LMFDB - Embedded newform 105.3.k.b.83.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(62,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("105.62");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.k (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:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			83.2
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	105.83
Dual form			105.3.k.b.62.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(2.70711 - 1.29289i) q^{3} -3.00000i q^{4} +(0.707107 + 4.94975i) q^{5} +(2.82843 + 1.00000i) q^{6} +7.00000i q^{7} +(4.94975 - 4.94975i) q^{8} +(5.65685 - 7.00000i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(2.70711 - 1.29289i) q^{3} -3.00000i q^{4} +(0.707107 + 4.94975i) q^{5} +(2.82843 + 1.00000i) q^{6} +7.00000i q^{7} +(4.94975 - 4.94975i) q^{8} +(5.65685 - 7.00000i) q^{9} +(-3.00000 + 4.00000i) q^{10} -9.89949i q^{11} +(-3.87868 - 8.12132i) q^{12} +(8.00000 - 8.00000i) q^{13} +(-4.94975 + 4.94975i) q^{14} +(8.31371 + 12.4853i) q^{15} -5.00000 q^{16} +(-18.3848 + 18.3848i) q^{17} +(8.94975 - 0.949747i) q^{18} -10.0000 q^{19} +(14.8492 - 2.12132i) q^{20} +(9.05025 + 18.9497i) q^{21} +(7.00000 - 7.00000i) q^{22} +(-24.0416 + 24.0416i) q^{23} +(7.00000 - 19.7990i) q^{24} +(-24.0000 + 7.00000i) q^{25} +11.3137 q^{26} +(6.26346 - 26.2635i) q^{27} +21.0000 q^{28} -4.24264 q^{29} +(-2.94975 + 14.7071i) q^{30} +14.0000i q^{31} +(-23.3345 - 23.3345i) q^{32} +(-12.7990 - 26.7990i) q^{33} -26.0000 q^{34} +(-34.6482 + 4.94975i) q^{35} +(-21.0000 - 16.9706i) q^{36} +(30.0000 - 30.0000i) q^{37} +(-7.07107 - 7.07107i) q^{38} +(11.3137 - 32.0000i) q^{39} +(28.0000 + 21.0000i) q^{40} -33.9411 q^{41} +(-7.00000 + 19.7990i) q^{42} +(36.0000 + 36.0000i) q^{43} -29.6985 q^{44} +(38.6482 + 23.0503i) q^{45} -34.0000 q^{46} +(-4.24264 + 4.24264i) q^{47} +(-13.5355 + 6.46447i) q^{48} -49.0000 q^{49} +(-21.9203 - 12.0208i) q^{50} +(-26.0000 + 73.5391i) q^{51} +(-24.0000 - 24.0000i) q^{52} +(70.7107 - 70.7107i) q^{53} +(23.0000 - 14.1421i) q^{54} +(49.0000 - 7.00000i) q^{55} +(34.6482 + 34.6482i) q^{56} +(-27.0711 + 12.9289i) q^{57} +(-3.00000 - 3.00000i) q^{58} +29.6985i q^{59} +(37.4558 - 24.9411i) q^{60} -14.0000i q^{61} +(-9.89949 + 9.89949i) q^{62} +(49.0000 + 39.5980i) q^{63} -13.0000i q^{64} +(45.2548 + 33.9411i) q^{65} +(9.89949 - 28.0000i) q^{66} +(32.0000 - 32.0000i) q^{67} +(55.1543 + 55.1543i) q^{68} +(-34.0000 + 96.1665i) q^{69} +(-28.0000 - 21.0000i) q^{70} -59.3970i q^{71} +(-6.64823 - 62.6482i) q^{72} +(39.0000 - 39.0000i) q^{73} +42.4264 q^{74} +(-55.9203 + 49.9792i) q^{75} +30.0000i q^{76} +69.2965 q^{77} +(30.6274 - 14.6274i) q^{78} +56.0000i q^{79} +(-3.53553 - 24.7487i) q^{80} +(-17.0000 - 79.1960i) q^{81} +(-24.0000 - 24.0000i) q^{82} +(-36.7696 - 36.7696i) q^{83} +(56.8492 - 27.1508i) q^{84} +(-104.000 - 78.0000i) q^{85} +50.9117i q^{86} +(-11.4853 + 5.48528i) q^{87} +(-49.0000 - 49.0000i) q^{88} +19.7990i q^{89} +(11.0294 + 43.6274i) q^{90} +(56.0000 + 56.0000i) q^{91} +(72.1249 + 72.1249i) q^{92} +(18.1005 + 37.8995i) q^{93} -6.00000 q^{94} +(-7.07107 - 49.4975i) q^{95} +(-93.3381 - 33.0000i) q^{96} +(113.000 + 113.000i) q^{97} +(-34.6482 - 34.6482i) q^{98} +(-69.2965 - 56.0000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{3}+O(q^{10}) $ 4 * q + 8 * q^3	$ 4 q + 8 q^{3} - 12 q^{10} - 24 q^{12} + 32 q^{13} - 12 q^{15} - 20 q^{16} + 16 q^{18} - 40 q^{19} + 56 q^{21} + 28 q^{22} + 28 q^{24} - 96 q^{25} - 40 q^{27} + 84 q^{28} + 8 q^{30} + 28 q^{33} - 104 q^{34} - 84 q^{36} + 120 q^{37} + 112 q^{40} - 28 q^{42} + 144 q^{43} + 16 q^{45} - 136 q^{46} - 40 q^{48} - 196 q^{49} - 104 q^{51} - 96 q^{52} + 92 q^{54} + 196 q^{55} - 80 q^{57} - 12 q^{58} + 48 q^{60} + 196 q^{63} + 128 q^{67} - 136 q^{69} - 112 q^{70} + 112 q^{72} + 156 q^{73} - 136 q^{75} + 32 q^{78} - 68 q^{81} - 96 q^{82} + 168 q^{84} - 416 q^{85} - 12 q^{87} - 196 q^{88} + 112 q^{90} + 224 q^{91} + 112 q^{93} - 24 q^{94} + 452 q^{97}+O(q^{100}) $ 4 * q + 8 * q^3 - 12 * q^10 - 24 * q^12 + 32 * q^13 - 12 * q^15 - 20 * q^16 + 16 * q^18 - 40 * q^19 + 56 * q^21 + 28 * q^22 + 28 * q^24 - 96 * q^25 - 40 * q^27 + 84 * q^28 + 8 * q^30 + 28 * q^33 - 104 * q^34 - 84 * q^36 + 120 * q^37 + 112 * q^40 - 28 * q^42 + 144 * q^43 + 16 * q^45 - 136 * q^46 - 40 * q^48 - 196 * q^49 - 104 * q^51 - 96 * q^52 + 92 * q^54 + 196 * q^55 - 80 * q^57 - 12 * q^58 + 48 * q^60 + 196 * q^63 + 128 * q^67 - 136 * q^69 - 112 * q^70 + 112 * q^72 + 156 * q^73 - 136 * q^75 + 32 * q^78 - 68 * q^81 - 96 * q^82 + 168 * q^84 - 416 * q^85 - 12 * q^87 - 196 * q^88 + 112 * q^90 + 224 * q^91 + 112 * q^93 - 24 * q^94 + 452 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.353553	+	0.353553i	0.861430	−	0.507877i	$-0.169569\pi$
$2$	0.707107	+	0.707107i	0.353553	+	0.353553i	−0.507877	+	0.861430i	$0.669569\pi$
$3$	2.70711	−	1.29289i	0.902369	−	0.430964i
$3$	2.70711	−	1.29289i	0.902369	−	0.430964i
$4$		−	3.00000i		−	0.750000i
$5$	0.707107	+	4.94975i	0.141421	+	0.989949i
$5$	0.707107	+	4.94975i	0.141421	+	0.989949i
$6$	2.82843	+	1.00000i	0.471405	+	0.166667i
$7$			7.00000i			1.00000i
$7$			7.00000i			1.00000i
$8$	4.94975	−	4.94975i	0.618718	−	0.618718i
$9$	5.65685	−	7.00000i	0.628539	−	0.777778i
$10$	−3.00000	+	4.00000i	−0.300000	+	0.400000i
$11$		−	9.89949i		−	0.899954i	−0.893040	−	0.449977i	$-0.851432\pi$
$11$		−	9.89949i		−	0.899954i	0.893040	−	0.449977i	$-0.148568\pi$
$12$	−3.87868	−	8.12132i	−0.323223	−	0.676777i
$13$	8.00000	−	8.00000i	0.615385	−	0.615385i	−0.328959	−	0.944344i	$-0.606698\pi$
$13$	8.00000	−	8.00000i	0.615385	−	0.615385i	0.944344	+	0.328959i	$0.106698\pi$
$14$	−4.94975	+	4.94975i	−0.353553	+	0.353553i
$15$	8.31371	+	12.4853i	0.554247	+	0.832352i
$16$	−5.00000			−0.312500
$17$	−18.3848	+	18.3848i	−1.08146	+	1.08146i	−0.0850836	+	0.996374i	$0.527116\pi$
$17$	−18.3848	+	18.3848i	−1.08146	+	1.08146i	−0.996374	+	0.0850836i	$0.972884\pi$
$18$	8.94975	−	0.949747i	0.497208	−	0.0527637i
$19$	−10.0000			−0.526316			−0.263158	−	0.964753i	$-0.584764\pi$
$19$	−10.0000			−0.526316			−0.263158	+	0.964753i	$0.584764\pi$
$20$	14.8492	−	2.12132i	0.742462	−	0.106066i
$21$	9.05025	+	18.9497i	0.430964	+	0.902369i
$22$	7.00000	−	7.00000i	0.318182	−	0.318182i
$23$	−24.0416	+	24.0416i	−1.04529	+	1.04529i	−0.0463637	+	0.998925i	$0.514763\pi$
$23$	−24.0416	+	24.0416i	−1.04529	+	1.04529i	−0.998925	+	0.0463637i	$0.985237\pi$
$24$	7.00000	−	19.7990i	0.291667	−	0.824958i
$25$	−24.0000	+	7.00000i	−0.960000	+	0.280000i
$26$	11.3137			0.435143
$27$	6.26346	−	26.2635i	0.231980	−	0.972721i
$28$	21.0000			0.750000
$29$	−4.24264			−0.146298			−0.0731490	−	0.997321i	$-0.523305\pi$
$29$	−4.24264			−0.146298			−0.0731490	+	0.997321i	$0.523305\pi$
$30$	−2.94975	+	14.7071i	−0.0983249	+	0.490237i
$31$			14.0000i			0.451613i	0.974172	+	0.225806i	$0.0725017\pi$
$31$			14.0000i			0.451613i	−0.974172	+	0.225806i	$0.927498\pi$
$32$	−23.3345	−	23.3345i	−0.729204	−	0.729204i
$33$	−12.7990	−	26.7990i	−0.387848	−	0.812091i
$34$	−26.0000			−0.764706
$35$	−34.6482	+	4.94975i	−0.989949	+	0.141421i
$36$	−21.0000	−	16.9706i	−0.583333	−	0.471405i
$37$	30.0000	−	30.0000i	0.810811	−	0.810811i	−0.173945	−	0.984755i	$-0.555651\pi$
$37$	30.0000	−	30.0000i	0.810811	−	0.810811i	0.984755	+	0.173945i	$0.0556514\pi$
$38$	−7.07107	−	7.07107i	−0.186081	−	0.186081i
$39$	11.3137	−	32.0000i	0.290095	−	0.820513i
$40$	28.0000	+	21.0000i	0.700000	+	0.525000i
$41$	−33.9411			−0.827832			−0.413916	−	0.910315i	$-0.635839\pi$
$41$	−33.9411			−0.827832			−0.413916	+	0.910315i	$0.635839\pi$
$42$	−7.00000	+	19.7990i	−0.166667	+	0.471405i
$43$	36.0000	+	36.0000i	0.837209	+	0.837209i	0.988491	−	0.151281i	$-0.0483400\pi$
$43$	36.0000	+	36.0000i	0.837209	+	0.837209i	−0.151281	+	0.988491i	$0.548340\pi$
$44$	−29.6985			−0.674966
$45$	38.6482	+	23.0503i	0.858850	+	0.512228i
$46$	−34.0000			−0.739130
$47$	−4.24264	+	4.24264i	−0.0902690	+	0.0902690i	−0.750799	−	0.660530i	$-0.770331\pi$
$47$	−4.24264	+	4.24264i	−0.0902690	+	0.0902690i	0.660530	+	0.750799i	$0.270331\pi$
$48$	−13.5355	+	6.46447i	−0.281990	+	0.134676i
$49$	−49.0000			−1.00000
$50$	−21.9203	−	12.0208i	−0.438406	−	0.240416i
$51$	−26.0000	+	73.5391i	−0.509804	+	1.44194i
$52$	−24.0000	−	24.0000i	−0.461538	−	0.461538i
$53$	70.7107	−	70.7107i	1.33416	−	1.33416i	0.432557	−	0.901606i	$-0.357611\pi$
$53$	70.7107	−	70.7107i	1.33416	−	1.33416i	0.901606	−	0.432557i	$-0.142389\pi$
$54$	23.0000	−	14.1421i	0.425926	−	0.261891i
$55$	49.0000	−	7.00000i	0.890909	−	0.127273i
$56$	34.6482	+	34.6482i	0.618718	+	0.618718i
$57$	−27.0711	+	12.9289i	−0.474931	+	0.226823i
$58$	−3.00000	−	3.00000i	−0.0517241	−	0.0517241i
$59$			29.6985i			0.503364i	0.967810	+	0.251682i	$0.0809837\pi$
$59$			29.6985i			0.503364i	−0.967810	+	0.251682i	$0.919016\pi$
$60$	37.4558	−	24.9411i	0.624264	−	0.415685i
$61$		−	14.0000i		−	0.229508i	−0.993394	−	0.114754i	$-0.963392\pi$
$61$		−	14.0000i		−	0.229508i	0.993394	−	0.114754i	$-0.0366080\pi$
$62$	−9.89949	+	9.89949i	−0.159669	+	0.159669i
$63$	49.0000	+	39.5980i	0.777778	+	0.628539i
$64$		−	13.0000i		−	0.203125i
$65$	45.2548	+	33.9411i	0.696228	+	0.522171i
$66$	9.89949	−	28.0000i	0.149992	−	0.424242i
$67$	32.0000	−	32.0000i	0.477612	−	0.477612i	−0.426755	−	0.904367i	$-0.640343\pi$
$67$	32.0000	−	32.0000i	0.477612	−	0.477612i	0.904367	+	0.426755i	$0.140343\pi$
$68$	55.1543	+	55.1543i	0.811093	+	0.811093i
$69$	−34.0000	+	96.1665i	−0.492754	+	1.39372i
$70$	−28.0000	−	21.0000i	−0.400000	−	0.300000i
$71$		−	59.3970i		−	0.836577i	−0.908314	−	0.418289i	$-0.862630\pi$
$71$		−	59.3970i		−	0.836577i	0.908314	−	0.418289i	$-0.137370\pi$
$72$	−6.64823	−	62.6482i	−0.0923366	−	0.870114i
$73$	39.0000	−	39.0000i	0.534247	−	0.534247i	−0.387587	−	0.921833i	$-0.626691\pi$
$73$	39.0000	−	39.0000i	0.534247	−	0.534247i	0.921833	+	0.387587i	$0.126691\pi$
$74$	42.4264			0.573330
$75$	−55.9203	+	49.9792i	−0.745604	+	0.666389i
$76$			30.0000i			0.394737i
$77$	69.2965			0.899954
$78$	30.6274	−	14.6274i	0.392659	−	0.187531i
$79$			56.0000i			0.708861i	0.935082	+	0.354430i	$0.115325\pi$
$79$			56.0000i			0.708861i	−0.935082	+	0.354430i	$0.884675\pi$
$80$	−3.53553	−	24.7487i	−0.0441942	−	0.309359i
$81$	−17.0000	−	79.1960i	−0.209877	−	0.977728i
$82$	−24.0000	−	24.0000i	−0.292683	−	0.292683i
$83$	−36.7696	−	36.7696i	−0.443007	−	0.443007i	0.450015	−	0.893021i	$-0.351419\pi$
$83$	−36.7696	−	36.7696i	−0.443007	−	0.443007i	−0.893021	+	0.450015i	$0.851419\pi$
$84$	56.8492	−	27.1508i	0.676777	−	0.323223i
$85$	−104.000	−	78.0000i	−1.22353	−	0.917647i
$86$			50.9117i			0.591996i
$87$	−11.4853	+	5.48528i	−0.132015	+	0.0630492i
$88$	−49.0000	−	49.0000i	−0.556818	−	0.556818i
$89$			19.7990i			0.222461i	0.993795	+	0.111230i	$0.0354791\pi$
$89$			19.7990i			0.222461i	−0.993795	+	0.111230i	$0.964521\pi$
$90$	11.0294	+	43.6274i	0.122549	+	0.484749i
$91$	56.0000	+	56.0000i	0.615385	+	0.615385i
$92$	72.1249	+	72.1249i	0.783966	+	0.783966i
$93$	18.1005	+	37.8995i	0.194629	+	0.407521i
$94$	−6.00000			−0.0638298
$95$	−7.07107	−	49.4975i	−0.0744323	−	0.521026i
$96$	−93.3381	−	33.0000i	−0.972272	−	0.343750i
$97$	113.000	+	113.000i	1.16495	+	1.16495i	0.983378	+	0.181571i	$0.0581181\pi$
$97$	113.000	+	113.000i	1.16495	+	1.16495i	0.181571	+	0.983378i	$0.441882\pi$
$98$	−34.6482	−	34.6482i	−0.353553	−	0.353553i
$99$	−69.2965	−	56.0000i	−0.699964	−	0.565657i
$100$	21.0000	+	72.0000i	0.210000	+	0.720000i
$101$	91.9239			0.910137			0.455069	−	0.890456i	$-0.349615\pi$
$101$	91.9239			0.910137			0.455069	+	0.890456i	$0.349615\pi$
$102$	−70.3848	+	33.6152i	−0.690047	+	0.329561i
$103$	−5.00000	+	5.00000i	−0.0485437	+	0.0485437i	−0.730962	−	0.682418i	$-0.760928\pi$
$103$	−5.00000	+	5.00000i	−0.0485437	+	0.0485437i	0.682418	+	0.730962i	$0.260928\pi$
$104$		−	79.1960i		−	0.761500i
$105$	−87.3970	+	58.1960i	−0.832352	+	0.554247i
$106$	100.000			0.943396
$107$	−4.24264	−	4.24264i	−0.0396508	−	0.0396508i	0.687003	−	0.726654i	$-0.258926\pi$
$107$	−4.24264	−	4.24264i	−0.0396508	−	0.0396508i	−0.726654	+	0.687003i	$0.758926\pi$
$108$	−78.7904	−	18.7904i	−0.729540	−	0.173985i
$109$			70.0000i			0.642202i	0.947045	+	0.321101i	$0.104053\pi$
$109$			70.0000i			0.642202i	−0.947045	+	0.321101i	$0.895947\pi$
$110$	39.5980	+	29.6985i	0.359982	+	0.269986i
$111$	42.4264	−	120.000i	0.382220	−	1.08108i
$112$		−	35.0000i		−	0.312500i
$113$	12.7279	−	12.7279i	0.112636	−	0.112636i	−0.648542	−	0.761179i	$-0.724621\pi$
$113$	12.7279	−	12.7279i	0.112636	−	0.112636i	0.761179	+	0.648542i	$0.224621\pi$
$114$	−28.2843	−	10.0000i	−0.248108	−	0.0877193i
$115$	−136.000	−	102.000i	−1.18261	−	0.886957i
$116$			12.7279i			0.109723i
$117$	−10.7452	−	101.255i	−0.0918390	−	0.865426i
$118$	−21.0000	+	21.0000i	−0.177966	+	0.177966i
$119$	−128.693	−	128.693i	−1.08146	−	1.08146i
$120$	102.950	+	20.6482i	0.857915	+	0.172069i
$121$	23.0000			0.190083
$122$	9.89949	−	9.89949i	0.0811434	−	0.0811434i
$123$	−91.8823	+	43.8823i	−0.747010	+	0.356766i
$124$	42.0000			0.338710
$125$	−51.6188	−	113.844i	−0.412950	−	0.910754i
$126$	6.64823	+	62.6482i	0.0527637	+	0.497208i
$127$	−111.000	+	111.000i	−0.874016	+	0.874016i	−0.992907	−	0.118892i	$-0.962066\pi$
$127$	−111.000	+	111.000i	−0.874016	+	0.874016i	0.118892	+	0.992907i	$0.462066\pi$
$128$	−84.1457	+	84.1457i	−0.657388	+	0.657388i
$129$	144.000	+	50.9117i	1.11628	+	0.394664i
$130$	8.00000	+	56.0000i	0.0615385	+	0.430769i
$131$	−38.1838			−0.291479			−0.145740	−	0.989323i	$-0.546556\pi$
$131$	−38.1838			−0.291479			−0.145740	+	0.989323i	$0.546556\pi$
$132$	−80.3970	+	38.3970i	−0.609068	+	0.290886i
$133$		−	70.0000i		−	0.526316i
$134$	45.2548			0.337723
$135$	134.426	+	12.4315i	0.995751	+	0.0920849i
$136$			182.000i			1.33824i
$137$	−18.3848	−	18.3848i	−0.134195	−	0.134195i	0.636818	−	0.771014i	$-0.280250\pi$
$137$	−18.3848	−	18.3848i	−0.134195	−	0.134195i	−0.771014	+	0.636818i	$0.780250\pi$
$138$	−92.0416	+	43.9584i	−0.666968	+	0.318539i
$139$	−138.000			−0.992806			−0.496403	−	0.868092i	$-0.665346\pi$
$139$	−138.000			−0.992806			−0.496403	+	0.868092i	$0.665346\pi$
$140$	14.8492	+	103.945i	0.106066	+	0.742462i
$141$	−6.00000	+	16.9706i	−0.0425532	+	0.120359i
$142$	42.0000	−	42.0000i	0.295775	−	0.295775i
$143$	−79.1960	−	79.1960i	−0.553818	−	0.553818i
$144$	−28.2843	+	35.0000i	−0.196419	+	0.243056i
$145$	−3.00000	−	21.0000i	−0.0206897	−	0.144828i
$146$	55.1543			0.377769
$147$	−132.648	+	63.3518i	−0.902369	+	0.430964i
$148$	−90.0000	−	90.0000i	−0.608108	−	0.608108i
$149$	199.404			1.33828			0.669141	−	0.743135i	$-0.266662\pi$
$149$	199.404			1.33828			0.669141	+	0.743135i	$0.266662\pi$
$150$	−74.8823	−	4.20101i	−0.499215	−	0.0280067i
$151$	78.0000			0.516556			0.258278	−	0.966071i	$-0.416845\pi$
$151$	78.0000			0.516556			0.258278	+	0.966071i	$0.416845\pi$
$152$	−49.4975	+	49.4975i	−0.325641	+	0.325641i
$153$	24.6934	+	232.693i	0.161395	+	1.52087i
$154$	49.0000	+	49.0000i	0.318182	+	0.318182i
$155$	−69.2965	+	9.89949i	−0.447074	+	0.0638677i
$156$	−96.0000	−	33.9411i	−0.615385	−	0.217571i
$157$	46.0000	+	46.0000i	0.292994	+	0.292994i	0.838262	−	0.545268i	$-0.183572\pi$
$157$	46.0000	+	46.0000i	0.292994	+	0.292994i	−0.545268	+	0.838262i	$0.683572\pi$
$158$	−39.5980	+	39.5980i	−0.250620	+	0.250620i
$159$	100.000	−	282.843i	0.628931	−	1.77888i
$160$	99.0000	−	132.000i	0.618750	−	0.825000i
$161$	−168.291	−	168.291i	−1.04529	−	1.04529i
$162$	43.9792	−	68.0208i	0.271476	−	0.419882i
$163$	−138.000	−	138.000i	−0.846626	−	0.846626i	0.143085	−	0.989710i	$-0.454298\pi$
$163$	−138.000	−	138.000i	−0.846626	−	0.846626i	−0.989710	+	0.143085i	$0.954298\pi$
$164$			101.823i			0.620874i
$165$	123.598	−	82.3015i	0.749079	−	0.498797i
$166$		−	52.0000i		−	0.313253i
$167$	91.9239	−	91.9239i	0.550442	−	0.550442i	−0.376126	−	0.926568i	$-0.622744\pi$
$167$	91.9239	−	91.9239i	0.550442	−	0.550442i	0.926568	+	0.376126i	$0.122744\pi$
$168$	138.593	+	49.0000i	0.824958	+	0.291667i
$169$			41.0000i			0.242604i
$170$	−18.3848	−	128.693i	−0.108146	−	0.757020i
$171$	−56.5685	+	70.0000i	−0.330810	+	0.409357i
$172$	108.000	−	108.000i	0.627907	−	0.627907i
$173$	223.446	+	223.446i	1.29159	+	1.29159i	0.933801	+	0.357793i	$0.116471\pi$
$173$	223.446	+	223.446i	1.29159	+	1.29159i	0.357793	+	0.933801i	$0.383529\pi$
$174$	−12.0000	−	4.24264i	−0.0689655	−	0.0243830i
$175$	−49.0000	−	168.000i	−0.280000	−	0.960000i
$176$			49.4975i			0.281236i
$177$	38.3970	+	80.3970i	0.216932	+	0.454220i
$178$	−14.0000	+	14.0000i	−0.0786517	+	0.0786517i
$179$	12.7279			0.0711057			0.0355529	−	0.999368i	$-0.488681\pi$
$179$	12.7279			0.0711057			0.0355529	+	0.999368i	$0.488681\pi$
$180$	69.1508	−	115.945i	0.384171	−	0.644137i
$181$		−	350.000i		−	1.93370i	−0.255342	−	0.966851i	$-0.582188\pi$
$181$		−	350.000i		−	1.93370i	0.255342	−	0.966851i	$-0.417812\pi$
$182$			79.1960i			0.435143i
$183$	−18.1005	−	37.8995i	−0.0989099	−	0.207101i
$184$			238.000i			1.29348i
$185$	169.706	+	127.279i	0.917328	+	0.687996i
$186$	−14.0000	+	39.5980i	−0.0752688	+	0.212892i
$187$	182.000	+	182.000i	0.973262	+	0.973262i
$188$	12.7279	+	12.7279i	0.0677017	+	0.0677017i
$189$	183.844	+	43.8442i	0.972721	+	0.231980i
$190$	30.0000	−	40.0000i	0.157895	−	0.210526i
$191$		−	118.794i		−	0.621958i	−0.950417	−	0.310979i	$-0.899343\pi$
$191$		−	118.794i		−	0.621958i	0.950417	−	0.310979i	$-0.100657\pi$
$192$	−16.8076	−	35.1924i	−0.0875396	−	0.183294i
$193$	67.0000	+	67.0000i	0.347150	+	0.347150i	0.859047	−	0.511897i	$-0.171057\pi$
$193$	67.0000	+	67.0000i	0.347150	+	0.347150i	−0.511897	+	0.859047i	$0.671057\pi$
$194$			159.806i			0.823743i
$195$	166.392	+	33.3726i	0.853292	+	0.171141i
$196$			147.000i			0.750000i
$197$	−56.5685	−	56.5685i	−0.287150	−	0.287150i	0.548802	−	0.835952i	$-0.315084\pi$
$197$	−56.5685	−	56.5685i	−0.287150	−	0.287150i	−0.835952	+	0.548802i	$0.815084\pi$
$198$	−9.40202	−	88.5980i	−0.0474850	−	0.447465i
$199$	120.000			0.603015			0.301508	−	0.953464i	$-0.402510\pi$
$199$	120.000			0.603015			0.301508	+	0.953464i	$0.402510\pi$
$200$	−84.1457	+	153.442i	−0.420729	+	0.767211i
$201$	45.2548	−	128.000i	0.225148	−	0.636816i
$202$	65.0000	+	65.0000i	0.321782	+	0.321782i
$203$		−	29.6985i		−	0.146298i
$204$	220.617	+	78.0000i	1.08146	+	0.382353i
$205$	−24.0000	−	168.000i	−0.117073	−	0.819512i
$206$	−7.07107			−0.0343256
$207$	32.2914	+	304.291i	0.155997	+	1.47001i
$208$	−40.0000	+	40.0000i	−0.192308	+	0.192308i
$209$			98.9949i			0.473660i
$210$	−102.950	−	20.6482i	−0.490237	−	0.0983249i
$211$	86.0000			0.407583			0.203791	−	0.979014i	$-0.434674\pi$
$211$	86.0000			0.407583			0.203791	+	0.979014i	$0.434674\pi$
$212$	−212.132	−	212.132i	−1.00062	−	1.00062i
$213$	−76.7939	−	160.794i	−0.360535	−	0.754901i
$214$		−	6.00000i		−	0.0280374i
$215$	−152.735	+	203.647i	−0.710396	+	0.947194i
$216$	−98.9949	−	161.000i	−0.458310	−	0.745370i
$217$	−98.0000			−0.451613
$218$	−49.4975	+	49.4975i	−0.227053	+	0.227053i
$219$	55.1543	−	156.000i	0.251846	−	0.712329i
$220$	−21.0000	−	147.000i	−0.0954545	−	0.668182i
$221$			294.156i			1.33102i
$222$	114.853	−	54.8528i	0.517355	−	0.247085i
$223$	−237.000	+	237.000i	−1.06278	+	1.06278i	−0.0648877	+	0.997893i	$0.520669\pi$
$223$	−237.000	+	237.000i	−1.06278	+	1.06278i	−0.997893	+	0.0648877i	$0.979331\pi$
$224$	163.342	−	163.342i	0.729204	−	0.729204i
$225$	−86.7645	+	207.598i	−0.385620	+	0.922658i
$226$	18.0000			0.0796460
$227$	−117.380	+	117.380i	−0.517091	+	0.517091i	−0.916690	−	0.399599i	$-0.869149\pi$
$227$	−117.380	+	117.380i	−0.517091	+	0.517091i	0.399599	+	0.916690i	$0.369149\pi$
$228$	38.7868	+	81.2132i	0.170118	+	0.356198i
$229$	−374.000			−1.63319			−0.816594	−	0.577213i	$-0.804140\pi$
$229$	−374.000			−1.63319			−0.816594	+	0.577213i	$0.804140\pi$
$230$	−24.0416	−	168.291i	−0.104529	−	0.731702i
$231$	187.593	−	89.5929i	0.812091	−	0.387848i
$232$	−21.0000	+	21.0000i	−0.0905172	+	0.0905172i
$233$	173.948	−	173.948i	0.746559	−	0.746559i	−0.227272	−	0.973831i	$-0.572981\pi$
$233$	173.948	−	173.948i	0.746559	−	0.746559i	0.973831	+	0.227272i	$0.0729807\pi$
$234$	64.0000	−	79.1960i	0.273504	−	0.338444i
$235$	−24.0000	−	18.0000i	−0.102128	−	0.0765957i
$236$	89.0955			0.377523
$237$	72.4020	+	151.598i	0.305494	+	0.639654i
$238$		−	182.000i		−	0.764706i
$239$	−291.328			−1.21895			−0.609473	−	0.792807i	$-0.708619\pi$
$239$	−291.328			−1.21895			−0.609473	+	0.792807i	$0.708619\pi$
$240$	−41.5685	−	62.4264i	−0.173202	−	0.260110i
$241$		−	14.0000i		−	0.0580913i	−0.999578	−	0.0290456i	$-0.990753\pi$
$241$		−	14.0000i		−	0.0580913i	0.999578	−	0.0290456i	$-0.00924682\pi$
$242$	16.2635	+	16.2635i	0.0672044	+	0.0672044i
$243$	−148.413	−	192.413i	−0.610752	−	0.791822i
$244$	−42.0000			−0.172131
$245$	−34.6482	−	242.538i	−0.141421	−	0.989949i
$246$	−96.0000	−	33.9411i	−0.390244	−	0.137972i
$247$	−80.0000	+	80.0000i	−0.323887	+	0.323887i
$248$	69.2965	+	69.2965i	0.279421	+	0.279421i
$249$	−147.078	−	52.0000i	−0.590676	−	0.208835i
$250$	44.0000	−	117.000i	0.176000	−	0.468000i
$251$	−439.820			−1.75227			−0.876136	−	0.482063i	$-0.839887\pi$
$251$	−439.820			−1.75227			−0.876136	+	0.482063i	$0.839887\pi$
$252$	118.794	−	147.000i	0.471405	−	0.583333i
$253$	238.000	+	238.000i	0.940711	+	0.940711i
$254$	−156.978			−0.618022
$255$	−382.385	−	76.6934i	−1.49955	−	0.300759i
$256$	−171.000			−0.667969
$257$	35.3553	−	35.3553i	0.137569	−	0.137569i	−0.634969	−	0.772538i	$-0.718987\pi$
$257$	35.3553	−	35.3553i	0.137569	−	0.137569i	0.772538	+	0.634969i	$0.218987\pi$
$258$	65.8234	+	137.823i	0.255129	+	0.534199i
$259$	210.000	+	210.000i	0.810811	+	0.810811i
$260$	101.823	−	135.765i	0.391628	−	0.522171i
$261$	−24.0000	+	29.6985i	−0.0919540	+	0.113787i
$262$	−27.0000	−	27.0000i	−0.103053	−	0.103053i
$263$	−315.370	+	315.370i	−1.19912	+	1.19912i	−0.224695	+	0.974429i	$0.572139\pi$
$263$	−315.370	+	315.370i	−1.19912	+	1.19912i	−0.974429	+	0.224695i	$0.927861\pi$
$264$	−196.000	−	69.2965i	−0.742424	−	0.262487i
$265$	400.000	+	300.000i	1.50943	+	1.13208i
$266$	49.4975	−	49.4975i	0.186081	−	0.186081i
$267$	25.5980	+	53.5980i	0.0958726	+	0.200741i
$268$	−96.0000	−	96.0000i	−0.358209	−	0.358209i
$269$		−	267.286i		−	0.993630i	−0.867857	−	0.496815i	$-0.834503\pi$
$269$		−	267.286i		−	0.993630i	0.867857	−	0.496815i	$-0.165497\pi$
$270$	86.2635	+	103.844i	0.319494	+	0.384608i
$271$			112.000i			0.413284i	0.978417	+	0.206642i	$0.0662536\pi$
$271$			112.000i			0.413284i	−0.978417	+	0.206642i	$0.933746\pi$
$272$	91.9239	−	91.9239i	0.337955	−	0.337955i
$273$	224.000	+	79.1960i	0.820513	+	0.290095i
$274$		−	26.0000i		−	0.0948905i
$275$	69.2965	+	237.588i	0.251987	+	0.863956i
$276$	288.500	+	102.000i	1.04529	+	0.369565i
$277$	102.000	−	102.000i	0.368231	−	0.368231i	−0.498601	−	0.866832i	$-0.666153\pi$
$277$	102.000	−	102.000i	0.368231	−	0.368231i	0.866832	+	0.498601i	$0.166153\pi$
$278$	−97.5807	−	97.5807i	−0.351010	−	0.351010i
$279$	98.0000	+	79.1960i	0.351254	+	0.283856i
$280$	−147.000	+	196.000i	−0.525000	+	0.700000i
$281$			296.985i			1.05689i	0.848969	+	0.528443i	$0.177224\pi$
$281$			296.985i			1.05689i	−0.848969	+	0.528443i	$0.822776\pi$
$282$	−16.2426	+	7.75736i	−0.0575980	+	0.0275084i
$283$	102.000	−	102.000i	0.360424	−	0.360424i	−0.503545	−	0.863969i	$-0.667971\pi$
$283$	102.000	−	102.000i	0.360424	−	0.360424i	0.863969	+	0.503545i	$0.167971\pi$
$284$	−178.191			−0.627433
$285$	−83.1371	−	124.853i	−0.291709	−	0.438080i
$286$		−	112.000i		−	0.391608i
$287$		−	237.588i		−	0.827832i
$288$	−295.342	+	31.3417i	−1.02549	+	0.108825i
$289$		−	387.000i		−	1.33910i
$290$	12.7279	−	16.9706i	0.0438894	−	0.0585192i
$291$	452.000	+	159.806i	1.55326	+	0.549162i
$292$	−117.000	−	117.000i	−0.400685	−	0.400685i
$293$	−185.262	−	185.262i	−0.632293	−	0.632293i	0.316349	−	0.948643i	$-0.397543\pi$
$293$	−185.262	−	185.262i	−0.632293	−	0.632293i	−0.948643	+	0.316349i	$0.897543\pi$
$294$	−138.593	−	49.0000i	−0.471405	−	0.166667i
$295$	−147.000	+	21.0000i	−0.498305	+	0.0711864i
$296$		−	296.985i		−	1.00333i
$297$	−259.995	−	62.0051i	−0.875404	−	0.208771i
$298$	141.000	+	141.000i	0.473154	+	0.473154i
$299$			384.666i			1.28651i
$300$	149.938	+	167.761i	0.499792	+	0.559203i
$301$	−252.000	+	252.000i	−0.837209	+	0.837209i
$302$	55.1543	+	55.1543i	0.182630	+	0.182630i
$303$	248.848	−	118.848i	0.821280	−	0.392237i
$304$	50.0000			0.164474
$305$	69.2965	−	9.89949i	0.227202	−	0.0324574i
$306$	−147.078	+	182.000i	−0.480648	+	0.594771i
$307$	−90.0000	−	90.0000i	−0.293160	−	0.293160i	0.545168	−	0.838327i	$-0.316466\pi$
$307$	−90.0000	−	90.0000i	−0.293160	−	0.293160i	−0.838327	+	0.545168i	$0.816466\pi$
$308$		−	207.889i		−	0.674966i
$309$	−7.07107	+	20.0000i	−0.0228837	+	0.0647249i
$310$	−56.0000	−	42.0000i	−0.180645	−	0.135484i
$311$	299.813			0.964030			0.482015	−	0.876163i	$-0.339905\pi$
$311$	299.813			0.964030			0.482015	+	0.876163i	$0.339905\pi$
$312$	−102.392	−	214.392i	−0.328179	−	0.687154i
$313$	177.000	−	177.000i	0.565495	−	0.565495i	−0.365368	−	0.930863i	$-0.619057\pi$
$313$	177.000	−	177.000i	0.565495	−	0.565495i	0.930863	+	0.365368i	$0.119057\pi$
$314$			65.0538i			0.207178i
$315$	−161.352	+	270.538i	−0.512228	+	0.858850i
$316$	168.000			0.531646
$317$	213.546	+	213.546i	0.673647	+	0.673647i	0.958555	−	0.284908i	$-0.0919629\pi$
$317$	213.546	+	213.546i	0.673647	+	0.673647i	−0.284908	+	0.958555i	$0.591963\pi$
$318$	270.711	−	129.289i	0.851291	−	0.406570i
$319$			42.0000i			0.131661i
$320$	64.3467	−	9.19239i	0.201083	−	0.0287262i
$321$	−16.9706	−	6.00000i	−0.0528678	−	0.0186916i
$322$		−	238.000i		−	0.739130i
$323$	183.848	−	183.848i	0.569188	−	0.569188i
$324$	−237.588	+	51.0000i	−0.733296	+	0.157407i
$325$	−136.000	+	248.000i	−0.418462	+	0.763077i
$326$		−	195.161i		−	0.598655i
$327$	90.5025	+	189.497i	0.276766	+	0.579503i
$328$	−168.000	+	168.000i	−0.512195	+	0.512195i
$329$	−29.6985	−	29.6985i	−0.0902690	−	0.0902690i
$330$	145.593	+	29.2010i	0.441191	+	0.0884879i
$331$	102.000			0.308157			0.154079	−	0.988059i	$-0.450759\pi$
$331$	102.000			0.308157			0.154079	+	0.988059i	$0.450759\pi$
$332$	−110.309	+	110.309i	−0.332255	+	0.332255i
$333$	−40.2944	−	379.706i	−0.121004	−	1.14026i
$334$	130.000			0.389222
$335$	181.019	+	135.765i	0.540356	+	0.405267i
$336$	−45.2513	−	94.7487i	−0.134676	−	0.281990i
$337$	253.000	−	253.000i	0.750742	−	0.750742i	−0.223876	−	0.974618i	$-0.571871\pi$
$337$	253.000	−	253.000i	0.750742	−	0.750742i	0.974618	+	0.223876i	$0.0718710\pi$
$338$	−28.9914	+	28.9914i	−0.0857733	+	0.0857733i
$339$	18.0000	−	50.9117i	0.0530973	−	0.150182i
$340$	−234.000	+	312.000i	−0.688235	+	0.917647i
$341$	138.593			0.406431
$342$	−89.4975	+	9.49747i	−0.261689	+	0.0277704i
$343$		−	343.000i		−	1.00000i
$344$	356.382			1.03599
$345$	−500.042	−	100.291i	−1.44940	−	0.290700i
$346$			316.000i			0.913295i
$347$	169.706	+	169.706i	0.489065	+	0.489065i	0.908011	−	0.418946i	$-0.137600\pi$
$347$	169.706	+	169.706i	0.489065	+	0.489065i	−0.418946	+	0.908011i	$0.637600\pi$
$348$	16.4558	+	34.4558i	0.0472869	+	0.0990110i
$349$	−446.000			−1.27794			−0.638968	−	0.769233i	$-0.720639\pi$
$349$	−446.000			−1.27794			−0.638968	+	0.769233i	$0.720639\pi$
$350$	84.1457	−	153.442i	0.240416	−	0.438406i
$351$	−160.000	−	260.215i	−0.455840	−	0.741354i
$352$	−231.000	+	231.000i	−0.656250	+	0.656250i
$353$	−97.5807	−	97.5807i	−0.276433	−	0.276433i	0.555250	−	0.831683i	$-0.312622\pi$
$353$	−97.5807	−	97.5807i	−0.276433	−	0.276433i	−0.831683	+	0.555250i	$0.812622\pi$
$354$	−29.6985	+	84.0000i	−0.0838940	+	0.237288i
$355$	294.000	−	42.0000i	0.828169	−	0.118310i
$356$	59.3970			0.166845
$357$	−514.774	−	182.000i	−1.44194	−	0.509804i
$358$	9.00000	+	9.00000i	0.0251397	+	0.0251397i
$359$	248.902			0.693319			0.346660	−	0.937991i	$-0.387316\pi$
$359$	248.902			0.693319			0.346660	+	0.937991i	$0.387316\pi$
$360$	305.392	−	77.2061i	0.848311	−	0.214461i
$361$	−261.000			−0.722992
$362$	247.487	−	247.487i	0.683667	−	0.683667i
$363$	62.2635	−	29.7365i	0.171525	−	0.0819189i
$364$	168.000	−	168.000i	0.461538	−	0.461538i
$365$	220.617	+	165.463i	0.604431	+	0.453323i
$366$	14.0000	−	39.5980i	0.0382514	−	0.108191i
$367$	−185.000	−	185.000i	−0.504087	−	0.504087i	0.408618	−	0.912705i	$-0.366011\pi$
$367$	−185.000	−	185.000i	−0.504087	−	0.504087i	−0.912705	+	0.408618i	$0.866011\pi$
$368$	120.208	−	120.208i	0.326653	−	0.326653i
$369$	−192.000	+	237.588i	−0.520325	+	0.643870i
$370$	30.0000	+	210.000i	0.0810811	+	0.567568i
$371$	494.975	+	494.975i	1.33416	+	1.33416i
$372$	113.698	−	54.3015i	0.305641	−	0.145972i
$373$	492.000	+	492.000i	1.31903	+	1.31903i	0.914540	+	0.404494i	$0.132552\pi$
$373$	492.000	+	492.000i	1.31903	+	1.31903i	0.404494	+	0.914540i	$0.367448\pi$
$374$			257.387i			0.688200i
$375$	−286.926	−	241.451i	−0.765136	−	0.643869i
$376$			42.0000i			0.111702i
$377$	−33.9411	+	33.9411i	−0.0900295	+	0.0900295i
$378$	98.9949	+	161.000i	0.261891	+	0.425926i
$379$		−	266.000i		−	0.701847i	−0.936404	−	0.350923i	$-0.885868\pi$
$379$		−	266.000i		−	0.701847i	0.936404	−	0.350923i	$-0.114132\pi$
$380$	−148.492	+	21.2132i	−0.390770	+	0.0558242i
$381$	−156.978	+	444.000i	−0.412015	+	1.16535i
$382$	84.0000	−	84.0000i	0.219895	−	0.219895i
$383$	134.350	+	134.350i	0.350784	+	0.350784i	0.860401	−	0.509617i	$-0.170213\pi$
$383$	134.350	+	134.350i	0.350784	+	0.350784i	−0.509617	+	0.860401i	$0.670213\pi$
$384$	−119.000	+	336.583i	−0.309896	+	0.876518i
$385$	49.0000	+	343.000i	0.127273	+	0.890909i
$386$			94.7523i			0.245472i
$387$	455.647	−	48.3532i	1.17738	−	0.124944i
$388$	339.000	−	339.000i	0.873711	−	0.873711i
$389$	329.512			0.847074			0.423537	−	0.905879i	$-0.360788\pi$
$389$	329.512			0.847074			0.423537	+	0.905879i	$0.360788\pi$
$390$	94.0589	+	141.255i	0.241177	+	0.362192i
$391$		−	884.000i		−	2.26087i
$392$	−242.538	+	242.538i	−0.618718	+	0.618718i
$393$	−103.368	+	49.3675i	−0.263022	+	0.125617i
$394$		−	80.0000i		−	0.203046i
$395$	−277.186	+	39.5980i	−0.701736	+	0.100248i
$396$	−168.000	+	207.889i	−0.424242	+	0.524973i
$397$	30.0000	+	30.0000i	0.0755668	+	0.0755668i	0.743880	−	0.668313i	$-0.232983\pi$
$397$	30.0000	+	30.0000i	0.0755668	+	0.0755668i	−0.668313	+	0.743880i	$0.732983\pi$
$398$	84.8528	+	84.8528i	0.213198	+	0.213198i
$399$	−90.5025	−	189.497i	−0.226823	−	0.474931i
$400$	120.000	−	35.0000i	0.300000	−	0.0875000i
$401$			79.1960i			0.197496i	0.995112	+	0.0987481i	$0.0314838\pi$
$401$			79.1960i			0.197496i	−0.995112	+	0.0987481i	$0.968516\pi$
$402$	122.510	−	58.5097i	0.304750	−	0.145546i
$403$	112.000	+	112.000i	0.277916	+	0.277916i
$404$		−	275.772i		−	0.682603i
$405$	379.979	−	140.146i	0.938220	−	0.346039i
$406$	21.0000	−	21.0000i	0.0517241	−	0.0517241i
$407$	−296.985	−	296.985i	−0.729693	−	0.729693i
$408$	235.307	+	492.693i	0.576732	+	1.20758i
$409$	302.000			0.738386			0.369193	−	0.929353i	$-0.379634\pi$
$409$	302.000			0.738386			0.369193	+	0.929353i	$0.379634\pi$
$410$	101.823	−	135.765i	0.248350	−	0.331133i
$411$	−73.5391	−	26.0000i	−0.178927	−	0.0632603i
$412$	15.0000	+	15.0000i	0.0364078	+	0.0364078i
$413$	−207.889			−0.503364
$414$	−192.333	+	238.000i	−0.464573	+	0.574879i
$415$	156.000	−	208.000i	0.375904	−	0.501205i
$416$	−373.352			−0.897482
$417$	−373.581	+	178.419i	−0.895877	+	0.427864i
$418$	−70.0000	+	70.0000i	−0.167464	+	0.167464i
$419$		−	366.281i		−	0.874180i	−0.899418	−	0.437090i	$-0.856009\pi$
$419$		−	366.281i		−	0.874180i	0.899418	−	0.437090i	$-0.143991\pi$
$420$	174.588	+	262.191i	0.415685	+	0.624264i
$421$	−614.000			−1.45843			−0.729216	−	0.684283i	$-0.760115\pi$
$421$	−614.000			−1.45843			−0.729216	+	0.684283i	$0.760115\pi$
$422$	60.8112	+	60.8112i	0.144102	+	0.144102i
$423$	5.69848	+	53.6985i	0.0134716	+	0.126947i
$424$		−	700.000i		−	1.65094i
$425$	312.541	−	569.928i	0.735391	−	1.34101i
$426$	59.3970	−	168.000i	0.139430	−	0.394366i
$427$	98.0000			0.229508
$428$	−12.7279	+	12.7279i	−0.0297381	+	0.0297381i
$429$	−316.784	−	112.000i	−0.738424	−	0.261072i
$430$	−252.000	+	36.0000i	−0.586047	+	0.0837209i
$431$		−	554.372i		−	1.28625i	−0.765763	−	0.643123i	$-0.777639\pi$
$431$		−	554.372i		−	1.28625i	0.765763	−	0.643123i	$-0.222361\pi$
$432$	−31.3173	+	131.317i	−0.0724937	+	0.303975i
$433$	−153.000	+	153.000i	−0.353349	+	0.353349i	−0.861354	−	0.508005i	$-0.830383\pi$
$433$	−153.000	+	153.000i	−0.353349	+	0.353349i	0.508005	+	0.861354i	$0.330383\pi$
$434$	−69.2965	−	69.2965i	−0.159669	−	0.159669i
$435$	−35.2721	−	52.9706i	−0.0810852	−	0.121771i
$436$	210.000			0.481651
$437$	240.416	−	240.416i	0.550152	−	0.550152i
$438$	149.309	−	71.3087i	0.340887	−	0.162805i
$439$	−248.000			−0.564920			−0.282460	−	0.959279i	$-0.591150\pi$
$439$	−248.000			−0.564920			−0.282460	+	0.959279i	$0.591150\pi$
$440$	207.889	−	277.186i	0.472476	−	0.629968i
$441$	−277.186	+	343.000i	−0.628539	+	0.777778i
$442$	−208.000	+	208.000i	−0.470588	+	0.470588i
$443$	−14.1421	+	14.1421i	−0.0319236	+	0.0319236i	−0.722888	−	0.690965i	$-0.757186\pi$
$443$	−14.1421	+	14.1421i	−0.0319236	+	0.0319236i	0.690965	+	0.722888i	$0.257186\pi$
$444$	−360.000	−	127.279i	−0.810811	−	0.286665i
$445$	−98.0000	+	14.0000i	−0.220225	+	0.0314607i
$446$	−335.169			−0.751499
$447$	539.808	−	257.808i	1.20762	−	0.576752i
$448$	91.0000			0.203125
$449$	−647.710			−1.44256			−0.721280	−	0.692643i	$-0.756446\pi$
$449$	−647.710			−1.44256			−0.721280	+	0.692643i	$0.756446\pi$
$450$	−208.146	+	85.4422i	−0.462546	+	0.189871i
$451$			336.000i			0.745011i
$452$	−38.1838	−	38.1838i	−0.0844774	−	0.0844774i
$453$	211.154	−	100.846i	0.466124	−	0.222617i
$454$	−166.000			−0.365639
$455$	−237.588	+	316.784i	−0.522171	+	0.696228i
$456$	−70.0000	+	197.990i	−0.153509	+	0.434188i
$457$	−313.000	+	313.000i	−0.684902	+	0.684902i	−0.961100	−	0.276199i	$-0.910925\pi$
$457$	−313.000	+	313.000i	−0.684902	+	0.684902i	0.276199	+	0.961100i	$0.410925\pi$
$458$	−264.458	−	264.458i	−0.577419	−	0.577419i
$459$	367.696	+	598.000i	0.801080	+	1.30283i
$460$	−306.000	+	408.000i	−0.665217	+	0.886957i
$461$	−142.836			−0.309839			−0.154919	−	0.987927i	$-0.549512\pi$
$461$	−142.836			−0.309839			−0.154919	+	0.987927i	$0.549512\pi$
$462$	196.000	+	69.2965i	0.424242	+	0.149992i
$463$	29.0000	+	29.0000i	0.0626350	+	0.0626350i	0.737730	−	0.675095i	$-0.235898\pi$
$463$	29.0000	+	29.0000i	0.0626350	+	0.0626350i	−0.675095	+	0.737730i	$0.735898\pi$
$464$	21.2132			0.0457181
$465$	−174.794	+	116.392i	−0.375901	+	0.250305i
$466$	246.000			0.527897
$467$	−350.725	+	350.725i	−0.751017	+	0.751017i	−0.974669	−	0.223652i	$-0.928202\pi$
$467$	−350.725	+	350.725i	−0.751017	+	0.751017i	0.223652	+	0.974669i	$0.428202\pi$
$468$	−303.765	+	32.2355i	−0.649069	+	0.0688793i
$469$	224.000	+	224.000i	0.477612	+	0.477612i
$470$	−4.24264	−	29.6985i	−0.00902690	−	0.0631883i
$471$	184.000	+	65.0538i	0.390658	+	0.138119i
$472$	147.000	+	147.000i	0.311441	+	0.311441i
$473$	356.382	−	356.382i	0.753450	−	0.753450i
$474$	−56.0000	+	158.392i	−0.118143	+	0.334160i
$475$	240.000	−	70.0000i	0.505263	−	0.147368i
$476$	−386.080	+	386.080i	−0.811093	+	0.811093i
$477$	−94.9747	−	894.975i	−0.199108	−	1.87626i
$478$	−206.000	−	206.000i	−0.430962	−	0.430962i
$479$			79.1960i			0.165336i	0.996577	+	0.0826680i	$0.0263441\pi$
$479$			79.1960i			0.165336i	−0.996577	+	0.0826680i	$0.973656\pi$
$480$	97.3417	−	485.335i	0.202795	−	1.01111i
$481$		−	480.000i		−	0.997921i
$482$	9.89949	−	9.89949i	0.0205384	−	0.0205384i
$483$	−673.166	−	238.000i	−1.39372	−	0.492754i
$484$		−	69.0000i		−	0.142562i
$485$	−479.418	+	639.225i	−0.988492	+	1.31799i
$486$	31.1127	−	241.000i	0.0640179	−	0.495885i
$487$	−101.000	+	101.000i	−0.207392	+	0.207392i	−0.803158	−	0.595766i	$-0.796849\pi$
$487$	−101.000	+	101.000i	−0.207392	+	0.207392i	0.595766	+	0.803158i	$0.296849\pi$
$488$	−69.2965	−	69.2965i	−0.142001	−	0.142001i
$489$	−552.000	−	195.161i	−1.12883	−	0.399103i
$490$	147.000	−	196.000i	0.300000	−	0.400000i
$491$		−	346.482i		−	0.705667i	−0.935686	−	0.352833i	$-0.885218\pi$
$491$		−	346.482i		−	0.705667i	0.935686	−	0.352833i	$-0.114782\pi$
$492$	131.647	+	275.647i	0.267575	+	0.560258i
$493$	78.0000	−	78.0000i	0.158215	−	0.158215i
$494$	−113.137			−0.229022
$495$	228.186	−	382.598i	0.460982	−	0.772925i
$496$		−	70.0000i		−	0.141129i
$497$	415.779			0.836577
$498$	−67.2304	−	140.770i	−0.135001	−	0.282670i
$499$			602.000i			1.20641i	0.797585	+	0.603206i	$0.206110\pi$
$499$			602.000i			1.20641i	−0.797585	+	0.603206i	$0.793890\pi$
$500$	−341.533	+	154.856i	−0.683065	+	0.309713i
$501$	130.000	−	367.696i	0.259481	−	0.733923i
$502$	−311.000	−	311.000i	−0.619522	−	0.619522i
$503$	626.497	+	626.497i	1.24552	+	1.24552i	0.957678	+	0.287842i	$0.0929379\pi$
$503$	626.497	+	626.497i	1.24552	+	1.24552i	0.287842	+	0.957678i	$0.407062\pi$
$504$	438.538	−	46.5376i	0.870114	−	0.0923366i
$505$	65.0000	+	455.000i	0.128713	+	0.900990i
$506$			336.583i			0.665183i
$507$	53.0086	+	110.991i	0.104553	+	0.218918i
$508$	333.000	+	333.000i	0.655512	+	0.655512i
$509$		−	386.080i		−	0.758507i	−0.925293	−	0.379254i	$-0.876181\pi$
$509$		−	386.080i		−	0.758507i	0.925293	−	0.379254i	$-0.123819\pi$
$510$	−216.156	−	324.617i	−0.423836	−	0.636505i
$511$	273.000	+	273.000i	0.534247	+	0.534247i
$512$	215.668	+	215.668i	0.421226	+	0.421226i
$513$	−62.6346	+	262.635i	−0.122095	+	0.511958i
$514$	50.0000			0.0972763
$515$	−28.2843	−	21.2132i	−0.0549209	−	0.0411907i
$516$	152.735	−	432.000i	0.295998	−	0.837209i
$517$	42.0000	+	42.0000i	0.0812379	+	0.0812379i
$518$			296.985i			0.573330i
$519$	893.783	+	316.000i	1.72213	+	0.608863i
$520$	392.000	−	56.0000i	0.753846	−	0.107692i
$521$	379.009			0.727465			0.363732	−	0.931503i	$-0.381502\pi$
$521$	379.009			0.727465			0.363732	+	0.931503i	$0.381502\pi$
$522$	−37.9706	+	4.02944i	−0.0727405	+	0.00771923i
$523$	−642.000	+	642.000i	−1.22753	+	1.22753i	−0.262639	+	0.964894i	$0.584593\pi$
$523$	−642.000	+	642.000i	−1.22753	+	1.22753i	−0.964894	+	0.262639i	$0.915407\pi$
$524$			114.551i			0.218609i
$525$	−349.854	−	391.442i	−0.666389	−	0.745604i
$526$	−446.000			−0.847909
$527$	−257.387	−	257.387i	−0.488400	−	0.488400i
$528$	63.9949	+	133.995i	0.121203	+	0.253778i
$529$		−	627.000i		−	1.18526i
$530$	70.7107	+	494.975i	0.133416	+	0.933915i
$531$	207.889	+	168.000i	0.391505	+	0.316384i
$532$	−210.000			−0.394737
$533$	−271.529	+	271.529i	−0.509435	+	0.509435i
$534$	−19.7990	+	56.0000i	−0.0370768	+	0.104869i
$535$	18.0000	−	24.0000i	0.0336449	−	0.0448598i
$536$		−	316.784i		−	0.591015i
$537$	34.4558	−	16.4558i	0.0641636	−	0.0306440i
$538$	189.000	−	189.000i	0.351301	−	0.351301i
$539$			485.075i			0.899954i
$540$	37.2944	−	403.279i	0.0690637	−	0.746813i
$541$	270.000			0.499076			0.249538	−	0.968365i	$-0.419721\pi$
$541$	270.000			0.499076			0.249538	+	0.968365i	$0.419721\pi$
$542$	−79.1960	+	79.1960i	−0.146118	+	0.146118i
$543$	−452.513	−	947.487i	−0.833357	−	1.74491i
$544$	858.000			1.57721
$545$	−346.482	+	49.4975i	−0.635747	+	0.0908211i
$546$	102.392	+	214.392i	0.187531	+	0.392659i
$547$	176.000	−	176.000i	0.321755	−	0.321755i	−0.527685	−	0.849440i	$-0.676940\pi$
$547$	176.000	−	176.000i	0.321755	−	0.321755i	0.849440	+	0.527685i	$0.176940\pi$
$548$	−55.1543	+	55.1543i	−0.100647	+	0.100647i
$549$	−98.0000	−	79.1960i	−0.178506	−	0.144255i
$550$	−119.000	+	217.000i	−0.216364	+	0.394545i
$551$	42.4264			0.0769989
$552$	307.709	+	644.291i	0.557443	+	1.16719i
$553$	−392.000			−0.708861
$554$	144.250			0.260379
$555$	623.970	+	125.147i	1.12427	+	0.225490i
$556$			414.000i			0.744604i
$557$	−364.867	−	364.867i	−0.655058	−	0.655058i	0.299149	−	0.954206i	$-0.403297\pi$
$557$	−364.867	−	364.867i	−0.655058	−	0.655058i	−0.954206	+	0.299149i	$0.903297\pi$
$558$	13.2965	+	125.296i	0.0238288	+	0.224546i
$559$	576.000			1.03041
$560$	173.241	−	24.7487i	0.309359	−	0.0441942i
$561$	728.000	+	257.387i	1.29768	+	0.458800i
$562$	−210.000	+	210.000i	−0.373665	+	0.373665i
$563$	615.183	+	615.183i	1.09269	+	1.09269i	0.995241	+	0.0974464i	$0.0310675\pi$
$563$	615.183	+	615.183i	1.09269	+	1.09269i	0.0974464	+	0.995241i	$0.468933\pi$
$564$	50.9117	+	18.0000i	0.0902690	+	0.0319149i
$565$	72.0000	+	54.0000i	0.127434	+	0.0955752i
$566$	144.250			0.254858
$567$	554.372	−	119.000i	0.977728	−	0.209877i
$568$	−294.000	−	294.000i	−0.517606	−	0.517606i
$569$	−28.2843			−0.0497087			−0.0248544	−	0.999691i	$-0.507912\pi$
$569$	−28.2843			−0.0497087			−0.0248544	+	0.999691i	$0.507912\pi$
$570$	29.4975	−	147.071i	0.0517500	−	0.258019i
$571$	−734.000			−1.28546			−0.642732	−	0.766091i	$-0.722199\pi$
$571$	−734.000			−1.28546			−0.642732	+	0.766091i	$0.722199\pi$
$572$	−237.588	+	237.588i	−0.415363	+	0.415363i
$573$	−153.588	−	321.588i	−0.268042	−	0.561235i
$574$	168.000	−	168.000i	0.292683	−	0.292683i
$575$	408.708	−	745.291i	0.710796	−	1.29616i
$576$	−91.0000	−	73.5391i	−0.157986	−	0.127672i
$577$	−647.000	−	647.000i	−1.12132	−	1.12132i	−0.991544	−	0.129773i	$-0.958575\pi$
$577$	−647.000	−	647.000i	−1.12132	−	1.12132i	−0.129773	−	0.991544i	$-0.541425\pi$
$578$	273.650	−	273.650i	0.473443	−	0.473443i
$579$	268.000	+	94.7523i	0.462867	+	0.163648i
$580$	−63.0000	+	9.00000i	−0.108621	+	0.0155172i
$581$	257.387	−	257.387i	0.443007	−	0.443007i
$582$	206.612	+	432.612i	0.355004	+	0.743320i
$583$	−700.000	−	700.000i	−1.20069	−	1.20069i
$584$		−	386.080i		−	0.661096i
$585$	493.588	−	124.784i	0.843740	−	0.213306i
$586$		−	262.000i		−	0.447099i
$587$	−630.739	+	630.739i	−1.07451	+	1.07451i	−0.0775226	+	0.996991i	$0.524701\pi$
$587$	−630.739	+	630.739i	−1.07451	+	1.07451i	−0.996991	+	0.0775226i	$0.975299\pi$
$588$	190.055	+	397.945i	0.323223	+	0.676777i
$589$		−	140.000i		−	0.237691i
$590$	−118.794	−	89.0955i	−0.201346	−	0.151009i
$591$	−226.274	−	80.0000i	−0.382867	−	0.135364i
$592$	−150.000	+	150.000i	−0.253378	+	0.253378i
$593$	−618.011	−	618.011i	−1.04218	−	1.04218i	−0.999070	−	0.0431072i	$-0.986274\pi$
$593$	−618.011	−	618.011i	−1.04218	−	1.04218i	−0.0431072	−	0.999070i	$-0.513726\pi$
$594$	−140.000	−	227.688i	−0.235690	−	0.383314i
$595$	546.000	−	728.000i	0.917647	−	1.22353i
$596$		−	598.212i		−	1.00371i
$597$	324.853	−	155.147i	0.544142	−	0.259878i
$598$	−272.000	+	272.000i	−0.454849	+	0.454849i
$599$	−96.1665			−0.160545			−0.0802726	−	0.996773i	$-0.525579\pi$
$599$	−96.1665			−0.160545			−0.0802726	+	0.996773i	$0.525579\pi$
$600$	−29.4071	+	524.176i	−0.0490118	+	0.873626i
$601$			476.000i			0.792013i	0.918248	+	0.396007i	$0.129604\pi$
$601$			476.000i			0.792013i	−0.918248	+	0.396007i	$0.870396\pi$
$602$	−356.382			−0.591996
$603$	−42.9807	−	405.019i	−0.0712780	−	0.671674i
$604$		−	234.000i		−	0.387417i
$605$	16.2635	+	113.844i	0.0268817	+	0.188172i
$606$	260.000	+	91.9239i	0.429043	+	0.151690i
$607$	345.000	+	345.000i	0.568369	+	0.568369i	0.931671	−	0.363302i	$-0.118351\pi$
$607$	345.000	+	345.000i	0.568369	+	0.568369i	−0.363302	+	0.931671i	$0.618351\pi$
$608$	233.345	+	233.345i	0.383792	+	0.383792i
$609$	−38.3970	−	80.3970i	−0.0630492	−	0.132015i
$610$	56.0000	+	42.0000i	0.0918033	+	0.0688525i
$611$			67.8823i			0.111100i
$612$	698.080	−	74.0803i	1.14065	−	0.121046i
$613$	116.000	+	116.000i	0.189233	+	0.189233i	0.795365	−	0.606131i	$-0.207279\pi$
$613$	116.000	+	116.000i	0.189233	+	0.189233i	−0.606131	+	0.795365i	$0.707279\pi$
$614$		−	127.279i		−	0.207295i
$615$	−282.177	−	423.765i	−0.458824	−	0.689048i
$616$	343.000	−	343.000i	0.556818	−	0.556818i
$617$	468.105	+	468.105i	0.758679	+	0.758679i	0.976082	−	0.217403i	$-0.0697587\pi$
$617$	468.105	+	468.105i	0.758679	+	0.758679i	−0.217403	+	0.976082i	$0.569759\pi$
$618$	−19.1421	+	9.14214i	−0.0309743	+	0.0147931i
$619$	1058.00			1.70921			0.854604	−	0.519280i	$-0.173800\pi$
$619$	1058.00			1.70921			0.854604	+	0.519280i	$0.173800\pi$
$620$	29.6985	+	207.889i	0.0479008	+	0.335305i
$621$	480.833	+	782.000i	0.774288	+	1.25926i
$622$	212.000	+	212.000i	0.340836	+	0.340836i
$623$	−138.593			−0.222461
$624$	−56.5685	+	160.000i	−0.0906547	+	0.256410i
$625$	527.000	−	336.000i	0.843200	−	0.537600i
$626$	250.316			0.399865
$627$	127.990	+	267.990i	0.204131	+	0.427416i
$628$	138.000	−	138.000i	0.219745	−	0.219745i
$629$			1103.09i			1.75371i
$630$	−305.392	+	77.2061i	−0.484749	+	0.122549i
$631$	128.000			0.202853			0.101426	−	0.994843i	$-0.467659\pi$
$631$	128.000			0.202853			0.101426	+	0.994843i	$0.467659\pi$
$632$	277.186	+	277.186i	0.438585	+	0.438585i
$633$	232.811	−	111.189i	0.367790	−	0.175654i
$634$			302.000i			0.476341i
$635$	−627.911	−	470.933i	−0.988836	−	0.741627i
$636$	−848.528	−	300.000i	−1.33416	−	0.471698i
$637$	−392.000	+	392.000i	−0.615385	+	0.615385i
$638$	−29.6985	+	29.6985i	−0.0465493	+	0.0465493i
$639$	−415.779	−	336.000i	−0.650671	−	0.525822i
$640$	−476.000	−	357.000i	−0.743750	−	0.557813i
$641$		−	277.186i		−	0.432427i	−0.976346	−	0.216214i	$-0.930629\pi$
$641$		−	277.186i		−	0.432427i	0.976346	−	0.216214i	$-0.0693708\pi$
$642$	−7.75736	−	16.2426i	−0.0120831	−	0.0253001i
$643$	−636.000	+	636.000i	−0.989114	+	0.989114i	−0.999941	−	0.0108278i	$-0.996553\pi$
$643$	−636.000	+	636.000i	−0.989114	+	0.989114i	0.0108278	+	0.999941i	$0.496553\pi$
$644$	−504.874	+	504.874i	−0.783966	+	0.783966i
$645$	−150.177	+	748.764i	−0.232832	+	1.16087i
$646$	260.000			0.402477
$647$	535.987	−	535.987i	0.828419	−	0.828419i	−0.158879	−	0.987298i	$-0.550788\pi$
$647$	535.987	−	535.987i	0.828419	−	0.828419i	0.987298	+	0.158879i	$0.0507881\pi$
$648$	−476.146	−	307.854i	−0.734793	−	0.475084i
$649$	294.000			0.453005
$650$	−271.529	+	79.1960i	−0.417737	+	0.121840i
$651$	−265.296	+	126.704i	−0.407521	+	0.194629i
$652$	−414.000	+	414.000i	−0.634969	+	0.634969i
$653$	−380.423	+	380.423i	−0.582578	+	0.582578i	−0.935611	−	0.353033i	$-0.885150\pi$
$653$	−380.423	+	380.423i	−0.582578	+	0.582578i	0.353033	+	0.935611i	$0.385150\pi$
$654$	−70.0000	+	197.990i	−0.107034	+	0.302737i
$655$	−27.0000	−	189.000i	−0.0412214	−	0.288550i
$656$	169.706			0.258698
$657$	−52.3827	−	493.617i	−0.0797301	−	0.751320i
$658$		−	42.0000i		−	0.0638298i
$659$	253.144			0.384134			0.192067	−	0.981382i	$-0.438481\pi$
$659$	253.144			0.384134			0.192067	+	0.981382i	$0.438481\pi$
$660$	−246.905	−	370.794i	−0.374098	−	0.561809i
$661$		−	1106.00i		−	1.67322i	−0.547797	−	0.836611i	$-0.684533\pi$
$661$		−	1106.00i		−	1.67322i	0.547797	−	0.836611i	$-0.315467\pi$
$662$	72.1249	+	72.1249i	0.108950	+	0.108950i
$663$	380.313	+	796.313i	0.573624	+	1.20108i
$664$	−364.000			−0.548193
$665$	346.482	−	49.4975i	0.521026	−	0.0744323i
$666$	240.000	−	296.985i	0.360360	−	0.445923i
$667$	102.000	−	102.000i	0.152924	−	0.152924i
$668$	−275.772	−	275.772i	−0.412832	−	0.412832i
$669$	−335.169	+	948.000i	−0.500999	+	1.41704i
$670$	32.0000	+	224.000i	0.0477612	+	0.334328i
$671$	−138.593			−0.206547
$672$	231.000	−	653.367i	0.343750	−	0.972272i
$673$	393.000	+	393.000i	0.583952	+	0.583952i	0.935987	−	0.352035i	$-0.114510\pi$
$673$	393.000	+	393.000i	0.583952	+	0.583952i	−0.352035	+	0.935987i	$0.614510\pi$
$674$	357.796			0.530855
$675$	33.5212	+	674.167i	0.0496611	+	0.998766i
$676$	123.000			0.181953
$677$	144.250	−	144.250i	0.213072	−	0.213072i	−0.592499	−	0.805571i	$-0.701859\pi$
$677$	144.250	−	144.250i	0.213072	−	0.213072i	0.805571	+	0.592499i	$0.201859\pi$
$678$	48.7279	−	23.2721i	0.0718701	−	0.0343246i
$679$	−791.000	+	791.000i	−1.16495	+	1.16495i
$680$	−900.854	+	128.693i	−1.32479	+	0.189255i
$681$	−166.000	+	469.519i	−0.243759	+	0.689455i
$682$	98.0000	+	98.0000i	0.143695	+	0.143695i
$683$	−592.555	+	592.555i	−0.867578	+	0.867578i	−0.992204	−	0.124626i	$-0.960227\pi$
$683$	−592.555	+	592.555i	−0.867578	+	0.867578i	0.124626	+	0.992204i	$0.460227\pi$
$684$	210.000	+	169.706i	0.307018	+	0.248108i
$685$	78.0000	−	104.000i	0.113869	−	0.151825i
$686$	242.538	−	242.538i	0.353553	−	0.353553i
$687$	−1012.46	+	483.542i	−1.47374	+	0.703846i
$688$	−180.000	−	180.000i	−0.261628	−	0.261628i
$689$		−	1131.37i		−	1.64205i
$690$	−282.666	−	424.500i	−0.409661	−	0.615217i
$691$		−	574.000i		−	0.830680i	−0.909666	−	0.415340i	$-0.863663\pi$
$691$		−	574.000i		−	0.830680i	0.909666	−	0.415340i	$-0.136337\pi$
$692$	670.337	−	670.337i	0.968695	−	0.968695i
$693$	392.000	−	485.075i	0.565657	−	0.699964i
$694$			240.000i			0.345821i
$695$	−97.5807	−	683.065i	−0.140404	−	0.982828i
$696$	−29.6985	+	84.0000i	−0.0426702	+	0.120690i
$697$	624.000	−	624.000i	0.895265	−	0.895265i
$698$	−315.370	−	315.370i	−0.451819	−	0.451819i
$699$	246.000	−	695.793i	0.351931	−	0.995412i
$700$	−504.000	+	147.000i	−0.720000	+	0.210000i
$701$			1118.64i			1.59578i	0.602802	+	0.797891i	$0.294051\pi$
$701$			1118.64i			1.59578i	−0.602802	+	0.797891i	$0.705949\pi$
$702$	70.8629	−	297.137i	0.100944	−	0.423272i
$703$	−300.000	+	300.000i	−0.426743	+	0.426743i
$704$	−128.693			−0.182803
$705$	−88.2426	−	17.6985i	−0.125167	−	0.0251042i
$706$		−	138.000i		−	0.195467i
$707$			643.467i			0.910137i
$708$	241.191	−	115.191i	0.340665	−	0.162699i
$709$			546.000i			0.770099i	0.922896	+	0.385049i	$0.125816\pi$
$709$			546.000i			0.770099i	−0.922896	+	0.385049i	$0.874184\pi$
$710$	237.588	+	178.191i	0.334631	+	0.250973i
$711$	392.000	+	316.784i	0.551336	+	0.445547i
$712$	98.0000	+	98.0000i	0.137640	+	0.137640i
$713$	−336.583	−	336.583i	−0.472066	−	0.472066i
$714$	−235.307	−	492.693i	−0.329561	−	0.690047i
$715$	336.000	−	448.000i	0.469930	−	0.626573i
$716$		−	38.1838i		−	0.0533293i
$717$	−788.656	+	376.656i	−1.09994	+	0.525322i
$718$	176.000	+	176.000i	0.245125	+	0.245125i
$719$		−	277.186i		−	0.385516i	−0.981246	−	0.192758i	$-0.938257\pi$
$719$		−	277.186i		−	0.385516i	0.981246	−	0.192758i	$-0.0617432\pi$
$720$	−193.241	−	115.251i	−0.268391	−	0.160071i
$721$	−35.0000	−	35.0000i	−0.0485437	−	0.0485437i
$722$	−184.555	−	184.555i	−0.255616	−	0.255616i
$723$	−18.1005	−	37.8995i	−0.0250353	−	0.0524198i
$724$	−1050.00			−1.45028
$725$	101.823	−	29.6985i	0.140446	−	0.0409634i
$726$	65.0538	+	23.0000i	0.0896058	+	0.0316804i
$727$	225.000	+	225.000i	0.309491	+	0.309491i	0.844712	−	0.535221i	$-0.179772\pi$
$727$	225.000	+	225.000i	0.309491	+	0.309491i	−0.535221	+	0.844712i	$0.679772\pi$
$728$	554.372			0.761500
$729$	−650.538	−	329.000i	−0.892371	−	0.451303i
$730$	39.0000	+	273.000i	0.0534247	+	0.373973i
$731$	−1323.70			−1.81081
$732$	−113.698	+	54.3015i	−0.155326	+	0.0741824i
$733$	−124.000	+	124.000i	−0.169168	+	0.169168i	−0.786614	−	0.617446i	$-0.788168\pi$
$733$	−124.000	+	124.000i	−0.169168	+	0.169168i	0.617446	+	0.786614i	$0.288168\pi$
$734$		−	261.630i		−	0.356443i
$735$	−407.372	−	611.779i	−0.554247	−	0.832352i
$736$	1122.00			1.52446
$737$	−316.784	−	316.784i	−0.429829	−	0.429829i
$738$	−303.765	+	32.2355i	−0.411605	+	0.0436795i
$739$		−	350.000i		−	0.473613i	−0.971557	−	0.236806i	$-0.923899\pi$
$739$		−	350.000i		−	0.473613i	0.971557	−	0.236806i	$-0.0761007\pi$
$740$	381.838	−	509.117i	0.515997	−	0.687996i
$741$	−113.137	+	320.000i	−0.152682	+	0.431849i
$742$			700.000i			0.943396i
$743$	666.095	−	666.095i	0.896493	−	0.896493i	−0.0986307	−	0.995124i	$-0.531446\pi$
$743$	666.095	−	666.095i	0.896493	−	0.896493i	0.995124	+	0.0986307i	$0.0314463\pi$
$744$	277.186	+	98.0000i	0.372562	+	0.131720i
$745$	141.000	+	987.000i	0.189262	+	1.32483i
$746$			695.793i			0.932698i
$747$	−465.387	+	49.3869i	−0.623008	+	0.0661136i
$748$	546.000	−	546.000i	0.729947	−	0.729947i
$749$	29.6985	−	29.6985i	0.0396508	−	0.0396508i
$750$	−32.1558	−	373.619i	−0.0428744	−	0.498158i
$751$	−1172.00			−1.56059			−0.780293	−	0.625414i	$-0.784930\pi$
$751$	−1172.00			−1.56059			−0.780293	+	0.625414i	$0.784930\pi$
$752$	21.2132	−	21.2132i	0.0282090	−	0.0282090i
$753$	−1190.64	+	568.641i	−1.58120	+	0.755167i
$754$	−48.0000			−0.0636605
$755$	55.1543	+	386.080i	0.0730521	+	0.511365i
$756$	131.533	−	551.533i	0.173985	−	0.729540i
$757$	302.000	−	302.000i	0.398943	−	0.398943i	−0.478917	−	0.877860i	$-0.658971\pi$
$757$	302.000	−	302.000i	0.398943	−	0.398943i	0.877860	+	0.478917i	$0.158971\pi$
$758$	188.090	−	188.090i	0.248140	−	0.248140i
$759$	952.000	+	336.583i	1.25428	+	0.443456i
$760$	−280.000	−	210.000i	−0.368421	−	0.276316i
$761$	−701.450			−0.921748			−0.460874	−	0.887466i	$-0.652464\pi$
$761$	−701.450			−0.921748			−0.460874	+	0.887466i	$0.652464\pi$
$762$	−424.955	+	202.955i	−0.557684	+	0.266346i
$763$	−490.000			−0.642202
$764$	−356.382			−0.466468
$765$	−1134.31	+	286.765i	−1.48276	+	0.374857i
$766$			190.000i			0.248042i
$767$	237.588	+	237.588i	0.309763	+	0.309763i
$768$	−462.915	+	221.085i	−0.602754	+	0.287871i
$769$	436.000			0.566970			0.283485	−	0.958977i	$-0.408509\pi$
$769$	436.000			0.566970			0.283485	+	0.958977i	$0.408509\pi$
$770$	−207.889	+	277.186i	−0.269986	+	0.359982i
$771$	50.0000	−	141.421i	0.0648508	−	0.183426i
$772$	201.000	−	201.000i	0.260363	−	0.260363i
$773$	684.479	+	684.479i	0.885484	+	0.885484i	0.994085	−	0.108601i	$-0.0346371\pi$
$773$	684.479	+	684.479i	0.885484	+	0.885484i	−0.108601	+	0.994085i	$0.534637\pi$
$774$	356.382	+	288.000i	0.460442	+	0.372093i
$775$	−98.0000	−	336.000i	−0.126452	−	0.433548i
$776$	1118.64			1.44155
$777$	840.000	+	296.985i	1.08108	+	0.382220i
$778$	233.000	+	233.000i	0.299486	+	0.299486i
$779$	339.411			0.435701
$780$	100.118	−	499.176i	0.128356	−	0.639969i
$781$	−588.000			−0.752881
$782$	625.082	−	625.082i	0.799338	−	0.799338i
$783$	−26.5736	+	111.426i	−0.0339382	+	0.142307i
$784$	245.000			0.312500
$785$	−195.161	+	260.215i	−0.248613	+	0.331484i
$786$	−108.000	−	38.1838i	−0.137405	−	0.0485799i
$787$	74.0000	+	74.0000i	0.0940280	+	0.0940280i	0.752556	−	0.658528i	$-0.228821\pi$
$787$	74.0000	+	74.0000i	0.0940280	+	0.0940280i	−0.658528	+	0.752556i	$0.728821\pi$
$788$	−169.706	+	169.706i	−0.215362	+	0.215362i
$789$	−446.000	+	1261.48i	−0.565272	+	1.59883i
$790$	−224.000	−	168.000i	−0.283544	−	0.212658i
$791$	89.0955	+	89.0955i	0.112636	+	0.112636i
$792$	−620.186	+	65.8141i	−0.783063	+	0.0830987i
$793$	−112.000	−	112.000i	−0.141236	−	0.141236i
$794$			42.4264i			0.0534338i
$795$	1470.71	+	294.975i	1.84995	+	0.371037i
$796$		−	360.000i		−	0.452261i
$797$	418.607	−	418.607i	0.525229	−	0.525229i	−0.393917	−	0.919146i	$-0.628880\pi$
$797$	418.607	−	418.607i	0.525229	−	0.525229i	0.919146	+	0.393917i	$0.128880\pi$
$798$	70.0000	−	197.990i	0.0877193	−	0.248108i
$799$		−	156.000i		−	0.195244i
$800$	723.370	+	396.687i	0.904213	+	0.495859i
$801$	138.593	+	112.000i	0.173025	+	0.139825i
$802$	−56.0000	+	56.0000i	−0.0698254	+	0.0698254i
$803$	−386.080	−	386.080i	−0.480797	−	0.480797i
$804$	−384.000	−	135.765i	−0.477612	−	0.168861i
$805$	714.000	−	952.000i	0.886957	−	1.18261i
$806$			158.392i			0.196516i
$807$	−345.573	−	723.573i	−0.428219	−	0.896620i
$808$	455.000	−	455.000i	0.563119	−	0.563119i
$809$	576.999			0.713225			0.356613	−	0.934252i	$-0.383932\pi$
$809$	576.999			0.713225			0.356613	+	0.934252i	$0.383932\pi$
$810$	367.784	+	169.588i	0.454054	+	0.209368i
$811$			462.000i			0.569667i	0.958577	+	0.284834i	$0.0919383\pi$
$811$			462.000i			0.569667i	−0.958577	+	0.284834i	$0.908062\pi$
$812$	−89.0955			−0.109723
$813$	144.804	+	303.196i	0.178111	+	0.372935i
$814$		−	420.000i		−	0.515971i
$815$	585.484	−	780.646i	0.718386	−	0.957848i
$816$	130.000	−	367.696i	0.159314	−	0.450607i
$817$	−360.000	−	360.000i	−0.440636	−	0.440636i
$818$	213.546	+	213.546i	0.261059	+	0.261059i
$819$	708.784	−	75.2162i	0.865426	−	0.0918390i
$820$	−504.000	+	72.0000i	−0.614634	+	0.0878049i
$821$		−	1059.25i		−	1.29019i	−0.764102	−	0.645095i	$-0.776818\pi$
$821$		−	1059.25i		−	1.29019i	0.764102	−	0.645095i	$-0.223182\pi$
$822$	−33.6152	−	70.3848i	−0.0408944	−	0.0856262i
$823$	1089.00	+	1089.00i	1.32321	+	1.32321i	0.911164	+	0.412044i	$0.135185\pi$
$823$	1089.00	+	1089.00i	1.32321	+	1.32321i	0.412044	+	0.911164i	$0.364815\pi$
$824$			49.4975i			0.0600698i
$825$	494.769	+	553.583i	0.599720	+	0.671009i
$826$	−147.000	−	147.000i	−0.177966	−	0.177966i
$827$	497.803	+	497.803i	0.601939	+	0.601939i	0.940827	−	0.338888i	$-0.110051\pi$
$827$	497.803	+	497.803i	0.601939	+	0.601939i	−0.338888	+	0.940827i	$0.610051\pi$
$828$	912.874	−	96.8742i	1.10251	−	0.116998i
$829$	−426.000			−0.513872			−0.256936	−	0.966428i	$-0.582713\pi$
$829$	−426.000			−0.513872			−0.256936	+	0.966428i	$0.582713\pi$
$830$	257.387	−	36.7696i	0.310105	−	0.0443007i
$831$	144.250	−	408.000i	0.173586	−	0.490975i
$832$	−104.000	−	104.000i	−0.125000	−	0.125000i
$833$	900.854	−	900.854i	1.08146	−	1.08146i
$834$	−390.323	−	138.000i	−0.468013	−	0.165468i
$835$	520.000	+	390.000i	0.622754	+	0.467066i
$836$	296.985			0.355245
$837$	367.688	+	87.6884i	0.439293	+	0.104765i
$838$	259.000	−	259.000i	0.309069	−	0.309069i
$839$			376.181i			0.448368i	0.974547	+	0.224184i	$0.0719717\pi$
$839$			376.181i			0.448368i	−0.974547	+	0.224184i	$0.928028\pi$
$840$	−144.538	+	720.648i	−0.172069	+	0.857915i
$841$	−823.000			−0.978597
$842$	−434.164	−	434.164i	−0.515634	−	0.515634i
$843$	383.970	+	803.970i	0.455480	+	0.953701i
$844$		−	258.000i		−	0.305687i
$845$	−202.940	+	28.9914i	−0.240165	+	0.0343093i
$846$	−33.9411	+	42.0000i	−0.0401195	+	0.0496454i
$847$			161.000i			0.190083i
$848$	−353.553	+	353.553i	−0.416926	+	0.416926i
$849$	144.250	−	408.000i	0.169906	−	0.480565i
$850$	624.000	−	182.000i	0.734118	−	0.214118i
$851$			1442.50i			1.69506i
$852$	−482.382	+	230.382i	−0.566176	+	0.270401i
$853$	750.000	−	750.000i	0.879250	−	0.879250i	−0.114207	−	0.993457i	$-0.536433\pi$
$853$	750.000	−	750.000i	0.879250	−	0.879250i	0.993457	+	0.114207i	$0.0364328\pi$
$854$	69.2965	+	69.2965i	0.0811434	+	0.0811434i
$855$	−386.482	−	230.503i	−0.452026	−	0.269594i
$856$	−42.0000			−0.0490654
$857$	−1087.53	+	1087.53i	−1.26900	+	1.26900i	−0.322390	+	0.946607i	$0.604486\pi$
$857$	−1087.53	+	1087.53i	−1.26900	+	1.26900i	−0.946607	+	0.322390i	$0.895514\pi$
$858$	−144.804	−	303.196i	−0.168769	−	0.353375i
$859$	−682.000			−0.793946			−0.396973	−	0.917830i	$-0.629939\pi$
$859$	−682.000			−0.793946			−0.396973	+	0.917830i	$0.629939\pi$
$860$	610.940	+	458.205i	0.710396	+	0.532797i
$861$	−307.176	−	643.176i	−0.356766	−	0.747010i
$862$	392.000	−	392.000i	0.454756	−	0.454756i
$863$	−83.4386	+	83.4386i	−0.0966844	+	0.0966844i	−0.753795	−	0.657110i	$-0.771779\pi$
$863$	−83.4386	+	83.4386i	−0.0966844	+	0.0966844i	0.657110	+	0.753795i	$0.271779\pi$
$864$	−759.000	+	466.690i	−0.878472	+	0.540151i
$865$	−948.000	+	1264.00i	−1.09595	+	1.46127i
$866$	−216.375			−0.249855
$867$	−500.350	−	1047.65i	−0.577105	−	1.20836i
$868$			294.000i			0.338710i
$869$	554.372			0.637942
$870$	12.5147	−	62.3970i	0.0143847	−	0.0717207i
$871$		−	512.000i		−	0.587830i
$872$	346.482	+	346.482i	0.397342	+	0.397342i
$873$	1430.22	−	151.775i	1.63829	−	0.173855i
$874$	340.000			0.389016
$875$	796.909	−	361.332i	0.910754	−	0.412950i
$876$	−468.000	−	165.463i	−0.534247	−	0.188885i
$877$	380.000	−	380.000i	0.433295	−	0.433295i	−0.456452	−	0.889748i	$-0.650880\pi$
$877$	380.000	−	380.000i	0.433295	−	0.433295i	0.889748	+	0.456452i	$0.150880\pi$
$878$	−175.362	−	175.362i	−0.199729	−	0.199729i
$879$	−741.048	−	262.000i	−0.843058	−	0.298066i
$880$	−245.000	+	35.0000i	−0.278409	+	0.0397727i
$881$	25.4558			0.0288943			0.0144471	−	0.999896i	$-0.495401\pi$
$881$	25.4558			0.0288943			0.0144471	+	0.999896i	$0.495401\pi$
$882$	−438.538	+	46.5376i	−0.497208	+	0.0527637i
$883$	−342.000	−	342.000i	−0.387316	−	0.387316i	0.486413	−	0.873729i	$-0.338305\pi$
$883$	−342.000	−	342.000i	−0.387316	−	0.387316i	−0.873729	+	0.486413i	$0.838305\pi$
$884$	882.469			0.998268
$885$	−370.794	+	246.905i	−0.418976	+	0.278988i
$886$	−20.0000			−0.0225734
$887$	94.7523	−	94.7523i	0.106823	−	0.106823i	−0.651675	−	0.758498i	$-0.725933\pi$
$887$	94.7523	−	94.7523i	0.106823	−	0.106823i	0.758498	+	0.651675i	$0.225933\pi$
$888$	−383.970	−	803.970i	−0.432398	−	0.905371i
$889$	−777.000	−	777.000i	−0.874016	−	0.874016i
$890$	−79.1960	−	59.3970i	−0.0889842	−	0.0667382i
$891$	−784.000	+	168.291i	−0.879910	+	0.188879i
$892$	711.000	+	711.000i	0.797085	+	0.797085i
$893$	42.4264	−	42.4264i	0.0475100	−	0.0475100i
$894$	564.000	+	199.404i	0.630872	+	0.223047i
$895$	9.00000	+	63.0000i	0.0100559	+	0.0703911i
$896$	−589.020	−	589.020i	−0.657388	−	0.657388i
$897$	497.332	+	1041.33i	0.554439	+	1.16091i
$898$	−458.000	−	458.000i	−0.510022	−	0.510022i
$899$		−	59.3970i		−	0.0660700i
$900$	622.794	+	260.294i	0.691993	+	0.289215i
$901$			2600.00i			2.88568i
$902$	−237.588	+	237.588i	−0.263401	+	0.263401i
$903$	−356.382	+	1008.00i	−0.394664	+	1.11628i
$904$		−	126.000i		−	0.139381i
$905$	1732.41	−	247.487i	1.91427	−	0.273467i
$906$	220.617	+	78.0000i	0.243507	+	0.0860927i
$907$	130.000	−	130.000i	0.143330	−	0.143330i	−0.631801	−	0.775131i	$-0.717684\pi$
$907$	130.000	−	130.000i	0.143330	−	0.143330i	0.775131	+	0.631801i	$0.217684\pi$
$908$	352.139	+	352.139i	0.387818	+	0.387818i
$909$	520.000	−	643.467i	0.572057	−	0.707885i
$910$	−392.000	+	56.0000i	−0.430769	+	0.0615385i
$911$		−	1069.15i		−	1.17360i	−0.809734	−	0.586798i	$-0.800388\pi$
$911$		−	1069.15i		−	1.17360i	0.809734	−	0.586798i	$-0.199612\pi$
$912$	135.355	−	64.6447i	0.148416	−	0.0708823i
$913$	−364.000	+	364.000i	−0.398686	+	0.398686i
$914$	−442.649			−0.484299
$915$	174.794	−	116.392i	0.191032	−	0.127204i
$916$			1122.00i			1.22489i
$917$		−	267.286i		−	0.291479i
$918$	−162.850	+	682.850i	−0.177396	+	0.743845i
$919$			1428.00i			1.55386i	0.629585	+	0.776931i	$0.283225\pi$
$919$			1428.00i			1.55386i	−0.629585	+	0.776931i	$0.716775\pi$
$920$	−1178.04	+	168.291i	−1.28048	+	0.182925i
$921$	−360.000	−	127.279i	−0.390879	−	0.138197i
$922$	−101.000	−	101.000i	−0.109544	−	0.109544i
$923$	−475.176	−	475.176i	−0.514817	−	0.514817i
$924$	−268.779	−	562.779i	−0.290886	−	0.609068i
$925$	−510.000	+	930.000i	−0.551351	+	1.00541i
$926$			41.0122i			0.0442896i
$927$	6.71573	+	63.2843i	0.00724458	+	0.0682678i
$928$	99.0000	+	99.0000i	0.106681	+	0.106681i
$929$		−	871.156i		−	0.937735i	−0.883269	−	0.468867i	$-0.844662\pi$
$929$		−	871.156i		−	0.937735i	0.883269	−	0.468867i	$-0.155338\pi$
$930$	−205.899	−	41.2965i	−0.221397	−	0.0444048i
$931$	490.000			0.526316
$932$	−521.845	−	521.845i	−0.559919	−	0.559919i
$933$	811.627	−	387.627i	0.869911	−	0.415463i
$934$	−496.000			−0.531049
$935$	−772.161	+	1029.55i	−0.825840	+	1.10112i
$936$	−554.372	−	448.000i	−0.592277	−	0.478632i
$937$	−1077.00	−	1077.00i	−1.14941	−	1.14941i	−0.986668	−	0.162745i	$-0.947965\pi$
$937$	−1077.00	−	1077.00i	−1.14941	−	1.14941i	−0.162745	−	0.986668i	$-0.552035\pi$
$938$			316.784i			0.337723i
$939$	250.316	−	708.000i	0.266577	−	0.753994i
$940$	−54.0000	+	72.0000i	−0.0574468	+	0.0765957i
$941$	250.316			0.266010			0.133005	−	0.991115i	$-0.457537\pi$
$941$	250.316			0.266010			0.133005	+	0.991115i	$0.457537\pi$
$942$	84.1076	+	176.108i	0.0892863	+	0.186951i
$943$	816.000	−	816.000i	0.865323	−	0.865323i
$944$		−	148.492i		−	0.157301i
$945$	−87.0202	+	940.985i	−0.0920849	+	0.995751i
$946$	504.000			0.532770
$947$	−885.298	−	885.298i	−0.934844	−	0.934844i	0.0631590	−	0.998003i	$-0.479882\pi$
$947$	−885.298	−	885.298i	−0.934844	−	0.934844i	−0.998003	+	0.0631590i	$0.979882\pi$
$948$	454.794	−	217.206i	0.479740	−	0.229120i
$949$		−	624.000i		−	0.657534i
$950$	219.203	+	120.208i	0.230740	+	0.126535i
$951$	854.185	+	302.000i	0.898197	+	0.317560i
$952$	−1274.00			−1.33824
$953$	−462.448	+	462.448i	−0.485255	+	0.485255i	−0.906805	−	0.421550i	$-0.861486\pi$
$953$	−462.448	+	462.448i	−0.485255	+	0.485255i	0.421550	+	0.906805i	$0.361486\pi$
$954$	565.685	−	700.000i	0.592962	−	0.733753i
$955$	588.000	−	84.0000i	0.615707	−	0.0879581i
$956$			873.984i			0.914209i
$957$	54.3015	+	113.698i	0.0567414	+	0.118807i
$958$	−56.0000	+	56.0000i	−0.0584551	+	0.0584551i
$959$	128.693	−	128.693i	0.134195	−	0.134195i
$960$	162.309	−	108.078i	0.169072	−	0.112581i
$961$	765.000			0.796046
$962$	339.411	−	339.411i	0.352818	−	0.352818i
$963$	−53.6985	+	5.69848i	−0.0557617	+	0.00591743i
$964$	−42.0000			−0.0435685
$965$	−284.257	+	379.009i	−0.294567	+	0.392756i
$966$	−307.709	−	644.291i	−0.318539	−	0.666968i
$967$	729.000	−	729.000i	0.753878	−	0.753878i	−0.221323	−	0.975201i	$-0.571037\pi$
$967$	729.000	−	729.000i	0.753878	−	0.753878i	0.975201	+	0.221323i	$0.0710374\pi$
$968$	113.844	−	113.844i	0.117608	−	0.117608i
$969$	260.000	−	735.391i	0.268318	−	0.758917i
$970$	−791.000	+	113.000i	−0.815464	+	0.116495i
$971$	892.369			0.919020			0.459510	−	0.888173i	$-0.348025\pi$
$971$	892.369			0.919020			0.459510	+	0.888173i	$0.348025\pi$
$972$	−577.238	+	445.238i	−0.593866	+	0.458064i
$973$		−	966.000i		−	0.992806i
$974$	−142.836			−0.146648
$975$	−47.5290	+	847.196i	−0.0487477	+	0.868919i
$976$			70.0000i			0.0717213i
$977$	−1087.53	−	1087.53i	−1.11313	−	1.11313i	−0.992725	−	0.120408i	$-0.961580\pi$
$977$	−1087.53	−	1087.53i	−1.11313	−	1.11313i	−0.120408	−	0.992725i	$-0.538420\pi$
$978$	−252.323	−	528.323i	−0.257999	−	0.540208i
$979$	196.000			0.200204
$980$	−727.613	+	103.945i	−0.742462	+	0.106066i
$981$	490.000	+	395.980i	0.499490	+	0.403649i
$982$	245.000	−	245.000i	0.249491	−	0.249491i
$983$	−1146.93	−	1146.93i	−1.16676	−	1.16676i	−0.982964	−	0.183798i	$-0.941161\pi$
$983$	−1146.93	−	1146.93i	−1.16676	−	1.16676i	−0.183798	−	0.982964i	$-0.558839\pi$
$984$	−237.588	+	672.000i	−0.241451	+	0.682927i
$985$	240.000	−	320.000i	0.243655	−	0.324873i
$986$	110.309			0.111875
$987$	−118.794	−	42.0000i	−0.120359	−	0.0425532i
$988$	240.000	+	240.000i	0.242915	+	0.242915i
$989$	−1731.00			−1.75025
$990$	431.889	−	109.186i	0.436252	−	0.110289i
$991$	1618.00			1.63269			0.816347	−	0.577562i	$-0.195996\pi$
$991$	1618.00			1.63269			0.816347	+	0.577562i	$0.195996\pi$
$992$	326.683	−	326.683i	0.329318	−	0.329318i
$993$	276.125	−	131.875i	0.278071	−	0.132805i
$994$	294.000	+	294.000i	0.295775	+	0.295775i
$995$	84.8528	+	593.970i	0.0852792	+	0.596954i
$996$	−156.000	+	441.235i	−0.156627	+	0.443007i
$997$	−192.000	−	192.000i	−0.192578	−	0.192578i	0.604231	−	0.796809i	$-0.293480\pi$
$997$	−192.000	−	192.000i	−0.192578	−	0.192578i	−0.796809	+	0.604231i	$0.793480\pi$
$998$	−425.678	+	425.678i	−0.426531	+	0.426531i
$999$	−600.000	−	975.807i	−0.600601	−	0.976784i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.k.b.83.2	yes	4
3.2	odd	2	inner	105.3.k.b.83.1	yes	4
5.2	odd	4		105.3.k.a.62.1	✓	4
7.6	odd	2		105.3.k.a.83.2	yes	4
15.2	even	4		105.3.k.a.62.2	yes	4
21.20	even	2		105.3.k.a.83.1	yes	4
35.27	even	4	inner	105.3.k.b.62.1	yes	4
105.62	odd	4	inner	105.3.k.b.62.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.k.a.62.1	✓	4	5.2	odd	4
105.3.k.a.62.2	yes	4	15.2	even	4
105.3.k.a.83.1	yes	4	21.20	even	2
105.3.k.a.83.2	yes	4	7.6	odd	2
105.3.k.b.62.1	yes	4	35.27	even	4	inner
105.3.k.b.62.2	yes	4	105.62	odd	4	inner
105.3.k.b.83.1	yes	4	3.2	odd	2	inner
105.3.k.b.83.2	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(2.70711 - 1.29289i) q^{3} -3.00000i q^{4} +(0.707107 + 4.94975i) q^{5} +(2.82843 + 1.00000i) q^{6} +7.00000i q^{7} +(4.94975 - 4.94975i) q^{8} +(5.65685 - 7.00000i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(2.70711 - 1.29289i) q^{3} -3.00000i q^{4} +(0.707107 + 4.94975i) q^{5} +(2.82843 + 1.00000i) q^{6} +7.00000i q^{7} +(4.94975 - 4.94975i) q^{8} +(5.65685 - 7.00000i) q^{9} +(-3.00000 + 4.00000i) q^{10} -9.89949i q^{11} +(-3.87868 - 8.12132i) q^{12} +(8.00000 - 8.00000i) q^{13} +(-4.94975 + 4.94975i) q^{14} +(8.31371 + 12.4853i) q^{15} -5.00000 q^{16} +(-18.3848 + 18.3848i) q^{17} +(8.94975 - 0.949747i) q^{18} -10.0000 q^{19} +(14.8492 - 2.12132i) q^{20} +(9.05025 + 18.9497i) q^{21} +(7.00000 - 7.00000i) q^{22} +(-24.0416 + 24.0416i) q^{23} +(7.00000 - 19.7990i) q^{24} +(-24.0000 + 7.00000i) q^{25} +11.3137 q^{26} +(6.26346 - 26.2635i) q^{27} +21.0000 q^{28} -4.24264 q^{29} +(-2.94975 + 14.7071i) q^{30} +14.0000i q^{31} +(-23.3345 - 23.3345i) q^{32} +(-12.7990 - 26.7990i) q^{33} -26.0000 q^{34} +(-34.6482 + 4.94975i) q^{35} +(-21.0000 - 16.9706i) q^{36} +(30.0000 - 30.0000i) q^{37} +(-7.07107 - 7.07107i) q^{38} +(11.3137 - 32.0000i) q^{39} +(28.0000 + 21.0000i) q^{40} -33.9411 q^{41} +(-7.00000 + 19.7990i) q^{42} +(36.0000 + 36.0000i) q^{43} -29.6985 q^{44} +(38.6482 + 23.0503i) q^{45} -34.0000 q^{46} +(-4.24264 + 4.24264i) q^{47} +(-13.5355 + 6.46447i) q^{48} -49.0000 q^{49} +(-21.9203 - 12.0208i) q^{50} +(-26.0000 + 73.5391i) q^{51} +(-24.0000 - 24.0000i) q^{52} +(70.7107 - 70.7107i) q^{53} +(23.0000 - 14.1421i) q^{54} +(49.0000 - 7.00000i) q^{55} +(34.6482 + 34.6482i) q^{56} +(-27.0711 + 12.9289i) q^{57} +(-3.00000 - 3.00000i) q^{58} +29.6985i q^{59} +(37.4558 - 24.9411i) q^{60} -14.0000i q^{61} +(-9.89949 + 9.89949i) q^{62} +(49.0000 + 39.5980i) q^{63} -13.0000i q^{64} +(45.2548 + 33.9411i) q^{65} +(9.89949 - 28.0000i) q^{66} +(32.0000 - 32.0000i) q^{67} +(55.1543 + 55.1543i) q^{68} +(-34.0000 + 96.1665i) q^{69} +(-28.0000 - 21.0000i) q^{70} -59.3970i q^{71} +(-6.64823 - 62.6482i) q^{72} +(39.0000 - 39.0000i) q^{73} +42.4264 q^{74} +(-55.9203 + 49.9792i) q^{75} +30.0000i q^{76} +69.2965 q^{77} +(30.6274 - 14.6274i) q^{78} +56.0000i q^{79} +(-3.53553 - 24.7487i) q^{80} +(-17.0000 - 79.1960i) q^{81} +(-24.0000 - 24.0000i) q^{82} +(-36.7696 - 36.7696i) q^{83} +(56.8492 - 27.1508i) q^{84} +(-104.000 - 78.0000i) q^{85} +50.9117i q^{86} +(-11.4853 + 5.48528i) q^{87} +(-49.0000 - 49.0000i) q^{88} +19.7990i q^{89} +(11.0294 + 43.6274i) q^{90} +(56.0000 + 56.0000i) q^{91} +(72.1249 + 72.1249i) q^{92} +(18.1005 + 37.8995i) q^{93} -6.00000 q^{94} +(-7.07107 - 49.4975i) q^{95} +(-93.3381 - 33.0000i) q^{96} +(113.000 + 113.000i) q^{97} +(-34.6482 - 34.6482i) q^{98} +(-69.2965 - 56.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{3}+O(q^{10}) \) 4 * q + 8 * q^3	\( 4 q + 8 q^{3} - 12 q^{10} - 24 q^{12} + 32 q^{13} - 12 q^{15} - 20 q^{16} + 16 q^{18} - 40 q^{19} + 56 q^{21} + 28 q^{22} + 28 q^{24} - 96 q^{25} - 40 q^{27} + 84 q^{28} + 8 q^{30} + 28 q^{33} - 104 q^{34} - 84 q^{36} + 120 q^{37} + 112 q^{40} - 28 q^{42} + 144 q^{43} + 16 q^{45} - 136 q^{46} - 40 q^{48} - 196 q^{49} - 104 q^{51} - 96 q^{52} + 92 q^{54} + 196 q^{55} - 80 q^{57} - 12 q^{58} + 48 q^{60} + 196 q^{63} + 128 q^{67} - 136 q^{69} - 112 q^{70} + 112 q^{72} + 156 q^{73} - 136 q^{75} + 32 q^{78} - 68 q^{81} - 96 q^{82} + 168 q^{84} - 416 q^{85} - 12 q^{87} - 196 q^{88} + 112 q^{90} + 224 q^{91} + 112 q^{93} - 24 q^{94} + 452 q^{97}+O(q^{100}) \) 4 * q + 8 * q^3 - 12 * q^10 - 24 * q^12 + 32 * q^13 - 12 * q^15 - 20 * q^16 + 16 * q^18 - 40 * q^19 + 56 * q^21 + 28 * q^22 + 28 * q^24 - 96 * q^25 - 40 * q^27 + 84 * q^28 + 8 * q^30 + 28 * q^33 - 104 * q^34 - 84 * q^36 + 120 * q^37 + 112 * q^40 - 28 * q^42 + 144 * q^43 + 16 * q^45 - 136 * q^46 - 40 * q^48 - 196 * q^49 - 104 * q^51 - 96 * q^52 + 92 * q^54 + 196 * q^55 - 80 * q^57 - 12 * q^58 + 48 * q^60 + 196 * q^63 + 128 * q^67 - 136 * q^69 - 112 * q^70 + 112 * q^72 + 156 * q^73 - 136 * q^75 + 32 * q^78 - 68 * q^81 - 96 * q^82 + 168 * q^84 - 416 * q^85 - 12 * q^87 - 196 * q^88 + 112 * q^90 + 224 * q^91 + 112 * q^93 - 24 * q^94 + 452 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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