LMFDB - Embedded newform 418.2.h.b.373.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(65,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("418.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.h (of order $6$, degree $2$, 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:	$10$ over $\Q(\zeta_{6})$
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} + 41 x^{18} + 707 x^{16} + 6667 x^{14} + 37400 x^{12} + 126976 x^{10} + 253280 x^{8} + \cdots + 2304 $ x^20 + 41x^18 + 707x^16 + 6667x^14 + 37400x^12 + 126976x^10 + 253280x^8 + 273276x^6 + 137476x^4 + 30336*x^2 + 2304
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			373.7
Root			$1.50467i$ of defining polynomial
Character	$\chi$	$=$	418.373
Dual form			418.2.h.b.65.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(1.30309 - 0.752337i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.28873 + 2.23214i) q^{5} +(1.30309 + 0.752337i) q^{6} +1.03498i q^{7} -1.00000 q^{8} +(-0.367978 + 0.637356i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(1.30309 - 0.752337i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.28873 + 2.23214i) q^{5} +(1.30309 + 0.752337i) q^{6} +1.03498i q^{7} -1.00000 q^{8} +(-0.367978 + 0.637356i) q^{9} +(-1.28873 + 2.23214i) q^{10} +(2.23821 - 2.44754i) q^{11} +1.50467i q^{12} +(-0.637909 + 1.10489i) q^{13} +(-0.896317 + 0.517489i) q^{14} +(3.35865 + 1.93912i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-5.42929 + 3.13460i) q^{17} -0.735955 q^{18} +(2.12959 - 3.80327i) q^{19} -2.57746 q^{20} +(0.778652 + 1.34867i) q^{21} +(3.23873 + 0.714574i) q^{22} +(2.61127 - 4.52285i) q^{23} +(-1.30309 + 0.752337i) q^{24} +(-0.821643 + 1.42313i) q^{25} -1.27582 q^{26} +5.62140i q^{27} +(-0.896317 - 0.517489i) q^{28} +(2.46827 - 4.27517i) q^{29} +3.87823i q^{30} +6.43113i q^{31} +(0.500000 - 0.866025i) q^{32} +(1.07520 - 4.87324i) q^{33} +(-5.42929 - 3.13460i) q^{34} +(-2.31022 + 1.33381i) q^{35} +(-0.367978 - 0.637356i) q^{36} -11.5218i q^{37} +(4.35852 - 0.0573582i) q^{38} +1.91969i q^{39} +(-1.28873 - 2.23214i) q^{40} +(5.43032 + 9.40559i) q^{41} +(-0.778652 + 1.34867i) q^{42} +(3.01253 - 1.73929i) q^{43} +(1.00053 + 3.16211i) q^{44} -1.89689 q^{45} +5.22254 q^{46} +(2.86068 - 4.95485i) q^{47} +(-1.30309 - 0.752337i) q^{48} +5.92882 q^{49} -1.64329 q^{50} +(-4.71655 + 8.16931i) q^{51} +(-0.637909 - 1.10489i) q^{52} +(-9.79731 - 5.65648i) q^{53} +(-4.86827 + 2.81070i) q^{54} +(8.34769 + 1.84178i) q^{55} -1.03498i q^{56} +(-0.0863055 - 6.55816i) q^{57} +4.93655 q^{58} +(-9.19565 + 5.30911i) q^{59} +(-3.35865 + 1.93912i) q^{60} +(-6.07379 - 3.50671i) q^{61} +(-5.56952 + 3.21556i) q^{62} +(-0.659650 - 0.380849i) q^{63} +1.00000 q^{64} -3.28837 q^{65} +(4.75795 - 1.50547i) q^{66} +(-6.53077 - 3.77054i) q^{67} -6.26920i q^{68} -7.85822i q^{69} +(-2.31022 - 1.33381i) q^{70} +(1.07615 - 0.621318i) q^{71} +(0.367978 - 0.637356i) q^{72} +(1.69396 - 0.978008i) q^{73} +(9.97820 - 5.76092i) q^{74} +2.47261i q^{75} +(2.22893 + 3.74591i) q^{76} +(2.53315 + 2.31649i) q^{77} +(-1.66250 + 0.959846i) q^{78} +(-6.29456 - 10.9025i) q^{79} +(1.28873 - 2.23214i) q^{80} +(3.12525 + 5.41309i) q^{81} +(-5.43032 + 9.40559i) q^{82} -2.31152i q^{83} -1.55730 q^{84} +(-13.9938 - 8.07930i) q^{85} +(3.01253 + 1.73929i) q^{86} -7.42789i q^{87} +(-2.23821 + 2.44754i) q^{88} +(-8.88019 - 5.12698i) q^{89} +(-0.948447 - 1.64276i) q^{90} +(-1.14354 - 0.660222i) q^{91} +(2.61127 + 4.52285i) q^{92} +(4.83838 + 8.38031i) q^{93} +5.72137 q^{94} +(11.2339 - 0.147838i) q^{95} -1.50467i q^{96} +(-4.43118 + 2.55834i) q^{97} +(2.96441 + 5.13451i) q^{98} +(0.736343 + 2.32717i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9}+O(q^{10}) $ 20 * q + 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 + 3 * q^6 - 20 * q^8 + 11 * q^9	$ 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9} - 2 q^{10} + q^{11} + 5 q^{13} - 6 q^{14} + 12 q^{15} - 10 q^{16} + 6 q^{17} + 22 q^{18} - 18 q^{19} - 4 q^{20} - 14 q^{21} + 2 q^{22} - 4 q^{23} - 3 q^{24} - 20 q^{25} + 10 q^{26} - 6 q^{28} + 5 q^{29} + 10 q^{32} - 13 q^{33} + 6 q^{34} - 12 q^{35} + 11 q^{36} - 12 q^{38} - 2 q^{40} - q^{41} + 14 q^{42} + 3 q^{43} + q^{44} + 12 q^{45} - 8 q^{46} + q^{47} - 3 q^{48} + 8 q^{49} - 40 q^{50} - 12 q^{51} + 5 q^{52} - 24 q^{53} + 27 q^{54} - 2 q^{55} + 32 q^{57} + 10 q^{58} - 51 q^{59} - 12 q^{60} + 27 q^{61} + 12 q^{63} + 20 q^{64} - 8 q^{65} - 8 q^{66} + 27 q^{67} - 12 q^{70} + 33 q^{71} - 11 q^{72} - 9 q^{73} - 12 q^{74} + 6 q^{76} - 22 q^{77} - 24 q^{79} + 2 q^{80} + 12 q^{81} + q^{82} + 28 q^{84} - 12 q^{85} + 3 q^{86} - q^{88} + 21 q^{89} + 6 q^{90} + 12 q^{91} - 4 q^{92} - 10 q^{93} + 2 q^{94} - 24 q^{95} + 24 q^{97} + 4 q^{98} + 3 q^{99}+O(q^{100}) $ 20 * q + 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 + 3 * q^6 - 20 * q^8 + 11 * q^9 - 2 * q^10 + q^11 + 5 * q^13 - 6 * q^14 + 12 * q^15 - 10 * q^16 + 6 * q^17 + 22 * q^18 - 18 * q^19 - 4 * q^20 - 14 * q^21 + 2 * q^22 - 4 * q^23 - 3 * q^24 - 20 * q^25 + 10 * q^26 - 6 * q^28 + 5 * q^29 + 10 * q^32 - 13 * q^33 + 6 * q^34 - 12 * q^35 + 11 * q^36 - 12 * q^38 - 2 * q^40 - q^41 + 14 * q^42 + 3 * q^43 + q^44 + 12 * q^45 - 8 * q^46 + q^47 - 3 * q^48 + 8 * q^49 - 40 * q^50 - 12 * q^51 + 5 * q^52 - 24 * q^53 + 27 * q^54 - 2 * q^55 + 32 * q^57 + 10 * q^58 - 51 * q^59 - 12 * q^60 + 27 * q^61 + 12 * q^63 + 20 * q^64 - 8 * q^65 - 8 * q^66 + 27 * q^67 - 12 * q^70 + 33 * q^71 - 11 * q^72 - 9 * q^73 - 12 * q^74 + 6 * q^76 - 22 * q^77 - 24 * q^79 + 2 * q^80 + 12 * q^81 + q^82 + 28 * q^84 - 12 * q^85 + 3 * q^86 - q^88 + 21 * q^89 + 6 * q^90 + 12 * q^91 - 4 * q^92 - 10 * q^93 + 2 * q^94 - 24 * q^95 + 24 * q^97 + 4 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	1.30309	−	0.752337i	0.752337	−	0.434362i	−0.0742006	−	0.997243i	$-0.523641\pi$
$3$	1.30309	−	0.752337i	0.752337	−	0.434362i	0.826538	+	0.562881i	$0.190307\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.28873	+	2.23214i	0.576337	+	0.998245i	0.995895	+	0.0905164i	$0.0288518\pi$
$5$	1.28873	+	2.23214i	0.576337	+	0.998245i	−0.419558	+	0.907729i	$0.637815\pi$
$6$	1.30309	+	0.752337i	0.531983	+	0.307140i
$7$			1.03498i			0.391185i	0.980685	+	0.195592i	$0.0626630\pi$
$7$			1.03498i			0.391185i	−0.980685	+	0.195592i	$0.937337\pi$
$8$	−1.00000			−0.353553
$9$	−0.367978	+	0.637356i	−0.122659	+	0.212452i
$10$	−1.28873	+	2.23214i	−0.407532	+	0.705866i
$11$	2.23821	−	2.44754i	0.674844	−	0.737960i
$11$	2.23821	−	2.44754i	0.674844	−	0.737960i
$12$			1.50467i			0.434362i
$13$	−0.637909	+	1.10489i	−0.176924	+	0.306442i	−0.940826	−	0.338891i	$-0.889948\pi$
$13$	−0.637909	+	1.10489i	−0.176924	+	0.306442i	0.763901	+	0.645333i	$0.223281\pi$
$14$	−0.896317	+	0.517489i	−0.239551	+	0.138305i
$15$	3.35865	+	1.93912i	0.867199	+	0.500678i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−5.42929	+	3.13460i	−1.31680	+	0.760253i	−0.983212	−	0.182468i	$-0.941592\pi$
$17$	−5.42929	+	3.13460i	−1.31680	+	0.760253i	−0.333584	+	0.942720i	$0.608258\pi$
$18$	−0.735955			−0.173466
$19$	2.12959	−	3.80327i	0.488561	−	0.872530i
$19$	2.12959	−	3.80327i	0.488561	−	0.872530i
$20$	−2.57746			−0.576337
$21$	0.778652	+	1.34867i	0.169916	+	0.294303i
$22$	3.23873	+	0.714574i	0.690500	+	0.152348i
$23$	2.61127	−	4.52285i	0.544487	−	0.943080i	−0.454152	−	0.890924i	$-0.650058\pi$
$23$	2.61127	−	4.52285i	0.544487	−	0.943080i	0.998639	−	0.0521554i	$-0.0166091\pi$
$24$	−1.30309	+	0.752337i	−0.265991	+	0.153570i
$25$	−0.821643	+	1.42313i	−0.164329	+	0.284626i
$26$	−1.27582			−0.250209
$27$			5.62140i			1.08184i
$28$	−0.896317	−	0.517489i	−0.169388	−	0.0977962i
$29$	2.46827	−	4.27517i	0.458347	−	0.793880i	−0.540527	−	0.841327i	$-0.681775\pi$
$29$	2.46827	−	4.27517i	0.458347	−	0.793880i	0.998874	+	0.0474467i	$0.0151084\pi$
$30$			3.87823i			0.708065i
$31$			6.43113i			1.15506i	0.816368	+	0.577532i	$0.195984\pi$
$31$			6.43113i			1.15506i	−0.816368	+	0.577532i	$0.804016\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	1.07520	−	4.87324i	0.187168	−	0.848322i
$34$	−5.42929	−	3.13460i	−0.931116	−	0.537580i
$35$	−2.31022	+	1.33381i	−0.390498	+	0.225454i
$36$	−0.367978	−	0.637356i	−0.0613296	−	0.106226i
$37$		−	11.5218i		−	1.89418i	−0.320972	−	0.947089i	$-0.604010\pi$
$37$		−	11.5218i		−	1.89418i	0.320972	−	0.947089i	$-0.395990\pi$
$38$	4.35852	−	0.0573582i	0.707046	−	0.00930474i
$39$			1.91969i			0.307397i
$40$	−1.28873	−	2.23214i	−0.203766	−	0.352933i
$41$	5.43032	+	9.40559i	0.848073	+	1.46891i	0.882925	+	0.469514i	$0.155571\pi$
$41$	5.43032	+	9.40559i	0.848073	+	1.46891i	−0.0348518	+	0.999392i	$0.511096\pi$
$42$	−0.778652	+	1.34867i	−0.120149	+	0.208104i
$43$	3.01253	−	1.73929i	0.459407	−	0.265239i	−0.252388	−	0.967626i	$-0.581216\pi$
$43$	3.01253	−	1.73929i	0.459407	−	0.265239i	0.711795	+	0.702387i	$0.247883\pi$
$44$	1.00053	+	3.16211i	0.150835	+	0.476706i
$45$	−1.89689			−0.282772
$46$	5.22254			0.770021
$47$	2.86068	−	4.95485i	0.417274	−	0.722739i	−0.578390	−	0.815760i	$-0.696319\pi$
$47$	2.86068	−	4.95485i	0.417274	−	0.722739i	0.995664	+	0.0930207i	$0.0296523\pi$
$48$	−1.30309	−	0.752337i	−0.188084	−	0.108591i
$49$	5.92882			0.846974
$50$	−1.64329			−0.232396
$51$	−4.71655	+	8.16931i	−0.660450	+	1.14393i
$52$	−0.637909	−	1.10489i	−0.0884621	−	0.153221i
$53$	−9.79731	−	5.65648i	−1.34576	−	0.776977i	−0.358118	−	0.933676i	$-0.616581\pi$
$53$	−9.79731	−	5.65648i	−1.34576	−	0.776977i	−0.987646	+	0.156699i	$0.949915\pi$
$54$	−4.86827	+	2.81070i	−0.662488	+	0.382488i
$55$	8.34769	+	1.84178i	1.12560	+	0.248346i
$56$		−	1.03498i		−	0.138305i
$57$	−0.0863055	−	6.55816i	−0.0114314	−	0.868649i
$58$	4.93655			0.648200
$59$	−9.19565	+	5.30911i	−1.19717	+	0.691188i	−0.959924	−	0.280262i	$-0.909579\pi$
$59$	−9.19565	+	5.30911i	−1.19717	+	0.691188i	−0.237248	+	0.971449i	$0.576245\pi$
$60$	−3.35865	+	1.93912i	−0.433600	+	0.250339i
$61$	−6.07379	−	3.50671i	−0.777669	−	0.448988i	0.0579344	−	0.998320i	$-0.481549\pi$
$61$	−6.07379	−	3.50671i	−0.777669	−	0.448988i	−0.835604	+	0.549333i	$0.814882\pi$
$62$	−5.56952	+	3.21556i	−0.707330	+	0.408377i
$63$	−0.659650	−	0.380849i	−0.0831080	−	0.0479824i
$64$	1.00000			0.125000
$65$	−3.28837			−0.407872
$66$	4.75795	−	1.50547i	0.585663	−	0.185310i
$67$	−6.53077	−	3.77054i	−0.797861	−	0.460645i	0.0448617	−	0.998993i	$-0.485715\pi$
$67$	−6.53077	−	3.77054i	−0.797861	−	0.460645i	−0.842723	+	0.538348i	$0.819049\pi$
$68$		−	6.26920i		−	0.760253i
$69$		−	7.85822i		−	0.946019i
$70$	−2.31022	−	1.33381i	−0.276124	−	0.159420i
$71$	1.07615	−	0.621318i	0.127716	−	0.0737368i	−0.434781	−	0.900536i	$-0.643174\pi$
$71$	1.07615	−	0.621318i	0.127716	−	0.0737368i	0.562497	+	0.826799i	$0.309841\pi$
$72$	0.367978	−	0.637356i	0.0433666	−	0.0751131i
$73$	1.69396	−	0.978008i	0.198263	−	0.114467i	−0.397582	−	0.917567i	$-0.630151\pi$
$73$	1.69396	−	0.978008i	0.198263	−	0.114467i	0.595845	+	0.803099i	$0.296817\pi$
$74$	9.97820	−	5.76092i	1.15994	−	0.669693i
$75$			2.47261i			0.285513i
$76$	2.22893	+	3.74591i	0.255676	+	0.429685i
$77$	2.53315	+	2.31649i	0.288679	+	0.263989i
$78$	−1.66250	+	0.959846i	−0.188241	+	0.108681i
$79$	−6.29456	−	10.9025i	−0.708193	−	1.22663i	−0.965527	−	0.260304i	$-0.916177\pi$
$79$	−6.29456	−	10.9025i	−0.708193	−	1.22663i	0.257334	−	0.966323i	$-0.417156\pi$
$80$	1.28873	−	2.23214i	0.144084	−	0.249561i
$81$	3.12525	+	5.41309i	0.347250	+	0.601455i
$82$	−5.43032	+	9.40559i	−0.599678	+	1.03867i
$83$		−	2.31152i		−	0.253722i	−0.991920	−	0.126861i	$-0.959510\pi$
$83$		−	2.31152i		−	0.253722i	0.991920	−	0.126861i	$-0.0404903\pi$
$84$	−1.55730			−0.169916
$85$	−13.9938	−	8.07930i	−1.51784	−	0.876323i
$86$	3.01253	+	1.73929i	0.324850	+	0.187552i
$87$		−	7.42789i		−	0.796354i
$88$	−2.23821	+	2.44754i	−0.238593	+	0.260908i
$89$	−8.88019	−	5.12698i	−0.941298	−	0.543459i	−0.0509314	−	0.998702i	$-0.516219\pi$
$89$	−8.88019	−	5.12698i	−0.941298	−	0.543459i	−0.890367	+	0.455243i	$0.849552\pi$
$90$	−0.948447	−	1.64276i	−0.0999751	−	0.173162i
$91$	−1.14354	−	0.660222i	−0.119875	−	0.0692101i
$92$	2.61127	+	4.52285i	0.272244	+	0.471540i
$93$	4.83838	+	8.38031i	0.501716	+	0.868998i
$94$	5.72137			0.590114
$95$	11.2339	−	0.147838i	1.15257	−	0.0151679i
$96$		−	1.50467i		−	0.153570i
$97$	−4.43118	+	2.55834i	−0.449918	+	0.259760i	−0.707795	−	0.706417i	$-0.750310\pi$
$97$	−4.43118	+	2.55834i	−0.449918	+	0.259760i	0.257878	+	0.966178i	$0.416977\pi$
$98$	2.96441	+	5.13451i	0.299451	+	0.518664i
$99$	0.736343	+	2.32717i	0.0740053	+	0.233890i
$100$	−0.821643	−	1.42313i	−0.0821643	−	0.142313i
$101$	14.8989	+	8.60187i	1.48249	+	0.855918i	0.999803	−	0.0198732i	$-0.00632625\pi$
$101$	14.8989	+	8.60187i	1.48249	+	0.855918i	0.482691	+	0.875791i	$0.339660\pi$
$102$	−9.43311			−0.934017
$103$			2.03133i			0.200153i	0.994980	+	0.100077i	$0.0319088\pi$
$103$			2.03133i			0.200153i	−0.994980	+	0.100077i	$0.968091\pi$
$104$	0.637909	−	1.10489i	0.0625522	−	0.108344i
$105$	−2.00694	+	3.47613i	−0.195858	+	0.339235i
$106$		−	11.3130i		−	1.09881i
$107$	14.7559			1.42651			0.713255	−	0.700905i	$-0.247220\pi$
$107$	14.7559			1.42651			0.713255	+	0.700905i	$0.247220\pi$
$108$	−4.86827	−	2.81070i	−0.468450	−	0.270460i
$109$	−5.03672	−	8.72385i	−0.482430	−	0.835593i	0.517367	−	0.855764i	$-0.326912\pi$
$109$	−5.03672	−	8.72385i	−0.482430	−	0.835593i	−0.999797	+	0.0201707i	$0.993579\pi$
$110$	2.57882	+	8.15021i	0.245880	+	0.777092i
$111$	−8.66830	−	15.0139i	−0.822759	−	1.42506i
$112$	0.896317	−	0.517489i	0.0846940	−	0.0488981i
$113$			12.6960i			1.19434i	0.802115	+	0.597169i	$0.203708\pi$
$113$			12.6960i			1.19434i	−0.802115	+	0.597169i	$0.796292\pi$
$114$	5.63638	−	3.35382i	0.527895	−	0.314114i
$115$	13.4609			1.25523
$116$	2.46827	+	4.27517i	0.229173	+	0.396940i
$117$	−0.469473	−	0.813151i	−0.0434028	−	0.0751758i
$118$	−9.19565	−	5.30911i	−0.846528	−	0.488743i
$119$	−3.24424	−	5.61920i	−0.297399	−	0.515111i
$120$	−3.35865	−	1.93912i	−0.306601	−	0.177016i
$121$	−0.980877	−	10.9562i	−0.0891706	−	0.996016i
$122$		−	7.01341i		−	0.634964i
$123$	14.1523	+	8.17086i	1.27607	+	0.736742i
$124$	−5.56952	−	3.21556i	−0.500158	−	0.288766i
$125$	8.65179			0.773839
$126$		−	0.761698i		−	0.0678574i
$127$	−5.37052	+	9.30202i	−0.476557	+	0.825420i	−0.999639	−	0.0268617i	$-0.991449\pi$
$127$	−5.37052	+	9.30202i	−0.476557	+	0.825420i	0.523082	+	0.852282i	$0.324782\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	2.61706	−	4.53288i	0.230419	−	0.399098i
$130$	−1.64418	−	2.84781i	−0.144204	−	0.249770i
$131$	−3.73979	+	2.15917i	−0.326747	+	0.188648i	−0.654396	−	0.756152i	$-0.727077\pi$
$131$	−3.73979	+	2.15917i	−0.326747	+	0.188648i	0.327649	+	0.944800i	$0.393744\pi$
$132$	3.68275	+	3.36777i	0.320542	+	0.293127i
$133$	3.93630	+	2.20408i	0.341321	+	0.191118i
$134$		−	7.54109i		−	0.651451i
$135$	−12.5478	+	7.24445i	−1.07994	+	0.623503i
$136$	5.42929	−	3.13460i	0.465558	−	0.268790i
$137$	4.24589	−	7.35410i	0.362751	−	0.628304i	−0.625661	−	0.780095i	$-0.715171\pi$
$137$	4.24589	−	7.35410i	0.362751	−	0.628304i	0.988413	+	0.151791i	$0.0485042\pi$
$138$	6.80542	−	3.92911i	0.579316	−	0.334468i
$139$	4.81963	+	2.78261i	0.408795	+	0.236018i	0.690272	−	0.723550i	$-0.257491\pi$
$139$	4.81963	+	2.78261i	0.408795	+	0.236018i	−0.281477	+	0.959568i	$0.590824\pi$
$140$		−	2.66761i		−	0.225454i
$141$		−	8.60880i		−	0.724992i
$142$	1.07615	+	0.621318i	0.0903088	+	0.0521398i
$143$	1.27649	+	4.03428i	0.106746	+	0.337363i
$144$	0.735955			0.0613296
$145$	12.7237			1.05665
$146$	1.69396	+	0.978008i	0.140193	+	0.0809405i
$147$	7.72576	−	4.46047i	0.637210	−	0.367894i
$148$	9.97820	+	5.76092i	0.820203	+	0.473544i
$149$	−10.0667	+	5.81202i	−0.824697	+	0.476139i	−0.852033	−	0.523487i	$-0.824631\pi$
$149$	−10.0667	+	5.81202i	−0.824697	+	0.476139i	0.0273366	+	0.999626i	$0.491297\pi$
$150$	−2.14134	+	1.23631i	−0.174840	+	0.100944i
$151$	−0.137030			−0.0111513			−0.00557566	−	0.999984i	$-0.501775\pi$
$151$	−0.137030			−0.0111513			−0.00557566	+	0.999984i	$0.501775\pi$
$152$	−2.12959	+	3.80327i	−0.172732	+	0.308486i
$153$		−	4.61385i		−	0.373008i
$154$	−0.739568	+	3.35202i	−0.0595961	+	0.270113i
$155$	−14.3552	+	8.28798i	−1.15304	+	0.665707i
$156$	−1.66250	−	0.959846i	−0.133107	−	0.0768492i
$157$	−8.92471	−	15.4581i	−0.712269	−	1.23369i	−0.964003	−	0.265890i	$-0.914334\pi$
$157$	−8.92471	−	15.4581i	−0.712269	−	1.23369i	0.251734	−	0.967797i	$-0.418999\pi$
$158$	6.29456	−	10.9025i	0.500768	−	0.867356i
$159$	−17.0223			−1.34996
$160$	2.57746			0.203766
$161$	4.68105	+	2.70261i	0.368919	+	0.212995i
$162$	−3.12525	+	5.41309i	−0.245543	+	0.425293i
$163$	−14.9577			−1.17158			−0.585788	−	0.810464i	$-0.699215\pi$
$163$	−14.9577			−1.17158			−0.585788	+	0.810464i	$0.699215\pi$
$164$	−10.8606			−0.848073
$165$	12.2634	−	3.88028i	0.954705	−	0.302079i
$166$	2.00184	−	1.15576i	0.155373	−	0.0897044i
$167$	−7.91092	+	13.7021i	−0.612166	+	1.06030i	0.378709	+	0.925516i	$0.376368\pi$
$167$	−7.91092	+	13.7021i	−0.612166	+	1.06030i	−0.990875	+	0.134786i	$0.956965\pi$
$168$	−0.778652	−	1.34867i	−0.0600743	−	0.104052i
$169$	5.68614	+	9.84869i	0.437396	+	0.757591i
$170$		−	16.1586i		−	1.23931i
$171$	1.64040	+	2.75682i	0.125444	+	0.210820i
$172$			3.47857i			0.265239i
$173$	−5.19007	−	8.98946i	−0.394593	−	0.683456i	0.598456	−	0.801156i	$-0.295781\pi$
$173$	−5.19007	−	8.98946i	−0.394593	−	0.683456i	−0.993049	+	0.117700i	$0.962448\pi$
$174$	6.43275	−	3.71395i	0.487665	−	0.281554i
$175$	−1.47291	−	0.850383i	−0.111341	−	0.0642829i
$176$	−3.23873	−	0.714574i	−0.244129	−	0.0538630i
$177$	−7.98848	+	13.8365i	−0.600451	+	1.04001i
$178$		−	10.2540i		−	0.768567i
$179$			7.87498i			0.588603i	0.955713	+	0.294302i	$0.0950870\pi$
$179$			7.87498i			0.588603i	−0.955713	+	0.294302i	$0.904913\pi$
$180$	0.948447	−	1.64276i	0.0706931	−	0.122444i
$181$	−6.56316	−	3.78924i	−0.487836	−	0.281652i	0.235840	−	0.971792i	$-0.424216\pi$
$181$	−6.56316	−	3.78924i	−0.487836	−	0.281652i	−0.723676	+	0.690140i	$0.757549\pi$
$182$		−	1.32044i		−	0.0978778i
$183$	−10.5529			−0.780093
$184$	−2.61127	+	4.52285i	−0.192505	+	0.333429i
$185$	25.7184	−	14.8485i	1.89085	−	1.09168i
$186$	−4.83838	+	8.38031i	−0.354767	+	0.614474i
$187$	−4.47981	+	20.3043i	−0.327596	+	1.48480i
$188$	2.86068	+	4.95485i	0.208637	+	0.361370i
$189$	−5.81802			−0.423199
$190$	5.74498	+	9.65493i	0.416785	+	0.700442i
$191$	18.3013			1.32423			0.662116	−	0.749401i	$-0.269659\pi$
$191$	18.3013			1.32423			0.662116	+	0.749401i	$0.269659\pi$
$192$	1.30309	−	0.752337i	0.0940421	−	0.0542953i
$193$	0.825790	+	1.43031i	0.0594417	+	0.102956i	0.894215	−	0.447638i	$-0.147735\pi$
$193$	0.825790	+	1.43031i	0.0594417	+	0.102956i	−0.834773	+	0.550594i	$0.814401\pi$
$194$	−4.43118	−	2.55834i	−0.318140	−	0.183678i
$195$	−4.28503	+	2.47396i	−0.306857	+	0.177164i
$196$	−2.96441	+	5.13451i	−0.211744	+	0.366751i
$197$			23.7846i			1.69458i	0.531127	+	0.847292i	$0.321769\pi$
$197$			23.7846i			1.69458i	−0.531127	+	0.847292i	$0.678231\pi$
$198$	−1.64722	+	1.80128i	−0.117063	+	0.128011i
$199$	−8.73397	+	15.1277i	−0.619135	+	1.07237i	0.370509	+	0.928829i	$0.379183\pi$
$199$	−8.73397	+	15.1277i	−0.619135	+	1.07237i	−0.989644	+	0.143544i	$0.954150\pi$
$200$	0.821643	−	1.42313i	0.0580990	−	0.100630i
$201$	−11.3469			−0.800347
$202$			17.2037i			1.21045i
$203$	4.42471	+	2.55461i	0.310554	+	0.179298i
$204$	−4.71655	−	8.16931i	−0.330225	−	0.571966i
$205$	−13.9964	+	24.2425i	−0.977552	+	1.69317i
$206$	−1.75919	+	1.01567i	−0.122568	+	0.0707648i
$207$	1.92178	+	3.32862i	0.133573	+	0.231355i
$208$	1.27582			0.0884621
$209$	−4.54219	−	13.7247i	−0.314190	−	0.949360i
$210$	−4.01389			−0.276984
$211$	6.40200	+	11.0886i	0.440732	+	0.763370i	0.997744	−	0.0671344i	$-0.0213856\pi$
$211$	6.40200	+	11.0886i	0.440732	+	0.763370i	−0.557012	+	0.830504i	$0.688052\pi$
$212$	9.79731	−	5.65648i	0.672882	−	0.388489i
$213$	0.934880	−	1.61926i	0.0640570	−	0.110950i
$214$	7.37797	+	12.7790i	0.504347	+	0.873555i
$215$	7.76468	+	4.48294i	0.529547	+	0.305734i
$216$		−	5.62140i		−	0.382488i
$217$	−6.65608			−0.451844
$218$	5.03672	−	8.72385i	0.341129	−	0.590854i
$219$	1.47158	−	2.54886i	0.0994404	−	0.172236i
$220$	−5.76888	+	6.30842i	−0.388938	+	0.425314i
$221$		−	7.99837i		−	0.538028i
$222$	8.66830	−	15.0139i	0.581778	−	1.00767i
$223$	6.33848	−	3.65952i	0.424456	−	0.245060i	−0.272526	−	0.962148i	$-0.587859\pi$
$223$	6.33848	−	3.65952i	0.424456	−	0.245060i	0.696982	+	0.717089i	$0.254526\pi$
$224$	0.896317	+	0.517489i	0.0598877	+	0.0345762i
$225$	−0.604693	−	1.04736i	−0.0403129	−	0.0698239i
$226$	−10.9951	+	6.34800i	−0.731380	+	0.422262i
$227$	13.0580			0.866690			0.433345	−	0.901228i	$-0.357333\pi$
$227$	13.0580			0.866690			0.433345	+	0.901228i	$0.357333\pi$
$228$	5.72268	+	3.20433i	0.378994	+	0.212212i
$229$	−7.77701			−0.513920			−0.256960	−	0.966422i	$-0.582721\pi$
$229$	−7.77701			−0.513920			−0.256960	+	0.966422i	$0.582721\pi$
$230$	6.73044	+	11.6575i	0.443792	+	0.768670i
$231$	5.04369	+	1.11281i	0.331851	+	0.0732175i
$232$	−2.46827	+	4.27517i	−0.162050	+	0.280679i
$233$	−13.4326	+	7.75529i	−0.879996	+	0.508066i	−0.870657	−	0.491891i	$-0.836306\pi$
$233$	−13.4326	+	7.75529i	−0.879996	+	0.508066i	−0.00933865	+	0.999956i	$0.502973\pi$
$234$	0.469473	−	0.813151i	0.0306904	−	0.0531573i
$235$	14.7466			0.961961
$236$		−	10.6182i		−	0.691188i
$237$	−16.4047	−	9.47126i	−1.06560	−	0.615224i
$238$	3.24424	−	5.61920i	0.210293	−	0.364238i
$239$			23.3081i			1.50768i	0.657061	+	0.753838i	$0.271799\pi$
$239$			23.3081i			1.50768i	−0.657061	+	0.753838i	$0.728201\pi$
$240$		−	3.87823i		−	0.250339i
$241$	−6.94125	+	12.0226i	−0.447125	+	0.774443i	−0.998198	−	0.0600142i	$-0.980885\pi$
$241$	−6.94125	+	12.0226i	−0.447125	+	0.774443i	0.551073	+	0.834457i	$0.314219\pi$
$242$	8.99789	−	6.32755i	0.578406	−	0.406751i
$243$	−6.45987	−	3.72961i	−0.414401	−	0.239254i
$244$	6.07379	−	3.50671i	0.388835	−	0.224494i
$245$	7.64064	+	13.2340i	0.488143	+	0.845488i
$246$			16.3417i			1.04191i
$247$	2.84372	+	4.77910i	0.180941	+	0.304087i
$248$		−	6.43113i		−	0.408377i
$249$	−1.73904	−	3.01211i	−0.110207	−	0.190885i
$250$	4.32589	+	7.49267i	0.273593	+	0.473878i
$251$	−1.89922	+	3.28955i	−0.119878	+	0.207635i	−0.919719	−	0.392577i	$-0.871584\pi$
$251$	−1.89922	+	3.28955i	−0.119878	+	0.207635i	0.799841	+	0.600212i	$0.204917\pi$
$252$	0.659650	−	0.380849i	0.0415540	−	0.0239912i
$253$	−5.22529	−	16.5142i	−0.328511	−	1.03824i
$254$	−10.7410			−0.673953
$255$	−24.3134			−1.52257
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	16.0217	+	9.25013i	0.999405	+	0.577007i	0.908072	−	0.418813i	$-0.137554\pi$
$257$	16.0217	+	9.25013i	0.999405	+	0.577007i	0.0913331	+	0.995820i	$0.470887\pi$
$258$	5.23412			0.325862
$259$	11.9248			0.740974
$260$	1.64418	−	2.84781i	0.101968	−	0.176614i
$261$	1.81654	+	3.14634i	0.112441	+	0.194753i
$262$	−3.73979	−	2.15917i	−0.231045	−	0.133394i
$263$	8.06674	−	4.65734i	0.497417	−	0.287184i	−0.230229	−	0.973136i	$-0.573948\pi$
$263$	8.06674	−	4.65734i	0.497417	−	0.287184i	0.727646	+	0.685953i	$0.240614\pi$
$264$	−1.07520	+	4.87324i	−0.0661740	+	0.299927i
$265$		−	29.1587i		−	1.79120i
$266$	0.0593645	+	4.51097i	0.00363987	+	0.276586i
$267$	−15.4289			−0.944232
$268$	6.53077	−	3.77054i	0.398930	−	0.230323i
$269$	13.5799	−	7.84037i	0.827982	−	0.478036i	−0.0251790	−	0.999683i	$-0.508016\pi$
$269$	13.5799	−	7.84037i	0.827982	−	0.478036i	0.853161	+	0.521647i	$0.174682\pi$
$270$	−12.5478	−	7.24445i	−0.763633	−	0.440883i
$271$	8.80397	−	5.08297i	0.534803	−	0.308769i	−0.208167	−	0.978093i	$-0.566750\pi$
$271$	8.80397	−	5.08297i	0.534803	−	0.308769i	0.742970	+	0.669325i	$0.233416\pi$
$272$	5.42929	+	3.13460i	0.329199	+	0.190063i
$273$	−1.98684			−0.120249
$274$	8.49179			0.513008
$275$	1.64415	+	5.19625i	0.0991461	+	0.313346i
$276$	6.80542	+	3.92911i	0.409638	+	0.236505i
$277$			0.710197i			0.0426716i	0.999772	+	0.0213358i	$0.00679192\pi$
$277$			0.710197i			0.0426716i	−0.999772	+	0.0213358i	$0.993208\pi$
$278$			5.56523i			0.333780i
$279$	−4.09892	−	2.36651i	−0.245396	−	0.141679i
$280$	2.31022	−	1.33381i	0.138062	−	0.0797101i
$281$	−7.18482	+	12.4445i	−0.428610	+	0.742375i	−0.996750	−	0.0805575i	$-0.974330\pi$
$281$	−7.18482	+	12.4445i	−0.428610	+	0.742375i	0.568140	+	0.822932i	$0.307663\pi$
$282$	7.45544	−	4.30440i	0.443965	−	0.256323i
$283$	0.730650	−	0.421841i	0.0434326	−	0.0250758i	−0.478126	−	0.878291i	$-0.658684\pi$
$283$	0.730650	−	0.421841i	0.0434326	−	0.0250758i	0.521559	+	0.853215i	$0.325351\pi$
$284$			1.24264i			0.0737368i
$285$	14.5275	−	8.64433i	0.860536	−	0.512046i
$286$	−2.85554	+	3.12261i	−0.168852	+	0.184644i
$287$	−9.73458	+	5.62026i	−0.574614	+	0.331753i
$288$	0.367978	+	0.637356i	0.0216833	+	0.0375566i
$289$	11.1515	−	19.3149i	0.655968	−	1.13617i
$290$	6.36187	+	11.0191i	0.373582	+	0.647063i
$291$	−3.84947	+	6.66748i	−0.225660	+	0.390854i
$292$			1.95602i			0.114467i
$293$	−3.44149			−0.201054			−0.100527	−	0.994934i	$-0.532053\pi$
$293$	−3.44149			−0.201054			−0.100527	+	0.994934i	$0.532053\pi$
$294$	7.72576	+	4.46047i	0.450576	+	0.260140i
$295$	−23.7014	−	13.6840i	−1.37995	−	0.796714i
$296$			11.5218i			0.669693i
$297$	13.7586	+	12.5818i	0.798354	+	0.730072i
$298$	−10.0667	−	5.81202i	−0.583149	−	0.336681i
$299$	3.33151	+	5.77034i	0.192666	+	0.333707i
$300$	−2.14134	−	1.23631i	−0.123631	−	0.0713781i
$301$	1.80012	+	3.11791i	0.103757	+	0.179713i
$302$	−0.0685149	−	0.118671i	−0.00394259	−	0.00682877i
$303$	25.8860			1.48711
$304$	−4.35852	+	0.0573582i	−0.249978	+	0.00328972i
$305$		−	18.0768i		−	1.03507i
$306$	3.99572	−	2.30693i	0.228420	−	0.131878i
$307$	−12.7937	−	22.1594i	−0.730177	−	1.26470i	−0.956808	−	0.290722i	$-0.906104\pi$
$307$	−12.7937	−	22.1594i	−0.730177	−	1.26470i	0.226631	−	0.973981i	$-0.427229\pi$
$308$	−3.27272	+	1.03552i	−0.186480	+	0.0590044i
$309$	1.52825	+	2.64700i	0.0869389	+	0.150583i
$310$	−14.3552	−	8.28798i	−0.815321	−	0.470726i
$311$	8.75086			0.496216			0.248108	−	0.968732i	$-0.420191\pi$
$311$	8.75086			0.496216			0.248108	+	0.968732i	$0.420191\pi$
$312$		−	1.91969i		−	0.108681i
$313$	−3.22013	+	5.57742i	−0.182012	+	0.315254i	−0.942566	−	0.334021i	$-0.891594\pi$
$313$	−3.22013	+	5.57742i	−0.182012	+	0.315254i	0.760553	+	0.649275i	$0.224928\pi$
$314$	8.92471	−	15.4581i	0.503651	−	0.872348i
$315$		−	1.96324i		−	0.110616i
$316$	12.5891			0.708193
$317$	−13.1671	−	7.60200i	−0.739535	−	0.426971i	0.0823651	−	0.996602i	$-0.473753\pi$
$317$	−13.1671	−	7.60200i	−0.739535	−	0.426971i	−0.821900	+	0.569631i	$0.807086\pi$
$318$	−8.51116	−	14.7418i	−0.477282	−	0.826677i
$319$	−4.93915	−	15.6099i	−0.276539	−	0.873987i
$320$	1.28873	+	2.23214i	0.0720421	+	0.124781i
$321$	19.2282	−	11.1014i	1.07322	−	0.619622i
$322$			5.40521i			0.301221i
$323$	0.359591	+	27.3245i	0.0200082	+	1.52037i
$324$	−6.25050			−0.347250
$325$	−1.04827	−	1.81565i	−0.0581474	−	0.100714i
$326$	−7.47884	−	12.9537i	−0.414215	−	0.717441i
$327$	−13.1265	−	7.57862i	−0.725900	−	0.419098i
$328$	−5.43032	−	9.40559i	−0.299839	−	0.519337i
$329$	5.12816	+	2.96075i	0.282725	+	0.163231i
$330$	9.49212	+	8.68028i	0.522524	+	0.477834i
$331$			3.32959i			0.183011i	0.995805	+	0.0915055i	$0.0291679\pi$
$331$			3.32959i			0.183011i	−0.995805	+	0.0915055i	$0.970832\pi$
$332$	2.00184	+	1.15576i	0.109865	+	0.0634306i
$333$	7.34351	+	4.23978i	0.402422	+	0.232338i
$334$	−15.8218			−0.865733
$335$		−	19.4368i		−	1.06195i
$336$	0.778652	−	1.34867i	0.0424790	−	0.0735757i
$337$	−10.5268	−	18.2330i	−0.573432	−	0.993213i	−0.996210	−	0.0869798i	$-0.972278\pi$
$337$	−10.5268	−	18.2330i	−0.573432	−	0.993213i	0.422778	−	0.906233i	$-0.361055\pi$
$338$	−5.68614	+	9.84869i	−0.309285	+	0.535698i
$339$	9.55167	+	16.5440i	0.518775	+	0.898545i
$340$	13.9938	−	8.07930i	0.758918	−	0.438162i
$341$	15.7404	+	14.3942i	0.852392	+	0.779489i
$342$	−1.56728	+	2.79904i	−0.0847489	+	0.151355i
$343$			13.3810i			0.722508i
$344$	−3.01253	+	1.73929i	−0.162425	+	0.0937761i
$345$	17.5407	−	10.1271i	0.944358	−	0.545225i
$346$	5.19007	−	8.98946i	0.279020	−	0.483276i
$347$	26.0648	−	15.0485i	1.39923	−	0.807848i	0.404921	−	0.914352i	$-0.367299\pi$
$347$	26.0648	−	15.0485i	1.39923	−	0.807848i	0.994312	+	0.106504i	$0.0339657\pi$
$348$	6.43275	+	3.71395i	0.344831	+	0.199088i
$349$		−	21.1004i		−	1.12948i	−0.825270	−	0.564738i	$-0.808977\pi$
$349$		−	21.1004i		−	1.12948i	0.825270	−	0.564738i	$-0.191023\pi$
$350$		−	1.70077i		−	0.0909097i
$351$	−6.21103	−	3.58594i	−0.331520	−	0.191403i
$352$	−1.00053	−	3.16211i	−0.0533283	−	0.168541i
$353$	−25.8530			−1.37602			−0.688008	−	0.725704i	$-0.741514\pi$
$353$	−25.8530			−1.37602			−0.688008	+	0.725704i	$0.741514\pi$
$354$	−15.9770			−0.849166
$355$	2.77374	+	1.60142i	0.147215	+	0.0849945i
$356$	8.88019	−	5.12698i	0.470649	−	0.271729i
$357$	−8.45506	−	4.88153i	−0.447489	−	0.258358i
$358$	−6.81993	+	3.93749i	−0.360444	+	0.208103i
$359$	1.56776	−	0.905146i	0.0827431	−	0.0477718i	−0.458058	−	0.888923i	$-0.651455\pi$
$359$	1.56776	−	0.905146i	0.0827431	−	0.0477718i	0.540801	+	0.841151i	$0.318121\pi$
$360$	1.89689			0.0999751
$361$	−9.92972	−	16.1988i	−0.522617	−	0.852568i
$362$		−	7.57848i		−	0.398316i
$363$	−9.52091	−	13.5389i	−0.499718	−	0.710608i
$364$	1.14354	−	0.660222i	0.0599377	−	0.0346050i
$365$	4.36611	+	2.52077i	0.228532	+	0.131943i
$366$	−5.27645	−	9.13908i	−0.275804	−	0.477707i
$367$	−11.8297	+	20.4896i	−0.617505	+	1.06955i	0.372434	+	0.928059i	$0.378523\pi$
$367$	−11.8297	+	20.4896i	−0.617505	+	1.06955i	−0.989939	+	0.141492i	$0.954810\pi$
$368$	−5.22254			−0.272244
$369$	−7.99295			−0.416096
$370$	25.7184	+	14.8485i	1.33703	+	0.771937i
$371$	5.85433	−	10.1400i	0.303942	−	0.526443i
$372$	−9.67675			−0.501716
$373$	5.06865			0.262445			0.131222	−	0.991353i	$-0.458110\pi$
$373$	5.06865			0.262445			0.131222	+	0.991353i	$0.458110\pi$
$374$	−19.8239	+	6.27251i	−1.02507	+	0.324344i
$375$	11.2740	−	6.50906i	0.582188	−	0.336126i
$376$	−2.86068	+	4.95485i	−0.147529	+	0.255527i
$377$	3.14907	+	5.45435i	0.162185	+	0.280913i
$378$	−2.90901	−	5.03855i	−0.149623	−	0.259155i
$379$			10.7288i			0.551102i	0.961286	+	0.275551i	$0.0888603\pi$
$379$			10.7288i			0.551102i	−0.961286	+	0.275551i	$0.911140\pi$
$380$	−5.48892	+	9.80277i	−0.281576	+	0.502871i
$381$			16.1618i			0.827993i
$382$	9.15063	+	15.8493i	0.468187	+	0.810923i
$383$	20.0577	−	11.5803i	1.02490	−	0.591726i	0.109381	−	0.994000i	$-0.465113\pi$
$383$	20.0577	−	11.5803i	1.02490	−	0.591726i	0.915519	+	0.402274i	$0.131780\pi$
$384$	1.30309	+	0.752337i	0.0664978	+	0.0383925i
$385$	−1.90621	+	8.63968i	−0.0971492	+	0.440319i
$386$	−0.825790	+	1.43031i	−0.0420316	+	0.0728009i
$387$			2.56008i			0.130136i
$388$		−	5.11668i		−	0.259760i
$389$	−7.84388	+	13.5860i	−0.397701	+	0.688838i	−0.993442	−	0.114339i	$-0.963525\pi$
$389$	−7.84388	+	13.5860i	−0.397701	+	0.688838i	0.595741	+	0.803176i	$0.296858\pi$
$390$	−4.28503	−	2.47396i	−0.216981	−	0.125274i
$391$			32.7412i			1.65579i
$392$	−5.92882			−0.299451
$393$	−3.24885	+	5.62717i	−0.163883	+	0.283853i
$394$	−20.5981	+	11.8923i	−1.03772	+	0.599126i
$395$	16.2240	−	28.1007i	0.816316	−	1.41390i
$396$	−2.38356	−	0.525894i	−0.119779	−	0.0264272i
$397$	−0.419461	−	0.726527i	−0.0210521	−	0.0364634i	0.855307	−	0.518121i	$-0.173368\pi$
$397$	−0.419461	−	0.726527i	−0.0210521	−	0.0364634i	−0.876360	+	0.481658i	$0.840035\pi$
$398$	−17.4679			−0.875588
$399$	6.78755	−	0.0893243i	0.339802	−	0.00447181i
$400$	1.64329			0.0821643
$401$	−2.38649	+	1.37784i	−0.119176	+	0.0688062i	−0.558403	−	0.829570i	$-0.688586\pi$
$401$	−2.38649	+	1.37784i	−0.119176	+	0.0688062i	0.439227	+	0.898376i	$0.355252\pi$
$402$	−5.67344	−	9.82669i	−0.282965	−	0.490111i
$403$	−7.10570	−	4.10248i	−0.353960	−	0.204359i
$404$	−14.8989	+	8.60187i	−0.741247	+	0.427959i
$405$	−8.05520	+	13.9520i	−0.400266	+	0.693281i
$406$			5.10922i			0.253566i
$407$	−28.2001	−	25.7882i	−1.39783	−	1.27827i
$408$	4.71655	−	8.16931i	0.233504	−	0.404441i
$409$	−11.6534	+	20.1842i	−0.576222	+	0.998046i	0.419686	+	0.907670i	$0.362140\pi$
$409$	−11.6534	+	20.1842i	−0.576222	+	0.998046i	−0.995908	+	0.0903763i	$0.971193\pi$
$410$	−27.9928			−1.38247
$411$		−	12.7774i		−	0.630261i
$412$	−1.75919	−	1.01567i	−0.0866689	−	0.0500383i
$413$	−5.49481	−	9.51730i	−0.270382	−	0.468316i
$414$	−1.92178	+	3.32862i	−0.0944502	+	0.163593i
$415$	5.15965	−	2.97892i	0.253277	−	0.146230i
$416$	0.637909	+	1.10489i	0.0312761	+	0.0541718i
$417$	8.37385			0.410069
$418$	9.61488	−	10.7960i	0.470279	−	0.528051i
$419$	37.3689			1.82559			0.912796	−	0.408416i	$-0.133919\pi$
$419$	37.3689			1.82559			0.912796	+	0.408416i	$0.133919\pi$
$420$	−2.00694	−	3.47613i	−0.0979288	−	0.169618i
$421$	11.5480	−	6.66723i	0.562814	−	0.324941i	−0.191460	−	0.981500i	$-0.561322\pi$
$421$	11.5480	−	6.66723i	0.562814	−	0.324941i	0.754274	+	0.656560i	$0.227989\pi$
$422$	−6.40200	+	11.0886i	−0.311644	+	0.539784i
$423$	2.10534	+	3.64655i	0.102365	+	0.177301i
$424$	9.79731	+	5.65648i	0.475799	+	0.274703i
$425$		−	10.3021i		−	0.499725i
$426$	1.86976			0.0905902
$427$	3.62936	−	6.28624i	0.175637	−	0.304212i
$428$	−7.37797	+	12.7790i	−0.356627	+	0.617697i
$429$	4.69852	+	4.29666i	0.226847	+	0.207445i
$430$			8.96588i			0.432373i
$431$	−0.486368	+	0.842415i	−0.0234275	+	0.0405777i	−0.877501	−	0.479574i	$-0.840791\pi$
$431$	−0.486368	+	0.842415i	−0.0234275	+	0.0405777i	0.854074	+	0.520152i	$0.174125\pi$
$432$	4.86827	−	2.81070i	0.234225	−	0.135230i
$433$	−7.42225	−	4.28524i	−0.356691	−	0.205935i	0.310938	−	0.950430i	$-0.399357\pi$
$433$	−7.42225	−	4.28524i	−0.356691	−	0.205935i	−0.667628	+	0.744495i	$0.732690\pi$
$434$	−3.32804	−	5.76433i	−0.159751	−	0.276697i
$435$	16.5801	−	9.57254i	0.794956	−	0.458968i
$436$	10.0734			0.482430
$437$	−11.6407	−	19.5632i	−0.556850	−	0.935833i
$438$	2.94317			0.140630
$439$	−16.7943	−	29.0886i	−0.801548	−	1.38832i	−0.918597	−	0.395195i	$-0.870677\pi$
$439$	−16.7943	−	29.0886i	−0.801548	−	1.38832i	0.117050	−	0.993126i	$-0.462656\pi$
$440$	−8.34769	−	1.84178i	−0.397961	−	0.0878036i
$441$	−2.18167	+	3.77877i	−0.103889	+	0.179941i
$442$	6.92679	−	3.99918i	0.329474	−	0.190222i
$443$	2.66659	−	4.61866i	0.126693	−	0.219439i	−0.795700	−	0.605691i	$-0.792897\pi$
$443$	2.66659	−	4.61866i	0.126693	−	0.219439i	0.922394	+	0.386251i	$0.126230\pi$
$444$	17.3366			0.822759
$445$		−	26.4292i		−	1.25286i
$446$	6.33848	+	3.65952i	0.300135	+	0.173283i
$447$	−8.74519	+	15.1471i	−0.413633	+	0.716434i
$448$			1.03498i			0.0488981i
$449$			1.68858i			0.0796891i	0.999206	+	0.0398446i	$0.0126863\pi$
$449$			1.68858i			0.0796891i	−0.999206	+	0.0398446i	$0.987314\pi$
$450$	0.604693	−	1.04736i	0.0285055	−	0.0493730i
$451$	35.1747	+	7.76073i	1.65631	+	0.365438i
$452$	−10.9951	−	6.34800i	−0.517164	−	0.298585i
$453$	−0.178562	+	0.103093i	−0.00838956	+	0.00484371i
$454$	6.52900	+	11.3086i	0.306421	+	0.530737i
$455$		−	3.40339i		−	0.159553i
$456$	0.0863055	+	6.55816i	0.00404162	+	0.307114i
$457$		−	30.9238i		−	1.44655i	−0.690558	−	0.723277i	$-0.742635\pi$
$457$		−	30.9238i		−	1.44655i	0.690558	−	0.723277i	$-0.257365\pi$
$458$	−3.88851	−	6.73509i	−0.181698	−	0.314710i
$459$	−17.6208	−	30.5202i	−0.822470	−	1.42456i
$460$	−6.73044	+	11.6575i	−0.313808	+	0.543532i
$461$	8.45094	−	4.87915i	0.393599	−	0.227245i	−0.290119	−	0.956991i	$-0.593695\pi$
$461$	8.45094	−	4.87915i	0.393599	−	0.227245i	0.683719	+	0.729746i	$0.260362\pi$
$462$	1.55813	+	4.92437i	0.0724905	+	0.229102i
$463$	−0.198973			−0.00924708			−0.00462354	−	0.999989i	$-0.501472\pi$
$463$	−0.198973			−0.00924708			−0.00462354	+	0.999989i	$0.501472\pi$
$464$	−4.93655			−0.229173
$465$	−12.4707	+	21.5999i	−0.578315	+	1.00167i
$466$	−13.4326	−	7.75529i	−0.622251	−	0.359257i
$467$	−6.26389			−0.289858			−0.144929	−	0.989442i	$-0.546295\pi$
$467$	−6.26389			−0.289858			−0.144929	+	0.989442i	$0.546295\pi$
$468$	0.938946			0.0434028
$469$	3.90243	−	6.75921i	0.180197	−	0.312111i
$470$	7.37329	+	12.7709i	0.340105	+	0.589079i
$471$	−23.2593	−	13.4288i	−1.07173	−	0.618766i
$472$	9.19565	−	5.30911i	0.423264	−	0.244372i
$473$	2.48570	−	11.2662i	0.114293	−	0.518019i
$474$		−	18.9425i		−	0.870059i
$475$	3.66278	+	6.15561i	0.168060	+	0.282439i
$476$	6.48849			0.297399
$477$	7.21038	−	4.16292i	0.330141	−	0.190607i
$478$	−20.1854	+	11.6540i	−0.923259	+	0.533044i
$479$	−3.18610	−	1.83950i	−0.145577	−	0.0840487i	0.425442	−	0.904985i	$-0.360118\pi$
$479$	−3.18610	−	1.83950i	−0.145577	−	0.0840487i	−0.571019	+	0.820937i	$0.693452\pi$
$480$	3.35865	−	1.93912i	0.153301	−	0.0885082i
$481$	12.7304	+	7.34988i	0.580455	+	0.335126i
$482$	−13.8825			−0.632330
$483$	8.13308			0.370068
$484$	9.97877	+	4.62863i	0.453580	+	0.210392i
$485$	−11.4212	−	6.59401i	−0.518608	−	0.299419i
$486$		−	7.45922i		−	0.338357i
$487$		−	13.3798i		−	0.606296i	−0.952943	−	0.303148i	$-0.901962\pi$
$487$		−	13.3798i		−	0.606296i	0.952943	−	0.303148i	$-0.0980377\pi$
$488$	6.07379	+	3.50671i	0.274948	+	0.158741i
$489$	−19.4911	+	11.2532i	−0.881420	+	0.508888i
$490$	−7.64064	+	13.2340i	−0.345169	+	0.597850i
$491$	−33.5410	+	19.3649i	−1.51368	+	0.873925i	−0.513810	+	0.857904i	$0.671766\pi$
$491$	−33.5410	+	19.3649i	−1.51368	+	0.873925i	−0.999872	+	0.0160208i	$0.994900\pi$
$492$	−14.1523	+	8.17086i	−0.638037	+	0.368371i
$493$			30.9482i			1.39384i
$494$	−2.71697	+	4.85228i	−0.122242	+	0.218315i
$495$	−4.24564	+	4.64272i	−0.190827	+	0.208675i
$496$	5.56952	−	3.21556i	0.250079	−	0.144383i
$497$	0.643050	+	1.11380i	0.0288447	+	0.0499605i
$498$	1.73904	−	3.01211i	0.0779284	−	0.134976i
$499$	0.925300	+	1.60267i	0.0414221	+	0.0717452i	0.885993	−	0.463698i	$-0.153478\pi$
$499$	0.925300	+	1.60267i	0.0414221	+	0.0717452i	−0.844571	+	0.535443i	$0.820144\pi$
$500$	−4.32589	+	7.49267i	−0.193460	+	0.335082i
$501$			23.8067i			1.06361i
$502$	−3.79845			−0.169533
$503$	3.46674	+	2.00152i	0.154574	+	0.0892435i	0.575292	−	0.817948i	$-0.304888\pi$
$503$	3.46674	+	2.00152i	0.154574	+	0.0892435i	−0.420718	+	0.907192i	$0.638222\pi$
$504$	0.659650	+	0.380849i	0.0293831	+	0.0169644i
$505$			44.3419i			1.97319i
$506$	11.6891	−	12.7824i	0.519644	−	0.568245i
$507$	14.8191	+	8.55579i	0.658138	+	0.379976i
$508$	−5.37052	−	9.30202i	−0.238278	−	0.412710i
$509$	0.212375	+	0.122615i	0.00941336	+	0.00543481i	0.504699	−	0.863295i	$-0.331603\pi$
$509$	0.212375	+	0.122615i	0.00941336	+	0.00543481i	−0.495286	+	0.868730i	$0.664937\pi$
$510$	−12.1567	−	21.0561i	−0.538309	−	0.932378i
$511$	1.01222	+	1.75321i	0.0447778	+	0.0775574i
$512$	−1.00000			−0.0441942
$513$	21.3797	+	11.9713i	0.943936	+	0.528544i
$514$			18.5003i			0.816011i
$515$	−4.53423	+	2.61784i	−0.199802	+	0.115356i
$516$	2.61706	+	4.53288i	0.115210	+	0.199549i
$517$	−5.72438	−	18.0916i	−0.251758	−	0.795668i
$518$	5.96242	+	10.3272i	0.261974	+	0.453752i
$519$	−13.5262	−	7.80936i	−0.593735	−	0.342793i
$520$	3.28837			0.144204
$521$			9.34318i			0.409332i	0.978832	+	0.204666i	$0.0656108\pi$
$521$			9.34318i			0.409332i	−0.978832	+	0.204666i	$0.934389\pi$
$522$	−1.81654	+	3.14634i	−0.0795078	+	0.137711i
$523$	19.8582	−	34.3954i	0.868339	−	1.50401i	0.00464596	−	0.999989i	$-0.498521\pi$
$523$	19.8582	−	34.3954i	0.868339	−	1.50401i	0.863693	−	0.504018i	$-0.168146\pi$
$524$		−	4.31834i		−	0.188648i
$525$	−2.55910			−0.111688
$526$	8.06674	+	4.65734i	0.351727	+	0.203069i
$527$	−20.1590	−	34.9165i	−0.878141	−	1.52098i
$528$	−4.75795	+	1.50547i	−0.207063	+	0.0655170i
$529$	−2.13746	−	3.70219i	−0.0929330	−	0.160965i
$530$	25.2522	−	14.5793i	1.09688	−	0.633286i
$531$		−	7.81454i		−	0.339122i
$532$	−3.87694	+	2.30690i	−0.168086	+	0.100017i
$533$	−13.8562			−0.600179
$534$	−7.71444	−	13.3618i	−0.333836	−	0.578221i
$535$	19.0164	+	32.9374i	0.822150	+	1.42401i
$536$	6.53077	+	3.77054i	0.282086	+	0.162863i
$537$	5.92464	+	10.2618i	0.255667	+	0.442828i
$538$	13.5799	+	7.84037i	0.585472	+	0.338022i
$539$	13.2699	−	14.5110i	0.571576	−	0.625033i
$540$		−	14.4889i		−	0.623503i
$541$	−6.22825	−	3.59588i	−0.267774	−	0.154599i	0.360102	−	0.932913i	$-0.382742\pi$
$541$	−6.22825	−	3.59588i	−0.267774	−	0.154599i	−0.627875	+	0.778314i	$0.716075\pi$
$542$	8.80397	+	5.08297i	0.378163	+	0.218332i
$543$	−11.4031			−0.489356
$544$			6.26920i			0.268790i
$545$	12.9819	−	22.4853i	0.556084	−	0.963166i
$546$	−0.993419	−	1.72065i	−0.0425144	−	0.0736371i
$547$	9.42822	−	16.3302i	0.403121	−	0.698227i	−0.590979	−	0.806687i	$-0.701259\pi$
$547$	9.42822	−	16.3302i	0.403121	−	0.698227i	0.994101	+	0.108460i	$0.0345919\pi$
$548$	4.24589	+	7.35410i	0.181376	+	0.314152i
$549$	4.47004	−	2.58078i	0.190777	−	0.110145i
$550$	−3.67801	+	4.02201i	−0.156831	+	0.171499i
$551$	−11.0032	−	18.4919i	−0.468754	−	0.787780i
$552$			7.85822i			0.334468i
$553$	11.2838	−	6.51473i	0.479838	−	0.277034i
$554$	−0.615049	+	0.355099i	−0.0261309	+	0.0150867i
$555$	22.3422	−	38.6978i	0.948373	−	1.64263i
$556$	−4.81963	+	2.78261i	−0.204398	+	0.118009i
$557$	−23.4342	−	13.5298i	−0.992940	−	0.573274i	−0.0867885	−	0.996227i	$-0.527660\pi$
$557$	−23.4342	−	13.5298i	−0.992940	−	0.573274i	−0.906152	+	0.422952i	$0.860994\pi$
$558$		−	4.73302i		−	0.200365i
$559$			4.43803i			0.187709i
$560$	2.31022	+	1.33381i	0.0976246	+	0.0563636i
$561$	9.43808	+	29.8285i	0.398476	+	1.25936i
$562$	−14.3696			−0.606146
$563$	−15.8265			−0.667007			−0.333503	−	0.942749i	$-0.608231\pi$
$563$	−15.8265			−0.667007			−0.333503	+	0.942749i	$0.608231\pi$
$564$	7.45544	+	4.30440i	0.313931	+	0.181248i
$565$	−28.3393	+	16.3617i	−1.19224	+	0.688342i
$566$	0.730650	+	0.421841i	0.0307115	+	0.0177313i
$567$	−5.60243	+	3.23457i	−0.235280	+	0.135839i
$568$	−1.07615	+	0.621318i	−0.0451544	+	0.0260699i
$569$	−15.2885			−0.640929			−0.320464	−	0.947261i	$-0.603839\pi$
$569$	−15.2885			−0.640929			−0.320464	+	0.947261i	$0.603839\pi$
$570$	14.7500	+	8.25904i	0.617808	+	0.345933i
$571$		−	10.6630i		−	0.446233i	−0.974792	−	0.223116i	$-0.928377\pi$
$571$		−	10.6630i		−	0.446233i	0.974792	−	0.223116i	$-0.0716230\pi$
$572$	−4.13203	−	0.911667i	−0.172769	−	0.0381187i
$573$	23.8481	−	13.7687i	0.996269	−	0.575196i
$574$	−9.73458	−	5.62026i	−0.406313	−	0.234585i
$575$	4.29106	+	7.43234i	0.178950	+	0.309950i
$576$	−0.367978	+	0.637356i	−0.0153324	+	0.0265565i
$577$	22.1114			0.920508			0.460254	−	0.887787i	$-0.347758\pi$
$577$	22.1114			0.920508			0.460254	+	0.887787i	$0.347758\pi$
$578$	22.3029			0.927679
$579$	2.15215	+	1.24255i	0.0894404	+	0.0516384i
$580$	−6.36187	+	11.0191i	−0.264162	+	0.457542i
$581$	2.39237			0.0992523
$582$	−7.69894			−0.319131
$583$	−35.7728	+	11.3189i	−1.48156	+	0.468782i
$584$	−1.69396	+	0.978008i	−0.0700965	+	0.0404702i
$585$	1.21005	−	2.09586i	0.0500293	−	0.0866532i
$586$	−1.72074	−	2.98042i	−0.0710833	−	0.123120i
$587$	6.96222	+	12.0589i	0.287362	+	0.497725i	0.973179	−	0.230049i	$-0.0738886\pi$
$587$	6.96222	+	12.0589i	0.287362	+	0.497725i	−0.685818	+	0.727773i	$0.740555\pi$
$588$			8.92094i			0.367894i
$589$	24.4593	+	13.6956i	1.00783	+	0.564319i
$590$		−	27.3680i		−	1.12672i
$591$	17.8941	+	30.9934i	0.736063	+	1.27490i
$592$	−9.97820	+	5.76092i	−0.410101	+	0.236772i
$593$	27.5467	+	15.9041i	1.13121	+	0.653103i	0.944238	−	0.329263i	$-0.106800\pi$
$593$	27.5467	+	15.9041i	1.13121	+	0.653103i	0.186969	+	0.982366i	$0.440134\pi$
$594$	−4.01690	+	18.2062i	−0.164815	+	0.747009i
$595$	8.36190	−	14.4832i	0.342804	−	0.593755i
$596$		−	11.6240i		−	0.476139i
$597$			26.2836i			1.07571i
$598$	−3.33151	+	5.77034i	−0.136235	+	0.235967i
$599$	9.14428	+	5.27945i	0.373625	+	0.215713i	0.675041	−	0.737780i	$-0.264126\pi$
$599$	9.14428	+	5.27945i	0.373625	+	0.215713i	−0.301416	+	0.953493i	$0.597459\pi$
$600$		−	2.47261i		−	0.100944i
$601$	−18.6740			−0.761727			−0.380863	−	0.924631i	$-0.624373\pi$
$601$	−18.6740			−0.761727			−0.380863	+	0.924631i	$0.624373\pi$
$602$	−1.80012	+	3.11791i	−0.0733676	+	0.127076i
$603$	4.80636	−	2.77495i	0.195730	−	0.113005i
$604$	0.0685149	−	0.118671i	0.00278783	−	0.00482867i
$605$	23.1917	−	16.3090i	0.942876	−	0.663055i
$606$	12.9430	+	22.4179i	0.525774	+	0.910667i
$607$	−26.0751			−1.05835			−0.529177	−	0.848511i	$-0.677499\pi$
$607$	−26.0751			−1.05835			−0.529177	+	0.848511i	$0.677499\pi$
$608$	−2.22893	−	3.74591i	−0.0903952	−	0.151917i
$609$	7.68771			0.311522
$610$	15.6549	−	9.03838i	0.633850	−	0.365953i
$611$	3.64972	+	6.32149i	0.147652	+	0.255740i
$612$	3.99572	+	2.30693i	0.161517	+	0.0932520i
$613$	14.9163	−	8.61192i	0.602463	−	0.347832i	−0.167547	−	0.985864i	$-0.553585\pi$
$613$	14.9163	−	8.61192i	0.602463	−	0.347832i	0.770010	+	0.638032i	$0.220251\pi$
$614$	12.7937	−	22.1594i	0.516313	−	0.894280i
$615$			42.1201i			1.69845i
$616$	−2.53315	−	2.31649i	−0.102063	−	0.0933342i
$617$	−16.8501	+	29.1853i	−0.678361	+	1.17496i	0.297113	+	0.954842i	$0.403976\pi$
$617$	−16.8501	+	29.1853i	−0.678361	+	1.17496i	−0.975474	+	0.220114i	$0.929357\pi$
$618$	−1.52825	+	2.64700i	−0.0614751	+	0.106478i
$619$	27.9306			1.12262			0.561312	−	0.827604i	$-0.310297\pi$
$619$	27.9306			1.12262			0.561312	+	0.827604i	$0.310297\pi$
$620$		−	16.5760i		−	0.665707i
$621$	25.4247	+	14.6790i	1.02026	+	0.589047i
$622$	4.37543	+	7.57846i	0.175439	+	0.303869i
$623$	5.30631	−	9.19080i	0.212593	−	0.368222i
$624$	1.66250	−	0.959846i	0.0665533	−	0.0384246i
$625$	15.2580	+	26.4277i	0.610321	+	1.05711i
$626$	−6.44025			−0.257404
$627$	−16.2445	−	14.4673i	−0.648743	−	0.577767i
$628$	17.8494			0.712269
$629$	36.1164	+	62.5554i	1.44005	+	2.49425i
$630$	1.70022	−	0.981622i	0.0677383	−	0.0391087i
$631$	21.4324	−	37.1220i	0.853211	−	1.47780i	−0.0250841	−	0.999685i	$-0.507985\pi$
$631$	21.4324	−	37.1220i	0.853211	−	1.47780i	0.878295	−	0.478119i	$-0.158681\pi$
$632$	6.29456	+	10.9025i	0.250384	+	0.433678i
$633$	16.6847	+	9.63292i	0.663158	+	0.382874i
$634$		−	15.2040i		−	0.603828i
$635$	−27.6846			−1.09863
$636$	8.51116	−	14.7418i	0.337489	−	0.584549i
$637$	−3.78205	+	6.55070i	−0.149850	+	0.259548i
$638$	11.0490	−	12.0824i	0.437434	−	0.478346i
$639$			0.914524i			0.0361780i
$640$	−1.28873	+	2.23214i	−0.0509415	+	0.0882332i
$641$	−16.4320	+	9.48701i	−0.649024	+	0.374714i	−0.788082	−	0.615570i	$-0.788926\pi$
$641$	−16.4320	+	9.48701i	−0.649024	+	0.374714i	0.139058	+	0.990284i	$0.455592\pi$
$642$	19.2282	+	11.1014i	0.758878	+	0.438139i
$643$	12.8034	+	22.1762i	0.504918	+	0.874544i	0.999984	+	0.00568864i	$0.00181076\pi$
$643$	12.8034	+	22.1762i	0.504918	+	0.874544i	−0.495065	+	0.868856i	$0.664856\pi$
$644$	−4.68105	+	2.70261i	−0.184459	+	0.106498i
$645$	13.4907			0.531197
$646$	−23.4839	+	13.9736i	−0.923961	+	0.549786i
$647$	−25.7999			−1.01430			−0.507149	−	0.861859i	$-0.669300\pi$
$647$	−25.7999			−1.01430			−0.507149	+	0.861859i	$0.669300\pi$
$648$	−3.12525	−	5.41309i	−0.122771	−	0.212646i
$649$	−7.58750	+	34.3896i	−0.297836	+	1.34991i
$650$	1.04827	−	1.81565i	0.0411165	−	0.0712158i
$651$	−8.67344	+	5.00761i	−0.339939	+	0.196264i
$652$	7.47884	−	12.9537i	0.292894	−	0.507307i
$653$	−19.2782			−0.754416			−0.377208	−	0.926129i	$-0.623116\pi$
$653$	−19.2782			−0.754416			−0.377208	+	0.926129i	$0.623116\pi$
$654$		−	15.1572i		−	0.592695i
$655$	−9.63916	−	5.56517i	−0.376633	−	0.217449i
$656$	5.43032	−	9.40559i	0.212018	−	0.367227i
$657$			1.43954i			0.0561618i
$658$			5.92149i			0.230844i
$659$	−24.1711	+	41.8657i	−0.941574	+	1.63085i	−0.179105	+	0.983830i	$0.557320\pi$
$659$	−24.1711	+	41.8657i	−0.941574	+	1.63085i	−0.762469	+	0.647024i	$0.776013\pi$
$660$	−2.77128	+	12.5606i	−0.107872	+	0.488919i
$661$	22.6189	+	13.0590i	0.879772	+	0.507936i	0.870583	−	0.492021i	$-0.163742\pi$
$661$	22.6189	+	13.0590i	0.879772	+	0.507936i	0.00918865	+	0.999958i	$0.497075\pi$
$662$	−2.88351	+	1.66480i	−0.112071	+	0.0647042i
$663$	−6.01747	−	10.4226i	−0.233699	−	0.404779i
$664$			2.31152i			0.0897044i
$665$	0.153010	+	11.6268i	0.00593345	+	0.450870i
$666$			8.47955i			0.328576i
$667$	−12.8907	−	22.3273i	−0.499128	−	0.864515i
$668$	−7.91092	−	13.7021i	−0.306083	−	0.530151i
$669$	5.50639	−	9.53734i	0.212889	−	0.368735i
$670$	16.8328	−	9.71842i	0.650307	−	0.375455i
$671$	−22.1772	+	7.01711i	−0.856141	+	0.270892i
$672$	1.55730			0.0600743
$673$	−16.5428			−0.637679			−0.318839	−	0.947809i	$-0.603293\pi$
$673$	−16.5428			−0.637679			−0.318839	+	0.947809i	$0.603293\pi$
$674$	10.5268	−	18.2330i	0.405477	−	0.702308i
$675$	−7.99997	−	4.61878i	−0.307919	−	0.177777i
$676$	−11.3723			−0.437396
$677$	−38.3734			−1.47481			−0.737405	−	0.675450i	$-0.763949\pi$
$677$	−38.3734			−1.47481			−0.737405	+	0.675450i	$0.763949\pi$
$678$	−9.55167	+	16.5440i	−0.366830	+	0.635367i
$679$	−2.64783	−	4.58617i	−0.101614	−	0.176001i
$680$	13.9938	+	8.07930i	0.536636	+	0.309827i
$681$	17.0157	−	9.82402i	0.652043	−	0.376457i
$682$	−4.59552	+	20.8287i	−0.175971	+	0.797572i
$683$			33.6671i			1.28824i	0.764926	+	0.644118i	$0.222775\pi$
$683$			33.6671i			1.28824i	−0.764926	+	0.644118i	$0.777225\pi$
$684$	−3.20768	+	0.0422131i	−0.122649	+	0.00161406i
$685$	21.8872			0.836268
$686$	−11.5883	+	6.69052i	−0.442444	+	0.255445i
$687$	−10.1341	+	5.85094i	−0.386641	+	0.223227i
$688$	−3.01253	−	1.73929i	−0.114852	−	0.0663097i
$689$	12.4996	−	7.21664i	0.476197	−	0.274932i
$690$	17.5407	+	10.1271i	0.667762	+	0.385533i
$691$	16.4600			0.626167			0.313083	−	0.949726i	$-0.398638\pi$
$691$	16.4600			0.626167			0.313083	+	0.949726i	$0.398638\pi$
$692$	10.3801			0.394593
$693$	−2.40857	+	0.762099i	−0.0914941	+	0.0289497i
$694$	26.0648	+	15.0485i	0.989407	+	0.571235i
$695$			14.3441i			0.544104i
$696$			7.42789i			0.281554i
$697$	−58.9656	−	34.0438i	−2.23348	−	1.28950i
$698$	18.2734	−	10.5502i	0.691660	−	0.399330i
$699$	−11.6692	+	20.2116i	−0.441369	+	0.764473i
$700$	1.47291	−	0.850383i	0.0556706	−	0.0321414i
$701$	21.9133	−	12.6517i	0.827656	−	0.477847i	−0.0253936	−	0.999678i	$-0.508084\pi$
$701$	21.9133	−	12.6517i	0.827656	−	0.477847i	0.853049	+	0.521830i	$0.174751\pi$
$702$		−	7.17188i		−	0.270685i
$703$	−43.8206	−	24.5367i	−1.65273	−	0.925421i
$704$	2.23821	−	2.44754i	0.0843555	−	0.0922450i
$705$	19.2161	−	11.0944i	0.723719	−	0.417839i
$706$	−12.9265	−	22.3893i	−0.486495	−	0.842634i
$707$	−8.90274	+	15.4200i	−0.334822	+	0.579929i
$708$	−7.98848	−	13.8365i	−0.300226	−	0.520006i
$709$	−22.3215	+	38.6620i	−0.838301	+	1.45198i	0.0530123	+	0.998594i	$0.483118\pi$
$709$	−22.3215	+	38.6620i	−0.838301	+	1.45198i	−0.891314	+	0.453387i	$0.850216\pi$
$710$			3.20284i			0.120200i
$711$	9.26503			0.347466
$712$	8.88019	+	5.12698i	0.332799	+	0.192142i
$713$	29.0870	+	16.7934i	1.08932	+	0.628918i
$714$		−	9.76306i		−	0.365373i
$715$	−7.36004	+	8.04840i	−0.275250	+	0.300993i
$716$	−6.81993	−	3.93749i	−0.254873	−	0.147151i
$717$	17.5355	+	30.3724i	0.654877	+	1.13428i
$718$	1.56776	+	0.905146i	0.0585082	+	0.0337797i
$719$	−18.1671	−	31.4663i	−0.677518	−	1.17350i	−0.975726	−	0.218995i	$-0.929722\pi$
$719$	−18.1671	−	31.4663i	−0.677518	−	1.17350i	0.298208	−	0.954501i	$-0.403611\pi$
$720$	0.948447	+	1.64276i	0.0353465	+	0.0612220i
$721$	−2.10238			−0.0782969
$722$	9.06370	−	16.6988i	0.337316	−	0.621464i
$723$			20.8886i			0.776856i
$724$	6.56316	−	3.78924i	0.243918	−	0.140826i
$725$	4.05608	+	7.02534i	0.150639	+	0.260914i
$726$	6.96457	−	15.0148i	0.258480	−	0.557251i
$727$	−2.43997	−	4.22615i	−0.0904934	−	0.156739i	0.817225	−	0.576318i	$-0.195511\pi$
$727$	−2.43997	−	4.22615i	−0.0904934	−	0.156739i	−0.907719	+	0.419579i	$0.862178\pi$
$728$	1.14354	+	0.660222i	0.0423823	+	0.0244695i
$729$	−29.9752			−1.11019
$730$			5.04155i			0.186596i
$731$	−10.9039	+	18.8862i	−0.403297	+	0.698531i
$732$	5.27645	−	9.13908i	0.195023	−	0.337790i
$733$			37.2391i			1.37546i	0.725967	+	0.687729i	$0.241392\pi$
$733$			37.2391i			1.37546i	−0.725967	+	0.687729i	$0.758608\pi$
$734$	−23.6594			−0.873284
$735$	19.9128	+	11.4967i	0.734496	+	0.424061i
$736$	−2.61127	−	4.52285i	−0.0962527	−	0.166715i
$737$	−23.8458	+	7.54506i	−0.878370	+	0.277926i
$738$	−3.99647	−	6.92209i	−0.147112	−	0.254806i
$739$	30.0495	−	17.3491i	1.10539	−	0.638197i	0.167758	−	0.985828i	$-0.446347\pi$
$739$	30.0495	−	17.3491i	1.10539	−	0.638197i	0.937631	+	0.347632i	$0.113014\pi$
$740$			29.6970i			1.09168i
$741$	7.30110	+	4.08815i	0.268213	+	0.150182i
$742$	11.7087			0.429839
$743$	−17.5229	−	30.3506i	−0.642853	−	1.11345i	−0.984793	−	0.173732i	$-0.944417\pi$
$743$	−17.5229	−	30.3506i	−0.642853	−	1.11345i	0.341940	−	0.939722i	$-0.388916\pi$
$744$	−4.83838	−	8.38031i	−0.177384	−	0.307237i
$745$	−25.9465	−	14.9802i	−0.950607	−	0.548833i
$746$	2.53433	+	4.38958i	0.0927883	+	0.160714i
$747$	1.47326	+	0.850588i	0.0539038	+	0.0311214i
$748$	−15.3441	−	14.0318i	−0.561036	−	0.513052i
$749$			15.2721i			0.558029i
$750$	11.2740	+	6.50906i	0.411669	+	0.237677i
$751$	5.60281	+	3.23478i	0.204449	+	0.118039i	0.598729	−	0.800952i	$-0.295673\pi$
$751$	5.60281	+	3.23478i	0.204449	+	0.118039i	−0.394280	+	0.918990i	$0.629006\pi$
$752$	−5.72137			−0.208637
$753$			5.71543i			0.208282i
$754$	−3.14907	+	5.45435i	−0.114682	+	0.198636i
$755$	−0.176594	−	0.305870i	−0.00642692	−	0.0111318i
$756$	2.90901	−	5.03855i	0.105800	−	0.183250i
$757$	−14.0964	−	24.4158i	−0.512344	−	0.887406i	−0.999898	−	0.0143129i	$-0.995444\pi$
$757$	−14.0964	−	24.4158i	−0.512344	−	0.887406i	0.487553	−	0.873093i	$-0.337889\pi$
$758$	−9.29142	+	5.36441i	−0.337480	+	0.194844i
$759$	−19.2333	−	17.5883i	−0.698124	−	0.638415i
$760$	−11.2339	+	0.147838i	−0.407497	+	0.00536266i
$761$		−	15.6802i		−	0.568408i	−0.958764	−	0.284204i	$-0.908271\pi$
$761$		−	15.6802i		−	0.568408i	0.958764	−	0.284204i	$-0.0917293\pi$
$762$	−13.9965	+	8.08088i	−0.507040	+	0.292740i
$763$	9.02899	−	5.21289i	0.326871	−	0.188719i
$764$	−9.15063	+	15.8493i	−0.331058	+	0.573409i
$765$	10.2988	−	5.94601i	0.372353	−	0.214978i
$766$	20.0577	+	11.5803i	0.724714	+	0.418414i
$767$		−	13.5469i		−	0.489151i
$768$			1.50467i			0.0542953i
$769$	3.73465	+	2.15620i	0.134675	+	0.0777546i	0.565824	−	0.824526i	$-0.308558\pi$
$769$	3.73465	+	2.15620i	0.134675	+	0.0777546i	−0.431149	+	0.902281i	$0.641892\pi$
$770$	−8.43528	+	2.66902i	−0.303987	+	0.0961847i
$771$	27.8369			1.00252
$772$	−1.65158			−0.0594417
$773$	−28.5174	−	16.4645i	−1.02570	−	0.592187i	−0.109949	−	0.993937i	$-0.535069\pi$
$773$	−28.5174	−	16.4645i	−1.02570	−	0.592187i	−0.915749	+	0.401750i	$0.868402\pi$
$774$	−2.21709	+	1.28004i	−0.0796917	+	0.0460100i
$775$	−9.15232	−	5.28409i	−0.328761	−	0.189810i
$776$	4.43118	−	2.55834i	0.159070	−	0.0918391i
$777$	15.5391	−	8.97150i	0.557462	−	0.321851i
$778$	−15.6878			−0.562434
$779$	47.3363	−	0.622947i	1.69600	−	0.0223194i
$780$		−	4.94792i		−	0.177164i
$781$	0.887954	−	4.02456i	0.0317735	−	0.144010i
$782$	−28.3547	+	16.3706i	−1.01396	+	0.585411i
$783$	24.0325	+	13.8751i	0.858850	+	0.495857i
$784$	−2.96441	−	5.13451i	−0.105872	−	0.183375i
$785$	23.0031	−	39.8425i	0.821014	−	1.42204i
$786$	−6.49770			−0.231765
$787$	41.9603			1.49572			0.747861	−	0.663856i	$-0.231081\pi$
$787$	41.9603			1.49572			0.747861	+	0.663856i	$0.231081\pi$
$788$	−20.5981	−	11.8923i	−0.733776	−	0.423646i
$789$	7.00777	−	12.1378i	0.249483	−	0.432118i
$790$	32.4479			1.15444
$791$	−13.1401			−0.467207
$792$	−0.736343	−	2.32717i	−0.0261648	−	0.0826925i
$793$	7.74906	−	4.47392i	0.275177	−	0.158874i
$794$	0.419461	−	0.726527i	0.0148861	−	0.0257835i
$795$	−21.9372	−	37.9963i	−0.778031	−	1.34759i
$796$	−8.73397	−	15.1277i	−0.309567	−	0.536186i
$797$		−	11.7067i		−	0.414674i	−0.978270	−	0.207337i	$-0.933520\pi$
$797$		−	11.7067i		−	0.414674i	0.978270	−	0.207337i	$-0.0664796\pi$
$798$	3.47113	+	5.83353i	0.122877	+	0.206505i
$799$			35.8684i			1.26893i
$800$	0.821643	+	1.42313i	0.0290495	+	0.0503152i
$801$	6.53543	−	3.77323i	0.230918	−	0.133321i
$802$	−2.38649	−	1.37784i	−0.0842700	−	0.0486533i
$803$	1.39772	−	6.33501i	0.0493244	−	0.223558i
$804$	5.67344	−	9.82669i	0.200087	−	0.346561i
$805$			13.9317i			0.491028i
$806$		−	8.20495i		−	0.289007i
$807$	11.7972	−	20.4334i	0.415281	−	0.719288i
$808$	−14.8989	−	8.60187i	−0.524140	−	0.302613i
$809$		−	40.9084i		−	1.43826i	−0.694874	−	0.719131i	$-0.744540\pi$
$809$		−	40.9084i		−	1.43826i	0.694874	−	0.719131i	$-0.255460\pi$
$810$	−16.1104			−0.566062
$811$	19.4964	−	33.7687i	0.684611	−	1.18578i	−0.288948	−	0.957345i	$-0.593306\pi$
$811$	19.4964	−	33.7687i	0.684611	−	1.18578i	0.973559	−	0.228436i	$-0.0733611\pi$
$812$	−4.42471	+	2.55461i	−0.155277	+	0.0896492i
$813$	7.64822	−	13.2471i	0.268235	−	0.464596i
$814$	8.23320	−	37.3161i	0.288573	−	1.30793i
$815$	−19.2764	−	33.3877i	−0.675222	−	1.16952i
$816$	9.43311			0.330225
$817$	−0.199525	−	15.1614i	−0.00698049	−	0.530432i
$818$	−23.3067			−0.814901
$819$	0.841593	−	0.485894i	0.0294076	−	0.0169785i
$820$	−13.9964	−	24.2425i	−0.488776	−	0.846585i
$821$	15.9807	+	9.22644i	0.557729	+	0.322005i	0.752233	−	0.658897i	$-0.228977\pi$
$821$	15.9807	+	9.22644i	0.557729	+	0.322005i	−0.194505	+	0.980902i	$0.562310\pi$
$822$	11.0655	−	6.38869i	0.385955	−	0.222831i
$823$	−12.2487	+	21.2154i	−0.426962	+	0.739521i	−0.996601	−	0.0823743i	$-0.973750\pi$
$823$	−12.2487	+	21.2154i	−0.426962	+	0.739521i	0.569639	+	0.821895i	$0.307083\pi$
$824$		−	2.03133i		−	0.0707648i
$825$	6.05181	+	5.53421i	0.210697	+	0.192676i
$826$	5.49481	−	9.51730i	0.191189	−	0.331149i
$827$	11.5078	−	19.9321i	0.400166	−	0.693109i	−0.593579	−	0.804776i	$-0.702286\pi$
$827$	11.5078	−	19.9321i	0.400166	−	0.693109i	0.993746	+	0.111667i	$0.0356190\pi$
$828$	−3.84356			−0.133573
$829$			12.1162i			0.420814i	0.977614	+	0.210407i	$0.0674790\pi$
$829$			12.1162i			0.420814i	−0.977614	+	0.210407i	$0.932521\pi$
$830$	5.15965	+	2.97892i	0.179094	+	0.103400i
$831$	0.534308	+	0.925448i	0.0185349	+	0.0321034i
$832$	−0.637909	+	1.10489i	−0.0221155	+	0.0383052i
$833$	−32.1893	+	18.5845i	−1.11529	+	0.643914i
$834$	4.18693	+	7.25197i	0.144981	+	0.251115i
$835$	−40.7801			−1.41126
$836$	14.1571	+	2.92872i	0.489632	+	0.101292i
$837$	−36.1519			−1.24959
$838$	18.6845	+	32.3624i	0.645444	+	1.11794i
$839$	−38.0663	+	21.9776i	−1.31420	+	0.758751i	−0.982788	−	0.184737i	$-0.940857\pi$
$839$	−38.0663	+	21.9776i	−1.31420	+	0.758751i	−0.331407	+	0.943488i	$0.607523\pi$
$840$	2.00694	−	3.47613i	0.0692461	−	0.119938i
$841$	2.31525	+	4.01014i	0.0798363	+	0.138281i
$842$	11.5480	+	6.66723i	0.397970	+	0.229768i
$843$			21.6216i			0.744688i
$844$	−12.8040			−0.440732
$845$	−14.6558	+	25.3846i	−0.504175	+	0.873256i
$846$	−2.10534	+	3.64655i	−0.0723830	+	0.125371i
$847$	11.3394	−	1.01519i	0.389627	−	0.0348822i
$848$			11.3130i			0.388489i
$849$	0.634733	−	1.09939i	0.0217840	−	0.0377310i
$850$	8.92188	−	5.15105i	0.306018	−	0.176680i
$851$	−52.1115	−	30.0866i	−1.78636	−	1.03136i
$852$	0.934880	+	1.61926i	0.0320285	+	0.0554750i
$853$	−31.2859	+	18.0629i	−1.07121	+	0.618462i	−0.928511	−	0.371305i	$-0.878911\pi$
$853$	−31.2859	+	18.0629i	−1.07121	+	0.618462i	−0.142696	+	0.989767i	$0.545577\pi$
$854$	7.25872			0.248388
$855$	−4.03960	+	7.21440i	−0.138151	+	0.246727i
$856$	−14.7559			−0.504347
$857$	6.10797	+	10.5793i	0.208644	+	0.361383i	0.951288	−	0.308304i	$-0.0997615\pi$
$857$	6.10797	+	10.5793i	0.208644	+	0.361383i	−0.742643	+	0.669687i	$0.766428\pi$
$858$	−1.37176	+	6.21737i	−0.0468312	+	0.212257i
$859$	−11.6292	+	20.1423i	−0.396782	+	0.687246i	−0.993327	−	0.115334i	$-0.963206\pi$
$859$	−11.6292	+	20.1423i	−0.396782	+	0.687246i	0.596545	+	0.802579i	$0.296540\pi$
$860$	−7.76468	+	4.48294i	−0.264773	+	0.152867i
$861$	−8.45666	+	14.6474i	−0.288202	+	0.499181i
$862$	−0.972737			−0.0331315
$863$		−	27.6194i		−	0.940177i	−0.882619	−	0.470088i	$-0.844222\pi$
$863$		−	27.6194i		−	0.940177i	0.882619	−	0.470088i	$-0.155778\pi$
$864$	4.86827	+	2.81070i	0.165622	+	0.0956219i
$865$	13.3772	−	23.1699i	0.454838	−	0.787802i
$866$		−	8.57048i		−	0.291237i
$867$		−	33.5586i		−	1.13971i
$868$	3.32804	−	5.76433i	0.112961	−	0.195654i
$869$	−40.7728	−	8.99585i	−1.38312	−	0.305163i
$870$	16.5801	+	9.57254i	0.562119	+	0.324540i
$871$	8.33208	−	4.81053i	0.282322	−	0.162999i
$872$	5.03672	+	8.72385i	0.170565	+	0.295427i
$873$		−	3.76565i		−	0.127448i
$874$	11.1219	−	19.8627i	0.376202	−	0.671867i
$875$			8.95441i			0.302714i
$876$	1.47158	+	2.54886i	0.0497202	+	0.0861179i
$877$	0.789626	+	1.36767i	0.0266638	+	0.0461830i	0.879049	−	0.476731i	$-0.158178\pi$
$877$	0.789626	+	1.36767i	0.0266638	+	0.0461830i	−0.852386	+	0.522914i	$0.824845\pi$
$878$	16.7943	−	29.0886i	0.566780	−	0.981691i
$879$	−4.48455	+	2.58916i	−0.151260	+	0.0873301i
$880$	−2.57882	−	8.15021i	−0.0869319	−	0.274743i
$881$	57.0988			1.92371			0.961853	−	0.273567i	$-0.0882034\pi$
$881$	57.0988			1.92371			0.961853	+	0.273567i	$0.0882034\pi$
$882$	−4.36335			−0.146922
$883$	4.44129	−	7.69253i	0.149461	−	0.258874i	−0.781567	−	0.623821i	$-0.785579\pi$
$883$	4.44129	−	7.69253i	0.149461	−	0.258874i	0.931028	+	0.364947i	$0.118913\pi$
$884$	6.92679	+	3.99918i	0.232973	+	0.134507i
$885$	−41.1800			−1.38425
$886$	5.33317			0.179172
$887$	0.00621394	−	0.0107629i	0.000208644	−	0.000361381i	−0.865921	−	0.500181i	$-0.833267\pi$
$887$	0.00621394	−	0.0107629i	0.000208644	−	0.000361381i	0.866130	+	0.499819i	$0.166600\pi$
$888$	8.66830	+	15.0139i	0.290889	+	0.503835i
$889$	−9.62738	−	5.55837i	−0.322892	−	0.186422i
$890$	22.8883	−	13.2146i	0.767218	−	0.442954i
$891$	20.2437	+	4.46645i	0.678190	+	0.149632i
$892$			7.31904i			0.245060i
$893$	−12.7526	−	21.4317i	−0.426748	−	0.717186i
$894$	−17.4904			−0.584966
$895$	−17.5781	+	10.1487i	−0.587570	+	0.339234i
$896$	−0.896317	+	0.517489i	−0.0299439	+	0.0172881i
$897$	8.68248	+	5.01283i	0.289900	+	0.167374i
$898$	−1.46236	+	0.844291i	−0.0487994	+	0.0281744i
$899$	27.4942	+	15.8738i	0.916983	+	0.529420i
$900$	1.20939			0.0403129
$901$	70.9233			2.36280
$902$	10.8664	+	34.3425i	0.361810	+	1.14348i
$903$	4.69143	+	2.70860i	0.156121	+	0.0901366i
$904$		−	12.6960i		−	0.422262i
$905$		−	19.5332i		−	0.649306i
$906$	−0.178562	−	0.103093i	−0.00593231	−	0.00342502i
$907$	26.6724	−	15.3993i	0.885644	−	0.511327i	0.0131288	−	0.999914i	$-0.495821\pi$
$907$	26.6724	−	15.3993i	0.885644	−	0.511327i	0.872515	+	0.488587i	$0.162488\pi$
$908$	−6.52900	+	11.3086i	−0.216673	+	0.375288i
$909$	−10.9649	+	6.33059i	−0.363683	+	0.209972i
$910$	2.94742	−	1.70169i	0.0977061	−	0.0564106i
$911$		−	34.4265i		−	1.14060i	−0.821437	−	0.570300i	$-0.806827\pi$
$911$		−	34.4265i		−	1.14060i	0.821437	−	0.570300i	$-0.193173\pi$
$912$	−5.63638	+	3.35382i	−0.186639	+	0.111056i
$913$	−5.65753	−	5.17366i	−0.187237	−	0.171223i
$914$	26.7808	−	15.4619i	0.885829	−	0.511434i
$915$	−13.5998	−	23.5556i	−0.449596	−	0.778724i
$916$	3.88851	−	6.73509i	0.128480	−	0.222534i
$917$	−2.23469	−	3.87060i	−0.0737961	−	0.127819i
$918$	17.6208	−	30.5202i	0.581574	−	1.00732i
$919$			4.94601i			0.163154i	0.996667	+	0.0815770i	$0.0259956\pi$
$919$			4.94601i			0.163154i	−0.996667	+	0.0815770i	$0.974004\pi$
$920$	−13.4609			−0.443792
$921$	−33.3427	−	19.2504i	−1.09868	−	0.634322i
$922$	8.45094	+	4.87915i	0.278317	+	0.160686i
$923$			1.58538i			0.0521833i
$924$	−3.48557	+	3.81156i	−0.114667	+	0.125391i
$925$	16.3970	+	9.46683i	0.539131	+	0.311268i
$926$	−0.0994867	−	0.172316i	−0.00326934	−	0.00566266i
$927$	−1.29468	−	0.747485i	−0.0425229	−	0.0245506i
$928$	−2.46827	−	4.27517i	−0.0810250	−	0.140339i
$929$	−15.3297	−	26.5517i	−0.502950	−	0.871135i	−0.999994	−	0.00340952i	$-0.998915\pi$
$929$	−15.3297	−	26.5517i	−0.502950	−	0.871135i	0.497044	−	0.867725i	$-0.334419\pi$
$930$	−24.9414			−0.817861
$931$	12.6259	−	22.5489i	0.413798	−	0.739010i
$932$		−	15.5106i		−	0.508066i
$933$	11.4031	−	6.58359i	0.373321	−	0.215537i
$934$	−3.13195	−	5.42469i	−0.102480	−	0.177501i
$935$	−51.0953	+	16.1671i	−1.67100	+	0.528721i
$936$	0.469473	+	0.813151i	0.0153452	+	0.0265787i
$937$	−38.8014	−	22.4020i	−1.26759	−	0.731842i	−0.293057	−	0.956095i	$-0.594672\pi$
$937$	−38.8014	−	22.4020i	−1.26759	−	0.731842i	−0.974531	+	0.224253i	$0.928006\pi$
$938$	7.80486			0.254838
$939$			9.69048i			0.316237i
$940$	−7.37329	+	12.7709i	−0.240490	+	0.416541i
$941$	8.65893	−	14.9977i	0.282273	−	0.488912i	−0.689671	−	0.724123i	$-0.742245\pi$
$941$	8.65893	−	14.9977i	0.282273	−	0.488912i	0.971944	+	0.235211i	$0.0755782\pi$
$942$		−	26.8576i		−	0.875067i
$943$	56.7201			1.84706
$944$	9.19565	+	5.30911i	0.299293	+	0.172797i
$945$	−7.49785	−	12.9867i	−0.243905	−	0.422456i
$946$	10.9996	−	3.48041i	0.357629	−	0.113158i
$947$	5.45613	+	9.45029i	0.177300	+	0.307093i	0.940955	−	0.338532i	$-0.109930\pi$
$947$	5.45613	+	9.45029i	0.177300	+	0.307093i	−0.763655	+	0.645625i	$0.776597\pi$
$948$	16.4047	−	9.47126i	0.532800	−	0.307612i
$949$			2.49552i			0.0810080i
$950$	−3.49952	+	6.24986i	−0.113539	+	0.202772i
$951$	−22.8771			−0.741840
$952$	3.24424	+	5.61920i	0.105147	+	0.182119i
$953$	18.8652	+	32.6755i	0.611105	+	1.05846i	0.991055	+	0.133457i	$0.0426078\pi$
$953$	18.8652	+	32.6755i	0.611105	+	1.05846i	−0.379950	+	0.925007i	$0.624059\pi$
$954$	7.21038	+	4.16292i	0.233445	+	0.134779i
$955$	23.5853	+	40.8510i	0.763204	+	1.32191i
$956$	−20.1854	−	11.6540i	−0.652842	−	0.376919i
$957$	−18.1800	−	16.6252i	−0.587678	−	0.537415i
$958$		−	3.67899i		−	0.118863i
$959$	7.61134	+	4.39441i	0.245783	+	0.141903i
$960$	3.35865	+	1.93912i	0.108400	+	0.0625847i
$961$	−10.3594			−0.334175
$962$			14.6998i			0.473940i
$963$	−5.42985	+	9.40478i	−0.174975	+	0.303065i
$964$	−6.94125	−	12.0226i	−0.223562	−	0.387222i
$965$	−2.12844	+	3.68656i	−0.0685169	+	0.118675i
$966$	4.06654	+	7.04346i	0.130839	+	0.226620i
$967$	39.0230	−	22.5300i	1.25490	−	0.724515i	0.282819	−	0.959173i	$-0.408731\pi$
$967$	39.0230	−	22.5300i	1.25490	−	0.724515i	0.972078	+	0.234659i	$0.0753972\pi$
$968$	0.980877	+	10.9562i	0.0315266	+	0.352145i
$969$	21.0258	+	35.3356i	0.675445	+	1.13514i
$970$		−	13.1880i		−	0.423442i
$971$	−4.01440	+	2.31771i	−0.128828	+	0.0743790i	−0.563029	−	0.826437i	$-0.690364\pi$
$971$	−4.01440	+	2.31771i	−0.128828	+	0.0743790i	0.434201	+	0.900816i	$0.357031\pi$
$972$	6.45987	−	3.72961i	0.207200	−	0.119627i
$973$	−2.87994	+	4.98821i	−0.0923267	+	0.159915i
$974$	11.5872	−	6.68989i	0.371279	−	0.214358i
$975$	−2.73197	−	1.57730i	−0.0874930	−	0.0505141i
$976$			7.01341i			0.224494i
$977$			8.29996i			0.265539i	0.991147	+	0.132770i	$0.0423870\pi$
$977$			8.29996i			0.265539i	−0.991147	+	0.132770i	$0.957613\pi$
$978$	−19.4911	−	11.2532i	−0.623258	−	0.359838i
$979$	−32.4242	+	10.2594i	−1.03628	+	0.327891i
$980$	−15.2813			−0.488143
$981$	7.41360			0.236698
$982$	−33.5410	−	19.3649i	−1.07033	−	0.617958i
$983$	−28.9764	+	16.7295i	−0.924204	+	0.533589i	−0.884974	−	0.465641i	$-0.845824\pi$
$983$	−28.9764	+	16.7295i	−0.924204	+	0.533589i	−0.0392301	+	0.999230i	$0.512491\pi$
$984$	−14.1523	−	8.17086i	−0.451160	−	0.260478i
$985$	−53.0907	+	30.6519i	−1.69161	+	0.976651i
$986$	−26.8019	+	15.4741i	−0.853548	+	0.492796i
$987$	8.90992			0.283606
$988$	−5.56068	+	0.0731787i	−0.176909	+	0.00232813i
$989$		−	18.1670i		−	0.577677i
$990$	−6.14353	−	1.35547i	−0.195254	−	0.0430797i
$991$	20.3493	−	11.7487i	0.646416	−	0.373209i	−0.140665	−	0.990057i	$-0.544924\pi$
$991$	20.3493	−	11.7487i	0.646416	−	0.373209i	0.787082	+	0.616848i	$0.211591\pi$
$992$	5.56952	+	3.21556i	0.176832	+	0.102094i
$993$	2.50498	+	4.33875i	0.0794930	+	0.137686i
$994$	−0.643050	+	1.11380i	−0.0203963	+	0.0353274i
$995$	−45.0229			−1.42732
$996$	3.47808			0.110207
$997$	2.48472	+	1.43455i	0.0786918	+	0.0454327i	0.538830	−	0.842415i	$-0.318867\pi$
$997$	2.48472	+	1.43455i	0.0786918	+	0.0454327i	−0.460138	+	0.887848i	$0.652200\pi$
$998$	−0.925300	+	1.60267i	−0.0292899	+	0.0507315i
$999$	64.7688			2.04919

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.h.b.373.7	yes	20
11.10	odd	2		418.2.h.a.373.7	yes	20
19.8	odd	6		418.2.h.a.65.7	✓	20
209.65	even	6	inner	418.2.h.b.65.7	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.h.a.65.7	✓	20	19.8	odd	6
418.2.h.a.373.7	yes	20	11.10	odd	2
418.2.h.b.65.7	yes	20	209.65	even	6	inner
418.2.h.b.373.7	yes	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.30309 - 0.752337i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.28873 + 2.23214i) q^{5} +(1.30309 + 0.752337i) q^{6} +1.03498i q^{7} -1.00000 q^{8} +(-0.367978 + 0.637356i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.30309 - 0.752337i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.28873 + 2.23214i) q^{5} +(1.30309 + 0.752337i) q^{6} +1.03498i q^{7} -1.00000 q^{8} +(-0.367978 + 0.637356i) q^{9} +(-1.28873 + 2.23214i) q^{10} +(2.23821 - 2.44754i) q^{11} +1.50467i q^{12} +(-0.637909 + 1.10489i) q^{13} +(-0.896317 + 0.517489i) q^{14} +(3.35865 + 1.93912i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-5.42929 + 3.13460i) q^{17} -0.735955 q^{18} +(2.12959 - 3.80327i) q^{19} -2.57746 q^{20} +(0.778652 + 1.34867i) q^{21} +(3.23873 + 0.714574i) q^{22} +(2.61127 - 4.52285i) q^{23} +(-1.30309 + 0.752337i) q^{24} +(-0.821643 + 1.42313i) q^{25} -1.27582 q^{26} +5.62140i q^{27} +(-0.896317 - 0.517489i) q^{28} +(2.46827 - 4.27517i) q^{29} +3.87823i q^{30} +6.43113i q^{31} +(0.500000 - 0.866025i) q^{32} +(1.07520 - 4.87324i) q^{33} +(-5.42929 - 3.13460i) q^{34} +(-2.31022 + 1.33381i) q^{35} +(-0.367978 - 0.637356i) q^{36} -11.5218i q^{37} +(4.35852 - 0.0573582i) q^{38} +1.91969i q^{39} +(-1.28873 - 2.23214i) q^{40} +(5.43032 + 9.40559i) q^{41} +(-0.778652 + 1.34867i) q^{42} +(3.01253 - 1.73929i) q^{43} +(1.00053 + 3.16211i) q^{44} -1.89689 q^{45} +5.22254 q^{46} +(2.86068 - 4.95485i) q^{47} +(-1.30309 - 0.752337i) q^{48} +5.92882 q^{49} -1.64329 q^{50} +(-4.71655 + 8.16931i) q^{51} +(-0.637909 - 1.10489i) q^{52} +(-9.79731 - 5.65648i) q^{53} +(-4.86827 + 2.81070i) q^{54} +(8.34769 + 1.84178i) q^{55} -1.03498i q^{56} +(-0.0863055 - 6.55816i) q^{57} +4.93655 q^{58} +(-9.19565 + 5.30911i) q^{59} +(-3.35865 + 1.93912i) q^{60} +(-6.07379 - 3.50671i) q^{61} +(-5.56952 + 3.21556i) q^{62} +(-0.659650 - 0.380849i) q^{63} +1.00000 q^{64} -3.28837 q^{65} +(4.75795 - 1.50547i) q^{66} +(-6.53077 - 3.77054i) q^{67} -6.26920i q^{68} -7.85822i q^{69} +(-2.31022 - 1.33381i) q^{70} +(1.07615 - 0.621318i) q^{71} +(0.367978 - 0.637356i) q^{72} +(1.69396 - 0.978008i) q^{73} +(9.97820 - 5.76092i) q^{74} +2.47261i q^{75} +(2.22893 + 3.74591i) q^{76} +(2.53315 + 2.31649i) q^{77} +(-1.66250 + 0.959846i) q^{78} +(-6.29456 - 10.9025i) q^{79} +(1.28873 - 2.23214i) q^{80} +(3.12525 + 5.41309i) q^{81} +(-5.43032 + 9.40559i) q^{82} -2.31152i q^{83} -1.55730 q^{84} +(-13.9938 - 8.07930i) q^{85} +(3.01253 + 1.73929i) q^{86} -7.42789i q^{87} +(-2.23821 + 2.44754i) q^{88} +(-8.88019 - 5.12698i) q^{89} +(-0.948447 - 1.64276i) q^{90} +(-1.14354 - 0.660222i) q^{91} +(2.61127 + 4.52285i) q^{92} +(4.83838 + 8.38031i) q^{93} +5.72137 q^{94} +(11.2339 - 0.147838i) q^{95} -1.50467i q^{96} +(-4.43118 + 2.55834i) q^{97} +(2.96441 + 5.13451i) q^{98} +(0.736343 + 2.32717i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9}+O(q^{10}) \) 20 * q + 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 + 3 * q^6 - 20 * q^8 + 11 * q^9	\( 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9} - 2 q^{10} + q^{11} + 5 q^{13} - 6 q^{14} + 12 q^{15} - 10 q^{16} + 6 q^{17} + 22 q^{18} - 18 q^{19} - 4 q^{20} - 14 q^{21} + 2 q^{22} - 4 q^{23} - 3 q^{24} - 20 q^{25} + 10 q^{26} - 6 q^{28} + 5 q^{29} + 10 q^{32} - 13 q^{33} + 6 q^{34} - 12 q^{35} + 11 q^{36} - 12 q^{38} - 2 q^{40} - q^{41} + 14 q^{42} + 3 q^{43} + q^{44} + 12 q^{45} - 8 q^{46} + q^{47} - 3 q^{48} + 8 q^{49} - 40 q^{50} - 12 q^{51} + 5 q^{52} - 24 q^{53} + 27 q^{54} - 2 q^{55} + 32 q^{57} + 10 q^{58} - 51 q^{59} - 12 q^{60} + 27 q^{61} + 12 q^{63} + 20 q^{64} - 8 q^{65} - 8 q^{66} + 27 q^{67} - 12 q^{70} + 33 q^{71} - 11 q^{72} - 9 q^{73} - 12 q^{74} + 6 q^{76} - 22 q^{77} - 24 q^{79} + 2 q^{80} + 12 q^{81} + q^{82} + 28 q^{84} - 12 q^{85} + 3 q^{86} - q^{88} + 21 q^{89} + 6 q^{90} + 12 q^{91} - 4 q^{92} - 10 q^{93} + 2 q^{94} - 24 q^{95} + 24 q^{97} + 4 q^{98} + 3 q^{99}+O(q^{100}) \) 20 * q + 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 + 3 * q^6 - 20 * q^8 + 11 * q^9 - 2 * q^10 + q^11 + 5 * q^13 - 6 * q^14 + 12 * q^15 - 10 * q^16 + 6 * q^17 + 22 * q^18 - 18 * q^19 - 4 * q^20 - 14 * q^21 + 2 * q^22 - 4 * q^23 - 3 * q^24 - 20 * q^25 + 10 * q^26 - 6 * q^28 + 5 * q^29 + 10 * q^32 - 13 * q^33 + 6 * q^34 - 12 * q^35 + 11 * q^36 - 12 * q^38 - 2 * q^40 - q^41 + 14 * q^42 + 3 * q^43 + q^44 + 12 * q^45 - 8 * q^46 + q^47 - 3 * q^48 + 8 * q^49 - 40 * q^50 - 12 * q^51 + 5 * q^52 - 24 * q^53 + 27 * q^54 - 2 * q^55 + 32 * q^57 + 10 * q^58 - 51 * q^59 - 12 * q^60 + 27 * q^61 + 12 * q^63 + 20 * q^64 - 8 * q^65 - 8 * q^66 + 27 * q^67 - 12 * q^70 + 33 * q^71 - 11 * q^72 - 9 * q^73 - 12 * q^74 + 6 * q^76 - 22 * q^77 - 24 * q^79 + 2 * q^80 + 12 * q^81 + q^82 + 28 * q^84 - 12 * q^85 + 3 * q^86 - q^88 + 21 * q^89 + 6 * q^90 + 12 * q^91 - 4 * q^92 - 10 * q^93 + 2 * q^94 - 24 * q^95 + 24 * q^97 + 4 * q^98 + 3 * q^99

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