LMFDB - Embedded newform 105.3.k.b.62.2

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			62.2
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	105.62
Dual form			105.3.k.b.83.2

$q$-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 $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

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

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	−0.507877	−	0.861430i	$-0.669569\pi$
$2$	0.707107	−	0.707107i	0.353553	−	0.353553i	0.861430	+	0.507877i	$0.169569\pi$
$3$	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	$0.148568\pi$
$11$			9.89949i			0.899954i	−0.893040	+	0.449977i	$0.851432\pi$
$12$	−3.87868	+	8.12132i	−0.323223	+	0.676777i
$13$	8.00000	+	8.00000i	0.615385	+	0.615385i	0.944344	−	0.328959i	$-0.106698\pi$
$13$	8.00000	+	8.00000i	0.615385	+	0.615385i	−0.328959	+	0.944344i	$0.606698\pi$
$14$	−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	−0.996374	−	0.0850836i	$-0.972884\pi$
$17$	−18.3848	−	18.3848i	−1.08146	−	1.08146i	−0.0850836	−	0.996374i	$-0.527116\pi$
$18$	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	−0.998925	−	0.0463637i	$-0.985237\pi$
$23$	−24.0416	−	24.0416i	−1.04529	−	1.04529i	−0.0463637	−	0.998925i	$-0.514763\pi$
$24$	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	$-0.927498\pi$
$31$		−	14.0000i		−	0.451613i	0.974172	−	0.225806i	$-0.0725017\pi$
$32$	−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	0.984755	−	0.173945i	$-0.0556514\pi$
$37$	30.0000	+	30.0000i	0.810811	+	0.810811i	−0.173945	+	0.984755i	$0.555651\pi$
$38$	−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	−0.151281	−	0.988491i	$-0.548340\pi$
$43$	36.0000	−	36.0000i	0.837209	−	0.837209i	0.988491	+	0.151281i	$0.0483400\pi$
$44$	−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	0.660530	−	0.750799i	$-0.270331\pi$
$47$	−4.24264	−	4.24264i	−0.0902690	−	0.0902690i	−0.750799	+	0.660530i	$0.770331\pi$
$48$	−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	0.901606	+	0.432557i	$0.142389\pi$
$53$	70.7107	+	70.7107i	1.33416	+	1.33416i	0.432557	+	0.901606i	$0.357611\pi$
$54$	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	$-0.919016\pi$
$59$		−	29.6985i		−	0.503364i	0.967810	−	0.251682i	$-0.0809837\pi$
$60$	37.4558	+	24.9411i	0.624264	+	0.415685i
$61$			14.0000i			0.229508i	0.993394	+	0.114754i	$0.0366080\pi$
$61$			14.0000i			0.229508i	−0.993394	+	0.114754i	$0.963392\pi$
$62$	−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	0.904367	−	0.426755i	$-0.140343\pi$
$67$	32.0000	+	32.0000i	0.477612	+	0.477612i	−0.426755	+	0.904367i	$0.640343\pi$
$68$	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	$0.137370\pi$
$71$			59.3970i			0.836577i	−0.908314	+	0.418289i	$0.862630\pi$
$72$	−6.64823	+	62.6482i	−0.0923366	+	0.870114i
$73$	39.0000	+	39.0000i	0.534247	+	0.534247i	0.921833	−	0.387587i	$-0.126691\pi$
$73$	39.0000	+	39.0000i	0.534247	+	0.534247i	−0.387587	+	0.921833i	$0.626691\pi$
$74$	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	$-0.884675\pi$
$79$		−	56.0000i		−	0.708861i	0.935082	−	0.354430i	$-0.115325\pi$
$80$	−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	−0.893021	−	0.450015i	$-0.851419\pi$
$83$	−36.7696	+	36.7696i	−0.443007	+	0.443007i	0.450015	+	0.893021i	$0.351419\pi$
$84$	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	$-0.964521\pi$
$89$		−	19.7990i		−	0.222461i	0.993795	−	0.111230i	$-0.0354791\pi$
$90$	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	0.181571	−	0.983378i	$-0.441882\pi$
$97$	113.000	−	113.000i	1.16495	−	1.16495i	0.983378	−	0.181571i	$-0.0581181\pi$
$98$	−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	0.682418	−	0.730962i	$-0.260928\pi$
$103$	−5.00000	−	5.00000i	−0.0485437	−	0.0485437i	−0.730962	+	0.682418i	$0.760928\pi$
$104$			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	−0.726654	−	0.687003i	$-0.758926\pi$
$107$	−4.24264	+	4.24264i	−0.0396508	+	0.0396508i	0.687003	+	0.726654i	$0.258926\pi$
$108$	−78.7904	+	18.7904i	−0.729540	+	0.173985i
$109$		−	70.0000i		−	0.642202i	−0.947045	−	0.321101i	$-0.895947\pi$
$109$		−	70.0000i		−	0.642202i	0.947045	−	0.321101i	$-0.104053\pi$
$110$	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	0.761179	−	0.648542i	$-0.224621\pi$
$113$	12.7279	+	12.7279i	0.112636	+	0.112636i	−0.648542	+	0.761179i	$0.724621\pi$
$114$	−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	0.118892	−	0.992907i	$-0.462066\pi$
$127$	−111.000	−	111.000i	−0.874016	−	0.874016i	−0.992907	+	0.118892i	$0.962066\pi$
$128$	−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	−0.771014	−	0.636818i	$-0.780250\pi$
$137$	−18.3848	+	18.3848i	−0.134195	+	0.134195i	0.636818	+	0.771014i	$0.280250\pi$
$138$	−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	−0.545268	−	0.838262i	$-0.683572\pi$
$157$	46.0000	−	46.0000i	0.292994	−	0.292994i	0.838262	+	0.545268i	$0.183572\pi$
$158$	−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	−0.989710	−	0.143085i	$-0.954298\pi$
$163$	−138.000	+	138.000i	−0.846626	+	0.846626i	0.143085	+	0.989710i	$0.454298\pi$
$164$		−	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	0.926568	−	0.376126i	$-0.122744\pi$
$167$	91.9239	+	91.9239i	0.550442	+	0.550442i	−0.376126	+	0.926568i	$0.622744\pi$
$168$	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	0.357793	−	0.933801i	$-0.383529\pi$
$173$	223.446	−	223.446i	1.29159	−	1.29159i	0.933801	−	0.357793i	$-0.116471\pi$
$174$	−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	$0.417812\pi$
$181$			350.000i			1.93370i	−0.255342	+	0.966851i	$0.582188\pi$
$182$		−	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	$0.100657\pi$
$191$			118.794i			0.621958i	−0.950417	+	0.310979i	$0.899343\pi$
$192$	−16.8076	+	35.1924i	−0.0875396	+	0.183294i
$193$	67.0000	−	67.0000i	0.347150	−	0.347150i	−0.511897	−	0.859047i	$-0.671057\pi$
$193$	67.0000	−	67.0000i	0.347150	−	0.347150i	0.859047	+	0.511897i	$0.171057\pi$
$194$		−	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	−0.835952	−	0.548802i	$-0.815084\pi$
$197$	−56.5685	+	56.5685i	−0.287150	+	0.287150i	0.548802	+	0.835952i	$0.315084\pi$
$198$	−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	−0.997893	−	0.0648877i	$-0.979331\pi$
$223$	−237.000	−	237.000i	−1.06278	−	1.06278i	−0.0648877	−	0.997893i	$-0.520669\pi$
$224$	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	0.399599	−	0.916690i	$-0.369149\pi$
$227$	−117.380	−	117.380i	−0.517091	−	0.517091i	−0.916690	+	0.399599i	$0.869149\pi$
$228$	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	0.973831	−	0.227272i	$-0.0729807\pi$
$233$	173.948	+	173.948i	0.746559	+	0.746559i	−0.227272	+	0.973831i	$0.572981\pi$
$234$	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	$0.00924682\pi$
$241$			14.0000i			0.0580913i	−0.999578	+	0.0290456i	$0.990753\pi$
$242$	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	0.772538	−	0.634969i	$-0.218987\pi$
$257$	35.3553	+	35.3553i	0.137569	+	0.137569i	−0.634969	+	0.772538i	$0.718987\pi$
$258$	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	−0.974429	−	0.224695i	$-0.927861\pi$
$263$	−315.370	−	315.370i	−1.19912	−	1.19912i	−0.224695	−	0.974429i	$-0.572139\pi$
$264$	−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	$0.165497\pi$
$269$			267.286i			0.993630i	−0.867857	+	0.496815i	$0.834503\pi$
$270$	86.2635	−	103.844i	0.319494	−	0.384608i
$271$		−	112.000i		−	0.413284i	−0.978417	−	0.206642i	$-0.933746\pi$
$271$		−	112.000i		−	0.413284i	0.978417	−	0.206642i	$-0.0662536\pi$
$272$	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	0.866832	−	0.498601i	$-0.166153\pi$
$277$	102.000	+	102.000i	0.368231	+	0.368231i	−0.498601	+	0.866832i	$0.666153\pi$
$278$	−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	$-0.822776\pi$
$281$		−	296.985i		−	1.05689i	0.848969	−	0.528443i	$-0.177224\pi$
$282$	−16.2426	−	7.75736i	−0.0575980	−	0.0275084i
$283$	102.000	+	102.000i	0.360424	+	0.360424i	0.863969	−	0.503545i	$-0.167971\pi$
$283$	102.000	+	102.000i	0.360424	+	0.360424i	−0.503545	+	0.863969i	$0.667971\pi$
$284$	−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	−0.948643	−	0.316349i	$-0.897543\pi$
$293$	−185.262	+	185.262i	−0.632293	+	0.632293i	0.316349	+	0.948643i	$0.397543\pi$
$294$	−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	−0.838327	−	0.545168i	$-0.816466\pi$
$307$	−90.0000	+	90.0000i	−0.293160	+	0.293160i	0.545168	+	0.838327i	$0.316466\pi$
$308$			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	0.930863	−	0.365368i	$-0.119057\pi$
$313$	177.000	+	177.000i	0.565495	+	0.565495i	−0.365368	+	0.930863i	$0.619057\pi$
$314$		−	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	−0.284908	−	0.958555i	$-0.591963\pi$
$317$	213.546	−	213.546i	0.673647	−	0.673647i	0.958555	+	0.284908i	$0.0919629\pi$
$318$	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	0.974618	−	0.223876i	$-0.0718710\pi$
$337$	253.000	+	253.000i	0.750742	+	0.750742i	−0.223876	+	0.974618i	$0.571871\pi$
$338$	−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	−0.418946	−	0.908011i	$-0.637600\pi$
$347$	169.706	−	169.706i	0.489065	−	0.489065i	0.908011	+	0.418946i	$0.137600\pi$
$348$	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	−0.831683	−	0.555250i	$-0.812622\pi$
$353$	−97.5807	+	97.5807i	−0.276433	+	0.276433i	0.555250	+	0.831683i	$0.312622\pi$
$354$	−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	−0.912705	−	0.408618i	$-0.866011\pi$
$367$	−185.000	+	185.000i	−0.504087	+	0.504087i	0.408618	+	0.912705i	$0.366011\pi$
$368$	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	0.404494	−	0.914540i	$-0.367448\pi$
$373$	492.000	−	492.000i	1.31903	−	1.31903i	0.914540	−	0.404494i	$-0.132552\pi$
$374$		−	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	$0.114132\pi$
$379$			266.000i			0.701847i	−0.936404	+	0.350923i	$0.885868\pi$
$380$	−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	−0.509617	−	0.860401i	$-0.670213\pi$
$383$	134.350	−	134.350i	0.350784	−	0.350784i	0.860401	+	0.509617i	$0.170213\pi$
$384$	−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	−0.668313	−	0.743880i	$-0.732983\pi$
$397$	30.0000	−	30.0000i	0.0755668	−	0.0755668i	0.743880	+	0.668313i	$0.232983\pi$
$398$	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	$-0.968516\pi$
$401$		−	79.1960i		−	0.197496i	0.995112	−	0.0987481i	$-0.0314838\pi$
$402$	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	$0.143991\pi$
$419$			366.281i			0.874180i	−0.899418	+	0.437090i	$0.856009\pi$
$420$	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	$0.222361\pi$
$431$			554.372i			1.28625i	−0.765763	+	0.643123i	$0.777639\pi$
$432$	−31.3173	−	131.317i	−0.0724937	−	0.303975i
$433$	−153.000	−	153.000i	−0.353349	−	0.353349i	0.508005	−	0.861354i	$-0.330383\pi$
$433$	−153.000	−	153.000i	−0.353349	−	0.353349i	−0.861354	+	0.508005i	$0.830383\pi$
$434$	−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	0.690965	−	0.722888i	$-0.257186\pi$
$443$	−14.1421	−	14.1421i	−0.0319236	−	0.0319236i	−0.722888	+	0.690965i	$0.757186\pi$
$444$	−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	0.276199	−	0.961100i	$-0.410925\pi$
$457$	−313.000	−	313.000i	−0.684902	−	0.684902i	−0.961100	+	0.276199i	$0.910925\pi$
$458$	−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	−0.675095	−	0.737730i	$-0.735898\pi$
$463$	29.0000	−	29.0000i	0.0626350	−	0.0626350i	0.737730	+	0.675095i	$0.235898\pi$
$464$	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	0.223652	−	0.974669i	$-0.428202\pi$
$467$	−350.725	−	350.725i	−0.751017	−	0.751017i	−0.974669	+	0.223652i	$0.928202\pi$
$468$	−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	$-0.973656\pi$
$479$		−	79.1960i		−	0.165336i	0.996577	−	0.0826680i	$-0.0263441\pi$
$480$	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	0.595766	−	0.803158i	$-0.296849\pi$
$487$	−101.000	−	101.000i	−0.207392	−	0.207392i	−0.803158	+	0.595766i	$0.796849\pi$
$488$	−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	$0.114782\pi$
$491$			346.482i			0.705667i	−0.935686	+	0.352833i	$0.885218\pi$
$492$	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	$-0.793890\pi$
$499$		−	602.000i		−	1.20641i	0.797585	−	0.603206i	$-0.206110\pi$
$500$	−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	0.287842	−	0.957678i	$-0.407062\pi$
$503$	626.497	−	626.497i	1.24552	−	1.24552i	0.957678	−	0.287842i	$-0.0929379\pi$
$504$	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	$0.123819\pi$
$509$			386.080i			0.758507i	−0.925293	+	0.379254i	$0.876181\pi$
$510$	−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	−0.964894	−	0.262639i	$-0.915407\pi$
$523$	−642.000	−	642.000i	−1.22753	−	1.22753i	−0.262639	−	0.964894i	$-0.584593\pi$
$524$		−	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	0.849440	−	0.527685i	$-0.176940\pi$
$547$	176.000	+	176.000i	0.321755	+	0.321755i	−0.527685	+	0.849440i	$0.676940\pi$
$548$	−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	−0.954206	−	0.299149i	$-0.903297\pi$
$557$	−364.867	+	364.867i	−0.655058	+	0.655058i	0.299149	+	0.954206i	$0.403297\pi$
$558$	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	0.0974464	−	0.995241i	$-0.468933\pi$
$563$	615.183	−	615.183i	1.09269	−	1.09269i	0.995241	−	0.0974464i	$-0.0310675\pi$
$564$	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	−0.129773	+	0.991544i	$0.541425\pi$
$577$	−647.000	+	647.000i	−1.12132	+	1.12132i	−0.991544	+	0.129773i	$0.958575\pi$
$578$	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	−0.996991	−	0.0775226i	$-0.975299\pi$
$587$	−630.739	−	630.739i	−1.07451	−	1.07451i	−0.0775226	−	0.996991i	$-0.524701\pi$
$588$	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	−0.0431072	+	0.999070i	$0.513726\pi$
$593$	−618.011	+	618.011i	−1.04218	+	1.04218i	−0.999070	+	0.0431072i	$0.986274\pi$
$594$	−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	$-0.870396\pi$
$601$		−	476.000i		−	0.792013i	0.918248	−	0.396007i	$-0.129604\pi$
$602$	−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	−0.363302	−	0.931671i	$-0.618351\pi$
$607$	345.000	−	345.000i	0.568369	−	0.568369i	0.931671	+	0.363302i	$0.118351\pi$
$608$	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	−0.606131	−	0.795365i	$-0.707279\pi$
$613$	116.000	−	116.000i	0.189233	−	0.189233i	0.795365	+	0.606131i	$0.207279\pi$
$614$			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	−0.217403	−	0.976082i	$-0.569759\pi$
$617$	468.105	−	468.105i	0.758679	−	0.758679i	0.976082	+	0.217403i	$0.0697587\pi$
$618$	−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	$0.0693708\pi$
$641$			277.186i			0.432427i	−0.976346	+	0.216214i	$0.930629\pi$
$642$	−7.75736	+	16.2426i	−0.0120831	+	0.0253001i
$643$	−636.000	−	636.000i	−0.989114	−	0.989114i	0.0108278	−	0.999941i	$-0.496553\pi$
$643$	−636.000	−	636.000i	−0.989114	−	0.989114i	−0.999941	+	0.0108278i	$0.996553\pi$
$644$	−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	0.987298	−	0.158879i	$-0.0507881\pi$
$647$	535.987	+	535.987i	0.828419	+	0.828419i	−0.158879	+	0.987298i	$0.550788\pi$
$648$	−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	0.353033	−	0.935611i	$-0.385150\pi$
$653$	−380.423	−	380.423i	−0.582578	−	0.582578i	−0.935611	+	0.353033i	$0.885150\pi$
$654$	−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	$0.315467\pi$
$661$			1106.00i			1.67322i	−0.547797	+	0.836611i	$0.684533\pi$
$662$	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	−0.352035	−	0.935987i	$-0.614510\pi$
$673$	393.000	−	393.000i	0.583952	−	0.583952i	0.935987	+	0.352035i	$0.114510\pi$
$674$	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	0.805571	−	0.592499i	$-0.201859\pi$
$677$	144.250	+	144.250i	0.213072	+	0.213072i	−0.592499	+	0.805571i	$0.701859\pi$
$678$	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	0.124626	−	0.992204i	$-0.460227\pi$
$683$	−592.555	−	592.555i	−0.867578	−	0.867578i	−0.992204	+	0.124626i	$0.960227\pi$
$684$	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	$0.136337\pi$
$691$			574.000i			0.830680i	−0.909666	+	0.415340i	$0.863663\pi$
$692$	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	$-0.705949\pi$
$701$		−	1118.64i		−	1.59578i	0.602802	−	0.797891i	$-0.294051\pi$
$702$	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	$-0.874184\pi$
$709$		−	546.000i		−	0.770099i	0.922896	−	0.385049i	$-0.125816\pi$
$710$	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	$0.0617432\pi$
$719$			277.186i			0.385516i	−0.981246	+	0.192758i	$0.938257\pi$
$720$	−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	−0.535221	−	0.844712i	$-0.679772\pi$
$727$	225.000	−	225.000i	0.309491	−	0.309491i	0.844712	+	0.535221i	$0.179772\pi$
$728$	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	0.617446	−	0.786614i	$-0.288168\pi$
$733$	−124.000	−	124.000i	−0.169168	−	0.169168i	−0.786614	+	0.617446i	$0.788168\pi$
$734$			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	$0.0761007\pi$
$739$			350.000i			0.473613i	−0.971557	+	0.236806i	$0.923899\pi$
$740$	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	0.995124	−	0.0986307i	$-0.0314463\pi$
$743$	666.095	+	666.095i	0.896493	+	0.896493i	−0.0986307	+	0.995124i	$0.531446\pi$
$744$	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	0.877860	−	0.478917i	$-0.158971\pi$
$757$	302.000	+	302.000i	0.398943	+	0.398943i	−0.478917	+	0.877860i	$0.658971\pi$
$758$	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	−0.108601	−	0.994085i	$-0.534637\pi$
$773$	684.479	−	684.479i	0.885484	−	0.885484i	0.994085	+	0.108601i	$0.0346371\pi$
$774$	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	−0.658528	−	0.752556i	$-0.728821\pi$
$787$	74.0000	−	74.0000i	0.0940280	−	0.0940280i	0.752556	+	0.658528i	$0.228821\pi$
$788$	−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	0.919146	−	0.393917i	$-0.128880\pi$
$797$	418.607	+	418.607i	0.525229	+	0.525229i	−0.393917	+	0.919146i	$0.628880\pi$
$798$	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	$-0.908062\pi$
$811$		−	462.000i		−	0.569667i	0.958577	−	0.284834i	$-0.0919383\pi$
$812$	−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	$0.223182\pi$
$821$			1059.25i			1.29019i	−0.764102	+	0.645095i	$0.776818\pi$
$822$	−33.6152	+	70.3848i	−0.0408944	+	0.0856262i
$823$	1089.00	−	1089.00i	1.32321	−	1.32321i	0.412044	−	0.911164i	$-0.364815\pi$
$823$	1089.00	−	1089.00i	1.32321	−	1.32321i	0.911164	−	0.412044i	$-0.135185\pi$
$824$		−	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	−0.338888	−	0.940827i	$-0.610051\pi$
$827$	497.803	−	497.803i	0.601939	−	0.601939i	0.940827	+	0.338888i	$0.110051\pi$
$828$	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	$-0.928028\pi$
$839$		−	376.181i		−	0.448368i	0.974547	−	0.224184i	$-0.0719717\pi$
$840$	−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	0.993457	−	0.114207i	$-0.0364328\pi$
$853$	750.000	+	750.000i	0.879250	+	0.879250i	−0.114207	+	0.993457i	$0.536433\pi$
$854$	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	−0.946607	−	0.322390i	$-0.895514\pi$
$857$	−1087.53	−	1087.53i	−1.26900	−	1.26900i	−0.322390	−	0.946607i	$-0.604486\pi$
$858$	−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	0.657110	−	0.753795i	$-0.271779\pi$
$863$	−83.4386	−	83.4386i	−0.0966844	−	0.0966844i	−0.753795	+	0.657110i	$0.771779\pi$
$864$	−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	0.889748	−	0.456452i	$-0.150880\pi$
$877$	380.000	+	380.000i	0.433295	+	0.433295i	−0.456452	+	0.889748i	$0.650880\pi$
$878$	−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	−0.873729	−	0.486413i	$-0.838305\pi$
$883$	−342.000	+	342.000i	−0.387316	+	0.387316i	0.486413	+	0.873729i	$0.338305\pi$
$884$	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	0.758498	−	0.651675i	$-0.225933\pi$
$887$	94.7523	+	94.7523i	0.106823	+	0.106823i	−0.651675	+	0.758498i	$0.725933\pi$
$888$	−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	0.775131	−	0.631801i	$-0.217684\pi$
$907$	130.000	+	130.000i	0.143330	+	0.143330i	−0.631801	+	0.775131i	$0.717684\pi$
$908$	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	$0.199612\pi$
$911$			1069.15i			1.17360i	−0.809734	+	0.586798i	$0.800388\pi$
$912$	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	$-0.716775\pi$
$919$		−	1428.00i		−	1.55386i	0.629585	−	0.776931i	$-0.283225\pi$
$920$	−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	$0.155338\pi$
$929$			871.156i			0.937735i	−0.883269	+	0.468867i	$0.844662\pi$
$930$	−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	−0.162745	+	0.986668i	$0.552035\pi$
$937$	−1077.00	+	1077.00i	−1.14941	+	1.14941i	−0.986668	+	0.162745i	$0.947965\pi$
$938$		−	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	−0.998003	−	0.0631590i	$-0.979882\pi$
$947$	−885.298	+	885.298i	−0.934844	+	0.934844i	0.0631590	+	0.998003i	$0.479882\pi$
$948$	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	0.421550	−	0.906805i	$-0.361486\pi$
$953$	−462.448	−	462.448i	−0.485255	−	0.485255i	−0.906805	+	0.421550i	$0.861486\pi$
$954$	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	0.975201	−	0.221323i	$-0.0710374\pi$
$967$	729.000	+	729.000i	0.753878	+	0.753878i	−0.221323	+	0.975201i	$0.571037\pi$
$968$	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	−0.120408	+	0.992725i	$0.538420\pi$
$977$	−1087.53	+	1087.53i	−1.11313	+	1.11313i	−0.992725	+	0.120408i	$0.961580\pi$
$978$	−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	−0.183798	+	0.982964i	$0.558839\pi$
$983$	−1146.93	+	1146.93i	−1.16676	+	1.16676i	−0.982964	+	0.183798i	$0.941161\pi$
$984$	−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	−0.796809	−	0.604231i	$-0.793480\pi$
$997$	−192.000	+	192.000i	−0.192578	+	0.192578i	0.604231	+	0.796809i	$0.293480\pi$
$998$	−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.62.2	yes	4
3.2	odd	2	inner	105.3.k.b.62.1	yes	4
5.3	odd	4		105.3.k.a.83.1	yes	4
7.6	odd	2		105.3.k.a.62.2	yes	4
15.8	even	4		105.3.k.a.83.2	yes	4
21.20	even	2		105.3.k.a.62.1	✓	4
35.13	even	4	inner	105.3.k.b.83.1	yes	4
105.83	odd	4	inner	105.3.k.b.83.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.k.a.62.1	✓	4	21.20	even	2
105.3.k.a.62.2	yes	4	7.6	odd	2
105.3.k.a.83.1	yes	4	5.3	odd	4
105.3.k.a.83.2	yes	4	15.8	even	4
105.3.k.b.62.1	yes	4	3.2	odd	2	inner
105.3.k.b.62.2	yes	4	1.1	even	1	trivial
105.3.k.b.83.1	yes	4	35.13	even	4	inner
105.3.k.b.83.2	yes	4	105.83	odd	4	inner

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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