LMFDB - Embedded newform 430.2.p.a.59.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(59,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 8]))

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

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

chi := DirichletCharacter("430.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.p (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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			59.16
Character	$\chi$	$=$	430.59
Dual form			430.2.p.a.379.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.974928 - 0.222521i) q^{2} +(-0.607117 - 0.138570i) q^{3} +(0.900969 - 0.433884i) q^{4} +(-1.73606 - 1.40929i) q^{5} -0.622730 q^{6} -0.713157i q^{7} +(0.781831 - 0.623490i) q^{8} +(-2.35352 - 1.13339i) q^{9} +O(q^{10})$	\(q+(0.974928 - 0.222521i) q^{2} +(-0.607117 - 0.138570i) q^{3} +(0.900969 - 0.433884i) q^{4} +(-1.73606 - 1.40929i) q^{5} -0.622730 q^{6} -0.713157i q^{7} +(0.781831 - 0.623490i) q^{8} +(-2.35352 - 1.13339i) q^{9} +(-2.00613 - 0.987643i) q^{10} +(-4.27215 - 2.05736i) q^{11} +(-0.607117 + 0.138570i) q^{12} +(1.64080 - 1.30849i) q^{13} +(-0.158692 - 0.695277i) q^{14} +(0.858707 + 1.09617i) q^{15} +(0.623490 - 0.781831i) q^{16} +(0.628662 + 0.501341i) q^{17} +(-2.54671 - 0.581271i) q^{18} +(-0.141698 + 0.0682384i) q^{19} +(-2.17560 - 0.516474i) q^{20} +(-0.0988226 + 0.432970i) q^{21} +(-4.62284 - 1.05513i) q^{22} +(2.65462 - 5.51238i) q^{23} +(-0.561060 + 0.270192i) q^{24} +(1.02782 + 4.89322i) q^{25} +(1.30849 - 1.64080i) q^{26} +(2.73242 + 2.17903i) q^{27} +(-0.309427 - 0.642533i) q^{28} +(-0.402880 - 1.76513i) q^{29} +(1.08110 + 0.877605i) q^{30} +(-0.288375 - 1.26345i) q^{31} +(0.433884 - 0.900969i) q^{32} +(2.30861 + 1.84105i) q^{33} +(0.724459 + 0.348881i) q^{34} +(-1.00504 + 1.23809i) q^{35} -2.61221 q^{36} +7.05804i q^{37} +(-0.122961 + 0.0980584i) q^{38} +(-1.17747 + 0.567042i) q^{39} +(-2.23598 - 0.0194078i) q^{40} +(-2.45190 - 10.7425i) q^{41} +0.444105i q^{42} +(-4.10385 - 5.11453i) q^{43} -4.74173 q^{44} +(2.48857 + 5.28442i) q^{45} +(1.36144 - 5.96488i) q^{46} +(1.14936 + 2.38668i) q^{47} +(-0.486870 + 0.388266i) q^{48} +6.49141 q^{49} +(2.09090 + 4.54182i) q^{50} +(-0.312200 - 0.391487i) q^{51} +(0.910574 - 1.89083i) q^{52} +(7.20751 + 5.74780i) q^{53} +(3.14879 + 1.51638i) q^{54} +(4.51731 + 9.59239i) q^{55} +(-0.444646 - 0.557569i) q^{56} +(0.0954833 - 0.0217935i) q^{57} +(-0.785557 - 1.63123i) q^{58} +(-0.450743 + 0.565214i) q^{59} +(1.24928 + 0.615035i) q^{60} +(-0.108093 + 0.473588i) q^{61} +(-0.562290 - 1.16761i) q^{62} +(-0.808288 + 1.67843i) q^{63} +(0.222521 - 0.974928i) q^{64} +(-4.69257 - 0.0407303i) q^{65} +(2.66040 + 1.28118i) q^{66} +(6.20330 + 12.8813i) q^{67} +(0.783929 + 0.178927i) q^{68} +(-2.37552 + 2.97881i) q^{69} +(-0.704345 + 1.43069i) q^{70} +(9.75178 - 4.69621i) q^{71} +(-2.54671 + 0.581271i) q^{72} +(9.54871 - 7.61484i) q^{73} +(1.57056 + 6.88108i) q^{74} +(0.0540474 - 3.11318i) q^{75} +(-0.0980584 + 0.122961i) q^{76} +(-1.46722 + 3.04671i) q^{77} +(-1.02177 + 0.814837i) q^{78} -4.61483 q^{79} +(-2.18424 + 0.478632i) q^{80} +(3.52911 + 4.42536i) q^{81} +(-4.78085 - 9.92753i) q^{82} +(-15.7000 - 3.58343i) q^{83} +(0.0988226 + 0.432970i) q^{84} +(-0.384863 - 1.75632i) q^{85} +(-5.13905 - 4.07311i) q^{86} +1.12747i q^{87} +(-4.62284 + 1.05513i) q^{88} +(-1.58261 + 6.93389i) q^{89} +(3.60208 + 4.59817i) q^{90} +(-0.933161 - 1.17015i) q^{91} -6.11828i q^{92} +0.807025i q^{93} +(1.65163 + 2.07108i) q^{94} +(0.342165 + 0.0812277i) q^{95} +(-0.388266 + 0.486870i) q^{96} +(2.68459 - 5.57461i) q^{97} +(6.32865 - 1.44447i) q^{98} +(7.72278 + 9.68406i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 22 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{9}+O(q^{10}) $ 132 * q + 22 * q^4 - 4 * q^5 - 4 * q^6 + 12 * q^9	$ 132 q + 22 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{9} + 8 q^{11} - 10 q^{14} - 20 q^{15} - 22 q^{16} - 4 q^{19} + 4 q^{20} - 24 q^{21} + 4 q^{24} - 16 q^{25} + 12 q^{26} + 40 q^{29} + 24 q^{31} - 4 q^{35} + 128 q^{36} - 56 q^{39} - 28 q^{41} - 8 q^{44} - 80 q^{45} - 12 q^{46} - 136 q^{49} - 56 q^{50} + 172 q^{51} + 16 q^{54} - 4 q^{56} + 16 q^{59} - 8 q^{60} - 44 q^{61} + 22 q^{64} + 42 q^{65} + 8 q^{66} - 62 q^{69} + 12 q^{70} - 8 q^{71} - 4 q^{74} - 122 q^{75} - 52 q^{76} - 64 q^{79} - 4 q^{80} - 56 q^{81} + 24 q^{84} - 72 q^{85} - 10 q^{86} + 16 q^{89} + 2 q^{90} - 24 q^{91} - 20 q^{94} + 106 q^{95} - 4 q^{96} - 104 q^{99}+O(q^{100}) $ 132 * q + 22 * q^4 - 4 * q^5 - 4 * q^6 + 12 * q^9 + 8 * q^11 - 10 * q^14 - 20 * q^15 - 22 * q^16 - 4 * q^19 + 4 * q^20 - 24 * q^21 + 4 * q^24 - 16 * q^25 + 12 * q^26 + 40 * q^29 + 24 * q^31 - 4 * q^35 + 128 * q^36 - 56 * q^39 - 28 * q^41 - 8 * q^44 - 80 * q^45 - 12 * q^46 - 136 * q^49 - 56 * q^50 + 172 * q^51 + 16 * q^54 - 4 * q^56 + 16 * q^59 - 8 * q^60 - 44 * q^61 + 22 * q^64 + 42 * q^65 + 8 * q^66 - 62 * q^69 + 12 * q^70 - 8 * q^71 - 4 * q^74 - 122 * q^75 - 52 * q^76 - 64 * q^79 - 4 * q^80 - 56 * q^81 + 24 * q^84 - 72 * q^85 - 10 * q^86 + 16 * q^89 + 2 * q^90 - 24 * q^91 - 20 * q^94 + 106 * q^95 - 4 * q^96 - 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$-1$	$e\left(\frac{4}{7}\right)$

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 $

$2$	0.974928	−	0.222521i	0.689378	−	0.157346i
$2$	0.974928	−	0.222521i	0.689378	−	0.157346i
$3$	−0.607117	−	0.138570i	−0.350519	−	0.0800037i	0.0436363	−	0.999047i	$-0.486106\pi$
$3$	−0.607117	−	0.138570i	−0.350519	−	0.0800037i	−0.394155	+	0.919044i	$0.628963\pi$
$4$	0.900969	−	0.433884i	0.450484	−	0.216942i
$5$	−1.73606	−	1.40929i	−0.776390	−	0.630252i
$5$	−1.73606	−	1.40929i	−0.776390	−	0.630252i
$6$	−0.622730			−0.254228
$7$		−	0.713157i		−	0.269548i	−0.990876	−	0.134774i	$-0.956969\pi$
$7$		−	0.713157i		−	0.269548i	0.990876	−	0.134774i	$-0.0430309\pi$
$8$	0.781831	−	0.623490i	0.276419	−	0.220437i
$9$	−2.35352	−	1.13339i	−0.784506	−	0.377798i
$10$	−2.00613	−	0.987643i	−0.634394	−	0.312320i
$11$	−4.27215	−	2.05736i	−1.28810	−	0.620317i	−0.340642	−	0.940193i	$-0.610644\pi$
$11$	−4.27215	−	2.05736i	−1.28810	−	0.620317i	−0.947459	+	0.319876i	$0.896359\pi$
$12$	−0.607117	+	0.138570i	−0.175260	+	0.0400019i
$13$	1.64080	−	1.30849i	0.455075	−	0.362910i	−0.368963	−	0.929444i	$-0.620287\pi$
$13$	1.64080	−	1.30849i	0.455075	−	0.362910i	0.824039	+	0.566534i	$0.191716\pi$
$14$	−0.158692	−	0.695277i	−0.0424123	−	0.185821i
$15$	0.858707	+	1.09617i	0.221717	+	0.283030i
$16$	0.623490	−	0.781831i	0.155872	−	0.195458i
$17$	0.628662	+	0.501341i	0.152473	+	0.121593i	0.696755	−	0.717309i	$-0.254626\pi$
$17$	0.628662	+	0.501341i	0.152473	+	0.121593i	−0.544282	+	0.838902i	$0.683198\pi$
$18$	−2.54671	−	0.581271i	−0.600266	−	0.137007i
$19$	−0.141698	+	0.0682384i	−0.0325078	+	0.0156550i	−0.450067	−	0.892995i	$-0.648600\pi$
$19$	−0.141698	+	0.0682384i	−0.0325078	+	0.0156550i	0.417559	+	0.908650i	$0.362886\pi$
$20$	−2.17560	−	0.516474i	−0.486480	−	0.115487i
$21$	−0.0988226	+	0.432970i	−0.0215648	+	0.0944818i
$22$	−4.62284	−	1.05513i	−0.985593	−	0.224955i
$23$	2.65462	−	5.51238i	0.553527	−	1.14941i	−0.417109	−	0.908856i	$-0.636957\pi$
$23$	2.65462	−	5.51238i	0.553527	−	1.14941i	0.970636	−	0.240554i	$-0.0773290\pi$
$24$	−0.561060	+	0.270192i	−0.114526	+	0.0551528i
$25$	1.02782	+	4.89322i	0.205564	+	0.978644i
$26$	1.30849	−	1.64080i	0.256616	−	0.321787i
$27$	2.73242	+	2.17903i	0.525854	+	0.419354i
$28$	−0.309427	−	0.642533i	−0.0584763	−	0.121427i
$29$	−0.402880	−	1.76513i	−0.0748129	−	0.327777i	0.923648	−	0.383243i	$-0.125193\pi$
$29$	−0.402880	−	1.76513i	−0.0748129	−	0.327777i	−0.998461	+	0.0554661i	$0.982336\pi$
$30$	1.08110	+	0.877605i	0.197381	+	0.160228i
$31$	−0.288375	−	1.26345i	−0.0517937	−	0.226923i	0.942406	−	0.334470i	$-0.108557\pi$
$31$	−0.288375	−	1.26345i	−0.0517937	−	0.226923i	−0.994200	+	0.107547i	$0.965700\pi$
$32$	0.433884	−	0.900969i	0.0767005	−	0.159270i
$33$	2.30861	+	1.84105i	0.401877	+	0.320486i
$34$	0.724459	+	0.348881i	0.124244	+	0.0598326i
$35$	−1.00504	+	1.23809i	−0.169883	+	0.209275i
$36$	−2.61221			−0.435368
$37$			7.05804i			1.16033i	0.814497	+	0.580167i	$0.197013\pi$
$37$			7.05804i			1.16033i	−0.814497	+	0.580167i	$0.802987\pi$
$38$	−0.122961	+	0.0980584i	−0.0199470	+	0.0159072i
$39$	−1.17747	+	0.567042i	−0.188547	+	0.0907993i
$40$	−2.23598	−	0.0194078i	−0.353540	−	0.00306864i
$41$	−2.45190	−	10.7425i	−0.382922	−	1.67769i	−0.688274	−	0.725451i	$-0.741631\pi$
$41$	−2.45190	−	10.7425i	−0.382922	−	1.67769i	0.305352	−	0.952240i	$-0.401226\pi$
$42$			0.444105i			0.0685268i
$43$	−4.10385	−	5.11453i	−0.625831	−	0.779959i
$43$	−4.10385	−	5.11453i	−0.625831	−	0.779959i
$44$	−4.74173			−0.714842
$45$	2.48857	+	5.28442i	0.370975	+	0.787755i
$46$	1.36144	−	5.96488i	0.200734	−	0.879473i
$47$	1.14936	+	2.38668i	0.167652	+	0.348133i	0.967820	−	0.251643i	$-0.0809708\pi$
$47$	1.14936	+	2.38668i	0.167652	+	0.348133i	−0.800168	+	0.599775i	$0.795257\pi$
$48$	−0.486870	+	0.388266i	−0.0702736	+	0.0560414i
$49$	6.49141			0.927344
$50$	2.09090	+	4.54182i	0.295697	+	0.642311i
$51$	−0.312200	−	0.391487i	−0.0437168	−	0.0548191i
$52$	0.910574	−	1.89083i	0.126274	−	0.262210i
$53$	7.20751	+	5.74780i	0.990027	+	0.789520i	0.977615	−	0.210403i	$-0.0674775\pi$
$53$	7.20751	+	5.74780i	0.990027	+	0.789520i	0.0124124	+	0.999923i	$0.496049\pi$
$54$	3.14879	+	1.51638i	0.428496	+	0.206353i
$55$	4.51731	+	9.59239i	0.609114	+	1.29344i
$56$	−0.444646	−	0.557569i	−0.0594184	−	0.0745083i
$57$	0.0954833	−	0.0217935i	0.0126471	−	0.00288661i
$58$	−0.785557	−	1.63123i	−0.103149	−	0.214190i
$59$	−0.450743	+	0.565214i	−0.0586818	+	0.0735846i	−0.810306	−	0.586007i	$-0.800699\pi$
$59$	−0.450743	+	0.565214i	−0.0586818	+	0.0735846i	0.751624	+	0.659591i	$0.229271\pi$
$60$	1.24928	+	0.615035i	0.161281	+	0.0794007i
$61$	−0.108093	+	0.473588i	−0.0138399	+	0.0606368i	−0.981376	−	0.192095i	$-0.938472\pi$
$61$	−0.108093	+	0.473588i	−0.0138399	+	0.0606368i	0.967536	+	0.252732i	$0.0813290\pi$
$62$	−0.562290	−	1.16761i	−0.0714109	−	0.148286i
$63$	−0.808288	+	1.67843i	−0.101835	+	0.211462i
$64$	0.222521	−	0.974928i	0.0278151	−	0.121866i
$65$	−4.69257	−	0.0407303i	−0.582041	−	0.00505198i
$66$	2.66040	+	1.28118i	0.327472	+	0.157702i
$67$	6.20330	+	12.8813i	0.757854	+	1.57370i	0.817802	+	0.575499i	$0.195192\pi$
$67$	6.20330	+	12.8813i	0.757854	+	1.57370i	−0.0599482	+	0.998201i	$0.519094\pi$
$68$	0.783929	+	0.178927i	0.0950654	+	0.0216980i
$69$	−2.37552	+	2.97881i	−0.285979	+	0.358606i
$70$	−0.704345	+	1.43069i	−0.0841853	+	0.171000i
$71$	9.75178	−	4.69621i	1.15732	−	0.557337i	0.246098	−	0.969245i	$-0.420852\pi$
$71$	9.75178	−	4.69621i	1.15732	−	0.557337i	0.911226	+	0.411908i	$0.135137\pi$
$72$	−2.54671	+	0.581271i	−0.300133	+	0.0685034i
$73$	9.54871	−	7.61484i	1.11759	−	0.891250i	0.122725	−	0.992441i	$-0.460837\pi$
$73$	9.54871	−	7.61484i	1.11759	−	0.891250i	0.994867	+	0.101191i	$0.0322653\pi$
$74$	1.57056	+	6.88108i	0.182574	+	0.799909i
$75$	0.0540474	−	3.11318i	0.00624086	−	0.359479i
$76$	−0.0980584	+	0.122961i	−0.0112481	+	0.0141046i
$77$	−1.46722	+	3.04671i	−0.167205	+	0.347205i
$78$	−1.02177	+	0.814837i	−0.115693	+	0.0922622i
$79$	−4.61483			−0.519209			−0.259605	−	0.965715i	$-0.583592\pi$
$79$	−4.61483			−0.519209			−0.259605	+	0.965715i	$0.583592\pi$
$80$	−2.18424	+	0.478632i	−0.244206	+	0.0535127i
$81$	3.52911	+	4.42536i	0.392123	+	0.491707i
$82$	−4.78085	−	9.92753i	−0.527956	−	1.09631i
$83$	−15.7000	−	3.58343i	−1.72330	−	0.393332i	−0.757545	−	0.652783i	$-0.773601\pi$
$83$	−15.7000	−	3.58343i	−1.72330	−	0.393332i	−0.965756	+	0.259451i	$0.916458\pi$
$84$	0.0988226	+	0.432970i	0.0107824	+	0.0472409i
$85$	−0.384863	−	1.75632i	−0.0417442	−	0.190500i
$86$	−5.13905	−	4.07311i	−0.554158	−	0.439215i
$87$			1.12747i			0.120877i
$88$	−4.62284	+	1.05513i	−0.492797	+	0.112478i
$89$	−1.58261	+	6.93389i	−0.167757	+	0.734991i	0.819134	+	0.573602i	$0.194454\pi$
$89$	−1.58261	+	6.93389i	−0.167757	+	0.734991i	−0.986891	+	0.161389i	$0.948403\pi$
$90$	3.60208	+	4.59817i	0.379692	+	0.484690i
$91$	−0.933161	−	1.17015i	−0.0978218	−	0.122665i
$92$		−	6.11828i		−	0.637874i
$93$			0.807025i			0.0836846i
$94$	1.65163	+	2.07108i	0.170353	+	0.213616i
$95$	0.342165	+	0.0812277i	0.0351054	+	0.00833378i
$96$	−0.388266	+	0.486870i	−0.0396272	+	0.0496910i
$97$	2.68459	−	5.57461i	0.272579	−	0.566016i	−0.719077	−	0.694931i	$-0.755435\pi$
$97$	2.68459	−	5.57461i	0.272579	−	0.566016i	0.991656	+	0.128914i	$0.0411493\pi$
$98$	6.32865	−	1.44447i	0.639291	−	0.145914i
$99$	7.72278	+	9.68406i	0.776169	+	0.973285i
$100$	3.04912	+	3.96268i	0.304912	+	0.396268i
$101$	3.80298	−	1.83142i	0.378411	−	0.182233i	−0.235003	−	0.971995i	$-0.575510\pi$
$101$	3.80298	−	1.83142i	0.378411	−	0.182233i	0.613414	+	0.789761i	$0.289796\pi$
$102$	−0.391487	−	0.312200i	−0.0387630	−	0.0309124i
$103$	−9.62614	−	7.67659i	−0.948492	−	0.756397i	0.0214408	−	0.999770i	$-0.493175\pi$
$103$	−9.62614	−	7.67659i	−0.948492	−	0.756397i	−0.969933	+	0.243373i	$0.921746\pi$
$104$	0.466995	−	2.04604i	0.0457927	−	0.200631i
$105$	0.781741	−	0.612393i	0.0762901	−	0.0597635i
$106$	8.30580	+	3.99986i	0.806731	+	0.388501i
$107$	−6.18007	−	1.41056i	−0.597449	−	0.136364i	−0.0869069	−	0.996216i	$-0.527698\pi$
$107$	−6.18007	−	1.41056i	−0.597449	−	0.136364i	−0.510543	+	0.859852i	$0.670555\pi$
$108$	3.40727	+	0.777686i	0.327864	+	0.0748329i
$109$	8.14183	+	3.92090i	0.779845	+	0.375554i	0.781068	−	0.624445i	$-0.214675\pi$
$109$	8.14183	+	3.92090i	0.779845	+	0.375554i	−0.00122292	+	0.999999i	$0.500389\pi$
$110$	6.53856	+	8.34669i	0.623427	+	0.795826i
$111$	0.978036	−	4.28506i	0.0928311	−	0.406719i
$112$	−0.557569	−	0.444646i	−0.0526853	−	0.0420151i
$113$	8.82178	+	7.03514i	0.829883	+	0.661810i	0.943375	−	0.331729i	$-0.107632\pi$
$113$	8.82178	+	7.03514i	0.829883	+	0.661810i	−0.113491	+	0.993539i	$0.536203\pi$
$114$	0.0882399	−	0.0424941i	0.00826442	−	0.00397994i
$115$	−12.3771	+	5.82871i	−1.15417	+	0.543530i
$116$	−1.12884	−	1.41552i	−0.104810	−	0.131428i
$117$	−5.34468	+	1.21989i	−0.494116	+	0.112779i
$118$	−0.313670	+	0.651343i	−0.0288757	+	0.0599610i
$119$	0.357535	−	0.448335i	0.0327752	−	0.0410988i
$120$	1.35481	+	0.321624i	0.123677	+	0.0293601i
$121$	7.16015	+	8.97854i	0.650922	+	0.816231i
$122$			0.485767i			0.0439793i
$123$			6.86169i			0.618698i
$124$	−0.808009	−	1.01321i	−0.0725614	−	0.0909891i
$125$	5.11158	−	9.94343i	0.457194	−	0.889367i
$126$	−0.414538	+	1.81621i	−0.0369299	+	0.161801i
$127$	−8.93193	+	2.03866i	−0.792581	+	0.180901i	−0.599599	−	0.800301i	$-0.704673\pi$
$127$	−8.93193	+	2.03866i	−0.792581	+	0.180901i	−0.192982	+	0.981202i	$0.561816\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	1.78279	+	3.67379i	0.156966	+	0.323459i
$130$	−4.58398	+	1.00448i	−0.402041	+	0.0880992i
$131$	−3.43651	−	15.0563i	−0.300249	−	1.31548i	−0.869752	−	0.493488i	$-0.835722\pi$
$131$	−3.43651	−	15.0563i	−0.300249	−	1.31548i	0.569503	−	0.821989i	$-0.307136\pi$
$132$	2.87878	+	0.657064i	0.250566	+	0.0571900i
$133$	0.0486647	+	0.101053i	0.00421976	+	0.00876243i
$134$	8.91413	+	11.1780i	0.770064	+	0.965629i
$135$	−1.67277	−	7.63368i	−0.143969	−	0.657003i
$136$	0.804089			0.0689501
$137$	13.0048	−	10.3710i	1.11107	−	0.886051i	0.116824	−	0.993153i	$-0.462729\pi$
$137$	13.0048	−	10.3710i	1.11107	−	0.886051i	0.994248	+	0.107102i	$0.0341571\pi$
$138$	−1.65311	+	3.43272i	−0.140722	+	0.292213i
$139$	−1.17948	+	1.47902i	−0.100042	+	0.125449i	−0.829332	−	0.558756i	$-0.811279\pi$
$139$	−1.17948	+	1.47902i	−0.100042	+	0.125449i	0.729290	+	0.684205i	$0.239850\pi$
$140$	−0.368327	+	1.55155i	−0.0311294	+	0.131130i
$141$	−0.367075	−	1.60826i	−0.0309133	−	0.135440i
$142$	8.46228	−	6.74844i	0.710138	−	0.566316i
$143$	−9.70177	+	2.21436i	−0.811302	+	0.185174i
$144$	−2.35352	+	1.13339i	−0.196126	+	0.0944495i
$145$	−1.78815	+	3.63215i	−0.148498	+	0.301634i
$146$	7.61484	−	9.54871i	0.630209	−	0.790257i
$147$	−3.94104	−	0.899517i	−0.325052	−	0.0741909i
$148$	3.06237	+	6.35907i	0.251725	+	0.522713i
$149$	−9.18917	−	4.42527i	−0.752806	−	0.362532i	0.0178021	−	0.999842i	$-0.494333\pi$
$149$	−9.18917	−	4.42527i	−0.752806	−	0.362532i	−0.770608	+	0.637309i	$0.780047\pi$
$150$	−0.640056	−	3.04715i	−0.0522603	−	0.248799i
$151$	3.91699	−	17.1614i	0.318760	−	1.39658i	−0.520971	−	0.853575i	$-0.674430\pi$
$151$	3.91699	−	17.1614i	0.318760	−	1.39658i	0.839731	−	0.543003i	$-0.182713\pi$
$152$	−0.0682384	+	0.141698i	−0.00553486	+	0.0114933i
$153$	−0.911350	−	1.89244i	−0.0736783	−	0.152995i
$154$	−0.752476	+	3.29681i	−0.0606363	+	0.265665i
$155$	−1.27993	+	2.59984i	−0.102807	+	0.208824i
$156$	−0.814837	+	1.02177i	−0.0652392	+	0.0818074i
$157$	1.11184	+	2.30877i	0.0887348	+	0.184260i	0.940613	−	0.339479i	$-0.110251\pi$
$157$	1.11184	+	2.30877i	0.0887348	+	0.184260i	−0.851879	+	0.523739i	$0.824537\pi$
$158$	−4.49913	+	1.02690i	−0.357931	+	0.0816955i
$159$	−3.57933	−	4.48833i	−0.283859	−	0.355948i
$160$	−2.02297	+	0.952671i	−0.159930	+	0.0753153i
$161$	−3.93119	−	1.89316i	−0.309821	−	0.149202i
$162$	4.42536	+	3.52911i	0.347689	+	0.277273i
$163$	2.94810	−	6.12179i	0.230913	−	0.479496i	−0.753028	−	0.657988i	$-0.771408\pi$
$163$	2.94810	−	6.12179i	0.230913	−	0.479496i	0.983941	+	0.178492i	$0.0571220\pi$
$164$	−6.87006	−	8.61479i	−0.536462	−	0.672702i
$165$	−1.41331	−	6.44967i	−0.110026	−	0.502106i
$166$	−16.1038			−1.24990
$167$	−3.41068	+	2.71993i	−0.263926	+	0.210474i	−0.746507	−	0.665377i	$-0.768271\pi$
$167$	−3.41068	+	2.71993i	−0.263926	+	0.210474i	0.482581	+	0.875851i	$0.339699\pi$
$168$	0.192690	+	0.400124i	0.0148663	+	0.0308703i
$169$	−1.91271	+	8.38012i	−0.147131	+	0.644625i
$170$	−0.766033	−	1.62665i	−0.0587520	−	0.124758i
$171$	0.410831			0.0314170
$172$	−5.91655	−	2.82744i	−0.451133	−	0.215590i
$173$		−	2.80732i		−	0.213437i	−0.994289	−	0.106718i	$-0.965966\pi$
$173$		−	2.80732i		−	0.213437i	0.994289	−	0.106718i	$-0.0340343\pi$
$174$	0.250885	+	1.09920i	0.0190196	+	0.0833301i
$175$	3.48963	−	0.732999i	0.263792	−	0.0554095i
$176$	−4.27215	+	2.05736i	−0.322025	+	0.155079i
$177$	0.351976	−	0.280691i	0.0264561	−	0.0210981i
$178$			7.11221i			0.533082i
$179$	−7.55744			−0.564869			−0.282435	−	0.959287i	$-0.591142\pi$
$179$	−7.55744			−0.564869			−0.282435	+	0.959287i	$0.591142\pi$
$180$	4.53495	+	3.68135i	0.338015	+	0.274392i
$181$	−8.88214	−	4.27741i	−0.660204	−	0.317937i	0.0736108	−	0.997287i	$-0.476548\pi$
$181$	−8.88214	−	4.27741i	−0.660204	−	0.317937i	−0.733815	+	0.679350i	$0.762262\pi$
$182$	−1.17015	−	0.933161i	−0.0867370	−	0.0691705i
$183$	0.131251	−	0.272545i	0.00970233	−	0.0201471i
$184$	−1.36144	−	5.96488i	−0.100367	−	0.439737i
$185$	9.94680	−	12.2532i	0.731303	−	0.900873i
$186$	0.179580	+	0.786791i	0.0131674	+	0.0576903i
$187$	−1.65430	−	3.43519i	−0.120974	−	0.251206i
$188$	2.07108	+	1.65163i	0.151049	+	0.120458i
$189$	1.55399	−	1.94864i	0.113036	−	0.141743i
$190$	0.351661	+	0.00305233i	0.0255122	+	0.000221439i
$191$	−15.9028	+	7.65839i	−1.15069	+	0.554141i	−0.909240	−	0.416273i	$-0.863336\pi$
$191$	−15.9028	+	7.65839i	−1.15069	+	0.554141i	−0.241447	+	0.970414i	$0.577622\pi$
$192$	−0.270192	+	0.561060i	−0.0194995	+	0.0404910i
$193$	19.2644	+	4.39698i	1.38669	+	0.316502i	0.849779	−	0.527140i	$-0.176736\pi$
$193$	19.2644	+	4.39698i	1.38669	+	0.316502i	0.536907	+	0.843642i	$0.319593\pi$
$194$	1.37682	−	6.03223i	0.0988496	−	0.433089i
$195$	2.84329	+	0.674979i	0.203612	+	0.0483363i
$196$	5.84856	−	2.81652i	0.417754	−	0.201180i
$197$	2.16002	+	0.493010i	0.153895	+	0.0351255i	0.298774	−	0.954324i	$-0.403422\pi$
$197$	2.16002	+	0.493010i	0.153895	+	0.0351255i	−0.144879	+	0.989449i	$0.546279\pi$
$198$	9.68406	+	7.72278i	0.688216	+	0.548834i
$199$	4.37485	−	5.48589i	0.310125	−	0.388884i	−0.602204	−	0.798342i	$-0.705711\pi$
$199$	4.37485	−	5.48589i	0.310125	−	0.388884i	0.912329	+	0.409458i	$0.134282\pi$
$200$	3.85446	+	3.18484i	0.272551	+	0.225202i
$201$	−1.98116	−	8.68005i	−0.139741	−	0.612243i
$202$	3.30011	−	2.63175i	0.232195	−	0.185169i
$203$	−1.25882	+	0.287317i	−0.0883516	+	0.0201657i
$204$	−0.451143	−	0.217259i	−0.0315863	−	0.0152112i
$205$	−10.8826	+	22.1050i	−0.760071	+	1.54388i
$206$	−11.0930	−	5.34211i	−0.772886	−	0.372202i
$207$	−12.4954	+	9.96474i	−0.868490	+	0.692598i
$208$		−	2.09866i		−	0.145516i
$209$	0.745748			0.0515844
$210$	0.625871	−	0.770993i	0.0431892	−	0.0532036i
$211$	−1.02334	+	0.492812i	−0.0704493	+	0.0339266i	−0.468777	−	0.883317i	$-0.655305\pi$
$211$	−1.02334	+	0.492812i	−0.0704493	+	0.0339266i	0.398327	+	0.917243i	$0.369591\pi$
$212$	8.98761	+	2.05136i	0.617272	+	0.140888i
$213$	−6.57123	+	1.49984i	−0.450253	+	0.102767i
$214$	−6.33900			−0.433325
$215$	−0.0833082	+	14.6626i	−0.00568158	+	0.999984i
$216$	3.49489			0.237797
$217$	−0.901042	+	0.205657i	−0.0611667	+	0.0139609i
$218$	8.81017	+	2.01086i	0.596700	+	0.136193i
$219$	−6.85238	+	3.29993i	−0.463041	+	0.222989i
$220$	8.23193	+	6.68245i	0.554997	+	0.450531i
$221$	1.68751			0.113514
$222$		−	4.39525i		−	0.294990i
$223$	−10.7299	+	8.55683i	−0.718529	+	0.573008i	−0.913029	−	0.407895i	$-0.866263\pi$
$223$	−10.7299	+	8.55683i	−0.718529	+	0.573008i	0.194500	+	0.980903i	$0.437692\pi$
$224$	−0.642533	−	0.309427i	−0.0429310	−	0.0206745i
$225$	3.12695	−	12.6812i	0.208463	−	0.845413i
$226$	10.1661	+	4.89572i	0.676237	+	0.325658i
$227$	11.8279	−	2.69965i	0.785047	−	0.179182i	0.188835	−	0.982009i	$-0.439529\pi$
$227$	11.8279	−	2.69965i	0.785047	−	0.179182i	0.596212	+	0.802827i	$0.296672\pi$
$228$	0.0765717	−	0.0610639i	0.00507108	−	0.00404405i
$229$	−5.26714	−	23.0769i	−0.348063	−	1.52496i	−0.781573	−	0.623814i	$-0.785582\pi$
$229$	−5.26714	−	23.0769i	−0.348063	−	1.52496i	0.433510	−	0.901149i	$-0.357275\pi$
$230$	−10.7698	+	8.43673i	−0.710138	+	0.556302i
$231$	1.31296	−	1.64640i	0.0863864	−	0.108325i
$232$	−1.41552	−	1.12884i	−0.0929338	−	0.0741122i
$233$	−2.71912	−	0.620621i	−0.178135	−	0.0406582i	0.132523	−	0.991180i	$-0.457692\pi$
$233$	−2.71912	−	0.620621i	−0.178135	−	0.0406582i	−0.310658	+	0.950522i	$0.600549\pi$
$234$	−4.93923	+	2.37861i	−0.322887	+	0.155494i
$235$	1.36815	−	5.76320i	0.0892480	−	0.375950i
$236$	−0.160868	+	0.704810i	−0.0104716	+	0.0458792i
$237$	2.80174	+	0.639479i	0.181993	+	0.0415387i
$238$	0.248807	−	0.516653i	0.0161278	−	0.0334897i
$239$	9.05068	−	4.35858i	0.585440	−	0.281933i	−0.117626	−	0.993058i	$-0.537528\pi$
$239$	9.05068	−	4.35858i	0.585440	−	0.281933i	0.703066	+	0.711125i	$0.251814\pi$
$240$	1.39241	+	0.0120858i	0.0898800	+	0.000780137i
$241$	0.309247	−	0.387784i	0.0199204	−	0.0249793i	−0.771772	−	0.635900i	$-0.780629\pi$
$241$	0.309247	−	0.387784i	0.0199204	−	0.0249793i	0.791692	+	0.610921i	$0.209201\pi$
$242$	8.97854	+	7.16015i	0.577162	+	0.460272i
$243$	−6.07848	−	12.6221i	−0.389935	−	0.809708i
$244$	0.108093	+	0.473588i	0.00691997	+	0.0303184i
$245$	−11.2695	−	9.14825i	−0.719981	−	0.584460i
$246$	1.52687	+	6.68965i	0.0973497	+	0.426517i
$247$	−0.143209	+	0.297377i	−0.00911217	+	0.0189216i
$248$	−1.01321	−	0.808009i	−0.0643390	−	0.0513087i
$249$	9.03519	+	4.35112i	0.572582	+	0.275741i
$250$	2.77081	−	10.8316i	0.175241	−	0.685048i
$251$	−0.421570			−0.0266093			−0.0133046	−	0.999911i	$-0.504235\pi$
$251$	−0.421570			−0.0266093			−0.0133046	+	0.999911i	$0.504235\pi$
$252$			1.86291i			0.117353i
$253$	−22.6819	+	18.0882i	−1.42600	+	1.13719i
$254$	−8.25435	+	3.97508i	−0.517924	+	0.249419i
$255$	−0.00971808	+	1.11963i	−0.000608570	+	0.0701137i
$256$	−0.222521	−	0.974928i	−0.0139076	−	0.0609330i
$257$		−	3.67828i		−	0.229445i	−0.993398	−	0.114723i	$-0.963402\pi$
$257$		−	3.67828i		−	0.229445i	0.993398	−	0.114723i	$-0.0365979\pi$
$258$	2.55559	+	3.18497i	0.159104	+	0.198288i
$259$	5.03349			0.312766
$260$	−4.24553	+	1.99933i	−0.263296	+	0.123993i
$261$	−1.05240	+	4.61089i	−0.0651422	+	0.285407i
$262$	−6.70070	−	13.9141i	−0.413970	−	0.859618i
$263$	12.2088	−	9.73622i	0.752829	−	0.600361i	−0.170057	−	0.985434i	$-0.554395\pi$
$263$	12.2088	−	9.73622i	0.752829	−	0.600361i	0.922886	+	0.385073i	$0.125824\pi$
$264$	2.95282			0.181733
$265$	−4.41239	−	20.1360i	−0.271051	−	1.23694i
$266$	0.0699310	+	0.0876907i	0.00428775	+	0.00537666i
$267$	1.92166	−	3.99038i	0.117604	−	0.244207i
$268$	11.1780	+	8.91413i	0.682803	+	0.544517i
$269$	−15.3856	−	7.40930i	−0.938075	−	0.451753i	−0.0985852	−	0.995129i	$-0.531432\pi$
$269$	−15.3856	−	7.40930i	−0.938075	−	0.451753i	−0.839490	+	0.543376i	$0.817146\pi$
$270$	−3.32948	−	7.07007i	−0.202626	−	0.430271i
$271$	7.32055	+	9.17968i	0.444692	+	0.557626i	0.952773	−	0.303683i	$-0.0982165\pi$
$271$	7.32055	+	9.17968i	0.444692	+	0.557626i	−0.508081	+	0.861309i	$0.669645\pi$
$272$	0.783929	−	0.178927i	0.0475327	−	0.0108490i
$273$	0.404390	+	0.839724i	0.0244748	+	0.0508224i
$274$	10.3710	−	13.0048i	0.626533	−	0.785647i
$275$	5.67610	−	23.0192i	0.342281	−	1.38811i
$276$	−0.847813	+	3.71451i	−0.0510323	+	0.223587i
$277$	9.49808	+	19.7230i	0.570684	+	1.18504i	0.964066	+	0.265663i	$0.0855909\pi$
$277$	9.49808	+	19.7230i	0.570684	+	1.18504i	−0.393381	+	0.919375i	$0.628695\pi$
$278$	−0.820795	+	1.70440i	−0.0492280	+	0.102223i
$279$	−0.753296	+	3.30041i	−0.0450986	+	0.197590i
$280$	−0.0138408	+	1.59461i	−0.000827147	+	0.0952961i
$281$	7.22507	+	3.47941i	0.431011	+	0.207564i	0.636795	−	0.771034i	$-0.280260\pi$
$281$	7.22507	+	3.47941i	0.431011	+	0.207564i	−0.205783	+	0.978598i	$0.565974\pi$
$282$	−0.715743	−	1.48626i	−0.0426219	−	0.0885052i
$283$	−0.0268026	−	0.00611753i	−0.00159325	−	0.000363649i	0.221724	−	0.975109i	$-0.428832\pi$
$283$	−0.0268026	−	0.00611753i	−0.00159325	−	0.000363649i	−0.223317	+	0.974746i	$0.571689\pi$
$284$	6.74844	−	8.46228i	0.400446	−	0.502144i
$285$	−0.196478	−	0.0967286i	−0.0116384	−	0.00572971i
$286$	−8.96578	+	4.31769i	−0.530158	+	0.255311i
$287$	−7.66107	+	1.74859i	−0.452218	+	0.103216i
$288$	−2.04231	+	1.62868i	−0.120344	+	0.0959712i
$289$	−3.63898	−	15.9434i	−0.214058	−	0.937849i
$290$	−0.935089	+	3.93898i	−0.0549103	+	0.231305i
$291$	−2.40234	+	3.01244i	−0.140828	+	0.176592i
$292$	5.29913	−	11.0038i	0.310108	−	0.643947i
$293$	−25.6583	+	20.4618i	−1.49897	+	1.19539i	−0.572004	+	0.820251i	$0.693834\pi$
$293$	−25.6583	+	20.4618i	−1.49897	+	1.19539i	−0.926968	+	0.375140i	$0.877595\pi$
$294$	−4.04239			−0.235757
$295$	1.57907	−	0.346020i	0.0919368	−	0.0201461i
$296$	4.40062	+	5.51820i	0.255781	+	0.320739i
$297$	−7.19024	−	14.9307i	−0.417220	−	0.866367i
$298$	−9.94349	−	2.26954i	−0.576011	−	0.131471i
$299$	−2.85721	−	12.5182i	−0.165237	−	0.723949i
$300$	−1.30206	−	2.82833i	−0.0751747	−	0.163294i
$301$	−3.64747	+	2.92669i	−0.210236	+	0.168692i
$302$		−	17.6028i		−	1.01293i
$303$	−2.56264	+	0.584905i	−0.147220	+	0.0336019i
$304$	−0.0349966	+	0.153330i	−0.00200719	+	0.00879409i
$305$	0.855079	−	0.669844i	0.0489617	−	0.0383552i
$306$	−1.30961	−	1.64220i	−0.0748653	−	0.0938781i
$307$		−	7.12662i		−	0.406737i	−0.979102	−	0.203369i	$-0.934811\pi$
$307$		−	7.12662i		−	0.406737i	0.979102	−	0.203369i	$-0.0651890\pi$
$308$			3.38160i			0.192684i
$309$	4.78044	+	5.99449i	0.271950	+	0.341015i
$310$	−0.669323	+	2.81947i	−0.0380150	+	0.160135i
$311$	−13.6309	+	17.0927i	−0.772940	+	0.969236i	−0.999989	−	0.00464705i	$-0.998521\pi$
$311$	−13.6309	+	17.0927i	−0.772940	+	0.969236i	0.227049	+	0.973883i	$0.427092\pi$
$312$	−0.567042	+	1.17747i	−0.0321024	+	0.0666613i
$313$	25.9646	−	5.92626i	1.46761	−	0.334972i	0.587298	−	0.809371i	$-0.300192\pi$
$313$	25.9646	−	5.92626i	1.46761	−	0.334972i	0.880310	+	0.474399i	$0.157335\pi$
$314$	1.59772	+	2.00347i	0.0901644	+	0.113063i
$315$	3.76863	−	1.77475i	0.212338	−	0.0999956i
$316$	−4.15782	+	2.00230i	−0.233896	+	0.112638i
$317$	−5.40430	−	4.30979i	−0.303536	−	0.242062i	0.459862	−	0.887990i	$-0.347899\pi$
$317$	−5.40430	−	4.30979i	−0.303536	−	0.242062i	−0.763398	+	0.645929i	$0.776470\pi$
$318$	−4.48833	−	3.57933i	−0.251693	−	0.200719i
$319$	−1.91035	+	8.36977i	−0.106959	+	0.468617i
$320$	−1.76026	+	1.37894i	−0.0984017	+	0.0770851i
$321$	3.55656	+	1.71275i	0.198508	+	0.0955963i
$322$	−4.25390	−	0.970924i	−0.237060	−	0.0541075i
$323$	−0.123291	−	0.0281404i	−0.00686010	−	0.00156577i
$324$	5.09971	+	2.45589i	0.283317	+	0.136438i
$325$	8.08918	+	6.68388i	0.448707	+	0.370755i
$326$	1.51196	−	6.62432i	0.0837396	−	0.366887i
$327$	−4.39972	−	3.50866i	−0.243305	−	0.194029i
$328$	−8.61479	−	6.87006i	−0.475672	−	0.379336i
$329$	1.70208	−	0.819677i	0.0938385	−	0.0451902i
$330$	−2.81306	−	5.97347i	−0.154854	−	0.328829i
$331$	7.25670	+	9.09961i	0.398864	+	0.500160i	0.940189	−	0.340654i	$-0.110648\pi$
$331$	7.25670	+	9.09961i	0.398864	+	0.500160i	−0.541325	+	0.840814i	$0.682077\pi$
$332$	−15.7000	+	3.58343i	−0.861651	+	0.196666i
$333$	7.99954	−	16.6112i	0.438372	−	0.910289i
$334$	−2.71993	+	3.41068i	−0.148828	+	0.186624i
$335$	7.38412	−	31.1050i	0.403437	−	1.69945i
$336$	0.276895	+	0.347215i	0.0151058	+	0.0189421i
$337$			28.1664i			1.53432i	0.641455	+	0.767161i	$0.278331\pi$
$337$			28.1664i			1.53432i	−0.641455	+	0.767161i	$0.721669\pi$
$338$			8.59563i			0.467541i
$339$	−4.38099	−	5.49359i	−0.237943	−	0.298371i
$340$	−1.10879	−	1.41541i	−0.0601326	−	0.0767613i
$341$	−1.36740	+	5.99096i	−0.0740487	+	0.324429i
$342$	0.400530	−	0.0914184i	0.0216582	−	0.00494334i
$343$		−	9.62150i		−	0.519512i
$344$	−6.39738	−	1.43999i	−0.344923	−	0.0776393i
$345$	8.32204	−	1.82360i	0.448043	−	0.0981796i
$346$	−0.624687	−	2.73693i	−0.0335834	−	0.147138i
$347$	27.1043	+	6.18638i	1.45503	+	0.332102i	0.875648	−	0.482951i	$-0.160435\pi$
$347$	27.1043	+	6.18638i	1.45503	+	0.332102i	0.579387	+	0.815053i	$0.303292\pi$
$348$	0.489190	+	1.01581i	0.0262233	+	0.0544533i
$349$	6.85268	+	8.59299i	0.366816	+	0.459972i	0.930647	−	0.365918i	$-0.119245\pi$
$349$	6.85268	+	8.59299i	0.366816	+	0.459972i	−0.563832	+	0.825890i	$0.690673\pi$
$350$	3.23903	−	1.49114i	0.173134	−	0.0797047i
$351$	7.33458			0.391491
$352$	−3.70723	+	2.95642i	−0.197596	+	0.157578i
$353$	11.5479	−	23.9795i	0.614635	−	1.27630i	−0.328692	−	0.944437i	$-0.606608\pi$
$353$	11.5479	−	23.9795i	0.614635	−	1.27630i	0.943327	−	0.331865i	$-0.107678\pi$
$354$	0.280691	−	0.351976i	0.0149186	−	0.0187073i
$355$	−23.5480	−	5.59014i	−1.24980	−	0.296694i
$356$	1.58261	+	6.93389i	0.0838784	+	0.367495i
$357$	−0.279192	+	0.222648i	−0.0147764	+	0.0117838i
$358$	−7.36796	+	1.68169i	−0.389409	+	0.0888800i
$359$	28.4171	−	13.6849i	1.49980	−	0.722263i	0.509400	−	0.860530i	$-0.329867\pi$
$359$	28.4171	−	13.6849i	1.49980	−	0.722263i	0.990395	+	0.138266i	$0.0441530\pi$
$360$	5.24043	+	2.57993i	0.276195	+	0.135974i
$361$	−11.8309	+	14.8355i	−0.622678	+	0.780814i
$362$	−9.61126	−	2.19371i	−0.505156	−	0.115299i
$363$	−3.10289	−	6.44321i	−0.162859	−	0.338181i
$364$	−1.34846	−	0.649382i	−0.0706783	−	0.0340369i
$365$	−27.3086	−	0.237033i	−1.42940	−	0.0124068i
$366$	0.0673130	−	0.294918i	0.00351851	−	0.0154156i
$367$	−15.1286	+	31.4149i	−0.789707	+	1.63984i	−0.0213928	+	0.999771i	$0.506810\pi$
$367$	−15.1286	+	31.4149i	−0.789707	+	1.63984i	−0.768314	+	0.640073i	$0.778904\pi$
$368$	−2.65462	−	5.51238i	−0.138382	−	0.287353i
$369$	−6.40486	+	28.0615i	−0.333424	+	1.46083i
$370$	6.97082	−	14.1594i	0.362396	−	0.736110i
$371$	4.09908	−	5.14009i	0.212814	−	0.266860i
$372$	0.350155	+	0.727104i	0.0181547	+	0.0376986i
$373$	−19.1853	+	4.37892i	−0.993378	+	0.226732i	−0.688167	−	0.725553i	$-0.741584\pi$
$373$	−19.1853	+	4.37892i	−0.993378	+	0.226732i	−0.305211	+	0.952285i	$0.598727\pi$
$374$	−2.37722	−	2.98095i	−0.122923	−	0.154141i
$375$	−4.48119	+	5.32851i	−0.231408	+	0.275163i
$376$	2.38668	+	1.14936i	0.123083	+	0.0592739i
$377$	−2.97070	−	2.36906i	−0.152999	−	0.122013i
$378$	1.08141	−	2.24558i	0.0556220	−	0.115500i
$379$	17.8485	+	22.3813i	0.916814	+	1.14965i	0.988348	+	0.152211i	$0.0486393\pi$
$379$	17.8485	+	22.3813i	0.916814	+	1.14965i	−0.0715336	+	0.997438i	$0.522789\pi$
$380$	0.343523	−	0.0752761i	0.0176224	−	0.00386158i
$381$	5.70523			0.292288
$382$	−13.7999	+	11.0051i	−0.706066	+	0.563069i
$383$	7.33524	+	15.2318i	0.374813	+	0.778308i	0.999998	−	0.00216927i	$-0.000690501\pi$
$383$	7.33524	+	15.2318i	0.374813	+	0.778308i	−0.625184	+	0.780477i	$0.714976\pi$
$384$	−0.138570	+	0.607117i	−0.00707140	+	0.0309818i
$385$	6.84088	−	3.22155i	0.348644	−	0.164185i
$386$	19.7599			1.00575
$387$	3.86170	+	16.6884i	0.196301	+	0.848320i
$388$		−	6.18736i		−	0.314115i
$389$	3.06851	+	13.4440i	0.155579	+	0.681638i	0.991205	+	0.132338i	$0.0422484\pi$
$389$	3.06851	+	13.4440i	0.155579	+	0.681638i	−0.835625	+	0.549300i	$0.814894\pi$
$390$	2.92220	+	0.0253640i	0.147971	+	0.00128436i
$391$	4.43244	−	2.13455i	0.224158	−	0.107949i
$392$	5.07519	−	4.04733i	0.256336	−	0.204421i
$393$			9.61715i			0.485121i
$394$	2.21556			0.111619
$395$	8.01163	+	6.50362i	0.403109	+	0.327233i
$396$	11.1597	+	5.37425i	0.560798	+	0.270066i
$397$	23.0251	+	18.3619i	1.15560	+	0.921558i	0.997825	−	0.0659177i	$-0.0209975\pi$
$397$	23.0251	+	18.3619i	1.15560	+	0.921558i	0.157772	+	0.987476i	$0.449569\pi$
$398$	3.04444	−	6.32184i	0.152604	−	0.316885i
$399$	−0.0155422	−	0.0680946i	−0.000778081	−	0.00340900i
$400$	4.46651	+	2.24729i	0.223325	+	0.112364i
$401$	2.02838	+	8.88693i	0.101293	+	0.443792i	0.999986	+	0.00521531i	$0.00166009\pi$
$401$	2.02838	+	8.88693i	0.101293	+	0.443792i	−0.898694	+	0.438577i	$0.855483\pi$
$402$	−3.86298	−	8.02157i	−0.192668	−	0.400080i
$403$	−2.12639	−	1.69574i	−0.105923	−	0.0844706i
$404$	2.63175	−	3.30011i	0.130934	−	0.164186i
$405$	0.109853	−	12.6562i	0.00545864	−	0.628893i
$406$	−1.16332	+	0.560226i	−0.0577346	+	0.0278035i
$407$	14.5209	−	30.1530i	0.719775	−	1.49463i
$408$	−0.488176	−	0.111423i	−0.0241683	−	0.00551626i
$409$	3.25607	−	14.2658i	0.161002	−	0.705396i	−0.828393	−	0.560147i	$-0.810745\pi$
$409$	3.25607	−	14.2658i	0.161002	−	0.705396i	0.989395	−	0.145249i	$-0.0463983\pi$
$410$	−5.69089	+	23.9724i	−0.281053	+	1.18391i
$411$	−9.33253	+	4.49431i	−0.460340	+	0.221688i
$412$	−12.0036	−	2.73974i	−0.591375	−	0.134977i
$413$	0.403087	+	0.321451i	0.0198346	+	0.0158176i
$414$	−9.96474	+	12.4954i	−0.489740	+	0.614115i
$415$	22.2061	+	28.3469i	1.09006	+	1.39149i
$416$	−0.466995	−	2.04604i	−0.0228963	−	0.100315i
$417$	0.921031	−	0.734498i	0.0451031	−	0.0359685i
$418$	0.727050	−	0.165944i	0.0355612	−	0.00811661i
$419$	15.9189	+	7.66615i	0.777690	+	0.374516i	0.780239	−	0.625481i	$-0.215097\pi$
$419$	15.9189	+	7.66615i	0.777690	+	0.374516i	−0.00254930	+	0.999997i	$0.500811\pi$
$420$	0.438617	−	0.890932i	0.0214023	−	0.0434730i
$421$	25.5238	+	12.2916i	1.24395	+	0.599056i	0.935884	−	0.352308i	$-0.114603\pi$
$421$	25.5238	+	12.2916i	1.24395	+	0.599056i	0.308068	+	0.951364i	$0.400317\pi$
$422$	−0.888017	+	0.708170i	−0.0432280	+	0.0344732i
$423$		−	6.91977i		−	0.336451i
$424$	9.21875			0.447702
$425$	−1.80702	+	3.59147i	−0.0876533	+	0.174212i
$426$	−6.07273	+	2.92447i	−0.294225	+	0.141691i
$427$	0.337743	+	0.0770876i	0.0163445	+	0.00373053i
$428$	−6.18007	+	1.41056i	−0.298725	+	0.0681820i
$429$	6.19695			0.299192
$430$	3.18153	+	14.3136i	0.153427	+	0.690261i
$431$	6.01486			0.289726			0.144863	−	0.989452i	$-0.453726\pi$
$431$	6.01486			0.289726			0.144863	+	0.989452i	$0.453726\pi$
$432$	3.40727	−	0.777686i	0.163932	−	0.0374164i
$433$	36.9142	+	8.42543i	1.77398	+	0.404900i	0.979347	−	0.202185i	$-0.0648044\pi$
$433$	36.9142	+	8.42543i	1.77398	+	0.404900i	0.794636	+	0.607086i	$0.207662\pi$
$434$	−0.832688	+	0.401001i	−0.0399703	+	0.0192487i
$435$	1.58893	−	1.95735i	0.0761832	−	0.0938480i
$436$	9.03675			0.432782
$437$			0.962242i			0.0460303i
$438$	−5.94627	+	4.74199i	−0.284124	+	0.226581i
$439$	−16.6358	−	8.01137i	−0.793982	−	0.382362i	−0.00749780	−	0.999972i	$-0.502387\pi$
$439$	−16.6358	−	8.01137i	−0.793982	−	0.382362i	−0.786484	+	0.617610i	$0.788101\pi$
$440$	9.51253	+	4.68313i	0.453492	+	0.223260i
$441$	−15.2776	−	7.35732i	−0.727507	−	0.350349i
$442$	1.64520	−	0.375506i	0.0782541	−	0.0178610i
$443$	−1.60692	+	1.28148i	−0.0763470	+	0.0608847i	−0.660920	−	0.750457i	$-0.729834\pi$
$443$	−1.60692	+	1.28148i	−0.0763470	+	0.0608847i	0.584573	+	0.811341i	$0.301262\pi$
$444$	−0.978036	−	4.28506i	−0.0464155	−	0.203360i
$445$	12.5194	−	9.80730i	0.593474	−	0.464911i
$446$	−8.55683	+	10.7299i	−0.405178	+	0.508077i
$447$	4.96569	+	3.96000i	0.234869	+	0.187302i
$448$	−0.695277	−	0.158692i	−0.0328487	−	0.00749751i
$449$	−8.93688	+	4.30377i	−0.421757	+	0.203108i	−0.632710	−	0.774389i	$-0.718058\pi$
$449$	−8.93688	+	4.30377i	−0.421757	+	0.203108i	0.210953	+	0.977496i	$0.432343\pi$
$450$	0.226716	−	13.0591i	0.0106875	−	0.615610i
$451$	−11.6262	+	50.9378i	−0.547458	+	2.39857i
$452$	11.0006	+	2.51081i	0.517424	+	0.118099i
$453$	−4.75614	+	9.87622i	−0.223463	+	0.464025i
$454$	10.9306	−	5.26392i	0.513001	−	0.247048i
$455$	−0.0290471	+	3.34654i	−0.00136175	+	0.156888i
$456$	0.0610639	−	0.0765717i	0.00285958	−	0.00358580i
$457$	19.4309	+	15.4956i	0.908937	+	0.724853i	0.961801	−	0.273748i	$-0.0882636\pi$
$457$	19.4309	+	15.4956i	0.908937	+	0.724853i	−0.0528641	+	0.998602i	$0.516835\pi$
$458$	−10.2702	−	21.3262i	−0.479894	−	0.996509i
$459$	0.625329	+	2.73975i	0.0291879	+	0.127880i
$460$	−8.62241	+	10.6217i	−0.402022	+	0.495240i
$461$	−6.70887	−	29.3935i	−0.312463	−	1.36899i	−0.850458	−	0.526042i	$-0.823675\pi$
$461$	−6.70887	−	29.3935i	−0.312463	−	1.36899i	0.537995	−	0.842948i	$-0.319182\pi$
$462$	0.913682	−	1.89728i	0.0425083	−	0.0882695i
$463$	7.69182	+	6.13402i	0.357469	+	0.285072i	0.785713	−	0.618591i	$-0.212296\pi$
$463$	7.69182	+	6.13402i	0.357469	+	0.285072i	−0.428244	+	0.903663i	$0.640868\pi$
$464$	−1.63123	−	0.785557i	−0.0757278	−	0.0364686i
$465$	1.13733	−	1.40105i	0.0527424	−	0.0649719i
$466$	−2.78904			−0.129200
$467$			7.20107i			0.333226i	0.986022	+	0.166613i	$0.0532830\pi$
$467$			7.20107i			0.333226i	−0.986022	+	0.166613i	$0.946717\pi$
$468$	−4.28610	+	3.41805i	−0.198125	+	0.158000i
$469$	9.18639	−	4.42393i	0.424188	−	0.204278i
$470$	0.0514115	−	5.92315i	0.00237144	−	0.273214i
$471$	−0.355092	−	1.55576i	−0.0163618	−	0.0716857i
$472$			0.722936i			0.0332758i
$473$	7.00982	+	30.2931i	0.322312	+	1.39288i
$474$	2.87379			0.131998
$475$	−0.479546	−	0.623224i	−0.0220031	−	0.0285955i
$476$	0.127603	−	0.559065i	0.00584867	−	0.0256247i
$477$	−10.4485	−	21.6965i	−0.478403	−	0.993414i
$478$	7.85389	−	6.26326i	0.359228	−	0.286475i
$479$	−17.8622			−0.816147			−0.408073	−	0.912949i	$-0.633799\pi$
$479$	−17.8622			−0.816147			−0.408073	+	0.912949i	$0.633799\pi$
$480$	1.36019	−	0.298059i	0.0620840	−	0.0136044i
$481$	9.23539	+	11.5808i	0.421097	+	0.528039i
$482$	0.215204	−	0.446875i	0.00980226	−	0.0203546i
$483$	2.12436	+	1.69412i	0.0966616	+	0.0770850i
$484$	10.3467	+	4.98271i	0.470305	+	0.226487i
$485$	−12.5169	+	5.89452i	−0.568361	+	0.267656i
$486$	−8.73477	−	10.9531i	−0.396217	−	0.496840i
$487$	−13.2496	+	3.02413i	−0.600396	+	0.137036i	−0.511907	−	0.859041i	$-0.671061\pi$
$487$	−13.2496	+	3.02413i	−0.600396	+	0.137036i	−0.0884885	+	0.996077i	$0.528204\pi$
$488$	0.210767	+	0.437661i	0.00954096	+	0.0198120i
$489$	−2.63814	+	3.30812i	−0.119301	+	0.149599i
$490$	−13.0226	−	6.41119i	−0.588302	−	0.289628i
$491$	−5.69244	+	24.9402i	−0.256896	+	1.12554i	0.667652	+	0.744473i	$0.267299\pi$
$491$	−5.69244	+	24.9402i	−0.256896	+	1.12554i	−0.924549	+	0.381064i	$0.875558\pi$
$492$	2.97718	+	6.18217i	0.134221	+	0.278714i
$493$	0.631658	−	1.31165i	0.0284484	−	0.0590738i
$494$	−0.0734459	+	0.321788i	−0.00330449	+	0.0144779i
$495$	0.240392	−	27.6957i	0.0108048	−	1.24483i
$496$	−1.16761	−	0.562290i	−0.0524271	−	0.0252476i
$497$	−3.34914	−	6.95455i	−0.150229	−	0.311954i
$498$	9.77688	+	2.23151i	0.438112	+	0.0999963i
$499$	12.0221	−	15.0752i	0.538181	−	0.674857i	−0.436177	−	0.899861i	$-0.643668\pi$
$499$	12.0221	−	15.0752i	0.538181	−	0.674857i	0.974358	+	0.225003i	$0.0722393\pi$
$500$	0.291088	−	11.1765i	0.0130178	−	0.499831i
$501$	2.44758	−	1.17869i	0.109350	−	0.0526601i
$502$	−0.411001	+	0.0938082i	−0.0183439	+	0.00418687i
$503$	26.2988	−	20.9726i	1.17261	−	0.935122i	0.173839	−	0.984774i	$-0.444383\pi$
$503$	26.2988	−	20.9726i	1.17261	−	0.935122i	0.998767	+	0.0496523i	$0.0158113\pi$
$504$	0.414538	+	1.81621i	0.0184650	+	0.0809003i
$505$	−9.18321	−	2.18004i	−0.408648	−	0.0970103i
$506$	−18.0882	+	22.6819i	−0.804118	+	1.00833i
$507$	2.32248	−	4.82267i	0.103145	−	0.214182i
$508$	−7.16285	+	5.71219i	−0.317800	+	0.253437i
$509$	−25.8617			−1.14630			−0.573151	−	0.819450i	$-0.694279\pi$
$509$	−25.8617			−1.14630			−0.573151	+	0.819450i	$0.694279\pi$
$510$	0.239666	+	1.09372i	0.0106126	+	0.0484306i
$511$	−5.43058	−	6.80973i	−0.240235	−	0.301245i
$512$	−0.433884	−	0.900969i	−0.0191751	−	0.0398176i
$513$	−0.535872	−	0.122309i	−0.0236593	−	0.00540009i
$514$	−0.818495	−	3.58606i	−0.0361023	−	0.158174i
$515$	5.89306	+	26.8930i	0.259679	+	1.18505i
$516$	3.20024	+	2.53645i	0.140883	+	0.111661i
$517$		−	12.5609i		−	0.552427i
$518$	4.90729	−	1.12006i	0.215614	−	0.0492125i
$519$	−0.389012	+	1.70437i	−0.0170757	+	0.0748136i
$520$	−3.69419	+	2.89392i	−0.162001	+	0.126907i
$521$	23.2658	+	29.1744i	1.01929	+	1.27815i	0.960025	+	0.279913i	$0.0903055\pi$
$521$	23.2658	+	29.1744i	1.01929	+	1.27815i	0.0592688	+	0.998242i	$0.481123\pi$
$522$			4.72946i			0.207003i
$523$			16.2682i			0.711360i	0.934608	+	0.355680i	$0.115751\pi$
$523$			16.2682i			0.711360i	−0.934608	+	0.355680i	$0.884249\pi$
$524$	−9.62888	−	12.0742i	−0.420640	−	0.527466i
$525$	−2.22019	−	0.0385443i	−0.0968970	−	0.00168221i
$526$	9.73622	−	12.2088i	0.424520	−	0.532331i
$527$	0.452131	−	0.938861i	0.0196952	−	0.0408974i
$528$	2.87878	−	0.657064i	0.125283	−	0.0285950i
$529$	−8.99902	−	11.2844i	−0.391262	−	0.490627i
$530$	−8.78244	−	18.6493i	−0.381485	−	0.810073i
$531$	1.70144	−	0.819371i	0.0738363	−	0.0355577i
$532$	0.0876907	+	0.0699310i	0.00380188	+	0.00303189i
$533$	−18.0795	−	14.4179i	−0.783110	−	0.624509i
$534$	0.985542	−	4.31794i	0.0426486	−	0.186856i
$535$	8.74109	+	11.1583i	0.377910	+	0.482415i
$536$	12.8813	+	6.20330i	0.556387	+	0.267942i
$537$	4.58825	+	1.04724i	0.197998	+	0.0451916i
$538$	−16.6485	−	3.79992i	−0.717770	−	0.163826i
$539$	−27.7323	−	13.3552i	−1.19451	−	0.575247i
$540$	−4.81924	−	6.15193i	−0.207387	−	0.264737i
$541$	−2.33582	+	10.2339i	−0.100425	+	0.439989i	0.899570	+	0.436776i	$0.143880\pi$
$541$	−2.33582	+	10.2339i	−0.100425	+	0.439989i	−0.999995	+	0.00321266i	$0.998977\pi$
$542$	9.17968	+	7.32055i	0.394301	+	0.314445i
$543$	4.79977	+	3.82769i	0.205978	+	0.164262i
$544$	0.724459	−	0.348881i	0.0310609	−	0.0149582i
$545$	−8.60905	−	18.2811i	−0.368771	−	0.783076i
$546$	0.581107	+	0.728685i	0.0248691	+	0.0311849i
$547$	−9.98503	+	2.27902i	−0.426929	+	0.0974438i	−0.430586	−	0.902550i	$-0.641693\pi$
$547$	−9.98503	+	2.27902i	−0.426929	+	0.0974438i	0.00365699	+	0.999993i	$0.498836\pi$
$548$	7.21710	−	14.9865i	0.308299	−	0.640190i
$549$	0.791162	−	0.992086i	0.0337660	−	0.0423412i
$550$	0.411540	−	23.7051i	0.0175481	−	1.01079i
$551$	0.177537	+	0.222624i	0.00756333	+	0.00948412i
$552$			3.81004i			0.162166i
$553$			3.29110i			0.139952i
$554$	13.6487	+	17.1150i	0.579879	+	0.727145i
$555$	−7.73680	+	6.06079i	−0.328409	+	0.257266i
$556$	−0.420952	+	1.84431i	−0.0178523	+	0.0782162i
$557$	−30.7014	+	7.00739i	−1.30086	+	0.296913i	−0.816189	−	0.577784i	$-0.803917\pi$
$557$	−30.7014	+	7.00739i	−1.30086	+	0.296913i	−0.484670	+	0.874697i	$0.661060\pi$
$558$			3.38528i			0.143310i
$559$	−13.4259	−	3.02206i	−0.567855	−	0.127819i
$560$	0.341340	+	1.55771i	0.0144242	+	0.0658252i
$561$	0.528338	+	2.31480i	0.0223064	+	0.0977309i
$562$	7.81816	+	1.78444i	0.329789	+	0.0752722i
$563$	−4.89748	−	10.1697i	−0.206404	−	0.428603i	0.771909	−	0.635733i	$-0.219302\pi$
$563$	−4.89748	−	10.1697i	−0.206404	−	0.428603i	−0.978313	+	0.207130i	$0.933588\pi$
$564$	−1.02852	−	1.28972i	−0.0433085	−	0.0543072i
$565$	−5.40064	−	24.6459i	−0.227206	−	1.03686i
$566$	−0.0274919			−0.00115557
$567$	3.15598	−	2.51681i	0.132539	−	0.105696i
$568$	4.69621	−	9.75178i	0.197049	−	0.409176i
$569$	17.0694	−	21.4043i	0.715586	−	0.897316i	−0.282493	−	0.959269i	$-0.591162\pi$
$569$	17.0694	−	21.4043i	0.715586	−	0.897316i	0.998079	+	0.0619532i	$0.0197330\pi$
$570$	−0.213076	−	0.0505829i	−0.00892478	−	0.00211869i
$571$	−4.07712	−	17.8630i	−0.170622	−	0.747545i	−0.985744	−	0.168255i	$-0.946187\pi$
$571$	−4.07712	−	17.8630i	−0.170622	−	0.747545i	0.815121	−	0.579290i	$-0.196670\pi$
$572$	−7.78021	+	6.20451i	−0.325307	+	0.259424i
$573$	10.7161	−	2.44588i	0.447671	−	0.102178i
$574$	−7.07989	+	3.40949i	−0.295509	+	0.142310i
$575$	29.7017	+	7.32390i	1.23865	+	0.305428i
$576$	−1.62868	+	2.04231i	−0.0678619	+	0.0850961i
$577$	−15.5453	−	3.54811i	−0.647159	−	0.147710i	−0.113672	−	0.993518i	$-0.536261\pi$
$577$	−15.5453	−	3.54811i	−0.647159	−	0.147710i	−0.533487	+	0.845808i	$0.679119\pi$
$578$	−7.09549	−	14.7339i	−0.295134	−	0.612851i
$579$	−11.0865	−	5.33897i	−0.460738	−	0.221880i
$580$	−0.0351383	+	4.04830i	−0.00145904	+	0.168097i
$581$	−2.55555	+	11.1966i	−0.106022	+	0.464513i
$582$	−1.67178	+	3.47148i	−0.0692974	+	0.143897i
$583$	−18.9663	−	39.3839i	−0.785503	−	1.63111i
$584$	2.71771	−	11.9070i	0.112459	−	0.492717i
$585$	10.9979	+	5.41439i	0.454706	+	0.223857i
$586$	−20.4618	+	25.6583i	−0.845269	+	1.05993i
$587$	0.246387	+	0.511628i	0.0101695	+	0.0211172i	0.905992	−	0.423295i	$-0.139127\pi$
$587$	0.246387	+	0.511628i	0.0101695	+	0.0211172i	−0.895822	+	0.444413i	$0.853412\pi$
$588$	−3.94104	+	0.899517i	−0.162526	+	0.0370955i
$589$	0.127078	+	0.159351i	0.00523617	+	0.00656595i
$590$	1.46248	−	0.688720i	0.0602093	−	0.0283542i
$591$	−1.24307	−	0.598629i	−0.0511329	−	0.0246243i
$592$	5.51820	+	4.40062i	0.226797	+	0.180864i
$593$	2.53235	−	5.25849i	0.103991	−	0.215940i	−0.842480	−	0.538727i	$-0.818905\pi$
$593$	2.53235	−	5.25849i	0.103991	−	0.215940i	0.946472	+	0.322787i	$0.104620\pi$
$594$	−10.3324	−	12.9564i	−0.423942	−	0.531606i
$595$	−1.25254	+	0.274468i	−0.0513490	+	0.0112521i
$596$	−10.1992			−0.417776
$597$	−3.41623	+	2.72435i	−0.139817	+	0.111500i
$598$	−5.57114	−	11.5686i	−0.227821	−	0.473075i
$599$	−5.33646	+	23.3805i	−0.218042	+	0.955303i	0.740881	+	0.671636i	$0.234408\pi$
$599$	−5.33646	+	23.3805i	−0.218042	+	0.955303i	−0.958923	+	0.283667i	$0.908449\pi$
$600$	−1.89878	−	2.46768i	−0.0775174	−	0.100743i
$601$	−35.4091			−1.44437			−0.722183	−	0.691702i	$-0.756861\pi$
$601$	−35.4091			−1.44437			−0.722183	+	0.691702i	$0.756861\pi$
$602$	−2.90477	+	3.66495i	−0.118389	+	0.149372i
$603$		−	37.3471i		−	1.52089i
$604$	−3.91699	−	17.1614i	−0.159380	−	0.698289i
$605$	0.222879	−	25.6780i	0.00906132	−	1.04396i
$606$	−2.36823	+	1.14048i	−0.0962029	+	0.0463289i
$607$	5.69196	−	4.53919i	0.231030	−	0.184240i	−0.501132	−	0.865371i	$-0.667083\pi$
$607$	5.69196	−	4.53919i	0.231030	−	0.184240i	0.732162	+	0.681131i	$0.238512\pi$
$608$			0.157273i			0.00637828i
$609$	0.804062			0.0325822
$610$	0.684586	−	0.843322i	0.0277181	−	0.0341451i
$611$	5.00882	+	2.41212i	0.202635	+	0.0975839i
$612$	−1.64220	−	1.30961i	−0.0663818	−	0.0529377i
$613$	−2.39293	+	4.96896i	−0.0966494	+	0.200695i	−0.943688	−	0.330837i	$-0.892669\pi$
$613$	−2.39293	+	4.96896i	−0.0966494	+	0.200695i	0.847039	+	0.531532i	$0.178383\pi$
$614$	−1.58582	−	6.94794i	−0.0639985	−	0.280396i
$615$	9.67009	−	11.9123i	0.389936	−	0.480351i
$616$	0.752476	+	3.29681i	0.0303181	+	0.132832i
$617$	−11.0169	−	22.8767i	−0.443522	−	0.920982i	−0.996159	−	0.0875607i	$-0.972093\pi$
$617$	−11.0169	−	22.8767i	−0.443522	−	0.920982i	0.552637	−	0.833422i	$-0.313621\pi$
$618$	5.99449	+	4.78044i	0.241134	+	0.192298i
$619$	29.8188	−	37.3916i	1.19852	−	1.50290i	0.383421	−	0.923574i	$-0.374746\pi$
$619$	29.8188	−	37.3916i	1.19852	−	1.50290i	0.815099	−	0.579322i	$-0.196683\pi$
$620$	−0.0251515	+	2.89772i	−0.00101011	+	0.116375i
$621$	19.2652	−	9.27761i	0.773084	−	0.372298i
$622$	−9.48571	+	19.6973i	−0.380343	+	0.789789i
$623$	4.94495	+	1.12865i	0.198115	+	0.0452185i
$624$	−0.290812	+	1.27413i	−0.0116418	+	0.0510061i
$625$	−22.8872	+	10.0587i	−0.915487	+	0.402349i
$626$	23.9949	−	11.5553i	0.959030	−	0.461845i
$627$	−0.452756	−	0.103339i	−0.0180813	−	0.00412695i
$628$	2.00347	+	1.59772i	0.0799473	+	0.0637558i
$629$	−3.53849	+	4.43712i	−0.141089	+	0.176920i
$630$	3.27922	−	2.56885i	0.130647	−	0.102345i
$631$	1.05668	+	4.62962i	0.0420658	+	0.184302i	0.991596	−	0.129374i	$-0.0412966\pi$
$631$	1.05668	+	4.62962i	0.0420658	+	0.184302i	−0.949530	+	0.313676i	$0.898439\pi$
$632$	−3.60802	+	2.87730i	−0.143519	+	0.114453i
$633$	0.689573	−	0.157391i	0.0274081	−	0.00625572i
$634$	−6.22782	−	2.99916i	−0.247338	−	0.119112i
$635$	18.3794	+	9.04842i	0.729366	+	0.359076i
$636$	−5.17227	−	2.49084i	−0.205094	−	0.0987681i
$637$	10.6511	−	8.49395i	0.422011	−	0.336543i
$638$			8.58501i			0.339884i
$639$	−28.2736			−1.11849
$640$	−1.40929	+	1.73606i	−0.0557069	+	0.0686239i
$641$	7.07907	−	3.40910i	0.279606	−	0.134651i	−0.288825	−	0.957382i	$-0.593265\pi$
$641$	7.07907	−	3.40910i	0.279606	−	0.134651i	0.568432	+	0.822731i	$0.307550\pi$
$642$	3.84851	+	0.878398i	0.151889	+	0.0346676i
$643$	23.6392	−	5.39549i	0.932239	−	0.212777i	0.270679	−	0.962670i	$-0.412752\pi$
$643$	23.6392	−	5.39549i	0.932239	−	0.212777i	0.661560	+	0.749892i	$0.269895\pi$
$644$	−4.36329			−0.171938
$645$	2.08239	−	8.89039i	0.0819939	−	0.350059i
$646$	−0.126462			−0.00497557
$647$	45.8202	−	10.4582i	1.80138	−	0.411153i	0.815519	−	0.578731i	$-0.196452\pi$
$647$	45.8202	−	10.4582i	1.80138	−	0.411153i	0.985859	+	0.167578i	$0.0535946\pi$
$648$	5.51833	+	1.25952i	0.216781	+	0.0494788i
$649$	3.08849	−	1.48734i	0.121234	−	0.0583831i
$650$	9.37367	+	4.71629i	0.367666	+	0.184988i
$651$	0.575536			0.0225570
$652$		−	6.79468i		−	0.266100i
$653$	−32.9675	+	26.2907i	−1.29012	+	1.02884i	−0.292762	+	0.956185i	$0.594574\pi$
$653$	−32.9675	+	26.2907i	−1.29012	+	1.02884i	−0.997357	+	0.0726510i	$0.976854\pi$
$654$	−5.07016	−	2.44166i	−0.198259	−	0.0954765i
$655$	−15.2527	+	30.9817i	−0.595972	+	1.21056i
$656$	−9.92753	−	4.78085i	−0.387605	−	0.186661i
$657$	−31.1037	+	7.09921i	−1.21347	+	0.276967i
$658$	1.47701	−	1.17787i	0.0575797	−	0.0459183i
$659$	7.35547	+	32.2264i	0.286528	+	1.25536i	0.889254	+	0.457414i	$0.151224\pi$
$659$	7.35547	+	32.2264i	0.286528	+	1.25536i	−0.602725	+	0.797949i	$0.705919\pi$
$660$	−4.07176	−	5.19773i	−0.158493	−	0.202322i
$661$	−7.46362	+	9.35908i	−0.290301	+	0.364026i	−0.905500	−	0.424346i	$-0.860504\pi$
$661$	−7.46362	+	9.35908i	−0.290301	+	0.364026i	0.615199	+	0.788372i	$0.289076\pi$
$662$	9.09961	+	7.25670i	0.353667	+	0.282040i
$663$	−1.02451	−	0.233839i	−0.0397889	−	0.00908155i
$664$	−14.5090	+	6.98717i	−0.563058	+	0.271155i
$665$	0.0579281	−	0.244017i	0.00224636	−	0.00946258i
$666$	4.10263	−	17.9748i	0.158974	−	0.696510i
$667$	−10.7996	−	2.46493i	−0.418161	−	0.0954424i
$668$	−1.89278	+	3.93041i	−0.0732340	+	0.152072i
$669$	7.70004	−	3.70814i	0.297701	−	0.143365i
$670$	0.277476	−	31.9682i	0.0107198	−	1.23504i
$671$	1.43613	−	1.80085i	0.0554413	−	0.0695212i
$672$	0.347215	+	0.276895i	0.0133941	+	0.0106814i
$673$	0.109187	+	0.226729i	0.00420885	+	0.00873978i	0.903063	−	0.429509i	$-0.141313\pi$
$673$	0.109187	+	0.226729i	0.00420885	+	0.00873978i	−0.898854	+	0.438249i	$0.855599\pi$
$674$	6.26761	+	27.4602i	0.241419	+	1.05773i
$675$	−7.85402	+	15.6100i	−0.302302	+	0.600828i
$676$	1.91271	+	8.38012i	0.0735657	+	0.322312i
$677$	7.75622	−	16.1060i	0.298096	−	0.619002i	−0.697093	−	0.716981i	$-0.745523\pi$
$677$	7.75622	−	16.1060i	0.298096	−	0.619002i	0.995189	+	0.0979787i	$0.0312377\pi$
$678$	−5.49359	−	4.38099i	−0.210980	−	0.168251i
$679$	−3.97558	−	1.91454i	−0.152569	−	0.0734732i
$680$	−1.39595	−	1.13319i	−0.0535322	−	0.0434559i
$681$	−7.55502			−0.289509
$682$			6.14503i			0.235305i
$683$	−8.81154	+	7.02697i	−0.337164	+	0.268880i	−0.777405	−	0.629000i	$-0.783464\pi$
$683$	−8.81154	+	7.02697i	−0.337164	+	0.268880i	0.440241	+	0.897880i	$0.354893\pi$
$684$	0.370146	−	0.178253i	0.0141529	−	0.00681566i
$685$	−37.1927	−	0.322824i	−1.42106	−	0.0123345i
$686$	−2.14098	−	9.38026i	−0.0817432	−	0.358140i
$687$			14.7402i			0.562375i
$688$	−6.55741	+	0.0196588i	−0.249999	+	0.000749483i
$689$	19.3470			0.737062
$690$	7.70760	−	3.62971i	0.293423	−	0.138181i
$691$	7.49011	−	32.8163i	0.284937	−	1.24839i	−0.606440	−	0.795129i	$-0.707403\pi$
$691$	7.49011	−	32.8163i	0.284937	−	1.24839i	0.891377	−	0.453262i	$-0.149740\pi$
$692$	−1.21805	−	2.52931i	−0.0463033	−	0.0961498i
$693$	6.90626	−	5.50756i	0.262347	−	0.209215i
$694$	27.8013			1.05532
$695$	4.13202	−	0.905447i	0.156736	−	0.0343456i
$696$	0.702965	+	0.881490i	0.0266458	+	0.0334128i
$697$	3.84423	−	7.98262i	0.145610	−	0.302363i
$698$	8.59299	+	6.85268i	0.325249	+	0.259378i
$699$	1.56482	+	0.753579i	0.0591870	+	0.0285030i
$700$	2.82602	−	2.17450i	0.106813	−	0.0821885i
$701$	6.08687	+	7.63270i	0.229898	+	0.288283i	0.883378	−	0.468661i	$-0.155263\pi$
$701$	6.08687	+	7.63270i	0.229898	+	0.288283i	−0.653480	+	0.756943i	$0.726692\pi$
$702$	7.15069	−	1.63210i	0.269885	−	0.0615996i
$703$	−0.481629	−	1.00011i	−0.0181650	−	0.0377200i
$704$	−2.95642	+	3.70723i	−0.111424	+	0.139722i
$705$	−1.62923	+	3.30935i	−0.0613605	+	0.124637i
$706$	5.92246	−	25.9480i	0.222895	−	0.976565i
$707$	−1.30609	−	2.71213i	−0.0491206	−	0.102000i
$708$	0.195332	−	0.405611i	0.00734102	−	0.0152438i
$709$	10.0077	−	43.8467i	0.375848	−	1.64670i	−0.334170	−	0.942513i	$-0.608456\pi$
$709$	10.0077	−	43.8467i	0.375848	−	1.64670i	0.710018	−	0.704184i	$-0.248687\pi$
$710$	−24.2015	−	0.210063i	−0.908267	−	0.00788354i
$711$	10.8611	+	5.23042i	0.407323	+	0.196156i
$712$	3.08587	+	6.40788i	0.115648	+	0.240145i
$713$	−7.73016	−	1.76436i	−0.289497	−	0.0660758i
$714$	−0.222648	+	0.279192i	−0.00833239	+	0.0104485i
$715$	19.9635	+	9.82830i	0.746594	+	0.367557i
$716$	−6.80902	+	3.27905i	−0.254465	+	0.122544i
$717$	−6.09879	+	1.39201i	−0.227764	+	0.0519855i
$718$	24.6594	−	19.6652i	0.920281	−	0.733899i
$719$	9.88669	+	43.3164i	0.368711	+	1.61543i	0.730324	+	0.683101i	$0.239369\pi$
$719$	9.88669	+	43.3164i	0.368711	+	1.61543i	−0.361612	+	0.932328i	$0.617774\pi$
$720$	5.68313	+	1.34914i	0.211798	+	0.0502794i
$721$	−5.47462	+	6.86495i	−0.203885	+	0.255664i
$722$	−8.23306	+	17.0961i	−0.306403	+	0.636252i
$723$	−0.241485	+	0.192577i	−0.00898091	+	0.00716203i
$724$	−9.85843			−0.366386
$725$	8.22308	−	3.78562i	0.305398	−	0.140594i
$726$	−4.45884	−	5.59121i	−0.165483	−	0.207509i
$727$	−20.1374	−	41.8158i	−0.746856	−	1.55086i	−0.832177	−	0.554510i	$-0.812906\pi$
$727$	−20.1374	−	41.8158i	−0.746856	−	1.55086i	0.0853207	−	0.996354i	$-0.472809\pi$
$728$	−1.45915	−	0.333041i	−0.0540796	−	0.0123433i
$729$	−1.83727	−	8.04961i	−0.0680471	−	0.298134i
$730$	−26.6767	+	5.84566i	−0.987349	+	0.216357i
$731$	−0.0158074	−	5.27274i	−0.000584657	−	0.195019i
$732$		−	0.302502i		−	0.0111808i
$733$	34.1602	−	7.79684i	1.26174	−	0.287983i	0.461215	−	0.887288i	$-0.347414\pi$
$733$	34.1602	−	7.79684i	1.26174	−	0.287983i	0.800520	+	0.599305i	$0.204556\pi$
$734$	−7.75884	+	33.9937i	−0.286384	+	1.25473i
$735$	5.57422	+	7.11568i	0.205608	+	0.262466i
$736$	−3.81468	−	4.78346i	−0.140611	−	0.176321i
$737$		−	67.7932i		−	2.49720i
$738$			28.7832i			1.05952i
$739$	−30.2408	−	37.9208i	−1.11243	−	1.39494i	−0.909479	−	0.415749i	$-0.863519\pi$
$739$	−30.2408	−	37.9208i	−1.11243	−	1.39494i	−0.202948	−	0.979190i	$-0.565052\pi$
$740$	3.64530	−	15.3555i	0.134004	−	0.564479i
$741$	0.128152	−	0.160698i	0.00470779	−	0.00590338i
$742$	2.85253	−	5.92335i	0.104720	−	0.217453i
$743$	−26.9356	+	6.14787i	−0.988171	+	0.225544i	−0.685914	−	0.727683i	$-0.740597\pi$
$743$	−26.9356	+	6.14787i	−0.988171	+	0.225544i	−0.302257	+	0.953226i	$0.597740\pi$
$744$	0.503172	+	0.630958i	0.0184472	+	0.0231320i
$745$	9.71649	+	20.6327i	0.355985	+	0.755924i
$746$	−17.7299	+	8.53827i	−0.649137	+	0.312608i
$747$	32.8888	+	26.2280i	1.20334	+	0.959631i
$748$	−2.98095	−	2.37722i	−0.108994	−	0.0869199i
$749$	−1.00595	+	4.40736i	−0.0367566	+	0.161041i
$750$	−3.18314	+	6.19207i	−0.116232	+	0.226102i
$751$	−40.4049	−	19.4580i	−1.47440	−	0.710032i	−0.487761	−	0.872977i	$-0.662186\pi$
$751$	−40.4049	−	19.4580i	−1.47440	−	0.710032i	−0.986635	+	0.162946i	$0.947901\pi$
$752$	2.58260	+	0.589460i	0.0941776	+	0.0214954i
$753$	0.255942	+	0.0584172i	0.00932706	+	0.00212884i
$754$	−3.42339	−	1.64862i	−0.124672	−	0.0600390i
$755$	−30.9855	+	24.2732i	−1.12768	+	0.883391i
$756$	0.554613	−	2.42992i	0.0201711	−	0.0883752i
$757$	−22.0873	−	17.6140i	−0.802775	−	0.640192i	0.133662	−	0.991027i	$-0.457326\pi$
$757$	−22.0873	−	17.6140i	−0.802775	−	0.640192i	−0.936437	+	0.350835i	$0.885898\pi$
$758$	22.3813	+	17.8485i	0.812925	+	0.648286i
$759$	16.2770	−	7.83861i	0.590819	−	0.284523i
$760$	0.318160	−	0.149830i	0.0115409	−	0.00543490i
$761$	−16.4418	−	20.6173i	−0.596014	−	0.747378i	0.388737	−	0.921349i	$-0.372912\pi$
$761$	−16.4418	−	20.6173i	−0.596014	−	0.747378i	−0.984751	+	0.173971i	$0.944340\pi$
$762$	5.56218	−	1.26953i	0.201497	−	0.0459903i
$763$	2.79622	−	5.80640i	0.101230	−	0.210206i
$764$	−11.0051	+	13.7999i	−0.398150	+	0.499264i
$765$	−1.08483	+	4.56974i	−0.0392220	+	0.165219i
$766$	10.5407	+	13.2176i	0.380852	+	0.477573i
$767$			1.51720i			0.0547827i
$768$			0.622730i			0.0224708i
$769$	−17.5100	−	21.9568i	−0.631425	−	0.791782i	0.358476	−	0.933539i	$-0.383296\pi$
$769$	−17.5100	−	21.9568i	−0.631425	−	0.791782i	−0.989902	+	0.141757i	$0.954725\pi$
$770$	5.95250	−	4.66302i	0.214513	−	0.168044i
$771$	−0.509702	+	2.23315i	−0.0183565	+	0.0804249i
$772$	19.2644	−	4.39698i	0.693343	−	0.158251i
$773$			28.5618i			1.02730i	0.858000	+	0.513649i	$0.171707\pi$
$773$			28.5618i			1.02730i	−0.858000	+	0.513649i	$0.828293\pi$
$774$	7.47840	+	15.4107i	0.268805	+	0.553926i
$775$	5.88596	−	2.70969i	0.211430	−	0.0973349i
$776$	−1.37682	−	6.03223i	−0.0494248	−	0.216544i
$777$	−3.05592	−	0.697493i	−0.109630	−	0.0250224i
$778$	5.98314	+	12.4241i	0.214506	+	0.445427i
$779$	1.08048	+	1.35488i	0.0387121	+	0.0485435i
$780$	2.85458	−	0.625523i	0.102210	−	0.0223973i
$781$	−51.3228			−1.83648
$782$	3.84633	−	3.06735i	0.137544	−	0.109688i
$783$	2.74544	−	5.70096i	0.0981139	−	0.203736i
$784$	4.04733	−	5.07519i	0.144547	−	0.181257i
$785$	1.32349	−	5.57507i	0.0472372	−	0.198983i
$786$	2.14002	+	9.37603i	0.0763319	+	0.334432i
$787$	5.45471	−	4.34998i	0.194439	−	0.155060i	−0.521431	−	0.853293i	$-0.674602\pi$
$787$	5.45471	−	4.34998i	0.194439	−	0.155060i	0.715870	+	0.698233i	$0.246030\pi$
$788$	2.16002	−	0.493010i	0.0769474	−	0.0175627i
$789$	−8.76135	+	4.21924i	−0.311912	+	0.150209i
$790$	9.25796	+	4.55781i	0.329383	+	0.162159i
$791$	5.01716	−	6.29132i	0.178390	−	0.223694i
$792$	12.0758	+	2.75623i	0.429096	+	0.0979383i
$793$	0.442327	+	0.918502i	0.0157075	+	0.0326169i
$794$	26.5337	+	12.7780i	0.941647	+	0.453473i
$795$	−0.111416	+	12.8363i	−0.00395152	+	0.455257i
$796$	1.56137	−	6.84079i	0.0553412	−	0.242465i
$797$	−21.9306	+	45.5393i	−0.776820	+	1.61308i	0.0131310	+	0.999914i	$0.495820\pi$
$797$	−21.9306	+	45.5393i	−0.776820	+	1.61308i	−0.789951	+	0.613170i	$0.789894\pi$
$798$	−0.0303050	−	0.0629289i	−0.00107278	−	0.00222766i
$799$	−0.473979	+	2.07664i	−0.0167682	+	0.0734661i
$800$	4.85459	+	1.19705i	0.171636	+	0.0423222i
$801$	11.5835	−	14.5253i	0.409284	−	0.513226i
$802$	3.95505	+	8.21276i	0.139658	+	0.290002i
$803$	−56.4600	+	12.8866i	−1.99243	+	0.454759i
$804$	−5.55110	−	6.96086i	−0.195772	−	0.245490i
$805$	4.15678	+	8.82682i	0.146507	+	0.311105i
$806$	−2.45041	−	1.18005i	−0.0863120	−	0.0415657i
$807$	8.31413	+	6.63030i	0.292671	+	0.233398i
$808$	1.83142	−	3.80298i	0.0644291	−	0.133789i
$809$	14.8993	+	18.6832i	0.523833	+	0.656866i	0.971418	−	0.237375i	$-0.0762872\pi$
$809$	14.8993	+	18.6832i	0.523833	+	0.656866i	−0.447585	+	0.894241i	$0.647716\pi$
$810$	−2.70918	−	12.3633i	−0.0951907	−	0.434404i
$811$	−17.7028			−0.621629			−0.310815	−	0.950471i	$-0.600602\pi$
$811$	−17.7028			−0.621629			−0.310815	+	0.950471i	$0.600602\pi$
$812$	−1.00949	+	0.805043i	−0.0354262	+	0.0282515i
$813$	−3.17240	−	6.58755i	−0.111261	−	0.231036i
$814$	7.44718	−	32.6282i	0.261023	−	1.14362i
$815$	−13.7454	+	6.47309i	−0.481482	+	0.226743i
$816$	−0.500731			−0.0175291
$817$	0.930516	+	0.444681i	0.0325546	+	0.0155574i
$818$		−	14.6326i		−	0.511618i
$819$	0.869972	+	3.81160i	0.0303993	+	0.133188i
$820$	−0.213849	+	24.6377i	−0.00746794	+	0.860385i
$821$	21.1255	−	10.1735i	0.737286	−	0.355058i	−0.0272590	−	0.999628i	$-0.508678\pi$
$821$	21.1255	−	10.1735i	0.737286	−	0.355058i	0.764545	+	0.644570i	$0.222964\pi$
$822$	−8.09846	+	6.45831i	−0.282466	+	0.225259i
$823$		−	22.0760i		−	0.769520i	−0.923017	−	0.384760i	$-0.874284\pi$
$823$		−	22.0760i		−	0.769520i	0.923017	−	0.384760i	$-0.125716\pi$
$824$	−12.3123			−0.428919
$825$	−6.63583	+	13.1888i	−0.231030	+	0.459174i
$826$	0.464510	+	0.223696i	0.0161624	+	0.00778338i
$827$	10.5843	+	8.44069i	0.368052	+	0.293511i	0.789998	−	0.613109i	$-0.210082\pi$
$827$	10.5843	+	8.44069i	0.368052	+	0.293511i	−0.421946	+	0.906621i	$0.638653\pi$
$828$	−6.93442	+	14.3995i	−0.240988	+	0.500416i
$829$	2.72647	+	11.9455i	0.0946943	+	0.414883i	0.999950	−	0.00998398i	$-0.00317805\pi$
$829$	2.72647	+	11.9455i	0.0946943	+	0.414883i	−0.905256	+	0.424867i	$0.860321\pi$
$830$	27.9572	+	22.6948i	0.970407	+	0.787749i
$831$	−3.03343	−	13.2903i	−0.105228	−	0.461036i
$832$	−0.910574	−	1.89083i	−0.0315685	−	0.0655526i
$833$	4.08090	+	3.25441i	0.141395	+	0.112759i
$834$	0.734498	−	0.921031i	0.0254336	−	0.0318927i
$835$	9.75430	+	0.0846650i	0.337562	+	0.00292995i
$836$	0.671895	−	0.323568i	0.0232380	−	0.0111908i
$837$	1.96514	−	4.08066i	0.0679253	−	0.141048i
$838$	17.2257	+	3.93165i	0.595051	+	0.135817i
$839$	−1.13153	+	4.95758i	−0.0390649	+	0.171155i	−0.990697	−	0.136085i	$-0.956548\pi$
$839$	−1.13153	+	4.95758i	−0.0390649	+	0.171155i	0.951632	+	0.307239i	$0.0994052\pi$
$840$	0.229369	−	0.966196i	0.00791397	−	0.0333369i
$841$	23.1747	−	11.1604i	0.799128	−	0.384840i
$842$	27.6190	+	6.30385i	0.951813	+	0.217245i
$843$	−3.90432	−	3.11359i	−0.134472	−	0.107238i
$844$	−0.708170	+	0.888017i	−0.0243762	+	0.0305668i
$845$	15.1306	−	11.8529i	0.520508	−	0.407751i
$846$	−1.53979	−	6.74627i	−0.0529392	−	0.231942i
$847$	6.40311	−	5.10631i	0.220014	−	0.175455i
$848$	8.98761	−	2.05136i	0.308636	−	0.0704441i
$849$	0.0154246	+	0.00742811i	0.000529372	+	0.000254932i
$850$	−0.962537	+	3.90353i	−0.0330147	+	0.133890i
$851$	38.9066	+	18.7364i	1.33370	+	0.642276i
$852$	−5.26971	+	4.20246i	−0.180537	+	0.143974i
$853$			29.0254i			0.993812i	0.867804	+	0.496906i	$0.165531\pi$
$853$			29.0254i			0.993812i	−0.867804	+	0.496906i	$0.834469\pi$
$854$	0.346429			0.0118545
$855$	−0.713228	−	0.578978i	−0.0243919	−	0.0198006i
$856$	−5.71124	+	2.75039i	−0.195206	+	0.0940063i
$857$	−27.5551	−	6.28926i	−0.941263	−	0.214837i	−0.275755	−	0.961228i	$-0.588928\pi$
$857$	−27.5551	−	6.28926i	−0.941263	−	0.214837i	−0.665508	+	0.746391i	$0.731785\pi$
$858$	6.04158	−	1.37895i	0.206256	−	0.0470766i
$859$	23.5557			0.803712			0.401856	−	0.915703i	$-0.368365\pi$
$859$	23.5557			0.803712			0.401856	+	0.915703i	$0.368365\pi$
$860$	6.28682	+	13.2467i	0.214379	+	0.451710i
$861$	4.89347			0.166769
$862$	5.86406	−	1.33843i	0.199731	−	0.0455872i
$863$	−10.0126	−	2.28531i	−0.340833	−	0.0777930i	0.0486784	−	0.998815i	$-0.484499\pi$
$863$	−10.0126	−	2.28531i	−0.340833	−	0.0777930i	−0.389512	+	0.921022i	$0.627356\pi$
$864$	3.14879	−	1.51638i	0.107124	−	0.0515882i
$865$	−3.95632	+	4.87368i	−0.134519	+	0.165710i
$866$	37.8635			1.28666
$867$			10.1838i			0.345859i
$868$	−0.722579	+	0.576238i	−0.0245259	+	0.0195588i
$869$	19.7152	+	9.49436i	0.668794	+	0.322074i
$870$	1.11354	−	2.26185i	0.0377524	−	0.0766838i
$871$	27.0334	+	13.0186i	0.915993	+	0.441119i
$872$	8.81017	−	2.01086i	0.298350	−	0.0680965i
$873$	−12.6365	+	10.0773i	−0.427680	+	0.341063i
$874$	0.214119	+	0.938117i	0.00724268	+	0.0317323i
$875$	−7.09123	−	3.64536i	−0.239727	−	0.123236i
$876$	−4.74199	+	5.94627i	−0.160217	+	0.200906i
$877$	−29.8392	−	23.7960i	−1.00760	−	0.803534i	−0.0270160	−	0.999635i	$-0.508600\pi$
$877$	−29.8392	−	23.7960i	−1.00760	−	0.803534i	−0.980584	+	0.196101i	$0.937172\pi$
$878$	−18.0014	−	4.10870i	−0.607517	−	0.138662i
$879$	18.4130	−	8.86722i	0.621054	−	0.299084i
$880$	10.3161	+	2.44898i	0.347756	+	0.0825551i
$881$	1.12038	−	4.90872i	0.0377466	−	0.165379i	−0.952542	−	0.304409i	$-0.901541\pi$
$881$	1.12038	−	4.90872i	0.0377466	−	0.165379i	0.990288	+	0.139030i	$0.0443983\pi$
$882$	−16.5318	−	3.77327i	−0.556653	−	0.127052i
$883$	−3.96926	+	8.24225i	−0.133576	+	0.277374i	−0.957019	−	0.290026i	$-0.906336\pi$
$883$	−3.96926	+	8.24225i	−0.133576	+	0.277374i	0.823443	+	0.567399i	$0.192050\pi$
$884$	1.52039	−	0.732182i	0.0511363	−	0.0246260i
$885$	−1.00663	−	0.00873728i	−0.0338374	−	0.000293700i
$886$	−1.28148	+	1.60692i	−0.0430520	+	0.0539855i
$887$	31.6800	+	25.2639i	1.06371	+	0.848280i	0.988850	−	0.148914i	$-0.0475779\pi$
$887$	31.6800	+	25.2639i	1.06371	+	0.848280i	0.0748591	+	0.997194i	$0.476149\pi$
$888$	−1.90703	−	3.95999i	−0.0639957	−	0.132888i
$889$	1.45388	+	6.36987i	0.0487616	+	0.213639i
$890$	10.0231	−	12.3472i	0.335976	−	0.413880i
$891$	−5.97232	−	26.1664i	−0.200080	−	0.876609i
$892$	−5.95466	+	12.3650i	−0.199377	+	0.414010i
$893$	−0.325726	−	0.259758i	−0.0109000	−	0.00869246i
$894$	5.72237	+	2.75575i	0.191385	+	0.0921660i
$895$	13.1202	+	10.6506i	0.438559	+	0.356010i
$896$	−0.713157			−0.0238249
$897$			7.99596i			0.266977i
$898$	−7.75513	+	6.18451i	−0.258792	+	0.206380i
$899$	−2.11398	+	1.01804i	−0.0705052	+	0.0339535i
$900$	−2.68488	−	12.7821i	−0.0894961	−	0.426070i
$901$	1.64948	+	7.22684i	0.0549521	+	0.240761i
$902$			52.2478i			1.73966i
$903$	2.61999	−	1.27141i	0.0871878	−	0.0423099i
$904$	11.2835			0.375283
$905$	9.39184	+	19.9433i	0.312195	+	0.662939i
$906$	−2.43923	+	10.6869i	−0.0810378	+	0.355050i
$907$	−15.5515	−	32.2929i	−0.516378	−	1.07227i	−0.982278	−	0.187432i	$-0.939984\pi$
$907$	−15.5515	−	32.2929i	−0.516378	−	1.07227i	0.465900	−	0.884837i	$-0.345731\pi$
$908$	9.48526	−	7.56424i	0.314779	−	0.251028i
$909$	−11.0261			−0.365713
$910$	0.716356	+	3.26910i	0.0237470	+	0.108369i
$911$	18.2248	+	22.8532i	0.603815	+	0.757160i	0.985967	−	0.166940i	$-0.0533885\pi$
$911$	18.2248	+	22.8532i	0.603815	+	0.757160i	−0.382152	+	0.924099i	$0.624817\pi$
$912$	0.0424941	−	0.0882399i	0.00140712	−	0.00292191i
$913$	59.7004	+	47.6095i	1.97580	+	1.57564i
$914$	22.3918	+	10.7833i	0.740654	+	0.356680i
$915$	−0.611953	+	0.288185i	−0.0202306	+	0.00952710i
$916$	−14.7582	−	18.5062i	−0.487625	−	0.611462i
$917$	−10.7375	+	2.45077i	−0.354585	+	0.0809316i
$918$	1.21930	+	2.53191i	0.0402429	+	0.0835653i
$919$	−1.12822	+	1.41475i	−0.0372167	+	0.0466682i	−0.800092	−	0.599878i	$-0.795216\pi$
$919$	−1.12822	+	1.41475i	−0.0372167	+	0.0466682i	0.762875	+	0.646546i	$0.223787\pi$
$920$	−6.04267	+	12.2741i	−0.199221	+	0.404664i
$921$	−0.987539	+	4.32669i	−0.0325405	+	0.142569i
$922$	−13.0813	−	27.1636i	−0.430810	−	0.894587i
$923$	9.85574	−	20.4656i	0.324406	−	0.673635i
$924$	0.468590	−	2.05303i	0.0154155	−	0.0675396i
$925$	−34.5365	+	7.25441i	−1.13555	+	0.238523i
$926$	8.86392	+	4.26864i	0.291287	+	0.140276i
$927$	13.9547	+	28.9772i	0.458332	+	0.951736i
$928$	−1.76513	−	0.402880i	−0.0579433	−	0.0132252i
$929$	−25.9165	+	32.4983i	−0.850293	+	1.06623i	0.146733	+	0.989176i	$0.453124\pi$
$929$	−25.9165	+	32.4983i	−0.850293	+	1.06623i	−0.997027	+	0.0770581i	$0.975447\pi$
$930$	0.797052	−	1.61900i	0.0261364	−	0.0530890i
$931$	−0.919822	+	0.442963i	−0.0301460	+	0.0145175i
$932$	−2.71912	+	0.620621i	−0.0890676	+	0.0203291i
$933$	10.6441	−	8.48840i	0.348473	−	0.277898i
$934$	1.60239	+	7.02052i	0.0524318	+	0.229719i
$935$	−1.96920	+	8.29508i	−0.0643997	+	0.271278i
$936$	−3.41805	+	4.28610i	−0.111723	+	0.140096i
$937$	7.22426	−	15.0013i	0.236006	−	0.490072i	−0.749004	−	0.662565i	$-0.769468\pi$
$937$	7.22426	−	15.0013i	0.236006	−	0.490072i	0.985011	+	0.172493i	$0.0551822\pi$
$938$	7.97165	−	6.35718i	0.260284	−	0.207569i
$939$	−16.5848			−0.541224
$940$	−1.26790	−	5.78608i	−0.0413544	−	0.188721i
$941$	16.4317	+	20.6047i	0.535659	+	0.671695i	0.973851	−	0.227186i	$-0.0729526\pi$
$941$	16.4317	+	20.6047i	0.535659	+	0.671695i	−0.438192	+	0.898881i	$0.644381\pi$
$942$	−0.692379	−	1.43774i	−0.0225589	−	0.0468441i
$943$	−65.7254	−	15.0014i	−2.14031	−	0.488512i
$944$	0.160868	+	0.704810i	0.00523582	+	0.0229396i
$945$	−5.44402	+	1.19295i	−0.177094	+	0.0388065i
$946$	13.5749	+	27.9738i	0.441359	+	0.909506i
$947$		−	44.8607i		−	1.45778i	−0.684632	−	0.728889i	$-0.740037\pi$
$947$		−	44.8607i		−	1.45778i	0.684632	−	0.728889i	$-0.259963\pi$
$948$	2.80174	−	0.639479i	0.0909964	−	0.0207693i
$949$	5.70353	−	24.9888i	0.185145	−	0.811171i
$950$	−0.606203	−	0.500890i	−0.0196678	−	0.0162510i
$951$	2.68383	+	3.36542i	0.0870293	+	0.109131i
$952$		−	0.573442i		−	0.0185854i
$953$			42.0305i			1.36150i	0.732516	+	0.680750i	$0.238346\pi$
$953$			42.0305i			1.36150i	−0.732516	+	0.680750i	$0.761654\pi$
$954$	−15.0144	−	18.8275i	−0.486110	−	0.609563i
$955$	38.4011	+	9.11618i	1.24263	+	0.294993i
$956$	6.26326	−	7.85389i	0.202568	−	0.254013i
$957$	2.31961	−	4.81671i	0.0749822	−	0.155702i
$958$	−17.4144	+	3.97472i	−0.562634	+	0.128417i
$959$	−7.39612	−	9.27445i	−0.238833	−	0.299488i
$960$	1.25977	−	0.593257i	0.0406588	−	0.0191473i
$961$	26.4169	−	12.7217i	0.852157	−	0.410377i
$962$	11.5808	+	9.23539i	0.373380	+	0.297761i
$963$	12.9462	+	10.3242i	0.417185	+	0.332694i
$964$	0.110369	−	0.483558i	0.00355475	−	0.0155744i
$965$	−27.2477	−	34.7826i	−0.877133	−	1.11969i
$966$	2.44807	+	1.17893i	0.0787654	+	0.0379314i
$967$	15.0585	+	3.43701i	0.484250	+	0.110527i	0.457674	−	0.889120i	$-0.348683\pi$
$967$	15.0585	+	3.43701i	0.484250	+	0.110527i	0.0265756	+	0.999647i	$0.491540\pi$
$968$	11.1961	+	2.55543i	0.359855	+	0.0821345i
$969$	0.0709527	+	0.0341690i	0.00227933	+	0.00109767i
$970$	−10.8914	+	8.53199i	−0.349701	+	0.273946i
$971$	0.919087	−	4.02678i	0.0294949	−	0.129226i	−0.958037	−	0.286644i	$-0.907460\pi$
$971$	0.919087	−	4.02678i	0.0294949	−	0.129226i	0.987532	+	0.157419i	$0.0503173\pi$
$972$	−10.9531	−	8.73477i	−0.351319	−	0.280168i
$973$	1.05478	+	0.841155i	0.0338145	+	0.0269662i
$974$	−12.2445	+	5.89662i	−0.392338	+	0.188940i
$975$	−3.98489	−	5.17882i	−0.127619	−	0.165855i
$976$	0.302871	+	0.379788i	0.00969467	+	0.0121567i
$977$	−8.85459	+	2.02100i	−0.283283	+	0.0646576i	−0.361802	−	0.932255i	$-0.617838\pi$
$977$	−8.85459	+	2.02100i	−0.283283	+	0.0646576i	0.0785183	+	0.996913i	$0.474981\pi$
$978$	−1.83587	+	3.81222i	−0.0587047	+	0.121901i
$979$	21.0267	−	26.3666i	0.672015	−	0.842680i
$980$	−14.1227	−	3.35265i	−0.451134	−	0.107096i
$981$	−14.7180	−	18.4558i	−0.469910	−	0.589248i
$982$			25.5816i			0.816342i
$983$			39.8220i			1.27013i	0.772461	+	0.635063i	$0.219026\pi$
$983$			39.8220i			1.27013i	−0.772461	+	0.635063i	$0.780974\pi$
$984$	4.27819	+	5.36469i	0.136384	+	0.171020i
$985$	−3.05513	−	3.89998i	−0.0973445	−	0.124264i
$986$	0.323951	−	1.41932i	0.0103167	−	0.0452004i
$987$	−1.14694	+	0.261782i	−0.0365076	+	0.00833262i
$988$			0.330063i			0.0105007i
$989$	−39.0874	+	9.04481i	−1.24291	+	0.287608i
$990$	−5.92852	−	27.0548i	−0.188421	−	0.859859i
$991$	9.71725	+	42.5741i	0.308679	+	1.35241i	0.856644	+	0.515909i	$0.172546\pi$
$991$	9.71725	+	42.5741i	0.308679	+	1.35241i	−0.547965	+	0.836501i	$0.684597\pi$
$992$	−1.26345	−	0.288375i	−0.0401147	−	0.00915592i
$993$	−3.14473	−	6.53009i	−0.0997949	−	0.207226i
$994$	−4.81270	−	6.03493i	−0.152650	−	0.191416i
$995$	−15.3262	+	3.35842i	−0.485873	+	0.106469i
$996$	10.0283			0.317759
$997$	19.4702	−	15.5270i	0.616628	−	0.491745i	−0.264649	−	0.964345i	$-0.585256\pi$
$997$	19.4702	−	15.5270i	0.616628	−	0.491745i	0.881277	+	0.472600i	$0.156685\pi$
$998$	8.36609	−	17.3724i	0.264824	−	0.549913i
$999$	−15.3797	+	19.2855i	−0.486591	+	0.610166i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.p.a.59.16	yes	132
5.4	even	2	inner	430.2.p.a.59.7	✓	132
43.35	even	7	inner	430.2.p.a.379.7	yes	132
215.164	even	14	inner	430.2.p.a.379.16	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.p.a.59.7	✓	132	5.4	even	2	inner
430.2.p.a.59.16	yes	132	1.1	even	1	trivial
430.2.p.a.379.7	yes	132	43.35	even	7	inner
430.2.p.a.379.16	yes	132	215.164	even	14	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.p (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.974928 - 0.222521i) q^{2} +(-0.607117 - 0.138570i) q^{3} +(0.900969 - 0.433884i) q^{4} +(-1.73606 - 1.40929i) q^{5} -0.622730 q^{6} -0.713157i q^{7} +(0.781831 - 0.623490i) q^{8} +(-2.35352 - 1.13339i) q^{9} +O(q^{10})\)	\(q+(0.974928 - 0.222521i) q^{2} +(-0.607117 - 0.138570i) q^{3} +(0.900969 - 0.433884i) q^{4} +(-1.73606 - 1.40929i) q^{5} -0.622730 q^{6} -0.713157i q^{7} +(0.781831 - 0.623490i) q^{8} +(-2.35352 - 1.13339i) q^{9} +(-2.00613 - 0.987643i) q^{10} +(-4.27215 - 2.05736i) q^{11} +(-0.607117 + 0.138570i) q^{12} +(1.64080 - 1.30849i) q^{13} +(-0.158692 - 0.695277i) q^{14} +(0.858707 + 1.09617i) q^{15} +(0.623490 - 0.781831i) q^{16} +(0.628662 + 0.501341i) q^{17} +(-2.54671 - 0.581271i) q^{18} +(-0.141698 + 0.0682384i) q^{19} +(-2.17560 - 0.516474i) q^{20} +(-0.0988226 + 0.432970i) q^{21} +(-4.62284 - 1.05513i) q^{22} +(2.65462 - 5.51238i) q^{23} +(-0.561060 + 0.270192i) q^{24} +(1.02782 + 4.89322i) q^{25} +(1.30849 - 1.64080i) q^{26} +(2.73242 + 2.17903i) q^{27} +(-0.309427 - 0.642533i) q^{28} +(-0.402880 - 1.76513i) q^{29} +(1.08110 + 0.877605i) q^{30} +(-0.288375 - 1.26345i) q^{31} +(0.433884 - 0.900969i) q^{32} +(2.30861 + 1.84105i) q^{33} +(0.724459 + 0.348881i) q^{34} +(-1.00504 + 1.23809i) q^{35} -2.61221 q^{36} +7.05804i q^{37} +(-0.122961 + 0.0980584i) q^{38} +(-1.17747 + 0.567042i) q^{39} +(-2.23598 - 0.0194078i) q^{40} +(-2.45190 - 10.7425i) q^{41} +0.444105i q^{42} +(-4.10385 - 5.11453i) q^{43} -4.74173 q^{44} +(2.48857 + 5.28442i) q^{45} +(1.36144 - 5.96488i) q^{46} +(1.14936 + 2.38668i) q^{47} +(-0.486870 + 0.388266i) q^{48} +6.49141 q^{49} +(2.09090 + 4.54182i) q^{50} +(-0.312200 - 0.391487i) q^{51} +(0.910574 - 1.89083i) q^{52} +(7.20751 + 5.74780i) q^{53} +(3.14879 + 1.51638i) q^{54} +(4.51731 + 9.59239i) q^{55} +(-0.444646 - 0.557569i) q^{56} +(0.0954833 - 0.0217935i) q^{57} +(-0.785557 - 1.63123i) q^{58} +(-0.450743 + 0.565214i) q^{59} +(1.24928 + 0.615035i) q^{60} +(-0.108093 + 0.473588i) q^{61} +(-0.562290 - 1.16761i) q^{62} +(-0.808288 + 1.67843i) q^{63} +(0.222521 - 0.974928i) q^{64} +(-4.69257 - 0.0407303i) q^{65} +(2.66040 + 1.28118i) q^{66} +(6.20330 + 12.8813i) q^{67} +(0.783929 + 0.178927i) q^{68} +(-2.37552 + 2.97881i) q^{69} +(-0.704345 + 1.43069i) q^{70} +(9.75178 - 4.69621i) q^{71} +(-2.54671 + 0.581271i) q^{72} +(9.54871 - 7.61484i) q^{73} +(1.57056 + 6.88108i) q^{74} +(0.0540474 - 3.11318i) q^{75} +(-0.0980584 + 0.122961i) q^{76} +(-1.46722 + 3.04671i) q^{77} +(-1.02177 + 0.814837i) q^{78} -4.61483 q^{79} +(-2.18424 + 0.478632i) q^{80} +(3.52911 + 4.42536i) q^{81} +(-4.78085 - 9.92753i) q^{82} +(-15.7000 - 3.58343i) q^{83} +(0.0988226 + 0.432970i) q^{84} +(-0.384863 - 1.75632i) q^{85} +(-5.13905 - 4.07311i) q^{86} +1.12747i q^{87} +(-4.62284 + 1.05513i) q^{88} +(-1.58261 + 6.93389i) q^{89} +(3.60208 + 4.59817i) q^{90} +(-0.933161 - 1.17015i) q^{91} -6.11828i q^{92} +0.807025i q^{93} +(1.65163 + 2.07108i) q^{94} +(0.342165 + 0.0812277i) q^{95} +(-0.388266 + 0.486870i) q^{96} +(2.68459 - 5.57461i) q^{97} +(6.32865 - 1.44447i) q^{98} +(7.72278 + 9.68406i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 22 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{9}+O(q^{10}) \) 132 * q + 22 * q^4 - 4 * q^5 - 4 * q^6 + 12 * q^9	\( 132 q + 22 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{9} + 8 q^{11} - 10 q^{14} - 20 q^{15} - 22 q^{16} - 4 q^{19} + 4 q^{20} - 24 q^{21} + 4 q^{24} - 16 q^{25} + 12 q^{26} + 40 q^{29} + 24 q^{31} - 4 q^{35} + 128 q^{36} - 56 q^{39} - 28 q^{41} - 8 q^{44} - 80 q^{45} - 12 q^{46} - 136 q^{49} - 56 q^{50} + 172 q^{51} + 16 q^{54} - 4 q^{56} + 16 q^{59} - 8 q^{60} - 44 q^{61} + 22 q^{64} + 42 q^{65} + 8 q^{66} - 62 q^{69} + 12 q^{70} - 8 q^{71} - 4 q^{74} - 122 q^{75} - 52 q^{76} - 64 q^{79} - 4 q^{80} - 56 q^{81} + 24 q^{84} - 72 q^{85} - 10 q^{86} + 16 q^{89} + 2 q^{90} - 24 q^{91} - 20 q^{94} + 106 q^{95} - 4 q^{96} - 104 q^{99}+O(q^{100}) \) 132 * q + 22 * q^4 - 4 * q^5 - 4 * q^6 + 12 * q^9 + 8 * q^11 - 10 * q^14 - 20 * q^15 - 22 * q^16 - 4 * q^19 + 4 * q^20 - 24 * q^21 + 4 * q^24 - 16 * q^25 + 12 * q^26 + 40 * q^29 + 24 * q^31 - 4 * q^35 + 128 * q^36 - 56 * q^39 - 28 * q^41 - 8 * q^44 - 80 * q^45 - 12 * q^46 - 136 * q^49 - 56 * q^50 + 172 * q^51 + 16 * q^54 - 4 * q^56 + 16 * q^59 - 8 * q^60 - 44 * q^61 + 22 * q^64 + 42 * q^65 + 8 * q^66 - 62 * q^69 + 12 * q^70 - 8 * q^71 - 4 * q^74 - 122 * q^75 - 52 * q^76 - 64 * q^79 - 4 * q^80 - 56 * q^81 + 24 * q^84 - 72 * q^85 - 10 * q^86 + 16 * q^89 + 2 * q^90 - 24 * q^91 - 20 * q^94 + 106 * q^95 - 4 * q^96 - 104 * q^99

Introduction

L-functions

Modular forms

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