LMFDB - Embedded newform 270.2.k.b.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,2,Mod(31,270)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("270.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	270.k (of order $9$, degree $6$, 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:	$2.15596085457$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			211.1
Root			$0.500000 + 0.258654i$ of defining polynomial
Character	$\chi$	$=$	270.211
Dual form			270.2.k.b.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.766044 + 0.642788i) q^{2} +(-1.31533 + 1.12691i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.939693 + 0.342020i) q^{5} +(0.283238 - 1.70874i) q^{6} +(-0.720122 - 4.08401i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.460168 - 2.96450i) q^{9} +(0.500000 - 0.866025i) q^{10} +(4.99329 + 1.81741i) q^{11} +(0.881381 + 1.49103i) q^{12} +(-1.76311 - 1.47942i) q^{13} +(3.17680 + 2.66565i) q^{14} +(0.850578 - 1.50881i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(1.73332 - 3.00220i) q^{17} +(1.55303 + 2.56673i) q^{18} +(1.95962 + 3.39416i) q^{19} +(0.173648 + 0.984808i) q^{20} +(5.54949 + 4.56030i) q^{21} +(-4.99329 + 1.81741i) q^{22} +(0.235711 - 1.33678i) q^{23} +(-1.63359 - 0.575653i) q^{24} +(0.766044 - 0.642788i) q^{25} +2.30157 q^{26} +(2.73544 + 4.41785i) q^{27} -4.14702 q^{28} +(2.58015 - 2.16500i) q^{29} +(0.318266 + 1.70256i) q^{30} +(1.32591 - 7.51961i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-8.61586 + 3.23648i) q^{33} +(0.601977 + 3.41398i) q^{34} +(2.07351 + 3.59142i) q^{35} +(-2.83955 - 0.967956i) q^{36} +(5.85967 - 10.1493i) q^{37} +(-3.68287 - 1.34046i) q^{38} +(3.98623 - 0.0409315i) q^{39} +(-0.766044 - 0.642788i) q^{40} +(-8.55777 - 7.18082i) q^{41} +(-7.18247 + 0.0737513i) q^{42} +(2.46761 + 0.898136i) q^{43} +(2.65688 - 4.60184i) q^{44} +(0.581502 + 2.94310i) q^{45} +(0.678702 + 1.17555i) q^{46} +(1.91147 + 10.8405i) q^{47} +(1.62143 - 0.609077i) q^{48} +(-9.58275 + 3.48784i) q^{49} +(-0.173648 + 0.984808i) q^{50} +(1.10331 + 5.90217i) q^{51} +(-1.76311 + 1.47942i) q^{52} -6.23155 q^{53} +(-4.93520 - 1.62596i) q^{54} -5.31375 q^{55} +(3.17680 - 2.66565i) q^{56} +(-6.40243 - 2.25612i) q^{57} +(-0.584872 + 3.31698i) q^{58} +(1.23587 - 0.449821i) q^{59} +(-1.33819 - 1.09966i) q^{60} +(-1.19514 - 6.77800i) q^{61} +(3.81781 + 6.61264i) q^{62} +(-12.4384 + 0.255468i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.16277 + 0.787183i) q^{65} +(4.51976 - 8.01746i) q^{66} +(-4.32375 - 3.62806i) q^{67} +(-2.65560 - 2.22832i) q^{68} +(1.19639 + 2.02393i) q^{69} +(-3.89692 - 1.41836i) q^{70} +(-0.424943 + 0.736023i) q^{71} +(2.79741 - 1.08373i) q^{72} +(2.93911 + 5.09069i) q^{73} +(2.03504 + 11.5413i) q^{74} +(-0.283238 + 1.70874i) q^{75} +(3.68287 - 1.34046i) q^{76} +(3.82655 - 21.7014i) q^{77} +(-3.02732 + 2.59365i) q^{78} +(1.60439 - 1.34625i) q^{79} +1.00000 q^{80} +(-8.57649 - 2.72833i) q^{81} +11.1714 q^{82} +(-10.3632 + 8.69578i) q^{83} +(5.45468 - 4.67330i) q^{84} +(-0.601977 + 3.41398i) q^{85} +(-2.46761 + 0.898136i) q^{86} +(-0.953986 + 5.75527i) q^{87} +(0.922723 + 5.23302i) q^{88} +(0.216147 + 0.374377i) q^{89} +(-2.33725 - 1.88077i) q^{90} +(-4.77233 + 8.26591i) q^{91} +(-1.27554 - 0.464260i) q^{92} +(6.72989 + 11.3849i) q^{93} +(-8.43242 - 7.07564i) q^{94} +(-3.00231 - 2.51923i) q^{95} +(-0.850578 + 1.50881i) q^{96} +(13.1192 + 4.77498i) q^{97} +(5.09887 - 8.83151i) q^{98} +(7.68546 - 13.9663i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} + 3 q^{6} - 12 q^{7} + 6 q^{8} - 3 q^{9} + 6 q^{10} + 3 q^{11} + 9 q^{12} + 9 q^{13} - 6 q^{14} - 9 q^{17} - 6 q^{18} - 3 q^{19} - 6 q^{21} - 3 q^{22} - 24 q^{23} - 3 q^{24} + 12 q^{26} - 9 q^{27}+ \cdots + 45 q^{99}+O(q^{100}) $ 12 * q + 3 * q^3 + 3 * q^6 - 12 * q^7 + 6 * q^8 - 3 * q^9 + 6 * q^10 + 3 * q^11 + 9 * q^12 + 9 * q^13 - 6 * q^14 - 9 * q^17 - 6 * q^18 - 3 * q^19 - 6 * q^21 - 3 * q^22 - 24 * q^23 - 3 * q^24 + 12 * q^26 - 9 * q^27 - 6 * q^28 + 6 * q^29 + 6 * q^30 + 21 * q^31 - 9 * q^33 + 18 * q^34 + 3 * q^35 - 3 * q^36 - 18 * q^38 - 24 * q^41 - 27 * q^42 + 33 * q^43 + 3 * q^44 + 15 * q^45 + 15 * q^46 - 18 * q^47 + 6 * q^48 - 30 * q^49 + 9 * q^51 + 9 * q^52 + 24 * q^53 - 18 * q^54 - 6 * q^55 - 6 * q^56 + 15 * q^57 + 39 * q^58 + 36 * q^59 - 3 * q^60 - 24 * q^61 - 60 * q^63 - 6 * q^64 - 9 * q^66 + 9 * q^67 + 9 * q^68 + 18 * q^69 - 6 * q^70 - 18 * q^71 + 12 * q^72 + 12 * q^73 - 12 * q^74 - 3 * q^75 + 18 * q^76 + 24 * q^77 - 24 * q^78 + 27 * q^79 + 12 * q^80 - 63 * q^81 + 6 * q^82 - 9 * q^83 - 3 * q^84 - 18 * q^85 - 33 * q^86 - 18 * q^87 - 3 * q^88 + 15 * q^89 - 15 * q^90 - 21 * q^91 + 3 * q^92 + 36 * q^93 - 54 * q^94 - 18 * q^95 + 36 * q^97 + 3 * q^98 + 45 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

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 $

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	−1.31533	+	1.12691i	−0.759404	+	0.650619i
$3$	−1.31533	+	1.12691i	−0.759404	+	0.650619i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−0.939693	+	0.342020i	−0.420243	+	0.152956i
$5$	−0.939693	+	0.342020i	−0.420243	+	0.152956i
$6$	0.283238	−	1.70874i	0.115631	−	0.697588i
$7$	−0.720122	−	4.08401i	−0.272181	−	1.54361i	−0.747778	−	0.663949i	$-0.768879\pi$
$7$	−0.720122	−	4.08401i	−0.272181	−	1.54361i	0.475597	−	0.879663i	$-0.342232\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	0.460168	−	2.96450i	0.153389	−	0.988166i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	4.99329	+	1.81741i	1.50553	+	0.547970i	0.957487	−	0.288477i	$-0.0931490\pi$
$11$	4.99329	+	1.81741i	1.50553	+	0.547970i	0.548048	+	0.836447i	$0.315371\pi$
$12$	0.881381	+	1.49103i	0.254433	+	0.430423i
$13$	−1.76311	−	1.47942i	−0.488997	−	0.410318i	0.364669	−	0.931137i	$-0.381182\pi$
$13$	−1.76311	−	1.47942i	−0.488997	−	0.410318i	−0.853667	+	0.520819i	$0.825626\pi$
$14$	3.17680	+	2.66565i	0.849035	+	0.712425i
$15$	0.850578	−	1.50881i	0.219618	−	0.389574i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	1.73332	−	3.00220i	0.420393	−	0.728141i	−0.575585	−	0.817742i	$-0.695226\pi$
$17$	1.73332	−	3.00220i	0.420393	−	0.728141i	0.995978	+	0.0896005i	$0.0285590\pi$
$18$	1.55303	+	2.56673i	0.366053	+	0.604983i
$19$	1.95962	+	3.39416i	0.449567	+	0.778673i	0.998358	−	0.0572870i	$-0.0182450\pi$
$19$	1.95962	+	3.39416i	0.449567	+	0.778673i	−0.548791	+	0.835960i	$0.684912\pi$
$20$	0.173648	+	0.984808i	0.0388289	+	0.220210i
$21$	5.54949	+	4.56030i	1.21100	+	0.995140i
$22$	−4.99329	+	1.81741i	−1.06457	+	0.387473i
$23$	0.235711	−	1.33678i	0.0491491	−	0.278738i	−0.950322	−	0.311270i	$-0.899246\pi$
$23$	0.235711	−	1.33678i	0.0491491	−	0.278738i	0.999471	+	0.0325313i	$0.0103569\pi$
$24$	−1.63359	−	0.575653i	−0.333456	−	0.117505i
$25$	0.766044	−	0.642788i	0.153209	−	0.128558i
$26$	2.30157			0.451375
$27$	2.73544	+	4.41785i	0.526435	+	0.850215i
$28$	−4.14702			−0.783713
$29$	2.58015	−	2.16500i	0.479122	−	0.402031i	−0.370987	−	0.928638i	$-0.620981\pi$
$29$	2.58015	−	2.16500i	0.479122	−	0.402031i	0.850109	+	0.526607i	$0.176536\pi$
$30$	0.318266	+	1.70256i	0.0581071	+	0.310843i
$31$	1.32591	−	7.51961i	0.238141	−	1.35056i	−0.597757	−	0.801677i	$-0.703941\pi$
$31$	1.32591	−	7.51961i	0.238141	−	1.35056i	0.835898	−	0.548885i	$-0.184948\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	−8.61586	+	3.23648i	−1.49983	+	0.563399i
$34$	0.601977	+	3.41398i	0.103238	+	0.585493i
$35$	2.07351	+	3.59142i	0.350487	+	0.607061i
$36$	−2.83955	−	0.967956i	−0.473259	−	0.161326i
$37$	5.85967	−	10.1493i	0.963324	−	1.66853i	0.249273	−	0.968433i	$-0.419808\pi$
$37$	5.85967	−	10.1493i	0.963324	−	1.66853i	0.714051	−	0.700094i	$-0.246858\pi$
$38$	−3.68287	−	1.34046i	−0.597441	−	0.217451i
$39$	3.98623	−	0.0409315i	0.638307	−	0.00655429i
$40$	−0.766044	−	0.642788i	−0.121122	−	0.101634i
$41$	−8.55777	−	7.18082i	−1.33650	−	1.12146i	−0.982511	−	0.186206i	$-0.940381\pi$
$41$	−8.55777	−	7.18082i	−1.33650	−	1.12146i	−0.353989	−	0.935250i	$-0.615175\pi$
$42$	−7.18247	+	0.0737513i	−1.10828	+	0.0113801i
$43$	2.46761	+	0.898136i	0.376307	+	0.136965i	0.523247	−	0.852181i	$-0.324720\pi$
$43$	2.46761	+	0.898136i	0.376307	+	0.136965i	−0.146940	+	0.989145i	$0.546943\pi$
$44$	2.65688	−	4.60184i	0.400539	−	0.693754i
$45$	0.581502	+	2.94310i	0.0866852	+	0.438732i
$46$	0.678702	+	1.17555i	0.100069	+	0.173325i
$47$	1.91147	+	10.8405i	0.278817	+	1.58125i	0.726569	+	0.687093i	$0.241114\pi$
$47$	1.91147	+	10.8405i	0.278817	+	1.58125i	−0.447752	+	0.894158i	$0.647775\pi$
$48$	1.62143	−	0.609077i	0.234033	−	0.0879126i
$49$	−9.58275	+	3.48784i	−1.36896	+	0.498262i
$50$	−0.173648	+	0.984808i	−0.0245576	+	0.139273i
$51$	1.10331	+	5.90217i	0.154495	+	0.826469i
$52$	−1.76311	+	1.47942i	−0.244499	+	0.205159i
$53$	−6.23155			−0.855969			−0.427984	−	0.903786i	$-0.640776\pi$
$53$	−6.23155			−0.855969			−0.427984	+	0.903786i	$0.640776\pi$
$54$	−4.93520	−	1.62596i	−0.671596	−	0.221265i
$55$	−5.31375			−0.716506
$56$	3.17680	−	2.66565i	0.424518	−	0.356213i
$57$	−6.40243	−	2.25612i	−0.848022	−	0.298830i
$58$	−0.584872	+	3.31698i	−0.0767975	+	0.435540i
$59$	1.23587	−	0.449821i	0.160897	−	0.0585617i	−0.260316	−	0.965523i	$-0.583827\pi$
$59$	1.23587	−	0.449821i	0.160897	−	0.0585617i	0.421213	+	0.906962i	$0.361604\pi$
$60$	−1.33819	−	1.09966i	−0.172760	−	0.141965i
$61$	−1.19514	−	6.77800i	−0.153023	−	0.867834i	−0.960571	−	0.278033i	$-0.910317\pi$
$61$	−1.19514	−	6.77800i	−0.153023	−	0.867834i	0.807549	−	0.589801i	$-0.200794\pi$
$62$	3.81781	+	6.61264i	0.484862	+	0.839806i
$63$	−12.4384	+	0.255468i	−1.56709	+	0.0321860i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	2.16277	+	0.787183i	0.268258	+	0.0976381i
$66$	4.51976	−	8.01746i	0.556344	−	0.986881i
$67$	−4.32375	−	3.62806i	−0.528230	−	0.443238i	0.339260	−	0.940693i	$-0.389823\pi$
$67$	−4.32375	−	3.62806i	−0.528230	−	0.443238i	−0.867490	+	0.497455i	$0.834268\pi$
$68$	−2.65560	−	2.22832i	−0.322039	−	0.270223i
$69$	1.19639	+	2.02393i	0.144029	+	0.243652i
$70$	−3.89692	−	1.41836i	−0.465771	−	0.169527i
$71$	−0.424943	+	0.736023i	−0.0504314	+	0.0873498i	−0.890139	−	0.455689i	$-0.849393\pi$
$71$	−0.424943	+	0.736023i	−0.0504314	+	0.0873498i	0.839708	+	0.543039i	$0.182726\pi$
$72$	2.79741	−	1.08373i	0.329678	−	0.127719i
$73$	2.93911	+	5.09069i	0.343997	+	0.595821i	0.985171	−	0.171575i	$-0.0548856\pi$
$73$	2.93911	+	5.09069i	0.343997	+	0.595821i	−0.641174	+	0.767396i	$0.721552\pi$
$74$	2.03504	+	11.5413i	0.236569	+	1.34165i
$75$	−0.283238	+	1.70874i	−0.0327055	+	0.197308i
$76$	3.68287	−	1.34046i	0.422455	−	0.153761i
$77$	3.82655	−	21.7014i	0.436076	−	2.47311i
$78$	−3.02732	+	2.59365i	−0.342776	+	0.293673i
$79$	1.60439	−	1.34625i	0.180508	−	0.151464i	−0.548057	−	0.836441i	$-0.684632\pi$
$79$	1.60439	−	1.34625i	0.180508	−	0.151464i	0.728565	+	0.684977i	$0.240188\pi$
$80$	1.00000			0.111803
$81$	−8.57649	−	2.72833i	−0.952943	−	0.303148i
$82$	11.1714			1.23367
$83$	−10.3632	+	8.69578i	−1.13751	+	0.954485i	−0.999354	−	0.0359249i	$-0.988562\pi$
$83$	−10.3632	+	8.69578i	−1.13751	+	0.954485i	−0.138157	+	0.990410i	$0.544118\pi$
$84$	5.45468	−	4.67330i	0.595155	−	0.509898i
$85$	−0.601977	+	3.41398i	−0.0652935	+	0.370298i
$86$	−2.46761	+	0.898136i	−0.266089	+	0.0968485i
$87$	−0.953986	+	5.75527i	−0.102278	+	0.617030i
$88$	0.922723	+	5.23302i	0.0983626	+	0.557842i
$89$	0.216147	+	0.374377i	0.0229115	+	0.0396839i	0.877254	−	0.480027i	$-0.159373\pi$
$89$	0.216147	+	0.374377i	0.0229115	+	0.0396839i	−0.854342	+	0.519711i	$0.826040\pi$
$90$	−2.33725	−	1.88077i	−0.246367	−	0.198250i
$91$	−4.77233	+	8.26591i	−0.500276	+	0.866503i
$92$	−1.27554	−	0.464260i	−0.132985	−	0.0484024i
$93$	6.72989	+	11.3849i	0.697857	+	1.18056i
$94$	−8.43242	−	7.07564i	−0.869738	−	0.729796i
$95$	−3.00231	−	2.51923i	−0.308030	−	0.258468i
$96$	−0.850578	+	1.50881i	−0.0868118	+	0.153993i
$97$	13.1192	+	4.77498i	1.33205	+	0.484826i	0.907300	−	0.420485i	$-0.138140\pi$
$97$	13.1192	+	4.77498i	1.33205	+	0.484826i	0.424750	+	0.905311i	$0.360362\pi$
$98$	5.09887	−	8.83151i	0.515064	−	0.892117i
$99$	7.68546	−	13.9663i	0.772418	−	1.40366i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	0.887767	+	5.03478i	0.0883361	+	0.500979i	0.996587	+	0.0825523i	$0.0263072\pi$
$101$	0.887767	+	5.03478i	0.0883361	+	0.500979i	−0.908251	+	0.418427i	$0.862582\pi$
$102$	−4.63903	−	3.81213i	−0.459332	−	0.377457i
$103$	7.20009	−	2.62062i	0.709446	−	0.258217i	0.0380077	−	0.999277i	$-0.487899\pi$
$103$	7.20009	−	2.62062i	0.709446	−	0.258217i	0.671439	+	0.741060i	$0.265677\pi$
$104$	0.399664	−	2.26660i	0.0391902	−	0.222259i
$105$	−6.77453	−	2.38724i	−0.661127	−	0.232971i
$106$	4.77364	−	4.00556i	0.463657	−	0.389054i
$107$	9.64856			0.932762			0.466381	−	0.884584i	$-0.345558\pi$
$107$	9.64856			0.932762			0.466381	+	0.884584i	$0.345558\pi$
$108$	4.82573	−	1.92673i	0.464357	−	0.185400i
$109$	−7.37858			−0.706740			−0.353370	−	0.935484i	$-0.614964\pi$
$109$	−7.37858			−0.706740			−0.353370	+	0.935484i	$0.614964\pi$
$110$	4.07057	−	3.41561i	0.388114	−	0.325666i
$111$	3.72986	+	19.9529i	0.354023	+	1.89384i
$112$	−0.720122	+	4.08401i	−0.0680451	+	0.385903i
$113$	−3.10269	+	1.12929i	−0.291876	+	0.106234i	−0.483808	−	0.875174i	$-0.660747\pi$
$113$	−3.10269	+	1.12929i	−0.291876	+	0.106234i	0.191932	+	0.981408i	$0.438525\pi$
$114$	6.35475	−	2.38711i	0.595177	−	0.223574i
$115$	0.235711	+	1.33678i	0.0219802	+	0.124656i
$116$	−1.68407	−	2.91690i	−0.156362	−	0.270827i
$117$	−5.19706	+	4.54594i	−0.480469	+	0.420272i
$118$	−0.657595	+	1.13899i	−0.0605365	+	0.104852i
$119$	−13.5092	−	4.91696i	−1.23839	−	0.450737i
$120$	1.73196	−	0.0177842i	0.158106	−	0.00162347i
$121$	13.2035	+	11.0791i	1.20032	+	1.00719i
$122$	5.27235	+	4.42402i	0.477336	+	0.400532i
$123$	19.3484	−	0.198674i	1.74458	−	0.0179138i
$124$	−7.17513	−	2.61153i	−0.644346	−	0.234523i
$125$	−0.500000	+	0.866025i	−0.0447214	+	0.0774597i
$126$	9.36418	−	8.19097i	0.834227	−	0.729709i
$127$	3.84212	+	6.65475i	0.340933	+	0.590514i	0.984606	−	0.174787i	$-0.0559237\pi$
$127$	3.84212	+	6.65475i	0.340933	+	0.590514i	−0.643673	+	0.765301i	$0.722590\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	−4.25783	+	1.59942i	−0.374881	+	0.140821i
$130$	−2.16277	+	0.787183i	−0.189687	+	0.0690406i
$131$	0.192737	−	1.09307i	0.0168395	−	0.0955017i	−0.975230	−	0.221195i	$-0.929004\pi$
$131$	0.192737	−	1.09307i	0.0168395	−	0.0955017i	0.992069	+	0.125693i	$0.0401155\pi$
$132$	1.69118	+	9.04697i	0.147199	+	0.787438i
$133$	12.4506	−	10.4473i	1.07961	−	0.905896i
$134$	5.64425			0.487589
$135$	−4.08146	−	3.21584i	−0.351276	−	0.276776i
$136$	3.46665			0.297262
$137$	6.57766	−	5.51931i	0.561967	−	0.471546i	−0.317002	−	0.948425i	$-0.602676\pi$
$137$	6.57766	−	5.51931i	0.561967	−	0.471546i	0.878969	+	0.476878i	$0.158232\pi$
$138$	−2.21745	−	0.781395i	−0.188762	−	0.0665167i
$139$	−0.448276	+	2.54230i	−0.0380223	+	0.215635i	−0.997899	−	0.0647868i	$-0.979363\pi$
$139$	−0.448276	+	2.54230i	−0.0380223	+	0.215635i	0.959877	+	0.280422i	$0.0904744\pi$
$140$	3.89692	−	1.41836i	0.329350	−	0.119874i
$141$	−14.7304	−	12.1048i	−1.24053	−	1.01940i
$142$	−0.147581	−	0.836974i	−0.0123847	−	0.0702373i
$143$	−6.11499	−	10.5915i	−0.511361	−	0.885703i
$144$	−1.44633	+	2.62833i	−0.120528	+	0.219027i
$145$	−1.68407	+	2.91690i	−0.139855	+	0.242235i
$146$	−5.52373	−	2.01047i	−0.457147	−	0.166388i
$147$	8.67398	−	15.3865i	0.715418	−	1.26906i
$148$	−8.97754	−	7.53305i	−0.737949	−	0.619213i
$149$	9.22757	+	7.74285i	0.755952	+	0.634319i	0.937070	−	0.349142i	$-0.113527\pi$
$149$	9.22757	+	7.74285i	0.755952	+	0.634319i	−0.181118	+	0.983461i	$0.557972\pi$
$150$	−0.881381	−	1.49103i	−0.0719645	−	0.121742i
$151$	5.27168	+	1.91873i	0.429003	+	0.156144i	0.547492	−	0.836811i	$-0.315583\pi$
$151$	5.27168	+	1.91873i	0.429003	+	0.156144i	−0.118489	+	0.992955i	$0.537805\pi$
$152$	−1.95962	+	3.39416i	−0.158946	+	0.275302i
$153$	−8.10241	−	6.51995i	−0.655041	−	0.527107i
$154$	11.0181	+	19.0839i	0.887864	+	1.53783i
$155$	1.32591	+	7.51961i	0.106500	+	0.603990i
$156$	0.651891	−	3.93277i	0.0521931	−	0.314874i
$157$	−21.2491	+	7.73403i	−1.69586	+	0.617243i	−0.995343	−	0.0963927i	$-0.969270\pi$
$157$	−21.2491	+	7.73403i	−1.69586	+	0.617243i	−0.700517	+	0.713636i	$0.747047\pi$
$158$	−0.363686	+	2.06257i	−0.0289333	+	0.164089i
$159$	8.19652	−	7.02236i	0.650026	−	0.556910i
$160$	−0.766044	+	0.642788i	−0.0605611	+	0.0508168i
$161$	−5.62918			−0.443642
$162$	8.32371	−	3.42284i	0.653973	−	0.268924i
$163$	23.8620			1.86902			0.934509	−	0.355941i	$-0.115840\pi$
$163$	23.8620			1.86902			0.934509	+	0.355941i	$0.115840\pi$
$164$	−8.55777	+	7.18082i	−0.668250	+	0.560728i
$165$	6.98932	−	5.98810i	0.544118	−	0.466173i
$166$	2.34915	−	13.3227i	0.182330	−	1.03404i
$167$	−15.3777	+	5.59703i	−1.18996	+	0.433111i	−0.859711	−	0.510782i	$-0.829356\pi$
$167$	−15.3777	+	5.59703i	−1.18996	+	0.433111i	−0.330252	+	0.943893i	$0.607134\pi$
$168$	−1.17459	+	7.08615i	−0.0906217	+	0.546709i
$169$	−1.33757	−	7.58575i	−0.102890	−	0.583519i
$170$	−1.73332	−	3.00220i	−0.132940	−	0.230258i
$171$	10.9637	−	4.24740i	0.838416	−	0.324807i
$172$	1.31299	−	2.27416i	0.100114	−	0.173403i
$173$	−13.1963	−	4.80306i	−1.00330	−	0.365170i	−0.212442	−	0.977174i	$-0.568142\pi$
$173$	−13.1963	−	4.80306i	−1.00330	−	0.365170i	−0.790855	+	0.612003i	$0.790364\pi$
$174$	−2.96862	−	5.02200i	−0.225051	−	0.380717i
$175$	−3.17680	−	2.66565i	−0.240143	−	0.201504i
$176$	−4.07057	−	3.41561i	−0.306831	−	0.257462i
$177$	−1.11867	+	1.98438i	−0.0840845	+	0.149155i
$178$	−0.406223	−	0.147853i	−0.0304477	−	0.0110821i
$179$	−6.04923	+	10.4776i	−0.452140	+	0.783130i	−0.998519	−	0.0544083i	$-0.982673\pi$
$179$	−6.04923	+	10.4776i	−0.452140	+	0.783130i	0.546378	+	0.837538i	$0.316006\pi$
$180$	2.99937	−	0.0616029i	0.223560	−	0.00459161i
$181$	1.60081	+	2.77268i	0.118987	+	0.206092i	0.919367	−	0.393402i	$-0.128702\pi$
$181$	1.60081	+	2.77268i	0.118987	+	0.206092i	−0.800379	+	0.599494i	$0.795369\pi$
$182$	−1.65741	−	9.39965i	−0.122856	−	0.696748i
$183$	9.21017	+	7.56847i	0.680835	+	0.559477i
$184$	1.27554	−	0.464260i	0.0940343	−	0.0342257i
$185$	−2.03504	+	11.5413i	−0.149619	+	0.848534i
$186$	−12.4735	−	4.39547i	−0.914600	−	0.322291i
$187$	14.1112	−	11.8407i	1.03191	−	0.865879i
$188$	11.0077			0.802822
$189$	16.0727	−	14.3530i	1.16912	−	1.04402i
$190$	3.91923			0.284331
$191$	14.3537	−	12.0442i	1.03860	−	0.871486i	0.0467475	−	0.998907i	$-0.485114\pi$
$191$	14.3537	−	12.0442i	1.03860	−	0.871486i	0.991849	+	0.127421i	$0.0406699\pi$
$192$	−0.318266	−	1.70256i	−0.0229688	−	0.122872i
$193$	−3.62795	+	20.5751i	−0.261146	+	1.48103i	0.518645	+	0.854990i	$0.326437\pi$
$193$	−3.62795	+	20.5751i	−0.261146	+	1.48103i	−0.779791	+	0.626041i	$0.784674\pi$
$194$	−13.1192	+	4.77498i	−0.941901	+	0.342824i
$195$	−3.73183	+	1.40183i	−0.267242	+	0.100387i
$196$	1.77082	+	10.0428i	0.126487	+	0.717344i
$197$	2.34408	+	4.06006i	0.167009	+	0.289268i	0.937367	−	0.348344i	$-0.113256\pi$
$197$	2.34408	+	4.06006i	0.167009	+	0.289268i	−0.770358	+	0.637611i	$0.779923\pi$
$198$	3.08996	+	15.6389i	0.219594	+	1.11141i
$199$	−7.57305	+	13.1169i	−0.536840	+	0.929833i	0.462232	+	0.886759i	$0.347049\pi$
$199$	−7.57305	+	13.1169i	−0.536840	+	0.929833i	−0.999072	+	0.0430745i	$0.986285\pi$
$200$	0.939693	+	0.342020i	0.0664463	+	0.0241845i
$201$	9.77562	−	0.100378i	0.689519	−	0.00708014i
$202$	−3.91636	−	3.28622i	−0.275554	−	0.231217i
$203$	−10.6999	−	8.97830i	−0.750988	−	0.630153i
$204$	6.00409	−	0.0616514i	0.420370	−	0.00431646i
$205$	10.4977	+	3.82084i	0.733188	+	0.266859i
$206$	−3.83109	+	6.63564i	−0.266925	+	0.462327i
$207$	−3.85442	−	1.31391i	−0.267901	−	0.0913229i
$208$	1.15079	+	1.99322i	0.0797926	+	0.138205i
$209$	3.61637	+	20.5094i	0.250149	+	1.41867i
$210$	6.72409	−	2.52585i	0.464006	−	0.174300i
$211$	−10.1459	+	3.69280i	−0.698471	+	0.254223i	−0.666758	−	0.745274i	$-0.732318\pi$
$211$	−10.1459	+	3.69280i	−0.698471	+	0.254223i	−0.0317131	+	0.999497i	$0.510096\pi$
$212$	−1.08210	+	6.13687i	−0.0743187	+	0.421482i
$213$	−0.270489	−	1.44698i	−0.0185336	−	0.0991455i
$214$	−7.39123	+	6.20198i	−0.505254	+	0.423958i
$215$	−2.62598			−0.179090
$216$	−2.45825	+	4.57788i	−0.167263	+	0.311485i
$217$	−31.6650			−2.14956
$218$	5.65232	−	4.74286i	0.382823	−	0.321227i
$219$	−9.60262	−	3.38382i	−0.648885	−	0.228657i
$220$	−0.922723	+	5.23302i	−0.0622100	+	0.352810i
$221$	−7.49755	+	2.72889i	−0.504340	+	0.183565i
$222$	−15.6827	−	12.8873i	−1.05255	−	0.864938i
$223$	−4.09799	−	23.2408i	−0.274421	−	1.55632i	−0.740793	−	0.671733i	$-0.765550\pi$
$223$	−4.09799	−	23.2408i	−0.274421	−	1.55632i	0.466372	−	0.884589i	$-0.345561\pi$
$224$	−2.07351	−	3.59142i	−0.138542	−	0.239962i
$225$	−1.55303	−	2.56673i	−0.103536	−	0.171115i
$226$	1.65091	−	2.85945i	0.109817	−	0.190208i
$227$	−2.65926	−	0.967893i	−0.176502	−	0.0642413i	0.252258	−	0.967660i	$-0.418827\pi$
$227$	−2.65926	−	0.967893i	−0.176502	−	0.0642413i	−0.428759	+	0.903419i	$0.641049\pi$
$228$	−3.33361	+	5.91339i	−0.220774	+	0.391624i
$229$	10.6984	+	8.97704i	0.706971	+	0.593219i	0.923748	−	0.383002i	$-0.125110\pi$
$229$	10.6984	+	8.97704i	0.706971	+	0.593219i	−0.216776	+	0.976221i	$0.569554\pi$
$230$	−1.03983	−	0.872523i	−0.0685645	−	0.0575325i
$231$	19.4223	+	32.8566i	1.27789	+	2.16181i
$232$	3.16502	+	1.15197i	0.207794	+	0.0756308i
$233$	4.18924	−	7.25597i	0.274446	−	0.475354i	−0.695549	−	0.718478i	$-0.744839\pi$
$233$	4.18924	−	7.25597i	0.274446	−	0.475354i	0.969995	+	0.243124i	$0.0781722\pi$
$234$	1.05911	−	6.82300i	0.0692361	−	0.446033i
$235$	−5.50387	−	9.53298i	−0.359033	−	0.621863i
$236$	−0.228380	−	1.29521i	−0.0148663	−	0.0843109i
$237$	−0.593209	+	3.57875i	−0.0385331	+	0.232465i
$238$	13.5092	−	4.91696i	0.875674	−	0.318719i
$239$	0.676069	−	3.83418i	0.0437313	−	0.248012i	−0.955104	−	0.296272i	$-0.904256\pi$
$239$	0.676069	−	3.83418i	0.0437313	−	0.248012i	0.998835	+	0.0482598i	$0.0153675\pi$
$240$	−1.31533	+	1.12691i	−0.0849040	+	0.0727414i
$241$	−15.7535	+	13.2188i	−1.01477	+	0.851496i	−0.988962	−	0.148170i	$-0.952662\pi$
$241$	−15.7535	+	13.2188i	−1.01477	+	0.851496i	−0.0258120	+	0.999667i	$0.508217\pi$
$242$	−17.2359			−1.10797
$243$	14.3555	−	6.07625i	0.920903	−	0.389792i
$244$	−6.88256			−0.440611
$245$	7.81193	−	6.55499i	0.499086	−	0.418783i
$246$	−14.6940	+	12.5891i	−0.936856	+	0.802651i
$247$	1.56637	−	8.88335i	0.0996660	−	0.565234i
$248$	7.17513	−	2.61153i	0.455621	−	0.165833i
$249$	3.83170	−	23.1162i	0.242824	−	1.46493i
$250$	−0.173648	−	0.984808i	−0.0109825	−	0.0622847i
$251$	−6.96101	−	12.0568i	−0.439375	−	0.761020i	0.558266	−	0.829662i	$-0.311467\pi$
$251$	−6.96101	−	12.0568i	−0.439375	−	0.761020i	−0.997641	+	0.0686421i	$0.978133\pi$
$252$	−1.90832	+	12.2938i	−0.120213	+	0.774438i
$253$	3.60646	−	6.24656i	0.226736	−	0.392718i
$254$	−7.22083	−	2.62817i	−0.453075	−	0.164906i
$255$	−3.05544	−	5.16887i	−0.191339	−	0.323687i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−14.9992	−	12.5858i	−0.935623	−	0.785081i	0.0411949	−	0.999151i	$-0.486884\pi$
$257$	−14.9992	−	12.5858i	−0.935623	−	0.785081i	−0.976818	+	0.214070i	$0.931328\pi$
$258$	2.23360	−	3.96211i	0.139058	−	0.246670i
$259$	−45.6694	−	16.6223i	−2.83776	−	1.03286i
$260$	1.15079	−	1.99322i	0.0713687	−	0.123614i
$261$	−5.23084	−	8.64511i	−0.323781	−	0.535119i
$262$	0.554965	+	0.961227i	0.0342858	+	0.0593848i
$263$	1.63261	+	9.25897i	0.100671	+	0.570933i	0.992861	+	0.119274i	$0.0380566\pi$
$263$	1.63261	+	9.25897i	0.100671	+	0.570933i	−0.892191	+	0.451659i	$0.850832\pi$
$264$	−7.11081	−	5.84331i	−0.437640	−	0.359631i
$265$	5.85574	−	2.13131i	0.359715	−	0.130926i
$266$	−2.82233	+	16.0062i	−0.173048	+	0.981403i
$267$	−0.706192	−	0.248851i	−0.0432182	−	0.0152295i
$268$	−4.32375	+	3.62806i	−0.264115	+	0.221619i
$269$	31.9051			1.94529			0.972644	−	0.232301i	$-0.0746254\pi$
$269$	31.9051			1.94529			0.972644	+	0.232301i	$0.0746254\pi$
$270$	5.19369	−	0.160035i	0.316078	−	0.00973942i
$271$	−13.2327			−0.803827			−0.401913	−	0.915678i	$-0.631655\pi$
$271$	−13.2327			−0.803827			−0.401913	+	0.915678i	$0.631655\pi$
$272$	−2.65560	+	2.22832i	−0.161020	+	0.135112i
$273$	−3.03773	−	16.2503i	−0.183852	−	0.983515i
$274$	−1.49103	+	8.45607i	−0.0900766	+	0.510850i
$275$	4.99329	−	1.81741i	0.301107	−	0.109594i
$276$	2.20093	−	0.826764i	0.132481	−	0.0497653i
$277$	1.00366	+	5.69204i	0.0603041	+	0.342002i	1.00000		9.54097e-6i	$-3.03698e-6\pi$
$277$	1.00366	+	5.69204i	0.0603041	+	0.342002i	−0.939696	+	0.342011i	$0.888892\pi$
$278$	−1.29076	−	2.23566i	−0.0774146	−	0.134086i
$279$	−21.6817	−	7.39094i	−1.29805	−	0.442484i
$280$	−2.07351	+	3.59142i	−0.123916	+	0.214629i
$281$	−12.2466	−	4.45740i	−0.730571	−	0.265906i	−0.0501645	−	0.998741i	$-0.515975\pi$
$281$	−12.2466	−	4.45740i	−0.730571	−	0.265906i	−0.680407	+	0.732835i	$0.738197\pi$
$282$	19.0650	−	0.195764i	1.13530	−	0.0116575i
$283$	12.2819	+	10.3058i	0.730084	+	0.612613i	0.930155	−	0.367168i	$-0.119673\pi$
$283$	12.2819	+	10.3058i	0.730084	+	0.612613i	−0.200070	+	0.979782i	$0.564117\pi$
$284$	0.651050	+	0.546296i	0.0386327	+	0.0324167i
$285$	6.78795	−	0.0697003i	0.402084	−	0.00412869i
$286$	11.4924	+	4.18290i	0.679561	+	0.247340i
$287$	−23.1639	+	40.1211i	−1.36732	+	2.36828i
$288$	−0.581502	−	2.94310i	−0.0342653	−	0.173424i
$289$	2.49118	+	4.31486i	0.146540	+	0.253815i
$290$	−0.584872	−	3.31698i	−0.0343449	−	0.194780i
$291$	−22.6369	+	8.50339i	−1.32700	+	0.498478i
$292$	5.52373	−	2.01047i	0.323252	−	0.117654i
$293$	−2.44881	+	13.8879i	−0.143061	+	0.811339i	0.825843	+	0.563901i	$0.190700\pi$
$293$	−2.44881	+	13.8879i	−0.143061	+	0.811339i	−0.968904	+	0.247438i	$0.920411\pi$
$294$	3.24559	+	17.3623i	0.189287	+	1.01259i
$295$	−1.00749	+	0.845388i	−0.0586585	+	0.0492204i
$296$	11.7193			0.681173
$297$	5.62980	+	27.0310i	0.326674	+	1.56850i
$298$	−12.0457			−0.697791
$299$	−2.39325	+	2.00817i	−0.138405	+	0.116136i
$300$	1.63359	+	0.575653i	0.0943155	+	0.0332354i
$301$	1.89102	−	10.7245i	0.108997	−	0.618151i
$302$	−5.27168	+	1.91873i	−0.303351	+	0.110411i
$303$	−6.84142	−	5.62194i	−0.393029	−	0.322972i
$304$	−0.680568	−	3.85969i	−0.0390332	−	0.221368i
$305$	3.44128	+	5.96047i	0.197047	+	0.341296i
$306$	10.3977	−	0.213556i	0.594400	−	0.0122082i
$307$	5.23802	−	9.07251i	0.298950	−	0.517796i	−0.676946	−	0.736032i	$-0.736697\pi$
$307$	5.23802	−	9.07251i	0.298950	−	0.517796i	0.975896	+	0.218237i	$0.0700304\pi$
$308$	−20.7073	−	7.53683i	−1.17991	−	0.429451i
$309$	−6.51728	+	11.5608i	−0.370755	+	0.657671i
$310$	−5.84922	−	4.90808i	−0.332213	−	0.278760i
$311$	10.0424	+	8.42659i	0.569453	+	0.477828i	0.881464	−	0.472250i	$-0.156558\pi$
$311$	10.0424	+	8.42659i	0.569453	+	0.477828i	−0.312011	+	0.950078i	$0.601003\pi$
$312$	2.02856	+	3.43171i	0.114845	+	0.194282i
$313$	12.5067	+	4.55205i	0.706918	+	0.257297i	0.670362	−	0.742034i	$-0.266139\pi$
$313$	12.5067	+	4.55205i	0.706918	+	0.257297i	0.0365565	+	0.999332i	$0.488361\pi$
$314$	11.3064	−	19.5833i	0.638057	−	1.10515i
$315$	11.6009	−	4.49425i	0.653638	−	0.253223i
$316$	−1.04719	−	1.81379i	−0.0589092	−	0.102034i
$317$	0.0689750	+	0.391177i	0.00387402	+	0.0219707i	0.986683	−	0.162652i	$-0.0520048\pi$
$317$	0.0689750	+	0.391177i	0.00387402	+	0.0219707i	−0.982809	+	0.184623i	$0.940894\pi$
$318$	−1.76501	+	10.6481i	−0.0989767	+	0.597114i
$319$	16.8181	−	6.12130i	0.941635	−	0.342727i
$320$	0.173648	−	0.984808i	0.00970723	−	0.0550524i
$321$	−12.6910	+	10.8730i	−0.708343	+	0.606873i
$322$	4.31220	−	3.61837i	0.240310	−	0.201644i
$323$	13.5866			0.755978
$324$	−4.17617	+	7.97243i	−0.232010	+	0.442913i
$325$	−2.30157			−0.127668
$326$	−18.2794	+	15.3382i	−1.01240	+	0.849505i
$327$	9.70524	−	8.31496i	0.536701	−	0.459819i
$328$	1.93989	−	11.0017i	0.107112	−	0.607465i
$329$	42.8963	−	15.6130i	2.36495	−	0.860771i
$330$	−1.50505	+	9.07979i	−0.0828505	+	0.499826i
$331$	2.37361	+	13.4614i	0.130465	+	0.739906i	0.977911	+	0.209023i	$0.0670284\pi$
$331$	2.37361	+	13.4614i	0.130465	+	0.739906i	−0.847445	+	0.530883i	$0.821860\pi$
$332$	6.76411	+	11.7158i	0.371229	+	0.642987i
$333$	−27.3910	−	22.0413i	−1.50102	−	1.20786i
$334$	8.18231	−	14.1722i	0.447716	−	0.775467i
$335$	5.30386	+	1.93045i	0.289781	+	0.105472i
$336$	−3.65510	−	6.18332i	−0.199402	−	0.337328i
$337$	16.0013	+	13.4267i	0.871645	+	0.731397i	0.964444	−	0.264288i	$-0.0851370\pi$
$337$	16.0013	+	13.4267i	0.871645	+	0.731397i	−0.0927991	+	0.995685i	$0.529581\pi$
$338$	5.90067	+	4.95125i	0.320954	+	0.269312i
$339$	2.80845	−	4.98181i	0.152534	−	0.270575i
$340$	3.25758	+	1.18566i	0.176667	+	0.0643016i
$341$	20.2869	−	35.1379i	1.09860	−	1.90282i
$342$	−5.66852	+	10.3010i	−0.306518	+	0.557016i
$343$	6.63056	+	11.4845i	0.358017	+	0.620103i
$344$	0.455996	+	2.58608i	0.0245856	+	0.139432i
$345$	−1.81646	−	1.49268i	−0.0977952	−	0.0803633i
$346$	13.1963	−	4.80306i	0.709438	−	0.258214i
$347$	2.70557	−	15.3441i	0.145243	−	0.823712i	−0.821929	−	0.569590i	$-0.807102\pi$
$347$	2.70557	−	15.3441i	0.145243	−	0.823712i	0.967172	−	0.254123i	$-0.0817867\pi$
$348$	5.50218	+	1.93888i	0.294948	+	0.103935i
$349$	4.50780	−	3.78249i	0.241297	−	0.202472i	−0.514117	−	0.857720i	$-0.671880\pi$
$349$	4.50780	−	3.78249i	0.241297	−	0.202472i	0.755414	+	0.655248i	$0.227436\pi$
$350$	4.14702			0.221667
$351$	1.71299	−	11.8360i	0.0914327	−	0.631759i
$352$	5.31375			0.283224
$353$	16.9610	−	14.2320i	0.902743	−	0.757491i	−0.0679815	−	0.997687i	$-0.521656\pi$
$353$	16.9610	−	14.2320i	0.902743	−	0.757491i	0.970725	+	0.240195i	$0.0772114\pi$
$354$	−0.418580	−	2.23919i	−0.0222473	−	0.119011i
$355$	0.147581	−	0.836974i	0.00783279	−	0.0444220i
$356$	0.406223	−	0.147853i	0.0215298	−	0.00783620i
$357$	23.3100	−	8.75623i	1.23370	−	0.463429i
$358$	−2.10087	−	11.9147i	−0.111035	−	0.629709i
$359$	5.22927	+	9.05736i	0.275990	+	0.478029i	0.970385	−	0.241565i	$-0.0776609\pi$
$359$	5.22927	+	9.05736i	0.275990	+	0.478029i	−0.694394	+	0.719595i	$0.744328\pi$
$360$	−2.25805	+	1.97515i	−0.119010	+	0.104099i
$361$	1.81981	−	3.15200i	0.0957793	−	0.165895i
$362$	−3.00854	−	1.09502i	−0.158125	−	0.0575528i
$363$	−29.8520	+	0.306527i	−1.56682	+	0.0160885i
$364$	7.31163	+	6.13518i	0.383233	+	0.321571i
$365$	−4.50298	−	3.77845i	−0.235697	−	0.197773i
$366$	−11.9203	+	0.122401i	−0.623085	+	0.00639798i
$367$	−10.7652	−	3.91820i	−0.561937	−	0.204528i	0.0454051	−	0.998969i	$-0.485542\pi$
$367$	−10.7652	−	3.91820i	−0.561937	−	0.204528i	−0.607342	+	0.794440i	$0.707764\pi$
$368$	−0.678702	+	1.17555i	−0.0353798	+	0.0612796i
$369$	−25.2255	+	22.0651i	−1.31319	+	1.14866i
$370$	−5.85967	−	10.1493i	−0.304630	−	0.527634i
$371$	4.48747	+	25.4497i	0.232978	+	1.32128i
$372$	12.3806	−	4.65067i	0.641904	−	0.241126i
$373$	33.3881	−	12.1523i	1.72877	−	0.629221i	0.730229	−	0.683202i	$-0.239413\pi$
$373$	33.3881	−	12.1523i	1.72877	−	0.629221i	0.998542	+	0.0539809i	$0.0171910\pi$
$374$	−3.19875	+	18.1410i	−0.165404	+	0.938051i
$375$	−0.318266	−	1.70256i	−0.0164352	−	0.0879198i
$376$	−8.43242	+	7.07564i	−0.434869	+	0.364898i
$377$	−7.75203			−0.399250
$378$	−3.08650	+	21.3263i	−0.158753	+	1.09691i
$379$	−11.4059			−0.585882			−0.292941	−	0.956131i	$-0.594634\pi$
$379$	−11.4059			−0.585882			−0.292941	+	0.956131i	$0.594634\pi$
$380$	−3.00231	+	2.51923i	−0.154015	+	0.129234i
$381$	−12.5529	−	4.42346i	−0.643106	−	0.226621i
$382$	−3.25372	+	18.4527i	−0.166475	+	0.944124i
$383$	7.92605	−	2.88484i	0.405002	−	0.147409i	−0.131483	−	0.991318i	$-0.541974\pi$
$383$	7.92605	−	2.88484i	0.405002	−	0.147409i	0.536485	+	0.843910i	$0.319752\pi$
$384$	1.33819	+	1.09966i	0.0682892	+	0.0561167i
$385$	3.82655	+	21.7014i	0.195019	+	1.10601i
$386$	−10.4463	−	18.0935i	−0.531701	−	0.920933i
$387$	3.79804	−	6.90193i	0.193065	−	0.350845i
$388$	6.98056	−	12.0907i	0.354384	−	0.613812i
$389$	−5.62049	−	2.04569i	−0.284970	−	0.103721i	0.195580	−	0.980688i	$-0.437341\pi$
$389$	−5.62049	−	2.04569i	−0.284970	−	0.103721i	−0.480551	+	0.876967i	$0.659563\pi$
$390$	1.95767	−	3.47264i	0.0991303	−	0.175844i
$391$	−3.60473	−	3.02473i	−0.182299	−	0.152967i
$392$	−7.81193	−	6.55499i	−0.394562	−	0.331077i
$393$	0.978271	+	1.65494i	0.0493473	+	0.0834805i
$394$	−4.40543	−	1.60344i	−0.221942	−	0.0807804i
$395$	−1.04719	+	1.81379i	−0.0526900	+	0.0912618i
$396$	−12.4195	−	9.99392i	−0.624106	−	0.502213i
$397$	1.89353	+	3.27969i	0.0950336	+	0.164603i	0.909623	−	0.415436i	$-0.136371\pi$
$397$	1.89353	+	3.27969i	0.0950336	+	0.164603i	−0.814589	+	0.580039i	$0.803037\pi$
$398$	−2.63009	−	14.9160i	−0.131835	−	0.747672i
$399$	−4.60350	+	27.7723i	−0.230463	+	1.39035i
$400$	−0.939693	+	0.342020i	−0.0469846	+	0.0171010i
$401$	−0.554152	+	3.14275i	−0.0276731	+	0.156942i	−0.995513	−	0.0946252i	$-0.969835\pi$
$401$	−0.554152	+	3.14275i	−0.0276731	+	0.156942i	0.967840	+	0.251567i	$0.0809458\pi$
$402$	−7.42404	+	6.36054i	−0.370277	+	0.317235i
$403$	−13.4624	+	11.2963i	−0.670610	+	0.562708i
$404$	5.11244			0.254354
$405$	8.99241	−	0.369540i	0.446836	−	0.0183626i
$406$	13.9678			0.693208
$407$	47.7044	−	40.0288i	2.36462	−	1.98415i
$408$	−4.55977	+	3.90658i	−0.225742	+	0.193405i
$409$	5.53091	−	31.3674i	0.273486	−	1.55102i	−0.470244	−	0.882536i	$-0.655834\pi$
$409$	5.53091	−	31.3674i	0.273486	−	1.55102i	0.743730	−	0.668480i	$-0.233055\pi$
$410$	−10.4977	+	3.82084i	−0.518443	+	0.188698i
$411$	−2.43203	+	14.6721i	−0.119963	+	0.723721i
$412$	−1.33052	−	7.54577i	−0.0655502	−	0.371754i
$413$	−2.72706	−	4.72340i	−0.134190	−	0.232423i
$414$	3.79722	−	1.47106i	0.186623	−	0.0722988i
$415$	6.76411	−	11.7158i	0.332037	−	0.575105i
$416$	−2.16277	−	0.787183i	−0.106038	−	0.0385948i
$417$	−2.27530	−	3.84912i	−0.111422	−	0.188492i
$418$	−15.9535	−	13.3866i	−0.780312	−	0.654759i
$419$	23.7059	+	19.8916i	1.15811	+	0.971767i	0.999878	−	0.0156356i	$-0.00497716\pi$
$419$	23.7059	+	19.8916i	1.15811	+	0.971767i	0.158229	+	0.987402i	$0.449422\pi$
$420$	−3.52736	+	6.25707i	−0.172118	+	0.305314i
$421$	−13.0700	−	4.75709i	−0.636993	−	0.231846i	0.00327938	−	0.999995i	$-0.498956\pi$
$421$	−13.0700	−	4.75709i	−0.636993	−	0.231846i	−0.640272	+	0.768148i	$0.721178\pi$
$422$	5.39851	−	9.35049i	0.262795	−	0.455175i
$423$	33.0163	−	0.678109i	1.60531	−	0.0329708i
$424$	−3.11577	−	5.39668i	−0.151315	−	0.262086i
$425$	−0.601977	−	3.41398i	−0.0292002	−	0.165602i
$426$	1.13731	+	0.934584i	0.0551028	+	0.0452808i
$427$	−26.8208	+	9.76197i	−1.29795	+	0.472415i
$428$	1.67546	−	9.50198i	0.0809862	−	0.459295i
$429$	19.9788	+	7.04023i	0.964585	+	0.339905i
$430$	2.01161	−	1.68794i	0.0970086	−	0.0813999i
$431$	−36.8412			−1.77458			−0.887289	−	0.461214i	$-0.847414\pi$
$431$	−36.8412			−1.77458			−0.887289	+	0.461214i	$0.847414\pi$
$432$	−1.05948	−	5.08699i	−0.0509742	−	0.244748i
$433$	−30.6173			−1.47137			−0.735686	−	0.677323i	$-0.763140\pi$
$433$	−30.6173			−1.47137			−0.735686	+	0.677323i	$0.763140\pi$
$434$	24.2568	−	20.3539i	1.16436	−	0.977018i
$435$	−1.07197	−	5.73447i	−0.0513968	−	0.274947i
$436$	−1.28128	+	7.26648i	−0.0613620	+	0.348001i
$437$	4.99915	−	1.81954i	0.239142	−	0.0870405i
$438$	9.53111	−	3.58029i	0.455414	−	0.171073i
$439$	3.01220	+	17.0831i	0.143765	+	0.815330i	0.968351	+	0.249593i	$0.0802969\pi$
$439$	3.01220	+	17.0831i	0.143765	+	0.815330i	−0.824586	+	0.565736i	$0.808592\pi$
$440$	−2.65688	−	4.60184i	−0.126662	−	0.219384i
$441$	5.93001	+	30.0130i	0.282381	+	1.42919i
$442$	3.98937	−	6.90978i	0.189755	−	0.328665i
$443$	10.0498	+	3.65782i	0.477480	+	0.173788i	0.569538	−	0.821965i	$-0.307122\pi$
$443$	10.0498	+	3.65782i	0.477480	+	0.173788i	−0.0920579	+	0.995754i	$0.529344\pi$
$444$	20.2974	−	0.208419i	0.963274	−	0.00989112i
$445$	−0.331156	−	0.277873i	−0.0156983	−	0.0131724i
$446$	18.0782	+	15.1694i	0.856026	+	0.718291i
$447$	−20.8627	+	0.214223i	−0.986773	+	0.0101324i
$448$	3.89692	+	1.41836i	0.184112	+	0.0670114i
$449$	0.931298	−	1.61306i	0.0439507	−	0.0761248i	−0.843213	−	0.537579i	$-0.819339\pi$
$449$	0.931298	−	1.61306i	0.0439507	−	0.0761248i	0.887164	+	0.461454i	$0.152672\pi$
$450$	2.83955	+	0.967956i	0.133858	+	0.0456299i
$451$	−29.6810	−	51.4089i	−1.39762	−	2.42075i
$452$	0.573353	+	3.25165i	0.0269683	+	0.152945i
$453$	−9.09620	+	3.41692i	−0.427377	+	0.160541i
$454$	2.65926	−	0.967893i	0.124805	−	0.0454255i
$455$	1.65741	−	9.39965i	0.0777006	−	0.440662i
$456$	−1.24736	−	6.67272i	−0.0584128	−	0.312479i
$457$	−1.19059	+	0.999027i	−0.0556936	+	0.0467325i	−0.670210	−	0.742172i	$-0.733796\pi$
$457$	−1.19059	+	0.999027i	−0.0556936	+	0.0467325i	0.614516	+	0.788904i	$0.289351\pi$
$458$	−13.9658			−0.652579
$459$	18.0047	−	0.554785i	0.840386	−	0.0258951i
$460$	1.35740			0.0632893
$461$	13.7332	−	11.5235i	0.639617	−	0.536703i	−0.264283	−	0.964445i	$-0.585135\pi$
$461$	13.7332	−	11.5235i	0.639617	−	0.536703i	0.903901	+	0.427742i	$0.140691\pi$
$462$	−35.9982	−	12.6852i	−1.67479	−	0.590170i
$463$	1.77975	−	10.0935i	0.0827121	−	0.469084i	−0.915115	−	0.403194i	$-0.867900\pi$
$463$	1.77975	−	10.0935i	0.0827121	−	0.469084i	0.997827	−	0.0658903i	$-0.0209887\pi$
$464$	−3.16502	+	1.15197i	−0.146932	+	0.0534790i
$465$	−10.2179	−	8.39657i	−0.473844	−	0.389382i
$466$	1.45491	+	8.25119i	0.0673973	+	0.382229i
$467$	15.9660	+	27.6539i	0.738817	+	1.27967i	0.953028	+	0.302881i	$0.0979486\pi$
$467$	15.9660	+	27.6539i	0.738817	+	1.27967i	−0.214211	+	0.976787i	$0.568718\pi$
$468$	3.57442	+	5.90750i	0.165227	+	0.273074i
$469$	−11.7034	+	20.2709i	−0.540413	+	0.936023i
$470$	10.3439	+	3.76487i	0.477128	+	0.173660i
$471$	19.2339	−	34.1185i	0.886253	−	1.57210i
$472$	1.00749	+	0.845388i	0.0463737	+	0.0389121i
$473$	10.6892	+	8.96932i	0.491491	+	0.412410i
$474$	−1.84595	−	3.12279i	−0.0847874	−	0.143435i
$475$	3.68287	+	1.34046i	0.168982	+	0.0615044i
$476$	−7.18812	+	12.4502i	−0.329467	+	0.570653i
$477$	−2.86756	+	18.4734i	−0.131296	+	0.845839i
$478$	1.94666	+	3.37172i	0.0890383	+	0.154219i
$479$	−5.24255	−	29.7320i	−0.239538	−	1.35849i	−0.832842	−	0.553511i	$-0.813288\pi$
$479$	−5.24255	−	29.7320i	−0.239538	−	1.35849i	0.593303	−	0.804979i	$-0.297823\pi$
$480$	0.283238	−	1.70874i	0.0129280	−	0.0779927i
$481$	−25.3462	+	9.22528i	−1.15569	+	0.420636i
$482$	3.57103	−	20.2523i	0.162656	−	0.922469i
$483$	7.40421	−	6.34355i	0.336903	−	0.288642i
$484$	13.2035	−	11.0791i	0.600159	−	0.503593i
$485$	−13.9611			−0.633942
$486$	−7.09118	+	13.8822i	−0.321663	+	0.629709i
$487$	5.15830			0.233745			0.116873	−	0.993147i	$-0.462713\pi$
$487$	5.15830			0.233745			0.116873	+	0.993147i	$0.462713\pi$
$488$	5.27235	−	4.42402i	0.238668	−	0.200266i
$489$	−31.3863	+	26.8902i	−1.41934	+	1.21602i
$490$	−1.77082	+	10.0428i	−0.0799975	+	0.453688i
$491$	−5.43587	+	1.97849i	−0.245317	+	0.0892882i	−0.461753	−	0.887009i	$-0.652779\pi$
$491$	−5.43587	+	1.97849i	−0.245317	+	0.0892882i	0.216435	+	0.976297i	$0.430557\pi$
$492$	3.16415	−	19.0889i	0.142651	−	0.860595i
$493$	−2.02755	−	11.4988i	−0.0913161	−	0.517879i
$494$	4.51020	+	7.81189i	0.202923	+	0.351473i
$495$	−2.44522	+	15.7526i	−0.109904	+	0.708027i
$496$	−3.81781	+	6.61264i	−0.171425	+	0.296916i
$497$	3.31194	+	1.20545i	0.148561	+	0.0540717i
$498$	11.9235	+	20.1710i	0.534306	+	0.903883i
$499$	−11.6638	−	9.78713i	−0.522145	−	0.438132i	0.343234	−	0.939250i	$-0.388478\pi$
$499$	−11.6638	−	9.78713i	−0.522145	−	0.438132i	−0.865379	+	0.501118i	$0.832922\pi$
$500$	0.766044	+	0.642788i	0.0342585	+	0.0287463i
$501$	13.9194	−	24.6911i	0.621872	−	1.10312i
$502$	13.0824	+	4.76161i	0.583897	+	0.212521i
$503$	−13.2501	+	22.9499i	−0.590794	+	1.02328i	0.403332	+	0.915054i	$0.367852\pi$
$503$	−13.2501	+	22.9499i	−0.590794	+	1.02328i	−0.994126	+	0.108231i	$0.965481\pi$
$504$	−6.44046	−	10.6443i	−0.286881	−	0.474133i
$505$	−2.55622	−	4.42751i	−0.113750	−	0.197021i
$506$	1.25251	+	7.10333i	0.0556808	+	0.315782i
$507$	10.3078	+	8.47042i	0.457784	+	0.376185i
$508$	7.22083	−	2.62817i	0.320372	−	0.116606i
$509$	−4.17017	+	23.6502i	−0.184839	+	1.04828i	0.741322	+	0.671149i	$0.234199\pi$
$509$	−4.17017	+	23.6502i	−0.184839	+	1.04828i	−0.926162	+	0.377127i	$0.876912\pi$
$510$	5.66309	+	1.99559i	0.250766	+	0.0883661i
$511$	18.6739	−	15.6693i	0.826087	−	0.693169i
$512$	−1.00000			−0.0441942
$513$	−9.63445	+	17.9418i	−0.425371	+	0.792149i
$514$	19.5800			0.863639
$515$	−5.86957	+	4.92515i	−0.258644	+	0.217028i
$516$	0.835758	+	4.47088i	0.0367922	+	0.196819i
$517$	−10.1571	+	57.6038i	−0.446709	+	2.53341i
$518$	45.6694	−	16.6223i	2.00660	−	0.730342i
$519$	22.7701	−	8.55340i	0.999495	−	0.375453i
$520$	0.399664	+	2.26660i	0.0175264	+	0.0993972i
$521$	7.44260	+	12.8910i	0.326066	+	0.564763i	0.981728	−	0.190292i	$-0.0609435\pi$
$521$	7.44260	+	12.8910i	0.326066	+	0.564763i	−0.655661	+	0.755055i	$0.727610\pi$
$522$	9.56403	+	3.26022i	0.418606	+	0.142696i
$523$	1.21875	−	2.11093i	0.0532921	−	0.0923046i	−0.838149	−	0.545442i	$-0.816362\pi$
$523$	1.21875	−	2.11093i	0.0532921	−	0.0923046i	0.891441	+	0.453137i	$0.149695\pi$
$524$	−1.04299	−	0.379618i	−0.0455633	−	0.0165837i
$525$	7.18247	−	0.0737513i	0.313468	−	0.00321877i
$526$	−7.20220	−	6.04337i	−0.314031	−	0.263503i
$527$	−20.2772	−	17.0146i	−0.883288	−	0.741166i
$528$	9.20320	−	0.0945006i	0.400518	−	0.00411261i
$529$	19.8815	+	7.23627i	0.864413	+	0.314621i
$530$	−3.11577	+	5.39668i	−0.135341	+	0.234417i
$531$	−0.764785	−	3.87074i	−0.0331888	−	0.167976i
$532$	−8.12656	−	14.0756i	−0.352331	−	0.610255i
$533$	4.46479	+	25.3211i	0.193392	+	1.09678i
$534$	0.700933	−	0.263300i	0.0303323	−	0.0113941i
$535$	−9.06668	+	3.30000i	−0.391987	+	0.142672i
$536$	0.980114	−	5.55850i	0.0423345	−	0.240091i
$537$	−3.85052	−	20.5983i	−0.166162	−	0.888884i
$538$	−24.4407	+	20.5082i	−1.05371	+	0.884171i
$539$	−54.1883			−2.33406
$540$	−3.87573	+	3.46103i	−0.166785	+	0.148939i
$541$	33.0610			1.42140			0.710701	−	0.703494i	$-0.248378\pi$
$541$	33.0610			1.42140			0.710701	+	0.703494i	$0.248378\pi$
$542$	10.1368	−	8.50579i	0.435413	−	0.365355i
$543$	−5.23014	−	1.84302i	−0.224447	−	0.0790916i
$544$	0.601977	−	3.41398i	0.0258095	−	0.146373i
$545$	6.93360	−	2.52362i	0.297003	−	0.108100i
$546$	12.7726	+	10.4959i	0.546615	+	0.449181i
$547$	2.56848	+	14.5666i	0.109820	+	0.622823i	0.989185	+	0.146674i	$0.0468567\pi$
$547$	2.56848	+	14.5666i	0.109820	+	0.622823i	−0.879364	+	0.476149i	$0.842032\pi$
$548$	−4.29326	−	7.43615i	−0.183399	−	0.317656i
$549$	−20.6433	+	0.423986i	−0.881036	+	0.0180953i
$550$	−2.65688	+	4.60184i	−0.113290	+	0.196223i
$551$	12.4045	+	4.51485i	0.528448	+	0.192339i
$552$	−1.15458	+	2.04807i	−0.0491421	+	0.0871716i
$553$	−6.65344	−	5.58290i	−0.282933	−	0.237409i
$554$	−4.42762	−	3.71522i	−0.188112	−	0.157844i
$555$	−10.3292	−	17.4739i	−0.438451	−	0.741725i
$556$	2.42583	+	0.882932i	0.102878	+	0.0374446i
$557$	0.647453	−	1.12142i	0.0274335	−	0.0475162i	−0.851983	−	0.523570i	$-0.824600\pi$
$557$	0.647453	−	1.12142i	0.0274335	−	0.0475162i	0.879416	+	0.476054i	$0.157933\pi$
$558$	21.3600	−	8.27496i	0.904240	−	0.350307i
$559$	−3.02193	−	5.23414i	−0.127814	−	0.221381i
$560$	−0.720122	−	4.08401i	−0.0304307	−	0.172581i
$561$	−5.21749	+	31.4764i	−0.220283	+	1.32894i
$562$	12.2466	−	4.45740i	0.516592	−	0.188024i
$563$	−7.36454	+	41.7664i	−0.310378	+	1.76024i	0.286663	+	0.958031i	$0.407454\pi$
$563$	−7.36454	+	41.7664i	−0.310378	+	1.76024i	−0.597041	+	0.802211i	$0.703657\pi$
$564$	−14.4788	+	12.4047i	−0.609666	+	0.522331i
$565$	2.52933	−	2.12236i	0.106410	−	0.0892885i
$566$	−16.0329			−0.673913
$567$	−4.96643	+	36.9912i	−0.208570	+	1.55349i
$568$	−0.849886			−0.0356604
$569$	−28.1881	+	23.6526i	−1.18171	+	0.991568i	−0.181739	+	0.983347i	$0.558173\pi$
$569$	−28.1881	+	23.6526i	−1.18171	+	0.991568i	−0.999966	+	0.00822145i	$0.997383\pi$
$570$	−5.15507	+	4.41661i	−0.215922	+	0.184991i
$571$	2.21513	−	12.5627i	0.0927005	−	0.525731i	−0.902727	−	0.430213i	$-0.858438\pi$
$571$	2.21513	−	12.5627i	0.0927005	−	0.525731i	0.995428	−	0.0955174i	$-0.0304505\pi$
$572$	−11.4924	+	4.18290i	−0.480522	+	0.174896i
$573$	−5.30714	+	32.0173i	−0.221709	+	1.33754i
$574$	−8.04475	−	45.6241i	−0.335782	−	1.90431i
$575$	−0.678702	−	1.17555i	−0.0283038	−	0.0490237i
$576$	2.33725	+	1.88077i	0.0973853	+	0.0783652i
$577$	21.0070	−	36.3851i	0.874531	−	1.51473i	0.0172696	−	0.999851i	$-0.494503\pi$
$577$	21.0070	−	36.3851i	0.874531	−	1.51473i	0.857261	−	0.514881i	$-0.172164\pi$
$578$	−4.68189	−	1.70407i	−0.194741	−	0.0708799i
$579$	−18.4143	−	31.1514i	−0.765272	−	1.29461i
$580$	2.58015	+	2.16500i	0.107135	+	0.0898968i
$581$	42.9765	+	36.0615i	1.78296	+	1.49608i
$582$	11.8750	−	21.0647i	0.492236	−	0.873161i
$583$	−31.1159	−	11.3253i	−1.28869	−	0.469045i
$584$	−2.93911	+	5.09069i	−0.121621	+	0.210654i
$585$	3.32884	−	6.04929i	0.137631	−	0.250107i
$586$	−7.05106	−	12.2128i	−0.291277	−	0.504506i
$587$	−0.0119437	−	0.0677362i	−0.000492970	−	0.00279577i	0.984560	−	0.175046i	$-0.0560074\pi$
$587$	−0.0119437	−	0.0677362i	−0.000492970	−	0.00279577i	−0.985053	+	0.172250i	$0.944896\pi$
$588$	−13.6465	−	11.2140i	−0.562773	−	0.462459i
$589$	28.1210	−	10.2352i	1.15871	−	0.421734i
$590$	0.228380	−	1.29521i	0.00940227	−	0.0533229i
$591$	−7.65854	−	2.69875i	−0.315030	−	0.111012i
$592$	−8.97754	+	7.53305i	−0.368975	+	0.309606i
$593$	−21.2698			−0.873444			−0.436722	−	0.899597i	$-0.643861\pi$
$593$	−21.2698			−0.873444			−0.436722	+	0.899597i	$0.643861\pi$
$594$	−21.6879	−	17.0882i	−0.889865	−	0.701137i
$595$	14.3762			0.589368
$596$	9.22757	−	7.74285i	0.377976	−	0.317160i
$597$	−4.82049	−	25.7871i	−0.197289	−	1.05540i
$598$	0.542505	−	3.07670i	0.0221847	−	0.125816i
$599$	−15.9096	+	5.79061i	−0.650047	+	0.236598i	−0.645933	−	0.763394i	$-0.723532\pi$
$599$	−15.9096	+	5.79061i	−0.650047	+	0.236598i	−0.00411359	+	0.999992i	$0.501309\pi$
$600$	−1.62143	+	0.609077i	−0.0661945	+	0.0248655i
$601$	−2.58308	−	14.6494i	−0.105366	−	0.597562i	−0.991073	−	0.133317i	$-0.957437\pi$
$601$	−2.58308	−	14.6494i	−0.105366	−	0.597562i	0.885707	−	0.464244i	$-0.153674\pi$
$602$	5.44498	+	9.43099i	0.221921	+	0.384378i
$603$	−12.7450	+	11.1482i	−0.519017	+	0.453991i
$604$	2.80500	−	4.85840i	0.114134	−	0.197686i
$605$	−16.1965	−	5.89504i	−0.658481	−	0.239668i
$606$	8.85455	−	0.0909206i	0.359691	−	0.00369340i
$607$	11.3694	+	9.54005i	0.461469	+	0.387219i	0.843671	−	0.536860i	$-0.180390\pi$
$607$	11.3694	+	9.54005i	0.461469	+	0.387219i	−0.382202	+	0.924079i	$0.624834\pi$
$608$	3.00231	+	2.51923i	0.121760	+	0.102168i
$609$	24.1916	−	0.248405i	0.980293	−	0.0100659i
$610$	−6.46749	−	2.35397i	−0.261861	−	0.0953096i
$611$	12.6675	−	21.9408i	0.512474	−	0.887631i
$612$	−7.82786	+	6.84713i	−0.316423	+	0.276779i
$613$	0.849082	+	1.47065i	0.0342941	+	0.0593991i	0.882663	−	0.470006i	$-0.155748\pi$
$613$	0.849082	+	1.47065i	0.0342941	+	0.0593991i	−0.848369	+	0.529405i	$0.822415\pi$
$614$	1.81914	+	10.3169i	0.0734147	+	0.416356i
$615$	−18.1136	+	6.80423i	−0.730410	+	0.274373i
$616$	20.7073	−	7.53683i	0.834320	−	0.303668i
$617$	−1.48988	+	8.44950i	−0.0599801	+	0.340164i	−1.00000		0.000956789i	$-0.999695\pi$
$617$	−1.48988	+	8.44950i	−0.0599801	+	0.340164i	0.940019	+	0.341121i	$0.110807\pi$
$618$	−2.43861	−	13.0453i	−0.0980952	−	0.524759i
$619$	−35.4075	+	29.7104i	−1.42315	+	1.19416i	−0.473519	+	0.880784i	$0.657016\pi$
$619$	−35.4075	+	29.7104i	−1.42315	+	1.19416i	−0.949628	+	0.313379i	$0.898539\pi$
$620$	7.63561			0.306654
$621$	6.55047	−	2.61535i	0.262862	−	0.104950i
$622$	−13.1094			−0.525641
$623$	1.37331	−	1.15234i	0.0550205	−	0.0461677i
$624$	−3.75983	−	1.32491i	−0.150514	−	0.0530387i
$625$	0.173648	−	0.984808i	0.00694593	−	0.0393923i
$626$	−12.5067	+	4.55205i	−0.499867	+	0.181937i
$627$	−27.8689	−	22.9013i	−1.11298	−	0.914590i
$628$	3.92667	+	22.2693i	0.156691	+	0.888640i
$629$	−20.3134	−	35.1839i	−0.809949	−	1.40287i
$630$	−5.99797	+	10.8997i	−0.238965	+	0.434256i
$631$	−21.8953	+	37.9238i	−0.871639	+	1.50972i	−0.0113377	+	0.999936i	$0.503609\pi$
$631$	−21.8953	+	37.9238i	−0.871639	+	1.50972i	−0.860301	+	0.509787i	$0.829724\pi$
$632$	1.96808	+	0.716322i	0.0782860	+	0.0284938i
$633$	9.18371	−	16.2907i	0.365020	−	0.647496i
$634$	−0.304281	−	0.255322i	−0.0120846	−	0.0101401i
$635$	−5.88647	−	4.93934i	−0.233598	−	0.196012i
$636$	−5.49237	−	9.29141i	−0.217787	−	0.368429i
$637$	22.0554	+	8.02750i	0.873866	+	0.318061i
$638$	−8.94875	+	15.4997i	−0.354284	+	0.613638i
$639$	1.98639	+	1.59844i	0.0785805	+	0.0632332i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−5.52091	−	31.3106i	−0.218063	−	1.23669i	−0.875512	−	0.483196i	$-0.839476\pi$
$641$	−5.52091	−	31.3106i	−0.218063	−	1.23669i	0.657449	−	0.753499i	$-0.271635\pi$
$642$	2.73284	−	16.4868i	0.107856	−	0.650684i
$643$	−33.5941	+	12.2273i	−1.32482	+	0.482196i	−0.905001	−	0.425410i	$-0.860130\pi$
$643$	−33.5941	+	12.2273i	−1.32482	+	0.482196i	−0.419823	+	0.907606i	$0.637908\pi$
$644$	−0.977497	+	5.54366i	−0.0385188	+	0.218451i
$645$	3.45402	−	2.95923i	0.136002	−	0.116519i
$646$	−10.4079	+	8.73329i	−0.409495	+	0.343607i
$647$	−4.52870			−0.178042			−0.0890209	−	0.996030i	$-0.528374\pi$
$647$	−4.52870			−0.178042			−0.0890209	+	0.996030i	$0.528374\pi$
$648$	−1.92544	−	8.79163i	−0.0756385	−	0.345368i
$649$	6.98859			0.274326
$650$	1.76311	−	1.47942i	0.0691547	−	0.0580277i
$651$	41.6498	−	35.6835i	1.63239	−	1.39855i
$652$	4.14359	−	23.4995i	0.162276	−	0.920311i
$653$	−1.72649	+	0.628391i	−0.0675628	+	0.0245908i	−0.375580	−	0.926790i	$-0.622557\pi$
$653$	−1.72649	+	0.628391i	−0.0675628	+	0.0245908i	0.308018	+	0.951381i	$0.400334\pi$
$654$	−2.08989	+	12.6080i	−0.0817212	+	0.493013i
$655$	0.192737	+	1.09307i	0.00753087	+	0.0427097i
$656$	5.58569	+	9.67470i	0.218085	+	0.377733i
$657$	16.4438	−	6.37042i	0.641535	−	0.248534i
$658$	−22.8246	+	39.5334i	−0.889797	+	1.54117i
$659$	−20.5410	−	7.47630i	−0.800162	−	0.291235i	−0.0906087	−	0.995887i	$-0.528881\pi$
$659$	−20.5410	−	7.47630i	−0.800162	−	0.291235i	−0.709554	+	0.704651i	$0.751103\pi$
$660$	−4.68344	−	7.92296i	−0.182303	−	0.308401i
$661$	16.2061	+	13.5985i	0.630342	+	0.528920i	0.901035	−	0.433746i	$-0.142808\pi$
$661$	16.2061	+	13.5985i	0.630342	+	0.528920i	−0.270693	+	0.962666i	$0.587253\pi$
$662$	−10.4711	−	8.78631i	−0.406972	−	0.341490i
$663$	6.78653	−	12.0384i	0.263567	−	0.467533i
$664$	−12.7124	−	4.62693i	−0.493336	−	0.179560i
$665$	−8.12656	+	14.0756i	−0.315135	+	0.545829i
$666$	35.1506	−	0.721946i	1.36206	−	0.0279748i
$667$	−2.28597	−	3.95941i	−0.0885131	−	0.153309i
$668$	2.84169	+	16.1160i	0.109948	+	0.623547i
$669$	31.5804	+	25.9512i	1.22097	+	1.00333i
$670$	−5.30386	+	1.93045i	−0.204906	+	0.0745797i
$671$	6.35070	−	36.0166i	0.245166	−	1.39041i
$672$	6.77453	+	2.38724i	0.261333	+	0.0920899i
$673$	−9.74912	+	8.18048i	−0.375801	+	0.315334i	−0.811051	−	0.584975i	$-0.801104\pi$
$673$	−9.74912	+	8.18048i	−0.375801	+	0.315334i	0.435250	+	0.900309i	$0.356660\pi$
$674$	−20.8882			−0.804582
$675$	4.93520	+	1.62596i	0.189956	+	0.0625833i
$676$	−7.70277			−0.296260
$677$	−18.9360	+	15.8892i	−0.727770	+	0.610672i	−0.929523	−	0.368765i	$-0.879781\pi$
$677$	−18.9360	+	15.8892i	−0.727770	+	0.610672i	0.201752	+	0.979437i	$0.435336\pi$
$678$	1.05085	+	5.62153i	0.0403578	+	0.215893i
$679$	10.0537	−	57.0174i	0.385826	−	2.18813i
$680$	−3.25758	+	1.18566i	−0.124923	+	0.0454681i
$681$	4.58852	−	1.72364i	0.175833	−	0.0660502i
$682$	7.04556	+	39.9573i	0.269788	+	1.53005i
$683$	9.11940	+	15.7953i	0.348944	+	0.604389i	0.986062	−	0.166377i	$-0.0532070\pi$
$683$	9.11940	+	15.7953i	0.348944	+	0.604389i	−0.637118	+	0.770766i	$0.719874\pi$
$684$	−2.27904	−	11.5347i	−0.0871413	−	0.441041i
$685$	−4.29326	+	7.43615i	−0.164037	+	0.284121i
$686$	−12.4614	−	4.53557i	−0.475778	−	0.173169i
$687$	−24.1882	+	0.248370i	−0.922837	+	0.00947591i
$688$	−2.01161	−	1.68794i	−0.0766921	−	0.0643523i
$689$	10.9869	+	9.21908i	0.418566	+	0.351219i
$690$	2.35097	−	0.0241403i	0.0894999	−	0.000919006i
$691$	3.44263	+	1.25302i	0.130964	+	0.0476670i	0.406671	−	0.913575i	$-0.366690\pi$
$691$	3.44263	+	1.25302i	0.130964	+	0.0476670i	−0.275707	+	0.961242i	$0.588912\pi$
$692$	−7.02161	+	12.1618i	−0.266922	+	0.462322i
$693$	−62.5730	−	21.3301i	−2.37695	−	0.810263i
$694$	7.79038	+	13.4933i	0.295719	+	0.512200i
$695$	−0.448276	−	2.54230i	−0.0170041	−	0.0964349i
$696$	−5.46120	+	2.05146i	−0.207006	+	0.0777604i
$697$	−36.3917	+	13.2455i	−1.37843	+	0.501709i
$698$	−1.02183	+	5.79511i	−0.0386770	+	0.219348i
$699$	2.66658	+	14.2648i	0.100859	+	0.539546i
$700$	−3.17680	+	2.66565i	−0.120072	+	0.100752i
$701$	30.6535			1.15777			0.578884	−	0.815410i	$-0.303488\pi$
$701$	30.6535			1.15777			0.578884	+	0.815410i	$0.303488\pi$
$702$	6.29580	+	10.1680i	0.237620	+	0.383766i
$703$	45.9308			1.73231
$704$	−4.07057	+	3.41561i	−0.153415	+	0.128731i
$705$	17.9822	+	6.33664i	0.677247	+	0.238652i
$706$	−3.84475	+	21.8046i	−0.144699	+	0.820629i
$707$	19.9228	−	7.25130i	0.749274	−	0.272713i
$708$	1.75997	+	1.44626i	0.0661438	+	0.0543538i
$709$	3.99524	+	22.6581i	0.150044	+	0.850943i	0.963178	+	0.268866i	$0.0866488\pi$
$709$	3.99524	+	22.6581i	0.150044	+	0.850943i	−0.813133	+	0.582077i	$0.802240\pi$
$710$	0.424943	+	0.736023i	0.0159478	+	0.0276224i
$711$	−3.25265	−	5.37572i	−0.121984	−	0.201605i
$712$	−0.216147	+	0.374377i	−0.00810045	+	0.0140304i
$713$	−9.73956	−	3.54491i	−0.364749	−	0.132758i
$714$	−12.2281	+	21.6911i	−0.457626	+	0.811767i
$715$	9.36870	+	7.86127i	0.350370	+	0.293995i
$716$	9.26795	+	7.77674i	0.346360	+	0.290630i
$717$	3.43151	+	5.80506i	0.128152	+	0.216794i
$718$	−9.82782	−	3.57703i	−0.366771	−	0.133494i
$719$	11.2985	−	19.5696i	0.421363	−	0.729822i	−0.574710	−	0.818357i	$-0.694885\pi$
$719$	11.2985	−	19.5696i	0.421363	−	0.729822i	0.996073	+	0.0885350i	$0.0282185\pi$
$720$	0.460168	−	2.96450i	0.0171494	−	0.110480i
$721$	−15.8876	−	27.5181i	−0.591685	−	1.02483i
$722$	0.632012	+	3.58432i	0.0235211	+	0.133395i
$723$	5.82472	−	35.1397i	0.216624	−	1.30686i
$724$	3.00854	−	1.09502i	0.111811	−	0.0406960i
$725$	0.584872	−	3.31698i	0.0217216	−	0.123189i
$726$	22.6709	−	19.4233i	0.841396	−	0.720866i
$727$	−4.51934	+	3.79218i	−0.167613	+	0.140644i	−0.722736	−	0.691124i	$-0.757116\pi$
$727$	−4.51934	+	3.79218i	−0.167613	+	0.140644i	0.555123	+	0.831768i	$0.312671\pi$
$728$	−9.54465			−0.353748
$729$	−12.0348	+	24.1695i	−0.445732	+	0.895167i
$730$	5.87823			0.217563
$731$	6.97355	−	5.85151i	0.257926	−	0.216426i
$732$	9.05281	−	7.75599i	0.334602	−	0.286670i
$733$	6.31471	−	35.8125i	0.233239	−	1.32276i	−0.613052	−	0.790043i	$-0.710058\pi$
$733$	6.31471	−	35.8125i	0.233239	−	1.32276i	0.846291	−	0.532721i	$-0.178831\pi$
$734$	10.7652	−	3.91820i	0.397350	−	0.144623i
$735$	−2.88839	+	17.4253i	−0.106540	+	0.642740i
$736$	−0.235711	−	1.33678i	−0.00868842	−	0.0492745i
$737$	−14.9961	−	25.9740i	−0.552388	−	0.956764i
$738$	5.14071	−	33.1175i	0.189232	−	1.21907i
$739$	−2.89605	+	5.01611i	−0.106533	+	0.184521i	−0.914364	−	0.404894i	$-0.867308\pi$
$739$	−2.89605	+	5.01611i	−0.106533	+	0.184521i	0.807830	+	0.589415i	$0.200642\pi$
$740$	11.0126	+	4.00825i	0.404831	+	0.147346i
$741$	7.95040	+	13.4497i	0.292065	+	0.494086i
$742$	−19.7964	−	16.6111i	−0.726748	−	0.609814i
$743$	−35.9534	−	30.1685i	−1.31900	−	1.10677i	−0.986516	−	0.163665i	$-0.947668\pi$
$743$	−35.9534	−	30.1685i	−1.31900	−	1.10677i	−0.332485	−	0.943108i	$-0.607887\pi$
$744$	−6.49469	+	11.5207i	−0.238107	+	0.422370i
$745$	−11.3193	−	4.11988i	−0.414707	−	0.150941i
$746$	−17.7654	+	30.7707i	−0.650439	+	1.12659i
$747$	21.0098	+	34.7233i	0.768708	+	1.27046i
$748$	−9.21045	−	15.9530i	−0.336767	−	0.583298i
$749$	−6.94814	−	39.4049i	−0.253880	−	1.43982i
$750$	1.33819	+	1.09966i	0.0488638	+	0.0401539i
$751$	43.3786	−	15.7885i	1.58291	−	0.576132i	0.607075	−	0.794645i	$-0.292343\pi$
$751$	43.3786	−	15.7885i	1.58291	−	0.576132i	0.975834	+	0.218513i	$0.0701207\pi$
$752$	1.91147	−	10.8405i	0.0697043	−	0.395313i
$753$	22.7429	+	8.01425i	0.828797	+	0.292056i
$754$	5.93840	−	4.98291i	0.216264	−	0.181467i
$755$	−5.61000			−0.204169
$756$	−11.3439	−	18.3209i	−0.412574	−	0.666324i
$757$	−17.9021			−0.650664			−0.325332	−	0.945600i	$-0.605476\pi$
$757$	−17.9021			−0.650664			−0.325332	+	0.945600i	$0.605476\pi$
$758$	8.73743	−	7.33158i	0.317358	−	0.266295i
$759$	2.29562	+	12.2804i	0.0833258	+	0.445750i
$760$	0.680568	−	3.85969i	0.0246868	−	0.140006i
$761$	−22.5316	+	8.20082i	−0.816769	+	0.297280i	−0.716417	−	0.697672i	$-0.754219\pi$
$761$	−22.5316	+	8.20082i	−0.816769	+	0.297280i	−0.100352	+	0.994952i	$0.531997\pi$
$762$	12.4594	−	4.68029i	0.451358	−	0.169549i
$763$	5.31348	+	30.1342i	0.192361	+	1.09093i
$764$	−9.36870	−	16.2271i	−0.338948	−	0.587075i
$765$	9.84372	+	3.35556i	0.355901	+	0.121321i
$766$	−4.21736	+	7.30468i	−0.152379	+	0.263929i
$767$	−2.84445	−	1.03530i	−0.102707	−	0.0373824i
$768$	−1.73196	+	0.0177842i	−0.0624967	+	0.000641731i
$769$	30.6223	+	25.6951i	1.10427	+	0.926590i	0.997705	−	0.0677160i	$-0.0215712\pi$
$769$	30.6223	+	25.6951i	1.10427	+	0.926590i	0.106562	+	0.994306i	$0.466016\pi$
$770$	−16.8807	−	14.1646i	−0.608339	−	0.510457i
$771$	33.9118	−	0.348215i	1.22131	−	0.0125407i
$772$	19.6326	+	7.14567i	0.706591	+	0.257178i
$773$	15.9011	−	27.5414i	0.571921	−	0.990597i	−0.424447	−	0.905453i	$-0.639532\pi$
$773$	15.9011	−	27.5414i	0.571921	−	0.990597i	0.996369	−	0.0851440i	$-0.0271350\pi$
$774$	1.52701	+	7.72852i	0.0548872	+	0.277796i
$775$	−3.81781	−	6.61264i	−0.137140	−	0.237533i
$776$	2.42432	+	13.7490i	0.0870281	+	0.493561i
$777$	78.8019	−	29.6013i	2.82700	−	1.06194i
$778$	5.62049	−	2.04569i	0.201504	−	0.0733416i
$779$	7.60288	−	43.1181i	0.272401	−	1.54486i
$780$	0.732511	+	3.91856i	0.0262281	+	0.140307i
$781$	−3.45952	+	2.90288i	−0.123791	+	0.103873i
$782$	4.70564			0.168273
$783$	16.6225	+	5.47648i	0.594039	+	0.195713i
$784$	10.1977			0.364205
$785$	17.3224	−	14.5352i	0.618263	−	0.518784i
$786$	−1.81317	−	0.638935i	−0.0646737	−	0.0227900i
$787$	3.34798	−	18.9873i	0.119343	−	0.676825i	−0.865166	−	0.501486i	$-0.832787\pi$
$787$	3.34798	−	18.9873i	0.119343	−	0.676825i	0.984508	−	0.175339i	$-0.0561021\pi$
$788$	4.40543	−	1.60344i	0.156937	−	0.0571203i
$789$	−12.5814	−	10.3388i	−0.447910	−	0.368070i
$790$	−0.363686	−	2.06257i	−0.0129394	−	0.0733829i
$791$	6.84633	+	11.8582i	0.243428	+	0.421629i
$792$	15.9379	−	0.327343i	0.566328	−	0.0116316i
$793$	−7.92035	+	13.7184i	−0.281260	+	0.487156i
$794$	−3.55867	−	1.29525i	−0.126293	−	0.0459667i
$795$	−5.30042	+	9.40224i	−0.187986	+	0.333463i
$796$	11.6026	+	9.73573i	0.411243	+	0.345074i
$797$	7.14932	+	5.99900i	0.253242	+	0.212495i	0.760567	−	0.649260i	$-0.224921\pi$
$797$	7.14932	+	5.99900i	0.253242	+	0.212495i	−0.507325	+	0.861755i	$0.669366\pi$
$798$	−14.3252	−	24.2339i	−0.507107	−	0.857870i
$799$	35.8586	+	13.0515i	1.26859	+	0.461728i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	1.20930	−	0.468490i	0.0427287	−	0.0165533i
$802$	−1.59562	−	2.76369i	−0.0563432	−	0.0975894i
$803$	5.42398	+	30.7609i	0.191408	+	1.08553i
$804$	1.59867	−	9.64454i	0.0563806	−	0.340137i
$805$	5.28970	−	1.92529i	0.186437	−	0.0678577i
$806$	3.05168	−	17.3069i	0.107491	−	0.609610i
$807$	−41.9656	+	35.9540i	−1.47726	+	1.26564i
$808$	−3.91636	+	3.28622i	−0.137777	+	0.115609i
$809$	18.3093			0.643721			0.321860	−	0.946787i	$-0.395692\pi$
$809$	18.3093			0.643721			0.321860	+	0.946787i	$0.395692\pi$
$810$	−6.65105	+	6.06329i	−0.233694	+	0.213042i
$811$	47.5025			1.66804			0.834020	−	0.551735i	$-0.186034\pi$
$811$	47.5025			1.66804			0.834020	+	0.551735i	$0.186034\pi$
$812$	−10.6999	+	8.97830i	−0.375494	+	0.315077i
$813$	17.4053	−	14.9120i	0.610429	−	0.522985i
$814$	−10.8137	+	61.3276i	−0.379020	+	2.14953i
$815$	−22.4230	+	8.16129i	−0.785442	+	0.285877i
$816$	0.981885	−	5.92358i	0.0343728	−	0.207367i
$817$	1.78715	+	10.1355i	0.0625246	+	0.354595i
$818$	15.9256	+	27.5840i	0.556826	+	0.964452i
$819$	22.3082	+	17.9513i	0.779512	+	0.627268i
$820$	5.58569	−	9.67470i	0.195061	−	0.337855i
$821$	−20.6127	−	7.50239i	−0.719387	−	0.261835i	−0.0437212	−	0.999044i	$-0.513921\pi$
$821$	−20.6127	−	7.50239i	−0.719387	−	0.261835i	−0.675665	+	0.737208i	$0.736144\pi$
$822$	−7.56800	−	12.8028i	−0.263964	−	0.446547i
$823$	43.2806	+	36.3167i	1.50867	+	1.26592i	0.866299	+	0.499526i	$0.166493\pi$
$823$	43.2806	+	36.3167i	1.50867	+	1.26592i	0.642369	+	0.766396i	$0.277952\pi$
$824$	5.86957	+	4.92515i	0.204476	+	0.171576i
$825$	−4.51976	+	8.01746i	−0.157358	+	0.279132i
$826$	5.12519	+	1.86542i	0.178328	+	0.0649061i
$827$	−13.8995	+	24.0747i	−0.483334	+	0.837160i	−0.999817	−	0.0191380i	$-0.993908\pi$
$827$	−13.8995	+	24.0747i	−0.483334	+	0.837160i	0.516482	+	0.856298i	$0.327241\pi$
$828$	−1.96326	+	3.56771i	−0.0682280	+	0.123986i
$829$	6.45022	+	11.1721i	0.224026	+	0.388024i	0.956027	−	0.293280i	$-0.0947468\pi$
$829$	6.45022	+	11.1721i	0.224026	+	0.388024i	−0.732001	+	0.681303i	$0.761413\pi$
$830$	2.34915	+	13.3227i	0.0815403	+	0.462438i
$831$	−7.73453	−	6.35586i	−0.268308	−	0.220482i
$832$	2.16277	−	0.787183i	0.0749805	−	0.0272907i
$833$	−6.13881	+	34.8149i	−0.212697	+	1.20627i
$834$	4.21715	+	1.48606i	0.146028	+	0.0514581i
$835$	12.5360	−	10.5190i	0.433827	−	0.364024i
$836$	20.8258			0.720276
$837$	36.8474	−	14.7118i	1.27363	−	0.508513i
$838$	−30.9458			−1.06900
$839$	−13.0201	+	10.9252i	−0.449505	+	0.377180i	−0.839252	−	0.543742i	$-0.817007\pi$
$839$	−13.0201	+	10.9252i	−0.449505	+	0.377180i	0.389747	+	0.920922i	$0.372563\pi$
$840$	−1.31985	−	7.06054i	−0.0455392	−	0.243612i
$841$	−3.06586	+	17.3874i	−0.105719	+	0.599564i
$842$	13.0700	−	4.75709i	0.450422	−	0.163940i
$843$	21.1313	−	7.93783i	0.727802	−	0.273393i
$844$	1.87488	+	10.6330i	0.0645361	+	0.366002i
$845$	3.85139	+	6.67080i	0.132492	+	0.229482i
$846$	−24.8560	+	21.7419i	−0.854568	+	0.747502i
$847$	35.7389	−	61.9016i	1.22800	−	2.12696i
$848$	5.85574	+	2.13131i	0.201087	+	0.0731896i
$849$	−27.7683	+	0.285132i	−0.953007	+	0.00978570i
$850$	2.65560	+	2.22832i	0.0910865	+	0.0764306i
$851$	−12.1862	−	10.2254i	−0.417736	−	0.350522i
$852$	−1.47197	+	0.0151145i	−0.0504288	+	0.000517815i
$853$	−0.445724	−	0.162230i	−0.0152613	−	0.00555466i	0.334378	−	0.942439i	$-0.391474\pi$
$853$	−0.445724	−	0.162230i	−0.0152613	−	0.00555466i	−0.349640	+	0.936884i	$0.613696\pi$
$854$	14.2710	−	24.7182i	0.488345	−	0.845839i
$855$	−8.84983	+	7.74106i	−0.302658	+	0.264739i
$856$	4.82428	+	8.35590i	0.164891	+	0.285599i
$857$	0.637461	+	3.61522i	0.0217752	+	0.123494i	0.993758	−	0.111560i	$-0.0355846\pi$
$857$	0.637461	+	3.61522i	0.0217752	+	0.123494i	−0.971982	+	0.235053i	$0.924474\pi$
$858$	−19.8300	+	7.44899i	−0.676985	+	0.254304i
$859$	17.0349	−	6.20021i	0.581225	−	0.211548i	−0.0346409	−	0.999400i	$-0.511029\pi$
$859$	17.0349	−	6.20021i	0.581225	−	0.211548i	0.615865	+	0.787851i	$0.288807\pi$
$860$	−0.455996	+	2.58608i	−0.0155493	+	0.0881846i
$861$	−14.7446	−	78.8760i	−0.502494	−	2.68809i
$862$	28.2220	−	23.6811i	0.961245	−	0.806580i
$863$	21.6446			0.736789			0.368395	−	0.929669i	$-0.379908\pi$
$863$	21.6446			0.736789			0.368395	+	0.929669i	$0.379908\pi$
$864$	4.08146	+	3.21584i	0.138854	+	0.109405i
$865$	14.0432			0.477484
$866$	23.4542	−	19.6804i	0.797006	−	0.668767i
$867$	−8.13915	−	2.86812i	−0.276420	−	0.0974063i
$868$	−5.49857	+	31.1840i	−0.186634	+	1.05845i
$869$	10.4579	−	3.80636i	0.354759	−	0.129122i
$870$	4.50722	+	3.70381i	0.152809	+	0.125571i
$871$	2.25580	+	12.7933i	0.0764350	+	0.433484i
$872$	−3.68929	−	6.39004i	−0.124935	−	0.216394i
$873$	20.1924	−	36.6944i	0.683411	−	1.24192i
$874$	−2.65999	+	4.60724i	−0.0899756	+	0.155842i
$875$	3.89692	+	1.41836i	0.131740	+	0.0479494i
$876$	−4.99989	+	8.86914i	−0.168931	+	0.299661i
$877$	−9.74664	−	8.17840i	−0.329121	−	0.276165i	0.463221	−	0.886243i	$-0.346694\pi$
$877$	−9.74664	−	8.17840i	−0.329121	−	0.276165i	−0.792341	+	0.610078i	$0.791138\pi$
$878$	−13.2883	−	11.1502i	−0.448457	−	0.376300i
$879$	−12.4294	−	21.0267i	−0.419232	−	0.709212i
$880$	4.99329	+	1.81741i	0.168324	+	0.0612649i
$881$	−13.2315	+	22.9177i	−0.445782	+	0.772117i	−0.998106	−	0.0615121i	$-0.980408\pi$
$881$	−13.2315	+	22.9177i	−0.445782	+	0.772117i	0.552324	+	0.833629i	$0.313741\pi$
$882$	−23.8347	−	19.1796i	−0.802554	−	0.645810i
$883$	6.04288	+	10.4666i	0.203359	+	0.352228i	0.949609	−	0.313438i	$-0.101481\pi$
$883$	6.04288	+	10.4666i	0.203359	+	0.352228i	−0.746250	+	0.665666i	$0.768147\pi$
$884$	1.38549	+	7.85752i	0.0465991	+	0.264277i
$885$	0.372511	−	2.24731i	0.0125218	−	0.0755425i
$886$	−10.0498	+	3.65782i	−0.337629	+	0.122887i
$887$	−5.87474	+	33.3173i	−0.197255	+	1.11869i	0.711917	+	0.702264i	$0.247827\pi$
$887$	−5.87474	+	33.3173i	−0.197255	+	1.11869i	−0.909171	+	0.416422i	$0.863284\pi$
$888$	−15.4148	+	13.2066i	−0.517286	+	0.443184i
$889$	24.4113	−	20.4835i	0.818729	−	0.686995i
$890$	0.432294			0.0144905
$891$	−37.8664	−	29.2104i	−1.26857	−	0.978584i
$892$	−23.5994			−0.790165
$893$	−33.0486	+	27.7311i	−1.10593	+	0.927985i
$894$	15.8441	−	13.5744i	0.529905	−	0.453996i
$895$	2.10087	−	11.9147i	0.0702245	−	0.398263i
$896$	−3.89692	+	1.41836i	−0.130187	+	0.0473842i
$897$	0.884880	−	5.33837i	0.0295453	−	0.178243i
$898$	0.323436	+	1.83430i	0.0107932	+	0.0612114i
$899$	−12.8589	−	22.2723i	−0.428869	−	0.742824i
$900$	−2.79741	+	1.08373i	−0.0932471	+	0.0361244i
$901$	−10.8013	+	18.7084i	−0.359843	+	0.623266i
$902$	55.7820	+	20.3030i	1.85734	+	0.676015i
$903$	9.59821	+	16.2373i	0.319408	+	0.540342i
$904$	−2.52933	−	2.12236i	−0.0841244	−	0.0705887i
$905$	−2.45258	−	2.05796i	−0.0815265	−	0.0684089i
$906$	4.77174	−	8.46444i	0.158531	−	0.281212i
$907$	5.84847	+	2.12867i	0.194195	+	0.0706813i	0.437287	−	0.899322i	$-0.355939\pi$
$907$	5.84847	+	2.12867i	0.194195	+	0.0706813i	−0.243092	+	0.970003i	$0.578162\pi$
$908$	−1.41496	+	2.45079i	−0.0469572	+	0.0813323i
$909$	15.3341	−	0.314942i	0.508600	−	0.0104460i
$910$	4.77233	+	8.26591i	0.158201	+	0.274012i
$911$	−2.15971	−	12.2483i	−0.0715543	−	0.405805i	−0.999456	−	0.0329797i	$-0.989500\pi$
$911$	−2.15971	−	12.2483i	−0.0715543	−	0.405805i	0.927902	−	0.372825i	$-0.121611\pi$
$912$	5.24468	+	4.30982i	0.173669	+	0.142712i
$913$	−67.5504	+	24.5863i	−2.23559	+	0.813689i
$914$	0.269886	−	1.53060i	0.00892702	−	0.0506277i
$915$	−11.2433	−	3.96197i	−0.371692	−	0.130979i
$916$	10.6984	−	8.97704i	0.353486	−	0.296610i
$917$	−4.60290			−0.152001
$918$	−13.4358	+	11.9982i	−0.443447	+	0.395999i
$919$	−13.6239			−0.449410			−0.224705	−	0.974427i	$-0.572142\pi$
$919$	−13.6239			−0.449410			−0.224705	+	0.974427i	$0.572142\pi$
$920$	−1.03983	+	0.872523i	−0.0342823	+	0.0287662i
$921$	3.33416	+	17.8361i	0.109864	+	0.587719i
$922$	−3.11306	+	17.6550i	−0.102523	+	0.581437i
$923$	1.83811	−	0.669016i	0.0605020	−	0.0220209i
$924$	35.7301	−	13.4217i	1.17543	−	0.441543i
$925$	−2.03504	−	11.5413i	−0.0669118	−	0.379476i
$926$	5.12459	+	8.87606i	0.168405	+	0.291685i
$927$	−4.45557	−	22.5506i	−0.146340	−	0.740658i
$928$	1.68407	−	2.91690i	0.0552824	−	0.0957519i
$929$	−11.5678	−	4.21032i	−0.379526	−	0.138136i	0.145211	−	0.989401i	$-0.453614\pi$
$929$	−11.5678	−	4.21032i	−0.379526	−	0.138136i	−0.524737	+	0.851265i	$0.675836\pi$
$930$	13.2246	−	0.135793i	0.433651	−	0.00445283i
$931$	−30.6168	−	25.6905i	−1.00342	−	0.841973i
$932$	−6.41828	−	5.38558i	−0.210238	−	0.176411i
$933$	−22.7050	+	0.233141i	−0.743329	+	0.00763268i
$934$	−30.0062	−	10.9214i	−0.981833	−	0.357358i
$935$	−9.21045	+	15.9530i	−0.301214	+	0.521718i
$936$	−6.53543	−	2.22782i	−0.213617	−	0.0728186i
$937$	−4.99354	−	8.64906i	−0.163132	−	0.282553i	0.772858	−	0.634578i	$-0.218826\pi$
$937$	−4.99354	−	8.64906i	−0.163132	−	0.282553i	−0.935990	+	0.352026i	$0.885493\pi$
$938$	−4.06455	−	23.0512i	−0.132712	−	0.752649i
$939$	−21.5801	+	8.10639i	−0.704239	+	0.264542i
$940$	−10.3439	+	3.76487i	−0.337381	+	0.122796i
$941$	8.00115	−	45.3768i	0.260830	−	1.47924i	−0.519822	−	0.854275i	$-0.674002\pi$
$941$	8.00115	−	45.3768i	0.260830	−	1.47924i	0.780652	−	0.624966i	$-0.214887\pi$
$942$	7.19687	+	38.4996i	0.234487	+	1.25439i
$943$	−11.6164	+	9.74728i	−0.378281	+	0.317415i
$944$	−1.31519			−0.0428058
$945$	−10.1944	+	18.9846i	−0.331624	+	0.617568i
$946$	−13.9538			−0.453676
$947$	23.4765	−	19.6991i	0.762884	−	0.640136i	−0.175991	−	0.984392i	$-0.556313\pi$
$947$	23.4765	−	19.6991i	0.762884	−	0.640136i	0.938876	+	0.344256i	$0.111869\pi$
$948$	3.42137	+	1.20564i	0.111121	+	0.0391574i
$949$	2.34931	−	13.3236i	0.0762619	−	0.432503i
$950$	−3.68287	+	1.34046i	−0.119488	+	0.0434902i
$951$	−0.531544	−	0.436797i	−0.0172365	−	0.0141641i
$952$	−2.49641	−	14.1578i	−0.0809090	−	0.458858i
$953$	−15.3236	−	26.5413i	−0.496381	−	0.859758i	0.503610	−	0.863931i	$-0.332005\pi$
$953$	−15.3236	−	26.5413i	−0.496381	−	0.859758i	−0.999991	+	0.00417334i	$0.998672\pi$
$954$	−9.67780	−	15.9947i	−0.313330	−	0.517847i
$955$	−9.36870	+	16.2271i	−0.303164	+	0.525096i
$956$	−3.65853	−	1.33160i	−0.118325	−	0.0430669i
$957$	−15.2232	+	27.0040i	−0.492097	+	0.872914i
$958$	23.1274	+	19.4062i	0.747212	+	0.626985i
$959$	−27.2777	−	22.8887i	−0.880841	−	0.739114i
$960$	0.881381	+	1.49103i	0.0284465	+	0.0481227i
$961$	−25.6561	−	9.33804i	−0.827615	−	0.301227i
$962$	13.4865	−	23.3592i	0.434821	−	0.753131i
$963$	4.43996	−	28.6031i	0.143076	−	0.921723i
$964$	10.2824	+	17.8096i	0.331173	+	0.573609i
$965$	−3.62795	−	20.5751i	−0.116788	−	0.662337i
$966$	−1.59440	+	9.61878i	−0.0512988	+	0.309479i
$967$	22.0780	−	8.03574i	0.709981	−	0.258412i	0.0383147	−	0.999266i	$-0.487801\pi$
$967$	22.0780	−	8.03574i	0.709981	−	0.258412i	0.671666	+	0.740854i	$0.265579\pi$
$968$	−2.99299	+	16.9741i	−0.0961984	+	0.545568i
$969$	−17.8708	+	15.3108i	−0.574093	+	0.491854i
$970$	10.6948	−	8.97404i	0.343391	−	0.288139i
$971$	24.9314			0.800086			0.400043	−	0.916496i	$-0.368995\pi$
$971$	24.9314			0.800086			0.400043	+	0.916496i	$0.368995\pi$
$972$	−3.49114	−	15.1925i	−0.111978	−	0.487300i
$973$	10.7056			0.343206
$974$	−3.95149	+	3.31569i	−0.126614	+	0.106242i
$975$	3.02732	−	2.59365i	0.0969517	−	0.0830634i
$976$	−1.19514	+	6.77800i	−0.0382556	+	0.216958i
$977$	−28.6024	+	10.4104i	−0.915073	+	0.333059i	−0.756276	−	0.654252i	$-0.772983\pi$
$977$	−28.6024	+	10.4104i	−0.915073	+	0.333059i	−0.158796	+	0.987311i	$0.550761\pi$
$978$	6.75862	−	40.7739i	0.216117	−	1.30380i
$979$	0.398887	+	2.26220i	0.0127485	+	0.0723003i
$980$	−5.09887	−	8.83151i	−0.162878	−	0.282112i
$981$	−3.39538	+	21.8738i	−0.108406	+	0.698376i
$982$	2.89236	−	5.00972i	0.0922991	−	0.159867i
$983$	27.0970	+	9.86252i	0.864262	+	0.314565i	0.735841	−	0.677154i	$-0.236787\pi$
$983$	27.0970	+	9.86252i	0.864262	+	0.314565i	0.128420	+	0.991720i	$0.459009\pi$
$984$	9.84624	+	16.6568i	0.313887	+	0.531001i
$985$	−3.59134	−	3.01349i	−0.114430	−	0.0960178i
$986$	8.94447	+	7.50530i	0.284850	+	0.239017i
$987$	−38.8283	+	68.8762i	−1.23592	+	2.19235i
$988$	−8.47639	−	3.08516i	−0.269670	−	0.0981519i
$989$	1.78226	−	3.08696i	0.0566724	−	0.0981595i
$990$	−8.25243	−	13.6389i	−0.262280	−	0.433474i
$991$	23.8089	+	41.2382i	0.756314	+	1.30997i	0.944719	+	0.327882i	$0.106335\pi$
$991$	23.8089	+	41.2382i	0.756314	+	1.30997i	−0.188405	+	0.982091i	$0.560332\pi$
$992$	−1.32591	−	7.51961i	−0.0420977	−	0.238748i
$993$	−18.2918	−	15.0313i	−0.580473	−	0.477004i
$994$	−3.31194	+	1.20545i	−0.105048	+	0.0382345i
$995$	2.63009	−	14.9160i	0.0833796	−	0.472869i
$996$	−22.0996	−	7.78757i	−0.700253	−	0.246759i
$997$	−9.48351	+	7.95761i	−0.300346	+	0.252020i	−0.780488	−	0.625171i	$-0.785029\pi$
$997$	−9.48351	+	7.95761i	−0.300346	+	0.252020i	0.480142	+	0.877191i	$0.340585\pi$
$998$	15.2261			0.481973
$999$	60.8666	−	1.87551i	1.92573	−	0.0593384i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.2.k.b.211.1	yes	12
3.2	odd	2		810.2.k.b.361.1		12
27.4	even	9		7290.2.a.k.1.1		6
27.11	odd	18		810.2.k.b.451.1		12
27.16	even	9	inner	270.2.k.b.151.1	✓	12
27.23	odd	18		7290.2.a.l.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.k.b.151.1	✓	12	27.16	even	9	inner
270.2.k.b.211.1	yes	12	1.1	even	1	trivial
810.2.k.b.361.1		12	3.2	odd	2
810.2.k.b.451.1		12	27.11	odd	18
7290.2.a.k.1.1		6	27.4	even	9
7290.2.a.l.1.1		6	27.23	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	270.k (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-1.31533 + 1.12691i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.939693 + 0.342020i) q^{5} +(0.283238 - 1.70874i) q^{6} +(-0.720122 - 4.08401i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.460168 - 2.96450i) q^{9} +(0.500000 - 0.866025i) q^{10} +(4.99329 + 1.81741i) q^{11} +(0.881381 + 1.49103i) q^{12} +(-1.76311 - 1.47942i) q^{13} +(3.17680 + 2.66565i) q^{14} +(0.850578 - 1.50881i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(1.73332 - 3.00220i) q^{17} +(1.55303 + 2.56673i) q^{18} +(1.95962 + 3.39416i) q^{19} +(0.173648 + 0.984808i) q^{20} +(5.54949 + 4.56030i) q^{21} +(-4.99329 + 1.81741i) q^{22} +(0.235711 - 1.33678i) q^{23} +(-1.63359 - 0.575653i) q^{24} +(0.766044 - 0.642788i) q^{25} +2.30157 q^{26} +(2.73544 + 4.41785i) q^{27} -4.14702 q^{28} +(2.58015 - 2.16500i) q^{29} +(0.318266 + 1.70256i) q^{30} +(1.32591 - 7.51961i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-8.61586 + 3.23648i) q^{33} +(0.601977 + 3.41398i) q^{34} +(2.07351 + 3.59142i) q^{35} +(-2.83955 - 0.967956i) q^{36} +(5.85967 - 10.1493i) q^{37} +(-3.68287 - 1.34046i) q^{38} +(3.98623 - 0.0409315i) q^{39} +(-0.766044 - 0.642788i) q^{40} +(-8.55777 - 7.18082i) q^{41} +(-7.18247 + 0.0737513i) q^{42} +(2.46761 + 0.898136i) q^{43} +(2.65688 - 4.60184i) q^{44} +(0.581502 + 2.94310i) q^{45} +(0.678702 + 1.17555i) q^{46} +(1.91147 + 10.8405i) q^{47} +(1.62143 - 0.609077i) q^{48} +(-9.58275 + 3.48784i) q^{49} +(-0.173648 + 0.984808i) q^{50} +(1.10331 + 5.90217i) q^{51} +(-1.76311 + 1.47942i) q^{52} -6.23155 q^{53} +(-4.93520 - 1.62596i) q^{54} -5.31375 q^{55} +(3.17680 - 2.66565i) q^{56} +(-6.40243 - 2.25612i) q^{57} +(-0.584872 + 3.31698i) q^{58} +(1.23587 - 0.449821i) q^{59} +(-1.33819 - 1.09966i) q^{60} +(-1.19514 - 6.77800i) q^{61} +(3.81781 + 6.61264i) q^{62} +(-12.4384 + 0.255468i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.16277 + 0.787183i) q^{65} +(4.51976 - 8.01746i) q^{66} +(-4.32375 - 3.62806i) q^{67} +(-2.65560 - 2.22832i) q^{68} +(1.19639 + 2.02393i) q^{69} +(-3.89692 - 1.41836i) q^{70} +(-0.424943 + 0.736023i) q^{71} +(2.79741 - 1.08373i) q^{72} +(2.93911 + 5.09069i) q^{73} +(2.03504 + 11.5413i) q^{74} +(-0.283238 + 1.70874i) q^{75} +(3.68287 - 1.34046i) q^{76} +(3.82655 - 21.7014i) q^{77} +(-3.02732 + 2.59365i) q^{78} +(1.60439 - 1.34625i) q^{79} +1.00000 q^{80} +(-8.57649 - 2.72833i) q^{81} +11.1714 q^{82} +(-10.3632 + 8.69578i) q^{83} +(5.45468 - 4.67330i) q^{84} +(-0.601977 + 3.41398i) q^{85} +(-2.46761 + 0.898136i) q^{86} +(-0.953986 + 5.75527i) q^{87} +(0.922723 + 5.23302i) q^{88} +(0.216147 + 0.374377i) q^{89} +(-2.33725 - 1.88077i) q^{90} +(-4.77233 + 8.26591i) q^{91} +(-1.27554 - 0.464260i) q^{92} +(6.72989 + 11.3849i) q^{93} +(-8.43242 - 7.07564i) q^{94} +(-3.00231 - 2.51923i) q^{95} +(-0.850578 + 1.50881i) q^{96} +(13.1192 + 4.77498i) q^{97} +(5.09887 - 8.83151i) q^{98} +(7.68546 - 13.9663i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} + 3 q^{6} - 12 q^{7} + 6 q^{8} - 3 q^{9} + 6 q^{10} + 3 q^{11} + 9 q^{12} + 9 q^{13} - 6 q^{14} - 9 q^{17} - 6 q^{18} - 3 q^{19} - 6 q^{21} - 3 q^{22} - 24 q^{23} - 3 q^{24} + 12 q^{26} - 9 q^{27}+ \cdots + 45 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 + 3 * q^6 - 12 * q^7 + 6 * q^8 - 3 * q^9 + 6 * q^10 + 3 * q^11 + 9 * q^12 + 9 * q^13 - 6 * q^14 - 9 * q^17 - 6 * q^18 - 3 * q^19 - 6 * q^21 - 3 * q^22 - 24 * q^23 - 3 * q^24 + 12 * q^26 - 9 * q^27 - 6 * q^28 + 6 * q^29 + 6 * q^30 + 21 * q^31 - 9 * q^33 + 18 * q^34 + 3 * q^35 - 3 * q^36 - 18 * q^38 - 24 * q^41 - 27 * q^42 + 33 * q^43 + 3 * q^44 + 15 * q^45 + 15 * q^46 - 18 * q^47 + 6 * q^48 - 30 * q^49 + 9 * q^51 + 9 * q^52 + 24 * q^53 - 18 * q^54 - 6 * q^55 - 6 * q^56 + 15 * q^57 + 39 * q^58 + 36 * q^59 - 3 * q^60 - 24 * q^61 - 60 * q^63 - 6 * q^64 - 9 * q^66 + 9 * q^67 + 9 * q^68 + 18 * q^69 - 6 * q^70 - 18 * q^71 + 12 * q^72 + 12 * q^73 - 12 * q^74 - 3 * q^75 + 18 * q^76 + 24 * q^77 - 24 * q^78 + 27 * q^79 + 12 * q^80 - 63 * q^81 + 6 * q^82 - 9 * q^83 - 3 * q^84 - 18 * q^85 - 33 * q^86 - 18 * q^87 - 3 * q^88 + 15 * q^89 - 15 * q^90 - 21 * q^91 + 3 * q^92 + 36 * q^93 - 54 * q^94 - 18 * q^95 + 36 * q^97 + 3 * q^98 + 45 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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