LMFDB - Embedded newform 672.2.bs.a.155.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(155,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1, 4, 0]))

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

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

chi := DirichletCharacter("672.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bs (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			155.14
Character	$\chi$	$=$	672.155
Dual form			672.2.bs.a.659.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.868232 - 1.11632i) q^{2} +(-1.73050 + 0.0733671i) q^{3} +(-0.492347 + 1.93845i) q^{4} +(-1.63009 + 3.93540i) q^{5} +(1.58437 + 1.86809i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.59141 - 1.13341i) q^{8} +(2.98923 - 0.253923i) q^{9} +O(q^{10})$	\(q+(-0.868232 - 1.11632i) q^{2} +(-1.73050 + 0.0733671i) q^{3} +(-0.492347 + 1.93845i) q^{4} +(-1.63009 + 3.93540i) q^{5} +(1.58437 + 1.86809i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.59141 - 1.13341i) q^{8} +(2.98923 - 0.253923i) q^{9} +(5.80847 - 1.59713i) q^{10} +(-1.91118 + 4.61399i) q^{11} +(0.709787 - 3.39061i) q^{12} +(3.99885 - 1.65638i) q^{13} +(1.40329 + 0.175426i) q^{14} +(2.53214 - 6.92978i) q^{15} +(-3.51519 - 1.90878i) q^{16} +2.12763 q^{17} +(-2.87881 - 3.11648i) q^{18} +(2.22926 + 5.38190i) q^{19} +(-6.82600 - 5.09744i) q^{20} +(1.17177 - 1.27552i) q^{21} +(6.81004 - 1.87252i) q^{22} +(-5.40417 + 5.40417i) q^{23} +(-4.40126 + 2.15148i) q^{24} +(-9.29460 - 9.29460i) q^{25} +(-5.32097 - 3.02588i) q^{26} +(-5.15423 + 0.658725i) q^{27} +(-1.02255 - 1.71883i) q^{28} +(-0.313330 + 0.129786i) q^{29} +(-9.93435 + 3.18997i) q^{30} +1.59660i q^{31} +(0.921182 + 5.58135i) q^{32} +(2.96877 - 8.12471i) q^{33} +(-1.84728 - 2.37512i) q^{34} +(-1.63009 - 3.93540i) q^{35} +(-0.979524 + 5.91950i) q^{36} +(-1.54413 - 0.639601i) q^{37} +(4.07242 - 7.16131i) q^{38} +(-6.79846 + 3.15974i) q^{39} +(0.236168 + 12.0458i) q^{40} +(-0.541581 - 0.541581i) q^{41} +(-2.44126 - 0.200619i) q^{42} +(-1.22767 - 0.508517i) q^{43} +(-8.00303 - 5.97641i) q^{44} +(-3.87345 + 12.1777i) q^{45} +(10.7249 + 1.34072i) q^{46} -7.60088i q^{47} +(6.22306 + 3.04524i) q^{48} -1.00000i q^{49} +(-2.30590 + 18.4456i) q^{50} +(-3.68186 + 0.156098i) q^{51} +(1.24198 + 8.56708i) q^{52} +(-6.41413 - 2.65682i) q^{53} +(5.21041 + 5.18185i) q^{54} +(-15.0425 - 15.0425i) q^{55} +(-1.03096 + 2.63384i) q^{56} +(-4.25258 - 9.14981i) q^{57} +(0.416926 + 0.237093i) q^{58} +(8.13626 + 3.37015i) q^{59} +(12.1864 + 8.32030i) q^{60} +(0.969280 + 2.34005i) q^{61} +(1.78232 - 1.38622i) q^{62} +(-1.93416 + 2.29326i) q^{63} +(5.43078 - 5.87424i) q^{64} +18.4371i q^{65} +(-11.6474 + 3.74003i) q^{66} +(1.45557 - 0.602916i) q^{67} +(-1.04753 + 4.12431i) q^{68} +(8.95540 - 9.74838i) q^{69} +(-2.97787 + 5.23655i) q^{70} +(-3.18672 - 3.18672i) q^{71} +(7.45852 - 4.04604i) q^{72} +(6.05729 - 6.05729i) q^{73} +(0.626666 + 2.27907i) q^{74} +(16.7662 + 15.4024i) q^{75} +(-11.5301 + 1.67154i) q^{76} +(-1.91118 - 4.61399i) q^{77} +(9.42992 + 4.84589i) q^{78} -6.59357 q^{79} +(13.2419 - 10.7222i) q^{80} +(8.87105 - 1.51807i) q^{81} +(-0.134361 + 1.07480i) q^{82} +(0.569240 - 0.235787i) q^{83} +(1.89562 + 2.89941i) q^{84} +(-3.46824 + 8.37308i) q^{85} +(0.498233 + 1.81198i) q^{86} +(0.532695 - 0.247582i) q^{87} +(0.276892 + 14.1229i) q^{88} +(-5.79385 + 5.79385i) q^{89} +(16.9573 - 6.24909i) q^{90} +(-1.65638 + 3.99885i) q^{91} +(-7.81499 - 13.1364i) q^{92} +(-0.117138 - 2.76291i) q^{93} +(-8.48503 + 6.59932i) q^{94} -24.8138 q^{95} +(-2.00359 - 9.59091i) q^{96} +11.6357 q^{97} +(-1.11632 + 0.868232i) q^{98} +(-4.54136 + 14.2776i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 16 q^{4}+O(q^{10}) $ 192 * q - 16 * q^4	$ 192 q - 16 q^{4} + 8 q^{10} + 16 q^{16} + 16 q^{22} + 24 q^{27} - 84 q^{30} + 40 q^{36} + 32 q^{37} + 24 q^{39} - 96 q^{46} - 72 q^{48} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 28 q^{60} - 16 q^{61} - 64 q^{64} - 12 q^{66} - 32 q^{67} + 56 q^{69} - 24 q^{70} + 60 q^{72} + 80 q^{75} - 56 q^{76} + 100 q^{78} - 32 q^{79} - 120 q^{82} - 56 q^{87} + 40 q^{88} + 60 q^{90} - 80 q^{93} + 216 q^{94} + 96 q^{96} - 64 q^{99}+O(q^{100}) $ 192 * q - 16 * q^4 + 8 * q^10 + 16 * q^16 + 16 * q^22 + 24 * q^27 - 84 * q^30 + 40 * q^36 + 32 * q^37 + 24 * q^39 - 96 * q^46 - 72 * q^48 + 16 * q^52 - 32 * q^55 - 72 * q^58 - 28 * q^60 - 16 * q^61 - 64 * q^64 - 12 * q^66 - 32 * q^67 + 56 * q^69 - 24 * q^70 + 60 * q^72 + 80 * q^75 - 56 * q^76 + 100 * q^78 - 32 * q^79 - 120 * q^82 - 56 * q^87 + 40 * q^88 + 60 * q^90 - 80 * q^93 + 216 * q^94 + 96 * q^96 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$e\left(\frac{1}{8}\right)$	$-1$	$1$

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 $

$2$	−0.868232	−	1.11632i	−0.613933	−	0.789358i
$2$	−0.868232	−	1.11632i	−0.613933	−	0.789358i
$3$	−1.73050	+	0.0733671i	−0.999102	+	0.0423585i
$3$	−1.73050	+	0.0733671i	−0.999102	+	0.0423585i
$4$	−0.492347	+	1.93845i	−0.246174	+	0.969226i
$5$	−1.63009	+	3.93540i	−0.729000	+	1.75996i	−0.0831001	+	0.996541i	$0.526482\pi$
$5$	−1.63009	+	3.93540i	−0.729000	+	1.75996i	−0.645900	+	0.763422i	$0.723518\pi$
$6$	1.58437	+	1.86809i	0.646818	+	0.762645i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	2.59141	−	1.13341i	0.916201	−	0.400720i
$9$	2.98923	−	0.253923i	0.996412	−	0.0846410i
$10$	5.80847	−	1.59713i	1.83680	−	0.505056i
$11$	−1.91118	+	4.61399i	−0.576241	+	1.39117i	0.319921	+	0.947444i	$0.396344\pi$
$11$	−1.91118	+	4.61399i	−0.576241	+	1.39117i	−0.896163	+	0.443726i	$0.853656\pi$
$12$	0.709787	−	3.39061i	0.204898	−	0.978783i
$13$	3.99885	−	1.65638i	1.10908	−	0.459396i	0.248459	−	0.968642i	$-0.420076\pi$
$13$	3.99885	−	1.65638i	1.10908	−	0.459396i	0.860621	+	0.509246i	$0.170076\pi$
$14$	1.40329	+	0.175426i	0.375045	+	0.0468846i
$15$	2.53214	−	6.92978i	0.653797	−	1.78926i
$16$	−3.51519	−	1.90878i	−0.878797	−	0.477196i
$17$	2.12763			0.516027			0.258013	−	0.966141i	$-0.416932\pi$
$17$	2.12763			0.516027			0.258013	+	0.966141i	$0.416932\pi$
$18$	−2.87881	−	3.11648i	−0.678542	−	0.734562i
$19$	2.22926	+	5.38190i	0.511427	+	1.23469i	0.943053	+	0.332641i	$0.107940\pi$
$19$	2.22926	+	5.38190i	0.511427	+	1.23469i	−0.431627	+	0.902052i	$0.642060\pi$
$20$	−6.82600	−	5.09744i	−1.52634	−	1.13982i
$21$	1.17177	−	1.27552i	0.255701	−	0.278342i
$22$	6.81004	−	1.87252i	1.45191	−	0.399223i
$23$	−5.40417	+	5.40417i	−1.12685	+	1.12685i	−0.136160	+	0.990687i	$0.543476\pi$
$23$	−5.40417	+	5.40417i	−1.12685	+	1.12685i	−0.990687	+	0.136160i	$0.956524\pi$
$24$	−4.40126	+	2.15148i	−0.898404	+	0.439169i
$25$	−9.29460	−	9.29460i	−1.85892	−	1.85892i
$26$	−5.32097	−	3.02588i	−1.04353	−	0.593424i
$27$	−5.15423	+	0.658725i	−0.991932	+	0.126772i
$28$	−1.02255	−	1.71883i	−0.193244	−	0.324829i
$29$	−0.313330	+	0.129786i	−0.0581839	+	0.0241006i	−0.411586	−	0.911371i	$-0.635025\pi$
$29$	−0.313330	+	0.129786i	−0.0581839	+	0.0241006i	0.353402	+	0.935472i	$0.385025\pi$
$30$	−9.93435	+	3.18997i	−1.81376	+	0.582407i
$31$			1.59660i			0.286758i	0.989668	+	0.143379i	$0.0457967\pi$
$31$			1.59660i			0.286758i	−0.989668	+	0.143379i	$0.954203\pi$
$32$	0.921182	+	5.58135i	0.162844	+	0.986652i
$33$	2.96877	−	8.12471i	0.516796	−	1.41433i
$34$	−1.84728	−	2.37512i	−0.316806	−	0.407330i
$35$	−1.63009	−	3.93540i	−0.275536	−	0.665203i
$36$	−0.979524	+	5.91950i	−0.163254	+	0.986584i
$37$	−1.54413	−	0.639601i	−0.253854	−	0.105150i	0.252128	−	0.967694i	$-0.418870\pi$
$37$	−1.54413	−	0.639601i	−0.253854	−	0.105150i	−0.505982	+	0.862544i	$0.668870\pi$
$38$	4.07242	−	7.16131i	0.660634	−	1.16172i
$39$	−6.79846	+	3.15974i	−1.08863	+	0.505963i
$40$	0.236168	+	12.0458i	0.0373415	+	1.90460i
$41$	−0.541581	−	0.541581i	−0.0845808	−	0.0845808i	0.663551	−	0.748131i	$-0.269049\pi$
$41$	−0.541581	−	0.541581i	−0.0845808	−	0.0845808i	−0.748131	+	0.663551i	$0.769049\pi$
$42$	−2.44126	−	0.200619i	−0.376695	−	0.0309561i
$43$	−1.22767	−	0.508517i	−0.187218	−	0.0775481i	0.287105	−	0.957899i	$-0.407307\pi$
$43$	−1.22767	−	0.508517i	−0.187218	−	0.0775481i	−0.474323	+	0.880351i	$0.657307\pi$
$44$	−8.00303	−	5.97641i	−1.20650	−	0.900977i
$45$	−3.87345	+	12.1777i	−0.577419	+	1.81535i
$46$	10.7249	+	1.34072i	1.58129	+	0.197678i
$47$		−	7.60088i		−	1.10870i	−0.832283	−	0.554351i	$-0.812966\pi$
$47$		−	7.60088i		−	1.10870i	0.832283	−	0.554351i	$-0.187034\pi$
$48$	6.22306	+	3.04524i	0.898222	+	0.439543i
$49$		−	1.00000i		−	0.142857i
$50$	−2.30590	+	18.4456i	−0.326103	+	2.60861i
$51$	−3.68186	+	0.156098i	−0.515564	+	0.0218581i
$52$	1.24198	+	8.56708i	0.172232	+	1.18804i
$53$	−6.41413	−	2.65682i	−0.881049	−	0.364943i	−0.104146	−	0.994562i	$-0.533211\pi$
$53$	−6.41413	−	2.65682i	−0.881049	−	0.364943i	−0.776904	+	0.629620i	$0.783211\pi$
$54$	5.21041	+	5.18185i	0.709048	+	0.705161i
$55$	−15.0425	−	15.0425i	−2.02833	−	2.02833i
$56$	−1.03096	+	2.63384i	−0.137768	+	0.351962i
$57$	−4.25258	−	9.14981i	−0.563268	−	1.21192i
$58$	0.416926	+	0.237093i	0.0547450	+	0.0311319i
$59$	8.13626	+	3.37015i	1.05925	+	0.438756i	0.843185	−	0.537623i	$-0.180678\pi$
$59$	8.13626	+	3.37015i	1.05925	+	0.438756i	0.216065	+	0.976379i	$0.430678\pi$
$60$	12.1864	+	8.32030i	1.57325	+	1.07415i
$61$	0.969280	+	2.34005i	0.124104	+	0.299612i	0.973705	−	0.227813i	$-0.0731575\pi$
$61$	0.969280	+	2.34005i	0.124104	+	0.299612i	−0.849601	+	0.527425i	$0.823157\pi$
$62$	1.78232	−	1.38622i	0.226354	−	0.176050i
$63$	−1.93416	+	2.29326i	−0.243681	+	0.288923i
$64$	5.43078	−	5.87424i	0.678847	−	0.734280i
$65$			18.4371i			2.28684i
$66$	−11.6474	+	3.74003i	−1.43369	+	0.460366i
$67$	1.45557	−	0.602916i	0.177826	−	0.0736580i	−0.291994	−	0.956420i	$-0.594319\pi$
$67$	1.45557	−	0.602916i	0.177826	−	0.0736580i	0.469820	+	0.882762i	$0.344319\pi$
$68$	−1.04753	+	4.12431i	−0.127032	+	0.500147i
$69$	8.95540	−	9.74838i	1.07810	−	1.17357i
$70$	−2.97787	+	5.23655i	−0.355923	+	0.625887i
$71$	−3.18672	−	3.18672i	−0.378194	−	0.378194i	0.492257	−	0.870450i	$-0.336172\pi$
$71$	−3.18672	−	3.18672i	−0.378194	−	0.378194i	−0.870450	+	0.492257i	$0.836172\pi$
$72$	7.45852	−	4.04604i	0.878995	−	0.476830i
$73$	6.05729	−	6.05729i	0.708952	−	0.708952i	−0.257363	−	0.966315i	$-0.582854\pi$
$73$	6.05729	−	6.05729i	0.708952	−	0.708952i	0.966315	+	0.257363i	$0.0828536\pi$
$74$	0.626666	+	2.27907i	0.0728484	+	0.264937i
$75$	16.7662	+	15.4024i	1.93599	+	1.77851i
$76$	−11.5301	+	1.67154i	−1.32260	+	0.191739i
$77$	−1.91118	−	4.61399i	−0.217799	−	0.525813i
$78$	9.42992	+	4.84589i	1.06773	+	0.548689i
$79$	−6.59357			−0.741835			−0.370918	−	0.928666i	$-0.620957\pi$
$79$	−6.59357			−0.741835			−0.370918	+	0.928666i	$0.620957\pi$
$80$	13.2419	−	10.7222i	1.48049	−	1.19877i
$81$	8.87105	−	1.51807i	0.985672	−	0.168675i
$82$	−0.134361	+	1.07480i	−0.0148377	+	0.118691i
$83$	0.569240	−	0.235787i	0.0624822	−	0.0258810i	−0.351223	−	0.936292i	$-0.614234\pi$
$83$	0.569240	−	0.235787i	0.0624822	−	0.0258810i	0.413706	+	0.910411i	$0.364234\pi$
$84$	1.89562	+	2.89941i	0.206830	+	0.316352i
$85$	−3.46824	+	8.37308i	−0.376184	+	0.908188i
$86$	0.498233	+	1.81198i	0.0537258	+	0.195391i
$87$	0.532695	−	0.247582i	0.0571109	−	0.0265435i
$88$	0.276892	+	14.1229i	0.0295167	+	1.50550i
$89$	−5.79385	+	5.79385i	−0.614147	+	0.614147i	−0.944024	−	0.329877i	$-0.892993\pi$
$89$	−5.79385	+	5.79385i	−0.614147	+	0.614147i	0.329877	+	0.944024i	$0.392993\pi$
$90$	16.9573	−	6.24909i	1.78746	−	0.658712i
$91$	−1.65638	+	3.99885i	−0.173635	+	0.419193i
$92$	−7.81499	−	13.1364i	−0.814769	−	1.36957i
$93$	−0.117138	−	2.76291i	−0.0121466	−	0.286500i
$94$	−8.48503	+	6.59932i	−0.875164	+	0.680668i
$95$	−24.8138			−2.54584
$96$	−2.00359	−	9.59091i	−0.204491	−	0.978869i
$97$	11.6357			1.18142			0.590712	−	0.806883i	$-0.298847\pi$
$97$	11.6357			1.18142			0.590712	+	0.806883i	$0.298847\pi$
$98$	−1.11632	+	0.868232i	−0.112765	+	0.0877046i
$99$	−4.54136	+	14.2776i	−0.456423	+	1.43495i
$100$	22.5933	−	13.4410i	2.25933	−	1.34410i
$101$	0.687953	−	1.66087i	0.0684539	−	0.165262i	−0.885950	−	0.463781i	$-0.846492\pi$
$101$	0.687953	−	1.66087i	0.0684539	−	0.165262i	0.954404	+	0.298519i	$0.0964925\pi$
$102$	3.37097	+	3.97461i	0.333775	+	0.393545i
$103$	0.241885	−	0.241885i	0.0238336	−	0.0238336i	−0.695090	−	0.718923i	$-0.744635\pi$
$103$	0.241885	−	0.241885i	0.0238336	−	0.0238336i	0.718923	+	0.695090i	$0.244635\pi$
$104$	8.48529	−	8.82466i	0.832051	−	0.865329i
$105$	3.10960	+	6.69059i	0.303466	+	0.652935i
$106$	2.60309	+	9.46697i	0.252834	+	0.919514i
$107$	1.61412	−	3.89683i	0.156043	−	0.376720i	−0.826453	−	0.563006i	$-0.809645\pi$
$107$	1.61412	−	3.89683i	0.156043	−	0.376720i	0.982496	+	0.186285i	$0.0596449\pi$
$108$	1.26077	−	10.3155i	0.121317	−	0.992614i
$109$	−11.2818	+	4.67306i	−1.08060	+	0.447598i	−0.850719	−	0.525621i	$-0.823833\pi$
$109$	−11.2818	+	4.67306i	−1.08060	+	0.447598i	−0.229879	+	0.973219i	$0.573833\pi$
$110$	−3.73188	+	29.8526i	−0.355821	+	2.84633i
$111$	2.71904	+	0.993539i	0.258080	+	0.0943026i
$112$	3.83533	−	1.13590i	0.362404	−	0.107332i
$113$	−2.15751			−0.202961			−0.101481	−	0.994838i	$-0.532358\pi$
$113$	−2.15751			−0.202961			−0.101481	+	0.994838i	$0.532358\pi$
$114$	−6.52191	+	12.6914i	−0.610833	+	1.18866i
$115$	−12.4582	−	30.0768i	−1.16174	−	2.80468i
$116$	−0.0973158	−	0.671275i	−0.00903555	−	0.0623263i
$117$	11.5329	−	5.96670i	1.06622	−	0.551621i
$118$	−3.30199	−	12.0088i	−0.303973	−	1.10550i
$119$	−1.50446	+	1.50446i	−0.137914	+	0.137914i
$120$	−1.29245	−	20.8278i	−0.117984	−	1.90131i
$121$	−9.85812	−	9.85812i	−0.896192	−	0.896192i
$122$	1.77069	−	3.11373i	0.160310	−	0.281904i
$123$	0.976938	+	0.897470i	0.0880876	+	0.0809221i
$124$	−3.09493	−	0.786081i	−0.277933	−	0.0705922i
$125$	32.0521	−	13.2764i	2.86682	−	1.18748i
$126$	4.23931	+	0.168061i	0.377668	+	0.0149721i
$127$		−	11.1821i		−	0.992250i	−0.868251	−	0.496125i	$-0.834756\pi$
$127$		−	11.1821i		−	0.992250i	0.868251	−	0.496125i	$-0.165244\pi$
$128$	−11.2727	−	0.962293i	−0.996376	−	0.0850555i
$129$	2.16178	+	0.789916i	0.190335	+	0.0695483i
$130$	20.5817	−	16.0077i	1.80514	−	1.40397i
$131$	−4.79520	−	11.5766i	−0.418959	−	1.01146i	−0.982650	−	0.185470i	$-0.940619\pi$
$131$	−4.79520	−	11.5766i	−0.418959	−	1.01146i	0.563691	−	0.825986i	$-0.309381\pi$
$132$	14.2877	+	9.75499i	1.24358	+	0.849063i
$133$	−5.38190	−	2.22926i	−0.466670	−	0.193301i
$134$	−1.93682	−	1.10141i	−0.167316	−	0.0951475i
$135$	5.80954	−	21.3577i	0.500006	−	1.83818i
$136$	5.51356	−	2.41147i	0.472784	−	0.206782i
$137$	9.14775	+	9.14775i	0.781545	+	0.781545i	0.980091	−	0.198547i	$-0.0636222\pi$
$137$	9.14775	+	9.14775i	0.781545	+	0.781545i	−0.198547	+	0.980091i	$0.563622\pi$
$138$	−18.6577	−	1.53326i	−1.58825	−	0.130519i
$139$	−13.1569	−	5.44978i	−1.11596	−	0.462244i	−0.252971	−	0.967474i	$-0.581408\pi$
$139$	−13.1569	−	5.44978i	−1.11596	−	0.462244i	−0.862985	+	0.505230i	$0.831408\pi$
$140$	8.43115	−	1.22228i	0.712562	−	0.103301i
$141$	0.557655	+	13.1533i	0.0469630	+	1.10771i
$142$	−0.790592	+	6.32421i	−0.0663450	+	0.530716i
$143$			21.6163i			1.80764i
$144$	−10.9924	−	4.81321i	−0.916034	−	0.401101i
$145$		−	1.44464i		−	0.119971i
$146$	−12.0210	−	1.50275i	−0.994866	−	0.124369i
$147$	0.0733671	+	1.73050i	0.00605122	+	0.142729i
$148$	2.00009	−	2.67832i	0.164406	−	0.220157i
$149$	−16.2558	−	6.73339i	−1.33173	−	0.551621i	−0.400582	−	0.916261i	$-0.631192\pi$
$149$	−16.2558	−	6.73339i	−1.33173	−	0.551621i	−0.931149	+	0.364640i	$0.881192\pi$
$150$	2.63704	−	32.0893i	0.215314	−	2.62008i
$151$	−4.29496	−	4.29496i	−0.349519	−	0.349519i	0.510411	−	0.859930i	$-0.329493\pi$
$151$	−4.29496	−	4.29496i	−0.349519	−	0.349519i	−0.859930	+	0.510411i	$0.829493\pi$
$152$	11.8768	+	11.4200i	0.963336	+	0.926288i
$153$	6.36000	−	0.540255i	0.514175	−	0.0436771i
$154$	−3.49135	+	6.13950i	−0.281341	+	0.494735i
$155$	−6.28325	−	2.60261i	−0.504683	−	0.209046i
$156$	−2.77779	−	14.7342i	−0.222401	−	1.17968i
$157$	7.73681	+	18.6783i	0.617464	+	1.49069i	0.854638	+	0.519224i	$0.173779\pi$
$157$	7.73681	+	18.6783i	0.617464	+	1.49069i	−0.237174	+	0.971467i	$0.576221\pi$
$158$	5.72475	+	7.36055i	0.455437	+	0.585574i
$159$	11.2946	+	4.12703i	0.895717	+	0.327295i
$160$	−23.4664	−	5.47290i	−1.85518	−	0.432671i
$161$		−	7.64265i		−	0.602325i
$162$	−9.39678	−	8.58490i	−0.738281	−	0.674494i
$163$	12.0374	−	4.98606i	0.942844	−	0.390539i	0.142307	−	0.989823i	$-0.454548\pi$
$163$	12.0374	−	4.98606i	0.942844	−	0.390539i	0.800537	+	0.599284i	$0.204548\pi$
$164$	1.31647	−	0.783183i	0.102799	−	0.0611563i
$165$	27.1346	+	24.9273i	2.11242	+	1.94059i
$166$	−0.757446	−	0.430737i	−0.0587892	−	0.0334317i
$167$	1.05988	+	1.05988i	0.0820161	+	0.0820161i	0.746925	−	0.664909i	$-0.231530\pi$
$167$	1.05988	+	1.05988i	0.0820161	+	0.0820161i	−0.664909	+	0.746925i	$0.731530\pi$
$168$	1.59084	−	4.63349i	0.122736	−	0.357482i
$169$	4.05479	−	4.05479i	0.311907	−	0.311907i
$170$	12.3583	−	3.39810i	0.947838	−	0.260622i
$171$	8.03036	+	15.5217i	0.614097	+	1.18698i
$172$	1.59018	−	2.12941i	0.121250	−	0.162366i
$173$	5.41297	+	13.0681i	0.411540	+	0.993546i	0.984725	+	0.174120i	$0.0557080\pi$
$173$	5.41297	+	13.0681i	0.411540	+	0.993546i	−0.573184	+	0.819427i	$0.694292\pi$
$174$	−0.738883	−	0.379700i	−0.0560146	−	0.0287850i
$175$	13.1446			0.993635
$176$	15.5252	−	12.5710i	1.17026	−	0.947576i
$177$	−14.3270	−	5.23510i	−1.07689	−	0.393494i
$178$	11.4982	+	1.43740i	0.861827	+	0.107737i
$179$	6.83314	−	2.83038i	0.510733	−	0.211552i	−0.112408	−	0.993662i	$-0.535856\pi$
$179$	6.83314	−	2.83038i	0.510733	−	0.211552i	0.623141	+	0.782110i	$0.285856\pi$
$180$	−21.6989	−	13.5042i	−1.61734	−	1.00654i
$181$	−5.69775	+	13.7556i	−0.423510	+	1.02244i	0.557794	+	0.829980i	$0.311648\pi$
$181$	−5.69775	+	13.7556i	−0.423510	+	1.02244i	−0.981304	+	0.192465i	$0.938352\pi$
$182$	5.90211	−	1.62288i	0.437494	−	0.120296i
$183$	−1.84902	−	3.97833i	−0.136683	−	0.294087i
$184$	−7.87927	+	20.1295i	−0.580868	+	1.48397i
$185$	5.03417	−	5.03417i	0.370120	−	0.370120i
$186$	−2.98259	+	2.52961i	−0.218694	+	0.185480i
$187$	−4.06628	+	9.81688i	−0.297356	+	0.717881i
$188$	14.7339	+	3.74227i	1.07458	+	0.272933i
$189$	3.17880	−	4.11038i	0.231224	−	0.298986i
$190$	21.5442	+	27.7002i	1.56298	+	2.00958i
$191$	21.2246			1.53576			0.767878	−	0.640596i	$-0.221313\pi$
$191$	21.2246			1.53576			0.767878	+	0.640596i	$0.221313\pi$
$192$	−8.96696	+	10.5638i	−0.647135	+	0.762376i
$193$	7.75753			0.558399			0.279200	−	0.960233i	$-0.409931\pi$
$193$	7.75753			0.558399			0.279200	+	0.960233i	$0.409931\pi$
$194$	−10.1025	−	12.9892i	−0.725314	−	0.932567i
$195$	−1.35268	−	31.9053i	−0.0968672	−	2.28479i
$196$	1.93845	+	0.492347i	0.138461	+	0.0351677i
$197$	2.49316	−	6.01902i	0.177630	−	0.428837i	−0.809838	−	0.586653i	$-0.800445\pi$
$197$	2.49316	−	6.01902i	0.177630	−	0.428837i	0.987469	+	0.157816i	$0.0504453\pi$
$198$	19.8813	−	7.32664i	1.41290	−	0.520682i
$199$	−15.0719	+	15.0719i	−1.06842	+	1.06842i	−0.0709341	+	0.997481i	$0.522598\pi$
$199$	−15.0719	+	15.0719i	−1.06842	+	1.06842i	−0.997481	+	0.0709341i	$0.977402\pi$
$200$	−34.6207	−	13.5515i	−2.44805	−	0.958238i
$201$	−2.47462	+	1.15014i	−0.174546	+	0.0811243i
$202$	−2.45136	+	0.674040i	−0.172477	+	0.0474253i
$203$	0.129786	−	0.313330i	0.00910916	−	0.0219915i
$204$	1.51017	−	7.21397i	0.105733	−	0.505079i
$205$	3.01417	−	1.24851i	0.210518	−	0.0871996i
$206$	−0.480033	−	0.0600091i	−0.0334455	−	0.00418103i
$207$	−14.7821	+	17.5266i	−1.02743	+	1.21818i
$208$	−17.2184	−	1.81045i	−1.19388	−	0.125532i
$209$	−29.0925			−2.01237
$210$	4.76900	−	9.28030i	0.329092	−	0.640402i
$211$	9.10875	+	21.9905i	0.627072	+	1.51389i	0.843244	+	0.537531i	$0.180643\pi$
$211$	9.10875	+	21.9905i	0.627072	+	1.51389i	−0.216171	+	0.976355i	$0.569357\pi$
$212$	8.30810	−	11.1254i	0.570603	−	0.764096i
$213$	5.74840	+	5.28080i	0.393874	+	0.361835i
$214$	−5.75154	+	1.58147i	−0.393167	+	0.108107i
$215$	4.00243	−	4.00243i	0.272964	−	0.272964i
$216$	−12.6101	+	7.54886i	−0.858009	+	0.513635i
$217$	−1.12897	−	1.12897i	−0.0766392	−	0.0766392i
$218$	15.0118	+	8.53679i	1.01673	+	0.578184i
$219$	−10.0377	+	10.9265i	−0.678286	+	0.738346i
$220$	36.5652	−	21.7530i	2.46523	−	1.46659i
$221$	8.50808	−	3.52416i	0.572315	−	0.237061i
$222$	−1.25165	−	3.89795i	−0.0840053	−	0.261613i
$223$			6.03823i			0.404350i	0.979349	+	0.202175i	$0.0648009\pi$
$223$			6.03823i			0.404350i	−0.979349	+	0.202175i	$0.935199\pi$
$224$	−4.59798	−	3.29523i	−0.307216	−	0.220172i
$225$	−30.1439	−	25.4236i	−2.00959	−	1.69491i
$226$	1.87321	+	2.40847i	0.124604	+	0.160209i
$227$	−9.39236	−	22.6752i	−0.623393	−	1.50500i	−0.847695	−	0.530483i	$-0.822010\pi$
$227$	−9.39236	−	22.6752i	−0.623393	−	1.50500i	0.224303	−	0.974520i	$-0.427990\pi$
$228$	19.8302	−	3.73853i	1.31329	−	0.247590i
$229$	−7.65456	−	3.17062i	−0.505827	−	0.209521i	0.115151	−	0.993348i	$-0.463265\pi$
$229$	−7.65456	−	3.17062i	−0.505827	−	0.209521i	−0.620979	+	0.783827i	$0.713265\pi$
$230$	−22.7588	+	40.0211i	−1.50067	+	2.63891i
$231$	3.64580	+	7.84427i	0.239876	+	0.516115i
$232$	−0.664866	+	0.691458i	−0.0436506	+	0.0453964i
$233$	2.88066	+	2.88066i	0.188719	+	0.188719i	0.795142	−	0.606423i	$-0.207396\pi$
$233$	2.88066	+	2.88066i	0.188719	+	0.188719i	−0.606423	+	0.795142i	$0.707396\pi$
$234$	−16.6740	−	7.69394i	−1.09001	−	0.502969i
$235$	29.9125	+	12.3902i	1.95127	+	0.808245i
$236$	−10.5387	+	14.1125i	−0.686013	+	0.918643i
$237$	11.4102	−	0.483752i	0.741169	−	0.0314231i
$238$	2.98569	+	0.373242i	0.193533	+	0.0241937i
$239$		−	1.14305i		−	0.0739375i	−0.999316	−	0.0369687i	$-0.988230\pi$
$239$		−	1.14305i		−	0.0739375i	0.999316	−	0.0369687i	$-0.0117702\pi$
$240$	−22.1284	+	19.5262i	−1.42838	+	1.26041i
$241$			19.2767i			1.24172i	0.783921	+	0.620861i	$0.213217\pi$
$241$			19.2767i			1.24172i	−0.783921	+	0.620861i	$0.786783\pi$
$242$	−2.44570	+	19.5640i	−0.157215	+	1.25762i
$243$	−15.2399	+	3.27786i	−0.977642	+	0.210275i
$244$	−5.01329	+	0.726785i	−0.320943	+	0.0465276i
$245$	3.93540	+	1.63009i	0.251423	+	0.104143i
$246$	0.153656	−	1.86979i	0.00979675	−	0.119213i
$247$	17.8289	+	17.8289i	1.13443	+	1.13443i
$248$	1.80960	+	4.13744i	0.114909	+	0.262727i
$249$	−0.967769	+	0.449792i	−0.0613299	+	0.0285044i
$250$	−42.6493	−	24.2534i	−2.69738	−	1.53392i
$251$	14.5500	+	6.02681i	0.918388	+	0.380409i	0.791262	−	0.611478i	$-0.209425\pi$
$251$	14.5500	+	6.02681i	0.918388	+	0.380409i	0.127126	+	0.991887i	$0.459425\pi$
$252$	−3.49309	−	4.87835i	−0.220044	−	0.307307i
$253$	−14.6064	−	35.2631i	−0.918300	−	2.21697i
$254$	−12.4828	+	9.70864i	−0.783241	+	0.609174i
$255$	5.38747	−	14.7440i	0.337377	−	0.923308i
$256$	8.71310	+	13.4195i	0.544568	+	0.838716i
$257$		−	23.8422i		−	1.48724i	−0.668604	−	0.743618i	$-0.733108\pi$
$257$		−	23.8422i		−	1.48724i	0.668604	−	0.743618i	$-0.266892\pi$
$258$	−0.995130	−	3.09908i	−0.0619541	−	0.192940i
$259$	1.54413	−	0.639601i	0.0959478	−	0.0397429i
$260$	−35.7394	−	9.07745i	−2.21646	−	0.562960i
$261$	−0.903662	+	0.467521i	−0.0559353	+	0.0289388i
$262$	−8.75991	+	15.4042i	−0.541189	+	0.951674i
$263$	7.41687	+	7.41687i	0.457344	+	0.457344i	0.897783	−	0.440439i	$-0.145177\pi$
$263$	7.41687	+	7.41687i	0.457344	+	0.457344i	−0.440439	+	0.897783i	$0.645177\pi$
$264$	−1.51531	−	24.4192i	−0.0932611	−	1.50290i
$265$	20.9113	−	20.9113i	1.28457	−	1.28457i
$266$	2.18417	+	7.94345i	0.133920	+	0.487044i
$267$	9.60116	−	10.4513i	0.587582	−	0.639610i
$268$	0.452079	+	3.11839i	0.0276151	+	0.190486i
$269$	−6.20161	−	14.9720i	−0.378119	−	0.912859i	−0.992319	−	0.123709i	$-0.960521\pi$
$269$	−6.20161	−	14.9720i	−0.378119	−	0.912859i	0.614200	−	0.789150i	$-0.289479\pi$
$270$	−28.8861	+	12.0581i	−1.75795	+	0.733835i
$271$	10.5268			0.639457			0.319728	−	0.947509i	$-0.396408\pi$
$271$	10.5268			0.639457			0.319728	+	0.947509i	$0.396408\pi$
$272$	−7.47903	−	4.06119i	−0.453483	−	0.246246i
$273$	2.57297	−	7.04151i	0.155723	−	0.426172i
$274$	2.26946	−	18.1542i	0.137103	−	1.09673i
$275$	60.6488	−	25.1216i	3.65726	−	1.51489i
$276$	14.4876	+	22.1592i	0.872051	+	1.33383i
$277$	−2.97329	+	7.17815i	−0.178647	+	0.431293i	−0.987683	−	0.156466i	$-0.949990\pi$
$277$	−2.97329	+	7.17815i	−0.178647	+	0.431293i	0.809036	+	0.587759i	$0.199990\pi$
$278$	5.33956	+	19.4190i	0.320245	+	1.16468i
$279$	0.405413	+	4.77261i	0.0242715	+	0.285728i
$280$	−8.68464	−	8.35065i	−0.519007	−	0.499047i
$281$	−4.53348	+	4.53348i	−0.270445	+	0.270445i	−0.829279	−	0.558834i	$-0.811249\pi$
$281$	−4.53348	+	4.53348i	−0.270445	+	0.270445i	0.558834	+	0.829279i	$0.311249\pi$
$282$	14.1991	−	12.0426i	0.845546	−	0.717128i
$283$	−3.53349	+	8.53060i	−0.210044	+	0.507091i	−0.993430	−	0.114445i	$-0.963491\pi$
$283$	−3.53349	+	8.53060i	−0.210044	+	0.507091i	0.783385	+	0.621536i	$0.213491\pi$
$284$	7.74627	−	4.60832i	0.459656	−	0.273454i
$285$	42.9402	−	1.82052i	2.54356	−	0.107838i
$286$	24.1307	−	18.7679i	1.42688	−	1.10977i
$287$	0.765911			0.0452103
$288$	4.17086	+	16.4500i	0.245770	+	0.969328i
$289$	−12.4732			−0.733716
$290$	−1.61268	+	1.25428i	−0.0947001	+	0.0736540i
$291$	−20.1355	+	0.853676i	−1.18036	+	0.0500434i
$292$	8.75947	+	14.7240i	0.512609	+	0.861660i
$293$	−10.9902	+	26.5328i	−0.642057	+	1.55006i	0.181842	+	0.983328i	$0.441794\pi$
$293$	−10.9902	+	26.5328i	−0.642057	+	1.55006i	−0.823900	+	0.566736i	$0.808206\pi$
$294$	1.86809	−	1.58437i	0.108949	−	0.0924025i
$295$	−26.5257	+	26.5257i	−1.54439	+	1.54439i
$296$	−4.72641	+	0.0926656i	−0.274717	+	0.00538608i
$297$	6.81129	−	25.0405i	0.395231	−	1.45300i
$298$	6.59721	+	23.9929i	0.382166	+	1.38987i
$299$	−12.6591	+	30.5618i	−0.732094	+	1.76743i
$300$	−38.1115	+	24.9171i	−2.20037	+	1.43859i
$301$	1.22767	−	0.508517i	0.0707617	−	0.0293104i
$302$	−1.06554	+	8.52358i	−0.0613147	+	0.490477i
$303$	−1.06865	+	2.92460i	−0.0613922	+	0.168014i
$304$	2.43663	−	23.1736i	0.139750	−	1.32910i
$305$	−10.7890			−0.617778
$306$	−6.12505	−	6.63073i	−0.350146	−	0.379054i
$307$	7.37154	+	17.7965i	0.420716	+	1.01570i	0.982137	+	0.188168i	$0.0602550\pi$
$307$	7.37154	+	17.7965i	0.420716	+	1.01570i	−0.561421	+	0.827531i	$0.689745\pi$
$308$	9.88495	−	1.43304i	0.563248	−	0.0816549i
$309$	−0.400834	+	0.436327i	−0.0228027	+	0.0248218i
$310$	2.54997	+	9.27379i	0.144829	+	0.526716i
$311$	5.83893	−	5.83893i	0.331095	−	0.331095i	−0.521907	−	0.853002i	$-0.674779\pi$
$311$	5.83893	−	5.83893i	0.331095	−	0.331095i	0.853002	+	0.521907i	$0.174779\pi$
$312$	−14.0363	+	15.8936i	−0.794650	+	0.899797i
$313$	16.8205	+	16.8205i	0.950752	+	0.950752i	0.998843	−	0.0480911i	$-0.0153138\pi$
$313$	16.8205	+	16.8205i	0.950752	+	0.950752i	−0.0480911	+	0.998843i	$0.515314\pi$
$314$	14.1337	−	24.8539i	0.797608	−	1.40258i
$315$	−5.87202	−	11.3499i	−0.330851	−	0.639495i
$316$	3.24633	−	12.7813i	0.182620	−	0.719006i
$317$	−24.0737	+	9.97165i	−1.35211	+	0.560064i	−0.936880	−	0.349651i	$-0.886300\pi$
$317$	−24.0737	+	9.97165i	−1.35211	+	0.560064i	−0.415234	+	0.909715i	$0.636300\pi$
$318$	−5.19920	−	16.1916i	−0.291557	−	0.907979i
$319$		−	1.69374i		−	0.0948315i
$320$	14.2648	+	30.9478i	0.797425	+	1.73004i
$321$	−2.50733	+	6.86186i	−0.139945	+	0.382992i
$322$	−8.53165	+	6.63559i	−0.475450	+	0.369787i
$323$	4.74304	+	11.4507i	0.263910	+	0.637135i
$324$	−1.42493	+	17.9435i	−0.0791627	+	0.996862i
$325$	−52.5630	−	21.7723i	−2.91567	−	1.20771i
$326$	−16.0173	−	9.10858i	−0.887117	−	0.504477i
$327$	19.1802	−	8.91443i	1.06067	−	0.492969i
$328$	−2.01729	−	0.789625i	−0.111386	−	0.0435998i
$329$	5.37463	+	5.37463i	0.296313	+	0.296313i
$330$	4.26781	−	51.9336i	0.234935	−	2.85885i
$331$	−5.52284	−	2.28764i	−0.303563	−	0.125740i	0.225702	−	0.974196i	$-0.427532\pi$
$331$	−5.52284	−	2.28764i	−0.303563	−	0.125740i	−0.529265	+	0.848456i	$0.677532\pi$
$332$	0.176798	+	1.21953i	0.00970304	+	0.0669306i
$333$	−4.77819	−	1.51983i	−0.261843	−	0.0832860i
$334$	0.262946	−	2.10339i	0.0143877	−	0.115092i
$335$			6.71105i			0.366664i
$336$	−6.55368	+	2.24706i	−0.357533	+	0.122587i
$337$			4.60763i			0.250994i	0.992094	+	0.125497i	$0.0400525\pi$
$337$			4.60763i			0.250994i	−0.992094	+	0.125497i	$0.959947\pi$
$338$	−8.04695	−	1.00595i	−0.437697	−	0.0547166i
$339$	3.73355	−	0.158290i	0.202779	−	0.00859713i
$340$	−14.5232	−	10.8455i	−0.787633	−	0.588179i
$341$	−7.36669	−	3.05138i	−0.398928	−	0.165242i
$342$	10.3550	−	22.4409i	0.559935	−	1.21347i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	−3.75775	+	0.0736741i	−0.202604	+	0.00397224i
$345$	23.7656	+	51.1339i	1.27950	+	2.75295i
$346$	9.88845	−	17.3887i	0.531606	−	0.934823i
$347$	−24.0952	−	9.98058i	−1.29350	−	0.535785i	−0.373474	−	0.927641i	$-0.621833\pi$
$347$	−24.0952	−	9.98058i	−1.29350	−	0.535785i	−0.920027	+	0.391855i	$0.871833\pi$
$348$	0.217654	+	1.15450i	0.0116675	+	0.0618876i
$349$	6.10478	+	14.7383i	0.326782	+	0.788920i	0.998827	+	0.0484110i	$0.0154157\pi$
$349$	6.10478	+	14.7383i	0.326782	+	0.788920i	−0.672046	+	0.740509i	$0.734584\pi$
$350$	−11.4125	−	14.6735i	−0.610025	−	0.784334i
$351$	−19.5199	+	11.1715i	−1.04189	+	0.596289i
$352$	−27.5128	−	6.41661i	−1.46644	−	0.342007i
$353$		−	4.96251i		−	0.264128i	−0.991241	−	0.132064i	$-0.957840\pi$
$353$		−	4.96251i		−	0.264128i	0.991241	−	0.132064i	$-0.0421604\pi$
$354$	6.59513	+	20.5388i	0.350527	+	1.09163i
$355$	17.7356	−	7.34634i	0.941310	−	0.389903i
$356$	−8.37851	−	14.0837i	−0.444060	−	0.746434i
$357$	2.49309	−	2.71385i	0.131948	−	0.143632i
$358$	−9.09236	−	5.17055i	−0.480546	−	0.273272i
$359$	−12.1121	−	12.1121i	−0.639251	−	0.639251i	0.311120	−	0.950371i	$-0.399296\pi$
$359$	−12.1121	−	12.1121i	−0.639251	−	0.639251i	−0.950371	+	0.311120i	$0.899296\pi$
$360$	3.76466	+	35.9477i	0.198415	+	1.89461i
$361$	−10.5603	+	10.5603i	−0.555804	+	0.555804i
$362$	20.3026	−	5.58251i	1.06708	−	0.293410i
$363$	17.7827	+	16.3362i	0.933349	+	0.857427i
$364$	−6.93605	−	5.17963i	−0.363548	−	0.271486i
$365$	13.9639	+	33.7118i	0.730903	+	1.76456i
$366$	−2.83572	+	5.51821i	−0.148225	+	0.288441i
$367$	−31.8005			−1.65997			−0.829987	−	0.557783i	$-0.811652\pi$
$367$	−31.8005			−1.65997			−0.829987	+	0.557783i	$0.811652\pi$
$368$	29.3121	−	8.68128i	1.52800	−	0.452543i
$369$	−1.75643	−	1.48139i	−0.0914363	−	0.0771182i
$370$	−9.99058	−	1.24893i	−0.519385	−	0.0649286i
$371$	6.41413	−	2.65682i	0.333005	−	0.137935i
$372$	5.41343	+	1.13324i	0.280673	+	0.0587560i
$373$	−13.3131	+	32.1406i	−0.689324	+	1.66417i	0.0568153	+	0.998385i	$0.481905\pi$
$373$	−13.3131	+	32.1406i	−0.689324	+	1.66417i	−0.746139	+	0.665790i	$0.768095\pi$
$374$	14.4893	−	3.98404i	0.749222	−	0.206010i
$375$	−54.4919	+	25.3263i	−2.81395	+	1.30785i
$376$	−8.61489	−	19.6970i	−0.444279	−	1.01579i
$377$	−1.03798	+	1.03798i	−0.0534589	+	0.0534589i
$378$	−7.34844	+	0.0201967i	−0.377963	+	0.00103881i
$379$	13.7444	−	33.1819i	0.706002	−	1.70444i	−0.00375580	−	0.999993i	$-0.501196\pi$
$379$	13.7444	−	33.1819i	0.706002	−	1.70444i	0.709758	−	0.704446i	$-0.248804\pi$
$380$	12.2170	−	48.1004i	0.626720	−	2.46750i
$381$	0.820398	+	19.3506i	0.0420303	+	0.991359i
$382$	−18.4278	−	23.6934i	−0.942850	−	1.21226i
$383$	3.99425			0.204097			0.102048	−	0.994779i	$-0.467460\pi$
$383$	3.99425			0.204097			0.102048	+	0.994779i	$0.467460\pi$
$384$	19.5780	+	0.838199i	0.999085	+	0.0427741i
$385$	21.2733			1.08419
$386$	−6.73533	−	8.65990i	−0.342820	−	0.440777i
$387$	−3.79891	−	1.20834i	−0.193110	−	0.0614235i
$388$	−5.72879	+	22.5552i	−0.290835	+	1.14507i
$389$	8.13067	−	19.6292i	0.412241	−	0.995239i	−0.572293	−	0.820049i	$-0.693946\pi$
$389$	8.13067	−	19.6292i	0.412241	−	0.995239i	0.984535	−	0.175190i	$-0.0560539\pi$
$390$	−34.4422	+	29.2112i	−1.74405	+	1.47917i
$391$	−11.4981	+	11.4981i	−0.581483	+	0.581483i
$392$	−1.13341	−	2.59141i	−0.0572457	−	0.130886i
$393$	9.14742	+	19.6815i	0.461426	+	0.992801i
$394$	−8.88380	+	2.44273i	−0.447559	+	0.123063i
$395$	10.7482	−	25.9483i	0.540798	−	1.30560i
$396$	−25.4405	−	15.8327i	−1.27843	−	0.795625i
$397$	22.4877	−	9.31470i	1.12862	−	0.467491i	0.261311	−	0.965255i	$-0.415845\pi$
$397$	22.4877	−	9.31470i	1.12862	−	0.467491i	0.867313	+	0.497763i	$0.165845\pi$
$398$	29.9109	+	3.73917i	1.49930	+	0.187428i
$399$	9.47692	+	3.46287i	0.474439	+	0.173360i
$400$	14.9309	+	50.4137i	0.746545	+	2.52068i
$401$	12.1671			0.607594			0.303797	−	0.952737i	$-0.401746\pi$
$401$	12.1671			0.607594			0.303797	+	0.952737i	$0.401746\pi$
$402$	3.43247	+	1.76389i	0.171196	+	0.0879748i
$403$	2.64457	+	6.38455i	0.131735	+	0.318037i
$404$	2.88080	+	2.15129i	0.143325	+	0.107031i
$405$	−8.48643	+	37.3857i	−0.421694	+	1.85771i
$406$	−0.462461	+	0.127161i	−0.0229516	+	0.00631088i
$407$	5.90223	−	5.90223i	0.292562	−	0.292562i
$408$	−9.36428	+	4.57756i	−0.463601	+	0.226623i
$409$	−9.42302	−	9.42302i	−0.465938	−	0.465938i	0.434658	−	0.900596i	$-0.356869\pi$
$409$	−9.42302	−	9.42302i	−0.465938	−	0.465938i	−0.900596	+	0.434658i	$0.856869\pi$
$410$	−4.01073	−	2.28078i	−0.198076	−	0.112640i
$411$	−16.5013	−	15.1590i	−0.813948	−	0.747738i
$412$	0.349791	+	0.587973i	0.0172329	+	0.0289674i
$413$	−8.13626	+	3.37015i	−0.400359	+	0.165834i
$414$	32.3996	+	1.28443i	1.59235	+	0.0631264i
$415$			2.62454i			0.128834i
$416$	12.9285	+	20.7931i	0.633871	+	1.01947i
$417$	23.1678	+	8.46553i	1.13453	+	0.414559i
$418$	25.2591	+	32.4766i	1.23546	+	1.58848i
$419$	−1.35388	−	3.26855i	−0.0661412	−	0.159679i	0.887353	−	0.461091i	$-0.152542\pi$
$419$	−1.35388	−	3.26855i	−0.0661412	−	0.159679i	−0.953494	+	0.301412i	$0.902542\pi$
$420$	−14.5004	+	2.73372i	−0.707547	+	0.133392i
$421$	−0.250284	−	0.103671i	−0.0121981	−	0.00505262i	0.376576	−	0.926386i	$-0.377101\pi$
$421$	−0.250284	−	0.103671i	−0.0121981	−	0.00505262i	−0.388774	+	0.921333i	$0.627101\pi$
$422$	16.6399	−	29.2611i	0.810019	−	1.42441i
$423$	−1.93004	−	22.7208i	−0.0938417	−	1.10472i
$424$	−19.6329	+	0.384921i	−0.953458	+	0.0186934i
$425$	−19.7755	−	19.7755i	−0.959253	−	0.959253i
$426$	0.904127	−	11.0020i	0.0438051	−	0.533050i
$427$	−2.34005	−	0.969280i	−0.113243	−	0.0469067i
$428$	6.75910	+	5.04748i	0.326713	+	0.243979i
$429$	−1.58592	−	37.4068i	−0.0765691	−	1.80602i
$430$	−7.94304	−	0.992963i	−0.383047	−	0.0478849i
$431$			31.7680i			1.53021i	0.643904	+	0.765106i	$0.277314\pi$
$431$			31.7680i			1.53021i	−0.643904	+	0.765106i	$0.722686\pi$
$432$	19.3754	+	7.52276i	0.932202	+	0.361939i
$433$		−	37.8533i		−	1.81911i	−0.415581	−	0.909556i	$-0.636422\pi$
$433$		−	37.8533i		−	1.81911i	0.415581	−	0.909556i	$-0.363578\pi$
$434$	−0.280085	+	2.24049i	−0.0134445	+	0.107547i
$435$	0.105989	+	2.49995i	0.00508179	+	0.119863i
$436$	−3.50396	−	24.1699i	−0.167809	−	1.15753i
$437$	−41.1320	−	17.0374i	−1.96761	−	0.815011i
$438$	20.9126	+	1.71856i	0.999241	+	0.0821159i
$439$	10.9006	+	10.9006i	0.520257	+	0.520257i	0.917649	−	0.397392i	$-0.130085\pi$
$439$	10.9006	+	10.9006i	0.520257	+	0.520257i	−0.397392	+	0.917649i	$0.630085\pi$
$440$	−56.0304	−	21.9319i	−2.67115	−	1.04556i
$441$	−0.253923	−	2.98923i	−0.0120916	−	0.142345i
$442$	−11.3211	−	6.43796i	−0.538489	−	0.306223i
$443$	28.7119	+	11.8929i	1.36414	+	0.565047i	0.940194	−	0.340639i	$-0.110643\pi$
$443$	28.7119	+	11.8929i	1.36414	+	0.565047i	0.423950	+	0.905686i	$0.360643\pi$
$444$	−3.26464	+	4.78157i	−0.154933	+	0.226923i
$445$	−13.3566	−	32.2456i	−0.633163	−	1.52859i
$446$	6.74060	−	5.24258i	0.319177	−	0.248243i
$447$	28.6247	+	10.4595i	1.35390	+	0.494716i
$448$	0.313574	+	7.99385i	0.0148150	+	0.377674i
$449$			20.0759i			0.947442i	0.880675	+	0.473721i	$0.157089\pi$
$449$			20.0759i			0.947442i	−0.880675	+	0.473721i	$0.842911\pi$
$450$	−2.20909	+	55.7239i	−0.104138	+	2.62685i
$451$	3.53391	−	1.46379i	0.166405	−	0.0689273i
$452$	1.06224	−	4.18222i	0.0499637	−	0.196715i
$453$	7.74753	+	7.11731i	0.364011	+	0.334400i
$454$	−17.1580	+	30.1722i	−0.805266	+	1.41605i
$455$	−13.0370	−	13.0370i	−0.611184	−	0.611184i
$456$	−21.3906	−	18.8910i	−1.00171	−	0.884651i
$457$	25.1945	−	25.1945i	1.17855	−	1.17855i	0.198435	−	0.980114i	$-0.436414\pi$
$457$	25.1945	−	25.1945i	1.17855	−	1.17855i	0.980114	−	0.198435i	$-0.0635860\pi$
$458$	3.10650	+	11.2978i	0.145157	+	0.527911i
$459$	−10.9663	+	1.40152i	−0.511864	+	0.0654176i
$460$	64.4363	−	9.34143i	3.00436	−	0.435547i
$461$	5.30608	+	12.8100i	0.247129	+	0.596622i	0.997958	−	0.0638745i	$-0.0203457\pi$
$461$	5.30608	+	12.8100i	0.247129	+	0.596622i	−0.750829	+	0.660497i	$0.770346\pi$
$462$	5.59133	−	10.8805i	0.260132	−	0.506208i
$463$	−11.7196			−0.544654			−0.272327	−	0.962205i	$-0.587793\pi$
$463$	−11.7196			−0.544654			−0.272327	+	0.962205i	$0.587793\pi$
$464$	1.34915	+	0.141858i	0.0626326	+	0.00658561i
$465$	11.0641	+	4.04282i	0.513085	+	0.187481i
$466$	0.714663	−	5.71683i	0.0331061	−	0.264827i
$467$	−18.0770	+	7.48775i	−0.836505	+	0.346492i	−0.759474	−	0.650537i	$-0.774544\pi$
$467$	−18.0770	+	7.48775i	−0.836505	+	0.346492i	−0.0770302	+	0.997029i	$0.524544\pi$
$468$	5.88796	+	25.2936i	0.272171	+	1.16920i
$469$	−0.602916	+	1.45557i	−0.0278401	+	0.0672119i
$470$	−12.1396	−	44.1495i	−0.559956	−	2.03646i
$471$	−14.7589	−	31.7551i	−0.680054	−	1.46320i
$472$	24.9041	−	0.488268i	1.14630	−	0.0224743i
$473$	4.69258	−	4.69258i	0.215765	−	0.215765i
$474$	−10.4467	−	12.3174i	−0.479832	−	0.565757i
$475$	29.3026	−	70.7427i	1.34450	−	3.24590i
$476$	−2.17561	−	3.65705i	−0.0997190	−	0.167621i
$477$	−19.8480	−	6.31317i	−0.908777	−	0.289060i
$478$	−1.27601	+	0.992428i	−0.0583632	+	0.0453926i
$479$	1.46363			0.0668747			0.0334374	−	0.999441i	$-0.489355\pi$
$479$	1.46363			0.0668747			0.0334374	+	0.999441i	$0.489355\pi$
$480$	41.0101	+	7.74918i	1.87185	+	0.353700i
$481$	−7.23417			−0.329850
$482$	21.5190	−	16.7366i	0.980163	−	0.762333i
$483$	0.560719	+	13.2256i	0.0255136	+	0.601784i
$484$	23.9631	−	14.2559i	1.08923	−	0.647994i
$485$	−18.9672	+	45.7910i	−0.861258	+	2.07926i
$486$	16.8909	+	14.1667i	0.766189	+	0.642616i
$487$	−4.87574	+	4.87574i	−0.220941	+	0.220941i	−0.808895	−	0.587954i	$-0.799934\pi$
$487$	−4.87574	+	4.87574i	−0.220941	+	0.220941i	0.587954	+	0.808895i	$0.299934\pi$
$488$	5.16402	+	4.96543i	0.233764	+	0.224774i
$489$	−20.4649	+	9.51152i	−0.925455	+	0.430126i
$490$	−1.59713	−	5.80847i	−0.0721508	−	0.262400i
$491$	−14.2824	+	34.4807i	−0.644554	+	1.55609i	0.175917	+	0.984405i	$0.443711\pi$
$491$	−14.2824	+	34.4807i	−0.644554	+	1.55609i	−0.820472	+	0.571687i	$0.806289\pi$
$492$	−2.22069	+	1.45188i	−0.100117	+	0.0654558i
$493$	−0.666652	+	0.276136i	−0.0300245	+	0.0124365i
$494$	4.42317	−	35.3824i	0.199008	−	1.59193i
$495$	−48.7851	−	41.1459i	−2.19273	−	1.84937i
$496$	3.04756	−	5.61234i	0.136839	−	0.252002i
$497$	4.50670			0.202153
$498$	1.34236	+	0.689818i	0.0601526	+	0.0309115i
$499$	−3.13217	−	7.56173i	−0.140215	−	0.338510i	0.838136	−	0.545462i	$-0.183646\pi$
$499$	−3.13217	−	7.56173i	−0.140215	−	0.338510i	−0.978351	+	0.206952i	$0.933646\pi$
$500$	9.95490	+	68.6680i	0.445197	+	3.07092i
$501$	−1.91188	−	1.75636i	−0.0854165	−	0.0784684i
$502$	−5.90492	−	21.4751i	−0.263549	−	0.958482i
$503$	17.6469	−	17.6469i	0.786835	−	0.786835i	−0.194139	−	0.980974i	$-0.562191\pi$
$503$	17.6469	−	17.6469i	0.786835	−	0.786835i	0.980974	+	0.194139i	$0.0621914\pi$
$504$	−2.41299	+	8.13495i	−0.107483	+	0.362360i
$505$	5.41474	+	5.41474i	0.240953	+	0.240953i
$506$	−26.6832	+	46.9220i	−1.18621	+	2.08594i
$507$	−6.71932	+	7.31429i	−0.298415	+	0.324839i
$508$	21.6759	+	5.50547i	0.961714	+	0.244266i
$509$	−3.64857	+	1.51129i	−0.161720	+	0.0669867i	−0.462075	−	0.886841i	$-0.652895\pi$
$509$	−3.64857	+	1.51129i	−0.161720	+	0.0669867i	0.300355	+	0.953828i	$0.402895\pi$
$510$	−21.1367	+	6.78709i	−0.935947	+	0.300537i
$511$			8.56630i			0.378951i
$512$	7.41545	−	21.3778i	0.327720	−	0.944775i
$513$	−15.0353	−	26.2711i	−0.663825	−	1.15990i
$514$	−26.6156	+	20.7006i	−1.17396	+	0.913063i
$515$	0.557617	+	1.34621i	0.0245716	+	0.0593210i
$516$	−2.59556	+	3.80160i	−0.114263	+	0.167356i
$517$	35.0704	+	14.5266i	1.54239	+	0.638880i
$518$	−2.05467	−	1.16843i	−0.0902769	−	0.0513378i
$519$	−10.3259	−	22.2171i	−0.453256	−	0.975222i
$520$	20.8967	+	47.7780i	0.916382	+	2.09520i
$521$	13.8410	+	13.8410i	0.606385	+	0.606385i	0.941999	−	0.335614i	$-0.108944\pi$
$521$	13.8410	+	13.8410i	0.606385	+	0.606385i	−0.335614	+	0.941999i	$0.608944\pi$
$522$	1.30649	+	0.602860i	0.0571836	+	0.0263865i
$523$	6.30027	+	2.60966i	0.275491	+	0.114112i	0.516152	−	0.856497i	$-0.327364\pi$
$523$	6.30027	+	2.60966i	0.275491	+	0.114112i	−0.240660	+	0.970609i	$0.577364\pi$
$524$	24.8017	−	3.59554i	1.08347	−	0.157072i
$525$	−22.7466	+	0.964378i	−0.992743	+	0.0420889i
$526$	1.84005	−	14.7192i	0.0802300	−	0.641786i
$527$			3.39698i			0.147975i
$528$	−25.9441	+	22.8931i	−1.12907	+	0.996296i
$529$		−	35.4101i		−	1.53957i
$530$	−41.4996	−	5.18788i	−1.80263	−	0.225347i
$531$	25.1769	+	8.00818i	1.09259	+	0.347525i
$532$	6.97107	−	9.33499i	0.302234	−	0.404723i
$533$	−3.06276	−	1.26864i	−0.132663	−	0.0549508i
$534$	−20.0031	−	1.64382i	−0.865617	−	0.0711349i
$535$	12.7044	+	12.7044i	0.549259	+	0.549259i
$536$	3.08862	−	3.21215i	0.133408	−	0.138744i
$537$	−11.6171	+	5.39929i	−0.501313	+	0.232996i
$538$	−11.3291	+	19.9221i	−0.488434	+	0.858905i
$539$	4.61399	+	1.91118i	0.198739	+	0.0823202i
$540$	38.5406	+	21.7769i	1.65852	+	0.937130i
$541$	6.80394	+	16.4262i	0.292524	+	0.706216i	1.00000		0.000521870i	$-0.000166116\pi$
$541$	6.80394	+	16.4262i	0.292524	+	0.706216i	−0.707476	+	0.706738i	$0.750166\pi$
$542$	−9.13969	−	11.7513i	−0.392583	−	0.504761i
$543$	8.85072	−	24.2220i	0.379821	−	1.03947i
$544$	1.95994	+	11.8751i	0.0840317	+	0.509139i
$545$		−	52.0158i		−	2.22811i
$546$	−10.0945	+	3.24140i	−0.432006	+	0.138719i
$547$	−33.0189	+	13.6769i	−1.41178	+	0.584780i	−0.952782	−	0.303655i	$-0.901793\pi$
$547$	−33.0189	+	13.6769i	−1.41178	+	0.584780i	−0.459002	+	0.888435i	$0.651793\pi$
$548$	−22.2363	+	13.2286i	−0.949889	+	0.565097i
$549$	3.49160	+	6.74883i	0.149018	+	0.288033i
$550$	−80.7010	−	45.8922i	−3.44110	−	1.95685i
$551$	−1.39699	−	1.39699i	−0.0595136	−	0.0595136i
$552$	12.1582	−	35.4121i	0.517488	−	1.50724i
$553$	4.66236	−	4.66236i	0.198264	−	0.198264i
$554$	10.5946	−	2.91315i	0.450122	−	0.123768i
$555$	−8.34227	+	9.08095i	−0.354110	+	0.385465i
$556$	17.0419	−	22.8209i	0.722738	−	0.967821i
$557$	−8.56822	−	20.6855i	−0.363047	−	0.876473i	−0.994851	−	0.101345i	$-0.967685\pi$
$557$	−8.56822	−	20.6855i	−0.363047	−	0.876473i	0.631804	−	0.775128i	$-0.282315\pi$
$558$	4.97577	−	4.59630i	0.210641	−	0.194577i
$559$	−5.75155			−0.243265
$560$	−1.78173	+	16.9452i	−0.0752918	+	0.716064i
$561$	6.31645	−	17.2864i	0.266681	−	0.729832i
$562$	8.99693	+	1.12471i	0.379513	+	0.0474430i
$563$	−17.9366	+	7.42959i	−0.755938	+	0.313120i	−0.727162	−	0.686466i	$-0.759161\pi$
$563$	−17.9366	+	7.42959i	−0.755938	+	0.313120i	−0.0287761	+	0.999586i	$0.509161\pi$
$564$	−25.7716	−	5.39500i	−1.08518	−	0.227171i
$565$	3.51694	−	8.49064i	0.147959	−	0.357204i
$566$	12.5908	−	3.46203i	0.529230	−	0.145520i
$567$	−5.19934	+	7.34622i	−0.218352	+	0.308512i
$568$	−11.8699	−	4.64623i	−0.498051	−	0.194952i
$569$	−6.47008	+	6.47008i	−0.271240	+	0.271240i	−0.829599	−	0.558359i	$-0.811431\pi$
$569$	−6.47008	+	6.47008i	−0.271240	+	0.271240i	0.558359	+	0.829599i	$0.311431\pi$
$570$	−39.3144	−	46.3545i	−1.64670	−	1.94158i
$571$	−1.22776	+	2.96408i	−0.0513802	+	0.124043i	−0.947486	−	0.319799i	$-0.896385\pi$
$571$	−1.22776	+	2.96408i	−0.0513802	+	0.124043i	0.896105	+	0.443842i	$0.146385\pi$
$572$	−41.9021	−	10.6427i	−1.75201	−	0.444994i
$573$	−36.7290	+	1.55719i	−1.53438	+	0.0650524i
$574$	−0.664989	−	0.855003i	−0.0277561	−	0.0356872i
$575$	100.459			4.18944
$576$	14.7423	−	18.9385i	0.614261	−	0.789103i
$577$	−35.8304			−1.49164			−0.745820	−	0.666148i	$-0.767942\pi$
$577$	−35.8304			−1.49164			−0.745820	+	0.666148i	$0.767942\pi$
$578$	10.8296	+	13.9241i	0.450452	+	0.579165i
$579$	−13.4244	+	0.569148i	−0.557898	+	0.0236530i
$580$	2.80037	+	0.711265i	0.116279	+	0.0295337i
$581$	−0.235787	+	0.569240i	−0.00978209	+	0.0236161i
$582$	18.4352	+	21.7365i	0.764166	+	0.901007i
$583$	24.5171	−	24.5171i	1.01539	−	1.01539i
$584$	8.83152	−	22.5623i	0.365451	−	0.933633i
$585$	4.68160	+	55.1128i	0.193561	+	2.27863i
$586$	39.1612	−	10.7680i	1.61774	−	0.444821i
$587$	−7.10159	+	17.1448i	−0.293114	+	0.707640i	0.706886	+	0.707328i	$0.250099\pi$
$587$	−7.10159	+	17.1448i	−0.293114	+	0.707640i	−1.00000		0.000312323i	$0.999901\pi$
$588$	−3.39061	−	0.709787i	−0.139826	−	0.0292711i
$589$	−8.59274	+	3.55923i	−0.354058	+	0.146655i
$590$	52.6418	+	6.58077i	2.16723	+	0.270926i
$591$	−3.87280	+	10.5988i	−0.159306	+	0.435976i
$592$	4.20706	+	5.19574i	0.172909	+	0.213543i
$593$	14.4685			0.594151			0.297076	−	0.954854i	$-0.403989\pi$
$593$	14.4685			0.594151			0.297076	+	0.954854i	$0.403989\pi$
$594$	−33.8670	+	14.1374i	−1.38958	+	0.580063i
$595$	−3.46824	−	8.37308i	−0.142184	−	0.343263i
$596$	21.0559	−	28.1960i	0.862482	−	1.15495i
$597$	24.9760	−	27.1876i	1.02220	−	1.11271i
$598$	45.1078	−	12.4031i	1.84459	−	0.507199i
$599$	7.78763	−	7.78763i	0.318194	−	0.318194i	−0.529879	−	0.848073i	$-0.677763\pi$
$599$	7.78763	−	7.78763i	0.318194	−	0.318194i	0.848073	+	0.529879i	$0.177763\pi$
$600$	60.9052	+	20.9108i	2.48644	+	0.853682i
$601$	20.7830	+	20.7830i	0.847757	+	0.847757i	0.989853	−	0.142096i	$-0.0453841\pi$
$601$	20.7830	+	20.7830i	0.847757	+	0.847757i	−0.142096	+	0.989853i	$0.545384\pi$
$602$	−1.63357	−	0.928963i	−0.0665793	−	0.0378617i
$603$	4.19794	−	2.17186i	0.170953	−	0.0884450i
$604$	10.4402	−	6.21096i	0.424805	−	0.252721i
$605$	54.8653	−	22.7259i	2.23059	−	0.923941i
$606$	4.19262	−	1.34627i	0.170314	−	0.0546886i
$607$		−	41.5005i		−	1.68446i	−0.539122	−	0.842228i	$-0.681244\pi$
$607$		−	41.5005i		−	1.68446i	0.539122	−	0.842228i	$-0.318756\pi$
$608$	−27.9847	+	17.4000i	−1.13493	+	0.705662i
$609$	−0.201605	+	0.551739i	−0.00816946	+	0.0223576i
$610$	9.36738	+	12.0440i	0.379274	+	0.487649i
$611$	−12.5899	−	30.3947i	−0.509333	−	1.22964i
$612$	−2.08407	+	12.5945i	−0.0842435	+	0.509104i
$613$	−5.18294	−	2.14685i	−0.209337	−	0.0867103i	0.275551	−	0.961286i	$-0.411140\pi$
$613$	−5.18294	−	2.14685i	−0.209337	−	0.0867103i	−0.484888	+	0.874576i	$0.661140\pi$
$614$	13.4664	−	23.6805i	0.543459	−	0.955666i
$615$	−5.12440	+	2.38168i	−0.206636	+	0.0960386i
$616$	−10.1822	−	9.79058i	−0.410251	−	0.394474i
$617$	7.93891	+	7.93891i	0.319608	+	0.319608i	0.848617	−	0.529008i	$-0.177436\pi$
$617$	7.93891	+	7.93891i	0.319608	+	0.319608i	−0.529008	+	0.848617i	$0.677436\pi$
$618$	0.835098	+	0.0686269i	0.0335926	+	0.00276058i
$619$	−14.2133	−	5.88734i	−0.571280	−	0.236632i	0.0782937	−	0.996930i	$-0.475053\pi$
$619$	−14.2133	−	5.88734i	−0.571280	−	0.236632i	−0.649574	+	0.760298i	$0.725053\pi$
$620$	8.13857	−	10.8984i	0.326853	−	0.437690i
$621$	24.2945	−	31.4142i	0.974903	−	1.26061i
$622$	−11.5877	−	1.44858i	−0.464623	−	0.0580827i
$623$		−	8.19375i		−	0.328275i
$624$	29.9291	+	1.86972i	1.19812	+	0.0748488i
$625$			82.0566i			3.28226i
$626$	4.17300	−	33.3812i	0.166787	−	1.33418i
$627$	50.3445	−	2.13444i	2.01057	−	0.0852412i
$628$	−40.0162	+	5.80121i	−1.59682	+	0.231494i
$629$	−3.28535	−	1.36084i	−0.130996	−	0.0542601i
$630$	−7.57187	+	16.4094i	−0.301670	+	0.653767i
$631$	9.95090	+	9.95090i	0.396139	+	0.396139i	0.876869	−	0.480730i	$-0.159628\pi$
$631$	9.95090	+	9.95090i	0.396139	+	0.396139i	−0.480730	+	0.876869i	$0.659628\pi$
$632$	−17.0866	+	7.47320i	−0.679670	+	0.297268i
$633$	−17.3760	−	37.3862i	−0.690636	−	1.48597i
$634$	32.0331	+	18.2163i	1.27220	+	0.723461i
$635$	44.0060	+	18.2279i	1.74632	+	0.723351i
$636$	−13.5609	+	19.8620i	−0.537725	+	0.787580i
$637$	−1.65638	−	3.99885i	−0.0656280	−	0.158440i
$638$	−1.89076	+	1.47056i	−0.0748560	+	0.0582201i
$639$	−10.3350	−	8.71666i	−0.408847	−	0.344826i
$640$	22.1626	−	42.7940i	0.876053	−	1.69158i
$641$			18.2915i			0.722469i	0.932475	+	0.361235i	$0.117645\pi$
$641$			18.2915i			0.722469i	−0.932475	+	0.361235i	$0.882355\pi$
$642$	9.83699	−	3.15871i	0.388235	−	0.124664i
$643$	−13.3174	+	5.51624i	−0.525186	+	0.217539i	−0.629493	−	0.777006i	$-0.716738\pi$
$643$	−13.3174	+	5.51624i	−0.525186	+	0.217539i	0.104307	+	0.994545i	$0.466738\pi$
$644$	14.8149	+	3.76284i	0.583789	+	0.148277i
$645$	−6.63255	+	7.21984i	−0.261156	+	0.284281i
$646$	8.66462	−	15.2366i	0.340905	−	0.599478i
$647$	−13.0294	−	13.0294i	−0.512237	−	0.512237i	0.402974	−	0.915211i	$-0.367976\pi$
$647$	−13.0294	−	13.0294i	−0.512237	−	0.512237i	−0.915211	+	0.402974i	$0.867976\pi$
$648$	21.2679	−	13.9884i	0.835482	−	0.549518i
$649$	−31.0997	+	31.0997i	−1.22077	+	1.22077i
$650$	21.3320	+	77.5807i	0.836709	+	3.04296i
$651$	2.03650	+	1.87084i	0.0798167	+	0.0733241i
$652$	3.73865	+	25.7888i	0.146417	+	1.00997i
$653$	−16.3633	−	39.5046i	−0.640347	−	1.54593i	−0.826213	−	0.563358i	$-0.809509\pi$
$653$	−16.3633	−	39.5046i	−0.640347	−	1.54593i	0.185866	−	0.982575i	$-0.440491\pi$
$654$	−26.6042	−	13.6715i	−1.04031	−	0.534598i
$655$	53.3753			2.08555
$656$	0.869999	+	2.93752i	0.0339677	+	0.114691i
$657$	16.5686	−	19.6447i	0.646401	−	0.766414i
$658$	1.33339	−	10.6662i	0.0519810	−	0.415814i
$659$	−41.4082	+	17.1518i	−1.61304	+	0.668141i	−0.993182	−	0.116577i	$-0.962808\pi$
$659$	−41.4082	+	17.1518i	−1.61304	+	0.668141i	−0.619853	+	0.784718i	$0.712808\pi$
$660$	−61.6800	+	40.3261i	−2.40089	+	1.56969i
$661$	−6.55997	+	15.8372i	−0.255153	+	0.615994i	−0.998605	−	0.0527948i	$-0.983187\pi$
$661$	−6.55997	+	15.8372i	−0.255153	+	0.615994i	0.743452	+	0.668789i	$0.233187\pi$
$662$	2.24137	+	8.15146i	0.0871133	+	0.316816i
$663$	−14.4646	+	6.72276i	−0.561760	+	0.261090i
$664$	1.20789	−	1.25620i	0.0468752	−	0.0487500i
$665$	17.5460	−	17.5460i	0.680406	−	0.680406i
$666$	2.45196	+	6.65356i	0.0950115	+	0.257820i
$667$	0.991905	−	2.39467i	0.0384067	−	0.0927221i
$668$	−2.57636	+	1.53270i	−0.0996823	+	0.0593019i
$669$	−0.443007	−	10.4491i	−0.0171277	−	0.403987i
$670$	7.49169	−	5.82675i	0.289429	−	0.225107i
$671$	−12.6494			−0.488325
$672$	8.19855	+	5.36505i	0.316266	+	0.206961i
$673$	46.7057			1.80037			0.900187	−	0.435504i	$-0.143430\pi$
$673$	46.7057			1.80037			0.900187	+	0.435504i	$0.143430\pi$
$674$	5.14360	−	4.00049i	0.198124	−	0.154093i
$675$	54.0291	+	41.7839i	2.07958	+	1.60826i
$676$	5.86365	+	9.85639i	0.225525	+	0.379092i
$677$	−11.8658	+	28.6465i	−0.456038	+	1.10097i	0.513949	+	0.857820i	$0.328182\pi$
$677$	−11.8658	+	28.6465i	−0.456038	+	1.10097i	−0.969988	+	0.243154i	$0.921818\pi$
$678$	−3.41829	−	4.03041i	−0.131279	−	0.154787i
$679$	−8.22766	+	8.22766i	−0.315749	+	0.315749i
$680$	0.502480	+	25.6290i	0.0192692	+	0.982827i
$681$	17.9171	+	38.5502i	0.686583	+	1.47725i
$682$	2.98967	+	10.8729i	0.114480	+	0.416345i
$683$	11.1057	−	26.8116i	0.424950	−	1.02592i	−0.555917	−	0.831238i	$-0.687633\pi$
$683$	11.1057	−	26.8116i	0.424950	−	1.02592i	0.980867	−	0.194681i	$-0.0623672\pi$
$684$	−34.0418	+	7.92440i	−1.30162	+	0.302997i
$685$	−50.9117	+	21.0883i	−1.94524	+	0.805743i
$686$	0.175426	−	1.40329i	0.00669779	−	0.0535779i
$687$	13.4788	+	4.92516i	0.514248	+	0.187906i
$688$	3.34484	+	4.13089i	0.127521	+	0.157489i
$689$	−30.0498			−1.14481
$690$	36.4478	−	70.9261i	1.38754	−	2.70011i
$691$	3.45765	+	8.34750i	0.131535	+	0.317554i	0.975901	−	0.218213i	$-0.0700227\pi$
$691$	3.45765	+	8.34750i	0.131535	+	0.317554i	−0.844366	+	0.535767i	$0.820023\pi$
$692$	−27.9969	+	4.05875i	−1.06428	+	0.154291i
$693$	−6.88455	−	13.3070i	−0.261523	−	0.505491i
$694$	9.77872	+	35.5635i	0.371195	+	1.34997i
$695$	42.8941	−	42.8941i	1.62706	−	1.62706i
$696$	1.09982	−	1.24534i	0.0416885	−	0.0472047i
$697$	−1.15229	−	1.15229i	−0.0436460	−	0.0436460i
$698$	11.1523	−	19.6111i	0.422119	−	0.742292i
$699$	−5.19632	−	4.77363i	−0.196543	−	0.180555i
$700$	−6.47169	+	25.4801i	−0.244607	+	0.963057i
$701$	3.90136	−	1.61600i	0.147352	−	0.0610354i	−0.307788	−	0.951455i	$-0.599589\pi$
$701$	3.90136	−	1.61600i	0.147352	−	0.0610354i	0.455141	+	0.890419i	$0.349589\pi$
$702$	29.4187	+	12.0910i	1.11034	+	0.456346i
$703$		−	9.73622i		−	0.367208i
$704$	16.7245	+	36.2842i	0.630328	+	1.36751i
$705$	−52.6725	−	19.2465i	−1.98376	−	0.724866i
$706$	−5.53975	+	4.30861i	−0.208491	+	0.162157i
$707$	0.687953	+	1.66087i	0.0258732	+	0.0624633i
$708$	17.2019	−	25.1948i	0.646485	−	0.946877i
$709$	38.0940	+	15.7791i	1.43065	+	0.592595i	0.957512	−	0.288393i	$-0.0931209\pi$
$709$	38.0940	+	15.7791i	1.43065	+	0.592595i	0.473139	+	0.880988i	$0.343121\pi$
$710$	−23.5995	−	13.4204i	−0.885675	−	0.503657i
$711$	−19.7097	+	1.67426i	−0.739173	+	0.0627897i
$712$	−8.44743	+	21.5810i	−0.316581	+	0.808783i
$713$	−8.62829	−	8.62829i	−0.323132	−	0.323132i
$714$	−5.19411	−	0.426843i	−0.194385	−	0.0159742i
$715$	−85.0685	−	35.2365i	−3.18138	−	1.31777i
$716$	2.12227	+	14.6392i	0.0793131	+	0.547094i
$717$	0.0838620	+	1.97804i	0.00313188	+	0.0738711i
$718$	−3.00488	+	24.0371i	−0.112141	+	0.897055i
$719$		−	0.739013i		−	0.0275605i	−0.999905	−	0.0137803i	$-0.995613\pi$
$719$		−	0.739013i		−	0.0275605i	0.999905	−	0.0137803i	$-0.00438654\pi$
$720$	36.8606	−	35.4135i	1.37371	−	1.31978i
$721$			0.342077i			0.0127396i
$722$	20.9574	+	2.61990i	0.779954	+	0.0975024i
$723$	−1.41428	−	33.3583i	−0.0525975	−	1.24061i
$724$	−23.8593	−	17.8173i	−0.886722	−	0.662176i
$725$	4.11859	+	1.70597i	0.152960	+	0.0633583i
$726$	2.79692	−	34.0348i	0.103803	−	1.26315i
$727$	19.5403	+	19.5403i	0.724710	+	0.724710i	0.969561	−	0.244851i	$-0.0787389\pi$
$727$	19.5403	+	19.5403i	0.724710	+	0.724710i	−0.244851	+	0.969561i	$0.578739\pi$
$728$	0.239976	+	12.2400i	0.00889410	+	0.453644i
$729$	26.1322	−	6.79044i	0.967858	−	0.251498i
$730$	25.5093	−	44.8578i	0.944142	−	1.66026i
$731$	−2.61203	−	1.08194i	−0.0966094	−	0.0400169i
$732$	8.62216	−	1.62551i	0.318684	−	0.0600806i
$733$	−20.4560	−	49.3852i	−0.755560	−	1.82408i	−0.525203	−	0.850977i	$-0.676010\pi$
$733$	−20.4560	−	49.3852i	−0.755560	−	1.82408i	−0.230358	−	0.973106i	$-0.573990\pi$
$734$	27.6102	+	35.4996i	1.01911	+	1.31031i
$735$	−6.92978	−	2.53214i	−0.255609	−	0.0933995i
$736$	−35.1408	−	25.1843i	−1.29531	−	0.928306i
$737$			7.86826i			0.289831i
$738$	−0.128720	+	3.24694i	−0.00473825	+	0.119521i
$739$	30.1692	−	12.4965i	1.10979	−	0.459691i	0.248926	−	0.968523i	$-0.419922\pi$
$739$	30.1692	−	12.4965i	1.10979	−	0.459691i	0.860866	+	0.508832i	$0.169922\pi$
$740$	7.27993	+	12.2371i	0.267616	+	0.449843i
$741$	−32.1609	−	29.5448i	−1.18146	−	1.08536i
$742$	−8.53482	−	4.85350i	−0.313323	−	0.178178i
$743$	6.42151	+	6.42151i	0.235582	+	0.235582i	0.815018	−	0.579436i	$-0.196727\pi$
$743$	6.42151	+	6.42151i	0.235582	+	0.235582i	−0.579436	+	0.815018i	$0.696727\pi$
$744$	−3.43505	−	7.02705i	−0.125935	−	0.257624i
$745$	52.9971	−	52.9971i	1.94167	−	1.94167i
$746$	47.4380	−	13.0438i	1.73683	−	0.477567i
$747$	1.64172	−	0.849366i	0.0600674	−	0.0310767i
$748$	−17.0275	−	12.7156i	−0.622588	−	0.464929i
$749$	1.61412	+	3.89683i	0.0589786	+	0.142387i
$750$	75.5839	+	38.8414i	2.75993	+	1.41829i
$751$	−53.6934			−1.95930			−0.979650	−	0.200712i	$-0.935675\pi$
$751$	−53.6934			−1.95930			−0.979650	+	0.200712i	$0.935675\pi$
$752$	−14.5084	+	26.7185i	−0.529068	+	0.974324i
$753$	−25.6209	−	9.36187i	−0.933677	−	0.341166i
$754$	2.05994	+	0.257513i	0.0750185	+	0.00937809i
$755$	23.9036	−	9.90119i	0.869940	−	0.360341i
$756$	6.40270	+	8.18569i	0.232864	+	0.297711i
$757$	−13.0057	+	31.3985i	−0.472699	+	1.14120i	0.490267	+	0.871572i	$0.336899\pi$
$757$	−13.0057	+	31.3985i	−0.472699	+	1.14120i	−0.962966	+	0.269624i	$0.913101\pi$
$758$	−48.9750	+	13.4664i	−1.77885	+	0.489122i
$759$	27.8636	+	59.9510i	1.01138	+	2.17608i
$760$	−64.3027	+	28.1242i	−2.33250	+	1.02017i
$761$	−13.3111	+	13.3111i	−0.482527	+	0.482527i	−0.905938	−	0.423411i	$-0.860833\pi$
$761$	−13.3111	+	13.3111i	−0.482527	+	0.482527i	0.423411	+	0.905938i	$0.360833\pi$
$762$	20.8892	−	17.7166i	0.756734	−	0.641805i
$763$	4.67306	−	11.2818i	0.169176	−	0.408428i
$764$	−10.4499	+	41.1428i	−0.378063	+	1.48849i
$765$	−8.24128	+	25.9098i	−0.297964	+	0.936770i
$766$	−3.46794	−	4.45887i	−0.125302	−	0.161105i
$767$	38.1179			1.37636
$768$	−16.0625	−	22.5831i	−0.579607	−	0.814896i
$769$	−1.57019			−0.0566225			−0.0283113	−	0.999599i	$-0.509013\pi$
$769$	−1.57019			−0.0566225			−0.0283113	+	0.999599i	$0.509013\pi$
$770$	−18.4701	−	23.7478i	−0.665617	−	0.855812i
$771$	1.74924	+	41.2589i	0.0629972	+	1.48590i
$772$	−3.81940	+	15.0376i	−0.137463	+	0.541215i
$773$	−6.12377	+	14.7841i	−0.220257	+	0.531747i	−0.994925	−	0.100621i	$-0.967917\pi$
$773$	−6.12377	+	14.7841i	−0.220257	+	0.531747i	0.774668	+	0.632368i	$0.217917\pi$
$774$	1.94944	+	5.28993i	0.0700711	+	0.190143i
$775$	14.8397	−	14.8397i	0.533060	−	0.533060i
$776$	30.1528	−	13.1880i	1.08242	−	0.473420i
$777$	−2.62519	+	1.22012i	−0.0941783	+	0.0437714i
$778$	−28.9718	+	7.96623i	−1.03869	+	0.285603i
$779$	1.70741	−	4.12206i	0.0611745	−	0.147688i
$780$	62.5129	+	13.0864i	2.23832	+	0.468568i
$781$	20.7939	−	8.61309i	0.744062	−	0.308201i
$782$	22.8186	+	2.85256i	0.815990	+	0.102007i
$783$	1.52948	−	0.875343i	0.0546592	−	0.0312822i
$784$	−1.90878	+	3.51519i	−0.0681708	+	0.125542i
$785$	−86.1183			−3.07369
$786$	14.0288	−	27.2996i	0.500392	−	0.973744i
$787$	−14.1609	−	34.1874i	−0.504781	−	1.21865i	−0.946852	−	0.321669i	$-0.895756\pi$
$787$	−14.1609	−	34.1874i	−0.504781	−	1.21865i	0.442072	−	0.896980i	$-0.354244\pi$
$788$	10.4401	+	7.79631i	0.371912	+	0.277732i
$789$	−13.3790	−	12.2907i	−0.476306	−	0.437561i
$790$	−38.2986	+	10.5308i	−1.36260	+	0.374668i
$791$	1.52559	−	1.52559i	0.0542436	−	0.0542436i
$792$	4.41381	+	42.1462i	0.156838	+	1.49760i
$793$	7.75200	+	7.75200i	0.275282	+	0.275282i
$794$	−29.9227	−	17.0162i	−1.06192	−	0.603881i
$795$	−34.6527	+	37.7211i	−1.22901	+	1.33783i
$796$	−21.7955	−	36.6366i	−0.772520	−	1.29855i
$797$	−25.3590	+	10.5040i	−0.898262	+	0.372072i	−0.783552	−	0.621327i	$-0.786594\pi$
$797$	−25.3590	+	10.5040i	−0.898262	+	0.372072i	−0.114710	+	0.993399i	$0.536594\pi$
$798$	−4.36249	−	13.5859i	−0.154430	−	0.480934i
$799$		−	16.1719i		−	0.572120i
$800$	43.3144	−	60.4384i	1.53139	−	2.13682i
$801$	−15.8480	+	18.7904i	−0.559961	+	0.663925i
$802$	−10.5638	−	13.5823i	−0.373021	−	0.479609i
$803$	16.3717	+	39.5248i	0.577745	+	1.39480i
$804$	−1.01111	−	5.36320i	−0.0356590	−	0.189146i
$805$	30.0768	+	12.4582i	1.06007	+	0.439095i
$806$	4.83111	−	8.49546i	0.170169	−	0.299240i
$807$	11.8303	+	25.4540i	0.416447	+	0.896023i
$808$	−0.0996708	−	5.08371i	−0.00350641	−	0.178844i
$809$	−23.4392	−	23.4392i	−0.824077	−	0.824077i	0.162613	−	0.986690i	$-0.448008\pi$
$809$	−23.4392	−	23.4392i	−0.824077	−	0.824077i	−0.986690	+	0.162613i	$0.948008\pi$
$810$	49.1026	−	22.9859i	1.72529	−	0.807641i
$811$	45.9343	+	19.0266i	1.61297	+	0.668114i	0.993173	−	0.116648i	$-0.0372150\pi$
$811$	45.9343	+	19.0266i	1.61297	+	0.668114i	0.619797	+	0.784762i	$0.287215\pi$
$812$	0.543476	+	0.405850i	0.0190723	+	0.0142426i
$813$	−18.2166	+	0.772320i	−0.638883	+	0.0270865i
$814$	−11.7133	−	1.46428i	−0.410550	−	0.0513231i
$815$			55.4998i			1.94407i
$816$	13.2404	+	6.47916i	0.463507	+	0.226816i
$817$		−	7.74081i		−	0.270817i
$818$	−2.33775	+	18.7005i	−0.0817376	+	0.653847i
$819$	−3.93590	+	12.3741i	−0.137531	+	0.432385i
$820$	0.936156	+	6.45751i	0.0326920	+	0.225506i
$821$	−14.0542	−	5.82146i	−0.490496	−	0.203170i	0.123706	−	0.992319i	$-0.460522\pi$
$821$	−14.0542	−	5.82146i	−0.490496	−	0.203170i	−0.614202	+	0.789149i	$0.710522\pi$
$822$	−2.59537	+	31.5823i	−0.0905241	+	1.10156i
$823$	−13.7350	−	13.7350i	−0.478771	−	0.478771i	0.425968	−	0.904738i	$-0.359934\pi$
$823$	−13.7350	−	13.7350i	−0.478771	−	0.478771i	−0.904738	+	0.425968i	$0.859934\pi$
$824$	0.352668	−	0.900976i	0.0122858	−	0.0313870i
$825$	−103.109	+	47.9224i	−3.58981	+	1.66844i
$826$	10.8263	+	6.15661i	0.376696	+	0.214216i
$827$	−0.334641	−	0.138613i	−0.0116366	−	0.00482004i	0.376858	−	0.926271i	$-0.377005\pi$
$827$	−0.334641	−	0.138613i	−0.0116366	−	0.00482004i	−0.388494	+	0.921451i	$0.627005\pi$
$828$	−26.6965	−	37.2835i	−0.927767	−	1.29569i
$829$	14.6349	+	35.3317i	0.508290	+	1.22712i	0.944867	+	0.327453i	$0.106190\pi$
$829$	14.6349	+	35.3317i	0.508290	+	1.22712i	−0.436578	+	0.899667i	$0.643810\pi$
$830$	2.92983	−	2.27871i	0.101696	−	0.0790952i
$831$	4.61862	−	12.6399i	0.160218	−	0.438473i
$832$	11.9869	−	32.4856i	0.415571	−	1.12623i
$833$		−	2.12763i		−	0.0737181i
$834$	−10.6648	−	33.2128i	−0.369292	−	1.15007i
$835$	−5.89876	+	2.44335i	−0.204135	+	0.0845555i
$836$	14.3236	−	56.3945i	0.495393	−	1.95044i
$837$	−1.05172	−	8.22923i	−0.0363527	−	0.284444i
$838$	−2.47327	+	4.34922i	−0.0854377	+	0.150241i
$839$	15.3445	+	15.3445i	0.529751	+	0.529751i	0.920498	−	0.390747i	$-0.127783\pi$
$839$	15.3445	+	15.3445i	0.529751	+	0.529751i	−0.390747	+	0.920498i	$0.627783\pi$
$840$	15.6414	+	13.8136i	0.539680	+	0.476615i
$841$	−20.4248	+	20.4248i	−0.704302	+	0.704302i
$842$	0.101574	+	0.369408i	0.00350048	+	0.0127306i
$843$	7.51256	−	8.17778i	0.258746	−	0.281658i
$844$	−47.1121	+	6.82992i	−1.62167	+	0.235096i
$845$	9.34752	+	22.5669i	0.321565	+	0.776325i
$846$	−23.6880	+	21.8815i	−0.814411	+	0.752301i
$847$	13.9415			0.479035
$848$	17.4756	+	21.5824i	0.600114	+	0.741143i
$849$	5.48882	−	15.0214i	0.188376	−	0.515533i
$850$	−4.90610	+	39.2456i	−0.168278	+	1.34611i
$851$	11.8013	−	4.88825i	0.404542	−	0.167567i
$852$	−13.0668	+	8.54301i	−0.447661	+	0.292679i
$853$	9.58832	−	23.1483i	0.328298	−	0.792581i	−0.670421	−	0.741981i	$-0.733887\pi$
$853$	9.58832	−	23.1483i	0.328298	−	0.792581i	0.998719	−	0.0506004i	$-0.0161135\pi$
$854$	0.949676	+	3.45380i	0.0324972	+	0.118187i
$855$	−74.1743	+	6.30080i	−2.53671	+	0.215483i
$856$	−0.233854	−	11.9277i	−0.00799295	−	0.407681i
$857$	4.80632	−	4.80632i	0.164181	−	0.164181i	−0.620235	−	0.784416i	$-0.712963\pi$
$857$	4.80632	−	4.80632i	0.164181	−	0.164181i	0.784416	+	0.620235i	$0.212963\pi$
$858$	−40.3811	+	34.2482i	−1.37859	+	1.16921i
$859$	−15.3632	+	37.0900i	−0.524184	+	1.26549i	0.411098	+	0.911591i	$0.365145\pi$
$859$	−15.3632	+	37.0900i	−0.524184	+	1.26549i	−0.935283	+	0.353902i	$0.884855\pi$
$860$	5.78793	+	9.72911i	0.197367	+	0.331760i
$861$	−1.32541	+	0.0561927i	−0.0451697	+	0.00191504i
$862$	35.4633	−	27.5820i	1.20789	−	0.939447i
$863$	−13.1338			−0.447079			−0.223539	−	0.974695i	$-0.571761\pi$
$863$	−13.1338			−0.447079			−0.223539	+	0.974695i	$0.571761\pi$
$864$	−8.42456	−	28.1607i	−0.286609	−	0.958048i
$865$	−60.2516			−2.04862
$866$	−42.2564	+	32.8654i	−1.43593	+	1.11681i
$867$	21.5848	−	0.915121i	0.733058	−	0.0310791i
$868$	2.74429	−	1.63260i	0.0931472	−	0.0554141i
$869$	12.6015	−	30.4227i	0.427476	−	1.03202i
$870$	2.69872	−	2.28885i	0.0914952	−	0.0775993i
$871$	4.82194	−	4.82194i	0.163385	−	0.163385i
$872$	−23.9392	+	24.8967i	−0.810683	+	0.843107i
$873$	34.7818	−	2.95457i	1.17718	−	0.0999969i
$874$	16.6929	+	60.7090i	0.564644	+	2.05351i
$875$	−13.2764	+	32.0521i	−0.448824	+	1.08356i
$876$	−16.2385	−	24.8373i	−0.548648	−	0.839173i
$877$	−34.8345	+	14.4289i	−1.17628	+	0.487229i	−0.883262	−	0.468879i	$-0.844658\pi$
$877$	−34.8345	+	14.4289i	−1.17628	+	0.487229i	−0.293013	+	0.956108i	$0.594658\pi$
$878$	2.70433	−	21.6328i	0.0912666	−	0.730072i
$879$	17.0719	−	46.7213i	0.575823	−	1.57587i
$880$	24.1643	+	81.5899i	0.814579	+	2.75040i
$881$	15.1865			0.511647			0.255823	−	0.966724i	$-0.417653\pi$
$881$	15.1865			0.511647			0.255823	+	0.966724i	$0.417653\pi$
$882$	−3.11648	+	2.87881i	−0.104937	+	0.0969345i
$883$	−9.14181	−	22.0703i	−0.307646	−	0.742724i	−0.999780	−	0.0209552i	$-0.993329\pi$
$883$	−9.14181	−	22.0703i	−0.307646	−	0.742724i	0.692134	−	0.721769i	$-0.256671\pi$
$884$	2.64249	+	18.2276i	0.0888764	+	0.613061i
$885$	43.9566	−	47.8488i	1.47758	−	1.60842i
$886$	−11.6523	−	42.3775i	−0.391468	−	1.42370i
$887$	−31.5049	+	31.5049i	−1.05783	+	1.05783i	−0.0596092	+	0.998222i	$0.518985\pi$
$887$	−31.5049	+	31.5049i	−1.05783	+	1.05783i	−0.998222	+	0.0596092i	$0.981015\pi$
$888$	8.17223	−	0.507120i	0.274242	−	0.0170178i
$889$	7.90693	+	7.90693i	0.265190	+	0.265190i
$890$	−24.3999	+	42.9069i	−0.817886	+	1.43824i
$891$	−9.94977	+	43.8322i	−0.333330	+	1.46843i
$892$	−11.7048	−	2.97291i	−0.391906	−	0.0995402i
$893$	40.9072	−	16.9443i	1.36891	−	0.567020i
$894$	−13.1767	−	41.0356i	−0.440696	−	1.37244i
$895$			31.5049i			1.05309i
$896$	8.65145	−	7.29057i	0.289025	−	0.243561i
$897$	19.6643	−	53.8158i	0.656572	−	1.79686i
$898$	22.4112	−	17.4306i	0.747871	−	0.581665i
$899$	−0.207215	−	0.500262i	−0.00691102	−	0.0166847i
$900$	64.1237	−	45.9152i	2.13746	−	1.53051i
$901$	−13.6469	−	5.65274i	−0.454645	−	0.188320i
$902$	−4.70231	−	2.67407i	−0.156570	−	0.0890366i
$903$	−2.08717	+	0.970058i	−0.0694566	+	0.0322815i
$904$	−5.59097	+	2.44533i	−0.185953	+	0.0813305i
$905$	−44.8458	−	44.8458i	−1.49072	−	1.49072i
$906$	1.21856	−	14.8282i	0.0404838	−	0.492634i
$907$	23.1684	+	9.59668i	0.769295	+	0.318652i	0.732587	−	0.680674i	$-0.238313\pi$
$907$	23.1684	+	9.59668i	0.769295	+	0.318652i	0.0367081	+	0.999326i	$0.488313\pi$
$908$	48.5790	−	7.04258i	1.61215	−	0.233716i
$909$	1.63472	−	5.13941i	0.0542203	−	0.170463i
$910$	−3.23434	+	25.8726i	−0.107217	+	0.857668i
$911$		−	10.9215i		−	0.361846i	−0.983497	−	0.180923i	$-0.942092\pi$
$911$		−	10.9215i		−	0.361846i	0.983497	−	0.180923i	$-0.0579085\pi$
$912$	−2.51639	+	40.2805i	−0.0833261	+	1.33382i
$913$			3.07710i			0.101837i
$914$	−49.9998	−	6.25050i	−1.65385	−	0.206748i
$915$	18.6704	−	0.791561i	0.617224	−	0.0261682i
$916$	9.91480	−	13.2769i	0.327594	−	0.438682i
$917$	11.5766	+	4.79520i	0.382294	+	0.158352i
$918$	11.0859	+	11.0251i	0.365888	+	0.363882i
$919$	12.5933	+	12.5933i	0.415414	+	0.415414i	0.883619	−	0.468206i	$-0.155099\pi$
$919$	12.5933	+	12.5933i	0.415414	+	0.415414i	−0.468206	+	0.883619i	$0.655099\pi$
$920$	−66.3737	−	63.8211i	−2.18828	−	2.10412i
$921$	−14.0621	−	30.2559i	−0.463362	−	0.996966i
$922$	9.69319	−	17.0454i	0.319228	−	0.561359i
$923$	−18.0216	−	7.46479i	−0.593188	−	0.245706i
$924$	−17.0007	+	3.20510i	−0.559283	+	0.105440i
$925$	8.40728	+	20.2970i	0.276430	+	0.667360i
$926$	10.1753	+	13.0828i	0.334381	+	0.429927i
$927$	0.661630	−	0.784470i	0.0217308	−	0.0257654i
$928$	−1.01301	−	1.62925i	−0.0332538	−	0.0534827i
$929$		−	8.38348i		−	0.275053i	−0.990498	−	0.137526i	$-0.956085\pi$
$929$		−	8.38348i		−	0.275053i	0.990498	−	0.137526i	$-0.0439152\pi$
$930$	−5.09310	−	15.8612i	−0.167009	−	0.520108i
$931$	5.38190	−	2.22926i	0.176385	−	0.0730610i
$932$	−7.00232	+	4.16574i	−0.229368	+	0.136453i
$933$	−9.67587	+	10.5326i	−0.316774	+	0.344823i
$934$	24.0538	+	13.6787i	0.787063	+	0.447580i
$935$	−32.0049	−	32.0049i	−1.04667	−	1.04667i
$936$	23.1237	−	28.5336i	0.755823	−	0.932650i
$937$	20.2999	−	20.2999i	0.663167	−	0.663167i	−0.292958	−	0.956125i	$-0.594640\pi$
$937$	20.2999	−	20.2999i	0.663167	−	0.663167i	0.956125	+	0.292958i	$0.0946396\pi$
$938$	2.14835	−	0.590723i	0.0701462	−	0.0192878i
$939$	−30.3419	−	27.8738i	−0.990171	−	0.909626i
$940$	−38.7450	+	51.8836i	−1.26372	+	1.69226i
$941$	6.55550	+	15.8264i	0.213703	+	0.515925i	0.993987	−	0.109501i	$-0.0349252\pi$
$941$	6.55550	+	15.8264i	0.213703	+	0.515925i	−0.780284	+	0.625426i	$0.784925\pi$
$942$	−22.6348	+	44.0465i	−0.737481	+	1.43511i
$943$	5.85359			0.190619
$944$	−22.1676	−	27.3771i	−0.721494	−	0.891047i
$945$	10.9942	+	19.2102i	0.357642	+	0.624906i
$946$	−9.31268	−	1.16418i	−0.302781	−	0.0378508i
$947$	−19.1765	+	7.94317i	−0.623153	+	0.258118i	−0.671841	−	0.740696i	$-0.734496\pi$
$947$	−19.1765	+	7.94317i	−0.623153	+	0.258118i	0.0486878	+	0.998814i	$0.484496\pi$
$948$	−4.68003	+	22.3562i	−0.152000	+	0.726096i
$949$	14.1890	−	34.2553i	0.460595	−	1.11197i
$950$	−104.413	+	28.7100i	−3.38761	+	0.931474i
$951$	40.9279	−	19.0221i	1.32718	−	0.616835i
$952$	−2.19351	+	5.60385i	−0.0710920	+	0.181622i
$953$	−42.0254	+	42.0254i	−1.36134	+	1.36134i	−0.489119	+	0.872217i	$0.662682\pi$
$953$	−42.0254	+	42.0254i	−1.36134	+	1.36134i	−0.872217	+	0.489119i	$0.837318\pi$
$954$	10.1851	+	27.6380i	0.329756	+	0.894814i
$955$	−34.5980	+	83.5271i	−1.11957	+	2.70287i
$956$	2.21574	+	0.562775i	0.0716621	+	0.0182015i
$957$	0.124265	+	2.93102i	0.00401692	+	0.0947464i
$958$	−1.27077	−	1.63388i	−0.0410566	−	0.0527881i
$959$	−12.9369			−0.417753
$960$	−26.9557	−	52.5085i	−0.869991	−	1.69471i
$961$	28.4509			0.917770
$962$	6.28094	+	8.07566i	0.202506	+	0.260370i
$963$	3.83548	−	12.0584i	0.123597	−	0.388576i
$964$	−37.3669	−	9.49083i	−1.20351	−	0.305679i
$965$	−12.6455	+	30.5290i	−0.407073	+	0.982762i
$966$	14.2772	−	12.1088i	0.459360	−	0.389594i
$967$	6.26193	−	6.26193i	0.201370	−	0.201370i	−0.599217	−	0.800587i	$-0.704521\pi$
$967$	6.26193	−	6.26193i	0.201370	−	0.201370i	0.800587	+	0.599217i	$0.204521\pi$
$968$	−36.7196	−	14.3731i	−1.18021	−	0.461970i
$969$	−9.04792	−	19.4674i	−0.290661	−	0.625384i
$970$	67.5854	−	18.5836i	2.17004	−	0.596685i
$971$	3.75817	−	9.07304i	0.120606	−	0.291168i	−0.852034	−	0.523486i	$-0.824631\pi$
$971$	3.75817	−	9.07304i	0.120606	−	0.291168i	0.972640	+	0.232319i	$0.0746312\pi$
$972$	1.14937	−	31.1557i	0.0368660	−	0.999320i
$973$	13.1569	−	5.44978i	0.421792	−	0.174712i
$974$	9.67617	+	1.20962i	0.310044	+	0.0387588i
$975$	92.5575	+	33.8205i	2.96421	+	1.08312i
$976$	1.05944	−	10.0759i	0.0339120	−	0.322520i
$977$	21.3356			0.682587			0.341293	−	0.939957i	$-0.389135\pi$
$977$	21.3356			0.682587			0.341293	+	0.939957i	$0.389135\pi$
$978$	28.3862	+	14.5872i	0.907690	+	0.466448i
$979$	−15.6597	−	37.8058i	−0.500486	−	1.20828i
$980$	−5.09744	+	6.82600i	−0.162832	+	0.218049i
$981$	−32.5373	+	16.8336i	−1.03884	+	0.537455i
$982$	50.8919	−	13.9935i	1.62403	−	0.446551i
$983$	−12.1533	+	12.1533i	−0.387631	+	0.387631i	−0.873841	−	0.486211i	$-0.838379\pi$
$983$	−12.1533	+	12.1533i	−0.387631	+	0.387631i	0.486211	+	0.873841i	$0.338379\pi$
$984$	3.54884	+	1.21844i	0.113133	+	0.0388425i
$985$	19.6231	+	19.6231i	0.625245	+	0.625245i
$986$	0.887065	+	0.504447i	0.0282499	+	0.0160649i
$987$	−9.69510	−	8.90646i	−0.308599	−	0.283496i
$988$	−43.3385	+	25.7825i	−1.37878	+	0.820249i
$989$	9.38264	−	3.88642i	0.298351	−	0.123581i
$990$	−3.57521	+	90.1840i	−0.113628	+	2.86624i
$991$			28.0241i			0.890214i	0.895477	+	0.445107i	$0.146834\pi$
$991$			28.0241i			0.890214i	−0.895477	+	0.445107i	$0.853166\pi$
$992$	−8.91117	+	1.47076i	−0.282930	+	0.0466966i
$993$	9.72509	+	3.55355i	0.308616	+	0.112768i
$994$	−3.91286	−	5.03092i	−0.124108	−	0.159571i
$995$	−34.7452	−	83.8823i	−1.10150	−	2.65925i
$996$	−0.395422	−	2.09743i	−0.0125294	−	0.0664595i
$997$	−20.8281	−	8.62729i	−0.659633	−	0.273229i	0.0276508	−	0.999618i	$-0.491197\pi$
$997$	−20.8281	−	8.62729i	−0.659633	−	0.273229i	−0.687284	+	0.726389i	$0.741197\pi$
$998$	−5.72187	+	10.0618i	−0.181123	+	0.318502i
$999$	8.38014	+	2.27949i	0.265136	+	0.0721200i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bs.a.155.14	✓	192
3.2	odd	2	inner	672.2.bs.a.155.35	yes	192
32.19	odd	8	inner	672.2.bs.a.659.35	yes	192
96.83	even	8	inner	672.2.bs.a.659.14	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.bs.a.155.14	✓	192	1.1	even	1	trivial
672.2.bs.a.155.35	yes	192	3.2	odd	2	inner
672.2.bs.a.659.14	yes	192	96.83	even	8	inner
672.2.bs.a.659.35	yes	192	32.19	odd	8	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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bs (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.868232 - 1.11632i) q^{2} +(-1.73050 + 0.0733671i) q^{3} +(-0.492347 + 1.93845i) q^{4} +(-1.63009 + 3.93540i) q^{5} +(1.58437 + 1.86809i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.59141 - 1.13341i) q^{8} +(2.98923 - 0.253923i) q^{9} +O(q^{10})\)	\(q+(-0.868232 - 1.11632i) q^{2} +(-1.73050 + 0.0733671i) q^{3} +(-0.492347 + 1.93845i) q^{4} +(-1.63009 + 3.93540i) q^{5} +(1.58437 + 1.86809i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.59141 - 1.13341i) q^{8} +(2.98923 - 0.253923i) q^{9} +(5.80847 - 1.59713i) q^{10} +(-1.91118 + 4.61399i) q^{11} +(0.709787 - 3.39061i) q^{12} +(3.99885 - 1.65638i) q^{13} +(1.40329 + 0.175426i) q^{14} +(2.53214 - 6.92978i) q^{15} +(-3.51519 - 1.90878i) q^{16} +2.12763 q^{17} +(-2.87881 - 3.11648i) q^{18} +(2.22926 + 5.38190i) q^{19} +(-6.82600 - 5.09744i) q^{20} +(1.17177 - 1.27552i) q^{21} +(6.81004 - 1.87252i) q^{22} +(-5.40417 + 5.40417i) q^{23} +(-4.40126 + 2.15148i) q^{24} +(-9.29460 - 9.29460i) q^{25} +(-5.32097 - 3.02588i) q^{26} +(-5.15423 + 0.658725i) q^{27} +(-1.02255 - 1.71883i) q^{28} +(-0.313330 + 0.129786i) q^{29} +(-9.93435 + 3.18997i) q^{30} +1.59660i q^{31} +(0.921182 + 5.58135i) q^{32} +(2.96877 - 8.12471i) q^{33} +(-1.84728 - 2.37512i) q^{34} +(-1.63009 - 3.93540i) q^{35} +(-0.979524 + 5.91950i) q^{36} +(-1.54413 - 0.639601i) q^{37} +(4.07242 - 7.16131i) q^{38} +(-6.79846 + 3.15974i) q^{39} +(0.236168 + 12.0458i) q^{40} +(-0.541581 - 0.541581i) q^{41} +(-2.44126 - 0.200619i) q^{42} +(-1.22767 - 0.508517i) q^{43} +(-8.00303 - 5.97641i) q^{44} +(-3.87345 + 12.1777i) q^{45} +(10.7249 + 1.34072i) q^{46} -7.60088i q^{47} +(6.22306 + 3.04524i) q^{48} -1.00000i q^{49} +(-2.30590 + 18.4456i) q^{50} +(-3.68186 + 0.156098i) q^{51} +(1.24198 + 8.56708i) q^{52} +(-6.41413 - 2.65682i) q^{53} +(5.21041 + 5.18185i) q^{54} +(-15.0425 - 15.0425i) q^{55} +(-1.03096 + 2.63384i) q^{56} +(-4.25258 - 9.14981i) q^{57} +(0.416926 + 0.237093i) q^{58} +(8.13626 + 3.37015i) q^{59} +(12.1864 + 8.32030i) q^{60} +(0.969280 + 2.34005i) q^{61} +(1.78232 - 1.38622i) q^{62} +(-1.93416 + 2.29326i) q^{63} +(5.43078 - 5.87424i) q^{64} +18.4371i q^{65} +(-11.6474 + 3.74003i) q^{66} +(1.45557 - 0.602916i) q^{67} +(-1.04753 + 4.12431i) q^{68} +(8.95540 - 9.74838i) q^{69} +(-2.97787 + 5.23655i) q^{70} +(-3.18672 - 3.18672i) q^{71} +(7.45852 - 4.04604i) q^{72} +(6.05729 - 6.05729i) q^{73} +(0.626666 + 2.27907i) q^{74} +(16.7662 + 15.4024i) q^{75} +(-11.5301 + 1.67154i) q^{76} +(-1.91118 - 4.61399i) q^{77} +(9.42992 + 4.84589i) q^{78} -6.59357 q^{79} +(13.2419 - 10.7222i) q^{80} +(8.87105 - 1.51807i) q^{81} +(-0.134361 + 1.07480i) q^{82} +(0.569240 - 0.235787i) q^{83} +(1.89562 + 2.89941i) q^{84} +(-3.46824 + 8.37308i) q^{85} +(0.498233 + 1.81198i) q^{86} +(0.532695 - 0.247582i) q^{87} +(0.276892 + 14.1229i) q^{88} +(-5.79385 + 5.79385i) q^{89} +(16.9573 - 6.24909i) q^{90} +(-1.65638 + 3.99885i) q^{91} +(-7.81499 - 13.1364i) q^{92} +(-0.117138 - 2.76291i) q^{93} +(-8.48503 + 6.59932i) q^{94} -24.8138 q^{95} +(-2.00359 - 9.59091i) q^{96} +11.6357 q^{97} +(-1.11632 + 0.868232i) q^{98} +(-4.54136 + 14.2776i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 16 q^{4}+O(q^{10}) \) 192 * q - 16 * q^4	\( 192 q - 16 q^{4} + 8 q^{10} + 16 q^{16} + 16 q^{22} + 24 q^{27} - 84 q^{30} + 40 q^{36} + 32 q^{37} + 24 q^{39} - 96 q^{46} - 72 q^{48} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 28 q^{60} - 16 q^{61} - 64 q^{64} - 12 q^{66} - 32 q^{67} + 56 q^{69} - 24 q^{70} + 60 q^{72} + 80 q^{75} - 56 q^{76} + 100 q^{78} - 32 q^{79} - 120 q^{82} - 56 q^{87} + 40 q^{88} + 60 q^{90} - 80 q^{93} + 216 q^{94} + 96 q^{96} - 64 q^{99}+O(q^{100}) \) 192 * q - 16 * q^4 + 8 * q^10 + 16 * q^16 + 16 * q^22 + 24 * q^27 - 84 * q^30 + 40 * q^36 + 32 * q^37 + 24 * q^39 - 96 * q^46 - 72 * q^48 + 16 * q^52 - 32 * q^55 - 72 * q^58 - 28 * q^60 - 16 * q^61 - 64 * q^64 - 12 * q^66 - 32 * q^67 + 56 * q^69 - 24 * q^70 + 60 * q^72 + 80 * q^75 - 56 * q^76 + 100 * q^78 - 32 * q^79 - 120 * q^82 - 56 * q^87 + 40 * q^88 + 60 * q^90 - 80 * q^93 + 216 * q^94 + 96 * q^96 - 64 * q^99

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