LMFDB - Embedded newform 675.2.ba.b.68.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(32,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([10, 9]))

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

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

chi := DirichletCharacter("675.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.ba (of order $36$, degree $12$, 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			68.5
Character	$\chi$	$=$	675.68
Dual form			675.2.ba.b.407.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.606324 + 0.865920i) q^{2} +(-1.47671 + 0.905161i) q^{3} +(0.301851 + 0.829330i) q^{4} +(0.111569 - 1.82754i) q^{6} +(2.61975 - 1.22161i) q^{7} +(-2.94330 - 0.788655i) q^{8} +(1.36137 - 2.67333i) q^{9} +(1.51740 + 1.80836i) q^{11} +(-1.19642 - 0.951458i) q^{12} +(4.45519 - 3.11956i) q^{13} +(-0.530600 + 3.00918i) q^{14} +(1.11535 - 0.935892i) q^{16} +(2.67549 - 0.716894i) q^{17} +(1.48946 + 2.79974i) q^{18} +(5.35751 - 3.09316i) q^{19} +(-2.76286 + 4.17526i) q^{21} +(-2.48593 + 0.217491i) q^{22} +(0.301527 - 0.646627i) q^{23} +(5.06027 - 1.49954i) q^{24} +5.74930i q^{26} +(0.409444 + 5.18000i) q^{27} +(1.80389 + 1.80389i) q^{28} +(-0.623300 - 3.53491i) q^{29} +(-5.18043 + 1.88552i) q^{31} +(-0.397007 - 4.53781i) q^{32} +(-3.87762 - 1.29695i) q^{33} +(-1.00144 + 2.75143i) q^{34} +(2.62800 + 0.322074i) q^{36} +(-1.14193 - 4.26173i) q^{37} +(-0.569956 + 6.51463i) q^{38} +(-3.75534 + 8.63936i) q^{39} +(5.70140 + 1.00531i) q^{41} +(-1.94025 - 4.92398i) q^{42} +(-1.44271 - 0.126221i) q^{43} +(-1.04170 + 1.80428i) q^{44} +(0.377104 + 0.653164i) q^{46} +(4.38688 + 9.40770i) q^{47} +(-0.799924 + 2.39162i) q^{48} +(0.871236 - 1.03830i) q^{49} +(-3.30202 + 3.48039i) q^{51} +(3.93195 + 2.75318i) q^{52} +(-7.22940 + 7.22940i) q^{53} +(-4.73372 - 2.78621i) q^{54} +(-8.67413 + 1.52948i) q^{56} +(-5.11170 + 9.41712i) q^{57} +(3.43887 + 1.60357i) q^{58} +(-6.27320 - 5.26384i) q^{59} +(2.64019 + 0.960952i) q^{61} +(1.50831 - 5.62907i) q^{62} +(0.300676 - 8.66650i) q^{63} +(6.69194 + 3.86359i) q^{64} +(3.47414 - 2.57134i) q^{66} +(4.28254 + 6.11610i) q^{67} +(1.40214 + 2.00246i) q^{68} +(0.140033 + 1.22781i) q^{69} +(-4.24004 - 2.44799i) q^{71} +(-6.11524 + 6.79476i) q^{72} +(-1.80353 + 6.73088i) q^{73} +(4.38269 + 1.59517i) q^{74} +(4.18242 + 3.50947i) q^{76} +(6.18430 + 2.88379i) q^{77} +(-5.20404 - 8.49007i) q^{78} +(12.8661 - 2.26863i) q^{79} +(-5.29336 - 7.27876i) q^{81} +(-4.32741 + 4.32741i) q^{82} +(3.90587 + 2.73492i) q^{83} +(-4.29664 - 1.03102i) q^{84} +(0.984048 - 1.17274i) q^{86} +(4.12010 + 4.65586i) q^{87} +(-3.03998 - 6.51925i) q^{88} +(-3.33276 - 5.77251i) q^{89} +(7.86060 - 13.6150i) q^{91} +(0.627283 + 0.0548802i) q^{92} +(5.94331 - 7.47350i) q^{93} +(-10.8062 - 1.90542i) q^{94} +(4.69371 + 6.34168i) q^{96} +(1.59893 - 18.2758i) q^{97} +(0.370833 + 1.38397i) q^{98} +(6.90008 - 1.59465i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.606324	+	0.865920i	−0.428736	+	0.612298i	−0.974159	−	0.225863i	$-0.927480\pi$
$2$	−0.606324	+	0.865920i	−0.428736	+	0.612298i	0.545424	+	0.838161i	$0.316369\pi$
$3$	−1.47671	+	0.905161i	−0.852581	+	0.522595i
$3$	−1.47671	+	0.905161i	−0.852581	+	0.522595i
$4$	0.301851	+	0.829330i	0.150926	+	0.414665i
$5$		0			0
$5$		0			0
$6$	0.111569	−	1.82754i	0.0455480	−	0.746089i
$7$	2.61975	−	1.22161i	0.990171	−	0.461725i	0.141096	−	0.989996i	$-0.454937\pi$
$7$	2.61975	−	1.22161i	0.990171	−	0.461725i	0.849076	+	0.528271i	$0.177160\pi$
$8$	−2.94330	−	0.788655i	−1.04061	−	0.278832i
$9$	1.36137	−	2.67333i	0.453789	−	0.891109i
$10$		0			0
$11$	1.51740	+	1.80836i	0.457512	+	0.545242i	0.944648	−	0.328084i	$-0.106403\pi$
$11$	1.51740	+	1.80836i	0.457512	+	0.545242i	−0.487136	+	0.873326i	$0.661959\pi$
$12$	−1.19642	−	0.951458i	−0.345378	−	0.274662i
$13$	4.45519	−	3.11956i	1.23565	−	0.865210i	0.241203	−	0.970475i	$-0.422458\pi$
$13$	4.45519	−	3.11956i	1.23565	−	0.865210i	0.994444	+	0.105265i	$0.0335690\pi$
$14$	−0.530600	+	3.00918i	−0.141809	+	0.804238i
$15$		0			0
$16$	1.11535	−	0.935892i	0.278838	−	0.233973i
$17$	2.67549	−	0.716894i	0.648901	−	0.173872i	0.0806688	−	0.996741i	$-0.474294\pi$
$17$	2.67549	−	0.716894i	0.648901	−	0.173872i	0.568232	+	0.822869i	$0.307628\pi$
$18$	1.48946	+	2.79974i	0.351069	+	0.659904i
$19$	5.35751	−	3.09316i	1.22910	−	0.709619i	0.262256	−	0.964998i	$-0.415534\pi$
$19$	5.35751	−	3.09316i	1.22910	−	0.709619i	0.966841	+	0.255379i	$0.0822003\pi$
$20$		0			0
$21$	−2.76286	+	4.17526i	−0.602906	+	0.911116i
$22$	−2.48593	+	0.217491i	−0.530002	+	0.0463692i
$23$	0.301527	−	0.646627i	0.0628728	−	0.134831i	−0.872361	−	0.488863i	$-0.837412\pi$
$23$	0.301527	−	0.646627i	0.0628728	−	0.134831i	0.935233	+	0.354032i	$0.115190\pi$
$24$	5.06027	−	1.49954i	1.03292	−	0.306093i
$25$		0			0
$26$			5.74930i			1.12753i
$27$	0.409444	+	5.18000i	0.0787976	+	0.996891i
$28$	1.80389	+	1.80389i	0.340903	+	0.340903i
$29$	−0.623300	−	3.53491i	−0.115744	−	0.656416i	−0.986379	−	0.164487i	$-0.947403\pi$
$29$	−0.623300	−	3.53491i	−0.115744	−	0.656416i	0.870635	−	0.491929i	$-0.163708\pi$
$30$		0			0
$31$	−5.18043	+	1.88552i	−0.930432	+	0.338650i	−0.762381	−	0.647129i	$-0.775970\pi$
$31$	−5.18043	+	1.88552i	−0.930432	+	0.338650i	−0.168051	+	0.985778i	$0.553747\pi$
$32$	−0.397007	−	4.53781i	−0.0701815	−	0.802178i
$33$	−3.87762	−	1.29695i	−0.675007	−	0.225769i
$34$	−1.00144	+	2.75143i	−0.171745	+	0.471866i
$35$		0			0
$36$	2.62800	+	0.322074i	0.438000	+	0.0536790i
$37$	−1.14193	−	4.26173i	−0.187732	−	0.700624i	−0.994029	−	0.109114i	$-0.965199\pi$
$37$	−1.14193	−	4.26173i	−0.187732	−	0.700624i	0.806298	−	0.591510i	$-0.201468\pi$
$38$	−0.569956	+	6.51463i	−0.0924591	+	1.05681i
$39$	−3.75534	+	8.63936i	−0.601335	+	1.38340i
$40$		0			0
$41$	5.70140	+	1.00531i	0.890409	+	0.157003i	0.600095	−	0.799928i	$-0.295129\pi$
$41$	5.70140	+	1.00531i	0.890409	+	0.157003i	0.290314	+	0.956932i	$0.406240\pi$
$42$	−1.94025	−	4.92398i	−0.299387	−	0.759786i
$43$	−1.44271	−	0.126221i	−0.220012	−	0.0192485i	−0.0233831	−	0.999727i	$-0.507444\pi$
$43$	−1.44271	−	0.126221i	−0.220012	−	0.0192485i	−0.196629	+	0.980478i	$0.562999\pi$
$44$	−1.04170	+	1.80428i	−0.157042	+	0.272005i
$45$		0			0
$46$	0.377104	+	0.653164i	0.0556010	+	0.0963037i
$47$	4.38688	+	9.40770i	0.639893	+	1.37225i	0.912081	+	0.410010i	$0.134475\pi$
$47$	4.38688	+	9.40770i	0.639893	+	1.37225i	−0.272188	+	0.962244i	$0.587747\pi$
$48$	−0.799924	+	2.39162i	−0.115459	+	0.345201i
$49$	0.871236	−	1.03830i	0.124462	−	0.148328i
$50$		0			0
$51$	−3.30202	+	3.48039i	−0.462375	+	0.487353i
$52$	3.93195	+	2.75318i	0.545263	+	0.381797i
$53$	−7.22940	+	7.22940i	−0.993035	+	0.993035i	−0.999976	−	0.00694140i	$-0.997790\pi$
$53$	−7.22940	+	7.22940i	−0.993035	+	0.993035i	0.00694140	+	0.999976i	$0.497790\pi$
$54$	−4.73372	−	2.78621i	−0.644177	−	0.379155i
$55$		0			0
$56$	−8.67413	+	1.52948i	−1.15913	+	0.204386i
$57$	−5.11170	+	9.41712i	−0.677061	+	1.24733i
$58$	3.43887	+	1.60357i	0.451546	+	0.210559i
$59$	−6.27320	−	5.26384i	−0.816701	−	0.685293i	0.135496	−	0.990778i	$-0.456737\pi$
$59$	−6.27320	−	5.26384i	−0.816701	−	0.685293i	−0.952197	+	0.305484i	$0.901182\pi$
$60$		0			0
$61$	2.64019	+	0.960952i	0.338042	+	0.123037i	0.505463	−	0.862848i	$-0.331322\pi$
$61$	2.64019	+	0.960952i	0.338042	+	0.123037i	−0.167421	+	0.985885i	$0.553544\pi$
$62$	1.50831	−	5.62907i	0.191555	−	0.714893i
$63$	0.300676	−	8.66650i	0.0378817	−	1.09188i
$64$	6.69194	+	3.86359i	0.836493	+	0.482949i
$65$		0			0
$66$	3.47414	−	2.57134i	0.427637	−	0.316510i
$67$	4.28254	+	6.11610i	0.523196	+	0.747201i	0.990592	−	0.136847i	$-0.0436968\pi$
$67$	4.28254	+	6.11610i	0.523196	+	0.747201i	−0.467396	+	0.884048i	$0.654808\pi$
$68$	1.40214	+	2.00246i	0.170034	+	0.242834i
$69$	0.140033	+	1.22781i	0.0168579	+	0.147811i
$70$		0			0
$71$	−4.24004	−	2.44799i	−0.503200	−	0.290523i	0.226834	−	0.973933i	$-0.427162\pi$
$71$	−4.24004	−	2.44799i	−0.503200	−	0.290523i	−0.730034	+	0.683411i	$0.760496\pi$
$72$	−6.11524	+	6.79476i	−0.720688	+	0.800770i
$73$	−1.80353	+	6.73088i	−0.211088	+	0.787790i	0.776420	+	0.630216i	$0.217034\pi$
$73$	−1.80353	+	6.73088i	−0.211088	+	0.787790i	−0.987507	+	0.157574i	$0.949633\pi$
$74$	4.38269	+	1.59517i	0.509478	+	0.185435i
$75$		0			0
$76$	4.18242	+	3.50947i	0.479756	+	0.402563i
$77$	6.18430	+	2.88379i	0.704767	+	0.328638i
$78$	−5.20404	−	8.49007i	−0.589242	−	0.961311i
$79$	12.8661	−	2.26863i	1.44754	−	0.255241i	0.606015	−	0.795453i	$-0.292767\pi$
$79$	12.8661	−	2.26863i	1.44754	−	0.255241i	0.841529	+	0.540212i	$0.181656\pi$
$80$		0			0
$81$	−5.29336	−	7.27876i	−0.588151	−	0.808751i
$82$	−4.32741	+	4.32741i	−0.477883	+	0.477883i
$83$	3.90587	+	2.73492i	0.428724	+	0.300196i	0.767951	−	0.640509i	$-0.221276\pi$
$83$	3.90587	+	2.73492i	0.428724	+	0.300196i	−0.339227	+	0.940705i	$0.610165\pi$
$84$	−4.29664	−	1.03102i	−0.468802	−	0.112493i
$85$		0			0
$86$	0.984048	−	1.17274i	0.106113	−	0.126460i
$87$	4.12010	+	4.65586i	0.441721	+	0.499161i
$88$	−3.03998	−	6.51925i	−0.324063	−	0.694955i
$89$	−3.33276	−	5.77251i	−0.353272	−	0.611885i	0.633549	−	0.773703i	$-0.281598\pi$
$89$	−3.33276	−	5.77251i	−0.353272	−	0.611885i	−0.986821	+	0.161818i	$0.948264\pi$
$90$		0			0
$91$	7.86060	−	13.6150i	0.824014	−	1.42723i
$92$	0.627283	+	0.0548802i	0.0653988	+	0.00572165i
$93$	5.94331	−	7.47350i	0.616292	−	0.774966i
$94$	−10.8062	−	1.90542i	−1.11457	−	0.196529i
$95$		0			0
$96$	4.69371	+	6.34168i	0.479050	+	0.647245i
$97$	1.59893	−	18.2758i	0.162346	−	1.85563i	−0.281548	−	0.959547i	$-0.590848\pi$
$97$	1.59893	−	18.2758i	0.162346	−	1.85563i	0.443894	−	0.896079i	$-0.353597\pi$
$98$	0.370833	+	1.38397i	0.0374597	+	0.139802i
$99$	6.90008	−	1.59465i	0.693484	−	0.160269i
$100$		0			0
$101$	−1.15191	+	3.16484i	−0.114619	+	0.314913i	−0.983716	−	0.179728i	$-0.942478\pi$
$101$	−1.15191	+	3.16484i	−0.114619	+	0.314913i	0.869097	+	0.494641i	$0.164701\pi$
$102$	−1.01165	−	4.96953i	−0.100168	−	0.492057i
$103$	0.316137	+	3.61346i	0.0311499	+	0.356045i	0.995734	+	0.0922694i	$0.0294121\pi$
$103$	0.316137	+	3.61346i	0.0311499	+	0.356045i	−0.964584	+	0.263775i	$0.915032\pi$
$104$	−15.5732	+	5.66819i	−1.52708	+	0.555812i
$105$		0			0
$106$	−1.87673	−	10.6434i	−0.182284	−	1.03378i
$107$	−4.03460	−	4.03460i	−0.390039	−	0.390039i	0.484662	−	0.874701i	$-0.338943\pi$
$107$	−4.03460	−	4.03460i	−0.390039	−	0.390039i	−0.874701	+	0.484662i	$0.838943\pi$
$108$	−4.17233	+	1.90315i	−0.401483	+	0.183131i
$109$			15.8226i			1.51553i	0.652527	+	0.757765i	$0.273709\pi$
$109$			15.8226i			1.51553i	−0.652527	+	0.757765i	$0.726291\pi$
$110$		0			0
$111$	5.54385	+	5.25972i	0.526199	+	0.499231i
$112$	1.77865	−	3.81433i	0.168067	−	0.360420i
$113$	−2.65880	+	0.232615i	−0.250119	+	0.0218825i	−0.211526	−	0.977372i	$-0.567843\pi$
$113$	−2.65880	+	0.232615i	−0.250119	+	0.0218825i	−0.0385931	+	0.999255i	$0.512288\pi$
$114$	−5.05513	−	10.1361i	−0.473456	−	0.949337i
$115$		0			0
$116$	2.74346	−	1.58394i	0.254724	−	0.147065i
$117$	−2.27446	−	16.1570i	−0.210273	−	1.49372i
$118$	8.36165	−	2.24050i	0.769753	−	0.206255i
$119$	6.13333	−	5.14648i	0.562242	−	0.471777i
$120$		0			0
$121$	0.942447	−	5.34488i	0.0856770	−	0.485898i
$122$	−2.43292	+	1.70355i	−0.220266	+	0.154232i
$123$	−9.32930	+	3.67613i	−0.841195	+	0.331466i
$124$	−3.12744	−	3.72713i	−0.280852	−	0.334707i
$125$		0			0
$126$	7.32219	+	5.51507i	0.652312	+	0.491321i
$127$	−3.15881	−	0.846401i	−0.280299	−	0.0751059i	0.115931	−	0.993257i	$-0.463015\pi$
$127$	−3.15881	−	0.846401i	−0.280299	−	0.0751059i	−0.396230	+	0.918151i	$0.629682\pi$
$128$	0.853671	−	0.398073i	0.0754546	−	0.0351850i
$129$	2.24472	−	1.11950i	0.197637	−	0.0985661i
$130$		0			0
$131$	0.497235	+	1.36614i	0.0434436	+	0.119360i	0.959517	−	0.281649i	$-0.0908815\pi$
$131$	0.497235	+	1.36614i	0.0434436	+	0.119360i	−0.916074	+	0.401010i	$0.868659\pi$
$132$	−0.0948693	−	3.60731i	−0.00825731	−	0.313976i
$133$	10.2567	−	14.6481i	0.889368	−	1.27015i
$134$	−7.89266			−0.681822
$135$		0			0
$136$	−8.44014			−0.723736
$137$	9.15193	−	13.0703i	0.781902	−	1.11667i	−0.208442	−	0.978035i	$-0.566839\pi$
$137$	9.15193	−	13.0703i	0.781902	−	1.11667i	0.990343	−	0.138637i	$-0.0442720\pi$
$138$	−1.14809	−	0.623196i	−0.0977322	−	0.0530499i
$139$	3.12149	+	8.57623i	0.264762	+	0.727426i	0.998830	+	0.0483514i	$0.0153967\pi$
$139$	3.12149	+	8.57623i	0.264762	+	0.727426i	−0.734069	+	0.679075i	$0.762381\pi$
$140$		0			0
$141$	−14.9937	−	9.92164i	−1.26269	−	0.835553i
$142$	4.69060	−	2.18726i	0.393626	−	0.183551i
$143$	12.4016	+	3.32299i	1.03707	+	0.277883i
$144$	−0.983543	−	4.25580i	−0.0819619	−	0.354650i
$145$		0			0
$146$	−4.73488	−	5.64281i	−0.391861	−	0.467002i
$147$	−0.346738	+	2.32188i	−0.0285985	+	0.191505i
$148$	3.18968	−	2.23344i	0.262190	−	0.183588i
$149$	−1.63395	+	9.26659i	−0.133858	+	0.759149i	0.841789	+	0.539806i	$0.181502\pi$
$149$	−1.63395	+	9.26659i	−0.133858	+	0.759149i	−0.975648	+	0.219343i	$0.929609\pi$
$150$		0			0
$151$	−0.808803	+	0.678666i	−0.0658194	+	0.0552291i	−0.675104	−	0.737723i	$-0.735901\pi$
$151$	−0.808803	+	0.678666i	−0.0658194	+	0.0552291i	0.609284	+	0.792952i	$0.291457\pi$
$152$	−18.2082	+	4.87887i	−1.47688	+	0.395729i
$153$	1.72582	−	8.12841i	0.139525	−	0.657143i
$154$	−6.24682	+	3.60660i	−0.503383	+	0.290628i
$155$		0			0
$156$	−8.29843	−	0.506611i	−0.664406	−	0.0405613i
$157$	−22.2338	+	1.94520i	−1.77445	+	0.155244i	−0.926860	−	0.375408i	$-0.877503\pi$
$157$	−22.2338	+	1.94520i	−1.77445	+	0.155244i	−0.847590	+	0.530652i	$0.821947\pi$
$158$	−5.83654	+	12.5165i	−0.464330	+	0.995759i
$159$	4.13198	−	17.2195i	0.327687	−	1.36560i
$160$		0			0
$161$		−	2.06235i		−	0.162536i
$162$	9.51231	−	0.170346i	0.747358	−	0.0133837i
$163$	1.74889	+	1.74889i	0.136983	+	0.136983i	0.772274	−	0.635290i	$-0.219119\pi$
$163$	1.74889	+	1.74889i	0.136983	+	0.136983i	−0.635290	+	0.772274i	$0.719119\pi$
$164$	0.887241	+	5.03179i	0.0692819	+	0.392917i
$165$		0			0
$166$	−4.73644	+	1.72392i	−0.367619	+	0.133802i
$167$	0.634893	+	7.25686i	0.0491295	+	0.561553i	0.980373	+	0.197154i	$0.0631699\pi$
$167$	0.634893	+	7.25686i	0.0491295	+	0.561553i	−0.931243	+	0.364399i	$0.881275\pi$
$168$	11.4248	−	10.1101i	0.881441	−	0.780011i
$169$	5.67082	−	15.5805i	0.436217	−	1.19850i
$170$		0			0
$171$	−0.975496	−	18.5333i	−0.0745981	−	1.41728i
$172$	−0.330806	−	1.23458i	−0.0252237	−	0.0941362i
$173$	1.78680	−	20.4232i	0.135848	−	1.55275i	−0.556295	−	0.830985i	$-0.687778\pi$
$173$	1.78680	−	20.4232i	0.135848	−	1.55275i	0.692143	−	0.721760i	$-0.256667\pi$
$174$	−6.52972	+	0.744716i	−0.495017	+	0.0564568i
$175$		0			0
$176$	3.38487	+	0.596843i	0.255144	+	0.0449887i
$177$	14.0283	+	2.09493i	1.05443	+	0.157464i
$178$	7.01926	+	0.614106i	0.526116	+	0.0460292i
$179$	−7.17079	+	12.4202i	−0.535970	+	0.928327i	0.463146	+	0.886282i	$0.346721\pi$
$179$	−7.17079	+	12.4202i	−0.535970	+	0.928327i	−0.999116	+	0.0420450i	$0.986613\pi$
$180$		0			0
$181$	1.03474	+	1.79221i	0.0769112	+	0.133214i	0.901916	−	0.431912i	$-0.142161\pi$
$181$	1.03474	+	1.79221i	0.0769112	+	0.133214i	−0.825005	+	0.565126i	$0.808828\pi$
$182$	7.02339	+	15.0617i	0.520609	+	1.11645i
$183$	−4.76862	+	0.970750i	−0.352507	+	0.0717599i
$184$	−1.39745	+	1.66542i	−0.103021	+	0.122776i
$185$		0			0
$186$	2.86788	+	9.67779i	0.210283	+	0.709610i
$187$	5.35618	+	3.75043i	0.391682	+	0.274259i
$188$	−6.47790	+	6.47790i	−0.472449	+	0.472449i
$189$	7.40057	+	13.0701i	0.538312	+	0.950710i
$190$		0			0
$191$	22.9618	−	4.04878i	1.66145	−	0.292959i	0.737467	−	0.675383i	$-0.236022\pi$
$191$	22.9618	−	4.04878i	1.66145	−	0.292959i	0.923987	+	0.382424i	$0.124911\pi$
$192$	−13.3793	+	0.351864i	−0.965564	+	0.0253936i
$193$	0.282417	+	0.131693i	0.0203288	+	0.00947948i	0.432756	−	0.901511i	$-0.357541\pi$
$193$	0.282417	+	0.131693i	0.0203288	+	0.00947948i	−0.412427	+	0.910991i	$0.635319\pi$
$194$	14.8559	+	12.4656i	1.06659	+	0.894977i
$195$		0			0
$196$	1.12408	+	0.409130i	0.0802911	+	0.0292236i
$197$	0.840756	−	3.13774i	0.0599014	−	0.223555i	−0.929486	−	0.368858i	$-0.879749\pi$
$197$	0.840756	−	3.13774i	0.0599014	−	0.223555i	0.989387	+	0.145303i	$0.0464156\pi$
$198$	−2.80284	+	6.94179i	−0.199189	+	0.493332i
$199$	−5.52277	−	3.18857i	−0.391499	−	0.226032i	0.291310	−	0.956629i	$-0.405909\pi$
$199$	−5.52277	−	3.18857i	−0.391499	−	0.226032i	−0.682809	+	0.730596i	$0.739242\pi$
$200$		0			0
$201$	−11.8601	−	5.15534i	−0.836550	−	0.363630i
$202$	−2.04207	−	2.91638i	−0.143679	−	0.205196i
$203$	−5.95116	−	8.49914i	−0.417690	−	0.596523i
$204$	−3.88311	−	1.68790i	−0.271872	−	0.118177i
$205$		0			0
$206$	−3.32065	−	1.91718i	−0.231360	−	0.133576i
$207$	−1.31816	−	1.68638i	−0.0916183	−	0.117211i
$208$	2.04954	−	7.64899i	0.142110	−	0.530362i
$209$	13.7230	+	4.99477i	0.949241	+	0.345495i
$210$		0			0
$211$	4.91430	+	4.12359i	0.338314	+	0.283879i	0.796077	−	0.605195i	$-0.206905\pi$
$211$	4.91430	+	4.12359i	0.338314	+	0.283879i	−0.457763	+	0.889074i	$0.651349\pi$
$212$	−8.17776	−	3.81335i	−0.561651	−	0.261902i
$213$	8.47715	−	0.222942i	0.580844	−	0.0152757i
$214$	5.93991	−	1.04737i	0.406044	−	0.0715965i
$215$		0			0
$216$	2.88011	−	15.5692i	0.195967	−	1.05935i
$217$	−11.2680	+	11.2680i	−0.764925	+	0.764925i
$218$	−13.7011	−	9.59362i	−0.927956	−	0.649762i
$219$	−3.42923	−	11.5721i	−0.231726	−	0.781968i
$220$		0			0
$221$	9.68341	−	11.5402i	0.651376	−	0.776280i
$222$	−7.91587	+	1.61143i	−0.531278	+	0.108152i
$223$	4.39023	+	9.41489i	0.293992	+	0.630467i	0.996714	−	0.0809965i	$-0.0258103\pi$
$223$	4.39023	+	9.41489i	0.293992	+	0.630467i	−0.702723	+	0.711464i	$0.748032\pi$
$224$	−6.58348	−	11.4029i	−0.439877	−	0.761889i
$225$		0			0
$226$	1.41067	−	2.44335i	0.0938361	−	0.162529i
$227$	3.11245	+	0.272304i	0.206580	+	0.0180734i	0.189976	−	0.981789i	$-0.439159\pi$
$227$	3.11245	+	0.272304i	0.206580	+	0.0180734i	0.0166042	+	0.999862i	$0.494714\pi$
$228$	−9.35287	−	1.39671i	−0.619409	−	0.0924996i
$229$	−23.1368	−	4.07964i	−1.52892	−	0.269590i	−0.654990	−	0.755638i	$-0.727327\pi$
$229$	−23.1368	−	4.07964i	−1.52892	−	0.269590i	−0.873933	+	0.486047i	$0.838438\pi$
$230$		0			0
$231$	−11.7427	+	1.33926i	−0.772616	+	0.0881170i
$232$	−0.953265	+	10.8959i	−0.0625849	+	0.715349i
$233$	0.858538	+	3.20411i	0.0562447	+	0.209908i	0.988329	−	0.152333i	$-0.0486785\pi$
$233$	0.858538	+	3.20411i	0.0562447	+	0.209908i	−0.932085	+	0.362241i	$0.882012\pi$
$234$	15.3698	+	7.82690i	1.00475	+	0.511661i
$235$		0			0
$236$	2.47188	−	6.79145i	0.160906	−	0.442085i
$237$	−16.9460	+	14.9960i	−1.10076	+	0.974093i
$238$	0.737653	+	8.43141i	0.0478149	+	0.546527i
$239$	15.9837	−	5.81759i	1.03390	−	0.376309i	0.231335	−	0.972874i	$-0.425691\pi$
$239$	15.9837	−	5.81759i	1.03390	−	0.376309i	0.802564	+	0.596566i	$0.203468\pi$
$240$		0			0
$241$	3.22231	+	18.2746i	0.207567	+	1.17717i	0.893349	+	0.449364i	$0.148349\pi$
$241$	3.22231	+	18.2746i	0.207567	+	1.17717i	−0.685782	+	0.727807i	$0.740540\pi$
$242$	4.05681	+	4.05681i	0.260782	+	0.260782i
$243$	14.4052	+	5.95729i	0.924096	+	0.382160i
$244$			2.47965i			0.158744i
$245$		0			0
$246$	2.47334	−	10.3074i	0.157695	−	0.657173i
$247$	14.2194	−	30.4937i	0.904761	−	1.94027i
$248$	16.7346	−	1.46409i	1.06265	−	0.0929695i
$249$	−8.24339	−	0.503250i	−0.522403	−	0.0318922i
$250$		0			0
$251$	−13.1493	+	7.59178i	−0.829979	+	0.479189i	−0.853846	−	0.520527i	$-0.825736\pi$
$251$	−13.1493	+	7.59178i	−0.829979	+	0.479189i	0.0238664	+	0.999715i	$0.492402\pi$
$252$	7.27814	−	2.36663i	0.458480	−	0.149084i
$253$	1.62687	−	0.435919i	0.102281	−	0.0274060i
$254$	2.64818	−	2.22208i	0.166161	−	0.139426i
$255$		0			0
$256$	−2.85653	+	16.2002i	−0.178533	+	1.01251i
$257$	−7.11815	+	4.98418i	−0.444018	+	0.310905i	−0.774118	−	0.633041i	$-0.781806\pi$
$257$	−7.11815	+	4.98418i	−0.444018	+	0.310905i	0.330100	+	0.943946i	$0.392917\pi$
$258$	−0.391636	+	2.62253i	−0.0243822	+	0.163271i
$259$	−8.19772	−	9.76966i	−0.509382	−	0.607057i
$260$		0			0
$261$	−10.2985	−	3.14602i	−0.637462	−	0.194734i
$262$	−1.48446	−	0.397759i	−0.0917099	−	0.0245736i
$263$	21.3889	−	9.97382i	1.31890	−	0.615012i	0.369541	−	0.929214i	$-0.379515\pi$
$263$	21.3889	−	9.97382i	1.31890	−	0.615012i	0.949356	+	0.314203i	$0.101737\pi$
$264$	10.3902	+	6.87540i	0.639470	+	0.423152i
$265$		0			0
$266$	6.46518	+	17.7629i	0.396406	+	1.08912i
$267$	10.1466	+	5.50766i	0.620961	+	0.337063i
$268$	−3.77957	+	5.39779i	−0.230874	+	0.329723i
$269$	−10.2124			−0.622659			−0.311330	−	0.950302i	$-0.600774\pi$
$269$	−10.2124			−0.622659			−0.311330	+	0.950302i	$0.600774\pi$
$270$		0			0
$271$	4.84409			0.294258			0.147129	−	0.989117i	$-0.452997\pi$
$271$	4.84409			0.294258			0.147129	+	0.989117i	$0.452997\pi$
$272$	2.31318	−	3.30356i	0.140257	−	0.200308i
$273$	0.715877	+	27.2205i	0.0433268	+	1.64746i
$274$	5.76881	+	15.8497i	0.348506	+	0.957514i
$275$		0			0
$276$	−0.975993	+	0.486750i	−0.0587479	+	0.0292989i
$277$	12.2491	−	5.71185i	0.735978	−	0.343192i	−0.0182248	−	0.999834i	$-0.505801\pi$
$277$	12.2491	−	5.71185i	0.735978	−	0.343192i	0.754203	+	0.656642i	$0.228024\pi$
$278$	−9.31897	−	2.49701i	−0.558914	−	0.149761i
$279$	−2.01184	+	16.4159i	−0.120446	+	0.982792i
$280$		0			0
$281$	−10.1156	−	12.0553i	−0.603445	−	0.719158i	0.374685	−	0.927152i	$-0.377751\pi$
$281$	−10.1156	−	12.0553i	−0.603445	−	0.719158i	−0.978130	+	0.207994i	$0.933306\pi$
$282$	17.6824	−	6.96758i	1.05297	−	0.414913i
$283$	−24.7001	+	17.2952i	−1.46827	+	1.02809i	−0.479680	+	0.877443i	$0.659247\pi$
$283$	−24.7001	+	17.2952i	−1.46827	+	1.02809i	−0.988587	+	0.150648i	$0.951864\pi$
$284$	0.750327	−	4.25532i	0.0445237	−	0.252507i
$285$		0			0
$286$	−10.3968	+	8.72397i	−0.614777	+	0.515859i
$287$	16.1643	−	4.33122i	0.954150	−	0.255664i
$288$	−12.6715	−	5.11629i	−0.746676	−	0.301480i
$289$	−8.07815	+	4.66392i	−0.475185	+	0.274348i
$290$		0			0
$291$	14.1814	+	28.4354i	0.831328	+	1.66691i
$292$	−6.12652	+	0.536001i	−0.358527	+	0.0313671i
$293$	−3.10333	+	6.65512i	−0.181299	+	0.388796i	−0.975863	−	0.218384i	$-0.929922\pi$
$293$	−3.10333	+	6.65512i	−0.181299	+	0.388796i	0.794564	+	0.607180i	$0.207699\pi$
$294$	−1.80033	−	1.70806i	−0.104997	−	0.0996160i
$295$		0			0
$296$			13.4441i			0.781424i
$297$	−8.74602	+	8.60053i	−0.507496	+	0.499053i
$298$	−7.03343	−	7.03343i	−0.407435	−	0.407435i
$299$	−0.673830	−	3.82148i	−0.0389686	−	0.221002i
$300$		0			0
$301$	−3.93374	+	1.43176i	−0.226737	+	0.0825254i
$302$	−0.0972742	−	1.11185i	−0.00559750	−	0.0639798i
$303$	−1.16365	−	5.71622i	−0.0668501	−	0.328388i
$304$	3.08065	−	8.46402i	0.176687	−	0.485445i
$305$		0			0
$306$	5.99214	+	6.42287i	0.342548	+	0.367171i
$307$	3.54038	+	13.2129i	0.202060	+	0.754099i	0.990326	+	0.138764i	$0.0443129\pi$
$307$	3.54038	+	13.2129i	0.202060	+	0.754099i	−0.788265	+	0.615336i	$0.789020\pi$
$308$	−0.524871	+	5.99930i	−0.0299073	+	0.341842i
$309$	−3.73760	−	5.04989i	−0.212625	−	0.287278i
$310$		0			0
$311$	3.80231	+	0.670449i	0.215609	+	0.0380177i	0.280409	−	0.959881i	$-0.409530\pi$
$311$	3.80231	+	0.670449i	0.215609	+	0.0380177i	−0.0648001	+	0.997898i	$0.520641\pi$
$312$	17.8666	−	22.4666i	1.01149	−	1.27192i
$313$	−24.5081	−	2.14418i	−1.38528	−	0.121196i	−0.629997	−	0.776597i	$-0.716944\pi$
$313$	−24.5081	−	2.14418i	−1.38528	−	0.121196i	−0.755281	+	0.655401i	$0.772500\pi$
$314$	11.7965	−	20.4321i	0.665714	−	1.15305i
$315$		0			0
$316$	5.76508	+	9.98541i	0.324311	+	0.561723i
$317$	6.97386	+	14.9555i	0.391691	+	0.839984i	0.998965	+	0.0454916i	$0.0144854\pi$
$317$	6.97386	+	14.9555i	0.391691	+	0.839984i	−0.607274	+	0.794493i	$0.707737\pi$
$318$	12.4054	+	14.0186i	0.695661	+	0.786123i
$319$	5.44660	−	6.49101i	0.304951	−	0.363427i
$320$		0			0
$321$	9.60991	+	2.30598i	0.536373	+	0.128707i
$322$	1.78583	+	1.25045i	0.0995203	+	0.0696849i
$323$	12.1165	−	12.1165i	0.674178	−	0.674178i
$324$	4.43868	−	6.58704i	0.246593	−	0.365947i
$325$		0			0
$326$	−2.57479	+	0.454005i	−0.142604	+	0.0251450i
$327$	−14.3220	−	23.3654i	−0.792009	−	1.29211i
$328$	−15.9881	−	7.45537i	−0.882794	−	0.411654i
$329$	22.9851	+	19.2867i	1.26721	+	1.06331i
$330$		0			0
$331$	−19.3973	−	7.06005i	−1.06617	−	0.388056i	−0.251429	−	0.967876i	$-0.580901\pi$
$331$	−19.3973	−	7.06005i	−1.06617	−	0.388056i	−0.814744	+	0.579820i	$0.803123\pi$
$332$	−1.08916	+	4.06479i	−0.0597752	+	0.223084i
$333$	−12.9476	−	2.74903i	−0.709523	−	0.150646i
$334$	−6.66881	−	3.85024i	−0.364901	−	0.210676i
$335$		0			0
$336$	0.826024	+	7.24263i	0.0450633	+	0.395118i
$337$	−6.00115	−	8.57053i	−0.326904	−	0.466867i	0.621735	−	0.783227i	$-0.286428\pi$
$337$	−6.00115	−	8.57053i	−0.326904	−	0.466867i	−0.948639	+	0.316361i	$0.897539\pi$
$338$	10.0531	+	14.3573i	0.546815	+	0.780933i
$339$	3.71573	−	2.75015i	0.201811	−	0.149367i
$340$		0			0
$341$	−11.2705	−	6.50701i	−0.610330	−	0.352374i
$342$	16.6398	+	10.3925i	0.899778	+	0.561961i
$343$	−4.22292	+	15.7602i	−0.228016	+	0.850968i
$344$	4.14679	+	1.50931i	0.223580	+	0.0813765i
$345$		0			0
$346$	16.6015	+	13.9303i	0.892500	+	0.748896i
$347$	−10.4146	−	4.85639i	−0.559083	−	0.260705i	0.122472	−	0.992472i	$-0.460918\pi$
$347$	−10.4146	−	4.85639i	−0.559083	−	0.260705i	−0.681554	+	0.731767i	$0.738696\pi$
$348$	−2.61759	+	4.82230i	−0.140317	+	0.258502i
$349$	−15.6377	+	2.75735i	−0.837067	+	0.147597i	−0.575719	−	0.817647i	$-0.695278\pi$
$349$	−15.6377	+	2.75735i	−0.837067	+	0.147597i	−0.261347	+	0.965245i	$0.584167\pi$
$350$		0			0
$351$	17.9835	+	21.8006i	0.959886	+	1.16363i
$352$	7.60358	−	7.60358i	0.405272	−	0.405272i
$353$	−7.10893	−	4.97772i	−0.378370	−	0.264938i	0.368885	−	0.929475i	$-0.379740\pi$
$353$	−7.10893	−	4.97772i	−0.378370	−	0.264938i	−0.747255	+	0.664538i	$0.768629\pi$
$354$	−10.3198	+	10.8772i	−0.548489	+	0.578118i
$355$		0			0
$356$	3.78131	−	4.50640i	0.200409	−	0.238838i
$357$	−4.39878	+	13.1515i	−0.232808	+	0.696053i
$358$	−6.40706	−	13.7400i	−0.338623	−	0.726180i
$359$	−10.2032	−	17.6725i	−0.538505	−	0.932718i	−0.998985	−	0.0450476i	$-0.985656\pi$
$359$	−10.2032	−	17.6725i	−0.538505	−	0.932718i	0.460480	−	0.887670i	$-0.347677\pi$
$360$		0			0
$361$	9.63526	−	16.6888i	0.507119	−	0.878356i
$362$	−2.17930	−	0.190664i	−0.114541	−	0.0100211i
$363$	3.44626	+	8.74593i	0.180881	+	0.459042i
$364$	13.6640	+	2.40933i	0.716189	+	0.126283i
$365$		0			0
$366$	2.05074	−	4.71784i	0.107194	−	0.246605i
$367$	−2.26163	+	25.8506i	−0.118056	+	1.34939i	0.673906	+	0.738818i	$0.264615\pi$
$367$	−2.26163	+	25.8506i	−0.118056	+	1.34939i	−0.791962	+	0.610571i	$0.790940\pi$
$368$	−0.268864	−	1.00341i	−0.0140155	−	0.0523066i
$369$	10.4492	−	13.8731i	0.543965	−	0.722206i
$370$		0			0
$371$	−10.1077	+	27.7707i	−0.524766	+	1.44178i
$372$	7.99199	+	2.67308i	0.414365	+	0.138593i
$373$	−0.416402	−	4.75950i	−0.0215605	−	0.246438i	−0.999325	−	0.0367323i	$-0.988305\pi$
$373$	−0.416402	−	4.75950i	−0.0215605	−	0.246438i	0.977765	−	0.209705i	$-0.0672505\pi$
$374$	−6.49515	+	2.36404i	−0.335856	+	0.122242i
$375$		0			0
$376$	−5.49248	−	31.1494i	−0.283253	−	1.60641i
$377$	−13.8043	−	13.8043i	−0.710956	−	0.710956i
$378$	−15.8048	−	1.51641i	−0.812911	−	0.0779958i
$379$			25.3002i			1.29958i	0.760112	+	0.649792i	$0.225144\pi$
$379$			25.3002i			1.29958i	−0.760112	+	0.649792i	$0.774856\pi$
$380$		0			0
$381$	5.43079	−	1.60934i	0.278228	−	0.0824491i
$382$	−10.4163	+	22.3379i	−0.532946	+	1.14291i
$383$	−12.2766	+	1.07406i	−0.627303	+	0.0548819i	−0.396375	−	0.918089i	$-0.629732\pi$
$383$	−12.2766	+	1.07406i	−0.627303	+	0.0548819i	−0.230929	+	0.972971i	$0.574176\pi$
$384$	−0.900307	+	1.36055i	−0.0459436	+	0.0694303i
$385$		0			0
$386$	−0.285272	+	0.164702i	−0.0145200	+	0.00838310i
$387$	−2.30149	+	3.68501i	−0.116991	+	0.187320i
$388$	15.6393	−	4.19054i	0.793965	−	0.212742i
$389$	−6.83430	+	5.73466i	−0.346513	+	0.290759i	−0.799388	−	0.600815i	$-0.794843\pi$
$389$	−6.83430	+	5.73466i	−0.346513	+	0.290759i	0.452875	+	0.891574i	$0.350398\pi$
$390$		0			0
$391$	0.343168	−	1.94620i	0.0173548	−	0.0984238i
$392$	−3.38317	+	2.36892i	−0.170876	+	0.119649i
$393$	−1.97085	−	1.56732i	−0.0994164	−	0.0790610i
$394$	2.20727	+	2.63052i	0.111200	+	0.132524i
$395$		0			0
$396$	3.40529	+	5.24109i	0.171122	+	0.263375i
$397$	13.1660	+	3.52782i	0.660782	+	0.177056i	0.573599	−	0.819136i	$-0.305547\pi$
$397$	13.1660	+	3.52782i	0.660782	+	0.177056i	0.0871833	+	0.996192i	$0.472213\pi$
$398$	6.10964	−	2.84897i	0.306249	−	0.142806i
$399$	−1.88733	+	30.9150i	−0.0944846	+	1.54768i
$400$		0			0
$401$	−1.00354	−	2.75721i	−0.0501146	−	0.137689i	0.912110	−	0.409945i	$-0.134452\pi$
$401$	−1.00354	−	2.75721i	−0.0501146	−	0.137689i	−0.962225	+	0.272257i	$0.912230\pi$
$402$	11.6552	−	7.14413i	0.581309	−	0.356317i
$403$	−17.1978	+	24.5610i	−0.856683	+	1.22347i
$404$	−2.97240			−0.147882
$405$		0			0
$406$	10.9679			0.544328
$407$	5.97399	−	8.53175i	0.296120	−	0.422903i
$408$	12.4637	−	7.63969i	0.617044	−	0.378221i
$409$	−9.80467	−	26.9381i	−0.484810	−	1.33200i	−0.905325	−	0.424719i	$-0.860373\pi$
$409$	−9.80467	−	26.9381i	−0.484810	−	1.33200i	0.420515	−	0.907285i	$-0.361849\pi$
$410$		0			0
$411$	−1.68404	+	27.5851i	−0.0830676	+	1.36067i
$412$	−2.90132	+	1.35291i	−0.142938	+	0.0666530i
$413$	−22.8645	−	6.12654i	−1.12509	−	0.301467i
$414$	2.25950	−	0.118928i	0.111048	−	0.00584500i
$415$		0			0
$416$	−15.9247	−	18.9783i	−0.780772	−	0.930488i
$417$	−12.3724	−	9.83918i	−0.605880	−	0.481827i
$418$	−12.6457	+	8.85459i	−0.618519	+	0.433092i
$419$	2.30839	−	13.0915i	0.112772	−	0.639563i	−0.875057	−	0.484020i	$-0.839176\pi$
$419$	2.30839	−	13.0915i	0.112772	−	0.639563i	0.987829	−	0.155543i	$-0.0497127\pi$
$420$		0			0
$421$	6.93437	−	5.81863i	0.337960	−	0.283582i	−0.457974	−	0.888966i	$-0.651425\pi$
$421$	6.93437	−	5.81863i	0.337960	−	0.283582i	0.795934	+	0.605383i	$0.206980\pi$
$422$	−6.55035	+	1.75516i	−0.318866	+	0.0854399i
$423$	31.1220	+	1.07975i	1.51320	+	0.0524993i
$424$	26.9798	−	15.5768i	1.31025	−	0.756476i
$425$		0			0
$426$	−4.94684	+	7.47571i	−0.239675	+	0.362199i
$427$	8.09054	−	0.707831i	0.391529	−	0.0342543i
$428$	2.12816	−	4.56386i	0.102869	−	0.220602i
$429$	−21.3214	+	6.31832i	−1.02941	+	0.305051i
$430$		0			0
$431$			0.295969i			0.0142563i	0.999975	+	0.00712817i	$0.00226899\pi$
$431$			0.295969i			0.0142563i	−0.999975	+	0.00712817i	$0.997731\pi$
$432$	5.30459	+	5.39433i	0.255217	+	0.259535i
$433$	−12.8171	−	12.8171i	−0.615949	−	0.615949i	0.328541	−	0.944490i	$-0.393443\pi$
$433$	−12.8171	−	12.8171i	−0.615949	−	0.615949i	−0.944490	+	0.328541i	$0.893443\pi$
$434$	−2.92514	−	16.5893i	−0.140411	−	0.796312i
$435$		0			0
$436$	−13.1221	+	4.77607i	−0.628437	+	0.228732i
$437$	−0.384686	−	4.39698i	−0.0184020	−	0.210336i
$438$	12.0997	+	4.04698i	0.578146	+	0.193372i
$439$	9.75841	−	26.8110i	0.465743	−	1.27962i	−0.455362	−	0.890306i	$-0.650490\pi$
$439$	9.75841	−	26.8110i	0.465743	−	1.27962i	0.921105	−	0.389313i	$-0.127288\pi$
$440$		0			0
$441$	−1.58964	−	3.74260i	−0.0756972	−	0.178219i
$442$	4.12164	+	15.3822i	0.196046	+	0.731655i
$443$	−3.51399	+	40.1651i	−0.166955	+	1.90830i	0.202878	+	0.979204i	$0.434970\pi$
$443$	−3.51399	+	40.1651i	−0.166955	+	1.90830i	−0.369833	+	0.929098i	$0.620585\pi$
$444$	−2.68863	+	6.18533i	−0.127597	+	0.293543i
$445$		0			0
$446$	−10.8144	−	1.90688i	−0.512079	−	0.0902933i
$447$	−5.97488	−	15.1631i	−0.282602	−	0.717190i
$448$	22.2510	+	1.94671i	1.05126	+	0.0919734i
$449$	3.91232	−	6.77634i	0.184634	−	0.319795i	−0.758819	−	0.651301i	$-0.774223\pi$
$449$	3.91232	−	6.77634i	0.184634	−	0.319795i	0.943453	+	0.331506i	$0.107557\pi$
$450$		0			0
$451$	6.83332	+	11.8357i	0.321768	+	0.557319i
$452$	−0.995476	−	2.13480i	−0.0468232	−	0.100413i
$453$	0.580068	−	1.73429i	0.0272540	−	0.0814841i
$454$	−2.12294	+	2.53003i	−0.0996347	+	0.118740i
$455$		0			0
$456$	22.4721	−	23.6860i	1.05235	−	1.10920i
$457$	−4.48957	−	3.14363i	−0.210013	−	0.147053i	0.463838	−	0.885920i	$-0.346472\pi$
$457$	−4.48957	−	3.14363i	−0.210013	−	0.147053i	−0.673851	+	0.738867i	$0.735361\pi$
$458$	17.5610	−	17.5610i	0.820573	−	0.820573i
$459$	4.80897	+	13.5655i	0.224464	+	0.633182i
$460$		0			0
$461$	29.6880	−	5.23480i	1.38271	−	0.243809i	0.567689	−	0.823243i	$-0.307837\pi$
$461$	29.6880	−	5.23480i	1.38271	−	0.243809i	0.815019	+	0.579434i	$0.196726\pi$
$462$	5.96021	−	10.9803i	0.277294	−	0.510850i
$463$	−0.163397	−	0.0761934i	−0.00759371	−	0.00354101i	0.418818	−	0.908070i	$-0.362445\pi$
$463$	−0.163397	−	0.0761934i	−0.00759371	−	0.00354101i	−0.426411	+	0.904529i	$0.640222\pi$
$464$	−4.00350	−	3.35933i	−0.185858	−	0.155953i
$465$		0			0
$466$	−3.29505	−	1.19930i	−0.152640	−	0.0555566i
$467$	3.26672	−	12.1916i	0.151166	−	0.564158i	−0.848238	−	0.529616i	$-0.822336\pi$
$467$	3.26672	−	12.1916i	0.151166	−	0.564158i	0.999403	−	0.0345422i	$-0.0109973\pi$
$468$	12.7130	−	6.76330i	0.587657	−	0.312634i
$469$	18.6907	+	10.7911i	0.863055	+	0.498285i
$470$		0			0
$471$	31.0722	−	22.9977i	1.43173	−	1.05968i
$472$	14.3126	+	20.4404i	0.658789	+	0.940848i
$473$	−1.96091	−	2.80048i	−0.0901629	−	0.128766i
$474$	−2.71055	−	23.7663i	−0.124500	−	1.09162i
$475$		0			0
$476$	6.11948	+	3.53308i	0.280486	+	0.161939i
$477$	9.48470	+	29.1684i	0.434274	+	1.33553i
$478$	−4.65373	+	17.3679i	−0.212857	+	0.794391i
$479$	33.4923	+	12.1902i	1.53030	+	0.556985i	0.963696	−	0.267003i	$-0.0860335\pi$
$479$	33.4923	+	12.1902i	1.53030	+	0.556985i	0.566607	+	0.823988i	$0.308256\pi$
$480$		0			0
$481$	−18.3822	−	15.4245i	−0.838157	−	0.703297i
$482$	−17.7781	−	8.29007i	−0.809771	−	0.377602i
$483$	1.86676	+	3.04550i	0.0849404	+	0.138575i
$484$	4.71715	−	0.831760i	0.214416	−	0.0378073i
$485$		0			0
$486$	−13.8928	+	8.86173i	−0.630189	+	0.401976i
$487$	−4.88907	+	4.88907i	−0.221545	+	0.221545i	−0.809149	−	0.587604i	$-0.800071\pi$
$487$	−4.88907	+	4.88907i	−0.221545	+	0.221545i	0.587604	+	0.809149i	$0.300071\pi$
$488$	−7.01302	−	4.91057i	−0.317464	−	0.222291i
$489$	−4.16563	−	0.999581i	−0.188376	−	0.0452026i
$490$		0			0
$491$	−16.6934	+	19.8944i	−0.753361	+	0.897821i	−0.997409	−	0.0719426i	$-0.977080\pi$
$491$	−16.6934	+	19.8944i	−0.753361	+	0.897821i	0.244048	+	0.969763i	$0.421525\pi$
$492$	−5.86479	−	6.62742i	−0.264405	−	0.298787i
$493$	−4.20179	−	9.01076i	−0.189239	−	0.405824i
$494$	17.7835	+	30.8019i	0.800117	+	1.38584i
$495$		0			0
$496$	−4.01336	+	6.95135i	−0.180205	+	0.312125i
$497$	−14.0983	−	1.23344i	−0.632396	−	0.0553275i
$498$	5.43393	−	6.83298i	0.243500	−	0.306193i
$499$	−11.0477	−	1.94801i	−0.494564	−	0.0872050i	−0.0791972	−	0.996859i	$-0.525236\pi$
$499$	−11.0477	−	1.94801i	−0.494564	−	0.0872050i	−0.415367	+	0.909654i	$0.636347\pi$
$500$		0			0
$501$	−7.50619	−	10.1416i	−0.335352	−	0.453095i
$502$	1.39889	−	15.9894i	0.0624354	−	0.713640i
$503$	−7.82118	−	29.1890i	−0.348729	−	1.30147i	−0.888195	−	0.459467i	$-0.848040\pi$
$503$	−7.82118	−	29.1890i	−0.348729	−	1.30147i	0.539466	−	0.842008i	$-0.318626\pi$
$504$	−7.71986	+	25.2710i	−0.343870	+	1.12566i
$505$		0			0
$506$	−0.608940	+	1.67305i	−0.0270707	+	0.0743761i
$507$	5.72864	+	28.1409i	0.254418	+	1.24978i
$508$	−0.251546	−	2.87518i	−0.0111605	−	0.127566i
$509$	−22.0511	+	8.02596i	−0.977399	+	0.355744i	−0.780829	−	0.624745i	$-0.785203\pi$
$509$	−22.0511	+	8.02596i	−0.977399	+	0.355744i	−0.196571	+	0.980490i	$0.562981\pi$
$510$		0			0
$511$	3.49769	+	19.8364i	0.154729	+	0.877511i
$512$	−10.9640	−	10.9640i	−0.484544	−	0.484544i
$513$	18.2162	+	26.4854i	0.804263	+	1.16936i
$514$		−	9.18578i		−	0.405167i
$515$		0			0
$516$	1.60600	+	1.52370i	0.0707004	+	0.0670769i
$517$	−10.3559	+	22.2083i	−0.455452	+	0.976719i
$518$	13.4302	−	1.17499i	0.590090	−	0.0516262i
$519$	15.8477	+	31.7765i	0.695636	+	1.39483i
$520$		0			0
$521$	−14.2319	+	8.21681i	−0.623512	+	0.359985i	−0.778235	−	0.627973i	$-0.783885\pi$
$521$	−14.2319	+	8.21681i	−0.623512	+	0.359985i	0.154723	+	0.987958i	$0.450551\pi$
$522$	8.96844	−	7.01018i	0.392538	−	0.306827i
$523$	14.1137	−	3.78176i	0.617150	−	0.165365i	0.0633182	−	0.997993i	$-0.479832\pi$
$523$	14.1137	−	3.78176i	0.617150	−	0.165365i	0.553832	+	0.832629i	$0.313165\pi$
$524$	−0.982891	+	0.824743i	−0.0429378	+	0.0360291i
$525$		0			0
$526$	−4.33208	+	24.5685i	−0.188888	+	1.07124i
$527$	−12.5084	+	8.75850i	−0.544876	+	0.381526i
$528$	−5.53872	+	2.18248i	−0.241042	+	0.0949804i
$529$	14.4569	+	17.2291i	0.628561	+	0.749090i
$530$		0			0
$531$	−22.6121	+	9.60430i	−0.981281	+	0.416791i
$532$	15.2441	+	4.08464i	0.660914	+	0.177091i
$533$	28.5370	−	13.3070i	1.23607	−	0.576390i
$534$	−10.9213	+	5.44671i	−0.472611	+	0.235702i
$535$		0			0
$536$	−7.78131	−	21.3790i	−0.336101	−	0.923431i
$537$	−0.653055	−	24.8318i	−0.0281814	−	1.07157i
$538$	6.19200	−	8.84309i	0.266956	−	0.381253i
$539$	3.19963			0.137818
$540$		0			0
$541$	−28.4337			−1.22246			−0.611230	−	0.791453i	$-0.709325\pi$
$541$	−28.4337			−1.22246			−0.611230	+	0.791453i	$0.709325\pi$
$542$	−2.93709	+	4.19460i	−0.126159	+	0.180173i
$543$	−3.15025	−	1.70998i	−0.135190	−	0.0733824i
$544$	−4.31531	−	11.8562i	−0.185017	−	0.508331i
$545$		0			0
$546$	−24.0048	−	15.8845i	−1.02731	−	0.679795i
$547$	−9.52924	+	4.44356i	−0.407441	+	0.189993i	−0.615524	−	0.788118i	$-0.711055\pi$
$547$	−9.52924	+	4.44356i	−0.407441	+	0.189993i	0.208083	+	0.978111i	$0.433278\pi$
$548$	13.6021	+	3.64467i	0.581053	+	0.155693i
$549$	6.16321	−	5.74989i	0.263039	−	0.245399i
$550$		0			0
$551$	−14.2734	−	17.0103i	−0.608066	−	0.724665i
$552$	0.556164	−	3.72426i	0.0236719	−	0.158515i
$553$	30.9344	−	21.6605i	1.31547	−	0.921099i
$554$	−2.48092	+	14.0700i	−0.105404	+	0.597776i
$555$		0			0
$556$	−6.17030	+	5.17749i	−0.261679	+	0.219575i
$557$	16.7541	−	4.48926i	0.709896	−	0.190216i	0.114237	−	0.993454i	$-0.463558\pi$
$557$	16.7541	−	4.48926i	0.709896	−	0.190216i	0.595659	+	0.803238i	$0.296891\pi$
$558$	−12.9950	−	11.6954i	−0.550122	−	0.495107i
$559$	−6.82132	+	3.93829i	−0.288511	+	0.166572i
$560$		0			0
$561$	−11.3043	−	0.690115i	−0.477267	−	0.0291367i
$562$	16.5722	−	1.44988i	0.699057	−	0.0611596i
$563$	9.91099	−	21.2542i	0.417699	−	0.895758i	−0.579058	−	0.815286i	$-0.696580\pi$
$563$	9.91099	−	21.2542i	0.417699	−	0.895758i	0.996757	−	0.0804714i	$-0.0256426\pi$
$564$	3.70246	−	15.4295i	0.155902	−	0.649701i
$565$		0			0
$566$		−	31.8748i		−	1.33980i
$567$	−22.7591	−	12.6021i	−0.955791	−	0.529238i
$568$	10.5491	+	10.5491i	0.442630	+	0.442630i
$569$	−6.84027	−	38.7931i	−0.286759	−	1.62629i	−0.698934	−	0.715186i	$-0.746342\pi$
$569$	−6.84027	−	38.7931i	−0.286759	−	1.62629i	0.412175	−	0.911105i	$-0.364769\pi$
$570$		0			0
$571$	31.4980	−	11.4643i	1.31815	−	0.479767i	0.415285	−	0.909691i	$-0.363682\pi$
$571$	31.4980	−	11.4643i	1.31815	−	0.479767i	0.902865	+	0.429924i	$0.141460\pi$
$572$	0.987576	+	11.2880i	0.0412926	+	0.471977i
$573$	−30.2431	+	26.7630i	−1.26343	+	1.11804i
$574$	−6.05032	+	16.6231i	−0.252536	+	0.693836i
$575$		0			0
$576$	19.4388	−	12.6300i	0.809951	−	0.526249i
$577$	−5.64888	−	21.0819i	−0.235166	−	0.877651i	−0.978074	−	0.208257i	$-0.933221\pi$
$577$	−5.64888	−	21.0819i	−0.235166	−	0.877651i	0.742908	−	0.669393i	$-0.233446\pi$
$578$	0.859390	−	9.82287i	0.0357459	−	0.408578i
$579$	−0.536252	+	0.0611597i	−0.0222859	+	0.00254171i
$580$		0			0
$581$	13.5734	+	2.39335i	0.563119	+	0.0992930i
$582$	−33.2213	−	4.96111i	−1.37707	−	0.205645i
$583$	−24.0432	−	2.10351i	−0.995769	−	0.0871185i
$584$	10.6167	−	18.3886i	0.439321	−	0.760927i
$585$		0			0
$586$	−3.88117	−	6.72239i	−0.160330	−	0.277699i
$587$	−10.3168	−	22.1244i	−0.425819	−	0.913173i	−0.995804	−	0.0915170i	$-0.970828\pi$
$587$	−10.3168	−	22.1244i	−0.425819	−	0.913173i	0.569984	−	0.821656i	$-0.306949\pi$
$588$	−2.03027	+	0.413302i	−0.0837268	+	0.0170443i
$589$	−21.9220	+	26.1256i	−0.903279	+	1.07649i
$590$		0			0
$591$	1.59861	+	5.39457i	0.0657580	+	0.221903i
$592$	−5.26217	−	3.68461i	−0.216274	−	0.151437i
$593$	−4.09490	+	4.09490i	−0.168157	+	0.168157i	−0.786169	−	0.618012i	$-0.787938\pi$
$593$	−4.09490	+	4.09490i	−0.168157	+	0.168157i	0.618012	+	0.786169i	$0.287938\pi$
$594$	−2.14445	−	12.7881i	−0.0879879	−	0.524700i
$595$		0			0
$596$	−8.17827	+	1.44205i	−0.334995	+	0.0590687i
$597$	11.0417	−	0.290389i	0.451908	−	0.0118848i
$598$	3.71765	+	1.73357i	0.152026	+	0.0708910i
$599$	−30.3866	−	25.4974i	−1.24156	−	1.04180i	−0.997400	−	0.0720615i	$-0.977042\pi$
$599$	−30.3866	−	25.4974i	−1.24156	−	1.04180i	−0.244163	−	0.969734i	$-0.578513\pi$
$600$		0			0
$601$	−22.4811	−	8.18244i	−0.917022	−	0.333769i	−0.159969	−	0.987122i	$-0.551139\pi$
$601$	−22.4811	−	8.18244i	−0.917022	−	0.333769i	−0.757053	+	0.653353i	$0.773362\pi$
$602$	1.14533	−	4.27441i	0.0466800	−	0.174212i
$603$	22.1805	−	3.12238i	0.903258	−	0.127153i
$604$	−0.806976	−	0.465908i	−0.0328354	−	0.0189575i
$605$		0			0
$606$	5.65534	+	2.45825i	0.229733	+	0.0998596i
$607$	−18.5771	−	26.5308i	−0.754020	−	1.07685i	−0.994349	−	0.106160i	$-0.966144\pi$
$607$	−18.5771	−	26.5308i	−0.754020	−	1.07685i	0.240329	−	0.970691i	$-0.422745\pi$
$608$	−16.1631	−	23.0833i	−0.655501	−	0.936152i
$609$	16.4813	+	7.16404i	0.667854	+	0.290301i
$610$		0			0
$611$	48.8923	+	28.2280i	1.97797	+	1.14198i
$612$	7.26207	−	1.02229i	0.293552	−	0.0413238i
$613$	3.95860	−	14.7737i	0.159886	−	0.596704i	−0.838751	−	0.544515i	$-0.816714\pi$
$613$	3.95860	−	14.7737i	0.159886	−	0.596704i	0.998637	−	0.0521885i	$-0.0166197\pi$
$614$	−13.5879	−	4.94560i	−0.548364	−	0.199588i
$615$		0			0
$616$	−15.9279	−	13.3651i	−0.641755	−	0.538497i
$617$	24.2804	+	11.3221i	0.977492	+	0.455812i	0.844646	−	0.535325i	$-0.179811\pi$
$617$	24.2804	+	11.3221i	0.977492	+	0.455812i	0.132845	+	0.991137i	$0.457589\pi$
$618$	6.63900	−	0.174600i	0.267060	−	0.00702345i
$619$	−18.6300	+	3.28497i	−0.748802	+	0.132034i	−0.535011	−	0.844845i	$-0.679692\pi$
$619$	−18.6300	+	3.28497i	−0.748802	+	0.132034i	−0.213792	+	0.976879i	$0.568581\pi$
$620$		0			0
$621$	3.47298	+	1.29715i	0.139366	+	0.0520529i
$622$	−2.88598	+	2.88598i	−0.115717	+	0.115717i
$623$	−15.7827	−	11.0512i	−0.632322	−	0.442757i
$624$	3.89698	+	13.1505i	0.156004	+	0.526443i
$625$		0			0
$626$	16.7165	−	19.9220i	0.668126	−	0.796242i
$627$	−24.7860	+	5.04570i	−0.989859	+	0.201506i
$628$	−8.32451	−	17.8520i	−0.332184	−	0.712371i
$629$	−6.11042	−	10.5836i	−0.243638	−	0.421994i
$630$		0			0
$631$	0.0126965	−	0.0219910i	0.000505440	−	0.000875448i	−0.865773	−	0.500438i	$-0.833172\pi$
$631$	0.0126965	−	0.0219910i	0.000505440	−	0.000875448i	0.866278	+	0.499562i	$0.166506\pi$
$632$	−39.6578	−	3.46961i	−1.57750	−	0.138014i
$633$	−10.9895	−	1.64112i	−0.436794	−	0.0652288i
$634$	−17.1787	−	3.02907i	−0.682253	−	0.120300i
$635$		0			0
$636$	15.5279	−	1.77096i	0.615722	−	0.0702232i
$637$	0.642490	−	7.34369i	0.0254564	−	0.290968i
$638$	2.31829	+	8.65198i	0.0917820	+	0.342535i
$639$	−12.3165	+	8.00241i	−0.487234	+	0.316570i
$640$		0			0
$641$	9.97230	−	27.3987i	0.393882	−	1.08218i	−0.571331	−	0.820720i	$-0.693573\pi$
$641$	9.97230	−	27.3987i	0.393882	−	1.08218i	0.965214	−	0.261463i	$-0.0842049\pi$
$642$	−7.82351	+	6.92324i	−0.308769	+	0.273238i
$643$	0.152914	+	1.74781i	0.00603033	+	0.0689270i	0.998614	−	0.0526401i	$-0.0167636\pi$
$643$	0.152914	+	1.74781i	0.00603033	+	0.0689270i	−0.992583	+	0.121567i	$0.961208\pi$
$644$	1.71037	−	0.622522i	0.0673979	−	0.0245308i
$645$		0			0
$646$	3.14539	+	17.8384i	0.123754	+	0.701842i
$647$	14.7341	+	14.7341i	0.579259	+	0.579259i	0.934699	−	0.355440i	$-0.115669\pi$
$647$	14.7341	+	14.7341i	0.579259	+	0.579259i	−0.355440	+	0.934699i	$0.615669\pi$
$648$	9.83953	+	25.5982i	0.386533	+	1.00559i
$649$		−	19.3315i		−	0.758830i
$650$		0			0
$651$	6.44028	−	26.8391i	0.252414	−	1.05191i
$652$	−0.922501	+	1.97831i	−0.0361279	+	0.0774766i
$653$	9.28810	−	0.812604i	0.363471	−	0.0317996i	0.0960426	−	0.995377i	$-0.469382\pi$
$653$	9.28810	−	0.812604i	0.363471	−	0.0317996i	0.267429	+	0.963578i	$0.413826\pi$
$654$	28.9164	+	1.76532i	1.13072	+	0.0690293i
$655$		0			0
$656$	7.29994	−	4.21462i	0.285015	−	0.164553i
$657$	15.5386	+	13.9846i	0.606218	+	0.545592i
$658$	−30.6372	+	8.20920i	−1.19436	+	0.320028i
$659$	14.0775	−	11.8125i	0.548383	−	0.460148i	−0.326010	−	0.945366i	$-0.605704\pi$
$659$	14.0775	−	11.8125i	0.548383	−	0.460148i	0.874393	+	0.485218i	$0.161260\pi$
$660$		0			0
$661$	4.43306	−	25.1412i	0.172426	−	0.977878i	−0.768647	−	0.639674i	$-0.779070\pi$
$661$	4.43306	−	25.1412i	0.172426	−	0.977878i	0.941073	−	0.338204i	$-0.109819\pi$
$662$	17.8745	−	12.5159i	0.694712	−	0.486443i
$663$	−3.85385	+	25.8067i	−0.149671	+	1.00225i
$664$	−9.33923	−	11.1301i	−0.362432	−	0.431930i
$665$		0			0
$666$	10.2309	−	9.54476i	0.396438	−	0.369852i
$667$	−2.47371	−	0.662829i	−0.0957825	−	0.0256648i
$668$	−5.82669	+	2.71703i	−0.225441	+	0.105125i
$669$	−15.0051	−	9.92922i	−0.580131	−	0.383886i
$670$		0			0
$671$	2.26847	+	6.23257i	0.0875733	+	0.240606i
$672$	20.0434	+	10.8797i	0.773191	+	0.419695i
$673$	2.68248	−	3.83098i	0.103402	−	0.147673i	−0.764117	−	0.645078i	$-0.776825\pi$
$673$	2.68248	−	3.83098i	0.103402	−	0.147673i	0.867518	+	0.497405i	$0.165714\pi$
$674$	11.0600			0.426017
$675$		0			0
$676$	14.6331			0.562810
$677$	22.5105	−	32.1483i	0.865147	−	1.23556i	−0.105347	−	0.994436i	$-0.533595\pi$
$677$	22.5105	−	32.1483i	0.865147	−	1.23556i	0.970495	−	0.241123i	$-0.0775158\pi$
$678$	0.128472	+	4.88500i	0.00493392	+	0.187607i
$679$	−18.1371	−	49.8312i	−0.696038	−	1.91235i
$680$		0			0
$681$	−4.84267	+	2.41515i	−0.185572	+	0.0925488i
$682$	12.4681	−	5.81397i	0.477428	−	0.222628i
$683$	−36.4765	−	9.77386i	−1.39574	−	0.373986i	−0.518924	−	0.854820i	$-0.673667\pi$
$683$	−36.4765	−	9.77386i	−1.39574	−	0.373986i	−0.876812	+	0.480834i	$0.840334\pi$
$684$	15.0758	−	6.40331i	0.576436	−	0.244837i
$685$		0			0
$686$	−11.0866	−	13.2125i	−0.423287	−	0.504454i
$687$	37.8592	−	14.9181i	1.44442	−	0.569160i
$688$	−1.72726	+	1.20944i	−0.0658513	+	0.0461096i
$689$	−9.65582	+	54.7609i	−0.367858	+	2.08622i
$690$		0			0
$691$	10.1478	−	8.51501i	0.386040	−	0.323926i	−0.429028	−	0.903291i	$-0.641144\pi$
$691$	10.1478	−	8.51501i	0.386040	−	0.323926i	0.815068	+	0.579365i	$0.196699\pi$
$692$	17.4769	−	4.68292i	0.664372	−	0.178018i
$693$	16.1284	−	12.6068i	0.612668	−	0.478892i
$694$	10.5198	−	6.07363i	0.399327	−	0.230552i
$695$		0			0
$696$	−8.45482	−	16.9529i	−0.320479	−	0.642599i
$697$	15.9747	−	1.39761i	0.605086	−	0.0529381i
$698$	7.09386	−	15.2128i	0.268507	−	0.575814i
$699$	−4.16805	−	3.95443i	−0.157650	−	0.149570i
$700$		0			0
$701$			1.42181i			0.0537011i	0.999639	+	0.0268505i	$0.00854782\pi$
$701$			1.42181i			0.0537011i	−0.999639	+	0.0268505i	$0.991452\pi$
$702$	−29.7814	+	2.35402i	−1.12402	+	0.0888467i
$703$	−19.3001	−	19.3001i	−0.727916	−	0.727916i
$704$	3.16755	+	17.9641i	0.119381	+	0.677046i
$705$		0			0
$706$	8.62062	−	3.13765i	0.324441	−	0.118087i
$707$	0.848488	+	9.69826i	0.0319107	+	0.364741i
$708$	2.49709	+	12.2665i	0.0938463	+	0.461002i
$709$	−12.4901	+	34.3163i	−0.469077	+	1.28878i	0.449410	+	0.893325i	$0.351634\pi$
$709$	−12.4901	+	34.3163i	−0.469077	+	1.28878i	−0.918487	+	0.395452i	$0.870588\pi$
$710$		0			0
$711$	11.4506	−	37.4836i	0.429432	−	1.40575i
$712$	5.25679	+	19.6186i	0.197007	+	0.735239i
$713$	−0.342810	+	3.91834i	−0.0128384	+	0.146743i
$714$	−8.72108	−	11.7831i	−0.326378	−	0.440971i
$715$		0			0
$716$	−12.4649	−	2.19790i	−0.465836	−	0.0821395i
$717$	−18.3375	+	23.0587i	−0.684826	+	0.861144i
$718$	21.4894	+	1.88008i	0.801977	+	0.0701639i
$719$	−12.9014	+	22.3459i	−0.481142	+	0.833363i	−0.999766	−	0.0216398i	$-0.993111\pi$
$719$	−12.9014	+	22.3459i	−0.481142	+	0.833363i	0.518624	+	0.855003i	$0.326445\pi$
$720$		0			0
$721$	5.24243	+	9.08015i	0.195238	+	0.338162i
$722$	8.60904	+	18.4622i	0.320395	+	0.687090i
$723$	−21.2999	−	24.0697i	−0.792152	−	0.895160i
$724$	−1.17400	+	1.39912i	−0.0436314	+	0.0519978i
$725$		0			0
$726$	−9.66282	−	2.31868i	−0.358621	−	0.0860543i
$727$	−1.32255	−	0.926059i	−0.0490507	−	0.0343456i	0.548794	−	0.835958i	$-0.315087\pi$
$727$	−1.32255	−	0.926059i	−0.0490507	−	0.0343456i	−0.597845	+	0.801612i	$0.703976\pi$
$728$	−33.8736	+	33.8736i	−1.25544	+	1.25544i
$729$	−26.6647	+	4.24184i	−0.987582	+	0.157105i
$730$		0			0
$731$	−3.95045	+	0.696570i	−0.146112	+	0.0257636i
$732$	−2.24449	−	3.66174i	−0.0829586	−	0.135342i
$733$	12.0574	+	5.62244i	0.445349	+	0.207669i	0.632338	−	0.774692i	$-0.282095\pi$
$733$	12.0574	+	5.62244i	0.445349	+	0.207669i	−0.186990	+	0.982362i	$0.559873\pi$
$734$	−21.0132	−	17.6322i	−0.775613	−	0.650816i
$735$		0			0
$736$	−3.05398	−	1.11156i	−0.112571	−	0.0409725i
$737$	−4.56182	+	17.0249i	−0.168037	+	0.627122i
$738$	5.67740	+	17.4598i	0.208988	+	0.642704i
$739$	−30.9063	−	17.8437i	−1.13691	−	0.656393i	−0.191243	−	0.981543i	$-0.561252\pi$
$739$	−30.9063	−	17.8437i	−1.13691	−	0.656393i	−0.945663	+	0.325150i	$0.894585\pi$
$740$		0			0
$741$	6.60366	+	57.9013i	0.242591	+	2.12706i
$742$	−17.9187	−	25.5905i	−0.657815	−	0.939457i
$743$	20.1985	+	28.8465i	0.741012	+	1.05828i	0.995825	+	0.0912848i	$0.0290974\pi$
$743$	20.1985	+	28.8465i	0.741012	+	1.05828i	−0.254813	+	0.966990i	$0.582014\pi$
$744$	−23.3869	+	17.3095i	−0.857407	+	0.634598i
$745$		0			0
$746$	4.37382	+	2.52523i	0.160137	+	0.0924551i
$747$	12.6286	−	6.71844i	0.462058	−	0.245815i
$748$	−1.49358	+	5.57411i	−0.0546106	+	0.203810i
$749$	−15.4983	−	5.64093i	−0.566296	−	0.206115i
$750$		0			0
$751$	19.0262	+	15.9649i	0.694275	+	0.582566i	0.920138	−	0.391593i	$-0.128076\pi$
$751$	19.0262	+	15.9649i	0.694275	+	0.582566i	−0.225864	+	0.974159i	$0.572520\pi$
$752$	13.6975	+	6.38726i	0.499497	+	0.232919i
$753$	12.5460	−	23.1132i	0.457203	−	0.842290i
$754$	20.3233	−	3.58354i	0.740130	−	0.130505i
$755$		0			0
$756$	−8.60555	+	10.0827i	−0.312981	+	0.366706i
$757$	−17.8009	+	17.8009i	−0.646986	+	0.646986i	−0.952263	−	0.305278i	$-0.901251\pi$
$757$	−17.8009	+	17.8009i	−0.646986	+	0.646986i	0.305278	+	0.952263i	$0.401251\pi$
$758$	−21.9080	−	15.3401i	−0.795733	−	0.557178i
$759$	−2.00785	+	2.11631i	−0.0728802	+	0.0768172i
$760$		0			0
$761$	−31.3105	+	37.3144i	−1.13500	+	1.35265i	−0.207765	+	0.978179i	$0.566619\pi$
$761$	−31.3105	+	37.3144i	−1.13500	+	1.35265i	−0.927240	+	0.374467i	$0.877826\pi$
$762$	−1.89925	+	5.67841i	−0.0688027	+	0.205707i
$763$	19.3290	+	41.4512i	0.699757	+	1.50063i
$764$	10.2888	+	17.8207i	0.372236	+	0.644731i
$765$		0			0
$766$	6.51352	−	11.2818i	0.235343	−	0.407626i
$767$	−44.3691	−	3.88180i	−1.60208	−	0.140164i
$768$	−10.4455	−	26.5086i	−0.376919	−	0.956547i
$769$	43.1365	+	7.60612i	1.55554	+	0.274284i	0.884287	−	0.466944i	$-0.154645\pi$
$769$	43.1365	+	7.60612i	1.55554	+	0.274284i	0.671254	+	0.741227i	$0.265756\pi$
$770$		0			0
$771$	5.99998	−	13.8033i	0.216084	−	0.497113i
$772$	−0.0239691	+	0.273968i	−0.000862668	+	0.00986034i
$773$	5.91076	+	22.0592i	0.212595	+	0.793416i	0.986999	+	0.160725i	$0.0513831\pi$
$773$	5.91076	+	22.0592i	0.212595	+	0.793416i	−0.774404	+	0.632691i	$0.781950\pi$
$774$	−1.79548	−	4.22722i	−0.0645371	−	0.151944i
$775$		0			0
$776$	−19.1194	+	52.5302i	−0.686347	+	1.88572i
$777$	20.9488	+	7.00674i	0.751534	+	0.251365i
$778$	−0.821958	−	9.39502i	−0.0294686	−	0.336828i
$779$	33.6549	−	12.2494i	1.20581	−	0.438879i
$780$		0			0
$781$	−2.00697	−	11.3821i	−0.0718150	−	0.407283i
$782$	1.47719	+	1.47719i	0.0528241	+	0.0528241i
$783$	18.0556	−	4.67604i	0.645255	−	0.167108i
$784$		−	1.97345i		−	0.0704805i
$785$		0			0
$786$	2.55215	−	0.756296i	0.0910322	−	0.0269762i
$787$	7.27876	−	15.6093i	0.259460	−	0.556413i	−0.732822	−	0.680421i	$-0.761797\pi$
$787$	7.27876	−	15.6093i	0.259460	−	0.556413i	0.992281	+	0.124008i	$0.0395748\pi$
$788$	2.85601	−	0.249868i	0.101741	−	0.00890119i
$789$	−22.5574	+	34.0889i	−0.803064	+	1.21360i
$790$		0			0
$791$	−6.68122	+	3.85740i	−0.237557	+	0.137153i
$792$	−21.5666	−	0.748235i	−0.766337	−	0.0265874i
$793$	14.7603	−	3.95501i	0.524154	−	0.140447i
$794$	−11.0377	+	9.26170i	−0.391712	+	0.328685i
$795$		0			0
$796$	0.977323	−	5.54267i	0.0346403	−	0.196455i
$797$	−26.9373	+	18.8617i	−0.954166	+	0.668115i	−0.943340	−	0.331827i	$-0.892335\pi$
$797$	−26.9373	+	18.8617i	−0.954166	+	0.668115i	−0.0108262	+	0.999941i	$0.503446\pi$
$798$	−25.6256	−	20.3787i	−0.907135	−	0.721400i
$799$	18.4814	+	22.0252i	0.653824	+	0.779197i
$800$		0			0
$801$	−19.9689	+	1.05106i	−0.705567	+	0.0371374i
$802$	2.99600	+	0.802775i	0.105792	+	0.0283470i
$803$	−14.9085	+	6.95197i	−0.526111	+	0.245330i
$804$	0.695477	−	11.3921i	0.0245276	−	0.401769i
$805$		0			0
$806$	−10.8404	−	29.7838i	−0.381838	−	1.04909i
$807$	15.0807	−	9.24384i	0.530867	−	0.325399i
$808$	5.88637	−	8.40661i	0.207082	−	0.295744i
$809$	0.589848			0.0207379			0.0103690	−	0.999946i	$-0.496699\pi$
$809$	0.589848			0.0207379			0.0103690	+	0.999946i	$0.496699\pi$
$810$		0			0
$811$	−48.5224			−1.70385			−0.851925	−	0.523664i	$-0.824565\pi$
$811$	−48.5224			−1.70385			−0.851925	+	0.523664i	$0.824565\pi$
$812$	5.25222	−	7.50095i	0.184317	−	0.263232i
$813$	−7.15334	+	4.38469i	−0.250879	+	0.153778i
$814$	3.76564	+	10.3460i	0.131985	+	0.362627i
$815$		0			0
$816$	−0.425646	+	6.97221i	−0.0149006	+	0.244076i
$817$	−8.11977	+	3.78631i	−0.284075	+	0.132466i
$818$	29.2711	+	7.84316i	1.02344	+	0.274230i
$819$	−25.6961	−	39.5489i	−0.897894	−	1.38195i
$820$		0			0
$821$	12.3182	+	14.6802i	0.429907	+	0.512343i	0.936895	−	0.349610i	$-0.113686\pi$
$821$	12.3182	+	14.6802i	0.429907	+	0.512343i	−0.506989	+	0.861953i	$0.669241\pi$
$822$	−22.8654	−	18.1837i	−0.797522	−	0.634230i
$823$	−0.511895	+	0.358433i	−0.0178435	+	0.0124942i	−0.582464	−	0.812856i	$-0.697911\pi$
$823$	−0.511895	+	0.358433i	−0.0178435	+	0.0124942i	0.564621	+	0.825351i	$0.309022\pi$
$824$	1.91929	−	10.8848i	0.0668615	−	0.379190i
$825$		0			0
$826$	19.1684	−	16.0842i	0.666954	−	0.559641i
$827$	−11.3875	+	3.05127i	−0.395981	+	0.106103i	−0.451314	−	0.892365i	$-0.649045\pi$
$827$	−11.3875	+	3.05127i	−0.395981	+	0.106103i	0.0553328	+	0.998468i	$0.482378\pi$
$828$	1.00068	−	1.60222i	0.0347759	−	0.0556811i
$829$	38.0844	−	21.9880i	1.32272	−	0.763675i	0.338562	−	0.940944i	$-0.390059\pi$
$829$	38.0844	−	21.9880i	1.32272	−	0.763675i	0.984163	+	0.177269i	$0.0567261\pi$
$830$		0			0
$831$	−12.9183	+	19.5222i	−0.448130	+	0.677217i
$832$	41.8666	−	3.66285i	1.45146	−	0.126986i
$833$	1.58663	−	3.40254i	0.0549735	−	0.117891i
$834$	16.0216	−	4.74780i	0.554784	−	0.164403i
$835$		0			0
$836$			12.8886i			0.445761i
$837$	−11.8881	−	26.0626i	−0.410913	−	0.900854i
$838$	9.93659	+	9.93659i	0.343254	+	0.343254i
$839$	−0.173429	−	0.983567i	−0.00598745	−	0.0339565i	0.981668	−	0.190601i	$-0.0610435\pi$
$839$	−0.173429	−	0.983567i	−0.00598745	−	0.0339565i	−0.987655	+	0.156644i	$0.949932\pi$
$840$		0			0
$841$	15.1440	−	5.51197i	0.522207	−	0.190068i
$842$	0.833993	+	9.53258i	0.0287413	+	0.328514i
$843$	25.8498	+	8.64597i	0.890314	+	0.297783i
$844$	−1.93642	+	5.32028i	−0.0666545	+	0.183132i
$845$		0			0
$846$	−19.8050	+	26.2945i	−0.680910	+	0.904024i
$847$	−4.06038	−	15.1535i	−0.139516	−	0.520682i
$848$	−1.29739	+	14.8293i	−0.0445527	+	0.509239i
$849$	20.8200	−	47.8976i	0.714541	−	1.64384i
$850$		0			0
$851$	−3.10007	−	0.546626i	−0.106269	−	0.0187381i
$852$	2.74373	+	6.96305i	0.0939986	+	0.238550i
$853$	−4.50805	−	0.394403i	−0.154353	−	0.0135041i	0.00971747	−	0.999953i	$-0.496907\pi$
$853$	−4.50805	−	0.394403i	−0.154353	−	0.0135041i	−0.164070	+	0.986449i	$0.552462\pi$
$854$	−4.29256	+	7.43494i	−0.146889	+	0.254418i
$855$		0			0
$856$	8.69313	+	15.0569i	0.297125	+	0.514635i
$857$	24.1963	+	51.8892i	0.826531	+	1.77250i	0.602881	+	0.797831i	$0.294019\pi$
$857$	24.1963	+	51.8892i	0.826531	+	1.77250i	0.223650	+	0.974670i	$0.428203\pi$
$858$	7.45653	−	22.2936i	0.254562	−	0.761091i
$859$	−20.9711	+	24.9924i	−0.715526	+	0.852730i	−0.994188	−	0.107659i	$-0.965665\pi$
$859$	−20.9711	+	24.9924i	−0.715526	+	0.852730i	0.278662	+	0.960389i	$0.410109\pi$
$860$		0			0
$861$	−19.9496	+	21.0273i	−0.679881	+	0.716608i
$862$	−0.256286	−	0.179453i	−0.00872913	−	0.00611220i
$863$	28.5706	−	28.5706i	0.972554	−	0.972554i	−0.0270792	−	0.999633i	$-0.508621\pi$
$863$	28.5706	−	28.5706i	0.972554	−	0.972554i	0.999633	+	0.0270792i	$0.00862062\pi$
$864$	23.3433	−	3.91447i	0.794154	−	0.133173i
$865$		0			0
$866$	18.8698	−	3.32726i	0.641223	−	0.113065i
$867$	7.70751	−	14.1993i	0.261761	−	0.482233i
$868$	−12.7462	−	5.94365i	−0.432634	−	0.201741i
$869$	23.6254	+	19.8241i	0.801437	+	0.672486i
$870$		0			0
$871$	38.1591	+	13.8888i	1.29297	+	0.470603i
$872$	12.4786	−	46.5707i	0.422578	−	1.57708i
$873$	−46.6805	−	29.1545i	−1.57989	−	0.986731i
$874$	4.04068	+	2.33289i	0.136678	+	0.0789111i
$875$		0			0
$876$	8.56194	−	6.33700i	0.289281	−	0.214108i
$877$	−20.3911	−	29.1215i	−0.688559	−	0.983364i	−0.999458	−	0.0329214i	$-0.989519\pi$
$877$	−20.3911	−	29.1215i	−0.688559	−	0.983364i	0.310899	−	0.950443i	$-0.399370\pi$
$878$	17.2994	+	24.7062i	0.583828	+	0.833792i
$879$	−1.44122	−	12.6367i	−0.0486112	−	0.426226i
$880$		0			0
$881$	−30.9752	−	17.8836i	−1.04358	−	0.602512i	−0.122736	−	0.992439i	$-0.539167\pi$
$881$	−30.9752	−	17.8836i	−1.04358	−	0.602512i	−0.920846	+	0.389927i	$0.872500\pi$
$882$	4.20463	+	0.892728i	0.141577	+	0.0300597i
$883$	−0.905746	+	3.38029i	−0.0304808	+	0.113756i	−0.979490	−	0.201492i	$-0.935421\pi$
$883$	−0.905746	+	3.38029i	−0.0304808	+	0.113756i	0.949009	+	0.315248i	$0.102088\pi$
$884$	12.4936	+	4.54730i	0.420205	+	0.152942i
$885$		0			0
$886$	−32.6492	−	27.3959i	−1.09687	−	0.920383i
$887$	25.7899	+	12.0260i	0.865939	+	0.403794i	0.804243	−	0.594301i	$-0.202571\pi$
$887$	25.7899	+	12.0260i	0.865939	+	0.403794i	0.0616962	+	0.998095i	$0.480349\pi$
$888$	−12.1691	−	19.8531i	−0.408368	−	0.666227i
$889$	−9.30926	+	1.64147i	−0.312222	+	0.0550532i
$890$		0			0
$891$	5.13050	−	20.6171i	0.171878	−	0.690698i
$892$	−6.48285	+	6.48285i	−0.217062	+	0.217062i
$893$	52.6023	+	36.8325i	1.76027	+	1.23255i
$894$	16.7527	+	4.01997i	0.560296	+	0.134448i
$895$		0			0
$896$	1.75011	−	2.08570i	0.0584672	−	0.0696785i
$897$	4.45411	+	5.03331i	0.148718	+	0.168057i
$898$	3.49564	+	7.49641i	0.116651	+	0.250159i
$899$	9.89411	+	17.1371i	0.329987	+	0.571554i
$900$		0			0
$901$	−14.1594	+	24.5249i	−0.471719	+	0.817042i
$902$	−14.3919	−	1.25913i	−0.479199	−	0.0419245i
$903$	4.51303	−	5.67497i	0.150184	−	0.188851i
$904$	8.00909	+	1.41222i	0.266378	+	0.0469697i
$905$		0			0
$906$	1.15005	+	1.55383i	0.0382078	+	0.0516227i
$907$	−2.85879	+	32.6761i	−0.0949246	+	1.08499i	0.788062	+	0.615596i	$0.211085\pi$
$907$	−2.85879	+	32.6761i	−0.0949246	+	1.08499i	−0.882987	+	0.469398i	$0.844471\pi$
$908$	0.713667	+	2.66344i	0.0236839	+	0.0883894i
$909$	6.89249	+	7.38793i	0.228609	+	0.245042i
$910$		0			0
$911$	9.92857	−	27.2785i	0.328948	−	0.903778i	−0.659430	−	0.751766i	$-0.729202\pi$
$911$	9.92857	−	27.2785i	0.328948	−	0.903778i	0.988379	−	0.152012i	$-0.0485753\pi$
$912$	3.11206	+	15.2874i	0.103051	+	0.506217i
$913$	0.981025	+	11.2132i	0.0324672	+	0.371102i
$914$	5.44427	−	1.98155i	0.180080	−	0.0655439i
$915$		0			0
$916$	−3.60050	−	20.4195i	−0.118964	−	0.674678i
$917$	2.97152	+	2.97152i	0.0981282	+	0.0981282i
$918$	−14.6624	−	4.06088i	−0.483932	−	0.134029i
$919$			28.2931i			0.933302i	0.884442	+	0.466651i	$0.154540\pi$
$919$			28.2931i			0.933302i	−0.884442	+	0.466651i	$0.845460\pi$
$920$		0			0
$921$	−17.1879	−	16.3070i	−0.566361	−	0.537335i
$922$	−13.4676	+	28.8814i	−0.443533	+	0.951159i
$923$	−26.5268	+	2.32080i	−0.873141	+	0.0763899i
$924$	−4.65525	−	9.33434i	−0.153147	−	0.307077i
$925$		0			0
$926$	0.165049	−	0.0952911i	0.00542385	−	0.00313146i
$927$	10.0903	+	4.07410i	0.331410	+	0.133811i
$928$	−15.7933	+	4.23180i	−0.518440	+	0.138916i
$929$	−25.1788	+	21.1275i	−0.826089	+	0.693171i	−0.954390	−	0.298564i	$-0.903492\pi$
$929$	−25.1788	+	21.1275i	−0.826089	+	0.693171i	0.128300	+	0.991735i	$0.459048\pi$
$930$		0			0
$931$	1.45603	−	8.25757i	0.0477195	−	0.270631i
$932$	−2.39811	+	1.67917i	−0.0785527	+	0.0550032i
$933$	−6.22178	+	2.45164i	−0.203692	+	0.0802630i
$934$	8.57623	+	10.2208i	0.280623	+	0.334433i
$935$		0			0
$936$	−6.04793	+	49.3488i	−0.197683	+	1.61302i
$937$	−4.87347	−	1.30584i	−0.159209	−	0.0426600i	0.178334	−	0.983970i	$-0.442929\pi$
$937$	−4.87347	−	1.30584i	−0.159209	−	0.0426600i	−0.337543	+	0.941310i	$0.609596\pi$
$938$	−20.6768	+	9.64174i	−0.675121	+	0.314814i
$939$	38.1322	−	19.0174i	1.24440	−	0.620610i
$940$		0			0
$941$	19.6715	+	54.0471i	0.641274	+	1.76189i	0.647687	+	0.761906i	$0.275736\pi$
$941$	19.6715	+	54.0471i	0.641274	+	1.76189i	−0.00641343	+	0.999979i	$0.502041\pi$
$942$	1.07432	+	40.8501i	0.0350034	+	1.33097i
$943$	2.36919	−	3.38355i	0.0771514	−	0.110184i
$944$	−11.9232			−0.388068
$945$		0			0
$946$	3.61394			0.117499
$947$	18.4673	−	26.3740i	0.600107	−	0.857041i	−0.398073	−	0.917354i	$-0.630321\pi$
$947$	18.4673	−	26.3740i	0.600107	−	0.857041i	0.998180	+	0.0603125i	$0.0192097\pi$
$948$	−17.5518	−	9.52727i	−0.570055	−	0.309431i
$949$	12.9623	+	35.6136i	0.420773	+	1.15607i
$950$		0			0
$951$	−23.8355	−	15.7725i	−0.772920	−	0.511459i
$952$	−22.1110	+	10.3105i	−0.716623	+	0.334167i
$953$	20.8927	+	5.59819i	0.676782	+	0.181343i	0.580808	−	0.814041i	$-0.302737\pi$
$953$	20.8927	+	5.59819i	0.676782	+	0.181343i	0.0959743	+	0.995384i	$0.469403\pi$
$954$	−31.0083	−	9.47252i	−1.00393	−	0.306684i
$955$		0			0
$956$	9.64940	+	11.4997i	0.312084	+	0.371927i
$957$	−2.16766	+	14.5154i	−0.0700706	+	0.469217i
$958$	−30.8629	+	21.6105i	−0.997136	+	0.698202i
$959$	8.00894	−	45.4210i	0.258622	−	1.46672i
$960$		0			0
$961$	−0.465741	+	0.390803i	−0.0150239	+	0.0126065i
$962$	24.5020	−	6.56528i	0.789975	−	0.211673i
$963$	−16.2784	+	5.29324i	−0.524563	+	0.170572i
$964$	−14.1830	+	8.18857i	−0.456804	+	0.263736i
$965$		0			0
$966$	−3.76902	−	0.230095i	−0.121266	−	0.00740317i
$967$	−10.9923	+	0.961701i	−0.353488	+	0.0309262i	−0.262517	−	0.964927i	$-0.584553\pi$
$967$	−10.9923	+	0.961701i	−0.353488	+	0.0309262i	−0.0909711	+	0.995854i	$0.528997\pi$
$968$	−6.98917	+	14.9883i	−0.224640	+	0.481743i
$969$	−6.92520	+	28.8599i	−0.222469	+	0.927114i
$970$		0			0
$971$		−	21.9387i		−	0.704047i	−0.935991	−	0.352023i	$-0.885494\pi$
$971$		−	21.9387i		−	0.704047i	0.935991	−	0.352023i	$-0.114506\pi$
$972$	−0.592321	+	13.7449i	−0.0189987	+	0.440868i
$973$	18.6543	+	18.6543i	0.598030	+	0.598030i
$974$	−1.26918	−	7.19790i	−0.0406673	−	0.230635i
$975$		0			0
$976$	3.84410	−	1.39914i	0.123046	−	0.0447853i
$977$	−0.479546	−	5.48124i	−0.0153420	−	0.175360i	−1.00000		0.000862648i	$-0.999725\pi$
$977$	−0.479546	−	5.48124i	−0.0153420	−	0.175360i	0.984658	−	0.174498i	$-0.0558301\pi$
$978$	3.39128	−	3.00104i	0.108441	−	0.0959625i
$979$	5.38167	−	14.7860i	0.171999	−	0.472563i
$980$		0			0
$981$	42.2990	+	21.5404i	1.35050	+	0.687731i
$982$	−7.10536	−	26.5176i	−0.226741	−	0.846209i
$983$	−2.39635	+	27.3904i	−0.0764316	+	0.873618i	0.857106	+	0.515139i	$0.172260\pi$
$983$	−2.39635	+	27.3904i	−0.0764316	+	0.873618i	−0.933538	+	0.358478i	$0.883296\pi$
$984$	30.3581	−	3.46235i	0.967782	−	0.110376i
$985$		0			0
$986$	10.3502	+	1.82503i	0.329619	+	0.0581207i
$987$	−51.4000	−	7.67583i	−1.63608	−	0.244324i
$988$	29.5815	+	2.58804i	0.941111	+	0.0823366i
$989$	−0.516635	+	0.894838i	−0.0164280	+	0.0284542i
$990$		0			0
$991$	7.95205	+	13.7734i	0.252605	+	0.437525i	0.964242	−	0.265022i	$-0.0853793\pi$
$991$	7.95205	+	13.7734i	0.252605	+	0.437525i	−0.711637	+	0.702547i	$0.752046\pi$
$992$	10.6128	+	22.7592i	0.336956	+	0.722606i
$993$	35.0348	−	7.13204i	1.11180	−	0.226328i
$994$	9.61620	−	11.4601i	0.305007	−	0.363494i
$995$		0			0
$996$	−2.07092	−	6.98839i	−0.0656195	−	0.221436i
$997$	−3.00447	−	2.10376i	−0.0951527	−	0.0666266i	0.525032	−	0.851083i	$-0.324053\pi$
$997$	−3.00447	−	2.10376i	−0.0951527	−	0.0666266i	−0.620185	+	0.784456i	$0.712942\pi$
$998$	8.38532	−	8.38532i	0.265433	−	0.265433i
$999$	21.6082	−	7.66011i	0.683652	−	0.242355i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.ba.b.68.5		192
5.2	odd	4	inner	675.2.ba.b.257.5		192
5.3	odd	4		135.2.q.a.122.12	yes	192
5.4	even	2		135.2.q.a.68.12	yes	192
15.8	even	4		405.2.r.a.152.5		192
15.14	odd	2		405.2.r.a.233.5		192
27.2	odd	18	inner	675.2.ba.b.218.5		192
135.2	even	36	inner	675.2.ba.b.407.5		192
135.29	odd	18		135.2.q.a.83.12	yes	192
135.79	even	18		405.2.r.a.8.5		192
135.83	even	36		135.2.q.a.2.12	✓	192
135.133	odd	36		405.2.r.a.332.5		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.12	✓	192	135.83	even	36
135.2.q.a.68.12	yes	192	5.4	even	2
135.2.q.a.83.12	yes	192	135.29	odd	18
135.2.q.a.122.12	yes	192	5.3	odd	4
405.2.r.a.8.5		192	135.79	even	18
405.2.r.a.152.5		192	15.8	even	4
405.2.r.a.233.5		192	15.14	odd	2
405.2.r.a.332.5		192	135.133	odd	36
675.2.ba.b.68.5		192	1.1	even	1	trivial
675.2.ba.b.218.5		192	27.2	odd	18	inner
675.2.ba.b.257.5		192	5.2	odd	4	inner
675.2.ba.b.407.5		192	135.2	even	36	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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.ba (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.606324 + 0.865920i) q^{2} +(-1.47671 + 0.905161i) q^{3} +(0.301851 + 0.829330i) q^{4} +(0.111569 - 1.82754i) q^{6} +(2.61975 - 1.22161i) q^{7} +(-2.94330 - 0.788655i) q^{8} +(1.36137 - 2.67333i) q^{9} +(1.51740 + 1.80836i) q^{11} +(-1.19642 - 0.951458i) q^{12} +(4.45519 - 3.11956i) q^{13} +(-0.530600 + 3.00918i) q^{14} +(1.11535 - 0.935892i) q^{16} +(2.67549 - 0.716894i) q^{17} +(1.48946 + 2.79974i) q^{18} +(5.35751 - 3.09316i) q^{19} +(-2.76286 + 4.17526i) q^{21} +(-2.48593 + 0.217491i) q^{22} +(0.301527 - 0.646627i) q^{23} +(5.06027 - 1.49954i) q^{24} +5.74930i q^{26} +(0.409444 + 5.18000i) q^{27} +(1.80389 + 1.80389i) q^{28} +(-0.623300 - 3.53491i) q^{29} +(-5.18043 + 1.88552i) q^{31} +(-0.397007 - 4.53781i) q^{32} +(-3.87762 - 1.29695i) q^{33} +(-1.00144 + 2.75143i) q^{34} +(2.62800 + 0.322074i) q^{36} +(-1.14193 - 4.26173i) q^{37} +(-0.569956 + 6.51463i) q^{38} +(-3.75534 + 8.63936i) q^{39} +(5.70140 + 1.00531i) q^{41} +(-1.94025 - 4.92398i) q^{42} +(-1.44271 - 0.126221i) q^{43} +(-1.04170 + 1.80428i) q^{44} +(0.377104 + 0.653164i) q^{46} +(4.38688 + 9.40770i) q^{47} +(-0.799924 + 2.39162i) q^{48} +(0.871236 - 1.03830i) q^{49} +(-3.30202 + 3.48039i) q^{51} +(3.93195 + 2.75318i) q^{52} +(-7.22940 + 7.22940i) q^{53} +(-4.73372 - 2.78621i) q^{54} +(-8.67413 + 1.52948i) q^{56} +(-5.11170 + 9.41712i) q^{57} +(3.43887 + 1.60357i) q^{58} +(-6.27320 - 5.26384i) q^{59} +(2.64019 + 0.960952i) q^{61} +(1.50831 - 5.62907i) q^{62} +(0.300676 - 8.66650i) q^{63} +(6.69194 + 3.86359i) q^{64} +(3.47414 - 2.57134i) q^{66} +(4.28254 + 6.11610i) q^{67} +(1.40214 + 2.00246i) q^{68} +(0.140033 + 1.22781i) q^{69} +(-4.24004 - 2.44799i) q^{71} +(-6.11524 + 6.79476i) q^{72} +(-1.80353 + 6.73088i) q^{73} +(4.38269 + 1.59517i) q^{74} +(4.18242 + 3.50947i) q^{76} +(6.18430 + 2.88379i) q^{77} +(-5.20404 - 8.49007i) q^{78} +(12.8661 - 2.26863i) q^{79} +(-5.29336 - 7.27876i) q^{81} +(-4.32741 + 4.32741i) q^{82} +(3.90587 + 2.73492i) q^{83} +(-4.29664 - 1.03102i) q^{84} +(0.984048 - 1.17274i) q^{86} +(4.12010 + 4.65586i) q^{87} +(-3.03998 - 6.51925i) q^{88} +(-3.33276 - 5.77251i) q^{89} +(7.86060 - 13.6150i) q^{91} +(0.627283 + 0.0548802i) q^{92} +(5.94331 - 7.47350i) q^{93} +(-10.8062 - 1.90542i) q^{94} +(4.69371 + 6.34168i) q^{96} +(1.59893 - 18.2758i) q^{97} +(0.370833 + 1.38397i) q^{98} +(6.90008 - 1.59465i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Introduction

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