LMFDB - Embedded newform 507.2.p.a.64.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(25,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("507.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.p (of order $26$, degree $12$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			64.1
Character	$\chi$	$=$	507.64
Dual form			507.2.p.a.103.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.32286 - 0.282046i) q^{2} +(-0.748511 + 0.663123i) q^{3} +(3.37425 + 0.831678i) q^{4} +(-0.0918625 - 0.175029i) q^{5} +(1.92572 - 1.32923i) q^{6} +(-0.0642964 - 0.0243844i) q^{7} +(-3.22762 - 1.22407i) q^{8} +(0.120537 - 0.992709i) q^{9} +(0.164018 + 0.432479i) q^{10} +(-4.19756 + 0.509676i) q^{11} +(-3.07717 + 1.61502i) q^{12} +(2.61965 - 2.47739i) q^{13} +(0.142474 + 0.0747762i) q^{14} +(0.184826 + 0.0700953i) q^{15} +(0.997726 + 0.523647i) q^{16} +(-0.724665 + 1.91078i) q^{17} +(-0.559980 + 2.27193i) q^{18} +4.20632i q^{19} +(-0.164399 - 0.666994i) q^{20} +(0.0642964 - 0.0243844i) q^{21} +9.89410 q^{22} -0.481984 q^{23} +(3.22762 - 1.22407i) q^{24} +(2.81813 - 4.08276i) q^{25} +(-6.78382 + 5.01576i) q^{26} +(0.568065 + 0.822984i) q^{27} +(-0.196672 - 0.135753i) q^{28} +(0.576613 - 4.74884i) q^{29} +(-0.409555 - 0.214951i) q^{30} +(-4.78369 + 3.30194i) q^{31} +(3.51189 + 2.42408i) q^{32} +(2.80394 - 3.16499i) q^{33} +(2.22223 - 4.23410i) q^{34} +(0.00163844 + 0.0134938i) q^{35} +(1.23234 - 3.24940i) q^{36} +(-2.82811 + 1.95210i) q^{37} +(1.18638 - 9.77070i) q^{38} +(-0.318025 + 3.59150i) q^{39} +(0.0822482 + 0.677375i) q^{40} +(-8.14240 - 9.19087i) q^{41} +(-0.156229 + 0.0385070i) q^{42} +(3.15732 - 4.57417i) q^{43} +(-14.5875 - 1.77124i) q^{44} +(-0.184826 + 0.0700953i) q^{45} +(1.11958 + 0.135942i) q^{46} +(-1.61732 - 6.56173i) q^{47} +(-1.09405 + 0.269659i) q^{48} +(-5.23604 - 4.63872i) q^{49} +(-7.69765 + 8.68885i) q^{50} +(-0.724665 - 1.91078i) q^{51} +(10.8997 - 6.18062i) q^{52} +(0.242681 - 0.639897i) q^{53} +(-1.08742 - 2.07190i) q^{54} +(0.474807 + 0.687876i) q^{55} +(0.177676 + 0.157407i) q^{56} +(-2.78931 - 3.14848i) q^{57} +(-2.67879 + 10.8683i) q^{58} +(-2.04396 - 3.89444i) q^{59} +(0.565353 + 0.390235i) q^{60} +(-2.13525 - 5.63019i) q^{61} +(12.0431 - 6.32073i) q^{62} +(-0.0319567 + 0.0608884i) q^{63} +(-9.16077 - 8.11573i) q^{64} +(-0.674263 - 0.230937i) q^{65} +(-7.40584 + 6.56100i) q^{66} +(-2.41701 - 9.80618i) q^{67} +(-4.03436 + 5.84478i) q^{68} +(0.360770 - 0.319614i) q^{69} -0.0318063i q^{70} +(-0.954864 - 1.07782i) q^{71} +(-1.60420 + 3.05654i) q^{72} +(-5.40032 + 0.655717i) q^{73} +(7.11988 - 3.73680i) q^{74} +(0.597974 + 4.92476i) q^{75} +(-3.49831 + 14.1932i) q^{76} +(0.282316 + 0.0695846i) q^{77} +(1.75170 - 8.25286i) q^{78} +(-6.75332 + 1.66454i) q^{79} -0.222735i q^{80} +(-0.970942 - 0.239316i) q^{81} +(16.3214 + 23.6457i) q^{82} +(0.797476 - 0.900164i) q^{83} +(0.237232 - 0.0288052i) q^{84} +(0.401013 - 0.0486918i) q^{85} +(-8.62415 + 9.73465i) q^{86} +(2.71746 + 3.93692i) q^{87} +(14.1720 + 3.49308i) q^{88} +5.70975i q^{89} +(0.449096 - 0.110692i) q^{90} +(-0.228844 + 0.0954084i) q^{91} +(-1.62633 - 0.400855i) q^{92} +(1.39105 - 5.64371i) q^{93} +(1.90610 + 15.6981i) q^{94} +(0.736230 - 0.386403i) q^{95} +(-4.23615 + 0.514362i) q^{96} +(4.54824 - 8.66595i) q^{97} +(10.8543 + 12.2519i) q^{98} +4.22839i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31}+ \cdots - 104 q^{98}+O(q^{100}) $ 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{26}\right)$

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 $

$2$	−2.32286	−	0.282046i	−1.64251	−	0.199437i	−0.753541	−	0.657401i	$-0.771656\pi$
$2$	−2.32286	−	0.282046i	−1.64251	−	0.199437i	−0.888971	+	0.457964i	$0.848579\pi$
$3$	−0.748511	+	0.663123i	−0.432153	+	0.382854i
$3$	−0.748511	+	0.663123i	−0.432153	+	0.382854i
$4$	3.37425	+	0.831678i	1.68713	+	0.415839i
$5$	−0.0918625	−	0.175029i	−0.0410822	−	0.0782756i	0.864050	−	0.503407i	$-0.167920\pi$
$5$	−0.0918625	−	0.175029i	−0.0410822	−	0.0782756i	−0.905132	+	0.425131i	$0.860228\pi$
$6$	1.92572	−	1.32923i	0.786171	−	0.542655i
$7$	−0.0642964	−	0.0243844i	−0.0243018	−	0.00921644i	0.342424	−	0.939546i	$-0.388752\pi$
$7$	−0.0642964	−	0.0243844i	−0.0243018	−	0.00921644i	−0.366726	+	0.930329i	$0.619521\pi$
$8$	−3.22762	−	1.22407i	−1.14114	−	0.432776i
$9$	0.120537	−	0.992709i	0.0401789	−	0.330903i
$10$	0.164018	+	0.432479i	0.0518669	+	0.136762i
$11$	−4.19756	+	0.509676i	−1.26561	+	0.153673i	−0.725678	−	0.688035i	$-0.758474\pi$
$11$	−4.19756	+	0.509676i	−1.26561	+	0.153673i	−0.539933	+	0.841708i	$0.681551\pi$
$12$	−3.07717	+	1.61502i	−0.888302	+	0.466217i
$13$	2.61965	−	2.47739i	0.726560	−	0.687103i
$13$	2.61965	−	2.47739i	0.726560	−	0.687103i
$14$	0.142474	+	0.0747762i	0.0380778	+	0.0199848i
$15$	0.184826	+	0.0700953i	0.0477219	+	0.0180985i
$16$	0.997726	+	0.523647i	0.249432	+	0.130912i
$17$	−0.724665	+	1.91078i	−0.175757	+	0.463433i	−0.993728	−	0.111827i	$-0.964330\pi$
$17$	−0.724665	+	1.91078i	−0.175757	+	0.463433i	0.817971	+	0.575260i	$0.195099\pi$
$18$	−0.559980	+	2.27193i	−0.131989	+	0.535499i
$19$			4.20632i			0.964996i	0.875897	+	0.482498i	$0.160270\pi$
$19$			4.20632i			0.964996i	−0.875897	+	0.482498i	$0.839730\pi$
$20$	−0.164399	−	0.666994i	−0.0367608	−	0.149144i
$21$	0.0642964	−	0.0243844i	0.0140306	−	0.00532111i
$22$	9.89410			2.10943
$23$	−0.481984			−0.100501			−0.0502503	−	0.998737i	$-0.516002\pi$
$23$	−0.481984			−0.100501			−0.0502503	+	0.998737i	$0.516002\pi$
$24$	3.22762	−	1.22407i	0.658835	−	0.249863i
$25$	2.81813	−	4.08276i	0.563625	−	0.816552i
$26$	−6.78382	+	5.01576i	−1.33042	+	0.983672i
$27$	0.568065	+	0.822984i	0.109324	+	0.158383i
$28$	−0.196672	−	0.135753i	−0.0371676	−	0.0256549i
$29$	0.576613	−	4.74884i	0.107074	−	0.881837i	−0.835879	−	0.548913i	$-0.815042\pi$
$29$	0.576613	−	4.74884i	0.107074	−	0.881837i	0.942954	−	0.332924i	$-0.108035\pi$
$30$	−0.409555	−	0.214951i	−0.0747742	−	0.0392445i
$31$	−4.78369	+	3.30194i	−0.859175	+	0.593046i	−0.914120	−	0.405443i	$-0.867117\pi$
$31$	−4.78369	+	3.30194i	−0.859175	+	0.593046i	0.0549447	+	0.998489i	$0.482502\pi$
$32$	3.51189	+	2.42408i	0.620820	+	0.428521i
$33$	2.80394	−	3.16499i	0.488103	−	0.550955i
$34$	2.22223	−	4.23410i	0.381109	−	0.726142i
$35$	0.00163844	+	0.0134938i	0.000276947	+	0.00228086i
$36$	1.23234	−	3.24940i	0.205389	−	0.541567i
$37$	−2.82811	+	1.95210i	−0.464938	+	0.320923i	−0.777400	−	0.629007i	$-0.783462\pi$
$37$	−2.82811	+	1.95210i	−0.464938	+	0.320923i	0.312462	+	0.949930i	$0.398846\pi$
$38$	1.18638	−	9.77070i	0.192456	−	1.58502i
$39$	−0.318025	+	3.59150i	−0.0509247	+	0.575100i
$40$	0.0822482	+	0.677375i	0.0130046	+	0.107102i
$41$	−8.14240	−	9.19087i	−1.27163	−	1.43537i	−0.848404	−	0.529349i	$-0.822436\pi$
$41$	−8.14240	−	9.19087i	−1.27163	−	1.43537i	−0.423225	−	0.906024i	$-0.639102\pi$
$42$	−0.156229	+	0.0385070i	−0.0241067	+	0.00594176i
$43$	3.15732	−	4.57417i	0.481487	−	0.697554i	−0.504681	−	0.863306i	$-0.668390\pi$
$43$	3.15732	−	4.57417i	0.481487	−	0.697554i	0.986167	+	0.165752i	$0.0530051\pi$
$44$	−14.5875	−	1.77124i	−2.19915	−	0.267025i
$45$	−0.184826	+	0.0700953i	−0.0275522	+	0.0104492i
$46$	1.11958	+	0.135942i	0.165073	+	0.0200435i
$47$	−1.61732	−	6.56173i	−0.235910	−	0.957126i	−0.962766	−	0.270336i	$-0.912865\pi$
$47$	−1.61732	−	6.56173i	−0.235910	−	0.957126i	0.726856	−	0.686790i	$-0.240981\pi$
$48$	−1.09405	+	0.269659i	−0.157913	+	0.0389220i
$49$	−5.23604	−	4.63872i	−0.748005	−	0.662675i
$50$	−7.69765	+	8.68885i	−1.08861	+	1.22879i
$51$	−0.724665	−	1.91078i	−0.101473	−	0.267563i
$52$	10.8997	−	6.18062i	1.51152	−	0.857098i
$53$	0.242681	−	0.639897i	0.0333348	−	0.0878966i	−0.917315	−	0.398161i	$-0.869648\pi$
$53$	0.242681	−	0.639897i	0.0333348	−	0.0878966i	0.950650	+	0.310265i	$0.100418\pi$
$54$	−1.08742	−	2.07190i	−0.147979	−	0.281950i
$55$	0.474807	+	0.687876i	0.0640229	+	0.0927532i
$56$	0.177676	+	0.157407i	0.0237429	+	0.0210344i
$57$	−2.78931	−	3.14848i	−0.369453	−	0.417026i
$58$	−2.67879	+	10.8683i	−0.351742	+	1.42707i
$59$	−2.04396	−	3.89444i	−0.266101	−	0.507012i	0.715340	−	0.698776i	$-0.246272\pi$
$59$	−2.04396	−	3.89444i	−0.266101	−	0.507012i	−0.981441	+	0.191764i	$0.938579\pi$
$60$	0.565353	+	0.390235i	0.0729868	+	0.0503791i
$61$	−2.13525	−	5.63019i	−0.273391	−	0.720873i	−0.999447	−	0.0332376i	$-0.989418\pi$
$61$	−2.13525	−	5.63019i	−0.273391	−	0.720873i	0.726057	−	0.687635i	$-0.241351\pi$
$62$	12.0431	−	6.32073i	1.52948	−	0.802733i
$63$	−0.0319567	+	0.0608884i	−0.00402617	+	0.00767122i
$64$	−9.16077	−	8.11573i	−1.14510	−	1.01447i
$65$	−0.674263	−	0.230937i	−0.0836320	−	0.0286442i
$66$	−7.40584	+	6.56100i	−0.911596	+	0.807603i
$67$	−2.41701	−	9.80618i	−0.295284	−	1.19802i	−0.911787	−	0.410663i	$-0.865297\pi$
$67$	−2.41701	−	9.80618i	−0.295284	−	1.19802i	0.616503	−	0.787353i	$-0.288549\pi$
$68$	−4.03436	+	5.84478i	−0.489238	+	0.708784i
$69$	0.360770	−	0.319614i	0.0434316	−	0.0384770i
$70$		−	0.0318063i		−	0.00380158i
$71$	−0.954864	−	1.07782i	−0.113321	−	0.127914i	0.689113	−	0.724654i	$-0.258001\pi$
$71$	−0.954864	−	1.07782i	−0.113321	−	0.127914i	−0.802434	+	0.596741i	$0.796462\pi$
$72$	−1.60420	+	3.05654i	−0.189056	+	0.360217i
$73$	−5.40032	+	0.655717i	−0.632059	+	0.0767459i	−0.430295	−	0.902688i	$-0.641590\pi$
$73$	−5.40032	+	0.655717i	−0.632059	+	0.0767459i	−0.201764	+	0.979434i	$0.564667\pi$
$74$	7.11988	−	3.73680i	0.827670	−	0.434395i
$75$	0.597974	+	4.92476i	0.0690480	+	0.568662i
$76$	−3.49831	+	14.1932i	−0.401283	+	1.62807i
$77$	0.282316	+	0.0695846i	0.0321729	+	0.00792991i
$78$	1.75170	−	8.25286i	0.198341	−	0.934452i
$79$	−6.75332	+	1.66454i	−0.759808	+	0.187276i	−0.600140	−	0.799895i	$-0.704889\pi$
$79$	−6.75332	+	1.66454i	−0.759808	+	0.187276i	−0.159668	+	0.987171i	$0.551042\pi$
$80$		−	0.222735i		−	0.0249025i
$81$	−0.970942	−	0.239316i	−0.107882	−	0.0265906i
$82$	16.3214	+	23.6457i	1.80240	+	2.61123i
$83$	0.797476	−	0.900164i	0.0875343	−	0.0988058i	−0.703111	−	0.711080i	$-0.748207\pi$
$83$	0.797476	−	0.900164i	0.0875343	−	0.0988058i	0.790646	+	0.612274i	$0.209745\pi$
$84$	0.237232	−	0.0288052i	0.0258842	−	0.00314291i
$85$	0.401013	−	0.0486918i	0.0434960	−	0.00528137i
$86$	−8.62415	+	9.73465i	−0.929966	+	1.04971i
$87$	2.71746	+	3.93692i	0.291342	+	0.422082i
$88$	14.1720	+	3.49308i	1.51074	+	0.372364i
$89$			5.70975i			0.605233i	0.953112	+	0.302616i	$0.0978601\pi$
$89$			5.70975i			0.605233i	−0.953112	+	0.302616i	$0.902140\pi$
$90$	0.449096	−	0.110692i	0.0473388	−	0.0116680i
$91$	−0.228844	+	0.0954084i	−0.0239893	+	0.0100015i
$92$	−1.62633	−	0.400855i	−0.169557	−	0.0417921i
$93$	1.39105	−	5.64371i	0.144245	−	0.585225i
$94$	1.90610	+	15.6981i	0.196599	+	1.61914i
$95$	0.736230	−	0.386403i	0.0755356	−	0.0396441i
$96$	−4.23615	+	0.514362i	−0.432351	+	0.0524969i
$97$	4.54824	−	8.66595i	0.461804	−	0.879894i	−0.537524	−	0.843248i	$-0.680640\pi$
$97$	4.54824	−	8.66595i	0.461804	−	0.879894i	0.999328	−	0.0366456i	$-0.0116673\pi$
$98$	10.8543	+	12.2519i	1.09644	+	1.23763i
$99$			4.22839i			0.424969i
$100$	12.9046	−	11.4325i	1.29046	−	1.14325i
$101$	0.729670	−	1.05711i	0.0726049	−	0.105186i	−0.784999	−	0.619497i	$-0.787337\pi$
$101$	0.729670	−	1.05711i	0.0726049	−	0.105186i	0.857604	+	0.514310i	$0.171952\pi$
$102$	1.14437	+	4.64288i	0.113309	+	0.459713i
$103$	2.91392	−	2.58151i	0.287117	−	0.254364i	−0.507253	−	0.861797i	$-0.669339\pi$
$103$	2.91392	−	2.58151i	0.287117	−	0.254364i	0.794371	+	0.607433i	$0.207801\pi$
$104$	−11.4877	+	4.78941i	−1.12646	+	0.469640i
$105$	−0.0101744	−	0.00901375i	−0.000992922	−	0.000879652i
$106$	−0.744195	+	1.41795i	−0.0722826	+	0.137723i
$107$	13.9084	−	7.29968i	1.34457	−	0.705686i	0.369848	−	0.929092i	$-0.379410\pi$
$107$	13.9084	−	7.29968i	1.34457	−	0.705686i	0.974725	+	0.223406i	$0.0717176\pi$
$108$	1.23234	+	3.24940i	0.118582	+	0.312674i
$109$	−3.72877	−	2.57378i	−0.357151	−	0.246524i	0.375955	−	0.926638i	$-0.377315\pi$
$109$	−3.72877	−	2.57378i	−0.357151	−	0.246524i	−0.733106	+	0.680114i	$0.761930\pi$
$110$	−0.908897	−	1.73176i	−0.0866599	−	0.165117i
$111$	0.822386	−	3.33655i	0.0780574	−	0.316691i
$112$	−0.0513814	−	0.0579976i	−0.00485508	−	0.00548026i
$113$	14.0359	+	12.4347i	1.32038	+	1.16976i	0.972679	+	0.232155i	$0.0745776\pi$
$113$	14.0359	+	12.4347i	1.32038	+	1.16976i	0.347706	+	0.937604i	$0.386961\pi$
$114$	5.59116	+	8.10019i	0.523660	+	0.758652i
$115$	0.0442762	+	0.0843613i	0.00412878	+	0.00786673i
$116$	5.89515	−	15.5442i	0.547351	−	1.44324i
$117$	−2.14356	−	2.89916i	−0.198172	−	0.268028i
$118$	3.64942	+	9.62273i	0.335956	+	0.885844i
$119$	0.0931867	−	0.105186i	0.00854241	−	0.00964239i
$120$	−0.510746	−	0.452482i	−0.0466245	−	0.0413057i
$121$	6.67936	−	1.64631i	0.607215	−	0.149665i
$122$	3.37192	+	13.6804i	0.305279	+	1.23857i
$123$	12.1894	+	1.48006i	1.09908	+	0.133452i
$124$	−18.8875	+	7.16309i	−1.69615	+	0.643264i
$125$	−1.95464	−	0.237336i	−0.174828	−	0.0212280i
$126$	0.0914043	−	0.132422i	0.00814295	−	0.0117971i
$127$	−7.73057	+	1.90541i	−0.685977	+	0.169078i	−0.566875	−	0.823804i	$-0.691848\pi$
$127$	−7.73057	+	1.90541i	−0.685977	+	0.169078i	−0.119102	+	0.992882i	$0.538002\pi$
$128$	13.3307	+	15.0473i	1.17828	+	1.33001i
$129$	0.669946	+	5.51750i	0.0589855	+	0.485789i
$130$	1.50108	+	0.726608i	0.131654	+	0.0637277i
$131$	−0.822178	+	6.77124i	−0.0718340	+	0.591606i	0.911697	+	0.410864i	$0.134773\pi$
$131$	−0.822178	+	6.77124i	−0.0718340	+	0.591606i	−0.983531	+	0.180742i	$0.942150\pi$
$132$	12.0935	−	8.34751i	1.05260	−	0.726557i
$133$	0.102569	−	0.270451i	0.00889383	−	0.0234511i
$134$	2.84857	+	23.4601i	0.246079	+	2.02664i
$135$	0.0918625	−	0.175029i	0.00790627	−	0.0150641i
$136$	4.67788	−	5.28024i	0.401125	−	0.452777i
$137$	13.1937	+	9.10696i	1.12721	+	0.778060i	0.977556	−	0.210678i	$-0.0675672\pi$
$137$	13.1937	+	9.10696i	1.12721	+	0.778060i	0.149659	+	0.988738i	$0.452183\pi$
$138$	−0.928165	+	0.640666i	−0.0790106	+	0.0545371i
$139$	−11.8853	−	6.23788i	−1.00810	−	0.529090i	−0.121971	−	0.992534i	$-0.538921\pi$
$139$	−11.8853	−	6.23788i	−1.00810	−	0.529090i	−0.886127	+	0.463443i	$0.846614\pi$
$140$	−0.00569397	+	0.0468941i	−0.000481228	+	0.00396327i
$141$	5.56181	+	3.83904i	0.468389	+	0.323306i
$142$	1.91402	+	2.77294i	0.160621	+	0.232700i
$143$	−9.73346	+	11.7341i	−0.813953	+	0.981258i
$144$	0.640092	−	0.927333i	0.0533410	−	0.0772777i
$145$	−0.884156	+	0.335316i	−0.0734252	+	0.0278465i
$146$	12.7291			1.05347
$147$	6.99527			0.576960
$148$	−11.1663	+	4.23481i	−0.917861	+	0.348099i
$149$	−5.37870	−	21.8223i	−0.440641	−	1.78775i	−0.599419	−	0.800435i	$-0.704602\pi$
$149$	−5.37870	−	21.8223i	−0.440641	−	1.78775i	0.158779	−	0.987314i	$-0.449244\pi$
$150$		−	11.6082i		−	0.947804i
$151$	−5.10116	+	20.6962i	−0.415127	+	1.68423i	0.275724	+	0.961237i	$0.411083\pi$
$151$	−5.10116	+	20.6962i	−0.415127	+	1.68423i	−0.690850	+	0.722998i	$0.742764\pi$
$152$	5.14885	−	13.5764i	0.417627	−	1.10119i
$153$	1.80950	+	0.949701i	0.146290	+	0.0767788i
$154$	−0.636155	−	0.241262i	−0.0512628	−	0.0194414i
$155$	1.01738	+	0.533961i	0.0817178	+	0.0428888i
$156$	−4.06007	+	11.8541i	−0.325066	+	0.949090i
$157$	−1.97830	+	1.03829i	−0.157885	+	0.0828646i	−0.541815	−	0.840498i	$-0.682263\pi$
$157$	−1.97830	+	1.03829i	−0.157885	+	0.0828646i	0.383930	+	0.923362i	$0.374570\pi$
$158$	16.1565	−	1.96176i	1.28534	−	0.156069i
$159$	0.242681	+	0.639897i	0.0192459	+	0.0507471i
$160$	0.101675	−	0.837367i	0.00803809	−	0.0661997i
$161$	0.0309898	+	0.0117529i	0.00244234	+	0.000926257i
$162$	2.18787	+	0.829748i	0.171895	+	0.0651911i
$163$	−9.80318	+	6.76664i	−0.767844	+	0.530004i	−0.886387	−	0.462944i	$-0.846793\pi$
$163$	−9.80318	+	6.76664i	−0.767844	+	0.530004i	0.118543	+	0.992949i	$0.462178\pi$
$164$	−19.8307	−	37.7842i	−1.54852	−	2.95045i
$165$	−0.811544	−	0.200028i	−0.0631786	−	0.0155721i
$166$	−2.10631	+	1.86603i	−0.163482	+	0.144832i
$167$	−2.19108	−	0.266045i	−0.169551	−	0.0205872i	0.0353209	−	0.999376i	$-0.488755\pi$
$167$	−2.19108	−	0.266045i	−0.169551	−	0.0205872i	−0.204872	+	0.978789i	$0.565678\pi$
$168$	−0.237373			−0.0183137
$169$	0.725120	−	12.9798i	0.0557784	−	0.998443i
$170$	−0.945231			−0.0724959
$171$	4.17565	+	0.507016i	0.319320	+	0.0387725i
$172$	14.4578	−	12.8085i	1.10240	−	0.976641i
$173$	−11.3306	−	2.79274i	−0.861448	−	0.212328i	−0.216245	−	0.976339i	$-0.569381\pi$
$173$	−11.3306	−	2.79274i	−0.861448	−	0.212328i	−0.645203	+	0.764011i	$0.723227\pi$
$174$	−5.20189	−	9.91138i	−0.394354	−	0.751380i
$175$	−0.280751	+	0.193789i	−0.0212228	+	0.0146490i
$176$	−4.45490	−	1.68952i	−0.335801	−	0.127353i
$177$	4.11241	+	1.55963i	0.309108	+	0.117229i
$178$	1.61042	−	13.2630i	0.120706	−	0.994102i
$179$	3.50296	+	9.23655i	0.261824	+	0.690372i	0.999878	+	0.0156308i	$0.00497564\pi$
$179$	3.50296	+	9.23655i	0.261824	+	0.690372i	−0.738054	+	0.674741i	$0.764255\pi$
$180$	−0.681947	+	0.0828033i	−0.0508293	+	0.00617179i
$181$	−3.35898	+	1.76293i	−0.249671	+	0.131037i	−0.584917	−	0.811093i	$-0.698873\pi$
$181$	−3.35898	+	1.76293i	−0.249671	+	0.131037i	0.335246	+	0.942131i	$0.391181\pi$
$182$	0.558482	−	0.157076i	0.0413974	−	0.0116432i
$183$	5.33177	+	2.79833i	0.394136	+	0.206858i
$184$	1.55566	+	0.589984i	0.114685	+	0.0434942i
$185$	0.601472	+	0.315677i	0.0442211	+	0.0232090i
$186$	−4.82300	+	12.7172i	−0.353640	+	0.932471i
$187$	2.06794	−	8.38997i	0.151223	−	0.613535i
$188$		−	23.4860i		−	1.71289i
$189$	−0.0164565	−	0.0667668i	−0.00119704	−	0.00485657i
$190$	−1.81914	+	0.689910i	−0.131975	+	0.0500514i
$191$	−9.65314			−0.698477			−0.349238	−	0.937034i	$-0.613560\pi$
$191$	−9.65314			−0.698477			−0.349238	+	0.937034i	$0.613560\pi$
$192$	12.2387			0.883249
$193$	−17.6326	+	6.68716i	−1.26922	+	0.481352i	−0.895033	−	0.446000i	$-0.852848\pi$
$193$	−17.6326	+	6.68716i	−1.26922	+	0.481352i	−0.374189	+	0.927353i	$0.622079\pi$
$194$	−13.0091	+	18.8470i	−0.934001	+	1.35313i
$195$	0.657833	−	0.274261i	0.0471084	−	0.0196402i
$196$	−13.8098	−	20.0069i	−0.986413	−	1.42907i
$197$	−2.93237	−	2.02407i	−0.208922	−	0.144209i	0.459009	−	0.888432i	$-0.348205\pi$
$197$	−2.93237	−	2.02407i	−0.208922	−	0.144209i	−0.667931	+	0.744223i	$0.732820\pi$
$198$	1.19260	−	9.82196i	0.0847545	−	0.698016i
$199$	15.3512	+	8.05692i	1.08822	+	0.571140i	0.910738	−	0.412985i	$-0.135514\pi$
$199$	15.3512	+	8.05692i	1.08822	+	0.571140i	0.177478	+	0.984125i	$0.443206\pi$
$200$	−14.0934	+	9.72800i	−0.996557	+	0.687873i
$201$	8.31185	+	5.73726i	0.586273	+	0.404675i
$202$	−1.99308	+	2.24972i	−0.140232	+	0.158290i
$203$	−0.152872	+	0.291273i	−0.0107295	+	0.0204434i
$204$	−0.856044	−	7.05016i	−0.0599351	−	0.493610i
$205$	−0.860692	+	2.26946i	−0.0601133	+	0.158506i
$206$	−7.49675	+	5.17463i	−0.522323	+	0.360534i
$207$	−0.0580967	+	0.478469i	−0.00403800	+	0.0332559i
$208$	3.91097	−	1.09998i	0.271177	−	0.0762700i
$209$	−2.14386	−	17.6563i	−0.148294	−	1.22131i
$210$	0.0210915	+	0.0238074i	0.00145545	+	0.00164286i
$211$	9.74571	−	2.40210i	0.670922	−	0.165367i	0.110883	−	0.993833i	$-0.464632\pi$
$211$	9.74571	−	2.40210i	0.670922	−	0.165367i	0.560039	+	0.828466i	$0.310786\pi$
$212$	1.35106	−	1.95734i	0.0927909	−	0.134431i
$213$	1.42945	+	0.173567i	0.0979444	+	0.0118926i
$214$	−34.3661	+	13.0333i	−2.34922	+	0.890940i
$215$	−1.09065	−	0.132429i	−0.0743820	−	0.00903161i
$216$	−0.826103	−	3.35163i	−0.0562092	−	0.228050i
$217$	0.388090	−	0.0956555i	0.0263452	−	0.00649352i
$218$	7.93548	+	7.03022i	0.537459	+	0.476147i
$219$	3.60737	−	4.07188i	0.243764	−	0.275152i
$220$	1.03003	+	2.71595i	0.0694443	+	0.183110i
$221$	2.83538	+	6.80086i	0.190728	+	0.457475i
$222$	−2.85135	+	7.51839i	−0.191370	+	0.504602i
$223$	−9.64284	−	18.3729i	−0.645732	−	1.23034i	−0.959732	−	0.280917i	$-0.909361\pi$
$223$	−9.64284	−	18.3729i	−0.645732	−	1.23034i	0.314000	−	0.949423i	$-0.398331\pi$
$224$	−0.166692	−	0.241495i	−0.0111376	−	0.0161356i
$225$	−3.71331	−	3.28970i	−0.247554	−	0.219313i
$226$	−29.0962	−	32.8429i	−1.93545	−	2.18468i
$227$	3.62063	−	14.6895i	0.240310	−	0.974975i	−0.719538	−	0.694453i	$-0.755646\pi$
$227$	3.62063	−	14.6895i	0.240310	−	0.974975i	0.959848	−	0.280522i	$-0.0905075\pi$
$228$	−6.79330	−	12.9436i	−0.449897	−	0.857208i
$229$	11.1555	+	7.70009i	0.737177	+	0.508836i	0.876495	−	0.481411i	$-0.159876\pi$
$229$	11.1555	+	7.70009i	0.737177	+	0.508836i	−0.139318	+	0.990248i	$0.544491\pi$
$230$	−0.0790538	−	0.208448i	−0.00521265	−	0.0137446i
$231$	−0.257460	+	0.135125i	−0.0169396	+	0.00889059i
$232$	−7.67402	+	14.6216i	−0.503824	+	0.959956i
$233$	−14.1473	−	12.5334i	−0.926820	−	0.821091i	0.0573432	−	0.998355i	$-0.481737\pi$
$233$	−14.1473	−	12.5334i	−0.926820	−	0.821091i	−0.984163	+	0.177263i	$0.943276\pi$
$234$	4.16149	+	7.33894i	0.272045	+	0.479762i
$235$	−0.999924	+	0.885855i	−0.0652279	+	0.0577868i
$236$	−3.65791	−	14.8407i	−0.238110	−	0.966049i
$237$	3.95114	−	5.72421i	0.256654	−	0.371828i
$238$	−0.246127	+	0.218050i	−0.0159541	+	0.0141341i
$239$			21.4743i			1.38906i	0.719464	+	0.694530i	$0.244388\pi$
$239$			21.4743i			1.38906i	−0.719464	+	0.694530i	$0.755612\pi$
$240$	0.147701	+	0.166720i	0.00953404	+	0.0107617i
$241$	−1.19543	+	2.27770i	−0.0770045	+	0.146720i	−0.920914	−	0.389766i	$-0.872556\pi$
$241$	−1.19543	+	2.27770i	−0.0770045	+	0.146720i	0.843910	+	0.536485i	$0.180248\pi$
$242$	−15.9796	+	1.94027i	−1.02721	+	0.124725i
$243$	0.885456	−	0.464723i	0.0568020	−	0.0298120i
$244$	−2.52236	−	20.7735i	−0.161478	−	1.32989i
$245$	−0.330918	+	1.34259i	−0.0211415	+	0.0857746i
$246$	−27.8967	−	6.87593i	−1.77863	−	0.438393i
$247$	10.4207	+	11.0191i	0.663052	+	0.701127i
$248$	19.4817	−	4.80182i	1.23709	−	0.304916i
$249$			1.20261i			0.0762121i
$250$	4.47341	+	1.10260i	0.282923	+	0.0697343i
$251$	−11.0635	−	16.0283i	−0.698325	−	1.01170i	−0.998330	−	0.0577605i	$-0.981604\pi$
$251$	−11.0635	−	16.0283i	−0.698325	−	1.01170i	0.300006	−	0.953937i	$-0.403011\pi$
$252$	−0.158470	+	0.178875i	−0.00998264	+	0.0112681i
$253$	2.02315	−	0.245655i	0.127195	−	0.0154442i
$254$	18.4945	−	2.24563i	1.16045	−	0.140904i
$255$	−0.267874	+	0.302367i	−0.0167749	+	0.0189350i
$256$	−12.8167	−	18.5682i	−0.801045	−	1.16051i
$257$	18.7692	+	4.62619i	1.17079	+	0.288574i	0.776323	−	0.630336i	$-0.217083\pi$
$257$	18.7692	+	4.62619i	1.17079	+	0.288574i	0.394468	+	0.918910i	$0.370929\pi$
$258$		−	13.0054i		−	0.809678i
$259$	0.229438	−	0.0565514i	0.0142566	−	0.00351393i
$260$	−2.08307	−	1.34001i	−0.129186	−	0.0831038i
$261$	−4.64471	−	1.14482i	−0.287500	−	0.0708625i
$262$	3.81961	−	15.4968i	0.235976	−	0.957393i
$263$	0.740989	+	6.10260i	0.0456914	+	0.376302i	0.997561	+	0.0697992i	$0.0222359\pi$
$263$	0.740989	+	6.10260i	0.0456914	+	0.376302i	−0.951870	+	0.306503i	$0.900841\pi$
$264$	−12.9242	+	6.78316i	−0.795431	+	0.417475i
$265$	−0.134294	+	0.0163063i	−0.00824962	+	0.00100169i
$266$	−0.314533	+	0.599292i	−0.0192852	+	0.0367449i
$267$	−3.78627	−	4.27381i	−0.231716	−	0.261553i
$268$		−	35.0987i		−	2.14399i
$269$	−4.05177	+	3.58956i	−0.247041	+	0.218859i	−0.777552	−	0.628819i	$-0.783539\pi$
$269$	−4.05177	+	3.58956i	−0.247041	+	0.218859i	0.530511	+	0.847678i	$0.322000\pi$
$270$	−0.262750	+	0.380660i	−0.0159905	+	0.0231662i
$271$	3.26557	+	13.2489i	0.198369	+	0.804816i	0.982811	+	0.184614i	$0.0591034\pi$
$271$	3.26557	+	13.2489i	0.198369	+	0.804816i	−0.784442	+	0.620202i	$0.787050\pi$
$272$	−1.72359	+	1.52697i	−0.104508	+	0.0925862i
$273$	0.108024	−	0.223166i	0.00653793	−	0.0135066i
$274$	−28.0786	−	24.8754i	−1.69629	−	1.50278i
$275$	−9.74837	+	18.5740i	−0.587849	+	1.12005i
$276$	1.48314	−	0.778414i	0.0892748	−	0.0468550i
$277$	3.86275	+	10.1852i	0.232090	+	0.611971i	0.999577	−	0.0290939i	$-0.00926218\pi$
$277$	3.86275	+	10.1852i	0.232090	+	0.611971i	−0.767487	+	0.641065i	$0.778493\pi$
$278$	25.8485	+	17.8419i	1.55029	+	1.07009i
$279$	2.70126	+	5.14681i	0.161720	+	0.308132i
$280$	0.0112291	−	0.0455583i	0.000671068	−	0.00272263i
$281$	−2.61998	−	2.95735i	−0.156295	−	0.176421i	0.665147	−	0.746712i	$-0.268369\pi$
$281$	−2.61998	−	2.95735i	−0.156295	−	0.176421i	−0.821442	+	0.570291i	$0.806830\pi$
$282$	−11.8365	−	10.4862i	−0.704855	−	0.624447i
$283$	15.1804	+	21.9926i	0.902380	+	1.30732i	0.951219	+	0.308517i	$0.0998326\pi$
$283$	15.1804	+	21.9926i	0.902380	+	1.30732i	−0.0488387	+	0.998807i	$0.515552\pi$
$284$	−2.32555	−	4.43097i	−0.137996	−	0.262930i
$285$	−0.294843	+	0.777438i	−0.0174650	+	0.0460514i
$286$	25.9191	−	24.5115i	1.53263	−	1.44940i
$287$	0.299413	+	0.789488i	0.0176738	+	0.0466020i
$288$	2.82972	−	3.19409i	0.166743	−	0.188214i
$289$	9.59873	+	8.50373i	0.564631	+	0.500219i
$290$	2.14835	−	0.529520i	0.126155	−	0.0310945i
$291$	2.34218	+	9.50260i	0.137301	+	0.557052i
$292$	−18.7674	−	2.27877i	−1.09828	−	0.133355i
$293$	−9.72343	+	3.68761i	−0.568049	+	0.215433i	−0.621873	−	0.783118i	$-0.713628\pi$
$293$	−9.72343	+	3.68761i	−0.568049	+	0.215433i	0.0538243	+	0.998550i	$0.482859\pi$
$294$	−16.2490	−	1.97299i	−0.947664	−	0.115067i
$295$	−0.493878	+	0.715506i	−0.0287547	+	0.0416584i
$296$	11.5176	−	2.83882i	0.669445	−	0.165003i
$297$	−2.80394	−	3.16499i	−0.162701	−	0.183652i
$298$	6.33909	+	52.2071i	0.367214	+	3.02428i
$299$	−1.26263	+	1.19406i	−0.0730197	+	0.0690542i
$300$	−2.07810	+	17.1147i	−0.119979	+	0.988117i
$301$	−0.314543	+	0.217113i	−0.0181299	+	0.0125142i
$302$	17.6866	−	46.6357i	1.01775	−	2.68358i
$303$	0.154827	+	1.27512i	0.00889461	+	0.0732537i
$304$	−2.20263	+	4.19676i	−0.126329	+	0.240700i
$305$	−0.789300	+	0.890936i	−0.0451952	+	0.0510148i
$306$	−3.93537	−	2.71639i	−0.224970	−	0.155286i
$307$	18.8657	−	13.0220i	1.07672	−	0.743206i	0.108699	−	0.994075i	$-0.465332\pi$
$307$	18.8657	−	13.0220i	1.07672	−	0.743206i	0.968021	+	0.250869i	$0.0807163\pi$
$308$	0.894733	+	0.469592i	0.0509822	+	0.0267575i
$309$	−0.469245	+	3.86458i	−0.0266944	+	0.219848i
$310$	−2.21263	−	1.52727i	−0.125669	−	0.0867429i
$311$	1.17733	+	1.70566i	0.0667604	+	0.0967191i	0.854942	−	0.518724i	$-0.173593\pi$
$311$	1.17733	+	1.70566i	0.0667604	+	0.0967191i	−0.788182	+	0.615443i	$0.788977\pi$
$312$	5.42272	−	11.2027i	0.307001	−	0.634228i
$313$	0.542882	−	0.786501i	0.0306855	−	0.0444556i	−0.807341	−	0.590085i	$-0.799094\pi$
$313$	0.542882	−	0.786501i	0.0306855	−	0.0444556i	0.838026	+	0.545630i	$0.183709\pi$
$314$	4.88816	−	1.85383i	0.275855	−	0.104618i
$315$	0.0135929			0.000765872
$316$	−24.1718			−1.35977
$317$	16.7707	−	6.36029i	0.941937	−	0.357230i	0.164633	−	0.986355i	$-0.447356\pi$
$317$	16.7707	−	6.36029i	0.941937	−	0.357230i	0.777304	+	0.629125i	$0.216587\pi$
$318$	−0.383234	−	1.55484i	−0.0214907	−	0.0871911i
$319$			20.2274i			1.13252i
$320$	−0.578961	+	2.34894i	−0.0323649	+	0.131310i
$321$	−5.56999	+	14.6868i	−0.310886	+	0.819740i
$322$	−0.0686702	−	0.0360409i	−0.00382684	−	0.00200848i
$323$	−8.03737	−	3.04817i	−0.447211	−	0.169605i
$324$	−3.07717	−	1.61502i	−0.170954	−	0.0897235i
$325$	−2.73207	−	17.6770i	−0.151548	−	0.980543i
$326$	24.6799	−	12.9530i	1.36689	−	0.717402i
$327$	4.49775	−	0.546126i	0.248726	−	0.0302008i
$328$	15.0303	+	39.6315i	0.829907	+	2.18829i
$329$	−0.0560159	+	0.461333i	−0.00308826	+	0.0254341i
$330$	1.82869	+	0.693530i	0.100666	+	0.0381776i
$331$	15.4842	+	5.87238i	0.851088	+	0.322775i	0.741295	−	0.671180i	$-0.234212\pi$
$331$	15.4842	+	5.87238i	0.851088	+	0.322775i	0.109793	+	0.993955i	$0.464981\pi$
$332$	3.43953	−	2.37414i	0.188769	−	0.130298i
$333$	1.59698	+	3.04279i	0.0875138	+	0.166744i
$334$	5.01454	+	1.23597i	0.274383	+	0.0676294i
$335$	−1.49434	+	1.32387i	−0.0816444	+	0.0723306i
$336$	0.0769190	+	0.00933966i	0.00419628	+	0.000509520i
$337$	−18.4016			−1.00240			−0.501200	−	0.865331i	$-0.667108\pi$
$337$	−18.4016			−1.00240			−0.501200	+	0.865331i	$0.667108\pi$
$338$	−5.34525	+	29.9457i	−0.290743	+	1.62883i
$339$	−18.7517			−1.01845
$340$	1.39362	+	0.169216i	0.0755794	+	0.00917700i
$341$	18.3969	−	16.2982i	0.996247	−	0.882598i
$342$	−9.55646	−	2.35546i	−0.516754	−	0.127368i
$343$	0.447243	+	0.852150i	0.0241488	+	0.0460118i
$344$	−15.7897	+	10.8989i	−0.851326	+	0.587628i
$345$	−0.0890832	−	0.0337848i	−0.00479608	−	0.00181891i
$346$	25.5317	+	9.68290i	1.37259	+	0.520556i
$347$	−3.76309	+	30.9919i	−0.202013	+	1.66373i	0.440723	+	0.897643i	$0.354722\pi$
$347$	−3.76309	+	30.9919i	−0.202013	+	1.66373i	−0.642737	+	0.766087i	$0.722201\pi$
$348$	5.89515	+	15.5442i	0.316013	+	0.833258i
$349$	−7.35668	+	0.893263i	−0.393794	+	0.0478152i	−0.315039	−	0.949079i	$-0.602018\pi$
$349$	−7.35668	+	0.893263i	−0.393794	+	0.0478152i	−0.0787551	+	0.996894i	$0.525094\pi$
$350$	0.706803	−	0.370959i	0.0377802	−	0.0198286i
$351$	3.52698	+	0.748613i	0.188256	+	0.0399580i
$352$	−15.9769	−	8.38530i	−0.851570	−	0.446938i
$353$	10.1295	+	3.84161i	0.539139	+	0.204468i	0.609117	−	0.793080i	$-0.291524\pi$
$353$	10.1295	+	3.84161i	0.539139	+	0.204468i	−0.0699785	+	0.997549i	$0.522293\pi$
$354$	−9.11268	−	4.78270i	−0.484333	−	0.254198i
$355$	−0.100934	+	0.266140i	−0.00535701	+	0.0141253i
$356$	−4.74868	+	19.2662i	−0.251680	+	1.02110i
$357$			0.140527i			0.00743748i
$358$	−5.53176	−	22.4432i	−0.292363	−	1.18616i
$359$	28.3545	−	10.7534i	1.49649	−	0.567544i	0.535600	−	0.844472i	$-0.320085\pi$
$359$	28.3545	−	10.7534i	1.49649	−	0.567544i	0.960891	+	0.276927i	$0.0893161\pi$
$360$	0.682350			0.0359630
$361$	1.30687			0.0687827
$362$	8.29966	−	3.14765i	0.436221	−	0.165437i
$363$	−3.90786	+	5.66152i	−0.205110	+	0.297153i
$364$	−0.851525	+	0.131608i	−0.0446320	+	0.00689812i
$365$	0.610857	+	0.884979i	0.0319737	+	0.0463219i
$366$	−11.5957	−	8.00393i	−0.606117	−	0.418372i
$367$	0.251891	−	2.07451i	0.0131486	−	0.108288i	−0.984657	−	0.174501i	$-0.944169\pi$
$367$	0.251891	−	2.07451i	0.0131486	−	0.108288i	0.997806	+	0.0662131i	$0.0210917\pi$
$368$	−0.480888	−	0.252389i	−0.0250680	−	0.0131567i
$369$	−10.1053	+	6.97520i	−0.526062	+	0.363114i
$370$	−1.30810	−	0.902917i	−0.0680049	−	0.0469404i
$371$	−0.0312070	+	0.0352255i	−0.00162019	+	0.00182881i
$372$	9.38750	−	17.8864i	0.486719	−	0.927366i
$373$	−4.28547	−	35.2940i	−0.221893	−	1.82746i	−0.498983	−	0.866612i	$-0.666293\pi$
$373$	−4.28547	−	35.2940i	−0.221893	−	1.82746i	0.277089	−	0.960844i	$-0.410630\pi$
$374$	−7.16991	+	18.9055i	−0.370747	+	0.977579i
$375$	1.62045	−	1.11851i	0.0836796	−	0.0577599i
$376$	−2.81195	+	23.1585i	−0.145015	+	1.19431i
$377$	−10.2542	−	13.8688i	−0.528117	−	0.714279i
$378$	0.0193949	+	0.159732i	0.000997567	+	0.00821571i
$379$	−10.1631	−	11.4718i	−0.522044	−	0.589265i	0.427062	−	0.904222i	$-0.359548\pi$
$379$	−10.1631	−	11.4718i	−0.522044	−	0.589265i	−0.949106	+	0.314957i	$0.898010\pi$
$380$	2.80559	−	0.691515i	0.143924	−	0.0354740i
$381$	4.52289	−	6.55254i	0.231715	−	0.335697i
$382$	22.4229	+	2.72263i	1.14726	+	0.139302i
$383$	−29.7898	+	11.2978i	−1.52219	+	0.577289i	−0.967076	−	0.254487i	$-0.918093\pi$
$383$	−29.7898	+	11.2978i	−1.52219	+	0.577289i	−0.555111	+	0.831776i	$0.687324\pi$
$384$	−19.9564	−	2.42315i	−1.01840	−	0.123656i
$385$	−0.0137549	−	0.0558058i	−0.000701015	−	0.00284413i
$386$	42.8442	−	10.5601i	2.18071	−	0.537497i
$387$	−4.16024	−	3.68566i	−0.211477	−	0.187352i
$388$	22.5542	−	25.4584i	1.14502	−	1.29246i
$389$	−3.20617	−	8.45397i	−0.162559	−	0.428633i	0.828843	−	0.559481i	$-0.188999\pi$
$389$	−3.20617	−	8.45397i	−0.162559	−	0.428633i	−0.991403	+	0.130847i	$0.958230\pi$
$390$	−1.60541	+	0.451530i	−0.0812930	+	0.0228641i
$391$	0.349277	−	0.920967i	0.0176637	−	0.0465753i
$392$	11.2218	+	21.3813i	0.566786	+	1.07992i
$393$	−3.87476	−	5.61355i	−0.195456	−	0.283166i
$394$	6.24060	+	5.52869i	0.314397	+	0.278531i
$395$	0.911722	+	1.02912i	0.0458737	+	0.0517807i
$396$	−3.51666	+	14.2676i	−0.176719	+	0.716976i
$397$	9.16829	+	17.4687i	0.460144	+	0.876730i	0.999402	+	0.0345897i	$0.0110124\pi$
$397$	9.16829	+	17.4687i	0.460144	+	0.876730i	−0.539258	+	0.842141i	$0.681295\pi$
$398$	−33.3862	−	23.0449i	−1.67350	−	1.15513i
$399$	0.102569	+	0.270451i	0.00513485	+	0.0135395i
$400$	4.94965	−	2.59777i	0.247482	−	0.129889i
$401$	4.34390	−	8.27661i	0.216924	−	0.413314i	−0.752540	−	0.658546i	$-0.771172\pi$
$401$	4.34390	−	8.27661i	0.216924	−	0.413314i	0.969464	+	0.245232i	$0.0788641\pi$
$402$	−17.6891	−	15.6712i	−0.882253	−	0.781608i
$403$	−4.35140	+	20.5010i	−0.216759	+	1.02123i
$404$	3.34127	−	2.96010i	0.166234	−	0.147271i
$405$	0.0473059	+	0.191928i	0.00235065	+	0.00953696i
$406$	0.437253	−	0.633470i	0.0217005	−	0.0314386i
$407$	10.8762	−	9.63547i	0.539113	−	0.477613i
$408$			7.05433i			0.349241i
$409$	−20.8841	−	23.5733i	−1.03265	−	1.16562i	−0.986006	−	0.166712i	$-0.946685\pi$
$409$	−20.8841	−	23.5733i	−1.03265	−	1.16562i	−0.0466467	−	0.998911i	$-0.514854\pi$
$410$	2.63936	−	5.02888i	0.130349	−	0.248359i
$411$	−15.9147	+	1.93239i	−0.785012	+	0.0953177i
$412$	11.9793	−	6.28722i	0.590178	−	0.309749i
$413$	0.0364556	+	0.300239i	0.00179386	+	0.0147738i
$414$	0.269901	−	1.09503i	0.0132649	−	0.0538179i
$415$	−0.230813	−	0.0568904i	−0.0113302	−	0.00279264i
$416$	15.2053	−	2.35006i	0.745502	−	0.115221i
$417$	13.0327	−	3.21228i	0.638216	−	0.157306i
$418$			41.6177i			2.03559i
$419$	−2.50456	−	0.617319i	−0.122356	−	0.0301580i	0.177662	−	0.984092i	$-0.443147\pi$
$419$	−2.50456	−	0.617319i	−0.122356	−	0.0301580i	−0.300018	+	0.953934i	$0.596993\pi$
$420$	−0.0268345	−	0.0388765i	−0.00130939	−	0.00189698i
$421$	15.8941	−	17.9408i	0.774632	−	0.874379i	−0.220248	−	0.975444i	$-0.570687\pi$
$421$	15.8941	−	17.9408i	0.774632	−	0.874379i	0.994880	+	0.101065i	$0.0322250\pi$
$422$	−23.3154	+	2.83101i	−1.13498	+	0.137811i
$423$	−6.70883	+	0.814599i	−0.326194	+	0.0396072i
$424$	−1.56656	+	1.76828i	−0.0760790	+	0.0858755i
$425$	5.75908	+	8.34347i	0.279356	+	0.404718i
$426$	−3.27146	−	0.806344i	−0.158503	−	0.0390675i
$427$			0.414068i			0.0200382i
$428$	53.0013	−	13.0637i	2.56192	−	0.631456i
$429$	−0.495573	−	15.2376i	−0.0239265	−	0.735679i
$430$	2.49609	+	0.615230i	0.120372	+	0.0296690i
$431$	−2.75449	+	11.1754i	−0.132679	+	0.538301i	0.866552	+	0.499088i	$0.166331\pi$
$431$	−2.75449	+	11.1754i	−0.132679	+	0.538301i	−0.999231	+	0.0392136i	$0.987515\pi$
$432$	0.135820	+	1.11858i	0.00653464	+	0.0538176i
$433$	8.92619	−	4.68483i	0.428965	−	0.225138i	−0.236401	−	0.971656i	$-0.575968\pi$
$433$	8.92619	−	4.68483i	0.428965	−	0.225138i	0.665366	+	0.746517i	$0.268275\pi$
$434$	−0.928458	+	0.112735i	−0.0445674	+	0.00541146i
$435$	0.439445	−	0.837292i	0.0210698	−	0.0401451i
$436$	−10.4412	−	11.7857i	−0.500045	−	0.564434i
$437$		−	2.02738i		−	0.0969826i
$438$	−9.52789	+	8.44097i	−0.455260	+	0.403325i
$439$	−17.8007	+	25.7887i	−0.849580	+	1.23083i	0.121623	+	0.992576i	$0.461190\pi$
$439$	−17.8007	+	25.7887i	−0.849580	+	1.23083i	−0.971203	+	0.238253i	$0.923425\pi$
$440$	−0.690483	−	2.80140i	−0.0329175	−	0.133551i
$441$	−5.23604	+	4.63872i	−0.249335	+	0.220892i
$442$	−4.66804	−	16.5972i	−0.222036	−	0.789447i
$443$	−10.3861	−	9.20127i	−0.493458	−	0.437166i	0.379333	−	0.925260i	$-0.376154\pi$
$443$	−10.3861	−	9.20127i	−0.493458	−	0.437166i	−0.872791	+	0.488095i	$0.837692\pi$
$444$	5.54987	−	10.5744i	0.263385	−	0.501839i
$445$	0.999375	−	0.524513i	0.0473749	−	0.0248643i
$446$	17.2170	+	45.3974i	0.815247	+	2.14963i
$447$	18.4969	+	12.7675i	0.874871	+	0.603880i
$448$	0.391107	+	0.745192i	0.0184781	+	0.0352070i
$449$	−3.32231	+	13.4792i	−0.156790	+	0.636121i	0.838974	+	0.544171i	$0.183156\pi$
$449$	−3.32231	+	13.4792i	−0.156790	+	0.636121i	−0.995764	+	0.0919492i	$0.970690\pi$
$450$	7.69765	+	8.68885i	0.362871	+	0.409596i
$451$	38.8626	+	34.4292i	1.82997	+	1.62121i
$452$	37.0189	+	53.6312i	1.74122	+	2.52260i
$453$	−9.90586	−	18.8740i	−0.465418	−	0.886780i
$454$	−12.5533	+	33.1004i	−0.589158	+	1.55348i
$455$	0.0377214	+	0.0312899i	0.00176841	+	0.00146689i
$456$	5.14885	+	13.5764i	0.241117	+	0.635773i
$457$	−15.6246	+	17.6365i	−0.730888	+	0.825002i	−0.990033	−	0.140837i	$-0.955021\pi$
$457$	−15.6246	+	17.6365i	−0.730888	+	0.825002i	0.259145	+	0.965838i	$0.416559\pi$
$458$	−23.7409	−	21.0326i	−1.10934	−	0.982790i
$459$	−1.98420	+	0.489062i	−0.0926146	+	0.0228274i
$460$	0.0792377	+	0.321480i	0.00369448	+	0.0149891i
$461$	38.5908	+	4.68578i	1.79735	+	0.218238i	0.949884	−	0.312604i	$-0.101201\pi$
$461$	38.5908	+	4.68578i	1.79735	+	0.218238i	0.847471	+	0.530842i	$0.178124\pi$
$462$	0.636155	−	0.241262i	0.0295966	−	0.0112245i
$463$	39.3621	+	4.77942i	1.82931	+	0.222119i	0.961506	−	0.274784i	$-0.0886065\pi$
$463$	39.3621	+	4.77942i	1.82931	+	0.222119i	0.867806	+	0.496903i	$0.165530\pi$
$464$	3.06202	−	4.43610i	0.142151	−	0.205941i
$465$	−1.11560	+	0.274971i	−0.0517347	+	0.0127515i
$466$	29.3272	+	33.1036i	1.35856	+	1.53349i
$467$	2.35441	+	19.3903i	0.108949	+	0.897275i	0.940022	+	0.341113i	$0.110804\pi$
$467$	2.35441	+	19.3903i	0.108949	+	0.897275i	−0.831073	+	0.556163i	$0.812273\pi$
$468$	−4.82174	−	11.5653i	−0.222885	−	0.534604i
$469$	−0.0837131	+	0.689439i	−0.00386551	+	0.0318353i
$470$	2.57254	−	1.77569i	0.118662	−	0.0819067i
$471$	0.792263	−	2.08902i	0.0365055	−	0.0962572i
$472$	1.83004	+	15.0717i	0.0842343	+	0.693732i
$473$	−10.9217	+	20.8095i	−0.502180	+	0.956824i
$474$	−10.7924	+	12.1821i	−0.495713	+	0.559545i
$475$	17.1734	+	11.8539i	0.787970	+	0.543896i
$476$	0.401916	−	0.277423i	0.0184218	−	0.0127157i
$477$	−0.605980	−	0.318043i	−0.0277459	−	0.0145622i
$478$	6.05676	−	49.8819i	0.277030	−	2.28155i
$479$	−27.5215	−	18.9967i	−1.25749	−	0.867983i	−0.262209	−	0.965011i	$-0.584451\pi$
$479$	−27.5215	−	18.9967i	−1.25749	−	0.867983i	−0.995282	+	0.0970282i	$0.969066\pi$
$480$	0.479172	+	0.694201i	0.0218711	+	0.0316858i
$481$	−2.57254	+	12.1201i	−0.117298	+	0.552630i
$482$	3.41924	−	4.95362i	0.155742	−	0.225631i
$483$	−0.0309898	+	0.0117529i	−0.00141009	+	0.000534775i
$484$	23.9070			1.08668
$485$	−1.93461			−0.0878461
$486$	−2.18787	+	0.829748i	−0.0992436	+	0.0376381i
$487$	−4.77549	−	19.3749i	−0.216398	−	0.877962i	−0.974238	−	0.225522i	$-0.927591\pi$
$487$	−4.77549	−	19.3749i	−0.216398	−	0.877962i	0.757840	−	0.652441i	$-0.226255\pi$
$488$			20.7858i			0.940930i
$489$	2.85067	−	11.5656i	0.128912	−	0.523015i
$490$	1.14735	−	3.02531i	0.0518319	−	0.136669i
$491$	−13.5186	−	7.09513i	−0.610088	−	0.320199i	0.131231	−	0.991352i	$-0.458107\pi$
$491$	−13.5186	−	7.09513i	−0.610088	−	0.320199i	−0.741319	+	0.671153i	$0.765799\pi$
$492$	39.8990	+	15.1317i	1.79879	+	0.682190i
$493$	8.65616	+	4.54310i	0.389854	+	0.204611i
$494$	−21.0979	−	28.5349i	−0.949239	−	1.28385i
$495$	0.740092	−	0.388430i	0.0332647	−	0.0174586i
$496$	−6.50186	+	0.789469i	−0.291942	+	0.0354482i
$497$	0.0351123	+	0.0925836i	0.00157500	+	0.00415294i
$498$	0.339191	−	2.79349i	0.0151995	−	0.125179i
$499$	25.3234	+	9.60389i	1.13363	+	0.429929i	0.848834	−	0.528659i	$-0.177305\pi$
$499$	25.3234	+	9.60389i	1.13363	+	0.429929i	0.284796	+	0.958588i	$0.408074\pi$
$500$	−6.39805	−	2.42646i	−0.286129	−	0.108515i
$501$	1.81647	−	1.25382i	0.0811538	−	0.0560164i
$502$	21.1784	+	40.3520i	0.945236	+	1.80100i
$503$	−32.0225	−	7.89283i	−1.42781	−	0.351924i	−0.551705	−	0.834040i	$-0.686022\pi$
$503$	−32.0225	−	7.89283i	−1.42781	−	0.351924i	−0.876108	+	0.482116i	$0.839869\pi$
$504$	0.177676	−	0.157407i	0.00791431	−	0.00701147i
$505$	−0.252055	−	0.0306050i	−0.0112163	−	0.00136190i
$506$	−4.76879			−0.211999
$507$	8.06441	+	10.1963i	0.358153	+	0.452835i
$508$	−27.6696			−1.22764
$509$	−15.7390	−	1.91106i	−0.697618	−	0.0847061i	−0.235958	−	0.971763i	$-0.575823\pi$
$509$	−15.7390	−	1.91106i	−0.697618	−	0.0847061i	−0.461660	+	0.887057i	$0.652746\pi$
$510$	0.707516	−	0.626804i	0.0313293	−	0.0277554i
$511$	0.363210	+	0.0895233i	0.0160675	+	0.00396028i
$512$	5.84974	+	11.1457i	0.258524	+	0.492577i
$513$	−3.46173	+	2.38946i	−0.152839	+	0.105497i
$514$	−42.2934	−	16.0398i	−1.86548	−	0.707485i
$515$	−0.719521	−	0.272878i	−0.0317059	−	0.0120245i
$516$	−2.32822	+	19.1746i	−0.102494	+	0.844116i
$517$	10.1331	+	26.7189i	0.445655	+	1.17510i
$518$	−0.548903	+	0.0666488i	−0.0241174	+	0.00292838i
$519$	10.3330	−	5.42317i	0.453568	−	0.238051i
$520$	1.89358	+	1.57072i	0.0830390	+	0.0688808i
$521$	12.3809	+	6.49797i	0.542415	+	0.284681i	0.713595	−	0.700558i	$-0.247066\pi$
$521$	12.3809	+	6.49797i	0.542415	+	0.284681i	−0.171180	+	0.985240i	$0.554758\pi$
$522$	10.4661	+	3.96928i	0.458090	+	0.173731i
$523$	−26.5778	−	13.9491i	−1.16217	−	0.609952i	−0.230431	−	0.973089i	$-0.574014\pi$
$523$	−26.5778	−	13.9491i	−1.16217	−	0.609952i	−0.931736	+	0.363136i	$0.881706\pi$
$524$	−8.40573	+	22.1641i	−0.367206	+	0.968243i
$525$	0.0816397	−	0.331225i	0.00356305	−	0.0144559i
$526$		−	14.3845i		−	0.627193i
$527$	−2.84273	−	11.5334i	−0.123831	−	0.502402i
$528$	4.45490	−	1.68952i	0.193875	−	0.0735270i
$529$	−22.7677			−0.989900
$530$	0.316546			0.0137499
$531$	−4.11241	+	1.55963i	−0.178464	+	0.0676823i
$532$	0.571021	−	0.827267i	0.0247569	−	0.0358666i
$533$	−44.0996	−	3.90499i	−1.91016	−	0.169144i
$534$	7.58956	+	10.9954i	0.328432	+	0.475817i
$535$	−2.55532	−	1.76381i	−0.110476	−	0.0762561i
$536$	−4.20232	+	34.6092i	−0.181512	+	1.49489i
$537$	−8.74697	−	4.59076i	−0.377460	−	0.198106i
$538$	10.4241	−	7.19526i	0.449416	−	0.310210i
$539$	24.3428	+	16.8026i	1.04852	+	0.723740i
$540$	0.455536	−	0.514193i	0.0196031	−	0.0221274i
$541$	17.8839	−	34.0749i	0.768888	−	1.46499i	−0.113030	−	0.993592i	$-0.536056\pi$
$541$	17.8839	−	34.0749i	0.768888	−	1.46499i	0.881918	−	0.471403i	$-0.156252\pi$
$542$	−3.84865	−	31.6965i	−0.165314	−	1.36148i
$543$	1.34519	−	3.54698i	0.0577278	−	0.152216i
$544$	−7.17684	+	4.95382i	−0.307705	+	0.212393i
$545$	−0.107954	+	0.889078i	−0.00462422	+	0.0380839i
$546$	−0.313869	+	0.487915i	−0.0134323	+	0.0208808i
$547$	−0.926892	−	7.63365i	−0.0396311	−	0.326391i	−0.999018	−	0.0442988i	$-0.985895\pi$
$547$	−0.926892	−	7.63365i	−0.0396311	−	0.326391i	0.959387	−	0.282092i	$-0.0910284\pi$
$548$	36.9448	+	41.7021i	1.57820	+	1.78142i
$549$	−5.84652	+	1.44104i	−0.249523	+	0.0615020i
$550$	27.8828	−	40.3952i	1.18893	−	1.72246i
$551$	19.9751	+	2.42542i	0.850970	+	0.103326i
$552$	−1.55566	+	0.589984i	−0.0662132	+	0.0251114i
$553$	0.474803	+	0.0576516i	0.0201907	+	0.00245159i
$554$	−6.09992	−	24.7483i	−0.259161	−	1.05146i
$555$	−0.659541	+	0.162562i	−0.0279960	+	0.00690038i
$556$	−34.9161	−	30.9329i	−1.48077	−	1.31185i
$557$	−1.59064	+	1.79546i	−0.0673977	+	0.0760763i	−0.781242	−	0.624228i	$-0.785414\pi$
$557$	−1.59064	+	1.79546i	−0.0673977	+	0.0760763i	0.713845	+	0.700304i	$0.246952\pi$
$558$	−4.82300	−	12.7172i	−0.204174	−	0.538363i
$559$	−3.06091	−	19.8046i	−0.129463	−	0.837646i
$560$	−0.00543126	+	0.0143211i	−0.000229513	+	0.000605175i
$561$	4.01570	+	7.65128i	0.169543	+	0.323037i
$562$	5.25175	+	7.60847i	0.221532	+	0.320944i
$563$	−14.9089	−	13.2081i	−0.628333	−	0.556655i	0.287718	−	0.957715i	$-0.407103\pi$
$563$	−14.9089	−	13.2081i	−0.628333	−	0.556655i	−0.916052	+	0.401060i	$0.868642\pi$
$564$	15.5741	+	17.5795i	0.655788	+	0.740232i
$565$	0.887068	−	3.59898i	0.0373192	−	0.151410i
$566$	−29.0590	−	55.3673i	−1.22144	−	2.32726i
$567$	0.0565925	+	0.0390630i	0.00237666	+	0.00164049i
$568$	1.76261	+	4.64761i	0.0739573	+	0.195009i
$569$	−1.51734	+	0.796363i	−0.0636104	+	0.0333853i	−0.496228	−	0.868192i	$-0.665282\pi$
$569$	−1.51734	+	0.796363i	−0.0636104	+	0.0333853i	0.432618	+	0.901577i	$0.357590\pi$
$570$	0.904154	−	1.72272i	0.0378708	−	0.0721568i
$571$	−21.1962	−	18.7782i	−0.887033	−	0.785843i	0.0906596	−	0.995882i	$-0.471102\pi$
$571$	−21.1962	−	18.7782i	−0.887033	−	0.785843i	−0.977693	+	0.210039i	$0.932641\pi$
$572$	−42.6022	+	31.4988i	−1.78129	+	1.31703i
$573$	7.22548	−	6.40122i	0.301849	−	0.267415i
$574$	−0.472823	−	1.91832i	−0.0197353	−	0.0800691i
$575$	−1.35829	+	1.96782i	−0.0566447	+	0.0820639i
$576$	−9.16077	+	8.11573i	−0.381699	+	0.338155i
$577$			12.0587i			0.502009i	0.967986	+	0.251004i	$0.0807608\pi$
$577$			12.0587i			0.502009i	−0.967986	+	0.251004i	$0.919239\pi$
$578$	−19.8981	−	22.4603i	−0.827650	−	0.934224i
$579$	8.76378	−	16.6980i	0.364210	−	0.693944i
$580$	−3.26224	+	0.396108i	−0.135457	+	0.0164475i
$581$	−0.0732248	+	0.0384313i	−0.00303788	+	0.00159440i
$582$	−2.76039	−	22.7338i	−0.114422	−	0.942347i
$583$	−0.692527	+	2.80969i	−0.0286816	+	0.116366i
$584$	18.2328	+	4.49398i	0.754479	+	0.185962i
$585$	−0.310526	+	0.641511i	−0.0128387	+	0.0265232i
$586$	23.6263	−	5.82335i	0.975992	−	0.240560i
$587$		−	37.6765i		−	1.55508i	−0.628835	−	0.777539i	$-0.716468\pi$
$587$		−	37.6765i		−	1.55508i	0.628835	−	0.777539i	$-0.283532\pi$
$588$	23.6038	+	5.81782i	0.973405	+	0.239923i
$589$	−13.8890	−	20.1217i	−0.572287	−	0.829101i
$590$	1.34902	−	1.52272i	0.0555381	−	0.0626896i
$591$	3.53711	−	0.429483i	0.145497	−	0.0176666i
$592$	−3.84389	+	0.466733i	−0.157983	+	0.0191826i
$593$	−30.3397	+	34.2465i	−1.24590	+	1.40633i	−0.366390	+	0.930461i	$0.619406\pi$
$593$	−30.3397	+	34.2465i	−1.24590	+	1.40633i	−0.879514	+	0.475873i	$0.842132\pi$
$594$	5.62049	+	8.14268i	0.230611	+	0.334098i
$595$	−0.0269710	−	0.00664776i	−0.00110570	−	0.000272532i
$596$		−	78.1072i		−	3.19939i
$597$	−16.8332	+	4.14902i	−0.688939	+	0.169808i
$598$	3.26969	−	2.41751i	0.133708	−	0.0988595i
$599$	−18.3400	−	4.52040i	−0.749351	−	0.184698i	−0.153896	−	0.988087i	$-0.549182\pi$
$599$	−18.3400	−	4.52040i	−0.749351	−	0.184698i	−0.595455	+	0.803389i	$0.703028\pi$
$600$	4.09823	−	16.6272i	0.167310	−	0.678802i
$601$	3.13577	+	25.8254i	0.127911	+	1.05344i	0.905405	+	0.424550i	$0.139568\pi$
$601$	3.13577	+	25.8254i	0.127911	+	1.05344i	−0.777494	+	0.628890i	$0.783509\pi$
$602$	0.791875	−	0.415608i	0.0322744	−	0.0169389i
$603$	−10.0260	+	1.21738i	−0.408291	+	0.0495755i
$604$	−34.4252	+	65.5917i	−1.40074	+	2.66889i
$605$	−0.901737	−	1.01785i	−0.0366608	−	0.0413815i
$606$		−	3.00559i		−	0.122094i
$607$	6.58296	−	5.83199i	0.267194	−	0.236713i	−0.518878	−	0.854848i	$-0.673650\pi$
$607$	6.58296	−	5.83199i	0.267194	−	0.236713i	0.786072	+	0.618135i	$0.212112\pi$
$608$	−10.1965	+	14.7721i	−0.413521	+	0.599089i
$609$	−0.0787235	−	0.319394i	−0.00319004	−	0.0129425i
$610$	2.08472	−	1.84690i	0.0844079	−	0.0747789i
$611$	−20.4927	−	13.1827i	−0.829047	−	0.533315i
$612$	5.31588	+	4.70946i	0.214882	+	0.190368i
$613$	20.9560	−	39.9283i	0.846405	−	1.61269i	0.0573602	−	0.998354i	$-0.481732\pi$
$613$	20.9560	−	39.9283i	0.846405	−	1.61269i	0.789045	−	0.614336i	$-0.210576\pi$
$614$	−47.4951	+	24.9274i	−1.91675	+	1.00599i
$615$	−0.860692	−	2.26946i	−0.0347064	−	0.0915134i
$616$	−0.826031	−	0.570168i	−0.0332818	−	0.0229727i
$617$	12.7264	+	24.2481i	0.512346	+	0.976194i	0.994952	+	0.100356i	$0.0319981\pi$
$617$	12.7264	+	24.2481i	0.512346	+	0.976194i	−0.482606	+	0.875838i	$0.660310\pi$
$618$	2.17998	−	8.84453i	0.0876917	−	0.355779i
$619$	19.5554	+	22.0735i	0.786000	+	0.887210i	0.995895	−	0.0905137i	$-0.0288509\pi$
$619$	19.5554	+	22.0735i	0.786000	+	0.887210i	−0.209896	+	0.977724i	$0.567312\pi$
$620$	2.98881	+	2.64785i	0.120033	+	0.106340i
$621$	−0.273798	−	0.396665i	−0.0109871	−	0.0159176i
$622$	−2.25370	−	4.29407i	−0.0903653	−	0.172177i
$623$	0.139229	−	0.367117i	0.00557809	−	0.0147082i
$624$	−2.19798	+	3.41680i	−0.0879896	+	0.136781i
$625$	−8.65783	−	22.8288i	−0.346313	−	0.913152i
$626$	−1.48287	+	1.67381i	−0.0592674	+	0.0668991i
$627$	13.3130	+	11.7943i	0.531669	+	0.471018i
$628$	−7.53880	+	1.85815i	−0.300831	+	0.0741481i
$629$	−1.68061	−	6.81852i	−0.0670105	−	0.271872i
$630$	−0.0315744	−	0.00383383i	−0.00125795	−	0.000152743i
$631$	24.2203	−	9.18556i	0.964196	−	0.365671i	0.178263	−	0.983983i	$-0.442952\pi$
$631$	24.2203	−	9.18556i	0.964196	−	0.365671i	0.785933	+	0.618312i	$0.212183\pi$
$632$	23.8347	+	2.89405i	0.948092	+	0.115119i
$633$	−5.70188	+	8.26060i	−0.226629	+	0.328329i
$634$	−40.7499	+	10.0440i	−1.61839	+	0.398897i
$635$	1.04365	+	1.17804i	0.0414161	+	0.0467491i
$636$	0.286678	+	2.36101i	0.0113675	+	0.0936200i
$637$	−25.2085	+	0.819856i	−0.998796	+	0.0324839i
$638$	5.70507	−	46.9855i	0.225866	−	1.86017i
$639$	−1.18506	+	0.817985i	−0.0468801	+	0.0323590i
$640$	1.40912	−	3.71555i	0.0557005	−	0.146870i
$641$	−4.57322	−	37.6639i	−0.180631	−	1.48763i	−0.747741	−	0.663991i	$-0.768862\pi$
$641$	−4.57322	−	37.6639i	−0.180631	−	1.48763i	0.567110	−	0.823642i	$-0.308062\pi$
$642$	17.0807	−	32.5445i	0.674121	−	1.28443i
$643$	−8.54875	+	9.64954i	−0.337130	+	0.380541i	−0.892489	−	0.451070i	$-0.851042\pi$
$643$	−8.54875	+	9.64954i	−0.337130	+	0.380541i	0.555359	+	0.831611i	$0.312581\pi$
$644$	0.0947928	+	0.0654308i	0.00373536	+	0.00257833i
$645$	0.904183	−	0.624112i	0.0356022	−	0.0245744i
$646$	17.8100	+	9.34740i	0.700724	+	0.367768i
$647$	4.11819	−	33.9163i	0.161903	−	1.33339i	−0.654568	−	0.756003i	$-0.727150\pi$
$647$	4.11819	−	33.9163i	0.161903	−	1.33339i	0.816471	−	0.577386i	$-0.195927\pi$
$648$	2.84089	+	1.96092i	0.111601	+	0.0770324i
$649$	10.5645	+	15.3054i	0.414694	+	0.600788i
$650$	1.36049	+	41.8318i	0.0533630	+	1.64078i
$651$	−0.227058	+	0.328950i	−0.00889910	+	0.0128926i
$652$	−38.7061	+	14.6793i	−1.51585	+	0.574885i
$653$	−1.05235			−0.0411816			−0.0205908	−	0.999788i	$-0.506555\pi$
$653$	−1.05235			−0.0411816			−0.0205908	+	0.999788i	$0.506555\pi$
$654$	−10.6017			−0.414559
$655$	1.26069	−	0.478118i	0.0492594	−	0.0186816i
$656$	−3.31111	−	13.4337i	−0.129277	−	0.524499i
$657$			5.43998i			0.212234i
$658$	0.260235	−	1.05581i	0.0101450	−	0.0411599i
$659$	12.8798	−	33.9613i	0.501727	−	1.32295i	−0.409976	−	0.912096i	$-0.634463\pi$
$659$	12.8798	−	33.9613i	0.501727	−	1.32295i	0.911703	−	0.410849i	$-0.134768\pi$
$660$	−2.57200	−	1.34989i	−0.100115	−	0.0525443i
$661$	26.0770	+	9.88968i	1.01428	+	0.384664i	0.805052	−	0.593204i	$-0.202137\pi$
$661$	26.0770	+	9.88968i	1.01428	+	0.384664i	0.209224	+	0.977868i	$0.432906\pi$
$662$	−34.3113	−	18.0080i	−1.33355	−	0.699900i
$663$	−6.63212	−	3.21031i	−0.257570	−	0.124678i
$664$	−3.67581	+	1.92922i	−0.142649	+	0.0748681i
$665$	−0.0567592	+	0.00689181i	−0.00220103	+	0.000267253i
$666$	−2.85135	−	7.51839i	−0.110488	−	0.291332i
$667$	−0.277918	+	2.28886i	−0.0107610	+	0.0886251i
$668$	−7.17199	−	2.71998i	−0.277493	−	0.105239i
$669$	19.4012	+	7.35792i	0.750096	+	0.284474i
$670$	3.84453	−	2.65369i	0.148527	−	0.102521i
$671$	11.8324	+	22.5448i	0.456785	+	0.870332i
$672$	0.284912	+	0.0702245i	0.0109907	+	0.00270897i
$673$	8.20573	−	7.26965i	0.316308	−	0.280224i	−0.489998	−	0.871724i	$-0.663002\pi$
$673$	8.20573	−	7.26965i	0.316308	−	0.280224i	0.806305	+	0.591500i	$0.201464\pi$
$674$	42.7444	+	5.19011i	1.64645	+	0.199916i
$675$	4.96093			0.190946
$676$	13.2417	−	43.1939i	0.509297	−	1.66130i
$677$	7.93325			0.304899			0.152450	−	0.988311i	$-0.451284\pi$
$677$	7.93325			0.304899			0.152450	+	0.988311i	$0.451284\pi$
$678$	43.5577	+	5.28886i	1.67282	+	0.203118i
$679$	−0.503750	+	0.446283i	−0.0193321	+	0.0171268i
$680$	−1.35392	−	0.333711i	−0.0519204	−	0.0127972i
$681$	7.03085	+	13.3962i	0.269423	+	0.513342i
$682$	−47.3303	+	32.6697i	−1.81237	+	1.25099i
$683$	7.37288	+	2.79616i	0.282115	+	0.106992i	0.491604	−	0.870819i	$-0.336411\pi$
$683$	7.37288	+	2.79616i	0.282115	+	0.106992i	−0.209489	+	0.977811i	$0.567180\pi$
$684$	13.6680	+	5.18360i	0.522610	+	0.198200i
$685$	0.381978	−	3.14587i	0.0145946	−	0.120198i
$686$	−0.798537	−	2.10557i	−0.0304883	−	0.0803910i
$687$	−13.4561	+	1.63387i	−0.513383	+	0.0623360i
$688$	5.54539	−	2.91045i	0.211416	−	0.110960i
$689$	−0.949533	−	2.27752i	−0.0361743	−	0.0867666i
$690$	0.197399	+	0.103603i	0.00751485	+	0.00394410i
$691$	−21.0629	−	7.98812i	−0.801272	−	0.303883i	−0.0802325	−	0.996776i	$-0.525566\pi$
$691$	−21.0629	−	7.98812i	−0.801272	−	0.303883i	−0.721040	+	0.692894i	$0.756336\pi$
$692$	−35.9096	−	18.8468i	−1.36508	−	0.716448i
$693$	0.103107	−	0.271870i	0.00391670	−	0.0103275i
$694$	17.4823	−	70.9284i	0.663619	−	2.69241i
$695$			2.65330i			0.100646i
$696$	−3.95184	−	16.0333i	−0.149794	−	0.607739i
$697$	23.4623	−	8.89807i	0.888698	−	0.337039i
$698$	17.3405			0.656347
$699$	18.9006			0.714886
$700$	−1.10849	+	0.420397i	−0.0418972	+	0.0158895i
$701$	−21.6932	+	31.4281i	−0.819342	+	1.18702i	0.160458	+	0.987043i	$0.448703\pi$
$701$	−21.6932	+	31.4281i	−0.819342	+	1.18702i	−0.979800	+	0.199979i	$0.935913\pi$
$702$	−7.98154	−	2.73370i	−0.301244	−	0.103177i
$703$	−8.21116	−	11.8959i	−0.309690	−	0.448663i
$704$	42.5892	+	29.3972i	1.60514	+	1.10795i
$705$	0.161023	−	1.32614i	0.00606448	−	0.0499455i
$706$	−22.4459	−	11.7805i	−0.844763	−	0.443366i
$707$	−0.0726922	+	0.0501758i	−0.00273387	+	0.00188705i
$708$	12.5792	+	8.68280i	0.472756	+	0.326320i
$709$	−1.72013	+	1.94163i	−0.0646009	+	0.0729194i	−0.779923	−	0.625876i	$-0.784742\pi$
$709$	−1.72013	+	1.94163i	−0.0646009	+	0.0729194i	0.715322	+	0.698795i	$0.246280\pi$
$710$	0.309519	−	0.589739i	0.0116160	−	0.0221325i
$711$	0.838385	+	6.90472i	0.0314419	+	0.258947i
$712$	6.98916	−	18.4289i	0.261930	−	0.690652i
$713$	2.30566	−	1.59148i	0.0863476	−	0.0596014i
$714$	0.0396352	−	0.326425i	0.00148331	−	0.0122161i
$715$	2.94796	+	0.625715i	0.110247	+	0.0234004i
$716$	4.13804	+	34.0798i	0.154646	+	1.27362i
$717$	−14.2401	−	16.0738i	−0.531807	−	0.600286i
$718$	−68.8965	+	16.9815i	−2.57119	+	0.633742i
$719$	13.4791	−	19.5278i	0.502684	−	0.728263i	−0.486703	−	0.873567i	$-0.661801\pi$
$719$	13.4791	−	19.5278i	0.502684	−	0.728263i	0.989387	+	0.145304i	$0.0464161\pi$
$720$	−0.221111	−	0.0268477i	−0.00824032	−	0.00100056i
$721$	−0.250303	+	0.0949276i	−0.00932179	+	0.00353529i
$722$	−3.03568	−	0.368598i	−0.112976	−	0.0137178i
$723$	−0.615604	−	2.49760i	−0.0228945	−	0.0928868i
$724$	−12.8002	+	3.15497i	−0.475716	+	0.117254i
$725$	−17.7634	−	15.7370i	−0.659717	−	0.584458i
$726$	10.6742	−	12.0487i	0.396158	−	0.447170i
$727$	16.7801	+	44.2454i	0.622338	+	1.64097i	0.759565	+	0.650432i	$0.225412\pi$
$727$	16.7801	+	44.2454i	0.622338	+	1.64097i	−0.137226	+	0.990540i	$0.543819\pi$
$728$	0.855407	−	0.0278204i	0.0317035	−	0.00103109i
$729$	−0.354605	+	0.935016i	−0.0131335	+	0.0346302i
$730$	−1.16933	−	2.22797i	−0.0432789	−	0.0824610i
$731$	6.45225	+	9.34770i	0.238645	+	0.345737i
$732$	15.6634	+	13.8766i	0.578937	+	0.512893i
$733$	5.67846	+	6.40966i	0.209739	+	0.236746i	0.843961	−	0.536405i	$-0.180218\pi$
$733$	5.67846	+	6.40966i	0.209739	+	0.236746i	−0.634222	+	0.773151i	$0.718679\pi$
$734$	−1.17021	+	4.74775i	−0.0431934	+	0.175243i
$735$	−0.642603	−	1.22438i	−0.0237028	−	0.0451619i
$736$	−1.69267	−	1.16837i	−0.0623928	−	0.0430666i
$737$	15.1435	+	39.9301i	0.557818	+	1.47084i
$738$	25.4406	−	13.3523i	0.936481	−	0.491503i
$739$	−22.4114	+	42.7013i	−0.824416	+	1.57079i	−0.00332522	+	0.999994i	$0.501058\pi$
$739$	−22.4114	+	42.7013i	−0.824416	+	1.57079i	−0.821090	+	0.570798i	$0.806634\pi$
$740$	1.76698	+	1.56541i	0.0649554	+	0.0575454i
$741$	−15.1070	−	1.33771i	−0.554969	−	0.0491421i
$742$	0.0824248	−	0.0730220i	0.00302591	−	0.00268072i
$743$	−5.75270	−	23.3396i	−0.211046	−	0.856247i	−0.976980	−	0.213329i	$-0.931569\pi$
$743$	−5.75270	−	23.3396i	−0.211046	−	0.856247i	0.765934	−	0.642919i	$-0.222277\pi$
$744$	−11.3981	+	16.5130i	−0.417874	+	0.605395i
$745$	−3.32544	+	2.94608i	−0.121835	+	0.107936i
$746$			83.1919i			3.04587i
$747$	−0.797476	−	0.900164i	−0.0291781	−	0.0329353i
$748$	13.9555	−	26.5900i	0.510264	−	0.972227i
$749$	−1.07226	+	0.130196i	−0.0391794	+	0.00475724i
$750$	−4.07955	+	2.14111i	−0.148964	+	0.0781824i
$751$	−5.00061	−	41.1837i	−0.182475	−	1.50282i	−0.739973	−	0.672637i	$-0.765162\pi$
$751$	−5.00061	−	41.1837i	−0.182475	−	1.50282i	0.557498	−	0.830178i	$-0.311762\pi$
$752$	1.82239	−	7.39371i	0.0664556	−	0.269621i
$753$	18.9099	+	4.66088i	0.689116	+	0.169852i
$754$	19.9074	+	35.1074i	0.724985	+	1.27854i
$755$	4.09105	−	1.00835i	0.148889	−	0.0366978i
$756$		−	0.238975i		−	0.00869142i
$757$	−29.2857	−	7.21827i	−1.06441	−	0.262353i	−0.332041	−	0.943265i	$-0.607737\pi$
$757$	−29.2857	−	7.21827i	−1.06441	−	0.262353i	−0.732365	+	0.680912i	$0.761584\pi$
$758$	20.3719	+	29.5138i	0.739941	+	1.07199i
$759$	−1.35145	+	1.52547i	−0.0490546	+	0.0553712i
$760$	−2.84926	+	0.345962i	−0.103353	+	0.0125494i
$761$	22.2285	−	2.69903i	0.805782	−	0.0978396i	0.292728	−	0.956196i	$-0.405437\pi$
$761$	22.2285	−	2.69903i	0.805782	−	0.0978396i	0.513054	+	0.858356i	$0.328514\pi$
$762$	−12.3542	+	13.9450i	−0.447544	+	0.505173i
$763$	0.176986	+	0.256409i	0.00640733	+	0.00928262i
$764$	−32.5721	−	8.02831i	−1.17842	−	0.290454i
$765$		−	0.403958i		−	0.0146051i
$766$	72.3840	−	17.8411i	2.61534	−	0.644624i
$767$	−15.0025	−	5.13838i	−0.541708	−	0.185536i
$768$	21.9065	+	5.39946i	0.790482	+	0.194836i
$769$	−2.53791	+	10.2967i	−0.0915195	+	0.371309i	−0.998787	−	0.0492455i	$-0.984318\pi$
$769$	−2.53791	+	10.2967i	−0.0915195	+	0.371309i	0.907267	+	0.420555i	$0.138164\pi$
$770$	0.0162109	+	0.133509i	0.000584200	+	0.00481132i
$771$	−17.1167	+	8.98353i	−0.616442	+	0.323534i
$772$	−65.0584	+	7.89952i	−2.34150	+	0.284310i
$773$	8.05247	−	15.3427i	0.289627	−	0.551839i	−0.696555	−	0.717504i	$-0.745285\pi$
$773$	8.05247	−	15.3427i	0.289627	−	0.551839i	0.986182	+	0.165665i	$0.0529770\pi$
$774$	8.62415	+	9.73465i	0.309989	+	0.349905i
$775$			28.8359i			1.03582i
$776$	−25.2877	+	22.4030i	−0.907777	+	0.804220i
$777$	−0.134236	+	0.194475i	−0.00481570	+	0.00697674i
$778$	5.06307	+	20.5417i	0.181520	+	0.736456i
$779$	38.6598	−	34.2496i	1.38513	−	1.22712i
$780$	2.44779	−	0.378319i	0.0876449	−	0.0135460i
$781$	4.55743	+	4.03753i	0.163078	+	0.144474i
$782$	−1.07108	+	2.04077i	−0.0383016	+	0.0729776i
$783$	4.23577	−	2.22310i	0.151374	−	0.0794473i
$784$	−2.79508	−	7.37001i	−0.0998242	−	0.263215i
$785$	0.363463	+	0.250880i	0.0129725	+	0.00895430i
$786$	7.41724	+	14.1324i	0.264564	+	0.504085i
$787$	−7.61330	+	30.8884i	−0.271385	+	1.10105i	0.664088	+	0.747654i	$0.268820\pi$
$787$	−7.61330	+	30.8884i	−0.271385	+	1.10105i	−0.935473	+	0.353398i	$0.885026\pi$
$788$	−8.21117	−	9.26849i	−0.292511	−	0.330176i
$789$	−4.60141	−	4.07649i	−0.163814	−	0.145127i
$790$	−1.82754	−	2.64765i	−0.0650211	−	0.0941993i
$791$	−0.599244	−	1.14176i	−0.0213067	−	0.0405964i
$792$	5.17586	−	13.6476i	0.183916	−	0.484947i
$793$	−19.5418	−	9.45929i	−0.693949	−	0.335909i
$794$	−16.3697	−	43.1633i	−0.580938	−	1.53181i
$795$	0.0897076	−	0.101259i	0.00318160	−	0.00359128i
$796$	45.0980	+	39.9533i	1.59846	+	1.41611i
$797$	32.1959	−	7.93558i	1.14044	−	0.281093i	0.376522	−	0.926408i	$-0.377120\pi$
$797$	32.1959	−	7.93558i	1.14044	−	0.281093i	0.763917	+	0.645315i	$0.223274\pi$
$798$	−0.161973	−	0.657150i	−0.00573378	−	0.0232629i
$799$	13.7101	+	1.66470i	0.485027	+	0.0588929i
$800$	19.7939	−	7.50684i	0.699820	−	0.265407i
$801$	5.66812	+	0.688235i	0.200273	+	0.0243176i
$802$	−12.4247	+	18.0002i	−0.438730	+	0.635610i
$803$	22.3339	−	5.50482i	0.788147	−	0.194261i
$804$	23.2747	+	26.2717i	0.820837	+	0.926533i
$805$	−0.000789702	−	0.00650378i	−2.78333e−5	−	0.000229228i
$806$	15.8899	−	46.3936i	0.559699	−	1.63414i
$807$	0.652479	−	5.37365i	0.0229683	−	0.189161i
$808$	−3.64908	+	2.51878i	−0.128374	+	0.0886102i
$809$	−5.87141	+	15.4816i	−0.206428	+	0.544305i	−0.997746	−	0.0670990i	$-0.978626\pi$
$809$	−5.87141	+	15.4816i	−0.206428	+	0.544305i	0.791319	+	0.611404i	$0.209395\pi$
$810$	−0.0557526	−	0.459164i	−0.00195895	−	0.0161334i
$811$	20.4442	−	38.9531i	0.717892	−	1.36783i	−0.203454	−	0.979085i	$-0.565217\pi$
$811$	20.4442	−	38.9531i	0.717892	−	1.36783i	0.921346	−	0.388744i	$-0.127091\pi$
$812$	−0.758073	+	0.855688i	−0.0266032	+	0.0300288i
$813$	−11.2300	−	7.75150i	−0.393853	−	0.271857i
$814$	−27.9816	+	19.3143i	−0.980753	+	0.676965i
$815$	2.08491	+	1.09424i	0.0730311	+	0.0383297i
$816$	0.277560	−	2.28591i	0.00971653	−	0.0800228i
$817$	19.2404	+	13.2807i	0.673137	+	0.464633i
$818$	41.8621	+	60.6477i	1.46367	+	2.12050i
$819$	0.0671287	+	0.238675i	0.00234567	+	0.00833999i
$820$	−4.79165	+	6.94190i	−0.167332	+	0.242422i
$821$	46.8980	−	17.7861i	1.63675	−	0.620738i	0.646866	−	0.762604i	$-0.276079\pi$
$821$	46.8980	−	17.7861i	1.63675	−	0.620738i	0.989886	+	0.141866i	$0.0453101\pi$
$822$	37.5126			1.30840
$823$	21.8796			0.762674			0.381337	−	0.924436i	$-0.375464\pi$
$823$	21.8796			0.762674			0.381337	+	0.924436i	$0.375464\pi$
$824$	−12.5650	+	4.76527i	−0.437722	+	0.166006i
$825$	−5.02006	−	20.3672i	−0.174776	−	0.709094i
$826$		−	0.707696i		−	0.0246239i
$827$	−4.03767	+	16.3815i	−0.140404	+	0.569640i	0.858025	+	0.513607i	$0.171691\pi$
$827$	−4.03767	+	16.3815i	−0.140404	+	0.569640i	−0.998429	+	0.0560323i	$0.982155\pi$
$828$	−0.593966	+	1.56616i	−0.0206417	+	0.0544278i
$829$	−49.3909	−	25.9223i	−1.71542	−	0.900319i	−0.973137	−	0.230228i	$-0.926053\pi$
$829$	−49.3909	−	25.9223i	−1.71542	−	0.900319i	−0.742279	−	0.670092i	$-0.766255\pi$
$830$	0.520102	+	0.197249i	0.0180530	+	0.00684660i
$831$	−9.64536	−	5.06228i	−0.334594	−	0.175608i
$832$	−44.1038	+	1.43439i	−1.52902	+	0.0497284i
$833$	12.6580	−	6.64342i	0.438573	−	0.230181i
$834$	−31.1793	+	3.78585i	−1.07965	+	0.131093i
$835$	0.154712	+	0.407943i	0.00535405	+	0.0141175i
$836$	7.45042	−	61.3597i	0.257678	−	2.12217i
$837$	−5.43489	−	2.06118i	−0.187857	−	0.0712448i
$838$	5.64364	+	2.14035i	0.194956	+	0.0739372i
$839$	−14.0309	+	9.68481i	−0.484399	+	0.334357i	−0.785108	−	0.619359i	$-0.787392\pi$
$839$	−14.0309	+	9.68481i	−0.484399	+	0.334357i	0.300708	+	0.953716i	$0.402777\pi$
$840$	0.0218056	+	0.0415472i	0.000752366	+	0.00143351i
$841$	5.93832	+	1.46366i	0.204770	+	0.0504712i
$842$	−41.9800	+	37.1910i	−1.44673	+	1.28169i
$843$	3.92217	+	0.476238i	0.135087	+	0.0164025i
$844$	34.8822			1.20070
$845$	−2.33845	+	1.06544i	−0.0804452	+	0.0366521i
$846$	15.8134			0.543677
$847$	−0.469603	−	0.0570202i	−0.0161358	−	0.00195924i
$848$	0.577209	−	0.511363i	0.0198215	−	0.0175603i
$849$	−25.9465	−	6.39523i	−0.890480	−	0.219484i
$850$	−11.0243	−	21.0050i	−0.378130	−	0.720467i
$851$	1.36310	−	0.940881i	0.0467265	−	0.0322530i
$852$	4.67898	+	1.77450i	0.160299	+	0.0607935i
$853$	−16.2695	−	6.17019i	−0.557056	−	0.211263i	0.0599785	−	0.998200i	$-0.480897\pi$
$853$	−16.2695	−	6.17019i	−0.557056	−	0.211263i	−0.617034	+	0.786936i	$0.711666\pi$
$854$	0.116786	−	0.961823i	0.00399635	−	0.0329129i
$855$	−0.294843	−	0.777438i	−0.0100834	−	0.0265878i
$856$	−53.8263	+	6.53569i	−1.83974	+	0.223385i
$857$	−33.2507	+	17.4513i	−1.13582	+	0.596125i	−0.924459	−	0.381283i	$-0.875482\pi$
$857$	−33.2507	+	17.4513i	−1.13582	+	0.596125i	−0.211363	+	0.977408i	$0.567790\pi$
$858$	−3.14657	+	35.5346i	−0.107422	+	1.21313i
$859$	32.5474	+	17.0822i	1.11050	+	0.582836i	0.917250	−	0.398313i	$-0.130404\pi$
$859$	32.5474	+	17.0822i	1.11050	+	0.582836i	0.193252	+	0.981149i	$0.438096\pi$
$860$	−3.57000	−	1.35392i	−0.121736	−	0.0461684i
$861$	−0.747641	−	0.392392i	−0.0254795	−	0.0133727i
$862$	9.55030	−	25.1821i	0.325284	−	0.857705i
$863$	−9.13311	+	37.0545i	−0.310895	+	1.26135i	0.582779	+	0.812631i	$0.301965\pi$
$863$	−9.13311	+	37.0545i	−0.310895	+	1.26135i	−0.893673	+	0.448718i	$0.851881\pi$
$864$			4.26727i			0.145175i
$865$	0.552045	+	2.23973i	0.0187701	+	0.0761533i
$866$	−22.0557	+	8.36461i	−0.749482	+	0.284241i
$867$	−12.8238			−0.435518
$868$	1.38907			0.0471480
$869$	27.4991	−	10.4290i	0.932843	−	0.353781i
$870$	−1.25692	+	1.82097i	−0.0426137	+	0.0617366i
$871$	−30.6254	−	19.7009i	−1.03770	−	0.667539i
$872$	8.88453	+	12.8715i	0.300868	+	0.435883i
$873$	−8.05453	−	5.55964i	−0.272605	−	0.188165i
$874$	−0.571815	+	4.70932i	−0.0193419	+	0.159295i
$875$	0.119889	+	0.0629225i	0.00405298	+	0.00212717i
$876$	15.5587	−	10.7394i	0.525679	−	0.362850i
$877$	22.4922	+	15.5252i	0.759506	+	0.524249i	0.883726	−	0.468006i	$-0.155027\pi$
$877$	22.4922	+	15.5252i	0.759506	+	0.524249i	−0.124219	+	0.992255i	$0.539643\pi$
$878$	48.6221	−	54.8830i	1.64092	−	1.85221i
$879$	4.83276	−	9.20805i	0.163005	−	0.310580i
$880$	0.113523	+	0.934943i	0.00382685	+	0.0315169i
$881$	−16.7025	+	44.0409i	−0.562722	+	1.48378i	0.287724	+	0.957713i	$0.407102\pi$
$881$	−16.7025	+	44.0409i	−0.562722	+	1.48378i	−0.850446	+	0.526063i	$0.823668\pi$
$882$	13.4709	−	9.29831i	0.453590	−	0.313090i
$883$	1.67735	−	13.8142i	0.0564473	−	0.464886i	−0.936888	−	0.349629i	$-0.886308\pi$
$883$	1.67735	−	13.8142i	0.0564473	−	0.464886i	0.993336	−	0.115257i	$-0.0367691\pi$
$884$	3.91117	+	25.3059i	0.131547	+	0.851131i
$885$	−0.104795	−	0.863065i	−0.00352265	−	0.0290116i
$886$	21.5303	+	24.3026i	0.723323	+	0.816463i
$887$	−26.5006	+	6.53182i	−0.889804	+	0.219317i	−0.657615	−	0.753354i	$-0.728435\pi$
$887$	−26.5006	+	6.53182i	−0.889804	+	0.219317i	−0.232188	+	0.972671i	$0.574589\pi$
$888$	−6.73853	+	9.76245i	−0.226130	+	0.327606i
$889$	0.543510	+	0.0659941i	0.0182287	+	0.00221337i
$890$	−2.46935	+	0.936500i	−0.0827727	+	0.0313915i
$891$	4.19756	+	0.509676i	0.140623	+	0.0170748i
$892$	−17.2570	−	70.0145i	−0.577808	−	2.34426i
$893$	27.6007	−	6.80297i	0.923623	−	0.227653i
$894$	−39.3646	−	34.8740i	−1.31655	−	1.16636i
$895$	1.29488	−	1.46161i	0.0432830	−	0.0488564i
$896$	−0.490199	−	1.29255i	−0.0163764	−	0.0431810i
$897$	0.153283	−	1.73104i	0.00511796	−	0.0577979i
$898$	11.5190	−	30.3732i	0.384395	−	1.01357i
$899$	12.9220	+	24.6209i	0.430974	+	0.821153i
$900$	−9.79366	−	14.1886i	−0.326455	−	0.472952i
$901$	1.04684	+	0.927422i	0.0348754	+	0.0308969i
$902$	−80.5617	−	90.9354i	−2.68241	−	3.02782i
$903$	0.0914660	−	0.371092i	0.00304380	−	0.0123492i
$904$	−30.0815	−	57.3154i	−1.00049	−	1.90628i
$905$	0.617128	+	0.425973i	0.0205140	+	0.0141598i
$906$	17.6866	+	46.6357i	0.587597	+	1.54937i
$907$	−5.99795	+	3.14797i	−0.199159	+	0.104527i	−0.561354	−	0.827576i	$-0.689720\pi$
$907$	−5.99795	+	3.14797i	−0.199159	+	0.104527i	0.362196	+	0.932102i	$0.382027\pi$
$908$	24.4338	−	46.5548i	0.810866	−	1.54498i
$909$	−0.961450	−	0.851771i	−0.0318893	−	0.0282515i
$910$	−0.0787965	−	0.0833213i	−0.00261208	−	0.00276208i
$911$	−1.24754	+	1.10523i	−0.0413330	+	0.0366178i	−0.683536	−	0.729916i	$-0.739559\pi$
$911$	−1.24754	+	1.10523i	−0.0413330	+	0.0366178i	0.642203	+	0.766534i	$0.278020\pi$
$912$	−1.13427	−	4.60193i	−0.0375596	−	0.152385i
$913$	−2.88866	+	4.18494i	−0.0956006	+	0.138501i
$914$	41.2681	−	36.5603i	1.36503	−	1.20931i
$915$		−	1.19028i		−	0.0393494i
$916$	31.2375	+	35.2599i	1.03212	+	1.16502i
$917$	0.217976	−	0.415318i	0.00719820	−	0.0137150i
$918$	4.74696	−	0.576386i	0.156673	−	0.0190236i
$919$	−36.9217	+	19.3780i	−1.21793	+	0.639221i	−0.946334	−	0.323190i	$-0.895245\pi$
$919$	−36.9217	+	19.3780i	−1.21793	+	0.639221i	−0.271599	+	0.962411i	$0.587552\pi$
$920$	−0.0396423	−	0.326484i	−0.00130697	−	0.0107638i
$921$	−5.48595	+	22.2574i	−0.180768	+	0.733405i
$922$	−88.3196	−	21.7688i	−2.90865	−	0.716918i
$923$	−5.17158	−	0.457940i	−0.170225	−	0.0150733i
$924$	−0.981115	+	0.241823i	−0.0322763	+	0.00795539i
$925$			17.0478i			0.560527i
$926$	−90.0847	−	22.2039i	−2.96037	−	0.729665i
$927$	−2.21145	−	3.20385i	−0.0726337	−	0.105228i
$928$	13.5366	−	15.2796i	0.444360	−	0.501579i
$929$	22.6958	−	2.75577i	0.744626	−	0.0904140i	0.260575	−	0.965454i	$-0.416088\pi$
$929$	22.6958	−	2.75577i	0.744626	−	0.0904140i	0.484051	+	0.875040i	$0.339165\pi$
$930$	2.66894	−	0.324068i	0.0875180	−	0.0106266i
$931$	19.5120	−	22.0244i	0.639478	−	0.721822i
$932$	−37.3128	−	54.0569i	−1.22222	−	1.77069i
$933$	−2.01231	−	0.495989i	−0.0658800	−	0.0162380i
$934$		−	45.7050i		−	1.49551i
$935$	−1.65846	+	0.408773i	−0.0542374	+	0.0133683i
$936$	3.36980	+	11.9813i	0.110145	+	0.391620i
$937$	41.8097	+	10.3052i	1.36586	+	0.336655i	0.853043	−	0.521841i	$-0.174754\pi$
$937$	41.8097	+	10.3052i	1.36586	+	0.336655i	0.512821	+	0.858496i	$0.328601\pi$
$938$	0.388908	−	1.57786i	0.0126983	−	0.0515190i
$939$	0.115193	+	0.948702i	0.00375919	+	0.0309597i
$940$	−4.11074	+	2.15748i	−0.134078	+	0.0703694i
$941$	−41.6368	+	5.05562i	−1.35732	+	0.164809i	−0.766630	−	0.642090i	$-0.778068\pi$
$941$	−41.6368	+	5.05562i	−1.35732	+	0.164809i	−0.590691	+	0.806898i	$0.701145\pi$
$942$	−2.42952	+	4.62906i	−0.0791580	+	0.150823i
$943$	3.92450	+	4.42985i	0.127799	+	0.144256i
$944$		−	4.95589i		−	0.161301i
$945$	−0.0101744	+	0.00901375i	−0.000330974	+	0.000293217i
$946$	31.2388	−	45.2573i	1.01566	−	1.47144i
$947$	1.31415	+	5.33170i	0.0427040	+	0.173257i	0.988422	−	0.151733i	$-0.0484853\pi$
$947$	1.31415	+	5.33170i	0.0427040	+	0.173257i	−0.945718	+	0.324990i	$0.894639\pi$
$948$	18.0928	−	16.0289i	0.587628	−	0.520593i
$949$	−12.5225	+	15.0964i	−0.406496	+	0.490050i
$950$	−36.5481	−	32.3788i	−1.18578	−	1.05051i
$951$	−8.33541	+	15.8818i	−0.270294	+	0.515002i
$952$	−0.429527	+	0.225433i	−0.0139210	+	0.00730632i
$953$	5.23347	+	13.7995i	0.169529	+	0.447010i	0.992674	−	0.120820i	$-0.0385523\pi$
$953$	5.23347	+	13.7995i	0.169529	+	0.447010i	−0.823146	+	0.567830i	$0.807783\pi$
$954$	1.31790	+	0.909683i	0.0426687	+	0.0294521i
$955$	0.886762	+	1.68958i	0.0286949	+	0.0546737i
$956$	−17.8597	+	72.4598i	−0.577625	+	2.34352i
$957$	−13.4133	−	15.1404i	−0.433589	−	0.489421i
$958$	58.5707	+	51.8891i	1.89233	+	1.67646i
$959$	−0.626240	−	0.907265i	−0.0202223	−	0.0292971i
$960$	−1.12427	−	2.14213i	−0.0362858	−	0.0691368i
$961$	0.988093	−	2.60539i	0.0318740	−	0.0840447i
$962$	9.39409	−	27.4278i	0.302878	−	0.884308i
$963$	−5.56999	−	14.6868i	−0.179490	−	0.473277i
$964$	−5.92800	+	6.69133i	−0.190928	+	0.215513i
$965$	2.79022	+	2.47192i	0.0898205	+	0.0795740i
$966$	0.0752999	−	0.0185598i	0.00242273	−	0.000597150i
$967$	2.33597	+	9.47738i	0.0751196	+	0.304772i	0.996469	−	0.0839638i	$-0.0267580\pi$
$967$	2.33597	+	9.47738i	0.0751196	+	0.304772i	−0.921349	+	0.388736i	$0.872912\pi$
$968$	−23.5736	−	2.86236i	−0.757685	−	0.0919996i
$969$	8.03737	−	3.04817i	0.258198	−	0.0979214i
$970$	4.49383	+	0.545650i	0.144288	+	0.0175198i
$971$	−24.0299	+	34.8133i	−0.771155	+	1.11721i	0.218792	+	0.975772i	$0.429788\pi$
$971$	−24.0299	+	34.8133i	−0.771155	+	1.11721i	−0.989947	+	0.141440i	$0.954827\pi$
$972$	3.37425	−	0.831678i	0.108229	−	0.0266761i
$973$	0.612074	+	0.690889i	0.0196222	+	0.0221489i
$974$	5.62818	+	46.3522i	0.180338	+	1.48522i
$975$	13.7670	+	11.4197i	0.440897	+	0.365724i
$976$	0.817839	−	6.73551i	0.0261784	−	0.215598i
$977$	16.4213	−	11.3348i	0.525365	−	0.362633i	−0.275669	−	0.961253i	$-0.588899\pi$
$977$	16.4213	−	11.3348i	0.525365	−	0.362633i	0.801033	+	0.598620i	$0.204284\pi$
$978$	−9.88375	+	26.0613i	−0.316047	+	0.833348i
$979$	−2.91012	−	23.9670i	−0.0930080	−	0.765989i
$980$	−2.23320	+	4.25500i	−0.0713369	+	0.135921i
$981$	−3.00447	+	3.39134i	−0.0959253	+	0.108277i
$982$	29.4008	+	20.2939i	0.938217	+	0.647604i
$983$	−46.3377	+	31.9846i	−1.47794	+	1.02015i	−0.488928	+	0.872324i	$0.662612\pi$
$983$	−46.3377	+	31.9846i	−1.47794	+	1.02015i	−0.989013	+	0.147825i	$0.952773\pi$
$984$	−37.5309	−	19.6977i	−1.19644	−	0.627940i
$985$	−0.0848966	+	0.699186i	−0.00270503	+	0.0222779i
$986$	−18.8257	−	12.9944i	−0.599532	−	0.413827i
$987$	−0.263992	−	0.382458i	−0.00840295	−	0.0121738i
$988$	25.9977	+	45.8478i	0.827096	+	1.45861i
$989$	−1.52178	+	2.20467i	−0.0483897	+	0.0701046i
$990$	−1.82869	+	0.693530i	−0.0581195	+	0.0220418i
$991$	16.1346			0.512532			0.256266	−	0.966606i	$-0.417508\pi$
$991$	16.1346			0.512532			0.256266	+	0.966606i	$0.417508\pi$
$992$	−24.8040			−0.787527
$993$	−15.4842	+	5.87238i	−0.491376	+	0.186354i
$994$	−0.0554482	−	0.224962i	−0.00175871	−	0.00713537i
$995$		−	3.42704i		−	0.108644i
$996$	−1.00018	+	4.05790i	−0.0316920	+	0.128579i
$997$	−5.40213	+	14.2442i	−0.171087	+	0.451120i	−0.992945	−	0.118572i	$-0.962168\pi$
$997$	−5.40213	+	14.2442i	−0.171087	+	0.451120i	0.821858	+	0.569692i	$0.192938\pi$
$998$	−56.1140	−	29.4509i	−1.77626	−	0.932251i
$999$	−3.21310	−	1.21857i	−0.101658	−	0.0385537i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.p.a.64.1	✓	168
169.103	even	26	inner	507.2.p.a.103.1	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.p.a.64.1	✓	168	1.1	even	1	trivial
507.2.p.a.103.1	yes	168	169.103	even	26	inner

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.p (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.32286 - 0.282046i) q^{2} +(-0.748511 + 0.663123i) q^{3} +(3.37425 + 0.831678i) q^{4} +(-0.0918625 - 0.175029i) q^{5} +(1.92572 - 1.32923i) q^{6} +(-0.0642964 - 0.0243844i) q^{7} +(-3.22762 - 1.22407i) q^{8} +(0.120537 - 0.992709i) q^{9} +(0.164018 + 0.432479i) q^{10} +(-4.19756 + 0.509676i) q^{11} +(-3.07717 + 1.61502i) q^{12} +(2.61965 - 2.47739i) q^{13} +(0.142474 + 0.0747762i) q^{14} +(0.184826 + 0.0700953i) q^{15} +(0.997726 + 0.523647i) q^{16} +(-0.724665 + 1.91078i) q^{17} +(-0.559980 + 2.27193i) q^{18} +4.20632i q^{19} +(-0.164399 - 0.666994i) q^{20} +(0.0642964 - 0.0243844i) q^{21} +9.89410 q^{22} -0.481984 q^{23} +(3.22762 - 1.22407i) q^{24} +(2.81813 - 4.08276i) q^{25} +(-6.78382 + 5.01576i) q^{26} +(0.568065 + 0.822984i) q^{27} +(-0.196672 - 0.135753i) q^{28} +(0.576613 - 4.74884i) q^{29} +(-0.409555 - 0.214951i) q^{30} +(-4.78369 + 3.30194i) q^{31} +(3.51189 + 2.42408i) q^{32} +(2.80394 - 3.16499i) q^{33} +(2.22223 - 4.23410i) q^{34} +(0.00163844 + 0.0134938i) q^{35} +(1.23234 - 3.24940i) q^{36} +(-2.82811 + 1.95210i) q^{37} +(1.18638 - 9.77070i) q^{38} +(-0.318025 + 3.59150i) q^{39} +(0.0822482 + 0.677375i) q^{40} +(-8.14240 - 9.19087i) q^{41} +(-0.156229 + 0.0385070i) q^{42} +(3.15732 - 4.57417i) q^{43} +(-14.5875 - 1.77124i) q^{44} +(-0.184826 + 0.0700953i) q^{45} +(1.11958 + 0.135942i) q^{46} +(-1.61732 - 6.56173i) q^{47} +(-1.09405 + 0.269659i) q^{48} +(-5.23604 - 4.63872i) q^{49} +(-7.69765 + 8.68885i) q^{50} +(-0.724665 - 1.91078i) q^{51} +(10.8997 - 6.18062i) q^{52} +(0.242681 - 0.639897i) q^{53} +(-1.08742 - 2.07190i) q^{54} +(0.474807 + 0.687876i) q^{55} +(0.177676 + 0.157407i) q^{56} +(-2.78931 - 3.14848i) q^{57} +(-2.67879 + 10.8683i) q^{58} +(-2.04396 - 3.89444i) q^{59} +(0.565353 + 0.390235i) q^{60} +(-2.13525 - 5.63019i) q^{61} +(12.0431 - 6.32073i) q^{62} +(-0.0319567 + 0.0608884i) q^{63} +(-9.16077 - 8.11573i) q^{64} +(-0.674263 - 0.230937i) q^{65} +(-7.40584 + 6.56100i) q^{66} +(-2.41701 - 9.80618i) q^{67} +(-4.03436 + 5.84478i) q^{68} +(0.360770 - 0.319614i) q^{69} -0.0318063i q^{70} +(-0.954864 - 1.07782i) q^{71} +(-1.60420 + 3.05654i) q^{72} +(-5.40032 + 0.655717i) q^{73} +(7.11988 - 3.73680i) q^{74} +(0.597974 + 4.92476i) q^{75} +(-3.49831 + 14.1932i) q^{76} +(0.282316 + 0.0695846i) q^{77} +(1.75170 - 8.25286i) q^{78} +(-6.75332 + 1.66454i) q^{79} -0.222735i q^{80} +(-0.970942 - 0.239316i) q^{81} +(16.3214 + 23.6457i) q^{82} +(0.797476 - 0.900164i) q^{83} +(0.237232 - 0.0288052i) q^{84} +(0.401013 - 0.0486918i) q^{85} +(-8.62415 + 9.73465i) q^{86} +(2.71746 + 3.93692i) q^{87} +(14.1720 + 3.49308i) q^{88} +5.70975i q^{89} +(0.449096 - 0.110692i) q^{90} +(-0.228844 + 0.0954084i) q^{91} +(-1.62633 - 0.400855i) q^{92} +(1.39105 - 5.64371i) q^{93} +(1.90610 + 15.6981i) q^{94} +(0.736230 - 0.386403i) q^{95} +(-4.23615 + 0.514362i) q^{96} +(4.54824 - 8.66595i) q^{97} +(10.8543 + 12.2519i) q^{98} +4.22839i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31}+ \cdots - 104 q^{98}+O(q^{100}) \) 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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