LMFDB - Embedded newform 418.2.f.h.191.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(115,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("418.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.f (of order $5$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 11 x^{18} - 3 x^{17} + 103 x^{16} + 50 x^{15} + 1002 x^{14} + 1120 x^{13} + \cdots + 1936 $ x^20 - x^19 + 11x^18 - 3x^17 + 103x^16 + 50x^15 + 1002x^14 + 1120x^13 + 7288x^12 + 5704x^11 + 24392x^10 + 10376x^9 + 48880x^8 + 21224x^7 + 77528x^6 + 44616x^5 + 147848x^4 + 67728x^3 + 115472x^2 - 24464x + 1936
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			191.1
Root			$-2.05454 + 1.49271i$ of defining polynomial
Character	$\chi$	$=$	418.191
Dual form			418.2.f.h.267.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-0.784763 + 2.41525i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.46809 + 1.06663i) q^{5} +(-2.05454 + 1.49271i) q^{6} +(-0.0865782 - 0.266460i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.79053 - 2.02744i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-0.784763 + 2.41525i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.46809 + 1.06663i) q^{5} +(-2.05454 + 1.49271i) q^{6} +(-0.0865782 - 0.266460i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.79053 - 2.02744i) q^{9} -1.81466 q^{10} +(-3.28363 + 0.466653i) q^{11} -2.53955 q^{12} +(0.680800 + 0.494630i) q^{13} +(0.0865782 - 0.266460i) q^{14} +(-1.42408 - 4.38286i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(3.48308 - 2.53061i) q^{17} +(-1.06589 - 3.28047i) q^{18} +(-0.309017 + 0.951057i) q^{19} +(-1.46809 - 1.06663i) q^{20} +0.711512 q^{21} +(-2.93081 - 1.55254i) q^{22} +3.84953 q^{23} +(-2.05454 - 1.49271i) q^{24} +(-0.527494 + 1.62346i) q^{25} +(0.260042 + 0.800328i) q^{26} +(0.923083 - 0.670659i) q^{27} +(0.226665 - 0.164682i) q^{28} +(2.44362 + 7.52067i) q^{29} +(1.42408 - 4.38286i) q^{30} +(-7.24528 - 5.26400i) q^{31} -1.00000 q^{32} +(1.44979 - 8.29701i) q^{33} +4.30533 q^{34} +(0.411319 + 0.298841i) q^{35} +(1.06589 - 3.28047i) q^{36} +(-0.494218 - 1.52105i) q^{37} +(-0.809017 + 0.587785i) q^{38} +(-1.72892 + 1.25613i) q^{39} +(-0.560761 - 1.72584i) q^{40} +(-2.18700 + 6.73091i) q^{41} +(0.575625 + 0.418216i) q^{42} -3.63697 q^{43} +(-1.45851 - 2.97872i) q^{44} +6.25929 q^{45} +(3.11434 + 2.26270i) q^{46} +(-2.36377 + 7.27493i) q^{47} +(-0.784763 - 2.41525i) q^{48} +(5.59961 - 4.06836i) q^{49} +(-1.38100 + 1.00335i) q^{50} +(3.37866 + 10.3984i) q^{51} +(-0.260042 + 0.800328i) q^{52} +(7.34890 + 5.33929i) q^{53} +1.14099 q^{54} +(4.32292 - 4.18751i) q^{55} +0.280173 q^{56} +(-2.05454 - 1.49271i) q^{57} +(-2.44362 + 7.52067i) q^{58} +(1.14652 + 3.52862i) q^{59} +(3.72828 - 2.70876i) q^{60} +(0.143837 - 0.104504i) q^{61} +(-2.76745 - 8.51734i) q^{62} +(-0.298633 + 0.919099i) q^{63} +(-0.809017 - 0.587785i) q^{64} -1.52706 q^{65} +(6.04976 - 5.86026i) q^{66} +8.01235 q^{67} +(3.48308 + 2.53061i) q^{68} +(-3.02097 + 9.29759i) q^{69} +(0.157110 + 0.483535i) q^{70} +(-3.04991 + 2.21589i) q^{71} +(2.79053 - 2.02744i) q^{72} +(0.184248 + 0.567056i) q^{73} +(0.494218 - 1.52105i) q^{74} +(-3.50711 - 2.54806i) q^{75} -1.00000 q^{76} +(0.408636 + 0.834556i) q^{77} -2.13706 q^{78} +(11.4673 + 8.33146i) q^{79} +(0.560761 - 1.72584i) q^{80} +(-2.30226 - 7.08562i) q^{81} +(-5.72565 + 4.15993i) q^{82} +(-2.61517 + 1.90003i) q^{83} +(0.219869 + 0.676688i) q^{84} +(-2.41426 + 7.43033i) q^{85} +(-2.94237 - 2.13776i) q^{86} -20.0820 q^{87} +(0.570884 - 3.26712i) q^{88} +13.3617 q^{89} +(5.06387 + 3.67912i) q^{90} +(0.0728568 - 0.224230i) q^{91} +(1.18957 + 3.66112i) q^{92} +(18.3997 - 13.3682i) q^{93} +(-6.18843 + 4.49616i) q^{94} +(-0.560761 - 1.72584i) q^{95} +(0.784763 - 2.41525i) q^{96} +(-7.80794 - 5.67280i) q^{97} +6.92150 q^{98} +(10.1092 + 5.35516i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 5 q^{2} - q^{3} - 5 q^{4} - q^{5} + q^{6} + 13 q^{7} + 5 q^{8} - 6 q^{9}+O(q^{10}) $ 20 * q + 5 * q^2 - q^3 - 5 * q^4 - q^5 + q^6 + 13 * q^7 + 5 * q^8 - 6 * q^9	\( 20 q + 5 q^{2} - q^{3} - 5 q^{4} - q^{5} + q^{6} + 13 q^{7} + 5 q^{8} - 6 q^{9} + 6 q^{10} + q^{11} + 4 q^{12} - 2 q^{13} - 13 q^{14} - 8 q^{15} - 5 q^{16} + 11 q^{17} + 6 q^{18} + 5 q^{19} - q^{20} + 2 q^{21} + 4 q^{22} + 28 q^{23} + q^{24} - 30 q^{25} - 13 q^{26} - 31 q^{27} - 2 q^{28} + 28 q^{29} + 8 q^{30} - q^{31} - 20 q^{32} + 9 q^{33} + 24 q^{34} - 11 q^{35} - 6 q^{36} + 8 q^{37} - 5 q^{38} + 18 q^{39} - 4 q^{40} - 5 q^{41} - 22 q^{42} - 44 q^{43} + 11 q^{44} - 4 q^{45} + 7 q^{46} - 39 q^{47} - q^{48} + 4 q^{49} - 25 q^{50} - 11 q^{51} + 13 q^{52} - q^{53} - 4 q^{54} + 8 q^{55} + 22 q^{56} + q^{57} - 28 q^{58} + 6 q^{59} + 7 q^{60} + 10 q^{61} + 11 q^{62} + 34 q^{63} - 5 q^{64} - 8 q^{65} + 41 q^{66} + 18 q^{67} + 11 q^{68} - 63 q^{69} + q^{70} - 3 q^{71} + 6 q^{72} + 5 q^{73} - 8 q^{74} + 5 q^{75} - 20 q^{76} + 36 q^{77} + 22 q^{78} + 19 q^{79} + 4 q^{80} + 63 q^{81} - 9 q^{83} - 23 q^{84} + 30 q^{85} - 26 q^{86} - 16 q^{87} - q^{88} + 44 q^{89} + 14 q^{90} - 68 q^{91} - 7 q^{92} + 27 q^{93} - 31 q^{94} - 4 q^{95} + q^{96} - 71 q^{97} + 6 q^{98} + 20 q^{99}+O(q^{100}) \) 20 * q + 5 * q^2 - q^3 - 5 * q^4 - q^5 + q^6 + 13 * q^7 + 5 * q^8 - 6 * q^9 + 6 * q^10 + q^11 + 4 * q^12 - 2 * q^13 - 13 * q^14 - 8 * q^15 - 5 * q^16 + 11 * q^17 + 6 * q^18 + 5 * q^19 - q^20 + 2 * q^21 + 4 * q^22 + 28 * q^23 + q^24 - 30 * q^25 - 13 * q^26 - 31 * q^27 - 2 * q^28 + 28 * q^29 + 8 * q^30 - q^31 - 20 * q^32 + 9 * q^33 + 24 * q^34 - 11 * q^35 - 6 * q^36 + 8 * q^37 - 5 * q^38 + 18 * q^39 - 4 * q^40 - 5 * q^41 - 22 * q^42 - 44 * q^43 + 11 * q^44 - 4 * q^45 + 7 * q^46 - 39 * q^47 - q^48 + 4 * q^49 - 25 * q^50 - 11 * q^51 + 13 * q^52 - q^53 - 4 * q^54 + 8 * q^55 + 22 * q^56 + q^57 - 28 * q^58 + 6 * q^59 + 7 * q^60 + 10 * q^61 + 11 * q^62 + 34 * q^63 - 5 * q^64 - 8 * q^65 + 41 * q^66 + 18 * q^67 + 11 * q^68 - 63 * q^69 + q^70 - 3 * q^71 + 6 * q^72 + 5 * q^73 - 8 * q^74 + 5 * q^75 - 20 * q^76 + 36 * q^77 + 22 * q^78 + 19 * q^79 + 4 * q^80 + 63 * q^81 - 9 * q^83 - 23 * q^84 + 30 * q^85 - 26 * q^86 - 16 * q^87 - q^88 + 44 * q^89 + 14 * q^90 - 68 * q^91 - 7 * q^92 + 27 * q^93 - 31 * q^94 - 4 * q^95 + q^96 - 71 * q^97 + 6 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−0.784763	+	2.41525i	−0.453083	+	1.39445i	0.420288	+	0.907391i	$0.361929\pi$
$3$	−0.784763	+	2.41525i	−0.453083	+	1.39445i	−0.873371	+	0.487055i	$0.838071\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−1.46809	+	1.06663i	−0.656550	+	0.477012i	−0.865496	−	0.500915i	$-0.832997\pi$
$5$	−1.46809	+	1.06663i	−0.656550	+	0.477012i	0.208946	+	0.977927i	$0.432997\pi$
$6$	−2.05454	+	1.49271i	−0.838761	+	0.609395i
$7$	−0.0865782	−	0.266460i	−0.0327235	−	0.100713i	0.933361	−	0.358940i	$-0.116862\pi$
$7$	−0.0865782	−	0.266460i	−0.0327235	−	0.100713i	−0.966084	+	0.258227i	$0.916862\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−2.79053	−	2.02744i	−0.930178	−	0.675814i
$10$	−1.81466			−0.573846
$11$	−3.28363	+	0.466653i	−0.990052	+	0.140701i
$11$	−3.28363	+	0.466653i	−0.990052	+	0.140701i
$12$	−2.53955			−0.733104
$13$	0.680800	+	0.494630i	0.188820	+	0.137186i	0.678179	−	0.734897i	$-0.262769\pi$
$13$	0.680800	+	0.494630i	0.188820	+	0.137186i	−0.489359	+	0.872082i	$0.662769\pi$
$14$	0.0865782	−	0.266460i	0.0231390	−	0.0712145i
$15$	−1.42408	−	4.38286i	−0.367695	−	1.13165i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	3.48308	−	2.53061i	0.844772	−	0.613763i	−0.0789276	−	0.996880i	$-0.525150\pi$
$17$	3.48308	−	2.53061i	0.844772	−	0.613763i	0.923700	+	0.383118i	$0.125150\pi$
$18$	−1.06589	−	3.28047i	−0.251233	−	0.773214i
$19$	−0.309017	+	0.951057i	−0.0708934	+	0.218187i
$19$	−0.309017	+	0.951057i	−0.0708934	+	0.218187i
$20$	−1.46809	−	1.06663i	−0.328275	−	0.238506i
$21$	0.711512			0.155265
$22$	−2.93081	−	1.55254i	−0.624850	−	0.331003i
$23$	3.84953			0.802683			0.401342	−	0.915928i	$-0.368544\pi$
$23$	3.84953			0.802683			0.401342	+	0.915928i	$0.368544\pi$
$24$	−2.05454	−	1.49271i	−0.419380	−	0.304698i
$25$	−0.527494	+	1.62346i	−0.105499	+	0.324692i
$26$	0.260042	+	0.800328i	0.0509985	+	0.156957i
$27$	0.923083	−	0.670659i	0.177647	−	0.129068i
$28$	0.226665	−	0.164682i	0.0428356	−	0.0311219i
$29$	2.44362	+	7.52067i	0.453768	+	1.39655i	0.872576	+	0.488479i	$0.162448\pi$
$29$	2.44362	+	7.52067i	0.453768	+	1.39655i	−0.418808	+	0.908075i	$0.637552\pi$
$30$	1.42408	−	4.38286i	0.260000	−	0.800197i
$31$	−7.24528	−	5.26400i	−1.30129	−	0.945443i	−0.301324	−	0.953522i	$-0.597428\pi$
$31$	−7.24528	−	5.26400i	−1.30129	−	0.945443i	−0.999967	+	0.00807878i	$0.997428\pi$
$32$	−1.00000			−0.176777
$33$	1.44979	−	8.29701i	0.252375	−	1.44432i
$34$	4.30533			0.738358
$35$	0.411319	+	0.298841i	0.0695257	+	0.0505134i
$36$	1.06589	−	3.28047i	0.177648	−	0.546745i
$37$	−0.494218	−	1.52105i	−0.0812490	−	0.250059i	0.902178	−	0.431364i	$-0.141968\pi$
$37$	−0.494218	−	1.52105i	−0.0812490	−	0.250059i	−0.983427	+	0.181306i	$0.941968\pi$
$38$	−0.809017	+	0.587785i	−0.131240	+	0.0953514i
$39$	−1.72892	+	1.25613i	−0.276849	+	0.201143i
$40$	−0.560761	−	1.72584i	−0.0886641	−	0.272880i
$41$	−2.18700	+	6.73091i	−0.341553	+	1.05119i	0.621851	+	0.783136i	$0.286381\pi$
$41$	−2.18700	+	6.73091i	−0.341553	+	1.05119i	−0.963403	+	0.268055i	$0.913619\pi$
$42$	0.575625	+	0.418216i	0.0888209	+	0.0645322i
$43$	−3.63697			−0.554633			−0.277316	−	0.960779i	$-0.589445\pi$
$43$	−3.63697			−0.554633			−0.277316	+	0.960779i	$0.589445\pi$
$44$	−1.45851	−	2.97872i	−0.219879	−	0.449058i
$45$	6.25929			0.933080
$46$	3.11434	+	2.26270i	0.459184	+	0.333617i
$47$	−2.36377	+	7.27493i	−0.344791	+	1.06116i	0.616904	+	0.787038i	$0.288387\pi$
$47$	−2.36377	+	7.27493i	−0.344791	+	1.06116i	−0.961696	+	0.274120i	$0.911613\pi$
$48$	−0.784763	−	2.41525i	−0.113271	−	0.348611i
$49$	5.59961	−	4.06836i	0.799945	−	0.581194i
$50$	−1.38100	+	1.00335i	−0.195303	+	0.141896i
$51$	3.37866	+	10.3984i	0.473107	+	1.45607i
$52$	−0.260042	+	0.800328i	−0.0360614	+	0.110986i
$53$	7.34890	+	5.33929i	1.00945	+	0.733407i	0.964093	−	0.265564i	$-0.0855580\pi$
$53$	7.34890	+	5.33929i	1.00945	+	0.733407i	0.0453552	+	0.998971i	$0.485558\pi$
$54$	1.14099			0.155270
$55$	4.32292	−	4.18751i	0.582903	−	0.564644i
$56$	0.280173			0.0374397
$57$	−2.05454	−	1.49271i	−0.272130	−	0.197714i
$58$	−2.44362	+	7.52067i	−0.320862	+	0.987513i
$59$	1.14652	+	3.52862i	0.149264	+	0.459387i	0.997535	−	0.0701760i	$-0.0223561\pi$
$59$	1.14652	+	3.52862i	0.149264	+	0.459387i	−0.848271	+	0.529563i	$0.822356\pi$
$60$	3.72828	−	2.70876i	0.481319	−	0.349699i
$61$	0.143837	−	0.104504i	0.0184165	−	0.0133804i	−0.578539	−	0.815655i	$-0.696377\pi$
$61$	0.143837	−	0.104504i	0.0184165	−	0.0133804i	0.596955	+	0.802274i	$0.296377\pi$
$62$	−2.76745	−	8.51734i	−0.351467	−	1.08170i
$63$	−0.298633	+	0.919099i	−0.0376243	+	0.115796i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−1.52706			−0.189409
$66$	6.04976	−	5.86026i	0.744674	−	0.721348i
$67$	8.01235			0.978864			0.489432	−	0.872042i	$-0.337204\pi$
$67$	8.01235			0.978864			0.489432	+	0.872042i	$0.337204\pi$
$68$	3.48308	+	2.53061i	0.422386	+	0.306881i
$69$	−3.02097	+	9.29759i	−0.363682	+	1.11930i
$70$	0.157110	+	0.483535i	0.0187782	+	0.0577935i
$71$	−3.04991	+	2.21589i	−0.361958	+	0.262978i	−0.753868	−	0.657025i	$-0.771814\pi$
$71$	−3.04991	+	2.21589i	−0.361958	+	0.262978i	0.391910	+	0.920003i	$0.371814\pi$
$72$	2.79053	−	2.02744i	0.328868	−	0.238936i
$73$	0.184248	+	0.567056i	0.0215645	+	0.0663688i	0.961260	−	0.275644i	$-0.0888912\pi$
$73$	0.184248	+	0.567056i	0.0215645	+	0.0663688i	−0.939695	+	0.342013i	$0.888891\pi$
$74$	0.494218	−	1.52105i	0.0574517	−	0.176818i
$75$	−3.50711	−	2.54806i	−0.404966	−	0.294225i
$76$	−1.00000			−0.114708
$77$	0.408636	+	0.834556i	0.0465683	+	0.0951064i
$78$	−2.13706			−0.241975
$79$	11.4673	+	8.33146i	1.29017	+	0.937362i	0.999809	−	0.0195555i	$-0.00622512\pi$
$79$	11.4673	+	8.33146i	1.29017	+	0.937362i	0.290359	+	0.956918i	$0.406225\pi$
$80$	0.560761	−	1.72584i	0.0626950	−	0.192955i
$81$	−2.30226	−	7.08562i	−0.255807	−	0.787292i
$82$	−5.72565	+	4.15993i	−0.632293	+	0.459387i
$83$	−2.61517	+	1.90003i	−0.287052	+	0.208555i	−0.721987	−	0.691906i	$-0.756771\pi$
$83$	−2.61517	+	1.90003i	−0.287052	+	0.208555i	0.434935	+	0.900462i	$0.356771\pi$
$84$	0.219869	+	0.676688i	0.0239897	+	0.0738327i
$85$	−2.41426	+	7.43033i	−0.261863	+	0.805932i
$86$	−2.94237	−	2.13776i	−0.317284	−	0.230520i
$87$	−20.0820			−2.15301
$88$	0.570884	−	3.26712i	0.0608565	−	0.348276i
$89$	13.3617			1.41633			0.708167	−	0.706045i	$-0.249522\pi$
$89$	13.3617			1.41633			0.708167	+	0.706045i	$0.249522\pi$
$90$	5.06387	+	3.67912i	0.533779	+	0.387813i
$91$	0.0728568	−	0.224230i	0.00763747	−	0.0235057i
$92$	1.18957	+	3.66112i	0.124021	+	0.381698i
$93$	18.3997	−	13.3682i	1.90796	−	1.38622i
$94$	−6.18843	+	4.49616i	−0.638288	+	0.463743i
$95$	−0.560761	−	1.72584i	−0.0575329	−	0.177068i
$96$	0.784763	−	2.41525i	0.0800945	−	0.246506i
$97$	−7.80794	−	5.67280i	−0.792776	−	0.575985i	0.116010	−	0.993248i	$-0.462990\pi$
$97$	−7.80794	−	5.67280i	−0.792776	−	0.575985i	−0.908786	+	0.417263i	$0.862990\pi$
$98$	6.92150			0.699177
$99$	10.1092	+	5.35516i	1.01601	+	0.538214i
$100$	−1.70701			−0.170701
$101$	−0.826015	−	0.600135i	−0.0821916	−	0.0597157i	0.545931	−	0.837830i	$-0.316176\pi$
$101$	−0.826015	−	0.600135i	−0.0821916	−	0.0597157i	−0.628122	+	0.778115i	$0.716176\pi$
$102$	−3.37866	+	10.3984i	−0.334537	+	1.02960i
$103$	−0.970905	−	2.98814i	−0.0956661	−	0.294430i	0.891761	−	0.452508i	$-0.149470\pi$
$103$	−0.970905	−	2.98814i	−0.0956661	−	0.294430i	−0.987427	+	0.158077i	$0.949470\pi$
$104$	−0.680800	+	0.494630i	−0.0667579	+	0.0485024i
$105$	−1.04456	+	0.758921i	−0.101939	+	0.0740631i
$106$	2.80703	+	8.63915i	0.272643	+	0.839108i
$107$	−4.07429	+	12.5394i	−0.393876	+	1.21223i	0.535957	+	0.844246i	$0.319951\pi$
$107$	−4.07429	+	12.5394i	−0.393876	+	1.21223i	−0.929833	+	0.367982i	$0.880049\pi$
$108$	0.923083	+	0.670659i	0.0888237	+	0.0645342i
$109$	12.9265			1.23813			0.619065	−	0.785340i	$-0.287512\pi$
$109$	12.9265			1.23813			0.619065	+	0.785340i	$0.287512\pi$
$110$	5.95868	−	0.846817i	0.568137	−	0.0807408i
$111$	4.06156			0.385506
$112$	0.226665	+	0.164682i	0.0214178	+	0.0155609i
$113$	2.37474	−	7.30869i	0.223397	−	0.687544i	−0.775054	−	0.631895i	$-0.782277\pi$
$113$	2.37474	−	7.30869i	0.223397	−	0.687544i	0.998450	−	0.0556487i	$-0.0177227\pi$
$114$	−0.784763	−	2.41525i	−0.0734998	−	0.226209i
$115$	−5.65146	+	4.10603i	−0.527002	+	0.382889i
$116$	−6.39747	+	4.64803i	−0.593990	+	0.431559i
$117$	−0.896961	−	2.76056i	−0.0829241	−	0.255214i
$118$	−1.14652	+	3.52862i	−0.105545	+	0.324835i
$119$	−0.975866	−	0.709008i	−0.0894575	−	0.0649947i
$120$	4.60841			0.420689
$121$	10.5645	−	3.06463i	0.960406	−	0.278603i
$122$	0.177793			0.0160966
$123$	−14.5406	−	10.5643i	−1.31108	−	0.952554i
$124$	2.76745	−	8.51734i	0.248524	−	0.764880i
$125$	−3.76103	−	11.5753i	−0.336397	−	1.03532i
$126$	−0.781832	+	0.568035i	−0.0696512	+	0.0506045i
$127$	−4.90241	+	3.56181i	−0.435019	+	0.316060i	−0.783653	−	0.621199i	$-0.786646\pi$
$127$	−4.90241	+	3.56181i	−0.435019	+	0.316060i	0.348634	+	0.937259i	$0.386646\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	2.85416	−	8.78420i	0.251295	−	0.773406i
$130$	−1.23542	−	0.897585i	−0.108354	−	0.0787234i
$131$	9.10748			0.795724			0.397862	−	0.917445i	$-0.369752\pi$
$131$	9.10748			0.795724			0.397862	+	0.917445i	$0.369752\pi$
$132$	8.33893	−	1.18509i	0.725811	−	0.103149i
$133$	0.280173			0.0242941
$134$	6.48212	+	4.70954i	0.559970	+	0.406842i
$135$	−0.639825	+	1.96918i	−0.0550673	+	0.169480i
$136$	1.33042	+	4.09461i	0.114083	+	0.351110i
$137$	9.98841	−	7.25700i	0.853367	−	0.620008i	−0.0727051	−	0.997353i	$-0.523163\pi$
$137$	9.98841	−	7.25700i	0.853367	−	0.620008i	0.926072	+	0.377346i	$0.123163\pi$
$138$	−7.90900	+	5.74623i	−0.673259	+	0.489151i
$139$	−3.13728	−	9.65555i	−0.266101	−	0.818973i	−0.991438	−	0.130580i	$-0.958316\pi$
$139$	−3.13728	−	9.65555i	−0.266101	−	0.818973i	0.725337	−	0.688394i	$-0.241684\pi$
$140$	−0.157110	+	0.483535i	−0.0132782	+	0.0408662i
$141$	−15.7158	−	11.4182i	−1.32351	−	0.961585i
$142$	−3.76990			−0.316363
$143$	−2.46632	−	1.30648i	−0.206244	−	0.109254i
$144$	3.44929			0.287441
$145$	−11.6092	−	8.43460i	−0.964094	−	0.700455i
$146$	−0.184248	+	0.567056i	−0.0152484	+	0.0469299i
$147$	5.43174	+	16.7172i	0.448002	+	1.37881i
$148$	1.29388	−	0.940059i	0.106356	−	0.0772724i
$149$	−1.69146	+	1.22892i	−0.138570	+	0.100677i	−0.654911	−	0.755706i	$-0.727294\pi$
$149$	−1.69146	+	1.22892i	−0.138570	+	0.100677i	0.516341	+	0.856383i	$0.327294\pi$
$150$	−1.33960	−	4.12285i	−0.109378	−	0.336629i
$151$	3.32499	−	10.2333i	0.270584	−	0.832772i	−0.719770	−	0.694212i	$-0.755753\pi$
$151$	3.32499	−	10.2333i	0.270584	−	0.832772i	0.990354	−	0.138559i	$-0.0442472\pi$
$152$	−0.809017	−	0.587785i	−0.0656199	−	0.0476757i
$153$	−14.8503			−1.20058
$154$	−0.159946	+	0.915360i	−0.0128888	+	0.0737618i
$155$	16.2515			1.30535
$156$	−1.72892	−	1.25613i	−0.138424	−	0.100571i
$157$	−0.909268	+	2.79844i	−0.0725675	+	0.223340i	−0.980762	−	0.195210i	$-0.937461\pi$
$157$	−0.909268	+	2.79844i	−0.0725675	+	0.223340i	0.908194	+	0.418549i	$0.137461\pi$
$158$	4.38011	+	13.4806i	0.348463	+	1.07246i
$159$	−18.6629	+	13.5594i	−1.48006	+	1.07533i
$160$	1.46809	−	1.06663i	0.116063	−	0.0843246i
$161$	−0.333286	−	1.02575i	−0.0262666	−	0.0808403i
$162$	2.30226	−	7.08562i	0.180883	−	0.556699i
$163$	−8.04447	−	5.84465i	−0.630092	−	0.457788i	0.226340	−	0.974048i	$-0.427324\pi$
$163$	−8.04447	−	5.84465i	−0.630092	−	0.457788i	−0.856432	+	0.516260i	$0.827324\pi$
$164$	−7.07730			−0.552644
$165$	6.72142	+	13.7271i	0.523262	+	1.06866i
$166$	−3.23253			−0.250893
$167$	−8.50028	−	6.17582i	−0.657771	−	0.477899i	0.208138	−	0.978099i	$-0.433260\pi$
$167$	−8.50028	−	6.17582i	−0.657771	−	0.477899i	−0.865910	+	0.500200i	$0.833260\pi$
$168$	−0.219869	+	0.676688i	−0.0169633	+	0.0522076i
$169$	−3.79839	−	11.6902i	−0.292184	−	0.899250i
$170$	−6.32062	+	4.59220i	−0.484769	+	0.352205i
$171$	2.79053	−	2.02744i	0.213398	−	0.155042i
$172$	−1.12389	−	3.45897i	−0.0856955	−	0.263744i
$173$	−2.15424	+	6.63007i	−0.163784	+	0.504075i	−0.998945	−	0.0459312i	$-0.985375\pi$
$173$	−2.15424	+	6.63007i	−0.163784	+	0.504075i	0.835161	+	0.550006i	$0.185375\pi$
$174$	−16.2467	−	11.8039i	−1.23166	−	0.894850i
$175$	0.478257			0.0361529
$176$	2.38222	−	2.30760i	0.179567	−	0.173942i
$177$	−9.42224			−0.708219
$178$	10.8098	+	7.85380i	0.810231	+	0.588667i
$179$	2.44985	−	7.53986i	0.183110	−	0.563556i	−0.816800	−	0.576920i	$-0.804254\pi$
$179$	2.44985	−	7.53986i	0.183110	−	0.563556i	0.999911	+	0.0133648i	$0.00425428\pi$
$180$	1.93423	+	5.95294i	0.144169	+	0.443706i
$181$	5.64535	−	4.10159i	0.419616	−	0.304869i	−0.357868	−	0.933772i	$-0.616496\pi$
$181$	5.64535	−	4.10159i	0.419616	−	0.304869i	0.777483	+	0.628904i	$0.216496\pi$
$182$	0.190742	−	0.138582i	0.0141387	−	0.0102724i
$183$	0.139525	+	0.429414i	0.0103140	+	0.0317432i
$184$	−1.18957	+	3.66112i	−0.0876963	+	0.269902i
$185$	2.34795	+	1.70589i	0.172625	+	0.125419i
$186$	22.7433			1.66762
$187$	−10.2562	+	9.93498i	−0.750011	+	0.726518i
$188$	−7.64932			−0.557884
$189$	−0.258623	−	0.187901i	−0.0188121	−	0.0136678i
$190$	0.560761	−	1.72584i	0.0406819	−	0.125206i
$191$	6.83204	+	21.0269i	0.494349	+	1.52145i	0.817968	+	0.575263i	$0.195100\pi$
$191$	6.83204	+	21.0269i	0.494349	+	1.52145i	−0.323619	+	0.946187i	$0.604900\pi$
$192$	2.05454	−	1.49271i	0.148273	−	0.107727i
$193$	18.9934	−	13.7995i	1.36717	−	0.993309i	0.369221	−	0.929342i	$-0.379625\pi$
$193$	18.9934	−	13.7995i	1.36717	−	0.993309i	0.997952	−	0.0639678i	$-0.0203755\pi$
$194$	−2.98237	−	9.17878i	−0.214121	−	0.658998i
$195$	1.19838	−	3.68824i	0.0858179	−	0.264120i
$196$	5.59961	+	4.06836i	0.399972	+	0.290597i
$197$	−16.2420			−1.15719			−0.578597	−	0.815613i	$-0.696400\pi$
$197$	−16.2420			−1.15719			−0.578597	+	0.815613i	$0.696400\pi$
$198$	5.03083	+	10.2745i	0.357525	+	0.730174i
$199$	2.06022			0.146045			0.0730226	−	0.997330i	$-0.476735\pi$
$199$	2.06022			0.146045			0.0730226	+	0.997330i	$0.476735\pi$
$200$	−1.38100	−	1.00335i	−0.0976513	−	0.0709478i
$201$	−6.28779	+	19.3518i	−0.443506	+	1.36497i
$202$	−0.315510	−	0.971039i	−0.0221992	−	0.0683221i
$203$	1.79240	−	1.30225i	0.125802	−	0.0914002i
$204$	−8.84545	+	6.42660i	−0.619305	+	0.449952i
$205$	−3.96867	−	12.2143i	−0.277184	−	0.853085i
$206$	0.970905	−	2.98814i	0.0676462	−	0.208194i
$207$	−10.7423	−	7.80470i	−0.746638	−	0.542464i
$208$	−0.841515			−0.0583485
$209$	0.570884	−	3.26712i	0.0394889	−	0.225992i
$210$	−1.29115			−0.0890980
$211$	10.8472	+	7.88095i	0.746751	+	0.542547i	0.894818	−	0.446431i	$-0.147305\pi$
$211$	10.8472	+	7.88095i	0.746751	+	0.542547i	−0.148067	+	0.988977i	$0.547305\pi$
$212$	−2.80703	+	8.63915i	−0.192788	+	0.593339i
$213$	−2.95848	−	9.10526i	−0.202712	−	0.623882i
$214$	−10.6666	+	7.74976i	−0.729156	+	0.529763i
$215$	5.33941	−	3.87931i	0.364144	−	0.264566i
$216$	0.352586	+	1.08515i	0.0239905	+	0.0738351i
$217$	−0.775365	+	2.38633i	−0.0526352	+	0.161995i
$218$	10.4577	+	7.59798i	0.708287	+	0.514600i
$219$	−1.51417			−0.102318
$220$	5.31842	+	2.81733i	0.358568	+	0.189945i
$221$	3.62300			0.243709
$222$	3.28587	+	2.38732i	0.220533	+	0.160227i
$223$	3.15621	−	9.71382i	0.211356	−	0.650486i	−0.788037	−	0.615628i	$-0.788902\pi$
$223$	3.15621	−	9.71382i	0.211356	−	0.650486i	0.999392	−	0.0348574i	$-0.0110977\pi$
$224$	0.0865782	+	0.266460i	0.00578475	+	0.0178036i
$225$	4.76346	−	3.46086i	0.317564	−	0.230724i
$226$	6.21714	−	4.51702i	0.413558	−	0.300468i
$227$	−1.34859	−	4.15055i	−0.0895094	−	0.275482i	0.896275	−	0.443500i	$-0.146263\pi$
$227$	−1.34859	−	4.15055i	−0.0895094	−	0.275482i	−0.985784	+	0.168018i	$0.946263\pi$
$228$	0.784763	−	2.41525i	0.0519722	−	0.159954i
$229$	15.3022	+	11.1177i	1.01120	+	0.734677i	0.964460	−	0.264230i	$-0.0851179\pi$
$229$	15.3022	+	11.1177i	1.01120	+	0.734677i	0.0467365	+	0.998907i	$0.485118\pi$
$230$	−6.98559			−0.460616
$231$	−2.33634	+	0.332029i	−0.153720	+	0.0218459i
$232$	−7.90770			−0.519166
$233$	11.3875	+	8.27352i	0.746022	+	0.542016i	0.894591	−	0.446885i	$-0.147467\pi$
$233$	11.3875	+	8.27352i	0.746022	+	0.542016i	−0.148569	+	0.988902i	$0.547467\pi$
$234$	0.896961	−	2.76056i	0.0586362	−	0.180464i
$235$	−4.28944	−	13.2015i	−0.279812	−	0.861173i
$236$	−3.00162	+	2.18080i	−0.195389	+	0.141958i
$237$	−29.1216	+	21.1581i	−1.89165	+	1.37437i
$238$	−0.372748	−	1.14720i	−0.0241616	−	0.0743619i
$239$	1.56063	−	4.80312i	0.100949	−	0.310688i	−0.887810	−	0.460211i	$-0.847774\pi$
$239$	1.56063	−	4.80312i	0.100949	−	0.310688i	0.988758	+	0.149523i	$0.0477737\pi$
$240$	3.72828	+	2.70876i	0.240660	+	0.174850i
$241$	−29.9451			−1.92894			−0.964468	−	0.264200i	$-0.914892\pi$
$241$	−29.9451			−1.92894			−0.964468	+	0.264200i	$0.914892\pi$
$242$	10.3482	+	3.73030i	0.665206	+	0.239793i
$243$	22.3433			1.43332
$244$	0.143837	+	0.104504i	0.00920824	+	0.00669018i
$245$	−3.88131	+	11.9454i	−0.247968	+	0.763166i
$246$	−5.55400	−	17.0934i	−0.354110	−	1.08984i
$247$	−0.680800	+	0.494630i	−0.0433182	+	0.0314725i
$248$	7.24528	−	5.26400i	0.460076	−	0.334265i
$249$	−2.53677	−	7.80736i	−0.160761	−	0.494771i
$250$	3.76103	−	11.5753i	0.237868	−	0.732083i
$251$	8.23300	+	5.98163i	0.519662	+	0.377557i	0.816477	−	0.577378i	$-0.195924\pi$
$251$	8.23300	+	5.98163i	0.519662	+	0.377557i	−0.296814	+	0.954935i	$0.595924\pi$
$252$	−0.966398			−0.0608774
$253$	−12.6404	+	1.79640i	−0.794698	+	0.112938i
$254$	−6.05972			−0.380220
$255$	−16.0515	−	11.6621i	−1.00518	−	0.730308i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	3.53917	+	10.8925i	0.220767	+	0.679452i	0.998694	+	0.0510968i	$0.0162717\pi$
$257$	3.53917	+	10.8925i	0.220767	+	0.679452i	−0.777926	+	0.628356i	$0.783728\pi$
$258$	7.47229	−	5.42893i	0.465204	−	0.337991i
$259$	−0.362510	+	0.263379i	−0.0225253	+	0.0163656i
$260$	−0.471888	−	1.45232i	−0.0292653	−	0.0900693i
$261$	8.42874	−	25.9410i	0.521726	−	1.60571i
$262$	7.36811	+	5.35324i	0.455203	+	0.330724i
$263$	−30.0451			−1.85266			−0.926331	−	0.376710i	$-0.877055\pi$
$263$	−30.0451			−1.85266			−0.926331	+	0.376710i	$0.877055\pi$
$264$	7.44291	+	3.94275i	0.458080	+	0.242659i
$265$	−16.4839			−1.01260
$266$	0.226665	+	0.164682i	0.0138977	+	0.0100973i
$267$	−10.4857	+	32.2718i	−0.641717	+	1.97500i
$268$	2.47595	+	7.62019i	0.151243	+	0.465477i
$269$	−16.8179	+	12.2189i	−1.02540	+	0.744999i	−0.967384	−	0.253316i	$-0.918479\pi$
$269$	−16.8179	+	12.2189i	−1.02540	+	0.744999i	−0.0580199	+	0.998315i	$0.518479\pi$
$270$	−1.67508	+	1.21702i	−0.101942	+	0.0740654i
$271$	−5.68339	−	17.4917i	−0.345241	−	1.06254i	−0.961455	−	0.274964i	$-0.911334\pi$
$271$	−5.68339	−	17.4917i	−0.345241	−	1.06254i	0.616214	−	0.787579i	$-0.288666\pi$
$272$	−1.33042	+	4.09461i	−0.0806685	+	0.248272i
$273$	0.484397	+	0.351935i	0.0293170	+	0.0213001i
$274$	12.3464			0.745870
$275$	0.974504	−	5.57700i	0.0587648	−	0.336306i
$276$	−9.77606			−0.588450
$277$	−13.0763	−	9.50050i	−0.785679	−	0.570829i	0.120999	−	0.992653i	$-0.461390\pi$
$277$	−13.0763	−	9.50050i	−0.785679	−	0.570829i	−0.906678	+	0.421823i	$0.861390\pi$
$278$	3.13728	−	9.65555i	0.188161	−	0.579101i
$279$	9.54574	+	29.3788i	0.571489	+	1.75886i
$280$	−0.411319	+	0.298841i	−0.0245810	+	0.0178592i
$281$	19.4421	−	14.1255i	1.15982	−	0.842660i	0.170066	−	0.985433i	$-0.445602\pi$
$281$	19.4421	−	14.1255i	1.15982	−	0.842660i	0.989755	+	0.142773i	$0.0456019\pi$
$282$	−6.00290	−	18.4750i	−0.357467	−	1.10017i
$283$	−3.65750	+	11.2566i	−0.217416	+	0.669136i	0.781558	+	0.623833i	$0.214425\pi$
$283$	−3.65750	+	11.2566i	−0.217416	+	0.669136i	−0.998973	+	0.0453035i	$0.985575\pi$
$284$	−3.04991	−	2.21589i	−0.180979	−	0.131489i
$285$	4.60841			0.272979
$286$	−1.22736	−	2.50663i	−0.0725752	−	0.148220i
$287$	1.98287			0.117045
$288$	2.79053	+	2.02744i	0.164434	+	0.119468i
$289$	0.474605	−	1.46068i	0.0279180	−	0.0859226i
$290$	−4.43433	−	13.6475i	−0.260393	−	0.801407i
$291$	19.8286	−	14.4063i	1.16237	−	0.844514i
$292$	−0.482366	+	0.350460i	−0.0282284	+	0.0205091i
$293$	−5.63548	−	17.3442i	−0.329228	−	1.01326i	−0.969496	−	0.245109i	$-0.921176\pi$
$293$	−5.63548	−	17.3442i	−0.329228	−	1.01326i	0.640267	−	0.768152i	$-0.278824\pi$
$294$	−5.43174	+	16.7172i	−0.316785	+	0.974965i
$295$	−5.44692	−	3.95742i	−0.317132	−	0.230410i
$296$	1.59932			0.0929588
$297$	−2.71810	+	2.63296i	−0.157720	+	0.152780i
$298$	−2.09076			−0.121114
$299$	2.62076	+	1.90409i	0.151562	+	0.110117i
$300$	1.33960	−	4.12285i	0.0773416	−	0.238033i
$301$	0.314883	+	0.969109i	0.0181495	+	0.0558585i
$302$	8.70494	−	6.32451i	0.500913	−	0.363935i
$303$	2.09770	−	1.52407i	0.120510	−	0.0875555i
$304$	−0.309017	−	0.951057i	−0.0177233	−	0.0545468i
$305$	−0.0996992	+	0.306843i	−0.00570876	+	0.0175698i
$306$	−12.0142	−	8.72880i	−0.686804	−	0.498993i
$307$	−0.500395			−0.0285591			−0.0142795	−	0.999898i	$-0.504545\pi$
$307$	−0.500395			−0.0285591			−0.0142795	+	0.999898i	$0.504545\pi$
$308$	−0.667434	+	0.646527i	−0.0380306	+	0.0368393i
$309$	7.97904			0.453912
$310$	13.1477	+	9.55238i	0.746741	+	0.542539i
$311$	0.651402	−	2.00481i	0.0369376	−	0.113682i	−0.930888	−	0.365306i	$-0.880964\pi$
$311$	0.651402	−	2.00481i	0.0369376	−	0.113682i	0.967825	+	0.251623i	$0.0809644\pi$
$312$	−0.660389	−	2.03247i	−0.0373872	−	0.115066i
$313$	−6.58236	+	4.78237i	−0.372057	+	0.270315i	−0.758063	−	0.652181i	$-0.773854\pi$
$313$	−6.58236	+	4.78237i	−0.372057	+	0.270315i	0.386006	+	0.922496i	$0.373854\pi$
$314$	−2.38049	+	1.72953i	−0.134339	+	0.0976030i
$315$	−0.541918	−	1.66785i	−0.0305336	−	0.0939729i
$316$	−4.38011	+	13.4806i	−0.246400	+	0.758342i
$317$	10.2772	+	7.46680i	0.577223	+	0.419377i	0.837722	−	0.546097i	$-0.183887\pi$
$317$	10.2772	+	7.46680i	0.577223	+	0.419377i	−0.260499	+	0.965474i	$0.583887\pi$
$318$	−23.0686			−1.29362
$319$	−11.5335	−	23.5548i	−0.645751	−	1.31882i
$320$	1.81466			0.101443
$321$	−27.0884	−	19.6809i	−1.51193	−	1.09848i
$322$	0.333286	−	1.02575i	0.0185733	−	0.0571627i
$323$	1.33042	+	4.09461i	0.0740265	+	0.227830i
$324$	6.02739	−	4.37916i	0.334855	−	0.243286i
$325$	−1.16213	+	0.844337i	−0.0644634	+	0.0468354i
$326$	−3.07271	−	9.45684i	−0.170182	−	0.523766i
$327$	−10.1442	+	31.2207i	−0.560976	+	1.72651i
$328$	−5.72565	−	4.15993i	−0.316146	−	0.229694i
$329$	2.14313			0.118155
$330$	−2.63087	+	15.0562i	−0.144825	+	0.828819i
$331$	35.8680			1.97148			0.985742	−	0.168267i	$-0.0538170\pi$
$331$	35.8680			1.97148			0.985742	+	0.168267i	$0.0538170\pi$
$332$	−2.61517	−	1.90003i	−0.143526	−	0.104278i
$333$	−1.70470	+	5.24654i	−0.0934171	+	0.287508i
$334$	−3.24682	−	9.99268i	−0.177658	−	0.546775i
$335$	−11.7629	+	8.54621i	−0.642673	+	0.466930i
$336$	−0.575625	+	0.418216i	−0.0314029	+	0.0228156i
$337$	−3.01398	−	9.27608i	−0.164182	−	0.505300i	0.834793	−	0.550564i	$-0.185587\pi$
$337$	−3.01398	−	9.27608i	−0.164182	−	0.505300i	−0.998975	+	0.0452636i	$0.985587\pi$
$338$	3.79839	−	11.6902i	0.206605	−	0.635866i
$339$	15.7887	+	11.4712i	0.857526	+	0.623029i
$340$	−7.81271			−0.423704
$341$	26.2473	+	13.9040i	1.42137	+	0.752945i
$342$	3.44929			0.186516
$343$	−3.15551	−	2.29261i	−0.170382	−	0.123790i
$344$	1.12389	−	3.45897i	0.0605959	−	0.186495i
$345$	−5.48203	−	16.8720i	−0.295143	−	0.908356i
$346$	−5.63987	+	4.09761i	−0.303201	+	0.220289i
$347$	22.1600	−	16.1002i	1.18961	−	0.864302i	0.196387	−	0.980526i	$-0.437079\pi$
$347$	22.1600	−	16.1002i	1.18961	−	0.864302i	0.993223	+	0.116224i	$0.0370790\pi$
$348$	−6.20567	−	19.0991i	−0.332659	−	1.02382i
$349$	−4.91550	+	15.1284i	−0.263121	+	0.809803i	0.728999	+	0.684514i	$0.239986\pi$
$349$	−4.91550	+	15.1284i	−0.263121	+	0.809803i	−0.992120	+	0.125289i	$0.960014\pi$
$350$	0.386918	+	0.281113i	0.0206817	+	0.0150261i
$351$	0.960163			0.0512497
$352$	3.28363	−	0.466653i	0.175018	−	0.0248727i
$353$	−3.96227			−0.210890			−0.105445	−	0.994425i	$-0.533627\pi$
$353$	−3.96227			−0.210890			−0.105445	+	0.994425i	$0.533627\pi$
$354$	−7.62275	−	5.53825i	−0.405145	−	0.294355i
$355$	2.11401	−	6.50626i	0.112200	−	0.345317i
$356$	4.12899	+	12.7077i	0.218836	+	0.673507i
$357$	2.47826	−	1.80056i	0.131163	−	0.0952957i
$358$	6.41379	−	4.65989i	0.338979	−	0.246283i
$359$	7.58383	+	23.3406i	0.400259	+	1.23187i	0.924790	+	0.380479i	$0.124241\pi$
$359$	7.58383	+	23.3406i	0.400259	+	1.23187i	−0.524531	+	0.851392i	$0.675759\pi$
$360$	−1.93423	+	5.95294i	−0.101943	+	0.313747i
$361$	−0.809017	−	0.587785i	−0.0425798	−	0.0309361i
$362$	6.97804			0.366758
$363$	−0.888741	+	27.9209i	−0.0466468	+	1.46546i
$364$	0.235770			0.0123577
$365$	−0.875331	−	0.635965i	−0.0458169	−	0.0332879i
$366$	−0.139525	+	0.429414i	−0.00729309	+	0.0224458i
$367$	6.97367	+	21.4627i	0.364022	+	1.12035i	0.950591	+	0.310446i	$0.100478\pi$
$367$	6.97367	+	21.4627i	0.364022	+	1.12035i	−0.586569	+	0.809900i	$0.699522\pi$
$368$	−3.11434	+	2.26270i	−0.162346	+	0.117951i
$369$	19.7494	−	14.3488i	1.02811	−	0.746969i
$370$	0.896838	+	2.76019i	0.0466244	+	0.143495i
$371$	0.786454	−	2.42046i	0.0408306	−	0.125664i
$372$	18.3997	+	13.3682i	0.953981	+	0.693108i
$373$	23.9780			1.24153			0.620766	−	0.783996i	$-0.286822\pi$
$373$	23.9780			1.24153			0.620766	+	0.783996i	$0.286822\pi$
$374$	−14.1371	+	2.00910i	−0.731013	+	0.103888i
$375$	30.9087			1.59612
$376$	−6.18843	−	4.49616i	−0.319144	−	0.231872i
$377$	−2.05634	+	6.32876i	−0.105907	+	0.325948i
$378$	−0.0987852	−	0.304030i	−0.00508096	−	0.0156376i
$379$	26.1097	−	18.9698i	1.34116	−	0.974413i	0.341765	−	0.939786i	$-0.388975\pi$
$379$	26.1097	−	18.9698i	1.34116	−	0.974413i	0.999400	−	0.0346278i	$-0.0110246\pi$
$380$	1.46809	−	1.06663i	0.0753115	−	0.0547170i
$381$	−4.75544	−	14.6357i	−0.243629	−	0.749812i
$382$	−6.83204	+	21.0269i	−0.349558	+	1.07583i
$383$	13.0524	+	9.48309i	0.666944	+	0.484564i	0.869001	−	0.494810i	$-0.164762\pi$
$383$	13.0524	+	9.48309i	0.666944	+	0.484564i	−0.202057	+	0.979374i	$0.564762\pi$
$384$	2.53955			0.129596
$385$	−1.49008	−	0.789340i	−0.0759413	−	0.0402285i
$386$	23.4771			1.19495
$387$	10.1491	+	7.37375i	0.515908	+	0.374829i
$388$	2.98237	−	9.17878i	0.151407	−	0.465982i
$389$	6.12751	+	18.8585i	0.310677	+	0.956166i	0.977497	+	0.210947i	$0.0676549\pi$
$389$	6.12751	+	18.8585i	0.310677	+	0.956166i	−0.666820	+	0.745219i	$0.732345\pi$
$390$	3.13741	−	2.27946i	0.158869	−	0.115425i
$391$	13.4082	−	9.74166i	0.678084	−	0.492657i
$392$	2.13886	+	6.58274i	0.108029	+	0.332479i
$393$	−7.14721	+	21.9968i	−0.360529	+	1.10959i
$394$	−13.1401	−	9.54681i	−0.661987	−	0.480961i
$395$	−25.7216			−1.29419
$396$	−1.96915	+	11.2693i	−0.0989533	+	0.566301i
$397$	−37.4262			−1.87837			−0.939185	−	0.343412i	$-0.888417\pi$
$397$	−37.4262			−1.87837			−0.939185	+	0.343412i	$0.888417\pi$
$398$	1.66675	+	1.21097i	0.0835469	+	0.0607004i
$399$	−0.219869	+	0.676688i	−0.0110072	+	0.0338768i
$400$	−0.527494	−	1.62346i	−0.0263747	−	0.0811730i
$401$	23.0514	−	16.7478i	1.15113	−	0.836346i	0.162501	−	0.986708i	$-0.448044\pi$
$401$	23.0514	−	16.7478i	1.15113	−	0.836346i	0.988631	+	0.150362i	$0.0480439\pi$
$402$	−16.4616	+	11.9601i	−0.821032	+	0.596515i
$403$	−2.32885	−	7.16746i	−0.116008	−	0.357037i
$404$	0.315510	−	0.971039i	0.0156972	−	0.0483110i
$405$	10.9377	+	7.94668i	0.543497	+	0.394874i
$406$	2.21553			0.109955
$407$	2.33263	+	4.76393i	0.115624	+	0.236139i
$408$	−10.9336			−0.541293
$409$	20.6758	+	15.0218i	1.02235	+	0.742782i	0.966764	−	0.255671i	$-0.0822965\pi$
$409$	20.6758	+	15.0218i	1.02235	+	0.742782i	0.0555885	+	0.998454i	$0.482297\pi$
$410$	3.96867	−	12.2143i	0.195999	−	0.603222i
$411$	9.68896	+	29.8195i	0.477921	+	1.47089i
$412$	2.54186	−	1.84677i	0.125229	−	0.0909839i
$413$	0.840973	−	0.611002i	0.0413816	−	0.0300655i
$414$	−4.10318	−	12.6283i	−0.201660	−	0.620646i
$415$	1.81267	−	5.57884i	0.0889807	−	0.273854i
$416$	−0.680800	−	0.494630i	−0.0333789	−	0.0242512i
$417$	25.7826			1.26258
$418$	2.38222	−	2.30760i	0.116518	−	0.112868i
$419$	−23.4672			−1.14645			−0.573225	−	0.819398i	$-0.694308\pi$
$419$	−23.4672			−1.14645			−0.573225	+	0.819398i	$0.694308\pi$
$420$	−1.04456	−	0.758921i	−0.0509695	−	0.0370315i
$421$	−9.03883	+	27.8186i	−0.440525	+	1.35580i	0.446792	+	0.894638i	$0.352567\pi$
$421$	−9.03883	+	27.8186i	−0.440525	+	1.35580i	−0.887317	+	0.461160i	$0.847433\pi$
$422$	4.14326	+	12.7516i	0.201691	+	0.620740i
$423$	21.3457	−	15.5085i	1.03786	−	0.754051i
$424$	−7.34890	+	5.33929i	−0.356894	+	0.259299i
$425$	2.27104	+	6.98953i	0.110161	+	0.339042i
$426$	2.95848	−	9.10526i	0.143339	−	0.441151i
$427$	−0.0402993	−	0.0292792i	−0.00195022	−	0.00141692i
$428$	−13.1847			−0.637306
$429$	5.09096	−	4.93149i	0.245794	−	0.238095i
$430$	6.59987			0.318274
$431$	−17.2589	−	12.5393i	−0.831331	−	0.603997i	0.0886047	−	0.996067i	$-0.471759\pi$
$431$	−17.2589	−	12.5393i	−0.831331	−	0.603997i	−0.919936	+	0.392070i	$0.871759\pi$
$432$	−0.352586	+	1.08515i	−0.0169638	+	0.0522093i
$433$	−9.49290	−	29.2161i	−0.456200	−	1.40404i	−0.869721	−	0.493544i	$-0.835701\pi$
$433$	−9.49290	−	29.2161i	−0.456200	−	1.40404i	0.413521	−	0.910494i	$-0.364299\pi$
$434$	−2.02993	+	1.47483i	−0.0974399	+	0.0707942i
$435$	29.4822	−	21.4200i	1.41356	−	1.02701i
$436$	3.99450	+	12.2938i	0.191302	+	0.588766i
$437$	−1.18957	+	3.66112i	−0.0569049	+	0.175135i
$438$	−1.22499	−	0.890008i	−0.0585323	−	0.0425262i
$439$	11.2316			0.536055			0.268027	−	0.963411i	$-0.413628\pi$
$439$	11.2316			0.536055			0.268027	+	0.963411i	$0.413628\pi$
$440$	2.64670	+	5.40536i	0.126177	+	0.257690i
$441$	−23.8743			−1.13687
$442$	2.93107	+	2.12954i	0.139417	+	0.101292i
$443$	8.54272	−	26.2918i	0.405877	−	1.24916i	−0.514284	−	0.857620i	$-0.671942\pi$
$443$	8.54272	−	26.2918i	0.405877	−	1.24916i	0.920161	−	0.391541i	$-0.128058\pi$
$444$	1.25509	+	3.86277i	0.0595639	+	0.183319i
$445$	−19.6162	+	14.2520i	−0.929895	+	0.675608i
$446$	8.26307	−	6.00347i	0.391268	−	0.284273i
$447$	−1.64075	−	5.04971i	−0.0776048	−	0.238843i
$448$	−0.0865782	+	0.266460i	−0.00409044	+	0.0125891i
$449$	28.5034	+	20.7089i	1.34516	+	0.977314i	0.999237	+	0.0390494i	$0.0124330\pi$
$449$	28.5034	+	20.7089i	1.34516	+	0.977314i	0.345919	+	0.938264i	$0.387567\pi$
$450$	5.88796			0.277561
$451$	4.04032	−	23.1224i	0.190251	−	1.08879i
$452$	7.68481			0.361463
$453$	22.1066	+	16.0614i	1.03866	+	0.754629i
$454$	1.34859	−	4.15055i	0.0632927	−	0.194795i
$455$	0.132210	+	0.406902i	0.00619812	+	0.0190759i
$456$	2.05454	−	1.49271i	0.0962124	−	0.0699024i
$457$	−4.48134	+	3.25588i	−0.209628	+	0.152304i	−0.687645	−	0.726047i	$-0.741356\pi$
$457$	−4.48134	+	3.25588i	−0.209628	+	0.152304i	0.478017	+	0.878350i	$0.341356\pi$
$458$	5.84491	+	17.9888i	0.273115	+	0.840561i
$459$	1.51800	−	4.67193i	0.0708542	−	0.218067i
$460$	−5.65146	−	4.10603i	−0.263501	−	0.191445i
$461$	35.3288			1.64543			0.822713	−	0.568456i	$-0.192459\pi$
$461$	35.3288			1.64543			0.822713	+	0.568456i	$0.192459\pi$
$462$	−2.08530	−	1.10465i	−0.0970171	−	0.0513930i
$463$	−34.9910			−1.62617			−0.813086	−	0.582144i	$-0.802214\pi$
$463$	−34.9910			−1.62617			−0.813086	+	0.582144i	$0.802214\pi$
$464$	−6.39747	−	4.64803i	−0.296995	−	0.215779i
$465$	−12.7536	+	39.2514i	−0.591432	+	1.82024i
$466$	4.34965	+	13.3868i	0.201494	+	0.620133i
$467$	9.41237	−	6.83849i	0.435552	−	0.316447i	−0.348313	−	0.937378i	$-0.613245\pi$
$467$	9.41237	−	6.83849i	0.435552	−	0.316447i	0.783865	+	0.620931i	$0.213245\pi$
$468$	2.34828	−	1.70612i	0.108549	−	0.0788655i
$469$	−0.693695	−	2.13497i	−0.0320318	−	0.0985839i
$470$	4.28944	−	13.2015i	0.197857	−	0.608941i
$471$	−6.04537	−	4.39222i	−0.278556	−	0.202383i
$472$	−3.71021			−0.170776
$473$	11.9425	−	1.69720i	0.549116	−	0.0780375i
$474$	−35.9963			−1.65337
$475$	−1.38100	−	1.00335i	−0.0633645	−	0.0460370i
$476$	0.372748	−	1.14720i	0.0170849	−	0.0525818i
$477$	−9.68226	−	29.7989i	−0.443320	−	1.36440i
$478$	4.08578	−	2.96849i	0.186879	−	0.135776i
$479$	−32.1377	+	23.3494i	−1.46841	+	1.06686i	−0.487337	+	0.873214i	$0.662032\pi$
$479$	−32.1377	+	23.3494i	−1.46841	+	1.06686i	−0.981071	+	0.193647i	$0.937968\pi$
$480$	1.42408	+	4.38286i	0.0650000	+	0.200049i
$481$	0.415892	−	1.27998i	0.0189630	−	0.0583622i
$482$	−24.2261	−	17.6013i	−1.10347	−	0.801718i
$483$	2.73899			0.124628
$484$	6.17924	+	9.10038i	0.280875	+	0.413654i
$485$	17.5135			0.795249
$486$	18.0761	+	13.1330i	0.819948	+	0.595727i
$487$	−3.51758	+	10.8260i	−0.159397	+	0.490573i	−0.998580	−	0.0532761i	$-0.983034\pi$
$487$	−3.51758	+	10.8260i	−0.159397	+	0.490573i	0.839183	+	0.543849i	$0.183034\pi$
$488$	0.0549410	+	0.169091i	0.00248706	+	0.00765438i
$489$	20.4293	−	14.8428i	0.923845	−	0.671213i
$490$	−10.1614	+	7.38269i	−0.459045	+	0.333516i
$491$	−1.63805	−	5.04141i	−0.0739243	−	0.227516i	0.907266	−	0.420556i	$-0.138165\pi$
$491$	−1.63805	−	5.04141i	−0.0739243	−	0.227516i	−0.981191	+	0.193041i	$0.938165\pi$
$492$	5.55400	−	17.0934i	0.250394	−	0.770632i
$493$	27.5432	+	20.0113i	1.24048	+	0.901264i
$494$	−0.841515			−0.0378615
$495$	−20.5532	+	2.92092i	−0.923798	+	0.131286i
$496$	8.95566			0.402121
$497$	0.854503	+	0.620833i	0.0383297	+	0.0278482i
$498$	2.53677	−	7.80736i	0.113675	−	0.349856i
$499$	−7.82066	−	24.0695i	−0.350101	−	1.07750i	−0.958796	−	0.284096i	$-0.908307\pi$
$499$	−7.82066	−	24.0695i	−0.350101	−	1.07750i	0.608695	−	0.793404i	$-0.291693\pi$
$500$	9.84650	−	7.15390i	0.440349	−	0.319932i
$501$	21.5868	−	15.6838i	0.964429	−	0.700699i
$502$	3.14473	+	9.67847i	0.140356	+	0.431971i
$503$	7.12611	−	21.9319i	0.317738	−	0.977896i	−0.656875	−	0.753999i	$-0.728122\pi$
$503$	7.12611	−	21.9319i	0.317738	−	0.977896i	0.974613	−	0.223897i	$-0.0718778\pi$
$504$	−0.781832	−	0.568035i	−0.0348256	−	0.0253023i
$505$	1.85279			0.0824480
$506$	−11.2822	−	5.97655i	−0.501556	−	0.265690i
$507$	31.2157			1.38634
$508$	−4.90241	−	3.56181i	−0.217509	−	0.158030i
$509$	5.13612	−	15.8073i	0.227654	−	0.700648i	−0.770357	−	0.637613i	$-0.779922\pi$
$509$	5.13612	−	15.8073i	0.227654	−	0.700648i	0.998011	−	0.0630353i	$-0.0200781\pi$
$510$	−6.13112	−	18.8697i	−0.271491	−	0.835562i
$511$	0.135146	−	0.0981893i	0.00597851	−	0.00434364i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	0.352586	+	1.08515i	0.0155671	+	0.0479105i
$514$	−3.53917	+	10.8925i	−0.156106	+	0.480445i
$515$	4.61262	+	3.35126i	0.203256	+	0.147674i
$516$	9.23625			0.406603
$517$	4.36688	−	24.9913i	0.192055	−	1.09911i
$518$	−0.448087			−0.0196878
$519$	−14.3227	−	10.4061i	−0.628697	−	0.456775i
$520$	0.471888	−	1.45232i	0.0206937	−	0.0636886i
$521$	9.55692	+	29.4132i	0.418696	+	1.28861i	0.908903	+	0.417008i	$0.136921\pi$
$521$	9.55692	+	29.4132i	0.418696	+	1.28861i	−0.490206	+	0.871606i	$0.663079\pi$
$522$	22.0667	−	16.0324i	0.965834	−	0.701720i
$523$	−6.66879	+	4.84516i	−0.291606	+	0.211864i	−0.723964	−	0.689838i	$-0.757682\pi$
$523$	−6.66879	+	4.84516i	−0.291606	+	0.211864i	0.432358	+	0.901702i	$0.357682\pi$
$524$	2.81437	+	8.66173i	0.122946	+	0.378389i
$525$	−0.375319	+	1.15511i	−0.0163802	+	0.0504132i
$526$	−24.3070	−	17.6601i	−1.05984	−	0.770016i
$527$	−38.5571			−1.67957
$528$	3.70396	+	7.56458i	0.161194	+	0.329206i
$529$	−8.18110			−0.355700
$530$	−13.3358	−	9.68899i	−0.579268	−	0.420863i
$531$	3.95467	−	12.1712i	0.171618	−	0.528186i
$532$	0.0865782	+	0.266460i	0.00375364	+	0.0115525i
$533$	−4.81822	+	3.50064i	−0.208700	+	0.151630i
$534$	−27.4520	+	19.9451i	−1.18797	+	0.863108i
$535$	−7.39345	−	22.7547i	−0.319647	−	0.983772i
$536$	−2.47595	+	7.62019i	−0.106945	+	0.329142i
$537$	16.2881	+	11.8340i	0.702884	+	0.510675i
$538$	−20.7880			−0.896236
$539$	−16.4886	+	15.9721i	−0.710212	+	0.687965i
$540$	−2.07052			−0.0891008
$541$	1.50911	+	1.09643i	0.0648818	+	0.0471394i	0.619753	−	0.784797i	$-0.287233\pi$
$541$	1.50911	+	1.09643i	0.0648818	+	0.0471394i	−0.554872	+	0.831936i	$0.687233\pi$
$542$	5.68339	−	17.4917i	0.244122	−	0.751331i
$543$	5.47610	+	16.8537i	0.235002	+	0.723262i
$544$	−3.48308	+	2.53061i	−0.149336	+	0.108499i
$545$	−18.9772	+	13.7878i	−0.812895	+	0.590603i
$546$	0.185023	+	0.569443i	0.00791826	+	0.0243699i
$547$	−14.0657	+	43.2899i	−0.601407	+	1.85094i	−0.0815846	+	0.996666i	$0.525998\pi$
$547$	−14.0657	+	43.2899i	−0.601407	+	1.85094i	−0.519823	+	0.854274i	$0.674002\pi$
$548$	9.98841	+	7.25700i	0.426684	+	0.310004i
$549$	−0.613259			−0.0261732
$550$	4.06647	−	3.93909i	0.173395	−	0.167963i
$551$	−7.90770			−0.336880
$552$	−7.90900	−	5.74623i	−0.336629	−	0.244576i
$553$	1.22719	−	3.77689i	0.0521853	−	0.160610i
$554$	−4.99471	−	15.3721i	−0.212205	−	0.653099i
$555$	−5.96273	+	4.33218i	−0.253104	+	0.183891i
$556$	8.21350	−	5.96746i	0.348330	−	0.253077i
$557$	−4.28770	−	13.1962i	−0.181676	−	0.559140i	0.818200	−	0.574934i	$-0.194972\pi$
$557$	−4.28770	−	13.1962i	−0.181676	−	0.559140i	−0.999875	+	0.0157941i	$0.994972\pi$
$558$	−9.54574	+	29.3788i	−0.404104	+	1.24370i
$559$	−2.47605	−	1.79895i	−0.104726	−	0.0760877i
$560$	−0.508419			−0.0214846
$561$	−15.9467	−	32.5680i	−0.673272	−	1.37502i
$562$	24.0318			1.01372
$563$	−31.5143	−	22.8965i	−1.32817	−	0.964971i	−0.999791	−	0.0204247i	$-0.993498\pi$
$563$	−31.5143	−	22.8965i	−1.32817	−	0.964971i	−0.328378	−	0.944547i	$-0.606502\pi$
$564$	6.00290	−	18.4750i	0.252768	−	0.777939i
$565$	4.30934	+	13.2628i	0.181295	+	0.557970i
$566$	−9.57545	+	6.95697i	−0.402486	+	0.292423i
$567$	−1.68871	+	1.22692i	−0.0709193	+	0.0515259i
$568$	−1.16496	−	3.58539i	−0.0488808	−	0.150440i
$569$	−2.16460	+	6.66194i	−0.0907446	+	0.279283i	−0.986121	−	0.166026i	$-0.946906\pi$
$569$	−2.16460	+	6.66194i	−0.0907446	+	0.279283i	0.895377	+	0.445309i	$0.146906\pi$
$570$	3.72828	+	2.70876i	0.156161	+	0.113457i
$571$	−23.7020			−0.991898			−0.495949	−	0.868352i	$-0.665180\pi$
$571$	−23.7020			−0.991898			−0.495949	+	0.868352i	$0.665180\pi$
$572$	0.480407	−	2.74933i	0.0200868	−	0.114955i
$573$	−56.1467			−2.34556
$574$	1.60417	+	1.16550i	0.0669569	+	0.0486470i
$575$	−2.03061	+	6.24956i	−0.0846821	+	0.260625i
$576$	1.06589	+	3.28047i	0.0444121	+	0.136686i
$577$	−22.6479	+	16.4547i	−0.942846	+	0.685018i	−0.949104	−	0.314963i	$-0.898008\pi$
$577$	−22.6479	+	16.4547i	−0.942846	+	0.685018i	0.00625796	+	0.999980i	$0.498008\pi$
$578$	1.24253	−	0.902753i	0.0516825	−	0.0375496i
$579$	18.4240	+	56.7031i	0.765673	+	2.35650i
$580$	4.43433	−	13.6475i	0.184126	−	0.566680i
$581$	0.732699	+	0.532337i	0.0303975	+	0.0220851i
$582$	24.5095			1.01595
$583$	−26.6227	−	14.1029i	−1.10260	−	0.584081i
$584$	−0.596238			−0.0246725
$585$	4.26132	+	3.09603i	0.176184	+	0.128005i
$586$	5.63548	−	17.3442i	0.232800	−	0.716484i
$587$	−14.1991	−	43.7003i	−0.586059	−	1.80370i	−0.594974	−	0.803745i	$-0.702838\pi$
$587$	−14.1991	−	43.7003i	−0.586059	−	1.80370i	0.00891517	−	0.999960i	$-0.497162\pi$
$588$	−14.2205	+	10.3318i	−0.586442	+	0.426075i
$589$	7.24528	−	5.26400i	0.298537	−	0.216900i
$590$	−2.08054	−	6.40324i	−0.0856544	−	0.263617i
$591$	12.7461	−	39.2285i	0.524305	−	1.61365i
$592$	1.29388	+	0.940059i	0.0531782	+	0.0386362i
$593$	1.84529			0.0757770			0.0378885	−	0.999282i	$-0.487937\pi$
$593$	1.84529			0.0757770			0.0378885	+	0.999282i	$0.487937\pi$
$594$	−3.74660	+	0.532448i	−0.153725	+	0.0218466i
$595$	2.18891			0.0897366
$596$	−1.69146	−	1.22892i	−0.0692849	−	0.0503384i
$597$	−1.61679	+	4.97595i	−0.0661706	+	0.203652i
$598$	1.00104	+	3.08089i	0.0409356	+	0.125987i
$599$	11.4966	−	8.35279i	0.469739	−	0.341286i	−0.327600	−	0.944816i	$-0.606240\pi$
$599$	11.4966	−	8.35279i	0.469739	−	0.341286i	0.797340	+	0.603531i	$0.206240\pi$
$600$	3.50711	−	2.54806i	0.143177	−	0.104024i
$601$	0.603596	+	1.85768i	0.0246212	+	0.0757762i	0.962612	−	0.270884i	$-0.0873158\pi$
$601$	0.603596	+	1.85768i	0.0246212	+	0.0757762i	−0.937991	+	0.346660i	$0.887316\pi$
$602$	−0.314883	+	0.969109i	−0.0128337	+	0.0394979i
$603$	−22.3587	−	16.2446i	−0.910518	−	0.661530i
$604$	10.7599			0.437814
$605$	−12.2408	+	15.7675i	−0.497658	+	0.641042i
$606$	2.59290			0.105329
$607$	−2.30543	−	1.67499i	−0.0935744	−	0.0679858i	0.540014	−	0.841656i	$-0.318419\pi$
$607$	−2.30543	−	1.67499i	−0.0935744	−	0.0679858i	−0.633589	+	0.773670i	$0.718419\pi$
$608$	0.309017	−	0.951057i	0.0125323	−	0.0385704i
$609$	1.73866	+	5.35105i	0.0704541	+	0.216835i
$610$	−0.261016	+	0.189639i	−0.0105682	+	0.00767826i
$611$	−5.20765	+	3.78358i	−0.210679	+	0.153067i
$612$	−4.58900	−	14.1235i	−0.185499	−	0.570909i
$613$	−12.9680	+	39.9115i	−0.523774	+	1.61201i	0.242952	+	0.970038i	$0.421884\pi$
$613$	−12.9680	+	39.9115i	−0.523774	+	1.61201i	−0.766727	+	0.641974i	$0.778116\pi$
$614$	−0.404828	−	0.294125i	−0.0163375	−	0.0118699i
$615$	32.6151			1.31517
$616$	−0.919985	+	0.130744i	−0.0370672	+	0.00526781i
$617$	−14.5978			−0.587684			−0.293842	−	0.955854i	$-0.594934\pi$
$617$	−14.5978			−0.587684			−0.293842	+	0.955854i	$0.594934\pi$
$618$	6.45518	+	4.68996i	0.259665	+	0.188658i
$619$	−2.72160	+	8.37622i	−0.109390	+	0.336669i	−0.990736	−	0.135804i	$-0.956638\pi$
$619$	−2.72160	+	8.37622i	−0.109390	+	0.336669i	0.881345	+	0.472472i	$0.156638\pi$
$620$	5.02198	+	15.4561i	0.201688	+	0.620731i
$621$	3.55344	−	2.58172i	0.142595	−	0.103601i
$622$	1.70539	−	1.23904i	0.0683800	−	0.0496810i
$623$	−1.15683	−	3.56036i	−0.0463474	−	0.142643i
$624$	0.660389	−	2.03247i	0.0264367	−	0.0813639i
$625$	10.9631	+	7.96513i	0.438522	+	0.318605i
$626$	−8.13625			−0.325190
$627$	7.44291	+	3.94275i	0.297241	+	0.157458i
$628$	−2.94245			−0.117417
$629$	−5.57058	−	4.04726i	−0.222114	−	0.161375i
$630$	0.541918	−	1.66785i	0.0215905	−	0.0664489i
$631$	−3.78359	−	11.6447i	−0.150622	−	0.463567i	0.847069	−	0.531483i	$-0.178365\pi$
$631$	−3.78359	−	11.6447i	−0.150622	−	0.463567i	−0.997691	+	0.0679158i	$0.978365\pi$
$632$	−11.4673	+	8.33146i	−0.456143	+	0.331408i
$633$	−27.5469	+	20.0140i	−1.09489	+	0.795486i
$634$	3.92553	+	12.0815i	0.155903	+	0.479819i
$635$	3.39805	−	10.4581i	0.134848	−	0.415018i
$636$	−18.6629	−	13.5594i	−0.740030	−	0.537664i
$637$	5.82455			0.230777
$638$	4.51438	−	25.8354i	0.178726	−	1.02283i
$639$	13.0035			0.514410
$640$	1.46809	+	1.06663i	0.0580314	+	0.0421623i
$641$	8.55740	−	26.3370i	0.337997	−	1.04025i	−0.627230	−	0.778834i	$-0.715811\pi$
$641$	8.55740	−	26.3370i	0.337997	−	1.04025i	0.965227	−	0.261414i	$-0.0841887\pi$
$642$	−10.3468	−	31.8443i	−0.408357	−	1.25679i
$643$	29.5209	−	21.4482i	1.16419	−	0.845833i	0.173887	−	0.984766i	$-0.444367\pi$
$643$	29.5209	−	21.4482i	1.16419	−	0.845833i	0.990302	+	0.138933i	$0.0443673\pi$
$644$	0.872553	−	0.633947i	0.0343834	−	0.0249810i
$645$	5.17933	+	15.9403i	0.203936	+	0.627650i
$646$	−1.33042	+	4.09461i	−0.0523447	+	0.161100i
$647$	21.3052	+	15.4791i	0.837594	+	0.608548i	0.921697	−	0.387909i	$-0.126803\pi$
$647$	21.3052	+	15.4791i	0.837594	+	0.608548i	−0.0841036	+	0.996457i	$0.526803\pi$
$648$	7.45027			0.292674
$649$	−5.41138	−	11.0516i	−0.212415	−	0.433815i
$650$	−1.43647			−0.0563430
$651$	−5.15510	−	3.74540i	−0.202044	−	0.146794i
$652$	3.07271	−	9.45684i	0.120337	−	0.370359i
$653$	−13.3642	−	41.1308i	−0.522982	−	1.60957i	−0.768272	−	0.640124i	$-0.778883\pi$
$653$	−13.3642	−	41.1308i	−0.522982	−	1.60957i	0.245290	−	0.969450i	$-0.421117\pi$
$654$	−26.5579	+	19.2954i	−1.03850	+	0.754511i
$655$	−13.3706	+	9.71432i	−0.522433	+	0.379570i
$656$	−2.18700	−	6.73091i	−0.0853882	−	0.262798i
$657$	0.635523	−	1.95594i	0.0247941	−	0.0763085i
$658$	1.73383	+	1.25970i	0.0675917	+	0.0491083i
$659$	−41.9096			−1.63256			−0.816282	−	0.577653i	$-0.803969\pi$
$659$	−41.9096			−1.63256			−0.816282	+	0.577653i	$0.803969\pi$
$660$	−10.9783	+	10.6344i	−0.427328	+	0.413942i
$661$	−36.3143			−1.41246			−0.706232	−	0.707981i	$-0.749606\pi$
$661$	−36.3143			−1.41246			−0.706232	+	0.707981i	$0.749606\pi$
$662$	29.0178	+	21.0827i	1.12781	+	0.819401i
$663$	−2.84319	+	8.75045i	−0.110420	+	0.339839i
$664$	−0.998905	−	3.07431i	−0.0387650	−	0.119307i
$665$	−0.411319	+	0.298841i	−0.0159503	+	0.0115886i
$666$	−4.46297	+	3.24254i	−0.172937	+	0.125646i
$667$	9.40678	+	28.9511i	0.364232	+	1.12099i
$668$	3.24682	−	9.99268i	0.125623	−	0.386628i
$669$	20.9844	+	15.2461i	0.811305	+	0.589448i
$670$	−14.5397			−0.561717
$671$	−0.423542	+	0.410274i	−0.0163506	+	0.0158385i
$672$	−0.711512			−0.0274472
$673$	30.6875	+	22.2958i	1.18292	+	0.859440i	0.992498	−	0.122262i	$-0.0390149\pi$
$673$	30.6875	+	22.2958i	1.18292	+	0.859440i	0.190420	+	0.981703i	$0.439015\pi$
$674$	3.01398	−	9.27608i	0.116094	−	0.357301i
$675$	0.601868	+	1.85236i	0.0231659	+	0.0712973i
$676$	9.94432	−	7.22497i	0.382474	−	0.277883i
$677$	−16.8963	+	12.2759i	−0.649376	+	0.471799i	−0.863059	−	0.505104i	$-0.831454\pi$
$677$	−16.8963	+	12.2759i	−0.649376	+	0.471799i	0.213682	+	0.976903i	$0.431454\pi$
$678$	6.03075	+	18.5608i	0.231610	+	0.712821i
$679$	−0.835579	+	2.57165i	−0.0320666	+	0.0986907i
$680$	−6.32062	−	4.59220i	−0.242385	−	0.176103i
$681$	11.0829			0.424699
$682$	13.0619	+	26.6764i	0.500167	+	1.02149i
$683$	−30.8027			−1.17863			−0.589315	−	0.807903i	$-0.700602\pi$
$683$	−30.8027			−1.17863			−0.589315	+	0.807903i	$0.700602\pi$
$684$	2.79053	+	2.02744i	0.106699	+	0.0775212i
$685$	−6.92335	+	21.3079i	−0.264528	+	0.814132i
$686$	−1.20530	−	3.70953i	−0.0460185	−	0.141630i
$687$	−38.8606	+	28.2339i	−1.48262	+	1.07719i
$688$	2.94237	−	2.13776i	0.112177	−	0.0815013i
$689$	2.36216	+	7.26997i	0.0899910	+	0.276964i
$690$	5.48203	−	16.8720i	0.208697	−	0.642305i
$691$	11.6856	+	8.49011i	0.444542	+	0.322979i	0.787437	−	0.616395i	$-0.211407\pi$
$691$	11.6856	+	8.49011i	0.444542	+	0.322979i	−0.342895	+	0.939374i	$0.611407\pi$
$692$	−6.97126			−0.265008
$693$	0.551702	−	3.15734i	0.0209574	−	0.119937i
$694$	27.3912			1.03976
$695$	14.9047	+	10.8289i	0.565368	+	0.410764i
$696$	6.20567	−	19.0991i	0.235225	−	0.723949i
$697$	9.41577	+	28.9788i	0.356648	+	1.09765i
$698$	−12.8690	+	9.34984i	−0.487097	+	0.353897i
$699$	−28.9191	+	21.0110i	−1.09382	+	0.794708i
$700$	0.147790	+	0.454850i	0.00558592	+	0.0171917i
$701$	−6.61749	+	20.3665i	−0.249939	+	0.769233i	0.744846	+	0.667237i	$0.232523\pi$
$701$	−6.61749	+	20.3665i	−0.249939	+	0.769233i	−0.994785	+	0.101996i	$0.967477\pi$
$702$	0.776788	+	0.564370i	0.0293180	+	0.0213008i
$703$	1.59932			0.0603197
$704$	2.93081	+	1.55254i	0.110459	+	0.0585135i
$705$	35.2512			1.32764
$706$	−3.20554	−	2.32896i	−0.120642	−	0.0876517i
$707$	−0.0883973	+	0.272059i	−0.00332452	+	0.0102318i
$708$	−2.91163	−	8.96108i	−0.109426	−	0.336778i
$709$	−22.1160	+	16.0682i	−0.830583	+	0.603454i	−0.919724	−	0.392565i	$-0.871588\pi$
$709$	−22.1160	+	16.0682i	−0.830583	+	0.603454i	0.0891410	+	0.996019i	$0.471588\pi$
$710$	5.53456	−	4.02109i	0.207708	−	0.150909i
$711$	−15.1083	−	46.4984i	−0.566604	−	1.74383i
$712$	−4.12899	+	12.7077i	−0.154740	+	0.476242i
$713$	−27.8909	−	20.2640i	−1.04452	−	0.758891i
$714$	3.06329			0.114641
$715$	5.01431	−	0.712609i	0.187525	−	0.0266501i
$716$	7.92788			0.296279
$717$	10.3760	+	7.53862i	0.387500	+	0.281535i
$718$	−7.58383	+	23.3406i	−0.283026	+	0.871064i
$719$	−7.72521	−	23.7758i	−0.288102	−	0.886686i	−0.985452	−	0.169956i	$-0.945638\pi$
$719$	−7.72521	−	23.7758i	−0.288102	−	0.886686i	0.697350	−	0.716731i	$-0.254362\pi$
$720$	−5.06387	+	3.67912i	−0.188719	+	0.137113i
$721$	−0.712161	+	0.517415i	−0.0265223	+	0.0192696i
$722$	−0.309017	−	0.951057i	−0.0115004	−	0.0353947i
$723$	23.4998	−	72.3250i	0.873968	−	2.68980i
$724$	5.64535	+	4.10159i	0.209808	+	0.152434i
$725$	−13.4985			−0.501322
$726$	−17.1305	+	22.0661i	−0.635772	+	0.818948i
$727$	49.8823			1.85003			0.925016	−	0.379928i	$-0.124051\pi$
$727$	49.8823			1.85003			0.925016	+	0.379928i	$0.124051\pi$
$728$	0.190742	+	0.138582i	0.00706936	+	0.00513619i
$729$	−10.6274	+	32.7077i	−0.393607	+	1.21140i
$730$	−0.334347	−	1.02901i	−0.0123747	−	0.0380855i
$731$	−12.6679	+	9.20375i	−0.468538	+	0.340413i
$732$	−0.365281	+	0.265392i	−0.0135012	+	0.00980919i
$733$	1.49057	+	4.58752i	0.0550556	+	0.169444i	0.974803	−	0.223067i	$-0.0716067\pi$
$733$	1.49057	+	4.58752i	0.0550556	+	0.169444i	−0.919748	+	0.392510i	$0.871607\pi$
$734$	−6.97367	+	21.4627i	−0.257403	+	0.792204i
$735$	−25.8053	−	18.7487i	−0.951844	−	0.691555i
$736$	−3.84953			−0.141896
$737$	−26.3096	+	3.73899i	−0.969126	+	0.137727i
$738$	24.4116			0.898605
$739$	13.7697	+	10.0043i	0.506526	+	0.368013i	0.811504	−	0.584347i	$-0.198649\pi$
$739$	13.7697	+	10.0043i	0.506526	+	0.368013i	−0.304978	+	0.952359i	$0.598649\pi$
$740$	−0.896838	+	2.76019i	−0.0329684	+	0.101466i
$741$	−0.660389	−	2.03247i	−0.0242600	−	0.0746646i
$742$	2.05896	−	1.49592i	0.0755869	−	0.0549171i
$743$	−27.4267	+	19.9266i	−1.00619	+	0.731037i	−0.963406	−	0.268047i	$-0.913622\pi$
$743$	−27.4267	+	19.9266i	−1.00619	+	0.731037i	−0.0427808	+	0.999084i	$0.513622\pi$
$744$	7.02807	+	21.6302i	0.257661	+	0.793000i
$745$	1.17242	−	3.60833i	0.0429540	−	0.132199i
$746$	19.3986	+	14.0939i	0.710233	+	0.516014i
$747$	11.1499			0.407954
$748$	−12.6181	−	6.68419i	−0.461363	−	0.244398i
$749$	3.69399			0.134975
$750$	25.0056	+	18.1677i	0.913076	+	0.663389i
$751$	3.28906	−	10.1227i	0.120019	−	0.369382i	−0.872941	−	0.487825i	$-0.837790\pi$
$751$	3.28906	−	10.1227i	0.120019	−	0.369382i	0.992961	+	0.118443i	$0.0377904\pi$
$752$	−2.36377	−	7.27493i	−0.0861978	−	0.265289i
$753$	−20.9081	+	15.1906i	−0.761933	+	0.553577i
$754$	−5.38356	+	3.91139i	−0.196058	+	0.142444i
$755$	6.03373	+	18.5699i	0.219590	+	0.675828i
$756$	0.0987852	−	0.304030i	0.00359278	−	0.0110574i
$757$	−13.3974	−	9.73378i	−0.486937	−	0.353780i	0.317068	−	0.948403i	$-0.397302\pi$
$757$	−13.3974	−	9.73378i	−0.486937	−	0.353780i	−0.804005	+	0.594622i	$0.797302\pi$
$758$	32.2734			1.17222
$759$	5.58100	−	31.9396i	0.202578	−	1.15933i
$760$	1.81466			0.0658247
$761$	15.3986	+	11.1878i	0.558201	+	0.405556i	0.830800	−	0.556571i	$-0.187883\pi$
$761$	15.3986	+	11.1878i	0.558201	+	0.405556i	−0.272599	+	0.962128i	$0.587883\pi$
$762$	4.75544	−	14.6357i	0.172271	−	0.530197i
$763$	−1.11915	−	3.44439i	−0.0405160	−	0.124695i
$764$	−17.8865	+	12.9953i	−0.647112	+	0.470154i
$765$	21.8016	−	15.8398i	0.788240	−	0.572690i
$766$	4.98556	+	15.3440i	0.180136	+	0.554400i
$767$	−0.964810	+	2.96938i	−0.0348373	+	0.107218i
$768$	2.05454	+	1.49271i	0.0741367	+	0.0538634i
$769$	18.7798			0.677215			0.338608	−	0.940928i	$-0.390044\pi$
$769$	18.7798			0.677215			0.338608	+	0.940928i	$0.390044\pi$
$770$	−0.741535	−	1.51443i	−0.0267231	−	0.0545764i
$771$	−29.0854			−1.04749
$772$	18.9934	+	13.7995i	0.683587	+	0.496655i
$773$	15.1511	−	46.6304i	0.544948	−	1.67718i	−0.176164	−	0.984361i	$-0.556369\pi$
$773$	15.1511	−	46.6304i	0.544948	−	1.67718i	0.721112	−	0.692818i	$-0.243631\pi$
$774$	3.87661	+	11.9310i	0.139342	+	0.428850i
$775$	12.3677	−	8.98569i	0.444263	−	0.322776i
$776$	7.80794	−	5.67280i	0.280289	−	0.203642i
$777$	−0.351642	−	1.08224i	−0.0126151	−	0.0388253i
$778$	−6.12751	+	18.8585i	−0.219682	+	0.676111i
$779$	−5.72565	−	4.15993i	−0.205143	−	0.149045i
$780$	3.87805			0.138856
$781$	8.98074	−	8.69942i	0.321356	−	0.311290i
$782$	16.5735			0.592667
$783$	7.29947	+	5.30338i	0.260862	+	0.189527i
$784$	−2.13886	+	6.58274i	−0.0763879	+	0.235098i
$785$	−1.65001	−	5.07822i	−0.0588915	−	0.181249i
$786$	−18.7116	+	13.5948i	−0.667422	+	0.484910i
$787$	2.40706	−	1.74883i	0.0858023	−	0.0623390i	−0.544057	−	0.839048i	$-0.683113\pi$
$787$	2.40706	−	1.74883i	0.0858023	−	0.0623390i	0.629859	+	0.776709i	$0.283113\pi$
$788$	−5.01906	−	15.4471i	−0.178796	−	0.550279i
$789$	23.5783	−	72.5666i	0.839410	−	2.58344i
$790$	−20.8092	−	15.1188i	−0.740358	−	0.537902i
$791$	−2.15308			−0.0765546
$792$	−8.21697	+	7.95958i	−0.291977	+	0.282832i
$793$	0.149615			0.00531299
$794$	−30.2785	−	21.9986i	−1.07454	−	0.780701i
$795$	12.9359	−	39.8127i	0.458791	−	1.41201i
$796$	0.636644	+	1.95939i	0.0225652	+	0.0694487i
$797$	24.9390	−	18.1192i	0.883384	−	0.641816i	−0.0507609	−	0.998711i	$-0.516165\pi$
$797$	24.9390	−	18.1192i	0.883384	−	0.641816i	0.934144	+	0.356895i	$0.116165\pi$
$798$	−0.575625	+	0.418216i	−0.0203769	+	0.0148047i
$799$	10.1768	+	31.3210i	0.360029	+	1.10806i
$800$	0.527494	−	1.62346i	0.0186497	−	0.0573980i
$801$	−37.2862	−	27.0900i	−1.31744	−	0.957179i
$802$	28.4931			1.00613
$803$	−0.869619	−	1.77602i	−0.0306882	−	0.0626745i
$804$	−20.3477			−0.717609
$805$	1.58339	+	1.15040i	0.0558071	+	0.0405462i
$806$	2.32885	−	7.16746i	0.0820303	−	0.252463i
$807$	−16.3137	−	50.2083i	−0.574268	−	1.76742i
$808$	0.826015	−	0.600135i	0.0290591	−	0.0211127i
$809$	−34.2801	+	24.9059i	−1.20522	+	0.875646i	−0.994788	−	0.101962i	$-0.967488\pi$
$809$	−34.2801	+	24.9059i	−1.20522	+	0.875646i	−0.210435	+	0.977608i	$0.567488\pi$
$810$	4.17782	+	12.8580i	0.146794	+	0.451784i
$811$	7.58107	−	23.3321i	0.266207	−	0.819302i	−0.725205	−	0.688533i	$-0.758255\pi$
$811$	7.58107	−	23.3321i	0.266207	−	0.819302i	0.991413	−	0.130769i	$-0.0417448\pi$
$812$	1.79240	+	1.30225i	0.0629008	+	0.0457001i
$813$	46.7069			1.63808
$814$	−0.913029	+	5.22519i	−0.0320017	+	0.183143i
$815$	18.0441			0.632057
$816$	−8.84545	−	6.42660i	−0.309653	−	0.224976i
$817$	1.12389	−	3.45897i	0.0393198	−	0.121014i
$818$	7.89745	+	24.3059i	0.276128	+	0.849834i
$819$	−0.657923	+	0.478009i	−0.0229897	+	0.0167030i
$820$	10.3901	−	7.54886i	0.362839	−	0.263618i
$821$	−12.7842	−	39.3458i	−0.446172	−	1.37318i	−0.881193	−	0.472756i	$-0.843259\pi$
$821$	−12.7842	−	39.3458i	−0.446172	−	1.37318i	0.435021	−	0.900420i	$-0.356741\pi$
$822$	−9.68896	+	29.8195i	−0.337941	+	1.04008i
$823$	24.0725	+	17.4897i	0.839115	+	0.609653i	0.922123	−	0.386896i	$-0.126453\pi$
$823$	24.0725	+	17.4897i	0.839115	+	0.609653i	−0.0830083	+	0.996549i	$0.526453\pi$
$824$	3.14192			0.109454
$825$	12.7051	+	6.73029i	0.442335	+	0.234319i
$826$	1.03950			0.0361688
$827$	35.1170	+	25.5140i	1.22114	+	0.887208i	0.996194	−	0.0871635i	$-0.0277802\pi$
$827$	35.1170	+	25.5140i	1.22114	+	0.887208i	0.224944	+	0.974372i	$0.427780\pi$
$828$	4.10318	−	12.6283i	0.142595	−	0.438863i
$829$	−14.8724	−	45.7725i	−0.516539	−	1.58975i	−0.780463	−	0.625202i	$-0.785017\pi$
$829$	−14.8724	−	45.7725i	−0.516539	−	1.58975i	0.263924	−	0.964544i	$-0.414983\pi$
$830$	4.74564	−	3.44791i	0.164724	−	0.119679i
$831$	33.2079	−	24.1269i	1.15197	−	0.836954i
$832$	−0.260042	−	0.800328i	−0.00901534	−	0.0277464i
$833$	9.20850	−	28.3409i	0.319056	−	0.981953i
$834$	20.8586	+	15.1546i	0.722273	+	0.524762i
$835$	19.0665			0.659823
$836$	3.28363	−	0.466653i	0.113567	−	0.0161395i
$837$	−10.2184			−0.353198
$838$	−18.9854	−	13.7937i	−0.655839	−	0.476495i
$839$	−1.09763	+	3.37814i	−0.0378942	+	0.116626i	−0.968214	−	0.250122i	$-0.919529\pi$
$839$	−1.09763	+	3.37814i	−0.0378942	+	0.116626i	0.930320	+	0.366749i	$0.119529\pi$
$840$	−0.398988	−	1.22796i	−0.0137664	−	0.0423686i
$841$	−27.1278	+	19.7095i	−0.935441	+	0.679638i
$842$	−23.6640	+	17.1929i	−0.815514	+	0.592505i
$843$	18.8593	+	58.0429i	0.649548	+	1.99910i
$844$	−4.14326	+	12.7516i	−0.142617	+	0.438929i
$845$	18.0456	+	13.1109i	0.620786	+	0.451028i
$846$	26.3847			0.907125
$847$	−1.73126	−	2.54968i	−0.0594867	−	0.0876081i
$848$	−9.08374			−0.311937
$849$	−24.3173	−	17.6675i	−0.834567	−	0.606349i
$850$	−2.27104	+	6.98953i	−0.0778959	+	0.239739i
$851$	−1.90251	−	5.85532i	−0.0652172	−	0.200718i
$852$	7.74539	−	5.62736i	0.265353	−	0.192790i
$853$	−1.36636	+	0.992716i	−0.0467831	+	0.0339899i	−0.610931	−	0.791684i	$-0.709205\pi$
$853$	−1.36636	+	0.992716i	−0.0467831	+	0.0339899i	0.564148	+	0.825674i	$0.309205\pi$
$854$	−0.0153930	−	0.0473747i	−0.000526737	−	0.00162113i
$855$	−1.93423	+	5.95294i	−0.0661492	+	0.203586i
$856$	−10.6666	−	7.74976i	−0.364578	−	0.264881i
$857$	−2.99660			−0.102362			−0.0511810	−	0.998689i	$-0.516299\pi$
$857$	−2.99660			−0.102362			−0.0511810	+	0.998689i	$0.516299\pi$
$858$	7.01733	−	0.997268i	0.239568	−	0.0340462i
$859$	−7.28751			−0.248647			−0.124323	−	0.992242i	$-0.539676\pi$
$859$	−7.28751			−0.248647			−0.124323	+	0.992242i	$0.539676\pi$
$860$	5.33941	+	3.87931i	0.182072	+	0.132283i
$861$	−1.55608	+	4.78912i	−0.0530311	+	0.163213i
$862$	−6.59230	−	20.2890i	−0.224535	−	0.691047i
$863$	−5.82883	+	4.23489i	−0.198416	+	0.144157i	−0.682557	−	0.730832i	$-0.739132\pi$
$863$	−5.82883	+	4.23489i	−0.198416	+	0.144157i	0.484141	+	0.874990i	$0.339132\pi$
$864$	−0.923083	+	0.670659i	−0.0314039	+	0.0228163i
$865$	−3.90921	−	12.0313i	−0.132917	−	0.409077i
$866$	9.49290	−	29.2161i	0.322582	−	0.992805i
$867$	3.15547	+	2.29258i	0.107165	+	0.0778602i
$868$	−2.50913			−0.0851656
$869$	−41.5422	−	22.0062i	−1.40922	−	0.746509i
$870$	36.4420			1.23550
$871$	5.45480	+	3.96315i	0.184829	+	0.134286i
$872$	−3.99450	+	12.2938i	−0.135271	+	0.416320i
$873$	10.2870	+	31.6603i	0.348164	+	1.07154i
$874$	−3.11434	+	2.26270i	−0.105344	+	0.0765369i
$875$	−2.75872	+	2.00433i	−0.0932619	+	0.0677587i
$876$	−0.467905	−	1.44006i	−0.0158090	−	0.0486552i
$877$	1.20419	−	3.70611i	0.0406625	−	0.125146i	−0.928665	−	0.370921i	$-0.879042\pi$
$877$	1.20419	−	3.70611i	0.0406625	−	0.125146i	0.969327	+	0.245774i	$0.0790422\pi$
$878$	9.08655	+	6.60176i	0.306656	+	0.222799i
$879$	46.3132			1.56211
$880$	−1.03596	+	5.92872i	−0.0349222	+	0.199857i
$881$	10.1047			0.340436			0.170218	−	0.985406i	$-0.445553\pi$
$881$	10.1047			0.340436			0.170218	+	0.985406i	$0.445553\pi$
$882$	−19.3147	−	14.0329i	−0.650360	−	0.472514i
$883$	15.7427	−	48.4510i	0.529783	−	1.63051i	−0.224875	−	0.974388i	$-0.572197\pi$
$883$	15.7427	−	48.4510i	0.529783	−	1.63051i	0.754658	−	0.656118i	$-0.227803\pi$
$884$	1.11957	+	3.44567i	0.0376551	+	0.115891i
$885$	13.8327	−	10.0500i	0.464981	−	0.337829i
$886$	22.3651	−	16.2492i	0.751371	−	0.545903i
$887$	1.61180	+	4.96060i	0.0541188	+	0.166561i	0.974463	−	0.224550i	$-0.0720911\pi$
$887$	1.61180	+	4.96060i	0.0541188	+	0.166561i	−0.920344	+	0.391110i	$0.872091\pi$
$888$	−1.25509	+	3.86277i	−0.0421181	+	0.129626i
$889$	1.37352	+	0.997924i	0.0460665	+	0.0334693i
$890$	−24.2469			−0.812758
$891$	10.8663	+	22.1922i	0.364035	+	0.743467i
$892$	10.2137			0.341981
$893$	−6.18843	−	4.49616i	−0.207088	−	0.150458i
$894$	1.64075	−	5.04971i	0.0548749	−	0.168888i
$895$	4.44564	+	13.6823i	0.148601	+	0.457348i
$896$	−0.226665	+	0.164682i	−0.00757234	+	0.00550162i
$897$	−6.65554	+	4.83553i	−0.222222	+	0.161454i
$898$	10.8873	+	33.5077i	0.363314	+	1.11817i
$899$	21.8842	−	67.3526i	0.729878	−	2.24633i
$900$	4.76346	+	3.46086i	0.158782	+	0.115362i
$901$	39.1085			1.30289
$902$	16.8597	−	16.3316i	0.561366	−	0.543782i
$903$	−2.58775			−0.0861149
$904$	6.21714	+	4.51702i	0.206779	+	0.150234i
$905$	−3.91301	+	12.0430i	−0.130073	+	0.400323i
$906$	8.44397	+	25.9879i	0.280532	+	0.863389i
$907$	28.9160	−	21.0087i	0.960139	−	0.697582i	0.00695580	−	0.999976i	$-0.497786\pi$
$907$	28.9160	−	21.0087i	0.960139	−	0.697582i	0.953183	+	0.302394i	$0.0977859\pi$
$908$	3.53067	−	2.56518i	0.117169	−	0.0851285i
$909$	1.08828	+	3.34940i	0.0360961	+	0.111092i
$910$	−0.132210	+	0.406902i	−0.00438273	+	0.0134887i
$911$	−17.0645	−	12.3981i	−0.565372	−	0.410767i	0.268049	−	0.963405i	$-0.413621\pi$
$911$	−17.0645	−	12.3981i	−0.565372	−	0.410767i	−0.833421	+	0.552638i	$0.813621\pi$
$912$	2.53955			0.0840927
$913$	7.70059	−	7.45938i	0.254852	−	0.246869i
$914$	−5.53923			−0.183222
$915$	−0.662862	−	0.481597i	−0.0219135	−	0.0159211i
$916$	−5.84491	+	17.9888i	−0.193121	+	0.594366i
$917$	−0.788509	−	2.42678i	−0.0260389	−	0.0801394i
$918$	3.97418	−	2.88741i	0.131167	−	0.0952987i
$919$	16.8305	−	12.2281i	0.555186	−	0.403366i	−0.274508	−	0.961585i	$-0.588515\pi$
$919$	16.8305	−	12.2281i	0.555186	−	0.403366i	0.829694	+	0.558219i	$0.188515\pi$
$920$	−2.15867	−	6.64370i	−0.0711692	−	0.219036i
$921$	0.392692	−	1.20858i	0.0129396	−	0.0398241i
$922$	28.5816	+	20.7658i	0.941285	+	0.683884i
$923$	−3.17243			−0.104422
$924$	−1.03775	−	2.11939i	−0.0341394	−	0.0697229i
$925$	2.73006			0.0897638
$926$	−28.3084	−	20.5672i	−0.930270	−	0.675881i
$927$	−3.34893	+	10.3070i	−0.109993	+	0.338525i
$928$	−2.44362	−	7.52067i	−0.0802156	−	0.246878i
$929$	−4.78127	+	3.47380i	−0.156868	+	0.113972i	−0.663451	−	0.748220i	$-0.730909\pi$
$929$	−4.78127	+	3.47380i	−0.156868	+	0.113972i	0.506582	+	0.862192i	$0.330909\pi$
$930$	−33.3892	+	24.2587i	−1.09488	+	0.795474i
$931$	2.13886	+	6.58274i	0.0700984	+	0.215741i
$932$	−4.34965	+	13.3868i	−0.142477	+	0.438501i
$933$	4.33092	+	3.14660i	0.141788	+	0.103015i
$934$	11.6343			0.380687
$935$	4.46015	−	25.5251i	0.145863	−	0.834759i
$936$	2.90263			0.0948754
$937$	6.79595	+	4.93755i	0.222014	+	0.161303i	0.693233	−	0.720714i	$-0.256186\pi$
$937$	6.79595	+	4.93755i	0.222014	+	0.161303i	−0.471219	+	0.882016i	$0.656186\pi$
$938$	0.693695	−	2.13497i	0.0226499	−	0.0697093i
$939$	−6.38502	−	19.6511i	−0.208367	−	0.641289i
$940$	11.2299	−	8.15900i	0.366279	−	0.266117i
$941$	−45.4903	+	33.0507i	−1.48294	+	1.07742i	−0.506349	+	0.862329i	$0.669005\pi$
$941$	−45.4903	+	33.0507i	−1.48294	+	1.07742i	−0.976594	+	0.215092i	$0.930995\pi$
$942$	−2.30913	−	7.10676i	−0.0752354	−	0.231551i
$943$	−8.41895	+	25.9109i	−0.274159	+	0.843773i
$944$	−3.00162	−	2.18080i	−0.0976944	−	0.0709791i
$945$	0.580103			0.0188707
$946$	10.6593	+	5.64654i	0.346562	+	0.183585i
$947$	1.33918			0.0435176			0.0217588	−	0.999763i	$-0.493073\pi$
$947$	1.33918			0.0435176			0.0217588	+	0.999763i	$0.493073\pi$
$948$	−29.1216	−	21.1581i	−0.945827	−	0.687184i
$949$	−0.155047	+	0.477186i	−0.00503304	+	0.0154901i
$950$	−0.527494	−	1.62346i	−0.0171142	−	0.0526720i
$951$	−26.0993	+	18.9623i	−0.846328	+	0.614894i
$952$	0.975866	−	0.709008i	0.0316280	−	0.0229791i
$953$	13.4518	+	41.4005i	0.435747	+	1.34109i	0.892319	+	0.451406i	$0.149077\pi$
$953$	13.4518	+	41.4005i	0.435747	+	1.34109i	−0.456572	+	0.889687i	$0.650923\pi$
$954$	9.68226	−	29.7989i	0.313475	−	0.964776i
$955$	−32.4580	−	23.5821i	−1.05031	−	0.763099i
$956$	5.05030			0.163338
$957$	65.9418	−	9.37132i	2.13160	−	0.302932i
$958$	−39.7244			−1.28344
$959$	−2.79848	−	2.03322i	−0.0903677	−	0.0656560i
$960$	−1.42408	+	4.38286i	−0.0459619	+	0.141456i
$961$	15.2048	+	46.7956i	0.490478	+	1.50954i
$962$	1.08882	−	0.791073i	0.0351049	−	0.0255052i
$963$	36.7923	−	26.7312i	1.18562	−	0.861400i
$964$	−9.25356	−	28.4795i	−0.298037	−	0.917264i
$965$	−13.1650	+	40.5178i	−0.423798	+	1.30432i
$966$	2.21589	+	1.60994i	0.0712950	+	0.0517989i
$967$	−4.52923			−0.145650			−0.0728251	−	0.997345i	$-0.523201\pi$
$967$	−4.52923			−0.145650			−0.0728251	+	0.997345i	$0.523201\pi$
$968$	−0.349961	+	10.9944i	−0.0112482	+	0.353374i
$969$	−10.9336			−0.351237
$970$	14.1688	+	10.2942i	0.454931	+	0.330527i
$971$	−5.85249	+	18.0121i	−0.187815	+	0.578036i	−0.999986	−	0.00538437i	$-0.998286\pi$
$971$	−5.85249	+	18.0121i	−0.187815	+	0.578036i	0.812170	+	0.583421i	$0.198286\pi$
$972$	6.90445	+	21.2497i	0.221460	+	0.681585i
$973$	−2.30120	+	1.67192i	−0.0737731	+	0.0535993i
$974$	−9.20915	+	6.69084i	−0.295080	+	0.214388i
$975$	−1.12729	−	3.46944i	−0.0361021	−	0.111111i
$976$	−0.0549410	+	0.169091i	−0.00175862	+	0.00541247i
$977$	1.89412	+	1.37616i	0.0605982	+	0.0440272i	0.617672	−	0.786436i	$-0.288076\pi$
$977$	1.89412	+	1.37616i	0.0605982	+	0.0440272i	−0.557074	+	0.830463i	$0.688076\pi$
$978$	25.2520			0.807470
$979$	−43.8748	+	6.23527i	−1.40225	+	0.199280i
$980$	−12.5602			−0.401220
$981$	−36.0717	−	26.2077i	−1.15168	−	0.836746i
$982$	1.63805	−	5.04141i	0.0522724	−	0.160878i
$983$	18.1479	+	55.8535i	0.578828	+	1.78145i	0.622757	+	0.782415i	$0.286012\pi$
$983$	18.1479	+	55.8535i	0.578828	+	1.78145i	−0.0439292	+	0.999035i	$0.513988\pi$
$984$	14.5406	−	10.5643i	0.463536	−	0.336779i
$985$	23.8447	−	17.3242i	0.759757	−	0.551996i
$986$	10.5206	+	32.3790i	0.335043	+	1.03116i
$987$	−1.68185	+	5.17620i	−0.0535339	+	0.164760i
$988$	−0.680800	−	0.494630i	−0.0216591	−	0.0157363i
$989$	−14.0006			−0.445194
$990$	−18.3448	−	9.71780i	−0.583035	−	0.308852i
$991$	0.797115			0.0253212			0.0126606	−	0.999920i	$-0.495970\pi$
$991$	0.797115			0.0253212			0.0126606	+	0.999920i	$0.495970\pi$
$992$	7.24528	+	5.26400i	0.230038	+	0.167132i
$993$	−28.1479	+	86.6302i	−0.893245	+	2.74913i
$994$	0.326391	+	1.00453i	0.0103525	+	0.0318617i
$995$	−3.02459	+	2.19750i	−0.0958861	+	0.0696653i
$996$	6.64134	−	4.82521i	0.210439	−	0.152893i
$997$	8.37656	+	25.7804i	0.265288	+	0.816473i	0.991627	+	0.129136i	$0.0412204\pi$
$997$	8.37656	+	25.7804i	0.265288	+	0.816473i	−0.726339	+	0.687337i	$0.758780\pi$
$998$	7.82066	−	24.0695i	0.247559	−	0.761908i
$999$	−1.47631	−	1.07260i	−0.0467084	−	0.0339356i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.f.h.191.1	✓	20
11.3	even	5	inner	418.2.f.h.267.1	yes	20
11.5	even	5		4598.2.a.cc.1.2		10
11.6	odd	10		4598.2.a.cd.1.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.h.191.1	✓	20	1.1	even	1	trivial
418.2.f.h.267.1	yes	20	11.3	even	5	inner
4598.2.a.cc.1.2		10	11.5	even	5
4598.2.a.cd.1.2		10	11.6	odd	10

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.784763 + 2.41525i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.46809 + 1.06663i) q^{5} +(-2.05454 + 1.49271i) q^{6} +(-0.0865782 - 0.266460i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.79053 - 2.02744i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.784763 + 2.41525i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.46809 + 1.06663i) q^{5} +(-2.05454 + 1.49271i) q^{6} +(-0.0865782 - 0.266460i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.79053 - 2.02744i) q^{9} -1.81466 q^{10} +(-3.28363 + 0.466653i) q^{11} -2.53955 q^{12} +(0.680800 + 0.494630i) q^{13} +(0.0865782 - 0.266460i) q^{14} +(-1.42408 - 4.38286i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(3.48308 - 2.53061i) q^{17} +(-1.06589 - 3.28047i) q^{18} +(-0.309017 + 0.951057i) q^{19} +(-1.46809 - 1.06663i) q^{20} +0.711512 q^{21} +(-2.93081 - 1.55254i) q^{22} +3.84953 q^{23} +(-2.05454 - 1.49271i) q^{24} +(-0.527494 + 1.62346i) q^{25} +(0.260042 + 0.800328i) q^{26} +(0.923083 - 0.670659i) q^{27} +(0.226665 - 0.164682i) q^{28} +(2.44362 + 7.52067i) q^{29} +(1.42408 - 4.38286i) q^{30} +(-7.24528 - 5.26400i) q^{31} -1.00000 q^{32} +(1.44979 - 8.29701i) q^{33} +4.30533 q^{34} +(0.411319 + 0.298841i) q^{35} +(1.06589 - 3.28047i) q^{36} +(-0.494218 - 1.52105i) q^{37} +(-0.809017 + 0.587785i) q^{38} +(-1.72892 + 1.25613i) q^{39} +(-0.560761 - 1.72584i) q^{40} +(-2.18700 + 6.73091i) q^{41} +(0.575625 + 0.418216i) q^{42} -3.63697 q^{43} +(-1.45851 - 2.97872i) q^{44} +6.25929 q^{45} +(3.11434 + 2.26270i) q^{46} +(-2.36377 + 7.27493i) q^{47} +(-0.784763 - 2.41525i) q^{48} +(5.59961 - 4.06836i) q^{49} +(-1.38100 + 1.00335i) q^{50} +(3.37866 + 10.3984i) q^{51} +(-0.260042 + 0.800328i) q^{52} +(7.34890 + 5.33929i) q^{53} +1.14099 q^{54} +(4.32292 - 4.18751i) q^{55} +0.280173 q^{56} +(-2.05454 - 1.49271i) q^{57} +(-2.44362 + 7.52067i) q^{58} +(1.14652 + 3.52862i) q^{59} +(3.72828 - 2.70876i) q^{60} +(0.143837 - 0.104504i) q^{61} +(-2.76745 - 8.51734i) q^{62} +(-0.298633 + 0.919099i) q^{63} +(-0.809017 - 0.587785i) q^{64} -1.52706 q^{65} +(6.04976 - 5.86026i) q^{66} +8.01235 q^{67} +(3.48308 + 2.53061i) q^{68} +(-3.02097 + 9.29759i) q^{69} +(0.157110 + 0.483535i) q^{70} +(-3.04991 + 2.21589i) q^{71} +(2.79053 - 2.02744i) q^{72} +(0.184248 + 0.567056i) q^{73} +(0.494218 - 1.52105i) q^{74} +(-3.50711 - 2.54806i) q^{75} -1.00000 q^{76} +(0.408636 + 0.834556i) q^{77} -2.13706 q^{78} +(11.4673 + 8.33146i) q^{79} +(0.560761 - 1.72584i) q^{80} +(-2.30226 - 7.08562i) q^{81} +(-5.72565 + 4.15993i) q^{82} +(-2.61517 + 1.90003i) q^{83} +(0.219869 + 0.676688i) q^{84} +(-2.41426 + 7.43033i) q^{85} +(-2.94237 - 2.13776i) q^{86} -20.0820 q^{87} +(0.570884 - 3.26712i) q^{88} +13.3617 q^{89} +(5.06387 + 3.67912i) q^{90} +(0.0728568 - 0.224230i) q^{91} +(1.18957 + 3.66112i) q^{92} +(18.3997 - 13.3682i) q^{93} +(-6.18843 + 4.49616i) q^{94} +(-0.560761 - 1.72584i) q^{95} +(0.784763 - 2.41525i) q^{96} +(-7.80794 - 5.67280i) q^{97} +6.92150 q^{98} +(10.1092 + 5.35516i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 5 q^{2} - q^{3} - 5 q^{4} - q^{5} + q^{6} + 13 q^{7} + 5 q^{8} - 6 q^{9}+O(q^{10}) \) 20 * q + 5 * q^2 - q^3 - 5 * q^4 - q^5 + q^6 + 13 * q^7 + 5 * q^8 - 6 * q^9	\( 20 q + 5 q^{2} - q^{3} - 5 q^{4} - q^{5} + q^{6} + 13 q^{7} + 5 q^{8} - 6 q^{9} + 6 q^{10} + q^{11} + 4 q^{12} - 2 q^{13} - 13 q^{14} - 8 q^{15} - 5 q^{16} + 11 q^{17} + 6 q^{18} + 5 q^{19} - q^{20} + 2 q^{21} + 4 q^{22} + 28 q^{23} + q^{24} - 30 q^{25} - 13 q^{26} - 31 q^{27} - 2 q^{28} + 28 q^{29} + 8 q^{30} - q^{31} - 20 q^{32} + 9 q^{33} + 24 q^{34} - 11 q^{35} - 6 q^{36} + 8 q^{37} - 5 q^{38} + 18 q^{39} - 4 q^{40} - 5 q^{41} - 22 q^{42} - 44 q^{43} + 11 q^{44} - 4 q^{45} + 7 q^{46} - 39 q^{47} - q^{48} + 4 q^{49} - 25 q^{50} - 11 q^{51} + 13 q^{52} - q^{53} - 4 q^{54} + 8 q^{55} + 22 q^{56} + q^{57} - 28 q^{58} + 6 q^{59} + 7 q^{60} + 10 q^{61} + 11 q^{62} + 34 q^{63} - 5 q^{64} - 8 q^{65} + 41 q^{66} + 18 q^{67} + 11 q^{68} - 63 q^{69} + q^{70} - 3 q^{71} + 6 q^{72} + 5 q^{73} - 8 q^{74} + 5 q^{75} - 20 q^{76} + 36 q^{77} + 22 q^{78} + 19 q^{79} + 4 q^{80} + 63 q^{81} - 9 q^{83} - 23 q^{84} + 30 q^{85} - 26 q^{86} - 16 q^{87} - q^{88} + 44 q^{89} + 14 q^{90} - 68 q^{91} - 7 q^{92} + 27 q^{93} - 31 q^{94} - 4 q^{95} + q^{96} - 71 q^{97} + 6 q^{98} + 20 q^{99}+O(q^{100}) \) 20 * q + 5 * q^2 - q^3 - 5 * q^4 - q^5 + q^6 + 13 * q^7 + 5 * q^8 - 6 * q^9 + 6 * q^10 + q^11 + 4 * q^12 - 2 * q^13 - 13 * q^14 - 8 * q^15 - 5 * q^16 + 11 * q^17 + 6 * q^18 + 5 * q^19 - q^20 + 2 * q^21 + 4 * q^22 + 28 * q^23 + q^24 - 30 * q^25 - 13 * q^26 - 31 * q^27 - 2 * q^28 + 28 * q^29 + 8 * q^30 - q^31 - 20 * q^32 + 9 * q^33 + 24 * q^34 - 11 * q^35 - 6 * q^36 + 8 * q^37 - 5 * q^38 + 18 * q^39 - 4 * q^40 - 5 * q^41 - 22 * q^42 - 44 * q^43 + 11 * q^44 - 4 * q^45 + 7 * q^46 - 39 * q^47 - q^48 + 4 * q^49 - 25 * q^50 - 11 * q^51 + 13 * q^52 - q^53 - 4 * q^54 + 8 * q^55 + 22 * q^56 + q^57 - 28 * q^58 + 6 * q^59 + 7 * q^60 + 10 * q^61 + 11 * q^62 + 34 * q^63 - 5 * q^64 - 8 * q^65 + 41 * q^66 + 18 * q^67 + 11 * q^68 - 63 * q^69 + q^70 - 3 * q^71 + 6 * q^72 + 5 * q^73 - 8 * q^74 + 5 * q^75 - 20 * q^76 + 36 * q^77 + 22 * q^78 + 19 * q^79 + 4 * q^80 + 63 * q^81 - 9 * q^83 - 23 * q^84 + 30 * q^85 - 26 * q^86 - 16 * q^87 - q^88 + 44 * q^89 + 14 * q^90 - 68 * q^91 - 7 * q^92 + 27 * q^93 - 31 * q^94 - 4 * q^95 + q^96 - 71 * q^97 + 6 * q^98 + 20 * q^99

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