LMFDB - Embedded newform 310.2.n.a.219.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [310,2,Mod(39,310)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(310, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 4]))

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

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

chi := DirichletCharacter("310.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 310 = 2 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	310.n (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:	$2.47536246266$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			219.4
Character	$\chi$	$=$	310.219
Dual form			310.2.n.a.109.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 + 0.809017i) q^{2} +(-0.00820391 - 0.0112917i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.91563 + 1.15341i) q^{5} +0.0139573 q^{6} +(1.51995 - 0.493860i) q^{7} +(0.951057 + 0.309017i) q^{8} +(0.926991 - 2.85298i) q^{9} +O(q^{10})$	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.00820391 - 0.0112917i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.91563 + 1.15341i) q^{5} +0.0139573 q^{6} +(1.51995 - 0.493860i) q^{7} +(0.951057 + 0.309017i) q^{8} +(0.926991 - 2.85298i) q^{9} +(-2.05911 + 0.871822i) q^{10} +(-0.445478 - 1.37104i) q^{11} +(-0.00820391 + 0.0112917i) q^{12} +(0.679815 + 0.935685i) q^{13} +(-0.493860 + 1.51995i) q^{14} +(-0.00269170 - 0.0310932i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-4.69574 - 1.52574i) q^{17} +(1.76324 + 2.42689i) q^{18} +(6.47369 + 4.70341i) q^{19} +(0.504995 - 2.17830i) q^{20} +(-0.0180460 - 0.0131112i) q^{21} +(1.37104 + 0.445478i) q^{22} +(8.04627 + 2.61439i) q^{23} +(-0.00431305 - 0.0132742i) q^{24} +(2.33929 + 4.41902i) q^{25} -1.15657 q^{26} +(-0.0796426 + 0.0258775i) q^{27} +(-0.939378 - 1.29294i) q^{28} +(-6.75195 - 4.90558i) q^{29} +(0.0267371 + 0.0160985i) q^{30} +(-0.639045 + 5.53097i) q^{31} -1.00000i q^{32} +(-0.0118267 + 0.0162781i) q^{33} +(3.99444 - 2.90213i) q^{34} +(3.48128 + 0.807066i) q^{35} -2.99981 q^{36} -5.84154i q^{37} +(-7.61028 + 2.47273i) q^{38} +(0.00498834 - 0.0153525i) q^{39} +(1.46545 + 1.68892i) q^{40} +(7.00420 + 5.08885i) q^{41} +(0.0212144 - 0.00689297i) q^{42} +(-2.55162 + 3.51200i) q^{43} +(-1.16628 + 0.847349i) q^{44} +(5.06643 - 4.39607i) q^{45} +(-6.84456 + 4.97287i) q^{46} +(-4.85011 - 6.67560i) q^{47} +(0.0132742 + 0.00431305i) q^{48} +(-3.59678 + 2.61322i) q^{49} +(-4.95006 - 0.704907i) q^{50} +(0.0212952 + 0.0655400i) q^{51} +(0.679815 - 0.935685i) q^{52} +(-12.8307 - 4.16896i) q^{53} +(0.0258775 - 0.0796426i) q^{54} +(0.727999 - 3.14022i) q^{55} +1.59817 q^{56} -0.111685i q^{57} +(7.93739 - 2.57902i) q^{58} +(-5.06197 + 3.67774i) q^{59} +(-0.0287396 + 0.0121683i) q^{60} -2.87018 q^{61} +(-4.09903 - 3.76802i) q^{62} -4.79418i q^{63} +(0.809017 + 0.587785i) q^{64} +(0.223047 + 2.57653i) q^{65} +(-0.00621767 - 0.0191360i) q^{66} -13.2637i q^{67} +4.93739i q^{68} +(-0.0364899 - 0.112304i) q^{69} +(-2.69917 + 2.34203i) q^{70} +(-1.59343 + 4.90406i) q^{71} +(1.76324 - 2.42689i) q^{72} +(13.2347 - 4.30021i) q^{73} +(4.72591 + 3.43357i) q^{74} +(0.0307069 - 0.0626678i) q^{75} +(2.47273 - 7.61028i) q^{76} +(-1.35420 - 1.86390i) q^{77} +(0.00948839 + 0.0130597i) q^{78} +(2.87558 - 8.85014i) q^{79} +(-2.22774 + 0.192852i) q^{80} +(-7.27973 - 5.28904i) q^{81} +(-8.23393 + 2.67537i) q^{82} +(-4.82271 + 6.63789i) q^{83} +(-0.00689297 + 0.0212144i) q^{84} +(-7.23551 - 8.33887i) q^{85} +(-1.34146 - 4.12860i) q^{86} +0.116486i q^{87} -1.44160i q^{88} +(-2.41371 - 7.42865i) q^{89} +(0.578519 + 6.68277i) q^{90} +(1.49538 + 1.08646i) q^{91} -8.46035i q^{92} +(0.0676968 - 0.0381597i) q^{93} +8.25149 q^{94} +(6.97624 + 16.4768i) q^{95} +(-0.0112917 + 0.00820391i) q^{96} +(-3.07681 + 0.999716i) q^{97} -4.44587i q^{98} -4.32451 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 16 q^{4} + 4 q^{5} - 16 q^{6} + 8 q^{9}+O(q^{10}) $ 64 * q + 16 * q^4 + 4 * q^5 - 16 * q^6 + 8 * q^9	$ 64 q + 16 q^{4} + 4 q^{5} - 16 q^{6} + 8 q^{9} - 4 q^{10} + 4 q^{11} - 14 q^{15} - 16 q^{16} + 16 q^{19} - 4 q^{20} + 32 q^{21} - 4 q^{24} - 8 q^{25} - 48 q^{26} - 40 q^{29} - 8 q^{30} - 60 q^{31} - 20 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{39} - 6 q^{40} + 28 q^{41} - 4 q^{44} - 22 q^{45} + 36 q^{46} + 32 q^{49} + 20 q^{50} - 4 q^{51} - 40 q^{54} + 32 q^{59} + 14 q^{60} - 64 q^{61} + 16 q^{64} + 48 q^{65} - 4 q^{66} - 20 q^{70} - 20 q^{71} - 4 q^{74} + 62 q^{75} + 24 q^{76} - 116 q^{79} - 6 q^{80} - 116 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{86} + 60 q^{89} - 82 q^{90} + 28 q^{91} + 16 q^{94} - 90 q^{95} + 4 q^{96} + 16 q^{99}+O(q^{100}) $ 64 * q + 16 * q^4 + 4 * q^5 - 16 * q^6 + 8 * q^9 - 4 * q^10 + 4 * q^11 - 14 * q^15 - 16 * q^16 + 16 * q^19 - 4 * q^20 + 32 * q^21 - 4 * q^24 - 8 * q^25 - 48 * q^26 - 40 * q^29 - 8 * q^30 - 60 * q^31 - 20 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^39 - 6 * q^40 + 28 * q^41 - 4 * q^44 - 22 * q^45 + 36 * q^46 + 32 * q^49 + 20 * q^50 - 4 * q^51 - 40 * q^54 + 32 * q^59 + 14 * q^60 - 64 * q^61 + 16 * q^64 + 48 * q^65 - 4 * q^66 - 20 * q^70 - 20 * q^71 - 4 * q^74 + 62 * q^75 + 24 * q^76 - 116 * q^79 - 6 * q^80 - 116 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^86 + 60 * q^89 - 82 * q^90 + 28 * q^91 + 16 * q^94 - 90 * q^95 + 4 * q^96 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/310\mathbb{Z}\right)^\times$.

$n$	$187$	$251$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$3$	−0.00820391	−	0.0112917i	−0.00473653	−	0.00651927i	0.806642	−	0.591040i	$-0.201283\pi$
$3$	−0.00820391	−	0.0112917i	−0.00473653	−	0.00651927i	−0.811379	+	0.584521i	$0.801283\pi$
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	1.91563	+	1.15341i	0.856697	+	0.515821i
$5$	1.91563	+	1.15341i	0.856697	+	0.515821i
$6$	0.0139573			0.00569805
$7$	1.51995	−	0.493860i	0.574485	−	0.186662i	−0.00734320	−	0.999973i	$-0.502337\pi$
$7$	1.51995	−	0.493860i	0.574485	−	0.186662i	0.581829	+	0.813311i	$0.302337\pi$
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$	0.926991	−	2.85298i	0.308997	−	0.950995i
$10$	−2.05911	+	0.871822i	−0.651147	+	0.275694i
$11$	−0.445478	−	1.37104i	−0.134317	−	0.413384i	0.861167	−	0.508323i	$-0.169734\pi$
$11$	−0.445478	−	1.37104i	−0.134317	−	0.413384i	−0.995483	+	0.0949391i	$0.969734\pi$
$12$	−0.00820391	+	0.0112917i	−0.00236826	+	0.00325964i
$13$	0.679815	+	0.935685i	0.188547	+	0.259512i	0.892817	−	0.450420i	$-0.148726\pi$
$13$	0.679815	+	0.935685i	0.188547	+	0.259512i	−0.704270	+	0.709932i	$0.748726\pi$
$14$	−0.493860	+	1.51995i	−0.131990	+	0.406223i
$15$	−0.00269170	−	0.0310932i	−0.000694994	−	0.00802824i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−4.69574	−	1.52574i	−1.13888	−	0.370046i	−0.321939	−	0.946761i	$-0.604334\pi$
$17$	−4.69574	−	1.52574i	−1.13888	−	0.370046i	−0.816946	+	0.576715i	$0.804334\pi$
$18$	1.76324	+	2.42689i	0.415600	+	0.572024i
$19$	6.47369	+	4.70341i	1.48517	+	1.07904i	0.975846	+	0.218459i	$0.0701028\pi$
$19$	6.47369	+	4.70341i	1.48517	+	1.07904i	0.509319	+	0.860578i	$0.329897\pi$
$20$	0.504995	−	2.17830i	0.112920	−	0.487082i
$21$	−0.0180460	−	0.0131112i	−0.00393796	−	0.00286110i
$22$	1.37104	+	0.445478i	0.292306	+	0.0949761i
$23$	8.04627	+	2.61439i	1.67776	+	0.545138i	0.984475	−	0.175523i	$-0.0561616\pi$
$23$	8.04627	+	2.61439i	1.67776	+	0.545138i	0.693287	+	0.720661i	$0.256162\pi$
$24$	−0.00431305	−	0.0132742i	−0.000880398	−	0.00270959i
$25$	2.33929	+	4.41902i	0.467858	+	0.883803i
$26$	−1.15657			−0.226822
$27$	−0.0796426	+	0.0258775i	−0.0153272	+	0.00498012i
$28$	−0.939378	−	1.29294i	−0.177526	−	0.244343i
$29$	−6.75195	−	4.90558i	−1.25381	−	0.910943i	−0.255369	−	0.966844i	$-0.582197\pi$
$29$	−6.75195	−	4.90558i	−1.25381	−	0.910943i	−0.998436	+	0.0559006i	$0.982197\pi$
$30$	0.0267371	+	0.0160985i	0.00488150	+	0.00293917i
$31$	−0.639045	+	5.53097i	−0.114776	+	0.993391i
$31$	−0.639045	+	5.53097i	−0.114776	+	0.993391i
$32$		−	1.00000i		−	0.176777i
$33$	−0.0118267	+	0.0162781i	−0.00205877	+	0.00283365i
$34$	3.99444	−	2.90213i	0.685040	−	0.497711i
$35$	3.48128	+	0.807066i	0.588444	+	0.136419i
$36$	−2.99981			−0.499968
$37$		−	5.84154i		−	0.960344i	−0.877174	−	0.480172i	$-0.840574\pi$
$37$		−	5.84154i		−	0.960344i	0.877174	−	0.480172i	$-0.159426\pi$
$38$	−7.61028	+	2.47273i	−1.23455	+	0.401130i
$39$	0.00498834	−	0.0153525i	0.000798774	−	0.00245837i
$40$	1.46545	+	1.68892i	0.231708	+	0.267042i
$41$	7.00420	+	5.08885i	1.09387	+	0.794744i	0.980049	−	0.198757i	$-0.0636903\pi$
$41$	7.00420	+	5.08885i	1.09387	+	0.794744i	0.113823	+	0.993501i	$0.463690\pi$
$42$	0.0212144	−	0.00689297i	0.00327345	−	0.00106361i
$43$	−2.55162	+	3.51200i	−0.389118	+	0.535575i	−0.957971	−	0.286864i	$-0.907387\pi$
$43$	−2.55162	+	3.51200i	−0.389118	+	0.535575i	0.568853	+	0.822439i	$0.307387\pi$
$44$	−1.16628	+	0.847349i	−0.175823	+	0.127743i
$45$	5.06643	−	4.39607i	0.755259	−	0.655327i
$46$	−6.84456	+	4.97287i	−1.00918	+	0.733209i
$47$	−4.85011	−	6.67560i	−0.707461	−	0.973736i	−0.999848	−	0.0174361i	$-0.994450\pi$
$47$	−4.85011	−	6.67560i	−0.707461	−	0.973736i	0.292387	−	0.956300i	$-0.405550\pi$
$48$	0.0132742	+	0.00431305i	0.00191597	+	0.000622535i
$49$	−3.59678	+	2.61322i	−0.513826	+	0.373316i
$50$	−4.95006	−	0.704907i	−0.700044	−	0.0996889i
$51$	0.0212952	+	0.0655400i	0.00298193	+	0.00917743i
$52$	0.679815	−	0.935685i	0.0942733	−	0.129756i
$53$	−12.8307	−	4.16896i	−1.76244	−	0.572651i	−0.764990	−	0.644042i	$-0.777256\pi$
$53$	−12.8307	−	4.16896i	−1.76244	−	0.572651i	−0.997448	+	0.0713914i	$0.977256\pi$
$54$	0.0258775	−	0.0796426i	0.00352148	−	0.0108380i
$55$	0.727999	−	3.14022i	0.0981633	−	0.423428i
$56$	1.59817			0.213564
$57$		−	0.111685i		−	0.0147931i
$58$	7.93739	−	2.57902i	1.04223	−	0.338641i
$59$	−5.06197	+	3.67774i	−0.659013	+	0.478801i	−0.866329	−	0.499473i	$-0.833527\pi$
$59$	−5.06197	+	3.67774i	−0.659013	+	0.478801i	0.207317	+	0.978274i	$0.433527\pi$
$60$	−0.0287396	+	0.0121683i	−0.00371027	+	0.00157092i
$61$	−2.87018			−0.367489			−0.183744	−	0.982974i	$-0.558822\pi$
$61$	−2.87018			−0.367489			−0.183744	+	0.982974i	$0.558822\pi$
$62$	−4.09903	−	3.76802i	−0.520577	−	0.478539i
$63$		−	4.79418i		−	0.604010i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	0.223047	+	2.57653i	0.0276656	+	0.319579i
$66$	−0.00621767	−	0.0191360i	−0.000765343	−	0.00235548i
$67$		−	13.2637i		−	1.62042i	−0.586140	−	0.810210i	$-0.699353\pi$
$67$		−	13.2637i		−	1.62042i	0.586140	−	0.810210i	$-0.300647\pi$
$68$			4.93739i			0.598747i
$69$	−0.0364899	−	0.112304i	−0.00439287	−	0.0135199i
$70$	−2.69917	+	2.34203i	−0.322613	+	0.279926i
$71$	−1.59343	+	4.90406i	−0.189105	+	0.582005i	−0.999995	−	0.00319370i	$-0.998983\pi$
$71$	−1.59343	+	4.90406i	−0.189105	+	0.582005i	0.810890	+	0.585199i	$0.198983\pi$
$72$	1.76324	−	2.42689i	0.207800	−	0.286012i
$73$	13.2347	−	4.30021i	1.54900	−	0.503301i	0.595159	−	0.803608i	$-0.297089\pi$
$73$	13.2347	−	4.30021i	1.54900	−	0.503301i	0.953843	+	0.300307i	$0.0970891\pi$
$74$	4.72591	+	3.43357i	0.549376	+	0.399145i
$75$	0.0307069	−	0.0626678i	0.00354573	−	0.00723626i
$76$	2.47273	−	7.61028i	0.283641	−	0.872959i
$77$	−1.35420	−	1.86390i	−0.154326	−	0.212411i
$78$	0.00948839	+	0.0130597i	0.00107435	+	0.00147871i
$79$	2.87558	−	8.85014i	0.323528	−	0.995718i	−0.648572	−	0.761153i	$-0.724633\pi$
$79$	2.87558	−	8.85014i	0.323528	−	0.995718i	0.972100	−	0.234565i	$-0.0753665\pi$
$80$	−2.22774	+	0.192852i	−0.249068	+	0.0215615i
$81$	−7.27973	−	5.28904i	−0.808859	−	0.587671i
$82$	−8.23393	+	2.67537i	−0.909285	+	0.295445i
$83$	−4.82271	+	6.63789i	−0.529361	+	0.728603i	−0.987033	−	0.160518i	$-0.948683\pi$
$83$	−4.82271	+	6.63789i	−0.529361	+	0.728603i	0.457672	+	0.889121i	$0.348683\pi$
$84$	−0.00689297	+	0.0212144i	−0.000752084	+	0.00231468i
$85$	−7.23551	−	8.33887i	−0.784801	−	0.904477i
$86$	−1.34146	−	4.12860i	−0.144654	−	0.445199i
$87$			0.116486i			0.0124886i
$88$		−	1.44160i		−	0.153675i
$89$	−2.41371	−	7.42865i	−0.255853	−	0.787435i	−0.993660	−	0.112423i	$-0.964139\pi$
$89$	−2.41371	−	7.42865i	−0.255853	−	0.787435i	0.737807	−	0.675011i	$-0.235861\pi$
$90$	0.578519	+	6.68277i	0.0609812	+	0.704426i
$91$	1.49538	+	1.08646i	0.156758	+	0.113892i
$92$		−	8.46035i		−	0.882052i
$93$	0.0676968	−	0.0381597i	0.00701983	−	0.00395697i
$94$	8.25149			0.851077
$95$	6.97624	+	16.4768i	0.715748	+	1.69049i
$96$	−0.0112917	+	0.00820391i	−0.00115246	+	0.000837308i
$97$	−3.07681	+	0.999716i	−0.312403	+	0.101506i	−0.461022	−	0.887389i	$-0.652517\pi$
$97$	−3.07681	+	0.999716i	−0.312403	+	0.101506i	0.148619	+	0.988894i	$0.452517\pi$
$98$		−	4.44587i		−	0.449100i
$99$	−4.32451			−0.434629
$100$	3.47985	−	3.59035i	0.347985	−	0.359035i
$101$	0.102865	−	0.316587i	0.0102355	−	0.0315016i	−0.945808	−	0.324725i	$-0.894728\pi$
$101$	0.102865	−	0.316587i	0.0102355	−	0.0315016i	0.956044	+	0.293224i	$0.0947281\pi$
$102$	−0.0655400	−	0.0212952i	−0.00648942	−	0.00210854i
$103$	−2.43250	+	3.34805i	−0.239682	+	0.329894i	−0.911864	−	0.410492i	$-0.865357\pi$
$103$	−2.43250	+	3.34805i	−0.239682	+	0.329894i	0.672183	+	0.740385i	$0.265357\pi$
$104$	0.357400	+	1.09996i	0.0350459	+	0.107860i
$105$	−0.0194469	−	0.0459307i	−0.00189783	−	0.00448238i
$106$	10.9145	−	7.92984i	1.06011	−	0.770214i
$107$	−1.78023	−	0.578430i	−0.172101	−	0.0559190i	0.221699	−	0.975115i	$-0.428840\pi$
$107$	−1.78023	−	0.578430i	−0.172101	−	0.0559190i	−0.393800	+	0.919196i	$0.628840\pi$
$108$	0.0492219	+	0.0677481i	0.00473637	+	0.00651906i
$109$	−9.81380	+	7.13014i	−0.939991	+	0.682944i	−0.948419	−	0.317021i	$-0.897317\pi$
$109$	−9.81380	+	7.13014i	−0.939991	+	0.682944i	0.00842741	+	0.999964i	$0.497317\pi$
$110$	2.11259	+	2.43474i	0.201427	+	0.232143i
$111$	−0.0659610	+	0.0479235i	−0.00626074	+	0.00454870i
$112$	−0.939378	+	1.29294i	−0.0887629	+	0.122172i
$113$	−9.60980	+	3.12241i	−0.904014	+	0.293732i	−0.723893	−	0.689912i	$-0.757649\pi$
$113$	−9.60980	+	3.12241i	−0.904014	+	0.293732i	−0.180121	+	0.983644i	$0.557649\pi$
$114$	0.0903553	+	0.0656470i	0.00846255	+	0.00614840i
$115$	12.3982	+	14.2889i	1.15614	+	1.33244i
$116$	−2.57902	+	7.93739i	−0.239456	+	0.736968i
$117$	3.29968	−	1.07213i	0.305055	−	0.0991184i
$118$		−	6.25694i		−	0.575998i
$119$	−7.89077			−0.723346
$120$	0.00704838	−	0.0304032i	0.000643426	−	0.00277542i
$121$	7.21789	−	5.24410i	0.656172	−	0.476737i
$122$	1.68705	−	2.32202i	0.152738	−	0.210226i
$123$		−	0.120838i		−	0.0108956i
$124$	5.45774	−	1.10140i	0.490120	−	0.0989083i
$125$	−0.615717	+	11.1634i	−0.0550714	+	0.998482i
$126$	3.87858	+	2.81795i	0.345531	+	0.251043i
$127$	7.36809	+	10.1413i	0.653813	+	0.899896i	0.999257	−	0.0385434i	$-0.0122718\pi$
$127$	7.36809	+	10.1413i	0.653813	+	0.899896i	−0.345444	+	0.938439i	$0.612272\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$	0.0605897			0.00533463
$130$	−2.21556	−	1.33400i	−0.194318	−	0.116999i
$131$	−2.02626	−	6.23619i	−0.177035	−	0.544858i	0.822685	−	0.568497i	$-0.192475\pi$
$131$	−2.02626	−	6.23619i	−0.177035	−	0.544858i	−0.999721	+	0.0236388i	$0.992475\pi$
$132$	0.0191360	+	0.00621767i	0.00166558	+	0.000541179i
$133$	12.1625	+	3.95183i	1.05462	+	0.342667i
$134$	10.7306	+	7.79621i	0.926980	+	0.673490i
$135$	−0.182413	−	0.0422889i	−0.0156996	−	0.00363965i
$136$	−3.99444	−	2.90213i	−0.342520	−	0.248855i
$137$	−1.03103	−	1.41909i	−0.0880868	−	0.121241i	0.762699	−	0.646753i	$-0.223874\pi$
$137$	−1.03103	−	1.41909i	−0.0880868	−	0.121241i	−0.850786	+	0.525512i	$0.823874\pi$
$138$	0.112304	+	0.0364899i	0.00955998	+	0.00310623i
$139$	−10.7420	+	7.80454i	−0.911126	+	0.661972i	−0.941299	−	0.337573i	$-0.890394\pi$
$139$	−10.7420	+	7.80454i	−0.911126	+	0.661972i	0.0301731	+	0.999545i	$0.490394\pi$
$140$	−0.308209	−	3.56029i	−0.0260485	−	0.300899i
$141$	−0.0355891	+	0.109532i	−0.00299714	+	0.00922426i
$142$	−3.03088	−	4.17164i	−0.254345	−	0.350076i
$143$	0.980018	−	1.34888i	0.0819532	−	0.112799i
$144$	0.926991	+	2.85298i	0.0772492	+	0.237749i
$145$	−7.27611	−	17.1850i	−0.604248	−	1.42714i
$146$	−4.30021	+	13.2347i	−0.355888	+	1.09531i
$147$	0.0590153	+	0.0191752i	0.00486750	+	0.00158155i
$148$	−5.55564	+	1.80514i	−0.456671	+	0.148381i
$149$	1.49376			0.122373			0.0611866	−	0.998126i	$-0.480512\pi$
$149$	1.49376			0.122373			0.0611866	+	0.998126i	$0.480512\pi$
$150$	0.0326502	+	0.0616777i	0.00266588	+	0.00503596i
$151$	−2.01343	−	6.19669i	−0.163850	−	0.504280i	0.835099	−	0.550099i	$-0.185410\pi$
$151$	−2.01343	−	6.19669i	−0.163850	−	0.504280i	−0.998950	+	0.0458195i	$0.985410\pi$
$152$	4.70341	+	6.47369i	0.381497	+	0.525085i
$153$	−8.70582	+	11.9825i	−0.703824	+	0.968730i
$154$	2.30391			0.185654
$155$	−7.60365	+	9.85822i	−0.610740	+	0.791831i
$156$	−0.0161426			−0.00129244
$157$	−7.87755	+	10.8425i	−0.628697	+	0.865327i	−0.997950	−	0.0640019i	$-0.979614\pi$
$157$	−7.87755	+	10.8425i	−0.628697	+	0.865327i	0.369253	+	0.929329i	$0.379614\pi$
$158$	5.46968	+	7.52838i	0.435145	+	0.598925i
$159$	0.0581875	+	0.179083i	0.00461457	+	0.0142022i
$160$	1.15341	−	1.91563i	0.0911851	−	0.151444i
$161$	13.5210			1.06561
$162$	8.55784	−	2.78061i	0.672368	−	0.218465i
$163$	19.6396	+	6.38130i	1.53830	+	0.499822i	0.950905	−	0.309482i	$-0.100156\pi$
$163$	19.6396	+	6.38130i	1.53830	+	0.499822i	0.587390	+	0.809304i	$0.300156\pi$
$164$	2.67537	−	8.23393i	0.208911	−	0.642962i
$165$	−0.0414309	+	0.0175418i	−0.00322539	+	0.00136562i
$166$	−2.53545	−	7.80330i	−0.196789	−	0.605654i
$167$	−2.68813	+	3.69990i	−0.208014	+	0.286307i	−0.900258	−	0.435357i	$-0.856622\pi$
$167$	−2.68813	+	3.69990i	−0.208014	+	0.286307i	0.692244	+	0.721663i	$0.256622\pi$
$168$	−0.0131112	−	0.0180460i	−0.00101155	−	0.00139228i
$169$	3.60386	−	11.0916i	0.277220	−	0.853196i
$170$	10.9992	−	0.952187i	0.843601	−	0.0730294i
$171$	19.4198	−	14.1093i	1.48507	−	1.07897i
$172$	4.12860	+	1.34146i	0.314803	+	0.102286i
$173$	6.78119	+	9.33351i	0.515564	+	0.709613i	0.984845	−	0.173435i	$-0.0554868\pi$
$173$	6.78119	+	9.33351i	0.515564	+	0.709613i	−0.469281	+	0.883049i	$0.655487\pi$
$174$	−0.0942391	−	0.0684687i	−0.00714425	−	0.00519060i
$175$	5.73797	+	5.56138i	0.433750	+	0.420401i
$176$	1.16628	+	0.847349i	0.0879113	+	0.0638713i
$177$	0.0830559	+	0.0269865i	0.00624287	+	0.00202843i
$178$	7.42865	+	2.41371i	0.556801	+	0.180915i
$179$	2.29637	+	7.06751i	0.171639	+	0.528250i	0.999464	−	0.0327359i	$-0.0104220\pi$
$179$	2.29637	+	7.06751i	0.171639	+	0.528250i	−0.827825	+	0.560986i	$0.810422\pi$
$180$	−5.74652	−	3.46000i	−0.428321	−	0.257894i
$181$	−6.67997			−0.496519			−0.248259	−	0.968694i	$-0.579858\pi$
$181$	−6.67997			−0.496519			−0.248259	+	0.968694i	$0.579858\pi$
$182$	−1.75792	+	0.571184i	−0.130306	+	0.0423390i
$183$	0.0235467	+	0.0324092i	0.00174062	+	0.00239576i
$184$	6.84456	+	4.97287i	0.504588	+	0.366605i
$185$	6.73770	−	11.1902i	0.495365	−	0.822724i
$186$	−0.00891935	+	0.0771975i	−0.000653999	+	0.00566040i
$187$			7.11772i			0.520500i
$188$	−4.85011	+	6.67560i	−0.353730	+	0.486868i
$189$	−0.108273	+	0.0786647i	−0.00787567	+	0.00572201i
$190$	−17.4306	−	4.04093i	−1.26455	−	0.293160i
$191$	−2.84401			−0.205785			−0.102893	−	0.994692i	$-0.532810\pi$
$191$	−2.84401			−0.205785			−0.102893	+	0.994692i	$0.532810\pi$
$192$		−	0.0139573i		−	0.00100728i
$193$	−1.13746	+	0.369582i	−0.0818759	+	0.0266031i	−0.349669	−	0.936873i	$-0.613706\pi$
$193$	−1.13746	+	0.369582i	−0.0818759	+	0.0266031i	0.267793	+	0.963477i	$0.413706\pi$
$194$	0.999716	−	3.07681i	0.0717754	−	0.220902i
$195$	0.0272636	−	0.0236562i	0.00195239	−	0.00169406i
$196$	3.59678	+	2.61322i	0.256913	+	0.186658i
$197$	5.61184	−	1.82340i	0.399827	−	0.129912i	−0.102199	−	0.994764i	$-0.532588\pi$
$197$	5.61184	−	1.82340i	0.399827	−	0.129912i	0.502027	+	0.864852i	$0.332588\pi$
$198$	2.54188	−	3.49860i	0.180644	−	0.248635i
$199$	−9.22558	+	6.70278i	−0.653984	+	0.475147i	−0.864626	−	0.502416i	$-0.832445\pi$
$199$	−9.22558	+	6.70278i	−0.653984	+	0.475147i	0.210642	+	0.977563i	$0.432445\pi$
$200$	0.859247	+	4.92562i	0.0607579	+	0.348294i
$201$	−0.149770	+	0.108814i	−0.0105640	+	0.00767517i
$202$	0.195662	+	0.269305i	0.0137667	+	0.0189482i
$203$	−12.6853	−	4.12169i	−0.890331	−	0.289286i
$204$	0.0557516	−	0.0405059i	0.00390339	−	0.00283598i
$205$	7.54794	+	17.8271i	0.527171	+	1.24510i
$206$	−1.27884	−	3.93587i	−0.0891012	−	0.274225i
$207$	14.9176	−	20.5324i	1.03685	−	1.42710i
$208$	−1.09996	−	0.357400i	−0.0762687	−	0.0247812i
$209$	3.56467	−	10.9709i	0.246574	−	0.758876i
$210$	0.0485893	+	0.0112645i	0.00335298	+	0.000777323i
$211$	−8.31022			−0.572099			−0.286050	−	0.958215i	$-0.592342\pi$
$211$	−8.31022			−0.572099			−0.286050	+	0.958215i	$0.592342\pi$
$212$			13.4910i			0.926569i
$213$	0.0684475	−	0.0222400i	0.00468995	−	0.00152386i
$214$	1.51435	−	1.10024i	0.103519	−	0.0752109i
$215$	−8.93873	+	3.78464i	−0.609617	+	0.258110i
$216$	−0.0837412			−0.00569787
$217$	1.76021	+	8.72237i	0.119491	+	0.592113i
$218$		−	12.1305i		−	0.821582i
$219$	−0.157133	−	0.114164i	−0.0106180	−	0.00771446i
$220$	−3.21149	+	0.278015i	−0.216519	+	0.0187437i
$221$	−1.76462	−	5.43095i	−0.118701	−	0.365325i
$222$		−	0.0815323i		−	0.00547209i
$223$		−	19.7329i		−	1.32141i	−0.750645	−	0.660705i	$-0.770257\pi$
$223$		−	19.7329i		−	1.32141i	0.750645	−	0.660705i	$-0.229743\pi$
$224$	−0.493860	−	1.51995i	−0.0329974	−	0.101556i
$225$	14.7759	−	2.57757i	0.985059	−	0.171838i
$226$	3.12241	−	9.60980i	0.207700	−	0.639235i
$227$	−8.69916	+	11.9734i	−0.577383	+	0.794700i	−0.993405	−	0.114654i	$-0.963424\pi$
$227$	−8.69916	+	11.9734i	−0.577383	+	0.794700i	0.416022	+	0.909355i	$0.363424\pi$
$228$	−0.106219	+	0.0345127i	−0.00703453	+	0.00228566i
$229$	−0.721043	−	0.523868i	−0.0476478	−	0.0346182i	0.563706	−	0.825975i	$-0.309375\pi$
$229$	−0.721043	−	0.523868i	−0.0476478	−	0.0346182i	−0.611354	+	0.791357i	$0.709375\pi$
$230$	−18.8474	+	1.63160i	−1.24276	+	0.107584i
$231$	−0.00993687	+	0.0305825i	−0.000653798	+	0.00201218i
$232$	−4.90558	−	6.75195i	−0.322067	−	0.443287i
$233$	−12.5874	−	17.3251i	−0.824628	−	1.13500i	−0.988899	−	0.148588i	$-0.952527\pi$
$233$	−12.5874	−	17.3251i	−0.824628	−	1.13500i	0.164271	−	0.986415i	$-0.447473\pi$
$234$	−1.07213	+	3.29968i	−0.0700873	+	0.215707i
$235$	−1.59132	−	18.3821i	−0.103806	−	1.19912i
$236$	5.06197	+	3.67774i	0.329506	+	0.239400i
$237$	−0.123524	+	0.0401354i	−0.00802376	+	0.00260708i
$238$	4.63808	−	6.38377i	0.300642	−	0.413798i
$239$	−2.15745	+	6.63993i	−0.139554	+	0.429502i	−0.996270	−	0.0862852i	$-0.972500\pi$
$239$	−2.15745	+	6.63993i	−0.139554	+	0.429502i	0.856717	+	0.515787i	$0.172500\pi$
$240$	0.0204538	+	0.0235728i	0.00132029	+	0.00152162i
$241$	5.50593	+	16.9455i	0.354668	+	1.09156i	0.956202	+	0.292708i	$0.0945565\pi$
$241$	5.50593	+	16.9455i	0.354668	+	1.09156i	−0.601534	+	0.798847i	$0.705443\pi$
$242$			8.92180i			0.573515i
$243$			0.376815i			0.0241727i
$244$	0.886934	+	2.72970i	0.0567802	+	0.174751i
$245$	−9.90422	+	0.857395i	−0.632757	+	0.0547769i
$246$	0.0977598	+	0.0710267i	0.00623294	+	0.00452850i
$247$			9.25478i			0.588867i
$248$	−2.31693	+	5.06279i	−0.147125	+	0.321487i
$249$	0.114518			0.00725729
$250$	−8.66945	−	7.05979i	−0.548304	−	0.446500i
$251$	13.5345	−	9.83336i	0.854287	−	0.620676i	−0.0720375	−	0.997402i	$-0.522950\pi$
$251$	13.5345	−	9.83336i	0.854287	−	0.620676i	0.926325	+	0.376726i	$0.122950\pi$
$252$	−4.55954	+	1.48148i	−0.287224	+	0.0933248i
$253$		−	12.1964i		−	0.766781i
$254$	−12.5353			−0.786538
$255$	−0.0348006	+	0.150113i	−0.00217930	+	0.00940041i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−17.6524	−	5.73562i	−1.10113	−	0.357778i	−0.298592	−	0.954381i	$-0.596517\pi$
$257$	−17.6524	−	5.73562i	−1.10113	−	0.357778i	−0.802537	+	0.596603i	$0.796517\pi$
$258$	−0.0356137	+	0.0490181i	−0.00221721	+	0.00305173i
$259$	−2.88491	−	8.87883i	−0.179259	−	0.551704i
$260$	2.38150	−	1.00832i	0.147695	−	0.0625335i
$261$	−20.2545	+	14.7158i	−1.25372	+	0.910884i
$262$	6.23619	+	2.02626i	0.385273	+	0.125183i
$263$	2.41074	+	3.31810i	0.148653	+	0.204603i	0.876849	−	0.480766i	$-0.159641\pi$
$263$	2.41074	+	3.31810i	0.148653	+	0.204603i	−0.728197	+	0.685368i	$0.759641\pi$
$264$	−0.0162781	+	0.0118267i	−0.00100185	+	0.000727884i
$265$	−19.7705	−	22.7853i	−1.21449	−	1.39969i
$266$	−10.3460	+	7.51683i	−0.634355	+	0.460886i
$267$	−0.0640802	+	0.0881989i	−0.00392165	+	0.00539768i
$268$	−12.6145	+	4.09871i	−0.770556	+	0.250369i
$269$	−14.8147	−	10.7635i	−0.903269	−	0.656263i	0.0360345	−	0.999351i	$-0.488527\pi$
$269$	−14.8147	−	10.7635i	−0.903269	−	0.656263i	−0.939304	+	0.343087i	$0.888527\pi$
$270$	0.141432	−	0.122719i	0.00860729	−	0.00746842i
$271$	−0.896693	+	2.75974i	−0.0544702	+	0.167642i	−0.974591	−	0.223993i	$-0.928091\pi$
$271$	−0.896693	+	2.75974i	−0.0544702	+	0.167642i	0.920120	+	0.391635i	$0.128091\pi$
$272$	4.69574	−	1.52574i	0.284721	−	0.0925115i
$273$		−	0.0257986i		−	0.00156140i
$274$	1.75409			0.105969
$275$	5.01654	−	5.17583i	0.302509	−	0.312114i
$276$	−0.0955318	+	0.0694079i	−0.00575034	+	0.00417787i
$277$	−3.93264	+	5.41282i	−0.236290	+	0.325225i	−0.910651	−	0.413177i	$-0.864419\pi$
$277$	−3.93264	+	5.41282i	−0.236290	+	0.325225i	0.674361	+	0.738402i	$0.264419\pi$
$278$		−	13.2779i		−	0.796354i
$279$	15.1874	+	6.95034i	0.909245	+	0.416106i
$280$	3.06150	+	1.84334i	0.182959	+	0.110161i
$281$	−1.79883	−	1.30692i	−0.107309	−	0.0779645i	0.532837	−	0.846218i	$-0.321126\pi$
$281$	−1.79883	−	1.30692i	−0.107309	−	0.0779645i	−0.640146	+	0.768254i	$0.721126\pi$
$282$	−0.0676945	−	0.0931735i	−0.00403115	−	0.00554840i
$283$	21.8869	−	7.11149i	1.30104	−	0.422734i	0.425098	−	0.905147i	$-0.360239\pi$
$283$	21.8869	−	7.11149i	1.30104	−	0.422734i	0.875944	+	0.482413i	$0.160239\pi$
$284$	5.15643			0.305978
$285$	0.128819	−	0.213948i	0.00763058	−	0.0126732i
$286$	0.515226	+	1.58570i	0.0304659	+	0.0937645i
$287$	13.1592	+	4.27568i	0.776762	+	0.252385i
$288$	−2.85298	−	0.926991i	−0.168114	−	0.0546235i
$289$	5.96881	+	4.33660i	0.351107	+	0.255094i
$290$	18.1798	+	4.21462i	1.06755	+	0.247491i
$291$	0.0365304	+	0.0265409i	0.00214145	+	0.00155585i
$292$	−8.17948	−	11.2581i	−0.478668	−	0.658830i
$293$	8.07780	+	2.62464i	0.471910	+	0.153333i	0.535311	−	0.844655i	$-0.320195\pi$
$293$	8.07780	+	2.62464i	0.471910	+	0.153333i	−0.0634006	+	0.997988i	$0.520195\pi$
$294$	−0.0502015	+	0.0364735i	−0.00292781	+	0.00212718i
$295$	−13.9388	+	1.20666i	−0.811549	+	0.0702547i
$296$	1.80514	−	5.55564i	0.104921	−	0.322915i
$297$	0.0709580	+	0.0976653i	0.00411740	+	0.00566712i
$298$	−0.878008	+	1.20847i	−0.0508616	+	0.0700050i
$299$	3.02373	+	9.30607i	0.174867	+	0.538184i
$300$	−0.0690896	−	0.00983861i	−0.00398889	−	0.000568032i
$301$	−2.14388	+	6.59819i	−0.123571	+	0.380313i
$302$	6.19669	+	2.01343i	0.356580	+	0.115860i
$303$	−0.00441871	+	0.00143573i	−0.000253848	+	8.24803e-5i
$304$	−8.00192			−0.458941
$305$	−5.49821	−	3.31049i	−0.314826	−	0.189558i
$306$	−4.57692	−	14.0863i	−0.261645	−	0.805261i
$307$	3.99602	+	5.50005i	0.228065	+	0.313904i	0.907679	−	0.419666i	$-0.137853\pi$
$307$	3.99602	+	5.50005i	0.228065	+	0.313904i	−0.679614	+	0.733570i	$0.737853\pi$
$308$	−1.35420	+	1.86390i	−0.0771629	+	0.106206i
$309$	0.0577613			0.00328593
$310$	−3.50616	−	11.9460i	−0.199136	−	0.678487i
$311$	22.0431			1.24995			0.624974	−	0.780646i	$-0.285110\pi$
$311$	22.0431			1.24995			0.624974	+	0.780646i	$0.285110\pi$
$312$	0.00948839	−	0.0130597i	0.000537174	−	0.000739357i
$313$	2.87377	+	3.95541i	0.162435	+	0.223573i	0.882474	−	0.470361i	$-0.155876\pi$
$313$	2.87377	+	3.95541i	0.162435	+	0.223573i	−0.720039	+	0.693934i	$0.755876\pi$
$314$	−4.14147	−	12.7461i	−0.233717	−	0.719307i
$315$	5.52966	−	9.18389i	0.311561	−	0.517454i
$316$	−9.30558			−0.523480
$317$	22.0267	−	7.15690i	1.23714	−	0.401971i	0.383845	−	0.923398i	$-0.374600\pi$
$317$	22.0267	−	7.15690i	1.23714	−	0.401971i	0.853296	+	0.521426i	$0.174600\pi$
$318$	−0.179083	−	0.0581875i	−0.0100425	−	0.00326300i
$319$	−3.71790	+	11.4425i	−0.208162	+	0.640658i
$320$	0.871822	+	2.05911i	0.0487363	+	0.115108i
$321$	0.00807334	+	0.0248472i	0.000450610	+	0.00138683i
$322$	−7.94746	+	10.9387i	−0.442895	+	0.609592i
$323$	−23.2226	−	31.9631i	−1.29214	−	1.77848i
$324$	−2.78061	+	8.55784i	−0.154478	+	0.475436i
$325$	−2.54452	+	5.19295i	−0.141145	+	0.288053i
$326$	−16.7065	+	12.1380i	−0.925286	+	0.672260i
$327$	0.161023	+	0.0523195i	0.00890459	+	0.00289328i
$328$	5.08885	+	7.00420i	0.280985	+	0.386742i
$329$	−10.6687	−	7.75127i	−0.588185	−	0.427341i
$330$	0.0101609	−	0.0438291i	0.000559340	−	0.00241271i
$331$	−6.00478	−	4.36273i	−0.330052	−	0.239797i	0.410400	−	0.911905i	$-0.365389\pi$
$331$	−6.00478	−	4.36273i	−0.330052	−	0.239797i	−0.740453	+	0.672108i	$0.765389\pi$
$332$	7.80330	+	2.53545i	0.428262	+	0.139151i
$333$	−16.6658	−	5.41506i	−0.913282	−	0.296743i
$334$	−1.41323	−	4.34949i	−0.0773288	−	0.237993i
$335$	15.2985	−	25.4084i	0.835846	−	1.38821i
$336$	0.0223061			0.00121690
$337$	5.79724	−	1.88364i	0.315796	−	0.102608i	−0.146830	−	0.989162i	$-0.546907\pi$
$337$	5.79724	−	1.88364i	0.315796	−	0.102608i	0.462626	+	0.886553i	$0.346907\pi$
$338$	6.85496	+	9.43504i	0.372860	+	0.513198i
$339$	0.114095	+	0.0828951i	0.00619681	+	0.00450224i
$340$	−5.69484	+	9.45823i	−0.308846	+	0.512944i
$341$	7.86785	−	1.58777i	0.426068	−	0.0859824i
$342$			24.0042i			1.29800i
$343$	−10.7520	+	14.7989i	−0.580553	+	0.799063i
$344$	−3.51200	+	2.55162i	−0.189354	+	0.137574i
$345$	0.0596317	−	0.257222i	0.00321046	−	0.0138483i
$346$	−11.5369			−0.620225
$347$			8.45573i			0.453927i	0.973903	+	0.226964i	$0.0728799\pi$
$347$			8.45573i			0.453927i	−0.973903	+	0.226964i	$0.927120\pi$
$348$	0.110785	−	0.0359961i	0.00593869	−	0.00192960i
$349$	−0.598922	+	1.84329i	−0.0320595	+	0.0986691i	−0.965806	−	0.259266i	$-0.916519\pi$
$349$	−0.598922	+	1.84329i	−0.0320595	+	0.0986691i	0.933746	+	0.357936i	$0.116519\pi$
$350$	−7.87195	+	1.37322i	−0.420773	+	0.0734016i
$351$	−0.0783554	−	0.0569285i	−0.00418230	−	0.00303862i
$352$	−1.37104	+	0.445478i	−0.0730766	+	0.0237440i
$353$	4.72132	−	6.49835i	0.251291	−	0.345872i	−0.664672	−	0.747135i	$-0.731429\pi$
$353$	4.72132	−	6.49835i	0.251291	−	0.345872i	0.915963	+	0.401263i	$0.131429\pi$
$354$	−0.0706516	+	0.0513314i	−0.00375509	+	0.00272823i
$355$	−8.70881	+	7.55650i	−0.462216	+	0.401057i
$356$	−6.31918	+	4.59116i	−0.334916	+	0.243331i
$357$	0.0647352	+	0.0891003i	0.00342615	+	0.00471569i
$358$	−7.06751	−	2.29637i	−0.373529	−	0.121367i
$359$	0.158439	−	0.115113i	0.00836209	−	0.00607542i	−0.583596	−	0.812044i	$-0.698355\pi$
$359$	0.158439	−	0.115113i	0.00836209	−	0.00607542i	0.591958	+	0.805968i	$0.298355\pi$
$360$	6.17692	−	2.61529i	0.325552	−	0.137838i
$361$	13.9152	+	42.8267i	0.732381	+	2.25404i
$362$	3.92639	−	5.40421i	0.206366	−	0.284039i
$363$	−0.118430	−	0.0384802i	−0.00621595	−	0.00201969i
$364$	0.571184	−	1.75792i	0.0299382	−	0.0921402i
$365$	30.3127	+	7.02739i	1.58664	+	0.367830i
$366$	−0.0400600			−0.00209397
$367$			17.9315i			0.936019i	0.883723	+	0.468010i	$0.155029\pi$
$367$			17.9315i			0.936019i	−0.883723	+	0.468010i	$0.844971\pi$
$368$	−8.04627	+	2.61439i	−0.419441	+	0.136285i
$369$	21.0112	−	15.2656i	1.09380	−	0.794693i
$370$	5.09278	+	12.0284i	0.264761	+	0.625325i
$371$	−21.5609			−1.11939
$372$	−0.0572114	−	0.0525915i	−0.00296628	−	0.00272674i
$373$			8.31057i			0.430305i	0.976580	+	0.215152i	$0.0690248\pi$
$373$			8.31057i			0.430305i	−0.976580	+	0.215152i	$0.930975\pi$
$374$	−5.75836	−	4.18369i	−0.297758	−	0.216334i
$375$	0.131105	−	0.0846308i	0.00677023	−	0.00437032i
$376$	−2.54985	−	7.84764i	−0.131499	−	0.404711i
$377$		−	9.65258i		−	0.497133i
$378$		−	0.133832i		−	0.00688359i
$379$	−2.51391	−	7.73702i	−0.129131	−	0.397424i	0.865500	−	0.500909i	$-0.167001\pi$
$379$	−2.51391	−	7.73702i	−0.129131	−	0.397424i	−0.994631	+	0.103485i	$0.967001\pi$
$380$	13.5146	−	11.7264i	0.693285	−	0.601553i
$381$	0.0540656	−	0.166397i	0.00276986	−	0.00852476i
$382$	1.67167	−	2.30085i	0.0855299	−	0.117722i
$383$	−14.6331	+	4.75459i	−0.747718	+	0.242948i	−0.657999	−	0.753019i	$-0.728597\pi$
$383$	−14.6331	+	4.75459i	−0.747718	+	0.242948i	−0.0897189	+	0.995967i	$0.528597\pi$
$384$	0.0112917	+	0.00820391i	0.000576228	+	0.000418654i
$385$	−0.444313	−	5.13250i	−0.0226443	−	0.261576i
$386$	0.369582	−	1.13746i	0.0188112	−	0.0578950i
$387$	7.65435	+	10.5353i	0.389093	+	0.535540i
$388$	1.90157	+	2.61729i	0.0965377	+	0.132873i
$389$	−10.4672	+	32.2146i	−0.530706	+	1.63335i	0.222041	+	0.975037i	$0.428728\pi$
$389$	−10.4672	+	32.2146i	−0.530706	+	1.63335i	−0.752748	+	0.658309i	$0.771272\pi$
$390$	0.00311314	+	0.0359615i	0.000157640	+	0.00182098i
$391$	−33.7943	−	24.5530i	−1.70905	−	1.24170i
$392$	−4.22827	+	1.37385i	−0.213560	+	0.0693898i
$393$	−0.0537940	+	0.0740410i	−0.00271355	+	0.00373488i
$394$	−1.82340	+	5.61184i	−0.0918615	+	0.282721i
$395$	15.7164	−	13.6369i	0.790778	−	0.686146i
$396$	1.33635	+	4.11285i	0.0671539	+	0.206678i
$397$		−	15.1531i		−	0.760512i	−0.924881	−	0.380256i	$-0.875836\pi$
$397$		−	15.1531i		−	0.760512i	0.924881	−	0.380256i	$-0.124164\pi$
$398$		−	11.4034i		−	0.571603i
$399$	−0.0551570	−	0.169756i	−0.00276130	−	0.00849841i
$400$	−4.48996	−	2.20006i	−0.224498	−	0.110003i
$401$	12.4395	+	9.03782i	0.621199	+	0.451327i	0.853340	−	0.521355i	$-0.174573\pi$
$401$	12.4395	+	9.03782i	0.621199	+	0.451327i	−0.232141	+	0.972682i	$0.574573\pi$
$402$		−	0.185126i		−	0.00923324i
$403$	−5.60967	+	3.16209i	−0.279438	+	0.157515i
$404$	−0.332880			−0.0165614
$405$	−7.84487	−	18.5284i	−0.389814	−	0.920682i
$406$	10.7907	−	7.83993i	0.535535	−	0.389089i
$407$	−8.00898	+	2.60228i	−0.396991	+	0.128990i
$408$			0.0689128i			0.00341169i
$409$	31.3896			1.55211			0.776057	−	0.630663i	$-0.217217\pi$
$409$	31.3896			1.55211			0.776057	+	0.630663i	$0.217217\pi$
$410$	−18.8590	−	4.37208i	−0.931378	−	0.215922i
$411$	−0.00756549	+	0.0232842i	−0.000373178	+	0.00114852i
$412$	3.93587	+	1.27884i	0.193907	+	0.0630041i
$413$	−5.87763	+	8.08987i	−0.289219	+	0.398076i
$414$	7.84266	+	24.1372i	0.385446	+	1.18628i
$415$	−16.8947	+	7.15319i	−0.829330	+	0.351136i
$416$	0.935685	−	0.679815i	0.0458757	−	0.0333307i
$417$	0.176253	+	0.0572681i	0.00863115	+	0.00280443i
$418$	6.78041	+	9.33244i	0.331641	+	0.456464i
$419$	16.9601	−	12.3222i	0.828554	−	0.601980i	−0.0905960	−	0.995888i	$-0.528877\pi$
$419$	16.9601	−	12.3222i	0.828554	−	0.601980i	0.919150	+	0.393908i	$0.128877\pi$
$420$	−0.0376733	+	0.0326885i	−0.00183827	+	0.00159504i
$421$	−9.83480	+	7.14540i	−0.479319	+	0.348246i	−0.801062	−	0.598581i	$-0.795731\pi$
$421$	−9.83480	+	7.14540i	−0.479319	+	0.348246i	0.321743	+	0.946827i	$0.395731\pi$
$422$	4.88463	−	6.72311i	0.237780	−	0.327276i
$423$	−23.5414	+	7.64906i	−1.14462	+	0.371910i
$424$	−10.9145	−	7.92984i	−0.530054	−	0.385107i
$425$	−4.24244	−	24.3197i	−0.205789	−	1.17968i
$426$	−0.0222400	+	0.0684475i	−0.00107753	+	0.00331629i
$427$	−4.36252	+	1.41747i	−0.211117	+	0.0685961i
$428$			1.87184i			0.0904788i
$429$	−0.0232711			−0.00112354
$430$	2.19222	−	9.45614i	0.105718	−	0.456016i
$431$	22.1371	−	16.0836i	1.06631	−	0.774718i	0.0910632	−	0.995845i	$-0.470973\pi$
$431$	22.1371	−	16.0836i	1.06631	−	0.774718i	0.975245	+	0.221127i	$0.0709735\pi$
$432$	0.0492219	−	0.0677481i	0.00236819	−	0.00325953i
$433$		−	36.6802i		−	1.76274i	−0.472428	−	0.881370i	$-0.656622\pi$
$433$		−	36.6802i		−	1.76274i	0.472428	−	0.881370i	$-0.343378\pi$
$434$	−8.09117	−	3.70284i	−0.388389	−	0.177742i
$435$	−0.134356	+	0.223144i	−0.00644188	+	0.0106989i
$436$	9.81380	+	7.13014i	0.469996	+	0.341472i
$437$	39.7925	+	54.7696i	1.90353	+	2.61999i
$438$	0.184721	−	0.0600194i	0.00882629	−	0.00286784i
$439$	−0.951941			−0.0454337			−0.0227168	−	0.999742i	$-0.507232\pi$
$439$	−0.951941			−0.0454337			−0.0227168	+	0.999742i	$0.507232\pi$
$440$	1.66275	−	2.76157i	0.0792685	−	0.131653i
$441$	4.12128	+	12.6840i	0.196251	+	0.604000i
$442$	5.43095	+	1.76462i	0.258324	+	0.0839346i
$443$	32.5950	+	10.5908i	1.54864	+	0.503183i	0.953743	−	0.300622i	$-0.0971943\pi$
$443$	32.5950	+	10.5908i	1.54864	+	0.503183i	0.594893	+	0.803805i	$0.297194\pi$
$444$	0.0659610	+	0.0479235i	0.00313037	+	0.00227435i
$445$	3.94449	−	17.0146i	0.186987	−	0.806567i
$446$	15.9642	+	11.5987i	0.755928	+	0.549214i
$447$	−0.0122546	−	0.0168671i	−0.000579624	−	0.000797784i
$448$	1.51995	+	0.493860i	0.0718107	+	0.0233327i
$449$	28.6849	−	20.8408i	1.35372	−	0.983537i	0.354906	−	0.934902i	$-0.384513\pi$
$449$	28.6849	−	20.8408i	1.35372	−	0.983537i	0.998817	−	0.0486349i	$-0.0154871\pi$
$450$	−6.59975	+	13.4690i	−0.311115	+	0.634935i
$451$	3.85679	−	11.8700i	0.181609	−	0.558936i
$452$	5.93918	+	8.17459i	0.279356	+	0.384500i
$453$	−0.0534533	+	0.0735721i	−0.00251145	+	0.00345672i
$454$	−4.57342	−	14.0755i	−0.214641	−	0.660597i
$455$	1.61147	+	3.80603i	0.0755467	+	0.178430i
$456$	0.0345127	−	0.106219i	0.00161620	−	0.00497416i
$457$	30.5683	+	9.93223i	1.42992	+	0.464610i	0.918741	−	0.394862i	$-0.129208\pi$
$457$	30.5683	+	9.93223i	1.42992	+	0.464610i	0.511183	+	0.859472i	$0.329208\pi$
$458$	0.847637	−	0.275414i	0.0396075	−	0.0128692i
$459$	0.413463			0.0192988
$460$	9.75825	−	16.2069i	0.454981	−	0.755651i
$461$	7.49143	+	23.0562i	0.348911	+	1.07384i	0.959457	+	0.281856i	$0.0909500\pi$
$461$	7.49143	+	23.0562i	0.348911	+	1.07384i	−0.610546	+	0.791981i	$0.709050\pi$
$462$	−0.0189011	−	0.0260151i	−0.000879356	−	0.00121033i
$463$	−3.76915	+	5.18779i	−0.175167	+	0.241097i	−0.887569	−	0.460675i	$-0.847607\pi$
$463$	−3.76915	+	5.18779i	−0.175167	+	0.241097i	0.712402	+	0.701772i	$0.247607\pi$
$464$	8.34587			0.387447
$465$	0.173696	+	0.00498226i	0.00805495	+	0.000231047i
$466$	21.4150			0.992029
$467$	10.7585	−	14.8078i	0.497842	−	0.685221i	−0.483968	−	0.875086i	$-0.660805\pi$
$467$	10.7585	−	14.8078i	0.497842	−	0.685221i	0.981810	+	0.189865i	$0.0608049\pi$
$468$	−2.03931	−	2.80687i	−0.0942672	−	0.129748i
$469$	−6.55042	−	20.1601i	−0.302470	−	0.930908i
$470$	15.8068	+	9.51735i	0.729114	+	0.439003i
$471$	0.187057			0.00861914
$472$	−5.95071	+	1.93350i	−0.273903	+	0.0889966i
$473$	5.95178	+	1.93385i	0.273663	+	0.0889185i
$474$	0.0401354	−	0.123524i	0.00184348	−	0.00567365i
$475$	−5.64061	+	39.6100i	−0.258809	+	1.81743i
$476$	2.43838	+	7.50457i	0.111763	+	0.343971i
$477$	−23.7880	+	32.7413i	−1.08918	+	1.49912i
$478$	−4.10371	−	5.64827i	−0.187699	−	0.258346i
$479$	8.54657	−	26.3036i	0.390503	−	1.20184i	−0.541906	−	0.840439i	$-0.682297\pi$
$479$	8.54657	−	26.3036i	0.390503	−	1.20184i	0.932409	−	0.361405i	$-0.117703\pi$
$480$	−0.0310932	+	0.00269170i	−0.00141921	+	0.000122859i
$481$	5.46584	−	3.97117i	0.249221	−	0.181070i
$482$	−16.9455	−	5.50593i	−0.771846	−	0.250788i
$483$	−0.110925	−	0.152676i	−0.00504728	−	0.00694698i
$484$	−7.21789	−	5.24410i	−0.328086	−	0.238368i
$485$	−7.04711	−	1.63373i	−0.319993	−	0.0741840i
$486$	−0.304850	−	0.221486i	−0.0138283	−	0.0100468i
$487$	−32.3487	−	10.5107i	−1.46586	−	0.476286i	−0.536004	−	0.844215i	$-0.680067\pi$
$487$	−32.3487	−	10.5107i	−1.46586	−	0.476286i	−0.929854	+	0.367929i	$0.880067\pi$
$488$	−2.72970	−	0.886934i	−0.123568	−	0.0401496i
$489$	−0.0890659	−	0.274117i	−0.00402770	−	0.0123960i
$490$	5.12791	−	8.51665i	0.231655	−	0.384743i
$491$	−41.3072			−1.86417			−0.932085	−	0.362240i	$-0.882012\pi$
$491$	−41.3072			−1.86417			−0.932085	+	0.362240i	$0.882012\pi$
$492$	−0.114924	+	0.0373409i	−0.00518116	+	0.00168346i
$493$	24.2208	+	33.3370i	1.09085	+	1.50142i
$494$	−7.48727	−	5.43982i	−0.336868	−	0.244749i
$495$	−8.28416	−	4.98793i	−0.372345	−	0.224191i
$496$	−2.73402	−	4.85027i	−0.122761	−	0.217784i
$497$			8.24083i			0.369652i
$498$	−0.0673121	+	0.0926471i	−0.00301633	+	0.00415162i
$499$	−6.91262	+	5.02231i	−0.309451	+	0.224830i	−0.731661	−	0.681669i	$-0.761255\pi$
$499$	−6.91262	+	5.02231i	−0.309451	+	0.224830i	0.422210	+	0.906498i	$0.361255\pi$
$500$	10.8073	−	2.86409i	0.483316	−	0.128086i
$501$	0.0638313			0.00285177
$502$			16.7295i			0.746675i
$503$	12.1071	−	3.93384i	0.539830	−	0.175401i	−0.0263960	−	0.999652i	$-0.508403\pi$
$503$	12.1071	−	3.93384i	0.539830	−	0.175401i	0.566226	+	0.824250i	$0.308403\pi$
$504$	1.48148	−	4.55954i	0.0659906	−	0.203098i
$505$	0.562207	−	0.487819i	0.0250179	−	0.0217076i
$506$	9.86709	+	7.16886i	0.438646	+	0.318695i
$507$	−0.154808	+	0.0503003i	−0.00687528	+	0.00223391i
$508$	7.36809	−	10.1413i	0.326906	−	0.449948i
$509$	−28.0960	+	20.4130i	−1.24534	+	0.904789i	−0.997942	−	0.0641260i	$-0.979574\pi$
$509$	−28.0960	+	20.4130i	−1.24534	+	0.904789i	−0.247394	+	0.968915i	$0.579574\pi$
$510$	−0.100988	−	0.116388i	−0.00447184	−	0.00515376i
$511$	17.9923	−	13.0722i	0.795932	−	0.578278i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$	−0.637294	−	0.207069i	−0.0281372	−	0.00914233i
$514$	15.0161	−	10.9098i	0.662330	−	0.481211i
$515$	−8.52146	+	3.60797i	−0.375500	+	0.158986i
$516$	−0.0187233	−	0.0576242i	−0.000824245	−	0.00253677i
$517$	−6.99189	+	9.62351i	−0.307503	+	0.423242i
$518$	8.87883	+	2.88491i	0.390113	+	0.126756i
$519$	0.0497590	−	0.153142i	0.00218418	−	0.00672221i
$520$	−0.584062	+	2.51935i	−0.0256128	+	0.110481i
$521$	−31.9539			−1.39993			−0.699964	−	0.714178i	$-0.746801\pi$
$521$	−31.9539			−1.39993			−0.699964	+	0.714178i	$0.746801\pi$
$522$		−	25.0360i		−	1.09580i
$523$	26.8047	−	8.70936i	1.17209	−	0.380834i	0.342665	−	0.939458i	$-0.388670\pi$
$523$	26.8047	−	8.70936i	1.17209	−	0.380834i	0.829421	+	0.558624i	$0.188670\pi$
$524$	−5.30482	+	3.85417i	−0.231742	+	0.168370i
$525$	0.0157237	−	0.110417i	0.000686240	−	0.00481898i
$526$	−4.10140			−0.178829
$527$	11.4396	−	24.9970i	0.498317	−	1.08889i
$528$		−	0.0201208i		−	0.000875646i
$529$	39.3000	+	28.5531i	1.70870	+	1.24144i
$530$	30.0545	−	2.60178i	1.30548	−	0.113014i
$531$	5.80013	+	17.8510i	0.251704	+	0.774666i
$532$		−	12.7884i		−	0.554447i
$533$			10.0132i			0.433720i
$534$	−0.0336890	−	0.103684i	−0.00145786	−	0.00448685i
$535$	−2.74309	−	3.16139i	−0.118594	−	0.136679i
$536$	4.09871	−	12.6145i	0.177037	−	0.544865i
$537$	0.0609650	−	0.0839112i	0.00263084	−	0.00362103i
$538$	17.4157	−	5.65872i	0.750846	−	0.243965i
$539$	5.18511	+	3.76720i	0.223338	+	0.162265i
$540$	0.0161497	+	0.186553i	0.000694971	+	0.00802798i
$541$	−4.34116	+	13.3607i	−0.186641	+	0.574422i	−0.999973	−	0.00737825i	$-0.997651\pi$
$541$	−4.34116	+	13.3607i	−0.186641	+	0.574422i	0.813332	+	0.581800i	$0.197651\pi$
$542$	−1.70561	−	2.34757i	−0.0732623	−	0.100837i
$543$	0.0548019	+	0.0754283i	0.00235177	+	0.00323694i
$544$	−1.52574	+	4.69574i	−0.0654155	+	0.201328i
$545$	−27.0236	+	2.33940i	−1.15756	+	0.100209i
$546$	0.0208715	+	0.0151640i	0.000893217	+	0.000648960i
$547$	−37.2933	+	12.1173i	−1.59455	+	0.518100i	−0.965751	−	0.259471i	$-0.916452\pi$
$547$	−37.2933	+	12.1173i	−1.59455	+	0.518100i	−0.628796	+	0.777571i	$0.716452\pi$
$548$	−1.03103	+	1.41909i	−0.0440434	+	0.0606206i
$549$	−2.66063	+	8.18858i	−0.113553	+	0.349480i
$550$	1.23869	+	7.10075i	0.0528178	+	0.302777i
$551$	−20.6371	−	63.5144i	−0.879169	−	2.70580i
$552$		−	0.118084i		−	0.00502598i
$553$		−	14.8719i		−	0.632416i
$554$	−2.06751	−	6.36315i	−0.0878402	−	0.270344i
$555$	−0.181633	+	0.0157237i	−0.00770987	+	0.000667433i
$556$	10.7420	+	7.80454i	0.455563	+	0.330986i
$557$		−	14.9720i		−	0.634386i	−0.948361	−	0.317193i	$-0.897260\pi$
$557$		−	14.9720i		−	0.634386i	0.948361	−	0.317193i	$-0.102740\pi$
$558$	−14.5499	+	8.20154i	−0.615945	+	0.347199i
$559$	−5.02075			−0.212355
$560$	−3.29080	+	1.39331i	−0.139061	+	0.0588783i
$561$	0.0803713	−	0.0583932i	0.00339328	−	0.00246536i
$562$	2.11465	−	0.687091i	0.0892010	−	0.0289832i
$563$			0.427944i			0.0180357i	0.999959	+	0.00901785i	$0.00287051\pi$
$563$			0.427944i			0.0180357i	−0.999959	+	0.00901785i	$0.997129\pi$
$564$	0.115169			0.00484948
$565$	−22.0103	−	5.10264i	−0.925979	−	0.214670i
$566$	−7.11149	+	21.8869i	−0.298918	+	0.919976i
$567$	−13.6768	−	4.44388i	−0.574374	−	0.186625i
$568$	−3.03088	+	4.17164i	−0.127173	+	0.175038i
$569$	−7.29530	−	22.4526i	−0.305835	−	0.941263i	−0.979364	−	0.202102i	$-0.935223\pi$
$569$	−7.29530	−	22.4526i	−0.305835	−	0.941263i	0.673530	−	0.739160i	$-0.264777\pi$
$570$	0.0973697	+	0.229972i	0.00407837	+	0.00963248i
$571$	1.65255	−	1.20065i	0.0691569	−	0.0502455i	−0.552670	−	0.833400i	$-0.686391\pi$
$571$	1.65255	−	1.20065i	0.0691569	−	0.0502455i	0.621827	+	0.783155i	$0.286391\pi$
$572$	−1.58570	−	0.515226i	−0.0663015	−	0.0215427i
$573$	0.0233320	+	0.0321137i	0.000974707	+	0.00134157i
$574$	−11.1939	+	8.13282i	−0.467223	+	0.339457i
$575$	7.26953	+	41.6724i	0.303160	+	1.73786i
$576$	2.42689	−	1.76324i	0.101121	−	0.0734684i
$577$	21.1567	−	29.1197i	0.880764	−	1.21227i	−0.0954451	−	0.995435i	$-0.530427\pi$
$577$	21.1567	−	29.1197i	0.880764	−	1.21227i	0.976209	−	0.216833i	$-0.0695726\pi$
$578$	−7.01676	+	2.27988i	−0.291859	+	0.0948306i
$579$	0.0135048	+	0.00981181i	0.000561240	+	0.000407765i
$580$	−14.0955	+	12.2305i	−0.585284	+	0.507842i
$581$	−4.05206	+	12.4710i	−0.168108	+	0.517383i
$582$	−0.0429440	+	0.0139534i	−0.00178009	+	0.000578385i
$583$			19.4486i			0.805480i
$584$	13.9158			0.575838
$585$	7.55757	+	1.75207i	0.312467	+	0.0724393i
$586$	−6.87138	+	4.99235i	−0.283854	+	0.206232i
$587$	−2.76463	+	3.80519i	−0.114109	+	0.157057i	−0.862251	−	0.506481i	$-0.830946\pi$
$587$	−2.76463	+	3.80519i	−0.114109	+	0.157057i	0.748142	+	0.663538i	$0.230946\pi$
$588$		−	0.0620524i		−	0.00255900i
$589$	−30.1514	+	32.8001i	−1.24237	+	1.35150i
$590$	7.21682	−	11.9860i	0.297112	−	0.493456i
$591$	−0.0666283	−	0.0484083i	−0.00274072	−	0.00199125i
$592$	3.43357	+	4.72591i	0.141119	+	0.194234i
$593$	0.739884	−	0.240403i	0.0303834	−	0.00987216i	−0.293786	−	0.955871i	$-0.594915\pi$
$593$	0.739884	−	0.240403i	0.0303834	−	0.00987216i	0.324169	+	0.945999i	$0.394915\pi$
$594$	−0.120721			−0.00495324
$595$	−15.1158	−	9.10129i	−0.619688	−	0.373117i
$596$	−0.461596	−	1.42065i	−0.0189077	−	0.0581919i
$597$	0.151372	+	0.0491836i	0.00619523	+	0.00201295i
$598$	−9.30607	−	3.02373i	−0.380554	−	0.123649i
$599$	−0.985268	−	0.715839i	−0.0402569	−	0.0292484i	0.567475	−	0.823391i	$-0.307920\pi$
$599$	−0.985268	−	0.715839i	−0.0402569	−	0.0292484i	−0.607732	+	0.794142i	$0.707920\pi$
$600$	0.0485695	−	0.0501117i	0.00198284	−	0.00204580i
$601$	7.63662	+	5.54833i	0.311504	+	0.226321i	0.732542	−	0.680722i	$-0.238334\pi$
$601$	7.63662	+	5.54833i	0.311504	+	0.226321i	−0.421038	+	0.907043i	$0.638334\pi$
$602$	−4.07791	−	5.61276i	−0.166203	−	0.228759i
$603$	−37.8412	−	12.2953i	−1.54101	−	0.500705i
$604$	−5.27122	+	3.82977i	−0.214483	+	0.155831i
$605$	19.8754	−	1.72059i	0.808051	−	0.0699518i
$606$	0.00143573	−	0.00441871i	5.83224e−5	−	0.000179498i
$607$	18.2533	+	25.1235i	0.740879	+	1.01973i	0.998568	+	0.0535044i	$0.0170391\pi$
$607$	18.2533	+	25.1235i	0.740879	+	1.01973i	−0.257689	+	0.966228i	$0.582961\pi$
$608$	4.70341	−	6.47369i	0.190748	−	0.262543i
$609$	0.0575278	+	0.177052i	0.00233114	+	0.00717452i
$610$	5.91001	−	2.50228i	0.239289	−	0.101315i
$611$	2.94908	−	9.07634i	0.119307	−	0.367189i
$612$	14.0863	+	4.57692i	0.569405	+	0.185011i
$613$	13.9097	−	4.51955i	0.561809	−	0.182543i	−0.0143259	−	0.999897i	$-0.504560\pi$
$613$	13.9097	−	4.51955i	0.561809	−	0.182543i	0.576135	+	0.817355i	$0.304560\pi$
$614$	−6.79843			−0.274362
$615$	0.139376	−	0.231481i	0.00562016	−	0.00933421i
$616$	−0.711947	−	2.19115i	−0.0286852	−	0.0882838i
$617$	−7.54642	−	10.3868i	−0.303807	−	0.418155i	0.629630	−	0.776895i	$-0.283206\pi$
$617$	−7.54642	−	10.3868i	−0.303807	−	0.418155i	−0.933437	+	0.358740i	$0.883206\pi$
$618$	−0.0339512	+	0.0467299i	−0.00136572	+	0.00187975i
$619$	−0.977191			−0.0392766			−0.0196383	−	0.999807i	$-0.506251\pi$
$619$	−0.977191			−0.0392766			−0.0196383	+	0.999807i	$0.506251\pi$
$620$	11.7254	+	4.18514i	0.470903	+	0.168079i
$621$	−0.708480			−0.0284303
$622$	−12.9566	+	17.8332i	−0.519512	+	0.715047i
$623$	−7.33743	−	10.0991i	−0.293968	−	0.404612i
$624$	0.00498834	+	0.0153525i	0.000199694	+	0.000614594i
$625$	−14.0554	+	20.6747i	−0.562217	+	0.826990i
$626$	−4.88915			−0.195410
$627$	−0.153125	+	0.0497533i	−0.00611522	+	0.00198696i
$628$	12.7461	+	4.14147i	0.508627	+	0.165263i
$629$	−8.91267	+	27.4304i	−0.355371	+	1.09372i
$630$	4.17967	+	9.87175i	0.166522	+	0.393300i
$631$	−3.22329	−	9.92028i	−0.128317	−	0.394920i	0.866174	−	0.499743i	$-0.166572\pi$
$631$	−3.22329	−	9.92028i	−0.128317	−	0.394920i	−0.994491	+	0.104823i	$0.966572\pi$
$632$	5.46968	−	7.52838i	0.217572	−	0.299463i
$633$	0.0681763	+	0.0938366i	0.00270976	+	0.00372967i
$634$	−7.15690	+	22.0267i	−0.284237	+	0.874791i
$635$	2.41747	+	27.9255i	0.0959343	+	1.10819i
$636$	0.152337	−	0.110679i	0.00604055	−	0.00438872i
$637$	−4.89029	−	1.58895i	−0.193760	−	0.0629566i
$638$	−7.07186	−	9.73358i	−0.279978	−	0.385356i
$639$	12.5141	+	9.09204i	0.495051	+	0.359675i
$640$	−2.17830	−	0.504995i	−0.0861048	−	0.0199617i
$641$	11.1299	+	8.08637i	0.439606	+	0.319392i	0.785478	−	0.618889i	$-0.212417\pi$
$641$	11.1299	+	8.08637i	0.439606	+	0.319392i	−0.345872	+	0.938282i	$0.612417\pi$
$642$	−0.0248472	−	0.00807334i	−0.000980640	−	0.000318629i
$643$	−11.5802	−	3.76264i	−0.456679	−	0.148384i	0.0716387	−	0.997431i	$-0.477177\pi$
$643$	−11.5802	−	3.76264i	−0.456679	−	0.148384i	−0.528318	+	0.849046i	$0.677177\pi$
$644$	−4.17823	−	12.8593i	−0.164645	−	0.506726i
$645$	0.116068	+	0.0698848i	0.00457016	+	0.00275171i
$646$	39.5086			1.55445
$647$	14.0368	−	4.56084i	0.551845	−	0.179305i	−0.0198037	−	0.999804i	$-0.506304\pi$
$647$	14.0368	−	4.56084i	0.551845	−	0.179305i	0.571648	+	0.820499i	$0.306304\pi$
$648$	−5.28904	−	7.27973i	−0.207773	−	0.285975i
$649$	7.29732	+	5.30181i	0.286445	+	0.208114i
$650$	−2.70555	−	5.11090i	−0.106121	−	0.200466i
$651$	0.0840499	−	0.0914333i	0.00329417	−	0.00358356i
$652$		−	20.6503i		−	0.808730i
$653$	−4.46639	+	6.14745i	−0.174783	+	0.240568i	−0.887417	−	0.460968i	$-0.847502\pi$
$653$	−4.46639	+	6.14745i	−0.174783	+	0.240568i	0.712634	+	0.701536i	$0.247502\pi$
$654$	−0.136974	+	0.0995177i	−0.00535612	+	0.00389145i
$655$	3.31131	−	14.2833i	0.129384	−	0.558096i
$656$	−8.65766			−0.338025
$657$		−	41.7446i		−	1.62861i
$658$	12.5418	−	4.07508i	0.488931	−	0.158863i
$659$	12.0671	−	37.1387i	0.470068	−	1.44672i	−0.382428	−	0.923985i	$-0.624912\pi$
$659$	12.0671	−	37.1387i	0.470068	−	1.44672i	0.852496	−	0.522734i	$-0.175088\pi$
$660$	0.0294861	+	0.0339825i	0.00114774	+	0.00132277i
$661$	−19.5905	−	14.2333i	−0.761982	−	0.553612i	0.137536	−	0.990497i	$-0.456082\pi$
$661$	−19.5905	−	14.2333i	−0.761982	−	0.553612i	−0.899518	+	0.436884i	$0.856082\pi$
$662$	7.05904	−	2.29362i	0.274357	−	0.0891441i
$663$	−0.0468479	+	0.0644806i	−0.00181942	+	0.00250422i
$664$	−6.63789	+	4.82271i	−0.257600	+	0.187157i
$665$	18.7408	+	21.5986i	0.726735	+	0.837557i
$666$	14.1768	−	10.3001i	0.549340	−	0.399119i
$667$	−41.5029	−	57.1238i	−1.60700	−	2.21184i
$668$	4.34949	+	1.41323i	0.168287	+	0.0546797i
$669$	−0.222818	+	0.161887i	−0.00861463	+	0.00625890i
$670$	11.5636	+	27.3114i	0.446740	+	1.05513i
$671$	1.27860	+	3.93513i	0.0493598	+	0.151914i
$672$	−0.0131112	+	0.0180460i	−0.000505776	+	0.000696140i
$673$	2.19464	+	0.713082i	0.0845972	+	0.0274873i	0.351010	−	0.936372i	$-0.385838\pi$
$673$	2.19464	+	0.713082i	0.0845972	+	0.0274873i	−0.266413	+	0.963859i	$0.585838\pi$
$674$	−1.88364	+	5.79724i	−0.0725550	+	0.223301i
$675$	−0.300660	−	0.291407i	−0.0115724	−	0.0112163i
$676$	−11.6623			−0.448552
$677$			11.9216i			0.458186i	0.973405	+	0.229093i	$0.0735760\pi$
$677$			11.9216i			0.458186i	−0.973405	+	0.229093i	$0.926424\pi$
$678$	−0.134127	+	0.0435805i	−0.00515112	+	0.00167370i
$679$	−4.18286	+	3.03903i	−0.160523	+	0.116627i
$680$	−4.30453	−	10.1666i	−0.165071	−	0.389872i
$681$	0.206567			0.00791566
$682$	−3.34008	+	7.29849i	−0.127898	+	0.279474i
$683$			32.9433i			1.26054i	0.776376	+	0.630269i	$0.217056\pi$
$683$			32.9433i			1.26054i	−0.776376	+	0.630269i	$0.782944\pi$
$684$	−19.4198	−	14.1093i	−0.742535	−	0.539483i
$685$	−0.338280	−	3.90766i	−0.0129250	−	0.149304i
$686$	−5.65266	−	17.3971i	−0.215820	−	0.664224i
$687$			0.0124396i			0.000474599i
$688$		−	4.34107i		−	0.165502i
$689$	−4.82170	−	14.8397i	−0.183692	−	0.565346i
$690$	0.173046	+	0.199434i	0.00658775	+	0.00759233i
$691$	−0.663085	+	2.04077i	−0.0252250	+	0.0776344i	−0.962877	−	0.269942i	$-0.912995\pi$
$691$	−0.663085	+	2.04077i	−0.0252250	+	0.0776344i	0.937652	+	0.347577i	$0.112995\pi$
$692$	6.78119	−	9.33351i	0.257782	−	0.354807i
$693$	−6.57301	+	2.13570i	−0.249688	+	0.0811286i
$694$	−6.84083	−	4.97015i	−0.259674	−	0.188664i
$695$	−29.5796	+	2.56066i	−1.12202	+	0.0971315i
$696$	−0.0359961	+	0.110785i	−0.00136443	+	0.00419928i
$697$	−25.1256	−	34.5825i	−0.951702	−	1.30990i
$698$	−1.13922	−	1.56800i	−0.0431200	−	0.0593496i
$699$	−0.0923638	+	0.284267i	−0.00349352	+	0.0107519i
$700$	3.51606	−	7.17570i	0.132895	−	0.271216i
$701$	8.54580	+	6.20889i	0.322771	+	0.234507i	0.737357	−	0.675504i	$-0.236074\pi$
$701$	8.54580	+	6.20889i	0.322771	+	0.234507i	−0.414586	+	0.910010i	$0.636074\pi$
$702$	0.0921123	−	0.0299291i	0.00347655	−	0.00112960i
$703$	27.4752	−	37.8163i	1.03625	−	1.42627i
$704$	0.445478	−	1.37104i	0.0167896	−	0.0516730i
$705$	−0.194511	+	0.168774i	−0.00732570	+	0.00635640i
$706$	2.48215	+	7.63926i	0.0934168	+	0.287507i
$707$		−	0.531997i		−	0.0200078i
$708$		−	0.0873302i		−	0.00328207i
$709$	−3.51469	−	10.8171i	−0.131997	−	0.406245i	0.863114	−	0.505010i	$-0.168511\pi$
$709$	−3.51469	−	10.8171i	−0.131997	−	0.406245i	−0.995111	+	0.0987643i	$0.968511\pi$
$710$	−0.994429	−	11.4872i	−0.0373202	−	0.431106i
$711$	−22.5837	−	16.4080i	−0.846953	−	0.615348i
$712$		−	7.81094i		−	0.292727i
$713$	−19.6020	+	42.8329i	−0.734102	+	1.60411i
$714$	−0.110134			−0.00412166
$715$	3.43316	−	1.45359i	0.128393	−	0.0543613i
$716$	6.01198	−	4.36796i	0.224678	−	0.163238i
$717$	0.0926757	−	0.0301122i	0.00346104	−	0.00112456i
$718$			0.195841i			0.00730874i
$719$	14.5268			0.541759			0.270879	−	0.962613i	$-0.412686\pi$
$719$	14.5268			0.541759			0.270879	+	0.962613i	$0.412686\pi$
$720$	−1.51489	+	6.53447i	−0.0564565	+	0.243525i
$721$	−2.04380	+	6.29018i	−0.0761152	+	0.234258i
$722$	−42.8267	−	13.9152i	−1.59385	−	0.517872i
$723$	0.146174	−	0.201191i	0.00543625	−	0.00748236i
$724$	2.06423	+	6.35303i	0.0767163	+	0.236109i
$725$	5.88306	−	41.3126i	0.218491	−	1.53431i
$726$	0.100742	−	0.0731936i	0.00373890	−	0.00271647i
$727$	15.9230	+	5.17371i	0.590553	+	0.191882i	0.589023	−	0.808116i	$-0.299513\pi$
$727$	15.9230	+	5.17371i	0.590553	+	0.191882i	0.00153043	+	0.999999i	$0.499513\pi$
$728$	1.08646	+	1.49538i	0.0402667	+	0.0554224i
$729$	−21.8349	+	15.8640i	−0.808702	+	0.587556i
$730$	−23.5026	+	20.3929i	−0.869871	+	0.754774i
$731$	17.3401	−	12.5983i	0.641348	−	0.465966i
$732$	0.0235467	−	0.0324092i	0.000870311	−	0.00119788i
$733$	25.2288	−	8.19734i	0.931848	−	0.302776i	0.196530	−	0.980498i	$-0.437033\pi$
$733$	25.2288	−	8.19734i	0.931848	−	0.302776i	0.735318	+	0.677722i	$0.237033\pi$
$734$	−14.5069	−	10.5399i	−0.535460	−	0.389035i
$735$	0.0909348	+	0.104802i	0.00335418	+	0.00386567i
$736$	2.61439	−	8.04627i	0.0963677	−	0.296589i
$737$	−18.1851	+	5.90868i	−0.669855	+	0.217649i
$738$			25.9713i			0.956017i
$739$	−7.39741			−0.272118			−0.136059	−	0.990701i	$-0.543444\pi$
$739$	−7.39741			−0.272118			−0.136059	+	0.990701i	$0.543444\pi$
$740$	−12.7246	−	2.94995i	−0.467766	−	0.108442i
$741$	0.104502	−	0.0759253i	0.00383899	−	0.00278919i
$742$	12.6732	−	17.4431i	0.465247	−	0.640358i
$743$		−	0.878251i		−	0.0322199i	−0.999870	−	0.0161099i	$-0.994872\pi$
$743$		−	0.878251i		−	0.0322199i	0.999870	−	0.0161099i	$-0.00512818\pi$
$744$	0.0761754	−	0.0153725i	0.00279273	−	0.000563585i
$745$	2.86149	+	1.72291i	0.104837	+	0.0631226i
$746$	−6.72339	−	4.88483i	−0.246161	−	0.178846i
$747$	14.4672	+	19.9124i	0.529326	+	0.728555i
$748$	6.76936	−	2.19950i	0.247512	−	0.0804216i
$749$	−2.99151			−0.109307
$750$	−0.00859375	+	0.155811i	−0.000313800	+	0.00568941i
$751$	2.50290	+	7.70312i	0.0913320	+	0.281091i	0.986280	−	0.165079i	$-0.0527878\pi$
$751$	2.50290	+	7.70312i	0.0913320	+	0.281091i	−0.894948	+	0.446170i	$0.852788\pi$
$752$	7.84764	+	2.54985i	0.286174	+	0.0929835i
$753$	−0.222071	−	0.0721552i	−0.00809271	−	0.00262948i
$754$	7.80910	+	5.67364i	0.284391	+	0.206622i
$755$	3.29034	−	14.1929i	0.119748	−	0.516532i
$756$	0.108273	+	0.0786647i	0.00393784	+	0.00286101i
$757$	−29.7732	−	40.9794i	−1.08213	−	1.48942i	−0.857158	−	0.515054i	$-0.827772\pi$
$757$	−29.7732	−	40.9794i	−1.08213	−	1.48942i	−0.224969	−	0.974366i	$-0.572228\pi$
$758$	7.73702	+	2.51391i	0.281021	+	0.0913093i
$759$	−0.137718	+	0.100058i	−0.00499885	+	0.00363188i
$760$	1.54319	+	17.8262i	0.0559772	+	0.646623i
$761$	10.4315	−	32.1049i	0.378142	−	1.16380i	−0.563193	−	0.826326i	$-0.690427\pi$
$761$	10.4315	−	32.1049i	0.378142	−	1.16380i	0.941334	−	0.337475i	$-0.109573\pi$
$762$	0.102839	+	0.141546i	0.00372546	+	0.00512765i
$763$	−11.3951	+	15.6841i	−0.412532	+	0.567801i
$764$	0.878847	+	2.70481i	0.0317956	+	0.0978567i
$765$	−30.4979	+	12.9127i	−1.10265	+	0.466861i
$766$	4.75459	−	14.6331i	0.171790	−	0.528716i
$767$	−6.88241	−	2.23623i	−0.248509	−	0.0807456i
$768$	−0.0132742	+	0.00431305i	−0.000478992	+	0.000155634i
$769$	44.9577			1.62121			0.810607	−	0.585590i	$-0.199137\pi$
$769$	44.9577			1.62121			0.810607	+	0.585590i	$0.199137\pi$
$770$	4.41344	+	2.65735i	0.159049	+	0.0957643i
$771$	0.0800540	+	0.246381i	0.00288307	+	0.00887319i
$772$	0.702986	+	0.967578i	0.0253010	+	0.0348239i
$773$	−3.16794	+	4.36030i	−0.113943	+	0.156829i	−0.862179	−	0.506603i	$-0.830901\pi$
$773$	−3.16794	+	4.36030i	−0.113943	+	0.156829i	0.748236	+	0.663432i	$0.230901\pi$
$774$	−13.0224			−0.468079
$775$	−25.9364	+	10.1146i	−0.931662	+	0.363327i
$776$	−3.23515			−0.116135
$777$	−0.0765897	+	0.105417i	−0.00274764	+	0.00378180i
$778$	−19.9097	−	27.4034i	−0.713798	−	0.982459i
$779$	21.4081	+	65.8872i	0.767023	+	2.36065i
$780$	−0.0309233	−	0.0186191i	−0.00110723	−	0.000666669i
$781$	7.43349			0.265991
$782$	39.7276	−	12.9083i	1.42066	−	0.461599i
$783$	0.664687	+	0.215970i	0.0237540	+	0.00771813i
$784$	1.37385	−	4.22827i	0.0490660	−	0.151010i
$785$	−27.5964	+	11.6842i	−0.984956	+	0.417028i
$786$	−0.0282812	−	0.0870405i	−0.00100876	−	0.00310463i
$787$	−1.01738	+	1.40030i	−0.0362656	+	0.0499153i	−0.826765	−	0.562548i	$-0.809821\pi$
$787$	−1.01738	+	1.40030i	−0.0362656	+	0.0499153i	0.790499	+	0.612463i	$0.209821\pi$
$788$	−3.46831	−	4.77372i	−0.123553	−	0.170057i
$789$	0.0176895	−	0.0544428i	0.000629764	−	0.00193821i
$790$	1.79460	+	20.7304i	0.0638490	+	0.737554i
$791$	−13.0643	+	9.49180i	−0.464514	+	0.337489i
$792$	−4.11285	−	1.33635i	−0.146144	−	0.0474850i
$793$	−1.95119	−	2.68558i	−0.0692888	−	0.0953679i
$794$	12.2591	+	8.90676i	0.435059	+	0.316089i
$795$	−0.0950900	+	0.410171i	−0.00337249	+	0.0145473i
$796$	9.22558	+	6.70278i	0.326992	+	0.237574i
$797$	−20.4057	−	6.63022i	−0.722808	−	0.234855i	−0.0755678	−	0.997141i	$-0.524077\pi$
$797$	−20.4057	−	6.63022i	−0.722808	−	0.234855i	−0.647240	+	0.762286i	$0.724077\pi$
$798$	0.169756	+	0.0551570i	0.00600928	+	0.00195253i
$799$	12.5896	+	38.7469i	0.445389	+	1.37077i
$800$	4.41902	−	2.33929i	0.156236	−	0.0827064i
$801$	−23.4313			−0.827904
$802$	−14.6235	+	4.75146i	−0.516374	+	0.167780i
$803$	−11.7915	−	16.2296i	−0.416113	−	0.572730i
$804$	0.149770	+	0.108814i	0.00528198	+	0.00383758i
$805$	25.9013	+	15.5953i	0.912902	+	0.549662i
$806$	0.739100	−	6.39695i	0.0260337	−	0.225323i
$807$			0.255586i			0.00899707i
$808$	0.195662	−	0.269305i	0.00688335	−	0.00947412i
$809$	24.0066	−	17.4418i	0.844027	−	0.613221i	−0.0794660	−	0.996838i	$-0.525322\pi$
$809$	24.0066	−	17.4418i	0.844027	−	0.613221i	0.923493	+	0.383616i	$0.125322\pi$
$810$	19.6009	+	4.54407i	0.688704	+	0.159662i
$811$	−19.6603			−0.690367			−0.345184	−	0.938535i	$-0.612183\pi$
$811$	−19.6603			−0.690367			−0.345184	+	0.938535i	$0.612183\pi$
$812$			13.3381i			0.468075i
$813$	0.0385185	−	0.0125154i	0.00135090	−	0.000438935i
$814$	2.60228	−	8.00898i	0.0912098	−	0.280715i
$815$	30.2621	+	34.8768i	1.06003	+	1.22168i
$816$	−0.0557516	−	0.0405059i	−0.00195170	−	0.00141799i
$817$	−33.0367	+	10.7343i	−1.15581	+	0.375545i
$818$	−18.4503	+	25.3947i	−0.645100	+	0.887904i
$819$	4.48584	−	3.25916i	0.156748	−	0.113884i
$820$	14.6221	−	12.6874i	0.510626	−	0.443063i
$821$	−5.76616	+	4.18936i	−0.201240	+	0.146210i	−0.683842	−	0.729631i	$-0.739692\pi$
$821$	−5.76616	+	4.18936i	−0.201240	+	0.146210i	0.482601	+	0.875840i	$0.339692\pi$
$822$	−0.0143904	−	0.0198067i	−0.000501923	−	0.000690838i
$823$	−17.5436	−	5.70027i	−0.611532	−	0.198699i	−0.0131549	−	0.999913i	$-0.504187\pi$
$823$	−17.5436	−	5.70027i	−0.611532	−	0.198699i	−0.598377	+	0.801215i	$0.704187\pi$
$824$	−3.34805	+	2.43250i	−0.116635	+	0.0847403i
$825$	−0.0995993	−	0.0141833i	−0.00346760	−	0.000493799i
$826$	−3.09006	−	9.51021i	−0.107517	−	0.330903i
$827$	17.3535	−	23.8850i	0.603440	−	0.830564i	−0.392578	−	0.919719i	$-0.628417\pi$
$827$	17.3535	−	23.8850i	0.603440	−	0.830564i	0.996018	+	0.0891547i	$0.0284166\pi$
$828$	−24.1372	−	7.84266i	−0.838827	−	0.272551i
$829$	16.1902	−	49.8283i	0.562309	−	1.73061i	−0.113507	−	0.993537i	$-0.536208\pi$
$829$	16.1902	−	49.8283i	0.562309	−	1.73061i	0.675816	−	0.737071i	$-0.263792\pi$
$830$	4.14342	−	17.8727i	0.143820	−	0.620369i
$831$	0.0933830			0.00323942
$832$			1.15657i			0.0400968i
$833$	20.8766	−	6.78323i	0.723333	−	0.235025i
$834$	−0.149930	+	0.108930i	−0.00519165	+	0.00377195i
$835$	−9.41697	+	3.98712i	−0.325888	+	0.137980i
$836$	−11.5355			−0.398965
$837$	−0.0922322	−	0.457038i	−0.00318801	−	0.0157975i
$838$			20.9638i			0.724183i
$839$	−17.6657	−	12.8349i	−0.609888	−	0.443110i	0.239487	−	0.970900i	$-0.423021\pi$
$839$	−17.6657	−	12.8349i	−0.609888	−	0.443110i	−0.849375	+	0.527790i	$0.823021\pi$
$840$	−0.00430178	−	0.0496921i	−0.000148425	−	0.00171454i
$841$	12.5626	+	38.6638i	0.433194	+	1.33323i
$842$		−	12.1565i		−	0.418940i
$843$			0.0310337i			0.00106886i
$844$	2.56800	+	7.90349i	0.0883942	+	0.272049i
$845$	19.6968	−	17.0906i	0.677590	−	0.587934i
$846$	7.64906	−	23.5414i	0.262980	−	0.809369i
$847$	8.38094	−	11.5354i	0.287973	−	0.396360i
$848$	12.8307	−	4.16896i	0.440610	−	0.143163i
$849$	−0.259859	−	0.188799i	−0.00891834	−	0.00647956i
$850$	22.1687	+	10.8626i	0.760380	+	0.372583i
$851$	15.2721	−	47.0026i	0.523520	−	1.61123i
$852$	−0.0423029	−	0.0582250i	−0.00144927	−	0.00199475i
$853$	8.49116	+	11.6871i	0.290732	+	0.400158i	0.929252	−	0.369447i	$-0.120453\pi$
$853$	8.49116	+	11.6871i	0.290732	+	0.400158i	−0.638520	+	0.769605i	$0.720453\pi$
$854$	1.41747	−	4.36252i	0.0485047	−	0.149282i
$855$	53.4750	−	4.62926i	1.82881	−	0.158317i
$856$	−1.51435	−	1.10024i	−0.0517594	−	0.0376054i
$857$	34.5576	−	11.2285i	1.18047	−	0.383557i	0.347926	−	0.937522i	$-0.386886\pi$
$857$	34.5576	−	11.2285i	1.18047	−	0.383557i	0.832540	+	0.553965i	$0.186886\pi$
$858$	0.0136784	−	0.0188267i	0.000466974	−	0.000642734i
$859$	11.8282	−	36.4036i	0.403574	−	1.24207i	−0.518505	−	0.855074i	$-0.673511\pi$
$859$	11.8282	−	36.4036i	0.403574	−	1.24207i	0.922080	−	0.387000i	$-0.126489\pi$
$860$	6.36163	+	7.33172i	0.216930	+	0.250010i
$861$	−0.0596770	−	0.183667i	−0.00203379	−	0.00625935i
$862$			27.3630i			0.931988i
$863$			20.9597i			0.713476i	0.934204	+	0.356738i	$0.116111\pi$
$863$			20.9597i			0.713476i	−0.934204	+	0.356738i	$0.883889\pi$
$864$	0.0258775	+	0.0796426i	0.000880369	+	0.00270950i
$865$	2.22491	+	25.7011i	0.0756491	+	0.873862i
$866$	29.6749	+	21.5601i	1.00839	+	0.732642i
$867$		−	0.102975i		−	0.00349722i
$868$	7.75153	−	4.36942i	0.263104	−	0.148308i
$869$	−13.4149			−0.455069
$870$	−0.101555	−	0.239857i	−0.00344304	−	0.00813192i
$871$	12.4106	−	9.01686i	0.420519	−	0.305525i
$872$	−11.5368	+	3.74854i	−0.390686	+	0.126941i
$873$			9.70481i			0.328458i
$874$	−67.6990			−2.28995
$875$	4.57729	+	17.2718i	0.154741	+	0.583893i
$876$	−0.0600194	+	0.184721i	−0.00202787	+	0.00624113i
$877$	17.6732	+	5.74235i	0.596780	+	0.193906i	0.591804	−	0.806082i	$-0.298416\pi$
$877$	17.6732	+	5.74235i	0.596780	+	0.193906i	0.00497614	+	0.999988i	$0.498416\pi$
$878$	0.559537	−	0.770137i	0.0188835	−	0.0259909i
$879$	−0.0366329	−	0.112744i	−0.00123560	−	0.00380277i
$880$	1.25681	+	2.96840i	0.0423672	+	0.100065i
$881$	34.1104	−	24.7826i	1.14921	−	0.834948i	0.160832	−	0.986982i	$-0.448582\pi$
$881$	34.1104	−	24.7826i	1.14921	−	0.834948i	0.988375	+	0.152034i	$0.0485824\pi$
$882$	−12.6840	−	4.12128i	−0.427092	−	0.138771i
$883$	13.0246	+	17.9268i	0.438311	+	0.603284i	0.969836	−	0.243759i	$-0.0783806\pi$
$883$	13.0246	+	17.9268i	0.438311	+	0.603284i	−0.531524	+	0.847043i	$0.678381\pi$
$884$	−4.61984	+	3.35651i	−0.155382	+	0.112892i
$885$	0.127978	+	0.147494i	0.00430194	+	0.00495795i
$886$	−27.7270	+	20.1448i	−0.931506	+	0.676779i
$887$	−0.106667	+	0.146815i	−0.00358153	+	0.00492956i	−0.810804	−	0.585318i	$-0.800970\pi$
$887$	−0.106667	+	0.146815i	−0.00358153	+	0.00492956i	0.807222	+	0.590247i	$0.200970\pi$
$888$	−0.0775418	+	0.0251949i	−0.00260213	+	0.000845485i
$889$	16.2075	+	11.7754i	0.543582	+	0.394935i
$890$	11.4466	+	13.1921i	0.383689	+	0.442199i
$891$	−4.00852	+	12.3369i	−0.134290	+	0.413303i
$892$	−18.7671	+	6.09779i	−0.628368	+	0.204169i
$893$		−	66.0278i		−	2.20954i
$894$	0.0208488			0.000697289
$895$	−3.75273	+	16.1874i	−0.125440	+	0.541085i
$896$	−1.29294	+	0.939378i	−0.0431942	+	0.0313824i
$897$	0.0802751	−	0.110489i	0.00268031	−	0.00368913i
$898$			35.4564i			1.18320i
$899$	31.4474	−	34.2099i	1.04883	−	1.14097i
$900$	−7.01742	−	13.2562i	−0.233914	−	0.441873i
$901$	53.8891	+	39.1527i	1.79531	+	1.30437i
$902$	7.33606	+	10.0972i	0.244264	+	0.336201i
$903$	0.0920931	−	0.0299229i	0.00306467	−	0.000995770i
$904$	−10.1043			−0.336065
$905$	−12.7964	−	7.70475i	−0.425366	−	0.256114i
$906$	−0.0281021	−	0.0864892i	−0.000933628	−	0.00287341i
$907$	−16.5362	−	5.37294i	−0.549076	−	0.178406i	0.0213239	−	0.999773i	$-0.493212\pi$
$907$	−16.5362	−	5.37294i	−0.549076	−	0.178406i	−0.570400	+	0.821367i	$0.693212\pi$
$908$	14.0755	+	4.57342i	0.467113	+	0.151774i
$909$	−0.807863	−	0.586947i	−0.0267951	−	0.0194678i
$910$	−4.02634	−	0.933428i	−0.133472	−	0.0309428i
$911$	36.4749	+	26.5005i	1.20847	+	0.878002i	0.995091	−	0.0989686i	$-0.0315543\pi$
$911$	36.4749	+	26.5005i	1.20847	+	0.878002i	0.213375	+	0.976970i	$0.431554\pi$
$912$	0.0656470	+	0.0903553i	0.00217379	+	0.00299196i
$913$	11.2492	+	3.65509i	0.372294	+	0.120966i
$914$	−26.0029	+	18.8922i	−0.860100	+	0.624899i
$915$	0.00772566	+	0.0892432i	0.000255402	+	0.00295029i
$916$	−0.275414	+	0.847637i	−0.00909993	+	0.0280067i
$917$	−6.15961	−	8.47797i	−0.203408	−	0.279967i
$918$	−0.243028	+	0.334499i	−0.00802111	+	0.0110401i
$919$	6.07527	+	18.6978i	0.200405	+	0.616782i	0.999871	+	0.0160710i	$0.00511578\pi$
$919$	6.07527	+	18.6978i	0.200405	+	0.616782i	−0.799466	+	0.600711i	$0.794884\pi$
$920$	7.37591	+	17.4208i	0.243177	+	0.574346i
$921$	0.0293220	−	0.0902437i	0.000966192	−	0.00297363i
$922$	−23.0562	−	7.49143i	−0.759317	−	0.246717i
$923$	−5.67189	+	1.84291i	−0.186692	+	0.0606601i
$924$	0.0321564			0.00105787
$925$	25.8139	−	13.6651i	0.848755	−	0.449305i
$926$	−1.98156	−	6.09862i	−0.0651181	−	0.200413i
$927$	7.29704	+	10.0435i	0.239666	+	0.329872i
$928$	−4.90558	+	6.75195i	−0.161033	+	0.221644i
$929$	−27.3436			−0.897116			−0.448558	−	0.893754i	$-0.648062\pi$
$929$	−27.3436			−0.897116			−0.448558	+	0.893754i	$0.648062\pi$
$930$	−0.106127	+	0.137594i	−0.00348003	+	0.00451190i
$931$	−35.5755			−1.16594
$932$	−12.5874	+	17.3251i	−0.412314	+	0.567502i
$933$	−0.180839	−	0.248904i	−0.00592042	−	0.00814875i
$934$	5.65606	+	17.4076i	0.185072	+	0.569593i
$935$	−8.20965	+	13.6349i	−0.268484	+	0.445910i
$936$	3.46948			0.113404
$937$	13.4908	−	4.38344i	0.440726	−	0.143201i	−0.0802443	−	0.996775i	$-0.525570\pi$
$937$	13.4908	−	4.38344i	0.440726	−	0.143201i	0.520971	+	0.853575i	$0.325570\pi$
$938$	20.1601	+	6.55042i	0.658251	+	0.213879i
$939$	0.0210872	−	0.0648996i	0.000688154	−	0.00211792i
$940$	−16.9907	+	7.19383i	−0.554176	+	0.234637i
$941$	0.653695	+	2.01187i	0.0213098	+	0.0655849i	0.961146	−	0.276041i	$-0.0890225\pi$
$941$	0.653695	+	2.01187i	0.0213098	+	0.0655849i	−0.939836	+	0.341626i	$0.889022\pi$
$942$	−0.109950	+	0.151333i	−0.00358235	+	0.00493068i
$943$	43.0534	+	59.2579i	1.40201	+	1.92970i
$944$	1.93350	−	5.95071i	0.0629301	−	0.193679i
$945$	−0.298143	+	0.0258098i	−0.00969859	+	0.000839594i
$946$	−5.06288	+	3.67840i	−0.164609	+	0.119595i
$947$	47.4614	+	15.4212i	1.54229	+	0.501120i	0.952007	−	0.306077i	$-0.0990165\pi$
$947$	47.4614	+	15.4212i	1.54229	+	0.501120i	0.590282	+	0.807197i	$0.299016\pi$
$948$	0.0763422	+	0.105076i	0.00247948	+	0.00341271i
$949$	13.0208	+	9.46014i	0.422672	+	0.307089i
$950$	−28.7297	−	27.8455i	−0.932114	−	0.903428i
$951$	−0.261518	−	0.190004i	−0.00848032	−	0.00616131i
$952$	−7.50457	−	2.43838i	−0.243225	−	0.0790284i
$953$	−12.8520	−	4.17586i	−0.416316	−	0.135269i	0.0933666	−	0.995632i	$-0.470237\pi$
$953$	−12.8520	−	4.17586i	−0.416316	−	0.135269i	−0.509683	+	0.860363i	$0.670237\pi$
$954$	−12.5061	−	38.4897i	−0.404899	−	1.24615i
$955$	−5.44807	−	3.28031i	−0.176295	−	0.106148i
$956$	6.98164			0.225802
$957$	0.159707	−	0.0518919i	0.00516259	−	0.00167743i
$958$	16.2565	+	22.3752i	0.525225	+	0.722910i
$959$	−2.26794	−	1.64776i	−0.0732357	−	0.0532088i
$960$	0.0160985	−	0.0267371i	0.000519577	−	0.000862936i
$961$	−30.1832	−	7.06907i	−0.973653	−	0.228035i
$962$			6.75615i			0.217827i
$963$	−3.30051	+	4.54276i	−0.106357	+	0.146388i
$964$	14.4147	−	10.4729i	0.464266	−	0.337309i
$965$	−2.60523	−	0.603970i	−0.0838652	−	0.0194425i
$966$	0.188717			0.00607188
$967$			24.9239i			0.801498i	0.916188	+	0.400749i	$0.131250\pi$
$967$			24.9239i			0.801498i	−0.916188	+	0.400749i	$0.868750\pi$
$968$	8.48514	−	2.75699i	0.272723	−	0.0886130i
$969$	−0.170403	+	0.524445i	−0.00547412	+	0.0168476i
$970$	5.46391	−	4.74095i	0.175436	−	0.152223i
$971$	8.74574	+	6.35415i	0.280664	+	0.203914i	0.719207	−	0.694796i	$-0.244505\pi$
$971$	8.74574	+	6.35415i	0.280664	+	0.203914i	−0.438543	+	0.898710i	$0.644505\pi$
$972$	0.358372	−	0.116442i	0.0114948	−	0.00373489i
$973$	−12.4729	+	17.1675i	−0.399864	+	0.550366i
$974$	27.5174	−	19.9926i	0.881715	−	0.640603i
$975$	0.0795123	−	0.0138705i	0.00254643	−	0.000444211i
$976$	2.32202	−	1.68705i	0.0743262	−	0.0540011i
$977$	25.9404	+	35.7039i	0.829908	+	1.14227i	0.987940	+	0.154836i	$0.0494850\pi$
$977$	25.9404	+	35.7039i	0.829908	+	1.14227i	−0.158032	+	0.987434i	$0.550515\pi$
$978$	0.274117	+	0.0890659i	0.00876529	+	0.00284801i
$979$	−9.10971	+	6.61859i	−0.291147	+	0.211531i
$980$	3.87600	+	9.15452i	0.123814	+	0.292431i
$981$	11.2449	+	34.6082i	0.359021	+	1.10495i
$982$	24.2798	−	33.4183i	0.774799	−	1.06642i
$983$	0.522020	+	0.169615i	0.0166499	+	0.00540987i	0.317330	−	0.948315i	$-0.397214\pi$
$983$	0.522020	+	0.169615i	0.0166499	+	0.00540987i	−0.300680	+	0.953725i	$0.597214\pi$
$984$	0.0373409	−	0.114924i	0.00119039	−	0.00366363i
$985$	12.8533	+	2.97979i	0.409542	+	0.0949441i
$986$	−41.2068			−1.31229
$987$			0.184059i			0.00585865i
$988$	8.80182	−	2.85988i	0.280023	−	0.0909850i
$989$	−29.7127	+	21.5876i	−0.944810	+	0.686445i
$990$	8.90463	−	3.77020i	0.283008	−	0.119825i
$991$	−17.3902			−0.552419			−0.276209	−	0.961097i	$-0.589078\pi$
$991$	−17.3902			−0.552419			−0.276209	+	0.961097i	$0.589078\pi$
$992$	5.53097	+	0.639045i	0.175608	+	0.0202897i
$993$			0.103596i			0.00328751i
$994$	−6.66697	−	4.84384i	−0.211464	−	0.153637i
$995$	−25.4039	+	2.19918i	−0.805357	+	0.0697186i
$996$	−0.0353881	−	0.108913i	−0.00112131	−	0.00345105i
$997$		−	35.0884i		−	1.11126i	−0.831429	−	0.555631i	$-0.812477\pi$
$997$		−	35.0884i		−	1.11126i	0.831429	−	0.555631i	$-0.187523\pi$
$998$		−	8.54447i		−	0.270470i
$999$	0.151164	+	0.465236i	0.00478263	+	0.0147194i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	310.2.n.a.219.4	yes	64
5.4	even	2	inner	310.2.n.a.219.13	yes	64
31.16	even	5	inner	310.2.n.a.109.13	yes	64
155.109	even	10	inner	310.2.n.a.109.4	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.2.n.a.109.4	✓	64	155.109	even	10	inner
310.2.n.a.109.13	yes	64	31.16	even	5	inner
310.2.n.a.219.4	yes	64	1.1	even	1	trivial
310.2.n.a.219.13	yes	64	5.4	even	2	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:	\( N \)	\(=\)	\( 310 = 2 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	310.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.00820391 - 0.0112917i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.91563 + 1.15341i) q^{5} +0.0139573 q^{6} +(1.51995 - 0.493860i) q^{7} +(0.951057 + 0.309017i) q^{8} +(0.926991 - 2.85298i) q^{9} +O(q^{10})\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.00820391 - 0.0112917i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.91563 + 1.15341i) q^{5} +0.0139573 q^{6} +(1.51995 - 0.493860i) q^{7} +(0.951057 + 0.309017i) q^{8} +(0.926991 - 2.85298i) q^{9} +(-2.05911 + 0.871822i) q^{10} +(-0.445478 - 1.37104i) q^{11} +(-0.00820391 + 0.0112917i) q^{12} +(0.679815 + 0.935685i) q^{13} +(-0.493860 + 1.51995i) q^{14} +(-0.00269170 - 0.0310932i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-4.69574 - 1.52574i) q^{17} +(1.76324 + 2.42689i) q^{18} +(6.47369 + 4.70341i) q^{19} +(0.504995 - 2.17830i) q^{20} +(-0.0180460 - 0.0131112i) q^{21} +(1.37104 + 0.445478i) q^{22} +(8.04627 + 2.61439i) q^{23} +(-0.00431305 - 0.0132742i) q^{24} +(2.33929 + 4.41902i) q^{25} -1.15657 q^{26} +(-0.0796426 + 0.0258775i) q^{27} +(-0.939378 - 1.29294i) q^{28} +(-6.75195 - 4.90558i) q^{29} +(0.0267371 + 0.0160985i) q^{30} +(-0.639045 + 5.53097i) q^{31} -1.00000i q^{32} +(-0.0118267 + 0.0162781i) q^{33} +(3.99444 - 2.90213i) q^{34} +(3.48128 + 0.807066i) q^{35} -2.99981 q^{36} -5.84154i q^{37} +(-7.61028 + 2.47273i) q^{38} +(0.00498834 - 0.0153525i) q^{39} +(1.46545 + 1.68892i) q^{40} +(7.00420 + 5.08885i) q^{41} +(0.0212144 - 0.00689297i) q^{42} +(-2.55162 + 3.51200i) q^{43} +(-1.16628 + 0.847349i) q^{44} +(5.06643 - 4.39607i) q^{45} +(-6.84456 + 4.97287i) q^{46} +(-4.85011 - 6.67560i) q^{47} +(0.0132742 + 0.00431305i) q^{48} +(-3.59678 + 2.61322i) q^{49} +(-4.95006 - 0.704907i) q^{50} +(0.0212952 + 0.0655400i) q^{51} +(0.679815 - 0.935685i) q^{52} +(-12.8307 - 4.16896i) q^{53} +(0.0258775 - 0.0796426i) q^{54} +(0.727999 - 3.14022i) q^{55} +1.59817 q^{56} -0.111685i q^{57} +(7.93739 - 2.57902i) q^{58} +(-5.06197 + 3.67774i) q^{59} +(-0.0287396 + 0.0121683i) q^{60} -2.87018 q^{61} +(-4.09903 - 3.76802i) q^{62} -4.79418i q^{63} +(0.809017 + 0.587785i) q^{64} +(0.223047 + 2.57653i) q^{65} +(-0.00621767 - 0.0191360i) q^{66} -13.2637i q^{67} +4.93739i q^{68} +(-0.0364899 - 0.112304i) q^{69} +(-2.69917 + 2.34203i) q^{70} +(-1.59343 + 4.90406i) q^{71} +(1.76324 - 2.42689i) q^{72} +(13.2347 - 4.30021i) q^{73} +(4.72591 + 3.43357i) q^{74} +(0.0307069 - 0.0626678i) q^{75} +(2.47273 - 7.61028i) q^{76} +(-1.35420 - 1.86390i) q^{77} +(0.00948839 + 0.0130597i) q^{78} +(2.87558 - 8.85014i) q^{79} +(-2.22774 + 0.192852i) q^{80} +(-7.27973 - 5.28904i) q^{81} +(-8.23393 + 2.67537i) q^{82} +(-4.82271 + 6.63789i) q^{83} +(-0.00689297 + 0.0212144i) q^{84} +(-7.23551 - 8.33887i) q^{85} +(-1.34146 - 4.12860i) q^{86} +0.116486i q^{87} -1.44160i q^{88} +(-2.41371 - 7.42865i) q^{89} +(0.578519 + 6.68277i) q^{90} +(1.49538 + 1.08646i) q^{91} -8.46035i q^{92} +(0.0676968 - 0.0381597i) q^{93} +8.25149 q^{94} +(6.97624 + 16.4768i) q^{95} +(-0.0112917 + 0.00820391i) q^{96} +(-3.07681 + 0.999716i) q^{97} -4.44587i q^{98} -4.32451 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 16 q^{4} + 4 q^{5} - 16 q^{6} + 8 q^{9}+O(q^{10}) \) 64 * q + 16 * q^4 + 4 * q^5 - 16 * q^6 + 8 * q^9	\( 64 q + 16 q^{4} + 4 q^{5} - 16 q^{6} + 8 q^{9} - 4 q^{10} + 4 q^{11} - 14 q^{15} - 16 q^{16} + 16 q^{19} - 4 q^{20} + 32 q^{21} - 4 q^{24} - 8 q^{25} - 48 q^{26} - 40 q^{29} - 8 q^{30} - 60 q^{31} - 20 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{39} - 6 q^{40} + 28 q^{41} - 4 q^{44} - 22 q^{45} + 36 q^{46} + 32 q^{49} + 20 q^{50} - 4 q^{51} - 40 q^{54} + 32 q^{59} + 14 q^{60} - 64 q^{61} + 16 q^{64} + 48 q^{65} - 4 q^{66} - 20 q^{70} - 20 q^{71} - 4 q^{74} + 62 q^{75} + 24 q^{76} - 116 q^{79} - 6 q^{80} - 116 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{86} + 60 q^{89} - 82 q^{90} + 28 q^{91} + 16 q^{94} - 90 q^{95} + 4 q^{96} + 16 q^{99}+O(q^{100}) \) 64 * q + 16 * q^4 + 4 * q^5 - 16 * q^6 + 8 * q^9 - 4 * q^10 + 4 * q^11 - 14 * q^15 - 16 * q^16 + 16 * q^19 - 4 * q^20 + 32 * q^21 - 4 * q^24 - 8 * q^25 - 48 * q^26 - 40 * q^29 - 8 * q^30 - 60 * q^31 - 20 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^39 - 6 * q^40 + 28 * q^41 - 4 * q^44 - 22 * q^45 + 36 * q^46 + 32 * q^49 + 20 * q^50 - 4 * q^51 - 40 * q^54 + 32 * q^59 + 14 * q^60 - 64 * q^61 + 16 * q^64 + 48 * q^65 - 4 * q^66 - 20 * q^70 - 20 * q^71 - 4 * q^74 + 62 * q^75 + 24 * q^76 - 116 * q^79 - 6 * q^80 - 116 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^86 + 60 * q^89 - 82 * q^90 + 28 * q^91 + 16 * q^94 - 90 * q^95 + 4 * q^96 + 16 * q^99

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