LMFDB - Embedded newform 816.2.u.a.205.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [816,2,Mod(205,816)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(816, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0, 0]))

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

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

chi := DirichletCharacter("816.205");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 816 = 2^{4} \cdot 3 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	816.u (of order $4$, degree $2$, 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:	$6.51579280494$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			205.14
Character	$\chi$	$=$	816.205
Dual form			816.2.u.a.613.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.359024 + 1.36788i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.74220 - 0.982204i) q^{4} +(2.64915 - 2.64915i) q^{5} +(-1.22111 + 0.713371i) q^{6} +1.00268i q^{7} +(1.96903 - 2.03050i) q^{8} +1.00000i q^{9} +(2.67262 + 4.57484i) q^{10} +(2.96004 - 2.96004i) q^{11} +(-0.537401 - 1.92645i) q^{12} +(-3.07604 - 3.07604i) q^{13} +(-1.37155 - 0.359986i) q^{14} +3.74647 q^{15} +(2.07055 + 3.42240i) q^{16} -1.00000 q^{17} +(-1.36788 - 0.359024i) q^{18} +(-2.51014 - 2.51014i) q^{19} +(-7.21738 + 2.01336i) q^{20} +(-0.709001 + 0.709001i) q^{21} +(2.98626 + 5.11171i) q^{22} -5.82426i q^{23} +(2.82809 - 0.0434604i) q^{24} -9.03603i q^{25} +(5.31203 - 3.10329i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(0.984836 - 1.74687i) q^{28} +(-2.02532 - 2.02532i) q^{29} +(-1.34507 + 5.12473i) q^{30} +9.91355 q^{31} +(-5.42482 + 1.60354i) q^{32} +4.18613 q^{33} +(0.359024 - 1.36788i) q^{34} +(2.65625 + 2.65625i) q^{35} +(0.982204 - 1.74220i) q^{36} +(-4.80507 + 4.80507i) q^{37} +(4.33478 - 2.53238i) q^{38} -4.35017i q^{39} +(-0.162823 - 10.5954i) q^{40} +7.46961i q^{41} +(-0.715282 - 1.22438i) q^{42} +(0.165656 - 0.165656i) q^{43} +(-8.06436 + 2.24963i) q^{44} +(2.64915 + 2.64915i) q^{45} +(7.96690 + 2.09105i) q^{46} +13.5858 q^{47} +(-0.955904 + 3.88410i) q^{48} +5.99464 q^{49} +(12.3602 + 3.24415i) q^{50} +(-0.707107 - 0.707107i) q^{51} +(2.33779 + 8.38038i) q^{52} +(-2.79442 + 2.79442i) q^{53} +(-0.713371 - 1.22111i) q^{54} -15.6832i q^{55} +(2.03593 + 1.97431i) q^{56} -3.54988i q^{57} +(3.49754 - 2.04326i) q^{58} +(-5.98782 + 5.98782i) q^{59} +(-6.52711 - 3.67980i) q^{60} +(-10.0269 - 10.0269i) q^{61} +(-3.55920 + 13.5606i) q^{62} -1.00268 q^{63} +(-0.245820 - 7.99622i) q^{64} -16.2978 q^{65} +(-1.50292 + 5.72613i) q^{66} +(1.87687 + 1.87687i) q^{67} +(1.74220 + 0.982204i) q^{68} +(4.11837 - 4.11837i) q^{69} +(-4.58710 + 2.67978i) q^{70} +12.1632i q^{71} +(2.03050 + 1.96903i) q^{72} +4.92646i q^{73} +(-4.84764 - 8.29790i) q^{74} +(6.38944 - 6.38944i) q^{75} +(1.90771 + 6.83866i) q^{76} +(2.96797 + 2.96797i) q^{77} +(5.95053 + 1.56182i) q^{78} +6.89893 q^{79} +(14.5517 + 3.58126i) q^{80} -1.00000 q^{81} +(-10.2175 - 2.68177i) q^{82} +(3.32968 + 3.32968i) q^{83} +(1.93161 - 0.538840i) q^{84} +(-2.64915 + 2.64915i) q^{85} +(0.167123 + 0.286072i) q^{86} -2.86424i q^{87} +(-0.181931 - 11.8388i) q^{88} +15.5369i q^{89} +(-4.57484 + 2.67262i) q^{90} +(3.08428 - 3.08428i) q^{91} +(-5.72061 + 10.1470i) q^{92} +(7.00994 + 7.00994i) q^{93} +(-4.87764 + 18.5838i) q^{94} -13.2995 q^{95} +(-4.96980 - 2.70205i) q^{96} -1.79560 q^{97} +(-2.15222 + 8.19996i) q^{98} +(2.96004 + 2.96004i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{4} + 12 q^{10} + 8 q^{11} - 8 q^{12} + 20 q^{14} + 24 q^{15} + 28 q^{16} - 64 q^{17} - 4 q^{18} - 48 q^{22} - 20 q^{26} + 16 q^{29} + 8 q^{30} - 24 q^{31} + 40 q^{32} - 24 q^{35} + 16 q^{37}+ \cdots + 8 q^{99}+O(q^{100}) $ 64 * q + 4 * q^4 + 12 * q^10 + 8 * q^11 - 8 * q^12 + 20 * q^14 + 24 * q^15 + 28 * q^16 - 64 * q^17 - 4 * q^18 - 48 * q^22 - 20 * q^26 + 16 * q^29 + 8 * q^30 - 24 * q^31 + 40 * q^32 - 24 * q^35 + 16 * q^37 - 12 * q^38 - 56 * q^40 + 8 * q^42 + 8 * q^43 + 24 * q^44 + 52 * q^46 + 64 * q^47 - 64 * q^49 + 68 * q^50 + 44 * q^52 - 16 * q^53 - 56 * q^56 + 4 * q^58 + 4 * q^60 + 76 * q^62 - 8 * q^63 + 52 * q^64 + 8 * q^66 + 16 * q^67 - 4 * q^68 - 136 * q^70 + 4 * q^72 - 84 * q^74 - 16 * q^75 - 20 * q^76 + 32 * q^77 + 24 * q^78 + 40 * q^79 + 56 * q^80 - 64 * q^81 + 64 * q^83 - 52 * q^84 - 44 * q^86 - 96 * q^88 - 20 * q^90 - 56 * q^91 + 32 * q^92 + 88 * q^94 - 48 * q^95 + 72 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/816\mathbb{Z}\right)^\times$.

$n$	$241$	$511$	$545$	$613$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.359024	+	1.36788i	−0.253868	+	0.967239i
$2$	−0.359024	+	1.36788i	−0.253868	+	0.967239i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	−1.74220	−	0.982204i	−0.871102	−	0.491102i
$5$	2.64915	−	2.64915i	1.18474	−	1.18474i	0.206235	−	0.978502i	$-0.433879\pi$
$5$	2.64915	−	2.64915i	1.18474	−	1.18474i	0.978502	−	0.206235i	$-0.0661212\pi$
$6$	−1.22111	+	0.713371i	−0.498515	+	0.291232i
$7$			1.00268i			0.378977i	0.981883	+	0.189488i	$0.0606830\pi$
$7$			1.00268i			0.378977i	−0.981883	+	0.189488i	$0.939317\pi$
$8$	1.96903	−	2.03050i	0.696158	−	0.717888i
$9$			1.00000i			0.333333i
$10$	2.67262	+	4.57484i	0.845157	+	1.44669i
$11$	2.96004	−	2.96004i	0.892486	−	0.892486i	−0.102271	−	0.994757i	$-0.532611\pi$
$11$	2.96004	−	2.96004i	0.892486	−	0.892486i	0.994757	+	0.102271i	$0.0326109\pi$
$12$	−0.537401	−	1.92645i	−0.155134	−	0.556118i
$13$	−3.07604	−	3.07604i	−0.853139	−	0.853139i	0.137379	−	0.990519i	$-0.456132\pi$
$13$	−3.07604	−	3.07604i	−0.853139	−	0.853139i	−0.990519	+	0.137379i	$0.956132\pi$
$14$	−1.37155	−	0.359986i	−0.366561	−	0.0962102i
$15$	3.74647			0.967334
$16$	2.07055	+	3.42240i	0.517637	+	0.855600i
$17$	−1.00000			−0.242536
$17$	−1.00000			−0.242536
$18$	−1.36788	−	0.359024i	−0.322413	−	0.0846227i
$19$	−2.51014	−	2.51014i	−0.575866	−	0.575866i	0.357895	−	0.933762i	$-0.383494\pi$
$19$	−2.51014	−	2.51014i	−0.575866	−	0.575866i	−0.933762	+	0.357895i	$0.883494\pi$
$20$	−7.21738	+	2.01336i	−1.61385	+	0.450200i
$21$	−0.709001	+	0.709001i	−0.154717	+	0.154717i
$22$	2.98626	+	5.11171i	0.636673	+	1.08982i
$23$		−	5.82426i		−	1.21444i	−0.794533	−	0.607221i	$-0.792284\pi$
$23$		−	5.82426i		−	1.21444i	0.794533	−	0.607221i	$-0.207716\pi$
$24$	2.82809	−	0.0434604i	0.577282	−	0.00887133i
$25$		−	9.03603i		−	1.80721i
$26$	5.31203	−	3.10329i	1.04177	−	0.608605i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	0.984836	−	1.74687i	0.186116	−	0.330128i
$29$	−2.02532	−	2.02532i	−0.376093	−	0.376093i	0.493598	−	0.869690i	$-0.335682\pi$
$29$	−2.02532	−	2.02532i	−0.376093	−	0.376093i	−0.869690	+	0.493598i	$0.835682\pi$
$30$	−1.34507	+	5.12473i	−0.245575	+	0.935643i
$31$	9.91355			1.78053			0.890263	−	0.455447i	$-0.150520\pi$
$31$	9.91355			1.78053			0.890263	+	0.455447i	$0.150520\pi$
$32$	−5.42482	+	1.60354i	−0.958981	+	0.283469i
$33$	4.18613			0.728711
$34$	0.359024	−	1.36788i	0.0615721	−	0.234590i
$35$	2.65625	+	2.65625i	0.448988	+	0.448988i
$36$	0.982204	−	1.74220i	0.163701	−	0.290367i
$37$	−4.80507	+	4.80507i	−0.789949	+	0.789949i	−0.981485	−	0.191537i	$-0.938653\pi$
$37$	−4.80507	+	4.80507i	−0.789949	+	0.789949i	0.191537	+	0.981485i	$0.438653\pi$
$38$	4.33478	−	2.53238i	0.703194	−	0.410806i
$39$		−	4.35017i		−	0.696585i
$40$	−0.162823	−	10.5954i	−0.0257446	−	1.67527i
$41$			7.46961i			1.16656i	0.812272	+	0.583278i	$0.198230\pi$
$41$			7.46961i			1.16656i	−0.812272	+	0.583278i	$0.801770\pi$
$42$	−0.715282	−	1.22438i	−0.110370	−	0.188926i
$43$	0.165656	−	0.165656i	0.0252623	−	0.0252623i	−0.694363	−	0.719625i	$-0.744314\pi$
$43$	0.165656	−	0.165656i	0.0252623	−	0.0252623i	0.719625	+	0.694363i	$0.244314\pi$
$44$	−8.06436	+	2.24963i	−1.21575	+	0.339144i
$45$	2.64915	+	2.64915i	0.394913	+	0.394913i
$46$	7.96690	+	2.09105i	1.17466	+	0.308308i
$47$	13.5858			1.98170			0.990849	−	0.134978i	$-0.0430963\pi$
$47$	13.5858			1.98170			0.990849	+	0.134978i	$0.0430963\pi$
$48$	−0.955904	+	3.88410i	−0.137973	+	0.560622i
$49$	5.99464			0.856376
$50$	12.3602	+	3.24415i	1.74800	+	0.458792i
$51$	−0.707107	−	0.707107i	−0.0990148	−	0.0990148i
$52$	2.33779	+	8.38038i	0.324193	+	1.16215i
$53$	−2.79442	+	2.79442i	−0.383843	+	0.383843i	−0.872485	−	0.488641i	$-0.837493\pi$
$53$	−2.79442	+	2.79442i	−0.383843	+	0.383843i	0.488641	+	0.872485i	$0.337493\pi$
$54$	−0.713371	−	1.22111i	−0.0970775	−	0.166172i
$55$		−	15.6832i		−	2.11472i
$56$	2.03593	+	1.97431i	0.272063	+	0.263828i
$57$		−	3.54988i		−	0.470193i
$58$	3.49754	−	2.04326i	0.459249	−	0.268294i
$59$	−5.98782	+	5.98782i	−0.779548	+	0.779548i	−0.979754	−	0.200206i	$-0.935839\pi$
$59$	−5.98782	+	5.98782i	−0.779548	+	0.779548i	0.200206	+	0.979754i	$0.435839\pi$
$60$	−6.52711	−	3.67980i	−0.842647	−	0.475060i
$61$	−10.0269	−	10.0269i	−1.28381	−	1.28381i	−0.938480	−	0.345334i	$-0.887766\pi$
$61$	−10.0269	−	10.0269i	−1.28381	−	1.28381i	−0.345334	−	0.938480i	$-0.612234\pi$
$62$	−3.55920	+	13.5606i	−0.452019	+	1.72219i
$63$	−1.00268			−0.126326
$64$	−0.245820	−	7.99622i	−0.0307275	−	0.999528i
$65$	−16.2978			−2.02149
$66$	−1.50292	+	5.72613i	−0.184997	+	0.704838i
$67$	1.87687	+	1.87687i	0.229296	+	0.229296i	0.812399	−	0.583103i	$-0.198161\pi$
$67$	1.87687	+	1.87687i	0.229296	+	0.229296i	−0.583103	+	0.812399i	$0.698161\pi$
$68$	1.74220	+	0.982204i	0.211273	+	0.119110i
$69$	4.11837	−	4.11837i	0.495794	−	0.495794i
$70$	−4.58710	+	2.67978i	−0.548263	+	0.320295i
$71$			12.1632i			1.44351i	0.692149	+	0.721755i	$0.256664\pi$
$71$			12.1632i			1.44351i	−0.692149	+	0.721755i	$0.743336\pi$
$72$	2.03050	+	1.96903i	0.239296	+	0.232053i
$73$			4.92646i			0.576599i	0.957540	+	0.288300i	$0.0930899\pi$
$73$			4.92646i			0.576599i	−0.957540	+	0.288300i	$0.906910\pi$
$74$	−4.84764	−	8.29790i	−0.563526	−	0.964612i
$75$	6.38944	−	6.38944i	0.737789	−	0.737789i
$76$	1.90771	+	6.83866i	0.218829	+	0.784448i
$77$	2.96797	+	2.96797i	0.338231	+	0.338231i
$78$	5.95053	+	1.56182i	0.673764	+	0.176841i
$79$	6.89893			0.776190			0.388095	−	0.921619i	$-0.373133\pi$
$79$	6.89893			0.776190			0.388095	+	0.921619i	$0.373133\pi$
$80$	14.5517	+	3.58126i	1.62693	+	0.400398i
$81$	−1.00000			−0.111111
$82$	−10.2175	−	2.68177i	−1.12834	−	0.296151i
$83$	3.32968	+	3.32968i	0.365479	+	0.365479i	0.865826	−	0.500346i	$-0.166794\pi$
$83$	3.32968	+	3.32968i	0.365479	+	0.365479i	−0.500346	+	0.865826i	$0.666794\pi$
$84$	1.93161	−	0.538840i	0.210756	−	0.0587923i
$85$	−2.64915	+	2.64915i	−0.287341	+	0.287341i
$86$	0.167123	+	0.286072i	0.0180214	+	0.0308479i
$87$		−	2.86424i		−	0.307078i
$88$	−0.181931	−	11.8388i	−0.0193939	−	1.26202i
$89$			15.5369i			1.64691i	0.567381	+	0.823455i	$0.307957\pi$
$89$			15.5369i			1.64691i	−0.567381	+	0.823455i	$0.692043\pi$
$90$	−4.57484	+	2.67262i	−0.482230	+	0.281719i
$91$	3.08428	−	3.08428i	0.323320	−	0.323320i
$92$	−5.72061	+	10.1470i	−0.596415	+	1.05790i
$93$	7.00994	+	7.00994i	0.726897	+	0.726897i
$94$	−4.87764	+	18.5838i	−0.503090	+	1.91677i
$95$	−13.2995			−1.36450
$96$	−4.96980	−	2.70205i	−0.507228	−	0.275777i
$97$	−1.79560			−0.182316			−0.0911578	−	0.995836i	$-0.529057\pi$
$97$	−1.79560			−0.182316			−0.0911578	+	0.995836i	$0.529057\pi$
$98$	−2.15222	+	8.19996i	−0.217407	+	0.828321i
$99$	2.96004	+	2.96004i	0.297495	+	0.297495i
$100$	−8.87523	+	15.7426i	−0.887523	+	1.57426i
$101$	3.50589	−	3.50589i	0.348849	−	0.348849i	−0.510832	−	0.859681i	$-0.670663\pi$
$101$	3.50589	−	3.50589i	0.348849	−	0.348849i	0.859681	+	0.510832i	$0.170663\pi$
$102$	1.22111	−	0.713371i	0.120908	−	0.0706342i
$103$		−	7.19968i		−	0.709406i	−0.934979	−	0.354703i	$-0.884582\pi$
$103$		−	7.19968i		−	0.709406i	0.934979	−	0.354703i	$-0.115418\pi$
$104$	−12.3027	+	0.189060i	−1.20638	+	0.0185389i
$105$			3.75651i			0.366597i
$106$	−2.81918	−	4.82570i	−0.273823	−	0.468714i
$107$	−7.17498	+	7.17498i	−0.693631	+	0.693631i	−0.963029	−	0.269398i	$-0.913175\pi$
$107$	−7.17498	+	7.17498i	−0.693631	+	0.693631i	0.269398	+	0.963029i	$0.413175\pi$
$108$	1.92645	−	0.537401i	0.185373	−	0.0517114i
$109$	13.4804	+	13.4804i	1.29119	+	1.29119i	0.934054	+	0.357133i	$0.116246\pi$
$109$	13.4804	+	13.4804i	1.29119	+	1.29119i	0.357133	+	0.934054i	$0.383754\pi$
$110$	21.4528	+	5.63064i	2.04544	+	0.536861i
$111$	−6.79539			−0.644990
$112$	−3.43157	+	2.07610i	−0.324253	+	0.196173i
$113$	0.160637			0.0151114			0.00755571	−	0.999971i	$-0.497595\pi$
$113$	0.160637			0.0151114			0.00755571	+	0.999971i	$0.497595\pi$
$114$	4.85582	+	1.27449i	0.454789	+	0.119367i
$115$	−15.4294	−	15.4294i	−1.43880	−	1.43880i
$116$	1.53924	+	5.51780i	0.142915	+	0.512315i
$117$	3.07604	−	3.07604i	0.284380	−	0.284380i
$118$	−6.04087	−	10.3404i	−0.556107	−	0.951912i
$119$		−	1.00268i		−	0.0919154i
$120$	7.37692	−	7.60719i	0.673418	−	0.694438i
$121$		−	6.52367i		−	0.593061i
$122$	17.3155	−	10.1157i	1.56767	−	0.915835i
$123$	−5.28181	+	5.28181i	−0.476245	+	0.476245i
$124$	−17.2714	−	9.73713i	−1.55102	−	0.874420i
$125$	−10.6921	−	10.6921i	−0.956328	−	0.956328i
$126$	0.359986	−	1.37155i	0.0320701	−	0.122187i
$127$	4.50169			0.399460			0.199730	−	0.979851i	$-0.435993\pi$
$127$	4.50169			0.399460			0.199730	+	0.979851i	$0.435993\pi$
$128$	11.0261	+	2.53458i	0.974583	+	0.224027i
$129$	0.234273			0.0206265
$130$	5.85130	−	22.2935i	0.513193	−	1.95527i
$131$	0.620957	+	0.620957i	0.0542533	+	0.0542533i	0.733713	−	0.679460i	$-0.237786\pi$
$131$	0.620957	+	0.620957i	0.0542533	+	0.0542533i	−0.679460	+	0.733713i	$0.737786\pi$
$132$	−7.29309	−	4.11163i	−0.634782	−	0.357872i
$133$	2.51687	−	2.51687i	0.218240	−	0.218240i
$134$	−3.24117	+	1.89349i	−0.279995	+	0.163573i
$135$			3.74647i			0.322445i
$136$	−1.96903	+	2.03050i	−0.168843	+	0.174114i
$137$		−	15.0862i		−	1.28890i	−0.764644	−	0.644452i	$-0.777085\pi$
$137$		−	15.0862i		−	1.28890i	0.764644	−	0.644452i	$-0.222915\pi$
$138$	4.15486	+	7.11204i	0.353685	+	0.605417i
$139$	−0.619897	+	0.619897i	−0.0525790	+	0.0525790i	−0.732907	−	0.680328i	$-0.761837\pi$
$139$	−0.619897	+	0.619897i	−0.0525790	+	0.0525790i	0.680328	+	0.732907i	$0.261837\pi$
$140$	−2.01875	−	7.23671i	−0.170615	−	0.611614i
$141$	9.60663	+	9.60663i	0.809025	+	0.809025i
$142$	−16.6379	−	4.36689i	−1.39622	−	0.366461i
$143$	−18.2104			−1.52283
$144$	−3.42240	+	2.07055i	−0.285200	+	0.172546i
$145$	−10.7308			−0.891142
$146$	−6.73882	−	1.76872i	−0.557709	−	0.146380i
$147$	4.23885	+	4.23885i	0.349614	+	0.349614i
$148$	13.0910	−	3.65185i	1.07607	−	0.300180i
$149$	7.29834	−	7.29834i	0.597903	−	0.597903i	−0.341851	−	0.939754i	$-0.611054\pi$
$149$	7.29834	−	7.29834i	0.597903	−	0.597903i	0.939754	+	0.341851i	$0.111054\pi$
$150$	6.44604	+	11.0340i	0.526317	+	0.900919i
$151$			5.88726i			0.479099i	0.970884	+	0.239549i	$0.0769997\pi$
$151$			5.88726i			0.479099i	−0.970884	+	0.239549i	$0.923000\pi$
$152$	−10.0394	+	0.154279i	−0.814302	+	0.0125137i
$153$		−	1.00000i		−	0.0808452i
$154$	−5.12540	+	2.99426i	−0.413017	+	0.241284i
$155$	26.2625	−	26.2625i	2.10946	−	2.10946i
$156$	−4.27276	+	7.57889i	−0.342095	+	0.606797i
$157$	−3.87474	−	3.87474i	−0.309238	−	0.309238i	0.535376	−	0.844614i	$-0.320170\pi$
$157$	−3.87474	−	3.87474i	−0.309238	−	0.309238i	−0.844614	+	0.535376i	$0.820170\pi$
$158$	−2.47688	+	9.43692i	−0.197050	+	0.750761i
$159$	−3.95191			−0.313407
$160$	−10.1231	+	18.6192i	−0.800305	+	1.47198i
$161$	5.83986			0.460246
$162$	0.359024	−	1.36788i	0.0282076	−	0.107471i
$163$	−8.98517	−	8.98517i	−0.703773	−	0.703773i	0.261445	−	0.965218i	$-0.415801\pi$
$163$	−8.98517	−	8.98517i	−0.703773	−	0.703773i	−0.965218	+	0.261445i	$0.915801\pi$
$164$	7.33668	−	13.0136i	0.572898	−	1.01619i
$165$	11.0897	−	11.0897i	0.863332	−	0.863332i
$166$	−5.75004	+	3.35917i	−0.446290	+	0.260722i
$167$		−	2.54190i		−	0.196698i	−0.995152	−	0.0983490i	$-0.968644\pi$
$167$		−	2.54190i		−	0.196698i	0.995152	−	0.0983490i	$-0.0313561\pi$
$168$	0.0435769	+	2.83567i	0.00336203	+	0.218777i
$169$			5.92401i			0.455693i
$170$	−2.67262	−	4.57484i	−0.204981	−	0.350874i
$171$	2.51014	−	2.51014i	0.191955	−	0.191955i
$172$	−0.451314	+	0.125898i	−0.0344123	+	0.00959965i
$173$	−5.78814	−	5.78814i	−0.440064	−	0.440064i	0.451969	−	0.892034i	$-0.350722\pi$
$173$	−5.78814	−	5.78814i	−0.440064	−	0.440064i	−0.892034	+	0.451969i	$0.850722\pi$
$174$	3.91794	+	1.02833i	0.297018	+	0.0779574i
$175$	9.06024			0.684890
$176$	16.2593	+	4.00154i	1.22559	+	0.301627i
$177$	−8.46806			−0.636498
$178$	−21.2527	−	5.57813i	−1.59296	−	0.418098i
$179$	12.2194	+	12.2194i	0.913324	+	0.913324i	0.996532	−	0.0832078i	$-0.0265165\pi$
$179$	12.2194	+	12.2194i	0.913324	+	0.913324i	−0.0832078	+	0.996532i	$0.526517\pi$
$180$	−2.01336	−	7.21738i	−0.150067	−	0.537952i
$181$	11.9536	−	11.9536i	0.888504	−	0.888504i	−0.105875	−	0.994379i	$-0.533764\pi$
$181$	11.9536	−	11.9536i	0.888504	−	0.888504i	0.994379	+	0.105875i	$0.0337644\pi$
$182$	3.11160	+	5.32626i	0.230647	+	0.394808i
$183$		−	14.1802i		−	1.04823i
$184$	−11.8261	−	11.4682i	−0.871834	−	0.845444i
$185$			25.4587i			1.87176i
$186$	−12.1055	+	7.07204i	−0.887619	+	0.518547i
$187$	−2.96004	+	2.96004i	−0.216460	+	0.216460i
$188$	−23.6693	−	13.3441i	−1.72626	−	0.973216i
$189$	−0.709001	−	0.709001i	−0.0515722	−	0.0515722i
$190$	4.77484	−	18.1922i	0.346403	−	1.31980i
$191$	−9.05641			−0.655299			−0.327649	−	0.944799i	$-0.606256\pi$
$191$	−9.05641			−0.655299			−0.327649	+	0.944799i	$0.606256\pi$
$192$	5.48036	−	5.82800i	0.395511	−	0.420600i
$193$	−11.7235			−0.843876			−0.421938	−	0.906625i	$-0.638650\pi$
$193$	−11.7235			−0.843876			−0.421938	+	0.906625i	$0.638650\pi$
$194$	0.644663	−	2.45617i	0.0462841	−	0.176343i
$195$	−11.5243	−	11.5243i	−0.825271	−	0.825271i
$196$	−10.4439	−	5.88796i	−0.745991	−	0.420568i
$197$	−5.02636	+	5.02636i	−0.358113	+	0.358113i	−0.863117	−	0.505004i	$-0.831491\pi$
$197$	−5.02636	+	5.02636i	−0.358113	+	0.358113i	0.505004	+	0.863117i	$0.331491\pi$
$198$	−5.11171	+	2.98626i	−0.363273	+	0.212224i
$199$			10.8789i			0.771185i	0.922669	+	0.385593i	$0.126003\pi$
$199$			10.8789i			0.771185i	−0.922669	+	0.385593i	$0.873997\pi$
$200$	−18.3476	−	17.7922i	−1.29737	−	1.25810i
$201$			2.65429i			0.187219i
$202$	3.53694	+	6.05434i	0.248858	+	0.425982i
$203$	2.03075	−	2.03075i	0.142530	−	0.142530i
$204$	0.537401	+	1.92645i	0.0376256	+	0.134878i
$205$	19.7881	+	19.7881i	1.38206	+	1.38206i
$206$	9.84832	+	2.58486i	0.686165	+	0.180095i
$207$	5.82426			0.404814
$208$	4.15835	−	16.8965i	0.288330	−	1.17156i
$209$	−14.8602			−1.02790
$210$	−5.13846	−	1.34867i	−0.354587	−	0.0930674i
$211$	−11.4994	−	11.4994i	−0.791649	−	0.791649i	0.190113	−	0.981762i	$-0.439114\pi$
$211$	−11.4994	−	11.4994i	−0.791649	−	0.791649i	−0.981762	+	0.190113i	$0.939114\pi$
$212$	7.61314	−	2.12376i	0.522873	−	0.145860i
$213$	−8.60070	+	8.60070i	−0.589310	+	0.589310i
$214$	−7.23854	−	12.3905i	−0.494816	−	0.846998i
$215$		−	0.877695i		−	0.0598583i
$216$	0.0434604	+	2.82809i	0.00295711	+	0.192427i
$217$			9.94011i			0.674778i
$218$	−23.2794	+	13.5998i	−1.57668	+	0.921095i
$219$	−3.48354	+	3.48354i	−0.235396	+	0.235396i
$220$	−15.4041	+	27.3233i	−1.03854	+	1.84214i
$221$	3.07604	+	3.07604i	0.206917	+	0.206917i
$222$	2.43971	−	9.29530i	0.163742	−	0.623860i
$223$	25.6500			1.71765			0.858825	−	0.512269i	$-0.171195\pi$
$223$	25.6500			1.71765			0.858825	+	0.512269i	$0.171195\pi$
$224$	−1.60784	−	5.43935i	−0.107428	−	0.363432i
$225$	9.03603			0.602402
$226$	−0.0576724	+	0.219732i	−0.00383631	+	0.0146164i
$227$	−18.1990	−	18.1990i	−1.20791	−	1.20791i	−0.971702	−	0.236211i	$-0.924094\pi$
$227$	−18.1990	−	18.1990i	−1.20791	−	1.20791i	−0.236211	−	0.971702i	$-0.575906\pi$
$228$	−3.48671	+	6.18461i	−0.230913	+	0.409586i
$229$	−12.5001	+	12.5001i	−0.826028	+	0.826028i	−0.986965	−	0.160937i	$-0.948549\pi$
$229$	−12.5001	+	12.5001i	−0.826028	+	0.826028i	0.160937	+	0.986965i	$0.448549\pi$
$230$	26.6451	−	15.5660i	1.75692	−	1.02639i
$231$			4.19734i			0.276165i
$232$	−8.10033	+	0.124481i	−0.531813	+	0.00817258i
$233$			5.67124i			0.371536i	0.982594	+	0.185768i	$0.0594772\pi$
$233$			5.67124i			0.371536i	−0.982594	+	0.185768i	$0.940523\pi$
$234$	3.10329	+	5.31203i	0.202868	+	0.347258i
$235$	35.9910	−	35.9910i	2.34779	−	2.34779i
$236$	16.3133	−	4.55074i	1.06190	−	0.296228i
$237$	4.87828	+	4.87828i	0.316878	+	0.316878i
$238$	1.37155	+	0.359986i	0.0889042	+	0.0233344i
$239$	10.1117			0.654071			0.327035	−	0.945012i	$-0.393950\pi$
$239$	10.1117			0.654071			0.327035	+	0.945012i	$0.393950\pi$
$240$	7.75725	+	12.8219i	0.500728	+	0.827651i
$241$	−11.5115			−0.741521			−0.370760	−	0.928729i	$-0.620903\pi$
$241$	−11.5115			−0.741521			−0.370760	+	0.928729i	$0.620903\pi$
$242$	8.92361	+	2.34215i	0.573631	+	0.150559i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	7.62044	+	27.3174i	0.487849	+	1.74882i
$245$	15.8807	−	15.8807i	1.01458	−	1.01458i
$246$	−5.32860	−	9.12119i	−0.339739	−	0.581546i
$247$			15.4426i			0.982589i
$248$	19.5201	−	20.1294i	1.23953	−	1.27822i
$249$			4.70887i			0.298413i
$250$	18.4642	−	10.7868i	1.16778	−	0.682217i
$251$	−14.0399	+	14.0399i	−0.886188	+	0.886188i	−0.994155	−	0.107967i	$-0.965566\pi$
$251$	−14.0399	+	14.0399i	−0.886188	+	0.886188i	0.107967	+	0.994155i	$0.465566\pi$
$252$	1.74687	+	0.984836i	0.110043	+	0.0620388i
$253$	−17.2400	−	17.2400i	−1.08387	−	1.08387i
$254$	−1.61621	+	6.15778i	−0.101410	+	0.386373i
$255$	−3.74647			−0.234613
$256$	−7.42566	+	14.1725i	−0.464104	+	0.885781i
$257$	−16.2046			−1.01081			−0.505407	−	0.862881i	$-0.668658\pi$
$257$	−16.2046			−1.01081			−0.505407	+	0.862881i	$0.668658\pi$
$258$	−0.0841094	+	0.320457i	−0.00523642	+	0.0199508i
$259$	−4.81794	−	4.81794i	−0.299372	−	0.299372i
$260$	28.3941	+	16.0078i	1.76093	+	0.992760i
$261$	2.02532	−	2.02532i	0.125364	−	0.125364i
$262$	−1.07233	+	0.626458i	−0.0662490	+	0.0387027i
$263$		−	16.6208i		−	1.02489i	−0.858721	−	0.512443i	$-0.828741\pi$
$263$		−	16.6208i		−	1.02489i	0.858721	−	0.512443i	$-0.171259\pi$
$264$	8.24262	−	8.49991i	0.507298	−	0.523133i
$265$			14.8057i			0.909507i
$266$	2.53916	+	4.34639i	0.155686	+	0.266495i
$267$	−10.9863	+	10.9863i	−0.672349	+	0.672349i
$268$	−1.42642	−	5.11335i	−0.0871324	−	0.312348i
$269$	−0.0719686	−	0.0719686i	−0.00438800	−	0.00438800i	0.704909	−	0.709297i	$-0.250988\pi$
$269$	−0.0719686	−	0.0719686i	−0.00438800	−	0.00438800i	−0.709297	+	0.704909i	$0.750988\pi$
$270$	−5.12473	−	1.34507i	−0.311881	−	0.0818585i
$271$	25.9768			1.57798			0.788989	−	0.614407i	$-0.210605\pi$
$271$	25.9768			1.57798			0.788989	+	0.614407i	$0.210605\pi$
$272$	−2.07055	−	3.42240i	−0.125545	−	0.207514i
$273$	4.36183			0.263990
$274$	20.6362	+	5.41632i	1.24668	+	0.327212i
$275$	−26.7470	−	26.7470i	−1.61291	−	1.61291i
$276$	−11.2201	+	3.12996i	−0.675372	+	0.188402i
$277$	−16.6842	+	16.6842i	−1.00246	+	1.00246i	−0.00245900	+	0.999997i	$0.500783\pi$
$277$	−16.6842	+	16.6842i	−1.00246	+	1.00246i	−0.999997	+	0.00245900i	$0.999217\pi$
$278$	−0.625388	−	1.07050i	−0.0375083	−	0.0642045i
$279$			9.91355i			0.593509i
$280$	10.6237	−	0.163259i	0.634890	−	0.00975662i
$281$			6.31754i			0.376873i	0.982085	+	0.188436i	$0.0603419\pi$
$281$			6.31754i			0.376873i	−0.982085	+	0.188436i	$0.939658\pi$
$282$	−16.5898	+	9.69173i	−0.987905	+	0.577134i
$283$	10.2201	−	10.2201i	0.607522	−	0.607522i	−0.334776	−	0.942298i	$-0.608661\pi$
$283$	10.2201	−	10.2201i	0.607522	−	0.607522i	0.942298	+	0.334776i	$0.108661\pi$
$284$	11.9468	−	21.1908i	0.708911	−	1.25744i
$285$	−9.40418	−	9.40418i	−0.557055	−	0.557055i
$286$	6.53796	−	24.9097i	0.386598	−	1.47294i
$287$	−7.48962			−0.442098
$288$	−1.60354	−	5.42482i	−0.0944897	−	0.319660i
$289$	1.00000			0.0588235
$290$	3.85260	−	14.6784i	0.226233	−	0.861948i
$291$	−1.26968	−	1.26968i	−0.0744300	−	0.0744300i
$292$	4.83880	−	8.58290i	0.283169	−	0.502277i
$293$	−8.93898	+	8.93898i	−0.522221	+	0.522221i	−0.918242	−	0.396021i	$-0.870391\pi$
$293$	−8.93898	+	8.93898i	−0.522221	+	0.522221i	0.396021	+	0.918242i	$0.370391\pi$
$294$	−7.32009	+	4.27640i	−0.426916	+	0.249405i
$295$			31.7253i			1.84712i
$296$	0.295331	+	19.2180i	0.0171658	+	1.11702i
$297$			4.18613i			0.242904i
$298$	7.36299	+	12.6035i	0.426527	+	0.730104i
$299$	−17.9156	+	17.9156i	−1.03609	+	1.03609i
$300$	−17.4074	+	4.85597i	−1.00502	+	0.280360i
$301$	0.166099	+	0.166099i	0.00957381	+	0.00957381i
$302$	−8.05309	−	2.11367i	−0.463403	−	0.121628i
$303$	4.95807			0.284834
$304$	3.39334	−	13.7881i	0.194622	−	0.790801i
$305$	−53.1256			−3.04196
$306$	1.36788	+	0.359024i	0.0781966	+	0.0205240i
$307$	−0.512512	−	0.512512i	−0.0292506	−	0.0292506i	0.692330	−	0.721581i	$-0.256584\pi$
$307$	−0.512512	−	0.512512i	−0.0292506	−	0.0292506i	−0.721581	+	0.692330i	$0.756584\pi$
$308$	−2.25565	−	8.08596i	−0.128528	−	0.460740i
$309$	5.09094	−	5.09094i	0.289614	−	0.289614i
$310$	26.4952	+	45.3529i	1.50482	+	2.57587i
$311$			7.32811i			0.415539i	0.978178	+	0.207770i	$0.0666204\pi$
$311$			7.32811i			0.415539i	−0.978178	+	0.207770i	$0.933380\pi$
$312$	−8.83301	−	8.56563i	−0.500071	−	0.484934i
$313$			0.917464i			0.0518581i	0.999664	+	0.0259291i	$0.00825440\pi$
$313$			0.917464i			0.0518581i	−0.999664	+	0.0259291i	$0.991746\pi$
$314$	6.69131	−	3.90906i	0.377613	−	0.220601i
$315$	−2.65625	+	2.65625i	−0.149663	+	0.149663i
$316$	−12.0193	−	6.77616i	−0.676141	−	0.381189i
$317$	18.3229	+	18.3229i	1.02911	+	1.02911i	0.999563	+	0.0295515i	$0.00940792\pi$
$317$	18.3229	+	18.3229i	1.02911	+	1.02911i	0.0295515	+	0.999563i	$0.490592\pi$
$318$	1.41883	−	5.40574i	0.0795640	−	0.303139i
$319$	−11.9901			−0.671315
$320$	−21.8344	−	20.5320i	−1.22058	−	1.14777i
$321$	−10.1470			−0.566348
$322$	−2.09665	+	7.98824i	−0.116842	+	0.445167i
$323$	2.51014	+	2.51014i	0.139668	+	0.139668i
$324$	1.74220	+	0.982204i	0.0967891	+	0.0545669i
$325$	−27.7952	+	27.7952i	−1.54180	+	1.54180i
$326$	15.5166	−	9.06477i	0.859382	−	0.502051i
$327$			19.0641i			1.05425i
$328$	15.1670	+	14.7079i	0.837457	+	0.812108i
$329$			13.6222i			0.751018i
$330$	11.1879	+	19.1509i	0.615876	+	1.05422i
$331$	−7.74298	+	7.74298i	−0.425593	+	0.425593i	−0.887124	−	0.461531i	$-0.847300\pi$
$331$	−7.74298	+	7.74298i	−0.425593	+	0.425593i	0.461531	+	0.887124i	$0.347300\pi$
$332$	−2.53055	−	9.07140i	−0.138882	−	0.497858i
$333$	−4.80507	−	4.80507i	−0.263316	−	0.263316i
$334$	3.47702	+	0.912602i	0.190254	+	0.0499354i
$335$	9.94422			0.543311
$336$	−3.89451	−	0.958465i	−0.212463	−	0.0522885i
$337$	−30.2297			−1.64672			−0.823358	−	0.567523i	$-0.807902\pi$
$337$	−30.2297			−1.64672			−0.823358	+	0.567523i	$0.807902\pi$
$338$	−8.10335	−	2.12686i	−0.440764	−	0.115686i
$339$	0.113587	+	0.113587i	0.00616921	+	0.00616921i
$340$	7.21738	−	2.01336i	0.391417	−	0.109190i
$341$	29.3445	−	29.3445i	1.58909	−	1.58909i
$342$	2.53238	+	4.33478i	0.136935	+	0.234398i
$343$			13.0294i			0.703524i
$344$	−0.0101816	−	0.662545i	−0.000548954	−	0.0357220i
$345$		−	21.8204i		−	1.17477i
$346$	9.99558	−	5.83942i	0.537366	−	0.313929i
$347$	2.54012	−	2.54012i	0.136361	−	0.136361i	−0.635632	−	0.771992i	$-0.719260\pi$
$347$	2.54012	−	2.54012i	0.136361	−	0.136361i	0.771992	+	0.635632i	$0.219260\pi$
$348$	−2.81327	+	4.99008i	−0.150807	+	0.267497i
$349$	−14.7496	−	14.7496i	−0.789529	−	0.789529i	0.191888	−	0.981417i	$-0.438539\pi$
$349$	−14.7496	−	14.7496i	−0.789529	−	0.789529i	−0.981417	+	0.191888i	$0.938539\pi$
$350$	−3.25284	+	12.3933i	−0.173872	+	0.662452i
$351$	4.35017			0.232195
$352$	−11.3111	+	20.8042i	−0.602885	+	1.10887i
$353$	−11.7154			−0.623547			−0.311773	−	0.950156i	$-0.600923\pi$
$353$	−11.7154			−0.623547			−0.311773	+	0.950156i	$0.600923\pi$
$354$	3.04023	−	11.5833i	0.161587	−	0.615646i
$355$	32.2223	+	32.2223i	1.71018	+	1.71018i
$356$	15.2604	−	27.0685i	0.808802	−	1.43463i
$357$	0.709001	−	0.709001i	0.0375243	−	0.0375243i
$358$	−21.1018	+	12.3277i	−1.11527	+	0.651539i
$359$			25.7580i			1.35945i	0.733465	+	0.679727i	$0.237902\pi$
$359$			25.7580i			1.35945i	−0.733465	+	0.679727i	$0.762098\pi$
$360$	10.5954	−	0.162823i	0.558425	−	0.00858154i
$361$		−	6.39836i		−	0.336756i
$362$	12.0595	+	20.6427i	0.633833	+	1.08496i
$363$	4.61293	−	4.61293i	0.242116	−	0.242116i
$364$	−8.40283	+	2.34405i	−0.440428	+	0.122862i
$365$	13.0510	+	13.0510i	0.683119	+	0.683119i
$366$	19.3968	+	5.09102i	1.01389	+	0.266112i
$367$	22.1046			1.15385			0.576926	−	0.816796i	$-0.304252\pi$
$367$	22.1046			1.15385			0.576926	+	0.816796i	$0.304252\pi$
$368$	19.9329	−	12.0594i	1.03908	−	0.628640i
$369$	−7.46961			−0.388852
$370$	−34.8246	−	9.14029i	−1.81044	−	0.475181i
$371$	−2.80191	−	2.80191i	−0.145468	−	0.145468i
$372$	−5.32755	−	19.0979i	−0.276221	−	0.990182i
$373$	24.7227	−	24.7227i	1.28010	−	1.28010i	0.339483	−	0.940612i	$-0.389748\pi$
$373$	24.7227	−	24.7227i	1.28010	−	1.28010i	0.940612	−	0.339483i	$-0.110252\pi$
$374$	−2.98626	−	5.11171i	−0.154416	−	0.264320i
$375$		−	15.1209i		−	0.780839i
$376$	26.7509	−	27.5860i	1.37957	−	1.42264i
$377$			12.4599i			0.641719i
$378$	1.22438	−	0.715282i	0.0629752	−	0.0367901i
$379$	4.81293	−	4.81293i	0.247224	−	0.247224i	−0.572607	−	0.819830i	$-0.694068\pi$
$379$	4.81293	−	4.81293i	0.247224	−	0.247224i	0.819830	+	0.572607i	$0.194068\pi$
$380$	23.1705	+	13.0628i	1.18862	+	0.670110i
$381$	3.18317	+	3.18317i	0.163079	+	0.163079i
$382$	3.25147	−	12.3881i	0.166360	−	0.633831i
$383$	−9.40034			−0.480335			−0.240168	−	0.970731i	$-0.577202\pi$
$383$	−9.40034			−0.480335			−0.240168	+	0.970731i	$0.577202\pi$
$384$	6.00444	+	9.58888i	0.306413	+	0.489331i
$385$	15.7252			0.801431
$386$	4.20902	−	16.0364i	0.214233	−	0.816230i
$387$	0.165656	+	0.165656i	0.00842075	+	0.00842075i
$388$	3.12830	+	1.76365i	0.158816	+	0.0895356i
$389$	13.0367	−	13.0367i	0.660985	−	0.660985i	−0.294627	−	0.955612i	$-0.595196\pi$
$389$	13.0367	−	13.0367i	0.660985	−	0.660985i	0.955612	+	0.294627i	$0.0951955\pi$
$390$	19.9014	−	11.6264i	1.00774	−	0.588724i
$391$			5.82426i			0.294545i
$392$	11.8036	−	12.1721i	0.596173	−	0.614783i
$393$			0.878166i			0.0442976i
$394$	−5.07089	−	8.68005i	−0.255468	−	0.437295i
$395$	18.2763	−	18.2763i	0.919582	−	0.919582i
$396$	−2.24963	−	8.06436i	−0.113048	−	0.405249i
$397$	8.96888	+	8.96888i	0.450135	+	0.450135i	0.895399	−	0.445264i	$-0.146890\pi$
$397$	8.96888	+	8.96888i	0.450135	+	0.450135i	−0.445264	+	0.895399i	$0.646890\pi$
$398$	−14.8811	−	3.90578i	−0.745920	−	0.195779i
$399$	3.55939			0.178192
$400$	30.9249	−	18.7095i	1.54625	−	0.935477i
$401$	30.7818			1.53717			0.768585	−	0.639747i	$-0.220961\pi$
$401$	30.7818			1.53717			0.768585	+	0.639747i	$0.220961\pi$
$402$	−3.63076	−	0.952954i	−0.181086	−	0.0475290i
$403$	−30.4945	−	30.4945i	−1.51904	−	1.51904i
$404$	−9.55146	+	2.66447i	−0.475203	+	0.132562i
$405$	−2.64915	+	2.64915i	−0.131638	+	0.131638i
$406$	2.04874	+	3.50691i	0.101677	+	0.174045i
$407$			28.4464i			1.41004i
$408$	−2.82809	+	0.0434604i	−0.140011	+	0.00215161i
$409$		−	17.5525i		−	0.867916i	−0.900933	−	0.433958i	$-0.857117\pi$
$409$		−	17.5525i		−	0.867916i	0.900933	−	0.433958i	$-0.142883\pi$
$410$	−34.1723	+	19.9634i	−1.68765	+	0.985924i
$411$	10.6676	−	10.6676i	0.526193	−	0.526193i
$412$	−7.07156	+	12.5433i	−0.348391	+	0.617965i
$413$	−6.00386	−	6.00386i	−0.295431	−	0.295431i
$414$	−2.09105	+	7.96690i	−0.102769	+	0.391552i
$415$	17.6417			0.865995
$416$	21.6195	+	11.7544i	1.05998	+	0.576306i
$417$	−0.876666			−0.0429305
$418$	5.33518	−	20.3271i	0.260952	−	0.994229i
$419$	6.51665	+	6.51665i	0.318359	+	0.318359i	0.848137	−	0.529777i	$-0.177725\pi$
$419$	6.51665	+	6.51665i	0.318359	+	0.318359i	−0.529777	+	0.848137i	$0.677725\pi$
$420$	3.68966	−	6.54460i	0.180037	−	0.319344i
$421$	−16.7912	+	16.7912i	−0.818355	+	0.818355i	−0.985870	−	0.167515i	$-0.946426\pi$
$421$	−16.7912	+	16.7912i	−0.818355	+	0.818355i	0.167515	+	0.985870i	$0.446426\pi$
$422$	19.8583	−	11.6012i	0.966688	−	0.564739i
$423$			13.5858i			0.660566i
$424$	0.171752	+	11.1764i	0.00834100	+	0.542772i
$425$			9.03603i			0.438312i
$426$	−8.67689	−	14.8526i	−0.420397	−	0.719611i
$427$	10.0538	−	10.0538i	0.486536	−	0.486536i
$428$	19.5476	−	5.45298i	0.944867	−	0.263580i
$429$	−12.8767	−	12.8767i	−0.621692	−	0.621692i
$430$	1.20058	+	0.315113i	0.0578973	+	0.0151961i
$431$	−31.1803			−1.50190			−0.750952	−	0.660357i	$-0.770405\pi$
$431$	−31.1803			−1.50190			−0.750952	+	0.660357i	$0.770405\pi$
$432$	−3.88410	−	0.955904i	−0.186874	−	0.0459909i
$433$	−3.95398			−0.190016			−0.0950081	−	0.995477i	$-0.530288\pi$
$433$	−3.95398			−0.190016			−0.0950081	+	0.995477i	$0.530288\pi$
$434$	−13.5969	−	3.56873i	−0.652672	−	0.171305i
$435$	−7.58780	−	7.58780i	−0.363807	−	0.363807i
$436$	−10.2451	−	36.7261i	−0.490650	−	1.75886i
$437$	−14.6197	+	14.6197i	−0.699356	+	0.699356i
$438$	−3.51440	−	6.01574i	−0.167924	−	0.287443i
$439$			15.3410i			0.732187i	0.930578	+	0.366094i	$0.119305\pi$
$439$			15.3410i			0.732187i	−0.930578	+	0.366094i	$0.880695\pi$
$440$	−31.8447	−	30.8807i	−1.51813	−	1.47218i
$441$			5.99464i			0.285459i
$442$	−5.31203	+	3.10329i	−0.252667	+	0.147608i
$443$	−16.9239	+	16.9239i	−0.804080	+	0.804080i	−0.983730	−	0.179651i	$-0.942503\pi$
$443$	−16.9239	+	16.9239i	−0.804080	+	0.804080i	0.179651	+	0.983730i	$0.442503\pi$
$444$	11.8390	+	6.67447i	0.561852	+	0.316756i
$445$	41.1597	+	41.1597i	1.95116	+	1.95116i
$446$	−9.20896	+	35.0862i	−0.436057	+	1.66138i
$447$	10.3214			0.488186
$448$	8.01764	−	0.246479i	0.378798	−	0.0116450i
$449$	35.2584			1.66395			0.831974	−	0.554815i	$-0.187211\pi$
$449$	35.2584			1.66395			0.831974	+	0.554815i	$0.187211\pi$
$450$	−3.24415	+	12.3602i	−0.152931	+	0.582667i
$451$	22.1103	+	22.1103i	1.04113	+	1.04113i
$452$	−0.279862	−	0.157778i	−0.0131636	−	0.00742125i
$453$	−4.16292	+	4.16292i	−0.195591	+	0.195591i
$454$	31.4280	−	18.3603i	1.47499	−	0.861690i
$455$		−	16.3415i		−	0.766099i
$456$	−7.20801	−	6.98983i	−0.337546	−	0.327329i
$457$		−	7.35355i		−	0.343985i	−0.985098	−	0.171992i	$-0.944980\pi$
$457$		−	7.35355i		−	0.343985i	0.985098	−	0.171992i	$-0.0550204\pi$
$458$	−12.6108	−	21.5865i	−0.589264	−	1.00867i
$459$	0.707107	−	0.707107i	0.0330049	−	0.0330049i
$460$	11.7263	+	42.0359i	0.546742	+	1.95993i
$461$	27.0467	+	27.0467i	1.25969	+	1.25969i	0.951240	+	0.308451i	$0.0998105\pi$
$461$	27.0467	+	27.0467i	1.25969	+	1.25969i	0.308451	+	0.951240i	$0.400189\pi$
$462$	−5.74147	−	1.50695i	−0.267117	−	0.0701095i
$463$	−13.6095			−0.632487			−0.316243	−	0.948678i	$-0.602422\pi$
$463$	−13.6095			−0.632487			−0.316243	+	0.948678i	$0.602422\pi$
$464$	2.73794	−	11.1250i	0.127105	−	0.516465i
$465$	37.1408			1.72236
$466$	−7.75759	−	2.03611i	−0.359364	−	0.0943210i
$467$	7.91908	+	7.91908i	0.366452	+	0.366452i	0.866181	−	0.499730i	$-0.166567\pi$
$467$	7.91908	+	7.91908i	0.366452	+	0.366452i	−0.499730	+	0.866181i	$0.666567\pi$
$468$	−8.38038	+	2.33779i	−0.387383	+	0.108064i
$469$	−1.88190	+	1.88190i	−0.0868979	+	0.0868979i
$470$	36.3098	+	62.1530i	1.67485	+	2.86690i
$471$		−	5.47971i		−	0.252492i
$472$	0.368026	+	23.9485i	0.0169398	+	1.10232i
$473$		−	0.980695i		−	0.0450924i
$474$	−8.42433	+	4.92149i	−0.386942	+	0.226052i
$475$	−22.6817	+	22.6817i	−1.04071	+	1.04071i
$476$	−0.984836	+	1.74687i	−0.0451399	+	0.0800677i
$477$	−2.79442	−	2.79442i	−0.127948	−	0.127948i
$478$	−3.63034	+	13.8316i	−0.166048	+	0.632642i
$479$	12.2181			0.558261			0.279130	−	0.960253i	$-0.409954\pi$
$479$	12.2181			0.558261			0.279130	+	0.960253i	$0.409954\pi$
$480$	−20.3239	+	6.00763i	−0.927656	+	0.274209i
$481$	29.5612			1.34787
$482$	4.13290	−	15.7464i	0.188248	−	0.717228i
$483$	4.12941	+	4.12941i	0.187894	+	0.187894i
$484$	−6.40758	+	11.3656i	−0.291254	+	0.516616i
$485$	−4.75682	+	4.75682i	−0.215996	+	0.215996i
$486$	1.22111	−	0.713371i	0.0553905	−	0.0323592i
$487$		−	23.6619i		−	1.07222i	−0.844147	−	0.536111i	$-0.819893\pi$
$487$		−	23.6619i		−	1.07222i	0.844147	−	0.536111i	$-0.180107\pi$
$488$	−40.1029	+	0.616277i	−1.81537	+	0.0278976i
$489$		−	12.7070i		−	0.574628i
$490$	16.0214	+	27.4245i	0.723773	+	1.23891i
$491$	−10.5576	+	10.5576i	−0.476456	+	0.476456i	−0.903996	−	0.427540i	$-0.859380\pi$
$491$	−10.5576	+	10.5576i	−0.476456	+	0.476456i	0.427540	+	0.903996i	$0.359380\pi$
$492$	14.3898	−	4.01417i	0.648742	−	0.180973i
$493$	2.02532	+	2.02532i	0.0912159	+	0.0912159i
$494$	−21.1236	−	5.54426i	−0.950398	−	0.249448i
$495$	15.6832			0.704908
$496$	20.5265	+	33.9281i	0.921666	+	1.52342i
$497$	−12.1958			−0.547057
$498$	−6.44118	−	1.69060i	−0.288636	−	0.0757575i
$499$	19.6185	+	19.6185i	0.878246	+	0.878246i	0.993353	−	0.115107i	$-0.0367212\pi$
$499$	19.6185	+	19.6185i	0.878246	+	0.878246i	−0.115107	+	0.993353i	$0.536721\pi$
$500$	8.12597	+	29.1296i	0.363405	+	1.30271i
$501$	1.79739	−	1.79739i	0.0803016	−	0.0803016i
$502$	−14.1642	−	24.2455i	−0.632180	−	1.08213i
$503$		−	11.5499i		−	0.514987i	−0.966280	−	0.257493i	$-0.917103\pi$
$503$		−	11.5499i		−	0.514987i	0.966280	−	0.257493i	$-0.0828965\pi$
$504$	−1.97431	+	2.03593i	−0.0879426	+	0.0906877i
$505$		−	18.5753i		−	0.826588i
$506$	29.7719	−	17.3928i	1.32352	−	0.773202i
$507$	−4.18891	+	4.18891i	−0.186036	+	0.186036i
$508$	−7.84286	−	4.42158i	−0.347971	−	0.196176i
$509$	−13.8432	−	13.8432i	−0.613588	−	0.613588i	0.330291	−	0.943879i	$-0.392853\pi$
$509$	−13.8432	−	13.8432i	−0.613588	−	0.613588i	−0.943879	+	0.330291i	$0.892853\pi$
$510$	1.34507	−	5.12473i	0.0595608	−	0.226927i
$511$	−4.93966			−0.218518
$512$	−16.7203	−	15.2457i	−0.738941	−	0.673771i
$513$	3.54988			0.156731
$514$	5.81783	−	22.1660i	0.256614	−	0.977699i
$515$	−19.0731	−	19.0731i	−0.840460	−	0.840460i
$516$	−0.408150	−	0.230104i	−0.0179678	−	0.0101297i
$517$	40.2146	−	40.2146i	1.76864	−	1.76864i
$518$	8.32013	−	4.86062i	0.365566	−	0.213563i
$519$		−	8.18567i		−	0.359311i
$520$	−32.0909	+	33.0926i	−1.40728	+	1.45121i
$521$			34.9447i			1.53096i	0.643461	+	0.765479i	$0.277498\pi$
$521$			34.9447i			1.53096i	−0.643461	+	0.765479i	$0.722502\pi$
$522$	2.04326	+	3.49754i	0.0894312	+	0.153083i
$523$	9.73962	−	9.73962i	0.425884	−	0.425884i	−0.461340	−	0.887224i	$-0.652631\pi$
$523$	9.73962	−	9.73962i	0.425884	−	0.425884i	0.887224	+	0.461340i	$0.152631\pi$
$524$	−0.471927	−	1.69174i	−0.0206162	−	0.0739040i
$525$	6.40656	+	6.40656i	0.279605	+	0.279605i
$526$	22.7354	+	5.96728i	0.991309	+	0.260186i
$527$	−9.91355			−0.431841
$528$	8.66758	+	14.3266i	0.377208	+	0.623486i
$529$	−10.9220			−0.474869
$530$	−20.2525	−	5.31560i	−0.879711	−	0.230895i
$531$	−5.98782	−	5.98782i	−0.259849	−	0.259849i
$532$	−6.85698	+	1.91282i	−0.297288	+	0.0829312i
$533$	22.9768	−	22.9768i	0.995235	−	0.995235i
$534$	−11.0836	−	18.9723i	−0.479634	−	0.821010i
$535$			38.0152i			1.64354i
$536$	7.50658	−	0.115357i	0.324235	−	0.00498265i
$537$			17.2809i			0.745726i
$538$	0.124283	−	0.0726062i	0.00535822	−	0.00313027i
$539$	17.7444	−	17.7444i	0.764304	−	0.764304i
$540$	3.67980	−	6.52711i	0.158353	−	0.280882i
$541$	−17.2716	−	17.2716i	−0.742563	−	0.742563i	0.230507	−	0.973071i	$-0.425961\pi$
$541$	−17.2716	−	17.2716i	−0.742563	−	0.742563i	−0.973071	+	0.230507i	$0.925961\pi$
$542$	−9.32629	+	35.5332i	−0.400598	+	1.52628i
$543$	16.9049			0.725461
$544$	5.42482	−	1.60354i	0.232587	−	0.0687514i
$545$	71.4232			3.05943
$546$	−1.56600	+	5.96647i	−0.0670186	+	0.255341i
$547$	−6.14127	−	6.14127i	−0.262582	−	0.262582i	0.563520	−	0.826102i	$-0.309447\pi$
$547$	−6.14127	−	6.14127i	−0.262582	−	0.262582i	−0.826102	+	0.563520i	$0.809447\pi$
$548$	−14.8178	+	26.2833i	−0.632984	+	1.12277i
$549$	10.0269	−	10.0269i	0.427938	−	0.427938i
$550$	46.1896	−	26.9840i	1.96953	−	1.15060i
$551$			10.1677i			0.433158i
$552$	−0.253125	−	16.4715i	−0.0107737	−	0.701076i
$553$			6.91741i			0.294158i
$554$	−16.8320	−	28.8120i	−0.715123	−	1.22411i
$555$	−18.0020	+	18.0020i	−0.764144	+	0.764144i
$556$	1.68885	−	0.471121i	0.0716233	−	0.0199800i
$557$	−10.8059	−	10.8059i	−0.457859	−	0.457859i	0.440093	−	0.897952i	$-0.354945\pi$
$557$	−10.8059	−	10.8059i	−0.457859	−	0.457859i	−0.897952	+	0.440093i	$0.854945\pi$
$558$	−13.5606	−	3.55920i	−0.574065	−	0.150673i
$559$	−1.01913			−0.0431044
$560$	−3.59086	+	14.5907i	−0.151741	+	0.616568i
$561$	−4.18613			−0.176738
$562$	−8.64165	−	2.26815i	−0.364526	−	0.0956760i
$563$	32.2165	+	32.2165i	1.35777	+	1.35777i	0.876666	+	0.481100i	$0.159763\pi$
$563$	32.2165	+	32.2165i	1.35777	+	1.35777i	0.481100	+	0.876666i	$0.340237\pi$
$564$	−7.30104	−	26.1724i	−0.307429	−	1.10206i
$565$	0.425551	−	0.425551i	0.0179031	−	0.0179031i
$566$	10.3106	+	17.6492i	0.433389	+	0.741850i
$567$		−	1.00268i		−	0.0421086i
$568$	24.6974	+	23.9498i	1.03628	+	1.00491i
$569$			0.396091i			0.0166050i	0.999966	+	0.00830250i	$0.00264280\pi$
$569$			0.396091i			0.0166050i	−0.999966	+	0.00830250i	$0.997357\pi$
$570$	16.2401	−	9.48748i	0.680224	−	0.397387i
$571$	−11.0925	+	11.0925i	−0.464206	+	0.464206i	−0.900031	−	0.435826i	$-0.856456\pi$
$571$	−11.0925	+	11.0925i	−0.464206	+	0.464206i	0.435826	+	0.900031i	$0.356456\pi$
$572$	31.7262	+	17.8863i	1.32654	+	0.747865i
$573$	−6.40385	−	6.40385i	−0.267525	−	0.267525i
$574$	2.68895	−	10.2449i	0.112235	−	0.427614i
$575$	−52.6282			−2.19475
$576$	7.99622	−	0.245820i	0.333176	−	0.0102425i
$577$	−41.1309			−1.71230			−0.856152	−	0.516725i	$-0.827151\pi$
$577$	−41.1309			−1.71230			−0.856152	+	0.516725i	$0.827151\pi$
$578$	−0.359024	+	1.36788i	−0.0149334	+	0.0568964i
$579$	−8.28977	−	8.28977i	−0.344511	−	0.344511i
$580$	18.6952	+	10.5398i	0.776276	+	0.437642i
$581$	−3.33860	+	3.33860i	−0.138508	+	0.138508i
$582$	2.19262	−	1.28093i	0.0908871	−	0.0530962i
$583$			16.5432i			0.685149i
$584$	10.0032	+	9.70037i	0.413934	+	0.401404i
$585$		−	16.2978i		−	0.673831i
$586$	−9.01817	−	15.4368i	−0.372537	−	0.637688i
$587$	−16.2394	+	16.2394i	−0.670270	+	0.670270i	−0.957778	−	0.287508i	$-0.907173\pi$
$587$	−16.2394	+	16.2394i	−0.670270	+	0.670270i	0.287508	+	0.957778i	$0.407173\pi$
$588$	−3.22152	−	11.5484i	−0.132853	−	0.476246i
$589$	−24.8844	−	24.8844i	−1.02535	−	1.02535i
$590$	−43.3965	−	11.3901i	−1.78661	−	0.468925i
$591$	−7.10835			−0.292398
$592$	−26.3940	−	6.49574i	−1.08479	−	0.266973i
$593$	14.8455			0.609631			0.304816	−	0.952411i	$-0.401405\pi$
$593$	14.8455			0.609631			0.304816	+	0.952411i	$0.401405\pi$
$594$	−5.72613	−	1.50292i	−0.234946	−	0.0616655i
$595$	−2.65625	−	2.65625i	−0.108896	−	0.108896i
$596$	−19.8837	+	5.54673i	−0.814466	+	0.227203i
$597$	−7.69255	+	7.69255i	−0.314835	+	0.314835i
$598$	−18.0743	−	30.9386i	−0.739115	−	1.26517i
$599$		−	17.6354i		−	0.720565i	−0.932843	−	0.360282i	$-0.882680\pi$
$599$		−	17.6354i		−	0.720565i	0.932843	−	0.360282i	$-0.117320\pi$
$600$	−0.392710	−	25.5547i	−0.0160323	−	1.04327i
$601$		−	26.6347i		−	1.08645i	−0.839587	−	0.543226i	$-0.817203\pi$
$601$		−	26.6347i		−	1.08645i	0.839587	−	0.543226i	$-0.182797\pi$
$602$	−0.286838	+	0.167571i	−0.0116906	+	0.00682968i
$603$	−1.87687	+	1.87687i	−0.0764320	+	0.0764320i
$604$	5.78250	−	10.2568i	0.235287	−	0.417344i
$605$	−17.2822	−	17.2822i	−0.702622	−	0.702622i
$606$	−1.78007	+	6.78206i	−0.0723102	+	0.275502i
$607$	−12.8818			−0.522855			−0.261427	−	0.965223i	$-0.584193\pi$
$607$	−12.8818			−0.522855			−0.261427	+	0.965223i	$0.584193\pi$
$608$	17.6422	+	9.59195i	0.715485	+	0.389005i
$609$	2.87191			0.116376
$610$	19.0734	−	72.6696i	0.772258	−	2.94231i
$611$	−41.7905	−	41.7905i	−1.69066	−	1.69066i
$612$	−0.982204	+	1.74220i	−0.0397033	+	0.0704244i
$613$	−9.50457	+	9.50457i	−0.383886	+	0.383886i	−0.872500	−	0.488614i	$-0.837503\pi$
$613$	−9.50457	+	9.50457i	−0.383886	+	0.383886i	0.488614	+	0.872500i	$0.337503\pi$
$614$	0.885061	−	0.517053i	0.0357181	−	0.0208665i
$615$			27.9847i			1.12845i
$616$	11.8705	−	0.182418i	0.478275	−	0.00734984i
$617$			22.8787i			0.921061i	0.887644	+	0.460530i	$0.152341\pi$
$617$			22.8787i			0.921061i	−0.887644	+	0.460530i	$0.847659\pi$
$618$	5.13604	+	8.79158i	0.206602	+	0.353649i
$619$	11.4318	−	11.4318i	0.459483	−	0.459483i	−0.439003	−	0.898486i	$-0.644668\pi$
$619$	11.4318	−	11.4318i	0.459483	−	0.459483i	0.898486	+	0.439003i	$0.144668\pi$
$620$	−71.5498	+	19.9595i	−2.87351	+	0.801593i
$621$	4.11837	+	4.11837i	0.165265	+	0.165265i
$622$	−10.0240	−	2.63097i	−0.401926	−	0.105492i
$623$	−15.5785			−0.624141
$624$	14.8880	−	9.00725i	0.595999	−	0.360578i
$625$	−11.4697			−0.458790
$626$	−1.25498	−	0.329391i	−0.0501592	−	0.0131651i
$627$	−10.5078	−	10.5078i	−0.419640	−	0.419640i
$628$	2.94480	+	10.5564i	0.117510	+	0.421245i
$629$	4.80507	−	4.80507i	0.191591	−	0.191591i
$630$	−2.67978	−	4.58710i	−0.106765	−	0.182754i
$631$		−	24.0059i		−	0.955659i	−0.878453	−	0.477830i	$-0.841424\pi$
$631$		−	24.0059i		−	0.955659i	0.878453	−	0.477830i	$-0.158576\pi$
$632$	13.5842	−	14.0082i	0.540351	−	0.557218i
$633$		−	16.2626i		−	0.646379i
$634$	−31.6419	+	18.4852i	−1.25666	+	0.734140i
$635$	11.9257	−	11.9257i	0.473256	−	0.473256i
$636$	6.88503	+	3.88158i	0.273009	+	0.153915i
$637$	−18.4397	−	18.4397i	−0.730608	−	0.730608i
$638$	4.30472	−	16.4010i	0.170425	−	0.649322i
$639$	−12.1632			−0.481170
$640$	35.9245	−	22.4955i	1.42004	−	0.889211i
$641$	25.0756			0.990426			0.495213	−	0.868771i	$-0.335090\pi$
$641$	25.0756			0.990426			0.495213	+	0.868771i	$0.335090\pi$
$642$	3.64300	−	13.8798i	0.143778	−	0.547793i
$643$	−4.51232	−	4.51232i	−0.177948	−	0.177948i	0.612512	−	0.790461i	$-0.290159\pi$
$643$	−4.51232	−	4.51232i	−0.177948	−	0.177948i	−0.790461	+	0.612512i	$0.790159\pi$
$644$	−10.1742	−	5.73594i	−0.400921	−	0.226028i
$645$	0.620624	−	0.620624i	0.0244370	−	0.0244370i
$646$	−4.33478	+	2.53238i	−0.170550	+	0.0996351i
$647$			2.28865i			0.0899760i	0.998988	+	0.0449880i	$0.0143250\pi$
$647$			2.28865i			0.0899760i	−0.998988	+	0.0449880i	$0.985675\pi$
$648$	−1.96903	+	2.03050i	−0.0773509	+	0.0797654i
$649$			35.4484i			1.39147i
$650$	−28.0414	−	47.9997i	−1.09987	−	1.88270i
$651$	−7.02872	+	7.02872i	−0.275477	+	0.275477i
$652$	6.82873	+	24.4793i	0.267434	+	0.958683i
$653$	−21.6871	−	21.6871i	−0.848681	−	0.848681i	0.141287	−	0.989969i	$-0.454876\pi$
$653$	−21.6871	−	21.6871i	−0.848681	−	0.848681i	−0.989969	+	0.141287i	$0.954876\pi$
$654$	−26.0775	−	6.84448i	−1.01971	−	0.267640i
$655$	3.29002			0.128552
$656$	−25.5640	+	15.4662i	−0.998106	+	0.603853i
$657$	−4.92646			−0.192200
$658$	−18.6336	−	4.89070i	−0.726413	−	0.190659i
$659$	12.6568	+	12.6568i	0.493039	+	0.493039i	0.909262	−	0.416223i	$-0.136647\pi$
$659$	12.6568	+	12.6568i	0.493039	+	0.493039i	−0.416223	+	0.909262i	$0.636647\pi$
$660$	−30.2129	+	8.42816i	−1.17603	+	0.328066i
$661$	−30.4752	+	30.4752i	−1.18535	+	1.18535i	−0.207008	+	0.978339i	$0.566373\pi$
$661$	−30.4752	+	30.4752i	−1.18535	+	1.18535i	−0.978339	+	0.207008i	$0.933627\pi$
$662$	−7.81158	−	13.3714i	−0.303606	−	0.519694i
$663$			4.35017i			0.168947i
$664$	13.3171	−	0.204650i	0.516805	−	0.00794195i
$665$		−	13.3351i		−	0.517115i
$666$	8.29790	−	4.84764i	0.321537	−	0.187842i
$667$	−11.7960	+	11.7960i	−0.456743	+	0.456743i
$668$	−2.49666	+	4.42851i	−0.0965988	+	0.171344i
$669$	18.1373	+	18.1373i	0.701228	+	0.701228i
$670$	−3.57021	+	13.6025i	−0.137929	+	0.525511i
$671$	−59.3601			−2.29157
$672$	2.70929	−	4.98312i	0.104513	−	0.192228i
$673$	−8.08932			−0.311821			−0.155910	−	0.987771i	$-0.549831\pi$
$673$	−8.08932			−0.311821			−0.155910	+	0.987771i	$0.549831\pi$
$674$	10.8532	−	41.3506i	0.418049	−	1.59277i
$675$	6.38944	+	6.38944i	0.245930	+	0.245930i
$676$	5.81859	−	10.3208i	0.223792	−	0.396955i
$677$	28.4416	−	28.4416i	1.09310	−	1.09310i	0.0979023	−	0.995196i	$-0.468787\pi$
$677$	28.4416	−	28.4416i	1.09310	−	1.09310i	0.995196	−	0.0979023i	$-0.0312133\pi$
$678$	−0.196155	+	0.114593i	−0.00753327	+	0.00440094i
$679$		−	1.80041i		−	0.0690934i
$680$	0.162823	+	10.5954i	0.00624399	+	0.406314i
$681$		−	25.7373i		−	0.986257i
$682$	29.6044	+	50.6752i	1.13361	+	1.94045i
$683$	−2.13638	+	2.13638i	−0.0817464	+	0.0817464i	−0.746798	−	0.665051i	$-0.768410\pi$
$683$	−2.13638	+	2.13638i	−0.0817464	+	0.0817464i	0.665051	+	0.746798i	$0.268410\pi$
$684$	−6.83866	+	1.90771i	−0.261483	+	0.0729430i
$685$	−39.9658	−	39.9658i	−1.52701	−	1.52701i
$686$	−17.8227	−	4.67788i	−0.680476	−	0.178602i
$687$	−17.6778			−0.674449
$688$	0.909938	+	0.223942i	0.0346911	+	0.00853771i
$689$	17.1915			0.654944
$690$	29.8478	+	7.83405i	1.13628	+	0.298237i
$691$	25.2514	+	25.2514i	0.960608	+	0.960608i	0.999253	−	0.0386446i	$-0.0123040\pi$
$691$	25.2514	+	25.2514i	0.960608	+	0.960608i	−0.0386446	+	0.999253i	$0.512304\pi$
$692$	4.39899	+	15.7693i	0.167224	+	0.599458i
$693$	−2.96797	+	2.96797i	−0.112744	+	0.112744i
$694$	2.56262	+	4.38654i	0.0972756	+	0.166511i
$695$			3.28440i			0.124585i
$696$	−5.81582	−	5.63978i	−0.220448	−	0.213775i
$697$		−	7.46961i		−	0.282931i
$698$	25.4712	−	14.8803i	0.964099	−	0.563227i
$699$	−4.01018	+	4.01018i	−0.151679	+	0.151679i
$700$	−15.7848	−	8.89901i	−0.596609	−	0.336351i
$701$	−36.2735	−	36.2735i	−1.37003	−	1.37003i	−0.860380	−	0.509653i	$-0.829774\pi$
$701$	−36.2735	−	36.2735i	−1.37003	−	1.37003i	−0.509653	−	0.860380i	$-0.670226\pi$
$702$	−1.56182	+	5.95053i	−0.0589469	+	0.224588i
$703$	24.1228			0.909810
$704$	−24.3968	−	22.9415i	−0.919488	−	0.864640i
$705$	50.8989			1.91696
$706$	4.20610	−	16.0253i	0.158299	−	0.603119i
$707$	3.51528	+	3.51528i	0.132206	+	0.132206i
$708$	14.7531	+	8.31737i	0.554455	+	0.312586i
$709$	34.8473	−	34.8473i	1.30872	−	1.30872i	0.386377	−	0.922341i	$-0.373726\pi$
$709$	34.8473	−	34.8473i	1.30872	−	1.30872i	0.922341	−	0.386377i	$-0.126274\pi$
$710$	−55.6448	+	32.5077i	−2.08831	+	1.21999i
$711$			6.89893i			0.258730i
$712$	31.5477	+	30.5927i	1.18230	+	1.14651i
$713$		−	57.7391i		−	2.16235i
$714$	0.715282	+	1.22438i	0.0267687	+	0.0458212i
$715$	−48.2421	+	48.2421i	−1.80415	+	1.80415i
$716$	−9.28677	−	33.2908i	−0.347063	−	1.24413i
$717$	7.15004	+	7.15004i	0.267023	+	0.267023i
$718$	−35.2339	−	9.24773i	−1.31492	−	0.345122i
$719$	34.1227			1.27256			0.636282	−	0.771457i	$-0.280472\pi$
$719$	34.1227			1.27256			0.636282	+	0.771457i	$0.280472\pi$
$720$	−3.58126	+	14.5517i	−0.133466	+	0.542309i
$721$	7.21897			0.268848
$722$	8.75220	+	2.29716i	0.325723	+	0.0854916i
$723$	−8.13986	−	8.13986i	−0.302725	−	0.302725i
$724$	−32.5665	+	9.08473i	−1.21032	+	0.337631i
$725$	−18.3009	+	18.3009i	−0.679677	+	0.679677i
$726$	4.65379	+	7.96610i	0.172719	+	0.295650i
$727$			15.4162i			0.571756i	0.958266	+	0.285878i	$0.0922851\pi$
$727$			15.4162i			0.571756i	−0.958266	+	0.285878i	$0.907715\pi$
$728$	−0.189567	−	12.3357i	−0.00702582	−	0.457190i
$729$		−	1.00000i		−	0.0370370i
$730$	−22.5378	+	13.1666i	−0.834161	+	0.487317i
$731$	−0.165656	+	0.165656i	−0.00612700	+	0.00612700i
$732$	−13.9278	+	24.7048i	−0.514788	+	0.913115i
$733$	−3.64144	−	3.64144i	−0.134500	−	0.134500i	0.636652	−	0.771151i	$-0.280319\pi$
$733$	−3.64144	−	3.64144i	−0.134500	−	0.134500i	−0.771151	+	0.636652i	$0.780319\pi$
$734$	−7.93609	+	30.2365i	−0.292927	+	1.11605i
$735$	22.4587			0.828402
$736$	9.33945	+	31.5955i	0.344257	+	1.16463i
$737$	11.1112			0.409287
$738$	2.68177	−	10.2175i	0.0987172	−	0.376113i
$739$	−17.1159	−	17.1159i	−0.629618	−	0.629618i	0.318354	−	0.947972i	$-0.396870\pi$
$739$	−17.1159	−	17.1159i	−0.629618	−	0.629618i	−0.947972	+	0.318354i	$0.896870\pi$
$740$	25.0057	−	44.3543i	0.919227	−	1.63050i
$741$	−10.9196	+	10.9196i	−0.401140	+	0.401140i
$742$	4.83863	−	2.82673i	0.177632	−	0.103772i
$743$			28.3698i			1.04079i	0.853927	+	0.520393i	$0.174215\pi$
$743$			28.3698i			1.04079i	−0.853927	+	0.520393i	$0.825785\pi$
$744$	28.0364	−	0.430847i	1.02787	−	0.0157956i
$745$		−	38.6689i		−	1.41672i
$746$	24.9418	+	42.6939i	0.913182	+	1.56313i
$747$	−3.32968	+	3.32968i	−0.121826	+	0.121826i
$748$	8.06436	−	2.24963i	0.294862	−	0.0822546i
$749$	−7.19420	−	7.19420i	−0.262870	−	0.262870i
$750$	20.6836	+	5.42876i	0.755258	+	0.198230i
$751$	−8.24674			−0.300928			−0.150464	−	0.988616i	$-0.548077\pi$
$751$	−8.24674			−0.300928			−0.150464	+	0.988616i	$0.548077\pi$
$752$	28.1301	+	46.4962i	1.02580	+	1.69554i
$753$	−19.8554			−0.723569
$754$	−17.0437	−	4.47341i	−0.620695	−	0.162912i
$755$	15.5963	+	15.5963i	0.567606	+	0.567606i
$756$	0.538840	+	1.93161i	0.0195974	+	0.0702519i
$757$	−8.48866	+	8.48866i	−0.308526	+	0.308526i	−0.844337	−	0.535812i	$-0.820006\pi$
$757$	−8.48866	+	8.48866i	−0.308526	+	0.308526i	0.535812	+	0.844337i	$0.320006\pi$
$758$	4.85557	+	8.31148i	0.176362	+	0.301887i
$759$		−	24.3811i		−	0.884978i
$760$	−26.1872	+	27.0046i	−0.949909	+	0.979560i
$761$			6.91360i			0.250618i	0.992118	+	0.125309i	$0.0399922\pi$
$761$			6.91360i			0.250618i	−0.992118	+	0.125309i	$0.960008\pi$
$762$	−5.49704	+	3.21137i	−0.199137	+	0.116336i
$763$	−13.5165	+	13.5165i	−0.489330	+	0.489330i
$764$	15.7781	+	8.89525i	0.570832	+	0.321819i
$765$	−2.64915	−	2.64915i	−0.0957804	−	0.0957804i
$766$	3.37495	−	12.8586i	0.121942	−	0.464599i
$767$	36.8375			1.33013
$768$	−15.2722	+	4.77074i	−0.551088	+	0.172149i
$769$	26.4086			0.952319			0.476160	−	0.879359i	$-0.342028\pi$
$769$	26.4086			0.952319			0.476160	+	0.879359i	$0.342028\pi$
$770$	−5.64573	+	21.5102i	−0.203458	+	0.775175i
$771$	−11.4584	−	11.4584i	−0.412663	−	0.412663i
$772$	20.4247	+	11.5149i	0.735102	+	0.414429i
$773$	0.794474	−	0.794474i	0.0285752	−	0.0285752i	−0.692675	−	0.721250i	$-0.743568\pi$
$773$	0.794474	−	0.794474i	0.0285752	−	0.0285752i	0.721250	+	0.692675i	$0.243568\pi$
$774$	−0.286072	+	0.167123i	−0.0102826	+	0.00600712i
$775$		−	89.5792i		−	3.21778i
$776$	−3.53560	+	3.64596i	−0.126921	+	0.130882i
$777$		−	6.81360i		−	0.244436i
$778$	13.1521	+	22.5131i	0.471527	+	0.807133i
$779$	18.7498	−	18.7498i	0.671781	−	0.671781i
$780$	8.75845	+	31.3968i	0.313603	+	1.12419i
$781$	36.0036	+	36.0036i	1.28831	+	1.28831i
$782$	−7.96690	−	2.09105i	−0.284896	−	0.0747757i
$783$	2.86424			0.102359
$784$	12.4122	+	20.5160i	0.443292	+	0.732716i
$785$	−20.5296			−0.732732
$786$	−1.20123	−	0.315282i	−0.0428464	−	0.0112457i
$787$	12.2136	+	12.2136i	0.435367	+	0.435367i	0.890449	−	0.455082i	$-0.150390\pi$
$787$	12.2136	+	12.2136i	0.435367	+	0.435367i	−0.455082	+	0.890449i	$0.650390\pi$
$788$	13.6939	−	3.82003i	0.487823	−	0.136083i
$789$	11.7527	−	11.7527i	0.418408	−	0.418408i
$790$	18.4382	+	31.5615i	0.656003	+	1.12291i
$791$			0.161067i			0.00572688i
$792$	11.8388	−	0.181931i	0.420672	−	0.00646464i
$793$			61.6863i			2.19054i
$794$	−15.4884	+	9.04833i	−0.549663	+	0.321113i
$795$	−10.4692	+	10.4692i	−0.371305	+	0.371305i
$796$	10.6853	−	18.9533i	0.378731	−	0.671781i
$797$	4.85051	+	4.85051i	0.171814	+	0.171814i	0.787776	−	0.615962i	$-0.211232\pi$
$797$	4.85051	+	4.85051i	0.171814	+	0.171814i	−0.615962	+	0.787776i	$0.711232\pi$
$798$	−1.27790	+	4.86882i	−0.0452373	+	0.172355i
$799$	−13.5858			−0.480632
$800$	14.4897	+	49.0188i	0.512287	+	1.73308i
$801$	−15.5369			−0.548970
$802$	−11.0514	+	42.1059i	−0.390239	+	1.48681i
$803$	14.5825	+	14.5825i	0.514606	+	0.514606i
$804$	2.60706	−	4.62432i	0.0919438	−	0.163087i
$805$	15.4707	−	15.4707i	0.545270	−	0.545270i
$806$	52.6611	−	30.7646i	1.85491	−	1.08364i
$807$		−	0.101779i		−	0.00358279i
$808$	−0.215480	−	14.0219i	−0.00758056	−	0.493288i
$809$			11.3855i			0.400293i	0.979766	+	0.200146i	$0.0641418\pi$
$809$			11.3855i			0.400293i	−0.979766	+	0.200146i	$0.935858\pi$
$810$	−2.67262	−	4.57484i	−0.0939064	−	0.160743i
$811$	9.35626	−	9.35626i	0.328543	−	0.328543i	−0.523490	−	0.852032i	$-0.675370\pi$
$811$	9.35626	−	9.35626i	0.328543	−	0.328543i	0.852032	+	0.523490i	$0.175370\pi$
$812$	−5.53258	+	1.54337i	−0.194156	+	0.0541615i
$813$	18.3684	+	18.3684i	0.644207	+	0.644207i
$814$	−38.9113	−	10.2129i	−1.36384	−	0.357963i
$815$	−47.6062			−1.66757
$816$	0.955904	−	3.88410i	0.0334633	−	0.135971i
$817$	−0.831639			−0.0290954
$818$	24.0098	+	6.30177i	0.839482	+	0.220336i
$819$	3.08428	+	3.08428i	0.107773	+	0.107773i
$820$	−15.0390	−	53.9110i	−0.525184	−	1.88265i
$821$	29.7729	−	29.7729i	1.03908	−	1.03908i	0.0398757	−	0.999205i	$-0.487304\pi$
$821$	29.7729	−	29.7729i	1.03908	−	1.03908i	0.999205	−	0.0398757i	$-0.0126962\pi$
$822$	10.7621	+	18.4219i	0.375371	+	0.642538i
$823$		−	36.4593i		−	1.27089i	−0.772146	−	0.635445i	$-0.780817\pi$
$823$		−	36.4593i		−	1.27089i	0.772146	−	0.635445i	$-0.219183\pi$
$824$	−14.6189	−	14.1764i	−0.509274	−	0.493859i
$825$		−	37.8260i		−	1.31693i
$826$	10.3681	−	6.05705i	0.360753	−	0.210752i
$827$	−9.11760	+	9.11760i	−0.317050	+	0.317050i	−0.847633	−	0.530583i	$-0.821973\pi$
$827$	−9.11760	+	9.11760i	−0.317050	+	0.317050i	0.530583	+	0.847633i	$0.321973\pi$
$828$	−10.1470	−	5.72061i	−0.352634	−	0.198805i
$829$	5.99789	+	5.99789i	0.208315	+	0.208315i	0.803551	−	0.595236i	$-0.202941\pi$
$829$	5.99789	+	5.99789i	0.208315	+	0.208315i	−0.595236	+	0.803551i	$0.702941\pi$
$830$	−6.33377	+	24.1317i	−0.219848	+	0.837624i
$831$	−23.5950			−0.818502
$832$	−23.8405	+	25.3528i	−0.826522	+	0.878951i
$833$	−5.99464			−0.207702
$834$	0.314744	−	1.19918i	0.0108987	−	0.0415241i
$835$	−6.73388	−	6.73388i	−0.233036	−	0.233036i
$836$	25.8896	+	14.5958i	0.895410	+	0.504806i
$837$	−7.00994	+	7.00994i	−0.242299	+	0.242299i
$838$	−11.2536	+	6.57438i	−0.388751	+	0.227108i
$839$		−	37.5084i		−	1.29493i	−0.762094	−	0.647467i	$-0.775829\pi$
$839$		−	37.5084i		−	1.29493i	0.762094	−	0.647467i	$-0.224171\pi$
$840$	7.62757	+	7.39668i	0.263176	+	0.255210i
$841$		−	20.7961i		−	0.717109i
$842$	−16.9400	−	28.9969i	−0.583790	−	0.999299i
$843$	−4.46717	+	4.46717i	−0.153858	+	0.153858i
$844$	8.73951	+	31.3290i	0.300826	+	1.07839i
$845$	15.6936	+	15.6936i	0.539877	+	0.539877i
$846$	−18.5838	−	4.87764i	−0.638925	−	0.167697i
$847$	6.54114			0.224756
$848$	−15.3496	−	3.77764i	−0.527108	−	0.129725i
$849$	14.4534			0.496040
$850$	−12.3602	−	3.24415i	−0.423952	−	0.111273i
$851$	27.9860	+	27.9860i	0.959347	+	0.959347i
$852$	23.4318	−	6.53653i	0.802761	−	0.223938i
$853$	3.22373	−	3.22373i	0.110378	−	0.110378i	−0.649761	−	0.760139i	$-0.725131\pi$
$853$	3.22373	−	3.22373i	0.110378	−	0.110378i	0.760139	+	0.649761i	$0.225131\pi$
$854$	10.1428	+	17.3619i	0.347080	+	0.594112i
$855$		−	13.2995i		−	0.454834i
$856$	0.440991	+	28.6965i	0.0150728	+	0.980827i
$857$		−	8.20890i		−	0.280411i	−0.990122	−	0.140205i	$-0.955224\pi$
$857$		−	8.20890i		−	0.280411i	0.990122	−	0.140205i	$-0.0447763\pi$
$858$	22.2368	−	12.9908i	0.759153	−	0.443497i
$859$	−6.87039	+	6.87039i	−0.234415	+	0.234415i	−0.814533	−	0.580118i	$-0.803006\pi$
$859$	−6.87039	+	6.87039i	−0.234415	+	0.234415i	0.580118	+	0.814533i	$0.303006\pi$
$860$	−0.862076	+	1.52912i	−0.0293965	+	0.0521427i
$861$	−5.29596	−	5.29596i	−0.180486	−	0.180486i
$862$	11.1945	−	42.6510i	0.381285	−	1.45270i
$863$	6.07761			0.206884			0.103442	−	0.994635i	$-0.467014\pi$
$863$	6.07761			0.206884			0.103442	+	0.994635i	$0.467014\pi$
$864$	2.70205	−	4.96980i	0.0919256	−	0.169076i
$865$	−30.6674			−1.04272
$866$	1.41957	−	5.40858i	0.0482391	−	0.183791i
$867$	0.707107	+	0.707107i	0.0240146	+	0.0240146i
$868$	9.76322	−	17.3177i	0.331385	−	0.587801i
$869$	20.4211	−	20.4211i	0.692738	−	0.692738i
$870$	13.1034	−	7.65502i	0.444248	−	0.259530i
$871$		−	11.5466i		−	0.391243i
$872$	53.9152	−	0.828536i	1.82580	−	0.0280578i
$873$		−	1.79560i		−	0.0607719i
$874$	−14.7492	−	25.2469i	−0.498900	−	0.853989i
$875$	10.7207	−	10.7207i	0.362426	−	0.362426i
$876$	9.49058	−	2.64749i	0.320657	−	0.0894502i
$877$	38.8630	+	38.8630i	1.31231	+	1.31231i	0.919709	+	0.392600i	$0.128424\pi$
$877$	38.8630	+	38.8630i	1.31231	+	1.31231i	0.392600	+	0.919709i	$0.371576\pi$
$878$	−20.9847	−	5.50779i	−0.708200	−	0.185879i
$879$	−12.6416			−0.426392
$880$	53.6742	−	32.4728i	1.80936	−	1.09466i
$881$	−54.0905			−1.82236			−0.911178	−	0.412012i	$-0.864826\pi$
$881$	−54.0905			−1.82236			−0.911178	+	0.412012i	$0.864826\pi$
$882$	−8.19996	−	2.15222i	−0.276107	−	0.0724689i
$883$	9.46592	+	9.46592i	0.318554	+	0.318554i	0.848211	−	0.529658i	$-0.177680\pi$
$883$	9.46592	+	9.46592i	0.318554	+	0.318554i	−0.529658	+	0.848211i	$0.677680\pi$
$884$	−2.33779	−	8.38038i	−0.0786283	−	0.281863i
$885$	−22.4332	+	22.4332i	−0.754084	+	0.754084i
$886$	−17.0738	−	29.2260i	−0.573607	−	0.981868i
$887$			39.0197i			1.31015i	0.755563	+	0.655076i	$0.227363\pi$
$887$			39.0197i			1.31015i	−0.755563	+	0.655076i	$0.772637\pi$
$888$	−13.3804	+	13.7980i	−0.449015	+	0.463031i
$889$			4.51375i			0.151386i
$890$	−71.0790	+	41.5243i	−2.38257	+	1.39190i
$891$	−2.96004	+	2.96004i	−0.0991651	+	0.0991651i
$892$	−44.6875	−	25.1935i	−1.49625	−	0.843542i
$893$	−34.1024	−	34.1024i	−1.14119	−	1.14119i
$894$	−3.70563	+	14.1185i	−0.123935	+	0.472192i
$895$	64.7424			2.16410
$896$	−2.54137	+	11.0557i	−0.0849012	+	0.369344i
$897$	−25.3365			−0.845962
$898$	−12.6586	+	48.2294i	−0.422423	+	1.60943i
$899$	−20.0781	−	20.0781i	−0.669643	−	0.669643i
$900$	−15.7426	−	8.87523i	−0.524754	−	0.295841i
$901$	2.79442	−	2.79442i	0.0930957	−	0.0930957i
$902$	−38.1825	+	22.3062i	−1.27134	+	0.742715i
$903$			0.234900i			0.00781699i
$904$	0.316299	−	0.326172i	0.0105199	−	0.0108483i
$905$		−	63.3339i		−	2.10529i
$906$	−4.19980	−	7.18898i	−0.139529	−	0.238838i
$907$	−10.5532	+	10.5532i	−0.350412	+	0.350412i	−0.860263	−	0.509851i	$-0.829701\pi$
$907$	−10.5532	+	10.5532i	−0.350412	+	0.350412i	0.509851	+	0.860263i	$0.329701\pi$
$908$	13.8313	+	49.5816i	0.459007	+	1.64542i
$909$	3.50589	+	3.50589i	0.116283	+	0.116283i
$910$	22.3532	+	5.86697i	0.741001	+	0.194488i
$911$	4.36641			0.144666			0.0723328	−	0.997381i	$-0.476956\pi$
$911$	4.36641			0.144666			0.0723328	+	0.997381i	$0.476956\pi$
$912$	12.1491	−	7.35020i	0.402297	−	0.243389i
$913$	19.7119			0.652370
$914$	10.0588	+	2.64010i	0.332715	+	0.0873268i
$915$	−37.5655	−	37.5655i	−1.24188	−	1.24188i
$916$	34.0553	−	9.50005i	1.12522	−	0.313890i
$917$	−0.622620	+	0.622620i	−0.0205607	+	0.0205607i
$918$	0.713371	+	1.22111i	0.0235447	+	0.0403025i
$919$		−	25.9609i		−	0.856371i	−0.903691	−	0.428186i	$-0.859153\pi$
$919$		−	25.9609i		−	0.856371i	0.903691	−	0.428186i	$-0.140847\pi$
$920$	−61.7102	+	0.948325i	−2.03452	+	0.0312653i
$921$		−	0.724802i		−	0.0238830i
$922$	−46.7071	+	27.2863i	−1.53822	+	0.898627i
$923$	37.4145	−	37.4145i	1.23151	−	1.23151i
$924$	4.12265	−	7.31263i	0.135625	−	0.240568i
$925$	43.4188	+	43.4188i	1.42760	+	1.42760i
$926$	4.88613	−	18.6162i	0.160568	−	0.611766i
$927$	7.19968			0.236469
$928$	14.2347	+	7.73931i	0.467277	+	0.254055i
$929$	−1.72136			−0.0564760			−0.0282380	−	0.999601i	$-0.508990\pi$
$929$	−1.72136			−0.0564760			−0.0282380	+	0.999601i	$0.508990\pi$
$930$	−13.3344	+	50.8043i	−0.437253	+	1.66594i
$931$	−15.0474	−	15.0474i	−0.493158	−	0.493158i
$932$	5.57032	−	9.88046i	0.182462	−	0.323645i
$933$	−5.18176	+	5.18176i	−0.169643	+	0.169643i
$934$	−13.6755	+	7.98924i	−0.447477	+	0.261416i
$935$			15.6832i			0.512896i
$936$	−0.189060	−	12.3027i	−0.00617964	−	0.402126i
$937$			26.9335i			0.879878i	0.898028	+	0.439939i	$0.145000\pi$
$937$			26.9335i			0.879878i	−0.898028	+	0.439939i	$0.855000\pi$
$938$	−1.89857	−	3.24986i	−0.0619904	−	0.106112i
$939$	−0.648745	+	0.648745i	−0.0211710	+	0.0211710i
$940$	−98.0541	+	27.3531i	−3.19817	+	0.892160i
$941$	−12.4070	−	12.4070i	−0.404457	−	0.404457i	0.475344	−	0.879800i	$-0.342324\pi$
$941$	−12.4070	−	12.4070i	−0.404457	−	0.404457i	−0.879800	+	0.475344i	$0.842324\pi$
$942$	7.49560	+	1.96735i	0.244220	+	0.0640996i
$943$	43.5049			1.41672
$944$	−32.8908	−	8.09465i	−1.07050	−	0.263458i
$945$	−3.75651			−0.122199
$946$	1.34148	+	0.352093i	0.0436151	+	0.0114475i
$947$	24.0506	+	24.0506i	0.781540	+	0.781540i	0.980091	−	0.198551i	$-0.0636235\pi$
$947$	24.0506	+	24.0506i	0.781540	+	0.781540i	−0.198551	+	0.980091i	$0.563624\pi$
$948$	−3.70749	−	13.2904i	−0.120414	−	0.431653i
$949$	15.1540	−	15.1540i	0.491919	−	0.491919i
$950$	−22.8827	−	39.1692i	−0.742412	−	1.27082i
$951$			25.9124i			0.840269i
$952$	−2.03593	−	1.97431i	−0.0659850	−	0.0639877i
$953$		−	16.5303i		−	0.535468i	−0.963493	−	0.267734i	$-0.913725\pi$
$953$		−	16.5303i		−	0.535468i	0.963493	−	0.267734i	$-0.0862748\pi$
$954$	4.82570	−	2.81918i	0.156238	−	0.0912742i
$955$	−23.9918	+	23.9918i	−0.776357	+	0.776357i
$956$	−17.6166	−	9.93174i	−0.569762	−	0.321215i
$957$	−8.47825	−	8.47825i	−0.274063	−	0.274063i
$958$	−4.38660	+	16.7130i	−0.141725	+	0.539972i
$959$	15.1267			0.488465
$960$	−0.920959	−	29.9576i	−0.0297238	−	0.966878i
$961$	67.2785			2.17027
$962$	−10.6132	+	40.4362i	−0.342182	+	1.30371i
$963$	−7.17498	−	7.17498i	−0.231210	−	0.231210i
$964$	20.0554	+	11.3066i	0.645940	+	0.364162i
$965$	−31.0574	+	31.0574i	−0.999772	+	0.999772i
$966$	−7.13110	+	4.16599i	−0.229439	+	0.134038i
$967$		−	36.4090i		−	1.17083i	−0.810732	−	0.585417i	$-0.800931\pi$
$967$		−	36.4090i		−	1.17083i	0.810732	−	0.585417i	$-0.199069\pi$
$968$	−13.2463	−	12.8453i	−0.425751	−	0.412864i
$969$			3.54988i			0.114039i
$970$	−4.79896	−	8.21459i	−0.154085	−	0.263754i
$971$	3.58188	−	3.58188i	0.114948	−	0.114948i	−0.647293	−	0.762241i	$-0.724099\pi$
$971$	3.58188	−	3.58188i	0.114948	−	0.114948i	0.762241	+	0.647293i	$0.224099\pi$
$972$	0.537401	+	1.92645i	0.0172371	+	0.0617908i
$973$	−0.621557	−	0.621557i	−0.0199262	−	0.0199262i
$974$	32.3667	+	8.49518i	1.03710	+	0.272203i
$975$	−39.3083			−1.25887
$976$	13.5549	−	55.0773i	0.433882	−	1.76298i
$977$	−28.4623			−0.910590			−0.455295	−	0.890341i	$-0.650466\pi$
$977$	−28.4623			−0.910590			−0.455295	+	0.890341i	$0.650466\pi$
$978$	17.3816	+	4.56210i	0.555803	+	0.145880i
$979$	45.9899	+	45.9899i	1.46984	+	1.46984i
$980$	−43.2655	+	12.0693i	−1.38207	+	0.385541i
$981$	−13.4804	+	13.4804i	−0.430395	+	0.430395i
$982$	−10.6511	−	18.2319i	−0.339890	−	0.581804i
$983$			2.45969i			0.0784520i	0.999230	+	0.0392260i	$0.0124892\pi$
$983$			2.45969i			0.0784520i	−0.999230	+	0.0392260i	$0.987511\pi$
$984$	0.324632	+	21.1247i	0.0103489	+	0.673432i
$985$			26.6312i			0.848541i
$986$	−3.49754	+	2.04326i	−0.111384	+	0.0650707i
$987$	−9.63237	+	9.63237i	−0.306602	+	0.306602i
$988$	15.1678	−	26.9041i	0.482551	−	0.855935i
$989$	−0.964822	−	0.964822i	−0.0306795	−	0.0306795i
$990$	−5.63064	+	21.4528i	−0.178954	+	0.681814i
$991$	10.5632			0.335550			0.167775	−	0.985825i	$-0.446342\pi$
$991$	10.5632			0.335550			0.167775	+	0.985825i	$0.446342\pi$
$992$	−53.7792	+	15.8968i	−1.70749	+	0.504724i
$993$	−10.9502			−0.347495
$994$	4.37859	−	16.6824i	0.138880	−	0.529135i
$995$	28.8199	+	28.8199i	0.913652	+	0.913652i
$996$	4.62508	−	8.20382i	0.146551	−	0.259948i
$997$	−15.7306	+	15.7306i	−0.498194	+	0.498194i	−0.910876	−	0.412681i	$-0.864592\pi$
$997$	−15.7306	+	15.7306i	−0.498194	+	0.498194i	0.412681	+	0.910876i	$0.364592\pi$
$998$	−33.8793	+	19.7923i	−1.07243	+	0.626515i
$999$		−	6.79539i		−	0.214997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	816.2.u.a.205.14	✓	64
16.5	even	4	inner	816.2.u.a.613.14	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
816.2.u.a.205.14	✓	64	1.1	even	1	trivial
816.2.u.a.613.14	yes	64	16.5	even	4	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:	\( N \)	\(=\)	\( 816 = 2^{4} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	816.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.359024 + 1.36788i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.74220 - 0.982204i) q^{4} +(2.64915 - 2.64915i) q^{5} +(-1.22111 + 0.713371i) q^{6} +1.00268i q^{7} +(1.96903 - 2.03050i) q^{8} +1.00000i q^{9} +(2.67262 + 4.57484i) q^{10} +(2.96004 - 2.96004i) q^{11} +(-0.537401 - 1.92645i) q^{12} +(-3.07604 - 3.07604i) q^{13} +(-1.37155 - 0.359986i) q^{14} +3.74647 q^{15} +(2.07055 + 3.42240i) q^{16} -1.00000 q^{17} +(-1.36788 - 0.359024i) q^{18} +(-2.51014 - 2.51014i) q^{19} +(-7.21738 + 2.01336i) q^{20} +(-0.709001 + 0.709001i) q^{21} +(2.98626 + 5.11171i) q^{22} -5.82426i q^{23} +(2.82809 - 0.0434604i) q^{24} -9.03603i q^{25} +(5.31203 - 3.10329i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(0.984836 - 1.74687i) q^{28} +(-2.02532 - 2.02532i) q^{29} +(-1.34507 + 5.12473i) q^{30} +9.91355 q^{31} +(-5.42482 + 1.60354i) q^{32} +4.18613 q^{33} +(0.359024 - 1.36788i) q^{34} +(2.65625 + 2.65625i) q^{35} +(0.982204 - 1.74220i) q^{36} +(-4.80507 + 4.80507i) q^{37} +(4.33478 - 2.53238i) q^{38} -4.35017i q^{39} +(-0.162823 - 10.5954i) q^{40} +7.46961i q^{41} +(-0.715282 - 1.22438i) q^{42} +(0.165656 - 0.165656i) q^{43} +(-8.06436 + 2.24963i) q^{44} +(2.64915 + 2.64915i) q^{45} +(7.96690 + 2.09105i) q^{46} +13.5858 q^{47} +(-0.955904 + 3.88410i) q^{48} +5.99464 q^{49} +(12.3602 + 3.24415i) q^{50} +(-0.707107 - 0.707107i) q^{51} +(2.33779 + 8.38038i) q^{52} +(-2.79442 + 2.79442i) q^{53} +(-0.713371 - 1.22111i) q^{54} -15.6832i q^{55} +(2.03593 + 1.97431i) q^{56} -3.54988i q^{57} +(3.49754 - 2.04326i) q^{58} +(-5.98782 + 5.98782i) q^{59} +(-6.52711 - 3.67980i) q^{60} +(-10.0269 - 10.0269i) q^{61} +(-3.55920 + 13.5606i) q^{62} -1.00268 q^{63} +(-0.245820 - 7.99622i) q^{64} -16.2978 q^{65} +(-1.50292 + 5.72613i) q^{66} +(1.87687 + 1.87687i) q^{67} +(1.74220 + 0.982204i) q^{68} +(4.11837 - 4.11837i) q^{69} +(-4.58710 + 2.67978i) q^{70} +12.1632i q^{71} +(2.03050 + 1.96903i) q^{72} +4.92646i q^{73} +(-4.84764 - 8.29790i) q^{74} +(6.38944 - 6.38944i) q^{75} +(1.90771 + 6.83866i) q^{76} +(2.96797 + 2.96797i) q^{77} +(5.95053 + 1.56182i) q^{78} +6.89893 q^{79} +(14.5517 + 3.58126i) q^{80} -1.00000 q^{81} +(-10.2175 - 2.68177i) q^{82} +(3.32968 + 3.32968i) q^{83} +(1.93161 - 0.538840i) q^{84} +(-2.64915 + 2.64915i) q^{85} +(0.167123 + 0.286072i) q^{86} -2.86424i q^{87} +(-0.181931 - 11.8388i) q^{88} +15.5369i q^{89} +(-4.57484 + 2.67262i) q^{90} +(3.08428 - 3.08428i) q^{91} +(-5.72061 + 10.1470i) q^{92} +(7.00994 + 7.00994i) q^{93} +(-4.87764 + 18.5838i) q^{94} -13.2995 q^{95} +(-4.96980 - 2.70205i) q^{96} -1.79560 q^{97} +(-2.15222 + 8.19996i) q^{98} +(2.96004 + 2.96004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{4} + 12 q^{10} + 8 q^{11} - 8 q^{12} + 20 q^{14} + 24 q^{15} + 28 q^{16} - 64 q^{17} - 4 q^{18} - 48 q^{22} - 20 q^{26} + 16 q^{29} + 8 q^{30} - 24 q^{31} + 40 q^{32} - 24 q^{35} + 16 q^{37}+ \cdots + 8 q^{99}+O(q^{100}) \) 64 * q + 4 * q^4 + 12 * q^10 + 8 * q^11 - 8 * q^12 + 20 * q^14 + 24 * q^15 + 28 * q^16 - 64 * q^17 - 4 * q^18 - 48 * q^22 - 20 * q^26 + 16 * q^29 + 8 * q^30 - 24 * q^31 + 40 * q^32 - 24 * q^35 + 16 * q^37 - 12 * q^38 - 56 * q^40 + 8 * q^42 + 8 * q^43 + 24 * q^44 + 52 * q^46 + 64 * q^47 - 64 * q^49 + 68 * q^50 + 44 * q^52 - 16 * q^53 - 56 * q^56 + 4 * q^58 + 4 * q^60 + 76 * q^62 - 8 * q^63 + 52 * q^64 + 8 * q^66 + 16 * q^67 - 4 * q^68 - 136 * q^70 + 4 * q^72 - 84 * q^74 - 16 * q^75 - 20 * q^76 + 32 * q^77 + 24 * q^78 + 40 * q^79 + 56 * q^80 - 64 * q^81 + 64 * q^83 - 52 * q^84 - 44 * q^86 - 96 * q^88 - 20 * q^90 - 56 * q^91 + 32 * q^92 + 88 * q^94 - 48 * q^95 + 72 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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