LMFDB - Embedded newform 714.2.bf.a.29.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [714,2,Mod(29,714)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(714, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 0, 13]))

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

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

chi := DirichletCharacter("714.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 714 = 2 \cdot 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	714.bf (of order $16$, degree $8$, 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:	$5.70131870432$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			29.12
Character	$\chi$	$=$	714.29
Dual form			714.2.bf.a.197.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.923880 + 0.382683i) q^{2} +(0.285068 - 1.70843i) q^{3} +(0.707107 - 0.707107i) q^{4} +(-0.344420 + 1.73152i) q^{5} +(0.390419 + 1.68748i) q^{6} +(-0.980785 + 0.195090i) q^{7} +(-0.382683 + 0.923880i) q^{8} +(-2.83747 - 0.974039i) q^{9} +O(q^{10})$	\(q+(-0.923880 + 0.382683i) q^{2} +(0.285068 - 1.70843i) q^{3} +(0.707107 - 0.707107i) q^{4} +(-0.344420 + 1.73152i) q^{5} +(0.390419 + 1.68748i) q^{6} +(-0.980785 + 0.195090i) q^{7} +(-0.382683 + 0.923880i) q^{8} +(-2.83747 - 0.974039i) q^{9} +(-0.344420 - 1.73152i) q^{10} +(0.224582 + 0.150061i) q^{11} +(-1.00647 - 1.40962i) q^{12} +(2.13539 + 2.13539i) q^{13} +(0.831470 - 0.555570i) q^{14} +(2.85999 + 1.08202i) q^{15} -1.00000i q^{16} +(-0.339200 + 4.10913i) q^{17} +(2.99423 - 0.185959i) q^{18} +(0.806580 + 1.94726i) q^{19} +(0.980825 + 1.46791i) q^{20} +(0.0537076 + 1.73122i) q^{21} +(-0.264913 - 0.0526945i) q^{22} +(-1.20657 + 1.80576i) q^{23} +(1.46929 + 0.917157i) q^{24} +(1.73987 + 0.720680i) q^{25} +(-2.79002 - 1.15567i) q^{26} +(-2.47295 + 4.56996i) q^{27} +(-0.555570 + 0.831470i) q^{28} +(5.50611 + 1.09523i) q^{29} +(-3.05636 + 0.0948175i) q^{30} +(-2.23008 - 3.33756i) q^{31} +(0.382683 + 0.923880i) q^{32} +(0.320390 - 0.340906i) q^{33} +(-1.25912 - 3.92615i) q^{34} -1.76544i q^{35} +(-2.69515 + 1.31765i) q^{36} +(-2.55287 + 1.70577i) q^{37} +(-1.49037 - 1.49037i) q^{38} +(4.25690 - 3.03944i) q^{39} +(-1.46791 - 0.980825i) q^{40} +(1.65627 + 8.32663i) q^{41} +(-0.712128 - 1.57888i) q^{42} +(-2.20675 + 5.32756i) q^{43} +(0.264913 - 0.0526945i) q^{44} +(2.66385 - 4.57765i) q^{45} +(0.423691 - 2.13004i) q^{46} +(6.17639 - 6.17639i) q^{47} +(-1.70843 - 0.285068i) q^{48} +(0.923880 - 0.382683i) q^{49} -1.88323 q^{50} +(6.92347 + 1.75088i) q^{51} +3.01990 q^{52} +(5.21670 - 2.16083i) q^{53} +(0.535862 - 5.16845i) q^{54} +(-0.337184 + 0.337184i) q^{55} +(0.195090 - 0.980785i) q^{56} +(3.55668 - 0.822885i) q^{57} +(-5.50611 + 1.09523i) q^{58} +(3.32402 - 8.02491i) q^{59} +(2.78742 - 1.25722i) q^{60} +(2.38324 + 11.9814i) q^{61} +(3.33756 + 2.23008i) q^{62} +(2.97298 + 0.401759i) q^{63} +(-0.707107 - 0.707107i) q^{64} +(-4.43294 + 2.96199i) q^{65} +(-0.165543 + 0.437564i) q^{66} +4.91685i q^{67} +(2.66574 + 3.14544i) q^{68} +(2.74106 + 2.57611i) q^{69} +(0.675604 + 1.63105i) q^{70} +(-0.565485 - 0.846308i) q^{71} +(1.98575 - 2.24873i) q^{72} +(5.02763 + 1.00006i) q^{73} +(1.70577 - 2.55287i) q^{74} +(1.72721 - 2.76701i) q^{75} +(1.94726 + 0.806580i) q^{76} +(-0.249543 - 0.103364i) q^{77} +(-2.76972 + 4.43712i) q^{78} +(-2.43902 + 3.65025i) q^{79} +(1.73152 + 0.344420i) q^{80} +(7.10250 + 5.52762i) q^{81} +(-4.71666 - 7.05897i) q^{82} +(3.99331 + 9.64069i) q^{83} +(1.26213 + 1.18618i) q^{84} +(-6.99820 - 2.00260i) q^{85} -5.76651i q^{86} +(3.44075 - 9.09459i) q^{87} +(-0.224582 + 0.150061i) q^{88} +(-2.15330 - 2.15330i) q^{89} +(-0.709282 + 5.24861i) q^{90} +(-2.51096 - 1.67777i) q^{91} +(0.423691 + 2.13004i) q^{92} +(-6.33771 + 2.85851i) q^{93} +(-3.34264 + 8.06984i) q^{94} +(-3.64951 + 0.725932i) q^{95} +(1.68748 - 0.390419i) q^{96} +(-0.490506 + 2.46594i) q^{97} +(-0.707107 + 0.707107i) q^{98} +(-0.491081 - 0.644546i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q+O(q^{10}) $ 144 * q	$ 144 q - 16 q^{11} + 32 q^{17} + 16 q^{24} + 32 q^{25} + 16 q^{29} + 32 q^{31} + 48 q^{38} - 16 q^{39} + 16 q^{43} - 64 q^{45} - 16 q^{46} + 32 q^{47} + 176 q^{50} - 64 q^{51} - 32 q^{52} - 128 q^{53} - 64 q^{54} - 16 q^{57} - 16 q^{58} - 16 q^{60} - 32 q^{61} - 32 q^{62} + 16 q^{70} - 16 q^{71} - 16 q^{72} - 16 q^{74} + 112 q^{75} + 16 q^{78} + 64 q^{79} + 32 q^{80} + 128 q^{82} - 144 q^{83} - 16 q^{85} + 112 q^{87} + 16 q^{88} + 96 q^{91} - 16 q^{92} - 32 q^{93} + 32 q^{97} + 16 q^{99}+O(q^{100}) $ 144 * q - 16 * q^11 + 32 * q^17 + 16 * q^24 + 32 * q^25 + 16 * q^29 + 32 * q^31 + 48 * q^38 - 16 * q^39 + 16 * q^43 - 64 * q^45 - 16 * q^46 + 32 * q^47 + 176 * q^50 - 64 * q^51 - 32 * q^52 - 128 * q^53 - 64 * q^54 - 16 * q^57 - 16 * q^58 - 16 * q^60 - 32 * q^61 - 32 * q^62 + 16 * q^70 - 16 * q^71 - 16 * q^72 - 16 * q^74 + 112 * q^75 + 16 * q^78 + 64 * q^79 + 32 * q^80 + 128 * q^82 - 144 * q^83 - 16 * q^85 + 112 * q^87 + 16 * q^88 + 96 * q^91 - 16 * q^92 - 32 * q^93 + 32 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/714\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$547$
$\chi(n)$	$-1$	$1$	$e\left(\frac{13}{16}\right)$

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 $

$2$	−0.923880	+	0.382683i	−0.653281	+	0.270598i
$2$	−0.923880	+	0.382683i	−0.653281	+	0.270598i
$3$	0.285068	−	1.70843i	0.164584	−	0.986363i
$3$	0.285068	−	1.70843i	0.164584	−	0.986363i
$4$	0.707107	−	0.707107i	0.353553	−	0.353553i
$5$	−0.344420	+	1.73152i	−0.154029	+	0.774358i	0.824114	+	0.566424i	$0.191674\pi$
$5$	−0.344420	+	1.73152i	−0.154029	+	0.774358i	−0.978143	+	0.207933i	$0.933326\pi$
$6$	0.390419	+	1.68748i	0.159388	+	0.688909i
$7$	−0.980785	+	0.195090i	−0.370702	+	0.0737372i
$7$	−0.980785	+	0.195090i	−0.370702	+	0.0737372i
$8$	−0.382683	+	0.923880i	−0.135299	+	0.326641i
$9$	−2.83747	−	0.974039i	−0.945824	−	0.324680i
$10$	−0.344420	−	1.73152i	−0.108915	−	0.547554i
$11$	0.224582	+	0.150061i	0.0677141	+	0.0452451i	0.588967	−	0.808157i	$-0.299535\pi$
$11$	0.224582	+	0.150061i	0.0677141	+	0.0452451i	−0.521252	+	0.853403i	$0.674535\pi$
$12$	−1.00647	−	1.40962i	−0.290543	−	0.406921i
$13$	2.13539	+	2.13539i	0.592251	+	0.592251i	0.938239	−	0.345988i	$-0.112456\pi$
$13$	2.13539	+	2.13539i	0.592251	+	0.592251i	−0.345988	+	0.938239i	$0.612456\pi$
$14$	0.831470	−	0.555570i	0.222220	−	0.148482i
$15$	2.85999	+	1.08202i	0.738447	+	0.279376i
$16$		−	1.00000i		−	0.250000i
$17$	−0.339200	+	4.10913i	−0.0822680	+	0.996610i
$17$	−0.339200	+	4.10913i	−0.0822680	+	0.996610i
$18$	2.99423	−	0.185959i	0.705747	−	0.0438310i
$19$	0.806580	+	1.94726i	0.185042	+	0.446731i	0.988993	−	0.147965i	$-0.0472723\pi$
$19$	0.806580	+	1.94726i	0.185042	+	0.446731i	−0.803950	+	0.594696i	$0.797272\pi$
$20$	0.980825	+	1.46791i	0.219319	+	0.328234i
$21$	0.0537076	+	1.73122i	0.0117200	+	0.377783i
$22$	−0.264913	−	0.0526945i	−0.0564796	−	0.0112345i
$23$	−1.20657	+	1.80576i	−0.251587	+	0.376527i	−0.935669	−	0.352878i	$-0.885203\pi$
$23$	−1.20657	+	1.80576i	−0.251587	+	0.376527i	0.684082	+	0.729405i	$0.260203\pi$
$24$	1.46929	+	0.917157i	0.299918	+	0.187214i
$25$	1.73987	+	0.720680i	0.347975	+	0.144136i
$26$	−2.79002	−	1.15567i	−0.547169	−	0.226645i
$27$	−2.47295	+	4.56996i	−0.475920	+	0.879489i
$28$	−0.555570	+	0.831470i	−0.104993	+	0.157133i
$29$	5.50611	+	1.09523i	1.02246	+	0.203380i	0.677721	−	0.735319i	$-0.262968\pi$
$29$	5.50611	+	1.09523i	1.02246	+	0.203380i	0.344738	+	0.938699i	$0.387968\pi$
$30$	−3.05636	+	0.0948175i	−0.558012	+	0.0173112i
$31$	−2.23008	−	3.33756i	−0.400535	−	0.599443i	0.575303	−	0.817941i	$-0.304884\pi$
$31$	−2.23008	−	3.33756i	−0.400535	−	0.599443i	−0.975837	+	0.218498i	$0.929884\pi$
$32$	0.382683	+	0.923880i	0.0676495	+	0.163320i
$33$	0.320390	−	0.340906i	0.0557728	−	0.0593441i
$34$	−1.25912	−	3.92615i	−0.215937	−	0.673329i
$35$		−	1.76544i		−	0.298414i
$36$	−2.69515	+	1.31765i	−0.449191	+	0.219608i
$37$	−2.55287	+	1.70577i	−0.419689	+	0.280427i	−0.747430	−	0.664340i	$-0.768713\pi$
$37$	−2.55287	+	1.70577i	−0.419689	+	0.280427i	0.327741	+	0.944767i	$0.393713\pi$
$38$	−1.49037	−	1.49037i	−0.241769	−	0.241769i
$39$	4.25690	−	3.03944i	0.681650	−	0.486699i
$40$	−1.46791	−	0.980825i	−0.232097	−	0.155082i
$41$	1.65627	+	8.32663i	0.258666	+	1.30040i	0.863621	+	0.504141i	$0.168191\pi$
$41$	1.65627	+	8.32663i	0.258666	+	1.30040i	−0.604955	+	0.796259i	$0.706809\pi$
$42$	−0.712128	−	1.57888i	−0.109884	−	0.243627i
$43$	−2.20675	+	5.32756i	−0.336526	+	0.812445i	0.661518	+	0.749929i	$0.269913\pi$
$43$	−2.20675	+	5.32756i	−0.336526	+	0.812445i	−0.998044	+	0.0625162i	$0.980087\pi$
$44$	0.264913	−	0.0526945i	0.0399371	−	0.00794399i
$45$	2.66385	−	4.57765i	0.397103	−	0.682396i
$46$	0.423691	−	2.13004i	0.0624698	−	0.314057i
$47$	6.17639	−	6.17639i	0.900919	−	0.900919i	−0.0945967	−	0.995516i	$-0.530156\pi$
$47$	6.17639	−	6.17639i	0.900919	−	0.900919i	0.995516	+	0.0945967i	$0.0301562\pi$
$48$	−1.70843	−	0.285068i	−0.246591	−	0.0411461i
$49$	0.923880	−	0.382683i	0.131983	−	0.0546691i
$50$	−1.88323			−0.266328
$51$	6.92347	+	1.75088i	0.969479	+	0.245172i
$52$	3.01990			0.418785
$53$	5.21670	−	2.16083i	0.716569	−	0.296813i	0.00554909	−	0.999985i	$-0.498234\pi$
$53$	5.21670	−	2.16083i	0.716569	−	0.296813i	0.711020	+	0.703172i	$0.248234\pi$
$54$	0.535862	−	5.16845i	0.0729215	−	0.703337i
$55$	−0.337184	+	0.337184i	−0.0454659	+	0.0454659i
$56$	0.195090	−	0.980785i	0.0260700	−	0.131063i
$57$	3.55668	−	0.822885i	0.471094	−	0.108994i
$58$	−5.50611	+	1.09523i	−0.722988	+	0.143811i
$59$	3.32402	−	8.02491i	0.432751	−	1.04475i	−0.545645	−	0.838016i	$-0.683715\pi$
$59$	3.32402	−	8.02491i	0.432751	−	1.04475i	0.978396	−	0.206738i	$-0.0662846\pi$
$60$	2.78742	−	1.25722i	0.359855	−	0.162306i
$61$	2.38324	+	11.9814i	0.305143	+	1.53406i	0.763806	+	0.645446i	$0.223328\pi$
$61$	2.38324	+	11.9814i	0.305143	+	1.53406i	−0.458664	+	0.888610i	$0.651672\pi$
$62$	3.33756	+	2.23008i	0.423870	+	0.283221i
$63$	2.97298	+	0.401759i	0.374560	+	0.0506169i
$64$	−0.707107	−	0.707107i	−0.0883883	−	0.0883883i
$65$	−4.43294	+	2.96199i	−0.549838	+	0.367390i
$66$	−0.165543	+	0.437564i	−0.0203769	+	0.0538604i
$67$			4.91685i			0.600689i	0.953831	+	0.300344i	$0.0971016\pi$
$67$			4.91685i			0.600689i	−0.953831	+	0.300344i	$0.902898\pi$
$68$	2.66574	+	3.14544i	0.323269	+	0.381441i
$69$	2.74106	+	2.57611i	0.329985	+	0.310127i
$70$	0.675604	+	1.63105i	0.0807501	+	0.194948i
$71$	−0.565485	−	0.846308i	−0.0671107	−	0.100438i	0.796396	−	0.604775i	$-0.206737\pi$
$71$	−0.565485	−	0.846308i	−0.0671107	−	0.100438i	−0.863507	+	0.504337i	$0.831737\pi$
$72$	1.98575	−	2.24873i	0.234023	−	0.265016i
$73$	5.02763	+	1.00006i	0.588439	+	0.117048i	0.480325	−	0.877091i	$-0.340519\pi$
$73$	5.02763	+	1.00006i	0.588439	+	0.117048i	0.108114	+	0.994138i	$0.465519\pi$
$74$	1.70577	−	2.55287i	0.198292	−	0.296765i
$75$	1.72721	−	2.76701i	0.199441	−	0.319507i
$76$	1.94726	+	0.806580i	0.223366	+	0.0925211i
$77$	−0.249543	−	0.103364i	−0.0284380	−	0.0117794i
$78$	−2.76972	+	4.43712i	−0.313609	+	0.502405i
$79$	−2.43902	+	3.65025i	−0.274411	+	0.410686i	−0.942920	−	0.333019i	$-0.891933\pi$
$79$	−2.43902	+	3.65025i	−0.274411	+	0.410686i	0.668509	+	0.743704i	$0.266933\pi$
$80$	1.73152	+	0.344420i	0.193589	+	0.0385073i
$81$	7.10250	+	5.52762i	0.789166	+	0.614180i
$82$	−4.71666	−	7.05897i	−0.520868	−	0.779533i
$83$	3.99331	+	9.64069i	0.438322	+	1.05820i	0.976528	+	0.215390i	$0.0691023\pi$
$83$	3.99331	+	9.64069i	0.438322	+	1.05820i	−0.538206	+	0.842813i	$0.680898\pi$
$84$	1.26213	+	1.18618i	0.137710	+	0.129423i
$85$	−6.99820	−	2.00260i	−0.759061	−	0.217212i
$86$		−	5.76651i		−	0.621819i
$87$	3.44075	−	9.09459i	0.368887	−	0.975042i
$88$	−0.224582	+	0.150061i	−0.0239406	+	0.0159966i
$89$	−2.15330	−	2.15330i	−0.228250	−	0.228250i	0.583711	−	0.811961i	$-0.301600\pi$
$89$	−2.15330	−	2.15330i	−0.228250	−	0.228250i	−0.811961	+	0.583711i	$0.801600\pi$
$90$	−0.709282	+	5.24861i	−0.0747649	+	0.553252i
$91$	−2.51096	−	1.67777i	−0.263220	−	0.175878i
$92$	0.423691	+	2.13004i	0.0441728	+	0.222072i
$93$	−6.33771	+	2.85851i	−0.657190	+	0.296414i
$94$	−3.34264	+	8.06984i	−0.344767	+	0.832341i
$95$	−3.64951	+	0.725932i	−0.374432	+	0.0744791i
$96$	1.68748	−	0.390419i	0.172227	−	0.0398470i
$97$	−0.490506	+	2.46594i	−0.0498033	+	0.250378i	−0.997664	−	0.0683055i	$-0.978241\pi$
$97$	−0.490506	+	2.46594i	−0.0498033	+	0.250378i	0.947861	+	0.318684i	$0.103241\pi$
$98$	−0.707107	+	0.707107i	−0.0714286	+	0.0714286i
$99$	−0.491081	−	0.644546i	−0.0493555	−	0.0647793i
$100$	1.73987	−	0.720680i	0.173987	−	0.0720680i
$101$	−15.0948			−1.50199			−0.750993	−	0.660310i	$-0.770425\pi$
$101$	−15.0948			−1.50199			−0.750993	+	0.660310i	$0.770425\pi$
$102$	−7.06648	+	1.03189i	−0.699686	+	0.102173i
$103$	3.17820			0.313157			0.156579	−	0.987666i	$-0.449954\pi$
$103$	3.17820			0.313157			0.156579	+	0.987666i	$0.449954\pi$
$104$	−2.79002	+	1.15567i	−0.273584	+	0.113322i
$105$	−3.01613	−	0.503270i	−0.294344	−	0.0491142i
$106$	−3.99269	+	3.99269i	−0.387804	+	0.387804i
$107$	1.61157	−	8.10190i	0.155796	−	0.783240i	−0.821309	−	0.570483i	$-0.806756\pi$
$107$	1.61157	−	8.10190i	0.155796	−	0.783240i	0.977105	−	0.212757i	$-0.0682441\pi$
$108$	1.48281	+	4.98009i	0.142683	+	0.479209i
$109$	−15.7682	+	3.13648i	−1.51032	+	0.300420i	−0.879645	−	0.475630i	$-0.842220\pi$
$109$	−15.7682	+	3.13648i	−1.51032	+	0.300420i	−0.630670	+	0.776051i	$0.717220\pi$
$110$	0.182483	−	0.440552i	0.0173990	−	0.0420050i
$111$	2.18645	+	4.84766i	0.207529	+	0.460119i
$112$	0.195090	+	0.980785i	0.0184343	+	0.0926755i
$113$	−0.241018	−	0.161043i	−0.0226730	−	0.0151496i	0.544182	−	0.838967i	$-0.316840\pi$
$113$	−0.241018	−	0.161043i	−0.0226730	−	0.0151496i	−0.566855	+	0.823818i	$0.691840\pi$
$114$	−2.97104	+	2.12133i	−0.278264	+	0.198681i
$115$	−2.71113	−	2.71113i	−0.252815	−	0.252815i
$116$	4.66785	−	3.11896i	0.433399	−	0.289588i
$117$	−3.97916	−	8.13907i	−0.367874	−	0.752457i
$118$			8.68610i			0.799620i
$119$	−0.468969	−	4.09635i	−0.0429903	−	0.375512i
$120$	−2.09413	+	2.22822i	−0.191167	+	0.203408i
$121$	−4.18160	−	10.0953i	−0.380145	−	0.917752i
$122$	−6.78689	−	10.1573i	−0.614456	−	0.919599i
$123$	14.6976	−	0.455965i	1.32524	−	0.0411129i
$124$	−3.93692	−	0.783101i	−0.353545	−	0.0703246i
$125$	−6.75124	+	10.1039i	−0.603849	+	0.903725i
$126$	−2.90042	+	0.766532i	−0.258390	+	0.0682881i
$127$	−9.98938	−	4.13774i	−0.886414	−	0.367165i	−0.107433	−	0.994212i	$-0.534263\pi$
$127$	−9.98938	−	4.13774i	−0.886414	−	0.367165i	−0.778981	+	0.627048i	$0.784263\pi$
$128$	0.923880	+	0.382683i	0.0816602	+	0.0338248i
$129$	8.47270	+	5.28879i	0.745979	+	0.465652i
$130$	2.96199	−	4.43294i	0.259784	−	0.388794i
$131$	1.05510	+	0.209872i	0.0921844	+	0.0183366i	0.240967	−	0.970533i	$-0.422535\pi$
$131$	1.05510	+	0.209872i	0.0921844	+	0.0183366i	−0.148783	+	0.988870i	$0.547535\pi$
$132$	−0.0145066	−	0.467607i	−0.00126264	−	0.0407000i
$133$	−1.17097	−	1.75248i	−0.101536	−	0.151960i
$134$	−1.88160	−	4.54258i	−0.162545	−	0.392419i
$135$	−7.06122	−	5.85594i	−0.607733	−	0.503999i
$136$	−3.66653	−	1.88588i	−0.314403	−	0.161712i
$137$			11.1077i			0.948996i	0.880257	+	0.474498i	$0.157370\pi$
$137$			11.1077i			0.948996i	−0.880257	+	0.474498i	$0.842630\pi$
$138$	−3.51824	−	1.33105i	−0.299493	−	0.113307i
$139$	16.7126	−	11.1670i	1.41755	−	0.947174i	0.418302	−	0.908308i	$-0.362625\pi$
$139$	16.7126	−	11.1670i	1.41755	−	0.947174i	0.999244	−	0.0388663i	$-0.0123747\pi$
$140$	−1.24835	−	1.24835i	−0.105505	−	0.105505i
$141$	−8.79124	−	12.3126i	−0.740356	−	1.03691i
$142$	0.846308	+	0.565485i	0.0710206	+	0.0474545i
$143$	0.159132	+	0.800011i	0.0133073	+	0.0669002i
$144$	−0.974039	+	2.83747i	−0.0811699	+	0.236456i
$145$	−3.79283	+	9.15670i	−0.314977	+	0.760422i
$146$	−5.02763	+	1.00006i	−0.416089	+	0.0827653i
$147$	−0.390419	−	1.68748i	−0.0322013	−	0.139181i
$148$	−0.598987	+	3.01131i	−0.0492364	+	0.247528i
$149$	6.53357	−	6.53357i	0.535251	−	0.535251i	−0.386879	−	0.922130i	$-0.626447\pi$
$149$	6.53357	−	6.53357i	0.535251	−	0.535251i	0.922130	+	0.386879i	$0.126447\pi$
$150$	−0.536848	+	3.21736i	−0.0438335	+	0.262697i
$151$	−16.4640	+	6.81960i	−1.33982	+	0.554972i	−0.933440	−	0.358733i	$-0.883209\pi$
$151$	−16.4640	+	6.81960i	−1.33982	+	0.554972i	−0.406380	+	0.913704i	$0.633209\pi$
$152$	−2.10769			−0.170957
$153$	4.96492	−	11.3291i	0.401390	−	0.915907i
$154$	0.270103			0.0217655
$155$	6.54712	−	2.71190i	0.525877	−	0.217825i
$156$	0.860878	−	5.15929i	0.0689254	−	0.413074i
$157$	5.29152	−	5.29152i	0.422309	−	0.422309i	−0.463689	−	0.885998i	$-0.653474\pi$
$157$	5.29152	−	5.29152i	0.422309	−	0.422309i	0.885998	+	0.463689i	$0.153474\pi$
$158$	0.856470	−	4.30577i	0.0681371	−	0.342548i
$159$	−2.20451	−	9.52835i	−0.174829	−	0.755648i
$160$	−1.73152	+	0.344420i	−0.136888	+	0.0272288i
$161$	0.831100	−	2.00645i	0.0654998	−	0.158131i
$162$	−8.67718	−	2.38884i	−0.681744	−	0.187685i
$163$	1.19556	+	6.01050i	0.0936437	+	0.470779i	0.998941	+	0.0460011i	$0.0146478\pi$
$163$	1.19556	+	6.01050i	0.0936437	+	0.470779i	−0.905298	+	0.424778i	$0.860352\pi$
$164$	7.05897	+	4.71666i	0.551213	+	0.368309i
$165$	0.479935	+	0.672176i	0.0373629	+	0.0523288i
$166$	−7.37867	−	7.37867i	−0.572696	−	0.572696i
$167$	5.30499	−	3.54468i	0.410512	−	0.274296i	−0.333120	−	0.942885i	$-0.608101\pi$
$167$	5.30499	−	3.54468i	0.410512	−	0.274296i	0.743632	+	0.668589i	$0.233101\pi$
$168$	−1.61999	−	0.612889i	−0.124985	−	0.0472854i
$169$		−	3.88020i		−	0.298477i
$170$	7.23185	−	0.827936i	0.554658	−	0.0634998i
$171$	−0.391945	−	6.31093i	−0.0299728	−	0.482609i
$172$	2.20675	+	5.32756i	0.168263	+	0.406223i
$173$	3.65558	+	5.47096i	0.277929	+	0.415950i	0.944004	−	0.329935i	$-0.107027\pi$
$173$	3.65558	+	5.47096i	0.277929	+	0.415950i	−0.666075	+	0.745885i	$0.732027\pi$
$174$	0.301513	+	9.71902i	0.0228577	+	0.736797i
$175$	−1.84704	−	0.367399i	−0.139623	−	0.0277728i
$176$	0.150061	−	0.224582i	0.0113113	−	0.0169285i
$177$	−12.7624	−	7.96651i	−0.959282	−	0.598800i
$178$	2.81343	+	1.16536i	0.210875	+	0.0873474i
$179$	−6.40447	−	2.65282i	−0.478692	−	0.198281i	0.130272	−	0.991478i	$-0.458415\pi$
$179$	−6.40447	−	2.65282i	−0.478692	−	0.198281i	−0.608965	+	0.793197i	$0.708415\pi$
$180$	−1.35326	−	5.12051i	−0.100866	−	0.381660i
$181$	9.21762	−	13.7951i	0.685141	−	1.02539i	−0.312020	−	0.950076i	$-0.601005\pi$
$181$	9.21762	−	13.7951i	0.685141	−	1.02539i	0.997160	−	0.0753097i	$-0.0239945\pi$
$182$	2.96187	+	0.589153i	0.219549	+	0.0436709i
$183$	21.1487	−	0.656097i	1.56336	−	0.0485001i
$184$	−1.20657	−	1.80576i	−0.0889495	−	0.133122i
$185$	−2.07431	−	5.00783i	−0.152506	−	0.368183i
$186$	4.76137	−	5.06626i	0.349121	−	0.371476i
$187$	−0.692799	+	0.871937i	−0.0506625	+	0.0637624i
$188$		−	8.73473i		−	0.637046i
$189$	1.53388	−	4.96460i	0.111573	−	0.361121i
$190$	3.09390	−	2.06728i	0.224455	−	0.149976i
$191$	−8.17859	−	8.17859i	−0.591782	−	0.591782i	0.346331	−	0.938113i	$-0.387428\pi$
$191$	−8.17859	−	8.17859i	−0.591782	−	0.591782i	−0.938113	+	0.346331i	$0.887428\pi$
$192$	−1.40962	+	1.00647i	−0.101730	+	0.0726357i
$193$	4.91949	+	3.28710i	0.354113	+	0.236611i	0.719884	−	0.694094i	$-0.244195\pi$
$193$	4.91949	+	3.28710i	0.354113	+	0.236611i	−0.365772	+	0.930705i	$0.619195\pi$
$194$	−0.490506	−	2.46594i	−0.0352163	−	0.177044i
$195$	3.79667	+	8.41774i	0.271885	+	0.602807i
$196$	0.382683	−	0.923880i	0.0273345	−	0.0659914i
$197$	−7.20801	+	1.43376i	−0.513550	+	0.102151i	−0.445060	−	0.895501i	$-0.646818\pi$
$197$	−7.20801	+	1.43376i	−0.513550	+	0.102151i	−0.0684891	+	0.997652i	$0.521818\pi$
$198$	0.700357	+	0.407554i	0.0497722	+	0.0289636i
$199$	3.45449	−	17.3669i	0.244882	−	1.23110i	−0.641126	−	0.767435i	$-0.721533\pi$
$199$	3.45449	−	17.3669i	0.244882	−	1.23110i	0.886008	−	0.463669i	$-0.153467\pi$
$200$	−1.33164	+	1.33164i	−0.0941613	+	0.0941613i
$201$	8.40010	+	1.40164i	0.592497	+	0.0988639i
$202$	13.9458	−	5.77652i	0.981220	−	0.406435i
$203$	−5.61398			−0.394024
$204$	6.13369	−	3.65757i	0.429444	−	0.256081i
$205$	−14.9881			−1.04682
$206$	−2.93627	+	1.21624i	−0.204580	+	0.0847397i
$207$	5.18249	−	3.94855i	0.360208	−	0.274443i
$208$	2.13539	−	2.13539i	0.148063	−	0.148063i
$209$	−0.111064	+	0.558356i	−0.00768245	+	0.0386223i
$210$	2.97913	−	0.689262i	0.205580	−	0.0475636i
$211$	−21.2137	+	4.21966i	−1.46041	+	0.290493i	−0.860449	−	0.509537i	$-0.829817\pi$
$211$	−21.2137	+	4.21966i	−1.46041	+	0.290493i	−0.599959	+	0.800030i	$0.704817\pi$
$212$	2.16083	−	5.21670i	0.148406	−	0.358284i
$213$	−1.60706	+	0.724837i	−0.110114	+	0.0496650i
$214$	1.61157	+	8.10190i	0.110164	+	0.553834i
$215$	−8.46471	−	5.65594i	−0.577288	−	0.385732i
$216$	−3.27573	−	4.03356i	−0.222885	−	0.274449i
$217$	2.83836	+	2.83836i	0.192680	+	0.192680i
$218$	13.3676	−	8.93194i	0.905368	−	0.604948i
$219$	3.14174	−	8.30427i	0.212299	−	0.561150i
$220$			0.476850i			0.0321492i
$221$	−9.49893	+	8.05028i	−0.638967	+	0.541520i
$222$	−3.87514	−	3.64193i	−0.260082	−	0.244431i
$223$	4.72582	+	11.4091i	0.316465	+	0.764013i	0.999436	+	0.0335684i	$0.0106872\pi$
$223$	4.72582	+	11.4091i	0.316465	+	0.764013i	−0.682972	+	0.730445i	$0.739313\pi$
$224$	−0.555570	−	0.831470i	−0.0371206	−	0.0555549i
$225$	−4.23488	−	3.73961i	−0.282325	−	0.249308i
$226$	0.284300	+	0.0565507i	0.0189113	+	0.00376170i
$227$	−4.34292	+	6.49964i	−0.288250	+	0.431396i	−0.947129	−	0.320852i	$-0.896031\pi$
$227$	−4.34292	+	6.49964i	−0.288250	+	0.431396i	0.658880	+	0.752248i	$0.271031\pi$
$228$	1.93309	−	3.09682i	0.128022	−	0.205092i
$229$	−19.0801	−	7.90323i	−1.26085	−	0.522260i	−0.350678	−	0.936496i	$-0.614049\pi$
$229$	−19.0801	−	7.90323i	−1.26085	−	0.522260i	−0.910169	+	0.414236i	$0.864049\pi$
$230$	3.54227	+	1.46726i	0.233570	+	0.0967480i
$231$	−0.247727	+	0.396860i	−0.0162992	+	0.0261115i
$232$	−3.11896	+	4.66785i	−0.204770	+	0.306460i
$233$	−16.7080	−	3.32343i	−1.09458	−	0.217725i	−0.385396	−	0.922751i	$-0.625935\pi$
$233$	−16.7080	−	3.32343i	−1.09458	−	0.217725i	−0.709181	+	0.705026i	$0.750935\pi$
$234$	6.79095	+	5.99676i	0.443938	+	0.392020i
$235$	8.56725	+	12.8218i	0.558866	+	0.836401i
$236$	−3.32402	−	8.02491i	−0.216376	−	0.522377i
$237$	5.54092	+	5.20747i	0.359921	+	0.338262i
$238$	2.00088	+	3.60507i	0.129697	+	0.233682i
$239$		−	18.4834i		−	1.19559i	−0.801648	−	0.597796i	$-0.796043\pi$
$239$		−	18.4834i		−	1.19559i	0.801648	−	0.597796i	$-0.203957\pi$
$240$	1.08202	−	2.85999i	0.0698440	−	0.184612i
$241$	4.68896	−	3.13306i	0.302043	−	0.201818i	−0.395308	−	0.918549i	$-0.629362\pi$
$241$	4.68896	−	3.13306i	0.302043	−	0.201818i	0.697351	+	0.716730i	$0.254362\pi$
$242$	7.72659	+	7.72659i	0.496684	+	0.496684i
$243$	11.4682	−	10.5584i	0.735688	−	0.677320i
$244$	10.1573	+	6.78689i	0.650255	+	0.434486i
$245$	0.344420	+	1.73152i	0.0220042	+	0.110623i
$246$	−13.4043	+	6.04579i	−0.854629	+	0.385466i
$247$	−2.43579	+	5.88052i	−0.154986	+	0.374168i
$248$	3.93692	−	0.783101i	0.249994	−	0.0497270i
$249$	17.6088	−	4.07403i	1.11591	−	0.258181i
$250$	2.37072	−	11.9184i	0.149938	−	0.753787i
$251$	8.23121	−	8.23121i	0.519550	−	0.519550i	−0.397886	−	0.917435i	$-0.630256\pi$
$251$	8.23121	−	8.23121i	0.519550	−	0.519550i	0.917435	+	0.397886i	$0.130256\pi$
$252$	2.38630	−	1.81813i	0.150323	−	0.114531i
$253$	−0.541948	+	0.224482i	−0.0340720	+	0.0141131i
$254$	10.8124			0.678432
$255$	−5.41626	+	11.3851i	−0.339179	+	0.712960i
$256$	−1.00000			−0.0625000
$257$	12.7404	−	5.27725i	0.794725	−	0.329186i	0.0518835	−	0.998653i	$-0.483478\pi$
$257$	12.7404	−	5.27725i	0.794725	−	0.329186i	0.742842	+	0.669467i	$0.233478\pi$
$258$	−9.85168	−	1.64385i	−0.613339	−	0.102342i
$259$	2.17104	−	2.17104i	0.134902	−	0.134902i
$260$	−1.04011	+	5.22901i	−0.0645051	+	0.324289i
$261$	−14.5566	−	8.47086i	−0.901033	−	0.524333i
$262$	−1.05510	+	0.209872i	−0.0651842	+	0.0129660i
$263$	−10.1730	+	24.5598i	−0.627293	+	1.51442i	0.215680	+	0.976464i	$0.430803\pi$
$263$	−10.1730	+	24.5598i	−0.627293	+	1.51442i	−0.842973	+	0.537956i	$0.819197\pi$
$264$	0.192348	+	0.426461i	0.0118382	+	0.0262469i
$265$	1.94477	+	9.77703i	0.119466	+	0.600598i
$266$	1.75248	+	1.17097i	0.107452	+	0.0717969i
$267$	−4.29261	+	3.06493i	−0.262703	+	0.187571i
$268$	3.47674	+	3.47674i	0.212376	+	0.212376i
$269$	−18.4406	+	12.3216i	−1.12434	+	0.751260i	−0.971511	−	0.236993i	$-0.923838\pi$
$269$	−18.4406	+	12.3216i	−1.12434	+	0.751260i	−0.152829	+	0.988253i	$0.548838\pi$
$270$	8.76469	+	2.70797i	0.533402	+	0.164802i
$271$			7.36575i			0.447437i	0.974654	+	0.223719i	$0.0718197\pi$
$271$			7.36575i			0.447437i	−0.974654	+	0.223719i	$0.928180\pi$
$272$	4.10913	+	0.339200i	0.249153	+	0.0205670i
$273$	−3.58214	+	3.81152i	−0.216801	+	0.230683i
$274$	−4.25074	−	10.2622i	−0.256796	−	0.619961i
$275$	0.282599	+	0.422939i	0.0170414	+	0.0255042i
$276$	3.75980	−	0.116640i	0.226314	−	0.00702093i
$277$	−19.7471	−	3.92794i	−1.18649	−	0.236007i	−0.437888	−	0.899030i	$-0.644273\pi$
$277$	−19.7471	−	3.92794i	−1.18649	−	0.236007i	−0.748599	+	0.663023i	$0.769273\pi$
$278$	−11.1670	+	16.7126i	−0.669753	+	1.00236i
$279$	3.07689	+	11.6424i	0.184209	+	0.697013i
$280$	1.63105	+	0.675604i	0.0974740	+	0.0403751i
$281$	14.2268	+	5.89292i	0.848698	+	0.351542i	0.764277	−	0.644888i	$-0.223096\pi$
$281$	14.2268	+	5.89292i	0.848698	+	0.351542i	0.0844206	+	0.996430i	$0.473096\pi$
$282$	12.8339	+	8.01112i	0.764247	+	0.477055i
$283$	14.9977	−	22.4457i	0.891522	−	1.33426i	−0.0505065	−	0.998724i	$-0.516084\pi$
$283$	14.9977	−	22.4457i	0.891522	−	1.33426i	0.942028	−	0.335533i	$-0.108916\pi$
$284$	−0.998289	−	0.198572i	−0.0592375	−	0.0117831i
$285$	0.199846	+	6.44187i	0.0118379	+	0.381584i
$286$	−0.453170	−	0.678216i	−0.0267965	−	0.0401038i
$287$	−3.24889	−	7.84351i	−0.191776	−	0.462988i
$288$	−0.185959	−	2.99423i	−0.0109577	−	0.176437i
$289$	−16.7699	−	2.78763i	−0.986464	−	0.163978i
$290$		−	9.91114i		−	0.582002i
$291$	4.07306	+	1.54096i	0.238767	+	0.0903324i
$292$	4.26222	−	2.84792i	0.249427	−	0.166662i
$293$	15.2625	+	15.2625i	0.891645	+	0.891645i	0.994678	−	0.103033i	$-0.0328548\pi$
$293$	15.2625	+	15.2625i	0.891645	+	0.891645i	−0.103033	+	0.994678i	$0.532855\pi$
$294$	1.00647	+	1.40962i	0.0586985	+	0.0822105i
$295$	12.7504	+	8.51954i	0.742357	+	0.496027i
$296$	−0.598987	−	3.01131i	−0.0348154	−	0.175029i
$297$	−1.24115	+	0.655238i	−0.0720191	+	0.0380208i
$298$	−3.53594	+	8.53652i	−0.204832	+	0.494507i
$299$	−6.43250	+	1.27950i	−0.372001	+	0.0739956i
$300$	−0.735248	−	3.17790i	−0.0424496	−	0.183476i
$301$	1.12499	−	5.65571i	0.0648434	−	0.325990i
$302$	12.6010	−	12.6010i	0.725105	−	0.725105i
$303$	−4.30304	+	25.7884i	−0.247203	+	1.48150i
$304$	1.94726	−	0.806580i	0.111683	−	0.0462605i
$305$	−21.5668			−1.23491
$306$	−0.251512	+	12.3668i	−0.0143780	+	0.706961i
$307$	26.6072			1.51855			0.759277	−	0.650767i	$-0.225553\pi$
$307$	26.6072			1.51855			0.759277	+	0.650767i	$0.225553\pi$
$308$	−0.249543	+	0.103364i	−0.0142190	+	0.00588970i
$309$	0.906003	−	5.42973i	0.0515407	−	0.308887i
$310$	−5.01095	+	5.01095i	−0.284603	+	0.284603i
$311$	−2.90987	+	14.6289i	−0.165004	+	0.829529i	0.806267	+	0.591552i	$0.201484\pi$
$311$	−2.90987	+	14.6289i	−0.165004	+	0.829529i	−0.971271	+	0.237977i	$0.923516\pi$
$312$	1.17903	+	5.09601i	0.0667493	+	0.288505i
$313$	−14.7704	+	2.93802i	−0.834873	+	0.166067i	−0.593975	−	0.804484i	$-0.702442\pi$
$313$	−14.7704	+	2.93802i	−0.834873	+	0.166067i	−0.240898	+	0.970550i	$0.577442\pi$
$314$	−2.86375	+	6.91371i	−0.161611	+	0.390163i
$315$	−1.71961	+	5.00938i	−0.0968888	+	0.282247i
$316$	0.856470	+	4.30577i	0.0481802	+	0.242218i
$317$	5.11998	+	3.42106i	0.287567	+	0.192146i	0.690984	−	0.722870i	$-0.257178\pi$
$317$	5.11998	+	3.42106i	0.287567	+	0.192146i	−0.403417	+	0.915016i	$0.632178\pi$
$318$	5.68304	+	7.95942i	0.318689	+	0.446342i
$319$	1.07222	+	1.07222i	0.0600330	+	0.0600330i
$320$	1.46791	−	0.980825i	0.0820586	−	0.0548298i
$321$	−13.3821	−	5.06285i	−0.746917	−	0.282580i
$322$			2.17177i			0.121028i
$323$	−8.27512	+	2.65383i	−0.460440	+	0.147663i
$324$	8.93084	−	1.11361i	0.496158	−	0.0618672i
$325$	2.17638	+	5.25425i	0.120724	+	0.291453i
$326$	−3.40468	−	5.09546i	−0.188568	−	0.282211i
$327$	0.863461	+	27.8329i	0.0477495	+	1.53916i
$328$	−8.32663	−	1.65627i	−0.459761	−	0.0914522i
$329$	−4.85276	+	7.26267i	−0.267541	+	0.400404i
$330$	−0.700633	−	0.437346i	−0.0385686	−	0.0240751i
$331$	21.9737	+	9.10182i	1.20779	+	0.500281i	0.893507	−	0.449049i	$-0.148237\pi$
$331$	21.9737	+	9.10182i	1.20779	+	0.500281i	0.314279	+	0.949331i	$0.398237\pi$
$332$	9.64069	+	3.99331i	0.529102	+	0.219161i
$333$	8.90518	−	2.35349i	0.488001	−	0.128970i
$334$	−3.54468	+	5.30499i	−0.193956	+	0.290276i
$335$	−8.51360	−	1.69346i	−0.465148	−	0.0925237i
$336$	1.73122	−	0.0537076i	0.0944457	−	0.00292999i
$337$	−1.77228	−	2.65240i	−0.0965423	−	0.144486i	0.780054	−	0.625712i	$-0.215192\pi$
$337$	−1.77228	−	2.65240i	−0.0965423	−	0.144486i	−0.876596	+	0.481226i	$0.840192\pi$
$338$	1.48489	+	3.58484i	0.0807674	+	0.194990i
$339$	−0.343837	+	0.365854i	−0.0186747	+	0.0198705i
$340$	−6.36452	+	3.53242i	−0.345165	+	0.191573i
$341$		−	1.08420i		−	0.0587130i
$342$	2.77720	+	5.68054i	0.150174	+	0.307169i
$343$	−0.831470	+	0.555570i	−0.0448951	+	0.0299980i
$344$	−4.07754	−	4.07754i	−0.219846	−	0.219846i
$345$	−5.40464	+	3.85893i	−0.290976	+	0.207758i
$346$	−5.47096	−	3.65558i	−0.294121	−	0.196525i
$347$	4.16680	+	20.9479i	0.223685	+	1.12454i	0.915454	+	0.402423i	$0.131832\pi$
$347$	4.16680	+	20.9479i	0.223685	+	1.12454i	−0.691769	+	0.722119i	$0.743168\pi$
$348$	−3.99787	−	8.86382i	−0.214308	−	0.475151i
$349$	12.1729	−	29.3880i	0.651602	−	1.57311i	−0.158852	−	0.987302i	$-0.550779\pi$
$349$	12.1729	−	29.3880i	0.651602	−	1.57311i	0.810453	−	0.585803i	$-0.199221\pi$
$350$	1.84704	−	0.367399i	0.0987285	−	0.0196383i
$351$	−15.0394	+	4.47793i	−0.802742	+	0.239014i
$352$	−0.0526945	+	0.264913i	−0.00280862	+	0.0141199i
$353$	−26.3679	+	26.3679i	−1.40342	+	1.40342i	−0.614525	+	0.788897i	$0.710652\pi$
$353$	−26.3679	+	26.3679i	−1.40342	+	1.40342i	−0.788897	+	0.614525i	$0.789348\pi$
$354$	14.8396	+	2.47613i	0.788716	+	0.131605i
$355$	1.66016	−	0.687661i	0.0881122	−	0.0364973i
$356$	−3.04523			−0.161397
$357$	−7.13202	−	0.366537i	−0.377466	−	0.0193992i
$358$	6.93215			0.366375
$359$	29.5771	−	12.2512i	1.56102	−	0.646596i	0.575755	−	0.817622i	$-0.304708\pi$
$359$	29.5771	−	12.2512i	1.56102	−	0.646596i	0.985266	+	0.171026i	$0.0547083\pi$
$360$	3.20979	+	4.21286i	0.169171	+	0.222037i
$361$	10.2938	−	10.2938i	0.541779	−	0.541779i
$362$	−3.23680	+	16.2725i	−0.170122	+	0.855263i
$363$	−18.4391	+	4.26613i	−0.967803	+	0.223914i
$364$	−2.96187	+	0.589153i	−0.155244	+	0.0308800i
$365$	−3.46323	+	8.36098i	−0.181274	+	0.437633i
$366$	−19.2878	+	8.69941i	−1.00819	+	0.454726i
$367$	3.17412	+	15.9574i	0.165687	+	0.832967i	0.970808	+	0.239856i	$0.0771004\pi$
$367$	3.17412	+	15.9574i	0.165687	+	0.832967i	−0.805121	+	0.593111i	$0.797900\pi$
$368$	1.80576	+	1.20657i	0.0941317	+	0.0628968i
$369$	3.41084	−	25.2398i	0.177561	−	1.31393i
$370$	3.83283	+	3.83283i	0.199259	+	0.199259i
$371$	−4.69491	+	3.13704i	−0.243747	+	0.162867i
$372$	−2.46016	+	6.50271i	−0.127554	+	0.337150i
$373$		−	36.5110i		−	1.89047i	−0.326395	−	0.945234i	$-0.605834\pi$
$373$		−	36.5110i		−	1.89047i	0.326395	−	0.945234i	$-0.394166\pi$
$374$	0.306387	−	1.07069i	0.0158429	−	0.0553639i
$375$	15.3373	+	14.4143i	0.792016	+	0.744354i
$376$	3.34264	+	8.06984i	0.172383	+	0.416170i
$377$	9.41895	+	14.0965i	0.485100	+	0.726004i
$378$	0.482749	+	5.17368i	0.0248299	+	0.266105i
$379$	31.6073	+	6.28708i	1.62356	+	0.322946i	0.921263	−	0.388941i	$-0.127159\pi$
$379$	31.6073	+	6.28708i	1.62356	+	0.322946i	0.702294	+	0.711887i	$0.252159\pi$
$380$	−2.06728	+	3.09390i	−0.106049	+	0.158714i
$381$	−9.91669	+	15.8866i	−0.508048	+	0.813897i
$382$	10.6858	+	4.42622i	0.546735	+	0.226465i
$383$	7.43574	+	3.07998i	0.379948	+	0.157380i	0.564480	−	0.825447i	$-0.309077\pi$
$383$	7.43574	+	3.07998i	0.379948	+	0.157380i	−0.184531	+	0.982827i	$0.559077\pi$
$384$	0.917157	−	1.46929i	0.0468035	−	0.0749796i
$385$	0.264924	−	0.396486i	0.0135018	−	0.0202068i
$386$	−5.80294	−	1.15428i	−0.295362	−	0.0587511i
$387$	11.4508	−	12.9673i	0.582079	−	0.659167i
$388$	1.39684	+	2.09052i	0.0709139	+	0.106130i
$389$	−6.25111	−	15.0915i	−0.316944	−	0.765170i	−0.999413	−	0.0342559i	$-0.989094\pi$
$389$	−6.25111	−	15.0915i	−0.316944	−	0.765170i	0.682469	−	0.730914i	$-0.260906\pi$
$390$	−6.72900	−	6.32405i	−0.340736	−	0.320231i
$391$	−7.01083	−	5.57046i	−0.354553	−	0.281710i
$392$			1.00000i			0.0505076i
$393$	0.659327	−	1.74274i	0.0332587	−	0.0879094i
$394$	6.11066	−	4.08301i	0.307850	−	0.205699i
$395$	−5.48042	−	5.48042i	−0.275750	−	0.275750i
$396$	−0.803009	−	0.108516i	−0.0403527	−	0.00545315i
$397$	13.9960	+	9.35184i	0.702440	+	0.469355i	0.854792	−	0.518971i	$-0.173685\pi$
$397$	13.9960	+	9.35184i	0.702440	+	0.469355i	−0.152352	+	0.988326i	$0.548685\pi$
$398$	3.45449	+	17.3669i	0.173158	+	0.870523i
$399$	−3.32781	+	1.50095i	−0.166599	+	0.0751414i
$400$	0.720680	−	1.73987i	0.0360340	−	0.0869937i
$401$	15.1137	−	3.00630i	0.754743	−	0.150128i	0.197300	−	0.980343i	$-0.436783\pi$
$401$	15.1137	−	3.00630i	0.754743	−	0.150128i	0.557443	+	0.830216i	$0.311783\pi$
$402$	−8.29706	+	1.91963i	−0.413820	+	0.0957426i
$403$	2.36489	−	11.8891i	0.117803	−	0.592238i
$404$	−10.6736	+	10.6736i	−0.531032	+	0.531032i
$405$	−12.0174	+	10.3943i	−0.597149	+	0.516495i
$406$	5.18664	−	2.14838i	0.257409	−	0.106622i
$407$	−0.829299			−0.0411068
$408$	−4.26710	+	5.72642i	−0.211253	+	0.283500i
$409$	22.9930			1.13693			0.568466	−	0.822707i	$-0.307537\pi$
$409$	22.9930			1.13693			0.568466	+	0.822707i	$0.307537\pi$
$410$	13.8472	−	5.73571i	0.683866	−	0.283267i
$411$	18.9768	+	3.16646i	0.936054	+	0.156190i
$412$	2.24733	−	2.24733i	0.110718	−	0.110718i
$413$	−1.69457	+	8.51919i	−0.0833845	+	0.419202i
$414$	−3.27695	+	5.63123i	−0.161053	+	0.276760i
$415$	−18.0684	+	3.59403i	−0.886942	+	0.176424i
$416$	−1.15567	+	2.79002i	−0.0566612	+	0.136792i
$417$	−14.3138	−	31.7357i	−0.700952	−	1.55411i
$418$	−0.111064	−	0.558356i	−0.00543231	−	0.0273101i
$419$	−13.3424	−	8.91512i	−0.651820	−	0.435532i	0.185203	−	0.982700i	$-0.440706\pi$
$419$	−13.3424	−	8.91512i	−0.651820	−	0.435532i	−0.837023	+	0.547168i	$0.815706\pi$
$420$	−2.48859	+	1.77686i	−0.121431	+	0.0867019i
$421$	−11.6405	−	11.6405i	−0.567325	−	0.567325i	0.364053	−	0.931378i	$-0.381393\pi$
$421$	−11.6405	−	11.6405i	−0.567325	−	0.567325i	−0.931378	+	0.364053i	$0.881393\pi$
$422$	17.9841	−	12.0166i	0.875451	−	0.584957i
$423$	−23.5414	+	11.5093i	−1.14462	+	0.559601i
$424$			5.64651i			0.274219i
$425$	−3.55153	+	6.90491i	−0.172275	+	0.334938i
$426$	1.20735	−	1.28466i	0.0584962	−	0.0622419i
$427$	−4.67489	−	11.2862i	−0.226234	−	0.546177i
$428$	−4.58936	−	6.86846i	−0.221835	−	0.331999i
$429$	1.41213	−	0.0438084i	0.0681781	−	0.00211509i
$430$	9.98481	+	1.98610i	0.481510	+	0.0957783i
$431$	−1.65688	+	2.47970i	−0.0798092	+	0.119443i	−0.869227	−	0.494414i	$-0.835383\pi$
$431$	−1.65688	+	2.47970i	−0.0798092	+	0.119443i	0.789417	+	0.613857i	$0.210383\pi$
$432$	4.56996	+	2.47295i	0.219872	+	0.118980i
$433$	33.1360	+	13.7254i	1.59241	+	0.659600i	0.990317	−	0.138823i	$-0.0443318\pi$
$433$	33.1360	+	13.7254i	1.59241	+	0.659600i	0.602098	+	0.798423i	$0.294332\pi$
$434$	−3.70849	−	1.53611i	−0.178013	−	0.0737356i
$435$	14.5624	+	9.09007i	0.698212	+	0.435835i
$436$	−8.93194	+	13.3676i	−0.427763	+	0.640192i
$437$	−4.48947	−	0.893011i	−0.214761	−	0.0427185i
$438$	0.275312	+	8.87444i	0.0131549	+	0.424037i
$439$	1.64440	+	2.46102i	0.0784830	+	0.117458i	0.868634	−	0.495454i	$-0.164998\pi$
$439$	1.64440	+	2.46102i	0.0784830	+	0.117458i	−0.790151	+	0.612912i	$0.789998\pi$
$440$	−0.182483	−	0.440552i	−0.00869952	−	0.0210025i
$441$	−2.99423	+	0.185959i	−0.142582	+	0.00885520i
$442$	5.69516	−	11.0726i	0.270891	−	0.526668i
$443$		−	27.1115i		−	1.28811i	−0.764981	−	0.644053i	$-0.777251\pi$
$443$		−	27.1115i		−	1.28811i	0.764981	−	0.644053i	$-0.222749\pi$
$444$	4.97387	+	1.88176i	0.236049	+	0.0893043i
$445$	4.47012	−	2.98684i	0.211904	−	0.141590i
$446$	−8.73218	−	8.73218i	−0.413481	−	0.413481i
$447$	−9.29964	−	13.0247i	−0.439858	−	0.616046i
$448$	0.831470	+	0.555570i	0.0392832	+	0.0262482i
$449$	0.188759	+	0.948954i	0.00890808	+	0.0447839i	0.984984	−	0.172648i	$-0.0552321\pi$
$449$	0.188759	+	0.948954i	0.00890808	+	0.0447839i	−0.976076	+	0.217431i	$0.930232\pi$
$450$	5.34360	+	1.83434i	0.251900	+	0.0864714i
$451$	−0.877534	+	2.11856i	−0.0413215	+	0.0997589i
$452$	−0.284300	+	0.0565507i	−0.0133723	+	0.00265992i
$453$	6.95747	+	30.0716i	0.326890	+	1.41289i
$454$	1.52503	−	7.66685i	0.0715732	−	0.359823i
$455$	3.76990	−	3.76990i	0.176736	−	0.176736i
$456$	−0.600837	+	3.60085i	−0.0281368	+	0.168625i
$457$	8.20105	−	3.39699i	0.383629	−	0.158904i	−0.182530	−	0.983200i	$-0.558429\pi$
$457$	8.20105	−	3.39699i	0.383629	−	0.158904i	0.566159	+	0.824296i	$0.308429\pi$
$458$	20.6521			0.965011
$459$	−17.9397	−	11.7118i	−0.837355	−	0.546660i
$460$	−3.83412			−0.178767
$461$	25.1425	−	10.4144i	1.17100	−	0.485045i	0.289479	−	0.957184i	$-0.406518\pi$
$461$	25.1425	−	10.4144i	1.17100	−	0.485045i	0.881524	+	0.472139i	$0.156518\pi$
$462$	0.0769977	−	0.461452i	0.00358226	−	0.0214687i
$463$	12.4730	−	12.4730i	0.579671	−	0.579671i	−0.355141	−	0.934813i	$-0.615567\pi$
$463$	12.4730	−	12.4730i	0.579671	−	0.579671i	0.934813	+	0.355141i	$0.115567\pi$
$464$	1.09523	−	5.50611i	0.0508449	−	0.255615i
$465$	−2.76673	−	11.9584i	−0.128304	−	0.554556i
$466$	16.7080	−	3.32343i	0.773983	−	0.153955i
$467$	14.7117	−	35.5173i	0.680778	−	1.64354i	−0.0818017	−	0.996649i	$-0.526067\pi$
$467$	14.7117	−	35.5173i	0.680778	−	1.64354i	0.762580	−	0.646894i	$-0.223933\pi$
$468$	−8.56888	−	2.94150i	−0.396097	−	0.135971i
$469$	−0.959230	−	4.82237i	−0.0442931	−	0.222677i
$470$	−12.8218	−	8.56725i	−0.591425	−	0.395178i
$471$	−7.53176	−	10.5486i	−0.347045	−	0.486056i
$472$	6.14200	+	6.14200i	0.282708	+	0.282708i
$473$	−1.29506	+	0.865329i	−0.0595468	+	0.0397879i
$474$	−7.11195	−	2.69066i	−0.326663	−	0.123586i
$475$			3.96927i			0.182122i
$476$	−3.22817	−	2.56494i	−0.147963	−	0.117564i
$477$	−16.9070	+	1.05002i	−0.774117	+	0.0480772i
$478$	7.07330	+	17.0764i	0.323525	+	0.781059i
$479$	15.0330	+	22.4985i	0.686876	+	1.02798i	0.997009	+	0.0772897i	$0.0246266\pi$
$479$	15.0330	+	22.4985i	0.686876	+	1.02798i	−0.310132	+	0.950693i	$0.600373\pi$
$480$	0.0948175	+	3.05636i	0.00432781	+	0.139503i
$481$	−9.09386	−	1.80888i	−0.414644	−	0.0824779i
$482$	−3.13306	+	4.68896i	−0.142707	+	0.213576i
$483$	−3.19096	−	1.99185i	−0.145194	−	0.0906324i
$484$	−10.0953	−	4.18160i	−0.458876	−	0.190073i
$485$	−4.10087	−	1.69864i	−0.186211	−	0.0771312i
$486$	−6.55476	+	14.1434i	−0.297330	+	0.641557i
$487$	−5.15114	+	7.70923i	−0.233420	+	0.349338i	−0.929626	−	0.368504i	$-0.879870\pi$
$487$	−5.15114	+	7.70923i	−0.233420	+	0.349338i	0.696206	+	0.717842i	$0.254870\pi$
$488$	−11.9814	−	2.38324i	−0.542371	−	0.107884i
$489$	10.6093	−	0.329134i	0.479771	−	0.0148840i
$490$	−0.980825	−	1.46791i	−0.0443092	−	0.0663134i
$491$	−8.40577	−	20.2933i	−0.379347	−	0.915825i	−0.992088	−	0.125541i	$-0.959933\pi$
$491$	−8.40577	−	20.2933i	−0.379347	−	0.915825i	0.612741	−	0.790284i	$-0.290067\pi$
$492$	10.0704	−	10.7152i	0.454007	−	0.483079i
$493$	−6.36813	+	22.2538i	−0.286806	+	1.00226i
$494$		−	6.36503i		−	0.286376i
$495$	1.28518	−	0.628320i	0.0577646	−	0.0282409i
$496$	−3.33756	+	2.23008i	−0.149861	+	0.100134i
$497$	0.719726	+	0.719726i	0.0322841	+	0.0322841i
$498$	−14.7094	+	10.5025i	−0.659142	+	0.470629i
$499$	15.5163	+	10.3677i	0.694607	+	0.464121i	0.852087	−	0.523401i	$-0.175337\pi$
$499$	15.5163	+	10.3677i	0.694607	+	0.464121i	−0.157480	+	0.987522i	$0.550337\pi$
$500$	2.37072	+	11.9184i	0.106022	+	0.533008i
$501$	−4.54356	−	10.0737i	−0.202991	−	0.450059i
$502$	−4.45470	+	10.7546i	−0.198823	+	0.480001i
$503$	−2.91142	+	0.579118i	−0.129814	+	0.0258216i	−0.259570	−	0.965724i	$-0.583581\pi$
$503$	−2.91142	+	0.579118i	−0.129814	+	0.0258216i	0.129756	+	0.991546i	$0.458581\pi$
$504$	−1.50889	+	2.59293i	−0.0672111	+	0.115498i
$505$	5.19894	−	26.1369i	0.231350	−	1.16307i
$506$	0.414789	−	0.414789i	0.0184396	−	0.0184396i
$507$	−6.62906	−	1.10612i	−0.294407	−	0.0491246i
$508$	−9.98938	+	4.13774i	−0.443207	+	0.183582i
$509$	−20.7193			−0.918368			−0.459184	−	0.888341i	$-0.651858\pi$
$509$	−20.7193			−0.918368			−0.459184	+	0.888341i	$0.651858\pi$
$510$	0.647099	−	12.5911i	0.0286540	−	0.557545i
$511$	−5.12612			−0.226766
$512$	0.923880	−	0.382683i	0.0408301	−	0.0169124i
$513$	−10.8935	−	1.12943i	−0.480960	−	0.0498657i
$514$	−9.75109	+	9.75109i	−0.430102	+	0.430102i
$515$	−1.09463	+	5.50310i	−0.0482354	+	0.242496i
$516$	9.73084	−	2.25136i	0.428377	−	0.0991105i
$517$	2.31394	−	0.460272i	0.101767	−	0.0202427i
$518$	−1.17496	+	2.83659i	−0.0516246	+	0.124633i
$519$	10.3889	−	4.68571i	0.456020	−	0.205680i
$520$	−1.04011	−	5.22901i	−0.0456120	−	0.229307i
$521$	24.3492	+	16.2696i	1.06676	+	0.712784i	0.959574	−	0.281455i	$-0.0908170\pi$
$521$	24.3492	+	16.2696i	1.06676	+	0.712784i	0.107183	+	0.994239i	$0.465817\pi$
$522$	16.6902	+	2.25547i	0.730512	+	0.0987192i
$523$	21.7979	+	21.7979i	0.953158	+	0.953158i	0.998951	−	0.0457931i	$-0.0145815\pi$
$523$	21.7979	+	21.7979i	0.953158	+	0.953158i	−0.0457931	+	0.998951i	$0.514582\pi$
$524$	0.894470	−	0.597666i	0.0390751	−	0.0261091i
$525$	−1.15421	+	3.05081i	−0.0503738	+	0.133148i
$526$		−	26.5833i		−	1.15909i
$527$	14.4709	−	8.03160i	0.630362	−	0.349862i
$528$	−0.340906	−	0.320390i	−0.0148360	−	0.0139432i
$529$	6.99676	+	16.8917i	0.304207	+	0.734421i
$530$	−5.53824	−	8.28857i	−0.240566	−	0.360032i
$531$	−17.2484	+	19.5327i	−0.748517	+	0.847648i
$532$	−2.06720	−	0.411191i	−0.0896243	−	0.0178274i
$533$	−14.2438	+	21.3174i	−0.616969	+	0.923359i
$534$	2.79295	−	4.47434i	0.120863	−	0.193624i
$535$	13.4735	+	5.58091i	0.582511	+	0.241284i
$536$	−4.54258	−	1.88160i	−0.196209	−	0.0812726i
$537$	−6.35787	+	10.1854i	−0.274362	+	0.439531i
$538$	12.3216	−	18.4406i	0.531221	−	0.795029i
$539$	0.264913	+	0.0526945i	0.0114106	+	0.00226971i
$540$	−9.13381	+	0.852263i	−0.393057	+	0.0366756i
$541$	2.50891	+	3.75485i	0.107867	+	0.161434i	0.881476	−	0.472229i	$-0.156551\pi$
$541$	2.50891	+	3.75485i	0.107867	+	0.161434i	−0.773609	+	0.633663i	$0.781551\pi$
$542$	−2.81875	−	6.80506i	−0.121076	−	0.292302i
$543$	−20.9404	−	19.6802i	−0.898639	−	0.844560i
$544$	−3.92615	+	1.25912i	−0.168332	+	0.0539841i
$545$		−	28.3831i		−	1.21580i
$546$	1.85086	−	4.89221i	0.0792097	−	0.209367i
$547$	17.9713	−	12.0081i	0.768398	−	0.513427i	−0.108504	−	0.994096i	$-0.534606\pi$
$547$	17.9713	−	12.0081i	0.768398	−	0.513427i	0.876902	+	0.480669i	$0.159606\pi$
$548$	7.85434	+	7.85434i	0.335521	+	0.335521i
$549$	4.90793	−	36.3181i	0.209465	−	1.55002i
$550$	−0.422939	−	0.282599i	−0.0180342	−	0.0120501i
$551$	2.30842	+	11.6052i	0.0983419	+	0.494398i
$552$	−3.42897	+	1.54658i	−0.145947	+	0.0658267i
$553$	1.68003	−	4.05594i	0.0714420	−	0.172476i
$554$	19.7471	−	3.92794i	0.838973	−	0.166882i
$555$	−9.14686	+	2.11625i	−0.388262	+	0.0898296i
$556$	3.92134	−	19.7139i	0.166302	−	0.836055i
$557$	12.0051	−	12.0051i	0.508673	−	0.508673i	−0.405446	−	0.914119i	$-0.632884\pi$
$557$	12.0051	−	12.0051i	0.508673	−	0.508673i	0.914119	+	0.405446i	$0.132884\pi$
$558$	−7.29803	−	9.57871i	−0.308950	−	0.405499i
$559$	−16.0887	+	6.66416i	−0.680480	+	0.281864i
$560$	−1.76544			−0.0746034
$561$	1.29215	+	1.43216i	0.0545546	+	0.0604659i
$562$	−15.3989			−0.649565
$563$	15.4002	−	6.37897i	0.649041	−	0.268841i	−0.0337779	−	0.999429i	$-0.510754\pi$
$563$	15.4002	−	6.37897i	0.649041	−	0.268841i	0.682819	+	0.730588i	$0.260754\pi$
$564$	−14.9227	−	2.48999i	−0.628359	−	0.104848i
$565$	0.361860	−	0.361860i	0.0152235	−	0.0152235i
$566$	−5.26650	+	26.4765i	−0.221367	+	1.11289i
$567$	−8.04441	−	4.03578i	−0.337833	−	0.169487i
$568$	0.998289	−	0.198572i	0.0418873	−	0.00833190i
$569$	−7.30648	+	17.6394i	−0.306304	+	0.739483i	0.693515	+	0.720442i	$0.256061\pi$
$569$	−7.30648	+	17.6394i	−0.306304	+	0.739483i	−0.999819	+	0.0190405i	$0.993939\pi$
$570$	−2.64983	−	5.87504i	−0.110989	−	0.246078i
$571$	−8.23246	−	41.3874i	−0.344518	−	1.73201i	−0.632669	−	0.774422i	$-0.718041\pi$
$571$	−8.23246	−	41.3874i	−0.344518	−	1.73201i	0.288151	−	0.957585i	$-0.406959\pi$
$572$	0.678216	+	0.453170i	0.0283576	+	0.0189480i
$573$	−16.3040	+	11.6411i	−0.681110	+	0.486314i
$574$	6.00316	+	6.00316i	0.250567	+	0.250567i
$575$	−3.40065	+	2.27224i	−0.141817	+	0.0947591i
$576$	1.31765	+	2.69515i	0.0549019	+	0.112298i
$577$			0.786991i			0.0327629i	0.999866	+	0.0163814i	$0.00521460\pi$
$577$			0.786991i			0.0327629i	−0.999866	+	0.0163814i	$0.994785\pi$
$578$	16.5601	−	3.84212i	0.688811	−	0.159811i
$579$	7.01817	−	7.46756i	0.291665	−	0.310341i
$580$	3.79283	+	9.15670i	0.157489	+	0.380211i
$581$	−5.79738	−	8.67639i	−0.240516	−	0.359957i
$582$	−4.35271	+	0.135034i	−0.180426	+	0.00559735i
$583$	1.49583	+	0.297540i	0.0619511	+	0.0123228i
$584$	−2.84792	+	4.26222i	−0.117848	+	0.176372i
$585$	15.4634	−	4.08672i	0.639334	−	0.168965i
$586$	−19.9414	−	8.26001i	−0.823772	−	0.341218i
$587$	7.06393	+	2.92598i	0.291560	+	0.120768i	0.523669	−	0.851922i	$-0.324563\pi$
$587$	7.06393	+	2.92598i	0.291560	+	0.120768i	−0.232109	+	0.972690i	$0.574563\pi$
$588$	−1.46929	−	0.917157i	−0.0605926	−	0.0378229i
$589$	4.70034	−	7.03455i	0.193674	−	0.289854i
$590$	−15.0401	−	2.99167i	−0.619192	−	0.123165i
$591$	0.394709	+	12.7231i	0.0162362	+	0.523359i
$592$	1.70577	+	2.55287i	0.0701068	+	0.104922i
$593$	−4.28168	−	10.3369i	−0.175827	−	0.424485i	0.811256	−	0.584691i	$-0.198784\pi$
$593$	−4.28168	−	10.3369i	−0.175827	−	0.424485i	−0.987084	+	0.160206i	$0.948784\pi$
$594$	0.895928	−	1.08033i	0.0367604	−	0.0443265i
$595$	7.25442	+	0.598837i	0.297402	+	0.0245499i
$596$		−	9.23986i		−	0.378480i
$597$	−28.6853	−	10.8525i	−1.17401	−	0.444163i
$598$	5.45321	−	3.64372i	0.222998	−	0.149003i
$599$	−17.4151	−	17.4151i	−0.711563	−	0.711563i	0.255299	−	0.966862i	$-0.417826\pi$
$599$	−17.4151	−	17.4151i	−0.711563	−	0.711563i	−0.966862	+	0.255299i	$0.917826\pi$
$600$	1.89541	+	2.65463i	0.0773798	+	0.108375i
$601$	−13.3540	−	8.92284i	−0.544720	−	0.363970i	0.252559	−	0.967582i	$-0.418728\pi$
$601$	−13.3540	−	8.92284i	−0.544720	−	0.363970i	−0.797279	+	0.603611i	$0.793728\pi$
$602$	1.12499	+	5.65571i	0.0458512	+	0.230509i
$603$	4.78920	−	13.9514i	0.195031	−	0.568146i
$604$	−6.81960	+	16.4640i	−0.277486	+	0.669910i
$605$	18.9204	−	3.76349i	0.769222	−	0.153008i
$606$	−5.89330	−	25.4721i	−0.239399	−	1.03473i
$607$	2.30659	−	11.5960i	0.0936218	−	0.470669i	−0.905322	−	0.424725i	$-0.860371\pi$
$607$	2.30659	−	11.5960i	0.0936218	−	0.470669i	0.998944	−	0.0459432i	$-0.0146293\pi$
$608$	−1.49037	+	1.49037i	−0.0604423	+	0.0604423i
$609$	−1.60037	+	9.59110i	−0.0648502	+	0.388651i
$610$	19.9251	−	8.25324i	0.806743	−	0.334164i
$611$	26.3780			1.06714
$612$	−4.50019	−	11.5216i	−0.181909	−	0.465735i
$613$	−8.80896			−0.355790			−0.177895	−	0.984049i	$-0.556929\pi$
$613$	−8.80896			−0.355790			−0.177895	+	0.984049i	$0.556929\pi$
$614$	−24.5819	+	10.1821i	−0.992044	+	0.410918i
$615$	−4.27264	+	25.6062i	−0.172290	+	1.03254i
$616$	0.190992	−	0.190992i	0.00769527	−	0.00769527i
$617$	−6.18280	+	31.0830i	−0.248910	+	1.25136i	0.630838	+	0.775915i	$0.282711\pi$
$617$	−6.18280	+	31.0830i	−0.248910	+	1.25136i	−0.879748	+	0.475441i	$0.842289\pi$
$618$	1.24083	+	5.36313i	0.0499135	+	0.215737i
$619$	−20.4187	+	4.06154i	−0.820699	+	0.163247i	−0.587544	−	0.809193i	$-0.699905\pi$
$619$	−20.4187	+	4.06154i	−0.820699	+	0.163247i	−0.233155	+	0.972440i	$0.574905\pi$
$620$	2.71190	−	6.54712i	0.108913	−	0.262939i
$621$	−5.26846	−	9.97953i	−0.211416	−	0.400465i
$622$	−2.90987	−	14.6289i	−0.116675	−	0.586565i
$623$	2.53202	+	1.69184i	0.101443	+	0.0677821i
$624$	−3.03944	−	4.25690i	−0.121675	−	0.170412i
$625$	−8.51168	−	8.51168i	−0.340467	−	0.340467i
$626$	12.5217	−	8.36676i	0.500470	−	0.334403i
$627$	0.922251	+	0.348914i	0.0368312	+	0.0139343i
$628$		−	7.48334i		−	0.298618i
$629$	−6.14330	−	11.0687i	−0.244950	−	0.441336i
$630$	−0.328300	−	5.28613i	−0.0130798	−	0.210605i
$631$	6.92395	+	16.7159i	0.275638	+	0.665449i	0.999705	−	0.0242804i	$-0.00772946\pi$
$631$	6.92395	+	16.7159i	0.275638	+	0.665449i	−0.724067	+	0.689729i	$0.757729\pi$
$632$	−2.43902	−	3.65025i	−0.0970191	−	0.145199i
$633$	1.16166	+	37.4450i	0.0461717	+	1.48830i
$634$	−6.03943	−	1.20132i	−0.239857	−	0.0477104i
$635$	10.6051	−	15.8717i	0.420851	−	0.629847i
$636$	−8.29639	−	5.17874i	−0.328973	−	0.205350i
$637$	2.79002	+	1.15567i	0.110545	+	0.0457891i
$638$	−1.40093	−	0.580283i	−0.0554632	−	0.0229736i
$639$	0.780211	+	2.95218i	0.0308647	+	0.116786i
$640$	−0.980825	+	1.46791i	−0.0387705	+	0.0580242i
$641$	−8.31520	−	1.65400i	−0.328431	−	0.0653289i	0.0281211	−	0.999605i	$-0.491048\pi$
$641$	−8.31520	−	1.65400i	−0.328431	−	0.0653289i	−0.356552	+	0.934276i	$0.616048\pi$
$642$	14.3009	−	0.443658i	0.564413	−	0.0175098i
$643$	−14.5308	−	21.7469i	−0.573039	−	0.857614i	0.425847	−	0.904795i	$-0.359976\pi$
$643$	−14.5308	−	21.7469i	−0.573039	−	0.857614i	−0.998886	+	0.0471813i	$0.984976\pi$
$644$	−0.831100	−	2.00645i	−0.0327499	−	0.0790653i
$645$	−12.0758	+	12.8490i	−0.475484	+	0.505931i
$646$	6.62964	−	5.61857i	0.260840	−	0.221060i
$647$		−	33.2953i		−	1.30897i	−0.756074	−	0.654486i	$-0.772885\pi$
$647$		−	33.2953i		−	1.30897i	0.756074	−	0.654486i	$-0.227115\pi$
$648$	−7.82486	+	4.44652i	−0.307389	+	0.174676i
$649$	1.95074	−	1.30345i	0.0765734	−	0.0511647i
$650$	−4.02143	−	4.02143i	−0.157733	−	0.157733i
$651$	5.65826	−	4.04001i	0.221765	−	0.158341i
$652$	5.09546	+	3.40468i	0.199554	+	0.133337i
$653$	2.21563	+	11.1387i	0.0867045	+	0.435893i	0.999615	+	0.0277339i	$0.00882910\pi$
$653$	2.21563	+	11.1387i	0.0867045	+	0.435893i	−0.912911	+	0.408159i	$0.866171\pi$
$654$	−11.4489	−	25.3838i	−0.447689	−	0.992586i
$655$	−0.726794	+	1.75464i	−0.0283982	+	0.0685593i
$656$	8.32663	−	1.65627i	0.325100	−	0.0646665i
$657$	−13.2917	−	7.73474i	−0.518557	−	0.301761i
$658$	1.70406	−	8.56690i	0.0664312	−	0.333972i
$659$	13.7955	−	13.7955i	0.537395	−	0.537395i	−0.385368	−	0.922763i	$-0.625926\pi$
$659$	13.7955	−	13.7955i	0.537395	−	0.537395i	0.922763	+	0.385368i	$0.125926\pi$
$660$	0.814665	+	0.135935i	0.0317108	+	0.00529125i
$661$	12.0712	−	5.00005i	0.469515	−	0.194479i	−0.135366	−	0.990796i	$-0.543221\pi$
$661$	12.0712	−	5.00005i	0.469515	−	0.194479i	0.604880	+	0.796316i	$0.293221\pi$
$662$	−23.7842			−0.924399
$663$	11.0455	+	18.5231i	0.428972	+	0.719379i
$664$	−10.4350			−0.404957
$665$	3.43776	−	1.42397i	0.133311	−	0.0552191i
$666$	−7.32667	+	5.58220i	−0.283903	+	0.216306i
$667$	−8.62123	+	8.62123i	−0.333815	+	0.333815i
$668$	1.24473	−	6.25766i	0.0481599	−	0.242116i
$669$	20.8389	−	4.82136i	0.805679	−	0.186404i
$670$	8.51360	−	1.69346i	0.328909	−	0.0654241i
$671$	−1.26270	+	3.04843i	−0.0487461	+	0.117683i
$672$	−1.57888	+	0.712128i	−0.0609068	+	0.0274709i
$673$	8.23516	+	41.4009i	0.317442	+	1.59589i	0.729006	+	0.684508i	$0.239983\pi$
$673$	8.23516	+	41.4009i	0.317442	+	1.59589i	−0.411564	+	0.911381i	$0.635017\pi$
$674$	2.65240	+	1.77228i	0.102167	+	0.0682657i
$675$	−7.59610	+	6.16895i	−0.292374	+	0.237443i
$676$	−2.74372	−	2.74372i	−0.105528	−	0.105528i
$677$	20.7331	−	13.8534i	0.796837	−	0.532430i	−0.0892164	−	0.996012i	$-0.528436\pi$
$677$	20.7331	−	13.8534i	0.796837	−	0.532430i	0.886054	+	0.463583i	$0.153436\pi$
$678$	0.177658	−	0.469586i	0.00682291	−	0.0180343i
$679$		−	2.51425i		−	0.0964880i
$680$	4.52825	−	5.69913i	0.173651	−	0.218552i
$681$	9.86615	+	9.27242i	0.378072	+	0.355320i
$682$	0.414907	+	1.00167i	0.0158876	+	0.0383561i
$683$	−7.84990	−	11.7482i	−0.300368	−	0.449533i	0.650329	−	0.759652i	$-0.274631\pi$
$683$	−7.84990	−	11.7482i	−0.300368	−	0.449533i	−0.950697	+	0.310120i	$0.899631\pi$
$684$	−4.73965	−	4.18535i	−0.181225	−	0.160031i
$685$	−19.2332	−	3.82572i	−0.734862	−	0.146173i
$686$	0.555570	−	0.831470i	0.0212118	−	0.0317457i
$687$	−18.9412	+	30.3440i	−0.722654	+	1.15770i
$688$	5.32756	+	2.20675i	0.203111	+	0.0841315i
$689$	15.7539	+	6.52548i	0.600176	+	0.248601i
$690$	3.51649	−	5.63345i	0.133871	−	0.214462i
$691$	−19.0792	+	28.5540i	−0.725807	+	1.08625i	0.266667	+	0.963789i	$0.414078\pi$
$691$	−19.0792	+	28.5540i	−0.725807	+	1.08625i	−0.992474	+	0.122458i	$0.960922\pi$
$692$	6.45344	+	1.28367i	0.245323	+	0.0487978i
$693$	0.607390	+	0.536356i	0.0230728	+	0.0203745i
$694$	−11.8660	−	17.7588i	−0.450428	−	0.674114i
$695$	13.5797	+	32.7843i	0.515108	+	1.24358i
$696$	7.08559	+	6.65918i	0.268579	+	0.252416i
$697$	−34.7770	+	3.98143i	−1.31727	+	0.150808i
$698$			31.8094i			1.20400i
$699$	−10.4408	+	27.5971i	−0.394906	+	1.04382i
$700$	−1.56585	+	1.04626i	−0.0591834	+	0.0395451i
$701$	10.0191	+	10.0191i	0.378417	+	0.378417i	0.870531	−	0.492114i	$-0.163776\pi$
$701$	10.0191	+	10.0191i	0.378417	+	0.378417i	−0.492114	+	0.870531i	$0.663776\pi$
$702$	12.1809	−	9.89239i	0.459740	−	0.373364i
$703$	−5.38067	−	3.59525i	−0.202936	−	0.135597i
$704$	−0.0526945	−	0.264913i	−0.00198600	−	0.00998428i
$705$	24.3474	−	10.9815i	0.916976	−	0.413586i
$706$	14.2702	−	34.4513i	0.537067	−	1.29659i
$707$	14.8047	−	2.94484i	0.556789	−	0.110752i
$708$	−14.6576	+	3.39122i	−0.550865	+	0.127450i
$709$	1.83943	−	9.24742i	0.0690811	−	0.347294i	−0.930750	−	0.365655i	$-0.880845\pi$
$709$	1.83943	−	9.24742i	0.0690811	−	0.347294i	0.999831	+	0.0183613i	$0.00584490\pi$
$710$	−1.27063	+	1.27063i	−0.0476860	+	0.0476860i
$711$	10.4761	−	7.98179i	0.392886	−	0.299341i
$712$	2.81343	−	1.16536i	0.105438	−	0.0436737i
$713$	8.71757			0.326476
$714$	6.72939	−	2.39067i	0.251841	−	0.0894685i
$715$	−1.44004			−0.0538544
$716$	−6.40447	+	2.65282i	−0.239346	+	0.0991404i
$717$	−31.5776	−	5.26903i	−1.17929	−	0.196776i
$718$	−22.6374	+	22.6374i	−0.844819	+	0.844819i
$719$	−0.304032	+	1.52847i	−0.0113385	+	0.0570023i	−0.986040	−	0.166507i	$-0.946751\pi$
$719$	−0.304032	+	1.52847i	−0.0113385	+	0.0570023i	0.974702	+	0.223509i	$0.0717512\pi$
$720$	−4.57765	−	2.66385i	−0.170599	−	0.0992757i
$721$	−3.11713	+	0.620036i	−0.116088	+	0.0230913i
$722$	−5.57096	+	13.4495i	−0.207330	+	0.500538i
$723$	−4.01595	−	8.90390i	−0.149355	−	0.331140i
$724$	−3.23680	−	16.2725i	−0.120295	−	0.604762i
$725$	8.79063	+	5.87371i	0.326476	+	0.218144i
$726$	15.4029	−	10.9977i	0.571657	−	0.408164i
$727$	−11.1752	−	11.1752i	−0.414466	−	0.414466i	0.468825	−	0.883291i	$-0.344677\pi$
$727$	−11.1752	−	11.1752i	−0.414466	−	0.414466i	−0.883291	+	0.468825i	$0.844677\pi$
$728$	2.51096	−	1.67777i	0.0930622	−	0.0621822i
$729$	−14.7690	−	22.6026i	−0.547001	−	0.837132i
$730$		−	9.04986i		−	0.334950i
$731$	−21.1431	−	10.8749i	−0.782006	−	0.402223i
$732$	14.4905	−	15.4183i	0.535583	−	0.569878i
$733$	13.9431	+	33.6616i	0.515000	+	1.24332i	0.940941	+	0.338570i	$0.109943\pi$
$733$	13.9431	+	33.6616i	0.515000	+	1.24332i	−0.425941	+	0.904751i	$0.640057\pi$
$734$	−9.03912	−	13.5280i	−0.333640	−	0.499327i
$735$	3.05636	−	0.0948175i	0.112736	−	0.00349740i
$736$	−2.13004	−	0.423691i	−0.0785143	−	0.0156175i
$737$	−0.737828	+	1.10424i	−0.0271782	+	0.0406751i
$738$	6.50767	+	24.6239i	0.239550	+	0.906416i
$739$	−19.6256	−	8.12920i	−0.721940	−	0.299038i	−0.00870503	−	0.999962i	$-0.502771\pi$
$739$	−19.6256	−	8.12920i	−0.721940	−	0.299038i	−0.713235	+	0.700925i	$0.752771\pi$
$740$	−5.00783	−	2.07431i	−0.184092	−	0.0762532i
$741$	9.35209	+	5.83773i	0.343558	+	0.214454i
$742$	3.13704	−	4.69491i	0.115164	−	0.172355i
$743$	−6.68001	−	1.32874i	−0.245066	−	0.0487466i	0.0710290	−	0.997474i	$-0.477372\pi$
$743$	−6.68001	−	1.32874i	−0.245066	−	0.0487466i	−0.316095	+	0.948728i	$0.602372\pi$
$744$	−0.215585	−	6.94919i	−0.00790372	−	0.254770i
$745$	9.06269	+	13.5633i	0.332031	+	0.496920i
$746$	13.9721	+	33.7318i	0.511557	+	1.23501i
$747$	−1.94049	−	31.2448i	−0.0709987	−	1.14319i
$748$	0.126670	+	1.10644i	0.00463151	+	0.0404553i
$749$			8.26062i			0.301837i
$750$	−19.6860	−	7.44777i	−0.718830	−	0.271954i
$751$	−3.31195	+	2.21297i	−0.120855	+	0.0807526i	−0.614528	−	0.788895i	$-0.710654\pi$
$751$	−3.31195	+	2.21297i	−0.120855	+	0.0807526i	0.493674	+	0.869647i	$0.335654\pi$
$752$	−6.17639	−	6.17639i	−0.225230	−	0.225230i
$753$	−11.7160	−	16.4089i	−0.426955	−	0.597974i
$754$	−14.0965	−	9.41895i	−0.513362	−	0.343018i
$755$	−6.13773	−	30.8565i	−0.223375	−	1.12298i
$756$	−2.42588	−	4.59512i	−0.0882285	−	0.167123i
$757$	−12.5572	+	30.3157i	−0.456398	+	1.10184i	0.513448	+	0.858121i	$0.328368\pi$
$757$	−12.5572	+	30.3157i	−0.456398	+	1.10184i	−0.969845	+	0.243721i	$0.921632\pi$
$758$	−31.6073	+	6.28708i	−1.14803	+	0.228357i
$759$	0.229020	+	0.989874i	0.00831291	+	0.0359302i
$760$	0.725932	−	3.64951i	0.0263323	−	0.132382i
$761$	18.5116	−	18.5116i	0.671046	−	0.671046i	−0.286911	−	0.957957i	$-0.592628\pi$
$761$	18.5116	−	18.5116i	0.671046	−	0.671046i	0.957957	+	0.286911i	$0.0926283\pi$
$762$	3.08228	−	18.4723i	0.111659	−	0.669180i
$763$	14.8533	−	6.15243i	0.537725	−	0.222733i
$764$	−11.5663			−0.418453
$765$	17.9066	+	12.4988i	0.647414	+	0.451896i
$766$	−8.04838			−0.290800
$767$	24.2344	−	10.0382i	0.875054	−	0.362459i
$768$	−0.285068	+	1.70843i	−0.0102865	+	0.0616477i
$769$	−14.4009	+	14.4009i	−0.519310	+	0.519310i	−0.917363	−	0.398052i	$-0.869686\pi$
$769$	−14.4009	+	14.4009i	−0.519310	+	0.519310i	0.398052	+	0.917363i	$0.369686\pi$
$770$	−0.0930288	+	0.467688i	−0.00335253	+	0.0168543i
$771$	−5.38393	−	23.2705i	−0.193898	−	0.838066i
$772$	5.80294	−	1.15428i	0.208852	−	0.0415433i
$773$	10.2684	−	24.7900i	0.369327	−	0.891634i	−0.624534	−	0.780998i	$-0.714711\pi$
$773$	10.2684	−	24.7900i	0.369327	−	0.891634i	0.993861	−	0.110637i	$-0.0352890\pi$
$774$	−5.61680	+	16.3623i	−0.201892	+	0.588131i
$775$	−1.47476	−	7.41410i	−0.0529748	−	0.266322i
$776$	−2.09052	−	1.39684i	−0.0750454	−	0.0501437i
$777$	−3.09017	−	4.32796i	−0.110859	−	0.155265i
$778$	11.5505	+	11.5505i	0.414107	+	0.414107i
$779$	−14.8782	+	9.94127i	−0.533066	+	0.356183i
$780$	8.63689	+	3.26759i	0.309250	+	0.116998i
$781$		−	0.274923i		−	0.00983753i
$782$	8.60889	+	2.46351i	0.307853	+	0.0880949i
$783$	−18.6215	+	22.4542i	−0.665478	+	0.802449i
$784$	−0.382683	−	0.923880i	−0.0136673	−	0.0329957i
$785$	7.33985	+	10.9849i	0.261971	+	0.392067i
$786$	0.0577770	+	1.86239i	0.00206084	+	0.0664293i
$787$	−41.0880	−	8.17291i	−1.46463	−	0.291333i	−0.602539	−	0.798089i	$-0.705844\pi$
$787$	−41.0880	−	8.17291i	−1.46463	−	0.291333i	−0.862089	+	0.506757i	$0.830844\pi$
$788$	−4.08301	+	6.11066i	−0.145451	+	0.217683i
$789$	39.0587	+	24.3811i	1.39053	+	0.867988i
$790$	7.16052	+	2.96598i	0.254760	+	0.105525i
$791$	0.267805	+	0.110928i	0.00952203	+	0.00394415i
$792$	0.783411	−	0.207042i	0.0278373	−	0.00735693i
$793$	−20.4957	+	30.6740i	−0.727825	+	1.08927i
$794$	−16.5094	−	3.28393i	−0.585898	−	0.116542i
$795$	17.2578	−	0.535388i	0.612070	−	0.0189883i
$796$	−9.83754	−	14.7229i	−0.348682	−	0.521840i
$797$	−19.8773	−	47.9881i	−0.704091	−	1.69983i	−0.714263	−	0.699877i	$-0.753238\pi$
$797$	−19.8773	−	47.9881i	−0.704091	−	1.69983i	0.0101723	−	0.999948i	$-0.496762\pi$
$798$	2.50010	−	2.66019i	0.0885027	−	0.0941697i
$799$	23.2846	+	27.4746i	0.823748	+	0.971982i
$800$			1.88323i			0.0665821i
$801$	4.01254	+	8.20734i	0.141776	+	0.289992i
$802$	−12.8128	+	8.56123i	−0.452435	+	0.302307i
$803$	0.979046	+	0.979046i	0.0345498	+	0.0345498i
$804$	6.93087	−	4.94866i	0.244433	−	0.174526i
$805$	3.18796	+	2.13012i	0.112361	+	0.0750770i
$806$	2.36489	+	11.8891i	0.0832996	+	0.418775i
$807$	15.7938	+	35.0169i	0.555967	+	1.23265i
$808$	5.77652	−	13.9458i	0.203217	−	0.490610i
$809$	20.9327	−	4.16376i	0.735953	−	0.146390i	0.187138	−	0.982334i	$-0.440079\pi$
$809$	20.9327	−	4.16376i	0.735953	−	0.146390i	0.548815	+	0.835944i	$0.315079\pi$
$810$	7.12491	−	14.2019i	0.250344	−	0.499004i
$811$	−6.24691	+	31.4053i	−0.219359	+	1.10279i	0.701433	+	0.712736i	$0.252544\pi$
$811$	−6.24691	+	31.4053i	−0.219359	+	1.10279i	−0.920792	+	0.390055i	$0.872456\pi$
$812$	−3.96968	+	3.96968i	−0.139309	+	0.139309i
$813$	12.5839	+	2.09974i	0.441336	+	0.0736411i
$814$	0.766172	−	0.317359i	0.0268543	−	0.0111234i
$815$	−10.8191			−0.378975
$816$	1.75088	−	6.92347i	0.0612931	−	0.242370i
$817$	−12.1540			−0.425216
$818$	−21.2428	+	8.79905i	−0.742737	+	0.307652i
$819$	5.49056	+	7.20638i	0.191856	+	0.251811i
$820$	−10.5982	+	10.5982i	−0.370106	+	0.370106i
$821$	−4.02912	+	20.2558i	−0.140617	+	0.706931i	0.844569	+	0.535446i	$0.179856\pi$
$821$	−4.02912	+	20.2558i	−0.140617	+	0.706931i	−0.985187	+	0.171485i	$0.945144\pi$
$822$	−18.7440	+	4.33667i	−0.653772	+	0.151259i
$823$	−24.2295	+	4.81955i	−0.844588	+	0.167999i	−0.598375	−	0.801216i	$-0.704187\pi$
$823$	−24.2295	+	4.81955i	−0.844588	+	0.167999i	−0.246214	+	0.969216i	$0.579187\pi$
$824$	−1.21624	+	2.93627i	−0.0423699	+	0.102290i
$825$	0.803123	−	0.362234i	0.0279611	−	0.0126114i
$826$	−1.69457	−	8.51919i	−0.0589617	−	0.296421i
$827$	−24.2998	−	16.2366i	−0.844986	−	0.564602i	0.0560093	−	0.998430i	$-0.482162\pi$
$827$	−24.2998	−	16.2366i	−0.844986	−	0.564602i	−0.900995	+	0.433829i	$0.857162\pi$
$828$	0.872528	−	6.45662i	0.0303225	−	0.224383i
$829$	−1.51882	−	1.51882i	−0.0527508	−	0.0527508i	0.680239	−	0.732990i	$-0.261876\pi$
$829$	−1.51882	−	1.51882i	−0.0527508	−	0.0527508i	−0.732990	+	0.680239i	$0.761876\pi$
$830$	15.3176	−	10.2349i	0.531683	−	0.355259i
$831$	−12.3399	+	32.6168i	−0.428065	+	1.13146i
$832$		−	3.01990i		−	0.104696i
$833$	1.25912	+	3.92615i	0.0436258	+	0.136033i
$834$	25.3690	+	23.8423i	0.878457	+	0.825592i
$835$	4.31053	+	10.4065i	0.149172	+	0.360133i
$836$	0.316283	+	0.473351i	0.0109389	+	0.0163712i
$837$	20.7674	−	1.93778i	0.717826	−	0.0669793i
$838$	15.7385	+	3.13057i	0.543676	+	0.108144i
$839$	−13.0668	+	19.5558i	−0.451116	+	0.675143i	−0.985418	−	0.170151i	$-0.945574\pi$
$839$	−13.0668	+	19.5558i	−0.451116	+	0.675143i	0.534302	+	0.845294i	$0.320574\pi$
$840$	1.61918	−	2.59395i	0.0558672	−	0.0894997i
$841$	2.32519	+	0.963127i	0.0801791	+	0.0332113i
$842$	15.2091	+	6.29982i	0.524140	+	0.217106i
$843$	14.1232	−	22.6256i	0.486430	−	0.779266i
$844$	−12.0166	+	17.9841i	−0.413627	+	0.619037i
$845$	6.71864	+	1.33642i	0.231128	+	0.0459742i
$846$	17.3450	−	19.6421i	0.596333	−	0.675309i
$847$	6.07074	+	9.08551i	0.208593	+	0.312182i
$848$	−2.16083	−	5.21670i	−0.0742031	−	0.179142i
$849$	−34.0715	−	32.0211i	−1.16933	−	1.09896i
$850$	0.638790	−	7.73842i	0.0219103	−	0.265426i
$851$		−	6.66800i		−	0.228576i
$852$	−0.623827	+	1.64890i	−0.0213720	+	0.0564904i
$853$	28.2415	−	18.8704i	0.966972	−	0.646110i	0.0314972	−	0.999504i	$-0.489972\pi$
$853$	28.2415	−	18.8704i	0.966972	−	0.646110i	0.935475	+	0.353394i	$0.114972\pi$
$854$	8.63808	+	8.63808i	0.295589	+	0.295589i
$855$	11.0625	+	1.49495i	0.378328	+	0.0511262i
$856$	6.86846	+	4.58936i	0.234759	+	0.156861i
$857$	2.56903	+	12.9154i	0.0877563	+	0.441181i	0.999535	+	0.0304983i	$0.00970943\pi$
$857$	2.56903	+	12.9154i	0.0877563	+	0.441181i	−0.911779	+	0.410682i	$0.865291\pi$
$858$	−1.28787	+	0.580871i	−0.0439671	+	0.0198306i
$859$	15.9308	−	38.4604i	0.543552	−	1.31225i	−0.378649	−	0.925540i	$-0.623611\pi$
$859$	15.9308	−	38.4604i	0.543552	−	1.31225i	0.922201	−	0.386711i	$-0.126389\pi$
$860$	−9.98481	+	1.98610i	−0.340479	+	0.0677255i
$861$	−14.3263	+	3.31457i	−0.488237	+	0.112960i
$862$	0.581820	−	2.92500i	0.0198169	−	0.0996261i
$863$	−17.6620	+	17.6620i	−0.601221	+	0.601221i	−0.940636	−	0.339416i	$-0.889771\pi$
$863$	−17.6620	+	17.6620i	−0.601221	+	0.601221i	0.339416	+	0.940636i	$0.389771\pi$
$864$	−5.16845	−	0.535862i	−0.175834	−	0.0182304i
$865$	−10.7321	+	4.44539i	−0.364903	+	0.151148i
$866$	−35.8662			−1.21878
$867$	−9.54304	+	27.8555i	−0.324099	+	0.946023i
$868$	4.01404			0.136246
$869$	−1.09552	+	0.453780i	−0.0371630	+	0.0153934i
$870$	−16.9325	−	2.82535i	−0.574065	−	0.0957883i
$871$	−10.4994	+	10.4994i	−0.355759	+	0.355759i
$872$	3.13648	−	15.7682i	0.106215	−	0.533977i
$873$	3.79372	−	6.51926i	0.128398	−	0.220644i
$874$	4.48947	−	0.893011i	0.151859	−	0.0302066i
$875$	4.65034	−	11.2269i	0.157210	−	0.379539i
$876$	−3.65045	−	8.09355i	−0.123337	−	0.273456i
$877$	−5.02028	−	25.2387i	−0.169523	−	0.852249i	−0.968140	−	0.250409i	$-0.919435\pi$
$877$	−5.02028	−	25.2387i	−0.169523	−	0.852249i	0.798617	−	0.601839i	$-0.205565\pi$
$878$	−2.46102	−	1.64440i	−0.0830554	−	0.0554959i
$879$	30.4258	−	21.7241i	1.02624	−	0.732735i
$880$	0.337184	+	0.337184i	0.0113665	+	0.0113665i
$881$	40.0940	−	26.7900i	1.35080	−	0.902577i	0.351369	−	0.936237i	$-0.385716\pi$
$881$	40.0940	−	26.7900i	1.35080	−	0.902577i	0.999433	+	0.0336601i	$0.0107164\pi$
$882$	2.69515	−	1.31765i	0.0907503	−	0.0443675i
$883$		−	28.7300i		−	0.966841i	−0.875388	−	0.483421i	$-0.839394\pi$
$883$		−	28.7300i		−	0.966841i	0.875388	−	0.483421i	$-0.160606\pi$
$884$	−1.02435	+	12.4092i	−0.0344526	+	0.417365i
$885$	18.1898	−	19.3545i	0.611443	−	0.650595i
$886$	10.3751	+	25.0478i	0.348559	+	0.841496i
$887$	11.7750	+	17.6225i	0.395364	+	0.591704i	0.974736	−	0.223359i	$-0.0717022\pi$
$887$	11.7750	+	17.6225i	0.395364	+	0.591704i	−0.579372	+	0.815063i	$0.696702\pi$
$888$	−5.31537	+	0.164899i	−0.178372	+	0.00553364i
$889$	10.6047	+	2.10940i	0.355669	+	0.0707470i
$890$	−2.98684	+	4.47012i	−0.100119	+	0.149839i
$891$	0.765615	+	2.30721i	0.0256491	+	0.0772946i
$892$	11.4091	+	4.72582i	0.382007	+	0.158232i
$893$	17.0088	+	7.04526i	0.569177	+	0.235761i
$894$	13.5761	+	8.47441i	0.454052	+	0.283427i
$895$	6.79922	−	10.1758i	0.227273	−	0.340138i
$896$	−0.980785	−	0.195090i	−0.0327657	−	0.00651751i
$897$	0.352243	+	11.3542i	0.0117610	+	0.379107i
$898$	−0.537539	−	0.804485i	−0.0179379	−	0.0268460i
$899$	−8.62368	−	20.8194i	−0.287616	−	0.694366i
$900$	−5.63881	+	0.350203i	−0.187960	+	0.0116734i
$901$	7.10962	+	22.1690i	0.236856	+	0.738558i
$902$		−	2.29311i		−	0.0763521i
$903$	−9.34169	−	3.53423i	−0.310872	−	0.117612i
$904$	0.241018	−	0.161043i	0.00801613	−	0.00535621i
$905$	20.7118	+	20.7118i	0.688483	+	0.688483i
$906$	−17.9358	−	25.1201i	−0.595876	−	0.834558i
$907$	−15.6413	−	10.4512i	−0.519361	−	0.347026i	0.268099	−	0.963391i	$-0.413604\pi$
$907$	−15.6413	−	10.4512i	−0.519361	−	0.347026i	−0.787460	+	0.616365i	$0.788604\pi$
$908$	1.52503	+	7.66685i	0.0506099	+	0.254433i
$909$	42.8310	+	14.7029i	1.42061	+	0.487664i
$910$	−2.04026	+	4.92562i	−0.0676339	+	0.163283i
$911$	17.8563	−	3.55183i	0.591604	−	0.117677i	0.109796	−	0.993954i	$-0.464980\pi$
$911$	17.8563	−	3.55183i	0.591604	−	0.117677i	0.481808	+	0.876277i	$0.339980\pi$
$912$	−0.822885	−	3.55668i	−0.0272485	−	0.117774i
$913$	−0.549867	+	2.76437i	−0.0181979	+	0.0914873i
$914$	−6.27681	+	6.27681i	−0.207619	+	0.207619i
$915$	−6.14800	+	36.8453i	−0.203246	+	1.21807i
$916$	−19.0801	+	7.90323i	−0.630424	+	0.261130i
$917$	−1.07577			−0.0355250
$918$	21.0561	+	3.95506i	0.694953	+	0.130536i
$919$	−6.85794			−0.226223			−0.113111	−	0.993582i	$-0.536082\pi$
$919$	−6.85794			−0.226223			−0.113111	+	0.993582i	$0.536082\pi$
$920$	3.54227	−	1.46726i	0.116785	−	0.0483740i
$921$	7.58488	−	45.4566i	0.249930	−	1.49785i
$922$	−19.2432	+	19.2432i	−0.633742	+	0.633742i
$923$	0.599668	−	3.01473i	0.0197383	−	0.0992311i
$924$	0.105453	+	0.455792i	0.00346916	+	0.0149945i
$925$	−5.67098	+	1.12803i	−0.186461	+	0.0370894i
$926$	−6.75036	+	16.2968i	−0.221831	+	0.535546i
$927$	−9.01805	−	3.09569i	−0.296192	−	0.101676i
$928$	1.09523	+	5.50611i	0.0359528	+	0.180747i
$929$	11.6971	+	7.81573i	0.383768	+	0.256426i	0.732458	−	0.680813i	$-0.238373\pi$
$929$	11.6971	+	7.81573i	0.383768	+	0.256426i	−0.348689	+	0.937238i	$0.613373\pi$
$930$	7.13239	+	9.98932i	0.233880	+	0.327563i
$931$	1.49037	+	1.49037i	0.0488448	+	0.0488448i
$932$	−14.1644	+	9.46433i	−0.463969	+	0.310014i
$933$	24.1630	+	9.14154i	0.791060	+	0.299281i
$934$			38.4436i			1.25791i
$935$	−1.27116	−	1.49990i	−0.0415714	−	0.0490521i
$936$	9.04228	−	0.561578i	0.295556	−	0.0183558i
$937$	13.1214	+	31.6779i	0.428658	+	1.03487i	0.979713	+	0.200404i	$0.0642254\pi$
$937$	13.1214	+	31.6779i	0.428658	+	1.03487i	−0.551055	+	0.834469i	$0.685775\pi$
$938$	2.73166	+	4.08821i	0.0891917	+	0.133485i
$939$	0.808825	+	26.0718i	0.0263950	+	0.850820i
$940$	15.1243	+	3.00842i	0.493301	+	0.0981237i
$941$	22.8785	−	34.2402i	0.745819	−	1.11620i	−0.243425	−	0.969920i	$-0.578271\pi$
$941$	22.8785	−	34.2402i	0.745819	−	1.11620i	0.989244	−	0.146277i	$-0.0467292\pi$
$942$	10.9952	+	6.86340i	0.358244	+	0.223622i
$943$	−17.0343	−	7.05583i	−0.554713	−	0.229770i
$944$	−8.02491	−	3.32402i	−0.261188	−	0.108188i
$945$	8.06798	+	4.36584i	0.262451	+	0.142021i
$946$	0.865329	−	1.29506i	0.0281343	−	0.0421059i
$947$	−35.9153	−	7.14399i	−1.16709	−	0.232149i	−0.426742	−	0.904373i	$-0.640339\pi$
$947$	−35.9153	−	7.14399i	−1.16709	−	0.232149i	−0.740347	+	0.672225i	$0.765339\pi$
$948$	7.60026	−	0.235783i	0.246845	−	0.00765788i
$949$	8.60044	+	12.8715i	0.279182	+	0.417825i
$950$	−1.51897	−	3.66712i	−0.0492820	−	0.118977i
$951$	7.30420	−	7.77190i	0.236855	−	0.252021i
$952$	3.96400	+	1.13433i	0.128474	+	0.0367640i
$953$			19.4499i			0.630043i	0.949085	+	0.315021i	$0.102012\pi$
$953$			19.4499i			0.630043i	−0.949085	+	0.315021i	$0.897988\pi$
$954$	15.2182	−	7.44011i	0.492707	−	0.240882i
$955$	16.9782	−	11.3445i	0.549403	−	0.367099i
$956$	−13.0697	−	13.0697i	−0.422706	−	0.422706i
$957$	2.13748	−	1.52616i	0.0690948	−	0.0493338i
$958$	−22.4985	−	15.0330i	−0.726894	−	0.485695i
$959$	−2.16701	−	10.8943i	−0.0699763	−	0.351795i
$960$	−1.25722	−	2.78742i	−0.0405765	−	0.0899637i
$961$	5.69718	−	13.7542i	0.183780	−	0.443684i
$962$	9.09386	−	1.80888i	0.293198	−	0.0583207i
$963$	−12.4643	+	21.4192i	−0.401658	+	0.690223i
$964$	1.10019	−	5.53101i	0.0354346	−	0.178142i
$965$	−7.38604	+	7.38604i	−0.237765	+	0.237765i
$966$	3.71032	+	0.619102i	0.119377	+	0.0199193i
$967$	49.2839	−	20.4141i	1.58486	−	0.656472i	0.595690	−	0.803215i	$-0.296879\pi$
$967$	49.2839	−	20.4141i	1.58486	−	0.656472i	0.989175	+	0.146742i	$0.0468789\pi$
$968$	10.9270			0.351209
$969$	2.17492	+	14.8940i	0.0698683	+	0.478464i
$970$	4.43875			0.142520
$971$	37.0388	−	15.3420i	1.18863	−	0.492347i	0.301321	−	0.953523i	$-0.402572\pi$
$971$	37.0388	−	15.3420i	1.18863	−	0.492347i	0.887309	+	0.461176i	$0.152572\pi$
$972$	0.643374	−	15.5752i	0.0206362	−	0.499574i
$973$	−14.2129	+	14.2129i	−0.455645	+	0.455645i
$974$	1.80884	−	9.09365i	0.0579590	−	0.291379i
$975$	9.59693	−	2.22038i	0.307348	−	0.0711089i
$976$	11.9814	−	2.38324i	0.383514	−	0.0762857i
$977$	−5.62252	+	13.5740i	−0.179880	+	0.434270i	−0.987941	−	0.154829i	$-0.950517\pi$
$977$	−5.62252	+	13.5740i	−0.179880	+	0.434270i	0.808061	+	0.589099i	$0.200517\pi$
$978$	−9.67580	+	4.36410i	−0.309398	+	0.139549i
$979$	−0.160467	−	0.806721i	−0.00512854	−	0.0257829i
$980$	1.46791	+	0.980825i	0.0468906	+	0.0313313i
$981$	47.7968	+	6.45912i	1.52603	+	0.206224i
$982$	15.5318	+	15.5318i	0.495641	+	0.495641i
$983$	−38.2103	+	25.5313i	−1.21872	+	0.814322i	−0.987352	−	0.158545i	$-0.949320\pi$
$983$	−38.2103	+	25.5313i	−1.21872	+	0.814322i	−0.231367	+	0.972867i	$0.574320\pi$
$984$	−5.20328	+	13.7533i	−0.165874	+	0.438440i
$985$		−	12.9746i		−	0.413405i
$986$	−2.63278	−	22.9968i	−0.0838449	−	0.732368i
$987$	11.0244	+	10.3610i	0.350910	+	0.329793i
$988$	2.43579	+	5.88052i	0.0774928	+	0.187084i
$989$	−6.95770	−	10.4129i	−0.221242	−	0.331112i
$990$	−0.946904	+	1.07231i	−0.0300946	+	0.0340802i
$991$	−45.4632	−	9.04320i	−1.44419	−	0.287267i	−0.590072	−	0.807351i	$-0.700901\pi$
$991$	−45.4632	−	9.04320i	−1.44419	−	0.287267i	−0.854115	+	0.520084i	$0.825901\pi$
$992$	2.23008	−	3.33756i	0.0708052	−	0.105968i
$993$	21.8138	−	34.9460i	0.692241	−	1.10898i
$994$	−0.940367	−	0.389513i	−0.0298266	−	0.0123546i
$995$	28.8812	+	11.9630i	0.915596	+	0.379252i
$996$	9.57054	−	15.3321i	0.303254	−	0.485816i
$997$	30.9834	−	46.3699i	0.981253	−	1.46855i	0.100521	−	0.994935i	$-0.467949\pi$
$997$	30.9834	−	46.3699i	0.981253	−	1.46855i	0.880732	−	0.473615i	$-0.157051\pi$
$998$	−18.3028	−	3.64065i	−0.579364	−	0.115243i
$999$	−1.48219	−	15.8848i	−0.0468943	−	0.502572i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	714.2.bf.a.29.12	✓	144
3.2	odd	2		714.2.bf.b.29.17	yes	144
17.10	odd	16		714.2.bf.b.197.17	yes	144
51.44	even	16	inner	714.2.bf.a.197.12	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.2.bf.a.29.12	✓	144	1.1	even	1	trivial
714.2.bf.a.197.12	yes	144	51.44	even	16	inner
714.2.bf.b.29.17	yes	144	3.2	odd	2
714.2.bf.b.197.17	yes	144	17.10	odd	16

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:	\( N \)	\(=\)	\( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	714.bf (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.923880 + 0.382683i) q^{2} +(0.285068 - 1.70843i) q^{3} +(0.707107 - 0.707107i) q^{4} +(-0.344420 + 1.73152i) q^{5} +(0.390419 + 1.68748i) q^{6} +(-0.980785 + 0.195090i) q^{7} +(-0.382683 + 0.923880i) q^{8} +(-2.83747 - 0.974039i) q^{9} +O(q^{10})\)	\(q+(-0.923880 + 0.382683i) q^{2} +(0.285068 - 1.70843i) q^{3} +(0.707107 - 0.707107i) q^{4} +(-0.344420 + 1.73152i) q^{5} +(0.390419 + 1.68748i) q^{6} +(-0.980785 + 0.195090i) q^{7} +(-0.382683 + 0.923880i) q^{8} +(-2.83747 - 0.974039i) q^{9} +(-0.344420 - 1.73152i) q^{10} +(0.224582 + 0.150061i) q^{11} +(-1.00647 - 1.40962i) q^{12} +(2.13539 + 2.13539i) q^{13} +(0.831470 - 0.555570i) q^{14} +(2.85999 + 1.08202i) q^{15} -1.00000i q^{16} +(-0.339200 + 4.10913i) q^{17} +(2.99423 - 0.185959i) q^{18} +(0.806580 + 1.94726i) q^{19} +(0.980825 + 1.46791i) q^{20} +(0.0537076 + 1.73122i) q^{21} +(-0.264913 - 0.0526945i) q^{22} +(-1.20657 + 1.80576i) q^{23} +(1.46929 + 0.917157i) q^{24} +(1.73987 + 0.720680i) q^{25} +(-2.79002 - 1.15567i) q^{26} +(-2.47295 + 4.56996i) q^{27} +(-0.555570 + 0.831470i) q^{28} +(5.50611 + 1.09523i) q^{29} +(-3.05636 + 0.0948175i) q^{30} +(-2.23008 - 3.33756i) q^{31} +(0.382683 + 0.923880i) q^{32} +(0.320390 - 0.340906i) q^{33} +(-1.25912 - 3.92615i) q^{34} -1.76544i q^{35} +(-2.69515 + 1.31765i) q^{36} +(-2.55287 + 1.70577i) q^{37} +(-1.49037 - 1.49037i) q^{38} +(4.25690 - 3.03944i) q^{39} +(-1.46791 - 0.980825i) q^{40} +(1.65627 + 8.32663i) q^{41} +(-0.712128 - 1.57888i) q^{42} +(-2.20675 + 5.32756i) q^{43} +(0.264913 - 0.0526945i) q^{44} +(2.66385 - 4.57765i) q^{45} +(0.423691 - 2.13004i) q^{46} +(6.17639 - 6.17639i) q^{47} +(-1.70843 - 0.285068i) q^{48} +(0.923880 - 0.382683i) q^{49} -1.88323 q^{50} +(6.92347 + 1.75088i) q^{51} +3.01990 q^{52} +(5.21670 - 2.16083i) q^{53} +(0.535862 - 5.16845i) q^{54} +(-0.337184 + 0.337184i) q^{55} +(0.195090 - 0.980785i) q^{56} +(3.55668 - 0.822885i) q^{57} +(-5.50611 + 1.09523i) q^{58} +(3.32402 - 8.02491i) q^{59} +(2.78742 - 1.25722i) q^{60} +(2.38324 + 11.9814i) q^{61} +(3.33756 + 2.23008i) q^{62} +(2.97298 + 0.401759i) q^{63} +(-0.707107 - 0.707107i) q^{64} +(-4.43294 + 2.96199i) q^{65} +(-0.165543 + 0.437564i) q^{66} +4.91685i q^{67} +(2.66574 + 3.14544i) q^{68} +(2.74106 + 2.57611i) q^{69} +(0.675604 + 1.63105i) q^{70} +(-0.565485 - 0.846308i) q^{71} +(1.98575 - 2.24873i) q^{72} +(5.02763 + 1.00006i) q^{73} +(1.70577 - 2.55287i) q^{74} +(1.72721 - 2.76701i) q^{75} +(1.94726 + 0.806580i) q^{76} +(-0.249543 - 0.103364i) q^{77} +(-2.76972 + 4.43712i) q^{78} +(-2.43902 + 3.65025i) q^{79} +(1.73152 + 0.344420i) q^{80} +(7.10250 + 5.52762i) q^{81} +(-4.71666 - 7.05897i) q^{82} +(3.99331 + 9.64069i) q^{83} +(1.26213 + 1.18618i) q^{84} +(-6.99820 - 2.00260i) q^{85} -5.76651i q^{86} +(3.44075 - 9.09459i) q^{87} +(-0.224582 + 0.150061i) q^{88} +(-2.15330 - 2.15330i) q^{89} +(-0.709282 + 5.24861i) q^{90} +(-2.51096 - 1.67777i) q^{91} +(0.423691 + 2.13004i) q^{92} +(-6.33771 + 2.85851i) q^{93} +(-3.34264 + 8.06984i) q^{94} +(-3.64951 + 0.725932i) q^{95} +(1.68748 - 0.390419i) q^{96} +(-0.490506 + 2.46594i) q^{97} +(-0.707107 + 0.707107i) q^{98} +(-0.491081 - 0.644546i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q+O(q^{10}) \) 144 * q	\( 144 q - 16 q^{11} + 32 q^{17} + 16 q^{24} + 32 q^{25} + 16 q^{29} + 32 q^{31} + 48 q^{38} - 16 q^{39} + 16 q^{43} - 64 q^{45} - 16 q^{46} + 32 q^{47} + 176 q^{50} - 64 q^{51} - 32 q^{52} - 128 q^{53} - 64 q^{54} - 16 q^{57} - 16 q^{58} - 16 q^{60} - 32 q^{61} - 32 q^{62} + 16 q^{70} - 16 q^{71} - 16 q^{72} - 16 q^{74} + 112 q^{75} + 16 q^{78} + 64 q^{79} + 32 q^{80} + 128 q^{82} - 144 q^{83} - 16 q^{85} + 112 q^{87} + 16 q^{88} + 96 q^{91} - 16 q^{92} - 32 q^{93} + 32 q^{97} + 16 q^{99}+O(q^{100}) \) 144 * q - 16 * q^11 + 32 * q^17 + 16 * q^24 + 32 * q^25 + 16 * q^29 + 32 * q^31 + 48 * q^38 - 16 * q^39 + 16 * q^43 - 64 * q^45 - 16 * q^46 + 32 * q^47 + 176 * q^50 - 64 * q^51 - 32 * q^52 - 128 * q^53 - 64 * q^54 - 16 * q^57 - 16 * q^58 - 16 * q^60 - 32 * q^61 - 32 * q^62 + 16 * q^70 - 16 * q^71 - 16 * q^72 - 16 * q^74 + 112 * q^75 + 16 * q^78 + 64 * q^79 + 32 * q^80 + 128 * q^82 - 144 * q^83 - 16 * q^85 + 112 * q^87 + 16 * q^88 + 96 * q^91 - 16 * q^92 - 32 * q^93 + 32 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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