LMFDB - Embedded newform 546.2.o.b.265.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(265,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("546.265");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.o (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.836829184.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 14x^{6} + 61x^{4} + 84x^{2} + 4 $ x^8 + 14x^6 + 61x^4 + 84*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			265.1
Root			$-2.06644i$ of defining polynomial
Character	$\chi$	$=$	546.265
Dual form			546.2.o.b.307.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{3} -1.00000i q^{4} +(-2.16830 - 2.16830i) q^{5} +(0.707107 + 0.707107i) q^{6} +(2.62949 - 0.292893i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{3} -1.00000i q^{4} +(-2.16830 - 2.16830i) q^{5} +(0.707107 + 0.707107i) q^{6} +(2.62949 - 0.292893i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +3.06644 q^{10} +(0.516075 + 0.516075i) q^{11} -1.00000 q^{12} +(3.60525 - 0.0469777i) q^{13} +(-1.65222 + 2.06644i) q^{14} +(-2.16830 + 2.16830i) q^{15} -1.00000 q^{16} -2.57461 q^{17} +(0.707107 - 0.707107i) q^{18} +(-3.82052 - 3.82052i) q^{19} +(-2.16830 + 2.16830i) q^{20} +(-0.292893 - 2.62949i) q^{21} -0.729840 q^{22} -6.97248i q^{23} +(0.707107 - 0.707107i) q^{24} +4.40303i q^{25} +(-2.51608 + 2.58251i) q^{26} +1.00000i q^{27} +(-0.292893 - 2.62949i) q^{28} -6.32541 q^{29} -3.06644i q^{30} +(-4.33660 - 4.33660i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.516075 - 0.516075i) q^{33} +(1.82052 - 1.82052i) q^{34} +(-6.33660 - 5.06644i) q^{35} +1.00000i q^{36} +(-3.58251 - 3.58251i) q^{37} +5.40303 q^{38} +(-0.0469777 - 3.60525i) q^{39} -3.06644i q^{40} +(-0.176204 - 0.176204i) q^{41} +(2.06644 + 1.65222i) q^{42} +7.89486i q^{43} +(0.516075 - 0.516075i) q^{44} +(2.16830 + 2.16830i) q^{45} +(4.93029 + 4.93029i) q^{46} +(1.41421 - 1.41421i) q^{47} +1.00000i q^{48} +(6.82843 - 1.54032i) q^{49} +(-3.11341 - 3.11341i) q^{50} +2.57461i q^{51} +(-0.0469777 - 3.60525i) q^{52} -0.514936 q^{53} +(-0.707107 - 0.707107i) q^{54} -2.23801i q^{55} +(2.06644 + 1.65222i) q^{56} +(-3.82052 + 3.82052i) q^{57} +(4.47274 - 4.47274i) q^{58} +(-3.17834 + 3.17834i) q^{59} +(2.16830 + 2.16830i) q^{60} +6.41208i q^{61} +6.13287 q^{62} +(-2.62949 + 0.292893i) q^{63} +1.00000i q^{64} +(-7.91911 - 7.71538i) q^{65} +0.729840i q^{66} +(-3.96130 + 3.96130i) q^{67} +2.57461i q^{68} -6.97248 q^{69} +(8.06316 - 0.898138i) q^{70} +(8.12169 - 8.12169i) q^{71} +(-0.707107 - 0.707107i) q^{72} +(11.6056 - 11.6056i) q^{73} +5.06644 q^{74} +4.40303 q^{75} +(-3.82052 + 3.82052i) q^{76} +(1.50817 + 1.20586i) q^{77} +(2.58251 + 2.51608i) q^{78} +10.9455 q^{79} +(2.16830 + 2.16830i) q^{80} +1.00000 q^{81} +0.249190 q^{82} +(1.01118 + 1.01118i) q^{83} +(-2.62949 + 0.292893i) q^{84} +(5.58251 + 5.58251i) q^{85} +(-5.58251 - 5.58251i) q^{86} +6.32541i q^{87} +0.729840i q^{88} +(1.10977 - 1.10977i) q^{89} -3.06644 q^{90} +(9.46619 - 1.17948i) q^{91} -6.97248 q^{92} +(-4.33660 + 4.33660i) q^{93} +2.00000i q^{94} +16.5681i q^{95} +(-0.707107 - 0.707107i) q^{96} +(-9.34336 - 9.34336i) q^{97} +(-3.73926 + 5.91760i) q^{98} +(-0.516075 - 0.516075i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{5} - 8 q^{9}+O(q^{10}) $ 8 * q - 4 * q^5 - 8 * q^9	$ 8 q - 4 q^{5} - 8 q^{9} + 4 q^{10} - 8 q^{12} + 16 q^{13} - 4 q^{14} - 4 q^{15} - 8 q^{16} + 4 q^{17} - 8 q^{19} - 4 q^{20} - 8 q^{21} - 12 q^{22} - 16 q^{26} - 8 q^{28} + 12 q^{29} - 8 q^{31} - 8 q^{34} - 24 q^{35} - 4 q^{37} - 4 q^{38} - 4 q^{39} + 12 q^{41} - 4 q^{42} + 4 q^{45} + 24 q^{46} + 32 q^{49} - 8 q^{50} - 4 q^{52} + 40 q^{53} - 4 q^{56} - 8 q^{57} + 4 q^{58} - 8 q^{59} + 4 q^{60} + 8 q^{62} - 12 q^{65} + 32 q^{67} - 28 q^{69} + 8 q^{70} - 12 q^{71} + 20 q^{73} + 20 q^{74} - 12 q^{75} - 8 q^{76} + 8 q^{77} - 4 q^{78} + 24 q^{79} + 4 q^{80} + 8 q^{81} + 40 q^{82} + 44 q^{83} + 20 q^{85} - 20 q^{86} + 16 q^{89} - 4 q^{90} - 28 q^{91} - 28 q^{92} - 8 q^{93} - 8 q^{97} - 16 q^{98}+O(q^{100}) $ 8 * q - 4 * q^5 - 8 * q^9 + 4 * q^10 - 8 * q^12 + 16 * q^13 - 4 * q^14 - 4 * q^15 - 8 * q^16 + 4 * q^17 - 8 * q^19 - 4 * q^20 - 8 * q^21 - 12 * q^22 - 16 * q^26 - 8 * q^28 + 12 * q^29 - 8 * q^31 - 8 * q^34 - 24 * q^35 - 4 * q^37 - 4 * q^38 - 4 * q^39 + 12 * q^41 - 4 * q^42 + 4 * q^45 + 24 * q^46 + 32 * q^49 - 8 * q^50 - 4 * q^52 + 40 * q^53 - 4 * q^56 - 8 * q^57 + 4 * q^58 - 8 * q^59 + 4 * q^60 + 8 * q^62 - 12 * q^65 + 32 * q^67 - 28 * q^69 + 8 * q^70 - 12 * q^71 + 20 * q^73 + 20 * q^74 - 12 * q^75 - 8 * q^76 + 8 * q^77 - 4 * q^78 + 24 * q^79 + 4 * q^80 + 8 * q^81 + 40 * q^82 + 44 * q^83 + 20 * q^85 - 20 * q^86 + 16 * q^89 - 4 * q^90 - 28 * q^91 - 28 * q^92 - 8 * q^93 - 8 * q^97 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$		−	1.00000i		−	0.500000i
$5$	−2.16830	−	2.16830i	−0.969692	−	0.969692i	0.0298617	−	0.999554i	$-0.490493\pi$
$5$	−2.16830	−	2.16830i	−0.969692	−	0.969692i	−0.999554	+	0.0298617i	$0.990493\pi$
$6$	0.707107	+	0.707107i	0.288675	+	0.288675i
$7$	2.62949	−	0.292893i	0.993854	−	0.110703i
$7$	2.62949	−	0.292893i	0.993854	−	0.110703i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−1.00000			−0.333333
$10$	3.06644			0.969692
$11$	0.516075	+	0.516075i	0.155603	+	0.155603i	0.780615	−	0.625012i	$-0.214906\pi$
$11$	0.516075	+	0.516075i	0.155603	+	0.155603i	−0.625012	+	0.780615i	$0.714906\pi$
$12$	−1.00000			−0.288675
$13$	3.60525	−	0.0469777i	0.999915	−	0.0130293i
$13$	3.60525	−	0.0469777i	0.999915	−	0.0130293i
$14$	−1.65222	+	2.06644i	−0.441575	+	0.552278i
$15$	−2.16830	+	2.16830i	−0.559852	+	0.559852i
$16$	−1.00000			−0.250000
$17$	−2.57461			−0.624434			−0.312217	−	0.950011i	$-0.601072\pi$
$17$	−2.57461			−0.624434			−0.312217	+	0.950011i	$0.601072\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	−3.82052	−	3.82052i	−0.876488	−	0.876488i	0.116682	−	0.993169i	$-0.462774\pi$
$19$	−3.82052	−	3.82052i	−0.876488	−	0.876488i	−0.993169	+	0.116682i	$0.962774\pi$
$20$	−2.16830	+	2.16830i	−0.484846	+	0.484846i
$21$	−0.292893	−	2.62949i	−0.0639145	−	0.573802i
$22$	−0.729840			−0.155603
$23$		−	6.97248i		−	1.45386i	−0.686710	−	0.726931i	$-0.740946\pi$
$23$		−	6.97248i		−	1.45386i	0.686710	−	0.726931i	$-0.259054\pi$
$24$	0.707107	−	0.707107i	0.144338	−	0.144338i
$25$			4.40303i			0.880606i
$26$	−2.51608	+	2.58251i	−0.493443	+	0.506472i
$27$			1.00000i			0.192450i
$28$	−0.292893	−	2.62949i	−0.0553516	−	0.496927i
$29$	−6.32541			−1.17460			−0.587300	−	0.809369i	$-0.699809\pi$
$29$	−6.32541			−1.17460			−0.587300	+	0.809369i	$0.699809\pi$
$30$		−	3.06644i		−	0.559852i
$31$	−4.33660	−	4.33660i	−0.778876	−	0.778876i	0.200764	−	0.979640i	$-0.435658\pi$
$31$	−4.33660	−	4.33660i	−0.778876	−	0.778876i	−0.979640	+	0.200764i	$0.935658\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	0.516075	−	0.516075i	0.0898371	−	0.0898371i
$34$	1.82052	−	1.82052i	0.312217	−	0.312217i
$35$	−6.33660	−	5.06644i	−1.07108	−	0.856384i
$36$			1.00000i			0.166667i
$37$	−3.58251	−	3.58251i	−0.588961	−	0.588961i	0.348389	−	0.937350i	$-0.386729\pi$
$37$	−3.58251	−	3.58251i	−0.588961	−	0.588961i	−0.937350	+	0.348389i	$0.886729\pi$
$38$	5.40303			0.876488
$39$	−0.0469777	−	3.60525i	−0.00752245	−	0.577301i
$40$		−	3.06644i		−	0.484846i
$41$	−0.176204	−	0.176204i	−0.0275185	−	0.0275185i	0.693214	−	0.720732i	$-0.256194\pi$
$41$	−0.176204	−	0.176204i	−0.0275185	−	0.0275185i	−0.720732	+	0.693214i	$0.756194\pi$
$42$	2.06644	+	1.65222i	0.318858	+	0.254944i
$43$			7.89486i			1.20396i	0.798513	+	0.601978i	$0.205620\pi$
$43$			7.89486i			1.20396i	−0.798513	+	0.601978i	$0.794380\pi$
$44$	0.516075	−	0.516075i	0.0778013	−	0.0778013i
$45$	2.16830	+	2.16830i	0.323231	+	0.323231i
$46$	4.93029	+	4.93029i	0.726931	+	0.726931i
$47$	1.41421	−	1.41421i	0.206284	−	0.206284i	−0.596402	−	0.802686i	$-0.703403\pi$
$47$	1.41421	−	1.41421i	0.206284	−	0.206284i	0.802686	+	0.596402i	$0.203403\pi$
$48$			1.00000i			0.144338i
$49$	6.82843	−	1.54032i	0.975490	−	0.220046i
$50$	−3.11341	−	3.11341i	−0.440303	−	0.440303i
$51$			2.57461i			0.360517i
$52$	−0.0469777	−	3.60525i	−0.00651463	−	0.499958i
$53$	−0.514936			−0.0707319			−0.0353660	−	0.999374i	$-0.511260\pi$
$53$	−0.514936			−0.0707319			−0.0353660	+	0.999374i	$0.511260\pi$
$54$	−0.707107	−	0.707107i	−0.0962250	−	0.0962250i
$55$		−	2.23801i		−	0.301773i
$56$	2.06644	+	1.65222i	0.276139	+	0.220788i
$57$	−3.82052	+	3.82052i	−0.506040	+	0.506040i
$58$	4.47274	−	4.47274i	0.587300	−	0.587300i
$59$	−3.17834	+	3.17834i	−0.413785	+	0.413785i	−0.883055	−	0.469270i	$-0.844517\pi$
$59$	−3.17834	+	3.17834i	−0.413785	+	0.413785i	0.469270	+	0.883055i	$0.344517\pi$
$60$	2.16830	+	2.16830i	0.279926	+	0.279926i
$61$			6.41208i			0.820982i	0.911865	+	0.410491i	$0.134643\pi$
$61$			6.41208i			0.820982i	−0.911865	+	0.410491i	$0.865357\pi$
$62$	6.13287			0.778876
$63$	−2.62949	+	0.292893i	−0.331285	+	0.0369011i
$64$			1.00000i			0.125000i
$65$	−7.91911	−	7.71538i	−0.982244	−	0.956976i
$66$			0.729840i			0.0898371i
$67$	−3.96130	+	3.96130i	−0.483950	+	0.483950i	−0.906391	−	0.422441i	$-0.861173\pi$
$67$	−3.96130	+	3.96130i	−0.483950	+	0.483950i	0.422441	+	0.906391i	$0.361173\pi$
$68$			2.57461i			0.312217i
$69$	−6.97248			−0.839388
$70$	8.06316	−	0.898138i	0.963732	−	0.107348i
$71$	8.12169	−	8.12169i	0.963867	−	0.963867i	−0.0355021	−	0.999370i	$-0.511303\pi$
$71$	8.12169	−	8.12169i	0.963867	−	0.963867i	0.999370	+	0.0355021i	$0.0113031\pi$
$72$	−0.707107	−	0.707107i	−0.0833333	−	0.0833333i
$73$	11.6056	−	11.6056i	1.35833	−	1.35833i	0.482364	−	0.875971i	$-0.339778\pi$
$73$	11.6056	−	11.6056i	1.35833	−	1.35833i	0.875971	−	0.482364i	$-0.160222\pi$
$74$	5.06644			0.588961
$75$	4.40303			0.508418
$76$	−3.82052	+	3.82052i	−0.438244	+	0.438244i
$77$	1.50817	+	1.20586i	0.171872	+	0.137420i
$78$	2.58251	+	2.51608i	0.292412	+	0.284889i
$79$	10.9455			1.23146			0.615732	−	0.787956i	$-0.288860\pi$
$79$	10.9455			1.23146			0.615732	+	0.787956i	$0.288860\pi$
$80$	2.16830	+	2.16830i	0.242423	+	0.242423i
$81$	1.00000			0.111111
$82$	0.249190			0.0275185
$83$	1.01118	+	1.01118i	0.110992	+	0.110992i	0.760421	−	0.649430i	$-0.224992\pi$
$83$	1.01118	+	1.01118i	0.110992	+	0.110992i	−0.649430	+	0.760421i	$0.724992\pi$
$84$	−2.62949	+	0.292893i	−0.286901	+	0.0319573i
$85$	5.58251	+	5.58251i	0.605508	+	0.605508i
$86$	−5.58251	−	5.58251i	−0.601978	−	0.601978i
$87$			6.32541i			0.678156i
$88$			0.729840i			0.0778013i
$89$	1.10977	−	1.10977i	0.117635	−	0.117635i	−0.645839	−	0.763474i	$-0.723492\pi$
$89$	1.10977	−	1.10977i	0.117635	−	0.117635i	0.763474	+	0.645839i	$0.223492\pi$
$90$	−3.06644			−0.323231
$91$	9.46619	−	1.17948i	0.992327	−	0.123643i
$92$	−6.97248			−0.726931
$93$	−4.33660	+	4.33660i	−0.449684	+	0.449684i
$94$			2.00000i			0.206284i
$95$			16.5681i			1.69985i
$96$	−0.707107	−	0.707107i	−0.0721688	−	0.0721688i
$97$	−9.34336	−	9.34336i	−0.948675	−	0.948675i	0.0500709	−	0.998746i	$-0.484055\pi$
$97$	−9.34336	−	9.34336i	−0.948675	−	0.948675i	−0.998746	+	0.0500709i	$0.984055\pi$
$98$	−3.73926	+	5.91760i	−0.377722	+	0.597768i
$99$	−0.516075	−	0.516075i	−0.0518675	−	0.0518675i
$100$	4.40303			0.440303
$101$	−5.86058			−0.583149			−0.291575	−	0.956548i	$-0.594179\pi$
$101$	−5.86058			−0.583149			−0.291575	+	0.956548i	$0.594179\pi$
$102$	−1.82052	−	1.82052i	−0.180258	−	0.180258i
$103$	−9.16965			−0.903513			−0.451756	−	0.892141i	$-0.649202\pi$
$103$	−9.16965			−0.903513			−0.451756	+	0.892141i	$0.649202\pi$
$104$	2.58251	+	2.51608i	0.253236	+	0.246721i
$105$	−5.06644	+	6.33660i	−0.494434	+	0.618388i
$106$	0.364115	−	0.364115i	0.0353660	−	0.0353660i
$107$	7.91334			0.765011			0.382506	−	0.923953i	$-0.375061\pi$
$107$	7.91334			0.765011			0.382506	+	0.923953i	$0.375061\pi$
$108$	1.00000			0.0962250
$109$	9.90330	−	9.90330i	0.948564	−	0.948564i	−0.0501767	−	0.998740i	$-0.515978\pi$
$109$	9.90330	−	9.90330i	0.948564	−	0.948564i	0.998740	+	0.0501767i	$0.0159785\pi$
$110$	1.58251	+	1.58251i	0.150887	+	0.150887i
$111$	−3.58251	+	3.58251i	−0.340037	+	0.340037i
$112$	−2.62949	+	0.292893i	−0.248463	+	0.0276758i
$113$	11.9450			1.12369			0.561844	−	0.827243i	$-0.310092\pi$
$113$	11.9450			1.12369			0.561844	+	0.827243i	$0.310092\pi$
$114$		−	5.40303i		−	0.506040i
$115$	−15.1184	+	15.1184i	−1.40980	+	1.40980i
$116$			6.32541i			0.587300i
$117$	−3.60525	+	0.0469777i	−0.333305	+	0.00434309i
$118$		−	4.49485i		−	0.413785i
$119$	−6.76990	+	0.754084i	−0.620595	+	0.0691268i
$120$	−3.06644			−0.279926
$121$		−	10.4673i		−	0.951576i
$122$	−4.53402	−	4.53402i	−0.410491	−	0.410491i
$123$	−0.176204	+	0.176204i	−0.0158878	+	0.0158878i
$124$	−4.33660	+	4.33660i	−0.389438	+	0.389438i
$125$	−1.29440	+	1.29440i	−0.115775	+	0.115775i
$126$	1.65222	−	2.06644i	0.147192	−	0.184093i
$127$			19.2112i			1.70472i	0.522954	+	0.852361i	$0.324830\pi$
$127$			19.2112i			1.70472i	−0.522954	+	0.852361i	$0.675170\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	7.89486			0.695104
$130$	11.0553	−	0.144054i	0.969610	−	0.0126344i
$131$			9.83056i			0.858900i	0.903091	+	0.429450i	$0.141293\pi$
$131$			9.83056i			0.858900i	−0.903091	+	0.429450i	$0.858707\pi$
$132$	−0.516075	−	0.516075i	−0.0449186	−	0.0449186i
$133$	−11.1650	−	8.92701i	−0.968130	−	0.774070i
$134$		−	5.60212i		−	0.483950i
$135$	2.16830	−	2.16830i	0.186617	−	0.186617i
$136$	−1.82052	−	1.82052i	−0.156108	−	0.156108i
$137$	3.88019	+	3.88019i	0.331507	+	0.331507i	0.853159	−	0.521652i	$-0.174684\pi$
$137$	3.88019	+	3.88019i	0.331507	+	0.331507i	−0.521652	+	0.853159i	$0.674684\pi$
$138$	4.93029	−	4.93029i	0.419694	−	0.419694i
$139$		−	3.32681i		−	0.282176i	−0.989997	−	0.141088i	$-0.954940\pi$
$139$		−	3.32681i		−	0.282176i	0.989997	−	0.141088i	$-0.0450601\pi$
$140$	−5.06644	+	6.33660i	−0.428192	+	0.535540i
$141$	−1.41421	−	1.41421i	−0.119098	−	0.119098i
$142$			11.4858i			0.963867i
$143$	1.88482	+	1.83633i	0.157617	+	0.153562i
$144$	1.00000			0.0833333
$145$	13.7154	+	13.7154i	1.13900	+	1.13900i
$146$			16.4128i			1.35833i
$147$	−1.54032	−	6.82843i	−0.127043	−	0.563199i
$148$	−3.58251	+	3.58251i	−0.294481	+	0.294481i
$149$	8.02774	−	8.02774i	0.657658	−	0.657658i	−0.297168	−	0.954825i	$-0.596042\pi$
$149$	8.02774	−	8.02774i	0.657658	−	0.657658i	0.954825	+	0.297168i	$0.0960420\pi$
$150$	−3.11341	+	3.11341i	−0.254209	+	0.254209i
$151$	13.5417	+	13.5417i	1.10201	+	1.10201i	0.994169	+	0.107837i	$0.0343926\pi$
$151$	13.5417	+	13.5417i	1.10201	+	1.10201i	0.107837	+	0.994169i	$0.465607\pi$
$152$		−	5.40303i		−	0.438244i
$153$	2.57461			0.208145
$154$	−1.91911	+	0.213765i	−0.154646	+	0.0172257i
$155$			18.8061i			1.51054i
$156$	−3.60525	+	0.0469777i	−0.288651	+	0.00376122i
$157$			3.14458i			0.250965i	0.992096	+	0.125482i	$0.0400479\pi$
$157$			3.14458i			0.250965i	−0.992096	+	0.125482i	$0.959952\pi$
$158$	−7.73963	+	7.73963i	−0.615732	+	0.615732i
$159$			0.514936i			0.0408371i
$160$	−3.06644			−0.242423
$161$	−2.04219	−	18.3341i	−0.160947	−	1.44493i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	−15.2816	−	15.2816i	−1.19694	−	1.19694i	−0.975077	−	0.221867i	$-0.928785\pi$
$163$	−15.2816	−	15.2816i	−1.19694	−	1.19694i	−0.221867	−	0.975077i	$-0.571215\pi$
$164$	−0.176204	+	0.176204i	−0.0137592	+	0.0137592i
$165$	−2.23801			−0.174229
$166$	−1.43003			−0.110992
$167$	−9.21892	+	9.21892i	−0.713382	+	0.713382i	−0.967241	−	0.253860i	$-0.918300\pi$
$167$	−9.21892	+	9.21892i	−0.713382	+	0.713382i	0.253860	+	0.967241i	$0.418300\pi$
$168$	1.65222	−	2.06644i	0.127472	−	0.159429i
$169$	12.9956	−	0.338732i	0.999660	−	0.0260563i
$170$	−7.89486			−0.605508
$171$	3.82052	+	3.82052i	0.292163	+	0.292163i
$172$	7.89486			0.601978
$173$	17.4793			1.32892			0.664462	−	0.747322i	$-0.268661\pi$
$173$	17.4793			1.32892			0.664462	+	0.747322i	$0.268661\pi$
$174$	−4.47274	−	4.47274i	−0.339078	−	0.339078i
$175$	1.28962	+	11.5777i	0.0974860	+	0.875194i
$176$	−0.516075	−	0.516075i	−0.0389006	−	0.0389006i
$177$	3.17834	+	3.17834i	0.238899	+	0.238899i
$178$			1.56945i			0.117635i
$179$			18.3235i			1.36956i	0.728749	+	0.684781i	$0.240102\pi$
$179$			18.3235i			1.36956i	−0.728749	+	0.684781i	$0.759898\pi$
$180$	2.16830	−	2.16830i	0.161615	−	0.161615i
$181$	4.96432			0.368995			0.184498	−	0.982833i	$-0.440934\pi$
$181$	4.96432			0.368995			0.184498	+	0.982833i	$0.440934\pi$
$182$	−5.85959	+	7.52763i	−0.434342	+	0.557985i
$183$	6.41208			0.473994
$184$	4.93029	−	4.93029i	0.363466	−	0.363466i
$185$			15.5359i			1.14222i
$186$		−	6.13287i		−	0.449684i
$187$	−1.32869	−	1.32869i	−0.0971634	−	0.0971634i
$188$	−1.41421	−	1.41421i	−0.103142	−	0.103142i
$189$	0.292893	+	2.62949i	0.0213048	+	0.191267i
$190$	−11.7154	−	11.7154i	−0.849923	−	0.849923i
$191$	10.5427			0.762841			0.381421	−	0.924402i	$-0.375435\pi$
$191$	10.5427			0.762841			0.381421	+	0.924402i	$0.375435\pi$
$192$	1.00000			0.0721688
$193$	−13.6366	−	13.6366i	−0.981586	−	0.981586i	0.0182475	−	0.999833i	$-0.494191\pi$
$193$	−13.6366	−	13.6366i	−0.981586	−	0.981586i	−0.999833	+	0.0182475i	$0.994191\pi$
$194$	13.2135			0.948675
$195$	−7.71538	+	7.91911i	−0.552510	+	0.567099i
$196$	−1.54032	−	6.82843i	−0.110023	−	0.487745i
$197$	13.4673	−	13.4673i	0.959508	−	0.959508i	−0.0397038	−	0.999211i	$-0.512641\pi$
$197$	13.4673	−	13.4673i	0.959508	−	0.959508i	0.999211	+	0.0397038i	$0.0126414\pi$
$198$	0.729840			0.0518675
$199$	5.92452			0.419978			0.209989	−	0.977704i	$-0.432657\pi$
$199$	5.92452			0.419978			0.209989	+	0.977704i	$0.432657\pi$
$200$	−3.11341	+	3.11341i	−0.220152	+	0.220152i
$201$	3.96130	+	3.96130i	0.279409	+	0.279409i
$202$	4.14405	−	4.14405i	0.291575	−	0.291575i
$203$	−16.6326	+	1.85267i	−1.16738	+	0.130032i
$204$	2.57461			0.180258
$205$			0.764127i			0.0533689i
$206$	6.48392	−	6.48392i	0.451756	−	0.451756i
$207$			6.97248i			0.484621i
$208$	−3.60525	+	0.0469777i	−0.249979	+	0.00325731i
$209$		−	3.94335i		−	0.272767i
$210$	−0.898138	−	8.06316i	−0.0619774	−	0.556411i
$211$	−7.04407			−0.484934			−0.242467	−	0.970160i	$-0.577957\pi$
$211$	−7.04407			−0.484934			−0.242467	+	0.970160i	$0.577957\pi$
$212$			0.514936i			0.0353660i
$213$	−8.12169	−	8.12169i	−0.556489	−	0.556489i
$214$	−5.59557	+	5.59557i	−0.382506	+	0.382506i
$215$	17.1184	−	17.1184i	1.16747	−	1.16747i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	−12.6732	−	10.1329i	−0.860312	−	0.687864i
$218$			14.0054i			0.948564i
$219$	−11.6056	−	11.6056i	−0.784235	−	0.784235i
$220$	−2.23801			−0.150887
$221$	−9.28208	+	0.120949i	−0.624381	+	0.00813591i
$222$		−	5.06644i		−	0.340037i
$223$	9.71425	+	9.71425i	0.650514	+	0.650514i	0.953117	−	0.302603i	$-0.0978555\pi$
$223$	9.71425	+	9.71425i	0.650514	+	0.650514i	−0.302603	+	0.953117i	$0.597856\pi$
$224$	1.65222	−	2.06644i	0.110394	−	0.138070i
$225$		−	4.40303i		−	0.293535i
$226$	−8.44636	+	8.44636i	−0.561844	+	0.561844i
$227$	−13.9000	−	13.9000i	−0.922577	−	0.922577i	0.0746342	−	0.997211i	$-0.476221\pi$
$227$	−13.9000	−	13.9000i	−0.922577	−	0.922577i	−0.997211	+	0.0746342i	$0.976221\pi$
$228$	3.82052	+	3.82052i	0.253020	+	0.253020i
$229$	−5.97035	+	5.97035i	−0.394532	+	0.394532i	−0.876299	−	0.481768i	$-0.839995\pi$
$229$	−5.97035	+	5.97035i	−0.394532	+	0.394532i	0.481768	+	0.876299i	$0.339995\pi$
$230$		−	21.3807i		−	1.40980i
$231$	1.20586	−	1.50817i	0.0793397	−	0.0992302i
$232$	−4.47274	−	4.47274i	−0.293650	−	0.293650i
$233$		−	1.35293i		−	0.0886336i	−0.999018	−	0.0443168i	$-0.985889\pi$
$233$		−	1.35293i		−	0.0886336i	0.999018	−	0.0443168i	$-0.0141111\pi$
$234$	2.51608	−	2.58251i	0.164481	−	0.168824i
$235$	−6.13287			−0.400065
$236$	3.17834	+	3.17834i	0.206892	+	0.206892i
$237$		−	10.9455i		−	0.710986i
$238$	4.25382	−	5.32026i	0.275734	−	0.344861i
$239$	20.8904	−	20.8904i	1.35129	−	1.35129i	0.467071	−	0.884220i	$-0.345309\pi$
$239$	20.8904	−	20.8904i	1.35129	−	1.35129i	0.884220	−	0.467071i	$-0.154691\pi$
$240$	2.16830	−	2.16830i	0.139963	−	0.139963i
$241$	11.1816	−	11.1816i	0.720269	−	0.720269i	−0.248391	−	0.968660i	$-0.579902\pi$
$241$	11.1816	−	11.1816i	0.720269	−	0.720269i	0.968660	+	0.248391i	$0.0799018\pi$
$242$	7.40152	+	7.40152i	0.475788	+	0.475788i
$243$		−	1.00000i		−	0.0641500i
$244$	6.41208			0.410491
$245$	−18.1459	−	11.4662i	−1.15930	−	0.732548i
$246$		−	0.249190i		−	0.0158878i
$247$	−13.9534	−	13.5944i	−0.887833	−	0.864993i
$248$		−	6.13287i		−	0.389438i
$249$	1.01118	−	1.01118i	0.0640810	−	0.0640810i
$250$		−	1.83056i		−	0.115775i
$251$	20.6366			1.30257			0.651286	−	0.758832i	$-0.274230\pi$
$251$	20.6366			1.30257			0.651286	+	0.758832i	$0.274230\pi$
$252$	0.292893	+	2.62949i	0.0184505	+	0.165642i
$253$	3.59832	−	3.59832i	0.226225	−	0.226225i
$254$	−13.5844	−	13.5844i	−0.852361	−	0.852361i
$255$	5.58251	−	5.58251i	0.349590	−	0.349590i
$256$	1.00000			0.0625000
$257$	−9.21351			−0.574723			−0.287362	−	0.957822i	$-0.592778\pi$
$257$	−9.21351			−0.574723			−0.287362	+	0.957822i	$0.592778\pi$
$258$	−5.58251	+	5.58251i	−0.347552	+	0.347552i
$259$	−10.4695	−	8.37088i	−0.650541	−	0.520141i
$260$	−7.71538	+	7.91911i	−0.478488	+	0.491122i
$261$	6.32541			0.391533
$262$	−6.95126	−	6.95126i	−0.429450	−	0.429450i
$263$	9.50464			0.586081			0.293041	−	0.956100i	$-0.405333\pi$
$263$	9.50464			0.586081			0.293041	+	0.956100i	$0.405333\pi$
$264$	0.729840			0.0449186
$265$	1.11654	+	1.11654i	0.0685882	+	0.0685882i
$266$	14.2072	−	1.58251i	0.871100	−	0.0970300i
$267$	−1.10977	−	1.10977i	−0.0679167	−	0.0679167i
$268$	3.96130	+	3.96130i	0.241975	+	0.241975i
$269$		−	15.7423i		−	0.959824i	−0.877317	−	0.479912i	$-0.840669\pi$
$269$		−	15.7423i		−	0.959824i	0.877317	−	0.479912i	$-0.159331\pi$
$270$			3.06644i			0.186617i
$271$	−17.4746	+	17.4746i	−1.06151	+	1.06151i	−0.0635278	+	0.997980i	$0.520235\pi$
$271$	−17.4746	+	17.4746i	−1.06151	+	1.06151i	−0.997980	+	0.0635278i	$0.979765\pi$
$272$	2.57461			0.156108
$273$	−1.17948	−	9.46619i	−0.0713853	−	0.572920i
$274$	−5.48742			−0.331507
$275$	−2.27230	+	2.27230i	−0.137025	+	0.137025i
$276$			6.97248i			0.419694i
$277$			21.3991i			1.28575i	0.765971	+	0.642875i	$0.222259\pi$
$277$			21.3991i			1.28575i	−0.765971	+	0.642875i	$0.777741\pi$
$278$	2.35241	+	2.35241i	0.141088	+	0.141088i
$279$	4.33660	+	4.33660i	0.259625	+	0.259625i
$280$	−0.898138	−	8.06316i	−0.0536740	−	0.481866i
$281$	0.634274	+	0.634274i	0.0378376	+	0.0378376i	0.725772	−	0.687935i	$-0.241483\pi$
$281$	0.634274	+	0.634274i	0.0378376	+	0.0378376i	−0.687935	+	0.725772i	$0.741483\pi$
$282$	2.00000			0.119098
$283$	−11.6503			−0.692539			−0.346269	−	0.938135i	$-0.612552\pi$
$283$	−11.6503			−0.692539			−0.346269	+	0.938135i	$0.612552\pi$
$284$	−8.12169	−	8.12169i	−0.481934	−	0.481934i
$285$	16.5681			0.981407
$286$	−2.63125	+	0.0342862i	−0.155589	+	0.00202739i
$287$	−0.514936	−	0.411718i	−0.0303957	−	0.0243030i
$288$	−0.707107	+	0.707107i	−0.0416667	+	0.0416667i
$289$	−10.3714			−0.610083
$290$	−19.3965			−1.13900
$291$	−9.34336	+	9.34336i	−0.547718	+	0.547718i
$292$	−11.6056	−	11.6056i	−0.679167	−	0.679167i
$293$	16.3755	−	16.3755i	0.956668	−	0.956668i	−0.0424317	−	0.999099i	$-0.513510\pi$
$293$	16.3755	−	16.3755i	0.956668	−	0.956668i	0.999099	+	0.0424317i	$0.0135105\pi$
$294$	5.91760	+	3.73926i	0.345121	+	0.218078i
$295$	13.7832			0.802488
$296$		−	5.06644i		−	0.294481i
$297$	−0.516075	+	0.516075i	−0.0299457	+	0.0299457i
$298$			11.3529i			0.657658i
$299$	−0.327551	−	25.1375i	−0.0189428	−	1.45374i
$300$		−	4.40303i		−	0.254209i
$301$	2.31235	+	20.7595i	0.133282	+	1.19656i
$302$	−19.1508			−1.10201
$303$			5.86058i			0.336681i
$304$	3.82052	+	3.82052i	0.219122	+	0.219122i
$305$	13.9033	−	13.9033i	0.796100	−	0.796100i
$306$	−1.82052	+	1.82052i	−0.104072	+	0.104072i
$307$	14.8704	−	14.8704i	0.848697	−	0.848697i	−0.141274	−	0.989971i	$-0.545120\pi$
$307$	14.8704	−	14.8704i	0.848697	−	0.848697i	0.989971	+	0.141274i	$0.0451198\pi$
$308$	1.20586	−	1.50817i	0.0687102	−	0.0859359i
$309$			9.16965i			0.521643i
$310$	−13.2979	−	13.2979i	−0.755270	−	0.755270i
$311$	26.0489			1.47710			0.738549	−	0.674199i	$-0.235511\pi$
$311$	26.0489			1.47710			0.738549	+	0.674199i	$0.235511\pi$
$312$	2.51608	−	2.58251i	0.142445	−	0.146206i
$313$			13.1007i			0.740497i	0.928933	+	0.370248i	$0.120727\pi$
$313$			13.1007i			0.740497i	−0.928933	+	0.370248i	$0.879273\pi$
$314$	−2.22355	−	2.22355i	−0.125482	−	0.125482i
$315$	6.33660	+	5.06644i	0.357027	+	0.285461i
$316$		−	10.9455i		−	0.615732i
$317$	−15.6157	+	15.6157i	−0.877063	+	0.877063i	−0.993230	−	0.116167i	$-0.962939\pi$
$317$	−15.6157	+	15.6157i	−0.877063	+	0.877063i	0.116167	+	0.993230i	$0.462939\pi$
$318$	−0.364115	−	0.364115i	−0.0204185	−	0.0204185i
$319$	−3.26439	−	3.26439i	−0.182771	−	0.182771i
$320$	2.16830	−	2.16830i	0.121212	−	0.121212i
$321$		−	7.91334i		−	0.441679i
$322$	14.4082	+	11.5201i	0.802937	+	0.641990i
$323$	9.83633	+	9.83633i	0.547308	+	0.547308i
$324$		−	1.00000i		−	0.0555556i
$325$	0.206844	+	15.8740i	0.0114736	+	0.880532i
$326$	21.6114			1.19694
$327$	−9.90330	−	9.90330i	−0.547653	−	0.547653i
$328$		−	0.249190i		−	0.0137592i
$329$	3.30445	−	4.13287i	0.182180	−	0.227853i
$330$	1.58251	−	1.58251i	0.0871144	−	0.0871144i
$331$	−6.01634	+	6.01634i	−0.330688	+	0.330688i	−0.852848	−	0.522160i	$-0.825126\pi$
$331$	−6.01634	+	6.01634i	−0.330688	+	0.330688i	0.522160	+	0.852848i	$0.325126\pi$
$332$	1.01118	−	1.01118i	0.0554958	−	0.0554958i
$333$	3.58251	+	3.58251i	0.196320	+	0.196320i
$334$		−	13.0375i		−	0.713382i
$335$	17.1786			0.938565
$336$	0.292893	+	2.62949i	0.0159786	+	0.143450i
$337$		−	1.23748i		−	0.0674101i	−0.999432	−	0.0337050i	$-0.989269\pi$
$337$		−	1.23748i		−	0.0674101i	0.999432	−	0.0337050i	$-0.0107307\pi$
$338$	−8.94975	+	9.42879i	−0.486802	+	0.512858i
$339$		−	11.9450i		−	0.648761i
$340$	5.58251	−	5.58251i	0.302754	−	0.302754i
$341$		−	4.47602i		−	0.242390i
$342$	−5.40303			−0.292163
$343$	17.5041	−	6.05025i	0.945134	−	0.326683i
$344$	−5.58251	+	5.58251i	−0.300989	+	0.300989i
$345$	15.1184	+	15.1184i	0.813948	+	0.813948i
$346$	−12.3597	+	12.3597i	−0.664462	+	0.664462i
$347$	−12.1613			−0.652852			−0.326426	−	0.945223i	$-0.605844\pi$
$347$	−12.1613			−0.652852			−0.326426	+	0.945223i	$0.605844\pi$
$348$	6.32541			0.339078
$349$	17.9622	−	17.9622i	0.961494	−	0.961494i	−0.0377919	−	0.999286i	$-0.512032\pi$
$349$	17.9622	−	17.9622i	0.961494	−	0.961494i	0.999286	+	0.0377919i	$0.0120324\pi$
$350$	−9.09859	−	7.27479i	−0.486340	−	0.388854i
$351$	0.0469777	+	3.60525i	0.00250748	+	0.192434i
$352$	0.729840			0.0389006
$353$	21.2045	+	21.2045i	1.12860	+	1.12860i	0.990405	+	0.138195i	$0.0441300\pi$
$353$	21.2045	+	21.2045i	1.12860	+	1.12860i	0.138195	+	0.990405i	$0.455870\pi$
$354$	−4.49485			−0.238899
$355$	−35.2205			−1.86931
$356$	−1.10977	−	1.10977i	−0.0588176	−	0.0588176i
$357$	0.754084	+	6.76990i	0.0399104	+	0.358301i
$358$	−12.9567	−	12.9567i	−0.684781	−	0.684781i
$359$	20.4359	+	20.4359i	1.07857	+	1.07857i	0.996638	+	0.0819287i	$0.0261080\pi$
$359$	20.4359	+	20.4359i	1.07857	+	1.07857i	0.0819287	+	0.996638i	$0.473892\pi$
$360$			3.06644i			0.161615i
$361$			10.1928i			0.536461i
$362$	−3.51030	+	3.51030i	−0.184498	+	0.184498i
$363$	−10.4673			−0.549392
$364$	−1.17948	−	9.46619i	−0.0618215	−	0.496163i
$365$	−50.3289			−2.63433
$366$	−4.53402	+	4.53402i	−0.236997	+	0.236997i
$367$			1.09998i			0.0574185i	0.999588	+	0.0287092i	$0.00913969\pi$
$367$			1.09998i			0.0574185i	−0.999588	+	0.0287092i	$0.990860\pi$
$368$			6.97248i			0.363466i
$369$	0.176204	+	0.176204i	0.00917283	+	0.00917283i
$370$	−10.9855	−	10.9855i	−0.571111	−	0.571111i
$371$	−1.35402	+	0.150821i	−0.0702972	+	0.00783025i
$372$	4.33660	+	4.33660i	0.224842	+	0.224842i
$373$	20.6382			1.06861			0.534304	−	0.845293i	$-0.320574\pi$
$373$	20.6382			1.06861			0.534304	+	0.845293i	$0.320574\pi$
$374$	1.87905			0.0971634
$375$	1.29440	+	1.29440i	0.0668427	+	0.0668427i
$376$	2.00000			0.103142
$377$	−22.8047	+	0.297153i	−1.17450	+	0.0153042i
$378$	−2.06644	−	1.65222i	−0.106286	−	0.0849812i
$379$	−5.82027	+	5.82027i	−0.298967	+	0.298967i	−0.840609	−	0.541642i	$-0.817803\pi$
$379$	−5.82027	+	5.82027i	−0.298967	+	0.298967i	0.541642	+	0.840609i	$0.317803\pi$
$380$	16.5681			0.849923
$381$	19.2112			0.984221
$382$	−7.45480	+	7.45480i	−0.381421	+	0.381421i
$383$	−9.25710	−	9.25710i	−0.473016	−	0.473016i	0.429874	−	0.902889i	$-0.358558\pi$
$383$	−9.25710	−	9.25710i	−0.473016	−	0.473016i	−0.902889	+	0.429874i	$0.858558\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	−0.655498	−	5.88482i	−0.0334073	−	0.299918i
$386$	19.2851			0.981586
$387$		−	7.89486i		−	0.401318i
$388$	−9.34336	+	9.34336i	−0.474337	+	0.474337i
$389$		−	33.6641i		−	1.70684i	−0.521224	−	0.853420i	$-0.674524\pi$
$389$		−	33.6641i		−	1.70684i	0.521224	−	0.853420i	$-0.325476\pi$
$390$	−0.144054	−	11.0553i	−0.00729446	−	0.559805i
$391$			17.9514i			0.907841i
$392$	5.91760	+	3.73926i	0.298884	+	0.188861i
$393$	9.83056			0.495886
$394$			19.0457i			0.959508i
$395$	−23.7331	−	23.7331i	−1.19414	−	1.19414i
$396$	−0.516075	+	0.516075i	−0.0259338	+	0.0259338i
$397$	−24.1629	+	24.1629i	−1.21270	+	1.21270i	−0.242566	+	0.970135i	$0.577989\pi$
$397$	−24.1629	+	24.1629i	−1.21270	+	1.21270i	−0.970135	+	0.242566i	$0.922011\pi$
$398$	−4.18927	+	4.18927i	−0.209989	+	0.209989i
$399$	−8.92701	+	11.1650i	−0.446910	+	0.558950i
$400$		−	4.40303i		−	0.220152i
$401$	−8.28885	−	8.28885i	−0.413925	−	0.413925i	0.469178	−	0.883104i	$-0.344550\pi$
$401$	−8.28885	−	8.28885i	−0.413925	−	0.413925i	−0.883104	+	0.469178i	$0.844550\pi$
$402$	−5.60212			−0.279409
$403$	−15.8382	−	15.4308i	−0.788958	−	0.768661i
$404$			5.86058i			0.291575i
$405$	−2.16830	−	2.16830i	−0.107744	−	0.107744i
$406$	10.4510	−	13.0711i	0.518674	−	0.648706i
$407$		−	3.69769i		−	0.183288i
$408$	−1.82052	+	1.82052i	−0.0901292	+	0.0901292i
$409$	7.74077	+	7.74077i	0.382756	+	0.382756i	0.872094	−	0.489338i	$-0.162762\pi$
$409$	7.74077	+	7.74077i	0.382756	+	0.382756i	−0.489338	+	0.872094i	$0.662762\pi$
$410$	−0.540319	−	0.540319i	−0.0266845	−	0.0266845i
$411$	3.88019	−	3.88019i	0.191396	−	0.191396i
$412$			9.16965i			0.451756i
$413$	−7.42650	+	9.28833i	−0.365434	+	0.457049i
$414$	−4.93029	−	4.93029i	−0.242310	−	0.242310i
$415$		−	4.38508i		−	0.215255i
$416$	2.51608	−	2.58251i	0.123361	−	0.126618i
$417$	−3.32681			−0.162914
$418$	2.78837	+	2.78837i	0.136384	+	0.136384i
$419$			37.2548i			1.82002i	0.414592	+	0.910008i	$0.363924\pi$
$419$			37.2548i			1.82002i	−0.414592	+	0.910008i	$0.636076\pi$
$420$	6.33660	+	5.06644i	0.309194	+	0.247217i
$421$	26.1725	−	26.1725i	1.27557	−	1.27557i	0.332451	−	0.943121i	$-0.392125\pi$
$421$	26.1725	−	26.1725i	1.27557	−	1.27557i	0.943121	−	0.332451i	$-0.107875\pi$
$422$	4.98091	−	4.98091i	0.242467	−	0.242467i
$423$	−1.41421	+	1.41421i	−0.0687614	+	0.0687614i
$424$	−0.364115	−	0.364115i	−0.0176830	−	0.0176830i
$425$		−	11.3361i		−	0.549880i
$426$	11.4858			0.556489
$427$	1.87805	+	16.8605i	0.0908854	+	0.815936i
$428$		−	7.91334i		−	0.382506i
$429$	1.83633	−	1.88482i	0.0886590	−	0.0910000i
$430$			24.2091i			1.16747i
$431$	2.05151	−	2.05151i	0.0988177	−	0.0988177i	−0.655970	−	0.754787i	$-0.727740\pi$
$431$	2.05151	−	2.05151i	0.0988177	−	0.0988177i	0.754787	+	0.655970i	$0.227740\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	−15.7613			−0.757441			−0.378720	−	0.925511i	$-0.623636\pi$
$433$	−15.7613			−0.757441			−0.378720	+	0.925511i	$0.623636\pi$
$434$	16.1263	−	1.79628i	0.774088	−	0.0862240i
$435$	13.7154	−	13.7154i	0.657602	−	0.657602i
$436$	−9.90330	−	9.90330i	−0.474282	−	0.474282i
$437$	−26.6385	+	26.6385i	−1.27429	+	1.27429i
$438$	16.4128			0.784235
$439$	−10.8489			−0.517788			−0.258894	−	0.965906i	$-0.583358\pi$
$439$	−10.8489			−0.517788			−0.258894	+	0.965906i	$0.583358\pi$
$440$	1.58251	−	1.58251i	0.0754433	−	0.0754433i
$441$	−6.82843	+	1.54032i	−0.325163	+	0.0733485i
$442$	6.47790	−	6.64895i	0.308122	−	0.316258i
$443$	−9.19115			−0.436685			−0.218342	−	0.975872i	$-0.570065\pi$
$443$	−9.19115			−0.436685			−0.218342	+	0.975872i	$0.570065\pi$
$444$	3.58251	+	3.58251i	0.170018	+	0.170018i
$445$	−4.81261			−0.228140
$446$	−13.7380			−0.650514
$447$	−8.02774	−	8.02774i	−0.379699	−	0.379699i
$448$	0.292893	+	2.62949i	0.0138379	+	0.124232i
$449$	15.6122	+	15.6122i	0.736784	+	0.736784i	0.971954	−	0.235170i	$-0.0755648\pi$
$449$	15.6122	+	15.6122i	0.736784	+	0.736784i	−0.235170	+	0.971954i	$0.575565\pi$
$450$	3.11341	+	3.11341i	0.146768	+	0.146768i
$451$		−	0.181869i		−	0.00856389i
$452$		−	11.9450i		−	0.561844i
$453$	13.5417	−	13.5417i	0.636243	−	0.636243i
$454$	19.6576			0.922577
$455$	−23.0830	−	17.9681i	−1.08215	−	0.842356i
$456$	−5.40303			−0.253020
$457$	−26.7396	+	26.7396i	−1.25083	+	1.25083i	−0.295477	+	0.955350i	$0.595479\pi$
$457$	−26.7396	+	26.7396i	−1.25083	+	1.25083i	−0.955350	+	0.295477i	$0.904521\pi$
$458$		−	8.44334i		−	0.394532i
$459$		−	2.57461i		−	0.120172i
$460$	15.1184	+	15.1184i	0.704900	+	0.704900i
$461$	17.1846	+	17.1846i	0.800368	+	0.800368i	0.983153	−	0.182785i	$-0.0585111\pi$
$461$	17.1846	+	17.1846i	0.800368	+	0.800368i	−0.182785	+	0.983153i	$0.558511\pi$
$462$	0.213765	+	1.91911i	0.00994526	+	0.0892850i
$463$	−16.9948	−	16.9948i	−0.789816	−	0.789816i	0.191648	−	0.981464i	$-0.438617\pi$
$463$	−16.9948	−	16.9948i	−0.789816	−	0.789816i	−0.981464	+	0.191648i	$0.938617\pi$
$464$	6.32541			0.293650
$465$	18.8061			0.872110
$466$	0.956669	+	0.956669i	0.0443168	+	0.0443168i
$467$	−7.72653			−0.357541			−0.178771	−	0.983891i	$-0.557212\pi$
$467$	−7.72653			−0.357541			−0.178771	+	0.983891i	$0.557212\pi$
$468$	0.0469777	+	3.60525i	0.00217154	+	0.166653i
$469$	−9.25596	+	11.5764i	−0.427400	+	0.534550i
$470$	4.33660	−	4.33660i	0.200032	−	0.200032i
$471$	3.14458			0.144895
$472$	−4.49485			−0.206892
$473$	−4.07434	+	4.07434i	−0.187338	+	0.187338i
$474$	7.73963	+	7.73963i	0.355493	+	0.355493i
$475$	16.8219	−	16.8219i	0.771841	−	0.771841i
$476$	0.754084	+	6.76990i	0.0345634	+	0.310298i
$477$	0.514936			0.0235773
$478$			29.5436i			1.35129i
$479$	−26.0081	+	26.0081i	−1.18834	+	1.18834i	−0.210816	+	0.977526i	$0.567612\pi$
$479$	−26.0081	+	26.0081i	−1.18834	+	1.18834i	−0.977526	+	0.210816i	$0.932388\pi$
$480$			3.06644i			0.139963i
$481$	−13.0841	−	12.7475i	−0.596585	−	0.581238i
$482$			15.8131i			0.720269i
$483$	−18.3341	+	2.04219i	−0.834229	+	0.0929230i
$484$	−10.4673			−0.475788
$485$			40.5184i			1.83985i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	−12.7641	+	12.7641i	−0.578398	+	0.578398i	−0.934462	−	0.356064i	$-0.884119\pi$
$487$	−12.7641	+	12.7641i	−0.578398	+	0.578398i	0.356064	+	0.934462i	$0.384119\pi$
$488$	−4.53402	+	4.53402i	−0.205246	+	0.205246i
$489$	−15.2816	+	15.2816i	−0.691056	+	0.691056i
$490$	20.9389	−	4.72329i	0.945925	−	0.213377i
$491$			43.7292i			1.97347i	0.162337	+	0.986735i	$0.448097\pi$
$491$			43.7292i			1.97347i	−0.162337	+	0.986735i	$0.551903\pi$
$492$	0.176204	+	0.176204i	0.00794390	+	0.00794390i
$493$	16.2854			0.733460
$494$	19.4793	−	0.253822i	0.876413	−	0.0114200i
$495$			2.23801i			0.100591i
$496$	4.33660	+	4.33660i	0.194719	+	0.194719i
$497$	18.9771	−	23.7347i	0.851240	−	1.06465i
$498$			1.43003i			0.0640810i
$499$	6.31100	−	6.31100i	0.282519	−	0.282519i	−0.551594	−	0.834113i	$-0.685980\pi$
$499$	6.31100	−	6.31100i	0.282519	−	0.282519i	0.834113	+	0.551594i	$0.185980\pi$
$500$	1.29440	+	1.29440i	0.0578875	+	0.0578875i
$501$	9.21892	+	9.21892i	0.411871	+	0.411871i
$502$	−14.5923	+	14.5923i	−0.651286	+	0.651286i
$503$			23.4423i			1.04524i	0.852565	+	0.522620i	$0.175046\pi$
$503$			23.4423i			1.04524i	−0.852565	+	0.522620i	$0.824954\pi$
$504$	−2.06644	−	1.65222i	−0.0920464	−	0.0735959i
$505$	12.7075	+	12.7075i	0.565475	+	0.565475i
$506$			5.08880i			0.226225i
$507$	−0.338732	−	12.9956i	−0.0150436	−	0.577154i
$508$	19.2112			0.852361
$509$	16.5795	+	16.5795i	0.734874	+	0.734874i	0.971581	−	0.236707i	$-0.0760682\pi$
$509$	16.5795	+	16.5795i	0.734874	+	0.734874i	−0.236707	+	0.971581i	$0.576068\pi$
$510$			7.89486i			0.349590i
$511$	27.1176	−	33.9161i	1.19961	−	1.50036i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	3.82052	−	3.82052i	0.168680	−	0.168680i
$514$	6.51494	−	6.51494i	0.287362	−	0.287362i
$515$	19.8825	+	19.8825i	0.876130	+	0.876130i
$516$		−	7.89486i		−	0.347552i
$517$	1.45968			0.0641967
$518$	13.3221	−	1.48392i	0.585341	−	0.0651999i
$519$		−	17.4793i		−	0.767254i
$520$	−0.144054	−	11.0553i	−0.00631719	−	0.484805i
$521$		−	32.3153i		−	1.41576i	−0.706332	−	0.707880i	$-0.749652\pi$
$521$		−	32.3153i		−	1.41576i	0.706332	−	0.707880i	$-0.250348\pi$
$522$	−4.47274	+	4.47274i	−0.195767	+	0.195767i
$523$		−	11.3376i		−	0.495757i	−0.968791	−	0.247878i	$-0.920267\pi$
$523$		−	11.3376i		−	0.495757i	0.968791	−	0.247878i	$-0.0797333\pi$
$524$	9.83056			0.429450
$525$	11.5777	−	1.28962i	0.505293	−	0.0562836i
$526$	−6.72080	+	6.72080i	−0.293041	+	0.293041i
$527$	11.1650	+	11.1650i	0.486356	+	0.486356i
$528$	−0.516075	+	0.516075i	−0.0224593	+	0.0224593i
$529$	−25.6155			−1.11372
$530$	−1.57902			−0.0685882
$531$	3.17834	−	3.17834i	0.137928	−	0.137928i
$532$	−8.92701	+	11.1650i	−0.387035	+	0.484065i
$533$	−0.643537	−	0.626982i	−0.0278747	−	0.0271576i
$534$	1.56945			0.0679167
$535$	−17.1585	−	17.1585i	−0.741825	−	0.741825i
$536$	−5.60212			−0.241975
$537$	18.3235			0.790717
$538$	11.1315	+	11.1315i	0.479912	+	0.479912i
$539$	4.31890	+	2.72906i	0.186028	+	0.117549i
$540$	−2.16830	−	2.16830i	−0.0933087	−	0.0933087i
$541$	17.1266	+	17.1266i	0.736329	+	0.736329i	0.971866	−	0.235536i	$-0.0756847\pi$
$541$	17.1266	+	17.1266i	0.736329	+	0.736329i	−0.235536	+	0.971866i	$0.575685\pi$
$542$		−	24.7129i		−	1.06151i
$543$		−	4.96432i		−	0.213039i
$544$	−1.82052	+	1.82052i	−0.0780542	+	0.0780542i
$545$	−42.9466			−1.83963
$546$	7.52763	+	5.85959i	0.322153	+	0.250767i
$547$	0.145972			0.00624133			0.00312066	−	0.999995i	$-0.499007\pi$
$547$	0.145972			0.00624133			0.00312066	+	0.999995i	$0.499007\pi$
$548$	3.88019	−	3.88019i	0.165754	−	0.165754i
$549$		−	6.41208i		−	0.273661i
$550$		−	3.21351i		−	0.137025i
$551$	24.1664	+	24.1664i	1.02952	+	1.02952i
$552$	−4.93029	−	4.93029i	−0.209847	−	0.209847i
$553$	28.7810	−	3.20586i	1.22389	−	0.136327i
$554$	−15.1315	−	15.1315i	−0.642875	−	0.642875i
$555$	15.5359			0.659462
$556$	−3.32681			−0.141088
$557$	−18.1533	−	18.1533i	−0.769181	−	0.769181i	0.208782	−	0.977962i	$-0.433050\pi$
$557$	−18.1533	−	18.1533i	−0.769181	−	0.769181i	−0.977962	+	0.208782i	$0.933050\pi$
$558$	−6.13287			−0.259625
$559$	0.370882	+	28.4629i	0.0156866	+	1.20385i
$560$	6.33660	+	5.06644i	0.267770	+	0.214096i
$561$	−1.32869	+	1.32869i	−0.0560973	+	0.0560973i
$562$	−0.897000			−0.0378376
$563$	21.4249			0.902951			0.451476	−	0.892283i	$-0.350898\pi$
$563$	21.4249			0.902951			0.451476	+	0.892283i	$0.350898\pi$
$564$	−1.41421	+	1.41421i	−0.0595491	+	0.0595491i
$565$	−25.9002	−	25.9002i	−1.08963	−	1.08963i
$566$	8.23801	−	8.23801i	0.346269	−	0.346269i
$567$	2.62949	−	0.292893i	0.110428	−	0.0123004i
$568$	11.4858			0.481934
$569$		−	26.3627i		−	1.10518i	−0.833452	−	0.552591i	$-0.813639\pi$
$569$		−	26.3627i		−	1.10518i	0.833452	−	0.552591i	$-0.186361\pi$
$570$	−11.7154	+	11.7154i	−0.490703	+	0.490703i
$571$		−	21.5077i		−	0.900068i	−0.893012	−	0.450034i	$-0.851412\pi$
$571$		−	21.5077i		−	0.900068i	0.893012	−	0.450034i	$-0.148588\pi$
$572$	1.83633	−	1.88482i	0.0767810	−	0.0788083i
$573$		−	10.5427i		−	0.440426i
$574$	0.655244	−	0.0729862i	0.0273493	−	0.00304638i
$575$	30.7001			1.28028
$576$		−	1.00000i		−	0.0416667i
$577$	−11.5787	−	11.5787i	−0.482028	−	0.482028i	0.423751	−	0.905779i	$-0.360713\pi$
$577$	−11.5787	−	11.5787i	−0.482028	−	0.482028i	−0.905779	+	0.423751i	$0.860713\pi$
$578$	7.33369	−	7.33369i	0.305041	−	0.305041i
$579$	−13.6366	+	13.6366i	−0.566719	+	0.566719i
$580$	13.7154	−	13.7154i	0.569500	−	0.569500i
$581$	2.95506	+	2.36272i	0.122596	+	0.0980222i
$582$		−	13.2135i		−	0.547718i
$583$	−0.265746	−	0.265746i	−0.0110061	−	0.0110061i
$584$	16.4128			0.679167
$585$	7.91911	+	7.71538i	0.327415	+	0.318992i
$586$			23.1585i			0.956668i
$587$	−27.3890	−	27.3890i	−1.13047	−	1.13047i	−0.990099	−	0.140368i	$-0.955172\pi$
$587$	−27.3890	−	27.3890i	−1.13047	−	1.13047i	−0.140368	−	0.990099i	$-0.544828\pi$
$588$	−6.82843	+	1.54032i	−0.281600	+	0.0635217i
$589$			33.1361i			1.36535i
$590$	−9.74618	+	9.74618i	−0.401244	+	0.401244i
$591$	−13.4673	−	13.4673i	−0.553972	−	0.553972i
$592$	3.58251	+	3.58251i	0.147240	+	0.147240i
$593$	12.3499	−	12.3499i	0.507150	−	0.507150i	−0.406500	−	0.913651i	$-0.633251\pi$
$593$	12.3499	−	12.3499i	0.507150	−	0.507150i	0.913651	+	0.406500i	$0.133251\pi$
$594$		−	0.729840i		−	0.0299457i
$595$	16.3142	+	13.0441i	0.668818	+	0.534755i
$596$	−8.02774	−	8.02774i	−0.328829	−	0.328829i
$597$		−	5.92452i		−	0.242474i
$598$	18.0065	+	17.5433i	0.736341	+	0.717398i
$599$	−29.0798			−1.18817			−0.594084	−	0.804403i	$-0.702485\pi$
$599$	−29.0798			−1.18817			−0.594084	+	0.804403i	$0.702485\pi$
$600$	3.11341	+	3.11341i	0.127105	+	0.127105i
$601$		−	28.7194i		−	1.17149i	−0.810496	−	0.585744i	$-0.800802\pi$
$601$		−	28.7194i		−	1.17149i	0.810496	−	0.585744i	$-0.199198\pi$
$602$	−16.3142	−	13.0441i	−0.664919	−	0.531637i
$603$	3.96130	−	3.96130i	0.161317	−	0.161317i
$604$	13.5417	−	13.5417i	0.551003	−	0.551003i
$605$	−22.6963	+	22.6963i	−0.922736	+	0.922736i
$606$	−4.14405	−	4.14405i	−0.168341	−	0.168341i
$607$			22.9366i			0.930967i	0.885056	+	0.465484i	$0.154120\pi$
$607$			22.9366i			0.930967i	−0.885056	+	0.465484i	$0.845880\pi$
$608$	−5.40303			−0.219122
$609$	1.85267	+	16.6326i	0.0750740	+	0.673987i
$610$			19.6622i			0.796100i
$611$	5.03215	−	5.16502i	0.203579	−	0.208954i
$612$		−	2.57461i		−	0.104072i
$613$	−5.54006	+	5.54006i	−0.223761	+	0.223761i	−0.810080	−	0.586319i	$-0.800576\pi$
$613$	−5.54006	+	5.54006i	−0.223761	+	0.223761i	0.586319	+	0.810080i	$0.300576\pi$
$614$			21.0299i			0.848697i
$615$	0.764127			0.0308126
$616$	0.213765	+	1.91911i	0.00861285	+	0.0773230i
$617$	−3.86438	+	3.86438i	−0.155574	+	0.155574i	−0.780602	−	0.625028i	$-0.785087\pi$
$617$	−3.86438	+	3.86438i	−0.155574	+	0.155574i	0.625028	+	0.780602i	$0.285087\pi$
$618$	−6.48392	−	6.48392i	−0.260822	−	0.260822i
$619$	25.0182	−	25.0182i	1.00557	−	1.00557i	0.00558273	−	0.999984i	$-0.498223\pi$
$619$	25.0182	−	25.0182i	1.00557	−	1.00557i	0.999984	−	0.00558273i	$-0.00177705\pi$
$620$	18.8061			0.755270
$621$	6.97248			0.279796
$622$	−18.4194	+	18.4194i	−0.738549	+	0.738549i
$623$	2.59308	−	3.24317i	0.103890	−	0.129935i
$624$	0.0469777	+	3.60525i	0.00188061	+	0.144325i
$625$	27.6285			1.10514
$626$	−9.26361	−	9.26361i	−0.370248	−	0.370248i
$627$	−3.94335			−0.157482
$628$	3.14458			0.125482
$629$	9.22355	+	9.22355i	0.367767	+	0.367767i
$630$	−8.06316	+	0.898138i	−0.321244	+	0.0357827i
$631$	−8.12549	−	8.12549i	−0.323471	−	0.323471i	0.526626	−	0.850097i	$-0.323457\pi$
$631$	−8.12549	−	8.12549i	−0.323471	−	0.323471i	−0.850097	+	0.526626i	$0.823457\pi$
$632$	7.73963	+	7.73963i	0.307866	+	0.307866i
$633$			7.04407i			0.279977i
$634$		−	22.0839i		−	0.877063i
$635$	41.6557	−	41.6557i	1.65306	−	1.65306i
$636$	0.514936			0.0204185
$637$	24.5458	−	5.87401i	0.972540	−	0.232737i
$638$	4.61654			0.182771
$639$	−8.12169	+	8.12169i	−0.321289	+	0.321289i
$640$			3.06644i			0.121212i
$641$		−	42.7580i		−	1.68884i	−0.535682	−	0.844420i	$-0.679945\pi$
$641$		−	42.7580i		−	1.68884i	0.535682	−	0.844420i	$-0.320055\pi$
$642$	5.59557	+	5.59557i	0.220840	+	0.220840i
$643$	7.37341	+	7.37341i	0.290779	+	0.290779i	0.837388	−	0.546609i	$-0.184082\pi$
$643$	7.37341	+	7.37341i	0.290779	+	0.290779i	−0.546609	+	0.837388i	$0.684082\pi$
$644$	−18.3341	+	2.04219i	−0.722463	+	0.0804737i
$645$	−17.1184	−	17.1184i	−0.674037	−	0.674037i
$646$	−13.9107			−0.547308
$647$	22.7445			0.894178			0.447089	−	0.894490i	$-0.352461\pi$
$647$	22.7445			0.894178			0.447089	+	0.894490i	$0.352461\pi$
$648$	0.707107	+	0.707107i	0.0277778	+	0.0277778i
$649$	−3.28052			−0.128772
$650$	−11.3709	−	11.0784i	−0.446003	−	0.434529i
$651$	−10.1329	+	12.6732i	−0.397139	+	0.496702i
$652$	−15.2816	+	15.2816i	−0.598472	+	0.598472i
$653$	−28.5645			−1.11782			−0.558908	−	0.829230i	$-0.688780\pi$
$653$	−28.5645			−1.11782			−0.558908	+	0.829230i	$0.688780\pi$
$654$	14.0054			0.547653
$655$	21.3156	−	21.3156i	0.832869	−	0.832869i
$656$	0.176204	+	0.176204i	0.00687962	+	0.00687962i
$657$	−11.6056	+	11.6056i	−0.452778	+	0.452778i
$658$	0.585786	+	5.25898i	0.0228363	+	0.205016i
$659$	−24.6149			−0.958862			−0.479431	−	0.877580i	$-0.659157\pi$
$659$	−24.6149			−0.958862			−0.479431	+	0.877580i	$0.659157\pi$
$660$			2.23801i			0.0871144i
$661$	−14.7668	+	14.7668i	−0.574363	+	0.574363i	−0.933345	−	0.358981i	$-0.883124\pi$
$661$	−14.7668	+	14.7668i	−0.574363	+	0.574363i	0.358981	+	0.933345i	$0.383124\pi$
$662$		−	8.50839i		−	0.330688i
$663$	0.120949	+	9.28208i	0.00469727	+	0.360486i
$664$			1.43003i			0.0554958i
$665$	4.85267	+	43.5655i	0.188179	+	1.68940i
$666$	−5.06644			−0.196320
$667$			44.1038i			1.70771i
$668$	9.21892	+	9.21892i	0.356691	+	0.356691i
$669$	9.71425	−	9.71425i	0.375574	−	0.375574i
$670$	−12.1471	+	12.1471i	−0.469282	+	0.469282i
$671$	−3.30911	+	3.30911i	−0.127747	+	0.127747i
$672$	−2.06644	−	1.65222i	−0.0797145	−	0.0637359i
$673$		−	50.9335i		−	1.96334i	−0.190584	−	0.981671i	$-0.561038\pi$
$673$		−	50.9335i		−	1.96334i	0.190584	−	0.981671i	$-0.438962\pi$
$674$	0.875033	+	0.875033i	0.0337050	+	0.0337050i
$675$	−4.40303			−0.169473
$676$	−0.338732	−	12.9956i	−0.0130282	−	0.499830i
$677$		−	4.02891i		−	0.154844i	−0.996998	−	0.0774218i	$-0.975331\pi$
$677$		−	4.02891i		−	0.154844i	0.996998	−	0.0774218i	$-0.0246688\pi$
$678$	8.44636	+	8.44636i	0.324381	+	0.324381i
$679$	−27.3049	−	21.8317i	−1.04787	−	0.837822i
$680$			7.89486i			0.302754i
$681$	−13.9000	+	13.9000i	−0.532650	+	0.532650i
$682$	3.16502	+	3.16502i	0.121195	+	0.121195i
$683$	−17.3021	−	17.3021i	−0.662045	−	0.662045i	0.293817	−	0.955862i	$-0.405074\pi$
$683$	−17.3021	−	17.3021i	−0.662045	−	0.662045i	−0.955862	+	0.293817i	$0.905074\pi$
$684$	3.82052	−	3.82052i	0.146081	−	0.146081i
$685$		−	16.8268i		−	0.642920i
$686$	−8.09911	+	16.6555i	−0.309226	+	0.635908i
$687$	5.97035	+	5.97035i	0.227783	+	0.227783i
$688$		−	7.89486i		−	0.300989i
$689$	−1.85647	+	0.0241905i	−0.0707259	+	0.000921585i
$690$	−21.3807			−0.813948
$691$	2.49183	+	2.49183i	0.0947937	+	0.0947937i	0.752913	−	0.658120i	$-0.228648\pi$
$691$	2.49183	+	2.49183i	0.0947937	+	0.0947937i	−0.658120	+	0.752913i	$0.728648\pi$
$692$		−	17.4793i		−	0.664462i
$693$	−1.50817	−	1.20586i	−0.0572906	−	0.0458068i
$694$	8.59932	−	8.59932i	0.326426	−	0.326426i
$695$	−7.21351	+	7.21351i	−0.273624	+	0.273624i
$696$	−4.47274	+	4.47274i	−0.169539	+	0.169539i
$697$	0.453656	+	0.453656i	0.0171835	+	0.0171835i
$698$			25.4024i			0.961494i
$699$	−1.35293			−0.0511727
$700$	11.5777	−	1.28962i	0.437597	−	0.0487430i
$701$			0.236091i			0.00891703i	0.999990	+	0.00445852i	$0.00141919\pi$
$701$			0.236091i			0.00891703i	−0.999990	+	0.00445852i	$0.998581\pi$
$702$	−2.58251	−	2.51608i	−0.0974706	−	0.0949631i
$703$			27.3741i			1.03243i
$704$	−0.516075	+	0.516075i	−0.0194503	+	0.0194503i
$705$			6.13287i			0.230977i
$706$	−29.9876			−1.12860
$707$	−15.4103	+	1.71652i	−0.579565	+	0.0645565i
$708$	3.17834	−	3.17834i	0.119449	−	0.119449i
$709$	9.68526	+	9.68526i	0.363737	+	0.363737i	0.865187	−	0.501449i	$-0.167200\pi$
$709$	9.68526	+	9.68526i	0.363737	+	0.363737i	−0.501449	+	0.865187i	$0.667200\pi$
$710$	24.9047	−	24.9047i	0.934655	−	0.934655i
$711$	−10.9455			−0.410488
$712$	1.56945			0.0588176
$713$	−30.2368	+	30.2368i	−1.13238	+	1.13238i
$714$	−5.32026	−	4.25382i	−0.199106	−	0.159195i
$715$	−0.105136	−	8.06857i	−0.00393188	−	0.301747i
$716$	18.3235			0.684781
$717$	−20.8904	−	20.8904i	−0.780168	−	0.780168i
$718$	−28.9008			−1.07857
$719$	47.6518			1.77711			0.888556	−	0.458768i	$-0.151709\pi$
$719$	47.6518			1.77711			0.888556	+	0.458768i	$0.151709\pi$
$720$	−2.16830	−	2.16830i	−0.0808077	−	0.0808077i
$721$	−24.1115	+	2.68573i	−0.897959	+	0.100022i
$722$	−7.20737	−	7.20737i	−0.268231	−	0.268231i
$723$	−11.1816	−	11.1816i	−0.415847	−	0.415847i
$724$		−	4.96432i		−	0.184498i
$725$		−	27.8510i		−	1.03436i
$726$	7.40152	−	7.40152i	0.274696	−	0.274696i
$727$	−10.6947			−0.396644			−0.198322	−	0.980137i	$-0.563549\pi$
$727$	−10.6947			−0.396644			−0.198322	+	0.980137i	$0.563549\pi$
$728$	7.52763	+	5.85959i	0.278992	+	0.217171i
$729$	−1.00000			−0.0370370
$730$	35.5879	−	35.5879i	1.31717	−	1.31717i
$731$		−	20.3262i		−	0.751790i
$732$		−	6.41208i		−	0.236997i
$733$	1.22630	+	1.22630i	0.0452945	+	0.0452945i	0.729391	−	0.684097i	$-0.239803\pi$
$733$	1.22630	+	1.22630i	0.0452945	+	0.0452945i	−0.684097	+	0.729391i	$0.739803\pi$
$734$	−0.777803	−	0.777803i	−0.0287092	−	0.0287092i
$735$	−11.4662	+	18.1459i	−0.422937	+	0.669323i
$736$	−4.93029	−	4.93029i	−0.181733	−	0.181733i
$737$	−4.08866			−0.150608
$738$	−0.249190			−0.00917283
$739$	10.0141	+	10.0141i	0.368373	+	0.368373i	0.866884	−	0.498511i	$-0.166119\pi$
$739$	10.0141	+	10.0141i	0.368373	+	0.368373i	−0.498511	+	0.866884i	$0.666119\pi$
$740$	15.5359			0.571111
$741$	−13.5944	+	13.9534i	−0.499404	+	0.512591i
$742$	0.850789	−	1.06408i	0.0312335	−	0.0390637i
$743$	−17.3229	+	17.3229i	−0.635516	+	0.635516i	−0.949446	−	0.313930i	$-0.898354\pi$
$743$	−17.3229	+	17.3229i	−0.635516	+	0.635516i	0.313930	+	0.949446i	$0.398354\pi$
$744$	−6.13287			−0.224842
$745$	−34.8130			−1.27545
$746$	−14.5934	+	14.5934i	−0.534304	+	0.534304i
$747$	−1.01118	−	1.01118i	−0.0369972	−	0.0369972i
$748$	−1.32869	+	1.32869i	−0.0485817	+	0.0485817i
$749$	20.8080	−	2.31776i	0.760309	−	0.0846892i
$750$	−1.83056			−0.0668427
$751$		−	38.8207i		−	1.41659i	−0.705919	−	0.708293i	$-0.749466\pi$
$751$		−	38.8207i		−	1.41659i	0.705919	−	0.708293i	$-0.250534\pi$
$752$	−1.41421	+	1.41421i	−0.0515711	+	0.0515711i
$753$		−	20.6366i		−	0.752041i
$754$	15.9152	−	16.3355i	0.579598	−	0.594902i
$755$		−	58.7248i		−	2.13721i
$756$	2.62949	−	0.292893i	0.0956336	−	0.0106524i
$757$	−12.6121			−0.458395			−0.229198	−	0.973380i	$-0.573610\pi$
$757$	−12.6121			−0.458395			−0.229198	+	0.973380i	$0.573610\pi$
$758$		−	8.23110i		−	0.298967i
$759$	−3.59832	−	3.59832i	−0.130611	−	0.130611i
$760$	−11.7154	+	11.7154i	−0.424962	+	0.424962i
$761$	−30.3727	+	30.3727i	−1.10101	+	1.10101i	−0.106721	+	0.994289i	$0.534035\pi$
$761$	−30.3727	+	30.3727i	−1.10101	+	1.10101i	−0.994289	+	0.106721i	$0.965965\pi$
$762$	−13.5844	+	13.5844i	−0.492111	+	0.492111i
$763$	23.1400	−	28.9412i	0.837724	−	1.04774i
$764$		−	10.5427i		−	0.381421i
$765$	−5.58251	−	5.58251i	−0.201836	−	0.201836i
$766$	13.0915			0.473016
$767$	−11.3094	+	11.6080i	−0.408358	+	0.419141i
$768$		−	1.00000i		−	0.0360844i
$769$	0.566917	+	0.566917i	0.0204435	+	0.0204435i	0.717255	−	0.696811i	$-0.245398\pi$
$769$	0.566917	+	0.566917i	0.0204435	+	0.0204435i	−0.696811	+	0.717255i	$0.745398\pi$
$770$	4.62470	+	3.69769i	0.166663	+	0.133256i
$771$			9.21351i			0.331816i
$772$	−13.6366	+	13.6366i	−0.490793	+	0.490793i
$773$	23.9977	+	23.9977i	0.863137	+	0.863137i	0.991701	−	0.128564i	$-0.0410369\pi$
$773$	23.9977	+	23.9977i	0.863137	+	0.863137i	−0.128564	+	0.991701i	$0.541037\pi$
$774$	5.58251	+	5.58251i	0.200659	+	0.200659i
$775$	19.0942	−	19.0942i	0.685883	−	0.685883i
$776$		−	13.2135i		−	0.474337i
$777$	−8.37088	+	10.4695i	−0.300304	+	0.375590i
$778$	23.8041	+	23.8041i	0.853420	+	0.853420i
$779$			1.34638i			0.0482392i
$780$	7.91911	+	7.71538i	0.283550	+	0.276255i
$781$	8.38281			0.299960
$782$	−12.6935	−	12.6935i	−0.453920	−	0.453920i
$783$		−	6.32541i		−	0.226052i
$784$	−6.82843	+	1.54032i	−0.243872	+	0.0550114i
$785$	6.81838	−	6.81838i	0.243359	−	0.243359i
$786$	−6.95126	+	6.95126i	−0.247943	+	0.247943i
$787$	32.7888	−	32.7888i	1.16879	−	1.16879i	0.186302	−	0.982492i	$-0.440350\pi$
$787$	32.7888	−	32.7888i	1.16879	−	1.16879i	0.982492	−	0.186302i	$-0.0596504\pi$
$788$	−13.4673	−	13.4673i	−0.479754	−	0.479754i
$789$		−	9.50464i		−	0.338374i
$790$	33.5636			1.19414
$791$	31.4091	−	3.49860i	1.11678	−	0.124396i
$792$		−	0.729840i		−	0.0259338i
$793$	0.301224	+	23.1171i	0.0106968	+	0.820913i
$794$		−	34.1715i		−	1.21270i
$795$	1.11654	−	1.11654i	0.0395994	−	0.0395994i
$796$		−	5.92452i		−	0.209989i
$797$	0.606614			0.0214874			0.0107437	−	0.999942i	$-0.496580\pi$
$797$	0.606614			0.0214874			0.0107437	+	0.999942i	$0.496580\pi$
$798$	−1.58251	−	14.2072i	−0.0560203	−	0.502930i
$799$	−3.64104	+	3.64104i	−0.128811	+	0.128811i
$800$	3.11341	+	3.11341i	0.110076	+	0.110076i
$801$	−1.10977	+	1.10977i	−0.0392117	+	0.0392117i
$802$	11.7222			0.413925
$803$	11.9787			0.422721
$804$	3.96130	−	3.96130i	0.139704	−	0.139704i
$805$	−35.3256	+	44.1818i	−1.24506	+	1.55720i
$806$	22.1105	−	0.288108i	0.778810	−	0.0101482i
$807$	−15.7423			−0.554155
$808$	−4.14405	−	4.14405i	−0.145787	−	0.145787i
$809$	1.54084			0.0541732			0.0270866	−	0.999633i	$-0.491377\pi$
$809$	1.54084			0.0541732			0.0270866	+	0.999633i	$0.491377\pi$
$810$	3.06644			0.107744
$811$	−17.4392	−	17.4392i	−0.612373	−	0.612373i	0.331191	−	0.943564i	$-0.392550\pi$
$811$	−17.4392	−	17.4392i	−0.612373	−	0.612373i	−0.943564	+	0.331191i	$0.892550\pi$
$812$	1.85267	+	16.6326i	0.0650160	+	0.583690i
$813$	17.4746	+	17.4746i	0.612862	+	0.612862i
$814$	2.61466	+	2.61466i	0.0916438	+	0.0916438i
$815$			66.2699i			2.32133i
$816$		−	2.57461i		−	0.0901292i
$817$	30.1625	−	30.1625i	1.05525	−	1.05525i
$818$	−10.9471			−0.382756
$819$	−9.46619	+	1.17948i	−0.330776	+	0.0412143i
$820$	0.764127			0.0266845
$821$	−20.4659	+	20.4659i	−0.714266	+	0.714266i	−0.967425	−	0.253159i	$-0.918531\pi$
$821$	−20.4659	+	20.4659i	−0.714266	+	0.714266i	0.253159	+	0.967425i	$0.418531\pi$
$822$			5.48742i			0.191396i
$823$			7.39538i			0.257787i	0.991658	+	0.128893i	$0.0411425\pi$
$823$			7.39538i			0.257787i	−0.991658	+	0.128893i	$0.958858\pi$
$824$	−6.48392	−	6.48392i	−0.225878	−	0.225878i
$825$	2.27230	+	2.27230i	0.0791112	+	0.0791112i
$826$	−1.31651	−	11.8192i	−0.0458073	−	0.411241i
$827$	−0.405564	−	0.405564i	−0.0141029	−	0.0141029i	0.700020	−	0.714123i	$-0.253174\pi$
$827$	−0.405564	−	0.405564i	−0.0141029	−	0.0141029i	−0.714123	+	0.700020i	$0.753174\pi$
$828$	6.97248			0.242310
$829$	3.28950			0.114249			0.0571245	−	0.998367i	$-0.481807\pi$
$829$	3.28950			0.114249			0.0571245	+	0.998367i	$0.481807\pi$
$830$	3.10072	+	3.10072i	0.107628	+	0.107628i
$831$	21.3991			0.742328
$832$	0.0469777	+	3.60525i	0.00162866	+	0.124989i
$833$	−17.5805	+	3.96571i	−0.609128	+	0.137404i
$834$	2.35241	−	2.35241i	0.0814572	−	0.0814572i
$835$	39.9787			1.38352
$836$	−3.94335			−0.136384
$837$	4.33660	−	4.33660i	0.149895	−	0.149895i
$838$	−26.3431	−	26.3431i	−0.910008	−	0.910008i
$839$	−8.32703	+	8.32703i	−0.287481	+	0.287481i	−0.836083	−	0.548602i	$-0.815160\pi$
$839$	−8.32703	+	8.32703i	−0.287481	+	0.287481i	0.548602	+	0.836083i	$0.315160\pi$
$840$	−8.06316	+	0.898138i	−0.278206	+	0.0309887i
$841$	11.0109			0.379685
$842$			37.0136i			1.27557i
$843$	0.634274	−	0.634274i	0.0218456	−	0.0218456i
$844$			7.04407i			0.242467i
$845$	−28.9128	−	27.4438i	−0.994630	−	0.944097i
$846$		−	2.00000i		−	0.0687614i
$847$	−3.06581	−	27.5237i	−0.105343	−	0.945727i
$848$	0.514936			0.0176830
$849$			11.6503i			0.399837i
$850$	8.01581	+	8.01581i	0.274940	+	0.274940i
$851$	−24.9790	+	24.9790i	−0.856269	+	0.856269i
$852$	−8.12169	+	8.12169i	−0.278245	+	0.278245i
$853$	−11.6895	+	11.6895i	−0.400242	+	0.400242i	−0.878318	−	0.478076i	$-0.841334\pi$
$853$	−11.6895	+	11.6895i	−0.400242	+	0.400242i	0.478076	+	0.878318i	$0.341334\pi$
$854$	−13.2502	−	10.5942i	−0.453411	−	0.362525i
$855$		−	16.5681i		−	0.566616i
$856$	5.59557	+	5.59557i	0.191253	+	0.191253i
$857$	17.6693			0.603573			0.301787	−	0.953376i	$-0.402417\pi$
$857$	17.6693			0.603573			0.301787	+	0.953376i	$0.402417\pi$
$858$	0.0342862	+	2.63125i	0.00117051	+	0.0898295i
$859$			41.1971i			1.40563i	0.711374	+	0.702813i	$0.248073\pi$
$859$			41.1971i			1.40563i	−0.711374	+	0.702813i	$0.751927\pi$
$860$	−17.1184	−	17.1184i	−0.583733	−	0.583733i
$861$	−0.411718	+	0.514936i	−0.0140313	+	0.0175490i
$862$			2.90127i			0.0988177i
$863$	5.50354	−	5.50354i	0.187343	−	0.187343i	−0.607204	−	0.794546i	$-0.707709\pi$
$863$	5.50354	−	5.50354i	0.187343	−	0.187343i	0.794546	+	0.607204i	$0.207709\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$	−37.9002	−	37.9002i	−1.28865	−	1.28865i
$866$	11.1449	−	11.1449i	0.378720	−	0.378720i
$867$			10.3714i			0.352231i
$868$	−10.1329	+	12.6732i	−0.343932	+	0.430156i
$869$	5.64869	+	5.64869i	0.191619	+	0.191619i
$870$			19.3965i			0.657602i
$871$	−14.0954	+	14.4676i	−0.477603	+	0.490214i
$872$	14.0054			0.474282
$873$	9.34336	+	9.34336i	0.316225	+	0.316225i
$874$		−	37.6725i		−	1.27429i
$875$	−3.02450	+	3.78274i	−0.102247	+	0.127880i
$876$	−11.6056	+	11.6056i	−0.392117	+	0.392117i
$877$	14.6890	−	14.6890i	0.496012	−	0.496012i	−0.414182	−	0.910194i	$-0.635932\pi$
$877$	14.6890	−	14.6890i	0.496012	−	0.496012i	0.910194	+	0.414182i	$0.135932\pi$
$878$	7.67131	−	7.67131i	0.258894	−	0.258894i
$879$	−16.3755	−	16.3755i	−0.552332	−	0.552332i
$880$			2.23801i			0.0754433i
$881$	−9.22544			−0.310813			−0.155406	−	0.987851i	$-0.549669\pi$
$881$	−9.22544			−0.310813			−0.155406	+	0.987851i	$0.549669\pi$
$882$	3.73926	−	5.91760i	0.125907	−	0.199256i
$883$		−	26.4515i		−	0.890165i	−0.895490	−	0.445083i	$-0.853174\pi$
$883$		−	26.4515i		−	0.890165i	0.895490	−	0.445083i	$-0.146826\pi$
$884$	0.120949	+	9.28208i	0.00406795	+	0.312190i
$885$		−	13.7832i		−	0.463316i
$886$	6.49912	−	6.49912i	0.218342	−	0.218342i
$887$		−	11.7136i		−	0.393303i	−0.980473	−	0.196651i	$-0.936993\pi$
$887$		−	11.7136i		−	0.393303i	0.980473	−	0.196651i	$-0.0630067\pi$
$888$	−5.06644			−0.170018
$889$	5.62684	+	50.5157i	0.188718	+	1.69424i
$890$	3.40303	−	3.40303i	0.114070	−	0.114070i
$891$	0.516075	+	0.516075i	0.0172892	+	0.0172892i
$892$	9.71425	−	9.71425i	0.325257	−	0.325257i
$893$	−10.8061			−0.361611
$894$	11.3529			0.379699
$895$	39.7308	−	39.7308i	1.32805	−	1.32805i
$896$	−2.06644	−	1.65222i	−0.0690348	−	0.0551969i
$897$	−25.1375	+	0.327551i	−0.839317	+	0.0109366i
$898$	−22.0789			−0.736784
$899$	27.4308	+	27.4308i	0.914867	+	0.914867i
$900$	−4.40303			−0.146768
$901$	1.32576			0.0441674
$902$	0.128601	+	0.128601i	0.00428194	+	0.00428194i
$903$	20.7595	−	2.31235i	0.690832	−	0.0769503i
$904$	8.44636	+	8.44636i	0.280922	+	0.280922i
$905$	−10.7641	−	10.7641i	−0.357812	−	0.357812i
$906$			19.1508i			0.636243i
$907$			24.4074i			0.810436i	0.914220	+	0.405218i	$0.132804\pi$
$907$			24.4074i			0.810436i	−0.914220	+	0.405218i	$0.867196\pi$
$908$	−13.9000	+	13.9000i	−0.461288	+	0.461288i
$909$	5.86058			0.194383
$910$	29.0275	−	3.61680i	0.962252	−	0.119896i
$911$	−35.7796			−1.18543			−0.592715	−	0.805412i	$-0.701944\pi$
$911$	−35.7796			−1.18543			−0.592715	+	0.805412i	$0.701944\pi$
$912$	3.82052	−	3.82052i	0.126510	−	0.126510i
$913$			1.04369i			0.0345411i
$914$		−	37.8155i		−	1.25083i
$915$	−13.9033	−	13.9033i	−0.459629	−	0.459629i
$916$	5.97035	+	5.97035i	0.197266	+	0.197266i
$917$	2.87931	+	25.8494i	0.0950830	+	0.853621i
$918$	1.82052	+	1.82052i	0.0600861	+	0.0600861i
$919$	21.9957			0.725572			0.362786	−	0.931872i	$-0.381826\pi$
$919$	21.9957			0.725572			0.362786	+	0.931872i	$0.381826\pi$
$920$	−21.3807			−0.704900
$921$	−14.8704	−	14.8704i	−0.489995	−	0.489995i
$922$	−24.3027			−0.800368
$923$	28.8992	−	29.6622i	0.951227	−	0.976344i
$924$	−1.50817	−	1.20586i	−0.0496151	−	0.0396699i
$925$	15.7739	−	15.7739i	0.518643	−	0.518643i
$926$	24.0343			0.789816
$927$	9.16965			0.301171
$928$	−4.47274	+	4.47274i	−0.146825	+	0.146825i
$929$	−11.1005	−	11.1005i	−0.364196	−	0.364196i	0.501159	−	0.865355i	$-0.332907\pi$
$929$	−11.1005	−	11.1005i	−0.364196	−	0.364196i	−0.865355	+	0.501159i	$0.832907\pi$
$930$	−13.2979	+	13.2979i	−0.436055	+	0.436055i
$931$	−31.9730	−	20.2033i	−1.04787	−	0.662137i
$932$	−1.35293			−0.0443168
$933$		−	26.0489i		−	0.852803i
$934$	5.46348	−	5.46348i	0.178771	−	0.178771i
$935$			5.76199i			0.188437i
$936$	−2.58251	−	2.51608i	−0.0844120	−	0.0822405i
$937$			32.9296i			1.07576i	0.843020	+	0.537882i	$0.180775\pi$
$937$			32.9296i			1.07576i	−0.843020	+	0.537882i	$0.819225\pi$
$938$	−1.64082	−	14.7307i	−0.0535748	−	0.480975i
$939$	13.1007			0.427526
$940$			6.13287i			0.200032i
$941$	−16.5400	−	16.5400i	−0.539189	−	0.539189i	0.384102	−	0.923291i	$-0.374511\pi$
$941$	−16.5400	−	16.5400i	−0.539189	−	0.539189i	−0.923291	+	0.384102i	$0.874511\pi$
$942$	−2.22355	+	2.22355i	−0.0724473	+	0.0724473i
$943$	−1.22858	+	1.22858i	−0.0400081	+	0.0400081i
$944$	3.17834	−	3.17834i	0.103446	−	0.103446i
$945$	5.06644	−	6.33660i	0.164811	−	0.206129i
$946$		−	5.76199i		−	0.187338i
$947$	8.74592	+	8.74592i	0.284204	+	0.284204i	0.834783	−	0.550579i	$-0.185593\pi$
$947$	8.74592	+	8.74592i	0.284204	+	0.284204i	−0.550579	+	0.834783i	$0.685593\pi$
$948$	−10.9455			−0.355493
$949$	41.2959	−	42.3863i	1.34052	−	1.37592i
$950$			23.7897i			0.771841i
$951$	15.6157	+	15.6157i	0.506372	+	0.506372i
$952$	−5.32026	−	4.25382i	−0.172431	−	0.137867i
$953$		−	14.1171i		−	0.457296i	−0.973509	−	0.228648i	$-0.926569\pi$
$953$		−	14.1171i		−	0.457296i	0.973509	−	0.228648i	$-0.0734306\pi$
$954$	−0.364115	+	0.364115i	−0.0117887	+	0.0117887i
$955$	−22.8597	−	22.8597i	−0.739721	−	0.739721i
$956$	−20.8904	−	20.8904i	−0.675645	−	0.675645i
$957$	−3.26439	+	3.26439i	−0.105523	+	0.105523i
$958$		−	36.7810i		−	1.18834i
$959$	11.3394	+	9.06644i	0.366168	+	0.292771i
$960$	−2.16830	−	2.16830i	−0.0699815	−	0.0699815i
$961$			6.61213i			0.213295i
$962$	18.2657	−	0.238009i	0.588911	−	0.00767373i
$963$	−7.91334			−0.255004
$964$	−11.1816	−	11.1816i	−0.360134	−	0.360134i
$965$			59.1365i			1.90367i
$966$	11.5201	−	14.4082i	0.370653	−	0.463576i
$967$	−17.8079	+	17.8079i	−0.572664	+	0.572664i	−0.932872	−	0.360208i	$-0.882706\pi$
$967$	−17.8079	+	17.8079i	−0.572664	+	0.572664i	0.360208	+	0.932872i	$0.382706\pi$
$968$	7.40152	−	7.40152i	0.237894	−	0.237894i
$969$	9.83633	−	9.83633i	0.315989	−	0.315989i
$970$	−28.6508	−	28.6508i	−0.919923	−	0.919923i
$971$			21.1673i			0.679291i	0.940554	+	0.339646i	$0.110307\pi$
$971$			21.1673i			0.679291i	−0.940554	+	0.339646i	$0.889693\pi$
$972$	−1.00000			−0.0320750
$973$	−0.974400	−	8.74781i	−0.0312378	−	0.280442i
$974$		−	18.0512i		−	0.578398i
$975$	15.8740	−	0.206844i	0.508375	−	0.00662431i
$976$		−	6.41208i		−	0.205246i
$977$	19.6568	−	19.6568i	0.628877	−	0.628877i	−0.318908	−	0.947786i	$-0.603316\pi$
$977$	19.6568	−	19.6568i	0.628877	−	0.628877i	0.947786	+	0.318908i	$0.103316\pi$
$978$		−	21.6114i		−	0.691056i
$979$	1.14545			0.0366086
$980$	−11.4662	+	18.1459i	−0.366274	+	0.579651i
$981$	−9.90330	+	9.90330i	−0.316188	+	0.316188i
$982$	−30.9212	−	30.9212i	−0.986735	−	0.986735i
$983$	−17.7065	+	17.7065i	−0.564749	+	0.564749i	−0.930653	−	0.365904i	$-0.880760\pi$
$983$	−17.7065	+	17.7065i	−0.564749	+	0.564749i	0.365904	+	0.930653i	$0.380760\pi$
$984$	−0.249190			−0.00794390
$985$	−58.4024			−1.86085
$986$	−11.5155	+	11.5155i	−0.366730	+	0.366730i
$987$	−4.13287	−	3.30445i	−0.131551	−	0.105182i
$988$	−13.5944	+	13.9534i	−0.432497	+	0.443917i
$989$	55.0468			1.75039
$990$	−1.58251	−	1.58251i	−0.0502955	−	0.0502955i
$991$	26.3147			0.835913			0.417957	−	0.908467i	$-0.362746\pi$
$991$	26.3147			0.835913			0.417957	+	0.908467i	$0.362746\pi$
$992$	−6.13287			−0.194719
$993$	6.01634	+	6.01634i	0.190923	+	0.190923i
$994$	3.36411	+	30.2018i	0.106703	+	0.957943i
$995$	−12.8461	−	12.8461i	−0.407249	−	0.407249i
$996$	−1.01118	−	1.01118i	−0.0320405	−	0.0320405i
$997$		−	3.40444i		−	0.107820i	−0.998546	−	0.0539099i	$-0.982832\pi$
$997$		−	3.40444i		−	0.107820i	0.998546	−	0.0539099i	$-0.0171684\pi$
$998$			8.92510i			0.282519i
$999$	3.58251	−	3.58251i	0.113346	−	0.113346i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.o.b.265.1	✓	8
3.2	odd	2		1638.2.x.c.811.4		8
7.6	odd	2		546.2.o.c.265.2	yes	8
13.8	odd	4		546.2.o.c.307.2	yes	8
21.20	even	2		1638.2.x.a.811.3		8
39.8	even	4		1638.2.x.a.307.3		8
91.34	even	4	inner	546.2.o.b.307.1	yes	8
273.125	odd	4		1638.2.x.c.307.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.o.b.265.1	✓	8	1.1	even	1	trivial
546.2.o.b.307.1	yes	8	91.34	even	4	inner
546.2.o.c.265.2	yes	8	7.6	odd	2
546.2.o.c.307.2	yes	8	13.8	odd	4
1638.2.x.a.307.3		8	39.8	even	4
1638.2.x.a.811.3		8	21.20	even	2
1638.2.x.c.307.4		8	273.125	odd	4
1638.2.x.c.811.4		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{3} -1.00000i q^{4} +(-2.16830 - 2.16830i) q^{5} +(0.707107 + 0.707107i) q^{6} +(2.62949 - 0.292893i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{3} -1.00000i q^{4} +(-2.16830 - 2.16830i) q^{5} +(0.707107 + 0.707107i) q^{6} +(2.62949 - 0.292893i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +3.06644 q^{10} +(0.516075 + 0.516075i) q^{11} -1.00000 q^{12} +(3.60525 - 0.0469777i) q^{13} +(-1.65222 + 2.06644i) q^{14} +(-2.16830 + 2.16830i) q^{15} -1.00000 q^{16} -2.57461 q^{17} +(0.707107 - 0.707107i) q^{18} +(-3.82052 - 3.82052i) q^{19} +(-2.16830 + 2.16830i) q^{20} +(-0.292893 - 2.62949i) q^{21} -0.729840 q^{22} -6.97248i q^{23} +(0.707107 - 0.707107i) q^{24} +4.40303i q^{25} +(-2.51608 + 2.58251i) q^{26} +1.00000i q^{27} +(-0.292893 - 2.62949i) q^{28} -6.32541 q^{29} -3.06644i q^{30} +(-4.33660 - 4.33660i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.516075 - 0.516075i) q^{33} +(1.82052 - 1.82052i) q^{34} +(-6.33660 - 5.06644i) q^{35} +1.00000i q^{36} +(-3.58251 - 3.58251i) q^{37} +5.40303 q^{38} +(-0.0469777 - 3.60525i) q^{39} -3.06644i q^{40} +(-0.176204 - 0.176204i) q^{41} +(2.06644 + 1.65222i) q^{42} +7.89486i q^{43} +(0.516075 - 0.516075i) q^{44} +(2.16830 + 2.16830i) q^{45} +(4.93029 + 4.93029i) q^{46} +(1.41421 - 1.41421i) q^{47} +1.00000i q^{48} +(6.82843 - 1.54032i) q^{49} +(-3.11341 - 3.11341i) q^{50} +2.57461i q^{51} +(-0.0469777 - 3.60525i) q^{52} -0.514936 q^{53} +(-0.707107 - 0.707107i) q^{54} -2.23801i q^{55} +(2.06644 + 1.65222i) q^{56} +(-3.82052 + 3.82052i) q^{57} +(4.47274 - 4.47274i) q^{58} +(-3.17834 + 3.17834i) q^{59} +(2.16830 + 2.16830i) q^{60} +6.41208i q^{61} +6.13287 q^{62} +(-2.62949 + 0.292893i) q^{63} +1.00000i q^{64} +(-7.91911 - 7.71538i) q^{65} +0.729840i q^{66} +(-3.96130 + 3.96130i) q^{67} +2.57461i q^{68} -6.97248 q^{69} +(8.06316 - 0.898138i) q^{70} +(8.12169 - 8.12169i) q^{71} +(-0.707107 - 0.707107i) q^{72} +(11.6056 - 11.6056i) q^{73} +5.06644 q^{74} +4.40303 q^{75} +(-3.82052 + 3.82052i) q^{76} +(1.50817 + 1.20586i) q^{77} +(2.58251 + 2.51608i) q^{78} +10.9455 q^{79} +(2.16830 + 2.16830i) q^{80} +1.00000 q^{81} +0.249190 q^{82} +(1.01118 + 1.01118i) q^{83} +(-2.62949 + 0.292893i) q^{84} +(5.58251 + 5.58251i) q^{85} +(-5.58251 - 5.58251i) q^{86} +6.32541i q^{87} +0.729840i q^{88} +(1.10977 - 1.10977i) q^{89} -3.06644 q^{90} +(9.46619 - 1.17948i) q^{91} -6.97248 q^{92} +(-4.33660 + 4.33660i) q^{93} +2.00000i q^{94} +16.5681i q^{95} +(-0.707107 - 0.707107i) q^{96} +(-9.34336 - 9.34336i) q^{97} +(-3.73926 + 5.91760i) q^{98} +(-0.516075 - 0.516075i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{5} - 8 q^{9}+O(q^{10}) \) 8 * q - 4 * q^5 - 8 * q^9	\( 8 q - 4 q^{5} - 8 q^{9} + 4 q^{10} - 8 q^{12} + 16 q^{13} - 4 q^{14} - 4 q^{15} - 8 q^{16} + 4 q^{17} - 8 q^{19} - 4 q^{20} - 8 q^{21} - 12 q^{22} - 16 q^{26} - 8 q^{28} + 12 q^{29} - 8 q^{31} - 8 q^{34} - 24 q^{35} - 4 q^{37} - 4 q^{38} - 4 q^{39} + 12 q^{41} - 4 q^{42} + 4 q^{45} + 24 q^{46} + 32 q^{49} - 8 q^{50} - 4 q^{52} + 40 q^{53} - 4 q^{56} - 8 q^{57} + 4 q^{58} - 8 q^{59} + 4 q^{60} + 8 q^{62} - 12 q^{65} + 32 q^{67} - 28 q^{69} + 8 q^{70} - 12 q^{71} + 20 q^{73} + 20 q^{74} - 12 q^{75} - 8 q^{76} + 8 q^{77} - 4 q^{78} + 24 q^{79} + 4 q^{80} + 8 q^{81} + 40 q^{82} + 44 q^{83} + 20 q^{85} - 20 q^{86} + 16 q^{89} - 4 q^{90} - 28 q^{91} - 28 q^{92} - 8 q^{93} - 8 q^{97} - 16 q^{98}+O(q^{100}) \) 8 * q - 4 * q^5 - 8 * q^9 + 4 * q^10 - 8 * q^12 + 16 * q^13 - 4 * q^14 - 4 * q^15 - 8 * q^16 + 4 * q^17 - 8 * q^19 - 4 * q^20 - 8 * q^21 - 12 * q^22 - 16 * q^26 - 8 * q^28 + 12 * q^29 - 8 * q^31 - 8 * q^34 - 24 * q^35 - 4 * q^37 - 4 * q^38 - 4 * q^39 + 12 * q^41 - 4 * q^42 + 4 * q^45 + 24 * q^46 + 32 * q^49 - 8 * q^50 - 4 * q^52 + 40 * q^53 - 4 * q^56 - 8 * q^57 + 4 * q^58 - 8 * q^59 + 4 * q^60 + 8 * q^62 - 12 * q^65 + 32 * q^67 - 28 * q^69 + 8 * q^70 - 12 * q^71 + 20 * q^73 + 20 * q^74 - 12 * q^75 - 8 * q^76 + 8 * q^77 - 4 * q^78 + 24 * q^79 + 4 * q^80 + 8 * q^81 + 40 * q^82 + 44 * q^83 + 20 * q^85 - 20 * q^86 + 16 * q^89 - 4 * q^90 - 28 * q^91 - 28 * q^92 - 8 * q^93 - 8 * q^97 - 16 * q^98

Introduction

L-functions

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