LMFDB - Embedded newform 50.2.e.a.39.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,2,Mod(9,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7]))

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

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

chi := DirichletCharacter("50.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$50 = 2 \cdot 5^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	50.e (of order $10$ , degree $4$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.399252010106$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - x^{6} + x^{4} - x^{2} + 1$ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.2
Root			$0.587785 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	50.39
Dual form			50.2.e.a.9.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 + 0.809017i) q^{2} +(0.166977 + 0.0542543i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.44575 - 1.70582i) q^{5} +(0.0542543 + 0.166977i) q^{6} +1.27346i q^{7} +(-0.951057 + 0.309017i) q^{8} +(-2.40211 - 1.74524i) q^{9} +(0.530249 - 2.17229i) q^{10} +(3.52874 - 2.56378i) q^{11} +(-0.103198 + 0.142040i) q^{12} +(-2.51812 + 3.46589i) q^{13} +(-1.03025 + 0.748520i) q^{14} +(-0.148859 - 0.363271i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.0930960 + 0.0302487i) q^{17} -2.96917i q^{18} +(0.103198 + 0.317610i) q^{19} +(2.06909 - 0.847859i) q^{20} +(-0.0690905 + 0.212639i) q^{21} +(4.14828 + 1.34786i) q^{22} +(3.71113 + 5.10793i) q^{23} -0.175571 q^{24} +(-0.819639 + 4.93236i) q^{25} -4.28408 q^{26} +(-0.616005 - 0.847859i) q^{27} +(-1.21113 - 0.393520i) q^{28} +(1.44575 - 4.44955i) q^{29} +(0.206396 - 0.333955i) q^{30} +(2.48459 + 7.64677i) q^{31} -1.00000i q^{32} +(0.728316 - 0.236644i) q^{33} +(-0.0791922 - 0.0575365i) q^{34} +(2.17229 - 1.84110i) q^{35} +(2.40211 - 1.74524i) q^{36} +(2.41492 - 3.32385i) q^{37} +(-0.196294 + 0.270175i) q^{38} +(-0.608509 + 0.442107i) q^{39} +(1.90211 + 1.17557i) q^{40} +(-9.24846 - 6.71940i) q^{41} +(-0.212639 + 0.0690905i) q^{42} -10.2093i q^{43} +(1.34786 + 4.14828i) q^{44} +(0.495785 + 6.62074i) q^{45} +(-1.95106 + 6.00473i) q^{46} +(-11.1323 - 3.61710i) q^{47} +(-0.103198 - 0.142040i) q^{48} +5.37831 q^{49} +(-4.47214 + 2.23607i) q^{50} -0.0171861 q^{51} +(-2.51812 - 3.46589i) q^{52} +(-0.841616 - 0.273457i) q^{53} +(0.323853 - 0.996718i) q^{54} +(-9.47501 - 2.31282i) q^{55} +(-0.393520 - 1.21113i) q^{56} +0.0586326i q^{57} +(4.44955 - 1.44575i) q^{58} +(6.15537 + 4.47214i) q^{59} +(0.391491 - 0.0293163i) q^{60} +(1.35645 - 0.985520i) q^{61} +(-4.72597 + 6.50473i) q^{62} +(2.22249 - 3.05899i) q^{63} +(0.809017 - 0.587785i) q^{64} +(9.55275 - 0.715345i) q^{65} +(0.619543 + 0.450124i) q^{66} +(1.11179 - 0.361243i) q^{67} -0.0978870i q^{68} +(0.342548 + 1.05425i) q^{69} +(2.76632 + 0.675249i) q^{70} +(-0.728373 + 2.24170i) q^{71} +(2.82385 + 0.917526i) q^{72} +(-0.945424 - 1.30127i) q^{73} +4.10851 q^{74} +(-0.404463 + 0.779124i) q^{75} -0.333955 q^{76} +(3.26486 + 4.49370i) q^{77} +(-0.715345 - 0.232430i) q^{78} +(-2.51358 + 7.73601i) q^{79} +(0.166977 + 2.22982i) q^{80} +(2.69572 + 8.29657i) q^{81} -11.4317i q^{82} +(7.05722 - 2.29303i) q^{83} +(-0.180881 - 0.131418i) q^{84} +(0.186192 + 0.115073i) q^{85} +(8.25950 - 6.00088i) q^{86} +(0.482814 - 0.664536i) q^{87} +(-2.56378 + 3.52874i) q^{88} +(1.38197 - 1.00406i) q^{89} +(-5.06488 + 4.29267i) q^{90} +(-4.41367 - 3.20672i) q^{91} +(-6.00473 + 1.95106i) q^{92} +1.41164i q^{93} +(-3.61710 - 11.1323i) q^{94} +(0.392588 - 0.635220i) q^{95} +(0.0542543 - 0.166977i) q^{96} +(6.28402 + 2.04180i) q^{97} +(3.16129 + 4.35114i) q^{98} -12.9508 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q + 2 q^{4} - 10 q^{5} + 2 q^{6} - 4 q^{9} - 4 q^{11} - 10 q^{12} - 4 q^{14} - 20 q^{15} - 2 q^{16} + 10 q^{17} + 10 q^{19} + 16 q^{21} + 20 q^{22} + 10 q^{23} + 8 q^{24} + 10 q^{25} - 28 q^{26} + 10 q^{28}+ \cdots - 28 q^{99}+O(q^{100})$ 8 * q + 2 * q^4 - 10 * q^5 + 2 * q^6 - 4 * q^9 - 4 * q^11 - 10 * q^12 - 4 * q^14 - 20 * q^15 - 2 * q^16 + 10 * q^17 + 10 * q^19 + 16 * q^21 + 20 * q^22 + 10 * q^23 + 8 * q^24 + 10 * q^25 - 28 * q^26 + 10 * q^28 + 10 * q^29 + 20 * q^30 + 6 * q^31 - 30 * q^33 - 4 * q^34 + 10 * q^35 + 4 * q^36 - 10 * q^37 - 8 * q^39 - 14 * q^41 - 10 * q^42 - 6 * q^44 + 10 * q^45 - 8 * q^46 - 30 * q^47 - 10 * q^48 - 16 * q^49 + 16 * q^51 - 20 * q^54 - 10 * q^55 + 4 * q^56 - 14 * q^61 + 20 * q^63 + 2 * q^64 + 50 * q^65 + 24 * q^66 + 10 * q^67 - 8 * q^69 - 34 * q^71 + 36 * q^74 + 10 * q^75 + 40 * q^77 + 20 * q^78 - 12 * q^81 + 50 * q^83 + 14 * q^84 - 20 * q^85 + 22 * q^86 + 20 * q^87 - 10 * q^88 + 20 * q^89 - 30 * q^90 - 4 * q^91 - 10 * q^92 - 24 * q^94 + 2 * q^96 - 20 * q^97 - 40 * q^98 - 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$ .

$n$	$27$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

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

)

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

$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$3$	0.166977	+	0.0542543i	0.0964045	+	0.0313237i	0.356822	−	0.934172i	$-0.383860\pi$
$3$	0.166977	+	0.0542543i	0.0964045	+	0.0313237i	−0.260418	+	0.965496i	$0.583860\pi$
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	−1.44575	−	1.70582i	−0.646557	−	0.762866i
$5$	−1.44575	−	1.70582i	−0.646557	−	0.762866i
$6$	0.0542543	+	0.166977i	0.0221492	+	0.0681683i
$7$			1.27346i			0.481322i	0.970609	+	0.240661i	$0.0773642\pi$
$7$			1.27346i			0.481322i	−0.970609	+	0.240661i	$0.922636\pi$
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$	−2.40211	−	1.74524i	−0.800704	−	0.581746i
$10$	0.530249	−	2.17229i	0.167679	−	0.686938i
$11$	3.52874	−	2.56378i	1.06396	−	0.773009i	0.0891391	−	0.996019i	$-0.471588\pi$
$11$	3.52874	−	2.56378i	1.06396	−	0.773009i	0.974816	+	0.223011i	$0.0715884\pi$
$12$	−0.103198	+	0.142040i	−0.0297906	+	0.0410033i
$13$	−2.51812	+	3.46589i	−0.698400	+	0.961266i	0.301569	+	0.953444i	$0.402490\pi$
$13$	−2.51812	+	3.46589i	−0.698400	+	0.961266i	−0.999969	+	0.00782134i	$0.997510\pi$
$14$	−1.03025	+	0.748520i	−0.275346	+	0.200050i
$15$	−0.148859	−	0.363271i	−0.0384352	−	0.0937962i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−0.0930960	+	0.0302487i	−0.0225791	+	0.00733640i	−0.320285	−	0.947321i	$-0.603779\pi$
$17$	−0.0930960	+	0.0302487i	−0.0225791	+	0.00733640i	0.297706	+	0.954658i	$0.403779\pi$
$18$		−	2.96917i		−	0.699841i
$19$	0.103198	+	0.317610i	0.0236752	+	0.0728647i	0.962196	−	0.272358i	$-0.0878034\pi$
$19$	0.103198	+	0.317610i	0.0236752	+	0.0728647i	−0.938521	+	0.345223i	$0.887803\pi$
$20$	2.06909	−	0.847859i	0.462663	−	0.189587i
$21$	−0.0690905	+	0.212639i	−0.0150768	+	0.0464016i
$22$	4.14828	+	1.34786i	0.884417	+	0.287364i
$23$	3.71113	+	5.10793i	0.773824	+	1.06508i	0.995937	+	0.0900565i	$0.0287048\pi$
$23$	3.71113	+	5.10793i	0.773824	+	1.06508i	−0.222113	+	0.975021i	$0.571295\pi$
$24$	−0.175571			−0.0358382
$25$	−0.819639	+	4.93236i	−0.163928	+	0.986472i
$26$	−4.28408			−0.840177
$27$	−0.616005	−	0.847859i	−0.118550	−	0.163170i
$28$	−1.21113	−	0.393520i	−0.228882	−	0.0743683i
$29$	1.44575	−	4.44955i	0.268468	−	0.826260i	−0.722406	−	0.691469i	$-0.756964\pi$
$29$	1.44575	−	4.44955i	0.268468	−	0.826260i	0.990874	−	0.134791i	$-0.0430363\pi$
$30$	0.206396	−	0.333955i	0.0376825	−	0.0609716i
$31$	2.48459	+	7.64677i	0.446245	+	1.37340i	0.881113	+	0.472907i	$0.156795\pi$
$31$	2.48459	+	7.64677i	0.446245	+	1.37340i	−0.434867	+	0.900494i	$0.643205\pi$
$32$		−	1.00000i		−	0.176777i
$33$	0.728316	−	0.236644i	0.126784	−	0.0411945i
$34$	−0.0791922	−	0.0575365i	−0.0135814	−	0.00986743i
$35$	2.17229	−	1.84110i	0.367184	−	0.311202i
$36$	2.40211	−	1.74524i	0.400352	−	0.290873i
$37$	2.41492	−	3.32385i	0.397011	−	0.546438i	−0.562980	−	0.826470i	$-0.690345\pi$
$37$	2.41492	−	3.32385i	0.397011	−	0.546438i	0.959991	+	0.280032i	$0.0903452\pi$
$38$	−0.196294	+	0.270175i	−0.0318431	+	0.0438282i
$39$	−0.608509	+	0.442107i	−0.0974393	+	0.0707938i
$40$	1.90211	+	1.17557i	0.300750	+	0.185874i
$41$	−9.24846	−	6.71940i	−1.44437	−	1.04939i	−0.987107	−	0.160061i	$-0.948831\pi$
$41$	−9.24846	−	6.71940i	−1.44437	−	1.04939i	−0.457260	−	0.889333i	$-0.651169\pi$
$42$	−0.212639	+	0.0690905i	−0.0328109	+	0.0106609i
$43$		−	10.2093i		−	1.55690i	−0.627704	−	0.778452i	$-0.716005\pi$
$43$		−	10.2093i		−	1.55690i	0.627704	−	0.778452i	$-0.283995\pi$
$44$	1.34786	+	4.14828i	0.203197	+	0.625377i
$45$	0.495785	+	6.62074i	0.0739073	+	0.986962i
$46$	−1.95106	+	6.00473i	−0.287668	+	0.885350i
$47$	−11.1323	−	3.61710i	−1.62381	−	0.527608i	−0.650975	−	0.759099i	$-0.725640\pi$
$47$	−11.1323	−	3.61710i	−1.62381	−	0.527608i	−0.972837	+	0.231491i	$0.925640\pi$
$48$	−0.103198	−	0.142040i	−0.0148953	−	0.0205016i
$49$	5.37831			0.768329
$50$	−4.47214	+	2.23607i	−0.632456	+	0.316228i
$51$	−0.0171861			−0.00240653
$52$	−2.51812	−	3.46589i	−0.349200	−	0.480633i
$53$	−0.841616	−	0.273457i	−0.115605	−	0.0375623i	0.250643	−	0.968079i	$-0.419358\pi$
$53$	−0.841616	−	0.273457i	−0.115605	−	0.0375623i	−0.366248	+	0.930517i	$0.619358\pi$
$54$	0.323853	−	0.996718i	0.0440708	−	0.135636i
$55$	−9.47501	−	2.31282i	−1.27761	−	0.311860i
$56$	−0.393520	−	1.21113i	−0.0525863	−	0.161844i
$57$			0.0586326i			0.00776608i
$58$	4.44955	−	1.44575i	0.584254	−	0.189836i
$59$	6.15537	+	4.47214i	0.801361	+	0.582223i	0.911313	−	0.411714i	$-0.135070\pi$
$59$	6.15537	+	4.47214i	0.801361	+	0.582223i	−0.109952	+	0.993937i	$0.535070\pi$
$60$	0.391491	−	0.0293163i	0.0505413	−	0.00378472i
$61$	1.35645	−	0.985520i	0.173676	−	0.126183i	−0.497551	−	0.867434i	$-0.665767\pi$
$61$	1.35645	−	0.985520i	0.173676	−	0.126183i	0.671227	+	0.741252i	$0.265767\pi$
$62$	−4.72597	+	6.50473i	−0.600198	+	0.826102i
$63$	2.22249	−	3.05899i	0.280007	−	0.385396i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	9.55275	−	0.715345i	1.18487	−	0.0887276i
$66$	0.619543	+	0.450124i	0.0762604	+	0.0554064i
$67$	1.11179	−	0.361243i	0.135827	−	0.0441328i	−0.240315	−	0.970695i	$-0.577251\pi$
$67$	1.11179	−	0.361243i	0.135827	−	0.0441328i	0.376142	+	0.926562i	$0.377251\pi$
$68$		−	0.0978870i		−	0.0118705i
$69$	0.342548	+	1.05425i	0.0412379	+	0.126917i
$70$	2.76632	+	0.675249i	0.330638	+	0.0807077i
$71$	−0.728373	+	2.24170i	−0.0864419	+	0.266041i	−0.984929	−	0.172959i	$-0.944667\pi$
$71$	−0.728373	+	2.24170i	−0.0864419	+	0.266041i	0.898487	+	0.439000i	$0.144667\pi$
$72$	2.82385	+	0.917526i	0.332794	+	0.108131i
$73$	−0.945424	−	1.30127i	−0.110654	−	0.152302i	0.750098	−	0.661326i	$-0.230006\pi$
$73$	−0.945424	−	1.30127i	−0.110654	−	0.152302i	−0.860752	+	0.509025i	$0.830006\pi$
$74$	4.10851			0.477604
$75$	−0.404463	+	0.779124i	−0.0467033	+	0.0899655i
$76$	−0.333955			−0.0383073
$77$	3.26486	+	4.49370i	0.372066	+	0.512105i
$78$	−0.715345	−	0.232430i	−0.0809968	−	0.0263175i
$79$	−2.51358	+	7.73601i	−0.282800	+	0.870369i	0.704249	+	0.709953i	$0.251284\pi$
$79$	−2.51358	+	7.73601i	−0.282800	+	0.870369i	−0.987049	+	0.160417i	$0.948716\pi$
$80$	0.166977	+	2.22982i	0.0186686	+	0.249302i
$81$	2.69572	+	8.29657i	0.299524	+	0.921841i
$82$		−	11.4317i		−	1.26242i
$83$	7.05722	−	2.29303i	0.774630	−	0.251693i	0.105084	−	0.994463i	$-0.466489\pi$
$83$	7.05722	−	2.29303i	0.774630	−	0.251693i	0.669546	+	0.742771i	$0.266489\pi$
$84$	−0.180881	−	0.131418i	−0.0197358	−	0.0143389i
$85$	0.186192	+	0.115073i	0.0201954	+	0.0124814i
$86$	8.25950	−	6.00088i	0.890644	−	0.647091i
$87$	0.482814	−	0.664536i	0.0517631	−	0.0712458i
$88$	−2.56378	+	3.52874i	−0.273300	+	0.376165i
$89$	1.38197	−	1.00406i	0.146488	−	0.106430i	−0.512127	−	0.858910i	$-0.671142\pi$
$89$	1.38197	−	1.00406i	0.146488	−	0.106430i	0.658615	+	0.752480i	$0.271142\pi$
$90$	−5.06488	+	4.29267i	−0.533885	+	0.452487i
$91$	−4.41367	−	3.20672i	−0.462678	−	0.336155i
$92$	−6.00473	+	1.95106i	−0.626037	+	0.203412i
$93$			1.41164i			0.146380i
$94$	−3.61710	−	11.1323i	−0.373076	−	1.14821i
$95$	0.392588	−	0.635220i	0.0402786	−	0.0651722i
$96$	0.0542543	−	0.166977i	0.00553730	−	0.0170421i
$97$	6.28402	+	2.04180i	0.638046	+	0.207314i	0.610136	−	0.792297i	$-0.291115\pi$
$97$	6.28402	+	2.04180i	0.638046	+	0.207314i	0.0279099	+	0.999610i	$0.491115\pi$
$98$	3.16129	+	4.35114i	0.319338	+	0.439532i
$99$	−12.9508			−1.30161
$100$	−4.43767	−	2.30371i	−0.443767	−	0.230371i
$101$	−7.02311			−0.698825			−0.349413	−	0.936969i	$-0.613619\pi$
$101$	−7.02311			−0.698825			−0.349413	+	0.936969i	$0.613619\pi$
$102$	−0.0101017	−	0.0139038i	−0.00100022	−	0.00137668i
$103$	−12.1228	−	3.93893i	−1.19449	−	0.388114i	−0.356760	−	0.934196i	$-0.616119\pi$
$103$	−12.1228	−	3.93893i	−1.19449	−	0.388114i	−0.837732	+	0.546082i	$0.816119\pi$
$104$	1.32385	−	4.07440i	0.129814	−	0.399528i
$105$	0.462611	−	0.189566i	0.0451462	−	0.0184997i
$106$	−0.273457	−	0.841616i	−0.0265605	−	0.0817449i
$107$			12.2022i			1.17963i	0.807537	+	0.589817i	$0.200800\pi$
$107$			12.2022i			1.17963i	−0.807537	+	0.589817i	$0.799200\pi$
$108$	0.996718	−	0.323853i	0.0959092	−	0.0311628i
$109$	−4.08628	−	2.96885i	−0.391394	−	0.284365i	0.374632	−	0.927173i	$-0.377769\pi$
$109$	−4.08628	−	2.96885i	−0.391394	−	0.284365i	−0.766027	+	0.642809i	$0.777769\pi$
$110$	−3.69816	−	9.02488i	−0.352606	−	0.860489i
$111$	0.583571	−	0.423989i	0.0553901	−	0.0402432i
$112$	0.748520	−	1.03025i	0.0707284	−	0.0973494i
$113$	−8.24962	+	11.3546i	−0.776059	+	1.06815i	0.219647	+	0.975579i	$0.429509\pi$
$113$	−8.24962	+	11.3546i	−0.776059	+	1.06815i	−0.995706	+	0.0925736i	$0.970491\pi$
$114$	−0.0474348	+	0.0344634i	−0.00444268	+	0.00322779i
$115$	3.34786	−	13.7153i	0.312189	−	1.27896i
$116$	3.78501	+	2.74997i	0.351429	+	0.255328i
$117$	12.0976	−	3.93075i	1.11842	−	0.363398i
$118$			7.60845i			0.700415i
$119$	−0.0385205	−	0.118554i	−0.00353117	−	0.0108678i
$120$	0.253830	+	0.299492i	0.0231714	+	0.0273397i
$121$	2.47985	−	7.63220i	0.225441	−	0.693837i
$122$	1.59460	+	0.518118i	0.144369	+	0.0469082i
$123$	−1.17973	−	1.62376i	−0.106373	−	0.146409i
$124$	−8.04029			−0.722040
$125$	9.59871	−	5.73279i	0.858534	−	0.512756i
$126$	3.78112			0.336849
$127$	0.775266	+	1.06706i	0.0687937	+	0.0946864i	0.842027	−	0.539435i	$-0.181362\pi$
$127$	0.775266	+	1.06706i	0.0687937	+	0.0946864i	−0.773234	+	0.634121i	$0.781362\pi$
$128$	0.951057	+	0.309017i	0.0840623	+	0.0273135i
$129$	0.553898	−	1.70472i	0.0487680	−	0.150093i
$130$	6.19369	+	7.30786i	0.543222	+	0.640942i
$131$	−0.550197	−	1.69333i	−0.0480710	−	0.147947i	0.924140	−	0.382054i	$-0.124783\pi$
$131$	−0.550197	−	1.69333i	−0.0480710	−	0.147947i	−0.972211	+	0.234107i	$0.924783\pi$
$132$			0.765797i			0.0666541i
$133$	−0.404463	+	0.131418i	−0.0350714	+	0.0113954i
$134$	0.945746	+	0.687124i	0.0817000	+	0.0593585i
$135$	−0.555707	+	2.27658i	−0.0478276	+	0.195937i
$136$	0.0791922	−	0.0575365i	0.00679068	−	0.00493372i
$137$	5.61986	−	7.73508i	0.480137	−	0.660852i	−0.498394	−	0.866951i	$-0.666077\pi$
$137$	5.61986	−	7.73508i	0.480137	−	0.660852i	0.978531	+	0.206098i	$0.0660767\pi$
$138$	−0.651565	+	0.896802i	−0.0554649	+	0.0763409i
$139$	−3.72123	+	2.70363i	−0.315631	+	0.229319i	−0.734309	−	0.678816i	$-0.762494\pi$
$139$	−3.72123	+	2.70363i	−0.315631	+	0.229319i	0.418678	+	0.908135i	$0.362494\pi$
$140$	1.07971	+	2.63490i	0.0912523	+	0.222690i
$141$	−1.66260	−	1.20795i	−0.140016	−	0.101728i
$142$	−2.24170	+	0.728373i	−0.188119	+	0.0611237i
$143$			18.6861i			1.56261i
$144$	0.917526	+	2.82385i	0.0764605	+	0.235321i
$145$	−9.68031	+	3.96673i	−0.803906	+	0.329419i
$146$	0.497039	−	1.52973i	0.0411352	−	0.126601i
$147$	0.898056	+	0.291796i	0.0740704	+	0.0240669i
$148$	2.41492	+	3.32385i	0.198505	+	0.273219i
$149$	−2.03186			−0.166457			−0.0832284	−	0.996530i	$-0.526523\pi$
$149$	−2.03186			−0.166457			−0.0832284	+	0.996530i	$0.526523\pi$
$150$	−0.868062	+	0.130741i	−0.0708770	+	0.0106749i
$151$	18.9655			1.54339			0.771696	−	0.635992i	$-0.219409\pi$
$151$	18.9655			1.54339			0.771696	+	0.635992i	$0.219409\pi$
$152$	−0.196294	−	0.270175i	−0.0159215	−	0.0219141i
$153$	0.276418	+	0.0898138i	0.0223471	+	0.00726101i
$154$	−1.71644	+	5.28266i	−0.138315	+	0.425689i
$155$	9.45193	−	15.2935i	0.759197	−	1.22841i
$156$	−0.232430	−	0.715345i	−0.0186093	−	0.0572734i
$157$			14.2430i			1.13672i	0.822781	+	0.568359i	$0.192421\pi$
$157$			14.2430i			1.13672i	−0.822781	+	0.568359i	$0.807579\pi$
$158$	−7.73601	+	2.51358i	−0.615444	+	0.199970i
$159$	−0.125695	−	0.0913225i	−0.00996823	−	0.00724234i
$160$	−1.70582	+	1.44575i	−0.134857	+	0.114296i
$161$	−6.50473	+	4.72597i	−0.512645	+	0.372458i
$162$	−5.12756	+	7.05748i	−0.402859	+	0.554488i
$163$	11.5880	−	15.9495i	0.907641	−	1.24926i	−0.0603249	−	0.998179i	$-0.519214\pi$
$163$	11.5880	−	15.9495i	0.907641	−	1.24926i	0.967966	−	0.251082i	$-0.0807863\pi$
$164$	9.24846	−	6.71940i	0.722184	−	0.524697i
$165$	−1.45663	−	0.900248i	−0.113399	−	0.0700842i
$166$	6.00323	+	4.36160i	0.465941	+	0.338526i
$167$	−5.49885	+	1.78668i	−0.425514	+	0.138258i	−0.513942	−	0.857825i	$-0.671815\pi$
$167$	−5.49885	+	1.78668i	−0.425514	+	0.138258i	0.0884287	+	0.996083i	$0.471815\pi$
$168$		−	0.223582i		−	0.0172497i
$169$	−1.65427	−	5.09132i	−0.127252	−	0.391640i
$170$	0.0163449	+	0.218271i	0.00125360	+	0.0167406i
$171$	0.306412	−	0.943040i	0.0234319	−	0.0721161i
$172$	9.70962	+	3.15485i	0.740352	+	0.240555i
$173$	−6.18806	−	8.51713i	−0.470469	−	0.647545i	0.506169	−	0.862434i	$-0.331061\pi$
$173$	−6.18806	−	8.51713i	−0.470469	−	0.647545i	−0.976639	+	0.214889i	$0.931061\pi$
$174$	0.821412			0.0622711
$175$	−6.28115	−	1.04377i	−0.474811	−	0.0789020i
$176$	−4.36176			−0.328780
$177$	0.785175	+	1.08070i	0.0590174	+	0.0812305i
$178$	1.62460	+	0.527864i	0.121769	+	0.0395651i
$179$	−3.35558	+	10.3274i	−0.250808	+	0.771906i	0.743819	+	0.668381i	$0.233012\pi$
$179$	−3.35558	+	10.3274i	−0.250808	+	0.771906i	−0.994627	+	0.103525i	$0.966988\pi$
$180$	−6.44990	−	1.57440i	−0.480747	−	0.117349i
$181$	−3.17848	−	9.78234i	−0.236254	−	0.727116i	−0.996953	−	0.0780101i	$-0.975143\pi$
$181$	−3.17848	−	9.78234i	−0.236254	−	0.727116i	0.760698	−	0.649106i	$-0.224857\pi$
$182$		−	5.45559i		−	0.404395i
$183$	0.279966	−	0.0909663i	0.0206956	−	0.00672442i
$184$	−5.10793	−	3.71113i	−0.376562	−	0.273588i
$185$	−9.16125	+	0.686028i	−0.673549	+	0.0504378i
$186$	−1.14204	+	0.829740i	−0.0837384	+	0.0608395i
$187$	−0.250961	+	0.345418i	−0.0183521	+	0.0252594i
$188$	6.88014	−	9.46969i	0.501785	−	0.690648i
$189$	1.07971	−	0.784457i	0.0785375	−	0.0570608i
$190$	0.744661	−	0.0557630i	0.0540234	−	0.00404547i
$191$	7.79944	+	5.66662i	0.564347	+	0.410022i	0.833047	−	0.553202i	$-0.186594\pi$
$191$	7.79944	+	5.66662i	0.564347	+	0.410022i	−0.268700	+	0.963224i	$0.586594\pi$
$192$	0.166977	−	0.0542543i	0.0120506	−	0.00391546i
$193$		−	6.00000i		−	0.431889i	−0.976406	−	0.215945i	$-0.930717\pi$
$193$		−	6.00000i		−	0.431889i	0.976406	−	0.215945i	$-0.0692831\pi$
$194$	2.04180	+	6.28402i	0.146593	+	0.451167i
$195$	1.63390	+	0.398831i	0.117006	+	0.0285609i
$196$	−1.66199	+	5.11507i	−0.118713	+	0.365362i
$197$	−19.7330	−	6.41164i	−1.40592	−	0.456810i	−0.494818	−	0.868997i	$-0.664765\pi$
$197$	−19.7330	−	6.41164i	−1.40592	−	0.456810i	−0.911100	+	0.412186i	$0.864765\pi$
$198$	−7.61231	−	10.4774i	−0.540983	−	0.744600i
$199$	19.0629			1.35133			0.675666	−	0.737208i	$-0.263856\pi$
$199$	19.0629			1.35133			0.675666	+	0.737208i	$0.263856\pi$
$200$	−0.744661	−	4.94424i	−0.0526555	−	0.349610i
$201$	0.205243			0.0144767
$202$	−4.12808	−	5.68181i	−0.290451	−	0.399771i
$203$	5.66631	+	1.84110i	0.397697	+	0.129220i
$204$	0.00531079	−	0.0163449i	0.000371829	−	0.00114437i
$205$	1.90884	+	25.4908i	0.133319	+	1.78035i
$206$	−3.93893	−	12.1228i	−0.274438	−	0.844633i
$207$		−	18.7466i		−	1.30298i
$208$	4.07440	−	1.32385i	0.282509	−	0.0917927i
$209$	1.17844	+	0.856187i	0.0815144	+	0.0592237i
$210$	0.425277	+	0.262836i	0.0293469	+	0.0181374i
$211$	−13.7691	+	10.0039i	−0.947906	+	0.688694i	−0.950311	−	0.311303i	$-0.899235\pi$
$211$	−13.7691	+	10.0039i	−0.947906	+	0.688694i	0.00240468	+	0.999997i	$0.499235\pi$
$212$	0.520147	−	0.715921i	0.0357238	−	0.0491697i
$213$	−0.243244	+	0.334796i	−0.0166668	+	0.0229399i
$214$	−9.87181	+	7.17229i	−0.674823	+	0.490288i
$215$	−17.4152	+	14.7601i	−1.18771	+	1.00663i
$216$	0.847859	+	0.616005i	0.0576895	+	0.0419139i
$217$	−9.73784	+	3.16402i	−0.661048	+	0.214787i
$218$		−	5.05092i		−	0.342091i
$219$	−0.0872654	−	0.268575i	−0.00589685	−	0.0181486i
$220$	5.12756	−	8.29657i	0.345700	−	0.559354i
$221$	0.129588	−	0.398831i	0.00871703	−	0.0268283i
$222$	0.686028	+	0.222904i	0.0460432	+	0.0149603i
$223$	2.92595	+	4.02723i	0.195936	+	0.269683i	0.895669	−	0.444722i	$-0.146697\pi$
$223$	2.92595	+	4.02723i	0.195936	+	0.269683i	−0.699732	+	0.714405i	$0.746697\pi$
$224$	1.27346			0.0850865
$225$	10.5770	−	10.4176i	0.705134	−	0.694508i
$226$	−14.0351			−0.933600
$227$	0.603519	+	0.830673i	0.0400570	+	0.0551337i	0.828576	−	0.559877i	$-0.189152\pi$
$227$	0.603519	+	0.830673i	0.0400570	+	0.0551337i	−0.788519	+	0.615011i	$0.789152\pi$
$228$	−0.0557630	−	0.0181185i	−0.00369299	−	0.00119993i
$229$	1.26236	−	3.88514i	0.0834189	−	0.256737i	−0.900644	−	0.434558i	$-0.856905\pi$
$229$	1.26236	−	3.88514i	0.0834189	−	0.256737i	0.984063	+	0.177821i	$0.0569047\pi$
$230$	13.0637	−	5.35317i	0.861396	−	0.352978i
$231$	0.301356	+	0.927480i	0.0198278	+	0.0610237i
$232$			4.67853i			0.307161i
$233$	−4.19681	+	1.36363i	−0.274942	+	0.0893342i	−0.443243	−	0.896402i	$-0.646172\pi$
$233$	−4.19681	+	1.36363i	−0.274942	+	0.0893342i	0.168301	+	0.985736i	$0.446172\pi$
$234$	10.2908	+	7.47673i	0.672733	+	0.488769i
$235$	9.92435	+	24.2191i	0.647393	+	1.57988i
$236$	−6.15537	+	4.47214i	−0.400680	+	0.291111i
$237$	−0.839423	+	1.15537i	−0.0545264	+	0.0750492i
$238$	0.0732703	−	0.100848i	0.00474941	−	0.00653700i
$239$	17.5979	−	12.7856i	1.13831	−	0.827032i	0.151428	−	0.988468i	$-0.451613\pi$
$239$	17.5979	−	12.7856i	1.13831	−	0.827032i	0.986883	+	0.161437i	$0.0516128\pi$
$240$	−0.0930960	+	0.381390i	−0.00600932	+	0.0246186i
$241$	12.8328	+	9.32358i	0.826633	+	0.600584i	0.918605	−	0.395177i	$-0.129317\pi$
$241$	12.8328	+	9.32358i	0.826633	+	0.600584i	−0.0919714	+	0.995762i	$0.529317\pi$
$242$	7.63220	−	2.47985i	0.490617	−	0.159411i
$243$			4.67563i			0.299942i
$244$	0.518118	+	1.59460i	0.0331691	+	0.102084i
$245$	−7.77566	−	9.17442i	−0.496769	−	0.586132i
$246$	0.620220	−	1.90884i	0.0395438	−	0.121703i
$247$	−1.36067	−	0.442107i	−0.0865771	−	0.0281306i
$248$	−4.72597	−	6.50473i	−0.300099	−	0.413051i
$249$	1.30280			0.0825618
$250$	10.2799	+	4.39587i	0.650158	+	0.278019i
$251$	−8.49087			−0.535939			−0.267970	−	0.963427i	$-0.586353\pi$
$251$	−8.49087			−0.535939			−0.267970	+	0.963427i	$0.586353\pi$
$252$	2.22249	+	3.05899i	0.140003	+	0.192698i
$253$	26.1912	+	8.51005i	1.64663	+	0.535022i
$254$	−0.407581	+	1.25441i	−0.0255739	+	0.0787085i
$255$	0.0248467	+	0.0293163i	0.00155596	+	0.00183586i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$		−	9.98572i		−	0.622892i	−0.950264	−	0.311446i	$-0.899187\pi$
$257$		−	9.98572i		−	0.622892i	0.950264	−	0.311446i	$-0.100813\pi$
$258$	1.70472	−	0.553898i	0.106131	−	0.0344842i
$259$	4.23279	+	3.07530i	0.263013	+	0.191090i
$260$	−2.27163	+	9.30625i	−0.140880	+	0.577149i
$261$	−11.2384	+	8.16515i	−0.695637	+	0.505410i
$262$	1.04654	−	1.44043i	0.0646553	−	0.0889904i
$263$	4.54612	−	6.25720i	0.280326	−	0.385836i	−0.645516	−	0.763747i	$-0.723358\pi$
$263$	4.54612	−	6.25720i	0.280326	−	0.385836i	0.925842	+	0.377911i	$0.123358\pi$
$264$	−0.619543	+	0.450124i	−0.0381302	+	0.0277032i
$265$	0.750293	+	1.83099i	0.0460901	+	0.112477i
$266$	−0.344057	−	0.249972i	−0.0210955	−	0.0153268i
$267$	0.285232	−	0.0926774i	0.0174559	−	0.00567176i
$268$			1.16901i			0.0714084i
$269$	2.26777	+	6.97948i	0.138268	+	0.425546i	0.996084	−	0.0884112i	$-0.0281790\pi$
$269$	2.26777	+	6.97948i	0.138268	+	0.425546i	−0.857816	+	0.513957i	$0.828179\pi$
$270$	−2.16843	+	0.888565i	−0.131966	+	0.0540764i
$271$	4.10960	−	12.6481i	0.249641	−	0.768315i	−0.745198	−	0.666844i	$-0.767645\pi$
$271$	4.10960	−	12.6481i	0.249641	−	0.768315i	0.994838	−	0.101472i	$-0.0323551\pi$
$272$	0.0930960	+	0.0302487i	0.00564478	+	0.00183410i
$273$	−0.563005	−	0.774910i	−0.0340746	−	0.0468997i
$274$	9.56108			0.577606
$275$	9.75320	+	19.5064i	0.588140	+	1.17628i
$276$	−1.10851			−0.0667244
$277$	−11.5165	−	15.8511i	−0.691959	−	0.952399i	−0.999999	−	0.00102623i	$-0.999673\pi$
$277$	−11.5165	−	15.8511i	−0.691959	−	0.952399i	0.308041	−	0.951373i	$-0.400327\pi$
$278$	−4.37457	−	1.42138i	−0.262369	−	0.0852489i
$279$	7.37718	−	22.7046i	0.441660	−	1.35929i
$280$	−1.49704	+	2.42226i	−0.0894652	+	0.144758i
$281$	−3.55571	−	10.9433i	−0.212116	−	0.652825i	−0.999346	−	0.0361656i	$-0.988486\pi$
$281$	−3.55571	−	10.9433i	−0.212116	−	0.652825i	0.787230	−	0.616659i	$-0.211514\pi$
$282$		−	2.05509i		−	0.122379i
$283$	−18.6927	+	6.07363i	−1.11117	+	0.361040i	−0.806390	−	0.591384i	$-0.798582\pi$
$283$	−18.6927	+	6.07363i	−1.11117	+	0.361040i	−0.304776	+	0.952424i	$0.598582\pi$
$284$	−1.90690	−	1.38545i	−0.113154	−	0.0822111i
$285$	0.100017	−	0.0847679i	0.00592448	−	0.00502122i
$286$	−15.1174	+	10.9834i	−0.893911	+	0.649464i
$287$	8.55687	−	11.7775i	0.505096	−	0.695205i
$288$	−1.74524	+	2.40211i	−0.102839	+	0.141546i
$289$	−13.7455	+	9.98672i	−0.808561	+	0.587454i
$290$	−8.89910	−	5.49994i	−0.522573	−	0.322968i
$291$	0.938514	+	0.681870i	0.0550166	+	0.0399719i
$292$	1.52973	−	0.497039i	0.0895206	−	0.0290870i
$293$		−	6.12203i		−	0.357653i	−0.983881	−	0.178827i	$-0.942770\pi$
$293$		−	6.12203i		−	0.357653i	0.983881	−	0.178827i	$-0.0572301\pi$
$294$	0.291796	+	0.898056i	0.0170179	+	0.0523757i
$295$	−1.27044	−	16.9655i	−0.0739679	−	0.987770i
$296$	−1.26960	+	3.90742i	−0.0737939	+	0.227114i
$297$	−4.34745	−	1.41257i	−0.252264	−	0.0819657i
$298$	−1.19430	−	1.64381i	−0.0691839	−	0.0952235i
$299$	−27.0486			−1.56426
$300$	−0.616005	−	0.625430i	−0.0355651	−	0.0361092i
$301$	13.0011			0.749371
$302$	11.1477	+	15.3434i	0.641475	+	0.882915i
$303$	−1.17270	−	0.381034i	−0.0673699	−	0.0218898i
$304$	0.103198	−	0.317610i	0.00591880	−	0.0182162i
$305$	−3.64220	−	0.889050i	−0.208552	−	0.0509069i
$306$	0.0898138	+	0.276418i	0.00513431	+	0.0158018i
$307$			14.1935i			0.810064i	0.914302	+	0.405032i	$0.132740\pi$
$307$			14.1935i			0.810064i	−0.914302	+	0.405032i	$0.867260\pi$
$308$	−5.28266	+	1.71644i	−0.301008	+	0.0978033i
$309$	−1.81053	−	1.31542i	−0.102997	−	0.0748319i
$310$	17.9284	−	1.34255i	1.01827	−	0.0762516i
$311$	−5.81375	+	4.22394i	−0.329668	+	0.239518i	−0.740290	−	0.672288i	$-0.765312\pi$
$311$	−5.81375	+	4.22394i	−0.329668	+	0.239518i	0.410622	+	0.911806i	$0.365312\pi$
$312$	0.442107	−	0.608509i	0.0250294	−	0.0344500i
$313$	−0.367741	+	0.506152i	−0.0207859	+	0.0286094i	−0.819283	−	0.573389i	$-0.805629\pi$
$313$	−0.367741	+	0.506152i	−0.0207859	+	0.0286094i	0.798498	+	0.601998i	$0.205629\pi$
$314$	−11.5229	+	8.37184i	−0.650272	+	0.472450i
$315$	−8.43123	+	0.631362i	−0.475046	+	0.0355732i
$316$	−6.58064	−	4.78112i	−0.370190	−	0.268959i
$317$	6.85717	−	2.22803i	0.385137	−	0.125139i	−0.110048	−	0.993926i	$-0.535100\pi$
$317$	6.85717	−	2.22803i	0.385137	−	0.125139i	0.495185	+	0.868788i	$0.335100\pi$
$318$		−	0.155367i		−	0.00871255i
$319$	−6.30600	−	19.4079i	−0.353068	−	1.08663i
$320$	−2.17229	−	0.530249i	−0.121435	−	0.0296418i
$321$	−0.662023	+	2.03750i	−0.0369505	+	0.113722i
$322$	−7.64677	−	2.48459i	−0.426138	−	0.138461i
$323$	−0.0192146	−	0.0264466i	−0.00106913	−	0.00147153i
$324$	−8.72353			−0.484640
$325$	−15.0311	−	15.2611i	−0.833775	−	0.846531i
$326$	19.7147			1.09189
$327$	−0.521243	−	0.717430i	−0.0288248	−	0.0396739i
$328$	10.8722	+	3.53260i	0.600318	+	0.195055i
$329$	4.60623	−	14.1765i	0.253949	−	0.781576i
$330$	−0.127871	−	1.70759i	−0.00703906	−	0.0939999i
$331$	−7.48266	−	23.0292i	−0.411284	−	1.26580i	−0.915533	−	0.402244i	$-0.868231\pi$
$331$	−7.48266	−	23.0292i	−0.411284	−	1.26580i	0.504249	−	0.863558i	$-0.331769\pi$
$332$			7.42040i			0.407247i
$333$	−11.6018	+	3.76966i	−0.635776	+	0.206576i
$334$	−4.67760	−	3.39847i	−0.255947	−	0.185956i
$335$	−2.22358	−	1.37425i	−0.121487	−	0.0750832i
$336$	0.180881	−	0.131418i	0.00986788	−	0.00716944i
$337$	−13.0498	+	17.9615i	−0.710866	+	0.978423i	0.288912	+	0.957356i	$0.406706\pi$
$337$	−13.0498	+	17.9615i	−0.710866	+	0.978423i	−0.999778	+	0.0210674i	$0.993294\pi$
$338$	3.14661	−	4.33094i	0.171153	−	0.235572i
$339$	−1.99354	+	1.44839i	−0.108274	+	0.0786657i
$340$	−0.166977	+	0.141520i	−0.00905562	+	0.00767498i
$341$	28.3721	+	20.6135i	1.53644	+	1.11629i
$342$	0.943040	−	0.306412i	0.0509937	−	0.0165689i
$343$			15.7632i			0.851135i
$344$	3.15485	+	9.70962i	0.170098	+	0.523508i
$345$	1.30313	−	2.10851i	0.0701582	−	0.113518i
$346$	3.25325	−	10.0125i	0.174896	−	0.538275i
$347$	23.9270	+	7.77436i	1.28447	+	0.417349i	0.870152	−	0.492783i	$-0.164021\pi$
$347$	23.9270	+	7.77436i	1.28447	+	0.417349i	0.414317	+	0.910133i	$0.364021\pi$
$348$	0.482814	+	0.664536i	0.0258815	+	0.0356229i
$349$	25.4708			1.36342			0.681710	−	0.731622i	$-0.261236\pi$
$349$	25.4708			1.36342			0.681710	+	0.731622i	$0.261236\pi$
$350$	−2.84754	−	5.69507i	−0.152207	−	0.304415i
$351$	4.48976			0.239646
$352$	−2.56378	−	3.52874i	−0.136650	−	0.188082i
$353$	27.5059	+	8.93720i	1.46399	+	0.475679i	0.929286	−	0.369361i	$-0.120423\pi$
$353$	27.5059	+	8.93720i	1.46399	+	0.475679i	0.534703	+	0.845040i	$0.320423\pi$
$354$	−0.412791	+	1.27044i	−0.0219396	+	0.0675231i
$355$	4.87698	−	1.99846i	0.258843	−	0.106067i
$356$	0.527864	+	1.62460i	0.0279767	+	0.0861035i
$357$		−	0.0218857i		−	0.00115832i
$358$	−10.3274	+	3.35558i	−0.545820	+	0.177348i
$359$	−6.82792	−	4.96077i	−0.360364	−	0.261820i	0.392840	−	0.919607i	$-0.371493\pi$
$359$	−6.82792	−	4.96077i	−0.360364	−	0.261820i	−0.753204	+	0.657787i	$0.771493\pi$
$360$	−2.51744	−	6.14349i	−0.132681	−	0.323790i
$361$	15.2811	−	11.1024i	0.804268	−	0.584335i
$362$	6.04582	−	8.32136i	0.317761	−	0.437361i
$363$	0.828159	−	1.13986i	0.0434671	−	0.0598273i
$364$	4.41367	−	3.20672i	0.231339	−	0.168078i
$365$	−0.852880	+	3.49402i	−0.0446418	+	0.182885i
$366$	0.238153	+	0.173028i	0.0124485	+	0.00904433i
$367$	−2.85041	+	0.926153i	−0.148790	+	0.0483448i	−0.382465	−	0.923970i	$-0.624925\pi$
$367$	−2.85041	+	0.926153i	−0.148790	+	0.0483448i	0.233675	+	0.972315i	$0.424925\pi$
$368$		−	6.31375i		−	0.329127i
$369$	10.4889	+	32.2815i	0.546030	+	1.68051i
$370$	−5.93986	−	7.00837i	−0.308799	−	0.364348i
$371$	0.348236	−	1.07176i	0.0180795	−	0.0556431i
$372$	−1.34255	−	0.436220i	−0.0696079	−	0.0226170i
$373$	−10.3080	−	14.1877i	−0.533728	−	0.734613i	0.453965	−	0.891019i	$-0.350009\pi$
$373$	−10.3080	−	14.1877i	−0.533728	−	0.734613i	−0.987693	+	0.156406i	$0.950009\pi$
$374$	−0.426960			−0.0220776
$375$	1.91380	−	0.436475i	0.0988280	−	0.0225395i
$376$	11.7052			0.603649
$377$	11.7811	+	16.2153i	0.606757	+	0.835130i
$378$	1.26928	+	0.412413i	0.0652846	+	0.0212123i
$379$	−9.82469	+	30.2373i	−0.504661	+	1.55319i	0.296680	+	0.954977i	$0.404121\pi$
$379$	−9.82469	+	30.2373i	−0.504661	+	1.55319i	−0.801340	+	0.598209i	$0.795879\pi$
$380$	0.482814	+	0.569667i	0.0247678	+	0.0292233i
$381$	0.0715593	+	0.220237i	0.00366609	+	0.0112831i
$382$			9.64063i			0.493258i
$383$	−18.6755	+	6.06804i	−0.954273	+	0.310062i	−0.744451	−	0.667677i	$-0.767289\pi$
$383$	−18.6755	+	6.06804i	−0.954273	+	0.310062i	−0.209822	+	0.977740i	$0.567289\pi$
$384$	0.142040	+	0.103198i	0.00724842	+	0.00526629i
$385$	2.94528	−	12.0660i	0.150105	−	0.614941i
$386$	4.85410	−	3.52671i	0.247067	−	0.179505i
$387$	−17.8177	+	24.5239i	−0.905722	+	1.24662i
$388$	−3.88374	+	5.34551i	−0.197167	+	0.271377i
$389$	−23.8930	+	17.3593i	−1.21142	+	0.880150i	−0.995359	−	0.0962298i	$-0.969322\pi$
$389$	−23.8930	+	17.3593i	−1.21142	+	0.880150i	−0.216063	+	0.976379i	$0.569322\pi$
$390$	0.637724	+	1.55628i	0.0322924	+	0.0788054i
$391$	−0.500000	−	0.363271i	−0.0252861	−	0.0183714i
$392$	−5.11507	+	1.66199i	−0.258350	+	0.0839431i
$393$		−	0.312599i		−	0.0157685i
$394$	−6.41164	−	19.7330i	−0.323014	−	0.994134i
$395$	16.8302	−	6.89659i	0.846821	−	0.347005i
$396$	4.00203	−	12.3170i	0.201110	−	0.618951i
$397$	21.1823	+	6.88254i	1.06311	+	0.345425i	0.787800	−	0.615931i	$-0.211220\pi$
$397$	21.1823	+	6.88254i	1.06311	+	0.345425i	0.275308	+	0.961356i	$0.411220\pi$
$398$	11.2049	+	15.4222i	0.561650	+	0.773045i
$399$	−0.0746662			−0.00373798
$400$	3.56227	−	3.50859i	0.178114	−	0.175430i
$401$	7.37458			0.368269			0.184134	−	0.982901i	$-0.441052\pi$
$401$	7.37458			0.368269			0.184134	+	0.982901i	$0.441052\pi$
$402$	0.120639	+	0.166045i	0.00601692	+	0.00828157i
$403$	−32.7594	−	10.6442i	−1.63186	−	0.530224i
$404$	2.17026	−	6.67937i	0.107974	−	0.332311i
$405$	10.2551	−	16.5931i	0.509581	−	0.824519i
$406$	1.84110	+	5.66631i	0.0913720	+	0.281214i
$407$		−	17.9203i		−	0.888278i
$408$	0.0163449	−	0.00531079i	0.000809194	−	0.000262923i
$409$	−14.9117	−	10.8340i	−0.737335	−	0.535705i	0.154541	−	0.987986i	$-0.450610\pi$
$409$	−14.9117	−	10.8340i	−0.737335	−	0.535705i	−0.891875	+	0.452281i	$0.850610\pi$
$410$	−19.5005	+	16.5274i	−0.963059	+	0.816229i
$411$	1.35805	−	0.986682i	0.0669878	−	0.0486695i
$412$	7.49228	−	10.3122i	0.369118	−	0.508048i
$413$	−5.69507	+	7.83860i	−0.280236	+	0.385712i
$414$	15.1663	−	11.0190i	0.745385	−	0.541554i
$415$	−14.1144	−	8.72320i	−0.692850	−	0.428205i
$416$	3.46589	+	2.51812i	0.169929	+	0.123461i
$417$	−0.768046	+	0.249553i	−0.0376114	+	0.0122207i
$418$			1.45663i			0.0712462i
$419$	−3.58315	−	11.0278i	−0.175048	−	0.538744i	0.824587	−	0.565735i	$-0.191407\pi$
$419$	−3.58315	−	11.0278i	−0.175048	−	0.538744i	−0.999636	+	0.0269911i	$0.991407\pi$
$420$	0.0373331	+	0.498548i	0.00182167	+	0.0243266i
$421$	−0.902012	+	2.77611i	−0.0439614	+	0.135299i	−0.970628	−	0.240585i	$-0.922661\pi$
$421$	−0.902012	+	2.77611i	−0.0439614	+	0.135299i	0.926667	+	0.375884i	$0.122661\pi$
$422$	−16.1866	−	5.25934i	−0.787951	−	0.256021i
$423$	20.4283	+	28.1172i	0.993259	+	1.36710i
$424$	0.884927			0.0429759
$425$	−0.0728926	−	0.483976i	−0.00353581	−	0.0234763i
$426$	−0.413831			−0.0200502
$427$	1.25502	+	1.72738i	0.0607346	+	0.0835940i
$428$	−11.6050	−	3.77070i	−0.560949	−	0.182263i
$429$	−1.01380	+	3.12016i	−0.0489469	+	0.150643i
$430$	−22.1775	−	5.41347i	−1.06950	−	0.261061i
$431$	2.34092	+	7.20460i	0.112758	+	0.347033i	0.991473	−	0.130314i	$-0.0415984\pi$
$431$	2.34092	+	7.20460i	0.112758	+	0.347033i	−0.878715	+	0.477347i	$0.841598\pi$
$432$			1.04801i			0.0504225i
$433$	27.3735	−	8.89418i	1.31548	−	0.427427i	0.434543	−	0.900651i	$-0.356910\pi$
$433$	27.3735	−	8.89418i	1.31548	−	0.427427i	0.880942	+	0.473224i	$0.156910\pi$
$434$	−8.28350	−	6.01832i	−0.397621	−	0.288888i
$435$	−1.83161	+	0.137157i	−0.0878187	+	0.00657619i
$436$	4.08628	−	2.96885i	0.195697	−	0.142182i
$437$	−1.23935	+	1.70582i	−0.0592862	+	0.0816004i
$438$	0.165989	−	0.228464i	0.00793124	−	0.0109164i
$439$	14.3588	−	10.4323i	0.685310	−	0.497907i	−0.189805	−	0.981822i	$-0.560786\pi$
$439$	14.3588	−	10.4323i	0.685310	−	0.497907i	0.875115	+	0.483915i	$0.160786\pi$
$440$	9.72597	−	0.728316i	0.463667	−	0.0347211i
$441$	−12.9193	−	9.38642i	−0.615205	−	0.446972i
$442$	0.398831	−	0.129588i	0.0189704	−	0.00616387i
$443$		−	19.3439i		−	0.919058i	−0.888163	−	0.459529i	$-0.848018\pi$
$443$		−	19.3439i		−	0.919058i	0.888163	−	0.459529i	$-0.151982\pi$
$444$	0.222904	+	0.686028i	0.0105786	+	0.0325575i
$445$	−3.71071	−	0.905773i	−0.175905	−	0.0429378i
$446$	−1.53827	+	4.73429i	−0.0728390	+	0.224175i
$447$	−0.339276	−	0.110237i	−0.0160472	−	0.00521405i
$448$	0.748520	+	1.03025i	0.0353642	+	0.0486747i
$449$	−11.2932			−0.532960			−0.266480	−	0.963840i	$-0.585861\pi$
$449$	−11.2932			−0.532960			−0.266480	+	0.963840i	$0.585861\pi$
$450$	14.6450	+	2.43365i	0.690374	+	0.114723i
$451$	−49.8625			−2.34793
$452$	−8.24962	−	11.3546i	−0.388029	−	0.534076i
$453$	3.16681	+	1.02896i	0.148790	+	0.0483448i
$454$	−0.317289	+	0.976514i	−0.0148911	+	0.0458301i
$455$	0.910961	+	12.1650i	0.0427065	+	0.570305i
$456$	−0.0181185	−	0.0557630i	−0.000848476	−	0.00261134i
$457$		−	2.60741i		−	0.121970i	−0.998139	−	0.0609848i	$-0.980576\pi$
$457$		−	2.60741i		−	0.121970i	0.998139	−	0.0609848i	$-0.0194241\pi$
$458$	3.88514	−	1.26236i	0.181540	−	0.0589861i
$459$	0.0829943	+	0.0602989i	0.00387384	+	0.00281451i
$460$	12.0095	+	7.42226i	0.559944	+	0.346065i
$461$	1.58366	−	1.15060i	0.0737585	−	0.0535887i	−0.550295	−	0.834970i	$-0.685485\pi$
$461$	1.58366	−	1.15060i	0.0737585	−	0.0535887i	0.624053	+	0.781382i	$0.285485\pi$
$462$	−0.573214	+	0.788961i	−0.0266683	+	0.0367058i
$463$	−0.856972	+	1.17952i	−0.0398269	+	0.0548170i	−0.828466	−	0.560039i	$-0.810786\pi$
$463$	−0.856972	+	1.17952i	−0.0398269	+	0.0548170i	0.788639	+	0.614856i	$0.210786\pi$
$464$	−3.78501	+	2.74997i	−0.175715	+	0.127664i
$465$	2.40800	−	2.04087i	0.111668	−	0.0946431i
$466$	−3.57002	−	2.59377i	−0.165378	−	0.120154i
$467$	24.3331	−	7.90629i	1.12600	−	0.365860i	0.313945	−	0.949441i	$-0.398349\pi$
$467$	24.3331	−	7.90629i	1.12600	−	0.365860i	0.812055	+	0.583581i	$0.198349\pi$
$468$			12.7202i			0.587991i
$469$	0.460027	+	1.41582i	0.0212421	+	0.0653764i
$470$	−13.7603	+	22.2646i	−0.634714	+	1.02699i
$471$	−0.772745	+	2.37827i	−0.0356062	+	0.109585i
$472$	−7.23607	−	2.35114i	−0.333067	−	0.108220i
$473$	−26.1744	−	36.0260i	−1.20350	−	1.65648i
$474$	−1.42811			−0.0655954
$475$	−1.65115	+	0.248683i	−0.0757601	+	0.0114104i
$476$	0.124655			0.00571355
$477$	1.54441	+	2.12569i	0.0707136	+	0.0973289i
$478$	20.6875	+	6.72179i	0.946226	+	0.307447i
$479$	2.12209	−	6.53112i	0.0969608	−	0.298415i	−0.890799	−	0.454398i	$-0.849855\pi$
$479$	2.12209	−	6.53112i	0.0969608	−	0.298415i	0.987760	+	0.155983i	$0.0498545\pi$
$480$	−0.363271	+	0.148859i	−0.0165810	+	0.00679445i
$481$	5.43906	+	16.7397i	0.248000	+	0.763265i
$482$			15.8622i			0.722504i
$483$	−1.34255	+	0.436220i	−0.0610880	+	0.0198487i
$484$	6.49234	+	4.71696i	0.295106	+	0.214407i
$485$	−5.60215	−	13.6713i	−0.254381	−	0.620783i
$486$	−3.78266	+	2.74826i	−0.171585	+	0.124664i
$487$	24.8770	−	34.2403i	1.12728	−	1.55157i	0.334159	−	0.942517i	$-0.391548\pi$
$487$	24.8770	−	34.2403i	1.12728	−	1.55157i	0.793126	−	0.609058i	$-0.208452\pi$
$488$	−0.985520	+	1.35645i	−0.0446124	+	0.0614037i
$489$	2.80026	−	2.03451i	0.126632	−	0.0920036i
$490$	2.85184	−	11.6832i	0.128833	−	0.527795i
$491$	−10.4767	−	7.61178i	−0.472808	−	0.343515i	0.325727	−	0.945464i	$-0.394391\pi$
$491$	−10.4767	−	7.61178i	−0.472808	−	0.343515i	−0.798535	+	0.601949i	$0.794391\pi$
$492$	1.90884	−	0.620220i	0.0860572	−	0.0279617i
$493$			0.457967i			0.0206258i
$494$	−0.442107	−	1.36067i	−0.0198913	−	0.0612193i
$495$	18.7236	+	22.0918i	0.841564	+	0.992952i
$496$	2.48459	−	7.64677i	0.111561	−	0.343350i
$497$	−2.85471	−	0.927551i	−0.128051	−	0.0416064i
$498$	0.765768	+	1.05399i	0.0343149	+	0.0472304i
$499$	12.9767			0.580915			0.290458	−	0.956888i	$-0.406192\pi$
$499$	12.9767			0.580915			0.290458	+	0.956888i	$0.406192\pi$
$500$	2.48604	+	10.9004i	0.111179	+	0.487483i
$501$	−1.01512			−0.0453522
$502$	−4.99081	−	6.86926i	−0.222751	−	0.306590i
$503$	−20.2024	−	6.56414i	−0.900778	−	0.292681i	−0.178220	−	0.983991i	$-0.557034\pi$
$503$	−20.2024	−	6.56414i	−0.900778	−	0.292681i	−0.722558	+	0.691310i	$0.757034\pi$
$504$	−1.16843	+	3.59606i	−0.0520460	+	0.160181i
$505$	10.1536	+	11.9802i	0.451831	+	0.533110i
$506$	8.51005	+	26.1912i	0.378318	+	1.16434i
$507$		−	0.939887i		−	0.0417419i
$508$	−1.25441	+	0.407581i	−0.0556553	+	0.0180835i
$509$	11.5303	+	8.37728i	0.511073	+	0.371317i	0.813231	−	0.581942i	$-0.197707\pi$
$509$	11.5303	+	8.37728i	0.511073	+	0.371317i	−0.302157	+	0.953258i	$0.597707\pi$
$510$	−0.00911289	+	0.0373331i	−0.000403526	+	0.00165314i
$511$	1.65711	−	1.20396i	0.0733060	−	0.0532600i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$	0.205718	−	0.283147i	0.00908267	−	0.0125012i
$514$	8.07862	−	5.86946i	0.356332	−	0.258891i
$515$	10.8073	+	26.3739i	0.476229	+	1.16217i
$516$	1.45012	+	1.05358i	0.0638382	+	0.0463811i
$517$	−48.5564	+	15.7769i	−2.13551	+	0.693869i
$518$			5.23201i			0.229881i
$519$	−0.571175	−	1.75790i	−0.0250718	−	0.0771631i
$520$	−8.86415	+	3.63229i	−0.388719	+	0.159287i
$521$	−9.07543	+	27.9313i	−0.397602	+	1.22369i	0.529315	+	0.848426i	$0.322449\pi$
$521$	−9.07543	+	27.9313i	−0.397602	+	1.22369i	−0.926917	+	0.375268i	$0.877551\pi$
$522$	−13.2115	−	4.29267i	−0.578251	−	0.187885i
$523$	8.95773	+	12.3293i	0.391694	+	0.539121i	0.958635	−	0.284638i	$-0.0918733\pi$
$523$	8.95773	+	12.3293i	0.391694	+	0.539121i	−0.566941	+	0.823758i	$0.691873\pi$
$524$	1.78048			0.0777804
$525$	−0.992182	−	0.515066i	−0.0433024	−	0.0224793i
$526$	7.73433			0.337233
$527$	−0.462611	−	0.636729i	−0.0201516	−	0.0277363i
$528$	−0.728316	−	0.236644i	−0.0316959	−	0.0102986i
$529$	−5.21110	+	16.0381i	−0.226569	+	0.697309i
$530$	−1.04029	+	1.68323i	−0.0451875	+	0.0731149i
$531$	−6.98095	−	21.4852i	−0.302947	−	0.932376i
$532$		−	0.425277i		−	0.0184381i
$533$	46.5775	−	15.1339i	2.01749	−	0.655523i
$534$	0.242632	+	0.176283i	0.0104997	+	0.00762850i
$535$	20.8148	−	17.6413i	0.899902	−	0.762701i
$536$	−0.945746	+	0.687124i	−0.0408500	+	0.0296793i
$537$	−1.12061	+	1.54239i	−0.0483579	+	0.0665590i
$538$	−4.31355	+	5.93710i	−0.185970	+	0.255966i
$539$	18.9786	−	13.7888i	0.817468	−	0.593925i
$540$	−1.99344	−	1.23201i	−0.0857838	−	0.0530173i
$541$	−24.5392	−	17.8288i	−1.05502	−	0.766520i	−0.0818632	−	0.996644i	$-0.526087\pi$
$541$	−24.5392	−	17.8288i	−1.05502	−	0.766520i	−0.973161	+	0.230123i	$0.926087\pi$
$542$	12.6481	−	4.10960i	0.543281	−	0.176523i
$543$		−	1.80588i		−	0.0774976i
$544$	0.0302487	+	0.0930960i	0.00129690	+	0.00399146i
$545$	0.843389	+	11.2627i	0.0361268	+	0.482439i
$546$	0.295989	−	0.910961i	0.0126672	−	0.0389855i
$547$	29.5288	+	9.59449i	1.26256	+	0.410231i	0.862406	−	0.506217i	$-0.168956\pi$
$547$	29.5288	+	9.59449i	1.26256	+	0.410231i	0.400155	+	0.916448i	$0.368956\pi$
$548$	5.61986	+	7.73508i	0.240069	+	0.330426i
$549$	−4.97832			−0.212469
$550$	−10.0482	+	19.3561i	−0.428458	+	0.825346i
$551$	1.56242			0.0665613
$552$	−0.651565	−	0.896802i	−0.0277324	−	0.0381704i
$553$	−9.85148	−	3.20094i	−0.418928	−	0.136118i
$554$	6.05458	−	18.6341i	0.257234	−	0.791686i
$555$	−1.56694	−	0.382486i	−0.0665130	−	0.0162356i
$556$	−1.42138	−	4.37457i	−0.0602801	−	0.185523i
$557$		−	28.0537i		−	1.18867i	−0.804216	−	0.594337i	$-0.797415\pi$
$557$		−	28.0537i		−	1.18867i	0.804216	−	0.594337i	$-0.202585\pi$
$558$	22.7046	−	7.37718i	0.961163	−	0.312301i
$559$	35.3843	+	25.7082i	1.49660	+	1.08734i
$560$	−2.83959	+	0.212639i	−0.119994	+	0.00898563i
$561$	−0.0606452	+	0.0440613i	−0.00256044	+	0.00186027i
$562$	6.76336	−	9.30896i	0.285295	−	0.392675i
$563$	13.6142	−	18.7384i	0.573772	−	0.789729i	−0.419223	−	0.907883i	$-0.637698\pi$
$563$	13.6142	−	18.7384i	0.573772	−	0.789729i	0.992995	+	0.118154i	$0.0376976\pi$
$564$	1.66260	−	1.20795i	0.0700081	−	0.0508638i
$565$	31.2958	−	2.34354i	1.31662	−	0.0985936i
$566$	−15.9010	−	11.5527i	−0.668367	−	0.485597i
$567$	−10.5653	+	3.43288i	−0.443702	+	0.144167i
$568$		−	2.35706i		−	0.0989002i
$569$	4.16602	+	12.8217i	0.174649	+	0.537514i	0.999617	−	0.0276651i	$-0.00880719\pi$
$569$	4.16602	+	12.8217i	0.174649	+	0.537514i	−0.824968	+	0.565179i	$0.808807\pi$
$570$	0.127367	+	0.0310899i	0.00533482	+	0.00130221i
$571$	−12.0389	+	37.0519i	−0.503813	+	1.55058i	0.298945	+	0.954270i	$0.403365\pi$
$571$	−12.0389	+	37.0519i	−0.503813	+	1.55058i	−0.802758	+	0.596305i	$0.796635\pi$
$572$	−17.7716	−	5.77433i	−0.743067	−	0.241437i
$573$	0.994892	+	1.36935i	0.0415622	+	0.0572054i
$574$	14.5578			0.607632
$575$	−28.2360	+	14.1180i	−1.17752	+	0.588760i
$576$	−2.96917			−0.123716
$577$	−26.1132	−	35.9417i	−1.08711	−	1.49627i	−0.851449	−	0.524437i	$-0.824276\pi$
$577$	−26.1132	−	35.9417i	−1.08711	−	1.49627i	−0.235657	−	0.971836i	$-0.575724\pi$
$578$	−16.1588	−	5.25033i	−0.672119	−	0.218385i
$579$	0.325526	−	1.00186i	0.0135284	−	0.0416361i
$580$	−0.781209	−	10.4323i	−0.0324380	−	0.433178i
$581$	2.92007	+	8.98706i	0.121145	+	0.372846i
$582$			1.16007i			0.0480863i
$583$	−3.67093	+	1.19276i	−0.152034	+	0.0493989i
$584$	1.30127	+	0.945424i	0.0538467	+	0.0391219i
$585$	−24.1952	−	14.9535i	−1.00035	−	0.618250i
$586$	4.95283	−	3.59844i	0.204600	−	0.148650i
$587$	−23.0686	+	31.7512i	−0.952144	+	1.31051i	−0.00157480	+	0.999999i	$0.500501\pi$
$587$	−23.0686	+	31.7512i	−0.952144	+	1.31051i	−0.950569	+	0.310514i	$0.899499\pi$
$588$	−0.555029	+	0.763932i	−0.0228890	+	0.0315040i
$589$	−2.17229	+	1.57826i	−0.0895076	+	0.0650311i
$590$	12.9786	−	10.9999i	0.534322	−	0.452858i
$591$	−2.94711	−	2.14120i	−0.121228	−	0.0880771i
$592$	−3.90742	+	1.26960i	−0.160594	+	0.0521802i
$593$		−	23.5637i		−	0.967644i	−0.875167	−	0.483822i	$-0.839248\pi$
$593$		−	23.5637i		−	0.967644i	0.875167	−	0.483822i	$-0.160752\pi$
$594$	−1.41257	−	4.34745i	−0.0579585	−	0.178378i
$595$	−0.146541	+	0.237108i	−0.00600758	+	0.00972047i
$596$	0.627881	−	1.93242i	0.0257190	−	0.0791549i
$597$	3.18307	+	1.03424i	0.130275	+	0.0423288i
$598$	−15.8988	−	21.8828i	−0.650149	−	0.894854i
$599$	−39.2513			−1.60376			−0.801882	−	0.597483i	$-0.796168\pi$
$599$	−39.2513			−1.60376			−0.801882	+	0.597483i	$0.796168\pi$
$600$	0.143904	−	0.865977i	0.00587487	−	0.0353534i
$601$	−13.1067			−0.534635			−0.267317	−	0.963609i	$-0.586137\pi$
$601$	−13.1067			−0.534635			−0.267317	+	0.963609i	$0.586137\pi$
$602$	7.64186	+	10.5181i	0.311459	+	0.428687i
$603$	−3.30110	−	1.07259i	−0.134431	−	0.0436794i
$604$	−5.86067	+	18.0373i	−0.238467	+	0.733926i
$605$	−16.6044	+	6.80404i	−0.675065	+	0.276624i
$606$	−0.381034	−	1.17270i	−0.0154784	−	0.0476377i
$607$			6.14712i			0.249504i	0.992188	+	0.124752i	$0.0398135\pi$
$607$			6.14712i			0.249504i	−0.992188	+	0.124752i	$0.960186\pi$
$608$	0.317610	−	0.103198i	0.0128808	−	0.00418522i
$609$	0.846259	+	0.614843i	0.0342921	+	0.0249147i
$610$	−1.42158	−	3.46917i	−0.0575579	−	0.140463i
$611$	40.5689	−	29.4750i	1.64124	−	1.19243i
$612$	−0.170836	+	0.235136i	−0.00690564	+	0.00950479i
$613$	−13.0198	+	17.9202i	−0.525865	+	0.723790i	−0.986493	−	0.163803i	$-0.947624\pi$
$613$	−13.0198	+	17.9202i	−0.525865	+	0.723790i	0.460629	+	0.887593i	$0.347624\pi$
$614$	−11.4828	+	8.34271i	−0.463406	+	0.336684i
$615$	−1.06425	+	4.35994i	−0.0429146	+	0.175810i
$616$	−4.49370	−	3.26486i	−0.181056	−	0.131545i
$617$	11.5313	−	3.74675i	0.464233	−	0.150838i	−0.0675559	−	0.997715i	$-0.521520\pi$
$617$	11.5313	−	3.74675i	0.464233	−	0.150838i	0.531789	+	0.846877i	$0.321520\pi$
$618$		−	2.23793i		−	0.0900229i
$619$	−4.06963	−	12.5250i	−0.163572	−	0.503424i	0.835356	−	0.549709i	$-0.185262\pi$
$619$	−4.06963	−	12.5250i	−0.163572	−	0.503424i	−0.998928	+	0.0462856i	$0.985262\pi$
$620$	11.6242	+	13.7153i	0.466840	+	0.550819i
$621$	2.04473	−	6.29303i	0.0820521	−	0.252531i
$622$	−6.83447	−	2.22066i	−0.274037	−	0.0890402i
$623$	1.27862	+	1.75987i	0.0512270	+	0.0705079i
$624$	0.752158			0.0301104
$625$	−23.6564	−	8.08551i	−0.946255	−	0.323420i
$626$	−0.625638			−0.0250055
$627$	0.150321	+	0.206899i	0.00600325	+	0.00826276i
$628$	−13.5459	−	4.40134i	−0.540541	−	0.175633i
$629$	−0.124277	+	0.382486i	−0.00495526	+	0.0152507i
$630$	−5.46654	−	6.44990i	−0.217792	−	0.256970i
$631$	10.0018	+	30.7824i	0.398165	+	1.22543i	0.926469	+	0.376371i	$0.122828\pi$
$631$	10.0018	+	30.7824i	0.398165	+	1.22543i	−0.528304	+	0.849055i	$0.677172\pi$
$632$		−	8.13412i		−	0.323558i
$633$	−2.84189	+	0.923385i	−0.112955	+	0.0367013i
$634$	5.83306	+	4.23796i	0.231660	+	0.168311i
$635$	0.699377	−	2.86516i	0.0277539	−	0.113701i
$636$	0.125695	−	0.0913225i	0.00498412	−	0.00362117i
$637$	−13.5432	+	18.6406i	−0.536602	+	0.738569i
$638$	11.9947	−	16.5093i	0.474876	−	0.653610i
$639$	5.66193	−	4.11363i	0.223983	−	0.162733i
$640$	−0.847859	−	2.06909i	−0.0335146	−	0.0817880i
$641$	11.5106	+	8.36292i	0.454640	+	0.330315i	0.791425	−	0.611266i	$-0.209340\pi$
$641$	11.5106	+	8.36292i	0.454640	+	0.330315i	−0.336785	+	0.941582i	$0.609340\pi$
$642$	−2.03750	+	0.662023i	−0.0804136	+	0.0261280i
$643$			18.7825i			0.740708i	0.928891	+	0.370354i	$0.120764\pi$
$643$			18.7825i			0.740708i	−0.928891	+	0.370354i	$0.879236\pi$
$644$	−2.48459	−	7.64677i	−0.0979065	−	0.301325i
$645$	−3.70875	+	1.51975i	−0.146032	+	0.0598399i
$646$	0.0101017	−	0.0310899i	0.000397447	−	0.00122322i
$647$	−14.3035	−	4.64749i	−0.562328	−	0.182712i	0.0140402	−	0.999901i	$-0.495531\pi$
$647$	−14.3035	−	4.64749i	−0.562328	−	0.182712i	−0.576369	+	0.817190i	$0.695531\pi$
$648$	−5.12756	−	7.05748i	−0.201430	−	0.277244i
$649$	33.1863			1.30267
$650$	3.51140	−	21.1306i	0.137728	−	0.828811i
$651$	−1.79766			−0.0704559
$652$	11.5880	+	15.9495i	0.453820	+	0.624630i
$653$	−22.5809	−	7.33698i	−0.883659	−	0.287118i	−0.168183	−	0.985756i	$-0.553790\pi$
$653$	−22.5809	−	7.33698i	−0.883659	−	0.287118i	−0.715476	+	0.698637i	$0.753790\pi$
$654$	0.274034	−	0.843389i	0.0107156	−	0.0329791i
$655$	−2.09307	+	3.38667i	−0.0817832	+	0.132328i
$656$	3.53260	+	10.8722i	0.137925	+	0.424489i
$657$			4.77578i			0.186321i
$658$	14.1765	−	4.60623i	0.552658	−	0.179569i
$659$	−5.30922	−	3.85737i	−0.206818	−	0.150262i	0.479555	−	0.877512i	$-0.340798\pi$
$659$	−5.30922	−	3.85737i	−0.206818	−	0.150262i	−0.686373	+	0.727250i	$0.740798\pi$
$660$	1.30631	−	1.10715i	0.0508481	−	0.0430957i
$661$	25.9148	−	18.8282i	1.00797	−	0.732331i	0.0441853	−	0.999023i	$-0.485931\pi$
$661$	25.9148	−	18.8282i	1.00797	−	0.732331i	0.963782	+	0.266692i	$0.0859308\pi$
$662$	14.2329	−	19.5898i	0.553176	−	0.761381i
$663$	0.0432765	−	0.0595651i	0.00168072	−	0.00231332i
$664$	−6.00323	+	4.36160i	−0.232970	+	0.169263i
$665$	0.808926	+	0.499944i	0.0313688	+	0.0193870i
$666$	−9.86910	−	7.17032i	−0.382420	−	0.277844i
$667$	28.0933	−	9.12808i	1.08778	−	0.353441i
$668$		−	5.78183i		−	0.223706i
$669$	0.270074	+	0.831202i	0.0104417	+	0.0321361i
$670$	−0.195198	−	2.60668i	−0.00754114	−	0.100705i
$671$	2.25991	−	6.95529i	0.0872429	−	0.268506i
$672$	0.212639	+	0.0690905i	0.00820272	+	0.00266522i
$673$	29.2455	+	40.2530i	1.12733	+	1.55164i	0.793039	+	0.609171i	$0.208498\pi$
$673$	29.2455	+	40.2530i	1.12733	+	1.55164i	0.334294	+	0.942469i	$0.391502\pi$
$674$	−22.2016			−0.855173
$675$	4.68685	−	2.34342i	0.180397	−	0.0901984i
$676$	5.35333			0.205897
$677$	16.8590	+	23.2044i	0.647943	+	0.891818i	0.999008	−	0.0445337i	$-0.0141802\pi$
$677$	16.8590	+	23.2044i	0.647943	+	0.891818i	−0.351064	+	0.936351i	$0.614180\pi$
$678$	−2.34354	−	0.761463i	−0.0900032	−	0.0292438i
$679$	−2.60015	+	8.00244i	−0.0997846	+	0.307105i
$680$	−0.212639	−	0.0519044i	−0.00815432	−	0.00199044i
$681$	0.0557065	+	0.171447i	0.00213468	+	0.00656987i
$682$			35.0699i			1.34289i
$683$	33.3619	−	10.8399i	1.27656	−	0.414779i	0.409192	−	0.912449i	$-0.365811\pi$
$683$	33.3619	−	10.8399i	1.27656	−	0.414779i	0.867367	+	0.497670i	$0.165811\pi$
$684$	0.802198	+	0.582831i	0.0306728	+	0.0222851i
$685$	−21.3195	+	1.59649i	−0.814578	+	0.0609986i
$686$	−12.7527	+	9.26540i	−0.486902	+	0.353755i
$687$	0.421570	−	0.580242i	0.0160839	−	0.0221376i
$688$	−6.00088	+	8.25950i	−0.228781	+	0.314890i
$689$	3.06706	−	2.22835i	0.116846	−	0.0848934i
$690$	2.47178	−	0.185096i	0.0940990	−	0.00704648i
$691$	1.37666	+	1.00020i	0.0523704	+	0.0380493i	0.613663	−	0.789568i	$-0.289696\pi$
$691$	1.37666	+	1.00020i	0.0523704	+	0.0380493i	−0.561292	+	0.827618i	$0.689696\pi$
$692$	10.0125	−	3.25325i	0.380618	−	0.123670i
$693$		−	16.4923i		−	0.626492i
$694$	7.77436	+	23.9270i	0.295110	+	0.908257i
$695$	9.99186	+	2.43898i	0.379013	+	0.0925159i
$696$	−0.253830	+	0.781209i	−0.00962141	+	0.0296117i
$697$	1.06425	+	0.345795i	0.0403113	+	0.0130979i
$698$	14.9714	+	20.6063i	0.566674	+	0.779960i
$699$	−0.774756			−0.0293040
$700$	2.93367	−	5.65119i	0.110882	−	0.213595i
$701$	−5.26104			−0.198707			−0.0993534	−	0.995052i	$-0.531677\pi$
$701$	−5.26104			−0.198707			−0.0993534	+	0.995052i	$0.531677\pi$
$702$	2.63902	+	3.63229i	0.0996032	+	0.137092i
$703$	1.30490	+	0.423989i	0.0492154	+	0.0159910i
$704$	1.34786	−	4.14828i	0.0507993	−	0.156344i
$705$	0.343153	+	4.58248i	0.0129239	+	0.172586i
$706$	8.93720	+	27.5059i	0.336356	+	1.03520i
$707$		−	8.94363i		−	0.336360i
$708$	−1.27044	+	0.412791i	−0.0477461	+	0.0155136i
$709$	−35.0458	−	25.4622i	−1.31617	−	0.956254i	−0.999971	−	0.00756154i	$-0.997593\pi$
$709$	−35.0458	−	25.4622i	−1.31617	−	0.956254i	−0.316200	−	0.948693i	$-0.602407\pi$
$710$	4.48340	+	2.77089i	0.168259	+	0.103990i
$711$	19.5391	−	14.1960i	0.732773	−	0.532391i
$712$	−1.00406	+	1.38197i	−0.0376286	+	0.0517914i
$713$	−29.8386	+	41.0693i	−1.11746	+	1.53806i
$714$	0.0177059	−	0.0128641i	0.000662627	−	0.000481427i
$715$	31.8752	−	27.0154i	1.19206	−	1.01032i
$716$	−8.78501	−	6.38268i	−0.328311	−	0.238532i
$717$	3.63212	−	1.18015i	0.135644	−	0.0440734i
$718$		−	8.43977i		−	0.314970i
$719$	−7.61145	−	23.4256i	−0.283859	−	0.873629i	−0.986738	−	0.162319i	$-0.948103\pi$
$719$	−7.61145	−	23.4256i	−0.283859	−	0.873629i	0.702879	−	0.711309i	$-0.251897\pi$
$720$	3.49047	−	5.64771i	0.130082	−	0.210478i
$721$	5.01606	−	15.4378i	0.186808	−	0.574935i
$722$	17.9640	+	5.83686i	0.668551	+	0.217225i
$723$	1.63695	+	2.25306i	0.0608786	+	0.0837923i
$724$	10.2858			0.382267
$725$	20.7618	+	10.7780i	0.771074	+	0.400283i
$726$	1.40895			0.0522910
$727$	8.26374	+	11.3741i	0.306485	+	0.421841i	0.934281	−	0.356537i	$-0.116043\pi$
$727$	8.26374	+	11.3741i	0.306485	+	0.421841i	−0.627796	+	0.778378i	$0.716043\pi$
$728$	5.18858	+	1.68587i	0.192301	+	0.0624825i
$729$	7.83348	−	24.1090i	0.290129	−	0.892925i
$730$	−3.32803	+	1.36374i	−0.123176	+	0.0504743i
$731$	0.308818	+	0.950445i	0.0114221	+	0.0351535i
$732$			0.294373i			0.0108803i
$733$	−26.8518	+	8.72468i	−0.991794	+	0.322253i	−0.759582	−	0.650412i	$-0.774596\pi$
$733$	−26.8518	+	8.72468i	−0.991794	+	0.322253i	−0.232212	+	0.972665i	$0.574596\pi$
$734$	−2.42470	−	1.76165i	−0.0894974	−	0.0650236i
$735$	−0.800609	−	1.95378i	−0.0295309	−	0.0720664i
$736$	5.10793	−	3.71113i	0.188281	−	0.136794i
$737$	2.99707	−	4.12512i	0.110399	−	0.151951i
$738$	−19.9511	+	27.4603i	−0.734409	+	1.01083i
$739$	−28.0840	+	20.4042i	−1.03309	+	0.750582i	−0.968924	−	0.247357i	$-0.920438\pi$
$739$	−28.0840	+	20.4042i	−1.03309	+	0.750582i	−0.0641632	+	0.997939i	$0.520438\pi$
$740$	2.17853	−	8.92486i	0.0800844	−	0.328085i
$741$	−0.203214	−	0.147644i	−0.00746527	−	0.00542384i
$742$	1.07176	−	0.348236i	0.0393456	−	0.0127842i
$743$			35.3024i			1.29512i	0.762015	+	0.647559i	$0.224210\pi$
$743$			35.3024i			1.29512i	−0.762015	+	0.647559i	$0.775790\pi$
$744$	−0.436220	−	1.34255i	−0.0159926	−	0.0492202i
$745$	2.93756	+	3.46599i	0.107624	+	0.126984i
$746$	5.41923	−	16.6787i	0.198412	−	0.610650i
$747$	−20.9541	−	6.80840i	−0.766671	−	0.249106i
$748$	−0.250961	−	0.345418i	−0.00917603	−	0.0126297i
$749$	−15.5390			−0.567783
$750$	1.47802	+	1.29174i	0.0539695	+	0.0471677i
$751$	14.5513			0.530983			0.265491	−	0.964113i	$-0.414466\pi$
$751$	14.5513			0.530983			0.265491	+	0.964113i	$0.414466\pi$
$752$	6.88014	+	9.46969i	0.250893	+	0.345324i
$753$	−1.41778	−	0.460666i	−0.0516669	−	0.0167876i
$754$	−6.19369	+	19.0622i	−0.225561	+	0.694205i
$755$	−27.4193	−	32.3517i	−0.997891	−	1.17740i
$756$	0.412413	+	1.26928i	0.0149993	+	0.0461632i
$757$		−	23.9496i		−	0.870462i	−0.900319	−	0.435231i	$-0.856667\pi$
$757$		−	23.9496i		−	0.870462i	0.900319	−	0.435231i	$-0.143333\pi$
$758$	−30.2373	+	9.82469i	−1.09827	+	0.356849i
$759$	3.91164	+	2.84197i	0.141983	+	0.103157i
$760$	−0.177079	+	0.725446i	−0.00642334	+	0.0263147i
$761$	17.4988	−	12.7137i	0.634333	−	0.460870i	−0.223566	−	0.974689i	$-0.571770\pi$
$761$	17.4988	−	12.7137i	0.634333	−	0.460870i	0.857899	+	0.513819i	$0.171770\pi$
$762$	−0.136114	+	0.187345i	−0.00493088	+	0.00678678i
$763$	3.78071	−	5.20370i	0.136871	−	0.188387i
$764$	−7.79944	+	5.66662i	−0.282174	+	0.205011i
$765$	−0.246425	−	0.601368i	−0.00890950	−	0.0217425i
$766$	−15.8863	−	11.5421i	−0.573996	−	0.417033i
$767$	−30.9999	+	10.0725i	−1.11934	+	0.363696i
$768$			0.175571i			0.00633535i
$769$	−13.7177	−	42.2187i	−0.494672	−	1.52244i	−0.817467	−	0.575975i	$-0.804623\pi$
$769$	−13.7177	−	42.2187i	−0.494672	−	1.52244i	0.322795	−	0.946469i	$-0.395377\pi$
$770$	11.4928	−	4.70945i	0.414172	−	0.169717i
$771$	0.541768	−	1.66739i	0.0195113	−	0.0600496i
$772$	5.70634	+	1.85410i	0.205376	+	0.0667306i
$773$	6.81261	+	9.37675i	0.245032	+	0.337258i	0.913764	−	0.406246i	$-0.133162\pi$
$773$	6.81261	+	9.37675i	0.245032	+	0.337258i	−0.668731	+	0.743504i	$0.733162\pi$
$774$	−30.3132			−1.08959
$775$	−39.7531	+	5.98729i	−1.42797	+	0.215070i
$776$	−6.60741			−0.237192
$777$	0.539932	+	0.743152i	0.0193699	+	0.0266604i
$778$	−28.0879	−	9.12631i	−1.00700	−	0.327194i
$779$	1.17973	−	3.63083i	0.0422682	−	0.130088i
$780$	−0.884215	+	1.43069i	−0.0316600	+	0.0512269i
$781$	3.17699	+	9.77776i	0.113682	+	0.349876i
$782$		−	0.618034i		−	0.0221009i
$783$	−4.66318	+	1.51516i	−0.166648	+	0.0541473i
$784$	−4.35114	−	3.16129i	−0.155398	−	0.112903i
$785$	24.2960	−	20.5918i	0.867163	−	0.734953i
$786$	0.252898	−	0.183741i	0.00902057	−	0.00655383i
$787$	4.55658	−	6.27159i	0.162424	−	0.223558i	−0.720045	−	0.693927i	$-0.755879\pi$
$787$	4.55658	−	6.27159i	0.162424	−	0.223558i	0.882470	+	0.470369i	$0.155879\pi$
$788$	12.1957	−	16.7859i	0.434452	−	0.597972i
$789$	1.09858	−	0.798165i	0.0391105	−	0.0284154i
$790$	15.4720	+	9.56224i	0.550470	+	0.340209i
$791$	−14.4596	−	10.5055i	−0.514125	−	0.373534i
$792$	12.3170	−	4.00203i	0.437665	−	0.142206i
$793$			7.18297i			0.255075i
$794$	6.88254	+	21.1823i	0.244252	+	0.751731i
$795$	0.0259428	+	0.346441i	0.000920096	+	0.0122870i
$796$	−5.89076	+	18.1299i	−0.208792	+	0.642597i
$797$	38.4237	+	12.4846i	1.36104	+	0.442228i	0.896390	−	0.443267i	$-0.146181\pi$
$797$	38.4237	+	12.4846i	1.36104	+	0.442228i	0.464649	+	0.885495i	$0.346181\pi$
$798$	−0.0438877	−	0.0604062i	−0.00155361	−	0.00213836i
$799$	1.14579			0.0405350
$800$	4.93236	+	0.819639i	0.174385	+	0.0289786i
$801$	−5.07196			−0.179209
$802$	4.33467	+	5.96616i	0.153062	+	0.210672i
$803$	−6.67231	−	2.16797i	−0.235461	−	0.0765059i
$804$	−0.0634236	+	0.195198i	−0.00223678	+	0.00688409i
$805$	17.4658	+	4.26336i	0.615590	+	0.150264i
$806$	−10.6442	−	32.7594i	−0.374925	−	1.15390i
$807$			1.28845i			0.0453556i
$808$	6.67937	−	2.17026i	0.234980	−	0.0763495i
$809$	7.99707	+	5.81021i	0.281162	+	0.204276i	0.719424	−	0.694571i	$-0.244406\pi$
$809$	7.99707	+	5.81021i	0.281162	+	0.204276i	−0.438262	+	0.898847i	$0.644406\pi$
$810$	19.4519	−	1.45663i	0.683471	−	0.0511808i
$811$	−4.56597	+	3.31737i	−0.160333	+	0.116489i	−0.665059	−	0.746791i	$-0.731594\pi$
$811$	−4.56597	+	3.31737i	−0.160333	+	0.116489i	0.504726	+	0.863280i	$0.331594\pi$
$812$	−3.50197	+	4.82005i	−0.122895	+	0.169151i
$813$	1.37242	−	1.88898i	0.0481330	−	0.0662493i
$814$	14.4979	−	10.5333i	0.508150	−	0.369192i
$815$	−43.9602	+	3.29190i	−1.53986	+	0.115310i
$816$	0.0139038	+	0.0101017i	0.000486731	+	0.000353631i
$817$	3.24258	−	1.05358i	0.113443	−	0.0368600i
$818$		−	18.4318i		−	0.644454i
$819$	5.00565	+	15.4058i	0.174911	+	0.538322i
$820$	−24.8330	−	6.06166i	−0.867206	−	0.211682i
$821$	−2.57398	+	7.92189i	−0.0898325	+	0.276476i	−0.985873	−	0.167497i	$-0.946431\pi$
$821$	−2.57398	+	7.92189i	−0.0898325	+	0.276476i	0.896040	+	0.443973i	$0.146431\pi$
$822$	1.59649	+	0.518730i	0.0556838	+	0.0180928i
$823$	−5.29439	−	7.28710i	−0.184551	−	0.254012i	0.706710	−	0.707503i	$-0.250178\pi$
$823$	−5.29439	−	7.28710i	−0.184551	−	0.254012i	−0.891261	+	0.453491i	$0.850178\pi$
$824$	12.7466			0.444050
$825$	0.570259	+	3.78628i	0.0198539	+	0.131821i
$826$	−9.68904			−0.337125
$827$	−27.7260	−	38.1615i	−0.964126	−	1.32701i	−0.944959	−	0.327189i	$-0.893899\pi$
$827$	−27.7260	−	38.1615i	−0.964126	−	1.32701i	−0.0191672	−	0.999816i	$-0.506101\pi$
$828$	17.8291	+	5.79303i	0.619604	+	0.201322i
$829$	8.20305	−	25.2464i	0.284904	−	0.876844i	−0.701524	−	0.712646i	$-0.747497\pi$
$829$	8.20305	−	25.2464i	0.284904	−	0.876844i	0.986427	−	0.164197i	$-0.0525034\pi$
$830$	−1.23904	−	16.5462i	−0.0430077	−	0.574326i
$831$	−1.06300	−	3.27159i	−0.0368752	−	0.113490i
$832$			4.28408i			0.148524i
$833$	−0.500699	+	0.162687i	−0.0173482	+	0.00563677i
$834$	−0.653339	−	0.474678i	−0.0226233	−	0.0164368i
$835$	10.9977	+	6.79695i	0.380591	+	0.235218i
$836$	−1.17844	+	0.856187i	−0.0407572	+	0.0296118i
$837$	4.95286	−	6.81703i	0.171196	−	0.235631i
$838$	6.81556	−	9.38081i	0.235440	−	0.324055i
$839$	0.237312	−	0.172417i	0.00819291	−	0.00595250i	−0.583681	−	0.811983i	$-0.698388\pi$
$839$	0.237312	−	0.172417i	0.00819291	−	0.00595250i	0.591874	+	0.806030i	$0.298388\pi$
$840$	−0.381390	+	0.323242i	−0.0131592	+	0.0111529i
$841$	5.75320	+	4.17994i	0.198386	+	0.144136i
$842$	−2.77611	+	0.902012i	−0.0956710	+	0.0310854i
$843$		−	2.02020i		−	0.0695795i
$844$	−5.25934	−	16.1866i	−0.181034	−	0.557165i
$845$	−6.29322	+	10.1826i	−0.216493	+	0.350294i
$846$	−10.7398	+	33.0537i	−0.369242	+	1.13641i
$847$	9.71929	+	3.15799i	0.333959	+	0.108510i
$848$	0.520147	+	0.715921i	0.0178619	+	0.0245848i
$849$	−3.45078			−0.118430
$850$	0.348700	−	0.343446i	0.0119603	−	0.0117801i
$851$	25.9401			0.889215
$852$	−0.243244	−	0.334796i	−0.00833339	−	0.0114699i
$853$	47.9683	+	15.5859i	1.64240	+	0.533650i	0.977074	−	0.212899i	$-0.0682906\pi$
$853$	47.9683	+	15.5859i	1.64240	+	0.533650i	0.665330	+	0.746549i	$0.268291\pi$
$854$	−0.659802	+	2.03066i	−0.0225780	+	0.0694878i
$855$	−2.05165	+	0.840712i	−0.0701649	+	0.0287517i
$856$	−3.77070	−	11.6050i	−0.128880	−	0.396651i
$857$			42.6554i			1.45708i	0.685003	+	0.728540i	$0.259801\pi$
$857$			42.6554i			1.45708i	−0.685003	+	0.728540i	$0.740199\pi$
$858$	−3.12016	+	1.01380i	−0.106521	+	0.0346107i
$859$	−24.0952	−	17.5062i	−0.822118	−	0.597304i	0.0952006	−	0.995458i	$-0.469651\pi$
$859$	−24.0952	−	17.5062i	−0.822118	−	0.597304i	−0.917318	+	0.398155i	$0.869651\pi$
$860$	−8.65604	−	21.1240i	−0.295169	−	0.720321i
$861$	2.06779	−	1.50233i	0.0704700	−	0.0511994i
$862$	−4.45269	+	6.12860i	−0.151659	+	0.208741i
$863$	−16.1142	+	22.1793i	−0.548534	+	0.754992i	−0.989812	−	0.142378i	$-0.954525\pi$
$863$	−16.1142	+	22.1793i	−0.548534	+	0.754992i	0.441278	+	0.897370i	$0.354525\pi$
$864$	−0.847859	+	0.616005i	−0.0288447	+	0.0209569i
$865$	−5.58233	+	22.8693i	−0.189805	+	0.777580i
$866$	23.2853	+	16.9177i	0.791265	+	0.574888i
$867$	−2.83702	+	0.921803i	−0.0963502	+	0.0313061i
$868$		−	10.2390i		−	0.347533i
$869$	10.9637	+	33.7426i	0.371916	+	1.14464i
$870$	−1.18755	−	1.40118i	−0.0402618	−	0.0475045i
$871$	−1.54759	+	4.76300i	−0.0524382	+	0.161388i
$872$	4.80371	+	1.56082i	0.162674	+	0.0528560i
$873$	−11.5315	−	15.8718i	−0.390282	−	0.537177i
$874$	−2.10851			−0.0713214
$875$	7.30046	+	12.2235i	0.246801	+	0.413231i
$876$	0.282397			0.00954130
$877$	1.95893	+	2.69624i	0.0661484	+	0.0910455i	0.840809	−	0.541331i	$-0.182079\pi$
$877$	1.95893	+	2.69624i	0.0661484	+	0.0910455i	−0.774661	+	0.632377i	$0.782079\pi$
$878$	16.8798	+	5.48459i	0.569666	+	0.185096i
$879$	0.332147	−	1.02224i	0.0112030	−	0.0344794i
$880$	6.30600	+	7.44038i	0.212575	+	0.250815i
$881$	−2.40321	−	7.39632i	−0.0809662	−	0.249188i	0.902377	−	0.430948i	$-0.141821\pi$
$881$	−2.40321	−	7.39632i	−0.0809662	−	0.249188i	−0.983343	+	0.181760i	$0.941821\pi$
$882$		−	15.9691i		−	0.537709i
$883$	−5.35794	+	1.74090i	−0.180309	+	0.0585859i	−0.397780	−	0.917481i	$-0.630219\pi$
$883$	−5.35794	+	1.74090i	−0.180309	+	0.0585859i	0.217471	+	0.976067i	$0.430219\pi$
$884$	0.339266	+	0.246491i	0.0114107	+	0.00829039i
$885$	0.708317	−	2.90179i	0.0238098	−	0.0975425i
$886$	15.6496	−	11.3701i	0.525758	−	0.381985i
$887$	−12.9554	+	17.8316i	−0.435001	+	0.598728i	−0.969092	−	0.246699i	$-0.920654\pi$
$887$	−12.9554	+	17.8316i	−0.435001	+	0.598728i	0.534091	+	0.845427i	$0.320654\pi$
$888$	−0.423989	+	0.583571i	−0.0142281	+	0.0195833i
$889$	−1.35886	+	0.987268i	−0.0455746	+	0.0331119i
$890$	−1.44832	−	3.53443i	−0.0485477	−	0.118474i
$891$	30.7831	+	22.3652i	1.03127	+	0.749262i
$892$	−4.73429	+	1.53827i	−0.158516	+	0.0515049i
$893$		−	3.90900i		−	0.130810i
$894$	−0.110237	−	0.339276i	−0.00368689	−	0.0113471i
$895$	22.4680	−	9.20679i	0.751022	−	0.307749i
$896$	−0.393520	+	1.21113i	−0.0131466	+	0.0404610i
$897$	−4.51651	−	1.46750i	−0.150802	−	0.0489985i
$898$	−6.63799	−	9.13641i	−0.221513	−	0.304886i
$899$	37.6168			1.25459
$900$	6.63928	+	13.2786i	0.221309	+	0.442618i
$901$	0.0866228			0.00288582
$902$	−29.3084	−	40.3396i	−0.975864	−	1.34316i
$903$	2.17089	+	0.705366i	0.0722428	+	0.0234731i
$904$	4.33708	−	13.3482i	0.144249	−	0.443953i
$905$	−12.0916	+	19.5647i	−0.401940	+	0.650352i
$906$	1.02896	+	3.16681i	0.0341849	+	0.105210i
$907$		−	10.7033i		−	0.355398i	−0.984085	−	0.177699i	$-0.943135\pi$
$907$		−	10.7033i		−	0.355398i	0.984085	−	0.177699i	$-0.0568653\pi$
$908$	−0.976514	+	0.317289i	−0.0324068	+	0.0105296i
$909$	16.8703	+	12.2570i	0.559553	+	0.406539i
$910$	−9.30625	+	7.88740i	−0.308499	+	0.261465i
$911$	−44.2253	+	32.1316i	−1.46525	+	1.06457i	−0.483294	+	0.875458i	$0.660560\pi$
$911$	−44.2253	+	32.1316i	−1.46525	+	1.06457i	−0.981956	+	0.189108i	$0.939440\pi$
$912$	0.0344634	−	0.0474348i	0.00114120	−	0.00157072i
$913$	19.0243	−	26.1846i	0.629611	−	0.866585i
$914$	2.10944	−	1.53260i	0.0697741	−	0.0506939i
$915$	−0.559931	−	0.346056i	−0.0185108	−	0.0114403i
$916$	3.30489	+	2.40115i	0.109197	+	0.0793361i
$917$	2.15639	−	0.700653i	0.0712102	−	0.0231376i
$918$			0.102587i			0.00338586i
$919$	13.9687	+	42.9912i	0.460785	+	1.41815i	0.864207	+	0.503136i	$0.167821\pi$
$919$	13.9687	+	42.9912i	0.460785	+	1.41815i	−0.403422	+	0.915014i	$0.632179\pi$
$920$	1.05425	+	14.0786i	0.0347577	+	0.464156i
$921$	−0.770056	+	2.36999i	−0.0253742	+	0.0780938i
$922$	1.86171	+	0.604905i	0.0613120	+	0.0199215i
$923$	−5.93536	−	8.16933i	−0.195365	−	0.268897i
$924$	−0.975210			−0.0320820
$925$	14.4151	+	14.6356i	0.473965	+	0.481216i
$926$	−1.45797			−0.0479118
$927$	22.2459	+	30.6189i	0.730651	+	1.00566i
$928$	−4.44955	−	1.44575i	−0.146064	−	0.0474589i
$929$	−11.4615	+	35.2748i	−0.376039	+	1.15733i	0.566736	+	0.823899i	$0.308206\pi$
$929$	−11.4615	+	35.2748i	−0.376039	+	1.15733i	−0.942775	+	0.333429i	$0.891794\pi$
$930$	3.06649	+	0.748520i	0.100554	+	0.0245449i
$931$	0.555029	+	1.70820i	0.0181903	+	0.0559841i
$932$		−	4.41279i		−	0.144546i
$933$	−1.19993	+	0.389882i	−0.0392840	+	0.0127642i
$934$	20.6989	+	15.0387i	0.677290	+	0.492080i
$935$	0.952045	−	0.0712927i	0.0311352	−	0.00233152i
$936$	−10.2908	+	7.47673i	−0.336367	+	0.244385i
$937$	26.3755	−	36.3028i	0.861651	−	1.18596i	−0.119522	−	0.992831i	$-0.538136\pi$
$937$	26.3755	−	36.3028i	0.861651	−	1.18596i	0.981173	−	0.193129i	$-0.0618636\pi$
$938$	−0.875024	+	1.20437i	−0.0285705	+	0.0393240i
$939$	−0.0888654	+	0.0645645i	−0.00290001	+	0.00210698i
$940$	−26.1005	+	1.95450i	−0.851305	+	0.0637488i
$941$	−37.8128	−	27.4726i	−1.23266	−	0.895582i	−0.235575	−	0.971856i	$-0.575697\pi$
$941$	−37.8128	−	27.4726i	−1.23266	−	0.895582i	−0.997087	+	0.0762745i	$0.975697\pi$
$942$	−2.37827	+	0.772745i	−0.0774881	+	0.0251774i
$943$		−	72.1771i		−	2.35041i
$944$	−2.35114	−	7.23607i	−0.0765231	−	0.235514i
$945$	−2.89913	−	0.707669i	−0.0943087	−	0.0230205i
$946$	13.7607	−	42.3511i	0.447399	−	1.37695i
$947$	−32.6851	−	10.6200i	−1.06212	−	0.345105i	−0.274708	−	0.961528i	$-0.588581\pi$
$947$	−32.6851	−	10.6200i	−1.06212	−	0.345105i	−0.787415	+	0.616423i	$0.788581\pi$
$948$	−0.839423	−	1.15537i	−0.0272632	−	0.0375246i
$949$	6.89074			0.223683
$950$	−1.17171	−	1.18964i	−0.0380154	−	0.0385970i
$951$	1.26587			0.0410487
$952$	0.0732703	+	0.100848i	0.00237470	+	0.00326850i
$953$	14.4287	+	4.68815i	0.467390	+	0.151864i	0.533238	−	0.845965i	$-0.320975\pi$
$953$	14.4287	+	4.68815i	0.467390	+	0.151864i	−0.0658477	+	0.997830i	$0.520975\pi$
$954$	−0.811943	+	2.49890i	−0.0262876	+	0.0809050i
$955$	−1.60977	−	21.4969i	−0.0520909	−	0.695624i
$956$	6.72179	+	20.6875i	0.217398	+	0.669083i
$957$		−	3.58280i		−	0.115816i
$958$	6.53112	−	2.12209i	0.211011	−	0.0685617i
$959$	9.85029	+	7.15666i	0.318083	+	0.231101i
$960$	−0.333955	−	0.206396i	−0.0107783	−	0.00666139i
$961$	−27.2205	+	19.7768i	−0.878079	+	0.637962i
$962$	−10.3457	+	14.2396i	−0.333559	+	0.459105i
$963$	21.2958	−	29.3111i	0.686247	−	0.944538i
$964$	−12.8328	+	9.32358i	−0.413317	+	0.300292i
$965$	−10.2349	+	8.67447i	−0.329474	+	0.279241i
$966$	−1.14204	−	0.829740i	−0.0367445	−	0.0266965i
$967$	−50.8143	+	16.5106i	−1.63408	+	0.530944i	−0.975204	−	0.221309i	$-0.928967\pi$
$967$	−50.8143	+	16.5106i	−1.63408	+	0.530944i	−0.658874	+	0.752253i	$0.728967\pi$
$968$			8.02497i			0.257932i
$969$	−0.00177356	−	0.00545847i	−5.69751e−5	−	0.000175351i
$970$	7.76748	−	12.5680i	0.249399	−	0.403536i
$971$	8.39505	−	25.8373i	0.269410	−	0.829159i	−0.721234	−	0.692691i	$-0.756425\pi$
$971$	8.39505	−	25.8373i	0.269410	−	0.829159i	0.990645	−	0.136468i	$-0.0435750\pi$
$972$	−4.44679	−	1.44485i	−0.142631	−	0.0463435i
$973$	−3.44296	−	4.73883i	−0.110376	−	0.151920i
$974$	42.3233			1.35613
$975$	−1.68188	−	3.36375i	−0.0538631	−	0.107726i
$976$	−1.67667			−0.0536688
$977$	−6.69674	−	9.21727i	−0.214248	−	0.294886i	0.688344	−	0.725384i	$-0.258338\pi$
$977$	−6.69674	−	9.21727i	−0.214248	−	0.294886i	−0.902592	+	0.430498i	$0.858338\pi$
$978$	3.29190	+	1.06960i	0.105263	+	0.0342022i
$979$	2.30242	−	7.08611i	0.0735856	−	0.226473i
$980$	11.1282	−	4.56004i	0.355477	−	0.145665i
$981$	4.63434	+	14.2630i	0.147963	+	0.455384i
$982$		−	12.9499i		−	0.413249i
$983$	8.65482	−	2.81212i	0.276046	−	0.0896927i	−0.167723	−	0.985834i	$-0.553641\pi$
$983$	8.65482	−	2.81212i	0.276046	−	0.0896927i	0.443768	+	0.896142i	$0.353641\pi$
$984$	1.62376	+	1.17973i	0.0517635	+	0.0376084i
$985$	17.5918	+	42.9305i	0.560521	+	1.36788i
$986$	−0.370503	+	0.269186i	−0.0117992	+	0.00857264i
$987$	1.53827	−	2.11725i	0.0489637	−	0.0673928i
$988$	0.840938	−	1.15745i	0.0267538	−	0.0368235i
$989$	52.1484	−	37.8880i	1.65822	−	1.20477i
$990$	−6.86716	+	28.1329i	−0.218253	+	0.894124i
$991$	−4.04514	−	2.93897i	−0.128498	−	0.0933594i	0.521680	−	0.853141i	$-0.325306\pi$
$991$	−4.04514	−	2.93897i	−0.128498	−	0.0933594i	−0.650178	+	0.759782i	$0.725306\pi$
$992$	7.64677	−	2.48459i	0.242785	−	0.0788857i
$993$		−	4.25133i		−	0.134912i
$994$	−0.927551	−	2.85471i	−0.0294201	−	0.0905459i
$995$	−27.5601	−	32.5178i	−0.873714	−	1.03089i
$996$	−0.402588	+	1.23904i	−0.0127565	+	0.0392604i
$997$	−46.9380	−	15.2511i	−1.48654	−	0.483006i	−0.550481	−	0.834848i	$-0.685556\pi$
$997$	−46.9380	−	15.2511i	−1.48654	−	0.483006i	−0.936060	+	0.351841i	$0.885556\pi$
$998$	7.62749	+	10.4983i	0.241444	+	0.332319i
$999$	−4.30576			−0.136228

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.2.e.a.39.2	yes	8
3.2	odd	2		450.2.l.b.289.1		8
4.3	odd	2		400.2.y.a.289.2		8
5.2	odd	4		250.2.d.b.51.2		8
5.3	odd	4		250.2.d.c.51.1		8
5.4	even	2		250.2.e.a.199.1		8
25.3	odd	20		1250.2.a.h.1.2		4
25.4	even	10		1250.2.b.c.1249.6		8
25.9	even	10	inner	50.2.e.a.9.2	✓	8
25.12	odd	20		250.2.d.b.201.2		8
25.13	odd	20		250.2.d.c.201.1		8
25.16	even	5		250.2.e.a.49.1		8
25.21	even	5		1250.2.b.c.1249.3		8
25.22	odd	20		1250.2.a.i.1.3		4
75.59	odd	10		450.2.l.b.109.1		8
100.3	even	20		10000.2.a.o.1.3		4
100.47	even	20		10000.2.a.bb.1.2		4
100.59	odd	10		400.2.y.a.209.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.e.a.9.2	✓	8	25.9	even	10	inner
50.2.e.a.39.2	yes	8	1.1	even	1	trivial
250.2.d.b.51.2		8	5.2	odd	4
250.2.d.b.201.2		8	25.12	odd	20
250.2.d.c.51.1		8	5.3	odd	4
250.2.d.c.201.1		8	25.13	odd	20
250.2.e.a.49.1		8	25.16	even	5
250.2.e.a.199.1		8	5.4	even	2
400.2.y.a.209.2		8	100.59	odd	10
400.2.y.a.289.2		8	4.3	odd	2
450.2.l.b.109.1		8	75.59	odd	10
450.2.l.b.289.1		8	3.2	odd	2
1250.2.a.h.1.2		4	25.3	odd	20
1250.2.a.i.1.3		4	25.22	odd	20
1250.2.b.c.1249.3		8	25.21	even	5
1250.2.b.c.1249.6		8	25.4	even	10
10000.2.a.o.1.3		4	100.3	even	20
10000.2.a.bb.1.2		4	100.47	even	20

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	50.2.e.a.39.2

Level	$50$
Weight	$2$
Character	50.39
Analytic conductor	$0.399$
Analytic rank	$0$
Dimension	$8$
Inner twists	$2$