LMFDB - Embedded newform 130.2.g.d.57.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [130,2,Mod(57,130)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(130, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("130.57"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	130.g (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-4,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.03805522628$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{11})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 9 $ x^4 - 5*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			57.1
Root			$1.65831 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	130.57
Dual form			130.2.g.d.73.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +(-1.15831 + 1.15831i) q^{3} +1.00000 q^{4} +(1.50000 - 1.65831i) q^{5} +(1.15831 - 1.15831i) q^{6} +3.00000i q^{7} -1.00000 q^{8} +0.316625i q^{9} +(-1.50000 + 1.65831i) q^{10} +(3.31662 + 3.31662i) q^{11} +(-1.15831 + 1.15831i) q^{12} +(-2.00000 + 3.00000i) q^{13} -3.00000i q^{14} +(0.183375 + 3.65831i) q^{15} +1.00000 q^{16} +(3.15831 - 3.15831i) q^{17} -0.316625i q^{18} +(-2.00000 - 2.00000i) q^{19} +(1.50000 - 1.65831i) q^{20} +(-3.47494 - 3.47494i) q^{21} +(-3.31662 - 3.31662i) q^{22} +(3.31662 + 3.31662i) q^{23} +(1.15831 - 1.15831i) q^{24} +(-0.500000 - 4.97494i) q^{25} +(2.00000 - 3.00000i) q^{26} +(-3.84169 - 3.84169i) q^{27} +3.00000i q^{28} -6.31662i q^{29} +(-0.183375 - 3.65831i) q^{30} +(1.00000 - 1.00000i) q^{31} -1.00000 q^{32} -7.68338 q^{33} +(-3.15831 + 3.15831i) q^{34} +(4.97494 + 4.50000i) q^{35} +0.316625i q^{36} +3.00000i q^{37} +(2.00000 + 2.00000i) q^{38} +(-1.15831 - 5.79156i) q^{39} +(-1.50000 + 1.65831i) q^{40} +(-6.31662 + 6.31662i) q^{41} +(3.47494 + 3.47494i) q^{42} +(-2.47494 - 2.47494i) q^{43} +(3.31662 + 3.31662i) q^{44} +(0.525063 + 0.474937i) q^{45} +(-3.31662 - 3.31662i) q^{46} -9.31662i q^{47} +(-1.15831 + 1.15831i) q^{48} -2.00000 q^{49} +(0.500000 + 4.97494i) q^{50} +7.31662i q^{51} +(-2.00000 + 3.00000i) q^{52} +(9.63325 - 9.63325i) q^{53} +(3.84169 + 3.84169i) q^{54} +(10.4749 - 0.525063i) q^{55} -3.00000i q^{56} +4.63325 q^{57} +6.31662i q^{58} +(-0.316625 + 0.316625i) q^{59} +(0.183375 + 3.65831i) q^{60} +2.00000 q^{61} +(-1.00000 + 1.00000i) q^{62} -0.949874 q^{63} +1.00000 q^{64} +(1.97494 + 7.81662i) q^{65} +7.68338 q^{66} -4.94987 q^{67} +(3.15831 - 3.15831i) q^{68} -7.68338 q^{69} +(-4.97494 - 4.50000i) q^{70} +(-2.84169 + 2.84169i) q^{71} -0.316625i q^{72} -4.00000 q^{73} -3.00000i q^{74} +(6.34169 + 5.18338i) q^{75} +(-2.00000 - 2.00000i) q^{76} +(-9.94987 + 9.94987i) q^{77} +(1.15831 + 5.79156i) q^{78} +12.9499i q^{79} +(1.50000 - 1.65831i) q^{80} +7.94987 q^{81} +(6.31662 - 6.31662i) q^{82} -6.31662i q^{83} +(-3.47494 - 3.47494i) q^{84} +(-0.500000 - 9.97494i) q^{85} +(2.47494 + 2.47494i) q^{86} +(7.31662 + 7.31662i) q^{87} +(-3.31662 - 3.31662i) q^{88} +(-0.316625 + 0.316625i) q^{89} +(-0.525063 - 0.474937i) q^{90} +(-9.00000 - 6.00000i) q^{91} +(3.31662 + 3.31662i) q^{92} +2.31662i q^{93} +9.31662i q^{94} +(-6.31662 + 0.316625i) q^{95} +(1.15831 - 1.15831i) q^{96} +8.94987 q^{97} +2.00000 q^{98} +(-1.05013 + 1.05013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 2 q^{3} + 4 q^{4} + 6 q^{5} - 2 q^{6} - 4 q^{8} - 6 q^{10} + 2 q^{12} - 8 q^{13} + 14 q^{15} + 4 q^{16} + 6 q^{17} - 8 q^{19} + 6 q^{20} + 6 q^{21} - 2 q^{24} - 2 q^{25} + 8 q^{26} - 22 q^{27}+ \cdots - 44 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 2 * q^3 + 4 * q^4 + 6 * q^5 - 2 * q^6 - 4 * q^8 - 6 * q^10 + 2 * q^12 - 8 * q^13 + 14 * q^15 + 4 * q^16 + 6 * q^17 - 8 * q^19 + 6 * q^20 + 6 * q^21 - 2 * q^24 - 2 * q^25 + 8 * q^26 - 22 * q^27 - 14 * q^30 + 4 * q^31 - 4 * q^32 - 44 * q^33 - 6 * q^34 + 8 * q^38 + 2 * q^39 - 6 * q^40 - 12 * q^41 - 6 * q^42 + 10 * q^43 + 22 * q^45 + 2 * q^48 - 8 * q^49 + 2 * q^50 - 8 * q^52 + 12 * q^53 + 22 * q^54 + 22 * q^55 - 8 * q^57 + 12 * q^59 + 14 * q^60 + 8 * q^61 - 4 * q^62 + 36 * q^63 + 4 * q^64 - 12 * q^65 + 44 * q^66 + 20 * q^67 + 6 * q^68 - 44 * q^69 - 18 * q^71 - 16 * q^73 + 32 * q^75 - 8 * q^76 - 2 * q^78 + 6 * q^80 - 8 * q^81 + 12 * q^82 + 6 * q^84 - 2 * q^85 - 10 * q^86 + 16 * q^87 + 12 * q^89 - 22 * q^90 - 36 * q^91 - 12 * q^95 - 2 * q^96 - 4 * q^97 + 8 * q^98 - 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/130\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−1.15831	+	1.15831i	−0.668752	+	0.668752i	−0.957427	−	0.288675i	$-0.906785\pi$
$3$	−1.15831	+	1.15831i	−0.668752	+	0.668752i	0.288675	+	0.957427i	$0.406785\pi$
$4$	1.00000			0.500000
$5$	1.50000	−	1.65831i	0.670820	−	0.741620i
$5$	1.50000	−	1.65831i	0.670820	−	0.741620i
$6$	1.15831	−	1.15831i	0.472879	−	0.472879i
$7$			3.00000i			1.13389i	0.823754	+	0.566947i	$0.191875\pi$
$7$			3.00000i			1.13389i	−0.823754	+	0.566947i	$0.808125\pi$
$8$	−1.00000			−0.353553
$9$			0.316625i			0.105542i
$10$	−1.50000	+	1.65831i	−0.474342	+	0.524404i
$11$	3.31662	+	3.31662i	1.00000	+	1.00000i	1.00000			$0$
$11$	3.31662	+	3.31662i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$12$	−1.15831	+	1.15831i	−0.334376	+	0.334376i
$13$	−2.00000	+	3.00000i	−0.554700	+	0.832050i
$13$	−2.00000	+	3.00000i	−0.554700	+	0.832050i
$14$		−	3.00000i		−	0.801784i
$15$	0.183375	+	3.65831i	0.0473473	+	0.944572i
$16$	1.00000			0.250000
$17$	3.15831	−	3.15831i	0.766003	−	0.766003i	−0.211397	−	0.977400i	$-0.567801\pi$
$17$	3.15831	−	3.15831i	0.766003	−	0.766003i	0.977400	+	0.211397i	$0.0678013\pi$
$18$		−	0.316625i		−	0.0746292i
$19$	−2.00000	−	2.00000i	−0.458831	−	0.458831i	0.439440	−	0.898272i	$-0.355177\pi$
$19$	−2.00000	−	2.00000i	−0.458831	−	0.458831i	−0.898272	+	0.439440i	$0.855177\pi$
$20$	1.50000	−	1.65831i	0.335410	−	0.370810i
$21$	−3.47494	−	3.47494i	−0.758293	−	0.758293i
$22$	−3.31662	−	3.31662i	−0.707107	−	0.707107i
$23$	3.31662	+	3.31662i	0.691564	+	0.691564i	0.962576	−	0.271012i	$-0.0873583\pi$
$23$	3.31662	+	3.31662i	0.691564	+	0.691564i	−0.271012	+	0.962576i	$0.587358\pi$
$24$	1.15831	−	1.15831i	0.236440	−	0.236440i
$25$	−0.500000	−	4.97494i	−0.100000	−	0.994987i
$26$	2.00000	−	3.00000i	0.392232	−	0.588348i
$27$	−3.84169	−	3.84169i	−0.739333	−	0.739333i
$28$			3.00000i			0.566947i
$29$		−	6.31662i		−	1.17297i	−0.809961	−	0.586484i	$-0.800512\pi$
$29$		−	6.31662i		−	1.17297i	0.809961	−	0.586484i	$-0.199488\pi$
$30$	−0.183375	−	3.65831i	−0.0334796	−	0.667913i
$31$	1.00000	−	1.00000i	0.179605	−	0.179605i	−0.611578	−	0.791184i	$-0.709465\pi$
$31$	1.00000	−	1.00000i	0.179605	−	0.179605i	0.791184	+	0.611578i	$0.209465\pi$
$32$	−1.00000			−0.176777
$33$	−7.68338			−1.33750
$34$	−3.15831	+	3.15831i	−0.541646	+	0.541646i
$35$	4.97494	+	4.50000i	0.840918	+	0.760639i
$36$			0.316625i			0.0527708i
$37$			3.00000i			0.493197i	0.969118	+	0.246598i	$0.0793129\pi$
$37$			3.00000i			0.493197i	−0.969118	+	0.246598i	$0.920687\pi$
$38$	2.00000	+	2.00000i	0.324443	+	0.324443i
$39$	−1.15831	−	5.79156i	−0.185478	−	0.927392i
$40$	−1.50000	+	1.65831i	−0.237171	+	0.262202i
$41$	−6.31662	+	6.31662i	−0.986491	+	0.986491i	−0.999910	−	0.0134189i	$-0.995729\pi$
$41$	−6.31662	+	6.31662i	−0.986491	+	0.986491i	0.0134189	+	0.999910i	$0.495729\pi$
$42$	3.47494	+	3.47494i	0.536194	+	0.536194i
$43$	−2.47494	−	2.47494i	−0.377424	−	0.377424i	0.492748	−	0.870172i	$-0.335993\pi$
$43$	−2.47494	−	2.47494i	−0.377424	−	0.377424i	−0.870172	+	0.492748i	$0.835993\pi$
$44$	3.31662	+	3.31662i	0.500000	+	0.500000i
$45$	0.525063	+	0.474937i	0.0782717	+	0.0707995i
$46$	−3.31662	−	3.31662i	−0.489010	−	0.489010i
$47$		−	9.31662i		−	1.35897i	−0.733690	−	0.679485i	$-0.762203\pi$
$47$		−	9.31662i		−	1.35897i	0.733690	−	0.679485i	$-0.237797\pi$
$48$	−1.15831	+	1.15831i	−0.167188	+	0.167188i
$49$	−2.00000			−0.285714
$50$	0.500000	+	4.97494i	0.0707107	+	0.703562i
$51$			7.31662i			1.02453i
$52$	−2.00000	+	3.00000i	−0.277350	+	0.416025i
$53$	9.63325	−	9.63325i	1.32323	−	1.32323i	0.412082	−	0.911147i	$-0.364802\pi$
$53$	9.63325	−	9.63325i	1.32323	−	1.32323i	0.911147	−	0.412082i	$-0.135198\pi$
$54$	3.84169	+	3.84169i	0.522787	+	0.522787i
$55$	10.4749	−	0.525063i	1.41244	−	0.0707995i
$56$		−	3.00000i		−	0.400892i
$57$	4.63325			0.613689
$58$			6.31662i			0.829413i
$59$	−0.316625	+	0.316625i	−0.0412210	+	0.0412210i	−0.727417	−	0.686196i	$-0.759279\pi$
$59$	−0.316625	+	0.316625i	−0.0412210	+	0.0412210i	0.686196	+	0.727417i	$0.259279\pi$
$60$	0.183375	+	3.65831i	0.0236736	+	0.472286i
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$	−1.00000	+	1.00000i	−0.127000	+	0.127000i
$63$	−0.949874			−0.119673
$64$	1.00000			0.125000
$65$	1.97494	+	7.81662i	0.244961	+	0.969533i
$66$	7.68338			0.945758
$67$	−4.94987			−0.604723			−0.302362	−	0.953193i	$-0.597775\pi$
$67$	−4.94987			−0.604723			−0.302362	+	0.953193i	$0.597775\pi$
$68$	3.15831	−	3.15831i	0.383002	−	0.383002i
$69$	−7.68338			−0.924970
$70$	−4.97494	−	4.50000i	−0.594619	−	0.537853i
$71$	−2.84169	+	2.84169i	−0.337246	+	0.337246i	−0.855330	−	0.518084i	$-0.826646\pi$
$71$	−2.84169	+	2.84169i	−0.337246	+	0.337246i	0.518084	+	0.855330i	$0.326646\pi$
$72$		−	0.316625i		−	0.0373146i
$73$	−4.00000			−0.468165			−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000			−0.468165			−0.234082	+	0.972217i	$0.575209\pi$
$74$		−	3.00000i		−	0.348743i
$75$	6.34169	+	5.18338i	0.732275	+	0.598525i
$76$	−2.00000	−	2.00000i	−0.229416	−	0.229416i
$77$	−9.94987	+	9.94987i	−1.13389	+	1.13389i
$78$	1.15831	+	5.79156i	0.131153	+	0.655765i
$79$			12.9499i			1.45697i	0.685059	+	0.728487i	$0.259776\pi$
$79$			12.9499i			1.45697i	−0.685059	+	0.728487i	$0.740224\pi$
$80$	1.50000	−	1.65831i	0.167705	−	0.185405i
$81$	7.94987			0.883319
$82$	6.31662	−	6.31662i	0.697555	−	0.697555i
$83$		−	6.31662i		−	0.693340i	−0.937987	−	0.346670i	$-0.887312\pi$
$83$		−	6.31662i		−	0.693340i	0.937987	−	0.346670i	$-0.112688\pi$
$84$	−3.47494	−	3.47494i	−0.379147	−	0.379147i
$85$	−0.500000	−	9.97494i	−0.0542326	−	1.08193i
$86$	2.47494	+	2.47494i	0.266879	+	0.266879i
$87$	7.31662	+	7.31662i	0.784425	+	0.784425i
$88$	−3.31662	−	3.31662i	−0.353553	−	0.353553i
$89$	−0.316625	+	0.316625i	−0.0335622	+	0.0335622i	−0.723689	−	0.690127i	$-0.757555\pi$
$89$	−0.316625	+	0.316625i	−0.0335622	+	0.0335622i	0.690127	+	0.723689i	$0.257555\pi$
$90$	−0.525063	−	0.474937i	−0.0553465	−	0.0500628i
$91$	−9.00000	−	6.00000i	−0.943456	−	0.628971i
$92$	3.31662	+	3.31662i	0.345782	+	0.345782i
$93$			2.31662i			0.240223i
$94$			9.31662i			0.960936i
$95$	−6.31662	+	0.316625i	−0.648072	+	0.0324850i
$96$	1.15831	−	1.15831i	0.118220	−	0.118220i
$97$	8.94987			0.908722			0.454361	−	0.890818i	$-0.349868\pi$
$97$	8.94987			0.908722			0.454361	+	0.890818i	$0.349868\pi$
$98$	2.00000			0.202031
$99$	−1.05013	+	1.05013i	−0.105542	+	0.105542i
$100$	−0.500000	−	4.97494i	−0.0500000	−	0.497494i
$101$		−	19.2665i		−	1.91709i	−0.284944	−	0.958544i	$-0.591975\pi$
$101$		−	19.2665i		−	1.91709i	0.284944	−	0.958544i	$-0.408025\pi$
$102$		−	7.31662i		−	0.724454i
$103$	7.94987	+	7.94987i	0.783324	+	0.783324i	0.980390	−	0.197066i	$-0.0631413\pi$
$103$	7.94987	+	7.94987i	0.783324	+	0.783324i	−0.197066	+	0.980390i	$0.563141\pi$
$104$	2.00000	−	3.00000i	0.196116	−	0.294174i
$105$	−10.9749	+	0.550126i	−1.07104	+	0.0536868i
$106$	−9.63325	+	9.63325i	−0.935664	+	0.935664i
$107$	−9.63325	−	9.63325i	−0.931281	−	0.931281i	0.0665047	−	0.997786i	$-0.478815\pi$
$107$	−9.63325	−	9.63325i	−0.931281	−	0.931281i	−0.997786	+	0.0665047i	$0.978815\pi$
$108$	−3.84169	−	3.84169i	−0.369667	−	0.369667i
$109$	1.47494	+	1.47494i	0.141273	+	0.141273i	0.774206	−	0.632933i	$-0.218149\pi$
$109$	1.47494	+	1.47494i	0.141273	+	0.141273i	−0.632933	+	0.774206i	$0.718149\pi$
$110$	−10.4749	+	0.525063i	−0.998746	+	0.0500628i
$111$	−3.47494	−	3.47494i	−0.329826	−	0.329826i
$112$			3.00000i			0.283473i
$113$	2.68338	−	2.68338i	0.252431	−	0.252431i	−0.569536	−	0.821967i	$-0.692877\pi$
$113$	2.68338	−	2.68338i	0.252431	−	0.252431i	0.821967	+	0.569536i	$0.192877\pi$
$114$	−4.63325			−0.433944
$115$	10.4749	−	0.525063i	0.976793	−	0.0489624i
$116$		−	6.31662i		−	0.586484i
$117$	−0.949874	−	0.633250i	−0.0878159	−	0.0585439i
$118$	0.316625	−	0.316625i	0.0291477	−	0.0291477i
$119$	9.47494	+	9.47494i	0.868566	+	0.868566i
$120$	−0.183375	−	3.65831i	−0.0167398	−	0.333957i
$121$			11.0000i			1.00000i
$122$	−2.00000			−0.181071
$123$		−	14.6332i		−	1.31944i
$124$	1.00000	−	1.00000i	0.0898027	−	0.0898027i
$125$	−9.00000	−	6.63325i	−0.804984	−	0.593296i
$126$	0.949874			0.0846215
$127$	7.00000	−	7.00000i	0.621150	−	0.621150i	−0.324676	−	0.945825i	$-0.605255\pi$
$127$	7.00000	−	7.00000i	0.621150	−	0.621150i	0.945825	+	0.324676i	$0.105255\pi$
$128$	−1.00000			−0.0883883
$129$	5.73350			0.504807
$130$	−1.97494	−	7.81662i	−0.173213	−	0.685563i
$131$	−3.00000			−0.262111			−0.131056	−	0.991375i	$-0.541837\pi$
$131$	−3.00000			−0.262111			−0.131056	+	0.991375i	$0.541837\pi$
$132$	−7.68338			−0.668752
$133$	6.00000	−	6.00000i	0.520266	−	0.520266i
$134$	4.94987			0.427604
$135$	−12.1332	+	0.608187i	−1.04426	+	0.0523444i
$136$	−3.15831	+	3.15831i	−0.270823	+	0.270823i
$137$			5.68338i			0.485564i	0.970081	+	0.242782i	$0.0780599\pi$
$137$			5.68338i			0.485564i	−0.970081	+	0.242782i	$0.921940\pi$
$138$	7.68338			0.654052
$139$		−	15.9499i		−	1.35285i	−0.736511	−	0.676425i	$-0.763528\pi$
$139$		−	15.9499i		−	1.35285i	0.736511	−	0.676425i	$-0.236472\pi$
$140$	4.97494	+	4.50000i	0.420459	+	0.380319i
$141$	10.7916	+	10.7916i	0.908813	+	0.908813i
$142$	2.84169	−	2.84169i	0.238469	−	0.238469i
$143$	−16.5831	+	3.31662i	−1.38675	+	0.277350i
$144$			0.316625i			0.0263854i
$145$	−10.4749	−	9.47494i	−0.869896	−	0.786851i
$146$	4.00000			0.331042
$147$	2.31662	−	2.31662i	0.191072	−	0.191072i
$148$			3.00000i			0.246598i
$149$	15.3166	+	15.3166i	1.25479	+	1.25479i	0.953549	+	0.301238i	$0.0973998\pi$
$149$	15.3166	+	15.3166i	1.25479	+	1.25479i	0.301238	+	0.953549i	$0.402600\pi$
$150$	−6.34169	−	5.18338i	−0.517797	−	0.423221i
$151$	4.47494	+	4.47494i	0.364165	+	0.364165i	0.865344	−	0.501179i	$-0.167100\pi$
$151$	4.47494	+	4.47494i	0.364165	+	0.364165i	−0.501179	+	0.865344i	$0.667100\pi$
$152$	2.00000	+	2.00000i	0.162221	+	0.162221i
$153$	1.00000	+	1.00000i	0.0808452	+	0.0808452i
$154$	9.94987	−	9.94987i	0.801784	−	0.801784i
$155$	−0.158312	−	3.15831i	−0.0127160	−	0.253682i
$156$	−1.15831	−	5.79156i	−0.0927392	−	0.463696i
$157$	10.0000	+	10.0000i	0.798087	+	0.798087i	0.982794	−	0.184707i	$-0.0591335\pi$
$157$	10.0000	+	10.0000i	0.798087	+	0.798087i	−0.184707	+	0.982794i	$0.559134\pi$
$158$		−	12.9499i		−	1.03024i
$159$			22.3166i			1.76982i
$160$	−1.50000	+	1.65831i	−0.118585	+	0.131101i
$161$	−9.94987	+	9.94987i	−0.784160	+	0.784160i
$162$	−7.94987			−0.624601
$163$	2.94987			0.231052			0.115526	−	0.993304i	$-0.463145\pi$
$163$	2.94987			0.231052			0.115526	+	0.993304i	$0.463145\pi$
$164$	−6.31662	+	6.31662i	−0.493246	+	0.493246i
$165$	−11.5251	+	12.7414i	−0.897225	+	0.991919i
$166$			6.31662i			0.490265i
$167$			12.6332i			0.977590i	0.872399	+	0.488795i	$0.162563\pi$
$167$			12.6332i			0.977590i	−0.872399	+	0.488795i	$0.837437\pi$
$168$	3.47494	+	3.47494i	0.268097	+	0.268097i
$169$	−5.00000	−	12.0000i	−0.384615	−	0.923077i
$170$	0.500000	+	9.97494i	0.0383482	+	0.765043i
$171$	0.633250	−	0.633250i	0.0484258	−	0.0484258i
$172$	−2.47494	−	2.47494i	−0.188712	−	0.188712i
$173$	3.31662	+	3.31662i	0.252158	+	0.252158i	0.821855	−	0.569697i	$-0.192939\pi$
$173$	3.31662	+	3.31662i	0.252158	+	0.252158i	−0.569697	+	0.821855i	$0.692939\pi$
$174$	−7.31662	−	7.31662i	−0.554672	−	0.554672i
$175$	14.9248	−	1.50000i	1.12821	−	0.113389i
$176$	3.31662	+	3.31662i	0.250000	+	0.250000i
$177$		−	0.733501i		−	0.0551333i
$178$	0.316625	−	0.316625i	0.0237320	−	0.0237320i
$179$	−15.0000			−1.12115			−0.560576	−	0.828103i	$-0.689420\pi$
$179$	−15.0000			−1.12115			−0.560576	+	0.828103i	$0.689420\pi$
$180$	0.525063	+	0.474937i	0.0391359	+	0.0353997i
$181$		−	6.94987i		−	0.516580i	−0.966067	−	0.258290i	$-0.916841\pi$
$181$		−	6.94987i		−	0.516580i	0.966067	−	0.258290i	$-0.0831590\pi$
$182$	9.00000	+	6.00000i	0.667124	+	0.444750i
$183$	−2.31662	+	2.31662i	−0.171250	+	0.171250i
$184$	−3.31662	−	3.31662i	−0.244505	−	0.244505i
$185$	4.97494	+	4.50000i	0.365765	+	0.330847i
$186$		−	2.31662i		−	0.169863i
$187$	20.9499			1.53201
$188$		−	9.31662i		−	0.679485i
$189$	11.5251	−	11.5251i	0.838325	−	0.838325i
$190$	6.31662	−	0.316625i	0.458256	−	0.0229704i
$191$	5.05013			0.365414			0.182707	−	0.983167i	$-0.441514\pi$
$191$	5.05013			0.365414			0.182707	+	0.983167i	$0.441514\pi$
$192$	−1.15831	+	1.15831i	−0.0835940	+	0.0835940i
$193$	−10.9499			−0.788189			−0.394095	−	0.919070i	$-0.628942\pi$
$193$	−10.9499			−0.788189			−0.394095	+	0.919070i	$0.628942\pi$
$194$	−8.94987			−0.642564
$195$	−11.3417	−	6.76650i	−0.812195	−	0.484559i
$196$	−2.00000			−0.142857
$197$	3.94987			0.281417			0.140708	−	0.990051i	$-0.455062\pi$
$197$	3.94987			0.281417			0.140708	+	0.990051i	$0.455062\pi$
$198$	1.05013	−	1.05013i	0.0746292	−	0.0746292i
$199$	−16.9499			−1.20154			−0.600772	−	0.799420i	$-0.705140\pi$
$199$	−16.9499			−1.20154			−0.600772	+	0.799420i	$0.705140\pi$
$200$	0.500000	+	4.97494i	0.0353553	+	0.351781i
$201$	5.73350	−	5.73350i	0.404410	−	0.404410i
$202$			19.2665i			1.35559i
$203$	18.9499			1.33002
$204$			7.31662i			0.512266i
$205$	1.00000	+	19.9499i	0.0698430	+	1.39336i
$206$	−7.94987	−	7.94987i	−0.553894	−	0.553894i
$207$	−1.05013	+	1.05013i	−0.0729888	+	0.0729888i
$208$	−2.00000	+	3.00000i	−0.138675	+	0.208013i
$209$		−	13.2665i		−	0.917663i
$210$	10.9749	−	0.550126i	0.757343	−	0.0379623i
$211$	−19.9499			−1.37341			−0.686703	−	0.726938i	$-0.740943\pi$
$211$	−19.9499			−1.37341			−0.686703	+	0.726938i	$0.740943\pi$
$212$	9.63325	−	9.63325i	0.661614	−	0.661614i
$213$		−	6.58312i		−	0.451068i
$214$	9.63325	+	9.63325i	0.658515	+	0.658515i
$215$	−7.81662	+	0.391813i	−0.533089	+	0.0267214i
$216$	3.84169	+	3.84169i	0.261394	+	0.261394i
$217$	3.00000	+	3.00000i	0.203653	+	0.203653i
$218$	−1.47494	−	1.47494i	−0.0998954	−	0.0998954i
$219$	4.63325	−	4.63325i	0.313086	−	0.313086i
$220$	10.4749	−	0.525063i	0.706220	−	0.0353997i
$221$	3.15831	+	15.7916i	0.212451	+	1.06226i
$222$	3.47494	+	3.47494i	0.233223	+	0.233223i
$223$		−	15.9499i		−	1.06808i	−0.845458	−	0.534041i	$-0.820673\pi$
$223$		−	15.9499i		−	1.06808i	0.845458	−	0.534041i	$-0.179327\pi$
$224$		−	3.00000i		−	0.200446i
$225$	1.57519	−	0.158312i	0.105013	−	0.0105542i
$226$	−2.68338	+	2.68338i	−0.178495	+	0.178495i
$227$	−18.0000			−1.19470			−0.597351	−	0.801980i	$-0.703780\pi$
$227$	−18.0000			−1.19470			−0.597351	+	0.801980i	$0.703780\pi$
$228$	4.63325			0.306844
$229$	3.52506	−	3.52506i	0.232943	−	0.232943i	−0.580977	−	0.813920i	$-0.697329\pi$
$229$	3.52506	−	3.52506i	0.232943	−	0.232943i	0.813920	+	0.580977i	$0.197329\pi$
$230$	−10.4749	+	0.525063i	−0.690697	+	0.0346216i
$231$		−	23.0501i		−	1.51659i
$232$			6.31662i			0.414707i
$233$	6.79156	+	6.79156i	0.444930	+	0.444930i	0.893665	−	0.448735i	$-0.148125\pi$
$233$	6.79156	+	6.79156i	0.444930	+	0.444930i	−0.448735	+	0.893665i	$0.648125\pi$
$234$	0.949874	+	0.633250i	0.0620952	+	0.0413968i
$235$	−15.4499	−	13.9749i	−1.00784	−	0.911624i
$236$	−0.316625	+	0.316625i	−0.0206105	+	0.0206105i
$237$	−15.0000	−	15.0000i	−0.974355	−	0.974355i
$238$	−9.47494	−	9.47494i	−0.614169	−	0.614169i
$239$	11.8417	+	11.8417i	0.765975	+	0.765975i	0.977395	−	0.211420i	$-0.0678088\pi$
$239$	11.8417	+	11.8417i	0.765975	+	0.765975i	−0.211420	+	0.977395i	$0.567809\pi$
$240$	0.183375	+	3.65831i	0.0118368	+	0.236143i
$241$	16.0000	+	16.0000i	1.03065	+	1.03065i	0.999515	+	0.0311354i	$0.00991232\pi$
$241$	16.0000	+	16.0000i	1.03065	+	1.03065i	0.0311354	+	0.999515i	$0.490088\pi$
$242$		−	11.0000i		−	0.707107i
$243$	2.31662	−	2.31662i	0.148612	−	0.148612i
$244$	2.00000			0.128037
$245$	−3.00000	+	3.31662i	−0.191663	+	0.211891i
$246$			14.6332i			0.932982i
$247$	10.0000	−	2.00000i	0.636285	−	0.127257i
$248$	−1.00000	+	1.00000i	−0.0635001	+	0.0635001i
$249$	7.31662	+	7.31662i	0.463672	+	0.463672i
$250$	9.00000	+	6.63325i	0.569210	+	0.419524i
$251$		−	19.2665i		−	1.21609i	−0.793902	−	0.608045i	$-0.791954\pi$
$251$		−	19.2665i		−	1.21609i	0.793902	−	0.608045i	$-0.208046\pi$
$252$	−0.949874			−0.0598365
$253$			22.0000i			1.38313i
$254$	−7.00000	+	7.00000i	−0.439219	+	0.439219i
$255$	12.1332	+	10.9749i	0.759814	+	0.687277i
$256$	1.00000			0.0625000
$257$	−11.8417	+	11.8417i	−0.738664	+	0.738664i	−0.972319	−	0.233655i	$-0.924931\pi$
$257$	−11.8417	+	11.8417i	−0.738664	+	0.738664i	0.233655	+	0.972319i	$0.424931\pi$
$258$	−5.73350			−0.356952
$259$	−9.00000			−0.559233
$260$	1.97494	+	7.81662i	0.122480	+	0.484766i
$261$	2.00000			0.123797
$262$	3.00000			0.185341
$263$	−12.3166	+	12.3166i	−0.759476	+	0.759476i	−0.976227	−	0.216751i	$-0.930454\pi$
$263$	−12.3166	+	12.3166i	−0.759476	+	0.759476i	0.216751	+	0.976227i	$0.430454\pi$
$264$	7.68338			0.472879
$265$	−1.52506	−	30.4248i	−0.0936839	−	1.86898i
$266$	−6.00000	+	6.00000i	−0.367884	+	0.367884i
$267$		−	0.733501i		−	0.0448895i
$268$	−4.94987			−0.302362
$269$		−	13.2665i		−	0.808873i	−0.914566	−	0.404436i	$-0.867468\pi$
$269$		−	13.2665i		−	0.808873i	0.914566	−	0.404436i	$-0.132532\pi$
$270$	12.1332	−	0.608187i	0.738406	−	0.0370131i
$271$	−10.5251	−	10.5251i	−0.639352	−	0.639352i	0.311044	−	0.950396i	$-0.399321\pi$
$271$	−10.5251	−	10.5251i	−0.639352	−	0.639352i	−0.950396	+	0.311044i	$0.899321\pi$
$272$	3.15831	−	3.15831i	0.191501	−	0.191501i
$273$	17.3747	−	3.47494i	1.05156	−	0.210313i
$274$		−	5.68338i		−	0.343345i
$275$	14.8417	−	18.1583i	0.894987	−	1.09499i
$276$	−7.68338			−0.462485
$277$	−21.8997	+	21.8997i	−1.31583	+	1.31583i	−0.398783	+	0.917045i	$0.630567\pi$
$277$	−21.8997	+	21.8997i	−1.31583	+	1.31583i	−0.917045	+	0.398783i	$0.869433\pi$
$278$			15.9499i			0.956610i
$279$	0.316625	+	0.316625i	0.0189558	+	0.0189558i
$280$	−4.97494	−	4.50000i	−0.297309	−	0.268926i
$281$	−11.6834	−	11.6834i	−0.696972	−	0.696972i	0.266784	−	0.963756i	$-0.414039\pi$
$281$	−11.6834	−	11.6834i	−0.696972	−	0.696972i	−0.963756	+	0.266784i	$0.914039\pi$
$282$	−10.7916	−	10.7916i	−0.642628	−	0.642628i
$283$	7.94987	+	7.94987i	0.472571	+	0.472571i	0.902746	−	0.430175i	$-0.141548\pi$
$283$	7.94987	+	7.94987i	0.472571	+	0.472571i	−0.430175	+	0.902746i	$0.641548\pi$
$284$	−2.84169	+	2.84169i	−0.168623	+	0.168623i
$285$	6.94987	−	7.68338i	0.411675	−	0.455124i
$286$	16.5831	−	3.31662i	0.980581	−	0.196116i
$287$	−18.9499	−	18.9499i	−1.11858	−	1.11858i
$288$		−	0.316625i		−	0.0186573i
$289$		−	2.94987i		−	0.173522i
$290$	10.4749	+	9.47494i	0.615109	+	0.556387i
$291$	−10.3668	+	10.3668i	−0.607710	+	0.607710i
$292$	−4.00000			−0.234082
$293$	−22.8997			−1.33782			−0.668909	−	0.743344i	$-0.733238\pi$
$293$	−22.8997			−1.33782			−0.668909	+	0.743344i	$0.733238\pi$
$294$	−2.31662	+	2.31662i	−0.135108	+	0.135108i
$295$	0.0501256	+	1.00000i	0.00291843	+	0.0582223i
$296$		−	3.00000i		−	0.174371i
$297$		−	25.4829i		−	1.47867i
$298$	−15.3166	−	15.3166i	−0.887268	−	0.887268i
$299$	−16.5831	+	3.31662i	−0.959027	+	0.191805i
$300$	6.34169	+	5.18338i	0.366138	+	0.299262i
$301$	7.42481	−	7.42481i	0.427959	−	0.427959i
$302$	−4.47494	−	4.47494i	−0.257504	−	0.257504i
$303$	22.3166	+	22.3166i	1.28206	+	1.28206i
$304$	−2.00000	−	2.00000i	−0.114708	−	0.114708i
$305$	3.00000	−	3.31662i	0.171780	−	0.189909i
$306$	−1.00000	−	1.00000i	−0.0571662	−	0.0571662i
$307$		−	25.8997i		−	1.47818i	−0.673608	−	0.739088i	$-0.735257\pi$
$307$		−	25.8997i		−	1.47818i	0.673608	−	0.739088i	$-0.264743\pi$
$308$	−9.94987	+	9.94987i	−0.566947	+	0.566947i
$309$	−18.4169			−1.04770
$310$	0.158312	+	3.15831i	0.00899154	+	0.179380i
$311$		−	19.2665i		−	1.09250i	−0.837621	−	0.546251i	$-0.816054\pi$
$311$		−	19.2665i		−	1.09250i	0.837621	−	0.546251i	$-0.183946\pi$
$312$	1.15831	+	5.79156i	0.0655765	+	0.327883i
$313$	−15.4248	+	15.4248i	−0.871862	+	0.871862i	−0.992675	−	0.120813i	$-0.961450\pi$
$313$	−15.4248	+	15.4248i	−0.871862	+	0.871862i	0.120813	+	0.992675i	$0.461450\pi$
$314$	−10.0000	−	10.0000i	−0.564333	−	0.564333i
$315$	−1.42481	+	1.57519i	−0.0802790	+	0.0887518i
$316$			12.9499i			0.728487i
$317$	12.0000			0.673987			0.336994	−	0.941507i	$-0.390590\pi$
$317$	12.0000			0.673987			0.336994	+	0.941507i	$0.390590\pi$
$318$		−	22.3166i		−	1.25145i
$319$	20.9499	−	20.9499i	1.17297	−	1.17297i
$320$	1.50000	−	1.65831i	0.0838525	−	0.0927025i
$321$	22.3166			1.24559
$322$	9.94987	−	9.94987i	0.554485	−	0.554485i
$323$	−12.6332			−0.702933
$324$	7.94987			0.441660
$325$	15.9248	+	8.44987i	0.883350	+	0.468715i
$326$	−2.94987			−0.163378
$327$	−3.41688			−0.188954
$328$	6.31662	−	6.31662i	0.348777	−	0.348777i
$329$	27.9499			1.54093
$330$	11.5251	−	12.7414i	0.634434	−	0.701393i
$331$	1.00000	−	1.00000i	0.0549650	−	0.0549650i	−0.679090	−	0.734055i	$-0.737625\pi$
$331$	1.00000	−	1.00000i	0.0549650	−	0.0549650i	0.734055	+	0.679090i	$0.237625\pi$
$332$		−	6.31662i		−	0.346670i
$333$	−0.949874			−0.0520528
$334$		−	12.6332i		−	0.691261i
$335$	−7.42481	+	8.20844i	−0.405661	+	0.448475i
$336$	−3.47494	−	3.47494i	−0.189573	−	0.189573i
$337$	3.52506	−	3.52506i	0.192022	−	0.192022i	−0.604547	−	0.796569i	$-0.706646\pi$
$337$	3.52506	−	3.52506i	0.192022	−	0.192022i	0.796569	+	0.604547i	$0.206646\pi$
$338$	5.00000	+	12.0000i	0.271964	+	0.652714i
$339$			6.21637i			0.337627i
$340$	−0.500000	−	9.97494i	−0.0271163	−	0.540967i
$341$	6.63325			0.359211
$342$	−0.633250	+	0.633250i	−0.0342422	+	0.0342422i
$343$			15.0000i			0.809924i
$344$	2.47494	+	2.47494i	0.133440	+	0.133440i
$345$	−11.5251	+	12.7414i	−0.620489	+	0.685976i
$346$	−3.31662	−	3.31662i	−0.178303	−	0.178303i
$347$	0.791562	+	0.791562i	0.0424933	+	0.0424933i	0.728034	−	0.685541i	$-0.240434\pi$
$347$	0.791562	+	0.791562i	0.0424933	+	0.0424933i	−0.685541	+	0.728034i	$0.740434\pi$
$348$	7.31662	+	7.31662i	0.392212	+	0.392212i
$349$	−18.4248	+	18.4248i	−0.986258	+	0.986258i	−0.999907	−	0.0136493i	$-0.995655\pi$
$349$	−18.4248	+	18.4248i	−0.986258	+	0.986258i	0.0136493	+	0.999907i	$0.495655\pi$
$350$	−14.9248	+	1.50000i	−0.797765	+	0.0801784i
$351$	19.2084	−	3.84169i	1.02527	−	0.205054i
$352$	−3.31662	−	3.31662i	−0.176777	−	0.176777i
$353$			7.58312i			0.403609i	0.979426	+	0.201804i	$0.0646806\pi$
$353$			7.58312i			0.403609i	−0.979426	+	0.201804i	$0.935319\pi$
$354$			0.733501i			0.0389851i
$355$	0.449874	+	8.97494i	0.0238769	+	0.476340i
$356$	−0.316625	+	0.316625i	−0.0167811	+	0.0167811i
$357$	−21.9499			−1.16171
$358$	15.0000			0.792775
$359$	−22.2665	+	22.2665i	−1.17518	+	1.17518i	−0.194224	+	0.980957i	$0.562219\pi$
$359$	−22.2665	+	22.2665i	−1.17518	+	1.17518i	−0.980957	+	0.194224i	$0.937781\pi$
$360$	−0.525063	−	0.474937i	−0.0276732	−	0.0250314i
$361$		−	11.0000i		−	0.578947i
$362$			6.94987i			0.365277i
$363$	−12.7414	−	12.7414i	−0.668752	−	0.668752i
$364$	−9.00000	−	6.00000i	−0.471728	−	0.314485i
$365$	−6.00000	+	6.63325i	−0.314054	+	0.347200i
$366$	2.31662	−	2.31662i	0.121092	−	0.121092i
$367$	1.94987	+	1.94987i	0.101783	+	0.101783i	0.756164	−	0.654382i	$-0.227071\pi$
$367$	1.94987	+	1.94987i	0.101783	+	0.101783i	−0.654382	+	0.756164i	$0.727071\pi$
$368$	3.31662	+	3.31662i	0.172891	+	0.172891i
$369$	−2.00000	−	2.00000i	−0.104116	−	0.104116i
$370$	−4.97494	−	4.50000i	−0.258635	−	0.233944i
$371$	28.8997	+	28.8997i	1.50040	+	1.50040i
$372$			2.31662i			0.120111i
$373$	−20.0000	+	20.0000i	−1.03556	+	1.03556i	−0.0362168	+	0.999344i	$0.511531\pi$
$373$	−20.0000	+	20.0000i	−1.03556	+	1.03556i	−0.999344	+	0.0362168i	$0.988469\pi$
$374$	−20.9499			−1.08329
$375$	18.1082	−	2.74144i	0.935103	−	0.141567i
$376$			9.31662i			0.480468i
$377$	18.9499	+	12.6332i	0.975968	+	0.650645i
$378$	−11.5251	+	11.5251i	−0.592785	+	0.592785i
$379$	13.0000	+	13.0000i	0.667765	+	0.667765i	0.957198	−	0.289433i	$-0.0934668\pi$
$379$	13.0000	+	13.0000i	0.667765	+	0.667765i	−0.289433	+	0.957198i	$0.593467\pi$
$380$	−6.31662	+	0.316625i	−0.324036	+	0.0162425i
$381$			16.2164i			0.830790i
$382$	−5.05013			−0.258387
$383$		−	14.3668i		−	0.734107i	−0.930200	−	0.367053i	$-0.880367\pi$
$383$		−	14.3668i		−	0.734107i	0.930200	−	0.367053i	$-0.119633\pi$
$384$	1.15831	−	1.15831i	0.0591099	−	0.0591099i
$385$	1.57519	+	31.4248i	0.0802790	+	1.60156i
$386$	10.9499			0.557334
$387$	0.783626	−	0.783626i	0.0398340	−	0.0398340i
$388$	8.94987			0.454361
$389$	13.8997			0.704745			0.352373	−	0.935860i	$-0.385375\pi$
$389$	13.8997			0.704745			0.352373	+	0.935860i	$0.385375\pi$
$390$	11.3417	+	6.76650i	0.574309	+	0.342635i
$391$	20.9499			1.05948
$392$	2.00000			0.101015
$393$	3.47494	−	3.47494i	0.175287	−	0.175287i
$394$	−3.94987			−0.198992
$395$	21.4749	+	19.4248i	1.08052	+	0.977368i
$396$	−1.05013	+	1.05013i	−0.0527708	+	0.0527708i
$397$			18.0000i			0.903394i	0.892171	+	0.451697i	$0.149181\pi$
$397$			18.0000i			0.903394i	−0.892171	+	0.451697i	$0.850819\pi$
$398$	16.9499			0.849620
$399$			13.8997i			0.695858i
$400$	−0.500000	−	4.97494i	−0.0250000	−	0.248747i
$401$	−10.5831	−	10.5831i	−0.528496	−	0.528496i	0.391628	−	0.920124i	$-0.371912\pi$
$401$	−10.5831	−	10.5831i	−0.528496	−	0.528496i	−0.920124	+	0.391628i	$0.871912\pi$
$402$	−5.73350	+	5.73350i	−0.285961	+	0.285961i
$403$	1.00000	+	5.00000i	0.0498135	+	0.249068i
$404$		−	19.2665i		−	0.958544i
$405$	11.9248	−	13.1834i	0.592549	−	0.655087i
$406$	−18.9499			−0.940466
$407$	−9.94987	+	9.94987i	−0.493197	+	0.493197i
$408$		−	7.31662i		−	0.362227i
$409$	−23.9499	−	23.9499i	−1.18425	−	1.18425i	−0.978634	−	0.205611i	$-0.934082\pi$
$409$	−23.9499	−	23.9499i	−1.18425	−	1.18425i	−0.205611	−	0.978634i	$-0.565918\pi$
$410$	−1.00000	−	19.9499i	−0.0493865	−	0.985254i
$411$	−6.58312	−	6.58312i	−0.324722	−	0.324722i
$412$	7.94987	+	7.94987i	0.391662	+	0.391662i
$413$	−0.949874	−	0.949874i	−0.0467403	−	0.0467403i
$414$	1.05013	−	1.05013i	0.0516109	−	0.0516109i
$415$	−10.4749	−	9.47494i	−0.514194	−	0.465106i
$416$	2.00000	−	3.00000i	0.0980581	−	0.147087i
$417$	18.4749	+	18.4749i	0.904722	+	0.904722i
$418$			13.2665i			0.648886i
$419$			8.68338i			0.424211i	0.977247	+	0.212105i	$0.0680320\pi$
$419$			8.68338i			0.424211i	−0.977247	+	0.212105i	$0.931968\pi$
$420$	−10.9749	+	0.550126i	−0.535522	+	0.0268434i
$421$	−2.47494	+	2.47494i	−0.120621	+	0.120621i	−0.764841	−	0.644220i	$-0.777182\pi$
$421$	−2.47494	+	2.47494i	−0.120621	+	0.120621i	0.644220	+	0.764841i	$0.277182\pi$
$422$	19.9499			0.971145
$423$	2.94987			0.143428
$424$	−9.63325	+	9.63325i	−0.467832	+	0.467832i
$425$	−17.2916	−	14.1332i	−0.838764	−	0.685563i
$426$			6.58312i			0.318953i
$427$			6.00000i			0.290360i
$428$	−9.63325	−	9.63325i	−0.465641	−	0.465641i
$429$	15.3668	−	23.0501i	0.741914	−	1.11287i
$430$	7.81662	−	0.391813i	0.376951	−	0.0188949i
$431$	12.1583	−	12.1583i	0.585645	−	0.585645i	−0.350804	−	0.936449i	$-0.614092\pi$
$431$	12.1583	−	12.1583i	0.585645	−	0.585645i	0.936449	+	0.350804i	$0.114092\pi$
$432$	−3.84169	−	3.84169i	−0.184833	−	0.184833i
$433$	12.5251	+	12.5251i	0.601916	+	0.601916i	0.940821	−	0.338905i	$-0.110056\pi$
$433$	12.5251	+	12.5251i	0.601916	+	0.601916i	−0.338905	+	0.940821i	$0.610056\pi$
$434$	−3.00000	−	3.00000i	−0.144005	−	0.144005i
$435$	23.1082	−	1.15831i	1.10795	−	0.0555368i
$436$	1.47494	+	1.47494i	0.0706367	+	0.0706367i
$437$		−	13.2665i		−	0.634623i
$438$	−4.63325	+	4.63325i	−0.221385	+	0.221385i
$439$	33.8997			1.61795			0.808973	−	0.587845i	$-0.200024\pi$
$439$	33.8997			1.61795			0.808973	+	0.587845i	$0.200024\pi$
$440$	−10.4749	+	0.525063i	−0.499373	+	0.0250314i
$441$		−	0.633250i		−	0.0301547i
$442$	−3.15831	−	15.7916i	−0.150226	−	0.751128i
$443$	20.0581	−	20.0581i	0.952987	−	0.952987i	−0.0459562	−	0.998943i	$-0.514633\pi$
$443$	20.0581	−	20.0581i	0.952987	−	0.952987i	0.998943	+	0.0459562i	$0.0146335\pi$
$444$	−3.47494	−	3.47494i	−0.164913	−	0.164913i
$445$	0.0501256	+	1.00000i	0.00237618	+	0.0474045i
$446$			15.9499i			0.755248i
$447$	−35.4829			−1.67828
$448$			3.00000i			0.141737i
$449$	21.6332	−	21.6332i	1.02094	−	1.02094i	0.0211601	−	0.999776i	$-0.493264\pi$
$449$	21.6332	−	21.6332i	1.02094	−	1.02094i	0.999776	−	0.0211601i	$-0.00673596\pi$
$450$	−1.57519	+	0.158312i	−0.0742551	+	0.00746292i
$451$	−41.8997			−1.97298
$452$	2.68338	−	2.68338i	0.126215	−	0.126215i
$453$	−10.3668			−0.487072
$454$	18.0000			0.844782
$455$	−23.4499	+	5.92481i	−1.09935	+	0.277759i
$456$	−4.63325			−0.216972
$457$	2.00000			0.0935561			0.0467780	−	0.998905i	$-0.485105\pi$
$457$	2.00000			0.0935561			0.0467780	+	0.998905i	$0.485105\pi$
$458$	−3.52506	+	3.52506i	−0.164715	+	0.164715i
$459$	−24.2665			−1.13266
$460$	10.4749	−	0.525063i	0.488396	−	0.0244812i
$461$	4.10819	−	4.10819i	0.191337	−	0.191337i	−0.604936	−	0.796274i	$-0.706801\pi$
$461$	4.10819	−	4.10819i	0.191337	−	0.191337i	0.796274	+	0.604936i	$0.206801\pi$
$462$			23.0501i			1.07239i
$463$	9.89975			0.460080			0.230040	−	0.973181i	$-0.426114\pi$
$463$	9.89975			0.460080			0.230040	+	0.973181i	$0.426114\pi$
$464$		−	6.31662i		−	0.293242i
$465$	3.84169	+	3.47494i	0.178154	+	0.161146i
$466$	−6.79156	−	6.79156i	−0.314613	−	0.314613i
$467$	−8.36675	+	8.36675i	−0.387167	+	0.387167i	−0.873676	−	0.486509i	$-0.838270\pi$
$467$	−8.36675	+	8.36675i	−0.387167	+	0.387167i	0.486509	+	0.873676i	$0.338270\pi$
$468$	−0.949874	−	0.633250i	−0.0439080	−	0.0292720i
$469$		−	14.8496i		−	0.685692i
$470$	15.4499	+	13.9749i	0.712650	+	0.644616i
$471$	−23.1662			−1.06744
$472$	0.316625	−	0.316625i	0.0145738	−	0.0145738i
$473$		−	16.4169i		−	0.754849i
$474$	15.0000	+	15.0000i	0.688973	+	0.688973i
$475$	−8.94987	+	10.9499i	−0.410648	+	0.502415i
$476$	9.47494	+	9.47494i	0.434283	+	0.434283i
$477$	3.05013	+	3.05013i	0.139656	+	0.139656i
$478$	−11.8417	−	11.8417i	−0.541626	−	0.541626i
$479$	3.15831	−	3.15831i	0.144307	−	0.144307i	−0.631262	−	0.775569i	$-0.717463\pi$
$479$	3.15831	−	3.15831i	0.144307	−	0.144307i	0.775569	+	0.631262i	$0.217463\pi$
$480$	−0.183375	−	3.65831i	−0.00836989	−	0.166978i
$481$	−9.00000	−	6.00000i	−0.410365	−	0.273576i
$482$	−16.0000	−	16.0000i	−0.728780	−	0.728780i
$483$		−	23.0501i		−	1.04882i
$484$			11.0000i			0.500000i
$485$	13.4248	−	14.8417i	0.609589	−	0.673926i
$486$	−2.31662	+	2.31662i	−0.105084	+	0.105084i
$487$	2.00000			0.0906287			0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000			0.0906287			0.0453143	+	0.998973i	$0.485571\pi$
$488$	−2.00000			−0.0905357
$489$	−3.41688	+	3.41688i	−0.154516	+	0.154516i
$490$	3.00000	−	3.31662i	0.135526	−	0.149830i
$491$			32.6834i			1.47498i	0.675358	+	0.737490i	$0.263989\pi$
$491$			32.6834i			1.47498i	−0.675358	+	0.737490i	$0.736011\pi$
$492$		−	14.6332i		−	0.659718i
$493$	−19.9499	−	19.9499i	−0.898497	−	0.898497i
$494$	−10.0000	+	2.00000i	−0.449921	+	0.0899843i
$495$	0.166248	+	3.31662i	0.00747229	+	0.149071i
$496$	1.00000	−	1.00000i	0.0449013	−	0.0449013i
$497$	−8.52506	−	8.52506i	−0.382401	−	0.382401i
$498$	−7.31662	−	7.31662i	−0.327866	−	0.327866i
$499$	−8.94987	−	8.94987i	−0.400651	−	0.400651i	0.477811	−	0.878463i	$-0.341430\pi$
$499$	−8.94987	−	8.94987i	−0.400651	−	0.400651i	−0.878463	+	0.477811i	$0.841430\pi$
$500$	−9.00000	−	6.63325i	−0.402492	−	0.296648i
$501$	−14.6332	−	14.6332i	−0.653765	−	0.653765i
$502$			19.2665i			0.859906i
$503$	1.58312	−	1.58312i	0.0705880	−	0.0705880i	−0.670931	−	0.741519i	$-0.734106\pi$
$503$	1.58312	−	1.58312i	0.0705880	−	0.0705880i	0.741519	+	0.670931i	$0.234106\pi$
$504$	0.949874			0.0423108
$505$	−31.9499	−	28.8997i	−1.42175	−	1.28602i
$506$		−	22.0000i		−	0.978019i
$507$	19.6913	+	8.10819i	0.874522	+	0.360097i
$508$	7.00000	−	7.00000i	0.310575	−	0.310575i
$509$	15.3166	+	15.3166i	0.678897	+	0.678897i	0.959751	−	0.280853i	$-0.0906174\pi$
$509$	15.3166	+	15.3166i	0.678897	+	0.678897i	−0.280853	+	0.959751i	$0.590617\pi$
$510$	−12.1332	−	10.9749i	−0.537269	−	0.485978i
$511$		−	12.0000i		−	0.530849i
$512$	−1.00000			−0.0441942
$513$			15.3668i			0.678459i
$514$	11.8417	−	11.8417i	0.522314	−	0.522314i
$515$	25.1082	−	1.25856i	1.10640	−	0.0554589i
$516$	5.73350			0.252403
$517$	30.8997	−	30.8997i	1.35897	−	1.35897i
$518$	9.00000			0.395437
$519$	−7.68338			−0.337263
$520$	−1.97494	−	7.81662i	−0.0866067	−	0.342782i
$521$	10.8997			0.477527			0.238763	−	0.971078i	$-0.423258\pi$
$521$	10.8997			0.477527			0.238763	+	0.971078i	$0.423258\pi$
$522$	−2.00000			−0.0875376
$523$	−5.00000	+	5.00000i	−0.218635	+	0.218635i	−0.807923	−	0.589288i	$-0.799408\pi$
$523$	−5.00000	+	5.00000i	−0.218635	+	0.218635i	0.589288	+	0.807923i	$0.299408\pi$
$524$	−3.00000			−0.131056
$525$	−15.5501	+	19.0251i	−0.678663	+	0.830322i
$526$	12.3166	−	12.3166i	0.537030	−	0.537030i
$527$		−	6.31662i		−	0.275156i
$528$	−7.68338			−0.334376
$529$		−	1.00000i		−	0.0434783i
$530$	1.52506	+	30.4248i	0.0662445	+	1.32157i
$531$	−0.100251	−	0.100251i	−0.00435053	−	0.00435053i
$532$	6.00000	−	6.00000i	0.260133	−	0.260133i
$533$	−6.31662	−	31.5831i	−0.273603	−	1.36802i
$534$			0.733501i			0.0317417i
$535$	−30.4248	+	1.52506i	−1.31538	+	0.0659342i
$536$	4.94987			0.213802
$537$	17.3747	−	17.3747i	0.749773	−	0.749773i
$538$			13.2665i			0.571959i
$539$	−6.63325	−	6.63325i	−0.285714	−	0.285714i
$540$	−12.1332	+	0.608187i	−0.522132	+	0.0261722i
$541$	4.47494	+	4.47494i	0.192393	+	0.192393i	0.796729	−	0.604337i	$-0.206562\pi$
$541$	4.47494	+	4.47494i	0.192393	+	0.192393i	−0.604337	+	0.796729i	$0.706562\pi$
$542$	10.5251	+	10.5251i	0.452090	+	0.452090i
$543$	8.05013	+	8.05013i	0.345464	+	0.345464i
$544$	−3.15831	+	3.15831i	−0.135412	+	0.135412i
$545$	4.65831	−	0.233501i	0.199540	−	0.0100021i
$546$	−17.3747	+	3.47494i	−0.743568	+	0.148714i
$547$	21.5251	+	21.5251i	0.920345	+	0.920345i	0.997054	−	0.0767083i	$-0.0244410\pi$
$547$	21.5251	+	21.5251i	0.920345	+	0.920345i	−0.0767083	+	0.997054i	$0.524441\pi$
$548$			5.68338i			0.242782i
$549$			0.633250i			0.0270264i
$550$	−14.8417	+	18.1583i	−0.632852	+	0.774273i
$551$	−12.6332	+	12.6332i	−0.538195	+	0.538195i
$552$	7.68338			0.327026
$553$	−38.8496			−1.65205
$554$	21.8997	−	21.8997i	0.930431	−	0.930431i
$555$	−10.9749	+	0.550126i	−0.465860	+	0.0233515i
$556$		−	15.9499i		−	0.676425i
$557$			4.58312i			0.194193i	0.995275	+	0.0970966i	$0.0309556\pi$
$557$			4.58312i			0.194193i	−0.995275	+	0.0970966i	$0.969044\pi$
$558$	−0.316625	−	0.316625i	−0.0134038	−	0.0134038i
$559$	12.3747	−	2.47494i	0.523393	−	0.104679i
$560$	4.97494	+	4.50000i	0.210229	+	0.190160i
$561$	−24.2665	+	24.2665i	−1.02453	+	1.02453i
$562$	11.6834	+	11.6834i	0.492833	+	0.492833i
$563$	6.79156	+	6.79156i	0.286230	+	0.286230i	0.835588	−	0.549357i	$-0.185127\pi$
$563$	6.79156	+	6.79156i	0.286230	+	0.286230i	−0.549357	+	0.835588i	$0.685127\pi$
$564$	10.7916	+	10.7916i	0.454407	+	0.454407i
$565$	−0.424812	−	8.47494i	−0.0178720	−	0.356543i
$566$	−7.94987	−	7.94987i	−0.334158	−	0.334158i
$567$			23.8496i			1.00159i
$568$	2.84169	−	2.84169i	0.119235	−	0.119235i
$569$	−42.7995			−1.79425			−0.897124	−	0.441779i	$-0.854348\pi$
$569$	−42.7995			−1.79425			−0.897124	+	0.441779i	$0.854348\pi$
$570$	−6.94987	+	7.68338i	−0.291098	+	0.321821i
$571$			28.8997i			1.20942i	0.796447	+	0.604708i	$0.206710\pi$
$571$			28.8997i			1.20942i	−0.796447	+	0.604708i	$0.793290\pi$
$572$	−16.5831	+	3.31662i	−0.693375	+	0.138675i
$573$	−5.84962	+	5.84962i	−0.244372	+	0.244372i
$574$	18.9499	+	18.9499i	0.790952	+	0.790952i
$575$	14.8417	−	18.1583i	0.618941	−	0.757254i
$576$			0.316625i			0.0131927i
$577$	−41.8997			−1.74431			−0.872155	−	0.489230i	$-0.837278\pi$
$577$	−41.8997			−1.74431			−0.872155	+	0.489230i	$0.837278\pi$
$578$			2.94987i			0.122699i
$579$	12.6834	−	12.6834i	0.527103	−	0.527103i
$580$	−10.4749	−	9.47494i	−0.434948	−	0.393425i
$581$	18.9499			0.786173
$582$	10.3668	−	10.3668i	0.429716	−	0.429716i
$583$	63.8997			2.64646
$584$	4.00000			0.165521
$585$	−2.47494	+	0.625314i	−0.102326	+	0.0258536i
$586$	22.8997			0.945980
$587$	−24.9499			−1.02979			−0.514896	−	0.857253i	$-0.672169\pi$
$587$	−24.9499			−1.02979			−0.514896	+	0.857253i	$0.672169\pi$
$588$	2.31662	−	2.31662i	0.0955360	−	0.0955360i
$589$	−4.00000			−0.164817
$590$	−0.0501256	−	1.00000i	−0.00206364	−	0.0411693i
$591$	−4.57519	+	4.57519i	−0.188198	+	0.188198i
$592$			3.00000i			0.123299i
$593$	12.9499			0.531788			0.265894	−	0.964002i	$-0.414333\pi$
$593$	12.9499			0.531788			0.265894	+	0.964002i	$0.414333\pi$
$594$			25.4829i			1.04557i
$595$	29.9248	−	1.50000i	1.22680	−	0.0614940i
$596$	15.3166	+	15.3166i	0.627393	+	0.627393i
$597$	19.6332	−	19.6332i	0.803535	−	0.803535i
$598$	16.5831	−	3.31662i	0.678134	−	0.135627i
$599$		−	13.2665i		−	0.542054i	−0.962572	−	0.271027i	$-0.912637\pi$
$599$		−	13.2665i		−	0.542054i	0.962572	−	0.271027i	$-0.0873633\pi$
$600$	−6.34169	−	5.18338i	−0.258898	−	0.211610i
$601$	−6.05013			−0.246790			−0.123395	−	0.992358i	$-0.539378\pi$
$601$	−6.05013			−0.246790			−0.123395	+	0.992358i	$0.539378\pi$
$602$	−7.42481	+	7.42481i	−0.302613	+	0.302613i
$603$		−	1.56725i		−	0.0638235i
$604$	4.47494	+	4.47494i	0.182083	+	0.182083i
$605$	18.2414	+	16.5000i	0.741620	+	0.670820i
$606$	−22.3166	−	22.3166i	−0.906551	−	0.906551i
$607$	3.05013	+	3.05013i	0.123801	+	0.123801i	0.766293	−	0.642492i	$-0.222099\pi$
$607$	3.05013	+	3.05013i	0.123801	+	0.123801i	−0.642492	+	0.766293i	$0.722099\pi$
$608$	2.00000	+	2.00000i	0.0811107	+	0.0811107i
$609$	−21.9499	+	21.9499i	−0.889454	+	0.889454i
$610$	−3.00000	+	3.31662i	−0.121466	+	0.134286i
$611$	27.9499	+	18.6332i	1.13073	+	0.753821i
$612$	1.00000	+	1.00000i	0.0404226	+	0.0404226i
$613$		−	24.0000i		−	0.969351i	−0.874694	−	0.484675i	$-0.838938\pi$
$613$		−	24.0000i		−	0.969351i	0.874694	−	0.484675i	$-0.161062\pi$
$614$			25.8997i			1.04523i
$615$	−24.2665	−	21.9499i	−0.978520	−	0.885104i
$616$	9.94987	−	9.94987i	0.400892	−	0.400892i
$617$	12.0000			0.483102			0.241551	−	0.970388i	$-0.422344\pi$
$617$	12.0000			0.483102			0.241551	+	0.970388i	$0.422344\pi$
$618$	18.4169			0.740835
$619$	−21.8997	+	21.8997i	−0.880225	+	0.880225i	−0.993557	−	0.113332i	$-0.963848\pi$
$619$	−21.8997	+	21.8997i	−0.880225	+	0.880225i	0.113332	+	0.993557i	$0.463848\pi$
$620$	−0.158312	−	3.15831i	−0.00635798	−	0.126841i
$621$		−	25.4829i		−	1.02259i
$622$			19.2665i			0.772516i
$623$	−0.949874	−	0.949874i	−0.0380559	−	0.0380559i
$624$	−1.15831	−	5.79156i	−0.0463696	−	0.231848i
$625$	−24.5000	+	4.97494i	−0.980000	+	0.198997i
$626$	15.4248	−	15.4248i	0.616499	−	0.616499i
$627$	15.3668	+	15.3668i	0.613689	+	0.613689i
$628$	10.0000	+	10.0000i	0.399043	+	0.399043i
$629$	9.47494	+	9.47494i	0.377790	+	0.377790i
$630$	1.42481	−	1.57519i	0.0567659	−	0.0627570i
$631$	4.47494	+	4.47494i	0.178144	+	0.178144i	0.790546	−	0.612402i	$-0.209797\pi$
$631$	4.47494	+	4.47494i	0.178144	+	0.178144i	−0.612402	+	0.790546i	$0.709797\pi$
$632$		−	12.9499i		−	0.515118i
$633$	23.1082	−	23.1082i	0.918468	−	0.918468i
$634$	−12.0000			−0.476581
$635$	−1.10819	−	22.1082i	−0.0439771	−	0.877337i
$636$			22.3166i			0.884912i
$637$	4.00000	−	6.00000i	0.158486	−	0.237729i
$638$	−20.9499	+	20.9499i	−0.829413	+	0.829413i
$639$	−0.899749	−	0.899749i	−0.0355935	−	0.0355935i
$640$	−1.50000	+	1.65831i	−0.0592927	+	0.0655506i
$641$		−	5.36675i		−	0.211974i	−0.994368	−	0.105987i	$-0.966200\pi$
$641$		−	5.36675i		−	0.211974i	0.994368	−	0.105987i	$-0.0338002\pi$
$642$	−22.3166			−0.880767
$643$			12.9499i			0.510693i	0.966850	+	0.255347i	$0.0821896\pi$
$643$			12.9499i			0.510693i	−0.966850	+	0.255347i	$0.917810\pi$
$644$	−9.94987	+	9.94987i	−0.392080	+	0.392080i
$645$	8.60025	−	9.50794i	0.338635	−	0.374375i
$646$	12.6332			0.497049
$647$	6.63325	−	6.63325i	0.260780	−	0.260780i	−0.564591	−	0.825371i	$-0.690966\pi$
$647$	6.63325	−	6.63325i	0.260780	−	0.260780i	0.825371	+	0.564591i	$0.190966\pi$
$648$	−7.94987			−0.312301
$649$	−2.10025			−0.0824421
$650$	−15.9248	−	8.44987i	−0.624622	−	0.331431i
$651$	−6.94987			−0.272387
$652$	2.94987			0.115526
$653$	31.5831	−	31.5831i	1.23594	−	1.23594i	0.274299	−	0.961645i	$-0.411554\pi$
$653$	31.5831	−	31.5831i	1.23594	−	1.23594i	0.961645	−	0.274299i	$-0.0884457\pi$
$654$	3.41688			0.133610
$655$	−4.50000	+	4.97494i	−0.175830	+	0.194387i
$656$	−6.31662	+	6.31662i	−0.246623	+	0.246623i
$657$		−	1.26650i		−	0.0494108i
$658$	−27.9499			−1.08960
$659$			0.633250i			0.0246679i	0.999924	+	0.0123340i	$0.00392612\pi$
$659$			0.633250i			0.0246679i	−0.999924	+	0.0123340i	$0.996074\pi$
$660$	−11.5251	+	12.7414i	−0.448612	+	0.495960i
$661$	−12.8997	−	12.8997i	−0.501742	−	0.501742i	0.410237	−	0.911979i	$-0.365446\pi$
$661$	−12.8997	−	12.8997i	−0.501742	−	0.501742i	−0.911979	+	0.410237i	$0.865446\pi$
$662$	−1.00000	+	1.00000i	−0.0388661	+	0.0388661i
$663$	−21.9499	−	14.6332i	−0.852462	−	0.568308i
$664$			6.31662i			0.245133i
$665$	−0.949874	−	18.9499i	−0.0368345	−	0.734845i
$666$	0.949874			0.0368069
$667$	20.9499	−	20.9499i	0.811182	−	0.811182i
$668$			12.6332i			0.488795i
$669$	18.4749	+	18.4749i	0.714282	+	0.714282i
$670$	7.42481	−	8.20844i	0.286845	−	0.317120i
$671$	6.63325	+	6.63325i	0.256074	+	0.256074i
$672$	3.47494	+	3.47494i	0.134049	+	0.134049i
$673$	11.4248	+	11.4248i	0.440394	+	0.440394i	0.892144	−	0.451750i	$-0.149200\pi$
$673$	11.4248	+	11.4248i	0.440394	+	0.440394i	−0.451750	+	0.892144i	$0.649200\pi$
$674$	−3.52506	+	3.52506i	−0.135780	+	0.135780i
$675$	−17.1913	+	21.0330i	−0.661694	+	0.809560i
$676$	−5.00000	−	12.0000i	−0.192308	−	0.461538i
$677$	−2.68338	−	2.68338i	−0.103130	−	0.103130i	0.653659	−	0.756789i	$-0.273233\pi$
$677$	−2.68338	−	2.68338i	−0.103130	−	0.103130i	−0.756789	+	0.653659i	$0.773233\pi$
$678$		−	6.21637i		−	0.238738i
$679$			26.8496i			1.03039i
$680$	0.500000	+	9.97494i	0.0191741	+	0.382521i
$681$	20.8496	−	20.8496i	0.798959	−	0.798959i
$682$	−6.63325			−0.254000
$683$	−30.9499			−1.18426			−0.592132	−	0.805841i	$-0.701714\pi$
$683$	−30.9499			−1.18426			−0.592132	+	0.805841i	$0.701714\pi$
$684$	0.633250	−	0.633250i	0.0242129	−	0.0242129i
$685$	9.42481	+	8.52506i	0.360104	+	0.325726i
$686$		−	15.0000i		−	0.572703i
$687$			8.16625i			0.311562i
$688$	−2.47494	−	2.47494i	−0.0943561	−	0.0943561i
$689$	9.63325	+	48.1662i	0.366998	+	1.83499i
$690$	11.5251	−	12.7414i	0.438752	−	0.485058i
$691$	−14.0000	+	14.0000i	−0.532585	+	0.532585i	−0.921341	−	0.388756i	$-0.872905\pi$
$691$	−14.0000	+	14.0000i	−0.532585	+	0.532585i	0.388756	+	0.921341i	$0.372905\pi$
$692$	3.31662	+	3.31662i	0.126079	+	0.126079i
$693$	−3.15038	−	3.15038i	−0.119673	−	0.119673i
$694$	−0.791562	−	0.791562i	−0.0300473	−	0.0300473i
$695$	−26.4499	−	23.9248i	−1.00330	−	0.907520i
$696$	−7.31662	−	7.31662i	−0.277336	−	0.277336i
$697$			39.8997i			1.51131i
$698$	18.4248	−	18.4248i	0.697389	−	0.697389i
$699$	−15.7335			−0.595096
$700$	14.9248	−	1.50000i	0.564105	−	0.0566947i
$701$			45.4829i			1.71786i	0.512089	+	0.858932i	$0.328872\pi$
$701$			45.4829i			1.71786i	−0.512089	+	0.858932i	$0.671128\pi$
$702$	−19.2084	+	3.84169i	−0.724976	+	0.144995i
$703$	6.00000	−	6.00000i	0.226294	−	0.226294i
$704$	3.31662	+	3.31662i	0.125000	+	0.125000i
$705$	34.0831	−	1.70844i	1.28364	−	0.0643435i
$706$		−	7.58312i		−	0.285395i
$707$	57.7995			2.17377
$708$		−	0.733501i		−	0.0275666i
$709$	−29.9499	+	29.9499i	−1.12479	+	1.12479i	−0.133780	+	0.991011i	$0.542712\pi$
$709$	−29.9499	+	29.9499i	−1.12479	+	1.12479i	−0.991011	+	0.133780i	$0.957288\pi$
$710$	−0.449874	−	8.97494i	−0.0168835	−	0.336823i
$711$	−4.10025			−0.153771
$712$	0.316625	−	0.316625i	0.0118660	−	0.0118660i
$713$	6.63325			0.248417
$714$	21.9499			0.821453
$715$	−19.3747	+	32.4749i	−0.724572	+	1.21449i
$716$	−15.0000			−0.560576
$717$	−27.4327			−1.02449
$718$	22.2665	−	22.2665i	0.830978	−	0.830978i
$719$	6.94987			0.259187			0.129593	−	0.991567i	$-0.458633\pi$
$719$	6.94987			0.259187			0.129593	+	0.991567i	$0.458633\pi$
$720$	0.525063	+	0.474937i	0.0195679	+	0.0176999i
$721$	−23.8496	+	23.8496i	−0.888206	+	0.888206i
$722$			11.0000i			0.409378i
$723$	−37.0660			−1.37850
$724$		−	6.94987i		−	0.258290i
$725$	−31.4248	+	3.15831i	−1.16709	+	0.117297i
$726$	12.7414	+	12.7414i	0.472879	+	0.472879i
$727$	13.9499	−	13.9499i	0.517372	−	0.517372i	−0.399403	−	0.916775i	$-0.630783\pi$
$727$	13.9499	−	13.9499i	0.517372	−	0.517372i	0.916775	+	0.399403i	$0.130783\pi$
$728$	9.00000	+	6.00000i	0.333562	+	0.222375i
$729$			29.2164i			1.08209i
$730$	6.00000	−	6.63325i	0.222070	−	0.245508i
$731$	−15.6332			−0.578217
$732$	−2.31662	+	2.31662i	−0.0856249	+	0.0856249i
$733$		−	36.7995i		−	1.35922i	−0.733573	−	0.679610i	$-0.762149\pi$
$733$		−	36.7995i		−	1.35922i	0.733573	−	0.679610i	$-0.237851\pi$
$734$	−1.94987	−	1.94987i	−0.0719712	−	0.0719712i
$735$	−0.366750	−	7.31662i	−0.0135278	−	0.269878i
$736$	−3.31662	−	3.31662i	−0.122252	−	0.122252i
$737$	−16.4169	−	16.4169i	−0.604723	−	0.604723i
$738$	2.00000	+	2.00000i	0.0736210	+	0.0736210i
$739$	35.8997	−	35.8997i	1.32059	−	1.32059i	0.407299	−	0.913295i	$-0.366471\pi$
$739$	35.8997	−	35.8997i	1.32059	−	1.32059i	0.913295	−	0.407299i	$-0.133529\pi$
$740$	4.97494	+	4.50000i	0.182882	+	0.165423i
$741$	−9.26650	+	13.8997i	−0.340413	+	0.510620i
$742$	−28.8997	−	28.8997i	−1.06094	−	1.06094i
$743$			15.6332i			0.573528i	0.958001	+	0.286764i	$0.0925796\pi$
$743$			15.6332i			0.573528i	−0.958001	+	0.286764i	$0.907420\pi$
$744$		−	2.31662i		−	0.0849316i
$745$	48.3747	−	2.42481i	1.77231	−	0.0888382i
$746$	20.0000	−	20.0000i	0.732252	−	0.732252i
$747$	2.00000			0.0731762
$748$	20.9499			0.766003
$749$	28.8997	−	28.8997i	1.05597	−	1.05597i
$750$	−18.1082	+	2.74144i	−0.661217	+	0.100103i
$751$			13.8997i			0.507209i	0.967308	+	0.253605i	$0.0816162\pi$
$751$			13.8997i			0.507209i	−0.967308	+	0.253605i	$0.918384\pi$
$752$		−	9.31662i		−	0.339742i
$753$	22.3166	+	22.3166i	0.813263	+	0.813263i
$754$	−18.9499	−	12.6332i	−0.690114	−	0.460076i
$755$	14.1332	−	0.708438i	0.514362	−	0.0257827i
$756$	11.5251	−	11.5251i	0.419162	−	0.419162i
$757$	−5.00000	−	5.00000i	−0.181728	−	0.181728i	0.610380	−	0.792108i	$-0.291017\pi$
$757$	−5.00000	−	5.00000i	−0.181728	−	0.181728i	−0.792108	+	0.610380i	$0.791017\pi$
$758$	−13.0000	−	13.0000i	−0.472181	−	0.472181i
$759$	−25.4829	−	25.4829i	−0.924970	−	0.924970i
$760$	6.31662	−	0.316625i	0.229128	−	0.0114852i
$761$	−25.5831	−	25.5831i	−0.927388	−	0.927388i	0.0701490	−	0.997537i	$-0.477653\pi$
$761$	−25.5831	−	25.5831i	−0.927388	−	0.927388i	−0.997537	+	0.0701490i	$0.977653\pi$
$762$		−	16.2164i		−	0.587457i
$763$	−4.42481	+	4.42481i	−0.160189	+	0.160189i
$764$	5.05013			0.182707
$765$	3.15831	−	0.158312i	0.114189	−	0.00572380i
$766$			14.3668i			0.519092i
$767$	−0.316625	−	1.58312i	−0.0114327	−	0.0571633i
$768$	−1.15831	+	1.15831i	−0.0417970	+	0.0417970i
$769$	4.94987	+	4.94987i	0.178497	+	0.178497i	0.790700	−	0.612203i	$-0.209717\pi$
$769$	4.94987	+	4.94987i	0.178497	+	0.178497i	−0.612203	+	0.790700i	$0.709717\pi$
$770$	−1.57519	−	31.4248i	−0.0567659	−	1.13247i
$771$		−	27.4327i		−	0.987966i
$772$	−10.9499			−0.394095
$773$			22.5831i			0.812259i	0.913816	+	0.406129i	$0.133122\pi$
$773$			22.5831i			0.812259i	−0.913816	+	0.406129i	$0.866878\pi$
$774$	−0.783626	+	0.783626i	−0.0281669	+	0.0281669i
$775$	−5.47494	−	4.47494i	−0.196666	−	0.160744i
$776$	−8.94987			−0.321282
$777$	10.4248	−	10.4248i	0.373988	−	0.373988i
$778$	−13.8997			−0.498330
$779$	25.2665			0.905266
$780$	−11.3417	−	6.76650i	−0.406098	−	0.242280i
$781$	−18.8496			−0.674493
$782$	−20.9499			−0.749166
$783$	−24.2665	+	24.2665i	−0.867214	+	0.867214i
$784$	−2.00000			−0.0714286
$785$	31.5831	−	1.58312i	1.12725	−	0.0565041i
$786$	−3.47494	+	3.47494i	−0.123947	+	0.123947i
$787$		−	25.8997i		−	0.923226i	−0.887081	−	0.461613i	$-0.847271\pi$
$787$		−	25.8997i		−	0.923226i	0.887081	−	0.461613i	$-0.152729\pi$
$788$	3.94987			0.140708
$789$		−	28.5330i		−	1.01580i
$790$	−21.4749	−	19.4248i	−0.764044	−	0.691104i
$791$	8.05013	+	8.05013i	0.286230	+	0.286230i
$792$	1.05013	−	1.05013i	0.0373146	−	0.0373146i
$793$	−4.00000	+	6.00000i	−0.142044	+	0.213066i
$794$		−	18.0000i		−	0.638796i
$795$	37.0079	+	33.4749i	1.31254	+	1.18723i
$796$	−16.9499			−0.600772
$797$	−7.26650	+	7.26650i	−0.257393	+	0.257393i	−0.823993	−	0.566600i	$-0.808258\pi$
$797$	−7.26650	+	7.26650i	−0.257393	+	0.257393i	0.566600	+	0.823993i	$0.308258\pi$
$798$		−	13.8997i		−	0.492046i
$799$	−29.4248	−	29.4248i	−1.04098	−	1.04098i
$800$	0.500000	+	4.97494i	0.0176777	+	0.175891i
$801$	−0.100251	−	0.100251i	−0.00354220	−	0.00354220i
$802$	10.5831	+	10.5831i	0.373703	+	0.373703i
$803$	−13.2665	−	13.2665i	−0.468165	−	0.468165i
$804$	5.73350	−	5.73350i	0.202205	−	0.202205i
$805$	1.57519	+	31.4248i	0.0555181	+	1.10758i
$806$	−1.00000	−	5.00000i	−0.0352235	−	0.176117i
$807$	15.3668	+	15.3668i	0.540935	+	0.540935i
$808$			19.2665i			0.677793i
$809$		−	14.3668i		−	0.505108i	−0.967583	−	0.252554i	$-0.918729\pi$
$809$		−	14.3668i		−	0.505108i	0.967583	−	0.252554i	$-0.0812705\pi$
$810$	−11.9248	+	13.1834i	−0.418995	+	0.463217i
$811$	22.9499	−	22.9499i	0.805879	−	0.805879i	−0.178128	−	0.984007i	$-0.557004\pi$
$811$	22.9499	−	22.9499i	0.805879	−	0.805879i	0.984007	+	0.178128i	$0.0570042\pi$
$812$	18.9499			0.665010
$813$	24.3826			0.855136
$814$	9.94987	−	9.94987i	0.348743	−	0.348743i
$815$	4.42481	−	4.89181i	0.154994	−	0.171353i
$816$			7.31662i			0.256133i
$817$			9.89975i			0.346348i
$818$	23.9499	+	23.9499i	0.837388	+	0.837388i
$819$	1.89975	−	2.84962i	0.0663826	−	0.0995739i
$820$	1.00000	+	19.9499i	0.0349215	+	0.696680i
$821$	−24.7916	+	24.7916i	−0.865231	+	0.865231i	−0.991940	−	0.126709i	$-0.959559\pi$
$821$	−24.7916	+	24.7916i	−0.865231	+	0.865231i	0.126709	+	0.991940i	$0.459559\pi$
$822$	6.58312	+	6.58312i	0.229613	+	0.229613i
$823$	−27.8997	−	27.8997i	−0.972524	−	0.972524i	0.0271084	−	0.999632i	$-0.491370\pi$
$823$	−27.8997	−	27.8997i	−0.972524	−	0.972524i	−0.999632	+	0.0271084i	$0.991370\pi$
$824$	−7.94987	−	7.94987i	−0.276947	−	0.276947i
$825$	3.84169	+	38.2243i	0.133750	+	1.33080i
$826$	0.949874	+	0.949874i	0.0330504	+	0.0330504i
$827$		−	31.2665i		−	1.08724i	−0.839331	−	0.543621i	$-0.817053\pi$
$827$		−	31.2665i		−	1.08724i	0.839331	−	0.543621i	$-0.182947\pi$
$828$	−1.05013	+	1.05013i	−0.0364944	+	0.0364944i
$829$	−30.8496			−1.07145			−0.535726	−	0.844392i	$-0.679962\pi$
$829$	−30.8496			−1.07145			−0.535726	+	0.844392i	$0.679962\pi$
$830$	10.4749	+	9.47494i	0.363590	+	0.328880i
$831$		−	50.7335i		−	1.75993i
$832$	−2.00000	+	3.00000i	−0.0693375	+	0.104006i
$833$	−6.31662	+	6.31662i	−0.218858	+	0.218858i
$834$	−18.4749	−	18.4749i	−0.639735	−	0.639735i
$835$	20.9499	+	18.9499i	0.725000	+	0.655787i
$836$		−	13.2665i		−	0.458831i
$837$	−7.68338			−0.265576
$838$		−	8.68338i		−	0.299962i
$839$	21.6332	−	21.6332i	0.746863	−	0.746863i	−0.227026	−	0.973889i	$-0.572900\pi$
$839$	21.6332	−	21.6332i	0.746863	−	0.746863i	0.973889	+	0.227026i	$0.0729002\pi$
$840$	10.9749	−	0.550126i	0.378671	−	0.0189811i
$841$	−10.8997			−0.375853
$842$	2.47494	−	2.47494i	0.0852920	−	0.0852920i
$843$	27.0660			0.932202
$844$	−19.9499			−0.686703
$845$	−27.3997	−	9.70844i	−0.942580	−	0.333980i
$846$	−2.94987			−0.101419
$847$	−33.0000			−1.13389
$848$	9.63325	−	9.63325i	0.330807	−	0.330807i
$849$	−18.4169			−0.632066
$850$	17.2916	+	14.1332i	0.593096	+	0.484766i
$851$	−9.94987	+	9.94987i	−0.341077	+	0.341077i
$852$		−	6.58312i		−	0.225534i
$853$	4.05013			0.138674			0.0693368	−	0.997593i	$-0.477912\pi$
$853$	4.05013			0.138674			0.0693368	+	0.997593i	$0.477912\pi$
$854$		−	6.00000i		−	0.205316i
$855$	−0.100251	−	2.00000i	−0.00342852	−	0.0683986i
$856$	9.63325	+	9.63325i	0.329258	+	0.329258i
$857$	−15.3166	+	15.3166i	−0.523206	+	0.523206i	−0.918538	−	0.395332i	$-0.870629\pi$
$857$	−15.3166	+	15.3166i	−0.523206	+	0.523206i	0.395332	+	0.918538i	$0.370629\pi$
$858$	−15.3668	+	23.0501i	−0.524612	+	0.786918i
$859$			19.8997i			0.678971i	0.940611	+	0.339485i	$0.110253\pi$
$859$			19.8997i			0.678971i	−0.940611	+	0.339485i	$0.889747\pi$
$860$	−7.81662	+	0.391813i	−0.266545	+	0.0133607i
$861$	43.8997			1.49610
$862$	−12.1583	+	12.1583i	−0.414114	+	0.414114i
$863$			22.5831i			0.768738i	0.923179	+	0.384369i	$0.125581\pi$
$863$			22.5831i			0.768738i	−0.923179	+	0.384369i	$0.874419\pi$
$864$	3.84169	+	3.84169i	0.130697	+	0.130697i
$865$	10.4749	−	0.525063i	0.356159	−	0.0178527i
$866$	−12.5251	−	12.5251i	−0.425619	−	0.425619i
$867$	3.41688	+	3.41688i	0.116043	+	0.116043i
$868$	3.00000	+	3.00000i	0.101827	+	0.101827i
$869$	−42.9499	+	42.9499i	−1.45697	+	1.45697i
$870$	−23.1082	+	1.15831i	−0.783441	+	0.0392705i
$871$	9.89975	−	14.8496i	0.335440	−	0.503160i
$872$	−1.47494	−	1.47494i	−0.0499477	−	0.0499477i
$873$			2.83375i			0.0959080i
$874$			13.2665i			0.448746i
$875$	19.8997	−	27.0000i	0.672734	−	0.912767i
$876$	4.63325	−	4.63325i	0.156543	−	0.156543i
$877$	−6.05013			−0.204298			−0.102149	−	0.994769i	$-0.532572\pi$
$877$	−6.05013			−0.204298			−0.102149	+	0.994769i	$0.532572\pi$
$878$	−33.8997			−1.14406
$879$	26.5251	−	26.5251i	0.894668	−	0.894668i
$880$	10.4749	−	0.525063i	0.353110	−	0.0176999i
$881$			16.5831i			0.558700i	0.960189	+	0.279350i	$0.0901189\pi$
$881$			16.5831i			0.558700i	−0.960189	+	0.279350i	$0.909881\pi$
$882$			0.633250i			0.0213226i
$883$	−24.4248	−	24.4248i	−0.821960	−	0.821960i	0.164429	−	0.986389i	$-0.447422\pi$
$883$	−24.4248	−	24.4248i	−0.821960	−	0.821960i	−0.986389	+	0.164429i	$0.947422\pi$
$884$	3.15831	+	15.7916i	0.106226	+	0.531128i
$885$	−1.21637	−	1.10025i	−0.0408879	−	0.0369845i
$886$	−20.0581	+	20.0581i	−0.673864	+	0.673864i
$887$	5.36675	+	5.36675i	0.180198	+	0.180198i	0.791442	−	0.611244i	$-0.209331\pi$
$887$	5.36675	+	5.36675i	0.180198	+	0.180198i	−0.611244	+	0.791442i	$0.709331\pi$
$888$	3.47494	+	3.47494i	0.116611	+	0.116611i
$889$	21.0000	+	21.0000i	0.704317	+	0.704317i
$890$	−0.0501256	−	1.00000i	−0.00168021	−	0.0335201i
$891$	26.3668	+	26.3668i	0.883319	+	0.883319i
$892$		−	15.9499i		−	0.534041i
$893$	−18.6332	+	18.6332i	−0.623538	+	0.623538i
$894$	35.4829			1.18672
$895$	−22.5000	+	24.8747i	−0.752092	+	0.831469i
$896$		−	3.00000i		−	0.100223i
$897$	15.3668	−	23.0501i	0.513081	−	0.769621i
$898$	−21.6332	+	21.6332i	−0.721911	+	0.721911i
$899$	−6.31662	−	6.31662i	−0.210671	−	0.210671i
$900$	1.57519	−	0.158312i	0.0525063	−	0.00527708i
$901$		−	60.8496i		−	2.02719i
$902$	41.8997			1.39511
$903$			17.2005i			0.572397i
$904$	−2.68338	+	2.68338i	−0.0892477	+	0.0892477i
$905$	−11.5251	−	10.4248i	−0.383106	−	0.346532i
$906$	10.3668			0.344412
$907$	−32.3246	+	32.3246i	−1.07332	+	1.07332i	−0.0762291	+	0.997090i	$0.524288\pi$
$907$	−32.3246	+	32.3246i	−1.07332	+	1.07332i	−0.997090	+	0.0762291i	$0.975712\pi$
$908$	−18.0000			−0.597351
$909$	6.10025			0.202333
$910$	23.4499	−	5.92481i	0.777356	−	0.196406i
$911$	−11.0501			−0.366107			−0.183053	−	0.983103i	$-0.558598\pi$
$911$	−11.0501			−0.366107			−0.183053	+	0.983103i	$0.558598\pi$
$912$	4.63325			0.153422
$913$	20.9499	−	20.9499i	0.693340	−	0.693340i
$914$	−2.00000			−0.0661541
$915$	0.366750	+	7.31662i	0.0121244	+	0.241880i
$916$	3.52506	−	3.52506i	0.116471	−	0.116471i
$917$		−	9.00000i		−	0.297206i
$918$	24.2665			0.800914
$919$		−	10.1003i		−	0.333177i	−0.986027	−	0.166588i	$-0.946725\pi$
$919$		−	10.1003i		−	0.333177i	0.986027	−	0.166588i	$-0.0532751\pi$
$920$	−10.4749	+	0.525063i	−0.345348	+	0.0173108i
$921$	30.0000	+	30.0000i	0.988534	+	0.988534i
$922$	−4.10819	+	4.10819i	−0.135296	+	0.135296i
$923$	−2.84169	−	14.2084i	−0.0935353	−	0.467676i
$924$		−	23.0501i		−	0.758293i
$925$	14.9248	−	1.50000i	0.490725	−	0.0493197i
$926$	−9.89975			−0.325326
$927$	−2.51713	+	2.51713i	−0.0826733	+	0.0826733i
$928$			6.31662i			0.207353i
$929$	−13.5831	−	13.5831i	−0.445648	−	0.445648i	0.448257	−	0.893905i	$-0.352045\pi$
$929$	−13.5831	−	13.5831i	−0.445648	−	0.445648i	−0.893905	+	0.448257i	$0.852045\pi$
$930$	−3.84169	−	3.47494i	−0.125974	−	0.113948i
$931$	4.00000	+	4.00000i	0.131095	+	0.131095i
$932$	6.79156	+	6.79156i	0.222465	+	0.222465i
$933$	22.3166	+	22.3166i	0.730613	+	0.730613i
$934$	8.36675	−	8.36675i	0.273768	−	0.273768i
$935$	31.4248	−	34.7414i	1.02770	−	1.13617i
$936$	0.949874	+	0.633250i	0.0310476	+	0.0206984i
$937$	1.94987	+	1.94987i	0.0636996	+	0.0636996i	0.738239	−	0.674539i	$-0.235658\pi$
$937$	1.94987	+	1.94987i	0.0636996	+	0.0636996i	−0.674539	+	0.738239i	$0.735658\pi$
$938$			14.8496i			0.484857i
$939$		−	35.7335i		−	1.16612i
$940$	−15.4499	−	13.9749i	−0.503919	−	0.455812i
$941$	−1.74144	+	1.74144i	−0.0567692	+	0.0567692i	−0.734921	−	0.678152i	$-0.762781\pi$
$941$	−1.74144	+	1.74144i	−0.0567692	+	0.0567692i	0.678152	+	0.734921i	$0.262781\pi$
$942$	23.1662			0.754797
$943$	−41.8997			−1.36444
$944$	−0.316625	+	0.316625i	−0.0103053	+	0.0103053i
$945$	−1.82456	−	36.3997i	−0.0593530	−	1.18408i
$946$			16.4169i			0.533759i
$947$			5.68338i			0.184685i	0.995727	+	0.0923424i	$0.0294354\pi$
$947$			5.68338i			0.184685i	−0.995727	+	0.0923424i	$0.970565\pi$
$948$	−15.0000	−	15.0000i	−0.487177	−	0.487177i
$949$	8.00000	−	12.0000i	0.259691	−	0.389536i
$950$	8.94987	−	10.9499i	0.290372	−	0.355261i
$951$	−13.8997	+	13.8997i	−0.450730	+	0.450730i
$952$	−9.47494	−	9.47494i	−0.307084	−	0.307084i
$953$	−21.0079	−	21.0079i	−0.680514	−	0.680514i	0.279602	−	0.960116i	$-0.409797\pi$
$953$	−21.0079	−	21.0079i	−0.680514	−	0.680514i	−0.960116	+	0.279602i	$0.909797\pi$
$954$	−3.05013	−	3.05013i	−0.0987515	−	0.0987515i
$955$	7.57519	−	8.37469i	0.245127	−	0.270998i
$956$	11.8417	+	11.8417i	0.382988	+	0.382988i
$957$			48.5330i			1.56885i
$958$	−3.15831	+	3.15831i	−0.102040	+	0.102040i
$959$	−17.0501			−0.550577
$960$	0.183375	+	3.65831i	0.00591841	+	0.118072i
$961$			29.0000i			0.935484i
$962$	9.00000	+	6.00000i	0.290172	+	0.193448i
$963$	3.05013	−	3.05013i	0.0982889	−	0.0982889i
$964$	16.0000	+	16.0000i	0.515325	+	0.515325i
$965$	−16.4248	+	18.1583i	−0.528733	+	0.584537i
$966$			23.0501i			0.741626i
$967$	−36.0501			−1.15929			−0.579647	−	0.814868i	$-0.696810\pi$
$967$	−36.0501			−1.15929			−0.579647	+	0.814868i	$0.696810\pi$
$968$		−	11.0000i		−	0.353553i
$969$	14.6332	−	14.6332i	0.470088	−	0.470088i
$970$	−13.4248	+	14.8417i	−0.431045	+	0.476538i
$971$	20.0501			0.643439			0.321720	−	0.946835i	$-0.395739\pi$
$971$	20.0501			0.643439			0.321720	+	0.946835i	$0.395739\pi$
$972$	2.31662	−	2.31662i	0.0743058	−	0.0743058i
$973$	47.8496			1.53399
$974$	−2.00000			−0.0640841
$975$	−28.2335	+	8.65831i	−0.904196	+	0.277288i
$976$	2.00000			0.0640184
$977$	35.0501			1.12135			0.560676	−	0.828035i	$-0.310541\pi$
$977$	35.0501			1.12135			0.560676	+	0.828035i	$0.310541\pi$
$978$	3.41688	−	3.41688i	0.109260	−	0.109260i
$979$	−2.10025			−0.0671243
$980$	−3.00000	+	3.31662i	−0.0958315	+	0.105946i
$981$	−0.467002	+	0.467002i	−0.0149102	+	0.0149102i
$982$		−	32.6834i		−	1.04297i
$983$	−2.05013			−0.0653889			−0.0326944	−	0.999465i	$-0.510409\pi$
$983$	−2.05013			−0.0653889			−0.0326944	+	0.999465i	$0.510409\pi$
$984$			14.6332i			0.466491i
$985$	5.92481	−	6.55013i	0.188780	−	0.208704i
$986$	19.9499	+	19.9499i	0.635333	+	0.635333i
$987$	−32.3747	+	32.3747i	−1.03050	+	1.03050i
$988$	10.0000	−	2.00000i	0.318142	−	0.0636285i
$989$		−	16.4169i		−	0.522026i
$990$	−0.166248	−	3.31662i	−0.00528371	−	0.105409i
$991$	59.7995			1.89959			0.949797	−	0.312867i	$-0.101290\pi$
$991$	59.7995			1.89959			0.949797	+	0.312867i	$0.101290\pi$
$992$	−1.00000	+	1.00000i	−0.0317500	+	0.0317500i
$993$			2.31662i			0.0735159i
$994$	8.52506	+	8.52506i	0.270399	+	0.270399i
$995$	−25.4248	+	28.1082i	−0.806021	+	0.891089i
$996$	7.31662	+	7.31662i	0.231836	+	0.231836i
$997$	8.89975	+	8.89975i	0.281858	+	0.281858i	0.833850	−	0.551992i	$-0.186132\pi$
$997$	8.89975	+	8.89975i	0.281858	+	0.281858i	−0.551992	+	0.833850i	$0.686132\pi$
$998$	8.94987	+	8.94987i	0.283303	+	0.283303i
$999$	11.5251	−	11.5251i	0.364637	−	0.364637i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.2.g.d.57.1	✓	4
3.2	odd	2		1170.2.m.e.577.2		4
4.3	odd	2		1040.2.bg.k.577.2		4
5.2	odd	4		650.2.j.f.343.2		4
5.3	odd	4		130.2.j.d.83.1	yes	4
5.4	even	2		650.2.g.g.57.2		4
13.8	odd	4		130.2.j.d.47.1	yes	4
15.8	even	4		1170.2.w.e.343.1		4
20.3	even	4		1040.2.cd.i.993.2		4
39.8	even	4		1170.2.w.e.307.1		4
52.47	even	4		1040.2.cd.i.177.2		4
65.8	even	4	inner	130.2.g.d.73.1	yes	4
65.34	odd	4		650.2.j.f.307.2		4
65.47	even	4		650.2.g.g.593.2		4
195.8	odd	4		1170.2.m.e.73.1		4
260.203	odd	4		1040.2.bg.k.593.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.g.d.57.1	✓	4	1.1	even	1	trivial
130.2.g.d.73.1	yes	4	65.8	even	4	inner
130.2.j.d.47.1	yes	4	13.8	odd	4
130.2.j.d.83.1	yes	4	5.3	odd	4
650.2.g.g.57.2		4	5.4	even	2
650.2.g.g.593.2		4	65.47	even	4
650.2.j.f.307.2		4	65.34	odd	4
650.2.j.f.343.2		4	5.2	odd	4
1040.2.bg.k.577.2		4	4.3	odd	2
1040.2.bg.k.593.2		4	260.203	odd	4
1040.2.cd.i.177.2		4	52.47	even	4
1040.2.cd.i.993.2		4	20.3	even	4
1170.2.m.e.73.1		4	195.8	odd	4
1170.2.m.e.577.2		4	3.2	odd	2
1170.2.w.e.307.1		4	39.8	even	4
1170.2.w.e.343.1		4	15.8	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	130.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.15831 + 1.15831i) q^{3} +1.00000 q^{4} +(1.50000 - 1.65831i) q^{5} +(1.15831 - 1.15831i) q^{6} +3.00000i q^{7} -1.00000 q^{8} +0.316625i q^{9} +(-1.50000 + 1.65831i) q^{10} +(3.31662 + 3.31662i) q^{11} +(-1.15831 + 1.15831i) q^{12} +(-2.00000 + 3.00000i) q^{13} -3.00000i q^{14} +(0.183375 + 3.65831i) q^{15} +1.00000 q^{16} +(3.15831 - 3.15831i) q^{17} -0.316625i q^{18} +(-2.00000 - 2.00000i) q^{19} +(1.50000 - 1.65831i) q^{20} +(-3.47494 - 3.47494i) q^{21} +(-3.31662 - 3.31662i) q^{22} +(3.31662 + 3.31662i) q^{23} +(1.15831 - 1.15831i) q^{24} +(-0.500000 - 4.97494i) q^{25} +(2.00000 - 3.00000i) q^{26} +(-3.84169 - 3.84169i) q^{27} +3.00000i q^{28} -6.31662i q^{29} +(-0.183375 - 3.65831i) q^{30} +(1.00000 - 1.00000i) q^{31} -1.00000 q^{32} -7.68338 q^{33} +(-3.15831 + 3.15831i) q^{34} +(4.97494 + 4.50000i) q^{35} +0.316625i q^{36} +3.00000i q^{37} +(2.00000 + 2.00000i) q^{38} +(-1.15831 - 5.79156i) q^{39} +(-1.50000 + 1.65831i) q^{40} +(-6.31662 + 6.31662i) q^{41} +(3.47494 + 3.47494i) q^{42} +(-2.47494 - 2.47494i) q^{43} +(3.31662 + 3.31662i) q^{44} +(0.525063 + 0.474937i) q^{45} +(-3.31662 - 3.31662i) q^{46} -9.31662i q^{47} +(-1.15831 + 1.15831i) q^{48} -2.00000 q^{49} +(0.500000 + 4.97494i) q^{50} +7.31662i q^{51} +(-2.00000 + 3.00000i) q^{52} +(9.63325 - 9.63325i) q^{53} +(3.84169 + 3.84169i) q^{54} +(10.4749 - 0.525063i) q^{55} -3.00000i q^{56} +4.63325 q^{57} +6.31662i q^{58} +(-0.316625 + 0.316625i) q^{59} +(0.183375 + 3.65831i) q^{60} +2.00000 q^{61} +(-1.00000 + 1.00000i) q^{62} -0.949874 q^{63} +1.00000 q^{64} +(1.97494 + 7.81662i) q^{65} +7.68338 q^{66} -4.94987 q^{67} +(3.15831 - 3.15831i) q^{68} -7.68338 q^{69} +(-4.97494 - 4.50000i) q^{70} +(-2.84169 + 2.84169i) q^{71} -0.316625i q^{72} -4.00000 q^{73} -3.00000i q^{74} +(6.34169 + 5.18338i) q^{75} +(-2.00000 - 2.00000i) q^{76} +(-9.94987 + 9.94987i) q^{77} +(1.15831 + 5.79156i) q^{78} +12.9499i q^{79} +(1.50000 - 1.65831i) q^{80} +7.94987 q^{81} +(6.31662 - 6.31662i) q^{82} -6.31662i q^{83} +(-3.47494 - 3.47494i) q^{84} +(-0.500000 - 9.97494i) q^{85} +(2.47494 + 2.47494i) q^{86} +(7.31662 + 7.31662i) q^{87} +(-3.31662 - 3.31662i) q^{88} +(-0.316625 + 0.316625i) q^{89} +(-0.525063 - 0.474937i) q^{90} +(-9.00000 - 6.00000i) q^{91} +(3.31662 + 3.31662i) q^{92} +2.31662i q^{93} +9.31662i q^{94} +(-6.31662 + 0.316625i) q^{95} +(1.15831 - 1.15831i) q^{96} +8.94987 q^{97} +2.00000 q^{98} +(-1.05013 + 1.05013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 2 q^{3} + 4 q^{4} + 6 q^{5} - 2 q^{6} - 4 q^{8} - 6 q^{10} + 2 q^{12} - 8 q^{13} + 14 q^{15} + 4 q^{16} + 6 q^{17} - 8 q^{19} + 6 q^{20} + 6 q^{21} - 2 q^{24} - 2 q^{25} + 8 q^{26} - 22 q^{27}+ \cdots - 44 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 2 * q^3 + 4 * q^4 + 6 * q^5 - 2 * q^6 - 4 * q^8 - 6 * q^10 + 2 * q^12 - 8 * q^13 + 14 * q^15 + 4 * q^16 + 6 * q^17 - 8 * q^19 + 6 * q^20 + 6 * q^21 - 2 * q^24 - 2 * q^25 + 8 * q^26 - 22 * q^27 - 14 * q^30 + 4 * q^31 - 4 * q^32 - 44 * q^33 - 6 * q^34 + 8 * q^38 + 2 * q^39 - 6 * q^40 - 12 * q^41 - 6 * q^42 + 10 * q^43 + 22 * q^45 + 2 * q^48 - 8 * q^49 + 2 * q^50 - 8 * q^52 + 12 * q^53 + 22 * q^54 + 22 * q^55 - 8 * q^57 + 12 * q^59 + 14 * q^60 + 8 * q^61 - 4 * q^62 + 36 * q^63 + 4 * q^64 - 12 * q^65 + 44 * q^66 + 20 * q^67 + 6 * q^68 - 44 * q^69 - 18 * q^71 - 16 * q^73 + 32 * q^75 - 8 * q^76 - 2 * q^78 + 6 * q^80 - 8 * q^81 + 12 * q^82 + 6 * q^84 - 2 * q^85 - 10 * q^86 + 16 * q^87 + 12 * q^89 - 22 * q^90 - 36 * q^91 - 12 * q^95 - 2 * q^96 - 4 * q^97 + 8 * q^98 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more