LMFDB - Embedded newform 65.2.f.b.18.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,2,Mod(18,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("65.18");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.f (of order $4$, 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:	$0.519027613138$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.619810816.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{5} + 14x^{4} - 8x^{3} + 2x^{2} + 2x + 1 $ x^8 - 2x^5 + 14x^4 - 8x^3 + 2x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			18.3
Root			$-0.252709 + 0.252709i$ of defining polynomial
Character	$\chi$	$=$	65.18
Dual form			65.2.f.b.47.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.57942i q^{2} +(0.725850 + 0.725850i) q^{3} -0.494582 q^{4} +(0.146426 - 2.23127i) q^{5} +(-1.14643 + 1.14643i) q^{6} -4.24997 q^{7} +2.37769i q^{8} -1.94628i q^{9} +O(q^{10})$	\(q+1.57942i q^{2} +(0.725850 + 0.725850i) q^{3} -0.494582 q^{4} +(0.146426 - 2.23127i) q^{5} +(-1.14643 + 1.14643i) q^{6} -4.24997 q^{7} +2.37769i q^{8} -1.94628i q^{9} +(3.52412 + 0.231269i) q^{10} +(1.14643 + 1.14643i) q^{11} +(-0.358992 - 0.358992i) q^{12} +(-0.231269 - 3.59813i) q^{13} -6.71251i q^{14} +(1.72585 - 1.51328i) q^{15} -4.74455 q^{16} +(4.37769 + 4.37769i) q^{17} +3.07401 q^{18} +(-0.274150 - 0.274150i) q^{19} +(-0.0724196 + 1.10354i) q^{20} +(-3.08484 - 3.08484i) q^{21} +(-1.81069 + 1.81069i) q^{22} +(-1.64101 + 1.64101i) q^{23} +(-1.72585 + 1.72585i) q^{24} +(-4.95712 - 0.653431i) q^{25} +(5.68297 - 0.365271i) q^{26} +(3.59026 - 3.59026i) q^{27} +2.10196 q^{28} +2.79827i q^{29} +(2.39012 + 2.72585i) q^{30} +(-2.30527 + 2.30527i) q^{31} -2.73827i q^{32} +1.66427i q^{33} +(-6.91424 + 6.91424i) q^{34} +(-0.622306 + 9.48283i) q^{35} +0.962596i q^{36} -2.04288 q^{37} +(0.432999 - 0.432999i) q^{38} +(2.44384 - 2.77957i) q^{39} +(5.30527 + 0.348156i) q^{40} +(-0.883113 + 0.883113i) q^{41} +(4.87228 - 4.87228i) q^{42} +(0.944696 - 0.944696i) q^{43} +(-0.567001 - 0.567001i) q^{44} +(-4.34268 - 0.284986i) q^{45} +(-2.59185 - 2.59185i) q^{46} +0.483745 q^{47} +(-3.44384 - 3.44384i) q^{48} +11.0623 q^{49} +(1.03204 - 7.82940i) q^{50} +6.35510i q^{51} +(0.114381 + 1.77957i) q^{52} +(-7.24997 - 7.24997i) q^{53} +(5.67055 + 5.67055i) q^{54} +(2.72585 - 2.39012i) q^{55} -10.1051i q^{56} -0.397983i q^{57} -4.41966 q^{58} +(0.311554 - 0.311554i) q^{59} +(-0.853574 + 0.748443i) q^{60} +11.2857 q^{61} +(-3.64101 - 3.64101i) q^{62} +8.27164i q^{63} -5.16421 q^{64} +(-8.06225 - 0.0108364i) q^{65} -2.62858 q^{66} +7.11597i q^{67} +(-2.16513 - 2.16513i) q^{68} -2.38225 q^{69} +(-14.9774 - 0.982885i) q^{70} +(7.42752 - 7.42752i) q^{71} +4.62767 q^{72} -4.96796i q^{73} -3.22658i q^{74} +(-3.12383 - 4.07242i) q^{75} +(0.135589 + 0.135589i) q^{76} +(-4.87228 - 4.87228i) q^{77} +(4.39012 + 3.85985i) q^{78} +10.7928i q^{79} +(-0.694725 + 10.5864i) q^{80} -0.626863 q^{81} +(-1.39481 - 1.39481i) q^{82} +11.8340 q^{83} +(1.52571 + 1.52571i) q^{84} +(10.4088 - 9.12680i) q^{85} +(1.49208 + 1.49208i) q^{86} +(-2.03113 + 2.03113i) q^{87} +(-2.72585 + 2.72585i) q^{88} +(-1.10513 + 1.10513i) q^{89} +(0.450114 - 6.85893i) q^{90} +(0.982885 + 15.2919i) q^{91} +(0.811612 - 0.811612i) q^{92} -3.34657 q^{93} +0.764039i q^{94} +(-0.651844 + 0.571559i) q^{95} +(1.98758 - 1.98758i) q^{96} -10.7928i q^{97} +17.4720i q^{98} +(2.23127 - 2.23127i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{3} - 8 q^{4} - 2 q^{5} - 6 q^{6}+O(q^{10}) $ 8 * q - 6 * q^3 - 8 * q^4 - 2 * q^5 - 6 * q^6	$ 8 q - 6 q^{3} - 8 q^{4} - 2 q^{5} - 6 q^{6} + 6 q^{10} + 6 q^{11} - 2 q^{12} + 14 q^{13} + 2 q^{15} - 8 q^{16} + 16 q^{17} + 20 q^{18} - 14 q^{19} - 2 q^{20} - 12 q^{21} + 10 q^{22} - 14 q^{23} - 2 q^{24} - 12 q^{25} + 6 q^{26} + 12 q^{27} - 8 q^{28} - 14 q^{30} + 2 q^{31} - 24 q^{35} - 44 q^{37} - 2 q^{38} + 6 q^{39} + 22 q^{40} + 16 q^{41} + 24 q^{42} - 6 q^{43} - 10 q^{44} + 22 q^{45} + 2 q^{46} + 16 q^{47} - 14 q^{48} + 24 q^{49} + 44 q^{50} - 38 q^{52} - 24 q^{53} + 20 q^{54} + 10 q^{55} + 24 q^{58} - 22 q^{59} - 10 q^{60} + 20 q^{61} - 30 q^{62} + 48 q^{64} - 36 q^{66} + 4 q^{68} + 4 q^{69} - 68 q^{70} - 10 q^{71} - 16 q^{72} + 30 q^{75} + 6 q^{76} - 24 q^{77} + 2 q^{78} - 26 q^{80} - 20 q^{81} + 20 q^{82} + 48 q^{83} - 16 q^{84} + 32 q^{85} - 46 q^{86} + 16 q^{87} - 10 q^{88} + 28 q^{89} - 14 q^{90} + 20 q^{91} + 50 q^{92} - 40 q^{93} + 2 q^{95} + 30 q^{96} + 2 q^{99}+O(q^{100}) $ 8 * q - 6 * q^3 - 8 * q^4 - 2 * q^5 - 6 * q^6 + 6 * q^10 + 6 * q^11 - 2 * q^12 + 14 * q^13 + 2 * q^15 - 8 * q^16 + 16 * q^17 + 20 * q^18 - 14 * q^19 - 2 * q^20 - 12 * q^21 + 10 * q^22 - 14 * q^23 - 2 * q^24 - 12 * q^25 + 6 * q^26 + 12 * q^27 - 8 * q^28 - 14 * q^30 + 2 * q^31 - 24 * q^35 - 44 * q^37 - 2 * q^38 + 6 * q^39 + 22 * q^40 + 16 * q^41 + 24 * q^42 - 6 * q^43 - 10 * q^44 + 22 * q^45 + 2 * q^46 + 16 * q^47 - 14 * q^48 + 24 * q^49 + 44 * q^50 - 38 * q^52 - 24 * q^53 + 20 * q^54 + 10 * q^55 + 24 * q^58 - 22 * q^59 - 10 * q^60 + 20 * q^61 - 30 * q^62 + 48 * q^64 - 36 * q^66 + 4 * q^68 + 4 * q^69 - 68 * q^70 - 10 * q^71 - 16 * q^72 + 30 * q^75 + 6 * q^76 - 24 * q^77 + 2 * q^78 - 26 * q^80 - 20 * q^81 + 20 * q^82 + 48 * q^83 - 16 * q^84 + 32 * q^85 - 46 * q^86 + 16 * q^87 - 10 * q^88 + 28 * q^89 - 14 * q^90 + 20 * q^91 + 50 * q^92 - 40 * q^93 + 2 * q^95 + 30 * q^96 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$			1.57942i			1.11682i	0.829565	+	0.558411i	$0.188589\pi$
$2$			1.57942i			1.11682i	−0.829565	+	0.558411i	$0.811411\pi$
$3$	0.725850	+	0.725850i	0.419070	+	0.419070i	0.884883	−	0.465813i	$-0.154238\pi$
$3$	0.725850	+	0.725850i	0.419070	+	0.419070i	−0.465813	+	0.884883i	$0.654238\pi$
$4$	−0.494582			−0.247291
$5$	0.146426	−	2.23127i	0.0654836	−	0.997854i
$5$	0.146426	−	2.23127i	0.0654836	−	0.997854i
$6$	−1.14643	+	1.14643i	−0.468026	+	0.468026i
$7$	−4.24997			−1.60634			−0.803169	−	0.595751i	$-0.796854\pi$
$7$	−4.24997			−1.60634			−0.803169	+	0.595751i	$0.796854\pi$
$8$			2.37769i			0.840642i
$9$		−	1.94628i		−	0.648761i
$10$	3.52412	+	0.231269i	1.11442	+	0.0731335i
$11$	1.14643	+	1.14643i	0.345660	+	0.345660i	0.858490	−	0.512830i	$-0.171403\pi$
$11$	1.14643	+	1.14643i	0.345660	+	0.345660i	−0.512830	+	0.858490i	$0.671403\pi$
$12$	−0.358992	−	0.358992i	−0.103632	−	0.103632i
$13$	−0.231269	−	3.59813i	−0.0641424	−	0.997941i
$13$	−0.231269	−	3.59813i	−0.0641424	−	0.997941i
$14$		−	6.71251i		−	1.79399i
$15$	1.72585	−	1.51328i	0.445613	−	0.390728i
$16$	−4.74455			−1.18614
$17$	4.37769	+	4.37769i	1.06175	+	1.06175i	0.997964	+	0.0637831i	$0.0203166\pi$
$17$	4.37769	+	4.37769i	1.06175	+	1.06175i	0.0637831	+	0.997964i	$0.479683\pi$
$18$	3.07401			0.724550
$19$	−0.274150	−	0.274150i	−0.0628942	−	0.0628942i	0.674960	−	0.737854i	$-0.264161\pi$
$19$	−0.274150	−	0.274150i	−0.0628942	−	0.0628942i	−0.737854	+	0.674960i	$0.764161\pi$
$20$	−0.0724196	+	1.10354i	−0.0161935	+	0.246760i
$21$	−3.08484	−	3.08484i	−0.673168	−	0.673168i
$22$	−1.81069	+	1.81069i	−0.386041	+	0.386041i
$23$	−1.64101	+	1.64101i	−0.342174	+	0.342174i	−0.857184	−	0.515010i	$-0.827788\pi$
$23$	−1.64101	+	1.64101i	−0.342174	+	0.342174i	0.515010	+	0.857184i	$0.327788\pi$
$24$	−1.72585	+	1.72585i	−0.352288	+	0.352288i
$25$	−4.95712	−	0.653431i	−0.991424	−	0.130686i
$26$	5.68297	−	0.365271i	1.11452	−	0.0716356i
$27$	3.59026	−	3.59026i	0.690946	−	0.690946i
$28$	2.10196			0.397233
$29$			2.79827i			0.519626i	0.965659	+	0.259813i	$0.0836609\pi$
$29$			2.79827i			0.519626i	−0.965659	+	0.259813i	$0.916339\pi$
$30$	2.39012	+	2.72585i	0.436374	+	0.497670i
$31$	−2.30527	+	2.30527i	−0.414040	+	0.414040i	−0.883143	−	0.469104i	$-0.844577\pi$
$31$	−2.30527	+	2.30527i	−0.414040	+	0.414040i	0.469104	+	0.883143i	$0.344577\pi$
$32$		−	2.73827i		−	0.484063i
$33$			1.66427i			0.289712i
$34$	−6.91424	+	6.91424i	−1.18578	+	1.18578i
$35$	−0.622306	+	9.48283i	−0.105189	+	1.60289i
$36$			0.962596i			0.160433i
$37$	−2.04288			−0.335848			−0.167924	−	0.985800i	$-0.553706\pi$
$37$	−2.04288			−0.335848			−0.167924	+	0.985800i	$0.553706\pi$
$38$	0.432999	−	0.432999i	0.0702417	−	0.0702417i
$39$	2.44384	−	2.77957i	0.391327	−	0.445087i
$40$	5.30527	+	0.348156i	0.838838	+	0.0550483i
$41$	−0.883113	+	0.883113i	−0.137919	+	0.137919i	−0.772696	−	0.634777i	$-0.781092\pi$
$41$	−0.883113	+	0.883113i	−0.137919	+	0.137919i	0.634777	+	0.772696i	$0.281092\pi$
$42$	4.87228	−	4.87228i	0.751809	−	0.751809i
$43$	0.944696	−	0.944696i	0.144065	−	0.144065i	−0.631396	−	0.775461i	$-0.717518\pi$
$43$	0.944696	−	0.944696i	0.144065	−	0.144065i	0.775461	+	0.631396i	$0.217518\pi$
$44$	−0.567001	−	0.567001i	−0.0854787	−	0.0854787i
$45$	−4.34268	−	0.284986i	−0.647368	−	0.0424832i
$46$	−2.59185	−	2.59185i	−0.382147	−	0.382147i
$47$	0.483745			0.0705615			0.0352808	−	0.999377i	$-0.488767\pi$
$47$	0.483745			0.0705615			0.0352808	+	0.999377i	$0.488767\pi$
$48$	−3.44384	−	3.44384i	−0.497075	−	0.497075i
$49$	11.0623			1.58032
$50$	1.03204	−	7.82940i	0.145953	−	1.10724i
$51$			6.35510i			0.889892i
$52$	0.114381	+	1.77957i	0.0158618	+	0.246782i
$53$	−7.24997	−	7.24997i	−0.995860	−	0.995860i	0.00413141	−	0.999991i	$-0.498685\pi$
$53$	−7.24997	−	7.24997i	−0.995860	−	0.995860i	−0.999991	+	0.00413141i	$0.998685\pi$
$54$	5.67055	+	5.67055i	0.771664	+	0.771664i
$55$	2.72585	−	2.39012i	0.367554	−	0.322283i
$56$		−	10.1051i		−	1.35036i
$57$		−	0.397983i		−	0.0527142i
$58$	−4.41966			−0.580329
$59$	0.311554	−	0.311554i	0.0405608	−	0.0405608i	−0.686535	−	0.727096i	$-0.740869\pi$
$59$	0.311554	−	0.311554i	0.0405608	−	0.0405608i	0.727096	+	0.686535i	$0.240869\pi$
$60$	−0.853574	+	0.748443i	−0.110196	+	0.0966235i
$61$	11.2857			1.44498			0.722490	−	0.691381i	$-0.242998\pi$
$61$	11.2857			1.44498			0.722490	+	0.691381i	$0.242998\pi$
$62$	−3.64101	−	3.64101i	−0.462408	−	0.462408i
$63$			8.27164i			1.04213i
$64$	−5.16421			−0.645526
$65$	−8.06225	−	0.0108364i	−0.999999	−	0.00134409i
$66$	−2.62858			−0.323556
$67$			7.11597i			0.869354i	0.900586	+	0.434677i	$0.143137\pi$
$67$			7.11597i			0.869354i	−0.900586	+	0.434677i	$0.856863\pi$
$68$	−2.16513	−	2.16513i	−0.262560	−	0.262560i
$69$	−2.38225			−0.286789
$70$	−14.9774	−	0.982885i	−1.79014	−	0.117477i
$71$	7.42752	−	7.42752i	0.881485	−	0.881485i	−0.112201	−	0.993686i	$-0.535790\pi$
$71$	7.42752	−	7.42752i	0.881485	−	0.881485i	0.993686	+	0.112201i	$0.0357900\pi$
$72$	4.62767			0.545376
$73$		−	4.96796i		−	0.581455i	−0.956806	−	0.290728i	$-0.906103\pi$
$73$		−	4.96796i		−	0.581455i	0.956806	−	0.290728i	$-0.0938973\pi$
$74$		−	3.22658i		−	0.375082i
$75$	−3.12383	−	4.07242i	−0.360709	−	0.470243i
$76$	0.135589	+	0.135589i	0.0155532	+	0.0155532i
$77$	−4.87228	−	4.87228i	−0.555247	−	0.555247i
$78$	4.39012	+	3.85985i	0.497083	+	0.437042i
$79$			10.7928i			1.21428i	0.794593	+	0.607142i	$0.207684\pi$
$79$			10.7928i			1.21428i	−0.794593	+	0.607142i	$0.792316\pi$
$80$	−0.694725	+	10.5864i	−0.0776726	+	1.18359i
$81$	−0.626863			−0.0696515
$82$	−1.39481	−	1.39481i	−0.154031	−	0.154031i
$83$	11.8340			1.29895			0.649473	−	0.760385i	$-0.274990\pi$
$83$	11.8340			1.29895			0.649473	+	0.760385i	$0.274990\pi$
$84$	1.52571	+	1.52571i	0.166468	+	0.166468i
$85$	10.4088	−	9.12680i	1.12900	−	0.989941i
$86$	1.49208	+	1.49208i	0.160895	+	0.160895i
$87$	−2.03113	+	2.03113i	−0.217759	+	0.217759i
$88$	−2.72585	+	2.72585i	−0.290577	+	0.290577i
$89$	−1.10513	+	1.10513i	−0.117144	+	0.117144i	−0.763249	−	0.646105i	$-0.776397\pi$
$89$	−1.10513	+	1.10513i	−0.117144	+	0.117144i	0.646105	+	0.763249i	$0.276397\pi$
$90$	0.450114	−	6.85893i	0.0474462	−	0.722995i
$91$	0.982885	+	15.2919i	0.103034	+	1.60303i
$92$	0.811612	−	0.811612i	0.0846165	−	0.0846165i
$93$	−3.34657			−0.347023
$94$			0.764039i			0.0788046i
$95$	−0.651844	+	0.571559i	−0.0668778	+	0.0586407i
$96$	1.98758	−	1.98758i	0.202856	−	0.202856i
$97$		−	10.7928i		−	1.09584i	−0.836530	−	0.547921i	$-0.815419\pi$
$97$		−	10.7928i		−	1.09584i	0.836530	−	0.547921i	$-0.184581\pi$
$98$			17.4720i			1.76494i
$99$	2.23127	−	2.23127i	0.224251	−	0.224251i
$100$	2.45170	+	0.323175i	0.245170	+	0.0323175i
$101$			11.6588i			1.16009i	0.814583	+	0.580046i	$0.196966\pi$
$101$			11.6588i			1.16009i	−0.814583	+	0.580046i	$0.803034\pi$
$102$	−10.0374			−0.993851
$103$	3.67213	−	3.67213i	0.361826	−	0.361826i	−0.502659	−	0.864485i	$-0.667645\pi$
$103$	3.67213	−	3.67213i	0.361826	−	0.361826i	0.864485	+	0.502659i	$0.167645\pi$
$104$	8.55525	−	0.549886i	0.838911	−	0.0539208i
$105$	−7.33481	+	6.43141i	−0.715804	+	0.627642i
$106$	11.4508	−	11.4508i	1.11220	−	1.11220i
$107$	−2.58729	+	2.58729i	−0.250123	+	0.250123i	−0.821021	−	0.570898i	$-0.806595\pi$
$107$	−2.58729	+	2.58729i	−0.250123	+	0.250123i	0.570898	+	0.821021i	$0.306595\pi$
$108$	−1.77568	+	1.77568i	−0.170865	+	0.170865i
$109$	5.28110	+	5.28110i	0.505837	+	0.505837i	0.913246	−	0.407409i	$-0.133568\pi$
$109$	5.28110	+	5.28110i	0.505837	+	0.505837i	−0.407409	+	0.913246i	$0.633568\pi$
$110$	3.77501	+	4.30527i	0.359933	+	0.410492i
$111$	−1.48283	−	1.48283i	−0.140744	−	0.140744i
$112$	20.1642			1.90534
$113$	−1.43459	−	1.43459i	−0.134954	−	0.134954i	0.636403	−	0.771357i	$-0.280422\pi$
$113$	−1.43459	−	1.43459i	−0.134954	−	0.134954i	−0.771357	+	0.636403i	$0.780422\pi$
$114$	0.628584			0.0588723
$115$	3.42124	+	3.90181i	0.319033	+	0.363846i
$116$		−	1.38397i		−	0.128499i
$117$	−7.00297	+	0.450114i	−0.647425	+	0.0416131i
$118$	0.492076	+	0.492076i	0.0452992	+	0.0452992i
$119$	−18.6051	−	18.6051i	−1.70552	−	1.70552i
$120$	3.59813	+	4.10354i	0.328463	+	0.374601i
$121$		−	8.37142i		−	0.761038i
$122$			17.8248i			1.61378i
$123$	−1.28202			−0.115595
$124$	1.14015	−	1.14015i	0.102388	−	0.102388i
$125$	−2.18383	+	10.9650i	−0.195328	+	0.980738i
$126$	−13.0644			−1.16387
$127$	−14.0115	−	14.0115i	−1.24332	−	1.24332i	−0.958615	−	0.284705i	$-0.908104\pi$
$127$	−14.0115	−	14.0115i	−1.24332	−	1.24332i	−0.284705	−	0.958615i	$-0.591896\pi$
$128$		−	13.6330i		−	1.20500i
$129$	1.37142			0.120746
$130$	0.0171153	−	12.7337i	0.00150111	−	1.11682i
$131$	−12.9251			−1.12927			−0.564634	−	0.825341i	$-0.690983\pi$
$131$	−12.9251			−1.12927			−0.564634	+	0.825341i	$0.690983\pi$
$132$		−	0.823116i		−	0.0716431i
$133$	1.16513	+	1.16513i	0.101029	+	0.101029i
$134$	−11.2391			−0.970913
$135$	−7.48513	−	8.53654i	−0.644217	−	0.734709i
$136$	−10.4088	+	10.4088i	−0.892549	+	0.892549i
$137$	5.62139			0.480267			0.240134	−	0.970740i	$-0.422809\pi$
$137$	5.62139			0.480267			0.240134	+	0.970740i	$0.422809\pi$
$138$		−	3.76259i		−	0.320293i
$139$		−	8.53735i		−	0.724128i	−0.932153	−	0.362064i	$-0.882072\pi$
$139$		−	8.53735i		−	0.724128i	0.932153	−	0.362064i	$-0.117928\pi$
$140$	0.307781	−	4.69003i	0.0260122	−	0.396380i
$141$	0.351127	+	0.351127i	0.0295702	+	0.0295702i
$142$	11.7312	+	11.7312i	0.984461	+	0.984461i
$143$	3.85985	−	4.39012i	0.322777	−	0.367120i
$144$			9.23424i			0.769520i
$145$	6.24369	+	0.409739i	0.518510	+	0.0340270i
$146$	7.84651			0.649382
$147$	8.02954	+	8.02954i	0.662265	+	0.662265i
$148$	1.01037			0.0830520
$149$	7.43141	+	7.43141i	0.608805	+	0.608805i	0.942634	−	0.333829i	$-0.108341\pi$
$149$	7.43141	+	7.43141i	0.608805	+	0.608805i	−0.333829	+	0.942634i	$0.608341\pi$
$150$	6.43208	−	4.93386i	0.525177	−	0.402848i
$151$	−13.4492	−	13.4492i	−1.09448	−	1.09448i	−0.995044	−	0.0994360i	$-0.968296\pi$
$151$	−13.4492	−	13.4492i	−1.09448	−	1.09448i	−0.0994360	−	0.995044i	$-0.531704\pi$
$152$	0.651844	−	0.651844i	0.0528715	−	0.0528715i
$153$	8.52023	−	8.52023i	0.688820	−	0.688820i
$154$	7.69539	−	7.69539i	0.620112	−	0.620112i
$155$	4.80614	+	5.48124i	0.386038	+	0.440264i
$156$	−1.20868	+	1.37472i	−0.0967716	+	0.110066i
$157$	5.65971	−	5.65971i	0.451694	−	0.451694i	−0.444222	−	0.895917i	$-0.646520\pi$
$157$	5.65971	−	5.65971i	0.451694	−	0.451694i	0.895917	+	0.444222i	$0.146520\pi$
$158$	−17.0464			−1.35614
$159$		−	10.5248i		−	0.834670i
$160$	−6.10982	−	0.400954i	−0.483024	−	0.0316982i
$161$	6.97423	−	6.97423i	0.549647	−	0.549647i
$162$		−	0.990083i		−	0.0777883i
$163$		−	5.05372i		−	0.395838i	−0.980218	−	0.197919i	$-0.936582\pi$
$163$		−	5.05372i		−	0.395838i	0.980218	−	0.197919i	$-0.0634183\pi$
$164$	0.436771	−	0.436771i	0.0341061	−	0.0341061i
$165$	3.71343	+	0.243692i	0.289090	+	0.0189714i
$166$			18.6908i			1.45069i
$167$	8.81400			0.682048			0.341024	−	0.940055i	$-0.389226\pi$
$167$	8.81400			0.682048			0.341024	+	0.940055i	$0.389226\pi$
$168$	7.33481	−	7.33481i	0.565893	−	0.565893i
$169$	−12.8930	+	1.66427i	−0.991772	+	0.128021i
$170$	14.4151	+	16.4399i	1.10559	+	1.26089i
$171$	−0.533573	+	0.533573i	−0.0408033	+	0.0408033i
$172$	−0.467229	+	0.467229i	−0.0356259	+	0.0356259i
$173$	−11.9251	+	11.9251i	−0.906647	+	0.906647i	−0.996000	−	0.0893534i	$-0.971520\pi$
$173$	−11.9251	+	11.9251i	−0.906647	+	0.906647i	0.0893534	+	0.996000i	$0.471520\pi$
$174$	−3.20801	−	3.20801i	−0.243199	−	0.243199i
$175$	21.0676	+	2.77706i	1.59256	+	0.209926i
$176$	−5.43928	−	5.43928i	−0.410001	−	0.410001i
$177$	0.452283			0.0339957
$178$	−1.74547	−	1.74547i	−0.130829	−	0.130829i
$179$	−2.01256			−0.150426			−0.0752128	−	0.997168i	$-0.523964\pi$
$179$	−2.01256			−0.150426			−0.0752128	+	0.997168i	$0.523964\pi$
$180$	2.14781	+	0.140949i	0.160088	+	0.0105057i
$181$			8.38225i			0.623048i	0.950238	+	0.311524i	$0.100839\pi$
$181$			8.38225i			0.623048i	−0.950238	+	0.311524i	$0.899161\pi$
$182$	−24.1525	+	1.55239i	−1.79030	+	0.115071i
$183$	8.19170	+	8.19170i	0.605548	+	0.605548i
$184$	−3.90181	−	3.90181i	−0.287646	−	0.287646i
$185$	−0.299131	+	4.55822i	−0.0219925	+	0.335127i
$186$		−	5.28565i		−	0.387563i
$187$			10.0374i			0.734008i
$188$	−0.239252			−0.0174492
$189$	−15.2585	+	15.2585i	−1.10989	+	1.10989i
$190$	−0.902734	−	1.02954i	−0.0654912	−	0.0746906i
$191$	7.97649			0.577158			0.288579	−	0.957456i	$-0.406817\pi$
$191$	7.97649			0.577158			0.288579	+	0.957456i	$0.406817\pi$
$192$	−3.74844	−	3.74844i	−0.270521	−	0.270521i
$193$			21.2368i			1.52866i	0.644825	+	0.764330i	$0.276930\pi$
$193$			21.2368i			1.52866i	−0.644825	+	0.764330i	$0.723070\pi$
$194$	17.0464			1.22386
$195$	−5.84412	−	5.85985i	−0.418506	−	0.419633i
$196$	−5.47119			−0.390799
$197$		−	3.55914i		−	0.253578i	−0.991930	−	0.126789i	$-0.959533\pi$
$197$		−	3.55914i		−	0.253578i	0.991930	−	0.126789i	$-0.0404671\pi$
$198$	3.52412	+	3.52412i	0.250448	+	0.250448i
$199$	0.607376			0.0430558			0.0215279	−	0.999768i	$-0.493147\pi$
$199$	0.607376			0.0430558			0.0215279	+	0.999768i	$0.493147\pi$
$200$	1.55366	−	11.7865i	0.109860	−	0.833432i
$201$	−5.16513	+	5.16513i	−0.364320	+	0.364320i
$202$	−18.4142			−1.29562
$203$		−	11.8926i		−	0.834694i
$204$		−	3.14312i		−	0.220062i
$205$	1.84115	+	2.09977i	0.128592	+	0.146654i
$206$	5.79986	+	5.79986i	0.404095	+	0.404095i
$207$	3.19386	+	3.19386i	0.221989	+	0.221989i
$208$	1.09727	+	17.0715i	0.0760817	+	1.18370i
$209$		−	0.628584i		−	0.0434801i
$210$	−10.1579	−	11.5848i	−0.700964	−	0.799426i
$211$	−17.9890			−1.23842			−0.619209	−	0.785227i	$-0.712546\pi$
$211$	−17.9890			−1.23842			−0.619209	+	0.785227i	$0.712546\pi$
$212$	3.58570	+	3.58570i	0.246267	+	0.246267i
$213$	10.7825			0.738807
$214$	−4.08643	−	4.08643i	−0.279343	−	0.279343i
$215$	−1.96954	−	2.24620i	−0.134322	−	0.153189i
$216$	8.53654	+	8.53654i	0.580838	+	0.580838i
$217$	9.79735	−	9.79735i	0.665087	−	0.665087i
$218$	−8.34109	+	8.34109i	−0.564930	+	0.564930i
$219$	3.60599	−	3.60599i	0.243670	−	0.243670i
$220$	−1.34816	+	1.18211i	−0.0908927	+	0.0796977i
$221$	14.7391	−	16.7639i	0.991458	−	1.12766i
$222$	2.34201	−	2.34201i	0.157186	−	0.157186i
$223$	15.6643			1.04896			0.524478	−	0.851424i	$-0.324260\pi$
$223$	15.6643			1.04896			0.524478	+	0.851424i	$0.324260\pi$
$224$			11.6376i			0.777569i
$225$	−1.27176	+	9.64795i	−0.0847841	+	0.643197i
$226$	2.26582	−	2.26582i	0.150720	−	0.150720i
$227$			24.4976i			1.62597i	0.582288	+	0.812983i	$0.302158\pi$
$227$			24.4976i			1.62597i	−0.582288	+	0.812983i	$0.697842\pi$
$228$			0.196835i			0.0130357i
$229$	10.7265	−	10.7265i	0.708828	−	0.708828i	−0.257461	−	0.966289i	$-0.582886\pi$
$229$	10.7265	−	10.7265i	0.708828	−	0.708828i	0.966289	+	0.257461i	$0.0828857\pi$
$230$	−6.16262	+	5.40359i	−0.406351	+	0.356302i
$231$		−	7.07309i		−	0.465375i
$232$	−6.65343			−0.436819
$233$	−6.63712	+	6.63712i	−0.434812	+	0.434812i	−0.890262	−	0.455450i	$-0.849479\pi$
$233$	−6.63712	+	6.63712i	−0.434812	+	0.434812i	0.455450	+	0.890262i	$0.349479\pi$
$234$	−0.710921	−	11.0607i	−0.0464744	−	0.723058i
$235$	0.0708328	−	1.07937i	0.00462062	−	0.0704101i
$236$	−0.154089	+	0.154089i	−0.0100303	+	0.0100303i
$237$	−7.83395	+	7.83395i	−0.508870	+	0.508870i
$238$	29.3853	−	29.3853i	1.90477	−	1.90477i
$239$	−18.6766	−	18.6766i	−1.20809	−	1.20809i	−0.971646	−	0.236441i	$-0.924019\pi$
$239$	−18.6766	−	18.6766i	−1.20809	−	1.20809i	−0.236441	−	0.971646i	$-0.575981\pi$
$240$	−8.18839	+	7.17985i	−0.528558	+	0.463458i
$241$	2.88629	+	2.88629i	0.185922	+	0.185922i	0.793931	−	0.608008i	$-0.208031\pi$
$241$	2.88629	+	2.88629i	0.185922	+	0.185922i	−0.608008	+	0.793931i	$0.708031\pi$
$242$	13.2220			0.849944
$243$	−11.2258	−	11.2258i	−0.720135	−	0.720135i
$244$	−5.58168			−0.357330
$245$	1.61980	−	24.6829i	0.103485	−	1.57693i
$246$		−	2.02485i		−	0.129099i
$247$	−0.923023	+	1.04983i	−0.0587305	+	0.0667989i
$248$	−5.48124	−	5.48124i	−0.348059	−	0.348059i
$249$	8.58968	+	8.58968i	0.544349	+	0.544349i
$250$	−17.3184	−	3.44919i	−1.09531	−	0.218146i
$251$			17.7801i			1.12227i	0.827724	+	0.561136i	$0.189635\pi$
$251$			17.7801i			1.12227i	−0.827724	+	0.561136i	$0.810365\pi$
$252$		−	4.09100i		−	0.257709i
$253$	−3.76259			−0.236552
$254$	22.1301	−	22.1301i	1.38857	−	1.38857i
$255$	14.1799	+	0.930551i	0.887982	+	0.0582734i
$256$	11.2039			0.700245
$257$	−4.03204	−	4.03204i	−0.251512	−	0.251512i	0.570078	−	0.821590i	$-0.306913\pi$
$257$	−4.03204	−	4.03204i	−0.251512	−	0.251512i	−0.821590	+	0.570078i	$0.806913\pi$
$258$			2.16605i			0.134852i
$259$	8.68218			0.539485
$260$	3.98744	+	0.00535950i	0.247291	+	0.000332382i
$261$	5.44622			0.337113
$262$		−	20.4142i		−	1.26119i
$263$	−6.17438	−	6.17438i	−0.380728	−	0.380728i	0.490636	−	0.871365i	$-0.336764\pi$
$263$	−6.17438	−	6.17438i	−0.380728	−	0.380728i	−0.871365	+	0.490636i	$0.836764\pi$
$264$	−3.95712			−0.243544
$265$	−17.2382	+	15.1150i	−1.05894	+	0.928510i
$266$	−1.84023	+	1.84023i	−0.112832	+	0.112832i
$267$	−1.60432			−0.0981828
$268$		−	3.51943i		−	0.214983i
$269$			25.1885i			1.53577i	0.640589	+	0.767884i	$0.278690\pi$
$269$			25.1885i			1.53577i	−0.640589	+	0.767884i	$0.721310\pi$
$270$	13.4828	−	11.8222i	0.820539	−	0.719476i
$271$	−7.43070	−	7.43070i	−0.451383	−	0.451383i	0.444431	−	0.895813i	$-0.353406\pi$
$271$	−7.43070	−	7.43070i	−0.451383	−	0.451383i	−0.895813	+	0.444431i	$0.853406\pi$
$272$	−20.7702	−	20.7702i	−1.25938	−	1.25938i
$273$	−10.3862	+	11.8131i	−0.628603	+	0.714960i
$274$			8.87856i			0.536373i
$275$	−4.93386	−	6.43208i	−0.297523	−	0.387869i
$276$	1.17822			0.0709204
$277$	0.389450	+	0.389450i	0.0233998	+	0.0233998i	0.718710	−	0.695310i	$-0.244733\pi$
$277$	0.389450	+	0.389450i	0.0233998	+	0.0233998i	−0.695310	+	0.718710i	$0.744733\pi$
$278$	13.4841			0.808722
$279$	4.48672	+	4.48672i	0.268613	+	0.268613i
$280$	−22.5473	−	1.47965i	−1.34746	−	0.0884261i
$281$	−2.39890	−	2.39890i	−0.143107	−	0.143107i	0.631924	−	0.775030i	$-0.282266\pi$
$281$	−2.39890	−	2.39890i	−0.143107	−	0.143107i	−0.775030	+	0.631924i	$0.782266\pi$
$282$	−0.554578	+	0.554578i	−0.0330246	+	0.0330246i
$283$	−20.6500	+	20.6500i	−1.22752	+	1.22752i	−0.262615	+	0.964901i	$0.584585\pi$
$283$	−20.6500	+	20.6500i	−1.22752	+	1.22752i	−0.964901	+	0.262615i	$0.915415\pi$
$284$	−3.67352	+	3.67352i	−0.217983	+	0.217983i
$285$	−0.888007	−	0.0582750i	−0.0526010	−	0.00345192i
$286$	6.93386	+	6.09635i	0.410008	+	0.360485i
$287$	3.75320	−	3.75320i	0.221545	−	0.221545i
$288$	−5.32945			−0.314041
$289$			21.3284i			1.25461i
$290$	−0.647152	+	9.86144i	−0.0380021	+	0.579084i
$291$	7.83395	−	7.83395i	0.459234	−	0.459234i
$292$			2.45706i			0.143789i
$293$		−	15.0708i		−	0.880445i	−0.897889	−	0.440222i	$-0.854900\pi$
$293$		−	15.0708i		−	0.880445i	0.897889	−	0.440222i	$-0.145100\pi$
$294$	−12.6820	+	12.6820i	−0.739632	+	0.739632i
$295$	−0.649541	−	0.740780i	−0.0378177	−	0.0431299i
$296$		−	4.85735i		−	0.282328i
$297$	8.23194			0.477665
$298$	−11.7374	+	11.7374i	−0.679927	+	0.679927i
$299$	6.28407	+	5.52504i	0.363417	+	0.319521i
$300$	1.54499	+	2.01414i	0.0892001	+	0.116287i
$301$	−4.01493	+	4.01493i	−0.231417	+	0.231417i
$302$	21.2420	−	21.2420i	1.22234	−	1.22234i
$303$	−8.46254	+	8.46254i	−0.486160	+	0.486160i
$304$	1.30072	+	1.30072i	0.0746013	+	0.0746013i
$305$	1.65251	−	25.1813i	0.0946225	−	1.44188i
$306$	13.4571	+	13.4571i	0.769289	+	0.769289i
$307$	−12.2780			−0.700742			−0.350371	−	0.936611i	$-0.613944\pi$
$307$	−12.2780			−0.700742			−0.350371	+	0.936611i	$0.613944\pi$
$308$	2.40974	+	2.40974i	0.137308	+	0.137308i
$309$	5.33084			0.303261
$310$	−8.65720	+	7.59093i	−0.491696	+	0.431136i
$311$		−	21.1944i		−	1.20182i	−0.799315	−	0.600912i	$-0.794804\pi$
$311$		−	21.1944i		−	1.20182i	0.799315	−	0.600912i	$-0.205196\pi$
$312$	6.60896	+	5.81069i	0.374159	+	0.328966i
$313$	−5.71879	−	5.71879i	−0.323245	−	0.323245i	0.526766	−	0.850011i	$-0.323405\pi$
$313$	−5.71879	−	5.71879i	−0.323245	−	0.323245i	−0.850011	+	0.526766i	$0.823405\pi$
$314$	8.93908	+	8.93908i	0.504462	+	0.504462i
$315$	18.4563	+	1.21118i	1.03989	+	0.0682424i
$316$		−	5.33792i		−	0.300281i
$317$			9.88047i			0.554943i	0.960734	+	0.277471i	$0.0894963\pi$
$317$			9.88047i			0.554943i	−0.960734	+	0.277471i	$0.910504\pi$
$318$	16.6231			0.932178
$319$	−3.20801	+	3.20801i	−0.179614	+	0.179614i
$320$	−0.756174	+	11.5227i	−0.0422714	+	0.644141i
$321$	−3.75597			−0.209638
$322$	11.0153	+	11.0153i	0.613857	+	0.613857i
$323$		−	2.40029i		−	0.133556i
$324$	0.310035			0.0172242
$325$	−1.20470	+	17.9875i	−0.0668248	+	0.997765i
$326$	7.98197			0.442080
$327$			7.66657i			0.423962i
$328$	−2.09977	−	2.09977i	−0.115941	−	0.115941i
$329$	−2.05590			−0.113346
$330$	−0.384893	+	5.86508i	−0.0211876	+	0.322862i
$331$	3.87697	−	3.87697i	0.213097	−	0.213097i	−0.592484	−	0.805582i	$-0.701853\pi$
$331$	3.87697	−	3.87697i	0.213097	−	0.213097i	0.805582	+	0.592484i	$0.201853\pi$
$332$	−5.85286			−0.321217
$333$			3.97602i			0.217885i
$334$			13.9210i			0.761726i
$335$	15.8776	+	1.04196i	0.867488	+	0.0569284i
$336$	14.6362	+	14.6362i	0.798470	+	0.798470i
$337$	10.6060	+	10.6060i	0.577745	+	0.577745i	0.934281	−	0.356536i	$-0.116042\pi$
$337$	10.6060	+	10.6060i	0.577745	+	0.577745i	−0.356536	+	0.934281i	$0.616042\pi$
$338$	−2.62858	−	20.3636i	−0.142976	−	1.10763i
$339$		−	2.08259i		−	0.113111i
$340$	−5.14801	+	4.51395i	−0.279190	+	0.244803i
$341$	−5.28565			−0.286234
$342$	−0.842738	−	0.842738i	−0.0455700	−	0.0455700i
$343$	−17.2644			−0.932192
$344$	2.24620	+	2.24620i	0.121107	+	0.121107i
$345$	−0.348823	+	5.31544i	−0.0187800	+	0.286174i
$346$	−18.8348	−	18.8348i	−1.01256	−	1.01256i
$347$	9.02188	−	9.02188i	0.484320	−	0.484320i	−0.422188	−	0.906508i	$-0.638738\pi$
$347$	9.02188	−	9.02188i	0.484320	−	0.484320i	0.906508	+	0.422188i	$0.138738\pi$
$348$	1.00456	−	1.00456i	0.0538499	−	0.0538499i
$349$	12.4143	−	12.4143i	0.664522	−	0.664522i	−0.291921	−	0.956443i	$-0.594294\pi$
$349$	12.4143	−	12.4143i	0.664522	−	0.664522i	0.956443	+	0.291921i	$0.0942943\pi$
$350$	−4.38616	+	33.2747i	−0.234450	+	1.77861i
$351$	−13.7485	−	12.0879i	−0.733842	−	0.645204i
$352$	3.13923	−	3.13923i	0.167321	−	0.167321i
$353$	26.3713			1.40360			0.701801	−	0.712373i	$-0.252379\pi$
$353$	26.3713			1.40360			0.701801	+	0.712373i	$0.252379\pi$
$354$			0.714347i			0.0379671i
$355$	−15.4852	−	17.6604i	−0.821870	−	0.937315i
$356$	0.546578	−	0.546578i	0.0289686	−	0.0289686i
$357$		−	27.0090i		−	1.42947i
$358$		−	3.17868i		−	0.167999i
$359$	−16.3706	+	16.3706i	−0.864009	+	0.864009i	−0.991801	−	0.127792i	$-0.959211\pi$
$359$	−16.3706	+	16.3706i	−0.864009	+	0.864009i	0.127792	+	0.991801i	$0.459211\pi$
$360$	0.677610	−	10.3256i	0.0357132	−	0.544205i
$361$		−	18.8497i		−	0.992089i
$362$	−13.2391			−0.695833
$363$	6.07639	−	6.07639i	0.318928	−	0.318928i
$364$	−0.486117	−	7.56311i	−0.0254794	−	0.396415i
$365$	−11.0848	−	0.727437i	−0.580207	−	0.0380758i
$366$	−12.9382	+	12.9382i	−0.676289	+	0.676289i
$367$	22.1292	−	22.1292i	1.15513	−	1.15513i	0.169626	−	0.985509i	$-0.445744\pi$
$367$	22.1292	−	22.1292i	1.15513	−	1.15513i	0.985509	−	0.169626i	$-0.0542560\pi$
$368$	7.78585	−	7.78585i	0.405865	−	0.405865i
$369$	1.71879	+	1.71879i	0.0894765	+	0.0894765i
$370$	−7.19936	−	0.472454i	−0.374277	−	0.0245617i
$371$	30.8122	+	30.8122i	1.59969	+	1.59969i
$372$	1.65515			0.0858156
$373$	13.4134	+	13.4134i	0.694518	+	0.694518i	0.963223	−	0.268704i	$-0.0865955\pi$
$373$	13.4134	+	13.4134i	0.694518	+	0.694518i	−0.268704	+	0.963223i	$0.586595\pi$
$374$	−15.8533			−0.819756
$375$	−9.54407	+	6.37380i	−0.492854	+	0.329142i
$376$			1.15020i			0.0593170i
$377$	10.0685	−	0.647152i	0.518556	−	0.0333300i
$378$	−24.0997	−	24.0997i	−1.23955	−	1.23955i
$379$	12.8914	+	12.8914i	0.662189	+	0.662189i	0.955896	−	0.293707i	$-0.0948889\pi$
$379$	12.8914	+	12.8914i	0.662189	+	0.662189i	−0.293707	+	0.955896i	$0.594889\pi$
$380$	0.322390	−	0.282683i	0.0165383	−	0.0145013i
$381$		−	20.3405i		−	1.04208i
$382$			12.5983i			0.644583i
$383$	−19.8962			−1.01665			−0.508324	−	0.861166i	$-0.669735\pi$
$383$	−19.8962			−1.01665			−0.508324	+	0.861166i	$0.669735\pi$
$384$	9.89554	−	9.89554i	0.504979	−	0.504979i
$385$	−11.5848	+	10.1579i	−0.590415	+	0.517696i
$386$	−33.5420			−1.70724
$387$	−1.83864	−	1.83864i	−0.0934636	−	0.0934636i
$388$			5.33792i			0.270992i
$389$	−13.2861			−0.673633			−0.336816	−	0.941570i	$-0.609350\pi$
$389$	−13.2861			−0.673633			−0.336816	+	0.941570i	$0.609350\pi$
$390$	9.25520	−	9.23035i	0.468655	−	0.467397i
$391$	−14.3677			−0.726604
$392$			26.3027i			1.32848i
$393$	−9.38167	−	9.38167i	−0.473243	−	0.473243i
$394$	5.62139			0.283201
$395$	24.0816	+	1.58034i	1.21168	+	0.0795157i
$396$	−1.10354	+	1.10354i	−0.0554552	+	0.0554552i
$397$	3.61591			0.181477			0.0907386	−	0.995875i	$-0.471077\pi$
$397$	3.61591			0.181477			0.0907386	+	0.995875i	$0.471077\pi$
$398$			0.959305i			0.0480856i
$399$			1.69142i			0.0846768i
$400$	23.5193	+	3.10024i	1.17597	+	0.155012i
$401$	5.44634	+	5.44634i	0.271977	+	0.271977i	0.829896	−	0.557918i	$-0.188400\pi$
$401$	5.44634	+	5.44634i	0.271977	+	0.271977i	−0.557918	+	0.829896i	$0.688400\pi$
$402$	−8.15793	−	8.15793i	−0.406881	−	0.406881i
$403$	8.82781	+	7.76153i	0.439744	+	0.386630i
$404$		−	5.76623i		−	0.286880i
$405$	−0.0917890	+	1.39870i	−0.00456103	+	0.0695020i
$406$	18.7834			0.932205
$407$	−2.34201	−	2.34201i	−0.116089	−	0.116089i
$408$	−15.1105			−0.748081
$409$	−27.3844	−	27.3844i	−1.35407	−	1.35407i	−0.881053	−	0.473018i	$-0.843164\pi$
$409$	−27.3844	−	27.3844i	−1.35407	−	1.35407i	−0.473018	−	0.881053i	$-0.656836\pi$
$410$	−3.31643	+	2.90796i	−0.163787	+	0.143614i
$411$	4.08029	+	4.08029i	0.201266	+	0.201266i
$412$	−1.81617	+	1.81617i	−0.0894763	+	0.0894763i
$413$	−1.32409	+	1.32409i	−0.0651544	+	0.0651544i
$414$	−5.04447	+	5.04447i	−0.247922	+	0.247922i
$415$	1.73280	−	26.4047i	0.0850596	−	1.29616i
$416$	−9.85265	+	0.633277i	−0.483066	+	0.0310489i
$417$	6.19684	−	6.19684i	0.303460	−	0.303460i
$418$	0.992802			0.0485595
$419$		−	31.6412i		−	1.54577i	−0.634543	−	0.772887i	$-0.718812\pi$
$419$		−	31.6412i		−	1.54577i	0.634543	−	0.772887i	$-0.281188\pi$
$420$	3.62767	−	3.18086i	0.177012	−	0.155210i
$421$	−0.312270	+	0.312270i	−0.0152191	+	0.0152191i	−0.714675	−	0.699456i	$-0.753426\pi$
$421$	−0.312270	+	0.312270i	−0.0152191	+	0.0152191i	0.699456	+	0.714675i	$0.253426\pi$
$422$		−	28.4123i		−	1.38309i
$423$		−	0.941505i		−	0.0457775i
$424$	17.2382	−	17.2382i	0.837162	−	0.837162i
$425$	−18.8402	−	24.5613i	−0.913885	−	1.19140i
$426$			17.0302i			0.825116i
$427$	−47.9637			−2.32113
$428$	1.27963	−	1.27963i	0.0618531	−	0.0618531i
$429$	5.98824	−	0.384893i	0.289115	−	0.0185828i
$430$	3.54770	−	3.11074i	0.171085	−	0.150013i
$431$	−13.0481	+	13.0481i	−0.628505	+	0.628505i	−0.947692	−	0.319187i	$-0.896590\pi$
$431$	−13.0481	+	13.0481i	−0.628505	+	0.628505i	0.319187	+	0.947692i	$0.396590\pi$
$432$	−17.0342	+	17.0342i	−0.819557	+	0.819557i
$433$	−0.0391255	+	0.0391255i	−0.00188025	+	0.00188025i	−0.708046	−	0.706166i	$-0.750423\pi$
$433$	−0.0391255	+	0.0391255i	−0.00188025	+	0.00188025i	0.706166	+	0.708046i	$0.250423\pi$
$434$	15.4742	+	15.4742i	0.742784	+	0.742784i
$435$	4.23458	+	4.82940i	0.203032	+	0.231552i
$436$	−2.61193	−	2.61193i	−0.125089	−	0.125089i
$437$	0.899763			0.0430415
$438$	5.69539	+	5.69539i	0.272136	+	0.272136i
$439$	17.4097			0.830919			0.415460	−	0.909612i	$-0.363621\pi$
$439$	17.4097			0.830919			0.415460	+	0.909612i	$0.363621\pi$
$440$	5.68297	+	6.48124i	0.270925	+	0.308981i
$441$		−	21.5303i		−	1.02525i
$442$	26.4773	+	23.2793i	1.25940	+	1.10728i
$443$	17.8580	+	17.8580i	0.848460	+	0.848460i	0.989941	−	0.141481i	$-0.0451864\pi$
$443$	17.8580	+	17.8580i	0.848460	+	0.848460i	−0.141481	+	0.989941i	$0.545186\pi$
$444$	0.733379	+	0.733379i	0.0348046	+	0.0348046i
$445$	2.30403	+	2.62767i	0.109221	+	0.124563i
$446$			24.7405i			1.17150i
$447$			10.7882i			0.510264i
$448$	21.9477			1.03693
$449$	−9.22202	+	9.22202i	−0.435214	+	0.435214i	−0.890398	−	0.455184i	$-0.849574\pi$
$449$	−9.22202	+	9.22202i	−0.435214	+	0.435214i	0.455184	+	0.890398i	$0.349574\pi$
$450$	−15.2382	−	2.00865i	−0.718336	−	0.0946887i
$451$	−2.02485			−0.0953463
$452$	0.709520	+	0.709520i	0.0333730	+	0.0333730i
$453$		−	19.5242i		−	0.917327i
$454$	−38.6922			−1.81591
$455$	34.2643	+	0.0460545i	1.60634	+	0.00215907i
$456$	0.946283			0.0443137
$457$		−	10.5157i		−	0.491902i	−0.969282	−	0.245951i	$-0.920900\pi$
$457$		−	10.5157i		−	0.491902i	0.969282	−	0.245951i	$-0.0791003\pi$
$458$	16.9417	+	16.9417i	0.791635	+	0.791635i
$459$	31.4341			1.46722
$460$	−1.69208	−	1.92977i	−0.0788938	−	0.0899758i
$461$	−2.81936	+	2.81936i	−0.131311	+	0.131311i	−0.769707	−	0.638397i	$-0.779598\pi$
$461$	−2.81936	+	2.81936i	−0.131311	+	0.131311i	0.638397	+	0.769707i	$0.279598\pi$
$462$	11.1714			0.519741
$463$			32.9570i			1.53164i	0.643054	+	0.765821i	$0.277667\pi$
$463$			32.9570i			1.53164i	−0.643054	+	0.765821i	$0.722333\pi$
$464$		−	13.2765i		−	0.616348i
$465$	−0.490024	+	7.46709i	−0.0227243	+	0.346278i
$466$	−10.4828	−	10.4828i	−0.485608	−	0.485608i
$467$	7.26867	+	7.26867i	0.336354	+	0.336354i	0.854993	−	0.518639i	$-0.173561\pi$
$467$	7.26867	+	7.26867i	0.336354	+	0.336354i	−0.518639	+	0.854993i	$0.673561\pi$
$468$	3.46354	−	0.222618i	0.160102	−	0.0102905i
$469$		−	30.2427i		−	1.39648i
$470$	1.70478	+	0.111875i	0.0786355	+	0.00516041i
$471$	8.21620			0.378583
$472$	0.740780	+	0.740780i	0.0340971	+	0.0340971i
$473$	2.16605			0.0995950
$474$	−12.3731	−	12.3731i	−0.568317	−	0.568317i
$475$	1.17985	+	1.53813i	0.0541354	+	0.0705743i
$476$	9.20173	+	9.20173i	0.421761	+	0.421761i
$477$	−14.1105	+	14.1105i	−0.646075	+	0.646075i
$478$	29.4982	−	29.4982i	1.34922	−	1.34922i
$479$	−19.0701	+	19.0701i	−0.871336	+	0.871336i	−0.992618	−	0.121282i	$-0.961299\pi$
$479$	−19.0701	+	19.0701i	−0.871336	+	0.871336i	0.121282	+	0.992618i	$0.461299\pi$
$480$	−4.14379	−	4.72585i	−0.189137	−	0.215705i
$481$	0.472454	+	7.35054i	0.0215421	+	0.335156i
$482$	−4.55867	+	4.55867i	−0.207642	+	0.207642i
$483$	10.1245			0.460681
$484$			4.14035i			0.188198i
$485$	−24.0816	−	1.58034i	−1.09349	−	0.0717597i
$486$	17.7303	−	17.7303i	0.804262	−	0.804262i
$487$			40.7729i			1.84760i	0.382879	+	0.923799i	$0.374933\pi$
$487$			40.7729i			1.84760i	−0.382879	+	0.923799i	$0.625067\pi$
$488$			26.8338i			1.21471i
$489$	3.66824	−	3.66824i	0.165884	−	0.165884i
$490$	38.9847	+	2.55835i	1.76115	+	0.115575i
$491$		−	4.59799i		−	0.207504i	−0.994603	−	0.103752i	$-0.966915\pi$
$491$		−	4.59799i		−	0.207504i	0.994603	−	0.103752i	$-0.0330849\pi$
$492$	0.634061			0.0285857
$493$	−12.2500	+	12.2500i	−0.551711	+	0.551711i
$494$	−1.65812	−	1.45784i	−0.0746025	−	0.0655915i
$495$	−4.65184	−	5.30527i	−0.209085	−	0.238454i
$496$	10.9375	−	10.9375i	0.491108	−	0.491108i
$497$	−31.5667	+	31.5667i	−1.41596	+	1.41596i
$498$	−13.5667	+	13.5667i	−0.607941	+	0.607941i
$499$	−22.8147	−	22.8147i	−1.02132	−	1.02132i	−0.999768	−	0.0215572i	$-0.993138\pi$
$499$	−22.8147	−	22.8147i	−1.02132	−	1.02132i	−0.0215572	−	0.999768i	$-0.506862\pi$
$500$	1.08008	−	5.42308i	0.0483028	−	0.242528i
$501$	6.39765	+	6.39765i	0.285826	+	0.285826i
$502$	−28.0824			−1.25338
$503$	11.1978	+	11.1978i	0.499287	+	0.499287i	0.911216	−	0.411929i	$-0.135145\pi$
$503$	11.1978	+	11.1978i	0.499287	+	0.499287i	−0.411929	+	0.911216i	$0.635145\pi$
$504$	−19.6674			−0.876057
$505$	26.0139	+	1.70715i	1.15760	+	0.0759671i
$506$		−	5.94272i		−	0.264186i
$507$	−10.5664	−	8.15040i	−0.469271	−	0.361972i
$508$	6.92983	+	6.92983i	0.307462	+	0.307462i
$509$	4.71971	+	4.71971i	0.209197	+	0.209197i	0.803926	−	0.594729i	$-0.202741\pi$
$509$	4.71971	+	4.71971i	0.209197	+	0.209197i	−0.594729	+	0.803926i	$0.702741\pi$
$510$	−1.46974	+	22.3961i	−0.0650810	+	0.991718i
$511$			21.1137i			0.934014i
$512$		−	9.57031i		−	0.422952i
$513$	−1.96854			−0.0869131
$514$	6.36831	−	6.36831i	0.280894	−	0.280894i
$515$	−7.65582	−	8.73121i	−0.337356	−	0.384743i
$516$	−0.678277			−0.0298595
$517$	0.554578	+	0.554578i	0.0243903	+	0.0243903i
$518$			13.7129i			0.602508i
$519$	−17.3116			−0.759897
$520$	0.0257657	−	19.1696i	0.00112990	−	0.840641i
$521$	−14.8279			−0.649622			−0.324811	−	0.945779i	$-0.605301\pi$
$521$	−14.8279			−0.649622			−0.324811	+	0.945779i	$0.605301\pi$
$522$			8.60190i			0.376495i
$523$	−22.3472	−	22.3472i	−0.977176	−	0.977176i	0.0225689	−	0.999745i	$-0.492815\pi$
$523$	−22.3472	−	22.3472i	−0.977176	−	0.977176i	−0.999745	+	0.0225689i	$0.992815\pi$
$524$	6.39251			0.279258
$525$	13.2762	+	17.3077i	0.579421	+	0.755368i
$526$	9.75196	−	9.75196i	0.425206	−	0.425206i
$527$	−20.1836			−0.879210
$528$		−	7.89620i		−	0.343638i
$529$			17.6142i			0.765834i
$530$	−23.8731	−	27.2265i	−1.03698	−	1.18264i
$531$	−0.606372	−	0.606372i	−0.0263143	−	0.0263143i
$532$	−0.576251	−	0.576251i	−0.0249837	−	0.0249837i
$533$	3.38179	+	2.97331i	0.146481	+	0.128789i
$534$		−	2.53390i		−	0.109653i
$535$	5.39409	+	6.15179i	0.233207	+	0.265965i
$536$	−16.9196			−0.730815
$537$	−1.46082	−	1.46082i	−0.0630389	−	0.0630389i
$538$	−39.7833			−1.71518
$539$	12.6820	+	12.6820i	0.546255	+	0.546255i
$540$	3.70201	+	4.22202i	0.159309	+	0.181687i
$541$	30.7281	+	30.7281i	1.32111	+	1.32111i	0.912882	+	0.408223i	$0.133851\pi$
$541$	30.7281	+	30.7281i	1.32111	+	1.32111i	0.408223	+	0.912882i	$0.366149\pi$
$542$	11.7362	−	11.7362i	0.504114	−	0.504114i
$543$	−6.08426	+	6.08426i	−0.261101	+	0.261101i
$544$	11.9873	−	11.9873i	0.513952	−	0.513952i
$545$	12.5568	−	11.0103i	0.537876	−	0.471627i
$546$	−18.6579	−	16.4043i	−0.798483	−	0.702038i
$547$	10.0949	−	10.0949i	0.431627	−	0.431627i	−0.457555	−	0.889181i	$-0.651275\pi$
$547$	10.0949	−	10.0949i	0.431627	−	0.431627i	0.889181	+	0.457555i	$0.151275\pi$
$548$	−2.78024			−0.118766
$549$		−	21.9651i		−	0.937446i
$550$	10.1590	−	7.79266i	0.433181	−	0.332280i
$551$	0.767145	−	0.767145i	0.0326815	−	0.0326815i
$552$		−	5.66427i		−	0.241087i
$553$		−	45.8691i		−	1.95055i
$554$	−0.615107	+	0.615107i	−0.0261334	+	0.0261334i
$555$	−3.52571	+	3.09146i	−0.149658	+	0.131225i
$556$			4.22242i			0.179070i
$557$	37.4425			1.58649			0.793246	−	0.608902i	$-0.208390\pi$
$557$	37.4425			1.58649			0.793246	+	0.608902i	$0.208390\pi$
$558$	−7.08643	+	7.08643i	−0.299992	+	0.299992i
$559$	−3.61761	−	3.18066i	−0.153009	−	0.134527i
$560$	2.95256	−	44.9918i	0.124768	−	1.90125i
$561$	−7.28565	+	7.28565i	−0.307601	+	0.307601i
$562$	3.78889	−	3.78889i	0.159824	−	0.159824i
$563$	30.1530	−	30.1530i	1.27080	−	1.27080i	0.325127	−	0.945670i	$-0.394593\pi$
$563$	30.1530	−	30.1530i	1.27080	−	1.27080i	0.945670	−	0.325127i	$-0.105407\pi$
$564$	−0.173661	−	0.173661i	−0.00731244	−	0.00731244i
$565$	−3.41101	+	2.99088i	−0.143502	+	0.125827i
$566$	−32.6151	−	32.6151i	−1.37092	−	1.37092i
$567$	2.66415			0.111884
$568$	17.6604	+	17.6604i	0.741013	+	0.741013i
$569$	44.0021			1.84466			0.922331	−	0.386400i	$-0.126282\pi$
$569$	44.0021			1.84466			0.922331	+	0.386400i	$0.126282\pi$
$570$	0.0920410	−	1.40254i	0.00385517	−	0.0587460i
$571$			30.3749i			1.27115i	0.772039	+	0.635576i	$0.219237\pi$
$571$			30.3749i			1.27115i	−0.772039	+	0.635576i	$0.780763\pi$
$572$	−1.90901	+	2.17127i	−0.0798198	+	0.0907855i
$573$	5.78974	+	5.78974i	0.241870	+	0.241870i
$574$	5.92790	+	5.92790i	0.247426	+	0.247426i
$575$	9.20695	−	7.06239i	0.383957	−	0.294522i
$576$			10.0510i			0.418792i
$577$		−	17.8387i		−	0.742636i	−0.928506	−	0.371318i	$-0.878906\pi$
$577$		−	17.8387i		−	0.742636i	0.928506	−	0.371318i	$-0.121094\pi$
$578$	−33.6866			−1.40118
$579$	−15.4148	+	15.4148i	−0.640616	+	0.640616i
$580$	−3.08802	−	0.202649i	−0.128223	−	0.00841456i
$581$	−50.2940			−2.08654
$582$	12.3731	+	12.3731i	0.512883	+	0.512883i
$583$		−	16.6231i		−	0.688459i
$584$	11.8123			0.488796
$585$	−0.0210908	+	15.6914i	−0.000871996	+	0.648760i
$586$	23.8032			0.983300
$587$		−	9.44899i		−	0.390002i	−0.980803	−	0.195001i	$-0.937529\pi$
$587$		−	9.44899i		−	0.390002i	0.980803	−	0.195001i	$-0.0624710\pi$
$588$	−3.97126	−	3.97126i	−0.163772	−	0.163772i
$589$	1.26398			0.0520814
$590$	1.17001	−	1.02590i	0.0481684	−	0.0422356i
$591$	2.58340	−	2.58340i	0.106267	−	0.106267i
$592$	9.69256			0.398362
$593$		−	31.6013i		−	1.29771i	−0.760912	−	0.648855i	$-0.775248\pi$
$593$		−	31.6013i		−	1.29771i	0.760912	−	0.648855i	$-0.224752\pi$
$594$			13.0017i			0.533467i
$595$	−44.2372	+	38.7887i	−1.81355	+	1.59018i
$596$	−3.67544	−	3.67544i	−0.150552	−	0.150552i
$597$	0.440864	+	0.440864i	0.0180434	+	0.0180434i
$598$	−8.72638	+	9.92521i	−0.356848	+	0.405872i
$599$			16.7567i			0.684661i	0.939580	+	0.342331i	$0.111216\pi$
$599$			16.7567i			0.684661i	−0.939580	+	0.342331i	$0.888784\pi$
$600$	9.68297	−	7.42752i	0.395306	−	0.303227i
$601$	36.7570			1.49935			0.749675	−	0.661807i	$-0.230210\pi$
$601$	36.7570			1.49935			0.749675	+	0.661807i	$0.230210\pi$
$602$	−6.34128	−	6.34128i	−0.258451	−	0.258451i
$603$	13.8497			0.564003
$604$	6.65173	+	6.65173i	0.270655	+	0.270655i
$605$	−18.6789	−	1.22579i	−0.759404	−	0.0498355i
$606$	−13.3659	−	13.3659i	−0.542954	−	0.542954i
$607$	15.2660	−	15.2660i	0.619629	−	0.619629i	−0.325807	−	0.945436i	$-0.605636\pi$
$607$	15.2660	−	15.2660i	0.619629	−	0.619629i	0.945436	+	0.325807i	$0.105636\pi$
$608$	−0.750697	+	0.750697i	−0.0304448	+	0.0304448i
$609$	8.63222	−	8.63222i	0.349795	−	0.349795i
$610$	39.7720	+	2.61002i	1.61032	+	0.105677i
$611$	−0.111875	−	1.74058i	−0.00452598	−	0.0704162i
$612$	−4.21395	+	4.21395i	−0.170339	+	0.170339i
$613$	−22.8956			−0.924745			−0.462373	−	0.886686i	$-0.653002\pi$
$613$	−22.8956			−0.924745			−0.462373	+	0.886686i	$0.653002\pi$
$614$		−	19.3922i		−	0.782604i
$615$	−0.187720	+	2.86052i	−0.00756961	+	0.115347i
$616$	11.5848	−	11.5848i	0.466764	−	0.466764i
$617$			14.4562i			0.581984i	0.956725	+	0.290992i	$0.0939854\pi$
$617$			14.4562i			0.581984i	−0.956725	+	0.290992i	$0.906015\pi$
$618$			8.41966i			0.338688i
$619$	−1.00603	+	1.00603i	−0.0404356	+	0.0404356i	−0.727036	−	0.686600i	$-0.759102\pi$
$619$	−1.00603	+	1.00603i	−0.0404356	+	0.0404356i	0.686600	+	0.727036i	$0.259102\pi$
$620$	−2.37703	−	2.71092i	−0.0954637	−	0.108873i
$621$			11.7833i			0.472847i
$622$	33.4750			1.34222
$623$	4.69678	−	4.69678i	0.188172	−	0.188172i
$624$	−11.5949	+	13.1878i	−0.464168	+	0.527935i
$625$	24.1461	+	6.47827i	0.965842	+	0.259131i
$626$	9.03239	−	9.03239i	0.361007	−	0.361007i
$627$	0.456258	−	0.456258i	0.0182212	−	0.0182212i
$628$	−2.79919	+	2.79919i	−0.111700	+	0.111700i
$629$	−8.94311	−	8.94311i	−0.356585	−	0.356585i
$630$	−1.91297	+	29.1503i	−0.0762146	+	1.16137i
$631$	−18.7320	−	18.7320i	−0.745710	−	0.745710i	0.227961	−	0.973670i	$-0.426794\pi$
$631$	−18.7320	−	18.7320i	−0.745710	−	0.745710i	−0.973670	+	0.227961i	$0.926794\pi$
$632$	−25.6620			−1.02078
$633$	−13.0574	−	13.0574i	−0.518983	−	0.518983i
$634$	−15.6055			−0.619772
$635$	−33.3151	+	29.2118i	−1.32207	+	1.15923i
$636$			5.20537i			0.206406i
$637$	−2.55835	−	39.8034i	−0.101366	−	1.57707i
$638$	−5.06681	−	5.06681i	−0.200597	−	0.200597i
$639$	−14.4561	−	14.4561i	−0.571873	−	0.571873i
$640$	−30.4189	−	1.99623i	−1.20241	−	0.0789078i
$641$		−	9.96670i		−	0.393661i	−0.980438	−	0.196830i	$-0.936935\pi$
$641$		−	9.96670i		−	0.393661i	0.980438	−	0.196830i	$-0.0630649\pi$
$642$		−	5.93227i		−	0.234128i
$643$	15.9115			0.627489			0.313745	−	0.949507i	$-0.398416\pi$
$643$	15.9115			0.627489			0.313745	+	0.949507i	$0.398416\pi$
$644$	−3.44933	+	3.44933i	−0.135923	+	0.135923i
$645$	0.200811	−	3.06000i	0.00790691	−	0.120487i
$646$	3.79107			0.149158
$647$	18.1067	+	18.1067i	0.711846	+	0.711846i	0.966921	−	0.255075i	$-0.0821003\pi$
$647$	18.1067	+	18.1067i	0.711846	+	0.711846i	−0.255075	+	0.966921i	$0.582100\pi$
$648$		−	1.49049i		−	0.0585519i
$649$	0.714347			0.0280406
$650$	−28.4098	−	1.90273i	−1.11433	−	0.0746314i
$651$	14.2228			0.557436
$652$			2.49948i			0.0978871i
$653$	28.8486	+	28.8486i	1.12893	+	1.12893i	0.990351	+	0.138584i	$0.0442551\pi$
$653$	28.8486	+	28.8486i	1.12893	+	1.12893i	0.138584	+	0.990351i	$0.455745\pi$
$654$	−12.1088			−0.473490
$655$	−1.89257	+	28.8393i	−0.0739486	+	1.12685i
$656$	4.18997	−	4.18997i	0.163591	−	0.163591i
$657$	−9.66904			−0.377225
$658$		−	3.24714i		−	0.126587i
$659$		−	9.37689i		−	0.365272i	−0.983181	−	0.182636i	$-0.941537\pi$
$659$		−	9.37689i		−	0.365272i	0.983181	−	0.182636i	$-0.0584630\pi$
$660$	−1.83659	−	0.120525i	−0.0714893	−	0.00469145i
$661$	−8.37769	−	8.37769i	−0.325855	−	0.325855i	0.525153	−	0.851008i	$-0.324008\pi$
$661$	−8.37769	−	8.37769i	−0.325855	−	0.325855i	−0.851008	+	0.525153i	$0.824008\pi$
$662$	6.12338	+	6.12338i	0.237992	+	0.237992i
$663$	22.8665	−	1.46974i	0.888060	−	0.0570798i
$664$			28.1375i			1.09195i
$665$	2.77032	−	2.42911i	0.107428	−	0.0941968i
$666$	−6.27983			−0.243338
$667$	−4.59198	−	4.59198i	−0.177802	−	0.177802i
$668$	−4.35924			−0.168664
$669$	11.3699	+	11.3699i	0.439586	+	0.439586i
$670$	−1.64570	+	25.0775i	−0.0635789	+	0.968829i
$671$	12.9382	+	12.9382i	0.499472	+	0.499472i
$672$	−8.44714	+	8.44714i	−0.325856	+	0.325856i
$673$	−4.98824	+	4.98824i	−0.192283	+	0.192283i	−0.796682	−	0.604399i	$-0.793413\pi$
$673$	−4.98824	+	4.98824i	−0.192283	+	0.192283i	0.604399	+	0.796682i	$0.293413\pi$
$674$	−16.7514	+	16.7514i	−0.645238	+	0.645238i
$675$	−20.1433	+	15.4514i	−0.775317	+	0.594723i
$676$	6.37666	−	0.823116i	0.245256	−	0.0316583i
$677$	4.95712	−	4.95712i	0.190518	−	0.190518i	−0.605402	−	0.795920i	$-0.706988\pi$
$677$	4.95712	−	4.95712i	0.190518	−	0.190518i	0.795920	+	0.605402i	$0.206988\pi$
$678$	3.28929			0.126324
$679$			45.8691i			1.76029i
$680$	21.7008	+	24.7490i	0.832186	+	0.949081i
$681$	−17.7816	+	17.7816i	−0.681393	+	0.681393i
$682$		−	8.34829i		−	0.319673i
$683$			3.52220i			0.134773i	0.997727	+	0.0673865i	$0.0214661\pi$
$683$			3.52220i			0.134773i	−0.997727	+	0.0673865i	$0.978534\pi$
$684$	0.263895	−	0.263895i	0.0100903	−	0.0100903i
$685$	0.823116	−	12.5428i	0.0314497	−	0.479237i
$686$		−	27.2679i		−	1.04109i
$687$	15.5717			0.594097
$688$	−4.48216	+	4.48216i	−0.170881	+	0.170881i
$689$	−24.4096	+	27.7630i	−0.929933	+	1.05769i
$690$	−8.39534	−	0.550940i	−0.319605	−	0.0209739i
$691$	18.5922	−	18.5922i	0.707280	−	0.707280i	−0.258682	−	0.965962i	$-0.583288\pi$
$691$	18.5922	−	18.5922i	0.707280	−	0.707280i	0.965962	+	0.258682i	$0.0832883\pi$
$692$	5.89792	−	5.89792i	0.224205	−	0.224205i
$693$	−9.48283	+	9.48283i	−0.360223	+	0.360223i
$694$	14.2494	+	14.2494i	0.540899	+	0.540899i
$695$	−19.0491	−	1.25009i	−0.722574	−	0.0474185i
$696$	−4.82940	−	4.82940i	−0.183058	−	0.183058i
$697$	−7.73199			−0.292870
$698$	19.6074	+	19.6074i	0.742153	+	0.742153i
$699$	−9.63511			−0.364433
$700$	−10.4197	−	1.37348i	−0.393826	−	0.0519128i
$701$		−	4.94675i		−	0.186836i	−0.995627	−	0.0934180i	$-0.970221\pi$
$701$		−	4.94675i		−	0.186836i	0.995627	−	0.0934180i	$-0.0297793\pi$
$702$	19.0919	−	21.7148i	0.720578	−	0.819571i
$703$	0.560055	+	0.560055i	0.0211229	+	0.0211229i
$704$	−5.92038	−	5.92038i	−0.223133	−	0.223133i
$705$	0.834872	−	0.732044i	0.0314431	−	0.0275704i
$706$			41.6515i			1.56757i
$707$		−	49.5495i		−	1.86350i
$708$	−0.223691			−0.00840682
$709$	14.2124	−	14.2124i	0.533760	−	0.533760i	−0.387929	−	0.921689i	$-0.626810\pi$
$709$	14.2124	−	14.2124i	0.533760	−	0.533760i	0.921689	+	0.387929i	$0.126810\pi$
$710$	27.8932	−	24.4577i	1.04681	−	0.917882i
$711$	21.0058			0.787780
$712$	−2.62767	−	2.62767i	−0.0984759	−	0.0984759i
$713$		−	7.56595i		−	0.283347i
$714$	42.6587			1.59646
$715$	−9.23035	−	9.25520i	−0.345195	−	0.346125i
$716$	0.995374			0.0371989
$717$		−	27.1128i		−	1.01255i
$718$	−25.8562	−	25.8562i	−0.964944	−	0.964944i
$719$	44.0748			1.64371			0.821856	−	0.569695i	$-0.192939\pi$
$719$	44.0748			1.64371			0.821856	+	0.569695i	$0.192939\pi$
$720$	20.6041	+	1.35213i	0.767868	+	0.0503910i
$721$	−15.6065	+	15.6065i	−0.581215	+	0.581215i
$722$	29.7717			1.10799
$723$			4.19002i			0.155829i
$724$		−	4.14571i		−	0.154074i
$725$	1.82848	−	13.8714i	0.0679079	−	0.515169i
$726$	9.59721	+	9.59721i	0.356186	+	0.356186i
$727$	18.2981	+	18.2981i	0.678638	+	0.678638i	0.959692	−	0.281054i	$-0.0906840\pi$
$727$	18.2981	+	18.2981i	0.678638	+	0.678638i	−0.281054	+	0.959692i	$0.590684\pi$
$728$	−36.3595	+	2.33700i	−1.34757	+	0.0866150i
$729$		−	14.4159i		−	0.533922i
$730$	1.14893	−	17.5077i	0.0425239	−	0.647988i
$731$	8.27118			0.305921
$732$	−4.05146	−	4.05146i	−0.149746	−	0.149746i
$733$	19.8910			0.734691			0.367345	−	0.930085i	$-0.380267\pi$
$733$	19.8910			0.734691			0.367345	+	0.930085i	$0.380267\pi$
$734$	34.9514	+	34.9514i	1.29008	+	1.29008i
$735$	19.0918	−	16.7403i	0.704211	−	0.617476i
$736$	4.49353	+	4.49353i	0.165634	+	0.165634i
$737$	−8.15793	+	8.15793i	−0.300501	+	0.300501i
$738$	−2.71469	+	2.71469i	−0.0999293	+	0.0999293i
$739$	2.02107	−	2.02107i	0.0743464	−	0.0743464i	−0.668956	−	0.743302i	$-0.733258\pi$
$739$	2.02107	−	2.02107i	0.0743464	−	0.0743464i	0.743302	+	0.668956i	$0.233258\pi$
$740$	0.147945	−	2.25441i	0.00543855	−	0.0828738i
$741$	−1.43199	+	0.0920410i	−0.0526056	+	0.00338121i
$742$	−48.6655	+	48.6655i	−1.78657	+	1.78657i
$743$	−1.93043			−0.0708207			−0.0354104	−	0.999373i	$-0.511274\pi$
$743$	−1.93043			−0.0708207			−0.0354104	+	0.999373i	$0.511274\pi$
$744$		−	7.95712i		−	0.291722i
$745$	17.6696	−	15.4933i	0.647365	−	0.567632i
$746$	−21.1854	+	21.1854i	−0.775653	+	0.775653i
$747$		−	23.0322i		−	0.842705i
$748$		−	4.96432i		−	0.181513i
$749$	10.9959	−	10.9959i	0.401782	−	0.401782i
$750$	−10.0669	−	15.0741i	−0.367593	−	0.550430i
$751$		−	42.9887i		−	1.56868i	−0.620332	−	0.784339i	$-0.713002\pi$
$751$		−	42.9887i		−	1.56868i	0.620332	−	0.784339i	$-0.286998\pi$
$752$	−2.29516			−0.0836957
$753$	−12.9057	+	12.9057i	−0.470310	+	0.470310i
$754$	1.02213	+	15.9025i	0.0372237	+	0.579134i
$755$	−31.9781	+	28.0395i	−1.16380	+	1.02046i
$756$	7.54658	−	7.54658i	0.274466	−	0.274466i
$757$	−31.8767	+	31.8767i	−1.15858	+	1.15858i	−0.173798	+	0.984781i	$0.555604\pi$
$757$	−31.8767	+	31.8767i	−1.15858	+	1.15858i	−0.984781	+	0.173798i	$0.944396\pi$
$758$	−20.3611	+	20.3611i	−0.739547	+	0.739547i
$759$	−2.73108	−	2.73108i	−0.0991318	−	0.0991318i
$760$	−1.35899	−	1.54989i	−0.0492958	−	0.0562203i
$761$	19.0048	+	19.0048i	0.688923	+	0.688923i	0.961994	−	0.273071i	$-0.0880395\pi$
$761$	19.0048	+	19.0048i	0.688923	+	0.688923i	−0.273071	+	0.961994i	$0.588039\pi$
$762$	32.1263			1.16381
$763$	−22.4445	−	22.4445i	−0.812546	−	0.812546i
$764$	−3.94503			−0.142726
$765$	−17.7633	−	20.2585i	−0.642235	−	0.732448i
$766$		−	31.4246i		−	1.13542i
$767$	−1.19306	−	1.04896i	−0.0430790	−	0.0378757i
$768$	8.13237	+	8.13237i	0.293452	+	0.293452i
$769$	−21.9349	−	21.9349i	−0.790991	−	0.790991i	0.190664	−	0.981655i	$-0.438936\pi$
$769$	−21.9349	−	21.9349i	−0.790991	−	0.790991i	−0.981655	+	0.190664i	$0.938936\pi$
$770$	−16.0437	−	18.2973i	−0.578174	−	0.659389i
$771$		−	5.85332i		−	0.210802i
$772$		−	10.5033i		−	0.378024i
$773$	−15.1954			−0.546540			−0.273270	−	0.961937i	$-0.588105\pi$
$773$	−15.1954			−0.546540			−0.273270	+	0.961937i	$0.588105\pi$
$774$	2.90400	−	2.90400i	0.104382	−	0.104382i
$775$	12.9339	−	9.92118i	0.464598	−	0.356379i
$776$	25.6620			0.921211
$777$	6.30197	+	6.30197i	0.226082	+	0.226082i
$778$		−	20.9844i		−	0.752328i
$779$	0.484210			0.0173486
$780$	2.89040	+	2.89818i	0.103493	+	0.103771i
$781$	17.0302			0.609389
$782$		−	22.6926i		−	0.811487i
$783$	10.0465	+	10.0465i	0.359033	+	0.359033i
$784$	−52.4854			−1.87448
$785$	−11.7996	−	13.4571i	−0.421146	−	0.480303i
$786$	14.8176	−	14.8176i	0.528528	−	0.528528i
$787$	−23.9899			−0.855148			−0.427574	−	0.903980i	$-0.640632\pi$
$787$	−23.9899			−0.855148			−0.427574	+	0.903980i	$0.640632\pi$
$788$			1.76028i			0.0627075i
$789$		−	8.96335i		−	0.319104i
$790$	−2.49603	+	38.0351i	−0.0888049	+	1.35323i
$791$	6.09695	+	6.09695i	0.216782	+	0.216782i
$792$	5.30527	+	5.30527i	0.188515	+	0.188515i
$793$	−2.61002	−	40.6072i	−0.0926844	−	1.44200i
$794$			5.71106i			0.202678i
$795$	−23.4836	−	1.54110i	−0.832878	−	0.0546572i
$796$	−0.300397			−0.0106473
$797$	−24.2326	−	24.2326i	−0.858363	−	0.858363i	0.132782	−	0.991145i	$-0.457609\pi$
$797$	−24.2326	−	24.2326i	−0.858363	−	0.858363i	−0.991145	+	0.132782i	$0.957609\pi$
$798$	−2.67147			−0.0945689
$799$	2.11769	+	2.11769i	0.0749185	+	0.0749185i
$800$	−1.78927	+	13.5739i	−0.0632603	+	0.479912i
$801$	2.15090	+	2.15090i	0.0759982	+	0.0759982i
$802$	−8.60208	+	8.60208i	−0.303750	+	0.303750i
$803$	5.69539	−	5.69539i	0.200986	−	0.200986i
$804$	2.55458	−	2.55458i	0.0900930	−	0.0900930i
$805$	−14.5402	−	16.5826i	−0.512474	−	0.584460i
$806$	−12.2588	+	13.9429i	−0.431796	+	0.491116i
$807$	−18.2831	+	18.2831i	−0.643594	+	0.643594i
$808$	−27.7210			−0.975223
$809$			2.36679i			0.0832119i	0.999134	+	0.0416060i	$0.0132474\pi$
$809$			2.36679i			0.0832119i	−0.999134	+	0.0416060i	$0.986753\pi$
$810$	−2.20914	−	0.144974i	−0.0776213	−	0.00509386i
$811$	−19.8318	+	19.8318i	−0.696388	+	0.696388i	−0.963630	−	0.267241i	$-0.913888\pi$
$811$	−19.8318	+	19.8318i	−0.696388	+	0.696388i	0.267241	+	0.963630i	$0.413888\pi$
$812$			5.88185i			0.206412i
$813$		−	10.7871i		−	0.378322i
$814$	3.69903	−	3.69903i	0.129651	−	0.129651i
$815$	−11.2762	−	0.739995i	−0.394988	−	0.0259209i
$816$		−	30.1521i		−	1.05554i
$817$	−0.517976			−0.0181217
$818$	43.2516	−	43.2516i	1.51226	−	1.51226i
$819$	29.7624	−	1.91297i	1.03998	−	0.0668446i
$820$	−0.910600	−	1.03851i	−0.0317995	−	0.0362663i
$821$	−25.1402	+	25.1402i	−0.877398	+	0.877398i	−0.993265	−	0.115867i	$-0.963035\pi$
$821$	−25.1402	+	25.1402i	−0.877398	+	0.877398i	0.115867	+	0.993265i	$0.463035\pi$
$822$	−6.44450	+	6.44450i	−0.224778	+	0.224778i
$823$	−19.6596	+	19.6596i	−0.685290	+	0.685290i	−0.961187	−	0.275897i	$-0.911025\pi$
$823$	−19.6596	+	19.6596i	−0.685290	+	0.685290i	0.275897	+	0.961187i	$0.411025\pi$
$824$	8.73121	+	8.73121i	0.304166	+	0.304166i
$825$	1.08748	−	8.24997i	0.0378613	−	0.287227i
$826$	−2.09131	−	2.09131i	−0.0727659	−	0.0727659i
$827$	25.4881			0.886309			0.443155	−	0.896445i	$-0.353859\pi$
$827$	25.4881			0.886309			0.443155	+	0.896445i	$0.353859\pi$
$828$	−1.57963	−	1.57963i	−0.0548958	−	0.0548958i
$829$	−38.5661			−1.33946			−0.669728	−	0.742607i	$-0.733589\pi$
$829$	−38.5661			−1.33946			−0.669728	+	0.742607i	$0.733589\pi$
$830$	41.7043	+	2.73682i	1.44758	+	0.0949965i
$831$			0.565365i			0.0196123i
$832$	1.19432	+	18.5815i	0.0414056	+	0.644197i
$833$	48.4272	+	48.4272i	1.67790	+	1.67790i
$834$	9.78743	+	9.78743i	0.338911	+	0.338911i
$835$	1.29060	−	19.6664i	0.0446630	−	0.680584i
$836$			0.310886i			0.0107522i
$837$			16.5531i			0.572158i
$838$	49.9749			1.72635
$839$	7.16262	−	7.16262i	0.247281	−	0.247281i	−0.572573	−	0.819854i	$-0.694055\pi$
$839$	7.16262	−	7.16262i	0.247281	−	0.247281i	0.819854	+	0.572573i	$0.194055\pi$
$840$	−15.2919	−	17.4399i	−0.527622	−	0.601735i
$841$	21.1697			0.729989
$842$	−0.493208	−	0.493208i	−0.0169971	−	0.0169971i
$843$		−	3.48249i		−	0.119943i
$844$	8.89705			0.306249
$845$	1.82555	+	29.0115i	0.0628010	+	0.998026i
$846$	1.48704			0.0511254
$847$			35.5783i			1.22248i
$848$	34.3979	+	34.3979i	1.18123	+	1.18123i
$849$	−29.9776			−1.02883
$850$	38.7927	−	29.7567i	1.33058	−	1.02065i
$851$	3.35238	−	3.35238i	0.114918	−	0.114918i
$852$	−5.33285			−0.182700
$853$			5.58445i			0.191208i	0.995419	+	0.0956039i	$0.0304782\pi$
$853$			5.58445i			0.191208i	−0.995419	+	0.0956039i	$0.969522\pi$
$854$		−	75.7550i		−	2.59228i
$855$	1.11242	+	1.26867i	0.0380438	+	0.0433877i
$856$	−6.15179	−	6.15179i	−0.210264	−	0.210264i
$857$	−16.9197	−	16.9197i	−0.577966	−	0.577966i	0.356376	−	0.934343i	$-0.384012\pi$
$857$	−16.9197	−	16.9197i	−0.577966	−	0.577966i	−0.934343	+	0.356376i	$0.884012\pi$
$858$	0.607909	+	9.45798i	0.0207537	+	0.322890i
$859$		−	28.3026i		−	0.965674i	−0.875710	−	0.482837i	$-0.839606\pi$
$859$		−	28.3026i		−	0.965674i	0.875710	−	0.482837i	$-0.160394\pi$
$860$	0.974100	+	1.11093i	0.0332165	+	0.0378823i
$861$	5.44853			0.185685
$862$	−20.6085	−	20.6085i	−0.701928	−	0.701928i
$863$	−44.2714			−1.50702			−0.753508	−	0.657439i	$-0.771640\pi$
$863$	−44.2714			−1.50702			−0.753508	+	0.657439i	$0.771640\pi$
$864$	−9.83112	−	9.83112i	−0.334461	−	0.334461i
$865$	24.8619	+	28.3542i	0.845330	+	0.964071i
$866$	−0.0617958	−	0.0617958i	−0.00209991	−	0.00209991i
$867$	−15.4812	+	15.4812i	−0.525770	+	0.525770i
$868$	−4.84559	+	4.84559i	−0.164470	+	0.164470i
$869$	−12.3731	+	12.3731i	−0.419730	+	0.419730i
$870$	−7.62767	+	6.68819i	−0.258602	+	0.226751i
$871$	25.6042	−	1.64570i	0.867564	−	0.0557624i
$872$	−12.5568	+	12.5568i	−0.425228	+	0.425228i
$873$	−21.0058			−0.710939
$874$			1.42111i			0.0480697i
$875$	9.28121	−	46.6009i	0.313762	−	1.57540i
$876$	−1.78346	+	1.78346i	−0.0602575	+	0.0602575i
$877$			40.7540i			1.37616i	0.725633	+	0.688082i	$0.241547\pi$
$877$			40.7540i			1.37616i	−0.725633	+	0.688082i	$0.758453\pi$
$878$			27.4973i			0.927989i
$879$	10.9391	−	10.9391i	0.368968	−	0.368968i
$880$	−12.9329	+	11.3400i	−0.435969	+	0.382273i
$881$			6.83724i			0.230353i	0.993345	+	0.115176i	$0.0367433\pi$
$881$			6.83724i			0.230353i	−0.993345	+	0.115176i	$0.963257\pi$
$882$	34.0054			1.14502
$883$	9.20332	−	9.20332i	0.309716	−	0.309716i	−0.535083	−	0.844799i	$-0.679720\pi$
$883$	9.20332	−	9.20332i	0.309716	−	0.309716i	0.844799	+	0.535083i	$0.179720\pi$
$884$	−7.28968	+	8.29113i	−0.245178	+	0.278861i
$885$	0.0662259	−	1.00916i	0.00222616	−	0.0339227i
$886$	−28.2054	+	28.2054i	−0.947578	+	0.947578i
$887$	23.9871	−	23.9871i	0.805409	−	0.805409i	−0.178526	−	0.983935i	$-0.557133\pi$
$887$	23.9871	−	23.9871i	0.805409	−	0.805409i	0.983935	+	0.178526i	$0.0571330\pi$
$888$	3.52571	−	3.52571i	0.118315	−	0.118315i
$889$	59.5485	+	59.5485i	1.99719	+	1.99719i
$890$	−4.15020	+	3.63903i	−0.139115	+	0.121981i
$891$	−0.718652	−	0.718652i	−0.0240758	−	0.0240758i
$892$	−7.74726			−0.259397
$893$	−0.132619	−	0.132619i	−0.00443791	−	0.00443791i
$894$	−17.0391			−0.569874
$895$	−0.294690	+	4.49056i	−0.00985042	+	0.150103i
$896$			57.9400i			1.93564i
$897$	0.550940	+	8.57164i	0.0183954	+	0.286199i
$898$	−14.5655	−	14.5655i	−0.486056	−	0.486056i
$899$	−6.45078	−	6.45078i	−0.215146	−	0.215146i
$900$	0.628990	−	4.77170i	0.0209663	−	0.159057i
$901$		−	63.4763i		−	2.11470i
$902$		−	3.19809i		−	0.106485i
$903$	−5.82848			−0.193960
$904$	3.41101	−	3.41101i	0.113448	−	0.113448i
$905$	18.7031	+	1.22738i	0.621711	+	0.0407994i
$906$	30.8370			1.02449
$907$	−22.7917	−	22.7917i	−0.756787	−	0.756787i	0.218949	−	0.975736i	$-0.429737\pi$
$907$	−22.7917	−	22.7917i	−0.756787	−	0.756787i	−0.975736	+	0.218949i	$0.929737\pi$
$908$		−	12.1161i		−	0.402086i
$909$	22.6913			0.752623
$910$	−0.0727397	+	54.1179i	−0.00241130	+	1.79399i
$911$	−1.52357			−0.0504781			−0.0252391	−	0.999681i	$-0.508035\pi$
$911$	−1.52357			−0.0504781			−0.0252391	+	0.999681i	$0.508035\pi$
$912$			1.88825i			0.0625263i
$913$	13.5667	+	13.5667i	0.448994	+	0.448994i
$914$	16.6087			0.549367
$915$	19.4773	−	17.0784i	0.643901	−	0.564594i
$916$	−5.30514	+	5.30514i	−0.175287	+	0.175287i
$917$	54.9312			1.81399
$918$			49.6478i			1.63862i
$919$			8.64385i			0.285134i	0.989785	+	0.142567i	$0.0455357\pi$
$919$			8.64385i			0.285134i	−0.989785	+	0.142567i	$0.954464\pi$
$920$	−9.27732	+	8.13467i	−0.305864	+	0.268192i
$921$	−8.91198	−	8.91198i	−0.293660	−	0.293660i
$922$	−4.45297	−	4.45297i	−0.146651	−	0.146651i
$923$	−28.4429	−	25.0074i	−0.936210	−	0.823129i
$924$			3.49822i			0.115083i
$925$	10.1268	+	1.33488i	0.332967	+	0.0438906i
$926$	−52.0531			−1.71057
$927$	−7.14701	−	7.14701i	−0.234739	−	0.234739i
$928$	7.66243			0.251532
$929$	−9.39925	−	9.39925i	−0.308379	−	0.308379i	0.535901	−	0.844281i	$-0.319972\pi$
$929$	−9.39925	−	9.39925i	−0.308379	−	0.308379i	−0.844281	+	0.535901i	$0.819972\pi$
$930$	−11.7937	−	0.773956i	−0.386731	−	0.0253790i
$931$	−3.03271	−	3.03271i	−0.0993931	−	0.0993931i
$932$	3.28260	−	3.28260i	0.107525	−	0.107525i
$933$	15.3840	−	15.3840i	0.503649	−	0.503649i
$934$	−11.4803	+	11.4803i	−0.375648	+	0.375648i
$935$	22.3961	+	1.46974i	0.732432	+	0.0480655i
$936$	−1.07023	−	16.6509i	−0.0349817	−	0.544252i
$937$	−26.2070	+	26.2070i	−0.856144	+	0.856144i	−0.990881	−	0.134737i	$-0.956981\pi$
$937$	−26.2070	+	26.2070i	−0.856144	+	0.856144i	0.134737	+	0.990881i	$0.456981\pi$
$938$	47.7660			1.55961
$939$		−	8.30197i		−	0.270924i
$940$	−0.0350326	+	0.533835i	−0.00114264	+	0.0174118i
$941$	−14.9851	+	14.9851i	−0.488502	+	0.488502i	−0.907833	−	0.419332i	$-0.862264\pi$
$941$	−14.9851	+	14.9851i	−0.488502	+	0.488502i	0.419332	+	0.907833i	$0.362264\pi$
$942$			12.9769i			0.422809i
$943$		−	2.89839i		−	0.0943845i
$944$	−1.47818	+	1.47818i	−0.0481108	+	0.0481108i
$945$	31.8116	+	36.2801i	1.03483	+	1.18019i
$946$			3.42111i			0.111230i
$947$	1.74843			0.0568162			0.0284081	−	0.999596i	$-0.490956\pi$
$947$	1.74843			0.0568162			0.0284081	+	0.999596i	$0.490956\pi$
$948$	3.87453	−	3.87453i	0.125839	−	0.125839i
$949$	−17.8753	+	1.14893i	−0.580258	+	0.0372959i
$950$	−2.42936	+	1.86349i	−0.0788189	+	0.0604596i
$951$	−7.17174	+	7.17174i	−0.232560	+	0.232560i
$952$	44.2372	−	44.2372i	1.43374	−	1.43374i
$953$	−18.8510	+	18.8510i	−0.610644	+	0.610644i	−0.943114	−	0.332470i	$-0.892118\pi$
$953$	−18.8510	+	18.8510i	−0.610644	+	0.610644i	0.332470	+	0.943114i	$0.392118\pi$
$954$	−22.2865	−	22.2865i	−0.721551	−	0.721551i
$955$	1.16796	−	17.7977i	0.0377944	−	0.575920i
$956$	9.23709	+	9.23709i	0.298749	+	0.298749i
$957$	−4.65707			−0.150542
$958$	−30.1198	−	30.1198i	−0.973127	−	0.973127i
$959$	−23.8907			−0.771472
$960$	−8.91265	+	7.81491i	−0.287655	+	0.252225i
$961$			20.3714i			0.657142i
$962$	−11.6096	+	0.746206i	−0.374310	+	0.0240586i
$963$	5.03560	+	5.03560i	0.162270	+	0.162270i
$964$	−1.42750	−	1.42750i	−0.0459768	−	0.0459768i
$965$	47.3851	+	3.10962i	1.52538	+	0.100102i
$966$			15.9909i			0.514498i
$967$		−	25.1486i		−	0.808724i	−0.914599	−	0.404362i	$-0.867494\pi$
$967$		−	25.1486i		−	0.808724i	0.914599	−	0.404362i	$-0.132506\pi$
$968$	19.9047			0.639760
$969$	1.74225	−	1.74225i	0.0559691	−	0.0559691i
$970$	2.49603	−	38.0351i	0.0801428	−	1.22123i
$971$	1.51896			0.0487459			0.0243729	−	0.999703i	$-0.492241\pi$
$971$	1.51896			0.0487459			0.0243729	+	0.999703i	$0.492241\pi$
$972$	5.55207	+	5.55207i	0.178083	+	0.178083i
$973$			36.2835i			1.16319i
$974$	−64.3977			−2.06344
$975$	−13.9306	+	12.1818i	−0.446137	+	0.390129i
$976$	−53.5454			−1.71395
$977$		−	14.1070i		−	0.451322i	−0.974206	−	0.225661i	$-0.927546\pi$
$977$		−	14.1070i		−	0.451322i	0.974206	−	0.225661i	$-0.0724542\pi$
$978$	5.79371	+	5.79371i	0.185262	+	0.185262i
$979$	−2.53390			−0.0809839
$980$	−0.801123	+	12.2077i	−0.0255909	+	0.389960i
$981$	10.2785	−	10.2785i	0.328167	−	0.328167i
$982$	7.26218			0.231746
$983$			17.0799i			0.544764i	0.962189	+	0.272382i	$0.0878115\pi$
$983$			17.0799i			0.544764i	−0.962189	+	0.272382i	$0.912189\pi$
$984$		−	3.04824i		−	0.0971744i
$985$	−7.94139	−	0.521149i	−0.253034	−	0.0166052i
$986$	−19.3479	−	19.3479i	−0.616163	−	0.616163i
$987$	−1.49228	−	1.49228i	−0.0474997	−	0.0474997i
$988$	0.456510	−	0.519225i	0.0145235	−	0.0165188i
$989$			3.10051i			0.0985904i
$990$	8.37928	−	7.34724i	0.266311	−	0.233511i
$991$	−12.4584			−0.395755			−0.197878	−	0.980227i	$-0.563405\pi$
$991$	−12.4584			−0.395755			−0.197878	+	0.980227i	$0.563405\pi$
$992$	6.31247	+	6.31247i	0.200421	+	0.200421i
$993$	5.62820			0.178605
$994$	−49.8573	−	49.8573i	−1.58138	−	1.58138i
$995$	0.0889356	−	1.35522i	0.00281945	−	0.0429633i
$996$	−4.24830	−	4.24830i	−0.134612	−	0.134612i
$997$	−12.8217	+	12.8217i	−0.406066	+	0.406066i	−0.880364	−	0.474298i	$-0.842702\pi$
$997$	−12.8217	+	12.8217i	−0.406066	+	0.406066i	0.474298	+	0.880364i	$0.342702\pi$
$998$	36.0340	−	36.0340i	1.14064	−	1.14064i
$999$	−7.33448	+	7.33448i	−0.232053	+	0.232053i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.2.f.b.18.3	✓	8
3.2	odd	2		585.2.n.e.343.2		8
4.3	odd	2		1040.2.cd.n.993.1		8
5.2	odd	4		65.2.k.b.57.2	yes	8
5.3	odd	4		325.2.k.b.57.3		8
5.4	even	2		325.2.f.b.18.2		8
13.2	odd	12		845.2.o.c.488.2		16
13.3	even	3		845.2.t.c.188.2		16
13.4	even	6		845.2.t.d.418.2		16
13.5	odd	4		845.2.k.b.268.3		8
13.6	odd	12		845.2.o.c.258.2		16
13.7	odd	12		845.2.o.d.258.3		16
13.8	odd	4		65.2.k.b.8.2	yes	8
13.9	even	3		845.2.t.c.418.3		16
13.10	even	6		845.2.t.d.188.3		16
13.11	odd	12		845.2.o.d.488.3		16
13.12	even	2		845.2.f.b.408.2		8
15.2	even	4		585.2.w.e.577.3		8
20.7	even	4		1040.2.bg.n.577.1		8
39.8	even	4		585.2.w.e.73.3		8
52.47	even	4		1040.2.bg.n.593.1		8
65.2	even	12		845.2.t.d.657.2		16
65.7	even	12		845.2.t.c.427.2		16
65.8	even	4		325.2.f.b.307.3		8
65.12	odd	4		845.2.k.b.577.3		8
65.17	odd	12		845.2.o.c.587.2		16
65.22	odd	12		845.2.o.d.587.3		16
65.32	even	12		845.2.t.d.427.3		16
65.34	odd	4		325.2.k.b.268.3		8
65.37	even	12		845.2.t.c.657.3		16
65.42	odd	12		845.2.o.d.357.3		16
65.47	even	4	inner	65.2.f.b.47.2	yes	8
65.57	even	4		845.2.f.b.437.3		8
65.62	odd	12		845.2.o.c.357.2		16
195.47	odd	4		585.2.n.e.307.3		8
260.47	odd	4		1040.2.cd.n.177.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.f.b.18.3	✓	8	1.1	even	1	trivial
65.2.f.b.47.2	yes	8	65.47	even	4	inner
65.2.k.b.8.2	yes	8	13.8	odd	4
65.2.k.b.57.2	yes	8	5.2	odd	4
325.2.f.b.18.2		8	5.4	even	2
325.2.f.b.307.3		8	65.8	even	4
325.2.k.b.57.3		8	5.3	odd	4
325.2.k.b.268.3		8	65.34	odd	4
585.2.n.e.307.3		8	195.47	odd	4
585.2.n.e.343.2		8	3.2	odd	2
585.2.w.e.73.3		8	39.8	even	4
585.2.w.e.577.3		8	15.2	even	4
845.2.f.b.408.2		8	13.12	even	2
845.2.f.b.437.3		8	65.57	even	4
845.2.k.b.268.3		8	13.5	odd	4
845.2.k.b.577.3		8	65.12	odd	4
845.2.o.c.258.2		16	13.6	odd	12
845.2.o.c.357.2		16	65.62	odd	12
845.2.o.c.488.2		16	13.2	odd	12
845.2.o.c.587.2		16	65.17	odd	12
845.2.o.d.258.3		16	13.7	odd	12
845.2.o.d.357.3		16	65.42	odd	12
845.2.o.d.488.3		16	13.11	odd	12
845.2.o.d.587.3		16	65.22	odd	12
845.2.t.c.188.2		16	13.3	even	3
845.2.t.c.418.3		16	13.9	even	3
845.2.t.c.427.2		16	65.7	even	12
845.2.t.c.657.3		16	65.37	even	12
845.2.t.d.188.3		16	13.10	even	6
845.2.t.d.418.2		16	13.4	even	6
845.2.t.d.427.3		16	65.32	even	12
845.2.t.d.657.2		16	65.2	even	12
1040.2.bg.n.577.1		8	20.7	even	4
1040.2.bg.n.593.1		8	52.47	even	4
1040.2.cd.n.177.1		8	260.47	odd	4
1040.2.cd.n.993.1		8	4.3	odd	2

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.57942i q^{2} +(0.725850 + 0.725850i) q^{3} -0.494582 q^{4} +(0.146426 - 2.23127i) q^{5} +(-1.14643 + 1.14643i) q^{6} -4.24997 q^{7} +2.37769i q^{8} -1.94628i q^{9} +O(q^{10})\)	\(q+1.57942i q^{2} +(0.725850 + 0.725850i) q^{3} -0.494582 q^{4} +(0.146426 - 2.23127i) q^{5} +(-1.14643 + 1.14643i) q^{6} -4.24997 q^{7} +2.37769i q^{8} -1.94628i q^{9} +(3.52412 + 0.231269i) q^{10} +(1.14643 + 1.14643i) q^{11} +(-0.358992 - 0.358992i) q^{12} +(-0.231269 - 3.59813i) q^{13} -6.71251i q^{14} +(1.72585 - 1.51328i) q^{15} -4.74455 q^{16} +(4.37769 + 4.37769i) q^{17} +3.07401 q^{18} +(-0.274150 - 0.274150i) q^{19} +(-0.0724196 + 1.10354i) q^{20} +(-3.08484 - 3.08484i) q^{21} +(-1.81069 + 1.81069i) q^{22} +(-1.64101 + 1.64101i) q^{23} +(-1.72585 + 1.72585i) q^{24} +(-4.95712 - 0.653431i) q^{25} +(5.68297 - 0.365271i) q^{26} +(3.59026 - 3.59026i) q^{27} +2.10196 q^{28} +2.79827i q^{29} +(2.39012 + 2.72585i) q^{30} +(-2.30527 + 2.30527i) q^{31} -2.73827i q^{32} +1.66427i q^{33} +(-6.91424 + 6.91424i) q^{34} +(-0.622306 + 9.48283i) q^{35} +0.962596i q^{36} -2.04288 q^{37} +(0.432999 - 0.432999i) q^{38} +(2.44384 - 2.77957i) q^{39} +(5.30527 + 0.348156i) q^{40} +(-0.883113 + 0.883113i) q^{41} +(4.87228 - 4.87228i) q^{42} +(0.944696 - 0.944696i) q^{43} +(-0.567001 - 0.567001i) q^{44} +(-4.34268 - 0.284986i) q^{45} +(-2.59185 - 2.59185i) q^{46} +0.483745 q^{47} +(-3.44384 - 3.44384i) q^{48} +11.0623 q^{49} +(1.03204 - 7.82940i) q^{50} +6.35510i q^{51} +(0.114381 + 1.77957i) q^{52} +(-7.24997 - 7.24997i) q^{53} +(5.67055 + 5.67055i) q^{54} +(2.72585 - 2.39012i) q^{55} -10.1051i q^{56} -0.397983i q^{57} -4.41966 q^{58} +(0.311554 - 0.311554i) q^{59} +(-0.853574 + 0.748443i) q^{60} +11.2857 q^{61} +(-3.64101 - 3.64101i) q^{62} +8.27164i q^{63} -5.16421 q^{64} +(-8.06225 - 0.0108364i) q^{65} -2.62858 q^{66} +7.11597i q^{67} +(-2.16513 - 2.16513i) q^{68} -2.38225 q^{69} +(-14.9774 - 0.982885i) q^{70} +(7.42752 - 7.42752i) q^{71} +4.62767 q^{72} -4.96796i q^{73} -3.22658i q^{74} +(-3.12383 - 4.07242i) q^{75} +(0.135589 + 0.135589i) q^{76} +(-4.87228 - 4.87228i) q^{77} +(4.39012 + 3.85985i) q^{78} +10.7928i q^{79} +(-0.694725 + 10.5864i) q^{80} -0.626863 q^{81} +(-1.39481 - 1.39481i) q^{82} +11.8340 q^{83} +(1.52571 + 1.52571i) q^{84} +(10.4088 - 9.12680i) q^{85} +(1.49208 + 1.49208i) q^{86} +(-2.03113 + 2.03113i) q^{87} +(-2.72585 + 2.72585i) q^{88} +(-1.10513 + 1.10513i) q^{89} +(0.450114 - 6.85893i) q^{90} +(0.982885 + 15.2919i) q^{91} +(0.811612 - 0.811612i) q^{92} -3.34657 q^{93} +0.764039i q^{94} +(-0.651844 + 0.571559i) q^{95} +(1.98758 - 1.98758i) q^{96} -10.7928i q^{97} +17.4720i q^{98} +(2.23127 - 2.23127i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{3} - 8 q^{4} - 2 q^{5} - 6 q^{6}+O(q^{10}) \) 8 * q - 6 * q^3 - 8 * q^4 - 2 * q^5 - 6 * q^6	\( 8 q - 6 q^{3} - 8 q^{4} - 2 q^{5} - 6 q^{6} + 6 q^{10} + 6 q^{11} - 2 q^{12} + 14 q^{13} + 2 q^{15} - 8 q^{16} + 16 q^{17} + 20 q^{18} - 14 q^{19} - 2 q^{20} - 12 q^{21} + 10 q^{22} - 14 q^{23} - 2 q^{24} - 12 q^{25} + 6 q^{26} + 12 q^{27} - 8 q^{28} - 14 q^{30} + 2 q^{31} - 24 q^{35} - 44 q^{37} - 2 q^{38} + 6 q^{39} + 22 q^{40} + 16 q^{41} + 24 q^{42} - 6 q^{43} - 10 q^{44} + 22 q^{45} + 2 q^{46} + 16 q^{47} - 14 q^{48} + 24 q^{49} + 44 q^{50} - 38 q^{52} - 24 q^{53} + 20 q^{54} + 10 q^{55} + 24 q^{58} - 22 q^{59} - 10 q^{60} + 20 q^{61} - 30 q^{62} + 48 q^{64} - 36 q^{66} + 4 q^{68} + 4 q^{69} - 68 q^{70} - 10 q^{71} - 16 q^{72} + 30 q^{75} + 6 q^{76} - 24 q^{77} + 2 q^{78} - 26 q^{80} - 20 q^{81} + 20 q^{82} + 48 q^{83} - 16 q^{84} + 32 q^{85} - 46 q^{86} + 16 q^{87} - 10 q^{88} + 28 q^{89} - 14 q^{90} + 20 q^{91} + 50 q^{92} - 40 q^{93} + 2 q^{95} + 30 q^{96} + 2 q^{99}+O(q^{100}) \) 8 * q - 6 * q^3 - 8 * q^4 - 2 * q^5 - 6 * q^6 + 6 * q^10 + 6 * q^11 - 2 * q^12 + 14 * q^13 + 2 * q^15 - 8 * q^16 + 16 * q^17 + 20 * q^18 - 14 * q^19 - 2 * q^20 - 12 * q^21 + 10 * q^22 - 14 * q^23 - 2 * q^24 - 12 * q^25 + 6 * q^26 + 12 * q^27 - 8 * q^28 - 14 * q^30 + 2 * q^31 - 24 * q^35 - 44 * q^37 - 2 * q^38 + 6 * q^39 + 22 * q^40 + 16 * q^41 + 24 * q^42 - 6 * q^43 - 10 * q^44 + 22 * q^45 + 2 * q^46 + 16 * q^47 - 14 * q^48 + 24 * q^49 + 44 * q^50 - 38 * q^52 - 24 * q^53 + 20 * q^54 + 10 * q^55 + 24 * q^58 - 22 * q^59 - 10 * q^60 + 20 * q^61 - 30 * q^62 + 48 * q^64 - 36 * q^66 + 4 * q^68 + 4 * q^69 - 68 * q^70 - 10 * q^71 - 16 * q^72 + 30 * q^75 + 6 * q^76 - 24 * q^77 + 2 * q^78 - 26 * q^80 - 20 * q^81 + 20 * q^82 + 48 * q^83 - 16 * q^84 + 32 * q^85 - 46 * q^86 + 16 * q^87 - 10 * q^88 + 28 * q^89 - 14 * q^90 + 20 * q^91 + 50 * q^92 - 40 * q^93 + 2 * q^95 + 30 * q^96 + 2 * q^99

Introduction

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