LMFDB - Embedded newform 675.2.ba.b.218.5

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			218.5
Character	$\chi$	$=$	675.218
Dual form			675.2.ba.b.257.5

$q$-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 $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.865920	+	0.606324i	−0.612298	+	0.428736i	−0.838161	−	0.545424i	$-0.816369\pi$
$2$	−0.865920	+	0.606324i	−0.612298	+	0.428736i	0.225863	+	0.974159i	$0.427480\pi$
$3$	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	−0.528271	−	0.849076i	$-0.677160\pi$
$7$	1.22161	−	2.61975i	0.461725	−	0.990171i	0.989996	−	0.141096i	$-0.0450626\pi$
$8$	−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	−0.487136	−	0.873326i	$-0.661959\pi$
$11$	1.51740	−	1.80836i	0.457512	−	0.545242i	0.944648	+	0.328084i	$0.106403\pi$
$12$	0.951458	+	1.19642i	0.274662	+	0.345378i
$13$	−3.11956	+	4.45519i	−0.865210	+	1.23565i	0.105265	+	0.994444i	$0.466431\pi$
$13$	−3.11956	+	4.45519i	−0.865210	+	1.23565i	−0.970475	+	0.241203i	$0.922458\pi$
$14$	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	−0.822869	−	0.568232i	$-0.807628\pi$
$17$	0.716894	−	2.67549i	0.173872	−	0.648901i	0.996741	−	0.0806688i	$-0.0257056\pi$
$18$	2.79974	+	1.48946i	0.659904	+	0.351069i
$19$	−5.35751	−	3.09316i	−1.22910	−	0.709619i	−0.262256	−	0.964998i	$-0.584466\pi$
$19$	−5.35751	−	3.09316i	−1.22910	−	0.709619i	−0.966841	+	0.255379i	$0.917800\pi$
$20$		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	−0.488863	−	0.872361i	$-0.662588\pi$
$23$	−0.646627	+	0.301527i	−0.134831	+	0.0628728i	0.354032	+	0.935233i	$0.384810\pi$
$24$	−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	−0.870635	−	0.491929i	$-0.836292\pi$
$29$	0.623300	−	3.53491i	0.115744	−	0.656416i	0.986379	−	0.164487i	$-0.0525969\pi$
$30$		0			0
$31$	−5.18043	−	1.88552i	−0.930432	−	0.338650i	−0.168051	−	0.985778i	$-0.553747\pi$
$31$	−5.18043	−	1.88552i	−0.930432	−	0.338650i	−0.762381	+	0.647129i	$0.775970\pi$
$32$	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	0.591510	−	0.806298i	$-0.298532\pi$
$37$	4.26173	+	1.14193i	0.700624	+	0.187732i	0.109114	+	0.994029i	$0.465199\pi$
$38$	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	0.290314	−	0.956932i	$-0.406240\pi$
$41$	5.70140	−	1.00531i	0.890409	−	0.157003i	0.600095	+	0.799928i	$0.295129\pi$
$42$	4.92398	+	1.94025i	0.759786	+	0.299387i
$43$	−0.126221	−	1.44271i	−0.0192485	−	0.220012i	−0.999727	−	0.0233831i	$-0.992556\pi$
$43$	−0.126221	−	1.44271i	−0.0192485	−	0.220012i	0.980478	−	0.196629i	$-0.0629993\pi$
$44$	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	−0.410010	−	0.912081i	$-0.634475\pi$
$47$	−9.40770	−	4.38688i	−1.37225	−	0.639893i	−0.962244	+	0.272188i	$0.912253\pi$
$48$	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	−0.00694140	−	0.999976i	$-0.502210\pi$
$53$	7.22940	−	7.22940i	0.993035	−	0.993035i	0.999976	+	0.00694140i	$0.00220953\pi$
$54$	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	−0.135496	−	0.990778i	$-0.543263\pi$
$59$	6.27320	−	5.26384i	0.816701	−	0.685293i	0.952197	+	0.305484i	$0.0988184\pi$
$60$		0			0
$61$	2.64019	−	0.960952i	0.338042	−	0.123037i	−0.167421	−	0.985885i	$-0.553544\pi$
$61$	2.64019	−	0.960952i	0.338042	−	0.123037i	0.505463	+	0.862848i	$0.331322\pi$
$62$	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	0.136847	−	0.990592i	$-0.456303\pi$
$67$	−6.11610	−	4.28254i	−0.747201	−	0.523196i	−0.884048	+	0.467396i	$0.845192\pi$
$68$	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	−0.730034	−	0.683411i	$-0.760496\pi$
$71$	−4.24004	+	2.44799i	−0.503200	+	0.290523i	0.226834	+	0.973933i	$0.427162\pi$
$72$	−6.79476	+	6.11524i	−0.800770	+	0.720688i
$73$	6.73088	−	1.80353i	0.787790	−	0.211088i	0.157574	−	0.987507i	$-0.449633\pi$
$73$	6.73088	−	1.80353i	0.787790	−	0.211088i	0.630216	+	0.776420i	$0.282966\pi$
$74$	−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	−0.606015	−	0.795453i	$-0.707233\pi$
$79$	−12.8661	−	2.26863i	−1.44754	−	0.255241i	−0.841529	+	0.540212i	$0.818344\pi$
$80$		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	0.940705	−	0.339227i	$-0.110165\pi$
$83$	2.73492	+	3.90587i	0.300196	+	0.428724i	−0.640509	+	0.767951i	$0.721276\pi$
$84$	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	−0.633549	−	0.773703i	$-0.718402\pi$
$89$	3.33276	−	5.77251i	0.353272	−	0.611885i	0.986821	+	0.161818i	$0.0517357\pi$
$90$		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	0.896079	−	0.443894i	$-0.146403\pi$
$97$	18.2758	−	1.59893i	1.85563	−	0.162346i	0.959547	+	0.281548i	$0.0908478\pi$
$98$	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	0.869097	−	0.494641i	$-0.164701\pi$
$101$	−1.15191	−	3.16484i	−0.114619	−	0.314913i	−0.983716	+	0.179728i	$0.942478\pi$
$102$	4.96953	+	1.01165i	0.492057	+	0.100168i
$103$	3.61346	+	0.316137i	0.356045	+	0.0311499i	0.263775	−	0.964584i	$-0.415032\pi$
$103$	3.61346	+	0.316137i	0.356045	+	0.0311499i	0.0922694	+	0.995734i	$0.470588\pi$
$104$	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	0.874701	−	0.484662i	$-0.161057\pi$
$107$	4.03460	+	4.03460i	0.390039	+	0.390039i	−0.484662	+	0.874701i	$0.661057\pi$
$108$	1.90315	−	4.17233i	0.183131	−	0.401483i
$109$			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
$112$	3.81433	−	1.77865i	0.360420	−	0.168067i
$113$	0.232615	−	2.65880i	0.0218825	−	0.250119i	−0.977372	−	0.211526i	$-0.932157\pi$
$113$	0.232615	−	2.65880i	0.0218825	−	0.250119i	0.999255	−	0.0385931i	$-0.0122876\pi$
$114$	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	0.993257	−	0.115931i	$-0.0369850\pi$
$127$	0.846401	+	3.15881i	0.0751059	+	0.280299i	−0.918151	+	0.396230i	$0.870318\pi$
$128$	−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	−0.916074	−	0.401010i	$-0.868659\pi$
$131$	0.497235	−	1.36614i	0.0434436	−	0.119360i	0.959517	+	0.281649i	$0.0908815\pi$
$132$	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	0.138637	−	0.990343i	$-0.455728\pi$
$137$	13.0703	−	9.15193i	1.11667	−	0.781902i	0.978035	+	0.208442i	$0.0668391\pi$
$138$	−0.623196	−	1.14809i	−0.0530499	−	0.0977322i
$139$	−3.12149	+	8.57623i	−0.264762	+	0.727426i	0.734069	+	0.679075i	$0.237619\pi$
$139$	−3.12149	+	8.57623i	−0.264762	+	0.727426i	−0.998830	+	0.0483514i	$0.984603\pi$
$140$		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	0.975648	+	0.219343i	$0.0703913\pi$
$149$	1.63395	+	9.26659i	0.133858	+	0.759149i	−0.841789	+	0.539806i	$0.818498\pi$
$150$		0			0
$151$	−0.808803	−	0.678666i	−0.0658194	−	0.0552291i	0.609284	−	0.792952i	$-0.291457\pi$
$151$	−0.808803	−	0.678666i	−0.0658194	−	0.0552291i	−0.675104	+	0.737723i	$0.735901\pi$
$152$	−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	0.375408	+	0.926860i	$0.377503\pi$
$157$	−1.94520	+	22.2338i	−0.155244	+	1.77445i	−0.530652	+	0.847590i	$0.678053\pi$
$158$	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	0.772274	−	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
$167$	−7.25686	−	0.634893i	−0.561553	−	0.0491295i	−0.197154	−	0.980373i	$-0.563170\pi$
$167$	−7.25686	−	0.634893i	−0.561553	−	0.0491295i	−0.364399	+	0.931243i	$0.618725\pi$
$168$	−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	−0.830985	−	0.556295i	$-0.812222\pi$
$173$	−20.4232	+	1.78680i	−1.55275	+	0.135848i	−0.721760	+	0.692143i	$0.756667\pi$
$174$	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	0.999116	+	0.0420450i	$0.0133873\pi$
$179$	7.17079	+	12.4202i	0.535970	+	0.928327i	−0.463146	+	0.886282i	$0.653279\pi$
$180$		0			0
$181$	1.03474	−	1.79221i	0.0769112	−	0.133214i	−0.825005	−	0.565126i	$-0.808828\pi$
$181$	1.03474	−	1.79221i	0.0769112	−	0.133214i	0.901916	+	0.431912i	$0.142161\pi$
$182$	−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	0.923987	−	0.382424i	$-0.124911\pi$
$191$	22.9618	+	4.04878i	1.66145	+	0.292959i	0.737467	+	0.675383i	$0.236022\pi$
$192$	−0.351864	+	13.3793i	−0.0253936	+	0.965564i
$193$	0.131693	+	0.282417i	0.00947948	+	0.0203288i	0.910991	−	0.412427i	$-0.135319\pi$
$193$	0.131693	+	0.282417i	0.00947948	+	0.0203288i	−0.901511	+	0.432756i	$0.857541\pi$
$194$	−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	−0.145303	−	0.989387i	$-0.546416\pi$
$197$	3.13774	−	0.840756i	0.223555	−	0.0599014i	0.368858	+	0.929486i	$0.379749\pi$
$198$	6.94179	−	2.80284i	0.493332	−	0.199189i
$199$	5.52277	−	3.18857i	0.391499	−	0.226032i	−0.291310	−	0.956629i	$-0.594091\pi$
$199$	5.52277	−	3.18857i	0.391499	−	0.226032i	0.682809	+	0.730596i	$0.260758\pi$
$200$		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	−0.457763	−	0.889074i	$-0.651349\pi$
$211$	4.91430	−	4.12359i	0.338314	−	0.283879i	0.796077	+	0.605195i	$0.206905\pi$
$212$	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	0.711464	−	0.702723i	$-0.248032\pi$
$223$	9.41489	+	4.39023i	0.630467	+	0.293992i	−0.0809965	+	0.996714i	$0.525810\pi$
$224$	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	−0.999862	−	0.0166042i	$-0.994714\pi$
$227$	−0.272304	−	3.11245i	−0.0180734	−	0.206580i	0.981789	−	0.189976i	$-0.0608411\pi$
$228$	−1.39671	−	9.35287i	−0.0924996	−	0.619409i
$229$	23.1368	−	4.07964i	1.52892	−	0.269590i	0.654990	−	0.755638i	$-0.272673\pi$
$229$	23.1368	−	4.07964i	1.52892	−	0.269590i	0.873933	+	0.486047i	$0.161562\pi$
$230$		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	0.362241	−	0.932085i	$-0.382012\pi$
$233$	3.20411	+	0.858538i	0.209908	+	0.0562447i	−0.152333	+	0.988329i	$0.548679\pi$
$234$	−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	−0.231335	−	0.972874i	$-0.574309\pi$
$239$	−15.9837	−	5.81759i	−1.03390	−	0.376309i	−0.802564	+	0.596566i	$0.796532\pi$
$240$		0			0
$241$	3.22231	−	18.2746i	0.207567	−	1.17717i	−0.685782	−	0.727807i	$-0.740540\pi$
$241$	3.22231	−	18.2746i	0.207567	−	1.17717i	0.893349	−	0.449364i	$-0.148349\pi$
$242$	−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	0.0238664	−	0.999715i	$-0.492402\pi$
$251$	−13.1493	−	7.59178i	−0.829979	−	0.479189i	−0.853846	+	0.520527i	$0.825736\pi$
$252$	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	−0.943946	−	0.330100i	$-0.892917\pi$
$257$	−4.98418	+	7.11815i	−0.310905	+	0.444018i	0.633041	+	0.774118i	$0.281806\pi$
$258$	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	0.314203	+	0.949356i	$0.398263\pi$
$263$	−9.97382	+	21.3889i	−0.615012	+	1.31890i	−0.929214	+	0.369541i	$0.879515\pi$
$264$	−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	−0.656642	−	0.754203i	$-0.728024\pi$
$277$	5.71185	−	12.2491i	0.343192	−	0.735978i	0.999834	+	0.0182248i	$0.00580146\pi$
$278$	−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	−0.978130	−	0.207994i	$-0.933306\pi$
$281$	−10.1156	+	12.0553i	−0.603445	+	0.719158i	0.374685	+	0.927152i	$0.377751\pi$
$282$	6.96758	−	17.6824i	0.414913	−	1.05297i
$283$	17.2952	−	24.7001i	1.02809	−	1.46827i	0.150648	−	0.988587i	$-0.451864\pi$
$283$	17.2952	−	24.7001i	1.02809	−	1.46827i	0.877443	−	0.479680i	$-0.159247\pi$
$284$	−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	−0.218384	−	0.975863i	$-0.570078\pi$
$293$	6.65512	−	3.10333i	0.388796	−	0.181299i	0.607180	+	0.794564i	$0.292301\pi$
$294$	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	−0.138764	−	0.990326i	$-0.544313\pi$
$307$	−13.2129	−	3.54038i	−0.754099	−	0.202060i	−0.615336	+	0.788265i	$0.710980\pi$
$308$	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	−0.0648001	−	0.997898i	$-0.520641\pi$
$311$	3.80231	−	0.670449i	0.215609	−	0.0380177i	0.280409	+	0.959881i	$0.409530\pi$
$312$	22.4666	−	17.8666i	1.27192	−	1.01149i
$313$	−2.14418	−	24.5081i	−0.121196	−	1.38528i	−0.776597	−	0.629997i	$-0.783056\pi$
$313$	−2.14418	−	24.5081i	−0.121196	−	1.38528i	0.655401	−	0.755281i	$-0.272500\pi$
$314$	−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	−0.0454916	−	0.998965i	$-0.514485\pi$
$317$	−14.9555	−	6.97386i	−0.839984	−	0.391691i	−0.794493	+	0.607274i	$0.792263\pi$
$318$	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	−0.814744	−	0.579820i	$-0.803123\pi$
$331$	−19.3973	+	7.06005i	−1.06617	+	0.388056i	−0.251429	+	0.967876i	$0.580901\pi$
$332$	−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	0.783227	−	0.621735i	$-0.213572\pi$
$337$	8.57053	+	6.00115i	0.466867	+	0.326904i	−0.316361	+	0.948639i	$0.602461\pi$
$338$	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	0.992472	−	0.122472i	$-0.0390821\pi$
$347$	4.85639	+	10.4146i	0.260705	+	0.559083i	−0.731767	+	0.681554i	$0.761304\pi$
$348$	4.82230	−	2.61759i	0.258502	−	0.140317i
$349$	15.6377	+	2.75735i	0.837067	+	0.147597i	0.575719	−	0.817647i	$-0.304722\pi$
$349$	15.6377	+	2.75735i	0.837067	+	0.147597i	0.261347	+	0.965245i	$0.415833\pi$
$350$		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	0.664538	−	0.747255i	$-0.268629\pi$
$353$	−4.97772	−	7.10893i	−0.264938	−	0.378370i	−0.929475	+	0.368885i	$0.879740\pi$
$354$	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	−0.460480	−	0.887670i	$-0.652323\pi$
$359$	10.2032	−	17.6725i	0.538505	−	0.932718i	0.998985	−	0.0450476i	$-0.0143439\pi$
$360$		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	−0.738818	−	0.673906i	$-0.764615\pi$
$367$	−25.8506	+	2.26163i	−1.34939	+	0.118056i	−0.610571	+	0.791962i	$0.709060\pi$
$368$	−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	−0.0367323	−	0.999325i	$-0.511695\pi$
$373$	−4.75950	−	0.416402i	−0.246438	−	0.0215605i	−0.209705	+	0.977765i	$0.567250\pi$
$374$	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	$0.225144\pi$
$379$			25.3002i			1.29958i	−0.760112	+	0.649792i	$0.774856\pi$
$380$		0			0
$381$	5.43079	+	1.60934i	0.278228	+	0.0824491i
$382$	−22.3379	+	10.4163i	−1.14291	+	0.532946i
$383$	1.07406	−	12.2766i	0.0548819	−	0.627303i	−0.918089	−	0.396375i	$-0.870268\pi$
$383$	1.07406	−	12.2766i	0.0548819	−	0.627303i	0.972971	−	0.230929i	$-0.0741764\pi$
$384$	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	0.799388	−	0.600815i	$-0.205157\pi$
$389$	6.83430	+	5.73466i	0.346513	+	0.290759i	−0.452875	+	0.891574i	$0.649602\pi$
$390$		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	−0.996192	−	0.0871833i	$-0.972213\pi$
$397$	−3.52782	−	13.1660i	−0.177056	−	0.660782i	0.819136	−	0.573599i	$-0.194453\pi$
$398$	−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	−0.962225	−	0.272257i	$-0.912230\pi$
$401$	−1.00354	+	2.75721i	−0.0501146	+	0.137689i	0.912110	+	0.409945i	$0.134452\pi$
$402$	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	−0.420515	−	0.907285i	$-0.638151\pi$
$409$	9.80467	−	26.9381i	0.484810	−	1.33200i	0.905325	−	0.424719i	$-0.139627\pi$
$410$		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	−0.987829	−	0.155543i	$-0.950287\pi$
$419$	−2.30839	−	13.0915i	−0.112772	−	0.639563i	0.875057	−	0.484020i	$-0.160824\pi$
$420$		0			0
$421$	6.93437	+	5.81863i	0.337960	+	0.283582i	0.795934	−	0.605383i	$-0.206980\pi$
$421$	6.93437	+	5.81863i	0.337960	+	0.283582i	−0.457974	+	0.888966i	$0.651425\pi$
$422$	−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	$-0.997731\pi$
$431$		−	0.295969i		−	0.0142563i	0.999975	−	0.00712817i	$-0.00226899\pi$
$432$	−5.39433	−	5.30459i	−0.259535	−	0.255217i
$433$	−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
$437$	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	−0.921105	−	0.389313i	$-0.872712\pi$
$439$	−9.75841	−	26.8110i	−0.465743	−	1.27962i	0.455362	−	0.890306i	$-0.349510\pi$
$440$		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	0.929098	−	0.369833i	$-0.120585\pi$
$443$	40.1651	−	3.51399i	1.90830	−	0.166955i	0.979204	+	0.202878i	$0.0650296\pi$
$444$	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	0.758819	−	0.651301i	$-0.225777\pi$
$449$	−3.91232	−	6.77634i	−0.184634	−	0.319795i	−0.943453	+	0.331506i	$0.892443\pi$
$450$		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	0.885920	−	0.463838i	$-0.153528\pi$
$457$	3.14363	+	4.48957i	0.147053	+	0.210013i	−0.738867	+	0.673851i	$0.764639\pi$
$458$	−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	0.815019	−	0.579434i	$-0.196726\pi$
$461$	29.6880	+	5.23480i	1.38271	+	0.243809i	0.567689	+	0.823243i	$0.307837\pi$
$462$	10.9803	−	5.96021i	0.510850	−	0.277294i
$463$	−0.0761934	−	0.163397i	−0.00354101	−	0.00759371i	0.904529	−	0.426411i	$-0.140222\pi$
$463$	−0.0761934	−	0.163397i	−0.00354101	−	0.00759371i	−0.908070	+	0.418818i	$0.862445\pi$
$464$	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	0.0345422	−	0.999403i	$-0.489003\pi$
$467$	12.1916	−	3.26672i	0.564158	−	0.151166i	0.529616	+	0.848238i	$0.322336\pi$
$468$	−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	−0.963696	−	0.267003i	$-0.913966\pi$
$479$	−33.4923	+	12.1902i	−1.53030	+	0.556985i	−0.566607	+	0.823988i	$0.691744\pi$
$480$		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	−0.809149	−	0.587604i	$-0.800071\pi$
$487$	−4.88907	+	4.88907i	−0.221545	+	0.221545i	0.587604	+	0.809149i	$0.300071\pi$
$488$	−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	0.244048	−	0.969763i	$-0.421525\pi$
$491$	−16.6934	−	19.8944i	−0.753361	−	0.897821i	−0.997409	+	0.0719426i	$0.977080\pi$
$492$	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	0.0791972	−	0.996859i	$-0.474764\pi$
$499$	11.0477	−	1.94801i	0.494564	−	0.0872050i	0.415367	+	0.909654i	$0.363653\pi$
$500$		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	−0.459467	−	0.888195i	$-0.651960\pi$
$503$	−29.1890	−	7.82118i	−1.30147	−	0.348729i	−0.842008	+	0.539466i	$0.818626\pi$
$504$	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	0.780829	−	0.624745i	$-0.214797\pi$
$509$	22.0511	+	8.02596i	0.977399	+	0.355744i	0.196571	+	0.980490i	$0.437019\pi$
$510$		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	0.154723	−	0.987958i	$-0.450551\pi$
$521$	−14.2319	−	8.21681i	−0.623512	−	0.359985i	−0.778235	+	0.627973i	$0.783885\pi$
$522$	7.01018	−	8.96844i	0.306827	−	0.392538i
$523$	−3.78176	+	14.1137i	−0.165365	+	0.617150i	0.832629	+	0.553832i	$0.186835\pi$
$523$	−3.78176	+	14.1137i	−0.165365	+	0.617150i	−0.997993	+	0.0633182i	$0.979832\pi$
$524$	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	−0.978111	−	0.208083i	$-0.933278\pi$
$547$	−4.44356	+	9.52924i	−0.189993	+	0.407441i	0.788118	+	0.615524i	$0.211055\pi$
$548$	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	−0.803238	−	0.595659i	$-0.796891\pi$
$557$	4.48926	−	16.7541i	0.190216	−	0.709896i	0.993454	−	0.114237i	$-0.0364423\pi$
$558$	−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	−0.815286	−	0.579058i	$-0.803420\pi$
$563$	−21.2542	+	9.91099i	−0.895758	+	0.417699i	−0.0804714	+	0.996757i	$0.525643\pi$
$564$	−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	−0.412175	−	0.911105i	$-0.635231\pi$
$569$	6.84027	−	38.7931i	0.286759	−	1.62629i	0.698934	−	0.715186i	$-0.253658\pi$
$570$		0			0
$571$	31.4980	+	11.4643i	1.31815	+	0.479767i	0.902865	−	0.429924i	$-0.141460\pi$
$571$	31.4980	+	11.4643i	1.31815	+	0.479767i	0.415285	+	0.909691i	$0.363682\pi$
$572$	−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	0.669393	−	0.742908i	$-0.266554\pi$
$577$	21.0819	+	5.64888i	0.877651	+	0.235166i	0.208257	+	0.978074i	$0.433221\pi$
$578$	−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	0.821656	−	0.569984i	$-0.193051\pi$
$587$	22.1244	+	10.3168i	0.913173	+	0.425819i	0.0915170	+	0.995804i	$0.470828\pi$
$588$	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	−0.618012	−	0.786169i	$-0.712062\pi$
$593$	4.09490	−	4.09490i	0.168157	−	0.168157i	0.786169	+	0.618012i	$0.212062\pi$
$594$	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	0.244163	−	0.969734i	$-0.421487\pi$
$599$	30.3866	−	25.4974i	1.24156	−	1.04180i	0.997400	−	0.0720615i	$-0.0229578\pi$
$600$		0			0
$601$	−22.4811	+	8.18244i	−0.917022	+	0.333769i	−0.757053	−	0.653353i	$-0.773362\pi$
$601$	−22.4811	+	8.18244i	−0.917022	+	0.333769i	−0.159969	+	0.987122i	$0.551139\pi$
$602$	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	0.970691	−	0.240329i	$-0.0772554\pi$
$607$	26.5308	+	18.5771i	1.07685	+	0.754020i	0.106160	+	0.994349i	$0.466144\pi$
$608$	−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	−0.544515	−	0.838751i	$-0.683286\pi$
$613$	−14.7737	+	3.95860i	−0.596704	+	0.159886i	−0.0521885	+	0.998637i	$0.516620\pi$
$614$	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	−0.991137	−	0.132845i	$-0.957589\pi$
$617$	−11.3221	−	24.2804i	−0.455812	−	0.977492i	0.535325	−	0.844646i	$-0.320189\pi$
$618$	−0.174600	+	6.63900i	−0.00702345	+	0.267060i
$619$	18.6300	+	3.28497i	0.748802	+	0.132034i	0.535011	−	0.844845i	$-0.320308\pi$
$619$	18.6300	+	3.28497i	0.748802	+	0.132034i	0.213792	+	0.976879i	$0.431419\pi$
$620$		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	0.866278	−	0.499562i	$-0.166506\pi$
$631$	0.0126965	+	0.0219910i	0.000505440	+	0.000875448i	−0.865773	+	0.500438i	$0.833172\pi$
$632$	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	0.965214	+	0.261463i	$0.0842049\pi$
$641$	9.97230	+	27.3987i	0.393882	+	1.08218i	−0.571331	+	0.820720i	$0.693573\pi$
$642$	−6.92324	+	7.82351i	−0.273238	+	0.308769i
$643$	1.74781	+	0.152914i	0.0689270	+	0.00603033i	0.121567	−	0.992583i	$-0.461208\pi$
$643$	1.74781	+	0.152914i	0.0689270	+	0.00603033i	−0.0526401	+	0.998614i	$0.516764\pi$
$644$	−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	0.355440	−	0.934699i	$-0.384331\pi$
$647$	−14.7341	−	14.7341i	−0.579259	−	0.579259i	−0.934699	+	0.355440i	$0.884331\pi$
$648$	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	0.963578	+	0.267429i	$0.0861741\pi$
$653$	−0.812604	+	9.28810i	−0.0317996	+	0.363471i	−0.995377	+	0.0960426i	$0.969382\pi$
$654$	−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	0.326010	−	0.945366i	$-0.394296\pi$
$659$	−14.0775	−	11.8125i	−0.548383	−	0.460148i	−0.874393	+	0.485218i	$0.838740\pi$
$660$		0			0
$661$	4.43306	+	25.1412i	0.172426	+	0.977878i	0.941073	+	0.338204i	$0.109819\pi$
$661$	4.43306	+	25.1412i	0.172426	+	0.977878i	−0.768647	+	0.639674i	$0.779070\pi$
$662$	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	−0.645078	−	0.764117i	$-0.723175\pi$
$673$	−3.83098	+	2.68248i	−0.147673	+	0.103402i	0.497405	+	0.867518i	$0.334286\pi$
$674$	−11.0600			−0.426017
$675$		0			0
$676$	14.6331			0.562810
$677$	32.1483	−	22.5105i	1.23556	−	0.865147i	0.241123	−	0.970495i	$-0.422484\pi$
$677$	32.1483	−	22.5105i	1.23556	−	0.865147i	0.994436	+	0.105347i	$0.0335953\pi$
$678$	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	−0.854820	−	0.518924i	$-0.826333\pi$
$683$	−9.77386	−	36.4765i	−0.373986	−	1.39574i	0.480834	−	0.876812i	$-0.340334\pi$
$684$	−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	0.815068	−	0.579365i	$-0.196699\pi$
$691$	10.1478	+	8.51501i	0.386040	+	0.323926i	−0.429028	+	0.903291i	$0.641144\pi$
$692$	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	$-0.991452\pi$
$701$		−	1.42181i		−	0.0537011i	0.999639	−	0.0268505i	$-0.00854782\pi$
$702$	−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	0.918487	+	0.395452i	$0.129412\pi$
$709$	12.4901	+	34.3163i	0.469077	+	1.28878i	−0.449410	+	0.893325i	$0.648366\pi$
$710$		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	0.999766	−	0.0216398i	$-0.00688871\pi$
$719$	12.9014	+	22.3459i	0.481142	+	0.833363i	−0.518624	+	0.855003i	$0.673555\pi$
$720$		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	0.835958	−	0.548794i	$-0.184913\pi$
$727$	0.926059	+	1.32255i	0.0343456	+	0.0490507i	−0.801612	+	0.597845i	$0.796024\pi$
$728$	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	0.982362	−	0.186990i	$-0.0598731\pi$
$733$	5.62244	+	12.0574i	0.207669	+	0.445349i	−0.774692	+	0.632338i	$0.782095\pi$
$734$	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	0.191243	−	0.981543i	$-0.438748\pi$
$739$	30.9063	−	17.8437i	1.13691	−	0.656393i	0.945663	+	0.325150i	$0.105415\pi$
$740$		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	0.966990	−	0.254813i	$-0.0820138\pi$
$743$	28.8465	+	20.1985i	1.05828	+	0.741012i	0.0912848	+	0.995825i	$0.470903\pi$
$744$	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	−0.225864	−	0.974159i	$-0.572520\pi$
$751$	19.0262	−	15.9649i	0.694275	−	0.582566i	0.920138	+	0.391593i	$0.128076\pi$
$752$	−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	−0.952263	−	0.305278i	$-0.901251\pi$
$757$	−17.8009	+	17.8009i	−0.646986	+	0.646986i	0.305278	+	0.952263i	$0.401251\pi$
$758$	−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	−0.927240	−	0.374467i	$-0.877826\pi$
$761$	−31.3105	−	37.3144i	−1.13500	−	1.35265i	−0.207765	−	0.978179i	$-0.566619\pi$
$762$	−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	−0.884287	−	0.466944i	$-0.845355\pi$
$769$	−43.1365	+	7.60612i	−1.55554	+	0.274284i	−0.671254	+	0.741227i	$0.734244\pi$
$770$		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	0.632691	−	0.774404i	$-0.281950\pi$
$773$	22.0592	+	5.91076i	0.793416	+	0.212595i	0.160725	+	0.986999i	$0.448617\pi$
$774$	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	−0.124008	−	0.992281i	$-0.539575\pi$
$787$	15.6093	−	7.27876i	0.556413	−	0.259460i	0.680421	+	0.732822i	$0.261797\pi$
$788$	−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	0.331827	+	0.943340i	$0.392335\pi$
$797$	−18.8617	+	26.9373i	−0.668115	+	0.954166i	−0.999941	+	0.0108262i	$0.996554\pi$
$798$	−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	−0.506989	−	0.861953i	$-0.669241\pi$
$821$	12.3182	−	14.6802i	0.429907	−	0.512343i	0.936895	+	0.349610i	$0.113686\pi$
$822$	18.1837	+	22.8654i	0.634230	+	0.797522i
$823$	0.358433	−	0.511895i	0.0124942	−	0.0178435i	−0.812856	−	0.582464i	$-0.802089\pi$
$823$	0.358433	−	0.511895i	0.0124942	−	0.0178435i	0.825351	+	0.564621i	$0.190978\pi$
$824$	−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	−0.998468	−	0.0553328i	$-0.982378\pi$
$827$	−3.05127	+	11.3875i	−0.106103	+	0.395981i	0.892365	+	0.451314i	$0.149045\pi$
$828$	−1.60222	+	1.00068i	−0.0556811	+	0.0347759i
$829$	−38.0844	−	21.9880i	−1.32272	−	0.763675i	−0.338562	−	0.940944i	$-0.609941\pi$
$829$	−38.0844	−	21.9880i	−1.32272	−	0.763675i	−0.984163	+	0.177269i	$0.943274\pi$
$830$		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	−0.981668	−	0.190601i	$-0.938956\pi$
$839$	0.173429	−	0.983567i	0.00598745	−	0.0339565i	0.987655	+	0.156644i	$0.0500676\pi$
$840$		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	0.986449	−	0.164070i	$-0.0524623\pi$
$853$	−0.394403	−	4.50805i	−0.0135041	−	0.154353i	−0.999953	+	0.00971747i	$0.996907\pi$
$854$	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	−0.974670	−	0.223650i	$-0.928203\pi$
$857$	−51.8892	−	24.1963i	−1.77250	−	0.826531i	−0.797831	−	0.602881i	$-0.794019\pi$
$858$	−22.2936	+	7.45653i	−0.761091	+	0.254562i
$859$	20.9711	+	24.9924i	0.715526	+	0.852730i	0.994188	−	0.107659i	$-0.0343354\pi$
$859$	20.9711	+	24.9924i	0.715526	+	0.852730i	−0.278662	+	0.960389i	$0.589891\pi$
$860$		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	−0.999633	−	0.0270792i	$-0.991379\pi$
$863$	−28.5706	+	28.5706i	−0.972554	+	0.972554i	0.0270792	+	0.999633i	$0.491379\pi$
$864$	−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	0.950443	−	0.310899i	$-0.100630\pi$
$877$	29.1215	+	20.3911i	0.983364	+	0.688559i	0.0329214	+	0.999458i	$0.489519\pi$
$878$	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	−0.920846	−	0.389927i	$-0.872500\pi$
$881$	−30.9752	+	17.8836i	−1.04358	+	0.602512i	−0.122736	+	0.992439i	$0.539167\pi$
$882$	−0.892728	−	4.20463i	−0.0300597	−	0.141577i
$883$	3.38029	−	0.905746i	0.113756	−	0.0304808i	−0.201492	−	0.979490i	$-0.564579\pi$
$883$	3.38029	−	0.905746i	0.113756	−	0.0304808i	0.315248	+	0.949009i	$0.397912\pi$
$884$	−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	−0.998095	−	0.0616962i	$-0.980349\pi$
$887$	−12.0260	−	25.7899i	−0.403794	−	0.865939i	0.594301	−	0.804243i	$-0.297429\pi$
$888$	−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	−0.615596	−	0.788062i	$-0.711085\pi$
$907$	−32.6761	+	2.85879i	−1.08499	+	0.0949246i	−0.469398	+	0.882987i	$0.655529\pi$
$908$	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	0.988379	+	0.152012i	$0.0485753\pi$
$911$	9.92857	+	27.2785i	0.328948	+	0.903778i	−0.659430	+	0.751766i	$0.729202\pi$
$912$	−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	$0.154540\pi$
$919$			28.2931i			0.933302i	−0.884442	+	0.466651i	$0.845460\pi$
$920$		0			0
$921$	−17.1879	+	16.3070i	−0.566361	+	0.537335i
$922$	−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	0.954390	−	0.298564i	$-0.0965076\pi$
$929$	25.1788	+	21.1275i	0.826089	+	0.693171i	−0.128300	+	0.991735i	$0.540952\pi$
$930$		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	0.983970	−	0.178334i	$-0.0570708\pi$
$937$	1.30584	+	4.87347i	0.0426600	+	0.159209i	−0.941310	+	0.337543i	$0.890404\pi$
$938$	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	−0.00641343	−	0.999979i	$-0.502041\pi$
$941$	19.6715	−	54.0471i	0.641274	−	1.76189i	0.647687	−	0.761906i	$-0.275736\pi$
$942$	−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	−0.0603125	−	0.998180i	$-0.519210\pi$
$947$	26.3740	−	18.4673i	0.857041	−	0.600107i	0.917354	+	0.398073i	$0.130321\pi$
$948$	−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	0.995384	+	0.0959743i	$0.0305967\pi$
$953$	5.59819	+	20.8927i	0.181343	+	0.676782i	−0.814041	+	0.580808i	$0.802737\pi$
$954$	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	0.964927	+	0.262517i	$0.0845527\pi$
$967$	−0.961701	+	10.9923i	−0.0309262	+	0.353488i	−0.995854	+	0.0909711i	$0.971003\pi$
$968$	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	$0.114506\pi$
$971$			21.9387i			0.704047i	−0.935991	+	0.352023i	$0.885494\pi$
$972$	−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	0.174498	−	0.984658i	$-0.444170\pi$
$977$	5.48124	+	0.479546i	0.175360	+	0.0153420i	0.000862648		1.00000i	$0.499725\pi$
$978$	−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	0.358478	−	0.933538i	$-0.383296\pi$
$983$	27.3904	−	2.39635i	0.873618	−	0.0764316i	0.515139	+	0.857106i	$0.327740\pi$
$984$	−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	−0.711637	−	0.702547i	$-0.752046\pi$
$991$	7.95205	−	13.7734i	0.252605	−	0.437525i	0.964242	+	0.265022i	$0.0853793\pi$
$992$	−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	0.851083	−	0.525032i	$-0.175947\pi$
$997$	2.10376	+	3.00447i	0.0666266	+	0.0951527i	−0.784456	+	0.620185i	$0.787058\pi$
$998$	−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.218.5		192
5.2	odd	4	inner	675.2.ba.b.407.5		192
5.3	odd	4		135.2.q.a.2.12	✓	192
5.4	even	2		135.2.q.a.83.12	yes	192
15.8	even	4		405.2.r.a.332.5		192
15.14	odd	2		405.2.r.a.8.5		192
27.14	odd	18	inner	675.2.ba.b.68.5		192
135.13	odd	36		405.2.r.a.152.5		192
135.14	odd	18		135.2.q.a.68.12	yes	192
135.68	even	36		135.2.q.a.122.12	yes	192
135.94	even	18		405.2.r.a.233.5		192
135.122	even	36	inner	675.2.ba.b.257.5		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.12	✓	192	5.3	odd	4
135.2.q.a.68.12	yes	192	135.14	odd	18
135.2.q.a.83.12	yes	192	5.4	even	2
135.2.q.a.122.12	yes	192	135.68	even	36
405.2.r.a.8.5		192	15.14	odd	2
405.2.r.a.152.5		192	135.13	odd	36
405.2.r.a.233.5		192	135.94	even	18
405.2.r.a.332.5		192	15.8	even	4
675.2.ba.b.68.5		192	27.14	odd	18	inner
675.2.ba.b.218.5		192	1.1	even	1	trivial
675.2.ba.b.257.5		192	135.122	even	36	inner
675.2.ba.b.407.5		192	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
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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