LMFDB - Embedded newform 850.2.v.d.143.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [850,2,Mod(107,850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(850, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([4, 5]))

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

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

chi := DirichletCharacter("850.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.v (of order $16$, degree $8$, 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:	$6.78728417181$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 170)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			143.2
Character	$\chi$	$=$	850.143
Dual form			850.2.v.d.107.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.382683 + 0.923880i) q^{2} +(-1.51925 + 0.302197i) q^{3} +(-0.707107 + 0.707107i) q^{4} +(-0.860584 - 1.28795i) q^{6} +(-0.134383 - 0.201119i) q^{7} +(-0.923880 - 0.382683i) q^{8} +(-0.554854 + 0.229828i) q^{9} +O(q^{10})$	\(q+(0.382683 + 0.923880i) q^{2} +(-1.51925 + 0.302197i) q^{3} +(-0.707107 + 0.707107i) q^{4} +(-0.860584 - 1.28795i) q^{6} +(-0.134383 - 0.201119i) q^{7} +(-0.923880 - 0.382683i) q^{8} +(-0.554854 + 0.229828i) q^{9} +(1.18040 - 0.788717i) q^{11} +(0.860584 - 1.28795i) q^{12} +0.250606 q^{13} +(0.134383 - 0.201119i) q^{14} -1.00000i q^{16} +(-3.42934 - 2.28902i) q^{17} +(-0.424667 - 0.424667i) q^{18} +(-5.56274 - 2.30416i) q^{19} +(0.264939 + 0.264939i) q^{21} +(1.18040 + 0.788717i) q^{22} +(0.605259 - 3.04284i) q^{23} +(1.51925 + 0.302197i) q^{24} +(0.0959029 + 0.231530i) q^{26} +(4.63737 - 3.09859i) q^{27} +(0.237236 + 0.0471892i) q^{28} +(0.237131 + 1.19214i) q^{29} +(4.24419 + 2.83588i) q^{31} +(0.923880 - 0.382683i) q^{32} +(-1.55497 + 1.55497i) q^{33} +(0.802430 - 4.04427i) q^{34} +(0.229828 - 0.554854i) q^{36} +(-1.26779 - 6.37360i) q^{37} -6.02107i q^{38} +(-0.380733 + 0.0757325i) q^{39} +(0.171169 - 0.860522i) q^{41} +(-0.143384 + 0.346160i) q^{42} +(3.38747 - 8.17809i) q^{43} +(-0.276961 + 1.39237i) q^{44} +(3.04284 - 0.605259i) q^{46} -10.2201i q^{47} +(0.302197 + 1.51925i) q^{48} +(2.65639 - 6.41310i) q^{49} +(5.90175 + 2.44125i) q^{51} +(-0.177206 + 0.177206i) q^{52} +(-1.82801 + 0.757188i) q^{53} +(4.63737 + 3.09859i) q^{54} +(0.0471892 + 0.237236i) q^{56} +(9.14748 + 1.81955i) q^{57} +(-1.01065 + 0.675292i) q^{58} +(0.520057 + 1.25553i) q^{59} +(-8.99481 - 1.78918i) q^{61} +(-0.995828 + 5.00636i) q^{62} +(0.120786 + 0.0807066i) q^{63} +(0.707107 + 0.707107i) q^{64} +(-2.03166 - 0.841542i) q^{66} +(7.69457 + 7.69457i) q^{67} +(4.04349 - 0.806326i) q^{68} +4.80573i q^{69} +(-0.548870 + 0.821442i) q^{71} +0.600569 q^{72} +(-8.70593 + 13.0293i) q^{73} +(5.40328 - 3.61035i) q^{74} +(5.56274 - 2.30416i) q^{76} +(-0.317252 - 0.131410i) q^{77} +(-0.215668 - 0.322770i) q^{78} +(-5.86124 - 8.77197i) q^{79} +(-4.83492 + 4.83492i) q^{81} +(0.860522 - 0.171169i) q^{82} +(0.0730601 + 0.176383i) q^{83} -0.374680 q^{84} +8.85190 q^{86} +(-0.720521 - 1.73949i) q^{87} +(-1.39237 + 0.276961i) q^{88} +(5.17953 - 5.17953i) q^{89} +(-0.0336774 - 0.0504017i) q^{91} +(1.72363 + 2.57960i) q^{92} +(-7.30496 - 3.02581i) q^{93} +(9.44214 - 3.91106i) q^{94} +(-1.28795 + 0.860584i) q^{96} +(-5.27043 + 7.88775i) q^{97} +6.94149 q^{98} +(-0.473679 + 0.708911i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q+O(q^{10}) $ 40 * q	$ 40 q + 16 q^{18} - 8 q^{26} - 24 q^{27} + 8 q^{28} + 8 q^{29} - 16 q^{31} + 32 q^{33} + 8 q^{34} - 32 q^{39} - 56 q^{41} + 24 q^{42} - 16 q^{43} + 16 q^{44} + 16 q^{49} - 32 q^{51} + 16 q^{52} - 16 q^{53} - 24 q^{54} - 8 q^{56} + 120 q^{57} - 16 q^{58} + 24 q^{61} + 8 q^{62} + 24 q^{63} - 16 q^{67} + 24 q^{71} - 56 q^{72} - 88 q^{73} + 32 q^{74} - 24 q^{77} - 32 q^{78} - 104 q^{79} + 48 q^{81} - 16 q^{82} - 16 q^{83} + 96 q^{86} - 136 q^{87} - 16 q^{89} + 48 q^{91} + 8 q^{92} + 8 q^{93} - 8 q^{94} - 16 q^{97} - 72 q^{98} + 160 q^{99}+O(q^{100}) $ 40 * q + 16 * q^18 - 8 * q^26 - 24 * q^27 + 8 * q^28 + 8 * q^29 - 16 * q^31 + 32 * q^33 + 8 * q^34 - 32 * q^39 - 56 * q^41 + 24 * q^42 - 16 * q^43 + 16 * q^44 + 16 * q^49 - 32 * q^51 + 16 * q^52 - 16 * q^53 - 24 * q^54 - 8 * q^56 + 120 * q^57 - 16 * q^58 + 24 * q^61 + 8 * q^62 + 24 * q^63 - 16 * q^67 + 24 * q^71 - 56 * q^72 - 88 * q^73 + 32 * q^74 - 24 * q^77 - 32 * q^78 - 104 * q^79 + 48 * q^81 - 16 * q^82 - 16 * q^83 + 96 * q^86 - 136 * q^87 - 16 * q^89 + 48 * q^91 + 8 * q^92 + 8 * q^93 - 8 * q^94 - 16 * q^97 - 72 * q^98 + 160 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/850\mathbb{Z}\right)^\times$.

$n$	$477$	$751$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{11}{16}\right)$

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 $

$2$	0.382683	+	0.923880i	0.270598	+	0.653281i
$2$	0.382683	+	0.923880i	0.270598	+	0.653281i
$3$	−1.51925	+	0.302197i	−0.877137	+	0.174473i	−0.613068	−	0.790030i	$-0.710065\pi$
$3$	−1.51925	+	0.302197i	−0.877137	+	0.174473i	−0.264069	+	0.964504i	$0.585065\pi$
$4$	−0.707107	+	0.707107i	−0.353553	+	0.353553i
$5$		0			0
$5$		0			0
$6$	−0.860584	−	1.28795i	−0.351332	−	0.525805i
$7$	−0.134383	−	0.201119i	−0.0507922	−	0.0760159i	0.805204	−	0.592997i	$-0.202056\pi$
$7$	−0.134383	−	0.201119i	−0.0507922	−	0.0760159i	−0.855997	+	0.516982i	$0.827056\pi$
$8$	−0.923880	−	0.382683i	−0.326641	−	0.135299i
$9$	−0.554854	+	0.229828i	−0.184951	+	0.0766093i
$10$		0			0
$11$	1.18040	−	0.788717i	0.355904	−	0.237807i	−0.364745	−	0.931107i	$-0.618844\pi$
$11$	1.18040	−	0.788717i	0.355904	−	0.237807i	0.720649	+	0.693300i	$0.243844\pi$
$12$	0.860584	−	1.28795i	0.248429	−	0.371800i
$13$	0.250606			0.0695057			0.0347529	−	0.999396i	$-0.488936\pi$
$13$	0.250606			0.0695057			0.0347529	+	0.999396i	$0.488936\pi$
$14$	0.134383	−	0.201119i	0.0359155	−	0.0537513i
$15$		0			0
$16$		−	1.00000i		−	0.250000i
$17$	−3.42934	−	2.28902i	−0.831737	−	0.555170i
$17$	−3.42934	−	2.28902i	−0.831737	−	0.555170i
$18$	−0.424667	−	0.424667i	−0.100095	−	0.100095i
$19$	−5.56274	−	2.30416i	−1.27618	−	0.528611i	−0.361342	−	0.932433i	$-0.617681\pi$
$19$	−5.56274	−	2.30416i	−1.27618	−	0.528611i	−0.914837	+	0.403822i	$0.867681\pi$
$20$		0			0
$21$	0.264939	+	0.264939i	0.0578144	+	0.0578144i
$22$	1.18040	+	0.788717i	0.251662	+	0.168155i
$23$	0.605259	−	3.04284i	0.126205	−	0.634477i	−0.864960	−	0.501841i	$-0.832656\pi$
$23$	0.605259	−	3.04284i	0.126205	−	0.634477i	0.991165	−	0.132635i	$-0.0423439\pi$
$24$	1.51925	+	0.302197i	0.310115	+	0.0616857i
$25$		0			0
$26$	0.0959029	+	0.231530i	0.0188081	+	0.0454068i
$27$	4.63737	−	3.09859i	0.892462	−	0.596324i
$28$	0.237236	+	0.0471892i	0.0448334	+	0.00891792i
$29$	0.237131	+	1.19214i	0.0440342	+	0.221375i	0.996536	−	0.0831567i	$-0.0265002\pi$
$29$	0.237131	+	1.19214i	0.0440342	+	0.221375i	−0.952502	+	0.304531i	$0.901500\pi$
$30$		0			0
$31$	4.24419	+	2.83588i	0.762279	+	0.509339i	0.874902	−	0.484299i	$-0.160925\pi$
$31$	4.24419	+	2.83588i	0.762279	+	0.509339i	−0.112623	+	0.993638i	$0.535925\pi$
$32$	0.923880	−	0.382683i	0.163320	−	0.0676495i
$33$	−1.55497	+	1.55497i	−0.270685	+	0.270685i
$34$	0.802430	−	4.04427i	0.137616	−	0.693586i
$35$		0			0
$36$	0.229828	−	0.554854i	0.0383047	−	0.0924756i
$37$	−1.26779	−	6.37360i	−0.208423	−	1.04781i	−0.933345	−	0.358982i	$-0.883124\pi$
$37$	−1.26779	−	6.37360i	−0.208423	−	1.04781i	0.724921	−	0.688832i	$-0.241876\pi$
$38$		−	6.02107i		−	0.976746i
$39$	−0.380733	+	0.0757325i	−0.0609660	+	0.0121269i
$40$		0			0
$41$	0.171169	−	0.860522i	0.0267320	−	0.134391i	−0.965115	−	0.261827i	$-0.915675\pi$
$41$	0.171169	−	0.860522i	0.0267320	−	0.134391i	0.991847	+	0.127436i	$0.0406749\pi$
$42$	−0.143384	+	0.346160i	−0.0221246	+	0.0534136i
$43$	3.38747	−	8.17809i	0.516585	−	1.24715i	−0.423404	−	0.905941i	$-0.639165\pi$
$43$	3.38747	−	8.17809i	0.516585	−	1.24715i	0.939989	−	0.341205i	$-0.110835\pi$
$44$	−0.276961	+	1.39237i	−0.0417534	+	0.209908i
$45$		0			0
$46$	3.04284	−	0.605259i	0.448643	−	0.0892406i
$47$		−	10.2201i		−	1.49075i	−0.666643	−	0.745377i	$-0.732269\pi$
$47$		−	10.2201i		−	1.49075i	0.666643	−	0.745377i	$-0.267731\pi$
$48$	0.302197	+	1.51925i	0.0436183	+	0.219284i
$49$	2.65639	−	6.41310i	0.379485	−	0.916158i
$50$		0			0
$51$	5.90175	+	2.44125i	0.826410	+	0.341844i
$52$	−0.177206	+	0.177206i	−0.0245740	+	0.0245740i
$53$	−1.82801	+	0.757188i	−0.251097	+	0.104008i	−0.504682	−	0.863305i	$-0.668390\pi$
$53$	−1.82801	+	0.757188i	−0.251097	+	0.104008i	0.253585	+	0.967313i	$0.418390\pi$
$54$	4.63737	+	3.09859i	0.631066	+	0.421665i
$55$		0			0
$56$	0.0471892	+	0.237236i	0.00630592	+	0.0317020i
$57$	9.14748	+	1.81955i	1.21161	+	0.241005i
$58$	−1.01065	+	0.675292i	−0.132704	+	0.0886702i
$59$	0.520057	+	1.25553i	0.0677056	+	0.163456i	0.954110	−	0.299455i	$-0.0968049\pi$
$59$	0.520057	+	1.25553i	0.0677056	+	0.163456i	−0.886405	+	0.462911i	$0.846805\pi$
$60$		0			0
$61$	−8.99481	−	1.78918i	−1.15167	−	0.229081i	−0.417907	−	0.908490i	$-0.637236\pi$
$61$	−8.99481	−	1.78918i	−1.15167	−	0.229081i	−0.733760	+	0.679409i	$0.762236\pi$
$62$	−0.995828	+	5.00636i	−0.126470	+	0.635809i
$63$	0.120786	+	0.0807066i	0.0152176	+	0.0101681i
$64$	0.707107	+	0.707107i	0.0883883	+	0.0883883i
$65$		0			0
$66$	−2.03166	−	0.841542i	−0.250080	−	0.103587i
$67$	7.69457	+	7.69457i	0.940041	+	0.940041i	0.998301	−	0.0582603i	$-0.0185553\pi$
$67$	7.69457	+	7.69457i	0.940041	+	0.940041i	−0.0582603	+	0.998301i	$0.518555\pi$
$68$	4.04349	−	0.806326i	0.490346	−	0.0977814i
$69$			4.80573i			0.578542i
$70$		0			0
$71$	−0.548870	+	0.821442i	−0.0651389	+	0.0974872i	−0.862609	−	0.505871i	$-0.831171\pi$
$71$	−0.548870	+	0.821442i	−0.0651389	+	0.0974872i	0.797470	+	0.603358i	$0.206171\pi$
$72$	0.600569			0.0707778
$73$	−8.70593	+	13.0293i	−1.01895	+	1.52497i	−0.177876	+	0.984053i	$0.556923\pi$
$73$	−8.70593	+	13.0293i	−1.01895	+	1.52497i	−0.841076	+	0.540917i	$0.818077\pi$
$74$	5.40328	−	3.61035i	0.628118	−	0.419695i
$75$		0			0
$76$	5.56274	−	2.30416i	0.638090	−	0.264306i
$77$	−0.317252	−	0.131410i	−0.0361542	−	0.0149756i
$78$	−0.215668	−	0.322770i	−0.0244196	−	0.0365465i
$79$	−5.86124	−	8.77197i	−0.659441	−	0.986924i	−0.998927	−	0.0463124i	$-0.985253\pi$
$79$	−5.86124	−	8.77197i	−0.659441	−	0.986924i	0.339486	−	0.940611i	$-0.389747\pi$
$80$		0			0
$81$	−4.83492	+	4.83492i	−0.537213	+	0.537213i
$82$	0.860522	−	0.171169i	0.0950288	−	0.0189024i
$83$	0.0730601	+	0.176383i	0.00801939	+	0.0193605i	0.927839	−	0.372982i	$-0.121665\pi$
$83$	0.0730601	+	0.176383i	0.00801939	+	0.0193605i	−0.919819	+	0.392343i	$0.871665\pi$
$84$	−0.374680			−0.0408810
$85$		0			0
$86$	8.85190			0.954525
$87$	−0.720521	−	1.73949i	−0.0772480	−	0.186493i
$88$	−1.39237	+	0.276961i	−0.148428	+	0.0295241i
$89$	5.17953	−	5.17953i	0.549029	−	0.549029i	−0.377131	−	0.926160i	$-0.623089\pi$
$89$	5.17953	−	5.17953i	0.549029	−	0.549029i	0.926160	+	0.377131i	$0.123089\pi$
$90$		0			0
$91$	−0.0336774	−	0.0504017i	−0.00353035	−	0.00528354i
$92$	1.72363	+	2.57960i	0.179701	+	0.268942i
$93$	−7.30496	−	3.02581i	−0.757489	−	0.313762i
$94$	9.44214	−	3.91106i	0.973882	−	0.403395i
$95$		0			0
$96$	−1.28795	+	0.860584i	−0.131451	+	0.0878329i
$97$	−5.27043	+	7.88775i	−0.535131	+	0.800880i	−0.996256	−	0.0864553i	$-0.972446\pi$
$97$	−5.27043	+	7.88775i	−0.535131	+	0.800880i	0.461125	+	0.887335i	$0.347446\pi$
$98$	6.94149			0.701197
$99$	−0.473679	+	0.708911i	−0.0476066	+	0.0712483i
$100$		0			0
$101$		−	16.9065i		−	1.68226i	−0.540832	−	0.841131i	$-0.681890\pi$
$101$		−	16.9065i		−	1.68226i	0.540832	−	0.841131i	$-0.318110\pi$
$102$	0.00307642	+	6.38673i	0.000304611	+	0.632380i
$103$	2.75429	+	2.75429i	0.271388	+	0.271388i	0.829659	−	0.558271i	$-0.188535\pi$
$103$	2.75429	+	2.75429i	0.271388	+	0.271388i	−0.558271	+	0.829659i	$0.688535\pi$
$104$	−0.231530	−	0.0959029i	−0.0227034	−	0.00940406i
$105$		0			0
$106$	−1.39910	−	1.39910i	−0.135893	−	0.135893i
$107$	−0.825553	−	0.551617i	−0.0798093	−	0.0533268i	0.515025	−	0.857175i	$-0.327782\pi$
$107$	−0.825553	−	0.551617i	−0.0798093	−	0.0533268i	−0.594835	+	0.803848i	$0.702782\pi$
$108$	−1.08808	+	5.47015i	−0.104701	+	0.526365i
$109$	−6.16805	−	1.22690i	−0.590792	−	0.117516i	−0.109364	−	0.994002i	$-0.534881\pi$
$109$	−6.16805	−	1.22690i	−0.590792	−	0.117516i	−0.481427	+	0.876486i	$0.659881\pi$
$110$		0			0
$111$	3.85216	+	9.29994i	0.365631	+	0.882712i
$112$	−0.201119	+	0.134383i	−0.0190040	+	0.0126980i
$113$	−7.01434	−	1.39524i	−0.659854	−	0.131253i	−0.146206	−	0.989254i	$-0.546706\pi$
$113$	−7.01434	−	1.39524i	−0.659854	−	0.131253i	−0.513648	+	0.858001i	$0.671706\pi$
$114$	1.81955	+	9.14748i	0.170416	+	0.856740i
$115$		0			0
$116$	−1.01065	−	0.675292i	−0.0938362	−	0.0626993i
$117$	−0.139050	+	0.0575964i	−0.0128552	+	0.00532479i
$118$	−0.960940	+	0.960940i	−0.0884617	+	0.0884617i
$119$	0.000480394		0.997313i	4.40377e−5		0.0914235i
$120$		0			0
$121$	−3.43825	+	8.30067i	−0.312568	+	0.754607i
$122$	−1.78918	−	8.99481i	−0.161985	−	0.814352i
$123$			1.35907i			0.122543i
$124$	−5.00636	+	0.995828i	−0.449585	+	0.0894280i
$125$		0			0
$126$	−0.0283404	+	0.142477i	−0.00252476	+	0.0126928i
$127$	6.00272	−	14.4919i	0.532655	−	1.28594i	−0.397103	−	0.917774i	$-0.629984\pi$
$127$	6.00272	−	14.4919i	0.532655	−	1.28594i	0.929759	−	0.368170i	$-0.120016\pi$
$128$	−0.382683	+	0.923880i	−0.0338248	+	0.0816602i
$129$	−2.67501	+	13.4482i	−0.235522	+	1.18405i
$130$		0			0
$131$	−5.73305	+	1.14038i	−0.500899	+	0.0996350i	−0.439072	−	0.898452i	$-0.644693\pi$
$131$	−5.73305	+	1.14038i	−0.500899	+	0.0996350i	−0.0618271	+	0.998087i	$0.519693\pi$
$132$		−	2.19906i		−	0.191403i
$133$	0.284129	+	1.42841i	0.0246371	+	0.123859i
$134$	−4.16427	+	10.0534i	−0.359738	+	0.868485i
$135$		0			0
$136$	2.29233	+	3.42713i	0.196565	+	0.293874i
$137$	−10.2123	+	10.2123i	−0.872492	+	0.872492i	−0.992744	−	0.120251i	$-0.961630\pi$
$137$	−10.2123	+	10.2123i	−0.872492	+	0.872492i	0.120251	+	0.992744i	$0.461630\pi$
$138$	−4.43992	+	1.83907i	−0.377951	+	0.156552i
$139$	−16.7907	−	11.2192i	−1.42417	−	0.951598i	−0.998917	−	0.0465215i	$-0.985186\pi$
$139$	−16.7907	−	11.2192i	−1.42417	−	0.951598i	−0.425249	−	0.905076i	$-0.639814\pi$
$140$		0			0
$141$	3.08848	+	15.5268i	0.260097	+	1.30760i
$142$	−0.968957	−	0.192737i	−0.0813130	−	0.0161742i
$143$	0.295815	−	0.197658i	0.0247373	−	0.0165290i
$144$	0.229828	+	0.554854i	0.0191523	+	0.0462378i
$145$		0			0
$146$	−15.3692	−	3.05712i	−1.27196	−	0.253009i
$147$	−2.09770	+	10.5458i	−0.173015	+	0.869806i
$148$	5.40328	+	3.61035i	0.444147	+	0.296769i
$149$	9.07239	+	9.07239i	0.743239	+	0.743239i	0.973200	−	0.229961i	$-0.0738598\pi$
$149$	9.07239	+	9.07239i	0.743239	+	0.743239i	−0.229961	+	0.973200i	$0.573860\pi$
$150$		0			0
$151$	6.66259	+	2.75974i	0.542194	+	0.224584i	0.636935	−	0.770918i	$-0.280202\pi$
$151$	6.66259	+	2.75974i	0.542194	+	0.224584i	−0.0947404	+	0.995502i	$0.530202\pi$
$152$	4.25754	+	4.25754i	0.345332	+	0.345332i
$153$	2.42886	+	0.481915i	0.196362	+	0.0389605i
$154$		−	0.343391i		−	0.0276712i
$155$		0			0
$156$	0.215668	−	0.322770i	0.0172672	−	0.0258423i
$157$	−24.9767			−1.99336			−0.996680	−	0.0814150i	$-0.974056\pi$
$157$	−24.9767			−1.99336			−0.996680	+	0.0814150i	$0.974056\pi$
$158$	5.86124	−	8.77197i	0.466295	−	0.697860i
$159$	2.54838	−	1.70277i	0.202100	−	0.135039i
$160$		0			0
$161$	−0.693311	+	0.287179i	−0.0546405	+	0.0226328i
$162$	−6.31713	−	2.61664i	−0.496320	−	0.205583i
$163$	3.78546	+	5.66535i	0.296500	+	0.443744i	0.949571	−	0.313553i	$-0.101519\pi$
$163$	3.78546	+	5.66535i	0.296500	+	0.443744i	−0.653070	+	0.757297i	$0.726519\pi$
$164$	0.487447	+	0.729516i	0.0380632	+	0.0569656i
$165$		0			0
$166$	−0.134997	+	0.134997i	−0.0104778	+	0.0104778i
$167$	−16.4048	+	3.26312i	−1.26944	+	0.252508i	−0.783449	−	0.621456i	$-0.786542\pi$
$167$	−16.4048	+	3.26312i	−1.26944	+	0.252508i	−0.485992	+	0.873963i	$0.661542\pi$
$168$	−0.143384	−	0.346160i	−0.0110623	−	0.0267068i
$169$	−12.9372			−0.995169
$170$		0			0
$171$	3.61607			0.276528
$172$	3.38747	+	8.17809i	0.258292	+	0.623573i
$173$	10.8217	−	2.15257i	0.822758	−	0.163657i	0.234279	−	0.972169i	$-0.424727\pi$
$173$	10.8217	−	2.15257i	0.822758	−	0.163657i	0.588479	+	0.808513i	$0.299727\pi$
$174$	1.33135	−	1.33135i	0.100929	−	0.100929i
$175$		0			0
$176$	−0.788717	−	1.18040i	−0.0594518	−	0.0889759i
$177$	−1.16951	−	1.75030i	−0.0879058	−	0.131560i
$178$	6.76738	+	2.80314i	0.507236	+	0.210104i
$179$	13.8487	−	5.73630i	1.03510	−	0.428751i	0.200547	−	0.979684i	$-0.435728\pi$
$179$	13.8487	−	5.73630i	1.03510	−	0.428751i	0.834550	+	0.550933i	$0.185728\pi$
$180$		0			0
$181$	−14.6146	+	9.76518i	−1.08630	+	0.725840i	−0.963799	−	0.266628i	$-0.914090\pi$
$181$	−14.6146	+	9.76518i	−1.08630	+	0.725840i	−0.122498	+	0.992469i	$0.539090\pi$
$182$	0.0336774	−	0.0504017i	0.00249633	−	0.00373603i
$183$	14.2060			1.05014
$184$	−1.72363	+	2.57960i	−0.127068	+	0.190170i
$185$		0			0
$186$		−	7.90683i		−	0.579757i
$187$	−5.85338	+	0.00281951i	−0.428041	+	0.000206183i
$188$	7.22670	+	7.22670i	0.527061	+	0.527061i
$189$	−1.24637	−	0.516264i	−0.0906602	−	0.0375527i
$190$		0			0
$191$	−6.51300	−	6.51300i	−0.471264	−	0.471264i	0.431059	−	0.902324i	$-0.358140\pi$
$191$	−6.51300	−	6.51300i	−0.471264	−	0.471264i	−0.902324	+	0.431059i	$0.858140\pi$
$192$	−1.28795	−	0.860584i	−0.0929501	−	0.0621073i
$193$	1.83080	−	9.20405i	0.131784	−	0.662522i	−0.857258	−	0.514887i	$-0.827834\pi$
$193$	1.83080	−	9.20405i	0.131784	−	0.662522i	0.989042	−	0.147635i	$-0.0471661\pi$
$194$	−9.30424	−	1.85073i	−0.668005	−	0.132875i
$195$		0			0
$196$	2.65639	+	6.41310i	0.189742	+	0.458079i
$197$	−5.57335	+	3.72400i	−0.397085	+	0.265324i	−0.738041	−	0.674755i	$-0.764249\pi$
$197$	−5.57335	+	3.72400i	−0.397085	+	0.265324i	0.340956	+	0.940079i	$0.389249\pi$
$198$	−0.836218	−	0.166334i	−0.0594274	−	0.0118208i
$199$	4.92775	+	24.7735i	0.349319	+	1.75614i	0.611613	+	0.791157i	$0.290521\pi$
$199$	4.92775	+	24.7735i	0.349319	+	1.75614i	−0.262294	+	0.964988i	$0.584479\pi$
$200$		0			0
$201$	−14.0152	−	9.36467i	−0.988557	−	0.660533i
$202$	15.6196	−	6.46985i	1.09899	−	0.455217i
$203$	0.207895	−	0.207895i	0.0145914	−	0.0145914i
$204$	−5.89939	+	2.44694i	−0.413040	+	0.171320i
$205$		0			0
$206$	−1.49061	+	3.59866i	−0.103856	+	0.250730i
$207$	0.363500	+	1.82744i	0.0252650	+	0.127016i
$208$		−	0.250606i		−	0.0173764i
$209$	−8.38358	+	1.66760i	−0.579904	+	0.115350i
$210$		0			0
$211$	4.01313	−	20.1754i	0.276275	−	1.38893i	−0.554436	−	0.832227i	$-0.687066\pi$
$211$	4.01313	−	20.1754i	0.276275	−	1.38893i	0.830711	−	0.556704i	$-0.187934\pi$
$212$	0.757188	−	1.82801i	0.0520039	−	0.125548i
$213$	0.585631	−	1.41384i	0.0401268	−	0.0968746i
$214$	0.193702	−	0.973807i	0.0132412	−	0.0665681i
$215$		0			0
$216$	−5.47015	+	1.08808i	−0.372197	+	0.0740345i
$217$		−	1.23468i		−	0.0838157i
$218$	−1.22690	−	6.16805i	−0.0830962	−	0.417753i
$219$	9.28902	−	22.4257i	0.627694	−	1.51539i
$220$		0			0
$221$	−0.859415	−	0.573644i	−0.0578105	−	0.0385875i
$222$	−7.11787	+	7.11787i	−0.477720	+	0.477720i
$223$	−4.24146	+	1.75687i	−0.284029	+	0.117649i	−0.520150	−	0.854075i	$-0.674124\pi$
$223$	−4.24146	+	1.75687i	−0.284029	+	0.117649i	0.236121	+	0.971724i	$0.424124\pi$
$224$	−0.201119	−	0.134383i	−0.0134378	−	0.00897887i
$225$		0			0
$226$	−1.39524	−	7.01434i	−0.0928100	−	0.466587i
$227$	18.5039	+	3.68065i	1.22815	+	0.244293i	0.766193	−	0.642611i	$-0.222149\pi$
$227$	18.5039	+	3.68065i	1.22815	+	0.244293i	0.461953	+	0.886904i	$0.347149\pi$
$228$	−7.75486	+	5.18163i	−0.513578	+	0.343162i
$229$	7.85190	+	18.9562i	0.518868	+	1.25266i	0.938599	+	0.345010i	$0.112124\pi$
$229$	7.85190	+	18.9562i	0.518868	+	1.25266i	−0.419731	+	0.907649i	$0.637876\pi$
$230$		0			0
$231$	0.521696	+	0.103772i	0.0343250	+	0.00682768i
$232$	0.237131	−	1.19214i	0.0155684	−	0.0782677i
$233$	9.03059	+	6.03405i	0.591614	+	0.395304i	0.815029	−	0.579420i	$-0.196721\pi$
$233$	9.03059	+	6.03405i	0.591614	+	0.395304i	−0.223416	+	0.974723i	$0.571721\pi$
$234$	−0.106424	−	0.106424i	−0.00695717	−	0.00695717i
$235$		0			0
$236$	−1.25553	−	0.520057i	−0.0817279	−	0.0338528i
$237$	11.5555	+	11.5555i	0.750612	+	0.750612i
$238$	−0.921213	+	0.382099i	−0.0597134	+	0.0247678i
$239$			7.02173i			0.454198i	0.973872	+	0.227099i	$0.0729241\pi$
$239$			7.02173i			0.454198i	−0.973872	+	0.227099i	$0.927076\pi$
$240$		0			0
$241$	−9.37504	+	14.0307i	−0.603900	+	0.903800i	−0.999896	−	0.0144526i	$-0.995399\pi$
$241$	−9.37504	+	14.0307i	−0.603900	+	0.903800i	0.395996	+	0.918252i	$0.370399\pi$
$242$	−8.98458			−0.577551
$243$	−3.41144	+	5.10558i	−0.218844	+	0.327523i
$244$	7.62543	−	5.09515i	0.488168	−	0.326184i
$245$		0			0
$246$	−1.25562	+	0.520094i	−0.0800553	+	0.0331600i
$247$	−1.39406	−	0.577438i	−0.0887018	−	0.0367415i
$248$	−2.83588	−	4.24419i	−0.180078	−	0.269506i
$249$	−0.164299	−	0.245890i	−0.0104120	−	0.0155827i
$250$		0			0
$251$	19.5290	−	19.5290i	1.23266	−	1.23266i	0.269721	−	0.962939i	$-0.413069\pi$
$251$	19.5290	−	19.5290i	1.23266	−	1.23266i	0.962939	−	0.269721i	$-0.0869313\pi$
$252$	−0.142477	+	0.0283404i	−0.00897519	+	0.00178528i
$253$	−1.68550	−	4.06915i	−0.105966	−	0.255825i
$254$	15.6859			0.984219
$255$		0			0
$256$	−1.00000			−0.0625000
$257$	0.305941	+	0.738606i	0.0190841	+	0.0460730i	0.933134	−	0.359528i	$-0.117062\pi$
$257$	0.305941	+	0.738606i	0.0190841	+	0.0460730i	−0.914050	+	0.405601i	$0.867062\pi$
$258$	−13.4482	+	2.67501i	−0.837249	+	0.166539i
$259$	−1.11148	+	1.11148i	−0.0690642	+	0.0690642i
$260$		0			0
$261$	−0.405560	−	0.606963i	−0.0251035	−	0.0375701i
$262$	−3.24751	−	4.86025i	−0.200632	−	0.300267i
$263$	6.89733	+	2.85697i	0.425308	+	0.176168i	0.585062	−	0.810989i	$-0.301070\pi$
$263$	6.89733	+	2.85697i	0.425308	+	0.176168i	−0.159754	+	0.987157i	$0.551070\pi$
$264$	2.03166	−	0.841542i	0.125040	−	0.0517934i
$265$		0			0
$266$	−1.21095	+	0.809132i	−0.0742482	+	0.0496110i
$267$	−6.30374	+	9.43421i	−0.385782	+	0.577364i
$268$	−10.8818			−0.664709
$269$	11.5222	−	17.2442i	0.702519	−	1.05139i	−0.292933	−	0.956133i	$-0.594631\pi$
$269$	11.5222	−	17.2442i	0.702519	−	1.05139i	0.995452	−	0.0952616i	$-0.0303687\pi$
$270$		0			0
$271$		−	20.6843i		−	1.25648i	−0.778018	−	0.628242i	$-0.783775\pi$
$271$		−	20.6843i		−	1.25648i	0.778018	−	0.628242i	$-0.216225\pi$
$272$	−2.28902	+	3.42934i	−0.138792	+	0.207934i
$273$	0.0663954	+	0.0663954i	0.00401843	+	0.00401843i
$274$	−13.3430	−	5.52684i	−0.806078	−	0.333888i
$275$		0			0
$276$	−3.39817	−	3.39817i	−0.204546	−	0.204546i
$277$	17.0637	+	11.4016i	1.02526	+	0.685054i	0.950045	−	0.312114i	$-0.101037\pi$
$277$	17.0637	+	11.4016i	1.02526	+	0.685054i	0.0752111	+	0.997168i	$0.476037\pi$
$278$	3.93965	−	19.8060i	0.236284	−	1.18788i
$279$	−3.00667	−	0.598064i	−0.180005	−	0.0358051i
$280$		0			0
$281$	−8.90415	−	21.4965i	−0.531177	−	1.28237i	−0.930744	−	0.365671i	$-0.880840\pi$
$281$	−8.90415	−	21.4965i	−0.531177	−	1.28237i	0.399568	−	0.916704i	$-0.369160\pi$
$282$	−13.1630	+	8.79525i	−0.783846	+	0.523749i
$283$	−16.7691	−	3.33557i	−0.996817	−	0.198279i	−0.330386	−	0.943846i	$-0.607179\pi$
$283$	−16.7691	−	3.33557i	−0.996817	−	0.198279i	−0.666431	+	0.745567i	$0.732179\pi$
$284$	−0.192737	−	0.968957i	−0.0114369	−	0.0574970i
$285$		0			0
$286$	0.295815	+	0.197658i	0.0174919	+	0.0116877i
$287$	−0.196070	+	0.0812147i	−0.0115736	+	0.00479395i
$288$	−0.424667	+	0.424667i	−0.0250237	+	0.0250237i
$289$	6.52075	+	15.6997i	0.383573	+	0.923510i
$290$		0			0
$291$	5.62342	−	13.5761i	0.329651	−	0.795847i
$292$	−3.05712	−	15.3692i	−0.178904	−	0.899412i
$293$		−	31.7214i		−	1.85318i	−0.376071	−	0.926591i	$-0.622725\pi$
$293$		−	31.7214i		−	1.85318i	0.376071	−	0.926591i	$-0.377275\pi$
$294$	−10.5458	+	2.09770i	−0.615045	+	0.122340i
$295$		0			0
$296$	−1.26779	+	6.37360i	−0.0736887	+	0.370458i
$297$	3.03003	−	7.31514i	0.175820	−	0.424468i
$298$	−4.90994	+	11.8536i	−0.284425	+	0.686663i
$299$	0.151682	−	0.762556i	0.00877199	−	0.0440998i
$300$		0			0
$301$	−2.09999	+	0.417714i	−0.121041	+	0.0240766i
$302$			7.21154i			0.414977i
$303$	5.10910	+	25.6852i	0.293510	+	1.47557i
$304$	−2.30416	+	5.56274i	−0.132153	+	0.319045i
$305$		0			0
$306$	0.484255	+	2.42840i	0.0276830	+	0.138822i
$307$	10.0231	−	10.0231i	0.572047	−	0.572047i	−0.360653	−	0.932700i	$-0.617446\pi$
$307$	10.0231	−	10.0231i	0.572047	−	0.572047i	0.932700	+	0.360653i	$0.117446\pi$
$308$	0.317252	−	0.131410i	0.0180771	−	0.00748779i
$309$	−5.01679	−	3.35211i	−0.285395	−	0.190695i
$310$		0			0
$311$	5.82573	+	29.2879i	0.330347	+	1.66077i	0.687097	+	0.726566i	$0.258885\pi$
$311$	5.82573	+	29.2879i	0.330347	+	1.66077i	−0.356750	+	0.934200i	$0.616115\pi$
$312$	0.380733	+	0.0757325i	0.0215548	+	0.00428751i
$313$	0.788463	−	0.526834i	0.0445666	−	0.0297784i	−0.533087	−	0.846060i	$-0.678968\pi$
$313$	0.788463	−	0.526834i	0.0445666	−	0.0297784i	0.577654	+	0.816282i	$0.303968\pi$
$314$	−9.55818	−	23.0755i	−0.539399	−	1.30223i
$315$		0			0
$316$	10.3472	+	2.05819i	0.582078	+	0.115782i
$317$	1.79766	−	9.03747i	0.100967	−	0.507595i	−0.896895	−	0.442243i	$-0.854183\pi$
$317$	1.79766	−	9.03747i	0.100967	−	0.507595i	0.997862	−	0.0653519i	$-0.0208170\pi$
$318$	2.54838	+	1.70277i	0.142906	+	0.0954868i
$319$	1.22017	+	1.22017i	0.0683164	+	0.0683164i
$320$		0			0
$321$	1.42092	+	0.588562i	0.0793078	+	0.0328504i
$322$	−0.530637	−	0.530637i	−0.0295712	−	0.0295712i
$323$	13.8022	+	20.6350i	0.767977	+	1.14816i
$324$		−	6.83761i		−	0.379867i
$325$		0			0
$326$	−3.78546	+	5.66535i	−0.209657	+	0.313775i
$327$	9.74154			0.538708
$328$	−0.487447	+	0.729516i	−0.0269147	+	0.0402808i
$329$	−2.05546	+	1.37341i	−0.113321	+	0.0757187i
$330$		0			0
$331$	−14.0014	+	5.79957i	−0.769587	+	0.318773i	−0.732705	−	0.680546i	$-0.761743\pi$
$331$	−14.0014	+	5.79957i	−0.769587	+	0.318773i	−0.0368818	+	0.999320i	$0.511743\pi$
$332$	−0.176383	−	0.0730601i	−0.00968026	−	0.00400969i
$333$	2.16827	+	3.24504i	0.118820	+	0.177827i
$334$	−9.29257	−	13.9073i	−0.508467	−	0.760975i
$335$		0			0
$336$	0.264939	−	0.264939i	0.0144536	−	0.0144536i
$337$	15.0655	−	2.99672i	0.820671	−	0.163242i	0.233140	−	0.972443i	$-0.425100\pi$
$337$	15.0655	−	2.99672i	0.820671	−	0.163242i	0.587531	+	0.809202i	$0.300100\pi$
$338$	−4.95085	−	11.9524i	−0.269291	−	0.650125i
$339$	11.0781			0.601682
$340$		0			0
$341$	7.24654			0.392422
$342$	1.38381	+	3.34081i	0.0748278	+	0.180650i
$343$	−3.30743	+	0.657888i	−0.178584	+	0.0355226i
$344$	−6.25924	+	6.25924i	−0.337475	+	0.337475i
$345$		0			0
$346$	6.12999	+	9.17418i	0.329550	+	0.493207i
$347$	−11.6216	−	17.3930i	−0.623883	−	0.933706i	−0.999975	−	0.00712393i	$-0.997732\pi$
$347$	−11.6216	−	17.3930i	−0.623883	−	0.933706i	0.376092	−	0.926582i	$-0.377268\pi$
$348$	1.73949	+	0.720521i	0.0932465	+	0.0386240i
$349$	−2.52921	+	1.04763i	−0.135386	+	0.0560785i	−0.449348	−	0.893357i	$-0.648344\pi$
$349$	−2.52921	+	1.04763i	−0.135386	+	0.0560785i	0.313962	+	0.949436i	$0.398344\pi$
$350$		0			0
$351$	1.16215	−	0.776527i	0.0620312	−	0.0414479i
$352$	0.788717	−	1.18040i	0.0420388	−	0.0629154i
$353$	−10.1837			−0.542025			−0.271013	−	0.962576i	$-0.587358\pi$
$353$	−10.1837			−0.542025			−0.271013	+	0.962576i	$0.587358\pi$
$354$	1.16951	−	1.75030i	0.0621588	−	0.0930272i
$355$		0			0
$356$			7.32495i			0.388222i
$357$	−0.302114	−	1.51502i	−0.0159896	−	0.0801832i
$358$	10.5993	+	10.5993i	0.560190	+	0.560190i
$359$	20.3347	+	8.42291i	1.07322	+	0.444544i	0.848128	−	0.529792i	$-0.177730\pi$
$359$	20.3347	+	8.42291i	1.07322	+	0.444544i	0.225097	+	0.974336i	$0.427730\pi$
$360$		0			0
$361$	12.1999	+	12.1999i	0.642099	+	0.642099i
$362$	−14.6146	−	9.76518i	−0.768128	−	0.513247i
$363$	2.71511	−	13.6498i	0.142506	−	0.716428i
$364$	0.0594529	+	0.0118259i	0.00311618	+	0.000619847i
$365$		0			0
$366$	5.43641	+	13.1246i	0.284165	+	0.686036i
$367$	1.58128	−	1.05658i	0.0825421	−	0.0551529i	−0.513614	−	0.858021i	$-0.671694\pi$
$367$	1.58128	−	1.05658i	0.0825421	−	0.0551529i	0.596156	+	0.802868i	$0.296694\pi$
$368$	−3.04284	−	0.605259i	−0.158619	−	0.0315513i
$369$	0.102799	+	0.516803i	0.00535148	+	0.0269037i
$370$		0			0
$371$	0.397940	+	0.265895i	0.0206600	+	0.0138046i
$372$	7.30496	−	3.02581i	0.378745	−	0.156881i
$373$	−4.01050	+	4.01050i	−0.207656	+	0.207656i	−0.803270	−	0.595615i	$-0.796909\pi$
$373$	−4.01050	+	4.01050i	−0.207656	+	0.207656i	0.595615	+	0.803270i	$0.296909\pi$
$374$	−2.24260	−	5.40674i	−0.115962	−	0.279576i
$375$		0			0
$376$	−3.91106	+	9.44214i	−0.201698	+	0.486941i
$377$	0.0594266	+	0.298758i	0.00306063	+	0.0153868i
$378$		−	1.34906i		−	0.0693883i
$379$	−1.89732	+	0.377400i	−0.0974587	+	0.0193857i	−0.243579	−	0.969881i	$-0.578321\pi$
$379$	−1.89732	+	0.377400i	−0.0974587	+	0.0193857i	0.146120	+	0.989267i	$0.453321\pi$
$380$		0			0
$381$	−4.74022	+	23.8307i	−0.242849	+	1.22088i
$382$	3.52481	−	8.50965i	0.180345	−	0.435392i
$383$	10.8982	−	26.3105i	0.556870	−	1.34440i	−0.355362	−	0.934729i	$-0.615642\pi$
$383$	10.8982	−	26.3105i	0.556870	−	1.34440i	0.912232	−	0.409674i	$-0.134358\pi$
$384$	0.302197	−	1.51925i	0.0154214	−	0.0775287i
$385$		0			0
$386$	9.20405	−	1.83080i	0.468474	−	0.0931852i
$387$			5.31618i			0.270237i
$388$	−1.85073	−	9.30424i	−0.0939565	−	0.472351i
$389$	9.59778	−	23.1711i	0.486627	−	1.17482i	−0.469780	−	0.882784i	$-0.655667\pi$
$389$	9.59778	−	23.1711i	0.486627	−	1.17482i	0.956407	−	0.292038i	$-0.0943333\pi$
$390$		0			0
$391$	−9.04078	+	9.04949i	−0.457212	+	0.457652i
$392$	−4.90838	+	4.90838i	−0.247910	+	0.247910i
$393$	8.36530	−	3.46502i	0.421973	−	0.174787i
$394$	−5.57335	−	3.72400i	−0.280781	−	0.187612i
$395$		0			0
$396$	−0.166334	−	0.836218i	−0.00835860	−	0.0420215i
$397$	4.51435	+	0.897961i	0.226569	+	0.0450674i	0.307069	−	0.951687i	$-0.400652\pi$
$397$	4.51435	+	0.897961i	0.226569	+	0.0450674i	−0.0805001	+	0.996755i	$0.525652\pi$
$398$	−21.0019	+	14.0330i	−1.05273	+	0.703413i
$399$	−0.863324	−	2.08425i	−0.0432203	−	0.104343i
$400$		0			0
$401$	36.0272	+	7.16626i	1.79911	+	0.357866i	0.977295	−	0.211884i	$-0.0679600\pi$
$401$	36.0272	+	7.16626i	1.79911	+	0.357866i	0.821818	+	0.569750i	$0.192960\pi$
$402$	3.28843	−	16.5321i	0.164012	−	0.824545i
$403$	1.06362	+	0.710689i	0.0529828	+	0.0354019i
$404$	11.9547	+	11.9547i	0.594769	+	0.594769i
$405$		0			0
$406$	0.271628	+	0.112512i	0.0134807	+	0.00558388i
$407$	−6.52346	−	6.52346i	−0.323356	−	0.323356i
$408$	−4.51827	−	4.51392i	−0.223688	−	0.223473i
$409$			37.5509i			1.85677i	0.371618	+	0.928386i	$0.378803\pi$
$409$			37.5509i			1.85677i	−0.371618	+	0.928386i	$0.621197\pi$
$410$		0			0
$411$	12.4288	−	18.6010i	0.613069	−	0.917522i
$412$	−3.89516			−0.191901
$413$	0.182624	−	0.273316i	0.00898632	−	0.0134490i
$414$	−1.54923	+	1.03516i	−0.0761404	+	0.0508754i
$415$		0			0
$416$	0.231530	−	0.0959029i	0.0113517	−	0.00470203i
$417$	28.8996	+	11.9706i	1.41522	+	0.586202i
$418$	−4.74892	−	7.10726i	−0.232277	−	0.347627i
$419$	−14.3243	−	21.4378i	−0.699787	−	1.04731i	−0.995749	−	0.0921057i	$-0.970640\pi$
$419$	−14.3243	−	21.4378i	−0.699787	−	1.04731i	0.295962	−	0.955200i	$-0.404360\pi$
$420$		0			0
$421$	3.63694	−	3.63694i	0.177254	−	0.177254i	−0.612904	−	0.790158i	$-0.709999\pi$
$421$	3.63694	−	3.63694i	0.177254	−	0.177254i	0.790158	+	0.612904i	$0.209999\pi$
$422$	20.1754	−	4.01313i	0.982122	−	0.195356i
$423$	2.34886	+	5.67066i	0.114206	+	0.275717i
$424$	1.97863			0.0960906
$425$		0			0
$426$	1.53033			0.0741446
$427$	0.848916	+	2.04946i	0.0410819	+	0.0991805i
$428$	0.973807	−	0.193702i	0.0470707	−	0.00936295i
$429$	−0.389685	+	0.389685i	−0.0188142	+	0.0188142i
$430$		0			0
$431$	2.44173	+	3.65430i	0.117614	+	0.176022i	0.885605	−	0.464438i	$-0.153744\pi$
$431$	2.44173	+	3.65430i	0.117614	+	0.176022i	−0.767992	+	0.640460i	$0.778744\pi$
$432$	−3.09859	−	4.63737i	−0.149081	−	0.223116i
$433$	−21.4595	−	8.88880i	−1.03128	−	0.427169i	−0.198103	−	0.980181i	$-0.563478\pi$
$433$	−21.4595	−	8.88880i	−1.03128	−	0.427169i	−0.833173	+	0.553013i	$0.813478\pi$
$434$	1.14070	−	0.472493i	0.0547552	−	0.0226804i
$435$		0			0
$436$	5.22902	−	3.49392i	0.250424	−	0.167328i
$437$	−10.3781	+	15.5319i	−0.496452	+	0.742993i
$438$	24.2734			1.15983
$439$	5.19233	−	7.77087i	0.247816	−	0.370883i	−0.686618	−	0.727018i	$-0.740906\pi$
$439$	5.19233	−	7.77087i	0.247816	−	0.370883i	0.934435	+	0.356135i	$0.115906\pi$
$440$		0			0
$441$			4.16885i			0.198517i
$442$	0.201094	−	1.01352i	0.00956507	−	0.0482082i
$443$	0.680053	+	0.680053i	0.0323103	+	0.0323103i	0.723077	−	0.690767i	$-0.242727\pi$
$443$	0.680053	+	0.680053i	0.0323103	+	0.0323103i	−0.690767	+	0.723077i	$0.742727\pi$
$444$	−9.29994	−	3.85216i	−0.441356	−	0.182816i
$445$		0			0
$446$	−3.24627	−	3.24627i	−0.153715	−	0.153715i
$447$	−16.5248	−	11.0415i	−0.781598	−	0.522247i
$448$	0.0471892	−	0.237236i	0.00222948	−	0.0112084i
$449$	−1.16763	−	0.232256i	−0.0551039	−	0.0109609i	0.167461	−	0.985879i	$-0.446443\pi$
$449$	−1.16763	−	0.232256i	−0.0551039	−	0.0109609i	−0.222565	+	0.974918i	$0.571443\pi$
$450$		0			0
$451$	−0.476661	−	1.15076i	−0.0224451	−	0.0541873i
$452$	5.94647	−	3.97331i	0.279699	−	0.186889i
$453$	−10.9561	−	2.17930i	−0.514762	−	0.102393i
$454$	3.68065	+	18.5039i	0.172742	+	0.868430i
$455$		0			0
$456$	−7.75486	−	5.18163i	−0.363154	−	0.242652i
$457$	16.5093	−	6.83836i	0.772270	−	0.319885i	0.0384787	−	0.999259i	$-0.487749\pi$
$457$	16.5093	−	6.83836i	0.772270	−	0.319885i	0.733792	+	0.679375i	$0.237749\pi$
$458$	−14.5084	+	14.5084i	−0.677934	+	0.677934i
$459$	−22.9959	+	0.0110768i	−1.07335	+	0.000517023i
$460$		0			0
$461$	1.95502	−	4.71984i	0.0910545	−	0.219825i	−0.871791	−	0.489878i	$-0.837041\pi$
$461$	1.95502	−	4.71984i	0.0910545	−	0.219825i	0.962845	+	0.270053i	$0.0870413\pi$
$462$	0.103772	+	0.521696i	0.00482790	+	0.0242715i
$463$			30.5132i			1.41807i	0.705174	+	0.709034i	$0.250869\pi$
$463$			30.5132i			1.41807i	−0.705174	+	0.709034i	$0.749131\pi$
$464$	1.19214	−	0.237131i	0.0553437	−	0.0110085i
$465$		0			0
$466$	−2.11888	+	10.6523i	−0.0981550	+	0.493459i
$467$	4.55023	−	10.9852i	0.210559	−	0.508335i	−0.782950	−	0.622084i	$-0.786286\pi$
$467$	4.55023	−	10.9852i	0.210559	−	0.508335i	0.993509	+	0.113749i	$0.0362860\pi$
$468$	0.0575964	−	0.139050i	0.00266239	−	0.00642759i
$469$	0.513502	−	2.58155i	0.0237113	−	0.119205i
$470$		0			0
$471$	37.9458	−	7.54789i	1.74845	−	0.347788i
$472$		−	1.35897i		−	0.0625518i
$473$	−2.45163	−	12.3252i	−0.112726	−	0.566711i
$474$	−6.25381	+	15.0980i	−0.287247	+	0.693475i
$475$		0			0
$476$	−0.705546	−	0.704867i	−0.0323387	−	0.0323075i
$477$	0.840257	−	0.840257i	0.0384727	−	0.0384727i
$478$	−6.48723	+	2.68710i	−0.296719	+	0.122905i
$479$	3.46289	+	2.31383i	0.158223	+	0.105722i	0.632161	−	0.774837i	$-0.282168\pi$
$479$	3.46289	+	2.31383i	0.158223	+	0.105722i	−0.473938	+	0.880558i	$0.657168\pi$
$480$		0			0
$481$	−0.317716	−	1.59727i	−0.0144866	−	0.0728290i
$482$	−16.5504	−	3.29208i	−0.753850	−	0.149950i
$483$	0.966525	−	0.645811i	0.0439784	−	0.0293854i
$484$	−3.43825	−	8.30067i	−0.156284	−	0.377303i
$485$		0			0
$486$	−6.02244	−	1.19794i	−0.273184	−	0.0543396i
$487$	−1.98391	+	9.97377i	−0.0898994	+	0.451955i	0.909447	+	0.415819i	$0.136505\pi$
$487$	−1.98391	+	9.97377i	−0.0898994	+	0.451955i	−0.999347	+	0.0361360i	$0.988495\pi$
$488$	7.62543	+	5.09515i	0.345187	+	0.230647i
$489$	−7.46310	−	7.46310i	−0.337493	−	0.337493i
$490$		0			0
$491$	−9.31628	−	3.85893i	−0.420438	−	0.174151i	0.162426	−	0.986721i	$-0.448068\pi$
$491$	−9.31628	−	3.85893i	−0.420438	−	0.174151i	−0.582864	+	0.812570i	$0.698068\pi$
$492$	−0.961009	−	0.961009i	−0.0433256	−	0.0433256i
$493$	1.91563	−	4.63105i	0.0862756	−	0.208572i
$494$		−	1.50892i		−	0.0678894i
$495$		0			0
$496$	2.83588	−	4.24419i	0.127335	−	0.190570i
$497$	0.238967			0.0107191
$498$	0.164299	−	0.245890i	0.00736239	−	0.0110186i
$499$	25.8286	−	17.2581i	1.15624	−	0.772578i	0.178824	−	0.983881i	$-0.442771\pi$
$499$	25.8286	−	17.2581i	1.15624	−	0.772578i	0.977421	+	0.211303i	$0.0677707\pi$
$500$		0			0
$501$	23.9368	−	9.91495i	1.06942	−	0.442967i
$502$	25.5159	+	10.5690i	1.13883	+	0.471718i
$503$	−3.09637	−	4.63404i	−0.138060	−	0.206622i	0.755996	−	0.654576i	$-0.227153\pi$
$503$	−3.09637	−	4.63404i	−0.138060	−	0.206622i	−0.894056	+	0.447954i	$0.852153\pi$
$504$	−0.0807066	−	0.120786i	−0.00359496	−	0.00538023i
$505$		0			0
$506$	3.11439	−	3.11439i	0.138451	−	0.138451i
$507$	19.6548	−	3.90958i	0.872899	−	0.173630i
$508$	6.00272	+	14.4919i	0.266328	+	0.642972i
$509$	44.5099			1.97287			0.986433	−	0.164167i	$-0.0524937\pi$
$509$	44.5099			1.97287			0.986433	+	0.164167i	$0.0524937\pi$
$510$		0			0
$511$	3.79038			0.167677
$512$	−0.382683	−	0.923880i	−0.0169124	−	0.0408301i
$513$	−32.9361	+	6.55140i	−1.45417	+	0.289252i
$514$	−0.565305	+	0.565305i	−0.0249345	+	0.0249345i
$515$		0			0
$516$	−7.61780	−	11.4008i	−0.335355	−	0.501894i
$517$	−8.06076	−	12.0638i	−0.354512	−	0.530565i
$518$	−1.45222	−	0.601530i	−0.0638070	−	0.0264297i
$519$	−15.7903	+	6.54056i	−0.693117	+	0.287099i
$520$		0			0
$521$	−18.5333	+	12.3835i	−0.811957	+	0.542533i	−0.890822	−	0.454353i	$-0.849871\pi$
$521$	−18.5333	+	12.3835i	−0.811957	+	0.542533i	0.0788644	+	0.996885i	$0.474871\pi$
$522$	0.405560	−	0.606963i	0.0177509	−	0.0265661i
$523$	−15.7551			−0.688922			−0.344461	−	0.938801i	$-0.611938\pi$
$523$	−15.7551			−0.688922			−0.344461	+	0.938801i	$0.611938\pi$
$524$	3.24751	−	4.86025i	0.141868	−	0.212321i
$525$		0			0
$526$			7.46562i			0.325516i
$527$	−8.06338	−	19.4402i	−0.351246	−	0.846830i
$528$	1.55497	+	1.55497i	0.0676713	+	0.0676713i
$529$	12.3567	+	5.11830i	0.537247	+	0.222535i
$530$		0			0
$531$	−0.577111	−	0.577111i	−0.0250445	−	0.0250445i
$532$	−1.21095	−	0.809132i	−0.0525014	−	0.0350803i
$533$	0.0428959	−	0.215652i	0.00185803	−	0.00934094i
$534$	−11.1284	−	2.21358i	−0.481573	−	0.0957909i
$535$		0			0
$536$	−4.16427	−	10.0534i	−0.179869	−	0.434242i
$537$	−19.3060	+	12.8999i	−0.833116	+	0.556670i
$538$	20.3409	+	4.04605i	0.876957	+	0.174438i
$539$	−1.92252	−	9.66516i	−0.0828088	−	0.416308i
$540$		0			0
$541$	−30.9603	−	20.6870i	−1.33109	−	0.889404i	−0.332530	−	0.943093i	$-0.607902\pi$
$541$	−30.9603	−	20.6870i	−1.33109	−	0.889404i	−0.998558	+	0.0536885i	$0.982902\pi$
$542$	19.1098	−	7.91555i	0.820838	−	0.340002i
$543$	19.2522	−	19.2522i	0.826191	−	0.826191i
$544$	−4.04427	−	0.802430i	−0.173397	−	0.0344039i
$545$		0			0
$546$	−0.0359330	+	0.0867498i	−0.00153779	+	0.00371255i
$547$	3.45355	+	17.3622i	0.147663	+	0.742352i	0.981669	+	0.190596i	$0.0610421\pi$
$547$	3.45355	+	17.3622i	0.147663	+	0.742352i	−0.834005	+	0.551756i	$0.813958\pi$
$548$		−	14.4423i		−	0.616945i
$549$	5.40201	−	1.07453i	0.230552	−	0.0458597i
$550$		0			0
$551$	1.42778	−	7.17795i	0.0608256	−	0.305791i
$552$	1.83907	−	4.43992i	0.0782762	−	0.188976i
$553$	−0.976556	+	2.35762i	−0.0415274	+	0.100256i
$554$	−4.00370	+	20.1280i	−0.170101	+	0.855155i
$555$		0			0
$556$	19.8060	−	3.93965i	0.839960	−	0.167078i
$557$			18.8677i			0.799448i	0.916636	+	0.399724i	$0.130894\pi$
$557$			18.8677i			0.799448i	−0.916636	+	0.399724i	$0.869106\pi$
$558$	−0.598064	−	3.00667i	−0.0253181	−	0.127282i
$559$	0.848923	−	2.04948i	0.0359056	−	0.0866838i
$560$		0			0
$561$	8.89187	−	1.77316i	0.375415	−	0.0748627i
$562$	16.4527	−	16.4527i	0.694016	−	0.694016i
$563$	7.07939	−	2.93238i	0.298361	−	0.123585i	−0.228481	−	0.973548i	$-0.573376\pi$
$563$	7.07939	−	2.93238i	0.298361	−	0.123585i	0.526842	+	0.849963i	$0.323376\pi$
$564$	−13.1630	−	8.79525i	−0.554263	−	0.370347i
$565$		0			0
$566$	−3.33557	−	16.7691i	−0.140205	−	0.704856i
$567$	1.62213	+	0.322661i	0.0681230	+	0.0135505i
$568$	0.821442	−	0.548870i	0.0344669	−	0.0230301i
$569$	−12.8952	−	31.1318i	−0.540596	−	1.30511i	−0.924303	−	0.381660i	$-0.875353\pi$
$569$	−12.8952	−	31.1318i	−0.540596	−	1.30511i	0.383707	−	0.923455i	$-0.374647\pi$
$570$		0			0
$571$	−1.88068	−	0.374090i	−0.0787038	−	0.0156552i	0.155581	−	0.987823i	$-0.450275\pi$
$571$	−1.88068	−	0.374090i	−0.0787038	−	0.0156552i	−0.234285	+	0.972168i	$0.575275\pi$
$572$	−0.0694081	+	0.348938i	−0.00290210	+	0.0145898i
$573$	11.8631	+	7.92664i	0.495586	+	0.331140i
$574$	−0.150065	−	0.150065i	−0.00626360	−	0.00626360i
$575$		0			0
$576$	−0.554854	−	0.229828i	−0.0231189	−	0.00957617i
$577$	−9.67382	−	9.67382i	−0.402726	−	0.402726i	0.476466	−	0.879193i	$-0.341917\pi$
$577$	−9.67382	−	9.67382i	−0.402726	−	0.402726i	−0.879193	+	0.476466i	$0.841917\pi$
$578$	−12.0092	+	12.0324i	−0.499518	+	0.500481i
$579$			14.5365i			0.604115i
$580$		0			0
$581$	0.0256559	−	0.0383967i	0.00106438	−	0.00159296i
$582$	14.6947			0.609115
$583$	−1.56058	+	2.33557i	−0.0646325	+	0.0967293i
$584$	13.0293	−	8.70593i	0.539158	−	0.360254i
$585$		0			0
$586$	29.3067	−	12.1392i	1.21065	−	0.501467i
$587$	11.4820	+	4.75599i	0.473912	+	0.196301i	0.606839	−	0.794825i	$-0.292437\pi$
$587$	11.4820	+	4.75599i	0.473912	+	0.196301i	−0.132926	+	0.991126i	$0.542437\pi$
$588$	−5.97373	−	8.94033i	−0.246353	−	0.368693i
$589$	−17.0750	−	25.5545i	−0.703563	−	1.05296i
$590$		0			0
$591$	7.34191	−	7.34191i	0.302006	−	0.302006i
$592$	−6.37360	+	1.26779i	−0.261953	+	0.0521058i
$593$	−11.4482	−	27.6385i	−0.470122	−	1.13498i	−0.964109	−	0.265507i	$-0.914461\pi$
$593$	−11.4482	−	27.6385i	−0.470122	−	1.13498i	0.493987	−	0.869470i	$-0.335539\pi$
$594$	7.91785			0.324874
$595$		0			0
$596$	−12.8303			−0.525549
$597$	−14.9729	−	36.1478i	−0.612801	−	1.47943i
$598$	0.762556	−	0.151682i	0.0311832	−	0.00620273i
$599$	−11.2916	+	11.2916i	−0.461360	+	0.461360i	−0.899101	−	0.437741i	$-0.855779\pi$
$599$	−11.2916	+	11.2916i	−0.461360	+	0.461360i	0.437741	+	0.899101i	$0.355779\pi$
$600$		0			0
$601$	9.39260	+	14.0570i	0.383132	+	0.573398i	0.972044	−	0.234800i	$-0.0754434\pi$
$601$	9.39260	+	14.0570i	0.383132	+	0.573398i	−0.588912	+	0.808197i	$0.700443\pi$
$602$	−1.18955	−	1.78029i	−0.0484824	−	0.0725590i
$603$	−6.03779	−	2.50093i	−0.245878	−	0.101846i
$604$	−6.66259	+	2.75974i	−0.271097	+	0.112292i
$605$		0			0
$606$	−21.7748	+	14.5495i	−0.884542	+	0.591032i
$607$	−24.2596	+	36.3070i	−0.984666	+	1.47366i	−0.107072	+	0.994251i	$0.534148\pi$
$607$	−24.2596	+	36.3070i	−0.984666	+	1.47366i	−0.877594	+	0.479405i	$0.840852\pi$
$608$	−6.02107			−0.244186
$609$	−0.253019	+	0.378669i	−0.0102528	+	0.0153445i
$610$		0			0
$611$		−	2.56122i		−	0.103616i
$612$	−2.05823	+	1.37670i	−0.0831991	+	0.0556498i
$613$	−14.2688	−	14.2688i	−0.576311	−	0.576311i	0.357574	−	0.933885i	$-0.383604\pi$
$613$	−14.2688	−	14.2688i	−0.576311	−	0.576311i	−0.933885	+	0.357574i	$0.883604\pi$
$614$	13.0958	+	5.42445i	0.528503	+	0.218913i
$615$		0			0
$616$	0.242814	+	0.242814i	0.00978326	+	0.00978326i
$617$	14.3887	+	9.61423i	0.579268	+	0.387054i	0.810408	−	0.585866i	$-0.199246\pi$
$617$	14.3887	+	9.61423i	0.579268	+	0.387054i	−0.231140	+	0.972921i	$0.574246\pi$
$618$	1.17710	−	5.91770i	0.0473501	−	0.238045i
$619$	−1.23501	−	0.245658i	−0.0496392	−	0.00987384i	0.170208	−	0.985408i	$-0.445556\pi$
$619$	−1.23501	−	0.245658i	−0.0496392	−	0.00987384i	−0.219847	+	0.975534i	$0.570556\pi$
$620$		0			0
$621$	−6.62172	−	15.9862i	−0.265720	−	0.641506i
$622$	−24.8291	+	16.5903i	−0.995556	+	0.665209i
$623$	−1.73774	−	0.345659i	−0.0696212	−	0.0138485i
$624$	0.0757325	+	0.380733i	0.00303172	+	0.0152415i
$625$		0			0
$626$	0.788463	+	0.526834i	0.0315133	+	0.0210565i
$627$	12.2328	−	5.06698i	0.488530	−	0.202356i
$628$	17.6612	−	17.6612i	0.704759	−	0.704759i
$629$	−10.2416	+	24.7592i	−0.408361	+	0.987216i
$630$		0			0
$631$	−3.78090	+	9.12791i	−0.150515	+	0.363376i	−0.981096	−	0.193522i	$-0.938009\pi$
$631$	−3.78090	+	9.12791i	−0.150515	+	0.363376i	0.830580	+	0.556899i	$0.188009\pi$
$632$	2.05819	+	10.3472i	0.0818706	+	0.411591i
$633$			31.8641i			1.26649i
$634$	9.03747	−	1.79766i	0.358924	−	0.0713943i
$635$		0			0
$636$	−0.597935	+	3.00602i	−0.0237096	+	0.119196i
$637$	0.665710	−	1.60716i	0.0263764	−	0.0636782i
$638$	−0.660351	+	1.59423i	−0.0261435	+	0.0631161i
$639$	0.115752	−	0.581926i	0.00457909	−	0.0230206i
$640$		0			0
$641$	−21.2165	+	4.22022i	−0.838001	+	0.166689i	−0.595392	−	0.803435i	$-0.703003\pi$
$641$	−21.2165	+	4.22022i	−0.838001	+	0.166689i	−0.242609	+	0.970124i	$0.578003\pi$
$642$			1.53799i			0.0606995i
$643$	−8.79438	−	44.2123i	−0.346816	−	1.74356i	−0.622781	−	0.782396i	$-0.713997\pi$
$643$	−8.79438	−	44.2123i	−0.346816	−	1.74356i	0.275965	−	0.961168i	$-0.411003\pi$
$644$	0.287179	−	0.693311i	0.0113164	−	0.0273203i
$645$		0			0
$646$	−13.7824	+	20.6483i	−0.542260	+	0.812396i
$647$	−3.89261	+	3.89261i	−0.153034	+	0.153034i	−0.779472	−	0.626438i	$-0.784512\pi$
$647$	−3.89261	+	3.89261i	−0.153034	+	0.153034i	0.626438	+	0.779472i	$0.284512\pi$
$648$	6.31713	−	2.61664i	0.248160	−	0.102791i
$649$	1.60413	+	1.07185i	0.0629676	+	0.0420736i
$650$		0			0
$651$	0.373117	+	1.87579i	0.0146236	+	0.0735179i
$652$	−6.68273	−	1.32928i	−0.261716	−	0.0520586i
$653$	22.7903	−	15.2280i	0.891854	−	0.595918i	−0.0229854	−	0.999736i	$-0.507317\pi$
$653$	22.7903	−	15.2280i	0.891854	−	0.595918i	0.914839	+	0.403818i	$0.132317\pi$
$654$	3.72793	+	9.00001i	0.145773	+	0.351928i
$655$		0			0
$656$	−0.860522	−	0.171169i	−0.0335977	−	0.00668301i
$657$	1.83601	−	9.23025i	0.0716296	−	0.360106i
$658$	−2.05546	−	1.37341i	−0.0801300	−	0.0535412i
$659$	1.15499	+	1.15499i	0.0449919	+	0.0449919i	0.729245	−	0.684253i	$-0.239872\pi$
$659$	1.15499	+	1.15499i	0.0449919	+	0.0449919i	−0.684253	+	0.729245i	$0.739872\pi$
$660$		0			0
$661$	−19.9073	−	8.24587i	−0.774303	−	0.320727i	−0.0396893	−	0.999212i	$-0.512637\pi$
$661$	−19.9073	−	8.24587i	−0.774303	−	0.320727i	−0.734614	+	0.678485i	$0.762637\pi$
$662$	−10.7162	−	10.7162i	−0.416497	−	0.416497i
$663$	1.47902	+	0.611794i	0.0574402	+	0.0237601i
$664$		−	0.190915i		−	0.00740895i
$665$		0			0
$666$	−2.16827	+	3.24504i	−0.0840187	+	0.125743i
$667$	3.77102			0.146014
$668$	9.29257	−	13.9073i	0.359540	−	0.538090i
$669$	5.91290	−	3.95087i	0.228606	−	0.152749i
$670$		0			0
$671$	−12.0286	+	4.98242i	−0.464360	+	0.192344i
$672$	0.346160	+	0.143384i	0.0133534	+	0.00553116i
$673$	23.3052	+	34.8788i	0.898351	+	1.34448i	0.938498	+	0.345284i	$0.112217\pi$
$673$	23.3052	+	34.8788i	0.898351	+	1.34448i	−0.0401469	+	0.999194i	$0.512783\pi$
$674$	8.53393	+	12.7719i	0.328715	+	0.491956i
$675$		0			0
$676$	9.14798	−	9.14798i	0.351845	−	0.351845i
$677$	11.8494	−	2.35700i	0.455411	−	0.0905869i	0.0379458	−	0.999280i	$-0.487919\pi$
$677$	11.8494	−	2.35700i	0.455411	−	0.0905869i	0.417465	+	0.908693i	$0.362919\pi$
$678$	4.23942	+	10.2349i	0.162814	+	0.393068i
$679$	2.29464			0.0880600
$680$		0			0
$681$	−29.2242			−1.11987
$682$	2.77313	+	6.69493i	0.106189	+	0.256362i
$683$	22.9053	−	4.55614i	0.876446	−	0.174336i	0.263689	−	0.964608i	$-0.415061\pi$
$683$	22.9053	−	4.55614i	0.876446	−	0.174336i	0.612757	+	0.790272i	$0.290061\pi$
$684$	−2.55695	+	2.55695i	−0.0977673	+	0.0977673i
$685$		0			0
$686$	−1.87351	−	2.80390i	−0.0715308	−	0.107053i
$687$	−17.6575	−	26.4262i	−0.673674	−	1.00822i
$688$	−8.17809	−	3.38747i	−0.311787	−	0.129146i
$689$	−0.458112	+	0.189756i	−0.0174527	+	0.00722913i
$690$		0			0
$691$	−23.0135	+	15.3771i	−0.875474	+	0.584973i	−0.910082	−	0.414428i	$-0.863982\pi$
$691$	−23.0135	+	15.3771i	−0.875474	+	0.584973i	0.0346081	+	0.999401i	$0.488982\pi$
$692$	−6.12999	+	9.17418i	−0.233027	+	0.348750i
$693$	0.206230			0.00783404
$694$	11.6216	−	17.3930i	0.441152	−	0.660230i
$695$		0			0
$696$			1.88281i			0.0713678i
$697$	−2.55675	+	2.55921i	−0.0968438	+	0.0969372i
$698$	−1.93577	−	1.93577i	−0.0732701	−	0.0732701i
$699$	−15.5432	−	6.43819i	−0.587896	−	0.243515i
$700$		0			0
$701$	4.84755	+	4.84755i	0.183089	+	0.183089i	0.792701	−	0.609611i	$-0.208674\pi$
$701$	4.84755	+	4.84755i	0.183089	+	0.183089i	−0.609611	+	0.792701i	$0.708674\pi$
$702$	1.16215	+	0.776527i	0.0438627	+	0.0293081i
$703$	−7.63343	+	38.3759i	−0.287900	+	1.44737i
$704$	1.39237	+	0.276961i	0.0524771	+	0.0104383i
$705$		0			0
$706$	−3.89714	−	9.40854i	−0.146671	−	0.354095i
$707$	−3.40022	+	2.27196i	−0.127879	+	0.0854457i
$708$	2.06462	+	0.410678i	0.0775930	+	0.0154342i
$709$	8.65704	+	43.5219i	0.325122	+	1.63450i	0.704818	+	0.709388i	$0.251028\pi$
$709$	8.65704	+	43.5219i	0.325122	+	1.63450i	−0.379696	+	0.925111i	$0.623972\pi$
$710$		0			0
$711$	5.26818	+	3.52008i	0.197572	+	0.132013i
$712$	−6.76738	+	2.80314i	−0.253618	+	0.105052i
$713$	11.1980	−	11.1980i	0.419367	−	0.419367i
$714$	1.28408	−	0.858890i	0.0480555	−	0.0321431i
$715$		0			0
$716$	−5.73630	+	13.8487i	−0.214376	+	0.517548i
$717$	−2.12194	−	10.6677i	−0.0792454	−	0.398394i
$718$			22.0101i			0.821411i
$719$	−45.6966	+	9.08963i	−1.70420	+	0.338986i	−0.948703	−	0.316169i	$-0.897603\pi$
$719$	−45.6966	+	9.08963i	−1.70420	+	0.338986i	−0.755494	+	0.655155i	$0.772603\pi$
$720$		0			0
$721$	0.183809	−	0.924072i	0.00684542	−	0.0344142i
$722$	−6.60252	+	15.9399i	−0.245721	+	0.593222i
$723$	10.0029	−	24.1493i	0.372014	−	0.898121i
$724$	3.42908	−	17.2391i	0.127441	−	0.640687i
$725$		0			0
$726$	13.6498	−	2.71511i	0.506591	−	0.100767i
$727$			43.0062i			1.59501i	0.603311	+	0.797506i	$0.293848\pi$
$727$			43.0062i			1.59501i	−0.603311	+	0.797506i	$0.706152\pi$
$728$	0.0118259	+	0.0594529i	0.000438298	+	0.00220347i
$729$	11.4898	−	27.7389i	0.425550	−	1.02737i
$730$		0			0
$731$	−30.3366	+	20.2914i	−1.12204	+	0.750506i
$732$	−10.0452	+	10.0452i	−0.371280	+	0.371280i
$733$	26.0810	−	10.8031i	0.963325	−	0.399022i	0.155102	−	0.987898i	$-0.450429\pi$
$733$	26.0810	−	10.8031i	0.963325	−	0.399022i	0.808223	+	0.588876i	$0.200429\pi$
$734$	1.58128	+	1.05658i	0.0583661	+	0.0389990i
$735$		0			0
$736$	−0.605259	−	3.04284i	−0.0223101	−	0.112161i
$737$	15.1515	+	3.01382i	0.558112	+	0.111015i
$738$	−0.438125	+	0.292746i	−0.0161276	+	0.0107761i
$739$	−2.98911	−	7.21635i	−0.109956	−	0.265458i	0.859317	−	0.511443i	$-0.170889\pi$
$739$	−2.98911	−	7.21635i	−0.109956	−	0.265458i	−0.969274	+	0.245985i	$0.920889\pi$
$740$		0			0
$741$	2.29242	+	0.455990i	0.0842140	+	0.0167512i
$742$	−0.0933698	+	0.469402i	−0.00342771	+	0.0172323i
$743$	−2.95821	−	1.97661i	−0.108526	−	0.0725149i	0.500123	−	0.865955i	$-0.333288\pi$
$743$	−2.95821	−	1.97661i	−0.108526	−	0.0725149i	−0.608649	+	0.793440i	$0.708288\pi$
$744$	5.59097	+	5.59097i	0.204975	+	0.204975i
$745$		0			0
$746$	−5.23997	−	2.17046i	−0.191849	−	0.0794664i
$747$	−0.0810754	−	0.0810754i	−0.00296639	−	0.00296639i
$748$	4.13697	−	4.14096i	0.151263	−	0.151408i
$749$			0.240163i			0.00877536i
$750$		0			0
$751$	7.02525	−	10.5140i	0.256355	−	0.383663i	−0.680860	−	0.732413i	$-0.738394\pi$
$751$	7.02525	−	10.5140i	0.256355	−	0.383663i	0.937216	+	0.348751i	$0.113394\pi$
$752$	−10.2201			−0.372689
$753$	−23.7677	+	35.5709i	−0.866145	+	1.29628i
$754$	−0.253275	+	0.169233i	−0.00922371	+	0.00616309i
$755$		0			0
$756$	1.24637	−	0.516264i	0.0453301	−	0.0187763i
$757$	−15.2559	−	6.31920i	−0.554485	−	0.229675i	0.0878041	−	0.996138i	$-0.472015\pi$
$757$	−15.2559	−	6.31920i	−0.554485	−	0.229675i	−0.642289	+	0.766463i	$0.722015\pi$
$758$	−1.07474	−	1.60847i	−0.0390365	−	0.0584222i
$759$	3.79036	+	5.67268i	0.137581	+	0.205905i
$760$		0			0
$761$	4.49157	−	4.49157i	0.162819	−	0.162819i	−0.620995	−	0.783814i	$-0.713271\pi$
$761$	4.49157	−	4.49157i	0.162819	−	0.162819i	0.783814	+	0.620995i	$0.213271\pi$
$762$	−23.8307	+	4.74022i	−0.863295	+	0.171720i
$763$	0.582130	+	1.40539i	0.0210745	+	0.0508784i
$764$	9.21078			0.333234
$765$		0			0
$766$	28.4783			1.02896
$767$	0.130330	+	0.314644i	0.00470593	+	0.0113611i
$768$	1.51925	−	0.302197i	0.0548211	−	0.0109046i
$769$	−10.8129	+	10.8129i	−0.389923	+	0.389923i	−0.874660	−	0.484737i	$-0.838915\pi$
$769$	−10.8129	+	10.8129i	−0.389923	+	0.389923i	0.484737	+	0.874660i	$0.338915\pi$
$770$		0			0
$771$	−0.688003	−	1.02967i	−0.0247778	−	0.0370827i
$772$	5.21367	+	7.80281i	0.187644	+	0.280829i
$773$	6.03868	+	2.50130i	0.217196	+	0.0899656i	0.488629	−	0.872492i	$-0.337497\pi$
$773$	6.03868	+	2.50130i	0.217196	+	0.0899656i	−0.271432	+	0.962458i	$0.587497\pi$
$774$	−4.91151	+	2.03441i	−0.176541	+	0.0731255i
$775$		0			0
$776$	7.88775	−	5.27043i	0.283154	−	0.189197i
$777$	1.35273	−	2.02450i	0.0485289	−	0.0726286i
$778$	25.0802			0.899169
$779$	−2.93495	+	4.39246i	−0.105155	+	0.157376i
$780$		0			0
$781$			1.40253i			0.0501865i
$782$	−11.8204	−	4.88950i	−0.422696	−	0.174848i
$783$	4.79362	+	4.79362i	0.171310	+	0.171310i
$784$	−6.41310	−	2.65639i	−0.229039	−	0.0948712i
$785$		0			0
$786$	6.40252	+	6.40252i	0.228370	+	0.228370i
$787$	−4.21424	−	2.81586i	−0.150221	−	0.100375i	0.478188	−	0.878257i	$-0.341294\pi$
$787$	−4.21424	−	2.81586i	−0.150221	−	0.100375i	−0.628409	+	0.777883i	$0.716294\pi$
$788$	1.30769	−	6.57422i	0.0465846	−	0.234197i
$789$	−11.3421	−	2.25609i	−0.403790	−	0.0803188i
$790$		0			0
$791$	0.662002	+	1.59822i	0.0235381	+	0.0568260i
$792$	0.708911	−	0.473679i	0.0251901	−	0.0168315i
$793$	−2.25416	−	0.448380i	−0.0800475	−	0.0159224i
$794$	0.897961	+	4.51435i	0.0318674	+	0.160208i
$795$		0			0
$796$	−21.0019	−	14.0330i	−0.744394	−	0.497388i
$797$	−6.65852	+	2.75805i	−0.235857	+	0.0976951i	−0.497482	−	0.867475i	$-0.665742\pi$
$797$	−6.65852	+	2.75805i	−0.235857	+	0.0976951i	0.261625	+	0.965170i	$0.415742\pi$
$798$	1.59522	−	1.59522i	0.0564700	−	0.0564700i
$799$	−23.3940	+	35.0482i	−0.827622	+	1.23992i
$800$		0			0
$801$	−1.68348	+	4.06428i	−0.0594828	+	0.143604i
$802$	7.16626	+	36.0272i	0.253049	+	1.27216i
$803$			22.2463i			0.785056i
$804$	16.5321	−	3.28843i	0.583041	−	0.115974i
$805$		0			0
$806$	−0.249561	+	1.25463i	−0.00879040	+	0.0441923i
$807$	−12.2939	+	29.6801i	−0.432765	+	1.04479i
$808$	−6.46985	+	15.6196i	−0.227608	+	0.549495i
$809$	−0.369390	+	1.85705i	−0.0129871	+	0.0652904i	−0.986735	−	0.162337i	$-0.948097\pi$
$809$	−0.369390	+	1.85705i	−0.0129871	+	0.0652904i	0.973748	+	0.227627i	$0.0730968\pi$
$810$		0			0
$811$	19.7489	−	3.92829i	0.693476	−	0.137941i	0.164246	−	0.986419i	$-0.447481\pi$
$811$	19.7489	−	3.92829i	0.693476	−	0.137941i	0.529230	+	0.848478i	$0.322481\pi$
$812$			0.294008i			0.0103177i
$813$	6.25074	+	31.4246i	0.219223	+	1.10211i
$814$	3.53047	−	8.52331i	0.123743	−	0.298742i
$815$		0			0
$816$	2.44125	−	5.90175i	0.0854610	−	0.206602i
$817$	−37.6873	+	37.6873i	−1.31851	+	1.31851i
$818$	−34.6925	+	14.3701i	−1.21299	+	0.502439i
$819$	0.0302697	+	0.0202256i	0.00105771	+	0.000706740i
$820$		0			0
$821$	−1.61477	−	8.11799i	−0.0563558	−	0.283320i	0.942323	−	0.334705i	$-0.108637\pi$
$821$	−1.61477	−	8.11799i	−0.0563558	−	0.283320i	−0.998679	+	0.0513847i	$0.983637\pi$
$822$	21.9414	+	4.36442i	0.765295	+	0.152227i
$823$	0.0322708	−	0.0215627i	0.00112489	−	0.000751627i	−0.555008	−	0.831845i	$-0.687285\pi$
$823$	0.0322708	−	0.0215627i	0.00112489	−	0.000751627i	0.556133	+	0.831094i	$0.312285\pi$
$824$	−1.49061	−	3.59866i	−0.0519279	−	0.125365i
$825$		0			0
$826$	0.322398	+	0.0641289i	0.0112177	+	0.00223133i
$827$	10.1422	−	50.9885i	0.352680	−	1.77304i	−0.243207	−	0.969974i	$-0.578199\pi$
$827$	10.1422	−	50.9885i	0.352680	−	1.77304i	0.595887	−	0.803068i	$-0.296801\pi$
$828$	−1.54923	−	1.03516i	−0.0538394	−	0.0359743i
$829$	−0.678814	−	0.678814i	−0.0235762	−	0.0235762i	0.695220	−	0.718797i	$-0.255307\pi$
$829$	−0.678814	−	0.678814i	−0.0235762	−	0.0235762i	−0.718797	+	0.695220i	$0.755307\pi$
$830$		0			0
$831$	−29.3694	−	12.1652i	−1.01881	−	0.422006i
$832$	0.177206	+	0.177206i	0.00614350	+	0.00614350i
$833$	−23.7894	+	15.9122i	−0.824255	+	0.551324i
$834$			31.2807i			1.08316i
$835$		0			0
$836$	4.74892	−	7.10726i	0.164245	−	0.245810i
$837$	28.4691			0.984036
$838$	14.3243	−	21.4378i	0.494824	−	0.740557i
$839$	−24.5010	+	16.3711i	−0.845870	+	0.565192i	−0.901263	−	0.433273i	$-0.857359\pi$
$839$	−24.5010	+	16.3711i	−0.845870	+	0.565192i	0.0553933	+	0.998465i	$0.482359\pi$
$840$		0			0
$841$	25.4275	−	10.5324i	0.876812	−	0.363187i
$842$	4.75190	+	1.96830i	0.163761	+	0.0678321i
$843$	20.0238	+	29.9677i	0.689655	+	1.03214i
$844$	11.4284	+	17.1039i	0.393383	+	0.588739i
$845$		0			0
$846$	−4.34013	+	4.34013i	−0.149217	+	0.149217i
$847$	2.13147	−	0.423975i	0.0732381	−	0.0145680i
$848$	0.757188	+	1.82801i	0.0260019	+	0.0627742i
$849$	26.4843			0.908940
$850$		0			0
$851$	−20.1612			−0.691117
$852$	0.585631	+	1.41384i	0.0200634	+	0.0484373i
$853$	−12.7168	+	2.52953i	−0.435414	+	0.0866093i	−0.407931	−	0.913013i	$-0.633749\pi$
$853$	−12.7168	+	2.52953i	−0.435414	+	0.0866093i	−0.0274838	+	0.999622i	$0.508749\pi$
$854$	−1.56859	+	1.56859i	−0.0536761	+	0.0536761i
$855$		0			0
$856$	0.551617	+	0.825553i	0.0188539	+	0.0282168i
$857$	−14.5080	−	21.7128i	−0.495584	−	0.741694i	0.496395	−	0.868097i	$-0.334657\pi$
$857$	−14.5080	−	21.7128i	−0.495584	−	0.741694i	−0.991979	+	0.126403i	$0.959657\pi$
$858$	−0.509148	−	0.210896i	−0.0173820	−	0.00719987i
$859$	39.8276	−	16.4971i	1.35890	−	0.562874i	0.420143	−	0.907458i	$-0.361980\pi$
$859$	39.8276	−	16.4971i	1.35890	−	0.562874i	0.938756	+	0.344583i	$0.111980\pi$
$860$		0			0
$861$	0.273335	−	0.182637i	0.00931524	−	0.00622424i
$862$	−2.44173	+	3.65430i	−0.0831655	+	0.124466i
$863$	−23.8428			−0.811618			−0.405809	−	0.913958i	$-0.633010\pi$
$863$	−23.8428			−0.811618			−0.405809	+	0.913958i	$0.633010\pi$
$864$	3.09859	−	4.63737i	0.105416	−	0.157767i
$865$		0			0
$866$		−	23.2276i		−	0.789305i
$867$	−14.6510	−	21.8811i	−0.497574	−	0.743122i
$868$	0.873052	+	0.873052i	0.0296333	+	0.0296333i
$869$	−13.8372	−	5.73156i	−0.469395	−	0.194430i
$870$		0			0
$871$	1.92831	+	1.92831i	0.0653382	+	0.0653382i
$872$	5.22902	+	3.49392i	0.177077	+	0.118319i
$873$	1.11149	−	5.58784i	0.0376183	−	0.189120i
$874$	−18.3212	−	3.64430i	−0.619722	−	0.123270i
$875$		0			0
$876$	9.28902	+	22.4257i	0.313847	+	0.757694i
$877$	−19.6574	+	13.1347i	−0.663785	+	0.443527i	−0.841283	−	0.540594i	$-0.818199\pi$
$877$	−19.6574	+	13.1347i	−0.663785	+	0.443527i	0.177499	+	0.984121i	$0.443199\pi$
$878$	9.16636	+	1.82330i	0.309350	+	0.0615335i
$879$	9.58609	+	48.1925i	0.323331	+	1.62549i
$880$		0			0
$881$	2.09659	+	1.40090i	0.0706359	+	0.0471974i	0.590387	−	0.807120i	$-0.298975\pi$
$881$	2.09659	+	1.40090i	0.0706359	+	0.0471974i	−0.519751	+	0.854318i	$0.673975\pi$
$882$	−3.85151	+	1.59535i	−0.129687	+	0.0537182i
$883$	14.0335	−	14.0335i	0.472267	−	0.472267i	−0.430381	−	0.902647i	$-0.641621\pi$
$883$	14.0335	−	14.0335i	0.472267	−	0.472267i	0.902647	+	0.430381i	$0.141621\pi$
$884$	1.01333	−	0.202070i	0.0340818	−	0.00679636i
$885$		0			0
$886$	−0.368042	+	0.888533i	−0.0123646	+	0.0298508i
$887$	−2.53061	−	12.7222i	−0.0849697	−	0.427171i	−0.999731	−	0.0231775i	$-0.992622\pi$
$887$	−2.53061	−	12.7222i	−0.0849697	−	0.427171i	0.914762	−	0.403994i	$-0.132378\pi$
$888$		−	10.0662i		−	0.337799i
$889$	−3.72125	+	0.740203i	−0.124807	+	0.0248256i
$890$		0			0
$891$	−1.89375	+	9.52051i	−0.0634429	+	0.318949i
$892$	1.75687	−	4.24146i	0.0588243	−	0.142014i
$893$	−23.5488	+	56.8517i	−0.788029	+	1.90247i
$894$	3.87727	−	19.4924i	0.129675	−	0.651923i
$895$		0			0
$896$	0.237236	−	0.0471892i	0.00792550	−	0.00157648i
$897$			1.20435i			0.0402120i
$898$	−0.232256	−	1.16763i	−0.00775049	−	0.0389644i
$899$	−2.37433	+	5.73214i	−0.0791883	+	0.191178i
$900$		0			0
$901$	8.00210	+	1.58771i	0.266588	+	0.0528943i
$902$	0.880756	−	0.880756i	0.0293260	−	0.0293260i
$903$	3.06417	−	1.26922i	0.101969	−	0.0422370i
$904$	5.94647	+	3.97331i	0.197777	+	0.132150i
$905$		0			0
$906$	−2.17930	−	10.9561i	−0.0724025	−	0.363992i
$907$	2.58672	+	0.514531i	0.0858907	+	0.0170847i	0.237849	−	0.971302i	$-0.423558\pi$
$907$	2.58672	+	0.514531i	0.0858907	+	0.0170847i	−0.151958	+	0.988387i	$0.548558\pi$
$908$	−15.6868	+	10.4816i	−0.520586	+	0.347844i
$909$	3.88559	+	9.38065i	0.128877	+	0.311136i
$910$		0			0
$911$	56.7789	+	11.2940i	1.88117	+	0.374188i	0.995867	−	0.0908286i	$-0.0289516\pi$
$911$	56.7789	+	11.2940i	1.88117	+	0.374188i	0.885302	+	0.465016i	$0.153952\pi$
$912$	1.81955	−	9.14748i	0.0602512	−	0.302903i
$913$	0.225356	+	0.150578i	0.00745820	+	0.00498341i
$914$	12.6356	+	12.6356i	0.417950	+	0.417950i
$915$		0			0
$916$	−18.9562	−	7.85190i	−0.626329	−	0.259434i
$917$	0.999779	+	0.999779i	0.0330156	+	0.0330156i
$918$	−8.81037	−	21.2412i	−0.290786	−	0.701063i
$919$		−	38.7156i		−	1.27711i	−0.769576	−	0.638556i	$-0.779532\pi$
$919$		−	38.7156i		−	1.27711i	0.769576	−	0.638556i	$-0.220468\pi$
$920$		0			0
$921$	−12.1986	+	18.2565i	−0.401957	+	0.601571i
$922$	5.10872			0.168247
$923$	−0.137550	+	0.205859i	−0.00452752	+	0.00677592i
$924$	−0.442272	+	0.295517i	−0.0145497	+	0.00972179i
$925$		0			0
$926$	−28.1905	+	11.6769i	−0.926398	+	0.383727i
$927$	−2.16124	−	0.895216i	−0.0709845	−	0.0294028i
$928$	0.675292	+	1.01065i	0.0221676	+	0.0331761i
$929$	7.38689	+	11.0553i	0.242356	+	0.362711i	0.932628	−	0.360838i	$-0.117509\pi$
$929$	7.38689	+	11.0553i	0.242356	+	0.362711i	−0.690272	+	0.723550i	$0.742509\pi$
$930$		0			0
$931$	−29.5537	+	29.5537i	−0.968582	+	0.968582i
$932$	−10.6523	+	2.11888i	−0.348928	+	0.0694061i
$933$	−17.7014	−	42.7350i	−0.579519	−	1.39908i
$934$	11.8903			0.389063
$935$		0			0
$936$	0.150507			0.00491946
$937$	−3.11305	−	7.51556i	−0.101699	−	0.245523i	0.864838	−	0.502051i	$-0.167421\pi$
$937$	−3.11305	−	7.51556i	−0.101699	−	0.245523i	−0.966537	+	0.256529i	$0.917421\pi$
$938$	2.58155	−	0.513502i	0.0842905	−	0.0167664i
$939$	−1.03866	+	1.03866i	−0.0338954	+	0.0338954i
$940$		0			0
$941$	6.66132	+	9.96938i	0.217153	+	0.324992i	0.924013	−	0.382361i	$-0.124889\pi$
$941$	6.66132	+	9.96938i	0.217153	+	0.324992i	−0.706860	+	0.707353i	$0.749889\pi$
$942$	21.4946	+	32.1689i	0.700331	+	1.04812i
$943$	−2.51483	−	1.04168i	−0.0818942	−	0.0339217i
$944$	1.25553	−	0.520057i	0.0408640	−	0.0169264i
$945$		0			0
$946$	10.4488	−	6.98164i	0.339719	−	0.226993i
$947$	−17.5643	+	26.2868i	−0.570763	+	0.854207i	−0.998771	−	0.0495681i	$-0.984216\pi$
$947$	−17.5643	+	26.2868i	−0.570763	+	0.854207i	0.428008	+	0.903775i	$0.359216\pi$
$948$	−16.3420			−0.530763
$949$	−2.18176	+	3.26524i	−0.0708230	+	0.105994i
$950$		0			0
$951$			14.2734i			0.462846i
$952$	0.381211	−	0.921580i	0.0123551	−	0.0298686i
$953$	35.4000	+	35.4000i	1.14672	+	1.14672i	0.987194	+	0.159524i	$0.0509959\pi$
$953$	35.4000	+	35.4000i	1.14672	+	1.14672i	0.159524	+	0.987194i	$0.449004\pi$
$954$	1.09785	+	0.454744i	0.0355442	+	0.0147229i
$955$		0			0
$956$	−4.96511	−	4.96511i	−0.160583	−	0.160583i
$957$	−2.22247	−	1.48501i	−0.0718422	−	0.0480034i
$958$	−0.812508	+	4.08476i	−0.0262510	+	0.131972i
$959$	3.42624	+	0.681521i	0.110639	+	0.0220075i
$960$		0			0
$961$	−1.89224	−	4.56827i	−0.0610399	−	0.147363i
$962$	1.35410	−	0.904778i	0.0436578	−	0.0291712i
$963$	0.584839	+	0.116332i	0.0188462	+	0.00374873i
$964$	−3.29208	−	16.5504i	−0.106031	−	0.533052i
$965$		0			0
$966$	0.966525	+	0.645811i	0.0310974	+	0.0207786i
$967$	6.17012	−	2.55575i	0.198418	−	0.0821873i	−0.281262	−	0.959631i	$-0.590753\pi$
$967$	6.17012	−	2.55575i	0.198418	−	0.0821873i	0.479680	+	0.877444i	$0.340753\pi$
$968$	6.35306	−	6.35306i	0.204195	−	0.204195i
$969$	−27.2048	−	27.1786i	−0.873945	−	0.873103i
$970$		0			0
$971$	−0.716696	+	1.73026i	−0.0229999	+	0.0555266i	−0.934962	−	0.354747i	$-0.884567\pi$
$971$	−0.716696	+	1.73026i	−0.0229999	+	0.0555266i	0.911962	+	0.410274i	$0.134567\pi$
$972$	−1.19794	−	6.02244i	−0.0384239	−	0.193170i
$973$			4.88460i			0.156593i
$974$	−9.97377	+	1.98391i	−0.319580	+	0.0635685i
$975$		0			0
$976$	−1.78918	+	8.99481i	−0.0572702	+	0.287917i
$977$	−7.94869	+	19.1898i	−0.254301	+	0.613938i	−0.998542	−	0.0539735i	$-0.982811\pi$
$977$	−7.94869	+	19.1898i	−0.254301	+	0.613938i	0.744241	+	0.667911i	$0.232811\pi$
$978$	4.03900	−	9.75101i	0.129153	−	0.311803i
$979$	2.02872	−	10.1991i	0.0648383	−	0.325964i
$980$		0			0
$981$	3.70434	−	0.736839i	0.118270	−	0.0235255i
$982$		−	10.0839i		−	0.321789i
$983$	2.00524	+	10.0810i	0.0639571	+	0.321534i	0.999498	−	0.0316845i	$-0.0100872\pi$
$983$	2.00524	+	10.0810i	0.0639571	+	0.321534i	−0.935541	+	0.353219i	$0.885087\pi$
$984$	0.520094	−	1.25562i	0.0165800	−	0.0400276i
$985$		0			0
$986$	5.01161	−	0.00241404i	0.159602	−	7.68786e-5i
$987$	2.70770	−	2.70770i	0.0861871	−	0.0861871i
$988$	1.39406	−	0.577438i	0.0443509	−	0.0183707i
$989$	−22.8343	−	15.2574i	−0.726090	−	0.485157i
$990$		0			0
$991$	3.19987	+	16.0868i	0.101647	+	0.511015i	0.997743	+	0.0671536i	$0.0213918\pi$
$991$	3.19987	+	16.0868i	0.101647	+	0.511015i	−0.896095	+	0.443861i	$0.853608\pi$
$992$	5.00636	+	0.995828i	0.158952	+	0.0316176i
$993$	19.5190	−	13.0422i	0.619416	−	0.413880i
$994$	0.0914486	+	0.220776i	0.00290057	+	0.00700260i
$995$		0			0
$996$	0.290047	+	0.0576940i	0.00919050	+	0.00182810i
$997$	3.12344	−	15.7026i	0.0989204	−	0.497306i	−0.899282	−	0.437370i	$-0.855910\pi$
$997$	3.12344	−	15.7026i	0.0989204	−	0.497306i	0.998202	−	0.0599366i	$-0.0190899\pi$
$998$	25.8286	+	17.2581i	0.817588	+	0.546295i
$999$	−25.6284	−	25.6284i	−0.810846	−	0.810846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.v.d.143.2		40
5.2	odd	4		850.2.s.d.7.4		40
5.3	odd	4		170.2.o.b.7.2	✓	40
5.4	even	2		170.2.r.b.143.4	yes	40
17.5	odd	16		850.2.s.d.243.4		40
85.22	even	16	inner	850.2.v.d.107.2		40
85.39	odd	16		170.2.o.b.73.2	yes	40
85.73	even	16		170.2.r.b.107.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.o.b.7.2	✓	40	5.3	odd	4
170.2.o.b.73.2	yes	40	85.39	odd	16
170.2.r.b.107.4	yes	40	85.73	even	16
170.2.r.b.143.4	yes	40	5.4	even	2
850.2.s.d.7.4		40	5.2	odd	4
850.2.s.d.243.4		40	17.5	odd	16
850.2.v.d.107.2		40	85.22	even	16	inner
850.2.v.d.143.2		40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.v (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.382683 + 0.923880i) q^{2} +(-1.51925 + 0.302197i) q^{3} +(-0.707107 + 0.707107i) q^{4} +(-0.860584 - 1.28795i) q^{6} +(-0.134383 - 0.201119i) q^{7} +(-0.923880 - 0.382683i) q^{8} +(-0.554854 + 0.229828i) q^{9} +O(q^{10})\)	\(q+(0.382683 + 0.923880i) q^{2} +(-1.51925 + 0.302197i) q^{3} +(-0.707107 + 0.707107i) q^{4} +(-0.860584 - 1.28795i) q^{6} +(-0.134383 - 0.201119i) q^{7} +(-0.923880 - 0.382683i) q^{8} +(-0.554854 + 0.229828i) q^{9} +(1.18040 - 0.788717i) q^{11} +(0.860584 - 1.28795i) q^{12} +0.250606 q^{13} +(0.134383 - 0.201119i) q^{14} -1.00000i q^{16} +(-3.42934 - 2.28902i) q^{17} +(-0.424667 - 0.424667i) q^{18} +(-5.56274 - 2.30416i) q^{19} +(0.264939 + 0.264939i) q^{21} +(1.18040 + 0.788717i) q^{22} +(0.605259 - 3.04284i) q^{23} +(1.51925 + 0.302197i) q^{24} +(0.0959029 + 0.231530i) q^{26} +(4.63737 - 3.09859i) q^{27} +(0.237236 + 0.0471892i) q^{28} +(0.237131 + 1.19214i) q^{29} +(4.24419 + 2.83588i) q^{31} +(0.923880 - 0.382683i) q^{32} +(-1.55497 + 1.55497i) q^{33} +(0.802430 - 4.04427i) q^{34} +(0.229828 - 0.554854i) q^{36} +(-1.26779 - 6.37360i) q^{37} -6.02107i q^{38} +(-0.380733 + 0.0757325i) q^{39} +(0.171169 - 0.860522i) q^{41} +(-0.143384 + 0.346160i) q^{42} +(3.38747 - 8.17809i) q^{43} +(-0.276961 + 1.39237i) q^{44} +(3.04284 - 0.605259i) q^{46} -10.2201i q^{47} +(0.302197 + 1.51925i) q^{48} +(2.65639 - 6.41310i) q^{49} +(5.90175 + 2.44125i) q^{51} +(-0.177206 + 0.177206i) q^{52} +(-1.82801 + 0.757188i) q^{53} +(4.63737 + 3.09859i) q^{54} +(0.0471892 + 0.237236i) q^{56} +(9.14748 + 1.81955i) q^{57} +(-1.01065 + 0.675292i) q^{58} +(0.520057 + 1.25553i) q^{59} +(-8.99481 - 1.78918i) q^{61} +(-0.995828 + 5.00636i) q^{62} +(0.120786 + 0.0807066i) q^{63} +(0.707107 + 0.707107i) q^{64} +(-2.03166 - 0.841542i) q^{66} +(7.69457 + 7.69457i) q^{67} +(4.04349 - 0.806326i) q^{68} +4.80573i q^{69} +(-0.548870 + 0.821442i) q^{71} +0.600569 q^{72} +(-8.70593 + 13.0293i) q^{73} +(5.40328 - 3.61035i) q^{74} +(5.56274 - 2.30416i) q^{76} +(-0.317252 - 0.131410i) q^{77} +(-0.215668 - 0.322770i) q^{78} +(-5.86124 - 8.77197i) q^{79} +(-4.83492 + 4.83492i) q^{81} +(0.860522 - 0.171169i) q^{82} +(0.0730601 + 0.176383i) q^{83} -0.374680 q^{84} +8.85190 q^{86} +(-0.720521 - 1.73949i) q^{87} +(-1.39237 + 0.276961i) q^{88} +(5.17953 - 5.17953i) q^{89} +(-0.0336774 - 0.0504017i) q^{91} +(1.72363 + 2.57960i) q^{92} +(-7.30496 - 3.02581i) q^{93} +(9.44214 - 3.91106i) q^{94} +(-1.28795 + 0.860584i) q^{96} +(-5.27043 + 7.88775i) q^{97} +6.94149 q^{98} +(-0.473679 + 0.708911i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q+O(q^{10}) \) 40 * q	\( 40 q + 16 q^{18} - 8 q^{26} - 24 q^{27} + 8 q^{28} + 8 q^{29} - 16 q^{31} + 32 q^{33} + 8 q^{34} - 32 q^{39} - 56 q^{41} + 24 q^{42} - 16 q^{43} + 16 q^{44} + 16 q^{49} - 32 q^{51} + 16 q^{52} - 16 q^{53} - 24 q^{54} - 8 q^{56} + 120 q^{57} - 16 q^{58} + 24 q^{61} + 8 q^{62} + 24 q^{63} - 16 q^{67} + 24 q^{71} - 56 q^{72} - 88 q^{73} + 32 q^{74} - 24 q^{77} - 32 q^{78} - 104 q^{79} + 48 q^{81} - 16 q^{82} - 16 q^{83} + 96 q^{86} - 136 q^{87} - 16 q^{89} + 48 q^{91} + 8 q^{92} + 8 q^{93} - 8 q^{94} - 16 q^{97} - 72 q^{98} + 160 q^{99}+O(q^{100}) \) 40 * q + 16 * q^18 - 8 * q^26 - 24 * q^27 + 8 * q^28 + 8 * q^29 - 16 * q^31 + 32 * q^33 + 8 * q^34 - 32 * q^39 - 56 * q^41 + 24 * q^42 - 16 * q^43 + 16 * q^44 + 16 * q^49 - 32 * q^51 + 16 * q^52 - 16 * q^53 - 24 * q^54 - 8 * q^56 + 120 * q^57 - 16 * q^58 + 24 * q^61 + 8 * q^62 + 24 * q^63 - 16 * q^67 + 24 * q^71 - 56 * q^72 - 88 * q^73 + 32 * q^74 - 24 * q^77 - 32 * q^78 - 104 * q^79 + 48 * q^81 - 16 * q^82 - 16 * q^83 + 96 * q^86 - 136 * q^87 - 16 * q^89 + 48 * q^91 + 8 * q^92 + 8 * q^93 - 8 * q^94 - 16 * q^97 - 72 * q^98 + 160 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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