LMFDB - Embedded newform 504.2.bf.b.115.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(115,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4, 1]))

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

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

chi := DirichletCharacter("504.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$90$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			115.1
Character	$\chi$	$=$	504.115
Dual form			504.2.bf.b.355.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41416 - 0.0128144i) q^{2} +(1.65702 + 0.504266i) q^{3} +(1.99967 + 0.0362430i) q^{4} +(2.12331 - 3.67768i) q^{5} +(-2.33682 - 0.734345i) q^{6} +(2.60163 + 0.481180i) q^{7} +(-2.82738 - 0.0768778i) q^{8} +(2.49143 + 1.67116i) q^{9} +O(q^{10})$	\(q+(-1.41416 - 0.0128144i) q^{2} +(1.65702 + 0.504266i) q^{3} +(1.99967 + 0.0362430i) q^{4} +(2.12331 - 3.67768i) q^{5} +(-2.33682 - 0.734345i) q^{6} +(2.60163 + 0.481180i) q^{7} +(-2.82738 - 0.0768778i) q^{8} +(2.49143 + 1.67116i) q^{9} +(-3.04982 + 5.17360i) q^{10} +(1.13867 + 1.97224i) q^{11} +(3.29522 + 1.06842i) q^{12} +(1.27225 + 2.20361i) q^{13} +(-3.67294 - 0.713802i) q^{14} +(5.37290 - 5.02328i) q^{15} +(3.99737 + 0.144948i) q^{16} +(-4.08493 - 2.35844i) q^{17} +(-3.50186 - 2.39520i) q^{18} +(-4.57481 + 2.64127i) q^{19} +(4.37921 - 7.27720i) q^{20} +(4.06831 + 2.10924i) q^{21} +(-1.58498 - 2.80364i) q^{22} +(1.03515 + 0.597642i) q^{23} +(-4.64626 - 1.55314i) q^{24} +(-6.51690 - 11.2876i) q^{25} +(-1.77093 - 3.13255i) q^{26} +(3.28564 + 4.02549i) q^{27} +(5.18496 + 1.05649i) q^{28} +(-2.81842 - 1.62722i) q^{29} +(-7.66248 + 7.03485i) q^{30} -5.17158 q^{31} +(-5.65105 - 0.256203i) q^{32} +(0.892268 + 3.84223i) q^{33} +(5.74651 + 3.38754i) q^{34} +(7.29369 - 8.54626i) q^{35} +(4.92148 + 3.43207i) q^{36} +(-0.0738513 + 0.0426381i) q^{37} +(6.50333 - 3.67654i) q^{38} +(0.996945 + 4.29298i) q^{39} +(-6.28614 + 10.2350i) q^{40} +(-3.43230 + 1.98164i) q^{41} +(-5.72619 - 3.03492i) q^{42} +(-3.65838 + 6.33650i) q^{43} +(2.20549 + 3.98509i) q^{44} +(11.4361 - 5.61430i) q^{45} +(-1.45620 - 0.858423i) q^{46} +8.98167 q^{47} +(6.55063 + 2.25592i) q^{48} +(6.53693 + 2.50370i) q^{49} +(9.07126 + 16.0459i) q^{50} +(-5.57954 - 5.96787i) q^{51} +(2.46422 + 4.45260i) q^{52} +(-8.95026 - 5.16743i) q^{53} +(-4.59483 - 5.73477i) q^{54} +9.67101 q^{55} +(-7.31880 - 1.56049i) q^{56} +(-8.91245 + 2.06971i) q^{57} +(3.96484 + 2.33726i) q^{58} -0.601814i q^{59} +(10.9261 - 9.85018i) q^{60} +2.64414 q^{61} +(7.31341 + 0.0662705i) q^{62} +(5.67765 + 5.54656i) q^{63} +(7.98818 + 0.434726i) q^{64} +10.8056 q^{65} +(-1.21257 - 5.44494i) q^{66} -0.653746 q^{67} +(-8.08305 - 4.86415i) q^{68} +(1.41389 + 1.51229i) q^{69} +(-10.4239 + 11.9923i) q^{70} -8.89379i q^{71} +(-6.91575 - 4.91654i) q^{72} +(3.31848 + 1.91592i) q^{73} +(0.104984 - 0.0593505i) q^{74} +(-5.10667 - 21.9900i) q^{75} +(-9.24384 + 5.11586i) q^{76} +(2.01340 + 5.67893i) q^{77} +(-1.35482 - 6.08371i) q^{78} -15.1455i q^{79} +(9.02074 - 14.3933i) q^{80} +(3.41446 + 8.32715i) q^{81} +(4.87920 - 2.75836i) q^{82} +(-1.34472 - 0.776375i) q^{83} +(8.05883 + 4.36523i) q^{84} +(-17.3472 + 10.0154i) q^{85} +(5.25472 - 8.91392i) q^{86} +(-3.84963 - 4.11757i) q^{87} +(-3.06784 - 5.66380i) q^{88} +(-9.92258 + 5.72880i) q^{89} +(-16.2443 + 7.79295i) q^{90} +(2.24960 + 6.34515i) q^{91} +(2.04829 + 1.23260i) q^{92} +(-8.56941 - 2.60785i) q^{93} +(-12.7015 - 0.115094i) q^{94} +22.4329i q^{95} +(-9.23471 - 3.27417i) q^{96} +(9.40404 + 5.42943i) q^{97} +(-9.21215 - 3.62439i) q^{98} +(-0.458999 + 6.81659i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9}+O(q^{10}) $ 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9	$ 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9} - 8 q^{11} + 12 q^{12} + 10 q^{14} + 14 q^{16} - 18 q^{17} + 8 q^{18} - 6 q^{19} + 36 q^{20} - 16 q^{22} - 12 q^{24} - 78 q^{25} - 6 q^{26} + 16 q^{28} + q^{30} - 26 q^{32} - 36 q^{33} - 12 q^{34} - 12 q^{35} + 2 q^{36} - 27 q^{38} + 24 q^{40} - 42 q^{41} + 22 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} - 9 q^{48} + 2 q^{49} + 15 q^{50} + 9 q^{52} - 51 q^{54} + 14 q^{56} - 26 q^{57} + 19 q^{58} + 37 q^{60} - 8 q^{64} + 24 q^{65} + 6 q^{66} + 28 q^{67} + 12 q^{68} + 27 q^{70} - 28 q^{72} + 18 q^{73} + 49 q^{74} - 18 q^{75} - 12 q^{76} - 33 q^{78} - 63 q^{80} - 22 q^{81} - 54 q^{82} + 6 q^{83} + 31 q^{84} - 13 q^{86} + 29 q^{88} - 66 q^{89} - 51 q^{90} + 2 q^{91} - 60 q^{92} - 45 q^{96} - 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) $ 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9 - 8 * q^11 + 12 * q^12 + 10 * q^14 + 14 * q^16 - 18 * q^17 + 8 * q^18 - 6 * q^19 + 36 * q^20 - 16 * q^22 - 12 * q^24 - 78 * q^25 - 6 * q^26 + 16 * q^28 + q^30 - 26 * q^32 - 36 * q^33 - 12 * q^34 - 12 * q^35 + 2 * q^36 - 27 * q^38 + 24 * q^40 - 42 * q^41 + 22 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 - 9 * q^48 + 2 * q^49 + 15 * q^50 + 9 * q^52 - 51 * q^54 + 14 * q^56 - 26 * q^57 + 19 * q^58 + 37 * q^60 - 8 * q^64 + 24 * q^65 + 6 * q^66 + 28 * q^67 + 12 * q^68 + 27 * q^70 - 28 * q^72 + 18 * q^73 + 49 * q^74 - 18 * q^75 - 12 * q^76 - 33 * q^78 - 63 * q^80 - 22 * q^81 - 54 * q^82 + 6 * q^83 + 31 * q^84 - 13 * q^86 + 29 * q^88 - 66 * q^89 - 51 * q^90 + 2 * q^91 - 60 * q^92 - 45 * q^96 - 6 * q^97 + 31 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.41416	−	0.0128144i	−0.999959	−	0.00906113i
$2$	−1.41416	−	0.0128144i	−0.999959	−	0.00906113i
$3$	1.65702	+	0.504266i	0.956681	+	0.291138i
$3$	1.65702	+	0.504266i	0.956681	+	0.291138i
$4$	1.99967	+	0.0362430i	0.999836	+	0.0181215i
$5$	2.12331	−	3.67768i	0.949573	−	1.64471i	0.203249	−	0.979127i	$-0.434850\pi$
$5$	2.12331	−	3.67768i	0.949573	−	1.64471i	0.746325	−	0.665582i	$-0.231817\pi$
$6$	−2.33682	−	0.734345i	−0.954004	−	0.299795i
$7$	2.60163	+	0.481180i	0.983323	+	0.181869i
$7$	2.60163	+	0.481180i	0.983323	+	0.181869i
$8$	−2.82738	−	0.0768778i	−0.999631	−	0.0271804i
$9$	2.49143	+	1.67116i	0.830477	+	0.557053i
$10$	−3.04982	+	5.17360i	−0.964437	+	1.63604i
$11$	1.13867	+	1.97224i	0.343322	+	0.594651i	0.985047	−	0.172283i	$-0.0551144\pi$
$11$	1.13867	+	1.97224i	0.343322	+	0.594651i	−0.641725	+	0.766935i	$0.721781\pi$
$12$	3.29522	+	1.06842i	0.951248	+	0.308427i
$13$	1.27225	+	2.20361i	0.352860	+	0.611171i	0.986749	−	0.162253i	$-0.0518760\pi$
$13$	1.27225	+	2.20361i	0.352860	+	0.611171i	−0.633890	+	0.773424i	$0.718543\pi$
$14$	−3.67294	−	0.713802i	−0.981634	−	0.190772i
$15$	5.37290	−	5.02328i	1.38728	−	1.29700i
$16$	3.99737	+	0.144948i	0.999343	+	0.0362371i
$17$	−4.08493	−	2.35844i	−0.990742	−	0.572005i	−0.0852459	−	0.996360i	$-0.527168\pi$
$17$	−4.08493	−	2.35844i	−0.990742	−	0.572005i	−0.905496	+	0.424355i	$0.860501\pi$
$18$	−3.50186	−	2.39520i	−0.825395	−	0.564555i
$19$	−4.57481	+	2.64127i	−1.04953	+	0.605948i	−0.922518	−	0.385953i	$-0.873873\pi$
$19$	−4.57481	+	2.64127i	−1.04953	+	0.605948i	−0.127014	+	0.991901i	$0.540539\pi$
$20$	4.37921	−	7.27720i	0.979222	−	1.62723i
$21$	4.06831	+	2.10924i	0.887777	+	0.460273i
$22$	−1.58498	−	2.80364i	−0.337920	−	0.597738i
$23$	1.03515	+	0.597642i	0.215843	+	0.124617i	0.604024	−	0.796966i	$-0.293563\pi$
$23$	1.03515	+	0.597642i	0.215843	+	0.124617i	−0.388181	+	0.921583i	$0.626896\pi$
$24$	−4.64626	−	1.55314i	−0.948414	−	0.317034i
$25$	−6.51690	−	11.2876i	−1.30338	−	2.25752i
$26$	−1.77093	−	3.13255i	−0.347307	−	0.614343i
$27$	3.28564	+	4.02549i	0.632322	+	0.774706i
$28$	5.18496	+	1.05649i	0.979866	+	0.199658i
$29$	−2.81842	−	1.62722i	−0.523368	−	0.302167i	0.214943	−	0.976626i	$-0.431043\pi$
$29$	−2.81842	−	1.62722i	−0.523368	−	0.302167i	−0.738312	+	0.674460i	$0.764377\pi$
$30$	−7.66248	+	7.03485i	−1.39897	+	1.28438i
$31$	−5.17158			−0.928843			−0.464421	−	0.885614i	$-0.653738\pi$
$31$	−5.17158			−0.928843			−0.464421	+	0.885614i	$0.653738\pi$
$32$	−5.65105	−	0.256203i	−0.998974	−	0.0452908i
$33$	0.892268	+	3.84223i	0.155324	+	0.668846i
$34$	5.74651	+	3.38754i	0.985518	+	0.580959i
$35$	7.29369	−	8.54626i	1.23286	−	1.44458i
$36$	4.92148	+	3.43207i	0.820246	+	0.572011i
$37$	−0.0738513	+	0.0426381i	−0.0121411	+	0.00700966i	−0.506058	−	0.862499i	$-0.668898\pi$
$37$	−0.0738513	+	0.0426381i	−0.0121411	+	0.00700966i	0.493917	+	0.869509i	$0.335565\pi$
$38$	6.50333	−	3.67654i	1.05498	−	0.596413i
$39$	0.996945	+	4.29298i	0.159639	+	0.687426i
$40$	−6.28614	+	10.2350i	−0.993926	+	1.61829i
$41$	−3.43230	+	1.98164i	−0.536035	+	0.309480i	−0.743470	−	0.668769i	$-0.766822\pi$
$41$	−3.43230	+	1.98164i	−0.536035	+	0.309480i	0.207436	+	0.978249i	$0.433488\pi$
$42$	−5.72619	−	3.03492i	−0.883570	−	0.468299i
$43$	−3.65838	+	6.33650i	−0.557898	+	0.966308i	0.439774	+	0.898109i	$0.355059\pi$
$43$	−3.65838	+	6.33650i	−0.557898	+	0.966308i	−0.997672	+	0.0681990i	$0.978275\pi$
$44$	2.20549	+	3.98509i	0.332490	+	0.600775i
$45$	11.4361	−	5.61430i	1.70479	−	0.836931i
$46$	−1.45620	−	0.858423i	−0.214705	−	0.126568i
$47$	8.98167			1.31011			0.655056	−	0.755581i	$-0.272645\pi$
$47$	8.98167			1.31011			0.655056	+	0.755581i	$0.272645\pi$
$48$	6.55063	+	2.25592i	0.945503	+	0.325614i
$49$	6.53693	+	2.50370i	0.933847	+	0.357672i
$50$	9.07126	+	16.0459i	1.28287	+	2.26924i
$51$	−5.57954	−	5.96787i	−0.781291	−	0.835669i
$52$	2.46422	+	4.45260i	0.341726	+	0.617465i
$53$	−8.95026	−	5.16743i	−1.22941	−	0.709802i	−0.262505	−	0.964931i	$-0.584549\pi$
$53$	−8.95026	−	5.16743i	−1.22941	−	0.709802i	−0.966907	+	0.255129i	$0.917882\pi$
$54$	−4.59483	−	5.73477i	−0.625277	−	0.780403i
$55$	9.67101			1.30404
$56$	−7.31880	−	1.56049i	−0.978016	−	0.208529i
$57$	−8.91245	+	2.06971i	−1.18048	+	0.274140i
$58$	3.96484	+	2.33726i	0.520609	+	0.306897i
$59$		−	0.601814i		−	0.0783495i	−0.999232	−	0.0391747i	$-0.987527\pi$
$59$		−	0.601814i		−	0.0783495i	0.999232	−	0.0391747i	$-0.0124729\pi$
$60$	10.9261	−	9.85018i	1.41055	−	1.27165i
$61$	2.64414			0.338548			0.169274	−	0.985569i	$-0.445858\pi$
$61$	2.64414			0.338548			0.169274	+	0.985569i	$0.445858\pi$
$62$	7.31341	+	0.0662705i	0.928804	+	0.00841636i
$63$	5.67765	+	5.54656i	0.715316	+	0.698801i
$64$	7.98818	+	0.434726i	0.998522	+	0.0543407i
$65$	10.8056			1.34026
$66$	−1.21257	−	5.44494i	−0.149257	−	0.670226i
$67$	−0.653746			−0.0798678			−0.0399339	−	0.999202i	$-0.512715\pi$
$67$	−0.653746			−0.0798678			−0.0399339	+	0.999202i	$0.512715\pi$
$68$	−8.08305	−	4.86415i	−0.980214	−	0.589865i
$69$	1.41389	+	1.51229i	0.170212	+	0.182059i
$70$	−10.4239	+	11.9923i	−1.24590	+	1.43335i
$71$		−	8.89379i		−	1.05550i	−0.849400	−	0.527750i	$-0.823036\pi$
$71$		−	8.89379i		−	1.05550i	0.849400	−	0.527750i	$-0.176964\pi$
$72$	−6.91575	−	4.91654i	−0.815029	−	0.579420i
$73$	3.31848	+	1.91592i	0.388398	+	0.224242i	0.681466	−	0.731850i	$-0.261343\pi$
$73$	3.31848	+	1.91592i	0.388398	+	0.224242i	−0.293068	+	0.956092i	$0.594676\pi$
$74$	0.104984	−	0.0593505i	0.0122041	−	0.00689936i
$75$	−5.10667	−	21.9900i	−0.589668	−	2.53919i
$76$	−9.24384	+	5.11586i	−1.06034	+	0.586829i
$77$	2.01340	+	5.67893i	0.229448	+	0.647174i
$78$	−1.35482	−	6.08371i	−0.153403	−	0.688845i
$79$		−	15.1455i		−	1.70400i	−0.523542	−	0.852000i	$-0.675390\pi$
$79$		−	15.1455i		−	1.70400i	0.523542	−	0.852000i	$-0.324610\pi$
$80$	9.02074	−	14.3933i	1.00855	−	1.60922i
$81$	3.41446	+	8.32715i	0.379384	+	0.925239i
$82$	4.87920	−	2.75836i	0.538817	−	0.304610i
$83$	−1.34472	−	0.776375i	−0.147602	−	0.0852183i	0.424380	−	0.905484i	$-0.360492\pi$
$83$	−1.34472	−	0.776375i	−0.147602	−	0.0852183i	−0.571982	+	0.820266i	$0.693825\pi$
$84$	8.05883	+	4.36523i	0.879291	+	0.476286i
$85$	−17.3472	+	10.0154i	−1.88156	+	1.08632i
$86$	5.25472	−	8.91392i	0.566631	−	0.961213i
$87$	−3.84963	−	4.11757i	−0.412724	−	0.441450i
$88$	−3.06784	−	5.66380i	−0.327032	−	0.603763i
$89$	−9.92258	+	5.72880i	−1.05179	+	0.607252i	−0.923150	−	0.384439i	$-0.874395\pi$
$89$	−9.92258	+	5.72880i	−1.05179	+	0.607252i	−0.128641	+	0.991691i	$0.541061\pi$
$90$	−16.2443	+	7.79295i	−1.71230	+	0.821449i
$91$	2.24960	+	6.34515i	0.235822	+	0.665152i
$92$	2.04829	+	1.23260i	0.213549	+	0.128508i
$93$	−8.56941	−	2.60785i	−0.888606	−	0.270422i
$94$	−12.7015	−	0.115094i	−1.31006	−	0.0118711i
$95$			22.4329i			2.30157i
$96$	−9.23471	−	3.27417i	−0.942513	−	0.334168i
$97$	9.40404	+	5.42943i	0.954836	+	0.551275i	0.894580	−	0.446908i	$-0.147475\pi$
$97$	9.40404	+	5.42943i	0.954836	+	0.551275i	0.0602559	+	0.998183i	$0.480808\pi$
$98$	−9.21215	−	3.62439i	−0.930568	−	0.366119i
$99$	−0.458999	+	6.81659i	−0.0461311	+	0.685093i
$100$	−12.6226	−	22.8077i	−1.26226	−	2.28077i
$101$	7.49747	+	12.9860i	0.746026	+	1.29215i	0.949714	+	0.313119i	$0.101374\pi$
$101$	7.49747	+	12.9860i	0.746026	+	1.29215i	−0.203688	+	0.979036i	$0.565293\pi$
$102$	7.81386	+	8.51100i	0.773687	+	0.842714i
$103$	1.48222	−	2.56728i	0.146048	−	0.252962i	−0.783716	−	0.621120i	$-0.786678\pi$
$103$	1.48222	−	2.56728i	0.146048	−	0.252962i	0.929763	+	0.368158i	$0.120011\pi$
$104$	−3.42774	−	6.32825i	−0.336117	−	0.620536i
$105$	16.3954	−	10.4834i	1.60003	−	1.02307i
$106$	12.5908	+	7.42225i	1.22293	+	0.720912i
$107$	4.38115	+	7.58837i	0.423541	+	0.733595i	0.996283	−	0.0861408i	$-0.0274535\pi$
$107$	4.38115	+	7.58837i	0.423541	+	0.733595i	−0.572742	+	0.819736i	$0.694120\pi$
$108$	6.42431	+	8.16874i	0.618180	+	0.786037i
$109$	−15.8196	−	9.13342i	−1.51524	−	0.874823i	−0.999840	−	0.0178722i	$-0.994311\pi$
$109$	−15.8196	−	9.13342i	−1.51524	−	0.874823i	−0.515398	−	0.856951i	$-0.672356\pi$
$110$	−13.6763	−	0.123928i	−1.30398	−	0.0118161i
$111$	−0.143874	+	0.0334114i	−0.0136559	+	0.00317127i
$112$	10.3299	+	2.30056i	0.976087	+	0.217382i
$113$	3.78832	+	6.56156i	0.356375	+	0.617260i	0.987352	−	0.158542i	$-0.0506792\pi$
$113$	3.78832	+	6.56156i	0.356375	+	0.617260i	−0.630977	+	0.775801i	$0.717346\pi$
$114$	12.6301	−	2.81268i	1.18292	−	0.263432i
$115$	4.39587	−	2.53796i	0.409917	−	0.236666i
$116$	−5.57695	−	3.35605i	−0.517807	−	0.311601i
$117$	−0.512846	+	7.61627i	−0.0474126	+	0.704125i
$118$	−0.00771186	+	0.851058i	−0.000709934	+	0.0783463i
$119$	−9.49264	−	8.10136i	−0.870189	−	0.742651i
$120$	−15.5774	+	13.7897i	−1.42202	+	1.25882i
$121$	2.90686	−	5.03483i	0.264260	−	0.457712i
$122$	−3.73923	−	0.0338830i	−0.338534	−	0.00306762i
$123$	−6.68666	+	1.55282i	−0.602916	+	0.140013i
$124$	−10.3415	−	0.187434i	−0.928690	−	0.0168320i
$125$	−34.1165			−3.05147
$126$	−7.95800	−	7.91645i	−0.708955	−	0.705254i
$127$			8.22619i			0.729957i	0.931016	+	0.364978i	$0.118924\pi$
$127$			8.22619i			0.729957i	−0.931016	+	0.364978i	$0.881076\pi$
$128$	−11.2910	−	0.717133i	−0.997989	−	0.0633862i
$129$	−9.25730	+	8.65491i	−0.815059	+	0.762023i
$130$	−15.2807	−	0.138466i	−1.34021	−	0.0121443i
$131$	−6.10138	−	3.52263i	−0.533080	−	0.307774i	0.209190	−	0.977875i	$-0.432917\pi$
$131$	−6.10138	−	3.52263i	−0.533080	−	0.307774i	−0.742270	+	0.670101i	$0.766251\pi$
$132$	1.64499	+	7.71553i	0.143178	+	0.671551i
$133$	−13.1729	+	4.67028i	−1.14223	+	0.404965i
$134$	0.924499	+	0.00837734i	0.0798645	+	0.000723692i
$135$	21.7809	−	3.53619i	1.87460	−	0.304347i
$136$	11.3684	+	6.98224i	0.974829	+	0.598723i
$137$	−7.01998	−	12.1590i	−0.599757	−	1.03881i	−0.992857	−	0.119314i	$-0.961930\pi$
$137$	−7.01998	−	12.1590i	−0.599757	−	1.03881i	0.393099	−	0.919496i	$-0.371403\pi$
$138$	−1.98008	−	2.15674i	−0.168555	−	0.183594i
$139$	8.13323	−	4.69573i	0.689852	−	0.398286i	−0.113705	−	0.993515i	$-0.536272\pi$
$139$	8.13323	−	4.69573i	0.689852	−	0.398286i	0.803557	+	0.595228i	$0.202938\pi$
$140$	14.8947	−	16.8254i	1.25883	−	1.42200i
$141$	14.8828	+	4.52915i	1.25336	+	0.381423i
$142$	−0.113968	+	12.5772i	−0.00956401	+	1.05546i
$143$	−2.89736	+	5.01837i	−0.242289	+	0.419657i
$144$	9.71695	+	7.04137i	0.809746	+	0.586781i
$145$	−11.9688	+	6.91018i	−0.993953	+	0.573859i
$146$	−4.66829	−	2.75194i	−0.386351	−	0.227752i
$147$	9.56929	+	7.44504i	0.789262	+	0.614057i
$148$	−0.149224	+	0.0825856i	−0.0122661	+	0.00678849i
$149$	−10.1520	−	5.86127i	−0.831686	−	0.480174i	0.0227438	−	0.999741i	$-0.492760\pi$
$149$	−10.1520	−	5.86127i	−0.831686	−	0.480174i	−0.854429	+	0.519567i	$0.826093\pi$
$150$	6.93984	+	31.1627i	0.566636	+	2.54443i
$151$	10.4083	−	6.00925i	0.847018	−	0.489026i	−0.0126255	−	0.999920i	$-0.504019\pi$
$151$	10.4083	−	6.00925i	0.847018	−	0.489026i	0.859644	+	0.510894i	$0.170686\pi$
$152$	13.1378	−	7.11617i	1.06561	−	0.577197i
$153$	−6.23601	−	12.7025i	−0.504151	−	1.02693i
$154$	−2.77448	−	8.05669i	−0.223574	−	0.649226i
$155$	−10.9809	+	19.0194i	−0.882004	+	1.52768i
$156$	1.83797	+	8.62067i	0.147155	+	0.690206i
$157$	−13.8537			−1.10565			−0.552824	−	0.833298i	$-0.686450\pi$
$157$	−13.8537			−1.10565			−0.552824	+	0.833298i	$0.686450\pi$
$158$	−0.194080	+	21.4181i	−0.0154402	+	1.70393i
$159$	−12.2250	−	13.0759i	−0.969505	−	1.03698i
$160$	−12.9412	+	20.2388i	−1.02309	+	1.60001i
$161$	2.40549	+	2.05293i	0.189579	+	0.161794i
$162$	−4.72187	−	11.8196i	−0.370985	−	0.928639i
$163$	0.00317992	+	0.00550779i	0.000249071	+	0.000431403i	0.866150	−	0.499784i	$-0.166587\pi$
$163$	0.00317992	+	0.00550779i	0.000249071	+	0.000431403i	−0.865901	+	0.500216i	$0.833254\pi$
$164$	−6.93529	+	3.83823i	−0.541555	+	0.299715i
$165$	16.0250	+	4.87676i	1.24755	+	0.379655i
$166$	1.89170	+	1.11515i	0.146824	+	0.0865522i
$167$	3.34808	+	5.79904i	0.259082	+	0.448743i	0.965996	−	0.258556i	$-0.0832467\pi$
$167$	3.34808	+	5.79904i	0.259082	+	0.448743i	−0.706914	+	0.707299i	$0.749913\pi$
$168$	−11.3405	−	6.27638i	−0.874939	−	0.484234i
$169$	3.26274	−	5.65124i	0.250980	−	0.434710i
$170$	24.6599	−	13.9410i	1.89133	−	1.06923i
$171$	−15.8118	−	1.06470i	−1.20916	−	0.0814193i
$172$	−7.54521	+	12.5383i	−0.575317	+	0.956039i
$173$	−11.2303			−0.853821			−0.426910	−	0.904294i	$-0.640398\pi$
$173$	−11.2303			−0.853821			−0.426910	+	0.904294i	$0.640398\pi$
$174$	5.39122	+	5.87221i	0.408707	+	0.445171i
$175$	−11.5232	−	32.5019i	−0.871070	−	2.45691i
$176$	4.26582	+	8.04881i	0.321548	+	0.606702i
$177$	0.303474	−	0.997217i	0.0228105	−	0.0749554i
$178$	14.1055	−	7.97427i	1.05725	−	0.597696i
$179$	−0.886186	+	1.53492i	−0.0662367	+	0.114725i	−0.897242	−	0.441539i	$-0.854433\pi$
$179$	−0.886186	+	1.53492i	−0.0662367	+	0.114725i	0.831005	+	0.556265i	$0.187766\pi$
$180$	23.0719	−	10.8123i	1.71968	−	0.805900i
$181$	9.79489			0.728049			0.364024	−	0.931389i	$-0.381403\pi$
$181$	9.79489			0.728049			0.364024	+	0.931389i	$0.381403\pi$
$182$	−3.09997	−	9.00185i	−0.229785	−	0.667262i
$183$	4.38140	+	1.33335i	0.323882	+	0.0985642i
$184$	−2.88081	−	1.76934i	−0.212376	−	0.130438i
$185$			0.362136i			0.0266247i
$186$	12.0851	+	3.79772i	0.886119	+	0.278462i
$187$		−	10.7419i		−	0.785528i
$188$	17.9604	+	0.325523i	1.30990	+	0.0237412i
$189$	6.61103	+	12.0538i	0.480882	+	0.876785i
$190$	0.287464	−	31.7236i	0.0208548	−	2.30147i
$191$			16.9687i			1.22781i	0.789380	+	0.613905i	$0.210402\pi$
$191$			16.9687i			1.22781i	−0.789380	+	0.613905i	$0.789598\pi$
$192$	13.0174	+	4.74852i	0.939447	+	0.342695i
$193$	14.2094			1.02282			0.511408	−	0.859338i	$-0.329124\pi$
$193$	14.2094			1.02282			0.511408	+	0.859338i	$0.329124\pi$
$194$	−13.2292	−	7.79856i	−0.949801	−	0.559904i
$195$	17.9050	+	5.44888i	1.28221	+	0.390202i
$196$	12.9810	+	5.24350i	0.927212	+	0.374536i
$197$			0.762030i			0.0542924i	0.999631	+	0.0271462i	$0.00864197\pi$
$197$			0.762030i			0.0542924i	−0.999631	+	0.0271462i	$0.991358\pi$
$198$	0.736446	−	9.63383i	0.0523369	−	0.684647i
$199$	5.87373	−	10.1736i	0.416378	−	0.721187i	−0.579194	−	0.815189i	$-0.696633\pi$
$199$	5.87373	−	10.1736i	0.416378	−	0.721187i	0.995572	+	0.0940024i	$0.0299661\pi$
$200$	17.5580	+	32.4153i	1.24154	+	2.29211i
$201$	−1.08327	−	0.329662i	−0.0764080	−	0.0232526i
$202$	−10.4362	−	18.4603i	−0.734287	−	1.29886i
$203$	−6.54950	−	5.58958i	−0.459685	−	0.392312i
$204$	−10.9409	−	12.1360i	−0.766020	−	0.849690i
$205$			16.8305i			1.17550i
$206$	−2.12899	+	3.61154i	−0.148334	+	0.251628i
$207$	1.58024	+	3.21888i	0.109834	+	0.223727i
$208$	4.76626	+	8.99305i	0.330481	+	0.623556i
$209$	−10.4184	−	6.01506i	−0.720655	−	0.416071i
$210$	−23.3200	+	14.6150i	−1.60923	+	1.00853i
$211$	−3.50875	−	6.07733i	−0.241552	−	0.418381i	0.719604	−	0.694384i	$-0.244323\pi$
$211$	−3.50875	−	6.07733i	−0.241552	−	0.418381i	−0.961157	+	0.276003i	$0.910990\pi$
$212$	−17.7103	−	10.6576i	−1.21635	−	0.731964i
$213$	4.48484	−	14.7372i	0.307296	−	1.00978i
$214$	−6.09838	−	10.7873i	−0.416877	−	0.737403i
$215$	15.5358	+	26.9087i	1.05953	+	1.83516i
$216$	−8.98030	−	11.6342i	−0.611032	−	0.791606i
$217$	−13.4545	−	2.48846i	−0.913352	−	0.168928i
$218$	22.2543	+	13.1188i	1.50725	+	0.888517i
$219$	4.53265	+	4.84812i	0.306288	+	0.327606i
$220$	19.3388	+	0.350506i	1.30382	+	0.0236311i
$221$		−	12.0021i		−	0.807350i
$222$	0.203888	−	0.0454053i	0.0136841	−	0.00304740i
$223$	−1.22301	+	2.11832i	−0.0818988	+	0.141853i	−0.904066	−	0.427394i	$-0.859432\pi$
$223$	−1.22301	+	2.11832i	−0.0818988	+	0.141853i	0.822167	+	0.569247i	$0.192765\pi$
$224$	−14.5786	−	3.38572i	−0.974077	−	0.226218i
$225$	2.62696	−	39.0130i	0.175131	−	2.60087i
$226$	−5.27319	−	9.32761i	−0.350767	−	0.620463i
$227$	4.56904	−	2.63794i	0.303258	−	0.175086i	−0.340648	−	0.940191i	$-0.610646\pi$
$227$	4.56904	−	2.63794i	0.303258	−	0.175086i	0.643905	+	0.765105i	$0.277313\pi$
$228$	−17.8970	+	3.81573i	−1.18526	+	0.252703i
$229$	3.77684	−	6.54168i	0.249581	−	0.432286i	−0.713829	−	0.700320i	$-0.753041\pi$
$229$	3.77684	−	6.54168i	0.249581	−	0.432286i	0.963409	+	0.268034i	$0.0863739\pi$
$230$	−6.24897	+	3.53274i	−0.412045	+	0.232942i
$231$	0.472547	+	10.4254i	0.0310913	+	0.685940i
$232$	7.84366	+	4.81744i	0.514962	+	0.316280i
$233$	1.36944	+	2.37193i	0.0897148	+	0.155391i	0.907391	−	0.420288i	$-0.138071\pi$
$233$	1.36944	+	2.37193i	0.0897148	+	0.155391i	−0.817676	+	0.575679i	$0.804738\pi$
$234$	0.822841	−	10.7640i	0.0537908	−	0.703666i
$235$	19.0709	−	33.0317i	1.24405	−	2.15475i
$236$	0.0218115	−	1.20343i	0.00141981	−	0.0783366i
$237$	7.63736	−	25.0964i	0.496100	−	1.63018i
$238$	13.3203	+	11.5782i	0.863424	+	0.750505i
$239$	−6.92925	+	4.00061i	−0.448216	+	0.258778i	−0.707076	−	0.707137i	$-0.749986\pi$
$239$	−6.92925	+	4.00061i	−0.448216	+	0.258778i	0.258860	+	0.965915i	$0.416653\pi$
$240$	22.2056	−	19.3011i	1.43337	−	1.24588i
$241$	−12.3497	+	7.13011i	−0.795515	+	0.459291i	−0.841900	−	0.539633i	$-0.818563\pi$
$241$	−12.3497	+	7.13011i	−0.795515	+	0.459291i	0.0463858	+	0.998924i	$0.485230\pi$
$242$	−4.17527	+	7.08278i	−0.268396	+	0.455298i
$243$	1.45872	+	15.5201i	0.0935772	+	0.995612i
$244$	5.28742	+	0.0958317i	0.338492	+	0.00613500i
$245$	23.0878	−	18.7246i	1.47502	−	1.19627i
$246$	9.47587	−	2.11025i	0.604160	−	0.134544i
$247$	−11.6406	−	6.72072i	−0.740675	−	0.427629i
$248$	14.6220	+	0.397579i	0.928499	+	0.0252463i
$249$	−1.83673	−	1.96457i	−0.116398	−	0.124499i
$250$	48.2460	+	0.437181i	3.05134	+	0.0276498i
$251$			19.8384i			1.25219i	0.779748	+	0.626094i	$0.215347\pi$
$251$			19.8384i			1.25219i	−0.779748	+	0.626094i	$0.784653\pi$
$252$	11.1524	+	11.2971i	0.702536	+	0.711649i
$253$			2.72207i			0.171135i
$254$	0.105413	−	11.6331i	0.00661423	−	0.729927i
$255$	−33.7950	+	7.84811i	−2.11633	+	0.491468i
$256$	15.9580	+	1.15882i	0.997374	+	0.0724265i
$257$	15.7995	+	9.12186i	0.985547	+	0.569006i	0.903940	−	0.427659i	$-0.140661\pi$
$257$	15.7995	+	9.12186i	0.985547	+	0.569006i	0.0816070	+	0.996665i	$0.473995\pi$
$258$	13.2022	−	12.1208i	0.821931	−	0.754606i
$259$	−0.212650	+	0.0753926i	−0.0132134	+	0.00468467i
$260$	21.6076	+	0.391626i	1.34004	+	0.0242876i
$261$	−4.30257	−	8.76413i	−0.266322	−	0.542486i
$262$	8.58316	+	5.05973i	0.530269	+	0.312591i
$263$	18.6396	−	10.7616i	1.14937	−	0.663588i	0.200635	−	0.979666i	$-0.435699\pi$
$263$	18.6396	−	10.7616i	1.14937	−	0.663588i	0.948733	+	0.316078i	$0.102366\pi$
$264$	−2.22740	−	10.9320i	−0.137087	−	0.672820i
$265$	−38.0084	+	21.9441i	−2.33483	+	1.34802i
$266$	18.6883	−	6.43571i	1.14585	−	0.394598i
$267$	−19.3307	+	4.48912i	−1.18302	+	0.274730i
$268$	−1.30728	−	0.0236937i	−0.0798547	−	0.00144732i
$269$	−9.08071	+	15.7283i	−0.553661	+	0.958968i	0.444346	+	0.895855i	$0.353436\pi$
$269$	−9.08071	+	15.7283i	−0.553661	+	0.958968i	−0.998006	+	0.0631130i	$0.979897\pi$
$270$	−30.8469	+	4.72161i	−1.87728	+	0.287348i
$271$	−3.48971	−	6.04435i	−0.211985	−	0.367168i	0.740351	−	0.672221i	$-0.234659\pi$
$271$	−3.48971	−	6.04435i	−0.211985	−	0.367168i	−0.952336	+	0.305052i	$0.901326\pi$
$272$	−15.9872	−	10.0197i	−0.969363	−	0.607531i
$273$	0.527983	+	11.6484i	0.0319550	+	0.704995i
$274$	9.77153	+	17.2846i	0.590320	+	1.04420i
$275$	14.8412	−	25.7057i	0.894958	−	1.55011i
$276$	2.77250	+	3.07533i	0.166885	+	0.185113i
$277$	12.8227	−	7.40319i	0.770442	−	0.444815i	−0.0625905	−	0.998039i	$-0.519936\pi$
$277$	12.8227	−	7.40319i	0.770442	−	0.444815i	0.833032	+	0.553225i	$0.186603\pi$
$278$	−11.5618	+	6.53626i	−0.693433	+	0.392019i
$279$	−12.8846	−	8.64252i	−0.771382	−	0.517414i
$280$	−21.2791	+	23.6028i	−1.27167	+	1.41054i
$281$	7.27227	−	12.5959i	0.433827	−	0.751411i	−0.563372	−	0.826203i	$-0.690496\pi$
$281$	7.27227	−	12.5959i	0.433827	−	0.751411i	0.997199	+	0.0747925i	$0.0238295\pi$
$282$	−20.9886	−	6.59564i	−1.24985	−	0.392765i
$283$			21.9980i			1.30765i	0.756647	+	0.653823i	$0.226836\pi$
$283$			21.9980i			1.30765i	−0.756647	+	0.653823i	$0.773164\pi$
$284$	0.322338	−	17.7847i	0.0191272	−	1.05533i
$285$	−11.3122	+	37.1718i	−0.670074	+	2.20187i
$286$	4.16162	−	7.05962i	0.246082	−	0.417444i
$287$	−9.88308	+	3.50393i	−0.583380	+	0.206830i
$288$	−13.6510	−	10.0821i	−0.804396	−	0.594094i
$289$	2.62446	+	4.54569i	0.154380	+	0.267394i
$290$	17.0143	−	9.61869i	0.999112	−	0.564829i
$291$	12.8448	+	13.7388i	0.752976	+	0.805383i
$292$	6.56643	+	3.95149i	0.384271	+	0.231243i
$293$	9.02688	+	15.6350i	0.527356	+	0.913407i	0.999492	+	0.0318815i	$0.0101499\pi$
$293$	9.02688	+	15.6350i	0.527356	+	0.913407i	−0.472136	+	0.881526i	$0.656517\pi$
$294$	−13.4371	−	10.6511i	−0.783666	−	0.621183i
$295$	−2.21328	−	1.27784i	−0.128862	−	0.0743986i
$296$	0.212084	−	0.114877i	0.0123271	−	0.00667707i
$297$	−4.19794	+	11.0638i	−0.243589	+	0.641985i
$298$	14.2814	+	8.41884i	0.827301	+	0.487690i
$299$			3.04141i			0.175889i
$300$	−9.41469	−	44.1579i	−0.543557	−	2.54946i
$301$	−12.5667	+	14.7249i	−0.724335	+	0.848728i
$302$	−14.7960	+	8.36464i	−0.851414	+	0.481331i
$303$	5.87505	+	25.2988i	0.337513	+	1.45338i
$304$	−18.6701	+	9.89501i	−1.07080	+	0.567518i
$305$	5.61434	−	9.72431i	0.321476	−	0.556813i
$306$	8.65591	+	18.0432i	0.494825	+	1.03146i
$307$			16.7995i			0.958800i	0.877597	+	0.479400i	$0.159146\pi$
$307$			16.7995i			0.958800i	−0.877597	+	0.479400i	$0.840854\pi$
$308$	3.82031	+	11.4290i	0.217682	+	0.651226i
$309$	3.75066	−	3.50660i	0.213368	−	0.199484i
$310$	15.7724	−	26.7557i	0.895810	−	1.51962i
$311$	9.60658			0.544739			0.272370	−	0.962193i	$-0.412193\pi$
$311$	9.60658			0.544739			0.272370	+	0.962193i	$0.412193\pi$
$312$	−2.48871	−	12.2145i	−0.140895	−	0.691511i
$313$			23.2026i			1.31149i	0.754984	+	0.655743i	$0.227645\pi$
$313$			23.2026i			1.31149i	−0.754984	+	0.655743i	$0.772355\pi$
$314$	19.5913	+	0.177527i	1.10560	+	0.0100184i
$315$	32.4539	−	9.10351i	1.82857	−	0.512925i
$316$	0.548918	−	30.2860i	0.0308791	−	1.70372i
$317$		−	0.619137i		−	0.0347742i	−0.999849	−	0.0173871i	$-0.994465\pi$
$317$		−	0.619137i		−	0.0347742i	0.999849	−	0.0173871i	$-0.00553476\pi$
$318$	17.1205	+	18.6479i	0.960069	+	1.04572i
$319$		−	7.41146i		−	0.414962i
$320$	18.5602	−	28.4549i	1.03754	−	1.59068i
$321$	3.43309	+	14.7833i	0.191616	+	0.825126i
$322$	−3.37543	−	2.93399i	−0.188105	−	0.163505i
$323$	24.9170			1.38642
$324$	6.52599	+	16.7753i	0.362555	+	0.931962i
$325$	16.5823	−	28.7214i	0.919820	−	1.59317i
$326$	−0.00442632	−	0.00782961i	−0.000245151	−	0.000433642i
$327$	−21.6076	−	23.1115i	−1.19491	−	1.27807i
$328$	9.85676	−	5.33898i	0.544249	−	0.294796i
$329$	23.3670	+	4.32180i	1.28826	+	0.238269i
$330$	−22.5994	−	7.10185i	−1.24406	−	0.390944i
$331$	−21.0990			−1.15970			−0.579852	−	0.814722i	$-0.696890\pi$
$331$	−21.0990			−1.15970			−0.579852	+	0.814722i	$0.696890\pi$
$332$	−2.66086	−	1.60123i	−0.146034	−	0.0878791i
$333$	−0.255251	−	0.0171874i	−0.0139876	−	0.000941865i
$334$	−4.66039	−	8.24365i	−0.255005	−	0.451072i
$335$	−1.38811	+	2.40427i	−0.0758403	+	0.131359i
$336$	15.9568	+	9.02111i	0.870515	+	0.492142i
$337$	2.48017	+	4.29578i	0.135103	+	0.234006i	0.925637	−	0.378413i	$-0.123530\pi$
$337$	2.48017	+	4.29578i	0.135103	+	0.234006i	−0.790534	+	0.612419i	$0.790197\pi$
$338$	−4.68644	+	7.94992i	−0.254909	+	0.432418i
$339$	2.96855	+	12.7830i	0.161229	+	0.694275i
$340$	−35.0516	+	19.3988i	−1.90094	+	1.05205i
$341$	−5.88872	−	10.1996i	−0.318892	−	0.552337i
$342$	22.3467	+	1.70826i	1.20837	+	0.0923723i
$343$	15.8019	+	9.65914i	0.853224	+	0.521545i
$344$	10.8308	−	17.6345i	0.583956	−	0.950787i
$345$	8.56386	−	1.98876i	0.461063	−	0.107071i
$346$	15.8813	+	0.143909i	0.853786	+	0.00773658i
$347$	−12.5438			−0.673385			−0.336693	−	0.941615i	$-0.609308\pi$
$347$	−12.5438			−0.673385			−0.336693	+	0.941615i	$0.609308\pi$
$348$	−7.54877	−	8.37331i	−0.404657	−	0.448856i
$349$	2.90769	−	5.03626i	0.155645	−	0.269585i	−0.777649	−	0.628699i	$-0.783588\pi$
$349$	2.90769	−	5.03626i	0.155645	−	0.269585i	0.933294	+	0.359114i	$0.116921\pi$
$350$	15.8791	+	46.1104i	0.848771	+	2.46471i
$351$	−4.69043	+	12.3617i	−0.250356	+	0.659819i
$352$	−5.92939	−	11.4369i	−0.316038	−	0.609590i
$353$	8.52413	−	4.92141i	0.453694	−	0.261940i	−0.255695	−	0.966757i	$-0.582304\pi$
$353$	8.52413	−	4.92141i	0.453694	−	0.261940i	0.709389	+	0.704817i	$0.248971\pi$
$354$	−0.441939	+	1.40633i	−0.0234888	+	0.0747457i
$355$	−32.7085	−	18.8843i	−1.73599	−	1.00227i
$356$	−20.0495	+	11.0961i	−1.06262	+	0.588092i
$357$	−11.6443	−	18.2109i	−0.616279	−	0.963825i
$358$	1.27287	−	2.15926i	0.0672735	−	0.114120i
$359$	−27.5240	+	15.8910i	−1.45266	+	0.838693i	−0.998632	−	0.0522952i	$-0.983346\pi$
$359$	−27.5240	+	15.8910i	−1.45266	+	0.838693i	−0.454027	+	0.890988i	$0.650013\pi$
$360$	−32.7658	+	14.9946i	−1.72691	+	0.790285i
$361$	4.45257	−	7.71208i	0.234346	−	0.405899i
$362$	−13.8515	−	0.125515i	−0.728019	−	0.00659694i
$363$	7.35562	−	6.87698i	0.386070	−	0.360948i
$364$	4.26849	+	12.7697i	0.223730	+	0.669317i
$365$	14.0923	−	8.13620i	0.737626	−	0.425868i
$366$	−6.17889	−	1.94171i	−0.322976	−	0.101495i
$367$	16.8255	+	29.1426i	0.878283	+	1.52123i	0.853224	+	0.521545i	$0.174644\pi$
$367$	16.8255	+	29.1426i	0.878283	+	1.52123i	0.0250592	+	0.999686i	$0.492023\pi$
$368$	4.05124	+	2.53904i	0.211185	+	0.132357i
$369$	−11.8630	−	0.798799i	−0.617561	−	0.0415838i
$370$	0.00464054	−	0.512116i	0.000241250	−	0.0266236i
$371$	−20.7988	−	17.7504i	−1.07982	−	0.921556i
$372$	−17.0415	−	5.52543i	−0.883560	−	0.286480i
$373$	28.5054	+	16.4576i	1.47595	+	0.852142i	0.999632	−	0.0271296i	$-0.00863669\pi$
$373$	28.5054	+	16.4576i	1.47595	+	0.852142i	0.476321	+	0.879271i	$0.341970\pi$
$374$	−0.137651	+	15.1908i	−0.00711777	+	0.785496i
$375$	−56.5317	−	17.2038i	−2.91928	−	0.888399i
$376$	−25.3946	−	0.690491i	−1.30963	−	0.0356093i
$377$		−	8.28093i		−	0.426490i
$378$	−9.19457	−	17.1307i	−0.472918	−	0.881107i
$379$	9.40072			0.482883			0.241441	−	0.970415i	$-0.422380\pi$
$379$	9.40072			0.482883			0.241441	+	0.970415i	$0.422380\pi$
$380$	−0.813036	+	44.8585i	−0.0417079	+	2.30119i
$381$	−4.14819	+	13.6310i	−0.212518	+	0.698336i
$382$	0.217443	−	23.9964i	0.0111253	−	1.22776i
$383$	−8.60018	+	14.8959i	−0.439449	+	0.761147i	−0.997647	−	0.0685602i	$-0.978159\pi$
$383$	−8.60018	+	14.8959i	−0.439449	+	0.761147i	0.558198	+	0.829708i	$0.311493\pi$
$384$	−18.3477	−	6.88195i	−0.936303	−	0.351193i
$385$	25.1604	+	4.65350i	1.28229	+	0.237164i
$386$	−20.0943	−	0.182085i	−1.02277	−	0.00926787i
$387$	−19.7039	+	9.67322i	−1.00161	+	0.491718i
$388$	18.6082	+	11.1979i	0.944689	+	0.568487i
$389$	13.1980	−	7.61985i	0.669163	−	0.386341i	−0.126596	−	0.991954i	$-0.540405\pi$
$389$	13.1980	−	7.61985i	0.669163	−	0.386341i	0.795759	+	0.605613i	$0.207072\pi$
$390$	−25.2507	−	7.93500i	−1.27862	−	0.401804i
$391$	−2.81900	−	4.88265i	−0.142563	−	0.246926i
$392$	−18.2899	−	7.58147i	−0.923781	−	0.382922i
$393$	−8.33376	−	8.91379i	−0.420383	−	0.449641i
$394$	0.00976494	−	1.07763i	0.000491950	−	0.0542902i
$395$	−55.7003	−	32.1586i	−2.80259	−	1.61807i
$396$	−1.16490	+	13.6143i	−0.0585384	+	0.684144i
$397$	−9.59121	−	16.6125i	−0.481369	−	0.833755i	0.518403	−	0.855137i	$-0.326527\pi$
$397$	−9.59121	−	16.6125i	−0.481369	−	0.833755i	−0.999771	+	0.0213814i	$0.993194\pi$
$398$	−8.43673	+	14.3118i	−0.422895	+	0.717385i
$399$	−24.1828	+	1.09612i	−1.21065	+	0.0548747i
$400$	−24.4143	−	46.0653i	−1.22072	−	2.30327i
$401$	11.9579	−	20.7116i	0.597147	−	1.03429i	−0.396093	−	0.918211i	$-0.629634\pi$
$401$	11.9579	−	20.7116i	0.597147	−	1.03429i	0.993240	−	0.116079i	$-0.0370325\pi$
$402$	1.52769	+	0.480075i	0.0761942	+	0.0239440i
$403$	−6.57956	−	11.3961i	−0.327751	−	0.567681i
$404$	14.5218	+	26.2395i	0.722487	+	1.30546i
$405$	37.8746	+	5.12384i	1.88200	+	0.254606i
$406$	9.19039	+	7.98847i	0.456111	+	0.396461i
$407$	−0.168185	−	0.0971015i	−0.00833661	−	0.00481314i
$408$	15.3167	+	17.3024i	0.758289	+	0.856596i
$409$		−	33.0948i		−	1.63643i	−0.574910	−	0.818217i	$-0.694963\pi$
$409$		−	33.0948i		−	1.63643i	0.574910	−	0.818217i	$-0.305037\pi$
$410$	0.215673	−	23.8010i	0.0106513	−	1.17545i
$411$	−5.50089	−	23.6876i	−0.271339	−	1.16842i
$412$	3.05700	−	5.08000i	0.150608	−	0.250274i
$413$	0.289581	−	1.56570i	0.0142493	−	0.0770428i
$414$	−2.19346	−	4.57224i	−0.107803	−	0.224713i
$415$	−5.71052	+	3.29697i	−0.280319	+	0.161842i
$416$	−6.62500	−	12.7787i	−0.324817	−	0.626525i
$417$	15.8448	−	3.67960i	0.775925	−	0.180191i
$418$	14.6562	+	8.63974i	0.716856	+	0.422584i
$419$	−20.7162	+	11.9605i	−1.01205	+	0.584310i	−0.911793	−	0.410651i	$-0.865301\pi$
$419$	−20.7162	+	11.9605i	−1.01205	+	0.584310i	−0.100262	+	0.994961i	$0.531968\pi$
$420$	33.1653	−	20.3691i	1.61830	−	0.993909i
$421$	−8.00858	−	4.62375i	−0.390314	−	0.225348i	0.291982	−	0.956424i	$-0.405685\pi$
$421$	−8.00858	−	4.62375i	−0.390314	−	0.225348i	−0.682296	+	0.731076i	$0.739019\pi$
$422$	4.88404	+	8.63926i	0.237751	+	0.420553i
$423$	22.3772	+	15.0098i	1.08802	+	0.729801i
$424$	24.9085	+	15.2984i	1.20967	+	0.742955i
$425$			61.4788i			2.98216i
$426$	−6.53111	+	20.7832i	−0.316433	+	1.00695i
$427$	6.87907	+	1.27231i	0.332902	+	0.0615713i
$428$	8.48583	+	15.3330i	0.410178	+	0.741150i
$429$	−7.33157	+	6.85450i	−0.353971	+	0.330938i
$430$	−21.6252	−	38.2522i	−1.04286	−	1.84468i
$431$	−0.314868	−	0.181789i	−0.0151666	−	0.00875647i	0.492398	−	0.870370i	$-0.336121\pi$
$431$	−0.314868	−	0.181789i	−0.0151666	−	0.00875647i	−0.507564	+	0.861614i	$0.669454\pi$
$432$	12.5505	+	16.5676i	0.603834	+	0.797110i
$433$		−	20.1586i		−	0.968761i	−0.874858	−	0.484380i	$-0.839045\pi$
$433$		−	20.1586i		−	0.968761i	0.874858	−	0.484380i	$-0.160955\pi$
$434$	18.9949	+	3.69148i	0.911784	+	0.177197i
$435$	−23.3171	+	5.41485i	−1.11797	+	0.259622i
$436$	−31.3029	−	18.8372i	−1.49914	−	0.902138i
$437$	−6.31412			−0.302045
$438$	−6.34774	−	6.91408i	−0.303307	−	0.330368i
$439$	−33.2358			−1.58626			−0.793129	−	0.609053i	$-0.791550\pi$
$439$	−33.2358			−1.58626			−0.793129	+	0.609053i	$0.791550\pi$
$440$	−27.3436	−	0.743486i	−1.30356	−	0.0354443i
$441$	12.1022	+	17.1621i	0.576297	+	0.817241i
$442$	−0.153800	+	16.9729i	−0.00731550	+	0.807317i
$443$	23.4559			1.11442			0.557211	−	0.830371i	$-0.311871\pi$
$443$	23.4559			1.11442			0.557211	+	0.830371i	$0.311871\pi$
$444$	−0.288912	+	0.0615975i	−0.0137112	+	0.00292329i
$445$			48.6561i			2.30652i
$446$	1.75667	−	2.97996i	0.0831808	−	0.141105i
$447$	−13.8665	−	14.8316i	−0.655861	−	0.701509i
$448$	20.5731	+	4.97475i	0.971987	+	0.235035i
$449$	−12.1148			−0.571732			−0.285866	−	0.958270i	$-0.592281\pi$
$449$	−12.1148			−0.571732			−0.285866	+	0.958270i	$0.592281\pi$
$450$	−4.21486	+	55.1368i	−0.198690	+	2.59917i
$451$	−7.81651	−	4.51287i	−0.368065	−	0.212503i
$452$	7.33758	+	13.2583i	0.345131	+	0.623616i
$453$	20.2771	−	4.70888i	0.952700	−	0.221243i
$454$	−6.49513	+	3.67190i	−0.304832	+	0.172331i
$455$	28.1120	+	5.19942i	1.31791	+	0.243753i
$456$	25.3580	−	5.16669i	1.18750	−	0.241953i
$457$	−8.70221			−0.407072			−0.203536	−	0.979067i	$-0.565243\pi$
$457$	−8.70221			−0.407072			−0.203536	+	0.979067i	$0.565243\pi$
$458$	−5.42486	+	9.20255i	−0.253487	+	0.430007i
$459$	−3.92777	−	24.1928i	−0.183333	−	1.12922i
$460$	8.88229	−	4.91576i	0.414139	−	0.229199i
$461$	8.45435	−	14.6434i	0.393758	−	0.682009i	−0.599184	−	0.800612i	$-0.704508\pi$
$461$	8.45435	−	14.6434i	0.393758	−	0.682009i	0.992942	+	0.118602i	$0.0378414\pi$
$462$	−0.534660	−	14.7492i	−0.0248746	−	0.686194i
$463$	35.0814	−	20.2542i	1.63037	−	0.941295i	0.646392	−	0.763006i	$-0.276277\pi$
$463$	35.0814	−	20.2542i	1.63037	−	0.941295i	0.983978	−	0.178289i	$-0.0570562\pi$
$464$	−11.0304	−	6.91312i	−0.512075	−	0.320934i
$465$	−27.7864	+	25.9783i	−1.28856	+	1.20471i
$466$	−1.90620	−	3.37183i	−0.0883031	−	0.156197i
$467$	19.0373	−	10.9912i	0.880939	−	0.508610i	0.00997120	−	0.999950i	$-0.496826\pi$
$467$	19.0373	−	10.9912i	0.880939	−	0.508610i	0.870968	+	0.491340i	$0.163493\pi$
$468$	−1.30156	+	15.2115i	−0.0601646	+	0.703150i
$469$	−1.70080	−	0.314570i	−0.0785358	−	0.0145255i
$470$	−27.3925	+	46.4676i	−1.26352	+	2.14339i
$471$	−22.9559	−	6.98597i	−1.05775	−	0.321896i
$472$	−0.0462661	+	1.70156i	−0.00212957	+	0.0783205i
$473$	−16.6628			−0.766155
$474$	−11.1220	+	35.3923i	−0.510851	+	1.62562i
$475$	59.6271	+	34.4257i	2.73588	+	1.57956i
$476$	−18.6885	−	16.5441i	−0.856588	−	0.758298i
$477$	−13.6633	−	27.8316i	−0.625602	−	1.27432i
$478$	9.85031	−	5.56868i	0.450542	−	0.254706i
$479$	−18.1101	−	31.3677i	−0.827474	−	1.43323i	−0.900014	−	0.435861i	$-0.856444\pi$
$479$	−18.1101	−	31.3677i	−0.827474	−	1.43323i	0.0725406	−	0.997365i	$-0.476889\pi$
$480$	−31.6495	+	27.0102i	−1.44460	+	1.23284i
$481$	−0.187915	−	0.108493i	−0.00856820	−	0.00494685i
$482$	17.5558	−	9.92483i	0.799644	−	0.452063i
$483$	2.95072	+	4.61476i	0.134262	+	0.209979i
$484$	5.99524	−	9.96265i	0.272511	−	0.452848i
$485$	39.9354	−	23.0567i	1.81337	−	1.04695i
$486$	−1.86398	−	21.9665i	−0.0845520	−	0.996419i
$487$	−6.42689	−	3.71056i	−0.291230	−	0.168142i	0.347266	−	0.937767i	$-0.387110\pi$
$487$	−6.42689	−	3.71056i	−0.291230	−	0.168142i	−0.638496	+	0.769625i	$0.720443\pi$
$488$	−7.47600	−	0.203276i	−0.338423	−	0.00920186i
$489$	0.00249180	+	0.0107300i	0.000112683	+	0.000485229i
$490$	−32.8896	+	26.1837i	−1.48580	+	1.18286i
$491$	15.6451	+	27.0980i	0.706052	+	1.22292i	0.966311	+	0.257379i	$0.0828588\pi$
$491$	15.6451	+	27.0980i	0.706052	+	1.22292i	−0.260259	+	0.965539i	$0.583808\pi$
$492$	−13.4274	+	2.86279i	−0.605354	+	0.129065i
$493$	7.67538	+	13.2942i	0.345682	+	0.598739i
$494$	16.3755	+	9.65331i	0.736770	+	0.434323i
$495$	24.0946	+	16.1618i	1.08297	+	0.726418i
$496$	−20.6727	−	0.749611i	−0.928233	−	0.0336585i
$497$	4.27952	−	23.1383i	0.191963	−	1.03790i
$498$	2.57225	+	2.80174i	0.115265	+	0.125549i
$499$	−4.87271	+	8.43978i	−0.218132	+	0.377817i	−0.954237	−	0.299051i	$-0.903330\pi$
$499$	−4.87271	+	8.43978i	−0.218132	+	0.377817i	0.736105	+	0.676868i	$0.236663\pi$
$500$	−68.2217	−	1.23648i	−3.05097	−	0.0552972i
$501$	2.62357	+	11.2974i	0.117213	+	0.504733i
$502$	0.254216	−	28.0546i	0.0113462	−	1.25214i
$503$	18.1773			0.810488			0.405244	−	0.914209i	$-0.367187\pi$
$503$	18.1773			0.810488			0.405244	+	0.914209i	$0.367187\pi$
$504$	−15.6265	−	16.1187i	−0.696058	−	0.717985i
$505$	63.6778			2.83362
$506$	0.0348816	−	3.84943i	0.00155068	−	0.171128i
$507$	8.25616	−	7.71892i	0.366669	−	0.342809i
$508$	−0.298142	+	16.4497i	−0.0132279	+	0.729837i
$509$	12.4696	−	21.5979i	0.552704	−	0.957311i	−0.445375	−	0.895344i	$-0.646930\pi$
$509$	12.4696	−	21.5979i	0.552704	−	0.957311i	0.998078	−	0.0619664i	$-0.0197372\pi$
$510$	47.8920	−	10.6654i	2.12069	−	0.472271i
$511$	7.71154	+	6.58131i	0.341138	+	0.291140i
$512$	−22.5522	−	1.84325i	−0.996677	−	0.0814609i
$513$	−25.6636	−	9.73757i	−1.13307	−	0.429924i
$514$	−22.2261	−	13.1022i	−0.980351	−	0.577913i
$515$	−6.29443	−	10.9023i	−0.277366	−	0.480412i
$516$	−18.8252	+	16.9715i	−0.828735	+	0.747127i
$517$	10.2272	+	17.7140i	0.449790	+	0.779059i
$518$	0.301687	−	0.103892i	0.0132554	−	0.00456475i
$519$	−18.6088	−	5.66304i	−0.816834	−	0.248580i
$520$	−30.5514	−	0.830707i	−1.33977	−	0.0364289i
$521$	5.36787	+	3.09914i	0.235171	+	0.135776i	0.612955	−	0.790118i	$-0.289981\pi$
$521$	5.36787	+	3.09914i	0.235171	+	0.135776i	−0.377784	+	0.925894i	$0.623314\pi$
$522$	5.97220	+	12.4490i	0.261396	+	0.544877i
$523$	−9.84372	+	5.68328i	−0.430436	+	0.248512i	−0.699532	−	0.714601i	$-0.746608\pi$
$523$	−9.84372	+	5.68328i	−0.430436	+	0.248512i	0.269096	+	0.963113i	$0.413275\pi$
$524$	−12.0731	−	7.26524i	−0.527415	−	0.317383i
$525$	−2.70450	−	59.6671i	−0.118034	−	2.60408i
$526$	−26.4972	+	14.9797i	−1.15533	+	0.653146i
$527$	21.1255	+	12.1968i	0.920243	+	0.531303i
$528$	3.00981	+	15.4881i	0.130985	+	0.674035i
$529$	−10.7856	−	18.6813i	−0.468941	−	0.812230i
$530$	54.0309	−	30.5454i	2.34695	−	1.32681i
$531$	1.00573	−	1.49938i	0.0436448	−	0.0650674i
$532$	−26.5107	+	8.86161i	−1.14938	+	0.384199i
$533$	−8.73350	−	5.04229i	−0.378290	−	0.218406i
$534$	27.3942	−	6.10060i	1.18546	−	0.263999i
$535$	37.2101			1.60873
$536$	1.84839	+	0.0502586i	0.0798383	+	0.00217084i
$537$	−2.24244	+	2.09652i	−0.0967683	+	0.0904715i
$538$	13.0431	−	22.1258i	0.562327	−	0.953912i
$539$	2.50552	+	15.7433i	0.107920	+	0.678110i
$540$	43.6828	−	6.28181i	1.87981	−	0.270326i
$541$	5.84542	−	3.37486i	0.251314	−	0.145096i	−0.369052	−	0.929409i	$-0.620317\pi$
$541$	5.84542	−	3.37486i	0.251314	−	0.145096i	0.620366	+	0.784312i	$0.286984\pi$
$542$	4.85753	+	8.59237i	0.208649	+	0.369074i
$543$	16.2303	+	4.93923i	0.696510	+	0.211963i
$544$	22.4799	+	14.3742i	0.963819	+	0.616290i
$545$	−67.1796	+	38.7862i	−2.87766	+	1.66142i
$546$	−0.597383	−	16.4795i	−0.0255656	−	0.705256i
$547$	−8.00398	+	13.8633i	−0.342225	+	0.592752i	−0.984846	−	0.173433i	$-0.944514\pi$
$547$	−8.00398	+	13.8633i	−0.342225	+	0.592752i	0.642620	+	0.766185i	$0.277847\pi$
$548$	−13.5970	−	24.5684i	−0.580834	−	1.04951i
$549$	6.58770	+	4.41878i	0.281156	+	0.188589i
$550$	−21.3172	+	36.1617i	−0.908967	+	1.54194i
$551$	17.1917			0.732389
$552$	−3.88134	−	4.38453i	−0.165201	−	0.186618i
$553$	7.28771	−	39.4029i	0.309905	−	1.67558i
$554$	−18.2282	+	10.3049i	−0.774440	+	0.437815i
$555$	−0.182613	+	0.600066i	−0.00775148	+	0.0254714i
$556$	16.4340	−	9.09514i	0.696956	−	0.385720i
$557$	0.468298	+	0.270372i	0.0198424	+	0.0114560i	0.509888	−	0.860241i	$-0.329687\pi$
$557$	0.468298	+	0.270372i	0.0198424	+	0.0114560i	−0.490046	+	0.871697i	$0.663020\pi$
$558$	18.1101	+	12.3870i	0.766662	+	0.524383i
$559$	−18.6176			−0.787439
$560$	30.3944	−	33.1054i	1.28440	−	1.39896i
$561$	5.41679	−	17.7996i	0.228697	−	0.751500i
$562$	−10.4455	+	17.7194i	−0.440618	+	0.747449i
$563$			1.39028i			0.0585933i	0.999571	+	0.0292966i	$0.00932674\pi$
$563$			1.39028i			0.0585933i	−0.999571	+	0.0292966i	$0.990673\pi$
$564$	29.5966	+	9.59621i	1.24624	+	0.404074i
$565$	32.1751			1.35362
$566$	0.281891	−	31.1086i	0.0118487	−	1.30759i
$567$	4.87629	+	23.3071i	0.204785	+	0.978807i
$568$	−0.683735	+	25.1462i	−0.0286889	+	1.05511i
$569$	−2.54401			−0.106650			−0.0533252	−	0.998577i	$-0.516982\pi$
$569$	−2.54401			−0.106650			−0.0533252	+	0.998577i	$0.516982\pi$
$570$	16.4735	−	52.4217i	0.689998	−	2.19570i
$571$	45.2500			1.89365			0.946827	−	0.321743i	$-0.104269\pi$
$571$	45.2500			1.89365			0.946827	+	0.321743i	$0.104269\pi$
$572$	−5.97564	+	9.93008i	−0.249854	+	0.415197i
$573$	−8.55673	+	28.1174i	−0.357463	+	1.17462i
$574$	14.0211	−	4.82846i	0.585230	−	0.201536i
$575$		−	15.5791i		−	0.649692i
$576$	19.1755	+	14.4326i	0.798979	+	0.601359i
$577$	−22.5732	−	13.0327i	−0.939736	−	0.542557i	−0.0498586	−	0.998756i	$-0.515877\pi$
$577$	−22.5732	−	13.0327i	−0.939736	−	0.542557i	−0.889878	+	0.456199i	$0.849210\pi$
$578$	−3.65314	−	6.46194i	−0.151950	−	0.268781i
$579$	23.5453	+	7.16533i	0.978509	+	0.297781i
$580$	−24.1841	+	13.3843i	−1.00419	+	0.555753i
$581$	−3.12489	−	2.66689i	−0.129642	−	0.110641i
$582$	−17.9885	−	19.5934i	−0.745647	−	0.812173i
$583$		−	23.5360i		−	0.974762i
$584$	−9.23531	−	5.67217i	−0.382160	−	0.234716i
$585$	26.9213	+	18.0578i	1.11306	+	0.746598i
$586$	−12.5651	−	22.2260i	−0.519058	−	0.918148i
$587$	22.2539	+	12.8483i	0.918517	+	0.530306i	0.883162	−	0.469069i	$-0.155410\pi$
$587$	22.2539	+	12.8483i	0.918517	+	0.530306i	0.0353554	+	0.999375i	$0.488744\pi$
$588$	18.8656	+	15.2345i	0.778005	+	0.628258i
$589$	23.6590	−	13.6595i	0.974851	−	0.562830i
$590$	3.11355	+	1.83542i	0.128183	+	0.0755631i
$591$	−0.384266	+	1.26270i	−0.0158066	+	0.0519405i
$592$	−0.301392	+	0.159736i	−0.0123871	+	0.00656510i
$593$	13.7270	−	7.92527i	0.563699	−	0.325452i	−0.190930	−	0.981604i	$-0.561150\pi$
$593$	13.7270	−	7.92527i	0.563699	−	0.325452i	0.754629	+	0.656152i	$0.227817\pi$
$594$	6.07832	−	15.5921i	0.249397	−	0.639751i
$595$	−49.9501	+	17.7092i	−2.04775	+	0.726007i
$596$	−20.0883	−	12.0886i	−0.822848	−	0.495167i
$597$	14.8631	−	13.8959i	0.608306	−	0.568723i
$598$	0.0389737	−	4.30102i	0.00159375	−	0.175882i
$599$		−	21.9021i		−	0.894896i	−0.894310	−	0.447448i	$-0.852333\pi$
$599$		−	21.9021i		−	0.894896i	0.894310	−	0.447448i	$-0.147667\pi$
$600$	12.7480	+	62.5668i	0.520434	+	2.55428i
$601$	12.7082	+	7.33710i	0.518379	+	0.299286i	0.736271	−	0.676686i	$-0.236585\pi$
$601$	12.7082	+	7.33710i	0.518379	+	0.299286i	−0.217892	+	0.975973i	$0.569918\pi$
$602$	17.9600	−	20.6622i	0.731996	−	0.842130i
$603$	−1.62876	−	1.09251i	−0.0663284	−	0.0444906i
$604$	21.0310	−	11.6393i	0.855741	−	0.473597i
$605$	−12.3443	−	21.3810i	−0.501868	−	0.869261i
$606$	−7.98405	−	35.8517i	−0.324330	−	1.45637i
$607$	2.57047	−	4.45219i	0.104332	−	0.180709i	−0.809133	−	0.587626i	$-0.800063\pi$
$607$	2.57047	−	4.45219i	0.104332	−	0.180709i	0.913465	+	0.406917i	$0.133396\pi$
$608$	26.5292	−	13.7538i	1.07590	−	0.557792i
$609$	−8.03402	−	12.5647i	−0.325555	−	0.509149i
$610$	−8.06415	+	13.6797i	−0.326508	+	0.553877i
$611$	11.4270	+	19.7921i	0.462285	+	0.800702i
$612$	−12.0096	−	25.6268i	−0.485459	−	1.03590i
$613$	5.42641	+	3.13294i	0.219170	+	0.126538i	0.605566	−	0.795795i	$-0.292947\pi$
$613$	5.42641	+	3.13294i	0.219170	+	0.126538i	−0.386396	+	0.922333i	$0.626280\pi$
$614$	0.215275	−	23.7571i	0.00868780	−	0.958760i
$615$	−8.48707	+	27.8885i	−0.342232	+	1.12457i
$616$	−5.25606	−	16.2113i	−0.211773	−	0.653171i
$617$	−21.4387	−	37.1329i	−0.863089	−	1.49491i	−0.868933	−	0.494931i	$-0.835194\pi$
$617$	−21.4387	−	37.1329i	−0.863089	−	1.49491i	0.00584388	−	0.999983i	$-0.498140\pi$
$618$	−5.34896	+	4.91082i	−0.215167	+	0.197542i
$619$	3.38714	−	1.95557i	0.136141	−	0.0786008i	−0.430383	−	0.902646i	$-0.641621\pi$
$619$	3.38714	−	1.95557i	0.136141	−	0.0786008i	0.566523	+	0.824046i	$0.308288\pi$
$620$	−22.6474	+	37.6346i	−0.909543	+	1.51144i
$621$	0.995320	+	6.13060i	0.0399408	+	0.246013i
$622$	−13.5852	−	0.123102i	−0.544717	−	0.00493595i
$623$	−28.5714	+	10.1297i	−1.14469	+	0.405836i
$624$	3.36290	+	17.3051i	0.134624	+	0.692760i
$625$	−39.8554	+	69.0315i	−1.59421	+	2.76126i
$626$	0.297326	−	32.8120i	0.0118835	−	1.31143i
$627$	−14.2303	−	15.2207i	−0.568303	−	0.607857i
$628$	−27.7029	−	0.502101i	−1.10547	−	0.0200360i
$629$	0.402237			0.0160382
$630$	−46.0115	+	12.4579i	−1.83314	+	0.496335i
$631$			41.8475i			1.66592i	0.553331	+	0.832962i	$0.313357\pi$
$631$			41.8475i			1.66592i	−0.553331	+	0.832962i	$0.686643\pi$
$632$	−1.16435	+	42.8221i	−0.0463154	+	1.70337i
$633$	−2.74948	−	11.8396i	−0.109282	−	0.470582i
$634$	−0.00793385	+	0.875556i	−0.000315093	+	0.0347728i
$635$	30.2533	+	17.4668i	1.20057	+	0.693147i
$636$	−23.9721	−	26.5905i	−0.950554	−	1.05438i
$637$	2.79945	+	17.5902i	0.110918	+	0.696948i
$638$	−0.0949732	+	10.4810i	−0.00376002	+	0.414945i
$639$	14.8629	−	22.1583i	0.587969	−	0.876568i
$640$	−26.6116	+	40.0019i	−1.05192	+	1.58121i
$641$	−5.03260	−	8.71671i	−0.198776	−	0.344289i	0.749356	−	0.662167i	$-0.230363\pi$
$641$	−5.03260	−	8.71671i	−0.198776	−	0.344289i	−0.948132	+	0.317878i	$0.897030\pi$
$642$	−4.66548	−	20.9499i	−0.184132	−	0.826828i
$643$	−5.36960	+	3.10014i	−0.211756	+	0.122258i	−0.602127	−	0.798400i	$-0.705680\pi$
$643$	−5.36960	+	3.10014i	−0.211756	+	0.122258i	0.390371	+	0.920658i	$0.372347\pi$
$644$	4.73579	+	4.19237i	0.186616	+	0.165203i
$645$	12.1739	+	52.4225i	0.479347	+	2.06413i
$646$	−35.2366	−	0.319296i	−1.38636	−	0.0125625i
$647$	21.1016	−	36.5491i	0.829591	−	1.43689i	−0.0687683	−	0.997633i	$-0.521907\pi$
$647$	21.1016	−	36.5491i	0.829591	−	1.43689i	0.898359	−	0.439261i	$-0.144760\pi$
$648$	−9.01381	−	23.8065i	−0.354096	−	0.935209i
$649$	1.18692	−	0.685268i	0.0465906	−	0.0268991i
$650$	−23.8180	+	40.4040i	−0.934218	+	1.58477i
$651$	−21.0396	−	10.9081i	−0.824605	−	0.427522i
$652$	0.00615918	+	0.0111290i	0.000241212	+	0.000435846i
$653$	4.19200	+	2.42025i	0.164046	+	0.0947117i	0.579775	−	0.814777i	$-0.303140\pi$
$653$	4.19200	+	2.42025i	0.164046	+	0.0947117i	−0.415730	+	0.909488i	$0.636474\pi$
$654$	30.2604	+	32.9602i	1.18328	+	1.28885i
$655$	−25.9102	+	14.9593i	−1.01240	+	0.584507i
$656$	−14.0074	+	7.42384i	−0.546897	+	0.289852i
$657$	5.06595	+	10.3191i	0.197641	+	0.402586i
$658$	−32.9891	−	6.41113i	−1.28605	−	0.249932i
$659$	4.69428	−	8.13074i	0.182863	−	0.316729i	−0.759991	−	0.649933i	$-0.774797\pi$
$659$	4.69428	−	8.13074i	0.182863	−	0.316729i	0.942854	+	0.333205i	$0.108130\pi$
$660$	31.8681	+	10.3327i	1.24046	+	0.402200i
$661$	−47.5300			−1.84870			−0.924352	−	0.381541i	$-0.875394\pi$
$661$	−47.5300			−1.84870			−0.924352	+	0.381541i	$0.875394\pi$
$662$	29.8372	+	0.270370i	1.15966	+	0.0105082i
$663$	6.05226	−	19.8878i	0.235050	−	0.772376i
$664$	3.74236	+	2.29849i	0.145232	+	0.0891987i
$665$	−10.7943	+	58.3621i	−0.418584	+	2.26318i
$666$	0.360744	+	0.0275766i	0.0139785	+	0.00106857i
$667$	−1.94499	−	3.36882i	−0.0753102	−	0.130441i
$668$	6.48488	+	11.7175i	0.250908	+	0.453364i
$669$	−3.09475	+	2.89337i	−0.119650	+	0.111864i
$670$	1.99381	−	3.38222i	0.0770275	−	0.130667i
$671$	3.01081	+	5.21487i	0.116231	+	0.201318i
$672$	−22.4498	−	12.9617i	−0.866020	−	0.500009i
$673$	15.6249	−	27.0631i	0.602295	−	1.04321i	−0.390178	−	0.920739i	$-0.627587\pi$
$673$	15.6249	−	27.0631i	0.602295	−	1.04321i	0.992473	−	0.122466i	$-0.0390801\pi$
$674$	−3.45229	−	6.10668i	−0.132977	−	0.235220i
$675$	24.0259	−	63.3207i	0.924757	−	2.43721i
$676$	6.72923	−	11.1824i	0.258817	−	0.430091i
$677$	−28.1325			−1.08122			−0.540610	−	0.841273i	$-0.681807\pi$
$677$	−28.1325			−1.08122			−0.540610	+	0.841273i	$0.681807\pi$
$678$	−4.03418	−	18.1151i	−0.154932	−	0.695707i
$679$	21.8533	+	18.6504i	0.838652	+	0.715736i
$680$	49.8170	−	26.9837i	1.91040	−	1.03478i
$681$	8.90121	−	2.06710i	0.341095	−	0.0792115i
$682$	8.19687	+	14.4992i	0.313874	+	0.555204i
$683$	−5.78832	+	10.0257i	−0.221484	+	0.383622i	−0.955259	−	0.295771i	$-0.904423\pi$
$683$	−5.78832	+	10.0257i	−0.221484	+	0.383622i	0.733775	+	0.679393i	$0.237757\pi$
$684$	−31.5798	−	2.70211i	−1.20748	−	0.103318i
$685$	−59.6224			−2.27805
$686$	−22.2226	−	13.8620i	−0.848463	−	0.529255i
$687$	9.55704	−	8.93516i	0.364624	−	0.340897i
$688$	−15.5424	+	24.7991i	−0.592548	+	0.945456i
$689$		−	26.2971i		−	1.00184i
$690$	−12.1361	+	2.70267i	−0.462014	+	0.102889i
$691$			3.17609i			0.120824i	0.998174	+	0.0604120i	$0.0192415\pi$
$691$			3.17609i			0.120824i	−0.998174	+	0.0604120i	$0.980759\pi$
$692$	−22.4568	−	0.407019i	−0.853681	−	0.0154725i
$693$	−4.47415	+	17.5134i	−0.169959	+	0.665278i
$694$	17.7389	+	0.160741i	0.673358	+	0.00610163i
$695$		−	39.8819i		−	1.51281i
$696$	10.5678	+	11.9379i	0.400573	+	0.452505i
$697$	18.6943			0.708096
$698$	−4.17646	+	7.08479i	−0.158081	+	0.268163i
$699$	1.07310	+	4.62090i	0.0405883	+	0.174779i
$700$	−21.8646	−	65.4108i	−0.826404	−	2.47230i
$701$			26.9986i			1.01972i	0.860257	+	0.509861i	$0.170303\pi$
$701$			26.9986i			1.01972i	−0.860257	+	0.509861i	$0.829697\pi$
$702$	6.79140	−	17.4213i	0.256325	−	0.657524i
$703$	0.225237	−	0.390122i	0.00849498	−	0.0147137i
$704$	8.23852	+	16.2496i	0.310501	+	0.612429i
$705$	48.2576	−	45.1174i	1.81749	−	1.69922i
$706$	−12.1175	+	6.85040i	−0.456048	+	0.257818i
$707$	13.2570	+	37.3923i	0.498581	+	1.40628i
$708$	0.642991	−	1.98311i	0.0241651	−	0.0745298i
$709$			20.4366i			0.767512i	0.923435	+	0.383756i	$0.125370\pi$
$709$			20.4366i			0.767512i	−0.923435	+	0.383756i	$0.874630\pi$
$710$	46.0130	+	27.1245i	1.72684	+	1.01796i
$711$	25.3105	−	37.7339i	0.949218	−	1.41513i
$712$	28.4953	−	15.4347i	1.06791	−	0.578439i
$713$	−5.35334	−	3.09075i	−0.200484	−	0.115750i
$714$	16.2334	+	25.9023i	0.607521	+	0.969370i
$715$	12.3040	+	21.3111i	0.460142	+	0.796990i
$716$	−1.82771	+	3.03722i	−0.0683048	+	0.113506i
$717$	−13.4993	+	3.13490i	−0.504140	+	0.117075i
$718$	39.1268	−	22.1196i	1.46020	−	0.825496i
$719$	−11.9894	−	20.7662i	−0.447129	−	0.774450i	0.551069	−	0.834460i	$-0.314220\pi$
$719$	−11.9894	−	20.7662i	−0.447129	−	0.774450i	−0.998198	+	0.0600100i	$0.980887\pi$
$720$	46.5280	−	20.7848i	1.73400	−	0.774605i
$721$	5.09151	−	5.96590i	0.189618	−	0.222182i
$722$	−6.39545	+	10.8490i	−0.238014	+	0.403759i
$723$	−24.0592	+	5.58719i	−0.894771	+	0.207790i
$724$	19.5866	+	0.354996i	0.727929	+	0.0131933i
$725$			42.4176i			1.57535i
$726$	−10.4901	+	9.63086i	−0.389324	+	0.357435i
$727$	−7.64970	+	13.2497i	−0.283712	+	0.491403i	−0.972296	−	0.233753i	$-0.924899\pi$
$727$	−7.64970	+	13.2497i	−0.283712	+	0.491403i	0.688584	+	0.725156i	$0.258232\pi$
$728$	−5.87267	−	18.1131i	−0.217656	−	0.671316i
$729$	−5.40911	+	26.4526i	−0.200337	+	0.979727i
$730$	−20.0330	+	11.3253i	−0.741454	+	0.419167i
$731$	29.8885	−	17.2561i	1.10547	−	0.638241i
$732$	8.71303	+	2.82506i	0.322043	+	0.104417i
$733$	0.619591	−	1.07316i	0.0228851	−	0.0396382i	−0.854356	−	0.519688i	$-0.826048\pi$
$733$	0.619591	−	1.07316i	0.0228851	−	0.0396382i	0.877241	+	0.480050i	$0.159381\pi$
$734$	−23.4204	−	41.4278i	−0.864463	−	1.52913i
$735$	47.6991	−	19.3847i	1.75941	−	0.715015i
$736$	−5.69654	−	3.64251i	−0.209977	−	0.134265i
$737$	−0.744401	−	1.28934i	−0.0274204	−	0.0474935i
$738$	16.7658	+	1.28164i	0.617159	+	0.0471779i
$739$	−0.161138	+	0.279099i	−0.00592755	+	0.0102668i	−0.868974	−	0.494858i	$-0.835220\pi$
$739$	−0.161138	+	0.279099i	−0.00592755	+	0.0102668i	0.863046	+	0.505125i	$0.168553\pi$
$740$	−0.0131249	+	0.724152i	−0.000482480	+	0.0266204i
$741$	−15.8997	−	17.0063i	−0.584091	−	0.624744i
$742$	29.1852	+	25.3684i	1.07142	+	0.931303i
$743$	−36.8715	+	21.2877i	−1.35268	+	0.780972i	−0.988624	−	0.150405i	$-0.951942\pi$
$743$	−36.8715	+	21.2877i	−1.35268	+	0.780972i	−0.364058	+	0.931376i	$0.618609\pi$
$744$	24.0285	+	8.03219i	0.880928	+	0.294474i
$745$	−43.1118	+	24.8906i	−1.57949	+	0.911921i
$746$	−40.1002	−	23.6389i	−1.46817	−	0.865481i
$747$	−2.05284	−	4.18153i	−0.0751093	−	0.152994i
$748$	0.389320	−	21.4803i	0.0142350	−	0.785399i
$749$	7.74674	+	21.8502i	0.283060	+	0.798390i
$750$	79.7241	+	25.0532i	2.91111	+	0.914815i
$751$	−6.76213	−	3.90412i	−0.246753	−	0.142463i	0.371523	−	0.928424i	$-0.378836\pi$
$751$	−6.76213	−	3.90412i	−0.246753	−	0.142463i	−0.618277	+	0.785960i	$0.712169\pi$
$752$	35.9031	+	1.30188i	1.30925	+	0.0474746i
$753$	−10.0038	+	32.8726i	−0.364560	+	1.19794i
$754$	−0.106115	+	11.7105i	−0.00386448	+	0.426472i
$755$		−	51.0380i		−	1.85746i
$756$	12.7830	+	24.3433i	0.464914	+	0.885356i
$757$		−	23.6804i		−	0.860679i	−0.902667	−	0.430339i	$-0.858394\pi$
$757$		−	23.6804i		−	0.860679i	0.902667	−	0.430339i	$-0.141606\pi$
$758$	−13.2941	−	0.120464i	−0.482863	−	0.00437546i
$759$	−1.37265	+	4.51052i	−0.0498239	+	0.163722i
$760$	1.72459	−	63.4264i	0.0625575	−	2.30072i
$761$	17.9794	+	10.3804i	0.651753	+	0.376290i	0.789127	−	0.614230i	$-0.210533\pi$
$761$	17.9794	+	10.3804i	0.651753	+	0.376290i	−0.137375	+	0.990519i	$0.543866\pi$
$762$	6.04086	−	19.2232i	0.218837	−	0.696381i
$763$	−36.7618	−	31.3738i	−1.33087	−	1.13581i
$764$	−0.614996	+	33.9318i	−0.0222498	+	1.22761i
$765$	−59.9566	−	4.03721i	−2.16773	−	0.145966i
$766$	12.3529	−	20.9550i	0.446327	−	0.757134i
$767$	1.32616	−	0.765659i	0.0478849	−	0.0276464i
$768$	25.8583	+	9.96727i	0.933082	+	0.359663i
$769$	43.5853	−	25.1640i	1.57173	−	0.907437i	0.575770	−	0.817612i	$-0.304702\pi$
$769$	43.5853	−	25.1640i	1.57173	−	0.907437i	0.995958	−	0.0898254i	$-0.0286309\pi$
$770$	−35.5210	−	6.90318i	−1.28009	−	0.248773i
$771$	21.5803	+	23.0823i	0.777195	+	0.831288i
$772$	28.4142	+	0.514992i	1.02265	+	0.0185350i
$773$	3.64135	−	6.30701i	0.130970	−	0.226847i	−0.793081	−	0.609117i	$-0.791524\pi$
$773$	3.64135	−	6.30701i	0.130970	−	0.226847i	0.924051	+	0.382270i	$0.124857\pi$
$774$	27.9883	−	13.4269i	1.00602	−	0.482622i
$775$	33.7026	+	58.3747i	1.21063	+	2.09688i
$776$	−26.1714	−	16.0740i	−0.939499	−	0.577024i
$777$	−0.390384	+	0.0176947i	−0.0140049	+	0.000634796i
$778$	−18.7616	+	10.6065i	−0.672636	+	0.380262i
$779$	10.4681	−	18.1312i	0.375057	−	0.649618i
$780$	35.6067	+	11.5449i	1.27492	+	0.413374i
$781$	17.5407	−	10.1271i	0.627654	−	0.362376i
$782$	3.92394	+	6.94096i	0.140320	+	0.248208i
$783$	−2.70999	−	16.6920i	−0.0968471	−	0.596523i
$784$	25.7676	+	10.9558i	0.920273	+	0.391277i
$785$	−29.4158	+	50.9496i	−1.04989	+	1.81847i
$786$	11.6710	+	12.7123i	0.416291	+	0.453432i
$787$		−	5.56884i		−	0.198508i	−0.995062	−	0.0992539i	$-0.968354\pi$
$787$		−	5.56884i		−	0.198508i	0.995062	−	0.0992539i	$-0.0316456\pi$
$788$	−0.0276183	+	1.52381i	−0.000983860	+	0.0542835i
$789$	36.3129	−	8.43284i	1.29277	−	0.300217i
$790$	78.3568	+	46.1910i	2.78781	+	1.64340i
$791$	6.69850	+	18.8936i	0.238171	+	0.671779i
$792$	1.82181	−	19.2378i	0.0647351	−	0.683586i
$793$	3.36402	+	5.82665i	0.119460	+	0.206910i
$794$	13.3506	+	23.6155i	0.473794	+	0.838083i
$795$	−74.0463	+	17.1955i	−2.62615	+	0.609863i
$796$	12.1142	−	20.1310i	0.429378	−	0.713523i
$797$	5.83009	+	10.0980i	0.206512	+	0.357690i	0.950614	−	0.310377i	$-0.100455\pi$
$797$	5.83009	+	10.0980i	0.206512	+	0.357690i	−0.744101	+	0.668067i	$0.767122\pi$
$798$	34.2122	−	1.24020i	1.21110	−	0.0439026i
$799$	−36.6895	−	21.1827i	−1.29798	−	0.749390i
$800$	33.9354	+	65.4564i	1.19980	+	2.31423i
$801$	−34.2952	−	2.30928i	−1.21176	−	0.0815945i
$802$	−17.1757	+	29.1362i	−0.606495	+	1.02884i
$803$			8.72643i			0.307949i
$804$	−2.15424	−	0.698477i	−0.0759741	−	0.0246334i
$805$	12.6576	−	4.48762i	0.446123	−	0.158168i
$806$	9.15848	+	16.2002i	0.322594	+	0.570628i
$807$	−22.9781	+	21.4829i	−0.808869	+	0.756235i
$808$	−20.1999	−	37.2928i	−0.710629	−	1.31195i
$809$	19.8711	−	34.4178i	0.698632	−	1.21007i	−0.270309	−	0.962774i	$-0.587126\pi$
$809$	19.8711	−	34.4178i	0.698632	−	1.21007i	0.968941	−	0.247293i	$-0.0795410\pi$
$810$	−53.4949	−	7.73125i	−1.87962	−	0.271648i
$811$		−	16.9925i		−	0.596686i	−0.954459	−	0.298343i	$-0.903566\pi$
$811$		−	16.9925i		−	0.596686i	0.954459	−	0.298343i	$-0.0964339\pi$
$812$	−12.8943	−	11.4147i	−0.452500	−	0.400578i
$813$	−2.73455	−	11.7754i	−0.0959050	−	0.412980i
$814$	0.236595	+	0.139472i	0.00829265	+	0.00488848i
$815$	0.0270078			0.000946043
$816$	−21.4385	−	24.6646i	−0.750496	−	0.863432i
$817$		−	38.6510i		−	1.35223i
$818$	−0.424089	+	46.8012i	−0.0148279	+	1.63637i
$819$	−4.99903	+	19.5679i	−0.174680	+	0.683759i
$820$	−0.609989	+	33.6555i	−0.0213017	+	1.17530i
$821$		−	43.0459i		−	1.50231i	−0.660124	−	0.751156i	$-0.729496\pi$
$821$		−	43.0459i		−	1.50231i	0.660124	−	0.751156i	$-0.270504\pi$
$822$	7.47558	+	33.5684i	0.260741	+	1.17083i
$823$			0.332797i			0.0116006i	0.999983	+	0.00580029i	$0.00184630\pi$
$823$			0.332797i			0.0116006i	−0.999983	+	0.00580029i	$0.998154\pi$
$824$	−4.38817	+	7.14474i	−0.152869	+	0.248899i
$825$	37.5547	−	35.1110i	1.30749	−	1.22241i
$826$	−0.429576	+	2.21043i	−0.0149468	+	0.0769105i
$827$	−29.6740			−1.03187			−0.515933	−	0.856629i	$-0.672555\pi$
$827$	−29.6740			−1.03187			−0.515933	+	0.856629i	$0.672555\pi$
$828$	3.04330	+	6.49397i	0.105762	+	0.225681i
$829$	−13.4646	+	23.3213i	−0.467643	+	0.809982i	−0.999316	−	0.0369676i	$-0.988230\pi$
$829$	−13.4646	+	23.3213i	−0.467643	+	0.809982i	0.531673	+	0.846950i	$0.321563\pi$
$830$	8.11782	−	4.58926i	0.281774	−	0.159295i
$831$	24.9807	−	5.80118i	0.866569	−	0.201241i
$832$	9.20502	+	18.1559i	0.319127	+	0.629442i
$833$	−20.7981	−	25.6444i	−0.720612	−	0.888526i
$834$	−22.4542	+	5.00048i	−0.777526	+	0.173152i
$835$	28.4360			0.984069
$836$	−20.6154	−	12.4057i	−0.712997	−	0.429062i
$837$	−16.9920	−	20.8181i	−0.587328	−	0.719579i
$838$	29.4493	−	16.6486i	1.01731	−	0.575116i
$839$	7.47056	−	12.9394i	0.257912	−	0.446717i	−0.707770	−	0.706443i	$-0.750299\pi$
$839$	7.47056	−	12.9394i	0.257912	−	0.446717i	0.965683	+	0.259725i	$0.0836321\pi$
$840$	−47.1620	+	28.3800i	−1.62724	+	0.979205i
$841$	−9.20432	−	15.9424i	−0.317390	−	0.549736i
$842$	11.2661	+	6.64133i	0.388256	+	0.228875i
$843$	18.4020	−	17.2046i	0.633799	−	0.592557i
$844$	−6.79609	−	12.2798i	−0.233931	−	0.422690i
$845$	−13.8556	−	23.9987i	−0.476648	−	0.825579i
$846$	−31.4525	−	21.5129i	−1.08136	−	0.739630i
$847$	9.98522	−	11.7000i	0.343096	−	0.402017i
$848$	−35.0285	−	21.9535i	−1.20288	−	0.753886i
$849$	−11.0929	+	36.4512i	−0.380706	+	1.25100i
$850$	0.787811	−	86.9405i	0.0270217	−	2.98204i
$851$	−0.101929			−0.00349409
$852$	9.50233	−	29.3070i	0.325544	−	1.00404i
$853$	15.8940	−	27.5292i	0.544200	−	0.942581i	−0.454457	−	0.890769i	$-0.650167\pi$
$853$	15.8940	−	27.5292i	0.544200	−	0.942581i	0.998657	−	0.0518128i	$-0.0164999\pi$
$854$	−9.71178	−	1.88739i	−0.332330	−	0.0645853i
$855$	−37.4889	+	55.8901i	−1.28210	+	1.91140i
$856$	−11.8038	−	21.7920i	−0.403445	−	0.744836i
$857$	8.22552	−	4.74901i	0.280979	−	0.162223i	−0.352888	−	0.935666i	$-0.614800\pi$
$857$	8.22552	−	4.74901i	0.280979	−	0.162223i	0.633866	+	0.773443i	$0.281467\pi$
$858$	10.4558	−	9.59937i	0.356956	−	0.327717i
$859$	−29.0142	−	16.7513i	−0.989950	−	0.571548i	−0.0846909	−	0.996407i	$-0.526990\pi$
$859$	−29.0142	−	16.7513i	−0.989950	−	0.571548i	−0.905259	+	0.424859i	$0.860324\pi$
$860$	30.0912	+	54.3717i	1.02610	+	1.85406i
$861$	−18.1434	+	0.822377i	−0.618325	+	0.0280265i
$862$	0.442942	+	0.261113i	0.0150867	+	0.00889353i
$863$	−4.35124	+	2.51219i	−0.148118	+	0.0855160i	−0.572227	−	0.820095i	$-0.693921\pi$
$863$	−4.35124	+	2.51219i	−0.148118	+	0.0855160i	0.424109	+	0.905611i	$0.360587\pi$
$864$	−17.5360	−	23.5900i	−0.596586	−	0.802549i
$865$	−23.8453	+	41.3013i	−0.810766	+	1.40429i
$866$	−0.258320	+	28.5074i	−0.00877806	+	0.968721i
$867$	2.05654	+	8.85572i	0.0698437	+	0.300756i
$868$	−26.8144	−	5.46374i	−0.910141	−	0.185451i
$869$	29.8705	−	17.2457i	1.01329	−	0.585021i
$870$	33.0434	−	7.35865i	1.12027	−	0.249482i
$871$	−0.831731	−	1.44060i	−0.0281821	−	0.0488129i
$872$	44.0258	+	27.0398i	1.49090	+	0.915685i
$873$	14.3561	+	29.2427i	0.485880	+	0.989715i
$874$	8.92915	+	0.0809115i	0.302033	+	0.00273687i
$875$	−88.7583	−	16.4162i	−3.00058	−	0.554968i
$876$	8.88810	+	9.85893i	0.300301	+	0.333102i
$877$	−5.19447	−	2.99903i	−0.175405	−	0.101270i	0.409727	−	0.912208i	$-0.365624\pi$
$877$	−5.19447	−	2.99903i	−0.175405	−	0.101270i	−0.585132	+	0.810938i	$0.698957\pi$
$878$	47.0006	+	0.425896i	1.58619	+	0.0143733i
$879$	7.07351	+	30.4595i	0.238584	+	1.02737i
$880$	38.6586	+	1.40180i	1.30318	+	0.0472545i
$881$		−	40.7513i		−	1.37295i	−0.727156	−	0.686473i	$-0.759158\pi$
$881$		−	40.7513i		−	1.37295i	0.727156	−	0.686473i	$-0.240842\pi$
$882$	−16.8945	−	24.4249i	−0.568868	−	0.822429i
$883$	−9.75434			−0.328260			−0.164130	−	0.986439i	$-0.552482\pi$
$883$	−9.75434			−0.328260			−0.164130	+	0.986439i	$0.552482\pi$
$884$	0.434993	−	24.0003i	0.0146304	−	0.807217i
$885$	−3.02308	−	3.23348i	−0.101620	−	0.108692i
$886$	−33.1703	−	0.300572i	−1.11438	−	0.0100979i
$887$	10.5541	−	18.2802i	0.354371	−	0.613789i	−0.632639	−	0.774447i	$-0.718028\pi$
$887$	10.5541	−	18.2802i	0.354371	−	0.613789i	0.987010	+	0.160658i	$0.0513616\pi$
$888$	0.409356	−	0.0834062i	0.0137371	−	0.00279893i
$889$	−3.95828	+	21.4015i	−0.132757	+	0.717783i
$890$	0.623497	−	68.8073i	0.0208997	−	2.30643i
$891$	−12.5352	+	16.2160i	−0.419944	+	0.543256i
$892$	−2.52239	+	4.19161i	−0.0844560	+	0.140346i
$893$	−41.0894	+	23.7230i	−1.37500	+	0.793859i
$894$	19.4193	+	21.1518i	0.649478	+	0.707423i
$895$	3.76330	+	6.51822i	0.125793	+	0.217880i
$896$	−29.0298	−	7.29870i	−0.969817	−	0.243832i
$897$	−1.53368	+	5.03967i	−0.0512080	+	0.168270i
$898$	17.1322	+	0.155243i	0.571708	+	0.00518053i
$899$	14.5757	+	8.41528i	0.486127	+	0.280665i
$900$	6.66701	−	77.9180i	0.222234	−	2.59727i
$901$	24.3741	+	42.2172i	0.812020	+	1.40646i
$902$	10.9959	+	6.48206i	0.366125	+	0.215829i
$903$	−28.2486	+	18.0624i	−0.940055	+	0.601080i
$904$	−10.2066	−	18.8433i	−0.339466	−	0.626718i
$905$	20.7976	−	36.0225i	0.691336	−	1.19743i
$906$	−28.7353	+	6.39926i	−0.954666	+	0.212601i
$907$	−21.1941	−	36.7092i	−0.703738	−	1.21891i	−0.967145	−	0.254225i	$-0.918180\pi$
$907$	−21.1941	−	36.7092i	−0.703738	−	1.21891i	0.263407	−	0.964685i	$-0.415154\pi$
$908$	9.23218	−	5.10941i	0.306381	−	0.169562i
$909$	−3.02223	+	44.8832i	−0.100241	+	1.48868i
$910$	−39.6882	−	7.71302i	−1.31565	−	0.255684i
$911$	31.0127	+	17.9052i	1.02750	+	0.593225i	0.916266	−	0.400569i	$-0.131188\pi$
$911$	31.0127	+	17.9052i	1.02750	+	0.593225i	0.111230	+	0.993795i	$0.464521\pi$
$912$	−35.9264	+	6.98156i	−1.18964	+	0.231183i
$913$		−	3.53614i		−	0.117029i
$914$	12.3063	+	0.111513i	0.407056	+	0.00368853i
$915$	14.2067	−	13.2823i	0.469659	−	0.439098i
$916$	7.78953	−	12.9443i	0.257373	−	0.427692i
$917$	−14.1785	−	12.1004i	−0.468215	−	0.399592i
$918$	5.24446	+	34.2628i	0.173093	+	1.13084i
$919$	−16.1803	+	9.34170i	−0.533739	+	0.308154i	−0.742538	−	0.669804i	$-0.766378\pi$
$919$	−16.1803	+	9.34170i	−0.533739	+	0.308154i	0.208799	+	0.977959i	$0.433045\pi$
$920$	−12.6239	+	6.83783i	−0.416198	+	0.225437i
$921$	−8.47143	+	27.8372i	−0.279143	+	0.917265i
$922$	−12.1434	+	20.5996i	−0.399922	+	0.678413i
$923$	19.5984	−	11.3152i	0.645090	−	0.372443i
$924$	0.567091	+	20.8645i	0.0186559	+	0.686391i
$925$	0.962563	+	0.555736i	0.0316489	+	0.0182725i
$926$	−49.8701	+	28.1931i	−1.63883	+	0.926483i
$927$	7.98319	−	3.91918i	0.262202	−	0.128723i
$928$	15.5102	+	9.91758i	0.509146	+	0.325560i
$929$			2.49452i			0.0818425i	0.999162	+	0.0409213i	$0.0130293\pi$
$929$			2.49452i			0.0818425i	−0.999162	+	0.0409213i	$0.986971\pi$
$930$	39.6271	−	36.3812i	1.29942	−	1.19299i
$931$	−36.5181	+	5.81182i	−1.19683	+	0.190475i
$932$	2.65246	+	4.79272i	0.0868842	+	0.156991i
$933$	15.9183	+	4.84428i	0.521142	+	0.158594i
$934$	−27.0625	+	15.2993i	−0.885512	+	0.500607i
$935$	−39.5054	−	22.8085i	−1.29197	−	0.745916i
$936$	2.03553	−	21.4947i	0.0665335	−	0.702576i
$937$			44.9799i			1.46943i	0.678377	+	0.734714i	$0.262684\pi$
$937$			44.9799i			1.46943i	−0.678377	+	0.734714i	$0.737316\pi$
$938$	2.40117	+	0.466645i	0.0784010	+	0.0152365i
$939$	−11.7003	+	38.4471i	−0.381824	+	1.25467i
$940$	39.3326	−	65.3614i	1.28289	−	2.13185i
$941$	−2.42012			−0.0788936			−0.0394468	−	0.999222i	$-0.512560\pi$
$941$	−2.42012			−0.0788936			−0.0394468	+	0.999222i	$0.512560\pi$
$942$	32.3737	+	10.1734i	1.05479	+	0.331468i
$943$	−4.73724			−0.154266
$944$	0.0872319	−	2.40567i	0.00283916	−	0.0782980i
$945$	58.3673	+	1.28070i	1.89869	+	0.0416611i
$946$	23.5637	+	0.213523i	0.766123	+	0.00694223i
$947$	38.9350			1.26522			0.632608	−	0.774472i	$-0.281984\pi$
$947$	38.9350			1.26522			0.632608	+	0.774472i	$0.281984\pi$
$948$	16.1818	−	49.9077i	0.525560	−	1.62093i
$949$			9.75016i			0.316504i
$950$	−83.8808	−	49.4474i	−2.72145	−	1.60428i
$951$	0.312210	−	1.02592i	0.0101241	−	0.0332678i
$952$	26.2165	+	23.6354i	0.849682	+	0.766029i
$953$	28.2533			0.915214			0.457607	−	0.889154i	$-0.348707\pi$
$953$	28.2533			0.915214			0.457607	+	0.889154i	$0.348707\pi$
$954$	18.9655	+	39.5333i	0.614029	+	1.27994i
$955$	62.4054	+	36.0298i	2.01939	+	1.16590i
$956$	−14.0012	+	7.74876i	−0.452832	+	0.250613i
$957$	3.73735	−	12.2809i	0.120811	−	0.396986i
$958$	25.2086	+	44.5909i	0.814453	+	1.44067i
$959$	−12.4127	−	35.0110i	−0.400828	−	1.13056i
$960$	45.1034	−	37.7911i	1.45571	−	1.21970i
$961$	−4.25480			−0.137252
$962$	0.264351	+	0.155834i	0.00852302	+	0.00502428i
$963$	−1.76604	+	26.2275i	−0.0569099	+	0.845169i
$964$	−24.9538	+	13.8103i	−0.803707	+	0.444799i
$965$	30.1710	−	52.2577i	0.971240	−	1.68224i
$966$	−4.11364	−	6.56380i	−0.132354	−	0.211187i
$967$	11.0324	−	6.36956i	0.354778	−	0.204831i	−0.312010	−	0.950079i	$-0.601002\pi$
$967$	11.0324	−	6.36956i	0.354778	−	0.204831i	0.666788	+	0.745248i	$0.267669\pi$
$968$	−8.60587	+	14.0119i	−0.276603	+	0.450360i
$969$	41.2880	+	12.5648i	1.32636	+	0.403640i
$970$	−56.7703	+	32.0940i	−1.82279	+	1.03048i
$971$	−27.6079	+	15.9394i	−0.885981	+	0.511521i	−0.872626	−	0.488390i	$-0.837584\pi$
$971$	−27.6079	+	15.9394i	−0.885981	+	0.511521i	−0.0133550	+	0.999911i	$0.504251\pi$
$972$	2.35447	+	31.0879i	0.0755198	+	0.997144i
$973$	23.4191	−	8.30298i	0.750783	−	0.266181i
$974$	9.04107	+	5.32967i	0.289695	+	0.170774i
$975$	41.9604	−	39.2300i	1.34381	−	1.25636i
$976$	10.5696	+	0.383264i	0.338325	+	0.0122680i
$977$	38.1317			1.21994			0.609971	−	0.792424i	$-0.291181\pi$
$977$	38.1317			1.21994			0.609971	+	0.792424i	$0.291181\pi$
$978$	−0.00338630	−	0.0152059i	−0.000108282	−	0.000486230i
$979$	−22.5971	−	13.0464i	−0.722206	−	0.416966i
$980$	46.8466	−	36.6063i	1.49646	−	1.16935i
$981$	−24.1499	−	49.1923i	−0.771048	−	1.57059i
$982$	−21.7773	−	38.5213i	−0.694942	−	1.22927i
$983$	0.589697	+	1.02138i	0.0188084	+	0.0325771i	0.875276	−	0.483623i	$-0.160679\pi$
$983$	0.589697	+	1.02138i	0.0188084	+	0.0325771i	−0.856468	+	0.516200i	$0.827346\pi$
$984$	19.0251	−	3.87637i	0.606499	−	0.123574i
$985$	2.80250	+	1.61803i	0.0892952	+	0.0515546i
$986$	−10.6838	−	18.8984i	−0.340242	−	0.601846i
$987$	36.5402	+	18.9445i	1.16309	+	0.603009i
$988$	−23.0338	−	13.8611i	−0.732804	−	0.440981i
$989$	−7.57392	+	4.37280i	−0.240837	+	0.139047i
$990$	−33.8665	−	23.1640i	−1.07635	−	0.736201i
$991$	21.9075	+	12.6483i	0.695914	+	0.401786i	0.805824	−	0.592155i	$-0.201723\pi$
$991$	21.9075	+	12.6483i	0.695914	+	0.401786i	−0.109910	+	0.993942i	$0.535056\pi$
$992$	29.2248	+	1.32497i	0.927889	+	0.0420680i
$993$	−34.9614	−	10.6395i	−1.10947	−	0.337634i
$994$	−6.34841	+	32.6664i	−0.201359	+	1.03611i
$995$	−24.9435	−	43.2034i	−0.790762	−	1.36964i
$996$	−3.60166	−	3.99506i	−0.114123	−	0.126588i
$997$	−3.54802	−	6.14536i	−0.112367	−	0.194625i	0.804357	−	0.594146i	$-0.202510\pi$
$997$	−3.54802	−	6.14536i	−0.112367	−	0.194625i	−0.916724	+	0.399521i	$0.869177\pi$
$998$	6.99892	−	11.8727i	0.221547	−	0.375824i
$999$	−0.414288	−	0.157194i	−0.0131075	−	0.00497340i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bf.b.115.1	✓	180
7.5	odd	6		504.2.cz.b.187.60	yes	180
8.3	odd	2	inner	504.2.bf.b.115.2	yes	180
9.4	even	3		504.2.cz.b.283.61	yes	180
56.19	even	6		504.2.cz.b.187.61	yes	180
63.40	odd	6	inner	504.2.bf.b.355.1	yes	180
72.67	odd	6		504.2.cz.b.283.60	yes	180
504.355	even	6	inner	504.2.bf.b.355.2	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bf.b.115.1	✓	180	1.1	even	1	trivial
504.2.bf.b.115.2	yes	180	8.3	odd	2	inner
504.2.bf.b.355.1	yes	180	63.40	odd	6	inner
504.2.bf.b.355.2	yes	180	504.355	even	6	inner
504.2.cz.b.187.60	yes	180	7.5	odd	6
504.2.cz.b.187.61	yes	180	56.19	even	6
504.2.cz.b.283.60	yes	180	72.67	odd	6
504.2.cz.b.283.61	yes	180	9.4	even	3

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41416 - 0.0128144i) q^{2} +(1.65702 + 0.504266i) q^{3} +(1.99967 + 0.0362430i) q^{4} +(2.12331 - 3.67768i) q^{5} +(-2.33682 - 0.734345i) q^{6} +(2.60163 + 0.481180i) q^{7} +(-2.82738 - 0.0768778i) q^{8} +(2.49143 + 1.67116i) q^{9} +O(q^{10})\)	\(q+(-1.41416 - 0.0128144i) q^{2} +(1.65702 + 0.504266i) q^{3} +(1.99967 + 0.0362430i) q^{4} +(2.12331 - 3.67768i) q^{5} +(-2.33682 - 0.734345i) q^{6} +(2.60163 + 0.481180i) q^{7} +(-2.82738 - 0.0768778i) q^{8} +(2.49143 + 1.67116i) q^{9} +(-3.04982 + 5.17360i) q^{10} +(1.13867 + 1.97224i) q^{11} +(3.29522 + 1.06842i) q^{12} +(1.27225 + 2.20361i) q^{13} +(-3.67294 - 0.713802i) q^{14} +(5.37290 - 5.02328i) q^{15} +(3.99737 + 0.144948i) q^{16} +(-4.08493 - 2.35844i) q^{17} +(-3.50186 - 2.39520i) q^{18} +(-4.57481 + 2.64127i) q^{19} +(4.37921 - 7.27720i) q^{20} +(4.06831 + 2.10924i) q^{21} +(-1.58498 - 2.80364i) q^{22} +(1.03515 + 0.597642i) q^{23} +(-4.64626 - 1.55314i) q^{24} +(-6.51690 - 11.2876i) q^{25} +(-1.77093 - 3.13255i) q^{26} +(3.28564 + 4.02549i) q^{27} +(5.18496 + 1.05649i) q^{28} +(-2.81842 - 1.62722i) q^{29} +(-7.66248 + 7.03485i) q^{30} -5.17158 q^{31} +(-5.65105 - 0.256203i) q^{32} +(0.892268 + 3.84223i) q^{33} +(5.74651 + 3.38754i) q^{34} +(7.29369 - 8.54626i) q^{35} +(4.92148 + 3.43207i) q^{36} +(-0.0738513 + 0.0426381i) q^{37} +(6.50333 - 3.67654i) q^{38} +(0.996945 + 4.29298i) q^{39} +(-6.28614 + 10.2350i) q^{40} +(-3.43230 + 1.98164i) q^{41} +(-5.72619 - 3.03492i) q^{42} +(-3.65838 + 6.33650i) q^{43} +(2.20549 + 3.98509i) q^{44} +(11.4361 - 5.61430i) q^{45} +(-1.45620 - 0.858423i) q^{46} +8.98167 q^{47} +(6.55063 + 2.25592i) q^{48} +(6.53693 + 2.50370i) q^{49} +(9.07126 + 16.0459i) q^{50} +(-5.57954 - 5.96787i) q^{51} +(2.46422 + 4.45260i) q^{52} +(-8.95026 - 5.16743i) q^{53} +(-4.59483 - 5.73477i) q^{54} +9.67101 q^{55} +(-7.31880 - 1.56049i) q^{56} +(-8.91245 + 2.06971i) q^{57} +(3.96484 + 2.33726i) q^{58} -0.601814i q^{59} +(10.9261 - 9.85018i) q^{60} +2.64414 q^{61} +(7.31341 + 0.0662705i) q^{62} +(5.67765 + 5.54656i) q^{63} +(7.98818 + 0.434726i) q^{64} +10.8056 q^{65} +(-1.21257 - 5.44494i) q^{66} -0.653746 q^{67} +(-8.08305 - 4.86415i) q^{68} +(1.41389 + 1.51229i) q^{69} +(-10.4239 + 11.9923i) q^{70} -8.89379i q^{71} +(-6.91575 - 4.91654i) q^{72} +(3.31848 + 1.91592i) q^{73} +(0.104984 - 0.0593505i) q^{74} +(-5.10667 - 21.9900i) q^{75} +(-9.24384 + 5.11586i) q^{76} +(2.01340 + 5.67893i) q^{77} +(-1.35482 - 6.08371i) q^{78} -15.1455i q^{79} +(9.02074 - 14.3933i) q^{80} +(3.41446 + 8.32715i) q^{81} +(4.87920 - 2.75836i) q^{82} +(-1.34472 - 0.776375i) q^{83} +(8.05883 + 4.36523i) q^{84} +(-17.3472 + 10.0154i) q^{85} +(5.25472 - 8.91392i) q^{86} +(-3.84963 - 4.11757i) q^{87} +(-3.06784 - 5.66380i) q^{88} +(-9.92258 + 5.72880i) q^{89} +(-16.2443 + 7.79295i) q^{90} +(2.24960 + 6.34515i) q^{91} +(2.04829 + 1.23260i) q^{92} +(-8.56941 - 2.60785i) q^{93} +(-12.7015 - 0.115094i) q^{94} +22.4329i q^{95} +(-9.23471 - 3.27417i) q^{96} +(9.40404 + 5.42943i) q^{97} +(-9.21215 - 3.62439i) q^{98} +(-0.458999 + 6.81659i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9}+O(q^{10}) \) 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9	\( 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9} - 8 q^{11} + 12 q^{12} + 10 q^{14} + 14 q^{16} - 18 q^{17} + 8 q^{18} - 6 q^{19} + 36 q^{20} - 16 q^{22} - 12 q^{24} - 78 q^{25} - 6 q^{26} + 16 q^{28} + q^{30} - 26 q^{32} - 36 q^{33} - 12 q^{34} - 12 q^{35} + 2 q^{36} - 27 q^{38} + 24 q^{40} - 42 q^{41} + 22 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} - 9 q^{48} + 2 q^{49} + 15 q^{50} + 9 q^{52} - 51 q^{54} + 14 q^{56} - 26 q^{57} + 19 q^{58} + 37 q^{60} - 8 q^{64} + 24 q^{65} + 6 q^{66} + 28 q^{67} + 12 q^{68} + 27 q^{70} - 28 q^{72} + 18 q^{73} + 49 q^{74} - 18 q^{75} - 12 q^{76} - 33 q^{78} - 63 q^{80} - 22 q^{81} - 54 q^{82} + 6 q^{83} + 31 q^{84} - 13 q^{86} + 29 q^{88} - 66 q^{89} - 51 q^{90} + 2 q^{91} - 60 q^{92} - 45 q^{96} - 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) \) 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9 - 8 * q^11 + 12 * q^12 + 10 * q^14 + 14 * q^16 - 18 * q^17 + 8 * q^18 - 6 * q^19 + 36 * q^20 - 16 * q^22 - 12 * q^24 - 78 * q^25 - 6 * q^26 + 16 * q^28 + q^30 - 26 * q^32 - 36 * q^33 - 12 * q^34 - 12 * q^35 + 2 * q^36 - 27 * q^38 + 24 * q^40 - 42 * q^41 + 22 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 - 9 * q^48 + 2 * q^49 + 15 * q^50 + 9 * q^52 - 51 * q^54 + 14 * q^56 - 26 * q^57 + 19 * q^58 + 37 * q^60 - 8 * q^64 + 24 * q^65 + 6 * q^66 + 28 * q^67 + 12 * q^68 + 27 * q^70 - 28 * q^72 + 18 * q^73 + 49 * q^74 - 18 * q^75 - 12 * q^76 - 33 * q^78 - 63 * q^80 - 22 * q^81 - 54 * q^82 + 6 * q^83 + 31 * q^84 - 13 * q^86 + 29 * q^88 - 66 * q^89 - 51 * q^90 + 2 * q^91 - 60 * q^92 - 45 * q^96 - 6 * q^97 + 31 * q^98 + 4 * q^99

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