LMFDB - Embedded newform 456.2.bk.a.61.5

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			61.5
Character	$\chi$	$=$	456.61
Dual form			456.2.bk.a.157.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.31763 + 0.513660i) q^{2} +(0.984808 - 0.173648i) q^{3} +(1.47231 - 1.35363i) q^{4} +(0.782380 + 0.932405i) q^{5} +(-1.20842 + 0.734660i) q^{6} +(-1.79007 + 3.10050i) q^{7} +(-1.24466 + 2.53985i) q^{8} +(0.939693 - 0.342020i) q^{9} +(-1.50983 - 0.826689i) q^{10} +(-5.51234 + 3.18255i) q^{11} +(1.21488 - 1.58873i) q^{12} +(0.0530119 + 0.00934743i) q^{13} +(0.766056 - 5.00480i) q^{14} +(0.932405 + 0.782380i) q^{15} +(0.335379 - 3.98592i) 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} +(5.62849 - 7.02490i) q^{22} +(4.19254 + 3.51795i) q^{23} +(-0.784706 + 2.71740i) q^{24} +(0.610982 - 3.46505i) q^{25} +(-0.0746516 + 0.0149136i) q^{26} +(0.866025 - 0.500000i) q^{27} +(1.56138 + 6.98798i) q^{28} +(1.38766 + 3.81257i) q^{29} +(-1.63044 - 0.551951i) q^{30} +(2.70891 - 4.69196i) q^{31} +(1.60550 + 5.42424i) q^{32} +(-4.87595 + 4.09141i) q^{33} +(10.0597 - 0.227864i) q^{34} +(-4.29143 + 0.756696i) q^{35} +(0.920548 - 1.77555i) q^{36} +1.63372i q^{37} +(-2.28895 - 5.72370i) q^{38} +0.0538297 q^{39} +(-3.34196 + 0.826606i) q^{40} +(-0.104577 - 0.593088i) q^{41} +(-0.114656 - 5.06179i) q^{42} +(1.27465 + 1.51907i) q^{43} +(-3.80787 + 12.1474i) q^{44} +(1.05410 + 0.608584i) q^{45} +(-7.33125 - 2.48183i) q^{46} +(4.54888 - 1.65566i) q^{47} +(-0.361863 - 3.98360i) q^{48} +(-2.90872 - 5.03804i) q^{49} +(0.974807 + 4.87949i) q^{50} +(-7.00699 - 1.23552i) q^{51} +(0.0907028 - 0.0579962i) q^{52} +(-8.44443 + 10.0637i) q^{53} +(-0.884273 + 1.10366i) 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} +(2.43184 - 0.110225i) q^{60} +(6.19143 - 7.37866i) q^{61} +(-1.15927 + 7.57374i) q^{62} +(-0.621685 + 3.52575i) q^{63} +(-4.90167 - 6.32247i) q^{64} +(0.0327599 + 0.0567418i) q^{65} +(4.32312 - 7.89555i) q^{66} +(2.64384 + 7.26389i) q^{67} +(-13.1379 + 5.46748i) q^{68} +(4.73973 + 2.73648i) q^{69} +(5.26585 - 3.20138i) q^{70} +(5.72109 - 4.80057i) q^{71} +(-0.300914 + 2.81237i) q^{72} +(1.33009 + 7.54329i) q^{73} +(-0.839176 - 2.15264i) q^{74} -3.51850i q^{75} +(5.95602 + 6.36599i) q^{76} -22.7880i q^{77} +(-0.0709278 + 0.0276502i) q^{78} +(1.03823 + 5.88807i) q^{79} +(3.97888 - 2.80579i) q^{80} +(0.766044 - 0.642788i) q^{81} +(0.442440 + 0.727755i) q^{82} +(6.95877 + 4.01765i) q^{83} +(2.75111 + 6.61068i) q^{84} +(-2.96198 - 8.13797i) q^{85} +(-2.45980 - 1.34684i) q^{86} +(2.02863 + 3.51369i) q^{87} +(-1.22224 - 17.9617i) q^{88} +(2.02146 - 11.4642i) q^{89} +(-1.70152 - 0.260442i) q^{90} +(-0.123877 + 0.147631i) q^{91} +(10.9347 - 0.495624i) 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} +(6.42046 + 5.14420i) 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 $

$2$	−1.31763	+	0.513660i	−0.931706	+	0.363212i
$2$	−1.31763	+	0.513660i	−0.931706	+	0.363212i
$3$	0.984808	−	0.173648i	0.568579	−	0.100256i
$3$	0.984808	−	0.173648i	0.568579	−	0.100256i
$4$	1.47231	−	1.35363i	0.736154	−	0.676814i
$5$	0.782380	+	0.932405i	0.349891	+	0.416984i	0.912072	−	0.410030i	$-0.134482\pi$
$5$	0.782380	+	0.932405i	0.349891	+	0.416984i	−0.562181	+	0.827014i	$0.690037\pi$
$6$	−1.20842	+	0.734660i	−0.493335	+	0.299924i
$7$	−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	$0.930126\pi$
$8$	−1.24466	+	2.53985i	−0.440052	+	0.897972i
$9$	0.939693	−	0.342020i	0.313231	−	0.114007i
$10$	−1.50983	−	0.826689i	−0.477450	−	0.261422i
$11$	−5.51234	+	3.18255i	−1.66203	+	0.959575i	−0.690291	+	0.723532i	$0.742517\pi$
$11$	−5.51234	+	3.18255i	−1.66203	+	0.959575i	−0.971743	+	0.236043i	$0.924149\pi$
$12$	1.21488	−	1.58873i	0.350707	−	0.458626i
$13$	0.0530119	+	0.00934743i	0.0147029	+	0.00259251i	0.180995	−	0.983484i	$-0.442068\pi$
$13$	0.0530119	+	0.00934743i	0.0147029	+	0.00259251i	−0.166292	+	0.986077i	$0.553179\pi$
$14$	0.766056	−	5.00480i	0.204737	−	1.33759i
$15$	0.932405	+	0.782380i	0.240746	+	0.202010i
$16$	0.335379	−	3.98592i	0.0838448	−	0.996479i
$17$	−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
$22$	5.62849	−	7.02490i	1.20000	−	1.49771i
$23$	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	$0.528934\pi$
$24$	−0.784706	+	2.71740i	−0.160177	+	0.554686i
$25$	0.610982	−	3.46505i	0.122196	−	0.693010i
$26$	−0.0746516	+	0.0149136i	−0.0146404	+	0.00292480i
$27$	0.866025	−	0.500000i	0.166667	−	0.0962250i
$28$	1.56138	+	6.98798i	0.295074	+	1.32060i
$29$	1.38766	+	3.81257i	0.257683	+	0.707977i	0.999309	+	0.0371643i	$0.0118325\pi$
$29$	1.38766	+	3.81257i	0.257683	+	0.707977i	−0.741626	+	0.670813i	$0.765945\pi$
$30$	−1.63044	−	0.551951i	−0.297677	−	0.100772i
$31$	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	$0.00492769\pi$
$32$	1.60550	+	5.42424i	0.283815	+	0.958879i
$33$	−4.87595	+	4.09141i	−0.848794	+	0.712223i
$34$	10.0597	−	0.227864i	1.72522	−	0.0390784i
$35$	−4.29143	+	0.756696i	−0.725385	+	0.127905i
$36$	0.920548	−	1.77555i	0.153425	−	0.295926i
$37$			1.63372i			0.268582i	0.990942	+	0.134291i	$0.0428757\pi$
$37$			1.63372i			0.268582i	−0.990942	+	0.134291i	$0.957124\pi$
$38$	−2.28895	−	5.72370i	−0.371317	−	0.928506i
$39$	0.0538297			0.00861965
$40$	−3.34196	+	0.826606i	−0.528410	+	0.130698i
$41$	−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	$0.959419\pi$
$42$	−0.114656	−	5.06179i	−0.0176918	−	0.781051i
$43$	1.27465	+	1.51907i	0.194382	+	0.231656i	0.854428	−	0.519570i	$-0.173908\pi$
$43$	1.27465	+	1.51907i	0.194382	+	0.231656i	−0.660046	+	0.751225i	$0.729463\pi$
$44$	−3.80787	+	12.1474i	−0.574058	+	1.83128i
$45$	1.05410	+	0.608584i	0.157136	+	0.0907223i
$46$	−7.33125	−	2.48183i	−1.08093	−	0.365926i
$47$	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	$0.274033\pi$
$48$	−0.361863	−	3.98360i	−0.0522304	−	0.574983i
$49$	−2.90872	−	5.03804i	−0.415531	−	0.719720i
$50$	0.974807	+	4.87949i	0.137858	+	0.690065i
$51$	−7.00699	−	1.23552i	−0.981174	−	0.173007i
$52$	0.0907028	−	0.0579962i	0.0125782	−	0.00804262i
$53$	−8.44443	+	10.0637i	−1.15993	+	1.38235i	−0.249663	+	0.968333i	$0.580320\pi$
$53$	−8.44443	+	10.0637i	−1.15993	+	1.38235i	−0.910268	+	0.414019i	$0.864125\pi$
$54$	−0.884273	+	1.10366i	−0.120334	+	0.150189i
$55$	−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	$-0.989113\pi$
$59$	−1.62716	+	4.47058i	−0.211838	+	0.582020i	0.787577	+	0.616216i	$0.211335\pi$
$60$	2.43184	−	0.110225i	0.313949	−	0.0142300i
$61$	6.19143	−	7.37866i	0.792731	−	0.944741i	−0.206702	−	0.978404i	$-0.566273\pi$
$61$	6.19143	−	7.37866i	0.792731	−	0.944741i	0.999433	+	0.0336634i	$0.0107174\pi$
$62$	−1.15927	+	7.57374i	−0.147227	+	0.961865i
$63$	−0.621685	+	3.52575i	−0.0783250	+	0.444203i
$64$	−4.90167	−	6.32247i	−0.612708	−	0.790309i
$65$	0.0327599	+	0.0567418i	0.00406337	+	0.00703796i
$66$	4.32312	−	7.89555i	0.532139	−	0.971875i
$67$	2.64384	+	7.26389i	0.322996	+	0.887425i	0.989835	+	0.142223i	$0.0454250\pi$
$67$	2.64384	+	7.26389i	0.322996	+	0.887425i	−0.666838	+	0.745202i	$0.732353\pi$
$68$	−13.1379	+	5.46748i	−1.59320	+	0.663030i
$69$	4.73973	+	2.73648i	0.570596	+	0.329434i
$70$	5.26585	−	3.20138i	0.629389	−	0.382638i
$71$	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	$0.131633\pi$
$72$	−0.300914	+	2.81237i	−0.0354630	+	0.331442i
$73$	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	$0.796493\pi$
$74$	−0.839176	−	2.15264i	−0.0975523	−	0.250240i
$75$		−	3.51850i		−	0.406282i
$76$	5.95602	+	6.36599i	0.683203	+	0.730229i
$77$		−	22.7880i		−	2.59693i
$78$	−0.0709278	+	0.0276502i	−0.00803099	+	0.00313076i
$79$	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	$0.835255\pi$
$80$	3.97888	−	2.80579i	0.444852	−	0.313697i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	0.442440	+	0.727755i	0.0488593	+	0.0803671i
$83$	6.95877	+	4.01765i	0.763824	+	0.440994i	0.830667	−	0.556770i	$-0.187959\pi$
$83$	6.95877	+	4.01765i	0.763824	+	0.440994i	−0.0668431	+	0.997763i	$0.521293\pi$
$84$	2.75111	+	6.61068i	0.300171	+	0.721284i
$85$	−2.96198	−	8.13797i	−0.321272	−	0.882687i
$86$	−2.45980	−	1.34684i	−0.265247	−	0.145233i
$87$	2.02863	+	3.51369i	0.217492	+	0.376707i
$88$	−1.22224	−	17.9617i	−0.130291	−	1.91472i
$89$	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	$-0.156087\pi$
$90$	−1.70152	−	0.260442i	−0.179356	−	0.0274530i
$91$	−0.123877	+	0.147631i	−0.0129858	+	0.0154759i
$92$	10.9347	−	0.495624i	1.14002	−	0.0516724i
$93$	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	$0.732232\pi$
$98$	6.42046	+	5.14420i	0.648564	+	0.519642i
$99$	−4.09141	+	4.87595i	−0.411202	+	0.490052i
$100$	−3.79084	−	5.92866i	−0.379084	−	0.592866i
$101$	6.29814	+	1.11053i	0.626689	+	0.110502i	0.477968	−	0.878377i	$-0.341373\pi$
$101$	6.29814	+	1.11053i	0.626689	+	0.110502i	0.148721	+	0.988879i	$0.452485\pi$
$102$	9.86726	−	1.97124i	0.977005	−	0.195182i
$103$	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	$0.476166\pi$
$104$	−0.0897226	+	0.123008i	−0.00879803	+	0.0120619i
$105$	−4.09484	+	1.49040i	−0.399615	+	0.145448i
$106$	5.95734	−	17.5978i	0.578628	−	1.70925i
$107$	−12.5343	−	7.23667i	−1.21173	−	0.699595i	−0.248597	−	0.968607i	$-0.579970\pi$
$107$	−12.5343	−	7.23667i	−1.21173	−	0.699595i	−0.963137	+	0.269012i	$0.913303\pi$
$108$	0.598241	−	1.90843i	0.0575658	−	0.183639i
$109$	6.40684	+	7.63538i	0.613664	+	0.731336i	0.979967	−	0.199159i	$-0.0638211\pi$
$109$	6.40684	+	7.63538i	0.613664	+	0.731336i	−0.366303	+	0.930496i	$0.619377\pi$
$110$	10.9537	−	0.248114i	1.04439	−	0.0236568i
$111$	0.283693	+	1.60890i	0.0269269	+	0.152710i
$112$	11.7580	+	8.17492i	1.11102	+	0.772457i
$113$	15.0800			1.41861			0.709304	−	0.704902i	$-0.249009\pi$
$113$	15.0800			1.41861			0.709304	+	0.704902i	$0.249009\pi$
$114$	−3.24808	−	5.23927i	−0.304211	−	0.490703i
$115$			6.66152i			0.621190i
$116$	7.20388	+	3.73490i	0.668863	+	0.346777i
$117$	0.0530119	−	0.00934743i	0.00490095	−	0.000864170i
$118$	−0.152361	−	6.72639i	−0.0140260	−	0.619214i
$119$	19.5135	−	16.3737i	1.78880	−	1.50098i
$120$	−3.14765	+	1.39437i	−0.287340	+	0.127288i
$121$	14.7573	−	25.5603i	1.34157	−	2.32367i
$122$	−4.36791	+	12.9026i	−0.395452	+	1.16815i
$123$	−0.205977	−	0.565918i	−0.0185724	−	0.0510271i
$124$	−2.36283	−	10.5749i	−0.212189	−	0.949651i
$125$	8.97934	−	5.18422i	0.803136	−	0.463691i
$126$	−0.991885	−	4.96498i	−0.0883641	−	0.442316i
$127$	−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	$0.884468\pi$
$128$	9.70619	+	5.81290i	0.857914	+	0.513793i
$129$	1.51907	+	1.27465i	0.133746	+	0.112227i
$130$	−0.0723115	−	0.0579374i	−0.00634214	−	0.00508144i
$131$	5.14262	−	14.1292i	0.449312	−	1.23448i	−0.483891	−	0.875128i	$-0.660777\pi$
$131$	5.14262	−	14.1292i	0.449312	−	1.23448i	0.933204	−	0.359348i	$-0.117001\pi$
$132$	−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
$136$	14.5025	−	13.9525i	1.24358	−	1.19642i
$137$	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	$0.666950\pi$
$138$	−7.65084	−	1.17107i	−0.651283	−	0.0996881i
$139$	−15.8721	−	2.79869i	−1.34626	−	0.237381i	−0.546376	−	0.837540i	$-0.683993\pi$
$139$	−15.8721	−	2.79869i	−1.34626	−	0.237381i	−0.799881	+	0.600158i	$0.795104\pi$
$140$	−5.29403	+	6.92310i	−0.447427	+	0.585108i
$141$	4.19227	−	2.42041i	0.353053	−	0.203835i
$142$	−5.07244	+	9.26407i	−0.425669	+	0.777424i
$143$	−0.321968	+	0.117187i	−0.0269244	+	0.00979966i
$144$	−1.04811	−	3.86024i	−0.0873425	−	0.321687i
$145$	−2.46918	+	4.27675i	−0.205054	+	0.355165i
$146$	−5.62725	−	9.25607i	−0.465714	−	0.766038i
$147$	−3.73937	−	4.45641i	−0.308418	−	0.367559i
$148$	2.21145	+	2.40534i	0.181780	+	0.197718i
$149$	6.59194	−	1.16234i	0.540033	−	0.0952223i	0.103023	−	0.994679i	$-0.467149\pi$
$149$	6.59194	−	1.16234i	0.540033	−	0.0952223i	0.437010	+	0.899457i	$0.356037\pi$
$150$	1.80731	+	4.63609i	0.147566	+	0.378535i
$151$	−11.1184			−0.904803			−0.452401	−	0.891814i	$-0.649433\pi$
$151$	−11.1184			−0.904803			−0.452401	+	0.891814i	$0.649433\pi$
$152$	−11.1178	−	5.32866i	−0.901772	−	0.432211i
$153$	−7.11508			−0.575220
$154$	11.7053	+	30.0262i	0.943237	+	2.41958i
$155$	6.49420	−	1.14510i	0.521627	−	0.0919769i
$156$	0.0792539	−	0.0728654i	0.00634539	−	0.00583390i
$157$	1.73586	+	2.06872i	0.138537	+	0.165102i	0.830852	−	0.556493i	$-0.187854\pi$
$157$	1.73586	+	2.06872i	0.138537	+	0.165102i	−0.692315	+	0.721595i	$0.743409\pi$
$158$	−4.39246	−	7.22501i	−0.349445	−	0.574791i
$159$	−6.56860	+	11.3771i	−0.520924	+	0.902266i
$160$	−3.80148	+	5.74079i	−0.300533	+	0.453850i
$161$	−18.4123	+	6.70155i	−1.45110	+	0.528156i
$162$	−0.679191	+	1.24044i	−0.0533622	+	0.0974585i
$163$	5.09870	−	2.94374i	0.399361	−	0.230571i	−0.286847	−	0.957976i	$-0.592607\pi$
$163$	5.09870	−	2.94374i	0.399361	−	0.230571i	0.686208	+	0.727405i	$0.259274\pi$
$164$	−0.956792	−	0.731649i	−0.0747129	−	0.0571322i
$165$	−7.62970	−	1.34532i	−0.593971	−	0.104733i
$166$	−11.2328	−	1.71934i	−0.871834	−	0.133447i
$167$	−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	$0.967666\pi$
$168$	−7.02059	−	7.29731i	−0.541650	−	0.563000i
$169$	−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	$-0.940389\pi$
$173$	−1.44932	+	3.98197i	−0.110190	+	0.302743i	0.872326	+	0.488925i	$0.162611\pi$
$174$	−4.47783	−	3.58772i	−0.339463	−	0.271985i
$175$	9.64967	+	8.09703i	0.729446	+	0.612078i
$176$	10.8367	+	23.0391i	0.816844	+	1.73664i
$177$	−0.826130	+	4.68522i	−0.0620958	+	0.352163i
$178$	3.22519	+	16.1440i	0.241738	+	1.21004i
$179$	2.07451	−	1.19772i	0.155056	−	0.0895216i	−0.420465	−	0.907309i	$-0.638133\pi$
$179$	2.07451	−	1.19772i	0.155056	−	0.0895216i	0.575520	+	0.817787i	$0.304800\pi$
$180$	2.37575	−	0.530835i	0.177078	−	0.0395661i
$181$	−1.18379	−	3.25243i	−0.0879903	−	0.241751i	0.887891	−	0.460054i	$-0.152170\pi$
$181$	−1.18379	−	3.25243i	−0.0879903	−	0.241751i	−0.975881	+	0.218303i	$0.929948\pi$
$182$	0.0873922	−	0.258153i	0.00647794	−	0.0191356i
$183$	4.81608	−	8.34169i	0.356015	−	0.616636i
$184$	−14.1533	+	6.26977i	−1.04340	+	0.462213i
$185$	−1.52329	+	1.27819i	−0.111994	+	0.0939745i
$186$	0.173508	+	7.65998i	0.0127222	+	0.561657i
$187$	44.6002	−	7.86422i	3.26149	−	0.575088i
$188$	4.45620	−	8.59513i	0.325002	−	0.626864i
$189$			3.58014i			0.260417i
$190$	3.54597	−	6.61234i	0.257252	−	0.479709i
$191$	−23.4516			−1.69690			−0.848451	−	0.529274i	$-0.822464\pi$
$191$	−23.4516			−1.69690			−0.848451	+	0.529274i	$0.822464\pi$
$192$	−5.92509	−	5.37525i	−0.427606	−	0.387926i
$193$	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	$0.940183\pi$
$194$	10.3433	−	0.234289i	0.742605	−	0.0168209i
$195$	0.0421153	+	0.0501911i	0.00301594	+	0.00359426i
$196$	−11.1022	−	3.48023i	−0.793012	−	0.248588i
$197$	10.3541	+	5.97796i	0.737701	+	0.425912i	0.821233	−	0.570593i	$-0.193287\pi$
$197$	10.3541	+	5.97796i	0.737701	+	0.425912i	−0.0835317	+	0.996505i	$0.526620\pi$
$198$	2.88639	−	8.52630i	0.205127	−	0.605938i
$199$	−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	$0.469478\pi$
$200$	8.04024	+	5.86459i	0.568531	+	0.414689i
$201$	3.86503	+	6.69444i	0.272619	+	0.472189i
$202$	−8.86907	+	1.77183i	−0.624026	+	0.124665i
$203$	−14.3049	−	2.52234i	−1.00401	−	0.177033i
$204$	−11.9889	+	7.66579i	−0.839389	+	0.536713i
$205$	0.471179	−	0.561529i	0.0329086	−	0.0392189i
$206$	−20.1841	−	16.1719i	−1.40629	−	1.12675i
$207$	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	$-0.916991\pi$
$211$	−0.876074	+	2.40699i	−0.0603114	+	0.165704i	0.905877	+	0.423540i	$0.139213\pi$
$212$	1.18969	+	26.2474i	0.0817080	+	1.80268i
$213$	4.80057	−	5.72109i	0.328929	−	0.392003i
$214$	20.2327	+	3.09691i	1.38308	+	0.211701i
$215$	−0.419125	+	2.37698i	−0.0285841	+	0.162108i
$216$	0.192022	+	2.82190i	0.0130654	+	0.192006i
$217$	9.69827	+	16.7979i	0.658362	+	1.14032i
$218$	−12.3638	−	6.76968i	−0.837385	−	0.458501i
$219$	2.61976	+	7.19772i	0.177027	+	0.486377i
$220$	−14.3055	+	5.95338i	−0.964474	+	0.401377i
$221$	−0.331690	−	0.191501i	−0.0223119	−	0.0128818i
$222$	−1.20023	−	1.97422i	−0.0805542	−	0.132501i
$223$	−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	$0.309384\pi$
$224$	−19.6918	−	4.73194i	−1.31571	−	0.316166i
$225$	−0.610982	−	3.46505i	−0.0407321	−	0.231003i
$226$	−19.8699	+	7.74600i	−1.32173	+	0.515256i
$227$			5.25834i			0.349008i	0.984656	+	0.174504i	$0.0558323\pi$
$227$			5.25834i			0.349008i	−0.984656	+	0.174504i	$0.944168\pi$
$228$	6.97098	+	5.23502i	0.461664	+	0.346698i
$229$		−	9.57101i		−	0.632470i	−0.948681	−	0.316235i	$-0.897581\pi$
$229$		−	9.57101i		−	0.632470i	0.948681	−	0.316235i	$-0.102419\pi$
$230$	−3.42175	−	8.77743i	−0.225624	−	0.578767i
$231$	−3.95709	−	22.4418i	−0.260358	−	1.47656i
$232$	−11.4105	−	1.22088i	−0.749138	−	0.0801549i
$233$	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	$0.214705\pi$
$234$	−0.0650488	+	0.0395466i	−0.00425237	+	0.00258524i
$235$	5.10270	+	2.94604i	0.332863	+	0.192179i
$236$	3.65583	+	8.78464i	0.237974	+	0.571832i
$237$	2.04490	+	5.61833i	0.132831	+	0.364950i
$238$	−17.3010	+	31.5978i	−1.12146	+	2.04818i
$239$	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	$0.544577\pi$
$240$	3.43121	−	3.45409i	0.221484	−	0.222961i
$241$	−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	$0.982272\pi$
$242$	−6.31533	+	41.2593i	−0.405965	+	2.65225i
$243$	0.642788	−	0.766044i	0.0412348	−	0.0491418i
$244$	−0.872275	−	19.2446i	−0.0558417	−	1.23201i
$245$	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
$250$	−9.16854	+	11.4432i	−0.579869	+	0.723733i
$251$	0.492247	−	0.586637i	0.0310704	−	0.0370282i	−0.750285	−	0.661114i	$-0.770084\pi$
$251$	0.492247	−	0.586637i	0.0310704	−	0.0370282i	0.781356	+	0.624086i	$0.214528\pi$
$252$	3.85725	+	6.03252i	0.242984	+	0.380013i
$253$	−34.3068	−	6.04921i	−2.15685	−	0.380310i
$254$	−3.19701	−	16.0030i	−0.200598	−	1.00411i
$255$	−4.33012	−	7.49999i	−0.271163	−	0.469668i
$256$	−15.7750	−	2.67359i	−0.985940	−	0.167099i
$257$	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	$0.375993\pi$
$258$	−2.65631	−	0.899234i	−0.165374	−	0.0559839i
$259$	−5.06534	−	2.92448i	−0.314745	−	0.181718i
$260$	0.125040	+	0.0391967i	0.00775465	+	0.00243087i
$261$	2.60795	+	3.10804i	0.161428	+	0.192383i
$262$	0.481536	+	21.2587i	0.0297494	+	1.31336i
$263$	−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	$-0.382496\pi$
$264$	−4.32268	−	17.4766i	−0.266043	−	1.07561i
$265$	−15.9902			−0.982268
$266$	21.8437	+	3.14895i	1.33932	+	0.193075i
$267$		−	11.6411i		−	0.712424i
$268$	13.7252	+	7.11590i	0.838397	+	0.434673i
$269$	−10.3763	+	1.82963i	−0.632656	+	0.111554i	−0.480774	−	0.876844i	$-0.659644\pi$
$269$	−10.3763	+	1.82963i	−0.632656	+	0.111554i	−0.151882	+	0.988399i	$0.548533\pi$
$270$	−1.72089	+	0.0389804i	−0.104730	+	0.00237227i
$271$	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	$0.229848\pi$
$272$	−11.9421	+	25.8336i	−0.724094	+	1.56639i
$273$	−0.0963591	+	0.166899i	−0.00583192	+	0.0101012i
$274$	−5.41776	−	1.83406i	−0.327299	−	0.110800i
$275$	7.65976	+	21.0450i	0.461901	+	1.26906i
$276$	10.6825	−	2.38689i	0.643012	−	0.143674i
$277$	−0.567859	+	0.327853i	−0.0341193	+	0.0196988i	−0.516963	−	0.856008i	$-0.672937\pi$
$277$	−0.567859	+	0.327853i	−0.0341193	+	0.0196988i	0.482843	+	0.875707i	$0.339604\pi$
$278$	22.3512	−	4.46524i	1.34054	−	0.267807i
$279$	0.940793	−	5.33550i	0.0563238	−	0.319428i
$280$	3.41946	−	11.8414i	0.204352	−	0.707660i
$281$	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	$0.623774\pi$
$282$	−4.28060	+	5.34261i	−0.254906	+	0.318148i
$283$	1.94793	−	5.35189i	0.115792	−	0.318137i	−0.868235	−	0.496153i	$-0.834746\pi$
$283$	1.94793	−	5.35189i	0.115792	−	0.318137i	0.984028	+	0.178016i	$0.0569678\pi$
$284$	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
$288$	3.36387	+	4.54801i	0.198218	+	0.267994i
$289$	25.7577	+	21.6133i	1.51516	+	1.27137i
$290$	1.05668	−	6.90350i	0.0620504	−	0.405387i
$291$	−7.20455	−	1.27036i	−0.422338	−	0.0744696i
$292$	12.1691	+	9.30560i	0.712143	+	0.544569i
$293$	−11.7846	+	6.80384i	−0.688464	+	0.397485i	−0.803036	−	0.595930i	$-0.796784\pi$
$293$	−11.7846	+	6.80384i	−0.688464	+	0.397485i	0.114573	+	0.993415i	$0.463450\pi$
$294$	7.21619	+	3.95114i	0.420857	+	0.230435i
$295$	−5.44145	+	1.98053i	−0.316813	+	0.115311i
$296$	−4.14940	−	2.03342i	−0.241179	−	0.118190i
$297$	−3.18255	+	5.51234i	−0.184670	+	0.319858i
$298$	−8.08870	+	4.91755i	−0.468566	+	0.284866i
$299$	0.189371	+	0.225683i	0.0109516	+	0.0130516i
$300$	−4.76275	−	5.18032i	−0.274977	−	0.299086i
$301$	−6.99157	+	1.23280i	−0.402988	+	0.0710576i
$302$	14.6500	−	5.71108i	0.843011	−	0.328635i
$303$	6.39530			0.367401
$304$	17.3863	+	1.31044i	0.997172	+	0.0751591i
$305$	11.7240			0.671311
$306$	9.37506	−	3.65473i	0.535936	−	0.208927i
$307$	−3.04647	+	0.537175i	−0.173871	+	0.0306582i	−0.259906	−	0.965634i	$-0.583692\pi$
$307$	−3.04647	+	0.537175i	−0.173871	+	0.0306582i	0.0860346	+	0.996292i	$0.472580\pi$
$308$	−30.8465	−	33.5509i	−1.75764	−	1.91174i
$309$	11.7555	+	14.0097i	0.668749	+	0.796984i
$310$	−7.96878	+	4.84463i	−0.452596	+	0.275157i
$311$	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	$-0.00327336\pi$
$312$	−0.0669994	+	0.136719i	−0.00379310	+	0.00774021i
$313$	−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	$0.441482\pi$
$314$	−3.34985	−	1.83417i	−0.189043	−	0.103508i
$315$	−3.77382	+	2.17882i	−0.212631	+	0.122762i
$316$	9.49884	+	7.26368i	0.534352	+	0.408614i
$317$	30.5658	+	5.38958i	1.71675	+	0.302709i	0.943494	−	0.331389i	$-0.107517\pi$
$317$	30.5658	+	5.38958i	1.71675	+	0.302709i	0.773253	+	0.634098i	$0.218628\pi$
$318$	2.81101	−	18.3649i	0.157634	−	1.02985i
$319$	−19.7830	−	16.5999i	−1.10763	−	0.929416i
$320$	2.06013	−	9.51692i	0.115165	−	0.532012i
$321$	−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
$326$	−5.20614	+	6.49776i	−0.288341	+	0.359878i
$327$	7.63538	+	6.40684i	0.422237	+	0.354299i
$328$	1.63652	+	0.472579i	0.0903616	+	0.0260938i
$329$	−3.00946	+	17.0675i	−0.165917	+	0.940963i
$330$	10.7442	−	2.14643i	0.591447	−	0.118157i
$331$	−25.4444	+	14.6903i	−1.39855	+	0.807453i	−0.994241	−	0.107170i	$-0.965821\pi$
$331$	−25.4444	+	14.6903i	−1.39855	+	0.807453i	−0.404308	+	0.914623i	$0.632488\pi$
$332$	15.6838	−	3.50438i	0.860763	−	0.192328i
$333$	0.558765	+	1.53520i	0.0306202	+	0.0841282i
$334$	24.1281	+	8.16802i	1.32023	+	0.446934i
$335$	−4.70440	+	8.14825i	−0.257029	+	0.445187i
$336$	12.9989	+	6.00897i	0.709148	+	0.327816i
$337$	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	$0.0941747\pi$
$338$	18.3760	−	0.416239i	0.999521	−	0.0226404i
$339$	14.8509	−	2.61862i	0.806591	−	0.142224i
$340$	−15.3767	−	7.97217i	−0.833920	−	0.432352i
$341$			34.4849i			1.86746i
$342$	−4.10853	−	4.59565i	−0.222164	−	0.248504i
$343$	−4.23377			−0.228602
$344$	−5.44470	+	1.34670i	−0.293559	+	0.0726092i
$345$	1.15676	+	6.56032i	0.0622779	+	0.353196i
$346$	−0.135709	−	5.99122i	−0.00729575	−	0.322090i
$347$	−8.08388	−	9.63400i	−0.433966	−	0.517180i	0.504096	−	0.863647i	$-0.331826\pi$
$347$	−8.08388	−	9.63400i	−0.433966	−	0.517180i	−0.938062	+	0.346467i	$0.887381\pi$
$348$	7.74299	+	2.42722i	0.415068	+	0.130113i
$349$	−12.2870	−	7.09390i	−0.657708	−	0.379728i	0.133695	−	0.991023i	$-0.457316\pi$
$349$	−12.2870	−	7.09390i	−0.657708	−	0.379728i	−0.791403	+	0.611295i	$0.790649\pi$
$350$	−16.8738	−	5.71226i	−0.901944	−	0.305333i
$351$	0.0505834	−	0.0184108i	0.00269994	−	0.000982698i
$352$	−26.1130	−	24.7907i	−1.39183	−	1.32135i
$353$	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	$0.831172\pi$
$354$	−1.31807	−	6.59774i	−0.0700547	−	0.350666i
$355$	8.95214	+	1.57850i	0.475130	+	0.0837783i
$356$	−12.5421	−	19.6152i	−0.664731	−	1.03960i
$357$	16.3737	−	19.5135i	0.866590	−	1.03276i
$358$	−2.11822	+	2.64374i	−0.111951	+	0.139726i
$359$	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
$364$	0.0174523	+	0.385041i	0.000914748	+	0.0201816i
$365$	−5.99277	+	7.14190i	−0.313676	+	0.373824i
$366$	−2.06103	+	13.4651i	−0.107732	+	0.703832i
$367$	−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	$0.930909\pi$
$368$	15.4284	−	15.5312i	0.804259	−	0.809622i
$369$	−0.301119	−	0.521553i	−0.0156756	−	0.0271510i
$370$	1.35058	−	2.46664i	0.0702133	−	0.128234i
$371$	−16.0862	−	44.1966i	−0.835156	−	2.29457i
$372$	−4.16324	−	10.0039i	−0.215854	−	0.518678i
$373$	8.56227	+	4.94343i	0.443337	+	0.255961i	0.705012	−	0.709195i	$-0.250941\pi$
$373$	8.56227	+	4.94343i	0.443337	+	0.255961i	−0.261675	+	0.965156i	$0.584275\pi$
$374$	−54.7271	+	33.2715i	−2.82987	+	1.72043i
$375$	7.94269	−	6.66471i	0.410159	−	0.344164i
$376$	−1.45667	+	13.6142i	−0.0751219	+	0.702098i
$377$	0.0379249	+	0.215083i	0.00195323	+	0.0110773i
$378$	−1.83898	−	4.71731i	−0.0945867	−	0.242632i
$379$		−	10.0112i		−	0.514239i	−0.966380	−	0.257119i	$-0.917227\pi$
$379$		−	10.0112i		−	0.514239i	0.966380	−	0.257119i	$-0.0827734\pi$
$380$	−1.27580	+	10.5340i	−0.0654471	+	0.540385i
$381$			11.5394i			0.591181i
$382$	30.9006	−	12.0462i	1.58101	−	0.616335i
$383$	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	$0.909588\pi$
$384$	10.5681	+	4.03913i	0.539303	+	0.206121i
$385$	21.2476	−	17.8289i	1.08288	−	0.908644i
$386$	−0.273274	−	0.449499i	−0.0139093	−	0.0228789i
$387$	1.71733	+	0.991501i	0.0872968	+	0.0504008i
$388$	−13.5083	+	5.62164i	−0.685780	+	0.285395i
$389$	−2.23914	−	6.15197i	−0.113529	−	0.311917i	0.869896	−	0.493235i	$-0.164186\pi$
$389$	−2.23914	−	6.15197i	−0.113529	−	0.311917i	−0.983425	+	0.181318i	$0.941964\pi$
$390$	−0.0812736	−	0.0445004i	−0.00411545	−	0.00225337i
$391$	−19.4703	−	33.7235i	−0.984655	−	1.70547i
$392$	16.4162	−	1.11707i	0.829144	−	0.0564207i
$393$	2.61097	−	14.8076i	0.131706	−	0.746943i
$394$	−16.7136	−	2.55825i	−0.842017	−	0.128883i
$395$	−4.67778	+	5.57476i	−0.235364	+	0.280496i
$396$	0.576415	+	12.7171i	0.0289659	+	0.639061i
$397$	−10.7647	+	29.5758i	−0.540265	+	1.48437i	0.306225	+	0.951959i	$0.400934\pi$
$397$	−10.7647	+	29.5758i	−0.540265	+	1.48437i	−0.846489	+	0.532406i	$0.821288\pi$
$398$	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	$0.352481\pi$
$402$	−8.53135	−	6.83549i	−0.425505	−	0.340923i
$403$	0.187462	−	0.223409i	0.00933815	−	0.0111288i
$404$	10.7761	−	6.89030i	0.536129	−	0.342805i
$405$	1.19868	+	0.211359i	0.0595627	+	0.0105025i
$406$	20.1442	−	4.02433i	0.999740	−	0.199724i
$407$	−5.19940	−	9.00563i	−0.257725	−	0.446392i
$408$	11.8593	−	16.2589i	0.587124	−	0.804935i
$409$	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	$0.185503\pi$
$410$	−0.332406	+	0.981915i	−0.0164163	+	0.0484933i
$411$	3.50264	+	2.02225i	0.172772	+	0.0997502i
$412$	34.9021	+	10.9409i	1.71950	+	0.539017i
$413$	−10.9483	−	13.0477i	−0.538730	−	0.642034i
$414$	−7.73796	+	0.175275i	−0.380300	+	0.00861428i
$415$	1.69833	+	9.63171i	0.0833678	+	0.472802i
$416$	0.0344078	+	0.302557i	0.00168698	+	0.0148341i
$417$	−16.1170			−0.789252
$418$	30.8334	+	24.2663i	1.50811	+	1.18690i
$419$			30.7096i			1.50026i	0.661290	+	0.750130i	$0.270009\pi$
$419$			30.7096i			1.50026i	−0.661290	+	0.750130i	$0.729991\pi$
$420$	−4.01141	+	7.73722i	−0.195737	+	0.377538i
$421$	18.6776	−	3.29337i	0.910291	−	0.160509i	0.301156	−	0.953575i	$-0.402628\pi$
$421$	18.6776	−	3.29337i	0.910291	−	0.160509i	0.609135	+	0.793066i	$0.291517\pi$
$422$	−0.0820324	−	3.62153i	−0.00399327	−	0.176294i
$423$	3.70828	−	3.11162i	0.180303	−	0.151292i
$424$	−15.0498	−	33.9734i	−0.730884	−	1.64989i
$425$	−12.5172	+	21.6804i	−0.607174	+	1.05166i
$426$	−3.38668	+	10.0041i	−0.164085	+	0.484703i
$427$	11.7944	+	32.4048i	0.570771	+	1.56818i
$428$	−28.2501	+	6.31215i	−1.36552	+	0.305109i
$429$	−0.296728	+	0.171316i	−0.0143262	+	0.00827121i
$430$	−0.668704	−	3.34727i	−0.0322478	−	0.161420i
$431$	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	$-0.121249\pi$
$432$	−1.70251	−	3.61959i	−0.0819121	−	0.174148i
$433$	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	$0.566268\pi$
$434$	−21.4072	−	17.1518i	−1.02758	−	0.823315i
$435$	−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	$0.178958\pi$
$440$	15.7913	−	15.1925i	0.752821	−	0.724274i
$441$	−4.45641	−	3.73937i	−0.212210	−	0.178065i
$442$	0.535412	+	0.0819525i	0.0254669	+	0.00389808i
$443$	0.820741	+	0.144719i	0.0389946	+	0.00687580i	0.193111	−	0.981177i	$-0.438142\pi$
$443$	0.820741	+	0.144719i	0.0389946	+	0.00687580i	−0.154117	+	0.988053i	$0.549253\pi$
$444$	2.59554	+	1.98478i	0.123179	+	0.0941936i
$445$	12.2709	−	7.08459i	0.581695	−	0.335842i
$446$	2.01085	−	3.67253i	0.0952166	−	0.173899i
$447$	6.28996	−	2.28936i	0.297505	−	0.108283i
$448$	28.3771	−	3.87992i	1.34069	−	0.183309i
$449$	−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	$0.302037\pi$
$450$	2.58490	+	4.25182i	0.121854	+	0.200433i
$451$	2.46400	+	2.93648i	0.116025	+	0.138274i
$452$	22.2024	−	20.4127i	1.04431	−	0.960135i
$453$	−10.9495	+	1.93069i	−0.514452	+	0.0907118i
$454$	−2.70100	−	6.92856i	−0.126764	−	0.325173i
$455$	−0.234570			−0.0109968
$456$	−11.8742	−	3.31712i	−0.556061	−	0.155338i
$457$	4.84691			0.226729			0.113364	−	0.993553i	$-0.463837\pi$
$457$	4.84691			0.226729			0.113364	+	0.993553i	$0.463837\pi$
$458$	4.91624	+	12.6111i	0.229721	+	0.589276i
$459$	−7.00699	+	1.23552i	−0.327058	+	0.0576692i
$460$	9.01722	+	9.80780i	0.420430	+	0.457291i
$461$	−3.76126	−	4.48250i	−0.175179	−	0.208771i	0.671309	−	0.741177i	$-0.265732\pi$
$461$	−3.76126	−	4.48250i	−0.175179	−	0.208771i	−0.846489	+	0.532407i	$0.821288\pi$
$462$	16.7414	+	27.5374i	0.778882	+	1.28116i
$463$	−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	$0.820063\pi$
$464$	15.6620	−	4.25245i	0.727090	−	0.197415i
$465$	6.19670	−	2.25541i	0.287365	−	0.104592i
$466$	−4.08176	+	7.45475i	−0.189084	+	0.345335i
$467$	22.5274	−	13.0062i	1.04244	−	0.601854i	0.121918	−	0.992540i	$-0.461095\pi$
$467$	22.5274	−	13.0062i	1.04244	−	0.601854i	0.920524	+	0.390686i	$0.127762\pi$
$468$	0.0653969	−	0.0855208i	0.00302297	−	0.00395320i
$469$	−27.2543	−	4.80567i	−1.25849	−	0.221905i
$470$	−8.23674	−	1.26075i	−0.379932	−	0.0581541i
$471$	2.06872	+	1.73586i	0.0953217	+	0.0799844i
$472$	−9.32936	−	9.69707i	−0.429418	−	0.446344i
$473$	−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
$478$	−26.8815	−	21.5380i	−1.22953	−	0.985127i
$479$	−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	$0.776345\pi$
$480$	−2.74685	+	6.31370i	−0.125376	+	0.288180i
$481$	−0.0152711	+	0.0866067i	−0.000696302	+	0.00394892i
$482$	−1.96297	−	9.82586i	−0.0894110	−	0.447556i
$483$	−16.9689	+	9.79700i	−0.772112	+	0.445779i
$484$	−12.8720	−	57.6085i	−0.585089	−	2.61857i
$485$	−3.04549	−	8.36742i	−0.138289	−	0.379945i
$486$	−0.453471	+	1.33954i	−0.0205699	+	0.0607627i
$487$	−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	$0.322286\pi$
$488$	11.0345	+	24.9092i	0.499508	+	1.12759i
$489$	4.51007	−	3.78440i	0.203952	−	0.171136i
$490$	0.226766	+	10.0112i	0.0102442	+	0.452259i
$491$	−15.5963	+	2.75005i	−0.703852	+	0.124108i	−0.514108	−	0.857726i	$-0.671877\pi$
$491$	−15.5963	+	2.75005i	−0.703852	+	0.124108i	−0.189744	+	0.981834i	$0.560766\pi$
$492$	−1.06931	−	0.554389i	−0.0482080	−	0.0249938i
$493$		−	28.8677i		−	1.30014i
$494$	−0.0678397	−	0.324820i	−0.00305225	−	0.0146143i
$495$	−7.74740			−0.348220
$496$	−17.7933	−	12.3711i	−0.798941	−	0.555477i
$497$	4.64297	+	26.3316i	0.208266	+	1.18113i
$498$	−11.3607	+	0.257334i	−0.509085	+	0.0115314i
$499$	−11.4788	−	13.6799i	−0.513860	−	0.612394i	0.445258	−	0.895402i	$-0.353112\pi$
$499$	−11.4788	−	13.6799i	−0.513860	−	0.612394i	−0.959117	+	0.283008i	$0.908668\pi$
$500$	6.20283	−	19.7875i	0.277399	−	0.884922i
$501$	−15.5990	−	9.00611i	−0.696913	−	0.402363i
$502$	−0.347269	+	1.02582i	−0.0154994	+	0.0457846i
$503$	−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	$0.623962\pi$
$504$	−8.18110	−	5.96733i	−0.364415	−	0.265806i
$505$	3.89208	+	6.74128i	0.173195	+	0.299983i
$506$	48.3109	−	9.65137i	2.14768	−	0.429056i
$507$	−12.7996	−	2.25692i	−0.568452	−	0.100233i
$508$	12.4326	+	19.4438i	0.551605	+	0.862681i
$509$	−16.1642	+	19.2638i	−0.716467	+	0.853852i	−0.994282	−	0.106782i	$-0.965945\pi$
$509$	−16.1642	+	19.2638i	−0.716467	+	0.853852i	0.277815	+	0.960635i	$0.410390\pi$
$510$	9.55795	+	7.65802i	0.423233	+	0.339103i
$511$	−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
$516$	3.96194	−	0.179578i	0.174414	−	0.00790547i
$517$	−19.8058	+	23.6036i	−0.871056	+	1.03808i
$518$	8.17645	+	1.25152i	0.359252	+	0.0549887i
$519$	−0.735838	+	4.17314i	−0.0322997	+	0.183181i
$520$	−0.184890	+	0.0125812i	−0.00810798	+	0.000551723i
$521$	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	$0.656747\pi$
$522$	−5.03280	−	2.75565i	−0.220280	−	0.120612i
$523$	5.99868	+	16.4812i	0.262304	+	0.720675i	0.999011	+	0.0444624i	$0.0141575\pi$
$523$	5.99868	+	16.4812i	0.262304	+	0.720675i	−0.736707	+	0.676212i	$0.763620\pi$
$524$	−11.5542	−	27.7638i	−0.504748	−	1.21287i
$525$	10.9091	+	6.29837i	0.476112	+	0.274884i
$526$	20.3926	+	33.5430i	0.889157	+	1.46255i
$527$	−29.5296	+	24.7783i	−1.28633	+	1.07936i
$528$	14.6727	+	20.8073i	0.638548	+	0.905522i
$529$	1.20744	+	6.84772i	0.0524973	+	0.297727i
$530$	21.0692	−	8.21350i	0.915186	−	0.356772i
$531$			4.75750i			0.206458i
$532$	−30.3994	+	7.07105i	−1.31798	+	0.306569i
$533$		−	0.0324183i		−	0.00140419i
$534$	5.97956	+	15.3387i	0.258761	+	0.663770i
$535$	−3.05907	−	17.3488i	−0.132255	−	0.750056i
$536$	−21.7399	−	2.32608i	−0.939019	−	0.100471i
$537$	1.83501	−	1.53975i	0.0791865	−	0.0664453i
$538$	12.7324	−	7.74068i	0.548932	−	0.333724i
$539$	32.0677	+	18.5143i	1.38125	+	0.797466i
$540$	2.24748	−	0.935316i	0.0967162	−	0.0402496i
$541$	−7.15711	−	19.6640i	−0.307708	−	0.845421i	−0.993103	−	0.117249i	$-0.962592\pi$
$541$	−7.15711	−	19.6640i	−0.307708	−	0.845421i	0.685394	−	0.728172i	$-0.259630\pi$
$542$	−3.35443	+	6.12639i	−0.144085	+	0.263151i
$543$	−1.73058	−	2.99746i	−0.0742664	−	0.128633i
$544$	2.46555	−	40.1734i	0.105710	−	1.72242i
$545$	−2.10667	+	11.9475i	−0.0902400	+	0.511776i
$546$	0.0412366	−	0.269407i	0.00176476	−	0.0115296i
$547$	2.13431	−	2.54357i	0.0912566	−	0.108755i	−0.718484	−	0.695544i	$-0.755164\pi$
$547$	2.13431	−	2.54357i	0.0912566	−	0.108755i	0.809740	+	0.586788i	$0.199608\pi$
$548$	8.08070	−	0.366264i	0.345190	−	0.0156460i
$549$	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
$554$	0.579824	−	0.723676i	0.0246343	−	0.0307461i
$555$	−1.27819	+	1.52329i	−0.0542562	+	0.0646600i
$556$	−27.1571	+	17.3645i	−1.15172	+	0.736417i
$557$	−17.3845	−	3.06536i	−0.736607	−	0.129884i	−0.207256	−	0.978287i	$-0.566453\pi$
$557$	−17.3845	−	3.06536i	−0.736607	−	0.129884i	−0.529351	+	0.848403i	$0.677564\pi$
$558$	1.50101	+	7.51348i	0.0635430	+	0.318071i
$559$	0.0533722	+	0.0924434i	0.00225740	+	0.00390994i
$560$	1.57687	+	17.3591i	0.0666348	+	0.733555i
$561$	42.5570	−	15.4895i	1.79676	−	0.653966i
$562$	−13.6694	−	4.62746i	−0.576607	−	0.195198i
$563$	16.1289	+	9.31200i	0.679750	+	0.392454i	0.799761	−	0.600319i	$-0.204960\pi$
$563$	16.1289	+	9.31200i	0.679750	+	0.392454i	−0.120011	+	0.992773i	$0.538293\pi$
$564$	2.89598	−	9.23836i	0.121943	−	0.389005i
$565$	11.7983	+	14.0607i	0.496359	+	0.591537i
$566$	0.182397	+	8.05239i	0.00766672	+	0.338467i
$567$	0.621685	+	3.52575i	0.0261083	+	0.148068i
$568$	5.07193	+	20.5058i	0.212813	+	0.860403i
$569$	−29.5469			−1.23867			−0.619336	−	0.785126i	$-0.712598\pi$
$569$	−29.5469			−1.23867			−0.619336	+	0.785126i	$0.712598\pi$
$570$	2.34388	−	7.12763i	0.0981744	−	0.298544i
$571$		−	21.8770i		−	0.915525i	−0.889075	−	0.457762i	$-0.848651\pi$
$571$		−	21.8770i		−	0.915525i	0.889075	−	0.457762i	$-0.151349\pi$
$572$	−0.315409	+	0.608361i	−0.0131879	+	0.0254368i
$573$	−23.0954	+	4.07234i	−0.964823	+	0.170124i
$574$	−3.04840	+	0.0690502i	−0.127238	+	0.00288210i
$575$	14.7514	−	12.3779i	0.615178	−	0.516195i
$576$	−6.76847	−	4.26471i	−0.282020	−	0.177696i
$577$	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	$-0.0488740\pi$
$578$	−45.0411	−	15.2477i	−1.87346	−	0.634220i
$579$	0.127222	+	0.349541i	0.00528718	+	0.0145264i
$580$	2.15373	+	9.63904i	0.0894289	+	0.400240i
$581$	−24.9134	+	14.3838i	−1.03358	+	0.596739i
$582$	10.1455	−	2.02682i	0.420543	−	0.0840145i
$583$	14.5204	−	82.3492i	0.601373	−	3.41056i
$584$	−20.8143	−	6.01058i	−0.861303	−	0.248719i
$585$	0.0501911	+	0.0421153i	0.00207515	+	0.00174125i
$586$	12.0329	−	15.0182i	0.497075	−	0.620398i
$587$	4.56129	−	12.5320i	0.188264	−	0.517252i	−0.809270	−	0.587438i	$-0.800137\pi$
$587$	4.56129	−	12.5320i	0.188264	−	0.517252i	0.997534	+	0.0701852i	$0.0223590\pi$
$588$	−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
$592$	6.51187	+	0.547916i	0.267636	+	0.0225192i
$593$	−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	$0.757251\pi$
$594$	1.36196	−	8.89798i	0.0558821	−	0.365089i
$595$	30.5339	+	5.38395i	1.25177	+	0.220720i
$596$	8.13199	−	10.6344i	0.333099	−	0.435600i
$597$	−6.12018	+	3.53349i	−0.250482	+	0.144616i
$598$	−0.365445	−	0.200095i	−0.0149442	−	0.00818250i
$599$	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	$0.287107\pi$
$600$	8.93647	+	4.37932i	0.364830	+	0.178785i
$601$	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	$0.0765770\pi$
$602$	8.57908	−	5.21567i	0.349657	−	0.212575i
$603$	4.96879	+	5.92158i	0.202345	+	0.241145i
$604$	−16.3697	+	15.0502i	−0.666074	+	0.612384i
$605$	35.3784	−	6.23816i	1.43834	−	0.253617i
$606$	−8.42666	+	3.28501i	−0.342309	+	0.133444i
$607$	6.35400			0.257901			0.128950	−	0.991651i	$-0.458839\pi$
$607$	6.35400			0.257901			0.128950	+	0.991651i	$0.458839\pi$
$608$	−23.5818	+	7.20395i	−0.956370	+	0.292159i
$609$	−14.5256			−0.588606
$610$	−15.4479	+	6.02212i	−0.625465	+	0.243829i
$611$	0.256621	−	0.0452492i	0.0103818	−	0.00183059i
$612$	−10.4756	+	9.63118i	−0.423450	+	0.389317i
$613$	4.25695	+	5.07324i	0.171937	+	0.204906i	0.845131	−	0.534560i	$-0.179523\pi$
$613$	4.25695	+	5.07324i	0.171937	+	0.204906i	−0.673194	+	0.739466i	$0.735078\pi$
$614$	3.73820	−	2.27265i	0.150862	−	0.0917167i
$615$	0.366512	−	0.634818i	0.0147792	−	0.0255983i
$616$	57.8780	+	28.3632i	2.33197	+	1.14279i
$617$	−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	$0.534604\pi$
$618$	−22.6857	−	12.4213i	−0.912552	−	0.499657i
$619$	28.7267	−	16.5854i	1.15462	−	0.666622i	0.204613	−	0.978843i	$-0.434406\pi$
$619$	28.7267	−	16.5854i	1.15462	−	0.666622i	0.950009	+	0.312221i	$0.101073\pi$
$620$	8.01142	−	10.4767i	0.321746	−	0.420754i
$621$	5.38982	+	0.950371i	0.216286	+	0.0381371i
$622$	−3.84048	+	25.0906i	−0.153989	+	1.00604i
$623$	31.9263	+	26.7893i	1.27910	+	1.07329i
$624$	0.0180534	−	0.214561i	0.000722713	−	0.00858930i
$625$	−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
$630$	3.85334	−	4.80934i	0.153521	−	0.191609i
$631$	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	$0.496649\pi$
$632$	−16.2470	−	4.69168i	−0.646272	−	0.186625i
$633$	−0.444794	+	2.52255i	−0.0176790	+	0.100263i
$634$	−43.0429	+	8.59894i	−1.70945	+	0.341508i
$635$	−12.1637	+	7.02269i	−0.482700	+	0.278687i
$636$	5.72943	+	25.6421i	0.227187	+	1.01678i
$637$	−0.107104	−	0.294265i	−0.00424361	−	0.0116592i
$638$	34.5934	+	11.7108i	1.36957	+	0.463636i
$639$	3.73418	−	6.46779i	0.147722	−	0.255862i
$640$	2.17396	+	13.5980i	0.0859332	+	0.537508i
$641$	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	$0.192161\pi$
$642$	20.4631	−	0.463516i	0.807615	−	0.0182935i
$643$	−40.6218	+	7.16272i	−1.60197	+	0.282470i	−0.902010	−	0.431715i	$-0.857909\pi$
$643$	−40.6218	+	7.16272i	−1.60197	+	0.282470i	−0.699957	+	0.714185i	$0.746798\pi$
$644$	−18.0372	+	34.7902i	−0.710766	+	1.37093i
$645$			2.41365i			0.0950372i
$646$	1.37526	+	43.8387i	0.0541090	+	1.72481i
$647$	−11.9278			−0.468930			−0.234465	−	0.972125i	$-0.575334\pi$
$647$	−11.9278			−0.468930			−0.234465	+	0.972125i	$0.575334\pi$
$648$	0.679123	+	2.74569i	0.0266785	+	0.107861i
$649$	−5.25840	−	29.8219i	−0.206410	−	1.17061i
$650$	0.00606563	+	0.267783i	0.000237914	+	0.0105033i
$651$	12.4679	+	14.8586i	0.488654	+	0.582355i
$652$	3.52213	−	11.2358i	0.137937	−	0.440029i
$653$	5.20649	+	3.00597i	0.203746	+	0.117633i	0.598401	−	0.801196i	$-0.295803\pi$
$653$	5.20649	+	3.00597i	0.203746	+	0.117633i	−0.394656	+	0.918829i	$0.629136\pi$
$654$	−13.3516	−	4.51987i	−0.522087	−	0.176741i
$655$	17.1976	−	6.25943i	0.671967	−	0.244576i
$656$	−2.39907	+	0.217928i	−0.0936681	+	0.00850864i
$657$	3.82983	+	6.63346i	0.149416	+	0.258796i
$658$	−4.80153	−	24.0346i	−0.187183	−	0.936964i
$659$	15.6571	+	2.76077i	0.609914	+	0.107544i	0.470070	−	0.882629i	$-0.344229\pi$
$659$	15.6571	+	2.76077i	0.609914	+	0.107544i	0.139844	+	0.990174i	$0.455340\pi$
$660$	−13.0543	+	8.34705i	−0.508139	+	0.324909i
$661$	−17.7491	+	21.1526i	−0.690360	+	0.822739i	−0.991399	−	0.130872i	$-0.958222\pi$
$661$	−17.7491	+	21.1526i	−0.690360	+	0.822739i	0.301039	+	0.953612i	$0.402667\pi$
$662$	25.9805	−	32.4262i	1.00976	−	1.26028i
$663$	−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
$668$	−35.9875	+	1.63116i	−1.39240	+	0.0631115i
$669$	−1.90308	+	2.26800i	−0.0735771	+	0.0876858i
$670$	2.01323	−	13.1529i	0.0777780	−	0.508139i
$671$	−10.6463	+	60.3782i	−0.410996	+	2.33088i
$672$	−20.2143	−	1.24061i	−0.779784	−	0.0478576i
$673$	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	$0.779619\pi$
$674$	−13.5991	+	24.8369i	−0.523819	+	0.956681i
$675$	−1.20340	−	3.30631i	−0.0463188	−	0.127260i
$676$	−23.9990	+	9.98744i	−0.923037	+	0.384132i
$677$	14.9007	+	8.60294i	0.572681	+	0.330638i	0.758220	−	0.651999i	$-0.226070\pi$
$677$	14.9007	+	8.60294i	0.572681	+	0.330638i	−0.185538	+	0.982637i	$0.559403\pi$
$678$	−18.2230	+	11.0787i	−0.699849	+	0.425475i
$679$	20.0636	−	16.8354i	0.769972	−	0.646083i
$680$	24.3559	+	2.60599i	0.934004	+	0.0999350i
$681$	0.913102	+	5.17846i	0.0349901	+	0.198439i
$682$	−17.7135	−	45.4384i	−0.678286	−	1.73993i
$683$			15.8039i			0.604721i	0.953194	+	0.302361i	$0.0977747\pi$
$683$			15.8039i			0.604721i	−0.953194	+	0.302361i	$0.902225\pi$
$684$	7.77413	+	3.94499i	0.297251	+	0.150840i
$685$			4.92283i			0.188092i
$686$	5.57855	−	2.17472i	0.212990	−	0.0830310i
$687$	−1.66199	−	9.42560i	−0.0634088	−	0.359609i
$688$	6.48236	−	4.57118i	0.247138	−	0.174275i
$689$	−0.541725	+	0.454561i	−0.0206381	+	0.0173174i
$690$	−4.89395	−	8.04990i	−0.186310	−	0.306454i
$691$	−26.1559	−	15.1011i	−0.995016	−	0.574473i	−0.0882460	−	0.996099i	$-0.528126\pi$
$691$	−26.1559	−	15.1011i	−0.995016	−	0.574473i	−0.906770	+	0.421626i	$0.861459\pi$
$692$	3.25626	+	7.82452i	0.123785	+	0.297444i
$693$	−7.79395	−	21.4137i	−0.296068	−	0.813439i
$694$	15.6002	+	8.54170i	0.592175	+	0.324238i
$695$	−9.80854	−	16.9889i	−0.372059	−	0.644425i
$696$	−11.4492	+	0.779082i	−0.433980	+	0.0295310i
$697$	−0.744077	+	4.21987i	−0.0281839	+	0.159839i
$698$	19.8336	+	3.03582i	0.750713	+	0.114907i
$699$	3.86299	−	4.60373i	0.146112	−	0.174129i
$700$	25.1677	−	1.14074i	0.951248	−	0.0431161i
$701$	15.5397	−	42.6950i	0.586926	−	1.61257i	−0.189165	−	0.981945i	$-0.560578\pi$
$701$	15.5397	−	42.6950i	0.586926	−	1.61257i	0.776091	−	0.630621i	$-0.217200\pi$
$702$	−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
$706$	−0.281653	−	0.225666i	−0.0106001	−	0.00849304i
$707$	−14.7173	+	17.5394i	−0.553502	+	0.659638i
$708$	5.12573	+	8.01636i	0.192637	+	0.301273i
$709$	6.74244	+	1.18887i	0.253218	+	0.0446491i	0.298816	−	0.954311i	$-0.403408\pi$
$709$	6.74244	+	1.18887i	0.253218	+	0.0446491i	−0.0455983	+	0.998960i	$0.514519\pi$
$710$	−12.6064	+	2.51847i	−0.473111	+	0.0945164i
$711$	2.98945	+	5.17788i	0.112113	+	0.194186i
$712$	26.6014	+	19.4032i	0.996931	+	0.727167i
$713$	27.8633	−	10.1414i	1.04349	−	0.379799i
$714$	−11.5513	+	34.1221i	−0.432296	+	1.27699i
$715$	−0.361167	−	0.208520i	−0.0135069	−	0.00779821i
$716$	1.43305	−	4.57152i	0.0535555	−	0.170846i
$717$	15.6562	+	18.6584i	0.584693	+	0.696810i
$718$	−37.7109	+	0.854199i	−1.40736	+	0.0318784i
$719$	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	$0.864739\pi$
$720$	2.77929	−	3.99744i	0.103578	−	0.148976i
$721$	−65.4750			−2.43842
$722$	24.8611	−	10.1943i	0.925236	−	0.379393i
$723$			7.08522i			0.263502i
$724$	−6.14548	−	3.18617i	−0.228395	−	0.118413i
$725$	14.0586	−	2.47891i	0.522123	−	0.0920644i
$726$	0.945218	+	41.7291i	0.0350803	+	1.54871i
$727$	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	$0.0247330\pi$
$728$	−0.220776	−	0.498378i	−0.00818249	−	0.0184711i
$729$	0.500000	−	0.866025i	0.0185185	−	0.0320750i
$730$	4.22775	−	12.4886i	0.156476	−	0.462225i
$731$	−4.82563	−	13.2583i	−0.178483	−	0.490377i
$732$	−4.20080	−	18.8007i	−0.155266	−	0.694894i
$733$	10.2689	−	5.92878i	0.379292	−	0.218984i	−0.298218	−	0.954498i	$-0.596392\pi$
$733$	10.2689	−	5.92878i	0.379292	−	0.218984i	0.677510	+	0.735513i	$0.263059\pi$
$734$	−4.05134	−	20.2794i	−0.149538	−	0.748526i
$735$	1.22957	−	6.97322i	0.0453532	−	0.257211i
$736$	−12.3511	+	28.3894i	−0.455269	+	1.04645i
$737$	−37.6914	−	31.6269i	−1.38838	−	1.16499i
$738$	0.664665	+	0.532542i	0.0244666	+	0.0196032i
$739$	−2.56191	+	7.03879i	−0.0942414	+	0.258926i	−0.977852	−	0.209296i	$-0.932883\pi$
$739$	−2.56191	+	7.03879i	−0.0942414	+	0.258926i	0.883611	+	0.468222i	$0.155105\pi$
$740$	−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	$0.546206\pi$
$744$	10.6242	+	11.0430i	0.389503	+	0.404855i
$745$	6.24117	+	5.23697i	0.228659	+	0.191868i
$746$	−13.8212	−	2.11553i	−0.506028	−	0.0774549i
$747$	7.91322	+	1.39531i	0.289529	+	0.0510519i
$748$	55.0200	−	71.9506i	2.01173	−	2.63078i
$749$	44.8745	−	25.9083i	1.63968	−	0.946669i
$750$	−7.04215	+	12.8615i	−0.257143	+	0.469635i
$751$	−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	$0.606036\pi$
$752$	−5.07371	−	18.6867i	−0.185019	−	0.681434i
$753$	0.382900	−	0.663203i	0.0139537	−	0.0241685i
$754$	−0.160451	−	0.263920i	−0.00584327	−	0.00961139i
$755$	−8.69882	−	10.3669i	−0.316583	−	0.377288i
$756$	4.84619	+	5.27107i	0.176254	+	0.191707i
$757$	17.1406	−	3.02236i	0.622987	−	0.109849i	0.146761	−	0.989172i	$-0.453115\pi$
$757$	17.1406	−	3.02236i	0.622987	−	0.109849i	0.476227	+	0.879323i	$0.342004\pi$
$758$	5.14233	+	13.1910i	0.186778	+	0.479120i
$759$	−34.8360			−1.26447
$760$	−3.72988	−	14.5353i	−0.135297	−	0.527252i
$761$	37.6324			1.36417			0.682087	−	0.731271i	$-0.261073\pi$
$761$	37.6324			1.36417			0.682087	+	0.731271i	$0.261073\pi$
$762$	−5.92732	−	15.2047i	−0.214724	−	0.550808i
$763$	−35.1422	+	6.19651i	−1.27223	+	0.224329i
$764$	−34.5280	+	31.7448i	−1.24918	+	1.14849i
$765$	−5.56670	−	6.63413i	−0.201264	−	0.239858i
$766$	−3.14255	−	5.16908i	−0.113545	−	0.186767i
$767$	−0.128047	+	0.221784i	−0.00462352	+	0.00800817i
$768$	−15.9996	+	0.106339i	−0.577338	+	0.00383719i
$769$	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	$0.319102\pi$
$770$	−18.8386	+	34.4059i	−0.678895	+	1.23990i
$771$	1.12464	−	0.649313i	0.0405031	−	0.0233844i
$772$	0.590964	+	0.451905i	0.0212693	+	0.0162644i
$773$	−12.6202	−	2.22528i	−0.453917	−	0.0800378i	−0.0579847	−	0.998317i	$-0.518467\pi$
$773$	−12.6202	−	2.22528i	−0.453917	−	0.0800378i	−0.395932	+	0.918280i	$0.629579\pi$
$774$	−2.77210	−	0.424310i	−0.0996412	−	0.0152515i
$775$	−14.6028	−	12.2532i	−0.524548	−	0.440148i
$776$	14.9114	−	14.3459i	0.535287	−	0.514989i
$777$	−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
$782$	42.9771	+	34.4341i	1.53686	+	1.23136i
$783$	3.10804	+	2.60795i	0.111072	+	0.0932007i
$784$	−21.0567	+	9.90424i	−0.752026	+	0.353723i
$785$	−0.570780	+	3.23706i	−0.0203720	+	0.115536i
$786$	4.16575	+	20.8521i	0.148587	+	0.743769i
$787$	14.4541	−	8.34506i	0.515232	−	0.297469i	−0.219750	−	0.975556i	$-0.570524\pi$
$787$	14.4541	−	8.34506i	0.515232	−	0.297469i	0.734982	+	0.678087i	$0.237191\pi$
$788$	23.3364	−	5.21425i	0.831325	−	0.185750i
$789$	−9.49372	−	26.0838i	−0.337986	−	0.928608i
$790$	3.30006	−	9.74826i	0.117411	−	0.346828i
$791$	−26.9943	+	46.7555i	−0.959807	+	1.66244i
$792$	−7.29179	−	16.4604i	−0.259102	−	0.584896i
$793$	0.397191	−	0.333283i	0.0141047	−	0.0118352i
$794$	−1.00797	−	44.4994i	−0.0357714	−	1.57922i
$795$	−15.7472	+	2.77666i	−0.558497	+	0.0984781i
$796$	−6.50549	+	12.5478i	−0.230581	+	0.444744i
$797$		−	29.2527i		−	1.03618i	−0.855325	−	0.518092i	$-0.826642\pi$
$797$		−	29.2527i		−	1.03618i	0.855325	−	0.518092i	$-0.173358\pi$
$798$	22.0586	−	0.692001i	0.780867	−	0.0244966i
$799$	−34.4428			−1.21850
$800$	19.7762	−	2.24902i	0.699194	−	0.0795147i
$801$	−2.02146	−	11.4642i	−0.0714246	−	0.405069i
$802$	−41.1104	+	0.931202i	−1.45166	+	0.0328819i
$803$	−31.3388	−	37.3481i	−1.10592	−	1.31799i
$804$	14.7523	+	4.62445i	0.520274	+	0.163092i
$805$	−20.6540	−	11.9246i	−0.727958	−	0.420287i
$806$	−0.132250	+	0.390662i	−0.00465831	+	0.0137605i
$807$	−9.90098	+	3.60366i	−0.348531	+	0.126855i
$808$	−10.6596	+	14.6141i	−0.375004	+	0.514122i
$809$	−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	$0.849726\pi$
$810$	−1.68798	+	0.337218i	−0.0593096	+	0.0118486i
$811$	−8.39251	−	1.47983i	−0.294701	−	0.0519637i	0.0243430	−	0.999704i	$-0.492251\pi$
$811$	−8.39251	−	1.47983i	−0.294701	−	0.0519637i	−0.319044	+	0.947740i	$0.603362\pi$
$812$	−24.4755	+	15.6499i	−0.858922	+	0.549202i
$813$	3.17464	−	3.78339i	0.111340	−	0.132689i
$814$	11.4767	+	9.19538i	0.402259	+	0.322298i
$815$	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
$820$	−0.0663817	−	1.46455i	−0.00231815	−	0.0511441i
$821$	−9.95381	+	11.8625i	−0.347390	+	0.414004i	−0.911241	−	0.411873i	$-0.864875\pi$
$821$	−9.95381	+	11.8625i	−0.347390	+	0.414004i	0.563851	+	0.825877i	$0.309319\pi$
$822$	−5.65394	−	0.865416i	−0.197204	−	0.0301849i
$823$	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	$-0.287900\pi$
$824$	−51.6080	+	3.51176i	−1.79785	+	0.122338i
$825$	11.1978	+	19.3952i	0.389858	+	0.675254i
$826$	21.1279	+	11.5683i	0.735133	+	0.402514i
$827$	5.12484	+	14.0804i	0.178208	+	0.489623i	0.996347	−	0.0853977i	$-0.0272161\pi$
$827$	5.12484	+	14.0804i	0.178208	+	0.489623i	−0.818139	+	0.575021i	$0.804994\pi$
$828$	10.1057	−	4.20562i	0.351199	−	0.146156i
$829$	41.6975	+	24.0741i	1.44821	+	0.836127i	0.998375	−	0.0569831i	$-0.0181481\pi$
$829$	41.6975	+	24.0741i	1.44821	+	0.836127i	0.449839	+	0.893110i	$0.351481\pi$
$830$	−7.18520	−	11.8187i	−0.249402	−	0.410233i
$831$	−0.502301	+	0.421480i	−0.0174246	+	0.0146210i
$832$	−0.200748	−	0.380984i	−0.00695968	−	0.0132083i
$833$	7.18756	+	40.7627i	0.249034	+	1.41234i
$834$	21.2363	−	8.27865i	0.735352	−	0.286666i
$835$		−	21.9239i		−	0.758707i
$836$	−53.0917	−	16.1361i	−1.83622	−	0.558080i
$837$		−	5.41781i		−	0.187267i
$838$	−15.7743	−	40.4639i	−0.544913	−	1.39780i
$839$	−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	$-0.190984\pi$
$840$	1.31127	−	12.2553i	0.0452432	−	0.422848i
$841$	9.60517	−	8.05970i	0.331213	−	0.277921i
$842$	−22.9185	+	13.9334i	−0.789825	+	0.480176i
$843$	8.83739	+	5.10227i	0.304376	+	0.175731i
$844$	1.96832	+	4.72971i	0.0677525	+	0.162803i
$845$	−5.41064	−	14.8656i	−0.186132	−	0.511393i
$846$	−3.28784	+	6.00476i	−0.113038	+	0.206448i
$847$	52.8331	+	91.5097i	1.81537	+	3.14431i
$848$	37.2809	+	37.0339i	1.28023	+	1.27175i
$849$	0.988989	−	5.60884i	0.0339420	−	0.192495i
$850$	5.35671	−	34.9964i	0.183734	−	1.20037i
$851$	−5.74736	+	6.84943i	−0.197017	+	0.234796i
$852$	−0.676324	−	14.9214i	−0.0231705	−	0.511198i
$853$	6.53123	−	17.9444i	0.223625	−	0.614405i	−0.776247	−	0.630429i	$-0.782879\pi$
$853$	6.53123	−	17.9444i	0.223625	−	0.614405i	0.999872	+	0.0160247i	$0.00510103\pi$
$854$	−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	$0.775765\pi$
$858$	0.302980	−	0.378148i	0.0103436	−	0.0129098i
$859$	18.5756	−	22.1376i	0.633792	−	0.755324i	−0.349584	−	0.936905i	$-0.613677\pi$
$859$	18.5756	−	22.1376i	0.633792	−	0.755324i	0.983376	+	0.181581i	$0.0581215\pi$
$860$	2.60046	+	4.06698i	0.0886750	+	0.138683i
$861$	2.12334	+	0.374402i	0.0723633	+	0.0127596i
$862$	6.06605	+	30.3642i	0.206611	+	1.03421i
$863$	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	$0.828906\pi$
$864$	4.10252	+	3.89478i	0.139571	+	0.132503i
$865$	−4.84672	+	1.76406i	−0.164794	+	0.0599799i
$866$	−26.2338	−	8.88086i	−0.891460	−	0.301784i
$867$	29.1195	+	16.8122i	0.988952	+	0.570971i
$868$	37.0170	+	11.6038i	1.25644	+	0.393859i
$869$	−24.4621	−	29.1528i	−0.829821	−	0.988942i
$870$	−0.158154	−	6.98211i	−0.00536191	−	0.236716i
$871$	0.0722563	+	0.409786i	0.00244831	+	0.0138851i
$872$	−27.3670	+	6.76900i	−0.926764	+	0.229227i
$873$	−7.31569			−0.247599
$874$	10.5392	−	32.0492i	0.356494	−	1.08408i
$875$			37.1205i			1.25490i
$876$	13.6001	+	7.05108i	0.459506	+	0.238234i
$877$	3.72820	−	0.657381i	0.125892	−	0.0221982i	−0.110347	−	0.993893i	$-0.535196\pi$
$877$	3.72820	−	0.657381i	0.125892	−	0.0221982i	0.236239	+	0.971695i	$0.424085\pi$
$878$	−57.9062	+	1.31165i	−1.95424	+	0.0442660i
$879$	−10.4241	+	8.74685i	−0.351596	+	0.295024i
$880$	−13.0034	+	28.1295i	−0.438343	+	0.948245i
$881$	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	$0.00132247\pi$
$882$	7.79267	+	2.63804i	0.262393	+	0.0888274i
$883$	−15.4289	−	42.3906i	−0.519225	−	1.42656i	−0.871376	−	0.490615i	$-0.836772\pi$
$883$	−15.4289	−	42.3906i	−0.519225	−	1.42656i	0.352152	−	0.935943i	$-0.385450\pi$
$884$	−0.747572	+	0.167036i	−0.0251436	+	0.00561804i
$885$	−5.01487	+	2.89534i	−0.168573	+	0.0973256i
$886$	−1.15577	+	0.230896i	−0.0388289	+	0.00775709i
$887$	−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	$0.0906800\pi$
$888$	−4.43947	−	1.28199i	−0.148979	−	0.0430208i
$889$	−31.6474	−	26.5553i	−1.06142	−	0.890636i
$890$	−12.5294	+	15.6379i	−0.419987	+	0.524184i
$891$	−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
$896$	−35.3977	+	19.6885i	−1.18255	+	0.657746i
$897$	0.225683	+	0.189371i	0.00753534	+	0.00632290i
$898$	3.74123	−	24.4422i	0.124846	−	0.815647i
$899$	21.6475	+	3.81704i	0.721985	+	0.127305i
$900$	−5.58994	−	4.27457i	−0.186331	−	0.142486i
$901$	80.9493	−	46.7361i	2.69681	−	1.55700i
$902$	−4.75500	−	2.60354i	−0.158324	−	0.0866885i
$903$	−6.67128	+	2.42815i	−0.222006	+	0.0808037i
$904$	−18.7694	+	38.3010i	−0.624262	+	1.27387i
$905$	2.10641	−	3.64841i	0.0700194	−	0.121277i
$906$	13.4357	−	8.16825i	0.446371	−	0.271372i
$907$	−21.1712	−	25.2308i	−0.702977	−	0.837775i	0.289883	−	0.957062i	$-0.406384\pi$
$907$	−21.1712	−	25.2308i	−0.702977	−	0.837775i	−0.992860	+	0.119287i	$0.961939\pi$
$908$	7.11784	+	7.74190i	0.236214	+	0.256924i
$909$	6.29814	−	1.11053i	0.208896	−	0.0368340i
$910$	0.309077	−	0.120489i	0.0102458	−	0.00399418i
$911$	25.3280			0.839155			0.419578	−	0.907719i	$-0.362178\pi$
$911$	25.3280			0.839155			0.419578	+	0.907719i	$0.362178\pi$
$912$	17.3497	−	1.72856i	0.574506	−	0.0572384i
$913$	−51.1455			−1.69267
$914$	−6.38645	+	2.48966i	−0.211245	+	0.0823507i
$915$	11.5458	−	2.03584i	0.381694	−	0.0673029i
$916$	−12.9556	−	14.0915i	−0.428065	−	0.465595i
$917$	34.6019	+	41.2370i	1.14266	+	1.36177i
$918$	8.59799	−	5.22717i	0.283776	−	0.172522i
$919$	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	$0.0130218\pi$
$920$	−16.9193	−	8.29129i	−0.557811	−	0.273356i
$921$	−2.90691	+	1.05803i	−0.0957860	+	0.0348632i
$922$	7.25844	+	3.97427i	0.239044	+	0.130886i
$923$	0.348159	−	0.201010i	0.0114598	−	0.00661632i
$924$	−36.2039	−	27.6848i	−1.19102	−	0.910762i
$925$	5.66092	+	0.998173i	0.186130	+	0.0328197i
$926$	8.15961	−	53.3084i	0.268141	−	1.75182i
$927$	14.0097	+	11.7555i	0.460139	+	0.386102i
$928$	−18.4524	+	13.6481i	−0.605731	+	0.448021i
$929$	−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
$934$	−23.0020	+	28.7088i	−0.752649	+	0.939379i
$935$	42.2269	+	35.4326i	1.38097	+	1.15877i
$936$	−0.0422405	+	0.146277i	−0.00138067	+	0.00478120i
$937$	−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	$0.908801\pi$
$938$	38.3796	−	7.66734i	1.25314	−	0.250347i
$939$	−5.04005	+	2.90987i	−0.164476	+	0.0949601i
$940$	11.5006	−	2.56967i	0.375108	−	0.0838135i
$941$	−17.5750	−	48.2869i	−0.572929	−	1.57411i	−0.799853	−	0.600196i	$-0.795089\pi$
$941$	−17.5750	−	48.2869i	−0.572929	−	1.57411i	0.226924	−	0.973912i	$-0.427133\pi$
$942$	−3.61746	−	1.22461i	−0.117863	−	0.0399000i
$943$	1.64801	−	2.85444i	0.0536667	−	0.0929534i
$944$	17.2737	+	7.98506i	0.562209	+	0.259892i
$945$	−3.33814	+	2.80103i	−0.108590	+	0.0911177i
$946$	17.8456	−	0.404226i	0.580212	−	0.0131425i
$947$	−22.6753	+	3.99827i	−0.736848	+	0.129926i	−0.529463	−	0.848333i	$-0.677607\pi$
$947$	−22.6753	+	3.99827i	−0.736848	+	0.129926i	−0.207385	+	0.978259i	$0.566495\pi$
$948$	10.6159	+	5.50387i	0.344787	+	0.178757i
$949$			0.412317i			0.0133844i
$950$	−21.2314	+	4.43425i	−0.688837	+	0.143866i
$951$	31.0373			1.00645
$952$	17.2993	+	69.9409i	0.560673	+	2.26680i
$953$	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	$0.801478\pi$
$954$	−0.420725	−	18.5740i	−0.0136215	−	0.601357i
$955$	−18.3481	−	21.8664i	−0.593731	−	0.707581i
$956$	46.4832	+	14.5712i	1.50337	+	0.471267i
$957$	−22.3650	−	12.9124i	−0.722957	−	0.417400i
$958$	9.92169	+	3.35877i	0.320555	+	0.108517i
$959$	−13.6066	+	4.95241i	−0.439381	+	0.159922i
$960$	0.376240	−	9.73007i	0.0121431	−	0.314037i
$961$	0.823658	+	1.42662i	0.0265696	+	0.0460199i
$962$	−0.0243647	−	0.121960i	−0.000785549	−	0.00393214i
$963$	−14.2535	−	2.51327i	−0.459311	−	0.0809889i
$964$	7.63362	+	11.9386i	0.245862	+	0.384515i
$965$	−0.291025	+	0.346830i	−0.00936842	+	0.0111648i
$966$	17.3264	−	21.6251i	0.557469	−	0.695776i
$967$	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	$-0.589516\pi$
$971$	17.2197	−	47.3108i	0.552607	−	1.51828i	0.830137	−	0.557559i	$-0.188262\pi$
$972$	−0.0905586	−	1.99795i	−0.00290467	−	0.0640842i
$973$	37.0896	−	44.2016i	1.18904	−	1.41704i
$974$	4.43535	−	28.9771i	0.142118	−	0.928485i
$975$	0.0328890	−	0.186523i	0.00105329	−	0.00597350i
$976$	−27.3342	−	27.1532i	−0.874948	−	0.869152i
$977$	−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	$0.936327\pi$
$978$	−3.99872	+	7.30308i	−0.127865	+	0.233527i
$979$	25.3426	+	69.6282i	0.809953	+	2.22533i
$980$	−5.44113	−	13.0746i	−0.173811	−	0.417652i
$981$	8.63191	+	4.98364i	0.275596	+	0.159115i
$982$	19.1376	−	11.6348i	0.610706	−	0.371280i
$983$	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	$0.0276950\pi$
$984$	1.69372	+	0.181221i	0.0539938	+	0.00577713i
$985$	2.52699	+	14.3313i	0.0805166	+	0.456632i
$986$	14.8282	+	38.0370i	0.472225	+	1.21135i
$987$			17.3308i			0.551646i
$988$	0.256235	+	0.393147i	0.00815191	+	0.0125077i
$989$			10.8529i			0.345102i
$990$	10.2082	−	3.97953i	0.324439	−	0.126478i
$991$	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	$0.703682\pi$
$992$	29.7995	+	7.16082i	0.946134	+	0.227356i
$993$	−22.5069	+	18.8855i	−0.714234	+	0.599313i
$994$	−19.6432	−	32.3104i	−0.623044	−	1.02482i
$995$	−7.44928	−	4.30084i	−0.236158	−	0.136346i
$996$	14.8370	−	6.17461i	0.470130	−	0.195650i
$997$	−8.58190	−	23.5786i	−0.271792	−	0.746741i	−0.998228	−	0.0595073i	$-0.981047\pi$
$997$	−8.58190	−	23.5786i	−0.271792	−	0.746741i	0.726436	−	0.687234i	$-0.241175\pi$
$998$	22.1516	+	12.1288i	0.701195	+	0.383931i
$999$	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.61.5	✓	240
8.5	even	2	inner	456.2.bk.a.61.14	yes	240
19.5	even	9	inner	456.2.bk.a.157.14	yes	240
152.5	even	18	inner	456.2.bk.a.157.5	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bk.a.61.5	✓	240	1.1	even	1	trivial
456.2.bk.a.61.14	yes	240	8.5	even	2	inner
456.2.bk.a.157.5	yes	240	152.5	even	18	inner
456.2.bk.a.157.14	yes	240	19.5	even	9	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+(-1.31763 + 0.513660i) q^{2} +(0.984808 - 0.173648i) q^{3} +(1.47231 - 1.35363i) q^{4} +(0.782380 + 0.932405i) q^{5} +(-1.20842 + 0.734660i) q^{6} +(-1.79007 + 3.10050i) q^{7} +(-1.24466 + 2.53985i) q^{8} +(0.939693 - 0.342020i) q^{9} +(-1.50983 - 0.826689i) q^{10} +(-5.51234 + 3.18255i) q^{11} +(1.21488 - 1.58873i) q^{12} +(0.0530119 + 0.00934743i) q^{13} +(0.766056 - 5.00480i) q^{14} +(0.932405 + 0.782380i) q^{15} +(0.335379 - 3.98592i) 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} +(5.62849 - 7.02490i) q^{22} +(4.19254 + 3.51795i) q^{23} +(-0.784706 + 2.71740i) q^{24} +(0.610982 - 3.46505i) q^{25} +(-0.0746516 + 0.0149136i) q^{26} +(0.866025 - 0.500000i) q^{27} +(1.56138 + 6.98798i) q^{28} +(1.38766 + 3.81257i) q^{29} +(-1.63044 - 0.551951i) q^{30} +(2.70891 - 4.69196i) q^{31} +(1.60550 + 5.42424i) q^{32} +(-4.87595 + 4.09141i) q^{33} +(10.0597 - 0.227864i) q^{34} +(-4.29143 + 0.756696i) q^{35} +(0.920548 - 1.77555i) q^{36} +1.63372i q^{37} +(-2.28895 - 5.72370i) q^{38} +0.0538297 q^{39} +(-3.34196 + 0.826606i) q^{40} +(-0.104577 - 0.593088i) q^{41} +(-0.114656 - 5.06179i) q^{42} +(1.27465 + 1.51907i) q^{43} +(-3.80787 + 12.1474i) q^{44} +(1.05410 + 0.608584i) q^{45} +(-7.33125 - 2.48183i) q^{46} +(4.54888 - 1.65566i) q^{47} +(-0.361863 - 3.98360i) q^{48} +(-2.90872 - 5.03804i) q^{49} +(0.974807 + 4.87949i) q^{50} +(-7.00699 - 1.23552i) q^{51} +(0.0907028 - 0.0579962i) q^{52} +(-8.44443 + 10.0637i) q^{53} +(-0.884273 + 1.10366i) 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} +(2.43184 - 0.110225i) q^{60} +(6.19143 - 7.37866i) q^{61} +(-1.15927 + 7.57374i) q^{62} +(-0.621685 + 3.52575i) q^{63} +(-4.90167 - 6.32247i) q^{64} +(0.0327599 + 0.0567418i) q^{65} +(4.32312 - 7.89555i) q^{66} +(2.64384 + 7.26389i) q^{67} +(-13.1379 + 5.46748i) q^{68} +(4.73973 + 2.73648i) q^{69} +(5.26585 - 3.20138i) q^{70} +(5.72109 - 4.80057i) q^{71} +(-0.300914 + 2.81237i) q^{72} +(1.33009 + 7.54329i) q^{73} +(-0.839176 - 2.15264i) q^{74} -3.51850i q^{75} +(5.95602 + 6.36599i) q^{76} -22.7880i q^{77} +(-0.0709278 + 0.0276502i) q^{78} +(1.03823 + 5.88807i) q^{79} +(3.97888 - 2.80579i) q^{80} +(0.766044 - 0.642788i) q^{81} +(0.442440 + 0.727755i) q^{82} +(6.95877 + 4.01765i) q^{83} +(2.75111 + 6.61068i) q^{84} +(-2.96198 - 8.13797i) q^{85} +(-2.45980 - 1.34684i) q^{86} +(2.02863 + 3.51369i) q^{87} +(-1.22224 - 17.9617i) q^{88} +(2.02146 - 11.4642i) q^{89} +(-1.70152 - 0.260442i) q^{90} +(-0.123877 + 0.147631i) q^{91} +(10.9347 - 0.495624i) 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} +(6.42046 + 5.14420i) 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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