LMFDB - Embedded newform 62.2.d.a.47.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [62,2,Mod(33,62)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(62, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("62.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	62.d (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:	$0.495072492532$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.511890625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 7x^{6} - 5x^{5} + 16x^{4} + 15x^{3} + 63x^{2} + 81x + 81 $ x^8 - 3x^7 + 7x^6 - 5x^5 + 16x^4 + 15x^3 + 63x^2 + 81*x + 81
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			47.1
Root			$-0.448193 - 1.37940i$ of defining polynomial
Character	$\chi$	$=$	62.47
Dual form			62.2.d.a.33.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(-2.48240 - 1.80357i) q^{3} +(0.309017 - 0.951057i) q^{4} -3.34677 q^{5} +3.06842 q^{6} +(0.778353 - 2.39552i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.98240 + 6.10121i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(-2.48240 - 1.80357i) q^{3} +(0.309017 - 0.951057i) q^{4} -3.34677 q^{5} +3.06842 q^{6} +(0.778353 - 2.39552i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.98240 + 6.10121i) q^{9} +(2.70759 - 1.96718i) q^{10} +(0.532018 - 1.63738i) q^{11} +(-2.48240 + 1.80357i) q^{12} +(-1.89284 - 1.37523i) q^{13} +(0.778353 + 2.39552i) q^{14} +(8.30803 + 6.03614i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.244144 - 0.751397i) q^{17} +(-5.19000 - 3.77075i) q^{18} +(-0.326615 + 0.237300i) q^{19} +(-1.03421 + 3.18297i) q^{20} +(-6.25268 + 4.54284i) q^{21} +(0.532018 + 1.63738i) q^{22} +(-1.56623 - 4.82035i) q^{23} +(0.948193 - 2.91824i) q^{24} +6.20087 q^{25} +2.33968 q^{26} +(3.23826 - 9.96634i) q^{27} +(-2.03775 - 1.48051i) q^{28} +(4.20759 - 3.05700i) q^{29} -10.2693 q^{30} +(-2.94366 - 4.72598i) q^{31} +1.00000 q^{32} +(-4.27382 + 3.10511i) q^{33} +(0.639176 + 0.464389i) q^{34} +(-2.60497 + 8.01727i) q^{35} +6.41519 q^{36} +5.88930 q^{37} +(0.124756 - 0.383959i) q^{38} +(2.21847 + 6.82775i) q^{39} +(-1.03421 - 3.18297i) q^{40} +(-6.27601 + 4.55979i) q^{41} +(2.38831 - 7.35047i) q^{42} +(-6.18645 + 4.49472i) q^{43} +(-1.39284 - 1.01196i) q^{44} +(-6.63465 - 20.4193i) q^{45} +(4.10044 + 2.97914i) q^{46} +(3.91519 + 2.84455i) q^{47} +(0.948193 + 2.91824i) q^{48} +(0.530422 + 0.385374i) q^{49} +(-5.01661 + 3.64478i) q^{50} +(-0.749135 + 2.30560i) q^{51} +(-1.89284 + 1.37523i) q^{52} +(-0.812562 - 2.50081i) q^{53} +(3.23826 + 9.96634i) q^{54} +(-1.78054 + 5.47995i) q^{55} +2.51880 q^{56} +1.23878 q^{57} +(-1.60716 + 4.94632i) q^{58} +(3.53202 + 2.56616i) q^{59} +(8.30803 - 6.03614i) q^{60} +9.60897 q^{61} +(5.15933 + 2.09315i) q^{62} +16.1586 q^{63} +(-0.809017 + 0.587785i) q^{64} +(6.33491 + 4.60258i) q^{65} +(1.63245 - 5.02418i) q^{66} -8.86119 q^{67} -0.790065 q^{68} +(-4.80584 + 14.7909i) q^{69} +(-2.60497 - 8.01727i) q^{70} +(-3.67558 - 11.3123i) q^{71} +(-5.19000 + 3.77075i) q^{72} +(2.42471 - 7.46249i) q^{73} +(-4.76454 + 3.46164i) q^{74} +(-15.3931 - 11.1837i) q^{75} +(0.124756 + 0.383959i) q^{76} +(-3.50829 - 2.54892i) q^{77} +(-5.80803 - 4.21978i) q^{78} +(-0.647345 - 1.99232i) q^{79} +(2.70759 + 1.96718i) q^{80} +(-10.4437 + 7.58776i) q^{81} +(2.39722 - 7.37789i) q^{82} +(9.91519 - 7.20381i) q^{83} +(2.38831 + 7.35047i) q^{84} +(0.817093 + 2.51475i) q^{85} +(2.36301 - 7.27261i) q^{86} -15.9584 q^{87} +1.72165 q^{88} +(4.52530 - 13.9274i) q^{89} +(17.3697 + 12.6198i) q^{90} +(-4.76769 + 3.46393i) q^{91} -5.06842 q^{92} +(-1.21628 + 17.0409i) q^{93} -4.83944 q^{94} +(1.09310 - 0.794187i) q^{95} +(-2.48240 - 1.80357i) q^{96} +(-5.80449 + 17.8644i) q^{97} -0.655638 q^{98} +11.0447 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 4 q^{5} + 6 q^{6} + 2 q^{7} - 2 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 4 * q^5 + 6 * q^6 + 2 * q^7 - 2 * q^8	\( 8 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 4 q^{5} + 6 q^{6} + 2 q^{7} - 2 q^{8} + q^{10} - 2 q^{11} - 4 q^{12} - 11 q^{13} + 2 q^{14} + 21 q^{15} - 2 q^{16} - 7 q^{17} - 5 q^{18} - 14 q^{19} + q^{20} - 7 q^{21} - 2 q^{22} + 3 q^{23} + q^{24} + 14 q^{26} + 5 q^{27} + 2 q^{28} + 13 q^{29} - 14 q^{30} + 15 q^{31} + 8 q^{32} + 2 q^{33} + 3 q^{34} - 28 q^{35} + 10 q^{36} + 52 q^{37} + 21 q^{38} - 16 q^{39} + q^{40} - 11 q^{41} - 17 q^{42} - 22 q^{43} - 7 q^{44} - 19 q^{45} + 8 q^{46} - 10 q^{47} + q^{48} - 10 q^{49} - 15 q^{50} + 28 q^{51} - 11 q^{52} + 7 q^{53} + 5 q^{54} - 7 q^{55} - 8 q^{56} - 20 q^{57} - 17 q^{58} + 22 q^{59} + 21 q^{60} + 4 q^{61} + 5 q^{62} + 66 q^{63} - 2 q^{64} - 18 q^{66} - 26 q^{67} + 8 q^{68} + 4 q^{69} - 28 q^{70} - 15 q^{71} - 5 q^{72} - 29 q^{73} - 23 q^{74} - 34 q^{75} + 21 q^{76} + 34 q^{77} - q^{78} - 2 q^{79} + q^{80} - 45 q^{81} + 9 q^{82} + 38 q^{83} - 17 q^{84} + 25 q^{85} + 18 q^{86} - 20 q^{87} + 18 q^{88} + q^{89} + 46 q^{90} + 38 q^{91} - 22 q^{92} + 21 q^{93} - 20 q^{94} - 12 q^{95} - 4 q^{96} - 10 q^{97} + 60 q^{98} + 14 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 4 * q^5 + 6 * q^6 + 2 * q^7 - 2 * q^8 + q^10 - 2 * q^11 - 4 * q^12 - 11 * q^13 + 2 * q^14 + 21 * q^15 - 2 * q^16 - 7 * q^17 - 5 * q^18 - 14 * q^19 + q^20 - 7 * q^21 - 2 * q^22 + 3 * q^23 + q^24 + 14 * q^26 + 5 * q^27 + 2 * q^28 + 13 * q^29 - 14 * q^30 + 15 * q^31 + 8 * q^32 + 2 * q^33 + 3 * q^34 - 28 * q^35 + 10 * q^36 + 52 * q^37 + 21 * q^38 - 16 * q^39 + q^40 - 11 * q^41 - 17 * q^42 - 22 * q^43 - 7 * q^44 - 19 * q^45 + 8 * q^46 - 10 * q^47 + q^48 - 10 * q^49 - 15 * q^50 + 28 * q^51 - 11 * q^52 + 7 * q^53 + 5 * q^54 - 7 * q^55 - 8 * q^56 - 20 * q^57 - 17 * q^58 + 22 * q^59 + 21 * q^60 + 4 * q^61 + 5 * q^62 + 66 * q^63 - 2 * q^64 - 18 * q^66 - 26 * q^67 + 8 * q^68 + 4 * q^69 - 28 * q^70 - 15 * q^71 - 5 * q^72 - 29 * q^73 - 23 * q^74 - 34 * q^75 + 21 * q^76 + 34 * q^77 - q^78 - 2 * q^79 + q^80 - 45 * q^81 + 9 * q^82 + 38 * q^83 - 17 * q^84 + 25 * q^85 + 18 * q^86 - 20 * q^87 + 18 * q^88 + q^89 + 46 * q^90 + 38 * q^91 - 22 * q^92 + 21 * q^93 - 20 * q^94 - 12 * q^95 - 4 * q^96 - 10 * q^97 + 60 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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
$3$	−2.48240	−	1.80357i	−1.43322	−	1.04129i	−0.989407	−	0.145171i	$-0.953627\pi$
$3$	−2.48240	−	1.80357i	−1.43322	−	1.04129i	−0.443809	−	0.896121i	$-0.646373\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−3.34677			−1.49672			−0.748361	−	0.663292i	$-0.769159\pi$
$5$	−3.34677			−1.49672			−0.748361	+	0.663292i	$0.769159\pi$
$6$	3.06842			1.25268
$7$	0.778353	−	2.39552i	0.294190	−	0.905423i	−0.689303	−	0.724473i	$-0.742083\pi$
$7$	0.778353	−	2.39552i	0.294190	−	0.905423i	0.983492	−	0.180949i	$-0.0579170\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	1.98240	+	6.10121i	0.660801	+	2.03374i
$10$	2.70759	−	1.96718i	0.856216	−	0.622078i
$11$	0.532018	−	1.63738i	0.160410	−	0.493690i	−0.838259	−	0.545272i	$-0.816426\pi$
$11$	0.532018	−	1.63738i	0.160410	−	0.493690i	0.998669	+	0.0515821i	$0.0164264\pi$
$12$	−2.48240	+	1.80357i	−0.716608	+	0.520646i
$13$	−1.89284	−	1.37523i	−0.524980	−	0.381420i	0.293497	−	0.955960i	$-0.405181\pi$
$13$	−1.89284	−	1.37523i	−0.524980	−	0.381420i	−0.818477	+	0.574540i	$0.805181\pi$
$14$	0.778353	+	2.39552i	0.208023	+	0.640230i
$15$	8.30803	+	6.03614i	2.14512	+	1.55852i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−0.244144	−	0.751397i	−0.0592135	−	0.182240i	0.917075	−	0.398716i	$-0.130544\pi$
$17$	−0.244144	−	0.751397i	−0.0592135	−	0.182240i	−0.976288	+	0.216475i	$0.930544\pi$
$18$	−5.19000	−	3.77075i	−1.22329	−	0.888775i
$19$	−0.326615	+	0.237300i	−0.0749306	+	0.0544402i	−0.624620	−	0.780929i	$-0.714746\pi$
$19$	−0.326615	+	0.237300i	−0.0749306	+	0.0544402i	0.549689	+	0.835369i	$0.314746\pi$
$20$	−1.03421	+	3.18297i	−0.231256	+	0.711733i
$21$	−6.25268	+	4.54284i	−1.36445	+	0.991328i
$22$	0.532018	+	1.63738i	0.113427	+	0.349091i
$23$	−1.56623	−	4.82035i	−0.326581	−	1.00511i	−0.970722	−	0.240206i	$-0.922785\pi$
$23$	−1.56623	−	4.82035i	−0.326581	−	1.00511i	0.644141	−	0.764907i	$-0.277215\pi$
$24$	0.948193	−	2.91824i	0.193549	−	0.595683i
$25$	6.20087			1.24017
$26$	2.33968			0.458849
$27$	3.23826	−	9.96634i	0.623203	−	1.91802i
$28$	−2.03775	−	1.48051i	−0.385099	−	0.279791i
$29$	4.20759	−	3.05700i	0.781331	−	0.567670i	−0.124047	−	0.992276i	$-0.539588\pi$
$29$	4.20759	−	3.05700i	0.781331	−	0.567670i	0.905378	+	0.424606i	$0.139588\pi$
$30$	−10.2693			−1.87491
$31$	−2.94366	−	4.72598i	−0.528697	−	0.848810i
$31$	−2.94366	−	4.72598i	−0.528697	−	0.848810i
$32$	1.00000			0.176777
$33$	−4.27382	+	3.10511i	−0.743977	+	0.540531i
$34$	0.639176	+	0.464389i	0.109618	+	0.0796420i
$35$	−2.60497	+	8.01727i	−0.440320	+	1.35517i
$36$	6.41519			1.06920
$37$	5.88930			0.968195			0.484097	−	0.875014i	$-0.339148\pi$
$37$	5.88930			0.968195			0.484097	+	0.875014i	$0.339148\pi$
$38$	0.124756	−	0.383959i	0.0202381	−	0.0622863i
$39$	2.21847	+	6.82775i	0.355240	+	1.09331i
$40$	−1.03421	−	3.18297i	−0.163523	−	0.503271i
$41$	−6.27601	+	4.55979i	−0.980148	+	0.712120i	−0.957742	−	0.287629i	$-0.907133\pi$
$41$	−6.27601	+	4.55979i	−0.980148	+	0.712120i	−0.0224066	+	0.999749i	$0.507133\pi$
$42$	2.38831	−	7.35047i	0.368524	−	1.13420i
$43$	−6.18645	+	4.49472i	−0.943425	+	0.685438i	−0.949243	−	0.314545i	$-0.898148\pi$
$43$	−6.18645	+	4.49472i	−0.943425	+	0.685438i	0.00581761	+	0.999983i	$0.498148\pi$
$44$	−1.39284	−	1.01196i	−0.209979	−	0.152559i
$45$	−6.63465	−	20.4193i	−0.989035	−	3.04394i
$46$	4.10044	+	2.97914i	0.604576	+	0.439250i
$47$	3.91519	+	2.84455i	0.571089	+	0.414920i	0.835501	−	0.549490i	$-0.185178\pi$
$47$	3.91519	+	2.84455i	0.571089	+	0.414920i	−0.264412	+	0.964410i	$0.585178\pi$
$48$	0.948193	+	2.91824i	0.136860	+	0.421211i
$49$	0.530422	+	0.385374i	0.0757746	+	0.0550534i
$50$	−5.01661	+	3.64478i	−0.709456	+	0.515450i
$51$	−0.749135	+	2.30560i	−0.104900	+	0.322848i
$52$	−1.89284	+	1.37523i	−0.262490	+	0.190710i
$53$	−0.812562	−	2.50081i	−0.111614	−	0.343512i	0.879612	−	0.475692i	$-0.157802\pi$
$53$	−0.812562	−	2.50081i	−0.111614	−	0.343512i	−0.991226	+	0.132180i	$0.957802\pi$
$54$	3.23826	+	9.96634i	0.440671	+	1.35625i
$55$	−1.78054	+	5.47995i	−0.240088	+	0.738916i
$56$	2.51880			0.336589
$57$	1.23878			0.164080
$58$	−1.60716	+	4.94632i	−0.211030	+	0.649484i
$59$	3.53202	+	2.56616i	0.459830	+	0.334086i	0.793464	−	0.608617i	$-0.208275\pi$
$59$	3.53202	+	2.56616i	0.459830	+	0.334086i	−0.333635	+	0.942702i	$0.608275\pi$
$60$	8.30803	−	6.03614i	1.07256	−	0.779262i
$61$	9.60897			1.23030			0.615151	−	0.788409i	$-0.289095\pi$
$61$	9.60897			1.23030			0.615151	+	0.788409i	$0.289095\pi$
$62$	5.15933	+	2.09315i	0.655236	+	0.265831i
$63$	16.1586			2.03579
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	6.33491	+	4.60258i	0.785749	+	0.570880i
$66$	1.63245	−	5.02418i	0.200941	−	0.618434i
$67$	−8.86119			−1.08257			−0.541283	−	0.840840i	$-0.682061\pi$
$67$	−8.86119			−1.08257			−0.541283	+	0.840840i	$0.682061\pi$
$68$	−0.790065			−0.0958095
$69$	−4.80584	+	14.7909i	−0.578555	+	1.78061i
$70$	−2.60497	−	8.01727i	−0.311353	−	0.958246i
$71$	−3.67558	−	11.3123i	−0.436211	−	1.34252i	−0.891841	−	0.452349i	$-0.850586\pi$
$71$	−3.67558	−	11.3123i	−0.436211	−	1.34252i	0.455630	−	0.890169i	$-0.349414\pi$
$72$	−5.19000	+	3.77075i	−0.611647	+	0.444388i
$73$	2.42471	−	7.46249i	0.283791	−	0.873419i	−0.702968	−	0.711222i	$-0.748142\pi$
$73$	2.42471	−	7.46249i	0.283791	−	0.873419i	0.986758	−	0.162197i	$-0.0518579\pi$
$74$	−4.76454	+	3.46164i	−0.553867	+	0.402408i
$75$	−15.3931	−	11.1837i	−1.77744	−	1.29138i
$76$	0.124756	+	0.383959i	0.0143105	+	0.0440431i
$77$	−3.50829	−	2.54892i	−0.399807	−	0.290477i
$78$	−5.80803	−	4.21978i	−0.657630	−	0.477796i
$79$	−0.647345	−	1.99232i	−0.0728320	−	0.224154i	0.908014	−	0.418941i	$-0.137598\pi$
$79$	−0.647345	−	1.99232i	−0.0728320	−	0.224154i	−0.980846	+	0.194787i	$0.937598\pi$
$80$	2.70759	+	1.96718i	0.302718	+	0.219938i
$81$	−10.4437	+	7.58776i	−1.16041	+	0.843085i
$82$	2.39722	−	7.37789i	0.264729	−	0.814752i
$83$	9.91519	−	7.20381i	1.08833	−	0.790720i	0.109216	−	0.994018i	$-0.465166\pi$
$83$	9.91519	−	7.20381i	1.08833	−	0.790720i	0.979117	+	0.203298i	$0.0651659\pi$
$84$	2.38831	+	7.35047i	0.260586	+	0.802002i
$85$	0.817093	+	2.51475i	0.0886261	+	0.272763i
$86$	2.36301	−	7.27261i	0.254810	−	0.784226i
$87$	−15.9584			−1.71093
$88$	1.72165			0.183528
$89$	4.52530	−	13.9274i	0.479680	−	1.47630i	−0.359859	−	0.933007i	$-0.617175\pi$
$89$	4.52530	−	13.9274i	0.479680	−	1.47630i	0.839540	−	0.543298i	$-0.182825\pi$
$90$	17.3697	+	12.6198i	1.83093	+	1.33025i
$91$	−4.76769	+	3.46393i	−0.499790	+	0.363119i
$92$	−5.06842			−0.528419
$93$	−1.21628	+	17.0409i	−0.126122	+	1.76706i
$94$	−4.83944			−0.499150
$95$	1.09310	−	0.794187i	0.112150	−	0.0814819i
$96$	−2.48240	−	1.80357i	−0.253359	−	0.184076i
$97$	−5.80449	+	17.8644i	−0.589356	+	1.81385i	−0.00833268	+	0.999965i	$0.502652\pi$
$97$	−5.80449	+	17.8644i	−0.589356	+	1.81385i	−0.581024	+	0.813887i	$0.697348\pi$
$98$	−0.655638			−0.0662294
$99$	11.0447			1.11003
$100$	1.91617	−	5.89738i	0.191617	−	0.589738i
$101$	−2.92191	−	8.99271i	−0.290741	−	0.894809i	−0.984619	−	0.174716i	$-0.944099\pi$
$101$	−2.92191	−	8.99271i	−0.290741	−	0.894809i	0.693878	−	0.720093i	$-0.255901\pi$
$102$	−0.749135	−	2.30560i	−0.0741754	−	0.228288i
$103$	1.05754	−	0.768349i	0.104203	−	0.0757077i	−0.534464	−	0.845191i	$-0.679486\pi$
$103$	1.05754	−	0.768349i	0.104203	−	0.0757077i	0.638666	+	0.769484i	$0.279486\pi$
$104$	0.723001	−	2.22517i	0.0708961	−	0.218196i
$105$	20.9263	−	15.2038i	2.04220	−	1.48374i
$106$	2.12731	+	1.54558i	0.206623	+	0.150120i
$107$	4.63903	+	14.2775i	0.448472	+	1.38025i	0.878631	+	0.477501i	$0.158457\pi$
$107$	4.63903	+	14.2775i	0.448472	+	1.38025i	−0.430160	+	0.902753i	$0.641543\pi$
$108$	−8.47787	−	6.15953i	−0.815784	−	0.592701i
$109$	−5.71333	−	4.15098i	−0.547238	−	0.397591i	0.279528	−	0.960137i	$-0.409822\pi$
$109$	−5.71333	−	4.15098i	−0.547238	−	0.397591i	−0.826766	+	0.562546i	$0.809822\pi$
$110$	−1.78054	−	5.47995i	−0.169768	−	0.522493i
$111$	−14.6196	−	10.6218i	−1.38763	−	1.00817i
$112$	−2.03775	+	1.48051i	−0.192550	+	0.139895i
$113$	1.67792	−	5.16410i	0.157845	−	0.485797i	−0.840593	−	0.541667i	$-0.817793\pi$
$113$	1.67792	−	5.16410i	0.157845	−	0.485797i	0.998438	+	0.0558701i	$0.0177933\pi$
$114$	−1.00219	+	0.728134i	−0.0938638	+	0.0681960i
$115$	5.24180	+	16.1326i	0.488801	+	1.50437i
$116$	−1.60716	−	4.94632i	−0.149221	−	0.459255i
$117$	4.63819	−	14.2749i	0.428801	−	1.31971i
$118$	−4.36581			−0.401906
$119$	−1.99002			−0.182425
$120$	−3.17339	+	9.76668i	−0.289689	+	0.891571i
$121$	6.50120	+	4.72340i	0.591019	+	0.429400i
$122$	−7.77382	+	5.64801i	−0.703809	+	0.511347i
$123$	23.8035			2.14629
$124$	−5.40431	+	1.33918i	−0.485322	+	0.120262i
$125$	−4.01904			−0.359474
$126$	−13.0726	+	9.49778i	−1.16460	+	0.846129i
$127$	−3.38098	−	2.45643i	−0.300013	−	0.217972i	0.427586	−	0.903975i	$-0.359364\pi$
$127$	−3.38098	−	2.45643i	−0.300013	−	0.217972i	−0.727600	+	0.686002i	$0.759364\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	23.4638			2.06587
$130$	−7.83038			−0.686769
$131$	2.13918	−	6.58371i	0.186901	−	0.575221i	−0.813075	−	0.582159i	$-0.802208\pi$
$131$	2.13918	−	6.58371i	0.186901	−	0.575221i	0.999976	+	0.00693742i	$0.00220827\pi$
$132$	1.63245	+	5.02418i	0.142087	+	0.437299i
$133$	0.314235	+	0.967116i	0.0272476	+	0.0838596i
$134$	7.16885	−	5.20848i	0.619295	−	0.449944i
$135$	−10.8377	+	33.3550i	−0.932761	+	2.87074i
$136$	0.639176	−	0.464389i	0.0548089	−	0.0398210i
$137$	2.87365	+	2.08783i	0.245512	+	0.178375i	0.703736	−	0.710462i	$-0.251514\pi$
$137$	2.87365	+	2.08783i	0.245512	+	0.178375i	−0.458223	+	0.888837i	$0.651514\pi$
$138$	−4.80584	−	14.7909i	−0.409100	−	1.25908i
$139$	1.99646	+	1.45051i	0.169337	+	0.123031i	0.669226	−	0.743059i	$-0.266626\pi$
$139$	1.99646	+	1.45051i	0.169337	+	0.123031i	−0.499889	+	0.866090i	$0.666626\pi$
$140$	6.81989	+	4.95494i	0.576386	+	0.418769i
$141$	−4.58872	−	14.1226i	−0.386440	−	1.18934i
$142$	9.62278	+	6.99136i	0.807526	+	0.586702i
$143$	−3.25881	+	2.36766i	−0.272515	+	0.197994i
$144$	1.98240	−	6.10121i	0.165200	−	0.508434i
$145$	−14.0819	+	10.2311i	−1.16943	+	0.849644i
$146$	2.42471	+	7.46249i	0.200670	+	0.617600i
$147$	−0.621671	−	1.91331i	−0.0512746	−	0.157807i
$148$	1.81989	−	5.60105i	0.149594	−	0.460404i
$149$	−14.2287			−1.16566			−0.582829	−	0.812595i	$-0.698054\pi$
$149$	−14.2287			−1.16566			−0.582829	+	0.812595i	$0.698054\pi$
$150$	19.0269			1.55354
$151$	−1.46345	+	4.50404i	−0.119094	+	0.366533i	−0.992779	−	0.119959i	$-0.961724\pi$
$151$	−1.46345	+	4.50404i	−0.119094	+	0.366533i	0.873685	+	0.486492i	$0.161724\pi$
$152$	−0.326615	−	0.237300i	−0.0264920	−	0.0192475i
$153$	4.10044	−	2.97914i	0.331501	−	0.240849i
$154$	4.33649			0.349444
$155$	9.85176	+	15.8168i	0.791313	+	1.27043i
$156$	7.17912			0.574790
$157$	14.8602	−	10.7966i	1.18597	−	0.861660i	0.193141	−	0.981171i	$-0.438133\pi$
$157$	14.8602	−	10.7966i	1.18597	−	0.861660i	0.992833	+	0.119511i	$0.0381327\pi$
$158$	1.69477	+	1.23132i	0.134829	+	0.0979588i
$159$	−2.49328	+	7.67352i	−0.197730	+	0.608550i
$160$	−3.34677			−0.264585
$161$	−12.7663			−1.00613
$162$	3.98912	−	12.2773i	0.313415	−	0.964593i
$163$	−3.91753	−	12.0569i	−0.306845	−	0.944370i	−0.978982	−	0.203944i	$-0.934624\pi$
$163$	−3.91753	−	12.0569i	−0.306845	−	0.944370i	0.672138	−	0.740426i	$-0.265376\pi$
$164$	2.39722	+	7.37789i	0.187192	+	0.576117i
$165$	14.3035	−	10.3921i	1.11353	−	0.809024i
$166$	−3.78726	+	11.6560i	−0.293949	+	0.904681i
$167$	−18.6653	+	13.5611i	−1.44436	+	1.04939i	−0.457255	+	0.889336i	$0.651167\pi$
$167$	−18.6653	+	13.5611i	−1.44436	+	1.04939i	−0.987108	+	0.160056i	$0.948833\pi$
$168$	−6.25268	−	4.54284i	−0.482405	−	0.350488i
$169$	−2.32563	−	7.15755i	−0.178894	−	0.550581i
$170$	−2.13918	−	1.55420i	−0.164067	−	0.119202i
$171$	−2.09530	−	1.52232i	−0.160231	−	0.116415i
$172$	2.36301	+	7.27261i	0.180178	+	0.554531i
$173$	16.3838	+	11.9035i	1.24564	+	0.905007i	0.997960	−	0.0638358i	$-0.0203334\pi$
$173$	16.3838	+	11.9035i	1.24564	+	0.905007i	0.247675	+	0.968843i	$0.420333\pi$
$174$	12.9107	−	9.38014i	0.978754	−	0.711107i
$175$	4.82646	−	14.8543i	0.364846	−	1.12288i
$176$	−1.39284	+	1.01196i	−0.104989	+	0.0762793i
$177$	−4.13964	−	12.7405i	−0.311154	−	0.957634i
$178$	4.52530	+	13.9274i	0.339185	+	1.04391i
$179$	−2.45235	+	7.54755i	−0.183297	+	0.564130i	−0.999915	−	0.0130484i	$-0.995846\pi$
$179$	−2.45235	+	7.54755i	−0.183297	+	0.564130i	0.816618	+	0.577179i	$0.195846\pi$
$180$	−21.4702			−1.60029
$181$	−24.2847			−1.80507			−0.902533	−	0.430620i	$-0.858295\pi$
$181$	−24.2847			−1.80507			−0.902533	+	0.430620i	$0.858295\pi$
$182$	1.82110	−	5.60476i	0.134989	−	0.415452i
$183$	−23.8533	−	17.3305i	−1.76329	−	1.28110i
$184$	4.10044	−	2.97914i	0.302288	−	0.219625i
$185$	−19.7101			−1.44912
$186$	−9.03239	−	14.5013i	−0.662287	−	1.06328i
$187$	−1.36021			−0.0994687
$188$	3.91519	−	2.84455i	0.285544	−	0.207460i
$189$	−21.3541	−	15.5146i	−1.55328	−	1.12852i
$190$	−0.417529	+	1.28502i	−0.0302907	+	0.0932253i
$191$	11.3915			0.824257			0.412129	−	0.911126i	$-0.364785\pi$
$191$	11.3915			0.824257			0.412129	+	0.911126i	$0.364785\pi$
$192$	3.06842			0.221444
$193$	−3.13502	+	9.64861i	−0.225664	+	0.694522i	0.772560	+	0.634942i	$0.218976\pi$
$193$	−3.13502	+	9.64861i	−0.225664	+	0.694522i	−0.998224	+	0.0595797i	$0.981024\pi$
$194$	−5.80449	−	17.8644i	−0.416738	−	1.28259i
$195$	−7.42471	−	22.8509i	−0.531695	−	1.63639i
$196$	0.530422	−	0.385374i	0.0378873	−	0.0275267i
$197$	−0.723369	+	2.22630i	−0.0515379	+	0.158617i	−0.973513	−	0.228632i	$-0.926575\pi$
$197$	−0.723369	+	2.22630i	−0.0515379	+	0.158617i	0.921975	+	0.387249i	$0.126575\pi$
$198$	−8.93534	+	6.49191i	−0.635007	+	0.461360i
$199$	9.63624	+	7.00114i	0.683095	+	0.496298i	0.874383	−	0.485236i	$-0.161266\pi$
$199$	9.63624	+	7.00114i	0.683095	+	0.496298i	−0.191288	+	0.981534i	$0.561266\pi$
$200$	1.91617	+	5.89738i	0.135494	+	0.417008i
$201$	21.9970	+	15.9818i	1.55155	+	1.12727i
$202$	7.64966	+	5.55780i	0.538228	+	0.391046i
$203$	−4.04811	−	12.4588i	−0.284122	−	0.874437i
$204$	1.96126	+	1.42494i	0.137316	+	0.0997657i
$205$	21.0044	−	15.2606i	1.46701	−	1.06584i
$206$	−0.403945	+	1.24322i	−0.0281442	+	0.0866189i
$207$	26.3051	−	19.1118i	1.82833	−	1.32836i
$208$	0.723001	+	2.22517i	0.0501311	+	0.154288i
$209$	0.214785	+	0.661042i	0.0148570	+	0.0457252i
$210$	−7.99313	+	24.6003i	−0.551578	+	1.69758i
$211$	20.5097			1.41195			0.705974	−	0.708237i	$-0.250509\pi$
$211$	20.5097			1.41195			0.705974	+	0.708237i	$0.250509\pi$
$212$	−2.62950			−0.180595
$213$	−11.2782	+	34.7107i	−0.772770	+	2.37834i
$214$	−12.1451	−	8.82395i	−0.830224	−	0.603193i
$215$	20.7046	−	15.0428i	1.41204	−	1.02591i
$216$	10.4792			0.713021
$217$	−13.6124	+	3.37313i	−0.924069	+	0.228983i
$218$	7.06206			0.478303
$219$	−19.4782	+	14.1518i	−1.31622	+	0.956288i
$220$	4.66152	+	3.38679i	0.314280	+	0.228338i
$221$	−0.571218	+	1.75803i	−0.0384243	+	0.118258i
$222$	18.0708			1.21283
$223$	−3.53346			−0.236618			−0.118309	−	0.992977i	$-0.537747\pi$
$223$	−3.53346			−0.236618			−0.118309	+	0.992977i	$0.537747\pi$
$224$	0.778353	−	2.39552i	0.0520059	−	0.160058i
$225$	12.2926	+	37.8328i	0.819508	+	2.52219i
$226$	1.67792	+	5.16410i	0.111613	+	0.343511i
$227$	−0.453928	+	0.329798i	−0.0301283	+	0.0218895i	−0.602747	−	0.797932i	$-0.705927\pi$
$227$	−0.453928	+	0.329798i	−0.0301283	+	0.0218895i	0.572619	+	0.819821i	$0.305927\pi$
$228$	0.382803	−	1.17815i	0.0253517	−	0.0780246i
$229$	−4.02016	+	2.92081i	−0.265659	+	0.193013i	−0.712638	−	0.701532i	$-0.752500\pi$
$229$	−4.02016	+	2.92081i	−0.265659	+	0.193013i	0.446979	+	0.894544i	$0.352500\pi$
$230$	−13.7232	−	9.97050i	−0.904882	−	0.657435i
$231$	4.11183	+	12.6549i	0.270539	+	0.832632i
$232$	4.20759	+	3.05700i	0.276242	+	0.200702i
$233$	7.68606	+	5.58425i	0.503530	+	0.365836i	0.810364	−	0.585927i	$-0.199269\pi$
$233$	7.68606	+	5.58425i	0.503530	+	0.365836i	−0.306833	+	0.951763i	$0.599269\pi$
$234$	4.63819	+	14.2749i	0.303208	+	0.933178i
$235$	−13.1032	−	9.52006i	−0.854761	−	0.621020i
$236$	3.53202	−	2.56616i	0.229915	−	0.167043i
$237$	−1.98632	+	6.11328i	−0.129026	+	0.397100i
$238$	1.60996	−	1.16970i	0.104358	−	0.0758206i
$239$	−3.81989	−	11.7564i	−0.247088	−	0.760460i	−0.995286	−	0.0969838i	$-0.969081\pi$
$239$	−3.81989	−	11.7564i	−0.247088	−	0.760460i	0.748198	−	0.663476i	$-0.230919\pi$
$240$	−3.17339	−	9.76668i	−0.204841	−	0.630436i
$241$	6.15504	−	18.9433i	0.396481	−	1.22024i	−0.531321	−	0.847171i	$-0.678304\pi$
$241$	6.15504	−	18.9433i	0.396481	−	1.22024i	0.927802	−	0.373073i	$-0.121696\pi$
$242$	−8.03593			−0.516569
$243$	8.17277			0.524283
$244$	2.96934	−	9.13868i	0.190092	−	0.585044i
$245$	−1.77520	−	1.28976i	−0.113413	−	0.0823997i
$246$	−19.2574	+	13.9913i	−1.22781	+	0.892055i
$247$	0.944572			0.0601017
$248$	3.58503	−	4.26000i	0.227650	−	0.270510i
$249$	−37.6061			−2.38319
$250$	3.25148	−	2.36233i	0.205641	−	0.149407i
$251$	19.9146	+	14.4688i	1.25700	+	0.913261i	0.998606	−	0.0527792i	$-0.0168080\pi$
$251$	19.9146	+	14.4688i	1.25700	+	0.913261i	0.258390	+	0.966041i	$0.416808\pi$
$252$	4.99328	−	15.3677i	0.314547	−	0.968076i
$253$	−8.72603			−0.548601
$254$	4.17912			0.262221
$255$	2.50718	−	7.71631i	0.157006	−	0.483214i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	6.33567	+	19.4992i	0.395208	+	1.21633i	0.928799	+	0.370583i	$0.120842\pi$
$257$	6.33567	+	19.4992i	0.395208	+	1.21633i	−0.533591	+	0.845742i	$0.679158\pi$
$258$	−18.9826	+	13.7917i	−1.18181	+	0.858633i
$259$	4.58395	−	14.1079i	0.284833	−	0.876625i
$260$	6.33491	−	4.60258i	0.392874	−	0.285440i
$261$	26.9925	+	19.6112i	1.67079	+	1.21390i
$262$	2.13918	+	6.58371i	0.132159	+	0.406743i
$263$	−4.10167	−	2.98003i	−0.252920	−	0.183757i	0.454100	−	0.890951i	$-0.349961\pi$
$263$	−4.10167	−	2.98003i	−0.252920	−	0.183757i	−0.707020	+	0.707194i	$0.749961\pi$
$264$	−4.27382	−	3.10511i	−0.263036	−	0.191106i
$265$	2.71946	+	8.36963i	0.167055	+	0.514142i
$266$	−0.822678	−	0.597710i	−0.0504416	−	0.0366480i
$267$	−36.3527	+	26.4118i	−2.22475	+	1.61638i
$268$	−2.73826	+	8.42749i	−0.167266	+	0.514791i
$269$	4.28568	−	3.11373i	0.261303	−	0.189848i	−0.449418	−	0.893321i	$-0.648369\pi$
$269$	4.28568	−	3.11373i	0.261303	−	0.189848i	0.710721	+	0.703474i	$0.248369\pi$
$270$	−10.8377	−	33.3550i	−0.659562	−	2.02992i
$271$	−2.41473	−	7.43177i	−0.146684	−	0.451448i	0.850539	−	0.525911i	$-0.176276\pi$
$271$	−2.41473	−	7.43177i	−0.146684	−	0.451448i	−0.997224	+	0.0744634i	$0.976276\pi$
$272$	−0.244144	+	0.751397i	−0.0148034	+	0.0455601i
$273$	18.0828			1.09442
$274$	−3.55202			−0.214586
$275$	3.29898	−	10.1532i	0.198936	−	0.612262i
$276$	12.5819	+	9.14125i	0.757338	+	0.550239i
$277$	0.833554	−	0.605612i	0.0500834	−	0.0363877i	−0.562462	−	0.826823i	$-0.690146\pi$
$277$	0.833554	−	0.605612i	0.0500834	−	0.0363877i	0.612545	+	0.790435i	$0.290146\pi$
$278$	−2.46775			−0.148006
$279$	22.9986	−	27.3287i	1.37689	−	1.63613i
$280$	−8.42985			−0.503780
$281$	−5.71370	+	4.15124i	−0.340851	+	0.247642i	−0.745021	−	0.667041i	$-0.767560\pi$
$281$	−5.71370	+	4.15124i	−0.340851	+	0.247642i	0.404170	+	0.914684i	$0.367560\pi$
$282$	12.0134	+	8.72827i	0.715390	+	0.519761i
$283$	6.70026	−	20.6213i	0.398289	−	1.22581i	−0.528081	−	0.849194i	$-0.677088\pi$
$283$	6.70026	−	20.6213i	0.398289	−	1.22581i	0.926370	−	0.376614i	$-0.122912\pi$
$284$	−11.8944			−0.705804
$285$	−4.14590			−0.245582
$286$	1.24475	−	3.83096i	0.0736038	−	0.226529i
$287$	6.03813	+	18.5835i	0.356420	+	1.09695i
$288$	1.98240	+	6.10121i	0.116814	+	0.359517i
$289$	13.2483	−	9.62545i	0.779312	−	0.566203i
$290$	5.37879	−	16.5542i	0.315853	−	0.972097i
$291$	46.6287	−	33.8778i	2.73342	−	1.98595i
$292$	−6.34797	−	4.61207i	−0.371487	−	0.269901i
$293$	−2.77555	−	8.54227i	−0.162149	−	0.499045i	0.836665	−	0.547714i	$-0.184502\pi$
$293$	−2.77555	−	8.54227i	−0.162149	−	0.499045i	−0.998815	+	0.0486695i	$0.984502\pi$
$294$	1.62756	+	1.18249i	0.0949210	+	0.0689641i
$295$	−11.8209	−	8.58835i	−0.688237	−	0.500033i
$296$	1.81989	+	5.60105i	0.105779	+	0.325555i
$297$	−14.5959	−	10.6045i	−0.846940	−	0.615338i
$298$	11.5112	−	8.36341i	0.666828	−	0.484479i
$299$	−3.66447	+	11.2781i	−0.211922	+	0.652229i
$300$	−15.3931	+	11.1837i	−0.888719	+	0.645692i
$301$	5.95196	+	18.3183i	0.343066	+	1.05585i
$302$	−1.46345	−	4.50404i	−0.0842121	−	0.259178i
$303$	−8.96564	+	27.5934i	−0.515063	+	1.58520i
$304$	0.403718			0.0231548
$305$	−32.1590			−1.84142
$306$	−1.56623	+	4.82035i	−0.0895353	+	0.275561i
$307$	11.7641	+	8.54715i	0.671415	+	0.487812i	0.870499	−	0.492171i	$-0.163796\pi$
$307$	11.7641	+	8.54715i	0.671415	+	0.487812i	−0.199083	+	0.979983i	$0.563796\pi$
$308$	−3.50829	+	2.54892i	−0.199904	+	0.145238i
$309$	−4.01102			−0.228179
$310$	−17.2671	−	7.00531i	−0.980705	−	0.397875i
$311$	−10.6398			−0.603327			−0.301663	−	0.953414i	$-0.597542\pi$
$311$	−10.6398			−0.603327			−0.301663	+	0.953414i	$0.597542\pi$
$312$	−5.80803	+	4.21978i	−0.328815	+	0.238898i
$313$	−2.73252	−	1.98529i	−0.154451	−	0.112215i	0.507876	−	0.861430i	$-0.330431\pi$
$313$	−2.73252	−	1.98529i	−0.154451	−	0.112215i	−0.662327	+	0.749215i	$0.730431\pi$
$314$	−5.67609	+	17.4692i	−0.320320	+	0.985845i
$315$	−54.0791			−3.04701
$316$	−2.09485			−0.117845
$317$	2.02016	−	6.21740i	0.113463	−	0.349204i	−0.878160	−	0.478367i	$-0.841229\pi$
$317$	2.02016	−	6.21740i	0.113463	−	0.349204i	0.991623	+	0.129163i	$0.0412290\pi$
$318$	−2.49328	−	7.67352i	−0.139816	−	0.430310i
$319$	−2.76696	−	8.51583i	−0.154920	−	0.476795i
$320$	2.70759	−	1.96718i	0.151359	−	0.109969i
$321$	14.2345	−	43.8092i	0.794491	−	2.44519i
$322$	10.3282	−	7.50387i	0.575567	−	0.418174i
$323$	0.258047	+	0.187482i	0.0143581	+	0.0104318i
$324$	3.98912	+	12.2773i	0.221618	+	0.682070i
$325$	−11.7373	−	8.52763i	−0.651067	−	0.473028i
$326$	10.2562	+	7.45158i	0.568040	+	0.412705i
$327$	6.69620	+	20.6088i	0.370301	+	1.13967i
$328$	−6.27601	−	4.55979i	−0.346535	−	0.251772i
$329$	9.86158	−	7.16486i	0.543687	−	0.395012i
$330$	−5.46345	+	16.8148i	−0.300753	+	0.925623i
$331$	−22.6560	+	16.4606i	−1.24529	+	0.904754i	−0.997939	−	0.0641730i	$-0.979559\pi$
$331$	−22.6560	+	16.4606i	−1.24529	+	0.904754i	−0.247348	+	0.968927i	$0.579559\pi$
$332$	−3.78726	−	11.6560i	−0.207853	−	0.639706i
$333$	11.6750	+	35.9318i	0.639784	+	1.96905i
$334$	7.12950	−	21.9424i	0.390109	−	1.20063i
$335$	29.6564			1.62030
$336$	7.72874			0.421637
$337$	9.18116	−	28.2567i	0.500130	−	1.53924i	−0.308677	−	0.951167i	$-0.599886\pi$
$337$	9.18116	−	28.2567i	0.500130	−	1.53924i	0.808807	−	0.588074i	$-0.200114\pi$
$338$	6.08857	+	4.42361i	0.331175	+	0.240613i
$339$	−13.4791	+	9.79312i	−0.732083	+	0.531889i
$340$	2.64417			0.143400
$341$	−9.30432	+	2.30560i	−0.503857	+	0.124855i
$342$	2.58993			0.140047
$343$	15.6003	−	11.3343i	0.842337	−	0.611994i
$344$	−6.18645	−	4.49472i	−0.333551	−	0.242339i
$345$	16.0840	−	49.5016i	0.865936	−	2.66508i
$346$	−20.2515			−1.08873
$347$	−9.82039			−0.527186			−0.263593	−	0.964634i	$-0.584908\pi$
$347$	−9.82039			−0.527186			−0.263593	+	0.964634i	$0.584908\pi$
$348$	−4.93143	+	15.1774i	−0.264353	+	0.813593i
$349$	0.317093	+	0.975911i	0.0169736	+	0.0522393i	0.959185	−	0.282781i	$-0.0912569\pi$
$349$	0.317093	+	0.975911i	0.0169736	+	0.0522393i	−0.942211	+	0.335020i	$0.891257\pi$
$350$	4.82646	+	14.8543i	0.257985	+	0.793997i
$351$	−19.8355	+	14.4113i	−1.05874	+	0.769221i
$352$	0.532018	−	1.63738i	0.0283567	−	0.0872729i
$353$	−16.9992	+	12.3507i	−0.904778	+	0.657360i	−0.939689	−	0.342031i	$-0.888885\pi$
$353$	−16.9992	+	12.3507i	−0.904778	+	0.657360i	0.0349109	+	0.999390i	$0.488885\pi$
$354$	10.8377	+	7.87406i	0.576018	+	0.418501i
$355$	12.3013	+	37.8595i	0.652886	+	2.00938i
$356$	−11.8474	−	8.60763i	−0.627910	−	0.456203i
$357$	4.94003	+	3.58914i	0.261454	+	0.189957i
$358$	−2.45235	−	7.54755i	−0.129611	−	0.398900i
$359$	24.6099	+	17.8802i	1.29886	+	0.943680i	0.999944	−	0.0105988i	$-0.00337376\pi$
$359$	24.6099	+	17.8802i	1.29886	+	0.943680i	0.298920	+	0.954278i	$0.403374\pi$
$360$	17.3697	−	12.6198i	0.915465	−	0.665124i
$361$	−5.82096	+	17.9151i	−0.306366	+	0.942898i
$362$	19.6467	−	14.2742i	1.03261	−	0.750234i
$363$	−7.61961	−	23.4508i	−0.399926	−	1.23085i
$364$	1.82110	+	5.60476i	0.0954514	+	0.293769i
$365$	−8.11495	+	24.9752i	−0.424756	+	1.30726i
$366$	29.4843			1.54117
$367$	25.8054			1.34703			0.673516	−	0.739172i	$-0.264783\pi$
$367$	25.8054			1.34703			0.673516	+	0.739172i	$0.264783\pi$
$368$	−1.56623	+	4.82035i	−0.0816452	+	0.251278i
$369$	−40.2618	−	29.2519i	−2.09595	−	1.52279i
$370$	15.9458	−	11.5853i	0.828984	−	0.602292i
$371$	−6.62320			−0.343859
$372$	15.8310	+	6.42267i	0.820798	+	0.333000i
$373$	12.4846			0.646430			0.323215	−	0.946326i	$-0.395236\pi$
$373$	12.4846			0.646430			0.323215	+	0.946326i	$0.395236\pi$
$374$	1.10044	−	0.799514i	0.0569022	−	0.0413419i
$375$	9.97688	+	7.24863i	0.515204	+	0.374318i
$376$	−1.49547	+	4.60258i	−0.0771229	+	0.237360i
$377$	−12.1684			−0.626704
$378$	26.3951			1.35762
$379$	0.582244	−	1.79196i	0.0299079	−	0.0920470i	−0.934988	−	0.354678i	$-0.884590\pi$
$379$	0.582244	−	1.79196i	0.0299079	−	0.0920470i	0.964896	+	0.262631i	$0.0845903\pi$
$380$	−0.417529	−	1.28502i	−0.0214188	−	0.0659202i
$381$	3.96261	+	12.1957i	0.203011	+	0.624803i
$382$	−9.21589	+	6.69573i	−0.471526	+	0.342584i
$383$	4.02861	−	12.3988i	0.205852	−	0.633548i	−0.793825	−	0.608146i	$-0.791913\pi$
$383$	4.02861	−	12.3988i	0.205852	−	0.633548i	0.999677	−	0.0254019i	$-0.00808656\pi$
$384$	−2.48240	+	1.80357i	−0.126680	+	0.0920381i
$385$	11.7415	+	8.53066i	0.598400	+	0.434763i
$386$	−3.13502	−	9.64861i	−0.159568	−	0.491101i
$387$	−39.6873	−	28.8345i	−2.01742	−	1.46574i
$388$	15.1963	+	11.0408i	0.771477	+	0.560511i
$389$	3.18962	+	9.81664i	0.161720	+	0.497723i	0.998780	−	0.0493885i	$-0.0157272\pi$
$389$	3.18962	+	9.81664i	0.161720	+	0.497723i	−0.837060	+	0.547112i	$0.815727\pi$
$390$	19.4381	+	14.1226i	0.984289	+	0.715128i
$391$	−3.23961	+	2.35372i	−0.163834	+	0.119033i
$392$	−0.202603	+	0.623548i	−0.0102330	+	0.0314939i
$393$	−17.1845	+	12.4853i	−0.866842	+	0.629798i
$394$	−0.723369	−	2.22630i	−0.0364428	−	0.112159i
$395$	2.16651	+	6.66784i	0.109009	+	0.335496i
$396$	3.41300	−	10.5041i	0.171510	−	0.527852i
$397$	14.8604			0.745824			0.372912	−	0.927867i	$-0.378359\pi$
$397$	14.8604			0.745824			0.372912	+	0.927867i	$0.378359\pi$
$398$	−11.9110			−0.597047
$399$	0.964204	−	2.96752i	0.0482706	−	0.148562i
$400$	−5.01661	−	3.64478i	−0.250831	−	0.182239i
$401$	−9.88612	+	7.18269i	−0.493689	+	0.358686i	−0.806601	−	0.591096i	$-0.798695\pi$
$401$	−9.88612	+	7.18269i	−0.493689	+	0.358686i	0.312912	+	0.949782i	$0.398695\pi$
$402$	−27.1898			−1.35611
$403$	−0.927418	+	12.9937i	−0.0461980	+	0.647264i
$404$	−9.45550			−0.470429
$405$	34.9525	−	25.3945i	1.73681	−	1.26186i
$406$	10.5981	+	7.69997i	0.525975	+	0.382143i
$407$	3.13321	−	9.64304i	0.155308	−	0.477988i
$408$	−2.42425			−0.120018
$409$	14.9660			0.740021			0.370010	−	0.929028i	$-0.379354\pi$
$409$	14.9660			0.740021			0.370010	+	0.929028i	$0.379354\pi$
$410$	−8.02296	+	24.6921i	−0.396226	+	1.21946i
$411$	−3.36801	−	10.3657i	−0.166131	−	0.511300i
$412$	−0.403945	−	1.24322i	−0.0199009	−	0.0612488i
$413$	8.89645	−	6.46365i	0.437766	−	0.318056i
$414$	−10.0476	+	30.9235i	−0.493815	+	1.51981i
$415$	−33.1839	+	24.1095i	−1.62893	+	1.18349i
$416$	−1.89284	−	1.37523i	−0.0928042	−	0.0674262i
$417$	−2.33991	−	7.20150i	−0.114586	−	0.352659i
$418$	−0.562315	−	0.408546i	−0.0275037	−	0.0199826i
$419$	−12.3701	−	8.98739i	−0.604318	−	0.439063i	0.243091	−	0.970003i	$-0.421839\pi$
$419$	−12.3701	−	8.98739i	−0.604318	−	0.439063i	−0.847409	+	0.530941i	$0.821839\pi$
$420$	−7.99313	−	24.6003i	−0.390025	−	1.20037i
$421$	−17.3497	−	12.6053i	−0.845572	−	0.614344i	0.0783493	−	0.996926i	$-0.475035\pi$
$421$	−17.3497	−	12.6053i	−0.845572	−	0.614344i	−0.923922	+	0.382582i	$0.875035\pi$
$422$	−16.5927	+	12.0553i	−0.807721	+	0.586844i
$423$	−9.59371	+	29.5264i	−0.466462	+	1.43562i
$424$	2.12731	−	1.54558i	0.103311	−	0.0750602i
$425$	−1.51390	−	4.65932i	−0.0734351	−	0.226010i
$426$	−11.2782	−	34.7107i	−0.546431	−	1.68174i
$427$	7.47917	−	23.0185i	0.361942	−	1.11394i
$428$	15.0122			0.725642
$429$	12.3599			0.596742
$430$	−7.90847	+	24.3398i	−0.381380	+	1.17377i
$431$	−7.24276	−	5.26218i	−0.348872	−	0.253470i	0.399524	−	0.916723i	$-0.369175\pi$
$431$	−7.24276	−	5.26218i	−0.348872	−	0.253470i	−0.748396	+	0.663253i	$0.769175\pi$
$432$	−8.47787	+	6.15953i	−0.407892	+	0.296351i
$433$	5.18109			0.248987			0.124494	−	0.992220i	$-0.460269\pi$
$433$	5.18109			0.248987			0.124494	+	0.992220i	$0.460269\pi$
$434$	9.02998	−	10.7301i	0.433453	−	0.515061i
$435$	53.4093			2.56078
$436$	−5.71333	+	4.15098i	−0.273619	+	0.198796i
$437$	1.65542	+	1.20273i	0.0791895	+	0.0575345i
$438$	7.44003	−	22.8980i	0.355498	−	1.09411i
$439$	−2.26810			−0.108251			−0.0541253	−	0.998534i	$-0.517237\pi$
$439$	−2.26810			−0.108251			−0.0541253	+	0.998534i	$0.517237\pi$
$440$	−5.76196			−0.274691
$441$	−1.29974	+	4.00018i	−0.0618923	+	0.190485i
$442$	−0.571218	−	1.75803i	−0.0271701	−	0.0836209i
$443$	−6.83506	−	21.0361i	−0.324743	−	0.999457i	−0.971556	−	0.236809i	$-0.923899\pi$
$443$	−6.83506	−	21.0361i	−0.324743	−	0.999457i	0.646813	−	0.762649i	$-0.276101\pi$
$444$	−14.6196	+	10.6218i	−0.693816	+	0.504087i
$445$	−15.1451	+	46.6119i	−0.717948	+	2.20962i
$446$	2.85863	−	2.07692i	0.135360	−	0.0983449i
$447$	35.3213	+	25.6624i	1.67064	+	1.21379i
$448$	0.778353	+	2.39552i	0.0367737	+	0.113178i
$449$	13.4381	+	9.76338i	0.634185	+	0.460763i	0.857848	−	0.513904i	$-0.171801\pi$
$449$	13.4381	+	9.76338i	0.634185	+	0.460763i	−0.223662	+	0.974667i	$0.571801\pi$
$450$	−32.1825	−	23.3820i	−1.51710	−	1.10224i
$451$	4.12717	+	12.7021i	0.194341	+	0.598120i
$452$	−4.39284	−	3.19159i	−0.206622	−	0.150120i
$453$	11.7562	−	8.54140i	0.552356	−	0.401310i
$454$	0.173385	−	0.533625i	0.00813737	−	0.0250443i
$455$	15.9564	−	11.5930i	0.748046	−	0.543488i
$456$	0.382803	+	1.17815i	0.0179264	+	0.0551717i
$457$	−11.2417	−	34.5984i	−0.525865	−	1.61845i	−0.762599	−	0.646872i	$-0.776077\pi$
$457$	−11.2417	−	34.5984i	−0.525865	−	1.61845i	0.236734	−	0.971575i	$-0.423923\pi$
$458$	1.53556	−	4.72598i	0.0717521	−	0.220830i
$459$	−8.27927			−0.386443
$460$	16.9628			0.790896
$461$	1.07920	−	3.32144i	0.0502634	−	0.154695i	−0.922774	−	0.385341i	$-0.874084\pi$
$461$	1.07920	−	3.32144i	0.0502634	−	0.154695i	0.973038	+	0.230646i	$0.0740839\pi$
$462$	−10.7649	−	7.82116i	−0.500829	−	0.363873i
$463$	−4.90751	+	3.56551i	−0.228071	+	0.165703i	−0.695952	−	0.718088i	$-0.745018\pi$
$463$	−4.90751	+	3.56551i	−0.228071	+	0.165703i	0.467881	+	0.883791i	$0.345018\pi$
$464$	−5.20087			−0.241444
$465$	4.07061	−	57.0319i	0.188770	−	2.64479i
$466$	−9.50049			−0.440102
$467$	−2.48066	+	1.80230i	−0.114791	+	0.0834006i	−0.643700	−	0.765278i	$-0.722601\pi$
$467$	−2.48066	+	1.80230i	−0.114791	+	0.0834006i	0.528909	+	0.848679i	$0.322601\pi$
$468$	−12.1429	−	8.82236i	−0.561308	−	0.407814i
$469$	−6.89713	+	21.2272i	−0.318480	+	0.980180i
$470$	16.1965			0.747088
$471$	−56.3614			−2.59700
$472$	−1.34911	+	4.15214i	−0.0620979	+	0.191118i
$473$	4.06828	+	12.5209i	0.187060	+	0.575710i
$474$	−1.98632	−	6.11328i	−0.0912349	−	0.280792i
$475$	−2.02530	+	1.47146i	−0.0929270	+	0.0675154i
$476$	−0.614949	+	1.89262i	−0.0281862	+	0.0867481i
$477$	13.6471	−	9.91521i	0.624859	−	0.453986i
$478$	10.0006	+	7.26587i	0.457417	+	0.332333i
$479$	1.62355	+	4.99678i	0.0741820	+	0.228309i	0.981272	−	0.192629i	$-0.0617013\pi$
$479$	1.62355	+	4.99678i	0.0741820	+	0.228309i	−0.907090	+	0.420937i	$0.861701\pi$
$480$	8.30803	+	6.03614i	0.379208	+	0.275511i
$481$	−11.1475	−	8.09914i	−0.508283	−	0.369289i
$482$	6.15504	+	18.9433i	0.280355	+	0.862843i
$483$	31.6912	+	23.0250i	1.44200	+	1.04767i
$484$	6.50120	−	4.72340i	0.295509	−	0.214700i
$485$	19.4263	−	59.7879i	0.882102	−	2.71483i
$486$	−6.61191	+	4.80383i	−0.299922	+	0.217906i
$487$	−2.09983	−	6.46260i	−0.0951522	−	0.292848i	0.892141	−	0.451757i	$-0.149203\pi$
$487$	−2.09983	−	6.46260i	−0.0951522	−	0.292848i	−0.987293	+	0.158908i	$0.949203\pi$
$488$	2.96934	+	9.13868i	0.134416	+	0.413688i
$489$	−12.0206	+	36.9957i	−0.543591	+	1.67300i
$490$	2.19427			0.0991269
$491$	23.1009			1.04253			0.521264	−	0.853395i	$-0.325461\pi$
$491$	23.1009			1.04253			0.521264	+	0.853395i	$0.325461\pi$
$492$	7.35568	−	22.6385i	0.331620	−	1.02062i
$493$	−3.32427	−	2.41523i	−0.149718	−	0.108776i
$494$	−0.764175	+	0.555205i	−0.0343818	+	0.0249799i
$495$	−36.9641			−1.66141
$496$	−0.396387	+	5.55364i	−0.0177983	+	0.249366i
$497$	−29.9597			−1.34387
$498$	30.4239	−	22.1043i	1.36333	−	0.990517i
$499$	−20.3630	−	14.7946i	−0.911573	−	0.662297i	0.0298390	−	0.999555i	$-0.490501\pi$
$499$	−20.3630	−	14.7946i	−0.911573	−	0.662297i	−0.941412	+	0.337258i	$0.890501\pi$
$500$	−1.24195	+	3.82234i	−0.0555418	+	0.170940i
$501$	70.7932			3.16281
$502$	−24.6158			−1.09866
$503$	−2.30850	+	7.10483i	−0.102931	+	0.316789i	−0.989239	−	0.146307i	$-0.953261\pi$
$503$	−2.30850	+	7.10483i	−0.102931	+	0.316789i	0.886308	+	0.463096i	$0.153261\pi$
$504$	4.99328	+	15.3677i	0.222418	+	0.684533i
$505$	9.77896	+	30.0966i	0.435158	+	1.33928i
$506$	7.05951	−	5.12903i	0.313833	−	0.228013i
$507$	−7.13600	+	21.9623i	−0.316921	+	0.975382i
$508$	−3.38098	+	2.45643i	−0.150007	+	0.108986i
$509$	−27.6648	−	20.0996i	−1.22622	−	0.890901i	−0.229619	−	0.973281i	$-0.573748\pi$
$509$	−27.6648	−	20.0996i	−1.22622	−	0.890901i	−0.996601	+	0.0823797i	$0.973748\pi$
$510$	2.50718	+	7.71631i	0.111020	+	0.341684i
$511$	−15.9893	−	11.6169i	−0.707325	−	0.513901i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	1.30734	+	4.02359i	0.0577206	+	0.177646i
$514$	−16.5870	−	12.0512i	−0.731621	−	0.531554i
$515$	−3.53935	+	2.57149i	−0.155962	+	0.113313i
$516$	7.25072	−	22.3154i	0.319195	−	0.982381i
$517$	6.74057	−	4.89731i	0.296450	−	0.215384i
$518$	4.58395	+	14.1079i	0.201407	+	0.619868i
$519$	−19.2023	−	59.0986i	−0.842888	−	2.59414i
$520$	−2.41972	+	7.44713i	−0.106112	+	0.326578i
$521$	−6.22092			−0.272543			−0.136272	−	0.990671i	$-0.543512\pi$
$521$	−6.22092			−0.272543			−0.136272	+	0.990671i	$0.543512\pi$
$522$	−33.3646			−1.46033
$523$	−5.94426	+	18.2945i	−0.259924	+	0.799964i	0.732895	+	0.680342i	$0.238169\pi$
$523$	−5.94426	+	18.2945i	−0.259924	+	0.799964i	−0.992819	+	0.119623i	$0.961831\pi$
$524$	−5.60044	−	4.06896i	−0.244656	−	0.177753i
$525$	−38.7721	+	28.1696i	−1.69215	+	1.22942i
$526$	5.06994			0.221060
$527$	−2.83241	+	3.36568i	−0.123382	+	0.146611i
$528$	5.28273			0.229901
$529$	−2.17533	+	1.58047i	−0.0945797	+	0.0687162i
$530$	−7.11963	−	5.17271i	−0.309257	−	0.224688i
$531$	−8.65480	+	26.6367i	−0.375586	+	1.15594i
$532$	1.01689			0.0440876
$533$	18.1503			0.786175
$534$	13.8855	−	42.7352i	0.600884	−	1.84933i
$535$	−15.5258	−	47.7834i	−0.671237	−	2.06586i
$536$	−2.73826	−	8.42749i	−0.118275	−	0.364012i
$537$	19.7003	−	14.3131i	0.850129	−	0.617655i
$538$	−1.63699	+	5.03812i	−0.0705755	+	0.217209i
$539$	0.913200	−	0.663478i	0.0393343	−	0.0285780i
$540$	28.3735	+	20.6145i	1.22100	+	0.887109i
$541$	7.03792	+	21.6605i	0.302584	+	0.931258i	0.980568	+	0.196181i	$0.0628539\pi$
$541$	7.03792	+	21.6605i	0.302584	+	0.931258i	−0.677984	+	0.735077i	$0.737146\pi$
$542$	6.32184	+	4.59309i	0.271546	+	0.197290i
$543$	60.2844	+	43.7992i	2.58705	+	1.87960i
$544$	−0.244144	−	0.751397i	−0.0104676	−	0.0322159i
$545$	19.1212	+	13.8924i	0.819062	+	0.595084i
$546$	−14.6293	+	10.6288i	−0.626075	+	0.454870i
$547$	0.683801	−	2.10452i	0.0292372	−	0.0899830i	−0.935373	−	0.353662i	$-0.884936\pi$
$547$	0.683801	−	2.10452i	0.0292372	−	0.0899830i	0.964610	+	0.263680i	$0.0849361\pi$
$548$	2.87365	−	2.08783i	0.122756	−	0.0891876i
$549$	19.0488	+	58.6263i	0.812985	+	2.50211i
$550$	3.29898	+	10.1532i	0.140669	+	0.432934i
$551$	−0.648839	+	1.99692i	−0.0276415	+	0.0850717i
$552$	−15.5520			−0.661938
$553$	−5.27651			−0.224380
$554$	−0.318389	+	0.979901i	−0.0135271	+	0.0416320i
$555$	48.9285	+	35.5486i	2.07690	+	1.50895i
$556$	1.99646	−	1.45051i	0.0846686	−	0.0615153i
$557$	30.0188			1.27194			0.635969	−	0.771715i	$-0.280601\pi$
$557$	30.0188			1.27194			0.635969	+	0.771715i	$0.280601\pi$
$558$	−2.54289	+	35.6276i	−0.107649	+	1.50824i
$559$	17.8913			0.756719
$560$	6.81989	−	4.95494i	0.288193	−	0.209385i
$561$	3.37660	+	2.45324i	0.142560	+	0.103576i
$562$	2.18244	−	6.71685i	0.0920606	−	0.283333i
$563$	−4.60946			−0.194265			−0.0971327	−	0.995271i	$-0.530967\pi$
$563$	−4.60946			−0.194265			−0.0971327	+	0.995271i	$0.530967\pi$
$564$	−14.8494			−0.625273
$565$	−5.61560	+	17.2830i	−0.236250	+	0.727103i
$566$	6.70026	+	20.6213i	0.281633	+	0.866777i
$567$	10.0478	+	30.9240i	0.421968	+	1.29869i
$568$	9.62278	−	6.99136i	0.403763	−	0.293351i
$569$	4.81521	−	14.8197i	0.201864	−	0.621274i	−0.797963	−	0.602706i	$-0.794089\pi$
$569$	4.81521	−	14.8197i	0.201864	−	0.621274i	0.999828	−	0.0185682i	$-0.00591078\pi$
$570$	3.35410	−	2.43690i	0.140488	−	0.102070i
$571$	−1.51012	−	1.09716i	−0.0631964	−	0.0459149i	0.555739	−	0.831357i	$-0.312436\pi$
$571$	−1.51012	−	1.09716i	−0.0631964	−	0.0459149i	−0.618935	+	0.785442i	$0.712436\pi$
$572$	1.24475	+	3.83096i	0.0520458	+	0.160180i
$573$	−28.2782	−	20.5453i	−1.18134	−	0.858293i
$574$	−15.8080	−	11.4852i	−0.659814	−	0.479383i
$575$	−9.71198	−	29.8904i	−0.405017	−	1.24652i
$576$	−5.19000	−	3.77075i	−0.216250	−	0.157115i
$577$	24.4672	−	17.7765i	1.01858	−	0.740045i	0.0525919	−	0.998616i	$-0.483252\pi$
$577$	24.4672	−	17.7765i	1.01858	−	0.740045i	0.965992	+	0.258571i	$0.0832518\pi$
$578$	−5.06040	+	15.5743i	−0.210485	+	0.647806i
$579$	25.1843	−	18.2975i	1.04662	−	0.760418i
$580$	5.37879	+	16.5542i	0.223342	+	0.687376i
$581$	−9.53937	−	29.3592i	−0.395760	−	1.21802i
$582$	−17.8106	+	54.8154i	−0.738273	+	2.27217i
$583$	−4.52708			−0.187492
$584$	7.84653			0.324692
$585$	−15.5230	+	47.7747i	−0.641795	+	1.97524i
$586$	7.26649	+	5.27941i	0.300176	+	0.218091i
$587$	−17.1362	+	12.4502i	−0.707287	+	0.513874i	−0.882297	−	0.470692i	$-0.844004\pi$
$587$	−17.1362	+	12.4502i	−0.707287	+	0.513874i	0.175010	+	0.984567i	$0.444004\pi$
$588$	−2.01177			−0.0829640
$589$	2.08292	+	0.845044i	0.0858250	+	0.0348194i
$590$	14.6114			0.601541
$591$	5.81098	−	4.22192i	0.239032	−	0.173667i
$592$	−4.76454	−	3.46164i	−0.195821	−	0.142273i
$593$	12.9021	−	39.7085i	0.529824	−	1.63063i	−0.224750	−	0.974417i	$-0.572156\pi$
$593$	12.9021	−	39.7085i	0.529824	−	1.63063i	0.754574	−	0.656215i	$-0.227844\pi$
$594$	18.0415			0.740253
$595$	6.66013			0.273039
$596$	−4.39690	+	13.5323i	−0.180104	+	0.554304i
$597$	−11.2940	−	34.7593i	−0.462232	−	1.42260i
$598$	−3.66447	−	11.2781i	−0.149851	−	0.461195i
$599$	5.28226	−	3.83779i	0.215827	−	0.156808i	−0.474619	−	0.880191i	$-0.657414\pi$
$599$	5.28226	−	3.83779i	0.215827	−	0.156808i	0.690446	+	0.723384i	$0.257414\pi$
$600$	5.87963	−	18.0956i	0.240035	−	0.738751i
$601$	4.23546	−	3.07724i	0.172768	−	0.125523i	−0.498041	−	0.867154i	$-0.665947\pi$
$601$	4.23546	−	3.07724i	0.172768	−	0.125523i	0.670809	+	0.741630i	$0.265947\pi$
$602$	−15.5824	−	11.3213i	−0.635093	−	0.461422i
$603$	−17.5664	−	54.0640i	−0.715361	−	2.20165i
$604$	3.83136	+	2.78365i	0.155896	+	0.113265i
$605$	−21.7580	−	15.8081i	−0.884590	−	0.642692i
$606$	−8.96564	−	27.5934i	−0.364204	−	1.12091i
$607$	−16.4180	−	11.9284i	−0.666386	−	0.484157i	0.202428	−	0.979297i	$-0.435117\pi$
$607$	−16.4180	−	11.9284i	−0.666386	−	0.484157i	−0.868813	+	0.495140i	$0.835117\pi$
$608$	−0.326615	+	0.237300i	−0.0132460	+	0.00962377i
$609$	−12.4213	+	38.2288i	−0.503336	+	1.54911i
$610$	26.0172	−	18.9026i	1.05341	−	0.765344i
$611$	−3.49892	−	10.7686i	−0.141551	−	0.435650i
$612$	−1.56623	−	4.82035i	−0.0633110	−	0.194851i
$613$	−0.456496	+	1.40495i	−0.0184377	+	0.0567454i	−0.959852	−	0.280507i	$-0.909497\pi$
$613$	−0.456496	+	1.40495i	−0.0184377	+	0.0567454i	0.941414	+	0.337252i	$0.109497\pi$
$614$	−14.5413			−0.586839
$615$	−79.6648			−3.21240
$616$	1.34005	−	4.12425i	0.0539921	−	0.166171i
$617$	16.6778	+	12.1171i	0.671421	+	0.487816i	0.870501	−	0.492167i	$-0.163795\pi$
$617$	16.6778	+	12.1171i	0.671421	+	0.487816i	−0.199079	+	0.979983i	$0.563795\pi$
$618$	3.24498	−	2.35762i	0.130532	−	0.0948372i
$619$	−2.74094			−0.110168			−0.0550839	−	0.998482i	$-0.517543\pi$
$619$	−2.74094			−0.110168			−0.0550839	+	0.998482i	$0.517543\pi$
$620$	18.0870	−	4.48193i	0.726391	−	0.179999i
$621$	−53.1131			−2.13135
$622$	8.60777	−	6.25391i	0.345140	−	0.250759i
$623$	−29.8412	−	21.6809i	−1.19556	−	0.868627i
$624$	2.21847	−	6.82775i	0.0888099	−	0.273329i
$625$	−17.5535			−0.702142
$626$	3.37758			0.134995
$627$	0.659051	−	2.02835i	0.0263200	−	0.0810046i
$628$	−5.67609	−	17.4692i	−0.226501	−	0.697098i
$629$	−1.43783	−	4.42520i	−0.0573302	−	0.176444i
$630$	43.7509	−	31.7869i	1.74308	−	1.26642i
$631$	−12.8289	+	39.4831i	−0.510709	+	1.57180i	0.280248	+	0.959928i	$0.409583\pi$
$631$	−12.8289	+	39.4831i	−0.510709	+	1.57180i	−0.790957	+	0.611872i	$0.790417\pi$
$632$	1.69477	−	1.23132i	0.0674143	−	0.0489794i
$633$	−50.9134	−	36.9908i	−2.02363	−	1.47025i
$634$	2.02016	+	6.21740i	0.0802306	+	0.246924i
$635$	11.3154	+	8.22109i	0.449036	+	0.326244i
$636$	6.52749	+	4.74250i	0.258832	+	0.188052i
$637$	−0.474027	−	1.45890i	−0.0187816	−	0.0578039i
$638$	7.24399	+	5.26307i	0.286792	+	0.208367i
$639$	61.7320	−	44.8509i	2.44208	−	1.77427i
$640$	−1.03421	+	3.18297i	−0.0408807	+	0.125818i
$641$	7.93753	−	5.76696i	0.313514	−	0.227781i	−0.419889	−	0.907575i	$-0.637931\pi$
$641$	7.93753	−	5.76696i	0.313514	−	0.227781i	0.733403	+	0.679794i	$0.237931\pi$
$642$	14.2345	+	43.8092i	0.561790	+	1.72901i
$643$	11.7291	+	36.0983i	0.462549	+	1.42358i	0.862039	+	0.506842i	$0.169187\pi$
$643$	11.7291	+	36.0983i	0.462549	+	1.42358i	−0.399490	+	0.916738i	$0.630813\pi$
$644$	−3.94502	+	12.1415i	−0.155455	+	0.478443i
$645$	−78.5280			−3.09204
$646$	−0.318964			−0.0125495
$647$	−9.54343	+	29.3717i	−0.375191	+	1.15472i	0.568159	+	0.822919i	$0.307656\pi$
$647$	−9.54343	+	29.3717i	−0.375191	+	1.15472i	−0.943350	+	0.331800i	$0.892344\pi$
$648$	−10.4437	−	7.58776i	−0.410266	−	0.298076i
$649$	6.08089	−	4.41803i	0.238696	−	0.173423i
$650$	14.5081			0.569053
$651$	39.8751	+	16.1774i	1.56283	+	0.634044i
$652$	−12.6774			−0.496485
$653$	3.12889	−	2.27327i	0.122443	−	0.0889601i	−0.524878	−	0.851177i	$-0.675889\pi$
$653$	3.12889	−	2.27327i	0.122443	−	0.0889601i	0.647321	+	0.762217i	$0.275889\pi$
$654$	−17.5309	−	12.7369i	−0.685512	−	0.498053i
$655$	−7.15933	+	22.0342i	−0.279738	+	0.860946i
$656$	7.75758			0.302883
$657$	50.3370			1.96383
$658$	−3.76679	+	11.5930i	−0.146845	+	0.451942i
$659$	9.22225	+	28.3832i	0.359248	+	1.10565i	0.953505	+	0.301376i	$0.0974460\pi$
$659$	9.22225	+	28.3832i	0.359248	+	1.10565i	−0.594258	+	0.804275i	$0.702554\pi$
$660$	−5.46345	−	16.8148i	−0.212665	−	0.654514i
$661$	−33.3584	+	24.2363i	−1.29749	+	0.942684i	−0.999928	−	0.0120174i	$-0.996175\pi$
$661$	−33.3584	+	24.2363i	−1.29749	+	0.942684i	−0.297565	+	0.954701i	$0.596175\pi$
$662$	8.65382	−	26.6337i	0.336340	−	1.03515i
$663$	4.58872	−	3.33390i	0.178211	−	0.129478i
$664$	9.91519	+	7.20381i	0.384784	+	0.279562i
$665$	−1.05167	−	3.23671i	−0.0407821	−	0.125514i
$666$	−30.5654	−	22.2071i	−1.18439	−	0.860507i
$667$	−21.3258	−	15.4941i	−0.825740	−	0.599935i
$668$	7.12950	+	21.9424i	0.275849	+	0.848975i
$669$	8.77148	+	6.37285i	0.339125	+	0.246389i
$670$	−23.9925	+	17.4316i	−0.926911	+	0.673441i
$671$	5.11215	−	15.7336i	0.197352	−	0.607388i
$672$	−6.25268	+	4.54284i	−0.241202	+	0.175244i
$673$	−12.5044	−	38.4845i	−0.482008	−	1.48347i	−0.836268	−	0.548321i	$-0.815267\pi$
$673$	−12.5044	−	38.4845i	−0.482008	−	1.48347i	0.354260	−	0.935147i	$-0.384733\pi$
$674$	9.18116	+	28.2567i	0.353645	+	1.08841i
$675$	20.0800	−	61.8000i	0.772881	−	2.37868i
$676$	−7.52589			−0.289457
$677$	43.9447			1.68893			0.844466	−	0.535609i	$-0.179918\pi$
$677$	43.9447			1.68893			0.844466	+	0.535609i	$0.179918\pi$
$678$	5.14855	−	15.8456i	0.197729	−	0.608547i
$679$	38.2766	+	27.8096i	1.46892	+	1.06723i
$680$	−2.13918	+	1.55420i	−0.0820337	+	0.0596009i
$681$	1.72165			0.0659737
$682$	6.17216	−	7.33421i	0.236344	−	0.280841i
$683$	−4.87945			−0.186707			−0.0933535	−	0.995633i	$-0.529759\pi$
$683$	−4.87945			−0.186707			−0.0933535	+	0.995633i	$0.529759\pi$
$684$	−2.09530	+	1.52232i	−0.0801156	+	0.0582074i
$685$	−9.61744	−	6.98748i	−0.367463	−	0.266978i
$686$	−5.95879	+	18.3393i	−0.227507	+	0.700196i
$687$	15.2475			0.581730
$688$	7.64688			0.291534
$689$	−1.90114	+	5.85109i	−0.0724275	+	0.222909i
$690$	16.0840	+	49.5016i	0.612309	+	1.88449i
$691$	11.0165	+	33.9054i	0.419088	+	1.28982i	0.908543	+	0.417792i	$0.137196\pi$
$691$	11.0165	+	33.9054i	0.419088	+	1.28982i	−0.489455	+	0.872029i	$0.662804\pi$
$692$	16.3838	−	11.9035i	0.622818	−	0.452504i
$693$	8.59666	−	26.4578i	0.326560	−	1.00505i
$694$	7.94487	−	5.77228i	0.301583	−	0.219113i
$695$	−6.68168	−	4.85452i	−0.253451	−	0.184143i
$696$	−4.93143	−	15.1774i	−0.186925	−	0.575297i
$697$	4.95846	+	3.60253i	0.187815	+	0.136456i
$698$	−0.830159	−	0.603146i	−0.0314220	−	0.0228294i
$699$	−9.00830	−	27.7247i	−0.340725	−	1.04864i
$700$	−12.6358	−	9.18048i	−0.477590	−	0.346990i
$701$	16.4492	−	11.9511i	0.621279	−	0.451386i	−0.232089	−	0.972695i	$-0.574556\pi$
$701$	16.4492	−	11.9511i	0.621279	−	0.451386i	0.853368	+	0.521309i	$0.174556\pi$
$702$	7.57649	−	23.3180i	0.285956	−	0.880083i
$703$	−1.92353	+	1.39753i	−0.0725474	+	0.0527087i
$704$	0.532018	+	1.63738i	0.0200512	+	0.0617112i
$705$	15.3574	+	47.2652i	0.578393	+	1.78011i
$706$	6.49313	−	19.9838i	0.244372	−	0.752100i
$707$	−23.8165			−0.895713
$708$	−13.3961			−0.503458
$709$	−2.96678	+	9.13080i	−0.111420	+	0.342914i	−0.991183	−	0.132497i	$-0.957701\pi$
$709$	−2.96678	+	9.13080i	−0.111420	+	0.342914i	0.879764	+	0.475411i	$0.157701\pi$
$710$	−32.2052	−	23.3985i	−1.20864	−	0.878129i
$711$	10.8723	−	7.89917i	0.407742	−	0.296242i
$712$	14.6442			0.548813
$713$	−18.1704	+	21.5914i	−0.680488	+	0.808606i
$714$	−6.10621			−0.228519
$715$	10.9065	−	7.92402i	0.407879	−	0.296342i
$716$	6.42033	+	4.66464i	0.239939	+	0.174326i
$717$	−11.7210	+	36.0736i	−0.437730	+	1.34719i
$718$	−30.4196			−1.13525
$719$	−36.7351			−1.36999			−0.684994	−	0.728549i	$-0.740195\pi$
$719$	−36.7351			−1.36999			−0.684994	+	0.728549i	$0.740195\pi$
$720$	−6.63465	+	20.4193i	−0.247259	+	0.760984i
$721$	−1.01746	−	3.13141i	−0.0378921	−	0.116620i
$722$	−5.82096	−	17.9151i	−0.216634	−	0.666730i
$723$	−49.4448	+	35.9238i	−1.83887	+	1.33602i
$724$	−7.50438	+	23.0961i	−0.278898	+	0.858360i
$725$	26.0908	−	18.9560i	0.968986	−	0.704010i
$726$	19.9484	+	14.4934i	0.740355	+	0.537899i
$727$	5.13927	+	15.8170i	0.190605	+	0.586622i	1.00000		0.000643148i	$-0.000204720\pi$
$727$	5.13927	+	15.8170i	0.190605	+	0.586622i	−0.809395	+	0.587265i	$0.800205\pi$
$728$	−4.76769	−	3.46393i	−0.176702	−	0.128382i
$729$	11.0429	+	8.02313i	0.408996	+	0.297153i
$730$	−8.11495	−	24.9752i	−0.300348	−	0.924375i
$731$	4.88770	+	3.55112i	0.180778	+	0.131343i
$732$	−23.8533	+	17.3305i	−0.881645	+	0.640552i
$733$	1.09540	−	3.37129i	0.0404594	−	0.124521i	−0.928787	−	0.370615i	$-0.879147\pi$
$733$	1.09540	−	3.37129i	0.0404594	−	0.124521i	0.969246	+	0.246093i	$0.0791470\pi$
$734$	−20.8770	+	15.1681i	−0.770585	+	0.559863i
$735$	2.08059	+	6.40340i	0.0767437	+	0.236193i
$736$	−1.56623	−	4.82035i	−0.0577319	−	0.177681i
$737$	−4.71432	+	14.5092i	−0.173654	+	0.534452i
$738$	49.7663			1.83192
$739$	9.42152			0.346576			0.173288	−	0.984871i	$-0.444561\pi$
$739$	9.42152			0.346576			0.173288	+	0.984871i	$0.444561\pi$
$740$	−6.09076	+	18.7454i	−0.223901	+	0.689096i
$741$	−2.34481	−	1.70360i	−0.0861386	−	0.0625834i
$742$	5.35828	−	3.89302i	0.196709	−	0.142917i
$743$	0.492369			0.0180633			0.00903163	−	0.999959i	$-0.497125\pi$
$743$	0.492369			0.0180633			0.00903163	+	0.999959i	$0.497125\pi$
$744$	−16.5827	+	4.10917i	−0.607951	+	0.150649i
$745$	47.6201			1.74467
$746$	−10.1003	+	7.33829i	−0.369798	+	0.268674i
$747$	63.6078	+	46.2138i	2.32729	+	1.69087i
$748$	−0.420329	+	1.29364i	−0.0153688	+	0.0473002i
$749$	37.8128			1.38165
$750$	−12.3321			−0.450305
$751$	12.6383	−	38.8968i	0.461179	−	1.41936i	−0.402546	−	0.915400i	$-0.631875\pi$
$751$	12.6383	−	38.8968i	0.461179	−	1.41936i	0.863725	−	0.503964i	$-0.168125\pi$
$752$	−1.49547	−	4.60258i	−0.0545341	−	0.167839i
$753$	−23.3405	−	71.8347i	−0.850575	−	2.61780i
$754$	9.84443	−	7.15240i	0.358513	−	0.260475i
$755$	4.89783	−	15.0740i	0.178250	−	0.548598i
$756$	−21.3541	+	15.5146i	−0.776640	+	0.564262i
$757$	11.8157	+	8.58462i	0.429449	+	0.312013i	0.781429	−	0.623995i	$-0.214491\pi$
$757$	11.8157	+	8.58462i	0.429449	+	0.312013i	−0.351979	+	0.936008i	$0.614491\pi$
$758$	0.582244	+	1.79196i	0.0211481	+	0.0650870i
$759$	21.6615	+	15.7380i	0.786263	+	0.571254i
$760$	1.09310	+	0.794187i	0.0396511	+	0.0288082i
$761$	16.6393	+	51.2106i	0.603175	+	1.85638i	0.508877	+	0.860839i	$0.330061\pi$
$761$	16.6393	+	51.2106i	0.603175	+	1.85638i	0.0942985	+	0.995544i	$0.469939\pi$
$762$	−10.3743	−	7.53734i	−0.375820	−	0.273049i
$763$	−14.3907	+	10.4555i	−0.520980	+	0.378514i
$764$	3.52016	−	10.8339i	0.127355	−	0.391958i
$765$	−13.7232	+	9.97050i	−0.496164	+	0.360484i
$766$	4.02861	+	12.3988i	0.145560	+	0.447986i
$767$	−3.15649	−	9.71468i	−0.113974	−	0.350777i
$768$	0.948193	−	2.91824i	0.0342150	−	0.105303i
$769$	41.8213			1.50811			0.754057	−	0.656809i	$-0.228094\pi$
$769$	41.8213			1.50811			0.754057	+	0.656809i	$0.228094\pi$
$770$	−14.5132			−0.523021
$771$	19.4405	−	59.8316i	0.700132	−	2.15478i
$772$	8.20759	+	5.96317i	0.295398	+	0.214619i
$773$	−15.9544	+	11.5915i	−0.573839	+	0.416919i	−0.836498	−	0.547970i	$-0.815401\pi$
$773$	−15.9544	+	11.5915i	−0.573839	+	0.416919i	0.262658	+	0.964889i	$0.415401\pi$
$774$	49.0561			1.76329
$775$	−18.2533	−	29.3052i	−0.655677	−	1.05267i
$776$	−18.7837			−0.674296
$777$	−36.8239	+	26.7541i	−1.32105	+	0.959799i
$778$	−8.35053	−	6.06702i	−0.299381	−	0.217513i
$779$	0.967802	−	2.97859i	0.0346751	−	0.106719i
$780$	−24.0269			−0.860300
$781$	−20.4780			−0.732760
$782$	1.23742	−	3.80839i	0.0442501	−	0.136188i
$783$	−16.8418	−	51.8336i	−0.601876	−	1.85238i
$784$	−0.202603	−	0.623548i	−0.00723583	−	0.0222696i
$785$	−49.7337	+	36.1336i	−1.77507	+	1.28967i
$786$	6.56389	−	20.2016i	0.234126	−	0.720566i
$787$	−3.06647	+	2.22792i	−0.109308	+	0.0794168i	−0.641096	−	0.767460i	$-0.721520\pi$
$787$	−3.06647	+	2.22792i	−0.109308	+	0.0794168i	0.531789	+	0.846877i	$0.321520\pi$
$788$	1.89380	+	1.37593i	0.0674640	+	0.0490154i
$789$	4.80728	+	14.7953i	0.171144	+	0.526726i
$790$	−5.67201	−	4.12095i	−0.201801	−	0.146617i
$791$	−11.0647	−	8.03897i	−0.393415	−	0.285833i
$792$	3.41300	+	10.5041i	0.121276	+	0.373248i
$793$	−18.1883	−	13.2145i	−0.645884	−	0.469262i
$794$	−12.0223	+	8.73475i	−0.426657	+	0.309985i
$795$	8.34443	−	25.6815i	0.295946	−	0.910829i
$796$	9.63624	−	7.00114i	0.341548	−	0.248149i
$797$	3.83584	+	11.8055i	0.135872	+	0.418172i	0.995725	−	0.0923708i	$-0.0294445\pi$
$797$	3.83584	+	11.8055i	0.135872	+	0.418172i	−0.859852	+	0.510543i	$0.829444\pi$
$798$	0.964204	+	2.96752i	0.0341325	+	0.105049i
$799$	1.18152	−	3.63634i	0.0417991	−	0.128644i
$800$	6.20087			0.219234
$801$	93.9451			3.31939
$802$	3.77616	−	11.6218i	0.133341	−	0.410381i
$803$	−10.9290	−	7.94036i	−0.385675	−	0.280209i
$804$	21.9970	−	15.9818i	0.775776	−	0.563634i
$805$	42.7260			1.50589
$806$	−6.88723	−	11.0573i	−0.242592	−	0.389476i
$807$	−16.2546			−0.572190
$808$	7.64966	−	5.55780i	0.269114	−	0.195523i
$809$	18.7740	+	13.6401i	0.660059	+	0.479561i	0.866683	−	0.498859i	$-0.166248\pi$
$809$	18.7740	+	13.6401i	0.660059	+	0.479561i	−0.206624	+	0.978420i	$0.566248\pi$
$810$	−13.3507	+	41.0892i	−0.469095	+	1.44373i
$811$	39.4836			1.38646			0.693228	−	0.720718i	$-0.256188\pi$
$811$	39.4836			1.38646			0.693228	+	0.720718i	$0.256188\pi$
$812$	−13.1000			−0.459719
$813$	−7.40940	+	22.8038i	−0.259859	+	0.799763i
$814$	3.13321	+	9.64304i	0.109819	+	0.337988i
$815$	13.1111	+	40.3517i	0.459261	+	1.41346i
$816$	1.96126	−	1.42494i	0.0686578	−	0.0498828i
$817$	0.953992	−	2.93608i	0.0333759	−	0.102721i
$818$	−12.1077	+	8.79679i	−0.423337	+	0.307573i
$819$	−30.5857	−	22.2218i	−1.06875	−	0.776492i
$820$	−8.02296	−	24.6921i	−0.280174	−	0.862286i
$821$	14.5456	+	10.5680i	0.507644	+	0.368825i	0.811929	−	0.583756i	$-0.198418\pi$
$821$	14.5456	+	10.5680i	0.507644	+	0.368825i	−0.304285	+	0.952581i	$0.598418\pi$
$822$	8.81755	+	6.40633i	0.307547	+	0.223446i
$823$	1.14856	+	3.53490i	0.0400362	+	0.123219i	0.969077	−	0.246759i	$-0.0793654\pi$
$823$	1.14856	+	3.53490i	0.0400362	+	0.123219i	−0.929041	+	0.369977i	$0.879365\pi$
$824$	1.05754	+	0.768349i	0.0368412	+	0.0267667i
$825$	−26.5014	+	19.2544i	−0.922661	+	0.670353i
$826$	−3.39814	+	10.4584i	−0.118237	+	0.363895i
$827$	−31.4516	+	22.8509i	−1.09368	+	0.794605i	−0.980017	−	0.198914i	$-0.936259\pi$
$827$	−31.4516	+	22.8509i	−1.09368	+	0.794605i	−0.113663	+	0.993519i	$0.536259\pi$
$828$	−10.0476	−	30.9235i	−0.349180	−	1.07466i
$829$	6.49478	+	19.9889i	0.225573	+	0.694243i	0.998233	+	0.0594223i	$0.0189259\pi$
$829$	6.49478	+	19.9889i	0.225573	+	0.694243i	−0.772660	+	0.634820i	$0.781074\pi$
$830$	12.6751	−	39.0100i	0.439959	−	1.35406i
$831$	−3.16148			−0.109671
$832$	2.33968			0.0811139
$833$	0.160070	−	0.492644i	0.00554609	−	0.0170691i
$834$	6.12596	+	4.45077i	0.212125	+	0.154118i
$835$	62.4684	−	45.3860i	2.16181	−	1.57065i
$836$	0.695060			0.0240392
$837$	−56.6330	+	14.0336i	−1.95752	+	0.485072i
$838$	15.2903			0.528193
$839$	−16.9514	+	12.3159i	−0.585227	+	0.425192i	−0.840605	−	0.541649i	$-0.817800\pi$
$839$	−16.9514	+	12.3159i	−0.585227	+	0.425192i	0.255378	+	0.966841i	$0.417800\pi$
$840$	20.9263	+	15.2038i	0.722025	+	0.524582i
$841$	−0.602869	+	1.85544i	−0.0207886	+	0.0639807i
$842$	21.4454			0.739057
$843$	21.6708			0.746380
$844$	6.33786	−	19.5059i	0.218158	−	0.671422i
$845$	7.78334	+	23.9547i	0.267755	+	0.824066i
$846$	−9.59371	−	29.5264i	−0.329839	−	1.01514i
$847$	16.3752	−	11.8973i	0.562660	−	0.408796i
$848$	−0.812562	+	2.50081i	−0.0279035	+	0.0858781i
$849$	−53.8247	+	39.1059i	−1.84726	+	1.34211i
$850$	3.96345	+	2.87962i	0.135945	+	0.0987700i
$851$	−9.22398	−	28.3885i	−0.316194	−	0.973145i
$852$	29.5267	+	21.4524i	1.01157	+	0.734948i
$853$	−43.0571	−	31.2828i	−1.47425	−	1.07110i	−0.979355	−	0.202150i	$-0.935207\pi$
$853$	−43.0571	−	31.2828i	−1.47425	−	1.07110i	−0.494894	−	0.868954i	$-0.664793\pi$
$854$	7.47917	+	23.0185i	0.255932	+	0.787677i
$855$	7.01247	+	5.09486i	0.239821	+	0.174241i
$856$	−12.1451	+	8.82395i	−0.415112	+	0.301596i
$857$	−4.36225	+	13.4256i	−0.149012	+	0.458611i	−0.997505	−	0.0705951i	$-0.977510\pi$
$857$	−4.36225	+	13.4256i	−0.149012	+	0.458611i	0.848493	+	0.529206i	$0.177510\pi$
$858$	−9.99938	+	7.26498i	−0.341373	+	0.248022i
$859$	−6.54750	−	20.1511i	−0.223398	−	0.687548i	−0.998450	−	0.0556511i	$-0.982277\pi$
$859$	−6.54750	−	20.1511i	−0.223398	−	0.687548i	0.775052	−	0.631897i	$-0.217723\pi$
$860$	−7.90847	−	24.3398i	−0.269676	−	0.829979i
$861$	18.5275	−	57.0218i	0.631416	−	1.94330i
$862$	8.95255			0.304925
$863$	3.42261			0.116507			0.0582535	−	0.998302i	$-0.481447\pi$
$863$	3.42261			0.116507			0.0582535	+	0.998302i	$0.481447\pi$
$864$	3.23826	−	9.96634i	0.110168	−	0.339062i
$865$	−54.8327	−	39.8383i	−1.86437	−	1.35454i
$866$	−4.19159	+	3.04537i	−0.142436	+	0.103486i
$867$	−50.2478			−1.70650
$868$	−0.998419	+	13.9885i	−0.0338886	+	0.474801i
$869$	−3.60659			−0.122345
$870$	−43.2090	+	31.3932i	−1.46492	+	1.06433i
$871$	16.7728	+	12.1862i	0.568326	+	0.412913i
$872$	2.18230	−	6.71642i	0.0739019	−	0.227447i
$873$	−120.501			−4.07834
$874$	−2.04621			−0.0692141
$875$	−3.12823	+	9.62771i	−0.105754	+	0.325476i
$876$	7.44003	+	22.8980i	0.251375	+	0.773653i
$877$	−15.1673	−	46.6803i	−0.512165	−	1.57628i	−0.788382	−	0.615186i	$-0.789081\pi$
$877$	−15.1673	−	46.6803i	−0.512165	−	1.57628i	0.276218	−	0.961095i	$-0.410919\pi$
$878$	1.83493	−	1.33316i	0.0619260	−	0.0449919i
$879$	−8.51655	+	26.2113i	−0.287256	+	0.884084i
$880$	4.66152	−	3.38679i	0.157140	−	0.114169i
$881$	−21.4239	−	15.5654i	−0.721789	−	0.524411i	0.165166	−	0.986266i	$-0.447184\pi$
$881$	−21.4239	−	15.5654i	−0.721789	−	0.524411i	−0.886955	+	0.461855i	$0.847184\pi$
$882$	−1.29974	−	4.00018i	−0.0437644	−	0.134693i
$883$	−13.4921	−	9.80261i	−0.454047	−	0.329884i	0.337145	−	0.941453i	$-0.390539\pi$
$883$	−13.4921	−	9.80261i	−0.454047	−	0.329884i	−0.791191	+	0.611569i	$0.790539\pi$
$884$	1.49547	+	1.08652i	0.0502981	+	0.0365437i
$885$	13.8544	+	42.6395i	0.465711	+	1.43331i
$886$	17.8944	+	13.0011i	0.601175	+	0.436779i
$887$	−13.8834	+	10.0869i	−0.466160	+	0.338685i	−0.795943	−	0.605372i	$-0.793024\pi$
$887$	−13.8834	+	10.0869i	−0.466160	+	0.338685i	0.329783	+	0.944057i	$0.393024\pi$
$888$	5.58419	−	17.1864i	0.187393	−	0.576737i
$889$	−8.51602	+	6.18725i	−0.285618	+	0.207514i
$890$	−15.1451	−	46.6119i	−0.507666	−	1.56243i
$891$	6.86787	+	21.1371i	0.230082	+	0.708120i
$892$	−1.09190	+	3.36052i	−0.0365595	+	0.112519i
$893$	−1.95377			−0.0653804
$894$	−43.6595			−1.46019
$895$	8.20744	−	25.2599i	0.274345	−	0.844346i
$896$	−2.03775	−	1.48051i	−0.0680766	−	0.0494605i
$897$	29.4375	−	21.3876i	0.982890	−	0.714112i
$898$	−16.6105			−0.554298
$899$	−26.8330	−	10.8862i	−0.894932	−	0.363076i
$900$	39.7798			1.32599
$901$	−1.68072	+	1.22111i	−0.0559928	+	0.0406811i
$902$	−10.8051	−	7.85035i	−0.359770	−	0.261388i
$903$	18.2631	−	56.2081i	0.607758	−	1.87049i
$904$	5.42985			0.180594
$905$	81.2753			2.70168
$906$	−4.49048	+	13.8203i	−0.149186	+	0.459148i
$907$	−11.5936	−	35.6815i	−0.384960	−	1.18479i	−0.936509	−	0.350643i	$-0.885963\pi$
$907$	−11.5936	−	35.6815i	−0.384960	−	1.18479i	0.551549	−	0.834143i	$-0.314037\pi$
$908$	0.173385	+	0.533625i	0.00575399	+	0.0177090i
$909$	49.0740	−	35.6544i	1.62768	−	1.18258i
$910$	−6.09479	+	18.7578i	−0.202040	+	0.621817i
$911$	21.1009	−	15.3307i	0.699104	−	0.507929i	−0.180536	−	0.983568i	$-0.557783\pi$
$911$	21.1009	−	15.3307i	0.699104	−	0.507929i	0.879640	+	0.475640i	$0.157783\pi$
$912$	−1.00219	−	0.728134i	−0.0331858	−	0.0241109i
$913$	−6.52033	−	20.0675i	−0.215792	−	0.664138i
$914$	29.4312	+	21.3830i	0.973497	+	0.707287i
$915$	79.8316	+	58.0011i	2.63915	+	1.91746i
$916$	1.53556	+	4.72598i	0.0507364	+	0.156151i
$917$	−14.1064	−	10.2489i	−0.465834	−	0.338448i
$918$	6.69807	−	4.86643i	0.221069	−	0.160616i
$919$	−15.6792	+	48.2557i	−0.517210	+	1.59181i	0.262016	+	0.965064i	$0.415613\pi$
$919$	−15.6792	+	48.2557i	−0.517210	+	1.59181i	−0.779225	+	0.626744i	$0.784387\pi$
$920$	−13.7232	+	9.97050i	−0.452441	+	0.328718i
$921$	−13.7880	−	42.4350i	−0.454328	−	1.39828i
$922$	1.07920	+	3.32144i	0.0355416	+	0.109386i
$923$	−8.59968	+	26.4671i	−0.283062	+	0.871175i
$924$	13.3062			0.437741
$925$	36.5188			1.20073
$926$	1.87450	−	5.76912i	0.0615999	−	0.189585i
$927$	6.78433	+	4.92910i	0.222827	+	0.161893i
$928$	4.20759	−	3.05700i	0.138121	−	0.100351i
$929$	−46.0097			−1.50953			−0.754764	−	0.655996i	$-0.772249\pi$
$929$	−46.0097			−1.50953			−0.754764	+	0.655996i	$0.772249\pi$
$930$	30.2293	+	48.5324i	0.991258	+	1.59144i
$931$	−0.264693			−0.00867495
$932$	7.68606	−	5.58425i	0.251765	−	0.182918i
$933$	26.4122	+	19.1896i	0.864698	+	0.628240i
$934$	0.947526	−	2.91619i	0.0310040	−	0.0954205i
$935$	4.55232			0.148877
$936$	15.0095			0.490601
$937$	11.1062	−	34.1815i	0.362825	−	1.11666i	−0.588507	−	0.808492i	$-0.700284\pi$
$937$	11.1062	−	34.1815i	0.362825	−	1.11666i	0.951332	−	0.308168i	$-0.0997158\pi$
$938$	−6.89713	−	21.2272i	−0.225199	−	0.693092i
$939$	3.20260	+	9.85660i	0.104513	+	0.321658i
$940$	−13.1032	+	9.52006i	−0.427380	+	0.310510i
$941$	5.65993	−	17.4195i	0.184509	−	0.567859i	−0.815431	−	0.578854i	$-0.803500\pi$
$941$	5.65993	−	17.4195i	0.184509	−	0.567859i	0.999940	+	0.0109954i	$0.00350002\pi$
$942$	45.5973	−	33.1284i	1.48564	−	1.07938i
$943$	31.8095	+	23.1109i	1.03586	+	0.752595i
$944$	−1.34911	−	4.15214i	−0.0439098	−	0.135141i
$945$	71.4672	+	51.9240i	2.32483	+	1.68909i
$946$	−10.6509	−	7.73832i	−0.346290	−	0.251595i
$947$	−16.2732	−	50.0836i	−0.528807	−	1.62750i	−0.756663	−	0.653805i	$-0.773172\pi$
$947$	−16.2732	−	50.0836i	−0.528807	−	1.62750i	0.227857	−	0.973695i	$-0.426828\pi$
$948$	5.20026	+	3.77821i	0.168897	+	0.122711i
$949$	−14.8522	+	10.7908i	−0.482124	+	0.350284i
$950$	0.773594	−	2.38088i	0.0250987	−	0.0772459i
$951$	−16.2284	+	11.7906i	−0.526241	+	0.382336i
$952$	−0.614949	−	1.89262i	−0.0199306	−	0.0613402i
$953$	15.3296	+	47.1796i	0.496574	+	1.52830i	0.814489	+	0.580178i	$0.197017\pi$
$953$	15.3296	+	47.1796i	0.496574	+	1.52830i	−0.317915	+	0.948119i	$0.602983\pi$
$954$	−5.21274	+	16.0431i	−0.168769	+	0.519416i
$955$	−38.1246			−1.23368
$956$	−12.3614			−0.399797
$957$	−8.49019	+	26.1301i	−0.274449	+	0.844667i
$958$	−4.25051	−	3.08818i	−0.137328	−	0.0997745i
$959$	7.23815	−	5.25882i	0.233732	−	0.169816i
$960$	−10.2693			−0.331440
$961$	−13.6697	+	27.8234i	−0.440958	+	0.897528i
$962$	13.7791			0.444255
$963$	−77.9133	+	56.6073i	−2.51072	+	1.82415i
$964$	−16.1141	−	11.7076i	−0.519001	−	0.377076i
$965$	10.4922	−	32.2917i	0.337756	−	1.03951i
$966$	−39.1725			−1.26035
$967$	56.5038			1.81704			0.908520	−	0.417841i	$-0.137213\pi$
$967$	56.5038			1.81704			0.908520	+	0.417841i	$0.137213\pi$
$968$	−2.48324	+	7.64262i	−0.0798143	+	0.245643i
$969$	−0.302439	−	0.930812i	−0.00971575	−	0.0299020i
$970$	19.4263	+	59.7879i	0.623740	+	1.91968i
$971$	1.37242	−	0.997121i	0.0440430	−	0.0319991i	−0.565546	−	0.824717i	$-0.691335\pi$
$971$	1.37242	−	0.997121i	0.0440430	−	0.0319991i	0.609589	+	0.792718i	$0.291335\pi$
$972$	2.52552	−	7.77276i	0.0810062	−	0.249311i
$973$	5.02868	−	3.65355i	0.161212	−	0.117127i
$974$	5.49742	+	3.99411i	0.176149	+	0.127979i
$975$	13.7565	+	42.3380i	0.440559	+	1.35590i
$976$	−7.77382	−	5.64801i	−0.248834	−	0.180788i
$977$	16.5809	+	12.0467i	0.530470	+	0.385409i	0.820533	−	0.571599i	$-0.193677\pi$
$977$	16.5809	+	12.0467i	0.530470	+	0.385409i	−0.290064	+	0.957007i	$0.593677\pi$
$978$	−12.0206	−	36.9957i	−0.384377	−	1.18299i
$979$	−20.3970	−	14.8193i	−0.651891	−	0.473627i
$980$	−1.77520	+	1.28976i	−0.0567067	+	0.0411998i
$981$	13.9999	−	43.0871i	0.446981	−	1.37567i
$982$	−18.6890	+	13.5784i	−0.596390	+	0.433303i
$983$	3.38925	+	10.4310i	0.108100	+	0.332699i	0.990446	−	0.137904i	$-0.0440365\pi$
$983$	3.38925	+	10.4310i	0.108100	+	0.332699i	−0.882345	+	0.470603i	$0.844037\pi$
$984$	7.35568	+	22.6385i	0.234491	+	0.721688i
$985$	2.42095	−	7.45091i	0.0771378	−	0.237406i
$986$	4.10903			0.130858
$987$	−37.4027			−1.19054
$988$	0.291889	−	0.898341i	0.00928622	−	0.0285800i
$989$	31.3555	+	22.7811i	0.997048	+	0.724398i
$990$	29.9045	−	21.7269i	0.950429	−	0.690527i
$991$	−32.5863			−1.03514			−0.517569	−	0.855642i	$-0.673163\pi$
$991$	−32.5863			−1.03514			−0.517569	+	0.855642i	$0.673163\pi$
$992$	−2.94366	−	4.72598i	−0.0934614	−	0.150050i
$993$	85.9291			2.72688
$994$	24.2379	−	17.6099i	0.768779	−	0.558551i
$995$	−32.2503	−	23.4312i	−1.02240	−	0.742819i
$996$	−11.6209	+	35.7655i	−0.368223	+	1.13327i
$997$	−33.2453			−1.05289			−0.526445	−	0.850209i	$-0.676475\pi$
$997$	−33.2453			−1.05289			−0.526445	+	0.850209i	$0.676475\pi$
$998$	25.1701			0.796744
$999$	19.0711	−	58.6947i	0.603382	−	1.85702i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.2.d.a.47.1	yes	8
3.2	odd	2		558.2.i.i.109.2		8
4.3	odd	2		496.2.n.e.481.2		8
31.2	even	5	inner	62.2.d.a.33.1	✓	8
31.8	even	5		1922.2.a.r.1.4		4
31.23	odd	10		1922.2.a.n.1.1		4
93.2	odd	10		558.2.i.i.343.2		8
124.95	odd	10		496.2.n.e.33.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.2.d.a.33.1	✓	8	31.2	even	5	inner
62.2.d.a.47.1	yes	8	1.1	even	1	trivial
496.2.n.e.33.2		8	124.95	odd	10
496.2.n.e.481.2		8	4.3	odd	2
558.2.i.i.109.2		8	3.2	odd	2
558.2.i.i.343.2		8	93.2	odd	10
1922.2.a.n.1.1		4	31.23	odd	10
1922.2.a.r.1.4		4	31.8	even	5

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:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	62.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-2.48240 - 1.80357i) q^{3} +(0.309017 - 0.951057i) q^{4} -3.34677 q^{5} +3.06842 q^{6} +(0.778353 - 2.39552i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.98240 + 6.10121i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-2.48240 - 1.80357i) q^{3} +(0.309017 - 0.951057i) q^{4} -3.34677 q^{5} +3.06842 q^{6} +(0.778353 - 2.39552i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.98240 + 6.10121i) q^{9} +(2.70759 - 1.96718i) q^{10} +(0.532018 - 1.63738i) q^{11} +(-2.48240 + 1.80357i) q^{12} +(-1.89284 - 1.37523i) q^{13} +(0.778353 + 2.39552i) q^{14} +(8.30803 + 6.03614i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.244144 - 0.751397i) q^{17} +(-5.19000 - 3.77075i) q^{18} +(-0.326615 + 0.237300i) q^{19} +(-1.03421 + 3.18297i) q^{20} +(-6.25268 + 4.54284i) q^{21} +(0.532018 + 1.63738i) q^{22} +(-1.56623 - 4.82035i) q^{23} +(0.948193 - 2.91824i) q^{24} +6.20087 q^{25} +2.33968 q^{26} +(3.23826 - 9.96634i) q^{27} +(-2.03775 - 1.48051i) q^{28} +(4.20759 - 3.05700i) q^{29} -10.2693 q^{30} +(-2.94366 - 4.72598i) q^{31} +1.00000 q^{32} +(-4.27382 + 3.10511i) q^{33} +(0.639176 + 0.464389i) q^{34} +(-2.60497 + 8.01727i) q^{35} +6.41519 q^{36} +5.88930 q^{37} +(0.124756 - 0.383959i) q^{38} +(2.21847 + 6.82775i) q^{39} +(-1.03421 - 3.18297i) q^{40} +(-6.27601 + 4.55979i) q^{41} +(2.38831 - 7.35047i) q^{42} +(-6.18645 + 4.49472i) q^{43} +(-1.39284 - 1.01196i) q^{44} +(-6.63465 - 20.4193i) q^{45} +(4.10044 + 2.97914i) q^{46} +(3.91519 + 2.84455i) q^{47} +(0.948193 + 2.91824i) q^{48} +(0.530422 + 0.385374i) q^{49} +(-5.01661 + 3.64478i) q^{50} +(-0.749135 + 2.30560i) q^{51} +(-1.89284 + 1.37523i) q^{52} +(-0.812562 - 2.50081i) q^{53} +(3.23826 + 9.96634i) q^{54} +(-1.78054 + 5.47995i) q^{55} +2.51880 q^{56} +1.23878 q^{57} +(-1.60716 + 4.94632i) q^{58} +(3.53202 + 2.56616i) q^{59} +(8.30803 - 6.03614i) q^{60} +9.60897 q^{61} +(5.15933 + 2.09315i) q^{62} +16.1586 q^{63} +(-0.809017 + 0.587785i) q^{64} +(6.33491 + 4.60258i) q^{65} +(1.63245 - 5.02418i) q^{66} -8.86119 q^{67} -0.790065 q^{68} +(-4.80584 + 14.7909i) q^{69} +(-2.60497 - 8.01727i) q^{70} +(-3.67558 - 11.3123i) q^{71} +(-5.19000 + 3.77075i) q^{72} +(2.42471 - 7.46249i) q^{73} +(-4.76454 + 3.46164i) q^{74} +(-15.3931 - 11.1837i) q^{75} +(0.124756 + 0.383959i) q^{76} +(-3.50829 - 2.54892i) q^{77} +(-5.80803 - 4.21978i) q^{78} +(-0.647345 - 1.99232i) q^{79} +(2.70759 + 1.96718i) q^{80} +(-10.4437 + 7.58776i) q^{81} +(2.39722 - 7.37789i) q^{82} +(9.91519 - 7.20381i) q^{83} +(2.38831 + 7.35047i) q^{84} +(0.817093 + 2.51475i) q^{85} +(2.36301 - 7.27261i) q^{86} -15.9584 q^{87} +1.72165 q^{88} +(4.52530 - 13.9274i) q^{89} +(17.3697 + 12.6198i) q^{90} +(-4.76769 + 3.46393i) q^{91} -5.06842 q^{92} +(-1.21628 + 17.0409i) q^{93} -4.83944 q^{94} +(1.09310 - 0.794187i) q^{95} +(-2.48240 - 1.80357i) q^{96} +(-5.80449 + 17.8644i) q^{97} -0.655638 q^{98} +11.0447 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 4 q^{5} + 6 q^{6} + 2 q^{7} - 2 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 4 * q^5 + 6 * q^6 + 2 * q^7 - 2 * q^8	\( 8 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 4 q^{5} + 6 q^{6} + 2 q^{7} - 2 q^{8} + q^{10} - 2 q^{11} - 4 q^{12} - 11 q^{13} + 2 q^{14} + 21 q^{15} - 2 q^{16} - 7 q^{17} - 5 q^{18} - 14 q^{19} + q^{20} - 7 q^{21} - 2 q^{22} + 3 q^{23} + q^{24} + 14 q^{26} + 5 q^{27} + 2 q^{28} + 13 q^{29} - 14 q^{30} + 15 q^{31} + 8 q^{32} + 2 q^{33} + 3 q^{34} - 28 q^{35} + 10 q^{36} + 52 q^{37} + 21 q^{38} - 16 q^{39} + q^{40} - 11 q^{41} - 17 q^{42} - 22 q^{43} - 7 q^{44} - 19 q^{45} + 8 q^{46} - 10 q^{47} + q^{48} - 10 q^{49} - 15 q^{50} + 28 q^{51} - 11 q^{52} + 7 q^{53} + 5 q^{54} - 7 q^{55} - 8 q^{56} - 20 q^{57} - 17 q^{58} + 22 q^{59} + 21 q^{60} + 4 q^{61} + 5 q^{62} + 66 q^{63} - 2 q^{64} - 18 q^{66} - 26 q^{67} + 8 q^{68} + 4 q^{69} - 28 q^{70} - 15 q^{71} - 5 q^{72} - 29 q^{73} - 23 q^{74} - 34 q^{75} + 21 q^{76} + 34 q^{77} - q^{78} - 2 q^{79} + q^{80} - 45 q^{81} + 9 q^{82} + 38 q^{83} - 17 q^{84} + 25 q^{85} + 18 q^{86} - 20 q^{87} + 18 q^{88} + q^{89} + 46 q^{90} + 38 q^{91} - 22 q^{92} + 21 q^{93} - 20 q^{94} - 12 q^{95} - 4 q^{96} - 10 q^{97} + 60 q^{98} + 14 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 4 * q^5 + 6 * q^6 + 2 * q^7 - 2 * q^8 + q^10 - 2 * q^11 - 4 * q^12 - 11 * q^13 + 2 * q^14 + 21 * q^15 - 2 * q^16 - 7 * q^17 - 5 * q^18 - 14 * q^19 + q^20 - 7 * q^21 - 2 * q^22 + 3 * q^23 + q^24 + 14 * q^26 + 5 * q^27 + 2 * q^28 + 13 * q^29 - 14 * q^30 + 15 * q^31 + 8 * q^32 + 2 * q^33 + 3 * q^34 - 28 * q^35 + 10 * q^36 + 52 * q^37 + 21 * q^38 - 16 * q^39 + q^40 - 11 * q^41 - 17 * q^42 - 22 * q^43 - 7 * q^44 - 19 * q^45 + 8 * q^46 - 10 * q^47 + q^48 - 10 * q^49 - 15 * q^50 + 28 * q^51 - 11 * q^52 + 7 * q^53 + 5 * q^54 - 7 * q^55 - 8 * q^56 - 20 * q^57 - 17 * q^58 + 22 * q^59 + 21 * q^60 + 4 * q^61 + 5 * q^62 + 66 * q^63 - 2 * q^64 - 18 * q^66 - 26 * q^67 + 8 * q^68 + 4 * q^69 - 28 * q^70 - 15 * q^71 - 5 * q^72 - 29 * q^73 - 23 * q^74 - 34 * q^75 + 21 * q^76 + 34 * q^77 - q^78 - 2 * q^79 + q^80 - 45 * q^81 + 9 * q^82 + 38 * q^83 - 17 * q^84 + 25 * q^85 + 18 * q^86 - 20 * q^87 + 18 * q^88 + q^89 + 46 * q^90 + 38 * q^91 - 22 * q^92 + 21 * q^93 - 20 * q^94 - 12 * q^95 - 4 * q^96 - 10 * q^97 + 60 * q^98 + 14 * q^99

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