173871	−	0.0306582i	−0.0860346	−	0.996292i	$-0.527420\pi$
$307$	3.04647	−	0.537175i	0.173871	−	0.0306582i	0.259906	+	0.965634i	$0.416308\pi$
$308$	−38.3976	−	24.5518i	−2.18791	−	1.39897i
$309$	−11.7555	−	14.0097i	−0.668749	−	0.796984i
$310$	5.83124	+	7.27795i	0.331192	+	0.413360i
$311$	8.97418	−	15.5437i	0.508879	−	0.881405i	−0.491068	−	0.871121i	$-0.663393\pi$
$311$	8.97418	−	15.5437i	0.508879	−	0.881405i	0.999947	−	0.0102834i	$-0.00327336\pi$
$312$	0.151902	+	0.0103365i	0.00859977	+	0.000585188i
$313$	−5.46877	+	1.99047i	−0.309113	+	0.112508i	−0.491919	−	0.870641i	$-0.663704\pi$
$313$	−5.46877	+	1.99047i	−0.309113	+	0.112508i	0.182806	+	0.983149i	$0.441482\pi$
$314$	−1.38715	+	3.55830i	−0.0782815	+	0.200806i
$315$	3.77382	−	2.17882i	0.212631	−	0.122762i
$316$	−11.0400	−	4.59440i	−0.621046	−	0.258455i
$317$	−30.5658	−	5.38958i	−1.71675	−	0.302709i	−0.773253	−	0.634098i	$-0.781372\pi$
$317$	−30.5658	−	5.38958i	−1.71675	−	0.302709i	−0.943494	+	0.331389i	$0.892483\pi$
$318$	18.5740	+	0.420725i	1.04158	+	0.0235931i
$319$	−19.7830	−	16.5999i	−1.10763	−	0.929416i
$320$	−5.19087	−	8.23837i	−0.290178	−	0.460539i
$321$	−13.6005	−	4.95017i	−0.759105	−	0.276292i
$322$	20.8184	+	18.2878i	1.16016	+	1.01914i
$323$	−10.3530	+	29.2349i	−0.576059	+	1.62667i
$324$	0.257757	+	1.98332i	0.0143199	+	0.110184i
$325$	−0.0647786	+	0.177978i	−0.00359327	+	0.00987243i
$326$	7.11453	+	4.32530i	0.394038	+	0.239556i
$327$	7.63538	+	6.40684i	0.422237	+	0.354299i
$328$	−0.181221	−	1.69372i	−0.0100063	−	0.0935199i
$329$	−3.00946	+	17.0675i	−0.165917	+	0.940963i
$330$	−3.51322	−	10.3779i	−0.193397	−	0.571287i
$331$	25.4444	−	14.6903i	1.39855	−	0.807453i	0.404308	−	0.914623i	$-0.367512\pi$
$331$	25.4444	−	14.6903i	1.39855	−	0.807453i	0.994241	+	0.107170i	$0.0341789\pi$
$332$	14.2671	−	7.39687i	0.783008	−	0.405956i
$333$	−0.558765	−	1.53520i	−0.0306202	−	0.0841282i
$334$	−4.99031	+	24.9795i	−0.273058	+	1.36682i
$335$	−4.70440	+	8.14825i	−0.257029	+	0.445187i
$336$	−14.2702	+	1.20071i	−0.778501	+	0.0655039i
$337$	15.3382	−	12.8703i	0.835524	−	0.701088i	−0.121028	−	0.992649i	$-0.538619\pi$
$337$	15.3382	−	12.8703i	0.835524	−	0.701088i	0.956552	+	0.291561i	$0.0941747\pi$
$338$	2.78104	+	18.1691i	0.151268	+	0.988267i
$339$	−14.8509	+	2.61862i	−0.806591	+	0.142224i
$340$	−16.9037	−	3.77693i	−0.916730	−	0.204833i
$341$		−	34.4849i		−	1.86746i
$342$	−4.02782	+	4.66655i	−0.217800	+	0.252338i
$343$	−4.23377			−0.228602
$344$	−3.30524	−	4.53142i	−0.178207	−	0.244318i
$345$	1.15676	+	6.56032i	0.0622779	+	0.353196i
$346$	−5.92377	+	0.906718i	−0.318464	+	0.0487455i
$347$	8.08388	+	9.63400i	0.433966	+	0.517180i	0.938062	−	0.346467i	$-0.112619\pi$
$347$	8.08388	+	9.63400i	0.433966	+	0.517180i	−0.504096	+	0.863647i	$0.668174\pi$
$348$	−8.10619	−	0.367420i	−0.434538	−	0.0196958i
$349$	12.2870	+	7.09390i	0.657708	+	0.379728i	0.791403	−	0.611295i	$-0.209351\pi$
$349$	12.2870	+	7.09390i	0.657708	+	0.379728i	−0.133695	+	0.991023i	$0.542684\pi$
$350$	3.48995	−	17.4693i	0.186546	−	0.933773i
$351$	0.0505834	−	0.0184108i	0.00269994	−	0.000982698i
$352$	−4.06856	+	35.7759i	−0.216855	+	1.90686i
$353$	0.127600	+	0.221009i	0.00679144	+	0.0117631i	0.869401	−	0.494107i	$-0.164505\pi$
$353$	0.127600	+	0.221009i	0.00679144	+	0.0117631i	−0.862610	+	0.505870i	$0.831172\pi$
$354$	6.37285	−	2.15739i	0.338713	−	0.114664i
$355$	−8.95214	−	1.57850i	−0.475130	−	0.0837783i
$356$	17.1393	+	15.7577i	0.908380	+	0.835158i
$357$	−16.3737	+	19.5135i	−0.866590	+	1.03276i
$358$	2.89469	+	1.75983i	0.152989	+	0.0930099i
$359$	25.0639	+	9.12251i	1.32282	+	0.481468i	0.904362	−	0.426767i	$-0.140348\pi$
$359$	25.0639	+	9.12251i	1.32282	+	0.481468i	0.418461	+	0.908235i	$0.362570\pi$
$360$	−2.85770	−	1.91977i	−0.150614	−	0.101181i
$361$	−18.9971	+	0.331088i	−0.999848	+	0.0174257i
$362$	3.23044	−	3.67744i	0.169788	−	0.193282i
$363$	−10.0946	+	27.7346i	−0.529827	+	1.45569i
$364$	0.115292	+	0.367789i	0.00604294	+	0.0192774i
$365$	5.99277	−	7.14190i	0.313676	−	0.373824i
$366$	−13.6184	−	0.308475i	−0.711847	−	0.0161242i
$367$	−2.53927	+	14.4009i	−0.132549	+	0.751721i	0.843987	+	0.536364i	$0.180203\pi$
$367$	−2.53927	+	14.4009i	−0.132549	+	0.751721i	−0.976535	+	0.215357i	$0.930909\pi$
$368$	5.73627	−	21.1270i	0.299024	−	1.10132i
$369$	−0.301119	−	0.521553i	−0.0156756	−	0.0271510i
$370$	2.62013	+	1.02142i	0.136214	+	0.0531010i
$371$	16.0862	+	44.1966i	0.835156	+	2.29457i
$372$	−6.58202	−	8.60743i	−0.341262	−	0.446274i
$373$	−8.56227	−	4.94343i	−0.443337	−	0.255961i	0.261675	−	0.965156i	$-0.415725\pi$
$373$	−8.56227	−	4.94343i	−0.443337	−	0.255961i	−0.705012	+	0.709195i	$0.749059\pi$
$374$	40.0471	+	49.9827i	2.07079	+	2.58454i
$375$	7.94269	−	6.66471i	0.410159	−	0.344164i
$376$	13.1544	−	3.79862i	0.678387	−	0.195899i
$377$	0.0379249	+	0.215083i	0.00195323	+	0.0110773i
$378$	−4.44097	+	2.43160i	−0.228419	+	0.125068i
$379$			10.0112i			0.514239i	0.966380	+	0.257119i	$0.0827734\pi$
$379$			10.0112i			0.514239i	−0.966380	+	0.257119i	$0.917227\pi$
$380$	−1.45917	−	10.5102i	−0.0748537	−	0.539163i
$381$		−	11.5394i		−	0.591181i
$382$	15.9281	+	29.0904i	0.814954	+	1.48840i
$383$	0.742791	+	4.21258i	0.0379548	+	0.215253i	0.997886	−	0.0649818i	$-0.0206989\pi$
$383$	0.742791	+	4.21258i	0.0379548	+	0.215253i	−0.959932	+	0.280234i	$0.909588\pi$
$384$	5.81290	+	9.70619i	0.296638	+	0.495317i
$385$	21.2476	−	17.8289i	1.08288	−	0.908644i
$386$	0.410532	−	0.328926i	0.0208955	−	0.0167419i
$387$	−1.71733	−	0.991501i	−0.0872968	−	0.0504008i
$388$	11.6226	−	8.88772i	0.590050	−	0.451206i
$389$	2.23914	+	6.15197i	0.113529	+	0.311917i	0.983425	−	0.181318i	$-0.0580363\pi$
$389$	2.23914	+	6.15197i	0.113529	+	0.311917i	−0.869896	+	0.493235i	$0.835814\pi$
$390$	−0.0336549	+	0.0863310i	−0.00170418	+	0.00437154i
$391$	−19.4703	−	33.7235i	−0.984655	−	1.70547i
$392$	−7.24069	−	14.7754i	−0.365710	−	0.746270i
$393$	2.61097	−	14.8076i	0.131706	−	0.746943i
$394$	−0.382895	+	16.9039i	−0.0192899	+	0.851606i
$395$	4.67778	−	5.57476i	0.235364	−	0.280496i
$396$	3.80787	+	12.1474i	0.191353	+	0.610428i
$397$	10.7647	−	29.5758i	0.540265	−	1.48437i	−0.306225	−	0.951959i	$-0.599066\pi$
$397$	10.7647	−	29.5758i	0.540265	−	1.48437i	0.846489	−	0.532406i	$-0.178712\pi$
$398$	7.50856	+	6.59588i	0.376370	+	0.330621i
$399$	−14.7103	−	5.20941i	−0.736437	−	0.260797i
$400$	−13.6065	+	3.59743i	−0.680324	+	0.179871i
$401$	27.3233	+	9.94488i	1.36446	+	0.496623i	0.917431	−	0.397895i	$-0.130259\pi$
$401$	27.3233	+	9.94488i	1.36446	+	0.496623i	0.447031	+	0.894519i	$0.352481\pi$
$402$	5.67898	−	9.34115i	0.283242	−	0.465894i
$403$	−0.187462	+	0.223409i	−0.00933815	+	0.0111288i
$404$	8.65687	−	9.41585i	0.430695	−	0.468456i
$405$	−1.19868	−	0.211359i	−0.0595627	−	0.0105025i
$406$	−6.58693	−	19.4576i	−0.326904	−	0.965662i
$407$	−5.19940	−	9.00563i	−0.257725	−	0.446392i
$408$	19.5358	+	4.83201i	0.967165	+	0.239220i
$409$	22.6665	−	8.24992i	1.12078	−	0.407932i	0.285846	−	0.958275i	$-0.407725\pi$
$409$	22.6665	−	8.24992i	1.12078	−	0.407932i	0.834939	+	0.550343i	$0.185503\pi$
$410$	1.01657	+	0.203086i	0.0502046	+	0.0100297i
$411$	−3.50264	−	2.02225i	−0.172772	−	0.0997502i
$412$	−36.5392	−	1.65617i	−1.80016	−	0.0815936i
$413$	10.9483	+	13.0477i	0.538730	+	0.642034i
$414$	−1.17107	−	7.65084i	−0.0575550	−	0.376018i
$415$	1.69833	+	9.63171i	0.0833678	+	0.472802i
$416$	0.220838	−	0.209655i	0.0108275	−	0.0102792i
$417$	−16.1170			−0.789252
$418$	−20.0901	+	33.7037i	−0.982640	+	1.64850i
$419$		−	30.7096i		−	1.50026i	−0.661290	−	0.750130i	$-0.729991\pi$
$419$		−	30.7096i		−	1.50026i	0.661290	−	0.750130i	$-0.270009\pi$
$420$	1.90047	−	8.50554i	0.0927332	−	0.415028i
$421$	−18.6776	+	3.29337i	−0.910291	+	0.160509i	−0.609135	−	0.793066i	$-0.708483\pi$
$421$	−18.6776	+	3.29337i	−0.910291	+	0.160509i	−0.301156	+	0.953575i	$0.597372\pi$
$422$	−3.58076	+	0.548087i	−0.174309	+	0.0266804i
$423$	3.70828	−	3.11162i	0.180303	−	0.151292i
$424$	25.7618	−	26.7772i	1.25110	−	1.30041i
$425$	−12.5172	+	21.6804i	−0.607174	+	1.05166i
$426$	10.3572	+	2.06912i	0.501808	+	0.100249i
$427$	−11.7944	−	32.4048i	−0.570771	−	1.56818i
$428$	−25.6982	+	13.3234i	−1.24217	+	0.644011i
$429$	0.296728	−	0.171316i	0.0143262	−	0.00827121i
$430$	3.23317	−	1.09452i	0.155917	−	0.0527824i
$431$	3.80203	−	21.5624i	0.183137	−	1.03862i	−0.745188	−	0.666855i	$-0.767640\pi$
$431$	3.80203	−	21.5624i	0.183137	−	1.03862i	0.928325	−	0.371769i	$-0.121249\pi$
$432$	3.26897	+	2.30518i	0.157278	+	0.110908i
$433$	15.0024	+	12.5885i	0.720967	+	0.604963i	0.927653	−	0.373444i	$-0.121823\pi$
$433$	15.0024	+	12.5885i	0.720967	+	0.604963i	−0.206686	+	0.978407i	$0.566268\pi$
$434$	14.2499	−	23.4391i	0.684016	−	1.12511i
$435$	1.68902	−	4.64054i	0.0809823	−	0.222497i
$436$	19.7683	−	2.56914i	0.946730	−	0.123039i
$437$	15.1746	−	18.4078i	0.725899	−	0.880562i
$438$	−7.14906	+	8.13829i	−0.341595	+	0.388862i
$439$	38.4864	+	14.0079i	1.83685	+	0.668560i	0.990777	+	0.135500i	$0.0432642\pi$
$439$	38.4864	+	14.0079i	1.83685	+	0.668560i	0.846077	+	0.533060i	$0.178958\pi$
$440$	−20.0351	−	8.87533i	−0.955137	−	0.423115i
$441$	−4.45641	−	3.73937i	−0.212210	−	0.178065i
$442$	0.0122659	−	0.541509i	0.000583428	−	0.0257569i
$443$	−0.820741	−	0.144719i	−0.0389946	−	0.00687580i	0.154117	−	0.988053i	$-0.450747\pi$
$443$	−0.820741	−	0.144719i	−0.0389946	−	0.00687580i	−0.193111	+	0.981177i	$0.561858\pi$
$444$	−3.01664	−	1.25541i	−0.143163	−	0.0595791i
$445$	−12.2709	+	7.08459i	−0.581695	+	0.335842i
$446$	3.90106	+	1.52077i	0.184721	+	0.0720106i
$447$	6.28996	−	2.28936i	0.297505	−	0.108283i
$448$	−17.5487	+	22.6354i	−0.829097	+	1.06942i
$449$	−8.74227	+	15.1421i	−0.412573	+	0.714598i	−0.995170	−	0.0981635i	$-0.968703\pi$
$449$	−8.74227	+	15.1421i	−0.412573	+	0.714598i	0.582597	+	0.812761i	$0.302037\pi$
$450$	−3.88322	+	3.11132i	−0.183057	+	0.146669i
$451$	−2.46400	−	2.93648i	−0.116025	−	0.138274i
$452$	−16.2472	+	25.4098i	−0.764205	+	1.19517i
$453$	10.9495	−	1.93069i	0.514452	−	0.0907118i
$454$	−6.52268	+	3.57142i	−0.306124	+	0.167615i
$455$	−0.234570			−0.0109968
$456$	1.41842	+	12.2470i	0.0664234	+	0.573517i
$457$	4.84691			0.226729			0.113364	−	0.993553i	$-0.463837\pi$
$457$	4.84691			0.226729			0.113364	+	0.993553i	$0.463837\pi$
$458$	11.8723	−	6.50054i	0.554756	−	0.303750i
$459$	7.00699	−	1.23552i	0.327058	−	0.0576692i
$460$	11.2246	+	7.17712i	0.523351	+	0.334635i
$461$	3.76126	+	4.48250i	0.175179	+	0.208771i	0.846489	−	0.532407i	$-0.178712\pi$
$461$	3.76126	+	4.48250i	0.175179	+	0.208771i	−0.671309	+	0.741177i	$0.734268\pi$
$462$	−25.1501	+	20.1508i	−1.17009	+	0.937500i
$463$	−19.0669	+	33.0248i	−0.886112	+	1.53479i	−0.0416783	+	0.999131i	$0.513270\pi$
$463$	−19.0669	+	33.0248i	−0.886112	+	1.53479i	−0.844434	+	0.535660i	$0.820063\pi$
$464$	−11.5137	+	11.4375i	−0.534511	+	0.530971i
$465$	6.19670	−	2.25541i	0.287365	−	0.104592i
$466$	−7.91864	−	3.08697i	−0.366824	−	0.143001i
$467$	−22.5274	+	13.0062i	−1.04244	+	0.601854i	−0.920524	−	0.390686i	$-0.872238\pi$
$467$	−22.5274	+	13.0062i	−1.04244	+	0.601854i	−0.121918	+	0.992540i	$0.538905\pi$
$468$	0.0413647	−	0.0993958i	0.00191208	−	0.00459457i
$469$	27.2543	+	4.80567i	1.25849	+	0.221905i
$470$	−0.188697	+	8.33053i	−0.00870395	+	0.384259i
$471$	2.06872	+	1.73586i	0.0953217	+	0.0799844i
$472$	5.45013	−	12.3031i	0.250863	−	0.566296i
$473$	−11.8608	−	4.31698i	−0.545360	−	0.198495i
$474$	−5.58034	+	6.35250i	−0.256314	+	0.291780i
$475$	−15.1264	−	2.53150i	−0.694048	−	0.116153i
$476$	6.56585	+	50.5211i	0.300945	+	2.31563i
$477$	4.49318	−	12.3449i	0.205729	−	0.565235i
$478$	17.8940	−	29.4332i	0.818450	−	1.34624i
$479$	−5.67394	−	4.76100i	−0.259249	−	0.217536i	0.503894	−	0.863766i	$-0.331900\pi$
$479$	−5.67394	−	4.76100i	−0.259249	−	0.217536i	−0.763143	+	0.646230i	$0.776345\pi$
$480$	−6.69476	+	1.60875i	−0.305573	+	0.0734292i
$481$	−0.0152711	+	0.0866067i	−0.000696302	+	0.00394892i
$482$	9.49093	−	3.21295i	0.432300	−	0.146346i
$483$	16.9689	−	9.79700i	0.772112	−	0.445779i
$484$	27.1696	+	52.4046i	1.23498	+	2.38203i
$485$	3.04549	+	8.36742i	0.138289	+	0.379945i
$486$	1.38681	+	0.277052i	0.0629070	+	0.0125673i
$487$	−10.3643	+	17.9514i	−0.469649	+	0.813456i	−0.999398	−	0.0346984i	$-0.988953\pi$
$487$	−10.3643	+	17.9514i	−0.469649	+	0.813456i	0.529749	+	0.848155i	$0.322286\pi$
$488$	−18.8885	+	19.6330i	−0.855041	+	0.888742i
$489$	4.51007	−	3.78440i	0.203952	−	0.171136i
$490$	9.89847	−	1.51510i	0.447167	−	0.0684454i
$491$	15.5963	−	2.75005i	0.703852	−	0.124108i	0.189744	−	0.981834i	$-0.439234\pi$
$491$	15.5963	−	2.75005i	0.703852	−	0.124108i	0.514108	+	0.857726i	$0.328123\pi$
$492$	−1.17549	−	0.262650i	−0.0529952	−	0.0118412i
$493$			28.8677i			1.30014i
$494$	0.313368	−	0.109136i	0.0140991	−	0.00491028i
$495$	−7.74740			−0.348220
$496$	−21.5824	−	1.96051i	−0.969078	−	0.0880293i
$497$	4.64297	+	26.3316i	0.208266	+	1.18113i
$498$	−1.71934	−	11.2328i	−0.0770455	−	0.503354i
$499$	11.4788	+	13.6799i	0.513860	+	0.612394i	0.959117	−	0.283008i	$-0.0913324\pi$
$499$	11.4788	+	13.6799i	0.513860	+	0.612394i	−0.445258	+	0.895402i	$0.646888\pi$
$500$	0.938952	−	20.7156i	0.0419912	−	0.926431i
$501$	15.5990	+	9.00611i	0.696913	+	0.402363i
$502$	1.06202	+	0.212166i	0.0474003	+	0.00946945i
$503$	−28.3747	+	10.3276i	−1.26517	+	0.460483i	−0.885500	−	0.464640i	$-0.846184\pi$
$503$	−28.3747	+	10.3276i	−1.26517	+	0.460483i	−0.379667	+	0.925123i	$0.623962\pi$
$504$	−2.43136	+	9.82995i	−0.108301	+	0.437861i
$505$	3.89208	+	6.74128i	0.173195	+	0.299983i
$506$	−15.7971	−	46.6642i	−0.702268	−	2.07447i
$507$	12.7996	+	2.25692i	0.568452	+	0.100233i
$508$	−16.9895	−	15.6201i	−0.753789	−	0.693028i
$509$	16.1642	−	19.2638i	0.716467	−	0.853852i	−0.277815	−	0.960635i	$-0.589610\pi$
$509$	16.1642	−	19.2638i	0.716467	−	0.853852i	0.994282	+	0.106782i	$0.0340548\pi$
$510$	−6.36234	+	10.4652i	−0.281729	+	0.463407i
$511$	−25.7689	−	9.37911i	−1.13995	−	0.414907i
$512$	22.1590	+	4.58020i	0.979299	+	0.202418i
$513$	2.21226	+	3.75578i	0.0976736	+	0.165822i
$514$	−1.37977	−	1.21206i	−0.0608592	−	0.0534616i
$515$	7.61337	−	20.9176i	0.335485	−	0.921738i
$516$	−3.78442	+	1.18631i	−0.166600	+	0.0522245i
$517$	19.8058	−	23.6036i	0.871056	−	1.03808i
$518$	0.187316	−	8.26955i	0.00823019	−	0.363343i
$519$	−0.735838	+	4.17314i	−0.0322997	+	0.183181i
$520$	0.0815496	+	0.166410i	0.00357618	+	0.00729758i
$521$	12.0231	+	20.8246i	0.526741	+	0.912342i	0.999514	+	0.0311583i	$0.00991959\pi$
$521$	12.0231	+	20.8246i	0.526741	+	0.912342i	−0.472773	+	0.881184i	$0.656747\pi$
$522$	−2.08405	+	5.34597i	−0.0912164	+	0.233987i
$523$	−5.99868	−	16.4812i	−0.262304	−	0.720675i	−0.999011	−	0.0444624i	$-0.985843\pi$
$523$	−5.99868	−	16.4812i	−0.262304	−	0.720675i	0.736707	−	0.676212i	$-0.236380\pi$
$524$	−18.2670	−	23.8881i	−0.797998	−	1.04356i
$525$	−10.9091	−	6.29837i	−0.476112	−	0.274884i
$526$	−30.6351	+	24.5455i	−1.33575	+	1.07023i
$527$	−29.5296	+	24.7783i	−1.28633	+	1.07936i
$528$	23.0391	+	10.8367i	1.00265	+	0.471605i
$529$	1.20744	+	6.84772i	0.0524973	+	0.297727i
$530$	10.8604	+	19.8349i	0.471744	+	0.861573i
$531$		−	4.75750i		−	0.206458i
$532$	−27.5822	+	14.6065i	−1.19584	+	0.633271i
$533$			0.0324183i			0.00140419i
$534$	14.4401	−	7.90653i	0.624885	−	0.342149i
$535$	−3.05907	−	17.3488i	−0.132255	−	0.750056i
$536$	−6.06583	−	21.0057i	−0.262004	−	0.907306i
$537$	1.83501	−	1.53975i	0.0791865	−	0.0664453i
$538$	−9.31706	−	11.6286i	−0.401687	−	0.501344i
$539$	−32.0677	−	18.5143i	−1.38125	−	0.797466i
$540$	−1.93375	+	1.47872i	−0.0832153	+	0.0636339i
$541$	7.15711	+	19.6640i	0.307708	+	0.845421i	0.993103	+	0.117249i	$0.0374076\pi$
$541$	7.15711	+	19.6640i	0.307708	+	0.845421i	−0.685394	+	0.728172i	$0.740370\pi$
$542$	−6.50761	−	2.53690i	−0.279526	−	0.108969i
$543$	−1.73058	−	2.99746i	−0.0742664	−	0.128633i
$544$	33.5584	−	22.2219i	1.43880	−	0.952757i
$545$	−2.10667	+	11.9475i	−0.0902400	+	0.511776i
$546$	0.272475	+	0.00617190i	0.0116608	+	0.000264133i
$547$	−2.13431	+	2.54357i	−0.0912566	+	0.108755i	−0.809740	−	0.586788i	$-0.800392\pi$
$547$	−2.13431	+	2.54357i	−0.0912566	+	0.108755i	0.718484	+	0.695544i	$0.244836\pi$
$548$	−7.71864	+	2.41959i	−0.329724	+	0.103360i
$549$	−3.29439	+	9.05127i	−0.140601	+	0.386299i
$550$	−20.9027	+	23.7951i	−0.891295	+	1.01462i
$551$	−16.5653	+	6.19326i	−0.705705	+	0.263842i
$552$	−12.8496	−	8.63222i	−0.546914	−	0.367412i
$553$	−20.1144	−	7.32105i	−0.855352	−	0.311323i
$554$	−0.792368	−	0.481722i	−0.0336645	−	0.0204664i
$555$	1.27819	−	1.52329i	0.0542562	−	0.0646600i
$556$	−21.8164	+	23.7292i	−0.925222	+	1.00634i
$557$	17.3845	+	3.06536i	0.736607	+	0.129884i	0.529351	−	0.848403i	$-0.322436\pi$
$557$	17.3845	+	3.06536i	0.736607	+	0.129884i	0.207256	+	0.978287i	$0.433547\pi$
$558$	−7.25737	+	2.45682i	−0.307229	+	0.104006i
$559$	0.0533722	+	0.0924434i	0.00225740	+	0.00390994i
$560$	−9.95025	−	14.3114i	−0.420475	−	0.604768i
$561$	42.5570	−	15.4895i	1.79676	−	0.653966i
$562$	2.82718	−	14.1518i	0.119257	−	0.596956i
$563$	−16.1289	−	9.31200i	−0.679750	−	0.392454i	0.120011	−	0.992773i	$-0.461707\pi$
$563$	−16.1289	−	9.31200i	−0.679750	−	0.392454i	−0.799761	+	0.600319i	$0.795040\pi$
$564$	0.438378	−	9.67170i	0.0184590	−	0.407252i
$565$	−11.7983	−	14.0607i	−0.496359	−	0.591537i
$566$	7.96173	−	1.21866i	0.334657	−	0.0512240i
$567$	0.621685	+	3.52575i	0.0261083	+	0.148068i
$568$	17.0662	−	12.4482i	0.716081	−	0.522313i
$569$	−29.5469			−1.23867			−0.619336	−	0.785126i	$-0.712598\pi$
$569$	−29.5469			−1.23867			−0.619336	+	0.785126i	$0.712598\pi$
$570$	−7.37027	−	1.40574i	−0.308706	−	0.0588798i
$571$			21.8770i			0.915525i	0.889075	+	0.457762i	$0.151349\pi$
$571$			21.8770i			0.915525i	−0.889075	+	0.457762i	$0.848651\pi$
$572$	0.149430	−	0.668773i	0.00624796	−	0.0279628i
$573$	23.0954	−	4.07234i	0.964823	−	0.170124i
$574$	−0.461348	−	3.01408i	−0.0192563	−	0.125805i
$575$	14.7514	−	12.3779i	0.615178	−	0.516195i
$576$	7.81890	−	1.69256i	0.325788	−	0.0705235i
$577$	15.0507	−	26.0685i	0.626567	−	1.08525i	−0.361668	−	0.932307i	$-0.617793\pi$
$577$	15.0507	−	26.0685i	0.626567	−	1.08525i	0.988236	−	0.152939i	$-0.0488740\pi$
$578$	9.31568	−	46.6306i	0.387481	−	1.93958i
$579$	−0.127222	−	0.349541i	−0.00528718	−	0.0145264i
$580$	−4.54600	−	8.76833i	−0.188762	−	0.364085i
$581$	24.9134	−	14.3838i	1.03358	−	0.596739i
$582$	−3.31745	−	9.79965i	−0.137513	−	0.406208i
$583$	14.5204	−	82.3492i	0.601373	−	3.41056i
$584$	2.30489	+	21.5418i	0.0953772	+	0.891407i
$585$	0.0501911	+	0.0421153i	0.00207515	+	0.00174125i
$586$	−16.4438	−	9.99703i	−0.679286	−	0.412973i
$587$	−4.56129	+	12.5320i	−0.188264	+	0.517252i	−0.997534	−	0.0701852i	$-0.977641\pi$
$587$	−4.56129	+	12.5320i	−0.188264	+	0.517252i	0.809270	+	0.587438i	$0.199863\pi$
$588$	−11.5378	+	1.49949i	−0.475812	+	0.0618377i
$589$	−20.5539	−	11.6292i	−0.846909	−	0.479173i
$590$	6.15251	+	5.40466i	0.253295	+	0.222506i
$591$	11.2349	+	4.08917i	0.462142	+	0.168206i
$592$	−5.93176	+	2.74206i	−0.243794	+	0.112698i
$593$	−4.09736	−	3.43809i	−0.168258	−	0.141186i	0.554770	−	0.832004i	$-0.312806\pi$
$593$	−4.09736	−	3.43809i	−0.168258	−	0.141186i	−0.723029	+	0.690818i	$0.757251\pi$
$594$	8.99931	+	0.203846i	0.369246	+	0.00836389i
$595$	−30.5339	−	5.38395i	−1.25177	−	0.220720i
$596$	5.14363	−	12.3597i	0.210691	−	0.506273i
$597$	6.12018	−	3.53349i	0.250482	−	0.144616i
$598$	−0.151328	+	0.388185i	−0.00618828	+	0.0158741i
$599$	14.4585	−	5.26245i	0.590756	−	0.215018i	−0.0293057	−	0.999570i	$-0.509330\pi$
$599$	14.4585	−	5.26245i	0.590756	−	0.215018i	0.620062	+	0.784553i	$0.287107\pi$
$600$	−0.675629	+	9.92887i	−0.0275824	+	0.405344i
$601$	6.84618	−	11.8579i	0.279262	−	0.483695i	−0.691940	−	0.721955i	$-0.743244\pi$
$601$	6.84618	−	11.8579i	0.279262	−	0.483695i	0.971201	+	0.238260i	$0.0765770\pi$
$602$	−6.27783	−	7.83534i	−0.255865	−	0.319345i
$603$	−4.96879	−	5.92158i	−0.202345	−	0.241145i
$604$	11.9790	−	18.7345i	0.487417	−	0.762294i
$605$	−35.3784	+	6.23816i	−1.43834	+	0.253617i
$606$	−4.34363	−	7.93301i	−0.176448	−	0.322257i
$607$	6.35400			0.257901			0.128950	−	0.991651i	$-0.458839\pi$
$607$	6.35400			0.257901			0.128950	+	0.991651i	$0.458839\pi$
$608$	19.9513	+	14.4895i	0.809132	+	0.587627i
$609$	−14.5256			−0.588606
$610$	−7.96280	−	14.5429i	−0.322404	−	0.588825i
$611$	−0.256621	+	0.0452492i	−0.0103818	+	0.00183059i
$612$	7.66579	−	11.9889i	0.309871	−	0.484621i
$613$	−4.25695	−	5.07324i	−0.171937	−	0.204906i	0.673194	−	0.739466i	$-0.264922\pi$
$613$	−4.25695	−	5.07324i	−0.171937	−	0.204906i	−0.845131	+	0.534560i	$0.820477\pi$
$614$	−2.73547	−	3.41413i	−0.110395	−	0.137783i
$615$	0.366512	−	0.634818i	0.0147792	−	0.0255983i
$616$	−4.37579	+	64.3054i	−0.176306	+	2.59094i
$617$	−20.6318	+	7.50935i	−0.830604	+	0.302315i	−0.722107	−	0.691782i	$-0.756826\pi$
$617$	−20.6318	+	7.50935i	−0.830604	+	0.302315i	−0.108497	+	0.994097i	$0.534604\pi$
$618$	−9.39399	+	24.0973i	−0.377882	+	0.969337i
$619$	−28.7267	+	16.5854i	−1.15462	+	0.666622i	−0.950009	−	0.312221i	$-0.898927\pi$
$619$	−28.7267	+	16.5854i	−1.15462	+	0.666622i	−0.204613	+	0.978843i	$0.565594\pi$
$620$	5.06736	−	12.1764i	0.203510	−	0.489017i
$621$	−5.38982	−	0.950371i	−0.216286	−	0.0381371i
$622$	−25.3763	−	0.574806i	−1.01750	−	0.0230476i
$623$	31.9263	+	26.7893i	1.27910	+	1.07329i
$624$	−0.0903487	−	0.195446i	−0.00361684	−	0.00782412i
$625$	−4.67250	−	1.70065i	−0.186900	−	0.0680260i
$626$	6.18341	+	5.43180i	0.247139	+	0.217098i
$627$	18.0186	+	21.0976i	0.719592	+	0.842556i
$628$	5.35601	−	0.696080i	0.213728	−	0.0277766i
$629$	−3.97566	+	10.9230i	−0.158520	+	0.435530i
$630$	−5.26585	−	3.20138i	−0.209796	−	0.127546i
$631$	25.0470	+	21.0170i	0.997107	+	0.836672i	0.986581	−	0.163272i	$-0.0522050\pi$
$631$	25.0470	+	21.0170i	0.997107	+	0.836672i	0.0105260	+	0.999945i	$0.496649\pi$
$632$	1.79913	+	16.8149i	0.0715656	+	0.668861i
$633$	−0.444794	+	2.52255i	−0.0176790	+	0.100263i
$634$	14.0745	+	41.5757i	0.558971	+	1.65118i
$635$	12.1637	−	7.02269i	0.482700	−	0.278687i
$636$	−12.0934	−	23.3258i	−0.479535	−	0.924928i
$637$	0.107104	+	0.294265i	0.00424361	+	0.0116592i
$638$	−7.15482	+	35.8142i	−0.283262	+	1.41790i
$639$	3.73418	−	6.46779i	0.147722	−	0.255862i
$640$	−6.69364	+	12.0344i	−0.264589	+	0.475702i
$641$	10.3080	−	8.64943i	0.407141	−	0.341632i	−0.416105	−	0.909317i	$-0.636605\pi$
$641$	10.3080	−	8.64943i	0.407141	−	0.341632i	0.823246	+	0.567685i	$0.192161\pi$
$642$	3.09691	+	20.2327i	0.122225	+	0.798523i
$643$	40.6218	−	7.16272i	1.60197	−	0.282470i	0.699957	−	0.714185i	$-0.253202\pi$
$643$	40.6218	−	7.16272i	1.60197	−	0.282470i	0.902010	+	0.431715i	$0.142091\pi$
$644$	8.54540	−	38.2450i	0.336736	−	1.50706i
$645$		−	2.41365i		−	0.0950372i
$646$	43.2959	−	7.01367i	1.70345	−	0.275949i
$647$	−11.9278			−0.468930			−0.234465	−	0.972125i	$-0.575334\pi$
$647$	−11.9278			−0.468930			−0.234465	+	0.972125i	$0.575334\pi$
$648$	2.28513	−	1.66679i	0.0897684	−	0.0654775i
$649$	−5.25840	−	29.8219i	−0.206410	−	1.17061i
$650$	0.264768	−	0.0405266i	0.0103851	−	0.00158958i
$651$	−12.4679	−	14.8586i	−0.488654	−	0.582355i
$652$	0.533162	−	11.7629i	0.0208802	−	0.460670i
$653$	−5.20649	−	3.00597i	−0.203746	−	0.117633i	0.394656	−	0.918829i	$-0.370864\pi$
$653$	−5.20649	−	3.00597i	−0.203746	−	0.117633i	−0.598401	+	0.801196i	$0.704197\pi$
$654$	2.76145	−	13.8227i	0.107981	−	0.540511i
$655$	17.1976	−	6.25943i	0.671967	−	0.244576i
$656$	−1.97788	+	1.37515i	−0.0772232	+	0.0536907i
$657$	3.82983	+	6.63346i	0.149416	+	0.258796i
$658$	23.2153	−	7.85903i	0.905027	−	0.306377i
$659$	−15.6571	−	2.76077i	−0.609914	−	0.107544i	−0.139844	−	0.990174i	$-0.544660\pi$
$659$	−15.6571	−	2.76077i	−0.609914	−	0.107544i	−0.470070	+	0.882629i	$0.655771\pi$
$660$	−10.4871	+	11.4066i	−0.408210	+	0.443999i
$661$	17.7491	−	21.1526i	0.690360	−	0.822739i	−0.301039	−	0.953612i	$-0.597333\pi$
$661$	17.7491	−	21.1526i	0.690360	−	0.822739i	0.991399	+	0.130872i	$0.0417778\pi$
$662$	−35.5041	−	21.5848i	−1.37991	−	0.838916i
$663$	−0.359905	−	0.130995i	−0.0139775	−	0.00508741i
$664$	−18.8655	−	12.6736i	−0.732123	−	0.491832i
$665$	−3.46122	−	18.6765i	−0.134220	−	0.724243i
$666$	−1.52482	+	1.73581i	−0.0590854	+	0.0672612i
$667$	7.59464	−	20.8661i	0.294066	−	0.807938i
$668$	34.3751	−	10.7757i	1.33001	−	0.416923i
$669$	1.90308	−	2.26800i	0.0735771	−	0.0876858i
$670$	13.3026	+	0.301321i	0.513925	+	0.0116411i
$671$	−10.6463	+	60.3782i	−0.410996	+	2.33088i
$672$	11.1816	+	16.8858i	0.431338	+	0.651384i
$673$	4.35698	+	7.54652i	0.167949	+	0.290897i	0.937699	−	0.347449i	$-0.112952\pi$
$673$	4.35698	+	7.54652i	0.167949	+	0.290897i	−0.769749	+	0.638346i	$0.779619\pi$
$674$	−26.3824	−	10.2848i	−1.01621	−	0.396155i
$675$	1.20340	+	3.30631i	0.0463188	+	0.127260i
$676$	20.6489	−	15.7900i	0.794187	−	0.607307i
$677$	−14.9007	−	8.60294i	−0.572681	−	0.330638i	0.185538	−	0.982637i	$-0.440597\pi$
$677$	−14.9007	−	8.60294i	−0.572681	−	0.330638i	−0.758220	+	0.651999i	$0.773930\pi$
$678$	13.3348	+	16.6432i	0.512122	+	0.639178i
$679$	20.0636	−	16.8354i	0.769972	−	0.646083i
$680$	6.79574	+	23.5333i	0.260605	+	0.902461i
$681$	0.913102	+	5.17846i	0.0349901	+	0.198439i
$682$	−42.7766	+	23.4218i	−1.63800	+	0.896868i
$683$		−	15.8039i		−	0.604721i	−0.953194	−	0.302361i	$-0.902225\pi$
$683$		−	15.8039i		−	0.604721i	0.953194	−	0.302361i	$-0.0977747\pi$
$684$	8.52425	+	1.82681i	0.325933	+	0.0698499i
$685$		−	4.92283i		−	0.188092i
$686$	2.87554	+	5.25175i	0.109788	+	0.200513i
$687$	−1.66199	−	9.42560i	−0.0634088	−	0.359609i
$688$	−3.37608	+	7.17766i	−0.128712	+	0.273646i
$689$	−0.541725	+	0.454561i	−0.0206381	+	0.0173174i
$690$	7.35204	−	5.89060i	0.279887	−	0.224251i
$691$	26.1559	+	15.1011i	0.995016	+	0.574473i	0.906770	−	0.421626i	$-0.138541\pi$
$691$	26.1559	+	15.1011i	0.995016	+	0.574473i	0.0882460	+	0.996099i	$0.471874\pi$
$692$	5.14810	+	6.73227i	0.195701	+	0.255922i
$693$	7.79395	+	21.4137i	0.296068	+	0.813439i
$694$	6.45993	−	16.5709i	0.245216	−	0.629023i
$695$	−9.80854	−	16.9889i	−0.372059	−	0.644425i
$696$	5.04989	+	10.3048i	0.191415	+	0.390603i
$697$	−0.744077	+	4.21987i	−0.0281839	+	0.159839i
$698$	0.454372	−	20.0594i	0.0171982	−	0.759261i
$699$	−3.86299	+	4.60373i	−0.146112	+	0.174129i
$700$	−24.0400	+	7.53589i	−0.908627	+	0.284830i
$701$	−15.5397	+	42.6950i	−0.586926	+	1.61257i	0.189165	+	0.981945i	$0.439422\pi$
$701$	−15.5397	+	42.6950i	−0.586926	+	1.61257i	−0.776091	+	0.630621i	$0.782800\pi$
$702$	−0.0571934	−	0.0502414i	−0.00215862	−	0.00189624i
$703$	−7.12095	+	0.0620485i	−0.268572	+	0.00234020i
$704$	47.1413	−	19.2518i	1.77670	−	0.725580i
$705$	5.53675	+	2.01521i	0.208526	+	0.0758973i
$706$	0.187485	−	0.308387i	0.00705608	−	0.0116063i
$707$	14.7173	−	17.5394i	0.553502	−	0.659638i
$708$	−7.00450	−	6.43988i	−0.263245	−	0.242026i
$709$	−6.74244	−	1.18887i	−0.253218	−	0.0446491i	0.0455983	−	0.998960i	$-0.485481\pi$
$709$	−6.74244	−	1.18887i	−0.253218	−	0.0446491i	−0.298816	+	0.954311i	$0.596592\pi$
$710$	4.12216	+	12.1767i	0.154702	+	0.456985i
$711$	2.98945	+	5.17788i	0.112113	+	0.194186i
$712$	7.90573	−	31.9628i	0.296280	−	1.19786i
$713$	27.8633	−	10.1414i	1.04349	−	0.379799i
$714$	35.3262	+	7.05734i	1.32205	+	0.264114i
$715$	0.361167	+	0.208520i	0.0135069	+	0.00779821i
$716$	0.216927	−	4.78595i	0.00810695	−	0.178859i
$717$	−15.6562	−	18.6584i	−0.584693	−	0.696810i
$718$	−5.70720	−	37.2863i	−0.212991	−	1.39151i
$719$	2.30757	+	13.0869i	0.0860578	+	0.488058i	0.997123	+	0.0757964i	$0.0241499\pi$
$719$	2.30757	+	13.0869i	0.0860578	+	0.488058i	−0.911066	+	0.412262i	$0.864739\pi$
$720$	−0.440448	+	4.84871i	−0.0164145	+	0.180701i
$721$	−65.4750			−2.43842
$722$	13.3134	+	23.3400i	0.495472	+	0.868624i
$723$		−	7.08522i		−	0.263502i
$724$	−6.75575	−	1.50949i	−0.251075	−	0.0560999i
$725$	−14.0586	+	2.47891i	−0.522123	+	0.0920644i
$726$	41.2593	−	6.31533i	1.53128	−	0.234384i
$727$	29.4884	−	24.7437i	1.09366	−	0.917693i	0.0966807	−	0.995315i	$-0.469177\pi$
$727$	29.4884	−	24.7437i	1.09366	−	0.917693i	0.996983	+	0.0776228i	$0.0247330\pi$
$728$	0.377917	−	0.392812i	0.0140065	−	0.0145586i
$729$	0.500000	−	0.866025i	0.0185185	−	0.0320750i
$730$	−12.9294	−	2.58298i	−0.478537	−	0.0956003i
$731$	4.82563	+	13.2583i	0.178483	+	0.490377i
$732$	8.86686	+	17.1024i	0.327729	+	0.632123i
$733$	−10.2689	+	5.92878i	−0.379292	+	0.218984i	−0.677510	−	0.735513i	$-0.736941\pi$
$733$	−10.2689	+	5.92878i	−0.379292	+	0.218984i	0.298218	+	0.954498i	$0.403608\pi$
$734$	19.5882	−	6.63114i	0.723012	−	0.244760i
$735$	1.22957	−	6.97322i	0.0453532	−	0.257211i
$736$	−30.1028	+	7.23372i	−1.10961	+	0.266638i
$737$	−37.6914	−	31.6269i	−1.38838	−	1.16499i
$738$	−0.442440	+	0.727755i	−0.0162864	+	0.0267890i
$739$	2.56191	−	7.03879i	0.0942414	−	0.258926i	−0.883611	−	0.468222i	$-0.844895\pi$
$739$	2.56191	−	7.03879i	0.0942414	−	0.258926i	0.977852	+	0.209296i	$0.0671171\pi$
$740$	−0.512554	−	3.94386i	−0.0188418	−	0.144979i
$741$	−0.00204444	−	0.234629i	−7.51045e−5	−	0.00861933i
$742$	43.8978	−	49.9720i	1.61154	−	1.83453i
$743$	10.3736	+	3.77567i	0.380569	+	0.138516i	0.525219	−	0.850967i	$-0.323983\pi$
$743$	10.3736	+	3.77567i	0.380569	+	0.138516i	−0.144650	+	0.989483i	$0.546206\pi$
$744$	−6.20658	+	14.0107i	−0.227544	+	0.513657i
$745$	6.24117	+	5.23697i	0.228659	+	0.191868i
$746$	−0.316632	+	13.9785i	−0.0115927	+	0.511791i
$747$	−7.91322	−	1.39531i	−0.289529	−	0.0510519i
$748$	34.8011	−	83.6240i	1.27245	−	3.05760i
$749$	−44.8745	+	25.9083i	−1.63968	+	0.946669i
$750$	−13.6618	−	5.32585i	−0.498858	−	0.194473i
$751$	−32.4725	+	11.8190i	−1.18494	+	0.431282i	−0.857944	−	0.513744i	$-0.828258\pi$
$751$	−32.4725	+	11.8190i	−1.18494	+	0.431282i	−0.326995	+	0.945026i	$0.606036\pi$
$752$	−13.6463	−	13.7373i	−0.497630	−	0.500948i
$753$	0.382900	−	0.663203i	0.0139537	−	0.0241685i
$754$	0.241040	−	0.193126i	0.00877816	−	0.00703324i
$755$	8.69882	+	10.3669i	0.316583	+	0.377288i
$756$	6.03252	+	3.85725i	0.219401	+	0.140287i
$757$	−17.1406	+	3.02236i	−0.622987	+	0.109849i	−0.476227	−	0.879323i	$-0.657996\pi$
$757$	−17.1406	+	3.02236i	−0.622987	+	0.109849i	−0.146761	+	0.989172i	$0.546885\pi$
$758$	12.4183	−	6.79949i	0.451052	−	0.246969i
$759$	−34.8360			−1.26447
$760$	−12.0463	+	8.94845i	−0.436964	+	0.324595i
$761$	37.6324			1.36417			0.682087	−	0.731271i	$-0.261073\pi$
$761$	37.6324			1.36417			0.682087	+	0.731271i	$0.261073\pi$
$762$	−14.3140	+	7.83745i	−0.518541	+	0.283921i
$763$	35.1422	−	6.19651i	1.27223	−	0.224329i
$764$	25.2668	−	39.5159i	0.914121	−	1.42964i
$765$	5.56670	+	6.63413i	0.201264	+	0.239858i
$766$	4.72097	−	3.78253i	0.170575	−	0.136668i
$767$	−0.128047	+	0.221784i	−0.00462352	+	0.00800817i
$768$	8.09192	−	13.8029i	0.291992	−	0.498070i
$769$	11.3349	−	4.12556i	0.408747	−	0.148772i	−0.129460	−	0.991585i	$-0.541324\pi$
$769$	11.3349	−	4.12556i	0.408747	−	0.148772i	0.538206	+	0.842813i	$0.319102\pi$
$770$	−36.5469	−	14.2473i	−1.31706	−	0.513436i
$771$	−1.12464	+	0.649313i	−0.0405031	+	0.0233844i
$772$	−0.686843	−	0.285838i	−0.0247200	−	0.0102875i
$773$	12.6202	+	2.22528i	0.453917	+	0.0800378i	0.395932	−	0.918280i	$-0.370421\pi$
$773$	12.6202	+	2.22528i	0.453917	+	0.0800378i	0.0579847	+	0.998317i	$0.481533\pi$
$774$	−0.0635066	+	2.80367i	−0.00228270	+	0.100776i
$775$	−14.6028	−	12.2532i	−0.524548	−	0.440148i
$776$	−18.9187	−	8.38077i	−0.679142	−	0.300852i
$777$	−5.49622	−	2.00046i	−0.197176	−	0.0717661i
$778$	6.11038	−	6.95588i	0.219068	−	0.249380i
$779$	−2.58114	+	0.478351i	−0.0924790	+	0.0171387i
$780$	0.129947	−	0.0168882i	0.00465284	−	0.000604695i
$781$	16.2586	−	44.6700i	0.581777	−	1.59842i
$782$	−28.6081	+	47.0565i	−1.02302	+	1.68274i
$783$	3.10804	+	2.60795i	0.111072	+	0.0932007i
$784$	−13.4102	+	19.0170i	−0.478937	+	0.679178i
$785$	−0.570780	+	3.23706i	−0.0203720	+	0.115536i
$786$	−20.1413	+	6.81840i	−0.718417	+	0.243204i
$787$	−14.4541	+	8.34506i	−0.515232	+	0.297469i	−0.734982	−	0.678087i	$-0.762809\pi$
$787$	−14.4541	+	8.34506i	−0.515232	+	0.297469i	0.219750	+	0.975556i	$0.429476\pi$
$788$	21.2284	−	11.0060i	0.756230	−	0.392073i
$789$	9.49372	+	26.0838i	0.337986	+	0.928608i
$790$	−10.0923	−	2.01620i	−0.359067	−	0.0717330i
$791$	−26.9943	+	46.7555i	−0.959807	+	1.66244i
$792$	12.4818	−	12.9738i	0.443523	−	0.461004i
$793$	0.397191	−	0.333283i	0.0141047	−	0.0118352i
$794$	−43.9983	+	6.73458i	−1.56144	+	0.239001i
$795$	15.7472	−	2.77666i	0.558497	−	0.0984781i
$796$	3.08207	−	13.7938i	0.109241	−	0.488909i
$797$			29.2527i			1.03618i	0.855325	+	0.518092i	$0.173358\pi$
$797$			29.2527i			1.03618i	−0.855325	+	0.518092i	$0.826642\pi$
$798$	3.52912	+	21.7855i	0.124929	+	0.771198i
$799$	−34.4428			−1.21850
$800$	13.7038	+	14.4347i	0.484502	+	0.510345i
$801$	−2.02146	−	11.4642i	−0.0714246	−	0.405069i
$802$	−6.22168	−	40.6475i	−0.219695	−	1.43531i
$803$	31.3388	+	37.3481i	1.10592	+	1.31799i
$804$	−15.4443	−	0.700024i	−0.544678	−	0.0246880i
$805$	20.6540	+	11.9246i	0.727958	+	0.420287i
$806$	0.404448	+	0.0807991i	0.0142461	+	0.00284603i
$807$	−9.90098	+	3.60366i	−0.348531	+	0.126855i
$808$	−17.5595	−	4.34319i	−0.617741	−	0.152793i
$809$	−1.46413	−	2.53595i	−0.0514761	−	0.0891592i	0.839139	−	0.543917i	$-0.183059\pi$
$809$	−1.46413	−	2.53595i	−0.0514761	−	0.0891592i	−0.890615	+	0.454758i	$0.849726\pi$
$810$	0.551951	+	1.63044i	0.0193936	+	0.0572879i
$811$	8.39251	+	1.47983i	0.294701	+	0.0519637i	0.319044	−	0.947740i	$-0.396638\pi$
$811$	8.39251	+	1.47983i	0.294701	+	0.0519637i	−0.0243430	+	0.999704i	$0.507749\pi$
$812$	−19.6622	+	21.3861i	−0.690009	+	0.750505i
$813$	−3.17464	+	3.78339i	−0.111340	+	0.132689i
$814$	−7.63959	+	12.5661i	−0.267767	+	0.440442i
$815$	6.73388	+	2.45093i	0.235878	+	0.0858524i
$816$	−7.27468	−	27.5149i	−0.254665	−	0.963214i
$817$	−6.57280	+	5.61355i	−0.229953	+	0.196393i
$818$	−25.6284	−	22.5132i	−0.896076	−	0.787156i
$819$	0.0659135	−	0.181096i	0.00230320	−	0.00632800i
$820$	−0.438526	−	1.39893i	−0.0153140	−	0.0488526i
$821$	9.95381	−	11.8625i	0.347390	−	0.414004i	−0.563851	−	0.825877i	$-0.690681\pi$
$821$	9.95381	−	11.8625i	0.347390	−	0.414004i	0.911241	+	0.411873i	$0.135125\pi$
$822$	−0.129527	+	5.71832i	−0.00451778	+	0.199449i
$823$	8.78243	−	49.8076i	0.306136	−	1.73619i	−0.311971	−	0.950092i	$-0.600989\pi$
$823$	8.78243	−	49.8076i	0.306136	−	1.73619i	0.618108	−	0.786094i	$-0.287900\pi$
$824$	22.7627	+	46.4497i	0.792976	+	1.61815i
$825$	11.1978	+	19.3952i	0.389858	+	0.675254i
$826$	8.74892	−	22.4426i	0.304414	−	0.780878i
$827$	−5.12484	−	14.0804i	−0.178208	−	0.489623i	0.818139	−	0.575021i	$-0.195006\pi$
$827$	−5.12484	−	14.0804i	−0.178208	−	0.489623i	−0.996347	+	0.0853977i	$0.972784\pi$
$828$	−8.69505	+	6.64902i	−0.302174	+	0.231070i
$829$	−41.6975	−	24.0741i	−1.44821	−	0.836127i	−0.449839	−	0.893110i	$-0.648519\pi$
$829$	−41.6975	−	24.0741i	−1.44821	−	0.836127i	−0.998375	+	0.0569831i	$0.981852\pi$
$830$	10.7941	−	8.64845i	0.374669	−	0.300192i
$831$	−0.502301	+	0.421480i	−0.0174246	+	0.0146210i
$832$	−0.410056	−	0.131541i	−0.0142161	−	0.00456036i
$833$	7.18756	+	40.7627i	0.249034	+	1.41234i
$834$	10.9465	+	19.9922i	0.379047	+	0.692274i
$835$			21.9239i			0.758707i
$836$	55.4526	+	2.02944i	1.91787	+	0.0701898i
$837$			5.41781i			0.187267i
$838$	−38.0935	+	20.8576i	−1.31592	+	0.720515i
$839$	−4.15201	−	23.5472i	−0.143343	−	0.812940i	−0.968682	−	0.248303i	$-0.920127\pi$
$839$	−4.15201	−	23.5472i	−0.143343	−	0.812940i	0.825339	−	0.564637i	$-0.190984\pi$
$840$	−11.8414	+	3.41946i	−0.408568	+	0.117983i
$841$	9.60517	−	8.05970i	0.331213	−	0.277921i
$842$	16.7709	+	20.9317i	0.577963	+	0.721354i
$843$	−8.83739	−	5.10227i	−0.304376	−	0.175731i
$844$	3.11189	+	4.06948i	0.107116	+	0.140077i
$845$	5.41064	+	14.8656i	0.186132	+	0.511393i
$846$	−6.37841	−	2.48653i	−0.219294	−	0.0854887i
$847$	52.8331	+	91.5097i	1.81537	+	3.14431i
$848$	−50.7127	−	13.7692i	−1.74148	−	0.472837i
$849$	0.988989	−	5.60884i	0.0339420	−	0.192495i
$850$	35.3949	+	0.801740i	1.21404	+	0.0274995i
$851$	5.74736	−	6.84943i	0.197017	−	0.234796i
$852$	−4.46788	−	14.2528i	−0.153067	−	0.488294i
$853$	−6.53123	+	17.9444i	−0.223625	+	0.614405i	−0.999872	−	0.0160247i	$-0.994899\pi$
$853$	−6.53123	+	17.9444i	−0.223625	+	0.614405i	0.776247	+	0.630429i	$0.217121\pi$
$854$	−32.1857	+	36.6393i	−1.10137	+	1.25377i
$855$	−2.61262	+	4.61765i	−0.0893497	+	0.157920i
$856$	33.9809	+	22.8280i	1.16144	+	0.780245i
$857$	−27.2072	−	9.90261i	−0.929380	−	0.338267i	−0.167416	−	0.985886i	$-0.553542\pi$
$857$	−27.2072	−	9.90261i	−0.929380	−	0.338267i	−0.761964	+	0.647620i	$0.775765\pi$
$858$	−0.414042	−	0.251718i	−0.0141352	−	0.00859351i
$859$	−18.5756	+	22.1376i	−0.633792	+	0.755324i	−0.983376	−	0.181581i	$-0.941878\pi$
$859$	−18.5756	+	22.1376i	−0.633792	+	0.755324i	0.349584	+	0.936905i	$0.386323\pi$
$860$	−3.55363	−	3.26718i	−0.121178	−	0.111410i
$861$	−2.12334	−	0.374402i	−0.0723633	−	0.0127596i
$862$	−29.3292	+	9.92877i	−0.998958	+	0.338175i
$863$	0.408611	+	0.707734i	0.0139093	+	0.0240916i	0.872896	−	0.487906i	$-0.162239\pi$
$863$	0.408611	+	0.707734i	0.0139093	+	0.0240916i	−0.858987	+	0.511997i	$0.828906\pi$
$864$	0.639197	−	5.62063i	0.0217459	−	0.191218i
$865$	−4.84672	+	1.76406i	−0.164794	+	0.0599799i
$866$	5.42583	−	27.1595i	0.184377	−	0.922919i
$867$	−29.1195	−	16.8122i	−0.988952	−	0.570971i
$868$	−38.7533	−	1.75652i	−1.31537	−	0.0596203i
$869$	24.4621	+	29.1528i	0.829821	+	0.988942i
$870$	−6.90350	+	1.05668i	−0.234051	+	0.0358248i
$871$	0.0722563	+	0.409786i	0.00244831	+	0.0138851i
$872$	−16.6133	−	22.7765i	−0.562598	−	0.771311i
$873$	−7.31569			−0.247599
$874$	−33.1402	−	6.32086i	−1.12098	−	0.213806i
$875$		−	37.1205i		−	1.25490i
$876$	14.9507	+	3.34055i	0.505136	+	0.112867i
$877$	−3.72820	+	0.657381i	−0.125892	+	0.0221982i	−0.236239	−	0.971695i	$-0.575915\pi$
$877$	−3.72820	+	0.657381i	−0.125892	+	0.0221982i	0.110347	+	0.993893i	$0.464804\pi$
$878$	−8.76358	−	57.2542i	−0.295756	−	1.93224i
$879$	−10.4241	+	8.74685i	−0.351596	+	0.295024i
$880$	2.59832	+	30.8805i	0.0875892	+	1.04098i
$881$	14.7339	−	25.5199i	0.496398	−	0.859786i	−0.503594	−	0.863941i	$-0.667989\pi$
$881$	14.7339	−	25.5199i	0.496398	−	0.859786i	0.999991	+	0.00415465i	$0.00132247\pi$
$882$	−1.61173	+	8.06767i	−0.0542697	+	0.271653i
$883$	15.4289	+	42.3906i	0.519225	+	1.42656i	0.871376	+	0.490615i	$0.163228\pi$
$883$	15.4289	+	42.3906i	0.519225	+	1.42656i	−0.352152	+	0.935943i	$0.614550\pi$
$884$	−0.680042	+	0.352572i	−0.0228723	+	0.0118583i
$885$	5.01487	−	2.89534i	0.168573	−	0.0973256i
$886$	0.377924	+	1.11637i	0.0126966	+	0.0375053i
$887$	−1.13904	+	6.45982i	−0.0382453	+	0.216900i	−0.997941	−	0.0641423i	$-0.979569\pi$
$887$	−1.13904	+	6.45982i	−0.0382453	+	0.216900i	0.959696	+	0.281042i	$0.0906800\pi$
$888$	0.491609	+	4.59464i	0.0164973	+	0.154186i
$889$	−31.6474	−	26.5553i	−1.06142	−	0.890636i
$890$	17.1223	+	10.4095i	0.573940	+	0.348928i
$891$	2.17699	−	5.98124i	0.0729320	−	0.200379i
$892$	−0.763132	−	5.87194i	−0.0255515	−	0.196607i
$893$	−7.38933	−	19.7645i	−0.247275	−	0.661393i
$894$	−7.11190	−	6.24743i	−0.237857	−	0.208945i
$895$	2.73981	+	0.997209i	0.0915817	+	0.0333330i
$896$	39.9968	+	6.39442i	1.33620	+	0.213623i
$897$	0.225683	+	0.189371i	0.00753534	+	0.00632290i
$898$	24.7205	+	0.559951i	0.824935	+	0.0186858i
$899$	−21.6475	−	3.81704i	−0.721985	−	0.127305i
$900$	6.49686	+	2.70374i	0.216562	+	0.0901248i
$901$	−80.9493	+	46.7361i	−2.69681	+	1.55700i
$902$	−1.96901	+	5.05088i	−0.0655610	+	0.168176i
$903$	−6.67128	+	2.42815i	−0.222006	+	0.0808037i
$904$	42.5543	+	2.89569i	1.41534	+	0.0963092i
$905$	2.10641	−	3.64841i	0.0700194	−	0.121277i
$906$	−9.83170	−	12.2709i	−0.326636	−	0.407674i
$907$	21.1712	+	25.2308i	0.702977	+	0.837775i	0.992860	−	0.119287i	$-0.0380609\pi$
$907$	21.1712	+	25.2308i	0.702977	+	0.837775i	−0.289883	+	0.957062i	$0.593616\pi$
$908$	8.86028	+	5.66534i	0.294039	+	0.188011i
$909$	−6.29814	+	1.11053i	−0.208896	+	0.0368340i
$910$	0.159318	+	0.290971i	0.00528134	+	0.00964560i
$911$	25.3280			0.839155			0.419578	−	0.907719i	$-0.362178\pi$
$911$	25.3280			0.839155			0.419578	+	0.907719i	$0.362178\pi$
$912$	14.2283	−	10.0775i	0.471146	−	0.333699i
$913$	−51.1455			−1.69267
$914$	−3.29198	−	6.01232i	−0.108889	−	0.198870i
$915$	−11.5458	+	2.03584i	−0.381694	+	0.0673029i
$916$	−16.1271	−	10.3118i	−0.532855	−	0.340712i
$917$	−34.6019	−	41.2370i	−1.14266	−	1.36177i
$918$	−6.29167	−	7.85262i	−0.207656	−	0.259175i
$919$	14.0711	−	24.3719i	0.464163	−	0.803954i	−0.535000	−	0.844852i	$-0.679688\pi$
$919$	14.0711	−	24.3719i	0.464163	−	0.803954i	0.999163	+	0.0408979i	$0.0130218\pi$
$920$	1.27916	−	18.7981i	0.0421725	−	0.619757i
$921$	−2.90691	+	1.05803i	−0.0957860	+	0.0348632i
$922$	3.00567	−	7.71010i	0.0989865	−	0.253919i
$923$	−0.348159	+	0.201010i	−0.0114598	+	0.00661632i
$924$	42.0777	+	17.5111i	1.38425	+	0.576073i
$925$	−5.66092	−	0.998173i	−0.186130	−	0.0328197i
$926$	53.9154	+	1.22125i	1.77177	+	0.0401328i
$927$	14.0097	+	11.7555i	0.460139	+	0.386102i
$928$	22.0075	+	6.51392i	0.722433	+	0.213830i
$929$	−23.5051	−	8.55517i	−0.771178	−	0.280686i	−0.0736890	−	0.997281i	$-0.523477\pi$
$929$	−23.5051	−	8.55517i	−0.771178	−	0.280686i	−0.697489	+	0.716595i	$0.745699\pi$
$930$	−7.00645	−	6.15480i	−0.229751	−	0.201824i
$931$	−21.8490	+	12.8697i	−0.716072	+	0.421786i
$932$	1.54906	+	11.9193i	0.0507410	+	0.390428i
$933$	−6.13870	+	16.8659i	−0.200972	+	0.552166i
$934$	31.4338	+	19.1103i	1.02855	+	0.625307i
$935$	42.2269	+	35.4326i	1.38097	+	1.15877i
$936$	−0.151389	+	0.0161981i	−0.00494832	+	0.000529451i
$937$	−4.72951	+	26.8224i	−0.154506	+	0.876250i	0.804729	+	0.593642i	$0.202310\pi$
$937$	−4.72951	+	26.8224i	−0.154506	+	0.876250i	−0.959236	+	0.282607i	$0.908801\pi$
$938$	−12.5497	−	37.0714i	−0.409763	−	1.21042i
$939$	5.04005	−	2.90987i	0.164476	−	0.0949601i
$940$	10.4617	−	5.42395i	0.341223	−	0.176910i
$941$	17.5750	+	48.2869i	0.572929	+	1.57411i	0.799853	+	0.600196i	$0.204911\pi$
$941$	17.5750	+	48.2869i	0.572929	+	1.57411i	−0.226924	+	0.973912i	$0.572867\pi$
$942$	0.748185	−	3.74512i	0.0243772	−	0.122022i
$943$	1.64801	−	2.85444i	0.0536667	−	0.0929534i
$944$	−18.9630	+	1.59556i	−0.617192	+	0.0519312i
$945$	−3.33814	+	2.80103i	−0.108590	+	0.0911177i
$946$	2.70078	+	17.6447i	0.0878098	+	0.573679i
$947$	22.6753	−	3.99827i	0.736848	−	0.129926i	0.207385	−	0.978259i	$-0.433505\pi$
$947$	22.6753	−	3.99827i	0.736848	−	0.129926i	0.529463	+	0.848333i	$0.322393\pi$
$948$	11.6700	+	2.60754i	0.379025	+	0.0846888i
$949$		−	0.412317i		−	0.0133844i
$950$	7.13354	+	20.4829i	0.231443	+	0.664551i
$951$	31.0373			1.00645
$952$	58.2092	−	42.4581i	1.88657	−	1.37607i
$953$	4.65509	+	26.4004i	0.150793	+	0.855191i	0.962532	+	0.271170i	$0.0874105\pi$
$953$	4.65509	+	26.4004i	0.150793	+	0.855191i	−0.811738	+	0.584021i	$0.801478\pi$
$954$	−18.3649	+	2.81101i	−0.594586	+	0.0910099i
$955$	18.3481	+	21.8664i	0.593731	+	0.707581i
$956$	−48.6636	−	2.20572i	−1.57389	−	0.0713379i
$957$	22.3650	+	12.9124i	0.722957	+	0.417400i
$958$	−2.05207	+	10.2718i	−0.0662992	+	0.331868i
$959$	−13.6066	+	4.95241i	−0.439381	+	0.159922i
$960$	6.54259	+	7.21182i	0.211161	+	0.232761i
$961$	0.823658	+	1.42662i	0.0265696	+	0.0460199i
$962$	0.117803	−	0.0398795i	0.00379811	−	0.00128577i
$963$	14.2535	+	2.51327i	0.459311	+	0.0809889i
$964$	−10.4316	−	9.59076i	−0.335980	−	0.308898i
$965$	0.291025	−	0.346830i	0.00936842	−	0.0111648i
$966$	−23.6778	−	14.3949i	−0.761819	−	0.463150i
$967$	4.53476	+	1.65052i	0.145828	+	0.0530771i	0.413903	−	0.910321i	$-0.364165\pi$
$967$	4.53476	+	1.65052i	0.145828	+	0.0530771i	−0.268075	+	0.963398i	$0.586387\pi$
$968$	46.5517	−	69.2950i	1.49623	−	2.22723i
$969$	5.11918	−	30.5885i	0.164452	−	0.982644i
$970$	8.31084	−	9.46083i	0.266845	−	0.303769i
$971$	−17.2197	+	47.3108i	−0.552607	+	1.51828i	0.277530	+	0.960717i	$0.410484\pi$
$971$	−17.2197	+	47.3108i	−0.552607	+	1.51828i	−0.830137	+	0.557559i	$0.811738\pi$
$972$	−0.598241	−	1.90843i	−0.0191886	−	0.0612129i
$973$	−37.0896	+	44.2016i	−1.18904	+	1.41704i
$974$	29.3070	+	0.663841i	0.939057	+	0.0212708i
$975$	0.0328890	−	0.186523i	0.00105329	−	0.00597350i
$976$	37.1824	+	10.0956i	1.19018	+	0.323151i
$977$	−9.93809	−	17.2133i	−0.317948	−	0.550701i	0.662112	−	0.749405i	$-0.269660\pi$
$977$	−9.93809	−	17.2133i	−0.317948	−	0.550701i	−0.980060	+	0.198704i	$0.936327\pi$
$978$	−7.75753	−	3.02416i	−0.248058	−	0.0967019i
$979$	−25.3426	−	69.6282i	−0.809953	−	2.22533i
$980$	−8.60234	−	11.2494i	−0.274792	−	0.359350i
$981$	−8.63191	−	4.98364i	−0.275596	−	0.159115i
$982$	−14.0042	−	17.4785i	−0.446891	−	0.557763i
$983$	33.9749	−	28.5084i	1.08363	−	0.909275i	0.0874147	−	0.996172i	$-0.472139\pi$
$983$	33.9749	−	28.5084i	1.08363	−	0.909275i	0.996217	+	0.0868967i	$0.0276950\pi$
$984$	0.472579	+	1.63652i	0.0150653	+	0.0521703i
$985$	2.52699	+	14.3313i	0.0805166	+	0.456632i
$986$	35.8088	−	19.6067i	1.14038	−	0.624404i
$987$		−	17.3308i		−	0.551646i
$988$	−0.348214	−	0.314591i	−0.0110782	−	0.0100085i
$989$		−	10.8529i		−	0.345102i
$990$	5.26196	+	9.61021i	0.167236	+	0.305433i
$991$	7.50317	+	42.5526i	0.238346	+	1.35173i	0.835451	+	0.549565i	$0.185206\pi$
$991$	7.50317	+	42.5526i	0.238346	+	1.35173i	−0.597105	+	0.802163i	$0.703682\pi$
$992$	12.2267	+	28.1033i	0.388197	+	0.892280i
$993$	−22.5069	+	18.8855i	−0.714234	+	0.599313i
$994$	29.5094	−	23.6435i	0.935981	−	0.749926i
$995$	7.44928	+	4.30084i	0.236158	+	0.136346i
$996$	−12.7659	+	9.76195i	−0.404503	+	0.309319i
$997$	8.58190	+	23.5786i	0.271792	+	0.746741i	0.998228	+	0.0595073i	$0.0189530\pi$
$997$	8.58190	+	23.5786i	0.271792	+	0.746741i	−0.726436	+	0.687234i	$0.758825\pi$
$998$	9.17282	−	23.5300i	0.290361	−	0.744828i
$999$	0.816860	+	1.41484i	0.0258443	+	0.0447637i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.bk.a.61.14	yes	240
8.5	even	2	inner	456.2.bk.a.61.5	✓	240
19.5	even	9	inner	456.2.bk.a.157.5	yes	240
152.5	even	18	inner	456.2.bk.a.157.14	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bk.a.61.5	✓	240	8.5	even	2	inner
456.2.bk.a.61.14	yes	240	1.1	even	1	trivial
456.2.bk.a.157.5	yes	240	19.5	even	9	inner
456.2.bk.a.157.14	yes	240	152.5	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bk (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.679191 - 1.24044i) q^{2} +(-0.984808 + 0.173648i) q^{3} +(-1.07740 + 1.68500i) q^{4} +(-0.782380 - 0.932405i) q^{5} +(0.884273 + 1.10366i) q^{6} +(-1.79007 + 3.10050i) q^{7} +(2.82190 + 0.192022i) q^{8} +(0.939693 - 0.342020i) q^{9} +(-0.625210 + 1.60378i) q^{10} +(5.51234 - 3.18255i) q^{11} +(0.768436 - 1.84648i) q^{12} +(-0.0530119 - 0.00934743i) q^{13} +(5.06179 + 0.114656i) q^{14} +(0.932405 + 0.782380i) q^{15} +(-1.67842 - 3.63083i) q^{16} +(-6.68599 - 2.43350i) q^{17} +(-1.06249 - 0.933339i) q^{18} +(-0.0379798 - 4.35873i) q^{19} +(2.41403 - 0.313734i) q^{20} +(1.22448 - 3.36423i) q^{21} +(-7.69170 - 4.67619i) q^{22} +(4.19254 + 3.51795i) q^{23} +(-2.81237 + 0.300914i) q^{24} +(0.610982 - 3.46505i) q^{25} +(0.0244102 + 0.0721070i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(-3.29570 - 6.35674i) q^{28} +(-1.38766 - 3.81257i) q^{29} +(0.337218 - 1.68798i) q^{30} +(2.70891 - 4.69196i) q^{31} +(-3.36387 + 4.54801i) q^{32} +(-4.87595 + 4.09141i) q^{33} +(1.52244 + 9.94640i) q^{34} +(4.29143 - 0.756696i) q^{35} +(-0.436123 + 1.95187i) q^{36} -1.63372i q^{37} +(-5.38097 + 3.00752i) q^{38} +0.0538297 q^{39} +(-2.02876 - 2.78139i) q^{40} +(-0.104577 - 0.593088i) q^{41} +(-5.00480 + 0.766056i) q^{42} +(-1.27465 - 1.51907i) q^{43} +(-0.576415 + 12.7171i) q^{44} +(-1.05410 - 0.608584i) q^{45} +(1.51629 - 7.58997i) q^{46} +(4.54888 - 1.65566i) q^{47} +(2.28340 + 3.28421i) q^{48} +(-2.90872 - 5.03804i) q^{49} +(-4.71317 + 1.59554i) q^{50} +(7.00699 + 1.23552i) q^{51} +(0.0728654 - 0.0792539i) q^{52} +(8.44443 - 10.0637i) q^{53} +(1.20842 + 0.734660i) q^{54} +(-7.28017 - 2.64977i) q^{55} +(-5.64677 + 8.40556i) q^{56} +(0.794289 + 4.28592i) q^{57} +(-3.78680 + 4.31078i) q^{58} +(1.62716 - 4.47058i) q^{59} +(-2.32288 + 0.728160i) q^{60} +(-6.19143 + 7.37866i) q^{61} +(-7.65998 - 0.173508i) q^{62} +(-0.621685 + 3.52575i) q^{63} +(7.92626 + 1.08373i) q^{64} +(0.0327599 + 0.0567418i) q^{65} +(8.38686 + 3.26950i) q^{66} +(-2.64384 - 7.26389i) q^{67} +(11.3039 - 8.64400i) q^{68} +(-4.73973 - 2.73648i) q^{69} +(-3.85334 - 4.80934i) q^{70} +(5.72109 - 4.80057i) q^{71} +(2.71740 - 0.784706i) q^{72} +(1.33009 + 7.54329i) q^{73} +(-2.02654 + 1.10961i) q^{74} +3.51850i q^{75} +(7.38536 + 4.63211i) q^{76} +22.7880i q^{77} +(-0.0365606 - 0.0667727i) q^{78} +(1.03823 + 5.88807i) q^{79} +(-2.07224 + 4.40565i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-0.664665 + 0.532542i) q^{82} +(-6.95877 - 4.01765i) q^{83} +(4.34946 + 5.68787i) q^{84} +(2.96198 + 8.13797i) q^{85} +(-1.01859 + 2.61287i) q^{86} +(2.02863 + 3.51369i) q^{87} +(16.1664 - 7.92236i) q^{88} +(2.02146 - 11.4642i) q^{89} +(-0.0389804 + 1.72089i) q^{90} +(0.123877 - 0.147631i) q^{91} +(-10.4448 + 3.27416i) q^{92} +(-1.85300 + 5.09108i) q^{93} +(-5.14330 - 4.51812i) q^{94} +(-4.03439 + 3.44560i) q^{95} +(2.52302 - 5.06304i) q^{96} +(-6.87450 - 2.50211i) q^{97} +(-4.27384 + 7.02989i) q^{98} +(4.09141 - 4.87595i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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