LMFDB - Embedded newform 504.2.bt.a.11.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(11,504)]

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, 1, 4]))

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

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

chi := DirichletCharacter("504.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bt (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:	$184$
Relative dimension:	$92$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.14
Character	$\chi$	$=$	504.11
Dual form			504.2.bt.a.275.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25253 + 0.656631i) q^{2} +(0.406083 - 1.68377i) q^{3} +(1.13767 - 1.64490i) q^{4} +(1.72880 - 2.99437i) q^{5} +(0.596986 + 2.37563i) q^{6} +(-0.995123 - 2.45148i) q^{7} +(-0.344876 + 2.80732i) q^{8} +(-2.67019 - 1.36751i) q^{9} +O(q^{10})$	\(q+(-1.25253 + 0.656631i) q^{2} +(0.406083 - 1.68377i) q^{3} +(1.13767 - 1.64490i) q^{4} +(1.72880 - 2.99437i) q^{5} +(0.596986 + 2.37563i) q^{6} +(-0.995123 - 2.45148i) q^{7} +(-0.344876 + 2.80732i) q^{8} +(-2.67019 - 1.36751i) q^{9} +(-0.199181 + 4.88573i) q^{10} +(1.40306 - 0.810058i) q^{11} +(-2.30765 - 2.58355i) q^{12} +(3.62956 - 2.09553i) q^{13} +(2.85614 + 2.41712i) q^{14} +(-4.33981 - 4.12687i) q^{15} +(-1.41141 - 3.74272i) q^{16} +(2.55419 + 1.47466i) q^{17} +(4.24245 - 0.0404868i) q^{18} +(1.07327 + 1.85897i) q^{19} +(-2.95864 - 6.25032i) q^{20} +(-4.53183 + 0.680060i) q^{21} +(-1.22547 + 1.93592i) q^{22} +(-4.48342 + 7.76551i) q^{23} +(4.58685 + 1.72070i) q^{24} +(-3.47750 - 6.02321i) q^{25} +(-3.17015 + 5.00799i) q^{26} +(-3.38689 + 3.94068i) q^{27} +(-5.16456 - 1.15209i) q^{28} +(-5.12823 + 8.88235i) q^{29} +(8.14558 + 2.31939i) q^{30} -3.35151i q^{31} +(4.22541 + 3.76110i) q^{32} +(-0.794195 - 2.69139i) q^{33} +(-4.16752 - 0.169902i) q^{34} +(-9.06099 - 1.25834i) q^{35} +(-5.28722 + 2.83643i) q^{36} +(2.60454 - 1.50373i) q^{37} +(-2.56496 - 1.62367i) q^{38} +(-2.05449 - 6.96231i) q^{39} +(7.80994 + 5.88599i) q^{40} +(10.1507 - 5.86051i) q^{41} +(5.22972 - 3.82754i) q^{42} +(2.49182 - 4.31596i) q^{43} +(0.263757 - 3.22948i) q^{44} +(-8.71105 + 5.63140i) q^{45} +(0.516551 - 12.6705i) q^{46} -2.25898 q^{47} +(-6.87504 + 0.856634i) q^{48} +(-5.01946 + 4.87904i) q^{49} +(8.31070 + 5.26082i) q^{50} +(3.52022 - 3.70185i) q^{51} +(0.682310 - 8.35429i) q^{52} +(4.19874 - 7.27244i) q^{53} +(1.65462 - 7.15977i) q^{54} -5.60171i q^{55} +(7.22528 - 1.94818i) q^{56} +(3.56592 - 1.05226i) q^{57} +(0.590842 - 14.4928i) q^{58} +10.3963i q^{59} +(-11.7256 + 2.44353i) q^{60} +4.88188i q^{61} +(2.20070 + 4.19787i) q^{62} +(-0.695235 + 7.90675i) q^{63} +(-7.76212 - 1.93636i) q^{64} -14.4910i q^{65} +(2.76200 + 2.84956i) q^{66} -1.38538 q^{67} +(5.33151 - 2.52371i) q^{68} +(11.2547 + 10.7025i) q^{69} +(12.1754 - 4.37361i) q^{70} -1.74692 q^{71} +(4.75992 - 7.02447i) q^{72} +(5.08360 - 8.80506i) q^{73} +(-2.27487 + 3.59370i) q^{74} +(-11.5539 + 3.40940i) q^{75} +(4.27885 + 0.349461i) q^{76} +(-3.38206 - 2.63346i) q^{77} +(7.14498 + 7.37148i) q^{78} +1.17720i q^{79} +(-13.6471 - 2.24414i) q^{80} +(5.25986 + 7.30301i) q^{81} +(-8.86588 + 14.0057i) q^{82} +(-11.6631 - 6.73372i) q^{83} +(-4.03711 + 8.22811i) q^{84} +(8.83138 - 5.09880i) q^{85} +(-0.287092 + 7.04209i) q^{86} +(12.8734 + 12.2418i) q^{87} +(1.79021 + 4.21822i) q^{88} +(-1.01384 + 0.585338i) q^{89} +(7.21311 - 12.7734i) q^{90} +(-8.74899 - 6.81246i) q^{91} +(7.67284 + 16.2094i) q^{92} +(-5.64318 - 1.36099i) q^{93} +(2.82944 - 1.48331i) q^{94} +7.42191 q^{95} +(8.04871 - 5.58733i) q^{96} +(0.559596 - 0.969249i) q^{97} +(3.08331 - 9.40708i) q^{98} +(-4.85420 + 0.244316i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 2 q^{3} - 2 q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) $ 184 * q - 2 * q^3 - 2 * q^4 - 2 * q^6 - 2 * q^9	$ 184 q - 2 q^{3} - 2 q^{4} - 2 q^{6} - 2 q^{9} - 6 q^{10} - 6 q^{11} - 8 q^{12} + 12 q^{14} - 2 q^{16} + 2 q^{18} - 4 q^{19} - 6 q^{20} + 2 q^{22} - 8 q^{24} - 74 q^{25} - 6 q^{26} - 8 q^{27} + 3 q^{30} - 14 q^{33} - 4 q^{34} + 30 q^{35} - 38 q^{36} + 39 q^{38} + 6 q^{40} - 12 q^{41} - 20 q^{42} - 4 q^{43} + 9 q^{44} - 6 q^{46} - 5 q^{48} - 2 q^{49} - 21 q^{50} - 34 q^{51} + 9 q^{52} + 47 q^{54} - 24 q^{56} + 4 q^{57} - 3 q^{58} - 11 q^{60} - 8 q^{64} - 26 q^{66} - 4 q^{67} - 42 q^{68} - 3 q^{70} + 52 q^{72} - 4 q^{73} + 27 q^{74} + 30 q^{75} + 2 q^{76} - 29 q^{78} + 87 q^{80} + 14 q^{81} - 4 q^{82} - 72 q^{83} - 59 q^{84} - 27 q^{86} - 7 q^{88} - 24 q^{89} - 49 q^{90} - 36 q^{91} - 36 q^{92} - 18 q^{94} + 23 q^{96} - 4 q^{97} + 57 q^{98} + 10 q^{99}+O(q^{100}) $ 184 * q - 2 * q^3 - 2 * q^4 - 2 * q^6 - 2 * q^9 - 6 * q^10 - 6 * q^11 - 8 * q^12 + 12 * q^14 - 2 * q^16 + 2 * q^18 - 4 * q^19 - 6 * q^20 + 2 * q^22 - 8 * q^24 - 74 * q^25 - 6 * q^26 - 8 * q^27 + 3 * q^30 - 14 * q^33 - 4 * q^34 + 30 * q^35 - 38 * q^36 + 39 * q^38 + 6 * q^40 - 12 * q^41 - 20 * q^42 - 4 * q^43 + 9 * q^44 - 6 * q^46 - 5 * q^48 - 2 * q^49 - 21 * q^50 - 34 * q^51 + 9 * q^52 + 47 * q^54 - 24 * q^56 + 4 * q^57 - 3 * q^58 - 11 * q^60 - 8 * q^64 - 26 * q^66 - 4 * q^67 - 42 * q^68 - 3 * q^70 + 52 * q^72 - 4 * q^73 + 27 * q^74 + 30 * q^75 + 2 * q^76 - 29 * q^78 + 87 * q^80 + 14 * q^81 - 4 * q^82 - 72 * q^83 - 59 * q^84 - 27 * q^86 - 7 * q^88 - 24 * q^89 - 49 * q^90 - 36 * q^91 - 36 * q^92 - 18 * q^94 + 23 * q^96 - 4 * q^97 + 57 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.25253	+	0.656631i	−0.885674	+	0.464308i
$2$	−1.25253	+	0.656631i	−0.885674	+	0.464308i
$3$	0.406083	−	1.68377i	0.234452	−	0.972128i
$3$	0.406083	−	1.68377i	0.234452	−	0.972128i
$4$	1.13767	−	1.64490i	0.568836	−	0.822451i
$5$	1.72880	−	2.99437i	0.773143	−	1.33912i	−0.162689	−	0.986677i	$-0.552017\pi$
$5$	1.72880	−	2.99437i	0.773143	−	1.33912i	0.935832	−	0.352445i	$-0.114650\pi$
$6$	0.596986	+	2.37563i	0.243719	+	0.969846i
$7$	−0.995123	−	2.45148i	−0.376121	−	0.926570i
$7$	−0.995123	−	2.45148i	−0.376121	−	0.926570i
$8$	−0.344876	+	2.80732i	−0.121932	+	0.992538i
$9$	−2.67019	−	1.36751i	−0.890064	−	0.455835i
$10$	−0.199181	+	4.88573i	−0.0629867	+	1.54500i
$11$	1.40306	−	0.810058i	0.423039	−	0.244242i	−0.273338	−	0.961918i	$-0.588128\pi$
$11$	1.40306	−	0.810058i	0.423039	−	0.244242i	0.696377	+	0.717676i	$0.254794\pi$
$12$	−2.30765	−	2.58355i	−0.666162	−	0.745807i
$13$	3.62956	−	2.09553i	1.00666	−	0.581194i	0.0964467	−	0.995338i	$-0.469252\pi$
$13$	3.62956	−	2.09553i	1.00666	−	0.581194i	0.910211	+	0.414144i	$0.135919\pi$
$14$	2.85614	+	2.41712i	0.763335	+	0.646003i
$15$	−4.33981	−	4.12687i	−1.12053	−	1.06555i
$16$	−1.41141	−	3.74272i	−0.352852	−	0.935679i
$17$	2.55419	+	1.47466i	0.619483	+	0.357659i	0.776668	−	0.629911i	$-0.216909\pi$
$17$	2.55419	+	1.47466i	0.619483	+	0.357659i	−0.157185	+	0.987569i	$0.550242\pi$
$18$	4.24245	−	0.0404868i	0.999954	−	0.00954283i
$19$	1.07327	+	1.85897i	0.246226	+	0.426476i	0.962476	−	0.271368i	$-0.0874761\pi$
$19$	1.07327	+	1.85897i	0.246226	+	0.426476i	−0.716250	+	0.697844i	$0.754143\pi$
$20$	−2.95864	−	6.25032i	−0.661572	−	1.39761i
$21$	−4.53183	+	0.680060i	−0.988927	+	0.148401i
$22$	−1.22547	+	1.93592i	−0.261271	+	0.412739i
$23$	−4.48342	+	7.76551i	−0.934858	+	1.61922i	−0.159970	+	0.987122i	$0.551140\pi$
$23$	−4.48342	+	7.76551i	−0.934858	+	1.61922i	−0.774888	+	0.632099i	$0.782194\pi$
$24$	4.58685	+	1.72070i	0.936287	+	0.351237i
$25$	−3.47750	−	6.02321i	−0.695500	−	1.20464i
$26$	−3.17015	+	5.00799i	−0.621717	+	0.982148i
$27$	−3.38689	+	3.94068i	−0.651808	+	0.758384i
$28$	−5.16456	−	1.15209i	−0.976010	−	0.217725i
$29$	−5.12823	+	8.88235i	−0.952288	+	1.64941i	−0.211832	+	0.977306i	$0.567943\pi$
$29$	−5.12823	+	8.88235i	−0.952288	+	1.64941i	−0.740456	+	0.672105i	$0.765390\pi$
$30$	8.14558	+	2.31939i	1.48717	+	0.423461i
$31$		−	3.35151i		−	0.601948i	−0.953632	−	0.300974i	$-0.902688\pi$
$31$		−	3.35151i		−	0.601948i	0.953632	−	0.300974i	$-0.0973118\pi$
$32$	4.22541	+	3.76110i	0.746955	+	0.664875i
$33$	−0.794195	−	2.69139i	−0.138252	−	0.468511i
$34$	−4.16752	−	0.169902i	−0.714723	−	0.0291379i
$35$	−9.06099	−	1.25834i	−1.53159	−	0.212699i
$36$	−5.28722	+	2.83643i	−0.881203	+	0.472739i
$37$	2.60454	−	1.50373i	0.428184	−	0.247212i	−0.270389	−	0.962751i	$-0.587152\pi$
$37$	2.60454	−	1.50373i	0.428184	−	0.247212i	0.698573	+	0.715539i	$0.253819\pi$
$38$	−2.56496	−	1.62367i	−0.416092	−	0.263394i
$39$	−2.05449	−	6.96231i	−0.328982	−	1.11486i
$40$	7.80994	+	5.88599i	1.23486	+	0.930656i
$41$	10.1507	−	5.86051i	1.58527	−	0.915257i	0.591202	−	0.806524i	$-0.298654\pi$
$41$	10.1507	−	5.86051i	1.58527	−	0.915257i	0.994071	−	0.108734i	$-0.0346795\pi$
$42$	5.22972	−	3.82754i	0.806963	−	0.590602i
$43$	2.49182	−	4.31596i	0.379999	−	0.658178i	−0.611062	−	0.791582i	$-0.709258\pi$
$43$	2.49182	−	4.31596i	0.379999	−	0.658178i	0.991062	+	0.133404i	$0.0425909\pi$
$44$	0.263757	−	3.22948i	0.0397629	−	0.486862i
$45$	−8.71105	+	5.63140i	−1.29857	+	0.839480i
$46$	0.516551	−	12.6705i	0.0761613	−	1.86816i
$47$	−2.25898			−0.329505			−0.164753	−	0.986335i	$-0.552683\pi$
$47$	−2.25898			−0.329505			−0.164753	+	0.986335i	$0.552683\pi$
$48$	−6.87504	+	0.856634i	−0.992327	+	0.123644i
$49$	−5.01946	+	4.87904i	−0.717066	+	0.697006i
$50$	8.31070	+	5.26082i	1.17531	+	0.743993i
$51$	3.52022	−	3.70185i	0.492929	−	0.518362i
$52$	0.682310	−	8.35429i	0.0946193	−	1.15853i
$53$	4.19874	−	7.27244i	0.576742	−	0.998946i	−0.419108	−	0.907936i	$-0.637657\pi$
$53$	4.19874	−	7.27244i	0.576742	−	0.998946i	0.995850	−	0.0910099i	$-0.0290095\pi$
$54$	1.65462	−	7.15977i	0.225165	−	0.974321i
$55$		−	5.60171i		−	0.755335i
$56$	7.22528	−	1.94818i	0.965518	−	0.260336i
$57$	3.56592	−	1.05226i	0.472317	−	0.139375i
$58$	0.590842	−	14.4928i	0.0775814	−	1.90299i
$59$			10.3963i			1.35348i	0.736220	+	0.676742i	$0.236609\pi$
$59$			10.3963i			1.35348i	−0.736220	+	0.676742i	$0.763391\pi$
$60$	−11.7256	+	2.44353i	−1.51377	+	0.315458i
$61$			4.88188i			0.625061i	0.949908	+	0.312531i	$0.101177\pi$
$61$			4.88188i			0.625061i	−0.949908	+	0.312531i	$0.898823\pi$
$62$	2.20070	+	4.19787i	0.279490	+	0.533130i
$63$	−0.695235	+	7.90675i	−0.0875914	+	0.996156i
$64$	−7.76212	−	1.93636i	−0.970265	−	0.242045i
$65$		−	14.4910i		−	1.79739i
$66$	2.76200	+	2.84956i	0.339979	+	0.350756i
$67$	−1.38538			−0.169251			−0.0846257	−	0.996413i	$-0.526969\pi$
$67$	−1.38538			−0.169251			−0.0846257	+	0.996413i	$0.526969\pi$
$68$	5.33151	−	2.52371i	0.646541	−	0.306045i
$69$	11.2547	+	10.7025i	1.35491	+	1.28843i
$70$	12.1754	−	4.37361i	1.45524	−	0.522747i
$71$	−1.74692			−0.207321			−0.103661	−	0.994613i	$-0.533056\pi$
$71$	−1.74692			−0.207321			−0.103661	+	0.994613i	$0.533056\pi$
$72$	4.75992	−	7.02447i	0.560961	−	0.827842i
$73$	5.08360	−	8.80506i	0.594991	−	1.03055i	−0.398557	−	0.917143i	$-0.630489\pi$
$73$	5.08360	−	8.80506i	0.594991	−	1.03055i	0.993548	−	0.113411i	$-0.0361777\pi$
$74$	−2.27487	+	3.59370i	−0.264449	+	0.417759i
$75$	−11.5539	+	3.40940i	−1.33413	+	0.393684i
$76$	4.27885	+	0.349461i	0.490818	+	0.0400860i
$77$	−3.38206	−	2.63346i	−0.385421	−	0.300111i
$78$	7.14498	+	7.37148i	0.809010	+	0.834656i
$79$			1.17720i			0.132446i	0.997805	+	0.0662229i	$0.0210948\pi$
$79$			1.17720i			0.132446i	−0.997805	+	0.0662229i	$0.978905\pi$
$80$	−13.6471	−	2.24414i	−1.52579	−	0.250902i
$81$	5.25986	+	7.30301i	0.584429	+	0.811445i
$82$	−8.86588	+	14.0057i	−0.979073	+	1.54667i
$83$	−11.6631	−	6.73372i	−1.28020	−	0.739122i	−0.303313	−	0.952891i	$-0.598093\pi$
$83$	−11.6631	−	6.73372i	−1.28020	−	0.739122i	−0.976884	+	0.213769i	$0.931426\pi$
$84$	−4.03711	+	8.22811i	−0.440485	+	0.897760i
$85$	8.83138	−	5.09880i	0.957897	−	0.553042i
$86$	−0.287092	+	7.04209i	−0.0309579	+	0.759368i
$87$	12.8734	+	12.2418i	1.38017	+	1.31245i
$88$	1.79021	+	4.21822i	0.190837	+	0.449663i
$89$	−1.01384	+	0.585338i	−0.107466	+	0.0620457i	−0.552770	−	0.833334i	$-0.686429\pi$
$89$	−1.01384	+	0.585338i	−0.107466	+	0.0620457i	0.445303	+	0.895380i	$0.353096\pi$
$90$	7.21311	−	12.7734i	0.760329	−	1.34644i
$91$	−8.74899	−	6.81246i	−0.917143	−	0.714140i
$92$	7.67284	+	16.2094i	0.799949	+	1.68995i
$93$	−5.64318	−	1.36099i	−0.585171	−	0.141128i
$94$	2.82944	−	1.48331i	0.291834	−	0.152992i
$95$	7.42191			0.761471
$96$	8.04871	−	5.58733i	0.821468	−	0.570254i
$97$	0.559596	−	0.969249i	0.0568184	−	0.0984123i	−0.836217	−	0.548398i	$-0.815238\pi$
$97$	0.559596	−	0.969249i	0.0568184	−	0.0984123i	0.893036	+	0.449986i	$0.148571\pi$
$98$	3.08331	−	9.40708i	0.311461	−	0.950259i
$99$	−4.85420	+	0.244316i	−0.487866	+	0.0245547i
$100$	−13.8638	−	1.13228i	−1.38638	−	0.113228i
$101$	3.03097	+	5.24979i	0.301593	+	0.522374i	0.976497	−	0.215531i	$-0.0691484\pi$
$101$	3.03097	+	5.24979i	0.301593	+	0.522374i	−0.674904	+	0.737905i	$0.735815\pi$
$102$	−1.97844	+	6.94817i	−0.195894	+	0.687971i
$103$	6.47599	+	3.73892i	0.638099	+	0.368406i	0.783882	−	0.620910i	$-0.213237\pi$
$103$	6.47599	+	3.73892i	0.638099	+	0.368406i	−0.145783	+	0.989317i	$0.546570\pi$
$104$	4.63107	+	10.9120i	0.454114	+	1.07001i
$105$	−5.79829	+	14.7457i	−0.565855	+	1.43903i
$106$	−0.483753	+	11.8660i	−0.0469862	+	1.15253i
$107$	3.68993	−	2.13038i	0.356719	−	0.205952i	−0.310922	−	0.950436i	$-0.600638\pi$
$107$	3.68993	−	2.13038i	0.356719	−	0.205952i	0.667640	+	0.744484i	$0.267304\pi$
$108$	2.62886	+	10.0543i	0.252962	+	0.967476i
$109$	−0.661901	−	0.382149i	−0.0633986	−	0.0366032i	0.467966	−	0.883747i	$-0.344987\pi$
$109$	−0.661901	−	0.382149i	−0.0633986	−	0.0366032i	−0.531364	+	0.847143i	$0.678320\pi$
$110$	3.67826	+	7.01632i	0.350708	+	0.668980i
$111$	−1.47429	−	4.99610i	−0.139933	−	0.474209i
$112$	−7.77066	+	7.18449i	−0.734258	+	0.678871i
$113$	5.76170	−	3.32652i	0.542015	−	0.312932i	−0.203880	−	0.978996i	$-0.565355\pi$
$113$	5.76170	−	3.32652i	0.542015	−	0.312932i	0.745895	+	0.666063i	$0.232022\pi$
$114$	−3.77548	+	3.65948i	−0.353606	+	0.342741i
$115$	15.5019	+	26.8500i	1.44556	+	2.50378i
$116$	8.77636	+	18.5406i	0.814864	+	1.72145i
$117$	−12.5573	+	0.632018i	−1.16092	+	0.0584301i
$118$	−6.82654	−	13.0217i	−0.628434	−	1.19874i
$119$	1.07337	−	7.72901i	0.0983953	−	0.708517i
$120$	13.0822	−	10.7600i	1.19423	−	0.982247i
$121$	−4.18761	+	7.25316i	−0.380692	+	0.659378i
$122$	−3.20560	−	6.11472i	−0.290221	−	0.553600i
$123$	−5.74574	−	19.4713i	−0.518076	−	1.75567i
$124$	−5.51290	−	3.81291i	−0.495073	−	0.342410i
$125$	−6.75961			−0.604598
$126$	−4.32101	−	10.3600i	−0.384946	−	0.922939i
$127$		−	11.9603i		−	1.06130i	−0.847590	−	0.530652i	$-0.821947\pi$
$127$		−	11.9603i		−	1.06130i	0.847590	−	0.530652i	$-0.178053\pi$
$128$	10.9938	−	2.67150i	0.971722	−	0.236129i
$129$	−6.25522	−	5.94831i	−0.550741	−	0.523719i
$130$	9.51523	+	18.1504i	0.834541	+	1.59190i
$131$	−8.53946	−	4.93026i	−0.746096	−	0.430759i	0.0781856	−	0.996939i	$-0.475087\pi$
$131$	−8.53946	−	4.93026i	−0.746096	−	0.430759i	−0.824282	+	0.566180i	$0.808421\pi$
$132$	−5.33061	−	1.75555i	−0.463970	−	0.152801i
$133$	3.48917	−	4.48100i	0.302549	−	0.388552i
$134$	1.73524	−	0.909685i	0.149902	−	0.0785848i
$135$	5.94460	+	16.9543i	0.511629	+	1.45919i
$136$	−5.02074	+	6.66187i	−0.430525	+	0.571250i
$137$	6.33828	−	3.65941i	0.541516	−	0.312644i	−0.204177	−	0.978934i	$-0.565452\pi$
$137$	6.33828	−	3.65941i	0.541516	−	0.312644i	0.745693	+	0.666289i	$0.232118\pi$
$138$	−21.1245	−	6.01504i	−1.79824	−	0.512034i
$139$	0.612108	+	1.06020i	0.0519184	+	0.0899252i	0.890817	−	0.454363i	$-0.150133\pi$
$139$	0.612108	+	1.06020i	0.0519184	+	0.0899252i	−0.838898	+	0.544288i	$0.816800\pi$
$140$	−12.3783	+	13.4729i	−1.04616	+	1.13866i
$141$	−0.917332	+	3.80360i	−0.0772533	+	0.320321i
$142$	2.18807	−	1.14708i	0.183619	−	0.0962609i
$143$	3.39500	−	5.88030i	0.283904	−	0.491736i
$144$	−1.34946	+	11.9239i	−0.112455	+	0.993657i
$145$	17.7314	+	30.7116i	1.47251	+	2.55046i
$146$	−0.585701	+	14.3667i	−0.0484730	+	1.18899i
$147$	6.17688	+	10.4329i	0.509461	+	0.860494i
$148$	0.489620	−	5.99497i	0.0402465	−	0.492784i
$149$	−4.79806	+	8.31049i	−0.393073	+	0.680822i	−0.992853	−	0.119343i	$-0.961921\pi$
$149$	−4.79806	+	8.31049i	−0.393073	+	0.680822i	0.599780	+	0.800165i	$0.295255\pi$
$150$	12.2329	−	11.8570i	0.998810	−	0.968121i
$151$	−8.11547	+	4.68547i	−0.660427	+	0.381298i	−0.792440	−	0.609950i	$-0.791189\pi$
$151$	−8.11547	+	4.68547i	−0.660427	+	0.381298i	0.132012	+	0.991248i	$0.457856\pi$
$152$	−5.58886	+	2.37191i	−0.453317	+	0.192388i
$153$	−4.80358	−	7.43051i	−0.388346	−	0.600721i
$154$	5.96535	+	1.07773i	0.480701	+	0.0868463i
$155$	−10.0356	−	5.79408i	−0.806083	−	0.465392i
$156$	−13.7897	−	4.54139i	−1.10406	−	0.363602i
$157$			12.9218i			1.03127i	0.856808	+	0.515635i	$0.172444\pi$
$157$			12.9218i			1.03127i	−0.856808	+	0.515635i	$0.827556\pi$
$158$	−0.772988	−	1.47448i	−0.0614956	−	0.117304i
$159$	−10.5401	−	10.0230i	−0.835885	−	0.794872i
$160$	18.5670	−	6.15026i	1.46785	−	0.486221i
$161$	23.4985	+	3.26335i	1.85194	+	0.257188i
$162$	−11.3835	−	5.69346i	−0.894374	−	0.447321i
$163$	5.50445	+	9.53400i	0.431142	+	0.746760i	0.996972	−	0.0777619i	$-0.0247774\pi$
$163$	5.50445	+	9.53400i	0.431142	+	0.746760i	−0.565830	+	0.824522i	$0.691444\pi$
$164$	1.90820	−	23.3642i	0.149005	−	1.82444i
$165$	−9.43202	−	2.27476i	−0.734282	−	0.177090i
$166$	19.0300	+	0.775817i	1.47702	+	0.0602151i
$167$	−3.26694	−	5.65851i	−0.252804	−	0.437869i	0.711493	−	0.702693i	$-0.248019\pi$
$167$	−3.26694	−	5.65851i	−0.252804	−	0.437869i	−0.964297	+	0.264824i	$0.914686\pi$
$168$	−0.346224	−	12.9569i	−0.0267118	−	0.999643i
$169$	2.28246	−	3.95333i	0.175574	−	0.304103i
$170$	−7.71355	+	12.1854i	−0.591603	+	0.934575i
$171$	−0.323703	−	6.43150i	−0.0247542	−	0.491829i
$172$	−4.26446	−	9.00895i	−0.325162	−	0.686926i
$173$	2.10334			0.159914			0.0799570	−	0.996798i	$-0.474522\pi$
$173$	2.10334			0.159914			0.0799570	+	0.996798i	$0.474522\pi$
$174$	−24.1626	−	6.88012i	−1.83176	−	0.521581i
$175$	−11.3052	+	14.5188i	−0.854593	+	1.09752i
$176$	−5.01211	−	4.10794i	−0.377802	−	0.309648i
$177$	17.5050	+	4.22177i	1.31576	+	0.317327i
$178$	0.885510	−	1.39887i	0.0663718	−	0.104850i
$179$	9.83410	+	5.67772i	0.735035	+	0.424373i	0.820261	−	0.571989i	$-0.193828\pi$
$179$	9.83410	+	5.67772i	0.735035	+	0.424373i	−0.0852264	+	0.996362i	$0.527161\pi$
$180$	−0.647210	+	20.7355i	−0.0482402	+	1.54553i
$181$			1.85384i			0.137795i	0.997624	+	0.0688975i	$0.0219481\pi$
$181$			1.85384i			0.137795i	−0.997624	+	0.0688975i	$0.978052\pi$
$182$	15.4317	+	2.78797i	1.14387	+	0.206658i
$183$	8.21999	+	1.98245i	0.607639	+	0.146547i
$184$	−20.2541	−	15.2645i	−1.49315	−	1.12532i
$185$		−	10.3986i		−	0.764522i
$186$	7.96193	−	2.00080i	0.583797	−	0.146706i
$187$	4.77825			0.349421
$188$	−2.56997	+	3.71579i	−0.187434	+	0.271002i
$189$	13.0309	+	4.38142i	0.947855	+	0.318701i
$190$	−9.29617	+	4.87345i	−0.674415	+	0.353557i
$191$	−6.69915			−0.484734			−0.242367	−	0.970185i	$-0.577924\pi$
$191$	−6.69915			−0.484734			−0.242367	+	0.970185i	$0.577924\pi$
$192$	−6.41246	+	12.2833i	−0.462779	+	0.886473i
$193$	7.72671			0.556181			0.278091	−	0.960555i	$-0.410298\pi$
$193$	7.72671			0.556181			0.278091	+	0.960555i	$0.410298\pi$
$194$	−0.0644731	+	1.58146i	−0.00462890	+	0.113542i
$195$	−24.3995	−	5.88455i	−1.74729	−	0.421401i
$196$	2.31504	+	13.8073i	0.165360	+	0.986233i
$197$	24.6822			1.75854			0.879268	−	0.476328i	$-0.158032\pi$
$197$	24.6822			1.75854			0.879268	+	0.476328i	$0.158032\pi$
$198$	5.91962	−	3.49343i	0.420689	−	0.248268i
$199$	−3.83211	−	2.21247i	−0.271651	−	0.156838i	0.357987	−	0.933727i	$-0.383463\pi$
$199$	−3.83211	−	2.21247i	−0.271651	−	0.156838i	−0.629638	+	0.776889i	$0.716797\pi$
$200$	18.1084	−	7.68520i	1.28046	−	0.543426i
$201$	−0.562581	+	2.33267i	−0.0396814	+	0.164534i
$202$	−7.24356	−	4.58531i	−0.509655	−	0.322621i
$203$	26.8781	+	3.73269i	1.88647	+	0.261983i
$204$	−2.08433	−	10.0019i	−0.145932	−	0.700273i
$205$		−	40.5266i		−	2.83050i
$206$	−10.5665	−	0.430774i	−0.736201	−	0.0300135i
$207$	22.5910	−	14.6043i	1.57018	−	1.01507i
$208$	−12.9657	−	10.6268i	−0.899012	−	0.736834i
$209$	3.01174	+	1.73883i	0.208326	+	0.120277i
$210$	−2.41993	−	22.2768i	−0.166991	−	1.53724i
$211$	7.02842	+	12.1736i	0.483857	+	0.838064i	0.999828	−	0.0185415i	$-0.00590228\pi$
$211$	7.02842	+	12.1736i	0.483857	+	0.838064i	−0.515971	+	0.856606i	$0.672569\pi$
$212$	−7.18566	−	15.1802i	−0.493513	−	1.04258i
$213$	−0.709395	+	2.94142i	−0.0486069	+	0.201543i
$214$	−3.22288	+	5.09129i	−0.220311	+	0.348033i
$215$	−8.61572	−	14.9229i	−0.587587	−	1.01773i
$216$	−9.89470	−	10.8671i	−0.673249	−	0.739416i
$217$	−8.21613	+	3.33516i	−0.557748	+	0.226406i
$218$	1.07998	+	0.0440288i	0.0731457	+	0.00298200i
$219$	−12.7614	−	12.1352i	−0.862333	−	0.820023i
$220$	−9.21427	−	6.37291i	−0.621226	−	0.429662i
$221$	12.3608			0.831477
$222$	5.12719	+	5.28972i	0.344114	+	0.355022i
$223$	4.15022	+	2.39613i	0.277919	+	0.160457i	0.632481	−	0.774576i	$-0.282037\pi$
$223$	4.15022	+	2.39613i	0.277919	+	0.160457i	−0.354562	+	0.935033i	$0.615370\pi$
$224$	5.01543	−	14.1013i	0.335108	−	0.942180i
$225$	1.04883	+	20.8386i	0.0699217	+	1.38924i
$226$	−5.03241	+	7.94988i	−0.334751	+	0.528818i
$227$	−5.05670	+	2.91949i	−0.335625	+	0.193773i	−0.658336	−	0.752724i	$-0.728739\pi$
$227$	−5.05670	+	2.91949i	−0.335625	+	0.193773i	0.322711	+	0.946498i	$0.395406\pi$
$228$	2.32598	−	7.06271i	0.154042	−	0.467739i
$229$	−7.27048	−	4.19761i	−0.480447	−	0.277386i	0.240156	−	0.970734i	$-0.422801\pi$
$229$	−7.27048	−	4.19761i	−0.480447	−	0.277386i	−0.720603	+	0.693348i	$0.756135\pi$
$230$	−37.0471	−	23.4515i	−2.44282	−	1.54635i
$231$	−5.80755	+	4.62521i	−0.382109	+	0.304317i
$232$	−23.1670	−	17.4599i	−1.52099	−	1.14630i
$233$	−10.2853	+	5.93825i	−0.673815	+	0.389027i	−0.797521	−	0.603292i	$-0.793856\pi$
$233$	−10.2853	+	5.93825i	−0.673815	+	0.389027i	0.123705	+	0.992319i	$0.460522\pi$
$234$	15.3134	−	9.03711i	1.00107	−	0.590774i
$235$	−3.90532	+	6.76421i	−0.254755	+	0.441248i
$236$	17.1009	+	11.8276i	1.11317	+	0.769910i
$237$	1.98215	+	0.478043i	0.128754	+	0.0310522i
$238$	3.73068	+	10.3856i	0.241824	+	0.673201i
$239$	−7.54611	−	13.0702i	−0.488117	−	0.845444i	0.511789	−	0.859111i	$-0.328983\pi$
$239$	−7.54611	−	13.0702i	−0.488117	−	0.845444i	−0.999907	+	0.0136672i	$0.995649\pi$
$240$	−9.32049	+	22.0674i	−0.601635	+	1.42444i
$241$	−2.88202	−	4.99181i	−0.185647	−	0.321551i	0.758147	−	0.652084i	$-0.226105\pi$
$241$	−2.88202	−	4.99181i	−0.185647	−	0.321551i	−0.943794	+	0.330533i	$0.892772\pi$
$242$	0.482470	−	11.8345i	0.0310144	−	0.760752i
$243$	14.4326	−	5.89078i	0.925849	−	0.377894i
$244$	8.03022	+	5.55398i	0.514082	+	0.355557i
$245$	5.93200	+	23.4650i	0.378982	+	1.49912i
$246$	19.9822	+	20.6156i	1.27402	+	1.31440i
$247$	7.79102	+	4.49815i	0.495731	+	0.286210i
$248$	9.40876	+	1.15586i	0.597457	+	0.0733969i
$249$	−16.0743	+	16.9037i	−1.01867	+	1.07123i
$250$	8.46662	−	4.43857i	0.535476	−	0.280720i
$251$		−	15.7274i		−	0.992702i	−0.868122	−	0.496351i	$-0.834673\pi$
$251$		−	15.7274i		−	0.992702i	0.868122	−	0.496351i	$-0.165327\pi$
$252$	12.2149	+	10.1389i	0.769465	+	0.638689i
$253$			14.5273i			0.913325i
$254$	7.85350	+	14.9807i	0.492772	+	0.939970i
$255$	−4.99895	−	16.9406i	−0.313046	−	1.06086i
$256$	−12.0159	+	10.5650i	−0.750992	+	0.660312i
$257$	−10.9504	−	6.32219i	−0.683065	−	0.394367i	0.117944	−	0.993020i	$-0.462370\pi$
$257$	−10.9504	−	6.32219i	−0.683065	−	0.394367i	−0.801009	+	0.598653i	$0.795703\pi$
$258$	11.7407	+	3.34307i	0.730944	+	0.208131i
$259$	−6.27821	−	4.88857i	−0.390109	−	0.303761i
$260$	−23.8362	−	16.4860i	−1.47826	−	1.02242i
$261$	25.8400	−	16.7047i	1.59946	−	1.03400i
$262$	13.9333	+	0.568033i	0.860802	+	0.0350932i
$263$	−8.57262	−	14.8482i	−0.528610	−	0.915580i	−0.999443	−	0.0333578i	$-0.989380\pi$
$263$	−8.57262	−	14.8482i	−0.528610	−	0.915580i	0.470833	−	0.882222i	$-0.343953\pi$
$264$	7.82950	−	1.30136i	0.481872	−	0.0800934i
$265$	−14.5176	−	25.1452i	−0.891808	−	1.54466i
$266$	−1.42793	+	7.90369i	−0.0875518	+	0.484607i
$267$	0.573876	+	1.94477i	0.0351206	+	0.119018i
$268$	−1.57611	+	2.27882i	−0.0962763	+	0.139201i
$269$	−14.0158	+	24.2761i	−0.854559	+	1.48014i	0.0224943	+	0.999747i	$0.492839\pi$
$269$	−14.0158	+	24.2761i	−0.854559	+	1.48014i	−0.877053	+	0.480393i	$0.840494\pi$
$270$	−18.5785	−	17.3323i	−1.13065	−	1.05481i
$271$	11.5814	−	6.68654i	0.703522	−	0.406179i	−0.105136	−	0.994458i	$-0.533528\pi$
$271$	11.5814	−	6.68654i	0.703522	−	0.406179i	0.808658	+	0.588279i	$0.200194\pi$
$272$	1.91425	−	11.6410i	0.116068	−	0.705838i
$273$	−15.0235	+	11.9649i	−0.909262	+	0.724148i
$274$	−5.53602	+	8.74544i	−0.334443	+	0.528331i
$275$	−9.75829	−	5.63395i	−0.588447	−	0.339740i
$276$	30.4088	−	6.33698i	1.83039	−	0.381441i
$277$	16.6144	−	9.59234i	0.998264	−	0.576348i	0.0905296	−	0.995894i	$-0.471144\pi$
$277$	16.6144	−	9.59234i	0.998264	−	0.576348i	0.907734	+	0.419546i	$0.137811\pi$
$278$	−1.46285	−	0.926009i	−0.0877358	−	0.0555383i
$279$	−4.58320	+	8.94917i	−0.274389	+	0.535773i
$280$	6.65750	−	25.0032i	0.397862	−	1.49422i
$281$	−23.8575	−	13.7741i	−1.42322	−	0.821696i	−0.426647	−	0.904418i	$-0.640305\pi$
$281$	−23.8575	−	13.7741i	−1.42322	−	0.821696i	−0.996573	+	0.0827216i	$0.973639\pi$
$282$	−1.34858	−	5.36648i	−0.0803066	−	0.319570i
$283$	15.3322			0.911408			0.455704	−	0.890131i	$-0.349388\pi$
$283$	15.3322			0.911408			0.455704	+	0.890131i	$0.349388\pi$
$284$	−1.98742	+	2.87351i	−0.117932	+	0.170511i
$285$	3.01391	−	12.4968i	0.178529	−	0.740247i
$286$	−0.391150	+	9.59453i	−0.0231292	+	0.567336i
$287$	−24.4681	−	19.0523i	−1.44431	−	1.12462i
$288$	−6.13935	−	15.8211i	−0.361764	−	0.932270i
$289$	−4.15073	−	7.18928i	−0.244161	−	0.422899i
$290$	−42.3753	−	26.8243i	−2.48836	−	1.57518i
$291$	−1.40475	−	1.33583i	−0.0823481	−	0.0783077i
$292$	−8.69999	−	18.3793i	−0.509128	−	1.07557i
$293$	−7.15936	−	12.4004i	−0.418254	−	0.724438i	0.577510	−	0.816384i	$-0.304025\pi$
$293$	−7.15936	−	12.4004i	−0.418254	−	0.724438i	−0.995764	+	0.0919462i	$0.970691\pi$
$294$	−14.5873	−	9.01165i	−0.850750	−	0.525570i
$295$	31.1304	+	17.9731i	1.81248	+	1.04644i
$296$	3.32322	+	7.83039i	0.193158	+	0.455132i
$297$	−1.55984	+	8.27260i	−0.0905110	+	0.480025i
$298$	0.552803	−	13.5597i	0.0320230	−	0.785493i
$299$			37.5805i			2.17334i
$300$	−7.53639	+	22.8838i	−0.435113	+	1.32120i
$301$	−13.0601	−	1.81373i	−0.752774	−	0.104541i
$302$	7.08826	−	11.1976i	0.407883	−	0.644347i
$303$	10.0703	−	2.97162i	0.578523	−	0.170715i
$304$	5.44276	−	6.64072i	0.312163	−	0.380871i
$305$	14.6182	+	8.43980i	0.837034	+	0.483262i
$306$	10.8957	+	6.15277i	0.622868	+	0.351731i
$307$	24.6043			1.40424			0.702120	−	0.712059i	$-0.252237\pi$
$307$	24.6043			1.40424			0.702120	+	0.712059i	$0.252237\pi$
$308$	−8.17946	+	2.56713i	−0.466068	+	0.146276i
$309$	8.92529	−	9.38580i	0.507742	−	0.533940i
$310$	16.3745	+	0.667558i	0.930012	+	0.0379147i
$311$	20.8386			1.18165			0.590825	−	0.806800i	$-0.298802\pi$
$311$	20.8386			1.18165			0.590825	+	0.806800i	$0.298802\pi$
$312$	20.2540	−	3.36648i	1.14666	−	0.190589i
$313$	−27.9462			−1.57961			−0.789805	−	0.613357i	$-0.789819\pi$
$313$	−27.9462			−1.57961			−0.789805	+	0.613357i	$0.789819\pi$
$314$	−8.48484	−	16.1849i	−0.478827	−	0.913369i
$315$	22.4738	+	15.7510i	1.26626	+	0.887467i
$316$	1.93638	+	1.33927i	0.108930	+	0.0753399i
$317$	−12.2871			−0.690111			−0.345055	−	0.938582i	$-0.612140\pi$
$317$	−12.2871			−0.690111			−0.345055	+	0.938582i	$0.612140\pi$
$318$	19.7832	+	5.63311i	1.10939	+	0.315889i
$319$			16.6166i			0.930354i
$320$	−19.2173	+	19.8951i	−1.07428	+	1.11217i
$321$	−2.08866	−	7.07812i	−0.116578	−	0.395062i
$322$	−31.5754	+	11.3424i	−1.75963	+	0.632087i
$323$			6.33087i			0.352259i
$324$	17.9967	−	0.343526i	0.999818	−	0.0190848i
$325$	−25.2436	−	14.5744i	−1.40026	−	0.808441i
$326$	−13.1548	−	8.32724i	−0.728578	−	0.461203i
$327$	−0.912239	+	0.959308i	−0.0504470	+	0.0530498i
$328$	12.9516	+	30.5174i	0.715132	+	1.68504i
$329$	2.24796	+	5.53782i	0.123934	+	0.305310i
$330$	13.3076	−	3.34414i	0.732559	−	0.184089i
$331$	20.9034			1.14896			0.574478	−	0.818520i	$-0.305205\pi$
$331$	20.9034			1.14896			0.574478	+	0.818520i	$0.305205\pi$
$332$	−24.3451	+	11.5240i	−1.33611	+	0.632460i
$333$	−9.01099	+	0.453531i	−0.493799	+	0.0248534i
$334$	7.80750	+	4.94229i	0.427208	+	0.270430i
$335$	−2.39505	+	4.14835i	−0.130856	+	0.226649i
$336$	8.94153	+	16.0015i	0.487800	+	0.872955i
$337$	−3.56185	−	6.16931i	−0.194027	−	0.336064i	0.752554	−	0.658530i	$-0.228821\pi$
$337$	−3.56185	−	6.16931i	−0.194027	−	0.336064i	−0.946581	+	0.322466i	$0.895488\pi$
$338$	−0.262970	+	6.45041i	−0.0143037	+	0.350856i
$339$	−3.26138	−	11.0522i	−0.177134	−	0.600275i
$340$	1.66018	−	20.3275i	0.0900362	−	1.10241i
$341$	−2.71491	−	4.70237i	−0.147021	−	0.254648i
$342$	4.62857	+	7.84311i	0.250285	+	0.424107i
$343$	16.9558	+	7.44984i	0.915528	+	0.402253i
$344$	11.2569	+	8.48382i	0.606933	+	0.457417i
$345$	51.5044	−	15.1983i	2.77291	−	0.818249i
$346$	−2.63450	+	1.38112i	−0.141632	+	0.0742494i
$347$			9.01770i			0.484095i	0.970264	+	0.242048i	$0.0778190\pi$
$347$			9.01770i			0.484095i	−0.970264	+	0.242048i	$0.922181\pi$
$348$	34.7822	−	7.24836i	1.86452	−	0.388553i
$349$	1.99476	+	1.15167i	0.106777	+	0.0616477i	0.552437	−	0.833554i	$-0.313698\pi$
$349$	1.99476	+	1.15167i	0.106777	+	0.0616477i	−0.445661	+	0.895202i	$0.647031\pi$
$350$	4.62661	−	25.6086i	0.247302	−	1.36884i
$351$	−4.03512	+	21.4002i	−0.215379	+	1.14226i
$352$	8.97523	+	1.85422i	0.478381	+	0.0988304i
$353$	10.3701	−	5.98717i	0.551944	−	0.318665i	−0.197962	−	0.980210i	$-0.563432\pi$
$353$	10.3701	−	5.98717i	0.551944	−	0.318665i	0.749906	+	0.661545i	$0.230099\pi$
$354$	−24.6978	+	6.20645i	−1.31267	+	0.329869i
$355$	−3.02007	+	5.23092i	−0.160289	+	0.277628i
$356$	−0.190588	+	2.33358i	−0.0101011	+	0.123680i
$357$	−12.5780	−	4.94593i	−0.665700	−	0.261766i
$358$	−16.0457	−	0.654151i	−0.848041	−	0.0345730i
$359$	17.6165	+	30.5127i	0.929763	+	1.61040i	0.783717	+	0.621118i	$0.213321\pi$
$359$	17.6165	+	30.5127i	0.929763	+	1.61040i	0.146046	+	0.989278i	$0.453345\pi$
$360$	−12.8049	−	26.3969i	−0.674879	−	1.39124i
$361$	7.19617	−	12.4641i	0.378746	−	0.656007i
$362$	−1.21729	−	2.32199i	−0.0639793	−	0.122041i
$363$	10.5122	+	9.99638i	0.551745	+	0.524674i
$364$	−21.1593	+	6.64088i	−1.10905	+	0.348077i
$365$	−17.5771	−	30.4444i	−0.920026	−	1.59353i
$366$	−11.5975	+	2.91442i	−0.606213	+	0.152339i
$367$	−4.68528	+	2.70505i	−0.244570	+	0.141202i	−0.617275	−	0.786747i	$-0.711763\pi$
$367$	−4.68528	+	2.70505i	−0.244570	+	0.141202i	0.372706	+	0.927950i	$0.378430\pi$
$368$	35.3920	+	5.81988i	1.84494	+	0.303382i
$369$	−35.1186	+	1.76755i	−1.82820	+	0.0920149i
$370$	6.82805	+	13.0246i	0.354974	+	0.677117i
$371$	−22.0065	−	3.05615i	−1.14252	−	0.158667i
$372$	−8.65878	+	7.73412i	−0.448937	+	0.400995i
$373$	20.9108	+	12.0728i	1.08272	+	0.625108i	0.931628	−	0.363412i	$-0.118388\pi$
$373$	20.9108	+	12.0728i	1.08272	+	0.625108i	0.151090	+	0.988520i	$0.451722\pi$
$374$	−5.98491	+	3.13755i	−0.309473	+	0.162239i
$375$	−2.74496	+	11.3817i	−0.141749	+	0.587746i
$376$	0.779067	−	6.34167i	0.0401773	−	0.327047i
$377$			42.9853i			2.21386i
$378$	−19.1985	+	3.06860i	−0.987466	+	0.157832i
$379$	−25.5508			−1.31246			−0.656229	−	0.754561i	$-0.727850\pi$
$379$	−25.5508			−1.31246			−0.656229	+	0.754561i	$0.727850\pi$
$380$	8.44369	−	12.2083i	0.433152	−	0.626273i
$381$	−20.1384	−	4.85688i	−1.03172	−	0.248825i
$382$	8.39090	−	4.39887i	0.429316	−	0.225066i
$383$	1.45817	−	2.52563i	0.0745090	−	0.129053i	−0.826364	−	0.563137i	$-0.809594\pi$
$383$	1.45817	−	2.52563i	0.0745090	−	0.129053i	0.900873	+	0.434083i	$0.142928\pi$
$384$	−0.0338093	−	19.5959i	−0.00172532	−	0.999999i
$385$	−13.7325	+	5.57439i	−0.699871	+	0.284097i
$386$	−9.67795	+	5.07360i	−0.492595	+	0.258239i
$387$	−12.5557	+	8.11687i	−0.638244	+	0.412604i
$388$	−0.957683	−	2.02317i	−0.0486190	−	0.102711i
$389$	−5.11043	−	8.85152i	−0.259109	−	0.448790i	0.706894	−	0.707319i	$-0.250096\pi$
$389$	−5.11043	−	8.85152i	−0.259109	−	0.448790i	−0.966003	+	0.258529i	$0.916762\pi$
$390$	34.4252	−	8.65091i	1.74319	−	0.438056i
$391$	−22.9030	+	13.2231i	−1.15826	+	0.668720i
$392$	−11.9659	−	15.7739i	−0.604371	−	0.796703i
$393$	−11.7692	+	12.3764i	−0.593676	+	0.624308i
$394$	−30.9153	+	16.2071i	−1.55749	+	0.816502i
$395$	3.52498	+	2.03515i	0.177361	+	0.102399i
$396$	−5.12061	+	8.26264i	−0.257321	+	0.415213i
$397$	−13.8248	+	7.98175i	−0.693846	+	0.400592i	−0.805051	−	0.593205i	$-0.797862\pi$
$397$	−13.8248	+	7.98175i	−0.693846	+	0.400592i	0.111205	+	0.993797i	$0.464529\pi$
$398$	6.25262	+	0.254907i	0.313416	+	0.0127773i
$399$	−6.12811	−	7.69463i	−0.306789	−	0.385213i
$400$	−17.6350	+	21.5165i	−0.881750	+	1.07582i
$401$	4.87896	+	2.81687i	0.243644	+	0.140668i	0.616850	−	0.787081i	$-0.288408\pi$
$401$	4.87896	+	2.81687i	0.243644	+	0.140668i	−0.373207	+	0.927748i	$0.621742\pi$
$402$	−0.827054	−	3.29115i	−0.0412497	−	0.164148i
$403$	−7.02317	−	12.1645i	−0.349849	−	0.605956i
$404$	12.0836	+	0.986893i	0.601184	+	0.0490998i
$405$	30.9611	−	3.12452i	1.53847	−	0.155259i
$406$	−36.1166	+	12.9737i	−1.79244	+	0.643872i
$407$	2.43622	−	4.21966i	0.120759	−	0.209161i
$408$	9.17824	+	11.1591i	0.454391	+	0.552456i
$409$	−8.85640			−0.437921			−0.218960	−	0.975734i	$-0.570267\pi$
$409$	−8.85640			−0.437921			−0.218960	+	0.975734i	$0.570267\pi$
$410$	26.6110	+	50.7608i	1.31422	+	2.50690i
$411$	−3.58775	−	12.1583i	−0.176971	−	0.599723i
$412$	13.5177	−	6.39872i	0.665970	−	0.315242i
$413$	25.4863	−	10.3456i	1.25410	−	0.509074i
$414$	−18.7063	+	33.1263i	−0.919363	+	1.62807i
$415$	−40.3265	+	23.2825i	−1.97955	+	1.14289i
$416$	23.2179	+	4.79666i	1.13835	+	0.235176i
$417$	2.03371	−	0.600122i	0.0995912	−	0.0293881i
$418$	−4.91407	−	0.200337i	−0.240355	−	0.00979880i
$419$	13.6301	−	7.86937i	0.665876	−	0.384444i	−0.128636	−	0.991692i	$-0.541060\pi$
$419$	13.6301	−	7.86937i	0.665876	−	0.384444i	0.794512	+	0.607248i	$0.207727\pi$
$420$	17.6586	+	26.3133i	0.861654	+	1.28396i
$421$	18.6549	+	10.7704i	0.909185	+	0.524918i	0.880169	−	0.474661i	$-0.157429\pi$
$421$	18.6549	+	10.7704i	0.909185	+	0.524918i	0.0290159	+	0.999579i	$0.490763\pi$
$422$	−16.7969	−	10.6327i	−0.817659	−	0.517593i
$423$	6.03190	+	3.08916i	0.293281	+	0.150200i
$424$	18.9680	+	14.2953i	0.921169	+	0.694242i
$425$		−	20.5126i		−	0.995006i
$426$	−1.04289	−	4.15003i	−0.0505280	−	0.201070i
$427$	11.9678	−	4.85808i	0.579163	−	0.235099i
$428$	0.693658	−	8.49324i	0.0335292	−	0.410536i
$429$	−8.52245	−	8.10430i	−0.411468	−	0.391279i
$430$	20.5903	+	13.0340i	0.992952	+	0.628556i
$431$	−8.86197	+	15.3494i	−0.426866	+	0.739354i	−0.996593	−	0.0824805i	$-0.973716\pi$
$431$	−8.86197	+	15.3494i	−0.426866	+	0.739354i	0.569727	+	0.821834i	$0.307049\pi$
$432$	19.5291	+	7.11428i	0.939596	+	0.342286i
$433$	−26.3748			−1.26749			−0.633747	−	0.773540i	$-0.718484\pi$
$433$	−26.3748			−1.26749			−0.633747	+	0.773540i	$0.718484\pi$
$434$	8.10100	−	9.57236i	0.388860	−	0.459488i
$435$	58.9118	−	17.3841i	2.82461	−	0.833505i
$436$	−1.38162	+	0.654003i	−0.0661678	+	0.0313210i
$437$	−19.2478			−0.920745
$438$	23.9524	+	6.82025i	1.14449	+	0.325884i
$439$		−	14.6607i		−	0.699717i	−0.936802	−	0.349859i	$-0.886230\pi$
$439$		−	14.6607i		−	0.699717i	0.936802	−	0.349859i	$-0.113770\pi$
$440$	15.7258	+	1.93190i	0.749699	+	0.0920997i
$441$	20.0750	−	6.16383i	0.955954	−	0.293516i
$442$	−15.4823	+	8.11647i	−0.736417	+	0.386061i
$443$			21.5739i			1.02501i	0.858685	+	0.512503i	$0.171282\pi$
$443$			21.5739i			1.02501i	−0.858685	+	0.512503i	$0.828718\pi$
$444$	−9.89535	−	3.25887i	−0.469613	−	0.154659i
$445$			4.04773i			0.191881i
$446$	−6.77165	−	0.276067i	−0.320647	−	0.0130721i
$447$	12.0446	+	11.4536i	0.569689	+	0.541737i
$448$	2.97733	+	20.9556i	0.140666	+	0.990057i
$449$		−	31.8487i		−	1.50303i	−0.659715	−	0.751515i	$-0.729323\pi$
$449$		−	31.8487i		−	1.50303i	0.659715	−	0.751515i	$-0.270677\pi$
$450$	−14.9970	−	25.4123i	−0.706964	−	1.19795i
$451$	9.49470	−	16.4453i	0.447088	−	0.774379i
$452$	1.08312	−	13.2619i	0.0509459	−	0.623788i
$453$	4.59371	+	15.5673i	0.215831	+	0.731416i
$454$	4.41666	−	6.97714i	0.207284	−	0.327453i
$455$	−35.5243	+	14.4203i	−1.66540	+	0.676035i
$456$	1.72422	+	10.3736i	0.0807441	+	0.485787i
$457$	−0.0421800			−0.00197310			−0.000986549	−	1.00000i	$-0.500314\pi$
$457$	−0.0421800			−0.00197310			−0.000986549		1.00000i	$0.500314\pi$
$458$	11.8628	+	0.483622i	0.554311	+	0.0225982i
$459$	−14.4620	+	5.07073i	−0.675026	+	0.236681i
$460$	61.8017	+	5.04746i	2.88152	+	0.235339i
$461$	−6.19595	+	10.7317i	−0.288574	+	0.499825i	−0.973470	−	0.228816i	$-0.926514\pi$
$461$	−6.19595	+	10.7317i	−0.288574	+	0.499825i	0.684896	+	0.728641i	$0.259848\pi$
$462$	4.23709	−	9.60665i	0.197127	−	0.446942i
$463$	13.8147	−	7.97595i	0.642026	−	0.370674i	−0.143369	−	0.989669i	$-0.545793\pi$
$463$	13.8147	−	7.97595i	0.642026	−	0.370674i	0.785394	+	0.618996i	$0.212460\pi$
$464$	40.4821	+	6.65690i	1.87934	+	0.309039i
$465$	−13.8312	+	14.5449i	−0.641408	+	0.674503i
$466$	8.98348	−	14.1915i	0.416152	−	0.657409i
$467$	−31.6838	+	18.2926i	−1.46615	+	0.846482i	−0.999284	−	0.0378450i	$-0.987951\pi$
$467$	−31.6838	+	18.2926i	−1.46615	+	0.846482i	−0.466867	+	0.884328i	$0.654617\pi$
$468$	−13.2464	+	21.3745i	−0.612317	+	0.988036i
$469$	1.37863	+	3.39623i	0.0636591	+	0.156823i
$470$	0.449946	−	11.0367i	0.0207545	−	0.509087i
$471$	21.7574	+	5.24732i	1.00253	+	0.241784i
$472$	−29.1858	−	3.58544i	−1.34338	−	0.165033i
$473$		−	8.07408i		−	0.371247i
$474$	−2.79660	+	0.702774i	−0.128452	+	0.0322795i
$475$	7.46462	−	12.9291i	0.342500	−	0.593228i
$476$	−11.4923	−	10.5587i	−0.526750	−	0.483955i
$477$	−21.1566	+	13.6770i	−0.968692	+	0.626227i
$478$	18.0341	+	11.4159i	0.824859	+	0.522151i
$479$	12.9952	+	22.5083i	0.593764	+	1.02843i	0.993720	+	0.111895i	$0.0356920\pi$
$479$	12.9952	+	22.5083i	0.593764	+	1.02843i	−0.399956	+	0.916534i	$0.630975\pi$
$480$	−2.81590	−	33.7602i	−0.128528	−	1.54093i
$481$	6.30222	−	10.9158i	0.287357	−	0.497716i
$482$	6.88760	+	4.35998i	0.313722	+	0.198591i
$483$	15.0371	−	38.2410i	0.684212	−	1.74003i
$484$	7.16661	+	15.1399i	0.325755	+	0.688178i
$485$	−1.93486	−	3.35127i	−0.0878574	−	0.152174i
$486$	−14.2092	+	16.8553i	−0.644541	+	0.764570i
$487$	3.42857	+	1.97948i	0.155363	+	0.0896990i	0.575666	−	0.817685i	$-0.304743\pi$
$487$	3.42857	+	1.97948i	0.155363	+	0.0896990i	−0.420303	+	0.907384i	$0.638076\pi$
$488$	−13.7050	−	1.68365i	−0.620397	−	0.0762151i
$489$	18.2884	−	5.39666i	0.827028	−	0.244046i
$490$	−22.8379	−	25.4955i	−1.03171	−	1.15177i
$491$	13.3794	−	7.72462i	0.603805	−	0.348607i	−0.166732	−	0.986002i	$-0.553321\pi$
$491$	13.3794	−	7.72462i	0.603805	−	0.348607i	0.770537	+	0.637395i	$0.219988\pi$
$492$	−38.5652	−	12.7008i	−1.73865	−	0.572596i
$493$	−26.1970	+	15.1248i	−1.17985	+	0.681188i
$494$	−12.7121	−	0.518248i	−0.571945	−	0.0233171i
$495$	−7.66037	+	14.9577i	−0.344308	+	0.672297i
$496$	−12.5437	+	4.73034i	−0.563231	+	0.212398i
$497$	1.73840	+	4.28253i	0.0779779	+	0.192098i
$498$	9.03408	−	31.7272i	0.404827	−	1.42173i
$499$	−8.23068	+	14.2560i	−0.368456	+	0.638184i	−0.989324	−	0.145731i	$-0.953447\pi$
$499$	−8.23068	+	14.2560i	−0.368456	+	0.638184i	0.620869	+	0.783915i	$0.286780\pi$
$500$	−7.69021	+	11.1189i	−0.343917	+	0.497252i
$501$	−10.8543	+	3.20297i	−0.484935	+	0.143098i
$502$	10.3271	+	19.6990i	0.460920	+	0.879210i
$503$	24.0517			1.07241			0.536206	−	0.844087i	$-0.319857\pi$
$503$	24.0517			1.07241			0.536206	+	0.844087i	$0.319857\pi$
$504$	−21.9570	−	4.67860i	−0.978043	−	0.208401i
$505$	20.9598			0.932697
$506$	−9.53909	−	18.1959i	−0.424064	−	0.808908i
$507$	−5.72965	−	5.44853i	−0.254463	−	0.241978i
$508$	−19.6735	−	13.6069i	−0.872871	−	0.603708i
$509$	8.49082	−	14.7065i	0.376349	−	0.651855i	−0.614179	−	0.789167i	$-0.710513\pi$
$509$	8.49082	−	14.7065i	0.376349	−	0.651855i	0.990528	+	0.137311i	$0.0438461\pi$
$510$	17.3851	+	17.9362i	0.769823	+	0.794226i
$511$	−26.6442	−	3.70021i	−1.17867	−	0.163688i
$512$	8.11296	−	21.1230i	0.358545	−	0.933512i
$513$	−10.9607	−	2.06668i	−0.483925	−	0.0912463i
$514$	17.8670	+	0.728403i	0.788080	+	0.0321285i
$515$	22.3914	−	12.9277i	0.986683	−	0.569662i
$516$	−16.9008	+	3.52200i	−0.744015	+	0.155048i
$517$	−3.16948	+	1.82990i	−0.139394	+	0.0804790i
$518$	11.0736	+	2.00063i	0.486548	+	0.0879025i
$519$	0.854131	−	3.54155i	0.0374922	−	0.155457i
$520$	40.6809	+	4.99760i	1.78397	+	0.219159i
$521$	−6.28059	−	3.62610i	−0.275158	−	0.158862i	0.356072	−	0.934459i	$-0.384116\pi$
$521$	−6.28059	−	3.62610i	−0.275158	−	0.158862i	−0.631229	+	0.775596i	$0.717449\pi$
$522$	−21.3966	+	37.8905i	−0.936504	+	1.65842i
$523$	−2.72925	−	4.72720i	−0.119342	−	0.206706i	0.800165	−	0.599780i	$-0.204745\pi$
$523$	−2.72925	−	4.72720i	−0.119342	−	0.206706i	−0.919507	+	0.393074i	$0.871412\pi$
$524$	−17.8249	+	8.43756i	−0.778684	+	0.368596i
$525$	19.8556	+	24.9313i	0.866569	+	1.08809i
$526$	20.4873	+	12.9688i	0.893288	+	0.565467i
$527$	4.94235	−	8.56039i	0.215292	−	0.372897i
$528$	−8.95218	+	6.77109i	−0.389594	+	0.294674i
$529$	−28.7021	−	49.7135i	−1.24792	−	2.16146i
$530$	34.6948	+	21.9625i	1.50705	+	0.953988i
$531$	14.2170	−	27.7601i	0.616965	−	1.20469i
$532$	−3.40129	−	10.8372i	−0.147464	−	0.469854i
$533$	24.5617	−	42.5421i	1.06388	−	1.84270i
$534$	−1.99579	−	2.05906i	−0.0863663	−	0.0891041i
$535$		−	14.7320i		−	0.636920i
$536$	0.477786	−	3.88922i	0.0206372	−	0.167989i
$537$	13.5535	−	14.2528i	0.584875	−	0.615053i
$538$	1.61481	−	39.6098i	0.0696196	−	1.70770i
$539$	−3.09031	+	10.9116i	−0.133109	+	0.469998i
$540$	34.6511	+	9.51010i	1.49115	+	0.409249i
$541$	4.26423	−	2.46196i	0.183334	−	0.105848i	−0.405524	−	0.914084i	$-0.632911\pi$
$541$	4.26423	−	2.46196i	0.183334	−	0.105848i	0.588858	+	0.808237i	$0.299578\pi$
$542$	−10.1155	+	15.9798i	−0.434499	+	0.686393i
$543$	3.12145	+	0.752814i	0.133954	+	0.0323063i
$544$	5.24617	+	15.8376i	0.224928	+	0.679033i
$545$	−2.28859	+	1.32132i	−0.0980324	+	0.0565990i
$546$	10.9609	−	24.8513i	0.469081	−	1.06354i
$547$	7.18725	−	12.4487i	0.307305	−	0.532267i	−0.670467	−	0.741939i	$-0.733906\pi$
$547$	7.18725	−	12.4487i	0.307305	−	0.532267i	0.977772	+	0.209672i	$0.0672396\pi$
$548$	1.19152	−	14.5891i	0.0508990	−	0.623214i
$549$	6.67600	−	13.0356i	0.284925	−	0.556345i
$550$	15.9220	+	0.649109i	0.678916	+	0.0276781i
$551$	−22.0160			−0.937912
$552$	−33.9269	+	27.9046i	−1.44402	+	1.18770i
$553$	2.88588	−	1.17146i	0.122720	−	0.0498156i
$554$	−14.5115	+	22.9243i	−0.616533	+	0.973958i
$555$	−17.5089	−	4.22271i	−0.743212	−	0.179244i
$556$	2.44031	+	0.199304i	0.103492	+	0.00845239i
$557$	−8.31796	+	14.4071i	−0.352443	+	0.610450i	−0.986677	−	0.162692i	$-0.947982\pi$
$557$	−8.31796	+	14.4071i	−0.352443	+	0.610450i	0.634234	+	0.773141i	$0.281316\pi$
$558$	−0.135692	−	14.2186i	−0.00574429	−	0.601921i
$559$		−	20.8867i		−	0.883414i
$560$	8.07911	+	35.6888i	0.341405	+	1.50813i
$561$	1.94037	−	8.04550i	0.0819225	−	0.339681i
$562$	38.9268	+	1.58697i	1.64203	+	0.0669423i
$563$		−	18.9644i		−	0.799255i	−0.916678	−	0.399627i	$-0.869140\pi$
$563$		−	18.9644i		−	0.799255i	0.916678	−	0.399627i	$-0.130860\pi$
$564$	5.21293	+	5.83618i	0.219504	+	0.245747i
$565$		−	23.0035i		−	0.967766i
$566$	−19.2041	+	10.0676i	−0.807210	+	0.423174i
$567$	12.6689	−	20.1618i	0.532045	−	0.846716i
$568$	0.602471	−	4.90416i	0.0252791	−	0.205774i
$569$			24.5678i			1.02994i	0.857209	+	0.514969i	$0.172196\pi$
$569$			24.5678i			1.02994i	−0.857209	+	0.514969i	$0.827804\pi$
$570$	4.43077	+	17.6317i	0.185585	+	0.738510i
$571$	14.8138			0.619938			0.309969	−	0.950747i	$-0.399681\pi$
$571$	14.8138			0.619938			0.309969	+	0.950747i	$0.399681\pi$
$572$	−5.81013	−	12.2743i	−0.242934	−	0.513214i
$573$	−2.72042	+	11.2799i	−0.113647	+	0.471223i
$574$	43.1573	+	7.79705i	1.80135	+	0.325443i
$575$	62.3644			2.60077
$576$	18.0784	+	15.7852i	0.753266	+	0.657716i
$577$	−14.8512	+	25.7230i	−0.618262	+	1.07086i	0.371541	+	0.928416i	$0.378829\pi$
$577$	−14.8512	+	25.7230i	−0.618262	+	1.07086i	−0.989803	+	0.142444i	$0.954504\pi$
$578$	9.91963	+	6.27930i	0.412602	+	0.261184i
$579$	3.13769	−	13.0100i	0.130398	−	0.540679i
$580$	70.6901	+	5.77339i	2.93525	+	0.239727i
$581$	−4.90128	+	35.2928i	−0.203339	+	1.46419i
$582$	2.63665	+	0.750764i	0.109292	+	0.0311202i
$583$		−	13.6049i		−	0.563458i
$584$	22.9654	+	17.3080i	0.950316	+	0.716209i
$585$	−19.8165	+	38.6937i	−0.819311	+	1.59979i
$586$	17.1098	+	10.8308i	0.706799	+	0.447416i
$587$	−0.647855	−	0.374039i	−0.0267398	−	0.0154382i	0.486570	−	0.873641i	$-0.338248\pi$
$587$	−0.647855	−	0.374039i	−0.0267398	−	0.0154382i	−0.513310	+	0.858203i	$0.671581\pi$
$588$	24.1884	+	1.70889i	0.997514	+	0.0704734i
$589$	6.23033	−	3.59708i	0.256716	−	0.148215i
$590$	−50.7935	−	2.07075i	−2.09114	−	0.0852515i
$591$	10.0230	−	41.5593i	0.412293	−	1.70952i
$592$	−9.30412	−	7.62569i	−0.382397	−	0.313414i
$593$	−9.05519	+	5.22801i	−0.371852	+	0.214689i	−0.674267	−	0.738487i	$-0.735540\pi$
$593$	−9.05519	+	5.22801i	−0.371852	+	0.214689i	0.302415	+	0.953176i	$0.402207\pi$
$594$	−3.47830	−	11.3859i	−0.142716	−	0.467170i
$595$	−21.2879	−	16.5760i	−0.872718	−	0.679549i
$596$	8.21132	+	17.3470i	0.336349	+	0.710559i
$597$	−5.28146	+	5.55397i	−0.216156	+	0.227309i
$598$	−24.6765	−	47.0708i	−1.00910	−	1.92487i
$599$	−34.2488			−1.39937			−0.699684	−	0.714452i	$-0.746676\pi$
$599$	−34.2488			−1.39937			−0.699684	+	0.714452i	$0.746676\pi$
$600$	−5.58663	−	33.6113i	−0.228073	−	1.37217i
$601$	−23.6438	+	40.9523i	−0.964452	+	1.67048i	−0.253372	+	0.967369i	$0.581540\pi$
$601$	−23.6438	+	40.9523i	−0.964452	+	1.67048i	−0.711080	+	0.703111i	$0.751794\pi$
$602$	17.5492	−	6.30394i	0.715252	−	0.256930i
$603$	3.69924	+	1.89452i	0.150645	+	0.0771508i
$604$	−1.52560	+	18.6797i	−0.0620759	+	0.760065i
$605$	14.4791	+	25.0785i	0.588659	+	1.01959i
$606$	−10.6621	+	10.3345i	−0.433119	+	0.419811i
$607$	−8.97187	−	5.17991i	−0.364157	−	0.210246i	0.306746	−	0.951791i	$-0.400760\pi$
$607$	−8.97187	−	5.17991i	−0.364157	−	0.210246i	−0.670903	+	0.741545i	$0.734093\pi$
$608$	−2.45673	+	11.8916i	−0.0996334	+	0.482268i
$609$	17.1997	−	43.7408i	0.696969	−	1.77247i
$610$	−23.8516	−	0.972381i	−0.965721	−	0.0393706i
$611$	−8.19908	+	4.73374i	−0.331699	+	0.191507i
$612$	−17.6874	−	0.552069i	−0.714969	−	0.0223161i
$613$	−12.4399	−	7.18219i	−0.502444	−	0.290086i	0.227278	−	0.973830i	$-0.427017\pi$
$613$	−12.4399	−	7.18219i	−0.502444	−	0.290086i	−0.729722	+	0.683744i	$0.760351\pi$
$614$	−30.8176	+	16.1559i	−1.24370	+	0.652000i
$615$	−68.2376	−	16.4572i	−2.75161	−	0.663617i
$616$	8.55937	−	8.58630i	0.344867	−	0.345952i
$617$	−19.3123	+	11.1500i	−0.777486	+	0.448882i	−0.835538	−	0.549432i	$-0.814844\pi$
$617$	−19.3123	+	11.1500i	−0.777486	+	0.448882i	0.0580528	+	0.998314i	$0.481511\pi$
$618$	−5.01620	+	17.6166i	−0.201781	+	0.708645i
$619$	13.8838	+	24.0475i	0.558038	+	0.966550i	0.997660	+	0.0683670i	$0.0217789\pi$
$619$	13.8838	+	24.0475i	0.558038	+	0.966550i	−0.439623	+	0.898183i	$0.644888\pi$
$620$	−20.9480	+	9.91589i	−0.841291	+	0.398232i
$621$	−15.4165	−	43.9687i	−0.618644	−	1.76440i
$622$	−26.1010	+	13.6833i	−1.04656	+	0.548649i
$623$	2.44383	+	1.90291i	0.0979101	+	0.0762384i
$624$	−23.1583	+	17.5160i	−0.927072	+	0.701202i
$625$	5.70149	−	9.87527i	0.228060	−	0.395011i
$626$	35.0035	−	18.3503i	1.39902	−	0.733426i
$627$	4.15081	−	4.36498i	0.165767	−	0.174321i
$628$	21.2551	+	14.7007i	0.848169	+	0.586623i
$629$	8.87001			0.353670
$630$	−38.4917	−	4.97161i	−1.53355	−	0.198074i
$631$			26.0710i			1.03787i	0.854814	+	0.518935i	$0.173671\pi$
$631$			26.0710i			1.03787i	−0.854814	+	0.518935i	$0.826329\pi$
$632$	−3.30479	−	0.405990i	−0.131457	−	0.0161494i
$633$	23.3517	−	6.89079i	0.928147	−	0.273884i
$634$	15.3899	−	8.06807i	0.611213	−	0.320424i
$635$	−35.8135	−	20.6770i	−1.42122	−	0.820540i
$636$	−28.4780	+	5.93461i	−1.12922	+	0.235323i
$637$	−7.99427	+	28.2272i	−0.316744	+	1.11840i
$638$	−10.9110	−	20.8129i	−0.431971	−	0.823990i
$639$	4.66461	+	2.38892i	0.184529	+	0.0945043i
$640$	11.0066	−	37.5379i	0.435074	−	1.48382i
$641$	−42.3700	+	24.4623i	−1.67352	+	0.966205i	−0.707869	+	0.706343i	$0.750344\pi$
$641$	−42.3700	+	24.4623i	−1.67352	+	0.966205i	−0.965646	+	0.259861i	$0.916323\pi$
$642$	7.26383	+	7.49409i	0.286680	+	0.295768i
$643$	16.4873	+	28.5568i	0.650194	+	1.12617i	0.983075	+	0.183201i	$0.0586459\pi$
$643$	16.4873	+	28.5568i	0.650194	+	1.12617i	−0.332881	+	0.942969i	$0.608021\pi$
$644$	32.1015	−	34.9401i	1.26498	−	1.37683i
$645$	−28.6254	+	8.44700i	−1.12713	+	0.332600i
$646$	−4.15705	−	7.92962i	−0.163557	−	0.311987i
$647$	8.39914	−	14.5477i	0.330204	−	0.571930i	−0.652348	−	0.757920i	$-0.726216\pi$
$647$	8.39914	−	14.5477i	0.330204	−	0.571930i	0.982552	+	0.185990i	$0.0595491\pi$
$648$	−22.3159	+	12.2475i	−0.876651	+	0.481126i
$649$	8.42161	+	14.5867i	0.330577	+	0.572576i
$650$	41.1884	+	1.67917i	1.61554	+	0.0658624i
$651$	2.27922	+	15.1885i	0.0893298	+	0.595283i
$652$	21.9448	+	1.79227i	0.859423	+	0.0701906i
$653$	0.488441	−	0.846005i	0.0191142	−	0.0331067i	−0.856310	−	0.516462i	$-0.827249\pi$
$653$	0.488441	−	0.846005i	0.0191142	−	0.0331067i	0.875424	+	0.483355i	$0.160582\pi$
$654$	0.512698	−	1.80057i	0.0200481	−	0.0704078i
$655$	−29.5260	+	17.0469i	−1.15368	+	0.666076i
$656$	−36.2610	−	29.7196i	−1.41575	−	1.16036i
$657$	−25.6152	+	16.5594i	−0.999343	+	0.646042i
$658$	−6.45194	−	5.46022i	−0.251523	−	0.212861i
$659$	−29.8473	−	17.2324i	−1.16269	−	0.671277i	−0.210740	−	0.977542i	$-0.567587\pi$
$659$	−29.8473	−	17.2324i	−1.16269	−	0.671277i	−0.951946	+	0.306265i	$0.900921\pi$
$660$	−14.4723	+	12.9268i	−0.563334	+	0.503176i
$661$			24.6748i			0.959738i	0.877340	+	0.479869i	$0.159316\pi$
$661$			24.6748i			0.959738i	−0.877340	+	0.479869i	$0.840684\pi$
$662$	−26.1822	+	13.7258i	−1.01760	+	0.533469i
$663$	5.01951	−	20.8128i	0.194942	−	0.808301i
$664$	22.9261	−	30.4199i	0.889704	−	1.18052i
$665$	−7.38571	−	18.1946i	−0.286406	−	0.705557i
$666$	10.9888	−	6.48496i	0.425806	−	0.251287i
$667$	−45.9840	−	79.6466i	−1.78051	−	3.08393i
$668$	−13.0244	−	1.06373i	−0.503929	−	0.0411568i
$669$	5.71987	−	6.01500i	0.221143	−	0.232553i
$670$	0.275943	−	6.76860i	0.0106606	−	0.261494i
$671$	3.95461	+	6.84959i	0.152666	+	0.264425i
$672$	−21.7067	−	14.1711i	−0.837352	−	0.546664i
$673$	−4.54737	+	7.87628i	−0.175288	+	0.303608i	−0.940261	−	0.340454i	$-0.889419\pi$
$673$	−4.54737	+	7.87628i	−0.175288	+	0.303608i	0.764973	+	0.644063i	$0.222752\pi$
$674$	8.51230	+	5.38844i	0.327881	+	0.207555i
$675$	35.5134	+	6.69623i	1.36691	+	0.257738i
$676$	−3.90616	−	8.25202i	−0.150237	−	0.317385i
$677$	38.3691			1.47465			0.737323	−	0.675540i	$-0.236090\pi$
$677$	38.3691			1.47465			0.737323	+	0.675540i	$0.236090\pi$
$678$	11.3422	+	11.7018i	0.435595	+	0.449403i
$679$	−2.93296	−	0.407314i	−0.112557	−	0.0156313i
$680$	11.2682	+	26.5510i	0.432117	+	1.01818i
$681$	2.86232	+	9.69990i	0.109684	+	0.371701i
$682$	6.48824	+	4.10717i	0.248447	+	0.157272i
$683$	−7.44126	−	4.29622i	−0.284732	−	0.164390i	0.350832	−	0.936439i	$-0.385899\pi$
$683$	−7.44126	−	4.29622i	−0.284732	−	0.164390i	−0.635564	+	0.772048i	$0.719232\pi$
$684$	−10.9475	−	6.78448i	−0.418587	−	0.259411i
$685$		−	25.3056i		−	0.966876i
$686$	−26.1295	+	1.80256i	−0.997629	+	0.0688221i
$687$	−10.0202	+	10.5373i	−0.382296	+	0.402022i
$688$	−19.6704	−	3.23461i	−0.749927	−	0.123318i
$689$		−	35.1943i		−	1.34080i
$690$	−54.5313	+	52.8558i	−2.07597	+	2.01218i
$691$	35.6797			1.35732			0.678659	−	0.734453i	$-0.262561\pi$
$691$	35.6797			1.35732			0.678659	+	0.734453i	$0.262561\pi$
$692$	2.39291	−	3.45979i	0.0909648	−	0.131521i
$693$	5.42947	+	11.6568i	0.206248	+	0.442807i
$694$	−5.92130	−	11.2950i	−0.224769	−	0.428751i
$695$	4.23285			0.160561
$696$	−38.8063	+	31.9179i	−1.47095	+	1.20984i
$697$	34.5691			1.30940
$698$	−3.25472	−	0.132689i	−0.123193	−	0.00502234i
$699$	5.82196	+	19.7296i	0.220207	+	0.746243i
$700$	11.0205	+	35.1136i	0.416534	+	1.32717i
$701$	−38.1015			−1.43907			−0.719537	−	0.694454i	$-0.755646\pi$
$701$	−38.1015			−1.43907			−0.719537	+	0.694454i	$0.755646\pi$
$702$	−8.99795	−	29.4541i	−0.339606	−	1.11167i
$703$	5.59078	+	3.22784i	0.210860	+	0.121740i
$704$	−12.4593	+	3.57094i	−0.469577	+	0.134585i
$705$	9.80351	+	9.32250i	0.369222	+	0.351106i
$706$	−9.05750	+	14.3084i	−0.340883	+	0.538505i
$707$	9.85355	−	12.6545i	0.370581	−	0.475923i
$708$	26.8594	−	23.9911i	1.00944	−	0.901640i
$709$			11.0375i			0.414523i	0.978286	+	0.207262i	$0.0664551\pi$
$709$			11.0375i			0.414523i	−0.978286	+	0.207262i	$0.933545\pi$
$710$	0.347954	−	8.53497i	0.0130585	−	0.320312i
$711$	1.60983	−	3.14336i	0.0603734	−	0.117885i
$712$	−1.29359	−	3.04803i	−0.0484791	−	0.114230i
$713$	26.0262	+	15.0262i	0.974687	+	0.562736i
$714$	19.0020	−	2.06420i	0.711134	−	0.0772506i
$715$	−11.7385	−	20.3317i	−0.438996	−	0.760364i
$716$	20.5273	−	9.71675i	0.767140	−	0.363132i
$717$	−25.0717	+	7.39834i	−0.936319	+	0.276296i
$718$	−42.1008	−	26.6505i	−1.57119	−	0.994589i
$719$	18.5463	+	32.1231i	0.691660	+	1.19799i	0.971294	+	0.237883i	$0.0764535\pi$
$719$	18.5463	+	32.1231i	0.691660	+	1.19799i	−0.279634	+	0.960107i	$0.590213\pi$
$720$	33.3716	+	24.6548i	1.24368	+	0.918830i
$721$	2.72145	−	19.5964i	0.101352	−	0.729809i
$722$	−0.829097	+	20.3369i	−0.0308558	+	0.756862i
$723$	−9.57542	+	2.82559i	−0.356114	+	0.105085i
$724$	3.04939	+	2.10906i	0.113330	+	0.0783827i
$725$	71.3336			2.64926
$726$	−19.7307	−	5.61817i	−0.732277	−	0.208510i
$727$	12.0186	+	6.93893i	0.445744	+	0.257350i	0.706031	−	0.708181i	$-0.250484\pi$
$727$	12.0186	+	6.93893i	0.445744	+	0.257350i	−0.260287	+	0.965531i	$0.583817\pi$
$728$	22.1421	−	22.2118i	0.820641	−	0.823223i
$729$	−4.05793	−	26.6933i	−0.150294	−	0.988641i
$730$	42.0066	+	26.5909i	1.55473	+	0.984174i
$731$	12.7292	−	7.34920i	0.470806	−	0.271820i
$732$	12.6126	−	11.2657i	0.466175	−	0.416392i
$733$	−30.7926	−	17.7781i	−1.13735	−	0.656649i	−0.191577	−	0.981478i	$-0.561360\pi$
$733$	−30.7926	−	17.7781i	−1.13735	−	0.656649i	−0.945773	+	0.324829i	$0.894693\pi$
$734$	4.09224	−	6.46465i	0.151047	−	0.238615i
$735$	41.9187	−	0.459408i	1.54619	−	0.0169455i
$736$	−48.1512	+	15.9499i	−1.77488	+	0.587922i
$737$	−1.94378	+	1.12224i	−0.0716000	+	0.0413383i
$738$	42.8265	−	25.2739i	1.57647	−	0.930344i
$739$	−14.7653	+	25.5743i	−0.543151	+	0.940765i	0.455570	+	0.890200i	$0.349435\pi$
$739$	−14.7653	+	25.5743i	−0.543151	+	0.940765i	−0.998721	+	0.0505647i	$0.983898\pi$
$740$	−17.1047	−	11.8302i	−0.628782	−	0.434887i
$741$	10.7377	−	11.2917i	0.394458	−	0.414811i
$742$	29.5706	−	10.6222i	1.08557	−	0.389954i
$743$	−5.18532	−	8.98124i	−0.190231	−	0.329490i	0.755096	−	0.655615i	$-0.227590\pi$
$743$	−5.18532	−	8.98124i	−0.190231	−	0.329490i	−0.945327	+	0.326125i	$0.894257\pi$
$744$	5.76694	−	15.3729i	0.211426	−	0.563596i
$745$	16.5898	+	28.7344i	0.607803	+	1.05275i
$746$	−34.1188	−	1.39096i	−1.24918	−	0.0509265i
$747$	21.9344	+	33.9298i	0.802540	+	1.24142i
$748$	5.43608	−	7.85976i	0.198763	−	0.287381i
$749$	−8.89451	−	6.92577i	−0.324998	−	0.253062i
$750$	−4.03539	−	16.0583i	−0.147352	−	0.586367i
$751$	−36.0349	−	20.8048i	−1.31493	−	0.759177i	−0.332024	−	0.943271i	$-0.607731\pi$
$751$	−36.0349	−	20.8048i	−1.31493	−	0.759177i	−0.982909	+	0.184095i	$0.941065\pi$
$752$	3.18833	+	8.45471i	0.116266	+	0.308311i
$753$	−26.4813	−	6.38662i	−0.965033	−	0.232741i
$754$	−28.2255	−	53.8405i	−1.02791	−	1.96076i
$755$			32.4009i			1.17919i
$756$	22.0318	−	16.4499i	0.801290	−	0.598276i
$757$			25.8221i			0.938519i	0.883060	+	0.469259i	$0.155479\pi$
$757$			25.8221i			0.938519i	−0.883060	+	0.469259i	$0.844521\pi$
$758$	32.0032	−	16.7775i	1.16241	−	0.609385i
$759$	24.4607	+	5.89930i	0.887868	+	0.214131i
$760$	−2.55964	+	20.8357i	−0.0928479	+	0.755790i
$761$	28.6791	+	16.5579i	1.03962	+	0.600223i	0.919725	−	0.392563i	$-0.128412\pi$
$761$	28.6791	+	16.5579i	1.03962	+	0.600223i	0.119893	+	0.992787i	$0.461745\pi$
$762$	28.4132	−	7.14013i	1.02930	−	0.258660i
$763$	−0.278155	+	2.00292i	−0.0100699	+	0.0725105i
$764$	−7.62144	+	11.0195i	−0.275734	+	0.398670i
$765$	−30.5541	+	1.53782i	−1.10469	+	0.0555998i
$766$	−0.168001	+	4.12091i	−0.00607013	+	0.148894i
$767$	21.7857	+	37.7340i	0.786637	+	1.36250i
$768$	12.9096	+	24.5223i	0.465836	+	0.884871i
$769$	12.9810	+	22.4837i	0.468106	+	0.810784i	0.999336	−	0.0364443i	$-0.0116032\pi$
$769$	12.9810	+	22.4837i	0.468106	+	0.810784i	−0.531230	+	0.847228i	$0.678270\pi$
$770$	13.5400	−	15.9993i	0.487949	−	0.576573i
$771$	−15.0919	+	15.8706i	−0.543522	+	0.571565i
$772$	8.79046	−	12.7097i	0.316376	−	0.457432i
$773$	7.73961	−	13.4054i	0.278374	−	0.482159i	−0.692607	−	0.721316i	$-0.743538\pi$
$773$	7.73961	−	13.4054i	0.278374	−	0.482159i	0.970981	+	0.239157i	$0.0768711\pi$
$774$	10.3967	−	18.4111i	0.373701	−	0.661774i
$775$	−20.1868	+	11.6549i	−0.725132	+	0.418655i
$776$	2.52800	+	1.90524i	0.0907500	+	0.0683940i
$777$	−10.7807	+	8.58591i	−0.386756	+	0.308018i
$778$	12.2132	+	7.73115i	0.437863	+	0.277175i
$779$	21.7890	+	12.5799i	0.780670	+	0.450720i
$780$	−37.4382	+	33.4402i	−1.34050	+	1.19735i
$781$	−2.45103	+	1.41511i	−0.0877049	+	0.0506365i
$782$	20.0041	−	31.6012i	0.715345	−	1.13006i
$783$	−17.6338	−	50.2923i	−0.630179	−	1.79730i
$784$	25.3454	+	11.9001i	0.905191	+	0.425004i
$785$	38.6926	+	22.3392i	1.38100	+	0.797319i
$786$	6.61452	−	23.2299i	0.235932	−	0.828582i
$787$	−51.6301			−1.84041			−0.920206	−	0.391434i	$-0.871979\pi$
$787$	−51.6301			−1.84041			−0.920206	+	0.391434i	$0.871979\pi$
$788$	28.0803	−	40.5998i	1.00032	−	1.44631i
$789$	−28.4822	+	8.40475i	−1.01399	+	0.299217i
$790$	−5.75149	−	0.234477i	−0.204629	−	0.00834232i
$791$	−13.8885	−	10.8144i	−0.493817	−	0.384514i
$792$	0.988226	−	13.7116i	0.0351151	−	0.487220i
$793$	10.2301	+	17.7191i	0.363282	+	0.629223i
$794$	12.0749	−	19.0752i	0.428523	−	0.676953i
$795$	−48.2342	+	14.2333i	−1.71069	+	0.504803i
$796$	−7.99899	+	3.78638i	−0.283517	+	0.134205i
$797$	13.0775	+	22.6510i	0.463230	+	0.802338i	0.999120	−	0.0419498i	$-0.0133569\pi$
$797$	13.0775	+	22.6510i	0.463230	+	0.802338i	−0.535889	+	0.844288i	$0.680024\pi$
$798$	12.7282	+	5.61387i	0.450573	+	0.198729i
$799$	−5.76986	−	3.33123i	−0.204123	−	0.117850i
$800$	7.96000	−	38.5298i	0.281428	−	1.36223i
$801$	3.50759	−	0.176540i	0.123935	−	0.00623773i
$802$	−7.96069	−	0.324542i	−0.281102	−	0.0114600i
$803$		−	16.4721i		−	0.581286i
$804$	3.19699	+	3.57921i	0.112749	+	0.126229i
$805$	50.3959	−	64.7215i	1.77622	−	2.28113i
$806$	16.7843	+	10.6248i	0.591202	+	0.374242i
$807$	35.1839	+	33.4576i	1.23853	+	1.17776i
$808$	−15.7832	+	6.69838i	−0.555250	+	0.235648i
$809$	29.3197	+	16.9278i	1.03083	+	0.595148i	0.917221	−	0.398378i	$-0.130427\pi$
$809$	29.3197	+	16.9278i	1.03083	+	0.595148i	0.113605	+	0.993526i	$0.463760\pi$
$810$	−36.7282	+	24.2436i	−1.29050	+	0.851833i
$811$	31.1320			1.09319			0.546596	−	0.837396i	$-0.315923\pi$
$811$	31.1320			1.09319			0.546596	+	0.837396i	$0.315923\pi$
$812$	36.7183	−	39.9652i	1.28856	−	1.40250i
$813$	−6.55560	−	22.2158i	−0.229915	−	0.779143i
$814$	−0.280686	+	6.88496i	−0.00983805	+	0.241318i
$815$	38.0644			1.33334
$816$	−18.8234	−	7.95037i	−0.658952	−	0.278318i
$817$	10.6976			0.374263
$818$	11.0929	−	5.81538i	0.387855	−	0.203330i
$819$	14.0454	+	30.1549i	0.490786	+	1.05370i
$820$	−66.6623	−	46.1059i	−2.32795	−	1.61009i
$821$	−54.7036			−1.90917			−0.954584	−	0.297941i	$-0.903700\pi$
$821$	−54.7036			−1.90917			−0.954584	+	0.297941i	$0.903700\pi$
$822$	12.4773	+	12.8728i	0.435195	+	0.448990i
$823$		−	51.6441i		−	1.80020i	−0.435683	−	0.900100i	$-0.643493\pi$
$823$		−	51.6441i		−	1.80020i	0.435683	−	0.900100i	$-0.356507\pi$
$824$	−12.7298	+	16.8907i	−0.443462	+	0.588417i
$825$	−13.4490	+	14.1429i	−0.468234	+	0.492393i
$826$	−25.1291	+	29.6933i	−0.874354	+	1.03316i
$827$		−	3.69048i		−	0.128331i	−0.997939	−	0.0641653i	$-0.979561\pi$
$827$		−	3.69048i		−	0.128331i	0.997939	−	0.0641653i	$-0.0204385\pi$
$828$	1.67845	−	53.7748i	0.0583303	−	1.86881i
$829$	34.4538	+	19.8919i	1.19663	+	0.690875i	0.959803	−	0.280676i	$-0.0905587\pi$
$829$	34.4538	+	19.8919i	1.19663	+	0.690875i	0.236829	+	0.971551i	$0.423892\pi$
$830$	35.2222	−	55.6417i	1.22258	−	1.93135i
$831$	−9.40450	−	31.8702i	−0.326238	−	1.10557i
$832$	−32.2308	+	9.23760i	−1.11740	+	0.320256i
$833$	−20.0156	+	5.05999i	−0.693500	+	0.175318i
$834$	−2.15323	+	2.08707i	−0.0745602	+	0.0722693i
$835$	−22.5916			−0.781813
$836$	6.28657	−	2.97580i	0.217426	−	0.102920i
$837$	13.2072	+	11.3512i	0.456508	+	0.392355i
$838$	−11.9049	+	18.8066i	−0.411249	+	0.649663i
$839$	−27.8146	+	48.1762i	−0.960265	+	1.66323i	−0.238435	+	0.971159i	$0.576634\pi$
$839$	−27.8146	+	48.1762i	−0.960265	+	1.66323i	−0.721831	+	0.692070i	$0.756699\pi$
$840$	−39.3962	−	21.3631i	−1.35930	−	0.737097i
$841$	−38.0974	−	65.9867i	−1.31370	−	2.27540i
$842$	−30.4381	−	1.24090i	−1.04896	−	0.0427642i
$843$	−32.8807	+	34.5772i	−1.13247	+	1.19090i
$844$	28.0204	+	2.28848i	0.964502	+	0.0787726i
$845$	−7.89183	−	13.6690i	−0.271487	−	0.470230i
$846$	−9.58358	+	0.0914586i	−0.329490	+	0.00314441i
$847$	21.9481	+	3.04804i	0.754146	+	0.104732i
$848$	−33.1448	−	5.45035i	−1.13820	−	0.187166i
$849$	6.22617	−	25.8160i	0.213682	−	0.886004i
$850$	13.4692	+	25.6927i	0.461989	+	0.881251i
$851$			26.9675i			0.924433i
$852$	4.03129	+	4.51325i	0.138110	+	0.154621i
$853$	10.6239	+	6.13369i	0.363754	+	0.210014i	0.670726	−	0.741705i	$-0.265982\pi$
$853$	10.6239	+	6.13369i	0.363754	+	0.210014i	−0.306972	+	0.951719i	$0.599316\pi$
$854$	−11.8001	+	13.9433i	−0.403791	+	0.477131i
$855$	−19.8179	−	10.1495i	−0.677758	−	0.347105i
$856$	4.70810	+	11.0935i	0.160919	+	0.379169i
$857$	11.3673	−	6.56289i	0.388298	−	0.224184i	−0.293124	−	0.956074i	$-0.594695\pi$
$857$	11.3673	−	6.56289i	0.388298	−	0.224184i	0.681422	+	0.731890i	$0.261362\pi$
$858$	15.9962	+	4.55479i	0.546101	+	0.155498i
$859$	0.910393	−	1.57685i	0.0310622	−	0.0538013i	−0.850076	−	0.526659i	$-0.823444\pi$
$859$	0.910393	−	1.57685i	0.0310622	−	0.0538013i	0.881139	+	0.472858i	$0.156778\pi$
$860$	−34.3485	−	2.80531i	−1.17127	−	0.0956601i
$861$	−42.0158	+	33.4619i	−1.43189	+	1.14038i
$862$	1.02102	−	25.0446i	0.0347761	−	0.853024i
$863$	−15.0018	−	25.9838i	−0.510666	−	0.884499i	−0.999924	−	0.0123601i	$-0.996066\pi$
$863$	−15.0018	−	25.9838i	−0.510666	−	0.884499i	0.489258	−	0.872139i	$-0.337268\pi$
$864$	−29.1323	+	3.91257i	−0.991101	+	0.133108i
$865$	3.63625	−	6.29818i	0.123636	−	0.214144i
$866$	33.0353	−	17.3185i	1.12259	−	0.588508i
$867$	−13.7907	+	4.06945i	−0.468356	+	0.138206i
$868$	−3.86125	+	17.3091i	−0.131059	+	0.587508i
$869$	0.953603	+	1.65169i	0.0323488	+	0.0560297i
$870$	−62.3740	+	60.4575i	−2.11468	+	2.04970i
$871$	−5.02833	+	2.90311i	−0.170378	+	0.0983680i
$872$	1.30109	−	1.72638i	0.0440604	−	0.0584625i
$873$	−2.81968	+	1.82283i	−0.0954318	+	0.0616935i
$874$	24.1084	−	12.6387i	0.815479	−	0.427509i
$875$	6.72664	+	16.5710i	0.227402	+	0.560202i
$876$	−34.4795	+	7.18529i	−1.16496	+	0.242769i
$877$	14.8610	+	8.58000i	0.501820	+	0.289726i	0.729465	−	0.684018i	$-0.239769\pi$
$877$	14.8610	+	8.58000i	0.501820	+	0.289726i	−0.227645	+	0.973744i	$0.573103\pi$
$878$	9.62667	+	18.3630i	0.324884	+	0.619721i
$879$	−23.7867	+	7.01916i	−0.802306	+	0.236750i
$880$	−20.9656	+	7.90629i	−0.706751	+	0.266521i
$881$			37.1021i			1.25000i	0.780625	+	0.625000i	$0.214901\pi$
$881$			37.1021i			1.25000i	−0.780625	+	0.625000i	$0.785099\pi$
$882$	−21.0973	+	20.9023i	−0.710382	+	0.703817i
$883$	−31.1042			−1.04674			−0.523370	−	0.852105i	$-0.675326\pi$
$883$	−31.1042			−1.04674			−0.523370	+	0.852105i	$0.675326\pi$
$884$	14.0625	−	20.3323i	0.472974	−	0.683849i
$885$	42.9042	−	45.1179i	1.44221	−	1.51662i
$886$	−14.1661	−	27.0220i	−0.475919	−	0.907821i
$887$	−1.29831	+	2.24874i	−0.0435929	+	0.0755052i	−0.886999	−	0.461772i	$-0.847214\pi$
$887$	−1.29831	+	2.24874i	−0.0435929	+	0.0755052i	0.843406	+	0.537277i	$0.180547\pi$
$888$	14.5341	−	2.41576i	0.487733	−	0.0810676i
$889$	−29.3204	+	11.9020i	−0.983374	+	0.399179i
$890$	−2.65786	−	5.06991i	−0.0890918	−	0.169944i
$891$	13.2958	+	5.98578i	0.445425	+	0.200531i
$892$	8.66298	−	4.10069i	0.290058	−	0.137301i
$893$	−2.42450	−	4.19936i	−0.0811328	−	0.140526i
$894$	−22.6070	−	6.43717i	−0.756092	−	0.215291i
$895$	34.0024	−	19.6313i	1.13657	−	0.656201i
$896$	−17.4893	−	24.2925i	−0.584275	−	0.811555i
$897$	63.2771	+	15.2608i	2.11276	+	0.509544i
$898$	20.9128	+	39.8915i	0.697870	+	1.33120i
$899$	29.7693	+	17.1873i	0.992860	+	0.573228i
$900$	35.4707	+	21.9823i	1.18236	+	0.732743i
$901$	21.4488	−	12.3835i	0.714563	−	0.412553i
$902$	−1.09392	+	26.8328i	−0.0364235	+	0.893434i
$903$	−8.35741	+	21.2538i	−0.278117	+	0.707282i
$904$	7.35153	+	17.3222i	0.244508	+	0.576127i
$905$	5.55108	+	3.20492i	0.184524	+	0.106535i
$906$	−15.9757	−	16.4822i	−0.530759	−	0.547583i
$907$	−5.72640	−	9.91841i	−0.190142	−	0.329335i	0.755155	−	0.655546i	$-0.227561\pi$
$907$	−5.72640	−	9.91841i	−0.190142	−	0.329335i	−0.945297	+	0.326211i	$0.894228\pi$
$908$	−0.950595	+	11.6392i	−0.0315466	+	0.386260i
$909$	−0.914151	−	18.1628i	−0.0303205	−	0.602423i
$910$	35.0265	−	41.3882i	1.16112	−	1.37201i
$911$	3.81686	−	6.61099i	0.126458	−	0.219032i	−0.795844	−	0.605502i	$-0.792972\pi$
$911$	3.81686	−	6.61099i	0.126458	−	0.219032i	0.922302	+	0.386470i	$0.126306\pi$
$912$	−8.97126	−	11.8611i	−0.297068	−	0.392759i
$913$	−21.8188			−0.722098
$914$	0.0528318	−	0.0276967i	0.00174752	−	0.000916125i
$915$	20.1469	−	21.1864i	0.666037	−	0.700402i
$916$	−15.1761	+	7.18372i	−0.501432	+	0.237357i
$917$	−3.58859	+	25.8405i	−0.118506	+	0.853328i
$918$	14.7845	−	15.8474i	0.487960	−	0.523043i
$919$	48.3848	−	27.9350i	1.59607	−	0.921489i	0.603831	−	0.797112i	$-0.293640\pi$
$919$	48.3848	−	27.9350i	1.59607	−	0.921489i	0.992235	−	0.124377i	$-0.0396932\pi$
$920$	−80.7229	+	34.2588i	−2.66136	+	1.12948i
$921$	9.99138	−	41.4280i	0.329227	−	1.36510i
$922$	0.713858	−	17.5102i	0.0235097	−	0.576669i
$923$	−6.34054	+	3.66071i	−0.208701	+	0.120494i
$924$	1.00093	+	14.8148i	0.0329283	+	0.487372i
$925$	−18.1146	−	10.4585i	−0.595604	−	0.343872i
$926$	−12.0662	+	19.0613i	−0.396519	+	0.626394i
$927$	−12.1792	−	18.8396i	−0.400016	−	0.618773i
$928$	−55.0763	+	18.2438i	−1.80797	+	0.598883i
$929$		−	17.0652i		−	0.559892i	−0.960016	−	0.279946i	$-0.909683\pi$
$929$		−	17.0652i		−	0.559892i	0.960016	−	0.279946i	$-0.0903165\pi$
$930$	7.77345	−	27.3000i	0.254901	−	0.895201i
$931$	−14.4572	−	4.09446i	−0.473816	−	0.134190i
$932$	−1.93351	+	23.6742i	−0.0633343	+	0.775473i
$933$	8.46221	−	35.0875i	0.277040	−	1.14871i
$934$	27.6734	−	43.7167i	0.905502	−	1.43045i
$935$	8.26065	−	14.3079i	0.270152	−	0.467917i
$936$	2.55643	−	35.4703i	0.0835594	−	1.15938i
$937$	33.4837			1.09386			0.546932	−	0.837177i	$-0.315796\pi$
$937$	33.4837			1.09386			0.546932	+	0.837177i	$0.315796\pi$
$938$	−3.95684	−	3.34864i	−0.129196	−	0.109337i
$939$	−11.3485	+	47.0550i	−0.370343	+	1.53558i
$940$	6.68349	+	14.1193i	0.217991	+	0.460521i
$941$	−26.9691			−0.879168			−0.439584	−	0.898202i	$-0.644874\pi$
$941$	−26.9691			−0.879168			−0.439584	+	0.898202i	$0.644874\pi$
$942$	−30.6973	+	7.71412i	−1.00017	+	0.251340i
$943$			105.100i			3.42254i
$944$	38.9104	−	14.6734i	1.26643	−	0.477579i
$945$	35.6473	−	31.4446i	1.15961	−	1.02289i
$946$	5.30169	+	10.1130i	0.172373	+	0.328803i
$947$			36.8394i			1.19712i	0.801078	+	0.598560i	$0.204260\pi$
$947$			36.8394i			1.19712i	−0.801078	+	0.598560i	$0.795740\pi$
$948$	3.04136	−	2.71658i	0.0987789	−	0.0882304i
$949$		−	42.6113i		−	1.38322i
$950$	−0.860027	+	21.0956i	−0.0279029	+	0.684432i
$951$	−4.98958	+	20.6887i	−0.161798	+	0.670876i
$952$	21.3277	+	5.67884i	0.691233	+	0.184052i
$953$		−	30.5464i		−	0.989495i	−0.869037	−	0.494748i	$-0.835260\pi$
$953$		−	30.5464i		−	0.989495i	0.869037	−	0.494748i	$-0.164740\pi$
$954$	17.5185	−	31.0229i	0.567183	−	1.00440i
$955$	−11.5815	+	20.0597i	−0.374769	+	0.649118i
$956$	−30.0843	−	2.45704i	−0.972995	−	0.0794662i
$957$	27.9787	+	6.74774i	0.904422	+	0.218124i
$958$	−31.0565	−	19.6593i	−1.00339	−	0.635163i
$959$	−15.2783	−	11.8966i	−0.493363	−	0.384161i
$960$	25.6950	+	40.4367i	0.829302	+	1.30509i
$961$	19.7674			0.637658
$962$	−0.726103	+	17.8106i	−0.0234105	+	0.574236i
$963$	−12.7661	+	0.642530i	−0.411383	+	0.0207052i
$964$	−11.4898	−	0.938395i	−0.370063	−	0.0302237i
$965$	13.3579	−	23.1366i	0.430007	−	0.744795i
$966$	6.27577	+	57.7719i	0.201920	+	1.85878i
$967$	6.20470	−	3.58228i	0.199530	−	0.115198i	−0.396906	−	0.917859i	$-0.629916\pi$
$967$	6.20470	−	3.58228i	0.199530	−	0.115198i	0.596436	+	0.802661i	$0.296583\pi$
$968$	−18.9177	−	14.2574i	−0.608039	−	0.458251i
$969$	10.6598	+	2.57086i	0.342441	+	0.0825880i
$970$	4.62402	+	2.92709i	0.148468	+	0.0939832i
$971$	33.2083	−	19.1728i	1.06570	−	0.615284i	0.138699	−	0.990335i	$-0.455708\pi$
$971$	33.2083	−	19.1728i	1.06570	−	0.615284i	0.927005	+	0.375050i	$0.122375\pi$
$972$	6.72975	−	30.4419i	0.215857	−	0.976425i
$973$	1.98994	−	2.55560i	0.0637945	−	0.0819288i
$974$	−5.59418	−	0.228064i	−0.179249	−	0.00730763i
$975$	−34.7910	+	36.5861i	−1.11420	+	1.17169i
$976$	18.2715	−	6.89032i	0.584857	−	0.220554i
$977$			5.82554i			0.186376i	0.995649	+	0.0931878i	$0.0297057\pi$
$977$			5.82554i			0.186376i	−0.995649	+	0.0931878i	$0.970294\pi$
$978$	−19.3631	+	18.7682i	−0.619165	+	0.600141i
$979$	−0.948316	+	1.64253i	−0.0303083	+	0.0524955i
$980$	45.3463	+	16.9379i	1.44853	+	0.541062i
$981$	1.24481	+	1.92556i	0.0397438	+	0.0614785i
$982$	−11.6859	+	18.4607i	−0.372913	+	0.589104i
$983$	8.09591	+	14.0225i	0.258219	+	0.447249i	0.965765	−	0.259419i	$-0.0835309\pi$
$983$	8.09591	+	14.0225i	0.258219	+	0.447249i	−0.707546	+	0.706668i	$0.750198\pi$
$984$	56.6439	−	9.41495i	1.80574	−	0.300138i
$985$	42.6706	−	73.9077i	1.35960	−	2.35490i
$986$	22.8811	−	36.1461i	0.728683	−	1.15112i
$987$	10.2373	−	1.53624i	0.325857	−	0.0488990i
$988$	16.2626	−	7.69805i	0.517383	−	0.244908i
$989$	22.3438	+	38.7005i	0.710490	+	1.23061i
$990$	−0.226795	−	23.7650i	−0.00720803	−	0.755300i
$991$	9.67701	+	5.58702i	0.307400	+	0.177478i	0.645763	−	0.763538i	$-0.276540\pi$
$991$	9.67701	+	5.58702i	0.307400	+	0.177478i	−0.338362	+	0.941016i	$0.609873\pi$
$992$	12.6053	−	14.1615i	0.400220	−	0.449628i
$993$	8.48853	−	35.1966i	0.269375	−	1.11693i
$994$	−4.98944	−	4.22252i	−0.158255	−	0.133930i
$995$	−13.2499	+	7.64984i	−0.420051	+	0.242516i
$996$	9.51761	+	45.6714i	0.301577	+	1.44715i
$997$	−15.6164	+	9.01611i	−0.494575	+	0.285543i	−0.726470	−	0.687198i	$-0.758841\pi$
$997$	−15.6164	+	9.01611i	−0.494575	+	0.285543i	0.231895	+	0.972741i	$0.425507\pi$
$998$	0.948287	−	23.2606i	0.0300175	−	0.736300i
$999$	−2.89557	+	15.3567i	−0.0916118	+	0.485863i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bt.a.11.14	✓	184
7.2	even	3		504.2.cy.a.443.75	yes	184
8.3	odd	2	inner	504.2.bt.a.11.79	yes	184
9.5	odd	6		504.2.cy.a.347.45	yes	184
56.51	odd	6		504.2.cy.a.443.45	yes	184
63.23	odd	6	inner	504.2.bt.a.275.79	yes	184
72.59	even	6		504.2.cy.a.347.75	yes	184
504.275	even	6	inner	504.2.bt.a.275.14	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bt.a.11.14	✓	184	1.1	even	1	trivial
504.2.bt.a.11.79	yes	184	8.3	odd	2	inner
504.2.bt.a.275.14	yes	184	504.275	even	6	inner
504.2.bt.a.275.79	yes	184	63.23	odd	6	inner
504.2.cy.a.347.45	yes	184	9.5	odd	6
504.2.cy.a.347.75	yes	184	72.59	even	6
504.2.cy.a.443.45	yes	184	56.51	odd	6
504.2.cy.a.443.75	yes	184	7.2	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.bt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25253 + 0.656631i) q^{2} +(0.406083 - 1.68377i) q^{3} +(1.13767 - 1.64490i) q^{4} +(1.72880 - 2.99437i) q^{5} +(0.596986 + 2.37563i) q^{6} +(-0.995123 - 2.45148i) q^{7} +(-0.344876 + 2.80732i) q^{8} +(-2.67019 - 1.36751i) q^{9} +O(q^{10})\)	\(q+(-1.25253 + 0.656631i) q^{2} +(0.406083 - 1.68377i) q^{3} +(1.13767 - 1.64490i) q^{4} +(1.72880 - 2.99437i) q^{5} +(0.596986 + 2.37563i) q^{6} +(-0.995123 - 2.45148i) q^{7} +(-0.344876 + 2.80732i) q^{8} +(-2.67019 - 1.36751i) q^{9} +(-0.199181 + 4.88573i) q^{10} +(1.40306 - 0.810058i) q^{11} +(-2.30765 - 2.58355i) q^{12} +(3.62956 - 2.09553i) q^{13} +(2.85614 + 2.41712i) q^{14} +(-4.33981 - 4.12687i) q^{15} +(-1.41141 - 3.74272i) q^{16} +(2.55419 + 1.47466i) q^{17} +(4.24245 - 0.0404868i) q^{18} +(1.07327 + 1.85897i) q^{19} +(-2.95864 - 6.25032i) q^{20} +(-4.53183 + 0.680060i) q^{21} +(-1.22547 + 1.93592i) q^{22} +(-4.48342 + 7.76551i) q^{23} +(4.58685 + 1.72070i) q^{24} +(-3.47750 - 6.02321i) q^{25} +(-3.17015 + 5.00799i) q^{26} +(-3.38689 + 3.94068i) q^{27} +(-5.16456 - 1.15209i) q^{28} +(-5.12823 + 8.88235i) q^{29} +(8.14558 + 2.31939i) q^{30} -3.35151i q^{31} +(4.22541 + 3.76110i) q^{32} +(-0.794195 - 2.69139i) q^{33} +(-4.16752 - 0.169902i) q^{34} +(-9.06099 - 1.25834i) q^{35} +(-5.28722 + 2.83643i) q^{36} +(2.60454 - 1.50373i) q^{37} +(-2.56496 - 1.62367i) q^{38} +(-2.05449 - 6.96231i) q^{39} +(7.80994 + 5.88599i) q^{40} +(10.1507 - 5.86051i) q^{41} +(5.22972 - 3.82754i) q^{42} +(2.49182 - 4.31596i) q^{43} +(0.263757 - 3.22948i) q^{44} +(-8.71105 + 5.63140i) q^{45} +(0.516551 - 12.6705i) q^{46} -2.25898 q^{47} +(-6.87504 + 0.856634i) q^{48} +(-5.01946 + 4.87904i) q^{49} +(8.31070 + 5.26082i) q^{50} +(3.52022 - 3.70185i) q^{51} +(0.682310 - 8.35429i) q^{52} +(4.19874 - 7.27244i) q^{53} +(1.65462 - 7.15977i) q^{54} -5.60171i q^{55} +(7.22528 - 1.94818i) q^{56} +(3.56592 - 1.05226i) q^{57} +(0.590842 - 14.4928i) q^{58} +10.3963i q^{59} +(-11.7256 + 2.44353i) q^{60} +4.88188i q^{61} +(2.20070 + 4.19787i) q^{62} +(-0.695235 + 7.90675i) q^{63} +(-7.76212 - 1.93636i) q^{64} -14.4910i q^{65} +(2.76200 + 2.84956i) q^{66} -1.38538 q^{67} +(5.33151 - 2.52371i) q^{68} +(11.2547 + 10.7025i) q^{69} +(12.1754 - 4.37361i) q^{70} -1.74692 q^{71} +(4.75992 - 7.02447i) q^{72} +(5.08360 - 8.80506i) q^{73} +(-2.27487 + 3.59370i) q^{74} +(-11.5539 + 3.40940i) q^{75} +(4.27885 + 0.349461i) q^{76} +(-3.38206 - 2.63346i) q^{77} +(7.14498 + 7.37148i) q^{78} +1.17720i q^{79} +(-13.6471 - 2.24414i) q^{80} +(5.25986 + 7.30301i) q^{81} +(-8.86588 + 14.0057i) q^{82} +(-11.6631 - 6.73372i) q^{83} +(-4.03711 + 8.22811i) q^{84} +(8.83138 - 5.09880i) q^{85} +(-0.287092 + 7.04209i) q^{86} +(12.8734 + 12.2418i) q^{87} +(1.79021 + 4.21822i) q^{88} +(-1.01384 + 0.585338i) q^{89} +(7.21311 - 12.7734i) q^{90} +(-8.74899 - 6.81246i) q^{91} +(7.67284 + 16.2094i) q^{92} +(-5.64318 - 1.36099i) q^{93} +(2.82944 - 1.48331i) q^{94} +7.42191 q^{95} +(8.04871 - 5.58733i) q^{96} +(0.559596 - 0.969249i) q^{97} +(3.08331 - 9.40708i) q^{98} +(-4.85420 + 0.244316i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 2 q^{3} - 2 q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) \) 184 * q - 2 * q^3 - 2 * q^4 - 2 * q^6 - 2 * q^9	\( 184 q - 2 q^{3} - 2 q^{4} - 2 q^{6} - 2 q^{9} - 6 q^{10} - 6 q^{11} - 8 q^{12} + 12 q^{14} - 2 q^{16} + 2 q^{18} - 4 q^{19} - 6 q^{20} + 2 q^{22} - 8 q^{24} - 74 q^{25} - 6 q^{26} - 8 q^{27} + 3 q^{30} - 14 q^{33} - 4 q^{34} + 30 q^{35} - 38 q^{36} + 39 q^{38} + 6 q^{40} - 12 q^{41} - 20 q^{42} - 4 q^{43} + 9 q^{44} - 6 q^{46} - 5 q^{48} - 2 q^{49} - 21 q^{50} - 34 q^{51} + 9 q^{52} + 47 q^{54} - 24 q^{56} + 4 q^{57} - 3 q^{58} - 11 q^{60} - 8 q^{64} - 26 q^{66} - 4 q^{67} - 42 q^{68} - 3 q^{70} + 52 q^{72} - 4 q^{73} + 27 q^{74} + 30 q^{75} + 2 q^{76} - 29 q^{78} + 87 q^{80} + 14 q^{81} - 4 q^{82} - 72 q^{83} - 59 q^{84} - 27 q^{86} - 7 q^{88} - 24 q^{89} - 49 q^{90} - 36 q^{91} - 36 q^{92} - 18 q^{94} + 23 q^{96} - 4 q^{97} + 57 q^{98} + 10 q^{99}+O(q^{100}) \) 184 * q - 2 * q^3 - 2 * q^4 - 2 * q^6 - 2 * q^9 - 6 * q^10 - 6 * q^11 - 8 * q^12 + 12 * q^14 - 2 * q^16 + 2 * q^18 - 4 * q^19 - 6 * q^20 + 2 * q^22 - 8 * q^24 - 74 * q^25 - 6 * q^26 - 8 * q^27 + 3 * q^30 - 14 * q^33 - 4 * q^34 + 30 * q^35 - 38 * q^36 + 39 * q^38 + 6 * q^40 - 12 * q^41 - 20 * q^42 - 4 * q^43 + 9 * q^44 - 6 * q^46 - 5 * q^48 - 2 * q^49 - 21 * q^50 - 34 * q^51 + 9 * q^52 + 47 * q^54 - 24 * q^56 + 4 * q^57 - 3 * q^58 - 11 * q^60 - 8 * q^64 - 26 * q^66 - 4 * q^67 - 42 * q^68 - 3 * q^70 + 52 * q^72 - 4 * q^73 + 27 * q^74 + 30 * q^75 + 2 * q^76 - 29 * q^78 + 87 * q^80 + 14 * q^81 - 4 * q^82 - 72 * q^83 - 59 * q^84 - 27 * q^86 - 7 * q^88 - 24 * q^89 - 49 * q^90 - 36 * q^91 - 36 * q^92 - 18 * q^94 + 23 * q^96 - 4 * q^97 + 57 * q^98 + 10 * q^99

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