LMFDB - Embedded newform 294.2.j.a.251.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,2,Mod(41,294)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("294.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	294.j (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.34760181943$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			251.12
Character	$\chi$	$=$	294.251
Dual form			294.2.j.a.41.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.781831 + 0.623490i) q^{2} +(-1.67563 - 0.438472i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-1.24567 - 0.599884i) q^{5} +(-1.03668 - 1.38755i) q^{6} +(2.35011 - 1.21532i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(2.61548 + 1.46944i) q^{9} +O(q^{10})$	\(q+(0.781831 + 0.623490i) q^{2} +(-1.67563 - 0.438472i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-1.24567 - 0.599884i) q^{5} +(-1.03668 - 1.38755i) q^{6} +(2.35011 - 1.21532i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(2.61548 + 1.46944i) q^{9} +(-0.599884 - 1.24567i) q^{10} +(4.74543 + 3.78435i) q^{11} +(0.0546156 - 1.73119i) q^{12} +(3.67688 + 2.93221i) q^{13} +(2.59513 + 0.515095i) q^{14} +(1.82426 + 1.55138i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(1.02928 - 4.50956i) q^{17} +(1.12869 + 2.77958i) q^{18} -0.830794i q^{19} +(0.307656 - 1.34793i) q^{20} +(-4.47080 + 1.00597i) q^{21} +(1.35062 + 5.91746i) q^{22} +(-6.70486 + 1.53034i) q^{23} +(1.12208 - 1.31945i) q^{24} +(-1.92561 - 2.41464i) q^{25} +(1.04649 + 4.58499i) q^{26} +(-3.73828 - 3.60905i) q^{27} +(1.70779 + 2.02075i) q^{28} +(5.02565 + 1.14707i) q^{29} +(0.458992 + 2.35032i) q^{30} +3.29815i q^{31} +(-0.974928 - 0.222521i) q^{32} +(-6.29226 - 8.42192i) q^{33} +(3.61639 - 2.88397i) q^{34} +(-3.65651 + 0.104094i) q^{35} +(-0.850594 + 2.87689i) q^{36} +(0.766842 - 3.35975i) q^{37} +(0.517992 - 0.649541i) q^{38} +(-4.87540 - 6.52551i) q^{39} +(1.08095 - 0.862032i) q^{40} +(3.21630 + 1.54889i) q^{41} +(-4.12262 - 2.00100i) q^{42} +(2.30191 - 1.10854i) q^{43} +(-2.63352 + 5.46855i) q^{44} +(-2.37655 - 3.39942i) q^{45} +(-6.19623 - 2.98395i) q^{46} +(-1.68186 + 2.10898i) q^{47} +(1.69994 - 0.331980i) q^{48} +(4.04601 - 5.71225i) q^{49} -3.08844i q^{50} +(-3.70201 + 7.10506i) q^{51} +(-2.04051 + 4.23717i) q^{52} +(8.03549 - 1.83405i) q^{53} +(-0.672501 - 5.15245i) q^{54} +(-3.64108 - 7.56078i) q^{55} +(0.0752892 + 2.64468i) q^{56} +(-0.364280 + 1.39211i) q^{57} +(3.21403 + 4.03026i) q^{58} +(-8.71118 + 4.19508i) q^{59} +(-1.10655 + 2.12373i) q^{60} +(-6.90429 - 1.57586i) q^{61} +(-2.05636 + 2.57859i) q^{62} +(7.93250 + 0.274690i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(-2.82120 - 5.85828i) q^{65} +(0.331497 - 10.5077i) q^{66} -9.57648 q^{67} +4.62553 q^{68} +(11.9059 + 0.375607i) q^{69} +(-2.92368 - 2.19841i) q^{70} +(1.12963 - 0.257831i) q^{71} +(-2.45873 + 1.71891i) q^{72} +(-10.6284 + 8.47585i) q^{73} +(2.69431 - 2.14864i) q^{74} +(2.16786 + 4.89037i) q^{75} +(0.809965 - 0.184869i) q^{76} +(15.7515 + 3.12644i) q^{77} +(0.256852 - 8.14161i) q^{78} -15.0627 q^{79} +1.38259 q^{80} +(4.68152 + 7.68657i) q^{81} +(1.54889 + 3.21630i) q^{82} +(2.44958 + 3.07168i) q^{83} +(-1.97559 - 4.13486i) q^{84} +(-3.98736 + 4.99999i) q^{85} +(2.49087 + 0.568525i) q^{86} +(-7.91818 - 4.12568i) q^{87} +(-5.46855 + 2.63352i) q^{88} +(-5.74690 - 7.20638i) q^{89} +(0.261448 - 4.13953i) q^{90} +(12.2046 + 2.42244i) q^{91} +(-2.98395 - 6.19623i) q^{92} +(1.44615 - 5.52648i) q^{93} +(-2.62986 + 0.600248i) q^{94} +(-0.498380 + 1.03490i) q^{95} +(1.53605 + 0.800342i) q^{96} -14.5502i q^{97} +(6.72483 - 1.94337i) q^{98} +(6.85073 + 16.8710i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9}+O(q^{10}) $ 120 * q + 20 * q^4 - 14 * q^6 + 4 * q^7 - 10 * q^9	$ 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9} + 12 q^{15} - 20 q^{16} - 8 q^{18} - 12 q^{21} - 10 q^{22} - 24 q^{25} + 42 q^{27} - 4 q^{28} + 8 q^{30} + 10 q^{36} - 58 q^{37} + 8 q^{39} - 14 q^{40} - 2 q^{42} - 12 q^{43} + 14 q^{45} - 60 q^{46} - 36 q^{49} - 24 q^{51} - 42 q^{52} - 14 q^{55} + 34 q^{57} + 50 q^{58} - 12 q^{60} - 154 q^{61} + 20 q^{64} - 28 q^{67} + 28 q^{69} - 38 q^{70} + 8 q^{72} - 84 q^{75} - 16 q^{78} + 16 q^{79} + 22 q^{81} - 30 q^{84} - 32 q^{85} - 56 q^{87} - 4 q^{88} - 42 q^{90} + 88 q^{91} + 14 q^{93} + 112 q^{94} - 224 q^{99}+O(q^{100}) $ 120 * q + 20 * q^4 - 14 * q^6 + 4 * q^7 - 10 * q^9 + 12 * q^15 - 20 * q^16 - 8 * q^18 - 12 * q^21 - 10 * q^22 - 24 * q^25 + 42 * q^27 - 4 * q^28 + 8 * q^30 + 10 * q^36 - 58 * q^37 + 8 * q^39 - 14 * q^40 - 2 * q^42 - 12 * q^43 + 14 * q^45 - 60 * q^46 - 36 * q^49 - 24 * q^51 - 42 * q^52 - 14 * q^55 + 34 * q^57 + 50 * q^58 - 12 * q^60 - 154 * q^61 + 20 * q^64 - 28 * q^67 + 28 * q^69 - 38 * q^70 + 8 * q^72 - 84 * q^75 - 16 * q^78 + 16 * q^79 + 22 * q^81 - 30 * q^84 - 32 * q^85 - 56 * q^87 - 4 * q^88 - 42 * q^90 + 88 * q^91 + 14 * q^93 + 112 * q^94 - 224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$-1$	$e\left(\frac{9}{14}\right)$

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 $

$2$	0.781831	+	0.623490i	0.552838	+	0.440874i
$2$	0.781831	+	0.623490i	0.552838	+	0.440874i
$3$	−1.67563	−	0.438472i	−0.967427	−	0.253152i
$3$	−1.67563	−	0.438472i	−0.967427	−	0.253152i
$4$	0.222521	+	0.974928i	0.111260	+	0.487464i
$5$	−1.24567	−	0.599884i	−0.557082	−	0.268276i	0.134087	−	0.990970i	$-0.457190\pi$
$5$	−1.24567	−	0.599884i	−0.557082	−	0.268276i	−0.691169	+	0.722693i	$0.742904\pi$
$6$	−1.03668	−	1.38755i	−0.423222	−	0.566465i
$7$	2.35011	−	1.21532i	0.888257	−	0.459347i
$7$	2.35011	−	1.21532i	0.888257	−	0.459347i
$8$	−0.433884	+	0.900969i	−0.153401	+	0.318541i
$9$	2.61548	+	1.46944i	0.871828	+	0.489812i
$10$	−0.599884	−	1.24567i	−0.189700	−	0.393916i
$11$	4.74543	+	3.78435i	1.43080	+	1.14103i	0.966905	+	0.255136i	$0.0821203\pi$
$11$	4.74543	+	3.78435i	1.43080	+	1.14103i	0.463896	+	0.885890i	$0.346451\pi$
$12$	0.0546156	−	1.73119i	0.0157662	−	0.499751i
$13$	3.67688	+	2.93221i	1.01978	+	0.813249i	0.982539	−	0.186057i	$-0.0595709\pi$
$13$	3.67688	+	2.93221i	1.01978	+	0.813249i	0.0372432	+	0.999306i	$0.488142\pi$
$14$	2.59513	+	0.515095i	0.693576	+	0.137665i
$15$	1.82426	+	1.55138i	0.471021	+	0.400564i
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	1.02928	−	4.50956i	0.249637	−	1.09373i	−0.682290	−	0.731082i	$-0.739016\pi$
$17$	1.02928	−	4.50956i	0.249637	−	1.09373i	0.931926	−	0.362648i	$-0.118127\pi$
$18$	1.12869	+	2.77958i	0.266035	+	0.655153i
$19$		−	0.830794i		−	0.190597i	−0.995449	−	0.0952986i	$-0.969619\pi$
$19$		−	0.830794i		−	0.190597i	0.995449	−	0.0952986i	$-0.0303806\pi$
$20$	0.307656	−	1.34793i	0.0687939	−	0.301406i
$21$	−4.47080	+	1.00597i	−0.975608	+	0.219520i
$22$	1.35062	+	5.91746i	0.287953	+	1.26161i
$23$	−6.70486	+	1.53034i	−1.39806	+	0.319098i	−0.854142	−	0.520040i	$-0.825917\pi$
$23$	−6.70486	+	1.53034i	−1.39806	+	0.319098i	−0.543919	+	0.839138i	$0.683060\pi$
$24$	1.12208	−	1.31945i	0.229043	−	0.269331i
$25$	−1.92561	−	2.41464i	−0.385122	−	0.482928i
$26$	1.04649	+	4.58499i	0.205234	+	0.899191i
$27$	−3.73828	−	3.60905i	−0.719433	−	0.694562i
$28$	1.70779	+	2.02075i	0.322743	+	0.381886i
$29$	5.02565	+	1.14707i	0.933240	+	0.213006i	0.661998	−	0.749505i	$-0.269709\pi$
$29$	5.02565	+	1.14707i	0.933240	+	0.213006i	0.271242	+	0.962511i	$0.412566\pi$
$30$	0.458992	+	2.35032i	0.0838002	+	0.429108i
$31$			3.29815i			0.592365i	0.955131	+	0.296182i	$0.0957136\pi$
$31$			3.29815i			0.592365i	−0.955131	+	0.296182i	$0.904286\pi$
$32$	−0.974928	−	0.222521i	−0.172345	−	0.0393365i
$33$	−6.29226	−	8.42192i	−1.09534	−	1.46607i
$34$	3.61639	−	2.88397i	0.620205	−	0.494597i
$35$	−3.65651	+	0.104094i	−0.618064	+	0.0175951i
$36$	−0.850594	+	2.87689i	−0.141766	+	0.479481i
$37$	0.766842	−	3.35975i	0.126068	−	0.552340i	−0.871960	−	0.489576i	$-0.837151\pi$
$37$	0.766842	−	3.35975i	0.126068	−	0.552340i	0.998028	−	0.0627637i	$-0.0199914\pi$
$38$	0.517992	−	0.649541i	0.0840294	−	0.105369i
$39$	−4.87540	−	6.52551i	−0.780689	−	1.04492i
$40$	1.08095	−	0.862032i	0.170914	−	0.136299i
$41$	3.21630	+	1.54889i	0.502302	+	0.241896i	0.667836	−	0.744308i	$-0.267221\pi$
$41$	3.21630	+	1.54889i	0.502302	+	0.241896i	−0.165535	+	0.986204i	$0.552935\pi$
$42$	−4.12262	−	2.00100i	−0.636134	−	0.308761i
$43$	2.30191	−	1.10854i	0.351038	−	0.169051i	−0.250052	−	0.968232i	$-0.580448\pi$
$43$	2.30191	−	1.10854i	0.351038	−	0.169051i	0.601090	+	0.799182i	$0.294733\pi$
$44$	−2.63352	+	5.46855i	−0.397017	+	0.824415i
$45$	−2.37655	−	3.39942i	−0.354274	−	0.506756i
$46$	−6.19623	−	2.98395i	−0.913584	−	0.439959i
$47$	−1.68186	+	2.10898i	−0.245324	+	0.307627i	−0.889214	−	0.457491i	$-0.848748\pi$
$47$	−1.68186	+	2.10898i	−0.245324	+	0.307627i	0.643890	+	0.765118i	$0.277319\pi$
$48$	1.69994	−	0.331980i	0.245365	−	0.0479171i
$49$	4.04601	−	5.71225i	0.578001	−	0.816036i
$50$		−	3.08844i		−	0.436771i
$51$	−3.70201	+	7.10506i	−0.518385	+	0.994907i
$52$	−2.04051	+	4.23717i	−0.282968	+	0.587590i
$53$	8.03549	−	1.83405i	1.10376	−	0.251926i	0.368443	−	0.929650i	$-0.379891\pi$
$53$	8.03549	−	1.83405i	1.10376	−	0.251926i	0.735316	+	0.677724i	$0.237034\pi$
$54$	−0.672501	−	5.15245i	−0.0915157	−	0.701160i
$55$	−3.64108	−	7.56078i	−0.490963	−	1.01949i
$56$	0.0752892	+	2.64468i	0.0100609	+	0.353410i
$57$	−0.364280	+	1.39211i	−0.0482501	+	0.184389i
$58$	3.21403	+	4.03026i	0.422022	+	0.529199i
$59$	−8.71118	+	4.19508i	−1.13410	+	0.546153i	−0.904220	−	0.427066i	$-0.859547\pi$
$59$	−8.71118	+	4.19508i	−1.13410	+	0.546153i	−0.229879	+	0.973219i	$0.573833\pi$
$60$	−1.10655	+	2.12373i	−0.142855	+	0.274173i
$61$	−6.90429	−	1.57586i	−0.884004	−	0.201768i	−0.243664	−	0.969860i	$-0.578349\pi$
$61$	−6.90429	−	1.57586i	−0.884004	−	0.201768i	−0.640340	+	0.768092i	$0.721207\pi$
$62$	−2.05636	+	2.57859i	−0.261158	+	0.327482i
$63$	7.93250	+	0.274690i	0.999401	+	0.0346077i
$64$	−0.623490	−	0.781831i	−0.0779362	−	0.0977289i
$65$	−2.82120	−	5.85828i	−0.349926	−	0.726630i
$66$	0.331497	−	10.5077i	0.0408044	−	1.29341i
$67$	−9.57648			−1.16995			−0.584976	−	0.811050i	$-0.698896\pi$
$67$	−9.57648			−1.16995			−0.584976	+	0.811050i	$0.698896\pi$
$68$	4.62553			0.560928
$69$	11.9059	+	0.375607i	1.43330	+	0.0452178i
$70$	−2.92368	−	2.19841i	−0.349446	−	0.262761i
$71$	1.12963	−	0.257831i	0.134063	−	0.0305989i	−0.154963	−	0.987920i	$-0.549526\pi$
$71$	1.12963	−	0.257831i	0.134063	−	0.0305989i	0.289026	+	0.957321i	$0.406669\pi$
$72$	−2.45873	+	1.71891i	−0.289764	+	0.202575i
$73$	−10.6284	+	8.47585i	−1.24396	+	0.992023i	−0.244206	+	0.969723i	$0.578527\pi$
$73$	−10.6284	+	8.47585i	−1.24396	+	0.992023i	−0.999751	+	0.0222993i	$0.992901\pi$
$74$	2.69431	−	2.14864i	0.313208	−	0.249775i
$75$	2.16786	+	4.89037i	0.250323	+	0.564692i
$76$	0.809965	−	0.184869i	0.0929093	−	0.0212059i
$77$	15.7515	+	3.12644i	1.79505	+	0.356291i
$78$	0.256852	−	8.14161i	0.0290827	−	0.921856i
$79$	−15.0627			−1.69468			−0.847341	−	0.531049i	$-0.821798\pi$
$79$	−15.0627			−1.69468			−0.847341	+	0.531049i	$0.821798\pi$
$80$	1.38259			0.154578
$81$	4.68152	+	7.68657i	0.520169	+	0.854064i
$82$	1.54889	+	3.21630i	0.171046	+	0.355181i
$83$	2.44958	+	3.07168i	0.268877	+	0.337161i	0.897879	−	0.440243i	$-0.145108\pi$
$83$	2.44958	+	3.07168i	0.268877	+	0.337161i	−0.629002	+	0.777404i	$0.716536\pi$
$84$	−1.97559	−	4.13486i	−0.215555	−	0.451150i
$85$	−3.98736	+	4.99999i	−0.432490	+	0.542325i
$86$	2.49087	+	0.568525i	0.268597	+	0.0613056i
$87$	−7.91818	−	4.12568i	−0.848918	−	0.442319i
$88$	−5.46855	+	2.63352i	−0.582949	+	0.280734i
$89$	−5.74690	−	7.20638i	−0.609170	−	0.763875i	0.377606	−	0.925966i	$-0.376747\pi$
$89$	−5.74690	−	7.20638i	−0.609170	−	0.763875i	−0.986776	+	0.162091i	$0.948176\pi$
$90$	0.261448	−	4.13953i	0.0275590	−	0.436345i
$91$	12.2046	+	2.42244i	1.27939	+	0.253941i
$92$	−2.98395	−	6.19623i	−0.311098	−	0.646001i
$93$	1.44615	−	5.52648i	0.149958	−	0.573069i
$94$	−2.62986	+	0.600248i	−0.271249	+	0.0619109i
$95$	−0.498380	+	1.03490i	−0.0511328	+	0.106178i
$96$	1.53605	+	0.800342i	0.156773	+	0.0816846i
$97$		−	14.5502i		−	1.47735i	−0.674064	−	0.738673i	$-0.735453\pi$
$97$		−	14.5502i		−	1.47735i	0.674064	−	0.738673i	$-0.264547\pi$
$98$	6.72483	−	1.94337i	0.679310	−	0.196310i
$99$	6.85073	+	16.8710i	0.688525	+	1.69560i
$100$	1.92561	−	2.41464i	0.192561	−	0.241464i
$101$	9.32141	+	4.48895i	0.927515	+	0.446667i	0.835748	−	0.549113i	$-0.185034\pi$
$101$	9.32141	+	4.48895i	0.927515	+	0.446667i	0.0917665	+	0.995781i	$0.470749\pi$
$102$	−7.32428	+	3.24679i	−0.725212	+	0.321480i
$103$	5.22239	−	10.8444i	0.514577	−	1.06853i	−0.468181	−	0.883633i	$-0.655090\pi$
$103$	5.22239	−	10.8444i	0.514577	−	1.06853i	0.982758	−	0.184898i	$-0.0591953\pi$
$104$	−4.23717	+	2.04051i	−0.415489	+	0.200089i
$105$	6.17261	+	1.42886i	0.602385	+	0.139442i
$106$	7.42591	+	3.57613i	0.721268	+	0.347344i
$107$	−1.62625	+	1.29689i	−0.157216	+	0.125376i	−0.698938	−	0.715182i	$-0.746344\pi$
$107$	−1.62625	+	1.29689i	−0.157216	+	0.125376i	0.541722	+	0.840557i	$0.317772\pi$
$108$	2.68672	−	4.44764i	0.258530	−	0.427975i
$109$	10.0298	−	12.5770i	0.960682	−	1.20466i	−0.0181179	−	0.999836i	$-0.505767\pi$
$109$	10.0298	−	12.5770i	0.960682	−	1.20466i	0.978799	−	0.204821i	$-0.0656611\pi$
$110$	1.86736	−	8.18143i	0.178046	−	0.780068i
$111$	−2.75810	+	5.29347i	−0.261788	+	0.502434i
$112$	−1.59007	+	2.11464i	−0.150247	+	0.199814i
$113$	−3.80437	+	3.03389i	−0.357885	+	0.285404i	−0.785882	−	0.618376i	$-0.787791\pi$
$113$	−3.80437	+	3.03389i	−0.357885	+	0.285404i	0.427997	+	0.903780i	$0.359219\pi$
$114$	−1.15277	+	0.861267i	−0.107967	+	0.0806650i
$115$	9.27009	+	2.11584i	0.864441	+	0.197303i
$116$			5.15490i			0.478620i
$117$	5.30812	+	13.0721i	0.490736	+	1.20851i
$118$	−9.42627	−	2.15148i	−0.867758	−	0.198060i
$119$	−3.06163	−	11.8489i	−0.280659	−	1.08618i
$120$	−2.18926	+	0.970480i	−0.199851	+	0.0885923i
$121$	5.75004	+	25.1926i	0.522731	+	2.29023i
$122$	−4.41546	−	5.53681i	−0.399757	−	0.501279i
$123$	−4.71019	−	4.00562i	−0.424704	−	0.361175i
$124$	−3.21545	+	0.733907i	−0.288756	+	0.0659068i
$125$	2.48845	+	10.9026i	0.222574	+	0.975161i
$126$	6.03061	+	5.16059i	0.537250	+	0.459742i
$127$	−1.33968	+	5.86954i	−0.118878	+	0.520837i	0.880064	+	0.474854i	$0.157499\pi$
$127$	−1.33968	+	5.86954i	−0.118878	+	0.520837i	−0.998942	+	0.0459832i	$0.985358\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−4.34322	+	0.848183i	−0.382399	+	0.0746784i
$130$	1.44687	−	6.33917i	0.126899	−	0.555982i
$131$	−5.66821	+	2.72967i	−0.495234	+	0.238492i	−0.664793	−	0.747028i	$-0.731480\pi$
$131$	−5.66821	+	2.72967i	−0.495234	+	0.238492i	0.169559	+	0.985520i	$0.445766\pi$
$132$	6.81061	−	8.00856i	0.592787	−	0.697055i
$133$	−1.00968	−	1.95246i	−0.0875502	−	0.169299i
$134$	−7.48719	−	5.97084i	−0.646795	−	0.515802i
$135$	2.49166	+	6.73823i	0.214448	+	0.579935i
$136$	3.61639	+	2.88397i	0.310103	+	0.247299i
$137$	−9.69084	−	20.1232i	−0.827945	−	1.71925i	−0.683776	−	0.729692i	$-0.739664\pi$
$137$	−9.69084	−	20.1232i	−0.827945	−	1.71925i	−0.144169	−	0.989553i	$-0.546051\pi$
$138$	9.07422	+	7.71687i	0.772449	+	0.656903i
$139$	−0.346981	+	0.720513i	−0.0294305	+	0.0611131i	−0.915166	−	0.403078i	$-0.867940\pi$
$139$	−0.346981	+	0.720513i	−0.0294305	+	0.0611131i	0.885735	+	0.464191i	$0.153655\pi$
$140$	−0.915135	−	3.54167i	−0.0773430	−	0.299326i
$141$	3.74291	−	2.79643i	0.315209	−	0.235502i
$142$	1.04394	+	0.502734i	0.0876053	+	0.0421885i
$143$	6.35184	+	27.8292i	0.531167	+	2.32720i
$144$	−2.99403	−	0.189100i	−0.249503	−	0.0157583i
$145$	−5.57221	−	4.44369i	−0.462747	−	0.369028i
$146$	−13.5942			−1.12506
$147$	−9.28429	+	7.79757i	−0.765755	+	0.643132i
$148$	3.44616			0.283272
$149$	−9.36588	−	7.46904i	−0.767283	−	0.611888i	0.159624	−	0.987178i	$-0.448972\pi$
$149$	−9.36588	−	7.46904i	−0.767283	−	0.611888i	−0.926907	+	0.375290i	$0.877543\pi$
$150$	−1.35419	+	5.17509i	−0.110570	+	0.422544i
$151$	−0.0178195	−	0.0780722i	−0.00145013	−	0.00635342i	0.974198	−	0.225696i	$-0.0724658\pi$
$151$	−0.0178195	−	0.0780722i	−0.00145013	−	0.00635342i	−0.975648	+	0.219343i	$0.929609\pi$
$152$	0.748520	+	0.360468i	0.0607130	+	0.0292378i
$153$	9.31857	−	10.2822i	0.753362	−	0.831269i
$154$	10.3657	+	12.2652i	0.835291	+	0.988360i
$155$	1.97851	−	4.10841i	0.158917	−	0.329995i
$156$	5.27703	−	6.20523i	0.422500	−	0.496816i
$157$	−0.754870	−	1.56750i	−0.0602452	−	0.125100i	0.868672	−	0.495387i	$-0.164974\pi$
$157$	−0.754870	−	1.56750i	−0.0602452	−	0.125100i	−0.928918	+	0.370287i	$0.879259\pi$
$158$	−11.7765	−	9.39142i	−0.936886	−	0.747141i
$159$	−14.2687	−	0.450149i	−1.13158	−	0.0356991i
$160$	1.08095	+	0.862032i	0.0854569	+	0.0681496i
$161$	−13.8973	+	11.7450i	−1.09526	+	0.925636i
$162$	−1.13234	+	8.92848i	−0.0889652	+	0.701488i
$163$	16.4133	−	7.90424i	1.28559	−	0.619108i	0.338769	−	0.940869i	$-0.389989\pi$
$163$	16.4133	−	7.90424i	1.28559	−	0.619108i	0.946821	+	0.321762i	$0.104275\pi$
$164$	−0.794360	+	3.48032i	−0.0620291	+	0.271767i
$165$	2.78592	+	14.2656i	0.216883	+	1.11057i
$166$			3.92883i			0.304936i
$167$	1.87055	−	8.19541i	0.144748	−	0.634180i	−0.849547	−	0.527513i	$-0.823125\pi$
$167$	1.87055	−	8.19541i	0.144748	−	0.634180i	0.994295	−	0.106668i	$-0.0340181\pi$
$168$	1.03346	−	4.46452i	0.0797333	−	0.344445i
$169$	2.02879	+	8.88870i	0.156061	+	0.683746i
$170$	−6.23489	+	1.42307i	−0.478194	+	0.109145i
$171$	1.22080	−	2.17293i	0.0933568	−	0.166168i
$172$	1.59297	+	1.99752i	0.121463	+	0.152310i
$173$	1.09089	+	4.77951i	0.0829389	+	0.363379i	0.999318	−	0.0369330i	$-0.0117588\pi$
$173$	1.09089	+	4.77951i	0.0829389	+	0.363379i	−0.916379	+	0.400312i	$0.868902\pi$
$174$	−3.61837	−	8.16249i	−0.274308	−	0.618797i
$175$	−7.45994	−	3.33443i	−0.563919	−	0.252060i
$176$	−5.91746	−	1.35062i	−0.446045	−	0.101807i
$177$	16.4362	−	3.20981i	1.23542	−	0.241264i
$178$		−	9.21731i		−	0.690866i
$179$	5.74722	+	1.31176i	0.429567	+	0.0980459i	0.431837	−	0.901952i	$-0.357865\pi$
$179$	5.74722	+	1.31176i	0.429567	+	0.0980459i	−0.00227013	+	0.999997i	$0.500723\pi$
$180$	2.78536	−	3.07340i	0.207609	−	0.229078i
$181$	−6.48699	+	5.17320i	−0.482174	+	0.384521i	−0.834194	−	0.551472i	$-0.814067\pi$
$181$	−6.48699	+	5.17320i	−0.482174	+	0.384521i	0.352019	+	0.935993i	$0.385495\pi$
$182$	8.03159	+	9.50340i	0.595341	+	0.704439i
$183$	10.8781	+	5.66790i	0.804131	+	0.418983i
$184$	1.53034	−	6.70486i	0.112818	−	0.494289i
$185$	−2.97070	+	3.72514i	−0.218410	+	0.273877i
$186$	4.57635	−	3.41912i	0.335554	−	0.250702i
$187$	21.9502	−	17.5047i	1.60515	−	1.28007i
$188$	−2.43036	−	1.17040i	−0.177252	−	0.0853600i
$189$	−13.1715	−	3.93846i	−0.958086	−	0.286481i
$190$	−1.03490	+	0.498380i	−0.0750794	+	0.0361563i
$191$	4.47394	−	9.29022i	0.323723	−	0.672217i	−0.674067	−	0.738670i	$-0.735454\pi$
$191$	4.47394	−	9.29022i	0.323723	−	0.672217i	0.997790	+	0.0664534i	$0.0211684\pi$
$192$	0.701928	+	1.58344i	0.0506573	+	0.114275i
$193$	−9.21730	−	4.43882i	−0.663476	−	0.319513i	0.0716639	−	0.997429i	$-0.477169\pi$
$193$	−9.21730	−	4.43882i	−0.663476	−	0.319513i	−0.735140	+	0.677916i	$0.762883\pi$
$194$	9.07188	−	11.3758i	0.651323	−	0.816733i
$195$	2.15860	+	11.0533i	0.154580	+	0.791545i
$196$	6.46935	+	2.67347i	0.462097	+	0.190962i
$197$			4.24217i			0.302242i	0.988515	+	0.151121i	$0.0482883\pi$
$197$			4.24217i			0.302242i	−0.988515	+	0.151121i	$0.951712\pi$
$198$	−5.16279	+	17.4617i	−0.366904	+	1.24095i
$199$	−8.37738	+	17.3958i	−0.593857	+	1.23316i	0.360016	+	0.932946i	$0.382771\pi$
$199$	−8.37738	+	17.3958i	−0.593857	+	1.23316i	−0.953873	+	0.300211i	$0.902943\pi$
$200$	3.01101	−	0.687242i	0.212910	−	0.0485954i
$201$	16.0467	+	4.19902i	1.13184	+	0.296176i
$202$	4.48895	+	9.32141i	0.315842	+	0.655852i
$203$	13.2049	−	3.41202i	0.926801	−	0.239477i
$204$	−7.75069	−	2.02817i	−0.542657	−	0.142000i
$205$	−3.07730	−	3.85882i	−0.214928	−	0.269511i
$206$	10.8444	−	5.22239i	0.755565	−	0.363861i
$207$	−19.7852	−	5.84978i	−1.37517	−	0.406588i
$208$	−4.58499	−	1.04649i	−0.317912	−	0.0725613i
$209$	3.14402	−	3.94248i	0.217476	−	0.272707i
$210$	3.93507	+	4.96569i	0.271545	+	0.342665i
$211$	4.39127	+	5.50648i	0.302308	+	0.379082i	0.909662	−	0.415349i	$-0.136341\pi$
$211$	4.39127	+	5.50648i	0.302308	+	0.379082i	−0.607354	+	0.794431i	$0.707769\pi$
$212$	3.57613	+	7.42591i	0.245610	+	0.510013i
$213$	−2.00590	−	0.0632821i	−0.137442	−	0.00433602i
$214$	−2.08006			−0.142190
$215$	−3.53242			−0.240909
$216$	4.87362	−	1.80217i	0.331608	−	0.122622i
$217$	4.00829	+	7.75100i	0.272101	+	0.526172i
$218$	15.6832	−	3.57960i	1.06220	−	0.242441i
$219$	21.5257	−	9.54215i	1.45457	−	0.644799i
$220$	6.56100	−	5.23222i	0.442342	−	0.352756i
$221$	17.0075	−	13.5630i	1.14405	−	0.912349i
$222$	−5.45680	+	2.41895i	−0.366236	+	0.162350i
$223$	15.5958	−	3.55963i	1.04437	−	0.238371i	0.334275	−	0.942476i	$-0.391509\pi$
$223$	15.5958	−	3.55963i	1.04437	−	0.238371i	0.710096	+	0.704105i	$0.248652\pi$
$224$	−2.56162	+	0.661898i	−0.171155	+	0.0442249i
$225$	−1.48825	−	9.14501i	−0.0992164	−	0.609667i
$226$	−4.86597			−0.323680
$227$	−8.39289			−0.557055			−0.278528	−	0.960428i	$-0.589846\pi$
$227$	−8.39289			−0.557055			−0.278528	+	0.960428i	$0.589846\pi$
$228$	−1.43826	−	0.0453743i	−0.0952513	−	0.00300499i
$229$	11.4881	+	23.8554i	0.759158	+	1.57641i	0.816019	+	0.578025i	$0.196176\pi$
$229$	11.4881	+	23.8554i	0.759158	+	1.57641i	−0.0568614	+	0.998382i	$0.518109\pi$
$230$	5.92845	+	7.43404i	0.390910	+	0.490186i
$231$	−25.0228	−	12.1453i	−1.64638	−	0.799105i
$232$	−3.21403	+	4.03026i	−0.211011	+	0.264600i
$233$	−8.71642	−	1.98947i	−0.571031	−	0.130334i	−0.0727511	−	0.997350i	$-0.523178\pi$
$233$	−8.71642	−	1.98947i	−0.571031	−	0.130334i	−0.498280	+	0.867016i	$0.666035\pi$
$234$	−4.00026	+	13.5297i	−0.261505	+	0.884466i
$235$	3.36019	−	1.61818i	0.219195	−	0.105559i
$236$	−6.02832	−	7.55928i	−0.392410	−	0.492067i
$237$	25.2395	+	6.60456i	1.63948	+	0.429012i
$238$	4.99396	−	11.1727i	0.323710	−	0.724219i
$239$	−4.79479	−	9.95649i	−0.310149	−	0.644032i	0.686383	−	0.727241i	$-0.259198\pi$
$239$	−4.79479	−	9.95649i	−0.310149	−	0.644032i	−0.996532	+	0.0832086i	$0.973483\pi$
$240$	−2.31672	−	0.606228i	−0.149543	−	0.0391319i
$241$	−7.58309	+	1.73079i	−0.488470	+	0.111490i	−0.459660	−	0.888095i	$-0.652029\pi$
$241$	−7.58309	+	1.73079i	−0.488470	+	0.111490i	−0.0288096	+	0.999585i	$0.509172\pi$
$242$	−11.2118	+	23.2814i	−0.720719	+	1.49659i
$243$	−4.47415	−	14.9326i	−0.287017	−	0.957926i
$244$		−	7.08185i		−	0.453369i
$245$	−8.46669	+	4.68845i	−0.540917	+	0.299534i
$246$	−1.18511	−	6.06848i	−0.0755598	−	0.386912i
$247$	2.43606	−	3.05473i	0.155003	−	0.194368i
$248$	−2.97153	−	1.43101i	−0.188692	−	0.0908694i
$249$	−2.75775	−	6.22108i	−0.174766	−	0.394245i
$250$	−4.85213	+	10.0755i	−0.306875	+	0.637233i
$251$	−21.6571	+	10.4295i	−1.36699	+	0.658306i	−0.966183	−	0.257859i	$-0.916983\pi$
$251$	−21.6571	+	10.4295i	−1.36699	+	0.658306i	−0.400803	+	0.916164i	$0.631269\pi$
$252$	1.49734	+	7.79474i	0.0943238	+	0.491022i
$253$	−37.6088	−	18.1115i	−2.36445	−	1.13866i
$254$	−4.70701	+	3.75371i	−0.295344	+	0.235529i
$255$	8.87370	−	6.62980i	0.555693	−	0.415174i
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	5.32276	−	23.3205i	0.332025	−	1.45470i	−0.483179	−	0.875521i	$-0.660518\pi$
$257$	5.32276	−	23.3205i	0.332025	−	1.45470i	0.815204	−	0.579174i	$-0.196625\pi$
$258$	−3.92450	−	2.04481i	−0.244328	−	0.127305i
$259$	−2.28100	−	8.82774i	−0.141735	−	0.548529i
$260$	5.08362	−	4.05405i	0.315273	−	0.251422i
$261$	11.4590	+	10.3850i	0.709292	+	0.642817i
$262$	−6.13351	−	1.39993i	−0.378929	−	0.0864882i
$263$		−	3.51437i		−	0.216705i	−0.994113	−	0.108353i	$-0.965442\pi$
$263$		−	3.51437i		−	0.216705i	0.994113	−	0.108353i	$-0.0345575\pi$
$264$	10.3180	−	2.01499i	0.635029	−	0.124014i
$265$	−11.1098	−	2.53574i	−0.682470	−	0.155769i
$266$	0.427938	−	2.15602i	0.0262386	−	0.132194i
$267$	6.46989	+	14.5951i	0.395951	+	0.893206i
$268$	−2.13097	−	9.33637i	−0.130170	−	0.570310i
$269$	−3.99917	−	5.01481i	−0.243834	−	0.305758i	0.644822	−	0.764333i	$-0.276932\pi$
$269$	−3.99917	−	5.01481i	−0.243834	−	0.305758i	−0.888656	+	0.458575i	$0.848360\pi$
$270$	−2.25316	+	6.82169i	−0.137123	+	0.415155i
$271$	−1.14194	+	0.260641i	−0.0693682	+	0.0158328i	−0.257064	−	0.966394i	$-0.582755\pi$
$271$	−1.14194	+	0.260641i	−0.0693682	+	0.0158328i	0.187696	+	0.982227i	$0.439898\pi$
$272$	1.02928	+	4.50956i	0.0624092	+	0.273432i
$273$	−19.3883	−	9.41051i	−1.17343	−	0.569550i
$274$	4.97003	−	21.7751i	0.300251	−	1.31548i
$275$		−	18.7457i		−	1.13041i
$276$	2.28312	+	11.6910i	0.137428	+	0.703714i
$277$	−5.53892	+	24.2676i	−0.332801	+	1.45810i	0.480880	+	0.876787i	$0.340317\pi$
$277$	−5.53892	+	24.2676i	−0.332801	+	1.45810i	−0.813681	+	0.581312i	$0.802540\pi$
$278$	−0.720513	+	0.346981i	−0.0432135	+	0.0208105i
$279$	−4.84641	+	8.62625i	−0.290147	+	0.516440i
$280$	1.49272	−	3.33957i	0.0892069	−	0.199577i
$281$	−11.8913	−	9.48300i	−0.709376	−	0.565708i	0.200950	−	0.979602i	$-0.435597\pi$
$281$	−11.8913	−	9.48300i	−0.709376	−	0.565708i	−0.910325	+	0.413893i	$0.864169\pi$
$282$	4.66987	+	0.147325i	0.278087	+	0.00877308i
$283$	−11.3731	−	9.06971i	−0.676058	−	0.539138i	0.224174	−	0.974549i	$-0.428032\pi$
$283$	−11.3731	−	9.06971i	−0.676058	−	0.539138i	−0.900232	+	0.435411i	$0.856603\pi$
$284$	0.502734	+	1.04394i	0.0298318	+	0.0619463i
$285$	1.28888	−	1.51558i	0.0763464	−	0.0897753i
$286$	−12.3852	+	25.7181i	−0.732350	+	1.52074i
$287$	9.44104	−	0.268769i	0.557287	−	0.0158649i
$288$	−2.22293	−	2.01459i	−0.130987	−	0.118711i
$289$	−3.96027	−	1.90717i	−0.232957	−	0.112186i
$290$	−1.58593	−	6.94843i	−0.0931292	−	0.408026i
$291$	−6.37984	+	24.3807i	−0.373993	+	1.42922i
$292$	−10.6284	−	8.47585i	−0.621979	−	0.496011i
$293$	−4.09342			−0.239140			−0.119570	−	0.992826i	$-0.538152\pi$
$293$	−4.09342			−0.239140			−0.119570	+	0.992826i	$0.538152\pi$
$294$	−12.1204	+	0.307724i	−0.706879	+	0.0179469i
$295$	13.3678			0.778306
$296$	2.69431	+	2.14864i	0.156604	+	0.124887i
$297$	−4.08183	−	31.2735i	−0.236852	−	1.81467i
$298$	−2.66567	−	11.6791i	−0.154418	−	0.676550i
$299$	−29.1402	−	14.0332i	−1.68522	−	0.811561i
$300$	−4.28537	+	3.20172i	−0.247416	+	0.184851i
$301$	4.06250	−	5.40274i	0.234159	−	0.311409i
$302$	0.0347454	−	0.0721495i	0.00199937	−	0.00415174i
$303$	−13.6510	−	11.6090i	−0.784227	−	0.666920i
$304$	0.360468	+	0.748520i	0.0206743	+	0.0429306i
$305$	7.65515	+	6.10478i	0.438333	+	0.349559i
$306$	13.6964	−	2.22894i	0.782972	−	0.127420i
$307$	−5.41326	−	4.31693i	−0.308951	−	0.246380i	0.456723	−	0.889609i	$-0.349023\pi$
$307$	−5.41326	−	4.31693i	−0.308951	−	0.246380i	−0.765674	+	0.643229i	$0.777594\pi$
$308$	0.456978	+	16.0522i	0.0260387	+	0.914661i
$309$	−13.5058	+	15.8813i	−0.768316	+	0.903458i
$310$	4.10841	−	1.97851i	0.233342	−	0.112372i
$311$	−3.10733	+	13.6141i	−0.176201	+	0.771985i	0.807162	+	0.590330i	$0.201002\pi$
$311$	−3.10733	+	13.6141i	−0.176201	+	0.771985i	−0.983362	+	0.181655i	$0.941855\pi$
$312$	7.99464	−	1.56127i	0.452607	−	0.0883894i
$313$			17.0194i			0.961993i	0.876723	+	0.480996i	$0.159725\pi$
$313$			17.0194i			0.961993i	−0.876723	+	0.480996i	$0.840275\pi$
$314$	0.387142	−	1.69618i	0.0218477	−	0.0957209i
$315$	−9.71651	−	5.10076i	−0.547464	−	0.287395i
$316$	−3.35176	−	14.6850i	−0.188551	−	0.826097i
$317$	6.65967	−	1.52003i	0.374044	−	0.0853732i	−0.0313661	−	0.999508i	$-0.509986\pi$
$317$	6.65967	−	1.52003i	0.374044	−	0.0853732i	0.405410	+	0.914135i	$0.367129\pi$
$318$	−10.8751	−	9.24833i	−0.609843	−	0.518620i
$319$	19.5080	+	24.4622i	1.09224	+	1.36962i
$320$	0.307656	+	1.34793i	0.0171985	+	0.0753514i
$321$	3.29366	−	1.46005i	0.183834	−	0.0814921i
$322$	−18.1882	+	0.517786i	−1.01359	+	0.0288551i
$323$	−3.74652	−	0.855119i	−0.208462	−	0.0475801i
$324$	−6.45212	+	6.27456i	−0.358451	+	0.348587i
$325$		−	14.5246i		−	0.805681i
$326$	17.7607	+	4.05375i	0.983672	+	0.224517i
$327$	−22.3209	+	16.6766i	−1.23435	+	0.922218i
$328$	−2.79100	+	2.22575i	−0.154107	+	0.122896i
$329$	−1.38946	+	7.00033i	−0.0766036	+	0.385941i
$330$	−6.71633	+	12.8903i	−0.369722	+	0.709586i
$331$	0.780623	−	3.42013i	0.0429069	−	0.187988i	−0.948933	−	0.315478i	$-0.897835\pi$
$331$	0.780623	−	3.42013i	0.0429069	−	0.187988i	0.991840	+	0.127491i	$0.0406923\pi$
$332$	−2.44958	+	3.07168i	−0.134438	+	0.168580i
$333$	6.94261	−	7.66056i	0.380452	−	0.419796i
$334$	6.57221	−	5.24116i	0.359615	−	0.286784i
$335$	11.9292	+	5.74478i	0.651759	+	0.313871i
$336$	3.59158	−	2.84615i	0.195937	−	0.155270i
$337$	−1.66645	+	0.802519i	−0.0907771	+	0.0437160i	−0.478721	−	0.877967i	$-0.658900\pi$
$337$	−1.66645	+	0.802519i	−0.0907771	+	0.0437160i	0.387944	+	0.921683i	$0.373185\pi$
$338$	−3.95584	+	8.21439i	−0.215169	+	0.446804i
$339$	7.70500	−	3.41556i	0.418478	−	0.185508i
$340$	−5.76190	−	2.77479i	−0.312483	−	0.150484i
$341$	−12.4814	+	15.6511i	−0.675903	+	0.847556i
$342$	2.30926	−	0.937709i	0.124870	−	0.0507055i
$343$	2.56637	−	18.3416i	0.138571	−	0.990353i
$344$			2.55493i			0.137752i
$345$	−14.6055	−	7.61004i	−0.786335	−	0.409711i
$346$	−2.12708	+	4.41693i	−0.114353	+	0.237456i
$347$	−0.724949	+	0.165465i	−0.0389173	+	0.00888262i	−0.241935	−	0.970292i	$-0.577782\pi$
$347$	−0.724949	+	0.165465i	−0.0389173	+	0.00888262i	0.203018	+	0.979175i	$0.434925\pi$
$348$	2.26028	−	8.63771i	0.121164	−	0.463030i
$349$	5.19524	+	10.7880i	0.278095	+	0.577470i	0.992498	−	0.122265i	$-0.0390157\pi$
$349$	5.19524	+	10.7880i	0.278095	+	0.577470i	−0.714402	+	0.699735i	$0.753301\pi$
$350$	−3.75343	−	7.25816i	−0.200629	−	0.387965i
$351$	−3.16270	−	24.2315i	−0.168813	−	1.29338i
$352$	−3.78435	−	4.74543i	−0.201707	−	0.252932i
$353$	12.0433	−	5.79973i	0.640999	−	0.308689i	−0.0850040	−	0.996381i	$-0.527090\pi$
$353$	12.0433	−	5.79973i	0.640999	−	0.308689i	0.726003	+	0.687692i	$0.241376\pi$
$354$	14.8516	+	7.73825i	0.789353	+	0.411283i
$355$	−1.56182	−	0.356475i	−0.0828929	−	0.0189198i
$356$	5.74690	−	7.20638i	0.304585	−	0.381937i
$357$	−0.0652241	+	21.1968i	−0.00345202	+	1.12185i
$358$	3.67548	+	4.60891i	0.194255	+	0.243588i
$359$	11.6948	+	24.2846i	0.617230	+	1.28169i	0.941909	+	0.335867i	$0.109029\pi$
$359$	11.6948	+	24.2846i	0.617230	+	1.28169i	−0.324680	+	0.945824i	$0.605256\pi$
$360$	4.09392	−	0.666239i	0.215768	−	0.0351139i
$361$	18.3098			0.963673
$362$	−8.29717			−0.436090
$363$	1.41129	−	44.7347i	0.0740736	−	2.34796i
$364$	0.354078	+	12.4377i	0.0185587	+	0.651911i
$365$	18.3240	−	4.18233i	0.959122	−	0.218913i
$366$	4.97095	+	11.2137i	0.259836	+	0.586150i
$367$	17.7763	−	14.1761i	0.927915	−	0.739988i	−0.0378830	−	0.999282i	$-0.512061\pi$
$367$	17.7763	−	14.1761i	0.927915	−	0.739988i	0.965798	+	0.259294i	$0.0834900\pi$
$368$	5.37688	−	4.28792i	0.280289	−	0.223523i
$369$	6.13619	+	8.77724i	0.319437	+	0.456925i
$370$	−4.64517	+	1.06023i	−0.241491	+	0.0551187i
$371$	16.6553	−	14.0759i	0.864701	−	0.730783i
$372$	5.70972	+	0.180130i	0.296035	+	0.00933931i
$373$	−9.45599			−0.489613			−0.244806	−	0.969572i	$-0.578724\pi$
$373$	−9.45599			−0.489613			−0.244806	+	0.969572i	$0.578724\pi$
$374$	28.0753			1.45174
$375$	0.610767	−	19.3599i	0.0315399	−	0.999742i
$376$	−1.17040	−	2.43036i	−0.0603586	−	0.125336i
$377$	15.1152	+	18.9539i	0.778475	+	0.976177i
$378$	−7.84231	−	11.2915i	−0.403365	−	0.580773i
$379$	−16.2076	+	20.3237i	−0.832528	+	1.04396i	0.165800	+	0.986159i	$0.446979\pi$
$379$	−16.2076	+	20.3237i	−0.832528	+	1.04396i	−0.998328	+	0.0577977i	$0.981592\pi$
$380$	−1.11985	−	0.255599i	−0.0574471	−	0.0131119i
$381$	4.81845	−	9.24777i	0.246857	−	0.473778i
$382$	9.29022	−	4.47394i	0.475329	−	0.228906i
$383$	−0.874932	−	1.09713i	−0.0447069	−	0.0560607i	0.758975	−	0.651119i	$-0.225700\pi$
$383$	−0.874932	−	1.09713i	−0.0447069	−	0.0560607i	−0.803682	+	0.595059i	$0.797129\pi$
$384$	−0.438472	+	1.67563i	−0.0223757	+	0.0855092i
$385$	−17.7457	−	13.3436i	−0.904403	−	0.680051i
$386$	−4.43882	−	9.21730i	−0.225930	−	0.469148i
$387$	7.64954	+	0.483136i	0.388848	+	0.0245592i
$388$	14.1854	−	3.23772i	0.720153	−	0.164370i
$389$	9.23029	−	19.1669i	0.467994	−	0.971800i	−0.524716	−	0.851277i	$-0.675829\pi$
$389$	9.23029	−	19.1669i	0.467994	−	0.971800i	0.992711	−	0.120523i	$-0.0384572\pi$
$390$	−5.20398	+	9.98770i	−0.263514	+	0.505747i
$391$			31.8112i			1.60876i
$392$	3.39106	+	6.12378i	0.171274	+	0.309298i
$393$	10.6947	−	2.08856i	0.539477	−	0.105354i
$394$	−2.64495	+	3.31666i	−0.133251	+	0.167091i
$395$	18.7632	+	9.03586i	0.944077	+	0.454643i
$396$	−14.9236	+	10.4331i	−0.749939	+	0.524284i
$397$	−4.51275	+	9.37081i	−0.226488	+	0.470308i	−0.982984	−	0.183691i	$-0.941195\pi$
$397$	−4.51275	+	9.37081i	−0.226488	+	0.470308i	0.756496	+	0.653999i	$0.226910\pi$
$398$	−17.3958	+	8.37738i	−0.871974	+	0.419920i
$399$	0.835752	+	3.71431i	0.0418399	+	0.185948i
$400$	2.78259	+	1.34002i	0.139129	+	0.0670012i
$401$	−22.6214	+	18.0400i	−1.12966	+	0.900873i	−0.995929	−	0.0901449i	$-0.971267\pi$
$401$	−22.6214	+	18.0400i	−1.12966	+	0.900873i	−0.133730	+	0.991018i	$0.542696\pi$
$402$	9.92773	+	13.2878i	0.495150	+	0.662738i
$403$	−9.67086	+	12.1269i	−0.481740	+	0.604083i
$404$	−2.30220	+	10.0866i	−0.114539	+	0.501826i
$405$	−1.22058	−	12.3833i	−0.0606512	−	0.615332i
$406$	12.4513	+	5.56549i	0.617950	+	0.276210i
$407$	16.3535	−	13.0415i	0.810613	−	0.646442i
$408$	−4.79519	−	6.41816i	−0.237397	−	0.317746i
$409$	27.4471	+	6.26463i	1.35717	+	0.309766i	0.838358	−	0.545120i	$-0.183516\pi$
$409$	27.4471	+	6.26463i	1.35717	+	0.309766i	0.518816	+	0.854886i	$0.326373\pi$
$410$		−	4.93561i		−	0.243752i
$411$	7.41481	+	37.9683i	0.365745	+	1.87284i
$412$	11.7346	+	2.67835i	0.578122	+	0.131953i
$413$	−15.3739	+	20.4457i	−0.756498	+	1.00607i
$414$	−11.8214	−	16.9094i	−0.580991	−	0.831053i
$415$	−1.20873	−	5.29578i	−0.0593340	−	0.259959i
$416$	−2.93221	−	3.67688i	−0.143763	−	0.180274i
$417$	0.897337	−	1.05517i	0.0439428	−	0.0516721i
$418$	4.91619	−	1.12209i	0.240459	−	0.0548831i
$419$	−3.80551	−	16.6730i	−0.185911	−	0.814531i	−0.978743	−	0.205090i	$-0.934251\pi$
$419$	−3.80551	−	16.6730i	−0.185911	−	0.814531i	0.792832	−	0.609441i	$-0.208606\pi$
$420$	−0.0194958	+	6.33580i	−0.000951295	+	0.309156i
$421$	8.47058	−	37.1120i	0.412831	−	1.80873i	−0.157739	−	0.987481i	$-0.550420\pi$
$421$	8.47058	−	37.1120i	0.412831	−	1.80873i	0.570570	−	0.821249i	$-0.306722\pi$
$422$			7.04305i			0.342850i
$423$	−7.49789	+	3.04463i	−0.364560	+	0.148035i
$424$	−1.83405	+	8.03549i	−0.0890692	+	0.390238i
$425$	−12.8710	+	6.19832i	−0.624333	+	0.300663i
$426$	−1.52882	−	1.30013i	−0.0740716	−	0.0629917i
$427$	−18.1410	+	4.68746i	−0.877904	+	0.226842i
$428$	−1.62625	−	1.29689i	−0.0786080	−	0.0626878i
$429$	1.55900	−	49.4166i	0.0752690	−	2.38586i
$430$	−2.76176	−	2.20243i	−0.133184	−	0.106211i
$431$	−1.66281	−	3.45286i	−0.0800948	−	0.166319i	0.857075	−	0.515191i	$-0.172279\pi$
$431$	−1.66281	−	3.45286i	−0.0800948	−	0.166319i	−0.937170	+	0.348872i	$0.886565\pi$
$432$	4.93398	+	1.62966i	0.237386	+	0.0784072i
$433$	7.19915	−	14.9492i	0.345969	−	0.718412i	−0.653282	−	0.757115i	$-0.726608\pi$
$433$	7.19915	−	14.9492i	0.345969	−	0.718412i	0.999251	+	0.0387030i	$0.0123226\pi$
$434$	−1.69886	+	8.55910i	−0.0815478	+	0.410850i
$435$	7.38853	+	9.88924i	0.354253	+	0.474153i
$436$	14.4935	+	6.97970i	0.694113	+	0.334267i
$437$	1.27140	+	5.57036i	0.0608193	+	0.266467i
$438$	22.7789	+	5.96068i	1.08842	+	0.284812i
$439$	12.5092	+	9.97577i	0.597032	+	0.476117i	0.874769	−	0.484540i	$-0.161013\pi$
$439$	12.5092	+	9.97577i	0.597032	+	0.476117i	−0.277737	+	0.960657i	$0.589584\pi$
$440$	8.39183			0.400065
$441$	18.9761	−	8.99495i	0.903622	−	0.428331i
$442$	21.7534			1.03471
$443$	8.87808	+	7.08003i	0.421810	+	0.336383i	0.811281	−	0.584656i	$-0.198771\pi$
$443$	8.87808	+	7.08003i	0.421810	+	0.336383i	−0.389471	+	0.921039i	$0.627342\pi$
$444$	−5.77449	−	1.51104i	−0.274045	−	0.0717110i
$445$	2.83576	+	12.4243i	0.134428	+	0.588967i
$446$	14.4127	+	6.94077i	0.682459	+	0.328655i
$447$	12.4188	+	16.6220i	0.587389	+	0.786196i
$448$	−2.41544	−	1.07965i	−0.114119	−	0.0510087i
$449$	5.71113	−	11.8593i	0.269525	−	0.559675i	−0.721646	−	0.692262i	$-0.756614\pi$
$449$	5.71113	−	11.8593i	0.269525	−	0.559675i	0.991171	+	0.132587i	$0.0423285\pi$
$450$	4.53826	−	8.07776i	0.213936	−	0.380789i
$451$	9.40119	+	19.5218i	0.442685	+	0.919244i
$452$	−3.80437	−	3.03389i	−0.178943	−	0.142702i
$453$	−0.00437361	+	0.138634i	−0.000205490	+	0.00651357i
$454$	−6.56182	−	5.23288i	−0.307962	−	0.245591i
$455$	−13.7498	−	10.3389i	−0.644599	−	0.484696i
$456$	−1.09619	−	0.932217i	−0.0513337	−	0.0436551i
$457$	5.57952	−	2.68695i	0.260999	−	0.125690i	−0.298809	−	0.954313i	$-0.596589\pi$
$457$	5.57952	−	2.68695i	0.260999	−	0.125690i	0.559808	+	0.828623i	$0.310875\pi$
$458$	−5.89179	+	25.8136i	−0.275305	+	1.20619i
$459$	−20.1230	+	13.1433i	−0.939260	+	0.613477i
$460$			9.50849i			0.443336i
$461$	−6.01050	+	26.3337i	−0.279937	+	1.22648i	0.617935	+	0.786229i	$0.287969\pi$
$461$	−6.01050	+	26.3337i	−0.279937	+	1.22648i	−0.897872	+	0.440256i	$0.854888\pi$
$462$	−11.9911	−	25.0971i	−0.557877	−	1.16762i
$463$	3.18065	+	13.9354i	0.147817	+	0.647631i	0.993489	+	0.113927i	$0.0363430\pi$
$463$	3.18065	+	13.9354i	0.147817	+	0.647631i	−0.845672	+	0.533704i	$0.820800\pi$
$464$	−5.02565	+	1.14707i	−0.233310	+	0.0532515i
$465$	−5.11667	+	6.01666i	−0.237280	+	0.279016i
$466$	−5.57436	−	6.99002i	−0.258227	−	0.323807i
$467$	−0.827790	−	3.62678i	−0.0383055	−	0.167828i	0.952157	−	0.305609i	$-0.0988600\pi$
$467$	−0.827790	−	3.62678i	−0.0383055	−	0.167828i	−0.990463	+	0.137781i	$0.956003\pi$
$468$	−11.5632	+	8.08384i	−0.534508	+	0.373676i
$469$	−22.5058	+	11.6385i	−1.03922	+	0.537414i
$470$	3.63602	+	0.829898i	0.167717	+	0.0382804i
$471$	0.577578	+	2.95755i	0.0266134	+	0.136277i
$472$		−	9.66868i		−	0.445037i
$473$	15.1187	+	3.45074i	0.695157	+	0.158665i
$474$	15.6152	+	20.9002i	0.717228	+	0.959979i
$475$	−2.00607	+	1.59979i	−0.0920447	+	0.0734032i
$476$	10.8705	−	5.62149i	0.498249	−	0.257661i
$477$	23.7117	+	7.01071i	1.08568	+	0.320998i
$478$	2.45905	−	10.7738i	0.112474	−	0.492782i
$479$	11.5472	−	14.4797i	0.527605	−	0.661596i	−0.444600	−	0.895729i	$-0.646654\pi$
$479$	11.5472	−	14.4797i	0.527605	−	0.661596i	0.972204	+	0.234134i	$0.0752254\pi$
$480$	−1.43330	−	1.91842i	−0.0654211	−	0.0875633i
$481$	12.6711	−	10.1049i	0.577752	−	0.460742i
$482$	−7.00783	−	3.37479i	−0.319198	−	0.153718i
$483$	28.4366	−	13.5867i	1.29391	−	0.618217i
$484$	−23.2814	+	11.2118i	−1.05825	+	0.509625i
$485$	−8.72842	+	18.1247i	−0.396337	+	0.823002i
$486$	5.81228	−	14.4643i	0.263650	−	0.656116i
$487$	8.99791	+	4.33317i	0.407734	+	0.196354i	0.626497	−	0.779424i	$-0.284488\pi$
$487$	8.99791	+	4.33317i	0.407734	+	0.196354i	−0.218763	+	0.975778i	$0.570202\pi$
$488$	4.41546	−	5.53681i	0.199878	−	0.250640i
$489$	−30.9685	+	6.04781i	−1.40044	+	0.273491i
$490$	−9.54273	−	1.61331i	−0.431097	−	0.0728821i
$491$			16.5398i			0.746429i	0.927745	+	0.373214i	$0.121744\pi$
$491$			16.5398i			0.746429i	−0.927745	+	0.373214i	$0.878256\pi$
$492$	2.85708	−	5.48343i	0.128807	−	0.247212i
$493$	10.3456	−	21.4828i	0.465942	−	0.967538i
$494$	3.80918	−	0.869421i	0.171383	−	0.0391171i
$495$	1.58689	−	25.1254i	0.0713255	−	1.12930i
$496$	−1.43101	−	2.97153i	−0.0642543	−	0.133426i
$497$	2.34141	−	1.97879i	0.105027	−	0.0887610i
$498$	1.72268	−	6.58327i	0.0771952	−	0.295003i
$499$	−17.2470	−	21.6271i	−0.772083	−	0.968161i	0.227902	−	0.973684i	$-0.426813\pi$
$499$	−17.2470	−	21.6271i	−0.772083	−	0.968161i	−0.999985	+	0.00552287i	$0.998242\pi$
$500$	−10.0755	+	4.85213i	−0.450592	+	0.216994i
$501$	−6.72781	+	12.9123i	−0.300577	+	0.576880i
$502$	−23.4349	−	5.34887i	−1.04595	−	0.238732i
$503$	1.52518	−	1.91251i	0.0680043	−	0.0852747i	−0.746666	−	0.665199i	$-0.768347\pi$
$503$	1.52518	−	1.91251i	0.0680043	−	0.0852747i	0.814670	+	0.579925i	$0.196918\pi$
$504$	−3.68927	+	7.02775i	−0.164333	+	0.313041i
$505$	−8.91857	−	11.1835i	−0.396871	−	0.497661i
$506$	−18.1115	−	37.6088i	−0.805152	−	1.67192i
$507$	0.497946	−	15.7838i	0.0221146	−	0.700981i
$508$	−6.02049			−0.267116
$509$	16.8173			0.745415			0.372707	−	0.927949i	$-0.378429\pi$
$509$	16.8173			0.745415			0.372707	+	0.927949i	$0.378429\pi$
$510$	11.0714	+	0.349279i	0.490248	+	0.0154663i
$511$	−14.6770	+	32.8360i	−0.649272	+	1.45258i
$512$	0.974928	−	0.222521i	0.0430861	−	0.00983413i
$513$	−2.99838	+	3.10574i	−0.132382	+	0.137122i
$514$	18.7016	−	14.9140i	0.824893	−	0.657830i
$515$	−13.0108	+	10.3757i	−0.573323	+	0.457210i
$516$	−1.79337	−	4.04558i	−0.0789489	−	0.178097i
$517$	−15.9623	+	3.64329i	−0.702020	+	0.160232i
$518$	3.72064	−	8.32399i	0.163476	−	0.365735i
$519$	0.267748	−	8.48702i	0.0117529	−	0.372539i
$520$	6.50220			0.285140
$521$	−39.5633			−1.73330			−0.866651	−	0.498915i	$-0.833732\pi$
$521$	−39.5633			−1.73330			−0.866651	+	0.498915i	$0.833732\pi$
$522$	2.48402	+	15.2639i	0.108723	+	0.668082i
$523$	6.56141	+	13.6249i	0.286911	+	0.595776i	0.993754	−	0.111594i	$-0.0355957\pi$
$523$	6.56141	+	13.6249i	0.286911	+	0.595776i	−0.706843	+	0.707370i	$0.749881\pi$
$524$	−3.92253	−	4.91869i	−0.171356	−	0.214874i
$525$	11.0381	+	8.85826i	0.481740	+	0.386606i
$526$	2.19117	−	2.74764i	0.0955396	−	0.119803i
$527$	14.8732	+	3.39471i	0.647887	+	0.147876i
$528$	9.32327	+	4.85778i	0.405743	+	0.211408i
$529$	21.8910	−	10.5421i	0.951781	−	0.458354i
$530$	−7.10498	−	8.90937i	−0.308621	−	0.386998i
$531$	−28.9484	−	1.82835i	−1.25625	−	0.0793434i
$532$	1.67883	−	1.41883i	0.0727865	−	0.0615139i
$533$	7.28427	+	15.1259i	0.315517	+	0.655177i
$534$	−4.04153	+	15.4448i	−0.174894	+	0.668363i
$535$	2.80377	−	0.639942i	0.121217	−	0.0276671i
$536$	4.15508	−	8.62811i	0.179472	−	0.372677i
$537$	−9.05505	−	4.71803i	−0.390754	−	0.203598i
$538$		−	6.41418i		−	0.276535i
$539$	40.8172	−	11.7955i	1.75812	−	0.508070i
$540$	−6.01484	+	3.92859i	−0.258838	+	0.169060i
$541$	−16.5668	+	20.7741i	−0.712263	+	0.893150i	−0.997872	−	0.0651963i	$-0.979233\pi$
$541$	−16.5668	+	20.7741i	−0.712263	+	0.893150i	0.285609	+	0.958346i	$0.407804\pi$
$542$	−1.05532	−	0.508213i	−0.0453297	−	0.0218296i
$543$	13.1381	−	5.82402i	0.563810	−	0.249933i
$544$	−2.00694	+	4.16746i	−0.0860470	+	0.178678i
$545$	−20.0386	+	9.65008i	−0.858359	+	0.413364i
$546$	−9.29101	−	19.4458i	−0.397619	−	0.832204i
$547$	−42.0688	−	20.2593i	−1.79873	−	0.866224i	−0.925235	−	0.379395i	$-0.876132\pi$
$547$	−42.0688	−	20.2593i	−1.79873	−	0.866224i	−0.873497	−	0.486829i	$-0.838154\pi$
$548$	17.4623	−	13.9257i	0.745952	−	0.594877i
$549$	−15.7424	−	14.2670i	−0.671871	−	0.608903i
$550$	11.6877	−	14.6560i	0.498367	−	0.624933i
$551$	0.952981	−	4.17528i	0.0405984	−	0.177873i
$552$	−5.50419	+	10.5639i	−0.234274	+	0.449628i
$553$	−35.3989	+	18.3059i	−1.50531	+	0.778447i
$554$	−19.4611	+	15.5197i	−0.826823	+	0.659369i
$555$	6.61116	−	4.93939i	0.280628	−	0.209665i
$556$	−0.779659	−	0.177952i	−0.0330649	−	0.00754685i
$557$			34.5348i			1.46329i	0.681688	+	0.731643i	$0.261246\pi$
$557$			34.5348i			1.46329i	−0.681688	+	0.731643i	$0.738754\pi$
$558$	−9.16746	+	3.72258i	−0.388089	+	0.157590i
$559$	11.7143	+	2.67371i	0.495463	+	0.113086i
$560$	3.24924	−	1.68029i	0.137305	−	0.0710051i
$561$	−44.4557	+	19.7068i	−1.87692	+	0.832023i
$562$	−3.38444	−	14.8282i	−0.142764	−	0.625491i
$563$	16.1077	+	20.1984i	0.678857	+	0.851260i	0.995248	−	0.0973689i	$-0.0310427\pi$
$563$	16.1077	+	20.1984i	0.678857	+	0.851260i	−0.316391	+	0.948629i	$0.602471\pi$
$564$	3.55919	+	3.02680i	0.149869	+	0.127451i
$565$	6.55898	−	1.49704i	0.275938	−	0.0629812i
$566$	−3.23694	−	14.1820i	−0.136059	−	0.596112i
$567$	20.3437	+	12.3747i	0.854355	+	0.519690i
$568$	−0.257831	+	1.12963i	−0.0108184	+	0.0473983i
$569$			0.199932i			0.00838160i	0.999991	+	0.00419080i	$0.00133398\pi$
$569$			0.199932i			0.00838160i	−0.999991	+	0.00419080i	$0.998666\pi$
$570$	1.95263	−	0.381328i	0.0817868	−	0.0159721i
$571$	10.1609	−	44.5177i	0.425219	−	1.86301i	−0.0751135	−	0.997175i	$-0.523932\pi$
$571$	10.1609	−	44.5177i	0.425219	−	1.86301i	0.500333	−	0.865833i	$-0.333211\pi$
$572$	−25.7181	+	12.3852i	−1.07533	+	0.517850i
$573$	−11.5702	+	13.6053i	−0.483351	+	0.568369i
$574$	7.54888	+	5.67626i	0.315084	+	0.236923i
$575$	16.6062	+	13.2430i	0.692525	+	0.552271i
$576$	−0.481877	−	2.96105i	−0.0200782	−	0.123377i
$577$	22.9857	+	18.3305i	0.956906	+	0.763107i	0.971562	−	0.236785i	$-0.0760938\pi$
$577$	22.9857	+	18.3305i	0.956906	+	0.763107i	−0.0146558	+	0.999893i	$0.504665\pi$
$578$	−1.90717	−	3.96027i	−0.0793276	−	0.164726i
$579$	13.4985	+	11.4794i	0.560979	+	0.477066i
$580$	3.09234	−	6.42131i	0.128402	−	0.266630i
$581$	9.48985	+	4.24176i	0.393705	+	0.175978i
$582$	−20.1891	+	15.0838i	−0.836865	+	0.625246i
$583$	45.0725	+	21.7058i	1.86671	+	0.898962i
$584$	−3.02499	−	13.2534i	−0.125175	−	0.548428i
$585$	1.22956	−	19.4678i	0.0508362	−	0.804894i
$586$	−3.20037	−	2.55221i	−0.132206	−	0.105431i
$587$	1.85828			0.0766994			0.0383497	−	0.999264i	$-0.487790\pi$
$587$	1.85828			0.0766994			0.0383497	+	0.999264i	$0.487790\pi$
$588$	−9.66801	−	7.31639i	−0.398702	−	0.301723i
$589$	2.74008			0.112903
$590$	10.4514	+	8.33471i	0.430277	+	0.343135i
$591$	1.86007	−	7.10831i	0.0765132	−	0.292397i
$592$	0.766842	+	3.35975i	0.0315170	+	0.138085i
$593$	19.6723	+	9.47366i	0.807843	+	0.389037i	0.791759	−	0.610834i	$-0.209166\pi$
$593$	19.6723	+	9.47366i	0.807843	+	0.389037i	0.0160844	+	0.999871i	$0.494880\pi$
$594$	16.3074	−	26.9956i	0.669100	−	1.10764i
$595$	−3.29415	+	16.5964i	−0.135047	+	0.680387i
$596$	5.19767	−	10.7931i	0.212905	−	0.442102i
$597$	21.6650	−	25.4757i	0.886689	−	1.04265i
$598$	−14.0332	−	29.1402i	−0.573860	−	1.19163i
$599$	20.3117	+	16.1981i	0.829915	+	0.661835i	0.943383	−	0.331706i	$-0.107624\pi$
$599$	20.3117	+	16.1981i	0.829915	+	0.661835i	−0.113467	+	0.993542i	$0.536196\pi$
$600$	−5.34667	−	0.168677i	−0.218277	−	0.00688620i
$601$	1.73478	+	1.38344i	0.0707633	+	0.0564319i	0.658233	−	0.752815i	$-0.271304\pi$
$601$	1.73478	+	1.38344i	0.0707633	+	0.0564319i	−0.587469	+	0.809246i	$0.699876\pi$
$602$	6.54475	−	1.69110i	0.266744	−	0.0689241i
$603$	−25.0471	−	14.0720i	−1.02000	−	0.573057i
$604$	0.0721495	−	0.0347454i	0.00293572	−	0.00141377i
$605$	7.94996	−	34.8311i	0.323212	−	1.41608i
$606$	−3.43465	−	17.5875i	−0.139523	−	0.714444i
$607$			3.37845i			0.137127i	0.997647	+	0.0685635i	$0.0218416\pi$
$607$			3.37845i			0.137127i	−0.997647	+	0.0685635i	$0.978158\pi$
$608$	−0.184869	+	0.809965i	−0.00749743	+	0.0328484i
$609$	−23.6226	−	0.0726885i	−0.957236	−	0.00294549i
$610$	2.17877	+	9.54582i	0.0882159	+	0.386499i
$611$	−12.3680	+	2.82291i	−0.500354	+	0.114203i
$612$	12.0980	+	6.79693i	0.489033	+	0.274749i
$613$	10.8275	+	13.5772i	0.437318	+	0.548379i	0.950834	−	0.309701i	$-0.100229\pi$
$613$	10.8275	+	13.5772i	0.437318	+	0.548379i	−0.513516	+	0.858080i	$0.671657\pi$
$614$	−1.54069	−	6.75022i	−0.0621774	−	0.272417i
$615$	3.46444	+	7.81527i	0.139700	+	0.315142i
$616$	−9.65113	+	12.8351i	−0.388855	+	0.517140i
$617$	−23.2938	−	5.31666i	−0.937774	−	0.214041i	−0.273792	−	0.961789i	$-0.588278\pi$
$617$	−23.2938	−	5.31666i	−0.937774	−	0.214041i	−0.663982	+	0.747748i	$0.731135\pi$
$618$	−20.4611	+	3.99583i	−0.823066	+	0.160736i
$619$		−	10.3257i		−	0.415025i	−0.978232	−	0.207512i	$-0.933463\pi$
$619$		−	10.3257i		−	0.415025i	0.978232	−	0.207512i	$-0.0665367\pi$
$620$	4.44566	+	1.01469i	0.178542	+	0.0407511i
$621$	30.5878	+	18.4773i	1.22744	+	0.741470i
$622$	−10.9177	+	8.70655i	−0.437758	+	0.349101i
$623$	−22.2639	−	9.95147i	−0.891983	−	0.398697i
$624$	7.22390	+	3.76393i	0.289187	+	0.150678i
$625$	0.00430567	−	0.0188644i	0.000172227	−	0.000754575i
$626$	−10.6114	+	13.3063i	−0.424118	+	0.531827i
$627$	−6.99689	+	5.22757i	−0.279429	+	0.208769i
$628$	1.36023	−	1.08475i	0.0542791	−	0.0432861i
$629$	−14.3617	−	6.91624i	−0.572640	−	0.275769i
$630$	−4.41641	−	10.0461i	−0.175954	−	0.400245i
$631$	33.6812	−	16.2200i	1.34083	−	0.645708i	0.380551	−	0.924760i	$-0.375734\pi$
$631$	33.6812	−	16.2200i	1.34083	−	0.645708i	0.960276	+	0.279052i	$0.0900201\pi$
$632$	6.53545	−	13.5710i	0.259966	−	0.539825i
$633$	−4.94372	−	11.1523i	−0.196495	−	0.443263i
$634$	6.15446	+	2.96383i	0.244425	+	0.117709i
$635$	5.18985	−	6.50787i	0.205953	−	0.258257i
$636$	−2.73622	−	14.0111i	−0.108498	−	0.555577i
$637$	31.6262	−	9.13948i	1.25308	−	0.362119i
$638$			31.2883i			1.23872i
$639$	3.33340	+	0.985569i	0.131867	+	0.0389885i
$640$	−0.599884	+	1.24567i	−0.0237125	+	0.0492395i
$641$	−23.6755	+	5.40378i	−0.935126	+	0.213436i	−0.662824	−	0.748775i	$-0.730642\pi$
$641$	−23.6755	+	5.40378i	−0.935126	+	0.213436i	−0.272302	+	0.962212i	$0.587785\pi$
$642$	3.48541	+	0.912047i	0.137558	+	0.0359956i
$643$	−15.9437	−	33.1074i	−0.628757	−	1.30563i	−0.935329	−	0.353780i	$-0.884896\pi$
$643$	−15.9437	−	33.1074i	−0.628757	−	1.30563i	0.306572	−	0.951848i	$-0.400818\pi$
$644$	−14.5430	−	10.9354i	−0.573073	−	0.430913i
$645$	5.91904	+	1.54887i	0.233062	+	0.0609866i
$646$	−2.39599	−	3.00448i	−0.0942689	−	0.118209i
$647$	−26.0330	+	12.5368i	−1.02346	+	0.492874i	−0.868836	−	0.495099i	$-0.835132\pi$
$647$	−26.0330	+	12.5368i	−1.02346	+	0.492874i	−0.154626	+	0.987973i	$0.549417\pi$
$648$	−8.95660	+	0.882822i	−0.351848	+	0.0346805i
$649$	−57.2140	−	13.0587i	−2.24585	−	0.512600i
$650$	9.05596	−	11.3558i	0.355204	−	0.445412i
$651$	−3.31783	−	14.7453i	−0.130036	−	0.577916i
$652$	11.3584	+	14.2429i	0.444828	+	0.557797i
$653$	−7.58709	−	15.7548i	−0.296906	−	0.616531i	0.698139	−	0.715963i	$-0.254012\pi$
$653$	−7.58709	−	15.7548i	−0.296906	−	0.616531i	−0.995044	+	0.0994314i	$0.968298\pi$
$654$	−27.8489	−	0.878577i	−1.08898	−	0.0343551i
$655$	8.69822			0.339868
$656$	−3.56982			−0.139378
$657$	−40.2531	+	6.55073i	−1.57042	+	0.255568i
$658$	−5.45096	+	4.60676i	−0.212501	+	0.179590i
$659$	19.0078	−	4.33840i	0.740438	−	0.169000i	0.164366	−	0.986399i	$-0.447442\pi$
$659$	19.0078	−	4.33840i	0.740438	−	0.169000i	0.576072	+	0.817399i	$0.304585\pi$
$660$	−13.2880	+	5.89046i	−0.517234	+	0.229286i
$661$	−32.3616	+	25.8076i	−1.25872	+	1.00380i	−0.259446	+	0.965758i	$0.583540\pi$
$661$	−32.3616	+	25.8076i	−1.25872	+	1.00380i	−0.999276	+	0.0380399i	$0.987889\pi$
$662$	2.74273	−	2.18726i	0.106599	−	0.0850102i
$663$	−34.4454	+	15.2693i	−1.33775	+	0.593012i
$664$	−3.83032	+	0.874247i	−0.148645	+	0.0339273i
$665$	0.0864809	+	3.03781i	0.00335359	+	0.117801i
$666$	10.2042	−	1.66062i	0.395406	−	0.0643478i
$667$	−35.4517			−1.37270
$668$	8.40618			0.325245
$669$	−27.6936	−	0.873677i	−1.07070	−	0.0337783i
$670$	5.74478	+	11.9292i	0.221940	+	0.460863i
$671$	−26.8002	−	33.6064i	−1.03461	−	1.29736i
$672$	4.58255	+	0.0141009i	0.176776	+	0.000543953i
$673$	−17.9759	+	22.5411i	−0.692920	+	0.868894i	−0.996472	−	0.0839208i	$-0.973256\pi$
$673$	−17.9759	+	22.5411i	−0.692920	+	0.868894i	0.303553	+	0.952815i	$0.401827\pi$
$674$	−1.80324	−	0.411578i	−0.0694583	−	0.0158534i
$675$	−1.51608	+	15.9762i	−0.0583539	+	0.614925i
$676$	−8.21439	+	3.95584i	−0.315938	+	0.152148i
$677$	29.3180	+	36.7636i	1.12678	+	1.41294i	0.898296	+	0.439392i	$0.144806\pi$
$677$	29.3180	+	36.7636i	1.12678	+	1.41294i	0.228486	+	0.973547i	$0.426623\pi$
$678$	8.15358	+	2.13359i	0.313136	+	0.0819402i
$679$	−17.6831	−	34.1945i	−0.678614	−	1.31226i
$680$	−2.77479	−	5.76190i	−0.106408	−	0.220959i
$681$	14.0634	+	3.68005i	0.538910	+	0.141020i
$682$	−19.5166	+	4.45454i	−0.747331	+	0.170573i
$683$	6.92481	−	14.3795i	0.264971	−	0.550217i	−0.725454	−	0.688270i	$-0.758370\pi$
$683$	6.92481	−	14.3795i	0.264971	−	0.550217i	0.990425	+	0.138053i	$0.0440845\pi$
$684$	2.39010	+	0.706669i	0.0913879	+	0.0270202i
$685$			30.8804i			1.17988i
$686$	13.4423	−	12.7399i	0.513228	−	0.486413i
$687$	−8.78998	−	45.0100i	−0.335359	−	1.71724i
$688$	−1.59297	+	1.99752i	−0.0607314	+	0.0761548i
$689$	34.9233	+	16.8182i	1.33047	+	0.640722i
$690$	−6.67428	−	15.0562i	−0.254085	−	0.573179i
$691$	−0.799031	+	1.65921i	−0.0303966	+	0.0631191i	−0.915614	−	0.402058i	$-0.868295\pi$
$691$	−0.799031	+	1.65921i	−0.0303966	+	0.0631191i	0.885218	+	0.465177i	$0.154009\pi$
$692$	−4.41693	+	2.12708i	−0.167906	+	0.0808595i
$693$	36.6036	+	31.3229i	1.39046	+	1.18986i
$694$	−0.669953	−	0.322632i	−0.0254311	−	0.0122470i
$695$	0.864449	−	0.689375i	0.0327904	−	0.0261495i
$696$	7.15268	−	5.34397i	0.271122	−	0.202563i
$697$	10.2953	−	12.9099i	0.389961	−	0.488996i
$698$	−2.66443	+	11.6736i	−0.100850	+	0.441853i
$699$	13.7332	+	7.15552i	0.519437	+	0.270647i
$700$	1.59084	−	8.01489i	0.0601281	−	0.302934i
$701$	−5.66440	+	4.51721i	−0.213941	+	0.170613i	−0.724597	−	0.689173i	$-0.757974\pi$
$701$	−5.66440	+	4.51721i	−0.213941	+	0.170613i	0.510656	+	0.859785i	$0.329403\pi$
$702$	12.6354	−	20.9168i	0.476891	−	0.789455i
$703$	−2.79126	−	0.637088i	−0.105275	−	0.0240282i
$704$		−	6.06963i		−	0.228758i
$705$	−6.33997	+	1.23813i	−0.238777	+	0.0466306i
$706$	13.0319	+	2.97444i	0.490461	+	0.111945i
$707$	27.3618	−	0.778940i	1.02905	−	0.0292951i
$708$	6.78672	+	15.3098i	0.255060	+	0.575378i
$709$	0.312107	+	1.36743i	0.0117214	+	0.0513549i	0.980450	−	0.196766i	$-0.0630440\pi$
$709$	0.312107	+	1.36743i	0.0117214	+	0.0513549i	−0.968729	+	0.248121i	$0.920187\pi$
$710$	−0.998822	−	1.25248i	−0.0374851	−	0.0470049i
$711$	−39.3962	−	22.1336i	−1.47747	−	0.830076i
$712$	8.98621	−	2.05104i	0.336773	−	0.0768661i
$713$	−5.04729	−	22.1136i	−0.189023	−	0.828162i
$714$	−13.2670	+	16.5316i	−0.496503	+	0.618681i
$715$	8.78200	−	38.4764i	0.328428	−	1.43894i
$716$			5.89502i			0.220307i
$717$	3.66867	+	18.7858i	0.137009	+	0.701569i
$718$	−5.99780	+	26.2781i	−0.223836	+	0.980688i
$719$	45.0298	−	21.6852i	1.67933	−	0.808723i	0.682353	−	0.731023i	$-0.260957\pi$
$719$	45.0298	−	21.6852i	1.67933	−	0.808723i	0.996977	−	0.0777000i	$-0.0247576\pi$
$720$	3.61615	+	2.03163i	0.134766	+	0.0757144i
$721$	−0.906209	−	31.8324i	−0.0337490	−	1.18550i
$722$	14.3152	+	11.4160i	0.532755	+	0.424858i
$723$	13.4654	+	0.424806i	0.500782	+	0.0157987i
$724$	−6.48699	−	5.17320i	−0.241087	−	0.192261i
$725$	−6.90768	−	14.3439i	−0.256545	−	0.532721i
$726$	28.9950	−	34.0951i	1.07611	−	1.26539i
$727$	14.5220	−	30.1553i	0.538592	−	1.11840i	−0.437132	−	0.899397i	$-0.644006\pi$
$727$	14.5220	−	30.1553i	0.538592	−	1.11840i	0.975725	−	0.219001i	$-0.0702799\pi$
$728$	−7.47793	+	9.94493i	−0.277151	+	0.368583i
$729$	0.949508	+	26.9833i	0.0351670	+	0.999381i
$730$	16.9339	+	8.15495i	0.626753	+	0.301828i
$731$	−2.62973	−	11.5216i	−0.0972641	−	0.426142i
$732$	−3.10519	+	11.8666i	−0.114771	+	0.438601i
$733$	−5.64315	−	4.50026i	−0.208434	−	0.166221i	0.513709	−	0.857965i	$-0.328271\pi$
$733$	−5.64315	−	4.50026i	−0.208434	−	0.166221i	−0.722143	+	0.691744i	$0.756843\pi$
$734$	22.7367			0.839228
$735$	16.2428	−	4.14372i	0.599125	−	0.152843i
$736$	6.87729			0.253500
$737$	−45.4445	−	36.2408i	−1.67397	−	1.33495i
$738$	−0.675053	+	10.6882i	−0.0248490	+	0.393437i
$739$	10.2150	+	44.7547i	0.375764	+	1.64633i	0.710265	+	0.703934i	$0.248575\pi$
$739$	10.2150	+	44.7547i	0.375764	+	1.64633i	−0.334501	+	0.942395i	$0.608568\pi$
$740$	−4.29278	−	2.06729i	−0.157806	−	0.0759953i
$741$	−5.42136	+	4.05045i	−0.199159	+	0.148797i
$742$	21.7978	−	0.620544i	0.800223	−	0.0227809i
$743$	−0.569921	+	1.18345i	−0.0209084	+	0.0434167i	−0.911161	−	0.412049i	$-0.864813\pi$
$743$	−0.569921	+	1.18345i	−0.0209084	+	0.0434167i	0.890253	+	0.455466i	$0.150527\pi$
$744$	4.35173	+	3.70078i	0.159542	+	0.135677i
$745$	7.18626	+	14.9224i	0.263284	+	0.546715i
$746$	−7.39299	−	5.89571i	−0.270677	−	0.215857i
$747$	1.89321	+	11.6334i	0.0692690	+	0.425645i
$748$	21.9502	+	17.5047i	0.802577	+	0.640034i
$749$	−2.24574	+	5.02426i	−0.0820574	+	0.183582i
$750$	12.5482	−	14.7554i	0.458196	−	0.538790i
$751$	−18.9268	+	9.11468i	−0.690649	+	0.332599i	−0.746073	−	0.665864i	$-0.768063\pi$
$751$	−18.9268	+	9.11468i	−0.690649	+	0.332599i	0.0554240	+	0.998463i	$0.482349\pi$
$752$	0.600248	−	2.62986i	0.0218888	−	0.0959011i
$753$	40.8624	−	7.97999i	1.48911	−	0.290807i
$754$			24.2430i			0.882877i
$755$	−0.0246371	+	0.107942i	−0.000896634	+	0.00392841i
$756$	0.908779	−	13.7177i	0.0330520	−	0.498906i
$757$	1.27098	+	5.56851i	0.0461944	+	0.202391i	0.992759	−	0.120123i	$-0.0383290\pi$
$757$	1.27098	+	5.56851i	0.0461944	+	0.202391i	−0.946565	+	0.322514i	$0.895472\pi$
$758$	−25.3432	+	5.78442i	−0.920507	+	0.210100i
$759$	55.0772	+	46.8386i	1.99917	+	1.70013i
$760$	−0.716171	−	0.898051i	−0.0259783	−	0.0325757i
$761$	−0.858326	−	3.76057i	−0.0311143	−	0.136321i	0.956985	−	0.290137i	$-0.0937008\pi$
$761$	−0.858326	−	3.76057i	−0.0311143	−	0.136321i	−0.988099	+	0.153816i	$0.950844\pi$
$762$	9.53311	−	4.22595i	0.345348	−	0.153090i
$763$	8.28611	−	41.7467i	0.299977	−	1.51133i
$764$	10.0528	+	2.29450i	0.363699	+	0.0830119i
$765$	−17.7760	+	7.21823i	−0.642694	+	0.260976i
$766$		−	1.40328i		−	0.0507026i
$767$	−44.3308	−	10.1182i	−1.60069	−	0.365348i
$768$	−1.38755	+	1.03668i	−0.0500689	+	0.0374079i
$769$	22.4353	−	17.8916i	0.809038	−	0.645186i	−0.129029	−	0.991641i	$-0.541186\pi$
$769$	22.4353	−	17.8916i	0.809038	−	0.645186i	0.938067	+	0.346454i	$0.112614\pi$
$770$	−5.55454	−	21.4967i	−0.200172	−	0.774686i
$771$	−19.1444	+	36.7428i	−0.689469	+	1.32326i
$772$	2.27648	−	9.97393i	0.0819325	−	0.358970i
$773$	28.2228	−	35.3903i	1.01511	−	1.27290i	0.0534701	−	0.998569i	$-0.482972\pi$
$773$	28.2228	−	35.3903i	1.01511	−	1.27290i	0.961635	−	0.274332i	$-0.0884568\pi$
$774$	5.67942	+	5.14714i	0.204142	+	0.185010i
$775$	7.96383	−	6.35094i	0.286069	−	0.228133i
$776$	13.1092	+	6.31308i	0.470595	+	0.226626i
$777$	−0.0485938	+	15.7922i	−0.00174329	+	0.566542i
$778$	19.1669	−	9.23029i	0.687167	−	0.330922i
$779$	1.28681	−	2.67208i	0.0461047	−	0.0957373i
$780$	−10.2959	+	4.56407i	−0.368651	+	0.163420i
$781$	6.33632	+	3.05141i	0.226731	+	0.109188i
$782$	−19.8339	+	24.8710i	−0.709260	+	0.889384i
$783$	−14.6475	−	22.4259i	−0.523458	−	0.801437i
$784$	−1.16688	+	6.90206i	−0.0416742	+	0.246502i
$785$			2.40543i			0.0858535i
$786$	9.66367	+	5.03514i	0.344692	+	0.179598i
$787$	−0.198716	+	0.412637i	−0.00708345	+	0.0147089i	−0.904481	−	0.426515i	$-0.859741\pi$
$787$	−0.198716	+	0.412637i	−0.00708345	+	0.0147089i	0.897397	+	0.441224i	$0.145455\pi$
$788$	−4.13581	+	0.943972i	−0.147332	+	0.0336276i
$789$	−1.54095	+	5.88878i	−0.0548593	+	0.209646i
$790$	9.03586	+	18.7632i	0.321481	+	0.667563i
$791$	−5.25355	+	11.7535i	−0.186795	+	0.417905i
$792$	−18.1727	−	1.14777i	−0.645738	−	0.0407841i
$793$	−20.7655	−	26.0391i	−0.737404	−	0.924675i
$794$	−9.37081	+	4.51275i	−0.332558	+	0.160151i
$795$	17.5041	+	9.12031i	0.620806	+	0.323464i
$796$	−18.8238	−	4.29641i	−0.667192	−	0.152282i
$797$	−8.30571	+	10.4150i	−0.294203	+	0.368919i	−0.906862	−	0.421429i	$-0.861529\pi$
$797$	−8.30571	+	10.4150i	−0.294203	+	0.368919i	0.612658	+	0.790348i	$0.290100\pi$
$798$	−1.66242	+	3.42505i	−0.0588490	+	0.121245i
$799$	7.77949	+	9.75517i	0.275219	+	0.345113i
$800$	1.34002	+	2.78259i	0.0473770	+	0.0983793i
$801$	−4.44161	−	27.2929i	−0.156936	−	0.964346i
$802$	−28.9339			−1.02169
$803$	−82.5118			−2.91178
$804$	−0.523025	+	16.5787i	−0.0184457	+	0.584686i
$805$	24.3571	−	6.29365i	0.858476	−	0.221822i
$806$	−15.1220	+	3.45149i	−0.532649	+	0.121574i
$807$	4.50229	+	10.1565i	0.158488	+	0.357526i
$808$	−8.08881	+	6.45061i	−0.284563	+	0.226932i
$809$	7.87011	−	6.27621i	0.276698	−	0.220660i	−0.475301	−	0.879823i	$-0.657661\pi$
$809$	7.87011	−	6.27621i	0.276698	−	0.220660i	0.752000	+	0.659163i	$0.229089\pi$
$810$	6.76658	−	10.4427i	0.237754	−	0.366919i
$811$	7.95750	−	1.81625i	0.279426	−	0.0637771i	−0.0805113	−	0.996754i	$-0.525655\pi$
$811$	7.95750	−	1.81625i	0.279426	−	0.0637771i	0.359937	+	0.932977i	$0.382798\pi$
$812$	6.26483	+	12.1146i	0.219853	+	0.425138i
$813$	2.02776	+	0.0639719i	0.0711168	+	0.00224359i
$814$	20.9169			0.733137
$815$	−25.1872			−0.882271
$816$	0.252626	−	8.00768i	0.00884369	−	0.280325i
$817$	−0.920969	−	1.91241i	−0.0322206	−	0.0669069i
$818$	17.5531	+	22.0109i	0.613730	+	0.769593i
$819$	28.3614	+	24.2698i	0.991027	+	0.848054i
$820$	3.07730	−	3.85882i	0.107464	−	0.134756i
$821$	33.4681	+	7.63887i	1.16804	+	0.266598i	0.762198	−	0.647344i	$-0.224120\pi$
$821$	33.4681	+	7.63887i	1.16804	+	0.266598i	0.405845	+	0.913942i	$0.366977\pi$
$822$	−17.8757	+	34.3079i	−0.623488	+	1.19662i
$823$	−25.1416	+	12.1075i	−0.876380	+	0.422042i	−0.817301	−	0.576211i	$-0.804531\pi$
$823$	−25.1416	+	12.1075i	−0.876380	+	0.422042i	−0.0590788	+	0.998253i	$0.518816\pi$
$824$	7.50456	+	9.41042i	0.261434	+	0.327827i
$825$	−8.21946	+	31.4109i	−0.286165	+	1.09359i
$826$	−24.7675	+	6.39968i	−0.861771	+	0.222673i
$827$	−21.0682	−	43.7485i	−0.732612	−	1.52128i	−0.849181	−	0.528101i	$-0.822904\pi$
$827$	−21.0682	−	43.7485i	−0.732612	−	1.52128i	0.116570	−	0.993182i	$-0.462810\pi$
$828$	1.30049	−	20.5908i	0.0451953	−	0.715581i
$829$	−7.49540	+	1.71078i	−0.260326	+	0.0594177i	−0.350692	−	0.936491i	$-0.614054\pi$
$829$	−7.49540	+	1.71078i	−0.260326	+	0.0594177i	0.0903658	+	0.995909i	$0.471196\pi$
$830$	2.35684	−	4.89403i	0.0818072	−	0.169874i
$831$	19.9219	−	38.2349i	0.691081	−	1.32635i
$832$		−	4.70290i		−	0.163044i
$833$	−21.5953	−	24.1252i	−0.748232	−	0.835890i
$834$	1.35946	−	0.265487i	0.0470741	−	0.00919307i
$835$	−7.24639	+	9.08669i	−0.250772	+	0.314458i
$836$	4.54324	+	2.18791i	0.157131	+	0.0756704i
$837$	11.9032	−	12.3294i	0.411434	−	0.426166i
$838$	7.42020	−	15.4082i	0.256327	−	0.532268i
$839$	−19.1269	+	9.21104i	−0.660334	+	0.318000i	−0.733868	−	0.679293i	$-0.762287\pi$
$839$	−19.1269	+	9.21104i	−0.660334	+	0.318000i	0.0735333	+	0.997293i	$0.476572\pi$
$840$	−3.96555	+	4.94137i	−0.136825	+	0.170494i
$841$	−2.18669	−	1.05305i	−0.0754031	−	0.0363122i
$842$	29.7615	−	23.7340i	1.02565	−	0.817929i
$843$	15.7674	+	21.1040i	0.543059	+	0.726861i
$844$	−4.39127	+	5.50648i	−0.151154	+	0.189541i
$845$	2.80499	−	12.2894i	0.0964944	−	0.422770i
$846$	−7.76038	−	2.29447i	−0.266807	−	0.0788855i
$847$	44.1302	+	52.2171i	1.51633	+	1.79420i
$848$	−6.44396	+	5.13889i	−0.221287	+	0.176470i
$849$	15.0802	+	20.1843i	0.517552	+	0.692722i
$850$	−13.9275	−	3.17886i	−0.477710	−	0.109034i
$851$			23.7002i			0.812433i
$852$	−0.384659	−	1.96969i	−0.0131782	−	0.0674805i
$853$	37.7925	+	8.62589i	1.29399	+	0.295345i	0.813454	−	0.581630i	$-0.197585\pi$
$853$	37.7925	+	8.62589i	1.29399	+	0.295345i	0.480537	+	0.876975i	$0.340442\pi$
$854$	−17.1058	−	7.64592i	−0.585348	−	0.261638i
$855$	−2.82422	+	1.97442i	−0.0965864	+	0.0675238i
$856$	−0.462856	−	2.02791i	−0.0158201	−	0.0693124i
$857$	−23.4390	−	29.3916i	−0.800662	−	1.00400i	−0.999712	−	0.0240095i	$-0.992357\pi$
$857$	−23.4390	−	29.3916i	−0.800662	−	1.00400i	0.199049	−	0.979989i	$-0.436215\pi$
$858$	32.0296	−	37.6634i	1.09347	−	1.28581i
$859$	42.7070	−	9.74760i	1.45714	−	0.332584i	0.580712	−	0.814109i	$-0.302774\pi$
$859$	42.7070	−	9.74760i	1.45714	−	0.332584i	0.876432	+	0.481525i	$0.159917\pi$
$860$	−0.786038	−	3.44386i	−0.0268037	−	0.117434i
$861$	−15.9376	−	3.68928i	−0.543150	−	0.125730i
$862$	0.852787	−	3.73630i	0.0290460	−	0.127259i
$863$			4.69971i			0.159980i	0.996796	+	0.0799900i	$0.0254888\pi$
$863$			4.69971i			0.159980i	−0.996796	+	0.0799900i	$0.974511\pi$
$864$	2.84147	+	4.35041i	0.0966686	+	0.148004i
$865$	1.50826	−	6.60811i	0.0512823	−	0.224682i
$866$	14.9492	−	7.19915i	0.507994	−	0.244637i
$867$	5.79972	+	4.93218i	0.196969	+	0.167505i
$868$	−6.66474	+	5.63256i	−0.226216	+	0.191181i
$869$	−71.4789	−	57.0025i	−2.42475	−	1.93368i
$870$	−0.389252	+	12.3384i	−0.0131969	+	0.418311i
$871$	−35.2115	−	28.0803i	−1.19310	−	0.951463i
$872$	6.97970	+	14.4935i	0.236362	+	0.490812i
$873$	21.3805	−	38.0557i	0.723621	−	1.28799i
$874$	−2.47904	+	5.14779i	−0.0838549	+	0.174127i
$875$	19.0983	+	22.5981i	0.645640	+	0.763955i
$876$	14.0928	+	18.8626i	0.476152	+	0.637310i
$877$	−1.72902	−	0.832654i	−0.0583850	−	0.0281167i	0.404463	−	0.914554i	$-0.367458\pi$
$877$	−1.72902	−	0.832654i	−0.0583850	−	0.0281167i	−0.462848	+	0.886437i	$0.653173\pi$
$878$	3.56031	+	15.5987i	0.120155	+	0.526432i
$879$	6.85907	+	1.79485i	0.231351	+	0.0605389i
$880$	6.56100	+	5.23222i	0.221171	+	0.176378i
$881$	55.9337			1.88445			0.942227	−	0.334974i	$-0.108728\pi$
$881$	55.9337			1.88445			0.942227	+	0.334974i	$0.108728\pi$
$882$	20.4443	+	4.79885i	0.688397	+	0.161586i
$883$	53.7876			1.81010			0.905048	−	0.425309i	$-0.139834\pi$
$883$	53.7876			1.81010			0.905048	+	0.425309i	$0.139834\pi$
$884$	17.0075	+	13.5630i	0.572025	+	0.456175i
$885$	−22.3996	−	5.86143i	−0.752954	−	0.197030i
$886$	2.52683	+	11.0708i	0.0848907	+	0.371930i
$887$	36.2732	+	17.4683i	1.21794	+	0.586527i	0.928736	−	0.370741i	$-0.120896\pi$
$887$	36.2732	+	17.4683i	1.21794	+	0.586527i	0.289200	+	0.957269i	$0.406611\pi$
$888$	−3.57256	−	4.78172i	−0.119887	−	0.160464i
$889$	3.98495	+	15.4222i	0.133651	+	0.517244i
$890$	−5.52932	+	11.4817i	−0.185343	+	0.384869i
$891$	−6.87290	+	54.1926i	−0.230251	+	1.81552i
$892$	6.94077	+	14.4127i	0.232394	+	0.482572i
$893$	1.75213	+	1.39728i	0.0586328	+	0.0467581i
$894$	−0.654263	+	20.7386i	−0.0218818	+	0.693604i
$895$	−6.37224	−	5.08169i	−0.213001	−	0.169862i
$896$	−1.21532	−	2.35011i	−0.0406009	−	0.0785116i
$897$	42.6752	+	36.2917i	1.42488	+	1.21174i
$898$	11.8593	−	5.71113i	0.395750	−	0.190583i
$899$	−3.78321	+	16.5753i	−0.126177	+	0.552818i
$900$	8.58456	−	3.48589i	0.286152	−	0.116196i
$901$		−	38.1243i		−	1.27010i
$902$	−4.82148	+	21.1243i	−0.160538	+	0.703361i
$903$	−9.17621	+	7.27171i	−0.305365	+	0.241987i
$904$	−1.08278	−	4.74397i	−0.0360128	−	0.157782i
$905$	11.1840	−	2.55267i	0.371768	−	0.0848537i
$906$	−0.0898561	+	0.105661i	−0.00298527	+	0.00351036i
$907$	−6.55727	−	8.22255i	−0.217730	−	0.273025i	0.660956	−	0.750425i	$-0.270151\pi$
$907$	−6.55727	−	8.22255i	−0.217730	−	0.273025i	−0.878686	+	0.477399i	$0.841580\pi$
$908$	−1.86759	−	8.18246i	−0.0619782	−	0.271544i
$909$	17.7838	+	25.4380i	0.589850	+	0.843725i
$910$	−4.30379	−	16.6561i	−0.142669	−	0.552146i
$911$	24.7524	+	5.64956i	0.820082	+	0.187178i	0.611924	−	0.790917i	$-0.290396\pi$
$911$	24.7524	+	5.64956i	0.820082	+	0.187178i	0.208158	+	0.978095i	$0.433253\pi$
$912$	−0.275807	−	1.41230i	−0.00913288	−	0.0467659i
$913$			23.8465i			0.789206i
$914$	6.03753	+	1.37803i	0.199704	+	0.0455811i
$915$	−10.1504	−	13.5859i	−0.335563	−	0.449137i
$916$	−20.7009	+	16.5084i	−0.683977	+	0.545454i
$917$	−10.0035	+	13.3037i	−0.330345	+	0.439326i
$918$	−23.9275	−	2.27062i	−0.789725	−	0.0749417i
$919$	−10.9651	+	48.0411i	−0.361704	+	1.58473i	0.387164	+	0.922011i	$0.373455\pi$
$919$	−10.9651	+	48.0411i	−0.361704	+	1.58473i	−0.748868	+	0.662719i	$0.769402\pi$
$920$	−5.92845	+	7.43404i	−0.195455	+	0.245093i
$921$	7.17777	+	9.60715i	0.236516	+	0.316566i
$922$	−21.1180	+	16.8411i	−0.695485	+	0.554631i
$923$	4.90954	+	2.36431i	0.161599	+	0.0778221i
$924$	6.27273	−	27.0980i	0.206358	−	0.891459i
$925$	−9.58923	+	4.61793i	−0.315292	+	0.151837i
$926$	−6.20181	+	12.8782i	−0.203804	+	0.423204i
$927$	29.5942	−	20.6894i	0.972002	−	0.679529i
$928$	−4.64440	−	2.23663i	−0.152460	−	0.0734208i
$929$	23.2979	−	29.2147i	0.764380	−	0.958503i	−0.235530	−	0.971867i	$-0.575683\pi$
$929$	23.2979	−	29.2147i	0.764380	−	0.958503i	0.999911	+	0.0133644i	$0.00425414\pi$
$930$	−7.75170	+	1.51382i	−0.254188	+	0.0496403i
$931$	−4.74571	−	3.36140i	−0.155534	−	0.110166i
$932$		−	8.94058i		−	0.292858i
$933$	11.1761	−	21.4497i	0.365891	−	0.702233i
$934$	1.61407	−	3.35165i	0.0528140	−	0.109669i
$935$	−37.8435	+	8.63753i	−1.23761	+	0.282477i
$936$	−14.0806	−	0.889318i	−0.460240	−	0.0290683i
$937$	3.68446	+	7.65087i	0.120366	+	0.249943i	0.952443	−	0.304718i	$-0.0985622\pi$
$937$	3.68446	+	7.65087i	0.120366	+	0.249943i	−0.832076	+	0.554661i	$0.812848\pi$
$938$	−24.8522	−	4.93280i	−0.811452	−	0.161062i
$939$	7.46253	−	28.5182i	0.243530	−	0.930658i
$940$	2.32532	+	2.91586i	0.0758437	+	0.0951050i
$941$	−37.4120	+	18.0167i	−1.21960	+	0.587326i	−0.929199	−	0.369580i	$-0.879502\pi$
$941$	−37.4120	+	18.0167i	−1.21960	+	0.587326i	−0.290397	+	0.956906i	$0.593787\pi$
$942$	−1.39243	+	2.67242i	−0.0453679	+	0.0870721i
$943$	−23.9352	−	5.46305i	−0.779437	−	0.177901i
$944$	6.02832	−	7.55928i	0.196205	−	0.246034i
$945$	14.0448	+	12.8074i	0.456876	+	0.416625i
$946$	9.66875	+	12.1242i	0.314358	+	0.394193i
$947$	20.1529	+	41.8480i	0.654882	+	1.35988i	0.918566	+	0.395268i	$0.129348\pi$
$947$	20.1529	+	41.8480i	0.654882	+	1.35988i	−0.263684	+	0.964609i	$0.584938\pi$
$948$	−0.822656	+	26.0763i	−0.0267186	+	0.846920i
$949$	−63.9322			−2.07533
$950$	−2.56586			−0.0832474
$951$	−11.8256	−	0.373075i	−0.383473	−	0.0120978i
$952$	12.0038	+	2.38259i	0.389047	+	0.0772202i
$953$	−26.9086	+	6.14171i	−0.871655	+	0.198950i	−0.634876	−	0.772614i	$-0.718949\pi$
$953$	−26.9086	+	6.14171i	−0.871655	+	0.198950i	−0.236779	+	0.971564i	$0.576092\pi$
$954$	14.1675	+	20.2652i	0.458688	+	0.656110i
$955$	−11.1461	+	8.88873i	−0.360680	+	0.287633i
$956$	8.63992	−	6.89011i	0.279435	−	0.222842i
$957$	−21.9622	−	49.5433i	−0.709936	−	1.60151i
$958$	18.0559	−	4.12115i	0.583360	−	0.133148i
$959$	−47.2306	−	35.5143i	−1.52516	−	1.14682i
$960$	0.0755111	−	2.39353i	0.00243711	−	0.0772508i
$961$	20.1222			0.649104
$962$	16.2069			0.522533
$963$	−6.15915	+	1.00233i	−0.198476	+	0.0322997i
$964$	−3.37479	−	7.00783i	−0.108695	−	0.225707i
$965$	8.81896	+	11.0586i	0.283892	+	0.355990i
$966$	30.7038	+	7.10742i	0.987879	+	0.228677i
$967$	−12.4216	+	15.5762i	−0.399453	+	0.500898i	−0.940358	−	0.340185i	$-0.889510\pi$
$967$	−12.4216	+	15.5762i	−0.399453	+	0.500898i	0.540906	+	0.841083i	$0.318082\pi$
$968$	−25.1926	−	5.75004i	−0.809720	−	0.184813i
$969$	5.90284	+	3.07561i	0.189627	+	0.0988028i
$970$	−18.1247	+	8.72842i	−0.581950	+	0.280253i
$971$	−15.5220	−	19.4639i	−0.498123	−	0.624627i	0.467681	−	0.883897i	$-0.345089\pi$
$971$	−15.5220	−	19.4639i	−0.498123	−	0.624627i	−0.965805	+	0.259270i	$0.916518\pi$
$972$	13.5626	−	7.68479i	0.435021	−	0.246490i
$973$	0.0602094	+	2.11497i	0.00193023	+	0.0678030i
$974$	4.33317	+	8.99791i	0.138844	+	0.288312i
$975$	−6.36864	+	24.3379i	−0.203960	+	0.779437i
$976$	6.90429	−	1.57586i	0.221001	−	0.0504420i
$977$	−3.71165	+	7.70733i	−0.118746	+	0.246579i	−0.951867	−	0.306513i	$-0.900838\pi$
$977$	−3.71165	+	7.70733i	−0.118746	+	0.246579i	0.833120	+	0.553092i	$0.186552\pi$
$978$	−27.9829	−	14.5802i	−0.894793	−	0.466222i
$979$		−	55.9457i		−	1.78803i
$980$	−6.45492	−	7.21114i	−0.206195	−	0.230351i
$981$	44.7139	−	18.1567i	1.42760	−	0.579700i
$982$	−10.3124	+	12.9313i	−0.329081	+	0.412654i
$983$	−27.5426	−	13.2638i	−0.878471	−	0.423050i	−0.0604054	−	0.998174i	$-0.519239\pi$
$983$	−27.5426	−	13.2638i	−0.878471	−	0.423050i	−0.818066	+	0.575124i	$0.804954\pi$
$984$	5.65262	−	2.50576i	0.180199	−	0.0798807i
$985$	2.54481	−	5.28435i	0.0810844	−	0.168374i
$986$	21.4828	−	10.3456i	0.684153	−	0.329471i
$987$	5.39768	−	11.1207i	0.171810	−	0.353977i
$988$	3.52022	+	1.69525i	0.111993	+	0.0539330i
$989$	−13.7375	+	10.9553i	−0.436828	+	0.348359i
$990$	16.9061	−	18.6544i	0.537312	−	0.592877i
$991$	19.8869	−	24.9374i	0.631729	−	0.792163i	−0.358212	−	0.933640i	$-0.616614\pi$
$991$	19.8869	−	24.9374i	0.631729	−	0.792163i	0.989942	+	0.141477i	$0.0451851\pi$
$992$	0.733907	−	3.21545i	0.0233016	−	0.102091i
$993$	−2.80767	+	5.38860i	−0.0890987	+	0.171002i
$994$	3.06435	−	0.0872363i	0.0971952	−	0.00276697i
$995$	20.8710	−	16.6440i	0.661654	−	0.527651i
$996$	5.45145	−	4.07293i	0.172736	−	0.129056i
$997$	19.8963	+	4.54121i	0.630123	+	0.143822i	0.525643	−	0.850705i	$-0.323825\pi$
$997$	19.8963	+	4.54121i	0.630123	+	0.143822i	0.104481	+	0.994527i	$0.466682\pi$
$998$		−	27.6621i		−	0.875628i
$999$	−14.9922	+	9.79214i	−0.474332	+	0.309809i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.j.a.251.12	yes	120
3.2	odd	2	inner	294.2.j.a.251.9	yes	120
49.41	odd	14	inner	294.2.j.a.41.9	✓	120
147.41	even	14	inner	294.2.j.a.41.12	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.j.a.41.9	✓	120	49.41	odd	14	inner
294.2.j.a.41.12	yes	120	147.41	even	14	inner
294.2.j.a.251.9	yes	120	3.2	odd	2	inner
294.2.j.a.251.12	yes	120	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.j (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.781831 + 0.623490i) q^{2} +(-1.67563 - 0.438472i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-1.24567 - 0.599884i) q^{5} +(-1.03668 - 1.38755i) q^{6} +(2.35011 - 1.21532i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(2.61548 + 1.46944i) q^{9} +O(q^{10})\)	\(q+(0.781831 + 0.623490i) q^{2} +(-1.67563 - 0.438472i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-1.24567 - 0.599884i) q^{5} +(-1.03668 - 1.38755i) q^{6} +(2.35011 - 1.21532i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(2.61548 + 1.46944i) q^{9} +(-0.599884 - 1.24567i) q^{10} +(4.74543 + 3.78435i) q^{11} +(0.0546156 - 1.73119i) q^{12} +(3.67688 + 2.93221i) q^{13} +(2.59513 + 0.515095i) q^{14} +(1.82426 + 1.55138i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(1.02928 - 4.50956i) q^{17} +(1.12869 + 2.77958i) q^{18} -0.830794i q^{19} +(0.307656 - 1.34793i) q^{20} +(-4.47080 + 1.00597i) q^{21} +(1.35062 + 5.91746i) q^{22} +(-6.70486 + 1.53034i) q^{23} +(1.12208 - 1.31945i) q^{24} +(-1.92561 - 2.41464i) q^{25} +(1.04649 + 4.58499i) q^{26} +(-3.73828 - 3.60905i) q^{27} +(1.70779 + 2.02075i) q^{28} +(5.02565 + 1.14707i) q^{29} +(0.458992 + 2.35032i) q^{30} +3.29815i q^{31} +(-0.974928 - 0.222521i) q^{32} +(-6.29226 - 8.42192i) q^{33} +(3.61639 - 2.88397i) q^{34} +(-3.65651 + 0.104094i) q^{35} +(-0.850594 + 2.87689i) q^{36} +(0.766842 - 3.35975i) q^{37} +(0.517992 - 0.649541i) q^{38} +(-4.87540 - 6.52551i) q^{39} +(1.08095 - 0.862032i) q^{40} +(3.21630 + 1.54889i) q^{41} +(-4.12262 - 2.00100i) q^{42} +(2.30191 - 1.10854i) q^{43} +(-2.63352 + 5.46855i) q^{44} +(-2.37655 - 3.39942i) q^{45} +(-6.19623 - 2.98395i) q^{46} +(-1.68186 + 2.10898i) q^{47} +(1.69994 - 0.331980i) q^{48} +(4.04601 - 5.71225i) q^{49} -3.08844i q^{50} +(-3.70201 + 7.10506i) q^{51} +(-2.04051 + 4.23717i) q^{52} +(8.03549 - 1.83405i) q^{53} +(-0.672501 - 5.15245i) q^{54} +(-3.64108 - 7.56078i) q^{55} +(0.0752892 + 2.64468i) q^{56} +(-0.364280 + 1.39211i) q^{57} +(3.21403 + 4.03026i) q^{58} +(-8.71118 + 4.19508i) q^{59} +(-1.10655 + 2.12373i) q^{60} +(-6.90429 - 1.57586i) q^{61} +(-2.05636 + 2.57859i) q^{62} +(7.93250 + 0.274690i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(-2.82120 - 5.85828i) q^{65} +(0.331497 - 10.5077i) q^{66} -9.57648 q^{67} +4.62553 q^{68} +(11.9059 + 0.375607i) q^{69} +(-2.92368 - 2.19841i) q^{70} +(1.12963 - 0.257831i) q^{71} +(-2.45873 + 1.71891i) q^{72} +(-10.6284 + 8.47585i) q^{73} +(2.69431 - 2.14864i) q^{74} +(2.16786 + 4.89037i) q^{75} +(0.809965 - 0.184869i) q^{76} +(15.7515 + 3.12644i) q^{77} +(0.256852 - 8.14161i) q^{78} -15.0627 q^{79} +1.38259 q^{80} +(4.68152 + 7.68657i) q^{81} +(1.54889 + 3.21630i) q^{82} +(2.44958 + 3.07168i) q^{83} +(-1.97559 - 4.13486i) q^{84} +(-3.98736 + 4.99999i) q^{85} +(2.49087 + 0.568525i) q^{86} +(-7.91818 - 4.12568i) q^{87} +(-5.46855 + 2.63352i) q^{88} +(-5.74690 - 7.20638i) q^{89} +(0.261448 - 4.13953i) q^{90} +(12.2046 + 2.42244i) q^{91} +(-2.98395 - 6.19623i) q^{92} +(1.44615 - 5.52648i) q^{93} +(-2.62986 + 0.600248i) q^{94} +(-0.498380 + 1.03490i) q^{95} +(1.53605 + 0.800342i) q^{96} -14.5502i q^{97} +(6.72483 - 1.94337i) q^{98} +(6.85073 + 16.8710i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9}+O(q^{10}) \) 120 * q + 20 * q^4 - 14 * q^6 + 4 * q^7 - 10 * q^9	\( 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9} + 12 q^{15} - 20 q^{16} - 8 q^{18} - 12 q^{21} - 10 q^{22} - 24 q^{25} + 42 q^{27} - 4 q^{28} + 8 q^{30} + 10 q^{36} - 58 q^{37} + 8 q^{39} - 14 q^{40} - 2 q^{42} - 12 q^{43} + 14 q^{45} - 60 q^{46} - 36 q^{49} - 24 q^{51} - 42 q^{52} - 14 q^{55} + 34 q^{57} + 50 q^{58} - 12 q^{60} - 154 q^{61} + 20 q^{64} - 28 q^{67} + 28 q^{69} - 38 q^{70} + 8 q^{72} - 84 q^{75} - 16 q^{78} + 16 q^{79} + 22 q^{81} - 30 q^{84} - 32 q^{85} - 56 q^{87} - 4 q^{88} - 42 q^{90} + 88 q^{91} + 14 q^{93} + 112 q^{94} - 224 q^{99}+O(q^{100}) \) 120 * q + 20 * q^4 - 14 * q^6 + 4 * q^7 - 10 * q^9 + 12 * q^15 - 20 * q^16 - 8 * q^18 - 12 * q^21 - 10 * q^22 - 24 * q^25 + 42 * q^27 - 4 * q^28 + 8 * q^30 + 10 * q^36 - 58 * q^37 + 8 * q^39 - 14 * q^40 - 2 * q^42 - 12 * q^43 + 14 * q^45 - 60 * q^46 - 36 * q^49 - 24 * q^51 - 42 * q^52 - 14 * q^55 + 34 * q^57 + 50 * q^58 - 12 * q^60 - 154 * q^61 + 20 * q^64 - 28 * q^67 + 28 * q^69 - 38 * q^70 + 8 * q^72 - 84 * q^75 - 16 * q^78 + 16 * q^79 + 22 * q^81 - 30 * q^84 - 32 * q^85 - 56 * q^87 - 4 * q^88 - 42 * q^90 + 88 * q^91 + 14 * q^93 + 112 * q^94 - 224 * q^99

Introduction

L-functions

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Database

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