LMFDB - Embedded newform 819.2.dt.a.337.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(337,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("819.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.dt (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$84$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			337.6
Character	$\chi$	$=$	819.337
Dual form			819.2.dt.a.610.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.21181 + 1.27699i) q^{2} +(1.71517 + 0.241244i) q^{3} +(2.26141 - 3.91688i) q^{4} +(0.995531 + 0.574770i) q^{5} +(-4.10170 + 1.65667i) q^{6} +(0.866025 - 0.500000i) q^{7} +6.44325i q^{8} +(2.88360 + 0.827549i) q^{9} +O(q^{10})$	\(q+(-2.21181 + 1.27699i) q^{2} +(1.71517 + 0.241244i) q^{3} +(2.26141 - 3.91688i) q^{4} +(0.995531 + 0.574770i) q^{5} +(-4.10170 + 1.65667i) q^{6} +(0.866025 - 0.500000i) q^{7} +6.44325i q^{8} +(2.88360 + 0.827549i) q^{9} -2.93590 q^{10} +(-3.73474 + 2.15625i) q^{11} +(4.82363 - 6.17256i) q^{12} +(-0.744244 + 3.52790i) q^{13} +(-1.27699 + 2.21181i) q^{14} +(1.56884 + 1.22599i) q^{15} +(-3.70514 - 6.41750i) q^{16} -2.79866 q^{17} +(-7.43476 + 1.85195i) q^{18} -0.163153i q^{19} +(4.50261 - 2.59958i) q^{20} +(1.60600 - 0.648660i) q^{21} +(5.50703 - 9.53846i) q^{22} +(-3.77241 + 6.53400i) q^{23} +(-1.55440 + 11.0512i) q^{24} +(-1.83928 - 3.18572i) q^{25} +(-2.85897 - 8.75346i) q^{26} +(4.74622 + 2.11504i) q^{27} -4.52282i q^{28} +(2.90449 + 5.03073i) q^{29} +(-5.03557 - 0.708270i) q^{30} +(0.565281 + 0.326365i) q^{31} +(5.23014 + 3.01962i) q^{32} +(-6.92589 + 2.79735i) q^{33} +(6.19011 - 3.57386i) q^{34} +1.14954 q^{35} +(9.76242 - 9.42330i) q^{36} +5.98669i q^{37} +(0.208345 + 0.360864i) q^{38} +(-2.12759 + 5.87140i) q^{39} +(-3.70338 + 6.41445i) q^{40} +(4.39856 + 2.53951i) q^{41} +(-2.72384 + 3.48556i) q^{42} +(0.0944564 + 0.163603i) q^{43} +19.5047i q^{44} +(2.39506 + 2.48126i) q^{45} -19.2693i q^{46} +(3.08036 - 1.77845i) q^{47} +(-4.80676 - 11.9009i) q^{48} +(0.500000 - 0.866025i) q^{49} +(8.13628 + 4.69749i) q^{50} +(-4.80017 - 0.675160i) q^{51} +(12.1353 + 10.8932i) q^{52} +10.5546 q^{53} +(-13.1986 + 1.38281i) q^{54} -4.95740 q^{55} +(3.22162 + 5.58001i) q^{56} +(0.0393597 - 0.279835i) q^{57} +(-12.8484 - 7.41802i) q^{58} +(8.40422 + 4.85218i) q^{59} +(8.34987 - 3.37249i) q^{60} +(4.45539 + 7.71696i) q^{61} -1.66706 q^{62} +(2.91105 - 0.725123i) q^{63} -0.603551 q^{64} +(-2.76865 + 3.08437i) q^{65} +(11.7466 - 15.0315i) q^{66} +(2.80210 + 1.61779i) q^{67} +(-6.32892 + 10.9620i) q^{68} +(-8.04660 + 10.2968i) q^{69} +(-2.54257 + 1.46795i) q^{70} -11.6511i q^{71} +(-5.33210 + 18.5798i) q^{72} -7.32595i q^{73} +(-7.64495 - 13.2414i) q^{74} +(-2.38613 - 5.90777i) q^{75} +(-0.639051 - 0.368956i) q^{76} +(-2.15625 + 3.73474i) q^{77} +(-2.79190 - 15.7034i) q^{78} +(0.0472206 + 0.0817886i) q^{79} -8.51842i q^{80} +(7.63033 + 4.77264i) q^{81} -12.9717 q^{82} +(-10.7693 + 6.21763i) q^{83} +(1.09110 - 7.75740i) q^{84} +(-2.78615 - 1.60859i) q^{85} +(-0.417840 - 0.241240i) q^{86} +(3.76806 + 9.32924i) q^{87} +(-13.8933 - 24.0639i) q^{88} -11.6741i q^{89} +(-8.46598 - 2.42960i) q^{90} +(1.11942 + 3.42738i) q^{91} +(17.0619 + 29.5521i) q^{92} +(0.890818 + 0.696142i) q^{93} +(-4.54212 + 7.86719i) q^{94} +(0.0937755 - 0.162424i) q^{95} +(8.24210 + 6.44090i) q^{96} +(-4.86688 + 2.80990i) q^{97} +2.55398i q^{98} +(-12.5539 + 3.12710i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 84 q^{4} - 8 q^{9}+O(q^{10}) $ 168 * q + 84 * q^4 - 8 * q^9	$ 168 q + 84 q^{4} - 8 q^{9} - 24 q^{12} + 8 q^{14} - 84 q^{16} - 32 q^{23} + 84 q^{25} - 8 q^{26} + 48 q^{27} + 4 q^{29} + 80 q^{30} - 32 q^{35} + 4 q^{36} + 24 q^{38} + 24 q^{39} + 4 q^{48} + 84 q^{49} + 64 q^{51} + 18 q^{52} - 48 q^{53} - 24 q^{56} + 24 q^{62} - 240 q^{64} - 22 q^{65} - 132 q^{66} - 156 q^{68} - 52 q^{69} + 84 q^{74} - 60 q^{75} - 16 q^{77} - 148 q^{78} + 12 q^{79} - 8 q^{81} - 24 q^{82} + 88 q^{87} + 24 q^{88} - 164 q^{90} + 12 q^{91} + 128 q^{92} - 60 q^{94} - 96 q^{95}+O(q^{100}) $ 168 * q + 84 * q^4 - 8 * q^9 - 24 * q^12 + 8 * q^14 - 84 * q^16 - 32 * q^23 + 84 * q^25 - 8 * q^26 + 48 * q^27 + 4 * q^29 + 80 * q^30 - 32 * q^35 + 4 * q^36 + 24 * q^38 + 24 * q^39 + 4 * q^48 + 84 * q^49 + 64 * q^51 + 18 * q^52 - 48 * q^53 - 24 * q^56 + 24 * q^62 - 240 * q^64 - 22 * q^65 - 132 * q^66 - 156 * q^68 - 52 * q^69 + 84 * q^74 - 60 * q^75 - 16 * q^77 - 148 * q^78 + 12 * q^79 - 8 * q^81 - 24 * q^82 + 88 * q^87 + 24 * q^88 - 164 * q^90 + 12 * q^91 + 128 * q^92 - 60 * q^94 - 96 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$

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 $

$2$	−2.21181	+	1.27699i	−1.56399	+	0.902969i	−0.567141	+	0.823621i	$0.691951\pi$
$2$	−2.21181	+	1.27699i	−1.56399	+	0.902969i	−0.996847	+	0.0793484i	$0.974716\pi$
$3$	1.71517	+	0.241244i	0.990253	+	0.139282i
$3$	1.71517	+	0.241244i	0.990253	+	0.139282i
$4$	2.26141	−	3.91688i	1.13071	−	1.95844i
$5$	0.995531	+	0.574770i	0.445215	+	0.257045i	0.705807	−	0.708404i	$-0.250584\pi$
$5$	0.995531	+	0.574770i	0.445215	+	0.257045i	−0.260592	+	0.965449i	$0.583918\pi$
$6$	−4.10170	+	1.65667i	−1.67451	+	0.676331i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$8$			6.44325i			2.27803i
$9$	2.88360	+	0.827549i	0.961201	+	0.275850i
$10$	−2.93590			−0.928414
$11$	−3.73474	+	2.15625i	−1.12607	+	0.650135i	−0.942943	−	0.332955i	$-0.891954\pi$
$11$	−3.73474	+	2.15625i	−1.12607	+	0.650135i	−0.183124	+	0.983090i	$0.558621\pi$
$12$	4.82363	−	6.17256i	1.39246	−	1.78186i
$13$	−0.744244	+	3.52790i	−0.206416	+	0.978464i
$13$	−0.744244	+	3.52790i	−0.206416	+	0.978464i
$14$	−1.27699	+	2.21181i	−0.341290	+	0.591132i
$15$	1.56884	+	1.22599i	0.405073	+	0.316550i
$16$	−3.70514	−	6.41750i	−0.926286	−	1.60437i
$17$	−2.79866			−0.678775			−0.339387	−	0.940647i	$-0.610220\pi$
$17$	−2.79866			−0.678775			−0.339387	+	0.940647i	$0.610220\pi$
$18$	−7.43476	+	1.85195i	−1.75239	+	0.436509i
$19$		−	0.163153i		−	0.0374299i	−0.999825	−	0.0187149i	$-0.994043\pi$
$19$		−	0.163153i		−	0.0374299i	0.999825	−	0.0187149i	$-0.00595750\pi$
$20$	4.50261	−	2.59958i	1.00681	−	0.581284i
$21$	1.60600	−	0.648660i	0.350458	−	0.141549i
$22$	5.50703	−	9.53846i	1.17410	−	2.03361i
$23$	−3.77241	+	6.53400i	−0.786601	+	1.36243i	0.141437	+	0.989947i	$0.454828\pi$
$23$	−3.77241	+	6.53400i	−0.786601	+	1.36243i	−0.928038	+	0.372485i	$0.878506\pi$
$24$	−1.55440	+	11.0512i	−0.317290	+	2.25583i
$25$	−1.83928	−	3.18572i	−0.367856	−	0.637145i
$26$	−2.85897	−	8.75346i	−0.560691	−	1.71669i
$27$	4.74622	+	2.11504i	0.913411	+	0.407039i
$28$		−	4.52282i		−	0.854733i
$29$	2.90449	+	5.03073i	0.539351	+	0.934183i	0.998939	+	0.0460510i	$0.0146637\pi$
$29$	2.90449	+	5.03073i	0.539351	+	0.934183i	−0.459588	+	0.888132i	$0.652003\pi$
$30$	−5.03557	−	0.708270i	−0.919365	−	0.129312i
$31$	0.565281	+	0.326365i	0.101527	+	0.0586169i	0.549904	−	0.835228i	$-0.314664\pi$
$31$	0.565281	+	0.326365i	0.101527	+	0.0586169i	−0.448377	+	0.893845i	$0.647998\pi$
$32$	5.23014	+	3.01962i	0.924567	+	0.533799i
$33$	−6.92589	+	2.79735i	−1.20564	+	0.486957i
$34$	6.19011	−	3.57386i	1.06160	−	0.612912i
$35$	1.14954			0.194308
$36$	9.76242	−	9.42330i	1.62707	−	1.57055i
$37$			5.98669i			0.984206i	0.870537	+	0.492103i	$0.163772\pi$
$37$			5.98669i			0.984206i	−0.870537	+	0.492103i	$0.836228\pi$
$38$	0.208345	+	0.360864i	0.0337980	+	0.0585399i
$39$	−2.12759	+	5.87140i	−0.340687	+	0.940177i
$40$	−3.70338	+	6.41445i	−0.585556	+	1.01421i
$41$	4.39856	+	2.53951i	0.686940	+	0.396605i	0.802465	−	0.596700i	$-0.203522\pi$
$41$	4.39856	+	2.53951i	0.686940	+	0.396605i	−0.115525	+	0.993305i	$0.536855\pi$
$42$	−2.72384	+	3.48556i	−0.420298	+	0.537834i
$43$	0.0944564	+	0.163603i	0.0144045	+	0.0249493i	0.873138	−	0.487473i	$-0.162081\pi$
$43$	0.0944564	+	0.163603i	0.0144045	+	0.0249493i	−0.858733	+	0.512423i	$0.828748\pi$
$44$			19.5047i			2.94045i
$45$	2.39506	+	2.48126i	0.357035	+	0.369884i
$46$		−	19.2693i		−	2.84110i
$47$	3.08036	−	1.77845i	0.449317	−	0.259413i	−0.258225	−	0.966085i	$-0.583138\pi$
$47$	3.08036	−	1.77845i	0.449317	−	0.259413i	0.707542	+	0.706672i	$0.249804\pi$
$48$	−4.80676	−	11.9009i	−0.693796	−	1.71775i
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	8.13628	+	4.69749i	1.15064	+	0.664325i
$51$	−4.80017	−	0.675160i	−0.672158	−	0.0945413i
$52$	12.1353	+	10.8932i	1.68287	+	1.51061i
$53$	10.5546			1.44979			0.724896	−	0.688859i	$-0.241888\pi$
$53$	10.5546			1.44979			0.724896	+	0.688859i	$0.241888\pi$
$54$	−13.1986	+	1.38281i	−1.79611	+	0.188177i
$55$	−4.95740			−0.668456
$56$	3.22162	+	5.58001i	0.430507	+	0.745661i
$57$	0.0393597	−	0.279835i	0.00521332	−	0.0370650i
$58$	−12.8484	−	7.41802i	−1.68708	−	0.974034i
$59$	8.40422	+	4.85218i	1.09414	+	0.631700i	0.934675	−	0.355504i	$-0.115691\pi$
$59$	8.40422	+	4.85218i	1.09414	+	0.631700i	0.159462	+	0.987204i	$0.449024\pi$
$60$	8.34987	−	3.37249i	1.07796	−	0.435387i
$61$	4.45539	+	7.71696i	0.570454	+	0.988056i	0.996519	+	0.0833633i	$0.0265662\pi$
$61$	4.45539	+	7.71696i	0.570454	+	0.988056i	−0.426065	+	0.904693i	$0.640100\pi$
$62$	−1.66706			−0.211717
$63$	2.91105	−	0.725123i	0.366757	−	0.0913569i
$64$	−0.603551			−0.0754439
$65$	−2.76865	+	3.08437i	−0.343409	+	0.382569i
$66$	11.7466	−	15.0315i	1.44591	−	1.85025i
$67$	2.80210	+	1.61779i	0.342331	+	0.197645i	0.661302	−	0.750119i	$-0.270004\pi$
$67$	2.80210	+	1.61779i	0.342331	+	0.197645i	−0.318971	+	0.947764i	$0.603337\pi$
$68$	−6.32892	+	10.9620i	−0.767494	+	1.32934i
$69$	−8.04660	+	10.2968i	−0.968697	+	1.23959i
$70$	−2.54257	+	1.46795i	−0.303895	+	0.175454i
$71$		−	11.6511i		−	1.38273i	−0.722504	−	0.691367i	$-0.757009\pi$
$71$		−	11.6511i		−	1.38273i	0.722504	−	0.691367i	$-0.242991\pi$
$72$	−5.33210	+	18.5798i	−0.628394	+	2.18965i
$73$		−	7.32595i		−	0.857438i	−0.903438	−	0.428719i	$-0.858965\pi$
$73$		−	7.32595i		−	0.857438i	0.903438	−	0.428719i	$-0.141035\pi$
$74$	−7.64495	−	13.2414i	−0.888708	−	1.53929i
$75$	−2.38613	−	5.90777i	−0.275527	−	0.682170i
$76$	−0.639051	−	0.368956i	−0.0733042	−	0.0423222i
$77$	−2.15625	+	3.73474i	−0.245728	+	0.425613i
$78$	−2.79190	−	15.7034i	−0.316120	−	1.77806i
$79$	0.0472206	+	0.0817886i	0.00531274	+	0.00920193i	0.868670	−	0.495392i	$-0.164976\pi$
$79$	0.0472206	+	0.0817886i	0.00531274	+	0.00920193i	−0.863357	+	0.504594i	$0.831642\pi$
$80$		−	8.51842i		−	0.952388i
$81$	7.63033	+	4.77264i	0.847814	+	0.530294i
$82$	−12.9717			−1.43249
$83$	−10.7693	+	6.21763i	−1.18208	+	0.682474i	−0.956495	−	0.291750i	$-0.905763\pi$
$83$	−10.7693	+	6.21763i	−1.18208	+	0.682474i	−0.225585	+	0.974224i	$0.572429\pi$
$84$	1.09110	−	7.75740i	0.119049	−	0.846402i
$85$	−2.78615	−	1.60859i	−0.302201	−	0.174476i
$86$	−0.417840	−	0.241240i	−0.0450568	−	0.0260136i
$87$	3.76806	+	9.32924i	0.403978	+	1.00020i
$88$	−13.8933	−	24.0639i	−1.48103	−	2.56522i
$89$		−	11.6741i		−	1.23745i	−0.785606	−	0.618727i	$-0.787649\pi$
$89$		−	11.6741i		−	1.23745i	0.785606	−	0.618727i	$-0.212351\pi$
$90$	−8.46598	−	2.42960i	−0.892393	−	0.256103i
$91$	1.11942	+	3.42738i	0.117347	+	0.359287i
$92$	17.0619	+	29.5521i	1.77883	+	3.08102i
$93$	0.890818	+	0.696142i	0.0923735	+	0.0721865i
$94$	−4.54212	+	7.86719i	−0.468484	+	0.811438i
$95$	0.0937755	−	0.162424i	0.00962116	−	0.0166643i
$96$	8.24210	+	6.44090i	0.841206	+	0.657372i
$97$	−4.86688	+	2.80990i	−0.494157	+	0.285302i	−0.726297	−	0.687381i	$-0.758760\pi$
$97$	−4.86688	+	2.80990i	−0.494157	+	0.285302i	0.232140	+	0.972682i	$0.425427\pi$
$98$			2.55398i			0.257991i
$99$	−12.5539	+	3.12710i	−1.26172	+	0.314285i
$100$	−16.6375			−1.66375
$101$	−8.89708	−	15.4102i	−0.885293	−	1.53337i	−0.845378	−	0.534169i	$-0.820624\pi$
$101$	−8.89708	−	15.4102i	−0.885293	−	1.53337i	−0.0399154	−	0.999203i	$-0.512709\pi$
$102$	11.4793	−	4.63645i	1.13662	−	0.459077i
$103$	−1.08079	+	1.87198i	−0.106493	+	0.184451i	−0.914347	−	0.404931i	$-0.867295\pi$
$103$	−1.08079	+	1.87198i	−0.106493	+	0.184451i	0.807854	+	0.589382i	$0.200629\pi$
$104$	−22.7311	−	4.79534i	−2.22897	−	0.470222i
$105$	1.97165	+	0.277320i	0.192414	+	0.0270636i
$106$	−23.3449	+	13.4782i	−2.26746	+	1.30912i
$107$	−17.1550			−1.65844			−0.829218	−	0.558926i	$-0.811214\pi$
$107$	−17.1550			−1.65844			−0.829218	+	0.558926i	$0.811214\pi$
$108$	19.0175	−	13.8074i	1.82996	−	1.32862i
$109$			3.13351i			0.300135i	0.988676	+	0.150068i	$0.0479492\pi$
$109$			3.13351i			0.300135i	−0.988676	+	0.150068i	$0.952051\pi$
$110$	10.9648	−	6.33056i	1.04546	−	0.603595i
$111$	−1.44425	+	10.2682i	−0.137083	+	0.974613i
$112$	−6.41750	−	3.70514i	−0.606396	−	0.350103i
$113$	2.65546	−	4.59939i	0.249804	−	0.432674i	−0.713667	−	0.700485i	$-0.752967\pi$
$113$	2.65546	−	4.59939i	0.249804	−	0.432674i	0.963471	+	0.267811i	$0.0863003\pi$
$114$	0.270290	+	0.669205i	0.0253150	+	0.0626768i
$115$	−7.51109	+	4.33653i	−0.700413	+	0.404384i
$116$	26.2730			2.43939
$117$	−5.06561	+	9.55717i	−0.468316	+	0.883561i
$118$	−24.7848			−2.28162
$119$	−2.42371	+	1.39933i	−0.222181	+	0.128276i
$120$	−7.89937	+	10.1084i	−0.721111	+	0.922770i
$121$	3.79887	−	6.57983i	0.345351	−	0.598166i
$122$	−19.7090	−	11.3790i	−1.78437	−	1.03021i
$123$	6.93163	+	5.41681i	0.625004	+	0.488418i
$124$	2.55667	−	1.47609i	0.229595	−	0.132557i
$125$		−	9.97635i		−	0.892312i
$126$	−5.51272	+	5.32122i	−0.491112	+	0.474052i
$127$	0.408322			0.0362327			0.0181163	−	0.999836i	$-0.494233\pi$
$127$	0.408322			0.0362327			0.0181163	+	0.999836i	$0.494233\pi$
$128$	−9.12534	+	5.26852i	−0.806574	+	0.465675i
$129$	0.122540	+	0.303394i	0.0107891	+	0.0267124i
$130$	2.18503	−	10.3576i	0.191640	−	0.908420i
$131$	−6.74366	+	11.6804i	−0.589196	+	1.02052i	0.405142	+	0.914254i	$0.367222\pi$
$131$	−6.74366	+	11.6804i	−0.589196	+	1.02052i	−0.994338	+	0.106264i	$0.966111\pi$
$132$	−4.70540	+	33.4539i	−0.409552	+	2.91179i
$133$	−0.0815765	−	0.141295i	−0.00707358	−	0.0122518i
$134$	−8.26363			−0.713869
$135$	3.50935	+	4.83357i	0.302037	+	0.416007i
$136$		−	18.0324i		−	1.54627i
$137$	9.58109	−	5.53164i	0.818568	−	0.472600i	−0.0313546	−	0.999508i	$-0.509982\pi$
$137$	9.58109	−	5.53164i	0.818568	−	0.472600i	0.849922	+	0.526908i	$0.176649\pi$
$138$	4.64861	−	33.0501i	0.395716	−	2.81341i
$139$	11.0327	−	19.1092i	0.935779	−	1.62082i	0.162541	−	0.986702i	$-0.448031\pi$
$139$	11.0327	−	19.1092i	0.935779	−	1.62082i	0.773239	−	0.634115i	$-0.218636\pi$
$140$	2.59958	−	4.50261i	0.219705	−	0.380540i
$141$	5.71238	−	2.30722i	0.481069	−	0.194303i
$142$	14.8784	+	25.7701i	1.24857	+	2.16258i
$143$	−4.82750	−	14.7806i	−0.403696	−	1.23601i
$144$	−5.37337	−	21.5717i	−0.447781	−	1.79764i
$145$			6.67766i			0.554550i
$146$	9.35518	+	16.2036i	0.774240	+	1.34102i
$147$	1.06651	−	1.36476i	0.0879641	−	0.112563i
$148$	23.4492	+	13.5384i	1.92751	+	1.11285i
$149$	14.9338	+	8.62206i	1.22343	+	0.706347i	0.965647	−	0.259857i	$-0.0836754\pi$
$149$	14.9338	+	8.62206i	1.22343	+	0.706347i	0.257781	+	0.966203i	$0.417009\pi$
$150$	12.8219	+	10.0198i	1.04690	+	0.818114i
$151$	4.07043	−	2.35006i	0.331247	−	0.191245i	−0.325148	−	0.945663i	$-0.605414\pi$
$151$	4.07043	−	2.35006i	0.331247	−	0.191245i	0.656394	+	0.754418i	$0.272081\pi$
$152$	1.05124			0.0852664
$153$	−8.07022	−	2.31603i	−0.652439	−	0.187240i
$154$		−	11.0141i		−	0.887539i
$155$	0.375170	+	0.649813i	0.0301343	+	0.0521942i
$156$	18.1862	+	21.6112i	1.45606	+	1.73028i
$157$	1.62650	−	2.81718i	0.129809	−	0.224835i	−0.793794	−	0.608187i	$-0.791897\pi$
$157$	1.62650	−	2.81718i	0.129809	−	0.224835i	0.923602	+	0.383352i	$0.125230\pi$
$158$	−0.208886	−	0.120601i	−0.0166181	−	0.00959447i
$159$	18.1030	+	2.54625i	1.43566	+	0.201930i
$160$	3.47118	+	6.01225i	0.274421	+	0.475310i
$161$			7.54481i			0.594614i
$162$	−22.9715	−	0.812335i	−1.80481	−	0.0638231i
$163$			11.9409i			0.935286i	0.883917	+	0.467643i	$0.154897\pi$
$163$			11.9409i			0.935286i	−0.883917	+	0.467643i	$0.845103\pi$
$164$	19.8939	−	11.4858i	1.55345	−	0.896887i
$165$	−8.50278	−	1.19594i	−0.661940	−	0.0931041i
$166$	15.8797	−	27.5045i	1.23251	−	2.13476i
$167$	−1.65525	−	0.955660i	−0.128087	−	0.0739512i	0.434587	−	0.900630i	$-0.356894\pi$
$167$	−1.65525	−	0.955660i	−0.128087	−	0.0739512i	−0.562675	+	0.826679i	$0.690228\pi$
$168$	4.17948	+	10.3479i	0.322454	+	0.798355i
$169$	−11.8922	−	5.25124i	−0.914785	−	0.403941i
$170$	8.21660			0.630184
$171$	0.135017	−	0.470469i	0.0103250	−	0.0359776i
$172$	0.854419			0.0651489
$173$	−3.46480	−	6.00121i	−0.263424	−	0.456263i	0.703726	−	0.710472i	$-0.251518\pi$
$173$	−3.46480	−	6.00121i	−0.263424	−	0.456263i	−0.967149	+	0.254208i	$0.918185\pi$
$174$	−20.2476	−	15.8228i	−1.53497	−	1.19952i
$175$	−3.18572	−	1.83928i	−0.240818	−	0.139036i
$176$	27.6755	+	15.9785i	2.08612	+	1.20442i
$177$	13.2441	+	10.3498i	0.995487	+	0.777937i
$178$	14.9077	+	25.8210i	1.11738	+	1.93536i
$179$	−4.32615			−0.323351			−0.161676	−	0.986844i	$-0.551690\pi$
$179$	−4.32615			−0.323351			−0.161676	+	0.986844i	$0.551690\pi$
$180$	15.1350	−	3.77004i	1.12810	−	0.281002i
$181$	14.5589			1.08215			0.541077	−	0.840973i	$-0.318017\pi$
$181$	14.5589			1.08215			0.541077	+	0.840973i	$0.318017\pi$
$182$	−6.85267	−	6.15123i	−0.507954	−	0.455959i
$183$	5.78007	+	14.3107i	0.427275	+	1.05788i
$184$	−42.1002	−	24.3065i	−3.10366	−	1.79190i
$185$	−3.44097	+	5.95994i	−0.252985	+	0.438183i
$186$	−2.85929	−	0.402169i	−0.209653	−	0.0294884i
$187$	10.4523	−	6.03462i	0.764346	−	0.441295i
$188$		−	16.0872i		−	1.17328i
$189$	5.16787	−	0.541435i	0.375907	−	0.0393836i
$190$			0.479002i			0.0347504i
$191$	−8.70625	−	15.0797i	−0.629962	−	1.09113i	−0.987559	−	0.157250i	$-0.949737\pi$
$191$	−8.70625	−	15.0797i	−0.629962	−	1.09113i	0.357597	−	0.933876i	$-0.383596\pi$
$192$	−1.03519	−	0.145603i	−0.0747085	−	0.0105080i
$193$	16.0561	+	9.26999i	1.15574	+	0.667268i	0.950280	−	0.311397i	$-0.100797\pi$
$193$	16.0561	+	9.26999i	1.15574	+	0.667268i	0.205462	+	0.978665i	$0.434130\pi$
$194$	7.17642	−	12.4299i	0.515237	−	0.892417i
$195$	−5.49279	+	4.62229i	−0.393347	+	0.331009i
$196$	−2.26141	−	3.91688i	−0.161529	−	0.279777i
$197$			21.5434i			1.53490i	0.641106	+	0.767452i	$0.278476\pi$
$197$			21.5434i			1.53490i	−0.641106	+	0.767452i	$0.721524\pi$
$198$	23.7736	−	22.9478i	1.68952	−	1.63083i
$199$	−0.773398			−0.0548247			−0.0274124	−	0.999624i	$-0.508727\pi$
$199$	−0.773398			−0.0548247			−0.0274124	+	0.999624i	$0.508727\pi$
$200$	20.5264	−	11.8509i	1.45144	−	0.837987i
$201$	4.41579	+	3.45078i	0.311466	+	0.243399i
$202$	39.3574	+	22.7230i	2.76918	+	1.59878i
$203$	5.03073	+	2.90449i	0.353088	+	0.203855i
$204$	−13.4997	+	17.2749i	−0.945167	+	1.20948i
$205$	2.91927	+	5.05632i	0.203891	+	0.353149i
$206$		−	5.52061i		−	0.384639i
$207$	−16.2853	+	15.7196i	−1.13191	+	1.09259i
$208$	25.3978	−	8.29521i	1.76102	−	0.575169i
$209$	0.351800	+	0.609335i	0.0243345	+	0.0421486i
$210$	−4.71507	+	1.90440i	−0.325370	+	0.131416i
$211$	14.0884	−	24.4018i	0.969886	−	1.67989i	0.274014	−	0.961726i	$-0.411648\pi$
$211$	14.0884	−	24.4018i	0.969886	−	1.67989i	0.695872	−	0.718166i	$-0.255018\pi$
$212$	23.8684	−	41.3413i	1.63929	−	2.83933i
$213$	2.81076	−	19.9836i	0.192590	−	1.36926i
$214$	37.9436	−	21.9068i	2.59377	−	1.49752i
$215$			0.217163i			0.0148104i
$216$	−13.6277	+	30.5811i	−0.927248	+	2.08078i
$217$	0.652730			0.0443102
$218$	−4.00146	−	6.93073i	−0.271013	−	0.469408i
$219$	1.76734	−	12.5652i	0.119426	−	0.849080i
$220$	−11.2107	+	19.4175i	−0.755827	+	1.30913i
$221$	2.08288	−	9.87340i	0.140110	−	0.664157i
$222$	−9.91796	−	24.5556i	−0.665650	−	1.64806i
$223$	11.6732	−	6.73952i	0.781695	−	0.451312i	−0.0553355	−	0.998468i	$-0.517623\pi$
$223$	11.6732	−	6.73952i	0.781695	−	0.451312i	0.837031	+	0.547156i	$0.184290\pi$
$224$	6.03925			0.403514
$225$	−2.66741	−	10.7085i	−0.177827	−	0.713897i
$226$			13.5640i			0.902263i
$227$	12.8674	−	7.42902i	0.854042	−	0.493082i	−0.00797039	−	0.999968i	$-0.502537\pi$
$227$	12.8674	−	7.42902i	0.854042	−	0.493082i	0.862013	+	0.506887i	$0.169204\pi$
$228$	−1.00707	−	0.786989i	−0.0666949	−	0.0521196i
$229$	−13.2502	−	7.64999i	−0.875596	−	0.505526i	−0.00639215	−	0.999980i	$-0.502035\pi$
$229$	−13.2502	−	7.64999i	−0.875596	−	0.505526i	−0.869204	+	0.494454i	$0.835368\pi$
$230$	11.0754	−	19.1832i	0.730292	−	1.26490i
$231$	−4.59932	+	5.88553i	−0.302613	+	0.387239i
$232$	−32.4142	+	18.7144i	−2.12810	+	1.22866i
$233$	−17.5330			−1.14862			−0.574311	−	0.818637i	$-0.694730\pi$
$233$	−17.5330			−1.14862			−0.574311	+	0.818637i	$0.694730\pi$
$234$	−1.00023	−	27.6074i	−0.0653871	−	1.80475i
$235$	4.08879			0.266723
$236$	38.0108	−	21.9456i	2.47429	−	1.42853i
$237$	0.0612603	+	0.151673i	0.00397929	+	0.00985221i
$238$	3.57386	−	6.19011i	0.231659	−	0.401245i
$239$	−22.1548	−	12.7911i	−1.43308	−	0.827388i	−0.435723	−	0.900081i	$-0.643507\pi$
$239$	−22.1548	−	12.7911i	−1.43308	−	0.827388i	−0.997354	+	0.0726931i	$0.976841\pi$
$240$	2.05502	−	14.6105i	0.132651	−	0.943105i
$241$	−23.4915	+	13.5628i	−1.51322	+	0.873657i	−0.513338	+	0.858187i	$0.671591\pi$
$241$	−23.4915	+	13.5628i	−1.51322	+	0.873657i	−0.999880	+	0.0154704i	$0.995075\pi$
$242$			19.4045i			1.24737i
$243$	11.9359	+	10.0267i	0.765690	+	0.643210i
$244$	40.3019			2.58006
$245$	0.995531	−	0.574770i	0.0636021	−	0.0367207i
$246$	−22.2487	−	3.12935i	−1.41852	−	0.199520i
$247$	0.575588	+	0.121426i	0.0366238	+	0.00772613i
$248$	−2.10285	+	3.64224i	−0.133531	+	0.231283i
$249$	−19.9711	+	8.06627i	−1.26561	+	0.511179i
$250$	12.7397	+	22.0658i	0.805730	+	1.39557i
$251$	18.9335			1.19507			0.597536	−	0.801842i	$-0.296147\pi$
$251$	18.9335			1.19507			0.597536	+	0.801842i	$0.296147\pi$
$252$	3.74286	−	13.0420i	0.235778	−	0.821570i
$253$		−	32.5371i		−	2.04559i
$254$	−0.903131	+	0.521423i	−0.0566675	+	0.0327170i
$255$	−4.39066	−	3.43114i	−0.274954	−	0.214866i
$256$	14.0592	−	24.3513i	0.878703	−	1.52196i
$257$	9.02022	−	15.6235i	0.562666	−	0.974566i	−0.434597	−	0.900625i	$-0.643109\pi$
$257$	9.02022	−	15.6235i	0.562666	−	0.974566i	0.997263	−	0.0739406i	$-0.0235575\pi$
$258$	−0.658468	−	0.514568i	−0.0409944	−	0.0320356i
$259$	2.99335	+	5.18463i	0.185998	+	0.322157i
$260$	5.82004	+	17.8195i	0.360944	+	1.10512i
$261$	4.21223	+	16.9102i	0.260731	+	1.04672i
$262$		−	34.4464i		−	2.12810i
$263$	9.84549	+	17.0529i	0.607099	+	1.05153i	0.991716	+	0.128450i	$0.0410003\pi$
$263$	9.84549	+	17.0529i	0.607099	+	1.05153i	−0.384617	+	0.923076i	$0.625666\pi$
$264$	−18.0240	−	44.6252i	−1.10930	−	2.74649i
$265$	10.5075	+	6.06649i	0.645469	+	0.372662i
$266$	0.360864	+	0.208345i	0.0221260	+	0.0127745i
$267$	2.81631	−	20.0231i	0.172355	−	1.22539i
$268$	12.6734	−	7.31699i	0.774151	−	0.446957i
$269$	−12.3075			−0.750402			−0.375201	−	0.926943i	$-0.622426\pi$
$269$	−12.3075			−0.750402			−0.375201	+	0.926943i	$0.622426\pi$
$270$	−13.9345	−	6.20955i	−0.848024	−	0.377901i
$271$			26.4710i			1.60800i	0.594630	+	0.803999i	$0.297298\pi$
$271$			26.4710i			1.60800i	−0.594630	+	0.803999i	$0.702702\pi$
$272$	10.3694	+	17.9604i	0.628739	+	1.08901i
$273$	1.09316	+	6.14858i	0.0661608	+	0.372129i
$274$	−14.1277	+	24.4699i	−0.853487	+	1.47828i
$275$	13.7385	+	7.93191i	0.828461	+	0.478312i
$276$	22.1348	+	54.8029i	1.33236	+	3.29875i
$277$	7.29954	+	12.6432i	0.438587	+	0.759655i	0.997581	−	0.0695169i	$-0.0221458\pi$
$277$	7.29954	+	12.6432i	0.438587	+	0.759655i	−0.558994	+	0.829172i	$0.688812\pi$
$278$			56.3545i			3.37992i
$279$	1.35996	+	1.40890i	0.0814188	+	0.0843489i
$280$			7.40677i			0.442639i
$281$	−0.507808	+	0.293183i	−0.0302933	+	0.0174898i	−0.515070	−	0.857148i	$-0.672234\pi$
$281$	−0.507808	+	0.293183i	−0.0302933	+	0.0174898i	0.484777	+	0.874638i	$0.338901\pi$
$282$	−9.68842	+	12.3978i	−0.576937	+	0.738277i
$283$	−7.48454	+	12.9636i	−0.444910	+	0.770606i	−0.998046	−	0.0624847i	$-0.980098\pi$
$283$	−7.48454	+	12.9636i	−0.444910	+	0.770606i	0.553136	+	0.833091i	$0.313431\pi$
$284$	−45.6360	−	26.3480i	−2.70800	−	1.56346i
$285$	0.200025	−	0.255961i	0.0118484	−	0.0151619i
$286$	29.5522	+	26.5272i	1.74746	+	1.56859i
$287$	5.07902			0.299805
$288$	12.5828	+	13.0356i	0.741446	+	0.768129i
$289$	−9.16751			−0.539265
$290$	−8.52731	−	14.7697i	−0.500741	−	0.867309i
$291$	−9.02539	+	3.64534i	−0.529078	+	0.213693i
$292$	−28.6949	−	16.5670i	−1.67924	−	0.969510i
$293$	−10.1297	−	5.84839i	−0.591784	−	0.341667i	0.174019	−	0.984742i	$-0.444325\pi$
$293$	−10.1297	−	5.84839i	−0.591784	−	0.341667i	−0.765803	+	0.643076i	$0.777658\pi$
$294$	−0.616133	+	4.38051i	−0.0359336	+	0.255476i
$295$	5.57777	+	9.66099i	0.324751	+	0.562485i
$296$	−38.5737			−2.24205
$297$	−22.2865	+	2.33494i	−1.29319	+	0.135487i
$298$	−44.0412			−2.55124
$299$	−20.2437	−	18.1716i	−1.17072	−	1.05089i
$300$	−28.5361	−	4.01369i	−1.64753	−	0.231731i
$301$	0.163603	+	0.0944564i	0.00942994	+	0.00544438i
$302$	−6.00202	+	10.3958i	−0.345377	+	0.598211i
$303$	−11.5424	−	28.5775i	−0.663092	−	1.64173i
$304$	−1.04703	+	0.604505i	−0.0600515	+	0.0346708i
$305$			10.2433i			0.586530i
$306$	20.8074	−	5.18298i	1.18948	−	0.296291i
$307$			16.2718i			0.928683i	0.885656	+	0.464342i	$0.153709\pi$
$307$			16.2718i			0.928683i	−0.885656	+	0.464342i	$0.846291\pi$
$308$	9.75236	+	16.8916i	0.555692	+	0.962487i
$309$	−2.30533	+	2.95002i	−0.131146	+	0.167821i
$310$	−1.65961	−	0.958176i	−0.0942595	−	0.0544208i
$311$	7.20474	−	12.4790i	0.408543	−	0.707618i	−0.586183	−	0.810178i	$-0.699370\pi$
$311$	7.20474	−	12.4790i	0.408543	−	0.707618i	0.994727	+	0.102560i	$0.0327035\pi$
$312$	−37.8309	−	13.7086i	−2.14175	−	0.776095i
$313$	7.95132	+	13.7721i	0.449435	+	0.778445i	0.998349	−	0.0574341i	$-0.0182919\pi$
$313$	7.95132	+	13.7721i	0.449435	+	0.778445i	−0.548914	+	0.835879i	$0.684959\pi$
$314$			8.30809i			0.468853i
$315$	3.31482	+	0.951300i	0.186769	+	0.0535997i
$316$	0.427141			0.0240286
$317$	21.1621	−	12.2180i	1.18858	−	0.686229i	0.230599	−	0.973049i	$-0.425931\pi$
$317$	21.1621	−	12.2180i	1.18858	−	0.686229i	0.957985	+	0.286820i	$0.0925981\pi$
$318$	−43.2920	+	17.4855i	−2.42769	+	0.980540i
$319$	−21.6951	−	12.5257i	−1.21469	−	0.701302i
$320$	−0.600854	−	0.346903i	−0.0335887	−	0.0193925i
$321$	−29.4237	−	4.13854i	−1.64227	−	0.230991i
$322$	−9.63465	−	16.6877i	−0.536918	−	0.929970i
$323$			0.456610i			0.0254065i
$324$	35.9492	−	19.0942i	1.99718	−	1.06079i
$325$	12.6078	−	4.11784i	0.699355	−	0.228417i
$326$	−15.2485	−	26.4111i	−0.844534	−	1.46278i
$327$	−0.755940	+	5.37449i	−0.0418036	+	0.297210i
$328$	−16.3627	+	28.3410i	−0.903478	+	1.56487i
$329$	1.77845	−	3.08036i	0.0980490	−	0.169826i
$330$	20.3338	−	8.21276i	1.11934	−	0.452098i
$331$	−30.2892	+	17.4875i	−1.66485	+	0.961199i	−0.694495	+	0.719498i	$0.744372\pi$
$331$	−30.2892	+	17.4875i	−1.66485	+	0.961199i	−0.970351	+	0.241701i	$0.922295\pi$
$332$			56.2425i			3.08671i
$333$	−4.95428	+	17.2632i	−0.271493	+	0.946020i
$334$	4.88148			0.267103
$335$	1.85972	+	3.22113i	0.101607	+	0.175989i
$336$	−10.1132	−	7.90313i	−0.551722	−	0.431151i
$337$	−1.48812	+	2.57750i	−0.0810632	+	0.140406i	−0.903707	−	0.428152i	$-0.859165\pi$
$337$	−1.48812	+	2.57750i	−0.0810632	+	0.140406i	0.822644	+	0.568557i	$0.192498\pi$
$338$	33.0091	−	3.57148i	1.79546	−	0.194263i
$339$	5.66413	−	7.24811i	0.307633	−	0.393663i
$340$	−12.6013	+	7.27535i	−0.683400	+	0.394561i
$341$	−2.81490			−0.152436
$342$	0.302152	+	1.21300i	0.0163385	+	0.0655918i
$343$		−	1.00000i		−	0.0539949i
$344$	−1.05414	+	0.608606i	−0.0568352	+	0.0328138i
$345$	−13.9289	+	5.62587i	−0.749909	+	0.302887i
$346$	15.3270	+	8.84903i	0.823983	+	0.475727i
$347$	0.699266	−	1.21116i	0.0375386	−	0.0650187i	−0.846646	−	0.532157i	$-0.821382\pi$
$347$	0.699266	−	1.21116i	0.0375386	−	0.0650187i	0.884184	+	0.467138i	$0.154715\pi$
$348$	45.0626	+	6.33821i	2.41561	+	0.339764i
$349$	15.0476	−	8.68774i	0.805480	−	0.465044i	−0.0399035	−	0.999204i	$-0.512705\pi$
$349$	15.0476	−	8.68774i	0.805480	−	0.465044i	0.845384	+	0.534159i	$0.179372\pi$
$350$	9.39497			0.502182
$351$	−10.9940	+	15.1701i	−0.586816	+	0.809720i
$352$	−26.0443			−1.38817
$353$	19.6665	−	11.3544i	1.04674	−	0.604335i	0.125005	−	0.992156i	$-0.460105\pi$
$353$	19.6665	−	11.3544i	1.04674	−	0.604335i	0.921735	+	0.387821i	$0.126772\pi$
$354$	−42.5100	−	5.97918i	−2.25938	−	0.317790i
$355$	6.69671	−	11.5990i	0.355425	−	0.615613i
$356$	−45.7261	−	26.4000i	−2.42348	−	1.39920i
$357$	−4.49465	+	1.81538i	−0.237882	+	0.0960801i
$358$	9.56863	−	5.52445i	0.505718	−	0.291976i
$359$		−	24.0771i		−	1.27074i	−0.772208	−	0.635369i	$-0.780848\pi$
$359$		−	24.0771i		−	1.27074i	0.772208	−	0.635369i	$-0.219152\pi$
$360$	−15.9874	+	15.4320i	−0.842608	+	0.813337i
$361$	18.9734			0.998599
$362$	−32.2015	+	18.5916i	−1.69248	+	0.977151i
$363$	8.10304	−	10.3691i	0.425299	−	0.544234i
$364$	15.9561	+	3.36608i	0.836326	+	0.176431i
$365$	4.21074	−	7.29321i	0.220400	−	0.381744i
$366$	−31.0591	−	24.2716i	−1.62349	−	1.26869i
$367$	−0.521413	−	0.903114i	−0.0272175	−	0.0471421i	0.852096	−	0.523386i	$-0.175331\pi$
$367$	−0.521413	−	0.903114i	−0.0272175	−	0.0471421i	−0.879313	+	0.476244i	$0.841998\pi$
$368$	55.9092			2.91447
$369$	10.5821	+	10.9630i	0.550884	+	0.570709i
$370$		−	17.5764i		−	0.913751i
$371$	9.14059	−	5.27732i	0.474556	−	0.273985i
$372$	4.74121	−	1.91496i	0.245820	−	0.0992863i
$373$	9.54401	−	16.5307i	0.494170	−	0.855927i	−0.505808	−	0.862646i	$-0.668805\pi$
$373$	9.54401	−	16.5307i	0.494170	−	0.855927i	0.999977	+	0.00671902i	$0.00213875\pi$
$374$	−15.4123	+	26.6949i	−0.796952	+	1.38036i
$375$	2.40674	−	17.1111i	0.124283	−	0.883614i
$376$	11.4590	+	19.8475i	0.590951	+	1.02356i
$377$	−19.9096	+	6.50268i	−1.02540	+	0.334905i
$378$	−10.7389	+	7.79687i	−0.552352	+	0.401028i
$379$		−	31.1663i		−	1.60090i	−0.599397	−	0.800452i	$-0.704593\pi$
$379$		−	31.1663i		−	1.60090i	0.599397	−	0.800452i	$-0.295407\pi$
$380$	−0.424130	−	0.734615i	−0.0217574	−	0.0376849i
$381$	0.700340	+	0.0985052i	0.0358795	+	0.00504658i
$382$	38.5132	+	22.2356i	1.97051	+	1.13767i
$383$	1.21936	+	0.703997i	0.0623063	+	0.0359726i	0.530830	−	0.847479i	$-0.321880\pi$
$383$	1.21936	+	0.703997i	0.0623063	+	0.0359726i	−0.468523	+	0.883451i	$0.655214\pi$
$384$	−16.9225	+	6.83496i	−0.863572	+	0.348795i
$385$	−4.29324	+	2.47870i	−0.218804	+	0.126326i
$386$	−47.3508			−2.41009
$387$	0.136985	+	0.549934i	0.00696334	+	0.0279547i
$388$			25.4173i			1.29037i
$389$	−0.903187	−	1.56437i	−0.0457934	−	0.0793165i	0.842220	−	0.539134i	$-0.181248\pi$
$389$	−0.903187	−	1.56437i	−0.0457934	−	0.0793165i	−0.888014	+	0.459817i	$0.847915\pi$
$390$	6.24640	−	17.2379i	0.316299	−	0.872874i
$391$	10.5577	−	18.2864i	0.533925	−	0.924785i
$392$	5.58001	+	3.22162i	0.281833	+	0.162717i
$393$	−14.3843	+	18.4069i	−0.725593	+	0.928506i
$394$	−27.5107	−	47.6500i	−1.38597	−	2.40057i
$395$			0.108564i			0.00546245i
$396$	−16.1411	+	56.2438i	−0.811121	+	2.82636i
$397$		−	10.0994i		−	0.506874i	−0.967352	−	0.253437i	$-0.918439\pi$
$397$		−	10.0994i		−	0.506874i	0.967352	−	0.253437i	$-0.0815611\pi$
$398$	1.71061	−	0.987622i	0.0857452	−	0.0495050i
$399$	−0.105831	−	0.262024i	−0.00529817	−	0.0131176i
$400$	−13.6296	+	23.6071i	−0.681479	+	1.18036i
$401$	4.19753	+	2.42345i	0.209615	+	0.121021i	0.601132	−	0.799150i	$-0.294716\pi$
$401$	4.19753	+	2.42345i	0.209615	+	0.121021i	−0.391518	+	0.920171i	$0.628050\pi$
$402$	−14.1735	−	1.99355i	−0.706911	−	0.0994294i
$403$	−1.57209	+	1.75136i	−0.0783114	+	0.0872415i
$404$	−80.4799			−4.00402
$405$	4.85305	+	9.13700i	0.241150	+	0.454021i
$406$	−14.8360			−0.736301
$407$	−12.9088	−	22.3588i	−0.639867	−	1.10828i
$408$	4.35022	−	30.9287i	0.215368	−	1.53120i
$409$	23.9068	+	13.8026i	1.18212	+	0.682495i	0.956503	−	0.291722i	$-0.0942283\pi$
$409$	23.9068	+	13.8026i	1.18212	+	0.682495i	0.225613	+	0.974217i	$0.427562\pi$
$410$	−12.9138	−	7.45576i	−0.637765	−	0.368214i
$411$	17.7677	−	7.17632i	0.876414	−	0.353982i
$412$	4.88820	+	8.46662i	0.240824	+	0.417120i
$413$	9.70436			0.477520
$414$	15.9463	−	55.5650i	0.783717	−	2.73087i
$415$	−14.2948			−0.701706
$416$	−14.5454	+	16.2041i	−0.713149	+	0.794471i
$417$	23.5329	−	30.1138i	1.15241	−	1.47468i
$418$	−1.55623	−	0.898490i	−0.0761177	−	0.0439466i
$419$	1.59313	−	2.75937i	0.0778293	−	0.134804i	−0.824484	−	0.565885i	$-0.808534\pi$
$419$	1.59313	−	2.75937i	0.0778293	−	0.134804i	0.902313	+	0.431081i	$0.141868\pi$
$420$	5.54495	−	7.09560i	0.270566	−	0.346230i
$421$	−11.5043	+	6.64203i	−0.560687	+	0.323713i	−0.753421	−	0.657538i	$-0.771598\pi$
$421$	−11.5043	+	6.64203i	−0.560687	+	0.323713i	0.192734	+	0.981251i	$0.438264\pi$
$422$			71.9631i			3.50311i
$423$	10.3543	−	2.57919i	0.503443	−	0.125404i
$424$			68.0062i			3.30267i
$425$	5.14751	+	8.91576i	0.249691	+	0.432478i
$426$	19.3020	+	47.7894i	0.935186	+	2.31540i
$427$	7.71696	+	4.45539i	0.373450	+	0.215611i
$428$	−38.7945	+	67.1940i	−1.87520	+	3.24795i
$429$	−4.71424	−	26.5158i	−0.227606	−	1.28019i
$430$	−0.277315	−	0.480324i	−0.0133733	−	0.0231633i
$431$		−	33.8087i		−	1.62851i	−0.580510	−	0.814253i	$-0.697147\pi$
$431$		−	33.8087i		−	1.62851i	0.580510	−	0.814253i	$-0.302853\pi$
$432$	−4.01219	−	38.2954i	−0.193036	−	1.84249i
$433$	−20.1885			−0.970197			−0.485099	−	0.874460i	$-0.661216\pi$
$433$	−20.1885			−0.970197			−0.485099	+	0.874460i	$0.661216\pi$
$434$	−1.44372	+	0.833530i	−0.0693006	+	0.0400107i
$435$	−1.61095	+	11.4533i	−0.0772390	+	0.549144i
$436$	12.2736	+	7.08615i	0.587797	+	0.339365i
$437$	1.06604	+	0.615479i	0.0509957	+	0.0294424i
$438$	12.1367	+	30.0488i	0.579912	+	1.43579i
$439$	−10.7563	−	18.6304i	−0.513369	−	0.889182i	−0.999880	−	0.0155072i	$-0.995064\pi$
$439$	−10.7563	−	18.6304i	−0.513369	−	0.889182i	0.486510	−	0.873675i	$-0.338270\pi$
$440$		−	31.9418i		−	1.52276i
$441$	2.15848	−	2.08350i	0.102785	−	0.0992142i
$442$	8.00129	+	24.4979i	0.380583	+	1.16525i
$443$	16.1478	+	27.9687i	0.767203	+	1.32883i	0.939074	+	0.343715i	$0.111685\pi$
$443$	16.1478	+	27.9687i	0.767203	+	1.32883i	−0.171871	+	0.985119i	$0.554981\pi$
$444$	36.9532	+	28.8776i	1.75372	+	1.37047i
$445$	6.70993	−	11.6219i	0.318081	−	0.550933i
$446$	−17.2126	+	29.8131i	−0.815041	+	1.41169i
$447$	23.5340	+	18.3910i	1.11312	+	0.869864i
$448$	−0.522690	+	0.301775i	−0.0246948	+	0.0142576i
$449$		−	17.2086i		−	0.812123i	−0.913846	−	0.406062i	$-0.866902\pi$
$449$		−	17.2086i		−	0.812123i	0.913846	−	0.406062i	$-0.133098\pi$
$450$	19.5744	+	20.2788i	0.922746	+	0.955954i
$451$	−21.9033			−1.03139
$452$	−12.0102	−	20.8022i	−0.564911	−	0.978454i
$453$	7.54840	−	3.04878i	0.354655	−	0.143244i
$454$	−18.9736	+	32.8632i	−0.890475	+	1.54235i
$455$	−0.855538	+	4.05547i	−0.0401082	+	0.190123i
$456$	1.80305	+	0.253604i	0.0844353	+	0.0118761i
$457$	29.3541	−	16.9476i	1.37313	−	0.792775i	0.381806	−	0.924242i	$-0.375302\pi$
$457$	29.3541	−	16.9476i	1.37313	−	0.792775i	0.991321	+	0.131467i	$0.0419688\pi$
$458$	39.0759			1.82590
$459$	−13.2831	−	5.91927i	−0.620000	−	0.276288i
$460$			39.2267i			1.82896i
$461$	19.4282	−	11.2169i	0.904864	−	0.522423i	0.0260886	−	0.999660i	$-0.491695\pi$
$461$	19.4282	−	11.2169i	0.904864	−	0.522423i	0.878775	+	0.477236i	$0.158361\pi$
$462$	2.65708	−	18.8910i	0.123619	−	0.878888i
$463$	0.887929	+	0.512646i	0.0412656	+	0.0238247i	0.520491	−	0.853867i	$-0.325749\pi$
$463$	0.887929	+	0.512646i	0.0412656	+	0.0238247i	−0.479225	+	0.877692i	$0.659082\pi$
$464$	21.5231	−	37.2792i	0.999186	−	1.73064i
$465$	0.486715	+	1.20505i	0.0225709	+	0.0558827i
$466$	38.7796	−	22.3894i	1.79643	−	1.03717i
$467$	3.28554			0.152037			0.0760184	−	0.997106i	$-0.475779\pi$
$467$	3.28554			0.152037			0.0760184	+	0.997106i	$0.475779\pi$
$468$	25.9789	+	41.4541i	1.20087	+	1.91622i
$469$	3.23559			0.149406
$470$	−9.04365	+	5.22135i	−0.417152	+	0.240843i
$471$	3.46935	−	4.43955i	0.159859	−	0.204564i
$472$	−31.2638	+	54.1505i	−1.43903	+	2.49248i
$473$	−0.705541	−	0.407344i	−0.0324408	−	0.0187297i
$474$	−0.329181	−	0.257243i	−0.0151198	−	0.0118156i
$475$	−0.519761	+	0.300084i	−0.0238483	+	0.0137688i
$476$			12.6578i			0.580171i
$477$	30.4354	+	8.73448i	1.39354	+	0.399924i
$478$	65.3365			2.98842
$479$	−18.6166	+	10.7483i	−0.850616	+	0.491103i	−0.860859	−	0.508844i	$-0.830073\pi$
$479$	−18.6166	+	10.7483i	−0.850616	+	0.491103i	0.0102426	+	0.999948i	$0.496740\pi$
$480$	4.50323	+	11.1494i	0.205543	+	0.508899i
$481$	−21.1205	−	4.45556i	−0.963011	−	0.203156i
$482$	34.6392	−	59.9968i	1.57777	−	2.73278i
$483$	−1.82014	+	12.9406i	−0.0828193	+	0.588818i
$484$	−17.1816	−	29.7594i	−0.780982	−	1.35270i
$485$	−6.46018			−0.293341
$486$	−39.2040	−	6.93503i	−1.77833	−	0.314579i
$487$			14.4199i			0.653430i	0.945123	+	0.326715i	$0.105942\pi$
$487$			14.4199i			0.653430i	−0.945123	+	0.326715i	$0.894058\pi$
$488$	−49.7223	+	28.7072i	−2.25082	+	1.29951i
$489$	−2.88068	+	20.4807i	−0.130269	+	0.926170i
$490$	−1.46795	+	2.54257i	−0.0663153	+	0.114861i
$491$	4.93973	−	8.55586i	0.222927	−	0.386120i	−0.732769	−	0.680478i	$-0.761772\pi$
$491$	4.93973	−	8.55586i	0.222927	−	0.386120i	0.955695	+	0.294357i	$0.0951056\pi$
$492$	36.8923	−	14.9007i	1.66323	−	0.671776i
$493$	−8.12869	−	14.0793i	−0.366098	−	0.634100i
$494$	−1.42815	+	0.466450i	−0.0642556	+	0.0209866i
$495$	−14.2952	−	4.10249i	−0.642520	−	0.184393i
$496$		−	4.83692i		−	0.217184i
$497$	−5.82556	−	10.0902i	−0.261312	−	0.452606i
$498$	33.8717	−	43.3439i	1.51783	−	1.94229i
$499$	−6.46598	−	3.73314i	−0.289457	−	0.167118i	0.348240	−	0.937405i	$-0.386779\pi$
$499$	−6.46598	−	3.73314i	−0.289457	−	0.167118i	−0.637697	+	0.770287i	$0.720113\pi$
$500$	−39.0762	−	22.5606i	−1.74754	−	1.00894i
$501$	−2.60849	−	2.03844i	−0.116539	−	0.0910707i
$502$	−41.8773	+	24.1779i	−1.86908	+	1.07911i
$503$	−26.1876			−1.16765			−0.583824	−	0.811880i	$-0.698444\pi$
$503$	−26.1876			−1.16765			−0.583824	+	0.811880i	$0.698444\pi$
$504$	4.67215	+	18.7566i	0.208114	+	0.835485i
$505$		−	20.4551i		−	0.910240i
$506$	41.5495	+	71.9659i	1.84710	+	3.19927i
$507$	−19.1303	−	11.8757i	−0.849606	−	0.527418i
$508$	0.923384	−	1.59935i	0.0409685	−	0.0709596i
$509$	17.9288	+	10.3512i	0.794678	+	0.458808i	0.841607	−	0.540091i	$-0.181610\pi$
$509$	17.9288	+	10.3512i	0.794678	+	0.458808i	−0.0469287	+	0.998898i	$0.514943\pi$
$510$	14.0928	+	1.98221i	0.624041	+	0.0877735i
$511$	−3.66298	−	6.34446i	−0.162041	−	0.280662i
$512$			50.7401i			2.24241i
$513$	0.345075	−	0.774361i	0.0152354	−	0.0341889i
$514$			46.0750i			2.03228i
$515$	−2.15191	+	1.24241i	−0.0948245	+	0.0547470i
$516$	1.46547	+	0.206124i	0.0645138	+	0.00907409i
$517$	−7.66957	+	13.2841i	−0.337307	+	0.584233i
$518$	−13.2414	−	7.64495i	−0.581796	−	0.335900i
$519$	−4.49495	−	11.1289i	−0.197307	−	0.488506i
$520$	−19.8733	−	17.8391i	−0.871504	−	0.782296i
$521$	35.0560			1.53583			0.767915	−	0.640552i	$-0.221294\pi$
$521$	35.0560			1.53583			0.767915	+	0.640552i	$0.221294\pi$
$522$	−30.9109	−	32.0233i	−1.35293	−	1.40162i
$523$	7.62353			0.333354			0.166677	−	0.986012i	$-0.446696\pi$
$523$	7.62353			0.333354			0.166677	+	0.986012i	$0.446696\pi$
$524$	30.5004	+	52.8282i	1.33242	+	2.30781i
$525$	−5.02034	−	3.92321i	−0.219105	−	0.171223i
$526$	−43.5528	−	25.1452i	−1.89899	−	1.09638i
$527$	−1.58203	−	0.913384i	−0.0689142	−	0.0397877i
$528$	43.6134	+	34.0823i	1.89803	+	1.48324i
$529$	−16.9621	−	29.3792i	−0.737482	−	1.27736i
$530$	−30.9874			−1.34601
$531$	20.2190	+	20.9467i	0.877431	+	0.909008i
$532$	−0.737913			−0.0319926
$533$	−12.2327	+	13.6277i	−0.529859	+	0.590280i
$534$	19.3401	+	47.8837i	0.836929	+	2.07213i
$535$	−17.0783	−	9.86017i	−0.738360	−	0.426292i
$536$	−10.4238	+	18.0546i	−0.450241	+	0.779841i
$537$	−7.42007	−	1.04366i	−0.320200	−	0.0450372i
$538$	27.2219	−	15.7166i	1.17362	−	0.677590i
$539$			4.31251i			0.185753i
$540$	26.8686	−	2.81501i	1.15624	−	0.121139i
$541$			7.27899i			0.312948i	0.987682	+	0.156474i	$0.0500128\pi$
$541$			7.27899i			0.312948i	−0.987682	+	0.156474i	$0.949987\pi$
$542$	−33.8032	−	58.5489i	−1.45197	−	2.51489i
$543$	24.9709	+	3.51225i	1.07161	+	0.150725i
$544$	−14.6374	−	8.45089i	−0.627572	−	0.362329i
$545$	−1.80105	+	3.11950i	−0.0771483	+	0.133625i
$546$	−10.2695	−	12.2036i	−0.439495	−	0.522264i
$547$	1.74129	+	3.01601i	0.0744523	+	0.128955i	0.900848	−	0.434135i	$-0.142946\pi$
$547$	1.74129	+	3.01601i	0.0744523	+	0.128955i	−0.826396	+	0.563090i	$0.809612\pi$
$548$		−	50.0373i		−	2.13749i
$549$	6.46141	+	25.9397i	0.275766	+	1.10708i
$550$	−40.5159			−1.72760
$551$	0.820779	−	0.473877i	0.0349664	−	0.0201878i
$552$	−66.3450	−	51.8462i	−2.82383	−	2.20672i
$553$	0.0817886	+	0.0472206i	0.00347800	+	0.00200803i
$554$	−32.2904	−	18.6429i	−1.37189	−	0.792061i
$555$	−7.33964	+	9.39218i	−0.311551	+	0.398676i
$556$	−49.8988	−	86.4273i	−2.11618	−	3.66533i
$557$		−	24.8255i		−	1.05189i	−0.850518	−	0.525945i	$-0.823712\pi$
$557$		−	24.8255i		−	1.05189i	0.850518	−	0.525945i	$-0.176288\pi$
$558$	−4.80714	−	1.37957i	−0.203502	−	0.0584020i
$559$	−0.647475	+	0.211472i	−0.0273853	+	0.00894433i
$560$	−4.25921	−	7.37717i	−0.179984	−	0.311742i
$561$	19.3832	−	7.82884i	0.818360	−	0.330534i
$562$	0.748785	−	1.29693i	0.0315856	−	0.0547078i
$563$	−8.74727	+	15.1507i	−0.368653	+	0.638527i	−0.989355	−	0.145520i	$-0.953514\pi$
$563$	−8.74727	+	15.1507i	−0.368653	+	0.638527i	0.620702	+	0.784047i	$0.286848\pi$
$564$	3.88095	−	27.5923i	0.163417	−	1.16184i
$565$	5.28718	−	3.05255i	0.222433	−	0.128422i
$566$		−	38.2307i		−	1.60696i
$567$	8.99438	+	0.318066i	0.377728	+	0.0133575i
$568$	75.0710			3.14991
$569$	2.56451	+	4.44187i	0.107510	+	0.186213i	0.914761	−	0.403996i	$-0.132379\pi$
$569$	2.56451	+	4.44187i	0.107510	+	0.186213i	−0.807251	+	0.590208i	$0.799046\pi$
$570$	−0.115556	+	0.821569i	−0.00484012	+	0.0344117i
$571$	−1.91812	+	3.32227i	−0.0802707	+	0.139033i	−0.903366	−	0.428870i	$-0.858912\pi$
$571$	−1.91812	+	3.32227i	−0.0802707	+	0.139033i	0.823095	+	0.567903i	$0.192245\pi$
$572$	−68.8108	−	14.5163i	−2.87712	−	0.606955i
$573$	−11.2948	−	27.9645i	−0.471847	−	1.16823i
$574$	−11.2338	+	6.48586i	−0.468892	+	0.270715i
$575$	27.7540			1.15742
$576$	−1.74040	−	0.499468i	−0.0725167	−	0.0208112i
$577$			3.51179i			0.146198i	0.997325	+	0.0730989i	$0.0232889\pi$
$577$			3.51179i			0.146198i	−0.997325	+	0.0730989i	$0.976711\pi$
$578$	20.2768	−	11.7068i	0.843404	−	0.486940i
$579$	25.3026	+	19.7730i	1.05154	+	0.821739i
$580$	26.1556	+	15.1009i	1.08605	+	0.627033i
$581$	−6.21763	+	10.7693i	−0.257951	+	0.446784i
$582$	15.3074	−	19.5881i	0.634513	−	0.811955i
$583$	−39.4189	+	22.7585i	−1.63256	+	0.942560i
$584$	47.2029			1.95327
$585$	−10.5362	+	6.60290i	−0.435616	+	0.272996i
$586$	29.8734			1.23406
$587$	−2.28029	+	1.31653i	−0.0941178	+	0.0543389i	−0.546320	−	0.837576i	$-0.683972\pi$
$587$	−2.28029	+	1.31653i	−0.0941178	+	0.0543389i	0.452202	+	0.891915i	$0.350638\pi$
$588$	−2.93378	−	7.26366i	−0.120987	−	0.299548i
$589$	0.0532475	−	0.0922273i	0.00219402	−	0.00380016i
$590$	−24.6740	−	14.2455i	−1.01581	−	0.586479i
$591$	−5.19722	+	36.9506i	−0.213785	+	1.51994i
$592$	38.4196	−	22.1816i	1.57904	−	0.911656i
$593$			37.2703i			1.53051i	0.643729	+	0.765253i	$0.277386\pi$
$593$			37.2703i			1.53051i	−0.643729	+	0.765253i	$0.722614\pi$
$594$	46.3118	−	33.6241i	1.90020	−	1.37961i
$595$	−3.21717			−0.131891
$596$	67.5431	−	38.9961i	2.76667	−	1.59734i
$597$	−1.32651	−	0.186578i	−0.0542903	−	0.00763612i
$598$	67.9803	+	14.3411i	2.77992	+	0.586450i
$599$	−5.09848	+	8.83083i	−0.208318	+	0.360818i	−0.951185	−	0.308622i	$-0.900132\pi$
$599$	−5.09848	+	8.83083i	−0.208318	+	0.360818i	0.742867	+	0.669440i	$0.233466\pi$
$600$	38.0652	−	15.3745i	1.55401	−	0.627659i
$601$	15.5005	+	26.8477i	0.632279	+	1.09514i	0.987085	+	0.160199i	$0.0512136\pi$
$601$	15.5005	+	26.8477i	0.632279	+	1.09514i	−0.354806	+	0.934940i	$0.615453\pi$
$602$	−0.482480			−0.0196644
$603$	6.74134	+	6.98395i	0.274529	+	0.284408i
$604$		−	21.2578i		−	0.864969i
$605$	7.56378	−	4.36695i	0.307511	−	0.177542i
$606$	62.0227	+	48.4685i	2.51950	+	1.96890i
$607$	11.0996	−	19.2251i	0.450520	−	0.780324i	−0.547898	−	0.836545i	$-0.684572\pi$
$607$	11.0996	−	19.2251i	0.450520	−	0.780324i	0.998418	+	0.0562213i	$0.0179052\pi$
$608$	0.492661	−	0.853313i	0.0199800	−	0.0346064i
$609$	7.92786	+	6.19533i	0.321253	+	0.251047i
$610$	−13.0806	−	22.6563i	−0.529618	−	0.917325i
$611$	3.98165	+	12.1908i	0.161080	+	0.493188i
$612$	−27.3217	+	26.3726i	−1.10441	+	1.06605i
$613$		−	15.7967i		−	0.638023i	−0.947751	−	0.319011i	$-0.896649\pi$
$613$		−	15.7967i		−	0.638023i	0.947751	−	0.319011i	$-0.103351\pi$
$614$	−20.7790	−	35.9903i	−0.838572	−	1.45245i
$615$	3.78723	+	9.37670i	0.152716	+	0.378105i
$616$	−24.0639	−	13.8933i	−0.969561	−	0.559776i
$617$	−19.4580	−	11.2341i	−0.783350	−	0.452268i	0.0542659	−	0.998527i	$-0.482718\pi$
$617$	−19.4580	−	11.2341i	−0.783350	−	0.452268i	−0.837616	+	0.546259i	$0.816051\pi$
$618$	1.33182	−	9.46878i	0.0535735	−	0.380890i
$619$	−38.6243	+	22.2998i	−1.55244	+	0.896303i	−0.554500	+	0.832184i	$0.687091\pi$
$619$	−38.6243	+	22.2998i	−1.55244	+	0.896303i	−0.997942	+	0.0641194i	$0.979576\pi$
$620$	3.39365			0.136292
$621$	−31.7243	+	23.0330i	−1.27305	+	0.924283i
$622$			36.8016i			1.47561i
$623$	−5.83706	−	10.1101i	−0.233857	−	0.405052i
$624$	45.5627	−	8.10059i	1.82397	−	0.324283i
$625$	−3.46229	+	5.99686i	−0.138492	+	0.239874i
$626$	−35.1737	−	20.3075i	−1.40582	−	0.811652i
$627$	0.456397	+	1.12998i	0.0182267	+	0.0451271i
$628$	−7.35636	−	12.7416i	−0.293551	−	0.508445i
$629$		−	16.7547i		−	0.668054i
$630$	−8.54656	+	2.12889i	−0.340503	+	0.0848171i
$631$		−	2.73870i		−	0.109026i	−0.998513	−	0.0545130i	$-0.982639\pi$
$631$		−	2.73870i		−	0.109026i	0.998513	−	0.0545130i	$-0.0173606\pi$
$632$	−0.526984	+	0.304254i	−0.0209623	+	0.0121026i
$633$	30.0508	−	38.4545i	1.19441	−	1.52843i
$634$	−31.2044	+	54.0477i	−1.23929	+	2.14651i
$635$	0.406497	+	0.234691i	0.0161313	+	0.00931343i
$636$	50.9116	−	65.1491i	2.01878	−	2.58333i
$637$	2.68313	+	2.40849i	0.106310	+	0.0954277i
$638$	63.9806			2.53302
$639$	9.64187	−	33.5972i	0.381426	−	1.32908i
$640$	−12.1127			−0.478798
$641$	4.46795	+	7.73872i	0.176474	+	0.305661i	0.940670	−	0.339322i	$-0.110198\pi$
$641$	4.46795	+	7.73872i	0.176474	+	0.305661i	−0.764197	+	0.644983i	$0.776864\pi$
$642$	70.3646	−	28.4201i	2.77707	−	1.12165i
$643$	−27.1873	−	15.6966i	−1.07216	−	0.619014i	−0.143392	−	0.989666i	$-0.545801\pi$
$643$	−27.1873	−	15.6966i	−1.07216	−	0.619014i	−0.928772	+	0.370652i	$0.879134\pi$
$644$	29.5521	+	17.0619i	1.16452	+	0.672334i
$645$	−0.0523893	+	0.372471i	−0.00206283	+	0.0146660i
$646$	−0.583087	−	1.00994i	−0.0229412	−	0.0397354i
$647$	42.8459			1.68445			0.842223	−	0.539129i	$-0.181246\pi$
$647$	42.8459			1.68445			0.842223	+	0.539129i	$0.181246\pi$
$648$	−30.7513	+	49.1641i	−1.20803	+	1.93135i
$649$	−41.8501			−1.64276
$650$	−22.6277	+	25.2079i	−0.887529	+	0.988737i
$651$	1.11954	+	0.157467i	0.0438783	+	0.00617163i
$652$	46.7712	+	27.0034i	1.83170	+	1.05753i
$653$	11.7810	−	20.4053i	0.461026	−	0.798521i	−0.537986	−	0.842954i	$-0.680815\pi$
$653$	11.7810	−	20.4053i	0.461026	−	0.798521i	0.999012	+	0.0444328i	$0.0141481\pi$
$654$	−5.19118	−	12.8527i	−0.202991	−	0.502580i
$655$	−13.4270	+	7.75211i	−0.524638	+	0.302900i
$656$		−	37.6370i		−	1.46948i
$657$	6.06258	−	21.1251i	0.236524	−	0.824170i
$658$			9.08425i			0.354141i
$659$	−3.50988	−	6.07930i	−0.136726	−	0.236816i	0.789530	−	0.613712i	$-0.210325\pi$
$659$	−3.50988	−	6.07930i	−0.136726	−	0.236816i	−0.926255	+	0.376897i	$0.876991\pi$
$660$	−23.9126	+	30.5998i	−0.930799	+	1.19110i
$661$	−0.939214	−	0.542255i	−0.0365312	−	0.0210913i	0.481623	−	0.876378i	$-0.340047\pi$
$661$	−0.939214	−	0.542255i	−0.0365312	−	0.0210913i	−0.518154	+	0.855287i	$0.673381\pi$
$662$	44.6627	−	77.3581i	1.73587	−	3.00661i
$663$	5.95440	−	16.4321i	0.231250	−	0.638168i
$664$	−40.0617	−	69.3890i	−1.55470	−	2.69281i
$665$		−	0.187551i		−	0.00727291i
$666$	−11.0871	−	44.5096i	−0.429615	−	1.72471i
$667$	−43.8277			−1.69702
$668$	−7.48641	+	4.32228i	−0.289658	+	0.167234i
$669$	21.6474	−	8.74333i	0.836936	−	0.338036i
$670$	−8.22670	−	4.74969i	−0.317825	−	0.183496i
$671$	−33.2795	−	19.2139i	−1.28474	−	0.741745i
$672$	10.3583	+	1.45693i	0.399581	+	0.0562024i
$673$	8.21824	+	14.2344i	0.316790	+	0.548696i	0.979816	−	0.199900i	$-0.0640617\pi$
$673$	8.21824	+	14.2344i	0.316790	+	0.548696i	−0.663027	+	0.748596i	$0.730728\pi$
$674$		−	7.60128i		−	0.292790i
$675$	−1.99170	−	19.0103i	−0.0766605	−	0.731707i
$676$	−47.4616	+	34.7051i	−1.82545	+	1.33481i
$677$	10.6295	+	18.4108i	0.408525	+	0.707586i	0.994725	−	0.102580i	$-0.0327099\pi$
$677$	10.6295	+	18.4108i	0.408525	+	0.707586i	−0.586200	+	0.810167i	$0.699377\pi$
$678$	−3.27223	+	23.2645i	−0.125669	+	0.893468i
$679$	−2.80990	+	4.86688i	−0.107834	+	0.186774i
$680$	10.3645	−	17.9519i	0.397461	−	0.688422i
$681$	23.8620	−	9.63783i	0.914395	−	0.369322i
$682$	6.22604	−	3.59461i	0.238407	−	0.137645i
$683$		−	14.4868i		−	0.554323i	−0.960823	−	0.277161i	$-0.910606\pi$
$683$		−	14.4868i		−	0.554323i	0.960823	−	0.277161i	$-0.0893936\pi$
$684$	−1.53744	−	1.59277i	−0.0587855	−	0.0609010i
$685$	12.7177			0.485918
$686$	1.27699	+	2.21181i	0.0487557	+	0.0844474i
$687$	−20.8808	−	16.3175i	−0.796650	−	0.622553i
$688$	0.699949	−	1.21235i	0.0266853	−	0.0462203i
$689$	−7.85522	+	37.2358i	−0.299260	+	1.41857i
$690$	23.6240	−	30.2305i	0.899352	−	1.15086i
$691$	−17.4733	+	10.0882i	−0.664715	+	0.383774i	−0.794071	−	0.607825i	$-0.792042\pi$
$691$	−17.4733	+	10.0882i	−0.664715	+	0.383774i	0.129356	+	0.991598i	$0.458709\pi$
$692$	−31.3413			−1.19142
$693$	−9.30846	+	8.98511i	−0.353599	+	0.341316i
$694$			3.57183i			0.135585i
$695$	21.9667	−	12.6825i	0.833246	−	0.481075i
$696$	−60.1106	+	24.2785i	−2.27849	+	0.920276i
$697$	−12.3101	−	7.10722i	−0.466277	−	0.269205i
$698$	−22.1883	+	38.4313i	−0.839841	+	1.45465i
$699$	−30.0720	−	4.22972i	−1.13743	−	0.159983i
$700$	−14.4085	+	8.31873i	−0.544589	+	0.314419i
$701$	18.2309			0.688571			0.344285	−	0.938865i	$-0.388121\pi$
$701$	18.2309			0.688571			0.344285	+	0.938865i	$0.388121\pi$
$702$	4.94457	−	47.5927i	0.186621	−	1.79627i
$703$	0.976747			0.0368387
$704$	2.25411	−	1.30141i	0.0849549	−	0.0490487i
$705$	7.01297	+	0.986397i	0.264124	+	0.0371499i
$706$	−28.9990	+	50.2278i	−1.09139	+	1.89035i
$707$	−15.4102	−	8.89708i	−0.579560	−	0.334609i
$708$	70.4892	−	28.4704i	2.64915	−	1.06998i
$709$	32.6538	−	18.8527i	1.22634	−	0.708027i	0.260077	−	0.965588i	$-0.416252\pi$
$709$	32.6538	−	18.8527i	1.22634	−	0.708027i	0.966262	+	0.257561i	$0.0829187\pi$
$710$			34.2066i			1.28375i
$711$	0.0684816	+	0.274923i	0.00256826	+	0.0103104i
$712$	75.2192			2.81896
$713$	−4.26494	+	2.46236i	−0.159723	+	0.0922162i
$714$	7.62310	−	9.75491i	0.285287	−	0.365068i
$715$	3.68951	−	17.4892i	0.137980	−	0.654060i
$716$	−9.78320	+	16.9450i	−0.365615	+	0.633264i
$717$	−34.9135	−	27.2836i	−1.30387	−	1.01893i
$718$	30.7462	+	53.2540i	1.14744	+	1.98742i
$719$	27.2892			1.01771			0.508857	−	0.860851i	$-0.330068\pi$
$719$	27.2892			1.01771			0.508857	+	0.860851i	$0.330068\pi$
$720$	7.04941	−	24.5637i	0.262716	−	0.915436i
$721$			2.16157i			0.0805011i
$722$	−41.9656	+	24.2288i	−1.56180	+	0.901704i
$723$	−43.5638	+	17.5953i	−1.62015	+	0.654377i
$724$	32.9236	−	57.0254i	1.22360	−	2.11933i
$725$	10.6843	−	18.5058i	0.396807	−	0.687289i
$726$	−4.68121	+	33.2819i	−0.173736	+	1.23521i
$727$	−4.07151	−	7.05206i	−0.151004	−	0.261546i	0.780593	−	0.625040i	$-0.214917\pi$
$727$	−4.07151	−	7.05206i	−0.151004	−	0.261546i	−0.931597	+	0.363493i	$0.881584\pi$
$728$	−22.0834	+	7.21268i	−0.818466	+	0.267320i
$729$	18.0532	+	20.0769i	0.668638	+	0.743588i
$730$			21.5083i			0.796058i
$731$	−0.264351	−	0.457870i	−0.00977739	−	0.0169349i
$732$	69.1245	+	9.72260i	2.55492	+	0.359358i
$733$	16.1434	+	9.32039i	0.596270	+	0.344257i	0.767573	−	0.640962i	$-0.221464\pi$
$733$	16.1434	+	9.32039i	0.596270	+	0.344257i	−0.171303	+	0.985218i	$0.554798\pi$
$734$	2.30654	+	1.33168i	0.0851358	+	0.0491532i
$735$	1.84616	−	0.745661i	0.0680967	−	0.0275041i
$736$	−39.4604	+	22.7825i	−1.45453	+	0.839773i
$737$	−13.9535			−0.513984
$738$	−37.4053	−	10.7347i	−1.37691	−	0.395151i
$739$		−	12.5524i		−	0.461747i	−0.972984	−	0.230873i	$-0.925842\pi$
$739$		−	12.5524i		−	0.461747i	0.972984	−	0.230873i	$-0.0741583\pi$
$740$	15.5629	+	26.9557i	0.572104	+	0.990913i
$741$	0.957937	+	0.347123i	0.0351907	+	0.0127519i
$742$	−13.4782	+	23.3449i	−0.494800	+	0.857018i
$743$	12.5678	+	7.25604i	0.461069	+	0.266198i	0.712494	−	0.701679i	$-0.247566\pi$
$743$	12.5678	+	7.25604i	0.461069	+	0.266198i	−0.251425	+	0.967877i	$0.580899\pi$
$744$	−4.48541	+	5.73976i	−0.164443	+	0.210430i
$745$	9.91140	+	17.1671i	0.363126	+	0.628952i
$746$			48.7504i			1.78488i
$747$	−36.1997	+	9.01710i	−1.32448	+	0.329918i
$748$		−	54.5871i		−	1.99590i
$749$	−14.8567	+	8.57749i	−0.542850	+	0.313415i
$750$	16.5275	+	40.9200i	0.603499	+	1.49419i
$751$	0.367334	−	0.636241i	0.0134042	−	0.0232168i	−0.859245	−	0.511563i	$-0.829067\pi$
$751$	0.367334	−	0.636241i	0.0134042	−	0.0232168i	0.872650	+	0.488347i	$0.162400\pi$
$752$	−22.8264	−	13.1788i	−0.832392	−	0.480582i
$753$	32.4741	+	4.56759i	1.18342	+	0.166452i
$754$	35.7324	−	39.8071i	1.30130	−	1.44969i
$755$	5.40298			0.196635
$756$	9.56594	−	21.4663i	0.347910	−	0.780723i
$757$	17.8325			0.648132			0.324066	−	0.946035i	$-0.394950\pi$
$757$	17.8325			0.648132			0.324066	+	0.946035i	$0.394950\pi$
$758$	39.7991	+	68.9340i	1.44557	+	2.50379i
$759$	7.84938	−	55.8065i	0.284914	−	2.02565i
$760$	1.04654	+	0.604219i	0.0379619	+	0.0219173i
$761$	46.5789	+	26.8924i	1.68848	+	0.974847i	0.955680	+	0.294409i	$0.0951227\pi$
$761$	46.5789	+	26.8924i	1.68848	+	0.974847i	0.732805	+	0.680438i	$0.238211\pi$
$762$	−1.67481	+	0.676453i	−0.0606721	+	0.0245053i
$763$	1.56675	+	2.71370i	0.0567203	+	0.0982424i
$764$	−78.7536			−2.84921
$765$	−6.70297	−	6.94420i	−0.242346	−	0.251068i
$766$	−3.59599			−0.129928
$767$	−23.3728	+	26.0381i	−0.843943	+	0.940181i
$768$	29.9886	−	38.3749i	1.08212	−	1.38474i
$769$	25.4378	+	14.6865i	0.917311	+	0.529610i	0.882776	−	0.469794i	$-0.155672\pi$
$769$	25.4378	+	14.6865i	0.917311	+	0.529610i	0.0345349	+	0.999403i	$0.489005\pi$
$770$	6.33056	−	10.9648i	0.228137	−	0.395146i
$771$	19.2403	−	24.6208i	0.692921	−	0.886697i
$772$	72.6188	−	41.9265i	2.61361	−	1.50897i
$773$		−	8.37904i		−	0.301373i	−0.988582	−	0.150687i	$-0.951852\pi$
$773$		−	8.37904i		−	0.301373i	0.988582	−	0.150687i	$-0.0481484\pi$
$774$	−1.00525	−	1.04142i	−0.0361328	−	0.0374332i
$775$		−	2.40111i		−	0.0862502i
$776$	−18.1049	−	31.3585i	−0.649926	−	1.12571i
$777$	3.88333	+	9.61464i	0.139314	+	0.344923i
$778$	3.99536	+	2.30672i	0.143241	+	0.0827000i
$779$	0.414329	−	0.717639i	0.0148449	−	0.0257121i
$780$	5.68350	+	31.9675i	0.203502	+	1.14462i
$781$	25.1228	+	43.5139i	0.898964	+	1.55705i
$782$			53.9282i			1.92847i
$783$	3.14519	+	30.0201i	0.112400	+	1.07283i
$784$	−7.41029			−0.264653
$785$	3.23846	−	1.86972i	0.115586	−	0.0667333i
$786$	8.30999	−	59.0813i	0.296407	−	2.10736i
$787$	2.93477	+	1.69439i	0.104613	+	0.0603984i	0.551394	−	0.834245i	$-0.314096\pi$
$787$	2.93477	+	1.69439i	0.104613	+	0.0603984i	−0.446781	+	0.894644i	$0.647430\pi$
$788$	84.3830	+	48.7185i	3.00602	+	1.73553i
$789$	12.7728	+	31.6237i	0.454722	+	1.12584i
$790$	−0.138635	−	0.240123i	−0.00493242	−	0.00854321i
$791$		−	5.31091i		−	0.188834i
$792$	−20.1487	−	80.8880i	−0.715952	−	2.87423i
$793$	−30.5406	+	9.97489i	−1.08453	+	0.354219i
$794$	12.8968	+	22.3380i	0.457692	+	0.792746i
$795$	16.5586	+	12.9399i	0.587272	+	0.458932i
$796$	−1.74897	+	3.02931i	−0.0619907	+	0.107371i
$797$	−25.9840	+	45.0056i	−0.920401	+	1.59418i	−0.121606	+	0.992578i	$0.538804\pi$
$797$	−25.9840	+	45.0056i	−0.920401	+	1.59418i	−0.798795	+	0.601603i	$0.794529\pi$
$798$	0.568681	+	0.444403i	0.0201311	+	0.0157317i
$799$	−8.62088	+	4.97727i	−0.304985	+	0.176083i
$800$		−	22.2157i		−	0.785444i
$801$	9.66089	−	33.6635i	0.341351	−	1.18944i
$802$	−12.3789			−0.437113
$803$	15.7966	+	27.3605i	0.557451	+	0.965533i
$804$	23.5022	−	9.49249i	0.828859	−	0.334774i
$805$	−4.33653	+	7.51109i	−0.152843	+	0.264731i
$806$	1.24070	−	5.88123i	0.0437018	−	0.207157i
$807$	−21.1094	−	2.96911i	−0.743088	−	0.104518i
$808$	99.2917	−	57.3261i	3.49307	−	2.01673i
$809$	−56.1532			−1.97424			−0.987120	−	0.159980i	$-0.948857\pi$
$809$	−56.1532			−1.97424			−0.987120	+	0.159980i	$0.948857\pi$
$810$	−22.4019	−	14.0120i	−0.787123	−	0.492332i
$811$		−	35.1788i		−	1.23529i	−0.786456	−	0.617647i	$-0.788086\pi$
$811$		−	35.1788i		−	1.23529i	0.786456	−	0.617647i	$-0.211914\pi$
$812$	22.7531	−	13.1365i	0.798477	−	0.461001i
$813$	−6.38597	+	45.4022i	−0.223966	+	1.59232i
$814$	57.1039	+	32.9689i	2.00149	+	1.15556i
$815$	−6.86329	+	11.8876i	−0.240411	+	0.416403i
$816$	13.4525	+	33.3066i	0.470931	+	1.16597i
$817$	0.0266924	−	0.0154109i	0.000933848	−	0.000539157i
$818$	−70.5032			−2.46509
$819$	0.391636	+	10.8096i	0.0136849	+	0.377717i
$820$	26.4067			0.922161
$821$	20.7484	−	11.9791i	0.724125	−	0.418074i	−0.0921442	−	0.995746i	$-0.529372\pi$
$821$	20.7484	−	11.9791i	0.724125	−	0.418074i	0.816269	+	0.577672i	$0.196039\pi$
$822$	−30.1346	+	38.5618i	−1.05107	+	1.34500i
$823$	−1.29827	+	2.24866i	−0.0452547	+	0.0783835i	−0.887766	−	0.460296i	$-0.847743\pi$
$823$	−1.29827	+	2.24866i	−0.0452547	+	0.0783835i	0.842511	+	0.538679i	$0.181077\pi$
$824$	−12.0616	−	6.96377i	−0.420186	−	0.242594i
$825$	21.6502	+	16.9189i	0.753765	+	0.589040i
$826$	−21.4642	+	12.3924i	−0.746836	+	0.431186i
$827$		−	25.5476i		−	0.888378i	−0.895933	−	0.444189i	$-0.853492\pi$
$827$		−	25.5476i		−	0.888378i	0.895933	−	0.444189i	$-0.146508\pi$
$828$	24.7440	+	99.3361i	0.859913	+	3.45217i
$829$	28.8562			1.00222			0.501108	−	0.865385i	$-0.332926\pi$
$829$	28.8562			1.00222			0.501108	+	0.865385i	$0.332926\pi$
$830$	31.6175	−	18.2544i	1.09746	−	0.633619i
$831$	9.46985	+	23.4461i	0.328505	+	0.813338i
$832$	0.449189	−	2.12927i	0.0155728	−	0.0738191i
$833$	−1.39933	+	2.42371i	−0.0484839	+	0.0839766i
$834$	−13.5952	+	96.6574i	−0.470763	+	3.34697i
$835$	−1.09857	−	1.90278i	−0.0380176	−	0.0658483i
$836$	3.18225			0.110061
$837$	1.99267	+	2.74459i	0.0688769	+	0.0948669i
$838$			8.13763i			0.281110i
$839$	−29.8486	+	17.2331i	−1.03049	+	0.594952i	−0.917124	−	0.398601i	$-0.869496\pi$
$839$	−29.8486	+	17.2331i	−1.03049	+	0.594952i	−0.113363	+	0.993554i	$0.536162\pi$
$840$	−1.78684	+	12.7039i	−0.0616518	+	0.438325i
$841$	−2.37216	+	4.10871i	−0.0817988	+	0.141680i
$842$	16.9636	−	29.3818i	0.584605	−	1.01257i
$843$	−0.941705	+	0.380353i	−0.0324340	+	0.0131000i
$844$	−63.7194	−	110.365i	−2.19331	−	3.79893i
$845$	−8.82080	−	12.0631i	−0.303445	−	0.414982i
$846$	−19.6082	+	18.9270i	−0.674142	+	0.650724i
$847$		−	7.59773i		−	0.261061i
$848$	−39.1065	−	67.7344i	−1.34292	−	2.32601i
$849$	−15.9646	+	20.4292i	−0.547905	+	0.701127i
$850$	−22.7707	−	13.1467i	−0.781028	−	0.450927i
$851$	−39.1170	−	22.5842i	−1.34091	−	0.774178i
$852$	−71.9172	−	56.2006i	−2.46384	−	1.92540i
$853$	23.7398	−	13.7062i	0.812834	−	0.469290i	−0.0351051	−	0.999384i	$-0.511177\pi$
$853$	23.7398	−	13.7062i	0.812834	−	0.469290i	0.847939	+	0.530094i	$0.177843\pi$
$854$	−22.7580			−0.778762
$855$	0.404825	−	0.390762i	0.0138447	−	0.0133638i
$856$		−	110.534i		−	3.77797i
$857$	28.8553	+	49.9788i	0.985678	+	1.70724i	0.638886	+	0.769301i	$0.279395\pi$
$857$	28.8553	+	49.9788i	0.985678	+	1.70724i	0.346791	+	0.937942i	$0.387271\pi$
$858$	44.2875	+	52.6279i	1.51195	+	1.79669i
$859$	−11.4239	+	19.7868i	−0.389778	+	0.675115i	−0.992419	−	0.122897i	$-0.960782\pi$
$859$	−11.4239	+	19.7868i	−0.389778	+	0.675115i	0.602641	+	0.798012i	$0.294115\pi$
$860$	0.850601	+	0.491095i	0.0290052	+	0.0167462i
$861$	8.71137	+	1.22528i	0.296883	+	0.0417576i
$862$	43.1734	+	74.7784i	1.47049	+	2.54696i
$863$		−	28.0485i		−	0.954782i	−0.878691	−	0.477391i	$-0.841583\pi$
$863$		−	28.0485i		−	0.954782i	0.878691	−	0.477391i	$-0.158417\pi$
$864$	18.4368	+	25.3937i	0.627232	+	0.863913i
$865$		−	7.96585i		−	0.270847i
$866$	44.6532	−	25.7805i	1.51738	−	0.876058i
$867$	−15.7238	−	2.21161i	−0.534009	−	0.0751101i
$868$	1.47609	−	2.55667i	0.0501018	−	0.0867789i
$869$	−0.352714	−	0.203639i	−0.0119650	−	0.00690799i
$870$	−11.0627	−	27.3898i	−0.375059	−	0.928600i
$871$	−7.79286	+	8.68151i	−0.264051	+	0.294162i
$872$	−20.1900			−0.683718
$873$	−16.3595	+	4.07504i	−0.553685	+	0.137919i
$874$	−3.14385			−0.106342
$875$	−4.98817	−	8.63977i	−0.168631	−	0.292078i
$876$	−45.2199	−	35.3377i	−1.52784	−	1.19395i
$877$	−34.6232	−	19.9897i	−1.16914	−	0.675005i	−0.215665	−	0.976467i	$-0.569192\pi$
$877$	−34.6232	−	19.9897i	−1.16914	−	0.675005i	−0.953478	+	0.301462i	$0.902525\pi$
$878$	47.5818	+	27.4714i	1.60581	+	0.927113i
$879$	−15.9633	−	12.4747i	−0.538427	−	0.420761i
$880$	18.3679	+	31.8141i	0.619181	+	1.07245i
$881$	16.2736			0.548273			0.274136	−	0.961691i	$-0.411608\pi$
$881$	16.2736			0.548273			0.274136	+	0.961691i	$0.411608\pi$
$882$	−2.11354	+	7.36467i	−0.0711667	+	0.247981i
$883$	−48.3427			−1.62686			−0.813430	−	0.581663i	$-0.802402\pi$
$883$	−48.3427			−1.62686			−0.813430	+	0.581663i	$0.802402\pi$
$884$	−33.9627	−	30.4862i	−1.14229	−	1.02536i
$885$	7.23616	+	17.9158i	0.243241	+	0.602234i
$886$	−71.4316	−	41.2411i	−2.39979	−	1.38552i
$887$	−10.8823	+	18.8487i	−0.365392	+	0.632877i	−0.988839	−	0.148988i	$-0.952398\pi$
$887$	−10.8823	+	18.8487i	−0.365392	+	0.632877i	0.623447	+	0.781866i	$0.285732\pi$
$888$	−66.1604	−	9.30569i	−2.22020	−	0.312279i
$889$	0.353617	−	0.204161i	0.0118599	−	0.00684734i
$890$			34.2741i			1.14887i
$891$	−38.7883	−	1.37166i	−1.29946	−	0.0459525i
$892$		−	60.9634i		−	2.04120i
$893$	−0.290159	−	0.502570i	−0.00970981	−	0.0168179i
$894$	−75.5380	−	10.6247i	−2.52637	−	0.355342i
$895$	−4.30681	−	2.48654i	−0.143961	−	0.0831158i
$896$	−5.26852	+	9.12534i	−0.176009	+	0.304856i
$897$	−30.3376	−	36.0510i	−1.01294	−	1.20371i
$898$	21.9752	+	38.0622i	0.733322	+	1.27015i
$899$			3.79170i			0.126460i
$900$	−47.9758	−	13.7683i	−1.59919	−	0.458944i
$901$	−29.5388			−0.984082
$902$	48.4460	−	27.9703i	1.61308	−	0.931310i
$903$	0.257820	+	0.201477i	0.00857971	+	0.00670473i
$904$	29.6350	+	17.1098i	0.985645	+	0.569062i
$905$	14.4938	+	8.36801i	0.481791	+	0.278162i
$906$	−12.8024	+	16.3826i	−0.425331	+	0.544275i
$907$	16.2062	+	28.0699i	0.538117	+	0.932045i	0.999005	+	0.0445876i	$0.0141974\pi$
$907$	16.2062	+	28.0699i	0.538117	+	0.932045i	−0.460889	+	0.887458i	$0.652469\pi$
$908$		−	67.2003i		−	2.23012i
$909$	−12.9030	−	51.7997i	−0.427964	−	1.71809i
$910$	−3.28650	−	10.0624i	−0.108947	−	0.333567i
$911$	−13.0115	−	22.5367i	−0.431092	−	0.746673i	0.565876	−	0.824490i	$-0.308538\pi$
$911$	−13.0115	−	22.5367i	−0.431092	−	0.746673i	−0.996968	+	0.0778177i	$0.975205\pi$
$912$	−1.94167	+	0.784238i	−0.0642952	+	0.0259687i
$913$	26.8136	−	46.4425i	0.887401	−	1.53702i
$914$	−43.2839	+	74.9698i	−1.43170	+	2.47978i
$915$	−2.47114	+	17.5690i	−0.0816932	+	0.580813i
$916$	−59.9282	+	34.5996i	−1.98008	+	1.14320i
$917$			13.4873i			0.445390i
$918$	36.9385	−	3.87003i	1.21915	−	0.127730i
$919$	−11.2845			−0.372242			−0.186121	−	0.982527i	$-0.559592\pi$
$919$	−11.2845			−0.372242			−0.186121	+	0.982527i	$0.559592\pi$
$920$	−27.9413	−	48.3958i	−0.921198	−	1.59556i
$921$	−3.92549	+	27.9089i	−0.129349	+	0.919631i
$922$	−28.6478	+	49.6194i	−0.943464	+	1.63413i
$923$	41.1040	+	8.67127i	1.35296	+	0.285418i
$924$	12.6519	+	31.3246i	0.416218	+	1.03050i
$925$	19.0720	−	11.0112i	0.627082	−	0.362046i
$926$	−2.61858			−0.0860518
$927$	−4.66571	+	4.50363i	−0.153242	+	0.147919i
$928$			35.0819i			1.15162i
$929$	−1.41813	+	0.818756i	−0.0465272	+	0.0268625i	−0.523083	−	0.852282i	$-0.675218\pi$
$929$	−1.41813	+	0.818756i	−0.0465272	+	0.0268625i	0.476556	+	0.879144i	$0.341885\pi$
$930$	−2.61536	−	2.04380i	−0.0857609	−	0.0670190i
$931$	−0.141295	−	0.0815765i	−0.00463075	−	0.00267356i
$932$	−39.6492	+	68.6745i	−1.29875	+	2.24951i
$933$	15.3678	−	19.6654i	0.503120	−	0.643818i
$934$	−7.26700	+	4.19561i	−0.237784	+	0.137284i
$935$	13.8741			0.453731
$936$	−61.5792	−	32.6390i	−2.01278	−	1.06684i
$937$	16.2213			0.529925			0.264963	−	0.964259i	$-0.414640\pi$
$937$	16.2213			0.529925			0.264963	+	0.964259i	$0.414640\pi$
$938$	−7.15651	+	4.13182i	−0.233668	+	0.134909i
$939$	10.3154	+	25.5397i	0.336631	+	0.833455i
$940$	9.24644	−	16.0153i	0.301586	−	0.522362i
$941$	33.0382	+	19.0746i	1.07701	+	0.621814i	0.930089	−	0.367334i	$-0.119729\pi$
$941$	33.0382	+	19.0746i	1.07701	+	0.621814i	0.146924	+	0.989148i	$0.453063\pi$
$942$	−2.00428	+	14.2498i	−0.0653029	+	0.464283i
$943$	−33.1863	+	19.1601i	−1.08069	+	0.623939i
$944$		−	71.9121i		−	2.34054i
$945$	5.45597	+	2.43132i	0.177483	+	0.0790908i
$946$	2.08070			0.0676493
$947$	−46.1284	+	26.6323i	−1.49897	+	0.865433i	−0.999999	−	0.00118454i	$-0.999623\pi$
$947$	−46.1284	+	26.6323i	−1.49897	+	0.865433i	−0.498974	+	0.866617i	$0.666290\pi$
$948$	0.732619	+	0.103045i	0.0237944	+	0.00334676i
$949$	25.8453	+	5.45229i	0.838973	+	0.176989i
$950$	0.766409	−	1.32746i	0.0248656	−	0.0430685i
$951$	39.2441	−	15.8506i	1.27258	−	0.513991i
$952$	−9.01622	−	15.6166i	−0.292218	−	0.506136i
$953$	−1.69168			−0.0547988			−0.0273994	−	0.999625i	$-0.508723\pi$
$953$	−1.69168			−0.0547988			−0.0273994	+	0.999625i	$0.508723\pi$
$954$	−78.4713	+	19.5467i	−2.54060	+	0.632847i
$955$		−	20.0164i		−	0.647714i
$956$	−100.202	+	57.8519i	−3.24078	+	1.87106i
$957$	−34.1889	−	26.7174i	−1.10517	−	0.863651i
$958$	27.4510	−	47.5466i	0.886902	−	1.53616i
$959$	5.53164	−	9.58109i	0.178626	−	0.309390i
$960$	−0.946877	−	0.739949i	−0.0305603	−	0.0238818i
$961$	−15.2870	−	26.4778i	−0.493128	−	0.854123i
$962$	52.4043	−	17.1158i	1.68958	−	0.551835i
$963$	−49.4682	−	14.1966i	−1.59409	−	0.457479i
$964$			122.684i			3.95140i
$965$	10.6562	+	18.4571i	0.343036	+	0.594155i
$966$	−12.4992	−	30.9465i	−0.402156	−	0.995688i
$967$	−27.2380	−	15.7258i	−0.875914	−	0.505709i	−0.00660494	−	0.999978i	$-0.502102\pi$
$967$	−27.2380	−	15.7258i	−0.875914	−	0.505709i	−0.869309	+	0.494269i	$0.835436\pi$
$968$	42.3955	+	24.4770i	1.36264	+	0.786721i
$969$	−0.110154	+	0.783163i	−0.00353867	+	0.0251588i
$970$	14.2887	−	8.24959i	0.458783	−	0.264878i
$971$	27.8056			0.892325			0.446162	−	0.894952i	$-0.352790\pi$
$971$	27.8056			0.892325			0.446162	+	0.894952i	$0.352790\pi$
$972$	66.2652	−	24.0772i	2.12546	−	0.772276i
$973$		−	22.0653i		−	0.707383i
$974$	−18.4141	−	31.8942i	−0.590027	−	1.02196i
$975$	22.6179	−	4.02123i	0.724353	−	0.128783i
$976$	33.0157	−	57.1849i	1.05681	−	1.83044i
$977$	0.788886	+	0.455463i	0.0252387	+	0.0145716i	0.512566	−	0.858648i	$-0.328695\pi$
$977$	0.788886	+	0.455463i	0.0252387	+	0.0145716i	−0.487328	+	0.873219i	$0.662028\pi$
$978$	−19.7821	−	48.9781i	−0.632563	−	1.56615i
$979$	25.1724	+	43.5998i	0.804512	+	1.39346i
$980$		−	5.19917i		−	0.166081i
$981$	−2.59313	+	9.03579i	−0.0827922	+	0.288490i
$982$			25.2319i			0.805183i
$983$	−19.2978	+	11.1416i	−0.615505	+	0.355362i	−0.775117	−	0.631818i	$-0.782309\pi$
$983$	−19.2978	+	11.1416i	−0.615505	+	0.355362i	0.159612	+	0.987180i	$0.448976\pi$
$984$	−34.9019	+	44.6622i	−1.11263	+	1.42378i
$985$	−12.3825	+	21.4471i	−0.394539	+	0.683362i
$986$	35.9583	+	20.7605i	1.14514	+	0.661150i
$987$	3.79346	−	4.85430i	0.120747	−	0.154514i
$988$	1.77725	−	1.97992i	0.0565419	−	0.0629895i
$989$	−1.42531			−0.0453223
$990$	36.8571	−	9.18087i	1.17140	−	0.291787i
$991$	52.9607			1.68235			0.841176	−	0.540762i	$-0.181864\pi$
$991$	52.9607			1.68235			0.841176	+	0.540762i	$0.181864\pi$
$992$	1.97100	+	3.41387i	0.0625793	+	0.108390i
$993$	−56.1698	+	22.6869i	−1.78250	+	0.719946i
$994$	25.7701	+	14.8784i	0.817378	+	0.471913i
$995$	−0.769942	−	0.444526i	−0.0244088	−	0.0140924i
$996$	−13.5682	+	96.4654i	−0.429924	+	3.05662i
$997$	−21.0275	−	36.4208i	−0.665949	−	1.15346i	−0.979027	−	0.203730i	$-0.934694\pi$
$997$	−21.0275	−	36.4208i	−0.665949	−	1.15346i	0.313079	−	0.949727i	$-0.398640\pi$
$998$	19.0687			0.603610
$999$	−12.6621	+	28.4142i	−0.400610	+	0.898985i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.dt.a.337.6	✓	168
9.7	even	3	inner	819.2.dt.a.610.79	yes	168
13.12	even	2	inner	819.2.dt.a.337.79	yes	168
117.25	even	6	inner	819.2.dt.a.610.6	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.dt.a.337.6	✓	168	1.1	even	1	trivial
819.2.dt.a.337.79	yes	168	13.12	even	2	inner
819.2.dt.a.610.6	yes	168	117.25	even	6	inner
819.2.dt.a.610.79	yes	168	9.7	even	3	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.dt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.21181 + 1.27699i) q^{2} +(1.71517 + 0.241244i) q^{3} +(2.26141 - 3.91688i) q^{4} +(0.995531 + 0.574770i) q^{5} +(-4.10170 + 1.65667i) q^{6} +(0.866025 - 0.500000i) q^{7} +6.44325i q^{8} +(2.88360 + 0.827549i) q^{9} +O(q^{10})\)	\(q+(-2.21181 + 1.27699i) q^{2} +(1.71517 + 0.241244i) q^{3} +(2.26141 - 3.91688i) q^{4} +(0.995531 + 0.574770i) q^{5} +(-4.10170 + 1.65667i) q^{6} +(0.866025 - 0.500000i) q^{7} +6.44325i q^{8} +(2.88360 + 0.827549i) q^{9} -2.93590 q^{10} +(-3.73474 + 2.15625i) q^{11} +(4.82363 - 6.17256i) q^{12} +(-0.744244 + 3.52790i) q^{13} +(-1.27699 + 2.21181i) q^{14} +(1.56884 + 1.22599i) q^{15} +(-3.70514 - 6.41750i) q^{16} -2.79866 q^{17} +(-7.43476 + 1.85195i) q^{18} -0.163153i q^{19} +(4.50261 - 2.59958i) q^{20} +(1.60600 - 0.648660i) q^{21} +(5.50703 - 9.53846i) q^{22} +(-3.77241 + 6.53400i) q^{23} +(-1.55440 + 11.0512i) q^{24} +(-1.83928 - 3.18572i) q^{25} +(-2.85897 - 8.75346i) q^{26} +(4.74622 + 2.11504i) q^{27} -4.52282i q^{28} +(2.90449 + 5.03073i) q^{29} +(-5.03557 - 0.708270i) q^{30} +(0.565281 + 0.326365i) q^{31} +(5.23014 + 3.01962i) q^{32} +(-6.92589 + 2.79735i) q^{33} +(6.19011 - 3.57386i) q^{34} +1.14954 q^{35} +(9.76242 - 9.42330i) q^{36} +5.98669i q^{37} +(0.208345 + 0.360864i) q^{38} +(-2.12759 + 5.87140i) q^{39} +(-3.70338 + 6.41445i) q^{40} +(4.39856 + 2.53951i) q^{41} +(-2.72384 + 3.48556i) q^{42} +(0.0944564 + 0.163603i) q^{43} +19.5047i q^{44} +(2.39506 + 2.48126i) q^{45} -19.2693i q^{46} +(3.08036 - 1.77845i) q^{47} +(-4.80676 - 11.9009i) q^{48} +(0.500000 - 0.866025i) q^{49} +(8.13628 + 4.69749i) q^{50} +(-4.80017 - 0.675160i) q^{51} +(12.1353 + 10.8932i) q^{52} +10.5546 q^{53} +(-13.1986 + 1.38281i) q^{54} -4.95740 q^{55} +(3.22162 + 5.58001i) q^{56} +(0.0393597 - 0.279835i) q^{57} +(-12.8484 - 7.41802i) q^{58} +(8.40422 + 4.85218i) q^{59} +(8.34987 - 3.37249i) q^{60} +(4.45539 + 7.71696i) q^{61} -1.66706 q^{62} +(2.91105 - 0.725123i) q^{63} -0.603551 q^{64} +(-2.76865 + 3.08437i) q^{65} +(11.7466 - 15.0315i) q^{66} +(2.80210 + 1.61779i) q^{67} +(-6.32892 + 10.9620i) q^{68} +(-8.04660 + 10.2968i) q^{69} +(-2.54257 + 1.46795i) q^{70} -11.6511i q^{71} +(-5.33210 + 18.5798i) q^{72} -7.32595i q^{73} +(-7.64495 - 13.2414i) q^{74} +(-2.38613 - 5.90777i) q^{75} +(-0.639051 - 0.368956i) q^{76} +(-2.15625 + 3.73474i) q^{77} +(-2.79190 - 15.7034i) q^{78} +(0.0472206 + 0.0817886i) q^{79} -8.51842i q^{80} +(7.63033 + 4.77264i) q^{81} -12.9717 q^{82} +(-10.7693 + 6.21763i) q^{83} +(1.09110 - 7.75740i) q^{84} +(-2.78615 - 1.60859i) q^{85} +(-0.417840 - 0.241240i) q^{86} +(3.76806 + 9.32924i) q^{87} +(-13.8933 - 24.0639i) q^{88} -11.6741i q^{89} +(-8.46598 - 2.42960i) q^{90} +(1.11942 + 3.42738i) q^{91} +(17.0619 + 29.5521i) q^{92} +(0.890818 + 0.696142i) q^{93} +(-4.54212 + 7.86719i) q^{94} +(0.0937755 - 0.162424i) q^{95} +(8.24210 + 6.44090i) q^{96} +(-4.86688 + 2.80990i) q^{97} +2.55398i q^{98} +(-12.5539 + 3.12710i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 84 q^{4} - 8 q^{9}+O(q^{10}) \) 168 * q + 84 * q^4 - 8 * q^9	\( 168 q + 84 q^{4} - 8 q^{9} - 24 q^{12} + 8 q^{14} - 84 q^{16} - 32 q^{23} + 84 q^{25} - 8 q^{26} + 48 q^{27} + 4 q^{29} + 80 q^{30} - 32 q^{35} + 4 q^{36} + 24 q^{38} + 24 q^{39} + 4 q^{48} + 84 q^{49} + 64 q^{51} + 18 q^{52} - 48 q^{53} - 24 q^{56} + 24 q^{62} - 240 q^{64} - 22 q^{65} - 132 q^{66} - 156 q^{68} - 52 q^{69} + 84 q^{74} - 60 q^{75} - 16 q^{77} - 148 q^{78} + 12 q^{79} - 8 q^{81} - 24 q^{82} + 88 q^{87} + 24 q^{88} - 164 q^{90} + 12 q^{91} + 128 q^{92} - 60 q^{94} - 96 q^{95}+O(q^{100}) \) 168 * q + 84 * q^4 - 8 * q^9 - 24 * q^12 + 8 * q^14 - 84 * q^16 - 32 * q^23 + 84 * q^25 - 8 * q^26 + 48 * q^27 + 4 * q^29 + 80 * q^30 - 32 * q^35 + 4 * q^36 + 24 * q^38 + 24 * q^39 + 4 * q^48 + 84 * q^49 + 64 * q^51 + 18 * q^52 - 48 * q^53 - 24 * q^56 + 24 * q^62 - 240 * q^64 - 22 * q^65 - 132 * q^66 - 156 * q^68 - 52 * q^69 + 84 * q^74 - 60 * q^75 - 16 * q^77 - 148 * q^78 + 12 * q^79 - 8 * q^81 - 24 * q^82 + 88 * q^87 + 24 * q^88 - 164 * q^90 + 12 * q^91 + 128 * q^92 - 60 * q^94 - 96 * q^95

Introduction

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