LMFDB - Embedded newform 210.2.j.b.197.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(113,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("210.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.j (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:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 16x^{10} + 86x^{8} + 196x^{6} + 185x^{4} + 60x^{2} + 4 $ x^12 + 16x^10 + 86x^8 + 196x^6 + 185x^4 + 60*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			197.1
Root			$-0.297931i$ of defining polynomial
Character	$\chi$	$=$	210.197
Dual form			210.2.j.b.113.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.10458 - 1.33413i) q^{3} -1.00000i q^{4} +(-0.953972 + 2.02236i) q^{5} +(1.72443 + 0.162311i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.559788 + 2.94731i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.10458 - 1.33413i) q^{3} -1.00000i q^{4} +(-0.953972 + 2.02236i) q^{5} +(1.72443 + 0.162311i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.559788 + 2.94731i) q^{9} +(-0.755464 - 2.10458i) q^{10} +0.780604i q^{11} +(-1.33413 + 1.10458i) q^{12} +(-3.85292 + 3.85292i) q^{13} +1.00000 q^{14} +(3.75183 - 0.961147i) q^{15} -1.00000 q^{16} +(-2.97331 + 2.97331i) q^{17} +(-1.68823 - 2.47989i) q^{18} +5.79249i q^{19} +(2.02236 + 0.953972i) q^{20} +(-0.162311 + 1.72443i) q^{21} +(-0.551971 - 0.551971i) q^{22} +(-1.74679 - 1.74679i) q^{23} +(0.162311 - 1.72443i) q^{24} +(-3.17988 - 3.85855i) q^{25} -5.44886i q^{26} +(4.55042 - 2.50872i) q^{27} +(-0.707107 + 0.707107i) q^{28} +3.33651 q^{29} +(-1.97331 + 3.33257i) q^{30} +1.20515 q^{31} +(0.707107 - 0.707107i) q^{32} +(1.04143 - 0.862243i) q^{33} -4.20489i q^{34} +(2.10458 - 0.755464i) q^{35} +(2.94731 + 0.559788i) q^{36} +(-6.28770 - 6.28770i) q^{37} +(-4.09591 - 4.09591i) q^{38} +(9.39617 + 0.884411i) q^{39} +(-2.10458 + 0.755464i) q^{40} -0.410091i q^{41} +(-1.10458 - 1.33413i) q^{42} +(-0.397015 + 0.397015i) q^{43} +0.780604 q^{44} +(-5.42650 - 3.94374i) q^{45} +2.47033 q^{46} +(4.50070 - 4.50070i) q^{47} +(1.10458 + 1.33413i) q^{48} +1.00000i q^{49} +(4.97692 + 0.479893i) q^{50} +(7.25104 + 0.682501i) q^{51} +(3.85292 + 3.85292i) q^{52} +(7.69577 + 7.69577i) q^{53} +(-1.44370 + 4.99157i) q^{54} +(-1.57866 - 0.744674i) q^{55} -1.00000i q^{56} +(7.72791 - 6.39829i) q^{57} +(-2.35927 + 2.35927i) q^{58} -12.6753 q^{59} +(-0.961147 - 3.75183i) q^{60} +9.11230 q^{61} +(-0.852168 + 0.852168i) q^{62} +(2.47989 - 1.68823i) q^{63} +1.00000i q^{64} +(-4.11642 - 11.4676i) q^{65} +(-0.126701 + 1.34610i) q^{66} +(4.95979 + 4.95979i) q^{67} +(2.97331 + 2.97331i) q^{68} +(-0.400963 + 4.25991i) q^{69} +(-0.953972 + 2.02236i) q^{70} +1.88593i q^{71} +(-2.47989 + 1.68823i) q^{72} +(-8.48507 + 8.48507i) q^{73} +8.89215 q^{74} +(-1.63535 + 8.50445i) q^{75} +5.79249 q^{76} +(0.551971 - 0.551971i) q^{77} +(-7.26947 + 6.01872i) q^{78} -12.5532i q^{79} +(0.953972 - 2.02236i) q^{80} +(-8.37327 - 3.29974i) q^{81} +(0.289978 + 0.289978i) q^{82} +(3.60601 + 3.60601i) q^{83} +(1.72443 + 0.162311i) q^{84} +(-3.17665 - 8.84955i) q^{85} -0.561464i q^{86} +(-3.68545 - 4.45132i) q^{87} +(-0.551971 + 0.551971i) q^{88} -18.5847 q^{89} +(6.62576 - 1.04847i) q^{90} +5.44886 q^{91} +(-1.74679 + 1.74679i) q^{92} +(-1.33119 - 1.60782i) q^{93} +6.36495i q^{94} +(-11.7145 - 5.52587i) q^{95} +(-1.72443 - 0.162311i) q^{96} +(-8.82001 - 8.82001i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(-2.30068 - 0.436973i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} + 4 q^{5}+O(q^{10}) $ 12 * q + 4 * q^3 + 4 * q^5	$ 12 q + 4 q^{3} + 4 q^{5} - 4 q^{12} + 12 q^{14} - 12 q^{15} - 12 q^{16} - 28 q^{17} - 8 q^{18} - 4 q^{21} + 4 q^{22} + 24 q^{23} + 4 q^{24} + 20 q^{25} + 28 q^{27} - 8 q^{29} - 16 q^{30} - 8 q^{31} - 36 q^{33} + 8 q^{35} + 4 q^{36} - 20 q^{37} + 4 q^{38} + 40 q^{39} - 8 q^{40} + 4 q^{42} + 8 q^{43} - 8 q^{44} - 48 q^{45} + 8 q^{46} - 16 q^{47} - 4 q^{48} + 16 q^{50} + 8 q^{51} + 24 q^{53} + 4 q^{54} - 16 q^{55} + 44 q^{57} - 8 q^{58} - 32 q^{59} + 4 q^{60} - 28 q^{62} - 8 q^{66} + 28 q^{68} + 32 q^{69} + 4 q^{70} - 24 q^{73} - 8 q^{74} - 4 q^{75} - 4 q^{77} - 8 q^{78} - 4 q^{80} - 36 q^{81} + 32 q^{82} + 24 q^{83} - 36 q^{85} - 16 q^{87} + 4 q^{88} - 48 q^{89} - 8 q^{90} + 24 q^{91} + 24 q^{92} - 20 q^{93} + 8 q^{97} + 40 q^{99}+O(q^{100}) $ 12 * q + 4 * q^3 + 4 * q^5 - 4 * q^12 + 12 * q^14 - 12 * q^15 - 12 * q^16 - 28 * q^17 - 8 * q^18 - 4 * q^21 + 4 * q^22 + 24 * q^23 + 4 * q^24 + 20 * q^25 + 28 * q^27 - 8 * q^29 - 16 * q^30 - 8 * q^31 - 36 * q^33 + 8 * q^35 + 4 * q^36 - 20 * q^37 + 4 * q^38 + 40 * q^39 - 8 * q^40 + 4 * q^42 + 8 * q^43 - 8 * q^44 - 48 * q^45 + 8 * q^46 - 16 * q^47 - 4 * q^48 + 16 * q^50 + 8 * q^51 + 24 * q^53 + 4 * q^54 - 16 * q^55 + 44 * q^57 - 8 * q^58 - 32 * q^59 + 4 * q^60 - 28 * q^62 - 8 * q^66 + 28 * q^68 + 32 * q^69 + 4 * q^70 - 24 * q^73 - 8 * q^74 - 4 * q^75 - 4 * q^77 - 8 * q^78 - 4 * q^80 - 36 * q^81 + 32 * q^82 + 24 * q^83 - 36 * q^85 - 16 * q^87 + 4 * q^88 - 48 * q^89 - 8 * q^90 + 24 * q^91 + 24 * q^92 - 20 * q^93 + 8 * q^97 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−1.10458	−	1.33413i	−0.637732	−	0.770258i
$3$	−1.10458	−	1.33413i	−0.637732	−	0.770258i
$4$		−	1.00000i		−	0.500000i
$5$	−0.953972	+	2.02236i	−0.426629	+	0.904427i
$5$	−0.953972	+	2.02236i	−0.426629	+	0.904427i
$6$	1.72443	+	0.162311i	0.703995	+	0.0662633i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−0.559788	+	2.94731i	−0.186596	+	0.982437i
$10$	−0.755464	−	2.10458i	−0.238899	−	0.665528i
$11$			0.780604i			0.235361i	0.993052	+	0.117681i	$0.0375459\pi$
$11$			0.780604i			0.235361i	−0.993052	+	0.117681i	$0.962454\pi$
$12$	−1.33413	+	1.10458i	−0.385129	+	0.318866i
$13$	−3.85292	+	3.85292i	−1.06861	+	1.06861i	−0.0711428	+	0.997466i	$0.522665\pi$
$13$	−3.85292	+	3.85292i	−1.06861	+	1.06861i	−0.997466	+	0.0711428i	$0.977335\pi$
$14$	1.00000			0.267261
$15$	3.75183	−	0.961147i	0.968717	−	0.248167i
$16$	−1.00000			−0.250000
$17$	−2.97331	+	2.97331i	−0.721133	+	0.721133i	−0.968836	−	0.247703i	$-0.920324\pi$
$17$	−2.97331	+	2.97331i	−0.721133	+	0.721133i	0.247703	+	0.968836i	$0.420324\pi$
$18$	−1.68823	−	2.47989i	−0.397920	−	0.584516i
$19$			5.79249i			1.32889i	0.747338	+	0.664444i	$0.231332\pi$
$19$			5.79249i			1.32889i	−0.747338	+	0.664444i	$0.768668\pi$
$20$	2.02236	+	0.953972i	0.452213	+	0.213315i
$21$	−0.162311	+	1.72443i	−0.0354192	+	0.376301i
$22$	−0.551971	−	0.551971i	−0.117681	−	0.117681i
$23$	−1.74679	−	1.74679i	−0.364231	−	0.364231i	0.501137	−	0.865368i	$-0.332915\pi$
$23$	−1.74679	−	1.74679i	−0.364231	−	0.364231i	−0.865368	+	0.501137i	$0.832915\pi$
$24$	0.162311	−	1.72443i	0.0331316	−	0.351998i
$25$	−3.17988	−	3.85855i	−0.635975	−	0.771709i
$26$		−	5.44886i		−	1.06861i
$27$	4.55042	−	2.50872i	0.875728	−	0.482804i
$28$	−0.707107	+	0.707107i	−0.133631	+	0.133631i
$29$	3.33651			0.619574			0.309787	−	0.950806i	$-0.399742\pi$
$29$	3.33651			0.619574			0.309787	+	0.950806i	$0.399742\pi$
$30$	−1.97331	+	3.33257i	−0.360275	+	0.608442i
$31$	1.20515			0.216451			0.108225	−	0.994126i	$-0.465483\pi$
$31$	1.20515			0.216451			0.108225	+	0.994126i	$0.465483\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	1.04143	−	0.862243i	0.181289	−	0.150097i
$34$		−	4.20489i		−	0.721133i
$35$	2.10458	−	0.755464i	0.355740	−	0.127697i
$36$	2.94731	+	0.559788i	0.491218	+	0.0932981i
$37$	−6.28770	−	6.28770i	−1.03369	−	1.03369i	−0.999412	−	0.0342797i	$-0.989086\pi$
$37$	−6.28770	−	6.28770i	−1.03369	−	1.03369i	−0.0342797	−	0.999412i	$-0.510914\pi$
$38$	−4.09591	−	4.09591i	−0.664444	−	0.664444i
$39$	9.39617	+	0.884411i	1.50459	+	0.141619i
$40$	−2.10458	+	0.755464i	−0.332764	+	0.119449i
$41$		−	0.410091i		−	0.0640455i	−0.999487	−	0.0320227i	$-0.989805\pi$
$41$		−	0.410091i		−	0.0640455i	0.999487	−	0.0320227i	$-0.0101949\pi$
$42$	−1.10458	−	1.33413i	−0.170441	−	0.205860i
$43$	−0.397015	+	0.397015i	−0.0605442	+	0.0605442i	−0.736731	−	0.676186i	$-0.763631\pi$
$43$	−0.397015	+	0.397015i	−0.0605442	+	0.0605442i	0.676186	+	0.736731i	$0.263631\pi$
$44$	0.780604			0.117681
$45$	−5.42650	−	3.94374i	−0.808935	−	0.587899i
$46$	2.47033			0.364231
$47$	4.50070	−	4.50070i	0.656495	−	0.656495i	−0.298054	−	0.954549i	$-0.596338\pi$
$47$	4.50070	−	4.50070i	0.656495	−	0.656495i	0.954549	+	0.298054i	$0.0963376\pi$
$48$	1.10458	+	1.33413i	0.159433	+	0.192565i
$49$			1.00000i			0.142857i
$50$	4.97692	+	0.479893i	0.703842	+	0.0678671i
$51$	7.25104	+	0.682501i	1.01535	+	0.0955693i
$52$	3.85292	+	3.85292i	0.534304	+	0.534304i
$53$	7.69577	+	7.69577i	1.05710	+	1.05710i	0.998268	+	0.0588277i	$0.0187363\pi$
$53$	7.69577	+	7.69577i	1.05710	+	1.05710i	0.0588277	+	0.998268i	$0.481264\pi$
$54$	−1.44370	+	4.99157i	−0.196462	+	0.679266i
$55$	−1.57866	−	0.744674i	−0.212867	−	0.100412i
$56$		−	1.00000i		−	0.133631i
$57$	7.72791	−	6.39829i	1.02359	−	0.847474i
$58$	−2.35927	+	2.35927i	−0.309787	+	0.309787i
$59$	−12.6753			−1.65019			−0.825093	−	0.564996i	$-0.808878\pi$
$59$	−12.6753			−1.65019			−0.825093	+	0.564996i	$0.808878\pi$
$60$	−0.961147	−	3.75183i	−0.124084	−	0.484359i
$61$	9.11230			1.16671			0.583355	−	0.812217i	$-0.301740\pi$
$61$	9.11230			1.16671			0.583355	+	0.812217i	$0.301740\pi$
$62$	−0.852168	+	0.852168i	−0.108225	+	0.108225i
$63$	2.47989	−	1.68823i	0.312437	−	0.212697i
$64$			1.00000i			0.125000i
$65$	−4.11642	−	11.4676i	−0.510579	−	1.42238i
$66$	−0.126701	+	1.34610i	−0.0155958	+	0.165693i
$67$	4.95979	+	4.95979i	0.605934	+	0.605934i	0.941881	−	0.335947i	$-0.109056\pi$
$67$	4.95979	+	4.95979i	0.605934	+	0.605934i	−0.335947	+	0.941881i	$0.609056\pi$
$68$	2.97331	+	2.97331i	0.360567	+	0.360567i
$69$	−0.400963	+	4.25991i	−0.0482702	+	0.512833i
$70$	−0.953972	+	2.02236i	−0.114021	+	0.241718i
$71$			1.88593i			0.223819i	0.993718	+	0.111910i	$0.0356967\pi$
$71$			1.88593i			0.223819i	−0.993718	+	0.111910i	$0.964303\pi$
$72$	−2.47989	+	1.68823i	−0.292258	+	0.198960i
$73$	−8.48507	+	8.48507i	−0.993102	+	0.993102i	−0.999976	−	0.00687462i	$-0.997812\pi$
$73$	−8.48507	+	8.48507i	−0.993102	+	0.993102i	0.00687462	+	0.999976i	$0.497812\pi$
$74$	8.89215			1.03369
$75$	−1.63535	+	8.50445i	−0.188834	+	0.982009i
$76$	5.79249			0.664444
$77$	0.551971	−	0.551971i	0.0629029	−	0.0629029i
$78$	−7.26947	+	6.01872i	−0.823105	+	0.681486i
$79$		−	12.5532i		−	1.41234i	−0.708041	−	0.706172i	$-0.750421\pi$
$79$		−	12.5532i		−	1.41234i	0.708041	−	0.706172i	$-0.249579\pi$
$80$	0.953972	−	2.02236i	0.106657	−	0.226107i
$81$	−8.37327	−	3.29974i	−0.930364	−	0.366638i
$82$	0.289978	+	0.289978i	0.0320227	+	0.0320227i
$83$	3.60601	+	3.60601i	0.395811	+	0.395811i	0.876753	−	0.480942i	$-0.159705\pi$
$83$	3.60601	+	3.60601i	0.395811	+	0.395811i	−0.480942	+	0.876753i	$0.659705\pi$
$84$	1.72443	+	0.162311i	0.188151	+	0.0177096i
$85$	−3.17665	−	8.84955i	−0.344556	−	0.959868i
$86$		−	0.561464i		−	0.0605442i
$87$	−3.68545	−	4.45132i	−0.395122	−	0.477232i
$88$	−0.551971	+	0.551971i	−0.0588403	+	0.0588403i
$89$	−18.5847			−1.96998			−0.984988	−	0.172621i	$-0.944776\pi$
$89$	−18.5847			−1.96998			−0.984988	+	0.172621i	$0.944776\pi$
$90$	6.62576	−	1.04847i	0.698417	−	0.110518i
$91$	5.44886			0.571196
$92$	−1.74679	+	1.74679i	−0.182115	+	0.182115i
$93$	−1.33119	−	1.60782i	−0.138038	−	0.166723i
$94$			6.36495i			0.656495i
$95$	−11.7145	−	5.52587i	−1.20188	−	0.566942i
$96$	−1.72443	−	0.162311i	−0.175999	−	0.0165658i
$97$	−8.82001	−	8.82001i	−0.895536	−	0.895536i	0.0995012	−	0.995037i	$-0.468275\pi$
$97$	−8.82001	−	8.82001i	−0.895536	−	0.895536i	−0.995037	+	0.0995012i	$0.968275\pi$
$98$	−0.707107	−	0.707107i	−0.0714286	−	0.0714286i
$99$	−2.30068	−	0.436973i	−0.231227	−	0.0439175i
$100$	−3.85855	+	3.17988i	−0.385855	+	0.317988i
$101$			8.52395i			0.848165i	0.905624	+	0.424083i	$0.139403\pi$
$101$			8.52395i			0.848165i	−0.905624	+	0.424083i	$0.860597\pi$
$102$	−5.60986	+	4.64466i	−0.555459	+	0.459890i
$103$	7.68570	−	7.68570i	0.757294	−	0.757294i	−0.218535	−	0.975829i	$-0.570128\pi$
$103$	7.68570	−	7.68570i	0.757294	−	0.757294i	0.975829	+	0.218535i	$0.0701277\pi$
$104$	−5.44886			−0.534304
$105$	−3.33257	−	1.97331i	−0.325226	−	0.192575i
$106$	−10.8835			−1.05710
$107$	−8.53379	+	8.53379i	−0.824993	+	0.824993i	−0.986819	−	0.161827i	$-0.948261\pi$
$107$	−8.53379	+	8.53379i	−0.824993	+	0.824993i	0.161827	+	0.986819i	$0.448261\pi$
$108$	−2.50872	−	4.55042i	−0.241402	−	0.437864i
$109$			3.67769i			0.352259i	0.984367	+	0.176129i	$0.0563577\pi$
$109$			3.67769i			0.352259i	−0.984367	+	0.176129i	$0.943642\pi$
$110$	1.64285	−	0.589719i	0.156639	−	0.0562275i
$111$	−1.44330	+	15.3339i	−0.136992	+	1.45543i
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$	11.8416	+	11.8416i	1.11396	+	1.11396i	0.992609	+	0.121355i	$0.0387238\pi$
$113$	11.8416	+	11.8416i	1.11396	+	1.11396i	0.121355	+	0.992609i	$0.461276\pi$
$114$	−0.940186	+	9.98874i	−0.0880565	+	0.935531i
$115$	5.19902	−	1.86625i	0.484811	−	0.174028i
$116$		−	3.33651i		−	0.309787i
$117$	−9.19894	−	13.5126i	−0.850442	−	1.24924i
$118$	8.96281	−	8.96281i	0.825093	−	0.825093i
$119$	4.20489			0.385462
$120$	3.33257	+	1.97331i	0.304221	+	0.180138i
$121$	10.3907			0.944605
$122$	−6.44337	+	6.44337i	−0.583355	+	0.583355i
$123$	−0.547114	+	0.452980i	−0.0493316	+	0.0408438i
$124$		−	1.20515i		−	0.108225i
$125$	10.8369	−	2.74991i	0.969280	−	0.245959i
$126$	−0.559788	+	2.94731i	−0.0498699	+	0.262567i
$127$	12.5290	+	12.5290i	1.11177	+	1.11177i	0.992911	+	0.118863i	$0.0379248\pi$
$127$	12.5290	+	12.5290i	1.11177	+	1.11177i	0.118863	+	0.992911i	$0.462075\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	0.968204	+	0.0911319i	0.0852456	+	0.00802372i
$130$	11.0195	+	5.19806i	0.966478	+	0.455900i
$131$		−	11.8873i		−	1.03860i	−0.854591	−	0.519301i	$-0.826192\pi$
$131$		−	11.8873i		−	1.03860i	0.854591	−	0.519301i	$-0.173808\pi$
$132$	−0.862243	−	1.04143i	−0.0750486	−	0.0906444i
$133$	4.09591	−	4.09591i	0.355160	−	0.355160i
$134$	−7.01420			−0.605934
$135$	0.732569	+	11.5958i	0.0630495	+	0.998010i
$136$	−4.20489			−0.360567
$137$	−4.34731	+	4.34731i	−0.371416	+	0.371416i	−0.867993	−	0.496577i	$-0.834590\pi$
$137$	−4.34731	+	4.34731i	−0.371416	+	0.371416i	0.496577	+	0.867993i	$0.334590\pi$
$138$	−2.72869	−	3.29574i	−0.232281	−	0.280552i
$139$			11.6395i			0.987250i	0.869675	+	0.493625i	$0.164328\pi$
$139$			11.6395i			0.987250i	−0.869675	+	0.493625i	$0.835672\pi$
$140$	−0.755464	−	2.10458i	−0.0638484	−	0.177870i
$141$	−10.9759	−	1.03310i	−0.924338	−	0.0870030i
$142$	−1.33356	−	1.33356i	−0.111910	−	0.111910i
$143$	−3.00761	−	3.00761i	−0.251509	−	0.251509i
$144$	0.559788	−	2.94731i	0.0466490	−	0.245609i
$145$	−3.18293	+	6.74762i	−0.264328	+	0.560359i
$146$		−	11.9997i		−	0.993102i
$147$	1.33413	−	1.10458i	0.110037	−	0.0911046i
$148$	−6.28770	+	6.28770i	−0.516846	+	0.516846i
$149$	5.78924			0.474273			0.237137	−	0.971476i	$-0.423791\pi$
$149$	5.78924			0.474273			0.237137	+	0.971476i	$0.423791\pi$
$150$	−4.85718	−	7.16992i	−0.396587	−	0.585422i
$151$	0.326935			0.0266056			0.0133028	−	0.999912i	$-0.495765\pi$
$151$	0.326935			0.0266056			0.0133028	+	0.999912i	$0.495765\pi$
$152$	−4.09591	+	4.09591i	−0.332222	+	0.332222i
$153$	−7.09884	−	10.4277i	−0.573907	−	0.843028i
$154$			0.780604i			0.0629029i
$155$	−1.14968	+	2.43724i	−0.0923443	+	0.195764i
$156$	0.884411	−	9.39617i	0.0708095	−	0.752296i
$157$	15.7404	+	15.7404i	1.25622	+	1.25622i	0.952883	+	0.303339i	$0.0981014\pi$
$157$	15.7404	+	15.7404i	1.25622	+	1.25622i	0.303339	+	0.952883i	$0.401899\pi$
$158$	8.87644	+	8.87644i	0.706172	+	0.706172i
$159$	1.76651	−	18.7678i	0.140093	−	1.48838i
$160$	0.755464	+	2.10458i	0.0597247	+	0.166382i
$161$			2.47033i			0.194689i
$162$	8.25407	−	3.58753i	0.648501	−	0.281863i
$163$	0.261547	−	0.261547i	0.0204859	−	0.0204859i	−0.696790	−	0.717276i	$-0.745389\pi$
$163$	0.261547	−	0.261547i	0.0204859	−	0.0204859i	0.717276	+	0.696790i	$0.245389\pi$
$164$	−0.410091			−0.0320227
$165$	0.750275	+	2.92869i	0.0584089	+	0.227998i
$166$	−5.09967			−0.395811
$167$	7.48816	−	7.48816i	0.579451	−	0.579451i	−0.355301	−	0.934752i	$-0.615622\pi$
$167$	7.48816	−	7.48816i	0.579451	−	0.579451i	0.934752	+	0.355301i	$0.115622\pi$
$168$	−1.33413	+	1.10458i	−0.102930	+	0.0852205i
$169$		−	16.6901i		−	1.28385i
$170$	8.50380	+	4.01135i	0.652212	+	0.307656i
$171$	−17.0723	−	3.24257i	−1.30555	−	0.247965i
$172$	0.397015	+	0.397015i	0.0302721	+	0.0302721i
$173$	8.48843	+	8.48843i	0.645363	+	0.645363i	0.951869	−	0.306505i	$-0.0991598\pi$
$173$	8.48843	+	8.48843i	0.645363	+	0.645363i	−0.306505	+	0.951869i	$0.599160\pi$
$174$	5.75357	+	0.541553i	0.436177	+	0.0410550i
$175$	−0.479893	+	4.97692i	−0.0362765	+	0.376220i
$176$		−	0.780604i		−	0.0588403i
$177$	14.0010	+	16.9105i	1.05238	+	1.27107i
$178$	13.1414	−	13.1414i	0.984988	−	0.984988i
$179$	2.37051			0.177180			0.0885902	−	0.996068i	$-0.471764\pi$
$179$	2.37051			0.177180			0.0885902	+	0.996068i	$0.471764\pi$
$180$	−3.94374	+	5.42650i	−0.293949	+	0.404467i
$181$	−6.15369			−0.457400			−0.228700	−	0.973497i	$-0.573447\pi$
$181$	−6.15369			−0.457400			−0.228700	+	0.973497i	$0.573447\pi$
$182$	−3.85292	+	3.85292i	−0.285598	+	0.285598i
$183$	−10.0653	−	12.1570i	−0.744048	−	0.898669i
$184$		−	2.47033i		−	0.182115i
$185$	18.7143	−	6.71771i	1.37590	−	0.493896i
$186$	2.07819	+	0.195609i	0.152380	+	0.0143428i
$187$	−2.32098	−	2.32098i	−0.169727	−	0.169727i
$188$	−4.50070	−	4.50070i	−0.328247	−	0.328247i
$189$	−4.99157	−	1.44370i	−0.363083	−	0.105014i
$190$	12.1908	−	4.37602i	0.884412	−	0.317470i
$191$			9.64185i			0.697660i	0.937186	+	0.348830i	$0.113421\pi$
$191$			9.64185i			0.697660i	−0.937186	+	0.348830i	$0.886579\pi$
$192$	1.33413	−	1.10458i	0.0962823	−	0.0797165i
$193$	−6.77716	+	6.77716i	−0.487830	+	0.487830i	−0.907621	−	0.419791i	$-0.862104\pi$
$193$	−6.77716	+	6.77716i	−0.487830	+	0.487830i	0.419791	+	0.907621i	$0.362104\pi$
$194$	12.4734			0.895536
$195$	−10.7523	+	18.1587i	−0.769986	+	1.30037i
$196$	1.00000			0.0714286
$197$	−2.34224	+	2.34224i	−0.166878	+	0.166878i	−0.785606	−	0.618728i	$-0.787648\pi$
$197$	−2.34224	+	2.34224i	−0.166878	+	0.166878i	0.618728	+	0.785606i	$0.287648\pi$
$198$	1.93582	−	1.31784i	0.137572	−	0.0936549i
$199$		−	9.94617i		−	0.705066i	−0.935799	−	0.352533i	$-0.885320\pi$
$199$		−	9.94617i		−	0.705066i	0.935799	−	0.352533i	$-0.114680\pi$
$200$	0.479893	−	4.97692i	0.0339336	−	0.351921i
$201$	1.13848	−	12.0955i	0.0803024	−	0.853150i
$202$	−6.02735	−	6.02735i	−0.424083	−	0.424083i
$203$	−2.35927	−	2.35927i	−0.165588	−	0.165588i
$204$	0.682501	−	7.25104i	0.0477847	−	0.507674i
$205$	0.829352	+	0.391215i	0.0579244	+	0.0273237i
$206$			10.8692i			0.757294i
$207$	6.12616	−	4.17050i	0.425797	−	0.289869i
$208$	3.85292	−	3.85292i	0.267152	−	0.267152i
$209$	−4.52164			−0.312768
$210$	3.75183	−	0.961147i	0.258901	−	0.0663254i
$211$	−14.9895			−1.03192			−0.515960	−	0.856613i	$-0.672565\pi$
$211$	−14.9895			−1.03192			−0.515960	+	0.856613i	$0.672565\pi$
$212$	7.69577	−	7.69577i	0.528548	−	0.528548i
$213$	2.51607	−	2.08317i	0.172399	−	0.142737i
$214$		−	12.0686i		−	0.824993i
$215$	−0.424166	−	1.18165i	−0.0289279	−	0.0805877i
$216$	4.99157	+	1.44370i	0.339633	+	0.0982311i
$217$	−0.852168	−	0.852168i	−0.0578489	−	0.0578489i
$218$	−2.60052	−	2.60052i	−0.176129	−	0.176129i
$219$	20.6926	+	1.94769i	1.39828	+	0.131612i
$220$	−0.744674	+	1.57866i	−0.0502059	+	0.106433i
$221$		−	22.9119i		−	1.54122i
$222$	−9.82213	−	11.8633i	−0.659218	−	0.796210i
$223$	7.97398	−	7.97398i	0.533977	−	0.533977i	−0.387776	−	0.921754i	$-0.626757\pi$
$223$	7.97398	−	7.97398i	0.533977	−	0.533977i	0.921754	+	0.387776i	$0.126757\pi$
$224$	−1.00000			−0.0668153
$225$	13.1524	−	7.21211i	0.876826	−	0.480807i
$226$	−16.7465			−1.11396
$227$	20.3950	−	20.3950i	1.35366	−	1.35366i	0.472135	−	0.881526i	$-0.343484\pi$
$227$	20.3950	−	20.3950i	1.35366	−	1.35366i	0.881526	−	0.472135i	$-0.156516\pi$
$228$	−6.39829	−	7.72791i	−0.423737	−	0.511794i
$229$			19.5317i			1.29069i	0.763891	+	0.645346i	$0.223287\pi$
$229$			19.5317i			1.29069i	−0.763891	+	0.645346i	$0.776713\pi$
$230$	−2.35663	+	4.99590i	−0.155391	+	0.329420i
$231$	−1.34610	−	0.126701i	−0.0885667	−	0.00833630i
$232$	2.35927	+	2.35927i	0.154893	+	0.154893i
$233$	2.92961	+	2.92961i	0.191925	+	0.191925i	0.796527	−	0.604602i	$-0.206668\pi$
$233$	2.92961	+	2.92961i	0.191925	+	0.191925i	−0.604602	+	0.796527i	$0.706668\pi$
$234$	16.0595	+	3.05021i	1.04984	+	0.199398i
$235$	4.80849	+	13.3956i	0.313672	+	0.873831i
$236$			12.6753i			0.825093i
$237$	−16.7475	+	13.8660i	−1.08787	+	0.900696i
$238$	−2.97331	+	2.97331i	−0.192731	+	0.192731i
$239$	−12.0343			−0.778432			−0.389216	−	0.921147i	$-0.627254\pi$
$239$	−12.0343			−0.778432			−0.389216	+	0.921147i	$0.627254\pi$
$240$	−3.75183	+	0.961147i	−0.242179	+	0.0620418i
$241$	5.77972			0.372304			0.186152	−	0.982521i	$-0.440398\pi$
$241$	5.77972			0.372304			0.186152	+	0.982521i	$0.440398\pi$
$242$	−7.34730	+	7.34730i	−0.472303	+	0.472303i
$243$	4.84671	+	14.8158i	0.310917	+	0.950437i
$244$		−	9.11230i		−	0.583355i
$245$	−2.02236	−	0.953972i	−0.129204	−	0.0609470i
$246$	0.0665624	−	0.707173i	0.00424386	−	0.0450877i
$247$	−22.3180	−	22.3180i	−1.42006	−	1.42006i
$248$	0.852168	+	0.852168i	0.0541127	+	0.0541127i
$249$	0.827733	−	8.79401i	0.0524555	−	0.557298i
$250$	−5.71835	+	9.60731i	−0.361660	+	0.607620i
$251$		−	1.50663i		−	0.0950977i	−0.998869	−	0.0475489i	$-0.984859\pi$
$251$		−	1.50663i		−	0.0950977i	0.998869	−	0.0475489i	$-0.0151410\pi$
$252$	−1.68823	−	2.47989i	−0.106349	−	0.156219i
$253$	1.36355	−	1.36355i	0.0857257	−	0.0857257i
$254$	−17.7188			−1.11177
$255$	−8.29755	+	14.0131i	−0.519613	+	0.877536i
$256$	1.00000			0.0625000
$257$	−3.44942	+	3.44942i	−0.215169	+	0.215169i	−0.806459	−	0.591290i	$-0.798619\pi$
$257$	−3.44942	+	3.44942i	−0.215169	+	0.215169i	0.591290	+	0.806459i	$0.298619\pi$
$258$	−0.749064	+	0.620184i	−0.0466347	+	0.0386110i
$259$			8.89215i			0.552532i
$260$	−11.4676	+	4.11642i	−0.711189	+	0.255289i
$261$	−1.86774	+	9.83372i	−0.115610	+	0.608692i
$262$	8.40562	+	8.40562i	0.519301	+	0.519301i
$263$	−9.85402	−	9.85402i	−0.607625	−	0.607625i	0.334700	−	0.942325i	$-0.391365\pi$
$263$	−9.85402	−	9.85402i	−0.607625	−	0.607625i	−0.942325	+	0.334700i	$0.891365\pi$
$264$	1.34610	+	0.126701i	0.0828465	+	0.00779790i
$265$	−22.9052	+	8.22207i	−1.40705	+	0.505078i
$266$			5.79249i			0.355160i
$267$	20.5284	+	24.7944i	1.25632	+	1.51739i
$268$	4.95979	−	4.95979i	0.302967	−	0.302967i
$269$	9.17881			0.559642			0.279821	−	0.960052i	$-0.409725\pi$
$269$	9.17881			0.559642			0.279821	+	0.960052i	$0.409725\pi$
$270$	−8.71750	−	7.68149i	−0.530530	−	0.467480i
$271$	−7.85752			−0.477310			−0.238655	−	0.971104i	$-0.576707\pi$
$271$	−7.85752			−0.477310			−0.238655	+	0.971104i	$0.576707\pi$
$272$	2.97331	−	2.97331i	0.180283	−	0.180283i
$273$	−6.01872	−	7.26947i	−0.364270	−	0.439968i
$274$		−	6.14802i		−	0.371416i
$275$	3.01200	−	2.48222i	0.181630	−	0.149684i
$276$	4.25991	+	0.400963i	0.256417	+	0.0241351i
$277$	2.82887	+	2.82887i	0.169970	+	0.169970i	0.786966	−	0.616996i	$-0.211650\pi$
$277$	2.82887	+	2.82887i	0.169970	+	0.169970i	−0.616996	+	0.786966i	$0.711650\pi$
$278$	−8.23037	−	8.23037i	−0.493625	−	0.493625i
$279$	−0.674628	+	3.55194i	−0.0403889	+	0.212649i
$280$	2.02236	+	0.953972i	0.120859	+	0.0570107i
$281$			0.990734i			0.0591022i	0.999563	+	0.0295511i	$0.00940778\pi$
$281$			0.990734i			0.0591022i	−0.999563	+	0.0295511i	$0.990592\pi$
$282$	8.49165	−	7.03062i	0.505671	−	0.418668i
$283$	−16.0249	+	16.0249i	−0.952584	+	0.952584i	−0.998926	−	0.0463416i	$-0.985244\pi$
$283$	−16.0249	+	16.0249i	−0.952584	+	0.952584i	0.0463416	+	0.998926i	$0.485244\pi$
$284$	1.88593			0.111910
$285$	5.56743	+	21.7324i	0.329786	+	1.28732i
$286$	4.25340			0.251509
$287$	−0.289978	+	0.289978i	−0.0171169	+	0.0171169i
$288$	1.68823	+	2.47989i	0.0994801	+	0.146129i
$289$		−	0.681122i		−	0.0400660i
$290$	−2.52061	−	7.02196i	−0.148015	−	0.412344i
$291$	−2.02457	+	21.5095i	−0.118682	+	1.26091i
$292$	8.48507	+	8.48507i	0.496551	+	0.496551i
$293$	−0.328091	−	0.328091i	−0.0191673	−	0.0191673i	0.697458	−	0.716625i	$-0.254314\pi$
$293$	−0.328091	−	0.328091i	−0.0191673	−	0.0191673i	−0.716625	+	0.697458i	$0.754314\pi$
$294$	−0.162311	+	1.72443i	−0.00946618	+	0.100571i
$295$	12.0919	−	25.6341i	0.704018	−	1.49247i
$296$		−	8.89215i		−	0.516846i
$297$	1.95832	+	3.55208i	0.113633	+	0.206112i
$298$	−4.09361	+	4.09361i	−0.237137	+	0.237137i
$299$	13.4605			0.778440
$300$	8.50445	+	1.63535i	0.491005	+	0.0944171i
$301$	0.561464			0.0323622
$302$	−0.231178	+	0.231178i	−0.0133028	+	0.0133028i
$303$	11.3720	−	9.41542i	0.653306	−	0.540902i
$304$		−	5.79249i		−	0.332222i
$305$	−8.69288	+	18.4283i	−0.497753	+	1.05520i
$306$	12.3931	+	2.35385i	0.708468	+	0.134561i
$307$	−5.29402	−	5.29402i	−0.302146	−	0.302146i	0.539707	−	0.841853i	$-0.318535\pi$
$307$	−5.29402	−	5.29402i	−0.302146	−	0.302146i	−0.841853	+	0.539707i	$0.818535\pi$
$308$	−0.551971	−	0.551971i	−0.0314514	−	0.0314514i
$309$	−18.7432	−	1.76420i	−1.06626	−	0.100362i
$310$	−0.910446	−	2.53633i	−0.0517099	−	0.144054i
$311$			12.1390i			0.688340i	0.938907	+	0.344170i	$0.111840\pi$
$311$			12.1390i			0.688340i	−0.938907	+	0.344170i	$0.888160\pi$
$312$	6.01872	+	7.26947i	0.340743	+	0.411553i
$313$	12.2205	−	12.2205i	0.690745	−	0.690745i	−0.271651	−	0.962396i	$-0.587570\pi$
$313$	12.2205	−	12.2205i	0.690745	−	0.690745i	0.962396	+	0.271651i	$0.0875696\pi$
$314$	−22.2603			−1.25622
$315$	1.04847	+	6.62576i	0.0590743	+	0.373319i
$316$	−12.5532			−0.706172
$317$	−2.40772	+	2.40772i	−0.135231	+	0.135231i	−0.771482	−	0.636251i	$-0.780484\pi$
$317$	−2.40772	+	2.40772i	−0.135231	+	0.135231i	0.636251	+	0.771482i	$0.280484\pi$
$318$	12.0217	+	14.5199i	0.674144	+	0.814237i
$319$			2.60449i			0.145824i
$320$	−2.02236	−	0.953972i	−0.113053	−	0.0533286i
$321$	20.8114	+	1.95887i	1.16158	+	0.109333i
$322$	−1.74679	−	1.74679i	−0.0973447	−	0.0973447i
$323$	−17.2229	−	17.2229i	−0.958305	−	0.958305i
$324$	−3.29974	+	8.37327i	−0.183319	+	0.465182i
$325$	27.1185	+	2.61487i	1.50426	+	0.145047i
$326$			0.369883i			0.0204859i
$327$	4.90650	−	4.06232i	0.271330	−	0.224647i
$328$	0.289978	−	0.289978i	0.0160114	−	0.0160114i
$329$	−6.36495			−0.350911
$330$	−2.60142	−	1.54037i	−0.143204	−	0.0847947i
$331$	−15.2790			−0.839810			−0.419905	−	0.907568i	$-0.637937\pi$
$331$	−15.2790			−0.839810			−0.419905	+	0.907568i	$0.637937\pi$
$332$	3.60601	−	3.60601i	0.197905	−	0.197905i
$333$	22.0516	−	15.0120i	1.20842	−	0.822654i
$334$			10.5899i			0.579451i
$335$	−14.7620	+	5.29898i	−0.806532	+	0.289514i
$336$	0.162311	−	1.72443i	0.00885481	−	0.0940753i
$337$	11.4834	+	11.4834i	0.625541	+	0.625541i	0.946943	−	0.321402i	$-0.104154\pi$
$337$	11.4834	+	11.4834i	0.625541	+	0.625541i	−0.321402	+	0.946943i	$0.604154\pi$
$338$	11.8016	+	11.8016i	0.641925	+	0.641925i
$339$	2.71815	−	28.8782i	0.147630	−	1.56845i
$340$	−8.84955	+	3.17665i	−0.479934	+	0.172278i
$341$			0.940744i			0.0509441i
$342$	14.3648	−	9.77907i	0.776757	−	0.528792i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	−0.561464			−0.0302721
$345$	−8.23257	−	4.87473i	−0.443226	−	0.262446i
$346$	−12.0045			−0.645363
$347$	−12.0974	+	12.0974i	−0.649425	+	0.649425i	−0.952854	−	0.303429i	$-0.901868\pi$
$347$	−12.0974	+	12.0974i	−0.649425	+	0.649425i	0.303429	+	0.952854i	$0.401868\pi$
$348$	−4.45132	+	3.68545i	−0.238616	+	0.197561i
$349$		−	0.114169i		−	0.00611132i	−0.999995	−	0.00305566i	$-0.999027\pi$
$349$		−	0.114169i		−	0.00611132i	0.999995	−	0.00305566i	$-0.000972649\pi$
$350$	−3.17988	−	3.85855i	−0.169972	−	0.206248i
$351$	−7.86650	+	27.1983i	−0.419883	+	1.45174i
$352$	0.551971	+	0.551971i	0.0294201	+	0.0294201i
$353$	17.4937	+	17.4937i	0.931097	+	0.931097i	0.997775	−	0.0666780i	$-0.0212400\pi$
$353$	17.4937	+	17.4937i	0.931097	+	0.931097i	−0.0666780	+	0.997775i	$0.521240\pi$
$354$	−21.8577	−	2.05735i	−1.16172	−	0.109347i
$355$	−3.81404	−	1.79913i	−0.202428	−	0.0954877i
$356$			18.5847i			0.984988i
$357$	−4.64466	−	5.60986i	−0.245821	−	0.296905i
$358$	−1.67621	+	1.67621i	−0.0885902	+	0.0885902i
$359$	25.4743			1.34448			0.672240	−	0.740333i	$-0.265332\pi$
$359$	25.4743			1.34448			0.672240	+	0.740333i	$0.265332\pi$
$360$	−1.04847	−	6.62576i	−0.0552590	−	0.349208i
$361$	−14.5529			−0.765944
$362$	4.35131	−	4.35131i	0.228700	−	0.228700i
$363$	−11.4774	−	13.8625i	−0.602405	−	0.727590i
$364$		−	5.44886i		−	0.285598i
$365$	−9.06534	−	25.2544i	−0.474502	−	1.32187i
$366$	15.7135	+	1.47903i	0.821359	+	0.0773101i
$367$	−23.9590	−	23.9590i	−1.25065	−	1.25065i	−0.955428	−	0.295224i	$-0.904606\pi$
$367$	−23.9590	−	23.9590i	−1.25065	−	1.25065i	−0.295224	−	0.955428i	$-0.595394\pi$
$368$	1.74679	+	1.74679i	0.0910576	+	0.0910576i
$369$	1.20867	+	0.229564i	0.0629206	+	0.0119506i
$370$	−8.48286	+	17.9831i	−0.441003	+	0.934899i
$371$		−	10.8835i		−	0.565041i
$372$	−1.60782	+	1.33119i	−0.0833616	+	0.0690188i
$373$	4.14472	−	4.14472i	0.214605	−	0.214605i	−0.591615	−	0.806221i	$-0.701509\pi$
$373$	4.14472	−	4.14472i	0.214605	−	0.214605i	0.806221	+	0.591615i	$0.201509\pi$
$374$	3.28236			0.169727
$375$	−15.6390	−	11.4203i	−0.807593	−	0.589740i
$376$	6.36495			0.328247
$377$	−12.8553	+	12.8553i	−0.662082	+	0.662082i
$378$	4.55042	−	2.50872i	0.234048	−	0.129035i
$379$			13.5788i			0.697495i	0.937217	+	0.348748i	$0.113393\pi$
$379$			13.5788i			0.697495i	−0.937217	+	0.348748i	$0.886607\pi$
$380$	−5.52587	+	11.7145i	−0.283471	+	0.600941i
$381$	2.87595	−	30.5547i	0.147340	−	1.56537i
$382$	−6.81782	−	6.81782i	−0.348830	−	0.348830i
$383$	−11.0679	−	11.0679i	−0.565541	−	0.565541i	0.365335	−	0.930876i	$-0.380954\pi$
$383$	−11.0679	−	11.0679i	−0.565541	−	0.565541i	−0.930876	+	0.365335i	$0.880954\pi$
$384$	−0.162311	+	1.72443i	−0.00828291	+	0.0879994i
$385$	0.589719	+	1.64285i	0.0300548	+	0.0837272i
$386$		−	9.58435i		−	0.487830i
$387$	−0.947882	−	1.39237i	−0.0481835	−	0.0707782i
$388$	−8.82001	+	8.82001i	−0.447768	+	0.447768i
$389$	−29.1746			−1.47921			−0.739605	−	0.673041i	$-0.764988\pi$
$389$	−29.1746			−1.47921			−0.739605	+	0.673041i	$0.764988\pi$
$390$	−5.23715	−	20.4432i	−0.265193	−	1.03518i
$391$	10.3875			0.525317
$392$	−0.707107	+	0.707107i	−0.0357143	+	0.0357143i
$393$	−15.8592	+	13.1306i	−0.799992	+	0.662350i
$394$		−	3.31243i		−	0.166878i
$395$	25.3870	+	11.9754i	1.27736	+	0.602547i
$396$	−0.436973	+	2.30068i	−0.0219587	+	0.115614i
$397$	−10.4013	−	10.4013i	−0.522028	−	0.522028i	0.396155	−	0.918183i	$-0.370344\pi$
$397$	−10.4013	−	10.4013i	−0.522028	−	0.522028i	−0.918183	+	0.396155i	$0.870344\pi$
$398$	7.03301	+	7.03301i	0.352533	+	0.352533i
$399$	−9.98874	−	0.940186i	−0.500062	−	0.0470682i
$400$	3.17988	+	3.85855i	0.158994	+	0.192927i
$401$			3.08489i			0.154052i	0.997029	+	0.0770260i	$0.0245425\pi$
$401$			3.08489i			0.154052i	−0.997029	+	0.0770260i	$0.975458\pi$
$402$	7.74777	+	9.35783i	0.386424	+	0.466726i
$403$	−4.64334	+	4.64334i	−0.231301	+	0.231301i
$404$	8.52395			0.424083
$405$	14.6611	−	13.7859i	0.728517	−	0.685027i
$406$	3.33651			0.165588
$407$	4.90821	−	4.90821i	0.243291	−	0.243291i
$408$	4.64466	+	5.60986i	0.229945	+	0.277729i
$409$			2.47368i			0.122316i	0.998128	+	0.0611579i	$0.0194793\pi$
$409$			2.47368i			0.122316i	−0.998128	+	0.0611579i	$0.980521\pi$
$410$	−0.863071	+	0.309809i	−0.0426241	+	0.0153004i
$411$	10.6018	+	0.997893i	0.522950	+	0.0492224i
$412$	−7.68570	−	7.68570i	−0.378647	−	0.378647i
$413$	8.96281	+	8.96281i	0.441031	+	0.441031i
$414$	−1.38286	+	7.28083i	−0.0679640	+	0.357833i
$415$	−10.7327	+	3.85262i	−0.526846	+	0.189117i
$416$			5.44886i			0.267152i
$417$	15.5286	−	12.8568i	0.760437	−	0.629601i
$418$	3.19728	−	3.19728i	0.156384	−	0.156384i
$419$	23.6148			1.15366			0.576828	−	0.816865i	$-0.304290\pi$
$419$	23.6148			1.15366			0.576828	+	0.816865i	$0.304290\pi$
$420$	−1.97331	+	3.33257i	−0.0962876	+	0.162613i
$421$	−19.6409			−0.957240			−0.478620	−	0.878022i	$-0.658863\pi$
$421$	−19.6409			−0.957240			−0.478620	+	0.878022i	$0.658863\pi$
$422$	10.5992	−	10.5992i	0.515960	−	0.515960i
$423$	10.7455	+	15.7844i	0.522465	+	0.767464i
$424$			10.8835i			0.528548i
$425$	20.9274	+	2.01790i	1.01513	+	0.0978825i
$426$	−0.306108	+	3.25216i	−0.0148310	+	0.157568i
$427$	−6.44337	−	6.44337i	−0.311816	−	0.311816i
$428$	8.53379	+	8.53379i	0.412496	+	0.412496i
$429$	−0.690375	+	7.33469i	−0.0333316	+	0.354122i
$430$	1.13548	+	0.535621i	0.0547578	+	0.0258299i
$431$		−	28.9367i		−	1.39383i	−0.717153	−	0.696915i	$-0.754555\pi$
$431$		−	28.9367i		−	1.39383i	0.717153	−	0.696915i	$-0.245445\pi$
$432$	−4.55042	+	2.50872i	−0.218932	+	0.120701i
$433$	18.0810	−	18.0810i	0.868918	−	0.868918i	−0.123434	−	0.992353i	$-0.539391\pi$
$433$	18.0810	−	18.0810i	0.868918	−	0.868918i	0.992353	+	0.123434i	$0.0393908\pi$
$434$	1.20515			0.0578489
$435$	12.5180	−	3.20687i	0.600192	−	0.153758i
$436$	3.67769			0.176129
$437$	10.1183	−	10.1183i	0.484022	−	0.484022i
$438$	−16.0091	+	13.2547i	−0.764945	+	0.633333i
$439$			12.4892i			0.596076i	0.954554	+	0.298038i	$0.0963323\pi$
$439$			12.4892i			0.596076i	−0.954554	+	0.298038i	$0.903668\pi$
$440$	−0.589719	−	1.64285i	−0.0281137	−	0.0783197i
$441$	−2.94731	−	0.559788i	−0.140348	−	0.0266566i
$442$	16.2011	+	16.2011i	0.770609	+	0.770609i
$443$	−19.6631	−	19.6631i	−0.934224	−	0.934224i	0.0637426	−	0.997966i	$-0.479696\pi$
$443$	−19.6631	−	19.6631i	−0.934224	−	0.934224i	−0.997966	+	0.0637426i	$0.979696\pi$
$444$	15.3339	+	1.44330i	0.727714	+	0.0684958i
$445$	17.7293	−	37.5850i	0.840449	−	1.78170i
$446$			11.2769i			0.533977i
$447$	−6.39470	−	7.72358i	−0.302459	−	0.365313i
$448$	0.707107	−	0.707107i	0.0334077	−	0.0334077i
$449$	36.8034			1.73686			0.868431	−	0.495810i	$-0.165129\pi$
$449$	36.8034			1.73686			0.868431	+	0.495810i	$0.165129\pi$
$450$	−4.20041	+	14.3999i	−0.198009	+	0.678817i
$451$	0.320119			0.0150738
$452$	11.8416	−	11.8416i	0.556982	−	0.556982i
$453$	−0.361127	−	0.436173i	−0.0169672	−	0.0204932i
$454$			28.8428i			1.35366i
$455$	−5.19806	+	11.0195i	−0.243689	+	0.516604i
$456$	9.98874	+	0.940186i	0.467765	+	0.0440283i
$457$	0.564472	+	0.564472i	0.0264049	+	0.0264049i	0.720186	−	0.693781i	$-0.244056\pi$
$457$	0.564472	+	0.564472i	0.0264049	+	0.0264049i	−0.693781	+	0.720186i	$0.744056\pi$
$458$	−13.8110	−	13.8110i	−0.645346	−	0.645346i
$459$	−6.07059	+	20.9890i	−0.283351	+	0.979683i
$460$	−1.86625	−	5.19902i	−0.0870142	−	0.242406i
$461$		−	1.34252i		−	0.0625275i	−0.999511	−	0.0312638i	$-0.990047\pi$
$461$		−	1.34252i		−	0.0625275i	0.999511	−	0.0312638i	$-0.00995319\pi$
$462$	1.04143	−	0.862243i	0.0484515	−	0.0401152i
$463$	−27.2878	+	27.2878i	−1.26817	+	1.26817i	−0.321142	+	0.947031i	$0.604067\pi$
$463$	−27.2878	+	27.2878i	−1.26817	+	1.26817i	−0.947031	+	0.321142i	$0.895933\pi$
$464$	−3.33651			−0.154893
$465$	4.52150	−	1.15832i	0.209680	−	0.0537160i
$466$	−4.14309			−0.191925
$467$	−18.9254	+	18.9254i	−0.875765	+	0.875765i	−0.993093	−	0.117328i	$-0.962567\pi$
$467$	−18.9254	+	18.9254i	−0.875765	+	0.875765i	0.117328	+	0.993093i	$0.462567\pi$
$468$	−13.5126	+	9.19894i	−0.624619	+	0.425221i
$469$		−	7.01420i		−	0.323886i
$470$	−12.8722	−	6.07198i	−0.593751	−	0.280080i
$471$	3.61310	−	38.3863i	0.166483	−	1.76875i
$472$	−8.96281	−	8.96281i	−0.412547	−	0.412547i
$473$	−0.309911	−	0.309911i	−0.0142497	−	0.0142497i
$474$	2.03752	−	21.6471i	0.0935865	−	0.994283i
$475$	22.3506	−	18.4194i	1.02552	−	0.845140i
$476$		−	4.20489i		−	0.192731i
$477$	−26.9898	+	18.3738i	−1.23578	+	0.841280i
$478$	8.50951	−	8.50951i	0.389216	−	0.389216i
$479$	−15.7320			−0.718815			−0.359408	−	0.933181i	$-0.617021\pi$
$479$	−15.7320			−0.718815			−0.359408	+	0.933181i	$0.617021\pi$
$480$	1.97331	−	3.33257i	0.0900688	−	0.152111i
$481$	48.4521			2.20922
$482$	−4.08688	+	4.08688i	−0.186152	+	0.186152i
$483$	3.29574	−	2.72869i	0.149961	−	0.124160i
$484$		−	10.3907i		−	0.472303i
$485$	26.2513	−	9.42319i	1.19201	−	0.427885i
$486$	−13.9035	−	7.04924i	−0.630677	−	0.319760i
$487$	1.69131	+	1.69131i	0.0766404	+	0.0766404i	0.744388	−	0.667747i	$-0.232741\pi$
$487$	1.69131	+	1.69131i	0.0766404	+	0.0766404i	−0.667747	+	0.744388i	$0.732741\pi$
$488$	6.44337	+	6.44337i	0.291678	+	0.291678i
$489$	−0.637837	−	0.0600362i	−0.0288440	−	0.00271493i
$490$	2.10458	−	0.755464i	0.0950754	−	0.0341284i
$491$		−	8.25442i		−	0.372517i	−0.982501	−	0.186258i	$-0.940364\pi$
$491$		−	8.25442i		−	0.372517i	0.982501	−	0.186258i	$-0.0596361\pi$
$492$	0.452980	+	0.547114i	0.0204219	+	0.0246658i
$493$	−9.92046	+	9.92046i	−0.446795	+	0.446795i
$494$	31.5624			1.42006
$495$	3.07850	−	4.23595i	0.138368	−	0.190392i
$496$	−1.20515			−0.0541127
$497$	1.33356	−	1.33356i	0.0598182	−	0.0598182i
$498$	5.63301	+	6.80360i	0.252421	+	0.304877i
$499$			18.4475i			0.825823i	0.910771	+	0.412912i	$0.135488\pi$
$499$			18.4475i			0.825823i	−0.910771	+	0.412912i	$0.864512\pi$
$500$	−2.74991	−	10.8369i	−0.122980	−	0.484640i
$501$	−18.2615	−	1.71885i	−0.815862	−	0.0767927i
$502$	1.06535	+	1.06535i	0.0475489	+	0.0475489i
$503$	6.61830	+	6.61830i	0.295095	+	0.295095i	0.839089	−	0.543994i	$-0.183089\pi$
$503$	6.61830	+	6.61830i	0.295095	+	0.295095i	−0.543994	+	0.839089i	$0.683089\pi$
$504$	2.94731	+	0.559788i	0.131284	+	0.0249350i
$505$	−17.2385	−	8.13161i	−0.767103	−	0.361852i
$506$			1.92835i			0.0857257i
$507$	−22.2666	+	18.4356i	−0.988896	+	0.818752i
$508$	12.5290	−	12.5290i	0.555887	−	0.555887i
$509$	0.871429			0.0386254			0.0193127	−	0.999813i	$-0.493852\pi$
$509$	0.871429			0.0386254			0.0193127	+	0.999813i	$0.493852\pi$
$510$	−4.04152	−	15.7760i	−0.178961	−	0.698574i
$511$	11.9997			0.530835
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	14.5317	+	26.3582i	0.641592	+	1.16375i
$514$		−	4.87821i		−	0.215169i
$515$	8.21131	+	22.8752i	0.361833	+	1.00800i
$516$	0.0911319	−	0.968204i	0.00401186	−	0.0426228i
$517$	3.51327	+	3.51327i	0.154513	+	0.154513i
$518$	−6.28770	−	6.28770i	−0.276266	−	0.276266i
$519$	1.94846	−	20.7008i	0.0855278	−	0.908666i
$520$	5.19806	−	11.0195i	0.227950	−	0.483239i
$521$		−	3.35506i		−	0.146988i	−0.997296	−	0.0734939i	$-0.976585\pi$
$521$		−	3.35506i		−	0.146988i	0.997296	−	0.0734939i	$-0.0234150\pi$
$522$	−5.63280	−	8.27418i	−0.246541	−	0.362151i
$523$	−0.214504	+	0.214504i	−0.00937959	+	0.00937959i	−0.711781	−	0.702401i	$-0.752111\pi$
$523$	−0.214504	+	0.214504i	−0.00937959	+	0.00937959i	0.702401	+	0.711781i	$0.252111\pi$
$524$	−11.8873			−0.519301
$525$	7.16992	−	4.85718i	0.312921	−	0.211985i
$526$	13.9357			0.607625
$527$	−3.58328	+	3.58328i	−0.156090	+	0.156090i
$528$	−1.04143	+	0.862243i	−0.0453222	+	0.0375243i
$529$		−	16.8975i		−	0.734672i
$530$	10.3825	−	22.0103i	0.450988	−	0.956066i
$531$	7.09550	−	37.3581i	0.307919	−	1.62120i
$532$	−4.09591	−	4.09591i	−0.177580	−	0.177580i
$533$	1.58005	+	1.58005i	0.0684396	+	0.0684396i
$534$	−32.0480	−	3.01651i	−1.38685	−	0.130537i
$535$	−9.11740	−	25.3994i	−0.394179	−	1.09811i
$536$			7.01420i			0.302967i
$537$	−2.61843	−	3.16256i	−0.112994	−	0.136475i
$538$	−6.49040	+	6.49040i	−0.279821	+	0.279821i
$539$	−0.780604			−0.0336230
$540$	11.5958	−	0.732569i	0.499005	−	0.0315247i
$541$	37.7416			1.62264			0.811318	−	0.584605i	$-0.198750\pi$
$541$	37.7416			1.62264			0.811318	+	0.584605i	$0.198750\pi$
$542$	5.55610	−	5.55610i	0.238655	−	0.238655i
$543$	6.79726	+	8.20980i	0.291698	+	0.352316i
$544$			4.20489i			0.180283i
$545$	−7.43761	−	3.50841i	−0.318592	−	0.150284i
$546$	9.39617	+	0.884411i	0.402119	+	0.0378493i
$547$	13.1372	+	13.1372i	0.561704	+	0.561704i	0.929791	−	0.368087i	$-0.119987\pi$
$547$	13.1372	+	13.1372i	0.561704	+	0.561704i	−0.368087	+	0.929791i	$0.619987\pi$
$548$	4.34731	+	4.34731i	0.185708	+	0.185708i
$549$	−5.10096	+	26.8568i	−0.217704	+	1.14622i
$550$	−0.374607	+	3.88500i	−0.0159733	+	0.165657i
$551$			19.3267i			0.823344i
$552$	−3.29574	+	2.72869i	−0.140276	+	0.116141i
$553$	−8.87644	+	8.87644i	−0.377465	+	0.377465i
$554$	−4.00063			−0.169970
$555$	−29.6338	−	17.5470i	−1.25788	−	0.744827i
$556$	11.6395			0.493625
$557$	−2.16691	+	2.16691i	−0.0918149	+	0.0918149i	−0.751522	−	0.659708i	$-0.770680\pi$
$557$	−2.16691	+	2.16691i	−0.0918149	+	0.0918149i	0.659708	+	0.751522i	$0.270680\pi$
$558$	−2.03457	−	2.98864i	−0.0861302	−	0.126519i
$559$		−	3.05934i		−	0.129396i
$560$	−2.10458	+	0.755464i	−0.0889349	+	0.0319242i
$561$	−0.532764	+	5.66019i	−0.0224933	+	0.238973i
$562$	−0.700555	−	0.700555i	−0.0295511	−	0.0295511i
$563$	−20.7396	−	20.7396i	−0.874069	−	0.874069i	0.118844	−	0.992913i	$-0.462081\pi$
$563$	−20.7396	−	20.7396i	−0.874069	−	0.874069i	−0.992913	+	0.118844i	$0.962081\pi$
$564$	−1.03310	+	10.9759i	−0.0435015	+	0.462169i
$565$	−35.2445	+	12.6514i	−1.48275	+	0.532249i
$566$		−	22.6627i		−	0.952584i
$567$	3.58753	+	8.25407i	0.150662	+	0.346638i
$568$	−1.33356	+	1.33356i	−0.0559548	+	0.0559548i
$569$	−20.8701			−0.874918			−0.437459	−	0.899238i	$-0.644121\pi$
$569$	−20.8701			−0.874918			−0.437459	+	0.899238i	$0.644121\pi$
$570$	−19.3039	−	11.4304i	−0.808552	−	0.478765i
$571$	34.8812			1.45973			0.729865	−	0.683591i	$-0.239583\pi$
$571$	34.8812			1.45973			0.729865	+	0.683591i	$0.239583\pi$
$572$	−3.00761	+	3.00761i	−0.125754	+	0.125754i
$573$	12.8634	−	10.6502i	0.537378	−	0.444920i
$574$		−	0.410091i		−	0.0171169i
$575$	−1.18550	+	12.2946i	−0.0494386	+	0.512722i
$576$	−2.94731	−	0.559788i	−0.122805	−	0.0233245i
$577$	33.1884	+	33.1884i	1.38165	+	1.38165i	0.841693	+	0.539957i	$0.181559\pi$
$577$	33.1884	+	33.1884i	1.38165	+	1.38165i	0.539957	+	0.841693i	$0.318441\pi$
$578$	0.481626	+	0.481626i	0.0200330	+	0.0200330i
$579$	16.5275	+	1.55565i	0.686861	+	0.0646505i
$580$	6.74762	+	3.18293i	0.280180	+	0.132164i
$581$		−	5.09967i		−	0.211570i
$582$	−13.7779	−	16.6411i	−0.571112	−	0.689794i
$583$	−6.00735	+	6.00735i	−0.248799	+	0.248799i
$584$	−11.9997			−0.496551
$585$	36.1028	−	5.71294i	1.49267	−	0.236201i
$586$	0.463991			0.0191673
$587$	−12.2341	+	12.2341i	−0.504957	+	0.504957i	−0.912974	−	0.408017i	$-0.866220\pi$
$587$	−12.2341	+	12.2341i	−0.504957	+	0.504957i	0.408017	+	0.912974i	$0.366220\pi$
$588$	−1.10458	−	1.33413i	−0.0455523	−	0.0550185i
$589$			6.98081i			0.287639i
$590$	9.57576	+	26.6763i	0.394228	+	1.09825i
$591$	5.71205	+	0.537645i	0.234962	+	0.0221158i
$592$	6.28770	+	6.28770i	0.258423	+	0.258423i
$593$	−17.2595	−	17.2595i	−0.708762	−	0.708762i	0.257513	−	0.966275i	$-0.417097\pi$
$593$	−17.2595	−	17.2595i	−0.708762	−	0.708762i	−0.966275	+	0.257513i	$0.917097\pi$
$594$	−3.89644	−	1.12696i	−0.159873	−	0.0462396i
$595$	−4.01135	+	8.50380i	−0.164449	+	0.348622i
$596$		−	5.78924i		−	0.237137i
$597$	−13.2695	+	10.9864i	−0.543083	+	0.449643i
$598$	−9.51800	+	9.51800i	−0.389220	+	0.389220i
$599$	−15.9441			−0.651458			−0.325729	−	0.945463i	$-0.605610\pi$
$599$	−15.9441			−0.651458			−0.325729	+	0.945463i	$0.605610\pi$
$600$	−7.16992	+	4.85718i	−0.292711	+	0.198294i
$601$	4.32631			0.176474			0.0882369	−	0.996100i	$-0.471877\pi$
$601$	4.32631			0.176474			0.0882369	+	0.996100i	$0.471877\pi$
$602$	−0.397015	+	0.397015i	−0.0161811	+	0.0161811i
$603$	−17.3945	+	11.8416i	−0.708357	+	0.482227i
$604$		−	0.326935i		−	0.0133028i
$605$	−9.91239	+	21.0136i	−0.402996	+	0.854326i
$606$	−1.38353	+	14.6990i	−0.0562022	+	0.597104i
$607$	−11.2179	−	11.2179i	−0.455322	−	0.455322i	0.441795	−	0.897116i	$-0.354342\pi$
$607$	−11.2179	−	11.2179i	−0.455322	−	0.455322i	−0.897116	+	0.441795i	$0.854342\pi$
$608$	4.09591	+	4.09591i	0.166111	+	0.166111i
$609$	−0.541553	+	5.75357i	−0.0219448	+	0.233146i
$610$	−6.88402	−	19.1776i	−0.278726	−	0.776478i
$611$			34.6817i			1.40307i
$612$	−10.4277	+	7.09884i	−0.421514	+	0.286953i
$613$	−23.2421	+	23.2421i	−0.938741	+	0.938741i	−0.998229	−	0.0594881i	$-0.981053\pi$
$613$	−23.2421	+	23.2421i	−0.938741	+	0.938741i	0.0594881	+	0.998229i	$0.481053\pi$
$614$	7.48687			0.302146
$615$	−0.394158	−	1.53859i	−0.0158940	−	0.0620420i
$616$	0.780604			0.0314514
$617$	−18.0762	+	18.0762i	−0.727720	+	0.727720i	−0.970165	−	0.242445i	$-0.922051\pi$
$617$	−18.0762	+	18.0762i	−0.727720	+	0.727720i	0.242445	+	0.970165i	$0.422051\pi$
$618$	14.5009	−	12.0060i	0.583312	−	0.482951i
$619$			10.0672i			0.404634i	0.979320	+	0.202317i	$0.0648471\pi$
$619$			10.0672i			0.404634i	−0.979320	+	0.202317i	$0.935153\pi$
$620$	2.43724	+	1.14968i	0.0978820	+	0.0461721i
$621$	−12.3308	−	3.56641i	−0.494819	−	0.143115i
$622$	−8.58358	−	8.58358i	−0.344170	−	0.344170i
$623$	13.1414	+	13.1414i	0.526498	+	0.526498i
$624$	−9.39617	−	0.884411i	−0.376148	−	0.0354048i
$625$	−4.77678	+	24.5394i	−0.191071	+	0.981576i
$626$			17.2824i			0.690745i
$627$	4.99453	+	6.03244i	0.199462	+	0.240913i
$628$	15.7404	−	15.7404i	0.628111	−	0.628111i
$629$	37.3906			1.49086
$630$	−5.42650	−	3.94374i	−0.216197	−	0.157123i
$631$	11.7095			0.466149			0.233075	−	0.972459i	$-0.425121\pi$
$631$	11.7095			0.466149			0.233075	+	0.972459i	$0.425121\pi$
$632$	8.87644	−	8.87644i	0.353086	−	0.353086i
$633$	16.5572	+	19.9979i	0.658088	+	0.794845i
$634$		−	3.40503i		−	0.135231i
$635$	−37.2906	+	13.3859i	−1.47983	+	0.531203i
$636$	−18.7678	−	1.76651i	−0.744190	−	0.0700467i
$637$	−3.85292	−	3.85292i	−0.152658	−	0.152658i
$638$	−1.84165	−	1.84165i	−0.0729118	−	0.0729118i
$639$	−5.55843	−	1.05572i	−0.219888	−	0.0417638i
$640$	2.10458	−	0.755464i	0.0831910	−	0.0298623i
$641$			17.2227i			0.680255i	0.940379	+	0.340128i	$0.110470\pi$
$641$			17.2227i			0.680255i	−0.940379	+	0.340128i	$0.889530\pi$
$642$	−16.1010	+	13.3308i	−0.635458	+	0.526124i
$643$	−19.6141	+	19.6141i	−0.773505	+	0.773505i	−0.978717	−	0.205213i	$-0.934211\pi$
$643$	−19.6141	+	19.6141i	−0.773505	+	0.773505i	0.205213	+	0.978717i	$0.434211\pi$
$644$	2.47033			0.0973447
$645$	−1.10794	+	1.87112i	−0.0436251	+	0.0736753i
$646$	24.3568			0.958305
$647$	7.71110	−	7.71110i	0.303155	−	0.303155i	−0.539092	−	0.842247i	$-0.681233\pi$
$647$	7.71110	−	7.71110i	0.303155	−	0.303155i	0.842247	+	0.539092i	$0.181233\pi$
$648$	−3.58753	−	8.25407i	−0.140931	−	0.324250i
$649$		−	9.89441i		−	0.388390i
$650$	−21.0247	+	17.3267i	−0.824656	+	0.679609i
$651$	−0.195609	+	2.07819i	−0.00766652	+	0.0814508i
$652$	−0.261547	−	0.261547i	−0.0102430	−	0.0102430i
$653$	−28.8829	−	28.8829i	−1.13028	−	1.13028i	−0.990131	−	0.140145i	$-0.955243\pi$
$653$	−28.8829	−	28.8829i	−1.13028	−	1.13028i	−0.140145	−	0.990131i	$-0.544757\pi$
$654$	−0.596931	+	6.34192i	−0.0233418	+	0.247989i
$655$	24.0405	+	11.3402i	0.939339	+	0.443098i
$656$			0.410091i			0.0160114i
$657$	−20.2583	−	29.7580i	−0.790351	−	1.16097i
$658$	4.50070	−	4.50070i	0.175456	−	0.175456i
$659$	46.5136			1.81191			0.905956	−	0.423371i	$-0.139153\pi$
$659$	46.5136			1.81191			0.905956	+	0.423371i	$0.139153\pi$
$660$	2.92869	−	0.750275i	0.113999	−	0.0292044i
$661$	−8.72550			−0.339383			−0.169691	−	0.985497i	$-0.554277\pi$
$661$	−8.72550			−0.339383			−0.169691	+	0.985497i	$0.554277\pi$
$662$	10.8039	−	10.8039i	0.419905	−	0.419905i
$663$	−30.5673	+	25.3081i	−1.18714	+	0.982884i
$664$			5.09967i			0.197905i
$665$	4.37602	+	12.1908i	0.169695	+	0.472738i
$666$	−4.97773	+	26.2079i	−0.192883	+	1.01554i
$667$	−5.82817	−	5.82817i	−0.225668	−	0.225668i
$668$	−7.48816	−	7.48816i	−0.289726	−	0.289726i
$669$	−19.4462	−	1.83037i	−0.751835	−	0.0707662i
$670$	6.69135	−	14.1852i	0.258509	−	0.548023i
$671$			7.11310i			0.274598i
$672$	1.10458	+	1.33413i	0.0426103	+	0.0514651i
$673$	25.1132	−	25.1132i	0.968043	−	0.968043i	−0.0314620	−	0.999505i	$-0.510016\pi$
$673$	25.1132	−	25.1132i	0.968043	−	0.968043i	0.999505	+	0.0314620i	$0.0100163\pi$
$674$	−16.2400			−0.625541
$675$	−24.1498	−	9.58058i	−0.929526	−	0.368757i
$676$	−16.6901			−0.641925
$677$	9.97427	−	9.97427i	0.383342	−	0.383342i	−0.488962	−	0.872305i	$-0.662624\pi$
$677$	9.97427	−	9.97427i	0.383342	−	0.383342i	0.872305	+	0.488962i	$0.162624\pi$
$678$	18.4980	+	22.3420i	0.710410	+	0.858040i
$679$			12.4734i			0.478684i
$680$	4.01135	−	8.50380i	0.153828	−	0.326106i
$681$	−49.7374	−	4.68152i	−1.90594	−	0.179396i
$682$	−0.665206	−	0.665206i	−0.0254721	−	0.0254721i
$683$	−1.82278	−	1.82278i	−0.0697468	−	0.0697468i	0.671373	−	0.741120i	$-0.265705\pi$
$683$	−1.82278	−	1.82278i	−0.0697468	−	0.0697468i	−0.741120	+	0.671373i	$0.765705\pi$
$684$	−3.24257	+	17.0723i	−0.123983	+	0.652774i
$685$	−4.64461	−	12.9390i	−0.177461	−	0.494375i
$686$			1.00000i			0.0381802i
$687$	26.0578	−	21.5744i	0.994166	−	0.823115i
$688$	0.397015	−	0.397015i	0.0151360	−	0.0151360i
$689$	−59.3025			−2.25924
$690$	9.26825	−	2.37435i	0.352836	−	0.0903900i
$691$	−26.8515			−1.02148			−0.510740	−	0.859735i	$-0.670629\pi$
$691$	−26.8515			−1.02148			−0.510740	+	0.859735i	$0.670629\pi$
$692$	8.48843	−	8.48843i	0.322682	−	0.322682i
$693$	1.31784	+	1.93582i	0.0500607	+	0.0735355i
$694$		−	17.1084i		−	0.649425i
$695$	−23.5393	−	11.1038i	−0.892895	−	0.421189i
$696$	0.541553	−	5.75357i	0.0205275	−	0.218088i
$697$	1.21933	+	1.21933i	0.0461853	+	0.0461853i
$698$	0.0807296	+	0.0807296i	0.00305566	+	0.00305566i
$699$	0.672470	−	7.14447i	0.0254352	−	0.270229i
$700$	4.97692	+	0.479893i	0.188110	+	0.0181383i
$701$		−	40.3766i		−	1.52500i	−0.646987	−	0.762501i	$-0.723971\pi$
$701$		−	40.3766i		−	1.52500i	0.646987	−	0.762501i	$-0.276029\pi$
$702$	−13.6697	−	24.7946i	−0.515929	−	0.935811i
$703$	36.4214	−	36.4214i	1.37366	−	1.37366i
$704$	−0.780604			−0.0294201
$705$	12.5600	−	21.2117i	0.473037	−	0.798878i
$706$	−24.7399			−0.931097
$707$	6.02735	−	6.02735i	0.226682	−	0.226682i
$708$	16.9105	−	14.0010i	0.635535	−	0.526188i
$709$			14.0214i			0.526584i	0.964716	+	0.263292i	$0.0848082\pi$
$709$			14.0214i			0.526584i	−0.964716	+	0.263292i	$0.915192\pi$
$710$	3.96911	−	1.42476i	0.148958	−	0.0534701i
$711$	36.9981	+	7.02713i	1.38754	+	0.263538i
$712$	−13.1414	−	13.1414i	−0.492494	−	0.492494i
$713$	−2.10514	−	2.10514i	−0.0788380	−	0.0788380i
$714$	7.25104	+	0.682501i	0.271363	+	0.0255420i
$715$	8.95164	−	3.21329i	0.334772	−	0.120170i
$716$		−	2.37051i		−	0.0885902i
$717$	13.2929	+	16.0552i	0.496431	+	0.599594i
$718$	−18.0130	+	18.0130i	−0.672240	+	0.672240i
$719$	−15.3457			−0.572299			−0.286149	−	0.958185i	$-0.592375\pi$
$719$	−15.3457			−0.572299			−0.286149	+	0.958185i	$0.592375\pi$
$720$	5.42650	+	3.94374i	0.202234	+	0.146975i
$721$	−10.8692			−0.404791
$722$	10.2905	−	10.2905i	0.382972	−	0.382972i
$723$	−6.38419	−	7.71088i	−0.237430	−	0.286771i
$724$			6.15369i			0.228700i
$725$	−10.6097	−	12.8741i	−0.394034	−	0.478131i
$726$	17.9179	+	1.68652i	0.664997	+	0.0625927i
$727$	37.3012	+	37.3012i	1.38342	+	1.38342i	0.838459	+	0.544965i	$0.183457\pi$
$727$	37.3012	+	37.3012i	1.38342	+	1.38342i	0.544965	+	0.838459i	$0.316543\pi$
$728$	3.85292	+	3.85292i	0.142799	+	0.142799i
$729$	14.4126	−	22.8315i	0.533801	−	0.845610i
$730$	24.2677	+	11.4474i	0.898188	+	0.423686i
$731$		−	2.36089i		−	0.0873209i
$732$	−12.1570	+	10.0653i	−0.449334	+	0.372024i
$733$	0.763659	−	0.763659i	0.0282064	−	0.0282064i	−0.692863	−	0.721069i	$-0.743651\pi$
$733$	0.763659	−	0.763659i	0.0282064	−	0.0282064i	0.721069	+	0.692863i	$0.243651\pi$
$734$	33.8832			1.25065
$735$	0.961147	+	3.75183i	0.0354524	+	0.138388i
$736$	−2.47033			−0.0910576
$737$	−3.87163	+	3.87163i	−0.142613	+	0.142613i
$738$	−1.01698	+	0.692329i	−0.0374356	+	0.0254850i
$739$		−	5.91073i		−	0.217430i	−0.994073	−	0.108715i	$-0.965326\pi$
$739$		−	5.91073i		−	0.217430i	0.994073	−	0.108715i	$-0.0346736\pi$
$740$	−6.71771	−	18.7143i	−0.246948	−	0.687951i
$741$	−5.12294	+	54.4272i	−0.188196	+	1.99943i
$742$	7.69577	+	7.69577i	0.282521	+	0.282521i
$743$	29.0001	+	29.0001i	1.06391	+	1.06391i	0.997813	+	0.0660966i	$0.0210546\pi$
$743$	29.0001	+	29.0001i	1.06391	+	1.06391i	0.0660966	+	0.997813i	$0.478945\pi$
$744$	0.195609	−	2.07819i	0.00717138	−	0.0761902i
$745$	−5.52277	+	11.7079i	−0.202339	+	0.428945i
$746$			5.86152i			0.214605i
$747$	−12.6466	+	8.60942i	−0.462716	+	0.315002i
$748$	−2.32098	+	2.32098i	−0.0848633	+	0.0848633i
$749$	12.0686			0.440977
$750$	19.1338	−	2.98307i	0.698667	−	0.108926i
$751$	27.1470			0.990609			0.495304	−	0.868720i	$-0.335057\pi$
$751$	27.1470			0.990609			0.495304	+	0.868720i	$0.335057\pi$
$752$	−4.50070	+	4.50070i	−0.164124	+	0.164124i
$753$	−2.01004	+	1.66420i	−0.0732498	+	0.0606468i
$754$		−	18.1802i		−	0.662082i
$755$	−0.311887	+	0.661180i	−0.0113507	+	0.0240628i
$756$	−1.44370	+	4.99157i	−0.0525068	+	0.181542i
$757$	−21.7239	−	21.7239i	−0.789567	−	0.789567i	0.191856	−	0.981423i	$-0.438549\pi$
$757$	−21.7239	−	21.7239i	−0.789567	−	0.789567i	−0.981423	+	0.191856i	$0.938549\pi$
$758$	−9.60165	−	9.60165i	−0.348748	−	0.348748i
$759$	−3.32531	−	0.312993i	−0.120701	−	0.0113609i
$760$	−4.37602	−	12.1908i	−0.158735	−	0.442206i
$761$			27.8482i			1.00950i	0.863267	+	0.504748i	$0.168415\pi$
$761$			27.8482i			1.00950i	−0.863267	+	0.504748i	$0.831585\pi$
$762$	19.5718	+	23.6391i	0.709013	+	0.856353i
$763$	2.60052	−	2.60052i	0.0941451	−	0.0941451i
$764$	9.64185			0.348830
$765$	27.8606	−	4.40869i	1.00730	−	0.159396i
$766$	15.6523			0.565541
$767$	48.8371	−	48.8371i	1.76340	−	1.76340i
$768$	−1.10458	−	1.33413i	−0.0398582	−	0.0481412i
$769$		−	28.9571i		−	1.04422i	−0.852878	−	0.522110i	$-0.825145\pi$
$769$		−	28.9571i		−	1.04422i	0.852878	−	0.522110i	$-0.174855\pi$
$770$	−1.57866	−	0.744674i	−0.0568910	−	0.0268362i
$771$	8.41213	+	0.791789i	0.302955	+	0.0285156i
$772$	6.77716	+	6.77716i	0.243915	+	0.243915i
$773$	−26.3889	−	26.3889i	−0.949144	−	0.949144i	0.0496237	−	0.998768i	$-0.484198\pi$
$773$	−26.3889	−	26.3889i	−0.949144	−	0.949144i	−0.998768	+	0.0496237i	$0.984198\pi$
$774$	1.65481	+	0.314301i	0.0594808	+	0.0112973i
$775$	−3.83222	−	4.65012i	−0.137657	−	0.167037i
$776$		−	12.4734i		−	0.447768i
$777$	11.8633	−	9.82213i	0.425592	−	0.352367i
$778$	20.6295	−	20.6295i	0.739605	−	0.739605i
$779$	2.37545			0.0851093
$780$	18.1587	+	10.7523i	0.650187	+	0.384993i
$781$	−1.47217			−0.0526783
$782$	−7.34506	+	7.34506i	−0.262659	+	0.262659i
$783$	15.1825	−	8.37037i	0.542578	−	0.299133i
$784$		−	1.00000i		−	0.0357143i
$785$	−46.8487	+	16.8169i	−1.67210	+	0.600220i
$786$	1.92945	−	20.4989i	0.0688212	−	0.731171i
$787$	−15.9989	−	15.9989i	−0.570300	−	0.570300i	0.361912	−	0.932212i	$-0.382124\pi$
$787$	−15.9989	−	15.9989i	−0.570300	−	0.570300i	−0.932212	+	0.361912i	$0.882124\pi$
$788$	2.34224	+	2.34224i	0.0834390	+	0.0834390i
$789$	−2.26192	+	24.0311i	−0.0805264	+	0.855530i
$790$	−26.4192	+	9.48348i	−0.939954	+	0.337407i
$791$		−	16.7465i		−	0.595439i
$792$	−1.31784	−	1.93582i	−0.0468275	−	0.0687862i
$793$	−35.1090	+	35.1090i	−1.24676	+	1.24676i
$794$	14.7097			0.522028
$795$	36.2700	+	21.4764i	1.28636	+	0.761691i
$796$	−9.94617			−0.352533
$797$	20.6511	−	20.6511i	0.731499	−	0.731499i	−0.239418	−	0.970917i	$-0.576957\pi$
$797$	20.6511	−	20.6511i	0.731499	−	0.731499i	0.970917	+	0.239418i	$0.0769565\pi$
$798$	7.72791	−	6.39829i	0.273565	−	0.226497i
$799$			26.7639i			0.946840i
$800$	−4.97692	−	0.479893i	−0.175961	−	0.0169668i
$801$	10.4035	−	54.7749i	0.367590	−	1.93538i
$802$	−2.18135	−	2.18135i	−0.0770260	−	0.0770260i
$803$	−6.62348	−	6.62348i	−0.233737	−	0.233737i
$804$	−12.0955	−	1.13848i	−0.426575	−	0.0401512i
$805$	−4.99590	−	2.35663i	−0.176082	−	0.0830602i
$806$		−	6.56668i		−	0.231301i
$807$	−10.1388	−	12.2457i	−0.356902	−	0.431069i
$808$	−6.02735	+	6.02735i	−0.212041	+	0.212041i
$809$	15.4725			0.543983			0.271992	−	0.962300i	$-0.412318\pi$
$809$	15.4725			0.543983			0.271992	+	0.962300i	$0.412318\pi$
$810$	−0.618872	+	20.1151i	−0.0217449	+	0.706772i
$811$	23.4390			0.823054			0.411527	−	0.911398i	$-0.364996\pi$
$811$	23.4390			0.823054			0.411527	+	0.911398i	$0.364996\pi$
$812$	−2.35927	+	2.35927i	−0.0827940	+	0.0827940i
$813$	8.67929	+	10.4829i	0.304396	+	0.367652i
$814$			6.94125i			0.243291i
$815$	0.279434	+	0.778450i	0.00978813	+	0.0272679i
$816$	−7.25104	−	0.682501i	−0.253837	−	0.0238923i
$817$	−2.29970	−	2.29970i	−0.0804565	−	0.0804565i
$818$	−1.74916	−	1.74916i	−0.0611579	−	0.0611579i
$819$	−3.05021	+	16.0595i	−0.106583	+	0.561163i
$820$	0.391215	−	0.829352i	0.0136618	−	0.0289622i
$821$			26.9077i			0.939087i	0.882909	+	0.469543i	$0.155581\pi$
$821$			26.9077i			0.939087i	−0.882909	+	0.469543i	$0.844419\pi$
$822$	−8.20224	+	6.79101i	−0.286086	+	0.236864i
$823$	29.5001	−	29.5001i	1.02831	−	1.02831i	0.0287224	−	0.999587i	$-0.490856\pi$
$823$	29.5001	−	29.5001i	1.02831	−	1.02831i	0.999587	−	0.0287224i	$-0.00914388\pi$
$824$	10.8692			0.378647
$825$	−6.63861	−	1.27656i	−0.231127	−	0.0444442i
$826$	−12.6753			−0.441031
$827$	14.8938	−	14.8938i	0.517909	−	0.517909i	−0.399030	−	0.916938i	$-0.630653\pi$
$827$	14.8938	−	14.8938i	0.517909	−	0.517909i	0.916938	+	0.399030i	$0.130653\pi$
$828$	−4.17050	−	6.12616i	−0.144935	−	0.212899i
$829$		−	34.3997i		−	1.19475i	−0.801962	−	0.597375i	$-0.796210\pi$
$829$		−	34.3997i		−	1.19475i	0.801962	−	0.597375i	$-0.203790\pi$
$830$	4.86494	−	10.3134i	0.168864	−	0.357982i
$831$	0.649347	−	6.89880i	0.0225256	−	0.239317i
$832$	−3.85292	−	3.85292i	−0.133576	−	0.133576i
$833$	−2.97331	−	2.97331i	−0.103019	−	0.103019i
$834$	−1.88922	+	20.0715i	−0.0654184	+	0.695019i
$835$	8.00026	+	22.2872i	0.276860	+	0.771282i
$836$			4.52164i			0.156384i
$837$	5.48393	−	3.02338i	0.189552	−	0.104503i
$838$	−16.6982	+	16.6982i	−0.576828	+	0.576828i
$839$	19.6850			0.679602			0.339801	−	0.940497i	$-0.389640\pi$
$839$	19.6850			0.679602			0.339801	+	0.940497i	$0.389640\pi$
$840$	−0.961147	−	3.75183i	−0.0331627	−	0.129450i
$841$	−17.8677			−0.616128
$842$	13.8882	−	13.8882i	0.478620	−	0.478620i
$843$	1.32176	−	1.09435i	0.0455240	−	0.0376914i
$844$			14.9895i			0.515960i
$845$	33.7533	+	15.9218i	1.16115	+	0.547728i
$846$	−18.7595	−	3.56303i	−0.644964	−	0.122499i
$847$	−7.34730	−	7.34730i	−0.252456	−	0.252456i
$848$	−7.69577	−	7.69577i	−0.264274	−	0.264274i
$849$	39.0802	+	3.67841i	1.34123	+	0.126243i
$850$	−16.2248	+	13.3710i	−0.556505	+	0.458623i
$851$			21.9666i			0.753004i
$852$	−2.08317	−	2.51607i	−0.0713683	−	0.0861993i
$853$	0.519079	−	0.519079i	0.0177729	−	0.0177729i	−0.698164	−	0.715937i	$-0.746000\pi$
$853$	0.519079	−	0.519079i	0.0177729	−	0.0177729i	0.715937	+	0.698164i	$0.246000\pi$
$854$	9.11230			0.311816
$855$	22.8441	−	31.4329i	0.781251	−	1.07498i
$856$	−12.0686			−0.412496
$857$	−3.46899	+	3.46899i	−0.118498	+	0.118498i	−0.763869	−	0.645371i	$-0.776703\pi$
$857$	−3.46899	+	3.46899i	−0.118498	+	0.118498i	0.645371	+	0.763869i	$0.276703\pi$
$858$	−4.69824	−	5.67458i	−0.160395	−	0.193727i
$859$		−	30.0887i		−	1.02661i	−0.858205	−	0.513307i	$-0.828420\pi$
$859$		−	30.0887i		−	1.02661i	0.858205	−	0.513307i	$-0.171580\pi$
$860$	−1.18165	+	0.424166i	−0.0402939	+	0.0144639i
$861$	0.707173	+	0.0665624i	0.0241004	+	0.00226844i
$862$	20.4613	+	20.4613i	0.696915	+	0.696915i
$863$	10.2849	+	10.2849i	0.350102	+	0.350102i	0.860147	−	0.510046i	$-0.170372\pi$
$863$	10.2849	+	10.2849i	0.350102	+	0.350102i	−0.510046	+	0.860147i	$0.670372\pi$
$864$	1.44370	−	4.99157i	0.0491156	−	0.169817i
$865$	−25.2644	+	9.06894i	−0.859015	+	0.308353i
$866$			25.5704i			0.868918i
$867$	−0.908703	+	0.752356i	−0.0308612	+	0.0255514i
$868$	−0.852168	+	0.852168i	−0.0289245	+	0.0289245i
$869$	9.79907			0.332411
$870$	−6.58396	+	11.1192i	−0.223217	+	0.376975i
$871$	−38.2194			−1.29501
$872$	−2.60052	+	2.60052i	−0.0880647	+	0.0880647i
$873$	30.9326	−	21.0580i	1.04691	−	0.712704i
$874$			14.3094i			0.484022i
$875$	−9.60731	−	5.71835i	−0.324786	−	0.193316i
$876$	1.94769	−	20.6926i	0.0658062	−	0.699139i
$877$	25.3250	+	25.3250i	0.855164	+	0.855164i	0.990764	−	0.135600i	$-0.0432961\pi$
$877$	25.3250	+	25.3250i	0.855164	+	0.855164i	−0.135600	+	0.990764i	$0.543296\pi$
$878$	−8.83119	−	8.83119i	−0.298038	−	0.298038i
$879$	−0.0753109	+	0.800119i	−0.00254017	+	0.0269873i
$880$	1.57866	+	0.744674i	0.0532167	+	0.0251030i
$881$		−	9.27692i		−	0.312547i	−0.987714	−	0.156274i	$-0.950052\pi$
$881$		−	9.27692i		−	0.312547i	0.987714	−	0.156274i	$-0.0499482\pi$
$882$	2.47989	−	1.68823i	0.0835023	−	0.0568458i
$883$	13.4381	−	13.4381i	0.452228	−	0.452228i	−0.443866	−	0.896093i	$-0.646393\pi$
$883$	13.4381	−	13.4381i	0.452228	−	0.452228i	0.896093	+	0.443866i	$0.146393\pi$
$884$	−22.9119			−0.770609
$885$	−47.5556	+	12.1828i	−1.59856	+	0.409522i
$886$	27.8079			0.934224
$887$	39.1904	−	39.1904i	1.31589	−	1.31589i	0.398885	−	0.917001i	$-0.369397\pi$
$887$	39.1904	−	39.1904i	1.31589	−	1.31589i	0.917001	−	0.398885i	$-0.130603\pi$
$888$	−11.8633	+	9.82213i	−0.398105	+	0.329609i
$889$		−	17.7188i		−	0.594268i
$890$	14.0401	+	39.1131i	0.470625	+	1.31107i
$891$	2.57579	−	6.53621i	0.0862923	−	0.218971i
$892$	−7.97398	−	7.97398i	−0.266989	−	0.266989i
$893$	26.0703	+	26.0703i	0.872408	+	0.872408i
$894$	9.98313	+	0.939659i	0.333886	+	0.0314269i
$895$	−2.26140	+	4.79403i	−0.0755903	+	0.160247i
$896$			1.00000i			0.0334077i
$897$	−14.8682	−	17.9580i	−0.496436	−	0.599600i
$898$	−26.0240	+	26.0240i	−0.868431	+	0.868431i
$899$	4.02098			0.134107
$900$	−7.21211	−	13.1524i	−0.240404	−	0.438413i
$901$	−45.7638			−1.52461
$902$	−0.226358	+	0.226358i	−0.00753691	+	0.00753691i
$903$	−0.620184	−	0.749064i	−0.0206384	−	0.0249273i
$904$			16.7465i			0.556982i
$905$	5.87044	−	12.4450i	0.195140	−	0.413685i
$906$	0.563776	+	0.0530653i	0.0187302	+	0.00176297i
$907$	−23.8197	−	23.8197i	−0.790921	−	0.790921i	0.190723	−	0.981644i	$-0.438917\pi$
$907$	−23.8197	−	23.8197i	−0.790921	−	0.790921i	−0.981644	+	0.190723i	$0.938917\pi$
$908$	−20.3950	−	20.3950i	−0.676831	−	0.676831i
$909$	−25.1227	−	4.77161i	−0.833269	−	0.158264i
$910$	−4.11642	−	11.4676i	−0.136458	−	0.380147i
$911$			43.6041i			1.44467i	0.691544	+	0.722335i	$0.256931\pi$
$911$			43.6041i			1.44467i	−0.691544	+	0.722335i	$0.743069\pi$
$912$	−7.72791	+	6.39829i	−0.255897	+	0.211869i
$913$	−2.81487	+	2.81487i	−0.0931585	+	0.0931585i
$914$	−0.798284			−0.0264049
$915$	34.1878	−	8.75826i	1.13021	−	0.289539i
$916$	19.5317			0.645346
$917$	−8.40562	+	8.40562i	−0.277578	+	0.277578i
$918$	−10.5489	−	19.1340i	−0.348166	−	0.631517i
$919$		−	1.67169i		−	0.0551439i	−0.999620	−	0.0275720i	$-0.991222\pi$
$919$		−	1.67169i		−	0.0551439i	0.999620	−	0.0275720i	$-0.00877754\pi$
$920$	4.99590	+	2.35663i	0.164710	+	0.0776957i
$921$	−1.21520	+	12.9106i	−0.0400423	+	0.425418i
$922$	0.949307	+	0.949307i	0.0312638	+	0.0312638i
$923$	−7.26636	−	7.26636i	−0.239175	−	0.239175i
$924$	−0.126701	+	1.34610i	−0.00416815	+	0.0442833i
$925$	−4.26728	+	44.2555i	−0.140307	+	1.45511i
$926$		−	38.5908i		−	1.26817i
$927$	18.3498	+	26.9545i	0.602686	+	0.885302i
$928$	2.35927	−	2.35927i	0.0774467	−	0.0774467i
$929$	−35.1462			−1.15311			−0.576554	−	0.817059i	$-0.695603\pi$
$929$	−35.1462			−1.15311			−0.576554	+	0.817059i	$0.695603\pi$
$930$	−2.37813	+	4.01625i	−0.0779819	+	0.131698i
$931$	−5.79249			−0.189841
$932$	2.92961	−	2.92961i	0.0959625	−	0.0959625i
$933$	16.1950	−	13.4086i	0.530200	−	0.438976i
$934$		−	26.7646i		−	0.875765i
$935$	6.90800	−	2.47970i	0.225916	−	0.0810950i
$936$	3.05021	−	16.0595i	0.0996992	−	0.524920i
$937$	15.8397	+	15.8397i	0.517459	+	0.517459i	0.916802	−	0.399342i	$-0.130762\pi$
$937$	15.8397	+	15.8397i	0.517459	+	0.517459i	−0.399342	+	0.916802i	$0.630762\pi$
$938$	4.95979	+	4.95979i	0.161943	+	0.161943i
$939$	−29.8023	−	2.80513i	−0.972562	−	0.0915421i
$940$	13.3956	−	4.80849i	0.436916	−	0.156836i
$941$			14.3284i			0.467093i	0.972346	+	0.233546i	$0.0750331\pi$
$941$			14.3284i			0.467093i	−0.972346	+	0.233546i	$0.924967\pi$
$942$	24.5884	+	29.6981i	0.801133	+	0.967615i
$943$	−0.716343	+	0.716343i	−0.0233273	+	0.0233273i
$944$	12.6753			0.412547
$945$	7.68149	−	8.71750i	0.249879	−	0.283580i
$946$	0.438281			0.0142497
$947$	−19.8875	+	19.8875i	−0.646255	+	0.646255i	−0.952086	−	0.305831i	$-0.901066\pi$
$947$	−19.8875	+	19.8875i	−0.646255	+	0.646255i	0.305831	+	0.952086i	$0.401066\pi$
$948$	13.8660	+	16.7475i	0.450348	+	0.543935i
$949$		−	65.3846i		−	2.12247i
$950$	−2.77978	+	28.8287i	−0.0901878	+	0.935328i
$951$	5.87173	+	0.552675i	0.190404	+	0.0179217i
$952$	2.97331	+	2.97331i	0.0963655	+	0.0963655i
$953$	−0.913118	−	0.913118i	−0.0295788	−	0.0295788i	0.692163	−	0.721742i	$-0.256658\pi$
$953$	−0.913118	−	0.913118i	−0.0295788	−	0.0295788i	−0.721742	+	0.692163i	$0.756658\pi$
$954$	6.09244	−	32.0770i	0.197250	−	1.03853i
$955$	−19.4993	−	9.19805i	−0.630982	−	0.297642i
$956$			12.0343i			0.389216i
$957$	3.47472	−	2.87688i	0.112322	−	0.0929963i
$958$	11.1242	−	11.1242i	0.359408	−	0.359408i
$959$	6.14802			0.198530
$960$	0.961147	+	3.75183i	0.0310209	+	0.121090i
$961$	−29.5476			−0.953149
$962$	−34.2608	+	34.2608i	−1.10461	+	1.10461i
$963$	−20.3746	−	29.9288i	−0.656563	−	0.964444i
$964$		−	5.77972i		−	0.186152i
$965$	−7.24063	−	20.1711i	−0.233084	−	0.649330i
$966$	−0.400963	+	4.25991i	−0.0129008	+	0.137060i
$967$	−8.20069	−	8.20069i	−0.263716	−	0.263716i	0.562846	−	0.826562i	$-0.309707\pi$
$967$	−8.20069	−	8.20069i	−0.263716	−	0.263716i	−0.826562	+	0.562846i	$0.809707\pi$
$968$	7.34730	+	7.34730i	0.236151	+	0.236151i
$969$	−3.95338	+	42.0016i	−0.127001	+	1.34928i
$970$	−11.8992	+	25.2257i	−0.382062	+	0.809947i
$971$		−	24.9665i		−	0.801214i	−0.916250	−	0.400607i	$-0.868799\pi$
$971$		−	24.9665i		−	0.801214i	0.916250	−	0.400607i	$-0.131201\pi$
$972$	14.8158	−	4.84671i	0.475219	−	0.155458i
$973$	8.23037	−	8.23037i	0.263854	−	0.263854i
$974$	−2.39187			−0.0766404
$975$	−26.4661	−	39.0679i	−0.847594	−	1.25117i
$976$	−9.11230			−0.291678
$977$	−5.79833	+	5.79833i	−0.185505	+	0.185505i	−0.793750	−	0.608245i	$-0.791874\pi$
$977$	−5.79833	+	5.79833i	−0.185505	+	0.185505i	0.608245	+	0.793750i	$0.291874\pi$
$978$	0.493471	−	0.408567i	0.0157795	−	0.0130645i
$979$		−	14.5073i		−	0.463656i
$980$	−0.953972	+	2.02236i	−0.0304735	+	0.0646019i
$981$	−10.8393	−	2.05873i	−0.346072	−	0.0657301i
$982$	5.83675	+	5.83675i	0.186258	+	0.186258i
$983$	−6.34808	−	6.34808i	−0.202472	−	0.202472i	0.598586	−	0.801058i	$-0.295729\pi$
$983$	−6.34808	−	6.34808i	−0.202472	−	0.202472i	−0.801058	+	0.598586i	$0.795729\pi$
$984$	−0.707173	−	0.0665624i	−0.0225439	−	0.00212193i
$985$	−2.50242	−	6.97129i	−0.0797339	−	0.222124i
$986$		−	14.0297i		−	0.446795i
$987$	7.03062	+	8.49165i	0.223787	+	0.270292i
$988$	−22.3180	+	22.3180i	−0.710031	+	0.710031i
$989$	1.38700			0.0441041
$990$	0.818437	+	5.17210i	0.0260116	+	0.164380i
$991$	−61.4308			−1.95141			−0.975707	−	0.219080i	$-0.929694\pi$
$991$	−61.4308			−1.95141			−0.975707	+	0.219080i	$0.929694\pi$
$992$	0.852168	−	0.852168i	0.0270564	−	0.0270564i
$993$	16.8769	+	20.3841i	0.535574	+	0.646871i
$994$			1.88593i			0.0598182i
$995$	20.1147	+	9.48837i	0.637680	+	0.300802i
$996$	−8.79401	−	0.827733i	−0.278649	−	0.0262277i
$997$	−16.8640	−	16.8640i	−0.534088	−	0.534088i	0.387698	−	0.921786i	$-0.373270\pi$
$997$	−16.8640	−	16.8640i	−0.534088	−	0.534088i	−0.921786	+	0.387698i	$0.873270\pi$
$998$	−13.0443	−	13.0443i	−0.412912	−	0.412912i
$999$	−44.3858	−	12.8376i	−1.40430	−	0.406163i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.j.b.197.1	yes	12
3.2	odd	2		210.2.j.a.197.6	yes	12
5.2	odd	4		1050.2.j.c.743.1		12
5.3	odd	4		210.2.j.a.113.6	✓	12
5.4	even	2		1050.2.j.d.407.6		12
15.2	even	4		1050.2.j.d.743.6		12
15.8	even	4	inner	210.2.j.b.113.1	yes	12
15.14	odd	2		1050.2.j.c.407.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.j.a.113.6	✓	12	5.3	odd	4
210.2.j.a.197.6	yes	12	3.2	odd	2
210.2.j.b.113.1	yes	12	15.8	even	4	inner
210.2.j.b.197.1	yes	12	1.1	even	1	trivial
1050.2.j.c.407.1		12	15.14	odd	2
1050.2.j.c.743.1		12	5.2	odd	4
1050.2.j.d.407.6		12	5.4	even	2
1050.2.j.d.743.6		12	15.2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.10458 - 1.33413i) q^{3} -1.00000i q^{4} +(-0.953972 + 2.02236i) q^{5} +(1.72443 + 0.162311i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.559788 + 2.94731i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.10458 - 1.33413i) q^{3} -1.00000i q^{4} +(-0.953972 + 2.02236i) q^{5} +(1.72443 + 0.162311i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.559788 + 2.94731i) q^{9} +(-0.755464 - 2.10458i) q^{10} +0.780604i q^{11} +(-1.33413 + 1.10458i) q^{12} +(-3.85292 + 3.85292i) q^{13} +1.00000 q^{14} +(3.75183 - 0.961147i) q^{15} -1.00000 q^{16} +(-2.97331 + 2.97331i) q^{17} +(-1.68823 - 2.47989i) q^{18} +5.79249i q^{19} +(2.02236 + 0.953972i) q^{20} +(-0.162311 + 1.72443i) q^{21} +(-0.551971 - 0.551971i) q^{22} +(-1.74679 - 1.74679i) q^{23} +(0.162311 - 1.72443i) q^{24} +(-3.17988 - 3.85855i) q^{25} -5.44886i q^{26} +(4.55042 - 2.50872i) q^{27} +(-0.707107 + 0.707107i) q^{28} +3.33651 q^{29} +(-1.97331 + 3.33257i) q^{30} +1.20515 q^{31} +(0.707107 - 0.707107i) q^{32} +(1.04143 - 0.862243i) q^{33} -4.20489i q^{34} +(2.10458 - 0.755464i) q^{35} +(2.94731 + 0.559788i) q^{36} +(-6.28770 - 6.28770i) q^{37} +(-4.09591 - 4.09591i) q^{38} +(9.39617 + 0.884411i) q^{39} +(-2.10458 + 0.755464i) q^{40} -0.410091i q^{41} +(-1.10458 - 1.33413i) q^{42} +(-0.397015 + 0.397015i) q^{43} +0.780604 q^{44} +(-5.42650 - 3.94374i) q^{45} +2.47033 q^{46} +(4.50070 - 4.50070i) q^{47} +(1.10458 + 1.33413i) q^{48} +1.00000i q^{49} +(4.97692 + 0.479893i) q^{50} +(7.25104 + 0.682501i) q^{51} +(3.85292 + 3.85292i) q^{52} +(7.69577 + 7.69577i) q^{53} +(-1.44370 + 4.99157i) q^{54} +(-1.57866 - 0.744674i) q^{55} -1.00000i q^{56} +(7.72791 - 6.39829i) q^{57} +(-2.35927 + 2.35927i) q^{58} -12.6753 q^{59} +(-0.961147 - 3.75183i) q^{60} +9.11230 q^{61} +(-0.852168 + 0.852168i) q^{62} +(2.47989 - 1.68823i) q^{63} +1.00000i q^{64} +(-4.11642 - 11.4676i) q^{65} +(-0.126701 + 1.34610i) q^{66} +(4.95979 + 4.95979i) q^{67} +(2.97331 + 2.97331i) q^{68} +(-0.400963 + 4.25991i) q^{69} +(-0.953972 + 2.02236i) q^{70} +1.88593i q^{71} +(-2.47989 + 1.68823i) q^{72} +(-8.48507 + 8.48507i) q^{73} +8.89215 q^{74} +(-1.63535 + 8.50445i) q^{75} +5.79249 q^{76} +(0.551971 - 0.551971i) q^{77} +(-7.26947 + 6.01872i) q^{78} -12.5532i q^{79} +(0.953972 - 2.02236i) q^{80} +(-8.37327 - 3.29974i) q^{81} +(0.289978 + 0.289978i) q^{82} +(3.60601 + 3.60601i) q^{83} +(1.72443 + 0.162311i) q^{84} +(-3.17665 - 8.84955i) q^{85} -0.561464i q^{86} +(-3.68545 - 4.45132i) q^{87} +(-0.551971 + 0.551971i) q^{88} -18.5847 q^{89} +(6.62576 - 1.04847i) q^{90} +5.44886 q^{91} +(-1.74679 + 1.74679i) q^{92} +(-1.33119 - 1.60782i) q^{93} +6.36495i q^{94} +(-11.7145 - 5.52587i) q^{95} +(-1.72443 - 0.162311i) q^{96} +(-8.82001 - 8.82001i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(-2.30068 - 0.436973i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} + 4 q^{5}+O(q^{10}) \) 12 * q + 4 * q^3 + 4 * q^5	\( 12 q + 4 q^{3} + 4 q^{5} - 4 q^{12} + 12 q^{14} - 12 q^{15} - 12 q^{16} - 28 q^{17} - 8 q^{18} - 4 q^{21} + 4 q^{22} + 24 q^{23} + 4 q^{24} + 20 q^{25} + 28 q^{27} - 8 q^{29} - 16 q^{30} - 8 q^{31} - 36 q^{33} + 8 q^{35} + 4 q^{36} - 20 q^{37} + 4 q^{38} + 40 q^{39} - 8 q^{40} + 4 q^{42} + 8 q^{43} - 8 q^{44} - 48 q^{45} + 8 q^{46} - 16 q^{47} - 4 q^{48} + 16 q^{50} + 8 q^{51} + 24 q^{53} + 4 q^{54} - 16 q^{55} + 44 q^{57} - 8 q^{58} - 32 q^{59} + 4 q^{60} - 28 q^{62} - 8 q^{66} + 28 q^{68} + 32 q^{69} + 4 q^{70} - 24 q^{73} - 8 q^{74} - 4 q^{75} - 4 q^{77} - 8 q^{78} - 4 q^{80} - 36 q^{81} + 32 q^{82} + 24 q^{83} - 36 q^{85} - 16 q^{87} + 4 q^{88} - 48 q^{89} - 8 q^{90} + 24 q^{91} + 24 q^{92} - 20 q^{93} + 8 q^{97} + 40 q^{99}+O(q^{100}) \) 12 * q + 4 * q^3 + 4 * q^5 - 4 * q^12 + 12 * q^14 - 12 * q^15 - 12 * q^16 - 28 * q^17 - 8 * q^18 - 4 * q^21 + 4 * q^22 + 24 * q^23 + 4 * q^24 + 20 * q^25 + 28 * q^27 - 8 * q^29 - 16 * q^30 - 8 * q^31 - 36 * q^33 + 8 * q^35 + 4 * q^36 - 20 * q^37 + 4 * q^38 + 40 * q^39 - 8 * q^40 + 4 * q^42 + 8 * q^43 - 8 * q^44 - 48 * q^45 + 8 * q^46 - 16 * q^47 - 4 * q^48 + 16 * q^50 + 8 * q^51 + 24 * q^53 + 4 * q^54 - 16 * q^55 + 44 * q^57 - 8 * q^58 - 32 * q^59 + 4 * q^60 - 28 * q^62 - 8 * q^66 + 28 * q^68 + 32 * q^69 + 4 * q^70 - 24 * q^73 - 8 * q^74 - 4 * q^75 - 4 * q^77 - 8 * q^78 - 4 * q^80 - 36 * q^81 + 32 * q^82 + 24 * q^83 - 36 * q^85 - 16 * q^87 + 4 * q^88 - 48 * q^89 - 8 * q^90 + 24 * q^91 + 24 * q^92 - 20 * q^93 + 8 * q^97 + 40 * q^99

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