LMFDB - Embedded newform 1110.2.l.b.697.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(43,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1110.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.l (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			697.4
Character	$\chi$	$=$	1110.697
Dual form			1110.2.l.b.43.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.994632 - 2.00267i) q^{5} +(0.707107 - 0.707107i) q^{6} +(0.593998 + 0.593998i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.994632 - 2.00267i) q^{5} +(0.707107 - 0.707107i) q^{6} +(0.593998 + 0.593998i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(2.00267 - 0.994632i) q^{10} +2.21854i q^{11} +(0.707107 + 0.707107i) q^{12} +0.163340i q^{13} +(-0.593998 + 0.593998i) q^{14} +(-0.712794 + 2.11942i) q^{15} +1.00000 q^{16} +5.23332 q^{17} -1.00000 q^{18} +(-1.67943 - 1.67943i) q^{19} +(0.994632 + 2.00267i) q^{20} -0.840040i q^{21} -2.21854 q^{22} -3.86710i q^{23} +(-0.707107 + 0.707107i) q^{24} +(-3.02141 + 3.98385i) q^{25} -0.163340 q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.593998 - 0.593998i) q^{28} +(4.79365 - 4.79365i) q^{29} +(-2.11942 - 0.712794i) q^{30} +(-5.64797 - 5.64797i) q^{31} +1.00000i q^{32} +(1.56874 - 1.56874i) q^{33} +5.23332i q^{34} +(0.598775 - 1.78039i) q^{35} -1.00000i q^{36} +(-4.51960 + 4.07102i) q^{37} +(1.67943 - 1.67943i) q^{38} +(0.115499 - 0.115499i) q^{39} +(-2.00267 + 0.994632i) q^{40} -5.85724i q^{41} +0.840040 q^{42} -8.94207i q^{43} -2.21854i q^{44} +(2.00267 - 0.994632i) q^{45} +3.86710 q^{46} +(-7.97291 - 7.97291i) q^{47} +(-0.707107 - 0.707107i) q^{48} -6.29433i q^{49} +(-3.98385 - 3.02141i) q^{50} +(-3.70052 - 3.70052i) q^{51} -0.163340i q^{52} +(-7.94704 + 7.94704i) q^{53} +(0.707107 + 0.707107i) q^{54} +(4.44300 - 2.20663i) q^{55} +(0.593998 - 0.593998i) q^{56} +2.37508i q^{57} +(4.79365 + 4.79365i) q^{58} +(1.00057 + 1.00057i) q^{59} +(0.712794 - 2.11942i) q^{60} +(-7.50634 - 7.50634i) q^{61} +(5.64797 - 5.64797i) q^{62} +(-0.593998 + 0.593998i) q^{63} -1.00000 q^{64} +(0.327117 - 0.162463i) q^{65} +(1.56874 + 1.56874i) q^{66} +(5.39694 - 5.39694i) q^{67} -5.23332 q^{68} +(-2.73445 + 2.73445i) q^{69} +(1.78039 + 0.598775i) q^{70} +14.9530 q^{71} +1.00000 q^{72} +(0.258848 + 0.258848i) q^{73} +(-4.07102 - 4.51960i) q^{74} +(4.95347 - 0.680545i) q^{75} +(1.67943 + 1.67943i) q^{76} +(-1.31781 + 1.31781i) q^{77} +(0.115499 + 0.115499i) q^{78} +(-1.08732 - 1.08732i) q^{79} +(-0.994632 - 2.00267i) q^{80} -1.00000 q^{81} +5.85724 q^{82} +(-4.08091 + 4.08091i) q^{83} +0.840040i q^{84} +(-5.20523 - 10.4806i) q^{85} +8.94207 q^{86} -6.77925 q^{87} +2.21854 q^{88} +(12.5864 - 12.5864i) q^{89} +(0.994632 + 2.00267i) q^{90} +(-0.0970237 + 0.0970237i) q^{91} +3.86710i q^{92} +7.98744i q^{93} +(7.97291 - 7.97291i) q^{94} +(-1.69294 + 5.03378i) q^{95} +(0.707107 - 0.707107i) q^{96} -12.7909 q^{97} +6.29433 q^{98} -2.21854 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 40 q^{4} - 4 q^{7}+O(q^{10}) $ 40 * q - 40 * q^4 - 4 * q^7	$ 40 q - 40 q^{4} - 4 q^{7} + 4 q^{14} + 40 q^{16} + 24 q^{17} - 40 q^{18} + 4 q^{19} + 8 q^{22} + 8 q^{25} + 8 q^{26} + 4 q^{28} + 28 q^{31} - 4 q^{33} + 20 q^{35} + 20 q^{37} - 4 q^{38} + 4 q^{39} + 16 q^{42} - 16 q^{47} + 16 q^{51} + 20 q^{53} + 16 q^{55} - 4 q^{56} - 4 q^{59} - 8 q^{61} - 28 q^{62} + 4 q^{63} - 40 q^{64} - 4 q^{65} - 4 q^{66} + 16 q^{67} - 24 q^{68} - 8 q^{69} + 12 q^{70} + 40 q^{71} + 40 q^{72} + 8 q^{73} - 8 q^{74} + 16 q^{75} - 4 q^{76} - 24 q^{77} + 4 q^{78} - 12 q^{79} - 40 q^{81} - 24 q^{82} - 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{88} + 12 q^{89} - 24 q^{91} + 16 q^{94} - 28 q^{95} + 40 q^{97} - 56 q^{98} + 8 q^{99}+O(q^{100}) $ 40 * q - 40 * q^4 - 4 * q^7 + 4 * q^14 + 40 * q^16 + 24 * q^17 - 40 * q^18 + 4 * q^19 + 8 * q^22 + 8 * q^25 + 8 * q^26 + 4 * q^28 + 28 * q^31 - 4 * q^33 + 20 * q^35 + 20 * q^37 - 4 * q^38 + 4 * q^39 + 16 * q^42 - 16 * q^47 + 16 * q^51 + 20 * q^53 + 16 * q^55 - 4 * q^56 - 4 * q^59 - 8 * q^61 - 28 * q^62 + 4 * q^63 - 40 * q^64 - 4 * q^65 - 4 * q^66 + 16 * q^67 - 24 * q^68 - 8 * q^69 + 12 * q^70 + 40 * q^71 + 40 * q^72 + 8 * q^73 - 8 * q^74 + 16 * q^75 - 4 * q^76 - 24 * q^77 + 4 * q^78 - 12 * q^79 - 40 * q^81 - 24 * q^82 - 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^88 + 12 * q^89 - 24 * q^91 + 16 * q^94 - 28 * q^95 + 40 * q^97 - 56 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	−1.00000			−0.500000
$5$	−0.994632	−	2.00267i	−0.444813	−	0.895623i
$5$	−0.994632	−	2.00267i	−0.444813	−	0.895623i
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	0.593998	+	0.593998i	0.224510	+	0.224510i	0.810395	−	0.585884i	$-0.199253\pi$
$7$	0.593998	+	0.593998i	0.224510	+	0.224510i	−0.585884	+	0.810395i	$0.699253\pi$
$8$		−	1.00000i		−	0.353553i
$9$			1.00000i			0.333333i
$10$	2.00267	−	0.994632i	0.633301	−	0.314530i
$11$			2.21854i			0.668914i	0.942411	+	0.334457i	$0.108553\pi$
$11$			2.21854i			0.668914i	−0.942411	+	0.334457i	$0.891447\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$			0.163340i			0.0453024i	0.999743	+	0.0226512i	$0.00721072\pi$
$13$			0.163340i			0.0453024i	−0.999743	+	0.0226512i	$0.992789\pi$
$14$	−0.593998	+	0.593998i	−0.158753	+	0.158753i
$15$	−0.712794	+	2.11942i	−0.184043	+	0.547231i
$16$	1.00000			0.250000
$17$	5.23332			1.26927			0.634634	−	0.772813i	$-0.281151\pi$
$17$	5.23332			1.26927			0.634634	+	0.772813i	$0.281151\pi$
$18$	−1.00000			−0.235702
$19$	−1.67943	−	1.67943i	−0.385289	−	0.385289i	0.487715	−	0.873003i	$-0.337831\pi$
$19$	−1.67943	−	1.67943i	−0.385289	−	0.385289i	−0.873003	+	0.487715i	$0.837831\pi$
$20$	0.994632	+	2.00267i	0.222407	+	0.447812i
$21$		−	0.840040i		−	0.183312i
$22$	−2.21854			−0.472993
$23$		−	3.86710i		−	0.806346i	−0.915124	−	0.403173i	$-0.867907\pi$
$23$		−	3.86710i		−	0.806346i	0.915124	−	0.403173i	$-0.132093\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$	−3.02141	+	3.98385i	−0.604283	+	0.796770i
$26$	−0.163340			−0.0320336
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−0.593998	−	0.593998i	−0.112255	−	0.112255i
$29$	4.79365	−	4.79365i	0.890159	−	0.890159i	−0.104379	−	0.994538i	$-0.533285\pi$
$29$	4.79365	−	4.79365i	0.890159	−	0.890159i	0.994538	+	0.104379i	$0.0332854\pi$
$30$	−2.11942	−	0.712794i	−0.386951	−	0.130138i
$31$	−5.64797	−	5.64797i	−1.01441	−	1.01441i	−0.999895	−	0.0145112i	$-0.995381\pi$
$31$	−5.64797	−	5.64797i	−1.01441	−	1.01441i	−0.0145112	−	0.999895i	$-0.504619\pi$
$32$			1.00000i			0.176777i
$33$	1.56874	−	1.56874i	0.273083	−	0.273083i
$34$			5.23332i			0.897508i
$35$	0.598775	−	1.78039i	0.101212	−	0.300942i
$36$		−	1.00000i		−	0.166667i
$37$	−4.51960	+	4.07102i	−0.743018	+	0.669271i
$37$	−4.51960	+	4.07102i	−0.743018	+	0.669271i
$38$	1.67943	−	1.67943i	0.272440	−	0.272440i
$39$	0.115499	−	0.115499i	0.0184946	−	0.0184946i
$40$	−2.00267	+	0.994632i	−0.316651	+	0.157265i
$41$		−	5.85724i		−	0.914748i	−0.889275	−	0.457374i	$-0.848790\pi$
$41$		−	5.85724i		−	0.914748i	0.889275	−	0.457374i	$-0.151210\pi$
$42$	0.840040			0.129621
$43$		−	8.94207i		−	1.36365i	−0.731514	−	0.681826i	$-0.761186\pi$
$43$		−	8.94207i		−	1.36365i	0.731514	−	0.681826i	$-0.238814\pi$
$44$		−	2.21854i		−	0.334457i
$45$	2.00267	−	0.994632i	0.298541	−	0.148271i
$46$	3.86710			0.570173
$47$	−7.97291	−	7.97291i	−1.16297	−	1.16297i	−0.983823	−	0.179146i	$-0.942667\pi$
$47$	−7.97291	−	7.97291i	−1.16297	−	1.16297i	−0.179146	−	0.983823i	$-0.557333\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$		−	6.29433i		−	0.899190i
$50$	−3.98385	−	3.02141i	−0.563401	−	0.427292i
$51$	−3.70052	−	3.70052i	−0.518176	−	0.518176i
$52$		−	0.163340i		−	0.0226512i
$53$	−7.94704	+	7.94704i	−1.09161	+	1.09161i	−0.0962535	+	0.995357i	$0.530686\pi$
$53$	−7.94704	+	7.94704i	−1.09161	+	1.09161i	−0.995357	+	0.0962535i	$0.969314\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	4.44300	−	2.20663i	0.599095	−	0.297541i
$56$	0.593998	−	0.593998i	0.0793763	−	0.0793763i
$57$			2.37508i			0.314587i
$58$	4.79365	+	4.79365i	0.629438	+	0.629438i
$59$	1.00057	+	1.00057i	0.130263	+	0.130263i	0.769232	−	0.638969i	$-0.220639\pi$
$59$	1.00057	+	1.00057i	0.130263	+	0.130263i	−0.638969	+	0.769232i	$0.720639\pi$
$60$	0.712794	−	2.11942i	0.0920213	−	0.273615i
$61$	−7.50634	−	7.50634i	−0.961088	−	0.961088i	0.0381827	−	0.999271i	$-0.487843\pi$
$61$	−7.50634	−	7.50634i	−0.961088	−	0.961088i	−0.999271	+	0.0381827i	$0.987843\pi$
$62$	5.64797	−	5.64797i	0.717293	−	0.717293i
$63$	−0.593998	+	0.593998i	−0.0748367	+	0.0748367i
$64$	−1.00000			−0.125000
$65$	0.327117	−	0.162463i	0.0405739	−	0.0201511i
$66$	1.56874	+	1.56874i	0.193099	+	0.193099i
$67$	5.39694	−	5.39694i	0.659341	−	0.659341i	−0.295883	−	0.955224i	$-0.595614\pi$
$67$	5.39694	−	5.39694i	0.659341	−	0.659341i	0.955224	+	0.295883i	$0.0956138\pi$
$68$	−5.23332			−0.634634
$69$	−2.73445	+	2.73445i	−0.329189	+	0.329189i
$70$	1.78039	+	0.598775i	0.212798	+	0.0715673i
$71$	14.9530			1.77460			0.887299	−	0.461194i	$-0.152579\pi$
$71$	14.9530			1.77460			0.887299	+	0.461194i	$0.152579\pi$
$72$	1.00000			0.117851
$73$	0.258848	+	0.258848i	0.0302959	+	0.0302959i	0.722092	−	0.691797i	$-0.243181\pi$
$73$	0.258848	+	0.258848i	0.0302959	+	0.0302959i	−0.691797	+	0.722092i	$0.743181\pi$
$74$	−4.07102	−	4.51960i	−0.473246	−	0.525393i
$75$	4.95347	−	0.680545i	0.571977	−	0.0785826i
$76$	1.67943	+	1.67943i	0.192644	+	0.192644i
$77$	−1.31781	+	1.31781i	−0.150178	+	0.150178i
$78$	0.115499	+	0.115499i	0.0130777	+	0.0130777i
$79$	−1.08732	−	1.08732i	−0.122333	−	0.122333i	0.643290	−	0.765623i	$-0.277569\pi$
$79$	−1.08732	−	1.08732i	−0.122333	−	0.122333i	−0.765623	+	0.643290i	$0.777569\pi$
$80$	−0.994632	−	2.00267i	−0.111203	−	0.223906i
$81$	−1.00000			−0.111111
$82$	5.85724			0.646824
$83$	−4.08091	+	4.08091i	−0.447938	+	0.447938i	−0.894669	−	0.446731i	$-0.852588\pi$
$83$	−4.08091	+	4.08091i	−0.447938	+	0.447938i	0.446731	+	0.894669i	$0.352588\pi$
$84$			0.840040i			0.0916559i
$85$	−5.20523	−	10.4806i	−0.564587	−	1.13679i
$86$	8.94207			0.964248
$87$	−6.77925			−0.726812
$88$	2.21854			0.236497
$89$	12.5864	−	12.5864i	1.33415	−	1.33415i	0.432539	−	0.901615i	$-0.357618\pi$
$89$	12.5864	−	12.5864i	1.33415	−	1.33415i	0.901615	−	0.432539i	$-0.142382\pi$
$90$	0.994632	+	2.00267i	0.104843	+	0.211100i
$91$	−0.0970237	+	0.0970237i	−0.0101708	+	0.0101708i
$92$			3.86710i			0.403173i
$93$			7.98744i			0.828259i
$94$	7.97291	−	7.97291i	0.822343	−	0.822343i
$95$	−1.69294	+	5.03378i	−0.173692	+	0.516455i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$	−12.7909			−1.29872			−0.649359	−	0.760482i	$-0.724963\pi$
$97$	−12.7909			−1.29872			−0.649359	+	0.760482i	$0.724963\pi$
$98$	6.29433			0.635824
$99$	−2.21854			−0.222971
$100$	3.02141	−	3.98385i	0.302141	−	0.398385i
$101$			4.31584i			0.429442i	0.976675	+	0.214721i	$0.0688842\pi$
$101$			4.31584i			0.429442i	−0.976675	+	0.214721i	$0.931116\pi$
$102$	3.70052	−	3.70052i	0.366406	−	0.366406i
$103$	−13.9487			−1.37440			−0.687202	−	0.726467i	$-0.741161\pi$
$103$	−13.9487			−1.37440			−0.687202	+	0.726467i	$0.741161\pi$
$104$	0.163340			0.0160168
$105$	−1.68233	+	0.835531i	−0.164178	+	0.0815395i
$106$	−7.94704	−	7.94704i	−0.771885	−	0.771885i
$107$	5.53603	+	5.53603i	0.535189	+	0.535189i	0.922112	−	0.386923i	$-0.126462\pi$
$107$	5.53603	+	5.53603i	0.535189	+	0.535189i	−0.386923	+	0.922112i	$0.626462\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$	9.96395	+	9.96395i	0.954373	+	0.954373i	0.999004	−	0.0446302i	$-0.0142109\pi$
$109$	9.96395	+	9.96395i	0.954373	+	0.954373i	−0.0446302	+	0.999004i	$0.514211\pi$
$110$	2.20663	+	4.44300i	0.210394	+	0.423624i
$111$	6.07449	+	0.317197i	0.576565	+	0.0301070i
$112$	0.593998	+	0.593998i	0.0561275	+	0.0561275i
$113$	18.7870			1.76733			0.883665	−	0.468120i	$-0.155068\pi$
$113$	18.7870			1.76733			0.883665	+	0.468120i	$0.155068\pi$
$114$	−2.37508			−0.222447
$115$	−7.74455	+	3.84634i	−0.722183	+	0.358673i
$116$	−4.79365	+	4.79365i	−0.445080	+	0.445080i
$117$	−0.163340			−0.0151008
$118$	−1.00057	+	1.00057i	−0.0921100	+	0.0921100i
$119$	3.10858	+	3.10858i	0.284963	+	0.284963i
$120$	2.11942	+	0.712794i	0.193475	+	0.0650689i
$121$	6.07810			0.552555
$122$	7.50634	−	7.50634i	0.679592	−	0.679592i
$123$	−4.14170	+	4.14170i	−0.373444	+	0.373444i
$124$	5.64797	+	5.64797i	0.507203	+	0.507203i
$125$	10.9836	+	2.08844i	0.982399	+	0.186796i
$126$	−0.593998	−	0.593998i	−0.0529175	−	0.0529175i
$127$	4.61246	+	4.61246i	0.409290	+	0.409290i	0.881491	−	0.472201i	$-0.156540\pi$
$127$	4.61246	+	4.61246i	0.409290	+	0.409290i	−0.472201	+	0.881491i	$0.656540\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−6.32300	+	6.32300i	−0.556709	+	0.556709i
$130$	0.162463	+	0.327117i	0.0142490	+	0.0286901i
$131$	−11.9955	−	11.9955i	−1.04805	−	1.04805i	−0.998786	−	0.0492667i	$-0.984312\pi$
$131$	−11.9955	−	11.9955i	−1.04805	−	1.04805i	−0.0492667	−	0.998786i	$-0.515688\pi$
$132$	−1.56874	+	1.56874i	−0.136541	+	0.136541i
$133$		−	1.99516i		−	0.173002i
$134$	5.39694	+	5.39694i	0.466225	+	0.466225i
$135$	−2.11942	−	0.712794i	−0.182410	−	0.0613475i
$136$		−	5.23332i		−	0.448754i
$137$	−2.69211	−	2.69211i	−0.230002	−	0.230002i	0.582691	−	0.812694i	$-0.302000\pi$
$137$	−2.69211	−	2.69211i	−0.230002	−	0.230002i	−0.812694	+	0.582691i	$0.802000\pi$
$138$	−2.73445	−	2.73445i	−0.232772	−	0.232772i
$139$	−1.30467			−0.110661			−0.0553305	−	0.998468i	$-0.517621\pi$
$139$	−1.30467			−0.110661			−0.0553305	+	0.998468i	$0.517621\pi$
$140$	−0.598775	+	1.78039i	−0.0506058	+	0.150471i
$141$			11.2754i			0.949560i
$142$			14.9530i			1.25483i
$143$	−0.362376			−0.0303034
$144$			1.00000i			0.0833333i
$145$	−14.3681	−	4.83221i	−1.19320	−	0.401293i
$146$	−0.258848	+	0.258848i	−0.0214224	+	0.0214224i
$147$	−4.45077	+	4.45077i	−0.367093	+	0.367093i
$148$	4.51960	−	4.07102i	0.371509	−	0.334636i
$149$			9.07290i			0.743281i	0.928377	+	0.371640i	$0.121205\pi$
$149$			9.07290i			0.743281i	−0.928377	+	0.371640i	$0.878795\pi$
$150$	0.680545	+	4.95347i	0.0555663	+	0.404449i
$151$			0.0622104i			0.00506261i	0.999997	+	0.00253130i	$0.000805740\pi$
$151$			0.0622104i			0.00506261i	−0.999997	+	0.00253130i	$0.999194\pi$
$152$	−1.67943	+	1.67943i	−0.136220	+	0.136220i
$153$			5.23332i			0.423089i
$154$	−1.31781	−	1.31781i	−0.106192	−	0.106192i
$155$	−5.69340	+	16.9287i	−0.457305	+	1.35975i
$156$	−0.115499	+	0.115499i	−0.00924731	+	0.00924731i
$157$	−5.08868	−	5.08868i	−0.406121	−	0.406121i	0.474263	−	0.880383i	$-0.342715\pi$
$157$	−5.08868	−	5.08868i	−0.406121	−	0.406121i	−0.880383	+	0.474263i	$0.842715\pi$
$158$	1.08732	−	1.08732i	0.0865023	−	0.0865023i
$159$	11.2388			0.891296
$160$	2.00267	−	0.994632i	0.158325	−	0.0786326i
$161$	2.29705	−	2.29705i	0.181033	−	0.181033i
$162$		−	1.00000i		−	0.0785674i
$163$	−19.1109			−1.49688			−0.748441	−	0.663201i	$-0.769197\pi$
$163$	−19.1109			−1.49688			−0.748441	+	0.663201i	$0.769197\pi$
$164$			5.85724i			0.457374i
$165$	−4.70200	−	1.58136i	−0.366050	−	0.123109i
$166$	−4.08091	−	4.08091i	−0.316740	−	0.316740i
$167$	−7.28469			−0.563706			−0.281853	−	0.959458i	$-0.590949\pi$
$167$	−7.28469			−0.563706			−0.281853	+	0.959458i	$0.590949\pi$
$168$	−0.840040			−0.0648105
$169$	12.9733			0.997948
$170$	10.4806	−	5.20523i	0.803829	−	0.399223i
$171$	1.67943	−	1.67943i	0.128430	−	0.128430i
$172$			8.94207i			0.681826i
$173$	8.94815	+	8.94815i	0.680315	+	0.680315i	0.960071	−	0.279756i	$-0.0902536\pi$
$173$	8.94815	+	8.94815i	0.680315	+	0.680315i	−0.279756	+	0.960071i	$0.590254\pi$
$174$		−	6.77925i		−	0.513934i
$175$	−4.16111	+	0.571685i	−0.314551	+	0.0432154i
$176$			2.21854i			0.167228i
$177$		−	1.41502i		−	0.106359i
$178$	12.5864	+	12.5864i	0.943390	+	0.943390i
$179$	17.4301	−	17.4301i	1.30279	−	1.30279i	0.376287	−	0.926503i	$-0.377201\pi$
$179$	17.4301	−	17.4301i	1.30279	−	1.30279i	0.926503	−	0.376287i	$-0.122799\pi$
$180$	−2.00267	+	0.994632i	−0.149271	+	0.0741355i
$181$	3.39361			0.252245			0.126122	−	0.992015i	$-0.459747\pi$
$181$	3.39361			0.252245			0.126122	+	0.992015i	$0.459747\pi$
$182$	−0.0970237	−	0.0970237i	−0.00719188	−	0.00719188i
$183$			10.6156i			0.784725i
$184$	−3.86710			−0.285086
$185$	12.6483	+	5.00213i	0.929919	+	0.367764i
$186$	−7.98744			−0.585668
$187$			11.6103i			0.849030i
$188$	7.97291	+	7.97291i	0.581484	+	0.581484i
$189$	0.840040			0.0611039
$190$	−5.03378	−	1.69294i	−0.365189	−	0.122819i
$191$	1.08400	−	1.08400i	0.0784355	−	0.0784355i	−0.666801	−	0.745236i	$-0.732337\pi$
$191$	1.08400	−	1.08400i	0.0784355	−	0.0784355i	0.745236	+	0.666801i	$0.232337\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$		−	4.04039i		−	0.290834i	−0.989370	−	0.145417i	$-0.953548\pi$
$193$		−	4.04039i		−	0.290834i	0.989370	−	0.145417i	$-0.0464523\pi$
$194$		−	12.7909i		−	0.918332i
$195$	−0.346186	−	0.116428i	−0.0247909	−	0.00833757i
$196$			6.29433i			0.449595i
$197$	−12.3544	−	12.3544i	−0.880214	−	0.880214i	0.113342	−	0.993556i	$-0.463844\pi$
$197$	−12.3544	−	12.3544i	−0.880214	−	0.880214i	−0.993556	+	0.113342i	$0.963844\pi$
$198$		−	2.21854i		−	0.157664i
$199$	−5.19861	+	5.19861i	−0.368519	+	0.368519i	−0.866937	−	0.498418i	$-0.833915\pi$
$199$	−5.19861	+	5.19861i	−0.368519	+	0.368519i	0.498418	+	0.866937i	$0.333915\pi$
$200$	3.98385	+	3.02141i	0.281701	+	0.213646i
$201$	−7.63243			−0.538350
$202$	−4.31584			−0.303661
$203$	5.69484			0.399699
$204$	3.70052	+	3.70052i	0.259088	+	0.259088i
$205$	−11.7302	+	5.82580i	−0.819269	+	0.406892i
$206$		−	13.9487i		−	0.971850i
$207$	3.86710			0.268782
$208$			0.163340i			0.0113256i
$209$	3.72588	−	3.72588i	0.257725	−	0.257725i
$210$	−0.835531	−	1.68233i	−0.0576571	−	0.116092i
$211$	−15.2308			−1.04853			−0.524264	−	0.851556i	$-0.675660\pi$
$211$	−15.2308			−1.04853			−0.524264	+	0.851556i	$0.675660\pi$
$212$	7.94704	−	7.94704i	0.545805	−	0.545805i
$213$	−10.5734	−	10.5734i	−0.724477	−	0.724477i
$214$	−5.53603	+	5.53603i	−0.378435	+	0.378435i
$215$	−17.9081	+	8.89407i	−1.22132	+	0.606571i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$		−	6.70977i		−	0.455489i
$218$	−9.96395	+	9.96395i	−0.674844	+	0.674844i
$219$		−	0.366066i		−	0.0247365i
$220$	−4.44300	+	2.20663i	−0.299547	+	0.148771i
$221$			0.854812i			0.0575009i
$222$	−0.317197	+	6.07449i	−0.0212888	+	0.407693i
$223$	9.25821	−	9.25821i	0.619976	−	0.619976i	−0.325549	−	0.945525i	$-0.605549\pi$
$223$	9.25821	−	9.25821i	0.619976	−	0.619976i	0.945525	+	0.325549i	$0.105549\pi$
$224$	−0.593998	+	0.593998i	−0.0396882	+	0.0396882i
$225$	−3.98385	−	3.02141i	−0.265590	−	0.201428i
$226$			18.7870i			1.24969i
$227$	−12.5313			−0.831734			−0.415867	−	0.909425i	$-0.636522\pi$
$227$	−12.5313			−0.831734			−0.415867	+	0.909425i	$0.636522\pi$
$228$		−	2.37508i		−	0.157293i
$229$			7.37486i			0.487345i	0.969858	+	0.243672i	$0.0783521\pi$
$229$			7.37486i			0.487345i	−0.969858	+	0.243672i	$0.921648\pi$
$230$	−3.84634	−	7.74455i	−0.253620	−	0.510660i
$231$	1.86366			0.122620
$232$	−4.79365	−	4.79365i	−0.314719	−	0.314719i
$233$	18.4468	+	18.4468i	1.20849	+	1.20849i	0.971517	+	0.236971i	$0.0761545\pi$
$233$	18.4468	+	18.4468i	1.20849	+	1.20849i	0.236971	+	0.971517i	$0.423846\pi$
$234$		−	0.163340i		−	0.0106779i
$235$	−8.03703	+	23.8973i	−0.524278	+	1.55889i
$236$	−1.00057	−	1.00057i	−0.0651316	−	0.0651316i
$237$			1.53770i			0.0998843i
$238$	−3.10858	+	3.10858i	−0.201500	+	0.201500i
$239$	−10.9427	−	10.9427i	−0.707825	−	0.707825i	0.258252	−	0.966077i	$-0.416853\pi$
$239$	−10.9427	−	10.9427i	−0.707825	−	0.707825i	−0.966077	+	0.258252i	$0.916853\pi$
$240$	−0.712794	+	2.11942i	−0.0460106	+	0.136808i
$241$	11.4584	−	11.4584i	0.738102	−	0.738102i	−0.234108	−	0.972211i	$-0.575217\pi$
$241$	11.4584	−	11.4584i	0.738102	−	0.738102i	0.972211	+	0.234108i	$0.0752170\pi$
$242$			6.07810i			0.390715i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	7.50634	+	7.50634i	0.480544	+	0.480544i
$245$	−12.6055	+	6.26055i	−0.805336	+	0.399972i
$246$	−4.14170	−	4.14170i	−0.264065	−	0.264065i
$247$	0.274319	−	0.274319i	0.0174545	−	0.0174545i
$248$	−5.64797	+	5.64797i	−0.358647	+	0.358647i
$249$	5.77128			0.365740
$250$	−2.08844	+	10.9836i	−0.132085	+	0.694661i
$251$	−4.90961	−	4.90961i	−0.309892	−	0.309892i	0.534976	−	0.844867i	$-0.320321\pi$
$251$	−4.90961	−	4.90961i	−0.309892	−	0.309892i	−0.844867	+	0.534976i	$0.820321\pi$
$252$	0.593998	−	0.593998i	0.0374184	−	0.0374184i
$253$	8.57930			0.539376
$254$	−4.61246	+	4.61246i	−0.289412	+	0.289412i
$255$	−3.73028	+	11.0916i	−0.233599	+	0.694582i
$256$	1.00000			0.0625000
$257$	20.1402			1.25631			0.628155	−	0.778088i	$-0.283810\pi$
$257$	20.1402			1.25631			0.628155	+	0.778088i	$0.283810\pi$
$258$	−6.32300	−	6.32300i	−0.393653	−	0.393653i
$259$	−5.10281	−	0.266458i	−0.317073	−	0.0165569i
$260$	−0.327117	+	0.162463i	−0.0202869	+	0.0100756i
$261$	4.79365	+	4.79365i	0.296720	+	0.296720i
$262$	11.9955	−	11.9955i	0.741085	−	0.741085i
$263$	−5.00770	−	5.00770i	−0.308788	−	0.308788i	0.535651	−	0.844439i	$-0.320066\pi$
$263$	−5.00770	−	5.00770i	−0.308788	−	0.308788i	−0.844439	+	0.535651i	$0.820066\pi$
$264$	−1.56874	−	1.56874i	−0.0965493	−	0.0965493i
$265$	23.8197	+	8.01096i	1.46323	+	0.492109i
$266$	1.99516			0.122331
$267$	−17.7998			−1.08933
$268$	−5.39694	+	5.39694i	−0.329671	+	0.329671i
$269$		−	12.0216i		−	0.732969i	−0.930424	−	0.366485i	$-0.880561\pi$
$269$		−	12.0216i		−	0.732969i	0.930424	−	0.366485i	$-0.119439\pi$
$270$	0.712794	−	2.11942i	0.0433792	−	0.128984i
$271$	−11.5944			−0.704308			−0.352154	−	0.935942i	$-0.614551\pi$
$271$	−11.5944			−0.704308			−0.352154	+	0.935942i	$0.614551\pi$
$272$	5.23332			0.317317
$273$	0.137212			0.00830446
$274$	2.69211	−	2.69211i	0.162636	−	0.162636i
$275$	−8.83831	−	6.70311i	−0.532970	−	0.404213i
$276$	2.73445	−	2.73445i	0.164595	−	0.164595i
$277$			1.48164i			0.0890229i	0.999009	+	0.0445115i	$0.0141731\pi$
$277$			1.48164i			0.0890229i	−0.999009	+	0.0445115i	$0.985827\pi$
$278$		−	1.30467i		−	0.0782491i
$279$	5.64797	−	5.64797i	0.338135	−	0.338135i
$280$	−1.78039	−	0.598775i	−0.106399	−	0.0357837i
$281$	2.20394	−	2.20394i	0.131476	−	0.131476i	−0.638306	−	0.769782i	$-0.720365\pi$
$281$	2.20394	−	2.20394i	0.131476	−	0.131476i	0.769782	+	0.638306i	$0.220365\pi$
$282$	−11.2754			−0.671440
$283$	12.9583			0.770291			0.385145	−	0.922856i	$-0.374151\pi$
$283$	12.9583			0.770291			0.385145	+	0.922856i	$0.374151\pi$
$284$	−14.9530			−0.887299
$285$	4.75651	−	2.36233i	0.281751	−	0.139932i
$286$		−	0.362376i		−	0.0214277i
$287$	3.47919	−	3.47919i	0.205370	−	0.205370i
$288$	−1.00000			−0.0589256
$289$	10.3877			0.611040
$290$	4.83221	−	14.3681i	0.283757	−	0.843721i
$291$	9.04452	+	9.04452i	0.530199	+	0.530199i
$292$	−0.258848	−	0.258848i	−0.0151479	−	0.0151479i
$293$	−15.2639	+	15.2639i	−0.891729	+	0.891729i	−0.994686	−	0.102956i	$-0.967170\pi$
$293$	−15.2639	+	15.2639i	−0.891729	+	0.891729i	0.102956	+	0.994686i	$0.467170\pi$
$294$	−4.45077	−	4.45077i	−0.259574	−	0.259574i
$295$	1.00862	−	2.99902i	0.0587240	−	0.174610i
$296$	4.07102	+	4.51960i	0.236623	+	0.262697i
$297$	1.56874	+	1.56874i	0.0910276	+	0.0910276i
$298$	−9.07290			−0.525579
$299$	0.631653			0.0365294
$300$	−4.95347	+	0.680545i	−0.285989	+	0.0392913i
$301$	5.31157	−	5.31157i	0.306154	−	0.306154i
$302$	−0.0622104			−0.00357980
$303$	3.05176	−	3.05176i	0.175319	−	0.175319i
$304$	−1.67943	−	1.67943i	−0.0963222	−	0.0963222i
$305$	−7.56671	+	22.4988i	−0.433268	+	1.28828i
$306$	−5.23332			−0.299169
$307$	−20.5532	+	20.5532i	−1.17303	+	1.17303i	−0.191547	+	0.981483i	$0.561350\pi$
$307$	−20.5532	+	20.5532i	−1.17303	+	1.17303i	−0.981483	+	0.191547i	$0.938650\pi$
$308$	1.31781	−	1.31781i	0.0750889	−	0.0750889i
$309$	9.86320	+	9.86320i	0.561098	+	0.561098i
$310$	−16.9287	−	5.69340i	−0.961486	−	0.323363i
$311$	0.612480	+	0.612480i	0.0347305	+	0.0347305i	0.724259	−	0.689528i	$-0.242182\pi$
$311$	0.612480	+	0.612480i	0.0347305	+	0.0347305i	−0.689528	+	0.724259i	$0.742182\pi$
$312$	−0.115499	−	0.115499i	−0.00653884	−	0.00653884i
$313$		−	3.56579i		−	0.201550i	−0.994909	−	0.100775i	$-0.967868\pi$
$313$		−	3.56579i		−	0.201550i	0.994909	−	0.100775i	$-0.0321322\pi$
$314$	5.08868	−	5.08868i	0.287171	−	0.287171i
$315$	1.78039	+	0.598775i	0.100314	+	0.0337372i
$316$	1.08732	+	1.08732i	0.0611664	+	0.0611664i
$317$	4.20992	−	4.20992i	0.236453	−	0.236453i	−0.578927	−	0.815380i	$-0.696528\pi$
$317$	4.20992	−	4.20992i	0.236453	−	0.236453i	0.815380	+	0.578927i	$0.196528\pi$
$318$			11.2388i			0.630242i
$319$	10.6349	+	10.6349i	0.595439	+	0.595439i
$320$	0.994632	+	2.00267i	0.0556016	+	0.111953i
$321$		−	7.82913i		−	0.436980i
$322$	2.29705	+	2.29705i	0.128010	+	0.128010i
$323$	−8.78902	−	8.78902i	−0.489034	−	0.489034i
$324$	1.00000			0.0555556
$325$	−0.650723	−	0.493518i	−0.0360956	−	0.0273755i
$326$		−	19.1109i		−	1.05846i
$327$		−	14.0912i		−	0.779243i
$328$	−5.85724			−0.323412
$329$		−	9.47178i		−	0.522196i
$330$	1.58136	−	4.70200i	0.0870509	−	0.258837i
$331$	14.0919	−	14.0919i	0.774561	−	0.774561i	−0.204339	−	0.978900i	$-0.565505\pi$
$331$	14.0919	−	14.0919i	0.774561	−	0.774561i	0.978900	+	0.204339i	$0.0655045\pi$
$332$	4.08091	−	4.08091i	0.223969	−	0.223969i
$333$	−4.07102	−	4.51960i	−0.223090	−	0.247673i
$334$		−	7.28469i		−	0.398601i
$335$	−16.1763	−	5.44035i	−0.883805	−	0.297238i
$336$		−	0.840040i		−	0.0458279i
$337$	−17.5011	+	17.5011i	−0.953348	+	0.953348i	−0.998959	−	0.0456112i	$-0.985476\pi$
$337$	−17.5011	+	17.5011i	−0.953348	+	0.953348i	0.0456112	+	0.998959i	$0.485476\pi$
$338$			12.9733i			0.705656i
$339$	−13.2844	−	13.2844i	−0.721510	−	0.721510i
$340$	5.20523	+	10.4806i	0.282293	+	0.568393i
$341$	12.5302	−	12.5302i	0.678550	−	0.678550i
$342$	1.67943	+	1.67943i	0.0908134	+	0.0908134i
$343$	7.89681	−	7.89681i	0.426388	−	0.426388i
$344$	−8.94207			−0.482124
$345$	8.19600	+	2.75645i	0.441258	+	0.148402i
$346$	−8.94815	+	8.94815i	−0.481055	+	0.481055i
$347$			19.3835i			1.04056i	0.853996	+	0.520280i	$0.174173\pi$
$347$			19.3835i			1.04056i	−0.853996	+	0.520280i	$0.825827\pi$
$348$	6.77925			0.363406
$349$			14.5408i			0.778350i	0.921164	+	0.389175i	$0.127240\pi$
$349$			14.5408i			0.778350i	−0.921164	+	0.389175i	$0.872760\pi$
$350$	−0.571685	−	4.16111i	−0.0305579	−	0.222421i
$351$	0.115499	+	0.115499i	0.00616488	+	0.00616488i
$352$	−2.21854			−0.118248
$353$	26.3150			1.40060			0.700302	−	0.713847i	$-0.253049\pi$
$353$	26.3150			1.40060			0.700302	+	0.713847i	$0.253049\pi$
$354$	1.41502			0.0752075
$355$	−14.8728	−	29.9461i	−0.789365	−	1.58937i
$356$	−12.5864	+	12.5864i	−0.667077	+	0.667077i
$357$		−	4.39620i		−	0.232672i
$358$	17.4301	+	17.4301i	0.921212	+	0.921212i
$359$		−	6.12864i		−	0.323457i	−0.986835	−	0.161729i	$-0.948293\pi$
$359$		−	6.12864i		−	0.323457i	0.986835	−	0.161729i	$-0.0517069\pi$
$360$	−0.994632	−	2.00267i	−0.0524217	−	0.105550i
$361$		−	13.3590i		−	0.703105i
$362$			3.39361i			0.178364i
$363$	−4.29787	−	4.29787i	−0.225580	−	0.225580i
$364$	0.0970237	−	0.0970237i	0.00508542	−	0.00508542i
$365$	0.260930	−	0.775847i	0.0136577	−	0.0406097i
$366$	−10.6156			−0.554884
$367$	21.0105	+	21.0105i	1.09674	+	1.09674i	0.994789	+	0.101950i	$0.0325083\pi$
$367$	21.0105	+	21.0105i	1.09674	+	1.09674i	0.101950	+	0.994789i	$0.467492\pi$
$368$		−	3.86710i		−	0.201587i
$369$	5.85724			0.304916
$370$	−5.00213	+	12.6483i	−0.260048	+	0.657552i
$371$	−9.44106			−0.490155
$372$		−	7.98744i		−	0.414129i
$373$	2.15543	+	2.15543i	0.111604	+	0.111604i	0.760703	−	0.649100i	$-0.224854\pi$
$373$	2.15543	+	2.15543i	0.111604	+	0.111604i	−0.649100	+	0.760703i	$0.724854\pi$
$374$	−11.6103			−0.600355
$375$	−6.28979	−	9.24330i	−0.324803	−	0.477322i
$376$	−7.97291	+	7.97291i	−0.411171	+	0.411171i
$377$	0.782996	+	0.782996i	0.0403263	+	0.0403263i
$378$			0.840040i			0.0432070i
$379$			37.8733i			1.94542i	0.232022	+	0.972711i	$0.425466\pi$
$379$			37.8733i			1.94542i	−0.232022	+	0.972711i	$0.574534\pi$
$380$	1.69294	−	5.03378i	0.0868461	−	0.258228i
$381$		−	6.52301i		−	0.334184i
$382$	1.08400	+	1.08400i	0.0554622	+	0.0554622i
$383$			33.6750i			1.72071i	0.509695	+	0.860355i	$0.329758\pi$
$383$			33.6750i			1.72071i	−0.509695	+	0.860355i	$0.670242\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	3.94987	+	1.32840i	0.201304	+	0.0677017i
$386$	4.04039			0.205650
$387$	8.94207			0.454551
$388$	12.7909			0.649359
$389$	6.96706	+	6.96706i	0.353244	+	0.353244i	0.861315	−	0.508071i	$-0.169641\pi$
$389$	6.96706	+	6.96706i	0.353244	+	0.353244i	−0.508071	+	0.861315i	$0.669641\pi$
$390$	0.116428	−	0.346186i	0.00589555	−	0.0175298i
$391$		−	20.2378i		−	1.02347i
$392$	−6.29433			−0.317912
$393$			16.9642i			0.855731i
$394$	12.3544	−	12.3544i	0.622405	−	0.622405i
$395$	−1.09606	+	3.25902i	−0.0551489	+	0.163979i
$396$	2.21854			0.111486
$397$	−2.14584	+	2.14584i	−0.107697	+	0.107697i	−0.758902	−	0.651205i	$-0.774264\pi$
$397$	−2.14584	+	2.14584i	−0.107697	+	0.107697i	0.651205	+	0.758902i	$0.274264\pi$
$398$	−5.19861	−	5.19861i	−0.260583	−	0.260583i
$399$	−1.41079	+	1.41079i	−0.0706279	+	0.0706279i
$400$	−3.02141	+	3.98385i	−0.151071	+	0.199192i
$401$	3.17371	+	3.17371i	0.158488	+	0.158488i	0.781896	−	0.623409i	$-0.214253\pi$
$401$	3.17371	+	3.17371i	0.158488	+	0.158488i	−0.623409	+	0.781896i	$0.714253\pi$
$402$		−	7.63243i		−	0.380671i
$403$	0.922541	−	0.922541i	0.0459550	−	0.0459550i
$404$		−	4.31584i		−	0.214721i
$405$	0.994632	+	2.00267i	0.0494237	+	0.0995137i
$406$			5.69484i			0.282630i
$407$	−9.03170	−	10.0269i	−0.447685	−	0.497015i
$408$	−3.70052	+	3.70052i	−0.183203	+	0.183203i
$409$	−7.23143	+	7.23143i	−0.357571	+	0.357571i	−0.862917	−	0.505346i	$-0.831365\pi$
$409$	−7.23143	+	7.23143i	−0.357571	+	0.357571i	0.505346	+	0.862917i	$0.331365\pi$
$410$	−5.82580	−	11.7302i	−0.287716	−	0.579311i
$411$			3.80721i			0.187796i
$412$	13.9487			0.687202
$413$			1.18867i			0.0584908i
$414$			3.86710i			0.190058i
$415$	12.2317	+	4.11373i	0.600432	+	0.201935i
$416$	−0.163340			−0.00800841
$417$	0.922543	+	0.922543i	0.0451771	+	0.0451771i
$418$	3.72588	+	3.72588i	0.182239	+	0.182239i
$419$			1.66410i			0.0812966i	0.999174	+	0.0406483i	$0.0129423\pi$
$419$			1.66410i			0.0812966i	−0.999174	+	0.0406483i	$0.987058\pi$
$420$	1.68233	−	0.835531i	0.0820892	−	0.0407697i
$421$	−1.49656	−	1.49656i	−0.0729381	−	0.0729381i	0.669697	−	0.742635i	$-0.266424\pi$
$421$	−1.49656	−	1.49656i	−0.0729381	−	0.0729381i	−0.742635	+	0.669697i	$0.766424\pi$
$422$		−	15.2308i		−	0.741422i
$423$	7.97291	−	7.97291i	0.387656	−	0.387656i
$424$	7.94704	+	7.94704i	0.385943	+	0.385943i
$425$	−15.8120	+	20.8488i	−0.766996	+	1.01131i
$426$	10.5734	−	10.5734i	0.512283	−	0.512283i
$427$		−	8.91750i		−	0.431548i
$428$	−5.53603	−	5.53603i	−0.267594	−	0.267594i
$429$	0.256238	+	0.256238i	0.0123713	+	0.0123713i
$430$	−8.89407	−	17.9081i	−0.428910	−	0.863603i
$431$	1.82566	+	1.82566i	0.0879392	+	0.0879392i	0.749708	−	0.661769i	$-0.230194\pi$
$431$	1.82566	+	1.82566i	0.0879392	+	0.0879392i	−0.661769	+	0.749708i	$0.730194\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	8.92738	−	8.92738i	0.429023	−	0.429023i	−0.459273	−	0.888295i	$-0.651890\pi$
$433$	8.92738	−	8.92738i	0.429023	−	0.429023i	0.888295	+	0.459273i	$0.151890\pi$
$434$	6.70977			0.322079
$435$	6.74286	+	13.5766i	0.323295	+	0.650950i
$436$	−9.96395	−	9.96395i	−0.477187	−	0.477187i
$437$	−6.49454	+	6.49454i	−0.310676	+	0.310676i
$438$	0.366066			0.0174913
$439$	−12.1430	+	12.1430i	−0.579555	+	0.579555i	−0.934781	−	0.355225i	$-0.884404\pi$
$439$	−12.1430	+	12.1430i	−0.579555	+	0.579555i	0.355225	+	0.934781i	$0.384404\pi$
$440$	−2.20663	−	4.44300i	−0.105197	−	0.211812i
$441$	6.29433			0.299730
$442$	−0.854812			−0.0406593
$443$	−20.3377	−	20.3377i	−0.966271	−	0.966271i	0.0331781	−	0.999449i	$-0.489437\pi$
$443$	−20.3377	−	20.3377i	−0.966271	−	0.966271i	−0.999449	+	0.0331781i	$0.989437\pi$
$444$	−6.07449	−	0.317197i	−0.288282	−	0.0150535i
$445$	−37.7253	−	12.6876i	−1.78835	−	0.601451i
$446$	9.25821	+	9.25821i	0.438389	+	0.438389i
$447$	6.41551	−	6.41551i	0.303443	−	0.303443i
$448$	−0.593998	−	0.593998i	−0.0280638	−	0.0280638i
$449$	−5.53101	−	5.53101i	−0.261024	−	0.261024i	0.564446	−	0.825470i	$-0.309090\pi$
$449$	−5.53101	−	5.53101i	−0.261024	−	0.261024i	−0.825470	+	0.564446i	$0.809090\pi$
$450$	3.02141	−	3.98385i	0.142431	−	0.187800i
$451$	12.9945			0.611887
$452$	−18.7870			−0.883665
$453$	0.0439894	−	0.0439894i	0.00206680	−	0.00206680i
$454$		−	12.5313i		−	0.588125i
$455$	0.290810	+	0.0978040i	0.0136334	+	0.00458512i
$456$	2.37508			0.111223
$457$	−23.3394			−1.09177			−0.545884	−	0.837861i	$-0.683806\pi$
$457$	−23.3394			−1.09177			−0.545884	+	0.837861i	$0.683806\pi$
$458$	−7.37486			−0.344605
$459$	3.70052	−	3.70052i	0.172725	−	0.172725i
$460$	7.74455	−	3.84634i	0.361091	−	0.179337i
$461$	22.7009	−	22.7009i	1.05728	−	1.05728i	0.0590285	−	0.998256i	$-0.481200\pi$
$461$	22.7009	−	22.7009i	1.05728	−	1.05728i	0.998256	−	0.0590285i	$-0.0188003\pi$
$462$			1.86366i			0.0867052i
$463$		−	0.607463i		−	0.0282312i	−0.999900	−	0.0141156i	$-0.995507\pi$
$463$		−	0.607463i		−	0.0282312i	0.999900	−	0.0141156i	$-0.00449329\pi$
$464$	4.79365	−	4.79365i	0.222540	−	0.222540i
$465$	15.9962	−	7.94457i	0.741808	−	0.368420i
$466$	−18.4468	+	18.4468i	−0.854530	+	0.854530i
$467$	−8.76294			−0.405500			−0.202750	−	0.979230i	$-0.564988\pi$
$467$	−8.76294			−0.405500			−0.202750	+	0.979230i	$0.564988\pi$
$468$	0.163340			0.00755040
$469$	6.41155			0.296058
$470$	−23.8973	−	8.03703i	−1.10230	−	0.370721i
$471$			7.19648i			0.331596i
$472$	1.00057	−	1.00057i	0.0460550	−	0.0460550i
$473$	19.8383			0.912166
$474$	−1.53770			−0.0706288
$475$	11.7649	−	1.61635i	0.539810	−	0.0741632i
$476$	−3.10858	−	3.10858i	−0.142482	−	0.142482i
$477$	−7.94704	−	7.94704i	−0.363870	−	0.363870i
$478$	10.9427	−	10.9427i	0.500508	−	0.500508i
$479$	−6.88917	−	6.88917i	−0.314774	−	0.314774i	0.531982	−	0.846756i	$-0.321448\pi$
$479$	−6.88917	−	6.88917i	−0.314774	−	0.314774i	−0.846756	+	0.531982i	$0.821448\pi$
$480$	−2.11942	−	0.712794i	−0.0967377	−	0.0325344i
$481$	−0.664961	−	0.738233i	−0.0303196	−	0.0336605i
$482$	11.4584	+	11.4584i	0.521917	+	0.521917i
$483$	−3.24852			−0.147813
$484$	−6.07810			−0.276277
$485$	12.7222	+	25.6160i	0.577686	+	1.16316i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$	18.0453			0.817709			0.408855	−	0.912599i	$-0.365928\pi$
$487$	18.0453			0.817709			0.408855	+	0.912599i	$0.365928\pi$
$488$	−7.50634	+	7.50634i	−0.339796	+	0.339796i
$489$	13.5135	+	13.5135i	0.611100	+	0.611100i
$490$	−6.26055	−	12.6055i	−0.282823	−	0.569459i
$491$	41.7594			1.88457			0.942287	−	0.334807i	$-0.108671\pi$
$491$	41.7594			1.88457			0.942287	+	0.334807i	$0.108671\pi$
$492$	4.14170	−	4.14170i	0.186722	−	0.186722i
$493$	25.0867	−	25.0867i	1.12985	−	1.12985i
$494$	0.274319	+	0.274319i	0.0123422	+	0.0123422i
$495$	2.20663	+	4.44300i	0.0991805	+	0.199698i
$496$	−5.64797	−	5.64797i	−0.253601	−	0.253601i
$497$	8.88207	+	8.88207i	0.398415	+	0.398415i
$498$			5.77128i			0.258617i
$499$	−6.17352	+	6.17352i	−0.276365	+	0.276365i	−0.831656	−	0.555291i	$-0.812607\pi$
$499$	−6.17352	+	6.17352i	−0.276365	+	0.276365i	0.555291	+	0.831656i	$0.312607\pi$
$500$	−10.9836	−	2.08844i	−0.491199	−	0.0933980i
$501$	5.15105	+	5.15105i	0.230132	+	0.230132i
$502$	4.90961	−	4.90961i	0.219127	−	0.219127i
$503$			0.796966i			0.0355350i	0.999842	+	0.0177675i	$0.00565586\pi$
$503$			0.796966i			0.0355350i	−0.999842	+	0.0177675i	$0.994344\pi$
$504$	0.593998	+	0.593998i	0.0264588	+	0.0264588i
$505$	8.64322	−	4.29267i	0.384618	−	0.191021i
$506$			8.57930i			0.381396i
$507$	−9.17352	−	9.17352i	−0.407410	−	0.407410i
$508$	−4.61246	−	4.61246i	−0.204645	−	0.204645i
$509$	4.90293			0.217319			0.108659	−	0.994079i	$-0.465344\pi$
$509$	4.90293			0.217319			0.108659	+	0.994079i	$0.465344\pi$
$510$	−11.0916	−	3.73028i	−0.491144	−	0.165180i
$511$			0.307510i			0.0136035i
$512$			1.00000i			0.0441942i
$513$	−2.37508			−0.104862
$514$			20.1402i			0.888346i
$515$	13.8738	+	27.9347i	0.611353	+	1.23095i
$516$	6.32300	−	6.32300i	0.278354	−	0.278354i
$517$	17.6882	−	17.6882i	0.777925	−	0.777925i
$518$	0.266458	−	5.10281i	0.0117075	−	0.224205i
$519$		−	12.6546i		−	0.555475i
$520$	−0.162463	−	0.327117i	−0.00712449	−	0.0143450i
$521$		−	27.5443i		−	1.20674i	−0.797462	−	0.603369i	$-0.793825\pi$
$521$		−	27.5443i		−	1.20674i	0.797462	−	0.603369i	$-0.206175\pi$
$522$	−4.79365	+	4.79365i	−0.209813	+	0.209813i
$523$		−	43.9195i		−	1.92046i	−0.279204	−	0.960232i	$-0.590070\pi$
$523$		−	43.9195i		−	1.92046i	0.279204	−	0.960232i	$-0.409930\pi$
$524$	11.9955	+	11.9955i	0.524026	+	0.524026i
$525$	3.34659	+	2.53811i	0.146057	+	0.110772i
$526$	5.00770	−	5.00770i	0.218346	−	0.218346i
$527$	−29.5577	−	29.5577i	−1.28755	−	1.28755i
$528$	1.56874	−	1.56874i	0.0682707	−	0.0682707i
$529$	8.04553			0.349806
$530$	−8.01096	+	23.8197i	−0.347974	+	1.03466i
$531$	−1.00057	+	1.00057i	−0.0434211	+	0.0434211i
$532$			1.99516i			0.0865012i
$533$	0.956723			0.0414403
$534$		−	17.7998i		−	0.770274i
$535$	5.58056	−	16.5932i	0.241269	−	0.717386i
$536$	−5.39694	−	5.39694i	−0.233112	−	0.233112i
$537$	−24.6499			−1.06372
$538$	12.0216			0.518288
$539$	13.9642			0.601481
$540$	2.11942	+	0.712794i	0.0912052	+	0.0306738i
$541$	6.90527	−	6.90527i	0.296881	−	0.296881i	−0.542910	−	0.839791i	$-0.682678\pi$
$541$	6.90527	−	6.90527i	0.296881	−	0.296881i	0.839791	+	0.542910i	$0.182678\pi$
$542$		−	11.5944i		−	0.498021i
$543$	−2.39964	−	2.39964i	−0.102979	−	0.102979i
$544$			5.23332i			0.224377i
$545$	10.0441	−	29.8650i	0.430241	−	1.27928i
$546$			0.137212i			0.00587214i
$547$			19.7636i			0.845030i	0.906356	+	0.422515i	$0.138853\pi$
$547$			19.7636i			0.845030i	−0.906356	+	0.422515i	$0.861147\pi$
$548$	2.69211	+	2.69211i	0.115001	+	0.115001i
$549$	7.50634	−	7.50634i	0.320363	−	0.320363i
$550$	6.70311	−	8.83831i	0.285822	−	0.376867i
$551$	−16.1013			−0.685936
$552$	2.73445	+	2.73445i	0.116386	+	0.116386i
$553$		−	1.29173i		−	0.0549299i
$554$	−1.48164			−0.0629487
$555$	−5.40664	−	12.4807i	−0.229499	−	0.529777i
$556$	1.30467			0.0553305
$557$			32.5498i			1.37918i	0.724201	+	0.689589i	$0.242209\pi$
$557$			32.5498i			1.37918i	−0.724201	+	0.689589i	$0.757791\pi$
$558$	5.64797	+	5.64797i	0.239098	+	0.239098i
$559$	1.46060			0.0617767
$560$	0.598775	−	1.78039i	0.0253029	−	0.0752354i
$561$	8.20973	−	8.20973i	0.346615	−	0.346615i
$562$	2.20394	+	2.20394i	0.0929675	+	0.0929675i
$563$			9.04112i			0.381038i	0.981684	+	0.190519i	$0.0610170\pi$
$563$			9.04112i			0.381038i	−0.981684	+	0.190519i	$0.938983\pi$
$564$		−	11.2754i		−	0.474780i
$565$	−18.6861	−	37.6242i	−0.786132	−	1.58286i
$566$			12.9583i			0.544678i
$567$	−0.593998	−	0.593998i	−0.0249456	−	0.0249456i
$568$		−	14.9530i		−	0.627415i
$569$	−20.6513	+	20.6513i	−0.865749	+	0.865749i	−0.991999	−	0.126249i	$-0.959706\pi$
$569$	−20.6513	+	20.6513i	−0.865749	+	0.865749i	0.126249	+	0.991999i	$0.459706\pi$
$570$	2.36233	+	4.75651i	0.0989471	+	0.199228i
$571$	18.5622			0.776802			0.388401	−	0.921490i	$-0.373027\pi$
$571$	18.5622			0.776802			0.388401	+	0.921490i	$0.373027\pi$
$572$	0.362376			0.0151517
$573$	−1.53301			−0.0640423
$574$	3.47919	+	3.47919i	0.145219	+	0.145219i
$575$	15.4060	+	11.6841i	0.642473	+	0.487261i
$576$		−	1.00000i		−	0.0416667i
$577$	43.8508			1.82553			0.912766	−	0.408483i	$-0.133942\pi$
$577$	43.8508			1.82553			0.912766	+	0.408483i	$0.133942\pi$
$578$			10.3877i			0.432070i
$579$	−2.85699	+	2.85699i	−0.118732	+	0.118732i
$580$	14.3681	+	4.83221i	0.596601	+	0.200646i
$581$	−4.84810			−0.201133
$582$	−9.04452	+	9.04452i	−0.374907	+	0.374907i
$583$	−17.6308	−	17.6308i	−0.730193	−	0.730193i
$584$	0.258848	−	0.258848i	0.0107112	−	0.0107112i
$585$	0.162463	+	0.327117i	0.00671703	+	0.0135246i
$586$	−15.2639	−	15.2639i	−0.630548	−	0.630548i
$587$			29.8581i			1.23238i	0.787599	+	0.616188i	$0.211324\pi$
$587$			29.8581i			1.23238i	−0.787599	+	0.616188i	$0.788676\pi$
$588$	4.45077	−	4.45077i	0.183546	−	0.183546i
$589$			18.9708i			0.781678i
$590$	2.99902	+	1.00862i	0.123468	+	0.0415241i
$591$			17.4717i			0.718692i
$592$	−4.51960	+	4.07102i	−0.185755	+	0.167318i
$593$	28.1350	−	28.1350i	1.15537	−	1.15537i	0.169905	−	0.985460i	$-0.445654\pi$
$593$	28.1350	−	28.1350i	1.15537	−	1.15537i	0.985460	−	0.169905i	$-0.0543461\pi$
$594$	−1.56874	+	1.56874i	−0.0643662	+	0.0643662i
$595$	3.13359	−	9.31738i	0.128464	−	0.381975i
$596$		−	9.07290i		−	0.371640i
$597$	7.35194			0.300895
$598$			0.631653i			0.0258302i
$599$		−	18.0057i		−	0.735692i	−0.929887	−	0.367846i	$-0.880095\pi$
$599$		−	18.0057i		−	0.735692i	0.929887	−	0.367846i	$-0.119905\pi$
$600$	−0.680545	−	4.95347i	−0.0277831	−	0.202225i
$601$	−3.53685			−0.144271			−0.0721356	−	0.997395i	$-0.522981\pi$
$601$	−3.53685			−0.144271			−0.0721356	+	0.997395i	$0.522981\pi$
$602$	5.31157	+	5.31157i	0.216483	+	0.216483i
$603$	5.39694	+	5.39694i	0.219780	+	0.219780i
$604$		−	0.0622104i		−	0.00253130i
$605$	−6.04548	−	12.1725i	−0.245784	−	0.494881i
$606$	3.05176	+	3.05176i	0.123969	+	0.123969i
$607$			4.86568i			0.197492i	0.995113	+	0.0987459i	$0.0314831\pi$
$607$			4.86568i			0.197492i	−0.995113	+	0.0987459i	$0.968517\pi$
$608$	1.67943	−	1.67943i	0.0681101	−	0.0681101i
$609$	−4.02686	−	4.02686i	−0.163177	−	0.163177i
$610$	−22.4988	−	7.56671i	−0.910950	−	0.306367i
$611$	1.30230	−	1.30230i	0.0526853	−	0.0526853i
$612$		−	5.23332i		−	0.211545i
$613$	23.1044	+	23.1044i	0.933179	+	0.933179i	0.997903	−	0.0647244i	$-0.0206168\pi$
$613$	23.1044	+	23.1044i	0.933179	+	0.933179i	−0.0647244	+	0.997903i	$0.520617\pi$
$614$	−20.5532	−	20.5532i	−0.829458	−	0.829458i
$615$	12.4139	+	4.17501i	0.500578	+	0.168353i
$616$	1.31781	+	1.31781i	0.0530959	+	0.0530959i
$617$	−25.4761	+	25.4761i	−1.02563	+	1.02563i	−0.0259665	+	0.999663i	$0.508266\pi$
$617$	−25.4761	+	25.4761i	−1.02563	+	1.02563i	−0.999663	+	0.0259665i	$0.991734\pi$
$618$	−9.86320	+	9.86320i	−0.396756	+	0.396756i
$619$	31.1893			1.25360			0.626801	−	0.779179i	$-0.284364\pi$
$619$	31.1893			1.25360			0.626801	+	0.779179i	$0.284364\pi$
$620$	5.69340	−	16.9287i	0.228652	−	0.679873i
$621$	−2.73445	−	2.73445i	−0.109730	−	0.109730i
$622$	−0.612480	+	0.612480i	−0.0245582	+	0.0245582i
$623$	14.9526			0.599062
$624$	0.115499	−	0.115499i	0.00462366	−	0.00462366i
$625$	−6.74212	−	24.0737i	−0.269685	−	0.962949i
$626$	3.56579			0.142517
$627$	−5.26920			−0.210431
$628$	5.08868	+	5.08868i	0.203060	+	0.203060i
$629$	−23.6525	+	21.3050i	−0.943089	+	0.849484i
$630$	−0.598775	+	1.78039i	−0.0238558	+	0.0709326i
$631$	19.9604	+	19.9604i	0.794612	+	0.794612i	0.982240	−	0.187628i	$-0.0600800\pi$
$631$	19.9604	+	19.9604i	0.794612	+	0.794612i	−0.187628	+	0.982240i	$0.560080\pi$
$632$	−1.08732	+	1.08732i	−0.0432512	+	0.0432512i
$633$	10.7698	+	10.7698i	0.428060	+	0.428060i
$634$	4.20992	+	4.20992i	0.167197	+	0.167197i
$635$	4.64956	−	13.8250i	0.184512	−	0.548627i
$636$	−11.2388			−0.445648
$637$	1.02812			0.0407355
$638$	−10.6349	+	10.6349i	−0.421039	+	0.421039i
$639$			14.9530i			0.591533i
$640$	−2.00267	+	0.994632i	−0.0791627	+	0.0393163i
$641$	−0.397393			−0.0156961			−0.00784804	−	0.999969i	$-0.502498\pi$
$641$	−0.397393			−0.0156961			−0.00784804	+	0.999969i	$0.502498\pi$
$642$	7.82913			0.308991
$643$	21.4396			0.845495			0.422748	−	0.906247i	$-0.361066\pi$
$643$	21.4396			0.845495			0.422748	+	0.906247i	$0.361066\pi$
$644$	−2.29705	+	2.29705i	−0.0905165	+	0.0905165i
$645$	18.9520	+	6.37385i	0.746233	+	0.250970i
$646$	8.78902	−	8.78902i	0.345800	−	0.345800i
$647$		−	5.00707i		−	0.196848i	−0.995145	−	0.0984241i	$-0.968620\pi$
$647$		−	5.00707i		−	0.196848i	0.995145	−	0.0984241i	$-0.0313802\pi$
$648$			1.00000i			0.0392837i
$649$	−2.21980	+	2.21980i	−0.0871348	+	0.0871348i
$650$	0.493518	−	0.650723i	0.0193574	−	0.0255234i
$651$	−4.74452	+	4.74452i	−0.185953	+	0.185953i
$652$	19.1109			0.748441
$653$	−28.3624			−1.10991			−0.554954	−	0.831881i	$-0.687264\pi$
$653$	−28.3624			−1.10991			−0.554954	+	0.831881i	$0.687264\pi$
$654$	14.0912			0.551008
$655$	−12.0920	+	35.9542i	−0.472473	+	1.40485i
$656$		−	5.85724i		−	0.228687i
$657$	−0.258848	+	0.258848i	−0.0100986	+	0.0100986i
$658$	9.47178			0.369249
$659$	13.0798			0.509518			0.254759	−	0.967005i	$-0.418004\pi$
$659$	13.0798			0.509518			0.254759	+	0.967005i	$0.418004\pi$
$660$	4.70200	+	1.58136i	0.183025	+	0.0615543i
$661$	−21.4953	−	21.4953i	−0.836072	−	0.836072i	0.152267	−	0.988339i	$-0.451343\pi$
$661$	−21.4953	−	21.4953i	−0.836072	−	0.836072i	−0.988339	+	0.152267i	$0.951343\pi$
$662$	14.0919	+	14.0919i	0.547697	+	0.547697i
$663$	0.604443	−	0.604443i	0.0234746	−	0.0234746i
$664$	4.08091	+	4.08091i	0.158370	+	0.158370i
$665$	−3.99566	+	1.98445i	−0.154945	+	0.0769537i
$666$	4.51960	−	4.07102i	0.175131	−	0.157749i
$667$	−18.5375	−	18.5375i	−0.717776	−	0.717776i
$668$	7.28469			0.281853
$669$	−13.0931			−0.506208
$670$	5.44035	−	16.1763i	0.210179	−	0.624945i
$671$	16.6531	−	16.6531i	0.642885	−	0.642885i
$672$	0.840040			0.0324052
$673$	17.5609	−	17.5609i	0.676922	−	0.676922i	−0.282380	−	0.959303i	$-0.591124\pi$
$673$	17.5609	−	17.5609i	0.676922	−	0.676922i	0.959303	+	0.282380i	$0.0911240\pi$
$674$	−17.5011	−	17.5011i	−0.674119	−	0.674119i
$675$	0.680545	+	4.95347i	0.0261942	+	0.190659i
$676$	−12.9733			−0.498974
$677$	27.0147	−	27.0147i	1.03826	−	1.03826i	0.0390206	−	0.999238i	$-0.487576\pi$
$677$	27.0147	−	27.0147i	1.03826	−	1.03826i	0.999238	−	0.0390206i	$-0.0124238\pi$
$678$	13.2844	−	13.2844i	0.510184	−	0.510184i
$679$	−7.59776	−	7.59776i	−0.291575	−	0.291575i
$680$	−10.4806	+	5.20523i	−0.401914	+	0.199612i
$681$	8.86099	+	8.86099i	0.339554	+	0.339554i
$682$	12.5302	+	12.5302i	0.479807	+	0.479807i
$683$		−	24.3629i		−	0.932219i	−0.884727	−	0.466109i	$-0.845655\pi$
$683$		−	24.3629i		−	0.932219i	0.884727	−	0.466109i	$-0.154345\pi$
$684$	−1.67943	+	1.67943i	−0.0642148	+	0.0642148i
$685$	−2.71376	+	8.06907i	−0.103687	+	0.308303i
$686$	7.89681	+	7.89681i	0.301502	+	0.301502i
$687$	5.21481	−	5.21481i	0.198958	−	0.198958i
$688$		−	8.94207i		−	0.340913i
$689$	−1.29807	−	1.29807i	−0.0494526	−	0.0494526i
$690$	−2.75645	+	8.19600i	−0.104936	+	0.312016i
$691$			37.9850i			1.44502i	0.691361	+	0.722509i	$0.257011\pi$
$691$			37.9850i			1.44502i	−0.691361	+	0.722509i	$0.742989\pi$
$692$	−8.94815	−	8.94815i	−0.340158	−	0.340158i
$693$	−1.31781	−	1.31781i	−0.0500593	−	0.0500593i
$694$	−19.3835			−0.735787
$695$	1.29767	+	2.61284i	0.0492234	+	0.0991105i
$696$			6.77925i			0.256967i
$697$		−	30.6528i		−	1.16106i
$698$	−14.5408			−0.550377
$699$		−	26.0877i		−	0.986726i
$700$	4.16111	−	0.571685i	0.157275	−	0.0216077i
$701$	−2.11618	+	2.11618i	−0.0799271	+	0.0799271i	−0.745940	−	0.666013i	$-0.768000\pi$
$701$	−2.11618	+	2.11618i	−0.0799271	+	0.0799271i	0.666013	+	0.745940i	$0.268000\pi$
$702$	−0.115499	+	0.115499i	−0.00435923	+	0.00435923i
$703$	14.4274	+	0.753367i	0.544139	+	0.0284138i
$704$		−	2.21854i		−	0.0836142i
$705$	22.5810	−	11.2149i	0.850448	−	0.422377i
$706$			26.3150i			0.990376i
$707$	−2.56360	+	2.56360i	−0.0964141	+	0.0964141i
$708$			1.41502i			0.0531797i
$709$	−10.3418	−	10.3418i	−0.388395	−	0.388395i	0.485720	−	0.874114i	$-0.338557\pi$
$709$	−10.3418	−	10.3418i	−0.388395	−	0.388395i	−0.874114	+	0.485720i	$0.838557\pi$
$710$	29.9461	−	14.8728i	1.12386	−	0.558165i
$711$	1.08732	−	1.08732i	0.0407776	−	0.0407776i
$712$	−12.5864	−	12.5864i	−0.471695	−	0.471695i
$713$	−21.8413	+	21.8413i	−0.817962	+	0.817962i
$714$	4.39620			0.164524
$715$	0.360431	+	0.725721i	0.0134793	+	0.0271404i
$716$	−17.4301	+	17.4301i	−0.651395	+	0.651395i
$717$			15.4753i			0.577937i
$718$	6.12864			0.228719
$719$			8.49669i			0.316873i	0.987369	+	0.158436i	$0.0506453\pi$
$719$			8.49669i			0.316873i	−0.987369	+	0.158436i	$0.949355\pi$
$720$	2.00267	−	0.994632i	0.0746353	−	0.0370678i
$721$	−8.28548	−	8.28548i	−0.308568	−	0.308568i
$722$	13.3590			0.497170
$723$	−16.2047			−0.602658
$724$	−3.39361			−0.126122
$725$	4.61359	+	33.5808i	0.171344	+	1.24716i
$726$	4.29787	−	4.29787i	0.159509	−	0.159509i
$727$			4.28583i			0.158953i	0.996837	+	0.0794764i	$0.0253248\pi$
$727$			4.28583i			0.158953i	−0.996837	+	0.0794764i	$0.974675\pi$
$728$	0.0970237	+	0.0970237i	0.00359594	+	0.00359594i
$729$		−	1.00000i		−	0.0370370i
$730$	0.775847	+	0.260930i	0.0287154	+	0.00965745i
$731$		−	46.7967i		−	1.73084i
$732$		−	10.6156i		−	0.392363i
$733$	2.83283	+	2.83283i	0.104633	+	0.104633i	0.757485	−	0.652852i	$-0.226428\pi$
$733$	2.83283	+	2.83283i	0.104633	+	0.104633i	−0.652852	+	0.757485i	$0.726428\pi$
$734$	−21.0105	+	21.0105i	−0.775512	+	0.775512i
$735$	13.3403	+	4.48656i	0.492065	+	0.165489i
$736$	3.86710			0.142543
$737$	11.9733	+	11.9733i	0.441042	+	0.441042i
$738$			5.85724i			0.215608i
$739$	−41.7623			−1.53625			−0.768126	−	0.640299i	$-0.778810\pi$
$739$	−41.7623			−1.53625			−0.768126	+	0.640299i	$0.778810\pi$
$740$	−12.6483	−	5.00213i	−0.464960	−	0.183882i
$741$	−0.387946			−0.0142515
$742$		−	9.44106i		−	0.346592i
$743$	−36.8937	−	36.8937i	−1.35350	−	1.35350i	−0.881712	−	0.471788i	$-0.843609\pi$
$743$	−36.8937	−	36.8937i	−1.35350	−	1.35350i	−0.471788	−	0.881712i	$-0.656391\pi$
$744$	7.98744			0.292834
$745$	18.1701	−	9.02420i	0.665700	−	0.330621i
$746$	−2.15543	+	2.15543i	−0.0789157	+	0.0789157i
$747$	−4.08091	−	4.08091i	−0.149313	−	0.149313i
$748$		−	11.6103i		−	0.424515i
$749$			6.57679i			0.240311i
$750$	9.24330	−	6.28979i	0.337517	−	0.229671i
$751$		−	26.9870i		−	0.984768i	−0.870378	−	0.492384i	$-0.836125\pi$
$751$		−	26.9870i		−	0.984768i	0.870378	−	0.492384i	$-0.163875\pi$
$752$	−7.97291	−	7.97291i	−0.290742	−	0.290742i
$753$			6.94324i			0.253026i
$754$	−0.782996	+	0.782996i	−0.0285150	+	0.0285150i
$755$	0.124587	−	0.0618764i	0.00453419	−	0.00225191i
$756$	−0.840040			−0.0305520
$757$	−36.8457			−1.33918			−0.669590	−	0.742731i	$-0.733530\pi$
$757$	−36.8457			−1.33918			−0.669590	+	0.742731i	$0.733530\pi$
$758$	−37.8733			−1.37562
$759$	−6.06648	−	6.06648i	−0.220199	−	0.220199i
$760$	5.03378	+	1.69294i	0.182594	+	0.0614094i
$761$		−	38.2000i		−	1.38475i	−0.721538	−	0.692374i	$-0.756565\pi$
$761$		−	38.2000i		−	1.38475i	0.721538	−	0.692374i	$-0.243435\pi$
$762$	6.52301			0.236304
$763$			11.8371i			0.428533i
$764$	−1.08400	+	1.08400i	−0.0392177	+	0.0392177i
$765$	10.4806	−	5.20523i	0.378929	−	0.188196i
$766$	−33.6750			−1.21673
$767$	−0.163433	+	0.163433i	−0.00590124	+	0.00590124i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	−23.0452	+	23.0452i	−0.831031	+	0.831031i	−0.987658	−	0.156627i	$-0.949938\pi$
$769$	−23.0452	+	23.0452i	−0.831031	+	0.831031i	0.156627	+	0.987658i	$0.449938\pi$
$770$	−1.32840	+	3.94987i	−0.0478724	+	0.142343i
$771$	−14.2413	−	14.2413i	−0.512887	−	0.512887i
$772$			4.04039i			0.145417i
$773$	−15.2548	+	15.2548i	−0.548676	+	0.548676i	−0.926058	−	0.377382i	$-0.876824\pi$
$773$	−15.2548	+	15.2548i	−0.548676	+	0.548676i	0.377382	+	0.926058i	$0.376824\pi$
$774$			8.94207i			0.321416i
$775$	39.5655	−	5.43582i	1.42124	−	0.195260i
$776$			12.7909i			0.459166i
$777$	3.41982	+	3.79665i	0.122685	+	0.136204i
$778$	−6.96706	+	6.96706i	−0.249781	+	0.249781i
$779$	−9.83686	+	9.83686i	−0.352442	+	0.352442i
$780$	0.346186	+	0.116428i	0.0123954	+	0.00416879i
$781$			33.1738i			1.18705i
$782$	20.2378			0.723702
$783$		−	6.77925i		−	0.242271i
$784$		−	6.29433i		−	0.224798i
$785$	−5.12961	+	15.2523i	−0.183084	+	0.544379i
$786$	−16.9642			−0.605093
$787$	−24.1643	−	24.1643i	−0.861365	−	0.861365i	0.130132	−	0.991497i	$-0.458460\pi$
$787$	−24.1643	−	24.1643i	−0.861365	−	0.861365i	−0.991497	+	0.130132i	$0.958460\pi$
$788$	12.3544	+	12.3544i	0.440107	+	0.440107i
$789$			7.08196i			0.252124i
$790$	−3.25902	−	1.09606i	−0.115951	−	0.0389961i
$791$	11.1594	+	11.1594i	0.396784	+	0.396784i
$792$			2.21854i			0.0788322i
$793$	1.22609	−	1.22609i	0.0435396	−	0.0435396i
$794$	−2.14584	−	2.14584i	−0.0761529	−	0.0761529i
$795$	−11.1785	−	22.5077i	−0.396460	−	0.798266i
$796$	5.19861	−	5.19861i	0.184260	−	0.184260i
$797$			32.2456i			1.14220i	0.820881	+	0.571099i	$0.193483\pi$
$797$			32.2456i			1.14220i	−0.820881	+	0.571099i	$0.806517\pi$
$798$	−1.41079	−	1.41079i	−0.0499415	−	0.0499415i
$799$	−41.7248	−	41.7248i	−1.47612	−	1.47612i
$800$	−3.98385	−	3.02141i	−0.140850	−	0.106823i
$801$	12.5864	+	12.5864i	0.444718	+	0.444718i
$802$	−3.17371	+	3.17371i	−0.112068	+	0.112068i
$803$	−0.574263	+	0.574263i	−0.0202653	+	0.0202653i
$804$	7.63243			0.269175
$805$	−6.88497	−	2.31552i	−0.242663	−	0.0816115i
$806$	0.922541	+	0.922541i	0.0324951	+	0.0324951i
$807$	−8.50055	+	8.50055i	−0.299234	+	0.299234i
$808$	4.31584			0.151831
$809$	−16.4950	+	16.4950i	−0.579933	+	0.579933i	−0.934885	−	0.354952i	$-0.884497\pi$
$809$	−16.4950	+	16.4950i	−0.579933	+	0.579933i	0.354952	+	0.934885i	$0.384497\pi$
$810$	−2.00267	+	0.994632i	−0.0703668	+	0.0349478i
$811$	−36.1279			−1.26862			−0.634310	−	0.773078i	$-0.718716\pi$
$811$	−36.1279			−1.26862			−0.634310	+	0.773078i	$0.718716\pi$
$812$	−5.69484			−0.199850
$813$	8.19846	+	8.19846i	0.287533	+	0.287533i
$814$	10.0269	−	9.03170i	0.351443	−	0.316561i
$815$	19.0083	+	38.2729i	0.665833	+	1.34064i
$816$	−3.70052	−	3.70052i	−0.129544	−	0.129544i
$817$	−15.0176	+	15.0176i	−0.525400	+	0.525400i
$818$	−7.23143	−	7.23143i	−0.252841	−	0.252841i
$819$	−0.0970237	−	0.0970237i	−0.00339028	−	0.00339028i
$820$	11.7302	−	5.82580i	0.409635	−	0.203446i
$821$	−49.5091			−1.72788			−0.863939	−	0.503597i	$-0.832010\pi$
$821$	−49.5091			−1.72788			−0.863939	+	0.503597i	$0.832010\pi$
$822$	−3.80721			−0.132792
$823$	5.45635	−	5.45635i	0.190196	−	0.190196i	−0.605585	−	0.795781i	$-0.707061\pi$
$823$	5.45635	−	5.45635i	0.190196	−	0.190196i	0.795781	+	0.605585i	$0.207061\pi$
$824$			13.9487i			0.485925i
$825$	1.50981	+	10.9894i	0.0525650	+	0.382603i
$826$	−1.18867			−0.0413593
$827$	−9.24721			−0.321557			−0.160778	−	0.986991i	$-0.551400\pi$
$827$	−9.24721			−0.321557			−0.160778	+	0.986991i	$0.551400\pi$
$828$	−3.86710			−0.134391
$829$	15.9624	−	15.9624i	0.554396	−	0.554396i	−0.373311	−	0.927706i	$-0.621777\pi$
$829$	15.9624	−	15.9624i	0.554396	−	0.554396i	0.927706	+	0.373311i	$0.121777\pi$
$830$	−4.11373	+	12.2317i	−0.142790	+	0.424570i
$831$	1.04768	−	1.04768i	0.0363435	−	0.0363435i
$832$		−	0.163340i		−	0.00566280i
$833$		−	32.9403i		−	1.14131i
$834$	−0.922543	+	0.922543i	−0.0319451	+	0.0319451i
$835$	7.24559	+	14.5889i	0.250744	+	0.504869i
$836$	−3.72588	+	3.72588i	−0.128862	+	0.128862i
$837$	−7.98744			−0.276086
$838$	−1.66410			−0.0574854
$839$	8.15311			0.281477			0.140738	−	0.990047i	$-0.455052\pi$
$839$	8.15311			0.281477			0.140738	+	0.990047i	$0.455052\pi$
$840$	0.835531	+	1.68233i	0.0288286	+	0.0580458i
$841$		−	16.9582i		−	0.584766i
$842$	1.49656	−	1.49656i	0.0515750	−	0.0515750i
$843$	−3.11684			−0.107350
$844$	15.2308			0.524264
$845$	−12.9037	−	25.9813i	−0.443900	−	0.893785i
$846$	7.97291	+	7.97291i	0.274114	+	0.274114i
$847$	3.61038	+	3.61038i	0.124054	+	0.124054i
$848$	−7.94704	+	7.94704i	−0.272903	+	0.272903i
$849$	−9.16290	−	9.16290i	−0.314470	−	0.314470i
$850$	−20.8488	−	15.8120i	−0.715107	−	0.542348i
$851$	15.7430	+	17.4778i	0.539664	+	0.599130i
$852$	10.5734	+	10.5734i	0.362238	+	0.362238i
$853$	39.7229			1.36009			0.680044	−	0.733172i	$-0.261961\pi$
$853$	39.7229			1.36009			0.680044	+	0.733172i	$0.261961\pi$
$854$	8.91750			0.305151
$855$	−5.03378	−	1.69294i	−0.172152	−	0.0578974i
$856$	5.53603	−	5.53603i	0.189218	−	0.189218i
$857$	36.5325			1.24793			0.623964	−	0.781453i	$-0.285521\pi$
$857$	36.5325			1.24793			0.623964	+	0.781453i	$0.285521\pi$
$858$	−0.256238	+	0.256238i	−0.00874784	+	0.00874784i
$859$	7.62822	+	7.62822i	0.260272	+	0.260272i	0.825164	−	0.564893i	$-0.191082\pi$
$859$	7.62822	+	7.62822i	0.260272	+	0.260272i	−0.564893	+	0.825164i	$0.691082\pi$
$860$	17.9081	−	8.89407i	0.610660	−	0.303285i
$861$	−4.92032			−0.167684
$862$	−1.82566	+	1.82566i	−0.0621824	+	0.0621824i
$863$	−2.11127	+	2.11127i	−0.0718684	+	0.0718684i	−0.742127	−	0.670259i	$-0.766183\pi$
$863$	−2.11127	+	2.11127i	−0.0718684	+	0.0718684i	0.670259	+	0.742127i	$0.266183\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$	9.02011	−	26.8203i	0.306693	−	0.911919i
$866$	8.92738	+	8.92738i	0.303365	+	0.303365i
$867$	−7.34519	−	7.34519i	−0.249456	−	0.249456i
$868$			6.70977i			0.227744i
$869$	2.41225	−	2.41225i	0.0818300	−	0.0818300i
$870$	−13.5766	+	6.74286i	−0.460291	+	0.228604i
$871$	0.881537	+	0.881537i	0.0298698	+	0.0298698i
$872$	9.96395	−	9.96395i	0.337422	−	0.337422i
$873$		−	12.7909i		−	0.432906i
$874$	−6.49454	−	6.49454i	−0.219681	−	0.219681i
$875$	5.28368	+	7.76474i	0.178621	+	0.262496i
$876$			0.366066i			0.0123682i
$877$	−14.3455	−	14.3455i	−0.484412	−	0.484412i	0.422126	−	0.906537i	$-0.361284\pi$
$877$	−14.3455	−	14.3455i	−0.484412	−	0.484412i	−0.906537	+	0.422126i	$0.861284\pi$
$878$	−12.1430	−	12.1430i	−0.409807	−	0.409807i
$879$	21.5865			0.728094
$880$	4.44300	−	2.20663i	0.149774	−	0.0743854i
$881$			55.0941i			1.85617i	0.372373	+	0.928083i	$0.378544\pi$
$881$			55.0941i			1.85617i	−0.372373	+	0.928083i	$0.621456\pi$
$882$			6.29433i			0.211941i
$883$	−11.4724			−0.386078			−0.193039	−	0.981191i	$-0.561834\pi$
$883$	−11.4724			−0.386078			−0.193039	+	0.981191i	$0.561834\pi$
$884$		−	0.854812i		−	0.0287504i
$885$	−2.83383	+	1.40743i	−0.0952580	+	0.0473101i
$886$	20.3377	−	20.3377i	0.683257	−	0.683257i
$887$	5.30617	−	5.30617i	0.178164	−	0.178164i	−0.612391	−	0.790555i	$-0.709792\pi$
$887$	5.30617	−	5.30617i	0.178164	−	0.178164i	0.790555	+	0.612391i	$0.209792\pi$
$888$	0.317197	−	6.07449i	0.0106444	−	0.203846i
$889$			5.47959i			0.183779i
$890$	12.6876	−	37.7253i	0.425290	−	1.26455i
$891$		−	2.21854i		−	0.0743237i
$892$	−9.25821	+	9.25821i	−0.309988	+	0.309988i
$893$			26.7800i			0.896157i
$894$	6.41551	+	6.41551i	0.214567	+	0.214567i
$895$	−52.2435	−	17.5703i	−1.74631	−	0.587311i
$896$	0.593998	−	0.593998i	0.0198441	−	0.0198441i
$897$	−0.446646	−	0.446646i	−0.0149131	−	0.0149131i
$898$	5.53101	−	5.53101i	0.184572	−	0.184572i
$899$	−54.1488			−1.80597
$900$	3.98385	+	3.02141i	0.132795	+	0.100714i
$901$	−41.5894	+	41.5894i	−1.38555	+	1.38555i
$902$			12.9945i			0.432669i
$903$	−7.51170			−0.249974
$904$		−	18.7870i		−	0.624846i
$905$	−3.37539	−	6.79629i	−0.112202	−	0.225916i
$906$	0.0439894	+	0.0439894i	0.00146145	+	0.00146145i
$907$	31.7782			1.05518			0.527589	−	0.849500i	$-0.323096\pi$
$907$	31.7782			1.05518			0.527589	+	0.849500i	$0.323096\pi$
$908$	12.5313			0.415867
$909$	−4.31584			−0.143147
$910$	−0.0978040	+	0.290810i	−0.00324217	+	0.00964025i
$911$	−33.4412	+	33.4412i	−1.10796	+	1.10796i	−0.114539	+	0.993419i	$0.536539\pi$
$911$	−33.4412	+	33.4412i	−1.10796	+	1.10796i	−0.993419	+	0.114539i	$0.963461\pi$
$912$			2.37508i			0.0786467i
$913$	−9.05364	−	9.05364i	−0.299632	−	0.299632i
$914$		−	23.3394i		−	0.771997i
$915$	21.2595	−	10.5586i	0.702818	−	0.349056i
$916$		−	7.37486i		−	0.243672i
$917$		−	14.2506i		−	0.470597i
$918$	3.70052	+	3.70052i	0.122135	+	0.122135i
$919$	−2.92019	+	2.92019i	−0.0963281	+	0.0963281i	−0.753629	−	0.657300i	$-0.771698\pi$
$919$	−2.92019	+	2.92019i	−0.0963281	+	0.0963281i	0.657300	+	0.753629i	$0.271698\pi$
$920$	3.84634	+	7.74455i	0.126810	+	0.255330i
$921$	29.0665			0.957775
$922$	22.7009	+	22.7009i	0.747613	+	0.747613i
$923$			2.44243i			0.0803936i
$924$	−1.86366			−0.0613099
$925$	−2.56274	−	30.3056i	−0.0842624	−	0.996444i
$926$	0.607463			0.0199625
$927$		−	13.9487i		−	0.458134i
$928$	4.79365	+	4.79365i	0.157359	+	0.157359i
$929$	6.30230			0.206772			0.103386	−	0.994641i	$-0.467032\pi$
$929$	6.30230			0.206772			0.103386	+	0.994641i	$0.467032\pi$
$930$	7.94457	+	15.9962i	0.260513	+	0.524538i
$931$	−10.5709	+	10.5709i	−0.346448	+	0.346448i
$932$	−18.4468	−	18.4468i	−0.604244	−	0.604244i
$933$		−	0.866177i		−	0.0283574i
$934$		−	8.76294i		−	0.286732i
$935$	23.2517	−	11.5480i	0.760411	−	0.377660i
$936$			0.163340i			0.00533894i
$937$	−1.82017	−	1.82017i	−0.0594623	−	0.0594623i	0.676750	−	0.736213i	$-0.263388\pi$
$937$	−1.82017	−	1.82017i	−0.0594623	−	0.0594623i	−0.736213	+	0.676750i	$0.763388\pi$
$938$			6.41155i			0.209344i
$939$	−2.52139	+	2.52139i	−0.0822825	+	0.0822825i
$940$	8.03703	−	23.8973i	0.262139	−	0.779443i
$941$	−34.3191			−1.11877			−0.559385	−	0.828908i	$-0.688962\pi$
$941$	−34.3191			−1.11877			−0.559385	+	0.828908i	$0.688962\pi$
$942$	−7.19648			−0.234474
$943$	−22.6505			−0.737603
$944$	1.00057	+	1.00057i	0.0325658	+	0.0325658i
$945$	−0.835531	−	1.68233i	−0.0271798	−	0.0547261i
$946$			19.8383i			0.644999i
$947$	8.75872			0.284620			0.142310	−	0.989822i	$-0.454547\pi$
$947$	8.75872			0.284620			0.142310	+	0.989822i	$0.454547\pi$
$948$		−	1.53770i		−	0.0499421i
$949$	−0.0422803	+	0.0422803i	−0.00137248	+	0.00137248i
$950$	1.61635	+	11.7649i	0.0524413	+	0.381703i
$951$	−5.95373			−0.193063
$952$	3.10858	−	3.10858i	0.100750	−	0.100750i
$953$	−10.3887	−	10.3887i	−0.336523	−	0.336523i	0.518534	−	0.855057i	$-0.326478\pi$
$953$	−10.3887	−	10.3887i	−0.336523	−	0.336523i	−0.855057	+	0.518534i	$0.826478\pi$
$954$	7.94704	−	7.94704i	0.257295	−	0.257295i
$955$	−3.24908	−	1.09272i	−0.105138	−	0.0353595i
$956$	10.9427	+	10.9427i	0.353913	+	0.353913i
$957$		−	15.0400i		−	0.486174i
$958$	6.88917	−	6.88917i	0.222579	−	0.222579i
$959$		−	3.19821i		−	0.103276i
$960$	0.712794	−	2.11942i	0.0230053	−	0.0684039i
$961$			32.7992i			1.05804i
$962$	0.738233	−	0.664961i	0.0238016	−	0.0214392i
$963$	−5.53603	+	5.53603i	−0.178396	+	0.178396i
$964$	−11.4584	+	11.4584i	−0.369051	+	0.369051i
$965$	−8.09159	+	4.01870i	−0.260477	+	0.129367i
$966$		−	3.24852i		−	0.104519i
$967$	13.8109			0.444129			0.222065	−	0.975032i	$-0.428720\pi$
$967$	13.8109			0.444129			0.222065	+	0.975032i	$0.428720\pi$
$968$		−	6.07810i		−	0.195358i
$969$			12.4296i			0.399295i
$970$	−25.6160	+	12.7222i	−0.822479	+	0.408486i
$971$	−47.3586			−1.51981			−0.759905	−	0.650034i	$-0.774755\pi$
$971$	−47.3586			−1.51981			−0.759905	+	0.650034i	$0.774755\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	−0.774973	−	0.774973i	−0.0248445	−	0.0248445i
$974$			18.0453i			0.578208i
$975$	0.111160	+	0.809100i	0.00355998	+	0.0259119i
$976$	−7.50634	−	7.50634i	−0.240272	−	0.240272i
$977$			10.0505i			0.321543i	0.986992	+	0.160771i	$0.0513982\pi$
$977$			10.0505i			0.321543i	−0.986992	+	0.160771i	$0.948602\pi$
$978$	−13.5135	+	13.5135i	−0.432113	+	0.432113i
$979$	27.9233	+	27.9233i	0.892434	+	0.892434i
$980$	12.6055	−	6.26055i	0.402668	−	0.199986i
$981$	−9.96395	+	9.96395i	−0.318124	+	0.318124i
$982$			41.7594i			1.33259i
$983$	−16.0348	−	16.0348i	−0.511429	−	0.511429i	0.403535	−	0.914964i	$-0.367781\pi$
$983$	−16.0348	−	16.0348i	−0.511429	−	0.511429i	−0.914964	+	0.403535i	$0.867781\pi$
$984$	4.14170	+	4.14170i	0.132032	+	0.132032i
$985$	−12.4538	+	37.0299i	−0.396810	+	1.17987i
$986$	25.0867	+	25.0867i	0.798924	+	0.798924i
$987$	−6.69756	+	6.69756i	−0.213186	+	0.213186i
$988$	−0.274319	+	0.274319i	−0.00872725	+	0.00872725i
$989$	−34.5799			−1.09958
$990$	−4.44300	+	2.20663i	−0.141208	+	0.0701312i
$991$	18.3342	+	18.3342i	0.582404	+	0.582404i	0.935563	−	0.353160i	$-0.114893\pi$
$991$	18.3342	+	18.3342i	0.582404	+	0.582404i	−0.353160	+	0.935563i	$0.614893\pi$
$992$	5.64797	−	5.64797i	0.179323	−	0.179323i
$993$	−19.9290			−0.632426
$994$	−8.88207	+	8.88207i	−0.281722	+	0.281722i
$995$	15.5818	+	5.24042i	0.493977	+	0.166132i
$996$	−5.77128			−0.182870
$997$	36.8722			1.16775			0.583877	−	0.811842i	$-0.301535\pi$
$997$	36.8722			1.16775			0.583877	+	0.811842i	$0.301535\pi$
$998$	−6.17352	−	6.17352i	−0.195419	−	0.195419i
$999$	−0.317197	+	6.07449i	−0.0100357	+	0.192188i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.l.b.697.4	yes	40
5.3	odd	4		1110.2.o.b.253.17	yes	40
37.6	odd	4		1110.2.o.b.487.17	yes	40
185.43	even	4	inner	1110.2.l.b.43.4	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.b.43.4	✓	40	185.43	even	4	inner
1110.2.l.b.697.4	yes	40	1.1	even	1	trivial
1110.2.o.b.253.17	yes	40	5.3	odd	4
1110.2.o.b.487.17	yes	40	37.6	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.994632 - 2.00267i) q^{5} +(0.707107 - 0.707107i) q^{6} +(0.593998 + 0.593998i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.994632 - 2.00267i) q^{5} +(0.707107 - 0.707107i) q^{6} +(0.593998 + 0.593998i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(2.00267 - 0.994632i) q^{10} +2.21854i q^{11} +(0.707107 + 0.707107i) q^{12} +0.163340i q^{13} +(-0.593998 + 0.593998i) q^{14} +(-0.712794 + 2.11942i) q^{15} +1.00000 q^{16} +5.23332 q^{17} -1.00000 q^{18} +(-1.67943 - 1.67943i) q^{19} +(0.994632 + 2.00267i) q^{20} -0.840040i q^{21} -2.21854 q^{22} -3.86710i q^{23} +(-0.707107 + 0.707107i) q^{24} +(-3.02141 + 3.98385i) q^{25} -0.163340 q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.593998 - 0.593998i) q^{28} +(4.79365 - 4.79365i) q^{29} +(-2.11942 - 0.712794i) q^{30} +(-5.64797 - 5.64797i) q^{31} +1.00000i q^{32} +(1.56874 - 1.56874i) q^{33} +5.23332i q^{34} +(0.598775 - 1.78039i) q^{35} -1.00000i q^{36} +(-4.51960 + 4.07102i) q^{37} +(1.67943 - 1.67943i) q^{38} +(0.115499 - 0.115499i) q^{39} +(-2.00267 + 0.994632i) q^{40} -5.85724i q^{41} +0.840040 q^{42} -8.94207i q^{43} -2.21854i q^{44} +(2.00267 - 0.994632i) q^{45} +3.86710 q^{46} +(-7.97291 - 7.97291i) q^{47} +(-0.707107 - 0.707107i) q^{48} -6.29433i q^{49} +(-3.98385 - 3.02141i) q^{50} +(-3.70052 - 3.70052i) q^{51} -0.163340i q^{52} +(-7.94704 + 7.94704i) q^{53} +(0.707107 + 0.707107i) q^{54} +(4.44300 - 2.20663i) q^{55} +(0.593998 - 0.593998i) q^{56} +2.37508i q^{57} +(4.79365 + 4.79365i) q^{58} +(1.00057 + 1.00057i) q^{59} +(0.712794 - 2.11942i) q^{60} +(-7.50634 - 7.50634i) q^{61} +(5.64797 - 5.64797i) q^{62} +(-0.593998 + 0.593998i) q^{63} -1.00000 q^{64} +(0.327117 - 0.162463i) q^{65} +(1.56874 + 1.56874i) q^{66} +(5.39694 - 5.39694i) q^{67} -5.23332 q^{68} +(-2.73445 + 2.73445i) q^{69} +(1.78039 + 0.598775i) q^{70} +14.9530 q^{71} +1.00000 q^{72} +(0.258848 + 0.258848i) q^{73} +(-4.07102 - 4.51960i) q^{74} +(4.95347 - 0.680545i) q^{75} +(1.67943 + 1.67943i) q^{76} +(-1.31781 + 1.31781i) q^{77} +(0.115499 + 0.115499i) q^{78} +(-1.08732 - 1.08732i) q^{79} +(-0.994632 - 2.00267i) q^{80} -1.00000 q^{81} +5.85724 q^{82} +(-4.08091 + 4.08091i) q^{83} +0.840040i q^{84} +(-5.20523 - 10.4806i) q^{85} +8.94207 q^{86} -6.77925 q^{87} +2.21854 q^{88} +(12.5864 - 12.5864i) q^{89} +(0.994632 + 2.00267i) q^{90} +(-0.0970237 + 0.0970237i) q^{91} +3.86710i q^{92} +7.98744i q^{93} +(7.97291 - 7.97291i) q^{94} +(-1.69294 + 5.03378i) q^{95} +(0.707107 - 0.707107i) q^{96} -12.7909 q^{97} +6.29433 q^{98} -2.21854 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{4} - 4 q^{7}+O(q^{10}) \) 40 * q - 40 * q^4 - 4 * q^7	\( 40 q - 40 q^{4} - 4 q^{7} + 4 q^{14} + 40 q^{16} + 24 q^{17} - 40 q^{18} + 4 q^{19} + 8 q^{22} + 8 q^{25} + 8 q^{26} + 4 q^{28} + 28 q^{31} - 4 q^{33} + 20 q^{35} + 20 q^{37} - 4 q^{38} + 4 q^{39} + 16 q^{42} - 16 q^{47} + 16 q^{51} + 20 q^{53} + 16 q^{55} - 4 q^{56} - 4 q^{59} - 8 q^{61} - 28 q^{62} + 4 q^{63} - 40 q^{64} - 4 q^{65} - 4 q^{66} + 16 q^{67} - 24 q^{68} - 8 q^{69} + 12 q^{70} + 40 q^{71} + 40 q^{72} + 8 q^{73} - 8 q^{74} + 16 q^{75} - 4 q^{76} - 24 q^{77} + 4 q^{78} - 12 q^{79} - 40 q^{81} - 24 q^{82} - 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{88} + 12 q^{89} - 24 q^{91} + 16 q^{94} - 28 q^{95} + 40 q^{97} - 56 q^{98} + 8 q^{99}+O(q^{100}) \) 40 * q - 40 * q^4 - 4 * q^7 + 4 * q^14 + 40 * q^16 + 24 * q^17 - 40 * q^18 + 4 * q^19 + 8 * q^22 + 8 * q^25 + 8 * q^26 + 4 * q^28 + 28 * q^31 - 4 * q^33 + 20 * q^35 + 20 * q^37 - 4 * q^38 + 4 * q^39 + 16 * q^42 - 16 * q^47 + 16 * q^51 + 20 * q^53 + 16 * q^55 - 4 * q^56 - 4 * q^59 - 8 * q^61 - 28 * q^62 + 4 * q^63 - 40 * q^64 - 4 * q^65 - 4 * q^66 + 16 * q^67 - 24 * q^68 - 8 * q^69 + 12 * q^70 + 40 * q^71 + 40 * q^72 + 8 * q^73 - 8 * q^74 + 16 * q^75 - 4 * q^76 - 24 * q^77 + 4 * q^78 - 12 * q^79 - 40 * q^81 - 24 * q^82 - 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^88 + 12 * q^89 - 24 * q^91 + 16 * q^94 - 28 * q^95 + 40 * q^97 - 56 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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