LMFDB - Embedded newform 65.2.f.b.47.2

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			47.2
Root			$-0.252709 - 0.252709i$ of defining polynomial
Character	$\chi$	$=$	65.47
Dual form			65.2.f.b.18.3

$q$-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 $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

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	$-0.811411\pi$
$2$		−	1.57942i		−	1.11682i	0.829565	−	0.558411i	$-0.188589\pi$
$3$	0.725850	−	0.725850i	0.419070	−	0.419070i	−0.465813	−	0.884883i	$-0.654238\pi$
$3$	0.725850	−	0.725850i	0.419070	−	0.419070i	0.884883	+	0.465813i	$0.154238\pi$
$4$	−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	−0.512830	−	0.858490i	$-0.671403\pi$
$11$	1.14643	−	1.14643i	0.345660	−	0.345660i	0.858490	+	0.512830i	$0.171403\pi$
$12$	−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	0.0637831	−	0.997964i	$-0.479683\pi$
$17$	4.37769	−	4.37769i	1.06175	−	1.06175i	0.997964	−	0.0637831i	$-0.0203166\pi$
$18$	3.07401			0.724550
$19$	−0.274150	+	0.274150i	−0.0628942	+	0.0628942i	−0.737854	−	0.674960i	$-0.764161\pi$
$19$	−0.274150	+	0.274150i	−0.0628942	+	0.0628942i	0.674960	+	0.737854i	$0.264161\pi$
$20$	−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	0.515010	−	0.857184i	$-0.327788\pi$
$23$	−1.64101	−	1.64101i	−0.342174	−	0.342174i	−0.857184	+	0.515010i	$0.827788\pi$
$24$	−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	$-0.916339\pi$
$29$		−	2.79827i		−	0.519626i	0.965659	−	0.259813i	$-0.0836609\pi$
$30$	2.39012	−	2.72585i	0.436374	−	0.497670i
$31$	−2.30527	−	2.30527i	−0.414040	−	0.414040i	0.469104	−	0.883143i	$-0.344577\pi$
$31$	−2.30527	−	2.30527i	−0.414040	−	0.414040i	−0.883143	+	0.469104i	$0.844577\pi$
$32$			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	0.634777	−	0.772696i	$-0.281092\pi$
$41$	−0.883113	−	0.883113i	−0.137919	−	0.137919i	−0.772696	+	0.634777i	$0.781092\pi$
$42$	4.87228	+	4.87228i	0.751809	+	0.751809i
$43$	0.944696	+	0.944696i	0.144065	+	0.144065i	0.775461	−	0.631396i	$-0.217518\pi$
$43$	0.944696	+	0.944696i	0.144065	+	0.144065i	−0.631396	+	0.775461i	$0.717518\pi$
$44$	−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	−0.999991	−	0.00413141i	$-0.998685\pi$
$53$	−7.24997	+	7.24997i	−0.995860	+	0.995860i	0.00413141	+	0.999991i	$0.498685\pi$
$54$	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	0.727096	−	0.686535i	$-0.240869\pi$
$59$	0.311554	+	0.311554i	0.0405608	+	0.0405608i	−0.686535	+	0.727096i	$0.740869\pi$
$60$	−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	$-0.856863\pi$
$67$		−	7.11597i		−	0.869354i	0.900586	−	0.434677i	$-0.143137\pi$
$68$	−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	0.993686	−	0.112201i	$-0.0357900\pi$
$71$	7.42752	+	7.42752i	0.881485	+	0.881485i	−0.112201	+	0.993686i	$0.535790\pi$
$72$	4.62767			0.545376
$73$			4.96796i			0.581455i	0.956806	+	0.290728i	$0.0938973\pi$
$73$			4.96796i			0.581455i	−0.956806	+	0.290728i	$0.906103\pi$
$74$			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	$-0.792316\pi$
$79$		−	10.7928i		−	1.21428i	0.794593	−	0.607142i	$-0.207684\pi$
$80$	−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	0.646105	−	0.763249i	$-0.276397\pi$
$89$	−1.10513	−	1.10513i	−0.117144	−	0.117144i	−0.763249	+	0.646105i	$0.776397\pi$
$90$	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	$0.184581\pi$
$97$			10.7928i			1.09584i	−0.836530	+	0.547921i	$0.815419\pi$
$98$		−	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	$-0.803034\pi$
$101$		−	11.6588i		−	1.16009i	0.814583	−	0.580046i	$-0.196966\pi$
$102$	−10.0374			−0.993851
$103$	3.67213	+	3.67213i	0.361826	+	0.361826i	0.864485	−	0.502659i	$-0.167645\pi$
$103$	3.67213	+	3.67213i	0.361826	+	0.361826i	−0.502659	+	0.864485i	$0.667645\pi$
$104$	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	0.570898	−	0.821021i	$-0.306595\pi$
$107$	−2.58729	−	2.58729i	−0.250123	−	0.250123i	−0.821021	+	0.570898i	$0.806595\pi$
$108$	−1.77568	−	1.77568i	−0.170865	−	0.170865i
$109$	5.28110	−	5.28110i	0.505837	−	0.505837i	−0.407409	−	0.913246i	$-0.633568\pi$
$109$	5.28110	−	5.28110i	0.505837	−	0.505837i	0.913246	+	0.407409i	$0.133568\pi$
$110$	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	−0.771357	−	0.636403i	$-0.780422\pi$
$113$	−1.43459	+	1.43459i	−0.134954	+	0.134954i	0.636403	+	0.771357i	$0.280422\pi$
$114$	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	−0.284705	+	0.958615i	$0.591896\pi$
$127$	−14.0115	+	14.0115i	−1.24332	+	1.24332i	−0.958615	+	0.284705i	$0.908104\pi$
$128$			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	$0.117928\pi$
$139$			8.53735i			0.724128i	−0.932153	+	0.362064i	$0.882072\pi$
$140$	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	−0.333829	−	0.942634i	$-0.608341\pi$
$149$	7.43141	−	7.43141i	0.608805	−	0.608805i	0.942634	+	0.333829i	$0.108341\pi$
$150$	6.43208	+	4.93386i	0.525177	+	0.402848i
$151$	−13.4492	+	13.4492i	−1.09448	+	1.09448i	−0.0994360	+	0.995044i	$0.531704\pi$
$151$	−13.4492	+	13.4492i	−1.09448	+	1.09448i	−0.995044	+	0.0994360i	$0.968296\pi$
$152$	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	0.895917	−	0.444222i	$-0.146520\pi$
$157$	5.65971	+	5.65971i	0.451694	+	0.451694i	−0.444222	+	0.895917i	$0.646520\pi$
$158$	−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	$0.0634183\pi$
$163$			5.05372i			0.395838i	−0.980218	+	0.197919i	$0.936582\pi$
$164$	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	0.0893534	−	0.996000i	$-0.471520\pi$
$173$	−11.9251	−	11.9251i	−0.906647	−	0.906647i	−0.996000	+	0.0893534i	$0.971520\pi$
$174$	−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	$-0.899161\pi$
$181$		−	8.38225i		−	0.623048i	0.950238	−	0.311524i	$-0.100839\pi$
$182$	−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	$-0.723070\pi$
$193$		−	21.2368i		−	1.52866i	0.644825	−	0.764330i	$-0.276930\pi$
$194$	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	$0.0404671\pi$
$197$			3.55914i			0.253578i	−0.991930	+	0.126789i	$0.959533\pi$
$198$	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	$-0.697842\pi$
$227$		−	24.4976i		−	1.62597i	0.582288	−	0.812983i	$-0.302158\pi$
$228$		−	0.196835i		−	0.0130357i
$229$	10.7265	+	10.7265i	0.708828	+	0.708828i	0.966289	−	0.257461i	$-0.0828857\pi$
$229$	10.7265	+	10.7265i	0.708828	+	0.708828i	−0.257461	+	0.966289i	$0.582886\pi$
$230$	−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	0.455450	−	0.890262i	$-0.349479\pi$
$233$	−6.63712	−	6.63712i	−0.434812	−	0.434812i	−0.890262	+	0.455450i	$0.849479\pi$
$234$	−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	−0.236441	+	0.971646i	$0.575981\pi$
$239$	−18.6766	+	18.6766i	−1.20809	+	1.20809i	−0.971646	+	0.236441i	$0.924019\pi$
$240$	−8.18839	−	7.17985i	−0.528558	−	0.463458i
$241$	2.88629	−	2.88629i	0.185922	−	0.185922i	−0.608008	−	0.793931i	$-0.708031\pi$
$241$	2.88629	−	2.88629i	0.185922	−	0.185922i	0.793931	+	0.608008i	$0.208031\pi$
$242$	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	$-0.810365\pi$
$251$		−	17.7801i		−	1.12227i	0.827724	−	0.561136i	$-0.189635\pi$
$252$			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	−0.821590	−	0.570078i	$-0.806913\pi$
$257$	−4.03204	+	4.03204i	−0.251512	+	0.251512i	0.570078	+	0.821590i	$0.306913\pi$
$258$		−	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	−0.871365	−	0.490636i	$-0.836764\pi$
$263$	−6.17438	+	6.17438i	−0.380728	+	0.380728i	0.490636	+	0.871365i	$0.336764\pi$
$264$	−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	$-0.721310\pi$
$269$		−	25.1885i		−	1.53577i	0.640589	−	0.767884i	$-0.278690\pi$
$270$	13.4828	+	11.8222i	0.820539	+	0.719476i
$271$	−7.43070	+	7.43070i	−0.451383	+	0.451383i	−0.895813	−	0.444431i	$-0.853406\pi$
$271$	−7.43070	+	7.43070i	−0.451383	+	0.451383i	0.444431	+	0.895813i	$0.353406\pi$
$272$	−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	−0.695310	−	0.718710i	$-0.744733\pi$
$277$	0.389450	−	0.389450i	0.0233998	−	0.0233998i	0.718710	+	0.695310i	$0.244733\pi$
$278$	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	−0.775030	−	0.631924i	$-0.782266\pi$
$281$	−2.39890	+	2.39890i	−0.143107	+	0.143107i	0.631924	+	0.775030i	$0.282266\pi$
$282$	−0.554578	−	0.554578i	−0.0330246	−	0.0330246i
$283$	−20.6500	−	20.6500i	−1.22752	−	1.22752i	−0.964901	−	0.262615i	$-0.915415\pi$
$283$	−20.6500	−	20.6500i	−1.22752	−	1.22752i	−0.262615	−	0.964901i	$-0.584585\pi$
$284$	−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	$0.145100\pi$
$293$			15.0708i			0.880445i	−0.897889	+	0.440222i	$0.854900\pi$
$294$	−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	$0.205196\pi$
$311$			21.1944i			1.20182i	−0.799315	+	0.600912i	$0.794804\pi$
$312$	6.60896	−	5.81069i	0.374159	−	0.328966i
$313$	−5.71879	+	5.71879i	−0.323245	+	0.323245i	−0.850011	−	0.526766i	$-0.823405\pi$
$313$	−5.71879	+	5.71879i	−0.323245	+	0.323245i	0.526766	+	0.850011i	$0.323405\pi$
$314$	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	$-0.910504\pi$
$317$		−	9.88047i		−	0.554943i	0.960734	−	0.277471i	$-0.0894963\pi$
$318$	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	0.805582	−	0.592484i	$-0.201853\pi$
$331$	3.87697	+	3.87697i	0.213097	+	0.213097i	−0.592484	+	0.805582i	$0.701853\pi$
$332$	−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	−0.356536	−	0.934281i	$-0.616042\pi$
$337$	10.6060	−	10.6060i	0.577745	−	0.577745i	0.934281	+	0.356536i	$0.116042\pi$
$338$	−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	0.906508	−	0.422188i	$-0.138738\pi$
$347$	9.02188	+	9.02188i	0.484320	+	0.484320i	−0.422188	+	0.906508i	$0.638738\pi$
$348$	1.00456	+	1.00456i	0.0538499	+	0.0538499i
$349$	12.4143	+	12.4143i	0.664522	+	0.664522i	0.956443	−	0.291921i	$-0.0942943\pi$
$349$	12.4143	+	12.4143i	0.664522	+	0.664522i	−0.291921	+	0.956443i	$0.594294\pi$
$350$	−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	0.127792	−	0.991801i	$-0.459211\pi$
$359$	−16.3706	−	16.3706i	−0.864009	−	0.864009i	−0.991801	+	0.127792i	$0.959211\pi$
$360$	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	0.985509	+	0.169626i	$0.0542560\pi$
$367$	22.1292	+	22.1292i	1.15513	+	1.15513i	0.169626	+	0.985509i	$0.445744\pi$
$368$	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	−0.268704	−	0.963223i	$-0.586595\pi$
$373$	13.4134	−	13.4134i	0.694518	−	0.694518i	0.963223	+	0.268704i	$0.0865955\pi$
$374$	−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	−0.293707	−	0.955896i	$-0.594889\pi$
$379$	12.8914	−	12.8914i	0.662189	−	0.662189i	0.955896	+	0.293707i	$0.0948889\pi$
$380$	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	−0.557918	−	0.829896i	$-0.688400\pi$
$401$	5.44634	−	5.44634i	0.271977	−	0.271977i	0.829896	+	0.557918i	$0.188400\pi$
$402$	−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	−0.473018	+	0.881053i	$0.656836\pi$
$409$	−27.3844	+	27.3844i	−1.35407	+	1.35407i	−0.881053	+	0.473018i	$0.843164\pi$
$410$	−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	$0.281188\pi$
$419$			31.6412i			1.54577i	−0.634543	+	0.772887i	$0.718812\pi$
$420$	3.62767	+	3.18086i	0.177012	+	0.155210i
$421$	−0.312270	−	0.312270i	−0.0152191	−	0.0152191i	0.699456	−	0.714675i	$-0.253426\pi$
$421$	−0.312270	−	0.312270i	−0.0152191	−	0.0152191i	−0.714675	+	0.699456i	$0.753426\pi$
$422$			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	0.319187	−	0.947692i	$-0.396590\pi$
$431$	−13.0481	−	13.0481i	−0.628505	−	0.628505i	−0.947692	+	0.319187i	$0.896590\pi$
$432$	−17.0342	−	17.0342i	−0.819557	−	0.819557i
$433$	−0.0391255	−	0.0391255i	−0.00188025	−	0.00188025i	0.706166	−	0.708046i	$-0.250423\pi$
$433$	−0.0391255	−	0.0391255i	−0.00188025	−	0.00188025i	−0.708046	+	0.706166i	$0.750423\pi$
$434$	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	−0.141481	−	0.989941i	$-0.545186\pi$
$443$	17.8580	−	17.8580i	0.848460	−	0.848460i	0.989941	+	0.141481i	$0.0451864\pi$
$444$	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	0.455184	−	0.890398i	$-0.349574\pi$
$449$	−9.22202	−	9.22202i	−0.435214	−	0.435214i	−0.890398	+	0.455184i	$0.849574\pi$
$450$	−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	$0.0791003\pi$
$457$			10.5157i			0.491902i	−0.969282	+	0.245951i	$0.920900\pi$
$458$	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	0.638397	−	0.769707i	$-0.279598\pi$
$461$	−2.81936	−	2.81936i	−0.131311	−	0.131311i	−0.769707	+	0.638397i	$0.779598\pi$
$462$	11.1714			0.519741
$463$		−	32.9570i		−	1.53164i	−0.643054	−	0.765821i	$-0.722333\pi$
$463$		−	32.9570i		−	1.53164i	0.643054	−	0.765821i	$-0.277667\pi$
$464$			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	−0.518639	−	0.854993i	$-0.673561\pi$
$467$	7.26867	−	7.26867i	0.336354	−	0.336354i	0.854993	+	0.518639i	$0.173561\pi$
$468$	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	0.121282	−	0.992618i	$-0.461299\pi$
$479$	−19.0701	−	19.0701i	−0.871336	−	0.871336i	−0.992618	+	0.121282i	$0.961299\pi$
$480$	−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	$-0.625067\pi$
$487$		−	40.7729i		−	1.84760i	0.382879	−	0.923799i	$-0.374933\pi$
$488$		−	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	$0.0330849\pi$
$491$			4.59799i			0.207504i	−0.994603	+	0.103752i	$0.966915\pi$
$492$	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	−0.0215572	+	0.999768i	$0.506862\pi$
$499$	−22.8147	+	22.8147i	−1.02132	+	1.02132i	−0.999768	+	0.0215572i	$0.993138\pi$
$500$	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	−0.411929	−	0.911216i	$-0.635145\pi$
$503$	11.1978	−	11.1978i	0.499287	−	0.499287i	0.911216	+	0.411929i	$0.135145\pi$
$504$	−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	−0.594729	−	0.803926i	$-0.702741\pi$
$509$	4.71971	−	4.71971i	0.209197	−	0.209197i	0.803926	+	0.594729i	$0.202741\pi$
$510$	−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	−0.999745	−	0.0225689i	$-0.992815\pi$
$523$	−22.3472	+	22.3472i	−0.977176	+	0.977176i	0.0225689	+	0.999745i	$0.492815\pi$
$524$	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	0.408223	−	0.912882i	$-0.366149\pi$
$541$	30.7281	−	30.7281i	1.32111	−	1.32111i	0.912882	−	0.408223i	$-0.133851\pi$
$542$	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	0.889181	−	0.457555i	$-0.151275\pi$
$547$	10.0949	+	10.0949i	0.431627	+	0.431627i	−0.457555	+	0.889181i	$0.651275\pi$
$548$	−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	0.945670	+	0.325127i	$0.105407\pi$
$563$	30.1530	+	30.1530i	1.27080	+	1.27080i	0.325127	+	0.945670i	$0.394593\pi$
$564$	−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	$-0.780763\pi$
$571$		−	30.3749i		−	1.27115i	0.772039	−	0.635576i	$-0.219237\pi$
$572$	−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	$0.121094\pi$
$577$			17.8387i			0.742636i	−0.928506	+	0.371318i	$0.878906\pi$
$578$	−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	$0.0624710\pi$
$587$			9.44899i			0.390002i	−0.980803	+	0.195001i	$0.937529\pi$
$588$	−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	$0.224752\pi$
$593$			31.6013i			1.29771i	−0.760912	+	0.648855i	$0.775248\pi$
$594$		−	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	$-0.888784\pi$
$599$		−	16.7567i		−	0.684661i	0.939580	−	0.342331i	$-0.111216\pi$
$600$	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	0.945436	−	0.325807i	$-0.105636\pi$
$607$	15.2660	+	15.2660i	0.619629	+	0.619629i	−0.325807	+	0.945436i	$0.605636\pi$
$608$	−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	$-0.906015\pi$
$617$		−	14.4562i		−	0.581984i	0.956725	−	0.290992i	$-0.0939854\pi$
$618$		−	8.41966i		−	0.338688i
$619$	−1.00603	−	1.00603i	−0.0404356	−	0.0404356i	0.686600	−	0.727036i	$-0.259102\pi$
$619$	−1.00603	−	1.00603i	−0.0404356	−	0.0404356i	−0.727036	+	0.686600i	$0.759102\pi$
$620$	−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	−0.973670	−	0.227961i	$-0.926794\pi$
$631$	−18.7320	+	18.7320i	−0.745710	+	0.745710i	0.227961	+	0.973670i	$0.426794\pi$
$632$	−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	$0.0630649\pi$
$641$			9.96670i			0.393661i	−0.980438	+	0.196830i	$0.936935\pi$
$642$			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	−0.255075	−	0.966921i	$-0.582100\pi$
$647$	18.1067	−	18.1067i	0.711846	−	0.711846i	0.966921	+	0.255075i	$0.0821003\pi$
$648$			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	0.138584	−	0.990351i	$-0.455745\pi$
$653$	28.8486	−	28.8486i	1.12893	−	1.12893i	0.990351	−	0.138584i	$-0.0442551\pi$
$654$	−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	$0.0584630\pi$
$659$			9.37689i			0.365272i	−0.983181	+	0.182636i	$0.941537\pi$
$660$	−1.83659	+	0.120525i	−0.0714893	+	0.00469145i
$661$	−8.37769	+	8.37769i	−0.325855	+	0.325855i	−0.851008	−	0.525153i	$-0.824008\pi$
$661$	−8.37769	+	8.37769i	−0.325855	+	0.325855i	0.525153	+	0.851008i	$0.324008\pi$
$662$	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	0.604399	−	0.796682i	$-0.293413\pi$
$673$	−4.98824	−	4.98824i	−0.192283	−	0.192283i	−0.796682	+	0.604399i	$0.793413\pi$
$674$	−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	0.795920	−	0.605402i	$-0.206988\pi$
$677$	4.95712	+	4.95712i	0.190518	+	0.190518i	−0.605402	+	0.795920i	$0.706988\pi$
$678$	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	$-0.978534\pi$
$683$		−	3.52220i		−	0.134773i	0.997727	−	0.0673865i	$-0.0214661\pi$
$684$	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	0.965962	−	0.258682i	$-0.0832883\pi$
$691$	18.5922	+	18.5922i	0.707280	+	0.707280i	−0.258682	+	0.965962i	$0.583288\pi$
$692$	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	$0.0297793\pi$
$701$			4.94675i			0.186836i	−0.995627	+	0.0934180i	$0.970221\pi$
$702$	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	0.921689	−	0.387929i	$-0.126810\pi$
$709$	14.2124	+	14.2124i	0.533760	+	0.533760i	−0.387929	+	0.921689i	$0.626810\pi$
$710$	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	−0.281054	−	0.959692i	$-0.590684\pi$
$727$	18.2981	−	18.2981i	0.678638	−	0.678638i	0.959692	+	0.281054i	$0.0906840\pi$
$728$	−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	0.743302	−	0.668956i	$-0.233258\pi$
$739$	2.02107	+	2.02107i	0.0743464	+	0.0743464i	−0.668956	+	0.743302i	$0.733258\pi$
$740$	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	$0.286998\pi$
$751$			42.9887i			1.56868i	−0.620332	+	0.784339i	$0.713002\pi$
$752$	−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	−0.984781	−	0.173798i	$-0.944396\pi$
$757$	−31.8767	−	31.8767i	−1.15858	−	1.15858i	−0.173798	−	0.984781i	$-0.555604\pi$
$758$	−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	−0.273071	−	0.961994i	$-0.588039\pi$
$761$	19.0048	−	19.0048i	0.688923	−	0.688923i	0.961994	+	0.273071i	$0.0880395\pi$
$762$	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	−0.981655	−	0.190664i	$-0.938936\pi$
$769$	−21.9349	+	21.9349i	−0.790991	+	0.790991i	0.190664	+	0.981655i	$0.438936\pi$
$770$	−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	−0.991145	−	0.132782i	$-0.957609\pi$
$797$	−24.2326	+	24.2326i	−0.858363	+	0.858363i	0.132782	+	0.991145i	$0.457609\pi$
$798$	−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	$-0.986753\pi$
$809$		−	2.36679i		−	0.0832119i	0.999134	−	0.0416060i	$-0.0132474\pi$
$810$	−2.20914	+	0.144974i	−0.0776213	+	0.00509386i
$811$	−19.8318	−	19.8318i	−0.696388	−	0.696388i	0.267241	−	0.963630i	$-0.413888\pi$
$811$	−19.8318	−	19.8318i	−0.696388	−	0.696388i	−0.963630	+	0.267241i	$0.913888\pi$
$812$		−	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	0.115867	−	0.993265i	$-0.463035\pi$
$821$	−25.1402	−	25.1402i	−0.877398	−	0.877398i	−0.993265	+	0.115867i	$0.963035\pi$
$822$	−6.44450	−	6.44450i	−0.224778	−	0.224778i
$823$	−19.6596	−	19.6596i	−0.685290	−	0.685290i	0.275897	−	0.961187i	$-0.411025\pi$
$823$	−19.6596	−	19.6596i	−0.685290	−	0.685290i	−0.961187	+	0.275897i	$0.911025\pi$
$824$	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	0.819854	−	0.572573i	$-0.194055\pi$
$839$	7.16262	+	7.16262i	0.247281	+	0.247281i	−0.572573	+	0.819854i	$0.694055\pi$
$840$	−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	$-0.969522\pi$
$853$		−	5.58445i		−	0.191208i	0.995419	−	0.0956039i	$-0.0304782\pi$
$854$			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	−0.934343	−	0.356376i	$-0.884012\pi$
$857$	−16.9197	+	16.9197i	−0.577966	+	0.577966i	0.356376	+	0.934343i	$0.384012\pi$
$858$	0.607909	−	9.45798i	0.0207537	−	0.322890i
$859$			28.3026i			0.965674i	0.875710	+	0.482837i	$0.160394\pi$
$859$			28.3026i			0.965674i	−0.875710	+	0.482837i	$0.839606\pi$
$860$	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	$-0.758453\pi$
$877$		−	40.7540i		−	1.37616i	0.725633	−	0.688082i	$-0.241547\pi$
$878$		−	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	$-0.963257\pi$
$881$		−	6.83724i		−	0.230353i	0.993345	−	0.115176i	$-0.0367433\pi$
$882$	34.0054			1.14502
$883$	9.20332	+	9.20332i	0.309716	+	0.309716i	0.844799	−	0.535083i	$-0.179720\pi$
$883$	9.20332	+	9.20332i	0.309716	+	0.309716i	−0.535083	+	0.844799i	$0.679720\pi$
$884$	−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	0.983935	−	0.178526i	$-0.0571330\pi$
$887$	23.9871	+	23.9871i	0.805409	+	0.805409i	−0.178526	+	0.983935i	$0.557133\pi$
$888$	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	−0.975736	−	0.218949i	$-0.929737\pi$
$907$	−22.7917	+	22.7917i	−0.756787	+	0.756787i	0.218949	+	0.975736i	$0.429737\pi$
$908$			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	$-0.954464\pi$
$919$		−	8.64385i		−	0.285134i	0.989785	−	0.142567i	$-0.0455357\pi$
$920$	−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	−0.844281	−	0.535901i	$-0.819972\pi$
$929$	−9.39925	+	9.39925i	−0.308379	+	0.308379i	0.535901	+	0.844281i	$0.319972\pi$
$930$	−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	0.134737	−	0.990881i	$-0.456981\pi$
$937$	−26.2070	−	26.2070i	−0.856144	−	0.856144i	−0.990881	+	0.134737i	$0.956981\pi$
$938$	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	0.419332	−	0.907833i	$-0.362264\pi$
$941$	−14.9851	−	14.9851i	−0.488502	−	0.488502i	−0.907833	+	0.419332i	$0.862264\pi$
$942$		−	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	0.332470	−	0.943114i	$-0.392118\pi$
$953$	−18.8510	−	18.8510i	−0.610644	−	0.610644i	−0.943114	+	0.332470i	$0.892118\pi$
$954$	−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	$0.132506\pi$
$967$			25.1486i			0.808724i	−0.914599	+	0.404362i	$0.867494\pi$
$968$	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	$0.0724542\pi$
$977$			14.1070i			0.451322i	−0.974206	+	0.225661i	$0.927546\pi$
$978$	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	$-0.912189\pi$
$983$		−	17.0799i		−	0.544764i	0.962189	−	0.272382i	$-0.0878115\pi$
$984$			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	0.474298	−	0.880364i	$-0.342702\pi$
$997$	−12.8217	−	12.8217i	−0.406066	−	0.406066i	−0.880364	+	0.474298i	$0.842702\pi$
$998$	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.47.2	yes	8
3.2	odd	2		585.2.n.e.307.3		8
4.3	odd	2		1040.2.cd.n.177.1		8
5.2	odd	4		325.2.k.b.268.3		8
5.3	odd	4		65.2.k.b.8.2	yes	8
5.4	even	2		325.2.f.b.307.3		8
13.2	odd	12		845.2.o.d.357.3		16
13.3	even	3		845.2.t.c.657.3		16
13.4	even	6		845.2.t.d.427.3		16
13.5	odd	4		65.2.k.b.57.2	yes	8
13.6	odd	12		845.2.o.d.587.3		16
13.7	odd	12		845.2.o.c.587.2		16
13.8	odd	4		845.2.k.b.577.3		8
13.9	even	3		845.2.t.c.427.2		16
13.10	even	6		845.2.t.d.657.2		16
13.11	odd	12		845.2.o.c.357.2		16
13.12	even	2		845.2.f.b.437.3		8
15.8	even	4		585.2.w.e.73.3		8
20.3	even	4		1040.2.bg.n.593.1		8
39.5	even	4		585.2.w.e.577.3		8
52.31	even	4		1040.2.bg.n.577.1		8
65.3	odd	12		845.2.o.d.488.3		16
65.8	even	4		845.2.f.b.408.2		8
65.18	even	4	inner	65.2.f.b.18.3	✓	8
65.23	odd	12		845.2.o.c.488.2		16
65.28	even	12		845.2.t.c.188.2		16
65.33	even	12		845.2.t.d.418.2		16
65.38	odd	4		845.2.k.b.268.3		8
65.43	odd	12		845.2.o.c.258.2		16
65.44	odd	4		325.2.k.b.57.3		8
65.48	odd	12		845.2.o.d.258.3		16
65.57	even	4		325.2.f.b.18.2		8
65.58	even	12		845.2.t.c.418.3		16
65.63	even	12		845.2.t.d.188.3		16
195.83	odd	4		585.2.n.e.343.2		8
260.83	odd	4		1040.2.cd.n.993.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.f.b.18.3	✓	8	65.18	even	4	inner
65.2.f.b.47.2	yes	8	1.1	even	1	trivial
65.2.k.b.8.2	yes	8	5.3	odd	4
65.2.k.b.57.2	yes	8	13.5	odd	4
325.2.f.b.18.2		8	65.57	even	4
325.2.f.b.307.3		8	5.4	even	2
325.2.k.b.57.3		8	65.44	odd	4
325.2.k.b.268.3		8	5.2	odd	4
585.2.n.e.307.3		8	3.2	odd	2
585.2.n.e.343.2		8	195.83	odd	4
585.2.w.e.73.3		8	15.8	even	4
585.2.w.e.577.3		8	39.5	even	4
845.2.f.b.408.2		8	65.8	even	4
845.2.f.b.437.3		8	13.12	even	2
845.2.k.b.268.3		8	65.38	odd	4
845.2.k.b.577.3		8	13.8	odd	4
845.2.o.c.258.2		16	65.43	odd	12
845.2.o.c.357.2		16	13.11	odd	12
845.2.o.c.488.2		16	65.23	odd	12
845.2.o.c.587.2		16	13.7	odd	12
845.2.o.d.258.3		16	65.48	odd	12
845.2.o.d.357.3		16	13.2	odd	12
845.2.o.d.488.3		16	65.3	odd	12
845.2.o.d.587.3		16	13.6	odd	12
845.2.t.c.188.2		16	65.28	even	12
845.2.t.c.418.3		16	65.58	even	12
845.2.t.c.427.2		16	13.9	even	3
845.2.t.c.657.3		16	13.3	even	3
845.2.t.d.188.3		16	65.63	even	12
845.2.t.d.418.2		16	65.33	even	12
845.2.t.d.427.3		16	13.4	even	6
845.2.t.d.657.2		16	13.10	even	6
1040.2.bg.n.577.1		8	52.31	even	4
1040.2.bg.n.593.1		8	20.3	even	4
1040.2.cd.n.177.1		8	4.3	odd	2
1040.2.cd.n.993.1		8	260.83	odd	4

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

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