LMFDB - Embedded newform 170.2.g.e.89.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(89,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("170.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.g (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:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			89.1
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	170.89
Dual form			170.2.g.e.149.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.70711 - 1.70711i) q^{3} +1.00000 q^{4} +(2.12132 + 0.707107i) q^{5} +(1.70711 + 1.70711i) q^{6} +(1.00000 - 1.00000i) q^{7} -1.00000 q^{8} +2.82843i q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.70711 - 1.70711i) q^{3} +1.00000 q^{4} +(2.12132 + 0.707107i) q^{5} +(1.70711 + 1.70711i) q^{6} +(1.00000 - 1.00000i) q^{7} -1.00000 q^{8} +2.82843i q^{9} +(-2.12132 - 0.707107i) q^{10} +(-4.41421 - 4.41421i) q^{11} +(-1.70711 - 1.70711i) q^{12} -3.00000i q^{13} +(-1.00000 + 1.00000i) q^{14} +(-2.41421 - 4.82843i) q^{15} +1.00000 q^{16} +(2.12132 - 3.53553i) q^{17} -2.82843i q^{18} +1.24264i q^{19} +(2.12132 + 0.707107i) q^{20} -3.41421 q^{21} +(4.41421 + 4.41421i) q^{22} +(-2.82843 + 2.82843i) q^{23} +(1.70711 + 1.70711i) q^{24} +(4.00000 + 3.00000i) q^{25} +3.00000i q^{26} +(-0.292893 + 0.292893i) q^{27} +(1.00000 - 1.00000i) q^{28} +(-0.707107 + 0.707107i) q^{29} +(2.41421 + 4.82843i) q^{30} +(7.36396 - 7.36396i) q^{31} -1.00000 q^{32} +15.0711i q^{33} +(-2.12132 + 3.53553i) q^{34} +(2.82843 - 1.41421i) q^{35} +2.82843i q^{36} +(-3.24264 - 3.24264i) q^{37} -1.24264i q^{38} +(-5.12132 + 5.12132i) q^{39} +(-2.12132 - 0.707107i) q^{40} +(1.58579 + 1.58579i) q^{41} +3.41421 q^{42} +12.2426 q^{43} +(-4.41421 - 4.41421i) q^{44} +(-2.00000 + 6.00000i) q^{45} +(2.82843 - 2.82843i) q^{46} +4.41421i q^{47} +(-1.70711 - 1.70711i) q^{48} +5.00000i q^{49} +(-4.00000 - 3.00000i) q^{50} +(-9.65685 + 2.41421i) q^{51} -3.00000i q^{52} -3.00000 q^{53} +(0.292893 - 0.292893i) q^{54} +(-6.24264 - 12.4853i) q^{55} +(-1.00000 + 1.00000i) q^{56} +(2.12132 - 2.12132i) q^{57} +(0.707107 - 0.707107i) q^{58} +6.89949i q^{59} +(-2.41421 - 4.82843i) q^{60} +(1.87868 + 1.87868i) q^{61} +(-7.36396 + 7.36396i) q^{62} +(2.82843 + 2.82843i) q^{63} +1.00000 q^{64} +(2.12132 - 6.36396i) q^{65} -15.0711i q^{66} +2.48528i q^{67} +(2.12132 - 3.53553i) q^{68} +9.65685 q^{69} +(-2.82843 + 1.41421i) q^{70} +(2.29289 - 2.29289i) q^{71} -2.82843i q^{72} +(4.36396 + 4.36396i) q^{73} +(3.24264 + 3.24264i) q^{74} +(-1.70711 - 11.9497i) q^{75} +1.24264i q^{76} -8.82843 q^{77} +(5.12132 - 5.12132i) q^{78} +(8.24264 + 8.24264i) q^{79} +(2.12132 + 0.707107i) q^{80} +9.48528 q^{81} +(-1.58579 - 1.58579i) q^{82} -4.24264 q^{83} -3.41421 q^{84} +(7.00000 - 6.00000i) q^{85} -12.2426 q^{86} +2.41421 q^{87} +(4.41421 + 4.41421i) q^{88} -5.48528 q^{89} +(2.00000 - 6.00000i) q^{90} +(-3.00000 - 3.00000i) q^{91} +(-2.82843 + 2.82843i) q^{92} -25.1421 q^{93} -4.41421i q^{94} +(-0.878680 + 2.63604i) q^{95} +(1.70711 + 1.70711i) q^{96} +(-4.12132 - 4.12132i) q^{97} -5.00000i q^{98} +(12.4853 - 12.4853i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^6 + 4 * q^7 - 4 * q^8	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{6} + 4 q^{7} - 4 q^{8} - 12 q^{11} - 4 q^{12} - 4 q^{14} - 4 q^{15} + 4 q^{16} - 8 q^{21} + 12 q^{22} + 4 q^{24} + 16 q^{25} - 4 q^{27} + 4 q^{28} + 4 q^{30} + 4 q^{31} - 4 q^{32} + 4 q^{37} - 12 q^{39} + 12 q^{41} + 8 q^{42} + 32 q^{43} - 12 q^{44} - 8 q^{45} - 4 q^{48} - 16 q^{50} - 16 q^{51} - 12 q^{53} + 4 q^{54} - 8 q^{55} - 4 q^{56} - 4 q^{60} + 16 q^{61} - 4 q^{62} + 4 q^{64} + 16 q^{69} + 12 q^{71} - 8 q^{73} - 4 q^{74} - 4 q^{75} - 24 q^{77} + 12 q^{78} + 16 q^{79} + 4 q^{81} - 12 q^{82} - 8 q^{84} + 28 q^{85} - 32 q^{86} + 4 q^{87} + 12 q^{88} + 12 q^{89} + 8 q^{90} - 12 q^{91} - 44 q^{93} - 12 q^{95} + 4 q^{96} - 8 q^{97} + 16 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^6 + 4 * q^7 - 4 * q^8 - 12 * q^11 - 4 * q^12 - 4 * q^14 - 4 * q^15 + 4 * q^16 - 8 * q^21 + 12 * q^22 + 4 * q^24 + 16 * q^25 - 4 * q^27 + 4 * q^28 + 4 * q^30 + 4 * q^31 - 4 * q^32 + 4 * q^37 - 12 * q^39 + 12 * q^41 + 8 * q^42 + 32 * q^43 - 12 * q^44 - 8 * q^45 - 4 * q^48 - 16 * q^50 - 16 * q^51 - 12 * q^53 + 4 * q^54 - 8 * q^55 - 4 * q^56 - 4 * q^60 + 16 * q^61 - 4 * q^62 + 4 * q^64 + 16 * q^69 + 12 * q^71 - 8 * q^73 - 4 * q^74 - 4 * q^75 - 24 * q^77 + 12 * q^78 + 16 * q^79 + 4 * q^81 - 12 * q^82 - 8 * q^84 + 28 * q^85 - 32 * q^86 + 4 * q^87 + 12 * q^88 + 12 * q^89 + 8 * q^90 - 12 * q^91 - 44 * q^93 - 12 * q^95 + 4 * q^96 - 8 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−1.70711	−	1.70711i	−0.985599	−	0.985599i	0.0142992	−	0.999898i	$-0.495448\pi$
$3$	−1.70711	−	1.70711i	−0.985599	−	0.985599i	−0.999898	+	0.0142992i	$0.995448\pi$
$4$	1.00000			0.500000
$5$	2.12132	+	0.707107i	0.948683	+	0.316228i
$5$	2.12132	+	0.707107i	0.948683	+	0.316228i
$6$	1.70711	+	1.70711i	0.696923	+	0.696923i
$7$	1.00000	−	1.00000i	0.377964	−	0.377964i	−0.492403	−	0.870367i	$-0.663881\pi$
$7$	1.00000	−	1.00000i	0.377964	−	0.377964i	0.870367	+	0.492403i	$0.163881\pi$
$8$	−1.00000			−0.353553
$9$			2.82843i			0.942809i
$10$	−2.12132	−	0.707107i	−0.670820	−	0.223607i
$11$	−4.41421	−	4.41421i	−1.33094	−	1.33094i	−0.904534	−	0.426401i	$-0.859781\pi$
$11$	−4.41421	−	4.41421i	−1.33094	−	1.33094i	−0.426401	−	0.904534i	$-0.640219\pi$
$12$	−1.70711	−	1.70711i	−0.492799	−	0.492799i
$13$		−	3.00000i		−	0.832050i	−0.909353	−	0.416025i	$-0.863423\pi$
$13$		−	3.00000i		−	0.832050i	0.909353	−	0.416025i	$-0.136577\pi$
$14$	−1.00000	+	1.00000i	−0.267261	+	0.267261i
$15$	−2.41421	−	4.82843i	−0.623347	−	1.24669i
$16$	1.00000			0.250000
$17$	2.12132	−	3.53553i	0.514496	−	0.857493i
$17$	2.12132	−	3.53553i	0.514496	−	0.857493i
$18$		−	2.82843i		−	0.666667i
$19$			1.24264i			0.285081i	0.989789	+	0.142541i	$0.0455272\pi$
$19$			1.24264i			0.285081i	−0.989789	+	0.142541i	$0.954473\pi$
$20$	2.12132	+	0.707107i	0.474342	+	0.158114i
$21$	−3.41421			−0.745042
$22$	4.41421	+	4.41421i	0.941113	+	0.941113i
$23$	−2.82843	+	2.82843i	−0.589768	+	0.589768i	−0.937568	−	0.347801i	$-0.886929\pi$
$23$	−2.82843	+	2.82843i	−0.589768	+	0.589768i	0.347801	+	0.937568i	$0.386929\pi$
$24$	1.70711	+	1.70711i	0.348462	+	0.348462i
$25$	4.00000	+	3.00000i	0.800000	+	0.600000i
$26$			3.00000i			0.588348i
$27$	−0.292893	+	0.292893i	−0.0563673	+	0.0563673i
$28$	1.00000	−	1.00000i	0.188982	−	0.188982i
$29$	−0.707107	+	0.707107i	−0.131306	+	0.131306i	−0.769706	−	0.638399i	$-0.779597\pi$
$29$	−0.707107	+	0.707107i	−0.131306	+	0.131306i	0.638399	+	0.769706i	$0.279597\pi$
$30$	2.41421	+	4.82843i	0.440773	+	0.881546i
$31$	7.36396	−	7.36396i	1.32261	−	1.32261i	0.410947	−	0.911659i	$-0.365198\pi$
$31$	7.36396	−	7.36396i	1.32261	−	1.32261i	0.911659	−	0.410947i	$-0.134802\pi$
$32$	−1.00000			−0.176777
$33$			15.0711i			2.62354i
$34$	−2.12132	+	3.53553i	−0.363803	+	0.606339i
$35$	2.82843	−	1.41421i	0.478091	−	0.239046i
$36$			2.82843i			0.471405i
$37$	−3.24264	−	3.24264i	−0.533087	−	0.533087i	0.388403	−	0.921490i	$-0.373027\pi$
$37$	−3.24264	−	3.24264i	−0.533087	−	0.533087i	−0.921490	+	0.388403i	$0.873027\pi$
$38$		−	1.24264i		−	0.201583i
$39$	−5.12132	+	5.12132i	−0.820068	+	0.820068i
$40$	−2.12132	−	0.707107i	−0.335410	−	0.111803i
$41$	1.58579	+	1.58579i	0.247658	+	0.247658i	0.820009	−	0.572351i	$-0.193968\pi$
$41$	1.58579	+	1.58579i	0.247658	+	0.247658i	−0.572351	+	0.820009i	$0.693968\pi$
$42$	3.41421			0.526825
$43$	12.2426			1.86699			0.933493	−	0.358597i	$-0.116745\pi$
$43$	12.2426			1.86699			0.933493	+	0.358597i	$0.116745\pi$
$44$	−4.41421	−	4.41421i	−0.665468	−	0.665468i
$45$	−2.00000	+	6.00000i	−0.298142	+	0.894427i
$46$	2.82843	−	2.82843i	0.417029	−	0.417029i
$47$			4.41421i			0.643879i	0.946760	+	0.321940i	$0.104335\pi$
$47$			4.41421i			0.643879i	−0.946760	+	0.321940i	$0.895665\pi$
$48$	−1.70711	−	1.70711i	−0.246400	−	0.246400i
$49$			5.00000i			0.714286i
$50$	−4.00000	−	3.00000i	−0.565685	−	0.424264i
$51$	−9.65685	+	2.41421i	−1.35223	+	0.338058i
$52$		−	3.00000i		−	0.416025i
$53$	−3.00000			−0.412082			−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000			−0.412082			−0.206041	+	0.978543i	$0.566058\pi$
$54$	0.292893	−	0.292893i	0.0398577	−	0.0398577i
$55$	−6.24264	−	12.4853i	−0.841757	−	1.68351i
$56$	−1.00000	+	1.00000i	−0.133631	+	0.133631i
$57$	2.12132	−	2.12132i	0.280976	−	0.280976i
$58$	0.707107	−	0.707107i	0.0928477	−	0.0928477i
$59$			6.89949i			0.898238i	0.893472	+	0.449119i	$0.148262\pi$
$59$			6.89949i			0.898238i	−0.893472	+	0.449119i	$0.851738\pi$
$60$	−2.41421	−	4.82843i	−0.311674	−	0.623347i
$61$	1.87868	+	1.87868i	0.240540	+	0.240540i	0.817074	−	0.576533i	$-0.195595\pi$
$61$	1.87868	+	1.87868i	0.240540	+	0.240540i	−0.576533	+	0.817074i	$0.695595\pi$
$62$	−7.36396	+	7.36396i	−0.935224	+	0.935224i
$63$	2.82843	+	2.82843i	0.356348	+	0.356348i
$64$	1.00000			0.125000
$65$	2.12132	−	6.36396i	0.263117	−	0.789352i
$66$		−	15.0711i		−	1.85512i
$67$			2.48528i			0.303625i	0.988409	+	0.151813i	$0.0485111\pi$
$67$			2.48528i			0.303625i	−0.988409	+	0.151813i	$0.951489\pi$
$68$	2.12132	−	3.53553i	0.257248	−	0.428746i
$69$	9.65685			1.16255
$70$	−2.82843	+	1.41421i	−0.338062	+	0.169031i
$71$	2.29289	−	2.29289i	0.272116	−	0.272116i	−0.557835	−	0.829952i	$-0.688368\pi$
$71$	2.29289	−	2.29289i	0.272116	−	0.272116i	0.829952	+	0.557835i	$0.188368\pi$
$72$		−	2.82843i		−	0.333333i
$73$	4.36396	+	4.36396i	0.510763	+	0.510763i	0.914760	−	0.403997i	$-0.132379\pi$
$73$	4.36396	+	4.36396i	0.510763	+	0.510763i	−0.403997	+	0.914760i	$0.632379\pi$
$74$	3.24264	+	3.24264i	0.376949	+	0.376949i
$75$	−1.70711	−	11.9497i	−0.197120	−	1.37984i
$76$			1.24264i			0.142541i
$77$	−8.82843			−1.00609
$78$	5.12132	−	5.12132i	0.579875	−	0.579875i
$79$	8.24264	+	8.24264i	0.927370	+	0.927370i	0.997535	−	0.0701658i	$-0.0223528\pi$
$79$	8.24264	+	8.24264i	0.927370	+	0.927370i	−0.0701658	+	0.997535i	$0.522353\pi$
$80$	2.12132	+	0.707107i	0.237171	+	0.0790569i
$81$	9.48528			1.05392
$82$	−1.58579	−	1.58579i	−0.175121	−	0.175121i
$83$	−4.24264			−0.465690			−0.232845	−	0.972514i	$-0.574804\pi$
$83$	−4.24264			−0.465690			−0.232845	+	0.972514i	$0.574804\pi$
$84$	−3.41421			−0.372521
$85$	7.00000	−	6.00000i	0.759257	−	0.650791i
$86$	−12.2426			−1.32016
$87$	2.41421			0.258831
$88$	4.41421	+	4.41421i	0.470557	+	0.470557i
$89$	−5.48528			−0.581439			−0.290719	−	0.956808i	$-0.593895\pi$
$89$	−5.48528			−0.581439			−0.290719	+	0.956808i	$0.593895\pi$
$90$	2.00000	−	6.00000i	0.210819	−	0.632456i
$91$	−3.00000	−	3.00000i	−0.314485	−	0.314485i
$92$	−2.82843	+	2.82843i	−0.294884	+	0.294884i
$93$	−25.1421			−2.60712
$94$		−	4.41421i		−	0.455291i
$95$	−0.878680	+	2.63604i	−0.0901506	+	0.270452i
$96$	1.70711	+	1.70711i	0.174231	+	0.174231i
$97$	−4.12132	−	4.12132i	−0.418457	−	0.418457i	0.466215	−	0.884672i	$-0.345617\pi$
$97$	−4.12132	−	4.12132i	−0.418457	−	0.418457i	−0.884672	+	0.466215i	$0.845617\pi$
$98$		−	5.00000i		−	0.505076i
$99$	12.4853	−	12.4853i	1.25482	−	1.25482i
$100$	4.00000	+	3.00000i	0.400000	+	0.300000i
$101$		0			0			−	1.00000i	$-0.5\pi$
$101$		0			0				1.00000i	$0.5\pi$
$102$	9.65685	−	2.41421i	0.956171	−	0.239043i
$103$		0			0		1.00000			$0$
$103$		0			0		−1.00000			$\pi$
$104$			3.00000i			0.294174i
$105$	−7.24264	−	2.41421i	−0.706809	−	0.235603i
$106$	3.00000			0.291386
$107$	2.82843	+	2.82843i	0.273434	+	0.273434i	0.830481	−	0.557047i	$-0.188066\pi$
$107$	2.82843	+	2.82843i	0.273434	+	0.273434i	−0.557047	+	0.830481i	$0.688066\pi$
$108$	−0.292893	+	0.292893i	−0.0281837	+	0.0281837i
$109$	−12.6066	−	12.6066i	−1.20749	−	1.20749i	−0.971836	−	0.235657i	$-0.924276\pi$
$109$	−12.6066	−	12.6066i	−1.20749	−	1.20749i	−0.235657	−	0.971836i	$-0.575724\pi$
$110$	6.24264	+	12.4853i	0.595212	+	1.19042i
$111$			11.0711i			1.05082i
$112$	1.00000	−	1.00000i	0.0944911	−	0.0944911i
$113$	9.53553	−	9.53553i	0.897028	−	0.897028i	−0.0981446	−	0.995172i	$-0.531291\pi$
$113$	9.53553	−	9.53553i	0.897028	−	0.897028i	0.995172	+	0.0981446i	$0.0312908\pi$
$114$	−2.12132	+	2.12132i	−0.198680	+	0.198680i
$115$	−8.00000	+	4.00000i	−0.746004	+	0.373002i
$116$	−0.707107	+	0.707107i	−0.0656532	+	0.0656532i
$117$	8.48528			0.784465
$118$		−	6.89949i		−	0.635150i
$119$	−1.41421	−	5.65685i	−0.129641	−	0.518563i
$120$	2.41421	+	4.82843i	0.220387	+	0.440773i
$121$			27.9706i			2.54278i
$122$	−1.87868	−	1.87868i	−0.170088	−	0.170088i
$123$		−	5.41421i		−	0.488183i
$124$	7.36396	−	7.36396i	0.661303	−	0.661303i
$125$	6.36396	+	9.19239i	0.569210	+	0.822192i
$126$	−2.82843	−	2.82843i	−0.251976	−	0.251976i
$127$	−7.72792			−0.685742			−0.342871	−	0.939382i	$-0.611399\pi$
$127$	−7.72792			−0.685742			−0.342871	+	0.939382i	$0.611399\pi$
$128$	−1.00000			−0.0883883
$129$	−20.8995	−	20.8995i	−1.84010	−	1.84010i
$130$	−2.12132	+	6.36396i	−0.186052	+	0.558156i
$131$	10.4142	−	10.4142i	0.909894	−	0.909894i	−0.0863691	−	0.996263i	$-0.527526\pi$
$131$	10.4142	−	10.4142i	0.909894	−	0.909894i	0.996263	+	0.0863691i	$0.0275264\pi$
$132$			15.0711i			1.31177i
$133$	1.24264	+	1.24264i	0.107751	+	0.107751i
$134$		−	2.48528i		−	0.214696i
$135$	−0.828427	+	0.414214i	−0.0712997	+	0.0356498i
$136$	−2.12132	+	3.53553i	−0.181902	+	0.303170i
$137$			7.41421i			0.633439i	0.948519	+	0.316720i	$0.102581\pi$
$137$			7.41421i			0.633439i	−0.948519	+	0.316720i	$0.897419\pi$
$138$	−9.65685			−0.822046
$139$	−11.0000	+	11.0000i	−0.933008	+	0.933008i	−0.997893	−	0.0648849i	$-0.979332\pi$
$139$	−11.0000	+	11.0000i	−0.933008	+	0.933008i	0.0648849	+	0.997893i	$0.479332\pi$
$140$	2.82843	−	1.41421i	0.239046	−	0.119523i
$141$	7.53553	−	7.53553i	0.634606	−	0.634606i
$142$	−2.29289	+	2.29289i	−0.192415	+	0.192415i
$143$	−13.2426	+	13.2426i	−1.10741	+	1.10741i
$144$			2.82843i			0.235702i
$145$	−2.00000	+	1.00000i	−0.166091	+	0.0830455i
$146$	−4.36396	−	4.36396i	−0.361164	−	0.361164i
$147$	8.53553	−	8.53553i	0.703999	−	0.703999i
$148$	−3.24264	−	3.24264i	−0.266543	−	0.266543i
$149$	12.7279			1.04271			0.521356	−	0.853339i	$-0.325426\pi$
$149$	12.7279			1.04271			0.521356	+	0.853339i	$0.325426\pi$
$150$	1.70711	+	11.9497i	0.139385	+	0.975693i
$151$			12.0000i			0.976546i	0.872691	+	0.488273i	$0.162373\pi$
$151$			12.0000i			0.976546i	−0.872691	+	0.488273i	$0.837627\pi$
$152$		−	1.24264i		−	0.100791i
$153$	10.0000	+	6.00000i	0.808452	+	0.485071i
$154$	8.82843			0.711415
$155$	20.8284	−	10.4142i	1.67298	−	0.836490i
$156$	−5.12132	+	5.12132i	−0.410034	+	0.410034i
$157$			12.0000i			0.957704i	0.877896	+	0.478852i	$0.158947\pi$
$157$			12.0000i			0.957704i	−0.877896	+	0.478852i	$0.841053\pi$
$158$	−8.24264	−	8.24264i	−0.655749	−	0.655749i
$159$	5.12132	+	5.12132i	0.406147	+	0.406147i
$160$	−2.12132	−	0.707107i	−0.167705	−	0.0559017i
$161$			5.65685i			0.445823i
$162$	−9.48528			−0.745234
$163$	12.4853	−	12.4853i	0.977923	−	0.977923i	−0.0218388	−	0.999762i	$-0.506952\pi$
$163$	12.4853	−	12.4853i	0.977923	−	0.977923i	0.999762	+	0.0218388i	$0.00695206\pi$
$164$	1.58579	+	1.58579i	0.123829	+	0.123829i
$165$	−10.6569	+	31.9706i	−0.829635	+	2.48890i
$166$	4.24264			0.329293
$167$	13.0711	+	13.0711i	1.01147	+	1.01147i	0.999933	+	0.0115361i	$0.00367215\pi$
$167$	13.0711	+	13.0711i	1.01147	+	1.01147i	0.0115361	+	0.999933i	$0.496328\pi$
$168$	3.41421			0.263412
$169$	4.00000			0.307692
$170$	−7.00000	+	6.00000i	−0.536875	+	0.460179i
$171$	−3.51472			−0.268777
$172$	12.2426			0.933493
$173$	6.34315	+	6.34315i	0.482260	+	0.482260i	0.905853	−	0.423592i	$-0.139231\pi$
$173$	6.34315	+	6.34315i	0.482260	+	0.482260i	−0.423592	+	0.905853i	$0.639231\pi$
$174$	−2.41421			−0.183021
$175$	7.00000	−	1.00000i	0.529150	−	0.0755929i
$176$	−4.41421	−	4.41421i	−0.332734	−	0.332734i
$177$	11.7782	−	11.7782i	0.885302	−	0.885302i
$178$	5.48528			0.411139
$179$		−	23.3137i		−	1.74255i	−0.490797	−	0.871274i	$-0.663294\pi$
$179$		−	23.3137i		−	1.74255i	0.490797	−	0.871274i	$-0.336706\pi$
$180$	−2.00000	+	6.00000i	−0.149071	+	0.447214i
$181$	−14.0000	−	14.0000i	−1.04061	−	1.04061i	−0.999140	−	0.0414721i	$-0.986795\pi$
$181$	−14.0000	−	14.0000i	−1.04061	−	1.04061i	−0.0414721	−	0.999140i	$-0.513205\pi$
$182$	3.00000	+	3.00000i	0.222375	+	0.222375i
$183$		−	6.41421i		−	0.474152i
$184$	2.82843	−	2.82843i	0.208514	−	0.208514i
$185$	−4.58579	−	9.17157i	−0.337154	−	0.674307i
$186$	25.1421			1.84351
$187$	−24.9706	+	6.24264i	−1.82603	+	0.456507i
$188$			4.41421i			0.321940i
$189$			0.585786i			0.0426097i
$190$	0.878680	−	2.63604i	0.0637461	−	0.191238i
$191$	−21.2132			−1.53493			−0.767467	−	0.641089i	$-0.778483\pi$
$191$	−21.2132			−1.53493			−0.767467	+	0.641089i	$0.778483\pi$
$192$	−1.70711	−	1.70711i	−0.123200	−	0.123200i
$193$	1.51472	−	1.51472i	0.109032	−	0.109032i	−0.650486	−	0.759518i	$-0.725435\pi$
$193$	1.51472	−	1.51472i	0.109032	−	0.109032i	0.759518	+	0.650486i	$0.225435\pi$
$194$	4.12132	+	4.12132i	0.295894	+	0.295894i
$195$	−14.4853	+	7.24264i	−1.03731	+	0.518656i
$196$			5.00000i			0.357143i
$197$	14.6569	−	14.6569i	1.04426	−	1.04426i	0.0452834	−	0.998974i	$-0.485581\pi$
$197$	14.6569	−	14.6569i	1.04426	−	1.04426i	0.998974	−	0.0452834i	$-0.0144191\pi$
$198$	−12.4853	+	12.4853i	−0.887290	+	0.887290i
$199$	−2.87868	+	2.87868i	−0.204064	+	0.204064i	−0.801739	−	0.597675i	$-0.796091\pi$
$199$	−2.87868	+	2.87868i	−0.204064	+	0.204064i	0.597675	+	0.801739i	$0.296091\pi$
$200$	−4.00000	−	3.00000i	−0.282843	−	0.212132i
$201$	4.24264	−	4.24264i	0.299253	−	0.299253i
$202$		0			0
$203$			1.41421i			0.0992583i
$204$	−9.65685	+	2.41421i	−0.676115	+	0.169029i
$205$	2.24264	+	4.48528i	0.156633	+	0.313266i
$206$		0			0
$207$	−8.00000	−	8.00000i	−0.556038	−	0.556038i
$208$		−	3.00000i		−	0.208013i
$209$	5.48528	−	5.48528i	0.379425	−	0.379425i
$210$	7.24264	+	2.41421i	0.499790	+	0.166597i
$211$	−8.00000	−	8.00000i	−0.550743	−	0.550743i	0.375912	−	0.926655i	$-0.377329\pi$
$211$	−8.00000	−	8.00000i	−0.550743	−	0.550743i	−0.926655	+	0.375912i	$0.877329\pi$
$212$	−3.00000			−0.206041
$213$	−7.82843			−0.536395
$214$	−2.82843	−	2.82843i	−0.193347	−	0.193347i
$215$	25.9706	+	8.65685i	1.77118	+	0.590393i
$216$	0.292893	−	0.292893i	0.0199289	−	0.0199289i
$217$		−	14.7279i		−	0.999796i
$218$	12.6066	+	12.6066i	0.853827	+	0.853827i
$219$		−	14.8995i		−	1.00681i
$220$	−6.24264	−	12.4853i	−0.420879	−	0.841757i
$221$	−10.6066	−	6.36396i	−0.713477	−	0.428086i
$222$		−	11.0711i		−	0.743041i
$223$	−14.7574			−0.988226			−0.494113	−	0.869398i	$-0.664507\pi$
$223$	−14.7574			−0.988226			−0.494113	+	0.869398i	$0.664507\pi$
$224$	−1.00000	+	1.00000i	−0.0668153	+	0.0668153i
$225$	−8.48528	+	11.3137i	−0.565685	+	0.754247i
$226$	−9.53553	+	9.53553i	−0.634294	+	0.634294i
$227$	−13.9497	+	13.9497i	−0.925877	+	0.925877i	−0.997436	−	0.0715591i	$-0.977203\pi$
$227$	−13.9497	+	13.9497i	−0.925877	+	0.925877i	0.0715591	+	0.997436i	$0.477203\pi$
$228$	2.12132	−	2.12132i	0.140488	−	0.140488i
$229$		−	16.2426i		−	1.07334i	−0.843791	−	0.536672i	$-0.819681\pi$
$229$		−	16.2426i		−	1.07334i	0.843791	−	0.536672i	$-0.180319\pi$
$230$	8.00000	−	4.00000i	0.527504	−	0.263752i
$231$	15.0711	+	15.0711i	0.991603	+	0.991603i
$232$	0.707107	−	0.707107i	0.0464238	−	0.0464238i
$233$	−1.05025	−	1.05025i	−0.0688043	−	0.0688043i	0.671867	−	0.740672i	$-0.265493\pi$
$233$	−1.05025	−	1.05025i	−0.0688043	−	0.0688043i	−0.740672	+	0.671867i	$0.765493\pi$
$234$	−8.48528			−0.554700
$235$	−3.12132	+	9.36396i	−0.203612	+	0.610837i
$236$			6.89949i			0.449119i
$237$		−	28.1421i		−	1.82803i
$238$	1.41421	+	5.65685i	0.0916698	+	0.366679i
$239$	13.7574			0.889890			0.444945	−	0.895558i	$-0.353223\pi$
$239$	13.7574			0.889890			0.444945	+	0.895558i	$0.353223\pi$
$240$	−2.41421	−	4.82843i	−0.155837	−	0.311674i
$241$	11.2426	−	11.2426i	0.724202	−	0.724202i	−0.245256	−	0.969458i	$-0.578872\pi$
$241$	11.2426	−	11.2426i	0.724202	−	0.724202i	0.969458	+	0.245256i	$0.0788721\pi$
$242$		−	27.9706i		−	1.79802i
$243$	−15.3137	−	15.3137i	−0.982375	−	0.982375i
$244$	1.87868	+	1.87868i	0.120270	+	0.120270i
$245$	−3.53553	+	10.6066i	−0.225877	+	0.677631i
$246$			5.41421i			0.345198i
$247$	3.72792			0.237202
$248$	−7.36396	+	7.36396i	−0.467612	+	0.467612i
$249$	7.24264	+	7.24264i	0.458984	+	0.458984i
$250$	−6.36396	−	9.19239i	−0.402492	−	0.581378i
$251$	3.51472			0.221847			0.110924	−	0.993829i	$-0.464619\pi$
$251$	3.51472			0.221847			0.110924	+	0.993829i	$0.464619\pi$
$252$	2.82843	+	2.82843i	0.178174	+	0.178174i
$253$	24.9706			1.56989
$254$	7.72792			0.484893
$255$	−22.1924	−	1.70711i	−1.38974	−	0.106903i
$256$	1.00000			0.0625000
$257$	−18.7279			−1.16822			−0.584108	−	0.811676i	$-0.698555\pi$
$257$	−18.7279			−1.16822			−0.584108	+	0.811676i	$0.698555\pi$
$258$	20.8995	+	20.8995i	1.30115	+	1.30115i
$259$	−6.48528			−0.402976
$260$	2.12132	−	6.36396i	0.131559	−	0.394676i
$261$	−2.00000	−	2.00000i	−0.123797	−	0.123797i
$262$	−10.4142	+	10.4142i	−0.643392	+	0.643392i
$263$	13.2426			0.816576			0.408288	−	0.912853i	$-0.366126\pi$
$263$	13.2426			0.816576			0.408288	+	0.912853i	$0.366126\pi$
$264$		−	15.0711i		−	0.927560i
$265$	−6.36396	−	2.12132i	−0.390935	−	0.130312i
$266$	−1.24264	−	1.24264i	−0.0761912	−	0.0761912i
$267$	9.36396	+	9.36396i	0.573065	+	0.573065i
$268$			2.48528i			0.151813i
$269$	−12.7071	+	12.7071i	−0.774766	+	0.774766i	−0.978936	−	0.204170i	$-0.934551\pi$
$269$	−12.7071	+	12.7071i	−0.774766	+	0.774766i	0.204170	+	0.978936i	$0.434551\pi$
$270$	0.828427	−	0.414214i	0.0504165	−	0.0252082i
$271$	10.4853			0.636935			0.318468	−	0.947934i	$-0.396832\pi$
$271$	10.4853			0.636935			0.318468	+	0.947934i	$0.396832\pi$
$272$	2.12132	−	3.53553i	0.128624	−	0.214373i
$273$			10.2426i			0.619913i
$274$		−	7.41421i		−	0.447909i
$275$	−4.41421	−	30.8995i	−0.266187	−	1.86331i
$276$	9.65685			0.581274
$277$	−0.242641	−	0.242641i	−0.0145789	−	0.0145789i	0.699780	−	0.714359i	$-0.253281\pi$
$277$	−0.242641	−	0.242641i	−0.0145789	−	0.0145789i	−0.714359	+	0.699780i	$0.753281\pi$
$278$	11.0000	−	11.0000i	0.659736	−	0.659736i
$279$	20.8284	+	20.8284i	1.24697	+	1.24697i
$280$	−2.82843	+	1.41421i	−0.169031	+	0.0845154i
$281$			14.6569i			0.874355i	0.899375	+	0.437177i	$0.144022\pi$
$281$			14.6569i			0.874355i	−0.899375	+	0.437177i	$0.855978\pi$
$282$	−7.53553	+	7.53553i	−0.448735	+	0.448735i
$283$	−14.8787	+	14.8787i	−0.884446	+	0.884446i	−0.993983	−	0.109537i	$-0.965063\pi$
$283$	−14.8787	+	14.8787i	−0.884446	+	0.884446i	0.109537	+	0.993983i	$0.465063\pi$
$284$	2.29289	−	2.29289i	0.136058	−	0.136058i
$285$	6.00000	−	3.00000i	0.355409	−	0.177705i
$286$	13.2426	−	13.2426i	0.783054	−	0.783054i
$287$	3.17157			0.187212
$288$		−	2.82843i		−	0.166667i
$289$	−8.00000	−	15.0000i	−0.470588	−	0.882353i
$290$	2.00000	−	1.00000i	0.117444	−	0.0587220i
$291$			14.0711i			0.824861i
$292$	4.36396	+	4.36396i	0.255382	+	0.255382i
$293$		−	9.34315i		−	0.545832i	−0.962038	−	0.272916i	$-0.912012\pi$
$293$		−	9.34315i		−	0.545832i	0.962038	−	0.272916i	$-0.0879882\pi$
$294$	−8.53553	+	8.53553i	−0.497802	+	0.497802i
$295$	−4.87868	+	14.6360i	−0.284048	+	0.852143i
$296$	3.24264	+	3.24264i	0.188475	+	0.188475i
$297$	2.58579			0.150043
$298$	−12.7279			−0.737309
$299$	8.48528	+	8.48528i	0.490716	+	0.490716i
$300$	−1.70711	−	11.9497i	−0.0985599	−	0.689919i
$301$	12.2426	−	12.2426i	0.705654	−	0.705654i
$302$		−	12.0000i		−	0.690522i
$303$		0			0
$304$			1.24264i			0.0712703i
$305$	2.65685	+	5.31371i	0.152131	+	0.304262i
$306$	−10.0000	−	6.00000i	−0.571662	−	0.342997i
$307$			9.21320i			0.525825i	0.964820	+	0.262913i	$0.0846831\pi$
$307$			9.21320i			0.525825i	−0.964820	+	0.262913i	$0.915317\pi$
$308$	−8.82843			−0.503046
$309$		0			0
$310$	−20.8284	+	10.4142i	−1.18298	+	0.591488i
$311$	1.41421	−	1.41421i	0.0801927	−	0.0801927i	−0.665873	−	0.746065i	$-0.731941\pi$
$311$	1.41421	−	1.41421i	0.0801927	−	0.0801927i	0.746065	+	0.665873i	$0.231941\pi$
$312$	5.12132	−	5.12132i	0.289938	−	0.289938i
$313$	−5.51472	+	5.51472i	−0.311710	+	0.311710i	−0.845572	−	0.533862i	$-0.820740\pi$
$313$	−5.51472	+	5.51472i	−0.311710	+	0.311710i	0.533862	+	0.845572i	$0.320740\pi$
$314$		−	12.0000i		−	0.677199i
$315$	4.00000	+	8.00000i	0.225374	+	0.450749i
$316$	8.24264	+	8.24264i	0.463685	+	0.463685i
$317$	14.1421	−	14.1421i	0.794301	−	0.794301i	−0.187889	−	0.982190i	$-0.560164\pi$
$317$	14.1421	−	14.1421i	0.794301	−	0.794301i	0.982190	+	0.187889i	$0.0601645\pi$
$318$	−5.12132	−	5.12132i	−0.287189	−	0.287189i
$319$	6.24264			0.349521
$320$	2.12132	+	0.707107i	0.118585	+	0.0395285i
$321$		−	9.65685i		−	0.538993i
$322$		−	5.65685i		−	0.315244i
$323$	4.39340	+	2.63604i	0.244455	+	0.146673i
$324$	9.48528			0.526960
$325$	9.00000	−	12.0000i	0.499230	−	0.665640i
$326$	−12.4853	+	12.4853i	−0.691496	+	0.691496i
$327$			43.0416i			2.38021i
$328$	−1.58579	−	1.58579i	−0.0875604	−	0.0875604i
$329$	4.41421	+	4.41421i	0.243363	+	0.243363i
$330$	10.6569	−	31.9706i	0.586641	−	1.75992i
$331$		−	9.72792i		−	0.534695i	−0.963600	−	0.267347i	$-0.913853\pi$
$331$		−	9.72792i		−	0.534695i	0.963600	−	0.267347i	$-0.0861472\pi$
$332$	−4.24264			−0.232845
$333$	9.17157	−	9.17157i	0.502599	−	0.502599i
$334$	−13.0711	−	13.0711i	−0.715217	−	0.715217i
$335$	−1.75736	+	5.27208i	−0.0960148	+	0.288044i
$336$	−3.41421			−0.186261
$337$	−16.8492	−	16.8492i	−0.917837	−	0.917837i	0.0790351	−	0.996872i	$-0.474816\pi$
$337$	−16.8492	−	16.8492i	−0.917837	−	0.917837i	−0.996872	+	0.0790351i	$0.974816\pi$
$338$	−4.00000			−0.217571
$339$	−32.5563			−1.76822
$340$	7.00000	−	6.00000i	0.379628	−	0.325396i
$341$	−65.0122			−3.52061
$342$	3.51472			0.190054
$343$	12.0000	+	12.0000i	0.647939	+	0.647939i
$344$	−12.2426			−0.660079
$345$	20.4853	+	6.82843i	1.10289	+	0.367630i
$346$	−6.34315	−	6.34315i	−0.341010	−	0.341010i
$347$	14.2929	−	14.2929i	0.767283	−	0.767283i	−0.210345	−	0.977627i	$-0.567459\pi$
$347$	14.2929	−	14.2929i	0.767283	−	0.767283i	0.977627	+	0.210345i	$0.0674586\pi$
$348$	2.41421			0.129415
$349$			22.9706i			1.22959i	0.788688	+	0.614793i	$0.210760\pi$
$349$			22.9706i			1.22959i	−0.788688	+	0.614793i	$0.789240\pi$
$350$	−7.00000	+	1.00000i	−0.374166	+	0.0534522i
$351$	0.878680	+	0.878680i	0.0469005	+	0.0469005i
$352$	4.41421	+	4.41421i	0.235278	+	0.235278i
$353$		−	11.3137i		−	0.602168i	−0.953598	−	0.301084i	$-0.902652\pi$
$353$		−	11.3137i		−	0.602168i	0.953598	−	0.301084i	$-0.0973484\pi$
$354$	−11.7782	+	11.7782i	−0.626003	+	0.626003i
$355$	6.48528	−	3.24264i	0.344203	−	0.172101i
$356$	−5.48528			−0.290719
$357$	−7.24264	+	12.0711i	−0.383321	+	0.638869i
$358$			23.3137i			1.23217i
$359$		−	7.07107i		−	0.373197i	−0.982436	−	0.186598i	$-0.940254\pi$
$359$		−	7.07107i		−	0.373197i	0.982436	−	0.186598i	$-0.0597463\pi$
$360$	2.00000	−	6.00000i	0.105409	−	0.316228i
$361$	17.4558			0.918729
$362$	14.0000	+	14.0000i	0.735824	+	0.735824i
$363$	47.7487	−	47.7487i	2.50616	−	2.50616i
$364$	−3.00000	−	3.00000i	−0.157243	−	0.157243i
$365$	6.17157	+	12.3431i	0.323035	+	0.646070i
$366$			6.41421i			0.335276i
$367$	−9.75736	+	9.75736i	−0.509330	+	0.509330i	−0.914321	−	0.404991i	$-0.867275\pi$
$367$	−9.75736	+	9.75736i	−0.509330	+	0.509330i	0.404991	+	0.914321i	$0.367275\pi$
$368$	−2.82843	+	2.82843i	−0.147442	+	0.147442i
$369$	−4.48528	+	4.48528i	−0.233494	+	0.233494i
$370$	4.58579	+	9.17157i	0.238404	+	0.476807i
$371$	−3.00000	+	3.00000i	−0.155752	+	0.155752i
$372$	−25.1421			−1.30356
$373$			15.5147i			0.803322i	0.915788	+	0.401661i	$0.131567\pi$
$373$			15.5147i			0.803322i	−0.915788	+	0.401661i	$0.868433\pi$
$374$	24.9706	−	6.24264i	1.29120	−	0.322799i
$375$	4.82843	−	26.5563i	0.249339	−	1.37136i
$376$		−	4.41421i		−	0.227646i
$377$	2.12132	+	2.12132i	0.109254	+	0.109254i
$378$		−	0.585786i		−	0.0301296i
$379$	−16.4853	+	16.4853i	−0.846792	+	0.846792i	−0.989731	−	0.142939i	$-0.954345\pi$
$379$	−16.4853	+	16.4853i	−0.846792	+	0.846792i	0.142939	+	0.989731i	$0.454345\pi$
$380$	−0.878680	+	2.63604i	−0.0450753	+	0.135226i
$381$	13.1924	+	13.1924i	0.675867	+	0.675867i
$382$	21.2132			1.08536
$383$	−4.75736			−0.243090			−0.121545	−	0.992586i	$-0.538785\pi$
$383$	−4.75736			−0.243090			−0.121545	+	0.992586i	$0.538785\pi$
$384$	1.70711	+	1.70711i	0.0871154	+	0.0871154i
$385$	−18.7279	−	6.24264i	−0.954463	−	0.318154i
$386$	−1.51472	+	1.51472i	−0.0770971	+	0.0770971i
$387$			34.6274i			1.76021i
$388$	−4.12132	−	4.12132i	−0.209228	−	0.209228i
$389$			28.6274i			1.45147i	0.687976	+	0.725734i	$0.258500\pi$
$389$			28.6274i			1.45147i	−0.687976	+	0.725734i	$0.741500\pi$
$390$	14.4853	−	7.24264i	0.733491	−	0.366745i
$391$	4.00000	+	16.0000i	0.202289	+	0.809155i
$392$		−	5.00000i		−	0.252538i
$393$	−35.5563			−1.79358
$394$	−14.6569	+	14.6569i	−0.738402	+	0.738402i
$395$	11.6569	+	23.3137i	0.586520	+	1.17304i
$396$	12.4853	−	12.4853i	0.627409	−	0.627409i
$397$	−20.7279	+	20.7279i	−1.04030	+	1.04030i	−0.0411517	+	0.999153i	$0.513103\pi$
$397$	−20.7279	+	20.7279i	−1.04030	+	1.04030i	−0.999153	+	0.0411517i	$0.986897\pi$
$398$	2.87868	−	2.87868i	0.144295	−	0.144295i
$399$		−	4.24264i		−	0.212398i
$400$	4.00000	+	3.00000i	0.200000	+	0.150000i
$401$	−21.8995	−	21.8995i	−1.09361	−	1.09361i	−0.995140	−	0.0984684i	$-0.968606\pi$
$401$	−21.8995	−	21.8995i	−1.09361	−	1.09361i	−0.0984684	−	0.995140i	$-0.531394\pi$
$402$	−4.24264	+	4.24264i	−0.211604	+	0.211604i
$403$	−22.0919	−	22.0919i	−1.10048	−	1.10048i
$404$		0			0
$405$	20.1213	+	6.70711i	0.999836	+	0.333279i
$406$		−	1.41421i		−	0.0701862i
$407$			28.6274i			1.41901i
$408$	9.65685	−	2.41421i	0.478086	−	0.119521i
$409$	8.51472			0.421026			0.210513	−	0.977591i	$-0.432487\pi$
$409$	8.51472			0.421026			0.210513	+	0.977591i	$0.432487\pi$
$410$	−2.24264	−	4.48528i	−0.110756	−	0.221512i
$411$	12.6569	−	12.6569i	0.624317	−	0.624317i
$412$		0			0
$413$	6.89949	+	6.89949i	0.339502	+	0.339502i
$414$	8.00000	+	8.00000i	0.393179	+	0.393179i
$415$	−9.00000	−	3.00000i	−0.441793	−	0.147264i
$416$			3.00000i			0.147087i
$417$	37.5563			1.83914
$418$	−5.48528	+	5.48528i	−0.268294	+	0.268294i
$419$	11.3137	+	11.3137i	0.552711	+	0.552711i	0.927222	−	0.374511i	$-0.122190\pi$
$419$	11.3137	+	11.3137i	0.552711	+	0.552711i	−0.374511	+	0.927222i	$0.622190\pi$
$420$	−7.24264	−	2.41421i	−0.353405	−	0.117802i
$421$	23.2132			1.13134			0.565671	−	0.824631i	$-0.308617\pi$
$421$	23.2132			1.13134			0.565671	+	0.824631i	$0.308617\pi$
$422$	8.00000	+	8.00000i	0.389434	+	0.389434i
$423$	−12.4853			−0.607055
$424$	3.00000			0.145693
$425$	19.0919	−	7.77817i	0.926092	−	0.377297i
$426$	7.82843			0.379289
$427$	3.75736			0.181831
$428$	2.82843	+	2.82843i	0.136717	+	0.136717i
$429$	45.2132			2.18291
$430$	−25.9706	−	8.65685i	−1.25241	−	0.417471i
$431$	6.34315	+	6.34315i	0.305539	+	0.305539i	0.843176	−	0.537638i	$-0.180683\pi$
$431$	6.34315	+	6.34315i	0.305539	+	0.305539i	−0.537638	+	0.843176i	$0.680683\pi$
$432$	−0.292893	+	0.292893i	−0.0140918	+	0.0140918i
$433$	−14.2426			−0.684458			−0.342229	−	0.939617i	$-0.611182\pi$
$433$	−14.2426			−0.684458			−0.342229	+	0.939617i	$0.611182\pi$
$434$			14.7279i			0.706963i
$435$	5.12132	+	1.70711i	0.245549	+	0.0818495i
$436$	−12.6066	−	12.6066i	−0.603747	−	0.603747i
$437$	−3.51472	−	3.51472i	−0.168132	−	0.168132i
$438$			14.8995i			0.711925i
$439$	−12.9706	+	12.9706i	−0.619051	+	0.619051i	−0.945288	−	0.326237i	$-0.894219\pi$
$439$	−12.9706	+	12.9706i	−0.619051	+	0.619051i	0.326237	+	0.945288i	$0.394219\pi$
$440$	6.24264	+	12.4853i	0.297606	+	0.595212i
$441$	−14.1421			−0.673435
$442$	10.6066	+	6.36396i	0.504505	+	0.302703i
$443$		−	1.79899i		−	0.0854726i	−0.999086	−	0.0427363i	$-0.986392\pi$
$443$		−	1.79899i		−	0.0854726i	0.999086	−	0.0427363i	$-0.0136075\pi$
$444$			11.0711i			0.525410i
$445$	−11.6360	−	3.87868i	−0.551601	−	0.183867i
$446$	14.7574			0.698781
$447$	−21.7279	−	21.7279i	−1.02770	−	1.02770i
$448$	1.00000	−	1.00000i	0.0472456	−	0.0472456i
$449$	10.7990	+	10.7990i	0.509636	+	0.509636i	0.914415	−	0.404779i	$-0.132651\pi$
$449$	10.7990	+	10.7990i	0.509636	+	0.509636i	−0.404779	+	0.914415i	$0.632651\pi$
$450$	8.48528	−	11.3137i	0.400000	−	0.533333i
$451$		−	14.0000i		−	0.659234i
$452$	9.53553	−	9.53553i	0.448514	−	0.448514i
$453$	20.4853	−	20.4853i	0.962482	−	0.962482i
$454$	13.9497	−	13.9497i	0.654694	−	0.654694i
$455$	−4.24264	−	8.48528i	−0.198898	−	0.397796i
$456$	−2.12132	+	2.12132i	−0.0993399	+	0.0993399i
$457$	6.24264			0.292018			0.146009	−	0.989283i	$-0.453357\pi$
$457$	6.24264			0.292018			0.146009	+	0.989283i	$0.453357\pi$
$458$			16.2426i			0.758969i
$459$	0.414214	+	1.65685i	0.0193338	+	0.0773353i
$460$	−8.00000	+	4.00000i	−0.373002	+	0.186501i
$461$		−	16.2843i		−	0.758434i	−0.925308	−	0.379217i	$-0.876193\pi$
$461$		−	16.2843i		−	0.758434i	0.925308	−	0.379217i	$-0.123807\pi$
$462$	−15.0711	−	15.0711i	−0.701170	−	0.701170i
$463$		−	16.7574i		−	0.778781i	−0.921073	−	0.389390i	$-0.872686\pi$
$463$		−	16.7574i		−	0.778781i	0.921073	−	0.389390i	$-0.127314\pi$
$464$	−0.707107	+	0.707107i	−0.0328266	+	0.0328266i
$465$	−53.3345	−	17.7782i	−2.47333	−	0.824443i
$466$	1.05025	+	1.05025i	0.0486520	+	0.0486520i
$467$	6.72792			0.311331			0.155666	−	0.987810i	$-0.450248\pi$
$467$	6.72792			0.311331			0.155666	+	0.987810i	$0.450248\pi$
$468$	8.48528			0.392232
$469$	2.48528	+	2.48528i	0.114760	+	0.114760i
$470$	3.12132	−	9.36396i	0.143976	−	0.431927i
$471$	20.4853	−	20.4853i	0.943912	−	0.943912i
$472$		−	6.89949i		−	0.317575i
$473$	−54.0416	−	54.0416i	−2.48484	−	2.48484i
$474$			28.1421i			1.29261i
$475$	−3.72792	+	4.97056i	−0.171049	+	0.228065i
$476$	−1.41421	−	5.65685i	−0.0648204	−	0.259281i
$477$		−	8.48528i		−	0.388514i
$478$	−13.7574			−0.629247
$479$	−19.9497	+	19.9497i	−0.911527	+	0.911527i	−0.996392	−	0.0848652i	$-0.972954\pi$
$479$	−19.9497	+	19.9497i	−0.911527	+	0.911527i	0.0848652	+	0.996392i	$0.472954\pi$
$480$	2.41421	+	4.82843i	0.110193	+	0.220387i
$481$	−9.72792	+	9.72792i	−0.443555	+	0.443555i
$482$	−11.2426	+	11.2426i	−0.512088	+	0.512088i
$483$	9.65685	−	9.65685i	0.439402	−	0.439402i
$484$			27.9706i			1.27139i
$485$	−5.82843	−	11.6569i	−0.264655	−	0.529310i
$486$	15.3137	+	15.3137i	0.694644	+	0.694644i
$487$	2.75736	−	2.75736i	0.124948	−	0.124948i	−0.641868	−	0.766815i	$-0.721840\pi$
$487$	2.75736	−	2.75736i	0.124948	−	0.124948i	0.766815	+	0.641868i	$0.221840\pi$
$488$	−1.87868	−	1.87868i	−0.0850438	−	0.0850438i
$489$	−42.6274			−1.92768
$490$	3.53553	−	10.6066i	0.159719	−	0.479157i
$491$			12.8995i			0.582146i	0.956701	+	0.291073i	$0.0940123\pi$
$491$			12.8995i			0.582146i	−0.956701	+	0.291073i	$0.905988\pi$
$492$		−	5.41421i		−	0.244092i
$493$	1.00000	+	4.00000i	0.0450377	+	0.180151i
$494$	−3.72792			−0.167727
$495$	35.3137	−	17.6569i	1.58723	−	0.793617i
$496$	7.36396	−	7.36396i	0.330652	−	0.330652i
$497$		−	4.58579i		−	0.205701i
$498$	−7.24264	−	7.24264i	−0.324550	−	0.324550i
$499$	−25.4853	−	25.4853i	−1.14088	−	1.14088i	−0.988290	−	0.152588i	$-0.951239\pi$
$499$	−25.4853	−	25.4853i	−1.14088	−	1.14088i	−0.152588	−	0.988290i	$-0.548761\pi$
$500$	6.36396	+	9.19239i	0.284605	+	0.411096i
$501$		−	44.6274i		−	1.99381i
$502$	−3.51472			−0.156870
$503$	−1.07107	+	1.07107i	−0.0477566	+	0.0477566i	−0.730582	−	0.682825i	$-0.760751\pi$
$503$	−1.07107	+	1.07107i	−0.0477566	+	0.0477566i	0.682825	+	0.730582i	$0.260751\pi$
$504$	−2.82843	−	2.82843i	−0.125988	−	0.125988i
$505$		0			0
$506$	−24.9706			−1.11008
$507$	−6.82843	−	6.82843i	−0.303261	−	0.303261i
$508$	−7.72792			−0.342871
$509$		0			0			−	1.00000i	$-0.5\pi$
$509$		0			0				1.00000i	$0.5\pi$
$510$	22.1924	+	1.70711i	0.982695	+	0.0755920i
$511$	8.72792			0.386101
$512$	−1.00000			−0.0441942
$513$	−0.363961	−	0.363961i	−0.0160693	−	0.0160693i
$514$	18.7279			0.826053
$515$		0			0
$516$	−20.8995	−	20.8995i	−0.920049	−	0.920049i
$517$	19.4853	−	19.4853i	0.856962	−	0.856962i
$518$	6.48528			0.284947
$519$		−	21.6569i		−	0.950630i
$520$	−2.12132	+	6.36396i	−0.0930261	+	0.279078i
$521$	11.3137	+	11.3137i	0.495663	+	0.495663i	0.910085	−	0.414422i	$-0.136016\pi$
$521$	11.3137	+	11.3137i	0.495663	+	0.495663i	−0.414422	+	0.910085i	$0.636016\pi$
$522$	2.00000	+	2.00000i	0.0875376	+	0.0875376i
$523$		−	9.51472i		−	0.416050i	−0.978124	−	0.208025i	$-0.933297\pi$
$523$		−	9.51472i		−	0.416050i	0.978124	−	0.208025i	$-0.0667035\pi$
$524$	10.4142	−	10.4142i	0.454947	−	0.454947i
$525$	−13.6569	−	10.2426i	−0.596034	−	0.447025i
$526$	−13.2426			−0.577407
$527$	−10.4142	−	41.6569i	−0.453650	−	1.81460i
$528$			15.0711i			0.655884i
$529$			7.00000i			0.304348i
$530$	6.36396	+	2.12132i	0.276433	+	0.0921443i
$531$	−19.5147			−0.846867
$532$	1.24264	+	1.24264i	0.0538753	+	0.0538753i
$533$	4.75736	−	4.75736i	0.206064	−	0.206064i
$534$	−9.36396	−	9.36396i	−0.405218	−	0.405218i
$535$	4.00000	+	8.00000i	0.172935	+	0.345870i
$536$		−	2.48528i		−	0.107348i
$537$	−39.7990	+	39.7990i	−1.71745	+	1.71745i
$538$	12.7071	−	12.7071i	0.547842	−	0.547842i
$539$	22.0711	−	22.0711i	0.950668	−	0.950668i
$540$	−0.828427	+	0.414214i	−0.0356498	+	0.0178249i
$541$	−12.9706	+	12.9706i	−0.557648	+	0.557648i	−0.928637	−	0.370989i	$-0.879019\pi$
$541$	−12.9706	+	12.9706i	−0.557648	+	0.557648i	0.370989	+	0.928637i	$0.379019\pi$
$542$	−10.4853			−0.450381
$543$			47.7990i			2.05125i
$544$	−2.12132	+	3.53553i	−0.0909509	+	0.151585i
$545$	−17.8284	−	35.6569i	−0.763686	−	1.52737i
$546$		−	10.2426i		−	0.438345i
$547$	23.6066	+	23.6066i	1.00935	+	1.00935i	0.999956	+	0.00938949i	$0.00298881\pi$
$547$	23.6066	+	23.6066i	1.00935	+	1.00935i	0.00938949	+	0.999956i	$0.497011\pi$
$548$			7.41421i			0.316720i
$549$	−5.31371	+	5.31371i	−0.226784	+	0.226784i
$550$	4.41421	+	30.8995i	0.188223	+	1.31756i
$551$	−0.878680	−	0.878680i	−0.0374330	−	0.0374330i
$552$	−9.65685			−0.411023
$553$	16.4853			0.701025
$554$	0.242641	+	0.242641i	0.0103088	+	0.0103088i
$555$	−7.82843	+	23.4853i	−0.332298	+	0.996895i
$556$	−11.0000	+	11.0000i	−0.466504	+	0.466504i
$557$		−	4.79899i		−	0.203340i	−0.994818	−	0.101670i	$-0.967581\pi$
$557$		−	4.79899i		−	0.203340i	0.994818	−	0.101670i	$-0.0324185\pi$
$558$	−20.8284	−	20.8284i	−0.881738	−	0.881738i
$559$		−	36.7279i		−	1.55343i
$560$	2.82843	−	1.41421i	0.119523	−	0.0597614i
$561$	53.2843	+	31.9706i	2.24966	+	1.34980i
$562$		−	14.6569i		−	0.618262i
$563$	21.9411			0.924708			0.462354	−	0.886695i	$-0.347005\pi$
$563$	21.9411			0.924708			0.462354	+	0.886695i	$0.347005\pi$
$564$	7.53553	−	7.53553i	0.317303	−	0.317303i
$565$	26.9706	−	13.4853i	1.13466	−	0.567330i
$566$	14.8787	−	14.8787i	0.625398	−	0.625398i
$567$	9.48528	−	9.48528i	0.398344	−	0.398344i
$568$	−2.29289	+	2.29289i	−0.0962077	+	0.0962077i
$569$		−	2.31371i		−	0.0969957i	−0.998823	−	0.0484979i	$-0.984557\pi$
$569$		−	2.31371i		−	0.0969957i	0.998823	−	0.0484979i	$-0.0154434\pi$
$570$	−6.00000	+	3.00000i	−0.251312	+	0.125656i
$571$	22.2132	+	22.2132i	0.929594	+	0.929594i	0.997679	−	0.0680858i	$-0.0216892\pi$
$571$	22.2132	+	22.2132i	0.929594	+	0.929594i	−0.0680858	+	0.997679i	$0.521689\pi$
$572$	−13.2426	+	13.2426i	−0.553703	+	0.553703i
$573$	36.2132	+	36.2132i	1.51283	+	1.51283i
$574$	−3.17157			−0.132379
$575$	−19.7990	+	2.82843i	−0.825675	+	0.117954i
$576$			2.82843i			0.117851i
$577$		−	28.9706i		−	1.20606i	−0.797718	−	0.603030i	$-0.793960\pi$
$577$		−	28.9706i		−	1.20606i	0.797718	−	0.603030i	$-0.206040\pi$
$578$	8.00000	+	15.0000i	0.332756	+	0.623918i
$579$	−5.17157			−0.214923
$580$	−2.00000	+	1.00000i	−0.0830455	+	0.0415227i
$581$	−4.24264	+	4.24264i	−0.176014	+	0.176014i
$582$		−	14.0711i		−	0.583265i
$583$	13.2426	+	13.2426i	0.548454	+	0.548454i
$584$	−4.36396	−	4.36396i	−0.180582	−	0.180582i
$585$	18.0000	+	6.00000i	0.744208	+	0.248069i
$586$			9.34315i			0.385962i
$587$	24.0000			0.990586			0.495293	−	0.868726i	$-0.335061\pi$
$587$	24.0000			0.990586			0.495293	+	0.868726i	$0.335061\pi$
$588$	8.53553	−	8.53553i	0.351999	−	0.351999i
$589$	9.15076	+	9.15076i	0.377050	+	0.377050i
$590$	4.87868	−	14.6360i	0.200852	−	0.602556i
$591$	−50.0416			−2.05844
$592$	−3.24264	−	3.24264i	−0.133272	−	0.133272i
$593$	18.0000			0.739171			0.369586	−	0.929197i	$-0.379500\pi$
$593$	18.0000			0.739171			0.369586	+	0.929197i	$0.379500\pi$
$594$	−2.58579			−0.106096
$595$	1.00000	−	13.0000i	0.0409960	−	0.532948i
$596$	12.7279			0.521356
$597$	9.82843			0.402251
$598$	−8.48528	−	8.48528i	−0.346989	−	0.346989i
$599$	−12.0000			−0.490307			−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000			−0.490307			−0.245153	+	0.969484i	$0.578838\pi$
$600$	1.70711	+	11.9497i	0.0696923	+	0.487846i
$601$	3.27208	+	3.27208i	0.133471	+	0.133471i	0.770686	−	0.637215i	$-0.219914\pi$
$601$	3.27208	+	3.27208i	0.133471	+	0.133471i	−0.637215	+	0.770686i	$0.719914\pi$
$602$	−12.2426	+	12.2426i	−0.498973	+	0.498973i
$603$	−7.02944			−0.286261
$604$			12.0000i			0.488273i
$605$	−19.7782	+	59.3345i	−0.804097	+	2.41229i
$606$		0			0
$607$	−24.4558	−	24.4558i	−0.992632	−	0.992632i	0.00734096	−	0.999973i	$-0.497663\pi$
$607$	−24.4558	−	24.4558i	−0.992632	−	0.992632i	−0.999973	+	0.00734096i	$0.997663\pi$
$608$		−	1.24264i		−	0.0503957i
$609$	2.41421	−	2.41421i	0.0978289	−	0.0978289i
$610$	−2.65685	−	5.31371i	−0.107573	−	0.215146i
$611$	13.2426			0.535740
$612$	10.0000	+	6.00000i	0.404226	+	0.242536i
$613$			37.9706i			1.53362i	0.641876	+	0.766808i	$0.278156\pi$
$613$			37.9706i			1.53362i	−0.641876	+	0.766808i	$0.721844\pi$
$614$		−	9.21320i		−	0.371815i
$615$	3.82843	−	11.4853i	0.154377	−	0.463131i
$616$	8.82843			0.355707
$617$	7.43503	+	7.43503i	0.299323	+	0.299323i	0.840749	−	0.541426i	$-0.182115\pi$
$617$	7.43503	+	7.43503i	0.299323	+	0.299323i	−0.541426	+	0.840749i	$0.682115\pi$
$618$		0			0
$619$	14.2426	+	14.2426i	0.572460	+	0.572460i	0.932815	−	0.360355i	$-0.117344\pi$
$619$	14.2426	+	14.2426i	0.572460	+	0.572460i	−0.360355	+	0.932815i	$0.617344\pi$
$620$	20.8284	−	10.4142i	0.836490	−	0.418245i
$621$		−	1.65685i		−	0.0664873i
$622$	−1.41421	+	1.41421i	−0.0567048	+	0.0567048i
$623$	−5.48528	+	5.48528i	−0.219763	+	0.219763i
$624$	−5.12132	+	5.12132i	−0.205017	+	0.205017i
$625$	7.00000	+	24.0000i	0.280000	+	0.960000i
$626$	5.51472	−	5.51472i	0.220412	−	0.220412i
$627$	−18.7279			−0.747921
$628$			12.0000i			0.478852i
$629$	−18.3431	+	4.58579i	−0.731389	+	0.182847i
$630$	−4.00000	−	8.00000i	−0.159364	−	0.318728i
$631$		−	14.4853i		−	0.576650i	−0.957533	−	0.288325i	$-0.906902\pi$
$631$		−	14.4853i		−	0.576650i	0.957533	−	0.288325i	$-0.0930983\pi$
$632$	−8.24264	−	8.24264i	−0.327875	−	0.327875i
$633$			27.3137i			1.08562i
$634$	−14.1421	+	14.1421i	−0.561656	+	0.561656i
$635$	−16.3934	−	5.46447i	−0.650552	−	0.216851i
$636$	5.12132	+	5.12132i	0.203074	+	0.203074i
$637$	15.0000			0.594322
$638$	−6.24264			−0.247149
$639$	6.48528	+	6.48528i	0.256554	+	0.256554i
$640$	−2.12132	−	0.707107i	−0.0838525	−	0.0279508i
$641$	−27.5563	+	27.5563i	−1.08841	+	1.08841i	−0.0927179	+	0.995692i	$0.529555\pi$
$641$	−27.5563	+	27.5563i	−1.08841	+	1.08841i	−0.995692	+	0.0927179i	$0.970445\pi$
$642$			9.65685i			0.381126i
$643$	−12.2426	−	12.2426i	−0.482803	−	0.482803i	0.423223	−	0.906026i	$-0.360899\pi$
$643$	−12.2426	−	12.2426i	−0.482803	−	0.482803i	−0.906026	+	0.423223i	$0.860899\pi$
$644$			5.65685i			0.222911i
$645$	−29.5563	−	59.1127i	−1.16378	−	2.32756i
$646$	−4.39340	−	2.63604i	−0.172856	−	0.103714i
$647$		−	17.5269i		−	0.689054i	−0.938776	−	0.344527i	$-0.888039\pi$
$647$		−	17.5269i		−	0.689054i	0.938776	−	0.344527i	$-0.111961\pi$
$648$	−9.48528			−0.372617
$649$	30.4558	−	30.4558i	1.19550	−	1.19550i
$650$	−9.00000	+	12.0000i	−0.353009	+	0.470679i
$651$	−25.1421	+	25.1421i	−0.985398	+	0.985398i
$652$	12.4853	−	12.4853i	0.488961	−	0.488961i
$653$	−34.7990	+	34.7990i	−1.36179	+	1.36179i	−0.490154	+	0.871636i	$0.663059\pi$
$653$	−34.7990	+	34.7990i	−1.36179	+	1.36179i	−0.871636	+	0.490154i	$0.836941\pi$
$654$		−	43.0416i		−	1.68306i
$655$	29.4558	−	14.7279i	1.15094	−	0.575468i
$656$	1.58579	+	1.58579i	0.0619146	+	0.0619146i
$657$	−12.3431	+	12.3431i	−0.481552	+	0.481552i
$658$	−4.41421	−	4.41421i	−0.172084	−	0.172084i
$659$	−12.2132			−0.475759			−0.237879	−	0.971295i	$-0.576452\pi$
$659$	−12.2132			−0.475759			−0.237879	+	0.971295i	$0.576452\pi$
$660$	−10.6569	+	31.9706i	−0.414817	+	1.24445i
$661$			12.0000i			0.466746i	0.972387	+	0.233373i	$0.0749763\pi$
$661$			12.0000i			0.466746i	−0.972387	+	0.233373i	$0.925024\pi$
$662$			9.72792i			0.378086i
$663$	7.24264	+	28.9706i	0.281281	+	1.12512i
$664$	4.24264			0.164646
$665$	1.75736	+	3.51472i	0.0681475	+	0.136295i
$666$	−9.17157	+	9.17157i	−0.355391	+	0.355391i
$667$		−	4.00000i		−	0.154881i
$668$	13.0711	+	13.0711i	0.505735	+	0.505735i
$669$	25.1924	+	25.1924i	0.973994	+	0.973994i
$670$	1.75736	−	5.27208i	0.0678927	−	0.203678i
$671$		−	16.5858i		−	0.640287i
$672$	3.41421			0.131706
$673$	30.1213	−	30.1213i	1.16109	−	1.16109i	0.176855	−	0.984237i	$-0.443408\pi$
$673$	30.1213	−	30.1213i	1.16109	−	1.16109i	0.984237	−	0.176855i	$-0.0565922\pi$
$674$	16.8492	+	16.8492i	0.649009	+	0.649009i
$675$	−2.05025	+	0.292893i	−0.0789143	+	0.0112735i
$676$	4.00000			0.153846
$677$	19.5858	+	19.5858i	0.752743	+	0.752743i	0.974990	−	0.222247i	$-0.0713393\pi$
$677$	19.5858	+	19.5858i	0.752743	+	0.752743i	−0.222247	+	0.974990i	$0.571339\pi$
$678$	32.5563			1.25032
$679$	−8.24264			−0.316324
$680$	−7.00000	+	6.00000i	−0.268438	+	0.230089i
$681$	47.6274			1.82509
$682$	65.0122			2.48945
$683$	17.4645	+	17.4645i	0.668259	+	0.668259i	0.957313	−	0.289054i	$-0.0933406\pi$
$683$	17.4645	+	17.4645i	0.668259	+	0.668259i	−0.289054	+	0.957313i	$0.593341\pi$
$684$	−3.51472			−0.134389
$685$	−5.24264	+	15.7279i	−0.200311	+	0.600933i
$686$	−12.0000	−	12.0000i	−0.458162	−	0.458162i
$687$	−27.7279	+	27.7279i	−1.05789	+	1.05789i
$688$	12.2426			0.466746
$689$			9.00000i			0.342873i
$690$	−20.4853	−	6.82843i	−0.779861	−	0.259954i
$691$	−7.48528	−	7.48528i	−0.284754	−	0.284754i	0.550248	−	0.835001i	$-0.314533\pi$
$691$	−7.48528	−	7.48528i	−0.284754	−	0.284754i	−0.835001	+	0.550248i	$0.814533\pi$
$692$	6.34315	+	6.34315i	0.241130	+	0.241130i
$693$		−	24.9706i		−	0.948553i
$694$	−14.2929	+	14.2929i	−0.542551	+	0.542551i
$695$	−31.1127	+	15.5563i	−1.18017	+	0.590086i
$696$	−2.41421			−0.0915105
$697$	8.97056	−	2.24264i	0.339784	−	0.0849461i
$698$		−	22.9706i		−	0.869449i
$699$			3.58579i			0.135627i
$700$	7.00000	−	1.00000i	0.264575	−	0.0377964i
$701$	−12.0000			−0.453234			−0.226617	−	0.973984i	$-0.572767\pi$
$701$	−12.0000			−0.453234			−0.226617	+	0.973984i	$0.572767\pi$
$702$	−0.878680	−	0.878680i	−0.0331636	−	0.0331636i
$703$	4.02944	−	4.02944i	0.151973	−	0.151973i
$704$	−4.41421	−	4.41421i	−0.166367	−	0.166367i
$705$	21.3137	−	10.6569i	0.802721	−	0.401360i
$706$			11.3137i			0.425797i
$707$		0			0
$708$	11.7782	−	11.7782i	0.442651	−	0.442651i
$709$	−18.6066	+	18.6066i	−0.698786	+	0.698786i	−0.964149	−	0.265363i	$-0.914508\pi$
$709$	−18.6066	+	18.6066i	−0.698786	+	0.698786i	0.265363	+	0.964149i	$0.414508\pi$
$710$	−6.48528	+	3.24264i	−0.243388	+	0.121694i
$711$	−23.3137	+	23.3137i	−0.874332	+	0.874332i
$712$	5.48528			0.205570
$713$			41.6569i			1.56006i
$714$	7.24264	−	12.0711i	0.271049	−	0.451748i
$715$	−37.4558	+	18.7279i	−1.40077	+	0.700385i
$716$		−	23.3137i		−	0.871274i
$717$	−23.4853	−	23.4853i	−0.877074	−	0.877074i
$718$			7.07107i			0.263890i
$719$	21.7487	−	21.7487i	0.811091	−	0.811091i	−0.173706	−	0.984797i	$-0.555574\pi$
$719$	21.7487	−	21.7487i	0.811091	−	0.811091i	0.984797	+	0.173706i	$0.0555744\pi$
$720$	−2.00000	+	6.00000i	−0.0745356	+	0.223607i
$721$		0			0
$722$	−17.4558			−0.649639
$723$	−38.3848			−1.42755
$724$	−14.0000	−	14.0000i	−0.520306	−	0.520306i
$725$	−4.94975	+	0.707107i	−0.183829	+	0.0262613i
$726$	−47.7487	+	47.7487i	−1.77212	+	1.77212i
$727$		−	25.2426i		−	0.936198i	−0.883676	−	0.468099i	$-0.844939\pi$
$727$		−	25.2426i		−	0.936198i	0.883676	−	0.468099i	$-0.155061\pi$
$728$	3.00000	+	3.00000i	0.111187	+	0.111187i
$729$			23.8284i			0.882534i
$730$	−6.17157	−	12.3431i	−0.228420	−	0.456840i
$731$	25.9706	−	43.2843i	0.960556	−	1.60093i
$732$		−	6.41421i		−	0.237076i
$733$	0.970563			0.0358486			0.0179243	−	0.999839i	$-0.494294\pi$
$733$	0.970563			0.0358486			0.0179243	+	0.999839i	$0.494294\pi$
$734$	9.75736	−	9.75736i	0.360151	−	0.360151i
$735$	24.1421	−	12.0711i	0.890496	−	0.445248i
$736$	2.82843	−	2.82843i	0.104257	−	0.104257i
$737$	10.9706	−	10.9706i	0.404106	−	0.404106i
$738$	4.48528	−	4.48528i	0.165105	−	0.165105i
$739$		−	41.1838i		−	1.51497i	−0.652853	−	0.757485i	$-0.726428\pi$
$739$		−	41.1838i		−	1.51497i	0.652853	−	0.757485i	$-0.273572\pi$
$740$	−4.58579	−	9.17157i	−0.168577	−	0.337154i
$741$	−6.36396	−	6.36396i	−0.233786	−	0.233786i
$742$	3.00000	−	3.00000i	0.110133	−	0.110133i
$743$	−12.1716	−	12.1716i	−0.446532	−	0.446532i	0.447668	−	0.894200i	$-0.352255\pi$
$743$	−12.1716	−	12.1716i	−0.446532	−	0.446532i	−0.894200	+	0.447668i	$0.852255\pi$
$744$	25.1421			0.921755
$745$	27.0000	+	9.00000i	0.989203	+	0.329734i
$746$		−	15.5147i		−	0.568034i
$747$		−	12.0000i		−	0.439057i
$748$	−24.9706	+	6.24264i	−0.913014	+	0.228254i
$749$	5.65685			0.206697
$750$	−4.82843	+	26.5563i	−0.176309	+	0.969701i
$751$	6.63604	−	6.63604i	0.242153	−	0.242153i	−0.575588	−	0.817740i	$-0.695227\pi$
$751$	6.63604	−	6.63604i	0.242153	−	0.242153i	0.817740	+	0.575588i	$0.195227\pi$
$752$			4.41421i			0.160970i
$753$	−6.00000	−	6.00000i	−0.218652	−	0.218652i
$754$	−2.12132	−	2.12132i	−0.0772539	−	0.0772539i
$755$	−8.48528	+	25.4558i	−0.308811	+	0.926433i
$756$			0.585786i			0.0213048i
$757$	−34.9411			−1.26996			−0.634978	−	0.772530i	$-0.718991\pi$
$757$	−34.9411			−1.26996			−0.634978	+	0.772530i	$0.718991\pi$
$758$	16.4853	−	16.4853i	0.598772	−	0.598772i
$759$	−42.6274	−	42.6274i	−1.54728	−	1.54728i
$760$	0.878680	−	2.63604i	0.0318731	−	0.0956192i
$761$	3.51472			0.127408			0.0637042	−	0.997969i	$-0.479709\pi$
$761$	3.51472			0.127408			0.0637042	+	0.997969i	$0.479709\pi$
$762$	−13.1924	−	13.1924i	−0.477910	−	0.477910i
$763$	−25.2132			−0.912779
$764$	−21.2132			−0.767467
$765$	16.9706	+	19.7990i	0.613572	+	0.715834i
$766$	4.75736			0.171890
$767$	20.6985			0.747379
$768$	−1.70711	−	1.70711i	−0.0615999	−	0.0615999i
$769$	36.4558			1.31463			0.657316	−	0.753615i	$-0.271692\pi$
$769$	36.4558			1.31463			0.657316	+	0.753615i	$0.271692\pi$
$770$	18.7279	+	6.24264i	0.674907	+	0.224969i
$771$	31.9706	+	31.9706i	1.15139	+	1.15139i
$772$	1.51472	−	1.51472i	0.0545159	−	0.0545159i
$773$	−15.5147			−0.558026			−0.279013	−	0.960287i	$-0.590007\pi$
$773$	−15.5147			−0.558026			−0.279013	+	0.960287i	$0.590007\pi$
$774$		−	34.6274i		−	1.24466i
$775$	51.5477	−	7.36396i	1.85165	−	0.264521i
$776$	4.12132	+	4.12132i	0.147947	+	0.147947i
$777$	11.0711	+	11.0711i	0.397172	+	0.397172i
$778$		−	28.6274i		−	1.02634i
$779$	−1.97056	+	1.97056i	−0.0706027	+	0.0706027i
$780$	−14.4853	+	7.24264i	−0.518656	+	0.259328i
$781$	−20.2426			−0.724339
$782$	−4.00000	−	16.0000i	−0.143040	−	0.572159i
$783$		−	0.414214i		−	0.0148028i
$784$			5.00000i			0.178571i
$785$	−8.48528	+	25.4558i	−0.302853	+	0.908558i
$786$	35.5563			1.26825
$787$	−11.3640	−	11.3640i	−0.405081	−	0.405081i	0.474938	−	0.880019i	$-0.342471\pi$
$787$	−11.3640	−	11.3640i	−0.405081	−	0.405081i	−0.880019	+	0.474938i	$0.842471\pi$
$788$	14.6569	−	14.6569i	0.522129	−	0.522129i
$789$	−22.6066	−	22.6066i	−0.804816	−	0.804816i
$790$	−11.6569	−	23.3137i	−0.414732	−	0.829465i
$791$		−	19.0711i		−	0.678089i
$792$	−12.4853	+	12.4853i	−0.443645	+	0.443645i
$793$	5.63604	−	5.63604i	0.200142	−	0.200142i
$794$	20.7279	−	20.7279i	0.735606	−	0.735606i
$795$	7.24264	+	14.4853i	0.256870	+	0.513740i
$796$	−2.87868	+	2.87868i	−0.102032	+	0.102032i
$797$	4.97056			0.176066			0.0880332	−	0.996118i	$-0.471942\pi$
$797$	4.97056			0.176066			0.0880332	+	0.996118i	$0.471942\pi$
$798$			4.24264i			0.150188i
$799$	15.6066	+	9.36396i	0.552122	+	0.331273i
$800$	−4.00000	−	3.00000i	−0.141421	−	0.106066i
$801$		−	15.5147i		−	0.548186i
$802$	21.8995	+	21.8995i	0.773298	+	0.773298i
$803$		−	38.5269i		−	1.35959i
$804$	4.24264	−	4.24264i	0.149626	−	0.149626i
$805$	−4.00000	+	12.0000i	−0.140981	+	0.422944i
$806$	22.0919	+	22.0919i	0.778153	+	0.778153i
$807$	43.3848			1.52722
$808$		0			0
$809$	6.85786	+	6.85786i	0.241110	+	0.241110i	0.817309	−	0.576199i	$-0.195465\pi$
$809$	6.85786	+	6.85786i	0.241110	+	0.241110i	−0.576199	+	0.817309i	$0.695465\pi$
$810$	−20.1213	−	6.70711i	−0.706991	−	0.235664i
$811$	−7.48528	+	7.48528i	−0.262844	+	0.262844i	−0.826208	−	0.563365i	$-0.809507\pi$
$811$	−7.48528	+	7.48528i	−0.262844	+	0.262844i	0.563365	+	0.826208i	$0.309507\pi$
$812$			1.41421i			0.0496292i
$813$	−17.8995	−	17.8995i	−0.627763	−	0.627763i
$814$		−	28.6274i		−	1.00339i
$815$	35.3137	−	17.6569i	1.23699	−	0.618493i
$816$	−9.65685	+	2.41421i	−0.338058	+	0.0845144i
$817$			15.2132i			0.532243i
$818$	−8.51472			−0.297710
$819$	8.48528	−	8.48528i	0.296500	−	0.296500i
$820$	2.24264	+	4.48528i	0.0783164	+	0.156633i
$821$	6.02082	−	6.02082i	0.210128	−	0.210128i	−0.594194	−	0.804322i	$-0.702529\pi$
$821$	6.02082	−	6.02082i	0.210128	−	0.210128i	0.804322	+	0.594194i	$0.202529\pi$
$822$	−12.6569	+	12.6569i	−0.441458	+	0.441458i
$823$	−14.7279	+	14.7279i	−0.513383	+	0.513383i	−0.915561	−	0.402178i	$-0.868253\pi$
$823$	−14.7279	+	14.7279i	−0.513383	+	0.513383i	0.402178	+	0.915561i	$0.368253\pi$
$824$		0			0
$825$	−45.2132	+	60.2843i	−1.57412	+	2.09883i
$826$	−6.89949	−	6.89949i	−0.240064	−	0.240064i
$827$	−17.3137	+	17.3137i	−0.602057	+	0.602057i	−0.940858	−	0.338801i	$-0.889979\pi$
$827$	−17.3137	+	17.3137i	−0.602057	+	0.602057i	0.338801	+	0.940858i	$0.389979\pi$
$828$	−8.00000	−	8.00000i	−0.278019	−	0.278019i
$829$	14.0000			0.486240			0.243120	−	0.969996i	$-0.421829\pi$
$829$	14.0000			0.486240			0.243120	+	0.969996i	$0.421829\pi$
$830$	9.00000	+	3.00000i	0.312395	+	0.104132i
$831$			0.828427i			0.0287378i
$832$		−	3.00000i		−	0.104006i
$833$	17.6777	+	10.6066i	0.612495	+	0.367497i
$834$	−37.5563			−1.30047
$835$	18.4853	+	36.9706i	0.639710	+	1.27942i
$836$	5.48528	−	5.48528i	0.189712	−	0.189712i
$837$			4.31371i			0.149104i
$838$	−11.3137	−	11.3137i	−0.390826	−	0.390826i
$839$	−27.0208	−	27.0208i	−0.932862	−	0.932862i	0.0650217	−	0.997884i	$-0.479288\pi$
$839$	−27.0208	−	27.0208i	−0.932862	−	0.932862i	−0.997884	+	0.0650217i	$0.979288\pi$
$840$	7.24264	+	2.41421i	0.249895	+	0.0832983i
$841$			28.0000i			0.965517i
$842$	−23.2132			−0.799980
$843$	25.0208	−	25.0208i	0.861763	−	0.861763i
$844$	−8.00000	−	8.00000i	−0.275371	−	0.275371i
$845$	8.48528	+	2.82843i	0.291903	+	0.0973009i
$846$	12.4853			0.429253
$847$	27.9706	+	27.9706i	0.961080	+	0.961080i
$848$	−3.00000			−0.103020
$849$	50.7990			1.74342
$850$	−19.0919	+	7.77817i	−0.654846	+	0.266789i
$851$	18.3431			0.628795
$852$	−7.82843			−0.268197
$853$	−25.4853	−	25.4853i	−0.872599	−	0.872599i	0.120156	−	0.992755i	$-0.461661\pi$
$853$	−25.4853	−	25.4853i	−0.872599	−	0.872599i	−0.992755	+	0.120156i	$0.961661\pi$
$854$	−3.75736			−0.128574
$855$	−7.45584	−	2.48528i	−0.254984	−	0.0849948i
$856$	−2.82843	−	2.82843i	−0.0966736	−	0.0966736i
$857$	−1.43503	+	1.43503i	−0.0490197	+	0.0490197i	−0.731192	−	0.682172i	$-0.761036\pi$
$857$	−1.43503	+	1.43503i	−0.0490197	+	0.0490197i	0.682172	+	0.731192i	$0.261036\pi$
$858$	−45.2132			−1.54355
$859$			20.2721i			0.691674i	0.938295	+	0.345837i	$0.112405\pi$
$859$			20.2721i			0.691674i	−0.938295	+	0.345837i	$0.887595\pi$
$860$	25.9706	+	8.65685i	0.885589	+	0.295196i
$861$	−5.41421	−	5.41421i	−0.184516	−	0.184516i
$862$	−6.34315	−	6.34315i	−0.216048	−	0.216048i
$863$			7.11270i			0.242119i	0.992645	+	0.121060i	$0.0386292\pi$
$863$			7.11270i			0.242119i	−0.992645	+	0.121060i	$0.961371\pi$
$864$	0.292893	−	0.292893i	0.00996443	−	0.00996443i
$865$	8.97056	+	17.9411i	0.305008	+	0.610017i
$866$	14.2426			0.483985
$867$	−11.9497	+	39.2635i	−0.405835	+	1.33346i
$868$		−	14.7279i		−	0.499898i
$869$		−	72.7696i		−	2.46854i
$870$	−5.12132	−	1.70711i	−0.173629	−	0.0578763i
$871$	7.45584			0.252632
$872$	12.6066	+	12.6066i	0.426913	+	0.426913i
$873$	11.6569	−	11.6569i	0.394525	−	0.394525i
$874$	3.51472	+	3.51472i	0.118887	+	0.118887i
$875$	15.5563	+	2.82843i	0.525901	+	0.0956183i
$876$		−	14.8995i		−	0.503407i
$877$	−25.4853	+	25.4853i	−0.860577	+	0.860577i	−0.991405	−	0.130828i	$-0.958236\pi$
$877$	−25.4853	+	25.4853i	−0.860577	+	0.860577i	0.130828	+	0.991405i	$0.458236\pi$
$878$	12.9706	−	12.9706i	0.437735	−	0.437735i
$879$	−15.9497	+	15.9497i	−0.537972	+	0.537972i
$880$	−6.24264	−	12.4853i	−0.210439	−	0.420879i
$881$	−39.5563	+	39.5563i	−1.33269	+	1.33269i	−0.429730	+	0.902958i	$0.641391\pi$
$881$	−39.5563	+	39.5563i	−1.33269	+	1.33269i	−0.902958	+	0.429730i	$0.858609\pi$
$882$	14.1421			0.476190
$883$		−	6.72792i		−	0.226413i	−0.993572	−	0.113206i	$-0.963888\pi$
$883$		−	6.72792i		−	0.226413i	0.993572	−	0.113206i	$-0.0361121\pi$
$884$	−10.6066	−	6.36396i	−0.356739	−	0.214043i
$885$	33.3137	−	16.6569i	1.11983	−	0.559914i
$886$			1.79899i			0.0604382i
$887$	−22.4142	−	22.4142i	−0.752596	−	0.752596i	0.222367	−	0.974963i	$-0.428622\pi$
$887$	−22.4142	−	22.4142i	−0.752596	−	0.752596i	−0.974963	+	0.222367i	$0.928622\pi$
$888$		−	11.0711i		−	0.371521i
$889$	−7.72792	+	7.72792i	−0.259186	+	0.259186i
$890$	11.6360	+	3.87868i	0.390041	+	0.130014i
$891$	−41.8701	−	41.8701i	−1.40270	−	1.40270i
$892$	−14.7574			−0.494113
$893$	−5.48528			−0.183558
$894$	21.7279	+	21.7279i	0.726690	+	0.726690i
$895$	16.4853	−	49.4558i	0.551042	−	1.65313i
$896$	−1.00000	+	1.00000i	−0.0334077	+	0.0334077i
$897$		−	28.9706i		−	0.967299i
$898$	−10.7990	−	10.7990i	−0.360367	−	0.360367i
$899$			10.4142i			0.347333i
$900$	−8.48528	+	11.3137i	−0.282843	+	0.377124i
$901$	−6.36396	+	10.6066i	−0.212014	+	0.353357i
$902$			14.0000i			0.466149i
$903$	−41.7990			−1.39098
$904$	−9.53553	+	9.53553i	−0.317147	+	0.317147i
$905$	−19.7990	−	39.5980i	−0.658141	−	1.31628i
$906$	−20.4853	+	20.4853i	−0.680578	+	0.680578i
$907$	21.8492	−	21.8492i	0.725492	−	0.725492i	−0.244226	−	0.969718i	$-0.578534\pi$
$907$	21.8492	−	21.8492i	0.725492	−	0.725492i	0.969718	+	0.244226i	$0.0785339\pi$
$908$	−13.9497	+	13.9497i	−0.462939	+	0.462939i
$909$		0			0
$910$	4.24264	+	8.48528i	0.140642	+	0.281284i
$911$	−12.6863	−	12.6863i	−0.420316	−	0.420316i	0.464997	−	0.885312i	$-0.346055\pi$
$911$	−12.6863	−	12.6863i	−0.420316	−	0.420316i	−0.885312	+	0.464997i	$0.846055\pi$
$912$	2.12132	−	2.12132i	0.0702439	−	0.0702439i
$913$	18.7279	+	18.7279i	0.619804	+	0.619804i
$914$	−6.24264			−0.206488
$915$	4.53553	−	13.6066i	0.149940	−	0.449820i
$916$		−	16.2426i		−	0.536672i
$917$		−	20.8284i		−	0.687815i
$918$	−0.414214	−	1.65685i	−0.0136711	−	0.0546843i
$919$	11.2132			0.369889			0.184945	−	0.982749i	$-0.440789\pi$
$919$	11.2132			0.369889			0.184945	+	0.982749i	$0.440789\pi$
$920$	8.00000	−	4.00000i	0.263752	−	0.131876i
$921$	15.7279	−	15.7279i	0.518253	−	0.518253i
$922$			16.2843i			0.536294i
$923$	−6.87868	−	6.87868i	−0.226414	−	0.226414i
$924$	15.0711	+	15.0711i	0.495802	+	0.495802i
$925$	−3.24264	−	22.6985i	−0.106617	−	0.746322i
$926$			16.7574i			0.550681i
$927$		0			0
$928$	0.707107	−	0.707107i	0.0232119	−	0.0232119i
$929$	−26.6569	−	26.6569i	−0.874583	−	0.874583i	0.118385	−	0.992968i	$-0.462228\pi$
$929$	−26.6569	−	26.6569i	−0.874583	−	0.874583i	−0.992968	+	0.118385i	$0.962228\pi$
$930$	53.3345	+	17.7782i	1.74891	+	0.582969i
$931$	−6.21320			−0.203630
$932$	−1.05025	−	1.05025i	−0.0344022	−	0.0344022i
$933$	−4.82843			−0.158076
$934$	−6.72792			−0.220144
$935$	−57.3848	−	4.41421i	−1.87668	−	0.144360i
$936$	−8.48528			−0.277350
$937$	4.78680			0.156378			0.0781889	−	0.996939i	$-0.475086\pi$
$937$	4.78680			0.156378			0.0781889	+	0.996939i	$0.475086\pi$
$938$	−2.48528	−	2.48528i	−0.0811473	−	0.0811473i
$939$	18.8284			0.614442
$940$	−3.12132	+	9.36396i	−0.101806	+	0.305419i
$941$	33.1924	+	33.1924i	1.08204	+	1.08204i	0.996319	+	0.0857218i	$0.0273196\pi$
$941$	33.1924	+	33.1924i	1.08204	+	1.08204i	0.0857218	+	0.996319i	$0.472680\pi$
$942$	−20.4853	+	20.4853i	−0.667447	+	0.667447i
$943$	−8.97056			−0.292122
$944$			6.89949i			0.224559i
$945$	−0.414214	+	1.24264i	−0.0134744	+	0.0404231i
$946$	54.0416	+	54.0416i	1.75704	+	1.75704i
$947$	27.7071	+	27.7071i	0.900360	+	0.900360i	0.995467	−	0.0951071i	$-0.0303193\pi$
$947$	27.7071	+	27.7071i	0.900360	+	0.900360i	−0.0951071	+	0.995467i	$0.530319\pi$
$948$		−	28.1421i		−	0.914014i
$949$	13.0919	−	13.0919i	0.424981	−	0.424981i
$950$	3.72792	−	4.97056i	0.120950	−	0.161266i
$951$	−48.2843			−1.56572
$952$	1.41421	+	5.65685i	0.0458349	+	0.183340i
$953$			7.41421i			0.240170i	0.992764	+	0.120085i	$0.0383167\pi$
$953$			7.41421i			0.240170i	−0.992764	+	0.120085i	$0.961683\pi$
$954$			8.48528i			0.274721i
$955$	−45.0000	−	15.0000i	−1.45617	−	0.485389i
$956$	13.7574			0.444945
$957$	−10.6569	−	10.6569i	−0.344487	−	0.344487i
$958$	19.9497	−	19.9497i	0.644547	−	0.644547i
$959$	7.41421	+	7.41421i	0.239417	+	0.239417i
$960$	−2.41421	−	4.82843i	−0.0779184	−	0.155837i
$961$		−	77.4558i		−	2.49858i
$962$	9.72792	−	9.72792i	0.313641	−	0.313641i
$963$	−8.00000	+	8.00000i	−0.257796	+	0.257796i
$964$	11.2426	−	11.2426i	0.362101	−	0.362101i
$965$	4.28427	−	2.14214i	0.137916	−	0.0689578i
$966$	−9.65685	+	9.65685i	−0.310704	+	0.310704i
$967$	−2.97056			−0.0955269			−0.0477634	−	0.998859i	$-0.515209\pi$
$967$	−2.97056			−0.0955269			−0.0477634	+	0.998859i	$0.515209\pi$
$968$		−	27.9706i		−	0.899008i
$969$	−3.00000	−	12.0000i	−0.0963739	−	0.385496i
$970$	5.82843	+	11.6569i	0.187140	+	0.374279i
$971$		−	0.556349i		−	0.0178541i	−0.999960	−	0.00892705i	$-0.997158\pi$
$971$		−	0.556349i		−	0.0178541i	0.999960	−	0.00892705i	$-0.00284161\pi$
$972$	−15.3137	−	15.3137i	−0.491187	−	0.491187i
$973$			22.0000i			0.705288i
$974$	−2.75736	+	2.75736i	−0.0883515	+	0.0883515i
$975$	−35.8492	+	5.12132i	−1.14809	+	0.164014i
$976$	1.87868	+	1.87868i	0.0601351	+	0.0601351i
$977$	−24.7279			−0.791116			−0.395558	−	0.918441i	$-0.629449\pi$
$977$	−24.7279			−0.791116			−0.395558	+	0.918441i	$0.629449\pi$
$978$	42.6274			1.36307
$979$	24.2132	+	24.2132i	0.773857	+	0.773857i
$980$	−3.53553	+	10.6066i	−0.112938	+	0.338815i
$981$	35.6569	−	35.6569i	1.13844	−	1.13844i
$982$		−	12.8995i		−	0.411639i
$983$	38.0122	+	38.0122i	1.21240	+	1.21240i	0.970235	+	0.242166i	$0.0778578\pi$
$983$	38.0122	+	38.0122i	1.21240	+	1.21240i	0.242166	+	0.970235i	$0.422142\pi$
$984$			5.41421i			0.172599i
$985$	41.4558	−	20.7279i	1.32089	−	0.660447i
$986$	−1.00000	−	4.00000i	−0.0318465	−	0.127386i
$987$		−	15.0711i		−	0.479717i
$988$	3.72792			0.118601
$989$	−34.6274	+	34.6274i	−1.10109	+	1.10109i
$990$	−35.3137	+	17.6569i	−1.12234	+	0.561172i
$991$	16.8787	−	16.8787i	0.536169	−	0.536169i	−0.386233	−	0.922401i	$-0.626224\pi$
$991$	16.8787	−	16.8787i	0.536169	−	0.536169i	0.922401	+	0.386233i	$0.126224\pi$
$992$	−7.36396	+	7.36396i	−0.233806	+	0.233806i
$993$	−16.6066	+	16.6066i	−0.526995	+	0.526995i
$994$			4.58579i			0.145452i
$995$	−8.14214	+	4.07107i	−0.258123	+	0.129062i
$996$	7.24264	+	7.24264i	0.229492	+	0.229492i
$997$	−28.6985	+	28.6985i	−0.908890	+	0.908890i	−0.996183	−	0.0872926i	$-0.972178\pi$
$997$	−28.6985	+	28.6985i	−0.908890	+	0.908890i	0.0872926	+	0.996183i	$0.472178\pi$
$998$	25.4853	+	25.4853i	0.806722	+	0.806722i
$999$	1.89949			0.0600974

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.g.e.89.1	✓	4
3.2	odd	2		1530.2.n.o.1279.1		4
5.2	odd	4		850.2.h.h.701.1		4
5.3	odd	4		850.2.h.k.701.2		4
5.4	even	2		170.2.g.f.89.2	yes	4
15.14	odd	2		1530.2.n.j.1279.2		4
17.13	even	4		170.2.g.f.149.2	yes	4
51.47	odd	4		1530.2.n.j.829.2		4
85.13	odd	4		850.2.h.k.251.2		4
85.47	odd	4		850.2.h.h.251.1		4
85.64	even	4	inner	170.2.g.e.149.1	yes	4
255.149	odd	4		1530.2.n.o.829.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.g.e.89.1	✓	4	1.1	even	1	trivial
170.2.g.e.149.1	yes	4	85.64	even	4	inner
170.2.g.f.89.2	yes	4	5.4	even	2
170.2.g.f.149.2	yes	4	17.13	even	4
850.2.h.h.251.1		4	85.47	odd	4
850.2.h.h.701.1		4	5.2	odd	4
850.2.h.k.251.2		4	85.13	odd	4
850.2.h.k.701.2		4	5.3	odd	4
1530.2.n.j.829.2		4	51.47	odd	4
1530.2.n.j.1279.2		4	15.14	odd	2
1530.2.n.o.829.1		4	255.149	odd	4
1530.2.n.o.1279.1		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.70711 - 1.70711i) q^{3} +1.00000 q^{4} +(2.12132 + 0.707107i) q^{5} +(1.70711 + 1.70711i) q^{6} +(1.00000 - 1.00000i) q^{7} -1.00000 q^{8} +2.82843i q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.70711 - 1.70711i) q^{3} +1.00000 q^{4} +(2.12132 + 0.707107i) q^{5} +(1.70711 + 1.70711i) q^{6} +(1.00000 - 1.00000i) q^{7} -1.00000 q^{8} +2.82843i q^{9} +(-2.12132 - 0.707107i) q^{10} +(-4.41421 - 4.41421i) q^{11} +(-1.70711 - 1.70711i) q^{12} -3.00000i q^{13} +(-1.00000 + 1.00000i) q^{14} +(-2.41421 - 4.82843i) q^{15} +1.00000 q^{16} +(2.12132 - 3.53553i) q^{17} -2.82843i q^{18} +1.24264i q^{19} +(2.12132 + 0.707107i) q^{20} -3.41421 q^{21} +(4.41421 + 4.41421i) q^{22} +(-2.82843 + 2.82843i) q^{23} +(1.70711 + 1.70711i) q^{24} +(4.00000 + 3.00000i) q^{25} +3.00000i q^{26} +(-0.292893 + 0.292893i) q^{27} +(1.00000 - 1.00000i) q^{28} +(-0.707107 + 0.707107i) q^{29} +(2.41421 + 4.82843i) q^{30} +(7.36396 - 7.36396i) q^{31} -1.00000 q^{32} +15.0711i q^{33} +(-2.12132 + 3.53553i) q^{34} +(2.82843 - 1.41421i) q^{35} +2.82843i q^{36} +(-3.24264 - 3.24264i) q^{37} -1.24264i q^{38} +(-5.12132 + 5.12132i) q^{39} +(-2.12132 - 0.707107i) q^{40} +(1.58579 + 1.58579i) q^{41} +3.41421 q^{42} +12.2426 q^{43} +(-4.41421 - 4.41421i) q^{44} +(-2.00000 + 6.00000i) q^{45} +(2.82843 - 2.82843i) q^{46} +4.41421i q^{47} +(-1.70711 - 1.70711i) q^{48} +5.00000i q^{49} +(-4.00000 - 3.00000i) q^{50} +(-9.65685 + 2.41421i) q^{51} -3.00000i q^{52} -3.00000 q^{53} +(0.292893 - 0.292893i) q^{54} +(-6.24264 - 12.4853i) q^{55} +(-1.00000 + 1.00000i) q^{56} +(2.12132 - 2.12132i) q^{57} +(0.707107 - 0.707107i) q^{58} +6.89949i q^{59} +(-2.41421 - 4.82843i) q^{60} +(1.87868 + 1.87868i) q^{61} +(-7.36396 + 7.36396i) q^{62} +(2.82843 + 2.82843i) q^{63} +1.00000 q^{64} +(2.12132 - 6.36396i) q^{65} -15.0711i q^{66} +2.48528i q^{67} +(2.12132 - 3.53553i) q^{68} +9.65685 q^{69} +(-2.82843 + 1.41421i) q^{70} +(2.29289 - 2.29289i) q^{71} -2.82843i q^{72} +(4.36396 + 4.36396i) q^{73} +(3.24264 + 3.24264i) q^{74} +(-1.70711 - 11.9497i) q^{75} +1.24264i q^{76} -8.82843 q^{77} +(5.12132 - 5.12132i) q^{78} +(8.24264 + 8.24264i) q^{79} +(2.12132 + 0.707107i) q^{80} +9.48528 q^{81} +(-1.58579 - 1.58579i) q^{82} -4.24264 q^{83} -3.41421 q^{84} +(7.00000 - 6.00000i) q^{85} -12.2426 q^{86} +2.41421 q^{87} +(4.41421 + 4.41421i) q^{88} -5.48528 q^{89} +(2.00000 - 6.00000i) q^{90} +(-3.00000 - 3.00000i) q^{91} +(-2.82843 + 2.82843i) q^{92} -25.1421 q^{93} -4.41421i q^{94} +(-0.878680 + 2.63604i) q^{95} +(1.70711 + 1.70711i) q^{96} +(-4.12132 - 4.12132i) q^{97} -5.00000i q^{98} +(12.4853 - 12.4853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^6 + 4 * q^7 - 4 * q^8	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{6} + 4 q^{7} - 4 q^{8} - 12 q^{11} - 4 q^{12} - 4 q^{14} - 4 q^{15} + 4 q^{16} - 8 q^{21} + 12 q^{22} + 4 q^{24} + 16 q^{25} - 4 q^{27} + 4 q^{28} + 4 q^{30} + 4 q^{31} - 4 q^{32} + 4 q^{37} - 12 q^{39} + 12 q^{41} + 8 q^{42} + 32 q^{43} - 12 q^{44} - 8 q^{45} - 4 q^{48} - 16 q^{50} - 16 q^{51} - 12 q^{53} + 4 q^{54} - 8 q^{55} - 4 q^{56} - 4 q^{60} + 16 q^{61} - 4 q^{62} + 4 q^{64} + 16 q^{69} + 12 q^{71} - 8 q^{73} - 4 q^{74} - 4 q^{75} - 24 q^{77} + 12 q^{78} + 16 q^{79} + 4 q^{81} - 12 q^{82} - 8 q^{84} + 28 q^{85} - 32 q^{86} + 4 q^{87} + 12 q^{88} + 12 q^{89} + 8 q^{90} - 12 q^{91} - 44 q^{93} - 12 q^{95} + 4 q^{96} - 8 q^{97} + 16 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^6 + 4 * q^7 - 4 * q^8 - 12 * q^11 - 4 * q^12 - 4 * q^14 - 4 * q^15 + 4 * q^16 - 8 * q^21 + 12 * q^22 + 4 * q^24 + 16 * q^25 - 4 * q^27 + 4 * q^28 + 4 * q^30 + 4 * q^31 - 4 * q^32 + 4 * q^37 - 12 * q^39 + 12 * q^41 + 8 * q^42 + 32 * q^43 - 12 * q^44 - 8 * q^45 - 4 * q^48 - 16 * q^50 - 16 * q^51 - 12 * q^53 + 4 * q^54 - 8 * q^55 - 4 * q^56 - 4 * q^60 + 16 * q^61 - 4 * q^62 + 4 * q^64 + 16 * q^69 + 12 * q^71 - 8 * q^73 - 4 * q^74 - 4 * q^75 - 24 * q^77 + 12 * q^78 + 16 * q^79 + 4 * q^81 - 12 * q^82 - 8 * q^84 + 28 * q^85 - 32 * q^86 + 4 * q^87 + 12 * q^88 + 12 * q^89 + 8 * q^90 - 12 * q^91 - 44 * q^93 - 12 * q^95 + 4 * q^96 - 8 * q^97 + 16 * q^99

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