LMFDB - Embedded newform 456.2.bk.a.157.14

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			157.14
Character	$\chi$	$=$	456.157
Dual form			456.2.bk.a.61.14

$q$-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 $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$-1$	$1$	$1$

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	−0.912072	−	0.410030i	$-0.865518\pi$
$5$	−0.782380	+	0.932405i	−0.349891	+	0.416984i	0.562181	+	0.827014i	$0.309963\pi$
$6$	0.884273	−	1.10366i	0.361003	−	0.450567i
$7$	−1.79007	−	3.10050i	−0.676584	−	1.17188i	−0.976003	−	0.217756i	$-0.930126\pi$
$7$	−1.79007	−	3.10050i	−0.676584	−	1.17188i	0.299420	−	0.954122i	$-0.403207\pi$
$8$	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	0.971743	+	0.236043i	$0.0758507\pi$
$11$	5.51234	+	3.18255i	1.66203	+	0.959575i	0.690291	+	0.723532i	$0.257483\pi$
$12$	0.768436	+	1.84648i	0.221828	+	0.533034i
$13$	−0.0530119	+	0.00934743i	−0.0147029	+	0.00259251i	−0.180995	−	0.983484i	$-0.557932\pi$
$13$	−0.0530119	+	0.00934743i	−0.0147029	+	0.00259251i	0.166292	+	0.986077i	$0.446821\pi$
$14$	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	−0.983684	−	0.179904i	$-0.942421\pi$
$17$	−6.68599	+	2.43350i	−1.62159	+	0.590211i	−0.637906	+	0.770114i	$0.720199\pi$
$18$	−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	−0.0907749	−	0.995871i	$-0.528934\pi$
$23$	4.19254	−	3.51795i	0.874204	−	0.733544i	0.964979	+	0.262327i	$0.0844899\pi$
$24$	−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	0.741626	+	0.670813i	$0.234055\pi$
$29$	−1.38766	+	3.81257i	−0.257683	+	0.707977i	−0.999309	+	0.0371643i	$0.988168\pi$
$30$	0.337218	+	1.68798i	0.0615674	+	0.308182i
$31$	2.70891	+	4.69196i	0.486534	+	0.842701i	0.999880	−	0.0154802i	$-0.00492769\pi$
$31$	2.70891	+	4.69196i	0.486534	+	0.842701i	−0.513346	+	0.858182i	$0.671594\pi$
$32$	−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	$0.0428757\pi$
$37$			1.63372i			0.268582i	−0.990942	+	0.134291i	$0.957124\pi$
$38$	−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	−0.991884	−	0.127144i	$-0.959419\pi$
$41$	−0.104577	+	0.593088i	−0.0163323	+	0.0926248i	0.975552	+	0.219768i	$0.0705302\pi$
$42$	−5.00480	−	0.766056i	−0.772257	−	0.118205i
$43$	−1.27465	+	1.51907i	−0.194382	+	0.231656i	−0.854428	−	0.519570i	$-0.826092\pi$
$43$	−1.27465	+	1.51907i	−0.194382	+	0.231656i	0.660046	+	0.751225i	$0.270537\pi$
$44$	−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	0.651756	−	0.758428i	$-0.274033\pi$
$47$	4.54888	+	1.65566i	0.663522	+	0.241502i	0.0117659	+	0.999931i	$0.496255\pi$
$48$	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	0.910268	+	0.414019i	$0.135875\pi$
$53$	8.44443	+	10.0637i	1.15993	+	1.38235i	0.249663	+	0.968333i	$0.419680\pi$
$54$	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	0.999415	−	0.0341958i	$-0.0108870\pi$
$59$	1.62716	+	4.47058i	0.211838	+	0.582020i	−0.787577	+	0.616216i	$0.788665\pi$
$60$	−2.32288	−	0.728160i	−0.299883	−	0.0940051i
$61$	−6.19143	−	7.37866i	−0.792731	−	0.944741i	0.206702	−	0.978404i	$-0.433727\pi$
$61$	−6.19143	−	7.37866i	−0.792731	−	0.944741i	−0.999433	+	0.0336634i	$0.989283\pi$
$62$	−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	0.666838	+	0.745202i	$0.267647\pi$
$67$	−2.64384	+	7.26389i	−0.322996	+	0.887425i	−0.989835	+	0.142223i	$0.954575\pi$
$68$	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	0.915705	−	0.401852i	$-0.131633\pi$
$71$	5.72109	+	4.80057i	0.678969	+	0.569722i	−0.236736	+	0.971574i	$0.576078\pi$
$72$	2.71740	+	0.784706i	0.320248	+	0.0924785i
$73$	1.33009	−	7.54329i	0.155675	−	0.882875i	−0.802492	−	0.596663i	$-0.796493\pi$
$73$	1.33009	−	7.54329i	0.155675	−	0.882875i	0.958166	−	0.286212i	$-0.0923961\pi$
$74$	−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	−0.869029	−	0.494761i	$-0.835255\pi$
$79$	1.03823	−	5.88807i	0.116809	−	0.662459i	0.985838	−	0.167698i	$-0.0536334\pi$
$80$	−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	−0.830667	−	0.556770i	$-0.812041\pi$
$83$	−6.95877	+	4.01765i	−0.763824	+	0.440994i	0.0668431	+	0.997763i	$0.478707\pi$
$84$	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	0.882162	+	0.470946i	$0.156087\pi$
$89$	2.02146	+	11.4642i	0.214274	+	1.21521i	−0.667888	+	0.744262i	$0.732802\pi$
$90$	−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	−0.666557	−	0.745454i	$-0.732232\pi$
$97$	−6.87450	+	2.50211i	−0.698000	+	0.254051i	−0.0314430	+	0.999506i	$0.510010\pi$
$98$	−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	−0.477968	−	0.878377i	$-0.658627\pi$
$101$	−6.29814	+	1.11053i	−0.626689	+	0.110502i	−0.148721	+	0.988879i	$0.547515\pi$
$102$	−3.22648	+	9.53092i	−0.319470	+	0.943702i
$103$	9.14418	−	15.8382i	0.901003	−	1.56058i	0.0748082	−	0.997198i	$-0.476166\pi$
$103$	9.14418	−	15.8382i	0.901003	−	1.56058i	0.826195	−	0.563385i	$-0.190501\pi$
$104$	−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	0.248597	−	0.968607i	$-0.420030\pi$
$107$	12.5343	−	7.23667i	1.21173	−	0.699595i	0.963137	+	0.269012i	$0.0866971\pi$
$108$	0.0905586	+	1.99795i	0.00871401	+	0.192253i
$109$	−6.40684	+	7.63538i	−0.613664	+	0.731336i	−0.979967	−	0.199159i	$-0.936179\pi$
$109$	−6.40684	+	7.63538i	−0.613664	+	0.731336i	0.366303	+	0.930496i	$0.380623\pi$
$110$	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	−0.934852	−	0.355037i	$-0.884468\pi$
$127$	−2.00380	−	11.3641i	−0.177808	−	1.00840i	0.757044	−	0.653364i	$-0.226643\pi$
$128$	−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	−0.933204	−	0.359348i	$-0.882999\pi$
$131$	−5.14262	−	14.1292i	−0.449312	−	1.23448i	0.483891	−	0.875128i	$-0.339223\pi$
$132$	−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	−0.500770	−	0.865580i	$-0.666950\pi$
$137$	3.09827	−	2.59975i	0.264703	−	0.222112i	0.765473	+	0.643469i	$0.222505\pi$
$138$	−0.175275	−	7.73796i	−0.0149204	−	0.658699i
$139$	15.8721	−	2.79869i	1.34626	−	0.237381i	0.546376	−	0.837540i	$-0.316007\pi$
$139$	15.8721	−	2.79869i	1.34626	−	0.237381i	0.799881	+	0.600158i	$0.204896\pi$
$140$	−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	−0.103023	−	0.994679i	$-0.532851\pi$
$149$	−6.59194	−	1.16234i	−0.540033	−	0.0952223i	−0.437010	+	0.899457i	$0.643963\pi$
$150$	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	−0.830852	−	0.556493i	$-0.812146\pi$
$157$	−1.73586	+	2.06872i	−0.138537	+	0.165102i	0.692315	+	0.721595i	$0.256591\pi$
$158$	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	0.286847	−	0.957976i	$-0.407393\pi$
$163$	−5.09870	−	2.94374i	−0.399361	−	0.230571i	−0.686208	+	0.727405i	$0.740726\pi$
$164$	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	−0.994845	−	0.101405i	$-0.967666\pi$
$167$	−13.7982	+	11.5780i	−1.06773	+	0.895935i	−0.0728882	+	0.997340i	$0.523222\pi$
$168$	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	0.982515	−	0.186182i	$-0.0596113\pi$
$173$	1.44932	+	3.98197i	0.110190	+	0.302743i	−0.872326	+	0.488925i	$0.837389\pi$
$174$	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	0.420465	−	0.907309i	$-0.361867\pi$
$179$	−2.07451	−	1.19772i	−0.155056	−	0.0895216i	−0.575520	+	0.817787i	$0.695200\pi$
$180$	2.16115	+	1.12046i	0.161082	+	0.0835143i
$181$	1.18379	−	3.25243i	0.0879903	−	0.241751i	−0.887891	−	0.460054i	$-0.847830\pi$
$181$	1.18379	−	3.25243i	0.0879903	−	0.241751i	0.975881	+	0.218303i	$0.0700521\pi$
$182$	−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	−0.982395	−	0.186817i	$-0.940183\pi$
$193$	0.0645925	−	0.366322i	0.00464947	−	0.0263685i	0.987044	+	0.160448i	$0.0512940\pi$
$194$	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	−0.821233	−	0.570593i	$-0.806713\pi$
$197$	−10.3541	+	5.97796i	−0.737701	+	0.425912i	0.0835317	+	0.996505i	$0.473380\pi$
$198$	−8.82719	+	1.76346i	−0.627321	+	0.125324i
$199$	−6.64078	−	2.41705i	−0.470752	−	0.171340i	0.0957408	−	0.995406i	$-0.469478\pi$
$199$	−6.64078	−	2.41705i	−0.470752	−	0.171340i	−0.566493	+	0.824066i	$0.691700\pi$
$200$	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	0.966189	−	0.257836i	$-0.0830094\pi$
$211$	0.876074	+	2.40699i	0.0603114	+	0.165704i	−0.905877	+	0.423540i	$0.860787\pi$
$212$	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	0.563683	−	0.825991i	$-0.309384\pi$
$223$	−2.26800	−	1.90308i	−0.151876	−	0.127439i	−0.715560	+	0.698552i	$0.753828\pi$
$224$	−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	$0.0558323\pi$
$227$			5.25834i			0.349008i	−0.984656	+	0.174504i	$0.944168\pi$
$228$	−8.07752	+	3.27928i	−0.534947	+	0.217176i
$229$		−	9.57101i		−	0.632470i	−0.948681	−	0.316235i	$-0.897581\pi$
$229$		−	9.57101i		−	0.632470i	0.948681	−	0.316235i	$-0.102419\pi$
$230$	−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	0.781010	−	0.624518i	$-0.214705\pi$
$233$	4.60373	+	3.86299i	0.301601	+	0.253073i	−0.479409	+	0.877591i	$0.659149\pi$
$234$	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	−0.139586	−	0.990210i	$-0.544577\pi$
$239$	12.1784	−	21.0936i	0.787754	−	1.36443i	0.927340	−	0.374220i	$-0.122090\pi$
$240$	1.27573	+	4.69856i	0.0823478	+	0.303291i
$241$	−1.23034	−	6.97758i	−0.0792529	−	0.449466i	−0.998449	−	0.0556665i	$-0.982272\pi$
$241$	−1.23034	−	6.97758i	−0.0792529	−	0.449466i	0.919196	−	0.393799i	$-0.128839\pi$
$242$	−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	0.750285	−	0.661114i	$-0.229916\pi$
$251$	−0.492247	−	0.586637i	−0.0310704	−	0.0370282i	−0.781356	+	0.624086i	$0.785472\pi$
$252$	−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	0.379800	−	0.925069i	$-0.375993\pi$
$257$	1.22031	+	0.444156i	0.0761208	+	0.0277057i	−0.303679	+	0.952774i	$0.598215\pi$
$258$	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	0.360823	+	0.932634i	$0.382496\pi$
$263$	−4.82009	+	27.3361i	−0.297220	+	1.68562i	−0.658042	+	0.752981i	$0.728615\pi$
$264$	−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	0.480774	−	0.876844i	$-0.340356\pi$
$269$	10.3763	+	1.82963i	0.632656	+	0.111554i	0.151882	+	0.988399i	$0.451467\pi$
$270$	−0.260442	+	1.70152i	−0.0158500	+	0.103551i
$271$	3.78339	+	3.17464i	0.229825	+	0.192846i	0.750427	−	0.660954i	$-0.229848\pi$
$271$	3.78339	+	3.17464i	0.229825	+	0.192846i	−0.520602	+	0.853799i	$0.674292\pi$
$272$	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	0.516963	−	0.856008i	$-0.327063\pi$
$277$	0.567859	+	0.327853i	0.0341193	+	0.0196988i	−0.482843	+	0.875707i	$0.660396\pi$
$278$	−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	−0.379123	−	0.925346i	$-0.623774\pi$
$281$	7.81713	−	6.55935i	0.466331	−	0.391298i	0.845454	+	0.534048i	$0.179330\pi$
$282$	5.84973	−	3.55636i	0.348346	−	0.211778i
$283$	−1.94793	−	5.35189i	−0.115792	−	0.318137i	0.868235	−	0.496153i	$-0.165254\pi$
$283$	−1.94793	−	5.35189i	−0.115792	−	0.318137i	−0.984028	+	0.178016i	$0.943032\pi$
$284$	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	0.803036	−	0.595930i	$-0.203216\pi$
$293$	11.7846	+	6.80384i	0.688464	+	0.397485i	−0.114573	+	0.993415i	$0.536550\pi$
$294$	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	0.259906	−	0.965634i	$-0.416308\pi$
$307$	3.04647	+	0.537175i	0.173871	+	0.0306582i	−0.0860346	+	0.996292i	$0.527420\pi$
$308$	−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	0.999947	+	0.0102834i	$0.00327336\pi$
$311$	8.97418	+	15.5437i	0.508879	+	0.881405i	−0.491068	+	0.871121i	$0.663393\pi$
$312$	0.151902	−	0.0103365i	0.00859977	−	0.000585188i
$313$	−5.46877	−	1.99047i	−0.309113	−	0.112508i	0.182806	−	0.983149i	$-0.441482\pi$
$313$	−5.46877	−	1.99047i	−0.309113	−	0.112508i	−0.491919	+	0.870641i	$0.663704\pi$
$314$	−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	−0.943494	−	0.331389i	$-0.892483\pi$
$317$	−30.5658	+	5.38958i	−1.71675	+	0.302709i	−0.773253	+	0.634098i	$0.781372\pi$
$318$	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	0.994241	−	0.107170i	$-0.0341789\pi$
$331$	25.4444	+	14.6903i	1.39855	+	0.807453i	0.404308	+	0.914623i	$0.367512\pi$
$332$	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	0.956552	−	0.291561i	$-0.0941747\pi$
$337$	15.3382	+	12.8703i	0.835524	+	0.701088i	−0.121028	+	0.992649i	$0.538619\pi$
$338$	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	−0.504096	−	0.863647i	$-0.668174\pi$
$347$	8.08388	−	9.63400i	0.433966	−	0.517180i	0.938062	+	0.346467i	$0.112619\pi$
$348$	−8.10619	+	0.367420i	−0.434538	+	0.0196958i
$349$	12.2870	−	7.09390i	0.657708	−	0.379728i	−0.133695	−	0.991023i	$-0.542684\pi$
$349$	12.2870	−	7.09390i	0.657708	−	0.379728i	0.791403	+	0.611295i	$0.209351\pi$
$350$	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	−0.862610	−	0.505870i	$-0.831172\pi$
$353$	0.127600	−	0.221009i	0.00679144	−	0.0117631i	0.869401	+	0.494107i	$0.164505\pi$
$354$	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	0.418461	−	0.908235i	$-0.362570\pi$
$359$	25.0639	−	9.12251i	1.32282	−	0.481468i	0.904362	+	0.426767i	$0.140348\pi$
$360$	−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	−0.976535	−	0.215357i	$-0.930909\pi$
$367$	−2.53927	−	14.4009i	−0.132549	−	0.751721i	0.843987	−	0.536364i	$-0.180203\pi$
$368$	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	−0.705012	−	0.709195i	$-0.749059\pi$
$373$	−8.56227	+	4.94343i	−0.443337	+	0.255961i	0.261675	+	0.965156i	$0.415725\pi$
$374$	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	$-0.917227\pi$
$379$		−	10.0112i		−	0.514239i	0.966380	−	0.257119i	$-0.0827734\pi$
$380$	−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	−0.959932	−	0.280234i	$-0.909588\pi$
$383$	0.742791	−	4.21258i	0.0379548	−	0.215253i	0.997886	+	0.0649818i	$0.0206989\pi$
$384$	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	−0.869896	−	0.493235i	$-0.835814\pi$
$389$	2.23914	−	6.15197i	0.113529	−	0.311917i	0.983425	+	0.181318i	$0.0580363\pi$
$390$	−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	0.846489	+	0.532406i	$0.178712\pi$
$397$	10.7647	+	29.5758i	0.540265	+	1.48437i	−0.306225	+	0.951959i	$0.599066\pi$
$398$	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	0.447031	−	0.894519i	$-0.352481\pi$
$401$	27.3233	−	9.94488i	1.36446	−	0.496623i	0.917431	+	0.397895i	$0.130259\pi$
$402$	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	0.834939	−	0.550343i	$-0.185503\pi$
$409$	22.6665	+	8.24992i	1.12078	+	0.407932i	0.285846	+	0.958275i	$0.407725\pi$
$410$	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	$0.270009\pi$
$419$			30.7096i			1.50026i	−0.661290	+	0.750130i	$0.729991\pi$
$420$	1.90047	+	8.50554i	0.0927332	+	0.415028i
$421$	−18.6776	−	3.29337i	−0.910291	−	0.160509i	−0.301156	−	0.953575i	$-0.597372\pi$
$421$	−18.6776	−	3.29337i	−0.910291	−	0.160509i	−0.609135	+	0.793066i	$0.708483\pi$
$422$	−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	0.928325	+	0.371769i	$0.121249\pi$
$431$	3.80203	+	21.5624i	0.183137	+	1.03862i	−0.745188	+	0.666855i	$0.767640\pi$
$432$	3.26897	−	2.30518i	0.157278	−	0.110908i
$433$	15.0024	−	12.5885i	0.720967	−	0.604963i	−0.206686	−	0.978407i	$-0.566268\pi$
$433$	15.0024	−	12.5885i	0.720967	−	0.604963i	0.927653	+	0.373444i	$0.121823\pi$
$434$	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	0.846077	−	0.533060i	$-0.178958\pi$
$439$	38.4864	−	14.0079i	1.83685	−	0.668560i	0.990777	−	0.135500i	$-0.0432642\pi$
$440$	−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	−0.193111	−	0.981177i	$-0.561858\pi$
$443$	−0.820741	+	0.144719i	−0.0389946	+	0.00687580i	0.154117	+	0.988053i	$0.450747\pi$
$444$	−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	0.582597	−	0.812761i	$-0.302037\pi$
$449$	−8.74227	−	15.1421i	−0.412573	−	0.714598i	−0.995170	+	0.0981635i	$0.968703\pi$
$450$	−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	−0.671309	−	0.741177i	$-0.734268\pi$
$461$	3.76126	−	4.48250i	0.175179	−	0.208771i	0.846489	+	0.532407i	$0.178712\pi$
$462$	−25.1501	−	20.1508i	−1.17009	−	0.937500i
$463$	−19.0669	−	33.0248i	−0.886112	−	1.53479i	−0.844434	−	0.535660i	$-0.820063\pi$
$463$	−19.0669	−	33.0248i	−0.886112	−	1.53479i	−0.0416783	−	0.999131i	$-0.513270\pi$
$464$	−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	−0.121918	−	0.992540i	$-0.538905\pi$
$467$	−22.5274	−	13.0062i	−1.04244	−	0.601854i	−0.920524	+	0.390686i	$0.872238\pi$
$468$	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	−0.763143	−	0.646230i	$-0.776345\pi$
$479$	−5.67394	+	4.76100i	−0.259249	+	0.217536i	0.503894	+	0.863766i	$0.331900\pi$
$480$	−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	0.529749	−	0.848155i	$-0.322286\pi$
$487$	−10.3643	−	17.9514i	−0.469649	−	0.813456i	−0.999398	+	0.0346984i	$0.988953\pi$
$488$	−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	0.514108	−	0.857726i	$-0.328123\pi$
$491$	15.5963	+	2.75005i	0.703852	+	0.124108i	0.189744	+	0.981834i	$0.439234\pi$
$492$	−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	−0.445258	−	0.895402i	$-0.646888\pi$
$499$	11.4788	−	13.6799i	0.513860	−	0.612394i	0.959117	+	0.283008i	$0.0913324\pi$
$500$	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	−0.379667	−	0.925123i	$-0.623962\pi$
$503$	−28.3747	−	10.3276i	−1.26517	−	0.460483i	−0.885500	+	0.464640i	$0.846184\pi$
$504$	−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	0.994282	−	0.106782i	$-0.0340548\pi$
$509$	16.1642	+	19.2638i	0.716467	+	0.853852i	−0.277815	+	0.960635i	$0.589610\pi$
$510$	−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	−0.472773	−	0.881184i	$-0.656747\pi$
$521$	12.0231	−	20.8246i	0.526741	−	0.912342i	0.999514	−	0.0311583i	$-0.00991959\pi$
$522$	−2.08405	−	5.34597i	−0.0912164	−	0.233987i
$523$	−5.99868	+	16.4812i	−0.262304	+	0.720675i	0.736707	+	0.676212i	$0.236380\pi$
$523$	−5.99868	+	16.4812i	−0.262304	+	0.720675i	−0.999011	+	0.0444624i	$0.985843\pi$
$524$	−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	−0.685394	−	0.728172i	$-0.740370\pi$
$541$	7.15711	−	19.6640i	0.307708	−	0.845421i	0.993103	−	0.117249i	$-0.0374076\pi$
$542$	−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	0.718484	−	0.695544i	$-0.244836\pi$
$547$	−2.13431	−	2.54357i	−0.0912566	−	0.108755i	−0.809740	+	0.586788i	$0.800392\pi$
$548$	−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	0.207256	−	0.978287i	$-0.433547\pi$
$557$	17.3845	−	3.06536i	0.736607	−	0.129884i	0.529351	+	0.848403i	$0.322436\pi$
$558$	−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	−0.799761	−	0.600319i	$-0.795040\pi$
$563$	−16.1289	+	9.31200i	−0.679750	+	0.392454i	0.120011	+	0.992773i	$0.461707\pi$
$564$	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	$-0.848651\pi$
$571$		−	21.8770i		−	0.915525i	0.889075	−	0.457762i	$-0.151349\pi$
$572$	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	0.988236	+	0.152939i	$0.0488740\pi$
$577$	15.0507	+	26.0685i	0.626567	+	1.08525i	−0.361668	+	0.932307i	$0.617793\pi$
$578$	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	0.809270	−	0.587438i	$-0.199863\pi$
$587$	−4.56129	−	12.5320i	−0.188264	−	0.517252i	−0.997534	+	0.0701852i	$0.977641\pi$
$588$	−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	−0.723029	−	0.690818i	$-0.757251\pi$
$593$	−4.09736	+	3.43809i	−0.168258	+	0.141186i	0.554770	+	0.832004i	$0.312806\pi$
$594$	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	0.620062	−	0.784553i	$-0.287107\pi$
$599$	14.4585	+	5.26245i	0.590756	+	0.215018i	−0.0293057	+	0.999570i	$0.509330\pi$
$600$	−0.675629	−	9.92887i	−0.0275824	−	0.405344i
$601$	6.84618	+	11.8579i	0.279262	+	0.483695i	0.971201	−	0.238260i	$-0.0765770\pi$
$601$	6.84618	+	11.8579i	0.279262	+	0.483695i	−0.691940	+	0.721955i	$0.743244\pi$
$602$	−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	−0.845131	−	0.534560i	$-0.820477\pi$
$613$	−4.25695	+	5.07324i	−0.171937	+	0.204906i	0.673194	+	0.739466i	$0.264922\pi$
$614$	−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	−0.108497	−	0.994097i	$-0.534604\pi$
$617$	−20.6318	−	7.50935i	−0.830604	−	0.302315i	−0.722107	+	0.691782i	$0.756826\pi$
$618$	−9.39399	−	24.0973i	−0.377882	−	0.969337i
$619$	−28.7267	−	16.5854i	−1.15462	−	0.666622i	−0.204613	−	0.978843i	$-0.565594\pi$
$619$	−28.7267	−	16.5854i	−1.15462	−	0.666622i	−0.950009	+	0.312221i	$0.898927\pi$
$620$	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	0.0105260	−	0.999945i	$-0.496649\pi$
$631$	25.0470	−	21.0170i	0.997107	−	0.836672i	0.986581	+	0.163272i	$0.0522050\pi$
$632$	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	0.823246	−	0.567685i	$-0.192161\pi$
$641$	10.3080	+	8.64943i	0.407141	+	0.341632i	−0.416105	+	0.909317i	$0.636605\pi$
$642$	3.09691	−	20.2327i	0.122225	−	0.798523i
$643$	40.6218	+	7.16272i	1.60197	+	0.282470i	0.902010	−	0.431715i	$-0.142091\pi$
$643$	40.6218	+	7.16272i	1.60197	+	0.282470i	0.699957	+	0.714185i	$0.253202\pi$
$644$	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	−0.598401	−	0.801196i	$-0.704197\pi$
$653$	−5.20649	+	3.00597i	−0.203746	+	0.117633i	0.394656	+	0.918829i	$0.370864\pi$
$654$	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	−0.470070	−	0.882629i	$-0.655771\pi$
$659$	−15.6571	+	2.76077i	−0.609914	+	0.107544i	−0.139844	+	0.990174i	$0.544660\pi$
$660$	−10.4871	−	11.4066i	−0.408210	−	0.443999i
$661$	17.7491	+	21.1526i	0.690360	+	0.822739i	0.991399	−	0.130872i	$-0.0417778\pi$
$661$	17.7491	+	21.1526i	0.690360	+	0.822739i	−0.301039	+	0.953612i	$0.597333\pi$
$662$	−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	−0.769749	−	0.638346i	$-0.779619\pi$
$673$	4.35698	−	7.54652i	0.167949	−	0.290897i	0.937699	+	0.347449i	$0.112952\pi$
$674$	−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	−0.758220	−	0.651999i	$-0.773930\pi$
$677$	−14.9007	+	8.60294i	−0.572681	+	0.330638i	0.185538	+	0.982637i	$0.440597\pi$
$678$	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	$0.0977747\pi$
$683$			15.8039i			0.604721i	−0.953194	+	0.302361i	$0.902225\pi$
$684$	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	0.0882460	−	0.996099i	$-0.471874\pi$
$691$	26.1559	−	15.1011i	0.995016	−	0.574473i	0.906770	+	0.421626i	$0.138541\pi$
$692$	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	−0.776091	−	0.630621i	$-0.782800\pi$
$701$	−15.5397	−	42.6950i	−0.586926	−	1.61257i	0.189165	−	0.981945i	$-0.439422\pi$
$702$	−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	−0.298816	−	0.954311i	$-0.596592\pi$
$709$	−6.74244	+	1.18887i	−0.253218	+	0.0446491i	0.0455983	+	0.998960i	$0.485481\pi$
$710$	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	−0.911066	−	0.412262i	$-0.864739\pi$
$719$	2.30757	−	13.0869i	0.0860578	−	0.488058i	0.997123	−	0.0757964i	$-0.0241499\pi$
$720$	−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	0.996983	−	0.0776228i	$-0.0247330\pi$
$727$	29.4884	+	24.7437i	1.09366	+	0.917693i	0.0966807	+	0.995315i	$0.469177\pi$
$728$	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	0.298218	−	0.954498i	$-0.403608\pi$
$733$	−10.2689	−	5.92878i	−0.379292	−	0.218984i	−0.677510	+	0.735513i	$0.736941\pi$
$734$	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	0.977852	−	0.209296i	$-0.0671171\pi$
$739$	2.56191	+	7.03879i	0.0942414	+	0.258926i	−0.883611	+	0.468222i	$0.844895\pi$
$740$	−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	−0.144650	−	0.989483i	$-0.546206\pi$
$743$	10.3736	−	3.77567i	0.380569	−	0.138516i	0.525219	+	0.850967i	$0.323983\pi$
$744$	−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	−0.326995	−	0.945026i	$-0.606036\pi$
$751$	−32.4725	−	11.8190i	−1.18494	−	0.431282i	−0.857944	+	0.513744i	$0.828258\pi$
$752$	−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	−0.146761	−	0.989172i	$-0.546885\pi$
$757$	−17.1406	−	3.02236i	−0.622987	−	0.109849i	−0.476227	+	0.879323i	$0.657996\pi$
$758$	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	0.538206	−	0.842813i	$-0.319102\pi$
$769$	11.3349	+	4.12556i	0.408747	+	0.148772i	−0.129460	+	0.991585i	$0.541324\pi$
$770$	−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	0.0579847	−	0.998317i	$-0.481533\pi$
$773$	12.6202	−	2.22528i	0.453917	−	0.0800378i	0.395932	+	0.918280i	$0.370421\pi$
$774$	−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	0.219750	−	0.975556i	$-0.429476\pi$
$787$	−14.4541	−	8.34506i	−0.515232	−	0.297469i	−0.734982	+	0.678087i	$0.762809\pi$
$788$	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	$-0.826642\pi$
$797$		−	29.2527i		−	1.03618i	0.855325	−	0.518092i	$-0.173358\pi$
$798$	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	−0.890615	−	0.454758i	$-0.849726\pi$
$809$	−1.46413	+	2.53595i	−0.0514761	+	0.0891592i	0.839139	+	0.543917i	$0.183059\pi$
$810$	0.551951	−	1.63044i	0.0193936	−	0.0572879i
$811$	8.39251	−	1.47983i	0.294701	−	0.0519637i	−0.0243430	−	0.999704i	$-0.507749\pi$
$811$	8.39251	−	1.47983i	0.294701	−	0.0519637i	0.319044	+	0.947740i	$0.396638\pi$
$812$	−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	0.911241	−	0.411873i	$-0.135125\pi$
$821$	9.95381	+	11.8625i	0.347390	+	0.414004i	−0.563851	+	0.825877i	$0.690681\pi$
$822$	−0.129527	−	5.71832i	−0.00451778	−	0.199449i
$823$	8.78243	+	49.8076i	0.306136	+	1.73619i	0.618108	+	0.786094i	$0.287900\pi$
$823$	8.78243	+	49.8076i	0.306136	+	1.73619i	−0.311971	+	0.950092i	$0.600989\pi$
$824$	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	−0.996347	−	0.0853977i	$-0.972784\pi$
$827$	−5.12484	+	14.0804i	−0.178208	+	0.489623i	0.818139	+	0.575021i	$0.195006\pi$
$828$	−8.69505	−	6.64902i	−0.302174	−	0.231070i
$829$	−41.6975	+	24.0741i	−1.44821	+	0.836127i	−0.998375	−	0.0569831i	$-0.981852\pi$
$829$	−41.6975	+	24.0741i	−1.44821	+	0.836127i	−0.449839	+	0.893110i	$0.648519\pi$
$830$	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	0.825339	+	0.564637i	$0.190984\pi$
$839$	−4.15201	+	23.5472i	−0.143343	+	0.812940i	−0.968682	+	0.248303i	$0.920127\pi$
$840$	−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	0.776247	−	0.630429i	$-0.217121\pi$
$853$	−6.53123	−	17.9444i	−0.223625	−	0.614405i	−0.999872	+	0.0160247i	$0.994899\pi$
$854$	−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	−0.761964	−	0.647620i	$-0.775765\pi$
$857$	−27.2072	+	9.90261i	−0.929380	+	0.338267i	−0.167416	+	0.985886i	$0.553542\pi$
$858$	−0.414042	+	0.251718i	−0.0141352	+	0.00859351i
$859$	−18.5756	−	22.1376i	−0.633792	−	0.755324i	0.349584	−	0.936905i	$-0.386323\pi$
$859$	−18.5756	−	22.1376i	−0.633792	−	0.755324i	−0.983376	+	0.181581i	$0.941878\pi$
$860$	−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	−0.858987	−	0.511997i	$-0.828906\pi$
$863$	0.408611	−	0.707734i	0.0139093	−	0.0240916i	0.872896	+	0.487906i	$0.162239\pi$
$864$	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	0.110347	−	0.993893i	$-0.464804\pi$
$877$	−3.72820	−	0.657381i	−0.125892	−	0.0221982i	−0.236239	+	0.971695i	$0.575915\pi$
$878$	−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	0.999991	−	0.00415465i	$-0.00132247\pi$
$881$	14.7339	+	25.5199i	0.496398	+	0.859786i	−0.503594	+	0.863941i	$0.667989\pi$
$882$	−1.61173	−	8.06767i	−0.0542697	−	0.271653i
$883$	15.4289	−	42.3906i	0.519225	−	1.42656i	−0.352152	−	0.935943i	$-0.614550\pi$
$883$	15.4289	−	42.3906i	0.519225	−	1.42656i	0.871376	−	0.490615i	$-0.163228\pi$
$884$	−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	0.959696	−	0.281042i	$-0.0906800\pi$
$887$	−1.13904	−	6.45982i	−0.0382453	−	0.216900i	−0.997941	+	0.0641423i	$0.979569\pi$
$888$	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	−0.289883	−	0.957062i	$-0.593616\pi$
$907$	21.1712	−	25.2308i	0.702977	−	0.837775i	0.992860	+	0.119287i	$0.0380609\pi$
$908$	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	0.999163	−	0.0408979i	$-0.0130218\pi$
$919$	14.0711	+	24.3719i	0.464163	+	0.803954i	−0.535000	+	0.844852i	$0.679688\pi$
$920$	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	−0.697489	−	0.716595i	$-0.745699\pi$
$929$	−23.5051	+	8.55517i	−0.771178	+	0.280686i	−0.0736890	+	0.997281i	$0.523477\pi$
$930$	−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	−0.959236	−	0.282607i	$-0.908801\pi$
$937$	−4.72951	−	26.8224i	−0.154506	−	0.876250i	0.804729	−	0.593642i	$-0.202310\pi$
$938$	−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	−0.226924	−	0.973912i	$-0.572867\pi$
$941$	17.5750	−	48.2869i	0.572929	−	1.57411i	0.799853	−	0.600196i	$-0.204911\pi$
$942$	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	0.529463	−	0.848333i	$-0.322393\pi$
$947$	22.6753	+	3.99827i	0.736848	+	0.129926i	0.207385	+	0.978259i	$0.433505\pi$
$948$	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	−0.811738	−	0.584021i	$-0.801478\pi$
$953$	4.65509	−	26.4004i	0.150793	−	0.855191i	0.962532	−	0.271170i	$-0.0874105\pi$
$954$	−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	−0.268075	−	0.963398i	$-0.586387\pi$
$967$	4.53476	−	1.65052i	0.145828	−	0.0530771i	0.413903	+	0.910321i	$0.364165\pi$
$968$	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	−0.830137	−	0.557559i	$-0.811738\pi$
$971$	−17.2197	−	47.3108i	−0.552607	−	1.51828i	0.277530	−	0.960717i	$-0.410484\pi$
$972$	−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	−0.980060	−	0.198704i	$-0.936327\pi$
$977$	−9.93809	+	17.2133i	−0.317948	+	0.550701i	0.662112	+	0.749405i	$0.269660\pi$
$978$	−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	0.996217	−	0.0868967i	$-0.0276950\pi$
$983$	33.9749	+	28.5084i	1.08363	+	0.909275i	0.0874147	+	0.996172i	$0.472139\pi$
$984$	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	−0.597105	−	0.802163i	$-0.703682\pi$
$991$	7.50317	−	42.5526i	0.238346	−	1.35173i	0.835451	−	0.549565i	$-0.185206\pi$
$992$	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	−0.726436	−	0.687234i	$-0.758825\pi$
$997$	8.58190	−	23.5786i	0.271792	−	0.746741i	0.998228	−	0.0595073i	$-0.0189530\pi$
$998$	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.157.14	yes	240
8.5	even	2	inner	456.2.bk.a.157.5	yes	240
19.4	even	9	inner	456.2.bk.a.61.5	✓	240
152.61	even	18	inner	456.2.bk.a.61.14	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bk.a.61.5	✓	240	19.4	even	9	inner
456.2.bk.a.61.14	yes	240	152.61	even	18	inner
456.2.bk.a.157.5	yes	240	8.5	even	2	inner
456.2.bk.a.157.14	yes	240	1.1	even	1	trivial

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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