LMFDB - Embedded newform 350.2.m.b.29.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(29,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("350.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.m (of order $10$, degree $4$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.3
Character	$\chi$	$=$	350.29
Dual form			350.2.m.b.169.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{2} +(0.474883 - 0.653621i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.51703 + 1.64275i) q^{5} +(-0.653621 + 0.474883i) q^{6} -1.00000i q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.725345 + 2.23238i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 0.309017i) q^{2} +(0.474883 - 0.653621i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.51703 + 1.64275i) q^{5} +(-0.653621 + 0.474883i) q^{6} -1.00000i q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.725345 + 2.23238i) q^{9} +(1.95042 - 1.09356i) q^{10} +(-0.682171 + 2.09951i) q^{11} +(0.768378 - 0.249661i) q^{12} +(3.68486 - 1.19728i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(0.353325 + 1.77168i) q^{15} +(0.309017 + 0.951057i) q^{16} +(4.24814 + 5.84706i) q^{17} -2.34727i q^{18} +(-2.97211 + 2.15937i) q^{19} +(-2.19289 + 0.437327i) q^{20} +(-0.653621 - 0.474883i) q^{21} +(1.29757 - 1.78595i) q^{22} +(-0.381098 - 0.123826i) q^{23} -0.807920 q^{24} +(-0.397259 - 4.98419i) q^{25} -3.87449 q^{26} +(4.10872 + 1.33500i) q^{27} +(0.587785 - 0.809017i) q^{28} +(4.01796 + 2.91922i) q^{29} +(0.211446 - 1.79415i) q^{30} +(0.0333070 - 0.0241990i) q^{31} -1.00000i q^{32} +(1.04833 + 1.44290i) q^{33} +(-2.23338 - 6.87363i) q^{34} +(1.64275 + 1.51703i) q^{35} +(-0.725345 + 2.23238i) q^{36} +(4.21894 - 1.37082i) q^{37} +(3.49393 - 1.13525i) q^{38} +(0.967309 - 2.97707i) q^{39} +(2.22070 + 0.261716i) q^{40} +(0.612552 + 1.88524i) q^{41} +(0.474883 + 0.653621i) q^{42} -1.16327i q^{43} +(-1.78595 + 1.29757i) q^{44} +(-4.76761 - 2.19502i) q^{45} +(0.324181 + 0.235532i) q^{46} +(-7.55799 + 10.4027i) q^{47} +(0.768378 + 0.249661i) q^{48} -1.00000 q^{49} +(-1.16238 + 4.86301i) q^{50} +5.83913 q^{51} +(3.68486 + 1.19728i) q^{52} +(8.24589 - 11.3495i) q^{53} +(-3.49509 - 2.53933i) q^{54} +(-2.41409 - 4.30564i) q^{55} +(-0.809017 + 0.587785i) q^{56} +2.96808i q^{57} +(-2.91922 - 4.01796i) q^{58} +(-2.54230 - 7.82439i) q^{59} +(-0.755519 + 1.64100i) q^{60} +(-2.24702 + 6.91561i) q^{61} +(-0.0391548 + 0.0127221i) q^{62} +(2.23238 - 0.725345i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-3.62319 + 7.86962i) q^{65} +(-0.551139 - 1.69623i) q^{66} +(2.17223 + 2.98981i) q^{67} +7.22736i q^{68} +(-0.261913 + 0.190291i) q^{69} +(-1.09356 - 1.95042i) q^{70} +(-0.616048 - 0.447585i) q^{71} +(1.37969 - 1.89898i) q^{72} +(-10.7961 - 3.50786i) q^{73} -4.43605 q^{74} +(-3.44643 - 2.10725i) q^{75} -3.67373 q^{76} +(2.09951 + 0.682171i) q^{77} +(-1.83993 + 2.53245i) q^{78} +(-6.54826 - 4.75759i) q^{79} +(-2.03114 - 0.935140i) q^{80} +(-2.87318 + 2.08749i) q^{81} -1.98226i q^{82} +(-6.69265 - 9.21165i) q^{83} +(-0.249661 - 0.768378i) q^{84} +(-16.0498 - 1.89152i) q^{85} +(-0.359471 + 1.10634i) q^{86} +(3.81612 - 1.23993i) q^{87} +(2.09951 - 0.682171i) q^{88} +(-2.93193 + 9.02356i) q^{89} +(3.85597 + 3.56086i) q^{90} +(-1.19728 - 3.68486i) q^{91} +(-0.235532 - 0.324181i) q^{92} -0.0332619i q^{93} +(10.4027 - 7.55799i) q^{94} +(0.961475 - 8.15826i) q^{95} +(-0.653621 - 0.474883i) q^{96} +(1.80553 - 2.48510i) q^{97} +(0.951057 + 0.309017i) q^{98} -5.18171 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 10 q^{4} + 6 q^{5} - 2 q^{6} + 20 q^{9}+O(q^{10}) $ 40 * q + 10 * q^4 + 6 * q^5 - 2 * q^6 + 20 * q^9	$ 40 q + 10 q^{4} + 6 q^{5} - 2 q^{6} + 20 q^{9} - 4 q^{10} - 6 q^{11} + 10 q^{12} + 10 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{19} + 4 q^{20} - 2 q^{21} - 10 q^{22} - 10 q^{23} - 8 q^{24} - 10 q^{25} + 12 q^{26} - 30 q^{27} + 4 q^{29} - 22 q^{30} - 24 q^{31} - 60 q^{33} - 4 q^{35} - 20 q^{36} + 10 q^{37} + 10 q^{38} + 36 q^{39} - 6 q^{40} - 34 q^{41} + 6 q^{44} + 112 q^{45} - 6 q^{46} + 30 q^{47} + 10 q^{48} - 40 q^{49} - 16 q^{50} + 44 q^{51} + 10 q^{53} + 20 q^{54} + 34 q^{55} - 10 q^{56} + 20 q^{58} + 12 q^{59} + 2 q^{60} + 2 q^{61} + 10 q^{64} - 106 q^{65} + 10 q^{66} - 30 q^{67} + 84 q^{69} + 4 q^{70} + 16 q^{71} - 110 q^{73} - 60 q^{74} + 10 q^{75} + 32 q^{76} + 20 q^{77} - 20 q^{78} + 4 q^{79} - 4 q^{80} - 20 q^{81} + 10 q^{83} + 2 q^{84} - 42 q^{85} - 14 q^{86} - 20 q^{87} + 20 q^{88} - 38 q^{90} + 2 q^{91} - 30 q^{92} + 6 q^{94} + 64 q^{95} - 2 q^{96} + 30 q^{97} - 72 q^{99}+O(q^{100}) $ 40 * q + 10 * q^4 + 6 * q^5 - 2 * q^6 + 20 * q^9 - 4 * q^10 - 6 * q^11 + 10 * q^12 + 10 * q^14 - 12 * q^15 - 10 * q^16 - 2 * q^19 + 4 * q^20 - 2 * q^21 - 10 * q^22 - 10 * q^23 - 8 * q^24 - 10 * q^25 + 12 * q^26 - 30 * q^27 + 4 * q^29 - 22 * q^30 - 24 * q^31 - 60 * q^33 - 4 * q^35 - 20 * q^36 + 10 * q^37 + 10 * q^38 + 36 * q^39 - 6 * q^40 - 34 * q^41 + 6 * q^44 + 112 * q^45 - 6 * q^46 + 30 * q^47 + 10 * q^48 - 40 * q^49 - 16 * q^50 + 44 * q^51 + 10 * q^53 + 20 * q^54 + 34 * q^55 - 10 * q^56 + 20 * q^58 + 12 * q^59 + 2 * q^60 + 2 * q^61 + 10 * q^64 - 106 * q^65 + 10 * q^66 - 30 * q^67 + 84 * q^69 + 4 * q^70 + 16 * q^71 - 110 * q^73 - 60 * q^74 + 10 * q^75 + 32 * q^76 + 20 * q^77 - 20 * q^78 + 4 * q^79 - 4 * q^80 - 20 * q^81 + 10 * q^83 + 2 * q^84 - 42 * q^85 - 14 * q^86 - 20 * q^87 + 20 * q^88 - 38 * q^90 + 2 * q^91 - 30 * q^92 + 6 * q^94 + 64 * q^95 - 2 * q^96 + 30 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$	0.474883	−	0.653621i	0.274174	−	0.377368i	−0.649619	−	0.760260i	$-0.725072\pi$
$3$	0.474883	−	0.653621i	0.274174	−	0.377368i	0.923793	+	0.382891i	$0.125072\pi$
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	−1.51703	+	1.64275i	−0.678435	+	0.734660i
$5$	−1.51703	+	1.64275i	−0.678435	+	0.734660i
$6$	−0.653621	+	0.474883i	−0.266840	+	0.193870i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	0.725345	+	2.23238i	0.241782	+	0.744127i
$10$	1.95042	−	1.09356i	0.616776	−	0.345815i
$11$	−0.682171	+	2.09951i	−0.205682	+	0.633025i	0.794002	+	0.607915i	$0.207994\pi$
$11$	−0.682171	+	2.09951i	−0.205682	+	0.633025i	−0.999685	+	0.0251103i	$0.992006\pi$
$12$	0.768378	−	0.249661i	0.221812	−	0.0720709i
$13$	3.68486	−	1.19728i	1.02200	−	0.332067i	0.250375	−	0.968149i	$-0.419446\pi$
$13$	3.68486	−	1.19728i	1.02200	−	0.332067i	0.771621	+	0.636082i	$0.219446\pi$
$14$	−0.309017	+	0.951057i	−0.0825883	+	0.254181i
$15$	0.353325	+	1.77168i	0.0912282	+	0.457445i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	4.24814	+	5.84706i	1.03032	+	1.41812i	0.904703	+	0.426042i	$0.140092\pi$
$17$	4.24814	+	5.84706i	1.03032	+	1.41812i	0.125621	+	0.992078i	$0.459908\pi$
$18$		−	2.34727i		−	0.553256i
$19$	−2.97211	+	2.15937i	−0.681850	+	0.495393i	−0.873971	−	0.485978i	$-0.838463\pi$
$19$	−2.97211	+	2.15937i	−0.681850	+	0.495393i	0.192121	+	0.981371i	$0.438463\pi$
$20$	−2.19289	+	0.437327i	−0.490344	+	0.0977893i
$21$	−0.653621	−	0.474883i	−0.142632	−	0.103628i
$22$	1.29757	−	1.78595i	0.276642	−	0.380765i
$23$	−0.381098	−	0.123826i	−0.0794644	−	0.0258196i	0.269015	−	0.963136i	$-0.413302\pi$
$23$	−0.381098	−	0.123826i	−0.0794644	−	0.0258196i	−0.348479	+	0.937316i	$0.613302\pi$
$24$	−0.807920			−0.164916
$25$	−0.397259	−	4.98419i	−0.0794518	−	0.996839i
$26$	−3.87449			−0.759850
$27$	4.10872	+	1.33500i	0.790723	+	0.256922i
$28$	0.587785	−	0.809017i	0.111081	−	0.152890i
$29$	4.01796	+	2.91922i	0.746116	+	0.542085i	0.894620	−	0.446827i	$-0.147446\pi$
$29$	4.01796	+	2.91922i	0.746116	+	0.542085i	−0.148505	+	0.988912i	$0.547446\pi$
$30$	0.211446	−	1.79415i	0.0386045	−	0.327565i
$31$	0.0333070	−	0.0241990i	0.00598212	−	0.00434626i	−0.584790	−	0.811185i	$-0.698823\pi$
$31$	0.0333070	−	0.0241990i	0.00598212	−	0.00434626i	0.590772	+	0.806838i	$0.298823\pi$
$32$		−	1.00000i		−	0.176777i
$33$	1.04833	+	1.44290i	0.182491	+	0.251177i
$34$	−2.23338	−	6.87363i	−0.383021	−	1.17882i
$35$	1.64275	+	1.51703i	0.277676	+	0.256424i
$36$	−0.725345	+	2.23238i	−0.120891	+	0.372064i
$37$	4.21894	−	1.37082i	0.693589	−	0.225361i	0.0590539	−	0.998255i	$-0.481192\pi$
$37$	4.21894	−	1.37082i	0.693589	−	0.225361i	0.634535	+	0.772894i	$0.281192\pi$
$38$	3.49393	−	1.13525i	0.566790	−	0.184161i
$39$	0.967309	−	2.97707i	0.154893	−	0.476713i
$40$	2.22070	+	0.261716i	0.351123	+	0.0413809i
$41$	0.612552	+	1.88524i	0.0956646	+	0.294425i	0.987426	−	0.158080i	$-0.0505304\pi$
$41$	0.612552	+	1.88524i	0.0956646	+	0.294425i	−0.891762	+	0.452505i	$0.850530\pi$
$42$	0.474883	+	0.653621i	0.0732761	+	0.100856i
$43$		−	1.16327i		−	0.177397i	−0.996059	−	0.0886986i	$-0.971729\pi$
$43$		−	1.16327i		−	0.177397i	0.996059	−	0.0886986i	$-0.0282708\pi$
$44$	−1.78595	+	1.29757i	−0.269242	+	0.195615i
$45$	−4.76761	−	2.19502i	−0.710714	−	0.327215i
$46$	0.324181	+	0.235532i	0.0477979	+	0.0347272i
$47$	−7.55799	+	10.4027i	−1.10245	+	1.51739i	−0.270345	+	0.962764i	$0.587138\pi$
$47$	−7.55799	+	10.4027i	−1.10245	+	1.51739i	−0.832102	+	0.554623i	$0.812862\pi$
$48$	0.768378	+	0.249661i	0.110906	+	0.0360355i
$49$	−1.00000			−0.142857
$50$	−1.16238	+	4.86301i	−0.164386	+	0.687733i
$51$	5.83913			0.817642
$52$	3.68486	+	1.19728i	0.510998	+	0.166033i
$53$	8.24589	−	11.3495i	1.13266	−	1.55897i	0.349745	−	0.936845i	$-0.386268\pi$
$53$	8.24589	−	11.3495i	1.13266	−	1.55897i	0.782915	−	0.622128i	$-0.213732\pi$
$54$	−3.49509	−	2.53933i	−0.475621	−	0.345559i
$55$	−2.41409	−	4.30564i	−0.325516	−	0.580573i
$56$	−0.809017	+	0.587785i	−0.108109	+	0.0785461i
$57$			2.96808i			0.393132i
$58$	−2.91922	−	4.01796i	−0.383312	−	0.527584i
$59$	−2.54230	−	7.82439i	−0.330979	−	1.01865i	−0.968669	−	0.248356i	$-0.920110\pi$
$59$	−2.54230	−	7.82439i	−0.330979	−	1.01865i	0.637690	−	0.770293i	$-0.279890\pi$
$60$	−0.755519	+	1.64100i	−0.0975370	+	0.211852i
$61$	−2.24702	+	6.91561i	−0.287701	+	0.885453i	0.697875	+	0.716220i	$0.254129\pi$
$61$	−2.24702	+	6.91561i	−0.287701	+	0.885453i	−0.985576	+	0.169233i	$0.945871\pi$
$62$	−0.0391548	+	0.0127221i	−0.00497266	+	0.00161571i
$63$	2.23238	−	0.725345i	0.281254	−	0.0913849i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	−3.62319	+	7.86962i	−0.449402	+	0.976106i
$66$	−0.551139	−	1.69623i	−0.0678406	−	0.208792i
$67$	2.17223	+	2.98981i	0.265380	+	0.365264i	0.920823	−	0.389980i	$-0.127518\pi$
$67$	2.17223	+	2.98981i	0.265380	+	0.365264i	−0.655443	+	0.755244i	$0.727518\pi$
$68$			7.22736i			0.876447i
$69$	−0.261913	+	0.190291i	−0.0315306	+	0.0229083i
$70$	−1.09356	−	1.95042i	−0.130706	−	0.233119i
$71$	−0.616048	−	0.447585i	−0.0731114	−	0.0531186i	0.550629	−	0.834750i	$-0.314388\pi$
$71$	−0.616048	−	0.447585i	−0.0731114	−	0.0531186i	−0.623741	+	0.781631i	$0.714388\pi$
$72$	1.37969	−	1.89898i	0.162598	−	0.223797i
$73$	−10.7961	−	3.50786i	−1.26359	−	0.410564i	−0.400816	−	0.916159i	$-0.631273\pi$
$73$	−10.7961	−	3.50786i	−1.26359	−	0.410564i	−0.862771	+	0.505595i	$0.831273\pi$
$74$	−4.43605			−0.515681
$75$	−3.44643	−	2.10725i	−0.397959	−	0.243325i
$76$	−3.67373			−0.421406
$77$	2.09951	+	0.682171i	0.239261	+	0.0777406i
$78$	−1.83993	+	2.53245i	−0.208331	+	0.286743i
$79$	−6.54826	−	4.75759i	−0.736737	−	0.535271i	0.154950	−	0.987922i	$-0.450478\pi$
$79$	−6.54826	−	4.75759i	−0.736737	−	0.535271i	−0.891688	+	0.452651i	$0.850478\pi$
$80$	−2.03114	−	0.935140i	−0.227088	−	0.104552i
$81$	−2.87318	+	2.08749i	−0.319243	+	0.231943i
$82$		−	1.98226i		−	0.218904i
$83$	−6.69265	−	9.21165i	−0.734614	−	1.01111i	−0.998910	−	0.0466683i	$-0.985140\pi$
$83$	−6.69265	−	9.21165i	−0.734614	−	1.01111i	0.264296	−	0.964442i	$-0.414860\pi$
$84$	−0.249661	−	0.768378i	−0.0272403	−	0.0838369i
$85$	−16.0498	−	1.89152i	−1.74085	−	0.205164i
$86$	−0.359471	+	1.10634i	−0.0387627	+	0.119299i
$87$	3.81612	−	1.23993i	0.409131	−	0.132935i
$88$	2.09951	−	0.682171i	0.223808	−	0.0727197i
$89$	−2.93193	+	9.02356i	−0.310784	+	0.956495i	0.666671	+	0.745352i	$0.267719\pi$
$89$	−2.93193	+	9.02356i	−0.310784	+	0.956495i	−0.977455	+	0.211143i	$0.932281\pi$
$90$	3.85597	+	3.56086i	0.406455	+	0.375348i
$91$	−1.19728	−	3.68486i	−0.125509	−	0.386278i
$92$	−0.235532	−	0.324181i	−0.0245559	−	0.0337982i
$93$		−	0.0332619i		−	0.00344909i
$94$	10.4027	−	7.55799i	1.07295	−	0.779547i
$95$	0.961475	−	8.15826i	0.0986452	−	0.837020i
$96$	−0.653621	−	0.474883i	−0.0667099	−	0.0484676i
$97$	1.80553	−	2.48510i	0.183324	−	0.252324i	−0.707457	−	0.706756i	$-0.750158\pi$
$97$	1.80553	−	2.48510i	0.183324	−	0.252324i	0.890781	+	0.454432i	$0.150158\pi$
$98$	0.951057	+	0.309017i	0.0960712	+	0.0312154i
$99$	−5.18171			−0.520781
$100$	2.60825	−	4.26580i	0.260825	−	0.426580i
$101$	−2.20020			−0.218928			−0.109464	−	0.993991i	$-0.534913\pi$
$101$	−2.20020			−0.218928			−0.109464	+	0.993991i	$0.534913\pi$
$102$	−5.55334	−	1.80439i	−0.549863	−	0.178661i
$103$	10.6631	−	14.6765i	1.05067	−	1.44612i	0.162437	−	0.986719i	$-0.448064\pi$
$103$	10.6631	−	14.6765i	1.05067	−	1.44612i	0.888229	−	0.459400i	$-0.151936\pi$
$104$	−3.13453	−	2.27737i	−0.307366	−	0.223314i
$105$	1.77168	−	0.353325i	0.172898	−	0.0344810i
$106$	−11.3495	+	8.24589i	−1.10236	+	0.800912i
$107$		−	11.0225i		−	1.06558i	−0.846246	−	0.532792i	$-0.821143\pi$
$107$		−	11.0225i		−	1.06558i	0.846246	−	0.532792i	$-0.178857\pi$
$108$	2.53933	+	3.49509i	0.244347	+	0.336315i
$109$	−3.06105	−	9.42093i	−0.293195	−	0.902361i	−0.983822	−	0.179150i	$-0.942665\pi$
$109$	−3.06105	−	9.42093i	−0.293195	−	0.902361i	0.690627	−	0.723211i	$-0.257335\pi$
$110$	0.965422	+	4.84091i	0.0920494	+	0.461562i
$111$	1.10751	−	3.40856i	0.105120	−	0.323527i
$112$	0.951057	−	0.309017i	0.0898664	−	0.0291994i
$113$	−8.57680	+	2.78677i	−0.806837	+	0.262157i	−0.683258	−	0.730177i	$-0.739437\pi$
$113$	−8.57680	+	2.78677i	−0.806837	+	0.262157i	−0.123580	+	0.992335i	$0.539437\pi$
$114$	0.917188	−	2.82282i	0.0859026	−	0.264381i
$115$	0.781552	−	0.438201i	0.0728801	−	0.0408625i
$116$	1.53472	+	4.72339i	0.142495	+	0.438556i
$117$	5.34559	+	7.35757i	0.494200	+	0.680208i
$118$			8.22705i			0.757362i
$119$	5.84706	−	4.24814i	0.535999	−	0.389426i
$120$	1.22564	−	1.32721i	0.111885	−	0.121157i
$121$	4.95662	+	3.60119i	0.450602	+	0.327381i
$122$	4.27408	−	5.88277i	0.386957	−	0.532601i
$123$	1.52312	+	0.494893i	0.137336	+	0.0446230i
$124$	0.0411697			0.00369715
$125$	8.79044	+	6.90856i	0.786241	+	0.617920i
$126$	−2.34727			−0.209111
$127$	3.21697	+	1.04526i	0.285460	+	0.0927515i	0.448247	−	0.893910i	$-0.352048\pi$
$127$	3.21697	+	1.04526i	0.285460	+	0.0927515i	−0.162787	+	0.986661i	$0.552048\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	−0.760339	−	0.552418i	−0.0669441	−	0.0486377i
$130$	5.87771	−	6.36482i	0.515509	−	0.558232i
$131$	−8.43947	+	6.13164i	−0.737360	+	0.535723i	−0.891883	−	0.452266i	$-0.850616\pi$
$131$	−8.43947	+	6.13164i	−0.737360	+	0.535723i	0.154523	+	0.987989i	$0.450616\pi$
$132$			1.78352i			0.155236i
$133$	2.15937	+	2.97211i	0.187241	+	0.257715i
$134$	−1.14201	−	3.51474i	−0.0986544	−	0.303627i
$135$	−8.42611	+	4.72436i	−0.725205	+	0.406609i
$136$	2.23338	−	6.87363i	0.191511	−	0.589409i
$137$	−4.30171	+	1.39771i	−0.367520	+	0.119414i	−0.486954	−	0.873428i	$-0.661892\pi$
$137$	−4.30171	+	1.39771i	−0.367520	+	0.119414i	0.119434	+	0.992842i	$0.461892\pi$
$138$	0.307897	−	0.100042i	0.0262099	−	0.00851612i
$139$	−0.933471	+	2.87293i	−0.0791760	+	0.243679i	−0.982808	−	0.184631i	$-0.940891\pi$
$139$	−0.933471	+	2.87293i	−0.0791760	+	0.243679i	0.903632	+	0.428310i	$0.140891\pi$
$140$	0.437327	+	2.19289i	0.0369609	+	0.185333i
$141$	3.21025	+	9.88012i	0.270352	+	0.832056i
$142$	0.447585	+	0.616048i	0.0375605	+	0.0516976i
$143$			8.55314i			0.715249i
$144$	−1.89898	+	1.37969i	−0.158248	+	0.114974i
$145$	−10.8909	+	2.17197i	−0.904440	+	0.180372i
$146$	9.18370	+	6.67235i	0.760049	+	0.552208i
$147$	−0.474883	+	0.653621i	−0.0391677	+	0.0539098i
$148$	4.21894	+	1.37082i	0.346794	+	0.112680i
$149$	10.2695			0.841314			0.420657	−	0.907220i	$-0.361800\pi$
$149$	10.2695			0.841314			0.420657	+	0.907220i	$0.361800\pi$
$150$	2.62657	+	3.06912i	0.214458	+	0.250593i
$151$	20.2745			1.64992			0.824959	−	0.565193i	$-0.191198\pi$
$151$	20.2745			1.64992			0.824959	+	0.565193i	$0.191198\pi$
$152$	3.49393	+	1.13525i	0.283395	+	0.0920807i
$153$	−9.97151	+	13.7246i	−0.806148	+	1.10957i
$154$	−1.78595	−	1.29757i	−0.143916	−	0.104561i
$155$	−0.0107748	+	0.0914256i	−0.000865451	+	0.00734348i
$156$	2.53245	−	1.83993i	0.202758	−	0.147312i
$157$			6.29952i			0.502757i	0.967889	+	0.251378i	$0.0808838\pi$
$157$			6.29952i			0.502757i	−0.967889	+	0.251378i	$0.919116\pi$
$158$	4.75759	+	6.54826i	0.378494	+	0.520952i
$159$	−3.50243	−	10.7794i	−0.277761	−	0.854860i
$160$	1.64275	+	1.51703i	0.129871	+	0.119932i
$161$	−0.123826	+	0.381098i	−0.00975888	+	0.0300347i
$162$	3.37763	−	1.09746i	0.265372	−	0.0862245i
$163$	19.4329	−	6.31414i	1.52210	−	0.494562i	0.575732	−	0.817638i	$-0.304717\pi$
$163$	19.4329	−	6.31414i	1.52210	−	0.494562i	0.946373	+	0.323077i	$0.104717\pi$
$164$	−0.612552	+	1.88524i	−0.0478323	+	0.147213i
$165$	−3.96067	−	0.466777i	−0.308338	−	0.0363385i
$166$	3.51854	+	10.8289i	0.273091	+	0.840489i
$167$	3.03008	+	4.17054i	0.234474	+	0.322726i	0.909998	−	0.414612i	$-0.136083\pi$
$167$	3.03008	+	4.17054i	0.234474	+	0.322726i	−0.675524	+	0.737338i	$0.736083\pi$
$168$			0.807920i			0.0623324i
$169$	1.62748	−	1.18243i	0.125191	−	0.0909563i
$170$	14.6798	+	6.75860i	1.12589	+	0.518361i
$171$	−6.97634	−	5.06861i	−0.533494	−	0.387606i
$172$	0.683754	−	0.941106i	0.0521357	−	0.0717587i
$173$	0.187209	+	0.0608281i	0.0142333	+	0.00462467i	0.316125	−	0.948718i	$-0.397618\pi$
$173$	0.187209	+	0.0608281i	0.0142333	+	0.00462467i	−0.301892	+	0.953342i	$0.597618\pi$
$174$	−4.01251			−0.304188
$175$	−4.98419	+	0.397259i	−0.376770	+	0.0300300i
$176$	−2.20755			−0.166400
$177$	−6.32148	−	2.05397i	−0.475152	−	0.154386i
$178$	5.57687	−	7.67590i	0.418004	−	0.575333i
$179$	16.2106	+	11.7777i	1.21164	+	0.880306i	0.995378	−	0.0960307i	$-0.0306147\pi$
$179$	16.2106	+	11.7777i	1.21164	+	0.880306i	0.216258	+	0.976336i	$0.430615\pi$
$180$	−2.56688	−	4.57814i	−0.191324	−	0.341235i
$181$	14.1252	−	10.2626i	1.04992	−	0.762812i	0.0777234	−	0.996975i	$-0.475235\pi$
$181$	14.1252	−	10.2626i	1.04992	−	0.762812i	0.972197	+	0.234163i	$0.0752349\pi$
$182$			3.87449i			0.287196i
$183$	3.45312	+	4.75281i	0.255262	+	0.351338i
$184$	0.123826	+	0.381098i	0.00912859	+	0.0280949i
$185$	−4.14833	+	9.01023i	−0.304991	+	0.662445i
$186$	−0.0102785	+	0.0316339i	−0.000753655	+	0.00231951i
$187$	−15.1739	+	4.93030i	−1.10962	+	0.360539i
$188$	−12.2291	+	3.97347i	−0.891898	+	0.289795i
$189$	1.33500	−	4.10872i	0.0971072	−	0.298865i
$190$	−3.43546	+	7.46185i	−0.249234	+	0.541340i
$191$	−5.60544	−	17.2518i	−0.405595	−	1.24829i	−0.920397	−	0.390984i	$-0.872135\pi$
$191$	−5.60544	−	17.2518i	−0.405595	−	1.24829i	0.514802	−	0.857309i	$-0.327865\pi$
$192$	0.474883	+	0.653621i	0.0342718	+	0.0471710i
$193$			5.45759i			0.392846i	0.980519	+	0.196423i	$0.0629325\pi$
$193$			5.45759i			0.392846i	−0.980519	+	0.196423i	$0.937067\pi$
$194$	−2.48510	+	1.80553i	−0.178420	+	0.129630i
$195$	3.42315	+	6.10535i	0.245137	+	0.437213i
$196$	−0.809017	−	0.587785i	−0.0577869	−	0.0419847i
$197$	11.8097	−	16.2546i	0.841403	−	1.15809i	−0.144289	−	0.989536i	$-0.546090\pi$
$197$	11.8097	−	16.2546i	0.841403	−	1.15809i	0.985692	−	0.168556i	$-0.0539104\pi$
$198$	4.92810	+	1.60124i	0.350225	+	0.113795i
$199$	14.1282			1.00152			0.500761	−	0.865585i	$-0.333053\pi$
$199$	14.1282			1.00152			0.500761	+	0.865585i	$0.333053\pi$
$200$	−3.79879	+	3.25102i	−0.268615	+	0.229882i
$201$	2.98576			0.210599
$202$	2.09251	+	0.679899i	0.147229	+	0.0478375i
$203$	2.91922	−	4.01796i	0.204889	−	0.282005i
$204$	4.72396	+	3.43216i	0.330743	+	0.240299i
$205$	−4.02624	−	1.85369i	−0.281205	−	0.129467i
$206$	−14.6765	+	10.6631i	−1.02256	+	0.742934i
$207$		−	0.940573i		−	0.0653743i
$208$	2.27737	+	3.13453i	0.157907	+	0.217340i
$209$	−2.50611	−	7.71303i	−0.173352	−	0.533521i
$210$	−1.79415	−	0.211446i	−0.123808	−	0.0145911i
$211$	5.22362	−	16.0767i	0.359609	−	1.10676i	−0.593679	−	0.804702i	$-0.702325\pi$
$211$	5.22362	−	16.0767i	0.359609	−	1.10676i	0.953288	−	0.302061i	$-0.0976748\pi$
$212$	13.3421	−	4.33512i	0.916342	−	0.297737i
$213$	−0.585102	+	0.190111i	−0.0400905	+	0.0130262i
$214$	−3.40613	+	10.4830i	−0.232839	+	0.716603i
$215$	1.91096	+	1.76471i	0.130327	+	0.120352i
$216$	−1.33500	−	4.10872i	−0.0908355	−	0.279563i
$217$	−0.0241990	−	0.0333070i	−0.00164273	−	0.00226103i
$218$			9.90575i			0.670902i
$219$	−7.41970	+	5.39073i	−0.501377	+	0.364271i
$220$	0.577751	−	4.90231i	0.0389520	−	0.330513i
$221$	22.6544	+	16.4594i	1.52390	+	1.10718i
$222$	−2.10661	+	2.89950i	−0.141386	+	0.194602i
$223$	−17.9048	−	5.81761i	−1.19899	−	0.389576i	−0.359602	−	0.933106i	$-0.617088\pi$
$223$	−17.9048	−	5.81761i	−1.19899	−	0.389576i	−0.839390	+	0.543530i	$0.817088\pi$
$224$	−1.00000			−0.0668153
$225$	10.8385	−	4.50209i	0.722565	−	0.300140i
$226$	9.01818			0.599880
$227$	−16.5595	−	5.38051i	−1.09909	−	0.357117i	−0.297339	−	0.954772i	$-0.596099\pi$
$227$	−16.5595	−	5.38051i	−1.09909	−	0.357117i	−0.801753	+	0.597655i	$0.796099\pi$
$228$	−1.74460	+	2.40123i	−0.115539	+	0.159025i
$229$	23.1580	+	16.8253i	1.53032	+	1.11185i	0.956059	+	0.293176i	$0.0947121\pi$
$229$	23.1580	+	16.8253i	1.53032	+	1.11185i	0.574265	+	0.818669i	$0.305288\pi$
$230$	−0.878711	+	0.175241i	−0.0579405	+	0.0115551i
$231$	1.44290	−	1.04833i	0.0949360	−	0.0689750i
$232$		−	4.96647i		−	0.326065i
$233$	−15.2373	−	20.9724i	−0.998231	−	1.37395i	−0.926404	−	0.376531i	$-0.877117\pi$
$233$	−15.2373	−	20.9724i	−0.998231	−	1.37395i	−0.0718273	−	0.997417i	$-0.522883\pi$
$234$	−2.81034	−	8.64934i	−0.183718	−	0.565425i
$235$	−5.62334	−	28.1970i	−0.366826	−	1.83937i
$236$	2.54230	−	7.82439i	0.165490	−	0.509325i
$237$	−6.21932	+	2.02078i	−0.403989	+	0.131264i
$238$	−6.87363	+	2.23338i	−0.445551	+	0.144768i
$239$	−0.302006	+	0.929479i	−0.0195352	+	0.0601230i	−0.960349	−	0.278801i	$-0.910063\pi$
$239$	−0.302006	+	0.929479i	−0.0195352	+	0.0601230i	0.940814	+	0.338924i	$0.110063\pi$
$240$	−1.57578	+	0.883510i	−0.101716	+	0.0570303i
$241$	−0.691004	−	2.12669i	−0.0445115	−	0.136992i	0.926331	−	0.376711i	$-0.122945\pi$
$241$	−0.691004	−	2.12669i	−0.0445115	−	0.136992i	−0.970842	+	0.239718i	$0.922945\pi$
$242$	−3.60119	−	4.95662i	−0.231494	−	0.318624i
$243$			15.8298i			1.01548i
$244$	−5.88277	+	4.27408i	−0.376606	+	0.273620i
$245$	1.51703	−	1.64275i	0.0969193	−	0.104951i
$246$	−1.29565	−	0.941343i	−0.0826074	−	0.0600178i
$247$	−8.36645	+	11.5154i	−0.532344	+	0.732709i
$248$	−0.0391548	−	0.0127221i	−0.00248633	−	0.000807857i
$249$	−9.19916			−0.582973
$250$	−6.22534	−	9.28682i	−0.393725	−	0.587350i
$251$	−17.3655			−1.09610			−0.548051	−	0.836445i	$-0.684630\pi$
$251$	−17.3655			−1.09610			−0.548051	+	0.836445i	$0.684630\pi$
$252$	2.23238	+	0.725345i	0.140627	+	0.0456924i
$253$	0.519948	−	0.715647i	0.0326888	−	0.0449923i
$254$	−2.73652	−	1.98819i	−0.171704	−	0.124750i
$255$	−8.85812	+	9.59224i	−0.554717	+	0.600689i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$		−	8.48400i		−	0.529218i	−0.964356	−	0.264609i	$-0.914757\pi$
$257$		−	8.48400i		−	0.529218i	0.964356	−	0.264609i	$-0.0852428\pi$
$258$	0.552418	+	0.760339i	0.0343921	+	0.0473366i
$259$	−1.37082	−	4.21894i	−0.0851783	−	0.262152i
$260$	−7.55687	+	4.23699i	−0.468657	+	0.262767i
$261$	−3.60240	+	11.0871i	−0.222983	+	0.686271i
$262$	9.92119	−	3.22359i	0.612933	−	0.199154i
$263$	26.2487	−	8.52872i	1.61856	−	0.525903i	0.646962	−	0.762523i	$-0.276039\pi$
$263$	26.2487	−	8.52872i	1.61856	−	0.525903i	0.971602	+	0.236619i	$0.0760394\pi$
$264$	0.551139	−	1.69623i	0.0339203	−	0.104396i
$265$	6.13515	+	30.7634i	0.376879	+	1.88978i
$266$	−1.13525	−	3.49393i	−0.0696064	−	0.214227i
$267$	4.50566	+	6.20151i	0.275742	+	0.379526i
$268$			3.69561i			0.225746i
$269$	14.7304	−	10.7022i	0.898125	−	0.652526i	−0.0398584	−	0.999205i	$-0.512691\pi$
$269$	14.7304	−	10.7022i	0.898125	−	0.652526i	0.937984	+	0.346679i	$0.112691\pi$
$270$	9.47362	−	1.88932i	0.576546	−	0.114981i
$271$	−12.9817	−	9.43173i	−0.788580	−	0.572937i	0.118962	−	0.992899i	$-0.462043\pi$
$271$	−12.9817	−	9.43173i	−0.788580	−	0.572937i	−0.907542	+	0.419962i	$0.862043\pi$
$272$	−4.24814	+	5.84706i	−0.257581	+	0.354530i
$273$	−2.97707	−	0.967309i	−0.180181	−	0.0585442i
$274$	4.52308			0.273250
$275$	10.7353	+	2.56602i	0.647365	+	0.154737i
$276$	−0.323742			−0.0194870
$277$	−25.2560	−	8.20616i	−1.51748	−	0.493060i	−0.572424	−	0.819958i	$-0.693997\pi$
$277$	−25.2560	−	8.20616i	−1.51748	−	0.493060i	−0.945060	+	0.326897i	$0.893997\pi$
$278$	1.77557	−	2.44386i	0.106491	−	0.146573i
$279$	0.0781804	+	0.0568014i	0.00468054	+	0.00340061i
$280$	0.261716	−	2.22070i	0.0156405	−	0.132712i
$281$	2.93611	−	2.13321i	0.175153	−	0.127256i	−0.496754	−	0.867891i	$-0.665475\pi$
$281$	2.93611	−	2.13321i	0.175153	−	0.127256i	0.671908	+	0.740635i	$0.265475\pi$
$282$		−	10.3886i		−	0.618631i
$283$	7.44188	+	10.2429i	0.442374	+	0.608876i	0.970738	−	0.240143i	$-0.0771942\pi$
$283$	7.44188	+	10.2429i	0.442374	+	0.608876i	−0.528364	+	0.849018i	$0.677194\pi$
$284$	−0.235309	−	0.724208i	−0.0139630	−	0.0429738i
$285$	−4.87582	−	4.50266i	−0.288819	−	0.266715i
$286$	2.64306	−	8.13451i	0.156288	−	0.481004i
$287$	1.88524	−	0.612552i	0.111282	−	0.0361578i
$288$	2.23238	−	0.725345i	0.131544	−	0.0427414i
$289$	−10.8881	+	33.5103i	−0.640479	+	1.97119i
$290$	11.0290	+	1.29980i	0.647647	+	0.0763271i
$291$	−0.766897	−	2.36027i	−0.0449563	−	0.138361i
$292$	−6.67235	−	9.18370i	−0.390470	−	0.537436i
$293$		−	6.64445i		−	0.388173i	−0.980984	−	0.194086i	$-0.937826\pi$
$293$		−	6.64445i		−	0.388173i	0.980984	−	0.194086i	$-0.0621742\pi$
$294$	0.653621	−	0.474883i	0.0381200	−	0.0276958i
$295$	16.7103	+	7.69345i	0.972909	+	0.447930i
$296$	−3.58884	−	2.60745i	−0.208597	−	0.151555i
$297$	−5.60570	+	7.71558i	−0.325275	+	0.447703i
$298$	−9.76692	−	3.17346i	−0.565782	−	0.183834i
$299$	−1.55255			−0.0897862
$300$	−1.54960	−	3.73056i	−0.0894664	−	0.215384i
$301$	−1.16327			−0.0670498
$302$	−19.2822	−	6.26517i	−1.10957	−	0.360520i
$303$	−1.04484	+	1.43810i	−0.0600244	+	0.0826165i
$304$	−2.97211	−	2.15937i	−0.170462	−	0.123848i
$305$	−7.95183	−	14.1825i	−0.455321	−	0.812085i
$306$	13.7246	−	9.97151i	0.784583	−	0.570033i
$307$			3.83131i			0.218664i	0.994005	+	0.109332i	$0.0348712\pi$
$307$			3.83131i			0.218664i	−0.994005	+	0.109332i	$0.965129\pi$
$308$	1.29757	+	1.78595i	0.0739357	+	0.101764i
$309$	−4.52914	−	13.9393i	−0.257654	−	0.792977i
$310$	0.0384995	−	0.0836213i	0.00218662	−	0.00474937i
$311$	−3.65525	+	11.2497i	−0.207270	+	0.637913i	0.792342	+	0.610077i	$0.208862\pi$
$311$	−3.65525	+	11.2497i	−0.207270	+	0.637913i	−0.999613	+	0.0278358i	$0.991138\pi$
$312$	−2.97707	+	0.967309i	−0.168543	+	0.0547631i
$313$	15.5457	−	5.05110i	0.878694	−	0.285505i	0.165279	−	0.986247i	$-0.447147\pi$
$313$	15.5457	−	5.05110i	0.878694	−	0.285505i	0.713415	+	0.700742i	$0.247147\pi$
$314$	1.94666	−	5.99120i	0.109856	−	0.338103i
$315$	−2.19502	+	4.76761i	−0.123676	+	0.268625i
$316$	−2.50121	−	7.69795i	−0.140704	−	0.433043i
$317$	−20.7362	−	28.5410i	−1.16466	−	1.60302i	−0.692282	−	0.721627i	$-0.743394\pi$
$317$	−20.7362	−	28.5410i	−1.16466	−	1.60302i	−0.472382	−	0.881394i	$-0.656606\pi$
$318$			11.3341i			0.635585i
$319$	−8.86985	+	6.44432i	−0.496616	+	0.360813i
$320$	−1.09356	−	1.95042i	−0.0611320	−	0.109032i
$321$	−7.20453	−	5.23440i	−0.402117	−	0.292155i
$322$	0.235532	−	0.324181i	0.0131257	−	0.0180659i
$323$	−25.2519	−	8.20484i	−1.40505	−	0.456529i
$324$	−3.55145			−0.197303
$325$	−7.43134	−	17.8904i	−0.412216	−	0.992382i
$326$	−20.4330			−1.13168
$327$	−7.61136	−	2.47308i	−0.420909	−	0.136762i
$328$	1.16514	−	1.60368i	0.0643343	−	0.0885485i
$329$	10.4027	+	7.55799i	0.573518	+	0.416685i
$330$	3.62258	+	1.66785i	0.199417	+	0.0918119i
$331$	16.8671	−	12.2547i	0.927100	−	0.673578i	−0.0181810	−	0.999835i	$-0.505788\pi$
$331$	16.8671	−	12.2547i	0.927100	−	0.673578i	0.945281	+	0.326257i	$0.105788\pi$
$332$		−	11.3862i		−	0.624900i
$333$	6.12037	+	8.42396i	0.335394	+	0.461630i
$334$	−1.59301	−	4.90277i	−0.0871654	−	0.268268i
$335$	−8.20685	−	0.967201i	−0.448388	−	0.0528438i
$336$	0.249661	−	0.768378i	0.0136201	−	0.0419184i
$337$	4.96163	−	1.61213i	0.270277	−	0.0878185i	−0.170743	−	0.985316i	$-0.554617\pi$
$337$	4.96163	−	1.61213i	0.270277	−	0.0878185i	0.441020	+	0.897497i	$0.354617\pi$
$338$	−1.91322	+	0.621641i	−0.104065	+	0.0338128i
$339$	−2.25149	+	6.92937i	−0.122284	+	0.376352i
$340$	−11.8728	−	10.9641i	−0.643891	−	0.594612i
$341$	0.0280848	+	0.0864361i	0.00152088	+	0.00468078i
$342$	5.06861	+	6.97634i	0.274079	+	0.377237i
$343$			1.00000i			0.0539949i
$344$	−0.941106	+	0.683754i	−0.0507411	+	0.0368655i
$345$	0.0847284	−	0.718933i	0.00456162	−	0.0387061i
$346$	−0.159250	−	0.115702i	−0.00856133	−	0.00622017i
$347$	−12.3322	+	16.9738i	−0.662025	+	0.911199i	−0.999546	−	0.0301187i	$-0.990411\pi$
$347$	−12.3322	+	16.9738i	−0.662025	+	0.911199i	0.337521	+	0.941318i	$0.390411\pi$
$348$	3.81612	+	1.23993i	0.204566	+	0.0664674i
$349$	5.07035			0.271409			0.135705	−	0.990749i	$-0.456670\pi$
$349$	5.07035			0.271409			0.135705	+	0.990749i	$0.456670\pi$
$350$	4.86301	+	1.16238i	0.259939	+	0.0621321i
$351$	16.7384			0.893431
$352$	2.09951	+	0.682171i	0.111904	+	0.0363598i
$353$	−18.5448	+	25.5248i	−0.987042	+	1.35855i	−0.0540935	+	0.998536i	$0.517227\pi$
$353$	−18.5448	+	25.5248i	−0.987042	+	1.35855i	−0.932948	+	0.360011i	$0.882773\pi$
$354$	5.37738	+	3.90689i	0.285804	+	0.207649i
$355$	1.66983	−	0.333015i	0.0886255	−	0.0176746i
$356$	−7.67590	+	5.57687i	−0.406822	+	0.295573i
$357$		−	5.83913i		−	0.309040i
$358$	−11.7777	−	16.2106i	−0.622470	−	0.856756i
$359$	7.02342	+	21.6158i	0.370682	+	1.14084i	0.946346	+	0.323155i	$0.104743\pi$
$359$	7.02342	+	21.6158i	0.370682	+	1.14084i	−0.575664	+	0.817686i	$0.695257\pi$
$360$	1.02652	+	5.14728i	0.0541025	+	0.271286i
$361$	−1.70073	+	5.23430i	−0.0895120	+	0.275490i
$362$	−16.6052	+	5.39536i	−0.872751	+	0.283574i
$363$	4.70763	−	1.52960i	0.247087	−	0.0802833i
$364$	1.19728	−	3.68486i	0.0627547	−	0.193139i
$365$	22.1405	−	12.4138i	1.15889	−	0.649766i
$366$	−1.81541	−	5.58726i	−0.0948930	−	0.292051i
$367$	17.1490	+	23.6036i	0.895171	+	1.23210i	0.971983	+	0.235052i	$0.0755261\pi$
$367$	17.1490	+	23.6036i	0.895171	+	1.23210i	−0.0768112	+	0.997046i	$0.524474\pi$
$368$		−	0.400710i		−	0.0208885i
$369$	−3.76427	+	2.73490i	−0.195960	+	0.142373i
$370$	6.72961	−	7.28733i	0.349856	−	0.378850i
$371$	−11.3495	−	8.24589i	−0.589237	−	0.428105i
$372$	0.0195508	−	0.0269094i	0.00101366	−	0.00139519i
$373$	−22.1365	−	7.19260i	−1.14619	−	0.372419i	−0.326481	−	0.945204i	$-0.605863\pi$
$373$	−22.1365	−	7.19260i	−1.14619	−	0.372419i	−0.819706	+	0.572785i	$0.805863\pi$
$374$	15.9548			0.825002
$375$	8.69001	−	2.46486i	0.448750	−	0.127285i
$376$	12.8584			0.663122
$377$	18.3007	+	5.94627i	0.942536	+	0.306248i
$378$	−2.53933	+	3.49509i	−0.130609	+	0.179768i
$379$	1.33084	+	0.966910i	0.0683606	+	0.0496669i	0.621441	−	0.783461i	$-0.286548\pi$
$379$	1.33084	+	0.966910i	0.0683606	+	0.0496669i	−0.553080	+	0.833128i	$0.686548\pi$
$380$	5.57315	−	6.03503i	0.285897	−	0.309591i
$381$	2.21089	−	1.60630i	0.113267	−	0.0822934i
$382$			18.1396i			0.928101i
$383$	−7.27972	−	10.0197i	−0.371976	−	0.511982i	0.581460	−	0.813575i	$-0.302482\pi$
$383$	−7.27972	−	10.0197i	−0.371976	−	0.511982i	−0.953437	+	0.301593i	$0.902482\pi$
$384$	−0.249661	−	0.768378i	−0.0127405	−	0.0392111i
$385$	−4.30564	+	2.41409i	−0.219436	+	0.123034i
$386$	1.68649	−	5.19047i	0.0858400	−	0.264188i
$387$	2.59687	−	0.843773i	0.132006	−	0.0428914i
$388$	2.92141	−	0.949223i	0.148312	−	0.0481895i
$389$	−8.49255	+	26.1374i	−0.430589	+	1.32522i	0.466950	+	0.884284i	$0.345353\pi$
$389$	−8.49255	+	26.1374i	−0.430589	+	1.32522i	−0.897539	+	0.440934i	$0.854647\pi$
$390$	−1.36896	−	6.86434i	−0.0693198	−	0.347589i
$391$	−0.894937	−	2.75433i	−0.0452589	−	0.139293i
$392$	0.587785	+	0.809017i	0.0296876	+	0.0408615i
$393$			8.42803i			0.425138i
$394$	−16.2546	+	11.8097i	−0.818894	+	0.594962i
$395$	17.7494	−	3.53977i	0.893071	−	0.178105i
$396$	−4.19209	−	3.04573i	−0.210660	−	0.153054i
$397$	11.0389	−	15.1937i	0.554026	−	0.762552i	−0.436525	−	0.899692i	$-0.643791\pi$
$397$	11.0389	−	15.1937i	0.554026	−	0.762552i	0.990552	+	0.137140i	$0.0437911\pi$
$398$	−13.4367	−	4.36586i	−0.673523	−	0.218841i
$399$	2.96808			0.148590
$400$	4.61749	−	1.91802i	0.230874	−	0.0959008i
$401$	7.73550			0.386292			0.193146	−	0.981170i	$-0.438131\pi$
$401$	7.73550			0.386292			0.193146	+	0.981170i	$0.438131\pi$
$402$	−2.83963	−	0.922651i	−0.141628	−	0.0460176i
$403$	0.0937587	−	0.129048i	0.00467045	−	0.00642832i
$404$	−1.78000	−	1.29325i	−0.0885583	−	0.0643414i
$405$	0.929471	−	7.88670i	0.0461858	−	0.391893i
$406$	−4.01796	+	2.91922i	−0.199408	+	0.144878i
$407$			9.79281i			0.485412i
$408$	−3.43216	−	4.72396i	−0.169917	−	0.233871i
$409$	0.864425	+	2.66043i	0.0427431	+	0.131550i	0.970151	−	0.242502i	$-0.0779682\pi$
$409$	0.864425	+	2.66043i	0.0427431	+	0.131550i	−0.927408	+	0.374052i	$0.877968\pi$
$410$	3.25636	+	3.00714i	0.160820	+	0.148512i
$411$	−1.12924	+	3.47544i	−0.0557012	+	0.171431i
$412$	17.2533	−	5.60593i	0.850007	−	0.276184i
$413$	−7.82439	+	2.54230i	−0.385013	+	0.125098i
$414$	−0.290653	+	0.894538i	−0.0142848	+	0.0439642i
$415$	25.2854	+	2.97996i	1.24121	+	0.146280i
$416$	−1.19728	−	3.68486i	−0.0587016	−	0.180665i
$417$	1.43452	+	1.97444i	0.0702486	+	0.0966888i
$418$			8.10996i			0.396671i
$419$	22.1142	−	16.0669i	1.08035	−	0.784920i	0.102606	−	0.994722i	$-0.467282\pi$
$419$	22.1142	−	16.0669i	1.08035	−	0.784920i	0.977744	+	0.209802i	$0.0672820\pi$
$420$	1.64100	+	0.755519i	0.0800724	+	0.0368655i
$421$	−17.2405	−	12.5260i	−0.840250	−	0.610478i	0.0821903	−	0.996617i	$-0.473808\pi$
$421$	−17.2405	−	12.5260i	−0.840250	−	0.610478i	−0.922441	+	0.386139i	$0.873808\pi$
$422$	−9.93592	+	13.6756i	−0.483673	+	0.665719i
$423$	−28.7049	−	9.32679i	−1.39568	−	0.453484i
$424$	−14.0287			−0.681296
$425$	27.4553	−	23.4963i	1.33178	−	1.13974i
$426$	0.615213			0.0298072
$427$	6.91561	+	2.24702i	0.334670	+	0.108741i
$428$	6.47885	−	8.91738i	0.313167	−	0.431038i
$429$	5.59051	+	4.06174i	0.269912	+	0.196103i
$430$	−1.27211	−	2.26886i	−0.0613465	−	0.109414i
$431$	1.92061	−	1.39540i	0.0925124	−	0.0672142i	−0.540568	−	0.841301i	$-0.681790\pi$
$431$	1.92061	−	1.39540i	0.0925124	−	0.0672142i	0.633080	+	0.774086i	$0.281790\pi$
$432$			4.32016i			0.207854i
$433$	9.36402	+	12.8885i	0.450006	+	0.619380i	0.972399	−	0.233325i	$-0.0749606\pi$
$433$	9.36402	+	12.8885i	0.450006	+	0.619380i	−0.522393	+	0.852705i	$0.674961\pi$
$434$	0.0127221	+	0.0391548i	0.000610683	+	0.00187949i
$435$	−3.75226	+	8.14995i	−0.179907	+	0.390760i
$436$	3.06105	−	9.42093i	0.146597	−	0.451181i
$437$	1.40005	−	0.454905i	0.0669736	−	0.0217611i
$438$	8.72238	−	2.83407i	0.416771	−	0.135417i
$439$	−4.84628	+	14.9153i	−0.231300	+	0.711869i	0.766291	+	0.642494i	$0.222100\pi$
$439$	−4.84628	+	14.9153i	−0.231300	+	0.711869i	−0.997591	+	0.0693744i	$0.977900\pi$
$440$	−2.06437	+	4.48384i	−0.0984150	+	0.213758i
$441$	−0.725345	−	2.23238i	−0.0345402	−	0.106304i
$442$	−16.4594	−	22.6544i	−0.782892	−	1.07756i
$443$			18.4342i			0.875835i	0.899015	+	0.437917i	$0.144284\pi$
$443$			18.4342i			0.875835i	−0.899015	+	0.437917i	$0.855716\pi$
$444$	2.89950	−	2.10661i	0.137604	−	0.0999752i
$445$	−10.3756	−	18.5054i	−0.491852	−	0.877241i
$446$	15.2307	+	11.0658i	0.721195	+	0.523979i
$447$	4.87684	−	6.71239i	0.230666	−	0.317485i
$448$	0.951057	+	0.309017i	0.0449332	+	0.0145997i
$449$	11.0236			0.520238			0.260119	−	0.965577i	$-0.416238\pi$
$449$	11.0236			0.520238			0.260119	+	0.965577i	$0.416238\pi$
$450$	−11.6992	+	0.932472i	−0.551507	+	0.0439572i
$451$	−4.37594			−0.206055
$452$	−8.57680	−	2.78677i	−0.403419	−	0.131079i
$453$	9.62804	−	13.2519i	0.452365	−	0.622626i
$454$	14.0864	+	10.2343i	0.661105	+	0.480321i
$455$	7.86962	+	3.62319i	0.368933	+	0.169858i
$456$	2.40123	−	1.74460i	0.112448	−	0.0816982i
$457$			7.52876i			0.352181i	0.984374	+	0.176090i	$0.0563451\pi$
$457$			7.52876i			0.352181i	−0.984374	+	0.176090i	$0.943655\pi$
$458$	−16.8253	−	23.1580i	−0.786193	−	1.08210i
$459$	9.64856	+	29.6952i	0.450356	+	1.38605i
$460$	0.889857	+	0.104872i	0.0414898	+	0.00488969i
$461$	0.500230	−	1.53955i	0.0232980	−	0.0717039i	−0.938732	−	0.344649i	$-0.887998\pi$
$461$	0.500230	−	1.53955i	0.0232980	−	0.0717039i	0.962030	+	0.272945i	$0.0879978\pi$
$462$	−1.69623	+	0.551139i	−0.0789159	+	0.0256413i
$463$	−10.0816	+	3.27572i	−0.468534	+	0.152236i	−0.533762	−	0.845635i	$-0.679222\pi$
$463$	−10.0816	+	3.27572i	−0.468534	+	0.152236i	0.0652287	+	0.997870i	$0.479222\pi$
$464$	−1.53472	+	4.72339i	−0.0712477	+	0.219278i
$465$	0.0546409	+	0.0504591i	0.00253391	+	0.00233999i
$466$	8.01074	+	24.6545i	0.371091	+	1.14210i
$467$	−16.3361	−	22.4847i	−0.755943	−	1.04047i	−0.997541	−	0.0700896i	$-0.977671\pi$
$467$	−16.3361	−	22.4847i	−0.755943	−	1.04047i	0.241598	−	0.970376i	$-0.422329\pi$
$468$			9.09446i			0.420391i
$469$	2.98981	−	2.17223i	0.138057	−	0.100304i
$470$	−3.36525	+	28.5547i	−0.155228	+	1.31713i
$471$	4.11750	+	2.99154i	0.189724	+	0.137843i
$472$	−4.83574	+	6.65583i	−0.222583	+	0.306359i
$473$	2.44230	+	0.793550i	0.112297	+	0.0364875i
$474$	6.53938			0.300364
$475$	11.9434	+	13.9558i	0.548001	+	0.640334i
$476$	7.22736			0.331266
$477$	31.3175	+	10.1757i	1.43393	+	0.465912i
$478$	0.574450	−	0.790662i	0.0262747	−	0.0361641i
$479$	−28.9770	−	21.0530i	−1.32399	−	0.961938i	−0.999873	−	0.0159229i	$-0.994931\pi$
$479$	−28.9770	−	21.0530i	−1.32399	−	0.961938i	−0.324121	−	0.946015i	$-0.605069\pi$
$480$	1.77168	−	0.353325i	0.0808656	−	0.0161270i
$481$	13.9049	−	10.1025i	0.634010	−	0.460636i
$482$			2.23614i			0.101853i
$483$	0.190291	+	0.261913i	0.00865852	+	0.0119174i
$484$	1.89326	+	5.82686i	0.0860573	+	0.264857i
$485$	1.34336	+	6.73600i	0.0609989	+	0.305866i
$486$	4.89167	−	15.0550i	0.221891	−	0.682909i
$487$	−32.2053	+	10.4641i	−1.45936	+	0.474175i	−0.927875	−	0.372892i	$-0.878366\pi$
$487$	−32.2053	+	10.4641i	−1.45936	+	0.474175i	−0.531486	+	0.847067i	$0.678366\pi$
$488$	6.91561	−	2.24702i	0.313055	−	0.101718i
$489$	5.10132	−	15.7003i	0.230690	−	0.709990i
$490$	−1.95042	+	1.09356i	−0.0881108	+	0.0494021i
$491$	−11.1998	−	34.4693i	−0.505438	−	1.55558i	−0.800032	−	0.599957i	$-0.795184\pi$
$491$	−11.1998	−	34.4693i	−0.505438	−	1.55558i	0.294594	−	0.955623i	$-0.404816\pi$
$492$	0.941343	+	1.29565i	0.0424390	+	0.0584123i
$493$			35.8945i			1.61661i
$494$	11.5154	−	8.36645i	0.518104	−	0.376424i
$495$	7.86079	−	8.51225i	0.353316	−	0.382597i
$496$	0.0333070	+	0.0241990i	0.00149553	+	0.00108657i
$497$	−0.447585	+	0.616048i	−0.0200769	+	0.0276335i
$498$	8.74892	+	2.84270i	0.392048	+	0.127384i
$499$	−36.4342			−1.63102			−0.815509	−	0.578745i	$-0.803543\pi$
$499$	−36.4342			−1.63102			−0.815509	+	0.578745i	$0.803543\pi$
$500$	3.05087	+	10.7560i	0.136439	+	0.481024i
$501$	4.16489			0.186074
$502$	16.5156	+	5.36624i	0.737127	+	0.239507i
$503$	−3.31564	+	4.56359i	−0.147837	+	0.203480i	−0.876513	−	0.481379i	$-0.840136\pi$
$503$	−3.31564	+	4.56359i	−0.147837	+	0.203480i	0.728676	+	0.684859i	$0.240136\pi$
$504$	−1.89898	−	1.37969i	−0.0845872	−	0.0614562i
$505$	3.33776	−	3.61438i	0.148528	−	0.160838i
$506$	−0.715647	+	0.519948i	−0.0318144	+	0.0231145i
$507$		−	1.62527i		−	0.0721808i
$508$	1.98819	+	2.73652i	0.0882119	+	0.121413i
$509$	0.667896	+	2.05557i	0.0296040	+	0.0911117i	0.964767	−	0.263106i	$-0.0847470\pi$
$509$	0.667896	+	2.05557i	0.0296040	+	0.0911117i	−0.935163	+	0.354218i	$0.884747\pi$
$510$	11.3887	−	6.38545i	0.504302	−	0.282752i
$511$	−3.50786	+	10.7961i	−0.155179	+	0.477591i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	−15.0943	+	4.90445i	−0.666432	+	0.216537i
$514$	−2.62170	+	8.06877i	−0.115638	+	0.355898i
$515$	7.93362	+	39.7815i	0.349597	+	1.75298i
$516$	−0.290424	−	0.893832i	−0.0127852	−	0.0393487i
$517$	−16.6846	−	22.9645i	−0.733790	−	1.00998i
$518$			4.43605i			0.194909i
$519$	0.128661	−	0.0934778i	0.00564760	−	0.00410322i
$520$	8.49631	−	1.69442i	0.372588	−	0.0743052i
$521$	−14.3307	−	10.4119i	−0.627839	−	0.456152i	0.227812	−	0.973705i	$-0.426843\pi$
$521$	−14.3307	−	10.4119i	−0.627839	−	0.456152i	−0.855651	+	0.517554i	$0.826843\pi$
$522$	6.85218	−	9.43121i	0.299912	−	0.412793i
$523$	10.4029	+	3.38010i	0.454887	+	0.147802i	0.527494	−	0.849559i	$-0.323132\pi$
$523$	10.4029	+	3.38010i	0.454887	+	0.147802i	−0.0726070	+	0.997361i	$0.523132\pi$
$524$	−10.4318			−0.455714
$525$	−2.10725	+	3.44643i	−0.0919681	+	0.150414i
$526$	−27.5995			−1.20340
$527$	0.282986	+	0.0919476i	0.0123270	+	0.00400530i
$528$	−1.04833	+	1.44290i	−0.0456227	+	0.0627942i
$529$	−18.4775	−	13.4247i	−0.803369	−	0.583682i
$530$	3.67155	−	31.1536i	0.159482	−	1.35323i
$531$	15.6230	−	11.3508i	0.677980	−	0.492581i
$532$			3.67373i			0.159277i
$533$	4.51434	+	6.21345i	0.195538	+	0.269134i
$534$	−2.36877	−	7.29031i	−0.102507	−	0.315483i
$535$	18.1072	+	16.7214i	0.782842	+	0.722929i
$536$	1.14201	−	3.51474i	0.0493272	−	0.151814i
$537$	15.3963	−	5.00256i	0.664399	−	0.215876i
$538$	−17.3166	+	5.62649i	−0.746570	+	0.242575i
$539$	0.682171	−	2.09951i	0.0293832	−	0.0904321i
$540$	−9.59378	−	1.13066i	−0.412851	−	0.0486557i
$541$	5.02401	+	15.4623i	0.215999	+	0.664777i	0.999081	+	0.0428587i	$0.0136465\pi$
$541$	5.02401	+	15.4623i	0.215999	+	0.664777i	−0.783082	+	0.621919i	$0.786353\pi$
$542$	9.43173	+	12.9817i	0.405127	+	0.557610i
$543$		−	14.1061i		−	0.605350i
$544$	5.84706	−	4.24814i	0.250691	−	0.182137i
$545$	20.1199	+	9.26327i	0.861843	+	0.396795i
$546$	2.53245	+	1.83993i	0.108379	+	0.0787418i
$547$	−15.1828	+	20.8973i	−0.649169	+	0.893504i	−0.999063	−	0.0432851i	$-0.986218\pi$
$547$	−15.1828	+	20.8973i	−0.649169	+	0.893504i	0.349894	+	0.936789i	$0.386218\pi$
$548$	−4.30171	−	1.39771i	−0.183760	−	0.0597072i
$549$	−17.0681			−0.728450
$550$	−9.41697	−	5.75784i	−0.401541	−	0.245515i
$551$	−18.2455			−0.777284
$552$	0.307897	+	0.100042i	0.0131050	+	0.00425806i
$553$	−4.75759	+	6.54826i	−0.202313	+	0.278460i
$554$	21.4840	+	15.6090i	0.912768	+	0.663165i
$555$	3.91930	+	6.99024i	0.166365	+	0.296719i
$556$	−2.44386	+	1.77557i	−0.103643	+	0.0753008i
$557$		−	34.4325i		−	1.45895i	−0.684006	−	0.729477i	$-0.739764\pi$
$557$		−	34.4325i		−	1.45895i	0.684006	−	0.729477i	$-0.260236\pi$
$558$	−0.0568014	−	0.0781804i	−0.00240459	−	0.00330964i
$559$	−1.39277	−	4.28649i	−0.0589077	−	0.181299i
$560$	−0.935140	+	2.03114i	−0.0395169	+	0.0858312i
$561$	−3.98329	+	12.2593i	−0.168174	+	0.517588i
$562$	−3.45160	+	1.12149i	−0.145597	+	0.0473073i
$563$	41.3810	−	13.4455i	1.74400	−	0.566661i	0.748651	−	0.662965i	$-0.230702\pi$
$563$	41.3810	−	13.4455i	1.74400	−	0.566661i	0.995352	+	0.0963041i	$0.0307021\pi$
$564$	−3.21025	+	9.88012i	−0.135176	+	0.416028i
$565$	8.43326	−	18.3171i	0.354790	−	0.770608i
$566$	−3.91243	−	12.0412i	−0.164452	−	0.506130i
$567$	2.08749	+	2.87318i	0.0876663	+	0.120662i
$568$			0.761477i			0.0319509i
$569$	23.1196	−	16.7973i	0.969222	−	0.704181i	0.0139480	−	0.999903i	$-0.495560\pi$
$569$	23.1196	−	16.7973i	0.969222	−	0.704181i	0.955274	+	0.295722i	$0.0955601\pi$
$570$	3.24578	+	5.78900i	0.135951	+	0.242474i
$571$	6.50037	+	4.72280i	0.272032	+	0.197643i	0.715435	−	0.698680i	$-0.246229\pi$
$571$	6.50037	+	4.72280i	0.272032	+	0.197643i	−0.443402	+	0.896323i	$0.646229\pi$
$572$	−5.02741	+	6.91963i	−0.210206	+	0.289324i
$573$	−13.9380	−	4.52874i	−0.582270	−	0.189191i
$574$	−1.98226			−0.0827380
$575$	−0.465779	+	1.94866i	−0.0194243	+	0.0812646i
$576$	−2.34727			−0.0978027
$577$	23.9083	+	7.76827i	0.995315	+	0.323397i	0.760992	−	0.648761i	$-0.224713\pi$
$577$	23.9083	+	7.76827i	0.995315	+	0.323397i	0.234323	+	0.972159i	$0.424713\pi$
$578$	20.7105	−	28.5055i	0.861442	−	1.18567i
$579$	3.56719	+	2.59172i	0.148248	+	0.107708i
$580$	−10.0876	−	4.64435i	−0.418864	−	0.192846i
$581$	−9.21165	+	6.69265i	−0.382164	+	0.277658i
$582$			2.48173i			0.102871i
$583$	18.2032	+	25.0546i	0.753901	+	1.03766i
$584$	3.50786	+	10.7961i	0.145156	+	0.446745i
$585$	−20.1961	−	2.38016i	−0.835004	−	0.0984077i
$586$	−2.05325	+	6.31925i	−0.0848189	+	0.261046i
$587$	30.4035	−	9.87870i	1.25489	−	0.407738i	0.395217	−	0.918588i	$-0.370669\pi$
$587$	30.4035	−	9.87870i	1.25489	−	0.407738i	0.859670	+	0.510850i	$0.170669\pi$
$588$	−0.768378	+	0.249661i	−0.0316874	+	0.0102958i
$589$	−0.0467378	+	0.143844i	−0.00192580	+	0.00592700i
$590$	−13.5150	−	12.4807i	−0.556404	−	0.513821i
$591$	−5.01613	−	15.4381i	−0.206336	−	0.635037i
$592$	2.60745	+	3.58884i	0.107165	+	0.147501i
$593$		−	10.3732i		−	0.425975i	−0.977055	−	0.212987i	$-0.931681\pi$
$593$		−	10.3732i		−	0.425975i	0.977055	−	0.212987i	$-0.0683193\pi$
$594$	7.71558	−	5.60570i	0.316574	−	0.230005i
$595$	−1.89152	+	16.0498i	−0.0775446	+	0.657978i
$596$	8.30824	+	6.03629i	0.340319	+	0.247256i
$597$	6.70926	−	9.23450i	0.274592	−	0.377943i
$598$	1.47656	+	0.479764i	0.0603811	+	0.0196190i
$599$	−7.15550			−0.292366			−0.146183	−	0.989258i	$-0.546699\pi$
$599$	−7.15550			−0.292366			−0.146183	+	0.989258i	$0.546699\pi$
$600$	0.320954	+	4.02683i	0.0131029	+	0.164395i
$601$	−44.1245			−1.79987			−0.899937	−	0.436019i	$-0.856388\pi$
$601$	−44.1245			−1.79987			−0.899937	+	0.436019i	$0.856388\pi$
$602$	1.10634	+	0.359471i	0.0450909	+	0.0146509i
$603$	−5.09879	+	7.01789i	−0.207639	+	0.285790i
$604$	16.4024	+	11.9171i	0.667406	+	0.484898i
$605$	−13.4352	+	2.67938i	−0.546218	+	0.108932i
$606$	1.43810	−	1.04484i	0.0584187	−	0.0424437i
$607$			16.1603i			0.655927i	0.944690	+	0.327963i	$0.106362\pi$
$607$			16.1603i			0.655927i	−0.944690	+	0.327963i	$0.893638\pi$
$608$	2.15937	+	2.97211i	0.0875739	+	0.120535i
$609$	−1.23993	−	3.81612i	−0.0502446	−	0.154637i
$610$	3.18002	+	15.9456i	0.128755	+	0.645617i
$611$	−15.3952	+	47.3815i	−0.622822	+	1.91685i
$612$	−16.1342	+	5.24233i	−0.652188	+	0.211909i
$613$	−2.83798	+	0.922116i	−0.114625	+	0.0372439i	−0.365768	−	0.930706i	$-0.619194\pi$
$613$	−2.83798	+	0.922116i	−0.114625	+	0.0372439i	0.251143	+	0.967950i	$0.419194\pi$
$614$	1.18394	−	3.64379i	0.0477799	−	0.147051i
$615$	−3.12361	+	1.75135i	−0.125956	+	0.0706211i
$616$	−0.682171	−	2.09951i	−0.0274854	−	0.0845915i
$617$	5.35817	+	7.37489i	0.215712	+	0.296902i	0.903136	−	0.429354i	$-0.141259\pi$
$617$	5.35817	+	7.37489i	0.215712	+	0.296902i	−0.687424	+	0.726256i	$0.741259\pi$
$618$			14.6566i			0.589575i
$619$	−9.40340	+	6.83197i	−0.377955	+	0.274600i	−0.760502	−	0.649336i	$-0.775047\pi$
$619$	−9.40340	+	6.83197i	−0.377955	+	0.274600i	0.382547	+	0.923936i	$0.375047\pi$
$620$	−0.0624556	+	0.0676316i	−0.00250828	+	0.00271615i
$621$	−1.40052	−	1.01753i	−0.0562008	−	0.0408323i
$622$	6.95271	−	9.56958i	0.278778	−	0.383705i
$623$	9.02356	+	2.93193i	0.361521	+	0.117465i
$624$	3.13028			0.125311
$625$	−24.6844	+	3.96003i	−0.987375	+	0.158401i
$626$	−16.3457			−0.653306
$627$	−6.23151	−	2.02474i	−0.248863	−	0.0808603i
$628$	−3.70277	+	5.09642i	−0.147756	+	0.203369i
$629$	25.9379	+	18.8450i	1.03421	+	0.751398i
$630$	3.56086	−	3.85597i	0.141868	−	0.153626i
$631$	6.62172	−	4.81096i	0.263606	−	0.191521i	−0.448129	−	0.893969i	$-0.647909\pi$
$631$	6.62172	−	4.81096i	0.263606	−	0.191521i	0.711735	+	0.702448i	$0.247909\pi$
$632$			8.09410i			0.321966i
$633$	−8.02743	−	11.0488i	−0.319062	−	0.439151i
$634$	10.9017	+	33.5519i	0.432961	+	1.33252i
$635$	−6.59732	+	3.69899i	−0.261807	+	0.146790i
$636$	3.50243	−	10.7794i	0.138880	−	0.427430i
$637$	−3.68486	+	1.19728i	−0.145999	+	0.0474381i
$638$	10.4271	−	3.38798i	0.412814	−	0.134131i
$639$	0.552334	−	1.69991i	0.0218500	−	0.0672473i
$640$	0.437327	+	2.19289i	0.0172869	+	0.0866814i
$641$	9.41440	+	28.9745i	0.371846	+	1.14443i	0.945582	+	0.325385i	$0.105494\pi$
$641$	9.41440	+	28.9745i	0.371846	+	1.14443i	−0.573735	+	0.819041i	$0.694506\pi$
$642$	5.23440	+	7.20453i	0.206585	+	0.284340i
$643$		−	13.2221i		−	0.521428i	−0.965416	−	0.260714i	$-0.916042\pi$
$643$		−	13.2221i		−	0.521428i	0.965416	−	0.260714i	$-0.0839580\pi$
$644$	−0.324181	+	0.235532i	−0.0127745	+	0.00928124i
$645$	2.06094	−	0.411013i	0.0811494	−	0.0161836i
$646$	21.4805	+	15.6065i	0.845141	+	0.614031i
$647$	2.92504	−	4.02598i	0.114995	−	0.158278i	−0.747639	−	0.664105i	$-0.768813\pi$
$647$	2.92504	−	4.02598i	0.114995	−	0.158278i	0.862635	+	0.505827i	$0.168813\pi$
$648$	3.37763	+	1.09746i	0.132686	+	0.0431122i
$649$	18.1616			0.712907
$650$	1.53918	+	19.3112i	0.0603715	+	0.757448i
$651$	−0.0332619			−0.00130364
$652$	19.4329	+	6.31414i	0.761052	+	0.247281i
$653$	19.6928	−	27.1048i	0.770638	−	1.06069i	−0.225616	−	0.974216i	$-0.572440\pi$
$653$	19.6928	−	27.1048i	0.770638	−	1.06069i	0.996254	−	0.0864753i	$-0.0275604\pi$
$654$	6.47461	+	4.70408i	0.253177	+	0.183944i
$655$	2.73016	−	23.1658i	0.106676	−	0.905163i
$656$	−1.60368	+	1.16514i	−0.0626133	+	0.0454912i
$657$		−	26.6454i		−	1.03954i
$658$	−7.55799	−	10.4027i	−0.294641	−	0.405539i
$659$	−14.1320	−	43.4937i	−0.550503	−	1.69427i	−0.707533	−	0.706680i	$-0.750192\pi$
$659$	−14.1320	−	43.4937i	−0.550503	−	1.69427i	0.157030	−	0.987594i	$-0.449808\pi$
$660$	−2.92989	−	2.70565i	−0.114046	−	0.105317i
$661$	6.49794	−	19.9986i	0.252741	−	0.777855i	−0.741526	−	0.670924i	$-0.765898\pi$
$661$	6.49794	−	19.9986i	0.252741	−	0.777855i	0.994266	−	0.106931i	$-0.0341024\pi$
$662$	−19.8285	+	6.44266i	−0.770655	+	0.250401i
$663$	21.5164	−	6.99109i	0.835627	−	0.271512i
$664$	−3.51854	+	10.8289i	−0.136546	+	0.420244i
$665$	−8.15826	−	0.961475i	−0.316364	−	0.0372844i
$666$	−3.21767	−	9.90296i	−0.124682	−	0.383732i
$667$	−1.16976	−	1.61004i	−0.0452933	−	0.0623409i
$668$			5.15508i			0.199456i
$669$	−12.3052	+	8.94025i	−0.475746	+	0.345650i
$670$	7.50629	+	3.45592i	0.289993	+	0.133514i
$671$	−12.9865	−	9.43525i	−0.501339	−	0.364244i
$672$	−0.474883	+	0.653621i	−0.0183190	+	0.0252140i
$673$	−6.80267	−	2.21032i	−0.262224	−	0.0852016i	0.174955	−	0.984576i	$-0.444022\pi$
$673$	−6.80267	−	2.21032i	−0.262224	−	0.0852016i	−0.437178	+	0.899375i	$0.644022\pi$
$674$	−5.21697			−0.200950
$675$	5.02169	−	21.0090i	0.193285	−	0.808636i
$676$	2.01167			0.0773721
$677$	−21.8558	−	7.10138i	−0.839986	−	0.272928i	−0.142740	−	0.989760i	$-0.545591\pi$
$677$	−21.8558	−	7.10138i	−0.839986	−	0.272928i	−0.697246	+	0.716832i	$0.745591\pi$
$678$	4.28258	−	5.89447i	0.164472	−	0.226376i
$679$	−2.48510	−	1.80553i	−0.0953694	−	0.0692899i
$680$	7.90357	+	14.0964i	0.303088	+	0.540571i
$681$	−11.3806	+	8.26852i	−0.436107	+	0.316851i
$682$		−	0.0908843i		−	0.00348014i
$683$	16.8024	+	23.1265i	0.642925	+	0.884911i	0.998767	−	0.0496351i	$-0.0158058\pi$
$683$	16.8024	+	23.1265i	0.642925	+	0.884911i	−0.355842	+	0.934546i	$0.615806\pi$
$684$	−2.66472	−	8.20118i	−0.101888	−	0.313580i
$685$	4.22972	−	9.18700i	0.161609	−	0.351017i
$686$	0.309017	−	0.951057i	0.0117983	−	0.0363115i
$687$	21.9947	−	7.14651i	0.839150	−	0.272656i
$688$	1.10634	−	0.359471i	0.0421787	−	0.0137047i
$689$	16.7964	−	51.6940i	0.639891	−	1.96938i
$690$	−0.302744	+	0.657564i	−0.0115253	+	0.0250330i
$691$	6.16695	+	18.9799i	0.234602	+	0.722030i	0.997174	+	0.0751268i	$0.0239362\pi$
$691$	6.16695	+	18.9799i	0.234602	+	0.722030i	−0.762572	+	0.646903i	$0.776064\pi$
$692$	0.115702	+	0.159250i	0.00439832	+	0.00605377i
$693$			5.18171i			0.196837i
$694$	16.9738	−	12.3322i	0.644315	−	0.468122i
$695$	−3.30340	−	5.89177i	−0.125305	−	0.223488i
$696$	−3.24619	−	2.35849i	−0.123046	−	0.0893985i
$697$	−8.42091	+	11.5904i	−0.318965	+	0.439018i
$698$	−4.82219	−	1.56682i	−0.182522	−	0.0593051i
$699$	−20.9440			−0.792174
$700$	−4.26580	−	2.60825i	−0.161232	−	0.0985824i
$701$	36.0984			1.36342			0.681709	−	0.731623i	$-0.261237\pi$
$701$	36.0984			1.36342			0.681709	+	0.731623i	$0.261237\pi$
$702$	−15.9192	−	5.17246i	−0.600831	−	0.195222i
$703$	−9.57907	+	13.1845i	−0.361281	+	0.497261i
$704$	−1.78595	−	1.29757i	−0.0673104	−	0.0489039i
$705$	−21.1006	−	9.71478i	−0.794695	−	0.365880i
$706$	25.5248	−	18.5448i	0.960637	−	0.697944i
$707$			2.20020i			0.0827470i
$708$	−3.90689	−	5.37738i	−0.146830	−	0.202094i
$709$	−9.08077	−	27.9477i	−0.341035	−	1.04960i	−0.963672	−	0.267088i	$-0.913939\pi$
$709$	−9.08077	−	27.9477i	−0.341035	−	1.04960i	0.622637	−	0.782511i	$-0.286061\pi$
$710$	−1.69101	−	0.199291i	−0.0634625	−	0.00747925i
$711$	5.87101	−	18.0691i	0.220180	−	0.677645i
$712$	9.02356	−	2.93193i	0.338172	−	0.109879i
$713$	−0.0156897	+	0.00509790i	−0.000587584	+	0.000190918i
$714$	−1.80439	+	5.55334i	−0.0675276	+	0.207829i
$715$	−14.0507	−	12.9753i	−0.525465	−	0.485250i
$716$	6.19190	+	19.0567i	0.231402	+	0.712182i
$717$	0.464110	+	0.638792i	0.0173325	+	0.0238561i
$718$		−	22.7282i		−	0.848211i
$719$	−15.9127	+	11.5613i	−0.593445	+	0.431163i	−0.843546	−	0.537057i	$-0.819536\pi$
$719$	−15.9127	+	11.5613i	−0.593445	+	0.431163i	0.250101	+	0.968220i	$0.419536\pi$
$720$	0.614317	−	5.21257i	0.0228942	−	0.194261i
$721$	−14.6765	−	10.6631i	−0.546582	−	0.397115i
$722$	3.23498	−	4.45256i	0.120393	−	0.165707i
$723$	−1.71820	−	0.558276i	−0.0639004	−	0.0207625i
$724$	17.4598			0.648887
$725$	12.9538	−	21.1860i	0.481091	−	0.786827i
$726$	−4.94990			−0.183708
$727$	−17.0894	−	5.55269i	−0.633812	−	0.205938i	−0.0255490	−	0.999674i	$-0.508133\pi$
$727$	−17.0894	−	5.55269i	−0.633812	−	0.205938i	−0.608263	+	0.793736i	$0.708133\pi$
$728$	−2.27737	+	3.13453i	−0.0844049	+	0.116173i
$729$	1.72712	+	1.25483i	0.0639676	+	0.0464752i
$730$	−24.8929	+	4.96440i	−0.921329	+	0.183741i
$731$	6.80172	−	4.94174i	0.251571	−	0.182777i
$732$			5.87479i			0.217139i
$733$	−9.22394	−	12.6957i	−0.340694	−	0.468925i	0.603950	−	0.797022i	$-0.293593\pi$
$733$	−9.22394	−	12.6957i	−0.340694	−	0.468925i	−0.944644	+	0.328097i	$0.893593\pi$
$734$	−9.01577	−	27.7477i	−0.332778	−	1.02419i
$735$	−0.353325	−	1.77168i	−0.0130326	−	0.0653492i
$736$	−0.123826	+	0.381098i	−0.00456430	+	0.0140475i
$737$	−7.75896	+	2.52104i	−0.285805	+	0.0928637i
$738$	4.42516	−	1.43782i	0.162892	−	0.0529270i
$739$	−6.87246	+	21.1513i	−0.252807	+	0.778061i	0.741446	+	0.671012i	$0.234140\pi$
$739$	−6.87246	+	21.1513i	−0.252807	+	0.778061i	−0.994254	+	0.107049i	$0.965860\pi$
$740$	−8.65215	+	4.85110i	−0.318059	+	0.178330i
$741$	3.55364	+	10.9370i	0.130546	+	0.401780i
$742$	8.24589	+	11.3495i	0.302716	+	0.416653i
$743$			3.74802i			0.137501i	0.997634	+	0.0687507i	$0.0219013\pi$
$743$			3.74802i			0.137501i	−0.997634	+	0.0687507i	$0.978099\pi$
$744$	−0.0269094	+	0.0195508i	−0.000986547	+	0.000716768i
$745$	−15.5792	+	16.8703i	−0.570777	+	0.618080i
$746$	18.8305	+	13.6811i	0.689432	+	0.500902i
$747$	15.7094	−	21.6222i	0.574778	−	0.791114i
$748$	−15.1739	−	4.93030i	−0.554812	−	0.180269i
$749$	−11.0225			−0.402753
$750$	−9.02638	−	0.341144i	−0.329597	−	0.0124568i
$751$	12.5574			0.458225			0.229113	−	0.973400i	$-0.426418\pi$
$751$	12.5574			0.458225			0.229113	+	0.973400i	$0.426418\pi$
$752$	−12.2291	−	3.97347i	−0.445949	−	0.144898i
$753$	−8.24659	+	11.3505i	−0.300523	+	0.413634i
$754$	−15.5675	−	11.3105i	−0.566936	−	0.411903i
$755$	−30.7570	+	33.3060i	−1.11936	+	1.21213i
$756$	3.49509	−	2.53933i	0.127115	−	0.0923545i
$757$			32.3585i			1.17609i	0.808828	+	0.588045i	$0.200102\pi$
$757$			32.3585i			1.17609i	−0.808828	+	0.588045i	$0.799898\pi$
$758$	−0.966910	−	1.33084i	−0.0351198	−	0.0483382i
$759$	−0.220847	−	0.679698i	−0.00801625	−	0.0246715i
$760$	−7.16531	+	4.01746i	−0.259913	+	0.145728i
$761$	−9.16693	+	28.2129i	−0.332301	+	1.02272i	0.635735	+	0.771907i	$0.280697\pi$
$761$	−9.16693	+	28.2129i	−0.332301	+	1.02272i	−0.968036	+	0.250810i	$0.919303\pi$
$762$	−2.59905	+	0.844483i	−0.0941537	+	0.0305924i
$763$	−9.42093	+	3.06105i	−0.341061	+	0.110817i
$764$	5.60544	−	17.2518i	0.202798	−	0.624147i
$765$	−7.41905	−	37.2013i	−0.268236	−	1.34502i
$766$	3.82718	+	11.7788i	0.138281	+	0.425587i
$767$	−18.7360	−	25.7879i	−0.676519	−	0.931148i
$768$			0.807920i			0.0291533i
$769$	14.8367	−	10.7795i	0.535026	−	0.388719i	−0.287208	−	0.957868i	$-0.592727\pi$
$769$	14.8367	−	10.7795i	0.535026	−	0.388719i	0.822235	+	0.569149i	$0.192727\pi$
$770$	4.84091	−	0.965422i	0.174454	−	0.0347914i
$771$	−5.54532	−	4.02891i	−0.199710	−	0.145098i
$772$	−3.20789	+	4.41528i	−0.115454	+	0.158909i
$773$	−14.0924	−	4.57890i	−0.506869	−	0.164692i	0.0444089	−	0.999013i	$-0.485860\pi$
$773$	−14.0924	−	4.57890i	−0.506869	−	0.164692i	−0.551278	+	0.834322i	$0.685860\pi$
$774$	−2.73051			−0.0981460
$775$	−0.133844	−	0.156395i	−0.00480781	−	0.00561789i
$776$	−3.07175			−0.110269
$777$	−3.40856	−	1.10751i	−0.122282	−	0.0397317i
$778$	16.1538	−	22.2338i	0.579141	−	0.797120i
$779$	−5.89150	−	4.28043i	−0.211085	−	0.153362i
$780$	−0.819244	+	6.95141i	−0.0293336	+	0.248900i
$781$	1.35996	−	0.988067i	0.0486631	−	0.0353558i
$782$			2.89608i			0.103564i
$783$	12.6115	+	17.3582i	0.450698	+	0.620332i
$784$	−0.309017	−	0.951057i	−0.0110363	−	0.0339663i
$785$	−10.3485	−	9.55655i	−0.369355	−	0.341088i
$786$	2.60440	−	8.01553i	0.0928960	−	0.285905i
$787$	22.3234	−	7.25331i	0.795743	−	0.258553i	0.117195	−	0.993109i	$-0.462610\pi$
$787$	22.3234	−	7.25331i	0.795743	−	0.258553i	0.678548	+	0.734556i	$0.262610\pi$
$788$	19.1084	−	6.20870i	0.680709	−	0.221176i
$789$	6.89052	−	21.2069i	0.245309	−	0.754984i
$790$	−17.9746	−	2.11835i	−0.639506	−	0.0753677i
$791$	2.78677	+	8.57680i	0.0990861	+	0.304956i
$792$	3.04573	+	4.19209i	0.108225	+	0.148959i
$793$			28.1734i			1.00047i
$794$	−15.1937	+	11.0389i	−0.539205	+	0.391756i
$795$	23.0211	+	10.5990i	0.816475	+	0.375907i
$796$	11.4300	+	8.30436i	0.405124	+	0.294340i
$797$	22.4634	−	30.9183i	0.795696	−	1.09518i	−0.197679	−	0.980267i	$-0.563340\pi$
$797$	22.4634	−	30.9183i	0.795696	−	1.09518i	0.993375	−	0.114915i	$-0.0366596\pi$
$798$	−2.82282	−	0.917188i	−0.0999266	−	0.0324681i
$799$	−92.9325			−3.28771
$800$	−4.98419	+	0.397259i	−0.176218	+	0.0140452i
$801$	−22.2707			−0.786896
$802$	−7.35690	−	2.39040i	−0.259781	−	0.0844080i
$803$	14.7296	−	20.2735i	0.519795	−	0.715436i
$804$	2.41553	+	1.75499i	0.0851892	+	0.0618936i
$805$	−0.438201	−	0.781552i	−0.0154446	−	0.0275461i
$806$	−0.129048	+	0.0937587i	−0.00454551	+	0.00330251i
$807$		−	14.7104i		−	0.517830i
$808$	1.29325	+	1.78000i	0.0454962	+	0.0626202i
$809$	−1.70932	−	5.26075i	−0.0600965	−	0.184958i	0.916501	−	0.400032i	$-0.131001\pi$
$809$	−1.70932	−	5.26075i	−0.0600965	−	0.184958i	−0.976598	+	0.215074i	$0.931001\pi$
$810$	−3.32110	+	7.21348i	−0.116692	+	0.253456i
$811$	5.67936	−	17.4793i	0.199429	−	0.613780i	−0.800467	−	0.599377i	$-0.795415\pi$
$811$	5.67936	−	17.4793i	0.199429	−	0.613780i	0.999896	−	0.0144032i	$-0.00458485\pi$
$812$	4.72339	−	1.53472i	0.165759	−	0.0538582i
$813$	−12.3296	+	4.00611i	−0.432416	+	0.140501i
$814$	3.02615	−	9.31352i	0.106066	−	0.326439i
$815$	−19.1077	+	41.5022i	−0.669314	+	1.45376i
$816$	1.80439	+	5.55334i	0.0631663	+	0.194406i
$817$	2.51193	+	3.45738i	0.0878813	+	0.120958i
$818$		−	2.79734i		−	0.0978066i
$819$	7.35757	−	5.34559i	0.257094	−	0.186790i
$820$	−2.16772	−	3.86623i	−0.0757002	−	0.135015i
$821$	−17.7326	−	12.8835i	−0.618873	−	0.449638i	0.233654	−	0.972320i	$-0.424932\pi$
$821$	−17.7326	−	12.8835i	−0.618873	−	0.449638i	−0.852528	+	0.522682i	$0.824932\pi$
$822$	2.14794	−	2.95638i	0.0749180	−	0.103116i
$823$	14.1055	+	4.58316i	0.491687	+	0.159759i	0.544358	−	0.838853i	$-0.316773\pi$
$823$	14.1055	+	4.58316i	0.491687	+	0.159759i	−0.0526705	+	0.998612i	$0.516773\pi$
$824$	−18.1412			−0.631977
$825$	6.77524	−	5.79828i	0.235884	−	0.201870i
$826$	8.22705			0.286256
$827$	1.45271	+	0.472014i	0.0505157	+	0.0164135i	0.334166	−	0.942514i	$-0.391545\pi$
$827$	1.45271	+	0.472014i	0.0505157	+	0.0164135i	−0.283650	+	0.958928i	$0.591545\pi$
$828$	0.552855	−	0.760940i	0.0192130	−	0.0264445i
$829$	9.14670	+	6.64547i	0.317678	+	0.230807i	0.735184	−	0.677867i	$-0.237096\pi$
$829$	9.14670	+	6.64547i	0.317678	+	0.230807i	−0.417506	+	0.908674i	$0.637096\pi$
$830$	−23.1270	−	10.6477i	−0.802749	−	0.369588i
$831$	−17.3574	+	12.6109i	−0.602120	+	0.437466i
$832$			3.87449i			0.134324i
$833$	−4.24814	−	5.84706i	−0.147189	−	0.202589i
$834$	−0.754170	−	2.32110i	−0.0261148	−	0.0803730i
$835$	−11.4479	−	1.34917i	−0.396170	−	0.0466898i
$836$	2.50611	−	7.71303i	0.0866758	−	0.266761i
$837$	0.169155	−	0.0549618i	0.00584685	−	0.00189976i
$838$	−25.9968	+	8.44687i	−0.898045	+	0.291792i
$839$	1.70024	−	5.23281i	0.0586989	−	0.180657i	−0.917408	−	0.397948i	$-0.869722\pi$
$839$	1.70024	−	5.23281i	0.0586989	−	0.180657i	0.976107	+	0.217292i	$0.0697223\pi$
$840$	−1.32721	−	1.22564i	−0.0457931	−	0.0422885i
$841$	−1.33934	−	4.12206i	−0.0461841	−	0.142140i
$842$	12.5260	+	17.2405i	0.431673	+	0.594147i
$843$		−	2.93213i		−	0.100988i
$844$	13.6756	−	9.93592i	0.470734	−	0.342009i
$845$	−0.526487	+	4.46732i	−0.0181117	+	0.153681i
$846$	24.4179	+	17.7406i	0.839503	+	0.609935i
$847$	3.60119	−	4.95662i	0.123739	−	0.170311i
$848$	13.3421	+	4.33512i	0.458171	+	0.148869i
$849$	10.2290			0.351058
$850$	−33.3723	+	13.8622i	−1.14466	+	0.475470i
$851$	−1.77757			−0.0609344
$852$	−0.585102	−	0.190111i	−0.0200453	−	0.00651310i
$853$	−12.5099	+	17.2184i	−0.428331	+	0.589546i	−0.967569	−	0.252607i	$-0.918712\pi$
$853$	−12.5099	+	17.2184i	−0.428331	+	0.589546i	0.539239	+	0.842153i	$0.318712\pi$
$854$	−5.88277	−	4.27408i	−0.201304	−	0.146256i
$855$	18.9098	−	3.77117i	0.646700	−	0.128971i
$856$	−8.91738	+	6.47885i	−0.304790	+	0.221443i
$857$		−	9.05034i		−	0.309154i	−0.987981	−	0.154577i	$-0.950599\pi$
$857$		−	9.05034i		−	0.309154i	0.987981	−	0.154577i	$-0.0494014\pi$
$858$	−4.06174	−	5.59051i	−0.138666	−	0.190857i
$859$	1.69053	+	5.20291i	0.0576801	+	0.177521i	0.975746	−	0.218908i	$-0.0702494\pi$
$859$	1.69053	+	5.20291i	0.0576801	+	0.177521i	−0.918065	+	0.396429i	$0.870249\pi$
$860$	0.508730	+	2.55092i	0.0173476	+	0.0869857i
$861$	0.494893	−	1.52312i	0.0168659	−	0.0519079i
$862$	−2.25781	+	0.733606i	−0.0769013	+	0.0249867i
$863$	−6.25980	+	2.03393i	−0.213086	+	0.0692359i	−0.413615	−	0.910452i	$-0.635734\pi$
$863$	−6.25980	+	2.03393i	−0.213086	+	0.0692359i	0.200529	+	0.979688i	$0.435734\pi$
$864$	1.33500	−	4.10872i	0.0454177	−	0.139781i
$865$	−0.383927	+	0.215261i	−0.0130539	+	0.00731908i
$866$	−4.92295	−	15.1513i	−0.167289	−	0.514862i
$867$	16.7324	+	23.0302i	0.568263	+	0.782146i
$868$		−	0.0411697i		−	0.00139739i
$869$	14.4556	−	10.5026i	0.490374	−	0.356277i
$870$	6.08708	−	6.59155i	0.206371	−	0.223475i
$871$	11.5840	+	8.41627i	0.392509	+	0.285175i
$872$	−5.82245	+	8.01392i	−0.197173	+	0.271386i
$873$	6.85732	+	2.22808i	0.232085	+	0.0754091i
$874$	−1.47210			−0.0497946
$875$	6.90856	−	8.79044i	0.233552	−	0.297171i
$876$	−9.17125			−0.309868
$877$	−3.52880	−	1.14658i	−0.119159	−	0.0387172i	0.248830	−	0.968547i	$-0.419954\pi$
$877$	−3.52880	−	1.14658i	−0.119159	−	0.0387172i	−0.367990	+	0.929830i	$0.619954\pi$
$878$	9.21816	−	12.6877i	0.311098	−	0.428190i
$879$	−4.34295	−	3.15534i	−0.146484	−	0.106427i
$880$	3.34891	−	3.62646i	0.112892	−	0.122248i
$881$	−43.6473	+	31.7116i	−1.47051	+	1.06839i	−0.490049	+	0.871695i	$0.663021\pi$
$881$	−43.6473	+	31.7116i	−1.47051	+	1.06839i	−0.980465	+	0.196696i	$0.936979\pi$
$882$			2.34727i			0.0790365i
$883$	17.8439	+	24.5600i	0.600496	+	0.826511i	0.995754	−	0.0920588i	$-0.0293448\pi$
$883$	17.8439	+	24.5600i	0.600496	+	0.826511i	−0.395258	+	0.918570i	$0.629345\pi$
$884$	8.65320	+	26.6318i	0.291039	+	0.895725i
$885$	12.9640	−	7.26869i	0.435781	−	0.244334i
$886$	5.69648	−	17.5320i	0.191377	−	0.588997i
$887$	−32.9048	+	10.6914i	−1.10484	+	0.358983i	−0.803962	−	0.594681i	$-0.797278\pi$
$887$	−32.9048	+	10.6914i	−1.10484	+	0.358983i	−0.300874	+	0.953664i	$0.597278\pi$
$888$	−3.40856	+	1.10751i	−0.114384	+	0.0371656i
$889$	1.04526	−	3.21697i	0.0350568	−	0.107894i
$890$	4.14933	+	20.8059i	0.139086	+	0.697417i
$891$	−2.42270	−	7.45629i	−0.0811633	−	0.249795i
$892$	−11.0658	−	15.2307i	−0.370509	−	0.509962i
$893$		−	47.2384i		−	1.58077i
$894$	−6.71239	+	4.87684i	−0.224496	+	0.163106i
$895$	−43.9397	+	8.76290i	−1.46874	+	0.292911i
$896$	−0.809017	−	0.587785i	−0.0270274	−	0.0196365i
$897$	−0.737279	+	1.01478i	−0.0246170	+	0.0338824i
$898$	−10.4841	−	3.40649i	−0.349859	−	0.113676i
$899$	0.204468			0.00681940
$900$	11.4148	+	2.72843i	0.380492	+	0.0909475i
$901$	101.391			3.37782
$902$	4.16177	+	1.35224i	0.138572	+	0.0450247i
$903$	−0.552418	+	0.760339i	−0.0183833	+	0.0253025i
$904$	7.29586	+	5.30075i	0.242657	+	0.176300i
$905$	−4.56950	+	38.7729i	−0.151895	+	1.28885i
$906$	−13.2519	+	9.62804i	−0.440263	+	0.319870i
$907$			17.0168i			0.565032i	0.959263	+	0.282516i	$0.0911690\pi$
$907$			17.0168i			0.565032i	−0.959263	+	0.282516i	$0.908831\pi$
$908$	−10.2343	−	14.0864i	−0.339638	−	0.467472i
$909$	−1.59590	−	4.91169i	−0.0529328	−	0.162910i
$910$	−6.36482	−	5.87771i	−0.210992	−	0.194844i
$911$	−17.2413	+	53.0631i	−0.571228	+	1.75806i	0.0774489	+	0.996996i	$0.475323\pi$
$911$	−17.2413	+	53.0631i	−0.571228	+	1.75806i	−0.648677	+	0.761064i	$0.724677\pi$
$912$	−2.82282	+	0.917188i	−0.0934728	+	0.0303711i
$913$	23.9054	−	7.76735i	0.791155	−	0.257062i
$914$	2.32652	−	7.16028i	0.0769543	−	0.236841i
$915$	−13.0461	−	1.53753i	−0.431292	−	0.0508291i
$916$	8.84557	+	27.2239i	0.292266	+	0.899502i
$917$	6.13164	+	8.43947i	0.202484	+	0.278696i
$918$		−	31.2234i		−	1.03053i
$919$	48.0384	−	34.9019i	1.58464	−	1.15131i	0.673518	−	0.739170i	$-0.264782\pi$
$919$	48.0384	−	34.9019i	1.58464	−	1.15131i	0.911121	−	0.412138i	$-0.135218\pi$
$920$	−0.813897	−	0.374720i	−0.0268334	−	0.0123542i
$921$	2.50422	+	1.81943i	0.0825170	+	0.0599521i
$922$	−0.951493	+	1.30962i	−0.0313358	+	0.0431300i
$923$	−2.80594	−	0.911704i	−0.0923585	−	0.0300091i
$924$	1.78352			0.0586737
$925$	−8.50842	−	20.4834i	−0.279755	−	0.673491i
$926$	10.6005			0.348353
$927$	40.4980	+	13.1586i	1.33013	+	0.432185i
$928$	2.91922	−	4.01796i	0.0958280	−	0.131896i
$929$	4.27986	+	3.10950i	0.140418	+	0.102019i	0.655776	−	0.754955i	$-0.272341\pi$
$929$	4.27986	+	3.10950i	0.140418	+	0.102019i	−0.515359	+	0.856974i	$0.672341\pi$
$930$	−0.0363739	−	0.0648745i	−0.00119275	−	0.00212732i
$931$	2.97211	−	2.15937i	0.0974071	−	0.0707704i
$932$		−	25.9233i		−	0.849146i
$933$	5.61723	+	7.73146i	0.183900	+	0.253116i
$934$	8.58838	+	26.4323i	0.281020	+	0.864891i
$935$	14.9200	−	32.4063i	0.487935	−	1.05980i
$936$	2.81034	−	8.64934i	0.0918589	−	0.282713i
$937$	7.11671	−	2.31236i	0.232493	−	0.0755415i	−0.190454	−	0.981696i	$-0.560996\pi$
$937$	7.11671	−	2.31236i	0.232493	−	0.0755415i	0.422946	+	0.906155i	$0.360996\pi$
$938$	−3.51474	+	1.14201i	−0.114760	+	0.0372879i
$939$	4.08089	−	12.5597i	0.133175	−	0.409869i
$940$	12.0244	−	26.1172i	0.392194	−	0.851849i
$941$	6.64116	+	20.4394i	0.216495	+	0.666305i	0.999044	+	0.0437150i	$0.0139194\pi$
$941$	6.64116	+	20.4394i	0.216495	+	0.666305i	−0.782549	+	0.622590i	$0.786081\pi$
$942$	−2.99154	−	4.11750i	−0.0974696	−	0.134155i
$943$		−	0.794312i		−	0.0258664i
$944$	6.65583	−	4.83574i	0.216629	−	0.157390i
$945$	4.72436	+	8.42611i	0.153684	+	0.274102i
$946$	−2.07754	−	1.50942i	−0.0675467	−	0.0490755i
$947$	−13.9573	+	19.2106i	−0.453552	+	0.624261i	−0.973156	−	0.230146i	$-0.926079\pi$
$947$	−13.9573	+	19.2106i	−0.453552	+	0.624261i	0.519604	+	0.854407i	$0.326079\pi$
$948$	−6.21932	−	2.02078i	−0.201994	−	0.0656319i
$949$	−43.9820			−1.42772
$950$	−7.04628	−	16.9634i	−0.228612	−	0.550366i
$951$	−28.5023			−0.924250
$952$	−6.87363	−	2.23338i	−0.222776	−	0.0723842i
$953$	−16.1530	+	22.2327i	−0.523247	+	0.720188i	−0.986083	−	0.166256i	$-0.946832\pi$
$953$	−16.1530	+	22.2327i	−0.523247	+	0.720188i	0.462835	+	0.886444i	$0.346832\pi$
$954$	−26.6403	−	19.3553i	−0.862511	−	0.626651i
$955$	36.8439	+	16.9630i	1.19224	+	0.548911i
$956$	−0.790662	+	0.574450i	−0.0255718	+	0.0185790i
$957$			8.85782i			0.286333i
$958$	21.0530	+	28.9770i	0.680193	+	0.936206i
$959$	1.39771	+	4.30171i	0.0451344	+	0.138909i
$960$	−1.79415	−	0.211446i	−0.0579059	−	0.00682438i
$961$	−9.57900	+	29.4811i	−0.309000	+	0.951005i
$962$	−16.3462	+	5.31121i	−0.527024	+	0.171240i
$963$	24.6064	−	7.99510i	0.792930	−	0.257639i
$964$	0.691004	−	2.12669i	0.0222557	−	0.0684961i
$965$	−8.96546	−	8.27931i	−0.288608	−	0.266520i
$966$	−0.100042	−	0.307897i	−0.00321879	−	0.00990642i
$967$	2.91680	+	4.01463i	0.0937980	+	0.129102i	0.853337	−	0.521360i	$-0.174575\pi$
$967$	2.91680	+	4.01463i	0.0937980	+	0.129102i	−0.759539	+	0.650462i	$0.774575\pi$
$968$		−	6.12672i		−	0.196920i
$969$	−17.3546	+	12.6088i	−0.557509	+	0.405054i
$970$	0.803926	−	6.82144i	0.0258125	−	0.219023i
$971$	−21.8265	−	15.8579i	−0.700447	−	0.508905i	0.179631	−	0.983734i	$-0.442510\pi$
$971$	−21.8265	−	15.8579i	−0.700447	−	0.508905i	−0.880078	+	0.474829i	$0.842510\pi$
$972$	−9.30451	+	12.8066i	−0.298442	+	0.410771i
$973$	2.87293	+	0.933471i	0.0921018	+	0.0299257i
$974$	33.8626			1.08503
$975$	−15.2226	−	3.63859i	−0.487512	−	0.116528i
$976$	−7.27150			−0.232755
$977$	43.5473	+	14.1494i	1.39320	+	0.452678i	0.906986	−	0.421161i	$-0.138377\pi$
$977$	43.5473	+	14.1494i	1.39320	+	0.452678i	0.486215	+	0.873839i	$0.338377\pi$
$978$	−9.70329	+	13.3554i	−0.310277	+	0.427060i
$979$	−16.9449	−	12.3112i	−0.541563	−	0.393468i
$980$	2.19289	−	0.437327i	0.0700491	−	0.0139699i
$981$	18.8108	−	13.6668i	0.600583	−	0.436349i
$982$			36.2432i			1.15657i
$983$	−21.6744	−	29.8323i	−0.691306	−	0.951502i	−1.00000		0.000340016i	$-0.999892\pi$
$983$	−21.6744	−	29.8323i	−0.691306	−	0.951502i	0.308694	−	0.951162i	$-0.400108\pi$
$984$	−0.494893	−	1.52312i	−0.0157766	−	0.0485554i
$985$	8.78668	+	44.0590i	0.279967	+	1.40384i
$986$	11.0920	−	34.1377i	0.353241	−	1.08716i
$987$	9.88012	−	3.21025i	0.314488	−	0.102183i
$988$	−13.5372	+	4.39850i	−0.430676	+	0.139935i
$989$	−0.144044	+	0.443320i	−0.00458032	+	0.0140968i
$990$	−10.1065	+	5.66652i	−0.321205	+	0.180094i
$991$	11.4304	+	35.1791i	0.363098	+	1.11750i	0.951163	+	0.308688i	$0.0998899\pi$
$991$	11.4304	+	35.1791i	0.363098	+	1.11750i	−0.588065	+	0.808814i	$0.700110\pi$
$992$	−0.0241990	−	0.0333070i	−0.000768318	−	0.00105750i
$993$		−	16.8442i		−	0.534536i
$994$	0.616048	−	0.447585i	0.0195399	−	0.0141965i
$995$	−21.4329	+	23.2091i	−0.679468	+	0.735779i
$996$	−7.44228	−	5.40713i	−0.235818	−	0.171331i
$997$	16.3794	−	22.5443i	0.518740	−	0.713984i	−0.466623	−	0.884456i	$-0.654529\pi$
$997$	16.3794	−	22.5443i	0.518740	−	0.713984i	0.985362	+	0.170473i	$0.0545294\pi$
$998$	34.6509	+	11.2588i	1.09686	+	0.356390i
$999$	19.1645			0.606337

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.m.b.29.3	✓	40
25.12	odd	20		8750.2.a.bf.1.12		20
25.13	odd	20		8750.2.a.be.1.9		20
25.19	even	10	inner	350.2.m.b.169.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.m.b.29.3	✓	40	1.1	even	1	trivial
350.2.m.b.169.3	yes	40	25.19	even	10	inner
8750.2.a.be.1.9		20	25.13	odd	20
8750.2.a.bf.1.12		20	25.12	odd	20

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(0.474883 - 0.653621i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.51703 + 1.64275i) q^{5} +(-0.653621 + 0.474883i) q^{6} -1.00000i q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.725345 + 2.23238i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 0.309017i) q^{2} +(0.474883 - 0.653621i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.51703 + 1.64275i) q^{5} +(-0.653621 + 0.474883i) q^{6} -1.00000i q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.725345 + 2.23238i) q^{9} +(1.95042 - 1.09356i) q^{10} +(-0.682171 + 2.09951i) q^{11} +(0.768378 - 0.249661i) q^{12} +(3.68486 - 1.19728i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(0.353325 + 1.77168i) q^{15} +(0.309017 + 0.951057i) q^{16} +(4.24814 + 5.84706i) q^{17} -2.34727i q^{18} +(-2.97211 + 2.15937i) q^{19} +(-2.19289 + 0.437327i) q^{20} +(-0.653621 - 0.474883i) q^{21} +(1.29757 - 1.78595i) q^{22} +(-0.381098 - 0.123826i) q^{23} -0.807920 q^{24} +(-0.397259 - 4.98419i) q^{25} -3.87449 q^{26} +(4.10872 + 1.33500i) q^{27} +(0.587785 - 0.809017i) q^{28} +(4.01796 + 2.91922i) q^{29} +(0.211446 - 1.79415i) q^{30} +(0.0333070 - 0.0241990i) q^{31} -1.00000i q^{32} +(1.04833 + 1.44290i) q^{33} +(-2.23338 - 6.87363i) q^{34} +(1.64275 + 1.51703i) q^{35} +(-0.725345 + 2.23238i) q^{36} +(4.21894 - 1.37082i) q^{37} +(3.49393 - 1.13525i) q^{38} +(0.967309 - 2.97707i) q^{39} +(2.22070 + 0.261716i) q^{40} +(0.612552 + 1.88524i) q^{41} +(0.474883 + 0.653621i) q^{42} -1.16327i q^{43} +(-1.78595 + 1.29757i) q^{44} +(-4.76761 - 2.19502i) q^{45} +(0.324181 + 0.235532i) q^{46} +(-7.55799 + 10.4027i) q^{47} +(0.768378 + 0.249661i) q^{48} -1.00000 q^{49} +(-1.16238 + 4.86301i) q^{50} +5.83913 q^{51} +(3.68486 + 1.19728i) q^{52} +(8.24589 - 11.3495i) q^{53} +(-3.49509 - 2.53933i) q^{54} +(-2.41409 - 4.30564i) q^{55} +(-0.809017 + 0.587785i) q^{56} +2.96808i q^{57} +(-2.91922 - 4.01796i) q^{58} +(-2.54230 - 7.82439i) q^{59} +(-0.755519 + 1.64100i) q^{60} +(-2.24702 + 6.91561i) q^{61} +(-0.0391548 + 0.0127221i) q^{62} +(2.23238 - 0.725345i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-3.62319 + 7.86962i) q^{65} +(-0.551139 - 1.69623i) q^{66} +(2.17223 + 2.98981i) q^{67} +7.22736i q^{68} +(-0.261913 + 0.190291i) q^{69} +(-1.09356 - 1.95042i) q^{70} +(-0.616048 - 0.447585i) q^{71} +(1.37969 - 1.89898i) q^{72} +(-10.7961 - 3.50786i) q^{73} -4.43605 q^{74} +(-3.44643 - 2.10725i) q^{75} -3.67373 q^{76} +(2.09951 + 0.682171i) q^{77} +(-1.83993 + 2.53245i) q^{78} +(-6.54826 - 4.75759i) q^{79} +(-2.03114 - 0.935140i) q^{80} +(-2.87318 + 2.08749i) q^{81} -1.98226i q^{82} +(-6.69265 - 9.21165i) q^{83} +(-0.249661 - 0.768378i) q^{84} +(-16.0498 - 1.89152i) q^{85} +(-0.359471 + 1.10634i) q^{86} +(3.81612 - 1.23993i) q^{87} +(2.09951 - 0.682171i) q^{88} +(-2.93193 + 9.02356i) q^{89} +(3.85597 + 3.56086i) q^{90} +(-1.19728 - 3.68486i) q^{91} +(-0.235532 - 0.324181i) q^{92} -0.0332619i q^{93} +(10.4027 - 7.55799i) q^{94} +(0.961475 - 8.15826i) q^{95} +(-0.653621 - 0.474883i) q^{96} +(1.80553 - 2.48510i) q^{97} +(0.951057 + 0.309017i) q^{98} -5.18171 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 10 q^{4} + 6 q^{5} - 2 q^{6} + 20 q^{9}+O(q^{10}) \) 40 * q + 10 * q^4 + 6 * q^5 - 2 * q^6 + 20 * q^9	\( 40 q + 10 q^{4} + 6 q^{5} - 2 q^{6} + 20 q^{9} - 4 q^{10} - 6 q^{11} + 10 q^{12} + 10 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{19} + 4 q^{20} - 2 q^{21} - 10 q^{22} - 10 q^{23} - 8 q^{24} - 10 q^{25} + 12 q^{26} - 30 q^{27} + 4 q^{29} - 22 q^{30} - 24 q^{31} - 60 q^{33} - 4 q^{35} - 20 q^{36} + 10 q^{37} + 10 q^{38} + 36 q^{39} - 6 q^{40} - 34 q^{41} + 6 q^{44} + 112 q^{45} - 6 q^{46} + 30 q^{47} + 10 q^{48} - 40 q^{49} - 16 q^{50} + 44 q^{51} + 10 q^{53} + 20 q^{54} + 34 q^{55} - 10 q^{56} + 20 q^{58} + 12 q^{59} + 2 q^{60} + 2 q^{61} + 10 q^{64} - 106 q^{65} + 10 q^{66} - 30 q^{67} + 84 q^{69} + 4 q^{70} + 16 q^{71} - 110 q^{73} - 60 q^{74} + 10 q^{75} + 32 q^{76} + 20 q^{77} - 20 q^{78} + 4 q^{79} - 4 q^{80} - 20 q^{81} + 10 q^{83} + 2 q^{84} - 42 q^{85} - 14 q^{86} - 20 q^{87} + 20 q^{88} - 38 q^{90} + 2 q^{91} - 30 q^{92} + 6 q^{94} + 64 q^{95} - 2 q^{96} + 30 q^{97} - 72 q^{99}+O(q^{100}) \) 40 * q + 10 * q^4 + 6 * q^5 - 2 * q^6 + 20 * q^9 - 4 * q^10 - 6 * q^11 + 10 * q^12 + 10 * q^14 - 12 * q^15 - 10 * q^16 - 2 * q^19 + 4 * q^20 - 2 * q^21 - 10 * q^22 - 10 * q^23 - 8 * q^24 - 10 * q^25 + 12 * q^26 - 30 * q^27 + 4 * q^29 - 22 * q^30 - 24 * q^31 - 60 * q^33 - 4 * q^35 - 20 * q^36 + 10 * q^37 + 10 * q^38 + 36 * q^39 - 6 * q^40 - 34 * q^41 + 6 * q^44 + 112 * q^45 - 6 * q^46 + 30 * q^47 + 10 * q^48 - 40 * q^49 - 16 * q^50 + 44 * q^51 + 10 * q^53 + 20 * q^54 + 34 * q^55 - 10 * q^56 + 20 * q^58 + 12 * q^59 + 2 * q^60 + 2 * q^61 + 10 * q^64 - 106 * q^65 + 10 * q^66 - 30 * q^67 + 84 * q^69 + 4 * q^70 + 16 * q^71 - 110 * q^73 - 60 * q^74 + 10 * q^75 + 32 * q^76 + 20 * q^77 - 20 * q^78 + 4 * q^79 - 4 * q^80 - 20 * q^81 + 10 * q^83 + 2 * q^84 - 42 * q^85 - 14 * q^86 - 20 * q^87 + 20 * q^88 - 38 * q^90 + 2 * q^91 - 30 * q^92 + 6 * q^94 + 64 * q^95 - 2 * q^96 + 30 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more