LMFDB - Embedded newform 105.3.k.b.62.1

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			62.1
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	105.62
Dual form			105.3.k.b.83.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(1.29289 + 2.70711i) q^{3} +3.00000i q^{4} +(-0.707107 + 4.94975i) q^{5} +(-2.82843 - 1.00000i) q^{6} -7.00000i q^{7} +(-4.94975 - 4.94975i) q^{8} +(-5.65685 + 7.00000i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.29289 + 2.70711i) 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} +(-8.12132 + 3.87868i) q^{12} +(8.00000 + 8.00000i) q^{13} +(4.94975 + 4.94975i) q^{14} +(-14.3137 + 4.48528i) q^{15} -5.00000 q^{16} +(18.3848 + 18.3848i) q^{17} +(-0.949747 - 8.94975i) q^{18} -10.0000 q^{19} +(-14.8492 - 2.12132i) q^{20} +(18.9497 - 9.05025i) 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} +(-26.2635 - 6.26346i) q^{27} +21.0000 q^{28} +4.24264 q^{29} +(6.94975 - 13.2929i) q^{30} -14.0000i q^{31} +(23.3345 - 23.3345i) q^{32} +(26.7990 - 12.7990i) 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} +(-30.6482 - 32.9497i) q^{45} -34.0000 q^{46} +(4.24264 + 4.24264i) q^{47} +(-6.46447 - 13.5355i) 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} +(-12.9289 - 27.0711i) q^{57} +(-3.00000 + 3.00000i) q^{58} +29.6985i q^{59} +(-13.4558 - 42.9411i) 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} +(62.6482 - 6.64823i) q^{72} +(39.0000 + 39.0000i) q^{73} -42.4264 q^{74} +(-12.0797 - 74.0208i) q^{75} -30.0000i q^{76} -69.2965 q^{77} +(-14.6274 - 30.6274i) 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} +(27.1508 + 56.8492i) q^{84} +(-104.000 + 78.0000i) q^{85} +50.9117i q^{86} +(5.48528 + 11.4853i) q^{87} +(-49.0000 + 49.0000i) q^{88} +19.7990i q^{89} +(44.9706 + 1.62742i) q^{90} +(56.0000 - 56.0000i) q^{91} +(-72.1249 + 72.1249i) q^{92} +(37.8995 - 18.1005i) 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	−0.861430	−	0.507877i	$-0.830431\pi$
$2$	−0.707107	+	0.707107i	−0.353553	+	0.353553i	0.507877	+	0.861430i	$0.330431\pi$
$3$	1.29289	+	2.70711i	0.430964	+	0.902369i
$3$	1.29289	+	2.70711i	0.430964	+	0.902369i
$4$			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	$-0.148568\pi$
$12$	−8.12132	+	3.87868i	−0.676777	+	0.323223i
$13$	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
$15$	−14.3137	+	4.48528i	−0.954247	+	0.299019i
$16$	−5.00000			−0.312500
$17$	18.3848	+	18.3848i	1.08146	+	1.08146i	0.996374	+	0.0850836i	$0.0271157\pi$
$17$	18.3848	+	18.3848i	1.08146	+	1.08146i	0.0850836	+	0.996374i	$0.472884\pi$
$18$	−0.949747	−	8.94975i	−0.0527637	−	0.497208i
$19$	−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
$21$	18.9497	−	9.05025i	0.902369	−	0.430964i
$22$	7.00000	+	7.00000i	0.318182	+	0.318182i
$23$	24.0416	+	24.0416i	1.04529	+	1.04529i	0.998925	+	0.0463637i	$0.0147633\pi$
$23$	24.0416	+	24.0416i	1.04529	+	1.04529i	0.0463637	+	0.998925i	$0.485237\pi$
$24$	7.00000	−	19.7990i	0.291667	−	0.824958i
$25$	−24.0000	−	7.00000i	−0.960000	−	0.280000i
$26$	−11.3137			−0.435143
$27$	−26.2635	−	6.26346i	−0.972721	−	0.231980i
$28$	21.0000			0.750000
$29$	4.24264			0.146298			0.0731490	−	0.997321i	$-0.476695\pi$
$29$	4.24264			0.146298			0.0731490	+	0.997321i	$0.476695\pi$
$30$	6.94975	−	13.2929i	0.231658	−	0.443096i
$31$		−	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
$33$	26.7990	−	12.7990i	0.812091	−	0.387848i
$34$	−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	$-0.364161\pi$
$41$	33.9411			0.827832			0.413916	+	0.910315i	$0.364161\pi$
$42$	−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
$45$	−30.6482	−	32.9497i	−0.681072	−	0.732217i
$46$	−34.0000			−0.739130
$47$	4.24264	+	4.24264i	0.0902690	+	0.0902690i	0.750799	−	0.660530i	$-0.229669\pi$
$47$	4.24264	+	4.24264i	0.0902690	+	0.0902690i	−0.660530	+	0.750799i	$0.729669\pi$
$48$	−6.46447	−	13.5355i	−0.134676	−	0.281990i
$49$	−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	$-0.857611\pi$
$53$	−70.7107	−	70.7107i	−1.33416	−	1.33416i	−0.432557	−	0.901606i	$-0.642389\pi$
$54$	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
$57$	−12.9289	−	27.0711i	−0.226823	−	0.474931i
$58$	−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	$0.919016\pi$
$60$	−13.4558	−	42.9411i	−0.224264	−	0.715685i
$61$			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	$-0.862630\pi$
$71$		−	59.3970i		−	0.836577i	0.908314	−	0.418289i	$-0.137370\pi$
$72$	62.6482	−	6.64823i	0.870114	−	0.0923366i
$73$	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
$75$	−12.0797	−	74.0208i	−0.161063	−	0.986944i
$76$		−	30.0000i		−	0.394737i
$77$	−69.2965			−0.899954
$78$	−14.6274	−	30.6274i	−0.187531	−	0.392659i
$79$		−	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	−0.450015	−	0.893021i	$-0.648581\pi$
$83$	36.7696	−	36.7696i	0.443007	−	0.443007i	0.893021	+	0.450015i	$0.148581\pi$
$84$	27.1508	+	56.8492i	0.323223	+	0.676777i
$85$	−104.000	+	78.0000i	−1.22353	+	0.917647i
$86$			50.9117i			0.591996i
$87$	5.48528	+	11.4853i	0.0630492	+	0.132015i
$88$	−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	$0.964521\pi$
$90$	44.9706	+	1.62742i	0.499673	+	0.0180824i
$91$	56.0000	−	56.0000i	0.615385	−	0.615385i
$92$	−72.1249	+	72.1249i	−0.783966	+	0.783966i
$93$	37.8995	−	18.1005i	0.407521	−	0.194629i
$94$	−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	$-0.650385\pi$
$101$	−91.9239			−0.910137			−0.455069	+	0.890456i	$0.650385\pi$
$102$	−33.6152	−	70.3848i	−0.329561	−	0.690047i
$103$	−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
$105$	31.3970	+	100.196i	0.299019	+	0.954247i
$106$	100.000			0.943396
$107$	4.24264	−	4.24264i	0.0396508	−	0.0396508i	−0.687003	−	0.726654i	$-0.741074\pi$
$107$	4.24264	−	4.24264i	0.0396508	−	0.0396508i	0.726654	+	0.687003i	$0.241074\pi$
$108$	18.7904	−	78.7904i	0.173985	−	0.729540i
$109$		−	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	0.648542	−	0.761179i	$-0.275379\pi$
$113$	−12.7279	−	12.7279i	−0.112636	−	0.112636i	−0.761179	+	0.648542i	$0.775379\pi$
$114$	28.2843	+	10.0000i	0.248108	+	0.0877193i
$115$	−136.000	+	102.000i	−1.18261	+	0.886957i
$116$			12.7279i			0.109723i
$117$	−101.255	+	10.7452i	−0.865426	+	0.0918390i
$118$	−21.0000	−	21.0000i	−0.177966	−	0.177966i
$119$	128.693	−	128.693i	1.08146	−	1.08146i
$120$	93.0503	+	48.6482i	0.775419	+	0.405402i
$121$	23.0000			0.190083
$122$	−9.89949	−	9.89949i	−0.0811434	−	0.0811434i
$123$	43.8823	+	91.8823i	0.356766	+	0.747010i
$124$	42.0000			0.338710
$125$	51.6188	−	113.844i	0.412950	−	0.910754i
$126$	−62.6482	+	6.64823i	−0.497208	+	0.0527637i
$127$	−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	$-0.453444\pi$
$131$	38.1838			0.291479			0.145740	+	0.989323i	$0.453444\pi$
$132$	38.3970	+	80.3970i	0.290886	+	0.609068i
$133$			70.0000i			0.526316i
$134$	−45.2548			−0.337723
$135$	49.5736	−	125.569i	0.367212	−	0.930137i
$136$		−	182.000i		−	1.33824i
$137$	18.3848	−	18.3848i	0.134195	−	0.134195i	−0.636818	−	0.771014i	$-0.719750\pi$
$137$	18.3848	−	18.3848i	0.134195	−	0.134195i	0.771014	+	0.636818i	$0.219750\pi$
$138$	−43.9584	−	92.0416i	−0.318539	−	0.666968i
$139$	−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
$147$	−63.3518	−	132.648i	−0.430964	−	0.902369i
$148$	−90.0000	+	90.0000i	−0.608108	+	0.608108i
$149$	−199.404			−1.33828			−0.669141	−	0.743135i	$-0.733338\pi$
$149$	−199.404			−1.33828			−0.669141	+	0.743135i	$0.733338\pi$
$150$	60.8823	+	43.7990i	0.405882	+	0.291993i
$151$	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
$153$	−232.693	+	24.6934i	−1.52087	+	0.161395i
$154$	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
$162$	68.0208	+	43.9792i	0.419882	+	0.271476i
$163$	−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
$165$	44.4020	+	141.698i	0.269103	+	0.858779i
$166$			52.0000i			0.313253i
$167$	−91.9239	−	91.9239i	−0.550442	−	0.550442i	0.376126	−	0.926568i	$-0.377256\pi$
$167$	−91.9239	−	91.9239i	−0.550442	−	0.550442i	−0.926568	+	0.376126i	$0.877256\pi$
$168$	−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	$0.616471\pi$
$173$	−223.446	+	223.446i	−1.29159	+	1.29159i	−0.933801	+	0.357793i	$0.883529\pi$
$174$	−12.0000	−	4.24264i	−0.0689655	−	0.0243830i
$175$	−49.0000	+	168.000i	−0.280000	+	0.960000i
$176$			49.4975i			0.281236i
$177$	−80.3970	+	38.3970i	−0.454220	+	0.216932i
$178$	−14.0000	−	14.0000i	−0.0786517	−	0.0786517i
$179$	−12.7279			−0.0711057			−0.0355529	−	0.999368i	$-0.511319\pi$
$179$	−12.7279			−0.0711057			−0.0355529	+	0.999368i	$0.511319\pi$
$180$	98.8492	−	91.9447i	0.549162	−	0.510804i
$181$			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
$183$	−37.8995	+	18.1005i	−0.207101	+	0.0989099i
$184$		−	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
$189$	−43.8442	+	183.844i	−0.231980	+	0.972721i
$190$	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	$-0.100657\pi$
$192$	−35.1924	+	16.8076i	−0.183294	+	0.0875396i
$193$	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
$195$	−150.392	−	78.6274i	−0.771241	−	0.403218i
$196$		−	147.000i		−	0.750000i
$197$	56.5685	−	56.5685i	0.287150	−	0.287150i	−0.548802	−	0.835952i	$-0.684916\pi$
$197$	56.5685	−	56.5685i	0.287150	−	0.287150i	0.835952	+	0.548802i	$0.184916\pi$
$198$	−88.5980	+	9.40202i	−0.447465	+	0.0474850i
$199$	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
$207$	−304.291	+	32.2914i	−1.47001	+	0.155997i
$208$	−40.0000	−	40.0000i	−0.192308	−	0.192308i
$209$			98.9949i			0.473660i
$210$	−93.0503	−	48.6482i	−0.443096	−	0.231658i
$211$	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
$213$	160.794	−	76.7939i	0.754901	−	0.360535i
$214$			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
$222$	−54.8528	−	114.853i	−0.247085	−	0.517355i
$223$	−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
$225$	184.765	−	128.402i	0.821176	−	0.570676i
$226$	18.0000			0.0796460
$227$	117.380	+	117.380i	0.517091	+	0.517091i	0.916690	−	0.399599i	$-0.130851\pi$
$227$	117.380	+	117.380i	0.517091	+	0.517091i	−0.399599	+	0.916690i	$0.630851\pi$
$228$	81.2132	−	38.7868i	0.356198	−	0.170118i
$229$	−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
$231$	−89.5929	−	187.593i	−0.387848	−	0.812091i
$232$	−21.0000	−	21.0000i	−0.0905172	−	0.0905172i
$233$	−173.948	−	173.948i	−0.746559	−	0.746559i	0.227272	−	0.973831i	$-0.427019\pi$
$233$	−173.948	−	173.948i	−0.746559	−	0.746559i	−0.973831	+	0.227272i	$0.927019\pi$
$234$	64.0000	−	79.1960i	0.273504	−	0.338444i
$235$	−24.0000	+	18.0000i	−0.102128	+	0.0765957i
$236$	−89.0955			−0.377523
$237$	151.598	−	72.4020i	0.639654	−	0.305494i
$238$			182.000i			0.764706i
$239$	291.328			1.21895			0.609473	−	0.792807i	$-0.291381\pi$
$239$	291.328			1.21895			0.609473	+	0.792807i	$0.291381\pi$
$240$	71.5685	−	22.4264i	0.298202	−	0.0934434i
$241$			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
$243$	192.413	−	148.413i	0.791822	−	0.610752i
$244$	−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	$-0.160113\pi$
$251$	439.820			1.75227			0.876136	+	0.482063i	$0.160113\pi$
$252$	−118.794	+	147.000i	−0.471405	+	0.583333i
$253$	238.000	−	238.000i	0.940711	−	0.940711i
$254$	156.978			0.618022
$255$	−345.615	−	180.693i	−1.35535	−	0.708602i
$256$	−171.000			−0.667969
$257$	−35.3553	−	35.3553i	−0.137569	−	0.137569i	0.634969	−	0.772538i	$-0.281013\pi$
$257$	−35.3553	−	35.3553i	−0.137569	−	0.137569i	−0.772538	+	0.634969i	$0.781013\pi$
$258$	−137.823	+	65.8234i	−0.534199	+	0.255129i
$259$	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	$0.0721385\pi$
$263$	315.370	+	315.370i	1.19912	+	1.19912i	0.224695	+	0.974429i	$0.427861\pi$
$264$	−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
$267$	−53.5980	+	25.5980i	−0.200741	+	0.0958726i
$268$	−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	$-0.165497\pi$
$270$	53.7365	+	123.844i	0.199024	+	0.458682i
$271$		−	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	$0.177224\pi$
$281$			296.985i			1.05689i	−0.848969	+	0.528443i	$0.822776\pi$
$282$	−7.75736	−	16.2426i	−0.0275084	−	0.0575980i
$283$	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
$285$	143.137	−	44.8528i	0.502235	−	0.157378i
$286$			112.000i			0.391608i
$287$		−	237.588i		−	0.827832i
$288$	31.3417	+	295.342i	0.108825	+	1.02549i
$289$			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	$-0.602457\pi$
$293$	185.262	−	185.262i	0.632293	−	0.632293i	0.948643	+	0.316349i	$0.102457\pi$
$294$	138.593	+	49.0000i	0.471405	+	0.166667i
$295$	−147.000	−	21.0000i	−0.498305	−	0.0711864i
$296$		−	296.985i		−	1.00333i
$297$	−62.0051	+	259.995i	−0.208771	+	0.875404i
$298$	141.000	−	141.000i	0.473154	−	0.473154i
$299$			384.666i			1.28651i
$300$	222.062	−	36.2391i	0.740208	−	0.120797i
$301$	−252.000	−	252.000i	−0.837209	−	0.837209i
$302$	−55.1543	+	55.1543i	−0.182630	+	0.182630i
$303$	−118.848	−	248.848i	−0.392237	−	0.821280i
$304$	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	$-0.660095\pi$
$311$	−299.813			−0.964030			−0.482015	+	0.876163i	$0.660095\pi$
$312$	214.392	−	102.392i	0.687154	−	0.328179i
$313$	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
$315$	−230.648	+	214.538i	−0.732217	+	0.681072i
$316$	168.000			0.531646
$317$	−213.546	+	213.546i	−0.673647	+	0.673647i	−0.958555	−	0.284908i	$-0.908037\pi$
$317$	−213.546	+	213.546i	−0.673647	+	0.673647i	0.284908	+	0.958555i	$0.408037\pi$
$318$	129.289	+	270.711i	0.406570	+	0.851291i
$319$		−	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
$327$	189.497	−	90.5025i	0.579503	−	0.276766i
$328$	−168.000	−	168.000i	−0.512195	−	0.512195i
$329$	29.6985	−	29.6985i	0.0902690	−	0.0902690i
$330$	−131.593	−	68.7990i	−0.398766	−	0.208482i
$331$	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
$333$	−379.706	+	40.2944i	−1.14026	+	0.121004i
$334$	130.000			0.389222
$335$	−181.019	+	135.765i	−0.540356	+	0.405267i
$336$	−94.7487	+	45.2513i	−0.281990	+	0.134676i
$337$	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
$342$	9.49747	+	89.4975i	0.0277704	+	0.261689i
$343$			343.000i			1.00000i
$344$	−356.382			−1.03599
$345$	−451.958	−	236.291i	−1.31002	−	0.684903i
$346$		−	316.000i		−	0.913295i
$347$	−169.706	+	169.706i	−0.489065	+	0.489065i	−0.908011	−	0.418946i	$-0.862400\pi$
$347$	−169.706	+	169.706i	−0.489065	+	0.489065i	0.418946	+	0.908011i	$0.362400\pi$
$348$	−34.4558	+	16.4558i	−0.0990110	+	0.0472869i
$349$	−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	$-0.687378\pi$
$353$	97.5807	−	97.5807i	0.276433	−	0.276433i	0.831683	+	0.555250i	$0.187378\pi$
$354$	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	$-0.612684\pi$
$359$	−248.902			−0.693319			−0.346660	+	0.937991i	$0.612684\pi$
$360$	−11.3919	+	314.794i	−0.0316442	+	0.874428i
$361$	−261.000			−0.722992
$362$	−247.487	−	247.487i	−0.683667	−	0.683667i
$363$	29.7365	+	62.2635i	0.0819189	+	0.171525i
$364$	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
$372$	54.3015	+	113.698i	0.145972	+	0.305641i
$373$	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
$375$	374.926	−	7.45079i	0.999803	−	0.0198688i
$376$		−	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	−0.860401	−	0.509617i	$-0.829787\pi$
$383$	−134.350	+	134.350i	−0.350784	+	0.350784i	0.509617	+	0.860401i	$0.329787\pi$
$384$	−119.000	+	336.583i	−0.309896	+	0.876518i
$385$	49.0000	−	343.000i	0.127273	−	0.890909i
$386$			94.7523i			0.245472i
$387$	48.3532	+	455.647i	0.124944	+	1.17738i
$388$	339.000	+	339.000i	0.873711	+	0.873711i
$389$	−329.512			−0.847074			−0.423537	−	0.905879i	$-0.639212\pi$
$389$	−329.512			−0.847074			−0.423537	+	0.905879i	$0.639212\pi$
$390$	161.941	−	50.7452i	0.415234	−	0.130116i
$391$			884.000i			2.26087i
$392$	242.538	+	242.538i	0.618718	+	0.618718i
$393$	49.3675	+	103.368i	0.125617	+	0.263022i
$394$			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
$399$	−189.497	+	90.5025i	−0.474931	+	0.226823i
$400$	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	$0.968516\pi$
$402$	−58.5097	−	122.510i	−0.145546	−	0.304750i
$403$	112.000	−	112.000i	0.277916	−	0.277916i
$404$		−	275.772i		−	0.682603i
$405$	404.021	−	28.1457i	0.997582	−	0.0694956i
$406$	21.0000	+	21.0000i	0.0517241	+	0.0517241i
$407$	296.985	−	296.985i	0.729693	−	0.729693i
$408$	492.693	−	235.307i	1.20758	−	0.576732i
$409$	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
$417$	−178.419	−	373.581i	−0.427864	−	0.895877i
$418$	−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	$-0.143991\pi$
$420$	−300.588	+	94.1909i	−0.715685	+	0.224264i
$421$	−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
$423$	−53.6985	+	5.69848i	−0.126947	+	0.0134716i
$424$			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	$-0.222361\pi$
$432$	131.317	+	31.3173i	0.303975	+	0.0724937i
$433$	−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
$435$	−60.7279	+	19.0294i	−0.139604	+	0.0437458i
$436$	210.000			0.481651
$437$	−240.416	−	240.416i	−0.550152	−	0.550152i
$438$	−71.3087	−	149.309i	−0.162805	−	0.340887i
$439$	−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	$-0.242814\pi$
$443$	14.1421	+	14.1421i	0.0319236	+	0.0319236i	−0.690965	+	0.722888i	$0.742814\pi$
$444$	−360.000	−	127.279i	−0.810811	−	0.286665i
$445$	−98.0000	−	14.0000i	−0.220225	−	0.0314607i
$446$	335.169			0.751499
$447$	−257.808	−	539.808i	−0.576752	−	1.20762i
$448$	91.0000			0.203125
$449$	647.710			1.44256			0.721280	−	0.692643i	$-0.243554\pi$
$449$	647.710			1.44256			0.721280	+	0.692643i	$0.243554\pi$
$450$	−39.8543	+	221.442i	−0.0885651	+	0.492094i
$451$		−	336.000i		−	0.745011i
$452$	38.1838	−	38.1838i	0.0844774	−	0.0844774i
$453$	100.846	+	211.154i	0.222617	+	0.466124i
$454$	−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	$-0.450488\pi$
$461$	142.836			0.309839			0.154919	+	0.987927i	$0.450488\pi$
$462$	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
$465$	62.7939	+	200.392i	0.135041	+	0.430950i
$466$	246.000			0.527897
$467$	350.725	+	350.725i	0.751017	+	0.751017i	0.974669	−	0.223652i	$-0.0717979\pi$
$467$	350.725	+	350.725i	0.751017	+	0.751017i	−0.223652	+	0.974669i	$0.571798\pi$
$468$	−32.2355	−	303.765i	−0.0688793	−	0.649069i
$469$	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
$477$	894.975	−	94.9747i	1.87626	−	0.199108i
$478$	−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	$0.973656\pi$
$480$	−229.342	+	438.665i	−0.477795	+	0.913886i
$481$			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	$-0.885218\pi$
$491$		−	346.482i		−	0.705667i	0.935686	−	0.352833i	$-0.114782\pi$
$492$	−275.647	+	131.647i	−0.560258	+	0.267575i
$493$	78.0000	+	78.0000i	0.158215	+	0.158215i
$494$	113.137			0.229022
$495$	−326.186	+	303.402i	−0.658961	+	0.612933i
$496$			70.0000i			0.141129i
$497$	−415.779			−0.836577
$498$	−140.770	+	67.2304i	−0.282670	+	0.135001i
$499$		−	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	$0.592938\pi$
$503$	−626.497	+	626.497i	−1.24552	+	1.24552i	−0.957678	+	0.287842i	$0.907062\pi$
$504$	−46.5376	−	438.538i	−0.0923366	−	0.870114i
$505$	65.0000	−	455.000i	0.128713	−	0.900990i
$506$			336.583i			0.665183i
$507$	110.991	−	53.0086i	0.218918	−	0.104553i
$508$	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	$-0.123819\pi$
$510$	372.156	−	116.617i	0.729718	−	0.228661i
$511$	273.000	−	273.000i	0.534247	−	0.534247i
$512$	−215.668	+	215.668i	−0.421226	+	0.421226i
$513$	262.635	+	62.6346i	0.511958	+	0.122095i
$514$	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	$-0.618498\pi$
$521$	−379.009			−0.727465			−0.363732	+	0.931503i	$0.618498\pi$
$522$	−4.02944	−	37.9706i	−0.00771923	−	0.0727405i
$523$	−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
$525$	−518.146	+	84.5578i	−0.986944	+	0.161063i
$526$	−446.000			−0.847909
$527$	257.387	−	257.387i	0.488400	−	0.488400i
$528$	−133.995	+	63.9949i	−0.253778	+	0.121203i
$529$			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
$537$	−16.4558	−	34.4558i	−0.0306440	−	0.0641636i
$538$	189.000	+	189.000i	0.351301	+	0.351301i
$539$			485.075i			0.899954i
$540$	376.706	+	148.721i	0.697603	+	0.275409i
$541$	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
$543$	−947.487	+	452.513i	−1.74491	+	0.833357i
$544$	858.000			1.57721
$545$	346.482	+	49.4975i	0.635747	+	0.0908211i
$546$	−214.392	+	102.392i	−0.392659	+	0.187531i
$547$	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
$552$	644.291	−	307.709i	1.16719	−	0.557443i
$553$	−392.000			−0.708861
$554$	−144.250			−0.260379
$555$	−563.970	−	294.853i	−1.01616	−	0.531266i
$556$		−	414.000i		−	0.744604i
$557$	364.867	−	364.867i	0.655058	−	0.655058i	−0.299149	−	0.954206i	$-0.596703\pi$
$557$	364.867	−	364.867i	0.655058	−	0.655058i	0.954206	+	0.299149i	$0.0967027\pi$
$558$	−125.296	+	13.2965i	−0.224546	+	0.0238288i
$559$	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	$0.531067\pi$
$563$	−615.183	+	615.183i	−1.09269	+	1.09269i	−0.995241	+	0.0974464i	$0.968933\pi$
$564$	−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	$-0.492088\pi$
$569$	28.2843			0.0497087			0.0248544	+	0.999691i	$0.492088\pi$
$570$	−69.4975	+	132.929i	−0.121925	+	0.233209i
$571$	−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
$573$	321.588	−	153.588i	0.561235	−	0.268042i
$574$	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
$582$	−432.612	+	206.612i	−0.743320	+	0.355004i
$583$	−700.000	+	700.000i	−1.20069	+	1.20069i
$584$		−	386.080i		−	0.661096i
$585$	18.4121	−	508.784i	0.0314737	−	0.869716i
$586$			262.000i			0.447099i
$587$	630.739	+	630.739i	1.07451	+	1.07451i	0.996991	+	0.0775226i	$0.0247010\pi$
$587$	630.739	+	630.739i	1.07451	+	1.07451i	0.0775226	+	0.996991i	$0.475299\pi$
$588$	397.945	−	190.055i	0.676777	−	0.323223i
$589$			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	$-0.486274\pi$
$593$	618.011	−	618.011i	1.04218	−	1.04218i	0.999070	−	0.0431072i	$-0.0137257\pi$
$594$	−140.000	−	227.688i	−0.235690	−	0.383314i
$595$	546.000	+	728.000i	0.917647	+	1.22353i
$596$		−	598.212i		−	1.00371i
$597$	155.147	+	324.853i	0.259878	+	0.544142i
$598$	−272.000	−	272.000i	−0.454849	−	0.454849i
$599$	96.1665			0.160545			0.0802726	−	0.996773i	$-0.474421\pi$
$599$	96.1665			0.160545			0.0802726	+	0.996773i	$0.474421\pi$
$600$	−306.593	+	426.176i	−0.510988	+	0.710293i
$601$		−	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
$603$	−405.019	+	42.9807i	−0.671674	+	0.0712780i
$604$			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
$609$	80.3970	−	38.3970i	0.132015	−	0.0630492i
$610$	56.0000	−	42.0000i	0.0918033	−	0.0688525i
$611$			67.8823i			0.111100i
$612$	−74.0803	−	698.080i	−0.121046	−	1.14065i
$613$	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
$615$	−485.823	+	152.235i	−0.789957	+	0.247537i
$616$	343.000	+	343.000i	0.556818	+	0.556818i
$617$	−468.105	+	468.105i	−0.758679	+	0.758679i	−0.976082	−	0.217403i	$-0.930241\pi$
$617$	−468.105	+	468.105i	−0.758679	+	0.758679i	0.217403	+	0.976082i	$0.430241\pi$
$618$	9.14214	+	19.1421i	0.0147931	+	0.0309743i
$619$	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
$627$	−267.990	+	127.990i	−0.427416	+	0.204131i
$628$	138.000	+	138.000i	0.219745	+	0.219745i
$629$			1103.09i			1.75371i
$630$	11.3919	−	314.794i	0.0180824	−	0.499673i
$631$	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
$633$	111.189	+	232.811i	0.175654	+	0.367790i
$634$		−	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	$-0.0693708\pi$
$642$	−16.2426	+	7.75736i	−0.0253001	+	0.0120831i
$643$	−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
$645$	−353.823	+	676.764i	−0.548563	+	1.04925i
$646$	260.000			0.402477
$647$	−535.987	−	535.987i	−0.828419	−	0.828419i	0.158879	−	0.987298i	$-0.449212\pi$
$647$	−535.987	−	535.987i	−0.828419	−	0.828419i	−0.987298	+	0.158879i	$0.949212\pi$
$648$	−307.854	+	476.146i	−0.475084	+	0.734793i
$649$	294.000			0.453005
$650$	271.529	+	79.1960i	0.417737	+	0.121840i
$651$	−126.704	−	265.296i	−0.194629	−	0.407521i
$652$	−414.000	−	414.000i	−0.634969	−	0.634969i
$653$	380.423	+	380.423i	0.582578	+	0.582578i	0.935611	−	0.353033i	$-0.114850\pi$
$653$	380.423	+	380.423i	0.582578	+	0.582578i	−0.353033	+	0.935611i	$0.614850\pi$
$654$	−70.0000	+	197.990i	−0.107034	+	0.302737i
$655$	−27.0000	+	189.000i	−0.0412214	+	0.288550i
$656$	−169.706			−0.258698
$657$	−493.617	+	52.3827i	−0.751320	+	0.0797301i
$658$			42.0000i			0.0638298i
$659$	−253.144			−0.384134			−0.192067	−	0.981382i	$-0.561519\pi$
$659$	−253.144			−0.384134			−0.192067	+	0.981382i	$0.561519\pi$
$660$	−425.095	+	133.206i	−0.644084	+	0.201827i
$661$			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
$663$	−796.313	+	380.313i	−1.20108	+	0.573624i
$664$	−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
$675$	586.479	+	334.167i	0.868857	+	0.495062i
$676$	123.000			0.181953
$677$	−144.250	−	144.250i	−0.213072	−	0.213072i	0.592499	−	0.805571i	$-0.298141\pi$
$677$	−144.250	−	144.250i	−0.213072	−	0.213072i	−0.805571	+	0.592499i	$0.798141\pi$
$678$	23.2721	+	48.7279i	0.0343246	+	0.0718701i
$679$	−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	$-0.0397732\pi$
$683$	592.555	+	592.555i	0.867578	+	0.867578i	−0.124626	+	0.992204i	$0.539773\pi$
$684$	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
$687$	−483.542	−	1012.46i	−0.703846	−	1.47374i
$688$	−180.000	+	180.000i	−0.261628	+	0.261628i
$689$		−	1131.37i		−	1.64205i
$690$	486.666	−	152.500i	0.705313	−	0.221014i
$691$			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	$0.294051\pi$
$701$			1118.64i			1.59578i	−0.602802	+	0.797891i	$0.705949\pi$
$702$	297.137	+	70.8629i	0.423272	+	0.100944i
$703$	−300.000	−	300.000i	−0.426743	−	0.426743i
$704$	128.693			0.182803
$705$	−79.7574	−	41.6985i	−0.113131	−	0.0591468i
$706$			138.000i			0.195467i
$707$			643.467i			0.910137i
$708$	−115.191	−	241.191i	−0.162699	−	0.340665i
$709$		−	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
$714$	−492.693	+	235.307i	−0.690047	+	0.329561i
$715$	336.000	+	448.000i	0.469930	+	0.626573i
$716$		−	38.1838i		−	0.0533293i
$717$	376.656	+	788.656i	0.525322	+	1.09994i
$718$	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	$-0.0617432\pi$
$720$	153.241	+	164.749i	0.212835	+	0.228818i
$721$	−35.0000	+	35.0000i	−0.0485437	+	0.0485437i
$722$	184.555	−	184.555i	0.255616	−	0.255616i
$723$	−37.8995	+	18.1005i	−0.0524198	+	0.0250353i
$724$	−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
$732$	−54.3015	−	113.698i	−0.0741824	−	0.155326i
$733$	−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
$735$	701.372	−	219.779i	0.954247	−	0.299019i
$736$	1122.00			1.52446
$737$	316.784	−	316.784i	0.429829	−	0.429829i
$738$	−32.2355	−	303.765i	−0.0436795	−	0.411605i
$739$			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	0.0986307	−	0.995124i	$-0.468554\pi$
$743$	−666.095	−	666.095i	−0.896493	−	0.896493i	−0.995124	+	0.0986307i	$0.968554\pi$
$744$	−277.186	−	98.0000i	−0.372562	−	0.131720i
$745$	141.000	−	987.000i	0.189262	−	1.32483i
$746$			695.793i			0.932698i
$747$	49.3869	+	465.387i	0.0661136	+	0.623008i
$748$	546.000	+	546.000i	0.729947	+	0.729947i
$749$	−29.6985	−	29.6985i	−0.0396508	−	0.0396508i
$750$	−259.844	+	270.381i	−0.346459	+	0.360508i
$751$	−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
$753$	568.641	+	1190.64i	0.755167	+	1.58120i
$754$	−48.0000			−0.0636605
$755$	−55.1543	+	386.080i	−0.0730521	+	0.511365i
$756$	−551.533	−	131.533i	−0.729540	−	0.173985i
$757$	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	$-0.347536\pi$
$761$	701.450			0.921748			0.460874	+	0.887466i	$0.347536\pi$
$762$	202.955	+	424.955i	0.266346	+	0.557684i
$763$	−490.000			−0.642202
$764$	356.382			0.466468
$765$	42.3128	−	1169.23i	0.0553109	−	1.52841i
$766$		−	190.000i		−	0.248042i
$767$	−237.588	+	237.588i	−0.309763	+	0.309763i
$768$	−221.085	−	462.915i	−0.287871	−	0.602754i
$769$	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	$-0.965363\pi$
$773$	−684.479	+	684.479i	−0.885484	+	0.885484i	0.108601	+	0.994085i	$0.465363\pi$
$774$	−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
$780$	235.882	−	451.176i	0.302413	−	0.578430i
$781$	−588.000			−0.752881
$782$	−625.082	−	625.082i	−0.799338	−	0.799338i
$783$	−111.426	−	26.5736i	−0.142307	−	0.0339382i
$784$	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
$792$	−65.8141	−	620.186i	−0.0830987	−	0.783063i
$793$	−112.000	+	112.000i	−0.141236	+	0.141236i
$794$			42.4264i			0.0534338i
$795$	1329.29	+	694.975i	1.67206	+	0.874182i
$796$			360.000i			0.452261i
$797$	−418.607	−	418.607i	−0.525229	−	0.525229i	0.393917	−	0.919146i	$-0.371120\pi$
$797$	−418.607	−	418.607i	−0.525229	−	0.525229i	−0.919146	+	0.393917i	$0.871120\pi$
$798$	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
$807$	723.573	−	345.573i	0.896620	−	0.428219i
$808$	455.000	+	455.000i	0.563119	+	0.563119i
$809$	−576.999			−0.713225			−0.356613	−	0.934252i	$-0.616068\pi$
$809$	−576.999			−0.713225			−0.356613	+	0.934252i	$0.616068\pi$
$810$	−265.784	+	305.588i	−0.328128	+	0.377269i
$811$		−	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
$813$	303.196	−	144.804i	0.372935	−	0.178111i
$814$			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
$819$	75.2162	+	708.784i	0.0918390	+	0.865426i
$820$	−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	$-0.223182\pi$
$822$	−70.3848	+	33.6152i	−0.0856262	+	0.0408944i
$823$	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
$825$	−732.769	+	119.583i	−0.888204	+	0.144949i
$826$	−147.000	+	147.000i	−0.177966	+	0.177966i
$827$	−497.803	+	497.803i	−0.601939	+	0.601939i	−0.940827	−	0.338888i	$-0.889949\pi$
$827$	−497.803	+	497.803i	−0.601939	+	0.601939i	0.338888	+	0.940827i	$0.389949\pi$
$828$	−96.8742	−	912.874i	−0.116998	−	1.10251i
$829$	−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
$837$	−87.6884	+	367.688i	−0.104765	+	0.439293i
$838$	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	$0.928028\pi$
$840$	340.538	−	651.352i	0.405402	−	0.775419i
$841$	−823.000			−0.978597
$842$	434.164	−	434.164i	0.515634	−	0.515634i
$843$	−803.970	+	383.970i	−0.953701	+	0.455480i
$844$			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
$852$	230.382	+	482.382i	0.270401	+	0.566176i
$853$	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
$855$	306.482	+	329.497i	0.358459	+	0.385377i
$856$	−42.0000			−0.0490654
$857$	1087.53	+	1087.53i	1.26900	+	1.26900i	0.946607	+	0.322390i	$0.104486\pi$
$857$	1087.53	+	1087.53i	1.26900	+	1.26900i	0.322390	+	0.946607i	$0.395514\pi$
$858$	−303.196	+	144.804i	−0.353375	+	0.168769i
$859$	−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
$861$	643.176	−	307.176i	0.747010	−	0.356766i
$862$	392.000	+	392.000i	0.454756	+	0.454756i
$863$	83.4386	+	83.4386i	0.0966844	+	0.0966844i	0.753795	−	0.657110i	$-0.228221\pi$
$863$	83.4386	+	83.4386i	0.0966844	+	0.0966844i	−0.657110	+	0.753795i	$0.728221\pi$
$864$	−759.000	+	466.690i	−0.878472	+	0.540151i
$865$	−948.000	−	1264.00i	−1.09595	−	1.46127i
$866$	216.375			0.249855
$867$	−1047.65	+	500.350i	−1.20836	+	0.577105i
$868$		−	294.000i		−	0.338710i
$869$	−554.372			−0.637942
$870$	29.4853	−	56.3970i	0.0338911	−	0.0648241i
$871$			512.000i			0.587830i
$872$	−346.482	+	346.482i	−0.397342	+	0.397342i
$873$	151.775	+	1430.22i	0.173855	+	1.63829i
$874$	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	$-0.504599\pi$
$881$	−25.4558			−0.0288943			−0.0144471	+	0.999896i	$0.504599\pi$
$882$	46.5376	+	438.538i	0.0527637	+	0.497208i
$883$	−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
$885$	−133.206	−	425.095i	−0.150515	−	0.480334i
$886$	−20.0000			−0.0225734
$887$	−94.7523	−	94.7523i	−0.106823	−	0.106823i	0.651675	−	0.758498i	$-0.274067\pi$
$887$	−94.7523	−	94.7523i	−0.106823	−	0.106823i	−0.758498	+	0.651675i	$0.774067\pi$
$888$	803.970	−	383.970i	0.905371	−	0.432398i
$889$	−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
$897$	−1041.33	+	497.332i	−1.16091	+	0.554439i
$898$	−458.000	+	458.000i	−0.510022	+	0.510022i
$899$		−	59.3970i		−	0.0660700i
$900$	385.206	+	554.294i	0.428007	+	0.615882i
$901$		−	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	$-0.800388\pi$
$911$		−	1069.15i		−	1.17360i	0.809734	−	0.586798i	$-0.199612\pi$
$912$	64.6447	+	135.355i	0.0708823	+	0.148416i
$913$	−364.000	−	364.000i	−0.398686	−	0.398686i
$914$	442.649			0.484299
$915$	−62.7939	−	200.392i	−0.0686273	−	0.219008i
$916$		−	1122.00i		−	1.22489i
$917$		−	267.286i		−	0.291479i
$918$	682.850	+	162.850i	0.743845	+	0.177396i
$919$		−	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
$924$	562.779	−	268.779i	0.609068	−	0.290886i
$925$	−510.000	−	930.000i	−0.551351	−	1.00541i
$926$			41.0122i			0.0442896i
$927$	63.2843	−	6.71573i	0.0682678	−	0.00724458i
$928$	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	$-0.155338\pi$
$930$	−186.101	−	97.2965i	−0.200108	−	0.104620i
$931$	490.000			0.526316
$932$	521.845	−	521.845i	0.559919	−	0.559919i
$933$	−387.627	−	811.627i	−0.415463	−	0.869911i
$934$	−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	$-0.542463\pi$
$941$	−250.316			−0.266010			−0.133005	+	0.991115i	$0.542463\pi$
$942$	−176.108	+	84.1076i	−0.186951	+	0.0892863i
$943$	816.000	+	816.000i	0.865323	+	0.865323i
$944$		−	148.492i		−	0.157301i
$945$	−878.980	−	347.015i	−0.930137	−	0.367212i
$946$	504.000			0.532770
$947$	885.298	−	885.298i	0.934844	−	0.934844i	−0.0631590	−	0.998003i	$-0.520118\pi$
$947$	885.298	−	885.298i	0.934844	−	0.934844i	0.998003	+	0.0631590i	$0.0201175\pi$
$948$	217.206	+	454.794i	0.229120	+	0.479740i
$949$			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	$-0.138514\pi$
$953$	462.448	+	462.448i	0.485255	+	0.485255i	−0.421550	+	0.906805i	$0.638514\pi$
$954$	−565.685	+	700.000i	−0.592962	+	0.733753i
$955$	588.000	+	84.0000i	0.615707	+	0.0879581i
$956$			873.984i			0.914209i
$957$	113.698	−	54.3015i	0.118807	−	0.0567414i
$958$	−56.0000	−	56.0000i	−0.0584551	−	0.0584551i
$959$	−128.693	−	128.693i	−0.134195	−	0.134195i
$960$	−58.3087	−	186.078i	−0.0607382	−	0.193831i
$961$	765.000			0.796046
$962$	−339.411	−	339.411i	−0.352818	−	0.352818i
$963$	5.69848	+	53.6985i	0.00591743	+	0.0557617i
$964$	−42.0000			−0.0435685
$965$	284.257	+	379.009i	0.294567	+	0.392756i
$966$	−644.291	+	307.709i	−0.666968	+	0.318539i
$967$	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	$-0.651975\pi$
$971$	−892.369			−0.919020			−0.459510	+	0.888173i	$0.651975\pi$
$972$	445.238	+	577.238i	0.458064	+	0.593866i
$973$			966.000i			0.992806i
$974$	142.836			0.146648
$975$	495.529	−	688.804i	0.508235	−	0.706466i
$976$		−	70.0000i		−	0.0717213i
$977$	1087.53	−	1087.53i	1.11313	−	1.11313i	0.120408	−	0.992725i	$-0.461580\pi$
$977$	1087.53	−	1087.53i	1.11313	−	1.11313i	0.992725	−	0.120408i	$-0.0384202\pi$
$978$	528.323	−	252.323i	0.540208	−	0.257999i
$979$	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	$-0.441161\pi$
$983$	1146.93	−	1146.93i	1.16676	−	1.16676i	0.982964	−	0.183798i	$-0.0588393\pi$
$984$	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
$990$	16.1106	−	445.186i	0.0162733	−	0.449683i
$991$	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
$993$	131.875	+	276.125i	0.132805	+	0.278071i
$994$	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.62.1	yes	4
3.2	odd	2	inner	105.3.k.b.62.2	yes	4
5.3	odd	4		105.3.k.a.83.2	yes	4
7.6	odd	2		105.3.k.a.62.1	✓	4
15.8	even	4		105.3.k.a.83.1	yes	4
21.20	even	2		105.3.k.a.62.2	yes	4
35.13	even	4	inner	105.3.k.b.83.2	yes	4
105.83	odd	4	inner	105.3.k.b.83.1	yes	4

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.29289 + 2.70711i) q^{3} +3.00000i q^{4} +(-0.707107 + 4.94975i) q^{5} +(-2.82843 - 1.00000i) q^{6} -7.00000i q^{7} +(-4.94975 - 4.94975i) q^{8} +(-5.65685 + 7.00000i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.29289 + 2.70711i) 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} +(-8.12132 + 3.87868i) q^{12} +(8.00000 + 8.00000i) q^{13} +(4.94975 + 4.94975i) q^{14} +(-14.3137 + 4.48528i) q^{15} -5.00000 q^{16} +(18.3848 + 18.3848i) q^{17} +(-0.949747 - 8.94975i) q^{18} -10.0000 q^{19} +(-14.8492 - 2.12132i) q^{20} +(18.9497 - 9.05025i) 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} +(-26.2635 - 6.26346i) q^{27} +21.0000 q^{28} +4.24264 q^{29} +(6.94975 - 13.2929i) q^{30} -14.0000i q^{31} +(23.3345 - 23.3345i) q^{32} +(26.7990 - 12.7990i) 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} +(-30.6482 - 32.9497i) q^{45} -34.0000 q^{46} +(4.24264 + 4.24264i) q^{47} +(-6.46447 - 13.5355i) 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} +(-12.9289 - 27.0711i) q^{57} +(-3.00000 + 3.00000i) q^{58} +29.6985i q^{59} +(-13.4558 - 42.9411i) 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} +(62.6482 - 6.64823i) q^{72} +(39.0000 + 39.0000i) q^{73} -42.4264 q^{74} +(-12.0797 - 74.0208i) q^{75} -30.0000i q^{76} -69.2965 q^{77} +(-14.6274 - 30.6274i) 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} +(27.1508 + 56.8492i) q^{84} +(-104.000 + 78.0000i) q^{85} +50.9117i q^{86} +(5.48528 + 11.4853i) q^{87} +(-49.0000 + 49.0000i) q^{88} +19.7990i q^{89} +(44.9706 + 1.62742i) q^{90} +(56.0000 - 56.0000i) q^{91} +(-72.1249 + 72.1249i) q^{92} +(37.8995 - 18.1005i) 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

Related objects

Downloads

Learn more