LMFDB - Embedded newform 429.2.n.a.313.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(157,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 0]))

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

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

chi := DirichletCharacter("429.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.n (of order $5$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 9 x^{10} - 15 x^{9} + 29 x^{8} - 26 x^{7} + 43 x^{6} + 24 x^{5} + 16 x^{4} + \cdots + 1 $ x^12 - 3x^11 + 9x^10 - 15x^9 + 29x^8 - 26x^7 + 43x^6 + 24x^5 + 16x^4 - 17x^3 + 14x^2 - 5*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			313.1
Root			$-0.566948 + 1.74489i$ of defining polynomial
Character	$\chi$	$=$	429.313
Dual form			429.2.n.a.196.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.566948 - 1.74489i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-1.10516 + 0.802947i) q^{4} +(-0.477448 + 1.46943i) q^{5} +(-0.566948 + 1.74489i) q^{6} +(-0.675271 + 0.490613i) q^{7} +(-0.940958 - 0.683646i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.566948 - 1.74489i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-1.10516 + 0.802947i) q^{4} +(-0.477448 + 1.46943i) q^{5} +(-0.566948 + 1.74489i) q^{6} +(-0.675271 + 0.490613i) q^{7} +(-0.940958 - 0.683646i) q^{8} +(0.309017 + 0.951057i) q^{9} +2.83468 q^{10} +(-2.09568 + 2.57063i) q^{11} +1.36605 q^{12} +(0.309017 + 0.951057i) q^{13} +(1.23891 + 0.900119i) q^{14} +(1.24997 - 0.908160i) q^{15} +(-1.50368 + 4.62784i) q^{16} +(-1.22440 + 3.76833i) q^{17} +(1.48429 - 1.07840i) q^{18} +(1.21176 + 0.880396i) q^{19} +(-0.652220 - 2.00733i) q^{20} +0.834681 q^{21} +(5.67359 + 2.19931i) q^{22} +1.75538 q^{23} +(0.359414 + 1.10616i) q^{24} +(2.11381 + 1.53577i) q^{25} +(1.48429 - 1.07840i) q^{26} +(0.309017 - 0.951057i) q^{27} +(0.352347 - 1.08441i) q^{28} +(-6.88940 + 5.00544i) q^{29} +(-2.29331 - 1.66618i) q^{30} +(-0.487584 - 1.50063i) q^{31} +6.60139 q^{32} +(3.20642 - 0.847870i) q^{33} +7.26947 q^{34} +(-0.398517 - 1.22651i) q^{35} +(-1.10516 - 0.802947i) q^{36} +(4.46927 - 3.24711i) q^{37} +(0.849185 - 2.61352i) q^{38} +(0.309017 - 0.951057i) q^{39} +(1.45383 - 1.05627i) q^{40} +(-7.17922 - 5.21601i) q^{41} +(-0.473220 - 1.45642i) q^{42} +3.09803 q^{43} +(0.251990 - 4.52368i) q^{44} -1.54505 q^{45} +(-0.995206 - 3.06293i) q^{46} +(-1.80257 - 1.30964i) q^{47} +(3.93668 - 2.86017i) q^{48} +(-1.94783 + 5.99480i) q^{49} +(1.48133 - 4.55905i) q^{50} +(3.20553 - 2.32895i) q^{51} +(-1.10516 - 0.802947i) q^{52} +(0.153958 + 0.473834i) q^{53} -1.83468 q^{54} +(-2.77679 - 4.30680i) q^{55} +0.970807 q^{56} +(-0.462852 - 1.42451i) q^{57} +(12.6398 + 9.18338i) q^{58} +(4.72692 - 3.43430i) q^{59} +(-0.652220 + 2.00733i) q^{60} +(-3.39577 + 10.4511i) q^{61} +(-2.34199 + 1.70156i) q^{62} +(-0.675271 - 0.490613i) q^{63} +(-0.735286 - 2.26298i) q^{64} -1.54505 q^{65} +(-3.29731 - 5.11413i) q^{66} -8.43289 q^{67} +(-1.67260 - 5.14774i) q^{68} +(-1.42013 - 1.03178i) q^{69} +(-1.91418 + 1.39073i) q^{70} +(-1.46101 + 4.49653i) q^{71} +(0.359414 - 1.10616i) q^{72} +(-1.33175 + 0.967570i) q^{73} +(-8.19968 - 5.95741i) q^{74} +(-0.807402 - 2.48493i) q^{75} -2.04610 q^{76} +(0.153970 - 2.76404i) q^{77} -1.83468 q^{78} +(-0.734755 - 2.26134i) q^{79} +(-6.08238 - 4.41911i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-5.03110 + 15.4841i) q^{82} +(-3.49105 + 10.7444i) q^{83} +(-0.922457 + 0.670204i) q^{84} +(-4.95272 - 3.59836i) q^{85} +(-1.75642 - 5.40570i) q^{86} +8.51576 q^{87} +(3.72935 - 0.986147i) q^{88} -6.16923 q^{89} +(0.875965 + 2.69594i) q^{90} +(-0.675271 - 0.490613i) q^{91} +(-1.93997 + 1.40947i) q^{92} +(-0.487584 + 1.50063i) q^{93} +(-1.26321 + 3.88777i) q^{94} +(-1.87224 + 1.36026i) q^{95} +(-5.34064 - 3.88020i) q^{96} +(3.31764 + 10.2106i) q^{97} +11.5646 q^{98} +(-3.09241 - 1.19874i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 8 q^{5} + 3 q^{6} + 5 q^{7} - q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 8 * q^5 + 3 * q^6 + 5 * q^7 - q^8 - 3 * q^9	\( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 8 q^{5} + 3 q^{6} + 5 q^{7} - q^{8} - 3 q^{9} + 14 q^{10} - 6 q^{11} + 2 q^{12} - 3 q^{13} + 11 q^{14} - 2 q^{15} - 5 q^{16} - 14 q^{17} - 2 q^{18} - 2 q^{19} - 9 q^{20} - 10 q^{21} + 21 q^{22} - 6 q^{23} + 4 q^{24} + 19 q^{25} - 2 q^{26} - 3 q^{27} - 12 q^{28} - 12 q^{29} - q^{30} - 12 q^{31} + 26 q^{32} + 9 q^{33} - 24 q^{34} - 2 q^{35} - 3 q^{36} + 4 q^{37} - 13 q^{38} - 3 q^{39} + 4 q^{40} - 10 q^{41} + q^{42} + 28 q^{43} - 12 q^{45} - 5 q^{46} + 28 q^{47} + 10 q^{48} + 20 q^{49} - q^{50} + 11 q^{51} - 3 q^{52} - 29 q^{53} - 2 q^{54} + 4 q^{55} + 12 q^{56} + 8 q^{57} + 22 q^{58} - 11 q^{59} - 9 q^{60} - 18 q^{61} + 40 q^{62} + 5 q^{63} + 11 q^{64} - 12 q^{65} + 16 q^{66} - 72 q^{67} - 35 q^{68} + 4 q^{69} - 6 q^{70} + 10 q^{71} + 4 q^{72} - 11 q^{73} - 15 q^{74} - 11 q^{75} + 4 q^{76} + 20 q^{77} - 2 q^{78} - 7 q^{79} - 27 q^{80} - 3 q^{81} - 10 q^{82} + 16 q^{83} + 8 q^{84} - 26 q^{85} - 35 q^{86} + 28 q^{87} + 25 q^{88} - 62 q^{89} - 6 q^{90} + 5 q^{91} - 34 q^{92} - 12 q^{93} - q^{94} + 15 q^{95} + q^{96} + 54 q^{97} + 50 q^{98} - 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 8 * q^5 + 3 * q^6 + 5 * q^7 - q^8 - 3 * q^9 + 14 * q^10 - 6 * q^11 + 2 * q^12 - 3 * q^13 + 11 * q^14 - 2 * q^15 - 5 * q^16 - 14 * q^17 - 2 * q^18 - 2 * q^19 - 9 * q^20 - 10 * q^21 + 21 * q^22 - 6 * q^23 + 4 * q^24 + 19 * q^25 - 2 * q^26 - 3 * q^27 - 12 * q^28 - 12 * q^29 - q^30 - 12 * q^31 + 26 * q^32 + 9 * q^33 - 24 * q^34 - 2 * q^35 - 3 * q^36 + 4 * q^37 - 13 * q^38 - 3 * q^39 + 4 * q^40 - 10 * q^41 + q^42 + 28 * q^43 - 12 * q^45 - 5 * q^46 + 28 * q^47 + 10 * q^48 + 20 * q^49 - q^50 + 11 * q^51 - 3 * q^52 - 29 * q^53 - 2 * q^54 + 4 * q^55 + 12 * q^56 + 8 * q^57 + 22 * q^58 - 11 * q^59 - 9 * q^60 - 18 * q^61 + 40 * q^62 + 5 * q^63 + 11 * q^64 - 12 * q^65 + 16 * q^66 - 72 * q^67 - 35 * q^68 + 4 * q^69 - 6 * q^70 + 10 * q^71 + 4 * q^72 - 11 * q^73 - 15 * q^74 - 11 * q^75 + 4 * q^76 + 20 * q^77 - 2 * q^78 - 7 * q^79 - 27 * q^80 - 3 * q^81 - 10 * q^82 + 16 * q^83 + 8 * q^84 - 26 * q^85 - 35 * q^86 + 28 * q^87 + 25 * q^88 - 62 * q^89 - 6 * q^90 + 5 * q^91 - 34 * q^92 - 12 * q^93 - q^94 + 15 * q^95 + q^96 + 54 * q^97 + 50 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	−0.566948	−	1.74489i	−0.400893	−	1.23382i	−0.924277	−	0.381723i	$-0.875331\pi$
$2$	−0.566948	−	1.74489i	−0.400893	−	1.23382i	0.523384	−	0.852097i	$-0.324669\pi$
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$4$	−1.10516	+	0.802947i	−0.552581	+	0.401473i
$5$	−0.477448	+	1.46943i	−0.213521	+	0.657151i	0.785734	+	0.618564i	$0.212285\pi$
$5$	−0.477448	+	1.46943i	−0.213521	+	0.657151i	−0.999255	+	0.0385862i	$0.987715\pi$
$6$	−0.566948	+	1.74489i	−0.231455	+	0.712346i
$7$	−0.675271	+	0.490613i	−0.255228	+	0.185434i	−0.708041	−	0.706171i	$-0.750421\pi$
$7$	−0.675271	+	0.490613i	−0.255228	+	0.185434i	0.452812	+	0.891606i	$0.350421\pi$
$8$	−0.940958	−	0.683646i	−0.332679	−	0.241705i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	2.83468			0.896405
$11$	−2.09568	+	2.57063i	−0.631872	+	0.775073i
$11$	−2.09568	+	2.57063i	−0.631872	+	0.775073i
$12$	1.36605			0.394346
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$14$	1.23891	+	0.900119i	0.331112	+	0.240567i
$15$	1.24997	−	0.908160i	0.322742	−	0.234486i
$16$	−1.50368	+	4.62784i	−0.375919	+	1.15696i
$17$	−1.22440	+	3.76833i	−0.296961	+	0.913953i	0.685594	+	0.727984i	$0.259542\pi$
$17$	−1.22440	+	3.76833i	−0.296961	+	0.913953i	−0.982556	+	0.185969i	$0.940458\pi$
$18$	1.48429	−	1.07840i	0.349850	−	0.254181i
$19$	1.21176	+	0.880396i	0.277997	+	0.201977i	0.718043	−	0.695998i	$-0.245038\pi$
$19$	1.21176	+	0.880396i	0.277997	+	0.201977i	−0.440046	+	0.897975i	$0.645038\pi$
$20$	−0.652220	−	2.00733i	−0.145841	−	0.448852i
$21$	0.834681			0.182142
$22$	5.67359	+	2.19931i	1.20961	+	0.468895i
$23$	1.75538			0.366021			0.183011	−	0.983111i	$-0.441416\pi$
$23$	1.75538			0.366021			0.183011	+	0.983111i	$0.441416\pi$
$24$	0.359414	+	1.10616i	0.0733651	+	0.225794i
$25$	2.11381	+	1.53577i	0.422761	+	0.307154i
$26$	1.48429	−	1.07840i	0.291093	−	0.211491i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	0.352347	−	1.08441i	0.0665874	−	0.204935i
$29$	−6.88940	+	5.00544i	−1.27933	+	0.929487i	−0.999533	−	0.0305729i	$-0.990267\pi$
$29$	−6.88940	+	5.00544i	−1.27933	+	0.929487i	−0.279796	+	0.960059i	$0.590267\pi$
$30$	−2.29331	−	1.66618i	−0.418698	−	0.304202i
$31$	−0.487584	−	1.50063i	−0.0875728	−	0.269521i	0.897674	−	0.440660i	$-0.145255\pi$
$31$	−0.487584	−	1.50063i	−0.0875728	−	0.269521i	−0.985247	+	0.171138i	$0.945255\pi$
$32$	6.60139			1.16697
$33$	3.20642	−	0.847870i	0.558166	−	0.147595i
$34$	7.26947			1.24670
$35$	−0.398517	−	1.22651i	−0.0673616	−	0.207318i
$36$	−1.10516	−	0.802947i	−0.184194	−	0.133824i
$37$	4.46927	−	3.24711i	0.734743	−	0.533822i	−0.156318	−	0.987707i	$-0.549962\pi$
$37$	4.46927	−	3.24711i	0.734743	−	0.533822i	0.891060	+	0.453885i	$0.149962\pi$
$38$	0.849185	−	2.61352i	0.137756	−	0.423969i
$39$	0.309017	−	0.951057i	0.0494823	−	0.152291i
$40$	1.45383	−	1.05627i	0.229871	−	0.167011i
$41$	−7.17922	−	5.21601i	−1.12121	−	0.814604i	−0.136815	−	0.990597i	$-0.543686\pi$
$41$	−7.17922	−	5.21601i	−1.12121	−	0.814604i	−0.984391	+	0.175993i	$0.943686\pi$
$42$	−0.473220	−	1.45642i	−0.0730195	−	0.224731i
$43$	3.09803			0.472445			0.236222	−	0.971699i	$-0.424091\pi$
$43$	3.09803			0.472445			0.236222	+	0.971699i	$0.424091\pi$
$44$	0.251990	−	4.52368i	0.0379890	−	0.681970i
$45$	−1.54505			−0.230323
$46$	−0.995206	−	3.06293i	−0.146735	−	0.451604i
$47$	−1.80257	−	1.30964i	−0.262932	−	0.191031i	0.448507	−	0.893779i	$-0.351956\pi$
$47$	−1.80257	−	1.30964i	−0.262932	−	0.191031i	−0.711438	+	0.702748i	$0.751956\pi$
$48$	3.93668	−	2.86017i	0.568211	−	0.412829i
$49$	−1.94783	+	5.99480i	−0.278261	+	0.856400i
$50$	1.48133	−	4.55905i	0.209491	−	0.644747i
$51$	3.20553	−	2.32895i	0.448864	−	0.326119i
$52$	−1.10516	−	0.802947i	−0.153258	−	0.111349i
$53$	0.153958	+	0.473834i	0.0211478	+	0.0650861i	0.961073	−	0.276293i	$-0.0891060\pi$
$53$	0.153958	+	0.473834i	0.0211478	+	0.0650861i	−0.939926	+	0.341379i	$0.889106\pi$
$54$	−1.83468			−0.249668
$55$	−2.77679	−	4.30680i	−0.374422	−	0.580729i
$56$	0.970807			0.129730
$57$	−0.462852	−	1.42451i	−0.0613062	−	0.188681i
$58$	12.6398	+	9.18338i	1.65969	+	1.20584i
$59$	4.72692	−	3.43430i	0.615392	−	0.447108i	−0.235917	−	0.971773i	$-0.575809\pi$
$59$	4.72692	−	3.43430i	0.615392	−	0.447108i	0.851309	+	0.524665i	$0.175809\pi$
$60$	−0.652220	+	2.00733i	−0.0842012	+	0.259145i
$61$	−3.39577	+	10.4511i	−0.434784	+	1.33813i	0.458524	+	0.888682i	$0.348378\pi$
$61$	−3.39577	+	10.4511i	−0.434784	+	1.33813i	−0.893308	+	0.449445i	$0.851622\pi$
$62$	−2.34199	+	1.70156i	−0.297433	+	0.216098i
$63$	−0.675271	−	0.490613i	−0.0850762	−	0.0618115i
$64$	−0.735286	−	2.26298i	−0.0919108	−	0.282872i
$65$	−1.54505			−0.191640
$66$	−3.29731	−	5.11413i	−0.405870	−	0.629506i
$67$	−8.43289			−1.03024			−0.515121	−	0.857117i	$-0.672253\pi$
$67$	−8.43289			−1.03024			−0.515121	+	0.857117i	$0.672253\pi$
$68$	−1.67260	−	5.14774i	−0.202833	−	0.624255i
$69$	−1.42013	−	1.03178i	−0.170963	−	0.124212i
$70$	−1.91418	+	1.39073i	−0.228788	+	0.166224i
$71$	−1.46101	+	4.49653i	−0.173390	+	0.533640i	−0.999556	−	0.0297868i	$-0.990517\pi$
$71$	−1.46101	+	4.49653i	−0.173390	+	0.533640i	0.826166	+	0.563426i	$0.190517\pi$
$72$	0.359414	−	1.10616i	0.0423573	−	0.130362i
$73$	−1.33175	+	0.967570i	−0.155869	+	0.113245i	−0.662986	−	0.748632i	$-0.730711\pi$
$73$	−1.33175	+	0.967570i	−0.155869	+	0.113245i	0.507117	+	0.861877i	$0.330711\pi$
$74$	−8.19968	−	5.95741i	−0.953193	−	0.692535i
$75$	−0.807402	−	2.48493i	−0.0932308	−	0.286935i
$76$	−2.04610			−0.234704
$77$	0.153970	−	2.76404i	0.0175465	−	0.314991i
$78$	−1.83468			−0.207737
$79$	−0.734755	−	2.26134i	−0.0826664	−	0.254421i	0.901177	−	0.433451i	$-0.142704\pi$
$79$	−0.734755	−	2.26134i	−0.0826664	−	0.254421i	−0.983844	+	0.179030i	$0.942704\pi$
$80$	−6.08238	−	4.41911i	−0.680031	−	0.494071i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−5.03110	+	15.4841i	−0.555592	+	1.70994i
$83$	−3.49105	+	10.7444i	−0.383193	+	1.17935i	0.554590	+	0.832124i	$0.312875\pi$
$83$	−3.49105	+	10.7444i	−0.383193	+	1.17935i	−0.937783	+	0.347222i	$0.887125\pi$
$84$	−0.922457	+	0.670204i	−0.100648	+	0.0731253i
$85$	−4.95272	−	3.59836i	−0.537197	−	0.390297i
$86$	−1.75642	−	5.40570i	−0.189399	−	0.582912i
$87$	8.51576			0.912985
$88$	3.72935	−	0.986147i	0.397550	−	0.105124i
$89$	−6.16923			−0.653937			−0.326968	−	0.945035i	$-0.606027\pi$
$89$	−6.16923			−0.653937			−0.326968	+	0.945035i	$0.606027\pi$
$90$	0.875965	+	2.69594i	0.0923348	+	0.284177i
$91$	−0.675271	−	0.490613i	−0.0707876	−	0.0514302i
$92$	−1.93997	+	1.40947i	−0.202256	+	0.146948i
$93$	−0.487584	+	1.50063i	−0.0505602	+	0.155608i
$94$	−1.26321	+	3.88777i	−0.130291	+	0.400993i
$95$	−1.87224	+	1.36026i	−0.192087	+	0.139560i
$96$	−5.34064	−	3.88020i	−0.545076	−	0.396021i
$97$	3.31764	+	10.2106i	0.336855	+	1.03673i	0.965801	+	0.259285i	$0.0834868\pi$
$97$	3.31764	+	10.2106i	0.336855	+	1.03673i	−0.628946	+	0.777449i	$0.716513\pi$
$98$	11.5646			1.16820
$99$	−3.09241	−	1.19874i	−0.310799	−	0.120478i
$100$	−3.56924			−0.356924
$101$	2.36659	+	7.28361i	0.235484	+	0.724746i	0.997057	+	0.0766663i	$0.0244276\pi$
$101$	2.36659	+	7.28361i	0.235484	+	0.724746i	−0.761573	+	0.648080i	$0.775572\pi$
$102$	−5.88112	−	4.27289i	−0.582318	−	0.423079i
$103$	5.74057	−	4.17077i	0.565635	−	0.410958i	−0.267882	−	0.963452i	$-0.586324\pi$
$103$	5.74057	−	4.17077i	0.565635	−	0.410958i	0.833517	+	0.552494i	$0.186324\pi$
$104$	0.359414	−	1.10616i	0.0352434	−	0.108468i
$105$	−0.398517	+	1.22651i	−0.0388912	+	0.119695i
$106$	0.739500	−	0.537278i	0.0718266	−	0.0521851i
$107$	−13.4846	−	9.79711i	−1.30360	−	0.947123i	−0.303619	−	0.952794i	$-0.598195\pi$
$107$	−13.4846	−	9.79711i	−1.30360	−	0.947123i	−0.999984	+	0.00567100i	$0.998195\pi$
$108$	0.422134	+	1.29919i	0.0406199	+	0.125015i
$109$	−19.4175			−1.85986			−0.929928	−	0.367742i	$-0.880131\pi$
$109$	−19.4175			−1.85986			−0.929928	+	0.367742i	$0.880131\pi$
$110$	−5.94059	+	7.28691i	−0.566413	+	0.694779i
$111$	−5.52432			−0.524345
$112$	−1.25509	−	3.86277i	−0.118595	−	0.364998i
$113$	10.4142	+	7.56633i	0.979682	+	0.711781i	0.957638	−	0.287976i	$-0.0929824\pi$
$113$	10.4142	+	7.56633i	0.979682	+	0.711781i	0.0220447	+	0.999757i	$0.492982\pi$
$114$	−2.22320	+	1.61525i	−0.208221	+	0.151282i
$115$	−0.838101	+	2.57941i	−0.0781533	+	0.240531i
$116$	3.59479	−	11.0636i	0.333768	−	1.02723i
$117$	−0.809017	+	0.587785i	−0.0747936	+	0.0543408i
$118$	−8.67238	−	6.30085i	−0.798357	−	0.580041i
$119$	−1.02199	−	3.14535i	−0.0936853	−	0.288334i
$120$	−1.79703			−0.164046
$121$	−2.21624	−	10.7744i	−0.201476	−	0.979493i
$122$	20.1612			1.82531
$123$	2.74222	+	8.43968i	0.247258	+	0.760980i
$124$	1.74379	+	1.26693i	0.156597	+	0.113774i
$125$	−9.51582	+	6.91365i	−0.851121	+	0.618375i
$126$	−0.473220	+	1.45642i	−0.0421578	+	0.129748i
$127$	4.03118	−	12.4067i	0.357710	−	1.10092i	−0.596712	−	0.802455i	$-0.703527\pi$
$127$	4.03118	−	12.4067i	0.357710	−	1.10092i	0.954422	−	0.298462i	$-0.0964735\pi$
$128$	7.14950	−	5.19442i	0.631933	−	0.459126i
$129$	−2.50636	−	1.82097i	−0.220672	−	0.160328i
$130$	0.875965	+	2.69594i	0.0768272	+	0.236450i
$131$	18.0732			1.57906			0.789531	−	0.613711i	$-0.210324\pi$
$131$	18.0732			1.57906			0.789531	+	0.613711i	$0.210324\pi$
$132$	−2.86282	+	3.51162i	−0.249176	+	0.305647i
$133$	−1.25020			−0.108406
$134$	4.78101	+	14.7144i	0.413016	+	1.27113i
$135$	1.24997	+	0.908160i	0.107581	+	0.0781620i
$136$	3.72831	−	2.70878i	0.319700	−	0.232276i
$137$	4.02283	−	12.3810i	0.343693	−	1.05778i	−0.618586	−	0.785717i	$-0.712294\pi$
$137$	4.02283	−	12.3810i	0.343693	−	1.05778i	0.962280	−	0.272062i	$-0.0877057\pi$
$138$	−0.995206	+	3.06293i	−0.0847176	+	0.260734i
$139$	−10.8108	+	7.85447i	−0.916956	+	0.666208i	−0.942765	−	0.333459i	$-0.891784\pi$
$139$	−10.8108	+	7.85447i	−0.916956	+	0.666208i	0.0258083	+	0.999667i	$0.491784\pi$
$140$	1.42525	+	1.03550i	0.120455	+	0.0875159i
$141$	0.688520	+	2.11905i	0.0579838	+	0.178456i
$142$	8.67424			0.727926
$143$	−3.09241	−	1.19874i	−0.258600	−	0.100244i
$144$	−4.86600			−0.405500
$145$	−4.06583	−	12.5133i	−0.337649	−	1.03918i
$146$	2.44333	+	1.77518i	0.202211	+	0.146915i
$147$	5.09948	−	3.70499i	0.420598	−	0.305583i
$148$	−2.33200	+	7.17716i	−0.191689	+	0.589959i
$149$	−1.37468	+	4.23083i	−0.112618	+	0.346603i	−0.991443	−	0.130542i	$-0.958328\pi$
$149$	−1.37468	+	4.23083i	−0.112618	+	0.346603i	0.878825	+	0.477145i	$0.158328\pi$
$150$	−3.87816	+	2.81765i	−0.316650	+	0.230060i
$151$	−11.2631	−	8.18315i	−0.916581	−	0.665935i	0.0260897	−	0.999660i	$-0.491694\pi$
$151$	−11.2631	−	8.18315i	−0.916581	−	0.665935i	−0.942671	+	0.333725i	$0.891694\pi$
$152$	−0.538337	−	1.65683i	−0.0436649	−	0.134387i
$153$	−3.96225			−0.320329
$154$	−4.91022	+	1.29840i	−0.395677	+	0.104628i
$155$	2.43787			0.195815
$156$	0.422134	+	1.29919i	0.0337978	+	0.104019i
$157$	8.60119	+	6.24913i	0.686450	+	0.498735i	0.875491	−	0.483234i	$-0.160538\pi$
$157$	8.60119	+	6.24913i	0.686450	+	0.498735i	−0.189041	+	0.981969i	$0.560538\pi$
$158$	−3.52922	+	2.56413i	−0.280770	+	0.203991i
$159$	0.153958	−	0.473834i	0.0122097	−	0.0375775i
$160$	−3.15182	+	9.70030i	−0.249173	+	0.766876i
$161$	−1.18536	+	0.861211i	−0.0934191	+	0.0678729i
$162$	1.48429	+	1.07840i	0.116617	+	0.0847270i
$163$	−0.768082	−	2.36391i	−0.0601608	−	0.185156i	0.916460	−	0.400127i	$-0.131034\pi$
$163$	−0.768082	−	2.36391i	−0.0601608	−	0.185156i	−0.976620	+	0.214971i	$0.931034\pi$
$164$	12.1224			0.946599
$165$	−0.285010	+	5.11643i	−0.0221880	+	0.398314i
$166$	20.7269			1.60872
$167$	−5.46850	−	16.8303i	−0.423165	−	1.30237i	−0.904740	−	0.425964i	$-0.859935\pi$
$167$	−5.46850	−	16.8303i	−0.423165	−	1.30237i	0.481575	−	0.876405i	$-0.340065\pi$
$168$	−0.785400	−	0.570626i	−0.0605949	−	0.0440248i
$169$	−0.809017	+	0.587785i	−0.0622321	+	0.0452143i
$170$	−3.47079	+	10.6820i	−0.266198	+	0.819272i
$171$	−0.462852	+	1.42451i	−0.0353951	+	0.108935i
$172$	−3.42382	+	2.48755i	−0.261064	+	0.189674i
$173$	10.4033	+	7.55847i	0.790952	+	0.574660i	0.908246	−	0.418437i	$-0.137422\pi$
$173$	10.4033	+	7.55847i	0.790952	+	0.574660i	−0.117294	+	0.993097i	$0.537422\pi$
$174$	−4.82799	−	14.8590i	−0.366009	−	1.12646i
$175$	−2.18086			−0.164858
$176$	−8.74523	−	13.5639i	−0.659196	−	1.02242i
$177$	−5.84279			−0.439171
$178$	3.49763	+	10.7646i	0.262158	+	0.806841i
$179$	8.99073	+	6.53215i	0.671999	+	0.488236i	0.870694	−	0.491826i	$-0.163670\pi$
$179$	8.99073	+	6.53215i	0.671999	+	0.488236i	−0.198695	+	0.980061i	$0.563670\pi$
$180$	1.70753	−	1.24060i	0.127272	−	0.0924686i
$181$	0.542673	−	1.67018i	0.0403366	−	0.124143i	−0.928860	−	0.370430i	$-0.879210\pi$
$181$	0.542673	−	1.67018i	0.0403366	−	0.124143i	0.969197	+	0.246287i	$0.0792104\pi$
$182$	−0.473220	+	1.45642i	−0.0350774	+	0.107957i
$183$	8.89024	−	6.45914i	0.657186	−	0.477473i
$184$	−1.65174	−	1.20006i	−0.121768	−	0.0884693i
$185$	2.63757	+	8.11762i	0.193918	+	0.596819i
$186$	2.89486			0.212262
$187$	−7.12100	−	11.0447i	−0.520739	−	0.807668i
$188$	3.04370			0.221985
$189$	0.257931	+	0.793829i	0.0187617	+	0.0577426i
$190$	3.43496	+	2.49564i	0.249198	+	0.181053i
$191$	4.36059	−	3.16815i	0.315521	−	0.229240i	−0.418741	−	0.908106i	$-0.637528\pi$
$191$	4.36059	−	3.16815i	0.315521	−	0.229240i	0.734262	+	0.678866i	$0.237528\pi$
$192$	−0.735286	+	2.26298i	−0.0530647	+	0.163316i
$193$	2.96202	−	9.11616i	0.213211	−	0.656196i	−0.786065	−	0.618144i	$-0.787885\pi$
$193$	2.96202	−	9.11616i	0.213211	−	0.656196i	0.999276	−	0.0380516i	$-0.0121151\pi$
$194$	15.9355	−	11.5778i	1.14410	−	0.831238i
$195$	1.24997	+	0.908160i	0.0895126	+	0.0650347i
$196$	−2.66084	−	8.18923i	−0.190060	−	0.584945i
$197$	12.7324			0.907143			0.453572	−	0.891220i	$-0.350150\pi$
$197$	12.7324			0.907143			0.453572	+	0.891220i	$0.350150\pi$
$198$	−0.338436	+	6.07553i	−0.0240516	+	0.431769i
$199$	2.14932			0.152361			0.0761807	−	0.997094i	$-0.475727\pi$
$199$	2.14932			0.152361			0.0761807	+	0.997094i	$0.475727\pi$
$200$	−0.939080	−	2.89019i	−0.0664030	−	0.204367i
$201$	6.82236	+	4.95673i	0.481212	+	0.349621i
$202$	11.3673	−	8.25885i	0.799802	−	0.581090i
$203$	2.19648	−	6.76006i	0.154162	−	0.474463i
$204$	−1.67260	+	5.14774i	−0.117106	+	0.360414i
$205$	11.0923	−	8.05902i	0.774719	−	0.562866i
$206$	−10.5321	−	7.65203i	−0.733807	−	0.533142i
$207$	0.542441	+	1.66946i	0.0377023	+	0.116036i
$208$	−4.86600			−0.337397
$209$	−4.80263	+	1.26996i	−0.332205	+	0.0878446i
$210$	2.36605			0.163273
$211$	−6.28270	−	19.3362i	−0.432519	−	1.33116i	−0.895608	−	0.444844i	$-0.853259\pi$
$211$	−6.28270	−	19.3362i	−0.432519	−	1.33116i	0.463089	−	0.886312i	$-0.346741\pi$
$212$	−0.550612	−	0.400043i	−0.0378162	−	0.0274751i
$213$	3.82497	−	2.77901i	0.262083	−	0.190414i
$214$	−9.44979	+	29.0835i	−0.645975	+	1.98811i
$215$	−1.47915	+	4.55234i	−0.100877	+	0.310467i
$216$	−0.940958	+	0.683646i	−0.0640241	+	0.0465162i
$217$	1.06548	+	0.774117i	0.0723296	+	0.0525505i
$218$	11.0087	+	33.8812i	0.745602	+	2.29473i
$219$	1.64613			0.111235
$220$	6.52693	+	2.53010i	0.440046	+	0.170580i
$221$	−3.96225			−0.266530
$222$	3.13200	+	9.63930i	0.210206	+	0.646947i
$223$	17.5855	+	12.7766i	1.17761	+	0.855586i	0.991900	−	0.127018i	$-0.0405407\pi$
$223$	17.5855	+	12.7766i	1.17761	+	0.855586i	0.185712	+	0.982604i	$0.440541\pi$
$224$	−4.45773	+	3.23873i	−0.297844	+	0.216397i
$225$	−0.807402	+	2.48493i	−0.0538268	+	0.165662i
$226$	7.29810	−	22.4612i	0.485462	−	1.49410i
$227$	15.8779	−	11.5359i	1.05385	−	0.765668i	0.0809103	−	0.996721i	$-0.474217\pi$
$227$	15.8779	−	11.5359i	1.05385	−	0.765668i	0.972941	+	0.231054i	$0.0742173\pi$
$228$	1.65533	+	1.20267i	0.109627	+	0.0796487i
$229$	0.160178	+	0.492977i	0.0105849	+	0.0325768i	0.956209	−	0.292683i	$-0.0945481\pi$
$229$	0.160178	+	0.492977i	0.0105849	+	0.0325768i	−0.945625	+	0.325260i	$0.894548\pi$
$230$	4.97593			0.328103
$231$	−1.74923	+	2.14565i	−0.115091	+	0.141174i
$232$	9.90458			0.650267
$233$	−3.52545	−	10.8502i	−0.230960	−	0.710821i	−0.997632	−	0.0687819i	$-0.978089\pi$
$233$	−3.52545	−	10.8502i	−0.230960	−	0.710821i	0.766672	−	0.642039i	$-0.221911\pi$
$234$	1.48429	+	1.07840i	0.0970310	+	0.0704971i
$235$	2.78506	−	2.02347i	0.181678	−	0.131996i
$236$	−2.46644	+	7.59092i	−0.160552	+	0.494127i
$237$	−0.734755	+	2.26134i	−0.0477275	+	0.146890i
$238$	−4.90886	+	3.56650i	−0.318194	+	0.231182i
$239$	21.6097	+	15.7004i	1.39782	+	1.01557i	0.994956	+	0.100310i	$0.0319836\pi$
$239$	21.6097	+	15.7004i	1.39782	+	1.01557i	0.402859	+	0.915262i	$0.368016\pi$
$240$	2.32326	+	7.15027i	0.149966	+	0.461548i
$241$	2.56160			0.165007			0.0825037	−	0.996591i	$-0.473708\pi$
$241$	2.56160			0.165007			0.0825037	+	0.996591i	$0.473708\pi$
$242$	−17.5437	+	9.97562i	−1.12775	+	0.641257i
$243$	1.00000			0.0641500
$244$	−4.63881	−	14.2768i	−0.296969	−	0.913977i
$245$	−7.87898	−	5.72441i	−0.503369	−	0.365719i
$246$	13.1716	−	9.56971i	0.839789	−	0.610143i
$247$	−0.462852	+	1.42451i	−0.0294505	+	0.0906394i
$248$	−0.567104	+	1.74537i	−0.0360111	+	0.110831i
$249$	9.13969	−	6.64038i	0.579205	−	0.420817i
$250$	17.4585	+	12.6843i	1.10417	+	0.802228i
$251$	6.72921	+	20.7104i	0.424744	+	1.30723i	0.903239	+	0.429138i	$0.141183\pi$
$251$	6.72921	+	20.7104i	0.424744	+	1.30723i	−0.478495	+	0.878090i	$0.658817\pi$
$252$	1.14022			0.0718271
$253$	−3.67871	+	4.51242i	−0.231279	+	0.283693i
$254$	−23.9337			−1.50174
$255$	1.89177	+	5.82227i	0.118467	+	0.364604i
$256$	−16.9671	−	12.3273i	−1.06044	−	0.770456i
$257$	−7.15461	+	5.19813i	−0.446292	+	0.324250i	−0.788130	−	0.615509i	$-0.788951\pi$
$257$	−7.15461	+	5.19813i	−0.446292	+	0.324250i	0.341838	+	0.939759i	$0.388951\pi$
$258$	−1.75642	+	5.40570i	−0.109350	+	0.336544i
$259$	−1.42489	+	4.38536i	−0.0885384	+	0.272493i
$260$	1.70753	−	1.24060i	0.105897	−	0.0769385i
$261$	−6.88940	−	5.00544i	−0.426443	−	0.309829i
$262$	−10.2465	−	31.5356i	−0.633034	−	1.94828i
$263$	5.45172			0.336167			0.168084	−	0.985773i	$-0.446242\pi$
$263$	5.45172			0.336167			0.168084	+	0.985773i	$0.446242\pi$
$264$	−3.59675	−	1.39425i	−0.221364	−	0.0858099i
$265$	−0.769775			−0.0472869
$266$	0.708799	+	2.18146i	0.0434592	+	0.133754i
$267$	4.99101	+	3.62618i	0.305445	+	0.221919i
$268$	9.31971	−	6.77116i	0.569292	−	0.413615i
$269$	3.74998	−	11.5413i	0.228641	−	0.703683i	−0.769261	−	0.638935i	$-0.779375\pi$
$269$	3.74998	−	11.5413i	0.228641	−	0.703683i	0.997902	−	0.0647486i	$-0.0206245\pi$
$270$	0.875965	−	2.69594i	0.0533095	−	0.164070i
$271$	18.8568	−	13.7003i	1.14547	−	0.832234i	0.157599	−	0.987503i	$-0.449625\pi$
$271$	18.8568	−	13.7003i	1.14547	−	0.832234i	0.987872	+	0.155269i	$0.0496245\pi$
$272$	−15.5981	−	11.3327i	−0.945775	−	0.687146i
$273$	0.257931	+	0.793829i	0.0156107	+	0.0480447i
$274$	−23.8841			−1.44289
$275$	−8.37776	+	2.21532i	−0.505198	+	0.133589i
$276$	2.39794			0.144339
$277$	−1.98304	−	6.10317i	−0.119149	−	0.366704i	0.873641	−	0.486572i	$-0.161753\pi$
$277$	−1.98304	−	6.10317i	−0.119149	−	0.366704i	−0.992790	+	0.119868i	$0.961753\pi$
$278$	19.8343	+	14.4105i	1.18958	+	0.864281i
$279$	1.27651	−	0.927441i	0.0764228	−	0.0555244i
$280$	−0.463510	+	1.42654i	−0.0277000	+	0.0852519i
$281$	−8.63846	+	26.5864i	−0.515327	+	1.58601i	0.267359	+	0.963597i	$0.413849\pi$
$281$	−8.63846	+	26.5864i	−0.515327	+	1.58601i	−0.782686	+	0.622417i	$0.786151\pi$
$282$	3.30714	−	2.40278i	0.196937	−	0.143083i
$283$	9.65527	+	7.01497i	0.573946	+	0.416996i	0.836537	−	0.547911i	$-0.184577\pi$
$283$	9.65527	+	7.01497i	0.573946	+	0.416996i	−0.262590	+	0.964907i	$0.584577\pi$
$284$	−1.99582	−	6.14250i	−0.118430	−	0.364490i
$285$	2.31421			0.137082
$286$	−0.338436	+	6.07553i	−0.0200121	+	0.359254i
$287$	7.40696			0.437219
$288$	2.03994	+	6.27829i	0.120205	+	0.369952i
$289$	1.05218	+	0.764451i	0.0618927	+	0.0449677i
$290$	−19.5292	+	14.1888i	−1.14680	+	0.833196i
$291$	3.31764	−	10.2106i	0.194484	−	0.598559i
$292$	0.694886	−	2.13864i	0.0406652	−	0.125154i
$293$	−5.85520	+	4.25405i	−0.342064	+	0.248524i	−0.745532	−	0.666470i	$-0.767805\pi$
$293$	−5.85520	+	4.25405i	−0.342064	+	0.248524i	0.403468	+	0.914994i	$0.367805\pi$
$294$	−9.35592	−	6.79748i	−0.545649	−	0.396437i
$295$	2.78963	+	8.58559i	0.162418	+	0.499872i
$296$	−6.42527			−0.373461
$297$	1.79721	+	2.78748i	0.104285	+	0.161746i
$298$	8.16169			0.472794
$299$	0.542441	+	1.66946i	0.0313702	+	0.0965475i
$300$	2.88757	+	2.09795i	0.166714	+	0.121125i
$301$	−2.09201	+	1.51993i	−0.120581	+	0.0876074i
$302$	−7.89305	+	24.2923i	−0.454194	+	1.39786i
$303$	2.36659	−	7.28361i	0.135957	−	0.418432i
$304$	−5.89643	+	4.28401i	−0.338184	+	0.245705i
$305$	−13.7359	−	9.97972i	−0.786515	−	0.571437i
$306$	2.24639	+	6.91368i	0.128418	+	0.395228i
$307$	−14.1729			−0.808890			−0.404445	−	0.914562i	$-0.632535\pi$
$307$	−14.1729			−0.808890			−0.404445	+	0.914562i	$0.632535\pi$
$308$	2.04921	+	3.17834i	0.116765	+	0.181103i
$309$	−7.09574			−0.403662
$310$	−1.38215	−	4.25381i	−0.0785006	−	0.241600i
$311$	−3.99196	−	2.90033i	−0.226363	−	0.164463i	0.468823	−	0.883292i	$-0.344678\pi$
$311$	−3.99196	−	2.90033i	−0.226363	−	0.164463i	−0.695186	+	0.718830i	$0.744678\pi$
$312$	−0.940958	+	0.683646i	−0.0532712	+	0.0387038i
$313$	−7.07497	+	21.7745i	−0.399901	+	1.23077i	0.525177	+	0.850993i	$0.323999\pi$
$313$	−7.07497	+	21.7745i	−0.399901	+	1.23077i	−0.925078	+	0.379776i	$0.876001\pi$
$314$	6.02759	−	18.5510i	0.340157	−	1.04690i
$315$	1.04333	−	0.758024i	0.0587850	−	0.0427098i
$316$	2.62776	+	1.90918i	0.147823	+	0.107400i
$317$	−4.20091	−	12.9291i	−0.235947	−	0.726170i	−0.996994	−	0.0774736i	$-0.975315\pi$
$317$	−4.20091	−	12.9291i	−0.235947	−	0.726170i	0.761048	−	0.648696i	$-0.224685\pi$
$318$	−0.914072			−0.0512586
$319$	1.57087	−	28.1999i	0.0879517	−	1.57889i
$320$	3.67636			0.205515
$321$	5.15065	+	15.8521i	0.287481	+	0.884776i
$322$	2.17475	+	1.58005i	0.121194	+	0.0880526i
$323$	−4.80130	+	3.48835i	−0.267152	+	0.194097i
$324$	0.422134	−	1.29919i	0.0234519	−	0.0721775i
$325$	−0.807402	+	2.48493i	−0.0447866	+	0.137839i
$326$	−3.68929	+	2.68043i	−0.204331	+	0.148455i
$327$	15.7091	+	11.4133i	0.868713	+	0.631157i
$328$	3.18944	+	9.81609i	0.176107	+	0.542003i
$329$	1.85975			0.102531
$330$	9.08917	−	2.40344i	0.500342	−	0.132305i
$331$	−9.57063			−0.526049			−0.263025	−	0.964789i	$-0.584720\pi$
$331$	−9.57063			−0.526049			−0.263025	+	0.964789i	$0.584720\pi$
$332$	−4.76897	−	14.6774i	−0.261731	−	0.805525i
$333$	4.46927	+	3.24711i	0.244914	+	0.177941i
$334$	−26.2666	+	19.0838i	−1.43725	+	1.04422i
$335$	4.02627	−	12.3916i	0.219979	−	0.677024i
$336$	−1.25509	+	3.86277i	−0.0684709	+	0.210732i
$337$	−16.0925	+	11.6919i	−0.876617	+	0.636899i	−0.932354	−	0.361546i	$-0.882249\pi$
$337$	−16.0925	+	11.6919i	−0.876617	+	0.636899i	0.0557373	+	0.998445i	$0.482249\pi$
$338$	1.48429	+	1.07840i	0.0807346	+	0.0586571i
$339$	−3.97786	−	12.2426i	−0.216048	−	0.664926i
$340$	8.36284			0.453539
$341$	4.87938	+	1.89145i	0.264233	+	0.102428i
$342$	2.74802			0.148596
$343$	−3.43133	−	10.5605i	−0.185274	−	0.570216i
$344$	−2.91511	−	2.11795i	−0.157172	−	0.114192i
$345$	2.19418	−	1.59416i	0.118130	−	0.0858268i
$346$	7.29052	−	22.4379i	0.391941	−	1.20627i
$347$	1.20933	−	3.72192i	0.0649200	−	0.199803i	−0.913335	−	0.407209i	$-0.866502\pi$
$347$	1.20933	−	3.72192i	0.0649200	−	0.199803i	0.978255	+	0.207406i	$0.0665020\pi$
$348$	−9.41129	+	6.83770i	−0.504498	+	0.366539i
$349$	13.0260	+	9.46395i	0.697266	+	0.506594i	0.879041	−	0.476747i	$-0.158184\pi$
$349$	13.0260	+	9.46395i	0.697266	+	0.506594i	−0.181774	+	0.983340i	$0.558184\pi$
$350$	1.23643	+	3.80535i	0.0660902	+	0.203405i
$351$	1.00000			0.0533761
$352$	−13.8344	+	16.9697i	−0.737377	+	0.904488i
$353$	−21.8675			−1.16389			−0.581944	−	0.813229i	$-0.697708\pi$
$353$	−21.8675			−1.16389			−0.581944	+	0.813229i	$0.697708\pi$
$354$	3.31256	+	10.1950i	0.176060	+	0.541858i
$355$	−5.90979	−	4.29372i	−0.313659	−	0.227887i
$356$	6.81799	−	4.95356i	0.361353	−	0.262538i
$357$	−1.02199	+	3.14535i	−0.0540892	+	0.166470i
$358$	6.30058	−	19.3912i	0.332996	−	1.02486i
$359$	15.3996	−	11.1885i	0.812760	−	0.590505i	−0.101869	−	0.994798i	$-0.532482\pi$
$359$	15.3996	−	11.1885i	0.812760	−	0.590505i	0.914630	+	0.404293i	$0.132482\pi$
$360$	1.45383	+	1.05627i	0.0766236	+	0.0556703i
$361$	−5.17805	−	15.9364i	−0.272529	−	0.838759i
$362$	−3.22193			−0.169341
$363$	−4.54008	+	10.0194i	−0.238292	+	0.525880i
$364$	1.14022			0.0597638
$365$	−0.785940	−	2.41888i	−0.0411380	−	0.126610i
$366$	−16.3108	−	11.8505i	−0.852577	−	0.619433i
$367$	−0.465136	+	0.337941i	−0.0242799	+	0.0176404i	−0.599859	−	0.800106i	$-0.704777\pi$
$367$	−0.465136	+	0.337941i	−0.0242799	+	0.0176404i	0.575579	+	0.817746i	$0.304777\pi$
$368$	−2.63952	+	8.12361i	−0.137595	+	0.423472i
$369$	2.74222	−	8.43968i	0.142754	−	0.439352i
$370$	12.6689	−	9.20453i	0.658627	−	0.478521i
$371$	−0.336433	−	0.244433i	−0.0174667	−	0.0126903i
$372$	−0.666067	−	2.04994i	−0.0345340	−	0.106285i
$373$	4.60635			0.238508			0.119254	−	0.992864i	$-0.461950\pi$
$373$	4.60635			0.238508			0.119254	+	0.992864i	$0.461950\pi$
$374$	−15.2345	+	18.6871i	−0.787757	+	0.966286i
$375$	11.7622			0.607397
$376$	0.800809	+	2.46464i	0.0412986	+	0.127104i
$377$	−6.88940	−	5.00544i	−0.354822	−	0.257793i
$378$	1.23891	−	0.900119i	0.0637225	−	0.0462971i
$379$	−11.2329	+	34.5714i	−0.576997	+	1.77581i	0.0522807	+	0.998632i	$0.483351\pi$
$379$	−11.2329	+	34.5714i	−0.576997	+	1.77581i	−0.629277	+	0.777181i	$0.716649\pi$
$380$	0.976907	−	3.00661i	0.0501143	−	0.154236i
$381$	−10.5538	+	7.66777i	−0.540686	+	0.392832i
$382$	−8.00029	−	5.81255i	−0.409331	−	0.297396i
$383$	−6.06664	−	18.6712i	−0.309991	−	0.954054i	−0.977768	−	0.209692i	$-0.932754\pi$
$383$	−6.06664	−	18.6712i	−0.309991	−	0.954054i	0.667777	−	0.744362i	$-0.267246\pi$
$384$	−8.83727			−0.450975
$385$	3.98806	+	1.54593i	0.203250	+	0.0787881i
$386$	−17.5860			−0.895102
$387$	0.957343	+	2.94640i	0.0486645	+	0.149774i
$388$	−11.8651	−	8.62052i	−0.602361	−	0.437641i
$389$	−14.9467	+	10.8594i	−0.757829	+	0.550595i	−0.898244	−	0.439498i	$-0.855156\pi$
$389$	−14.9467	+	10.8594i	−0.757829	+	0.550595i	0.140415	+	0.990093i	$0.455156\pi$
$390$	0.875965	−	2.69594i	0.0443562	−	0.136514i
$391$	−2.14929	+	6.61483i	−0.108694	+	0.334526i
$392$	5.93115	−	4.30923i	0.299568	−	0.217649i
$393$	−14.6215	−	10.6231i	−0.737558	−	0.535867i
$394$	−7.21858	−	22.2165i	−0.363667	−	1.11925i
$395$	3.67370			0.184844
$396$	4.38014	−	1.15824i	0.220110	−	0.0582035i
$397$	22.7651			1.14255			0.571273	−	0.820760i	$-0.306450\pi$
$397$	22.7651			1.14255			0.571273	+	0.820760i	$0.306450\pi$
$398$	−1.21855	−	3.75032i	−0.0610805	−	0.187986i
$399$	1.01143	+	0.734850i	0.0506350	+	0.0367885i
$400$	−10.2858	+	7.47306i	−0.514290	+	0.373653i
$401$	9.43111	−	29.0260i	0.470967	−	1.44949i	−0.380353	−	0.924842i	$-0.624197\pi$
$401$	9.43111	−	29.0260i	0.470967	−	1.44949i	0.851320	−	0.524647i	$-0.175803\pi$
$402$	4.78101	−	14.7144i	0.238455	−	0.733889i
$403$	1.27651	−	0.927441i	0.0635876	−	0.0461991i
$404$	−8.46381	−	6.14932i	−0.421090	−	0.305940i
$405$	−0.477448	−	1.46943i	−0.0237246	−	0.0730167i
$406$	−13.0408			−0.647205
$407$	−1.01905	+	18.2937i	−0.0505123	+	0.906786i
$408$	−4.60845			−0.228152
$409$	−5.16397	−	15.8931i	−0.255342	−	0.785861i	−0.993762	−	0.111520i	$-0.964428\pi$
$409$	−5.16397	−	15.8931i	−0.255342	−	0.785861i	0.738420	−	0.674341i	$-0.235572\pi$
$410$	−20.3508	−	14.7857i	−1.00505	−	0.730215i
$411$	−10.5319	+	7.65187i	−0.519500	+	0.377439i
$412$	−2.99535	+	9.21875i	−0.147570	+	0.454175i
$413$	−1.50703	+	4.63817i	−0.0741563	+	0.228230i
$414$	2.60548	−	1.89300i	0.128053	−	0.0930356i
$415$	−14.1213	−	10.2597i	−0.693188	−	0.503631i
$416$	2.03994	+	6.27829i	0.100016	+	0.307819i
$417$	13.3628			0.654380
$418$	4.93877	+	7.66005i	0.241563	+	0.374665i
$419$	33.3642			1.62995			0.814974	−	0.579498i	$-0.196751\pi$
$419$	33.3642			1.62995			0.814974	+	0.579498i	$0.196751\pi$
$420$	−0.544396	−	1.67548i	−0.0265638	−	0.0817549i
$421$	15.4063	+	11.1933i	0.750855	+	0.545528i	0.896092	−	0.443869i	$-0.146394\pi$
$421$	15.4063	+	11.1933i	0.750855	+	0.545528i	−0.145237	+	0.989397i	$0.546394\pi$
$422$	−30.1774	+	21.9252i	−1.46901	+	1.06730i
$423$	0.688520	−	2.11905i	0.0334770	−	0.103032i
$424$	0.179067	−	0.551111i	0.00869625	−	0.0267643i
$425$	−8.37543	+	6.08511i	−0.406268	+	0.295171i
$426$	−7.01761	−	5.09859i	−0.340004	−	0.247028i
$427$	−2.83438	−	8.72334i	−0.137165	−	0.422152i
$428$	22.7692			1.10059
$429$	1.79721	+	2.78748i	0.0867701	+	0.134581i
$430$	8.78192			0.423502
$431$	1.95061	+	6.00335i	0.0939575	+	0.289171i	0.986981	−	0.160839i	$-0.0514201\pi$
$431$	1.95061	+	6.00335i	0.0939575	+	0.289171i	−0.893023	+	0.450011i	$0.851420\pi$
$432$	3.93668	+	2.86017i	0.189404	+	0.137610i
$433$	8.82377	−	6.41085i	0.424043	−	0.308086i	−0.355219	−	0.934783i	$-0.615594\pi$
$433$	8.82377	−	6.41085i	0.424043	−	0.308086i	0.779263	+	0.626697i	$0.215594\pi$
$434$	0.746674	−	2.29803i	0.0358415	−	0.110309i
$435$	−4.06583	+	12.5133i	−0.194942	+	0.599969i
$436$	21.4594	−	15.5912i	1.02772	−	0.746682i
$437$	2.12710	+	1.54543i	0.101753	+	0.0739278i
$438$	−0.933268	−	2.87230i	−0.0445933	−	0.137244i
$439$	−11.6936			−0.558104			−0.279052	−	0.960276i	$-0.590020\pi$
$439$	−11.6936			−0.558104			−0.279052	+	0.960276i	$0.590020\pi$
$440$	−0.331491	+	5.95086i	−0.0158032	+	0.283696i
$441$	−6.30331			−0.300158
$442$	2.24639	+	6.91368i	0.106850	+	0.328850i
$443$	27.5167	+	19.9921i	1.30736	+	0.949852i	0.999998	−	0.00174158i	$-0.000554362\pi$
$443$	27.5167	+	19.9921i	1.30736	+	0.949852i	0.307360	+	0.951593i	$0.400554\pi$
$444$	6.10526	−	4.43573i	0.289743	−	0.210510i
$445$	2.94548	−	9.06527i	0.139629	−	0.429735i
$446$	12.3237	−	37.9284i	0.583543	−	1.79596i
$447$	3.59896	−	2.61480i	0.170225	−	0.123676i
$448$	1.60676	+	1.16738i	0.0759125	+	0.0551537i
$449$	5.59627	+	17.2236i	0.264104	+	0.812830i	0.991898	+	0.127034i	$0.0405458\pi$
$449$	5.59627	+	17.2236i	0.264104	+	0.812830i	−0.727794	+	0.685796i	$0.759454\pi$
$450$	4.79367			0.225976
$451$	28.4538	−	7.52400i	1.33984	−	0.354291i
$452$	−17.5847			−0.827115
$453$	4.30213	+	13.2406i	0.202132	+	0.622098i
$454$	−29.1308	−	21.1648i	−1.36718	−	0.993313i
$455$	1.04333	−	0.758024i	0.0489121	−	0.0355367i
$456$	−0.538337	+	1.65683i	−0.0252099	+	0.0775882i
$457$	−6.09735	+	18.7657i	−0.285222	+	0.877823i	0.701110	+	0.713053i	$0.252688\pi$
$457$	−6.09735	+	18.7657i	−0.285222	+	0.877823i	−0.986332	+	0.164770i	$0.947312\pi$
$458$	0.769376	−	0.558984i	0.0359506	−	0.0261196i
$459$	3.20553	+	2.32895i	0.149621	+	0.108706i
$460$	−1.14489	−	3.52361i	−0.0533808	−	0.164289i
$461$	−23.9263			−1.11436			−0.557180	−	0.830392i	$-0.688117\pi$
$461$	−23.9263			−1.11436			−0.557180	+	0.830392i	$0.688117\pi$
$462$	4.73564	+	1.83573i	0.220322	+	0.0854057i
$463$	3.65825			0.170013			0.0850067	−	0.996380i	$-0.472909\pi$
$463$	3.65825			0.170013			0.0850067	+	0.996380i	$0.472909\pi$
$464$	−12.8050	−	39.4096i	−0.594455	−	1.82955i
$465$	−1.97228	−	1.43295i	−0.0914623	−	0.0664513i
$466$	−16.9336	+	12.3030i	−0.784435	+	0.569926i
$467$	3.38297	−	10.4117i	0.156545	−	0.481797i	−0.841769	−	0.539838i	$-0.818485\pi$
$467$	3.38297	−	10.4117i	0.156545	−	0.481797i	0.998314	+	0.0580412i	$0.0184855\pi$
$468$	0.422134	−	1.29919i	0.0195132	−	0.0600553i
$469$	5.69449	−	4.13729i	0.262947	−	0.191042i
$470$	−5.10970	−	3.71242i	−0.235693	−	0.171241i
$471$	−3.28536	−	10.1113i	−0.151382	−	0.465905i
$472$	−6.79568			−0.312796
$473$	−6.49248	+	7.96387i	−0.298524	+	0.366179i
$474$	4.36236			0.200370
$475$	1.20934	+	3.72197i	0.0554884	+	0.170776i
$476$	3.65501	+	2.65552i	0.167527	+	0.121715i
$477$	−0.403067	+	0.292846i	−0.0184552	+	0.0134085i
$478$	15.1438	−	46.6077i	0.692660	−	2.13179i
$479$	5.63826	−	17.3528i	0.257619	−	0.792868i	−0.735684	−	0.677325i	$-0.763139\pi$
$479$	5.63826	−	17.3528i	0.257619	−	0.792868i	0.993302	−	0.115543i	$-0.0368609\pi$
$480$	8.25157	−	5.99512i	0.376631	−	0.273638i
$481$	4.46927	+	3.24711i	0.203781	+	0.148056i
$482$	−1.45229	−	4.46970i	−0.0661502	−	0.203589i
$483$	1.46518			0.0666680
$484$	11.1006	+	10.1280i	0.504572	+	0.460362i
$485$	−16.5879			−0.753216
$486$	−0.566948	−	1.74489i	−0.0257173	−	0.0791496i
$487$	7.13632	+	5.18484i	0.323378	+	0.234948i	0.737615	−	0.675221i	$-0.235952\pi$
$487$	7.13632	+	5.18484i	0.323378	+	0.234948i	−0.414238	+	0.910169i	$0.635952\pi$
$488$	10.3401	−	7.51255i	0.468076	−	0.340077i
$489$	−0.768082	+	2.36391i	−0.0347339	+	0.106900i
$490$	−5.52147	+	16.9934i	−0.249435	+	0.767681i
$491$	−16.2029	+	11.7721i	−0.731227	+	0.531268i	−0.889951	−	0.456055i	$-0.849262\pi$
$491$	−16.2029	+	11.7721i	−0.731227	+	0.531268i	0.158724	+	0.987323i	$0.449262\pi$
$492$	−9.80721	−	7.12535i	−0.442143	−	0.321236i
$493$	−10.4267	−	32.0902i	−0.469596	−	1.44527i
$494$	2.74802			0.123639
$495$	3.23794	−	3.97176i	0.145535	−	0.178517i
$496$	7.67786			0.344746
$497$	−1.21948	−	3.75317i	−0.0547010	−	0.168353i
$498$	−16.7684	−	12.1830i	−0.751411	−	0.545932i
$499$	−21.8250	+	15.8568i	−0.977021	+	0.709847i	−0.957041	−	0.289953i	$-0.906360\pi$
$499$	−21.8250	+	15.8568i	−0.977021	+	0.709847i	−0.0199803	+	0.999800i	$0.506360\pi$
$500$	4.96522	−	15.2814i	0.222052	−	0.683405i
$501$	−5.46850	+	16.8303i	−0.244315	+	0.751923i
$502$	32.3221	−	23.4834i	1.44261	−	1.04812i
$503$	32.7835	+	23.8186i	1.46174	+	1.06202i	0.982905	+	0.184115i	$0.0589419\pi$
$503$	32.7835	+	23.8186i	1.46174	+	1.06202i	0.478838	+	0.877903i	$0.341058\pi$
$504$	0.299996	+	0.923293i	0.0133629	+	0.0411267i
$505$	−11.8327			−0.526548
$506$	9.95929	+	3.86062i	0.442744	+	0.171626i
$507$	1.00000			0.0444116
$508$	5.50682	+	16.9482i	0.244325	+	0.751956i
$509$	25.5683	+	18.5764i	1.13329	+	0.823386i	0.986171	−	0.165732i	$-0.0529988\pi$
$509$	25.5683	+	18.5764i	1.13329	+	0.823386i	0.147123	+	0.989118i	$0.452999\pi$
$510$	9.08665	−	6.60184i	0.402364	−	0.292334i
$511$	0.424587	−	1.30674i	0.0187826	−	0.0578069i
$512$	−6.42855	+	19.7850i	−0.284104	+	0.874383i
$513$	1.21176	−	0.880396i	0.0535006	−	0.0388704i
$514$	13.1264	+	9.53691i	0.578982	+	0.420655i
$515$	3.38784	+	10.4267i	0.149286	+	0.459456i
$516$	4.23207			0.186307
$517$	7.14421	−	1.88913i	0.314202	−	0.0830841i
$518$	8.45979			0.371702
$519$	−3.97372	−	12.2299i	−0.174427	−	0.536831i
$520$	1.45383	+	1.05627i	0.0637547	+	0.0463205i
$521$	28.1358	−	20.4418i	1.23265	−	0.895573i	0.235565	−	0.971859i	$-0.424306\pi$
$521$	28.1358	−	20.4418i	1.23265	−	0.895573i	0.997086	+	0.0762855i	$0.0243060\pi$
$522$	−4.82799	+	14.8590i	−0.211315	+	0.650362i
$523$	−3.65723	+	11.2558i	−0.159919	+	0.492181i	−0.998626	−	0.0524022i	$-0.983312\pi$
$523$	−3.65723	+	11.2558i	−0.159919	+	0.492181i	0.838707	+	0.544583i	$0.183312\pi$
$524$	−19.9738	+	14.5118i	−0.872559	+	0.633951i
$525$	1.76435	+	1.28188i	0.0770027	+	0.0559458i
$526$	−3.09084	−	9.51262i	−0.134767	−	0.414770i
$527$	6.25186			0.272336
$528$	−0.897612	+	16.1137i	−0.0390635	+	0.701260i
$529$	−19.9187			−0.866028
$530$	0.436422	+	1.34317i	0.0189570	+	0.0583435i
$531$	4.72692	+	3.43430i	0.205131	+	0.149036i
$532$	1.38167	−	1.00384i	0.0599032	−	0.0435222i
$533$	2.74222	−	8.43968i	0.118779	−	0.365563i
$534$	3.49763	−	10.7646i	0.151357	−	0.465830i
$535$	20.8344	−	15.1371i	0.900749	−	0.654432i
$536$	7.93500	+	5.76511i	0.342740	+	0.249015i
$537$	−3.43415	−	10.5692i	−0.148195	−	0.456096i
$538$	−22.2642			−0.959879
$539$	−11.3284	−	17.5703i	−0.487947	−	0.756808i
$540$	−2.11063			−0.0908270
$541$	5.24782	+	16.1511i	0.225621	+	0.694391i	0.998228	+	0.0595062i	$0.0189526\pi$
$541$	5.24782	+	16.1511i	0.225621	+	0.694391i	−0.772607	+	0.634885i	$0.781047\pi$
$542$	−34.5963	−	25.1357i	−1.48604	−	1.07967i
$543$	−1.42074	+	1.03223i	−0.0609697	+	0.0442971i
$544$	−8.08276	+	24.8762i	−0.346546	+	1.06656i
$545$	9.27083	−	28.5327i	0.397119	−	1.22221i
$546$	1.23891	−	0.900119i	0.0530203	−	0.0385215i
$547$	−25.1290	−	18.2573i	−1.07444	−	0.780626i	−0.0977350	−	0.995212i	$-0.531160\pi$
$547$	−25.1290	−	18.2573i	−1.07444	−	0.780626i	−0.976705	+	0.214586i	$0.931160\pi$
$548$	5.49540	+	16.9131i	0.234752	+	0.722492i
$549$	−10.9889			−0.468997
$550$	8.61523	+	13.3623i	0.367355	+	0.569768i
$551$	−12.7551			−0.543384
$552$	0.630907	+	1.94173i	0.0268532	+	0.0826456i
$553$	1.60560	+	1.16654i	0.0682773	+	0.0496063i
$554$	−9.52505	+	6.92035i	−0.404681	+	0.294018i
$555$	2.63757	−	8.11762i	0.111959	−	0.344574i
$556$	5.64090	−	17.3609i	0.239228	−	0.736267i
$557$	15.6295	−	11.3555i	0.662242	−	0.481147i	−0.205177	−	0.978725i	$-0.565777\pi$
$557$	15.6295	−	11.3555i	0.662242	−	0.481147i	0.867419	+	0.497578i	$0.165777\pi$
$558$	−2.34199	−	1.70156i	−0.0991445	−	0.0720327i
$559$	0.957343	+	2.94640i	0.0404913	+	0.124619i
$560$	6.27533			0.265181
$561$	−0.730900	+	13.1210i	−0.0308586	+	0.553967i
$562$	51.2878			2.16345
$563$	11.1542	+	34.3291i	0.470094	+	1.44680i	0.852462	+	0.522790i	$0.175109\pi$
$563$	11.1542	+	34.3291i	0.470094	+	1.44680i	−0.382368	+	0.924010i	$0.624891\pi$
$564$	−2.46241	−	1.78904i	−0.103686	−	0.0753323i
$565$	−16.0904	+	11.6904i	−0.676930	+	0.491819i
$566$	6.76628	−	20.8245i	0.284408	−	0.875317i
$567$	0.257931	−	0.793829i	0.0108321	−	0.0333377i
$568$	4.44878	−	3.23223i	0.186667	−	0.135621i
$569$	27.3632	+	19.8805i	1.14712	+	0.833434i	0.988096	−	0.153840i	$-0.0491641\pi$
$569$	27.3632	+	19.8805i	1.14712	+	0.833434i	0.159028	+	0.987274i	$0.449164\pi$
$570$	−1.31204	−	4.03803i	−0.0549552	−	0.169135i
$571$	−32.5069			−1.36037			−0.680185	−	0.733041i	$-0.738100\pi$
$571$	−32.5069			−1.36037			−0.680185	+	0.733041i	$0.738100\pi$
$572$	4.38014	−	1.15824i	0.183143	−	0.0484283i
$573$	−5.38999			−0.225170
$574$	−4.19936	−	12.9243i	−0.175278	−	0.539450i
$575$	3.71053	+	2.69585i	0.154740	+	0.112425i
$576$	1.92500	−	1.39860i	0.0802085	−	0.0582749i
$577$	1.53716	−	4.73090i	0.0639929	−	0.196950i	−0.913948	−	0.405831i	$-0.866982\pi$
$577$	1.53716	−	4.73090i	0.0639929	−	0.196950i	0.977941	+	0.208881i	$0.0669822\pi$
$578$	0.737350	−	2.26933i	0.0306697	−	0.0943917i
$579$	−7.75467	+	5.63410i	−0.322273	+	0.234145i
$580$	14.5409	+	10.5646i	0.603780	+	0.438672i
$581$	−2.91391	−	8.96811i	−0.120890	−	0.372060i
$582$	−19.6973			−0.816481
$583$	−1.54070	−	0.597237i	−0.0638092	−	0.0247350i
$584$	1.91459			0.0792263
$585$	−0.477448	−	1.46943i	−0.0197400	−	0.0607536i
$586$	10.7424	+	7.80482i	0.443765	+	0.322414i
$587$	−13.6095	+	9.88786i	−0.561723	+	0.408116i	−0.832089	−	0.554642i	$-0.812855\pi$
$587$	−13.6095	+	9.88786i	−0.561723	+	0.408116i	0.270366	+	0.962758i	$0.412855\pi$
$588$	−2.66084	+	8.18923i	−0.109731	+	0.337718i
$589$	0.730313	−	2.24767i	0.0300920	−	0.0926138i
$590$	13.3993	−	9.73516i	0.551640	−	0.400790i
$591$	−10.3007	−	7.48390i	−0.423714	−	0.307846i
$592$	8.30679	+	25.5657i	0.341407	+	1.05074i
$593$	2.27552			0.0934445			0.0467222	−	0.998908i	$-0.485122\pi$
$593$	2.27552			0.0934445			0.0467222	+	0.998908i	$0.485122\pi$
$594$	3.84491	−	4.71628i	0.157758	−	0.193511i
$595$	5.10983			0.209483
$596$	−1.87789	−	5.77955i	−0.0769213	−	0.236739i
$597$	−1.73884	−	1.26334i	−0.0711659	−	0.0517050i
$598$	2.60548	−	1.89300i	0.106546	−	0.0774103i
$599$	6.79506	−	20.9130i	0.277638	−	0.854483i	−0.710871	−	0.703323i	$-0.751699\pi$
$599$	6.79506	−	20.9130i	0.277638	−	0.854483i	0.988509	−	0.151161i	$-0.0483011\pi$
$600$	−0.939080	+	2.89019i	−0.0383378	+	0.117992i
$601$	−23.2877	+	16.9195i	−0.949925	+	0.690161i	−0.950789	−	0.309839i	$-0.899725\pi$
$601$	−23.2877	+	16.9195i	−0.949925	+	0.690161i	0.000864048		1.00000i	$0.499725\pi$
$602$	3.83817	+	2.78859i	0.156432	+	0.113654i
$603$	−2.60591	−	8.02016i	−0.106121	−	0.326606i
$604$	19.0182			0.773840
$605$	16.8904	+	1.88761i	0.686694	+	0.0767424i
$606$	−14.0508			−0.570774
$607$	8.93501	+	27.4991i	0.362661	+	1.11616i	0.951433	+	0.307856i	$0.0996116\pi$
$607$	8.93501	+	27.4991i	0.362661	+	1.11616i	−0.588772	+	0.808299i	$0.700388\pi$
$608$	7.99931	+	5.81184i	0.324415	+	0.235701i
$609$	−5.75045	+	4.17794i	−0.233020	+	0.169299i
$610$	−9.62592	+	29.6255i	−0.389742	+	1.19950i
$611$	0.688520	−	2.11905i	0.0278545	−	0.0857274i
$612$	4.37893	−	3.18148i	0.177008	−	0.128604i
$613$	25.8923	+	18.8119i	1.04578	+	0.759805i	0.971406	−	0.237426i	$-0.0763036\pi$
$613$	25.8923	+	18.8119i	1.04578	+	0.759805i	0.0743755	+	0.997230i	$0.476304\pi$
$614$	8.03529	+	24.7301i	0.324278	+	0.998024i
$615$	−13.7108			−0.552874
$616$	−2.03450	+	2.49558i	−0.0819725	+	0.100550i
$617$	−20.8138			−0.837932			−0.418966	−	0.908002i	$-0.637607\pi$
$617$	−20.8138			−0.837932			−0.418966	+	0.908002i	$0.637607\pi$
$618$	4.02291	+	12.3812i	0.161825	+	0.498047i
$619$	18.3855	+	13.3579i	0.738976	+	0.536898i	0.892390	−	0.451264i	$-0.149027\pi$
$619$	18.3855	+	13.3579i	0.738976	+	0.536898i	−0.153414	+	0.988162i	$0.549027\pi$
$620$	−2.69424	+	1.95748i	−0.108203	+	0.0786144i
$621$	0.542441	−	1.66946i	0.0217674	−	0.0669932i
$622$	−2.79751	+	8.60985i	−0.112170	+	0.345223i
$623$	4.16590	−	3.02670i	0.166903	−	0.121262i
$624$	3.93668	+	2.86017i	0.157593	+	0.114498i
$625$	−1.57883	−	4.85913i	−0.0631530	−	0.194365i
$626$	42.0052			1.67887
$627$	4.63187	+	1.79550i	0.184979	+	0.0717055i
$628$	−14.5234			−0.579548
$629$	6.76399	+	20.8174i	0.269698	+	0.830045i
$630$	−1.91418	−	1.39073i	−0.0762627	−	0.0554081i
$631$	0.516644	−	0.375364i	0.0205673	−	0.0149430i	−0.577454	−	0.816423i	$-0.695954\pi$
$631$	0.516644	−	0.375364i	0.0205673	−	0.0149430i	0.598021	+	0.801480i	$0.295954\pi$
$632$	−0.854585	+	2.63014i	−0.0339936	+	0.104621i
$633$	−6.28270	+	19.3362i	−0.249715	+	0.768543i
$634$	−20.1781	+	14.6602i	−0.801374	+	0.582232i
$635$	16.3062	+	11.8471i	0.647090	+	0.470138i
$636$	0.210315	+	0.647283i	0.00833953	+	0.0256664i
$637$	−6.30331			−0.249746
$638$	−50.0961	+	13.2469i	−1.98332	+	0.524448i
$639$	−4.72793			−0.187034
$640$	4.21934	+	12.9858i	0.166784	+	0.513308i
$641$	5.65575	+	4.10914i	0.223389	+	0.162301i	0.693851	−	0.720119i	$-0.255913\pi$
$641$	5.65575	+	4.10914i	0.223389	+	0.162301i	−0.470462	+	0.882420i	$0.655913\pi$
$642$	24.7399	−	17.9746i	0.976405	−	0.709400i
$643$	−14.4992	+	44.6241i	−0.571794	+	1.75980i	0.0750503	+	0.997180i	$0.476088\pi$
$643$	−14.4992	+	44.6241i	−0.571794	+	1.75980i	−0.646845	+	0.762622i	$0.723912\pi$
$644$	0.618502	−	1.90355i	0.0243724	−	0.0750105i
$645$	3.87245	−	2.81350i	0.152478	−	0.110782i
$646$	8.80886	+	6.40001i	0.346580	+	0.251805i
$647$	−14.3973	−	44.3103i	−0.566016	−	1.74202i	−0.664914	−	0.746920i	$-0.731532\pi$
$647$	−14.3973	−	44.3103i	−0.566016	−	1.74202i	0.0988980	−	0.995098i	$-0.468468\pi$
$648$	1.16309			0.0456904
$649$	−1.07780	+	19.3483i	−0.0423072	+	0.759489i
$650$	4.79367			0.188023
$651$	−0.406978	−	1.25255i	−0.0159507	−	0.0490912i
$652$	2.74695	+	1.99578i	0.107579	+	0.0781606i
$653$	0.286183	−	0.207924i	0.0111992	−	0.00813671i	−0.582172	−	0.813066i	$-0.697797\pi$
$653$	0.286183	−	0.207924i	0.0111992	−	0.00813671i	0.593371	+	0.804929i	$0.297797\pi$
$654$	11.0087	−	33.8812i	0.430474	−	1.32486i
$655$	−8.62900	+	26.5573i	−0.337163	+	1.03768i
$656$	34.9341	−	25.3811i	1.36395	−	0.990966i
$657$	−1.33175	−	0.967570i	−0.0519563	−	0.0377485i
$658$	−1.05438	−	3.24505i	−0.0411040	−	0.126505i
$659$	−16.4906			−0.642383			−0.321191	−	0.947014i	$-0.604083\pi$
$659$	−16.4906			−0.642383			−0.321191	+	0.947014i	$0.604083\pi$
$660$	−3.79324	−	5.88333i	−0.147652	−	0.229008i
$661$	19.9245			0.774972			0.387486	−	0.921876i	$-0.373344\pi$
$661$	19.9245			0.774972			0.387486	+	0.921876i	$0.373344\pi$
$662$	5.42605	+	16.6997i	0.210889	+	0.649051i
$663$	3.20553	+	2.32895i	0.124492	+	0.0904490i
$664$	10.6303	−	7.72334i	0.412534	−	0.299724i
$665$	0.596906	−	1.83709i	0.0231470	−	0.0712392i
$666$	3.13200	−	9.63930i	0.121362	−	0.373515i
$667$	−12.0935	+	8.78643i	−0.468261	+	0.340212i
$668$	19.5574	+	14.2093i	0.756700	+	0.549774i
$669$	−6.71707	−	20.6730i	−0.259697	−	0.799265i
$670$	−23.9046			−0.923514
$671$	−19.7494	−	30.6314i	−0.762418	−	1.18251i
$672$	5.51005			0.212555
$673$	3.67564	+	11.3125i	0.141686	+	0.436064i	0.996570	−	0.0827551i	$-0.0263719\pi$
$673$	3.67564	+	11.3125i	0.141686	+	0.436064i	−0.854884	+	0.518819i	$0.826372\pi$
$674$	29.5247	+	21.4509i	1.13725	+	0.826260i
$675$	2.11381	−	1.53577i	0.0813605	−	0.0591118i
$676$	0.422134	−	1.29919i	0.0162359	−	0.0499690i
$677$	−8.24716	+	25.3821i	−0.316964	+	0.975515i	0.657974	+	0.753040i	$0.271414\pi$
$677$	−8.24716	+	25.3821i	−0.316964	+	0.975515i	−0.974938	+	0.222475i	$0.928586\pi$
$678$	−19.1067	+	13.8818i	−0.733787	+	0.533128i
$679$	−7.24979	−	5.26728i	−0.278221	−	0.202140i
$680$	2.20029	+	6.77181i	0.0843774	+	0.259687i
$681$	−19.6261			−0.752075
$682$	0.534004	−	9.58631i	0.0204481	−	0.367079i
$683$	−16.2014			−0.619928			−0.309964	−	0.950748i	$-0.600317\pi$
$683$	−16.2014			−0.619928			−0.309964	+	0.950748i	$0.600317\pi$
$684$	−0.632280	−	1.94596i	−0.0241758	−	0.0744056i
$685$	16.2723	+	11.8226i	0.621734	+	0.451716i
$686$	−16.4816	+	11.9746i	−0.629269	+	0.457191i
$687$	0.160178	−	0.492977i	0.00611117	−	0.0188083i
$688$	−4.65843	+	14.3372i	−0.177601	+	0.546600i
$689$	−0.403067	+	0.292846i	−0.0153556	+	0.0111565i
$690$	−4.02561	−	2.92478i	−0.153252	−	0.111344i
$691$	−7.71714	−	23.7509i	−0.293574	−	0.903528i	−0.983697	−	0.179835i	$-0.942443\pi$
$691$	−7.71714	−	23.7509i	−0.293574	−	0.903528i	0.690123	−	0.723692i	$-0.257557\pi$
$692$	−17.5664			−0.667775
$693$	2.67634	−	0.707701i	0.101666	−	0.0268833i
$694$	−7.17995			−0.272547
$695$	−6.38005	−	19.6358i	−0.242009	−	0.744828i
$696$	−8.01297	−	5.82176i	−0.303731	−	0.220673i
$697$	28.4459	−	20.6671i	1.07746	−	0.782824i
$698$	9.12844	−	28.0945i	0.345517	−	1.06339i
$699$	−3.52545	+	10.8502i	−0.133345	+	0.410393i
$700$	2.41020	−	1.75112i	0.0910971	−	0.0661859i
$701$	10.9205	+	7.93419i	0.412461	+	0.299670i	0.774597	−	0.632455i	$-0.217953\pi$
$701$	10.9205	+	7.93419i	0.412461	+	0.299670i	−0.362137	+	0.932125i	$0.617953\pi$
$702$	−0.566948	−	1.74489i	−0.0213981	−	0.0658565i
$703$	8.27443			0.312076
$704$	7.35820	+	2.85234i	0.277322	+	0.107501i
$705$	−3.44253			−0.129653
$706$	12.3977	+	38.1562i	0.466594	+	1.43603i
$707$	−5.17152	−	3.75733i	−0.194495	−	0.141309i
$708$	6.45722	−	4.69145i	0.242677	−	0.176315i
$709$	5.15071	−	15.8523i	0.193439	−	0.595344i	−0.806552	−	0.591163i	$-0.798669\pi$
$709$	5.15071	−	15.8523i	0.193439	−	0.595344i	0.999991	−	0.00418136i	$-0.00133097\pi$
$710$	−4.14150	+	12.7462i	−0.155428	+	0.478357i
$711$	1.92361	−	1.39759i	0.0721412	−	0.0524136i
$712$	5.80498	+	4.21757i	0.217551	+	0.158060i
$713$	−0.855894	−	2.63417i	−0.0320535	−	0.0986505i
$714$	6.06769			0.227077
$715$	3.23794	−	3.97176i	0.121092	−	0.148535i
$716$	−15.1812			−0.567347
$717$	−8.25417	−	25.4037i	−0.308258	−	0.948720i
$718$	−28.2534	−	20.5273i	−1.05441	−	0.766071i
$719$	16.6655	−	12.1082i	0.621518	−	0.451559i	−0.231934	−	0.972732i	$-0.574505\pi$
$719$	16.6655	−	12.1082i	0.621518	−	0.451559i	0.853451	+	0.521173i	$0.174505\pi$
$720$	2.32326	−	7.15027i	0.0865829	−	0.266475i
$721$	−1.83021	+	5.63280i	−0.0681605	+	0.209776i
$722$	−24.8715	+	18.0702i	−0.925622	+	0.672504i
$723$	−2.07238	−	1.50567i	−0.0770726	−	0.0559965i
$724$	0.741321	+	2.28155i	0.0275510	+	0.0847932i
$725$	−22.2501			−0.826346
$726$	20.0566	+	2.24146i	0.744371	+	0.0831882i
$727$	−19.1211			−0.709161			−0.354580	−	0.935026i	$-0.615376\pi$
$727$	−19.1211			−0.709161			−0.354580	+	0.935026i	$0.615376\pi$
$728$	0.299996	+	0.923293i	0.0111186	+	0.0342195i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−3.77507	+	2.74275i	−0.139722	+	0.101514i
$731$	−3.79323	+	11.6744i	−0.140298	+	0.431792i
$732$	−4.63881	+	14.2768i	−0.171455	+	0.527685i
$733$	−14.4049	+	10.4657i	−0.532055	+	0.386561i	−0.821126	−	0.570747i	$-0.806654\pi$
$733$	−14.4049	+	10.4657i	−0.532055	+	0.386561i	0.289071	+	0.957308i	$0.406654\pi$
$734$	0.853376	+	0.620014i	0.0314987	+	0.0228851i
$735$	3.00950	+	9.26229i	0.111007	+	0.341645i
$736$	11.5879			0.427137
$737$	17.6727	−	21.6778i	0.650981	−	0.798513i
$738$	−16.2810			−0.599311
$739$	3.30155	+	10.1611i	0.121449	+	0.373783i	0.993238	−	0.116100i	$-0.0370394\pi$
$739$	3.30155	+	10.1611i	0.121449	+	0.373783i	−0.871788	+	0.489883i	$0.837039\pi$
$740$	−9.43296	−	6.85344i	−0.346762	−	0.251938i
$741$	1.21176	−	0.880396i	0.0445152	−	0.0323422i
$742$	−0.235767	+	0.725617i	−0.00865529	+	0.0266382i
$743$	−1.58783	+	4.88684i	−0.0582519	+	0.179281i	−0.975949	−	0.218001i	$-0.930046\pi$
$743$	−1.58783	+	4.88684i	−0.0582519	+	0.179281i	0.917697	+	0.397282i	$0.130046\pi$
$744$	1.48470	−	1.07870i	0.0544316	−	0.0395469i
$745$	−5.56059	−	4.04000i	−0.203724	−	0.148014i
$746$	−2.61156	−	8.03755i	−0.0956159	−	0.294275i
$747$	−11.2973			−0.413346
$748$	16.7381	+	6.48839i	0.612007	+	0.237239i
$749$	13.9123			0.508346
$750$	−6.66855	−	20.5237i	−0.243501	−	0.749419i
$751$	−41.6178	−	30.2371i	−1.51865	−	1.10337i	−0.962149	−	0.272523i	$-0.912142\pi$
$751$	−41.6178	−	30.2371i	−1.51865	−	1.10337i	−0.556505	−	0.830844i	$-0.687858\pi$
$752$	8.77130	−	6.37272i	0.319856	−	0.232389i
$753$	6.72921	−	20.7104i	0.245226	−	0.754728i
$754$	−4.82799	+	14.8590i	−0.175825	+	0.541134i
$755$	17.4022	−	12.6434i	0.633329	−	0.460141i
$756$	−0.922457	−	0.670204i	−0.0335494	−	0.0243751i
$757$	9.70112	+	29.8570i	0.352593	+	1.08517i	0.957392	+	0.288792i	$0.0932536\pi$
$757$	9.70112	+	29.8570i	0.352593	+	1.08517i	−0.604799	+	0.796378i	$0.706746\pi$
$758$	66.6916			2.42235
$759$	5.62847	−	1.48833i	0.204301	−	0.0540230i
$760$	2.69163			0.0976357
$761$	6.67424	+	20.5412i	0.241941	+	0.744618i	0.996125	+	0.0879542i	$0.0280329\pi$
$761$	6.67424	+	20.5412i	0.241941	+	0.744618i	−0.754183	+	0.656664i	$0.771967\pi$
$762$	19.3628	+	14.0679i	0.701441	+	0.509626i
$763$	13.1121	−	9.52646i	0.474688	−	0.344881i
$764$	−2.27530	+	7.00264i	−0.0823174	+	0.253347i
$765$	1.89177	−	5.82227i	0.0683970	−	0.210504i
$766$	−29.1396	+	21.1712i	−1.05286	+	0.764946i
$767$	4.72692	+	3.43430i	0.170679	+	0.124006i
$768$	6.48084	+	19.9460i	0.233857	+	0.719739i
$769$	54.0751			1.95000			0.974998	−	0.222213i	$-0.0713280\pi$
$769$	54.0751			1.95000			0.974998	+	0.222213i	$0.0713280\pi$
$770$	0.436456	−	7.83517i	0.0157288	−	0.282360i
$771$	8.84358			0.318494
$772$	4.04628	+	12.4532i	0.145629	+	0.448199i
$773$	−6.63688	−	4.82197i	−0.238712	−	0.173434i	0.461997	−	0.886881i	$-0.347133\pi$
$773$	−6.63688	−	4.82197i	−0.238712	−	0.173434i	−0.700709	+	0.713447i	$0.747133\pi$
$774$	4.59836	−	3.34091i	0.165285	−	0.120086i
$775$	1.27396	−	3.92086i	0.0457622	−	0.140841i
$776$	3.85871	−	11.8759i	0.138520	−	0.426319i
$777$	3.73041	−	2.71030i	0.133828	−	0.0972316i
$778$	27.4225	+	19.9236i	0.983143	+	0.714295i
$779$	−4.10735	−	12.6411i	−0.147161	−	0.452915i
$780$	−2.11063			−0.0755726
$781$	−8.49708	−	13.1790i	−0.304049	−	0.471582i
$782$	12.7607			0.456320
$783$	2.63151	+	8.09897i	0.0940427	+	0.289434i
$784$	−24.8141	−	18.0285i	−0.886218	−	0.643875i
$785$	−13.2893	+	9.65525i	−0.474316	+	0.344611i
$786$	−10.2465	+	31.5356i	−0.365482	+	1.12484i
$787$	−6.30417	+	19.4022i	−0.224719	+	0.691615i	0.773601	+	0.633673i	$0.218454\pi$
$787$	−6.30417	+	19.4022i	−0.224719	+	0.691615i	−0.998320	+	0.0579415i	$0.981546\pi$
$788$	−14.0713	+	10.2234i	−0.501270	+	0.364194i
$789$	−4.41053	−	3.20444i	−0.157019	−	0.114081i
$790$	−2.08280	−	6.41019i	−0.0741026	−	0.228064i
$791$	−10.7445			−0.382031
$792$	2.09031	+	3.24208i	0.0742760	+	0.115202i
$793$	−10.9889			−0.390229
$794$	−12.9066	−	39.7224i	−0.458038	−	1.40970i
$795$	0.622761	+	0.452462i	0.0220870	+	0.0160472i
$796$	−2.37535	+	1.72579i	−0.0841919	+	0.0611690i
$797$	15.1775	−	46.7114i	0.537613	−	1.65460i	−0.200321	−	0.979730i	$-0.564199\pi$
$797$	15.1775	−	46.7114i	0.537613	−	1.65460i	0.737934	−	0.674873i	$-0.235801\pi$
$798$	0.708799	−	2.18146i	0.0250912	−	0.0772228i
$799$	7.14223	−	5.18913i	0.252674	−	0.183578i
$800$	13.9541	+	10.1382i	0.493351	+	0.358440i
$801$	−1.90640	−	5.86728i	−0.0673592	−	0.207310i
$802$	−55.9940			−1.97722
$803$	0.303654	−	5.45114i	0.0107157	−	0.192366i
$804$	−11.5198			−0.406272
$805$	−0.699547	−	2.15298i	−0.0246558	−	0.0758827i
$806$	−2.34199	−	1.70156i	−0.0824932	−	0.0599348i
$807$	−9.81758	+	7.13289i	−0.345595	+	0.251090i
$808$	2.75255	−	8.47148i	0.0968343	−	0.298025i
$809$	13.8627	−	42.6649i	0.487385	−	1.50002i	−0.341110	−	0.940023i	$-0.610803\pi$
$809$	13.8627	−	42.6649i	0.487385	−	1.50002i	0.828496	−	0.559995i	$-0.189197\pi$
$810$	−2.29331	+	1.66618i	−0.0805785	+	0.0585437i
$811$	17.9764	+	13.0606i	0.631238	+	0.458621i	0.856829	−	0.515601i	$-0.172431\pi$
$811$	17.9764	+	13.0606i	0.631238	+	0.458621i	−0.225591	+	0.974222i	$0.572431\pi$
$812$	3.00051	+	9.23460i	0.105297	+	0.324071i
$813$	−23.3083			−0.817459
$814$	32.4982	−	8.59346i	1.13906	−	0.301201i
$815$	3.84033			0.134521
$816$	5.95795	+	18.3367i	0.208570	+	0.641912i
$817$	3.75407	+	2.72749i	0.131338	+	0.0954228i
$818$	−24.8039	+	18.0211i	−0.867247	+	0.630092i
$819$	0.257931	−	0.793829i	0.00901283	−	0.0277386i
$820$	−5.78780	+	17.8130i	−0.202119	+	0.622058i
$821$	−20.6955	+	15.0362i	−0.722278	+	0.524766i	−0.887111	−	0.461556i	$-0.847291\pi$
$821$	−20.6955	+	15.0362i	−0.722278	+	0.524766i	0.164833	+	0.986321i	$0.447291\pi$
$822$	19.3227	+	14.0387i	0.673956	+	0.489657i
$823$	−1.03612	−	3.18885i	−0.0361169	−	0.111156i	0.931373	−	0.364067i	$-0.118612\pi$
$823$	−1.03612	−	3.18885i	−0.0361169	−	0.111156i	−0.967490	+	0.252911i	$0.918612\pi$
$824$	−8.25297			−0.287506
$825$	8.07988	+	3.13209i	0.281305	+	0.109045i
$826$	8.94749			0.311323
$827$	−6.34493	−	19.5277i	−0.220635	−	0.679044i	−0.998705	−	0.0508675i	$-0.983801\pi$
$827$	−6.34493	−	19.5277i	−0.220635	−	0.679044i	0.778070	−	0.628177i	$-0.216199\pi$
$828$	−1.93997	−	1.40947i	−0.0674188	−	0.0489826i
$829$	45.6140	−	33.1405i	1.58424	−	1.15102i	0.672619	−	0.739989i	$-0.265169\pi$
$829$	45.6140	−	33.1405i	1.58424	−	1.15102i	0.911622	−	0.411029i	$-0.134831\pi$
$830$	−9.89602	+	30.4568i	−0.343496	+	1.05717i
$831$	−1.98304	+	6.10317i	−0.0687909	+	0.211717i
$832$	1.92500	−	1.39860i	0.0667375	−	0.0484876i
$833$	−20.2054	−	14.6801i	−0.700077	−	0.508636i
$834$	−7.57602	−	23.3166i	−0.262336	−	0.807388i
$835$	27.3420			0.946208
$836$	4.28798	−	5.25976i	0.148303	−	0.181913i
$837$	−1.57786			−0.0545387
$838$	−18.9158	−	58.2167i	−0.653434	−	2.01106i
$839$	−35.5956	−	25.8617i	−1.22890	−	0.892846i	−0.232090	−	0.972694i	$-0.574556\pi$
$839$	−35.5956	−	25.8617i	−1.22890	−	0.892846i	−0.996807	+	0.0798480i	$0.974556\pi$
$840$	1.21348	−	0.881648i	0.0418692	−	0.0304198i
$841$	13.4479	−	41.3882i	0.463719	−	1.42718i
$842$	10.7965	−	33.2282i	0.372072	−	1.14512i
$843$	22.6158	−	16.4313i	0.778929	−	0.565925i
$844$	22.4693	+	16.3249i	0.773425	+	0.561926i
$845$	−0.477448	−	1.46943i	−0.0164247	−	0.0505501i
$846$	−4.08785			−0.140543
$847$	6.78264	+	6.18834i	0.233054	+	0.212634i
$848$	−2.42433			−0.0832520
$849$	−3.68799	−	11.3505i	−0.126571	−	0.389547i
$850$	15.3662	+	11.1642i	0.527058	+	0.382930i
$851$	7.84524	−	5.69990i	0.268931	−	0.195390i
$852$	−1.99582	+	6.14250i	−0.0683757	+	0.210439i
$853$	5.35849	−	16.4918i	0.183471	−	0.564667i	−0.816447	−	0.577420i	$-0.804060\pi$
$853$	5.35849	−	16.4918i	0.183471	−	0.564667i	0.999919	+	0.0127532i	$0.00405956\pi$
$854$	−13.6143	+	9.89135i	−0.465871	+	0.338475i
$855$	−1.87224	−	1.36026i	−0.0640291	−	0.0465199i
$856$	5.99066	+	18.4373i	0.204756	+	0.630175i
$857$	−3.98802			−0.136228			−0.0681140	−	0.997678i	$-0.521698\pi$
$857$	−3.98802			−0.136228			−0.0681140	+	0.997678i	$0.521698\pi$
$858$	3.84491	−	4.71628i	0.131263	−	0.161011i
$859$	−4.45502			−0.152003			−0.0760017	−	0.997108i	$-0.524215\pi$
$859$	−4.45502			−0.152003			−0.0760017	+	0.997108i	$0.524215\pi$
$860$	−2.02059	−	6.21875i	−0.0689017	−	0.212058i
$861$	−5.99236	−	4.35370i	−0.204219	−	0.148374i
$862$	9.36927	−	6.80717i	0.319119	−	0.231853i
$863$	8.17101	−	25.1478i	0.278144	−	0.856040i	−0.710226	−	0.703974i	$-0.751407\pi$
$863$	8.17101	−	25.1478i	0.278144	−	0.856040i	0.988370	−	0.152066i	$-0.0485927\pi$
$864$	2.03994	−	6.27829i	0.0694002	−	0.213592i
$865$	−16.0737	+	11.6782i	−0.546523	+	0.397072i
$866$	−16.1888	−	11.7619i	−0.550118	−	0.399684i
$867$	−0.401895	−	1.23691i	−0.0136491	−	0.0420076i
$868$	−1.79910			−0.0610655
$869$	7.35289	+	2.85028i	0.249430	+	0.0966890i
$870$	24.1395			0.818405
$871$	−2.60591	−	8.02016i	−0.0882978	−	0.271753i
$872$	18.2710	+	13.2747i	0.618735	+	0.449537i
$873$	−8.68570	+	6.31053i	−0.293966	+	0.213579i
$874$	1.49064	−	4.58772i	0.0504216	−	0.155182i
$875$	3.03383	−	9.33717i	0.102562	−	0.315654i
$876$	−1.81924	+	1.32175i	−0.0614663	+	0.0446579i
$877$	−38.8229	−	28.2065i	−1.31096	−	0.952466i	−0.999998	−	0.00204293i	$-0.999350\pi$
$877$	−38.8229	−	28.2065i	−1.31096	−	0.952466i	−0.310959	−	0.950423i	$-0.600650\pi$
$878$	6.62964	+	20.4039i	0.223740	+	0.688600i
$879$	7.23742			0.244112
$880$	24.1066	−	6.37449i	0.812634	−	0.214884i
$881$	−33.5896			−1.13166			−0.565832	−	0.824521i	$-0.691445\pi$
$881$	−33.5896			−1.13166			−0.565832	+	0.824521i	$0.691445\pi$
$882$	3.57365	+	10.9985i	0.120331	+	0.370340i
$883$	−3.21974	−	2.33928i	−0.108353	−	0.0787231i	0.532289	−	0.846563i	$-0.321332\pi$
$883$	−3.21974	−	2.33928i	−0.108353	−	0.0787231i	−0.640642	+	0.767839i	$0.721332\pi$
$884$	4.37893	−	3.18148i	0.147279	−	0.107005i
$885$	2.78963	−	8.58559i	0.0937723	−	0.288601i
$886$	19.2833	−	59.3480i	0.647836	−	1.99383i
$887$	−19.3270	+	14.0419i	−0.648936	+	0.471479i	−0.862909	−	0.505360i	$-0.831360\pi$
$887$	−19.3270	+	14.0419i	−0.648936	+	0.471479i	0.213973	+	0.976840i	$0.431360\pi$
$888$	5.19815	+	3.77668i	0.174438	+	0.126737i
$889$	3.36475	+	10.3556i	0.112850	+	0.347317i
$890$	−17.4878			−0.586192
$891$	0.184466	−	3.31149i	0.00617984	−	0.110939i
$892$	−29.6938			−0.994221
$893$	−1.03128	−	3.17395i	−0.0345104	−	0.106212i
$894$	−6.60294	−	4.79732i	−0.220835	−	0.160446i
$895$	−13.8912	+	10.0925i	−0.464331	+	0.337356i
$896$	−2.27940	+	7.01528i	−0.0761495	+	0.234364i
$897$	0.542441	−	1.66946i	0.0181116	−	0.0557417i
$898$	26.8803	−	19.5297i	0.897009	−	0.651715i
$899$	10.8705	+	7.89786i	0.362551	+	0.263409i
$900$	−1.10296	−	3.39455i	−0.0367652	−	0.113152i
$901$	−1.97407			−0.0657657
$902$	−29.2603	−	45.3829i	−0.974262	−	1.51108i
$903$	2.58586			0.0860521
$904$	−4.62660	−	14.2392i	−0.153878	−	0.473589i
$905$	2.19512	+	1.59484i	0.0729681	+	0.0530144i
$906$	20.6643	−	15.0135i	0.686524	−	0.498789i
$907$	12.7122	−	39.1240i	0.422100	−	1.29909i	−0.483644	−	0.875265i	$-0.660687\pi$
$907$	12.7122	−	39.1240i	0.422100	−	1.29909i	0.905744	−	0.423826i	$-0.139313\pi$
$908$	−8.28486	+	25.4982i	−0.274943	+	0.846186i
$909$	−6.19581	+	4.50152i	−0.205502	+	0.149306i
$910$	−1.91418	−	1.39073i	−0.0634544	−	0.0461023i
$911$	10.7062	+	32.9502i	0.354711	+	1.09169i	0.956177	+	0.292790i	$0.0945838\pi$
$911$	10.7062	+	32.9502i	0.354711	+	1.09169i	−0.601465	+	0.798899i	$0.705416\pi$
$912$	7.28839			0.241343
$913$	−20.3036	−	31.4909i	−0.671951	−	1.04220i
$914$	36.2009			1.19742
$915$	5.24665	+	16.1475i	0.173449	+	0.533821i
$916$	−0.572857	−	0.416205i	−0.0189277	−	0.0137518i
$917$	−12.2043	+	8.86694i	−0.403021	+	0.292812i
$918$	2.24639	−	6.91368i	0.0741419	−	0.228185i
$919$	5.17441	−	15.9252i	0.170688	−	0.525324i	−0.828722	−	0.559660i	$-0.810932\pi$
$919$	5.17441	−	15.9252i	0.170688	−	0.525324i	0.999410	+	0.0343364i	$0.0109318\pi$
$920$	2.55202	−	1.85415i	0.0841376	−	0.0611295i
$921$	11.4661	+	8.33062i	0.377821	+	0.274503i
$922$	13.5650	+	41.7487i	0.446739	+	1.37492i
$923$	−4.72793			−0.155622
$924$	0.210332	−	3.77583i	0.00691940	−	0.124216i
$925$	14.4340			0.474586
$926$	−2.07404	−	6.38323i	−0.0681571	−	0.209766i
$927$	5.74057	+	4.17077i	0.188545	+	0.136986i
$928$	−45.4796	+	33.0429i	−1.49294	+	1.08468i
$929$	−8.60400	+	26.4804i	−0.282288	+	0.868794i	0.704910	+	0.709296i	$0.250987\pi$
$929$	−8.60400	+	26.4804i	−0.282288	+	0.868794i	−0.987198	+	0.159497i	$0.949013\pi$
$930$	−1.38215	+	4.25381i	−0.0453224	+	0.139488i
$931$	−7.63810	+	5.54941i	−0.250329	+	0.181874i
$932$	12.6083	+	9.16049i	0.412999	+	0.300062i
$933$	1.52479	+	4.69283i	0.0499195	+	0.153636i
$934$	−20.0852			−0.657208
$935$	19.6293	−	5.19057i	0.641948	−	0.169750i
$936$	1.16309			0.0380167
$937$	9.96998	+	30.6845i	0.325705	+	1.00242i	0.971121	+	0.238586i	$0.0766840\pi$
$937$	9.96998	+	30.6845i	0.325705	+	1.00242i	−0.645416	+	0.763831i	$0.723316\pi$
$938$	−10.4476	−	7.59061i	−0.341125	−	0.247842i
$939$	18.5225	−	13.4574i	0.604460	−	0.439166i
$940$	−1.45321	+	4.47252i	−0.0473984	+	0.145877i
$941$	−7.82142	+	24.0719i	−0.254971	+	0.784720i	0.738864	+	0.673854i	$0.235362\pi$
$941$	−7.82142	+	24.0719i	−0.254971	+	0.784720i	−0.993835	+	0.110866i	$0.964638\pi$
$942$	−15.7804	+	11.4652i	−0.514155	+	0.373555i
$943$	−12.6022	−	9.15606i	−0.410385	−	0.298162i
$944$	8.78567	+	27.0395i	0.285949	+	0.880061i
$945$	−1.28963			−0.0419516
$946$	17.5769	+	6.81353i	0.571475	+	0.221527i
$947$	−45.4202			−1.47596			−0.737978	−	0.674824i	$-0.764219\pi$
$947$	−45.4202			−1.47596			−0.737978	+	0.674824i	$0.764219\pi$
$948$	−1.00372	−	3.08912i	−0.0325992	−	0.100330i
$949$	−1.33175	−	0.967570i	−0.0432303	−	0.0314086i
$950$	5.80878	−	4.22033i	0.188462	−	0.136926i
$951$	−4.20091	+	12.9291i	−0.136224	+	0.419254i
$952$	−1.18866	+	3.65832i	−0.0385247	+	0.118567i
$953$	−25.4686	+	18.5040i	−0.825010	+	0.599405i	−0.918143	−	0.396249i	$-0.870312\pi$
$953$	−25.4686	+	18.5040i	−0.825010	+	0.599405i	0.0931335	+	0.995654i	$0.470312\pi$
$954$	0.739500	+	0.537278i	0.0239422	+	0.0173950i
$955$	2.57344	+	7.92023i	0.0832745	+	0.256293i
$956$	−36.4888			−1.18013
$957$	−17.8463	+	21.8908i	−0.576890	+	0.707630i
$958$	−33.4752			−1.08153
$959$	3.35778	+	10.3342i	0.108428	+	0.333708i
$960$	−2.97424	−	2.16091i	−0.0959930	−	0.0697430i
$961$	23.0654	−	16.7580i	0.744044	−	0.540580i
$962$	3.13200	−	9.63930i	0.100980	−	0.310783i
$963$	5.15065	−	15.8521i	0.165977	−	0.510826i
$964$	−2.83098	+	2.05683i	−0.0911798	+	0.0662460i
$965$	11.9814	+	8.70498i	0.385694	+	0.280223i
$966$	−0.830680	−	2.55657i	−0.0267267	−	0.0822563i
$967$	20.9984			0.675263			0.337631	−	0.941278i	$-0.390374\pi$
$967$	20.9984			0.675263			0.337631	+	0.941278i	$0.390374\pi$
$968$	−5.28051	+	11.6534i	−0.169722	+	0.374555i
$969$	5.93474			0.190651
$970$	9.40445	+	28.9439i	0.301959	+	0.929334i
$971$	1.94634	+	1.41410i	0.0624611	+	0.0453806i	0.618578	−	0.785724i	$-0.287709\pi$
$971$	1.94634	+	1.41410i	0.0624611	+	0.0453806i	−0.556117	+	0.831104i	$0.687709\pi$
$972$	−1.10516	+	0.802947i	−0.0354481	+	0.0257545i
$973$	3.44668	−	10.6078i	0.110496	−	0.340070i
$974$	5.00103	−	15.3916i	0.160243	−	0.493179i
$975$	2.11381	−	1.53577i	0.0676960	−	0.0491840i
$976$	−43.2599	−	31.4302i	−1.38472	−	1.00606i
$977$	−13.0907	−	40.2889i	−0.418808	−	1.28896i	−0.908801	−	0.417231i	$-0.863001\pi$
$977$	−13.0907	−	40.2889i	−0.418808	−	1.28896i	0.489993	−	0.871726i	$-0.336999\pi$
$978$	4.56022			0.145820
$979$	12.9287	−	15.8588i	0.413204	−	0.506849i
$980$	13.3039			0.424979
$981$	−6.00033	−	18.4671i	−0.191576	−	0.589609i
$982$	29.7272	+	21.5981i	0.948632	+	0.689222i
$983$	−38.4963	+	27.9692i	−1.22784	+	0.892078i	−0.996726	−	0.0808483i	$-0.974237\pi$
$983$	−38.4963	+	27.9692i	−1.22784	+	0.892078i	−0.231114	+	0.972927i	$0.574237\pi$
$984$	3.18944	−	9.81609i	0.101676	−	0.312926i
$985$	−6.07904	+	18.7094i	−0.193694	+	0.596130i
$986$	−50.0822	+	36.3869i	−1.59494	+	1.15879i
$987$	−1.50457	−	1.09313i	−0.0478910	−	0.0347948i
$988$	−0.632280	−	1.94596i	−0.0201155	−	0.0619092i
$989$	5.43820			0.172925
$990$	−8.76600	−	3.39806i	−0.278602	−	0.107997i
$991$	−48.1600			−1.52985			−0.764926	−	0.644118i	$-0.777225\pi$
$991$	−48.1600			−1.52985			−0.764926	+	0.644118i	$0.777225\pi$
$992$	−3.21874	−	9.90625i	−0.102195	−	0.314524i
$993$	7.74280	+	5.62548i	0.245710	+	0.178519i
$994$	−5.85746	+	4.25570i	−0.185788	+	0.134983i
$995$	−1.02619	+	3.15828i	−0.0325324	+	0.100124i
$996$	−4.76897	+	14.6774i	−0.151111	+	0.465070i
$997$	−37.3141	+	27.1103i	−1.18175	+	0.858592i	−0.992368	−	0.123311i	$-0.960649\pi$
$997$	−37.3141	+	27.1103i	−1.18175	+	0.858592i	−0.189383	+	0.981903i	$0.560649\pi$
$998$	40.0419	+	29.0922i	1.26750	+	0.920896i
$999$	−1.70711	−	5.25394i	−0.0540105	−	0.166227i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.n.a.313.1	yes	12
11.3	even	5		4719.2.a.bg.1.2		6
11.8	odd	10		4719.2.a.bh.1.5		6
11.9	even	5	inner	429.2.n.a.196.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.a.196.1	✓	12	11.9	even	5	inner
429.2.n.a.313.1	yes	12	1.1	even	1	trivial
4719.2.a.bg.1.2		6	11.3	even	5
4719.2.a.bh.1.5		6	11.8	odd	10

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.566948 - 1.74489i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-1.10516 + 0.802947i) q^{4} +(-0.477448 + 1.46943i) q^{5} +(-0.566948 + 1.74489i) q^{6} +(-0.675271 + 0.490613i) q^{7} +(-0.940958 - 0.683646i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.566948 - 1.74489i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-1.10516 + 0.802947i) q^{4} +(-0.477448 + 1.46943i) q^{5} +(-0.566948 + 1.74489i) q^{6} +(-0.675271 + 0.490613i) q^{7} +(-0.940958 - 0.683646i) q^{8} +(0.309017 + 0.951057i) q^{9} +2.83468 q^{10} +(-2.09568 + 2.57063i) q^{11} +1.36605 q^{12} +(0.309017 + 0.951057i) q^{13} +(1.23891 + 0.900119i) q^{14} +(1.24997 - 0.908160i) q^{15} +(-1.50368 + 4.62784i) q^{16} +(-1.22440 + 3.76833i) q^{17} +(1.48429 - 1.07840i) q^{18} +(1.21176 + 0.880396i) q^{19} +(-0.652220 - 2.00733i) q^{20} +0.834681 q^{21} +(5.67359 + 2.19931i) q^{22} +1.75538 q^{23} +(0.359414 + 1.10616i) q^{24} +(2.11381 + 1.53577i) q^{25} +(1.48429 - 1.07840i) q^{26} +(0.309017 - 0.951057i) q^{27} +(0.352347 - 1.08441i) q^{28} +(-6.88940 + 5.00544i) q^{29} +(-2.29331 - 1.66618i) q^{30} +(-0.487584 - 1.50063i) q^{31} +6.60139 q^{32} +(3.20642 - 0.847870i) q^{33} +7.26947 q^{34} +(-0.398517 - 1.22651i) q^{35} +(-1.10516 - 0.802947i) q^{36} +(4.46927 - 3.24711i) q^{37} +(0.849185 - 2.61352i) q^{38} +(0.309017 - 0.951057i) q^{39} +(1.45383 - 1.05627i) q^{40} +(-7.17922 - 5.21601i) q^{41} +(-0.473220 - 1.45642i) q^{42} +3.09803 q^{43} +(0.251990 - 4.52368i) q^{44} -1.54505 q^{45} +(-0.995206 - 3.06293i) q^{46} +(-1.80257 - 1.30964i) q^{47} +(3.93668 - 2.86017i) q^{48} +(-1.94783 + 5.99480i) q^{49} +(1.48133 - 4.55905i) q^{50} +(3.20553 - 2.32895i) q^{51} +(-1.10516 - 0.802947i) q^{52} +(0.153958 + 0.473834i) q^{53} -1.83468 q^{54} +(-2.77679 - 4.30680i) q^{55} +0.970807 q^{56} +(-0.462852 - 1.42451i) q^{57} +(12.6398 + 9.18338i) q^{58} +(4.72692 - 3.43430i) q^{59} +(-0.652220 + 2.00733i) q^{60} +(-3.39577 + 10.4511i) q^{61} +(-2.34199 + 1.70156i) q^{62} +(-0.675271 - 0.490613i) q^{63} +(-0.735286 - 2.26298i) q^{64} -1.54505 q^{65} +(-3.29731 - 5.11413i) q^{66} -8.43289 q^{67} +(-1.67260 - 5.14774i) q^{68} +(-1.42013 - 1.03178i) q^{69} +(-1.91418 + 1.39073i) q^{70} +(-1.46101 + 4.49653i) q^{71} +(0.359414 - 1.10616i) q^{72} +(-1.33175 + 0.967570i) q^{73} +(-8.19968 - 5.95741i) q^{74} +(-0.807402 - 2.48493i) q^{75} -2.04610 q^{76} +(0.153970 - 2.76404i) q^{77} -1.83468 q^{78} +(-0.734755 - 2.26134i) q^{79} +(-6.08238 - 4.41911i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-5.03110 + 15.4841i) q^{82} +(-3.49105 + 10.7444i) q^{83} +(-0.922457 + 0.670204i) q^{84} +(-4.95272 - 3.59836i) q^{85} +(-1.75642 - 5.40570i) q^{86} +8.51576 q^{87} +(3.72935 - 0.986147i) q^{88} -6.16923 q^{89} +(0.875965 + 2.69594i) q^{90} +(-0.675271 - 0.490613i) q^{91} +(-1.93997 + 1.40947i) q^{92} +(-0.487584 + 1.50063i) q^{93} +(-1.26321 + 3.88777i) q^{94} +(-1.87224 + 1.36026i) q^{95} +(-5.34064 - 3.88020i) q^{96} +(3.31764 + 10.2106i) q^{97} +11.5646 q^{98} +(-3.09241 - 1.19874i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 8 q^{5} + 3 q^{6} + 5 q^{7} - q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 8 * q^5 + 3 * q^6 + 5 * q^7 - q^8 - 3 * q^9	\( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 8 q^{5} + 3 q^{6} + 5 q^{7} - q^{8} - 3 q^{9} + 14 q^{10} - 6 q^{11} + 2 q^{12} - 3 q^{13} + 11 q^{14} - 2 q^{15} - 5 q^{16} - 14 q^{17} - 2 q^{18} - 2 q^{19} - 9 q^{20} - 10 q^{21} + 21 q^{22} - 6 q^{23} + 4 q^{24} + 19 q^{25} - 2 q^{26} - 3 q^{27} - 12 q^{28} - 12 q^{29} - q^{30} - 12 q^{31} + 26 q^{32} + 9 q^{33} - 24 q^{34} - 2 q^{35} - 3 q^{36} + 4 q^{37} - 13 q^{38} - 3 q^{39} + 4 q^{40} - 10 q^{41} + q^{42} + 28 q^{43} - 12 q^{45} - 5 q^{46} + 28 q^{47} + 10 q^{48} + 20 q^{49} - q^{50} + 11 q^{51} - 3 q^{52} - 29 q^{53} - 2 q^{54} + 4 q^{55} + 12 q^{56} + 8 q^{57} + 22 q^{58} - 11 q^{59} - 9 q^{60} - 18 q^{61} + 40 q^{62} + 5 q^{63} + 11 q^{64} - 12 q^{65} + 16 q^{66} - 72 q^{67} - 35 q^{68} + 4 q^{69} - 6 q^{70} + 10 q^{71} + 4 q^{72} - 11 q^{73} - 15 q^{74} - 11 q^{75} + 4 q^{76} + 20 q^{77} - 2 q^{78} - 7 q^{79} - 27 q^{80} - 3 q^{81} - 10 q^{82} + 16 q^{83} + 8 q^{84} - 26 q^{85} - 35 q^{86} + 28 q^{87} + 25 q^{88} - 62 q^{89} - 6 q^{90} + 5 q^{91} - 34 q^{92} - 12 q^{93} - q^{94} + 15 q^{95} + q^{96} + 54 q^{97} + 50 q^{98} - 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 8 * q^5 + 3 * q^6 + 5 * q^7 - q^8 - 3 * q^9 + 14 * q^10 - 6 * q^11 + 2 * q^12 - 3 * q^13 + 11 * q^14 - 2 * q^15 - 5 * q^16 - 14 * q^17 - 2 * q^18 - 2 * q^19 - 9 * q^20 - 10 * q^21 + 21 * q^22 - 6 * q^23 + 4 * q^24 + 19 * q^25 - 2 * q^26 - 3 * q^27 - 12 * q^28 - 12 * q^29 - q^30 - 12 * q^31 + 26 * q^32 + 9 * q^33 - 24 * q^34 - 2 * q^35 - 3 * q^36 + 4 * q^37 - 13 * q^38 - 3 * q^39 + 4 * q^40 - 10 * q^41 + q^42 + 28 * q^43 - 12 * q^45 - 5 * q^46 + 28 * q^47 + 10 * q^48 + 20 * q^49 - q^50 + 11 * q^51 - 3 * q^52 - 29 * q^53 - 2 * q^54 + 4 * q^55 + 12 * q^56 + 8 * q^57 + 22 * q^58 - 11 * q^59 - 9 * q^60 - 18 * q^61 + 40 * q^62 + 5 * q^63 + 11 * q^64 - 12 * q^65 + 16 * q^66 - 72 * q^67 - 35 * q^68 + 4 * q^69 - 6 * q^70 + 10 * q^71 + 4 * q^72 - 11 * q^73 - 15 * q^74 - 11 * q^75 + 4 * q^76 + 20 * q^77 - 2 * q^78 - 7 * q^79 - 27 * q^80 - 3 * q^81 - 10 * q^82 + 16 * q^83 + 8 * q^84 - 26 * q^85 - 35 * q^86 + 28 * q^87 + 25 * q^88 - 62 * q^89 - 6 * q^90 + 5 * q^91 - 34 * q^92 - 12 * q^93 - q^94 + 15 * q^95 + q^96 + 54 * q^97 + 50 * q^98 - 6 * q^99

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