LMFDB - Embedded newform 924.2.bu.b.223.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [924,2,Mod(223,924)] 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("924.223"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(924, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 0, 5, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 924 = 2^{2} \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	924.bu (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [192,2,48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.37817714677$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			223.16
Character	$\chi$	$=$	924.223
Dual form			924.2.bu.b.895.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.636345 - 1.26296i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-1.19013 + 1.60736i) q^{4} +(0.381488 - 0.525073i) q^{5} +(-1.00450 + 0.995476i) q^{6} +(2.39317 - 1.12816i) q^{7} +(2.78736 + 0.480250i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.905904 - 0.147676i) q^{10} +(2.59042 + 2.07116i) q^{11} +(1.89646 + 0.635180i) q^{12} +(2.65571 + 3.65527i) q^{13} +(-2.94770 - 2.30457i) q^{14} +(-0.617261 - 0.200560i) q^{15} +(-1.16719 - 3.82592i) q^{16} +(-3.39103 + 4.66735i) q^{17} +(1.25716 + 0.647720i) q^{18} +(0.0757255 + 0.233059i) q^{19} +(0.389960 + 1.23809i) q^{20} +(-1.81247 - 1.92742i) q^{21} +(0.967390 - 4.58957i) q^{22} +8.55411i q^{23} +(-0.404596 - 2.79934i) q^{24} +(1.41492 + 4.35466i) q^{25} +(2.92650 - 5.68006i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-1.03483 + 5.18933i) q^{28} +(-2.06422 + 6.35301i) q^{29} +(0.139492 + 0.907200i) q^{30} +(2.34153 - 1.70122i) q^{31} +(-4.08925 + 3.90872i) q^{32} +(1.16931 - 3.10366i) q^{33} +(8.05254 + 1.31268i) q^{34} +(0.320599 - 1.68697i) q^{35} +(0.0180544 - 1.99992i) q^{36} +(0.730589 - 2.24852i) q^{37} +(0.246157 - 0.243944i) q^{38} +(2.65571 - 3.65527i) q^{39} +(1.31551 - 1.28036i) q^{40} +(5.30938 - 1.72512i) q^{41} +(-1.28089 + 3.51558i) q^{42} -2.48287i q^{43} +(-6.41203 + 1.69878i) q^{44} +0.649026i q^{45} +(10.8035 - 5.44337i) q^{46} +(-3.75656 - 11.5615i) q^{47} +(-3.27799 + 2.29234i) q^{48} +(4.45451 - 5.39975i) q^{49} +(4.59939 - 4.55805i) q^{50} +(5.48680 + 1.78277i) q^{51} +(-9.03595 - 0.0815724i) q^{52} +(0.458500 - 0.333120i) q^{53} +(0.227534 - 1.39579i) q^{54} +(2.07573 - 0.570037i) q^{55} +(7.21241 - 1.99526i) q^{56} +(0.198252 - 0.144039i) q^{57} +(9.33714 - 1.43569i) q^{58} +(-1.60166 + 4.92941i) q^{59} +(1.05699 - 0.753465i) q^{60} +(-0.541491 + 0.745298i) q^{61} +(-3.63859 - 1.87469i) q^{62} +(-1.27300 + 2.31937i) q^{63} +(7.53872 + 2.67726i) q^{64} +2.93240 q^{65} +(-4.66388 + 0.498212i) q^{66} +2.11653i q^{67} +(-3.46633 - 11.0053i) q^{68} +(8.13544 - 2.64336i) q^{69} +(-2.33458 + 0.668591i) q^{70} +(-2.28843 + 3.14975i) q^{71} +(-2.53730 + 1.24984i) q^{72} +(6.54886 + 2.12785i) q^{73} +(-3.30469 + 0.508133i) q^{74} +(3.70430 - 2.69133i) q^{75} +(-0.464732 - 0.155653i) q^{76} +(8.53592 + 2.03423i) q^{77} +(-6.30640 - 1.02803i) q^{78} +(-5.95596 - 8.19768i) q^{79} +(-2.45416 - 0.846685i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-5.55736 - 5.60775i) q^{82} +(-8.46913 - 6.15318i) q^{83} +(5.25512 - 0.619413i) q^{84} +(1.15706 + 3.56108i) q^{85} +(-3.13576 + 1.57996i) q^{86} +6.67995 q^{87} +(6.22575 + 7.01712i) q^{88} +3.88247i q^{89} +(0.819693 - 0.413005i) q^{90} +(10.4793 + 5.75161i) q^{91} +(-13.7495 - 10.1805i) q^{92} +(-2.34153 - 1.70122i) q^{93} +(-12.2112 + 12.1015i) q^{94} +(0.151262 + 0.0491479i) q^{95} +(4.98106 + 2.68125i) q^{96} +(0.854405 + 1.17599i) q^{97} +(-9.65427 - 2.18976i) q^{98} +(-3.31309 - 0.152995i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 2 q^{2} + 48 q^{3} - 2 q^{4} - 2 q^{6} + 2 q^{8} - 48 q^{9} + 2 q^{12} + 13 q^{14} + 6 q^{16} - 3 q^{18} + 6 q^{20} + 24 q^{22} + 3 q^{24} + 56 q^{25} - 18 q^{26} + 48 q^{27} + 16 q^{29} + 12 q^{31}+ \cdots + 50 q^{98}+O(q^{100}) $ 192 * q + 2 * q^2 + 48 * q^3 - 2 * q^4 - 2 * q^6 + 2 * q^8 - 48 * q^9 + 2 * q^12 + 13 * q^14 + 6 * q^16 - 3 * q^18 + 6 * q^20 + 24 * q^22 + 3 * q^24 + 56 * q^25 - 18 * q^26 + 48 * q^27 + 16 * q^29 + 12 * q^31 - 8 * q^32 + 24 * q^34 + 14 * q^35 - 2 * q^36 - 24 * q^37 - 36 * q^38 - 36 * q^40 + 2 * q^42 + 29 * q^44 - 23 * q^46 + 8 * q^47 - 11 * q^48 + 16 * q^49 - 14 * q^50 - 40 * q^52 + 8 * q^53 - 2 * q^54 - 4 * q^55 - 8 * q^56 + 7 * q^58 - 40 * q^59 - 6 * q^60 - 56 * q^64 - 16 * q^65 + 11 * q^66 - 78 * q^68 + 86 * q^70 - 3 * q^72 + 28 * q^74 - 36 * q^75 - 56 * q^76 + 28 * q^77 - 12 * q^78 + 6 * q^80 - 48 * q^81 + 8 * q^83 + 15 * q^84 - 60 * q^85 - 51 * q^86 - 16 * q^87 - 4 * q^88 + 8 * q^91 - 47 * q^92 - 12 * q^93 + 64 * q^94 - 2 * q^96 + 50 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/924\mathbb{Z}\right)^\times$.

$n$	$463$	$617$	$661$	$673$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.636345	−	1.26296i	−0.449964	−	0.893047i
$2$	−0.636345	−	1.26296i	−0.449964	−	0.893047i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	−1.19013	+	1.60736i	−0.595064	+	0.803678i
$5$	0.381488	−	0.525073i	0.170607	−	0.234820i	−0.715149	−	0.698972i	$-0.753641\pi$
$5$	0.381488	−	0.525073i	0.170607	−	0.234820i	0.885755	+	0.464152i	$0.153641\pi$
$6$	−1.00450	+	0.995476i	−0.410087	+	0.406401i
$7$	2.39317	−	1.12816i	0.904533	−	0.426404i
$7$	2.39317	−	1.12816i	0.904533	−	0.426404i
$8$	2.78736	+	0.480250i	0.985480	+	0.169794i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−0.905904	−	0.147676i	−0.286472	−	0.0466991i
$11$	2.59042	+	2.07116i	0.781041	+	0.624479i
$11$	2.59042	+	2.07116i	0.781041	+	0.624479i
$12$	1.89646	+	0.635180i	0.547460	+	0.183361i
$13$	2.65571	+	3.65527i	0.736560	+	1.01379i	0.998809	+	0.0487880i	$0.0155359\pi$
$13$	2.65571	+	3.65527i	0.736560	+	1.01379i	−0.262249	+	0.965000i	$0.584464\pi$
$14$	−2.94770	−	2.30457i	−0.787806	−	0.615923i
$15$	−0.617261	−	0.200560i	−0.159376	−	0.0517844i
$16$	−1.16719	−	3.82592i	−0.291797	−	0.956480i
$17$	−3.39103	+	4.66735i	−0.822445	+	1.13200i	0.166837	+	0.985984i	$0.446645\pi$
$17$	−3.39103	+	4.66735i	−0.822445	+	1.13200i	−0.989282	+	0.146015i	$0.953355\pi$
$18$	1.25716	+	0.647720i	0.296316	+	0.152669i
$19$	0.0757255	+	0.233059i	0.0173726	+	0.0534675i	0.959367	−	0.282161i	$-0.0910513\pi$
$19$	0.0757255	+	0.233059i	0.0173726	+	0.0534675i	−0.941994	+	0.335629i	$0.891051\pi$
$20$	0.389960	+	1.23809i	0.0871976	+	0.276846i
$21$	−1.81247	−	1.92742i	−0.395514	−	0.420597i
$22$	0.967390	−	4.58957i	0.206248	−	0.978500i
$23$			8.55411i			1.78365i	0.452376	+	0.891827i	$0.350576\pi$
$23$			8.55411i			1.78365i	−0.452376	+	0.891827i	$0.649424\pi$
$24$	−0.404596	−	2.79934i	−0.0825878	−	0.571413i
$25$	1.41492	+	4.35466i	0.282983	+	0.870933i
$26$	2.92650	−	5.68006i	0.573934	−	1.11395i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−1.03483	+	5.18933i	−0.195564	+	0.980691i
$29$	−2.06422	+	6.35301i	−0.383315	+	1.17972i	0.554380	+	0.832264i	$0.312956\pi$
$29$	−2.06422	+	6.35301i	−0.383315	+	1.17972i	−0.937695	+	0.347460i	$0.887044\pi$
$30$	0.139492	+	0.907200i	0.0254676	+	0.165631i
$31$	2.34153	−	1.70122i	0.420551	−	0.305548i	−0.357308	−	0.933986i	$-0.616305\pi$
$31$	2.34153	−	1.70122i	0.420551	−	0.305548i	0.777860	+	0.628438i	$0.216305\pi$
$32$	−4.08925	+	3.90872i	−0.722884	+	0.690970i
$33$	1.16931	−	3.10366i	0.203551	−	0.540278i
$34$	8.05254	+	1.31268i	1.38100	+	0.225123i
$35$	0.320599	−	1.68697i	0.0541911	−	0.285150i
$36$	0.0180544	−	1.99992i	0.00300906	−	0.333320i
$37$	0.730589	−	2.24852i	0.120108	−	0.369654i	−0.872870	−	0.487953i	$-0.837744\pi$
$37$	0.730589	−	2.24852i	0.120108	−	0.369654i	0.992978	+	0.118298i	$0.0377439\pi$
$38$	0.246157	−	0.243944i	0.0399319	−	0.0395730i
$39$	2.65571	−	3.65527i	0.425253	−	0.585311i
$40$	1.31551	−	1.28036i	0.208000	−	0.202442i
$41$	5.30938	−	1.72512i	0.829185	−	0.269419i	0.136483	−	0.990642i	$-0.456420\pi$
$41$	5.30938	−	1.72512i	0.829185	−	0.269419i	0.692702	+	0.721224i	$0.256420\pi$
$42$	−1.28089	+	3.51558i	−0.197646	+	0.542466i
$43$		−	2.48287i		−	0.378634i	−0.981916	−	0.189317i	$-0.939373\pi$
$43$		−	2.48287i		−	0.378634i	0.981916	−	0.189317i	$-0.0606274\pi$
$44$	−6.41203	+	1.69878i	−0.966650	+	0.256100i
$45$			0.649026i			0.0967511i
$46$	10.8035	−	5.44337i	1.59289	−	0.802581i
$47$	−3.75656	−	11.5615i	−0.547950	−	1.68642i	−0.713870	−	0.700278i	$-0.753059\pi$
$47$	−3.75656	−	11.5615i	−0.547950	−	1.68642i	0.165920	−	0.986139i	$-0.446941\pi$
$48$	−3.27799	+	2.29234i	−0.473137	+	0.330870i
$49$	4.45451	−	5.39975i	0.636359	−	0.771393i
$50$	4.59939	−	4.55805i	0.650451	−	0.644606i
$51$	5.48680	+	1.78277i	0.768306	+	0.249638i
$52$	−9.03595	−	0.0815724i	−1.25306	−	0.0113121i
$53$	0.458500	−	0.333120i	0.0629798	−	0.0457575i	−0.555850	−	0.831283i	$-0.687607\pi$
$53$	0.458500	−	0.333120i	0.0629798	−	0.0457575i	0.618830	+	0.785525i	$0.287607\pi$
$54$	0.227534	−	1.39579i	0.0309635	−	0.189943i
$55$	2.07573	−	0.570037i	0.279891	−	0.0768638i
$56$	7.21241	−	1.99526i	0.963799	−	0.266628i
$57$	0.198252	−	0.144039i	0.0262591	−	0.0190784i
$58$	9.33714	−	1.43569i	1.22603	−	0.188515i
$59$	−1.60166	+	4.92941i	−0.208519	+	0.641755i	0.791032	+	0.611775i	$0.209544\pi$
$59$	−1.60166	+	4.92941i	−0.208519	+	0.641755i	−0.999551	+	0.0299796i	$0.990456\pi$
$60$	1.05699	−	0.753465i	0.136457	−	0.0972719i
$61$	−0.541491	+	0.745298i	−0.0693308	+	0.0954256i	−0.842274	−	0.539049i	$-0.818784\pi$
$61$	−0.541491	+	0.745298i	−0.0693308	+	0.0954256i	0.772943	+	0.634475i	$0.218784\pi$
$62$	−3.63859	−	1.87469i	−0.462102	−	0.238086i
$63$	−1.27300	+	2.31937i	−0.160383	+	0.292213i
$64$	7.53872	+	2.67726i	0.942340	+	0.334657i
$65$	2.93240			0.363720
$66$	−4.66388	+	0.498212i	−0.574084	+	0.0613257i
$67$			2.11653i			0.258575i	0.991607	+	0.129287i	$0.0412690\pi$
$67$			2.11653i			0.258575i	−0.991607	+	0.129287i	$0.958731\pi$
$68$	−3.46633	−	11.0053i	−0.420355	−	1.33459i
$69$	8.13544	−	2.64336i	0.979392	−	0.318224i
$70$	−2.33458	+	0.668591i	−0.279036	+	0.0799119i
$71$	−2.28843	+	3.14975i	−0.271586	+	0.373806i	−0.922924	−	0.384981i	$-0.874208\pi$
$71$	−2.28843	+	3.14975i	−0.271586	+	0.373806i	0.651338	+	0.758788i	$0.274208\pi$
$72$	−2.53730	+	1.24984i	−0.299024	+	0.147295i
$73$	6.54886	+	2.12785i	0.766486	+	0.249046i	0.666060	−	0.745898i	$-0.267979\pi$
$73$	6.54886	+	2.12785i	0.766486	+	0.249046i	0.100426	+	0.994945i	$0.467979\pi$
$74$	−3.30469	+	0.508133i	−0.384163	+	0.0590692i
$75$	3.70430	−	2.69133i	0.427736	−	0.310768i
$76$	−0.464732	−	0.155653i	−0.0533085	−	0.0178546i
$77$	8.53592	+	2.03423i	0.972758	+	0.231823i
$78$	−6.30640	−	1.02803i	−0.714059	−	0.116402i
$79$	−5.95596	−	8.19768i	−0.670098	−	0.922311i	0.329664	−	0.944098i	$-0.393064\pi$
$79$	−5.95596	−	8.19768i	−0.670098	−	0.922311i	−0.999763	+	0.0217871i	$0.993064\pi$
$80$	−2.45416	−	0.846685i	−0.274383	−	0.0946622i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−5.55736	−	5.60775i	−0.613707	−	0.619272i
$83$	−8.46913	−	6.15318i	−0.929608	−	0.675399i	0.0162891	−	0.999867i	$-0.494815\pi$
$83$	−8.46913	−	6.15318i	−0.929608	−	0.675399i	−0.945897	+	0.324468i	$0.894815\pi$
$84$	5.25512	−	0.619413i	0.573381	−	0.0675835i
$85$	1.15706	+	3.56108i	0.125501	+	0.386253i
$86$	−3.13576	+	1.57996i	−0.338138	+	0.170372i
$87$	6.67995			0.716165
$88$	6.22575	+	7.01712i	0.663668	+	0.748028i
$89$			3.88247i			0.411541i	0.978600	+	0.205771i	$0.0659701\pi$
$89$			3.88247i			0.411541i	−0.978600	+	0.205771i	$0.934030\pi$
$90$	0.819693	−	0.413005i	0.0864032	−	0.0435345i
$91$	10.4793	+	5.75161i	1.09853	+	0.602932i
$92$	−13.7495	−	10.1805i	−1.43348	−	1.06139i
$93$	−2.34153	−	1.70122i	−0.242805	−	0.176408i
$94$	−12.2112	+	12.1015i	−1.25949	+	1.24817i
$95$	0.151262	+	0.0491479i	0.0155191	+	0.00504246i
$96$	4.98106	+	2.68125i	0.508377	+	0.273653i
$97$	0.854405	+	1.17599i	0.0867517	+	0.119403i	0.850187	−	0.526481i	$-0.176489\pi$
$97$	0.854405	+	1.17599i	0.0867517	+	0.119403i	−0.763435	+	0.645884i	$0.776489\pi$
$98$	−9.65427	−	2.18976i	−0.975229	−	0.221199i
$99$	−3.31309	−	0.152995i	−0.332978	−	0.0153765i
$100$	−8.68343	−	2.90834i	−0.868343	−	0.290834i
$101$	−9.34365	−	12.8604i	−0.929728	−	1.27966i	−0.959966	−	0.280118i	$-0.909626\pi$
$101$	−9.34365	−	12.8604i	−0.929728	−	1.27966i	0.0302378	−	0.999543i	$-0.490374\pi$
$102$	−1.23994	−	8.06406i	−0.122772	−	0.798461i
$103$	3.55090	−	10.9285i	0.349880	−	1.07682i	−0.609039	−	0.793140i	$-0.708445\pi$
$103$	3.55090	−	10.9285i	0.349880	−	1.07682i	0.958919	−	0.283680i	$-0.0915554\pi$
$104$	5.64696	+	11.4639i	0.553730	+	1.12413i
$105$	−1.70347	+	0.216394i	−0.166242	+	0.0211179i
$106$	−0.712480	−	0.367087i	−0.0692022	−	0.0356546i
$107$	4.56558	−	1.48345i	0.441372	−	0.143410i	−0.0798968	−	0.996803i	$-0.525459\pi$
$107$	4.56558	−	1.48345i	0.441372	−	0.143410i	0.521268	+	0.853393i	$0.325459\pi$
$108$	−1.90761	+	0.600838i	−0.183560	+	0.0578157i
$109$	9.39584			0.899958			0.449979	−	0.893039i	$-0.351431\pi$
$109$	9.39584			0.899958			0.449979	+	0.893039i	$0.351431\pi$
$110$	−2.04081	−	2.25882i	−0.194584	−	0.215370i
$111$	−2.36423			−0.224403
$112$	−7.10952	−	7.83930i	−0.671787	−	0.740745i
$113$	−1.18640	−	3.65137i	−0.111607	−	0.343492i	0.879617	−	0.475682i	$-0.157799\pi$
$113$	−1.18640	−	3.65137i	−0.111607	−	0.343492i	−0.991224	+	0.132191i	$0.957799\pi$
$114$	−0.308072	−	0.158726i	−0.0288535	−	0.0148660i
$115$	4.49153	+	3.26329i	0.418837	+	0.304303i
$116$	−7.75486	−	10.8788i	−0.720020	−	1.01007i
$117$	−4.29702	−	1.39619i	−0.397260	−	0.129078i
$118$	7.24485	−	1.11397i	0.666943	−	0.102550i
$119$	−2.84979	+	14.9954i	−0.261240	+	1.37462i
$120$	−1.62421	−	0.855472i	−0.148269	−	0.0780935i
$121$	2.42057	+	10.7304i	0.220051	+	0.975488i
$122$	1.28586	+	0.209613i	0.116416	+	0.0189775i
$123$	−3.28138	−	4.51643i	−0.295872	−	0.407232i
$124$	−0.0522545	+	5.78835i	−0.00469260	+	0.519809i
$125$	5.91259	+	1.92112i	0.528838	+	0.171830i
$126$	3.73933	+	0.131825i	0.333126	+	0.0117439i
$127$	4.59855	−	6.32937i	0.408056	−	0.561640i	−0.554687	−	0.832059i	$-0.687162\pi$
$127$	4.59855	−	6.32937i	0.408056	−	0.561640i	0.962743	+	0.270419i	$0.0871621\pi$
$128$	−1.41597	−	11.2248i	−0.125155	−	0.992137i
$129$	−2.36135	+	0.767249i	−0.207905	+	0.0675525i
$130$	−1.86602	−	3.70350i	−0.163661	−	0.324819i
$131$	−4.38163			−0.382825			−0.191412	−	0.981510i	$-0.561307\pi$
$131$	−4.38163			−0.382825			−0.191412	+	0.981510i	$0.561307\pi$
$132$	3.59706	+	5.57325i	0.313084	+	0.485089i
$133$	0.444152	+	0.472320i	0.0385129	+	0.0409553i
$134$	2.67309	−	1.34684i	0.230919	−	0.116349i
$135$	0.617261	−	0.200560i	0.0531253	−	0.0172615i
$136$	−11.6935	+	11.3810i	−1.00271	+	0.975916i
$137$	−5.95775	−	4.32856i	−0.509005	−	0.369814i	0.303441	−	0.952850i	$-0.401864\pi$
$137$	−5.95775	−	4.32856i	−0.509005	−	0.369814i	−0.812446	+	0.583037i	$0.801864\pi$
$138$	−8.51541	−	8.59263i	−0.724880	−	0.731453i
$139$	0.156199	−	0.480732i	0.0132486	−	0.0407751i	−0.944214	−	0.329334i	$-0.893176\pi$
$139$	0.156199	−	0.480732i	0.0132486	−	0.0407751i	0.957462	+	0.288558i	$0.0931759\pi$
$140$	2.33000	+	2.52303i	0.196921	+	0.213235i
$141$	−9.83479	+	7.14540i	−0.828239	+	0.601751i
$142$	5.43423	+	0.885859i	0.456031	+	0.0743397i
$143$	−0.691254	+	14.9691i	−0.0578056	+	1.25178i
$144$	3.19309	+	2.40918i	0.266091	+	0.200765i
$145$	2.54832	+	3.50746i	0.211626	+	0.291279i
$146$	−1.47995	−	9.62499i	−0.122481	−	0.796570i
$147$	−6.51199	−	2.56788i	−0.537100	−	0.211795i
$148$	2.74468	+	3.85035i	0.225611	+	0.316496i
$149$	−3.69870	−	2.68726i	−0.303009	−	0.220149i	0.425882	−	0.904779i	$-0.359964\pi$
$149$	−3.69870	−	2.68726i	−0.303009	−	0.220149i	−0.728891	+	0.684630i	$0.759964\pi$
$150$	−5.75625	−	2.96576i	−0.469996	−	0.242153i
$151$	3.96371	−	1.28789i	0.322562	−	0.104807i	−0.143260	−	0.989685i	$-0.545759\pi$
$151$	3.96371	−	1.28789i	0.322562	−	0.104807i	0.465822	+	0.884878i	$0.345759\pi$
$152$	0.0991475	+	0.685987i	0.00804192	+	0.0556409i
$153$		−	5.76916i		−	0.466409i
$154$	−2.86264	−	12.0750i	−0.230678	−	0.973030i
$155$		−	1.87847i		−	0.150882i
$156$	2.71468	+	8.61890i	0.217348	+	0.690064i
$157$	−10.1531	+	3.29894i	−0.810306	+	0.263284i	−0.684727	−	0.728799i	$-0.740079\pi$
$157$	−10.1531	+	3.29894i	−0.810306	+	0.263284i	−0.125579	+	0.992084i	$0.540079\pi$
$158$	−6.56328	+	12.7387i	−0.522147	+	1.01344i
$159$	−0.458500	−	0.333120i	−0.0363614	−	0.0264181i
$160$	0.492363	+	3.63828i	0.0389247	+	0.287631i
$161$	9.65039	+	20.4714i	0.760558	+	1.61337i
$162$	−1.39779	+	0.214925i	−0.109820	+	0.0168861i
$163$	−10.7510	−	14.7975i	−0.842085	−	1.15903i	−0.985552	−	0.169375i	$-0.945825\pi$
$163$	−10.7510	−	14.7975i	−0.842085	−	1.15903i	0.143467	−	0.989655i	$-0.454175\pi$
$164$	−3.54596	+	10.5872i	−0.276893	+	0.826720i
$165$	−1.18357	−	1.79798i	−0.0921410	−	0.139973i
$166$	−2.38192	+	14.6117i	−0.184873	+	1.13409i
$167$	−11.8030	+	8.57538i	−0.913343	+	0.663583i	−0.941858	−	0.336011i	$-0.890922\pi$
$167$	−11.8030	+	8.57538i	−0.913343	+	0.663583i	0.0285150	+	0.999593i	$0.490922\pi$
$168$	−4.12637	−	6.24284i	−0.318356	−	0.481646i
$169$	−2.29097	+	7.05089i	−0.176229	+	0.542376i
$170$	3.76120	−	3.72740i	0.288471	−	0.285878i
$171$	−0.198252	−	0.144039i	−0.0151607	−	0.0110149i
$172$	3.99085	+	2.95493i	0.304300	+	0.225312i
$173$	22.4640	−	7.29899i	1.70791	−	0.554932i	0.717923	−	0.696123i	$-0.245093\pi$
$173$	22.4640	−	7.29899i	1.70791	−	0.554932i	0.989982	+	0.141191i	$0.0450930\pi$
$174$	−4.25075	−	8.43649i	−0.322249	−	0.639569i
$175$	8.29889	+	8.82520i	0.627337	+	0.667122i
$176$	4.90060	−	12.3282i	0.369397	−	0.929272i
$177$	5.18309			0.389585
$178$	4.90340	−	2.47059i	0.367526	−	0.185179i
$179$	−7.63429	+	2.48053i	−0.570614	+	0.185404i	−0.580091	−	0.814551i	$-0.696983\pi$
$179$	−7.63429	+	2.48053i	−0.570614	+	0.185404i	0.00947761	+	0.999955i	$0.496983\pi$
$180$	−1.04322	−	0.772425i	−0.0777567	−	0.0575731i
$181$	−12.7780	+	17.5875i	−0.949785	+	1.30727i	0.00183830	+	0.999998i	$0.499415\pi$
$181$	−12.7780	+	17.5875i	−0.949785	+	1.30727i	−0.951623	+	0.307268i	$0.900585\pi$
$182$	0.595604	−	16.8949i	0.0441491	−	1.25233i
$183$	0.876150	+	0.284679i	0.0647669	+	0.0210440i
$184$	−4.10811	+	23.8434i	−0.302854	+	1.75776i
$185$	−0.901927	−	1.24140i	−0.0663110	−	0.0912692i
$186$	−0.658550	+	4.03982i	−0.0482872	+	0.296214i
$187$	−18.4510	+	5.06703i	−1.34927	+	0.370538i
$188$	23.0542	+	7.72154i	1.68140	+	0.563151i
$189$	2.59923	+	0.493969i	0.189066	+	0.0359310i
$190$	−0.0341829	−	0.222312i	−0.00247989	−	0.0161282i
$191$	1.44195	+	0.468517i	0.104336	+	0.0339007i	0.360720	−	0.932674i	$-0.382531\pi$
$191$	1.44195	+	0.468517i	0.104336	+	0.0339007i	−0.256384	+	0.966575i	$0.582531\pi$
$192$	0.216629	−	7.99707i	0.0156338	−	0.577139i
$193$	8.63782	+	6.27574i	0.621764	+	0.451738i	0.853537	−	0.521032i	$-0.174453\pi$
$193$	8.63782	+	6.27574i	0.621764	+	0.451738i	−0.231773	+	0.972770i	$0.574453\pi$
$194$	0.941527	−	1.82741i	0.0675977	−	0.131201i
$195$	−0.906162	−	2.78888i	−0.0648916	−	0.199716i
$196$	3.37788	+	13.5864i	0.241277	+	0.970456i
$197$	25.9410			1.84822			0.924111	−	0.382125i	$-0.124808\pi$
$197$	25.9410			1.84822			0.924111	+	0.382125i	$0.124808\pi$
$198$	1.91505	+	4.28166i	0.136096	+	0.304284i
$199$	18.6134			1.31947			0.659734	−	0.751499i	$-0.270669\pi$
$199$	18.6134			1.31947			0.659734	+	0.751499i	$0.270669\pi$
$200$	1.85255	+	12.8175i	0.130995	+	0.906335i
$201$	2.01294	−	0.654043i	0.141982	−	0.0461326i
$202$	−10.2964	+	19.9843i	−0.724452	+	1.40609i
$203$	2.22718	+	17.5326i	0.156318	+	1.23055i
$204$	−9.39555	+	6.69752i	−0.657820	+	0.468920i
$205$	1.11965	−	3.44592i	0.0781997	−	0.240674i
$206$	−16.0619	+	2.46969i	−1.11908	+	0.172071i
$207$	−5.02798	−	6.92042i	−0.349469	−	0.481002i
$208$	10.8851	−	14.4269i	0.754743	−	1.00033i
$209$	−0.286543	+	0.760562i	−0.0198206	+	0.0526092i
$210$	1.35729	+	2.01371i	0.0936622	+	0.138959i
$211$	−2.81837	−	3.87915i	−0.194025	−	0.267052i	0.700910	−	0.713250i	$-0.252778\pi$
$211$	−2.81837	−	3.87915i	−0.194025	−	0.267052i	−0.894934	+	0.446198i	$0.852778\pi$
$212$	−0.0102321	+	1.13343i	−0.000702741	+	0.0778441i
$213$	3.70275	+	1.20310i	0.253708	+	0.0824348i
$214$	−4.77882	−	4.82216i	−0.326673	−	0.329636i
$215$	−1.30369	−	0.947185i	−0.0889108	−	0.0645975i
$216$	1.97274	+	2.02690i	0.134228	+	0.137913i
$217$	3.68443	−	6.71293i	0.250115	−	0.455703i
$218$	−5.97900	−	11.8666i	−0.404949	−	0.803704i
$219$		−	6.88588i		−	0.465305i
$220$	−1.55413	+	4.01485i	−0.104779	+	0.270681i
$221$	−26.0660			−1.75339
$222$	1.50447	+	2.98593i	0.100973	+	0.200403i
$223$	5.37664	+	16.5476i	0.360046	+	1.10811i	0.953025	+	0.302891i	$0.0979517\pi$
$223$	5.37664	+	16.5476i	0.360046	+	1.10811i	−0.592979	+	0.805218i	$0.702048\pi$
$224$	−5.37660	+	13.9675i	−0.359239	+	0.933245i
$225$	−3.70430	−	2.69133i	−0.246953	−	0.179422i
$226$	−3.85656	+	3.82191i	−0.256535	+	0.254229i
$227$	8.42588	−	25.9322i	0.559245	−	1.72118i	−0.125214	−	0.992130i	$-0.539962\pi$
$227$	8.42588	−	25.9322i	0.559245	−	1.72118i	0.684460	−	0.729051i	$-0.260038\pi$
$228$	−0.00442427	+	0.490086i	−0.000293005	+	0.0324567i
$229$	−5.07817	−	6.98950i	−0.335575	−	0.461879i	0.607568	−	0.794268i	$-0.292145\pi$
$229$	−5.07817	−	6.98950i	−0.335575	−	0.461879i	−0.943142	+	0.332389i	$0.892145\pi$
$230$	1.26323	−	7.74920i	0.0832951	−	0.510967i
$231$	−0.703071	−	8.74675i	−0.0462587	−	0.575494i
$232$	−8.80474	+	16.7168i	−0.578059	+	1.09751i
$233$	16.9037	−	12.2812i	1.10740	−	0.804570i	0.125144	−	0.992139i	$-0.460061\pi$
$233$	16.9037	−	12.2812i	1.10740	−	0.804570i	0.982251	+	0.187569i	$0.0600607\pi$
$234$	0.971064	+	6.31542i	0.0634804	+	0.412852i
$235$	−7.50371	−	2.43810i	−0.489488	−	0.159044i
$236$	−6.01713	−	8.44108i	−0.391682	−	0.549467i
$237$	−5.95596	+	8.19768i	−0.386881	+	0.532497i
$238$	20.7520	−	5.94308i	1.34515	−	0.385232i
$239$	10.8548	−	3.52695i	0.702140	−	0.228139i	0.0638776	−	0.997958i	$-0.479653\pi$
$239$	10.8548	−	3.52695i	0.702140	−	0.228139i	0.638263	+	0.769818i	$0.279653\pi$
$240$	−0.0468691	+	2.59568i	−0.00302539	+	0.167551i
$241$			13.8880i			0.894603i	0.894383	+	0.447302i	$0.147615\pi$
$241$			13.8880i			0.894603i	−0.894383	+	0.447302i	$0.852385\pi$
$242$	12.0117	−	9.88530i	0.772141	−	0.635451i
$243$	−1.00000			−0.0641500
$244$	−0.553516	−	1.75737i	−0.0354352	−	0.112504i
$245$	−1.13592	−	4.39889i	−0.0725713	−	0.281034i
$246$	−3.61597	+	7.01825i	−0.230546	+	0.447467i
$247$	−0.650789	+	0.895734i	−0.0414087	+	0.0569942i
$248$	7.34369	−	3.61739i	0.466325	−	0.229705i
$249$	−3.23492	+	9.95606i	−0.205005	+	0.630940i
$250$	−1.33616	−	8.68986i	−0.0845061	−	0.549595i
$251$	−16.6757	+	12.1156i	−1.05256	+	0.764729i	−0.972697	−	0.232077i	$-0.925448\pi$
$251$	−16.6757	+	12.1156i	−1.05256	+	0.764729i	−0.0798613	+	0.996806i	$0.525448\pi$
$252$	−2.21302	−	4.80651i	−0.139407	−	0.302782i
$253$	−17.7170	+	22.1587i	−1.11386	+	1.39311i
$254$	−10.9200	−	1.78012i	−0.685181	−	0.111695i
$255$	3.02923	−	2.20087i	0.189698	−	0.137824i
$256$	−13.2754	+	8.93113i	−0.829709	+	0.558195i
$257$	−5.24337	−	1.70367i	−0.327072	−	0.106272i	0.140878	−	0.990027i	$-0.455007\pi$
$257$	−5.24337	−	1.70367i	−0.327072	−	0.106272i	−0.467950	+	0.883755i	$0.655007\pi$
$258$	2.47164	+	2.49405i	0.153877	+	0.155273i
$259$	−0.788267	−	6.20531i	−0.0489806	−	0.385579i
$260$	−3.48994	+	4.71341i	−0.216437	+	0.292313i
$261$	−2.06422	−	6.35301i	−0.127772	−	0.393241i
$262$	2.78823	+	5.53382i	0.172257	+	0.341880i
$263$			23.4306i			1.44479i	0.691480	+	0.722396i	$0.256959\pi$
$263$			23.4306i			1.44479i	−0.691480	+	0.722396i	$0.743041\pi$
$264$	4.74981	−	8.08945i	0.292331	−	0.497871i
$265$		−	0.367827i		−	0.0225954i
$266$	0.313886	−	0.861504i	0.0192456	−	0.0528222i
$267$	3.69245	−	1.19975i	0.225974	−	0.0734235i
$268$	−3.40201	−	2.51894i	−0.207811	−	0.153869i
$269$	−13.3915	+	18.4318i	−0.816493	+	1.12381i	0.173796	+	0.984782i	$0.444397\pi$
$269$	−13.3915	+	18.4318i	−0.816493	+	1.12381i	−0.990289	+	0.139024i	$0.955603\pi$
$270$	−0.646090	−	0.651949i	−0.0393198	−	0.0396764i
$271$	6.37245	−	19.6124i	0.387099	−	1.19137i	−0.547848	−	0.836578i	$-0.684553\pi$
$271$	6.37245	−	19.6124i	0.387099	−	1.19137i	0.934946	−	0.354789i	$-0.115447\pi$
$272$	21.8149	+	7.52614i	1.32272	+	0.456339i
$273$	2.23183	−	11.7437i	0.135077	−	0.710763i
$274$	−1.67560	+	10.2788i	−0.101227	+	0.620968i
$275$	−5.35399	+	14.2109i	−0.322858	+	0.856952i
$276$	−5.43339	+	16.2225i	−0.327052	+	0.976479i
$277$	3.77376	−	2.74180i	0.226743	−	0.164739i	−0.468614	−	0.883403i	$-0.655246\pi$
$277$	3.77376	−	2.74180i	0.226743	−	0.164739i	0.695357	+	0.718665i	$0.255246\pi$
$278$	−0.706541	+	0.108638i	−0.0423755	+	0.00651570i
$279$	−0.894385	+	2.75263i	−0.0535454	+	0.164796i
$280$	1.70379	−	4.54821i	0.101821	−	0.271808i
$281$	−19.8662	−	14.4336i	−1.18512	−	0.861039i	−0.192378	−	0.981321i	$-0.561620\pi$
$281$	−19.8662	−	14.4336i	−1.18512	−	0.861039i	−0.992740	+	0.120282i	$0.961620\pi$
$282$	15.2827	+	7.87400i	0.910069	+	0.468890i
$283$	2.27822	+	7.01163i	0.135426	+	0.416798i	0.995656	−	0.0931078i	$-0.0296801\pi$
$283$	2.27822	+	7.01163i	0.135426	+	0.416798i	−0.860230	+	0.509906i	$0.829680\pi$
$284$	−2.33924	−	7.42692i	−0.138809	−	0.440707i
$285$		−	0.159046i		−	0.00942106i
$286$	19.3452	−	8.65248i	1.14391	−	0.511632i
$287$	10.7600	−	10.1183i	0.635144	−	0.597266i
$288$	1.01078	−	5.56582i	0.0595610	−	0.327969i
$289$	−5.03180	−	15.4863i	−0.295988	−	0.910958i
$290$	2.80817	−	5.45038i	0.164901	−	0.320057i
$291$	0.854405	−	1.17599i	0.0500861	−	0.0689376i
$292$	−11.2142	+	7.99393i	−0.656262	+	0.467809i
$293$	−14.2815	−	4.64033i	−0.834332	−	0.271091i	−0.139463	−	0.990227i	$-0.544538\pi$
$293$	−14.2815	−	4.64033i	−0.834332	−	0.271091i	−0.694869	+	0.719136i	$0.744538\pi$
$294$	0.900749	+	9.85843i	0.0525328	+	0.574955i
$295$	1.97729	+	2.72150i	0.115122	+	0.158452i
$296$	3.11626	−	5.91656i	0.181129	−	0.343893i
$297$	0.878296	+	3.19822i	0.0509639	+	0.185579i
$298$	−1.04025	+	6.38134i	−0.0602601	+	0.369661i
$299$	−31.2675	+	22.7172i	−1.80825	+	1.31377i
$300$	−0.0826666	+	9.15716i	−0.00477276	+	0.528689i
$301$	−2.80107	−	5.94193i	−0.161451	−	0.342487i
$302$	−4.14884	−	4.18646i	−0.238739	−	0.240904i
$303$	−9.34365	+	12.8604i	−0.536779	+	0.738812i
$304$	0.803281	−	0.561744i	0.0460713	−	0.0322182i
$305$	0.184764	+	0.568644i	0.0105795	+	0.0325605i
$306$	−7.28621	+	3.67118i	−0.416525	+	0.209867i
$307$	−27.1599			−1.55010			−0.775049	−	0.631901i	$-0.782275\pi$
$307$	−27.1599			−1.55010			−0.775049	+	0.631901i	$0.782275\pi$
$308$	−13.4286	+	11.2993i	−0.765164	+	0.643835i
$309$	−11.4909			−0.653697
$310$	−2.37243	+	1.19536i	−0.134745	+	0.0678917i
$311$	6.28106	+	19.3311i	0.356166	+	1.09617i	0.955330	+	0.295541i	$0.0954998\pi$
$311$	6.28106	+	19.3311i	0.356166	+	1.09617i	−0.599164	+	0.800626i	$0.704500\pi$
$312$	9.15784	−	8.91313i	0.518461	−	0.504607i
$313$	17.3464	−	23.8753i	0.980477	−	1.34951i	0.0439057	−	0.999036i	$-0.486020\pi$
$313$	17.3464	−	23.8753i	0.980477	−	1.34951i	0.936572	−	0.350476i	$-0.113980\pi$
$314$	10.6273	+	10.7237i	0.599734	+	0.605173i
$315$	0.732205	+	1.55323i	0.0412551	+	0.0875145i
$316$	20.2650	+	0.182943i	1.13999	+	0.0102913i
$317$	−7.69305	+	5.58933i	−0.432085	+	0.313928i	−0.782482	−	0.622673i	$-0.786047\pi$
$317$	−7.69305	+	5.58933i	−0.432085	+	0.313928i	0.350397	+	0.936601i	$0.386047\pi$
$318$	−0.128952	+	0.791045i	−0.00723127	+	0.0443596i
$319$	−18.5053	+	12.1816i	−1.03610	+	0.682041i
$320$	4.28169	−	2.93704i	0.239354	−	0.164185i
$321$	−2.82169	−	3.88372i	−0.157491	−	0.216768i
$322$	19.7136	−	25.2149i	1.09859	−	1.40517i
$323$	−1.34456	−	0.436873i	−0.0748132	−	0.0243083i
$324$	1.16092	+	1.62858i	0.0644954	+	0.0904767i
$325$	−12.1599	+	16.7366i	−0.674507	+	0.928380i
$326$	−11.8473	+	22.9944i	−0.656160	+	1.27354i
$327$	−2.90347	−	8.93597i	−0.160562	−	0.494160i
$328$	15.6276	−	2.25870i	0.862891	−	0.124716i
$329$	−22.0333	−	23.4306i	−1.21473	−	1.29177i
$330$	−1.51762	+	2.63894i	−0.0835420	+	0.145269i
$331$		−	15.9666i		−	0.877604i	−0.898584	−	0.438802i	$-0.855403\pi$
$331$		−	15.9666i		−	0.877604i	0.898584	−	0.438802i	$-0.144597\pi$
$332$	19.9697	−	6.28982i	1.09598	−	0.345199i
$333$	0.730589	+	2.24852i	0.0400360	+	0.123218i
$334$	18.3411	+	9.44979i	1.00358	+	0.517070i
$335$	1.11133	+	0.807429i	0.0607185	+	0.0441146i
$336$	−5.25866	+	9.18404i	−0.286883	+	0.501030i
$337$	10.5927	−	32.6009i	0.577021	−	1.77589i	−0.0521729	−	0.998638i	$-0.516615\pi$
$337$	10.5927	−	32.6009i	0.577021	−	1.77589i	0.629193	−	0.777249i	$-0.283385\pi$
$338$	10.3628	−	1.59340i	0.563664	−	0.0866694i
$339$	−3.10604	+	2.25667i	−0.168697	+	0.122565i
$340$	−7.10097	−	2.37833i	−0.385104	−	0.128983i
$341$	9.58906	+	0.442811i	0.519277	+	0.0239796i
$342$	−0.0557579	+	0.342042i	−0.00301504	+	0.0184955i
$343$	4.56862	−	17.9479i	0.246682	−	0.969096i
$344$	1.19240	−	6.92064i	0.0642898	−	0.373136i
$345$	1.71561	−	5.28011i	0.0923655	−	0.284272i
$346$	−23.5132	−	23.7264i	−1.26408	−	1.27554i
$347$	16.0901	−	22.1461i	0.863761	−	1.18886i	−0.116899	−	0.993144i	$-0.537295\pi$
$347$	16.0901	−	22.1461i	0.863761	−	1.18886i	0.980660	−	0.195721i	$-0.0627047\pi$
$348$	−7.95000	+	10.7371i	−0.426165	+	0.575566i
$349$	−1.13355	+	0.368313i	−0.0606775	+	0.0197153i	−0.339198	−	0.940715i	$-0.610156\pi$
$349$	−1.13355	+	0.368313i	−0.0606775	+	0.0197153i	0.278521	+	0.960430i	$0.410156\pi$
$350$	5.86490	−	16.0970i	0.313492	−	0.860422i
$351$			4.51816i			0.241161i
$352$	−18.6885	+	1.65572i	−0.996098	+	0.0882504i
$353$			16.4875i			0.877539i	0.898600	+	0.438769i	$0.144585\pi$
$353$			16.4875i			0.877539i	−0.898600	+	0.438769i	$0.855415\pi$
$354$	−3.29824	−	6.54603i	−0.175299	−	0.347917i
$355$	0.780841	+	2.40318i	0.0414427	+	0.127548i
$356$	−6.24052	−	4.62064i	−0.330747	−	0.244894i
$357$	15.1421	−	1.92352i	0.801404	−	0.101803i
$358$	7.99085	+	8.06332i	0.422330	+	0.426160i
$359$	28.8793	+	9.38345i	1.52419	+	0.495240i	0.946963	−	0.321343i	$-0.104134\pi$
$359$	28.8793	+	9.38345i	1.52419	+	0.495240i	0.577228	+	0.816583i	$0.304134\pi$
$360$	−0.311695	+	1.80907i	−0.0164278	+	0.0953462i
$361$	15.3227	−	11.1326i	0.806460	−	0.585928i
$362$	30.3435	+	4.94644i	1.59482	+	0.259979i
$363$	9.45719	−	5.61796i	0.496374	−	0.294867i
$364$	−21.7166	+	9.99877i	−1.13826	+	0.524078i
$365$	3.61559	−	2.62688i	0.189249	−	0.137497i
$366$	−0.197997	−	1.28770i	−0.0103495	−	0.0673089i
$367$	4.35401	−	13.4003i	0.227277	−	0.699488i	−0.770775	−	0.637107i	$-0.780131\pi$
$367$	4.35401	−	13.4003i	0.227277	−	0.699488i	0.998052	−	0.0623804i	$-0.0198692\pi$
$368$	32.7273	−	9.98424i	1.70603	−	0.520464i
$369$	−3.28138	+	4.51643i	−0.170822	+	0.235116i
$370$	−0.993895	+	1.92905i	−0.0516701	+	0.100287i
$371$	0.721455	−	1.31447i	0.0374561	−	0.0682440i
$372$	5.52119	−	1.73900i	0.286260	−	0.0901630i
$373$	−3.52046			−0.182283			−0.0911414	−	0.995838i	$-0.529052\pi$
$373$	−3.52046			−0.182283			−0.0911414	+	0.995838i	$0.529052\pi$
$374$	18.1407	+	20.0785i	0.938033	+	1.03824i
$375$		−	6.21687i		−	0.321038i
$376$	−4.91846	−	34.0301i	−0.253650	−	1.75497i
$377$	−28.7039	+	9.32645i	−1.47832	+	0.480337i
$378$	−1.03015	−	3.59705i	−0.0529850	−	0.185013i
$379$	−13.8298	+	19.0351i	−0.710388	+	0.977765i	0.289401	+	0.957208i	$0.406544\pi$
$379$	−13.8298	+	19.0351i	−0.710388	+	0.977765i	−0.999789	+	0.0205572i	$0.993456\pi$
$380$	−0.259019	+	0.184639i	−0.0132874	+	0.00947177i
$381$	−7.44062	−	2.41760i	−0.381194	−	0.123858i
$382$	−0.325859	−	2.11926i	−0.0166724	−	0.108431i
$383$	11.7088	−	8.50696i	0.598293	−	0.434685i	−0.246980	−	0.969021i	$-0.579438\pi$
$383$	11.7088	−	8.50696i	0.598293	−	0.434685i	0.845272	+	0.534335i	$0.179438\pi$
$384$	−10.2378	+	4.81530i	−0.522446	+	0.245730i
$385$	4.32447	−	3.70594i	0.220396	−	0.188872i
$386$	2.42937	−	14.9027i	0.123651	−	0.758530i
$387$	1.45939	+	2.00868i	0.0741852	+	0.102107i
$388$	−2.90708	−	0.0262438i	−0.147585	−	0.00133233i
$389$	11.7011	−	36.0123i	0.593269	−	1.82589i	0.0301088	−	0.999547i	$-0.490415\pi$
$389$	11.7011	−	36.0123i	0.593269	−	1.82589i	0.563160	−	0.826348i	$-0.309585\pi$
$390$	−2.94561	+	2.91914i	−0.149157	+	0.147816i
$391$	−39.9250	−	29.0072i	−2.01910	−	1.46696i
$392$	15.0095	−	12.9118i	0.758097	−	0.652142i
$393$	1.35400	+	4.16718i	0.0683002	+	0.210206i
$394$	−16.5075	−	32.7624i	−0.831633	−	1.65055i
$395$	−6.57651			−0.330900
$396$	4.18893	−	5.14324i	0.210501	−	0.258457i
$397$		−	0.770638i		−	0.0386772i	−0.999813	−	0.0193386i	$-0.993844\pi$
$397$		−	0.770638i		−	0.0386772i	0.999813	−	0.0193386i	$-0.00615606\pi$
$398$	−11.8446	−	23.5080i	−0.593714	−	1.17835i
$399$	0.311952	−	0.568368i	0.0156171	−	0.0284540i
$400$	15.0091	−	10.4961i	0.750457	−	0.524803i
$401$	25.1926	+	18.3035i	1.25806	+	0.914034i	0.998661	−	0.0517366i	$-0.0164756\pi$
$401$	25.1926	+	18.3035i	1.25806	+	0.914034i	0.259399	+	0.965770i	$0.416476\pi$
$402$	−2.10695	−	2.12606i	−0.105085	−	0.106038i
$403$	12.4368	+	4.04097i	0.619523	+	0.201295i
$404$	31.7914	+	0.286999i	1.58168	+	0.0142787i
$405$	−0.381488	−	0.525073i	−0.0189563	−	0.0260911i
$406$	20.7257	−	13.9696i	1.02860	−	0.693301i
$407$	6.54958	−	4.31145i	0.324651	−	0.213711i
$408$	14.4375	+	7.60425i	0.714763	+	0.376467i
$409$	−8.89765	−	12.2466i	−0.439960	−	0.605553i	0.530243	−	0.847846i	$-0.322101\pi$
$409$	−8.89765	−	12.2466i	−0.439960	−	0.605553i	−0.970203	+	0.242292i	$0.922101\pi$
$410$	−5.06454	+	0.778728i	−0.250120	+	0.0384587i
$411$	−2.27566	+	7.00375i	−0.112250	+	0.345470i
$412$	13.3400	+	18.7139i	0.657216	+	0.921969i
$413$	1.72811	+	13.6038i	0.0850348	+	0.669401i
$414$	−5.54067	+	10.7539i	−0.272309	+	0.528526i
$415$	−6.46174	+	2.09955i	−0.317194	+	0.103063i
$416$	−25.1472	−	4.56688i	−1.23294	−	0.223910i
$417$	−0.505471			−0.0247530
$418$	1.14290	−	0.122088i	0.0559010	−	0.00597154i
$419$	−24.8690			−1.21493			−0.607464	−	0.794347i	$-0.707813\pi$
$419$	−24.8690			−1.21493			−0.607464	+	0.794347i	$0.707813\pi$
$420$	1.67953	−	2.99562i	0.0819526	−	0.146171i
$421$	−0.794546	−	2.44536i	−0.0387238	−	0.119180i	0.929826	−	0.368000i	$-0.119957\pi$
$421$	−0.794546	−	2.44536i	−0.0387238	−	0.119180i	−0.968550	+	0.248820i	$0.919957\pi$
$422$	−3.10575	+	6.02796i	−0.151186	+	0.293437i
$423$	9.83479	+	7.14540i	0.478184	+	0.347421i
$424$	1.43798	−	0.708329i	0.0698346	−	0.0343995i
$425$	−25.1228	−	8.16288i	−1.21863	−	0.395958i
$426$	−0.836767	−	5.44201i	−0.0405415	−	0.263666i
$427$	−0.455064	+	2.39451i	−0.0220221	+	0.115879i
$428$	−3.04920	+	9.10401i	−0.147389	+	0.440059i
$429$	14.4500	−	3.96828i	0.697655	−	0.191590i
$430$	−0.366659	+	2.24924i	−0.0176819	+	0.108468i
$431$	9.10193	+	12.5277i	0.438425	+	0.603440i	0.969861	−	0.243658i	$-0.0783475\pi$
$431$	9.10193	+	12.5277i	0.438425	+	0.603440i	−0.531436	+	0.847098i	$0.678348\pi$
$432$	1.30455	−	3.78129i	0.0627650	−	0.181927i
$433$	−24.9249	−	8.09858i	−1.19781	−	0.389193i	−0.358857	−	0.933393i	$-0.616833\pi$
$433$	−24.9249	−	8.09858i	−1.19781	−	0.389193i	−0.838956	+	0.544200i	$0.816833\pi$
$434$	−10.8227	−	0.381539i	−0.519507	−	0.0183145i
$435$	2.54832	−	3.50746i	0.122183	−	0.168170i
$436$	−11.1823	+	15.1025i	−0.535533	+	0.723276i
$437$	−1.99361	+	0.647764i	−0.0953675	+	0.0309868i
$438$	−8.69658	+	4.38180i	−0.415539	+	0.209370i
$439$	40.0226			1.91017			0.955087	−	0.296326i	$-0.0957614\pi$
$439$	40.0226			1.91017			0.955087	+	0.296326i	$0.0957614\pi$
$440$	6.05955	−	0.592029i	0.288878	−	0.0282239i
$441$	−0.429883	+	6.98679i	−0.0204706	+	0.332704i
$442$	16.5870	+	32.9203i	0.788962	+	1.56586i
$443$	−13.8641	+	4.50471i	−0.658702	+	0.214025i	−0.619247	−	0.785196i	$-0.712562\pi$
$443$	−13.8641	+	4.50471i	−0.658702	+	0.214025i	−0.0394550	+	0.999221i	$0.512562\pi$
$444$	2.81374	−	3.80017i	0.133534	−	0.180348i
$445$	2.03858	+	1.48112i	0.0966381	+	0.0702117i
$446$	17.4775	−	17.3205i	0.827585	−	0.820147i
$447$	−1.41278	+	4.34808i	−0.0668221	+	0.205657i
$448$	21.0618	−	2.09775i	0.995077	−	0.0991095i
$449$	26.6688	−	19.3760i	1.25858	−	0.914411i	0.259892	−	0.965638i	$-0.416313\pi$
$449$	26.6688	−	19.3760i	1.25858	−	0.914411i	0.998687	+	0.0512262i	$0.0163130\pi$
$450$	−1.04183	+	6.39099i	−0.0491121	+	0.301274i
$451$	17.3265	+	6.52780i	0.815875	+	0.307382i
$452$	7.28101	+	2.43863i	0.342470	+	0.114703i
$453$	−2.44971	−	3.37173i	−0.115097	−	0.158418i
$454$	−38.1131	+	5.86030i	−1.78873	+	0.275037i
$455$	7.01773	−	3.30822i	0.328996	−	0.155092i
$456$	0.621774	−	0.306276i	0.0291172	−	0.0143427i
$457$	−26.4287	−	19.2016i	−1.23628	−	0.898213i	−0.238939	−	0.971035i	$-0.576800\pi$
$457$	−26.4287	−	19.2016i	−1.23628	−	0.898213i	−0.997345	+	0.0728216i	$0.976800\pi$
$458$	−5.59598	+	10.8612i	−0.261483	+	0.507513i
$459$	−5.48680	+	1.78277i	−0.256102	+	0.0832126i
$460$	−10.5908	+	3.33576i	−0.493797	+	0.155530i
$461$			13.8047i			0.642947i	0.946919	+	0.321473i	$0.104178\pi$
$461$			13.8047i			0.642947i	−0.946919	+	0.321473i	$0.895822\pi$
$462$	−10.5994	+	6.45391i	−0.493128	+	0.300263i
$463$			32.9125i			1.52957i	0.644283	+	0.764787i	$0.277156\pi$
$463$			32.9125i			1.52957i	−0.644283	+	0.764787i	$0.722844\pi$
$464$	26.7154	+	0.482389i	1.24023	+	0.0223943i
$465$	−1.78653	+	0.580479i	−0.0828484	+	0.0269191i
$466$	−26.2672	−	13.5335i	−1.21681	−	0.626928i
$467$	−1.47576	−	1.07220i	−0.0682899	−	0.0496155i	0.553117	−	0.833104i	$-0.313438\pi$
$467$	−1.47576	−	1.07220i	−0.0682899	−	0.0496155i	−0.621406	+	0.783488i	$0.713438\pi$
$468$	7.35818	−	5.24520i	0.340132	−	0.242460i
$469$	2.38778	+	5.06520i	0.110257	+	0.233889i
$470$	1.69573	+	11.0284i	0.0782181	+	0.508700i
$471$	6.27497	+	8.63675i	0.289135	+	0.397960i
$472$	−6.83176	+	12.9708i	−0.314457	+	0.597031i
$473$	5.14243	−	6.43168i	0.236449	−	0.295729i
$474$	14.1434	+	2.30558i	0.649627	+	0.105899i
$475$	−0.907750	+	0.659519i	−0.0416504	+	0.0302608i
$476$	−20.7113	−	22.4271i	−0.949301	−	1.02794i
$477$	−0.175131	+	0.538999i	−0.00801871	+	0.0246791i
$478$	−11.3618	−	11.4648i	−0.519677	−	0.524390i
$479$	28.0439	+	20.3751i	1.28136	+	0.930960i	0.999593	−	0.0285240i	$-0.00908072\pi$
$479$	28.0439	+	20.3751i	1.28136	+	0.930960i	0.281763	+	0.959484i	$0.409081\pi$
$480$	3.30806	−	1.59256i	0.150992	−	0.0726899i
$481$	10.1592	−	3.30091i	0.463218	−	0.150509i
$482$	17.5399	−	8.83755i	0.798922	−	0.402539i
$483$	16.4873	−	15.5041i	0.750200	−	0.705460i
$484$	−20.1283	−	8.87981i	−0.914923	−	0.403628i
$485$	0.943425			0.0428387
$486$	0.636345	+	1.26296i	0.0288652	+	0.0572890i
$487$	4.78859	−	1.55591i	0.216992	−	0.0705049i	−0.198504	−	0.980100i	$-0.563608\pi$
$487$	4.78859	−	1.55591i	0.216992	−	0.0705049i	0.415496	+	0.909595i	$0.363608\pi$
$488$	−1.86726	+	1.81736i	−0.0845268	+	0.0822681i
$489$	−10.7510	+	14.7975i	−0.486178	+	0.669166i
$490$	−4.83277	+	4.23383i	−0.218322	+	0.191265i
$491$	−9.09804	−	2.95613i	−0.410589	−	0.133408i	0.0964373	−	0.995339i	$-0.469255\pi$
$491$	−9.09804	−	2.95613i	−0.410589	−	0.133408i	−0.507026	+	0.861931i	$0.669255\pi$
$492$	11.1648	+	0.100790i	0.503346	+	0.00454398i
$493$	−22.6519	−	31.1777i	−1.02019	−	1.40417i
$494$	1.54540	+	0.251923i	0.0695309	+	0.0113346i
$495$	−1.34424	+	1.68125i	−0.0604190	+	0.0755666i
$496$	−9.24174	−	6.97287i	−0.414967	−	0.313091i
$497$	−1.92317	+	10.1196i	−0.0862661	+	0.453926i
$498$	14.6326	−	2.24992i	0.655703	−	0.100821i
$499$	11.5154	+	3.74157i	0.515499	+	0.167496i	0.555202	−	0.831716i	$-0.312641\pi$
$499$	11.5154	+	3.74157i	0.515499	+	0.167496i	−0.0397027	+	0.999212i	$0.512641\pi$
$500$	−10.1247	+	7.21726i	−0.452789	+	0.322766i
$501$	11.8030	+	8.57538i	0.527319	+	0.383120i
$502$	25.9130	+	13.3510i	1.15655	+	0.595883i
$503$	−9.37161	−	28.8428i	−0.417859	−	1.28604i	−0.909668	−	0.415335i	$-0.863664\pi$
$503$	−9.37161	−	28.8428i	−0.417859	−	1.28604i	0.491809	−	0.870703i	$-0.336336\pi$
$504$	−4.66218	+	5.85355i	−0.207670	+	0.260738i
$505$	−10.3172			−0.459107
$506$	39.2597	+	8.27516i	1.74531	+	0.367876i
$507$	7.41374			0.329256
$508$	4.70067	+	14.9243i	0.208559	+	0.662158i
$509$	−24.7783	+	8.05097i	−1.09828	+	0.356853i	−0.801441	−	0.598074i	$-0.795933\pi$
$509$	−24.7783	+	8.05097i	−1.09828	+	0.356853i	−0.296840	+	0.954927i	$0.595933\pi$
$510$	−4.70724	−	2.42528i	−0.208440	−	0.107393i
$511$	18.0731	−	2.29584i	0.799506	−	0.101562i
$512$	19.7274	+	11.0829i	0.871834	+	0.489801i
$513$	−0.0757255	+	0.233059i	−0.00334336	+	0.0102898i
$514$	1.18492	+	7.70628i	0.0522647	+	0.339909i
$515$	−4.38366	−	6.03359i	−0.193167	−	0.265872i
$516$	1.57707	−	4.70865i	0.0694265	−	0.207287i
$517$	14.2147	−	37.7296i	0.625161	−	1.65935i
$518$	−7.33544	+	4.94427i	−0.322301	+	0.217239i
$519$	−13.8835	−	19.1090i	−0.609418	−	0.838792i
$520$	8.17365	+	1.40829i	0.358438	+	0.0617574i
$521$	5.71583	+	1.85719i	0.250415	+	0.0813648i	0.431535	−	0.902096i	$-0.357972\pi$
$521$	5.71583	+	1.85719i	0.250415	+	0.0813648i	−0.181120	+	0.983461i	$0.557972\pi$
$522$	−6.71003	+	6.64973i	−0.293690	+	0.291051i
$523$	−10.7443	−	7.80623i	−0.469818	−	0.341342i	0.327553	−	0.944833i	$-0.393776\pi$
$523$	−10.7443	−	7.80623i	−0.469818	−	0.341342i	−0.797370	+	0.603490i	$0.793776\pi$
$524$	5.21470	−	7.04284i	0.227805	−	0.307668i
$525$	5.82876	−	10.6198i	0.254388	−	0.463488i
$526$	29.5918	−	14.9099i	1.29027	−	0.650104i
$527$			16.6976i			0.727361i
$528$	−13.2392	−	0.851132i	−0.576161	−	0.0370408i
$529$	−50.1727			−2.18142
$530$	−0.464550	+	0.234065i	−0.0201788	+	0.0101671i
$531$	−1.60166	−	4.92941i	−0.0695062	−	0.213918i
$532$	−1.28778	+	0.151789i	−0.0558325	+	0.00658089i
$533$	20.4059	+	14.8258i	0.883879	+	0.642175i
$534$	−3.86491	−	3.89996i	−0.167251	−	0.168768i
$535$	0.962796	−	2.96318i	0.0416253	−	0.128110i
$536$	−1.01646	+	5.89951i	−0.0439044	+	0.254820i
$537$	4.71825	+	6.49412i	0.203608	+	0.280242i
$538$	31.8002	+	5.18390i	1.37100	+	0.223494i
$539$	22.7228	−	4.76161i	0.978742	−	0.205097i
$540$	−0.412248	+	1.23085i	−0.0177403	+	0.0529673i
$541$	2.93339	−	2.13123i	0.126116	−	0.0916288i	−0.522939	−	0.852370i	$-0.675164\pi$
$541$	2.93339	−	2.13123i	0.126116	−	0.0916288i	0.649055	+	0.760741i	$0.275164\pi$
$542$	−28.8247	+	4.43211i	−1.23813	+	0.190375i
$543$	20.6753	+	6.71782i	0.887263	+	0.288289i
$544$	−4.37660	−	32.3405i	−0.187645	−	1.38659i
$545$	3.58440	−	4.93350i	0.153539	−	0.211328i
$546$	−16.2521	+	4.65436i	−0.695524	+	0.199188i
$547$	21.9098	−	7.11894i	0.936797	−	0.304384i	0.199458	−	0.979906i	$-0.436082\pi$
$547$	21.9098	−	7.11894i	0.936797	−	0.304384i	0.737339	+	0.675523i	$0.236082\pi$
$548$	14.0480	−	4.42468i	0.600102	−	0.189013i
$549$		−	0.921239i		−	0.0393175i
$550$	21.3548	−	2.28120i	0.910572	−	0.0972706i
$551$	−1.63694			−0.0697360
$552$	23.9458	−	3.46096i	1.01920	−	0.147308i
$553$	−23.5019	−	12.8992i	−0.999403	−	0.548528i
$554$	−5.86419	−	3.02137i	−0.249145	−	0.128366i
$555$	−0.901927	+	1.24140i	−0.0382847	+	0.0526943i
$556$	0.586810	+	0.823201i	0.0248863	+	0.0349115i
$557$	7.37996	−	22.7132i	0.312699	−	0.962388i	−0.663993	−	0.747739i	$-0.731139\pi$
$557$	7.37996	−	22.7132i	0.312699	−	0.962388i	0.976691	−	0.214649i	$-0.0688607\pi$
$558$	4.04560	−	0.622055i	0.171264	−	0.0263337i
$559$	9.07555	−	6.59377i	0.383855	−	0.278887i
$560$	−6.82841	+	0.742420i	−0.288553	+	0.0313730i
$561$	10.5207	+	15.9822i	0.444185	+	0.674768i
$562$	−5.58732	+	34.2750i	−0.235687	+	1.44580i
$563$	−8.48436	+	6.16425i	−0.357573	+	0.259792i	−0.752039	−	0.659118i	$-0.770930\pi$
$563$	−8.48436	+	6.16425i	−0.357573	+	0.259792i	0.394466	+	0.918911i	$0.370930\pi$
$564$	0.219477	−	24.3120i	0.00924166	−	1.02372i
$565$	−2.36983	−	0.770005i	−0.0996996	−	0.0323944i
$566$	7.40567	−	7.33911i	0.311283	−	0.308486i
$567$	−0.333413	−	2.62466i	−0.0140020	−	0.110225i
$568$	−7.89133	+	7.68046i	−0.331113	+	0.322265i
$569$	−0.410567	−	1.26360i	−0.0172119	−	0.0529727i	0.942082	−	0.335383i	$-0.108866\pi$
$569$	−0.410567	−	1.26360i	−0.0172119	−	0.0529727i	−0.959294	+	0.282411i	$0.908866\pi$
$570$	−0.200868	+	0.101208i	−0.00841345	+	0.00423914i
$571$		−	41.4842i		−	1.73606i	−0.496512	−	0.868030i	$-0.665386\pi$
$571$		−	41.4842i		−	1.73606i	0.496512	−	0.868030i	$-0.334614\pi$
$572$	−23.2380	−	18.9262i	−0.971628	−	0.791345i
$573$		−	1.51615i		−	0.0633382i
$574$	−19.6261	−	7.15071i	−0.819179	−	0.298465i
$575$	−37.2503	+	12.1033i	−1.55344	+	0.504744i
$576$	−7.67260	+	2.26520i	−0.319692	+	0.0943835i
$577$	9.47514	−	13.0414i	0.394455	−	0.542921i	−0.564886	−	0.825169i	$-0.691080\pi$
$577$	9.47514	−	13.0414i	0.394455	−	0.542921i	0.959342	+	0.282248i	$0.0910800\pi$
$578$	−16.3566	+	16.2096i	−0.680344	+	0.674230i
$579$	3.29935	−	10.1544i	0.137116	−	0.422001i
$580$	−8.67056	−	0.0782739i	−0.360026	−	0.00325015i
$581$	−27.2098	−	5.17108i	−1.12885	−	0.214532i
$582$	−2.02892	−	0.330744i	−0.0841015	−	0.0137098i
$583$	1.87765	+	0.0867077i	0.0777644	+	0.00359107i
$584$	17.2321	+	9.07618i	0.713070	+	0.375575i
$585$	−2.37236	+	1.72362i	−0.0980851	+	0.0712630i
$586$	3.22740	+	20.9898i	0.133323	+	0.867079i
$587$	1.92872	−	5.93600i	0.0796069	−	0.245005i	−0.903330	−	0.428945i	$-0.858885\pi$
$587$	1.92872	−	5.93600i	0.0796069	−	0.245005i	0.982937	+	0.183940i	$0.0588853\pi$
$588$	11.8776	−	7.41098i	0.489824	−	0.305624i
$589$	0.573799	+	0.416889i	0.0236430	+	0.0171776i
$590$	2.17891	−	4.22905i	0.0897041	−	0.174107i
$591$	−8.01622	−	24.6714i	−0.329743	−	1.01484i
$592$	−9.45540	−	0.170732i	−0.388614	−	0.00701704i
$593$			8.53991i			0.350692i	0.984507	+	0.175346i	$0.0561044\pi$
$593$			8.53991i			0.350692i	−0.984507	+	0.175346i	$0.943896\pi$
$594$	3.48032	−	3.14442i	0.142799	−	0.129017i
$595$	6.78651	+	7.21691i	0.278220	+	0.295864i
$596$	8.72132	−	2.74694i	0.357239	−	0.112519i
$597$	−5.75186	−	17.7024i	−0.235408	−	0.724511i
$598$	48.5878	+	25.0336i	1.98690	+	1.02370i
$599$	2.52948	−	3.48152i	0.103352	−	0.142251i	−0.754209	−	0.656635i	$-0.771979\pi$
$599$	2.52948	−	3.48152i	0.103352	−	0.142251i	0.857560	+	0.514384i	$0.171979\pi$
$600$	11.6177	−	5.72271i	0.474291	−	0.233629i
$601$	20.6678	+	6.71539i	0.843059	+	0.273926i	0.698536	−	0.715575i	$-0.253835\pi$
$601$	20.6678	+	6.71539i	0.843059	+	0.273926i	0.144523	+	0.989501i	$0.453835\pi$
$602$	−5.72196	+	7.31876i	−0.233210	+	0.298290i
$603$	−1.24406	−	1.71231i	−0.0506622	−	0.0697305i
$604$	−2.64723	+	7.90384i	−0.107714	+	0.321603i
$605$	6.55765	+	2.82253i	0.266606	+	0.114752i
$606$	22.1880	+	3.61697i	0.901325	+	0.146929i
$607$	−34.6200	+	25.1529i	−1.40518	+	1.02092i	−0.411182	+	0.911553i	$0.634884\pi$
$607$	−34.6200	+	25.1529i	−1.40518	+	1.02092i	−0.994001	+	0.109371i	$0.965116\pi$
$608$	−1.22062	−	0.657047i	−0.0495028	−	0.0266468i
$609$	15.9862	−	7.53604i	0.647795	−	0.305376i
$610$	0.600601	−	0.595203i	0.0243176	−	0.0240991i
$611$	32.2840	−	44.4351i	1.30607	−	1.79765i
$612$	9.27310	+	6.86605i	0.374843	+	0.277544i
$613$	8.40766	+	25.8761i	0.339582	+	1.04513i	0.964421	+	0.264373i	$0.0851648\pi$
$613$	8.40766	+	25.8761i	0.339582	+	1.04513i	−0.624838	+	0.780754i	$0.714835\pi$
$614$	17.2831	+	34.3018i	0.697489	+	1.38431i
$615$	−3.62326			−0.146104
$616$	22.8157	+	9.76951i	0.919271	+	0.393625i
$617$	−1.29447			−0.0521134			−0.0260567	−	0.999660i	$-0.508295\pi$
$617$	−1.29447			−0.0521134			−0.0260567	+	0.999660i	$0.508295\pi$
$618$	7.31221	+	14.5126i	0.294140	+	0.583782i
$619$	10.4581	+	32.1868i	0.420348	+	1.29370i	0.907379	+	0.420313i	$0.138080\pi$
$619$	10.4581	+	32.1868i	0.420348	+	1.29370i	−0.487032	+	0.873384i	$0.661920\pi$
$620$	3.01937	+	2.23562i	0.121261	+	0.0897847i
$621$	−5.02798	+	6.92042i	−0.201766	+	0.277707i
$622$	20.4175	−	20.2340i	0.818666	−	0.811309i
$623$	4.38005	+	9.29141i	0.175483	+	0.372253i
$624$	−17.0845	−	5.89415i	−0.683926	−	0.235955i
$625$	−15.2572	+	11.0850i	−0.610287	+	0.443400i
$626$	−41.1918	−	6.71487i	−1.64636	−	0.268380i
$627$	0.811884	+	0.0374918i	0.0324235	+	0.00149728i
$628$	6.78093	−	20.2458i	0.270588	−	0.807896i
$629$	8.01719	+	11.0347i	0.319666	+	0.439983i
$630$	1.49573	−	1.91313i	0.0595913	−	0.0762211i
$631$	33.4557	+	10.8704i	1.33185	+	0.432744i	0.886548	−	0.462636i	$-0.153096\pi$
$631$	33.4557	+	10.8704i	1.33185	+	0.432744i	0.445302	+	0.895380i	$0.353096\pi$
$632$	−12.6645	−	25.7102i	−0.503765	−	1.02270i
$633$	−2.81837	+	3.87915i	−0.112020	+	0.154182i
$634$	11.9545	+	6.15926i	0.474775	+	0.244615i
$635$	−1.56909	−	4.82915i	−0.0622673	−	0.191639i
$636$	1.08112	−	0.340517i	0.0428690	−	0.0135024i
$637$	31.5674	+	1.94228i	1.25075	+	0.0769559i
$638$	27.1607	+	15.6197i	1.07530	+	0.618390i
$639$		−	3.89330i		−	0.154017i
$640$	−6.43399	−	3.53862i	−0.254326	−	0.139876i
$641$	0.258520	+	0.795644i	0.0102109	+	0.0314260i	0.956032	−	0.293262i	$-0.0947408\pi$
$641$	0.258520	+	0.795644i	0.0102109	+	0.0314260i	−0.945821	+	0.324688i	$0.894741\pi$
$642$	−3.10941	+	6.03506i	−0.122718	+	0.238185i
$643$	3.83643	+	2.78733i	0.151294	+	0.109921i	0.660857	−	0.750512i	$-0.270193\pi$
$643$	3.83643	+	2.78733i	0.151294	+	0.109921i	−0.509563	+	0.860433i	$0.670193\pi$
$644$	−44.3901	−	8.85201i	−1.74921	−	0.348818i
$645$	−0.497964	+	1.53258i	−0.0196073	+	0.0603452i
$646$	0.303850	+	1.97612i	0.0119548	+	0.0777495i
$647$	30.0167	−	21.8084i	1.18008	−	0.857378i	0.187899	−	0.982188i	$-0.439832\pi$
$647$	30.0167	−	21.8084i	1.18008	−	0.857378i	0.992181	+	0.124811i	$0.0398323\pi$
$648$	1.31809	−	2.50253i	0.0517793	−	0.0983086i
$649$	−14.3586	+	9.45195i	−0.563624	+	0.371021i
$650$	28.8755	+	4.70713i	1.13259	+	0.184629i
$651$	−7.52293	−	1.42969i	−0.294847	−	0.0560340i
$652$	36.5800	+	0.330227i	1.43258	+	0.0129327i
$653$	−6.92073	+	21.2998i	−0.270829	+	0.833526i	0.719464	+	0.694530i	$0.244388\pi$
$653$	−6.92073	+	21.2998i	−0.270829	+	0.833526i	−0.990293	+	0.138996i	$0.955612\pi$
$654$	−9.43815	+	9.35333i	−0.369061	+	0.365744i
$655$	−1.67154	+	2.30068i	−0.0653124	+	0.0898949i
$656$	−12.7972	−	18.2997i	−0.499647	−	0.714484i
$657$	−6.54886	+	2.12785i	−0.255495	+	0.0830155i
$658$	−15.5711	+	42.7371i	−0.607025	+	1.66606i
$659$			2.88781i			0.112493i	0.998417	+	0.0562466i	$0.0179133\pi$
$659$			2.88781i			0.112493i	−0.998417	+	0.0562466i	$0.982087\pi$
$660$	4.29860	+	0.237409i	0.167323	+	0.00924113i
$661$			29.9390i			1.16449i	0.813013	+	0.582246i	$0.197826\pi$
$661$			29.9390i			1.16449i	−0.813013	+	0.582246i	$0.802174\pi$
$662$	−20.1652	+	10.1603i	−0.783741	+	0.394890i
$663$	8.05483	+	24.7902i	0.312824	+	0.962773i
$664$	−20.6514	−	21.2184i	−0.801431	−	0.823434i
$665$	0.417441	−	0.0530280i	0.0161877	−	0.00205634i
$666$	2.37488	−	2.35354i	0.0920248	−	0.0911978i
$667$	−54.3443	−	17.6575i	−2.10422	−	0.683702i
$668$	0.263400	−	29.1774i	0.0101913	−	1.12891i
$669$	14.0762	−	10.2270i	0.544218	−	0.395398i
$670$	0.312559	−	1.91737i	0.0120752	−	0.0740744i
$671$	−2.94632	+	0.809120i	−0.113742	+	0.0312357i
$672$	14.9454	+	0.797247i	0.576531	+	0.0307545i
$673$	14.3690	−	10.4397i	0.553885	−	0.402421i	−0.275331	−	0.961349i	$-0.588787\pi$
$673$	14.3690	−	10.4397i	0.553885	−	0.402421i	0.829216	+	0.558929i	$0.188787\pi$
$674$	−47.9143	+	7.36734i	−1.84559	+	0.283779i
$675$	−1.41492	+	4.35466i	−0.0544602	+	0.167611i
$676$	−8.60673	−	12.0739i	−0.331028	−	0.464380i
$677$	8.59547	−	11.8306i	0.330351	−	0.454689i	−0.611242	−	0.791444i	$-0.709330\pi$
$677$	8.59547	−	11.8306i	0.330351	−	0.454689i	0.941592	+	0.336756i	$0.109330\pi$
$678$	4.82659	+	2.48678i	0.185364	+	0.0955041i
$679$	3.37144	+	1.85043i	0.129384	+	0.0710131i
$680$	1.51494	+	10.4817i	0.0580955	+	0.401954i
$681$	−27.2667			−1.04486
$682$	−5.54270	−	12.3924i	−0.212241	−	0.474528i
$683$			19.9554i			0.763571i	0.924251	+	0.381786i	$0.124691\pi$
$683$			19.9554i			0.763571i	−0.924251	+	0.381786i	$0.875309\pi$
$684$	0.467467	−	0.147237i	0.0178740	−	0.00562975i
$685$	−4.54562	+	1.47696i	−0.173679	+	0.0564318i
$686$	−25.5747	+	5.65109i	−0.976446	+	0.215760i
$687$	−5.07817	+	6.98950i	−0.193744	+	0.266666i
$688$	−9.49926	+	2.89797i	−0.362156	+	0.110484i
$689$	2.43528	+	0.791271i	0.0927768	+	0.0301450i
$690$	−7.76029	+	1.19323i	−0.295429	+	0.0454254i
$691$	−29.2718	+	21.2672i	−1.11355	+	0.809043i	−0.983219	−	0.182427i	$-0.941605\pi$
$691$	−29.2718	+	21.2672i	−1.11355	+	0.809043i	−0.130333	+	0.991470i	$0.541605\pi$
$692$	−15.0030	+	44.7944i	−0.570327	+	1.70283i
$693$	−8.10140	+	3.37156i	−0.307747	+	0.128075i
$694$	−38.2085	−	6.22854i	−1.45037	−	0.236432i
$695$	−0.192831	−	0.265409i	−0.00731451	−	0.0100676i
$696$	18.6194	+	3.20804i	0.705766	+	0.121601i
$697$	−9.95251	+	30.6307i	−0.376978	+	1.16022i
$698$	1.18649	+	1.19725i	0.0449094	+	0.0453167i
$699$	−16.9037	−	12.2812i	−0.639355	−	0.464519i
$700$	−24.0620	+	2.83615i	−0.909457	+	0.107196i
$701$	−6.37932	−	19.6335i	−0.240944	−	0.741548i	−0.996277	−	0.0862076i	$-0.972525\pi$
$701$	−6.37932	−	19.6335i	−0.240944	−	0.741548i	0.755334	−	0.655340i	$-0.227475\pi$
$702$	5.70625	−	2.87511i	0.215368	−	0.108514i
$703$	0.579363			0.0218511
$704$	13.9834	+	22.5491i	0.527020	+	0.849853i
$705$			7.88987i			0.297150i
$706$	20.8230	−	10.4917i	0.783683	−	0.394861i
$707$	−36.8695	−	20.2361i	−1.38662	−	0.761055i
$708$	−6.16854	+	8.33107i	−0.231828	+	0.313101i
$709$	3.24718	+	2.35922i	0.121951	+	0.0886023i	0.647089	−	0.762415i	$-0.275986\pi$
$709$	3.24718	+	2.35922i	0.121951	+	0.0886023i	−0.525138	+	0.851017i	$0.675986\pi$
$710$	2.53823	−	2.51542i	0.0952583	−	0.0944022i
$711$	9.63695	+	3.13123i	0.361414	+	0.117430i
$712$	−1.86456	+	10.8218i	−0.0698772	+	0.405566i
$713$	14.5524	+	20.0297i	0.544993	+	0.750118i
$714$	−12.0649	−	17.8998i	−0.451518	−	0.669884i
$715$	7.59616	+	6.07348i	0.284080	+	0.227135i
$716$	5.09869	−	15.2232i	0.190547	−	0.568917i
$717$	−6.70865	−	9.23367i	−0.250539	−	0.344838i
$718$	−6.52630	−	42.4445i	−0.243559	−	1.58401i
$719$	1.51371	−	4.65873i	0.0564520	−	0.173741i	−0.918855	−	0.394596i	$-0.870885\pi$
$719$	1.51371	−	4.65873i	0.0564520	−	0.173741i	0.975307	+	0.220854i	$0.0708846\pi$
$720$	2.48312	−	0.757535i	0.0925405	−	0.0282316i
$721$	−3.83123	−	30.1598i	−0.142683	−	1.12321i
$722$	−23.8106	−	12.2678i	−0.886139	−	0.456560i
$723$	13.2082	−	4.29162i	0.491220	−	0.159607i
$724$	−13.0618	−	41.4702i	−0.485438	−	1.54123i
$725$	−30.5859			−1.13593
$726$	−13.1133	−	8.36908i	−0.486680	−	0.310606i
$727$	−15.3122			−0.567900			−0.283950	−	0.958839i	$-0.591645\pi$
$727$	−15.3122			−0.567900			−0.283950	+	0.958839i	$0.591645\pi$
$728$	26.4473	+	21.0645i	0.980201	+	0.780701i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−5.61841	−	2.89474i	−0.207947	−	0.107139i
$731$	11.5884	+	8.41948i	0.428613	+	0.311406i
$732$	−1.50031	+	1.06948i	−0.0554531	+	0.0395292i
$733$	38.6171	+	12.5474i	1.42635	+	0.463450i	0.917615	−	0.397470i	$-0.130112\pi$
$733$	38.6171	+	12.5474i	1.42635	+	0.463450i	0.508739	+	0.860921i	$0.330112\pi$
$734$	−19.6946	+	3.02826i	−0.726942	+	0.111775i
$735$	−3.83257	+	2.43966i	−0.141366	+	0.0899880i
$736$	−33.4356	−	34.9799i	−1.23245	−	1.28937i
$737$	−4.38367	+	5.48270i	−0.161475	+	0.201958i
$738$	7.79215	+	1.27023i	0.286833	+	0.0467580i
$739$	−28.2924	−	38.9411i	−1.04075	−	1.43247i	−0.896560	−	0.442921i	$-0.853942\pi$
$739$	−28.2924	−	38.9411i	−1.04075	−	1.43247i	−0.144191	−	0.989550i	$-0.546058\pi$
$740$	3.06877	+	0.0277035i	0.112810	+	0.00101840i
$741$	1.05300	+	0.342140i	0.0386829	+	0.0125688i
$742$	−2.11922	−	0.0747099i	−0.0777990	−	0.00274269i
$743$	−9.32940	+	12.8408i	−0.342262	+	0.471084i	−0.945101	−	0.326780i	$-0.894036\pi$
$743$	−9.32940	+	12.8408i	−0.342262	+	0.471084i	0.602838	+	0.797864i	$0.294036\pi$
$744$	−5.70967	−	5.86643i	−0.209327	−	0.215074i
$745$	−2.82202	+	0.916930i	−0.103391	+	0.0335937i
$746$	2.24023	+	4.44620i	0.0820207	+	0.162787i
$747$	10.4684			0.383019
$748$	13.8146	−	35.6878i	0.505112	−	1.30488i
$749$	9.25264	−	8.70085i	0.338084	−	0.317922i
$750$	−7.85165	+	3.95608i	−0.286702	+	0.144455i
$751$	−46.9202	+	15.2453i	−1.71214	+	0.556309i	−0.990688	−	0.136153i	$-0.956526\pi$
$751$	−46.9202	+	15.2453i	−1.71214	+	0.556309i	−0.721455	+	0.692462i	$0.756526\pi$
$752$	−39.8488	+	27.8667i	−1.45313	+	1.01619i
$753$	16.6757	+	12.1156i	0.607695	+	0.441516i
$754$	30.0445	+	30.3170i	1.09416	+	1.10408i
$755$	0.835872	−	2.57255i	0.0304205	−	0.0936247i
$756$	−3.88740	+	3.59000i	−0.141383	+	0.130567i
$757$	−18.6838	+	13.5746i	−0.679075	+	0.493377i	−0.873051	−	0.487629i	$-0.837862\pi$
$757$	−18.6838	+	13.5746i	−0.679075	+	0.493377i	0.193975	+	0.981006i	$0.437862\pi$
$758$	32.8410	+	5.35357i	1.19284	+	0.194450i
$759$	26.5491	+	10.0024i	0.963670	+	0.363064i
$760$	0.398017	+	0.209636i	0.0144376	+	0.00760430i
$761$	11.9515	+	16.4499i	0.433243	+	0.596308i	0.968694	−	0.248259i	$-0.0798583\pi$
$761$	11.9515	+	16.4499i	0.433243	+	0.596308i	−0.535451	+	0.844566i	$0.679858\pi$
$762$	1.68147	+	10.9356i	0.0609132	+	0.396156i
$763$	22.4858	−	10.6000i	0.814041	−	0.383746i
$764$	−2.46918	+	1.76013i	−0.0893317	+	0.0636792i
$765$	−3.02923	−	2.20087i	−0.109522	−	0.0795725i
$766$	−18.1948	−	9.37439i	−0.657404	−	0.338711i
$767$	−22.2719	+	7.23656i	−0.804190	+	0.261297i
$768$	12.5963	+	9.86574i	0.454530	+	0.355999i
$769$			36.5363i			1.31753i	0.752348	+	0.658766i	$0.228921\pi$
$769$			36.5363i			1.31753i	−0.752348	+	0.658766i	$0.771079\pi$
$770$	−7.43231	−	3.10337i	−0.267842	−	0.111838i
$771$			5.51320i			0.198553i
$772$	−20.3675	+	6.41511i	−0.733041	+	0.230885i
$773$	46.1579	−	14.9976i	1.66019	−	0.539427i	0.679275	−	0.733884i	$-0.262294\pi$
$773$	46.1579	−	14.9976i	1.66019	−	0.539427i	0.980911	+	0.194457i	$0.0622944\pi$
$774$	1.60821	−	3.12137i	0.0578057	−	0.112195i
$775$	10.7213	+	7.78949i	0.385121	+	0.279807i
$776$	1.81676	+	3.68823i	0.0652180	+	0.132400i
$777$	−5.65801	+	2.66723i	−0.202980	+	0.0956864i
$778$	−52.9279	+	8.13824i	−1.89756	+	0.291770i
$779$	0.804111	+	1.10676i	0.0288103	+	0.0396539i
$780$	5.56117	+	1.86260i	0.199122	+	0.0666918i
$781$	−12.4516	+	3.41947i	−0.445554	+	0.122358i
$782$	−11.2288	+	68.8823i	−0.401542	+	2.46322i
$783$	−5.40419	+	3.92637i	−0.193130	+	0.140317i
$784$	−25.8583	−	10.7401i	−0.923510	−	0.383575i
$785$	−2.14110	+	6.58963i	−0.0764192	+	0.235194i
$786$	4.40136	−	4.36181i	0.156991	−	0.155581i
$787$	9.13509	+	6.63703i	0.325631	+	0.236585i	0.738574	−	0.674172i	$-0.235499\pi$
$787$	9.13509	+	6.63703i	0.325631	+	0.236585i	−0.412944	+	0.910757i	$0.635499\pi$
$788$	−30.8732	+	41.6965i	−1.09981	+	1.48537i
$789$	22.2838	−	7.24045i	0.793324	−	0.257767i
$790$	4.18493	+	8.30586i	0.148893	+	0.295509i
$791$	−6.95858	−	7.39989i	−0.247419	−	0.263110i
$792$	−9.16130	−	2.01756i	−0.325533	−	0.0716910i
$793$	−4.16230			−0.147808
$794$	−0.973284	+	0.490392i	−0.0345406	+	0.0174034i
$795$	−0.349824	+	0.113665i	−0.0124070	+	0.00403128i
$796$	−22.1523	+	29.9184i	−0.785169	+	1.06043i
$797$	15.2213	−	20.9503i	0.539165	−	0.742097i	−0.449327	−	0.893367i	$-0.648336\pi$
$797$	15.2213	−	20.9503i	0.539165	−	0.742097i	0.988492	+	0.151270i	$0.0483363\pi$
$798$	−0.916335	−	0.0323040i	−0.0324379	−	0.00114355i
$799$	66.7001	+	21.6722i	2.35968	+	0.766707i
$800$	−22.8071	−	12.2768i	−0.806352	−	0.434050i
$801$	−2.28206	−	3.14099i	−0.0806327	−	0.110981i
$802$	7.08537	−	43.4646i	0.250193	−	1.53479i
$803$	12.5572	+	19.0758i	0.443133	+	0.673170i
$804$	−1.34437	+	4.01390i	−0.0474124	+	0.141559i
$805$	14.4305	+	2.74244i	0.508608	+	0.0966582i
$806$	−2.81054	−	18.2787i	−0.0989971	−	0.643838i
$807$	21.6679	+	7.04031i	0.762745	+	0.247831i
$808$	−19.8679	−	40.3339i	−0.698949	−	1.41894i
$809$	20.9885	+	15.2491i	0.737918	+	0.536129i	0.892058	−	0.451920i	$-0.149261\pi$
$809$	20.9885	+	15.2491i	0.737918	+	0.536129i	−0.154141	+	0.988049i	$0.549261\pi$
$810$	−0.420388	+	0.815931i	−0.0147709	+	0.0286689i
$811$	−14.8960	−	45.8453i	−0.523070	−	1.60984i	−0.768100	−	0.640329i	$-0.778798\pi$
$811$	−14.8960	−	45.8453i	−0.523070	−	1.60984i	0.245030	−	0.969515i	$-0.421202\pi$
$812$	−30.8317	−	17.2862i	−1.08198	−	0.606625i
$813$	−20.6217			−0.723234
$814$	−9.61298	−	5.52828i	−0.336935	−	0.193766i
$815$	−11.8712			−0.415829
$816$	0.416617	−	23.0729i	0.0145845	−	0.807713i
$817$	0.578656	−	0.188017i	0.0202446	−	0.00657787i
$818$	−9.80492	+	19.0304i	−0.342821	+	0.665382i
$819$	−11.8586	+	1.50641i	−0.414374	+	0.0526384i
$820$	4.20630	+	5.90077i	0.146890	+	0.206064i
$821$	−14.1541	+	43.5619i	−0.493982	+	1.52032i	0.324556	+	0.945867i	$0.394785\pi$
$821$	−14.1541	+	43.5619i	−0.493982	+	1.52032i	−0.818537	+	0.574453i	$0.805215\pi$
$822$	10.2936	−	1.58275i	0.359029	−	0.0552046i
$823$	21.5134	+	29.6107i	0.749912	+	1.03216i	0.997987	+	0.0634240i	$0.0202021\pi$
$823$	21.5134	+	29.6107i	0.749912	+	1.03216i	−0.248075	+	0.968741i	$0.579798\pi$
$824$	15.1460	−	28.7564i	0.527637	−	1.00178i
$825$	15.1699	+	0.700527i	0.528147	+	0.0243892i
$826$	16.0814	−	10.8393i	0.559544	−	0.377147i
$827$	−28.4086	−	39.1010i	−0.987862	−	1.35968i	−0.932484	−	0.361210i	$-0.882364\pi$
$827$	−28.4086	−	39.1010i	−0.987862	−	1.35968i	−0.0553780	−	0.998465i	$-0.517636\pi$
$828$	17.1075	+	0.154439i	0.594527	+	0.00536712i
$829$	−7.45912	−	2.42361i	−0.259066	−	0.0841756i	0.176605	−	0.984282i	$-0.443489\pi$
$829$	−7.45912	−	2.42361i	−0.259066	−	0.0841756i	−0.435670	+	0.900106i	$0.643489\pi$
$830$	6.76354	+	6.82487i	0.234766	+	0.236895i
$831$	−3.77376	−	2.74180i	−0.130910	−	0.0951118i
$832$	10.2345	+	34.6660i	0.354819	+	1.20183i
$833$	10.0972	+	39.1015i	0.349846	+	1.35479i
$834$	0.321654	+	0.638389i	0.0111380	+	0.0221056i
$835$			9.46884i			0.327683i
$836$	−0.881471	−	1.36574i	−0.0304863	−	0.0472352i
$837$	2.89429			0.100041
$838$	15.8252	+	31.4085i	0.546674	+	1.08499i
$839$	−10.9472	−	33.6919i	−0.377938	−	1.16318i	−0.941475	−	0.337084i	$-0.890559\pi$
$839$	−10.9472	−	33.6919i	−0.377938	−	1.16318i	0.563536	−	0.826091i	$-0.309441\pi$
$840$	−4.85211	−	0.214925i	−0.167414	−	0.00741561i
$841$	−12.6382	−	9.18219i	−0.435800	−	0.316627i
$842$	−2.58279	+	2.55957i	−0.0890087	+	0.0882088i
$843$	−7.58821	+	23.3541i	−0.261352	+	0.804358i
$844$	9.58940	+	0.0865687i	0.330081	+	0.00297982i
$845$	2.82825	+	3.89276i	0.0972949	+	0.133915i
$846$	2.76601	−	16.9679i	0.0950975	−	0.583368i
$847$	17.8984	+	22.9488i	0.614996	+	0.788530i
$848$	−1.80964	−	1.36537i	−0.0621434	−	0.0468870i
$849$	5.96445	−	4.33343i	0.204699	−	0.148723i
$850$	5.67738	+	36.9234i	0.194732	+	1.26646i
$851$	19.2341	+	6.24953i	0.659336	+	0.214231i
$852$	−6.34056	+	4.51980i	−0.217224	+	0.154846i
$853$	13.7596	−	18.9385i	0.471121	−	0.648443i	−0.505647	−	0.862740i	$-0.668746\pi$
$853$	13.7596	−	18.9385i	0.471121	−	0.648443i	0.976768	+	0.214298i	$0.0687463\pi$
$854$	3.31375	−	0.949010i	0.113394	−	0.0324745i
$855$	−0.151262	+	0.0491479i	−0.00517304	+	0.00168082i
$856$	13.4383	−	1.94228i	0.459313	−	0.0663857i
$857$		−	31.3735i		−	1.07170i	−0.844314	−	0.535849i	$-0.819992\pi$
$857$		−	31.3735i		−	1.07170i	0.844314	−	0.535849i	$-0.180008\pi$
$858$	−14.2070	−	15.7246i	−0.485019	−	0.536830i
$859$	−48.7636			−1.66379			−0.831897	−	0.554930i	$-0.812745\pi$
$859$	−48.7636			−1.66379			−0.831897	+	0.554930i	$0.812745\pi$
$860$	3.07402	−	0.968219i	0.104823	−	0.0330160i
$861$	−12.9481	−	7.10666i	−0.441271	−	0.242194i
$862$	10.0300	−	19.4673i	0.341625	−	0.663060i
$863$	3.45315	−	4.75286i	0.117547	−	0.161789i	−0.746189	−	0.665734i	$-0.768119\pi$
$863$	3.45315	−	4.75286i	0.117547	−	0.161789i	0.863736	+	0.503945i	$0.168119\pi$
$864$	−5.60576	+	0.758619i	−0.190712	+	0.0258087i
$865$	4.73724	−	14.5797i	0.161071	−	0.495725i
$866$	5.63266	+	36.6326i	0.191405	+	1.24483i
$867$	−13.1734	+	9.57105i	−0.447393	+	0.325050i
$868$	6.40512	+	13.9114i	0.217404	+	0.472185i
$869$	1.55028	−	33.5712i	0.0525896	−	1.13883i
$870$	−6.05139	−	0.986465i	−0.205161	−	0.0334443i
$871$	−7.73647	+	5.62087i	−0.262140	+	0.190456i
$872$	26.1896	+	4.51235i	0.886890	+	0.152807i
$873$	−1.38246	−	0.449187i	−0.0467891	−	0.0152027i
$874$	2.08673	+	2.10565i	0.0705846	+	0.0712247i
$875$	16.3172	−	2.07279i	0.551621	−	0.0700730i
$876$	11.0681	+	8.19509i	0.373955	+	0.276886i
$877$	10.8396	+	33.3608i	0.366027	+	1.12651i	0.949336	+	0.314264i	$0.101758\pi$
$877$	10.8396	+	33.3608i	0.366027	+	1.12651i	−0.583309	+	0.812250i	$0.698242\pi$
$878$	−25.4682	−	50.5469i	−0.859510	−	1.70587i
$879$			15.0164i			0.506491i
$880$	−4.60368	−	7.27623i	−0.155190	−	0.245282i
$881$			18.6064i			0.626864i	0.949611	+	0.313432i	$0.101479\pi$
$881$			18.6064i			0.626864i	−0.949611	+	0.313432i	$0.898521\pi$
$882$	9.09758	−	3.90309i	0.306331	−	0.131424i
$883$	10.1525	−	3.29874i	0.341658	−	0.111011i	−0.133162	−	0.991094i	$-0.542513\pi$
$883$	10.1525	−	3.29874i	0.341658	−	0.111011i	0.474820	+	0.880083i	$0.342513\pi$
$884$	31.0219	−	41.8973i	1.04338	−	1.40916i
$885$	1.97729	−	2.72150i	0.0664658	−	0.0914823i
$886$	14.5116	+	14.6432i	0.487527	+	0.491948i
$887$	0.0103855	−	0.0319634i	0.000348712	−	0.00107323i	−0.950882	−	0.309554i	$-0.899820\pi$
$887$	0.0103855	−	0.0319634i	0.000348712	−	0.00107323i	0.951231	+	0.308480i	$0.0998204\pi$
$888$	−6.58997	−	1.13542i	−0.221145	−	0.0381023i
$889$	3.86458	−	20.3351i	0.129614	−	0.682019i
$890$	0.573347	−	3.51715i	0.0192186	−	0.117895i
$891$	2.77028	−	1.82361i	0.0928078	−	0.0610933i
$892$	−32.9968	−	11.0516i	−1.10481	−	0.370035i
$893$	2.41005	−	1.75100i	0.0806491	−	0.0585950i
$894$	6.39047	−	0.982603i	0.213729	−	0.0328632i
$895$	−1.60993	+	4.95485i	−0.0538140	+	0.165623i
$896$	−16.0520	−	25.2653i	−0.536258	−	0.844054i
$897$	31.2675	+	22.7172i	1.04399	+	0.758505i
$898$	−41.4417	−	21.3518i	−1.38293	−	0.712518i
$899$	5.97444	+	18.3874i	0.199259	+	0.613256i
$900$	8.73452	−	2.75110i	0.291151	−	0.0917032i
$901$			3.26960i			0.108926i
$902$	−2.78133	−	26.0366i	−0.0926080	−	0.866925i
$903$	−4.78553	+	4.50013i	−0.159252	+	0.149755i
$904$	−1.55335	−	10.7474i	−0.0516638	−	0.357454i
$905$	4.36004	+	13.4188i	0.144933	+	0.446057i
$906$	−2.69950	+	5.23947i	−0.0896848	+	0.174070i
$907$	−33.4098	+	45.9847i	−1.10935	+	1.52690i	−0.286992	+	0.957933i	$0.592655\pi$
$907$	−33.4098	+	45.9847i	−1.10935	+	1.52690i	−0.822363	+	0.568963i	$0.807345\pi$
$908$	31.6544	+	44.4060i	1.05049	+	1.47367i
$909$	15.1183	+	4.91225i	0.501444	+	0.162929i
$910$	−8.64384	−	6.75794i	−0.286541	−	0.224023i
$911$	−26.1913	−	36.0493i	−0.867758	−	1.19437i	−0.979664	−	0.200647i	$-0.935696\pi$
$911$	−26.1913	−	36.0493i	−0.867758	−	1.19437i	0.111906	−	0.993719i	$-0.464304\pi$
$912$	−0.782477	−	0.590377i	−0.0259104	−	0.0195493i
$913$	−9.19437	−	33.4803i	−0.304289	−	1.10804i
$914$	−7.43302	+	45.5973i	−0.245862	+	1.50822i
$915$	0.483718	−	0.351442i	0.0159912	−	0.0116183i
$916$	17.2783	+	0.155980i	0.570890	+	0.00515374i
$917$	−10.4860	+	4.94318i	−0.346278	+	0.163238i
$918$	5.74306	+	5.79514i	0.189549	+	0.191268i
$919$	−0.455751	+	0.627288i	−0.0150338	+	0.0206923i	−0.816468	−	0.577391i	$-0.804071\pi$
$919$	−0.455751	+	0.627288i	−0.0150338	+	0.0206923i	0.801434	+	0.598083i	$0.204071\pi$
$920$	10.9523	+	11.2530i	0.361087	+	0.371001i
$921$	8.39288	+	25.8306i	0.276555	+	0.851148i
$922$	17.4347	−	8.78453i	0.574182	−	0.289303i
$923$	−17.5906			−0.579000
$924$	14.8959	+	9.27968i	0.490039	+	0.305279i
$925$	10.8253			0.355933
$926$	41.5671	−	20.9437i	1.36598	−	0.688253i
$927$	3.55090	+	10.9285i	0.116627	+	0.358940i
$928$	−16.3910	−	34.0474i	−0.538061	−	1.11766i
$929$	18.8815	−	25.9882i	0.619483	−	0.852645i	−0.377832	−	0.925874i	$-0.623330\pi$
$929$	18.8815	−	25.9882i	0.619483	−	0.852645i	0.997315	+	0.0732288i	$0.0233303\pi$
$930$	1.86997	+	1.88693i	0.0613188	+	0.0618749i
$931$	1.59578	+	0.629267i	0.0522997	+	0.0206234i
$932$	−0.377229	+	41.7864i	−0.0123565	+	1.36876i
$933$	16.4440	−	11.9473i	0.538353	−	0.391137i
$934$	−0.415053	+	2.54611i	−0.0135810	+	0.0833112i
$935$	−4.37829	+	11.6212i	−0.143185	+	0.380053i
$936$	−11.3068	−	5.95532i	−0.369575	−	0.194656i
$937$	−21.4641	−	29.5428i	−0.701200	−	0.965120i	−0.999942	−	0.0107855i	$-0.996567\pi$
$937$	−21.4641	−	29.5428i	−0.701200	−	0.965120i	0.298741	−	0.954334i	$-0.403433\pi$
$938$	4.87769	−	6.23889i	0.159262	−	0.203707i
$939$	−28.0671	−	9.11955i	−0.915935	−	0.297605i
$940$	12.8493	−	9.15948i	0.419097	−	0.298749i
$941$	−20.0031	+	27.5320i	−0.652084	+	0.897517i	−0.999187	−	0.0403103i	$-0.987165\pi$
$941$	−20.0031	+	27.5320i	−0.652084	+	0.897517i	0.347103	+	0.937827i	$0.387165\pi$
$942$	6.91481	−	13.4210i	0.225297	−	0.437279i
$943$	14.7569	+	45.4170i	0.480550	+	1.47898i
$944$	20.7290	+	0.374294i	0.674671	+	0.0121822i
$945$	1.25094	−	1.17634i	0.0406932	−	0.0382664i
$946$	−11.3953	−	2.40190i	−0.370493	−	0.0780926i
$947$		−	21.1389i		−	0.686921i	−0.939167	−	0.343461i	$-0.888401\pi$
$947$		−	21.1389i		−	0.686921i	0.939167	−	0.343461i	$-0.111599\pi$
$948$	−6.08823	−	19.3296i	−0.197736	−	0.627798i
$949$	9.61398	+	29.5888i	0.312083	+	0.960493i
$950$	1.41059	+	0.726768i	0.0457655	+	0.0235795i
$951$	7.69305	+	5.58933i	0.249464	+	0.181246i
$952$	−15.1449	+	40.4289i	−0.490849	+	1.31031i
$953$	−9.29830	+	28.6172i	−0.301201	+	0.927003i	0.679866	+	0.733336i	$0.262038\pi$
$953$	−9.29830	+	28.6172i	−0.301201	+	0.927003i	−0.981067	+	0.193666i	$0.937962\pi$
$954$	0.792177	−	0.121806i	0.0256477	−	0.00394361i
$955$	0.796092	−	0.578394i	0.0257609	−	0.0187164i
$956$	−7.24958	+	21.6451i	−0.234468	+	0.700052i
$957$	17.3039	+	13.8353i	0.559355	+	0.447230i
$958$	7.88727	−	48.3838i	0.254826	−	1.56321i
$959$	−19.1412	−	3.63768i	−0.618102	−	0.117467i
$960$	−4.11640	−	3.16453i	−0.132856	−	0.102135i
$961$	−6.99092	+	21.5158i	−0.225513	+	0.694059i
$962$	−10.6337	−	10.7301i	−0.342843	−	0.345952i
$963$	−2.82169	+	3.88372i	−0.0909275	+	0.125151i
$964$	−22.3229	−	16.5285i	−0.718973	−	0.532346i
$965$	6.59045	−	2.14137i	0.212154	−	0.0689330i
$966$	−30.0727	−	10.9569i	−0.967572	−	0.352532i
$967$		−	31.0643i		−	0.998959i	−0.866326	−	0.499480i	$-0.833525\pi$
$967$		−	31.0643i		−	0.998959i	0.866326	−	0.499480i	$-0.166475\pi$
$968$	1.59372	+	31.0719i	0.0512242	+	0.998687i
$969$			1.41375i			0.0454162i
$970$	−0.600344	−	1.19151i	−0.0192759	−	0.0382570i
$971$	7.81103	+	24.0399i	0.250668	+	0.771476i	0.994652	+	0.103279i	$0.0329336\pi$
$971$	7.81103	+	24.0399i	0.250668	+	0.771476i	−0.743985	+	0.668197i	$0.767066\pi$
$972$	1.19013	−	1.60736i	0.0381734	−	0.0515560i
$973$	−0.168531	−	1.32669i	−0.00540285	−	0.0425317i
$974$	−5.01225	−	5.05770i	−0.160603	−	0.162059i
$975$	19.6751	+	6.39281i	0.630106	+	0.204734i
$976$	3.48347	+	1.20180i	0.111503	+	0.0384687i
$977$	7.16576	−	5.20623i	0.229253	−	0.166562i	−0.467229	−	0.884136i	$-0.654748\pi$
$977$	7.16576	−	5.20623i	0.229253	−	0.166562i	0.696482	+	0.717574i	$0.254748\pi$
$978$	25.5300	+	4.16176i	0.816359	+	0.133079i
$979$	−8.04124	+	10.0572i	−0.256999	+	0.321431i
$980$	8.42247	+	3.40941i	0.269046	+	0.108910i
$981$	−7.60139	+	5.52273i	−0.242694	+	0.176327i
$982$	2.05602	+	13.3716i	0.0656104	+	0.426704i
$983$	8.22611	−	25.3174i	0.262372	−	0.807498i	−0.729915	−	0.683538i	$-0.760440\pi$
$983$	8.22611	−	25.3174i	0.262372	−	0.807498i	0.992287	−	0.123960i	$-0.0395596\pi$
$984$	−6.97735	−	14.1648i	−0.222430	−	0.451556i
$985$	9.89619	−	13.6209i	0.315319	−	0.433999i
$986$	−24.9617	+	48.4482i	−0.794941	+	1.54290i
$987$	−15.4752	+	28.1954i	−0.492580	+	0.897468i
$988$	−0.665241	−	2.11209i	−0.0211641	−	0.0671945i
$989$	21.2387			0.675352
$990$	2.97875	+	0.627862i	0.0946709	+	0.0199548i
$991$		−	48.8458i		−	1.55164i	−0.630956	−	0.775818i	$-0.717337\pi$
$991$		−	48.8458i		−	1.55164i	0.630956	−	0.775818i	$-0.282663\pi$
$992$	−2.92550	+	16.1091i	−0.0928849	+	0.511464i
$993$	−15.1851	+	4.93395i	−0.481886	+	0.156574i
$994$	14.0044	−	4.01067i	0.444193	−	0.127211i
$995$	7.10079	−	9.77340i	0.225110	−	0.309837i
$996$	−12.1530	−	17.0487i	−0.385081	−	0.540207i
$997$	38.9696	+	12.6620i	1.23418	+	0.401009i	0.852226	−	0.523173i	$-0.175252\pi$
$997$	38.9696	+	12.6620i	1.23418	+	0.401009i	0.381952	+	0.924182i	$0.375252\pi$
$998$	−2.60231	−	16.9244i	−0.0823746	−	0.535732i
$999$	1.91271	−	1.38966i	0.0605153	−	0.0439670i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	924.2.bu.b.223.16	yes	192
4.3	odd	2		924.2.bu.a.223.36	yes	192
7.6	odd	2		924.2.bu.a.223.16	✓	192
11.4	even	5	inner	924.2.bu.b.895.36	yes	192
28.27	even	2	inner	924.2.bu.b.223.36	yes	192
44.15	odd	10		924.2.bu.a.895.16	yes	192
77.48	odd	10		924.2.bu.a.895.36	yes	192
308.279	even	10	inner	924.2.bu.b.895.16	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
924.2.bu.a.223.16	✓	192	7.6	odd	2
924.2.bu.a.223.36	yes	192	4.3	odd	2
924.2.bu.a.895.16	yes	192	44.15	odd	10
924.2.bu.a.895.36	yes	192	77.48	odd	10
924.2.bu.b.223.16	yes	192	1.1	even	1	trivial
924.2.bu.b.223.36	yes	192	28.27	even	2	inner
924.2.bu.b.895.16	yes	192	308.279	even	10	inner
924.2.bu.b.895.36	yes	192	11.4	even	5	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:	\( N \)	\(=\)	\( 924 = 2^{2} \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	924.bu (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.636345 - 1.26296i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-1.19013 + 1.60736i) q^{4} +(0.381488 - 0.525073i) q^{5} +(-1.00450 + 0.995476i) q^{6} +(2.39317 - 1.12816i) q^{7} +(2.78736 + 0.480250i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.905904 - 0.147676i) q^{10} +(2.59042 + 2.07116i) q^{11} +(1.89646 + 0.635180i) q^{12} +(2.65571 + 3.65527i) q^{13} +(-2.94770 - 2.30457i) q^{14} +(-0.617261 - 0.200560i) q^{15} +(-1.16719 - 3.82592i) q^{16} +(-3.39103 + 4.66735i) q^{17} +(1.25716 + 0.647720i) q^{18} +(0.0757255 + 0.233059i) q^{19} +(0.389960 + 1.23809i) q^{20} +(-1.81247 - 1.92742i) q^{21} +(0.967390 - 4.58957i) q^{22} +8.55411i q^{23} +(-0.404596 - 2.79934i) q^{24} +(1.41492 + 4.35466i) q^{25} +(2.92650 - 5.68006i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-1.03483 + 5.18933i) q^{28} +(-2.06422 + 6.35301i) q^{29} +(0.139492 + 0.907200i) q^{30} +(2.34153 - 1.70122i) q^{31} +(-4.08925 + 3.90872i) q^{32} +(1.16931 - 3.10366i) q^{33} +(8.05254 + 1.31268i) q^{34} +(0.320599 - 1.68697i) q^{35} +(0.0180544 - 1.99992i) q^{36} +(0.730589 - 2.24852i) q^{37} +(0.246157 - 0.243944i) q^{38} +(2.65571 - 3.65527i) q^{39} +(1.31551 - 1.28036i) q^{40} +(5.30938 - 1.72512i) q^{41} +(-1.28089 + 3.51558i) q^{42} -2.48287i q^{43} +(-6.41203 + 1.69878i) q^{44} +0.649026i q^{45} +(10.8035 - 5.44337i) q^{46} +(-3.75656 - 11.5615i) q^{47} +(-3.27799 + 2.29234i) q^{48} +(4.45451 - 5.39975i) q^{49} +(4.59939 - 4.55805i) q^{50} +(5.48680 + 1.78277i) q^{51} +(-9.03595 - 0.0815724i) q^{52} +(0.458500 - 0.333120i) q^{53} +(0.227534 - 1.39579i) q^{54} +(2.07573 - 0.570037i) q^{55} +(7.21241 - 1.99526i) q^{56} +(0.198252 - 0.144039i) q^{57} +(9.33714 - 1.43569i) q^{58} +(-1.60166 + 4.92941i) q^{59} +(1.05699 - 0.753465i) q^{60} +(-0.541491 + 0.745298i) q^{61} +(-3.63859 - 1.87469i) q^{62} +(-1.27300 + 2.31937i) q^{63} +(7.53872 + 2.67726i) q^{64} +2.93240 q^{65} +(-4.66388 + 0.498212i) q^{66} +2.11653i q^{67} +(-3.46633 - 11.0053i) q^{68} +(8.13544 - 2.64336i) q^{69} +(-2.33458 + 0.668591i) q^{70} +(-2.28843 + 3.14975i) q^{71} +(-2.53730 + 1.24984i) q^{72} +(6.54886 + 2.12785i) q^{73} +(-3.30469 + 0.508133i) q^{74} +(3.70430 - 2.69133i) q^{75} +(-0.464732 - 0.155653i) q^{76} +(8.53592 + 2.03423i) q^{77} +(-6.30640 - 1.02803i) q^{78} +(-5.95596 - 8.19768i) q^{79} +(-2.45416 - 0.846685i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-5.55736 - 5.60775i) q^{82} +(-8.46913 - 6.15318i) q^{83} +(5.25512 - 0.619413i) q^{84} +(1.15706 + 3.56108i) q^{85} +(-3.13576 + 1.57996i) q^{86} +6.67995 q^{87} +(6.22575 + 7.01712i) q^{88} +3.88247i q^{89} +(0.819693 - 0.413005i) q^{90} +(10.4793 + 5.75161i) q^{91} +(-13.7495 - 10.1805i) q^{92} +(-2.34153 - 1.70122i) q^{93} +(-12.2112 + 12.1015i) q^{94} +(0.151262 + 0.0491479i) q^{95} +(4.98106 + 2.68125i) q^{96} +(0.854405 + 1.17599i) q^{97} +(-9.65427 - 2.18976i) q^{98} +(-3.31309 - 0.152995i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 2 q^{2} + 48 q^{3} - 2 q^{4} - 2 q^{6} + 2 q^{8} - 48 q^{9} + 2 q^{12} + 13 q^{14} + 6 q^{16} - 3 q^{18} + 6 q^{20} + 24 q^{22} + 3 q^{24} + 56 q^{25} - 18 q^{26} + 48 q^{27} + 16 q^{29} + 12 q^{31}+ \cdots + 50 q^{98}+O(q^{100}) \) 192 * q + 2 * q^2 + 48 * q^3 - 2 * q^4 - 2 * q^6 + 2 * q^8 - 48 * q^9 + 2 * q^12 + 13 * q^14 + 6 * q^16 - 3 * q^18 + 6 * q^20 + 24 * q^22 + 3 * q^24 + 56 * q^25 - 18 * q^26 + 48 * q^27 + 16 * q^29 + 12 * q^31 - 8 * q^32 + 24 * q^34 + 14 * q^35 - 2 * q^36 - 24 * q^37 - 36 * q^38 - 36 * q^40 + 2 * q^42 + 29 * q^44 - 23 * q^46 + 8 * q^47 - 11 * q^48 + 16 * q^49 - 14 * q^50 - 40 * q^52 + 8 * q^53 - 2 * q^54 - 4 * q^55 - 8 * q^56 + 7 * q^58 - 40 * q^59 - 6 * q^60 - 56 * q^64 - 16 * q^65 + 11 * q^66 - 78 * q^68 + 86 * q^70 - 3 * q^72 + 28 * q^74 - 36 * q^75 - 56 * q^76 + 28 * q^77 - 12 * q^78 + 6 * q^80 - 48 * q^81 + 8 * q^83 + 15 * q^84 - 60 * q^85 - 51 * q^86 - 16 * q^87 - 4 * q^88 + 8 * q^91 - 47 * q^92 - 12 * q^93 + 64 * q^94 - 2 * q^96 + 50 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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