LMFDB - Embedded newform 850.2.v.d.107.2

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			107.2
Character	$\chi$	$=$	850.107
Dual form			850.2.v.d.143.2

$q$-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 $\left(\mathbb{Z}/850\mathbb{Z}\right)^\times$.

$n$	$477$	$751$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{16}\right)$

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	−0.264069	−	0.964504i	$-0.585065\pi$
$3$	−1.51925	−	0.302197i	−0.877137	−	0.174473i	−0.613068	+	0.790030i	$0.710065\pi$
$4$	−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	−0.855997	−	0.516982i	$-0.827056\pi$
$7$	−0.134383	+	0.201119i	−0.0507922	+	0.0760159i	0.805204	+	0.592997i	$0.202056\pi$
$8$	−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	0.720649	−	0.693300i	$-0.243844\pi$
$11$	1.18040	+	0.788717i	0.355904	+	0.237807i	−0.364745	+	0.931107i	$0.618844\pi$
$12$	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	−0.914837	−	0.403822i	$-0.867681\pi$
$19$	−5.56274	+	2.30416i	−1.27618	+	0.528611i	−0.361342	+	0.932433i	$0.617681\pi$
$20$		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	0.991165	+	0.132635i	$0.0423439\pi$
$23$	0.605259	+	3.04284i	0.126205	+	0.634477i	−0.864960	+	0.501841i	$0.832656\pi$
$24$	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	−0.952502	−	0.304531i	$-0.901500\pi$
$29$	0.237131	−	1.19214i	0.0440342	−	0.221375i	0.996536	+	0.0831567i	$0.0265002\pi$
$30$		0			0
$31$	4.24419	−	2.83588i	0.762279	−	0.509339i	−0.112623	−	0.993638i	$-0.535925\pi$
$31$	4.24419	−	2.83588i	0.762279	−	0.509339i	0.874902	+	0.484299i	$0.160925\pi$
$32$	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	0.724921	+	0.688832i	$0.241876\pi$
$37$	−1.26779	+	6.37360i	−0.208423	+	1.04781i	−0.933345	+	0.358982i	$0.883124\pi$
$38$			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	0.991847	−	0.127436i	$-0.0406749\pi$
$41$	0.171169	+	0.860522i	0.0267320	+	0.134391i	−0.965115	+	0.261827i	$0.915675\pi$
$42$	−0.143384	−	0.346160i	−0.0221246	−	0.0534136i
$43$	3.38747	+	8.17809i	0.516585	+	1.24715i	0.939989	+	0.341205i	$0.110835\pi$
$43$	3.38747	+	8.17809i	0.516585	+	1.24715i	−0.423404	+	0.905941i	$0.639165\pi$
$44$	−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	$0.267731\pi$
$47$			10.2201i			1.49075i	−0.666643	+	0.745377i	$0.732269\pi$
$48$	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	0.253585	−	0.967313i	$-0.418390\pi$
$53$	−1.82801	−	0.757188i	−0.251097	−	0.104008i	−0.504682	+	0.863305i	$0.668390\pi$
$54$	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	−0.886405	−	0.462911i	$-0.846805\pi$
$59$	0.520057	−	1.25553i	0.0677056	−	0.163456i	0.954110	+	0.299455i	$0.0968049\pi$
$60$		0			0
$61$	−8.99481	+	1.78918i	−1.15167	+	0.229081i	−0.733760	−	0.679409i	$-0.762236\pi$
$61$	−8.99481	+	1.78918i	−1.15167	+	0.229081i	−0.417907	+	0.908490i	$0.637236\pi$
$62$	−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	−0.0582603	−	0.998301i	$-0.518555\pi$
$67$	7.69457	−	7.69457i	0.940041	−	0.940041i	0.998301	+	0.0582603i	$0.0185553\pi$
$68$	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	0.797470	−	0.603358i	$-0.206171\pi$
$71$	−0.548870	−	0.821442i	−0.0651389	−	0.0974872i	−0.862609	+	0.505871i	$0.831171\pi$
$72$	0.600569			0.0707778
$73$	−8.70593	−	13.0293i	−1.01895	−	1.52497i	−0.841076	−	0.540917i	$-0.818077\pi$
$73$	−8.70593	−	13.0293i	−1.01895	−	1.52497i	−0.177876	−	0.984053i	$-0.556923\pi$
$74$	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	0.339486	+	0.940611i	$0.389747\pi$
$79$	−5.86124	+	8.77197i	−0.659441	+	0.986924i	−0.998927	+	0.0463124i	$0.985253\pi$
$80$		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	−0.919819	−	0.392343i	$-0.871665\pi$
$83$	0.0730601	−	0.176383i	0.00801939	−	0.0193605i	0.927839	+	0.372982i	$0.121665\pi$
$84$	−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	0.926160	−	0.377131i	$-0.123089\pi$
$89$	5.17953	+	5.17953i	0.549029	+	0.549029i	−0.377131	+	0.926160i	$0.623089\pi$
$90$		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	0.461125	−	0.887335i	$-0.347446\pi$
$97$	−5.27043	−	7.88775i	−0.535131	−	0.800880i	−0.996256	+	0.0864553i	$0.972446\pi$
$98$	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	$0.318110\pi$
$101$			16.9065i			1.68226i	−0.540832	+	0.841131i	$0.681890\pi$
$102$	0.00307642	−	6.38673i	0.000304611	−	0.632380i
$103$	2.75429	−	2.75429i	0.271388	−	0.271388i	−0.558271	−	0.829659i	$-0.688535\pi$
$103$	2.75429	−	2.75429i	0.271388	−	0.271388i	0.829659	+	0.558271i	$0.188535\pi$
$104$	−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	−0.594835	−	0.803848i	$-0.702782\pi$
$107$	−0.825553	+	0.551617i	−0.0798093	+	0.0533268i	0.515025	+	0.857175i	$0.327782\pi$
$108$	−1.08808	−	5.47015i	−0.104701	−	0.526365i
$109$	−6.16805	+	1.22690i	−0.590792	+	0.117516i	−0.481427	−	0.876486i	$-0.659881\pi$
$109$	−6.16805	+	1.22690i	−0.590792	+	0.117516i	−0.109364	+	0.994002i	$0.534881\pi$
$110$		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	−0.513648	−	0.858001i	$-0.671706\pi$
$113$	−7.01434	+	1.39524i	−0.659854	+	0.131253i	−0.146206	+	0.989254i	$0.546706\pi$
$114$	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	0.929759	+	0.368170i	$0.120016\pi$
$127$	6.00272	+	14.4919i	0.532655	+	1.28594i	−0.397103	+	0.917774i	$0.629984\pi$
$128$	−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	−0.0618271	−	0.998087i	$-0.519693\pi$
$131$	−5.73305	−	1.14038i	−0.500899	−	0.0996350i	−0.439072	+	0.898452i	$0.644693\pi$
$132$			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	0.120251	−	0.992744i	$-0.461630\pi$
$137$	−10.2123	−	10.2123i	−0.872492	−	0.872492i	−0.992744	+	0.120251i	$0.961630\pi$
$138$	−4.43992	−	1.83907i	−0.377951	−	0.156552i
$139$	−16.7907	+	11.2192i	−1.42417	+	0.951598i	−0.425249	+	0.905076i	$0.639814\pi$
$139$	−16.7907	+	11.2192i	−1.42417	+	0.951598i	−0.998917	+	0.0465215i	$0.985186\pi$
$140$		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	−0.229961	−	0.973200i	$-0.573860\pi$
$149$	9.07239	−	9.07239i	0.743239	−	0.743239i	0.973200	+	0.229961i	$0.0738598\pi$
$150$		0			0
$151$	6.66259	−	2.75974i	0.542194	−	0.224584i	−0.0947404	−	0.995502i	$-0.530202\pi$
$151$	6.66259	−	2.75974i	0.542194	−	0.224584i	0.636935	+	0.770918i	$0.280202\pi$
$152$	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	−0.653070	−	0.757297i	$-0.726519\pi$
$163$	3.78546	−	5.66535i	0.296500	−	0.443744i	0.949571	+	0.313553i	$0.101519\pi$
$164$	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	−0.485992	−	0.873963i	$-0.661542\pi$
$167$	−16.4048	−	3.26312i	−1.26944	−	0.252508i	−0.783449	+	0.621456i	$0.786542\pi$
$168$	−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	0.588479	−	0.808513i	$-0.299727\pi$
$173$	10.8217	+	2.15257i	0.822758	+	0.163657i	0.234279	+	0.972169i	$0.424727\pi$
$174$	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	0.834550	−	0.550933i	$-0.185728\pi$
$179$	13.8487	+	5.73630i	1.03510	+	0.428751i	0.200547	+	0.979684i	$0.435728\pi$
$180$		0			0
$181$	−14.6146	−	9.76518i	−1.08630	−	0.725840i	−0.122498	−	0.992469i	$-0.539090\pi$
$181$	−14.6146	−	9.76518i	−1.08630	−	0.725840i	−0.963799	+	0.266628i	$0.914090\pi$
$182$	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	−0.902324	−	0.431059i	$-0.858140\pi$
$191$	−6.51300	+	6.51300i	−0.471264	+	0.471264i	0.431059	+	0.902324i	$0.358140\pi$
$192$	−1.28795	+	0.860584i	−0.0929501	+	0.0621073i
$193$	1.83080	+	9.20405i	0.131784	+	0.662522i	0.989042	+	0.147635i	$0.0471661\pi$
$193$	1.83080	+	9.20405i	0.131784	+	0.662522i	−0.857258	+	0.514887i	$0.827834\pi$
$194$	−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	0.340956	−	0.940079i	$-0.389249\pi$
$197$	−5.57335	−	3.72400i	−0.397085	−	0.265324i	−0.738041	+	0.674755i	$0.764249\pi$
$198$	−0.836218	+	0.166334i	−0.0594274	+	0.0118208i
$199$	4.92775	−	24.7735i	0.349319	−	1.75614i	−0.262294	−	0.964988i	$-0.584479\pi$
$199$	4.92775	−	24.7735i	0.349319	−	1.75614i	0.611613	−	0.791157i	$-0.290521\pi$
$200$		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	0.830711	+	0.556704i	$0.187934\pi$
$211$	4.01313	+	20.1754i	0.276275	+	1.38893i	−0.554436	+	0.832227i	$0.687066\pi$
$212$	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	0.236121	−	0.971724i	$-0.424124\pi$
$223$	−4.24146	−	1.75687i	−0.284029	−	0.117649i	−0.520150	+	0.854075i	$0.674124\pi$
$224$	−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	0.461953	−	0.886904i	$-0.347149\pi$
$227$	18.5039	−	3.68065i	1.22815	−	0.244293i	0.766193	+	0.642611i	$0.222149\pi$
$228$	−7.75486	−	5.18163i	−0.513578	−	0.343162i
$229$	7.85190	−	18.9562i	0.518868	−	1.25266i	−0.419731	−	0.907649i	$-0.637876\pi$
$229$	7.85190	−	18.9562i	0.518868	−	1.25266i	0.938599	−	0.345010i	$-0.112124\pi$
$230$		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	−0.223416	−	0.974723i	$-0.571721\pi$
$233$	9.03059	−	6.03405i	0.591614	−	0.395304i	0.815029	+	0.579420i	$0.196721\pi$
$234$	−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	$-0.927076\pi$
$239$		−	7.02173i		−	0.454198i	0.973872	−	0.227099i	$-0.0729241\pi$
$240$		0			0
$241$	−9.37504	−	14.0307i	−0.603900	−	0.903800i	0.395996	−	0.918252i	$-0.370399\pi$
$241$	−9.37504	−	14.0307i	−0.603900	−	0.903800i	−0.999896	+	0.0144526i	$0.995399\pi$
$242$	−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	0.962939	+	0.269721i	$0.0869313\pi$
$251$	19.5290	+	19.5290i	1.23266	+	1.23266i	0.269721	+	0.962939i	$0.413069\pi$
$252$	−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	−0.914050	−	0.405601i	$-0.867062\pi$
$257$	0.305941	−	0.738606i	0.0190841	−	0.0460730i	0.933134	+	0.359528i	$0.117062\pi$
$258$	−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	−0.159754	−	0.987157i	$-0.551070\pi$
$263$	6.89733	−	2.85697i	0.425308	−	0.176168i	0.585062	+	0.810989i	$0.301070\pi$
$264$	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	0.995452	+	0.0952616i	$0.0303687\pi$
$269$	11.5222	+	17.2442i	0.702519	+	1.05139i	−0.292933	+	0.956133i	$0.594631\pi$
$270$		0			0
$271$			20.6843i			1.25648i	0.778018	+	0.628242i	$0.216225\pi$
$271$			20.6843i			1.25648i	−0.778018	+	0.628242i	$0.783775\pi$
$272$	−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	0.0752111	−	0.997168i	$-0.476037\pi$
$277$	17.0637	−	11.4016i	1.02526	−	0.685054i	0.950045	+	0.312114i	$0.101037\pi$
$278$	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	0.399568	+	0.916704i	$0.369160\pi$
$281$	−8.90415	+	21.4965i	−0.531177	+	1.28237i	−0.930744	+	0.365671i	$0.880840\pi$
$282$	−13.1630	−	8.79525i	−0.783846	−	0.523749i
$283$	−16.7691	+	3.33557i	−0.996817	+	0.198279i	−0.666431	−	0.745567i	$-0.732179\pi$
$283$	−16.7691	+	3.33557i	−0.996817	+	0.198279i	−0.330386	+	0.943846i	$0.607179\pi$
$284$	−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	$0.377275\pi$
$293$			31.7214i			1.85318i	−0.376071	+	0.926591i	$0.622725\pi$
$294$	−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	0.932700	−	0.360653i	$-0.117446\pi$
$307$	10.0231	+	10.0231i	0.572047	+	0.572047i	−0.360653	+	0.932700i	$0.617446\pi$
$308$	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	−0.356750	−	0.934200i	$-0.616115\pi$
$311$	5.82573	−	29.2879i	0.330347	−	1.66077i	0.687097	−	0.726566i	$-0.258885\pi$
$312$	0.380733	−	0.0757325i	0.0215548	−	0.00428751i
$313$	0.788463	+	0.526834i	0.0445666	+	0.0297784i	0.577654	−	0.816282i	$-0.303968\pi$
$313$	0.788463	+	0.526834i	0.0445666	+	0.0297784i	−0.533087	+	0.846060i	$0.678968\pi$
$314$	−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	0.997862	+	0.0653519i	$0.0208170\pi$
$317$	1.79766	+	9.03747i	0.100967	+	0.507595i	−0.896895	+	0.442243i	$0.854183\pi$
$318$	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	−0.0368818	−	0.999320i	$-0.511743\pi$
$331$	−14.0014	−	5.79957i	−0.769587	−	0.318773i	−0.732705	+	0.680546i	$0.761743\pi$
$332$	−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	0.587531	−	0.809202i	$-0.300100\pi$
$337$	15.0655	+	2.99672i	0.820671	+	0.163242i	0.233140	+	0.972443i	$0.425100\pi$
$338$	−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	0.376092	+	0.926582i	$0.377268\pi$
$347$	−11.6216	+	17.3930i	−0.623883	+	0.933706i	−0.999975	+	0.00712393i	$0.997732\pi$
$348$	1.73949	−	0.720521i	0.0932465	−	0.0386240i
$349$	−2.52921	−	1.04763i	−0.135386	−	0.0560785i	0.313962	−	0.949436i	$-0.398344\pi$
$349$	−2.52921	−	1.04763i	−0.135386	−	0.0560785i	−0.449348	+	0.893357i	$0.648344\pi$
$350$		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	0.225097	−	0.974336i	$-0.427730\pi$
$359$	20.3347	−	8.42291i	1.07322	−	0.444544i	0.848128	+	0.529792i	$0.177730\pi$
$360$		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	0.596156	−	0.802868i	$-0.296694\pi$
$367$	1.58128	+	1.05658i	0.0825421	+	0.0551529i	−0.513614	+	0.858021i	$0.671694\pi$
$368$	−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	0.595615	−	0.803270i	$-0.296909\pi$
$373$	−4.01050	−	4.01050i	−0.207656	−	0.207656i	−0.803270	+	0.595615i	$0.796909\pi$
$374$	−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	0.146120	−	0.989267i	$-0.453321\pi$
$379$	−1.89732	−	0.377400i	−0.0974587	−	0.0193857i	−0.243579	+	0.969881i	$0.578321\pi$
$380$		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	0.912232	+	0.409674i	$0.134358\pi$
$383$	10.8982	+	26.3105i	0.556870	+	1.34440i	−0.355362	+	0.934729i	$0.615642\pi$
$384$	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	0.956407	+	0.292038i	$0.0943333\pi$
$389$	9.59778	+	23.1711i	0.486627	+	1.17482i	−0.469780	+	0.882784i	$0.655667\pi$
$390$		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	−0.0805001	−	0.996755i	$-0.525652\pi$
$397$	4.51435	−	0.897961i	0.226569	−	0.0450674i	0.307069	+	0.951687i	$0.400652\pi$
$398$	−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	0.821818	−	0.569750i	$-0.192960\pi$
$401$	36.0272	−	7.16626i	1.79911	−	0.357866i	0.977295	+	0.211884i	$0.0679600\pi$
$402$	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	$-0.621197\pi$
$409$		−	37.5509i		−	1.85677i	0.371618	−	0.928386i	$-0.378803\pi$
$410$		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	0.295962	+	0.955200i	$0.404360\pi$
$419$	−14.3243	+	21.4378i	−0.699787	+	1.04731i	−0.995749	+	0.0921057i	$0.970640\pi$
$420$		0			0
$421$	3.63694	+	3.63694i	0.177254	+	0.177254i	0.790158	−	0.612904i	$-0.209999\pi$
$421$	3.63694	+	3.63694i	0.177254	+	0.177254i	−0.612904	+	0.790158i	$0.709999\pi$
$422$	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	−0.767992	−	0.640460i	$-0.778744\pi$
$431$	2.44173	−	3.65430i	0.117614	−	0.176022i	0.885605	+	0.464438i	$0.153744\pi$
$432$	−3.09859	+	4.63737i	−0.149081	+	0.223116i
$433$	−21.4595	+	8.88880i	−1.03128	+	0.427169i	−0.833173	−	0.553013i	$-0.813478\pi$
$433$	−21.4595	+	8.88880i	−1.03128	+	0.427169i	−0.198103	+	0.980181i	$0.563478\pi$
$434$	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	0.934435	−	0.356135i	$-0.115906\pi$
$439$	5.19233	+	7.77087i	0.247816	+	0.370883i	−0.686618	+	0.727018i	$0.740906\pi$
$440$		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	−0.690767	−	0.723077i	$-0.742727\pi$
$443$	0.680053	−	0.680053i	0.0323103	−	0.0323103i	0.723077	+	0.690767i	$0.242727\pi$
$444$	−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	−0.222565	−	0.974918i	$-0.571443\pi$
$449$	−1.16763	+	0.232256i	−0.0551039	+	0.0109609i	0.167461	+	0.985879i	$0.446443\pi$
$450$		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	0.733792	−	0.679375i	$-0.237749\pi$
$457$	16.5093	+	6.83836i	0.772270	+	0.319885i	0.0384787	+	0.999259i	$0.487749\pi$
$458$	−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	0.962845	−	0.270053i	$-0.0870413\pi$
$461$	1.95502	+	4.71984i	0.0910545	+	0.219825i	−0.871791	+	0.489878i	$0.837041\pi$
$462$	0.103772	−	0.521696i	0.00482790	−	0.0242715i
$463$		−	30.5132i		−	1.41807i	−0.705174	−	0.709034i	$-0.749131\pi$
$463$		−	30.5132i		−	1.41807i	0.705174	−	0.709034i	$-0.250869\pi$
$464$	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	0.993509	−	0.113749i	$-0.0362860\pi$
$467$	4.55023	+	10.9852i	0.210559	+	0.508335i	−0.782950	+	0.622084i	$0.786286\pi$
$468$	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	−0.473938	−	0.880558i	$-0.657168\pi$
$479$	3.46289	−	2.31383i	0.158223	−	0.105722i	0.632161	+	0.774837i	$0.282168\pi$
$480$		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	−0.999347	−	0.0361360i	$-0.988495\pi$
$487$	−1.98391	−	9.97377i	−0.0898994	−	0.451955i	0.909447	−	0.415819i	$-0.136505\pi$
$488$	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	−0.582864	−	0.812570i	$-0.698068\pi$
$491$	−9.31628	+	3.85893i	−0.420438	+	0.174151i	0.162426	+	0.986721i	$0.448068\pi$
$492$	−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	0.977421	−	0.211303i	$-0.0677707\pi$
$499$	25.8286	+	17.2581i	1.15624	+	0.772578i	0.178824	+	0.983881i	$0.442771\pi$
$500$		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	−0.894056	−	0.447954i	$-0.852153\pi$
$503$	−3.09637	+	4.63404i	−0.138060	+	0.206622i	0.755996	+	0.654576i	$0.227153\pi$
$504$	−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	0.0788644	−	0.996885i	$-0.474871\pi$
$521$	−18.5333	−	12.3835i	−0.811957	−	0.542533i	−0.890822	+	0.454353i	$0.849871\pi$
$522$	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	−0.998558	−	0.0536885i	$-0.982902\pi$
$541$	−30.9603	+	20.6870i	−1.33109	+	0.889404i	−0.332530	+	0.943093i	$0.607902\pi$
$542$	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	−0.834005	−	0.551756i	$-0.813958\pi$
$547$	3.45355	−	17.3622i	0.147663	−	0.742352i	0.981669	−	0.190596i	$-0.0610421\pi$
$548$			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	$-0.869106\pi$
$557$		−	18.8677i		−	0.799448i	0.916636	−	0.399724i	$-0.130894\pi$
$558$	−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	0.526842	−	0.849963i	$-0.323376\pi$
$563$	7.07939	+	2.93238i	0.298361	+	0.123585i	−0.228481	+	0.973548i	$0.573376\pi$
$564$	−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	0.383707	+	0.923455i	$0.374647\pi$
$569$	−12.8952	+	31.1318i	−0.540596	+	1.30511i	−0.924303	+	0.381660i	$0.875353\pi$
$570$		0			0
$571$	−1.88068	+	0.374090i	−0.0787038	+	0.0156552i	−0.234285	−	0.972168i	$-0.575275\pi$
$571$	−1.88068	+	0.374090i	−0.0787038	+	0.0156552i	0.155581	+	0.987823i	$0.450275\pi$
$572$	−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	−0.879193	−	0.476466i	$-0.841917\pi$
$577$	−9.67382	+	9.67382i	−0.402726	+	0.402726i	0.476466	+	0.879193i	$0.341917\pi$
$578$	−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	−0.132926	−	0.991126i	$-0.542437\pi$
$587$	11.4820	−	4.75599i	0.473912	−	0.196301i	0.606839	+	0.794825i	$0.292437\pi$
$588$	−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	0.493987	+	0.869470i	$0.335539\pi$
$593$	−11.4482	+	27.6385i	−0.470122	+	1.13498i	−0.964109	+	0.265507i	$0.914461\pi$
$594$	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	0.437741	−	0.899101i	$-0.355779\pi$
$599$	−11.2916	−	11.2916i	−0.461360	−	0.461360i	−0.899101	+	0.437741i	$0.855779\pi$
$600$		0			0
$601$	9.39260	−	14.0570i	0.383132	−	0.573398i	−0.588912	−	0.808197i	$-0.700443\pi$
$601$	9.39260	−	14.0570i	0.383132	−	0.573398i	0.972044	+	0.234800i	$0.0754434\pi$
$602$	−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	−0.877594	−	0.479405i	$-0.840852\pi$
$607$	−24.2596	−	36.3070i	−0.984666	−	1.47366i	−0.107072	−	0.994251i	$-0.534148\pi$
$608$	−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	−0.933885	−	0.357574i	$-0.883604\pi$
$613$	−14.2688	+	14.2688i	−0.576311	+	0.576311i	0.357574	+	0.933885i	$0.383604\pi$
$614$	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	−0.231140	−	0.972921i	$-0.574246\pi$
$617$	14.3887	−	9.61423i	0.579268	−	0.387054i	0.810408	+	0.585866i	$0.199246\pi$
$618$	1.17710	+	5.91770i	0.0473501	+	0.238045i
$619$	−1.23501	+	0.245658i	−0.0496392	+	0.00987384i	−0.219847	−	0.975534i	$-0.570556\pi$
$619$	−1.23501	+	0.245658i	−0.0496392	+	0.00987384i	0.170208	+	0.985408i	$0.445556\pi$
$620$		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	0.830580	−	0.556899i	$-0.188009\pi$
$631$	−3.78090	−	9.12791i	−0.150515	−	0.363376i	−0.981096	+	0.193522i	$0.938009\pi$
$632$	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	−0.242609	−	0.970124i	$-0.578003\pi$
$641$	−21.2165	−	4.22022i	−0.838001	−	0.166689i	−0.595392	+	0.803435i	$0.703003\pi$
$642$		−	1.53799i		−	0.0606995i
$643$	−8.79438	+	44.2123i	−0.346816	+	1.74356i	0.275965	+	0.961168i	$0.411003\pi$
$643$	−8.79438	+	44.2123i	−0.346816	+	1.74356i	−0.622781	+	0.782396i	$0.713997\pi$
$644$	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	0.626438	−	0.779472i	$-0.284512\pi$
$647$	−3.89261	−	3.89261i	−0.153034	−	0.153034i	−0.779472	+	0.626438i	$0.784512\pi$
$648$	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	0.914839	−	0.403818i	$-0.132317\pi$
$653$	22.7903	+	15.2280i	0.891854	+	0.595918i	−0.0229854	+	0.999736i	$0.507317\pi$
$654$	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	−0.684253	−	0.729245i	$-0.739872\pi$
$659$	1.15499	−	1.15499i	0.0449919	−	0.0449919i	0.729245	+	0.684253i	$0.239872\pi$
$660$		0			0
$661$	−19.9073	+	8.24587i	−0.774303	+	0.320727i	−0.734614	−	0.678485i	$-0.762637\pi$
$661$	−19.9073	+	8.24587i	−0.774303	+	0.320727i	−0.0396893	+	0.999212i	$0.512637\pi$
$662$	−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	−0.0401469	−	0.999194i	$-0.512783\pi$
$673$	23.3052	−	34.8788i	0.898351	−	1.34448i	0.938498	−	0.345284i	$-0.112217\pi$
$674$	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	0.417465	−	0.908693i	$-0.362919\pi$
$677$	11.8494	+	2.35700i	0.455411	+	0.0905869i	0.0379458	+	0.999280i	$0.487919\pi$
$678$	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	0.612757	−	0.790272i	$-0.290061\pi$
$683$	22.9053	+	4.55614i	0.876446	+	0.174336i	0.263689	+	0.964608i	$0.415061\pi$
$684$	−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	0.0346081	−	0.999401i	$-0.488982\pi$
$691$	−23.0135	−	15.3771i	−0.875474	−	0.584973i	−0.910082	+	0.414428i	$0.863982\pi$
$692$	−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	−0.609611	−	0.792701i	$-0.708674\pi$
$701$	4.84755	−	4.84755i	0.183089	−	0.183089i	0.792701	+	0.609611i	$0.208674\pi$
$702$	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	−0.379696	−	0.925111i	$-0.623972\pi$
$709$	8.65704	−	43.5219i	0.325122	−	1.63450i	0.704818	−	0.709388i	$-0.251028\pi$
$710$		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	−0.755494	−	0.655155i	$-0.772603\pi$
$719$	−45.6966	−	9.08963i	−1.70420	−	0.338986i	−0.948703	+	0.316169i	$0.897603\pi$
$720$		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	$-0.706152\pi$
$727$		−	43.0062i		−	1.59501i	0.603311	−	0.797506i	$-0.293848\pi$
$728$	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	0.808223	−	0.588876i	$-0.200429\pi$
$733$	26.0810	+	10.8031i	0.963325	+	0.399022i	0.155102	+	0.987898i	$0.450429\pi$
$734$	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	−0.969274	−	0.245985i	$-0.920889\pi$
$739$	−2.98911	+	7.21635i	−0.109956	+	0.265458i	0.859317	+	0.511443i	$0.170889\pi$
$740$		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	−0.608649	−	0.793440i	$-0.708288\pi$
$743$	−2.95821	+	1.97661i	−0.108526	+	0.0725149i	0.500123	+	0.865955i	$0.333288\pi$
$744$	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	0.937216	−	0.348751i	$-0.113394\pi$
$751$	7.02525	+	10.5140i	0.256355	+	0.383663i	−0.680860	+	0.732413i	$0.738394\pi$
$752$	−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	−0.642289	−	0.766463i	$-0.722015\pi$
$757$	−15.2559	+	6.31920i	−0.554485	+	0.229675i	0.0878041	+	0.996138i	$0.472015\pi$
$758$	−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	0.783814	−	0.620995i	$-0.213271\pi$
$761$	4.49157	+	4.49157i	0.162819	+	0.162819i	−0.620995	+	0.783814i	$0.713271\pi$
$762$	−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	0.484737	−	0.874660i	$-0.338915\pi$
$769$	−10.8129	−	10.8129i	−0.389923	−	0.389923i	−0.874660	+	0.484737i	$0.838915\pi$
$770$		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	−0.271432	−	0.962458i	$-0.587497\pi$
$773$	6.03868	−	2.50130i	0.217196	−	0.0899656i	0.488629	+	0.872492i	$0.337497\pi$
$774$	−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	−0.628409	−	0.777883i	$-0.716294\pi$
$787$	−4.21424	+	2.81586i	−0.150221	+	0.100375i	0.478188	+	0.878257i	$0.341294\pi$
$788$	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	0.261625	−	0.965170i	$-0.415742\pi$
$797$	−6.65852	−	2.75805i	−0.235857	−	0.0976951i	−0.497482	+	0.867475i	$0.665742\pi$
$798$	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	0.973748	−	0.227627i	$-0.0730968\pi$
$809$	−0.369390	−	1.85705i	−0.0129871	−	0.0652904i	−0.986735	+	0.162337i	$0.948097\pi$
$810$		0			0
$811$	19.7489	+	3.92829i	0.693476	+	0.137941i	0.529230	−	0.848478i	$-0.322481\pi$
$811$	19.7489	+	3.92829i	0.693476	+	0.137941i	0.164246	+	0.986419i	$0.447481\pi$
$812$		−	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	−0.998679	−	0.0513847i	$-0.983637\pi$
$821$	−1.61477	+	8.11799i	−0.0563558	+	0.283320i	0.942323	+	0.334705i	$0.108637\pi$
$822$	21.9414	−	4.36442i	0.765295	−	0.152227i
$823$	0.0322708	+	0.0215627i	0.00112489	+	0.000751627i	0.556133	−	0.831094i	$-0.312285\pi$
$823$	0.0322708	+	0.0215627i	0.00112489	+	0.000751627i	−0.555008	+	0.831845i	$0.687285\pi$
$824$	−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	0.595887	+	0.803068i	$0.296801\pi$
$827$	10.1422	+	50.9885i	0.352680	+	1.77304i	−0.243207	+	0.969974i	$0.578199\pi$
$828$	−1.54923	+	1.03516i	−0.0538394	+	0.0359743i
$829$	−0.678814	+	0.678814i	−0.0235762	+	0.0235762i	−0.718797	−	0.695220i	$-0.755307\pi$
$829$	−0.678814	+	0.678814i	−0.0235762	+	0.0235762i	0.695220	+	0.718797i	$0.255307\pi$
$830$		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	0.0553933	−	0.998465i	$-0.482359\pi$
$839$	−24.5010	−	16.3711i	−0.845870	−	0.565192i	−0.901263	+	0.433273i	$0.857359\pi$
$840$		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	−0.0274838	−	0.999622i	$-0.508749\pi$
$853$	−12.7168	−	2.52953i	−0.435414	−	0.0866093i	−0.407931	+	0.913013i	$0.633749\pi$
$854$	−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	−0.991979	−	0.126403i	$-0.959657\pi$
$857$	−14.5080	+	21.7128i	−0.495584	+	0.741694i	0.496395	+	0.868097i	$0.334657\pi$
$858$	−0.509148	+	0.210896i	−0.0173820	+	0.00719987i
$859$	39.8276	+	16.4971i	1.35890	+	0.562874i	0.938756	−	0.344583i	$-0.111980\pi$
$859$	39.8276	+	16.4971i	1.35890	+	0.562874i	0.420143	+	0.907458i	$0.361980\pi$
$860$		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	0.177499	−	0.984121i	$-0.443199\pi$
$877$	−19.6574	−	13.1347i	−0.663785	−	0.443527i	−0.841283	+	0.540594i	$0.818199\pi$
$878$	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	−0.519751	−	0.854318i	$-0.673975\pi$
$881$	2.09659	−	1.40090i	0.0706359	−	0.0471974i	0.590387	+	0.807120i	$0.298975\pi$
$882$	−3.85151	−	1.59535i	−0.129687	−	0.0537182i
$883$	14.0335	+	14.0335i	0.472267	+	0.472267i	0.902647	−	0.430381i	$-0.141621\pi$
$883$	14.0335	+	14.0335i	0.472267	+	0.472267i	−0.430381	+	0.902647i	$0.641621\pi$
$884$	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	0.914762	+	0.403994i	$0.132378\pi$
$887$	−2.53061	+	12.7222i	−0.0849697	+	0.427171i	−0.999731	+	0.0231775i	$0.992622\pi$
$888$			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	−0.151958	−	0.988387i	$-0.548558\pi$
$907$	2.58672	−	0.514531i	0.0858907	−	0.0170847i	0.237849	+	0.971302i	$0.423558\pi$
$908$	−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	0.885302	−	0.465016i	$-0.153952\pi$
$911$	56.7789	−	11.2940i	1.88117	−	0.374188i	0.995867	+	0.0908286i	$0.0289516\pi$
$912$	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	$0.220468\pi$
$919$			38.7156i			1.27711i	−0.769576	+	0.638556i	$0.779532\pi$
$920$		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	−0.690272	−	0.723550i	$-0.742509\pi$
$929$	7.38689	−	11.0553i	0.242356	−	0.362711i	0.932628	+	0.360838i	$0.117509\pi$
$930$		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	−0.966537	−	0.256529i	$-0.917421\pi$
$937$	−3.11305	+	7.51556i	−0.101699	+	0.245523i	0.864838	+	0.502051i	$0.167421\pi$
$938$	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	−0.706860	−	0.707353i	$-0.749889\pi$
$941$	6.66132	−	9.96938i	0.217153	−	0.324992i	0.924013	+	0.382361i	$0.124889\pi$
$942$	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	0.428008	−	0.903775i	$-0.359216\pi$
$947$	−17.5643	−	26.2868i	−0.570763	−	0.854207i	−0.998771	+	0.0495681i	$0.984216\pi$
$948$	−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	0.159524	−	0.987194i	$-0.449004\pi$
$953$	35.4000	−	35.4000i	1.14672	−	1.14672i	0.987194	−	0.159524i	$-0.0509959\pi$
$954$	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	0.479680	−	0.877444i	$-0.340753\pi$
$967$	6.17012	+	2.55575i	0.198418	+	0.0821873i	−0.281262	+	0.959631i	$0.590753\pi$
$968$	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	0.911962	−	0.410274i	$-0.134567\pi$
$971$	−0.716696	−	1.73026i	−0.0229999	−	0.0555266i	−0.934962	+	0.354747i	$0.884567\pi$
$972$	−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	0.744241	−	0.667911i	$-0.232811\pi$
$977$	−7.94869	−	19.1898i	−0.254301	−	0.613938i	−0.998542	+	0.0539735i	$0.982811\pi$
$978$	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	−0.935541	−	0.353219i	$-0.885087\pi$
$983$	2.00524	−	10.0810i	0.0639571	−	0.321534i	0.999498	+	0.0316845i	$0.0100872\pi$
$984$	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	−0.896095	−	0.443861i	$-0.853608\pi$
$991$	3.19987	−	16.0868i	0.101647	−	0.511015i	0.997743	−	0.0671536i	$-0.0213918\pi$
$992$	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	0.998202	+	0.0599366i	$0.0190899\pi$
$997$	3.12344	+	15.7026i	0.0989204	+	0.497306i	−0.899282	+	0.437370i	$0.855910\pi$
$998$	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.107.2		40
5.2	odd	4		170.2.o.b.73.2	yes	40
5.3	odd	4		850.2.s.d.243.4		40
5.4	even	2		170.2.r.b.107.4	yes	40
17.7	odd	16		850.2.s.d.7.4		40
85.7	even	16		170.2.r.b.143.4	yes	40
85.24	odd	16		170.2.o.b.7.2	✓	40
85.58	even	16	inner	850.2.v.d.143.2		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.o.b.7.2	✓	40	85.24	odd	16
170.2.o.b.73.2	yes	40	5.2	odd	4
170.2.r.b.107.4	yes	40	5.4	even	2
170.2.r.b.143.4	yes	40	85.7	even	16
850.2.s.d.7.4		40	17.7	odd	16
850.2.s.d.243.4		40	5.3	odd	4
850.2.v.d.107.2		40	1.1	even	1	trivial
850.2.v.d.143.2		40	85.58	even	16	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
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

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