LMFDB - Embedded newform 722.2.e.s.595.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [722,2,Mod(99,722)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(722, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("722.99"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,6,12,0,0,-6,6,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			595.3
Character	$\chi$	$=$	722.595
Dual form			722.2.e.s.415.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.766044 + 0.642788i) q^{2} +(1.20664 + 0.439181i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.641755 + 3.63957i) q^{5} +(-1.20664 + 0.439181i) q^{6} +(0.221232 - 0.383185i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.03503 - 0.868497i) q^{9} +(-2.83108 - 2.37556i) q^{10} +(2.01484 + 3.48980i) q^{11} +(0.642040 - 1.11205i) q^{12} +(4.59650 - 1.67299i) q^{13} +(0.0768330 + 0.435741i) q^{14} +(-0.824064 + 4.67350i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.204452 - 0.171556i) q^{17} +1.35114 q^{18} +3.69572 q^{20} +(0.435234 - 0.365205i) q^{21} +(-3.78665 - 1.37823i) q^{22} +(-1.59918 + 9.06939i) q^{23} +(0.222978 + 1.26457i) q^{24} +(-8.13617 + 2.96132i) q^{25} +(-2.44575 + 4.23616i) q^{26} +(-2.79360 - 4.83866i) q^{27} +(-0.338947 - 0.284410i) q^{28} +(0.171273 + 0.143715i) q^{29} +(-2.37280 - 4.10980i) q^{30} +(1.73993 - 3.01364i) q^{31} +(0.939693 - 0.342020i) q^{32} +(0.898528 + 5.09581i) q^{33} +(-0.0463455 + 0.262838i) q^{34} +(1.53660 + 0.559278i) q^{35} +(-1.03503 + 0.868497i) q^{36} -1.44903 q^{37} +6.28106 q^{39} +(-2.83108 + 2.37556i) q^{40} +(-7.39042 - 2.68989i) q^{41} +(-0.0986596 + 0.559526i) q^{42} +(-0.978546 - 5.54961i) q^{43} +(3.78665 - 1.37823i) q^{44} +(2.49672 - 4.32444i) q^{45} +(-4.60465 - 7.97549i) q^{46} +(1.68429 + 1.41328i) q^{47} +(-0.983662 - 0.825390i) q^{48} +(3.40211 + 5.89263i) q^{49} +(4.32916 - 7.49833i) q^{50} +(0.322044 - 0.117214i) q^{51} +(-0.849399 - 4.81718i) q^{52} +(-1.72648 + 9.79136i) q^{53} +(5.25026 + 1.91094i) q^{54} +(-11.4083 + 9.57273i) q^{55} +0.442463 q^{56} -0.223582 q^{58} +(2.68845 - 2.25588i) q^{59} +(4.45940 + 1.62309i) q^{60} +(0.708406 - 4.01757i) q^{61} +(0.604270 + 3.42699i) q^{62} +(-0.561777 + 0.204470i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(9.03879 + 15.6556i) q^{65} +(-3.96383 - 3.32605i) q^{66} +(-0.113193 - 0.0949801i) q^{67} +(-0.133446 - 0.231136i) q^{68} +(-5.91273 + 10.2412i) q^{69} +(-1.53660 + 0.559278i) q^{70} +(-1.99159 - 11.2949i) q^{71} +(0.234623 - 1.33061i) q^{72} +(-1.33649 - 0.486442i) q^{73} +(1.11002 - 0.931417i) q^{74} -11.1180 q^{75} +1.78298 q^{77} +(-4.81157 + 4.03739i) q^{78} +(9.58804 + 3.48976i) q^{79} +(0.641755 - 3.63957i) q^{80} +(-0.541955 - 3.07358i) q^{81} +(7.39042 - 2.68989i) q^{82} +(1.64439 - 2.84817i) q^{83} +(-0.284079 - 0.492039i) q^{84} +(0.755596 + 0.634021i) q^{85} +(4.31683 + 3.62225i) q^{86} +(0.143548 + 0.248633i) q^{87} +(-2.01484 + 3.48980i) q^{88} +(-5.60127 + 2.03870i) q^{89} +(0.867101 + 4.91757i) q^{90} +(0.375828 - 2.13143i) q^{91} +(8.65391 + 3.14977i) q^{92} +(3.42300 - 2.87224i) q^{93} -2.19868 q^{94} +1.28408 q^{96} +(-3.12911 + 2.62563i) q^{97} +(-6.39388 - 2.32718i) q^{98} +(0.945455 - 5.36194i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{7} + 12 q^{8} - 6 q^{11} + 6 q^{12} - 24 q^{18} - 12 q^{20} - 54 q^{26} - 12 q^{27} - 12 q^{30} + 78 q^{31} - 24 q^{37} - 36 q^{39} + 66 q^{45} - 30 q^{46} + 36 q^{49} + 18 q^{50} + 12 q^{56}+ \cdots + 12 q^{96}+O(q^{100}) $ 24 * q + 6 * q^7 + 12 * q^8 - 6 * q^11 + 6 * q^12 - 24 * q^18 - 12 * q^20 - 54 * q^26 - 12 * q^27 - 12 * q^30 + 78 * q^31 - 24 * q^37 - 36 * q^39 + 66 * q^45 - 30 * q^46 + 36 * q^49 + 18 * q^50 + 12 * q^56 - 12 * q^58 - 12 * q^64 - 12 * q^65 - 18 * q^68 - 60 * q^69 - 48 * q^75 + 24 * q^77 + 36 * q^83 + 12 * q^84 + 78 * q^87 + 6 * q^88 + 72 * q^94 + 12 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	1.20664	+	0.439181i	0.696654	+	0.253561i	0.665981	−	0.745968i	$-0.268013\pi$
$3$	1.20664	+	0.439181i	0.696654	+	0.253561i	0.0306722	+	0.999529i	$0.490235\pi$
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	0.641755	+	3.63957i	0.287001	+	1.62767i	0.698048	+	0.716051i	$0.254052\pi$
$5$	0.641755	+	3.63957i	0.287001	+	1.62767i	−0.411046	+	0.911614i	$0.634837\pi$
$6$	−1.20664	+	0.439181i	−0.492609	+	0.179295i
$7$	0.221232	−	0.383185i	0.0836177	−	0.144830i	−0.821184	−	0.570664i	$-0.806686\pi$
$7$	0.221232	−	0.383185i	0.0836177	−	0.144830i	0.904801	+	0.425834i	$0.140019\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−1.03503	−	0.868497i	−0.345011	−	0.289499i
$10$	−2.83108	−	2.37556i	−0.895267	−	0.751218i
$11$	2.01484	+	3.48980i	0.607496	+	1.05221i	0.991652	+	0.128946i	$0.0411593\pi$
$11$	2.01484	+	3.48980i	0.607496	+	1.05221i	−0.384156	+	0.923268i	$0.625507\pi$
$12$	0.642040	−	1.11205i	0.185341	−	0.321020i
$13$	4.59650	−	1.67299i	1.27484	−	0.464004i	0.386117	−	0.922450i	$-0.373816\pi$
$13$	4.59650	−	1.67299i	1.27484	−	0.464004i	0.888722	+	0.458446i	$0.151594\pi$
$14$	0.0768330	+	0.435741i	0.0205345	+	0.116457i
$15$	−0.824064	+	4.67350i	−0.212772	+	1.20669i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	0.204452	−	0.171556i	0.0495869	−	0.0416083i	−0.617657	−	0.786447i	$-0.711918\pi$
$17$	0.204452	−	0.171556i	0.0495869	−	0.0416083i	0.667244	+	0.744839i	$0.267474\pi$
$18$	1.35114			0.318467
$19$		0			0
$19$		0			0
$20$	3.69572			0.826388
$21$	0.435234	−	0.365205i	0.0949759	−	0.0796943i
$22$	−3.78665	−	1.37823i	−0.807317	−	0.293839i
$23$	−1.59918	+	9.06939i	−0.333452	+	1.89110i	0.108561	+	0.994090i	$0.465376\pi$
$23$	−1.59918	+	9.06939i	−0.333452	+	1.89110i	−0.442013	+	0.897009i	$0.645735\pi$
$24$	0.222978	+	1.26457i	0.0455152	+	0.258129i
$25$	−8.13617	+	2.96132i	−1.62723	+	0.592265i
$26$	−2.44575	+	4.23616i	−0.479650	+	0.830779i
$27$	−2.79360	−	4.83866i	−0.537629	−	0.931201i
$28$	−0.338947	−	0.284410i	−0.0640549	−	0.0537484i
$29$	0.171273	+	0.143715i	0.0318047	+	0.0266873i	0.658551	−	0.752536i	$-0.271169\pi$
$29$	0.171273	+	0.143715i	0.0318047	+	0.0266873i	−0.626747	+	0.779223i	$0.715614\pi$
$30$	−2.37280	−	4.10980i	−0.433211	−	0.750344i
$31$	1.73993	−	3.01364i	0.312500	−	0.541266i	−0.666403	−	0.745592i	$-0.732167\pi$
$31$	1.73993	−	3.01364i	0.312500	−	0.541266i	0.978903	+	0.204326i	$0.0655002\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	0.898528	+	5.09581i	0.156414	+	0.887066i
$34$	−0.0463455	+	0.262838i	−0.00794818	+	0.0450764i
$35$	1.53660	+	0.559278i	0.259734	+	0.0945353i
$36$	−1.03503	+	0.868497i	−0.172506	+	0.144749i
$37$	−1.44903			−0.238219			−0.119109	−	0.992881i	$-0.538004\pi$
$37$	−1.44903			−0.238219			−0.119109	+	0.992881i	$0.538004\pi$
$38$		0			0
$39$	6.28106			1.00577
$40$	−2.83108	+	2.37556i	−0.447634	+	0.375609i
$41$	−7.39042	−	2.68989i	−1.15419	−	0.420091i	−0.307172	−	0.951654i	$-0.599383\pi$
$41$	−7.39042	−	2.68989i	−1.15419	−	0.420091i	−0.847019	+	0.531563i	$0.821605\pi$
$42$	−0.0986596	+	0.559526i	−0.0152235	+	0.0863368i
$43$	−0.978546	−	5.54961i	−0.149227	−	0.846307i	−0.963876	−	0.266353i	$-0.914181\pi$
$43$	−0.978546	−	5.54961i	−0.149227	−	0.846307i	0.814649	−	0.579955i	$-0.196930\pi$
$44$	3.78665	−	1.37823i	0.570859	−	0.207776i
$45$	2.49672	−	4.32444i	0.372189	−	0.644650i
$46$	−4.60465	−	7.97549i	−0.678919	−	1.17592i
$47$	1.68429	+	1.41328i	0.245678	+	0.206149i	0.757309	−	0.653057i	$-0.226514\pi$
$47$	1.68429	+	1.41328i	0.245678	+	0.206149i	−0.511630	+	0.859206i	$0.670958\pi$
$48$	−0.983662	−	0.825390i	−0.141979	−	0.119135i
$49$	3.40211	+	5.89263i	0.486016	+	0.841805i
$50$	4.32916	−	7.49833i	0.612236	−	1.06042i
$51$	0.322044	−	0.117214i	0.0450951	−	0.0164133i
$52$	−0.849399	−	4.81718i	−0.117790	−	0.668022i
$53$	−1.72648	+	9.79136i	−0.237150	+	1.34495i	0.600887	+	0.799334i	$0.294814\pi$
$53$	−1.72648	+	9.79136i	−0.237150	+	1.34495i	−0.838037	+	0.545613i	$0.816297\pi$
$54$	5.25026	+	1.91094i	0.714470	+	0.260046i
$55$	−11.4083	+	9.57273i	−1.53830	+	1.29079i
$56$	0.442463			0.0591267
$57$		0			0
$58$	−0.223582			−0.0293577
$59$	2.68845	−	2.25588i	0.350007	−	0.293690i	−0.450786	−	0.892632i	$-0.648856\pi$
$59$	2.68845	−	2.25588i	0.350007	−	0.293690i	0.800793	+	0.598942i	$0.204412\pi$
$60$	4.45940	+	1.62309i	0.575706	+	0.209540i
$61$	0.708406	−	4.01757i	0.0907021	−	0.514397i	−0.905278	−	0.424820i	$-0.860337\pi$
$61$	0.708406	−	4.01757i	0.0907021	−	0.514397i	0.995980	−	0.0895771i	$-0.0285515\pi$
$62$	0.604270	+	3.42699i	0.0767424	+	0.435228i
$63$	−0.561777	+	0.204470i	−0.0707772	+	0.0257608i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	9.03879	+	15.6556i	1.12112	+	1.94184i
$66$	−3.96383	−	3.32605i	−0.487914	−	0.409409i
$67$	−0.113193	−	0.0949801i	−0.0138287	−	0.0116037i	0.635847	−	0.771815i	$-0.280651\pi$
$67$	−0.113193	−	0.0949801i	−0.0138287	−	0.0116037i	−0.649676	+	0.760211i	$0.725095\pi$
$68$	−0.133446	−	0.231136i	−0.0161828	−	0.0280294i
$69$	−5.91273	+	10.2412i	−0.711810	+	1.23289i
$70$	−1.53660	+	0.559278i	−0.183659	+	0.0668465i
$71$	−1.99159	−	11.2949i	−0.236358	−	1.34046i	−0.839734	−	0.542998i	$-0.817289\pi$
$71$	−1.99159	−	11.2949i	−0.236358	−	1.34046i	0.603376	−	0.797457i	$-0.293822\pi$
$72$	0.234623	−	1.33061i	0.0276506	−	0.156814i
$73$	−1.33649	−	0.486442i	−0.156424	−	0.0569337i	0.262621	−	0.964899i	$-0.415413\pi$
$73$	−1.33649	−	0.486442i	−0.156424	−	0.0569337i	−0.419045	+	0.907965i	$0.637635\pi$
$74$	1.11002	−	0.931417i	0.129037	−	0.108275i
$75$	−11.1180			−1.28379
$76$		0			0
$77$	1.78298			0.203190
$78$	−4.81157	+	4.03739i	−0.544803	+	0.457144i
$79$	9.58804	+	3.48976i	1.07874	+	0.392629i	0.819438	−	0.573168i	$-0.194286\pi$
$79$	9.58804	+	3.48976i	1.07874	+	0.392629i	0.259301	+	0.965797i	$0.416508\pi$
$80$	0.641755	−	3.63957i	0.0717503	−	0.406916i
$81$	−0.541955	−	3.07358i	−0.0602172	−	0.341509i
$82$	7.39042	−	2.68989i	0.816136	−	0.297049i
$83$	1.64439	−	2.84817i	0.180495	−	0.312627i	−0.761554	−	0.648101i	$-0.775563\pi$
$83$	1.64439	−	2.84817i	0.180495	−	0.312627i	0.942049	+	0.335475i	$0.108897\pi$
$84$	−0.284079	−	0.492039i	−0.0309956	−	0.0536859i
$85$	0.755596	+	0.634021i	0.0819559	+	0.0687692i
$86$	4.31683	+	3.62225i	0.465496	+	0.390597i
$87$	0.143548	+	0.248633i	0.0153900	+	0.0266562i
$88$	−2.01484	+	3.48980i	−0.214782	+	0.372014i
$89$	−5.60127	+	2.03870i	−0.593733	+	0.216101i	−0.621371	−	0.783517i	$-0.713424\pi$
$89$	−5.60127	+	2.03870i	−0.593733	+	0.216101i	0.0276373	+	0.999618i	$0.491202\pi$
$90$	0.867101	+	4.91757i	0.0914005	+	0.518358i
$91$	0.375828	−	2.13143i	0.0393975	−	0.223434i
$92$	8.65391	+	3.14977i	0.902233	+	0.328386i
$93$	3.42300	−	2.87224i	0.354948	−	0.297837i
$94$	−2.19868			−0.226776
$95$		0			0
$96$	1.28408			0.131056
$97$	−3.12911	+	2.62563i	−0.317713	+	0.266593i	−0.787671	−	0.616096i	$-0.788713\pi$
$97$	−3.12911	+	2.62563i	−0.317713	+	0.266593i	0.469958	+	0.882689i	$0.344269\pi$
$98$	−6.39388	−	2.32718i	−0.645880	−	0.235081i
$99$	0.945455	−	5.36194i	0.0950218	−	0.538895i
$100$	1.50350	+	8.52679i	0.150350	+	0.852679i
$101$	−0.399630	+	0.145453i	−0.0397647	+	0.0144732i	−0.361826	−	0.932246i	$-0.617847\pi$
$101$	−0.399630	+	0.145453i	−0.0397647	+	0.0144732i	0.322061	+	0.946719i	$0.395624\pi$
$102$	−0.171356	+	0.296797i	−0.0169668	+	0.0293873i
$103$	−2.26809	−	3.92845i	−0.223482	−	0.387081i	0.732381	−	0.680895i	$-0.238409\pi$
$103$	−2.26809	−	3.92845i	−0.223482	−	0.387081i	−0.955863	+	0.293813i	$0.905076\pi$
$104$	3.74710	+	3.14419i	0.367433	+	0.308313i
$105$	1.60850	+	1.34969i	0.156974	+	0.131717i
$106$	−4.97120	−	8.61038i	−0.482846	−	0.836314i
$107$	−1.58576	+	2.74661i	−0.153301	+	0.265525i	−0.932439	−	0.361327i	$-0.882324\pi$
$107$	−1.58576	+	2.74661i	−0.153301	+	0.265525i	0.779138	+	0.626852i	$0.215657\pi$
$108$	−5.25026	+	1.91094i	−0.505206	+	0.183880i
$109$	1.17753	+	6.67810i	0.112787	+	0.639646i	0.987822	+	0.155587i	$0.0497268\pi$
$109$	1.17753	+	6.67810i	0.112787	+	0.639646i	−0.875035	+	0.484059i	$0.839162\pi$
$110$	2.58606	−	14.6663i	0.246571	−	1.39837i
$111$	−1.74845	−	0.636385i	−0.165956	−	0.0604030i
$112$	−0.338947	+	0.284410i	−0.0320275	+	0.0268742i
$113$	10.0444			0.944893			0.472447	−	0.881359i	$-0.343371\pi$
$113$	10.0444			0.944893			0.472447	+	0.881359i	$0.343371\pi$
$114$		0			0
$115$	−34.0350			−3.17378
$116$	0.171273	−	0.143715i	0.0159023	−	0.0133436i
$117$	−6.21052	−	2.26044i	−0.574163	−	0.208978i
$118$	−0.609423	+	3.45621i	−0.0561019	+	0.318170i
$119$	−0.0205062	−	0.116296i	−0.00187980	−	0.0106609i
$120$	−4.45940	+	1.62309i	−0.407086	+	0.148167i
$121$	−2.61913	+	4.53647i	−0.238103	+	0.412406i
$122$	2.03977	+	3.53299i	0.184672	+	0.319862i
$123$	−7.73623	−	6.49146i	−0.697552	−	0.585316i
$124$	−2.66572	−	2.23681i	−0.239389	−	0.200871i
$125$	−6.76007	−	11.7088i	−0.604639	−	1.04727i
$126$	0.298915	−	0.517736i	0.0266295	−	0.0461236i
$127$	13.2314	−	4.81584i	1.17410	−	0.427337i	0.319985	−	0.947423i	$-0.396322\pi$
$127$	13.2314	−	4.81584i	1.17410	−	0.427337i	0.854114	+	0.520086i	$0.174100\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	1.25653	−	7.12614i	0.110631	−	0.627421i
$130$	−16.9874	−	6.18289i	−1.48989	−	0.542276i
$131$	12.1353	−	10.1827i	1.06027	−	0.889669i	0.0661303	−	0.997811i	$-0.478935\pi$
$131$	12.1353	−	10.1827i	1.06027	−	0.889669i	0.994135	+	0.108142i	$0.0344903\pi$
$132$	5.17442			0.450375
$133$		0			0
$134$	0.147763			0.0127648
$135$	15.8179	−	13.2728i	1.36138	−	1.14234i
$136$	0.250797	+	0.0912828i	0.0215057	+	0.00782743i
$137$	0.383317	−	2.17390i	0.0327490	−	0.185729i	−0.964045	−	0.265739i	$-0.914384\pi$
$137$	0.383317	−	2.17390i	0.0327490	−	0.185729i	0.996794	+	0.0800100i	$0.0254952\pi$
$138$	−2.05347	−	11.6458i	−0.174803	−	0.991358i
$139$	16.0353	−	5.83638i	1.36010	−	0.495036i	0.444014	−	0.896020i	$-0.353554\pi$
$139$	16.0353	−	5.83638i	1.36010	−	0.495036i	0.916085	+	0.400984i	$0.131332\pi$
$140$	0.817610	−	1.41614i	0.0691007	−	0.119686i
$141$	1.41164	+	2.44503i	0.118881	+	0.205909i
$142$	8.78585	+	7.37221i	0.737293	+	0.618662i
$143$	15.0996	+	12.6701i	1.26269	+	1.05952i
$144$	0.675571	+	1.17012i	0.0562975	+	0.0975102i
$145$	−0.413147	+	0.715592i	−0.0343100	+	0.0594267i
$146$	1.33649	−	0.486442i	0.110608	−	0.0402582i
$147$	1.51719	+	8.60443i	0.125136	+	0.709681i
$148$	−0.251621	+	1.42701i	−0.0206831	+	0.117300i
$149$	−12.7289	−	4.63292i	−1.04279	−	0.379544i	−0.236852	−	0.971546i	$-0.576116\pi$
$149$	−12.7289	−	4.63292i	−1.04279	−	0.379544i	−0.805937	+	0.592002i	$0.798338\pi$
$150$	8.51686	−	7.14650i	0.695399	−	0.583509i
$151$	9.15317			0.744875			0.372437	−	0.928057i	$-0.378522\pi$
$151$	9.15317			0.744875			0.372437	+	0.928057i	$0.378522\pi$
$152$		0			0
$153$	−0.360610			−0.0291536
$154$	−1.36584	+	1.14608i	−0.110063	+	0.0923537i
$155$	12.0850	+	4.39857i	0.970688	+	0.353302i
$156$	1.09069	−	6.18564i	0.0873255	−	0.495247i
$157$	−2.84614	−	16.1413i	−0.227147	−	1.28821i	−0.858538	−	0.512750i	$-0.828627\pi$
$157$	−2.84614	−	16.1413i	−0.227147	−	1.28821i	0.631391	−	0.775464i	$-0.282484\pi$
$158$	−9.58804	+	3.48976i	−0.762783	+	0.277630i
$159$	−6.38342	+	11.0564i	−0.506238	+	0.876830i
$160$	1.84786	+	3.20059i	0.146086	+	0.253028i
$161$	3.12146	+	2.61922i	0.246006	+	0.206423i
$162$	2.39082	+	2.00614i	0.187841	+	0.157617i
$163$	6.88612	+	11.9271i	0.539363	+	0.934204i	0.998938	+	0.0460652i	$0.0146682\pi$
$163$	6.88612	+	11.9271i	0.539363	+	0.934204i	−0.459576	+	0.888139i	$0.651998\pi$
$164$	−3.93236	+	6.81105i	−0.307066	+	0.531854i
$165$	−17.9699	+	6.54052i	−1.39896	+	0.509178i
$166$	0.571090	+	3.23881i	0.0443252	+	0.251381i
$167$	1.79427	−	10.1758i	0.138845	−	0.787429i	−0.833260	−	0.552882i	$-0.813528\pi$
$167$	1.79427	−	10.1758i	0.138845	−	0.787429i	0.972105	−	0.234547i	$-0.0753607\pi$
$168$	0.533894	+	0.194322i	0.0411908	+	0.0149922i
$169$	8.37033	−	7.02354i	0.643871	−	0.540272i
$170$	−0.986361			−0.0756504
$171$		0			0
$172$	−5.63522			−0.429682
$173$	7.51644	−	6.30704i	0.571464	−	0.479515i	−0.310667	−	0.950519i	$-0.600552\pi$
$173$	7.51644	−	6.30704i	0.571464	−	0.479515i	0.882131	+	0.471003i	$0.156108\pi$
$174$	−0.269782	−	0.0981928i	−0.0204521	−	0.00744397i
$175$	−0.665245	+	3.77279i	−0.0502878	+	0.285196i
$176$	−0.699745	−	3.96845i	−0.0527453	−	0.299133i
$177$	4.23473	−	1.54132i	0.318302	−	0.115852i
$178$	2.98037	−	5.16216i	0.223388	−	0.386920i
$179$	−4.39915	−	7.61955i	−0.328808	−	0.569512i	0.653468	−	0.756955i	$-0.273314\pi$
$179$	−4.39915	−	7.61955i	−0.328808	−	0.569512i	−0.982276	+	0.187442i	$0.939980\pi$
$180$	−3.82519	−	3.20972i	−0.285113	−	0.239238i
$181$	−11.1289	−	9.33826i	−0.827205	−	0.694107i	0.127443	−	0.991846i	$-0.459323\pi$
$181$	−11.1289	−	9.33826i	−0.827205	−	0.694107i	−0.954647	+	0.297739i	$0.903768\pi$
$182$	1.08215	+	1.87434i	0.0802145	+	0.138936i
$183$	2.61923	−	4.53664i	0.193619	−	0.335358i
$184$	−8.65391	+	3.14977i	−0.637975	+	0.232204i
$185$	−0.929920	−	5.27384i	−0.0683691	−	0.387740i
$186$	−0.775931	+	4.40052i	−0.0568940	+	0.322662i
$187$	1.01063	+	0.367840i	0.0739047	+	0.0268991i
$188$	1.68429	−	1.41328i	0.122839	−	0.103074i
$189$	−2.47214			−0.179821
$190$		0			0
$191$	12.7302			0.921122			0.460561	−	0.887628i	$-0.347648\pi$
$191$	12.7302			0.921122			0.460561	+	0.887628i	$0.347648\pi$
$192$	−0.983662	+	0.825390i	−0.0709897	+	0.0595674i
$193$	16.4240	+	5.97785i	1.18223	+	0.430295i	0.856987	−	0.515337i	$-0.172333\pi$
$193$	16.4240	+	5.97785i	1.18223	+	0.430295i	0.325238	+	0.945632i	$0.394556\pi$
$194$	0.709311	−	4.02270i	0.0509255	−	0.288813i
$195$	4.03090	+	22.8604i	0.288659	+	1.63707i
$196$	6.39388	−	2.32718i	0.456706	−	0.166227i
$197$	12.2556	−	21.2274i	0.873178	−	1.51239i	0.0144872	−	0.999895i	$-0.495388\pi$
$197$	12.2556	−	21.2274i	0.873178	−	1.51239i	0.858691	−	0.512494i	$-0.171278\pi$
$198$	2.72233	+	4.71521i	0.193467	+	0.335095i
$199$	12.6138	+	10.5842i	0.894166	+	0.750294i	0.969041	−	0.246898i	$-0.0794114\pi$
$199$	12.6138	+	10.5842i	0.894166	+	0.750294i	−0.0748752	+	0.997193i	$0.523856\pi$
$200$	−6.63266	−	5.56547i	−0.469000	−	0.393538i
$201$	−0.0948696	−	0.164319i	−0.00669159	−	0.0115902i
$202$	0.212639	−	0.368301i	0.0149612	−	0.0259136i
$203$	0.0929607	−	0.0338349i	0.00652456	−	0.00237475i
$204$	−0.0595113	−	0.337505i	−0.00416662	−	0.0236301i
$205$	5.04722	−	28.6242i	0.352513	−	1.99920i
$206$	4.26262	+	1.55147i	0.296990	+	0.108096i
$207$	9.53194	−	7.99825i	0.662516	−	0.555917i
$208$	−4.89149			−0.339164
$209$		0			0
$210$	−2.09975			−0.144897
$211$	−21.0512	+	17.6641i	−1.44923	+	1.21605i	−0.516086	+	0.856537i	$0.672612\pi$
$211$	−21.0512	+	17.6641i	−1.44923	+	1.21605i	−0.933141	+	0.359510i	$0.882944\pi$
$212$	9.34281	+	3.40050i	0.641667	+	0.233548i
$213$	2.55736	−	14.5035i	0.175227	−	0.993764i
$214$	−0.550728	−	3.12333i	−0.0376470	−	0.213507i
$215$	19.5702	−	7.12297i	1.33468	−	0.485783i
$216$	2.79360	−	4.83866i	0.190081	−	0.329229i
$217$	−0.769854	−	1.33343i	−0.0522611	−	0.0905189i
$218$	−5.19464	−	4.35882i	−0.351825	−	0.295216i
$219$	−1.39902	−	1.17392i	−0.0945372	−	0.0793261i
$220$	7.44627	+	12.8973i	0.502027	+	0.869536i
$221$	0.652752	−	1.13060i	0.0439089	−	0.0760524i
$222$	1.74845	−	0.636385i	0.117349	−	0.0427114i
$223$	−3.53732	−	20.0611i	−0.236876	−	1.34339i	−0.838626	−	0.544707i	$-0.816641\pi$
$223$	−3.53732	−	20.0611i	−0.236876	−	1.34339i	0.601750	−	0.798684i	$-0.294470\pi$
$224$	0.0768330	−	0.435741i	0.00513362	−	0.0291142i
$225$	10.9931	+	4.00116i	0.732874	+	0.266744i
$226$	−7.69442	+	6.45638i	−0.511825	+	0.429472i
$227$	22.1493			1.47010			0.735051	−	0.678011i	$-0.237158\pi$
$227$	22.1493			1.47010			0.735051	+	0.678011i	$0.237158\pi$
$228$		0			0
$229$	12.7148			0.840216			0.420108	−	0.907474i	$-0.361992\pi$
$229$	12.7148			0.840216			0.420108	+	0.907474i	$0.361992\pi$
$230$	26.0723	−	21.8773i	1.71916	−	1.44254i
$231$	2.15142	+	0.783052i	0.141553	+	0.0515210i
$232$	−0.0388245	+	0.220185i	−0.00254896	+	0.0144558i
$233$	−1.50757	−	8.54987i	−0.0987644	−	0.560120i	−0.993529	−	0.113582i	$-0.963768\pi$
$233$	−1.50757	−	8.54987i	−0.0987644	−	0.560120i	0.894764	−	0.446539i	$-0.147343\pi$
$234$	6.21052	−	2.26044i	0.405994	−	0.147770i
$235$	−4.06285	+	7.03706i	−0.265031	+	0.459047i
$236$	−1.75476	−	3.03934i	−0.114225	−	0.197844i
$237$	10.0367	+	8.42177i	0.651952	+	0.547053i
$238$	0.0904625	+	0.0759070i	0.00586381	+	0.00492032i
$239$	−10.9375	−	18.9442i	−0.707485	−	1.22540i	−0.965787	−	0.259336i	$-0.916496\pi$
$239$	−10.9375	−	18.9442i	−0.707485	−	1.22540i	0.258302	−	0.966064i	$-0.416837\pi$
$240$	2.37280	−	4.10980i	0.153163	−	0.265287i
$241$	−17.8196	+	6.48580i	−1.14786	+	0.417787i	−0.844746	−	0.535167i	$-0.820249\pi$
$241$	−17.8196	+	6.48580i	−1.14786	+	0.417787i	−0.303114	+	0.952954i	$0.598026\pi$
$242$	−0.909614	−	5.15868i	−0.0584722	−	0.331612i
$243$	−2.21471	+	12.5603i	−0.142074	+	0.805741i
$244$	−3.83352	−	1.39529i	−0.245416	−	0.0893241i
$245$	−19.2633	+	16.1639i	−1.23069	+	1.03267i
$246$	10.0989			0.643884
$247$		0			0
$248$	3.47985			0.220971
$249$	3.23505	−	2.71453i	0.205013	−	0.172026i
$250$	12.7048	+	4.62416i	0.803521	+	0.292458i
$251$	0.504058	−	2.85866i	0.0318159	−	0.180437i	−0.964759	−	0.263136i	$-0.915243\pi$
$251$	0.504058	−	2.85866i	0.0318159	−	0.180437i	0.996575	+	0.0826996i	$0.0263542\pi$
$252$	0.103812	+	0.588748i	0.00653955	+	0.0370876i
$253$	−34.8724	+	12.6925i	−2.19241	+	0.797972i
$254$	−7.04029	+	12.1941i	−0.441747	+	0.765129i
$255$	0.633283	+	1.09688i	0.0396577	+	0.0686892i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−17.5463	−	14.7231i	−1.09451	−	0.918399i	−0.0974623	−	0.995239i	$-0.531073\pi$
$257$	−17.5463	−	14.7231i	−1.09451	−	0.918399i	−0.997043	+	0.0768399i	$0.975517\pi$
$258$	3.61803	+	6.26662i	0.225249	+	0.390143i
$259$	−0.320571	+	0.555245i	−0.0199193	+	0.0345013i
$260$	16.9874	−	6.18289i	1.05351	−	0.383447i
$261$	−0.0524574	−	0.297501i	−0.00324703	−	0.0184148i
$262$	−2.75085	+	15.6008i	−0.169948	+	0.963823i
$263$	4.75706	+	1.73143i	0.293333	+	0.106765i	0.484495	−	0.874794i	$-0.339003\pi$
$263$	4.75706	+	1.73143i	0.293333	+	0.106765i	−0.191162	+	0.981559i	$0.561226\pi$
$264$	−3.96383	+	3.32605i	−0.243957	+	0.204704i
$265$	−36.7443			−2.25719
$266$		0			0
$267$	−7.65407			−0.468421
$268$	−0.113193	+	0.0949801i	−0.00691436	+	0.00580184i
$269$	−19.4910	−	7.09416i	−1.18839	−	0.432539i	−0.329232	−	0.944249i	$-0.606790\pi$
$269$	−19.4910	−	7.09416i	−1.18839	−	0.432539i	−0.859158	+	0.511711i	$0.829012\pi$
$270$	−3.58562	+	20.3350i	−0.218214	+	1.23755i
$271$	1.09306	+	6.19907i	0.0663989	+	0.376567i	0.999841	+	0.0178384i	$0.00567843\pi$
$271$	1.09306	+	6.19907i	0.0663989	+	0.376567i	−0.933442	+	0.358728i	$0.883210\pi$
$272$	−0.250797	+	0.0912828i	−0.0152068	+	0.00553483i
$273$	1.38957	−	2.40681i	0.0841006	−	0.145667i
$274$	1.10372	+	1.91169i	0.0666780	+	0.115490i
$275$	−26.7275	−	22.4270i	−1.61173	−	1.35240i
$276$	9.05883	+	7.60127i	0.545278	+	0.457542i
$277$	−3.58804	−	6.21467i	−0.215584	−	0.373403i	0.737869	−	0.674944i	$-0.235832\pi$
$277$	−3.58804	−	6.21467i	−0.215584	−	0.373403i	−0.953453	+	0.301541i	$0.902499\pi$
$278$	−8.53222	+	14.7782i	−0.511729	+	0.886340i
$279$	−4.41822	+	1.60810i	−0.264512	+	0.0962745i
$280$	0.283953	+	1.61038i	0.0169694	+	0.0962385i
$281$	−0.481685	+	2.73177i	−0.0287349	+	0.162964i	−0.995799	−	0.0915709i	$-0.970811\pi$
$281$	−0.481685	+	2.73177i	−0.0287349	+	0.162964i	0.967064	+	0.254535i	$0.0819223\pi$
$282$	−2.65301	−	0.965618i	−0.157985	−	0.0575017i
$283$	5.93578	−	4.98071i	0.352846	−	0.296073i	−0.449086	−	0.893489i	$-0.648250\pi$
$283$	5.93578	−	4.98071i	0.352846	−	0.296073i	0.801931	+	0.597416i	$0.203806\pi$
$284$	−11.4691			−0.680567
$285$		0			0
$286$	−19.7111			−1.16554
$287$	−2.66572	+	2.23681i	−0.157353	+	0.132035i
$288$	−1.26966	−	0.462117i	−0.0748153	−	0.0272305i
$289$	−2.93965	+	16.6716i	−0.172921	+	0.980681i
$290$	−0.143485	−	0.813741i	−0.00842570	−	0.0477845i
$291$	−4.92883	+	1.79395i	−0.288933	+	0.105163i
$292$	−0.711130	+	1.23171i	−0.0416157	+	0.0720806i
$293$	−0.391435	−	0.677985i	−0.0228679	−	0.0396083i	0.854365	−	0.519673i	$-0.173946\pi$
$293$	−0.391435	−	0.677985i	−0.0228679	−	0.0396083i	−0.877233	+	0.480065i	$0.840613\pi$
$294$	−6.69306	−	5.61614i	−0.390347	−	0.327540i
$295$	9.93576	+	8.33709i	0.578482	+	0.485404i
$296$	−0.724514	−	1.25490i	−0.0421115	−	0.0729393i
$297$	11.2573	−	19.4982i	0.653215	−	1.13140i
$298$	12.7289	−	4.63292i	0.737363	−	0.268378i
$299$	7.82237	+	44.3628i	0.452379	+	2.56557i
$300$	−1.93062	+	10.9491i	−0.111464	+	0.632145i
$301$	−2.34301	−	0.852786i	−0.135049	−	0.0491538i
$302$	−7.01174	+	5.88355i	−0.403480	+	0.338560i
$303$	−0.546090			−0.0313720
$304$		0			0
$305$	15.0769			0.863298
$306$	0.276243	−	0.231796i	0.0157918	−	0.0132509i
$307$	−26.4700	−	9.63429i	−1.51072	−	0.549858i	−0.551911	−	0.833903i	$-0.686101\pi$
$307$	−26.4700	−	9.63429i	−1.51072	−	0.549858i	−0.958811	+	0.284045i	$0.908324\pi$
$308$	0.309612	−	1.75590i	0.0176418	−	0.100051i
$309$	−1.01147	−	5.73632i	−0.0575404	−	0.326328i
$310$	−12.0850	+	4.39857i	−0.686380	+	0.249822i
$311$	−1.93414	+	3.35002i	−0.109675	+	0.189962i	−0.915639	−	0.402003i	$-0.868314\pi$
$311$	−1.93414	+	3.35002i	−0.109675	+	0.189962i	0.805964	+	0.591965i	$0.201648\pi$
$312$	3.14053	+	5.43956i	0.177798	+	0.307954i
$313$	23.2784	+	19.5329i	1.31577	+	1.10406i	0.987183	+	0.159591i	$0.0510175\pi$
$313$	23.2784	+	19.5329i	1.31577	+	1.10406i	0.328589	+	0.944473i	$0.393427\pi$
$314$	12.5557	+	10.5355i	0.708558	+	0.594551i
$315$	−1.10471	−	1.91341i	−0.0622432	−	0.107808i
$316$	5.10169	−	8.83638i	0.286992	−	0.497085i
$317$	5.00671	−	1.82229i	0.281205	−	0.102350i	−0.197567	−	0.980289i	$-0.563304\pi$
$317$	5.00671	−	1.82229i	0.281205	−	0.102350i	0.478772	+	0.877939i	$0.341082\pi$
$318$	−2.21694	−	12.5729i	−0.124320	−	0.705052i
$319$	−0.156450	+	0.887273i	−0.00875953	+	0.0496777i
$320$	−3.47284	−	1.26401i	−0.194138	−	0.0706603i
$321$	−3.11970	+	2.61774i	−0.174124	+	0.146108i
$322$	−4.07478			−0.227079
$323$		0			0
$324$	−3.12099			−0.173389
$325$	−32.4436	+	27.2234i	−1.79965	+	1.51008i
$326$	−12.9417	−	4.71039i	−0.716773	−	0.260884i
$327$	−1.51204	+	8.57521i	−0.0836160	+	0.474210i
$328$	−1.36569	−	7.74524i	−0.0754079	−	0.427659i
$329$	0.914166	−	0.332729i	0.0503996	−	0.0183440i
$330$	9.56159	−	16.5612i	0.526348	−	0.911662i
$331$	−10.2740	−	17.7951i	−0.564711	−	0.978108i	−0.997077	−	0.0764094i	$-0.975654\pi$
$331$	−10.2740	−	17.7951i	−0.564711	−	0.978108i	0.432366	−	0.901698i	$-0.357679\pi$
$332$	−2.51935	−	2.11399i	−0.138267	−	0.116020i
$333$	1.49979	+	1.25848i	0.0821882	+	0.0689641i
$334$	5.16640	+	8.94847i	0.282693	+	0.489638i
$335$	0.273045	−	0.472928i	0.0149180	−	0.0258388i
$336$	−0.533894	+	0.194322i	−0.0291263	+	0.0106011i
$337$	−2.30647	−	13.0806i	−0.125641	−	0.712547i	−0.980925	−	0.194387i	$-0.937728\pi$
$337$	−2.30647	−	13.0806i	−0.125641	−	0.712547i	0.855284	−	0.518160i	$-0.173383\pi$
$338$	−1.89740	+	10.7607i	−0.103205	+	0.585304i
$339$	12.1199	+	4.41129i	0.658263	+	0.239588i
$340$	0.755596	−	0.634021i	0.0409780	−	0.0343846i
$341$	14.0227			0.759370
$342$		0			0
$343$	6.10787			0.329794
$344$	4.31683	−	3.62225i	0.232748	−	0.195299i
$345$	−41.0679	−	14.9475i	−2.21102	−	0.804747i
$346$	−1.70384	+	9.66295i	−0.0915989	+	0.519483i
$347$	5.23416	+	29.6844i	0.280984	+	1.59354i	0.719286	+	0.694714i	$0.244469\pi$
$347$	5.23416	+	29.6844i	0.280984	+	1.59354i	−0.438302	+	0.898828i	$0.644420\pi$
$348$	0.269782	−	0.0981928i	0.0144619	−	0.00526368i
$349$	−17.5326	+	30.3674i	−0.938501	+	1.62553i	−0.170232	+	0.985404i	$0.554452\pi$
$349$	−17.5326	+	30.3674i	−0.938501	+	1.62553i	−0.768269	+	0.640127i	$0.778882\pi$
$350$	−1.91550	−	3.31774i	−0.102388	−	0.177341i
$351$	−20.9358	−	17.5672i	−1.11747	−	0.937670i
$352$	3.08691	+	2.59022i	0.164533	+	0.138059i
$353$	−6.77053	−	11.7269i	−0.360359	−	0.624160i	0.627661	−	0.778487i	$-0.284012\pi$
$353$	−6.77053	−	11.7269i	−0.360359	−	0.624160i	−0.988020	+	0.154327i	$0.950679\pi$
$354$	−2.25325	+	3.90275i	−0.119759	+	0.207429i
$355$	39.8304	−	14.4971i	2.11398	−	0.769425i
$356$	1.03507	+	5.87019i	0.0548587	+	0.311119i
$357$	0.0263316	−	0.149334i	0.00139361	−	0.00790358i
$358$	8.26770	+	3.00920i	0.436962	+	0.159041i
$359$	−18.0076	+	15.1102i	−0.950403	+	0.797483i	−0.979365	−	0.202097i	$-0.935224\pi$
$359$	−18.0076	+	15.1102i	−0.950403	+	0.797483i	0.0289620	+	0.999581i	$0.490780\pi$
$360$	4.99344			0.263177
$361$		0			0
$362$	14.5278			0.763562
$363$	−5.15268	+	4.32361i	−0.270445	+	0.226931i
$364$	−2.03378	−	0.740236i	−0.106599	−	0.0387989i
$365$	0.912742	−	5.17642i	0.0477751	−	0.270946i
$366$	0.909649	+	5.15888i	0.0475481	+	0.269659i
$367$	11.9274	−	4.34122i	0.622606	−	0.226610i	−0.0114041	−	0.999935i	$-0.503630\pi$
$367$	11.9274	−	4.34122i	0.622606	−	0.226610i	0.634010	+	0.773325i	$0.281408\pi$
$368$	4.60465	−	7.97549i	0.240034	−	0.415751i
$369$	5.31318	+	9.20269i	0.276593	+	0.479073i
$370$	4.10232	+	3.44225i	0.213269	+	0.178954i
$371$	3.36995	+	2.82772i	0.174959	+	0.146808i
$372$	−2.23420	−	3.86975i	−0.115838	−	0.200637i
$373$	1.32475	−	2.29454i	0.0685930	−	0.118807i	−0.829689	−	0.558226i	$-0.811482\pi$
$373$	1.32475	−	2.29454i	0.0685930	−	0.118807i	0.898282	+	0.439419i	$0.144816\pi$
$374$	−1.01063	+	0.367840i	−0.0522585	+	0.0190205i
$375$	−3.01470	−	17.0972i	−0.155678	−	0.882895i
$376$	−0.381797	+	2.16528i	−0.0196897	+	0.111666i
$377$	1.02769	+	0.374049i	0.0529288	+	0.0192645i
$378$	1.89377	−	1.58906i	0.0974048	−	0.0817323i
$379$	−18.1672			−0.933187			−0.466593	−	0.884472i	$-0.654519\pi$
$379$	−18.1672			−0.933187			−0.466593	+	0.884472i	$0.654519\pi$
$380$		0			0
$381$	18.0806			0.926297
$382$	−9.75187	+	8.18279i	−0.498949	+	0.418668i
$383$	21.6207	+	7.86931i	1.10477	+	0.402103i	0.829072	−	0.559142i	$-0.188869\pi$
$383$	21.6207	+	7.86931i	1.10477	+	0.402103i	0.275696	+	0.961245i	$0.411092\pi$
$384$	0.222978	−	1.26457i	0.0113788	−	0.0645324i
$385$	1.14424	+	6.48929i	0.0583157	+	0.330725i
$386$	−16.4240	+	5.97785i	−0.835960	+	0.304264i
$387$	−3.80699	+	6.59390i	−0.193520	+	0.335187i
$388$	2.04238	+	3.53750i	0.103686	+	0.179590i
$389$	−12.6938	−	10.6514i	−0.643603	−	0.540047i	0.261519	−	0.965198i	$-0.415776\pi$
$389$	−12.6938	−	10.6514i	−0.643603	−	0.540047i	−0.905122	+	0.425151i	$0.860221\pi$
$390$	−17.7822	−	14.9210i	−0.900437	−	0.755557i
$391$	1.22895	+	2.12860i	0.0621506	+	0.107648i
$392$	−3.40211	+	5.89263i	−0.171833	+	0.297623i
$393$	19.1150	−	6.95729i	0.964223	−	0.350949i
$394$	4.25634	+	24.1389i	0.214431	+	1.21610i
$395$	−6.54806	+	37.1359i	−0.329469	+	1.86851i
$396$	−5.11630	−	1.86218i	−0.257104	−	0.0935782i
$397$	−13.6316	+	11.4383i	−0.684152	+	0.574072i	−0.917216	−	0.398390i	$-0.869569\pi$
$397$	−13.6316	+	11.4383i	−0.684152	+	0.574072i	0.233064	+	0.972461i	$0.425125\pi$
$398$	−16.4661			−0.825371
$399$		0			0
$400$	8.65833			0.432916
$401$	−23.4574	+	19.6831i	−1.17141	+	0.982927i	−0.999997	−	0.00227274i	$-0.999277\pi$
$401$	−23.4574	+	19.6831i	−1.17141	+	0.982927i	−0.171410	+	0.985200i	$0.554832\pi$
$402$	0.178297	+	0.0648946i	0.00889262	+	0.00323665i
$403$	2.95578	−	16.7631i	0.147238	−	0.835028i
$404$	0.0738486	+	0.418817i	0.00367411	+	0.0208369i
$405$	10.8387	−	3.94497i	0.538580	−	0.196027i
$406$	−0.0494633	+	0.0856730i	−0.00245482	+	0.00425188i
$407$	−2.91955	−	5.05682i	−0.144717	−	0.250657i
$408$	0.262532	+	0.220291i	0.0129973	+	0.0109060i
$409$	−7.00416	−	5.87719i	−0.346333	−	0.290608i	0.452982	−	0.891519i	$-0.350360\pi$
$409$	−7.00416	−	5.87719i	−0.346333	−	0.290608i	−0.799316	+	0.600911i	$0.794804\pi$
$410$	14.5329	+	25.1717i	0.717729	+	1.24314i
$411$	1.41726	−	2.45477i	0.0699083	−	0.121085i
$412$	−4.26262	+	1.55147i	−0.210004	+	0.0764352i
$413$	−0.269647	−	1.52925i	−0.0132685	−	0.0752493i
$414$	−2.16072	+	12.2540i	−0.106193	+	0.602252i
$415$	11.4214	+	4.15705i	0.560654	+	0.204061i
$416$	3.74710	−	3.14419i	0.183717	−	0.154157i
$417$	21.9121			1.07304
$418$		0			0
$419$	12.6157			0.616315			0.308158	−	0.951335i	$-0.400288\pi$
$419$	12.6157			0.616315			0.308158	+	0.951335i	$0.400288\pi$
$420$	1.60850	−	1.34969i	0.0784869	−	0.0658583i
$421$	31.2498	+	11.3740i	1.52302	+	0.554335i	0.961901	−	0.273399i	$-0.0881480\pi$
$421$	31.2498	+	11.3740i	1.52302	+	0.554335i	0.561121	+	0.827734i	$0.310370\pi$
$422$	4.77193	−	27.0630i	0.232294	−	1.31740i
$423$	−0.515861	−	2.92559i	−0.0250820	−	0.142247i
$424$	−9.34281	+	3.40050i	−0.453727	+	0.165143i
$425$	−1.15542	+	2.00125i	−0.0560463	+	0.0970750i
$426$	7.36363	+	12.7542i	0.356769	+	0.617942i
$427$	−1.38275	−	1.16026i	−0.0669159	−	0.0561491i
$428$	2.42952	+	2.03861i	0.117435	+	0.0985399i
$429$	12.6553	+	21.9196i	0.611004	+	1.05829i
$430$	−10.4131	+	18.0360i	−0.502164	+	0.869773i
$431$	−21.6049	+	7.86354i	−1.04067	+	0.378773i	−0.805135	−	0.593092i	$-0.797907\pi$
$431$	−21.6049	+	7.86354i	−1.04067	+	0.378773i	−0.235537	+	0.971865i	$0.575685\pi$
$432$	0.970209	+	5.50233i	0.0466792	+	0.264731i
$433$	−6.02720	+	34.1819i	−0.289649	+	1.64268i	0.398543	+	0.917150i	$0.369516\pi$
$433$	−6.02720	+	34.1819i	−0.289649	+	1.64268i	−0.688191	+	0.725529i	$0.741595\pi$
$434$	1.44685	+	0.526611i	0.0694511	+	0.0252781i
$435$	−0.812794	+	0.682015i	−0.0389705	+	0.0327001i
$436$	6.78112			0.324757
$437$		0			0
$438$	1.82629			0.0872637
$439$	27.9467	−	23.4501i	1.33382	−	1.11921i	0.350655	−	0.936505i	$-0.385959\pi$
$439$	27.9467	−	23.4501i	1.33382	−	1.11921i	0.983168	−	0.182706i	$-0.0584856\pi$
$440$	−13.9944	−	5.09355i	−0.667157	−	0.242825i
$441$	1.59643	−	9.05380i	0.0760204	−	0.431133i
$442$	0.226699	+	1.28567i	0.0107829	+	0.0611531i
$443$	−11.0492	+	4.02157i	−0.524963	+	0.191071i	−0.590888	−	0.806754i	$-0.701222\pi$
$443$	−11.0492	+	4.02157i	−0.524963	+	0.191071i	0.0659252	+	0.997825i	$0.479000\pi$
$444$	−0.930333	+	1.61138i	−0.0441517	+	0.0764729i
$445$	−11.0146	−	19.0779i	−0.522143	−	0.904378i
$446$	15.6048	+	13.0940i	0.738908	+	0.620017i
$447$	−13.3244	−	11.1805i	−0.630225	−	0.528821i
$448$	0.221232	+	0.383185i	0.0104522	+	0.0181038i
$449$	−4.34551	+	7.52664i	−0.205077	+	0.355204i	−0.950157	−	0.311771i	$-0.899078\pi$
$449$	−4.34551	+	7.52664i	−0.205077	+	0.355204i	0.745080	+	0.666975i	$0.232411\pi$
$450$	−10.9931	+	4.00116i	−0.518220	+	0.188617i
$451$	−5.50330	−	31.2108i	−0.259140	−	1.46966i
$452$	1.74418	−	9.89175i	0.0820395	−	0.465269i
$453$	11.0446	+	4.01990i	0.518920	+	0.188871i
$454$	−16.9674	+	14.2373i	−0.796318	+	0.668190i
$455$	7.99866			0.374983
$456$		0			0
$457$	−13.0286			−0.609454			−0.304727	−	0.952440i	$-0.598565\pi$
$457$	−13.0286			−0.609454			−0.304727	+	0.952440i	$0.598565\pi$
$458$	−9.74008	+	8.17290i	−0.455124	+	0.381894i
$459$	−1.40126	−	0.510016i	−0.0654051	−	0.0238055i
$460$	−5.91011	+	33.5179i	−0.275560	+	1.56278i
$461$	1.57023	+	8.90522i	0.0731329	+	0.414758i	0.999292	+	0.0376243i	$0.0119790\pi$
$461$	1.57023	+	8.90522i	0.0731329	+	0.414758i	−0.926159	+	0.377133i	$0.876910\pi$
$462$	−2.15142	+	0.783052i	−0.100093	+	0.0364309i
$463$	8.86025	−	15.3464i	0.411771	−	0.713208i	−0.583313	−	0.812248i	$-0.698244\pi$
$463$	8.86025	−	15.3464i	0.411771	−	0.713208i	0.995083	+	0.0990396i	$0.0315771\pi$
$464$	−0.111791	−	0.193627i	−0.00518976	−	0.00898892i
$465$	12.6504	+	10.6150i	0.586650	+	0.492258i
$466$	6.65062	+	5.58053i	0.308084	+	0.258513i
$467$	3.93886	+	6.82231i	0.182269	+	0.315699i	0.942653	−	0.333775i	$-0.108323\pi$
$467$	3.93886	+	6.82231i	0.182269	+	0.315699i	−0.760384	+	0.649474i	$0.774989\pi$
$468$	−3.30455	+	5.72364i	−0.152753	+	0.264576i
$469$	−0.0614368	+	0.0223612i	−0.00283689	+	0.00103254i
$470$	−1.41101	−	8.00225i	−0.0650851	−	0.369116i
$471$	3.65467	−	20.7267i	0.168398	−	0.955035i
$472$	3.29788	+	1.20033i	0.151797	+	0.0552496i
$473$	17.3954	−	14.5965i	0.799842	−	0.671147i
$474$	−13.1019			−0.601792
$475$		0			0
$476$	−0.118090			−0.00541266
$477$	10.2907	−	8.63495i	0.471180	−	0.395367i
$478$	20.5557	+	7.48166i	0.940195	+	0.342203i
$479$	−5.24067	+	29.7213i	−0.239452	+	1.35800i	0.593579	+	0.804776i	$0.297715\pi$
$479$	−5.24067	+	29.7213i	−0.239452	+	1.35800i	−0.833031	+	0.553226i	$0.813397\pi$
$480$	0.824064	+	4.67350i	0.0376132	+	0.213315i
$481$	−6.66045	+	2.42421i	−0.303691	+	0.110534i
$482$	9.48160	−	16.4226i	0.431875	−	0.748030i
$483$	2.61617	+	4.53134i	0.119040	+	0.206183i
$484$	4.01274	+	3.36709i	0.182397	+	0.153049i
$485$	−11.5643	−	9.70359i	−0.525107	−	0.440617i
$486$	−6.37701	−	11.0453i	−0.289267	−	0.501025i
$487$	17.8850	−	30.9777i	0.810445	−	1.40373i	−0.102107	−	0.994773i	$-0.532558\pi$
$487$	17.8850	−	30.9777i	0.810445	−	1.40373i	0.912553	−	0.408959i	$-0.134108\pi$
$488$	3.83352	−	1.39529i	0.173535	−	0.0631617i
$489$	3.07091	+	17.4160i	0.138871	+	0.787578i
$490$	4.36664	−	24.7645i	0.197265	−	1.11874i
$491$	17.1707	+	6.24961i	0.774901	+	0.282041i	0.699045	−	0.715078i	$-0.253609\pi$
$491$	17.1707	+	6.24961i	0.774901	+	0.282041i	0.0758562	+	0.997119i	$0.475831\pi$
$492$	−7.73623	+	6.49146i	−0.348776	+	0.292658i
$493$	0.0596724			0.00268751
$494$		0			0
$495$	20.1219			0.904413
$496$	−2.66572	+	2.23681i	−0.119694	+	0.100436i
$497$	−4.76863	−	1.73564i	−0.213902	−	0.0778540i
$498$	−0.733325	+	4.15889i	−0.0328611	+	0.186365i
$499$	3.07322	+	17.4291i	0.137576	+	0.780234i	0.973031	+	0.230675i	$0.0740933\pi$
$499$	3.07322	+	17.4291i	0.137576	+	0.780234i	−0.835455	+	0.549559i	$0.814796\pi$
$500$	−12.7048	+	4.62416i	−0.568175	+	0.206799i
$501$	6.63407	−	11.4905i	0.296388	−	0.513360i
$502$	1.45138	+	2.51386i	0.0647782	+	0.112199i
$503$	−7.80618	−	6.55017i	−0.348061	−	0.292057i	0.451950	−	0.892043i	$-0.350728\pi$
$503$	−7.80618	−	6.55017i	−0.348061	−	0.292057i	−0.800011	+	0.599986i	$0.795173\pi$
$504$	−0.457965	−	0.384278i	−0.0203994	−	0.0171171i
$505$	−0.785853	−	1.36114i	−0.0349700	−	0.0605698i
$506$	18.5552	−	32.1386i	0.824881	−	1.42874i
$507$	13.1846	−	4.79879i	0.585548	−	0.213122i
$508$	−2.44507	−	13.8667i	−0.108482	−	0.615234i
$509$	1.46493	−	8.30805i	0.0649320	−	0.368248i	−0.934976	−	0.354710i	$-0.884580\pi$
$509$	1.46493	−	8.30805i	0.0649320	−	0.368248i	0.999908	−	0.0135377i	$-0.00430932\pi$
$510$	−1.19018	−	0.433191i	−0.0527022	−	0.0191820i
$511$	−0.482070	+	0.404505i	−0.0213255	+	0.0178942i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	22.9050			1.01030
$515$	12.8423	−	10.7760i	0.565900	−	0.474846i
$516$	−6.79968	−	2.47488i	−0.299339	−	0.108951i
$517$	−1.53851	+	8.72535i	−0.0676638	+	0.383741i
$518$	−0.111333	−	0.631402i	−0.00489170	−	0.0277422i
$519$	11.8396	−	4.30925i	0.519699	−	0.189155i
$520$	−9.03879	+	15.6556i	−0.396377	+	0.686545i
$521$	4.48183	+	7.76275i	0.196352	+	0.340092i	0.947343	−	0.320221i	$-0.103757\pi$
$521$	4.48183	+	7.76275i	0.196352	+	0.340092i	−0.750991	+	0.660313i	$0.770424\pi$
$522$	0.231415	+	0.194180i	0.0101287	+	0.00849902i
$523$	1.63928	+	1.37552i	0.0716809	+	0.0601474i	0.677924	−	0.735132i	$-0.262880\pi$
$523$	1.63928	+	1.37552i	0.0716809	+	0.0601474i	−0.606243	+	0.795279i	$0.707324\pi$
$524$	−7.92075	−	13.7191i	−0.346020	−	0.599324i
$525$	−2.45965	+	4.26024i	−0.107348	+	0.185932i
$526$	−4.75706	+	1.73143i	−0.207418	+	0.0754939i
$527$	−0.161275	−	0.914639i	−0.00702527	−	0.0398423i
$528$	0.898528	−	5.09581i	0.0391034	−	0.221767i
$529$	−58.0835	−	21.1407i	−2.52537	−	0.919160i
$530$	28.1478	−	23.6188i	1.22266	−	1.02594i
$531$	−4.74186			−0.205779
$532$		0			0
$533$	−38.4702			−1.66633
$534$	5.86336	−	4.91994i	0.253732	−	0.212907i
$535$	−11.0142	−	4.00882i	−0.476183	−	0.173317i
$536$	0.0256588	−	0.145518i	0.00110829	−	0.00628542i
$537$	−1.96183	−	11.1261i	−0.0846591	−	0.480126i
$538$	19.4910	−	7.09416i	0.840318	−	0.305851i
$539$	−13.7094	+	23.7454i	−0.590506	+	1.02279i
$540$	−10.3244	−	17.8823i	−0.444290	−	0.769533i
$541$	−8.97157	−	7.52804i	−0.385718	−	0.323656i	0.429224	−	0.903198i	$-0.358787\pi$
$541$	−8.97157	−	7.52804i	−0.385718	−	0.323656i	−0.814942	+	0.579542i	$0.803231\pi$
$542$	−4.82202	−	4.04616i	−0.207124	−	0.173797i
$543$	−9.32739	−	16.1555i	−0.400277	−	0.693299i
$544$	0.133446	−	0.231136i	0.00572147	−	0.00990988i
$545$	−23.5497	+	8.57140i	−1.00876	+	0.367158i
$546$	0.482593	+	2.73692i	0.0206531	+	0.117129i
$547$	4.33941	−	24.6100i	0.185540	−	1.05225i	−0.739720	−	0.672915i	$-0.765042\pi$
$547$	4.33941	−	24.6100i	0.185540	−	1.05225i	0.925260	−	0.379334i	$-0.123847\pi$
$548$	−2.07431	−	0.754987i	−0.0886102	−	0.0322515i
$549$	−4.22247	+	3.54307i	−0.180211	+	0.151215i
$550$	34.8902			1.48772
$551$		0			0
$552$	−11.8255			−0.503325
$553$	3.45840	−	2.90194i	0.147066	−	0.123403i
$554$	6.74331	+	2.45436i	0.286496	+	0.104276i
$555$	1.19409	−	6.77203i	0.0506864	−	0.287457i
$556$	−2.96321	−	16.8052i	−0.125668	−	0.712699i
$557$	−8.64109	+	3.14510i	−0.366135	+	0.133262i	−0.518534	−	0.855057i	$-0.673522\pi$
$557$	−8.64109	+	3.14510i	−0.366135	+	0.133262i	0.152399	+	0.988319i	$0.451300\pi$
$558$	2.35089	−	4.07185i	0.0995209	−	0.172375i
$559$	−13.7823	−	23.8717i	−0.582930	−	1.00966i
$560$	−1.25265	−	1.05110i	−0.0529342	−	0.0444170i
$561$	1.05792	+	0.887700i	0.0446654	+	0.0374787i
$562$	−1.38696	−	2.40228i	−0.0585052	−	0.101334i
$563$	9.86122	−	17.0801i	0.415601	−	0.719842i	−0.579890	−	0.814694i	$-0.696905\pi$
$563$	9.86122	−	17.0801i	0.415601	−	0.719842i	0.995491	+	0.0948526i	$0.0302380\pi$
$564$	2.65301	−	0.965618i	0.111712	−	0.0406598i
$565$	6.44601	+	36.5571i	0.271186	+	1.53797i
$566$	−1.34553	+	7.63089i	−0.0565569	+	0.320750i
$567$	−1.29765	−	0.472305i	−0.0544960	−	0.0198349i
$568$	8.78585	−	7.37221i	0.368646	−	0.309331i
$569$	−22.1469			−0.928446			−0.464223	−	0.885718i	$-0.653666\pi$
$569$	−22.1469			−0.928446			−0.464223	+	0.885718i	$0.653666\pi$
$570$		0			0
$571$	−3.02145			−0.126444			−0.0632218	−	0.998000i	$-0.520138\pi$
$571$	−3.02145			−0.126444			−0.0632218	+	0.998000i	$0.520138\pi$
$572$	15.0996	−	12.6701i	0.631345	−	0.529762i
$573$	15.3607	+	5.59084i	0.641703	+	0.233561i
$574$	0.604270	−	3.42699i	0.0252217	−	0.143040i
$575$	−13.8462	−	78.5258i	−0.577427	−	3.27475i
$576$	1.26966	−	0.462117i	0.0529024	−	0.0192549i
$577$	−1.15469	+	1.99998i	−0.0480704	+	0.0832603i	−0.889059	−	0.457792i	$-0.848641\pi$
$577$	−1.15469	+	1.99998i	−0.0480704	+	0.0832603i	0.840989	+	0.541052i	$0.181974\pi$
$578$	−8.46438	−	14.6607i	−0.352072	−	0.609807i
$579$	17.1925	+	14.4262i	0.714496	+	0.599533i
$580$	0.632978	+	0.531132i	0.0262830	+	0.0220540i
$581$	−0.727582	−	1.26021i	−0.0301852	−	0.0522823i
$582$	2.62258	−	4.54243i	0.108709	−	0.188290i
$583$	−37.6485	+	13.7029i	−1.55924	+	0.567517i
$584$	−0.246973	−	1.40065i	−0.0102198	−	0.0579594i
$585$	4.24142	−	24.0543i	0.175361	−	0.994522i
$586$	0.735657	+	0.267757i	0.0303897	+	0.0110610i
$587$	21.5174	−	18.0553i	0.888120	−	0.745221i	−0.0797125	−	0.996818i	$-0.525400\pi$
$587$	21.5174	−	18.0553i	0.888120	−	0.745221i	0.967832	+	0.251597i	$0.0809558\pi$
$588$	8.73716			0.360315
$589$		0			0
$590$	−12.9702			−0.533975
$591$	24.1108	−	20.2314i	0.991786	−	0.832207i
$592$	1.36164	+	0.495597i	0.0559631	+	0.0203689i
$593$	−2.10008	+	11.9102i	−0.0862401	+	0.489092i	0.910842	+	0.412755i	$0.135433\pi$
$593$	−2.10008	+	11.9102i	−0.0862401	+	0.489092i	−0.997082	+	0.0763367i	$0.975678\pi$
$594$	3.90962	+	22.1726i	0.160414	+	0.909752i
$595$	0.410109	−	0.149267i	0.0168128	−	0.00611937i
$596$	−6.77288	+	11.7310i	−0.277428	+	0.480519i
$597$	10.5719	+	18.3110i	0.432679	+	0.749421i
$598$	−34.5082	−	28.9558i	−1.41114	−	1.18409i
$599$	−14.9398	−	12.5360i	−0.610424	−	0.512206i	0.284353	−	0.958720i	$-0.408221\pi$
$599$	−14.9398	−	12.5360i	−0.610424	−	0.512206i	−0.894777	+	0.446513i	$0.852666\pi$
$600$	−5.55899	−	9.62845i	−0.226945	−	0.393080i
$601$	−19.4816	+	33.7431i	−0.794671	+	1.37641i	0.128376	+	0.991726i	$0.459023\pi$
$601$	−19.4816	+	33.7431i	−0.794671	+	1.37641i	−0.923048	+	0.384685i	$0.874310\pi$
$602$	2.34301	−	0.852786i	0.0954940	−	0.0347570i
$603$	0.0346686	+	0.196615i	0.00141181	+	0.00800680i
$604$	1.58943	−	9.01412i	0.0646731	−	0.366779i
$605$	−18.1916	−	6.62121i	−0.739595	−	0.269191i
$606$	0.418329	−	0.351020i	0.0169935	−	0.0142592i
$607$	−8.46029			−0.343393			−0.171696	−	0.985150i	$-0.554925\pi$
$607$	−8.46029			−0.343393			−0.171696	+	0.985150i	$0.554925\pi$
$608$		0			0
$609$	0.127030			0.00514750
$610$	−11.5495	+	9.69122i	−0.467627	+	0.392386i
$611$	10.1062	+	3.67836i	0.408854	+	0.148811i
$612$	−0.0626193	+	0.355132i	−0.00253123	+	0.0143553i
$613$	−0.506172	−	2.87064i	−0.0204441	−	0.115944i	0.972878	−	0.231319i	$-0.0743041\pi$
$613$	−0.506172	−	2.87064i	−0.0204441	−	0.115944i	−0.993322	+	0.115375i	$0.963193\pi$
$614$	26.4700	−	9.63429i	1.06824	−	0.388808i
$615$	18.6614	−	32.3225i	0.752500	−	1.30337i
$616$	0.891491	+	1.54411i	0.0359192	+	0.0622139i
$617$	−2.31273	−	1.94061i	−0.0931069	−	0.0781260i	0.595046	−	0.803692i	$-0.297134\pi$
$617$	−2.31273	−	1.94061i	−0.0931069	−	0.0781260i	−0.688153	+	0.725566i	$0.741578\pi$
$618$	4.46207	+	3.74412i	0.179491	+	0.150611i
$619$	1.96406	+	3.40186i	0.0789423	+	0.136732i	0.902794	−	0.430074i	$-0.141512\pi$
$619$	1.96406	+	3.40186i	0.0789423	+	0.136732i	−0.823852	+	0.566806i	$0.808179\pi$
$620$	6.43028	−	11.1376i	0.258246	−	0.447295i
$621$	48.3512	−	17.5984i	1.94027	−	0.706200i
$622$	−0.671718	−	3.80950i	−0.0269334	−	0.152747i
$623$	−0.457982	+	2.59734i	−0.0183487	+	0.104060i
$624$	−5.90227	−	2.14825i	−0.236280	−	0.0859988i
$625$	5.11335	−	4.29061i	0.204534	−	0.171624i
$626$	−30.3878			−1.21454
$627$		0			0
$628$	−16.3903			−0.654043
$629$	−0.296256	+	0.248589i	−0.0118125	+	0.00991188i
$630$	2.07617	+	0.755664i	0.0827166	+	0.0301064i
$631$	1.76022	−	9.98271i	0.0700733	−	0.397406i	−0.929517	−	0.368780i	$-0.879776\pi$
$631$	1.76022	−	9.98271i	0.0700733	−	0.397406i	0.999590	−	0.0286260i	$-0.00911317\pi$
$632$	1.77180	+	10.0484i	0.0704783	+	0.399703i
$633$	−33.1590	+	12.0689i	−1.31795	+	0.479695i
$634$	−2.66402	+	4.61421i	−0.105802	+	0.183254i
$635$	26.0189	+	45.0661i	1.03253	+	1.78839i
$636$	9.77996	+	8.20636i	0.387801	+	0.325404i
$637$	25.4961	+	21.3938i	1.01019	+	0.847652i
$638$	−0.450480	−	0.780255i	−0.0178347	−	0.0308906i
$639$	−7.74820	+	13.4203i	−0.306514	+	0.530898i
$640$	3.47284	−	1.26401i	0.137276	−	0.0499644i
$641$	−1.43786	−	8.15451i	−0.0567921	−	0.322084i	0.943155	−	0.332353i	$-0.107842\pi$
$641$	−1.43786	−	8.15451i	−0.0567921	−	0.322084i	−0.999947	+	0.0102688i	$0.996731\pi$
$642$	0.707178	−	4.01060i	0.0279101	−	0.158286i
$643$	−34.6315	−	12.6048i	−1.36573	−	0.497086i	−0.447911	−	0.894078i	$-0.647832\pi$
$643$	−34.6315	−	12.6048i	−1.36573	−	0.497086i	−0.917822	+	0.396992i	$0.870054\pi$
$644$	3.12146	−	2.61922i	0.123003	−	0.103212i
$645$	26.7425			1.05298
$646$		0			0
$647$	−20.1901			−0.793753			−0.396876	−	0.917872i	$-0.629906\pi$
$647$	−20.1901			−0.793753			−0.396876	+	0.917872i	$0.629906\pi$
$648$	2.39082	−	2.00614i	0.0939203	−	0.0788085i
$649$	13.2894	+	4.83693i	0.521653	+	0.189866i
$650$	7.35437	−	41.7087i	0.288462	−	1.63595i
$651$	−0.343321	−	1.94707i	−0.0134558	−	0.0763117i
$652$	12.9417	−	4.71039i	0.506835	−	0.184473i
$653$	11.0194	−	19.0861i	0.431221	−	0.746897i	−0.565757	−	0.824572i	$-0.691416\pi$
$653$	11.0194	−	19.0861i	0.431221	−	0.746897i	0.996979	+	0.0776744i	$0.0247495\pi$
$654$	−4.35375	−	7.54091i	−0.170245	−	0.294873i
$655$	44.8486	+	37.6325i	1.75238	+	1.47042i
$656$	6.02473	+	5.05535i	0.235226	+	0.197378i
$657$	0.960837	+	1.66422i	0.0374858	+	0.0649273i
$658$	−0.486417	+	0.842500i	−0.0189625	+	0.0328441i
$659$	−25.5799	+	9.31034i	−0.996453	+	0.362679i	−0.788216	−	0.615399i	$-0.788995\pi$
$659$	−25.5799	+	9.31034i	−0.996453	+	0.362679i	−0.208237	+	0.978078i	$0.566773\pi$
$660$	3.32071	+	18.8327i	0.129258	+	0.733060i
$661$	1.54690	−	8.77291i	0.0601675	−	0.341227i	−0.939832	−	0.341636i	$-0.889019\pi$
$661$	1.54690	−	8.77291i	0.0601675	−	0.341227i	1.00000		0.000409002i	$0.000130189\pi$
$662$	19.3088	+	7.02784i	0.750459	+	0.273145i
$663$	1.28417	−	1.07755i	0.0498732	−	0.0418486i
$664$	3.28878			0.127629
$665$		0			0
$666$	−1.95784			−0.0758648
$667$	−1.57731	+	1.32352i	−0.0610736	+	0.0512469i
$668$	−9.70966	−	3.53403i	−0.375678	−	0.136736i
$669$	4.54219	−	25.7601i	0.175611	−	0.995941i
$670$	0.0948275	+	0.537793i	0.00366351	+	0.0207768i
$671$	15.4478	−	5.62255i	0.596357	−	0.217056i
$672$	0.284079	−	0.492039i	0.0109586	−	0.0189808i
$673$	17.8505	+	30.9180i	0.688087	+	1.19180i	0.972456	+	0.233086i	$0.0748824\pi$
$673$	17.8505	+	30.9180i	0.688087	+	1.19180i	−0.284370	+	0.958715i	$0.591784\pi$
$674$	10.1749	+	8.53777i	0.391923	+	0.328863i
$675$	37.0581	+	31.0954i	1.42637	+	1.19686i
$676$	−5.46334	−	9.46279i	−0.210129	−	0.363953i
$677$	−13.6924	+	23.7160i	−0.526243	+	0.911480i	0.473290	+	0.880907i	$0.343066\pi$
$677$	−13.6924	+	23.7160i	−0.526243	+	0.911480i	−0.999533	+	0.0305727i	$0.990267\pi$
$678$	−12.1199	+	4.41129i	−0.465462	+	0.169414i
$679$	0.313844	+	1.77990i	0.0120442	+	0.0683062i
$680$	−0.171280	+	0.971376i	−0.00656828	+	0.0372506i
$681$	26.7263	+	9.72756i	1.02415	+	0.372761i
$682$	−10.7420	+	9.01360i	−0.411332	+	0.345148i
$683$	38.1521			1.45985			0.729925	−	0.683528i	$-0.239555\pi$
$683$	38.1521			1.45985			0.729925	+	0.683528i	$0.239555\pi$
$684$		0			0
$685$	8.15806			0.311703
$686$	−4.67890	+	3.92606i	−0.178641	+	0.149898i
$687$	15.3421	+	5.58408i	0.585339	+	0.213046i
$688$	−0.978546	+	5.54961i	−0.0373067	+	0.211577i
$689$	8.44507	+	47.8944i	0.321731	+	1.82463i
$690$	41.0679	−	14.9475i	1.56343	−	0.569042i
$691$	14.1029	−	24.4269i	0.536499	−	0.929244i	−0.462590	−	0.886572i	$-0.653080\pi$
$691$	14.1029	−	24.4269i	0.536499	−	0.929244i	0.999089	−	0.0426714i	$-0.0135868\pi$
$692$	−4.90601	−	8.49745i	−0.186498	−	0.323025i
$693$	−1.84545	−	1.54851i	−0.0701028	−	0.0588232i
$694$	−23.0904	−	19.3751i	−0.876498	−	0.735469i
$695$	31.5327	+	54.6162i	1.19610	+	2.07171i
$696$	−0.143548	+	0.248633i	−0.00544118	+	0.00942440i
$697$	−1.97245	+	0.717914i	−0.0747119	+	0.0271929i
$698$	−6.08902	−	34.5326i	−0.230473	−	1.30708i
$699$	1.93584	−	10.9787i	0.0732203	−	0.415253i
$700$	3.59996	+	1.31028i	0.136066	+	0.0495238i
$701$	32.6448	−	27.3923i	1.23298	−	1.03459i	0.234938	−	0.972010i	$-0.424511\pi$
$701$	32.6448	−	27.3923i	1.23298	−	1.03459i	0.998040	−	0.0625810i	$-0.0199332\pi$
$702$	27.3298			1.03150
$703$		0			0
$704$	−4.02967			−0.151874
$705$	−7.99293	+	6.70687i	−0.301031	+	0.252595i
$706$	12.7244	+	4.63132i	0.478890	+	0.174302i
$707$	−0.0326753	+	0.185311i	−0.00122888	+	0.00696934i
$708$	−0.782547	−	4.43804i	−0.0294099	−	0.166792i
$709$	21.3208	−	7.76015i	0.800721	−	0.291439i	0.0909359	−	0.995857i	$-0.471014\pi$
$709$	21.3208	−	7.76015i	0.800721	−	0.291439i	0.709785	+	0.704418i	$0.248792\pi$
$710$	−21.1933	+	36.7079i	−0.795371	+	1.37762i
$711$	−6.89310	−	11.9392i	−0.258511	−	0.447755i
$712$	−4.56620	−	3.83149i	−0.171125	−	0.143591i
$713$	24.5494	+	20.5994i	0.919384	+	0.771454i
$714$	0.0758187	+	0.131322i	0.00283744	+	0.00491460i
$715$	−36.4233	+	63.0871i	−1.36216	+	2.35932i
$716$	−8.26770	+	3.00920i	−0.308979	+	0.112459i
$717$	−4.87762	−	27.6624i	−0.182158	−	1.03307i
$718$	4.08199	−	23.1501i	0.152338	−	0.863954i
$719$	35.5508	+	12.9394i	1.32582	+	0.482560i	0.905320	−	0.424731i	$-0.139631\pi$
$719$	35.5508	+	12.9394i	1.32582	+	0.482560i	0.420503	+	0.907291i	$0.361854\pi$
$720$	−3.82519	+	3.20972i	−0.142557	+	0.119619i
$721$	−2.00709			−0.0747481
$722$		0			0
$723$	−24.3503			−0.905596
$724$	−11.1289	+	9.33826i	−0.413602	+	0.347054i
$725$	−1.81910	−	0.662097i	−0.0675596	−	0.0245897i
$726$	1.16802	−	6.62415i	0.0433492	−	0.245845i
$727$	−3.39314	−	19.2434i	−0.125845	−	0.713700i	−0.980803	−	0.195003i	$-0.937528\pi$
$727$	−3.39314	−	19.2434i	−0.125845	−	0.713700i	0.854958	−	0.518697i	$-0.173583\pi$
$728$	2.03378	−	0.740236i	0.0753770	−	0.0274350i
$729$	−12.8701	+	22.2916i	−0.476670	+	0.825616i
$730$	2.62814	+	4.55206i	0.0972717	+	0.168479i
$731$	−1.15213	−	0.966753i	−0.0426131	−	0.0357567i
$732$	−4.01290	−	3.36722i	−0.148321	−	0.124456i
$733$	−17.5550	−	30.4062i	−0.648410	−	1.12308i	−0.983503	−	0.180894i	$-0.942101\pi$
$733$	−17.5550	−	30.4062i	−0.648410	−	1.12308i	0.335092	−	0.942185i	$-0.391232\pi$
$734$	−6.34644	+	10.9924i	−0.234251	+	0.405735i
$735$	−30.3428	+	11.0439i	−1.11921	+	0.407359i
$736$	1.59918	+	9.06939i	0.0589465	+	0.334302i
$737$	0.103396	−	0.586390i	0.00380865	−	0.0216000i
$738$	−9.98550	−	3.63443i	−0.367571	−	0.133785i
$739$	−12.4693	+	10.4630i	−0.458689	+	0.384886i	−0.842649	−	0.538464i	$-0.819005\pi$
$739$	−12.4693	+	10.4630i	−0.458689	+	0.384886i	0.383959	+	0.923350i	$0.374560\pi$
$740$	−5.35520			−0.196861
$741$		0			0
$742$	−4.39915			−0.161498
$743$	−25.5158	+	21.4103i	−0.936085	+	0.785468i	−0.976900	−	0.213698i	$-0.931449\pi$
$743$	−25.5158	+	21.4103i	−0.936085	+	0.785468i	0.0408149	+	0.999167i	$0.487005\pi$
$744$	4.19893	+	1.52828i	0.153940	+	0.0560296i
$745$	8.69306	−	49.3008i	0.318489	−	1.80624i
$746$	0.460081	+	2.60925i	0.0168448	+	0.0955314i
$747$	−4.17562	+	1.51980i	−0.152778	+	0.0556066i
$748$	0.537746	−	0.931403i	0.0196619	−	0.0340555i
$749$	0.701639	+	1.21528i	0.0256373	+	0.0444052i
$750$	13.2992	+	11.1594i	0.485620	+	0.407484i
$751$	−14.7539	−	12.3800i	−0.538379	−	0.451754i	0.332604	−	0.943067i	$-0.392073\pi$
$751$	−14.7539	−	12.3800i	−0.538379	−	0.451754i	−0.870983	+	0.491313i	$0.836517\pi$
$752$	−1.09934	−	1.90411i	−0.0400888	−	0.0694358i
$753$	1.86368	−	3.22800i	0.0679164	−	0.117635i
$754$	−1.02769	+	0.374049i	−0.0374263	+	0.0136221i
$755$	5.87409	+	33.3136i	0.213780	+	1.21241i
$756$	−0.429282	+	2.43458i	−0.0156128	+	0.0885448i
$757$	22.5013	+	8.18982i	0.817825	+	0.297664i	0.716852	−	0.697225i	$-0.245582\pi$
$757$	22.5013	+	8.18982i	0.817825	+	0.297664i	0.100973	+	0.994889i	$0.467804\pi$
$758$	13.9169	−	11.6777i	0.505484	−	0.424152i
$759$	−47.6528			−1.72969
$760$		0			0
$761$	−44.7968			−1.62388			−0.811941	−	0.583739i	$-0.801589\pi$
$761$	−44.7968			−1.62388			−0.811941	+	0.583739i	$0.801589\pi$
$762$	−13.8505	+	11.6220i	−0.501752	+	0.421020i
$763$	2.81945	+	1.02620i	0.102071	+	0.0371508i
$764$	2.21057	−	12.5368i	0.0799756	−	0.453564i
$765$	−0.231423	−	1.31247i	−0.00836712	−	0.0474523i
$766$	−21.6207	+	7.86931i	−0.781189	+	0.284330i
$767$	8.58341	−	14.8669i	0.309929	−	0.536813i
$768$	0.642040	+	1.11205i	0.0231676	+	0.0401275i
$769$	−24.3117	−	20.4000i	−0.876704	−	0.735642i	0.0887948	−	0.996050i	$-0.471698\pi$
$769$	−24.3117	−	20.4000i	−0.876704	−	0.735642i	−0.965499	+	0.260408i	$0.916143\pi$
$770$	−5.04777	−	4.23559i	−0.181909	−	0.152640i
$771$	−14.7059	−	25.4714i	−0.529621	−	0.917330i
$772$	8.73903	−	15.1364i	0.314525	−	0.544772i
$773$	−20.8900	+	7.60334i	−0.751361	+	0.273473i	−0.689178	−	0.724592i	$-0.742028\pi$
$773$	−20.8900	+	7.60334i	−0.751361	+	0.273473i	−0.0621827	+	0.998065i	$0.519806\pi$
$774$	−1.32215	−	7.49830i	−0.0475238	−	0.269521i
$775$	−5.23197	+	29.6720i	−0.187938	+	1.06585i
$776$	−3.83842	−	1.39707i	−0.137791	−	0.0501519i
$777$	−0.630667	+	0.529192i	−0.0226250	+	0.0189847i
$778$	16.5706			0.594086
$779$		0			0
$780$	23.2130			0.831160
$781$	35.4041	−	29.7076i	1.26686	−	1.06302i
$782$	−2.30967	−	0.840650i	−0.0825936	−	0.0300616i
$783$	0.216921	−	1.23022i	0.00775212	−	0.0439644i
$784$	−1.18154	−	6.70085i	−0.0421979	−	0.239316i
$785$	56.9208	−	20.7175i	2.03159	−	0.739439i
$786$	−10.1709	+	17.6165i	−0.362783	+	0.628358i
$787$	12.2298	+	21.1826i	0.435945	+	0.755080i	0.997372	−	0.0724468i	$-0.0230807\pi$
$787$	12.2298	+	21.1826i	0.435945	+	0.755080i	−0.561427	+	0.827526i	$0.689747\pi$
$788$	−18.7767	−	15.7555i	−0.668893	−	0.561268i
$789$	4.97965	+	4.17842i	0.177280	+	0.148756i
$790$	−18.8544	−	32.6568i	−0.670810	−	1.16188i
$791$	2.22213	−	3.84884i	0.0790098	−	0.136849i
$792$	5.11630	−	1.86218i	0.181800	−	0.0661698i
$793$	−3.46516	−	19.6519i	−0.123052	−	0.697860i
$794$	3.09004	−	17.5245i	0.109661	−	0.621921i
$795$	−44.3372	−	16.1374i	−1.57248	−	0.572335i
$796$	12.6138	−	10.5842i	0.447083	−	0.375147i
$797$	−41.6933			−1.47685			−0.738426	−	0.674334i	$-0.764431\pi$
$797$	−41.6933			−1.47685			−0.738426	+	0.674334i	$0.764431\pi$
$798$		0			0
$799$	0.586812			0.0207599
$800$	−6.63266	+	5.56547i	−0.234500	+	0.196769i
$801$	7.56810	+	2.75456i	0.267406	+	0.0973278i
$802$	5.31736	−	30.1563i	0.187763	−	1.06485i
$803$	−0.995220	−	5.64417i	−0.0351205	−	0.199178i
$804$	−0.178297	+	0.0648946i	−0.00628803	+	0.00228866i
$805$	−7.52962	+	13.0417i	−0.265384	+	0.459659i
$806$	8.51084	+	14.7412i	0.299781	+	0.519237i
$807$	−20.4030	−	17.1202i	−0.718221	−	0.602659i
$808$	−0.325781	−	0.273363i	−0.0114609	−	0.00961688i
$809$	24.6244	+	42.6507i	0.865748	+	1.49952i	0.866303	+	0.499519i	$0.166490\pi$
$809$	24.6244	+	42.6507i	0.865748	+	1.49952i	−0.000555336		1.00000i	$0.500177\pi$
$810$	−5.76716	+	9.98901i	−0.202637	+	0.350978i
$811$	48.9068	−	17.8006i	1.71735	−	0.625064i	0.719744	−	0.694240i	$-0.244259\pi$
$811$	48.9068	−	17.8006i	1.71735	−	0.625064i	0.997604	+	0.0691759i	$0.0220370\pi$
$812$	−0.0171784	−	0.0974238i	−0.000602845	−	0.00341890i
$813$	−1.40358	+	7.96010i	−0.0492257	+	0.279173i
$814$	5.48697	+	1.99709i	0.192318	+	0.0699981i
$815$	−38.9904	+	32.7168i	−1.36577	+	1.14602i
$816$	−0.342712			−0.0119973
$817$		0			0
$818$	9.14328			0.319687
$819$	−2.24013	+	1.87969i	−0.0782765	+	0.0656818i
$820$	−27.3129	−	9.94109i	−0.953808	−	0.347158i
$821$	−7.33807	+	41.6162i	−0.256100	+	1.45242i	0.537132	+	0.843498i	$0.319508\pi$
$821$	−7.33807	+	41.6162i	−0.256100	+	1.45242i	−0.793233	+	0.608919i	$0.791604\pi$
$822$	0.492209	+	2.79146i	0.0171678	+	0.0973633i
$823$	−30.5185	+	11.1078i	−1.06381	+	0.387195i	−0.813858	−	0.581064i	$-0.802637\pi$
$823$	−30.5185	+	11.1078i	−1.06381	+	0.387195i	−0.249951	+	0.968259i	$0.580414\pi$
$824$	2.26809	−	3.92845i	0.0790127	−	0.136854i
$825$	−22.4009	−	38.7995i	−0.779899	−	1.35083i
$826$	1.18954	+	0.998144i	0.0413895	+	0.0347299i
$827$	16.4819	+	13.8300i	0.573133	+	0.480916i	0.882684	−	0.469967i	$-0.155734\pi$
$827$	16.4819	+	13.8300i	0.573133	+	0.480916i	−0.309551	+	0.950883i	$0.600179\pi$
$828$	−6.22153	−	10.7760i	−0.216213	−	0.374492i
$829$	2.82531	−	4.89357i	0.0981269	−	0.169961i	−0.812782	−	0.582567i	$-0.802048\pi$
$829$	2.82531	−	4.89357i	0.0981269	−	0.169961i	0.910909	+	0.412607i	$0.135382\pi$
$830$	−11.4214	+	4.15705i	−0.396442	+	0.144293i
$831$	−1.60011	−	9.07466i	−0.0555071	−	0.314797i
$832$	−0.849399	+	4.81718i	−0.0294476	+	0.167006i
$833$	1.70648	+	0.621109i	0.0591261	+	0.0215201i
$834$	−16.7856	+	14.0848i	−0.581239	+	0.487717i
$835$	38.1871			1.32152
$836$		0			0
$837$	−19.4427			−0.672037
$838$	−9.66416	+	8.10919i	−0.333843	+	0.280127i
$839$	−10.0327	−	3.65162i	−0.346369	−	0.126068i	0.162977	−	0.986630i	$-0.447890\pi$
$839$	−10.0327	−	3.65162i	−0.346369	−	0.126068i	−0.509346	+	0.860562i	$0.670113\pi$
$840$	−0.364618	+	2.06785i	−0.0125805	+	0.0713477i
$841$	−5.02712	−	28.5102i	−0.173349	−	0.983110i
$842$	−31.2498	+	11.3740i	−1.07694	+	0.391974i
$843$	−1.78096	+	3.08471i	−0.0613395	+	0.106243i
$844$	13.7402	+	23.7988i	0.472958	+	0.819187i
$845$	30.9344	+	25.9570i	1.06417	+	0.892949i
$846$	2.27571	+	1.90955i	0.0782404	+	0.0656515i
$847$	1.15887	+	2.00722i	0.0398192	+	0.0689689i
$848$	4.97120	−	8.61038i	0.170712	−	0.295682i
$849$	9.34978	−	3.40304i	0.320884	−	0.116792i
$850$	−0.401274	−	2.27574i	−0.0137636	−	0.0780572i
$851$	2.31725	−	13.1418i	0.0794344	−	0.450495i
$852$	−13.8391	−	5.03702i	−0.474120	−	0.172565i
$853$	7.86465	−	6.59923i	0.269281	−	0.225953i	−0.498141	−	0.867096i	$-0.665984\pi$
$853$	7.86465	−	6.59923i	0.269281	−	0.225953i	0.767422	+	0.641143i	$0.221539\pi$
$854$	1.80505			0.0617676
$855$		0			0
$856$	−3.17151			−0.108400
$857$	28.6031	−	24.0009i	0.977065	−	0.819855i	−0.00657938	−	0.999978i	$-0.502094\pi$
$857$	28.6031	−	24.0009i	0.977065	−	0.819855i	0.983644	+	0.180124i	$0.0576499\pi$
$858$	−23.7842	−	8.65674i	−0.811979	−	0.295536i
$859$	−4.21774	+	23.9200i	−0.143907	+	0.816139i	0.824331	+	0.566109i	$0.191552\pi$
$859$	−4.21774	+	23.9200i	−0.143907	+	0.816139i	−0.968238	+	0.250030i	$0.919559\pi$
$860$	−3.61643	−	20.5098i	−0.123319	−	0.699378i
$861$	−4.19893	+	1.52828i	−0.143099	+	0.0520838i
$862$	11.4957	−	19.9112i	0.391546	−	0.678178i
$863$	−11.7864	−	20.4146i	−0.401214	−	0.694922i	0.592659	−	0.805453i	$-0.298078\pi$
$863$	−11.7864	−	20.4146i	−0.401214	−	0.694922i	−0.993873	+	0.110531i	$0.964745\pi$
$864$	−4.28005	−	3.59139i	−0.145610	−	0.122182i
$865$	27.7786	+	23.3090i	0.944502	+	0.792531i
$866$	−17.3546	−	30.0591i	−0.589734	−	1.02145i
$867$	−10.8689	+	18.8256i	−0.369128	+	0.639349i
$868$	−1.44685	+	0.526611i	−0.0491094	+	0.0178743i
$869$	7.13977	+	40.4916i	0.242200	+	1.37358i
$870$	0.184245	−	1.04491i	0.00624651	−	0.0354257i
$871$	−0.679192	−	0.247206i	−0.0230135	−	0.00837624i
$872$	−5.19464	+	4.35882i	−0.175913	+	0.147608i
$873$	5.51908			0.186793
$874$		0			0
$875$	−5.98217			−0.202234
$876$	−1.39902	+	1.17392i	−0.0472686	+	0.0396631i
$877$	−29.5422	−	10.7525i	−0.997570	−	0.363086i	−0.208923	−	0.977932i	$-0.566996\pi$
$877$	−29.5422	−	10.7525i	−0.997570	−	0.363086i	−0.788647	+	0.614846i	$0.789218\pi$
$878$	−6.33500	+	35.9276i	−0.213796	+	1.21250i
$879$	−0.174563	−	0.989995i	−0.00588786	−	0.0333917i
$880$	13.9944	−	5.09355i	0.471751	−	0.171703i
$881$	20.8800	−	36.1653i	0.703466	−	1.21844i	−0.263776	−	0.964584i	$-0.584968\pi$
$881$	20.8800	−	36.1653i	0.703466	−	1.21844i	0.967242	−	0.253855i	$-0.0816985\pi$
$882$	4.59673	+	7.96178i	0.154780	+	0.268087i
$883$	0.415993	+	0.349060i	0.0139993	+	0.0117468i	0.649760	−	0.760139i	$-0.274869\pi$
$883$	0.415993	+	0.349060i	0.0139993	+	0.0117468i	−0.635761	+	0.771886i	$0.719314\pi$
$884$	−1.00007	−	0.839162i	−0.0336362	−	0.0282241i
$885$	8.32739	+	14.4235i	0.279922	+	0.484839i
$886$	5.87915	−	10.1830i	0.197514	−	0.342104i
$887$	10.6418	−	3.87331i	0.357318	−	0.130053i	−0.157123	−	0.987579i	$-0.550222\pi$
$887$	10.6418	−	3.87331i	0.357318	−	0.130053i	0.514441	+	0.857526i	$0.328000\pi$
$888$	−0.323101	−	1.83240i	−0.0108426	−	0.0614913i
$889$	1.08185	−	6.13550i	0.0362842	−	0.205778i
$890$	20.7007	+	7.53444i	0.693889	+	0.252555i
$891$	9.63422	−	8.08407i	0.322759	−	0.270827i
$892$	−20.3706			−0.682058
$893$		0			0
$894$	17.3938			0.581737
$895$	24.9087	−	20.9009i	0.832607	−	0.698640i
$896$	−0.415780	−	0.151331i	−0.0138902	−	0.00505563i
$897$	−10.0445	+	56.9654i	−0.335377	+	1.90202i
$898$	−1.50918	−	8.55898i	−0.0503620	−	0.285617i
$899$	0.731110	−	0.266102i	0.0243839	−	0.00887501i
$900$	5.84931	−	10.1313i	0.194977	−	0.337710i
$901$	1.32678	+	2.29805i	0.0442014	+	0.0765591i
$902$	24.2777	+	20.3714i	0.808358	+	0.678293i
$903$	−2.45264	−	2.05801i	−0.0816188	−	0.0684863i
$904$	5.02218	+	8.69866i	0.167035	+	0.289313i
$905$	26.8452	−	46.4973i	0.892366	−	1.54562i
$906$	−11.0446	+	4.01990i	−0.366932	+	0.133552i
$907$	−1.89725	−	10.7599i	−0.0629972	−	0.357275i	−0.999969	−	0.00787011i	$-0.997495\pi$
$907$	−1.89725	−	10.7599i	−0.0629972	−	0.357275i	0.936972	−	0.349405i	$-0.113616\pi$
$908$	3.84619	−	21.8128i	0.127640	−	0.723884i
$909$	0.539957	+	0.196528i	0.0179092	+	0.00651843i
$910$	−6.12733	+	5.14144i	−0.203119	+	0.170437i
$911$	−47.4159			−1.57096			−0.785479	−	0.618888i	$-0.787584\pi$
$911$	−47.4159			−1.57096			−0.785479	+	0.618888i	$0.787584\pi$
$912$		0			0
$913$	13.2527			0.438600
$914$	9.98051	−	8.37464i	0.330126	−	0.277009i
$915$	18.1923	+	6.62147i	0.601420	+	0.218899i
$916$	2.20790	−	12.5216i	0.0729509	−	0.413725i
$917$	−1.21715	−	6.90280i	−0.0401938	−	0.227951i
$918$	1.40126	−	0.510016i	0.0462484	−	0.0168330i
$919$	−2.55534	+	4.42599i	−0.0842930	+	0.146000i	−0.905090	−	0.425221i	$-0.860197\pi$
$919$	−2.55534	+	4.42599i	−0.0842930	+	0.146000i	0.820797	+	0.571220i	$0.193530\pi$
$920$	−17.0175	−	29.4752i	−0.561050	−	0.971767i
$921$	−27.7085	−	23.2502i	−0.913028	−	0.766121i
$922$	−6.92703	−	5.81247i	−0.228130	−	0.191424i
$923$	−28.0505	−	48.5850i	−0.923295	−	1.59919i
$924$	1.14475	−	1.98276i	0.0376594	−	0.0652279i
$925$	11.7895	−	4.29104i	0.387637	−	0.141089i
$926$	3.07713	+	17.4513i	0.101121	+	0.573485i
$927$	−1.06429	+	6.03591i	−0.0349560	+	0.198245i
$928$	0.210098	+	0.0764694i	0.00689680	+	0.00251023i
$929$	−32.8206	+	27.5397i	−1.07681	+	0.903549i	−0.995652	−	0.0931519i	$-0.970306\pi$
$929$	−32.8206	+	27.5397i	−1.07681	+	0.903549i	−0.0811564	+	0.996701i	$0.525861\pi$
$930$	−16.5140			−0.541514
$931$		0			0
$932$	−8.68176			−0.284381
$933$	−3.80507	+	3.19283i	−0.124572	+	0.104529i
$934$	−7.40264	−	2.69434i	−0.242222	−	0.0881615i
$935$	−0.690201	+	3.91433i	−0.0225720	+	0.128012i
$936$	−1.14766	−	6.50869i	−0.0375124	−	0.212743i
$937$	3.45699	−	1.25824i	0.112935	−	0.0411049i	−0.284935	−	0.958547i	$-0.591972\pi$
$937$	3.45699	−	1.25824i	0.112935	−	0.0411049i	0.397869	+	0.917442i	$0.369750\pi$
$938$	0.0326898	−	0.0566205i	0.00106736	−	0.00184872i
$939$	19.5102	+	33.7926i	0.636690	+	1.10278i
$940$	6.22464	+	5.22310i	0.203025	+	0.170359i
$941$	−14.0795	−	11.8141i	−0.458978	−	0.385129i	0.383777	−	0.923426i	$-0.374623\pi$
$941$	−14.0795	−	11.8141i	−0.458978	−	0.385129i	−0.842755	+	0.538297i	$0.819068\pi$
$942$	10.5232	+	18.2267i	0.342865	+	0.593859i
$943$	36.2143	−	62.7250i	1.17930	−	2.04261i
$944$	−3.29788	+	1.20033i	−0.107337	+	0.0390674i
$945$	−1.58650	−	8.99752i	−0.0516090	−	0.292689i
$946$	−3.94322	+	22.3631i	−0.128205	+	0.727087i
$947$	−43.9391	−	15.9925i	−1.42783	−	0.519687i	−0.491520	−	0.870866i	$-0.663559\pi$
$947$	−43.9391	−	15.9925i	−1.42783	−	0.519687i	−0.936308	+	0.351179i	$0.885781\pi$
$948$	10.0367	−	8.42177i	0.325976	−	0.273526i
$949$	−6.95697			−0.225833
$950$		0			0
$951$	6.84162			0.221855
$952$	0.0904625	−	0.0759070i	0.00293191	−	0.00246016i
$953$	23.5441	+	8.56934i	0.762667	+	0.277588i	0.693926	−	0.720047i	$-0.255880\pi$
$953$	23.5441	+	8.56934i	0.762667	+	0.277588i	0.0687410	+	0.997635i	$0.478102\pi$
$954$	−2.33272	+	13.2295i	−0.0755246	+	0.428321i
$955$	8.16964	+	46.3323i	0.264363	+	1.49928i
$956$	−20.5557	+	7.48166i	−0.664818	+	0.241974i
$957$	−0.578452	+	1.00191i	−0.0186987	+	0.0323871i
$958$	−15.0899	−	26.1365i	−0.487533	−	0.844432i
$959$	−0.748203	−	0.627817i	−0.0241607	−	0.0202733i
$960$	−3.63534	−	3.05041i	−0.117330	−	0.0984515i
$961$	9.44531	+	16.3598i	0.304687	+	0.527734i
$962$	3.54395	−	6.13831i	0.114262	−	0.197907i
$963$	4.02673	−	1.46561i	0.129760	−	0.0472287i
$964$	3.29293	+	18.6751i	0.106058	+	0.601485i
$965$	−11.2166	+	63.6126i	−0.361076	+	2.04776i
$966$	−4.91679	−	1.78957i	−0.158195	−	0.0575783i
$967$	5.44372	−	4.56782i	0.175058	−	0.146891i	−0.551049	−	0.834473i	$-0.685772\pi$
$967$	5.44372	−	4.56782i	0.175058	−	0.146891i	0.726107	+	0.687582i	$0.241328\pi$
$968$	−5.23826			−0.168364
$969$		0			0
$970$	15.0961			0.484707
$971$	−46.5405	+	39.0521i	−1.49355	+	1.25324i	−0.603520	+	0.797348i	$0.706236\pi$
$971$	−46.5405	+	39.0521i	−1.49355	+	1.25324i	−0.890035	+	0.455893i	$0.849320\pi$
$972$	11.9849	+	4.36213i	0.384415	+	0.139915i
$973$	1.31111	−	7.43568i	0.0420323	−	0.238377i
$974$	6.21139	+	35.2265i	0.199026	+	1.12873i
$975$	−51.1038	+	18.6002i	−1.63663	+	0.595685i
$976$	−2.03977	+	3.53299i	−0.0652916	+	0.113088i
$977$	−19.2706	−	33.3776i	−0.616520	−	1.06784i	−0.990116	−	0.140253i	$-0.955208\pi$
$977$	−19.2706	−	33.3776i	−0.616520	−	1.06784i	0.373595	−	0.927592i	$-0.378125\pi$
$978$	−13.5472	−	11.3675i	−0.433193	−	0.363492i
$979$	−18.4003	−	15.4397i	−0.588075	−	0.493454i
$980$	12.5732	+	21.7775i	0.401638	+	0.695657i
$981$	4.58112	−	7.93474i	0.146264	−	0.253337i
$982$	−17.1707	+	6.24961i	−0.547938	+	0.199433i
$983$	1.30328	+	7.39126i	0.0415682	+	0.235745i	0.998512	−	0.0545275i	$-0.0173653\pi$
$983$	1.30328	+	7.39126i	0.0415682	+	0.235745i	−0.956944	+	0.290272i	$0.906254\pi$
$984$	1.75366	−	9.94550i	0.0559046	−	0.317051i
$985$	85.1237	+	30.9825i	2.71227	+	0.987184i
$986$	−0.0457117	+	0.0383566i	−0.00145576	+	0.00122152i
$987$	1.24920			0.0397624
$988$		0			0
$989$	51.8964			1.65021
$990$	−15.4143	+	12.9341i	−0.489898	+	0.411073i
$991$	−20.1302	−	7.32680i	−0.639457	−	0.232743i	0.00188507	−	0.999998i	$-0.499400\pi$
$991$	−20.1302	−	7.32680i	−0.639457	−	0.232743i	−0.641342	+	0.767255i	$0.721622\pi$
$992$	0.604270	−	3.42699i	0.0191856	−	0.108807i
$993$	−4.58176	−	25.9844i	−0.145398	−	0.824591i
$994$	4.76863	−	1.73564i	0.151252	−	0.0550511i
$995$	−30.4270	+	52.7012i	−0.964602	+	1.67074i
$996$	−2.11153	−	3.65727i	−0.0669063	−	0.115885i
$997$	−31.4082	−	26.3546i	−0.994709	−	0.834660i	−0.00846600	−	0.999964i	$-0.502695\pi$
$997$	−31.4082	−	26.3546i	−0.994709	−	0.834660i	−0.986243	+	0.165305i	$0.947139\pi$
$998$	−13.5574	−	11.3760i	−0.429153	−	0.360102i
$999$	4.04801	+	7.01136i	0.128073	+	0.221830i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.e.s.595.3		24
19.2	odd	18		722.2.e.r.423.3		24
19.3	odd	18		722.2.e.r.415.2		24
19.4	even	9		722.2.a.m.1.2	✓	4
19.5	even	9	inner	722.2.e.s.245.2		24
19.6	even	9		722.2.c.n.653.3		8
19.7	even	3	inner	722.2.e.s.389.2		24
19.8	odd	6		722.2.e.r.99.3		24
19.9	even	9		722.2.c.n.429.3		8
19.10	odd	18		722.2.c.m.429.2		8
19.11	even	3	inner	722.2.e.s.99.2		24
19.12	odd	6		722.2.e.r.389.3		24
19.13	odd	18		722.2.c.m.653.2		8
19.14	odd	18		722.2.e.r.245.3		24
19.15	odd	18		722.2.a.n.1.3	yes	4
19.16	even	9	inner	722.2.e.s.415.3		24
19.17	even	9	inner	722.2.e.s.423.2		24
19.18	odd	2		722.2.e.r.595.2		24
57.23	odd	18		6498.2.a.ca.1.1		4
57.53	even	18		6498.2.a.bx.1.1		4
76.15	even	18		5776.2.a.bt.1.2		4
76.23	odd	18		5776.2.a.bv.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.a.m.1.2	✓	4	19.4	even	9
722.2.a.n.1.3	yes	4	19.15	odd	18
722.2.c.m.429.2		8	19.10	odd	18
722.2.c.m.653.2		8	19.13	odd	18
722.2.c.n.429.3		8	19.9	even	9
722.2.c.n.653.3		8	19.6	even	9
722.2.e.r.99.3		24	19.8	odd	6
722.2.e.r.245.3		24	19.14	odd	18
722.2.e.r.389.3		24	19.12	odd	6
722.2.e.r.415.2		24	19.3	odd	18
722.2.e.r.423.3		24	19.2	odd	18
722.2.e.r.595.2		24	19.18	odd	2
722.2.e.s.99.2		24	19.11	even	3	inner
722.2.e.s.245.2		24	19.5	even	9	inner
722.2.e.s.389.2		24	19.7	even	3	inner
722.2.e.s.415.3		24	19.16	even	9	inner
722.2.e.s.423.2		24	19.17	even	9	inner
722.2.e.s.595.3		24	1.1	even	1	trivial
5776.2.a.bt.1.2		4	76.15	even	18
5776.2.a.bv.1.3		4	76.23	odd	18
6498.2.a.bx.1.1		4	57.53	even	18
6498.2.a.ca.1.1		4	57.23	odd	18

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(1.20664 + 0.439181i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.641755 + 3.63957i) q^{5} +(-1.20664 + 0.439181i) q^{6} +(0.221232 - 0.383185i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.03503 - 0.868497i) q^{9} +(-2.83108 - 2.37556i) q^{10} +(2.01484 + 3.48980i) q^{11} +(0.642040 - 1.11205i) q^{12} +(4.59650 - 1.67299i) q^{13} +(0.0768330 + 0.435741i) q^{14} +(-0.824064 + 4.67350i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.204452 - 0.171556i) q^{17} +1.35114 q^{18} +3.69572 q^{20} +(0.435234 - 0.365205i) q^{21} +(-3.78665 - 1.37823i) q^{22} +(-1.59918 + 9.06939i) q^{23} +(0.222978 + 1.26457i) q^{24} +(-8.13617 + 2.96132i) q^{25} +(-2.44575 + 4.23616i) q^{26} +(-2.79360 - 4.83866i) q^{27} +(-0.338947 - 0.284410i) q^{28} +(0.171273 + 0.143715i) q^{29} +(-2.37280 - 4.10980i) q^{30} +(1.73993 - 3.01364i) q^{31} +(0.939693 - 0.342020i) q^{32} +(0.898528 + 5.09581i) q^{33} +(-0.0463455 + 0.262838i) q^{34} +(1.53660 + 0.559278i) q^{35} +(-1.03503 + 0.868497i) q^{36} -1.44903 q^{37} +6.28106 q^{39} +(-2.83108 + 2.37556i) q^{40} +(-7.39042 - 2.68989i) q^{41} +(-0.0986596 + 0.559526i) q^{42} +(-0.978546 - 5.54961i) q^{43} +(3.78665 - 1.37823i) q^{44} +(2.49672 - 4.32444i) q^{45} +(-4.60465 - 7.97549i) q^{46} +(1.68429 + 1.41328i) q^{47} +(-0.983662 - 0.825390i) q^{48} +(3.40211 + 5.89263i) q^{49} +(4.32916 - 7.49833i) q^{50} +(0.322044 - 0.117214i) q^{51} +(-0.849399 - 4.81718i) q^{52} +(-1.72648 + 9.79136i) q^{53} +(5.25026 + 1.91094i) q^{54} +(-11.4083 + 9.57273i) q^{55} +0.442463 q^{56} -0.223582 q^{58} +(2.68845 - 2.25588i) q^{59} +(4.45940 + 1.62309i) q^{60} +(0.708406 - 4.01757i) q^{61} +(0.604270 + 3.42699i) q^{62} +(-0.561777 + 0.204470i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(9.03879 + 15.6556i) q^{65} +(-3.96383 - 3.32605i) q^{66} +(-0.113193 - 0.0949801i) q^{67} +(-0.133446 - 0.231136i) q^{68} +(-5.91273 + 10.2412i) q^{69} +(-1.53660 + 0.559278i) q^{70} +(-1.99159 - 11.2949i) q^{71} +(0.234623 - 1.33061i) q^{72} +(-1.33649 - 0.486442i) q^{73} +(1.11002 - 0.931417i) q^{74} -11.1180 q^{75} +1.78298 q^{77} +(-4.81157 + 4.03739i) q^{78} +(9.58804 + 3.48976i) q^{79} +(0.641755 - 3.63957i) q^{80} +(-0.541955 - 3.07358i) q^{81} +(7.39042 - 2.68989i) q^{82} +(1.64439 - 2.84817i) q^{83} +(-0.284079 - 0.492039i) q^{84} +(0.755596 + 0.634021i) q^{85} +(4.31683 + 3.62225i) q^{86} +(0.143548 + 0.248633i) q^{87} +(-2.01484 + 3.48980i) q^{88} +(-5.60127 + 2.03870i) q^{89} +(0.867101 + 4.91757i) q^{90} +(0.375828 - 2.13143i) q^{91} +(8.65391 + 3.14977i) q^{92} +(3.42300 - 2.87224i) q^{93} -2.19868 q^{94} +1.28408 q^{96} +(-3.12911 + 2.62563i) q^{97} +(-6.39388 - 2.32718i) q^{98} +(0.945455 - 5.36194i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{7} + 12 q^{8} - 6 q^{11} + 6 q^{12} - 24 q^{18} - 12 q^{20} - 54 q^{26} - 12 q^{27} - 12 q^{30} + 78 q^{31} - 24 q^{37} - 36 q^{39} + 66 q^{45} - 30 q^{46} + 36 q^{49} + 18 q^{50} + 12 q^{56}+ \cdots + 12 q^{96}+O(q^{100}) \) 24 * q + 6 * q^7 + 12 * q^8 - 6 * q^11 + 6 * q^12 - 24 * q^18 - 12 * q^20 - 54 * q^26 - 12 * q^27 - 12 * q^30 + 78 * q^31 - 24 * q^37 - 36 * q^39 + 66 * q^45 - 30 * q^46 + 36 * q^49 + 18 * q^50 + 12 * q^56 - 12 * q^58 - 12 * q^64 - 12 * q^65 - 18 * q^68 - 60 * q^69 - 48 * q^75 + 24 * q^77 + 36 * q^83 + 12 * q^84 + 78 * q^87 + 6 * q^88 + 72 * q^94 + 12 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more