LMFDB - Embedded newform 675.2.ba.b.257.5

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			257.5
Character	$\chi$	$=$	675.257
Dual form			675.2.ba.b.218.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.865920 - 0.606324i) q^{2} +(0.905161 + 1.47671i) q^{3} +(-0.301851 - 0.829330i) q^{4} +(0.111569 - 1.82754i) q^{6} +(1.22161 + 2.61975i) q^{7} +(-0.788655 + 2.94330i) q^{8} +(-1.36137 + 2.67333i) q^{9} +(1.51740 + 1.80836i) q^{11} +(0.951458 - 1.19642i) q^{12} +(-3.11956 - 4.45519i) q^{13} +(0.530600 - 3.00918i) q^{14} +(1.11535 - 0.935892i) q^{16} +(0.716894 + 2.67549i) q^{17} +(2.79974 - 1.48946i) q^{18} +(-5.35751 + 3.09316i) q^{19} +(-2.76286 + 4.17526i) q^{21} +(-0.217491 - 2.48593i) q^{22} +(-0.646627 - 0.301527i) q^{23} +(-5.06027 + 1.49954i) q^{24} +5.74930i q^{26} +(-5.18000 + 0.409444i) q^{27} +(1.80389 - 1.80389i) q^{28} +(0.623300 + 3.53491i) q^{29} +(-5.18043 + 1.88552i) q^{31} +(4.53781 - 0.397007i) q^{32} +(-1.29695 + 3.87762i) q^{33} +(1.00144 - 2.75143i) q^{34} +(2.62800 + 0.322074i) q^{36} +(4.26173 - 1.14193i) q^{37} +(6.51463 + 0.569956i) q^{38} +(3.75534 - 8.63936i) q^{39} +(5.70140 + 1.00531i) q^{41} +(4.92398 - 1.94025i) q^{42} +(-0.126221 + 1.44271i) q^{43} +(1.04170 - 1.80428i) q^{44} +(0.377104 + 0.653164i) q^{46} +(-9.40770 + 4.38688i) q^{47} +(2.39162 + 0.799924i) q^{48} +(-0.871236 + 1.03830i) q^{49} +(-3.30202 + 3.48039i) q^{51} +(-2.75318 + 3.93195i) q^{52} +(7.22940 + 7.22940i) q^{53} +(4.73372 + 2.78621i) q^{54} +(-8.67413 + 1.52948i) q^{56} +(-9.41712 - 5.11170i) q^{57} +(1.60357 - 3.43887i) q^{58} +(6.27320 + 5.26384i) q^{59} +(2.64019 + 0.960952i) q^{61} +(5.62907 + 1.50831i) q^{62} +(-8.66650 - 0.300676i) q^{63} +(-6.69194 - 3.86359i) q^{64} +(3.47414 - 2.57134i) q^{66} +(-6.11610 + 4.28254i) q^{67} +(2.00246 - 1.40214i) q^{68} +(-0.140033 - 1.22781i) q^{69} +(-4.24004 - 2.44799i) q^{71} +(-6.79476 - 6.11524i) q^{72} +(6.73088 + 1.80353i) q^{73} +(-4.38269 - 1.59517i) q^{74} +(4.18242 + 3.50947i) q^{76} +(-2.88379 + 6.18430i) q^{77} +(-8.49007 + 5.20404i) q^{78} +(-12.8661 + 2.26863i) q^{79} +(-5.29336 - 7.27876i) q^{81} +(-4.32741 - 4.32741i) q^{82} +(2.73492 - 3.90587i) q^{83} +(4.29664 + 1.03102i) q^{84} +(0.984048 - 1.17274i) q^{86} +(-4.65586 + 4.12010i) q^{87} +(-6.51925 + 3.03998i) q^{88} +(3.33276 + 5.77251i) q^{89} +(7.86060 - 13.6150i) q^{91} +(-0.0548802 + 0.627283i) q^{92} +(-7.47350 - 5.94331i) q^{93} +(10.8062 + 1.90542i) q^{94} +(4.69371 + 6.34168i) q^{96} +(18.2758 + 1.59893i) q^{97} +(1.38397 - 0.370833i) 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 $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.865920	−	0.606324i	−0.612298	−	0.428736i	0.225863	−	0.974159i	$-0.427480\pi$
$2$	−0.865920	−	0.606324i	−0.612298	−	0.428736i	−0.838161	+	0.545424i	$0.816369\pi$
$3$	0.905161	+	1.47671i	0.522595	+	0.852581i
$3$	0.905161	+	1.47671i	0.522595	+	0.852581i
$4$	−0.301851	−	0.829330i	−0.150926	−	0.414665i
$5$		0			0
$5$		0			0
$6$	0.111569	−	1.82754i	0.0455480	−	0.746089i
$7$	1.22161	+	2.61975i	0.461725	+	0.990171i	0.989996	+	0.141096i	$0.0450626\pi$
$7$	1.22161	+	2.61975i	0.461725	+	0.990171i	−0.528271	+	0.849076i	$0.677160\pi$
$8$	−0.788655	+	2.94330i	−0.278832	+	1.04061i
$9$	−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	$0.661959\pi$
$12$	0.951458	−	1.19642i	0.274662	−	0.345378i
$13$	−3.11956	−	4.45519i	−0.865210	−	1.23565i	−0.970475	−	0.241203i	$-0.922458\pi$
$13$	−3.11956	−	4.45519i	−0.865210	−	1.23565i	0.105265	−	0.994444i	$-0.466431\pi$
$14$	0.530600	−	3.00918i	0.141809	−	0.804238i
$15$		0			0
$16$	1.11535	−	0.935892i	0.278838	−	0.233973i
$17$	0.716894	+	2.67549i	0.173872	+	0.648901i	0.996741	+	0.0806688i	$0.0257056\pi$
$17$	0.716894	+	2.67549i	0.173872	+	0.648901i	−0.822869	+	0.568232i	$0.807628\pi$
$18$	2.79974	−	1.48946i	0.659904	−	0.351069i
$19$	−5.35751	+	3.09316i	−1.22910	+	0.709619i	−0.966841	−	0.255379i	$-0.917800\pi$
$19$	−5.35751	+	3.09316i	−1.22910	+	0.709619i	−0.262256	+	0.964998i	$0.584466\pi$
$20$		0			0
$21$	−2.76286	+	4.17526i	−0.602906	+	0.911116i
$22$	−0.217491	−	2.48593i	−0.0463692	−	0.530002i
$23$	−0.646627	−	0.301527i	−0.134831	−	0.0628728i	0.354032	−	0.935233i	$-0.384810\pi$
$23$	−0.646627	−	0.301527i	−0.134831	−	0.0628728i	−0.488863	+	0.872361i	$0.662588\pi$
$24$	−5.06027	+	1.49954i	−1.03292	+	0.306093i
$25$		0			0
$26$			5.74930i			1.12753i
$27$	−5.18000	+	0.409444i	−0.996891	+	0.0787976i
$28$	1.80389	−	1.80389i	0.340903	−	0.340903i
$29$	0.623300	+	3.53491i	0.115744	+	0.656416i	0.986379	+	0.164487i	$0.0525969\pi$
$29$	0.623300	+	3.53491i	0.115744	+	0.656416i	−0.870635	+	0.491929i	$0.836292\pi$
$30$		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	$0.553747\pi$
$32$	4.53781	−	0.397007i	0.802178	−	0.0701815i
$33$	−1.29695	+	3.87762i	−0.225769	+	0.675007i
$34$	1.00144	−	2.75143i	0.171745	−	0.471866i
$35$		0			0
$36$	2.62800	+	0.322074i	0.438000	+	0.0536790i
$37$	4.26173	−	1.14193i	0.700624	−	0.187732i	0.109114	−	0.994029i	$-0.465199\pi$
$37$	4.26173	−	1.14193i	0.700624	−	0.187732i	0.591510	+	0.806298i	$0.298532\pi$
$38$	6.51463	+	0.569956i	1.05681	+	0.0924591i
$39$	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	$0.406240\pi$
$42$	4.92398	−	1.94025i	0.759786	−	0.299387i
$43$	−0.126221	+	1.44271i	−0.0192485	+	0.220012i	0.980478	+	0.196629i	$0.0629993\pi$
$43$	−0.126221	+	1.44271i	−0.0192485	+	0.220012i	−0.999727	+	0.0233831i	$0.992556\pi$
$44$	1.04170	−	1.80428i	0.157042	−	0.272005i
$45$		0			0
$46$	0.377104	+	0.653164i	0.0556010	+	0.0963037i
$47$	−9.40770	+	4.38688i	−1.37225	+	0.639893i	−0.962244	−	0.272188i	$-0.912253\pi$
$47$	−9.40770	+	4.38688i	−1.37225	+	0.639893i	−0.410010	+	0.912081i	$0.634475\pi$
$48$	2.39162	+	0.799924i	0.345201	+	0.115459i
$49$	−0.871236	+	1.03830i	−0.124462	+	0.148328i
$50$		0			0
$51$	−3.30202	+	3.48039i	−0.462375	+	0.487353i
$52$	−2.75318	+	3.93195i	−0.381797	+	0.545263i
$53$	7.22940	+	7.22940i	0.993035	+	0.993035i	0.999976	−	0.00694140i	$-0.00220953\pi$
$53$	7.22940	+	7.22940i	0.993035	+	0.993035i	−0.00694140	+	0.999976i	$0.502210\pi$
$54$	4.73372	+	2.78621i	0.644177	+	0.379155i
$55$		0			0
$56$	−8.67413	+	1.52948i	−1.15913	+	0.204386i
$57$	−9.41712	−	5.11170i	−1.24733	−	0.677061i
$58$	1.60357	−	3.43887i	0.210559	−	0.451546i
$59$	6.27320	+	5.26384i	0.816701	+	0.685293i	0.952197	−	0.305484i	$-0.0988184\pi$
$59$	6.27320	+	5.26384i	0.816701	+	0.685293i	−0.135496	+	0.990778i	$0.543263\pi$
$60$		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	$0.553544\pi$
$62$	5.62907	+	1.50831i	0.714893	+	0.191555i
$63$	−8.66650	−	0.300676i	−1.09188	−	0.0378817i
$64$	−6.69194	−	3.86359i	−0.836493	−	0.482949i
$65$		0			0
$66$	3.47414	−	2.57134i	0.427637	−	0.316510i
$67$	−6.11610	+	4.28254i	−0.747201	+	0.523196i	−0.884048	−	0.467396i	$-0.845192\pi$
$67$	−6.11610	+	4.28254i	−0.747201	+	0.523196i	0.136847	+	0.990592i	$0.456303\pi$
$68$	2.00246	−	1.40214i	0.242834	−	0.170034i
$69$	−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	$0.760496\pi$
$72$	−6.79476	−	6.11524i	−0.800770	−	0.720688i
$73$	6.73088	+	1.80353i	0.787790	+	0.211088i	0.630216	−	0.776420i	$-0.282966\pi$
$73$	6.73088	+	1.80353i	0.787790	+	0.211088i	0.157574	+	0.987507i	$0.449633\pi$
$74$	−4.38269	−	1.59517i	−0.509478	−	0.185435i
$75$		0			0
$76$	4.18242	+	3.50947i	0.479756	+	0.402563i
$77$	−2.88379	+	6.18430i	−0.328638	+	0.704767i
$78$	−8.49007	+	5.20404i	−0.961311	+	0.589242i
$79$	−12.8661	+	2.26863i	−1.44754	+	0.255241i	−0.841529	−	0.540212i	$-0.818344\pi$
$79$	−12.8661	+	2.26863i	−1.44754	+	0.255241i	−0.606015	+	0.795453i	$0.707233\pi$
$80$		0			0
$81$	−5.29336	−	7.27876i	−0.588151	−	0.808751i
$82$	−4.32741	−	4.32741i	−0.477883	−	0.477883i
$83$	2.73492	−	3.90587i	0.300196	−	0.428724i	−0.640509	−	0.767951i	$-0.721276\pi$
$83$	2.73492	−	3.90587i	0.300196	−	0.428724i	0.940705	+	0.339227i	$0.110165\pi$
$84$	4.29664	+	1.03102i	0.468802	+	0.112493i
$85$		0			0
$86$	0.984048	−	1.17274i	0.106113	−	0.126460i
$87$	−4.65586	+	4.12010i	−0.499161	+	0.441721i
$88$	−6.51925	+	3.03998i	−0.694955	+	0.324063i
$89$	3.33276	+	5.77251i	0.353272	+	0.611885i	0.986821	−	0.161818i	$-0.0517357\pi$
$89$	3.33276	+	5.77251i	0.353272	+	0.611885i	−0.633549	+	0.773703i	$0.718402\pi$
$90$		0			0
$91$	7.86060	−	13.6150i	0.824014	−	1.42723i
$92$	−0.0548802	+	0.627283i	−0.00572165	+	0.0653988i
$93$	−7.47350	−	5.94331i	−0.774966	−	0.616292i
$94$	10.8062	+	1.90542i	1.11457	+	0.196529i
$95$		0			0
$96$	4.69371	+	6.34168i	0.479050	+	0.647245i
$97$	18.2758	+	1.59893i	1.85563	+	0.162346i	0.959547	−	0.281548i	$-0.0908478\pi$
$97$	18.2758	+	1.59893i	1.85563	+	0.162346i	0.896079	+	0.443894i	$0.146403\pi$
$98$	1.38397	−	0.370833i	0.139802	−	0.0374597i
$99$	−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	$0.164701\pi$
$102$	4.96953	−	1.01165i	0.492057	−	0.100168i
$103$	3.61346	−	0.316137i	0.356045	−	0.0311499i	0.0922694	−	0.995734i	$-0.470588\pi$
$103$	3.61346	−	0.316137i	0.356045	−	0.0311499i	0.263775	+	0.964584i	$0.415032\pi$
$104$	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	$-0.661057\pi$
$107$	4.03460	−	4.03460i	0.390039	−	0.390039i	0.874701	+	0.484662i	$0.161057\pi$
$108$	1.90315	+	4.17233i	0.183131	+	0.401483i
$109$		−	15.8226i		−	1.51553i	−0.652527	−	0.757765i	$-0.726291\pi$
$109$		−	15.8226i		−	1.51553i	0.652527	−	0.757765i	$-0.273709\pi$
$110$		0			0
$111$	5.54385	+	5.25972i	0.526199	+	0.499231i
$112$	3.81433	+	1.77865i	0.360420	+	0.168067i
$113$	0.232615	+	2.65880i	0.0218825	+	0.250119i	0.999255	+	0.0385931i	$0.0122876\pi$
$113$	0.232615	+	2.65880i	0.0218825	+	0.250119i	−0.977372	+	0.211526i	$0.932157\pi$
$114$	5.05513	+	10.1361i	0.473456	+	0.949337i
$115$		0			0
$116$	2.74346	−	1.58394i	0.254724	−	0.147065i
$117$	16.1570	−	2.27446i	1.49372	−	0.210273i
$118$	−2.24050	−	8.36165i	−0.206255	−	0.769753i
$119$	−6.13333	+	5.14648i	−0.562242	+	0.471777i
$120$		0			0
$121$	0.942447	−	5.34488i	0.0856770	−	0.485898i
$122$	−1.70355	−	2.43292i	−0.154232	−	0.220266i
$123$	3.67613	+	9.32930i	0.331466	+	0.841195i
$124$	3.12744	+	3.72713i	0.280852	+	0.334707i
$125$		0			0
$126$	7.32219	+	5.51507i	0.652312	+	0.491321i
$127$	0.846401	−	3.15881i	0.0751059	−	0.280299i	−0.918151	−	0.396230i	$-0.870318\pi$
$127$	0.846401	−	3.15881i	0.0751059	−	0.280299i	0.993257	+	0.115931i	$0.0369850\pi$
$128$	−0.398073	−	0.853671i	−0.0351850	−	0.0754546i
$129$	−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	$0.868659\pi$
$132$	3.60731	−	0.0948693i	0.313976	−	0.00825731i
$133$	−14.6481	−	10.2567i	−1.27015	−	0.889368i
$134$	7.89266			0.681822
$135$		0			0
$136$	−8.44014			−0.723736
$137$	13.0703	+	9.15193i	1.11667	+	0.781902i	0.978035	−	0.208442i	$-0.0668391\pi$
$137$	13.0703	+	9.15193i	1.11667	+	0.781902i	0.138637	+	0.990343i	$0.455728\pi$
$138$	−0.623196	+	1.14809i	−0.0530499	+	0.0977322i
$139$	−3.12149	−	8.57623i	−0.264762	−	0.727426i	−0.998830	−	0.0483514i	$-0.984603\pi$
$139$	−3.12149	−	8.57623i	−0.264762	−	0.727426i	0.734069	−	0.679075i	$-0.237619\pi$
$140$		0			0
$141$	−14.9937	−	9.92164i	−1.26269	−	0.835553i
$142$	2.18726	+	4.69060i	0.183551	+	0.393626i
$143$	3.32299	−	12.4016i	0.277883	−	1.03707i
$144$	0.983543	+	4.25580i	0.0819619	+	0.354650i
$145$		0			0
$146$	−4.73488	−	5.64281i	−0.391861	−	0.467002i
$147$	−2.32188	−	0.346738i	−0.191505	−	0.0285985i
$148$	−2.23344	−	3.18968i	−0.183588	−	0.262190i
$149$	1.63395	−	9.26659i	0.133858	−	0.759149i	−0.841789	−	0.539806i	$-0.818498\pi$
$149$	1.63395	−	9.26659i	0.133858	−	0.759149i	0.975648	−	0.219343i	$-0.0703913\pi$
$150$		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	$0.291457\pi$
$152$	−4.87887	−	18.2082i	−0.395729	−	1.47688i
$153$	−8.12841	−	1.72582i	−0.657143	−	0.139525i
$154$	6.24682	−	3.60660i	0.503383	−	0.290628i
$155$		0			0
$156$	−8.29843	−	0.506611i	−0.664406	−	0.0405613i
$157$	−1.94520	−	22.2338i	−0.155244	−	1.77445i	−0.530652	−	0.847590i	$-0.678053\pi$
$157$	−1.94520	−	22.2338i	−0.155244	−	1.77445i	0.375408	−	0.926860i	$-0.377503\pi$
$158$	12.5165	+	5.83654i	0.995759	+	0.464330i
$159$	−4.13198	+	17.2195i	−0.327687	+	1.36560i
$160$		0			0
$161$		−	2.06235i		−	0.162536i
$162$	0.170346	+	9.51231i	0.0133837	+	0.747358i
$163$	1.74889	−	1.74889i	0.136983	−	0.136983i	−0.635290	−	0.772274i	$-0.719119\pi$
$163$	1.74889	−	1.74889i	0.136983	−	0.136983i	0.772274	+	0.635290i	$0.219119\pi$
$164$	−0.887241	−	5.03179i	−0.0692819	−	0.392917i
$165$		0			0
$166$	−4.73644	+	1.72392i	−0.367619	+	0.133802i
$167$	−7.25686	+	0.634893i	−0.561553	+	0.0491295i	−0.364399	−	0.931243i	$-0.618725\pi$
$167$	−7.25686	+	0.634893i	−0.561553	+	0.0491295i	−0.197154	+	0.980373i	$0.563170\pi$
$168$	−10.1101	−	11.4248i	−0.780011	−	0.881441i
$169$	−5.67082	+	15.5805i	−0.436217	+	1.19850i
$170$		0			0
$171$	−0.975496	−	18.5333i	−0.0745981	−	1.41728i
$172$	1.23458	−	0.330806i	0.0941362	−	0.0252237i
$173$	−20.4232	−	1.78680i	−1.55275	−	0.135848i	−0.721760	−	0.692143i	$-0.756667\pi$
$173$	−20.4232	−	1.78680i	−1.55275	−	0.135848i	−0.830985	+	0.556295i	$0.812222\pi$
$174$	6.52972	−	0.744716i	0.495017	−	0.0564568i
$175$		0			0
$176$	3.38487	+	0.596843i	0.255144	+	0.0449887i
$177$	−2.09493	+	14.0283i	−0.157464	+	1.05443i
$178$	0.614106	−	7.01926i	0.0460292	−	0.526116i
$179$	7.17079	−	12.4202i	0.535970	−	0.928327i	−0.463146	−	0.886282i	$-0.653279\pi$
$179$	7.17079	−	12.4202i	0.535970	−	0.928327i	0.999116	−	0.0420450i	$-0.0133873\pi$
$180$		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	$0.808828\pi$
$182$	−15.0617	+	7.02339i	−1.11645	+	0.520609i
$183$	0.970750	+	4.76862i	0.0717599	+	0.352507i
$184$	1.39745	−	1.66542i	0.103021	−	0.122776i
$185$		0			0
$186$	2.86788	+	9.67779i	0.210283	+	0.709610i
$187$	−3.75043	+	5.35618i	−0.274259	+	0.391682i
$188$	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	$0.124911\pi$
$192$	−0.351864	−	13.3793i	−0.0253936	−	0.965564i
$193$	0.131693	−	0.282417i	0.00947948	−	0.0203288i	−0.901511	−	0.432756i	$-0.857541\pi$
$193$	0.131693	−	0.282417i	0.00947948	−	0.0203288i	0.910991	+	0.412427i	$0.135319\pi$
$194$	−14.8559	−	12.4656i	−1.06659	−	0.894977i
$195$		0			0
$196$	1.12408	+	0.409130i	0.0802911	+	0.0292236i
$197$	3.13774	+	0.840756i	0.223555	+	0.0599014i	0.368858	−	0.929486i	$-0.379749\pi$
$197$	3.13774	+	0.840756i	0.223555	+	0.0599014i	−0.145303	+	0.989387i	$0.546416\pi$
$198$	6.94179	+	2.80284i	0.493332	+	0.199189i
$199$	5.52277	+	3.18857i	0.391499	+	0.226032i	0.682809	−	0.730596i	$-0.260758\pi$
$199$	5.52277	+	3.18857i	0.391499	+	0.226032i	−0.291310	+	0.956629i	$0.594091\pi$
$200$		0			0
$201$	−11.8601	−	5.15534i	−0.836550	−	0.363630i
$202$	2.91638	−	2.04207i	0.205196	−	0.143679i
$203$	−8.49914	+	5.95116i	−0.596523	+	0.417690i
$204$	3.88311	+	1.68790i	0.271872	+	0.118177i
$205$		0			0
$206$	−3.32065	−	1.91718i	−0.231360	−	0.133576i
$207$	1.68638	−	1.31816i	0.117211	−	0.0916183i
$208$	−7.64899	−	2.04954i	−0.530362	−	0.142110i
$209$	−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	$0.651349\pi$
$212$	3.81335	−	8.17776i	0.261902	−	0.561651i
$213$	−0.222942	−	8.47715i	−0.0152757	−	0.580844i
$214$	−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
$218$	−9.59362	+	13.7011i	−0.649762	+	0.927956i
$219$	3.42923	+	11.5721i	0.231726	+	0.781968i
$220$		0			0
$221$	9.68341	−	11.5402i	0.651376	−	0.776280i
$222$	−1.61143	−	7.91587i	−0.108152	−	0.531278i
$223$	9.41489	−	4.39023i	0.630467	−	0.293992i	−0.0809965	−	0.996714i	$-0.525810\pi$
$223$	9.41489	−	4.39023i	0.630467	−	0.293992i	0.711464	+	0.702723i	$0.248032\pi$
$224$	6.58348	+	11.4029i	0.439877	+	0.761889i
$225$		0			0
$226$	1.41067	−	2.44335i	0.0938361	−	0.162529i
$227$	−0.272304	+	3.11245i	−0.0180734	+	0.206580i	0.981789	+	0.189976i	$0.0608411\pi$
$227$	−0.272304	+	3.11245i	−0.0180734	+	0.206580i	−0.999862	+	0.0166042i	$0.994714\pi$
$228$	−1.39671	+	9.35287i	−0.0924996	+	0.619409i
$229$	23.1368	+	4.07964i	1.52892	+	0.269590i	0.873933	−	0.486047i	$-0.161562\pi$
$229$	23.1368	+	4.07964i	1.52892	+	0.269590i	0.654990	+	0.755638i	$0.272673\pi$
$230$		0			0
$231$	−11.7427	+	1.33926i	−0.772616	+	0.0881170i
$232$	−10.8959	−	0.953265i	−0.715349	−	0.0625849i
$233$	3.20411	−	0.858538i	0.209908	−	0.0562447i	−0.152333	−	0.988329i	$-0.548679\pi$
$233$	3.20411	−	0.858538i	0.209908	−	0.0562447i	0.362241	+	0.932085i	$0.382012\pi$
$234$	−15.3698	−	7.82690i	−1.00475	−	0.511661i
$235$		0			0
$236$	2.47188	−	6.79145i	0.160906	−	0.442085i
$237$	−14.9960	−	16.9460i	−0.974093	−	1.10076i
$238$	8.43141	−	0.737653i	0.546527	−	0.0478149i
$239$	−15.9837	+	5.81759i	−1.03390	+	0.376309i	−0.802564	−	0.596566i	$-0.796532\pi$
$239$	−15.9837	+	5.81759i	−1.03390	+	0.376309i	−0.231335	+	0.972874i	$0.574309\pi$
$240$		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
$243$	5.95729	−	14.4052i	0.382160	−	0.924096i
$244$		−	2.47965i		−	0.158744i
$245$		0			0
$246$	2.47334	−	10.3074i	0.157695	−	0.657173i
$247$	30.4937	+	14.2194i	1.94027	+	0.904761i
$248$	−1.46409	−	16.7346i	−0.0929695	−	1.06265i
$249$	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	$0.492402\pi$
$252$	2.36663	+	7.27814i	0.149084	+	0.458480i
$253$	−0.435919	−	1.62687i	−0.0274060	−	0.102281i
$254$	−2.64818	+	2.22208i	−0.166161	+	0.139426i
$255$		0			0
$256$	−2.85653	+	16.2002i	−0.178533	+	1.01251i
$257$	−4.98418	−	7.11815i	−0.310905	−	0.444018i	0.633041	−	0.774118i	$-0.281806\pi$
$257$	−4.98418	−	7.11815i	−0.310905	−	0.444018i	−0.943946	+	0.330100i	$0.892917\pi$
$258$	2.62253	+	0.391636i	0.163271	+	0.0243822i
$259$	8.19772	+	9.76966i	0.509382	+	0.607057i
$260$		0			0
$261$	−10.2985	−	3.14602i	−0.637462	−	0.194734i
$262$	0.397759	−	1.48446i	0.0245736	−	0.0917099i
$263$	−9.97382	−	21.3889i	−0.615012	−	1.31890i	−0.929214	−	0.369541i	$-0.879515\pi$
$263$	−9.97382	−	21.3889i	−0.615012	−	1.31890i	0.314203	−	0.949356i	$-0.398263\pi$
$264$	−10.3902	−	6.87540i	−0.639470	−	0.423152i
$265$		0			0
$266$	6.46518	+	17.7629i	0.396406	+	1.08912i
$267$	−5.50766	+	10.1466i	−0.337063	+	0.620961i
$268$	5.39779	+	3.77957i	0.329723	+	0.230874i
$269$	10.2124			0.622659			0.311330	−	0.950302i	$-0.399226\pi$
$269$	10.2124			0.622659			0.311330	+	0.950302i	$0.399226\pi$
$270$		0			0
$271$	4.84409			0.294258			0.147129	−	0.989117i	$-0.452997\pi$
$271$	4.84409			0.294258			0.147129	+	0.989117i	$0.452997\pi$
$272$	3.30356	+	2.31318i	0.200308	+	0.140257i
$273$	27.2205	−	0.715877i	1.64746	−	0.0433268i
$274$	−5.76881	−	15.8497i	−0.348506	−	0.957514i
$275$		0			0
$276$	−0.975993	+	0.486750i	−0.0587479	+	0.0292989i
$277$	5.71185	+	12.2491i	0.343192	+	0.735978i	0.999834	−	0.0182248i	$-0.00580146\pi$
$277$	5.71185	+	12.2491i	0.343192	+	0.735978i	−0.656642	+	0.754203i	$0.728024\pi$
$278$	−2.49701	+	9.31897i	−0.149761	+	0.558914i
$279$	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	$0.933306\pi$
$282$	6.96758	+	17.6824i	0.414913	+	1.05297i
$283$	17.2952	+	24.7001i	1.02809	+	1.46827i	0.877443	+	0.479680i	$0.159247\pi$
$283$	17.2952	+	24.7001i	1.02809	+	1.46827i	0.150648	+	0.988587i	$0.451864\pi$
$284$	−0.750327	+	4.25532i	−0.0445237	+	0.252507i
$285$		0			0
$286$	−10.3968	+	8.72397i	−0.614777	+	0.515859i
$287$	4.33122	+	16.1643i	0.255664	+	0.954150i
$288$	−5.11629	+	12.6715i	−0.301480	+	0.746676i
$289$	8.07815	−	4.66392i	0.475185	−	0.274348i
$290$		0			0
$291$	14.1814	+	28.4354i	0.831328	+	1.66691i
$292$	−0.536001	−	6.12652i	−0.0313671	−	0.358527i
$293$	6.65512	+	3.10333i	0.388796	+	0.181299i	0.607180	−	0.794564i	$-0.292301\pi$
$293$	6.65512	+	3.10333i	0.388796	+	0.181299i	−0.218384	+	0.975863i	$0.570078\pi$
$294$	1.80033	+	1.70806i	0.104997	+	0.0996160i
$295$		0			0
$296$			13.4441i			0.781424i
$297$	−8.60053	−	8.74602i	−0.499053	−	0.507496i
$298$	−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
$302$	1.11185	−	0.0972742i	0.0639798	−	0.00559750i
$303$	−5.71622	+	1.16365i	−0.328388	+	0.0668501i
$304$	−3.08065	+	8.46402i	−0.176687	+	0.485445i
$305$		0			0
$306$	5.99214	+	6.42287i	0.342548	+	0.367171i
$307$	−13.2129	+	3.54038i	−0.754099	+	0.202060i	−0.615336	−	0.788265i	$-0.710980\pi$
$307$	−13.2129	+	3.54038i	−0.754099	+	0.202060i	−0.138764	+	0.990326i	$0.544313\pi$
$308$	5.99930	+	0.524871i	0.341842	+	0.0299073i
$309$	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	$0.520641\pi$
$312$	22.4666	+	17.8666i	1.27192	+	1.01149i
$313$	−2.14418	+	24.5081i	−0.121196	+	1.38528i	0.655401	+	0.755281i	$0.272500\pi$
$313$	−2.14418	+	24.5081i	−0.121196	+	1.38528i	−0.776597	+	0.629997i	$0.783056\pi$
$314$	−11.7965	+	20.4321i	−0.665714	+	1.15305i
$315$		0			0
$316$	5.76508	+	9.98541i	0.324311	+	0.561723i
$317$	−14.9555	+	6.97386i	−0.839984	+	0.391691i	−0.794493	−	0.607274i	$-0.792263\pi$
$317$	−14.9555	+	6.97386i	−0.839984	+	0.391691i	−0.0454916	+	0.998965i	$0.514485\pi$
$318$	14.0186	−	12.4054i	0.786123	−	0.695661i
$319$	−5.44660	+	6.49101i	−0.304951	+	0.363427i
$320$		0			0
$321$	9.60991	+	2.30598i	0.536373	+	0.128707i
$322$	−1.25045	+	1.78583i	−0.0696849	+	0.0995203i
$323$	−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
$327$	23.3654	−	14.3220i	1.29211	−	0.792009i
$328$	−7.45537	+	15.9881i	−0.411654	+	0.882794i
$329$	−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	$0.803123\pi$
$332$	−4.06479	−	1.08916i	−0.223084	−	0.0597752i
$333$	−2.74903	+	12.9476i	−0.150646	+	0.709523i
$334$	6.66881	+	3.85024i	0.364901	+	0.210676i
$335$		0			0
$336$	0.826024	+	7.24263i	0.0450633	+	0.395118i
$337$	8.57053	−	6.00115i	0.466867	−	0.326904i	−0.316361	−	0.948639i	$-0.602461\pi$
$337$	8.57053	−	6.00115i	0.466867	−	0.326904i	0.783227	+	0.621735i	$0.213572\pi$
$338$	14.3573	−	10.0531i	0.780933	−	0.546815i
$339$	−3.71573	+	2.75015i	−0.201811	+	0.149367i
$340$		0			0
$341$	−11.2705	−	6.50701i	−0.610330	−	0.352374i
$342$	−10.3925	+	16.6398i	−0.561961	+	0.899778i
$343$	15.7602	+	4.22292i	0.850968	+	0.228016i
$344$	−4.14679	−	1.50931i	−0.223580	−	0.0813765i
$345$		0			0
$346$	16.6015	+	13.9303i	0.892500	+	0.748896i
$347$	4.85639	−	10.4146i	0.260705	−	0.559083i	−0.731767	−	0.681554i	$-0.761304\pi$
$347$	4.85639	−	10.4146i	0.260705	−	0.559083i	0.992472	+	0.122472i	$0.0390821\pi$
$348$	4.82230	+	2.61759i	0.258502	+	0.140317i
$349$	15.6377	−	2.75735i	0.837067	−	0.147597i	0.261347	−	0.965245i	$-0.415833\pi$
$349$	15.6377	−	2.75735i	0.837067	−	0.147597i	0.575719	+	0.817647i	$0.304722\pi$
$350$		0			0
$351$	17.9835	+	21.8006i	0.959886	+	1.16363i
$352$	7.60358	+	7.60358i	0.405272	+	0.405272i
$353$	−4.97772	+	7.10893i	−0.264938	+	0.378370i	−0.929475	−	0.368885i	$-0.879740\pi$
$353$	−4.97772	+	7.10893i	−0.264938	+	0.378370i	0.664538	+	0.747255i	$0.268629\pi$
$354$	10.3198	−	10.8772i	0.548489	−	0.578118i
$355$		0			0
$356$	3.78131	−	4.50640i	0.200409	−	0.238838i
$357$	−13.1515	−	4.39878i	−0.696053	−	0.232808i
$358$	−13.7400	+	6.40706i	−0.726180	+	0.338623i
$359$	10.2032	+	17.6725i	0.538505	+	0.932718i	0.998985	+	0.0450476i	$0.0143439\pi$
$359$	10.2032	+	17.6725i	0.538505	+	0.932718i	−0.460480	+	0.887670i	$0.652323\pi$
$360$		0			0
$361$	9.63526	−	16.6888i	0.507119	−	0.878356i
$362$	0.190664	−	2.17930i	0.0100211	−	0.114541i
$363$	8.74593	−	3.44626i	0.459042	−	0.180881i
$364$	−13.6640	−	2.40933i	−0.716189	−	0.126283i
$365$		0			0
$366$	2.05074	−	4.71784i	0.107194	−	0.246605i
$367$	−25.8506	−	2.26163i	−1.34939	−	0.118056i	−0.610571	−	0.791962i	$-0.709060\pi$
$367$	−25.8506	−	2.26163i	−1.34939	−	0.118056i	−0.738818	+	0.673906i	$0.764615\pi$
$368$	−1.00341	+	0.268864i	−0.0523066	+	0.0140155i
$369$	−10.4492	+	13.8731i	−0.543965	+	0.722206i
$370$		0			0
$371$	−10.1077	+	27.7707i	−0.524766	+	1.44178i
$372$	−2.67308	+	7.99199i	−0.138593	+	0.414365i
$373$	−4.75950	+	0.416402i	−0.246438	+	0.0215605i	−0.209705	−	0.977765i	$-0.567250\pi$
$373$	−4.75950	+	0.416402i	−0.246438	+	0.0215605i	−0.0367323	+	0.999325i	$0.511695\pi$
$374$	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
$378$	−1.51641	+	15.8048i	−0.0779958	+	0.812911i
$379$		−	25.3002i		−	1.29958i	−0.760112	−	0.649792i	$-0.774856\pi$
$379$		−	25.3002i		−	1.29958i	0.760112	−	0.649792i	$-0.225144\pi$
$380$		0			0
$381$	5.43079	−	1.60934i	0.278228	−	0.0824491i
$382$	−22.3379	−	10.4163i	−1.14291	−	0.532946i
$383$	1.07406	+	12.2766i	0.0548819	+	0.627303i	0.972971	+	0.230929i	$0.0741764\pi$
$383$	1.07406	+	12.2766i	0.0548819	+	0.627303i	−0.918089	+	0.396375i	$0.870268\pi$
$384$	0.900307	−	1.36055i	0.0459436	−	0.0694303i
$385$		0			0
$386$	−0.285272	+	0.164702i	−0.0145200	+	0.00838310i
$387$	−3.68501	−	2.30149i	−0.187320	−	0.116991i
$388$	−4.19054	−	15.6393i	−0.212742	−	0.793965i
$389$	6.83430	−	5.73466i	0.346513	−	0.290759i	−0.452875	−	0.891574i	$-0.649602\pi$
$389$	6.83430	−	5.73466i	0.346513	−	0.290759i	0.799388	+	0.600815i	$0.205157\pi$
$390$		0			0
$391$	0.343168	−	1.94620i	0.0173548	−	0.0984238i
$392$	−2.36892	−	3.38317i	−0.119649	−	0.170876i
$393$	−1.56732	+	1.97085i	−0.0790610	+	0.0994164i
$394$	−2.20727	−	2.63052i	−0.111200	−	0.132524i
$395$		0			0
$396$	3.40529	+	5.24109i	0.171122	+	0.263375i
$397$	−3.52782	+	13.1660i	−0.177056	+	0.660782i	0.819136	+	0.573599i	$0.194453\pi$
$397$	−3.52782	+	13.1660i	−0.177056	+	0.660782i	−0.996192	+	0.0871833i	$0.972213\pi$
$398$	−2.84897	−	6.10964i	−0.142806	−	0.306249i
$399$	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	$0.912230\pi$
$402$	7.14413	+	11.6552i	0.356317	+	0.581309i
$403$	24.5610	+	17.1978i	1.22347	+	0.856683i
$404$	2.97240			0.147882
$405$		0			0
$406$	10.9679			0.544328
$407$	8.53175	+	5.97399i	0.422903	+	0.296120i
$408$	−7.63969	−	12.4637i	−0.378221	−	0.617044i
$409$	9.80467	+	26.9381i	0.484810	+	1.33200i	0.905325	+	0.424719i	$0.139627\pi$
$409$	9.80467	+	26.9381i	0.484810	+	1.33200i	−0.420515	+	0.907285i	$0.638151\pi$
$410$		0			0
$411$	−1.68404	+	27.5851i	−0.0830676	+	1.36067i
$412$	−1.35291	−	2.90132i	−0.0666530	−	0.142938i
$413$	−6.12654	+	22.8645i	−0.301467	+	1.12509i
$414$	−2.25950	+	0.118928i	−0.111048	+	0.00584500i
$415$		0			0
$416$	−15.9247	−	18.9783i	−0.780772	−	0.930488i
$417$	9.83918	−	12.3724i	0.481827	−	0.605880i
$418$	8.85459	+	12.6457i	0.433092	+	0.618519i
$419$	−2.30839	+	13.0915i	−0.112772	+	0.639563i	0.875057	+	0.484020i	$0.160824\pi$
$419$	−2.30839	+	13.0915i	−0.112772	+	0.639563i	−0.987829	+	0.155543i	$0.950287\pi$
$420$		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	$0.206980\pi$
$422$	−1.75516	−	6.55035i	−0.0854399	−	0.318866i
$423$	1.07975	−	31.1220i	0.0524993	−	1.51320i
$424$	−26.9798	+	15.5768i	−1.31025	+	0.756476i
$425$		0			0
$426$	−4.94684	+	7.47571i	−0.239675	+	0.362199i
$427$	0.707831	+	8.09054i	0.0342543	+	0.391529i
$428$	−4.56386	−	2.12816i	−0.220602	−	0.102869i
$429$	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	$0.997731\pi$
$432$	−5.39433	+	5.30459i	−0.259535	+	0.255217i
$433$	−12.8171	+	12.8171i	−0.615949	+	0.615949i	−0.944490	−	0.328541i	$-0.893443\pi$
$433$	−12.8171	+	12.8171i	−0.615949	+	0.615949i	0.328541	+	0.944490i	$0.393443\pi$
$434$	2.92514	+	16.5893i	0.140411	+	0.796312i
$435$		0			0
$436$	−13.1221	+	4.77607i	−0.628437	+	0.228732i
$437$	4.39698	−	0.384686i	0.210336	−	0.0184020i
$438$	4.04698	−	12.0997i	0.193372	−	0.578146i
$439$	−9.75841	+	26.8110i	−0.465743	+	1.27962i	0.455362	+	0.890306i	$0.349510\pi$
$439$	−9.75841	+	26.8110i	−0.465743	+	1.27962i	−0.921105	+	0.389313i	$0.872712\pi$
$440$		0			0
$441$	−1.58964	−	3.74260i	−0.0756972	−	0.178219i
$442$	−15.3822	+	4.12164i	−0.731655	+	0.196046i
$443$	40.1651	+	3.51399i	1.90830	+	0.166955i	0.979204	−	0.202878i	$-0.0650296\pi$
$443$	40.1651	+	3.51399i	1.90830	+	0.166955i	0.929098	+	0.369833i	$0.120585\pi$
$444$	2.68863	−	6.18533i	0.127597	−	0.293543i
$445$		0			0
$446$	−10.8144	−	1.90688i	−0.512079	−	0.0902933i
$447$	15.1631	−	5.97488i	0.717190	−	0.282602i
$448$	1.94671	−	22.2510i	0.0919734	−	1.05126i
$449$	−3.91232	+	6.77634i	−0.184634	+	0.319795i	−0.943453	−	0.331506i	$-0.892443\pi$
$449$	−3.91232	+	6.77634i	−0.184634	+	0.319795i	0.758819	+	0.651301i	$0.225777\pi$
$450$		0			0
$451$	6.83332	+	11.8357i	0.321768	+	0.557319i
$452$	2.13480	−	0.995476i	0.100413	−	0.0468232i
$453$	−1.73429	−	0.580068i	−0.0814841	−	0.0272540i
$454$	2.12294	−	2.53003i	0.0996347	−	0.118740i
$455$		0			0
$456$	22.4721	−	23.6860i	1.05235	−	1.10920i
$457$	3.14363	−	4.48957i	0.147053	−	0.210013i	−0.738867	−	0.673851i	$-0.764639\pi$
$457$	3.14363	−	4.48957i	0.147053	−	0.210013i	0.885920	+	0.463838i	$0.153528\pi$
$458$	−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	$0.196726\pi$
$462$	10.9803	+	5.96021i	0.510850	+	0.277294i
$463$	−0.0761934	+	0.163397i	−0.00354101	+	0.00759371i	−0.908070	−	0.418818i	$-0.862445\pi$
$463$	−0.0761934	+	0.163397i	−0.00354101	+	0.00759371i	0.904529	+	0.426411i	$0.140222\pi$
$464$	4.00350	+	3.35933i	0.185858	+	0.155953i
$465$		0			0
$466$	−3.29505	−	1.19930i	−0.152640	−	0.0555566i
$467$	12.1916	+	3.26672i	0.564158	+	0.151166i	0.529616	−	0.848238i	$-0.322336\pi$
$467$	12.1916	+	3.26672i	0.564158	+	0.151166i	0.0345422	+	0.999403i	$0.489003\pi$
$468$	−6.76330	−	12.7130i	−0.312634	−	0.587657i
$469$	−18.6907	−	10.7911i	−0.863055	−	0.498285i
$470$		0			0
$471$	31.0722	−	22.9977i	1.43173	−	1.05968i
$472$	−20.4404	+	14.3126i	−0.940848	+	0.658789i
$473$	−2.80048	+	1.96091i	−0.128766	+	0.0901629i
$474$	2.71055	+	23.7663i	0.124500	+	1.09162i
$475$		0			0
$476$	6.11948	+	3.53308i	0.280486	+	0.161939i
$477$	−29.1684	+	9.48470i	−1.33553	+	0.434274i
$478$	17.3679	+	4.65373i	0.794391	+	0.212857i
$479$	−33.4923	−	12.1902i	−1.53030	−	0.556985i	−0.566607	−	0.823988i	$-0.691744\pi$
$479$	−33.4923	−	12.1902i	−1.53030	−	0.556985i	−0.963696	+	0.267003i	$0.913966\pi$
$480$		0			0
$481$	−18.3822	−	15.4245i	−0.838157	−	0.703297i
$482$	8.29007	−	17.7781i	0.377602	−	0.809771i
$483$	3.04550	−	1.86676i	0.138575	−	0.0849404i
$484$	−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	0.587604	−	0.809149i	$-0.300071\pi$
$487$	−4.88907	−	4.88907i	−0.221545	−	0.221545i	−0.809149	+	0.587604i	$0.800071\pi$
$488$	−4.91057	+	7.01302i	−0.222291	+	0.317464i
$489$	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	$0.421525\pi$
$492$	6.62742	−	5.86479i	0.298787	−	0.264405i
$493$	−9.01076	+	4.20179i	−0.405824	+	0.189239i
$494$	−17.7835	−	30.8019i	−0.800117	−	1.38584i
$495$		0			0
$496$	−4.01336	+	6.95135i	−0.180205	+	0.312125i
$497$	1.23344	−	14.0983i	0.0553275	−	0.632396i
$498$	−6.83298	−	5.43393i	−0.306193	−	0.243500i
$499$	11.0477	+	1.94801i	0.494564	+	0.0872050i	0.415367	−	0.909654i	$-0.363653\pi$
$499$	11.0477	+	1.94801i	0.494564	+	0.0872050i	0.0791972	+	0.996859i	$0.474764\pi$
$500$		0			0
$501$	−7.50619	−	10.1416i	−0.335352	−	0.453095i
$502$	15.9894	+	1.39889i	0.713640	+	0.0624354i
$503$	−29.1890	+	7.82118i	−1.30147	+	0.348729i	−0.842008	−	0.539466i	$-0.818626\pi$
$503$	−29.1890	+	7.82118i	−1.30147	+	0.348729i	−0.459467	+	0.888195i	$0.651960\pi$
$504$	7.71986	−	25.2710i	0.343870	−	1.12566i
$505$		0			0
$506$	−0.608940	+	1.67305i	−0.0270707	+	0.0743761i
$507$	−28.1409	+	5.72864i	−1.24978	+	0.254418i
$508$	−2.87518	+	0.251546i	−0.127566	+	0.0111605i
$509$	22.0511	−	8.02596i	0.977399	−	0.355744i	0.196571	−	0.980490i	$-0.437019\pi$
$509$	22.0511	−	8.02596i	0.977399	−	0.355744i	0.780829	+	0.624745i	$0.214797\pi$
$510$		0			0
$511$	3.49769	+	19.8364i	0.154729	+	0.877511i
$512$	10.9640	−	10.9640i	0.484544	−	0.484544i
$513$	26.4854	−	18.2162i	1.16936	−	0.804263i
$514$			9.18578i			0.405167i
$515$		0			0
$516$	1.60600	+	1.52370i	0.0707004	+	0.0670769i
$517$	−22.2083	−	10.3559i	−0.976719	−	0.455452i
$518$	−1.17499	−	13.4302i	−0.0516262	−	0.590090i
$519$	−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	$0.450551\pi$
$522$	7.01018	+	8.96844i	0.306827	+	0.392538i
$523$	−3.78176	−	14.1137i	−0.165365	−	0.617150i	−0.997993	−	0.0633182i	$-0.979832\pi$
$523$	−3.78176	−	14.1137i	−0.165365	−	0.617150i	0.832629	−	0.553832i	$-0.186835\pi$
$524$	0.982891	−	0.824743i	0.0429378	−	0.0360291i
$525$		0			0
$526$	−4.33208	+	24.5685i	−0.188888	+	1.07124i
$527$	−8.75850	−	12.5084i	−0.381526	−	0.544876i
$528$	2.18248	+	5.53872i	0.0949804	+	0.241042i
$529$	−14.4569	−	17.2291i	−0.628561	−	0.749090i
$530$		0			0
$531$	−22.6121	+	9.60430i	−0.981281	+	0.416791i
$532$	−4.08464	+	15.2441i	−0.177091	+	0.660914i
$533$	−13.3070	−	28.5370i	−0.576390	−	1.23607i
$534$	10.9213	−	5.44671i	0.472611	−	0.235702i
$535$		0			0
$536$	−7.78131	−	21.3790i	−0.336101	−	0.923431i
$537$	24.8318	−	0.653055i	1.07157	−	0.0281814i
$538$	−8.84309	−	6.19200i	−0.381253	−	0.266956i
$539$	−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	$0.709325\pi$
$542$	−4.19460	−	2.93709i	−0.180173	−	0.126159i
$543$	−1.70998	+	3.15025i	−0.0733824	+	0.135190i
$544$	4.31531	+	11.8562i	0.185017	+	0.508331i
$545$		0			0
$546$	−24.0048	−	15.8845i	−1.02731	−	0.679795i
$547$	−4.44356	−	9.52924i	−0.189993	−	0.407441i	0.788118	−	0.615524i	$-0.211055\pi$
$547$	−4.44356	−	9.52924i	−0.189993	−	0.407441i	−0.978111	+	0.208083i	$0.933278\pi$
$548$	3.64467	−	13.6021i	0.155693	−	0.581053i
$549$	−6.16321	+	5.74989i	−0.263039	+	0.245399i
$550$		0			0
$551$	−14.2734	−	17.0103i	−0.608066	−	0.724665i
$552$	3.72426	+	0.556164i	0.158515	+	0.0236719i
$553$	−21.6605	−	30.9344i	−0.921099	−	1.31547i
$554$	2.48092	−	14.0700i	0.105404	−	0.597776i
$555$		0			0
$556$	−6.17030	+	5.17749i	−0.261679	+	0.219575i
$557$	4.48926	+	16.7541i	0.190216	+	0.709896i	0.993454	+	0.114237i	$0.0364423\pi$
$557$	4.48926	+	16.7541i	0.190216	+	0.709896i	−0.803238	+	0.595659i	$0.796891\pi$
$558$	−11.6954	+	12.9950i	−0.495107	+	0.550122i
$559$	6.82132	−	3.93829i	0.288511	−	0.166572i
$560$		0			0
$561$	−11.3043	−	0.690115i	−0.477267	−	0.0291367i
$562$	1.44988	+	16.5722i	0.0611596	+	0.699057i
$563$	−21.2542	−	9.91099i	−0.895758	−	0.417699i	−0.0804714	−	0.996757i	$-0.525643\pi$
$563$	−21.2542	−	9.91099i	−0.895758	−	0.417699i	−0.815286	+	0.579058i	$0.803420\pi$
$564$	−3.70246	+	15.4295i	−0.155902	+	0.649701i
$565$		0			0
$566$		−	31.8748i		−	1.33980i
$567$	12.6021	−	22.7591i	0.529238	−	0.955791i
$568$	10.5491	−	10.5491i	0.442630	−	0.442630i
$569$	6.84027	+	38.7931i	0.286759	+	1.62629i	0.698934	+	0.715186i	$0.253658\pi$
$569$	6.84027	+	38.7931i	0.286759	+	1.62629i	−0.412175	+	0.911105i	$0.635231\pi$
$570$		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	$0.141460\pi$
$572$	−11.2880	+	0.987576i	−0.471977	+	0.0412926i
$573$	26.7630	+	30.2431i	1.11804	+	1.26343i
$574$	6.05032	−	16.6231i	0.252536	−	0.693836i
$575$		0			0
$576$	19.4388	−	12.6300i	0.809951	−	0.526249i
$577$	21.0819	−	5.64888i	0.877651	−	0.235166i	0.208257	−	0.978074i	$-0.433221\pi$
$577$	21.0819	−	5.64888i	0.877651	−	0.235166i	0.669393	+	0.742908i	$0.266554\pi$
$578$	−9.82287	−	0.859390i	−0.408578	−	0.0357459i
$579$	0.536252	−	0.0611597i	0.0222859	−	0.00254171i
$580$		0			0
$581$	13.5734	+	2.39335i	0.563119	+	0.0992930i
$582$	4.96111	−	33.2213i	0.205645	−	1.37707i
$583$	−2.10351	+	24.0432i	−0.0871185	+	0.995769i
$584$	−10.6167	+	18.3886i	−0.439321	+	0.760927i
$585$		0			0
$586$	−3.88117	−	6.72239i	−0.160330	−	0.277699i
$587$	22.1244	−	10.3168i	0.913173	−	0.425819i	0.0915170	−	0.995804i	$-0.470828\pi$
$587$	22.1244	−	10.3168i	0.913173	−	0.425819i	0.821656	+	0.569984i	$0.193051\pi$
$588$	0.413302	+	2.03027i	0.0170443	+	0.0837268i
$589$	21.9220	−	26.1256i	0.903279	−	1.07649i
$590$		0			0
$591$	1.59861	+	5.39457i	0.0657580	+	0.221903i
$592$	3.68461	−	5.26217i	0.151437	−	0.216274i
$593$	4.09490	+	4.09490i	0.168157	+	0.168157i	0.786169	−	0.618012i	$-0.212062\pi$
$593$	4.09490	+	4.09490i	0.168157	+	0.168157i	−0.618012	+	0.786169i	$0.712062\pi$
$594$	2.14445	+	12.7881i	0.0879879	+	0.524700i
$595$		0			0
$596$	−8.17827	+	1.44205i	−0.334995	+	0.0590687i
$597$	0.290389	+	11.0417i	0.0118848	+	0.451908i
$598$	1.73357	−	3.71765i	0.0708910	−	0.152026i
$599$	30.3866	+	25.4974i	1.24156	+	1.04180i	0.997400	+	0.0720615i	$0.0229578\pi$
$599$	30.3866	+	25.4974i	1.24156	+	1.04180i	0.244163	+	0.969734i	$0.421487\pi$
$600$		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	$0.773362\pi$
$602$	4.27441	+	1.14533i	0.174212	+	0.0466800i
$603$	−3.12238	−	22.1805i	−0.127153	−	0.903258i
$604$	0.806976	+	0.465908i	0.0328354	+	0.0189575i
$605$		0			0
$606$	5.65534	+	2.45825i	0.229733	+	0.0998596i
$607$	26.5308	−	18.5771i	1.07685	−	0.754020i	0.106160	−	0.994349i	$-0.466144\pi$
$607$	26.5308	−	18.5771i	1.07685	−	0.754020i	0.970691	+	0.240329i	$0.0772554\pi$
$608$	−23.0833	+	16.1631i	−0.936152	+	0.655501i
$609$	−16.4813	−	7.16404i	−0.667854	−	0.290301i
$610$		0			0
$611$	48.8923	+	28.2280i	1.97797	+	1.14198i
$612$	1.02229	+	7.26207i	0.0413238	+	0.293552i
$613$	−14.7737	−	3.95860i	−0.596704	−	0.159886i	−0.0521885	−	0.998637i	$-0.516620\pi$
$613$	−14.7737	−	3.95860i	−0.596704	−	0.159886i	−0.544515	+	0.838751i	$0.683286\pi$
$614$	13.5879	+	4.94560i	0.548364	+	0.199588i
$615$		0			0
$616$	−15.9279	−	13.3651i	−0.641755	−	0.538497i
$617$	−11.3221	+	24.2804i	−0.455812	+	0.977492i	0.535325	+	0.844646i	$0.320189\pi$
$617$	−11.3221	+	24.2804i	−0.455812	+	0.977492i	−0.991137	+	0.132845i	$0.957589\pi$
$618$	−0.174600	−	6.63900i	−0.00702345	−	0.267060i
$619$	18.6300	−	3.28497i	0.748802	−	0.132034i	0.213792	−	0.976879i	$-0.431419\pi$
$619$	18.6300	−	3.28497i	0.748802	−	0.132034i	0.535011	+	0.844845i	$0.320308\pi$
$620$		0			0
$621$	3.47298	+	1.29715i	0.139366	+	0.0520529i
$622$	−2.88598	−	2.88598i	−0.115717	−	0.115717i
$623$	−11.0512	+	15.7827i	−0.442757	+	0.632322i
$624$	−3.89698	−	13.1505i	−0.156004	−	0.526443i
$625$		0			0
$626$	16.7165	−	19.9220i	0.668126	−	0.796242i
$627$	−5.04570	−	24.7860i	−0.201506	−	0.989859i
$628$	−17.8520	+	8.32451i	−0.712371	+	0.332184i
$629$	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	$0.166506\pi$
$632$	3.46961	−	39.6578i	0.138014	−	1.57750i
$633$	−1.64112	+	10.9895i	−0.0652288	+	0.436794i
$634$	17.1787	+	3.02907i	0.682253	+	0.120300i
$635$		0			0
$636$	15.5279	−	1.77096i	0.615722	−	0.0702232i
$637$	7.34369	+	0.642490i	0.290968	+	0.0254564i
$638$	8.65198	−	2.31829i	0.342535	−	0.0917820i
$639$	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	$-0.0842049\pi$
$642$	−6.92324	−	7.82351i	−0.273238	−	0.308769i
$643$	1.74781	−	0.152914i	0.0689270	−	0.00603033i	−0.0526401	−	0.998614i	$-0.516764\pi$
$643$	1.74781	−	0.152914i	0.0689270	−	0.00603033i	0.121567	+	0.992583i	$0.461208\pi$
$644$	−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	$-0.884331\pi$
$647$	−14.7341	+	14.7341i	−0.579259	+	0.579259i	0.355440	+	0.934699i	$0.384331\pi$
$648$	25.5982	−	9.83953i	1.00559	−	0.386533i
$649$			19.3315i			0.758830i
$650$		0			0
$651$	6.44028	−	26.8391i	0.252414	−	1.05191i
$652$	−1.97831	−	0.922501i	−0.0774766	−	0.0361279i
$653$	−0.812604	−	9.28810i	−0.0317996	−	0.363471i	−0.995377	−	0.0960426i	$-0.969382\pi$
$653$	−0.812604	−	9.28810i	−0.0317996	−	0.363471i	0.963578	−	0.267429i	$-0.0861741\pi$
$654$	−28.9164	−	1.76532i	−1.13072	−	0.0690293i
$655$		0			0
$656$	7.29994	−	4.21462i	0.285015	−	0.164553i
$657$	−13.9846	+	15.5386i	−0.545592	+	0.606218i
$658$	8.20920	+	30.6372i	0.320028	+	1.19436i
$659$	−14.0775	+	11.8125i	−0.548383	+	0.460148i	−0.874393	−	0.485218i	$-0.838740\pi$
$659$	−14.0775	+	11.8125i	−0.548383	+	0.460148i	0.326010	+	0.945366i	$0.394296\pi$
$660$		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	$-0.109819\pi$
$662$	12.5159	+	17.8745i	0.486443	+	0.694712i
$663$	25.8067	+	3.85385i	1.00225	+	0.149671i
$664$	9.33923	+	11.1301i	0.362432	+	0.431930i
$665$		0			0
$666$	10.2309	−	9.54476i	0.396438	−	0.369852i
$667$	0.662829	−	2.47371i	0.0256648	−	0.0957825i
$668$	2.71703	+	5.82669i	0.105125	+	0.225441i
$669$	15.0051	+	9.92922i	0.580131	+	0.383886i
$670$		0			0
$671$	2.26847	+	6.23257i	0.0875733	+	0.240606i
$672$	−10.8797	+	20.0434i	−0.419695	+	0.773191i
$673$	−3.83098	−	2.68248i	−0.147673	−	0.103402i	0.497405	−	0.867518i	$-0.334286\pi$
$673$	−3.83098	−	2.68248i	−0.147673	−	0.103402i	−0.645078	+	0.764117i	$0.723175\pi$
$674$	−11.0600			−0.426017
$675$		0			0
$676$	14.6331			0.562810
$677$	32.1483	+	22.5105i	1.23556	+	0.865147i	0.994436	−	0.105347i	$-0.0335953\pi$
$677$	32.1483	+	22.5105i	1.23556	+	0.865147i	0.241123	+	0.970495i	$0.422484\pi$
$678$	4.88500	−	0.128472i	0.187607	−	0.00493392i
$679$	18.1371	+	49.8312i	0.696038	+	1.91235i
$680$		0			0
$681$	−4.84267	+	2.41515i	−0.185572	+	0.0925488i
$682$	5.81397	+	12.4681i	0.222628	+	0.477428i
$683$	−9.77386	+	36.4765i	−0.373986	+	1.39574i	0.480834	+	0.876812i	$0.340334\pi$
$683$	−9.77386	+	36.4765i	−0.373986	+	1.39574i	−0.854820	+	0.518924i	$0.826333\pi$
$684$	−15.0758	+	6.40331i	−0.576436	+	0.244837i
$685$		0			0
$686$	−11.0866	−	13.2125i	−0.423287	−	0.504454i
$687$	14.9181	+	37.8592i	0.569160	+	1.44442i
$688$	1.20944	+	1.72726i	0.0461096	+	0.0658513i
$689$	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	$0.196699\pi$
$692$	4.68292	+	17.4769i	0.178018	+	0.664372i
$693$	−12.6068	−	16.1284i	−0.478892	−	0.612668i
$694$	−10.5198	+	6.07363i	−0.399327	+	0.230552i
$695$		0			0
$696$	−8.45482	−	16.9529i	−0.320479	−	0.642599i
$697$	1.39761	+	15.9747i	0.0529381	+	0.605086i
$698$	−15.2128	−	7.09386i	−0.575814	−	0.268507i
$699$	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	$0.991452\pi$
$702$	−2.35402	−	29.7814i	−0.0888467	−	1.12402i
$703$	−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
$707$	−9.69826	+	0.848488i	−0.364741	+	0.0319107i
$708$	12.2665	−	2.49709i	0.461002	−	0.0938463i
$709$	12.4901	−	34.3163i	0.469077	−	1.28878i	−0.449410	−	0.893325i	$-0.648366\pi$
$709$	12.4901	−	34.3163i	0.469077	−	1.28878i	0.918487	−	0.395452i	$-0.129412\pi$
$710$		0			0
$711$	11.4506	−	37.4836i	0.429432	−	1.40575i
$712$	−19.6186	+	5.25679i	−0.735239	+	0.197007i
$713$	3.91834	+	0.342810i	0.146743	+	0.0128384i
$714$	8.72108	+	11.7831i	0.326378	+	0.440971i
$715$		0			0
$716$	−12.4649	−	2.19790i	−0.465836	−	0.0821395i
$717$	−23.0587	−	18.3375i	−0.861144	−	0.684826i
$718$	1.88008	−	21.4894i	0.0701639	−	0.801977i
$719$	12.9014	−	22.3459i	0.481142	−	0.833363i	−0.518624	−	0.855003i	$-0.673555\pi$
$719$	12.9014	−	22.3459i	0.481142	−	0.833363i	0.999766	+	0.0216398i	$0.00688871\pi$
$720$		0			0
$721$	5.24243	+	9.08015i	0.195238	+	0.338162i
$722$	−18.4622	+	8.60904i	−0.687090	+	0.320395i
$723$	−24.0697	+	21.2999i	−0.895160	+	0.792152i
$724$	1.17400	−	1.39912i	0.0436314	−	0.0519978i
$725$		0			0
$726$	−9.66282	−	2.31868i	−0.358621	−	0.0860543i
$727$	0.926059	−	1.32255i	0.0343456	−	0.0490507i	−0.801612	−	0.597845i	$-0.796024\pi$
$727$	0.926059	−	1.32255i	0.0343456	−	0.0490507i	0.835958	+	0.548794i	$0.184913\pi$
$728$	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
$732$	3.66174	−	2.24449i	0.135342	−	0.0829586i
$733$	5.62244	−	12.0574i	0.207669	−	0.445349i	−0.774692	−	0.632338i	$-0.782095\pi$
$733$	5.62244	−	12.0574i	0.207669	−	0.445349i	0.982362	+	0.186990i	$0.0598731\pi$
$734$	21.0132	+	17.6322i	0.775613	+	0.650816i
$735$		0			0
$736$	−3.05398	−	1.11156i	−0.112571	−	0.0409725i
$737$	−17.0249	−	4.56182i	−0.627122	−	0.168037i
$738$	17.4598	−	5.67740i	0.642704	−	0.208988i
$739$	30.9063	+	17.8437i	1.13691	+	0.656393i	0.945663	−	0.325150i	$-0.105415\pi$
$739$	30.9063	+	17.8437i	1.13691	+	0.656393i	0.191243	+	0.981543i	$0.438748\pi$
$740$		0			0
$741$	6.60366	+	57.9013i	0.242591	+	2.12706i
$742$	25.5905	−	17.9187i	0.939457	−	0.657815i
$743$	28.8465	−	20.1985i	1.05828	−	0.741012i	0.0912848	−	0.995825i	$-0.470903\pi$
$743$	28.8465	−	20.1985i	1.05828	−	0.741012i	0.966990	+	0.254813i	$0.0820138\pi$
$744$	23.3869	−	17.3095i	0.857407	−	0.634598i
$745$		0			0
$746$	4.37382	+	2.52523i	0.160137	+	0.0924551i
$747$	6.71844	+	12.6286i	0.245815	+	0.462058i
$748$	5.57411	+	1.49358i	0.203810	+	0.0546106i
$749$	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	$0.572520\pi$
$752$	−6.38726	+	13.6975i	−0.232919	+	0.499497i
$753$	−23.1132	−	12.5460i	−0.842290	−	0.457203i
$754$	−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	0.305278	−	0.952263i	$-0.401251\pi$
$757$	−17.8009	−	17.8009i	−0.646986	−	0.646986i	−0.952263	+	0.305278i	$0.901251\pi$
$758$	−15.3401	+	21.9080i	−0.557178	+	0.795733i
$759$	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	$0.877826\pi$
$762$	−5.67841	−	1.89925i	−0.205707	−	0.0688027i
$763$	41.4512	−	19.3290i	1.50063	−	0.699757i
$764$	−10.2888	−	17.8207i	−0.372236	−	0.644731i
$765$		0			0
$766$	6.51352	−	11.2818i	0.235343	−	0.407626i
$767$	3.88180	−	44.3691i	0.140164	−	1.60208i
$768$	−26.5086	+	10.4455i	−0.956547	+	0.376919i
$769$	−43.1365	−	7.60612i	−1.55554	−	0.274284i	−0.671254	−	0.741227i	$-0.734244\pi$
$769$	−43.1365	−	7.60612i	−1.55554	−	0.274284i	−0.884287	+	0.466944i	$0.845355\pi$
$770$		0			0
$771$	5.99998	−	13.8033i	0.216084	−	0.497113i
$772$	−0.273968	−	0.0239691i	−0.00986034	−	0.000862668i
$773$	22.0592	−	5.91076i	0.793416	−	0.212595i	0.160725	−	0.986999i	$-0.448617\pi$
$773$	22.0592	−	5.91076i	0.793416	−	0.212595i	0.632691	+	0.774404i	$0.281950\pi$
$774$	1.79548	+	4.22722i	0.0645371	+	0.151944i
$775$		0			0
$776$	−19.1194	+	52.5302i	−0.686347	+	1.88572i
$777$	−7.00674	+	20.9488i	−0.251365	+	0.751534i
$778$	−9.39502	+	0.821958i	−0.336828	+	0.0294686i
$779$	−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
$783$	−4.67604	−	18.0556i	−0.167108	−	0.645255i
$784$			1.97345i			0.0704805i
$785$		0			0
$786$	2.55215	−	0.756296i	0.0910322	−	0.0269762i
$787$	15.6093	+	7.27876i	0.556413	+	0.259460i	0.680421	−	0.732822i	$-0.261797\pi$
$787$	15.6093	+	7.27876i	0.556413	+	0.259460i	−0.124008	+	0.992281i	$0.539575\pi$
$788$	−0.249868	−	2.85601i	−0.00890119	−	0.101741i
$789$	22.5574	−	34.0889i	0.803064	−	1.21360i
$790$		0			0
$791$	−6.68122	+	3.85740i	−0.237557	+	0.137153i
$792$	0.748235	−	21.5666i	0.0265874	−	0.766337i
$793$	−3.95501	−	14.7603i	−0.140447	−	0.524154i
$794$	11.0377	−	9.26170i	0.391712	−	0.328685i
$795$		0			0
$796$	0.977323	−	5.54267i	0.0346403	−	0.196455i
$797$	−18.8617	−	26.9373i	−0.668115	−	0.954166i	−0.999941	−	0.0108262i	$-0.996554\pi$
$797$	−18.8617	−	26.9373i	−0.668115	−	0.954166i	0.331827	−	0.943340i	$-0.392335\pi$
$798$	−20.3787	+	25.6256i	−0.721400	+	0.907135i
$799$	−18.4814	−	22.0252i	−0.653824	−	0.779197i
$800$		0			0
$801$	−19.9689	+	1.05106i	−0.705567	+	0.0371374i
$802$	−0.802775	+	2.99600i	−0.0283470	+	0.105792i
$803$	6.95197	+	14.9085i	0.245330	+	0.526111i
$804$	−0.695477	+	11.3921i	−0.0245276	+	0.401769i
$805$		0			0
$806$	−10.8404	−	29.7838i	−0.381838	−	1.04909i
$807$	9.24384	+	15.0807i	0.325399	+	0.530867i
$808$	−8.40661	−	5.88637i	−0.295744	−	0.207082i
$809$	−0.589848			−0.0207379			−0.0103690	−	0.999946i	$-0.503301\pi$
$809$	−0.589848			−0.0207379			−0.0103690	+	0.999946i	$0.503301\pi$
$810$		0			0
$811$	−48.5224			−1.70385			−0.851925	−	0.523664i	$-0.824565\pi$
$811$	−48.5224			−1.70385			−0.851925	+	0.523664i	$0.824565\pi$
$812$	7.50095	+	5.25222i	0.263232	+	0.184317i
$813$	4.38469	+	7.15334i	0.153778	+	0.250879i
$814$	−3.76564	−	10.3460i	−0.131985	−	0.362627i
$815$		0			0
$816$	−0.425646	+	6.97221i	−0.0149006	+	0.244076i
$817$	−3.78631	−	8.11977i	−0.132466	−	0.284075i
$818$	7.84316	−	29.2711i	0.274230	−	1.02344i
$819$	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	$0.669241\pi$
$822$	18.1837	−	22.8654i	0.634230	−	0.797522i
$823$	0.358433	+	0.511895i	0.0124942	+	0.0178435i	0.825351	−	0.564621i	$-0.190978\pi$
$823$	0.358433	+	0.511895i	0.0124942	+	0.0178435i	−0.812856	+	0.582464i	$0.802089\pi$
$824$	−1.91929	+	10.8848i	−0.0668615	+	0.379190i
$825$		0			0
$826$	19.1684	−	16.0842i	0.666954	−	0.559641i
$827$	−3.05127	−	11.3875i	−0.106103	−	0.395981i	0.892365	−	0.451314i	$-0.149045\pi$
$827$	−3.05127	−	11.3875i	−0.106103	−	0.395981i	−0.998468	+	0.0553328i	$0.982378\pi$
$828$	−1.60222	−	1.00068i	−0.0556811	−	0.0347759i
$829$	−38.0844	+	21.9880i	−1.32272	+	0.763675i	−0.984163	−	0.177269i	$-0.943274\pi$
$829$	−38.0844	+	21.9880i	−1.32272	+	0.763675i	−0.338562	+	0.940944i	$0.609941\pi$
$830$		0			0
$831$	−12.9183	+	19.5222i	−0.448130	+	0.677217i
$832$	3.66285	+	41.8666i	0.126986	+	1.45146i
$833$	−3.40254	−	1.58663i	−0.117891	−	0.0549735i
$834$	−16.0216	+	4.74780i	−0.554784	+	0.164403i
$835$		0			0
$836$			12.8886i			0.445761i
$837$	26.0626	−	11.8881i	0.900854	−	0.410913i
$838$	9.93659	−	9.93659i	0.343254	−	0.343254i
$839$	0.173429	+	0.983567i	0.00598745	+	0.0339565i	0.987655	−	0.156644i	$-0.0500676\pi$
$839$	0.173429	+	0.983567i	0.00598745	+	0.0339565i	−0.981668	+	0.190601i	$0.938956\pi$
$840$		0			0
$841$	15.1440	−	5.51197i	0.522207	−	0.190068i
$842$	−9.53258	+	0.833993i	−0.328514	+	0.0287413i
$843$	8.64597	−	25.8498i	0.297783	−	0.890314i
$844$	1.93642	−	5.32028i	0.0666545	−	0.183132i
$845$		0			0
$846$	−19.8050	+	26.2945i	−0.680910	+	0.904024i
$847$	15.1535	−	4.06038i	0.520682	−	0.139516i
$848$	14.8293	+	1.29739i	0.509239	+	0.0445527i
$849$	−20.8200	+	47.8976i	−0.714541	+	1.64384i
$850$		0			0
$851$	−3.10007	−	0.546626i	−0.106269	−	0.0187381i
$852$	−6.96305	+	2.74373i	−0.238550	+	0.0939986i
$853$	−0.394403	+	4.50805i	−0.0135041	+	0.154353i	−0.999953	−	0.00971747i	$-0.996907\pi$
$853$	−0.394403	+	4.50805i	−0.0135041	+	0.154353i	0.986449	+	0.164070i	$0.0524623\pi$
$854$	4.29256	−	7.43494i	0.146889	−	0.254418i
$855$		0			0
$856$	8.69313	+	15.0569i	0.297125	+	0.514635i
$857$	−51.8892	+	24.1963i	−1.77250	+	0.826531i	−0.797831	+	0.602881i	$0.794019\pi$
$857$	−51.8892	+	24.1963i	−1.77250	+	0.826531i	−0.974670	+	0.223650i	$0.928203\pi$
$858$	−22.2936	−	7.45653i	−0.761091	−	0.254562i
$859$	20.9711	−	24.9924i	0.715526	−	0.852730i	−0.278662	−	0.960389i	$-0.589891\pi$
$859$	20.9711	−	24.9924i	0.715526	−	0.852730i	0.994188	+	0.107659i	$0.0343354\pi$
$860$		0			0
$861$	−19.9496	+	21.0273i	−0.679881	+	0.716608i
$862$	0.179453	−	0.256286i	0.00611220	−	0.00872913i
$863$	−28.5706	−	28.5706i	−0.972554	−	0.972554i	0.0270792	−	0.999633i	$-0.491379\pi$
$863$	−28.5706	−	28.5706i	−0.972554	−	0.972554i	−0.999633	+	0.0270792i	$0.991379\pi$
$864$	−23.3433	+	3.91447i	−0.794154	+	0.133173i
$865$		0			0
$866$	18.8698	−	3.32726i	0.641223	−	0.113065i
$867$	14.1993	+	7.70751i	0.482233	+	0.261761i
$868$	−5.94365	+	12.7462i	−0.201741	+	0.432634i
$869$	−23.6254	−	19.8241i	−0.801437	−	0.672486i
$870$		0			0
$871$	38.1591	+	13.8888i	1.29297	+	0.470603i
$872$	46.5707	+	12.4786i	1.57708	+	0.422578i
$873$	−29.1545	+	46.6805i	−0.986731	+	1.57989i
$874$	−4.04068	−	2.33289i	−0.136678	−	0.0789111i
$875$		0			0
$876$	8.56194	−	6.33700i	0.289281	−	0.214108i
$877$	29.1215	−	20.3911i	0.983364	−	0.688559i	0.0329214	−	0.999458i	$-0.489519\pi$
$877$	29.1215	−	20.3911i	0.983364	−	0.688559i	0.950443	+	0.310899i	$0.100630\pi$
$878$	24.7062	−	17.2994i	0.833792	−	0.583828i
$879$	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	$0.872500\pi$
$882$	−0.892728	+	4.20463i	−0.0300597	+	0.141577i
$883$	3.38029	+	0.905746i	0.113756	+	0.0304808i	0.315248	−	0.949009i	$-0.397912\pi$
$883$	3.38029	+	0.905746i	0.113756	+	0.0304808i	−0.201492	+	0.979490i	$0.564579\pi$
$884$	−12.4936	−	4.54730i	−0.420205	−	0.152942i
$885$		0			0
$886$	−32.6492	−	27.3959i	−1.09687	−	0.920383i
$887$	−12.0260	+	25.7899i	−0.403794	+	0.865939i	0.594301	+	0.804243i	$0.297429\pi$
$887$	−12.0260	+	25.7899i	−0.403794	+	0.865939i	−0.998095	+	0.0616962i	$0.980349\pi$
$888$	−19.8531	+	12.1691i	−0.666227	+	0.408368i
$889$	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
$893$	36.8325	−	52.6023i	1.23255	−	1.76027i
$894$	−16.7527	−	4.01997i	−0.560296	−	0.134448i
$895$		0			0
$896$	1.75011	−	2.08570i	0.0584672	−	0.0696785i
$897$	−5.03331	+	4.45411i	−0.168057	+	0.148718i
$898$	7.49641	−	3.49564i	0.250159	−	0.116651i
$899$	−9.89411	−	17.1371i	−0.329987	−	0.571554i
$900$		0			0
$901$	−14.1594	+	24.5249i	−0.471719	+	0.817042i
$902$	1.25913	−	14.3919i	0.0419245	−	0.479199i
$903$	−5.67497	−	4.51303i	−0.188851	−	0.150184i
$904$	−8.00909	−	1.41222i	−0.266378	−	0.0469697i
$905$		0			0
$906$	1.15005	+	1.55383i	0.0382078	+	0.0516227i
$907$	−32.6761	−	2.85879i	−1.08499	−	0.0949246i	−0.469398	−	0.882987i	$-0.655529\pi$
$907$	−32.6761	−	2.85879i	−1.08499	−	0.0949246i	−0.615596	+	0.788062i	$0.711085\pi$
$908$	2.66344	−	0.713667i	0.0883894	−	0.0236839i
$909$	−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	$-0.0485753\pi$
$912$	−15.2874	+	3.11206i	−0.506217	+	0.103051i
$913$	11.2132	−	0.981025i	0.371102	−	0.0324672i
$914$	−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
$918$	−4.06088	+	14.6624i	−0.134029	+	0.483932i
$919$		−	28.2931i		−	0.933302i	−0.884442	−	0.466651i	$-0.845460\pi$
$919$		−	28.2931i		−	0.933302i	0.884442	−	0.466651i	$-0.154540\pi$
$920$		0			0
$921$	−17.1879	−	16.3070i	−0.566361	−	0.537335i
$922$	−28.8814	−	13.4676i	−0.951159	−	0.443533i
$923$	2.32080	+	26.5268i	0.0763899	+	0.873141i
$924$	4.65525	+	9.33434i	0.153147	+	0.307077i
$925$		0			0
$926$	0.165049	−	0.0952911i	0.00542385	−	0.00313146i
$927$	−4.07410	+	10.0903i	−0.133811	+	0.331410i
$928$	4.23180	+	15.7933i	0.138916	+	0.518440i
$929$	25.1788	−	21.1275i	0.826089	−	0.693171i	−0.128300	−	0.991735i	$-0.540952\pi$
$929$	25.1788	−	21.1275i	0.826089	−	0.693171i	0.954390	+	0.298564i	$0.0965076\pi$
$930$		0			0
$931$	1.45603	−	8.25757i	0.0477195	−	0.270631i
$932$	−1.67917	−	2.39811i	−0.0550032	−	0.0785527i
$933$	2.45164	+	6.22178i	0.0802630	+	0.203692i
$934$	−8.57623	−	10.2208i	−0.280623	−	0.334433i
$935$		0			0
$936$	−6.04793	+	49.3488i	−0.197683	+	1.61302i
$937$	1.30584	−	4.87347i	0.0426600	−	0.159209i	−0.941310	−	0.337543i	$-0.890404\pi$
$937$	1.30584	−	4.87347i	0.0426600	−	0.159209i	0.983970	+	0.178334i	$0.0570708\pi$
$938$	9.64174	+	20.6768i	0.314814	+	0.675121i
$939$	−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	$0.502041\pi$
$942$	−40.8501	+	1.07432i	−1.33097	+	0.0350034i
$943$	−3.38355	−	2.36919i	−0.110184	−	0.0771514i
$944$	11.9232			0.388068
$945$		0			0
$946$	3.61394			0.117499
$947$	26.3740	+	18.4673i	0.857041	+	0.600107i	0.917354	−	0.398073i	$-0.130321\pi$
$947$	26.3740	+	18.4673i	0.857041	+	0.600107i	−0.0603125	+	0.998180i	$0.519210\pi$
$948$	−9.52727	+	17.5518i	−0.309431	+	0.570055i
$949$	−12.9623	−	35.6136i	−0.420773	−	1.15607i
$950$		0			0
$951$	−23.8355	−	15.7725i	−0.772920	−	0.511459i
$952$	−10.3105	−	22.1110i	−0.334167	−	0.716623i
$953$	5.59819	−	20.8927i	0.181343	−	0.676782i	−0.814041	−	0.580808i	$-0.802737\pi$
$953$	5.59819	−	20.8927i	0.181343	−	0.676782i	0.995384	−	0.0959743i	$-0.0305967\pi$
$954$	31.0083	+	9.47252i	1.00393	+	0.306684i
$955$		0			0
$956$	9.64940	+	11.4997i	0.312084	+	0.371927i
$957$	−14.5154	−	2.16766i	−0.469217	−	0.0700706i
$958$	21.6105	+	30.8629i	0.698202	+	0.997136i
$959$	−8.00894	+	45.4210i	−0.258622	+	1.46672i
$960$		0			0
$961$	−0.465741	+	0.390803i	−0.0150239	+	0.0126065i
$962$	6.56528	+	24.5020i	0.211673	+	0.789975i
$963$	5.29324	+	16.2784i	0.170572	+	0.524563i
$964$	14.1830	−	8.18857i	0.456804	−	0.263736i
$965$		0			0
$966$	−3.76902	−	0.230095i	−0.121266	−	0.00740317i
$967$	−0.961701	−	10.9923i	−0.0309262	−	0.353488i	−0.995854	−	0.0909711i	$-0.971003\pi$
$967$	−0.961701	−	10.9923i	−0.0309262	−	0.353488i	0.964927	−	0.262517i	$-0.0845527\pi$
$968$	14.9883	+	6.98917i	0.481743	+	0.224640i
$969$	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	$-0.114506\pi$
$972$	−13.7449	−	0.592321i	−0.440868	−	0.0189987i
$973$	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
$977$	5.48124	−	0.479546i	0.175360	−	0.0153420i	0.000862648	−	1.00000i	$-0.499725\pi$
$977$	5.48124	−	0.479546i	0.175360	−	0.0153420i	0.174498	+	0.984658i	$0.444170\pi$
$978$	−3.00104	−	3.39128i	−0.0959625	−	0.108441i
$979$	−5.38167	+	14.7860i	−0.171999	+	0.472563i
$980$		0			0
$981$	42.2990	+	21.5404i	1.35050	+	0.687731i
$982$	26.5176	−	7.10536i	0.846209	−	0.226741i
$983$	27.3904	+	2.39635i	0.873618	+	0.0764316i	0.515139	−	0.857106i	$-0.327740\pi$
$983$	27.3904	+	2.39635i	0.873618	+	0.0764316i	0.358478	+	0.933538i	$0.383296\pi$
$984$	−30.3581	+	3.46235i	−0.967782	+	0.110376i
$985$		0			0
$986$	10.3502	+	1.82503i	0.329619	+	0.0581207i
$987$	7.67583	−	51.4000i	0.244324	−	1.63608i
$988$	2.58804	−	29.5815i	0.0823366	−	0.941111i
$989$	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	$0.752046\pi$
$992$	−22.7592	+	10.6128i	−0.722606	+	0.336956i
$993$	−7.13204	−	35.0348i	−0.226328	−	1.11180i
$994$	−9.61620	+	11.4601i	−0.305007	+	0.363494i
$995$		0			0
$996$	−2.07092	−	6.98839i	−0.0656195	−	0.221436i
$997$	2.10376	−	3.00447i	0.0666266	−	0.0951527i	−0.784456	−	0.620185i	$-0.787058\pi$
$997$	2.10376	−	3.00447i	0.0666266	−	0.0951527i	0.851083	+	0.525032i	$0.175947\pi$
$998$	−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.257.5		192
5.2	odd	4		135.2.q.a.68.12	yes	192
5.3	odd	4	inner	675.2.ba.b.68.5		192
5.4	even	2		135.2.q.a.122.12	yes	192
15.2	even	4		405.2.r.a.233.5		192
15.14	odd	2		405.2.r.a.152.5		192
27.2	odd	18	inner	675.2.ba.b.407.5		192
135.2	even	36		135.2.q.a.83.12	yes	192
135.29	odd	18		135.2.q.a.2.12	✓	192
135.52	odd	36		405.2.r.a.8.5		192
135.79	even	18		405.2.r.a.332.5		192
135.83	even	36	inner	675.2.ba.b.218.5		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.12	✓	192	135.29	odd	18
135.2.q.a.68.12	yes	192	5.2	odd	4
135.2.q.a.83.12	yes	192	135.2	even	36
135.2.q.a.122.12	yes	192	5.4	even	2
405.2.r.a.8.5		192	135.52	odd	36
405.2.r.a.152.5		192	15.14	odd	2
405.2.r.a.233.5		192	15.2	even	4
405.2.r.a.332.5		192	135.79	even	18
675.2.ba.b.68.5		192	5.3	odd	4	inner
675.2.ba.b.218.5		192	135.83	even	36	inner
675.2.ba.b.257.5		192	1.1	even	1	trivial
675.2.ba.b.407.5		192	27.2	odd	18	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+(-0.865920 - 0.606324i) q^{2} +(0.905161 + 1.47671i) q^{3} +(-0.301851 - 0.829330i) q^{4} +(0.111569 - 1.82754i) q^{6} +(1.22161 + 2.61975i) q^{7} +(-0.788655 + 2.94330i) q^{8} +(-1.36137 + 2.67333i) q^{9} +(1.51740 + 1.80836i) q^{11} +(0.951458 - 1.19642i) q^{12} +(-3.11956 - 4.45519i) q^{13} +(0.530600 - 3.00918i) q^{14} +(1.11535 - 0.935892i) q^{16} +(0.716894 + 2.67549i) q^{17} +(2.79974 - 1.48946i) q^{18} +(-5.35751 + 3.09316i) q^{19} +(-2.76286 + 4.17526i) q^{21} +(-0.217491 - 2.48593i) q^{22} +(-0.646627 - 0.301527i) q^{23} +(-5.06027 + 1.49954i) q^{24} +5.74930i q^{26} +(-5.18000 + 0.409444i) q^{27} +(1.80389 - 1.80389i) q^{28} +(0.623300 + 3.53491i) q^{29} +(-5.18043 + 1.88552i) q^{31} +(4.53781 - 0.397007i) q^{32} +(-1.29695 + 3.87762i) q^{33} +(1.00144 - 2.75143i) q^{34} +(2.62800 + 0.322074i) q^{36} +(4.26173 - 1.14193i) q^{37} +(6.51463 + 0.569956i) q^{38} +(3.75534 - 8.63936i) q^{39} +(5.70140 + 1.00531i) q^{41} +(4.92398 - 1.94025i) q^{42} +(-0.126221 + 1.44271i) q^{43} +(1.04170 - 1.80428i) q^{44} +(0.377104 + 0.653164i) q^{46} +(-9.40770 + 4.38688i) q^{47} +(2.39162 + 0.799924i) q^{48} +(-0.871236 + 1.03830i) q^{49} +(-3.30202 + 3.48039i) q^{51} +(-2.75318 + 3.93195i) q^{52} +(7.22940 + 7.22940i) q^{53} +(4.73372 + 2.78621i) q^{54} +(-8.67413 + 1.52948i) q^{56} +(-9.41712 - 5.11170i) q^{57} +(1.60357 - 3.43887i) q^{58} +(6.27320 + 5.26384i) q^{59} +(2.64019 + 0.960952i) q^{61} +(5.62907 + 1.50831i) q^{62} +(-8.66650 - 0.300676i) q^{63} +(-6.69194 - 3.86359i) q^{64} +(3.47414 - 2.57134i) q^{66} +(-6.11610 + 4.28254i) q^{67} +(2.00246 - 1.40214i) q^{68} +(-0.140033 - 1.22781i) q^{69} +(-4.24004 - 2.44799i) q^{71} +(-6.79476 - 6.11524i) q^{72} +(6.73088 + 1.80353i) q^{73} +(-4.38269 - 1.59517i) q^{74} +(4.18242 + 3.50947i) q^{76} +(-2.88379 + 6.18430i) q^{77} +(-8.49007 + 5.20404i) q^{78} +(-12.8661 + 2.26863i) q^{79} +(-5.29336 - 7.27876i) q^{81} +(-4.32741 - 4.32741i) q^{82} +(2.73492 - 3.90587i) q^{83} +(4.29664 + 1.03102i) q^{84} +(0.984048 - 1.17274i) q^{86} +(-4.65586 + 4.12010i) q^{87} +(-6.51925 + 3.03998i) q^{88} +(3.33276 + 5.77251i) q^{89} +(7.86060 - 13.6150i) q^{91} +(-0.0548802 + 0.627283i) q^{92} +(-7.47350 - 5.94331i) q^{93} +(10.8062 + 1.90542i) q^{94} +(4.69371 + 6.34168i) q^{96} +(18.2758 + 1.59893i) q^{97} +(1.38397 - 0.370833i) 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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