LMFDB - Embedded newform 133.2.s.d.103.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [133,2,Mod(31,133)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(133, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("133.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 133 = 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	133.s (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:	$1.06201034688$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 26x^{14} + 265x^{12} + 1335x^{10} + 3450x^{8} + 4344x^{6} + 2376x^{4} + 423x^{2} + 9 $ x^16 + 26x^14 + 265x^12 + 1335x^10 + 3450x^8 + 4344x^6 + 2376x^4 + 423*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			103.4
Root			$0.525923i$ of defining polynomial
Character	$\chi$	$=$	133.103
Dual form			133.2.s.d.31.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.455463 + 0.262961i) q^{2} -0.0953773 q^{3} +(-0.861703 + 1.49251i) q^{4} +(-3.27538 + 1.89104i) q^{5} +(0.0434408 - 0.0250806i) q^{6} +(-0.941581 - 2.47253i) q^{7} -1.95822i q^{8} -2.99090 q^{9} +O(q^{10})$	\(q+(-0.455463 + 0.262961i) q^{2} -0.0953773 q^{3} +(-0.861703 + 1.49251i) q^{4} +(-3.27538 + 1.89104i) q^{5} +(0.0434408 - 0.0250806i) q^{6} +(-0.941581 - 2.47253i) q^{7} -1.95822i q^{8} -2.99090 q^{9} +(0.994541 - 1.72259i) q^{10} +(0.250365 + 0.433645i) q^{11} +(0.0821869 - 0.142352i) q^{12} +(3.23751 + 5.60753i) q^{13} +(1.07904 + 0.878547i) q^{14} +(0.312397 - 0.180362i) q^{15} +(-1.20847 - 2.09313i) q^{16} +3.98151i q^{17} +(1.36224 - 0.786492i) q^{18} +(3.19319 + 2.96708i) q^{19} -6.51805i q^{20} +(0.0898054 + 0.235824i) q^{21} +(-0.228064 - 0.131673i) q^{22} -2.32375 q^{23} +0.186770i q^{24} +(4.65206 - 8.05760i) q^{25} +(-2.94913 - 1.70268i) q^{26} +0.571396 q^{27} +(4.50165 + 0.725268i) q^{28} +(-5.67542 + 3.27670i) q^{29} +(-0.0948566 + 0.164296i) q^{30} +(-2.24721 - 3.89229i) q^{31} +(4.49257 + 2.59378i) q^{32} +(-0.0238792 - 0.0413599i) q^{33} +(-1.04698 - 1.81343i) q^{34} +(7.75969 + 6.31791i) q^{35} +(2.57727 - 4.46396i) q^{36} +(0.502008 + 0.289835i) q^{37} +(-2.23460 - 0.511707i) q^{38} +(-0.308785 - 0.534831i) q^{39} +(3.70308 + 6.41392i) q^{40} +(2.62442 - 4.54562i) q^{41} +(-0.102916 - 0.0837935i) q^{42} +(0.670487 - 1.16132i) q^{43} -0.862961 q^{44} +(9.79633 - 5.65591i) q^{45} +(1.05838 - 0.611057i) q^{46} +7.35971i q^{47} +(0.115260 + 0.199637i) q^{48} +(-5.22685 + 4.65618i) q^{49} +4.89325i q^{50} -0.379745i q^{51} -11.1591 q^{52} +(-7.15122 - 4.12876i) q^{53} +(-0.260250 + 0.150255i) q^{54} +(-1.64008 - 0.946901i) q^{55} +(-4.84178 + 1.84383i) q^{56} +(-0.304558 - 0.282992i) q^{57} +(1.72329 - 2.98483i) q^{58} -5.63983 q^{59} +0.621674i q^{60} -1.47410i q^{61} +(2.04704 + 1.18186i) q^{62} +(2.81618 + 7.39511i) q^{63} +2.10561 q^{64} +(-21.2081 - 12.2445i) q^{65} +(0.0217521 + 0.0125586i) q^{66} +(4.87051 + 2.81199i) q^{67} +(-5.94245 - 3.43087i) q^{68} +0.221633 q^{69} +(-5.19561 - 0.837074i) q^{70} +(5.27310 + 3.04442i) q^{71} +5.85686i q^{72} +7.24094i q^{73} -0.304861 q^{74} +(-0.443701 + 0.768512i) q^{75} +(-7.17998 + 2.20914i) q^{76} +(0.836464 - 1.02735i) q^{77} +(0.281280 + 0.162397i) q^{78} +(7.77277 - 4.48761i) q^{79} +(7.91637 + 4.57052i) q^{80} +8.91821 q^{81} +2.76048i q^{82} +8.36460i q^{83} +(-0.429355 - 0.0691742i) q^{84} +(-7.52918 - 13.0409i) q^{85} +0.705249i q^{86} +(0.541306 - 0.312523i) q^{87} +(0.849174 - 0.490271i) q^{88} -3.57155 q^{89} +(-2.97457 + 5.15211i) q^{90} +(10.8164 - 13.2848i) q^{91} +(2.00238 - 3.46823i) q^{92} +(0.214333 + 0.371236i) q^{93} +(-1.93532 - 3.35207i) q^{94} +(-16.0698 - 3.67985i) q^{95} +(-0.428489 - 0.247388i) q^{96} +(-1.29625 + 2.24517i) q^{97} +(1.15624 - 3.49518i) q^{98} +(-0.748818 - 1.29699i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 10 q^{4} + 9 q^{5} - 6 q^{6} + 2 q^{7} + 16 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 10 * q^4 + 9 * q^5 - 6 * q^6 + 2 * q^7 + 16 * q^9	$ 16 q - 8 q^{3} + 10 q^{4} + 9 q^{5} - 6 q^{6} + 2 q^{7} + 16 q^{9} - 2 q^{10} - 9 q^{11} - 17 q^{12} + 15 q^{13} + 3 q^{14} - 12 q^{15} - 22 q^{16} - 3 q^{18} + 8 q^{19} - 10 q^{21} - 27 q^{22} + 30 q^{23} + 13 q^{25} - 9 q^{26} - 38 q^{27} + 35 q^{28} - 18 q^{29} - 32 q^{30} - 27 q^{31} + 27 q^{32} - 12 q^{33} - 16 q^{34} - 6 q^{35} + 4 q^{36} - 39 q^{37} + 27 q^{38} - 9 q^{39} + 9 q^{40} + 9 q^{41} + 48 q^{42} - 9 q^{43} + 18 q^{44} + 75 q^{45} - 36 q^{46} + 35 q^{48} - 8 q^{49} + 18 q^{53} - 18 q^{54} + 15 q^{56} - 22 q^{57} - 20 q^{58} + 18 q^{59} - 45 q^{62} - 46 q^{63} - 22 q^{64} - 36 q^{65} - 45 q^{66} + 18 q^{67} + 63 q^{68} + 30 q^{69} - 19 q^{70} - 9 q^{71} + 18 q^{74} + 10 q^{75} + 98 q^{76} + 30 q^{77} + 54 q^{78} + 21 q^{79} + 27 q^{80} + 40 q^{81} - 34 q^{84} + 31 q^{85} - 48 q^{87} + 18 q^{88} + 24 q^{89} + 28 q^{90} + 15 q^{91} + 54 q^{92} + 6 q^{93} - 49 q^{94} - 66 q^{95} - 69 q^{96} + q^{97} + 15 q^{98} + 18 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 + 10 * q^4 + 9 * q^5 - 6 * q^6 + 2 * q^7 + 16 * q^9 - 2 * q^10 - 9 * q^11 - 17 * q^12 + 15 * q^13 + 3 * q^14 - 12 * q^15 - 22 * q^16 - 3 * q^18 + 8 * q^19 - 10 * q^21 - 27 * q^22 + 30 * q^23 + 13 * q^25 - 9 * q^26 - 38 * q^27 + 35 * q^28 - 18 * q^29 - 32 * q^30 - 27 * q^31 + 27 * q^32 - 12 * q^33 - 16 * q^34 - 6 * q^35 + 4 * q^36 - 39 * q^37 + 27 * q^38 - 9 * q^39 + 9 * q^40 + 9 * q^41 + 48 * q^42 - 9 * q^43 + 18 * q^44 + 75 * q^45 - 36 * q^46 + 35 * q^48 - 8 * q^49 + 18 * q^53 - 18 * q^54 + 15 * q^56 - 22 * q^57 - 20 * q^58 + 18 * q^59 - 45 * q^62 - 46 * q^63 - 22 * q^64 - 36 * q^65 - 45 * q^66 + 18 * q^67 + 63 * q^68 + 30 * q^69 - 19 * q^70 - 9 * q^71 + 18 * q^74 + 10 * q^75 + 98 * q^76 + 30 * q^77 + 54 * q^78 + 21 * q^79 + 27 * q^80 + 40 * q^81 - 34 * q^84 + 31 * q^85 - 48 * q^87 + 18 * q^88 + 24 * q^89 + 28 * q^90 + 15 * q^91 + 54 * q^92 + 6 * q^93 - 49 * q^94 - 66 * q^95 - 69 * q^96 + q^97 + 15 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/133\mathbb{Z}\right)^\times$.

$n$	$78$	$115$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.455463	+	0.262961i	−0.322061	+	0.185942i	−0.652311	−	0.757952i	$-0.726200\pi$
$2$	−0.455463	+	0.262961i	−0.322061	+	0.185942i	0.330250	+	0.943893i	$0.392867\pi$
$3$	−0.0953773			−0.0550661			−0.0275331	−	0.999621i	$-0.508765\pi$
$3$	−0.0953773			−0.0550661			−0.0275331	+	0.999621i	$0.508765\pi$
$4$	−0.861703	+	1.49251i	−0.430851	+	0.746256i
$5$	−3.27538	+	1.89104i	−1.46479	+	0.845698i	−0.999227	−	0.0393150i	$-0.987482\pi$
$5$	−3.27538	+	1.89104i	−1.46479	+	0.845698i	−0.465566	+	0.885013i	$0.654149\pi$
$6$	0.0434408	−	0.0250806i	0.0177346	−	0.0102391i
$7$	−0.941581	−	2.47253i	−0.355884	−	0.934530i
$7$	−0.941581	−	2.47253i	−0.355884	−	0.934530i
$8$		−	1.95822i		−	0.692337i
$9$	−2.99090			−0.996968
$10$	0.994541	−	1.72259i	0.314501	−	0.544732i
$11$	0.250365	+	0.433645i	0.0754880	+	0.130749i	0.901298	−	0.433199i	$-0.142615\pi$
$11$	0.250365	+	0.433645i	0.0754880	+	0.130749i	−0.825810	+	0.563948i	$0.809282\pi$
$12$	0.0821869	−	0.142352i	0.0237253	−	0.0410934i
$13$	3.23751	+	5.60753i	0.897923	+	1.55525i	0.830145	+	0.557547i	$0.188258\pi$
$13$	3.23751	+	5.60753i	0.897923	+	1.55525i	0.0677777	+	0.997700i	$0.478409\pi$
$14$	1.07904	+	0.878547i	0.288384	+	0.234802i
$15$	0.312397	−	0.180362i	0.0806604	−	0.0465693i
$16$	−1.20847	−	2.09313i	−0.302117	−	0.523282i
$17$			3.98151i			0.965657i	0.875715	+	0.482828i	$0.160391\pi$
$17$			3.98151i			0.965657i	−0.875715	+	0.482828i	$0.839609\pi$
$18$	1.36224	−	0.786492i	0.321084	−	0.185378i
$19$	3.19319	+	2.96708i	0.732568	+	0.680694i
$19$	3.19319	+	2.96708i	0.732568	+	0.680694i
$20$		−	6.51805i		−	1.45748i
$21$	0.0898054	+	0.235824i	0.0195971	+	0.0514609i
$22$	−0.228064	−	0.131673i	−0.0486234	−	0.0280727i
$23$	−2.32375			−0.484536			−0.242268	−	0.970209i	$-0.577891\pi$
$23$	−2.32375			−0.484536			−0.242268	+	0.970209i	$0.577891\pi$
$24$			0.186770i			0.0381243i
$25$	4.65206	−	8.05760i	0.930411	−	1.61152i
$26$	−2.94913	−	1.70268i	−0.578371	−	0.333923i
$27$	0.571396			0.109965
$28$	4.50165	+	0.725268i	0.850732	+	0.137063i
$29$	−5.67542	+	3.27670i	−1.05390	+	0.608468i	−0.923738	−	0.383025i	$-0.874882\pi$
$29$	−5.67542	+	3.27670i	−1.05390	+	0.608468i	−0.130160	+	0.991493i	$0.541549\pi$
$30$	−0.0948566	+	0.164296i	−0.0173184	+	0.0299963i
$31$	−2.24721	−	3.89229i	−0.403612	−	0.699076i	0.590547	−	0.807003i	$-0.298912\pi$
$31$	−2.24721	−	3.89229i	−0.403612	−	0.699076i	−0.994159	+	0.107927i	$0.965579\pi$
$32$	4.49257	+	2.59378i	0.794181	+	0.458521i
$33$	−0.0238792	−	0.0413599i	−0.00415683	−	0.00719984i
$34$	−1.04698	−	1.81343i	−0.179556	−	0.311000i
$35$	7.75969	+	6.31791i	1.31163	+	1.06792i
$36$	2.57727	−	4.46396i	0.429545	−	0.743993i
$37$	0.502008	+	0.289835i	0.0825297	+	0.0476485i	0.540697	−	0.841217i	$-0.318161\pi$
$37$	0.502008	+	0.289835i	0.0825297	+	0.0476485i	−0.458167	+	0.888866i	$0.651494\pi$
$38$	−2.23460	−	0.511707i	−0.362501	−	0.0830098i
$39$	−0.308785	−	0.534831i	−0.0494451	−	0.0856415i
$40$	3.70308	+	6.41392i	0.585508	+	1.01413i
$41$	2.62442	−	4.54562i	0.409865	−	0.709907i	−0.585009	−	0.811027i	$-0.698909\pi$
$41$	2.62442	−	4.54562i	0.409865	−	0.709907i	0.994874	+	0.101120i	$0.0322425\pi$
$42$	−0.102916	−	0.0837935i	−0.0158802	−	0.0129296i
$43$	0.670487	−	1.16132i	0.102248	−	0.177099i	−0.810362	−	0.585929i	$-0.800730\pi$
$43$	0.670487	−	1.16132i	0.102248	−	0.177099i	0.912611	+	0.408830i	$0.134063\pi$
$44$	−0.862961			−0.130096
$45$	9.79633	−	5.65591i	1.46035	−	0.843134i
$46$	1.05838	−	0.611057i	0.156050	−	0.0900955i
$47$			7.35971i			1.07352i	0.843734	+	0.536762i	$0.180353\pi$
$47$			7.35971i			1.07352i	−0.843734	+	0.536762i	$0.819647\pi$
$48$	0.115260	+	0.199637i	0.0166364	+	0.0288151i
$49$	−5.22685	+	4.65618i	−0.746693	+	0.665169i
$50$			4.89325i			0.692009i
$51$		−	0.379745i		−	0.0531750i
$52$	−11.1591			−1.54748
$53$	−7.15122	−	4.12876i	−0.982296	−	0.567129i	−0.0793331	−	0.996848i	$-0.525279\pi$
$53$	−7.15122	−	4.12876i	−0.982296	−	0.567129i	−0.902962	+	0.429720i	$0.858612\pi$
$54$	−0.260250	+	0.150255i	−0.0354155	+	0.0204471i
$55$	−1.64008	−	0.946901i	−0.221148	−	0.127680i
$56$	−4.84178	+	1.84383i	−0.647009	+	0.246392i
$57$	−0.304558	−	0.282992i	−0.0403397	−	0.0374832i
$58$	1.72329	−	2.98483i	0.226279	−	0.391927i
$59$	−5.63983			−0.734243			−0.367121	−	0.930173i	$-0.619657\pi$
$59$	−5.63983			−0.734243			−0.367121	+	0.930173i	$0.619657\pi$
$60$			0.621674i			0.0802578i
$61$		−	1.47410i		−	0.188739i	−0.995537	−	0.0943696i	$-0.969916\pi$
$61$		−	1.47410i		−	0.188739i	0.995537	−	0.0943696i	$-0.0300836\pi$
$62$	2.04704	+	1.18186i	0.259975	+	0.150097i
$63$	2.81618	+	7.39511i	0.354805	+	0.931696i
$64$	2.10561			0.263201
$65$	−21.2081	−	12.2445i	−2.63054	−	1.51874i
$66$	0.0217521	+	0.0125586i	0.00267750	+	0.00154586i
$67$	4.87051	+	2.81199i	0.595028	+	0.343539i	0.767083	−	0.641548i	$-0.221707\pi$
$67$	4.87051	+	2.81199i	0.595028	+	0.343539i	−0.172055	+	0.985087i	$0.555041\pi$
$68$	−5.94245	−	3.43087i	−0.720628	−	0.416055i
$69$	0.221633			0.0266815
$70$	−5.19561	−	0.837074i	−0.620995	−	0.100049i
$71$	5.27310	+	3.04442i	0.625801	+	0.361307i	0.779124	−	0.626870i	$-0.215664\pi$
$71$	5.27310	+	3.04442i	0.625801	+	0.361307i	−0.153323	+	0.988176i	$0.548997\pi$
$72$			5.85686i			0.690237i
$73$			7.24094i			0.847488i	0.905782	+	0.423744i	$0.139284\pi$
$73$			7.24094i			0.847488i	−0.905782	+	0.423744i	$0.860716\pi$
$74$	−0.304861			−0.0354394
$75$	−0.443701	+	0.768512i	−0.0512341	+	0.0887401i
$76$	−7.17998	+	2.20914i	−0.823600	+	0.253405i
$77$	0.836464	−	1.02735i	0.0953239	−	0.117077i
$78$	0.281280	+	0.162397i	0.0318487	+	0.0183878i
$79$	7.77277	−	4.48761i	0.874505	−	0.504896i	0.00566234	−	0.999984i	$-0.498198\pi$
$79$	7.77277	−	4.48761i	0.874505	−	0.504896i	0.868843	+	0.495088i	$0.164864\pi$
$80$	7.91637	+	4.57052i	0.885077	+	0.511000i
$81$	8.91821			0.990912
$82$			2.76048i			0.304844i
$83$			8.36460i			0.918134i	0.888402	+	0.459067i	$0.151816\pi$
$83$			8.36460i			0.918134i	−0.888402	+	0.459067i	$0.848184\pi$
$84$	−0.429355	−	0.0691742i	−0.0468465	−	0.00754752i
$85$	−7.52918	−	13.0409i	−0.816654	−	1.41449i
$86$			0.705249i			0.0760490i
$87$	0.541306	−	0.312523i	0.0580341	−	0.0335060i
$88$	0.849174	−	0.490271i	0.0905223	−	0.0522631i
$89$	−3.57155			−0.378584			−0.189292	−	0.981921i	$-0.560619\pi$
$89$	−3.57155			−0.378584			−0.189292	+	0.981921i	$0.560619\pi$
$90$	−2.97457	+	5.15211i	−0.313548	+	0.543080i
$91$	10.8164	−	13.2848i	1.13387	−	1.39262i
$92$	2.00238	−	3.46823i	0.208763	−	0.361588i
$93$	0.214333	+	0.371236i	0.0222253	+	0.0384954i
$94$	−1.93532	−	3.35207i	−0.199613	−	0.345740i
$95$	−16.0698	−	3.67985i	−1.64872	−	0.377544i
$96$	−0.428489	−	0.247388i	−0.0437325	−	0.0252490i
$97$	−1.29625	+	2.24517i	−0.131614	+	0.227962i	−0.924299	−	0.381669i	$-0.875349\pi$
$97$	−1.29625	+	2.24517i	−0.131614	+	0.227962i	0.792685	+	0.609632i	$0.208683\pi$
$98$	1.15624	−	3.49518i	0.116798	−	0.353066i
$99$	−0.748818	−	1.29699i	−0.0752591	−	0.130353i
$100$	8.01738	+	13.8865i	0.801738	+	1.38865i
$101$	0.631076	+	0.364352i	0.0627945	+	0.0362544i	0.531069	−	0.847329i	$-0.321791\pi$
$101$	0.631076	+	0.364352i	0.0627945	+	0.0362544i	−0.468274	+	0.883583i	$0.655124\pi$
$102$	0.0998584	+	0.172960i	0.00988745	+	0.0171256i
$103$	−7.53304	+	13.0476i	−0.742252	+	1.28562i	0.209215	+	0.977870i	$0.432909\pi$
$103$	−7.53304	+	13.0476i	−0.742252	+	1.28562i	−0.951468	+	0.307749i	$0.900424\pi$
$104$	10.9808	−	6.33976i	1.07676	−	0.621665i
$105$	−0.740098	−	0.602586i	−0.0722262	−	0.0588063i
$106$	4.34282			0.421812
$107$	13.7419	+	7.93389i	1.32848	+	0.766998i	0.985065	−	0.172185i	$-0.0550828\pi$
$107$	13.7419	+	7.93389i	1.32848	+	0.766998i	0.343415	+	0.939184i	$0.388416\pi$
$108$	−0.492374	+	0.852816i	−0.0473787	+	0.0820623i
$109$			8.02167i			0.768336i	0.923263	+	0.384168i	$0.125512\pi$
$109$			8.02167i			0.768336i	−0.923263	+	0.384168i	$0.874488\pi$
$110$	0.995993			0.0949642
$111$	−0.0478802	−	0.0276437i	−0.00454459	−	0.00262382i
$112$	−4.03746	+	4.95883i	−0.381504	+	0.468565i
$113$		−	7.80154i		−	0.733907i	−0.930239	−	0.366954i	$-0.880401\pi$
$113$		−	7.80154i		−	0.733907i	0.930239	−	0.366954i	$-0.119599\pi$
$114$	0.213131	+	0.0488052i	0.0199615	+	0.00457103i
$115$	7.61116	−	4.39431i	0.709745	−	0.409771i
$116$		−	11.2942i		−	1.04864i
$117$	−9.68307	−	16.7716i	−0.895200	−	1.55053i
$118$	2.56873	−	1.48306i	0.236471	−	0.136526i
$119$	9.84441	−	3.74891i	0.902436	−	0.343662i
$120$	−0.353190	−	0.611742i	−0.0322416	−	0.0558442i
$121$	5.37463	−	9.30914i	0.488603	−	0.846285i
$122$	0.387632	+	0.671398i	0.0350945	+	0.0607855i
$123$	−0.250310	+	0.433549i	−0.0225697	+	0.0390918i
$124$	7.74572			0.695586
$125$			16.2785i			1.45599i
$126$	−3.22729	−	2.62765i	−0.287510	−	0.234090i
$127$	−10.8927	+	6.28893i	−0.966574	+	0.558052i	−0.898190	−	0.439607i	$-0.855118\pi$
$127$	−10.8927	+	6.28893i	−0.966574	+	0.558052i	−0.0683841	+	0.997659i	$0.521784\pi$
$128$	−9.94416	+	5.74126i	−0.878948	+	0.507461i
$129$	−0.0639493	+	0.110763i	−0.00563042	+	0.00975217i
$130$	12.8793			1.12959
$131$	12.3525	−	7.13172i	1.07924	−	0.623102i	0.148551	−	0.988905i	$-0.452539\pi$
$131$	12.3525	−	7.13172i	1.07924	−	0.623102i	0.930692	+	0.365803i	$0.119206\pi$
$132$	0.0823069			0.00716390
$133$	4.32956	−	10.6890i	0.375420	−	0.926855i
$134$	−2.95778			−0.255513
$135$	−1.87154	+	1.08053i	−0.161076	+	0.0929974i
$136$	7.79668			0.668560
$137$	−1.46367	+	2.53515i	−0.125050	+	0.216593i	−0.921752	−	0.387779i	$-0.873242\pi$
$137$	−1.46367	+	2.53515i	−0.125050	+	0.216593i	0.796703	+	0.604372i	$0.206576\pi$
$138$	−0.100946	+	0.0582810i	−0.00859307	+	0.00496121i
$139$	7.50628	−	4.33375i	0.636674	−	0.367584i	−0.146658	−	0.989187i	$-0.546852\pi$
$139$	7.50628	−	4.33375i	0.636674	−	0.367584i	0.783332	+	0.621603i	$0.213518\pi$
$140$	−16.1161	+	6.13727i	−1.36206	+	0.518694i
$141$		−	0.701950i		−	0.0591148i
$142$	−3.20226			−0.268728
$143$	−1.62112	+	2.80786i	−0.135565	+	0.234805i
$144$	3.61441	+	6.26034i	0.301201	+	0.521695i
$145$	12.3927	−	21.4649i	1.02916	−	1.78256i
$146$	−1.90409	−	3.29798i	−0.157583	−	0.272943i
$147$	0.498523	−	0.444094i	0.0411175	−	0.0366283i
$148$	−0.865164	+	0.499503i	−0.0711160	+	0.0410589i
$149$	1.48603	+	2.57389i	0.121741	+	0.210861i	0.920454	−	0.390850i	$-0.127819\pi$
$149$	1.48603	+	2.57389i	0.121741	+	0.210861i	−0.798714	+	0.601711i	$0.794486\pi$
$150$		−	0.466705i		−	0.0381063i
$151$	−19.9808	+	11.5359i	−1.62602	+	0.938781i	−0.640751	+	0.767749i	$0.721377\pi$
$151$	−19.9808	+	11.5359i	−1.62602	+	0.938781i	−0.985266	+	0.171032i	$0.945290\pi$
$152$	5.81020	−	6.25298i	0.471269	−	0.507183i
$153$		−	11.9083i		−	0.962729i
$154$	−0.110825	+	0.687876i	−0.00893053	+	0.0554307i
$155$	14.7209	+	8.49914i	1.18241	+	0.682667i
$156$	1.06432			0.0852140
$157$			3.68509i			0.294102i	0.989129	+	0.147051i	$0.0469782\pi$
$157$			3.68509i			0.294102i	−0.989129	+	0.147051i	$0.953022\pi$
$158$	−2.36014	+	4.08788i	−0.187762	+	0.325214i
$159$	0.682064	+	0.393790i	0.0540912	+	0.0312296i
$160$	−19.6198			−1.55108
$161$	2.18800	+	5.74556i	0.172439	+	0.452814i
$162$	−4.06191	+	2.34515i	−0.319134	+	0.184252i
$163$	6.83996	−	11.8472i	0.535747	−	0.927942i	−0.463379	−	0.886160i	$-0.653363\pi$
$163$	6.83996	−	11.8472i	0.535747	−	0.927942i	0.999127	−	0.0417817i	$-0.0133034\pi$
$164$	4.52293	+	7.83395i	0.353182	+	0.611729i
$165$	0.156426	+	0.0903129i	0.0121778	+	0.00703085i
$166$	−2.19957	−	3.80976i	−0.170720	−	0.295695i
$167$	−2.72098	−	4.71288i	−0.210556	−	0.364694i	0.741333	−	0.671138i	$-0.234194\pi$
$167$	−2.72098	−	4.71288i	−0.210556	−	0.364694i	−0.951889	+	0.306444i	$0.900861\pi$
$168$	0.461796	−	0.175859i	0.0356283	−	0.0135678i
$169$	−14.4629	+	25.0505i	−1.11253	+	1.92696i
$170$	6.85852	+	3.95977i	0.526025	+	0.303700i
$171$	−9.55052	−	8.87424i	−0.730346	−	0.678630i
$172$	1.15552	+	2.00142i	0.0881077	+	0.152607i
$173$	1.37842	+	2.38750i	0.104800	+	0.181518i	0.913656	−	0.406487i	$-0.133247\pi$
$173$	1.37842	+	2.38750i	0.104800	+	0.181518i	−0.808857	+	0.588006i	$0.799913\pi$
$174$	−0.164363	+	0.284685i	−0.0124603	+	0.0215819i
$175$	−24.3030	−	3.91549i	−1.83713	−	0.295983i
$176$	0.605117	−	1.04809i	0.0456124	−	0.0790030i
$177$	0.537911			0.0404319
$178$	1.62671	−	0.939180i	0.121927	−	0.0703945i
$179$	11.4241	−	6.59571i	0.853878	−	0.492987i	−0.00807964	−	0.999967i	$-0.502572\pi$
$179$	11.4241	−	6.59571i	0.853878	−	0.492987i	0.861957	+	0.506981i	$0.169239\pi$
$180$			19.4949i			1.45306i
$181$	−3.36396	−	5.82654i	−0.250041	−	0.433084i	0.713496	−	0.700659i	$-0.247111\pi$
$181$	−3.36396	−	5.82654i	−0.250041	−	0.433084i	−0.963537	+	0.267576i	$0.913777\pi$
$182$	−1.43309	+	8.89502i	−0.106228	+	0.659343i
$183$			0.140596i			0.0103931i
$184$			4.55043i			0.335462i
$185$	−2.19235			−0.161185
$186$	−0.195242	−	0.112723i	−0.0143158	−	0.00826523i
$187$	−1.72656	+	0.996831i	−0.126259	+	0.0728955i
$188$	−10.9845	−	6.34188i	−0.801124	−	0.462529i
$189$	−0.538016	−	1.41280i	−0.0391349	−	0.102766i
$190$	8.28683	−	2.54969i	0.601190	−	0.184974i
$191$	7.06621	−	12.2390i	0.511293	−	0.885585i	−0.488621	−	0.872496i	$-0.662500\pi$
$191$	7.06621	−	12.2390i	0.511293	−	0.885585i	0.999914	−	0.0130894i	$-0.00416660\pi$
$192$	−0.200828			−0.0144935
$193$			16.5010i			1.18777i	0.804552	+	0.593883i	$0.202406\pi$
$193$			16.5010i			1.18777i	−0.804552	+	0.593883i	$0.797594\pi$
$194$		−	1.36345i		−	0.0978902i
$195$	2.02277	+	1.16785i	0.144854	+	0.0836313i
$196$	−2.44542	−	11.8134i	−0.174673	−	0.843813i
$197$	13.0212			0.927724			0.463862	−	0.885907i	$-0.346463\pi$
$197$	13.0212			0.927724			0.463862	+	0.885907i	$0.346463\pi$
$198$	0.682117	+	0.393821i	0.0484760	+	0.0279876i
$199$	−7.87179	−	4.54478i	−0.558016	−	0.322171i	0.194333	−	0.980936i	$-0.437746\pi$
$199$	−7.87179	−	4.54478i	−0.558016	−	0.322171i	−0.752349	+	0.658765i	$0.771079\pi$
$200$	−15.7786	−	9.10977i	−1.11571	−	0.644158i
$201$	−0.464536	−	0.268200i	−0.0327659	−	0.0189174i
$202$	−0.383242			−0.0269648
$203$	13.4456	+	10.9474i	0.943698	+	0.768356i
$204$	0.566775	+	0.327228i	0.0396822	+	0.0229105i
$205$			19.8515i			1.38649i
$206$		−	7.92359i		−	0.552063i
$207$	6.95012			0.483067
$208$	7.82485	−	13.5530i	0.542555	−	0.939734i
$209$	−0.487196	+	2.12756i	−0.0337000	+	0.147167i
$210$	0.495544	+	0.0798379i	0.0341958	+	0.00550934i
$211$	−8.85486	−	5.11235i	−0.609594	−	0.351949i	0.163213	−	0.986591i	$-0.447814\pi$
$211$	−8.85486	−	5.11235i	−0.609594	−	0.351949i	−0.772806	+	0.634642i	$0.781148\pi$
$212$	12.3244	−	7.11552i	0.846447	−	0.488696i
$213$	−0.502934	−	0.290369i	−0.0344605	−	0.0198958i
$214$	−8.34523			−0.570468
$215$			5.07167i			0.345885i
$216$		−	1.11892i		−	0.0761330i
$217$	−7.50789	+	9.22122i	−0.509668	+	0.625977i
$218$	−2.10939	−	3.65357i	−0.142866	−	0.247451i
$219$		−	0.690622i		−	0.0466679i
$220$	2.82652	−	1.63189i	0.190564	−	0.110022i
$221$	−22.3264	+	12.8902i	−1.50184	+	0.867085i
$222$	0.0290769			0.00195151
$223$	−5.08432	+	8.80630i	−0.340471	+	0.589714i	−0.984520	−	0.175271i	$-0.943920\pi$
$223$	−5.08432	+	8.80630i	−0.340471	+	0.589714i	0.644049	+	0.764984i	$0.277253\pi$
$224$	2.18311	−	13.5503i	0.145865	−	0.905366i
$225$	−13.9139	+	24.0995i	−0.927590	+	1.60663i
$226$	2.05150	+	3.55331i	0.136464	+	0.236363i
$227$	2.96543	+	5.13627i	0.196822	+	0.340907i	0.947496	−	0.319766i	$-0.103604\pi$
$227$	2.96543	+	5.13627i	0.196822	+	0.340907i	−0.750674	+	0.660673i	$0.770271\pi$
$228$	0.684807	−	0.210702i	0.0453525	−	0.0139540i
$229$	−10.3529	−	5.97727i	−0.684141	−	0.394989i	0.117272	−	0.993100i	$-0.462585\pi$
$229$	−10.3529	−	5.97727i	−0.684141	−	0.394989i	−0.801413	+	0.598111i	$0.795918\pi$
$230$	−2.31107	+	4.00289i	−0.152387	+	0.263942i
$231$	−0.0797797	+	0.0979857i	−0.00524912	+	0.00644699i
$232$	6.41652	+	11.1137i	0.421265	+	0.729652i
$233$	−4.88593	−	8.46268i	−0.320088	−	0.554409i	0.660418	−	0.750898i	$-0.270379\pi$
$233$	−4.88593	−	8.46268i	−0.320088	−	0.554409i	−0.980506	+	0.196490i	$0.937046\pi$
$234$	8.82055	+	5.09255i	0.576617	+	0.332910i
$235$	−13.9175	−	24.1058i	−0.907878	−	1.57249i
$236$	4.85985	−	8.41751i	0.316349	−	0.547933i
$237$	−0.741346	+	0.428016i	−0.0481556	+	0.0278026i
$238$	−3.49794	+	4.29619i	−0.226738	+	0.278480i
$239$	2.12087			0.137188			0.0685939	−	0.997645i	$-0.478149\pi$
$239$	2.12087			0.137188			0.0685939	+	0.997645i	$0.478149\pi$
$240$	−0.755042	−	0.435924i	−0.0487378	−	0.0281388i
$241$	−0.321892	+	0.557534i	−0.0207349	+	0.0359139i	−0.876207	−	0.481936i	$-0.839934\pi$
$241$	−0.321892	+	0.557534i	−0.0207349	+	0.0359139i	0.855472	+	0.517849i	$0.173267\pi$
$242$			5.65329i			0.363407i
$243$	−2.56478			−0.164531
$244$	2.20011	+	1.27024i	0.140848	+	0.0813186i
$245$	8.31489	−	25.1349i	0.531219	−	1.60581i
$246$		−	0.263287i		−	0.0167866i
$247$	−6.29999	+	27.5118i	−0.400859	+	1.75054i
$248$	−7.62197	+	4.40055i	−0.483996	+	0.279435i
$249$		−	0.797793i		−	0.0505581i
$250$	−4.28062	−	7.41424i	−0.270730	−	0.468918i
$251$	−7.50985	+	4.33581i	−0.474017	+	0.273674i	−0.717920	−	0.696126i	$-0.754906\pi$
$251$	−7.50985	+	4.33581i	−0.474017	+	0.273674i	0.243903	+	0.969800i	$0.421572\pi$
$252$	−13.4640	−	2.16921i	−0.848152	−	0.136647i
$253$	−0.581787	−	1.00768i	−0.0365766	−	0.0633526i
$254$	3.30749	−	5.72874i	0.207530	−	0.359453i
$255$	0.718113	+	1.24381i	0.0449700	+	0.0778903i
$256$	0.913850	−	1.58284i	0.0571157	−	0.0989272i
$257$	21.2625			1.32632			0.663159	−	0.748479i	$-0.269215\pi$
$257$	21.2625			1.32632			0.663159	+	0.748479i	$0.269215\pi$
$258$		−	0.0672648i		−	0.00418772i
$259$	0.243945	−	1.51414i	0.0151580	−	0.0940838i
$260$	36.5502	−	21.1022i	2.26674	−	1.30871i
$261$	16.9746	−	9.80030i	1.05070	−	0.606623i
$262$	−3.75074	+	6.49647i	−0.231721	+	0.401353i
$263$	25.9429			1.59971			0.799854	−	0.600194i	$-0.204910\pi$
$263$	25.9429			1.59971			0.799854	+	0.600194i	$0.204910\pi$
$264$	−0.0809920	+	0.0467607i	−0.00498471	+	0.00287792i
$265$	31.2306			1.91848
$266$	0.838847	+	6.00695i	0.0514330	+	0.368310i
$267$	0.340645			0.0208471
$268$	−8.39387	+	4.84620i	−0.512737	+	0.296029i
$269$	−23.1092			−1.40899			−0.704497	−	0.709707i	$-0.748827\pi$
$269$	−23.1092			−1.40899			−0.704497	+	0.709707i	$0.748827\pi$
$270$	0.568277	−	0.984284i	0.0345842	−	0.0599016i
$271$	0.284893	−	0.164483i	0.0173060	−	0.00999164i	−0.491322	−	0.870978i	$-0.663486\pi$
$271$	0.284893	−	0.164483i	0.0173060	−	0.00999164i	0.508628	+	0.860986i	$0.330153\pi$
$272$	8.33380	−	4.81152i	0.505311	−	0.291741i
$273$	−1.03164	+	1.26707i	−0.0624378	+	0.0766864i
$274$		−	1.53956i		−	0.0930079i
$275$	4.65885			0.280939
$276$	−0.190982	+	0.330791i	−0.0114958	+	0.0199113i
$277$	−0.807544	−	1.39871i	−0.0485206	−	0.0840402i	0.840745	−	0.541431i	$-0.182117\pi$
$277$	−0.807544	−	1.39871i	−0.0485206	−	0.0840402i	−0.889266	+	0.457391i	$0.848784\pi$
$278$	−2.27922	+	3.94772i	−0.136698	+	0.236769i
$279$	6.72120	+	11.6415i	0.402388	+	0.696956i
$280$	12.3719	−	15.1952i	0.739362	−	0.908087i
$281$	−2.57348	+	1.48580i	−0.153521	+	0.0886353i	−0.574792	−	0.818299i	$-0.694917\pi$
$281$	−2.57348	+	1.48580i	−0.153521	+	0.0886353i	0.421272	+	0.906934i	$0.361584\pi$
$282$	0.184586	+	0.319712i	0.0109919	+	0.0190386i
$283$			5.15530i			0.306451i	0.988191	+	0.153225i	$0.0489660\pi$
$283$			5.15530i			0.306451i	−0.988191	+	0.153225i	$0.951034\pi$
$284$	−9.08768	+	5.24678i	−0.539255	+	0.311339i
$285$	1.53269	+	0.350974i	0.0907887	+	0.0207899i
$286$		−	1.70517i		−	0.100829i
$287$	−13.7103	−	2.20889i	−0.809294	−	0.130387i
$288$	−13.4368	−	7.75776i	−0.791773	−	0.457130i
$289$	1.14761			0.0675066
$290$			13.0353i			0.765457i
$291$	0.123633	−	0.214138i	0.00724748	−	0.0125530i
$292$	−10.8072	−	6.23954i	−0.632443	−	0.365141i
$293$	23.8404			1.39277			0.696384	−	0.717669i	$-0.254791\pi$
$293$	23.8404			1.39277			0.696384	+	0.717669i	$0.254791\pi$
$294$	−0.110279	+	0.333361i	−0.00643160	+	0.0194420i
$295$	18.4725	−	10.6651i	1.07551	−	0.620948i
$296$	0.567561	−	0.983045i	0.0329888	−	0.0571383i
$297$	0.143058	+	0.247783i	0.00830105	+	0.0143778i
$298$	−1.35367	−	0.781539i	−0.0784158	−	0.0452734i
$299$	−7.52317	−	13.0305i	−0.435076	−	0.753574i
$300$	−0.764676	−	1.32446i	−0.0441486	−	0.0764676i
$301$	−3.50272	−	0.564328i	−0.201893	−	0.0325273i
$302$	6.06701	−	10.5084i	0.349117	−	0.604689i
$303$	−0.0601904	−	0.0347509i	−0.00345785	−	0.00199639i
$304$	2.35161	−	10.2694i	0.134874	−	0.588989i
$305$	2.78758	+	4.82823i	0.159616	+	0.276464i
$306$	3.13142	+	5.42378i	0.179012	+	0.310057i
$307$	5.79219	−	10.0324i	0.330577	−	0.572577i	−0.652048	−	0.758178i	$-0.726090\pi$
$307$	5.79219	−	10.0324i	0.330577	−	0.572577i	0.982625	+	0.185601i	$0.0594232\pi$
$308$	0.812548	+	2.13370i	0.0462992	+	0.121579i
$309$	0.718481	−	1.24445i	0.0408730	−	0.0707940i
$310$	−8.93978			−0.507745
$311$	−3.46873	+	2.00267i	−0.196694	+	0.113561i	−0.595112	−	0.803642i	$-0.702892\pi$
$311$	−3.46873	+	2.00267i	−0.196694	+	0.113561i	0.398419	+	0.917204i	$0.369559\pi$
$312$	−1.04732	+	0.604670i	−0.0592927	+	0.0342327i
$313$			0.657071i			0.0371398i	0.999828	+	0.0185699i	$0.00591133\pi$
$313$			0.657071i			0.0371398i	−0.999828	+	0.0185699i	$0.994089\pi$
$314$	−0.969037	−	1.67842i	−0.0546859	−	0.0947188i
$315$	−23.2085	−	18.8963i	−1.30765	−	1.06468i
$316$			15.4679i			0.870140i
$317$			12.9827i			0.729184i	0.931167	+	0.364592i	$0.118791\pi$
$317$			12.9827i			0.729184i	−0.931167	+	0.364592i	$0.881209\pi$
$318$	−0.414206			−0.0232275
$319$	−2.84185	−	1.64074i	−0.159113	−	0.0918641i
$320$	−6.89667	+	3.98179i	−0.385535	+	0.222589i
$321$	−1.31067	−	0.756713i	−0.0731542	−	0.0422356i
$322$	−2.50741	−	2.04153i	−0.139733	−	0.113770i
$323$	−11.8134	+	12.7137i	−0.657317	+	0.707409i
$324$	−7.68485	+	13.3105i	−0.426936	+	0.739475i
$325$	60.2443			3.34175
$326$			7.19459i			0.398471i
$327$		−	0.765085i		−	0.0423093i
$328$	−8.90134	−	5.13919i	−0.491495	−	0.283765i
$329$	18.1971	−	6.92976i	1.00324	−	0.382050i
$330$	−0.0949952			−0.00522931
$331$	9.13797	+	5.27581i	0.502268	+	0.289985i	0.729650	−	0.683821i	$-0.239683\pi$
$331$	9.13797	+	5.27581i	0.502268	+	0.289985i	−0.227381	+	0.973806i	$0.573016\pi$
$332$	−12.4843	−	7.20780i	−0.685164	−	0.395579i
$333$	−1.50146	−	0.866868i	−0.0822794	−	0.0475040i
$334$	2.47861	+	1.43103i	0.135624	+	0.0783023i
$335$	−21.2703			−1.16212
$336$	0.385082	−	0.472960i	0.0210080	−	0.0258021i
$337$	−4.77707	−	2.75804i	−0.260223	−	0.150240i	0.364213	−	0.931316i	$-0.381338\pi$
$337$	−4.77707	−	2.75804i	−0.260223	−	0.150240i	−0.624436	+	0.781076i	$0.714671\pi$
$338$		−	15.2127i		−	0.827464i
$339$			0.744090i			0.0404134i
$340$	25.9517			1.40743
$341$	1.12525	−	1.94899i	0.0609356	−	0.105544i
$342$	6.68349	+	1.53047i	0.361402	+	0.0827581i
$343$	16.4341	+	8.53940i	0.887356	+	0.461084i
$344$	−2.27412	−	1.31296i	−0.122612	−	0.0707903i
$345$	−0.725932	+	0.419117i	−0.0390829	+	0.0225645i
$346$	−1.25564	−	0.724945i	−0.0675037	−	0.0389733i
$347$	−6.75082			−0.362403			−0.181202	−	0.983446i	$-0.557999\pi$
$347$	−6.75082			−0.362403			−0.181202	+	0.983446i	$0.557999\pi$
$348$			1.07721i			0.0577444i
$349$			33.3790i			1.78674i	0.449326	+	0.893368i	$0.351664\pi$
$349$			33.3790i			1.78674i	−0.449326	+	0.893368i	$0.648336\pi$
$350$	12.0987	−	4.60738i	0.646704	−	0.246275i
$351$	1.84990	+	3.20412i	0.0987403	+	0.171023i
$352$			2.59757i			0.138451i
$353$	12.4934	−	7.21306i	0.664956	−	0.383913i	−0.129207	−	0.991618i	$-0.541243\pi$
$353$	12.4934	−	7.21306i	0.664956	−	0.383913i	0.794163	+	0.607705i	$0.207910\pi$
$354$	−0.244999	+	0.141450i	−0.0130215	+	0.00751798i
$355$	−23.0285			−1.22223
$356$	3.07762	−	5.33059i	0.163113	−	0.282521i
$357$	−0.938933	+	0.357561i	−0.0496936	+	0.0189241i
$358$	−3.46883	+	6.00820i	−0.183334	+	0.317543i
$359$	−12.2986	−	21.3017i	−0.649093	−	1.12426i	−0.983340	−	0.181777i	$-0.941815\pi$
$359$	−12.2986	−	21.3017i	−0.649093	−	1.12426i	0.334246	−	0.942486i	$-0.391518\pi$
$360$	−11.0755	−	19.1834i	−0.583733	−	1.01105i
$361$	1.39291	+	18.9489i	0.0733110	+	0.997309i
$362$	3.06431	+	1.76918i	0.161057	+	0.0929861i
$363$	−0.512618	+	0.887881i	−0.0269055	+	0.0466017i
$364$	10.5072	+	27.5912i	0.550725	+	1.44617i
$365$	−13.6929	−	23.7168i	−0.716719	−	1.24139i
$366$	−0.0369713	−	0.0640361i	−0.00193252	−	0.00334722i
$367$	−7.80399	−	4.50564i	−0.407365	−	0.235192i	0.282292	−	0.959329i	$-0.408905\pi$
$367$	−7.80399	−	4.50564i	−0.407365	−	0.235192i	−0.689657	+	0.724136i	$0.742239\pi$
$368$	2.80818	+	4.86391i	0.146387	+	0.253549i
$369$	−7.84937	+	13.5955i	−0.408622	+	0.707754i
$370$	0.998535	−	0.576505i	0.0519114	−	0.0299711i
$371$	−3.47505	+	21.5692i	−0.180416	+	1.11982i
$372$	−0.738766			−0.0383032
$373$	−8.96563	−	5.17631i	−0.464223	−	0.268019i	0.249595	−	0.968350i	$-0.419702\pi$
$373$	−8.96563	−	5.17631i	−0.464223	−	0.268019i	−0.713818	+	0.700331i	$0.753036\pi$
$374$	0.524256	−	0.908038i	0.0271086	−	0.0469535i
$375$		−	1.55260i		−	0.0801759i
$376$	14.4120			0.743240
$377$	−36.7484	−	21.2167i	−1.89264	−	1.09272i
$378$	0.616557	+	0.501999i	0.0317123	+	0.0258200i
$379$			12.6862i			0.651645i	0.945431	+	0.325822i	$0.105641\pi$
$379$			12.6862i			0.651645i	−0.945431	+	0.325822i	$0.894359\pi$
$380$	19.3396	−	20.8134i	0.992099	−	1.06770i
$381$	1.03892	−	0.599821i	0.0532255	−	0.0307298i
$382$			7.43256i			0.380283i
$383$	11.9922	+	20.7711i	0.612772	+	1.06135i	0.990771	+	0.135546i	$0.0432788\pi$
$383$	11.9922	+	20.7711i	0.612772	+	1.06135i	−0.378000	+	0.925806i	$0.623388\pi$
$384$	0.948447	−	0.547586i	0.0484002	−	0.0279439i
$385$	−0.796977	+	4.94674i	−0.0406177	+	0.252109i
$386$	−4.33912	−	7.51557i	−0.220855	−	0.382533i
$387$	−2.00536	+	3.47339i	−0.101938	+	0.176562i
$388$	−2.23396	−	3.86933i	−0.113412	−	0.196436i
$389$	6.79691	−	11.7726i	0.344617	−	0.596894i	−0.640667	−	0.767819i	$-0.721342\pi$
$389$	6.79691	−	11.7726i	0.344617	−	0.596894i	0.985284	+	0.170924i	$0.0546754\pi$
$390$	−1.22840			−0.0622022
$391$		−	9.25204i		−	0.467896i
$392$	9.11784	+	10.2353i	0.460521	+	0.516963i
$393$	−1.17815	+	0.680205i	−0.0594298	+	0.0343118i
$394$	−5.93068	+	3.42408i	−0.298784	+	0.172503i
$395$	−16.9725	+	29.3972i	−0.853979	+	1.47913i
$396$	2.58103			0.129702
$397$	−19.7254	+	11.3885i	−0.989990	+	0.571571i	−0.905271	−	0.424834i	$-0.860333\pi$
$397$	−19.7254	+	11.3885i	−0.989990	+	0.571571i	−0.0847188	+	0.996405i	$0.526999\pi$
$398$	4.78040			0.239620
$399$	−0.412941	+	1.01949i	−0.0206729	+	0.0510383i
$400$	−22.4874			−1.12437
$401$	−26.3352	+	15.2047i	−1.31512	+	0.759284i	−0.982939	−	0.183932i	$-0.941117\pi$
$401$	−26.3352	+	15.2047i	−1.31512	+	0.759284i	−0.332180	+	0.943216i	$0.607784\pi$
$402$	0.282105			0.0140701
$403$	14.5507	−	25.2026i	0.724824	−	1.25543i
$404$	−1.08760	+	0.627926i	−0.0541101	+	0.0312405i
$405$	−29.2105	+	16.8647i	−1.45148	+	0.838013i
$406$	−9.00272	−	1.45044i	−0.446797	−	0.0719842i
$407$			0.290258i			0.0143876i
$408$	−0.743626			−0.0368150
$409$	14.5790	−	25.2515i	0.720883	−	1.24861i	−0.239763	−	0.970832i	$-0.577070\pi$
$409$	14.5790	−	25.2515i	0.720883	−	1.24861i	0.960646	−	0.277775i	$-0.0895970\pi$
$410$	−5.22018	−	9.04161i	−0.257806	−	0.446533i
$411$	0.139601	−	0.241796i	0.00688601	−	0.0119269i
$412$	−12.9825	−	22.4863i	−0.639601	−	1.10782i
$413$	5.31035	+	13.9447i	0.261305	+	0.686172i
$414$	−3.16552	+	1.82761i	−0.155577	+	0.0898223i
$415$	−15.8178	−	27.3972i	−0.776465	−	1.34488i
$416$			33.5896i			1.64686i
$417$	−0.715929	+	0.413342i	−0.0350592	+	0.0202414i
$418$	−0.337568	−	1.09714i	−0.0165110	−	0.0536628i
$419$			10.3513i			0.505692i	0.967507	+	0.252846i	$0.0813666\pi$
$419$			10.3513i			0.505692i	−0.967507	+	0.252846i	$0.918633\pi$
$420$	1.53711	−	0.585356i	0.0750034	−	0.0285625i
$421$	−7.61630	−	4.39727i	−0.371196	−	0.214310i	0.302785	−	0.953059i	$-0.402084\pi$
$421$	−7.61630	−	4.39727i	−0.371196	−	0.214310i	−0.673981	+	0.738749i	$0.735417\pi$
$422$	5.37741			0.261768
$423$		−	22.0122i		−	1.07027i
$424$	−8.08503	+	14.0037i	−0.392644	+	0.680079i
$425$	32.0814	+	18.5222i	1.55618	+	0.898458i
$426$	0.305423			0.0147978
$427$	−3.64477	+	1.38798i	−0.176383	+	0.0671693i
$428$	−23.6829	+	13.6733i	−1.14475	+	0.660924i
$429$	0.154618	−	0.267806i	0.00746502	−	0.0129298i
$430$	−1.33365	−	2.30996i	−0.0643145	−	0.111396i
$431$	−17.0534	−	9.84576i	−0.821431	−	0.474253i	0.0294787	−	0.999565i	$-0.490615\pi$
$431$	−17.0534	−	9.84576i	−0.821431	−	0.474253i	−0.850910	+	0.525312i	$0.823949\pi$
$432$	−0.690514	−	1.19601i	−0.0332224	−	0.0575428i
$433$	−3.09250	−	5.35637i	−0.148616	−	0.257411i	0.782100	−	0.623153i	$-0.214149\pi$
$433$	−3.09250	−	5.35637i	−0.148616	−	0.257411i	−0.930716	+	0.365742i	$0.880815\pi$
$434$	0.994736	−	6.17420i	0.0477489	−	0.296371i
$435$	−1.18199	+	2.04726i	−0.0566719	+	0.0981587i
$436$	−11.9724	−	6.91229i	−0.573376	−	0.331039i
$437$	−7.42018	−	6.89475i	−0.354955	−	0.329821i
$438$	0.181607	+	0.314552i	0.00867751	+	0.0150299i
$439$	−6.57109	−	11.3815i	−0.313621	−	0.543207i	0.665523	−	0.746378i	$-0.268209\pi$
$439$	−6.57109	−	11.3815i	−0.313621	−	0.543207i	−0.979143	+	0.203171i	$0.934875\pi$
$440$	−1.85424	+	3.21164i	−0.0883976	+	0.153109i
$441$	15.6330	−	13.9262i	0.744429	−	0.663152i
$442$	6.77922	−	11.7420i	0.322455	−	0.558508i
$443$	2.71598			0.129040			0.0645200	−	0.997916i	$-0.479448\pi$
$443$	2.71598			0.129040			0.0645200	+	0.997916i	$0.479448\pi$
$444$	0.0825170	−	0.0476412i	0.00391608	−	0.00226095i
$445$	11.6982	−	6.75394i	0.554547	−	0.320168i
$446$		−	5.34792i		−	0.253231i
$447$	−0.141734	−	0.245490i	−0.00670379	−	0.0116113i
$448$	−1.98260	−	5.20620i	−0.0936692	−	0.245970i
$449$		−	28.4895i		−	1.34450i	−0.740323	−	0.672252i	$-0.765327\pi$
$449$		−	28.4895i		−	1.34450i	0.740323	−	0.672252i	$-0.234673\pi$
$450$		−	14.6352i		−	0.689911i
$451$	2.62825			0.123759
$452$	11.6439	+	6.72261i	0.547683	+	0.316205i
$453$	1.90572	−	1.10027i	0.0895384	−	0.0516950i
$454$	−2.70128	−	1.55959i	−0.126778	−	0.0731950i
$455$	−10.3058	+	63.9669i	−0.483144	+	2.99882i
$456$	−0.554161	+	0.596392i	−0.0259510	+	0.0279286i
$457$	−14.0993	+	24.4207i	−0.659538	+	1.14235i	0.321198	+	0.947012i	$0.395915\pi$
$457$	−14.0993	+	24.4207i	−0.659538	+	1.14235i	−0.980735	+	0.195341i	$0.937419\pi$
$458$	6.28716			0.293780
$459$			2.27502i			0.106189i
$460$			15.1463i			0.706202i
$461$	14.7322	+	8.50562i	0.686146	+	0.396146i	0.802166	−	0.597100i	$-0.203681\pi$
$461$	14.7322	+	8.50562i	0.686146	+	0.396146i	−0.116021	+	0.993247i	$0.537014\pi$
$462$	0.0105702	−	0.0656078i	0.000491769	−	0.00305235i
$463$	−5.68128			−0.264031			−0.132016	−	0.991248i	$-0.542145\pi$
$463$	−5.68128			−0.264031			−0.132016	+	0.991248i	$0.542145\pi$
$464$	13.7171	+	7.91958i	0.636801	+	0.367657i
$465$	−1.40404	−	0.810625i	−0.0651110	−	0.0375918i
$466$	4.45072	+	2.56962i	0.206175	+	0.119035i
$467$	22.6989	+	13.1052i	1.05038	+	0.606437i	0.922755	−	0.385386i	$-0.125932\pi$
$467$	22.6989	+	13.1052i	1.05038	+	0.606437i	0.127624	+	0.991823i	$0.459265\pi$
$468$	33.3757			1.54279
$469$	2.36677	−	14.6902i	0.109287	−	0.678332i
$470$	12.6778	+	7.31953i	0.584783	+	0.337625i
$471$		−	0.351474i		−	0.0161951i
$472$			11.0440i			0.508343i
$473$	0.671467			0.0308741
$474$	0.225104	−	0.389891i	0.0103393	−	0.0179083i
$475$	38.7624	−	11.9264i	1.77854	−	0.547222i
$476$	−2.88766	+	17.9234i	−0.132356	+	0.821515i
$477$	21.3886	+	12.3487i	0.979317	+	0.565409i
$478$	−0.965977	+	0.557707i	−0.0441828	+	0.0255089i
$479$	20.2159	+	11.6716i	0.923686	+	0.533290i	0.884809	−	0.465954i	$-0.154289\pi$
$479$	20.2159	+	11.6716i	0.923686	+	0.533290i	0.0388770	+	0.999244i	$0.487622\pi$
$480$	1.87128			0.0854120
$481$			3.75337i			0.171139i
$482$		−	0.338581i		−	0.0154219i
$483$	−0.208686	−	0.547996i	−0.00949553	−	0.0249347i
$484$	9.26267	+	16.0434i	0.421031	+	0.729246i
$485$		−	9.80502i		−	0.445223i
$486$	1.16816	−	0.674439i	0.0529889	−	0.0305932i
$487$	37.5068	−	21.6546i	1.69960	−	0.981262i	0.753460	−	0.657494i	$-0.228383\pi$
$487$	37.5068	−	21.6546i	1.69960	−	0.981262i	0.946136	−	0.323769i	$-0.104950\pi$
$488$	−2.88662			−0.130671
$489$	−0.652377	+	1.12995i	−0.0295015	+	0.0510981i
$490$	2.82240	+	13.6345i	0.127503	+	0.615944i
$491$	15.4368	−	26.7373i	0.696652	−	1.20664i	−0.272969	−	0.962023i	$-0.588006\pi$
$491$	15.4368	−	26.7373i	0.696652	−	1.20664i	0.969621	−	0.244613i	$-0.0786610\pi$
$492$	−0.431385	−	0.747181i	−0.0194483	−	0.0336855i
$493$	−13.0462	−	22.5967i	−0.587572	−	1.01770i
$494$	−4.36514	−	14.1873i	−0.196397	−	0.638315i
$495$	4.90532	+	2.83209i	0.220478	+	0.127293i
$496$	−5.43137	+	9.40741i	−0.243876	+	0.422405i
$497$	2.56240	−	15.9045i	0.114939	−	0.713413i
$498$	0.209789	+	0.363365i	0.00940086	+	0.0162828i
$499$	−13.2477	−	22.9457i	−0.593050	−	1.02719i	−0.993819	−	0.111013i	$-0.964590\pi$
$499$	−13.2477	−	22.9457i	−0.593050	−	1.02719i	0.400769	−	0.916179i	$-0.368743\pi$
$500$	−24.2959	−	14.0272i	−1.08654	−	0.627316i
$501$	0.259520	+	0.449502i	0.0115945	+	0.0200823i
$502$	2.28030	−	3.94960i	0.101775	−	0.176279i
$503$	4.74004	−	2.73666i	0.211348	−	0.122022i	−0.390590	−	0.920565i	$-0.627729\pi$
$503$	4.74004	−	2.73666i	0.211348	−	0.122022i	0.601938	+	0.798543i	$0.294396\pi$
$504$	14.4813	−	5.51470i	0.645048	−	0.245644i
$505$	−2.75602			−0.122641
$506$	0.529964	+	0.305975i	0.0235598	+	0.0136023i
$507$	1.37943	−	2.38925i	0.0612627	−	0.106110i
$508$		−	21.6767i		−	0.961749i
$509$	−35.2880			−1.56411			−0.782057	−	0.623208i	$-0.785829\pi$
$509$	−35.2880			−1.56411			−0.782057	+	0.623208i	$0.785829\pi$
$510$	−0.654147	−	0.377672i	−0.0289661	−	0.0167236i
$511$	17.9035	−	6.81793i	0.792003	−	0.301607i
$512$		−	22.0038i		−	0.972441i
$513$	1.82458	+	1.69538i	0.0805570	+	0.0748527i
$514$	−9.68427	+	5.59121i	−0.427155	+	0.246618i
$515$		−	56.9811i		−	2.51089i
$516$	−0.110211	−	0.190890i	−0.00485175	−	0.00840347i
$517$	−3.19150	+	1.84262i	−0.140362	+	0.0810382i
$518$	0.287052	+	0.753780i	0.0126123	+	0.0331192i
$519$	−0.131470	−	0.227713i	−0.00577091	−	0.00999551i
$520$	−23.9775	+	41.5302i	−1.05148	+	1.82122i
$521$	18.3398	+	31.7655i	0.803482	+	1.39167i	0.917311	+	0.398172i	$0.130355\pi$
$521$	18.3398	+	31.7655i	0.803482	+	1.39167i	−0.113828	+	0.993500i	$0.536311\pi$
$522$	−5.15420	+	8.92734i	−0.225593	+	0.390739i
$523$	−15.7132			−0.687092			−0.343546	−	0.939136i	$-0.611628\pi$
$523$	−15.7132			−0.687092			−0.343546	+	0.939136i	$0.611628\pi$
$524$			24.5817i			1.07386i
$525$	2.31795	+	0.373449i	0.101164	+	0.0162987i
$526$	−11.8160	+	6.82198i	−0.515203	+	0.297453i
$527$	15.4972	−	8.94730i	0.675067	−	0.389750i
$528$	−0.0577144	+	0.0999643i	−0.00251170	+	0.00435039i
$529$	−17.6002			−0.765225
$530$	−14.2244	+	8.21243i	−0.617866	+	0.356725i
$531$	16.8682			0.732016
$532$	12.2227	+	15.6727i	0.529921	+	0.679496i
$533$	33.9863			1.47211
$534$	−0.155151	+	0.0895765i	−0.00671404	+	0.00387635i
$535$	−60.0132			−2.59460
$536$	5.50651	−	9.53755i	0.237845	−	0.411960i
$537$	−1.08960	+	0.629081i	−0.0470197	+	0.0271469i
$538$	10.5254	−	6.07683i	0.453781	−	0.261991i
$539$	−3.32775	−	1.10085i	−0.143336	−	0.0474171i
$540$		−	3.72439i		−	0.160272i
$541$	32.4459			1.39496			0.697480	−	0.716605i	$-0.254305\pi$
$541$	32.4459			1.39496			0.697480	+	0.716605i	$0.254305\pi$
$542$	−0.0865054	+	0.149832i	−0.00371573	+	0.00643582i
$543$	0.320845	+	0.555720i	0.0137688	+	0.0238482i
$544$	−10.3272	+	17.8872i	−0.442774	+	0.766906i
$545$	−15.1693	−	26.2740i	−0.649781	−	1.12545i
$546$	0.136684	−	0.848384i	0.00584955	−	0.0363075i
$547$	28.9651	−	16.7230i	1.23846	−	0.715024i	0.269679	−	0.962950i	$-0.413082\pi$
$547$	28.9651	−	16.7230i	1.23846	−	0.715024i	0.968779	+	0.247926i	$0.0797490\pi$
$548$	−2.52250	−	4.36909i	−0.107756	−	0.186638i
$549$			4.40889i			0.188167i
$550$	−2.12193	+	1.22510i	−0.0904795	+	0.0522384i
$551$	−27.8449	−	6.37627i	−1.18623	−	0.271638i
$552$		−	0.434008i		−	0.0184726i
$553$	−18.4145	−	14.9930i	−0.783063	−	0.637567i
$554$	0.735612	+	0.424706i	0.0312532	+	0.0180440i
$555$	0.209101			0.00887584
$556$			14.9376i			0.633496i
$557$	−5.19908	+	9.00507i	−0.220292	+	0.381557i	−0.954897	−	0.296939i	$-0.904034\pi$
$557$	−5.19908	+	9.00507i	−0.220292	+	0.381557i	0.734605	+	0.678495i	$0.237368\pi$
$558$	−6.12251	−	3.53483i	−0.259186	−	0.149641i
$559$	8.68283			0.367245
$560$	3.84687	−	23.8770i	0.162560	−	1.00899i
$561$	0.164675	−	0.0950750i	0.00695257	−	0.00401407i
$562$	0.781415	−	1.35345i	0.0329620	−	0.0570919i
$563$	−15.6560	−	27.1171i	−0.659824	−	1.14285i	−0.980661	−	0.195714i	$-0.937298\pi$
$563$	−15.6560	−	27.1171i	−0.659824	−	1.14285i	0.320837	−	0.947134i	$-0.396036\pi$
$564$	1.04767	+	0.604872i	0.0441148	+	0.0254697i
$565$	14.7530	+	25.5530i	0.620664	+	1.07502i
$566$	−1.35564	−	2.34805i	−0.0569820	−	0.0986957i
$567$	−8.39721	−	22.0506i	−0.352650	−	0.926037i
$568$	5.96166	−	10.3259i	0.250146	−	0.433265i
$569$	8.86611	+	5.11885i	0.371687	+	0.214593i	0.674195	−	0.738553i	$-0.264491\pi$
$569$	8.86611	+	5.11885i	0.371687	+	0.214593i	−0.302508	+	0.953147i	$0.597824\pi$
$570$	−0.790375	+	0.243183i	−0.0331052	+	0.0101858i
$571$	16.4733	+	28.5326i	0.689386	+	1.19405i	0.972037	+	0.234828i	$0.0754528\pi$
$571$	16.4733	+	28.5326i	0.689386	+	1.19405i	−0.282651	+	0.959223i	$0.591214\pi$
$572$	−2.79384	−	4.83908i	−0.116816	−	0.202332i
$573$	−0.673956	+	1.16733i	−0.0281549	+	0.0487657i
$574$	6.82538	−	2.59921i	0.284886	−	0.108489i
$575$	−10.8102	+	18.7239i	−0.450818	+	0.780839i
$576$	−6.29768			−0.262403
$577$	38.0398	−	21.9623i	1.58362	−	0.914303i	0.589294	−	0.807919i	$-0.299406\pi$
$577$	38.0398	−	21.9623i	1.58362	−	0.914303i	0.994325	−	0.106384i	$-0.0339274\pi$
$578$	−0.522694	+	0.301778i	−0.0217412	+	0.0125523i
$579$		−	1.57382i		−	0.0654056i
$580$	21.3577	+	36.9927i	0.886831	+	1.53604i
$581$	20.6818	−	7.87595i	0.858024	−	0.326749i
$582$			0.130042i			0.00539043i
$583$		−	4.13479i		−	0.171246i
$584$	14.1794			0.586747
$585$	63.4314	+	36.6221i	2.62256	+	1.51414i
$586$	−10.8584	+	6.26909i	−0.448556	+	0.258974i
$587$	−15.4136	−	8.89904i	−0.636187	−	0.367303i	0.146957	−	0.989143i	$-0.453052\pi$
$587$	−15.4136	−	8.89904i	−0.636187	−	0.367303i	−0.783144	+	0.621840i	$0.786385\pi$
$588$	0.233237	+	1.12673i	0.00961854	+	0.0464655i
$589$	4.37294	−	19.0965i	0.180184	−	0.786856i
$590$	−5.60904	+	9.71513i	−0.230920	+	0.399966i
$591$	−1.24193			−0.0510862
$592$		−	1.40102i		−	0.0575817i
$593$			26.0165i			1.06837i	0.845368	+	0.534185i	$0.179381\pi$
$593$			26.0165i			1.06837i	−0.845368	+	0.534185i	$0.820619\pi$
$594$	−0.130315	−	0.0752373i	−0.00534688	−	0.00308703i
$595$	−25.1548	+	30.8952i	−1.03125	+	1.26658i
$596$	−5.12208			−0.209809
$597$	0.750790	+	0.433469i	0.0307278	+	0.0177407i
$598$	6.85304	+	3.95661i	0.280242	+	0.161798i
$599$	−16.0577	−	9.27092i	−0.656100	−	0.378800i	0.134689	−	0.990888i	$-0.456996\pi$
$599$	−16.0577	−	9.27092i	−0.656100	−	0.378800i	−0.790789	+	0.612088i	$0.790330\pi$
$600$	1.50492	+	0.868865i	0.0614380	+	0.0354713i
$601$	−4.97240			−0.202828			−0.101414	−	0.994844i	$-0.532337\pi$
$601$	−4.97240			−0.202828			−0.101414	+	0.994844i	$0.532337\pi$
$602$	1.74375	−	0.664049i	0.0710701	−	0.0270646i
$603$	−14.5672	−	8.41039i	−0.593223	−	0.342498i
$604$		−	39.7622i		−	1.61790i
$605$			40.6546i			1.65284i
$606$	0.0365526			0.00148485
$607$	14.8132	−	25.6572i	0.601248	−	1.04139i	−0.391384	−	0.920227i	$-0.628004\pi$
$607$	14.8132	−	25.6572i	0.601248	−	1.04139i	0.992632	−	0.121165i	$-0.0386629\pi$
$608$	6.64965	+	21.6122i	0.269679	+	0.876492i
$609$	−1.28241	−	1.04413i	−0.0519658	−	0.0423104i
$610$	−2.53928	−	1.46605i	−0.102812	−	0.0593588i
$611$	−41.2698	+	23.8271i	−1.66960	+	0.963942i
$612$	17.7733	+	10.2614i	0.718442	+	0.414793i
$613$	−6.61507			−0.267180			−0.133590	−	0.991037i	$-0.542651\pi$
$613$	−6.61507			−0.267180			−0.133590	+	0.991037i	$0.542651\pi$
$614$			6.09248i			0.245873i
$615$		−	1.89338i		−	0.0763485i
$616$	−2.01178	−	1.63798i	−0.0810569	−	0.0659962i
$617$	−11.7406	−	20.3354i	−0.472660	−	0.818671i	0.526851	−	0.849958i	$-0.323373\pi$
$617$	−11.7406	−	20.3354i	−0.472660	−	0.818671i	−0.999510	+	0.0312871i	$0.990039\pi$
$618$			0.755731i			0.0304000i
$619$	−20.4530	+	11.8086i	−0.822076	+	0.474626i	−0.851132	−	0.524952i	$-0.824083\pi$
$619$	−20.4530	+	11.8086i	−0.822076	+	0.474626i	0.0290556	+	0.999578i	$0.490750\pi$
$620$	−25.3701	+	14.6475i	−1.01889	+	0.588256i
$621$	−1.32778			−0.0532821
$622$	1.05325	−	1.82429i	0.0422316	−	0.0731472i
$623$	3.36290	+	8.83078i	0.134732	+	0.353798i
$624$	−0.746313	+	1.29265i	−0.0298764	+	0.0517475i
$625$	−7.52298	−	13.0302i	−0.300919	−	0.521208i
$626$	−0.172784	−	0.299271i	−0.00690585	−	0.0119613i
$627$	0.0464674	−	0.202921i	0.00185573	−	0.00810390i
$628$	−5.50005	−	3.17545i	−0.219476	−	0.126714i
$629$	−1.15398	+	1.99875i	−0.0460121	+	0.0796954i
$630$	15.5396	+	2.50361i	0.619112	+	0.0997461i
$631$	6.46921	+	11.2050i	0.257535	+	0.446064i	0.965581	−	0.260102i	$-0.0837563\pi$
$631$	6.46921	+	11.2050i	0.257535	+	0.446064i	−0.708046	+	0.706166i	$0.750423\pi$
$632$	−8.78775	−	15.2208i	−0.349558	−	0.605452i
$633$	0.844553	+	0.487603i	0.0335680	+	0.0193805i
$634$	−3.41396	−	5.91315i	−0.135586	−	0.234841i
$635$	23.7852	−	41.1972i	0.943887	−	1.63486i
$636$	−1.17547	+	0.678660i	−0.0466105	+	0.0269106i
$637$	−43.0316	−	14.2353i	−1.70497	−	0.564023i
$638$	1.72581			0.0683255
$639$	−15.7713	−	9.10558i	−0.623904	−	0.360211i
$640$	21.7139	−	37.6096i	0.858318	−	1.48665i
$641$		−	10.7300i		−	0.423808i	−0.977291	−	0.211904i	$-0.932034\pi$
$641$		−	10.7300i		−	0.423808i	0.977291	−	0.211904i	$-0.0679664\pi$
$642$	0.795946			0.0314135
$643$	−12.2385	−	7.06592i	−0.482641	−	0.278653i	0.238876	−	0.971050i	$-0.423221\pi$
$643$	−12.2385	−	7.06592i	−0.482641	−	0.278653i	−0.721516	+	0.692397i	$0.756555\pi$
$644$	−10.4607	−	1.68534i	−0.412210	−	0.0664119i
$645$		−	0.483722i		−	0.0190465i
$646$	2.03736	−	8.89709i	0.0801590	−	0.350051i
$647$	−16.5108	+	9.53250i	−0.649106	+	0.374761i	−0.788113	−	0.615530i	$-0.788942\pi$
$647$	−16.5108	+	9.53250i	−0.649106	+	0.374761i	0.139008	+	0.990291i	$0.455609\pi$
$648$		−	17.4639i		−	0.686045i
$649$	−1.41202	−	2.44568i	−0.0554265	−	0.0960015i
$650$	−27.4390	+	15.8419i	−1.07625	+	0.621371i
$651$	0.716082	−	0.879495i	0.0280655	−	0.0344701i
$652$	11.7880	+	20.4175i	0.461655	+	0.799610i
$653$	−3.46541	+	6.00227i	−0.135612	+	0.234887i	−0.925831	−	0.377937i	$-0.876633\pi$
$653$	−3.46541	+	6.00227i	−0.135612	+	0.234887i	0.790219	+	0.612825i	$0.209967\pi$
$654$	0.201188	+	0.348468i	0.00786707	+	0.0136262i
$655$	−26.9727	+	46.7182i	−1.05391	+	1.82543i
$656$	−12.6861			−0.495309
$657$		−	21.6570i		−	0.844918i
$658$	−6.46586	+	7.94139i	−0.252065	+	0.309588i
$659$	−29.2801	+	16.9049i	−1.14059	+	0.658520i	−0.946577	−	0.322478i	$-0.895484\pi$
$659$	−29.2801	+	16.9049i	−1.14059	+	0.658520i	−0.194014	+	0.980999i	$0.562151\pi$
$660$	−0.269586	+	0.155646i	−0.0104936	+	0.00605850i
$661$	−4.45317	+	7.71312i	−0.173208	+	0.300006i	−0.939540	−	0.342440i	$-0.888747\pi$
$661$	−4.45317	+	7.71312i	−0.173208	+	0.300006i	0.766331	+	0.642445i	$0.222080\pi$
$662$	−5.54934			−0.215681
$663$	2.12943	−	1.22943i	0.0827003	−	0.0477470i
$664$	16.3798			0.635658
$665$	6.03242	+	43.1979i	0.233927	+	1.67514i
$666$	0.911811			0.0353319
$667$	13.1883	−	7.61425i	0.510652	−	0.294825i
$668$	9.37872			0.362873
$669$	0.484929	−	0.839922i	0.0187484	−	0.0324732i
$670$	9.68784	−	5.59328i	0.374274	−	0.216087i
$671$	0.639237	−	0.369064i	0.0246775	−	0.0142475i
$672$	−0.208219	+	1.29239i	−0.00803222	+	0.0498550i
$673$			27.6596i			1.06620i	0.846052	+	0.533100i	$0.178973\pi$
$673$			27.6596i			1.06620i	−0.846052	+	0.533100i	$0.821027\pi$
$674$	2.90103			0.111744
$675$	2.65817	−	4.60408i	0.102313	−	0.177211i
$676$	−24.9254	−	43.1721i	−0.958671	−	1.66047i
$677$	−18.7168	+	32.4184i	−0.719345	+	1.24594i	0.241915	+	0.970297i	$0.422224\pi$
$677$	−18.7168	+	32.4184i	−0.719345	+	1.24594i	−0.961260	+	0.275644i	$0.911109\pi$
$678$	−0.195667	−	0.338905i	−0.00751454	−	0.0130156i
$679$	6.77178	+	1.09101i	0.259877	+	0.0418692i
$680$	−25.5371	+	14.7438i	−0.979301	+	0.565400i
$681$	−0.282835	−	0.489884i	−0.0108382	−	0.0187724i
$682$			1.18359i			0.0453219i
$683$	−20.3872	+	11.7705i	−0.780093	+	0.450387i	−0.836463	−	0.548023i	$-0.815381\pi$
$683$	−20.3872	+	11.7705i	−0.780093	+	0.450387i	0.0563703	+	0.998410i	$0.482047\pi$
$684$	21.4746	−	6.60731i	0.821103	−	0.252637i
$685$		−	11.0714i		−	0.423018i
$686$	−9.73064	+	0.432148i	−0.371517	+	0.0164995i
$687$	0.987435	+	0.570096i	0.0376730	+	0.0217505i
$688$	−3.24105			−0.123564
$689$		−	53.4675i		−	2.03695i
$690$	0.220423	−	0.381784i	0.00839137	−	0.0145343i
$691$	23.8453	+	13.7671i	0.907116	+	0.523724i	0.879502	−	0.475895i	$-0.157876\pi$
$691$	23.8453	+	13.7671i	0.907116	+	0.523724i	0.0276141	+	0.999619i	$0.491209\pi$
$692$	−4.75117			−0.180612
$693$	−2.50178	+	3.07270i	−0.0950349	+	0.116722i
$694$	3.07475	−	1.77521i	0.116716	−	0.0673859i
$695$	−16.3906	+	28.3893i	−0.621730	+	1.07687i
$696$	−0.611990	−	1.06000i	−0.0231974	−	0.0401791i
$697$	18.0984	+	10.4491i	0.685527	+	0.395789i
$698$	−8.77738	−	15.2029i	−0.332229	−	0.575437i
$699$	0.466007	+	0.807148i	0.0176260	+	0.0305291i
$700$	26.7859	−	32.8985i	1.01241	−	1.24345i
$701$	−11.2086	+	19.4139i	−0.423344	+	0.733253i	−0.996264	−	0.0863582i	$-0.972477\pi$
$701$	−11.2086	+	19.4139i	−0.423344	+	0.733253i	0.572920	+	0.819611i	$0.305810\pi$
$702$	−1.68512	−	0.972904i	−0.0636007	−	0.0367199i
$703$	0.743046	+	2.41499i	0.0280245	+	0.0910832i
$704$	0.527172	+	0.913088i	0.0198685	+	0.0344133i
$705$	1.32741	+	2.29915i	0.0499933	+	0.0865909i
$706$	−3.79351	+	6.57056i	−0.142771	+	0.247286i
$707$	0.306664	−	1.90343i	0.0115333	−	0.0715857i
$708$	−0.463520	+	0.802840i	−0.0174201	+	0.0301726i
$709$	38.4014			1.44219			0.721097	−	0.692835i	$-0.243638\pi$
$709$	38.4014			1.44219			0.721097	+	0.692835i	$0.243638\pi$
$710$	10.4886	−	6.05561i	0.393631	−	0.227263i
$711$	−23.2476	+	13.4220i	−0.871853	+	0.503365i
$712$			6.99390i			0.262107i
$713$	5.22197	+	9.04472i	0.195564	+	0.338727i
$714$	0.333624	−	0.409759i	0.0124856	−	0.0153348i
$715$		−	12.2624i		−	0.458587i
$716$			22.7342i			0.849616i
$717$	−0.202283			−0.00755440
$718$	11.2031	+	6.46810i	0.418095	+	0.241387i
$719$	28.8776	−	16.6725i	1.07695	−	0.621779i	0.146880	−	0.989154i	$-0.453077\pi$
$719$	28.8776	−	16.6725i	1.07695	−	0.621779i	0.930073	+	0.367376i	$0.119744\pi$
$720$	−23.6771	−	13.6700i	−0.882394	−	0.509450i
$721$	39.3536	+	6.34032i	1.46561	+	0.236126i
$722$	−5.61724	−	8.26422i	−0.209052	−	0.307562i
$723$	0.0307012	−	0.0531761i	0.00114179	−	0.00197764i
$724$	11.5949			0.430922
$725$			60.9736i			2.26450i
$726$		−	0.539195i		−	0.0200114i
$727$	−36.2422	−	20.9245i	−1.34415	−	0.776045i	−0.356736	−	0.934205i	$-0.616110\pi$
$727$	−36.2422	−	20.9245i	−1.34415	−	0.776045i	−0.987413	+	0.158160i	$0.949444\pi$
$728$	−26.0146	−	21.1810i	−0.964164	−	0.785020i
$729$	−26.5100			−0.981852
$730$	12.4732	+	7.20141i	0.461654	+	0.266536i
$731$	4.62379	+	2.66955i	0.171017	+	0.0987368i
$732$	−0.209841	−	0.121152i	−0.00775595	−	0.00447790i
$733$	30.0634	+	17.3571i	1.11042	+	0.641099i	0.938937	−	0.344089i	$-0.111812\pi$
$733$	30.0634	+	17.3571i	1.11042	+	0.641099i	0.171479	+	0.985188i	$0.445145\pi$
$734$	4.73924			0.174928
$735$	−0.793051	+	2.39730i	−0.0292521	+	0.0884258i
$736$	−10.4396	−	6.02732i	−0.384809	−	0.222170i
$737$			2.81610i			0.103732i
$738$		−	8.25633i		−	0.303920i
$739$	49.9556			1.83765			0.918823	−	0.394670i	$-0.129141\pi$
$739$	49.9556			1.83765			0.918823	+	0.394670i	$0.129141\pi$
$740$	1.88916	−	3.27212i	0.0694468	−	0.120285i
$741$	0.600876	−	2.62400i	0.0220737	−	0.0963952i
$742$	−4.08911	−	10.7378i	−0.150116	−	0.394196i
$743$	45.9883	+	26.5514i	1.68715	+	0.974075i	0.956686	+	0.291121i	$0.0940283\pi$
$743$	45.9883	+	26.5514i	1.68715	+	0.974075i	0.730461	+	0.682954i	$0.239305\pi$
$744$	0.726963	−	0.419712i	0.0266518	−	0.0153874i
$745$	−9.73464	−	5.62030i	−0.356650	−	0.205912i
$746$	5.44468			0.199344
$747$		−	25.0177i		−	0.915350i
$748$		−	3.43589i		−	0.125628i
$749$	6.67771	−	41.4477i	0.243998	−	1.51447i
$750$	0.408274	+	0.707151i	0.0149080	+	0.0258215i
$751$			35.6016i			1.29912i	0.760310	+	0.649560i	$0.225047\pi$
$751$			35.6016i			1.29912i	−0.760310	+	0.649560i	$0.774953\pi$
$752$	15.4048	−	8.89398i	0.561756	−	0.324330i
$753$	0.716269	−	0.413538i	0.0261023	−	0.0150702i
$754$	22.3167			0.812726
$755$	43.6298	−	75.5690i	1.58785	−	2.75024i
$756$	2.57223	+	0.414416i	0.0935510	+	0.0150722i
$757$	4.57602	−	7.92590i	0.166318	−	0.288072i	−0.770804	−	0.637072i	$-0.780145\pi$
$757$	4.57602	−	7.92590i	0.166318	−	0.288072i	0.937123	+	0.349000i	$0.113479\pi$
$758$	−3.33597	−	5.77807i	−0.121168	−	0.209869i
$759$	0.0554893	+	0.0961103i	0.00201413	+	0.00348858i
$760$	−7.20596	+	31.4682i	−0.261388	+	1.14147i
$761$	−31.3017	−	18.0721i	−1.13469	−	0.655111i	−0.189577	−	0.981866i	$-0.560712\pi$
$761$	−31.3017	−	18.0721i	−1.13469	−	0.655111i	−0.945109	+	0.326754i	$0.894045\pi$
$762$	−0.315459	+	0.546392i	−0.0114279	+	0.0197937i
$763$	19.8338	−	7.55305i	0.718033	−	0.273439i
$764$	12.1779	+	21.0928i	0.440582	+	0.763111i
$765$	22.5191	+	39.0041i	0.814178	+	1.41020i
$766$	−10.9240	−	6.30696i	−0.394699	−	0.227880i
$767$	−18.2590	−	31.6255i	−0.659293	−	1.14193i
$768$	−0.0871606	+	0.150967i	−0.00314514	+	0.00544754i
$769$	−30.1085	+	17.3831i	−1.08574	+	0.626852i	−0.932439	−	0.361328i	$-0.882324\pi$
$769$	−30.1085	+	17.3831i	−1.08574	+	0.626852i	−0.153301	+	0.988180i	$0.548990\pi$
$770$	−0.937808	−	2.46263i	−0.0337963	−	0.0887470i
$771$	−2.02796			−0.0730352
$772$	−24.6279	−	14.2189i	−0.886378	−	0.511750i
$773$	−15.7905	+	27.3500i	−0.567945	+	0.983709i	0.428824	+	0.903388i	$0.358928\pi$
$773$	−15.7905	+	27.3500i	−0.567945	+	0.983709i	−0.996769	+	0.0803214i	$0.974405\pi$
$774$		−	2.10933i		−	0.0758184i
$775$	−41.8167			−1.50210
$776$	4.39654	+	2.53834i	0.157827	+	0.0911212i
$777$	−0.0232668	+	0.144414i	−0.000834692	+	0.00518083i
$778$			7.14930i			0.256315i
$779$	21.8675	−	6.72818i	0.783483	−	0.241062i
$780$	−3.48606	+	2.01267i	−0.124821	+	0.0720653i
$781$			3.04887i			0.109097i
$782$	2.43293	+	4.21396i	0.0870013	+	0.150691i
$783$	−3.24291	+	1.87230i	−0.115892	+	0.0669104i
$784$	16.0625	+	5.31363i	0.573659	+	0.189772i
$785$	−6.96865	−	12.0701i	−0.248722	−	0.430799i
$786$	0.357735	−	0.619616i	0.0127600	−	0.0221010i
$787$	4.87936	+	8.45130i	0.173930	+	0.301256i	0.939791	−	0.341751i	$-0.111020\pi$
$787$	4.87936	+	8.45130i	0.173930	+	0.301256i	−0.765860	+	0.643007i	$0.777687\pi$
$788$	−11.2204	+	19.4344i	−0.399711	+	0.692320i
$789$	−2.47437			−0.0880897
$790$		−	17.8524i		−	0.635161i
$791$	−19.2896	+	7.34578i	−0.685858	+	0.261186i
$792$	−2.53980	+	1.46635i	−0.0902478	+	0.0521046i
$793$	8.26606	−	4.77241i	0.293536	−	0.169473i
$794$	5.98946	−	10.3740i	0.212558	−	0.368161i
$795$	−2.97869			−0.105643
$796$	13.5663	−	7.83249i	0.480844	−	0.277615i
$797$	11.3046			0.400430			0.200215	−	0.979752i	$-0.435836\pi$
$797$	11.3046			0.400430			0.200215	+	0.979752i	$0.435836\pi$
$798$	−0.0800070	−	0.572927i	−0.00283222	−	0.0202814i
$799$	−29.3027			−1.03666
$800$	41.7994	−	24.1329i	1.47783	−	0.853226i
$801$	10.6822			0.377436
$802$	7.99648	−	13.8503i	0.282365	−	0.489071i
$803$	−3.14000	+	1.81288i	−0.110808	+	0.0639751i
$804$	0.800584	−	0.462218i	0.0282344	−	0.0163012i
$805$	−18.0316	−	14.6813i	−0.635530	−	0.517447i
$806$			15.3051i			0.539100i
$807$	2.20409			0.0775878
$808$	0.713483	−	1.23579i	0.0251002	−	0.0434749i
$809$	−17.9056	−	31.0135i	−0.629529	−	1.09038i	−0.987646	−	0.156699i	$-0.949915\pi$
$809$	−17.9056	−	31.0135i	−0.629529	−	1.09038i	0.358118	−	0.933676i	$-0.383419\pi$
$810$	8.86952	−	15.3625i	0.311643	−	0.539782i
$811$	11.8397	+	20.5069i	0.415747	+	0.720095i	0.995507	−	0.0946924i	$-0.0301868\pi$
$811$	11.8397	+	20.5069i	0.415747	+	0.720095i	−0.579759	+	0.814788i	$0.696853\pi$
$812$	−27.9252	+	10.6344i	−0.979984	+	0.373193i
$813$	−0.0271723	+	0.0156880i	−0.000952975	+	0.000550201i
$814$	−0.0763267	−	0.132202i	−0.00267525	−	0.00463367i
$815$			51.7386i			1.81232i
$816$	−0.794856	+	0.458910i	−0.0278255	+	0.0160651i
$817$	5.58671	−	1.71892i	0.195454	−	0.0601374i
$818$			15.3348i			0.536169i
$819$	−32.3509	+	39.7335i	−1.13043	+	1.38840i
$820$	−29.6286	−	17.1061i	−1.03468	−	0.597370i
$821$	−36.7056			−1.28104			−0.640518	−	0.767943i	$-0.721280\pi$
$821$	−36.7056			−1.28104			−0.640518	+	0.767943i	$0.721280\pi$
$822$			0.146839i			0.00512159i
$823$	10.9942	−	19.0426i	0.383235	−	0.663783i	−0.608288	−	0.793717i	$-0.708143\pi$
$823$	10.9942	−	19.0426i	0.383235	−	0.663783i	0.991523	+	0.129934i	$0.0414766\pi$
$824$	25.5501	+	14.7514i	0.890081	+	0.513888i
$825$	−0.444349			−0.0154702
$826$	−6.08557	−	4.95485i	−0.211744	−	0.172401i
$827$	44.3311	−	25.5946i	1.54154	−	0.890010i	0.542801	−	0.839861i	$-0.317364\pi$
$827$	44.3311	−	25.5946i	1.54154	−	0.890010i	0.998742	−	0.0501492i	$-0.0159697\pi$
$828$	−5.98894	+	10.3731i	−0.208130	+	0.360492i
$829$	−0.809507	−	1.40211i	−0.0281154	−	0.0486972i	0.851625	−	0.524151i	$-0.175617\pi$
$829$	−0.809507	−	1.40211i	−0.0281154	−	0.0486972i	−0.879741	+	0.475454i	$0.842284\pi$
$830$	14.4088	+	8.31894i	0.500137	+	0.288754i
$831$	0.0770214	+	0.133405i	0.00267184	+	0.00462777i
$832$	6.81693	+	11.8073i	0.236335	+	0.409343i
$833$	−18.5386	−	20.8107i	−0.642325	−	0.721049i
$834$	0.217386	−	0.376523i	0.00752745	−	0.0130379i
$835$	17.8245	+	10.2910i	0.616842	+	0.356134i
$836$	−2.75560	−	2.56047i	−0.0953044	−	0.0885558i
$837$	−1.28405	−	2.22404i	−0.0443833	−	0.0768740i
$838$	−2.72198	−	4.71461i	−0.0940293	−	0.162863i
$839$	13.9547	−	24.1703i	0.481771	−	0.834452i	−0.518010	−	0.855375i	$-0.673327\pi$
$839$	13.9547	−	24.1703i	0.481771	−	0.834452i	0.999781	+	0.0209224i	$0.00666030\pi$
$840$	−1.18000	+	1.44928i	−0.0407138	+	0.0500048i
$841$	6.97356	−	12.0786i	0.240468	−	0.416502i
$842$	4.62525			0.159397
$843$	0.245451	−	0.141711i	0.00845379	−	0.00488080i
$844$	15.2605	−	8.81066i	0.525288	−	0.303275i
$845$		−	109.400i		−	3.76346i
$846$	5.78836	+	10.0257i	0.199008	+	0.344692i
$847$	−28.0778	−	4.52366i	−0.964765	−	0.155435i
$848$			19.9579i			0.685357i
$849$		−	0.491699i		−	0.0168751i
$850$	−19.4825			−0.668244
$851$	−1.16654	−	0.673504i	−0.0399886	−	0.0230874i
$852$	0.866759	−	0.500423i	0.0296947	−	0.0171442i
$853$	8.89817	+	5.13736i	0.304668	+	0.175900i	0.644538	−	0.764572i	$-0.277050\pi$
$853$	8.89817	+	5.13736i	0.304668	+	0.175900i	−0.339870	+	0.940472i	$0.610383\pi$
$854$	1.29507	−	1.59061i	0.0443163	−	0.0544295i
$855$	48.0631	+	11.0061i	1.64372	+	0.376400i
$856$	15.5363	−	26.9097i	0.531021	−	0.919755i
$857$	−12.0088			−0.410211			−0.205106	−	0.978740i	$-0.565754\pi$
$857$	−12.0088			−0.410211			−0.205106	+	0.978740i	$0.565754\pi$
$858$			0.162634i			0.00555224i
$859$		−	4.35170i		−	0.148478i	−0.997240	−	0.0742390i	$-0.976347\pi$
$859$		−	4.35170i		−	0.148478i	0.997240	−	0.0742390i	$-0.0236528\pi$
$860$	−7.56953	−	4.37027i	−0.258119	−	0.149025i
$861$	1.30765	+	0.210678i	0.0445647	+	0.00717989i
$862$	10.3562			0.352734
$863$	23.1015	+	13.3377i	0.786385	+	0.454020i	0.838688	−	0.544612i	$-0.183323\pi$
$863$	23.1015	+	13.3377i	0.786385	+	0.454020i	−0.0523032	+	0.998631i	$0.516656\pi$
$864$	2.56704	+	1.48208i	0.0873323	+	0.0504213i
$865$	−9.02972	−	5.21331i	−0.307020	−	0.177258i
$866$	2.81704	+	1.62642i	0.0957268	+	0.0552679i
$867$	−0.109456			−0.00371733
$868$	−7.29322	−	19.1516i	−0.247548	−	0.650046i
$869$	3.89206	+	2.24708i	0.132029	+	0.0762271i
$870$		−	1.24327i		−	0.0421507i
$871$			36.4154i			1.23389i
$872$	15.7082			0.531947
$873$	3.87695	−	6.71508i	0.131215	−	0.227271i
$874$	5.19267	+	1.18908i	0.175645	+	0.0402213i
$875$	40.2491	−	15.3275i	1.36067	−	0.518165i
$876$	1.03076	+	0.595110i	0.0348262	+	0.0201069i
$877$	0.824304	−	0.475912i	0.0278348	−	0.0160704i	−0.486018	−	0.873949i	$-0.661551\pi$
$877$	0.824304	−	0.475912i	0.0278348	−	0.0160704i	0.513853	+	0.857878i	$0.328218\pi$
$878$	5.98577	+	3.45588i	0.202010	+	0.116630i
$879$	−2.27383			−0.0766944
$880$			4.57720i			0.154297i
$881$			43.9588i			1.48101i	0.672051	+	0.740505i	$0.265414\pi$
$881$			43.9588i			1.48101i	−0.672051	+	0.740505i	$0.734586\pi$
$882$	−3.45820	+	10.4537i	−0.116444	+	0.351995i
$883$	17.4000	+	30.1377i	0.585556	+	1.01421i	0.994806	+	0.101791i	$0.0324572\pi$
$883$	17.4000	+	30.1377i	0.585556	+	1.01421i	−0.409250	+	0.912422i	$0.634209\pi$
$884$		−	44.4299i		−	1.49434i
$885$	−1.76186	+	1.01721i	−0.0592243	+	0.0341932i
$886$	−1.23703	+	0.714197i	−0.0415587	+	0.0239939i
$887$	18.3274			0.615373			0.307686	−	0.951488i	$-0.400445\pi$
$887$	18.3274			0.615373			0.307686	+	0.951488i	$0.400445\pi$
$888$	−0.0541325	+	0.0937602i	−0.00181657	+	0.00314639i
$889$	25.8060	+	21.0111i	0.865505	+	0.704691i
$890$	−3.55205	+	6.15234i	−0.119065	+	0.206227i
$891$	2.23281	+	3.86734i	0.0748019	+	0.129561i
$892$	−8.76235	−	15.1768i	−0.293385	−	0.508158i
$893$	−21.8368	+	23.5010i	−0.730742	+	0.786429i
$894$	0.129109	+	0.0745411i	0.00431805	+	0.00249303i
$895$	−24.9455	+	43.2069i	−0.833836	+	1.44425i
$896$	23.5587	+	19.1814i	0.787041	+	0.640806i
$897$	0.717539	+	1.24281i	0.0239579	+	0.0414964i
$898$	7.49164	+	12.9759i	0.249999	+	0.433012i
$899$	25.5077	+	14.7269i	0.850731	+	0.491170i
$900$	−23.9792	−	41.5332i	−0.799307	−	1.38444i
$901$	16.4387	−	28.4726i	0.547652	−	0.948561i
$902$	−1.19707	+	0.691128i	−0.0398580	+	0.0230121i
$903$	0.334080	+	0.0538241i	0.0111175	+	0.00179115i
$904$	−15.2772			−0.508111
$905$	22.0364	+	12.7227i	0.732516	+	0.422918i
$906$	−0.578655	+	1.00226i	−0.0192245	+	0.0332979i
$907$			52.8134i			1.75364i	0.480818	+	0.876821i	$0.340340\pi$
$907$			52.8134i			1.75364i	−0.480818	+	0.876821i	$0.659660\pi$
$908$	−10.2213			−0.339205
$909$	−1.88749	−	1.08974i	−0.0626040	−	0.0361445i
$910$	−12.1269	−	31.8446i	−0.402004	−	1.05564i
$911$		−	16.3343i		−	0.541180i	−0.962695	−	0.270590i	$-0.912781\pi$
$911$		−	16.3343i		−	0.541180i	0.962695	−	0.270590i	$-0.0872189\pi$
$912$	−0.224290	+	0.979465i	−0.00742698	+	0.0324333i
$913$	−3.62727	+	2.09421i	−0.120045	+	0.0693081i
$914$		−	14.8303i		−	0.490543i
$915$	−0.265872	−	0.460504i	−0.00878946	−	0.0152238i
$916$	17.8423	−	10.3013i	0.589526	−	0.340363i
$917$	−29.2643	−	23.8269i	−0.966393	−	0.786834i
$918$	−0.598242	−	1.03619i	−0.0197449	−	0.0341992i
$919$	6.44387	−	11.1611i	0.212564	−	0.368171i	−0.739952	−	0.672659i	$-0.765152\pi$
$919$	6.44387	−	11.1611i	0.212564	−	0.368171i	0.952516	+	0.304488i	$0.0984854\pi$
$920$	−8.60504	−	14.9044i	−0.283700	−	0.491382i
$921$	−0.552443	+	0.956860i	−0.0182036	+	0.0315296i
$922$	−8.94660			−0.294641
$923$			39.4254i			1.29770i
$924$	−0.0774986	−	0.203507i	−0.00254952	−	0.00669488i
$925$	4.67074	−	2.69665i	0.153573	−	0.0886655i
$926$	2.58761	−	1.49396i	0.0850341	−	0.0490945i
$927$	22.5306	−	39.0241i	0.740002	−	1.28172i
$928$	−33.9962			−1.11598
$929$	−32.9693	+	19.0348i	−1.08169	+	0.624513i	−0.931351	−	0.364122i	$-0.881369\pi$
$929$	−32.9693	+	19.0348i	−1.08169	+	0.624513i	−0.150337	+	0.988635i	$0.548036\pi$
$930$	0.852652			0.0279596
$931$	−30.5056	−	0.640410i	−0.999780	−	0.0209886i
$932$	16.8409			0.551641
$933$	0.330838	−	0.191010i	0.0108312	−	0.00625338i
$934$	−13.7847			−0.451048
$935$	3.77009	−	6.52999i	0.123295	−	0.213553i
$936$	−32.8425	+	18.9616i	−1.07349	+	0.619780i
$937$	−32.0802	+	18.5215i	−1.04802	+	0.605072i	−0.922093	−	0.386968i	$-0.873522\pi$
$937$	−32.0802	+	18.5215i	−1.04802	+	0.605072i	−0.125922	+	0.992040i	$0.540189\pi$
$938$	2.78499	+	7.31322i	0.0909331	+	0.238785i
$939$		−	0.0626696i		−	0.00204515i
$940$	47.9710			1.56464
$941$	−5.00486	+	8.66866i	−0.163154	+	0.282590i	−0.935998	−	0.352005i	$-0.885500\pi$
$941$	−5.00486	+	8.66866i	−0.163154	+	0.282590i	0.772844	+	0.634596i	$0.218833\pi$
$942$	0.0924241	+	0.160083i	0.00301134	+	0.00521580i
$943$	−6.09850	+	10.5629i	−0.198594	+	0.343975i
$944$	6.81555	+	11.8049i	0.221827	+	0.384216i
$945$	4.43386	+	3.61003i	0.144233	+	0.117434i
$946$	−0.305828	+	0.176570i	−0.00994332	+	0.00574078i
$947$	27.6834	+	47.9490i	0.899589	+	1.55813i	0.828020	+	0.560699i	$0.189467\pi$
$947$	27.6834	+	47.9490i	0.899589	+	1.55813i	0.0715693	+	0.997436i	$0.477199\pi$
$948$		−	1.47529i		−	0.0479152i
$949$	−40.6038	+	23.4426i	−1.31805	+	0.760979i
$950$	−14.5186	+	15.6251i	−0.471047	+	0.506944i
$951$		−	1.23826i		−	0.0401533i
$952$	−7.34120	−	19.2776i	−0.237930	−	0.624789i
$953$	−13.7411	−	7.93342i	−0.445118	−	0.256989i	0.260648	−	0.965434i	$-0.416064\pi$
$953$	−13.7411	−	7.93342i	−0.445118	−	0.256989i	−0.705766	+	0.708445i	$0.749397\pi$
$954$	−12.9889			−0.420533
$955$			53.4499i			1.72960i
$956$	−1.82756	+	3.16543i	−0.0591075	+	0.102377i
$957$	0.271048	+	0.156490i	0.00876175	+	0.00505860i
$958$	−12.2768			−0.396644
$959$	7.64641	+	1.23193i	0.246916	+	0.0397810i
$960$	0.657786	−	0.379773i	0.0212299	−	0.0122571i
$961$	5.40006	−	9.35317i	0.174195	−	0.301715i
$962$	−0.986991	−	1.70952i	−0.0318219	−	0.0551171i
$963$	−41.1007	−	23.7295i	−1.32445	−	0.764673i
$964$	−0.554751	−	0.960857i	−0.0178673	−	0.0309471i
$965$	−31.2040	−	54.0469i	−1.00449	−	1.73983i
$966$	0.239150	+	0.194715i	0.00769453	+	0.00626487i
$967$	19.1716	−	33.2061i	0.616516	−	1.06784i	−0.373600	−	0.927590i	$-0.621877\pi$
$967$	19.1716	−	33.2061i	0.616516	−	1.06784i	0.990116	−	0.140248i	$-0.0447899\pi$
$968$	−18.2294	−	10.5247i	−0.585914	−	0.338278i
$969$	1.12673	−	1.21260i	0.0361959	−	0.0389543i
$970$	2.57834	+	4.46582i	0.0827856	+	0.143389i
$971$	24.4083	+	42.2763i	0.783298	+	1.35671i	0.930010	+	0.367533i	$0.119798\pi$
$971$	24.4083	+	42.2763i	0.783298	+	1.35671i	−0.146712	+	0.989179i	$0.546869\pi$
$972$	2.21008	−	3.82797i	0.0708884	−	0.122782i
$973$	−17.7831	−	14.4790i	−0.570100	−	0.464174i
$974$	−11.3886	+	19.7257i	−0.364915	+	0.632052i
$975$	−5.74594			−0.184017
$976$	−3.08548	+	1.78140i	−0.0987639	+	0.0570213i
$977$	−8.29456	+	4.78887i	−0.265366	+	0.153209i	−0.626780	−	0.779196i	$-0.715628\pi$
$977$	−8.29456	+	4.78887i	−0.265366	+	0.153209i	0.361414	+	0.932406i	$0.382294\pi$
$978$		−	0.686200i		−	0.0219423i
$979$	−0.894192	−	1.54879i	−0.0285785	−	0.0494994i
$980$	30.3492	+	34.0689i	0.969471	+	1.08829i
$981$		−	23.9920i		−	0.766007i
$982$			16.2371i			0.518147i
$983$	−18.7012			−0.596475			−0.298238	−	0.954492i	$-0.596399\pi$
$983$	−18.7012			−0.596475			−0.298238	+	0.954492i	$0.596399\pi$
$984$	0.848986	+	0.490162i	0.0270647	+	0.0156258i
$985$	−42.6494	+	24.6237i	−1.35892	+	0.784575i
$986$	11.8841	+	6.86130i	0.378467	+	0.218508i
$987$	−1.73559	+	0.660942i	−0.0552446	+	0.0210380i
$988$	−35.6330	−	33.1098i	−1.13364	−	1.05336i
$989$	−1.55805	+	2.69862i	−0.0495430	+	0.0858110i
$990$	−2.97892			−0.0946763
$991$		−	23.8916i		−	0.758943i	−0.925204	−	0.379471i	$-0.876106\pi$
$991$		−	23.8916i		−	0.758943i	0.925204	−	0.379471i	$-0.123894\pi$
$992$		−	23.3152i		−	0.740257i
$993$	−0.871555	−	0.503193i	−0.0276580	−	0.0159683i
$994$	3.01519	+	7.91771i	0.0956360	+	0.251134i
$995$	34.3774			1.08984
$996$	1.19072	+	0.687461i	0.0377293	+	0.0217830i
$997$	−18.4477	−	10.6508i	−0.584244	−	0.337313i	0.178574	−	0.983926i	$-0.442851\pi$
$997$	−18.4477	−	10.6508i	−0.584244	−	0.337313i	−0.762818	+	0.646613i	$0.776185\pi$
$998$	12.0677	+	6.96728i	0.381996	+	0.220545i
$999$	0.286846	+	0.165610i	0.00907540	+	0.00523968i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	133.2.s.d.103.4	yes	16
7.2	even	3		931.2.p.h.293.5		16
7.3	odd	6		133.2.i.d.122.4	yes	16
7.4	even	3		931.2.i.g.521.4		16
7.5	odd	6		931.2.p.g.293.5		16
7.6	odd	2		931.2.s.g.901.4		16
19.12	odd	6		133.2.i.d.12.5	✓	16
133.12	even	6		931.2.p.h.734.5		16
133.31	even	6	inner	133.2.s.d.31.4	yes	16
133.69	even	6		931.2.i.g.411.5		16
133.88	odd	6		931.2.s.g.31.4		16
133.107	odd	6		931.2.p.g.734.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.i.d.12.5	✓	16	19.12	odd	6
133.2.i.d.122.4	yes	16	7.3	odd	6
133.2.s.d.31.4	yes	16	133.31	even	6	inner
133.2.s.d.103.4	yes	16	1.1	even	1	trivial
931.2.i.g.411.5		16	133.69	even	6
931.2.i.g.521.4		16	7.4	even	3
931.2.p.g.293.5		16	7.5	odd	6
931.2.p.g.734.5		16	133.107	odd	6
931.2.p.h.293.5		16	7.2	even	3
931.2.p.h.734.5		16	133.12	even	6
931.2.s.g.31.4		16	133.88	odd	6
931.2.s.g.901.4		16	7.6	odd	2

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:	\( N \)	\(=\)	\( 133 = 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	133.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.455463 + 0.262961i) q^{2} -0.0953773 q^{3} +(-0.861703 + 1.49251i) q^{4} +(-3.27538 + 1.89104i) q^{5} +(0.0434408 - 0.0250806i) q^{6} +(-0.941581 - 2.47253i) q^{7} -1.95822i q^{8} -2.99090 q^{9} +O(q^{10})\)	\(q+(-0.455463 + 0.262961i) q^{2} -0.0953773 q^{3} +(-0.861703 + 1.49251i) q^{4} +(-3.27538 + 1.89104i) q^{5} +(0.0434408 - 0.0250806i) q^{6} +(-0.941581 - 2.47253i) q^{7} -1.95822i q^{8} -2.99090 q^{9} +(0.994541 - 1.72259i) q^{10} +(0.250365 + 0.433645i) q^{11} +(0.0821869 - 0.142352i) q^{12} +(3.23751 + 5.60753i) q^{13} +(1.07904 + 0.878547i) q^{14} +(0.312397 - 0.180362i) q^{15} +(-1.20847 - 2.09313i) q^{16} +3.98151i q^{17} +(1.36224 - 0.786492i) q^{18} +(3.19319 + 2.96708i) q^{19} -6.51805i q^{20} +(0.0898054 + 0.235824i) q^{21} +(-0.228064 - 0.131673i) q^{22} -2.32375 q^{23} +0.186770i q^{24} +(4.65206 - 8.05760i) q^{25} +(-2.94913 - 1.70268i) q^{26} +0.571396 q^{27} +(4.50165 + 0.725268i) q^{28} +(-5.67542 + 3.27670i) q^{29} +(-0.0948566 + 0.164296i) q^{30} +(-2.24721 - 3.89229i) q^{31} +(4.49257 + 2.59378i) q^{32} +(-0.0238792 - 0.0413599i) q^{33} +(-1.04698 - 1.81343i) q^{34} +(7.75969 + 6.31791i) q^{35} +(2.57727 - 4.46396i) q^{36} +(0.502008 + 0.289835i) q^{37} +(-2.23460 - 0.511707i) q^{38} +(-0.308785 - 0.534831i) q^{39} +(3.70308 + 6.41392i) q^{40} +(2.62442 - 4.54562i) q^{41} +(-0.102916 - 0.0837935i) q^{42} +(0.670487 - 1.16132i) q^{43} -0.862961 q^{44} +(9.79633 - 5.65591i) q^{45} +(1.05838 - 0.611057i) q^{46} +7.35971i q^{47} +(0.115260 + 0.199637i) q^{48} +(-5.22685 + 4.65618i) q^{49} +4.89325i q^{50} -0.379745i q^{51} -11.1591 q^{52} +(-7.15122 - 4.12876i) q^{53} +(-0.260250 + 0.150255i) q^{54} +(-1.64008 - 0.946901i) q^{55} +(-4.84178 + 1.84383i) q^{56} +(-0.304558 - 0.282992i) q^{57} +(1.72329 - 2.98483i) q^{58} -5.63983 q^{59} +0.621674i q^{60} -1.47410i q^{61} +(2.04704 + 1.18186i) q^{62} +(2.81618 + 7.39511i) q^{63} +2.10561 q^{64} +(-21.2081 - 12.2445i) q^{65} +(0.0217521 + 0.0125586i) q^{66} +(4.87051 + 2.81199i) q^{67} +(-5.94245 - 3.43087i) q^{68} +0.221633 q^{69} +(-5.19561 - 0.837074i) q^{70} +(5.27310 + 3.04442i) q^{71} +5.85686i q^{72} +7.24094i q^{73} -0.304861 q^{74} +(-0.443701 + 0.768512i) q^{75} +(-7.17998 + 2.20914i) q^{76} +(0.836464 - 1.02735i) q^{77} +(0.281280 + 0.162397i) q^{78} +(7.77277 - 4.48761i) q^{79} +(7.91637 + 4.57052i) q^{80} +8.91821 q^{81} +2.76048i q^{82} +8.36460i q^{83} +(-0.429355 - 0.0691742i) q^{84} +(-7.52918 - 13.0409i) q^{85} +0.705249i q^{86} +(0.541306 - 0.312523i) q^{87} +(0.849174 - 0.490271i) q^{88} -3.57155 q^{89} +(-2.97457 + 5.15211i) q^{90} +(10.8164 - 13.2848i) q^{91} +(2.00238 - 3.46823i) q^{92} +(0.214333 + 0.371236i) q^{93} +(-1.93532 - 3.35207i) q^{94} +(-16.0698 - 3.67985i) q^{95} +(-0.428489 - 0.247388i) q^{96} +(-1.29625 + 2.24517i) q^{97} +(1.15624 - 3.49518i) q^{98} +(-0.748818 - 1.29699i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 10 q^{4} + 9 q^{5} - 6 q^{6} + 2 q^{7} + 16 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 10 * q^4 + 9 * q^5 - 6 * q^6 + 2 * q^7 + 16 * q^9	\( 16 q - 8 q^{3} + 10 q^{4} + 9 q^{5} - 6 q^{6} + 2 q^{7} + 16 q^{9} - 2 q^{10} - 9 q^{11} - 17 q^{12} + 15 q^{13} + 3 q^{14} - 12 q^{15} - 22 q^{16} - 3 q^{18} + 8 q^{19} - 10 q^{21} - 27 q^{22} + 30 q^{23} + 13 q^{25} - 9 q^{26} - 38 q^{27} + 35 q^{28} - 18 q^{29} - 32 q^{30} - 27 q^{31} + 27 q^{32} - 12 q^{33} - 16 q^{34} - 6 q^{35} + 4 q^{36} - 39 q^{37} + 27 q^{38} - 9 q^{39} + 9 q^{40} + 9 q^{41} + 48 q^{42} - 9 q^{43} + 18 q^{44} + 75 q^{45} - 36 q^{46} + 35 q^{48} - 8 q^{49} + 18 q^{53} - 18 q^{54} + 15 q^{56} - 22 q^{57} - 20 q^{58} + 18 q^{59} - 45 q^{62} - 46 q^{63} - 22 q^{64} - 36 q^{65} - 45 q^{66} + 18 q^{67} + 63 q^{68} + 30 q^{69} - 19 q^{70} - 9 q^{71} + 18 q^{74} + 10 q^{75} + 98 q^{76} + 30 q^{77} + 54 q^{78} + 21 q^{79} + 27 q^{80} + 40 q^{81} - 34 q^{84} + 31 q^{85} - 48 q^{87} + 18 q^{88} + 24 q^{89} + 28 q^{90} + 15 q^{91} + 54 q^{92} + 6 q^{93} - 49 q^{94} - 66 q^{95} - 69 q^{96} + q^{97} + 15 q^{98} + 18 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 + 10 * q^4 + 9 * q^5 - 6 * q^6 + 2 * q^7 + 16 * q^9 - 2 * q^10 - 9 * q^11 - 17 * q^12 + 15 * q^13 + 3 * q^14 - 12 * q^15 - 22 * q^16 - 3 * q^18 + 8 * q^19 - 10 * q^21 - 27 * q^22 + 30 * q^23 + 13 * q^25 - 9 * q^26 - 38 * q^27 + 35 * q^28 - 18 * q^29 - 32 * q^30 - 27 * q^31 + 27 * q^32 - 12 * q^33 - 16 * q^34 - 6 * q^35 + 4 * q^36 - 39 * q^37 + 27 * q^38 - 9 * q^39 + 9 * q^40 + 9 * q^41 + 48 * q^42 - 9 * q^43 + 18 * q^44 + 75 * q^45 - 36 * q^46 + 35 * q^48 - 8 * q^49 + 18 * q^53 - 18 * q^54 + 15 * q^56 - 22 * q^57 - 20 * q^58 + 18 * q^59 - 45 * q^62 - 46 * q^63 - 22 * q^64 - 36 * q^65 - 45 * q^66 + 18 * q^67 + 63 * q^68 + 30 * q^69 - 19 * q^70 - 9 * q^71 + 18 * q^74 + 10 * q^75 + 98 * q^76 + 30 * q^77 + 54 * q^78 + 21 * q^79 + 27 * q^80 + 40 * q^81 - 34 * q^84 + 31 * q^85 - 48 * q^87 + 18 * q^88 + 24 * q^89 + 28 * q^90 + 15 * q^91 + 54 * q^92 + 6 * q^93 - 49 * q^94 - 66 * q^95 - 69 * q^96 + q^97 + 15 * q^98 + 18 * q^99

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