LMFDB - Embedded newform 930.2.y.b.29.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(29,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 3]))

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

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

chi := DirichletCharacter("930.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.y (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.4
Character	$\chi$	$=$	930.29
Dual form			930.2.y.b.449.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-1.57629 - 0.717859i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.323295 + 2.21257i) q^{5} +(-0.853296 - 1.50728i) q^{6} +(1.33289 - 0.433081i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.96936 + 2.26310i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-1.57629 - 0.717859i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.323295 + 2.21257i) q^{5} +(-0.853296 - 1.50728i) q^{6} +(1.33289 - 0.433081i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.96936 + 2.26310i) q^{9} +(-1.03897 + 1.98004i) q^{10} +(1.02107 + 3.14254i) q^{11} +(0.195625 - 1.72097i) q^{12} +(-0.0835654 + 0.0607138i) q^{13} +(1.33289 + 0.433081i) q^{14} +(1.07871 - 3.71973i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-3.89752 - 1.26638i) q^{17} +(0.263025 + 2.98845i) q^{18} +(-4.77952 - 3.47252i) q^{19} +(-2.00438 + 0.991195i) q^{20} +(-2.41190 - 0.274165i) q^{21} +(-1.02107 + 3.14254i) q^{22} +(6.90622 + 2.24397i) q^{23} +(1.16982 - 1.27731i) q^{24} +(-4.79096 + 1.43063i) q^{25} -0.103293 q^{26} +(-1.47968 - 4.98102i) q^{27} +(0.823770 + 1.13382i) q^{28} +(4.84636 + 3.52109i) q^{29} +(3.05910 - 2.37527i) q^{30} +(1.00204 + 5.47685i) q^{31} -1.00000 q^{32} +(0.646396 - 5.68652i) q^{33} +(-2.40880 - 3.31543i) q^{34} +(1.38914 + 2.80910i) q^{35} +(-1.54377 + 2.57231i) q^{36} -7.76183 q^{37} +(-1.82561 - 5.61866i) q^{38} +(0.175307 - 0.0357142i) q^{39} +(-2.20419 - 0.376251i) q^{40} +(-6.16670 + 8.48773i) q^{41} +(-1.79012 - 1.63949i) q^{42} +(8.51775 + 6.18851i) q^{43} +(-2.67320 + 1.94219i) q^{44} +(-4.37060 + 5.08900i) q^{45} +(4.26828 + 5.87478i) q^{46} +(-5.03340 + 3.65698i) q^{47} +(1.69719 - 0.345758i) q^{48} +(-4.07409 + 2.96000i) q^{49} +(-4.71687 - 1.65865i) q^{50} +(5.23452 + 4.79404i) q^{51} +(-0.0835654 - 0.0607138i) q^{52} +(2.91935 + 0.948555i) q^{53} +(1.73068 - 4.89946i) q^{54} +(-6.62299 + 3.27516i) q^{55} +1.40148i q^{56} +(5.04110 + 8.90471i) q^{57} +(1.85115 + 5.69724i) q^{58} +(6.45054 + 8.87841i) q^{59} +(3.87101 - 0.123545i) q^{60} -13.9399i q^{61} +(-2.40855 + 5.01985i) q^{62} +(3.60504 + 2.16357i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.161350 - 0.165266i) q^{65} +(3.86540 - 4.22055i) q^{66} -5.60504i q^{67} -4.09809i q^{68} +(-9.27532 - 8.49482i) q^{69} +(-0.527308 + 3.08912i) q^{70} +(-6.89810 - 2.24133i) q^{71} +(-2.76090 + 1.17363i) q^{72} +(-1.85505 - 5.70926i) q^{73} +(-6.27945 - 4.56229i) q^{74} +(8.57891 + 1.18415i) q^{75} +(1.82561 - 5.61866i) q^{76} +(2.72195 + 3.74644i) q^{77} +(0.162819 + 0.0741495i) q^{78} +(8.56476 + 2.78286i) q^{79} +(-1.56207 - 1.59998i) q^{80} +(-1.24327 + 8.91371i) q^{81} +(-9.97793 + 3.24203i) q^{82} +(-0.0264479 + 0.0364024i) q^{83} +(-0.484573 - 2.37858i) q^{84} +(1.54191 - 9.03295i) q^{85} +(3.25349 + 10.0132i) q^{86} +(-5.11161 - 9.02924i) q^{87} -3.30426 q^{88} +(1.04920 + 3.22910i) q^{89} +(-6.52712 + 1.54811i) q^{90} +(-0.0850892 + 0.117115i) q^{91} +7.26163i q^{92} +(2.35211 - 9.35241i) q^{93} -6.22163 q^{94} +(6.13801 - 11.6977i) q^{95} +(1.57629 + 0.717859i) q^{96} +(-10.9372 + 3.55370i) q^{97} -5.03585 q^{98} +(-5.10103 + 8.49957i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9}+O(q^{10}) $ 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9	$ 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9} + 2 q^{10} - 35 q^{15} - 32 q^{16} - 6 q^{18} - 8 q^{19} + 3 q^{20} + 20 q^{23} - 10 q^{25} - 48 q^{31} - 128 q^{32} + 8 q^{33} + 10 q^{34} - 16 q^{35} - 4 q^{36} - 12 q^{38} + 4 q^{39} - 3 q^{40} + 5 q^{45} + 10 q^{46} - 6 q^{47} + 46 q^{49} + 5 q^{50} + 34 q^{51} + 20 q^{53} + 35 q^{60} + 8 q^{62} - 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} - 6 q^{72} + 5 q^{75} + 12 q^{76} - 50 q^{77} - 4 q^{78} - 10 q^{79} - 2 q^{80} - 24 q^{81} + 40 q^{83} - 30 q^{85} + 4 q^{87} - 5 q^{90} + 20 q^{91} + 26 q^{93} - 4 q^{94} + 26 q^{95} + 124 q^{98}+O(q^{100}) $ 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9 + 2 * q^10 - 35 * q^15 - 32 * q^16 - 6 * q^18 - 8 * q^19 + 3 * q^20 + 20 * q^23 - 10 * q^25 - 48 * q^31 - 128 * q^32 + 8 * q^33 + 10 * q^34 - 16 * q^35 - 4 * q^36 - 12 * q^38 + 4 * q^39 - 3 * q^40 + 5 * q^45 + 10 * q^46 - 6 * q^47 + 46 * q^49 + 5 * q^50 + 34 * q^51 + 20 * q^53 + 35 * q^60 + 8 * q^62 - 36 * q^63 - 32 * q^64 - 8 * q^66 + 8 * q^69 + 16 * q^70 - 6 * q^72 + 5 * q^75 + 12 * q^76 - 50 * q^77 - 4 * q^78 - 10 * q^79 - 2 * q^80 - 24 * q^81 + 40 * q^83 - 30 * q^85 + 4 * q^87 - 5 * q^90 + 20 * q^91 + 26 * q^93 - 4 * q^94 + 26 * q^95 + 124 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−1.57629	−	0.717859i	−0.910069	−	0.414456i
$3$	−1.57629	−	0.717859i	−0.910069	−	0.414456i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	0.323295	+	2.21257i	0.144582	+	0.989493i
$5$	0.323295	+	2.21257i	0.144582	+	0.989493i
$6$	−0.853296	−	1.50728i	−0.348356	−	0.615344i
$7$	1.33289	−	0.433081i	0.503784	−	0.163689i	−0.0460895	−	0.998937i	$-0.514676\pi$
$7$	1.33289	−	0.433081i	0.503784	−	0.163689i	0.549873	+	0.835248i	$0.314676\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	1.96936	+	2.26310i	0.656452	+	0.754367i
$10$	−1.03897	+	1.98004i	−0.328550	+	0.626143i
$11$	1.02107	+	3.14254i	0.307865	+	0.947511i	0.978593	+	0.205807i	$0.0659819\pi$
$11$	1.02107	+	3.14254i	0.307865	+	0.947511i	−0.670728	+	0.741704i	$0.734018\pi$
$12$	0.195625	−	1.72097i	0.0564721	−	0.496801i
$13$	−0.0835654	+	0.0607138i	−0.0231769	+	0.0168390i	−0.599313	−	0.800515i	$-0.704560\pi$
$13$	−0.0835654	+	0.0607138i	−0.0231769	+	0.0168390i	0.576137	+	0.817353i	$0.304560\pi$
$14$	1.33289	+	0.433081i	0.356229	+	0.115746i
$15$	1.07871	−	3.71973i	0.278522	−	0.960430i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−3.89752	−	1.26638i	−0.945286	−	0.307142i	−0.204488	−	0.978869i	$-0.565553\pi$
$17$	−3.89752	−	1.26638i	−0.945286	−	0.307142i	−0.740799	+	0.671727i	$0.765553\pi$
$18$	0.263025	+	2.98845i	0.0619956	+	0.704384i
$19$	−4.77952	−	3.47252i	−1.09650	−	0.796651i	−0.116012	−	0.993248i	$-0.537011\pi$
$19$	−4.77952	−	3.47252i	−1.09650	−	0.796651i	−0.980484	+	0.196597i	$0.937011\pi$
$20$	−2.00438	+	0.991195i	−0.448193	+	0.221638i
$21$	−2.41190	−	0.274165i	−0.526320	−	0.0598277i
$22$	−1.02107	+	3.14254i	−0.217693	+	0.669991i
$23$	6.90622	+	2.24397i	1.44005	+	0.467899i	0.921912	−	0.387400i	$-0.126627\pi$
$23$	6.90622	+	2.24397i	1.44005	+	0.467899i	0.518134	+	0.855299i	$0.326627\pi$
$24$	1.16982	−	1.27731i	0.238789	−	0.260729i
$25$	−4.79096	+	1.43063i	−0.958192	+	0.286126i
$26$	−0.103293			−0.0202573
$27$	−1.47968	−	4.98102i	−0.284765	−	0.958597i
$28$	0.823770	+	1.13382i	0.155678	+	0.214272i
$29$	4.84636	+	3.52109i	0.899947	+	0.653849i	0.938452	−	0.345409i	$-0.112260\pi$
$29$	4.84636	+	3.52109i	0.899947	+	0.653849i	−0.0385057	+	0.999258i	$0.512260\pi$
$30$	3.05910	−	2.37527i	0.558512	−	0.433664i
$31$	1.00204	+	5.47685i	0.179971	+	0.983672i
$31$	1.00204	+	5.47685i	0.179971	+	0.983672i
$32$	−1.00000			−0.176777
$33$	0.646396	−	5.68652i	0.112523	−	0.989897i
$34$	−2.40880	−	3.31543i	−0.413105	−	0.568591i
$35$	1.38914	+	2.80910i	0.234808	+	0.474824i
$36$	−1.54377	+	2.57231i	−0.257296	+	0.428718i
$37$	−7.76183			−1.27604			−0.638018	−	0.770021i	$-0.720246\pi$
$37$	−7.76183			−1.27604			−0.638018	+	0.770021i	$0.720246\pi$
$38$	−1.82561	−	5.61866i	−0.296153	−	0.911467i
$39$	0.175307	−	0.0357142i	0.0280716	−	0.00571885i
$40$	−2.20419	−	0.376251i	−0.348512	−	0.0594905i
$41$	−6.16670	+	8.48773i	−0.963077	+	1.32556i	−0.0176092	+	0.999845i	$0.505605\pi$
$41$	−6.16670	+	8.48773i	−0.963077	+	1.32556i	−0.945468	+	0.325716i	$0.894395\pi$
$42$	−1.79012	−	1.63949i	−0.276222	−	0.252978i
$43$	8.51775	+	6.18851i	1.29895	+	0.943739i	0.999945	−	0.0105142i	$-0.00334684\pi$
$43$	8.51775	+	6.18851i	1.29895	+	0.943739i	0.299000	+	0.954253i	$0.403347\pi$
$44$	−2.67320	+	1.94219i	−0.403000	+	0.292797i
$45$	−4.37060	+	5.08900i	−0.651530	+	0.758623i
$46$	4.26828	+	5.87478i	0.629323	+	0.866189i
$47$	−5.03340	+	3.65698i	−0.734197	+	0.533425i	−0.890888	−	0.454222i	$-0.849917\pi$
$47$	−5.03340	+	3.65698i	−0.734197	+	0.533425i	0.156691	+	0.987648i	$0.449917\pi$
$48$	1.69719	−	0.345758i	0.244968	−	0.0499058i
$49$	−4.07409	+	2.96000i	−0.582013	+	0.422857i
$50$	−4.71687	−	1.65865i	−0.667066	−	0.234569i
$51$	5.23452	+	4.79404i	0.732979	+	0.671300i
$52$	−0.0835654	−	0.0607138i	−0.0115884	−	0.00841949i
$53$	2.91935	+	0.948555i	0.401004	+	0.130294i	0.502574	−	0.864534i	$-0.332387\pi$
$53$	2.91935	+	0.948555i	0.401004	+	0.130294i	−0.101570	+	0.994828i	$0.532387\pi$
$54$	1.73068	−	4.89946i	0.235516	−	0.666733i
$55$	−6.62299	+	3.27516i	−0.893043	+	0.441623i
$56$			1.40148i			0.187281i
$57$	5.04110	+	8.90471i	0.667711	+	1.17946i
$58$	1.85115	+	5.69724i	0.243067	+	0.748084i
$59$	6.45054	+	8.87841i	0.839789	+	1.15587i	0.986021	+	0.166620i	$0.0532853\pi$
$59$	6.45054	+	8.87841i	0.839789	+	1.15587i	−0.146232	+	0.989250i	$0.546715\pi$
$60$	3.87101	−	0.123545i	0.499746	−	0.0159496i
$61$		−	13.9399i		−	1.78482i	−0.451226	−	0.892410i	$-0.649013\pi$
$61$		−	13.9399i		−	1.78482i	0.451226	−	0.892410i	$-0.350987\pi$
$62$	−2.40855	+	5.01985i	−0.305886	+	0.637521i
$63$	3.60504	+	2.16357i	0.454192	+	0.272584i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−0.161350	−	0.165266i	−0.0200130	−	0.0204987i
$66$	3.86540	−	4.22055i	0.475798	−	0.519514i
$67$		−	5.60504i		−	0.684764i	−0.939561	−	0.342382i	$-0.888766\pi$
$67$		−	5.60504i		−	0.684764i	0.939561	−	0.342382i	$-0.111234\pi$
$68$		−	4.09809i		−	0.496967i
$69$	−9.27532	−	8.49482i	−1.11662	−	1.02266i
$70$	−0.527308	+	3.08912i	−0.0630254	+	0.369221i
$71$	−6.89810	−	2.24133i	−0.818654	−	0.265997i	−0.130395	−	0.991462i	$-0.541625\pi$
$71$	−6.89810	−	2.24133i	−0.818654	−	0.265997i	−0.688259	+	0.725465i	$0.741625\pi$
$72$	−2.76090	+	1.17363i	−0.325376	+	0.138314i
$73$	−1.85505	−	5.70926i	−0.217117	−	0.668218i	−0.998996	−	0.0447885i	$-0.985739\pi$
$73$	−1.85505	−	5.70926i	−0.217117	−	0.668218i	0.781879	−	0.623430i	$-0.214261\pi$
$74$	−6.27945	−	4.56229i	−0.729971	−	0.530355i
$75$	8.57891	+	1.18415i	0.990608	+	0.136734i
$76$	1.82561	−	5.61866i	0.209412	−	0.644504i
$77$	2.72195	+	3.74644i	0.310195	+	0.426947i
$78$	0.162819	+	0.0741495i	0.0184356	+	0.00839577i
$79$	8.56476	+	2.78286i	0.963611	+	0.313096i	0.748234	−	0.663435i	$-0.230902\pi$
$79$	8.56476	+	2.78286i	0.963611	+	0.313096i	0.215377	+	0.976531i	$0.430902\pi$
$80$	−1.56207	−	1.59998i	−0.174645	−	0.178883i
$81$	−1.24327	+	8.91371i	−0.138141	+	0.990413i
$82$	−9.97793	+	3.24203i	−1.10188	+	0.358022i
$83$	−0.0264479	+	0.0364024i	−0.00290303	+	0.00399568i	−0.810466	−	0.585786i	$-0.800786\pi$
$83$	−0.0264479	+	0.0364024i	−0.00290303	+	0.00399568i	0.807563	+	0.589781i	$0.200786\pi$
$84$	−0.484573	−	2.37858i	−0.0528712	−	0.259524i
$85$	1.54191	−	9.03295i	0.167244	−	0.979761i
$86$	3.25349	+	10.0132i	0.350833	+	1.07975i
$87$	−5.11161	−	9.02924i	−0.548022	−	0.968037i
$88$	−3.30426			−0.352235
$89$	1.04920	+	3.22910i	0.111215	+	0.342284i	0.991139	−	0.132831i	$-0.0424067\pi$
$89$	1.04920	+	3.22910i	0.111215	+	0.342284i	−0.879924	+	0.475114i	$0.842407\pi$
$90$	−6.52712	+	1.54811i	−0.688019	+	0.163185i
$91$	−0.0850892	+	0.117115i	−0.00891978	+	0.0122770i
$92$			7.26163i			0.757077i
$93$	2.35211	−	9.35241i	0.243903	−	0.969800i
$94$	−6.22163			−0.641712
$95$	6.13801	−	11.6977i	0.629747	−	1.20016i
$96$	1.57629	+	0.717859i	0.160879	+	0.0732662i
$97$	−10.9372	+	3.55370i	−1.11050	+	0.360824i	−0.806135	−	0.591731i	$-0.798445\pi$
$97$	−10.9372	+	3.55370i	−1.11050	+	0.360824i	−0.304366	+	0.952555i	$0.598445\pi$
$98$	−5.03585			−0.508698
$99$	−5.10103	+	8.49957i	−0.512673	+	0.854239i
$100$	−2.84110	−	4.11439i	−0.284110	−	0.411439i
$101$	4.77202	+	1.55052i	0.474834	+	0.154283i	0.536650	−	0.843805i	$-0.319689\pi$
$101$	4.77202	+	1.55052i	0.474834	+	0.154283i	−0.0618167	+	0.998088i	$0.519689\pi$
$102$	1.41695	+	6.95524i	0.140299	+	0.688671i
$103$	0.128896	−	0.177411i	0.0127005	−	0.0174808i	−0.802620	−	0.596491i	$-0.796561\pi$
$103$	0.128896	−	0.177411i	0.0127005	−	0.0174808i	0.815320	+	0.579011i	$0.196561\pi$
$104$	−0.0319191	−	0.0982370i	−0.00312993	−	0.00963293i
$105$	−0.173147	−	5.42515i	−0.0168974	−	0.529440i
$106$	1.80426	+	2.48335i	0.175245	+	0.241204i
$107$	5.45125	−	16.7772i	0.526992	−	1.62192i	−0.233349	−	0.972393i	$-0.574969\pi$
$107$	5.45125	−	16.7772i	0.526992	−	1.62192i	0.760342	−	0.649523i	$-0.225031\pi$
$108$	4.27998	−	2.94648i	0.411842	−	0.283525i
$109$	15.2530	−	11.0820i	1.46097	−	1.06146i	0.477865	−	0.878433i	$-0.341411\pi$
$109$	15.2530	−	11.0820i	1.46097	−	1.06146i	0.983108	−	0.183026i	$-0.0585893\pi$
$110$	−7.28320	−	1.24323i	−0.694426	−	0.118537i
$111$	12.2349	+	5.57190i	1.16128	+	0.528861i
$112$	−0.823770	+	1.13382i	−0.0778389	+	0.107136i
$113$	0.886528	+	2.72845i	0.0833975	+	0.256671i	0.984057	−	0.177855i	$-0.0569158\pi$
$113$	0.886528	+	2.72845i	0.0833975	+	0.256671i	−0.900659	+	0.434526i	$0.856916\pi$
$114$	−1.15572	+	10.1671i	−0.108243	+	0.952240i
$115$	−2.73219	+	16.0060i	−0.254778	+	1.49256i
$116$	−1.85115	+	5.69724i	−0.171875	+	0.528975i
$117$	−0.301972	−	0.0695499i	−0.0279173	−	0.00642989i
$118$			10.9743i			1.01027i
$119$	−5.74339			−0.526496
$120$	3.20433	+	2.17537i	0.292514	+	0.198584i
$121$	0.0662339	−	0.0481217i	0.00602126	−	0.00437470i
$122$	8.19366	−	11.2776i	0.741819	−	1.02103i
$123$	15.8135	−	8.95228i	1.42585	−	0.807200i
$124$	−4.89915	+	2.64543i	−0.439957	+	0.237567i
$125$	−4.71426	−	10.1378i	−0.421656	−	0.906756i
$126$	1.64482	+	3.86935i	0.146533	+	0.344709i
$127$	1.56035	−	1.13366i	0.138459	−	0.100596i	−0.516400	−	0.856348i	$-0.672728\pi$
$127$	1.56035	−	1.13366i	0.138459	−	0.100596i	0.654859	+	0.755751i	$0.272728\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	−8.98394	−	15.8694i	−0.790992	−	1.39722i
$130$	−0.0333940	−	0.228542i	−0.00292884	−	0.0200445i
$131$	12.8542	−	4.17658i	1.12308	−	0.364910i	0.312136	−	0.950038i	$-0.398956\pi$
$131$	12.8542	−	4.17658i	1.12308	−	0.364910i	0.810941	+	0.585128i	$0.198956\pi$
$132$	5.60795	−	1.14247i	0.488110	−	0.0994395i
$133$	−7.87444	−	2.55856i	−0.682800	−	0.221855i
$134$	3.29456	−	4.53457i	0.284606	−	0.391727i
$135$	10.5425	−	4.88424i	0.907353	−	0.420369i
$136$	2.40880	−	3.31543i	0.206553	−	0.284295i
$137$	2.44363	+	3.36337i	0.208774	+	0.287352i	0.900544	−	0.434766i	$-0.143169\pi$
$137$	2.44363	+	3.36337i	0.208774	+	0.287352i	−0.691770	+	0.722118i	$0.743169\pi$
$138$	−2.51076	−	12.3244i	−0.213730	−	1.04912i
$139$	5.77927	+	7.95449i	0.490191	+	0.674691i	0.980423	−	0.196901i	$-0.0630879\pi$
$139$	5.77927	+	7.95449i	0.490191	+	0.674691i	−0.490232	+	0.871592i	$0.663088\pi$
$140$	−2.24234	+	2.18921i	−0.189513	+	0.185022i
$141$	10.5593	−	2.15118i	0.889252	−	0.181162i
$142$	−4.26326	−	5.86788i	−0.357765	−	0.492421i
$143$	−0.276122	−	0.200614i	−0.0230905	−	0.0167762i
$144$	−2.92346	−	0.673329i	−0.243622	−	0.0561108i
$145$	−6.22386	+	11.8613i	−0.516863	+	0.985025i
$146$	1.85505	−	5.70926i	0.153525	−	0.472502i
$147$	8.54679	−	1.74119i	0.704928	−	0.143611i
$148$	−2.39854	−	7.38194i	−0.197159	−	0.606792i
$149$			5.71210i			0.467953i	0.972242	+	0.233977i	$0.0751739\pi$
$149$			5.71210i			0.467953i	−0.972242	+	0.233977i	$0.924826\pi$
$150$	6.24446	+	6.00056i	0.509858	+	0.489944i
$151$	16.0267	−	5.20741i	1.30424	−	0.423773i	0.427184	−	0.904165i	$-0.359506\pi$
$151$	16.0267	−	5.20741i	1.30424	−	0.423773i	0.877054	+	0.480392i	$0.159506\pi$
$152$	4.77952	−	3.47252i	0.387670	−	0.281659i
$153$	−4.80965	−	11.3144i	−0.388837	−	0.914718i
$154$			4.63086i			0.373165i
$155$	−11.7940	+	3.98772i	−0.947316	+	0.320301i
$156$	0.0881390	+	0.155691i	0.00705677	+	0.0124652i
$157$	0.559794	−	0.770491i	0.0446765	−	0.0614919i	−0.786094	−	0.618107i	$-0.787900\pi$
$157$	0.559794	−	0.770491i	0.0446765	−	0.0614919i	0.830771	+	0.556615i	$0.187900\pi$
$158$	5.29331	+	7.28562i	0.421114	+	0.579613i
$159$	−3.92081	−	3.59088i	−0.310940	−	0.284775i
$160$	−0.323295	−	2.21257i	−0.0255587	−	0.174919i
$161$	10.1770			0.802062
$162$	−6.24517	+	6.48057i	−0.490667	+	0.509162i
$163$	−2.91875	−	0.948361i	−0.228614	−	0.0742813i	0.192470	−	0.981303i	$-0.438350\pi$
$163$	−2.91875	−	0.948361i	−0.228614	−	0.0742813i	−0.421084	+	0.907022i	$0.638350\pi$
$164$	−9.97793	−	3.24203i	−0.779145	−	0.253160i
$165$	12.7908	−	0.408226i	0.995765	−	0.0317804i
$166$	−0.0427935	+	0.0139045i	−0.00332142	+	0.00107920i
$167$	−6.71211	+	9.23842i	−0.519399	+	0.714891i	−0.985469	−	0.169857i	$-0.945669\pi$
$167$	−6.71211	+	9.23842i	−0.519399	+	0.714891i	0.466070	+	0.884748i	$0.345669\pi$
$168$	1.00607	−	2.20913i	0.0776196	−	0.170438i
$169$	−4.01392	+	12.3536i	−0.308763	+	0.950276i
$170$	6.55687	−	6.40150i	0.502889	−	0.490973i
$171$	−1.55390	−	17.6552i	−0.118830	−	1.35012i
$172$	−3.25349	+	10.0132i	−0.248076	+	0.763501i
$173$	19.8952	−	14.4547i	1.51260	−	1.09897i	0.547600	−	0.836740i	$-0.315542\pi$
$173$	19.8952	−	14.4547i	1.51260	−	1.09897i	0.965005	−	0.262231i	$-0.0844583\pi$
$174$	1.17188	−	10.3093i	0.0888399	−	0.781549i
$175$	−5.76623	+	3.98174i	−0.435886	+	0.300991i
$176$	−2.67320	−	1.94219i	−0.201500	−	0.146398i
$177$	−3.79445	−	18.6255i	−0.285209	−	1.39998i
$178$	−1.04920	+	3.22910i	−0.0786406	+	0.242031i
$179$	−1.80853	−	5.56607i	−0.135176	−	0.416028i	0.860442	−	0.509549i	$-0.170188\pi$
$179$	−1.80853	−	5.56607i	−0.135176	−	0.416028i	−0.995617	+	0.0935212i	$0.970188\pi$
$180$	−6.19051	−	2.58410i	−0.461414	−	0.192607i
$181$		−	5.41166i		−	0.402246i	−0.979566	−	0.201123i	$-0.935541\pi$
$181$		−	5.41166i		−	0.402246i	0.979566	−	0.201123i	$-0.0644590\pi$
$182$	−0.137677	+	0.0447341i	−0.0102053	+	0.00331591i
$183$	−10.0069	+	21.9732i	−0.739729	+	1.62431i
$184$	−4.26828	+	5.87478i	−0.314662	+	0.433094i
$185$	−2.50936	−	17.1736i	−0.184492	−	1.26263i
$186$	7.40011	−	6.18372i	0.542602	−	0.453412i
$187$		−	13.5412i		−	0.990227i
$188$	−5.03340	−	3.65698i	−0.367099	−	0.266713i
$189$	−4.12944	−	5.99831i	−0.300372	−	0.436313i
$190$	11.8415	−	5.85578i	0.859071	−	0.424823i
$191$		−	17.0351i		−	1.23262i	−0.787504	−	0.616309i	$-0.788627\pi$
$191$		−	17.0351i		−	1.23262i	0.787504	−	0.616309i	$-0.211373\pi$
$192$	0.853296	+	1.50728i	0.0615813	+	0.108778i
$193$	−21.5608	+	7.00552i	−1.55198	+	0.504268i	−0.954650	−	0.297729i	$-0.903771\pi$
$193$	−21.5608	+	7.00552i	−1.55198	+	0.504268i	−0.597328	+	0.801997i	$0.703771\pi$
$194$	−10.9372	−	3.55370i	−0.785243	−	0.255141i
$195$	0.135696	+	0.376333i	0.00971740	+	0.0269498i
$196$	−4.07409	−	2.96000i	−0.291006	−	0.211429i
$197$	−11.5194	+	3.74289i	−0.820726	+	0.266670i	−0.689134	−	0.724634i	$-0.742009\pi$
$197$	−11.5194	+	3.74289i	−0.820726	+	0.266670i	−0.131592	+	0.991304i	$0.542009\pi$
$198$	−9.12274	+	3.87799i	−0.648325	+	0.275597i
$199$	−0.963613	−	1.32630i	−0.0683087	−	0.0940189i	0.773496	−	0.633802i	$-0.218506\pi$
$199$	−0.963613	−	1.32630i	−0.0683087	−	0.0940189i	−0.841804	+	0.539783i	$0.818506\pi$
$200$	0.119880	−	4.99856i	0.00847681	−	0.353452i
$201$	−4.02363	+	8.83514i	−0.283805	+	0.623183i
$202$	2.94927	+	4.05932i	0.207510	+	0.285613i
$203$	7.98457	+	2.59434i	0.560407	+	0.182087i
$204$	−2.94185	+	6.45976i	−0.205971	+	0.452274i
$205$	−20.7734	−	10.9002i	−1.45088	−	0.761305i
$206$	0.208559	−	0.0677649i	0.0145310	−	0.00472140i
$207$	8.52248	+	20.0486i	0.592353	+	1.39348i
$208$	0.0319191	−	0.0982370i	0.00221319	−	0.00681151i
$209$	6.03230	−	18.5655i	0.417263	−	1.28420i
$210$	3.04874	−	4.49081i	0.210383	−	0.309895i
$211$	3.31255			0.228045			0.114023	−	0.993478i	$-0.463626\pi$
$211$	3.31255			0.228045			0.114023	+	0.993478i	$0.463626\pi$
$212$			3.06959i			0.210820i
$213$	9.26442	+	8.48484i	0.634788	+	0.581372i
$214$	14.2716	−	10.3689i	0.975584	−	0.708803i
$215$	−10.9388	+	20.8469i	−0.746019	+	1.42174i
$216$	5.19448	+	0.131958i	0.353439	+	0.00897858i
$217$	3.70752	+	6.86607i	0.251683	+	0.466099i
$218$	18.8538			1.27694
$219$	−1.17435	+	10.3311i	−0.0793554	+	0.698111i
$220$	−5.16148	−	5.28675i	−0.347987	−	0.356433i
$221$	0.402584	−	0.130808i	0.0270807	−	0.00879907i
$222$	6.62313	+	11.6992i	0.444516	+	0.785201i
$223$	25.0105			1.67483			0.837415	−	0.546568i	$-0.184066\pi$
$223$	25.0105			1.67483			0.837415	+	0.546568i	$0.184066\pi$
$224$	−1.33289	+	0.433081i	−0.0890573	+	0.0289365i
$225$	−12.6728	−	8.02502i	−0.844851	−	0.535001i
$226$	−0.886528	+	2.72845i	−0.0589709	+	0.181494i
$227$	−3.01846	−	2.19304i	−0.200342	−	0.145557i	0.483091	−	0.875570i	$-0.339514\pi$
$227$	−3.01846	−	2.19304i	−0.200342	−	0.145557i	−0.683433	+	0.730013i	$0.739514\pi$
$228$	−6.91109	+	7.54608i	−0.457698	+	0.499751i
$229$	4.28760	−	5.90137i	0.283333	−	0.389974i	−0.643502	−	0.765445i	$-0.722519\pi$
$229$	4.28760	−	5.90137i	0.283333	−	0.389974i	0.926834	+	0.375471i	$0.122519\pi$
$230$	−11.6185	+	11.3432i	−0.766099	+	0.747946i
$231$	−1.60115	−	7.85944i	−0.105348	−	0.517113i
$232$	−4.84636	+	3.52109i	−0.318179	+	0.231171i
$233$	−11.7447	+	8.53299i	−0.769418	+	0.559015i	−0.901785	−	0.432186i	$-0.857742\pi$
$233$	−11.7447	+	8.53299i	−0.769418	+	0.559015i	0.132366	+	0.991201i	$0.457742\pi$
$234$	−0.203420	−	0.233762i	−0.0132980	−	0.0152815i
$235$	−9.71861	−	9.95449i	−0.633972	−	0.649359i
$236$	−6.45054	+	8.87841i	−0.419894	+	0.577935i
$237$	−11.5028	−	10.5349i	−0.747188	−	0.684314i
$238$	−4.64650	−	3.37588i	−0.301188	−	0.218826i
$239$	9.24006	−	28.4380i	0.597690	−	1.83950i	0.0568340	−	0.998384i	$-0.481899\pi$
$239$	9.24006	−	28.4380i	0.597690	−	1.83950i	0.540855	−	0.841116i	$-0.318101\pi$
$240$	1.31371	+	3.64337i	0.0847994	+	0.235179i
$241$	22.0541	−	7.16581i	1.42063	−	0.461590i	0.504827	−	0.863220i	$-0.331556\pi$
$241$	22.0541	−	7.16581i	1.42063	−	0.461590i	0.915802	+	0.401630i	$0.131556\pi$
$242$	0.0818696			0.00526278
$243$	8.35853	−	13.1581i	0.536200	−	0.844091i
$244$	13.2576	−	4.30766i	0.848732	−	0.275770i
$245$	−7.86635	−	8.05727i	−0.502563	−	0.514760i
$246$	18.0554	+	2.05238i	1.15117	+	0.130855i
$247$	0.610232			0.0388281
$248$	−5.51844	−	0.739449i	−0.350421	−	0.0469550i
$249$	0.0678212	−	0.0383947i	0.00429799	−	0.00243317i
$250$	2.14495	−	10.9727i	0.135659	−	0.693972i
$251$	1.40041	−	1.01746i	0.0883931	−	0.0642214i	−0.542711	−	0.839920i	$-0.682602\pi$
$251$	1.40041	−	1.01746i	0.0883931	−	0.0642214i	0.631104	+	0.775698i	$0.282602\pi$
$252$	−0.943658	+	4.09717i	−0.0594449	+	0.258098i
$253$			23.9943i			1.50851i
$254$	1.92870			0.121017
$255$	−8.91488	+	13.1316i	−0.558271	+	0.822336i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	9.02779	−	27.7847i	0.563138	−	1.73316i	−0.110281	−	0.993900i	$-0.535175\pi$
$257$	9.02779	−	27.7847i	0.563138	−	1.73316i	0.673419	−	0.739261i	$-0.264825\pi$
$258$	2.05964	−	18.1192i	0.128228	−	1.12806i
$259$	−10.3456	+	3.36150i	−0.642847	+	0.208874i
$260$	0.107317	−	0.204523i	0.00665555	−	0.0126840i
$261$	1.57563	+	17.9021i	0.0975293	+	1.10811i
$262$	12.8542	+	4.17658i	0.794135	+	0.258030i
$263$	7.20220	+	9.91298i	0.444107	+	0.611260i	0.971119	−	0.238598i	$-0.0766877\pi$
$263$	7.20220	+	9.91298i	0.444107	+	0.611260i	−0.527012	+	0.849858i	$0.676688\pi$
$264$	5.20846	+	2.37199i	0.320558	+	0.145986i
$265$	−1.15494	+	6.76594i	−0.0709471	+	0.415629i
$266$	−4.86667	−	6.69840i	−0.298395	−	0.410705i
$267$	0.664201	−	5.84316i	0.0406484	−	0.357595i
$268$	5.33071	−	1.73205i	0.325625	−	0.105802i
$269$	8.65416	+	6.28761i	0.527653	+	0.383362i	0.819479	−	0.573109i	$-0.194263\pi$
$269$	8.65416	+	6.28761i	0.527653	+	0.383362i	−0.291826	+	0.956471i	$0.594263\pi$
$270$	11.3999	+	2.24529i	0.693778	+	0.136644i
$271$	2.09351	+	0.680224i	0.127172	+	0.0413207i	0.371912	−	0.928268i	$-0.378702\pi$
$271$	2.09351	+	0.680224i	0.127172	+	0.0413207i	−0.244740	+	0.969589i	$0.578702\pi$
$272$	3.89752	−	1.26638i	0.236322	−	0.0767855i
$273$	0.218197	−	0.123525i	0.0132059	−	0.00747608i
$274$			4.15735i			0.251155i
$275$	−9.38772	−	13.5950i	−0.566101	−	0.819809i
$276$	5.21282	−	11.4464i	0.313775	−	0.688992i
$277$	19.0653	+	13.8517i	1.14552	+	0.832270i	0.987879	−	0.155226i	$-0.0496106\pi$
$277$	19.0653	+	13.8517i	1.14552	+	0.832270i	0.157643	+	0.987496i	$0.449611\pi$
$278$			9.83228i			0.589701i
$279$	−10.4213	+	13.0536i	−0.623908	+	0.781498i
$280$	−3.10088	+	0.453092i	−0.185313	+	0.0270774i
$281$	−2.69960	+	3.71568i	−0.161045	+	0.221659i	−0.881912	−	0.471414i	$-0.843744\pi$
$281$	−2.69960	+	3.71568i	−0.161045	+	0.221659i	0.720867	+	0.693073i	$0.243744\pi$
$282$	9.80707	+	4.46625i	0.584002	+	0.265961i
$283$	−4.03061	+	1.30963i	−0.239595	+	0.0778491i	−0.426353	−	0.904557i	$-0.640202\pi$
$283$	−4.03061	+	1.30963i	−0.239595	+	0.0778491i	0.186758	+	0.982406i	$0.440202\pi$
$284$		−	7.25309i		−	0.430392i
$285$	−18.0725	+	14.0327i	−1.07053	+	0.831223i
$286$	−0.105469	−	0.324601i	−0.00623652	−	0.0191940i
$287$	−4.54364	+	13.9839i	−0.268202	+	0.825442i
$288$	−1.96936	−	2.26310i	−0.116045	−	0.133355i
$289$	−0.166376	−	0.120879i	−0.00978682	−	0.00711054i
$290$	−12.0071	+	5.93768i	−0.705081	+	0.348673i
$291$	19.7912	+	2.24969i	1.16018	+	0.131879i
$292$	4.85659	−	3.52852i	0.284210	−	0.206491i
$293$	−8.17619	+	25.1637i	−0.477658	+	1.47008i	0.364681	+	0.931132i	$0.381178\pi$
$293$	−8.17619	+	25.1637i	−0.477658	+	1.47008i	−0.842339	+	0.538948i	$0.818822\pi$
$294$	7.93795	+	3.61503i	0.462950	+	0.210833i
$295$	−17.5587	+	17.1426i	−1.02231	+	0.998083i
$296$	2.39854	−	7.38194i	0.139412	−	0.429066i
$297$	14.1422	−	9.73594i	0.820612	−	0.564936i
$298$	−3.35749	+	4.62118i	−0.194494	+	0.267698i
$299$	−0.713360	+	0.231785i	−0.0412547	+	0.0134045i
$300$	1.52483	+	8.52496i	0.0880362	+	0.492189i
$301$	14.0333	+	4.55971i	0.808868	+	0.262817i
$302$	16.0267	+	5.20741i	0.922236	+	0.299653i
$303$	−6.40901	−	5.86970i	−0.368188	−	0.337206i
$304$	5.90781			0.338836
$305$	30.8430	−	4.50670i	1.76607	−	0.258053i
$306$	2.75936	−	11.9806i	0.157742	−	0.684886i
$307$	17.6271	+	24.2616i	1.00603	+	1.38468i	0.921552	+	0.388255i	$0.126922\pi$
$307$	17.6271	+	24.2616i	1.00603	+	1.38468i	0.0844773	+	0.996425i	$0.473078\pi$
$308$	−2.72195	+	3.74644i	−0.155097	+	0.213473i
$309$	−0.330534	+	0.187121i	−0.0188034	+	0.0106449i
$310$	−11.8855	−	3.70620i	−0.675049	−	0.210498i
$311$			17.2003i			0.975339i	0.873028	+	0.487669i	$0.162153\pi$
$311$			17.2003i			0.975339i	−0.873028	+	0.487669i	$0.837847\pi$
$312$	−0.0202066	+	0.177763i	−0.00114397	+	0.0100639i
$313$	−0.227572	+	0.165340i	−0.0128631	+	0.00934559i	−0.594198	−	0.804319i	$-0.702531\pi$
$313$	−0.227572	+	0.165340i	−0.0128631	+	0.00934559i	0.581335	+	0.813664i	$0.302531\pi$
$314$	0.905767	−	0.294301i	0.0511154	−	0.0166084i
$315$	−3.62156	+	8.67588i	−0.204052	+	0.488831i
$316$			9.00552i			0.506600i
$317$	−7.36714	−	22.6737i	−0.413780	−	1.27348i	−0.913338	−	0.407203i	$-0.866504\pi$
$317$	−7.36714	−	22.6737i	−0.413780	−	1.27348i	0.499558	−	0.866280i	$-0.333496\pi$
$318$	−1.06133	−	5.20967i	−0.0595167	−	0.292144i
$319$	−6.11666	+	18.8252i	−0.342467	+	1.05401i
$320$	1.03897	−	1.98004i	0.0580800	−	0.110687i
$321$	−20.6364	+	22.5325i	−1.15181	+	1.25764i
$322$	8.23339	+	5.98191i	0.458829	+	0.333359i
$323$	14.2307	+	19.5869i	0.791818	+	1.08984i
$324$	−8.86164	+	1.57207i	−0.492313	+	0.0873374i
$325$	0.313500	−	0.410429i	0.0173898	−	0.0227665i
$326$	−1.80389	−	2.48284i	−0.0999082	−	0.137512i
$327$	−31.9984	+	6.51883i	−1.76952	+	0.360492i
$328$	−6.16670	−	8.48773i	−0.340499	−	0.468657i
$329$	−5.12519	+	7.05421i	−0.282561	+	0.388911i
$330$	10.5879	+	7.18800i	0.582847	+	0.395686i
$331$	−7.01826	+	9.65981i	−0.385759	+	0.530951i	−0.957099	−	0.289762i	$-0.906424\pi$
$331$	−7.01826	+	9.65981i	−0.385759	+	0.530951i	0.571340	+	0.820713i	$0.306424\pi$
$332$	−0.0427935	−	0.0139045i	−0.00234860	−	0.000763107i
$333$	−15.2858	−	17.5658i	−0.837657	−	0.962601i
$334$	−10.8604	+	3.52876i	−0.594256	+	0.193085i
$335$	12.4016	−	1.81208i	0.677569	−	0.0990045i
$336$	2.11242	−	1.19588i	0.115242	−	0.0652404i
$337$	−7.79505	−	23.9907i	−0.424623	−	1.30686i	−0.903354	−	0.428895i	$-0.858903\pi$
$337$	−7.79505	−	23.9907i	−0.424623	−	1.30686i	0.478731	−	0.877962i	$-0.341097\pi$
$338$	−10.5086	+	7.63494i	−0.571592	+	0.415286i
$339$	0.561222	−	4.93722i	0.0304814	−	0.268153i
$340$	9.06733	−	1.32489i	0.491745	−	0.0718524i
$341$	−16.1881	+	8.74120i	−0.876633	+	0.473362i
$342$	9.12031	−	15.1967i	0.493170	−	0.821743i
$343$	−9.91477	+	13.6465i	−0.535347	+	0.736842i
$344$	−8.51775	+	6.18851i	−0.459246	+	0.333662i
$345$	15.7967	−	23.2687i	0.850468	−	1.25274i
$346$	24.5918			1.32207
$347$			21.0881i			1.13207i	0.824382	+	0.566033i	$0.191523\pi$
$347$			21.0881i			1.13207i	−0.824382	+	0.566033i	$0.808477\pi$
$348$	7.00775	−	7.65162i	0.375655	−	0.410170i
$349$	6.67374e−5	0	0.000205397i	3.57237e−6	0	1.09946e-5i	−0.951055	−	0.309022i	$-0.899998\pi$
$349$	6.67374e−5	0	0.000205397i	3.57237e−6	0	1.09946e-5i	0.951058	+	0.309011i	$0.0999982\pi$
$350$	−7.00539	−	0.168010i	−0.374454	−	0.00898050i
$351$	0.426067	+	0.326404i	0.0227418	+	0.0174221i
$352$	−1.02107	−	3.14254i	−0.0544233	−	0.167498i
$353$	4.31060	−	5.93303i	0.229430	−	0.315783i	−0.678745	−	0.734374i	$-0.737476\pi$
$353$	4.31060	−	5.93303i	0.229430	−	0.315783i	0.908175	+	0.418591i	$0.137476\pi$
$354$	7.87801	−	17.2987i	0.418711	−	0.919414i
$355$	2.72898	−	15.9872i	0.144839	−	0.848511i
$356$	−2.74683	+	1.99569i	−0.145582	+	0.105771i
$357$	9.05323	+	4.12295i	0.479148	+	0.218209i
$358$	1.80853	−	5.56607i	0.0955836	−	0.294176i
$359$	2.39278	+	3.29338i	0.126286	+	0.173818i	0.867478	−	0.497475i	$-0.165739\pi$
$359$	2.39278	+	3.29338i	0.126286	+	0.173818i	−0.741192	+	0.671293i	$0.765739\pi$
$360$	−3.48933	−	5.72927i	−0.183904	−	0.301959i
$361$	4.91404	+	15.1239i	0.258634	+	0.795993i
$362$	3.18089	−	4.37813i	0.167184	−	0.230109i
$363$	−0.138948	+	0.0283071i	−0.00729289	+	0.00148573i
$364$	−0.137677	−	0.0447341i	−0.00721625	−	0.00234470i
$365$	12.0324	−	5.95021i	0.629806	−	0.311448i
$366$	−21.0113	+	11.8948i	−1.09828	+	0.621753i
$367$	2.63316			0.137450			0.0687250	−	0.997636i	$-0.478107\pi$
$367$	2.63316			0.137450			0.0687250	+	0.997636i	$0.478107\pi$
$368$	−6.90622	+	2.24397i	−0.360011	+	0.116975i
$369$	−31.3530	+	2.75951i	−1.63217	+	0.143654i
$370$	8.06428	−	15.3687i	0.419242	−	0.798981i
$371$	4.30197			0.223347
$372$	9.62151	−	0.653060i	0.498852	−	0.0338596i
$373$		−	24.1431i		−	1.25008i	−0.780592	−	0.625041i	$-0.785082\pi$
$373$		−	24.1431i		−	1.25008i	0.780592	−	0.625041i	$-0.214918\pi$
$374$	7.95929	−	10.9550i	0.411565	−	0.566471i
$375$	0.153492	+	19.3643i	0.00792628	+	0.999969i
$376$	−1.92259	−	5.91712i	−0.0991499	−	0.305152i
$377$	−0.618767			−0.0318681
$378$	0.184936	−	7.27996i	0.00951209	−	0.374441i
$379$	−4.57340	−	14.0755i	−0.234920	−	0.723009i	−0.997132	−	0.0756817i	$-0.975887\pi$
$379$	−4.57340	−	14.0755i	−0.234920	−	0.723009i	0.762212	−	0.647327i	$-0.224113\pi$
$380$	13.0219	+	2.22282i	0.668009	+	0.114028i
$381$	−3.27336	+	0.666862i	−0.167700	+	0.0341644i
$382$	10.0130	−	13.7817i	0.512310	−	0.705134i
$383$	−4.87538	+	1.58411i	−0.249120	+	0.0809440i	−0.430915	−	0.902392i	$-0.641809\pi$
$383$	−4.87538	+	1.58411i	−0.249120	+	0.0809440i	0.181795	+	0.983336i	$0.441809\pi$
$384$	−0.195625	+	1.72097i	−0.00998295	+	0.0878228i
$385$	−7.40928	+	7.23372i	−0.377612	+	0.368664i
$386$	−21.5608	−	7.00552i	−1.09741	−	0.356572i
$387$	2.76927	+	31.4639i	0.140770	+	1.59940i
$388$	−6.75954	−	9.30371i	−0.343164	−	0.472324i
$389$	0.725286	−	2.23220i	0.0367735	−	0.113177i	−0.930985	−	0.365058i	$-0.881049\pi$
$389$	0.725286	−	2.23220i	0.0367735	−	0.113177i	0.967758	+	0.251881i	$0.0810491\pi$
$390$	−0.111423	+	0.384220i	−0.00564211	+	0.0194557i
$391$	−24.0754	−	17.4918i	−1.21754	−	0.884598i
$392$	−1.55616	−	4.78938i	−0.0785981	−	0.241900i
$393$	−23.2601	−	2.64401i	−1.17332	−	0.133373i
$394$	−11.5194	−	3.74289i	−0.580341	−	0.188564i
$395$	−3.38834	+	19.8499i	−0.170486	+	0.998754i
$396$	−9.65988	−	2.22485i	−0.485427	−	0.111803i
$397$			7.02987i			0.352819i	0.984317	+	0.176410i	$0.0564483\pi$
$397$			7.02987i			0.352819i	−0.984317	+	0.176410i	$0.943552\pi$
$398$		−	1.63940i		−	0.0821755i
$399$	10.5757	+	9.68576i	0.529446	+	0.484894i
$400$	3.03507	−	3.97346i	0.151753	−	0.198673i
$401$	16.4468	+	11.9493i	0.821314	+	0.596720i	0.917089	−	0.398683i	$-0.130533\pi$
$401$	16.4468	+	11.9493i	0.821314	+	0.596720i	−0.0957743	+	0.995403i	$0.530533\pi$
$402$	−8.44835	+	4.78275i	−0.421365	+	0.238542i
$403$	−0.416256	−	0.396838i	−0.0207352	−	0.0197679i
$404$			5.01760i			0.249635i
$405$	−20.1242	+	0.130944i	−0.999979	+	0.00650667i
$406$	4.93473	+	6.79208i	0.244907	+	0.337085i
$407$	−7.92539	−	24.3918i	−0.392847	−	1.20906i
$408$	−6.17696	+	3.49688i	−0.305805	+	0.173121i
$409$			4.19400i			0.207380i	0.994610	+	0.103690i	$0.0330650\pi$
$409$			4.19400i			0.207380i	−0.994610	+	0.103690i	$0.966935\pi$
$410$	−10.3990	−	21.0288i	−0.513572	−	1.03854i
$411$	−1.43744	−	7.05582i	−0.0709036	−	0.348038i
$412$	0.208559	+	0.0677649i	0.0102750	+	0.00333854i
$413$	12.4429	+	9.04031i	0.612276	+	0.444844i
$414$	−4.88947	+	21.2291i	−0.240304	+	1.04335i
$415$	−0.0890934	−	0.0467491i	−0.00437342	−	0.00229482i
$416$	0.0835654	−	0.0607138i	0.00409713	−	0.00297674i
$417$	−3.39959	−	16.6872i	−0.166479	−	0.817178i
$418$	15.7928	−	11.4741i	0.772449	−	0.561217i
$419$	0.349732	+	0.481365i	0.0170855	+	0.0235162i	0.817474	−	0.575965i	$-0.195374\pi$
$419$	0.349732	+	0.481365i	0.0170855	+	0.0235162i	−0.800389	+	0.599481i	$0.795374\pi$
$420$	5.10612	−	1.84114i	0.249153	−	0.0898382i
$421$	7.06744	−	5.13480i	0.344446	−	0.250255i	−0.402089	−	0.915600i	$-0.631716\pi$
$421$	7.06744	−	5.13480i	0.344446	−	0.250255i	0.746535	+	0.665346i	$0.231716\pi$
$422$	2.67991	+	1.94707i	0.130456	+	0.0947818i
$423$	−18.1887	−	4.18920i	−0.884364	−	0.203686i
$424$	−1.80426	+	2.48335i	−0.0876225	+	0.120602i
$425$	20.4846	+	0.491280i	0.993647	+	0.0238306i
$426$	2.50781	+	12.3099i	0.121504	+	0.596415i
$427$	−6.03710	−	18.5803i	−0.292156	−	0.899163i
$428$	17.6406			0.852692
$429$	0.291234	+	0.514442i	0.0140609	+	0.0248375i
$430$	−21.1031	+	10.4358i	−1.01768	+	0.503260i
$431$	15.7366	+	21.6596i	0.758007	+	1.04331i	0.997377	+	0.0723792i	$0.0230592\pi$
$431$	15.7366	+	21.6596i	0.758007	+	1.04331i	−0.239370	+	0.970928i	$0.576941\pi$
$432$	4.12486	+	3.15999i	0.198457	+	0.152035i
$433$	−7.80516			−0.375092			−0.187546	−	0.982256i	$-0.560053\pi$
$433$	−7.80516			−0.375092			−0.187546	+	0.982256i	$0.560053\pi$
$434$	−1.03632	+	7.73399i	−0.0497451	+	0.371243i
$435$	18.3253	−	14.2289i	0.878631	−	0.682224i
$436$	15.2530	+	11.0820i	0.730487	+	0.530730i
$437$	−25.2161	−	34.7070i	−1.20625	−	1.66026i
$438$	−7.02254	+	7.66777i	−0.335550	+	0.366380i
$439$	9.34926			0.446216			0.223108	−	0.974794i	$-0.428380\pi$
$439$	9.34926			0.446216			0.223108	+	0.974794i	$0.428380\pi$
$440$	−1.06825	−	7.31092i	−0.0509269	−	0.348534i
$441$	−14.7221	−	3.39079i	−0.701053	−	0.161466i
$442$	0.402584	+	0.130808i	0.0191490	+	0.00622188i
$443$	1.54994	−	4.77023i	0.0736399	−	0.226640i	−0.907461	−	0.420136i	$-0.861982\pi$
$443$	1.54994	−	4.77023i	0.0736399	−	0.226640i	0.981101	+	0.193495i	$0.0619825\pi$
$444$	−1.51841	+	13.3579i	−0.0720605	+	0.633936i
$445$	−6.80541	+	3.36538i	−0.322607	+	0.159534i
$446$	20.2340	+	14.7008i	0.958106	+	0.696104i
$447$	4.10048	−	9.00390i	0.193946	−	0.425870i
$448$	−1.33289	−	0.433081i	−0.0629730	−	0.0204612i
$449$	12.2979	−	8.93496i	0.580375	−	0.421667i	−0.258485	−	0.966015i	$-0.583223\pi$
$449$	12.2979	−	8.93496i	0.580375	−	0.421667i	0.838859	+	0.544349i	$0.183223\pi$
$450$	−5.53550	−	13.9412i	−0.260946	−	0.657196i
$451$	−32.9697	−	10.7125i	−1.55248	−	0.504432i
$452$	−2.32096	+	1.68628i	−0.109169	+	0.0793157i
$453$	−29.0009	−	3.29658i	−1.36258	−	0.154887i
$454$	−1.15295	−	3.54842i	−0.0541106	−	0.166535i
$455$	−0.286635	−	0.150403i	−0.0134377	−	0.00705102i
$456$	−10.0267	+	2.04267i	−0.469542	+	0.0956568i
$457$	−3.20611	+	9.86740i	−0.149976	+	0.461578i	−0.997617	−	0.0689917i	$-0.978022\pi$
$457$	−3.20611	+	9.86740i	−0.149976	+	0.461578i	0.847642	+	0.530569i	$0.178022\pi$
$458$	6.93748	−	2.25412i	0.324167	−	0.105328i
$459$	−0.540774	+	21.2874i	−0.0252412	+	0.993612i
$460$	−16.0669	+	2.34765i	−0.749122	+	0.109460i
$461$	2.27642	+	7.00611i	0.106024	+	0.326307i	0.989969	−	0.141282i	$-0.0451226\pi$
$461$	2.27642	+	7.00611i	0.106024	+	0.326307i	−0.883946	+	0.467589i	$0.845123\pi$
$462$	3.32430	−	7.29955i	0.154660	−	0.339606i
$463$	−3.30955	−	2.40453i	−0.153808	−	0.111748i	0.508220	−	0.861227i	$-0.330304\pi$
$463$	−3.30955	−	2.40453i	−0.153808	−	0.111748i	−0.662027	+	0.749480i	$0.730304\pi$
$464$	−5.99043			−0.278099
$465$	21.4533	+	2.18064i	0.994874	+	0.101125i
$466$	−14.5172			−0.672496
$467$	0.488331	+	0.354793i	0.0225973	+	0.0164179i	0.599027	−	0.800729i	$-0.295554\pi$
$467$	0.488331	+	0.354793i	0.0225973	+	0.0164179i	−0.576429	+	0.817147i	$0.695554\pi$
$468$	−0.0271685	−	0.308684i	−0.00125587	−	0.0142689i
$469$	−2.42744	−	7.47088i	−0.112089	−	0.344973i
$470$	−2.01142	−	13.7658i	−0.0927799	−	0.634969i
$471$	−1.43550	+	0.812661i	−0.0661444	+	0.0374454i
$472$	−10.4372	+	3.39125i	−0.480411	+	0.156095i
$473$	−10.7504	+	33.0863i	−0.494303	+	1.52131i
$474$	−3.11373	−	15.2841i	−0.143018	−	0.702021i
$475$	27.8664	+	9.79900i	1.27860	+	0.449609i
$476$	−1.77481	−	5.46229i	−0.0813481	−	0.250364i
$477$	3.60257	+	8.47484i	0.164950	+	0.388036i
$478$	24.1908	−	17.5756i	1.10646	−	0.803891i
$479$	−15.1482	−	4.92195i	−0.692139	−	0.224890i	−0.0582369	−	0.998303i	$-0.518548\pi$
$479$	−15.1482	−	4.92195i	−0.692139	−	0.224890i	−0.633902	+	0.773413i	$0.718548\pi$
$480$	−1.07871	+	3.71973i	−0.0492361	+	0.169782i
$481$	0.648620	−	0.471250i	0.0295745	−	0.0214872i
$482$	22.0541	+	7.16581i	1.00454	+	0.326394i
$483$	−16.0419	−	7.30567i	−0.729932	−	0.332419i
$484$	0.0662339	+	0.0481217i	0.00301063	+	0.00218735i
$485$	−11.3988	−	23.0504i	−0.517591	−	1.04666i
$486$	14.4963	−	5.73209i	0.657566	−	0.260013i
$487$	1.46513	−	4.50922i	0.0663915	−	0.204332i	−0.912357	−	0.409395i	$-0.865740\pi$
$487$	1.46513	−	4.50922i	0.0663915	−	0.204332i	0.978749	+	0.205063i	$0.0657398\pi$
$488$	13.2576	+	4.30766i	0.600144	+	0.194999i
$489$	3.92000	+	3.59014i	0.177269	+	0.162352i
$490$	−1.62807	−	11.1422i	−0.0735485	−	0.503353i
$491$	3.54056			0.159783			0.0798917	−	0.996804i	$-0.474543\pi$
$491$	3.54056			0.159783			0.0798917	+	0.996804i	$0.474543\pi$
$492$	13.4008	+	12.2731i	0.604153	+	0.553314i
$493$	−14.4297	−	19.8608i	−0.649883	−	0.894487i
$494$	0.493688	+	0.358685i	0.0222121	+	0.0161380i
$495$	−20.4551	−	8.53853i	−0.919386	−	0.383778i
$496$	−4.02988	−	3.84189i	−0.180947	−	0.172506i
$497$	−10.1651			−0.455966
$498$	0.0774363	+	0.00880231i	0.00347000	+	0.000394441i
$499$	−10.8506	−	14.9346i	−0.485741	−	0.668564i	0.493855	−	0.869544i	$-0.335587\pi$
$499$	−10.8506	−	14.9346i	−0.485741	−	0.668564i	−0.979595	+	0.200980i	$0.935587\pi$
$500$	8.18487	−	7.61629i	0.366038	−	0.340611i
$501$	17.2121	−	9.74406i	0.768979	−	0.435332i
$502$	1.73100			0.0772584
$503$	−10.6806	−	32.8715i	−0.476224	−	1.46567i	−0.844299	−	0.535872i	$-0.819983\pi$
$503$	−10.6806	−	32.8715i	−0.476224	−	1.46567i	0.368075	−	0.929796i	$-0.380017\pi$
$504$	−3.17169	+	2.76002i	−0.141278	+	0.122941i
$505$	−1.88788	+	11.0597i	−0.0840094	+	0.492151i
$506$	−14.1035	+	19.4118i	−0.626977	+	0.862959i
$507$	15.1952	−	16.5914i	0.674844	−	0.736848i
$508$	1.56035	+	1.13366i	0.0692293	+	0.0502980i
$509$	−6.79045	+	4.93355i	−0.300982	+	0.218676i	−0.728017	−	0.685559i	$-0.759558\pi$
$509$	−6.79045	+	4.93355i	−0.300982	+	0.218676i	0.427036	+	0.904235i	$0.359558\pi$
$510$	−14.9309	+	5.38369i	−0.661150	+	0.238394i
$511$	−4.94515	−	6.80641i	−0.218760	−	0.301098i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−10.2245	+	28.9451i	−0.451424	+	1.27796i
$514$	23.6351	−	17.1719i	1.04250	−	0.757419i
$515$	0.434206	+	0.227837i	0.0191334	+	0.0100397i
$516$	12.3165	−	13.4482i	0.542204	−	0.592022i
$517$	−16.6317	−	12.0836i	−0.731460	−	0.531437i
$518$	−10.3456	−	3.36150i	−0.454561	−	0.147696i
$519$	−41.7370	+	8.50282i	−1.83205	+	0.373232i
$520$	0.207037	−	0.102383i	0.00907919	−	0.00448979i
$521$		−	2.84602i		−	0.124687i	−0.998055	−	0.0623433i	$-0.980143\pi$
$521$		−	2.84602i		−	0.124687i	0.998055	−	0.0623433i	$-0.0198574\pi$
$522$	−9.24787	+	15.4092i	−0.404768	+	0.674444i
$523$	0.720451	+	2.21732i	0.0315031	+	0.0969567i	0.965572	−	0.260137i	$-0.0837677\pi$
$523$	0.720451	+	2.21732i	0.0315031	+	0.0969567i	−0.934069	+	0.357094i	$0.883768\pi$
$524$	7.94433	+	10.9344i	0.347050	+	0.477673i
$525$	11.9476	−	2.13702i	0.521434	−	0.0932673i
$526$			12.2531i			0.534261i
$527$	3.03033	−	22.6151i	0.132003	−	0.985128i
$528$	2.81951	+	4.98044i	0.122703	+	0.216746i
$529$	24.0531	+	17.4756i	1.04578	+	0.759807i
$530$	−4.91128	+	4.79491i	−0.213333	+	0.208278i
$531$	−7.38933	+	32.0830i	−0.320669	+	1.39228i
$532$		−	8.27967i		−	0.358969i
$533$		−	1.08368i		−	0.0469396i
$534$	3.97187	−	4.33681i	0.171880	−	0.187672i
$535$	38.8832	+	6.63730i	1.68107	+	0.286955i
$536$	5.33071	+	1.73205i	0.230251	+	0.0748132i
$537$	−1.14490	+	10.0720i	−0.0494060	+	0.434638i
$538$	3.30559	+	10.1736i	0.142514	+	0.438614i
$539$	−13.4619	−	9.78061i	−0.579843	−	0.421281i
$540$	7.90300	+	8.51719i	0.340091	+	0.366522i
$541$	−9.72862	+	29.9416i	−0.418266	+	1.28729i	0.491031	+	0.871142i	$0.336620\pi$
$541$	−9.72862	+	29.9416i	−0.418266	+	1.28729i	−0.909297	+	0.416148i	$0.863380\pi$
$542$	1.29386	+	1.78085i	0.0555762	+	0.0764940i
$543$	−3.88481	+	8.53033i	−0.166713	+	0.366071i
$544$	3.89752	+	1.26638i	0.167105	+	0.0542956i
$545$	29.4509	+	30.1657i	1.26154	+	1.29215i
$546$	0.249132	+	0.0283192i	0.0106618	+	0.00121195i
$547$	37.3735	−	12.1434i	1.59797	−	0.519213i	0.631369	−	0.775483i	$-0.282493\pi$
$547$	37.3735	−	12.1434i	1.59797	−	0.519213i	0.966605	+	0.256269i	$0.0824935\pi$
$548$	−2.44363	+	3.36337i	−0.104387	+	0.143676i
$549$	31.5474	−	27.4526i	1.34641	−	1.17165i
$550$	0.396115	−	16.5165i	0.0168904	−	0.704268i
$551$	−10.9362	−	33.6582i	−0.465898	−	1.43389i
$552$	10.9453	−	6.19631i	0.465862	−	0.263733i
$553$	12.6211			0.536702
$554$	7.28229	+	22.4126i	0.309395	+	0.952219i
$555$	−8.37276	+	28.8719i	−0.355404	+	1.22554i
$556$	−5.77927	+	7.95449i	−0.245096	+	0.337345i
$557$		−	6.01736i		−	0.254964i	−0.991841	−	0.127482i	$-0.959311\pi$
$557$		−	6.01736i		−	0.254964i	0.991841	−	0.127482i	$-0.0406895\pi$
$558$	−16.1037	+	4.43508i	−0.681725	+	0.187752i
$559$	−1.08752			−0.0459971
$560$	−2.77498	−	1.45609i	−0.117264	−	0.0615311i
$561$	−9.72064	+	21.3447i	−0.410406	+	0.901176i
$562$	−4.36805	+	1.41927i	−0.184255	+	0.0598681i
$563$	−9.11762			−0.384262			−0.192131	−	0.981369i	$-0.561540\pi$
$563$	−9.11762			−0.384262			−0.192131	+	0.981369i	$0.561540\pi$
$564$	5.30889	+	9.37772i	0.223544	+	0.394873i
$565$	−5.75029	+	2.84360i	−0.241916	+	0.119631i
$566$	−4.03061	−	1.30963i	−0.169419	−	0.0550477i
$567$	2.20323	+	12.4194i	0.0925270	+	0.521566i
$568$	4.26326	−	5.86788i	0.178882	−	0.246211i
$569$	8.80748	+	27.1066i	0.369229	+	1.13637i	0.947290	+	0.320376i	$0.103809\pi$
$569$	8.80748	+	27.1066i	0.369229	+	1.13637i	−0.578062	+	0.815993i	$0.696191\pi$
$570$	−22.8692	+	0.729882i	−0.957885	+	0.0305714i
$571$	−9.45769	−	13.0174i	−0.395792	−	0.544761i	0.563890	−	0.825850i	$-0.309304\pi$
$571$	−9.45769	−	13.0174i	−0.395792	−	0.544761i	−0.959682	+	0.281089i	$0.909304\pi$
$572$	0.105469	−	0.324601i	0.00440989	−	0.0135722i
$573$	−12.2288	+	26.8522i	−0.510866	+	1.12177i
$574$	−11.8954	+	8.64251i	−0.496504	+	0.360731i
$575$	−36.2977	−	0.870525i	−1.51372	−	0.0363034i
$576$	−0.263025	−	2.98845i	−0.0109594	−	0.124519i
$577$	−9.31123	+	12.8158i	−0.387632	+	0.533529i	−0.957586	−	0.288147i	$-0.906961\pi$
$577$	−9.31123	+	12.8158i	−0.387632	+	0.533529i	0.569954	+	0.821676i	$0.306961\pi$
$578$	−0.0635500	−	0.195587i	−0.00264333	−	0.00813533i
$579$	39.0149	+	4.43489i	1.62140	+	0.184308i
$580$	−13.2040	−	2.25390i	−0.548267	−	0.0935883i
$581$	−0.0194868	+	0.0599743i	−0.000808450	+	0.00248815i
$582$	14.6891	+	13.4530i	0.608881	+	0.557645i
$583$			10.1427i			0.420068i
$584$	6.00307			0.248409
$585$	0.0562582	−	0.690620i	0.00232599	−	0.0285536i
$586$	−21.4055	+	15.5520i	−0.884255	+	0.642449i
$587$	−4.97236	+	6.84387i	−0.205231	+	0.282477i	−0.899209	−	0.437520i	$-0.855857\pi$
$587$	−4.97236	+	6.84387i	−0.205231	+	0.282477i	0.693977	+	0.719997i	$0.255857\pi$
$588$	4.29707	+	7.59043i	0.177208	+	0.313024i
$589$	14.2292	−	29.6563i	0.586306	−	1.22197i
$590$	−24.2815	+	3.54794i	−0.999652	+	0.146066i
$591$	20.8448	+	2.36946i	0.857441	+	0.0974667i
$592$	6.27945	−	4.56229i	0.258084	−	0.187509i
$593$	0.358338	+	1.10285i	0.0147152	+	0.0452887i	0.958144	−	0.286285i	$-0.0924204\pi$
$593$	0.358338	+	1.10285i	0.0147152	+	0.0452887i	−0.943429	+	0.331574i	$0.892420\pi$
$594$	17.1639	+	0.436022i	0.704243	+	0.0178902i
$595$	−1.85681	−	12.7077i	−0.0761218	−	0.520964i
$596$	−5.43253	+	1.76514i	−0.222525	+	0.0723028i
$597$	0.566834	+	2.78237i	0.0231990	+	0.113875i
$598$	−0.713360	−	0.231785i	−0.0291715	−	0.00947839i
$599$	−8.39806	+	11.5589i	−0.343135	+	0.472285i	−0.945354	−	0.326046i	$-0.894284\pi$
$599$	−8.39806	+	11.5589i	−0.343135	+	0.472285i	0.602219	+	0.798331i	$0.294284\pi$
$600$	−3.77723	+	7.79311i	−0.154205	+	0.318152i
$601$	13.5850	−	18.6981i	0.554144	−	0.762713i	−0.436424	−	0.899741i	$-0.643755\pi$
$601$	13.5850	−	18.6981i	0.554144	−	0.762713i	0.990567	+	0.137028i	$0.0437551\pi$
$602$	8.67308	+	11.9375i	0.353488	+	0.486535i
$603$	12.6848	−	11.0383i	0.516564	−	0.449515i
$604$	9.90507	+	13.6332i	0.403032	+	0.554726i
$605$	0.127886	+	0.130990i	0.00519930	+	0.00532549i
$606$	−1.73487	−	8.51581i	−0.0704744	−	0.345931i
$607$	−2.11469	−	2.91063i	−0.0858328	−	0.118139i	0.763941	−	0.645286i	$-0.223262\pi$
$607$	−2.11469	−	2.91063i	−0.0858328	−	0.118139i	−0.849774	+	0.527147i	$0.823262\pi$
$608$	4.77952	+	3.47252i	0.193835	+	0.140829i
$609$	−10.7236	−	9.82122i	−0.434542	−	0.397976i
$610$	27.6015	+	14.4831i	1.11755	+	0.586403i
$611$	0.198589	−	0.611194i	0.00803405	−	0.0247263i
$612$	9.27440	−	8.07060i	0.374895	−	0.326235i
$613$	−10.7419	−	33.0603i	−0.433862	−	1.33529i	−0.894248	−	0.447572i	$-0.852289\pi$
$613$	−10.7419	−	33.0603i	−0.433862	−	1.33529i	0.460385	−	0.887719i	$-0.347711\pi$
$614$			29.9889i			1.21026i
$615$	24.9200	+	32.0943i	1.00487	+	1.29417i
$616$	−4.40421	+	1.43101i	−0.177450	+	0.0576572i
$617$	−34.7495	+	25.2470i	−1.39896	+	1.01640i	−0.404147	+	0.914694i	$0.632432\pi$
$617$	−34.7495	+	25.2470i	−1.39896	+	1.01640i	−0.994814	+	0.101710i	$0.967568\pi$
$618$	−0.377394	−	0.0428990i	−0.0151810	−	0.00172565i
$619$			8.63187i			0.346944i	0.984839	+	0.173472i	$0.0554986\pi$
$619$			8.63187i			0.346944i	−0.984839	+	0.173472i	$0.944501\pi$
$620$	−7.43709	−	9.98448i	−0.298681	−	0.400986i
$621$	0.958227	−	37.7203i	0.0384523	−	1.51367i
$622$	−10.1101	+	13.9153i	−0.405377	+	0.557954i
$623$	2.79692	+	3.84963i	0.112056	+	0.154232i
$624$	−0.120834	+	0.131936i	−0.00483723	+	0.00528168i
$625$	20.9066	−	13.7082i	0.836264	−	0.548327i
$626$	−0.281294			−0.0112428
$627$	−22.8360	+	24.9342i	−0.911983	+	0.995776i
$628$	0.905767	+	0.294301i	0.0361440	+	0.0117439i
$629$	30.2519	+	9.82942i	1.20622	+	0.391925i
$630$	−8.02946	+	4.89023i	−0.319901	+	0.194832i
$631$	9.24842	−	3.00500i	0.368174	−	0.119627i	−0.119086	−	0.992884i	$-0.537996\pi$
$631$	9.24842	−	3.00500i	0.368174	−	0.119627i	0.487260	+	0.873257i	$0.337996\pi$
$632$	−5.29331	+	7.28562i	−0.210557	+	0.289807i
$633$	−5.22153	−	2.37794i	−0.207537	−	0.0945148i
$634$	7.36714	−	22.6737i	0.292586	−	0.900488i
$635$	3.01276	+	3.08588i	0.119558	+	0.122459i
$636$	2.20353	−	4.83855i	0.0873757	−	0.191861i
$637$	0.160740	−	0.494707i	0.00636875	−	0.0196010i
$638$	−16.0136	+	11.6346i	−0.633986	+	0.460618i
$639$	−8.51247	−	20.0251i	−0.336748	−	0.792180i
$640$	2.00438	−	0.991195i	0.0792300	−	0.0391804i
$641$	15.4994	+	11.2609i	0.612188	+	0.444780i	0.850184	−	0.526486i	$-0.176491\pi$
$641$	15.4994	+	11.2609i	0.612188	+	0.444780i	−0.237996	+	0.971266i	$0.576491\pi$
$642$	−29.9395	+	6.09938i	−1.18162	+	0.240723i
$643$	15.1042	−	46.4858i	0.595650	−	1.83322i	0.0441856	−	0.999023i	$-0.485931\pi$
$643$	15.1042	−	46.4858i	0.595650	−	1.83322i	0.551464	−	0.834199i	$-0.314069\pi$
$644$	3.14487	+	9.67893i	0.123925	+	0.381403i
$645$	32.2078	−	25.0081i	1.26818	−	0.984694i
$646$			24.2107i			0.952558i
$647$	−21.8118	+	7.08708i	−0.857510	+	0.278622i	−0.704588	−	0.709616i	$-0.748868\pi$
$647$	−21.8118	+	7.08708i	−0.857510	+	0.278622i	−0.152922	+	0.988238i	$0.548868\pi$
$648$	−8.09326	−	3.93690i	−0.317933	−	0.154656i
$649$	−21.3143	+	29.3366i	−0.836658	+	1.15156i
$650$	0.494870	−	0.147773i	0.0194104	−	0.00579614i
$651$	−0.915251	−	13.4844i	−0.0358715	−	0.528494i
$652$		−	3.06896i		−	0.120190i
$653$	25.9642	+	18.8641i	1.01606	+	0.738210i	0.965471	−	0.260510i	$-0.0838906\pi$
$653$	25.9642	+	18.8641i	1.01606	+	0.738210i	0.0505877	+	0.998720i	$0.483891\pi$
$654$	−29.7189	−	13.5343i	−1.16210	−	0.529235i
$655$	13.3967	+	27.0906i	0.523452	+	1.05852i
$656$		−	10.4914i		−	0.409621i
$657$	9.26738	−	15.4417i	0.361555	−	0.602440i
$658$	−8.29273	+	2.69447i	−0.323284	+	0.105041i
$659$	−43.1842	−	14.0314i	−1.68222	−	0.546586i	−0.696878	−	0.717189i	$-0.745428\pi$
$659$	−43.1842	−	14.0314i	−1.68222	−	0.546586i	−0.985340	+	0.170604i	$0.945428\pi$
$660$	4.34083	+	12.0387i	0.168967	+	0.468604i
$661$	−33.4302	−	24.2884i	−1.30028	−	0.944711i	−0.300325	−	0.953837i	$-0.597095\pi$
$661$	−33.4302	−	24.2884i	−1.30028	−	0.944711i	−0.999958	+	0.00912623i	$0.997095\pi$
$662$	−11.3558	+	3.68972i	−0.441355	+	0.143405i
$663$	−0.728489	−	0.0828085i	−0.0282922	−	0.00321602i
$664$	−0.0264479	−	0.0364024i	−0.00102638	−	0.00141269i
$665$	3.11523	−	18.2499i	0.120804	−	0.707702i
$666$	−2.04156	−	23.1958i	−0.0791087	−	0.898820i
$667$	25.5688	+	35.1925i	0.990029	+	1.36266i
$668$	−10.8604	−	3.52876i	−0.420202	−	0.136532i
$669$	−39.4238	−	17.9540i	−1.52421	−	0.694143i
$670$	11.0982	+	5.82345i	0.428760	+	0.224979i
$671$	43.8066	−	14.2336i	1.69114	−	0.549483i
$672$	2.41190	+	0.274165i	0.0930412	+	0.0105761i
$673$	−9.20373	+	28.3262i	−0.354778	+	1.09189i	0.601361	+	0.798978i	$0.294625\pi$
$673$	−9.20373	+	28.3262i	−0.354778	+	1.09189i	−0.956138	+	0.292916i	$0.905375\pi$
$674$	7.79505	−	23.9907i	0.300254	−	0.924087i
$675$	14.2151	+	21.7470i	0.547139	+	0.837042i
$676$	−12.9893			−0.499590
$677$			14.8329i			0.570075i	0.958516	+	0.285037i	$0.0920060\pi$
$677$			14.8329i			0.570075i	−0.958516	+	0.285037i	$0.907994\pi$
$678$	3.35606	−	3.66442i	0.128889	−	0.140731i
$679$	−13.0390	+	9.47337i	−0.500390	+	0.363554i
$680$	8.11437	+	4.25778i	0.311172	+	0.163278i
$681$	3.18367	+	5.62369i	0.121998	+	0.215500i
$682$	−18.2344	−	2.44333i	−0.698230	−	0.0935600i
$683$	45.7239			1.74958			0.874789	−	0.484505i	$-0.161000\pi$
$683$	45.7239			1.74958			0.874789	+	0.484505i	$0.161000\pi$
$684$	16.3109	−	6.93359i	0.623662	−	0.265113i
$685$	−6.65169	+	6.49407i	−0.254148	+	0.248126i
$686$	−16.0424	+	5.21250i	−0.612503	+	0.199014i
$687$	−10.9948	+	6.22436i	−0.419479	+	0.237474i
$688$	−10.5285			−0.401396
$689$	−0.301547	+	0.0979786i	−0.0114880	+	0.00373269i
$690$	26.4568	−	9.53965i	1.00719	−	0.363168i
$691$	2.96197	−	9.11600i	0.112679	−	0.346789i	−0.878777	−	0.477232i	$-0.841640\pi$
$691$	2.96197	−	9.11600i	0.112679	−	0.346789i	0.991456	+	0.130443i	$0.0416401\pi$
$692$	19.8952	+	14.4547i	0.756302	+	0.549486i
$693$	−3.11809	+	13.5381i	−0.118446	+	0.514271i
$694$	−12.3953	+	17.0606i	−0.470517	+	0.647612i
$695$	−15.7315	+	15.3587i	−0.596729	+	0.582589i
$696$	10.1669	−	2.07124i	0.385375	−	0.0785101i
$697$	34.7835	−	25.2717i	1.31752	−	0.957234i
$698$	0.000174721	0	0.000126942i	6.61328e−6	0	4.80483e-6i
$699$	24.6384	−	5.01943i	0.931911	−	0.189852i
$700$	−5.56872	−	4.25359i	−0.210478	−	0.160770i
$701$	−24.0063	+	33.0419i	−0.906707	+	1.24797i	0.0615721	+	0.998103i	$0.480389\pi$
$701$	−24.0063	+	33.0419i	−0.906707	+	1.24797i	−0.968279	+	0.249872i	$0.919611\pi$
$702$	0.152840	+	0.514502i	0.00576858	+	0.0194186i
$703$	37.0978	+	26.9531i	1.39917	+	1.01656i
$704$	1.02107	−	3.14254i	0.0384831	−	0.118439i
$705$	8.17340	+	22.6677i	0.307828	+	0.853715i
$706$	6.97470	−	2.26622i	0.262496	−	0.0852902i
$707$	7.03207			0.264468
$708$	16.5413	−	9.36433i	0.621662	−	0.351933i
$709$	−1.41536	+	0.459878i	−0.0531549	+	0.0172711i	−0.335474	−	0.942050i	$-0.608896\pi$
$709$	−1.41536	+	0.459878i	−0.0531549	+	0.0172711i	0.282319	+	0.959321i	$0.408896\pi$
$710$	11.6048	−	11.3298i	0.435521	−	0.425201i
$711$	10.5692	+	24.8634i	0.396375	+	0.932450i
$712$	−3.39527			−0.127243
$713$	−5.36960	+	40.0729i	−0.201093	+	1.50074i
$714$	4.90081	+	8.65689i	0.183408	+	0.323976i
$715$	0.354605	−	0.675797i	0.0132615	−	0.0252734i
$716$	4.73478	−	3.44002i	0.176947	−	0.128560i
$717$	−34.9794	+	38.1933i	−1.30633	+	1.42636i
$718$			4.07084i			0.151922i
$719$	−49.3096			−1.83894			−0.919469	−	0.393163i	$-0.871381\pi$
$719$	−49.3096			−1.83894			−0.919469	+	0.393163i	$0.871381\pi$
$720$	0.544650	−	6.68606i	0.0202979	−	0.249175i
$721$	0.0949711	−	0.292291i	0.00353691	−	0.0108855i
$722$	−4.91404	+	15.1239i	−0.182882	+	0.562852i
$723$	−39.9076	−	4.53636i	−1.48418	−	0.168709i
$724$	5.14680	−	1.67230i	0.191279	−	0.0621504i
$725$	−28.2561	−	9.93605i	−1.04940	−	0.369016i
$726$	−0.129050	−	0.0587708i	−0.00478949	−	0.00218119i
$727$	12.0664	+	3.92062i	0.447519	+	0.145408i	0.524102	−	0.851655i	$-0.324401\pi$
$727$	12.0664	+	3.92062i	0.447519	+	0.145408i	−0.0765829	+	0.997063i	$0.524401\pi$
$728$	−0.0850892	−	0.117115i	−0.00315362	−	0.00434058i
$729$	−22.6211	+	14.7406i	−0.837818	+	0.545950i
$730$	13.2319	+	2.25866i	0.489734	+	0.0835968i
$731$	−25.3611	−	34.9065i	−0.938013	−	1.29106i
$732$	−23.9901	−	2.72699i	−0.886699	−	0.100793i
$733$	9.52379	−	3.09447i	0.351769	−	0.114297i	−0.127802	−	0.991800i	$-0.540792\pi$
$733$	9.52379	−	3.09447i	0.351769	−	0.114297i	0.479571	+	0.877503i	$0.340792\pi$
$734$	2.13027	+	1.54773i	0.0786298	+	0.0571279i
$735$	6.61564	+	18.3475i	0.244021	+	0.676757i
$736$	−6.90622	−	2.24397i	−0.254567	−	0.0827137i
$737$	17.6140	−	5.72315i	0.648821	−	0.210815i
$738$	−26.9871	−	16.1964i	−0.993410	−	0.596197i
$739$			5.27335i			0.193983i	0.995285	+	0.0969917i	$0.0309220\pi$
$739$			5.27335i			0.193983i	−0.995285	+	0.0969917i	$0.969078\pi$
$740$	15.5576	−	7.69348i	0.571910	−	0.282818i
$741$	−0.961901	−	0.438061i	−0.0353363	−	0.0160926i
$742$	3.48037	+	2.52863i	0.127768	+	0.0928290i
$743$			14.6805i			0.538574i	0.963060	+	0.269287i	$0.0867881\pi$
$743$			14.6805i			0.538574i	−0.963060	+	0.269287i	$0.913212\pi$
$744$	8.16783	+	5.12705i	0.299447	+	0.187967i
$745$	−12.6384	+	1.84669i	−0.463036	+	0.0676576i
$746$	14.1910	−	19.5322i	0.519568	−	0.715124i
$747$	−0.134468	+	0.0118350i	−0.00491991	+	0.000433021i
$748$	12.8784	−	4.18445i	0.470881	−	0.152999i
$749$		−	24.7230i		−	0.903358i
$750$	−11.2579	+	15.7563i	−0.411080	+	0.575338i
$751$	−0.527574	−	1.62371i	−0.0192514	−	0.0592499i	0.940969	−	0.338492i	$-0.109917\pi$
$751$	−0.527574	−	1.62371i	−0.0192514	−	0.0592499i	−0.960221	+	0.279242i	$0.909917\pi$
$752$	1.92259	−	5.91712i	0.0701096	−	0.215775i
$753$	−2.93784	+	0.598508i	−0.107061	+	0.0218108i
$754$	−0.500593	−	0.363702i	−0.0182305	−	0.0132452i
$755$	16.7031	+	33.7768i	0.607889	+	1.22926i
$756$	4.42867	−	5.78091i	0.161069	−	0.210250i
$757$	35.8132	−	26.0198i	1.30165	−	0.945705i	0.301681	−	0.953409i	$-0.402452\pi$
$757$	35.8132	−	26.0198i	1.30165	−	0.945705i	0.999970	+	0.00770367i	$0.00245218\pi$
$758$	4.57340	−	14.0755i	0.166113	−	0.511245i
$759$	17.2245	−	37.8219i	0.625210	−	1.37285i
$760$	9.22840	+	9.45238i	0.334749	+	0.342874i
$761$	12.3535	−	38.0202i	0.447815	−	1.37823i	−0.431553	−	0.902088i	$-0.642034\pi$
$761$	12.3535	−	38.0202i	0.447815	−	1.37823i	0.879367	−	0.476144i	$-0.157966\pi$
$762$	−3.04018	−	1.38453i	−0.110134	−	0.0501563i
$763$	15.5312	−	21.3768i	0.562265	−	0.773892i
$764$	16.2014	−	5.26414i	0.586145	−	0.190450i
$765$	23.4791	−	14.2996i	0.848888	−	0.517004i
$766$	−4.87538	−	1.58411i	−0.176155	−	0.0572361i
$767$	−1.07808	−	0.350291i	−0.0389274	−	0.0126483i
$768$	−1.16982	+	1.27731i	−0.0422124	+	0.0460908i
$769$	16.4446			0.593007			0.296503	−	0.955032i	$-0.404179\pi$
$769$	16.4446			0.593007			0.296503	+	0.955032i	$0.404179\pi$
$770$	−10.2461	+	1.49713i	−0.369244	+	0.0539529i
$771$	−34.1759	+	37.3159i	−1.23081	+	1.34390i
$772$	−13.3253	−	18.3407i	−0.479588	−	0.660096i
$773$	−21.8532	+	30.0784i	−0.786006	+	1.08184i	0.208588	+	0.978004i	$0.433113\pi$
$773$	−21.8532	+	30.0784i	−0.786006	+	1.08184i	−0.994594	+	0.103841i	$0.966887\pi$
$774$	−16.2537	+	27.0826i	−0.584225	+	0.973464i
$775$	−12.6361	−	24.8059i	−0.453900	−	0.891052i
$776$		−	11.5000i		−	0.412827i
$777$	18.7208	+	2.12802i	0.671604	+	0.0763423i
$778$	1.89882	−	1.37958i	0.0680761	−	0.0494602i
$779$	58.9477	−	19.1533i	2.11202	−	0.686237i
$780$	−0.315982	+	0.245348i	−0.0113140	+	0.00878487i
$781$		−	23.9661i		−	0.857575i
$782$	−9.19598	−	28.3023i	−0.328847	−	1.01209i
$783$	10.3675	−	29.3499i	0.370505	−	1.04888i
$784$	1.55616	−	4.78938i	0.0555773	−	0.171049i
$785$	1.88575	+	0.989490i	0.0673052	+	0.0353164i
$786$	−17.2637	−	15.8110i	−0.615776	−	0.563959i
$787$	−38.1794	−	27.7389i	−1.36095	−	0.988786i	−0.998384	−	0.0568272i	$-0.981902\pi$
$787$	−38.1794	−	27.7389i	−1.36095	−	0.988786i	−0.362564	−	0.931959i	$-0.618098\pi$
$788$	−7.11941	−	9.79902i	−0.253618	−	0.349076i
$789$	−4.23661	−	20.7959i	−0.150827	−	0.740352i
$790$	−14.4087	+	14.0673i	−0.512638	+	0.500490i
$791$	2.36328	+	3.25278i	0.0840286	+	0.115656i
$792$	−6.50727	−	7.47788i	−0.231226	−	0.265715i
$793$	0.846344	+	1.16489i	0.0300545	+	0.0413665i
$794$	−4.13205	+	5.68729i	−0.146641	+	0.201834i
$795$	6.67750	−	9.83598i	0.236827	−	0.348846i
$796$	0.963613	−	1.32630i	0.0341544	−	0.0470094i
$797$	−25.3699	−	8.24318i	−0.898648	−	0.291988i	−0.176969	−	0.984216i	$-0.556629\pi$
$797$	−25.3699	−	8.24318i	−0.898648	−	0.291988i	−0.721679	+	0.692228i	$0.756629\pi$
$798$	2.86276	+	14.0522i	0.101341	+	0.497442i
$799$	24.2489	−	7.87894i	0.857864	−	0.278737i
$800$	4.79096	−	1.43063i	0.169386	−	0.0505803i
$801$	−5.24153	+	8.73368i	−0.185200	+	0.308590i
$802$	6.28212	+	19.3344i	0.221829	+	0.682721i
$803$	16.0474	−	11.6591i	0.566301	−	0.411442i
$804$	−9.64609	−	1.09649i	−0.340191	−	0.0386701i
$805$	3.29018	+	22.5174i	0.115964	+	0.793635i
$806$	−0.103503	−	0.565718i	−0.00364573	−	0.0199266i
$807$	−9.12781	−	16.1235i	−0.321314	−	0.567576i
$808$	−2.94927	+	4.05932i	−0.103755	+	0.142806i
$809$	5.23875	−	3.80618i	0.184185	−	0.133818i	−0.491872	−	0.870667i	$-0.663687\pi$
$809$	5.23875	−	3.80618i	0.184185	−	0.133818i	0.676057	+	0.736849i	$0.263687\pi$
$810$	−16.3578	−	11.7228i	−0.574754	−	0.411896i
$811$	17.1558			0.602420			0.301210	−	0.953558i	$-0.402609\pi$
$811$	17.1558			0.602420			0.301210	+	0.953558i	$0.402609\pi$
$812$			8.39547i			0.294623i
$813$	−2.81167	−	2.57507i	−0.0986096	−	0.0903118i
$814$	7.92539	−	24.3918i	0.277785	−	0.854934i
$815$	1.15470	−	6.76456i	0.0404473	−	0.236952i
$816$	−7.05268	−	0.801690i	−0.246893	−	0.0280648i
$817$	−19.2210	−	59.1561i	−0.672458	−	2.06961i
$818$	−2.46517	+	3.39302i	−0.0861928	+	0.118634i
$819$	−0.432615	+	0.0380762i	−0.0151168	+	0.00133049i
$820$	3.94740	−	23.1250i	0.137849	−	0.807561i
$821$	−16.3110	+	11.8507i	−0.569259	+	0.413591i	−0.834836	−	0.550499i	$-0.814438\pi$
$821$	−16.3110	+	11.8507i	−0.569259	+	0.413591i	0.265577	+	0.964090i	$0.414438\pi$
$822$	2.98439	−	6.55318i	0.104093	−	0.228568i
$823$	−7.82351	+	24.0783i	−0.272710	+	0.839316i	0.717106	+	0.696964i	$0.245466\pi$
$823$	−7.82351	+	24.0783i	−0.272710	+	0.839316i	−0.989816	+	0.142352i	$0.954534\pi$
$824$	0.128896	+	0.177411i	0.00449032	+	0.00618040i
$825$	5.03844	+	28.1687i	0.175416	+	0.980707i
$826$	4.75277	+	14.6275i	0.165370	+	0.508957i
$827$	0.537927	−	0.740393i	0.0187055	−	0.0257460i	−0.799562	−	0.600584i	$-0.794935\pi$
$827$	0.537927	−	0.740393i	0.0187055	−	0.0257460i	0.818267	+	0.574838i	$0.194935\pi$
$828$	−16.4338	+	14.3007i	−0.571114	+	0.496985i
$829$	28.8786	+	9.38324i	1.00300	+	0.325893i	0.764062	−	0.645143i	$-0.223202\pi$
$829$	28.8786	+	9.38324i	1.00300	+	0.325893i	0.238934	+	0.971036i	$0.423202\pi$
$830$	−0.0445996	−	0.0901886i	−0.00154807	−	0.00313049i
$831$	−20.1087	−	35.5205i	−0.697565	−	1.23219i
$832$	0.103293			0.00358102
$833$	19.6273	−	6.37730i	0.680046	−	0.220960i
$834$	7.05819	−	15.4985i	0.244405	−	0.536669i
$835$	−22.6107	−	11.8643i	−0.782475	−	0.410581i
$836$	19.5209			0.675145
$837$	25.7976	−	13.0952i	0.891696	−	0.452635i
$838$			0.595000i			0.0205539i
$839$	13.3577	−	18.3852i	0.461158	−	0.634729i	−0.513591	−	0.858035i	$-0.671685\pi$
$839$	13.3577	−	18.3852i	0.461158	−	0.634729i	0.974748	+	0.223306i	$0.0716850\pi$
$840$	5.21313	+	1.51179i	0.179870	+	0.0521617i
$841$	2.12766	+	6.54828i	0.0733677	+	0.225803i
$842$	8.73584			0.301057
$843$	6.92268	−	3.91905i	0.238430	−	0.134979i
$844$	1.02363	+	3.15042i	0.0352350	+	0.108442i
$845$	−28.6309	−	4.88725i	−0.984933	−	0.168126i
$846$	−12.2526	−	14.0802i	−0.421253	−	0.484087i
$847$	0.0674417	−	0.0928255i	0.00231732	−	0.00318952i
$848$	−2.91935	+	0.948555i	−0.100251	+	0.0325735i
$849$	7.29353	+	0.829067i	0.250313	+	0.0284535i
$850$	16.2836	+	12.4380i	0.558523	+	0.426619i
$851$	−53.6049	−	17.4173i	−1.83755	−	0.597057i
$852$	−5.20670	+	11.4330i	−0.178379	+	0.391686i
$853$	19.7309	+	27.1573i	0.675573	+	0.929847i	0.999870	−	0.0161084i	$-0.00512769\pi$
$853$	19.7309	+	27.1573i	0.675573	+	0.929847i	−0.324297	+	0.945955i	$0.605128\pi$
$854$	6.03710	−	18.5803i	0.206585	−	0.635804i
$855$	38.5610	−	9.14595i	1.31876	−	0.312785i
$856$	14.2716	+	10.3689i	0.487792	+	0.354402i
$857$	8.10401	+	24.9416i	0.276828	+	0.851989i	0.988730	+	0.149710i	$0.0478340\pi$
$857$	8.10401	+	24.9416i	0.276828	+	0.851989i	−0.711902	+	0.702279i	$0.752166\pi$
$858$	−0.0667679	+	0.587375i	−0.00227942	+	0.0200527i
$859$	24.0920	+	7.82795i	0.822007	+	0.267086i	0.689675	−	0.724119i	$-0.257753\pi$
$859$	24.0920	+	7.82795i	0.822007	+	0.267086i	0.132332	+	0.991205i	$0.457753\pi$
$860$	−23.2068	−	3.96137i	−0.791346	−	0.135081i
$861$	17.2005	−	18.7809i	0.586192	−	0.640051i
$862$			26.7728i			0.911884i
$863$		−	21.0648i		−	0.717053i	−0.933519	−	0.358527i	$-0.883279\pi$
$863$		−	21.0648i		−	0.717053i	0.933519	−	0.358527i	$-0.116721\pi$
$864$	1.47968	+	4.98102i	0.0503398	+	0.169458i
$865$	38.4141	+	39.3465i	1.30612	+	1.33782i
$866$	−6.31451	−	4.58776i	−0.214576	−	0.155898i
$867$	0.175482	+	0.309975i	0.00595968	+	0.0105273i
$868$	−5.38433	+	5.64779i	−0.182756	+	0.191699i
$869$			29.7566i			1.00942i
$870$	23.1890	−	0.740090i	0.786182	−	0.0250914i
$871$	0.340303	+	0.468387i	0.0115307	+	0.0158707i
$872$	5.82613	+	17.9310i	0.197298	+	0.607220i
$873$	−29.5816	−	17.7534i	−1.00118	−	0.600862i
$874$		−	42.9003i		−	1.45112i
$875$	−10.6741	−	11.4709i	−0.360850	−	0.387788i
$876$	−10.1884	+	2.07561i	−0.344232	+	0.0701283i
$877$	−43.7849	−	14.2266i	−1.47851	−	0.480398i	−0.544844	−	0.838537i	$-0.683411\pi$
$877$	−43.7849	−	14.2266i	−1.47851	−	0.480398i	−0.933668	+	0.358140i	$0.883411\pi$
$878$	7.56371	+	5.49536i	0.255263	+	0.185459i
$879$	30.9520	−	33.7959i	1.04399	−	1.13991i
$880$	3.43302	−	6.54256i	0.115727	−	0.220550i
$881$	−21.2811	+	15.4616i	−0.716978	+	0.520915i	−0.885417	−	0.464797i	$-0.846127\pi$
$881$	−21.2811	+	15.4616i	−0.716978	+	0.520915i	0.168439	+	0.985712i	$0.446127\pi$
$882$	−9.91739	−	11.3966i	−0.333936	−	0.383745i
$883$	46.6379	−	33.8844i	1.56949	−	1.14030i	0.641850	−	0.766830i	$-0.278167\pi$
$883$	46.6379	−	33.8844i	1.56949	−	1.14030i	0.927642	−	0.373472i	$-0.121833\pi$
$884$	0.248811	+	0.342459i	0.00836841	+	0.0115181i
$885$	39.9835	−	14.4170i	1.34403	−	0.484623i
$886$	4.05780	−	2.94816i	0.136324	−	0.0990455i
$887$	15.1520	+	11.0085i	0.508753	+	0.369631i	0.812350	−	0.583170i	$-0.198188\pi$
$887$	15.1520	+	11.0085i	0.508753	+	0.369631i	−0.303597	+	0.952800i	$0.598188\pi$
$888$	−9.07997	+	9.91424i	−0.304704	+	0.332700i
$889$	1.58880	−	2.18680i	0.0532867	−	0.0733429i
$890$	−7.48381	−	1.27747i	−0.250858	−	0.0428210i
$891$	−29.2811	+	5.19454i	−0.980955	+	0.174024i
$892$	7.72868	+	23.7864i	0.258775	+	0.796429i
$893$	36.7562			1.23000
$894$	8.60972	−	4.87411i	0.287952	−	0.163015i
$895$	11.7307	−	5.80098i	0.392113	−	0.193905i
$896$	−0.823770	−	1.13382i	−0.0275202	−	0.0378783i
$897$	1.29085	+	0.146733i	0.0431002	+	0.00489927i
$898$	15.2011			0.507266
$899$	−14.4283	+	30.0711i	−0.481209	+	1.00293i
$900$	3.71614	−	14.5324i	0.123871	−	0.484413i
$901$	−10.1770	−	7.39402i	−0.339045	−	0.246330i
$902$	−20.3764	−	28.0457i	−0.678459	−	0.933819i
$903$	−18.8473	−	17.2614i	−0.627200	−	0.574422i
$904$	−2.86886			−0.0954170
$905$	11.9737	−	1.74956i	0.398019	−	0.0581574i
$906$	−21.5246	−	19.7133i	−0.715106	−	0.654931i
$907$	−15.5038	−	5.03748i	−0.514794	−	0.167267i	0.0400874	−	0.999196i	$-0.487236\pi$
$907$	−15.5038	−	5.03748i	−0.514794	−	0.167267i	−0.554881	+	0.831929i	$0.687236\pi$
$908$	1.15295	−	3.54842i	0.0382620	−	0.117758i
$909$	5.88882	+	13.8531i	0.195320	+	0.459478i
$910$	−0.143488	−	0.290159i	−0.00475657	−	0.00961867i
$911$	2.47095	+	1.79525i	0.0818663	+	0.0594793i	0.627966	−	0.778241i	$-0.283888\pi$
$911$	2.47095	+	1.79525i	0.0818663	+	0.0594793i	−0.546099	+	0.837720i	$0.683888\pi$
$912$	−9.31239	−	4.24097i	−0.308364	−	0.140433i
$913$	−0.141401	−	0.0459440i	−0.00467969	−	0.00152052i
$914$	−8.39371	+	6.09839i	−0.277639	+	0.201717i
$915$	−51.8526	−	15.0371i	−1.71419	−	0.497111i
$916$	6.93748	+	2.25412i	0.229221	+	0.0744784i
$917$	15.3244	−	11.1338i	0.506056	−	0.367671i
$918$	−12.9499	+	16.9040i	−0.427412	+	0.557916i
$919$	10.6001	+	32.6237i	0.349664	+	1.07616i	0.959039	+	0.283273i	$0.0914204\pi$
$919$	10.6001	+	32.6237i	0.349664	+	1.07616i	−0.609375	+	0.792882i	$0.708580\pi$
$920$	−14.3783	−	7.54459i	−0.474038	−	0.248738i
$921$	−10.3689	−	50.8969i	−0.341667	−	1.67711i
$922$	−2.27642	+	7.00611i	−0.0749700	+	0.230734i
$923$	0.712522	−	0.231513i	0.0234530	−	0.00762033i
$924$	6.97999	−	3.95149i	0.229625	−	0.129994i
$925$	37.1866	−	11.1043i	1.22269	−	0.365107i
$926$	−1.26414	−	3.89061i	−0.0415421	−	0.127853i
$927$	0.655342	−	0.0576792i	0.0215242	−	0.00189443i
$928$	−4.84636	−	3.52109i	−0.159090	−	0.115585i
$929$	−19.8791			−0.652211			−0.326105	−	0.945333i	$-0.605736\pi$
$929$	−19.8791			−0.652211			−0.326105	+	0.945333i	$0.605736\pi$
$930$	16.0744	+	14.3741i	0.527099	+	0.471346i
$931$	29.7508			0.975044
$932$	−11.7447	−	8.53299i	−0.384709	−	0.279508i
$933$	12.3474	−	27.1126i	0.404235	−	0.887626i
$934$	0.186526	+	0.574067i	0.00610331	+	0.0187841i
$935$	29.9608	−	4.37779i	0.979823	−	0.143169i
$936$	0.159460	−	0.265700i	0.00521212	−	0.00868468i
$937$	−45.0970	+	14.6529i	−1.47325	+	0.478689i	−0.932090	−	0.362227i	$-0.882016\pi$
$937$	−45.0970	+	14.6529i	−1.47325	+	0.478689i	−0.541164	+	0.840917i	$0.682016\pi$
$938$	2.42744	−	7.47088i	0.0792586	−	0.243933i
$939$	0.477409	−	0.0972596i	0.0155797	−	0.00317395i
$940$	6.46406	−	12.3191i	0.210835	−	0.401803i
$941$	10.0407	+	30.9022i	0.327318	+	1.00738i	0.970383	+	0.241571i	$0.0776626\pi$
$941$	10.0407	+	30.9022i	0.327318	+	1.00738i	−0.643065	+	0.765812i	$0.722337\pi$
$942$	−1.63901	−	0.186309i	−0.0534020	−	0.00607029i
$943$	−61.6347	+	44.7803i	−2.00710	+	1.45825i
$944$	−10.4372	−	3.39125i	−0.339702	−	0.110376i
$945$	11.9367	−	11.0759i	0.388300	−	0.360299i
$946$	−28.1449	+	20.4484i	−0.915068	+	0.664836i
$947$	−13.2725	−	4.31249i	−0.431298	−	0.140137i	0.0853194	−	0.996354i	$-0.472809\pi$
$947$	−13.2725	−	4.31249i	−0.431298	−	0.140137i	−0.516617	+	0.856217i	$0.672809\pi$
$948$	6.46470	−	14.1953i	0.209964	−	0.461041i
$949$	0.501649	+	0.364469i	0.0162842	+	0.0118312i
$950$	16.7846	+	24.3070i	0.544566	+	0.788623i
$951$	−4.66381	+	41.0288i	−0.151234	+	1.33045i
$952$	1.77481	−	5.46229i	0.0575218	−	0.177034i
$953$	27.2348	+	8.84913i	0.882222	+	0.286651i	0.714880	−	0.699247i	$-0.246481\pi$
$953$	27.2348	+	8.84913i	0.882222	+	0.286651i	0.167343	+	0.985899i	$0.446481\pi$
$954$	−2.06684	+	8.97382i	−0.0669165	+	0.290538i
$955$	37.6915	−	5.50737i	1.21967	−	0.178214i
$956$	29.9014			0.967082
$957$	23.1554	−	25.2829i	0.748508	−	0.817281i
$958$	−9.36211	−	12.8858i	−0.302476	−	0.416322i
$959$	4.71370	+	3.42470i	0.152213	+	0.110589i
$960$	−3.05910	+	2.37527i	−0.0987319	+	0.0766616i
$961$	−28.9919	+	10.9760i	−0.935221	+	0.354064i
$962$	0.801739			0.0258491
$963$	48.7041	−	20.7036i	1.56947	−	0.667165i
$964$	13.6302	+	18.7603i	0.438999	+	0.604230i
$965$	−22.4707	−	45.4399i	−0.723358	−	1.46276i
$966$	−8.68401	−	15.3396i	−0.279403	−	0.493544i
$967$	−11.2045			−0.360311			−0.180156	−	0.983638i	$-0.557660\pi$
$967$	−11.2045			−0.360311			−0.180156	+	0.983638i	$0.557660\pi$
$968$	0.0252991	+	0.0778626i	0.000813144	+	0.00250260i
$969$	−8.37105	−	41.0902i	−0.268917	−	1.32001i
$970$	4.32689	−	25.3482i	0.138928	−	0.813881i
$971$	30.5081	−	41.9907i	0.979050	−	1.34755i	0.0417104	−	0.999130i	$-0.486719\pi$
$971$	30.5081	−	41.9907i	0.979050	−	1.34755i	0.937340	−	0.348417i	$-0.113281\pi$
$972$	15.0970	+	3.88337i	0.484237	+	0.124559i
$973$	11.1481	+	8.09954i	0.357390	+	0.259659i
$974$	3.83577	−	2.78685i	0.122906	−	0.0892964i
$975$	−0.788795	+	0.421904i	−0.0252617	+	0.0135118i
$976$	8.19366	+	11.2776i	0.262273	+	0.360987i
$977$	29.0277	−	21.0899i	0.928679	−	0.674725i	−0.0169902	−	0.999856i	$-0.505408\pi$
$977$	29.0277	−	21.0899i	0.928679	−	0.674725i	0.945669	+	0.325131i	$0.105408\pi$
$978$	1.06112	+	5.20860i	0.0339308	+	0.166553i
$979$	−9.07625	+	6.59428i	−0.290078	+	0.210754i
$980$	5.23208	−	9.97118i	0.167133	−	0.318518i
$981$	55.1182	+	12.6948i	1.75979	+	0.405313i
$982$	2.86437	+	2.08109i	0.0914059	+	0.0664102i
$983$	9.56549	+	3.10802i	0.305092	+	0.0991304i	0.457562	−	0.889178i	$-0.348723\pi$
$983$	9.56549	+	3.10802i	0.305092	+	0.0991304i	−0.152470	+	0.988308i	$0.548723\pi$
$984$	3.62749	+	17.8059i	0.115640	+	0.567632i
$985$	−12.0056	−	24.2775i	−0.382530	−	0.773547i
$986$		−	24.5493i		−	0.781810i
$987$	13.1427	−	7.44030i	0.418337	−	0.236827i
$988$	0.188572	+	0.580365i	0.00599928	+	0.0184639i
$989$	44.9386	+	61.8527i	1.42897	+	1.96680i
$990$	−11.5297	−	18.9310i	−0.366437	−	0.601667i
$991$		−	52.7846i		−	1.67676i	−0.545089	−	0.838378i	$-0.683504\pi$
$991$		−	52.7846i		−	1.67676i	0.545089	−	0.838378i	$-0.316496\pi$
$992$	−1.00204	−	5.47685i	−0.0318146	−	0.173890i
$993$	17.9972	−	10.1885i	0.571123	−	0.323322i
$994$	−8.22371	−	5.97488i	−0.260840	−	0.189512i
$995$	2.62300	−	2.56085i	0.0831548	−	0.0811844i
$996$	0.0574734	+	0.0526371i	0.00182112	+	0.00166787i
$997$			22.3671i			0.708372i	0.935175	+	0.354186i	$0.115242\pi$
$997$			22.3671i			0.708372i	−0.935175	+	0.354186i	$0.884758\pi$
$998$		−	18.4602i		−	0.584347i
$999$	11.4850	+	38.6618i	0.363371	+	1.22321i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.y.b.29.4	yes	128
3.2	odd	2		930.2.y.a.29.19	✓	128
5.4	even	2		930.2.y.a.29.29	yes	128
15.14	odd	2	inner	930.2.y.b.29.14	yes	128
31.15	odd	10	inner	930.2.y.b.449.14	yes	128
93.77	even	10		930.2.y.a.449.29	yes	128
155.139	odd	10		930.2.y.a.449.19	yes	128
465.449	even	10	inner	930.2.y.b.449.4	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.y.a.29.19	✓	128	3.2	odd	2
930.2.y.a.29.29	yes	128	5.4	even	2
930.2.y.a.449.19	yes	128	155.139	odd	10
930.2.y.a.449.29	yes	128	93.77	even	10
930.2.y.b.29.4	yes	128	1.1	even	1	trivial
930.2.y.b.29.14	yes	128	15.14	odd	2	inner
930.2.y.b.449.4	yes	128	465.449	even	10	inner
930.2.y.b.449.14	yes	128	31.15	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-1.57629 - 0.717859i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.323295 + 2.21257i) q^{5} +(-0.853296 - 1.50728i) q^{6} +(1.33289 - 0.433081i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.96936 + 2.26310i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-1.57629 - 0.717859i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.323295 + 2.21257i) q^{5} +(-0.853296 - 1.50728i) q^{6} +(1.33289 - 0.433081i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.96936 + 2.26310i) q^{9} +(-1.03897 + 1.98004i) q^{10} +(1.02107 + 3.14254i) q^{11} +(0.195625 - 1.72097i) q^{12} +(-0.0835654 + 0.0607138i) q^{13} +(1.33289 + 0.433081i) q^{14} +(1.07871 - 3.71973i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-3.89752 - 1.26638i) q^{17} +(0.263025 + 2.98845i) q^{18} +(-4.77952 - 3.47252i) q^{19} +(-2.00438 + 0.991195i) q^{20} +(-2.41190 - 0.274165i) q^{21} +(-1.02107 + 3.14254i) q^{22} +(6.90622 + 2.24397i) q^{23} +(1.16982 - 1.27731i) q^{24} +(-4.79096 + 1.43063i) q^{25} -0.103293 q^{26} +(-1.47968 - 4.98102i) q^{27} +(0.823770 + 1.13382i) q^{28} +(4.84636 + 3.52109i) q^{29} +(3.05910 - 2.37527i) q^{30} +(1.00204 + 5.47685i) q^{31} -1.00000 q^{32} +(0.646396 - 5.68652i) q^{33} +(-2.40880 - 3.31543i) q^{34} +(1.38914 + 2.80910i) q^{35} +(-1.54377 + 2.57231i) q^{36} -7.76183 q^{37} +(-1.82561 - 5.61866i) q^{38} +(0.175307 - 0.0357142i) q^{39} +(-2.20419 - 0.376251i) q^{40} +(-6.16670 + 8.48773i) q^{41} +(-1.79012 - 1.63949i) q^{42} +(8.51775 + 6.18851i) q^{43} +(-2.67320 + 1.94219i) q^{44} +(-4.37060 + 5.08900i) q^{45} +(4.26828 + 5.87478i) q^{46} +(-5.03340 + 3.65698i) q^{47} +(1.69719 - 0.345758i) q^{48} +(-4.07409 + 2.96000i) q^{49} +(-4.71687 - 1.65865i) q^{50} +(5.23452 + 4.79404i) q^{51} +(-0.0835654 - 0.0607138i) q^{52} +(2.91935 + 0.948555i) q^{53} +(1.73068 - 4.89946i) q^{54} +(-6.62299 + 3.27516i) q^{55} +1.40148i q^{56} +(5.04110 + 8.90471i) q^{57} +(1.85115 + 5.69724i) q^{58} +(6.45054 + 8.87841i) q^{59} +(3.87101 - 0.123545i) q^{60} -13.9399i q^{61} +(-2.40855 + 5.01985i) q^{62} +(3.60504 + 2.16357i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.161350 - 0.165266i) q^{65} +(3.86540 - 4.22055i) q^{66} -5.60504i q^{67} -4.09809i q^{68} +(-9.27532 - 8.49482i) q^{69} +(-0.527308 + 3.08912i) q^{70} +(-6.89810 - 2.24133i) q^{71} +(-2.76090 + 1.17363i) q^{72} +(-1.85505 - 5.70926i) q^{73} +(-6.27945 - 4.56229i) q^{74} +(8.57891 + 1.18415i) q^{75} +(1.82561 - 5.61866i) q^{76} +(2.72195 + 3.74644i) q^{77} +(0.162819 + 0.0741495i) q^{78} +(8.56476 + 2.78286i) q^{79} +(-1.56207 - 1.59998i) q^{80} +(-1.24327 + 8.91371i) q^{81} +(-9.97793 + 3.24203i) q^{82} +(-0.0264479 + 0.0364024i) q^{83} +(-0.484573 - 2.37858i) q^{84} +(1.54191 - 9.03295i) q^{85} +(3.25349 + 10.0132i) q^{86} +(-5.11161 - 9.02924i) q^{87} -3.30426 q^{88} +(1.04920 + 3.22910i) q^{89} +(-6.52712 + 1.54811i) q^{90} +(-0.0850892 + 0.117115i) q^{91} +7.26163i q^{92} +(2.35211 - 9.35241i) q^{93} -6.22163 q^{94} +(6.13801 - 11.6977i) q^{95} +(1.57629 + 0.717859i) q^{96} +(-10.9372 + 3.55370i) q^{97} -5.03585 q^{98} +(-5.10103 + 8.49957i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9}+O(q^{10}) \) 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9	\( 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9} + 2 q^{10} - 35 q^{15} - 32 q^{16} - 6 q^{18} - 8 q^{19} + 3 q^{20} + 20 q^{23} - 10 q^{25} - 48 q^{31} - 128 q^{32} + 8 q^{33} + 10 q^{34} - 16 q^{35} - 4 q^{36} - 12 q^{38} + 4 q^{39} - 3 q^{40} + 5 q^{45} + 10 q^{46} - 6 q^{47} + 46 q^{49} + 5 q^{50} + 34 q^{51} + 20 q^{53} + 35 q^{60} + 8 q^{62} - 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} - 6 q^{72} + 5 q^{75} + 12 q^{76} - 50 q^{77} - 4 q^{78} - 10 q^{79} - 2 q^{80} - 24 q^{81} + 40 q^{83} - 30 q^{85} + 4 q^{87} - 5 q^{90} + 20 q^{91} + 26 q^{93} - 4 q^{94} + 26 q^{95} + 124 q^{98}+O(q^{100}) \) 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9 + 2 * q^10 - 35 * q^15 - 32 * q^16 - 6 * q^18 - 8 * q^19 + 3 * q^20 + 20 * q^23 - 10 * q^25 - 48 * q^31 - 128 * q^32 + 8 * q^33 + 10 * q^34 - 16 * q^35 - 4 * q^36 - 12 * q^38 + 4 * q^39 - 3 * q^40 + 5 * q^45 + 10 * q^46 - 6 * q^47 + 46 * q^49 + 5 * q^50 + 34 * q^51 + 20 * q^53 + 35 * q^60 + 8 * q^62 - 36 * q^63 - 32 * q^64 - 8 * q^66 + 8 * q^69 + 16 * q^70 - 6 * q^72 + 5 * q^75 + 12 * q^76 - 50 * q^77 - 4 * q^78 - 10 * q^79 - 2 * q^80 - 24 * q^81 + 40 * q^83 - 30 * q^85 + 4 * q^87 - 5 * q^90 + 20 * q^91 + 26 * q^93 - 4 * q^94 + 26 * q^95 + 124 * q^98

Introduction

L-functions

Modular forms

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