LMFDB - Embedded newform 756.2.cf.a.659.108

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(155,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 7, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("756.155"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.cf (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$108$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			659.108
Character	$\chi$	$=$	756.659
Dual form			756.2.cf.a.491.108

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41406 - 0.0209939i) q^{2} +(-0.283220 - 1.70874i) q^{3} +(1.99912 - 0.0593732i) q^{4} +(0.747603 - 2.05402i) q^{5} +(-0.436362 - 2.41031i) q^{6} +(0.984808 + 0.173648i) q^{7} +(2.82562 - 0.125927i) q^{8} +(-2.83957 + 0.967897i) q^{9} +(1.01403 - 2.92020i) q^{10} +(3.57896 - 1.30263i) q^{11} +(-0.667643 - 3.39915i) q^{12} +(0.135281 - 0.113514i) q^{13} +(1.39622 + 0.224874i) q^{14} +(-3.72152 - 0.695718i) q^{15} +(3.99295 - 0.237388i) q^{16} +(-5.31680 + 3.06966i) q^{17} +(-3.99500 + 1.42828i) q^{18} +(-1.99685 - 1.15288i) q^{19} +(1.37259 - 4.15062i) q^{20} +(0.0178022 - 1.73196i) q^{21} +(5.03350 - 1.91714i) q^{22} +(0.0492249 + 0.279169i) q^{23} +(-1.01545 - 4.79258i) q^{24} +(0.170124 + 0.142751i) q^{25} +(0.188912 - 0.163356i) q^{26} +(2.45811 + 4.57796i) q^{27} +(1.97906 + 0.288672i) q^{28} +(-4.88155 + 5.81761i) q^{29} +(-5.27705 - 0.905656i) q^{30} +(4.41115 - 0.777805i) q^{31} +(5.64128 - 0.419508i) q^{32} +(-3.23949 - 5.74657i) q^{33} +(-7.45382 + 4.45229i) q^{34} +(1.09292 - 1.89300i) q^{35} +(-5.61918 + 2.10354i) q^{36} +(0.564446 + 0.977649i) q^{37} +(-2.84787 - 1.58832i) q^{38} +(-0.232281 - 0.199011i) q^{39} +(1.85379 - 5.89804i) q^{40} +(-7.24325 - 8.63216i) q^{41} +(-0.0111873 - 2.44946i) q^{42} +(0.101877 + 0.279904i) q^{43} +(7.07742 - 2.81661i) q^{44} +(-0.134791 + 6.55615i) q^{45} +(0.0754678 + 0.393727i) q^{46} +(1.47637 - 8.37293i) q^{47} +(-1.53652 - 6.75567i) q^{48} +(0.939693 + 0.342020i) q^{49} +(0.243561 + 0.198286i) q^{50} +(6.75107 + 8.21564i) q^{51} +(0.263703 - 0.234961i) q^{52} +1.17351i q^{53} +(3.57201 + 6.42189i) q^{54} -8.32511i q^{55} +(2.80456 + 0.366651i) q^{56} +(-1.40443 + 3.73862i) q^{57} +(-6.78066 + 8.32892i) q^{58} +(-3.05479 - 1.11185i) q^{59} +(-7.48107 - 1.16986i) q^{60} +(-2.13712 + 12.1202i) q^{61} +(6.22129 - 1.19247i) q^{62} +(-2.96451 + 0.460106i) q^{63} +(7.96829 - 0.711642i) q^{64} +(-0.132025 - 0.362734i) q^{65} +(-4.70147 - 8.05797i) q^{66} +(4.21151 + 5.01908i) q^{67} +(-10.4467 + 6.45229i) q^{68} +(0.463084 - 0.163179i) q^{69} +(1.50571 - 2.69975i) q^{70} +(0.0796712 + 0.137995i) q^{71} +(-7.90168 + 3.09249i) q^{72} +(-4.16572 + 7.21524i) q^{73} +(0.818684 + 1.37060i) q^{74} +(0.195741 - 0.331126i) q^{75} +(-4.06040 - 2.18619i) q^{76} +(3.75078 - 0.661364i) q^{77} +(-0.332636 - 0.276536i) q^{78} +(-1.06892 + 1.27389i) q^{79} +(2.49754 - 8.37908i) q^{80} +(7.12635 - 5.49683i) q^{81} +(-10.4236 - 12.0543i) q^{82} +(6.85632 + 5.75314i) q^{83} +(-0.0672433 - 3.46345i) q^{84} +(2.33029 + 13.2157i) q^{85} +(0.149936 + 0.393662i) q^{86} +(11.3233 + 6.69363i) q^{87} +(9.94874 - 4.13144i) q^{88} +(1.26098 + 0.728026i) q^{89} +(-0.0529630 + 9.27360i) q^{90} +(0.152938 - 0.0882985i) q^{91} +(0.114982 + 0.555168i) q^{92} +(-2.57839 - 7.31721i) q^{93} +(1.91190 - 11.8708i) q^{94} +(-3.86091 + 3.23969i) q^{95} +(-2.31455 - 9.52065i) q^{96} +(12.1677 - 4.42868i) q^{97} +(1.33596 + 0.463908i) q^{98} +(-8.90189 + 7.16298i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66}+ \cdots + 36 q^{97}+O(q^{100}) $ 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.41406	−	0.0209939i	0.999890	−	0.0148449i
$2$	1.41406	−	0.0209939i	0.999890	−	0.0148449i
$3$	−0.283220	−	1.70874i	−0.163517	−	0.986541i
$3$	−0.283220	−	1.70874i	−0.163517	−	0.986541i
$4$	1.99912	−	0.0593732i	0.999559	−	0.0296866i
$5$	0.747603	−	2.05402i	0.334338	−	0.918587i	−0.652631	−	0.757676i	$-0.726335\pi$
$5$	0.747603	−	2.05402i	0.334338	−	0.918587i	0.986969	−	0.160911i	$-0.0514431\pi$
$6$	−0.436362	−	2.41031i	−0.178144	−	0.984004i
$7$	0.984808	+	0.173648i	0.372222	+	0.0656328i
$7$	0.984808	+	0.173648i	0.372222	+	0.0656328i
$8$	2.82562	−	0.125927i	0.999008	−	0.0445217i
$9$	−2.83957	+	0.967897i	−0.946524	+	0.322632i
$10$	1.01403	−	2.92020i	0.320665	−	0.923449i
$11$	3.57896	−	1.30263i	1.07910	−	0.392759i	0.259525	−	0.965736i	$-0.416434\pi$
$11$	3.57896	−	1.30263i	1.07910	−	0.392759i	0.819571	+	0.572978i	$0.194212\pi$
$12$	−0.667643	−	3.39915i	−0.192732	−	0.981251i
$13$	0.135281	−	0.113514i	0.0375203	−	0.0314832i	−0.623835	−	0.781556i	$-0.714426\pi$
$13$	0.135281	−	0.113514i	0.0375203	−	0.0314832i	0.661355	+	0.750073i	$0.269982\pi$
$14$	1.39622	+	0.224874i	0.373156	+	0.0601000i
$15$	−3.72152	−	0.695718i	−0.960893	−	0.179634i
$16$	3.99295	−	0.237388i	0.998237	−	0.0593471i
$17$	−5.31680	+	3.06966i	−1.28951	+	0.744501i	−0.978568	−	0.205926i	$-0.933979\pi$
$17$	−5.31680	+	3.06966i	−1.28951	+	0.744501i	−0.310947	+	0.950427i	$0.600646\pi$
$18$	−3.99500	+	1.42828i	−0.941631	+	0.336648i
$19$	−1.99685	−	1.15288i	−0.458110	−	0.264490i	0.253139	−	0.967430i	$-0.418537\pi$
$19$	−1.99685	−	1.15288i	−0.458110	−	0.264490i	−0.711249	+	0.702940i	$0.751870\pi$
$20$	1.37259	−	4.15062i	0.306921	−	0.928107i
$21$	0.0178022	−	1.73196i	0.00388476	−	0.377945i
$22$	5.03350	−	1.91714i	1.07315	−	0.408735i
$23$	0.0492249	+	0.279169i	0.0102641	+	0.0582107i	0.989510	−	0.144467i	$-0.0461468\pi$
$23$	0.0492249	+	0.279169i	0.0102641	+	0.0582107i	−0.979246	+	0.202678i	$0.935036\pi$
$24$	−1.01545	−	4.79258i	−0.207277	−	0.978282i
$25$	0.170124	+	0.142751i	0.0340247	+	0.0285501i
$26$	0.188912	−	0.163356i	0.0370488	−	0.0320367i
$27$	2.45811	+	4.57796i	0.473063	+	0.881029i
$28$	1.97906	+	0.288672i	0.374007	+	0.0545539i
$29$	−4.88155	+	5.81761i	−0.906482	+	1.08030i	0.0899540	+	0.995946i	$0.471328\pi$
$29$	−4.88155	+	5.81761i	−0.906482	+	1.08030i	−0.996436	+	0.0843568i	$0.973116\pi$
$30$	−5.27705	−	0.905656i	−0.963454	−	0.165349i
$31$	4.41115	−	0.777805i	0.792266	−	0.139698i	0.237152	−	0.971472i	$-0.423786\pi$
$31$	4.41115	−	0.777805i	0.792266	−	0.139698i	0.555114	+	0.831775i	$0.312675\pi$
$32$	5.64128	−	0.419508i	0.997246	−	0.0741593i
$33$	−3.23949	−	5.74657i	−0.563923	−	1.00035i
$34$	−7.45382	+	4.45229i	−1.27832	+	0.763562i
$35$	1.09292	−	1.89300i	0.184738	−	0.319975i
$36$	−5.61918	+	2.10354i	−0.936529	+	0.350589i
$37$	0.564446	+	0.977649i	0.0927943	+	0.160724i	0.908686	−	0.417480i	$-0.137087\pi$
$37$	0.564446	+	0.977649i	0.0927943	+	0.160724i	−0.815892	+	0.578205i	$0.803753\pi$
$38$	−2.84787	−	1.58832i	−0.461986	−	0.257660i
$39$	−0.232281	−	0.199011i	−0.0371947	−	0.0318672i
$40$	1.85379	−	5.89804i	0.293110	−	0.932561i
$41$	−7.24325	−	8.63216i	−1.13120	−	1.34812i	−0.929565	−	0.368658i	$-0.879817\pi$
$41$	−7.24325	−	8.63216i	−1.13120	−	1.34812i	−0.201640	−	0.979460i	$-0.564627\pi$
$42$	−0.0111873	−	2.44946i	−0.00172623	−	0.377961i
$43$	0.101877	+	0.279904i	0.0155361	+	0.0426850i	0.947218	−	0.320589i	$-0.103881\pi$
$43$	0.101877	+	0.279904i	0.0155361	+	0.0426850i	−0.931682	+	0.363274i	$0.881659\pi$
$44$	7.07742	−	2.81661i	1.06696	−	0.424620i
$45$	−0.134791	+	6.55615i	−0.0200935	+	0.977333i
$46$	0.0754678	+	0.393727i	0.0111271	+	0.0580519i
$47$	1.47637	−	8.37293i	0.215351	−	1.22132i	−0.664945	−	0.746893i	$-0.731545\pi$
$47$	1.47637	−	8.37293i	0.215351	−	1.22132i	0.880296	−	0.474425i	$-0.157344\pi$
$48$	−1.53652	−	6.75567i	−0.221777	−	0.975097i
$49$	0.939693	+	0.342020i	0.134242	+	0.0488600i
$50$	0.243561	+	0.198286i	0.0344448	+	0.0280419i
$51$	6.75107	+	8.21564i	0.945338	+	1.15042i
$52$	0.263703	−	0.234961i	0.0365691	−	0.0325832i
$53$			1.17351i			0.161195i	0.996747	+	0.0805973i	$0.0256828\pi$
$53$			1.17351i			0.161195i	−0.996747	+	0.0805973i	$0.974317\pi$
$54$	3.57201	+	6.42189i	0.486089	+	0.873909i
$55$		−	8.32511i		−	1.12256i
$56$	2.80456	+	0.366651i	0.374775	+	0.0489958i
$57$	−1.40443	+	3.73862i	−0.186021	+	0.495193i
$58$	−6.78066	+	8.32892i	−0.890345	+	1.09364i
$59$	−3.05479	−	1.11185i	−0.397700	−	0.144751i	0.135425	−	0.990788i	$-0.456760\pi$
$59$	−3.05479	−	1.11185i	−0.397700	−	0.144751i	−0.533124	+	0.846037i	$0.678982\pi$
$60$	−7.48107	−	1.16986i	−0.965802	−	0.151029i
$61$	−2.13712	+	12.1202i	−0.273630	+	1.55183i	0.469649	+	0.882853i	$0.344381\pi$
$61$	−2.13712	+	12.1202i	−0.273630	+	1.55183i	−0.743279	+	0.668982i	$0.766731\pi$
$62$	6.22129	−	1.19247i	0.790105	−	0.151444i
$63$	−2.96451	+	0.460106i	−0.373493	+	0.0579679i
$64$	7.96829	−	0.711642i	0.996036	−	0.0889552i
$65$	−0.132025	−	0.362734i	−0.0163756	−	0.0449917i
$66$	−4.70147	−	8.05797i	−0.578711	−	0.991867i
$67$	4.21151	+	5.01908i	0.514518	+	0.613179i	0.959275	−	0.282472i	$-0.0911545\pi$
$67$	4.21151	+	5.01908i	0.514518	+	0.613179i	−0.444757	+	0.895651i	$0.646710\pi$
$68$	−10.4467	+	6.45229i	−1.26684	+	0.782455i
$69$	0.463084	−	0.163179i	0.0557488	−	0.0196444i
$70$	1.50571	−	2.69975i	0.179967	−	0.322682i
$71$	0.0796712	+	0.137995i	0.00945523	+	0.0163769i	0.870714	−	0.491789i	$-0.163657\pi$
$71$	0.0796712	+	0.137995i	0.00945523	+	0.0163769i	−0.861259	+	0.508166i	$0.830324\pi$
$72$	−7.90168	+	3.09249i	−0.931222	+	0.364453i
$73$	−4.16572	+	7.21524i	−0.487560	+	0.844480i	−0.999898	−	0.0143048i	$-0.995446\pi$
$73$	−4.16572	+	7.21524i	−0.487560	+	0.844480i	0.512337	+	0.858784i	$0.328780\pi$
$74$	0.818684	+	1.37060i	0.0951700	+	0.159329i
$75$	0.195741	−	0.331126i	0.0226022	−	0.0382352i
$76$	−4.06040	−	2.18619i	−0.465760	−	0.250774i
$77$	3.75078	−	0.661364i	0.427441	−	0.0753695i
$78$	−0.332636	−	0.276536i	−0.0376637	−	0.0313115i
$79$	−1.06892	+	1.27389i	−0.120263	+	0.143324i	−0.822817	−	0.568307i	$-0.807599\pi$
$79$	−1.06892	+	1.27389i	−0.120263	+	0.143324i	0.702554	+	0.711631i	$0.252043\pi$
$80$	2.49754	−	8.37908i	0.279234	−	0.936810i
$81$	7.12635	−	5.49683i	0.791817	−	0.610759i
$82$	−10.4236	−	12.0543i	−1.15109	−	1.33118i
$83$	6.85632	+	5.75314i	0.752579	+	0.631489i	0.936184	−	0.351511i	$-0.114332\pi$
$83$	6.85632	+	5.75314i	0.752579	+	0.631489i	−0.183605	+	0.983000i	$0.558777\pi$
$84$	−0.0672433	−	3.46345i	−0.00733684	−	0.377893i
$85$	2.33029	+	13.2157i	0.252755	+	1.43345i
$86$	0.149936	+	0.393662i	0.0161680	+	0.0424496i
$87$	11.3233	+	6.69363i	1.21399	+	0.717633i
$88$	9.94874	−	4.13144i	1.06054	−	0.440413i
$89$	1.26098	+	0.728026i	0.133663	+	0.0771706i	0.565341	−	0.824858i	$-0.308745\pi$
$89$	1.26098	+	0.728026i	0.133663	+	0.0771706i	−0.431677	+	0.902028i	$0.642078\pi$
$90$	−0.0529630	+	9.27360i	−0.00558279	+	0.977524i
$91$	0.152938	−	0.0882985i	0.0160322	−	0.00925620i
$92$	0.114982	+	0.555168i	0.0119877	+	0.0578803i
$93$	−2.57839	−	7.31721i	−0.267367	−	0.758760i
$94$	1.91190	−	11.8708i	0.197197	−	1.22438i
$95$	−3.86091	+	3.23969i	−0.396121	+	0.332385i
$96$	−2.31455	−	9.52065i	−0.236228	−	0.971698i
$97$	12.1677	−	4.42868i	1.23544	−	0.449665i	0.359985	−	0.932958i	$-0.382782\pi$
$97$	12.1677	−	4.42868i	1.23544	−	0.449665i	0.875458	+	0.483293i	$0.160560\pi$
$98$	1.33596	+	0.463908i	0.134952	+	0.0468618i
$99$	−8.90189	+	7.16298i	−0.894674	+	0.719907i
$100$	0.348573	+	0.275275i	0.0348573	+	0.0275275i
$101$	12.8452	+	2.26495i	1.27814	+	0.225371i	0.771192	−	0.636603i	$-0.219661\pi$
$101$	12.8452	+	2.26495i	1.27814	+	0.225371i	0.506953	+	0.861974i	$0.330772\pi$
$102$	9.71887	+	11.4757i	0.962312	+	1.13626i
$103$	−3.09264	+	8.49696i	−0.304727	+	0.837231i	0.688935	+	0.724823i	$0.258078\pi$
$103$	−3.09264	+	8.49696i	−0.304727	+	0.837231i	−0.993662	+	0.112408i	$0.964144\pi$
$104$	0.367959	−	0.337784i	0.0360814	−	0.0331225i
$105$	−3.54417	−	1.33138i	−0.345876	−	0.129930i
$106$	0.0246367	+	1.65942i	0.00239293	+	0.161177i
$107$	9.29019			0.898117			0.449058	−	0.893502i	$-0.351759\pi$
$107$	9.29019			0.898117			0.449058	+	0.893502i	$0.351759\pi$
$108$	5.18585	+	9.00594i	0.499009	+	0.866597i
$109$	−7.22711			−0.692231			−0.346116	−	0.938192i	$-0.612500\pi$
$109$	−7.22711			−0.692231			−0.346116	+	0.938192i	$0.612500\pi$
$110$	−0.174777	−	11.7722i	−0.0166643	−	1.12243i
$111$	1.51068	−	1.24138i	0.143388	−	0.117827i
$112$	3.97351	+	0.459587i	0.375461	+	0.0434269i
$113$	4.92062	−	13.5193i	0.462893	−	1.27179i	−0.460406	−	0.887708i	$-0.652296\pi$
$113$	4.92062	−	13.5193i	0.462893	−	1.27179i	0.923299	−	0.384081i	$-0.125482\pi$
$114$	−1.90746	+	5.31611i	−0.178650	+	0.497900i
$115$	0.610219	+	0.107598i	0.0569032	+	0.0100336i
$116$	−9.41339	+	11.9199i	−0.874012	+	1.10674i
$117$	−0.274271	+	0.453271i	−0.0253563	+	0.0419049i
$118$	−4.34299	−	1.50809i	−0.399805	−	0.138831i
$119$	−5.76907	+	2.09977i	−0.528850	+	0.192486i
$120$	−10.6032	−	1.49720i	−0.967938	−	0.136675i
$121$	2.68559	−	2.25347i	0.244144	−	0.204861i
$122$	−2.76756	+	17.1836i	−0.250563	+	1.55573i
$123$	−12.6987	+	14.8216i	−1.14500	+	1.33642i
$124$	8.77223	−	1.81683i	0.787770	−	0.163156i
$125$	9.88539	−	5.70733i	0.884176	−	0.510479i
$126$	−4.18232	+	0.712853i	−0.372591	+	0.0635060i
$127$	−9.51426	−	5.49306i	−0.844254	−	0.487430i	0.0144542	−	0.999896i	$-0.495399\pi$
$127$	−9.51426	−	5.49306i	−0.844254	−	0.487430i	−0.858708	+	0.512465i	$0.828732\pi$
$128$	11.2527	−	1.17359i	0.994605	−	0.103731i
$129$	0.449429	−	0.253355i	0.0395700	−	0.0223067i
$130$	−0.194306	−	0.510156i	−0.0170417	−	0.0447436i
$131$	1.05923	+	6.00720i	0.0925455	+	0.524852i	0.995472	+	0.0950565i	$0.0303032\pi$
$131$	1.05923	+	6.00720i	0.0925455	+	0.524852i	−0.902926	+	0.429795i	$0.858586\pi$
$132$	−6.81732	−	11.2957i	−0.593371	−	0.983167i
$133$	−1.76632	−	1.48212i	−0.153160	−	0.128516i
$134$	6.06069	+	7.00886i	0.523564	+	0.605473i
$135$	11.2409	−	1.62651i	0.967464	−	0.139988i
$136$	−14.6367	+	9.34322i	−1.25509	+	0.801175i
$137$	−12.8919	+	15.3640i	−1.10143	+	1.31264i	−0.155660	+	0.987811i	$0.549750\pi$
$137$	−12.8919	+	15.3640i	−1.10143	+	1.31264i	−0.945774	+	0.324826i	$0.894694\pi$
$138$	0.651402	−	0.240466i	0.0554511	−	0.0204698i
$139$	−16.6832	+	2.94169i	−1.41505	+	0.249511i	−0.828312	−	0.560268i	$-0.810698\pi$
$139$	−16.6832	+	2.94169i	−1.41505	+	0.249511i	−0.586735	+	0.809779i	$0.699587\pi$
$140$	2.07249	−	3.84922i	0.175157	−	0.325318i
$141$	−14.7253	−	0.151356i	−1.24009	−	0.0127465i
$142$	0.115557	+	0.193460i	0.00969730	+	0.0162348i
$143$	0.336298	−	0.582485i	0.0281226	−	0.0487098i
$144$	−11.1085	+	4.53885i	−0.925709	+	0.378237i
$145$	8.30003	+	14.3761i	0.689280	+	1.19387i
$146$	−5.73909	+	10.2902i	−0.474971	+	0.851624i
$147$	0.318283	−	1.70256i	0.0262516	−	0.140424i
$148$	1.18644	+	1.92092i	0.0975248	+	0.157899i
$149$	−6.24398	−	7.44128i	−0.511527	−	0.609614i	0.447029	−	0.894520i	$-0.352482\pi$
$149$	−6.24398	−	7.44128i	−0.511527	−	0.609614i	−0.958556	+	0.284906i	$0.908038\pi$
$150$	0.269838	−	0.472341i	0.0220321	−	0.0385665i
$151$	7.50767	+	20.6272i	0.610966	+	1.67861i	0.728077	+	0.685496i	$0.240415\pi$
$151$	7.50767	+	20.6272i	0.610966	+	1.67861i	−0.117111	+	0.993119i	$0.537363\pi$
$152$	−5.78754	−	3.00616i	−0.469431	−	0.243832i
$153$	12.1263	−	13.8626i	0.980356	−	1.12073i
$154$	5.28994	−	1.01395i	0.426276	−	0.0817065i
$155$	1.70016	−	9.64209i	0.136560	−	0.774471i
$156$	−0.476173	−	0.384055i	−0.0381243	−	0.0307490i
$157$	8.95421	+	3.25907i	0.714624	+	0.260102i	0.673642	−	0.739058i	$-0.264729\pi$
$157$	8.95421	+	3.25907i	0.714624	+	0.260102i	0.0409823	+	0.999160i	$0.486951\pi$
$158$	−1.48477	+	1.82379i	−0.118122	+	0.145093i
$159$	2.00523	−	0.332363i	0.159025	−	0.0263581i
$160$	3.35576	−	11.9009i	0.265296	−	0.940852i
$161$			0.283475i			0.0223410i
$162$	9.96167	−	7.92244i	0.782663	−	0.622446i
$163$		−	12.7508i		−	0.998718i	−0.866395	−	0.499359i	$-0.833569\pi$
$163$		−	12.7508i		−	0.998718i	0.866395	−	0.499359i	$-0.166431\pi$
$164$	−14.9926	−	16.8267i	−1.17073	−	1.31394i
$165$	−14.2254	+	2.35784i	−1.10745	+	0.183557i
$166$	9.81602	+	7.99133i	0.761871	+	0.620247i
$167$	−0.976334	−	0.355357i	−0.0755510	−	0.0274983i	0.303968	−	0.952682i	$-0.401688\pi$
$167$	−0.976334	−	0.355357i	−0.0755510	−	0.0274983i	−0.379519	+	0.925184i	$0.623911\pi$
$168$	−0.167797	−	4.89610i	−0.0129458	−	0.377743i
$169$	−2.25201	+	12.7718i	−0.173232	+	0.982445i
$170$	3.57261	+	18.6389i	0.274007	+	1.42954i
$171$	6.78609	+	1.34095i	0.518945	+	0.102545i
$172$	0.220283	+	0.553513i	0.0167964	+	0.0422049i
$173$	−4.99923	−	13.7353i	−0.380084	−	1.04427i	−0.971320	−	0.237774i	$-0.923582\pi$
$173$	−4.99923	−	13.7353i	−0.380084	−	1.04427i	0.591236	−	0.806498i	$-0.298640\pi$
$174$	16.1524	+	9.22746i	1.22451	+	0.699532i
$175$	0.142751	+	0.170124i	0.0107909	+	0.0128601i
$176$	13.9814	−	6.05095i	1.05388	−	0.456108i
$177$	−1.03469	+	5.53473i	−0.0777719	+	0.416016i
$178$	1.79838	+	1.00300i	0.134794	+	0.0751779i
$179$	10.7107	+	18.5515i	0.800555	+	1.38660i	0.919251	+	0.393672i	$0.128795\pi$
$179$	10.7107	+	18.5515i	0.800555	+	1.38660i	−0.118696	+	0.992931i	$0.537871\pi$
$180$	0.119797	+	13.1145i	0.00892911	+	0.977499i
$181$	5.65404	−	9.79309i	0.420262	−	0.727914i	−0.575703	−	0.817659i	$-0.695272\pi$
$181$	5.65404	−	9.79309i	0.420262	−	0.727914i	0.995965	+	0.0897443i	$0.0286050\pi$
$182$	0.214409	−	0.128070i	0.0158930	−	0.00949318i
$183$	21.3156	+	0.219095i	1.57569	+	0.0161960i
$184$	0.174246	+	0.782626i	0.0128456	+	0.0576960i
$185$	2.43009	−	0.428491i	0.178664	−	0.0315033i
$186$	−3.79961	−	10.2928i	−0.278601	−	0.754707i
$187$	−15.0300	+	17.9120i	−1.09910	+	1.30986i
$188$	2.45432	−	16.8261i	0.179000	−	1.22717i
$189$	1.62581	+	4.93526i	0.118260	+	0.358987i
$190$	−5.39153	+	4.66216i	−0.391143	+	0.338228i
$191$	−13.0242	−	10.9286i	−0.942398	−	0.790765i	0.0356034	−	0.999366i	$-0.488665\pi$
$191$	−13.0242	−	10.9286i	−0.942398	−	0.790765i	−0.978001	+	0.208601i	$0.933109\pi$
$192$	−3.47279	−	13.4142i	−0.250627	−	0.968084i
$193$	0.219069	+	1.24240i	0.0157689	+	0.0894301i	0.991677	−	0.128754i	$-0.0410978\pi$
$193$	0.219069	+	1.24240i	0.0157689	+	0.0894301i	−0.975908	+	0.218184i	$0.929987\pi$
$194$	17.1129	−	6.51786i	1.22863	−	0.467955i
$195$	−0.582426	+	0.328329i	−0.0417084	+	0.0235121i
$196$	1.89886	+	0.627946i	0.135633	+	0.0448533i
$197$	−18.4993	−	10.6806i	−1.31802	−	0.760959i	−0.334609	−	0.942357i	$-0.608604\pi$
$197$	−18.4993	−	10.6806i	−1.31802	−	0.760959i	−0.983410	+	0.181398i	$0.941938\pi$
$198$	−12.4374	+	10.3158i	−0.883888	+	0.733109i
$199$	8.97138	−	5.17963i	0.635964	−	0.367174i	−0.147094	−	0.989122i	$-0.546992\pi$
$199$	8.97138	−	5.17963i	0.635964	−	0.367174i	0.783058	+	0.621948i	$0.213659\pi$
$200$	0.498681	+	0.381936i	0.0352621	+	0.0270070i
$201$	7.38352	−	8.61788i	0.520793	−	0.607858i
$202$	18.2114	+	2.93311i	1.28135	+	0.206373i
$203$	−5.81761	+	4.88155i	−0.408316	+	0.342618i
$204$	13.9840	+	16.0232i	0.979074	+	1.12185i
$205$	−23.1457	+	8.42436i	−1.61657	+	0.588383i
$206$	−4.19479	+	12.0801i	−0.292265	+	0.841662i
$207$	−0.409984	−	0.745075i	−0.0284959	−	0.0517863i
$208$	0.513224	−	0.485371i	0.0355857	−	0.0336545i
$209$	−8.64844	−	1.52495i	−0.598225	−	0.105483i
$210$	−5.03962	−	1.80825i	−0.347767	−	0.124781i
$211$	−2.82100	+	7.75062i	−0.194205	+	0.533575i	−0.998128	−	0.0611589i	$-0.980520\pi$
$211$	−2.82100	+	7.75062i	−0.194205	+	0.533575i	0.803923	+	0.594734i	$0.202743\pi$
$212$	0.0696754	+	2.34600i	0.00478532	+	0.161124i
$213$	0.213232	−	0.175220i	0.0146104	−	0.0120059i
$214$	13.1369	−	0.195038i	0.898018	−	0.0133325i
$215$	0.651093			0.0444042
$216$	7.52217	+	12.6260i	0.511819	+	0.859094i
$217$	4.47920			0.304068
$218$	−10.2195	+	0.151725i	−0.692155	+	0.0102761i
$219$	13.5088	+	5.07462i	0.912838	+	0.342911i
$220$	−0.494289	−	16.6429i	−0.0333249	−	1.12206i
$221$	−0.370813	+	1.01880i	−0.0249436	+	0.0685320i
$222$	2.11013	−	1.78710i	0.141623	−	0.119942i
$223$	−7.15724	−	1.26201i	−0.479284	−	0.0845107i	−0.0712135	−	0.997461i	$-0.522687\pi$
$223$	−7.15724	−	1.26201i	−0.479284	−	0.0845107i	−0.408071	+	0.912950i	$0.633798\pi$
$224$	5.62842	+	0.566463i	0.376065	+	0.0378484i
$225$	−0.621246	−	0.240689i	−0.0414164	−	0.0160459i
$226$	6.67422	−	19.2204i	0.443963	−	1.27852i
$227$	−14.2760	+	5.19605i	−0.947534	+	0.344874i	−0.769137	−	0.639085i	$-0.779313\pi$
$227$	−14.2760	+	5.19605i	−0.947534	+	0.344874i	−0.178397	+	0.983959i	$0.557091\pi$
$228$	−2.58565	+	7.55733i	−0.171239	+	0.500497i
$229$	−9.56396	+	8.02512i	−0.632004	+	0.530315i	−0.901551	−	0.432673i	$-0.857571\pi$
$229$	−9.56396	+	8.02512i	−0.632004	+	0.530315i	0.269547	+	0.962987i	$0.413126\pi$
$230$	0.865144	+	0.139339i	0.0570459	+	0.00918774i
$231$	−2.19240	−	6.22180i	−0.144249	−	0.409364i
$232$	−13.0608	+	17.0531i	−0.857486	+	1.11959i
$233$	17.8354	−	10.2973i	1.16844	−	0.674598i	0.215126	−	0.976586i	$-0.430984\pi$
$233$	17.8354	−	10.2973i	1.16844	−	0.674598i	0.953311	+	0.301989i	$0.0976505\pi$
$234$	−0.378319	+	0.646709i	−0.0247315	+	0.0422767i
$235$	−16.0945	−	9.29214i	−1.04989	−	0.606152i
$236$	−6.17290	−	2.04135i	−0.401821	−	0.132881i
$237$	2.47948	+	1.46571i	0.161060	+	0.0952083i
$238$	−8.11371	+	3.09031i	−0.525934	+	0.200315i
$239$	−3.86304	−	21.9084i	−0.249879	−	1.41713i	−0.808883	−	0.587970i	$-0.799927\pi$
$239$	−3.86304	−	21.9084i	−0.249879	−	1.41713i	0.559004	−	0.829165i	$-0.311184\pi$
$240$	−15.0250	−	1.89452i	−0.969860	−	0.122291i
$241$	12.3156	+	10.3340i	0.793317	+	0.665672i	0.946564	−	0.322516i	$-0.104529\pi$
$241$	12.3156	+	10.3340i	0.793317	+	0.665672i	−0.153247	+	0.988188i	$0.548973\pi$
$242$	3.75026	−	3.24292i	0.241076	−	0.208463i
$243$	−11.4110	−	10.6203i	−0.732014	−	0.681290i
$244$	−3.55274	+	24.3566i	−0.227441	+	1.55927i
$245$	1.40503	−	1.67445i	0.0897643	−	0.106977i
$246$	−17.6455	+	21.2252i	−1.12504	+	1.35327i
$247$	−0.401006	+	0.0707082i	−0.0255154	+	0.00449905i
$248$	12.3663	−	2.75326i	0.785261	−	0.174832i
$249$	7.88876	−	13.3451i	0.499930	−	0.845709i
$250$	13.8587	−	8.27803i	0.876500	−	0.523548i
$251$	11.4578	−	19.8455i	0.723210	−	1.25264i	−0.236496	−	0.971632i	$-0.575999\pi$
$251$	11.4578	−	19.8455i	0.723210	−	1.25264i	0.959706	−	0.281004i	$-0.0906675\pi$
$252$	−5.89908	+	1.09582i	−0.371607	+	0.0690301i
$253$	0.539828	+	0.935010i	0.0339387	+	0.0587836i
$254$	−13.5690	−	7.56776i	−0.851396	−	0.474843i
$255$	21.9222	−	7.72481i	1.37282	−	0.483746i
$256$	15.8873	−	1.89576i	0.992956	−	0.118485i
$257$	−4.21238	−	5.02012i	−0.262761	−	0.313147i	0.618492	−	0.785791i	$-0.287744\pi$
$257$	−4.21238	−	5.02012i	−0.262761	−	0.313147i	−0.881253	+	0.472645i	$0.843299\pi$
$258$	0.630200	−	0.367694i	0.0392345	−	0.0228916i
$259$	0.386104	+	1.06081i	0.0239913	+	0.0659156i
$260$	−0.285469	−	0.717310i	−0.0177041	−	0.0444857i
$261$	8.23068	−	21.2444i	0.509466	−	1.31499i
$262$	1.62393	+	8.47229i	0.100327	+	0.523420i
$263$	3.84540	−	21.8083i	0.237117	−	1.34476i	−0.600991	−	0.799256i	$-0.705227\pi$
$263$	3.84540	−	21.8083i	0.237117	−	1.34476i	0.838108	−	0.545504i	$-0.183662\pi$
$264$	−9.87722	−	15.8297i	−0.607901	−	0.974250i
$265$	2.41043	+	0.877323i	0.148071	+	0.0538935i
$266$	−2.52880	−	2.05872i	−0.155050	−	0.126228i
$267$	0.886872	−	2.36087i	0.0542757	−	0.144483i
$268$	8.71731	+	9.78369i	0.532495	+	0.597634i
$269$			17.6558i			1.07649i	0.842788	+	0.538246i	$0.180913\pi$
$269$			17.6558i			1.07649i	−0.842788	+	0.538246i	$0.819087\pi$
$270$	15.8612	−	2.53597i	0.965280	−	0.154334i
$271$		−	8.29896i		−	0.504126i	−0.967711	−	0.252063i	$-0.918891\pi$
$271$		−	8.29896i		−	0.504126i	0.967711	−	0.252063i	$-0.0811090\pi$
$272$	−20.5010	+	13.5191i	−1.24306	+	0.819718i
$273$	−0.194194	−	0.236322i	−0.0117532	−	0.0143029i
$274$	−17.9074	+	21.9963i	−1.08183	+	1.32884i
$275$	0.794817	+	0.289290i	0.0479292	+	0.0174448i
$276$	0.916072	−	0.353708i	0.0551411	−	0.0212907i
$277$	1.00431	−	5.69571i	0.0603429	−	0.342222i	−0.939657	−	0.342118i	$-0.888856\pi$
$277$	1.00431	−	5.69571i	0.0603429	−	0.342222i	1.00000		0.000103968i	$-3.30941e-5\pi$
$278$	−23.5292	+	4.50997i	−1.41119	+	0.270490i
$279$	−11.7729	+	6.47817i	−0.704828	+	0.387838i
$280$	2.84981	−	5.48652i	0.170309	−	0.327883i
$281$	−5.68165	−	15.6102i	−0.338939	−	0.931227i	−0.985696	−	0.168531i	$-0.946098\pi$
$281$	−5.68165	−	15.6102i	−0.338939	−	0.931227i	0.646757	−	0.762696i	$-0.276125\pi$
$282$	−20.8256	+	0.0951152i	−1.24015	+	0.00566403i
$283$	−17.3005	−	20.6180i	−1.02841	−	1.22561i	−0.973872	−	0.227099i	$-0.927076\pi$
$283$	−17.3005	−	20.6180i	−1.02841	−	1.22561i	−0.0545378	−	0.998512i	$-0.517369\pi$
$284$	0.167465	+	0.271137i	0.00993724	+	0.0160890i
$285$	6.62926	+	5.67974i	0.392683	+	0.336438i
$286$	0.463316	−	0.830728i	0.0273964	−	0.0491220i
$287$	−5.63424	−	9.75880i	−0.332579	−	0.576044i
$288$	−15.6128	+	6.65140i	−0.919992	+	0.391938i
$289$	10.3456	−	17.9191i	0.608565	−	1.05406i
$290$	12.0385	+	20.1544i	0.706927	+	1.18350i
$291$	−11.0136	−	19.5371i	−0.645629	−	1.14529i
$292$	−7.89937	+	14.6714i	−0.462276	+	0.858581i
$293$	−32.2588	+	5.68811i	−1.88458	+	0.332303i	−0.992763	−	0.120090i	$-0.961682\pi$
$293$	−32.2588	+	5.68811i	−1.88458	+	0.332303i	−0.891819	+	0.452392i	$0.850571\pi$
$294$	0.414328	−	2.41419i	0.0241641	−	0.140799i
$295$	−4.56754	+	5.44338i	−0.265932	+	0.316926i
$296$	1.71802	+	2.69139i	0.0998580	+	0.156434i
$297$	14.7609	+	13.1823i	0.856512	+	0.764915i
$298$	−8.98557	−	10.3913i	−0.520520	−	0.601953i
$299$	0.0383489	+	0.0321785i	0.00221777	+	0.00186093i
$300$	0.371650	−	0.673583i	0.0214572	−	0.0388893i
$301$	0.0517242	+	0.293342i	0.00298133	+	0.0169080i
$302$	11.0493	+	29.0104i	0.635817	+	1.66936i
$303$	0.232200	−	22.5906i	0.0133396	−	1.29779i
$304$	−8.24702	−	4.12938i	−0.472999	−	0.236836i
$305$	23.2975	+	13.4508i	1.33401	+	0.770191i
$306$	16.8563	−	19.8571i	0.963611	−	1.13516i
$307$	22.8520	−	13.1936i	1.30423	−	0.752999i	0.323105	−	0.946363i	$-0.395273\pi$
$307$	22.8520	−	13.1936i	1.30423	−	0.752999i	0.981127	+	0.193364i	$0.0619399\pi$
$308$	7.45899	−	1.54484i	0.425016	−	0.0880255i
$309$	15.3950	+	2.87801i	0.875790	+	0.163724i
$310$	2.20170	−	13.6702i	0.125048	−	0.776413i
$311$	−24.3635	+	20.4434i	−1.38153	+	1.15924i	−0.412883	+	0.910784i	$0.635478\pi$
$311$	−24.3635	+	20.4434i	−1.38153	+	1.15924i	−0.968644	+	0.248454i	$0.920077\pi$
$312$	−0.681398	−	0.533079i	−0.0385766	−	0.0301796i
$313$	10.2095	−	3.71596i	0.577076	−	0.210039i	−0.0369595	−	0.999317i	$-0.511767\pi$
$313$	10.2095	−	3.71596i	0.577076	−	0.210039i	0.614036	+	0.789278i	$0.289545\pi$
$314$	12.7302	+	4.42053i	0.718407	+	0.249465i
$315$	−1.27121	+	6.43314i	−0.0716244	+	0.362466i
$316$	−2.06126	+	2.61012i	−0.115955	+	0.146831i
$317$	−20.1104	−	3.54601i	−1.12951	−	0.199164i	−0.422500	−	0.906363i	$-0.638847\pi$
$317$	−20.1104	−	3.54601i	−1.12951	−	0.199164i	−0.707014	+	0.707199i	$0.749958\pi$
$318$	2.82853	−	0.512078i	0.158616	−	0.0287159i
$319$	−9.89265	+	27.1798i	−0.553882	+	1.52178i
$320$	4.49539	−	16.8991i	0.251300	−	0.944686i
$321$	−2.63117	−	15.8745i	−0.146857	−	0.886029i
$322$	0.00595125	+	0.400850i	0.000331650	+	0.0223385i
$323$	14.1558			0.787652
$324$	13.9201	−	11.4119i	0.773336	−	0.633996i
$325$	0.0392188			0.00217547
$326$	−0.267689	−	18.0303i	−0.0148259	−	0.998608i
$327$	2.04686	+	12.3492i	0.113192	+	0.682914i
$328$	−21.5537	−	23.4791i	−1.19010	−	1.29642i
$329$	2.90789	−	7.98936i	0.160317	−	0.440468i
$330$	−20.0661	+	3.63276i	−1.10460	+	0.199977i
$331$	11.3917	+	2.00866i	0.626144	+	0.110406i	0.477712	−	0.878516i	$-0.341466\pi$
$331$	11.3917	+	2.00866i	0.626144	+	0.110406i	0.148432	+	0.988923i	$0.452577\pi$
$332$	14.0482	+	11.0941i	0.770994	+	0.608869i
$333$	−2.54905	−	2.22978i	−0.139687	−	0.122191i
$334$	−1.38805	−	0.481998i	−0.0759509	−	0.0263737i
$335$	13.4579	−	4.89826i	0.735281	−	0.267620i
$336$	−0.340063	−	6.91985i	−0.0185520	−	0.377509i
$337$	−13.5389	+	11.3605i	−0.737510	+	0.618845i	−0.932168	−	0.362027i	$-0.882085\pi$
$337$	−13.5389	+	11.3605i	−0.737510	+	0.618845i	0.194657	+	0.980871i	$0.437641\pi$
$338$	−2.91634	+	18.1073i	−0.158628	+	0.984909i
$339$	−24.4946	−	4.57912i	−1.33036	−	0.248704i
$340$	5.44318	+	26.2814i	0.295198	+	1.42531i
$341$	14.7741	−	8.52984i	0.800063	−	0.461917i
$342$	9.62407	+	1.75371i	0.520410	+	0.0948300i
$343$	0.866025	+	0.500000i	0.0467610	+	0.0269975i
$344$	0.323113	+	0.778074i	0.0174211	+	0.0419510i
$345$	0.0110308	−	1.07318i	0.000593880	−	0.0577780i
$346$	−7.35755	−	19.3175i	−0.395545	−	1.03852i
$347$	−3.57866	−	20.2956i	−0.192112	−	1.08952i	−0.916471	−	0.400100i	$-0.868975\pi$
$347$	−3.57866	−	20.2956i	−0.192112	−	1.08952i	0.724359	−	0.689423i	$-0.242136\pi$
$348$	23.0341	+	12.7091i	1.23476	+	0.681277i
$349$	1.31685	+	1.10497i	0.0704894	+	0.0591476i	0.677352	−	0.735659i	$-0.263128\pi$
$349$	1.31685	+	1.10497i	0.0704894	+	0.0591476i	−0.606862	+	0.794807i	$0.707572\pi$
$350$	0.205429	+	0.237568i	0.0109807	+	0.0126985i
$351$	0.852200	+	0.340281i	0.0454871	+	0.0181629i
$352$	19.6434	−	8.84992i	1.04700	−	0.471702i
$353$	−18.0497	+	21.5107i	−0.960686	+	1.14490i	0.0286993	+	0.999588i	$0.490863\pi$
$353$	−18.0497	+	21.5107i	−0.960686	+	1.14490i	−0.989386	+	0.145313i	$0.953581\pi$
$354$	−1.34691	+	7.84815i	−0.0715876	+	0.417125i
$355$	0.343006	−	0.0604813i	0.0182049	−	0.00321001i
$356$	2.56407	+	1.38054i	0.135895	+	0.0731686i
$357$	5.22187	+	9.26313i	0.276371	+	0.490257i
$358$	15.5350	+	26.0080i	0.821051	+	1.37457i
$359$	12.4623	−	21.5853i	0.657734	−	1.13923i	−0.323467	−	0.946239i	$-0.604848\pi$
$359$	12.4623	−	21.5853i	0.657734	−	1.13923i	0.981201	−	0.192989i	$-0.0618182\pi$
$360$	0.444725	+	18.5422i	0.0234390	+	0.977259i
$361$	−6.84171	−	11.8502i	−0.360090	−	0.623695i
$362$	7.78955	−	13.9667i	0.409409	−	0.734073i
$363$	−4.61121	−	3.95073i	−0.242026	−	0.207360i
$364$	0.300498	−	0.185600i	0.0157504	−	0.00972806i
$365$	11.7060	+	13.9506i	0.612718	+	0.730208i
$366$	30.1460	−	0.137684i	1.57576	−	0.00719685i
$367$	−5.00710	−	13.7569i	−0.261368	−	0.718104i	−0.999076	−	0.0429832i	$-0.986314\pi$
$367$	−5.00710	−	13.7569i	−0.261368	−	0.718104i	0.737707	−	0.675121i	$-0.235908\pi$
$368$	0.262824	+	1.10302i	0.0137007	+	0.0574989i
$369$	28.9228	+	17.5009i	1.50566	+	0.911063i
$370$	3.42730	−	0.656928i	0.178177	−	0.0341521i
$371$	−0.203779	+	1.15569i	−0.0105797	+	0.0600003i
$372$	−5.58895	−	14.4749i	−0.289774	−	0.750488i
$373$	−4.89188	−	1.78050i	−0.253292	−	0.0921908i	0.212254	−	0.977215i	$-0.431920\pi$
$373$	−4.89188	−	1.78050i	−0.253292	−	0.0921908i	−0.465546	+	0.885024i	$0.654142\pi$
$374$	−20.8772	+	25.6442i	−1.07953	+	1.32603i
$375$	−12.5521	−	15.2751i	−0.648186	−	0.788803i
$376$	3.11730	−	23.8447i	0.160763	−	1.22969i
$377$			1.34114i			0.0690722i
$378$	2.40260	+	6.94460i	0.123576	+	0.357192i
$379$			37.0304i			1.90213i	0.308997	+	0.951063i	$0.400007\pi$
$379$			37.0304i			1.90213i	−0.308997	+	0.951063i	$0.599993\pi$
$380$	−7.52606	+	6.70575i	−0.386079	+	0.343998i
$381$	−6.69157	+	17.8131i	−0.342820	+	0.912594i
$382$	−18.6464	−	15.1802i	−0.954033	−	0.776688i
$383$	−23.5859	−	8.58457i	−1.20518	−	0.438651i	−0.340154	−	0.940370i	$-0.610479\pi$
$383$	−23.5859	−	8.58457i	−1.20518	−	0.438651i	−0.865031	+	0.501719i	$0.832701\pi$
$384$	−5.19233	−	18.8955i	−0.264970	−	0.964257i
$385$	1.44564	−	8.19863i	0.0736766	−	0.417841i
$386$	0.335859	+	1.75223i	0.0170948	+	0.0891862i
$387$	−0.560205	−	0.696202i	−0.0284768	−	0.0353899i
$388$	24.0617	−	9.57590i	1.22155	−	0.486143i
$389$	3.70320	+	10.1745i	0.187760	+	0.515866i	0.997480	−	0.0709505i	$-0.0226032\pi$
$389$	3.70320	+	10.1745i	0.187760	+	0.515866i	−0.809720	+	0.586816i	$0.800381\pi$
$390$	−0.816691	+	0.476503i	−0.0413548	+	0.0241287i
$391$	−1.11867	−	1.33318i	−0.0565736	−	0.0674218i
$392$	2.69829	+	0.848088i	0.136284	+	0.0428349i
$393$	9.96474	−	3.51131i	0.502655	−	0.177122i
$394$	−26.3833	−	14.7146i	−1.32917	−	0.741309i
$395$	1.81747	+	3.14795i	0.0914468	+	0.158390i
$396$	−17.3706	+	14.8482i	−0.872908	+	0.746150i
$397$	0.983315	−	1.70315i	0.0493512	−	0.0854788i	−0.840295	−	0.542130i	$-0.817618\pi$
$397$	0.983315	−	1.70315i	0.0493512	−	0.0854788i	0.889646	+	0.456651i	$0.150951\pi$
$398$	12.5773	−	7.51264i	0.630443	−	0.376574i
$399$	−2.03230	+	3.43795i	−0.101742	+	0.172113i
$400$	0.713182	+	0.529611i	0.0356591	+	0.0264805i
$401$	36.8083	−	6.49030i	1.83812	−	0.324110i	0.856676	−	0.515854i	$-0.172525\pi$
$401$	36.8083	−	6.49030i	1.83812	−	0.324110i	0.981445	+	0.191744i	$0.0614144\pi$
$402$	10.2598	−	12.3412i	0.511712	−	0.615522i
$403$	0.508454	−	0.605952i	0.0253279	−	0.0301846i
$404$	25.8135	+	3.76525i	1.28427	+	0.187328i
$405$	−5.96293	−	18.7471i	−0.296300	−	0.931552i
$406$	−8.12395	+	7.02493i	−0.403185	+	0.348642i
$407$	3.29365	+	2.76370i	0.163260	+	0.136991i
$408$	20.1105	+	22.3642i	0.995620	+	1.10719i
$409$	3.93598	+	22.3220i	0.194622	+	1.10375i	0.912957	+	0.408057i	$0.133793\pi$
$409$	3.93598	+	22.3220i	0.194622	+	1.10375i	−0.718335	+	0.695697i	$0.755095\pi$
$410$	−32.5525	+	12.3984i	−1.60766	+	0.612316i
$411$	29.9043	+	17.6776i	1.47507	+	0.871970i
$412$	−5.67806	+	17.1701i	−0.279738	+	0.845908i
$413$	−2.81531	−	1.62542i	−0.138532	−	0.0799816i
$414$	−0.595383	−	1.04497i	−0.0292615	−	0.0513575i
$415$	16.9429	−	9.78198i	0.831693	−	0.480178i
$416$	0.715539	−	0.697118i	0.0350822	−	0.0341790i
$417$	9.75158	+	27.6740i	0.477537	+	1.35520i
$418$	−12.2614	−	1.97481i	−0.599725	−	0.0965910i
$419$	8.17538	−	6.85996i	0.399393	−	0.335131i	−0.420866	−	0.907123i	$-0.638274\pi$
$419$	8.17538	−	6.85996i	0.399393	−	0.335131i	0.820259	+	0.571992i	$0.193829\pi$
$420$	−7.16427	−	2.45117i	−0.349581	−	0.119605i
$421$	−18.5983	+	6.76921i	−0.906424	+	0.329911i	−0.752824	−	0.658222i	$-0.771309\pi$
$421$	−18.5983	+	6.76921i	−0.906424	+	0.329911i	−0.153600	+	0.988133i	$0.549087\pi$
$422$	−3.82634	+	11.0191i	−0.186263	+	0.536399i
$423$	3.91187	+	25.2045i	0.190201	+	1.22549i
$424$	0.147777	+	3.31591i	0.00717667	+	0.161035i
$425$	−1.34271	−	0.236756i	−0.0651310	−	0.0114843i
$426$	0.297844	−	0.252248i	0.0144306	−	0.0122214i
$427$	−4.20931	+	11.5650i	−0.203703	+	0.559669i
$428$	18.5722	−	0.551589i	0.897721	−	0.0266621i
$429$	−1.09056	−	0.409674i	−0.0526528	−	0.0197792i
$430$	0.920683	−	0.0136690i	0.0443993	−	0.000659177i
$431$	−8.83068			−0.425359			−0.212680	−	0.977122i	$-0.568219\pi$
$431$	−8.83068			−0.425359			−0.212680	+	0.977122i	$0.568219\pi$
$432$	10.9018	+	17.6960i	0.524515	+	0.851401i
$433$	12.8952			0.619706			0.309853	−	0.950785i	$-0.399720\pi$
$433$	12.8952			0.619706			0.309853	+	0.950785i	$0.399720\pi$
$434$	6.33385	−	0.0940360i	0.304034	−	0.00451387i
$435$	22.2142	−	18.2542i	1.06509	−	0.875221i
$436$	−14.4478	+	0.429097i	−0.691926	+	0.0205500i
$437$	0.223554	−	0.614210i	0.0106940	−	0.0293816i
$438$	19.2087	+	6.89221i	0.917828	+	0.329323i
$439$	−19.6785	−	3.46985i	−0.939204	−	0.165607i	−0.316968	−	0.948436i	$-0.602665\pi$
$439$	−19.6785	−	3.46985i	−0.939204	−	0.165607i	−0.622237	+	0.782829i	$0.713776\pi$
$440$	−1.04835	−	23.5236i	−0.0499782	−	1.12144i
$441$	−2.99937	−	0.0616654i	−0.142827	−	0.00293645i
$442$	−0.502963	+	1.44843i	−0.0239235	+	0.0688947i
$443$	4.66514	−	1.69797i	0.221648	−	0.0806731i	−0.228809	−	0.973471i	$-0.573483\pi$
$443$	4.66514	−	1.69797i	0.221648	−	0.0806731i	0.450457	+	0.892798i	$0.351261\pi$
$444$	2.94633	−	2.57136i	0.139827	−	0.122031i
$445$	2.43809	−	2.04580i	0.115577	−	0.0969804i
$446$	−10.1472	−	1.63430i	−0.480486	−	0.0773864i
$447$	−10.9468	+	12.7768i	−0.517765	+	0.604324i
$448$	7.97080	+	0.682848i	0.376585	+	0.0322615i
$449$	1.65970	−	0.958226i	0.0783259	−	0.0452215i	−0.460326	−	0.887750i	$-0.652267\pi$
$449$	1.65970	−	0.958226i	0.0783259	−	0.0452215i	0.538651	+	0.842529i	$0.318934\pi$
$450$	−0.883531	−	0.327305i	−0.0416501	−	0.0154293i
$451$	−37.1678	−	21.4588i	−1.75016	−	1.01046i
$452$	9.03423	−	27.3188i	0.424934	−	1.28497i
$453$	33.1201	−	18.6707i	1.55612	−	0.877225i
$454$	−20.0781	+	7.64723i	−0.942310	+	0.358902i
$455$	−0.0670306	−	0.380149i	−0.00314244	−	0.0178217i
$456$	−3.49760	+	10.7408i	−0.163790	+	0.502984i
$457$	−29.7730	−	24.9826i	−1.39272	−	1.16863i	−0.964223	−	0.265094i	$-0.914597\pi$
$457$	−29.7730	−	24.9826i	−1.39272	−	1.16863i	−0.428502	−	0.903541i	$-0.640958\pi$
$458$	−13.3555	+	11.5488i	−0.624062	+	0.539638i
$459$	−27.1220	−	16.7946i	−1.26595	−	0.783903i
$460$	1.22629	+	0.178871i	0.0571760	+	0.00833989i
$461$	−7.39837	+	8.81703i	−0.344576	+	0.410650i	−0.910303	−	0.413943i	$-0.864151\pi$
$461$	−7.39837	+	8.81703i	−0.344576	+	0.410650i	0.565727	+	0.824593i	$0.308596\pi$
$462$	−3.23079	−	8.75195i	−0.150310	−	0.407178i
$463$	37.1225	−	6.54569i	1.72523	−	0.304204i	0.778837	−	0.627227i	$-0.215810\pi$
$463$	37.1225	−	6.54569i	1.72523	−	0.304204i	0.946391	+	0.323023i	$0.104699\pi$
$464$	−18.1108	+	24.3882i	−0.840771	+	1.13220i
$465$	−16.9573	−	0.174299i	−0.786377	−	0.00808290i
$466$	25.0041	−	14.9354i	1.15829	−	0.691869i
$467$	6.44932	−	11.1706i	0.298439	−	0.516911i	−0.677340	−	0.735670i	$-0.736867\pi$
$467$	6.44932	−	11.1706i	0.298439	−	0.516911i	0.975779	+	0.218759i	$0.0702007\pi$
$468$	−0.521387	+	0.922426i	−0.0241011	+	0.0426392i
$469$	3.27597	+	5.67415i	0.151270	+	0.262008i
$470$	−22.9536	−	12.8017i	−1.05877	−	0.590500i
$471$	3.03288	−	16.2234i	0.139748	−	0.747537i
$472$	−8.77169	−	2.75700i	−0.403750	−	0.126901i
$473$	0.729225	+	0.869056i	0.0335298	+	0.0399593i
$474$	3.53690	+	2.02055i	0.162455	+	0.0928069i
$475$	−0.175137	−	0.481185i	−0.00803584	−	0.0220783i
$476$	−11.4084	+	4.54022i	−0.522902	+	0.208100i
$477$	−1.13584	−	3.33228i	−0.0520066	−	0.152575i
$478$	−5.92250	−	30.8986i	−0.270889	−	1.41327i
$479$	−4.47199	+	25.3619i	−0.204330	+	1.15882i	0.694160	+	0.719821i	$0.255776\pi$
$479$	−4.47199	+	25.3619i	−0.204330	+	1.15882i	−0.898490	+	0.438994i	$0.855335\pi$
$480$	−21.2860	−	2.36353i	−0.971569	−	0.107880i
$481$	0.187336	+	0.0681848i	0.00854179	+	0.00310896i
$482$	17.6319	+	14.3543i	0.803111	+	0.653822i
$483$	0.484385	−	0.0802858i	0.0220403	−	0.00365313i
$484$	5.23501	−	4.66441i	0.237955	−	0.212019i
$485$		−	28.3036i		−	1.28520i
$486$	−16.3587	−	14.7781i	−0.742047	−	0.670348i
$487$		−	40.0991i		−	1.81706i	−0.417817	−	0.908531i	$-0.637205\pi$
$487$		−	40.0991i		−	1.81706i	0.417817	−	0.908531i	$-0.362795\pi$
$488$	−4.51244	+	34.5163i	−0.204269	+	1.56248i
$489$	−21.7877	+	3.61127i	−0.985276	+	0.163307i
$490$	1.95165	−	2.39727i	0.0881664	−	0.108298i
$491$	−0.150560	−	0.0547994i	−0.00679468	−	0.00247306i	0.338621	−	0.940923i	$-0.390040\pi$
$491$	−0.150560	−	0.0547994i	−0.00679468	−	0.00247306i	−0.345415	+	0.938450i	$0.612262\pi$
$492$	−24.5062	+	30.3841i	−1.10482	+	1.36982i
$493$	8.09619	−	45.9158i	0.364634	−	2.06794i
$494$	−0.565561	+	0.108404i	−0.0254458	+	0.00487733i
$495$	8.05785	+	23.6398i	0.362173	+	1.06253i
$496$	17.4289	−	4.15289i	0.782579	−	0.186470i
$497$	0.0544983	+	0.149733i	0.00244458	+	0.00671644i
$498$	10.8750	−	19.0363i	0.487320	−	0.853037i
$499$	16.6077	+	19.7923i	0.743463	+	0.886025i	0.996683	−	0.0813840i	$-0.0259340\pi$
$499$	16.6077	+	19.7923i	0.743463	+	0.886025i	−0.253220	+	0.967409i	$0.581490\pi$
$500$	19.4232	−	11.9966i	0.868632	−	0.536502i
$501$	−0.330694	+	1.76894i	−0.0147743	+	0.0790306i
$502$	15.7854	−	28.3032i	0.704535	−	1.26323i
$503$	−9.95792	−	17.2476i	−0.444002	−	0.769034i	0.553980	−	0.832530i	$-0.313108\pi$
$503$	−9.95792	−	17.2476i	−0.444002	−	0.769034i	−0.997982	+	0.0634960i	$0.979775\pi$
$504$	−8.31864	+	1.67340i	−0.370542	+	0.0745390i
$505$	14.2554	−	24.6910i	0.634356	−	1.09874i
$506$	0.782978	+	1.31082i	0.0348076	+	0.0582733i
$507$	22.4615	+	0.230874i	0.997548	+	0.0102535i
$508$	−19.3463	−	10.4164i	−0.858352	−	0.462152i
$509$	−30.5016	+	5.37826i	−1.35196	+	0.238387i	−0.802260	−	0.596975i	$-0.796369\pi$
$509$	−30.5016	+	5.37826i	−1.35196	+	0.238387i	−0.549700	+	0.835362i	$0.685258\pi$
$510$	30.8371	−	11.3836i	1.36549	−	0.504072i
$511$	−5.35534	+	6.38225i	−0.236906	+	0.282334i
$512$	22.4258	−	3.01425i	0.991088	−	0.133212i
$513$	0.369378	−	11.9754i	0.0163084	−	0.528728i
$514$	−6.06194	−	7.01031i	−0.267381	−	0.309211i
$515$	15.1409	+	12.7047i	0.667187	+	0.559836i
$516$	0.883420	−	0.533171i	0.0388904	−	0.0234715i
$517$	−5.62299	−	31.8895i	−0.247299	−	1.40250i
$518$	0.568243	+	1.49194i	0.0249672	+	0.0655522i
$519$	−22.0541	+	12.4325i	−0.968067	+	0.545725i
$520$	−0.418729	−	1.00833i	−0.0183625	−	0.0442180i
$521$	−10.5056	−	6.06544i	−0.460261	−	0.265732i	0.251893	−	0.967755i	$-0.418947\pi$
$521$	−10.5056	−	6.06544i	−0.460261	−	0.265732i	−0.712154	+	0.702023i	$0.752280\pi$
$522$	11.1927	−	30.2136i	0.489889	−	1.32241i
$523$	18.0467	−	10.4193i	0.789128	−	0.455604i	−0.0505272	−	0.998723i	$-0.516090\pi$
$523$	18.0467	−	10.4193i	0.789128	−	0.455604i	0.839656	+	0.543119i	$0.182757\pi$
$524$	2.47420	+	11.9462i	0.108086	+	0.521873i
$525$	0.250267	−	0.292106i	0.0109225	−	0.0127485i
$526$	4.97977	−	30.9190i	0.217128	−	1.34813i
$527$	−21.0656	+	17.6762i	−0.917633	+	0.769986i
$528$	−14.2993	−	22.1767i	−0.622297	−	0.965119i
$529$	21.5374	−	7.83898i	0.936409	−	0.340825i
$530$	3.42690	+	1.18998i	0.148855	+	0.0516895i
$531$	9.75045	+	0.200464i	0.423134	+	0.00869941i
$532$	−3.61908	−	2.85806i	−0.156907	−	0.123913i
$533$	−1.95975	−	0.345557i	−0.0848862	−	0.0149677i
$534$	1.20452	−	3.35703i	0.0521249	−	0.145273i
$535$	6.94538	−	19.0823i	0.300275	−	0.824998i
$536$	12.5322	+	13.6517i	0.541308	+	0.589664i
$537$	28.6661	−	23.5559i	1.23704	−	1.01651i
$538$	0.370664	+	24.9663i	0.0159805	+	1.07637i
$539$	3.80865			0.164050
$540$	22.3754	−	3.91899i	0.962882	−	0.168647i
$541$	11.3240			0.486856			0.243428	−	0.969919i	$-0.421728\pi$
$541$	11.3240			0.486856			0.243428	+	0.969919i	$0.421728\pi$
$542$	−0.174228	−	11.7352i	−0.00748372	−	0.504070i
$543$	−18.3352	−	6.88768i	−0.786837	−	0.295579i
$544$	−28.7058	+	19.5472i	−1.23075	+	0.838081i
$545$	−5.40301	+	14.8446i	−0.231439	+	0.635875i
$546$	−0.279563	−	0.330097i	−0.0119642	−	0.0141268i
$547$	9.15710	+	1.61464i	0.391529	+	0.0690372i	0.365947	−	0.930636i	$-0.380745\pi$
$547$	9.15710	+	1.61464i	0.391529	+	0.0690372i	0.0255819	+	0.999673i	$0.491856\pi$
$548$	−24.8603	+	31.4799i	−1.06198	+	1.34476i
$549$	−5.66261	−	36.4848i	−0.241674	−	1.55713i
$550$	1.12999	+	0.392386i	0.0481829	+	0.0167314i
$551$	16.4548	−	5.98905i	0.700997	−	0.255142i
$552$	1.28795	−	0.519396i	0.0548189	−	0.0221070i
$553$	−1.27389	+	1.06892i	−0.0541713	+	0.0454551i
$554$	1.30057	−	8.07514i	0.0552560	−	0.343080i
$555$	−1.42043	−	4.03104i	−0.0602939	−	0.171108i
$556$	−33.1770	+	6.87132i	−1.40702	+	0.291409i
$557$	−24.7086	+	14.2655i	−1.04694	+	0.604448i	−0.921790	−	0.387690i	$-0.873273\pi$
$557$	−24.7086	+	14.2655i	−1.04694	+	0.604448i	−0.125146	+	0.992138i	$0.539940\pi$
$558$	−16.5116	+	9.40767i	−0.698993	+	0.398259i
$559$	0.0455552	+	0.0263013i	0.00192678	+	0.00111243i
$560$	3.91461	−	7.81809i	0.165422	−	0.330375i
$561$	34.8637	+	20.6092i	1.47195	+	0.870123i
$562$	−8.36190	−	21.9545i	−0.352726	−	0.926093i
$563$	5.22300	+	29.6211i	0.220123	+	1.24838i	0.871792	+	0.489877i	$0.162958\pi$
$563$	5.22300	+	29.6211i	0.220123	+	1.24838i	−0.651668	+	0.758504i	$0.725931\pi$
$564$	−29.4466	+	0.571709i	−1.23993	+	0.0240733i
$565$	−24.0903	−	20.2142i	−1.01349	−	0.850416i
$566$	−24.8968	−	28.7918i	−1.04649	−	1.21021i
$567$	7.97260	−	4.17584i	0.334818	−	0.175369i
$568$	0.242498	+	0.379888i	0.0101750	+	0.0159397i
$569$	−15.2708	+	18.1990i	−0.640184	+	0.762942i	−0.984399	−	0.175949i	$-0.943701\pi$
$569$	−15.2708	+	18.1990i	−0.640184	+	0.762942i	0.344215	+	0.938891i	$0.388145\pi$
$570$	9.49339	+	7.89230i	0.397635	+	0.330572i
$571$	1.38001	−	0.243333i	0.0577515	−	0.0101831i	−0.144698	−	0.989476i	$-0.546221\pi$
$571$	1.38001	−	0.243333i	0.0577515	−	0.0101831i	0.202449	+	0.979293i	$0.435110\pi$
$572$	0.637715	−	1.18442i	0.0266642	−	0.0495232i
$573$	−14.9854	+	25.3501i	−0.626024	+	1.05902i
$574$	−8.17202	−	13.6812i	−0.341094	−	0.571043i
$575$	−0.0314772	+	0.0545200i	−0.00131269	+	0.00227364i
$576$	−21.9377	+	9.73324i	−0.914072	+	0.405552i
$577$	−0.778077	−	1.34767i	−0.0323918	−	0.0561042i	0.849375	−	0.527790i	$-0.176979\pi$
$577$	−0.778077	−	1.34767i	−0.0323918	−	0.0561042i	−0.881767	+	0.471686i	$0.843646\pi$
$578$	14.2531	−	25.5558i	0.592850	−	1.06298i
$579$	2.06090	−	0.726205i	0.0856479	−	0.0301800i
$580$	17.4463	+	28.2467i	0.724418	+	1.17288i
$581$	5.75314	+	6.85632i	0.238680	+	0.284448i
$582$	−15.9840	−	27.3954i	−0.662559	−	1.13558i
$583$	1.52866	+	4.19996i	0.0633106	+	0.173944i
$584$	−10.8622	+	20.9121i	−0.449479	+	0.865349i
$585$	0.725983	+	0.902225i	0.0300157	+	0.0373024i
$586$	−45.4965	+	8.72055i	−1.87944	+	0.360243i
$587$	−4.45061	+	25.2406i	−0.183696	+	1.04179i	0.743923	+	0.668265i	$0.232963\pi$
$587$	−4.45061	+	25.2406i	−0.183696	+	1.04179i	−0.927619	+	0.373527i	$0.878148\pi$
$588$	0.535200	−	3.42251i	0.0220713	−	0.141142i
$589$	−9.70515	−	3.53238i	−0.399894	−	0.145549i
$590$	−6.34449	+	7.79314i	−0.261198	+	0.320839i
$591$	−13.0109	+	34.6354i	−0.535198	+	1.42471i
$592$	2.48589	+	3.76971i	0.102169	+	0.154934i
$593$			44.3021i			1.81927i	0.415410	+	0.909634i	$0.363638\pi$
$593$			44.3021i			1.81927i	−0.415410	+	0.909634i	$0.636362\pi$
$594$	21.1495	+	18.3307i	0.867773	+	0.752116i
$595$			13.4196i			0.550150i
$596$	−12.9243	−	14.5053i	−0.529399	−	0.594160i
$597$	−11.3915	−	13.8628i	−0.466223	−	0.567365i
$598$	0.0549031	+	0.0446972i	0.00224515	+	0.00182780i
$599$	21.2864	+	7.74763i	0.869740	+	0.316559i	0.738062	−	0.674733i	$-0.235741\pi$
$599$	21.2864	+	7.74763i	0.869740	+	0.316559i	0.131678	+	0.991293i	$0.457963\pi$
$600$	0.511393	−	0.960287i	0.0208775	−	0.0392036i
$601$	−0.527176	+	2.98977i	−0.0215040	+	0.121955i	−0.993670	−	0.112337i	$-0.964166\pi$
$601$	−0.527176	+	2.98977i	−0.0215040	+	0.121955i	0.972166	+	0.234293i	$0.0752774\pi$
$602$	0.0792994	+	0.413717i	0.00323200	+	0.0168619i
$603$	−16.8169	−	10.1757i	−0.684835	−	0.414388i
$604$	16.2334	+	40.7904i	0.660529	+	1.65974i
$605$	−2.62093	−	7.20096i	−0.106556	−	0.292761i
$606$	−0.145919	−	31.9492i	−0.00592757	−	1.29785i
$607$	−18.2084	−	21.7000i	−0.739058	−	0.880775i	0.257275	−	0.966338i	$-0.417175\pi$
$607$	−18.2084	−	21.7000i	−0.739058	−	0.880775i	−0.996333	+	0.0855633i	$0.972731\pi$
$608$	−11.7485	−	5.66605i	−0.476463	−	0.229788i
$609$	9.98896	+	8.55822i	0.404773	+	0.346796i
$610$	33.2264	+	18.5311i	1.34530	+	0.750303i
$611$	−0.750723	−	1.30029i	−0.0303710	−	0.0526041i
$612$	23.4189	−	28.4330i	0.946654	−	1.14934i
$613$	−9.79418	+	16.9640i	−0.395583	+	0.685170i	−0.993175	−	0.116630i	$-0.962791\pi$
$613$	−9.79418	+	16.9640i	−0.395583	+	0.685170i	0.597592	+	0.801800i	$0.296124\pi$
$614$	32.0371	−	19.1363i	1.29291	−	0.772277i
$615$	20.9504	+	37.1641i	0.844800	+	1.49860i
$616$	10.5150	−	2.34109i	0.423662	−	0.0943252i
$617$	−10.1893	+	1.79665i	−0.410207	+	0.0723305i	−0.374944	−	0.927048i	$-0.622338\pi$
$617$	−10.1893	+	1.79665i	−0.410207	+	0.0723305i	−0.0352630	+	0.999378i	$0.511227\pi$
$618$	21.8298	+	3.74647i	0.878124	+	0.150705i
$619$	−6.67445	+	7.95429i	−0.268269	+	0.319710i	−0.883314	−	0.468781i	$-0.844693\pi$
$619$	−6.67445	+	7.95429i	−0.268269	+	0.319710i	0.615046	+	0.788492i	$0.289138\pi$
$620$	2.82634	−	19.3766i	0.113509	−	0.778184i
$621$	−1.15702	+	0.911576i	−0.0464297	+	0.0365803i
$622$	−34.0222	+	29.4196i	−1.36417	+	1.17962i
$623$	1.11540	+	0.935932i	0.0446876	+	0.0374973i
$624$	−0.974728	−	0.739499i	−0.0390204	−	0.0296036i
$625$	−4.13982	−	23.4781i	−0.165593	−	0.939124i
$626$	14.3588	−	5.46892i	0.573895	−	0.218582i
$627$	−0.156336	+	15.2098i	−0.00624348	+	0.607422i
$628$	18.0940	+	5.98362i	0.722031	+	0.238772i
$629$	−6.00209	−	3.46531i	−0.239319	−	0.138171i
$630$	−1.66250	+	9.12352i	−0.0662357	+	0.363490i
$631$	−13.6242	+	7.86596i	−0.542372	+	0.313139i	−0.746040	−	0.665901i	$-0.768047\pi$
$631$	−13.6242	+	7.86596i	−0.542372	+	0.313139i	0.203668	+	0.979040i	$0.434714\pi$
$632$	−2.85995	+	3.73413i	−0.113763	+	0.148536i
$633$	14.0427	+	2.62521i	0.558149	+	0.104343i
$634$	−28.5117	−	4.59207i	−1.13235	−	0.182374i
$635$	−18.3958	+	15.4359i	−0.730013	+	0.612554i
$636$	3.98896	−	0.783489i	0.158172	−	0.0310674i
$637$	0.165947	−	0.0603998i	0.00657506	−	0.00239313i
$638$	−13.4182	+	38.6415i	−0.531230	+	1.52983i
$639$	−0.359797	−	0.314732i	−0.0142333	−	0.0124506i
$640$	6.00196	−	23.9906i	0.237248	−	0.948313i
$641$	30.4646	+	5.37173i	1.20328	+	0.212171i	0.739115	−	0.673579i	$-0.235244\pi$
$641$	30.4646	+	5.37173i	1.20328	+	0.212171i	0.464164	+	0.885750i	$0.346355\pi$
$642$	−4.05389	−	22.3922i	−0.159994	−	0.883751i
$643$	16.3309	−	44.8688i	0.644028	−	1.76945i	0.00534211	−	0.999986i	$-0.498300\pi$
$643$	16.3309	−	44.8688i	0.644028	−	1.76945i	0.638686	−	0.769467i	$-0.279478\pi$
$644$	0.0168308	+	0.566700i	0.000663228	+	0.0223311i
$645$	−0.184402	−	1.11255i	−0.00726084	−	0.0438065i
$646$	20.0172	−	0.297187i	0.787566	−	0.0116927i
$647$	1.37617			0.0541026			0.0270513	−	0.999634i	$-0.491388\pi$
$647$	1.37617			0.0541026			0.0270513	+	0.999634i	$0.491388\pi$
$648$	19.4442	−	16.4294i	0.763840	−	0.645406i
$649$	−12.3813			−0.486008
$650$	0.0554576		0.000823356i	0.00217523		3.22947e-5i
$651$	−1.26860	−	7.65378i	−0.0497203	−	0.299975i
$652$	−0.757055	−	25.4903i	−0.0296486	−	0.998278i
$653$	−5.32442	+	14.6287i	−0.208361	+	0.572467i	−0.999218	−	0.0395339i	$-0.987413\pi$
$653$	−5.32442	+	14.6287i	−0.208361	+	0.572467i	0.790857	+	0.612000i	$0.209635\pi$
$654$	3.15364	+	17.4196i	0.123317	+	0.681159i
$655$	13.1308	+	2.31532i	0.513063	+	0.0904669i
$656$	−30.9711	−	32.7483i	−1.20922	−	1.27861i
$657$	4.84526	−	24.5202i	0.189031	−	0.956623i
$658$	3.94420	−	11.3585i	0.153761	−	0.442799i
$659$	−13.4743	+	4.90425i	−0.524885	+	0.191043i	−0.590853	−	0.806779i	$-0.701209\pi$
$659$	−13.4743	+	4.90425i	−0.524885	+	0.191043i	0.0659679	+	0.997822i	$0.478987\pi$
$660$	−28.2983	+	5.55820i	−1.10151	+	0.216353i
$661$	−25.7146	+	21.5771i	−1.00018	+	0.839252i	−0.987010	−	0.160661i	$-0.948637\pi$
$661$	−25.7146	+	21.5771i	−1.00018	+	0.839252i	−0.0131721	+	0.999913i	$0.504193\pi$
$662$	16.1507	+	2.60121i	0.627714	+	0.101099i
$663$	1.84589	+	0.345078i	0.0716883	+	0.0134017i
$664$	20.0978	+	15.3928i	0.779948	+	0.597356i
$665$	−4.36482	+	2.52003i	−0.169260	+	0.0977225i
$666$	−3.65131	−	3.09952i	−0.141486	−	0.120104i
$667$	−1.86439	−	1.07640i	−0.0721894	−	0.0416785i
$668$	−1.97291	−	0.652432i	−0.0763340	−	0.0252433i
$669$	−0.129380	+	12.5873i	−0.00500213	+	0.486652i
$670$	18.9273	−	7.20895i	0.731227	−	0.278506i
$671$	8.13954	+	46.1616i	0.314223	+	1.78205i
$672$	−0.626144	−	9.77793i	−0.0241540	−	0.377192i
$673$	−9.43320	−	7.91539i	−0.363623	−	0.305116i	0.442610	−	0.896714i	$-0.354053\pi$
$673$	−9.43320	−	7.91539i	−0.363623	−	0.305116i	−0.806233	+	0.591598i	$0.798497\pi$
$674$	−18.9063	+	16.3486i	−0.728242	+	0.629725i
$675$	−0.235325	+	1.12972i	−0.00905766	+	0.0434828i
$676$	−3.74373	+	25.6660i	−0.143990	+	0.987155i
$677$	−5.46389	+	6.51161i	−0.209994	+	0.250262i	−0.860753	−	0.509023i	$-0.830007\pi$
$677$	−5.46389	+	6.51161i	−0.209994	+	0.250262i	0.650758	+	0.759285i	$0.274451\pi$
$678$	−34.7329	−	5.96091i	−1.33391	−	0.228927i
$679$	12.7519	−	2.24850i	0.489373	−	0.0862896i
$680$	8.24872	+	37.0492i	0.316324	+	1.42077i
$681$	12.9219	+	22.9224i	0.495170	+	0.878388i
$682$	20.7124	−	12.3719i	0.793118	−	0.473743i
$683$	23.3781	−	40.4920i	0.894536	−	1.54938i	0.0601592	−	0.998189i	$-0.480839\pi$
$683$	23.3781	−	40.4920i	0.894536	−	1.54938i	0.834377	−	0.551194i	$-0.185828\pi$
$684$	13.6458	+	2.27781i	0.521761	+	0.0870941i
$685$	21.9200	+	37.9665i	0.837520	+	1.45063i
$686$	1.23511	+	0.688848i	0.0471566	+	0.0263003i
$687$	16.4215	+	14.0694i	0.626520	+	0.536783i
$688$	0.473235	+	1.09346i	0.0180419	+	0.0416877i
$689$	0.133211	+	0.158754i	0.00507493	+	0.00604806i
$690$	−0.00693200	−	1.51777i	−0.000263897	−	0.0577805i
$691$	0.243635	+	0.669382i	0.00926832	+	0.0254645i	0.944241	−	0.329257i	$-0.106798\pi$
$691$	0.243635	+	0.669382i	0.00926832	+	0.0254645i	−0.934972	+	0.354721i	$0.884576\pi$
$692$	−10.8096	−	27.1616i	−0.410918	−	1.03253i
$693$	−10.0105	+	5.50837i	−0.380267	+	0.209246i
$694$	−5.48651	−	28.6240i	−0.208265	−	1.08655i
$695$	−6.43008	+	36.4668i	−0.243907	+	1.38326i
$696$	32.8383	+	17.4878i	1.24473	+	0.662872i
$697$	65.0087	+	23.6612i	2.46238	+	0.896233i
$698$	1.88530	+	1.53484i	0.0713597	+	0.0580947i
$699$	−22.6467	−	27.5597i	−0.856577	−	1.04240i
$700$	0.295476	+	0.331622i	0.0111680	+	0.0125341i
$701$			28.6244i			1.08113i	0.841302	+	0.540565i	$0.181789\pi$
$701$			28.6244i			1.08113i	−0.841302	+	0.540565i	$0.818211\pi$
$702$	1.21220	+	0.463287i	0.0457517	+	0.0174856i
$703$		−	2.60296i		−	0.0981726i
$704$	27.5911	−	12.9267i	1.03988	−	0.487193i
$705$	−11.3196	+	30.1329i	−0.426319	+	1.13487i
$706$	−25.0717	+	30.7964i	−0.943584	+	1.15904i
$707$	12.2567	+	4.46109i	0.460962	+	0.167777i
$708$	−1.73985	+	11.1260i	−0.0653875	+	0.418141i
$709$	5.55408	−	31.4987i	0.208588	−	1.18296i	−0.683106	−	0.730320i	$-0.739371\pi$
$709$	5.55408	−	31.4987i	0.208588	−	1.18296i	0.891693	−	0.452640i	$-0.149518\pi$
$710$	0.483761	−	0.0927251i	0.0181552	−	0.00347991i
$711$	1.80228	−	4.65190i	0.0675908	−	0.174460i
$712$	3.65473	+	1.89834i	0.136967	+	0.0711432i
$713$	0.434277	+	1.19317i	0.0162638	+	0.0446845i
$714$	7.57850	+	12.9890i	0.283618	+	0.486100i
$715$	−0.945020	−	1.12623i	−0.0353417	−	0.0421186i
$716$	22.5134	+	36.4507i	0.841366	+	1.36223i
$717$	−36.3416	+	12.8058i	−1.35720	+	0.478241i
$718$	17.1692	−	30.7845i	0.640750	−	1.14887i
$719$	−1.01481	−	1.75770i	−0.0378459	−	0.0655511i	0.846482	−	0.532417i	$-0.178716\pi$
$719$	−1.01481	−	1.75770i	−0.0378459	−	0.0655511i	−0.884328	+	0.466866i	$0.845383\pi$
$720$	1.01814	+	26.2104i	0.0379438	+	0.976803i
$721$	−4.52114	+	7.83084i	−0.168376	+	0.291636i
$722$	−9.92336	−	16.6132i	−0.369309	−	0.618280i
$723$	14.1701	−	23.9709i	0.526991	−	0.891488i
$724$	10.7217	−	19.9132i	0.398467	−	0.740070i
$725$	−1.66093	+	0.292868i	−0.0616856	+	0.0108768i
$726$	−6.60346	−	5.48976i	−0.245077	−	0.203744i
$727$	−5.01434	+	5.97585i	−0.185971	+	0.221632i	−0.850972	−	0.525210i	$-0.823987\pi$
$727$	−5.01434	+	5.97585i	−0.185971	+	0.221632i	0.665001	+	0.746842i	$0.268431\pi$
$728$	0.421025	−	0.268757i	0.0156042	−	0.00996081i
$729$	−14.9154	+	22.5062i	−0.552423	+	0.833564i
$730$	16.8458	+	19.4812i	0.623490	+	0.721032i
$731$	−1.40087	−	1.17547i	−0.0518130	−	0.0434763i
$732$	42.6253	−	0.827576i	1.57548	−	0.0305881i
$733$	3.16145	+	17.9294i	0.116771	+	0.662239i	0.985858	+	0.167581i	$0.0535956\pi$
$733$	3.16145	+	17.9294i	0.116771	+	0.662239i	−0.869088	+	0.494658i	$0.835293\pi$
$734$	−7.36914	−	19.3479i	−0.272000	−	0.714145i
$735$	−3.25914	−	1.92660i	−0.120215	−	0.0710636i
$736$	0.394805	+	1.55422i	0.0145527	+	0.0572892i
$737$	21.6108	+	12.4770i	0.796046	+	0.459597i
$738$	41.2659	+	24.1401i	1.51902	+	0.888611i
$739$	−16.3268	+	9.42626i	−0.600590	+	0.346751i	−0.769274	−	0.638920i	$-0.779382\pi$
$739$	−16.3268	+	9.42626i	−0.600590	+	0.346751i	0.168684	+	0.985670i	$0.446048\pi$
$740$	4.83261	−	1.00089i	0.177650	−	0.0367933i
$741$	0.234395	+	0.665188i	0.00861070	+	0.0244363i
$742$	−0.263892	+	1.63849i	−0.00968780	+	0.0601507i
$743$	7.18364	−	6.02779i	0.263542	−	0.221138i	−0.501435	−	0.865195i	$-0.667194\pi$
$743$	7.18364	−	6.02779i	0.263542	−	0.221138i	0.764978	+	0.644057i	$0.222750\pi$
$744$	−8.20699	−	20.3510i	−0.300883	−	0.746104i
$745$	−19.9526	+	7.26215i	−0.731006	+	0.266064i
$746$	−6.95478	−	2.41503i	−0.254633	−	0.0884205i
$747$	−25.0375	−	9.70024i	−0.916073	−	0.354913i
$748$	−28.9832	+	36.7006i	−1.05973	+	1.34191i
$749$	9.14906	+	1.61323i	0.334299	+	0.0589460i
$750$	−18.0700	−	21.3364i	−0.659824	−	0.779094i
$751$	−10.8232	+	29.7365i	−0.394944	+	1.08510i	0.569771	+	0.821804i	$0.307032\pi$
$751$	−10.8232	+	29.7365i	−0.394944	+	1.08510i	−0.964715	+	0.263297i	$0.915190\pi$
$752$	3.90745	−	33.7832i	0.142490	−	1.23195i
$753$	−37.1558	−	13.9577i	−1.35403	−	0.508649i
$754$	0.0281558	+	1.89645i	0.00102537	+	0.0690646i
$755$	47.9814			1.74622
$756$	3.54320	+	9.76963i	0.128865	+	0.355318i
$757$	20.0872			0.730083			0.365041	−	0.930991i	$-0.381055\pi$
$757$	20.0872			0.730083			0.365041	+	0.930991i	$0.381055\pi$
$758$	0.777414	+	52.3632i	0.0282369	+	1.90192i
$759$	1.44480	−	1.18724i	0.0524428	−	0.0430940i
$760$	−10.5015	+	9.64032i	−0.380929	+	0.349691i
$761$	9.48243	−	26.0528i	0.343738	−	0.944412i	−0.640562	−	0.767907i	$-0.721298\pi$
$761$	9.48243	−	26.0528i	0.343738	−	0.944412i	0.984300	−	0.176505i	$-0.0564793\pi$
$762$	−9.08830	+	25.3293i	−0.329234	+	0.917582i
$763$	−7.11731	−	1.25497i	−0.257664	−	0.0454331i
$764$	−26.6858	−	21.0743i	−0.965457	−	0.762440i
$765$	−19.4085	−	35.2715i	−0.701715	−	1.27524i
$766$	−33.5321	−	11.6439i	−1.21156	−	0.420712i
$767$	−0.539467	+	0.196350i	−0.0194790	+	0.00708978i
$768$	−7.73895	−	26.6103i	−0.279255	−	0.960217i
$769$	−20.8017	+	17.4547i	−0.750130	+	0.629434i	−0.935537	−	0.353228i	$-0.885084\pi$
$769$	−20.8017	+	17.4547i	−0.750130	+	0.629434i	0.185407	+	0.982662i	$0.440640\pi$
$770$	1.87210	−	11.6237i	0.0674657	−	0.418889i
$771$	−7.38504	+	8.61965i	−0.265966	+	0.310429i
$772$	0.511711	+	2.47070i	0.0184169	+	0.0889226i
$773$	−6.38872	+	3.68853i	−0.229786	+	0.132667i	−0.610473	−	0.792037i	$-0.709021\pi$
$773$	−6.38872	+	3.68853i	−0.229786	+	0.132667i	0.380687	+	0.924704i	$0.375687\pi$
$774$	−0.806778	−	0.972709i	−0.0289990	−	0.0349633i
$775$	0.861473	+	0.497372i	0.0309450	+	0.0178661i
$776$	33.8237	−	14.0460i	1.21420	−	0.504223i
$777$	1.70330	−	0.960193i	0.0611054	−	0.0344467i
$778$	5.45014	+	14.3095i	0.195397	+	0.513022i
$779$	4.51182	+	25.5878i	0.161653	+	0.916778i
$780$	−1.14485	+	0.690949i	−0.0409920	+	0.0247399i
$781$	0.464896	+	0.390094i	0.0166353	+	0.0139587i
$782$	−1.60985	−	1.86171i	−0.0575683	−	0.0665746i
$783$	−38.6322	−	8.04725i	−1.38060	−	0.287585i
$784$	3.83334	+	1.14260i	0.136905	+	0.0408070i
$785$	13.3884	−	15.9557i	0.477852	−	0.569482i
$786$	14.0170	−	5.17439i	0.499970	−	0.184564i
$787$	18.6334	−	3.28558i	0.664210	−	0.117118i	0.168629	−	0.985680i	$-0.446066\pi$
$787$	18.6334	−	3.28558i	0.664210	−	0.117118i	0.495582	+	0.868561i	$0.334955\pi$
$788$	−37.6164	−	20.2533i	−1.34003	−	0.721496i
$789$	−38.3538	−	0.394226i	−1.36543	−	0.0140348i
$790$	2.63609	+	4.41322i	0.0937880	+	0.157015i
$791$	7.19347	−	12.4595i	0.255770	−	0.443007i
$792$	−24.2514	+	21.3609i	−0.861735	+	0.759026i
$793$	1.08671	+	1.88223i	0.0385901	+	0.0668400i
$794$	1.35471	−	2.42900i	0.0480768	−	0.0862020i
$795$	0.816435	−	4.36726i	0.0289560	−	0.154891i
$796$	17.6273	−	10.8873i	0.624784	−	0.385892i
$797$	14.5117	+	17.2943i	0.514030	+	0.612597i	0.959158	−	0.282870i	$-0.0912865\pi$
$797$	14.5117	+	17.2943i	0.514030	+	0.612597i	−0.445129	+	0.895467i	$0.646842\pi$
$798$	−2.80161	+	4.90412i	−0.0991759	+	0.173604i
$799$	17.8525	+	49.0492i	0.631574	+	1.73524i
$800$	1.01960	+	0.733928i	0.0360483	+	0.0259483i
$801$	−4.28529	−	0.846786i	−0.151413	−	0.0299197i
$802$	51.9129	−	9.95042i	1.83311	−	0.351361i
$803$	−5.51012	+	31.2494i	−0.194448	+	1.10277i
$804$	14.2489	−	17.6665i	0.502518	−	0.623051i
$805$	0.582264	+	0.211927i	0.0205221	+	0.00746944i
$806$	0.706262	−	0.867525i	0.0248770	−	0.0305573i
$807$	30.1691	−	5.00047i	1.06200	−	0.176025i
$808$	36.5809	+	4.78236i	1.28691	+	0.168243i
$809$		−	21.5151i		−	0.756431i	−0.925718	−	0.378215i	$-0.876538\pi$
$809$		−	21.5151i		−	0.756431i	0.925718	−	0.378215i	$-0.123462\pi$
$810$	−8.82550	−	26.3843i	−0.310097	−	0.927051i
$811$			31.6085i			1.10992i	0.831876	+	0.554962i	$0.187267\pi$
$811$			31.6085i			1.10992i	−0.831876	+	0.554962i	$0.812733\pi$
$812$	−11.3403	+	10.1042i	−0.397965	+	0.354588i
$813$	−14.1807	+	2.35043i	−0.497340	+	0.0824331i
$814$	4.71543	+	3.83888i	0.165276	+	0.134553i
$815$	−26.1904	−	9.53252i	−0.917409	−	0.333910i
$816$	28.9070	+	31.2020i	1.01195	+	1.09229i
$817$	0.119264	−	0.676380i	0.00417252	−	0.0236635i
$818$	6.03433	+	31.4820i	0.210985	+	1.10074i
$819$	−0.348813	+	0.398758i	−0.0121885	+	0.0139337i
$820$	−45.7709	+	18.2155i	−1.59839	+	0.636114i
$821$	−12.7115	−	34.9245i	−0.443633	−	1.21887i	−0.937086	−	0.349100i	$-0.886487\pi$
$821$	−12.7115	−	34.9245i	−0.443633	−	1.21887i	0.493452	−	0.869773i	$-0.335735\pi$
$822$	42.6576	+	24.3693i	1.48785	+	0.849977i
$823$	11.1923	+	13.3385i	0.390141	+	0.464952i	0.924988	−	0.379997i	$-0.124075\pi$
$823$	11.1923	+	13.3385i	0.390141	+	0.464952i	−0.534847	+	0.844949i	$0.679631\pi$
$824$	−7.66864	+	24.3987i	−0.267150	+	0.849967i
$825$	0.269212	−	1.44007i	0.00937277	−	0.0501367i
$826$	−4.01513	−	2.23933i	−0.139704	−	0.0779163i
$827$	−4.33266	−	7.50438i	−0.150661	−	0.260953i	0.780809	−	0.624769i	$-0.214807\pi$
$827$	−4.33266	−	7.50438i	−0.150661	−	0.260953i	−0.931471	+	0.363816i	$0.881474\pi$
$828$	−0.863845	−	1.46515i	−0.0300207	−	0.0509175i
$829$	9.71584	−	16.8283i	0.337445	−	0.584472i	−0.646506	−	0.762909i	$-0.723771\pi$
$829$	9.71584	−	16.8283i	0.337445	−	0.584472i	0.983951	+	0.178437i	$0.0571040\pi$
$830$	23.7528	−	14.1880i	0.824473	−	0.492472i
$831$	−10.0169	−	0.102960i	−0.347483	−	0.00357165i
$832$	0.997178	−	1.00079i	0.0345709	−	0.0346960i
$833$	−6.04605	+	1.06608i	−0.209483	+	0.0369375i
$834$	14.3703	+	38.9279i	0.497602	+	1.34796i
$835$	−1.45982	+	1.73975i	−0.0505192	+	0.0602064i
$836$	−17.3798	−	2.53508i	−0.601093	−	0.0876775i
$837$	14.4038	+	18.2821i	0.497869	+	0.631923i
$838$	11.4164	−	9.87201i	0.394374	−	0.341023i
$839$	21.3896	+	17.9480i	0.738450	+	0.619633i	0.932421	−	0.361374i	$-0.117692\pi$
$839$	21.3896	+	17.9480i	0.738450	+	0.619633i	−0.193971	+	0.981007i	$0.562137\pi$
$840$	−10.1822	−	3.31568i	−0.351318	−	0.114402i
$841$	−4.97921	−	28.2385i	−0.171697	−	0.973741i
$842$	−26.1569	+	9.96251i	−0.901426	+	0.343331i
$843$	−25.0646	+	14.1296i	−0.863271	+	0.486648i
$844$	−5.17933	+	15.6619i	−0.178280	+	0.539105i
$845$	24.5499	+	14.1739i	0.844543	+	0.487597i
$846$	6.06075	+	35.5585i	0.208373	+	1.22253i
$847$	3.03610	−	1.75289i	0.104322	−	0.0602301i
$848$	0.278579	+	4.68579i	0.00956643	+	0.160911i
$849$	−30.3309	+	35.4015i	−1.04095	+	1.21498i
$850$	−1.90364	−	0.306598i	−0.0652943	−	0.0105162i
$851$	−0.245144	+	0.205700i	−0.00840343	+	0.00705131i
$852$	0.415873	−	0.362946i	0.0142476	−	0.0124343i
$853$	2.49711	−	0.908875i	0.0854995	−	0.0311193i	−0.298916	−	0.954279i	$-0.596625\pi$
$853$	2.49711	−	0.908875i	0.0854995	−	0.0311193i	0.384416	+	0.923160i	$0.374403\pi$
$854$	−5.70941	+	16.4419i	−0.195372	+	0.562631i
$855$	7.82764	−	12.9363i	0.267700	−	0.442412i
$856$	26.2506	−	1.16988i	0.897226	−	0.0399857i
$857$	43.4043	+	7.65335i	1.48266	+	0.261434i	0.855642	−	0.517569i	$-0.173163\pi$
$857$	43.4043	+	7.65335i	1.48266	+	0.261434i	0.627021	+	0.779002i	$0.284274\pi$
$858$	−1.55072	−	0.556407i	−0.0529406	−	0.0189954i
$859$	−13.5716	+	37.2876i	−0.463056	+	1.27224i	0.460119	+	0.887857i	$0.347807\pi$
$859$	−13.5716	+	37.2876i	−0.463056	+	1.27224i	−0.923175	+	0.384379i	$0.874416\pi$
$860$	1.30161	−	0.0386575i	0.0443846	−	0.00131821i
$861$	−15.0795	+	12.3913i	−0.513908	+	0.422296i
$862$	−12.4871	+	0.185391i	−0.425312	+	0.00631443i
$863$	−49.8265			−1.69611			−0.848057	−	0.529904i	$-0.822228\pi$
$863$	−49.8265			−1.69611			−0.848057	+	0.529904i	$0.822228\pi$
$864$	15.7874	+	24.7943i	0.537097	+	0.843521i
$865$	−31.9500			−1.08633
$866$	18.2346	−	0.270722i	0.619637	−	0.00919949i
$867$	−33.5491	−	12.6029i	−1.13939	−	0.428016i
$868$	8.95445	−	0.265945i	0.303934	−	0.00902675i
$869$	−2.16621	+	5.95160i	−0.0734835	+	0.201894i
$870$	31.0290	−	26.2788i	1.05198	−	0.890936i
$871$	1.13948	+	0.200921i	0.0386097	+	0.00680793i
$872$	−20.4211	+	0.910084i	−0.691545	+	0.0308193i
$873$	−30.2646	+	24.3527i	−1.02430	+	0.824213i
$874$	0.303224	−	0.873221i	0.0102567	−	0.0295372i
$875$	10.7263	−	3.90404i	0.362614	−	0.131981i
$876$	27.3069	+	9.34272i	0.922615	+	0.315661i
$877$	−23.3679	+	19.6080i	−0.789078	+	0.662115i	−0.945517	−	0.325572i	$-0.894443\pi$
$877$	−23.3679	+	19.6080i	−0.789078	+	0.662115i	0.156439	+	0.987688i	$0.449999\pi$
$878$	−27.8994	−	4.49344i	−0.941559	−	0.151646i
$879$	18.8558	+	53.5109i	0.635991	+	1.80488i
$880$	−1.97628	−	33.2417i	−0.0666205	−	1.12058i
$881$	24.4412	−	14.1111i	0.823446	−	0.475417i	−0.0281576	−	0.999603i	$-0.508964\pi$
$881$	24.4412	−	14.1111i	0.823446	−	0.475417i	0.851603	+	0.524187i	$0.175631\pi$
$882$	−4.24257	−	0.0242300i	−0.142855	−	0.000815866i
$883$	0.679809	+	0.392488i	0.0228774	+	0.0132083i	0.511395	−	0.859346i	$-0.329129\pi$
$883$	0.679809	+	0.392488i	0.0228774	+	0.0132083i	−0.488518	+	0.872554i	$0.662462\pi$
$884$	−0.680810	+	2.05872i	−0.0228981	+	0.0692422i
$885$	10.5949	+	6.26305i	0.356145	+	0.210530i
$886$	6.56113	−	2.49897i	0.220426	−	0.0839546i
$887$	−5.70903	−	32.3775i	−0.191690	−	1.08713i	−0.917054	−	0.398764i	$-0.869439\pi$
$887$	−5.70903	−	32.3775i	−0.191690	−	1.08713i	0.725363	−	0.688366i	$-0.241672\pi$
$888$	4.11230	−	3.69791i	0.138000	−	0.124094i
$889$	−8.41585	−	7.06174i	−0.282259	−	0.236843i
$890$	3.40466	−	2.94407i	0.114124	−	0.0986854i
$891$	18.3445	−	28.9559i	0.614565	−	0.970060i
$892$	−14.3831	−	2.09797i	−0.481582	−	0.0702451i
$893$	−12.6011	+	15.0174i	−0.421681	+	0.502540i
$894$	−15.2112	+	18.2970i	−0.508737	+	0.611944i
$895$	46.1125	−	8.13088i	1.54137	−	0.271785i
$896$	11.2855	+	0.798248i	0.377023	+	0.0266676i
$897$	0.0441235	−	0.0746418i	0.00147324	−	0.00249222i
$898$	2.32679	−	1.38983i	0.0776460	−	0.0463792i
$899$	−17.0083	+	29.4592i	−0.567259	+	0.982521i
$900$	−1.25624	−	0.444280i	−0.0418745	−	0.0148093i
$901$	−3.60229	−	6.23935i	−0.120010	−	0.207863i
$902$	−53.0079	−	29.5637i	−1.76497	−	0.984365i
$903$	0.486596	−	0.171463i	0.0161929	−	0.00570595i
$904$	12.2014	−	38.8201i	0.405812	−	1.29114i
$905$	−15.8882	−	18.9349i	−0.528143	−	0.629416i
$906$	46.4418	−	27.0967i	1.54292	−	0.900228i
$907$	−2.67176	−	7.34061i	−0.0887145	−	0.243741i	0.887399	−	0.461002i	$-0.152510\pi$
$907$	−2.67176	−	7.34061i	−0.0887145	−	0.243741i	−0.976114	+	0.217261i	$0.930288\pi$
$908$	−28.2310	+	11.2351i	−0.936878	+	0.372851i
$909$	−38.6671	+	6.00132i	−1.28251	+	0.199051i
$910$	−0.102766	−	0.536146i	−0.00340666	−	0.0177731i
$911$	5.16034	−	29.2657i	0.170970	−	0.969617i	−0.771724	−	0.635958i	$-0.780605\pi$
$911$	5.16034	−	29.2657i	0.170970	−	0.969617i	0.942694	−	0.333660i	$-0.108284\pi$
$912$	−4.72031	+	15.2615i	−0.156305	+	0.505360i
$913$	32.0327	+	11.6590i	1.06013	+	0.385855i
$914$	−42.6253	−	34.7017i	−1.40992	−	1.14783i
$915$	16.3856	−	43.6188i	0.541691	−	1.44199i
$916$	−18.6430	+	16.6110i	−0.615983	+	0.548843i
$917$			6.09987i			0.201436i
$918$	−38.7047	−	23.1791i	−1.27745	−	0.765024i
$919$		−	32.7521i		−	1.08039i	−0.841539	−	0.540196i	$-0.818350\pi$
$919$		−	32.7521i		−	1.08039i	0.841539	−	0.540196i	$-0.181650\pi$
$920$	1.73780	+	0.227189i	0.0572935	+	0.00749019i
$921$	−29.0166	−	35.3114i	−0.956128	−	1.16355i
$922$	−10.2766	+	12.6231i	−0.338442	+	0.415720i
$923$	0.0264424	+	0.00962424i	0.000870362	+	0.000316786i
$924$	−4.75227	−	12.3079i	−0.156338	−	0.404901i
$925$	−0.0435344	+	0.246896i	−0.00143140	+	0.00811789i
$926$	52.3559	−	10.0353i	1.72052	−	0.329782i
$927$	0.557596	−	27.1211i	0.0183138	−	0.890774i
$928$	−25.0977	+	34.8666i	−0.823871	+	1.14455i
$929$	3.94064	+	10.8268i	0.129288	+	0.355216i	0.987399	−	0.158247i	$-0.0505844\pi$
$929$	3.94064	+	10.8268i	0.129288	+	0.355216i	−0.858111	+	0.513464i	$0.828362\pi$
$930$	−23.9823	+	0.109533i	−0.786411	+	0.00359172i
$931$	−1.48212	−	1.76632i	−0.0485745	−	0.0578889i
$932$	35.0437	−	21.6444i	1.14790	−	0.708987i
$933$	41.8326	+	35.8408i	1.36954	+	1.17338i
$934$	8.88520	−	15.9312i	0.290733	−	0.521285i
$935$	25.5552	+	44.2630i	0.835746	+	1.44755i
$936$	−0.717906	+	1.31531i	−0.0234655	+	0.0429923i
$937$	2.11278	−	3.65945i	0.0690217	−	0.119549i	−0.829449	−	0.558582i	$-0.811346\pi$
$937$	2.11278	−	3.65945i	0.0690217	−	0.119549i	0.898471	+	0.439033i	$0.144679\pi$
$938$	4.75154	+	7.95481i	0.155143	+	0.259734i
$939$	−9.24115	−	16.3930i	−0.301573	−	0.534964i
$940$	−32.7264	−	17.6205i	−1.06742	−	0.574717i
$941$	51.3277	−	9.05046i	1.67323	−	0.295036i	0.745009	−	0.667054i	$-0.232445\pi$
$941$	51.3277	−	9.05046i	1.67323	−	0.295036i	0.928226	+	0.372018i	$0.121334\pi$
$942$	3.94808	−	23.0046i	0.128635	−	0.749529i
$943$	2.05328	−	2.44700i	0.0668640	−	0.0796854i
$944$	−12.4616	−	3.71440i	−0.405589	−	0.120893i
$945$	11.3526	+	0.350167i	0.369300	+	0.0113909i
$946$	1.04941	+	1.21359i	0.0341193	+	0.0394571i
$947$	15.4993	+	13.0054i	0.503659	+	0.422620i	0.858891	−	0.512158i	$-0.171154\pi$
$947$	15.4993	+	13.0054i	0.503659	+	0.422620i	−0.355232	+	0.934778i	$0.615598\pi$
$948$	5.04380	+	2.78292i	0.163815	+	0.0903850i
$949$	0.255490	+	1.44895i	0.00829355	+	0.0470351i
$950$	−0.257756	−	0.676747i	−0.00836271	−	0.0219566i
$951$	−0.363533	+	35.3677i	−0.0117884	+	1.14688i
$952$	−16.0368	+	6.65963i	−0.519756	+	0.215840i
$953$	−6.76936	−	3.90829i	−0.219281	−	0.126602i	0.386336	−	0.922358i	$-0.373740\pi$
$953$	−6.76936	−	3.90829i	−0.219281	−	0.126602i	−0.605617	+	0.795756i	$0.707074\pi$
$954$	−1.67610	−	4.68819i	−0.0542658	−	0.151786i
$955$	−32.1845	+	18.5817i	−1.04147	+	0.601291i
$956$	−9.02344	−	43.5681i	−0.291839	−	1.40909i
$957$	49.2450	+	9.20608i	1.59187	+	0.297590i
$958$	−5.79120	+	35.9571i	−0.187105	+	1.16172i
$959$	−15.3640	+	12.8919i	−0.496130	+	0.416303i
$960$	−30.1493	−	2.89529i	−0.973063	−	0.0934451i
$961$	−10.2772	+	3.74060i	−0.331523	+	0.120664i
$962$	0.266336	+	0.0924843i	0.00858700	+	0.00298181i
$963$	−26.3802	+	8.99195i	−0.850090	+	0.289762i
$964$	25.2339	+	19.9277i	0.812729	+	0.641828i
$965$	2.71570	+	0.478851i	0.0874215	+	0.0154148i
$966$	0.683263	−	0.123698i	0.0219836	−	0.00397991i
$967$	12.7589	−	35.0547i	0.410297	−	1.12728i	−0.546736	−	0.837305i	$-0.684130\pi$
$967$	12.7589	−	35.0547i	0.410297	−	1.12728i	0.957034	−	0.289977i	$-0.0936478\pi$
$968$	7.30468	−	6.70565i	0.234781	−	0.215528i
$969$	−4.00922	−	24.1886i	−0.128795	−	0.777051i
$970$	−0.594205	−	40.0230i	−0.0190788	−	1.28506i
$971$	−50.9231			−1.63420			−0.817100	−	0.576496i	$-0.804420\pi$
$971$	−50.9231			−1.63420			−0.817100	+	0.576496i	$0.804420\pi$
$972$	−23.4424	−	20.5536i	−0.751916	−	0.659258i
$973$	−16.9405			−0.543088
$974$	−0.841837	−	56.7024i	−0.0269742	−	1.81686i
$975$	−0.0111075	−	0.0670146i	−0.000355726	−	0.00214619i
$976$	−5.65622	+	48.9027i	−0.181051	+	1.56534i
$977$	16.2384	−	44.6146i	0.519512	−	1.42735i	−0.351548	−	0.936170i	$-0.614345\pi$
$977$	16.2384	−	44.6146i	0.519512	−	1.42735i	0.871060	−	0.491177i	$-0.163433\pi$
$978$	−30.7333	+	5.56396i	−0.982743	+	0.177916i
$979$	5.46134	+	0.962981i	0.174545	+	0.0307770i
$980$	2.70941	−	3.43085i	0.0865490	−	0.109595i
$981$	20.5219	−	6.99510i	0.655214	−	0.223336i
$982$	−0.214051	−	0.0743287i	−0.00683065	−	0.00237192i
$983$	−27.9118	+	10.1591i	−0.890247	+	0.324024i	−0.746338	−	0.665567i	$-0.768190\pi$
$983$	−27.9118	+	10.1591i	−0.890247	+	0.324024i	−0.143910	+	0.989591i	$0.545967\pi$
$984$	−34.0152	+	43.4794i	−1.08437	+	1.38607i
$985$	−35.7682	+	30.0131i	−1.13967	+	0.956297i
$986$	10.4845	−	65.0975i	0.333895	−	2.07313i
$987$	−14.4753	−	2.70608i	−0.460754	−	0.0861354i
$988$	−0.797460	+	0.165163i	−0.0253706	+	0.00525454i
$989$	−0.0731255	+	0.0422190i	−0.00232526	+	0.00134249i
$990$	11.8906	+	33.2588i	0.377907	+	1.05703i
$991$	47.8654	+	27.6351i	1.52050	+	0.877858i	0.999708	+	0.0241722i	$0.00769501\pi$
$991$	47.8654	+	27.6351i	1.52050	+	0.877858i	0.520788	+	0.853686i	$0.325638\pi$
$992$	24.5582	−	6.23833i	0.779725	−	0.198067i
$993$	0.205926	−	20.0343i	0.00653486	−	0.635770i
$994$	0.0802072	+	0.210587i	0.00254402	+	0.00667941i
$995$	−3.93204	−	22.2997i	−0.124654	−	0.706949i
$996$	14.9782	−	27.1467i	0.474603	−	0.860177i
$997$	−11.8448	−	9.93898i	−0.375129	−	0.314771i	0.435658	−	0.900112i	$-0.356516\pi$
$997$	−11.8448	−	9.93898i	−0.375129	−	0.314771i	−0.810787	+	0.585342i	$0.800960\pi$
$998$	23.8998	+	27.6388i	0.756534	+	0.874890i
$999$	−3.08817	+	4.98717i	−0.0977053	+	0.157787i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.cf.a.659.108	yes	648
4.3	odd	2	inner	756.2.cf.a.659.48	yes	648
27.5	odd	18	inner	756.2.cf.a.491.48	✓	648
108.59	even	18	inner	756.2.cf.a.491.108	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.cf.a.491.48	✓	648	27.5	odd	18	inner
756.2.cf.a.491.108	yes	648	108.59	even	18	inner
756.2.cf.a.659.48	yes	648	4.3	odd	2	inner
756.2.cf.a.659.108	yes	648	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.cf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41406 - 0.0209939i) q^{2} +(-0.283220 - 1.70874i) q^{3} +(1.99912 - 0.0593732i) q^{4} +(0.747603 - 2.05402i) q^{5} +(-0.436362 - 2.41031i) q^{6} +(0.984808 + 0.173648i) q^{7} +(2.82562 - 0.125927i) q^{8} +(-2.83957 + 0.967897i) q^{9} +(1.01403 - 2.92020i) q^{10} +(3.57896 - 1.30263i) q^{11} +(-0.667643 - 3.39915i) q^{12} +(0.135281 - 0.113514i) q^{13} +(1.39622 + 0.224874i) q^{14} +(-3.72152 - 0.695718i) q^{15} +(3.99295 - 0.237388i) q^{16} +(-5.31680 + 3.06966i) q^{17} +(-3.99500 + 1.42828i) q^{18} +(-1.99685 - 1.15288i) q^{19} +(1.37259 - 4.15062i) q^{20} +(0.0178022 - 1.73196i) q^{21} +(5.03350 - 1.91714i) q^{22} +(0.0492249 + 0.279169i) q^{23} +(-1.01545 - 4.79258i) q^{24} +(0.170124 + 0.142751i) q^{25} +(0.188912 - 0.163356i) q^{26} +(2.45811 + 4.57796i) q^{27} +(1.97906 + 0.288672i) q^{28} +(-4.88155 + 5.81761i) q^{29} +(-5.27705 - 0.905656i) q^{30} +(4.41115 - 0.777805i) q^{31} +(5.64128 - 0.419508i) q^{32} +(-3.23949 - 5.74657i) q^{33} +(-7.45382 + 4.45229i) q^{34} +(1.09292 - 1.89300i) q^{35} +(-5.61918 + 2.10354i) q^{36} +(0.564446 + 0.977649i) q^{37} +(-2.84787 - 1.58832i) q^{38} +(-0.232281 - 0.199011i) q^{39} +(1.85379 - 5.89804i) q^{40} +(-7.24325 - 8.63216i) q^{41} +(-0.0111873 - 2.44946i) q^{42} +(0.101877 + 0.279904i) q^{43} +(7.07742 - 2.81661i) q^{44} +(-0.134791 + 6.55615i) q^{45} +(0.0754678 + 0.393727i) q^{46} +(1.47637 - 8.37293i) q^{47} +(-1.53652 - 6.75567i) q^{48} +(0.939693 + 0.342020i) q^{49} +(0.243561 + 0.198286i) q^{50} +(6.75107 + 8.21564i) q^{51} +(0.263703 - 0.234961i) q^{52} +1.17351i q^{53} +(3.57201 + 6.42189i) q^{54} -8.32511i q^{55} +(2.80456 + 0.366651i) q^{56} +(-1.40443 + 3.73862i) q^{57} +(-6.78066 + 8.32892i) q^{58} +(-3.05479 - 1.11185i) q^{59} +(-7.48107 - 1.16986i) q^{60} +(-2.13712 + 12.1202i) q^{61} +(6.22129 - 1.19247i) q^{62} +(-2.96451 + 0.460106i) q^{63} +(7.96829 - 0.711642i) q^{64} +(-0.132025 - 0.362734i) q^{65} +(-4.70147 - 8.05797i) q^{66} +(4.21151 + 5.01908i) q^{67} +(-10.4467 + 6.45229i) q^{68} +(0.463084 - 0.163179i) q^{69} +(1.50571 - 2.69975i) q^{70} +(0.0796712 + 0.137995i) q^{71} +(-7.90168 + 3.09249i) q^{72} +(-4.16572 + 7.21524i) q^{73} +(0.818684 + 1.37060i) q^{74} +(0.195741 - 0.331126i) q^{75} +(-4.06040 - 2.18619i) q^{76} +(3.75078 - 0.661364i) q^{77} +(-0.332636 - 0.276536i) q^{78} +(-1.06892 + 1.27389i) q^{79} +(2.49754 - 8.37908i) q^{80} +(7.12635 - 5.49683i) q^{81} +(-10.4236 - 12.0543i) q^{82} +(6.85632 + 5.75314i) q^{83} +(-0.0672433 - 3.46345i) q^{84} +(2.33029 + 13.2157i) q^{85} +(0.149936 + 0.393662i) q^{86} +(11.3233 + 6.69363i) q^{87} +(9.94874 - 4.13144i) q^{88} +(1.26098 + 0.728026i) q^{89} +(-0.0529630 + 9.27360i) q^{90} +(0.152938 - 0.0882985i) q^{91} +(0.114982 + 0.555168i) q^{92} +(-2.57839 - 7.31721i) q^{93} +(1.91190 - 11.8708i) q^{94} +(-3.86091 + 3.23969i) q^{95} +(-2.31455 - 9.52065i) q^{96} +(12.1677 - 4.42868i) q^{97} +(1.33596 + 0.463908i) q^{98} +(-8.90189 + 7.16298i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66}+ \cdots + 36 q^{97}+O(q^{100}) \) 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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