LMFDB - Embedded newform 310.2.n.a.219.13

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			219.13
Character	$\chi$	$=$	310.219
Dual form			310.2.n.a.109.13

$q$-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} +(0.192852 - 2.22774i) 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} +(0.0287396 + 0.0121683i) 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} +(-1.68892 - 1.46545i) 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} +(-2.34203 + 2.69917i) q^{35} -2.99981 q^{36} +5.84154i q^{37} +(7.61028 - 2.47273i) q^{38} +(0.00498834 - 0.0153525i) q^{39} +(-2.17830 + 0.504995i) 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} +(-1.51489 - 6.53447i) 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} +(-2.20006 - 4.48996i) 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} +(-2.43474 - 2.11259i) q^{55} +1.59817 q^{56} +0.111685i q^{57} +(-7.93739 + 2.57902i) q^{58} +(-5.06197 + 3.67774i) q^{59} +(0.00269170 - 0.0310932i) q^{60} -2.87018 q^{61} +(4.09903 + 3.76802i) q^{62} +4.79418i q^{63} +(0.809017 + 0.587785i) q^{64} +(-2.38150 - 1.00832i) q^{65} +(-0.00621767 - 0.0191360i) q^{66} +13.2637i q^{67} -4.93739i q^{68} +(-0.0364899 - 0.112304i) q^{69} +(0.807066 + 3.48128i) 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} +(0.0690896 - 0.00983861i) 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} +(-0.871822 + 2.05911i) 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} +(10.7551 - 2.49336i) q^{85} +(-1.34146 - 4.12860i) q^{86} -0.116486i q^{87} +1.44160i q^{88} +(-2.41371 - 7.42865i) q^{89} +(-6.17692 - 2.61529i) q^{90} +(1.49538 + 1.08646i) q^{91} +8.46035i q^{92} +(-0.0676968 + 0.0381597i) q^{93} +8.25149 q^{94} +(17.8262 + 1.54319i) 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	0.811379	−	0.584521i	$-0.198717\pi$
$3$	0.00820391	+	0.0112917i	0.00473653	+	0.00651927i	−0.806642	+	0.591040i	$0.798717\pi$
$4$	−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	−0.581829	−	0.813311i	$-0.697663\pi$
$7$	−1.51995	+	0.493860i	−0.574485	+	0.186662i	0.00734320	+	0.999973i	$0.497663\pi$
$8$	−0.951057	−	0.309017i	−0.336249	−	0.109254i
$9$	0.926991	−	2.85298i	0.308997	−	0.950995i
$10$	0.192852	−	2.22774i	0.0609852	−	0.704472i
$11$	−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	0.704270	−	0.709932i	$-0.251274\pi$
$13$	−0.679815	−	0.935685i	−0.188547	−	0.259512i	−0.892817	+	0.450420i	$0.851274\pi$
$14$	−0.493860	+	1.51995i	−0.131990	+	0.406223i
$15$	0.0287396	+	0.0121683i	0.00742054	+	0.00314184i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	4.69574	+	1.52574i	1.13888	+	0.370046i	0.816946	−	0.576715i	$-0.195666\pi$
$17$	4.69574	+	1.52574i	1.13888	+	0.370046i	0.321939	+	0.946761i	$0.395666\pi$
$18$	−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	$0.329897\pi$
$20$	−1.68892	−	1.46545i	−0.377654	−	0.327685i
$21$	−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	−0.693287	−	0.720661i	$-0.743838\pi$
$23$	−8.04627	−	2.61439i	−1.67776	−	0.545138i	−0.984475	+	0.175523i	$0.943838\pi$
$24$	−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
$35$	−2.34203	+	2.69917i	−0.395876	+	0.456244i
$36$	−2.99981			−0.499968
$37$			5.84154i			0.960344i	0.877174	+	0.480172i	$0.159426\pi$
$37$			5.84154i			0.960344i	−0.877174	+	0.480172i	$0.840574\pi$
$38$	7.61028	−	2.47273i	1.23455	−	0.401130i
$39$	0.00498834	−	0.0153525i	0.000798774	−	0.00245837i
$40$	−2.17830	+	0.504995i	−0.344419	+	0.0798467i
$41$	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	−0.568853	−	0.822439i	$-0.692613\pi$
$43$	2.55162	−	3.51200i	0.389118	−	0.535575i	0.957971	+	0.286864i	$0.0926128\pi$
$44$	−1.16628	+	0.847349i	−0.175823	+	0.127743i
$45$	−1.51489	−	6.53447i	−0.225826	−	0.974101i
$46$	−6.84456	+	4.97287i	−1.00918	+	0.733209i
$47$	4.85011	+	6.67560i	0.707461	+	0.973736i	0.999848	+	0.0174361i	$0.00555037\pi$
$47$	4.85011	+	6.67560i	0.707461	+	0.973736i	−0.292387	+	0.956300i	$0.594450\pi$
$48$	−0.0132742	−	0.00431305i	−0.00191597	−	0.000622535i
$49$	−3.59678	+	2.61322i	−0.513826	+	0.373316i
$50$	−2.20006	−	4.48996i	−0.311135	−	0.634976i
$51$	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	0.997448	−	0.0713914i	$-0.0227439\pi$
$53$	12.8307	+	4.16896i	1.76244	+	0.572651i	0.764990	+	0.644042i	$0.222744\pi$
$54$	0.0258775	−	0.0796426i	0.00352148	−	0.0108380i
$55$	−2.43474	−	2.11259i	−0.328300	−	0.284861i
$56$	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	$0.433527\pi$
$60$	0.00269170	−	0.0310932i	0.000347497	−	0.00401412i
$61$	−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
$65$	−2.38150	−	1.00832i	−0.295389	−	0.125067i
$66$	−0.00621767	−	0.0191360i	−0.000765343	−	0.00235548i
$67$			13.2637i			1.62042i	0.586140	+	0.810210i	$0.300647\pi$
$67$			13.2637i			1.62042i	−0.586140	+	0.810210i	$0.699353\pi$
$68$		−	4.93739i		−	0.598747i
$69$	−0.0364899	−	0.112304i	−0.00439287	−	0.0135199i
$70$	0.807066	+	3.48128i	0.0964628	+	0.416092i
$71$	−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	−0.953843	−	0.300307i	$-0.902911\pi$
$73$	−13.2347	+	4.30021i	−1.54900	+	0.503301i	−0.595159	+	0.803608i	$0.702911\pi$
$74$	4.72591	+	3.43357i	0.549376	+	0.399145i
$75$	0.0690896	−	0.00983861i	0.00797778	−	0.00113606i
$76$	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	$-0.0753665\pi$
$80$	−0.871822	+	2.05911i	−0.0974726	+	0.230215i
$81$	−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	−0.457672	−	0.889121i	$-0.651317\pi$
$83$	4.82271	−	6.63789i	0.529361	−	0.728603i	0.987033	+	0.160518i	$0.0513166\pi$
$84$	−0.00689297	+	0.0212144i	−0.000752084	+	0.00231468i
$85$	10.7551	−	2.49336i	1.16656	−	0.270443i
$86$	−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	$-0.235861\pi$
$90$	−6.17692	−	2.61529i	−0.651105	−	0.275676i
$91$	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
$95$	17.8262	+	1.54319i	1.82893	+	0.158328i
$96$	−0.0112917	+	0.00820391i	−0.00115246	+	0.000837308i
$97$	3.07681	−	0.999716i	0.312403	−	0.101506i	−0.148619	−	0.988894i	$-0.547483\pi$
$97$	3.07681	−	0.999716i	0.312403	−	0.101506i	0.461022	+	0.887389i	$0.347483\pi$
$98$			4.44587i			0.449100i
$99$	−4.32451			−0.434629
$100$	−4.92562	−	0.859247i	−0.492562	−	0.0859247i
$101$	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	−0.672183	−	0.740385i	$-0.734643\pi$
$103$	2.43250	−	3.34805i	0.239682	−	0.329894i	0.911864	+	0.410492i	$0.134643\pi$
$104$	0.357400	+	1.09996i	0.0350459	+	0.107860i
$105$	−0.0496921	−	0.00430178i	−0.00484945	−	0.000419811i
$106$	10.9145	−	7.92984i	1.06011	−	0.770214i
$107$	1.78023	+	0.578430i	0.172101	+	0.0559190i	0.393800	−	0.919196i	$-0.371160\pi$
$107$	1.78023	+	0.578430i	0.172101	+	0.0559190i	−0.221699	+	0.975115i	$0.571160\pi$
$108$	−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	$0.497317\pi$
$110$	−3.14022	+	0.727999i	−0.299409	+	0.0694120i
$111$	−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	0.180121	−	0.983644i	$-0.442351\pi$
$113$	9.60980	−	3.12241i	0.904014	−	0.293732i	0.723893	+	0.689912i	$0.242351\pi$
$114$	0.0903553	+	0.0656470i	0.00846255	+	0.00614840i
$115$	−18.4292	+	4.27243i	−1.71853	+	0.398406i
$116$	−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
$120$	−0.0235728	−	0.0204538i	−0.00215189	−	0.00186717i
$121$	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	0.345444	−	0.938439i	$-0.387728\pi$
$127$	−7.36809	−	10.1413i	−0.653813	−	0.899896i	−0.999257	+	0.0385434i	$0.987728\pi$
$128$	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
$135$	0.122719	−	0.141432i	0.0105619	−	0.0121726i
$136$	−3.99444	−	2.90213i	−0.342520	−	0.248855i
$137$	1.03103	+	1.41909i	0.0880868	+	0.121241i	0.850786	−	0.525512i	$-0.176126\pi$
$137$	1.03103	+	1.41909i	0.0880868	+	0.121241i	−0.762699	+	0.646753i	$0.776126\pi$
$138$	−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	$0.490394\pi$
$140$	3.29080	+	1.39331i	0.278123	+	0.117757i
$141$	−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
$145$	−18.5924	−	1.60952i	−1.54401	−	0.133663i
$146$	−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
$155$	5.15530	+	11.3324i	0.414084	+	0.910239i
$156$	−0.0161426			−0.00129244
$157$	7.87755	−	10.8425i	0.628697	−	0.865327i	−0.369253	−	0.929329i	$-0.620386\pi$
$157$	7.87755	−	10.8425i	0.628697	−	0.865327i	0.997950	+	0.0640019i	$0.0203864\pi$
$158$	−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	−0.587390	−	0.809304i	$-0.699844\pi$
$163$	−19.6396	−	6.38130i	−1.53830	−	0.499822i	−0.950905	+	0.309482i	$0.899844\pi$
$164$	2.67537	−	8.23393i	0.208911	−	0.642962i
$165$	0.00388034	−	0.0448239i	0.000302084	−	0.00348953i
$166$	−2.53545	−	7.80330i	−0.196789	−	0.605654i
$167$	2.68813	−	3.69990i	0.208014	−	0.286307i	−0.692244	−	0.721663i	$-0.743378\pi$
$167$	2.68813	−	3.69990i	0.208014	−	0.286307i	0.900258	+	0.435357i	$0.143378\pi$
$168$	0.0131112	+	0.0180460i	0.00101155	+	0.00139228i
$169$	3.60386	−	11.0916i	0.277220	−	0.853196i
$170$	4.30453	−	10.1666i	0.330142	−	0.779745i
$171$	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	0.469281	−	0.883049i	$-0.344513\pi$
$173$	−6.78119	−	9.33351i	−0.515564	−	0.709613i	−0.984845	+	0.173435i	$0.944513\pi$
$174$	−0.0942391	−	0.0684687i	−0.00714425	−	0.00519060i
$175$	−1.37322	+	7.87195i	−0.103806	+	0.595063i
$176$	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
$190$	11.7264	−	13.5146i	0.850724	−	0.980452i
$191$	−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	−0.267793	−	0.963477i	$-0.586294\pi$
$193$	1.13746	−	0.369582i	0.0818759	−	0.0266031i	0.349669	+	0.936873i	$0.386294\pi$
$194$	0.999716	−	3.07681i	0.0717754	−	0.220902i
$195$	−0.00815194	−	0.0351634i	−0.000583773	−	0.00251811i
$196$	3.59678	+	2.61322i	0.256913	+	0.186658i
$197$	−5.61184	+	1.82340i	−0.399827	+	0.129912i	−0.502027	−	0.864852i	$-0.667412\pi$
$197$	−5.61184	+	1.82340i	−0.399827	+	0.129912i	0.102199	+	0.994764i	$0.467412\pi$
$198$	−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	$0.432445\pi$
$200$	−3.59035	+	3.47985i	−0.253876	+	0.246063i
$201$	−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
$205$	19.2870	+	1.66965i	1.34706	+	0.116613i
$206$	−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
$210$	−0.0326885	+	0.0376733i	−0.00225572	+	0.00259970i
$211$	−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
$215$	0.837184	−	9.67076i	0.0570955	−	0.659540i
$216$	−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
$220$	−1.25681	+	2.96840i	−0.0847344	+	0.200130i
$221$	−1.76462	−	5.43095i	−0.118701	−	0.365325i
$222$			0.0815323i			0.00547209i
$223$			19.7329i			1.32141i	0.750645	+	0.660705i	$0.229743\pi$
$223$			19.7329i			1.32141i	−0.750645	+	0.660705i	$0.770257\pi$
$224$	−0.493860	−	1.51995i	−0.0329974	−	0.101556i
$225$	−10.4389	−	10.7704i	−0.695926	−	0.718023i
$226$	3.12241	−	9.60980i	0.207700	−	0.639235i
$227$	8.69916	−	11.9734i	0.577383	−	0.794700i	−0.416022	−	0.909355i	$-0.636576\pi$
$227$	8.69916	−	11.9734i	0.577383	−	0.794700i	0.993405	+	0.114654i	$0.0365761\pi$
$228$	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	$0.709375\pi$
$230$	−7.37591	+	17.4208i	−0.486353	+	1.14869i
$231$	−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	$0.0474728\pi$
$233$	12.5874	+	17.3251i	0.824628	+	1.13500i	−0.164271	+	0.986415i	$0.552527\pi$
$234$	−1.07213	+	3.29968i	−0.0700873	+	0.215707i
$235$	16.9907	+	7.19383i	1.10835	+	0.469274i
$236$	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	$0.172500\pi$
$240$	−0.0304032	+	0.00704838i	−0.00196252	+	0.000454971i
$241$	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
$245$	−3.87600	+	9.15452i	−0.247629	+	0.584861i
$246$	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
$250$	−9.39327	−	6.06354i	−0.594082	−	0.383492i
$251$	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
$255$	0.116388	+	0.100988i	0.00728852	+	0.00632413i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	17.6524	+	5.73562i	1.10113	+	0.357778i	0.802537	−	0.596603i	$-0.203483\pi$
$257$	17.6524	+	5.73562i	1.10113	+	0.357778i	0.298592	+	0.954381i	$0.403483\pi$
$258$	0.0356137	−	0.0490181i	0.00221721	−	0.00305173i
$259$	−2.88491	−	8.87883i	−0.179259	−	0.551704i
$260$	−0.223047	+	2.57653i	−0.0138328	+	0.159790i
$261$	−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	0.728197	−	0.685368i	$-0.240359\pi$
$263$	−2.41074	−	3.31810i	−0.148653	−	0.204603i	−0.876849	+	0.480766i	$0.840359\pi$
$264$	−0.0162781	+	0.0118267i	−0.00100185	+	0.000727884i
$265$	29.3875	−	6.81291i	1.80526	−	0.418514i
$266$	−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	$0.888527\pi$
$270$	−0.0422889	−	0.182413i	−0.00257362	−	0.0111013i
$271$	−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
$275$	−7.10075	−	1.23869i	−0.428191	−	0.0746956i
$276$	−0.0955318	+	0.0694079i	−0.00575034	+	0.00417787i
$277$	3.93264	−	5.41282i	0.236290	−	0.325225i	−0.674361	−	0.738402i	$-0.735581\pi$
$277$	3.93264	−	5.41282i	0.236290	−	0.325225i	0.910651	+	0.413177i	$0.135581\pi$
$278$			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	−0.875944	−	0.482413i	$-0.839761\pi$
$283$	−21.8869	+	7.11149i	−1.30104	+	0.422734i	−0.425098	+	0.905147i	$0.639761\pi$
$284$	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
$290$	−12.2305	+	14.0955i	−0.718197	+	0.827717i
$291$	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	0.0634006	−	0.997988i	$-0.479805\pi$
$293$	−8.07780	−	2.62464i	−0.471910	−	0.153333i	−0.535311	+	0.844655i	$0.679805\pi$
$294$	−0.0502015	+	0.0364735i	−0.00292781	+	0.00212718i
$295$	−5.45494	+	12.8837i	−0.317599	+	0.750119i
$296$	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
$300$	−0.0307069	−	0.0626678i	−0.00177287	−	0.00361813i
$301$	−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	0.679614	−	0.733570i	$-0.262147\pi$
$307$	−3.99602	−	5.50005i	−0.228065	−	0.313904i	−0.907679	+	0.419666i	$0.862147\pi$
$308$	1.35420	−	1.86390i	0.0771629	−	0.106206i
$309$	0.0577613			0.00328593
$310$	12.1983	+	2.49028i	0.692817	+	0.141438i
$311$	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	0.720039	−	0.693934i	$-0.244124\pi$
$313$	−2.87377	−	3.95541i	−0.162435	−	0.223573i	−0.882474	+	0.470361i	$0.844124\pi$
$314$	−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	−0.853296	−	0.521426i	$-0.825400\pi$
$317$	−22.0267	+	7.15690i	−1.23714	+	0.401971i	−0.383845	+	0.923398i	$0.625400\pi$
$318$	0.179083	+	0.0581875i	0.0100425	+	0.00326300i
$319$	−3.71790	+	11.4425i	−0.208162	+	0.640658i
$320$	2.22774	+	0.192852i	0.124534	+	0.0107808i
$321$	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
$325$	−5.72509	+	0.815274i	−0.317571	+	0.0452233i
$326$	−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
$330$	−0.0339825	−	0.0294861i	−0.00187067	−	0.00162315i
$331$	−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	−0.462626	−	0.886553i	$-0.653093\pi$
$337$	−5.79724	+	1.88364i	−0.315796	+	0.102608i	0.146830	+	0.989162i	$0.453093\pi$
$338$	−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
$345$	−0.199434	−	0.173046i	−0.0107372	−	0.00931648i
$346$	−11.5369			−0.620225
$347$		−	8.45573i		−	0.453927i	−0.973903	−	0.226964i	$-0.927120\pi$
$347$		−	8.45573i		−	0.453927i	0.973903	−	0.226964i	$-0.0728799\pi$
$348$	−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	$0.116519\pi$
$350$	5.56138	+	5.73797i	0.297268	+	0.306708i
$351$	−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	−0.915963	−	0.401263i	$-0.868571\pi$
$353$	−4.72132	+	6.49835i	−0.251291	+	0.345872i	0.664672	+	0.747135i	$0.268571\pi$
$354$	−0.0706516	+	0.0513314i	−0.00375509	+	0.00272823i
$355$	2.60397	+	11.2322i	0.138205	+	0.596146i
$356$	−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	$0.298355\pi$
$360$	−0.578519	+	6.68277i	−0.0304906	+	0.352213i
$361$	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
$365$	−20.3929	+	23.5026i	−1.06741	+	1.23018i
$366$	−0.0400600			−0.00209397
$367$		−	17.9315i		−	0.936019i	−0.883723	−	0.468010i	$-0.844971\pi$
$367$		−	17.9315i		−	0.936019i	0.883723	−	0.468010i	$-0.155029\pi$
$368$	8.04627	−	2.61439i	0.419441	−	0.136285i
$369$	21.0112	−	15.2656i	1.09380	−	0.794693i
$370$	13.0134	+	1.12655i	0.676535	+	0.0585667i
$371$	−21.5609			−1.11939
$372$	0.0572114	+	0.0525915i	0.00296628	+	0.00272674i
$373$		−	8.31057i		−	0.430305i	−0.976580	−	0.215152i	$-0.930975\pi$
$373$		−	8.31057i		−	0.430305i	0.976580	−	0.215152i	$-0.0690248\pi$
$374$	−5.75836	−	4.18369i	−0.297758	−	0.216334i
$375$	0.121002	−	0.0985358i	0.00624853	−	0.00508837i
$376$	−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	$0.967001\pi$
$380$	−4.04093	−	17.4306i	−0.207295	−	0.894169i
$381$	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	0.0897189	−	0.995967i	$-0.471403\pi$
$383$	14.6331	−	4.75459i	0.747718	−	0.242948i	0.657999	+	0.753019i	$0.271403\pi$
$384$	0.0112917	+	0.00820391i	0.000576228	+	0.000418654i
$385$	4.74400	+	2.00860i	0.241776	+	0.102368i
$386$	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	$0.771272\pi$
$390$	−0.0332394	−	0.0140735i	−0.00168314	−	0.000712638i
$391$	−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
$395$	−4.69927	−	20.2703i	−0.236446	−	1.01991i
$396$	1.33635	+	4.11285i	0.0671539	+	0.206678i
$397$			15.1531i			0.760512i	0.924881	+	0.380256i	$0.124164\pi$
$397$			15.1531i			0.760512i	−0.924881	+	0.380256i	$0.875836\pi$
$398$			11.4034i			0.571603i
$399$	−0.0551570	−	0.169756i	−0.00276130	−	0.00849841i
$400$	0.704907	+	4.95006i	0.0352453	+	0.247503i
$401$	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
$405$	−20.0457	−	1.73533i	−0.996080	−	0.0862293i
$406$	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	$0.217217\pi$
$410$	12.6874	−	14.6221i	0.626585	−	0.722134i
$411$	−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
$415$	1.58233	−	18.2783i	0.0776734	−	0.897247i
$416$	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	$0.128877\pi$
$420$	0.0112645	+	0.0485893i	0.000549650	+	0.00237092i
$421$	−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
$425$	17.7270	−	17.1814i	0.859884	−	0.833421i
$426$	−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
$430$	−7.33172	−	6.36163i	−0.353567	−	0.306785i
$431$	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	$0.343378\pi$
$433$			36.6802i			1.76274i	−0.472428	+	0.881370i	$0.656622\pi$
$434$	−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	−0.594893	−	0.803805i	$-0.702806\pi$
$443$	−32.5950	−	10.5908i	−1.54864	−	0.503183i	−0.953743	+	0.300622i	$0.902806\pi$
$444$	0.0659610	+	0.0479235i	0.00313037	+	0.00227435i
$445$	−13.1921	−	11.4466i	−0.625364	−	0.542619i
$446$	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	$-0.0154871\pi$
$450$	−14.8492	+	2.11458i	−0.699999	+	0.0996824i
$451$	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
$455$	4.11772	+	0.356466i	0.193042	+	0.0167114i
$456$	0.0345127	−	0.106219i	0.00161620	−	0.00497416i
$457$	−30.5683	−	9.93223i	−1.42992	−	0.464610i	−0.511183	−	0.859472i	$-0.670792\pi$
$457$	−30.5683	−	9.93223i	−1.42992	−	0.464610i	−0.918741	+	0.394862i	$0.870792\pi$
$458$	−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	−0.712402	−	0.701772i	$-0.752393\pi$
$463$	3.76915	−	5.18779i	0.175167	−	0.241097i	0.887569	+	0.460675i	$0.152393\pi$
$464$	8.34587			0.387447
$465$	−0.0856684	+	0.151182i	−0.00397278	+	0.00701090i
$466$	21.4150			0.992029
$467$	−10.7585	+	14.8078i	−0.497842	+	0.685221i	−0.981810	−	0.189865i	$-0.939195\pi$
$467$	−10.7585	+	14.8078i	−0.497842	+	0.685221i	0.483968	+	0.875086i	$0.339195\pi$
$468$	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
$475$	35.9283	−	17.6047i	1.64850	−	0.807759i
$476$	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	$-0.117703\pi$
$480$	−0.0121683	+	0.0287396i	−0.000555404	+	0.00131178i
$481$	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
$485$	4.74095	−	5.46391i	0.215275	−	0.248103i
$486$	−0.304850	−	0.221486i	−0.0138283	−	0.0100468i
$487$	32.3487	+	10.5107i	1.46586	+	0.476286i	0.929854	−	0.367929i	$-0.119933\pi$
$487$	32.3487	+	10.5107i	1.46586	+	0.476286i	0.536004	+	0.844215i	$0.319933\pi$
$488$	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	$0.361255\pi$
$500$	−10.4267	+	4.03525i	−0.466298	+	0.180462i
$501$	0.0638313			0.00285177
$502$		−	16.7295i		−	0.746675i
$503$	−12.1071	+	3.93384i	−0.539830	+	0.175401i	−0.566226	−	0.824250i	$-0.691597\pi$
$503$	−12.1071	+	3.93384i	−0.539830	+	0.175401i	0.0263960	+	0.999652i	$0.491597\pi$
$504$	1.48148	−	4.55954i	0.0659906	−	0.203098i
$505$	−0.168103	−	0.725111i	−0.00748047	−	0.0322670i
$506$	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	$0.579574\pi$
$510$	0.150113	−	0.0348006i	0.00664710	−	0.00154100i
$511$	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
$515$	0.798103	−	9.21932i	0.0351686	−	0.406252i
$516$	−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
$520$	1.95335	+	1.69490i	0.0856603	+	0.0743261i
$521$	−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	−0.829421	−	0.558624i	$-0.811330\pi$
$523$	−26.8047	+	8.70936i	−1.17209	+	0.380834i	−0.342665	+	0.939458i	$0.611330\pi$
$524$	−5.30482	+	3.85417i	−0.231742	+	0.168370i
$525$	−0.100154	+	0.0490748i	−0.00437106	+	0.00214180i
$526$	−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
$530$	11.7618	−	27.7795i	0.510899	−	1.20667i
$531$	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
$535$	4.07742	−	0.945270i	0.176282	−	0.0408676i
$536$	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
$540$	−0.172432	−	0.0730074i	−0.00742030	−	0.00314174i
$541$	−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
$545$	−10.5756	+	24.9781i	−0.453011	+	1.06994i
$546$	0.0208715	+	0.0151640i	0.000893217	+	0.000648960i
$547$	37.2933	−	12.1173i	1.59455	−	0.518100i	0.628796	−	0.777571i	$-0.283548\pi$
$547$	37.2933	−	12.1173i	1.59455	−	0.518100i	0.965751	+	0.259471i	$0.0835482\pi$
$548$	1.03103	−	1.41909i	0.0440434	−	0.0606206i
$549$	−2.66063	+	8.18858i	−0.113553	+	0.349480i
$550$	−5.17583	+	5.01654i	−0.220698	+	0.213906i
$551$	−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
$555$	−0.0710816	+	0.167884i	−0.00301725	+	0.00712627i
$556$	10.7420	+	7.80454i	0.455563	+	0.330986i
$557$			14.9720i			0.634386i	0.948361	+	0.317193i	$0.102740\pi$
$557$			14.9720i			0.634386i	−0.948361	+	0.317193i	$0.897260\pi$
$558$	14.5499	−	8.20154i	0.615945	−	0.347199i
$559$	−5.02075			−0.212355
$560$	0.308209	−	3.56029i	0.0130242	−	0.150450i
$561$	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	$-0.997129\pi$
$563$		−	0.427944i		−	0.0180357i	0.999959	−	0.00901785i	$-0.00287051\pi$
$564$	0.115169			0.00484948
$565$	14.8074	−	17.0654i	0.622953	−	0.717948i
$566$	−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	$-0.264777\pi$
$570$	0.248805	+	0.0215387i	0.0104213	+	0.000902159i
$571$	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
$575$	−30.3756	+	29.4408i	−1.26675	+	1.22777i
$576$	2.42689	−	1.76324i	0.101121	−	0.0734684i
$577$	−21.1567	+	29.1197i	−0.880764	+	1.21227i	0.0954451	+	0.995435i	$0.469573\pi$
$577$	−21.1567	+	29.1197i	−0.880764	+	1.21227i	−0.976209	+	0.216833i	$0.930427\pi$
$578$	7.01676	−	2.27988i	0.291859	−	0.0948306i
$579$	0.0135048	+	0.00981181i	0.000561240	+	0.000407765i
$580$	4.21462	+	18.1798i	0.175003	+	0.754874i
$581$	−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
$585$	−5.08436	+	5.85968i	−0.210212	+	0.242268i
$586$	−6.87138	+	4.99235i	−0.283854	+	0.206232i
$587$	2.76463	−	3.80519i	0.114109	−	0.157057i	−0.748142	−	0.663538i	$-0.769054\pi$
$587$	2.76463	−	3.80519i	0.114109	−	0.157057i	0.862251	+	0.506481i	$0.169054\pi$
$588$			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	−0.324169	−	0.945999i	$-0.605085\pi$
$593$	−0.739884	+	0.240403i	−0.0303834	+	0.00987216i	0.293786	+	0.955871i	$0.405085\pi$
$594$	−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	$0.707920\pi$
$600$	−0.0687484	−	0.0119928i	−0.00280664	−	0.000489603i
$601$	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
$605$	7.77822	−	18.3710i	0.316230	−	0.746886i
$606$	0.00143573	−	0.00441871i	5.83224e−5	−	0.000179498i
$607$	−18.2533	−	25.1235i	−0.740879	−	1.01973i	−0.998568	−	0.0535044i	$-0.982961\pi$
$607$	−18.2533	−	25.1235i	−0.740879	−	1.01973i	0.257689	−	0.966228i	$-0.417039\pi$
$608$	−4.70341	+	6.47369i	−0.190748	+	0.262543i
$609$	0.0575278	+	0.177052i	0.00233114	+	0.00717452i
$610$	−0.553520	+	6.39400i	−0.0224114	+	0.258886i
$611$	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	−0.576135	−	0.817355i	$-0.695440\pi$
$613$	−13.9097	+	4.51955i	−0.561809	+	0.182543i	0.0143259	+	0.999897i	$0.495440\pi$
$614$	−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	0.933437	−	0.358740i	$-0.116794\pi$
$617$	7.54642	+	10.3868i	0.303807	+	0.418155i	−0.629630	+	0.776895i	$0.716794\pi$
$618$	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	$0.506251\pi$
$620$	9.18466	−	8.40488i	0.368865	−	0.337548i
$621$	−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
$630$	10.6802	+	0.924568i	0.425508	+	0.0368357i
$631$	−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
$635$	−25.8116	−	10.9286i	−1.02430	−	0.433688i
$636$	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
$640$	1.46545	−	1.68892i	0.0579270	−	0.0667605i
$641$	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	0.528318	−	0.849046i	$-0.322823\pi$
$643$	11.5802	+	3.76264i	0.456679	+	0.148384i	−0.0716387	+	0.997431i	$0.522823\pi$
$644$	−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	−0.571648	−	0.820499i	$-0.693696\pi$
$647$	−14.0368	+	4.56084i	−0.551845	+	0.179305i	0.0198037	+	0.999804i	$0.493696\pi$
$648$	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	−0.712634	−	0.701536i	$-0.752498\pi$
$653$	4.46639	−	6.14745i	0.174783	−	0.240568i	0.887417	+	0.460968i	$0.152498\pi$
$654$	−0.136974	+	0.0995177i	−0.00535612	+	0.00389145i
$655$	−11.0744	−	9.60913i	−0.432714	−	0.375460i
$656$	−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	$-0.175088\pi$
$660$	−0.0438291	+	0.0101609i	−0.00170605	+	0.000395513i
$661$	−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
$665$	−27.8569	+	6.45807i	−1.08024	+	0.250433i
$666$	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
$670$	29.5480	+	2.55793i	1.14154	+	0.0988216i
$671$	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	0.266413	−	0.963859i	$-0.414162\pi$
$673$	−2.19464	−	0.713082i	−0.0845972	−	0.0274873i	−0.351010	+	0.936372i	$0.614162\pi$
$674$	−1.88364	+	5.79724i	−0.0725550	+	0.223301i
$675$	0.0719544	−	0.412477i	0.00276953	−	0.0158763i
$676$	−11.6623			−0.448552
$677$		−	11.9216i		−	0.458186i	−0.973405	−	0.229093i	$-0.926424\pi$
$677$		−	11.9216i		−	0.458186i	0.973405	−	0.229093i	$-0.0735760\pi$
$678$	0.134127	−	0.0435805i	0.00515112	−	0.00167370i
$679$	−4.18286	+	3.03903i	−0.160523	+	0.116627i
$680$	−10.9992	−	0.952187i	−0.421800	−	0.0365147i
$681$	0.206567			0.00791566
$682$	3.34008	−	7.29849i	0.127898	−	0.279474i
$683$		−	32.9433i		−	1.26054i	−0.776376	−	0.630269i	$-0.782944\pi$
$683$		−	32.9433i		−	1.26054i	0.776376	−	0.630269i	$-0.217056\pi$
$684$	−19.4198	−	14.1093i	−0.742535	−	0.539483i
$685$	3.61187	+	1.52926i	0.138002	+	0.0584299i
$686$	−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
$690$	−0.257222	+	0.0596317i	−0.00979226	+	0.00227014i
$691$	−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
$695$	−11.5759	+	27.3406i	−0.439100	+	1.03709i
$696$	−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
$700$	7.91102	−	1.12656i	0.299008	−	0.0425799i
$701$	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
$705$	0.0581597	+	0.250872i	0.00219042	+	0.00944838i
$706$	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	$0.968511\pi$
$710$	10.6177	+	4.49549i	0.398474	+	0.168713i
$711$	−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
$715$	−0.321543	+	3.71432i	−0.0120250	+	0.138908i
$716$	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	$0.412686\pi$
$720$	5.06643	+	4.39607i	0.188815	+	0.163832i
$721$	−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
$725$	−37.4726	+	18.3614i	−1.39170	+	0.681925i
$726$	0.100742	−	0.0731936i	0.00373890	−	0.00271647i
$727$	−15.9230	−	5.17371i	−0.590553	−	0.191882i	−0.00153043	−	0.999999i	$-0.500487\pi$
$727$	−15.9230	−	5.17371i	−0.590553	−	0.191882i	−0.589023	+	0.808116i	$0.700487\pi$
$728$	−1.08646	−	1.49538i	−0.0402667	−	0.0554224i
$729$	−21.8349	+	15.8640i	−0.808702	+	0.587556i
$730$	7.02739	+	30.3127i	0.260095	+	1.12192i
$731$	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	−0.735318	−	0.677722i	$-0.762967\pi$
$733$	−25.2288	+	8.19734i	−0.931848	+	0.302776i	−0.196530	+	0.980498i	$0.562967\pi$
$734$	−14.5069	−	10.5399i	−0.535460	−	0.389035i
$735$	−0.135169	+	0.0313362i	−0.00498577	+	0.00115585i
$736$	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	$0.543444\pi$
$740$	8.56050	−	9.86591i	0.314690	−	0.362678i
$741$	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	$0.00512818\pi$
$743$			0.878251i			0.0322199i	−0.999870	+	0.0161099i	$0.994872\pi$
$744$	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
$755$	−11.0043	−	9.54828i	−0.400488	−	0.347497i
$756$	0.108273	+	0.0786647i	0.00393784	+	0.00286101i
$757$	29.7732	+	40.9794i	1.08213	+	1.48942i	0.857158	+	0.515054i	$0.172228\pi$
$757$	29.7732	+	40.9794i	1.08213	+	1.48942i	0.224969	+	0.974366i	$0.427772\pi$
$758$	−7.73702	−	2.51391i	−0.281021	−	0.0913093i
$759$	−0.137718	+	0.100058i	−0.00499885	+	0.00363188i
$760$	−16.4768	−	6.97624i	−0.597677	−	0.253055i
$761$	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
$765$	2.85637	−	32.9955i	0.103272	−	1.19295i
$766$	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	−0.748236	−	0.663432i	$-0.769099\pi$
$773$	3.16794	−	4.36030i	0.113943	−	0.156829i	0.862179	+	0.506603i	$0.169099\pi$
$774$	−13.0224			−0.468079
$775$	22.9465	+	15.7625i	0.824264	+	0.566206i
$776$	−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
$785$	2.58462	−	29.8563i	0.0922491	−	1.06562i
$786$	−0.0282812	−	0.0870405i	−0.00100876	−	0.00310463i
$787$	1.01738	−	1.40030i	0.0362656	−	0.0499153i	−0.790499	−	0.612463i	$-0.790179\pi$
$787$	1.01738	−	1.40030i	0.0362656	−	0.0499153i	0.826765	+	0.562548i	$0.190179\pi$
$788$	3.46831	+	4.77372i	0.123553	+	0.170057i
$789$	0.0176895	−	0.0544428i	0.000629764	−	0.00193821i
$790$	−19.1612	−	8.11281i	−0.681725	−	0.288641i
$791$	−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
$795$	0.318022	+	0.275943i	0.0112791	+	0.00978668i
$796$	9.22558	+	6.70278i	0.326992	+	0.237574i
$797$	20.4057	+	6.63022i	0.722808	+	0.234855i	0.647240	−	0.762286i	$-0.275923\pi$
$797$	20.4057	+	6.63022i	0.722808	+	0.234855i	0.0755678	+	0.997141i	$0.475923\pi$
$798$	−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	$0.125322\pi$
$810$	−13.1865	+	15.1973i	−0.463326	+	0.533980i
$811$	−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
$815$	−44.9826	+	10.4283i	−1.57567	+	0.365288i
$816$	−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
$820$	−4.37208	−	18.8590i	−0.152680	−	0.658584i
$821$	−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	0.598377	−	0.801215i	$-0.295813\pi$
$823$	17.5436	+	5.70027i	0.611532	+	0.198699i	0.0131549	+	0.999913i	$0.495813\pi$
$824$	−3.34805	+	2.43250i	−0.116635	+	0.0847403i
$825$	−0.0442670	−	0.0903416i	−0.00154118	−	0.00314529i
$826$	−3.09006	−	9.51021i	−0.107517	−	0.330903i
$827$	−17.3535	+	23.8850i	−0.603440	+	0.830564i	−0.996018	−	0.0891547i	$-0.971583\pi$
$827$	−17.3535	+	23.8850i	−0.603440	+	0.830564i	0.392578	+	0.919719i	$0.371583\pi$
$828$	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	$-0.263792\pi$
$830$	−13.8574	−	12.0238i	−0.480997	−	0.417354i
$831$	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
$835$	0.881975	−	10.1882i	0.0305220	−	0.352576i
$836$	−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	$0.823021\pi$
$840$	0.0459307	+	0.0194469i	0.00158476	+	0.000670983i
$841$	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
$845$	−5.88943	−	25.4041i	−0.202602	−	0.873926i
$846$	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
$850$	−3.48040	−	24.4404i	−0.119377	−	0.838299i
$851$	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	0.638520	−	0.769605i	$-0.279547\pi$
$853$	−8.49116	−	11.6871i	−0.290732	−	0.400158i	−0.929252	+	0.369447i	$0.879547\pi$
$854$	1.41747	−	4.36252i	0.0485047	−	0.149282i
$855$	20.9274	−	49.4272i	0.715701	−	1.69038i
$856$	−1.51435	−	1.10024i	−0.0517594	−	0.0376054i
$857$	−34.5576	+	11.2285i	−1.18047	+	0.383557i	−0.832540	−	0.553965i	$-0.813114\pi$
$857$	−34.5576	+	11.2285i	−1.18047	+	0.383557i	−0.347926	+	0.937522i	$0.613114\pi$
$858$	−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	$-0.126489\pi$
$860$	−9.45614	+	2.19222i	−0.322452	+	0.0747540i
$861$	−0.0596770	−	0.183667i	−0.00203379	−	0.00625935i
$862$		−	27.3630i		−	0.931988i
$863$		−	20.9597i		−	0.713476i	−0.934204	−	0.356738i	$-0.883889\pi$
$863$		−	20.9597i		−	0.713476i	0.934204	−	0.356738i	$-0.116111\pi$
$864$	0.0258775	+	0.0796426i	0.000880369	+	0.00270950i
$865$	−23.7556	−	10.0581i	−0.807715	−	0.341985i
$866$	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
$870$	−0.259500	−	0.0224646i	−0.00879787	−	0.000761620i
$871$	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
$875$	6.44900	+	16.6636i	0.218016	+	0.563334i
$876$	−0.0600194	+	0.184721i	−0.00202787	+	0.00624113i
$877$	−17.6732	−	5.74235i	−0.596780	−	0.193906i	−0.00497614	−	0.999988i	$-0.501584\pi$
$877$	−17.6732	−	5.74235i	−0.596780	−	0.193906i	−0.591804	+	0.806082i	$0.701584\pi$
$878$	−0.559537	+	0.770137i	−0.0188835	+	0.0259909i
$879$	−0.0366329	−	0.112744i	−0.00123560	−	0.00380277i
$880$	3.21149	+	0.278015i	0.108259	+	0.00937187i
$881$	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	0.531524	−	0.847043i	$-0.321619\pi$
$883$	−13.0246	−	17.9268i	−0.438311	−	0.603284i	−0.969836	+	0.243759i	$0.921619\pi$
$884$	−4.61984	+	3.35651i	−0.155382	+	0.112892i
$885$	−0.190231	+	0.0441013i	−0.00639455	+	0.00148245i
$886$	−27.7270	+	20.1448i	−0.931506	+	0.676779i
$887$	0.106667	−	0.146815i	0.00358153	−	0.00492956i	−0.807222	−	0.590247i	$-0.799030\pi$
$887$	0.106667	−	0.146815i	0.00358153	−	0.00492956i	0.810804	+	0.585318i	$0.199030\pi$
$888$	0.0775418	−	0.0251949i	0.00260213	−	0.000845485i
$889$	16.2075	+	11.7754i	0.543582	+	0.394935i
$890$	−17.0146	+	3.94449i	−0.570329	+	0.132219i
$891$	−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
$895$	12.5507	+	10.8901i	0.419525	+	0.364015i
$896$	−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	0.570400	−	0.821367i	$-0.306788\pi$
$907$	16.5362	+	5.37294i	0.549076	+	0.178406i	−0.0213239	+	0.999773i	$0.506788\pi$
$908$	−14.0755	−	4.57342i	−0.467113	−	0.151774i
$909$	−0.807863	−	0.586947i	−0.0267951	−	0.0194678i
$910$	2.70872	−	3.12178i	0.0897933	−	0.103486i
$911$	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
$915$	−0.0824879	−	0.0349252i	−0.00272697	−	0.00115459i
$916$	−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	$0.794884\pi$
$920$	18.8474	+	1.63160i	0.621381	+	0.0537921i
$921$	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	$0.648062\pi$
$930$	0.0719542	+	0.158170i	0.00235947	+	0.00518659i
$931$	−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	−0.520971	−	0.853575i	$-0.674430\pi$
$937$	−13.4908	+	4.38344i	−0.440726	+	0.143201i	0.0802443	+	0.996775i	$0.474430\pi$
$938$	−20.1601	−	6.55042i	−0.658251	−	0.213879i
$939$	0.0210872	−	0.0648996i	0.000688154	−	0.00211792i
$940$	1.59132	−	18.3821i	0.0519031	−	0.599560i
$941$	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
$945$	−0.116678	+	0.275575i	−0.00379553	+	0.00896446i
$946$	−5.06288	+	3.67840i	−0.164609	+	0.119595i
$947$	−47.4614	−	15.4212i	−1.54229	−	0.501120i	−0.590282	−	0.807197i	$-0.700984\pi$
$947$	−47.4614	−	15.4212i	−1.54229	−	0.501120i	−0.952007	+	0.306077i	$0.900984\pi$
$948$	−0.0763422	−	0.105076i	−0.00247948	−	0.00341271i
$949$	13.0208	+	9.46014i	0.422672	+	0.307089i
$950$	6.87562	−	39.4144i	0.223075	−	1.27877i
$951$	−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	0.509683	−	0.860363i	$-0.329763\pi$
$953$	12.8520	+	4.17586i	0.416316	+	0.135269i	−0.0933666	+	0.995632i	$0.529763\pi$
$954$	−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
$965$	1.75267	−	2.01994i	0.0564204	−	0.0650240i
$966$	0.188717			0.00607188
$967$		−	24.9239i		−	0.801498i	−0.916188	−	0.400749i	$-0.868750\pi$
$967$		−	24.9239i		−	0.801498i	0.916188	−	0.400749i	$-0.131250\pi$
$968$	−8.48514	+	2.75699i	−0.272723	+	0.0886130i
$969$	−0.170403	+	0.524445i	−0.00547412	+	0.0168476i
$970$	−1.63373	−	7.04711i	−0.0524560	−	0.226269i
$971$	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
$975$	−0.0561740	−	0.0579576i	−0.00179901	−	0.00185613i
$976$	2.32202	−	1.68705i	0.0743262	−	0.0540011i
$977$	−25.9404	−	35.7039i	−0.829908	−	1.14227i	−0.987940	−	0.154836i	$-0.950515\pi$
$977$	−25.9404	−	35.7039i	−0.829908	−	1.14227i	0.158032	−	0.987434i	$-0.449485\pi$
$978$	−0.274117	−	0.0890659i	−0.00876529	−	0.00284801i
$979$	−9.10971	+	6.61859i	−0.291147	+	0.211531i
$980$	9.90422	+	0.857395i	0.316379	+	0.0273885i
$981$	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	0.300680	−	0.953725i	$-0.402786\pi$
$983$	−0.522020	−	0.169615i	−0.0166499	−	0.00540987i	−0.317330	+	0.948315i	$0.602786\pi$
$984$	0.0373409	−	0.114924i	0.00119039	−	0.00366363i
$985$	−8.64710	+	9.96571i	−0.275519	+	0.317534i
$986$	−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
$990$	−0.833990	+	9.63386i	−0.0265059	+	0.306184i
$991$	−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
$995$	−9.94177	+	23.4809i	−0.315175	+	0.744396i
$996$	−0.0353881	−	0.108913i	−0.00112131	−	0.00345105i
$997$			35.0884i			1.11126i	0.831429	+	0.555631i	$0.187523\pi$
$997$			35.0884i			1.11126i	−0.831429	+	0.555631i	$0.812477\pi$
$998$			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.219.13	yes	64
5.4	even	2	inner	310.2.n.a.219.4	yes	64
31.16	even	5	inner	310.2.n.a.109.4	✓	64
155.109	even	10	inner	310.2.n.a.109.13	yes	64

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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} +(0.192852 - 2.22774i) 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} +(0.0287396 + 0.0121683i) 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} +(-1.68892 - 1.46545i) 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} +(-2.34203 + 2.69917i) q^{35} -2.99981 q^{36} +5.84154i q^{37} +(7.61028 - 2.47273i) q^{38} +(0.00498834 - 0.0153525i) q^{39} +(-2.17830 + 0.504995i) 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} +(-1.51489 - 6.53447i) 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} +(-2.20006 - 4.48996i) 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} +(-2.43474 - 2.11259i) q^{55} +1.59817 q^{56} +0.111685i q^{57} +(-7.93739 + 2.57902i) q^{58} +(-5.06197 + 3.67774i) q^{59} +(0.00269170 - 0.0310932i) q^{60} -2.87018 q^{61} +(4.09903 + 3.76802i) q^{62} +4.79418i q^{63} +(0.809017 + 0.587785i) q^{64} +(-2.38150 - 1.00832i) q^{65} +(-0.00621767 - 0.0191360i) q^{66} +13.2637i q^{67} -4.93739i q^{68} +(-0.0364899 - 0.112304i) q^{69} +(0.807066 + 3.48128i) 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} +(0.0690896 - 0.00983861i) 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} +(-0.871822 + 2.05911i) 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} +(10.7551 - 2.49336i) q^{85} +(-1.34146 - 4.12860i) q^{86} -0.116486i q^{87} +1.44160i q^{88} +(-2.41371 - 7.42865i) q^{89} +(-6.17692 - 2.61529i) q^{90} +(1.49538 + 1.08646i) q^{91} +8.46035i q^{92} +(-0.0676968 + 0.0381597i) q^{93} +8.25149 q^{94} +(17.8262 + 1.54319i) 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

Introduction

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