LMFDB - Embedded newform 105.3.k.b.83.1

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			83.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	105.83
Dual form			105.3.k.b.62.1

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

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

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.353553	−	0.353553i	0.507877	−	0.861430i	$-0.330431\pi$
$2$	−0.707107	−	0.707107i	−0.353553	−	0.353553i	−0.861430	+	0.507877i	$0.830431\pi$
$3$	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	$0.148568\pi$
$11$			9.89949i			0.899954i	−0.893040	+	0.449977i	$0.851432\pi$
$12$	−8.12132	−	3.87868i	−0.676777	−	0.323223i
$13$	8.00000	−	8.00000i	0.615385	−	0.615385i	−0.328959	−	0.944344i	$-0.606698\pi$
$13$	8.00000	−	8.00000i	0.615385	−	0.615385i	0.944344	+	0.328959i	$0.106698\pi$
$14$	4.94975	−	4.94975i	0.353553	−	0.353553i
$15$	−14.3137	−	4.48528i	−0.954247	−	0.299019i
$16$	−5.00000			−0.312500
$17$	18.3848	−	18.3848i	1.08146	−	1.08146i	0.0850836	−	0.996374i	$-0.472884\pi$
$17$	18.3848	−	18.3848i	1.08146	−	1.08146i	0.996374	−	0.0850836i	$-0.0271157\pi$
$18$	−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	0.0463637	−	0.998925i	$-0.485237\pi$
$23$	24.0416	−	24.0416i	1.04529	−	1.04529i	0.998925	−	0.0463637i	$-0.0147633\pi$
$24$	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	$0.0725017\pi$
$31$			14.0000i			0.451613i	−0.974172	+	0.225806i	$0.927498\pi$
$32$	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	−0.173945	−	0.984755i	$-0.555651\pi$
$37$	30.0000	−	30.0000i	0.810811	−	0.810811i	0.984755	+	0.173945i	$0.0556514\pi$
$38$	7.07107	+	7.07107i	0.186081	+	0.186081i
$39$	−11.3137	−	32.0000i	−0.290095	−	0.820513i
$40$	28.0000	+	21.0000i	0.700000	+	0.525000i
$41$	33.9411			0.827832			0.413916	−	0.910315i	$-0.364161\pi$
$41$	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	0.988491	−	0.151281i	$-0.0483400\pi$
$43$	36.0000	+	36.0000i	0.837209	+	0.837209i	−0.151281	+	0.988491i	$0.548340\pi$
$44$	29.6985			0.674966
$45$	−30.6482	+	32.9497i	−0.681072	+	0.732217i
$46$	−34.0000			−0.739130
$47$	4.24264	−	4.24264i	0.0902690	−	0.0902690i	−0.660530	−	0.750799i	$-0.729669\pi$
$47$	4.24264	−	4.24264i	0.0902690	−	0.0902690i	0.750799	+	0.660530i	$0.229669\pi$
$48$	−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	−0.432557	+	0.901606i	$0.642389\pi$
$53$	−70.7107	+	70.7107i	−1.33416	+	1.33416i	−0.901606	+	0.432557i	$0.857611\pi$
$54$	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	$-0.919016\pi$
$59$		−	29.6985i		−	0.503364i	0.967810	−	0.251682i	$-0.0809837\pi$
$60$	−13.4558	+	42.9411i	−0.224264	+	0.715685i
$61$		−	14.0000i		−	0.229508i	−0.993394	−	0.114754i	$-0.963392\pi$
$61$		−	14.0000i		−	0.229508i	0.993394	−	0.114754i	$-0.0366080\pi$
$62$	9.89949	−	9.89949i	0.159669	−	0.159669i
$63$	49.0000	−	39.5980i	0.777778	−	0.628539i
$64$		−	13.0000i		−	0.203125i
$65$	−45.2548	−	33.9411i	−0.696228	−	0.522171i
$66$	−9.89949	−	28.0000i	−0.149992	−	0.424242i
$67$	32.0000	−	32.0000i	0.477612	−	0.477612i	−0.426755	−	0.904367i	$-0.640343\pi$
$67$	32.0000	−	32.0000i	0.477612	−	0.477612i	0.904367	+	0.426755i	$0.140343\pi$
$68$	−55.1543	−	55.1543i	−0.811093	−	0.811093i
$69$	−34.0000	−	96.1665i	−0.492754	−	1.39372i
$70$	−28.0000	−	21.0000i	−0.400000	−	0.300000i
$71$			59.3970i			0.836577i	0.908314	+	0.418289i	$0.137370\pi$
$71$			59.3970i			0.836577i	−0.908314	+	0.418289i	$0.862630\pi$
$72$	62.6482	+	6.64823i	0.870114	+	0.0923366i
$73$	39.0000	−	39.0000i	0.534247	−	0.534247i	−0.387587	−	0.921833i	$-0.626691\pi$
$73$	39.0000	−	39.0000i	0.534247	−	0.534247i	0.921833	+	0.387587i	$0.126691\pi$
$74$	−42.4264			−0.573330
$75$	−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	$0.115325\pi$
$79$			56.0000i			0.708861i	−0.935082	+	0.354430i	$0.884675\pi$
$80$	3.53553	+	24.7487i	0.0441942	+	0.309359i
$81$	−17.0000	+	79.1960i	−0.209877	+	0.977728i
$82$	−24.0000	−	24.0000i	−0.292683	−	0.292683i
$83$	36.7696	+	36.7696i	0.443007	+	0.443007i	0.893021	−	0.450015i	$-0.148581\pi$
$83$	36.7696	+	36.7696i	0.443007	+	0.443007i	−0.450015	+	0.893021i	$0.648581\pi$
$84$	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	$-0.964521\pi$
$89$		−	19.7990i		−	0.222461i	0.993795	−	0.111230i	$-0.0354791\pi$
$90$	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	0.983378	+	0.181571i	$0.0581181\pi$
$97$	113.000	+	113.000i	1.16495	+	1.16495i	0.181571	+	0.983378i	$0.441882\pi$
$98$	34.6482	+	34.6482i	0.353553	+	0.353553i
$99$	69.2965	−	56.0000i	0.699964	−	0.565657i
$100$	21.0000	+	72.0000i	0.210000	+	0.720000i
$101$	−91.9239			−0.910137			−0.455069	−	0.890456i	$-0.650385\pi$
$101$	−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	−0.730962	−	0.682418i	$-0.760928\pi$
$103$	−5.00000	+	5.00000i	−0.0485437	+	0.0485437i	0.682418	+	0.730962i	$0.260928\pi$
$104$			79.1960i			0.761500i
$105$	31.3970	−	100.196i	0.299019	−	0.954247i
$106$	100.000			0.943396
$107$	4.24264	+	4.24264i	0.0396508	+	0.0396508i	0.726654	−	0.687003i	$-0.241074\pi$
$107$	4.24264	+	4.24264i	0.0396508	+	0.0396508i	−0.687003	+	0.726654i	$0.741074\pi$
$108$	18.7904	+	78.7904i	0.173985	+	0.729540i
$109$			70.0000i			0.642202i	0.947045	+	0.321101i	$0.104053\pi$
$109$			70.0000i			0.642202i	−0.947045	+	0.321101i	$0.895947\pi$
$110$	−39.5980	−	29.6985i	−0.359982	−	0.269986i
$111$	−42.4264	−	120.000i	−0.382220	−	1.08108i
$112$		−	35.0000i		−	0.312500i
$113$	−12.7279	+	12.7279i	−0.112636	+	0.112636i	−0.761179	−	0.648542i	$-0.775379\pi$
$113$	−12.7279	+	12.7279i	−0.112636	+	0.112636i	0.648542	+	0.761179i	$0.275379\pi$
$114$	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	−0.992907	−	0.118892i	$-0.962066\pi$
$127$	−111.000	+	111.000i	−0.874016	+	0.874016i	0.118892	+	0.992907i	$0.462066\pi$
$128$	84.1457	−	84.1457i	0.657388	−	0.657388i
$129$	144.000	−	50.9117i	1.11628	−	0.394664i
$130$	8.00000	+	56.0000i	0.0615385	+	0.430769i
$131$	38.1838			0.291479			0.145740	−	0.989323i	$-0.453444\pi$
$131$	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	0.771014	−	0.636818i	$-0.219750\pi$
$137$	18.3848	+	18.3848i	0.134195	+	0.134195i	−0.636818	+	0.771014i	$0.719750\pi$
$138$	−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	0.838262	−	0.545268i	$-0.183572\pi$
$157$	46.0000	+	46.0000i	0.292994	+	0.292994i	−0.545268	+	0.838262i	$0.683572\pi$
$158$	39.5980	−	39.5980i	0.250620	−	0.250620i
$159$	100.000	+	282.843i	0.628931	+	1.77888i
$160$	99.0000	−	132.000i	0.618750	−	0.825000i
$161$	168.291	+	168.291i	1.04529	+	1.04529i
$162$	68.0208	−	43.9792i	0.419882	−	0.271476i
$163$	−138.000	−	138.000i	−0.846626	−	0.846626i	0.143085	−	0.989710i	$-0.454298\pi$
$163$	−138.000	−	138.000i	−0.846626	−	0.846626i	−0.989710	+	0.143085i	$0.954298\pi$
$164$		−	101.823i		−	0.620874i
$165$	44.4020	−	141.698i	0.269103	−	0.858779i
$166$		−	52.0000i		−	0.313253i
$167$	−91.9239	+	91.9239i	−0.550442	+	0.550442i	−0.926568	−	0.376126i	$-0.877256\pi$
$167$	−91.9239	+	91.9239i	−0.550442	+	0.550442i	0.376126	+	0.926568i	$0.377256\pi$
$168$	−138.593	+	49.0000i	−0.824958	+	0.291667i
$169$			41.0000i			0.242604i
$170$	18.3848	+	128.693i	0.108146	+	0.757020i
$171$	56.5685	+	70.0000i	0.330810	+	0.409357i
$172$	108.000	−	108.000i	0.627907	−	0.627907i
$173$	−223.446	−	223.446i	−1.29159	−	1.29159i	−0.933801	−	0.357793i	$-0.883529\pi$
$173$	−223.446	−	223.446i	−1.29159	−	1.29159i	−0.357793	−	0.933801i	$-0.616471\pi$
$174$	−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	$-0.582188\pi$
$181$		−	350.000i		−	1.93370i	0.255342	−	0.966851i	$-0.417812\pi$
$182$		−	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	$0.100657\pi$
$191$			118.794i			0.621958i	−0.950417	+	0.310979i	$0.899343\pi$
$192$	−35.1924	−	16.8076i	−0.183294	−	0.0875396i
$193$	67.0000	+	67.0000i	0.347150	+	0.347150i	0.859047	−	0.511897i	$-0.171057\pi$
$193$	67.0000	+	67.0000i	0.347150	+	0.347150i	−0.511897	+	0.859047i	$0.671057\pi$
$194$		−	159.806i		−	0.823743i
$195$	−150.392	+	78.6274i	−0.771241	+	0.403218i
$196$			147.000i			0.750000i
$197$	56.5685	+	56.5685i	0.287150	+	0.287150i	0.835952	−	0.548802i	$-0.184916\pi$
$197$	56.5685	+	56.5685i	0.287150	+	0.287150i	−0.548802	+	0.835952i	$0.684916\pi$
$198$	−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	−0.0648877	+	0.997893i	$0.520669\pi$
$223$	−237.000	+	237.000i	−1.06278	+	1.06278i	−0.997893	+	0.0648877i	$0.979331\pi$
$224$	−163.342	+	163.342i	−0.729204	+	0.729204i
$225$	184.765	+	128.402i	0.821176	+	0.570676i
$226$	18.0000			0.0796460
$227$	117.380	−	117.380i	0.517091	−	0.517091i	−0.399599	−	0.916690i	$-0.630851\pi$
$227$	117.380	−	117.380i	0.517091	−	0.517091i	0.916690	+	0.399599i	$0.130851\pi$
$228$	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	−0.973831	−	0.227272i	$-0.927019\pi$
$233$	−173.948	+	173.948i	−0.746559	+	0.746559i	0.227272	+	0.973831i	$0.427019\pi$
$234$	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	$-0.990753\pi$
$241$		−	14.0000i		−	0.0580913i	0.999578	−	0.0290456i	$-0.00924682\pi$
$242$	−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	−0.772538	−	0.634969i	$-0.781013\pi$
$257$	−35.3553	+	35.3553i	−0.137569	+	0.137569i	0.634969	+	0.772538i	$0.281013\pi$
$258$	−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	0.224695	−	0.974429i	$-0.427861\pi$
$263$	315.370	−	315.370i	1.19912	−	1.19912i	0.974429	−	0.224695i	$-0.0721385\pi$
$264$	−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	$0.165497\pi$
$269$			267.286i			0.993630i	−0.867857	+	0.496815i	$0.834503\pi$
$270$	53.7365	−	123.844i	0.199024	−	0.458682i
$271$			112.000i			0.413284i	0.978417	+	0.206642i	$0.0662536\pi$
$271$			112.000i			0.413284i	−0.978417	+	0.206642i	$0.933746\pi$
$272$	−91.9239	+	91.9239i	−0.337955	+	0.337955i
$273$	224.000	−	79.1960i	0.820513	−	0.290095i
$274$		−	26.0000i		−	0.0948905i
$275$	−69.2965	−	237.588i	−0.251987	−	0.863956i
$276$	−288.500	+	102.000i	−1.04529	+	0.369565i
$277$	102.000	−	102.000i	0.368231	−	0.368231i	−0.498601	−	0.866832i	$-0.666153\pi$
$277$	102.000	−	102.000i	0.368231	−	0.368231i	0.866832	+	0.498601i	$0.166153\pi$
$278$	97.5807	+	97.5807i	0.351010	+	0.351010i
$279$	98.0000	−	79.1960i	0.351254	−	0.283856i
$280$	−147.000	+	196.000i	−0.525000	+	0.700000i
$281$		−	296.985i		−	1.05689i	−0.848969	−	0.528443i	$-0.822776\pi$
$281$		−	296.985i		−	1.05689i	0.848969	−	0.528443i	$-0.177224\pi$
$282$	−7.75736	+	16.2426i	−0.0275084	+	0.0575980i
$283$	102.000	−	102.000i	0.360424	−	0.360424i	−0.503545	−	0.863969i	$-0.667971\pi$
$283$	102.000	−	102.000i	0.360424	−	0.360424i	0.863969	+	0.503545i	$0.167971\pi$
$284$	178.191			0.627433
$285$	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	0.948643	−	0.316349i	$-0.102457\pi$
$293$	185.262	+	185.262i	0.632293	+	0.632293i	−0.316349	+	0.948643i	$0.602457\pi$
$294$	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	0.545168	−	0.838327i	$-0.316466\pi$
$307$	−90.0000	−	90.0000i	−0.293160	−	0.293160i	−0.838327	+	0.545168i	$0.816466\pi$
$308$			207.889i			0.674966i
$309$	7.07107	+	20.0000i	0.0228837	+	0.0647249i
$310$	−56.0000	−	42.0000i	−0.180645	−	0.135484i
$311$	−299.813			−0.964030			−0.482015	−	0.876163i	$-0.660095\pi$
$311$	−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	−0.365368	−	0.930863i	$-0.619057\pi$
$313$	177.000	−	177.000i	0.565495	−	0.565495i	0.930863	+	0.365368i	$0.119057\pi$
$314$		−	65.0538i		−	0.207178i
$315$	−230.648	−	214.538i	−0.732217	−	0.681072i
$316$	168.000			0.531646
$317$	−213.546	−	213.546i	−0.673647	−	0.673647i	0.284908	−	0.958555i	$-0.408037\pi$
$317$	−213.546	−	213.546i	−0.673647	−	0.673647i	−0.958555	+	0.284908i	$0.908037\pi$
$318$	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	−0.223876	−	0.974618i	$-0.571871\pi$
$337$	253.000	−	253.000i	0.750742	−	0.750742i	0.974618	+	0.223876i	$0.0718710\pi$
$338$	28.9914	−	28.9914i	0.0857733	−	0.0857733i
$339$	18.0000	+	50.9117i	0.0530973	+	0.150182i
$340$	−234.000	+	312.000i	−0.688235	+	0.917647i
$341$	−138.593			−0.406431
$342$	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	0.418946	−	0.908011i	$-0.362400\pi$
$347$	−169.706	−	169.706i	−0.489065	−	0.489065i	−0.908011	+	0.418946i	$0.862400\pi$
$348$	−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	0.831683	−	0.555250i	$-0.187378\pi$
$353$	97.5807	+	97.5807i	0.276433	+	0.276433i	−0.555250	+	0.831683i	$0.687378\pi$
$354$	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	0.408618	−	0.912705i	$-0.366011\pi$
$367$	−185.000	−	185.000i	−0.504087	−	0.504087i	−0.912705	+	0.408618i	$0.866011\pi$
$368$	−120.208	+	120.208i	−0.326653	+	0.326653i
$369$	−192.000	−	237.588i	−0.520325	−	0.643870i
$370$	30.0000	+	210.000i	0.0810811	+	0.567568i
$371$	−494.975	−	494.975i	−1.33416	−	1.33416i
$372$	54.3015	−	113.698i	0.145972	−	0.305641i
$373$	492.000	+	492.000i	1.31903	+	1.31903i	0.914540	+	0.404494i	$0.132552\pi$
$373$	492.000	+	492.000i	1.31903	+	1.31903i	0.404494	+	0.914540i	$0.367448\pi$
$374$		−	257.387i		−	0.688200i
$375$	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	$-0.885868\pi$
$379$		−	266.000i		−	0.701847i	0.936404	−	0.350923i	$-0.114132\pi$
$380$	148.492	−	21.2132i	0.390770	−	0.0558242i
$381$	156.978	+	444.000i	0.412015	+	1.16535i
$382$	84.0000	−	84.0000i	0.219895	−	0.219895i
$383$	−134.350	−	134.350i	−0.350784	−	0.350784i	0.509617	−	0.860401i	$-0.329787\pi$
$383$	−134.350	−	134.350i	−0.350784	−	0.350784i	−0.860401	+	0.509617i	$0.829787\pi$
$384$	−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	0.743880	−	0.668313i	$-0.232983\pi$
$397$	30.0000	+	30.0000i	0.0755668	+	0.0755668i	−0.668313	+	0.743880i	$0.732983\pi$
$398$	−84.8528	−	84.8528i	−0.213198	−	0.213198i
$399$	−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	$-0.968516\pi$
$401$		−	79.1960i		−	0.197496i	0.995112	−	0.0987481i	$-0.0314838\pi$
$402$	−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	$0.143991\pi$
$419$			366.281i			0.874180i	−0.899418	+	0.437090i	$0.856009\pi$
$420$	−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	$0.222361\pi$
$431$			554.372i			1.28625i	−0.765763	+	0.643123i	$0.777639\pi$
$432$	131.317	−	31.3173i	0.303975	−	0.0724937i
$433$	−153.000	+	153.000i	−0.353349	+	0.353349i	−0.861354	−	0.508005i	$-0.830383\pi$
$433$	−153.000	+	153.000i	−0.353349	+	0.353349i	0.508005	+	0.861354i	$0.330383\pi$
$434$	69.2965	+	69.2965i	0.159669	+	0.159669i
$435$	−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	−0.690965	−	0.722888i	$-0.742814\pi$
$443$	14.1421	−	14.1421i	0.0319236	−	0.0319236i	0.722888	+	0.690965i	$0.242814\pi$
$444$	−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	−0.961100	−	0.276199i	$-0.910925\pi$
$457$	−313.000	+	313.000i	−0.684902	+	0.684902i	0.276199	+	0.961100i	$0.410925\pi$
$458$	264.458	+	264.458i	0.577419	+	0.577419i
$459$	−367.696	+	598.000i	−0.801080	+	1.30283i
$460$	−306.000	+	408.000i	−0.665217	+	0.886957i
$461$	142.836			0.309839			0.154919	−	0.987927i	$-0.450488\pi$
$461$	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	0.737730	−	0.675095i	$-0.235898\pi$
$463$	29.0000	+	29.0000i	0.0626350	+	0.0626350i	−0.675095	+	0.737730i	$0.735898\pi$
$464$	−21.2132			−0.0457181
$465$	62.7939	−	200.392i	0.135041	−	0.430950i
$466$	246.000			0.527897
$467$	350.725	−	350.725i	0.751017	−	0.751017i	−0.223652	−	0.974669i	$-0.571798\pi$
$467$	350.725	−	350.725i	0.751017	−	0.751017i	0.974669	+	0.223652i	$0.0717979\pi$
$468$	−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	$-0.973656\pi$
$479$		−	79.1960i		−	0.165336i	0.996577	−	0.0826680i	$-0.0263441\pi$
$480$	−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	−0.803158	−	0.595766i	$-0.796849\pi$
$487$	−101.000	+	101.000i	−0.207392	+	0.207392i	0.595766	+	0.803158i	$0.296849\pi$
$488$	69.2965	+	69.2965i	0.142001	+	0.142001i
$489$	−552.000	+	195.161i	−1.12883	+	0.399103i
$490$	147.000	−	196.000i	0.300000	−	0.400000i
$491$			346.482i			0.705667i	0.935686	+	0.352833i	$0.114782\pi$
$491$			346.482i			0.705667i	−0.935686	+	0.352833i	$0.885218\pi$
$492$	−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	$0.206110\pi$
$499$			602.000i			1.20641i	−0.797585	+	0.603206i	$0.793890\pi$
$500$	341.533	−	154.856i	0.683065	−	0.309713i
$501$	130.000	+	367.696i	0.259481	+	0.733923i
$502$	−311.000	−	311.000i	−0.619522	−	0.619522i
$503$	−626.497	−	626.497i	−1.24552	−	1.24552i	−0.957678	−	0.287842i	$-0.907062\pi$
$503$	−626.497	−	626.497i	−1.24552	−	1.24552i	−0.287842	−	0.957678i	$-0.592938\pi$
$504$	−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	$0.123819\pi$
$509$			386.080i			0.758507i	−0.925293	+	0.379254i	$0.876181\pi$
$510$	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	−0.262639	+	0.964894i	$0.584593\pi$
$523$	−642.000	+	642.000i	−1.22753	+	1.22753i	−0.964894	+	0.262639i	$0.915407\pi$
$524$		−	114.551i		−	0.218609i
$525$	−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	−0.527685	−	0.849440i	$-0.676940\pi$
$547$	176.000	−	176.000i	0.321755	−	0.321755i	0.849440	+	0.527685i	$0.176940\pi$
$548$	55.1543	−	55.1543i	0.100647	−	0.100647i
$549$	−98.0000	+	79.1960i	−0.178506	+	0.144255i
$550$	−119.000	+	217.000i	−0.216364	+	0.394545i
$551$	−42.4264			−0.0769989
$552$	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	0.954206	−	0.299149i	$-0.0967027\pi$
$557$	364.867	+	364.867i	0.655058	+	0.655058i	−0.299149	+	0.954206i	$0.596703\pi$
$558$	−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	−0.995241	−	0.0974464i	$-0.968933\pi$
$563$	−615.183	−	615.183i	−1.09269	−	1.09269i	−0.0974464	−	0.995241i	$-0.531067\pi$
$564$	−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	−0.991544	−	0.129773i	$-0.958575\pi$
$577$	−647.000	−	647.000i	−1.12132	−	1.12132i	−0.129773	−	0.991544i	$-0.541425\pi$
$578$	−273.650	+	273.650i	−0.473443	+	0.473443i
$579$	268.000	−	94.7523i	0.462867	−	0.163648i
$580$	−63.0000	+	9.00000i	−0.108621	+	0.0155172i
$581$	−257.387	+	257.387i	−0.443007	+	0.443007i
$582$	−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	0.0775226	−	0.996991i	$-0.475299\pi$
$587$	630.739	−	630.739i	1.07451	−	1.07451i	0.996991	−	0.0775226i	$-0.0247010\pi$
$588$	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	0.999070	+	0.0431072i	$0.0137257\pi$
$593$	618.011	+	618.011i	1.04218	+	1.04218i	0.0431072	+	0.999070i	$0.486274\pi$
$594$	−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	$0.129604\pi$
$601$			476.000i			0.792013i	−0.918248	+	0.396007i	$0.870396\pi$
$602$	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	0.931671	−	0.363302i	$-0.118351\pi$
$607$	345.000	+	345.000i	0.568369	+	0.568369i	−0.363302	+	0.931671i	$0.618351\pi$
$608$	−233.345	−	233.345i	−0.383792	−	0.383792i
$609$	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	0.795365	−	0.606131i	$-0.207279\pi$
$613$	116.000	+	116.000i	0.189233	+	0.189233i	−0.606131	+	0.795365i	$0.707279\pi$
$614$			127.279i			0.207295i
$615$	−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	0.217403	−	0.976082i	$-0.430241\pi$
$617$	−468.105	−	468.105i	−0.758679	−	0.758679i	−0.976082	+	0.217403i	$0.930241\pi$
$618$	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	$0.0693708\pi$
$641$			277.186i			0.432427i	−0.976346	+	0.216214i	$0.930629\pi$
$642$	−16.2426	−	7.75736i	−0.0253001	−	0.0120831i
$643$	−636.000	+	636.000i	−0.989114	+	0.989114i	−0.999941	−	0.0108278i	$-0.996553\pi$
$643$	−636.000	+	636.000i	−0.989114	+	0.989114i	0.0108278	+	0.999941i	$0.496553\pi$
$644$	504.874	−	504.874i	0.783966	−	0.783966i
$645$	−353.823	−	676.764i	−0.548563	−	1.04925i
$646$	260.000			0.402477
$647$	−535.987	+	535.987i	−0.828419	+	0.828419i	−0.987298	−	0.158879i	$-0.949212\pi$
$647$	−535.987	+	535.987i	−0.828419	+	0.828419i	0.158879	+	0.987298i	$0.449212\pi$
$648$	−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	−0.353033	−	0.935611i	$-0.614850\pi$
$653$	380.423	−	380.423i	0.582578	−	0.582578i	0.935611	+	0.353033i	$0.114850\pi$
$654$	−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	$-0.684533\pi$
$661$		−	1106.00i		−	1.67322i	0.547797	−	0.836611i	$-0.315467\pi$
$662$	−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	0.935987	−	0.352035i	$-0.114510\pi$
$673$	393.000	+	393.000i	0.583952	+	0.583952i	−0.352035	+	0.935987i	$0.614510\pi$
$674$	−357.796			−0.530855
$675$	586.479	−	334.167i	0.868857	−	0.495062i
$676$	123.000			0.181953
$677$	−144.250	+	144.250i	−0.213072	+	0.213072i	−0.805571	−	0.592499i	$-0.798141\pi$
$677$	−144.250	+	144.250i	−0.213072	+	0.213072i	0.592499	+	0.805571i	$0.298141\pi$
$678$	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	−0.124626	−	0.992204i	$-0.539773\pi$
$683$	592.555	−	592.555i	0.867578	−	0.867578i	0.992204	+	0.124626i	$0.0397732\pi$
$684$	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	$-0.863663\pi$
$691$		−	574.000i		−	0.830680i	0.909666	−	0.415340i	$-0.136337\pi$
$692$	−670.337	+	670.337i	−0.968695	+	0.968695i
$693$	392.000	+	485.075i	0.565657	+	0.699964i
$694$			240.000i			0.345821i
$695$	97.5807	+	683.065i	0.140404	+	0.982828i
$696$	29.6985	+	84.0000i	0.0426702	+	0.120690i
$697$	624.000	−	624.000i	0.895265	−	0.895265i
$698$	315.370	+	315.370i	0.451819	+	0.451819i
$699$	246.000	+	695.793i	0.351931	+	0.995412i
$700$	−504.000	+	147.000i	−0.720000	+	0.210000i
$701$		−	1118.64i		−	1.59578i	−0.602802	−	0.797891i	$-0.705949\pi$
$701$		−	1118.64i		−	1.59578i	0.602802	−	0.797891i	$-0.294051\pi$
$702$	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	$0.125816\pi$
$709$			546.000i			0.770099i	−0.922896	+	0.385049i	$0.874184\pi$
$710$	−237.588	−	178.191i	−0.334631	−	0.250973i
$711$	392.000	−	316.784i	0.551336	−	0.445547i
$712$	98.0000	+	98.0000i	0.137640	+	0.137640i
$713$	336.583	+	336.583i	0.472066	+	0.472066i
$714$	−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	$0.0617432\pi$
$719$			277.186i			0.385516i	−0.981246	+	0.192758i	$0.938257\pi$
$720$	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	0.844712	−	0.535221i	$-0.179772\pi$
$727$	225.000	+	225.000i	0.309491	+	0.309491i	−0.535221	+	0.844712i	$0.679772\pi$
$728$	−554.372			−0.761500
$729$	650.538	−	329.000i	0.892371	−	0.451303i
$730$	39.0000	+	273.000i	0.0534247	+	0.373973i
$731$	1323.70			1.81081
$732$	−54.3015	+	113.698i	−0.0741824	+	0.155326i
$733$	−124.000	+	124.000i	−0.169168	+	0.169168i	−0.786614	−	0.617446i	$-0.788168\pi$
$733$	−124.000	+	124.000i	−0.169168	+	0.169168i	0.617446	+	0.786614i	$0.288168\pi$
$734$			261.630i			0.356443i
$735$	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	$-0.923899\pi$
$739$		−	350.000i		−	0.473613i	0.971557	−	0.236806i	$-0.0761007\pi$
$740$	−381.838	+	509.117i	−0.515997	+	0.687996i
$741$	113.137	+	320.000i	0.152682	+	0.431849i
$742$			700.000i			0.943396i
$743$	−666.095	+	666.095i	−0.896493	+	0.896493i	−0.995124	−	0.0986307i	$-0.968554\pi$
$743$	−666.095	+	666.095i	−0.896493	+	0.896493i	0.0986307	+	0.995124i	$0.468554\pi$
$744$	−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	−0.478917	−	0.877860i	$-0.658971\pi$
$757$	302.000	−	302.000i	0.398943	−	0.398943i	0.877860	+	0.478917i	$0.158971\pi$
$758$	−188.090	+	188.090i	−0.248140	+	0.248140i
$759$	952.000	−	336.583i	1.25428	−	0.443456i
$760$	−280.000	−	210.000i	−0.368421	−	0.276316i
$761$	701.450			0.921748			0.460874	−	0.887466i	$-0.347536\pi$
$761$	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	0.108601	−	0.994085i	$-0.465363\pi$
$773$	−684.479	−	684.479i	−0.885484	−	0.885484i	−0.994085	+	0.108601i	$0.965363\pi$
$774$	−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	0.752556	−	0.658528i	$-0.228821\pi$
$787$	74.0000	+	74.0000i	0.0940280	+	0.0940280i	−0.658528	+	0.752556i	$0.728821\pi$
$788$	169.706	−	169.706i	0.215362	−	0.215362i
$789$	−446.000	−	1261.48i	−0.565272	−	1.59883i
$790$	−224.000	−	168.000i	−0.283544	−	0.212658i
$791$	−89.0955	−	89.0955i	−0.112636	−	0.112636i
$792$	−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	−0.919146	−	0.393917i	$-0.871120\pi$
$797$	−418.607	+	418.607i	−0.525229	+	0.525229i	0.393917	+	0.919146i	$0.371120\pi$
$798$	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	$0.0919383\pi$
$811$			462.000i			0.569667i	−0.958577	+	0.284834i	$0.908062\pi$
$812$	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	$0.223182\pi$
$821$			1059.25i			1.29019i	−0.764102	+	0.645095i	$0.776818\pi$
$822$	−70.3848	−	33.6152i	−0.0856262	−	0.0408944i
$823$	1089.00	+	1089.00i	1.32321	+	1.32321i	0.911164	+	0.412044i	$0.135185\pi$
$823$	1089.00	+	1089.00i	1.32321	+	1.32321i	0.412044	+	0.911164i	$0.364815\pi$
$824$		−	49.4975i		−	0.0600698i
$825$	−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	0.338888	−	0.940827i	$-0.389949\pi$
$827$	−497.803	−	497.803i	−0.601939	−	0.601939i	−0.940827	+	0.338888i	$0.889949\pi$
$828$	−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	$-0.928028\pi$
$839$		−	376.181i		−	0.448368i	0.974547	−	0.224184i	$-0.0719717\pi$
$840$	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	−0.114207	−	0.993457i	$-0.536433\pi$
$853$	750.000	−	750.000i	0.879250	−	0.879250i	0.993457	+	0.114207i	$0.0364328\pi$
$854$	−69.2965	−	69.2965i	−0.0811434	−	0.0811434i
$855$	306.482	−	329.497i	0.358459	−	0.385377i
$856$	−42.0000			−0.0490654
$857$	1087.53	−	1087.53i	1.26900	−	1.26900i	0.322390	−	0.946607i	$-0.395514\pi$
$857$	1087.53	−	1087.53i	1.26900	−	1.26900i	0.946607	−	0.322390i	$-0.104486\pi$
$858$	−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	−0.657110	−	0.753795i	$-0.728221\pi$
$863$	83.4386	−	83.4386i	0.0966844	−	0.0966844i	0.753795	+	0.657110i	$0.228221\pi$
$864$	−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	−0.456452	−	0.889748i	$-0.650880\pi$
$877$	380.000	−	380.000i	0.433295	−	0.433295i	0.889748	+	0.456452i	$0.150880\pi$
$878$	175.362	+	175.362i	0.199729	+	0.199729i
$879$	741.048	−	262.000i	0.843058	−	0.298066i
$880$	−245.000	+	35.0000i	−0.278409	+	0.0397727i
$881$	−25.4558			−0.0288943			−0.0144471	−	0.999896i	$-0.504599\pi$
$881$	−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	0.486413	−	0.873729i	$-0.338305\pi$
$883$	−342.000	−	342.000i	−0.387316	−	0.387316i	−0.873729	+	0.486413i	$0.838305\pi$
$884$	−882.469			−0.998268
$885$	−133.206	+	425.095i	−0.150515	+	0.480334i
$886$	−20.0000			−0.0225734
$887$	−94.7523	+	94.7523i	−0.106823	+	0.106823i	−0.758498	−	0.651675i	$-0.774067\pi$
$887$	−94.7523	+	94.7523i	−0.106823	+	0.106823i	0.651675	+	0.758498i	$0.274067\pi$
$888$	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	−0.631801	−	0.775131i	$-0.717684\pi$
$907$	130.000	−	130.000i	0.143330	−	0.143330i	0.775131	+	0.631801i	$0.217684\pi$
$908$	−352.139	−	352.139i	−0.387818	−	0.387818i
$909$	520.000	+	643.467i	0.572057	+	0.707885i
$910$	−392.000	+	56.0000i	−0.430769	+	0.0615385i
$911$			1069.15i			1.17360i	0.809734	+	0.586798i	$0.199612\pi$
$911$			1069.15i			1.17360i	−0.809734	+	0.586798i	$0.800388\pi$
$912$	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	$0.283225\pi$
$919$			1428.00i			1.55386i	−0.629585	+	0.776931i	$0.716775\pi$
$920$	1178.04	−	168.291i	1.28048	−	0.182925i
$921$	−360.000	+	127.279i	−0.390879	+	0.138197i
$922$	−101.000	−	101.000i	−0.109544	−	0.109544i
$923$	475.176	+	475.176i	0.514817	+	0.514817i
$924$	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	$0.155338\pi$
$929$			871.156i			0.937735i	−0.883269	+	0.468867i	$0.844662\pi$
$930$	−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	−0.986668	−	0.162745i	$-0.947965\pi$
$937$	−1077.00	−	1077.00i	−1.14941	−	1.14941i	−0.162745	−	0.986668i	$-0.552035\pi$
$938$		−	316.784i		−	0.337723i
$939$	−250.316	−	708.000i	−0.266577	−	0.753994i
$940$	−54.0000	+	72.0000i	−0.0574468	+	0.0765957i
$941$	−250.316			−0.266010			−0.133005	−	0.991115i	$-0.542463\pi$
$941$	−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	0.998003	−	0.0631590i	$-0.0201175\pi$
$947$	885.298	+	885.298i	0.934844	+	0.934844i	−0.0631590	+	0.998003i	$0.520118\pi$
$948$	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	−0.421550	−	0.906805i	$-0.638514\pi$
$953$	462.448	−	462.448i	0.485255	−	0.485255i	0.906805	+	0.421550i	$0.138514\pi$
$954$	−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	−0.221323	−	0.975201i	$-0.571037\pi$
$967$	729.000	−	729.000i	0.753878	−	0.753878i	0.975201	+	0.221323i	$0.0710374\pi$
$968$	−113.844	+	113.844i	−0.117608	+	0.117608i
$969$	260.000	+	735.391i	0.268318	+	0.758917i
$970$	−791.000	+	113.000i	−0.815464	+	0.116495i
$971$	−892.369			−0.919020			−0.459510	−	0.888173i	$-0.651975\pi$
$971$	−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	0.992725	+	0.120408i	$0.0384202\pi$
$977$	1087.53	+	1087.53i	1.11313	+	1.11313i	0.120408	+	0.992725i	$0.461580\pi$
$978$	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	0.982964	+	0.183798i	$0.0588393\pi$
$983$	1146.93	+	1146.93i	1.16676	+	1.16676i	0.183798	+	0.982964i	$0.441161\pi$
$984$	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	0.604231	−	0.796809i	$-0.293480\pi$
$997$	−192.000	−	192.000i	−0.192578	−	0.192578i	−0.796809	+	0.604231i	$0.793480\pi$
$998$	425.678	−	425.678i	0.426531	−	0.426531i
$999$	−600.000	+	975.807i	−0.600601	+	0.976784i

Twists

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

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

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