LMFDB - Embedded newform 210.3.e.a.71.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(71,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

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

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

chi := DirichletCharacter("210.71");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.e (of order $2$, degree $1$, 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:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 34 x^{14} - 80 x^{13} + 97 x^{12} - 80 x^{11} + 498 x^{10} - 3288 x^{9} + \cdots + 43046721 $ x^16 - 8x^15 + 34x^14 - 80x^13 + 97x^12 - 80x^11 + 498x^10 - 3288x^9 + 11844x^8 - 29592x^7 + 40338x^6 - 58320x^5 + 636417x^4 - 4723920x^3 + 18068994x^2 - 38263752*x + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.5
Root			$0.812085 - 2.88800i$ of defining polynomial
Character	$\chi$	$=$	210.71
Dual form			210.3.e.a.71.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(-0.812085 + 2.88800i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(4.08424 + 1.14846i) q^{6} -2.64575 q^{7} +2.82843i q^{8} +(-7.68104 - 4.69059i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(-0.812085 + 2.88800i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(4.08424 + 1.14846i) q^{6} -2.64575 q^{7} +2.82843i q^{8} +(-7.68104 - 4.69059i) q^{9} -3.16228 q^{10} -19.7741i q^{11} +(1.62417 - 5.77599i) q^{12} +18.5947 q^{13} +3.74166i q^{14} +(6.45775 + 1.81588i) q^{15} +4.00000 q^{16} -13.2896i q^{17} +(-6.63350 + 10.8626i) q^{18} -5.47422 q^{19} +4.47214i q^{20} +(2.14857 - 7.64092i) q^{21} -27.9648 q^{22} -34.8062i q^{23} +(-8.16849 - 2.29692i) q^{24} -5.00000 q^{25} -26.2969i q^{26} +(19.7841 - 18.3736i) q^{27} +5.29150 q^{28} +6.83287i q^{29} +(2.56804 - 9.13264i) q^{30} -31.4842 q^{31} -5.65685i q^{32} +(57.1076 + 16.0583i) q^{33} -18.7944 q^{34} +5.91608i q^{35} +(15.3621 + 9.38119i) q^{36} -10.1809 q^{37} +7.74172i q^{38} +(-15.1005 + 53.7014i) q^{39} +6.32456 q^{40} +28.9124i q^{41} +(-10.8059 - 3.03854i) q^{42} -19.1117 q^{43} +39.5483i q^{44} +(-10.4885 + 17.1753i) q^{45} -49.2233 q^{46} -45.1245i q^{47} +(-3.24834 + 11.5520i) q^{48} +7.00000 q^{49} +7.07107i q^{50} +(38.3804 + 10.7923i) q^{51} -37.1894 q^{52} +74.1324i q^{53} +(-25.9843 - 27.9789i) q^{54} -44.2163 q^{55} -7.48331i q^{56} +(4.44553 - 15.8095i) q^{57} +9.66313 q^{58} -32.5630i q^{59} +(-12.9155 - 3.63175i) q^{60} +71.7631 q^{61} +44.5254i q^{62} +(20.3221 + 12.4101i) q^{63} -8.00000 q^{64} -41.5790i q^{65} +(22.7098 - 80.7624i) q^{66} +66.6261 q^{67} +26.5793i q^{68} +(100.520 + 28.2655i) q^{69} +8.36660 q^{70} +101.245i q^{71} +(13.2670 - 21.7253i) q^{72} +45.9939 q^{73} +14.3979i q^{74} +(4.06042 - 14.4400i) q^{75} +10.9484 q^{76} +52.3174i q^{77} +(75.9452 + 21.3553i) q^{78} -140.809 q^{79} -8.94427i q^{80} +(36.9967 + 72.0572i) q^{81} +40.8883 q^{82} -100.622i q^{83} +(-4.29715 + 15.2818i) q^{84} -29.7165 q^{85} +27.0280i q^{86} +(-19.7333 - 5.54887i) q^{87} +55.9297 q^{88} -11.2035i q^{89} +(24.2896 + 14.8330i) q^{90} -49.1969 q^{91} +69.6123i q^{92} +(25.5678 - 90.9263i) q^{93} -63.8157 q^{94} +12.2407i q^{95} +(16.3370 + 4.59384i) q^{96} +102.496 q^{97} -9.89949i q^{98} +(-92.7524 + 151.886i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} - 32 q^{4} + 16 q^{6} - 4 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 - 32 * q^4 + 16 * q^6 - 4 * q^9	$ 16 q - 8 q^{3} - 32 q^{4} + 16 q^{6} - 4 q^{9} + 16 q^{12} - 20 q^{15} + 64 q^{16} - 32 q^{18} + 48 q^{19} + 28 q^{21} - 96 q^{22} - 32 q^{24} - 80 q^{25} + 64 q^{27} - 88 q^{33} + 160 q^{34} + 8 q^{36} + 80 q^{37} + 156 q^{39} - 336 q^{43} - 80 q^{45} + 32 q^{46} - 32 q^{48} + 112 q^{49} + 84 q^{51} - 32 q^{54} - 80 q^{55} - 264 q^{57} + 96 q^{58} + 40 q^{60} + 112 q^{61} + 112 q^{63} - 128 q^{64} + 240 q^{67} + 8 q^{69} + 64 q^{72} + 48 q^{73} + 40 q^{75} - 96 q^{76} + 208 q^{78} + 8 q^{79} - 124 q^{81} - 608 q^{82} - 56 q^{84} + 120 q^{85} - 120 q^{87} + 192 q^{88} + 160 q^{90} - 56 q^{91} + 104 q^{93} + 32 q^{94} + 64 q^{96} - 192 q^{97} - 52 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 - 32 * q^4 + 16 * q^6 - 4 * q^9 + 16 * q^12 - 20 * q^15 + 64 * q^16 - 32 * q^18 + 48 * q^19 + 28 * q^21 - 96 * q^22 - 32 * q^24 - 80 * q^25 + 64 * q^27 - 88 * q^33 + 160 * q^34 + 8 * q^36 + 80 * q^37 + 156 * q^39 - 336 * q^43 - 80 * q^45 + 32 * q^46 - 32 * q^48 + 112 * q^49 + 84 * q^51 - 32 * q^54 - 80 * q^55 - 264 * q^57 + 96 * q^58 + 40 * q^60 + 112 * q^61 + 112 * q^63 - 128 * q^64 + 240 * q^67 + 8 * q^69 + 64 * q^72 + 48 * q^73 + 40 * q^75 - 96 * q^76 + 208 * q^78 + 8 * q^79 - 124 * q^81 - 608 * q^82 - 56 * q^84 + 120 * q^85 - 120 * q^87 + 192 * q^88 + 160 * q^90 - 56 * q^91 + 104 * q^93 + 32 * q^94 + 64 * q^96 - 192 * q^97 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$	−0.812085	+	2.88800i	−0.270695	+	0.962665i
$3$	−0.812085	+	2.88800i	−0.270695	+	0.962665i
$4$	−2.00000			−0.500000
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$	4.08424	+	1.14846i	0.680707	+	0.191410i
$7$	−2.64575			−0.377964
$7$	−2.64575			−0.377964
$8$			2.82843i			0.353553i
$9$	−7.68104	−	4.69059i	−0.853449	−	0.521177i
$10$	−3.16228			−0.316228
$11$		−	19.7741i		−	1.79765i	−0.438309	−	0.898824i	$-0.644423\pi$
$11$		−	19.7741i		−	1.79765i	0.438309	−	0.898824i	$-0.355577\pi$
$12$	1.62417	−	5.77599i	0.135347	−	0.481333i
$13$	18.5947			1.43036			0.715181	−	0.698940i	$-0.246344\pi$
$13$	18.5947			1.43036			0.715181	+	0.698940i	$0.246344\pi$
$14$			3.74166i			0.267261i
$15$	6.45775	+	1.81588i	0.430517	+	0.121058i
$16$	4.00000			0.250000
$17$		−	13.2896i		−	0.781743i	−0.920445	−	0.390872i	$-0.872174\pi$
$17$		−	13.2896i		−	0.781743i	0.920445	−	0.390872i	$-0.127826\pi$
$18$	−6.63350	+	10.8626i	−0.368528	+	0.603479i
$19$	−5.47422			−0.288117			−0.144058	−	0.989569i	$-0.546015\pi$
$19$	−5.47422			−0.288117			−0.144058	+	0.989569i	$0.546015\pi$
$20$			4.47214i			0.223607i
$21$	2.14857	−	7.64092i	0.102313	−	0.363853i
$22$	−27.9648			−1.27113
$23$		−	34.8062i		−	1.51331i	−0.653814	−	0.756656i	$-0.726832\pi$
$23$		−	34.8062i		−	1.51331i	0.653814	−	0.756656i	$-0.273168\pi$
$24$	−8.16849	−	2.29692i	−0.340354	−	0.0957051i
$25$	−5.00000			−0.200000
$26$		−	26.2969i		−	1.01142i
$27$	19.7841	−	18.3736i	0.732743	−	0.680505i
$28$	5.29150			0.188982
$29$			6.83287i			0.235616i	0.993036	+	0.117808i	$0.0375867\pi$
$29$			6.83287i			0.235616i	−0.993036	+	0.117808i	$0.962413\pi$
$30$	2.56804	−	9.13264i	0.0856012	−	0.304421i
$31$	−31.4842			−1.01562			−0.507810	−	0.861469i	$-0.669545\pi$
$31$	−31.4842			−1.01562			−0.507810	+	0.861469i	$0.669545\pi$
$32$		−	5.65685i		−	0.176777i
$33$	57.1076	+	16.0583i	1.73053	+	0.486614i
$34$	−18.7944			−0.552776
$35$			5.91608i			0.169031i
$36$	15.3621	+	9.38119i	0.426724	+	0.260589i
$37$	−10.1809			−0.275159			−0.137580	−	0.990491i	$-0.543932\pi$
$37$	−10.1809			−0.275159			−0.137580	+	0.990491i	$0.543932\pi$
$38$			7.74172i			0.203729i
$39$	−15.1005	+	53.7014i	−0.387191	+	1.37696i
$40$	6.32456			0.158114
$41$			28.9124i			0.705180i	0.935778	+	0.352590i	$0.114699\pi$
$41$			28.9124i			0.705180i	−0.935778	+	0.352590i	$0.885301\pi$
$42$	−10.8059	−	3.03854i	−0.257283	−	0.0723462i
$43$	−19.1117			−0.444458			−0.222229	−	0.974995i	$-0.571333\pi$
$43$	−19.1117			−0.444458			−0.222229	+	0.974995i	$0.571333\pi$
$44$			39.5483i			0.898824i
$45$	−10.4885	+	17.1753i	−0.233077	+	0.381674i
$46$	−49.2233			−1.07007
$47$		−	45.1245i		−	0.960096i	−0.877242	−	0.480048i	$-0.840619\pi$
$47$		−	45.1245i		−	0.960096i	0.877242	−	0.480048i	$-0.159381\pi$
$48$	−3.24834	+	11.5520i	−0.0676737	+	0.240666i
$49$	7.00000			0.142857
$50$			7.07107i			0.141421i
$51$	38.3804	+	10.7923i	0.752557	+	0.211614i
$52$	−37.1894			−0.715181
$53$			74.1324i			1.39872i	0.714767	+	0.699362i	$0.246533\pi$
$53$			74.1324i			1.39872i	−0.714767	+	0.699362i	$0.753467\pi$
$54$	−25.9843	−	27.9789i	−0.481190	−	0.518128i
$55$	−44.2163			−0.803933
$56$		−	7.48331i		−	0.133631i
$57$	4.44553	−	15.8095i	0.0779918	−	0.277360i
$58$	9.66313			0.166606
$59$		−	32.5630i		−	0.551916i	−0.961170	−	0.275958i	$-0.911005\pi$
$59$		−	32.5630i		−	0.551916i	0.961170	−	0.275958i	$-0.0889950\pi$
$60$	−12.9155	−	3.63175i	−0.215258	−	0.0605292i
$61$	71.7631			1.17644			0.588222	−	0.808700i	$-0.299828\pi$
$61$	71.7631			1.17644			0.588222	+	0.808700i	$0.299828\pi$
$62$			44.5254i			0.718152i
$63$	20.3221	+	12.4101i	0.322573	+	0.196986i
$64$	−8.00000			−0.125000
$65$		−	41.5790i		−	0.639677i
$66$	22.7098	−	80.7624i	0.344088	−	1.22367i
$67$	66.6261			0.994419			0.497210	−	0.867631i	$-0.334358\pi$
$67$	66.6261			0.994419			0.497210	+	0.867631i	$0.334358\pi$
$68$			26.5793i			0.390872i
$69$	100.520	+	28.2655i	1.45681	+	0.409646i
$70$	8.36660			0.119523
$71$			101.245i			1.42599i	0.701170	+	0.712994i	$0.252661\pi$
$71$			101.245i			1.42599i	−0.701170	+	0.712994i	$0.747339\pi$
$72$	13.2670	−	21.7253i	0.184264	−	0.301740i
$73$	45.9939			0.630053			0.315026	−	0.949083i	$-0.397987\pi$
$73$	45.9939			0.630053			0.315026	+	0.949083i	$0.397987\pi$
$74$			14.3979i			0.194567i
$75$	4.06042	−	14.4400i	0.0541390	−	0.192533i
$76$	10.9484			0.144058
$77$			52.3174i			0.679447i
$78$	75.9452	+	21.3553i	0.973657	+	0.273786i
$79$	−140.809			−1.78239			−0.891195	−	0.453620i	$-0.850132\pi$
$79$	−140.809			−1.78239			−0.891195	+	0.453620i	$0.850132\pi$
$80$		−	8.94427i		−	0.111803i
$81$	36.9967	+	72.0572i	0.456749	+	0.889596i
$82$	40.8883			0.498637
$83$		−	100.622i		−	1.21231i	−0.795347	−	0.606154i	$-0.792712\pi$
$83$		−	100.622i		−	1.21231i	0.795347	−	0.606154i	$-0.207288\pi$
$84$	−4.29715	+	15.2818i	−0.0511565	+	0.181927i
$85$	−29.7165			−0.349606
$86$			27.0280i			0.314279i
$87$	−19.7333	−	5.54887i	−0.226819	−	0.0637801i
$88$	55.9297			0.635565
$89$		−	11.2035i		−	0.125882i	−0.998017	−	0.0629410i	$-0.979952\pi$
$89$		−	11.2035i		−	0.125882i	0.998017	−	0.0629410i	$-0.0200480\pi$
$90$	24.2896	+	14.8330i	0.269884	+	0.164811i
$91$	−49.1969			−0.540626
$92$			69.6123i			0.756656i
$93$	25.5678	−	90.9263i	0.274923	−	0.977702i
$94$	−63.8157			−0.678890
$95$			12.2407i			0.128850i
$96$	16.3370	+	4.59384i	0.170177	+	0.0478525i
$97$	102.496			1.05666			0.528332	−	0.849038i	$-0.322818\pi$
$97$	102.496			1.05666			0.528332	+	0.849038i	$0.322818\pi$
$98$		−	9.89949i		−	0.101015i
$99$	−92.7524	+	151.886i	−0.936893	+	1.53420i
$100$	10.0000			0.100000
$101$		−	141.006i		−	1.39610i	−0.716050	−	0.698049i	$-0.754052\pi$
$101$		−	141.006i		−	1.39610i	0.716050	−	0.698049i	$-0.245948\pi$
$102$	15.2626	−	54.2781i	0.149634	−	0.532138i
$103$	59.0361			0.573166			0.286583	−	0.958055i	$-0.407481\pi$
$103$	59.0361			0.573166			0.286583	+	0.958055i	$0.407481\pi$
$104$			52.5937i			0.505709i
$105$	−17.0856	−	4.80436i	−0.162720	−	0.0457558i
$106$	104.839			0.989048
$107$			90.2764i			0.843705i	0.906664	+	0.421852i	$0.138620\pi$
$107$			90.2764i			0.843705i	−0.906664	+	0.421852i	$0.861380\pi$
$108$	−39.5681	+	36.7473i	−0.366372	+	0.340253i
$109$	−92.1672			−0.845570			−0.422785	−	0.906230i	$-0.638948\pi$
$109$	−92.1672			−0.845570			−0.422785	+	0.906230i	$0.638948\pi$
$110$			62.5313i			0.568466i
$111$	8.26774	−	29.4024i	0.0744842	−	0.264886i
$112$	−10.5830			−0.0944911
$113$		−	148.929i		−	1.31795i	−0.752163	−	0.658977i	$-0.770989\pi$
$113$		−	148.929i		−	1.31795i	0.752163	−	0.658977i	$-0.229011\pi$
$114$	−22.3580	−	6.28693i	−0.196123	−	0.0551485i
$115$	−77.8289			−0.676773
$116$		−	13.6657i		−	0.117808i
$117$	−142.827	−	87.2202i	−1.22074	−	0.745471i
$118$	−46.0511			−0.390263
$119$			35.1611i			0.295471i
$120$	−5.13607	+	18.2653i	−0.0428006	+	0.152211i
$121$	−270.016			−2.23154
$122$		−	101.488i		−	0.831871i
$123$	−83.4988	−	23.4793i	−0.678852	−	0.190889i
$124$	62.9684			0.507810
$125$			11.1803i			0.0894427i
$126$	17.5506	−	28.7398i	0.139290	−	0.228094i
$127$	77.7817			0.612455			0.306227	−	0.951958i	$-0.400933\pi$
$127$	77.7817			0.612455			0.306227	+	0.951958i	$0.400933\pi$
$128$			11.3137i			0.0883883i
$129$	15.5203	−	55.1944i	0.120312	−	0.427864i
$130$	−58.8016			−0.452320
$131$			229.780i			1.75405i	0.480447	+	0.877024i	$0.340474\pi$
$131$			229.780i			1.75405i	−0.480447	+	0.877024i	$0.659526\pi$
$132$	−114.215	−	32.1165i	−0.865267	−	0.243307i
$133$	14.4834			0.108898
$134$		−	94.2235i		−	0.703160i
$135$	−41.0847	−	44.2385i	−0.304331	−	0.327693i
$136$	37.5888			0.276388
$137$			143.560i			1.04788i	0.851754	+	0.523941i	$0.175539\pi$
$137$			143.560i			1.04788i	−0.851754	+	0.523941i	$0.824461\pi$
$138$	39.9735	−	142.157i	0.289663	−	1.03012i
$139$	−257.958			−1.85581			−0.927906	−	0.372815i	$-0.878393\pi$
$139$	−257.958			−1.85581			−0.927906	+	0.372815i	$0.878393\pi$
$140$		−	11.8322i		−	0.0845154i
$141$	130.319	+	36.6449i	0.924251	+	0.259893i
$142$	143.182			1.00833
$143$		−	367.694i		−	2.57129i
$144$	−30.7241	−	18.7624i	−0.213362	−	0.130294i
$145$	15.2788			0.105371
$146$		−	65.0451i		−	0.445515i
$147$	−5.68459	+	20.2160i	−0.0386707	+	0.137524i
$148$	20.3618			0.137580
$149$		−	117.530i		−	0.788791i	−0.918941	−	0.394396i	$-0.870954\pi$
$149$		−	117.530i		−	0.788791i	0.918941	−	0.394396i	$-0.129046\pi$
$150$	−20.4212	−	5.74231i	−0.136141	−	0.0382820i
$151$	251.056			1.66262			0.831311	−	0.555808i	$-0.187591\pi$
$151$	251.056			1.66262			0.831311	+	0.555808i	$0.187591\pi$
$152$		−	15.4834i		−	0.101865i
$153$	−62.3363	+	102.078i	−0.407427	+	0.667178i
$154$	73.9880			0.480442
$155$			70.4008i			0.454199i
$156$	30.2009	−	107.403i	0.193596	−	0.688479i
$157$	18.6419			0.118738			0.0593690	−	0.998236i	$-0.481091\pi$
$157$	18.6419			0.118738			0.0593690	+	0.998236i	$0.481091\pi$
$158$			199.134i			1.26034i
$159$	−214.094	−	60.2018i	−1.34650	−	0.378628i
$160$	−12.6491			−0.0790569
$161$			92.0884i			0.571978i
$162$	101.904	−	52.3212i	0.629039	−	0.322970i
$163$	−14.1896			−0.0870529			−0.0435265	−	0.999052i	$-0.513859\pi$
$163$	−14.1896			−0.0870529			−0.0435265	+	0.999052i	$0.513859\pi$
$164$		−	57.8247i		−	0.352590i
$165$	35.9074	−	127.696i	0.217620	−	0.773918i
$166$	−142.300			−0.857231
$167$			173.839i			1.04095i	0.853877	+	0.520476i	$0.174245\pi$
$167$			173.839i			1.04095i	−0.853877	+	0.520476i	$0.825755\pi$
$168$	21.6118	+	6.07708i	0.128642	+	0.0361731i
$169$	176.763			1.04593
$170$			42.0255i			0.247209i
$171$	42.0477	+	25.6773i	0.245893	+	0.150160i
$172$	38.2233			0.222229
$173$		−	164.076i		−	0.948415i	−0.880413	−	0.474207i	$-0.842735\pi$
$173$		−	164.076i		−	0.948415i	0.880413	−	0.474207i	$-0.157265\pi$
$174$	−7.84728	+	27.9071i	−0.0450993	+	0.160386i
$175$	13.2288			0.0755929
$176$		−	79.0965i		−	0.449412i
$177$	94.0419	+	26.4439i	0.531310	+	0.149401i
$178$	−15.8441			−0.0890120
$179$		−	267.494i		−	1.49438i	−0.664611	−	0.747189i	$-0.731403\pi$
$179$		−	267.494i		−	1.49438i	0.664611	−	0.747189i	$-0.268597\pi$
$180$	20.9770	−	34.3506i	0.116539	−	0.190837i
$181$	188.355			1.04063			0.520317	−	0.853973i	$-0.325814\pi$
$181$	188.355			1.04063			0.520317	+	0.853973i	$0.325814\pi$
$182$			69.5750i			0.382280i
$183$	−58.2777	+	207.251i	−0.318457	+	1.13252i
$184$	98.4467			0.535036
$185$			22.7652i			0.123055i
$186$	−128.589	−	36.1584i	−0.691340	−	0.194400i
$187$	−262.791			−1.40530
$188$			90.2490i			0.480048i
$189$	−52.3437	+	48.6121i	−0.276951	+	0.257207i
$190$	17.3110			0.0911106
$191$		−	300.383i		−	1.57268i	−0.617791	−	0.786342i	$-0.711972\pi$
$191$		−	300.383i		−	1.57268i	0.617791	−	0.786342i	$-0.288028\pi$
$192$	6.49668	−	23.1040i	0.0338369	−	0.120333i
$193$	209.232			1.08410			0.542051	−	0.840345i	$-0.317648\pi$
$193$	209.232			1.08410			0.542051	+	0.840345i	$0.317648\pi$
$194$		−	144.952i		−	0.747175i
$195$	120.080	+	33.7657i	0.615795	+	0.173157i
$196$	−14.0000			−0.0714286
$197$		−	97.0683i		−	0.492733i	−0.969177	−	0.246366i	$-0.920763\pi$
$197$		−	97.0683i		−	0.492733i	0.969177	−	0.246366i	$-0.0792366\pi$
$198$	214.799	+	131.172i	1.08484	+	0.662483i
$199$	292.070			1.46769			0.733845	−	0.679317i	$-0.237724\pi$
$199$	292.070			1.46769			0.733845	+	0.679317i	$0.237724\pi$
$200$		−	14.1421i		−	0.0707107i
$201$	−54.1060	+	192.416i	−0.269184	+	0.957293i
$202$	−199.413			−0.987191
$203$		−	18.0781i		−	0.0890545i
$204$	−76.7608	−	21.5846i	−0.376279	−	0.105807i
$205$	64.6500			0.315366
$206$		−	83.4897i		−	0.405290i
$207$	−163.262	+	267.347i	−0.788703	+	1.29153i
$208$	74.3788			0.357590
$209$			108.248i			0.517933i
$210$	−6.79439	+	24.1627i	−0.0323542	+	0.115060i
$211$	−88.4332			−0.419115			−0.209557	−	0.977796i	$-0.567202\pi$
$211$	−88.4332			−0.419115			−0.209557	+	0.977796i	$0.567202\pi$
$212$		−	148.265i		−	0.699362i
$213$	−292.396	−	82.2196i	−1.37275	−	0.386008i
$214$	127.670			0.596590
$215$			42.7350i			0.198767i
$216$	51.9685	+	55.9578i	0.240595	+	0.259064i
$217$	83.2994			0.383868
$218$			130.344i			0.597909i
$219$	−37.3509	+	132.830i	−0.170552	+	0.606530i
$220$	88.4326			0.401966
$221$		−	247.117i		−	1.11818i
$222$	−41.5812	−	11.6924i	−0.187303	−	0.0526683i
$223$	330.233			1.48087			0.740433	−	0.672130i	$-0.234620\pi$
$223$	330.233			1.48087			0.740433	+	0.672130i	$0.234620\pi$
$224$			14.9666i			0.0668153i
$225$	38.4052	+	23.4530i	0.170690	+	0.104235i
$226$	−210.617			−0.931935
$227$			283.024i			1.24680i	0.781902	+	0.623402i	$0.214250\pi$
$227$			283.024i			1.24680i	−0.781902	+	0.623402i	$0.785750\pi$
$228$	−8.89106	+	31.6191i	−0.0389959	+	0.138680i
$229$	−17.0978			−0.0746629			−0.0373314	−	0.999303i	$-0.511886\pi$
$229$	−17.0978			−0.0746629			−0.0373314	+	0.999303i	$0.511886\pi$
$230$			110.067i			0.478551i
$231$	−151.093	−	42.4862i	−0.654080	−	0.183923i
$232$	−19.3263			−0.0833029
$233$			223.943i			0.961129i	0.876960	+	0.480564i	$0.159568\pi$
$233$			223.943i			0.961129i	−0.876960	+	0.480564i	$0.840432\pi$
$234$	−123.348	+	201.987i	−0.527128	+	0.863193i
$235$	−100.901			−0.429368
$236$			65.1261i			0.275958i
$237$	114.349	−	406.655i	0.482484	−	1.71584i
$238$	49.7253			0.208930
$239$			10.9304i			0.0457340i	0.999739	+	0.0228670i	$0.00727942\pi$
$239$			10.9304i			0.0457340i	−0.999739	+	0.0228670i	$0.992721\pi$
$240$	25.8310	+	7.26351i	0.107629	+	0.0302646i
$241$	177.306			0.735710			0.367855	−	0.929883i	$-0.380092\pi$
$241$	177.306			0.735710			0.367855	+	0.929883i	$0.380092\pi$
$242$			381.861i			1.57794i
$243$	−238.145	+	48.3296i	−0.980022	+	0.198887i
$244$	−143.526			−0.588222
$245$		−	15.6525i		−	0.0638877i
$246$	−33.2047	+	118.085i	−0.134979	+	0.480021i
$247$	−101.791			−0.412111
$248$		−	89.0508i		−	0.359076i
$249$	290.595	+	81.7132i	1.16705	+	0.328166i
$250$	15.8114			0.0632456
$251$			182.001i			0.725103i	0.931964	+	0.362551i	$0.118094\pi$
$251$			182.001i			0.725103i	−0.931964	+	0.362551i	$0.881906\pi$
$252$	−40.6442	−	24.8203i	−0.161287	−	0.0984932i
$253$	−688.262			−2.72040
$254$		−	110.000i		−	0.433071i
$255$	24.1323	−	85.8212i	0.0946366	−	0.336554i
$256$	16.0000			0.0625000
$257$			155.204i			0.603906i	0.953323	+	0.301953i	$0.0976386\pi$
$257$			155.204i			0.603906i	−0.953323	+	0.301953i	$0.902361\pi$
$258$	−78.0567	−	21.9490i	−0.302545	−	0.0850737i
$259$	26.9361			0.104000
$260$			83.1580i			0.319838i
$261$	32.0502	−	52.4835i	0.122798	−	0.201086i
$262$	324.958			1.24030
$263$			159.605i			0.606861i	0.952854	+	0.303431i	$0.0981321\pi$
$263$			159.605i			0.606861i	−0.952854	+	0.303431i	$0.901868\pi$
$264$	−45.4196	+	161.525i	−0.172044	+	0.611836i
$265$	165.765			0.625529
$266$		−	20.4827i		−	0.0770025i
$267$	32.3556	+	9.09818i	0.121182	+	0.0340756i
$268$	−133.252			−0.497210
$269$			198.340i			0.737323i	0.929564	+	0.368661i	$0.120184\pi$
$269$			198.340i			0.737323i	−0.929564	+	0.368661i	$0.879816\pi$
$270$	−62.5627	+	58.1026i	−0.231714	+	0.215195i
$271$	46.2341			0.170606			0.0853028	−	0.996355i	$-0.472814\pi$
$271$	46.2341			0.170606			0.0853028	+	0.996355i	$0.472814\pi$
$272$		−	53.1586i		−	0.195436i
$273$	39.9521	−	142.081i	0.146345	−	0.520442i
$274$	203.024			0.740965
$275$			98.8707i			0.359530i
$276$	−201.040	−	56.5311i	−0.728406	−	0.204823i
$277$	387.786			1.39995			0.699974	−	0.714168i	$-0.253195\pi$
$277$	387.786			1.39995			0.699974	+	0.714168i	$0.253195\pi$
$278$			364.807i			1.31226i
$279$	241.831	+	147.680i	0.866779	+	0.529318i
$280$	−16.7332			−0.0597614
$281$			46.9368i			0.167035i	0.996506	+	0.0835174i	$0.0266154\pi$
$281$			46.9368i			0.167035i	−0.996506	+	0.0835174i	$0.973385\pi$
$282$	51.8237	−	184.299i	0.183772	−	0.653544i
$283$	−32.3428			−0.114286			−0.0571428	−	0.998366i	$-0.518199\pi$
$283$	−32.3428			−0.114286			−0.0571428	+	0.998366i	$0.518199\pi$
$284$		−	202.490i		−	0.712994i
$285$	−35.3512	−	9.94051i	−0.124039	−	0.0348790i
$286$	−519.998			−1.81817
$287$		−	76.4949i		−	0.266533i
$288$	−26.5340	+	43.4505i	−0.0921320	+	0.150870i
$289$	112.386			0.388877
$290$		−	21.6074i		−	0.0745083i
$291$	−83.2358	+	296.009i	−0.286034	+	1.01721i
$292$	−91.9877			−0.315026
$293$			36.5402i			0.124711i	0.998054	+	0.0623553i	$0.0198612\pi$
$293$			36.5402i			0.124711i	−0.998054	+	0.0623553i	$0.980139\pi$
$294$	28.5897	+	8.03923i	0.0972439	+	0.0273443i
$295$	−72.8132			−0.246824
$296$		−	28.7959i		−	0.0972834i
$297$	−363.323	−	391.213i	−1.22331	−	1.31721i
$298$	−166.212			−0.557760
$299$		−	647.210i		−	2.16458i
$300$	−8.12085	+	28.8800i	−0.0270695	+	0.0962665i
$301$	50.5647			0.167989
$302$		−	355.047i		−	1.17565i
$303$	407.225	+	114.509i	1.34398	+	0.377917i
$304$	−21.8969			−0.0720292
$305$		−	160.467i		−	0.526122i
$306$	144.360	+	88.1568i	0.471766	+	0.288094i
$307$	−57.4988			−0.187292			−0.0936462	−	0.995606i	$-0.529852\pi$
$307$	−57.4988			−0.187292			−0.0936462	+	0.995606i	$0.529852\pi$
$308$		−	104.635i		−	0.339724i
$309$	−47.9423	+	170.496i	−0.155153	+	0.551767i
$310$	99.5618			0.321167
$311$		−	230.523i		−	0.741231i	−0.928786	−	0.370615i	$-0.879147\pi$
$311$		−	230.523i		−	0.741231i	0.928786	−	0.370615i	$-0.120853\pi$
$312$	−151.890	−	42.7106i	−0.486828	−	0.136893i
$313$	449.686			1.43670			0.718348	−	0.695684i	$-0.244899\pi$
$313$	449.686			1.43670			0.718348	+	0.695684i	$0.244899\pi$
$314$		−	26.3636i		−	0.0839605i
$315$	27.7499	−	45.4416i	0.0880950	−	0.144259i
$316$	281.618			0.891195
$317$			370.113i			1.16755i	0.811916	+	0.583775i	$0.198425\pi$
$317$			370.113i			1.16755i	−0.811916	+	0.583775i	$0.801575\pi$
$318$	−85.1382	+	302.775i	−0.267730	+	0.952122i
$319$	135.114			0.423555
$320$			17.8885i			0.0559017i
$321$	−260.718	−	73.3121i	−0.812205	−	0.228387i
$322$	130.233			0.404449
$323$			72.7504i			0.225233i
$324$	−73.9933	−	144.114i	−0.228374	−	0.444798i
$325$	−92.9735			−0.286072
$326$			20.0672i			0.0615557i
$327$	74.8475	−	266.178i	0.228892	−	0.814001i
$328$	−81.7765			−0.249319
$329$			119.388i			0.362882i
$330$	−180.590	−	50.7807i	−0.547243	−	0.153881i
$331$	−125.253			−0.378409			−0.189204	−	0.981938i	$-0.560591\pi$
$331$	−125.253			−0.378409			−0.189204	+	0.981938i	$0.560591\pi$
$332$			201.243i			0.606154i
$333$	78.1998	+	47.7544i	0.234834	+	0.143407i
$334$	245.845			0.736064
$335$		−	148.980i		−	0.444718i
$336$	8.59430	−	30.5637i	0.0255783	−	0.0909633i
$337$	5.34562			0.0158624			0.00793119	−	0.999969i	$-0.497475\pi$
$337$	5.34562			0.0158624			0.00793119	+	0.999969i	$0.497475\pi$
$338$		−	249.980i		−	0.739586i
$339$	430.106	+	120.943i	1.26875	+	0.356764i
$340$	59.4331			0.174803
$341$			622.573i			1.82573i
$342$	36.3133	−	59.4644i	0.106179	−	0.173873i
$343$	−18.5203			−0.0539949
$344$		−	54.0560i		−	0.157139i
$345$	63.2037	−	224.770i	0.183199	−	0.651506i
$346$	−232.038			−0.670630
$347$		−	277.074i		−	0.798485i	−0.916845	−	0.399242i	$-0.869273\pi$
$347$		−	277.074i		−	0.798485i	0.916845	−	0.399242i	$-0.130727\pi$
$348$	39.4666	+	11.0977i	0.113410	+	0.0318900i
$349$	371.020			1.06309			0.531547	−	0.847029i	$-0.321611\pi$
$349$	371.020			1.06309			0.531547	+	0.847029i	$0.321611\pi$
$350$		−	18.7083i		−	0.0534522i
$351$	367.879	−	341.652i	1.04809	−	0.973368i
$352$	−111.859			−0.317782
$353$			200.070i			0.566770i	0.959006	+	0.283385i	$0.0914575\pi$
$353$			200.070i			0.566770i	−0.959006	+	0.283385i	$0.908543\pi$
$354$	37.3974	−	132.995i	0.105642	−	0.375693i
$355$	226.391			0.637721
$356$			22.4070i			0.0629410i
$357$	−101.545	−	28.5538i	−0.284440	−	0.0799825i
$358$	−378.293			−1.05669
$359$		−	13.1711i		−	0.0366884i	−0.999832	−	0.0183442i	$-0.994161\pi$
$359$		−	13.1711i		−	0.0366884i	0.999832	−	0.0183442i	$-0.00583947\pi$
$360$	−48.5791	−	29.6659i	−0.134942	−	0.0824053i
$361$	−331.033			−0.916989
$362$		−	266.374i		−	0.735839i
$363$	219.276	−	779.806i	0.604066	−	2.14823i
$364$	98.3939			0.270313
$365$		−	102.845i		−	0.281768i
$366$	293.098	+	82.4171i	0.800814	+	0.225183i
$367$	347.808			0.947706			0.473853	−	0.880604i	$-0.342863\pi$
$367$	347.808			0.947706			0.473853	+	0.880604i	$0.342863\pi$
$368$		−	139.225i		−	0.378328i
$369$	135.616	−	222.077i	0.367523	−	0.601835i
$370$	32.1948			0.0870129
$371$		−	196.136i		−	0.528668i
$372$	−51.1357	+	181.853i	−0.137462	+	0.488851i
$373$	−558.926			−1.49846			−0.749230	−	0.662310i	$-0.769576\pi$
$373$	−558.926			−1.49846			−0.749230	+	0.662310i	$0.769576\pi$
$374$			371.643i			0.993697i
$375$	−32.2888	−	9.07938i	−0.0861034	−	0.0242117i
$376$	127.631			0.339445
$377$			127.055i			0.337016i
$378$	68.7479	+	74.0252i	0.181873	+	0.195834i
$379$	−585.239			−1.54417			−0.772083	−	0.635522i	$-0.780785\pi$
$379$	−585.239			−1.54417			−0.772083	+	0.635522i	$0.780785\pi$
$380$		−	24.4815i		−	0.0644249i
$381$	−63.1654	+	224.633i	−0.165788	+	0.589589i
$382$	−424.805			−1.11206
$383$		−	391.278i		−	1.02161i	−0.859696	−	0.510807i	$-0.829347\pi$
$383$		−	391.278i		−	1.02161i	0.859696	−	0.510807i	$-0.170653\pi$
$384$	−32.6739	−	9.18769i	−0.0850884	−	0.0239263i
$385$	116.985			0.303858
$386$		−	295.899i		−	0.766577i
$387$	146.797	+	89.6451i	0.379322	+	0.231641i
$388$	−204.993			−0.528332
$389$		−	412.091i		−	1.05936i	−0.848197	−	0.529680i	$-0.822312\pi$
$389$		−	412.091i		−	1.05936i	0.848197	−	0.529680i	$-0.177688\pi$
$390$	47.7519	−	169.819i	0.122441	−	0.435433i
$391$	−462.561			−1.18302
$392$			19.7990i			0.0505076i
$393$	−663.604	−	186.601i	−1.68856	−	0.474812i
$394$	−137.275			−0.348415
$395$			314.858i			0.797109i
$396$	185.505	−	303.772i	0.468447	−	0.767100i
$397$	−620.931			−1.56406			−0.782028	−	0.623243i	$-0.785815\pi$
$397$	−620.931			−1.56406			−0.782028	+	0.623243i	$0.785815\pi$
$398$		−	413.050i		−	1.03781i
$399$	−11.7618	+	41.8281i	−0.0294781	+	0.104832i
$400$	−20.0000			−0.0500000
$401$			517.392i			1.29025i	0.764075	+	0.645127i	$0.223196\pi$
$401$			517.392i			1.29025i	−0.764075	+	0.645127i	$0.776804\pi$
$402$	272.117	+	76.5175i	0.676908	+	0.190342i
$403$	−585.439			−1.45270
$404$			282.012i			0.698049i
$405$	161.125	−	82.7271i	0.397839	−	0.204264i
$406$	−25.5662			−0.0629710
$407$			201.318i			0.494639i
$408$	−30.5253	+	108.556i	−0.0748168	+	0.266069i
$409$	−46.7243			−0.114240			−0.0571202	−	0.998367i	$-0.518192\pi$
$409$	−46.7243			−0.114240			−0.0571202	+	0.998367i	$0.518192\pi$
$410$		−	91.4289i		−	0.222997i
$411$	−414.600	−	116.583i	−1.00876	−	0.283656i
$412$	−118.072			−0.286583
$413$			86.1537i			0.208605i
$414$	378.086	+	230.887i	0.913252	+	0.557697i
$415$	−224.997			−0.542161
$416$		−	105.187i		−	0.252855i
$417$	209.484	−	744.981i	0.502359	−	1.78652i
$418$	153.086			0.366234
$419$			165.753i			0.395591i	0.980243	+	0.197796i	$0.0633783\pi$
$419$			165.753i			0.395591i	−0.980243	+	0.197796i	$0.936622\pi$
$420$	34.1712	+	9.60871i	0.0813601	+	0.0228779i
$421$	660.766			1.56952			0.784758	−	0.619802i	$-0.212787\pi$
$421$	660.766			1.56952			0.784758	+	0.619802i	$0.212787\pi$
$422$			125.063i			0.296359i
$423$	−211.661	+	346.603i	−0.500380	+	0.819392i
$424$	−209.678			−0.494524
$425$			66.4482i			0.156349i
$426$	−116.276	+	413.510i	−0.272949	+	0.970680i
$427$	−189.867			−0.444654
$428$		−	180.553i		−	0.421852i
$429$	1061.90	+	298.599i	2.47529	+	0.696034i
$430$	60.4364			0.140550
$431$			182.301i			0.422972i	0.977381	+	0.211486i	$0.0678303\pi$
$431$			182.301i			0.422972i	−0.977381	+	0.211486i	$0.932170\pi$
$432$	79.1363	−	73.4946i	0.183186	−	0.170126i
$433$	116.523			0.269106			0.134553	−	0.990906i	$-0.457040\pi$
$433$	116.523			0.269106			0.134553	+	0.990906i	$0.457040\pi$
$434$		−	117.803i		−	0.271436i
$435$	−12.4076	+	44.1250i	−0.0285233	+	0.101437i
$436$	184.334			0.422785
$437$			190.537i			0.436010i
$438$	187.850	+	52.8222i	0.428881	+	0.120599i
$439$	377.751			0.860481			0.430240	−	0.902714i	$-0.358429\pi$
$439$	377.751			0.860481			0.430240	+	0.902714i	$0.358429\pi$
$440$		−	125.063i		−	0.284233i
$441$	−53.7673	−	32.8342i	−0.121921	−	0.0744539i
$442$	−349.476			−0.790669
$443$		−	152.788i		−	0.344893i	−0.985019	−	0.172447i	$-0.944833\pi$
$443$		−	152.788i		−	0.344893i	0.985019	−	0.172447i	$-0.0551672\pi$
$444$	−16.5355	+	58.8047i	−0.0372421	+	0.132443i
$445$	−25.0518			−0.0562961
$446$		−	467.020i		−	1.04713i
$447$	339.426	+	95.4442i	0.759342	+	0.213522i
$448$	21.1660			0.0472456
$449$		−	201.173i		−	0.448047i	−0.974584	−	0.224023i	$-0.928081\pi$
$449$		−	201.173i		−	0.448047i	0.974584	−	0.224023i	$-0.0719192\pi$
$450$	33.1675	−	54.3131i	0.0737056	−	0.120696i
$451$	571.717			1.26767
$452$			297.858i			0.658977i
$453$	−203.879	+	725.048i	−0.450063	+	1.60055i
$454$	400.257			0.881623
$455$			110.008i			0.241775i
$456$	44.7161	+	12.5739i	0.0980616	+	0.0275743i
$457$	−718.056			−1.57124			−0.785620	−	0.618710i	$-0.787656\pi$
$457$	−718.056			−1.57124			−0.785620	+	0.618710i	$0.787656\pi$
$458$			24.1799i			0.0527946i
$459$	−244.179	−	262.923i	−0.531981	−	0.572817i
$460$	155.658			0.338387
$461$		−	344.884i		−	0.748121i	−0.927404	−	0.374061i	$-0.877965\pi$
$461$		−	344.884i		−	0.748121i	0.927404	−	0.374061i	$-0.122035\pi$
$462$	−60.0845	+	213.677i	−0.130053	+	0.462505i
$463$	−561.331			−1.21238			−0.606189	−	0.795321i	$-0.707303\pi$
$463$	−561.331			−1.21238			−0.606189	+	0.795321i	$0.707303\pi$
$464$			27.3315i			0.0589040i
$465$	−203.317	−	57.1714i	−0.437242	−	0.122949i
$466$	316.703			0.679621
$467$			146.016i			0.312668i	0.987704	+	0.156334i	$0.0499676\pi$
$467$			146.016i			0.312668i	−0.987704	+	0.156334i	$0.950032\pi$
$468$	285.653	+	174.440i	0.610370	+	0.372736i
$469$	−176.276			−0.375855
$470$			142.696i			0.303609i
$471$	−15.1388	+	53.8377i	−0.0321418	+	0.114305i
$472$	92.1022			0.195132
$473$			377.917i			0.798978i
$474$	−575.097	−	161.713i	−1.21329	−	0.341168i
$475$	27.3711			0.0576234
$476$		−	70.3222i		−	0.147736i
$477$	347.725	−	569.414i	0.728983	−	1.19374i
$478$	15.4579			0.0323388
$479$		−	48.7573i		−	0.101790i	−0.998704	−	0.0508949i	$-0.983793\pi$
$479$		−	48.7573i		−	0.101790i	0.998704	−	0.0508949i	$-0.0162074\pi$
$480$	10.2721	−	36.5306i	0.0214003	−	0.0761054i
$481$	−189.310			−0.393577
$482$		−	250.749i		−	0.520226i
$483$	−265.951	−	74.7836i	−0.550623	−	0.154831i
$484$	540.033			1.11577
$485$		−	229.189i		−	0.472555i
$486$	68.3484	+	336.788i	0.140635	+	0.692980i
$487$	562.319			1.15466			0.577329	−	0.816511i	$-0.304095\pi$
$487$	562.319			1.15466			0.577329	+	0.816511i	$0.304095\pi$
$488$			202.977i			0.415936i
$489$	11.5232	−	40.9796i	0.0235648	−	0.0838028i
$490$	−22.1359			−0.0451754
$491$		−	124.234i		−	0.253022i	−0.991965	−	0.126511i	$-0.959622\pi$
$491$		−	124.234i		−	0.253022i	0.991965	−	0.126511i	$-0.0403778\pi$
$492$	166.998	+	46.9586i	0.339426	+	0.0954443i
$493$	90.8063			0.184191
$494$			143.955i			0.291407i
$495$	339.627	+	207.401i	0.686115	+	0.418991i
$496$	−125.937			−0.253905
$497$		−	267.870i		−	0.538973i
$498$	115.560	−	410.963i	0.232048	−	0.825227i
$499$	−751.671			−1.50635			−0.753177	−	0.657817i	$-0.771480\pi$
$499$	−751.671			−1.50635			−0.753177	+	0.657817i	$0.771480\pi$
$500$		−	22.3607i		−	0.0447214i
$501$	−502.046	−	141.172i	−1.00209	−	0.281780i
$502$	257.388			0.512725
$503$		−	725.516i		−	1.44238i	−0.692739	−	0.721189i	$-0.743596\pi$
$503$		−	725.516i		−	1.44238i	0.692739	−	0.721189i	$-0.256404\pi$
$504$	−35.1012	+	57.4796i	−0.0696452	+	0.114047i
$505$	−315.299			−0.624354
$506$			973.349i			1.92361i
$507$	−143.546	+	510.490i	−0.283129	+	1.00688i
$508$	−155.563			−0.306227
$509$			495.288i			0.973062i	0.873663	+	0.486531i	$0.161738\pi$
$509$			495.288i			0.973062i	−0.873663	+	0.486531i	$0.838262\pi$
$510$	−121.370	−	34.1283i	−0.237979	−	0.0669182i
$511$	−121.688			−0.238138
$512$		−	22.6274i		−	0.0441942i
$513$	−108.302	+	100.581i	−0.211116	+	0.196065i
$514$	219.492			0.427026
$515$		−	132.009i		−	0.256328i
$516$	−31.0406	+	110.389i	−0.0601562	+	0.213932i
$517$	−892.298			−1.72591
$518$		−	38.0934i		−	0.0735394i
$519$	473.850	+	133.243i	0.913006	+	0.256731i
$520$	117.603			0.226160
$521$			496.127i			0.952260i	0.879375	+	0.476130i	$0.157961\pi$
$521$			496.127i			0.952260i	−0.879375	+	0.476130i	$0.842039\pi$
$522$	−74.2229	−	45.3258i	−0.142189	−	0.0868311i
$523$	863.914			1.65184			0.825922	−	0.563785i	$-0.190655\pi$
$523$	863.914			1.65184			0.825922	+	0.563785i	$0.190655\pi$
$524$		−	459.560i		−	0.877024i
$525$	−10.7429	+	38.2046i	−0.0204626	+	0.0727706i
$526$	225.715			0.429116
$527$			418.414i			0.793954i
$528$	228.430	+	64.2331i	0.432633	+	0.121654i
$529$	−682.468			−1.29011
$530$		−	234.427i		−	0.442316i
$531$	−152.740	+	250.118i	−0.287646	+	0.471032i
$532$	−28.9669			−0.0544490
$533$			537.617i			1.00866i
$534$	12.8668	−	45.7578i	0.0240951	−	0.0856887i
$535$	201.864			0.377316
$536$			188.447i			0.351580i
$537$	772.521	+	217.228i	1.43859	+	0.404521i
$538$	280.495			0.521366
$539$		−	138.419i		−	0.256807i
$540$	82.1694	+	88.4770i	0.152166	+	0.163846i
$541$	−606.291			−1.12069			−0.560343	−	0.828261i	$-0.689331\pi$
$541$	−606.291			−1.12069			−0.560343	+	0.828261i	$0.689331\pi$
$542$		−	65.3849i		−	0.120636i
$543$	−152.960	+	543.968i	−0.281694	+	1.00178i
$544$	−75.1775			−0.138194
$545$			206.092i			0.378151i
$546$	−200.932	−	56.5008i	−0.368008	−	0.103481i
$547$	940.119			1.71868			0.859341	−	0.511404i	$-0.170874\pi$
$547$	940.119			1.71868			0.859341	+	0.511404i	$0.170874\pi$
$548$		−	287.120i		−	0.523941i
$549$	−551.215	−	336.611i	−1.00403	−	0.613135i
$550$	139.824			0.254226
$551$		−	37.4046i		−	0.0678850i
$552$	−79.9470	+	284.314i	−0.144832	+	0.515061i
$553$	372.545			0.673680
$554$		−	548.412i		−	0.989913i
$555$	−65.7457	−	18.4872i	−0.118461	−	0.0333103i
$556$	515.916			0.927906
$557$		−	302.696i		−	0.543439i	−0.962376	−	0.271720i	$-0.912408\pi$
$557$		−	302.696i		−	0.543439i	0.962376	−	0.271720i	$-0.0875923\pi$
$558$	208.851	−	342.001i	0.374284	−	0.612905i
$559$	−355.376			−0.635735
$560$			23.6643i			0.0422577i
$561$	213.409	−	758.939i	0.380407	−	1.35283i
$562$	66.3786			0.118111
$563$			705.188i			1.25255i	0.779601	+	0.626277i	$0.215422\pi$
$563$			705.188i			1.25255i	−0.779601	+	0.626277i	$0.784578\pi$
$564$	−260.639	−	73.2898i	−0.462125	−	0.129946i
$565$	−333.015			−0.589407
$566$			45.7396i			0.0808121i
$567$	−97.8840	−	190.646i	−0.172635	−	0.336236i
$568$	−286.365			−0.504163
$569$			428.736i			0.753491i	0.926317	+	0.376746i	$0.122957\pi$
$569$			428.736i			0.753491i	−0.926317	+	0.376746i	$0.877043\pi$
$570$	−14.0580	+	49.9941i	−0.0246632	+	0.0877090i
$571$	222.414			0.389517			0.194758	−	0.980851i	$-0.437608\pi$
$571$	222.414			0.389517			0.194758	+	0.980851i	$0.437608\pi$
$572$			735.388i			1.28564i
$573$	867.504	+	243.936i	1.51397	+	0.425718i
$574$	−108.180			−0.188467
$575$			174.031i			0.302662i
$576$	61.4483	+	37.5247i	0.106681	+	0.0651471i
$577$	−677.458			−1.17410			−0.587052	−	0.809549i	$-0.699712\pi$
$577$	−677.458			−1.17410			−0.587052	+	0.809549i	$0.699712\pi$
$578$		−	158.937i		−	0.274978i
$579$	−169.914	+	604.261i	−0.293461	+	1.04363i
$580$	−30.5575			−0.0526854
$581$			266.220i			0.458209i
$582$	418.620	+	117.713i	0.719279	+	0.202256i
$583$	1465.90			2.51441
$584$			130.090i			0.222757i
$585$	−195.030	+	319.370i	−0.333385	+	0.545931i
$586$	51.6757			0.0881837
$587$			681.642i			1.16123i	0.814178	+	0.580615i	$0.197188\pi$
$587$			681.642i			1.16123i	−0.814178	+	0.580615i	$0.802812\pi$
$588$	11.3692	−	40.4319i	0.0193353	−	0.0687618i
$589$	172.352			0.292617
$590$			102.973i			0.174531i
$591$	280.333	+	78.8277i	0.474337	+	0.133380i
$592$	−40.7235			−0.0687898
$593$		−	39.3230i		−	0.0663120i	−0.999450	−	0.0331560i	$-0.989444\pi$
$593$		−	39.3230i		−	0.0663120i	0.999450	−	0.0331560i	$-0.0105558\pi$
$594$	−553.258	+	513.816i	−0.931411	+	0.865010i
$595$	78.6226			0.132139
$596$			235.060i			0.394396i
$597$	−237.186	+	843.498i	−0.397296	+	1.41289i
$598$	−915.293			−1.53059
$599$		−	564.730i		−	0.942788i	−0.881923	−	0.471394i	$-0.843751\pi$
$599$		−	564.730i		−	0.942788i	0.881923	−	0.471394i	$-0.156249\pi$
$600$	40.8424	+	11.4846i	0.0680707	+	0.0191410i
$601$	−223.287			−0.371527			−0.185763	−	0.982595i	$-0.559476\pi$
$601$	−223.287			−0.371527			−0.185763	+	0.982595i	$0.559476\pi$
$602$		−	71.5093i		−	0.118786i
$603$	−511.757	−	312.516i	−0.848686	−	0.518268i
$604$	−502.112			−0.831311
$605$			603.775i			0.997975i
$606$	161.940	−	575.903i	0.267228	−	0.950334i
$607$	343.966			0.566665			0.283332	−	0.959022i	$-0.408560\pi$
$607$	343.966			0.566665			0.283332	+	0.959022i	$0.408560\pi$
$608$			30.9669i			0.0509324i
$609$	52.2094	+	14.6809i	0.0857297	+	0.0241066i
$610$	−226.935			−0.372024
$611$		−	839.076i		−	1.37328i
$612$	124.673	−	204.156i	0.203713	−	0.333589i
$613$	532.494			0.868668			0.434334	−	0.900752i	$-0.356984\pi$
$613$	532.494			0.868668			0.434334	+	0.900752i	$0.356984\pi$
$614$			81.3156i			0.132436i
$615$	−52.5013	+	186.709i	−0.0853679	+	0.303592i
$616$	−147.976			−0.240221
$617$		−	553.837i		−	0.897630i	−0.893625	−	0.448815i	$-0.851846\pi$
$617$		−	553.837i		−	0.897630i	0.893625	−	0.448815i	$-0.148154\pi$
$618$	241.118	+	67.8007i	0.390158	+	0.109710i
$619$	467.768			0.755684			0.377842	−	0.925870i	$-0.376666\pi$
$619$	467.768			0.755684			0.377842	+	0.925870i	$0.376666\pi$
$620$		−	140.802i		−	0.227099i
$621$	−639.516	−	688.607i	−1.02982	−	1.10887i
$622$	−326.008			−0.524129
$623$			29.6416i			0.0475789i
$624$	−60.4019	+	214.806i	−0.0967979	+	0.344240i
$625$	25.0000			0.0400000
$626$		−	635.952i		−	1.01590i
$627$	−312.620	−	87.9065i	−0.498596	−	0.140202i
$628$	−37.2838			−0.0593690
$629$			135.300i			0.215104i
$630$	−64.2642	−	39.2443i	−0.102007	−	0.0622926i
$631$	822.827			1.30400			0.652002	−	0.758217i	$-0.273929\pi$
$631$	822.827			1.30400			0.652002	+	0.758217i	$0.273929\pi$
$632$		−	398.267i		−	0.630170i
$633$	71.8152	−	255.395i	0.113452	−	0.403467i
$634$	523.419			0.825582
$635$		−	173.925i		−	0.273898i
$636$	428.188	+	120.404i	0.673252	+	0.189314i
$637$	130.163			0.204337
$638$		−	191.080i		−	0.299499i
$639$	474.900	−	777.668i	0.743192	−	1.21701i
$640$	25.2982			0.0395285
$641$		−	64.4367i		−	0.100525i	−0.998736	−	0.0502626i	$-0.983994\pi$
$641$		−	64.4367i		−	0.100525i	0.998736	−	0.0502626i	$-0.0160058\pi$
$642$	−103.679	+	368.711i	−0.161494	+	0.574316i
$643$	−367.448			−0.571458			−0.285729	−	0.958310i	$-0.592236\pi$
$643$	−367.448			−0.571458			−0.285729	+	0.958310i	$0.592236\pi$
$644$		−	184.177i		−	0.285989i
$645$	−123.419	−	34.7044i	−0.191347	−	0.0538053i
$646$	102.885			0.159264
$647$		−	335.963i		−	0.519262i	−0.965708	−	0.259631i	$-0.916399\pi$
$647$		−	335.963i		−	0.519262i	0.965708	−	0.259631i	$-0.0836010\pi$
$648$	−203.809	+	104.642i	−0.314520	+	0.161485i
$649$	−643.906			−0.992151
$650$			131.484i			0.202284i
$651$	−67.6462	+	240.568i	−0.103911	+	0.369537i
$652$	28.3793			0.0435265
$653$		−	365.159i		−	0.559202i	−0.960116	−	0.279601i	$-0.909798\pi$
$653$		−	365.159i		−	0.559202i	0.960116	−	0.279601i	$-0.0902022\pi$
$654$	−376.433	−	105.850i	−0.575586	−	0.161851i
$655$	513.804			0.784434
$656$			115.649i			0.176295i
$657$	−353.281	−	215.739i	−0.537718	−	0.328369i
$658$	168.840			0.256596
$659$		−	895.096i		−	1.35826i	−0.734016	−	0.679132i	$-0.762357\pi$
$659$		−	895.096i		−	1.35826i	0.734016	−	0.679132i	$-0.237643\pi$
$660$	−71.8148	+	255.393i	−0.108810	+	0.386959i
$661$	511.388			0.773658			0.386829	−	0.922151i	$-0.373570\pi$
$661$	511.388			0.773658			0.386829	+	0.922151i	$0.373570\pi$
$662$			177.135i			0.267575i
$663$	713.672	+	200.680i	1.07643	+	0.302684i
$664$	284.601			0.428616
$665$		−	32.3859i		−	0.0487006i
$666$	67.5349	−	110.591i	0.101404	−	0.166053i
$667$	237.826			0.356560
$668$		−	347.678i		−	0.520476i
$669$	−268.177	+	953.712i	−0.400863	+	1.42558i
$670$	−210.690			−0.314463
$671$		−	1419.05i		−	2.11483i
$672$	−43.2236	−	12.1542i	−0.0643208	−	0.0180866i
$673$	265.771			0.394904			0.197452	−	0.980313i	$-0.436733\pi$
$673$	265.771			0.394904			0.197452	+	0.980313i	$0.436733\pi$
$674$		−	7.55985i		−	0.0112164i
$675$	−98.9203	+	91.8682i	−0.146549	+	0.136101i
$676$	−353.525			−0.522967
$677$		−	788.674i		−	1.16495i	−0.812847	−	0.582477i	$-0.802083\pi$
$677$		−	788.674i		−	1.16495i	0.812847	−	0.582477i	$-0.197917\pi$
$678$	171.039	−	608.262i	0.252270	−	0.897141i
$679$	−271.180			−0.399382
$680$		−	84.0511i		−	0.123604i
$681$	−817.373	−	229.840i	−1.20025	−	0.337503i
$682$	880.451			1.29098
$683$		−	644.795i		−	0.944062i	−0.881582	−	0.472031i	$-0.843521\pi$
$683$		−	644.795i		−	0.944062i	0.881582	−	0.472031i	$-0.156479\pi$
$684$	−84.0954	−	51.3547i	−0.122946	−	0.0750800i
$685$	321.010			0.468627
$686$			26.1916i			0.0381802i
$687$	13.8849	−	49.3784i	0.0202109	−	0.0718753i
$688$	−76.4467			−0.111114
$689$			1378.47i			2.00068i
$690$	−317.872	−	89.3835i	−0.460684	−	0.129541i
$691$	−758.839			−1.09818			−0.549088	−	0.835765i	$-0.685025\pi$
$691$	−758.839			−1.09818			−0.549088	+	0.835765i	$0.685025\pi$
$692$			328.151i			0.474207i
$693$	245.400	−	401.852i	0.354112	−	0.579873i
$694$	−391.842			−0.564614
$695$			576.811i			0.829944i
$696$	15.6946	−	55.8142i	0.0225497	−	0.0801928i
$697$	384.235			0.551270
$698$		−	524.701i		−	0.751721i
$699$	−646.746	−	181.861i	−0.925245	−	0.260173i
$700$	−26.4575			−0.0377964
$701$		−	633.097i		−	0.903134i	−0.892237	−	0.451567i	$-0.850865\pi$
$701$		−	633.097i		−	0.903134i	0.892237	−	0.451567i	$-0.149135\pi$
$702$	−483.169	−	520.259i	−0.688275	−	0.741110i
$703$	55.7324			0.0792780
$704$			158.193i			0.224706i
$705$	81.9405	−	291.403i	0.116228	−	0.413337i
$706$	282.942			0.400767
$707$			373.067i			0.527676i
$708$	−188.084	−	52.8879i	−0.265655	−	0.0747004i
$709$	−906.040			−1.27791			−0.638956	−	0.769243i	$-0.720634\pi$
$709$	−906.040			−1.27791			−0.638956	+	0.769243i	$0.720634\pi$
$710$		−	320.165i		−	0.450937i
$711$	1081.56	+	660.477i	1.52118	+	0.928941i
$712$	31.6883			0.0445060
$713$			1095.84i			1.53695i
$714$	−40.3811	+	143.606i	−0.0565562	+	0.201129i
$715$	−822.189			−1.14991
$716$			534.988i			0.747189i
$717$	−31.5670	−	8.87642i	−0.0440265	−	0.0123799i
$718$	−18.6268			−0.0259426
$719$		−	144.683i		−	0.201228i	−0.994926	−	0.100614i	$-0.967919\pi$
$719$		−	144.683i		−	0.201228i	0.994926	−	0.100614i	$-0.0320806\pi$
$720$	−41.9539	+	68.7013i	−0.0582694	+	0.0954185i
$721$	−156.195			−0.216636
$722$			468.151i			0.648409i
$723$	−143.988	+	512.059i	−0.199153	+	0.708243i
$724$	−376.709			−0.520317
$725$		−	34.1643i		−	0.0471232i
$726$	−1102.81	−	310.103i	−1.51902	−	0.427139i
$727$	−194.850			−0.268019			−0.134009	−	0.990980i	$-0.542785\pi$
$727$	−194.850			−0.268019			−0.134009	+	0.990980i	$0.542785\pi$
$728$		−	139.150i		−	0.191140i
$729$	53.8185	−	727.011i	0.0738251	−	0.997271i
$730$	−145.445			−0.199240
$731$			253.987i			0.347452i
$732$	116.555	−	414.503i	0.159229	−	0.566261i
$733$	883.063			1.20472			0.602362	−	0.798223i	$-0.294226\pi$
$733$	883.063			1.20472			0.602362	+	0.798223i	$0.294226\pi$
$734$		−	491.875i		−	0.670129i
$735$	45.2043	+	12.7111i	0.0615024	+	0.0172941i
$736$	−196.893			−0.267518
$737$		−	1317.47i		−	1.78762i
$738$	−314.064	−	191.790i	−0.425561	−	0.259878i
$739$	−679.219			−0.919106			−0.459553	−	0.888150i	$-0.651990\pi$
$739$	−679.219			−0.919106			−0.459553	+	0.888150i	$0.651990\pi$
$740$		−	45.5303i		−	0.0615274i
$741$	82.6633	−	293.973i	0.111556	−	0.396725i
$742$	−277.378			−0.373825
$743$			1349.22i			1.81591i	0.419073	+	0.907953i	$0.362355\pi$
$743$			1349.22i			1.81591i	−0.419073	+	0.907953i	$0.637645\pi$
$744$	257.178	+	72.3168i	0.345670	+	0.0972000i
$745$	−262.805			−0.352758
$746$			790.440i			1.05957i
$747$	−471.975	+	772.878i	−0.631827	+	1.03464i
$748$	525.582			0.702650
$749$		−	238.849i		−	0.318891i
$750$	−12.8402	+	45.6632i	−0.0171202	+	0.0608843i
$751$	171.226			0.227997			0.113998	−	0.993481i	$-0.463634\pi$
$751$	171.226			0.227997			0.113998	+	0.993481i	$0.463634\pi$
$752$		−	180.498i		−	0.240024i
$753$	−525.618	−	147.800i	−0.698031	−	0.196282i
$754$	179.683			0.238306
$755$		−	561.378i		−	0.743547i
$756$	104.687	−	97.2242i	0.138475	−	0.128603i
$757$	−317.899			−0.419946			−0.209973	−	0.977707i	$-0.567338\pi$
$757$	−317.899			−0.419946			−0.209973	+	0.977707i	$0.567338\pi$
$758$			827.653i			1.09189i
$759$	558.927	−	1987.70i	0.736399	−	2.61884i
$760$	−34.6220			−0.0455553
$761$		−	423.830i		−	0.556938i	−0.960445	−	0.278469i	$-0.910173\pi$
$761$		−	423.830i		−	0.556938i	0.960445	−	0.278469i	$-0.0898269\pi$
$762$	317.680	+	89.3293i	0.416902	+	0.117230i
$763$	243.851			0.319596
$764$			600.766i			0.786342i
$765$	228.254	+	139.388i	0.298371	+	0.182207i
$766$	−553.351			−0.722390
$767$		−	605.500i		−	0.789439i
$768$	−12.9934	+	46.2079i	−0.0169184	+	0.0601666i
$769$	169.095			0.219889			0.109945	−	0.993938i	$-0.464933\pi$
$769$	169.095			0.219889			0.109945	+	0.993938i	$0.464933\pi$
$770$		−	165.442i		−	0.214860i
$771$	−448.228	−	126.039i	−0.581360	−	0.163474i
$772$	−418.464			−0.542051
$773$		−	603.486i		−	0.780706i	−0.920665	−	0.390353i	$-0.872353\pi$
$773$		−	603.486i		−	0.780706i	0.920665	−	0.390353i	$-0.127647\pi$
$774$	126.777	−	207.603i	0.163795	−	0.268221i
$775$	157.421			0.203124
$776$			289.904i			0.373587i
$777$	−21.8744	+	77.7913i	−0.0281524	+	0.100118i
$778$	−582.785			−0.749081
$779$		−	158.273i		−	0.203174i
$780$	−240.160	−	67.5313i	−0.307897	−	0.0865786i
$781$	2002.04			2.56343
$782$			654.160i			0.836522i
$783$	125.545	+	135.182i	0.160338	+	0.172646i
$784$	28.0000			0.0357143
$785$		−	41.6845i		−	0.0531013i
$786$	−263.894	+	938.478i	−0.335743	+	1.19399i
$787$	1458.37			1.85307			0.926536	−	0.376205i	$-0.122771\pi$
$787$	1458.37			1.85307			0.926536	+	0.376205i	$0.122771\pi$
$788$			194.137i			0.246366i
$789$	−460.937	−	129.612i	−0.584204	−	0.164274i
$790$	445.277			0.563641
$791$			394.029i			0.498140i
$792$	−429.598	−	262.343i	−0.542422	−	0.331242i
$793$	1334.41			1.68274
$794$			878.128i			1.10596i
$795$	−134.615	+	478.729i	−0.169327	+	0.602175i
$796$	−584.141			−0.733845
$797$		−	47.8528i		−	0.0600412i	−0.999549	−	0.0300206i	$-0.990443\pi$
$797$		−	47.8528i		−	0.0600412i	0.999549	−	0.0300206i	$-0.00955729\pi$
$798$	59.1538	+	16.6337i	0.0741276	+	0.0208442i
$799$	−599.688			−0.750548
$800$			28.2843i			0.0353553i
$801$	−52.5510	+	86.0544i	−0.0656068	+	0.107434i
$802$	731.703			0.912347
$803$		−	909.489i		−	1.13261i
$804$	108.212	−	384.832i	0.134592	−	0.478646i
$805$	205.916			0.255796
$806$			827.936i			1.02722i
$807$	−572.804	−	161.069i	−0.709795	−	0.199589i
$808$	398.825			0.493595
$809$		−	267.783i		−	0.331005i	−0.986209	−	0.165503i	$-0.947075\pi$
$809$		−	267.783i		−	0.331005i	0.986209	−	0.165503i	$-0.0529247\pi$
$810$	−116.994	−	227.865i	−0.144437	−	0.281315i
$811$	−658.395			−0.811831			−0.405915	−	0.913911i	$-0.633047\pi$
$811$	−658.395			−0.811831			−0.405915	+	0.913911i	$0.633047\pi$
$812$			36.1561i			0.0445273i
$813$	−37.5460	+	133.524i	−0.0461820	+	0.164236i
$814$	284.707			0.349763
$815$			31.7290i			0.0389313i
$816$	153.522	+	43.1692i	0.188139	+	0.0529035i
$817$	104.622			0.128056
$818$			66.0782i			0.0807802i
$819$	377.884	+	230.763i	0.461396	+	0.281762i
$820$	−129.300			−0.157683
$821$		−	1104.72i		−	1.34558i	−0.739833	−	0.672791i	$-0.765095\pi$
$821$		−	1104.72i		−	1.34558i	0.739833	−	0.672791i	$-0.234905\pi$
$822$	−164.873	+	586.333i	−0.200575	+	0.713301i
$823$	−1044.86			−1.26957			−0.634787	−	0.772688i	$-0.718912\pi$
$823$	−1044.86			−1.26957			−0.634787	+	0.772688i	$0.718912\pi$
$824$			166.979i			0.202645i
$825$	−285.538	−	80.2913i	−0.346107	−	0.0973228i
$826$	121.840			0.147506
$827$			1417.09i			1.71354i	0.515702	+	0.856768i	$0.327531\pi$
$827$			1417.09i			1.71354i	−0.515702	+	0.856768i	$0.672469\pi$
$828$	326.523	−	534.695i	0.394352	−	0.645767i
$829$	−1178.56			−1.42166			−0.710832	−	0.703362i	$-0.751681\pi$
$829$	−1178.56			−1.42166			−0.710832	+	0.703362i	$0.751681\pi$
$830$			318.193i			0.383365i
$831$	−314.915	+	1119.92i	−0.378959	+	1.34768i
$832$	−148.758			−0.178795
$833$		−	93.0275i		−	0.111678i
$834$	−1053.56	−	296.254i	−1.26326	−	0.355221i
$835$	388.715			0.465528
$836$		−	216.496i		−	0.258966i
$837$	−622.886	+	578.480i	−0.744188	+	0.691135i
$838$	234.410			0.279725
$839$			631.629i			0.752836i	0.926450	+	0.376418i	$0.122844\pi$
$839$			631.629i			0.752836i	−0.926450	+	0.376418i	$0.877156\pi$
$840$	13.5888	−	48.3254i	0.0161771	−	0.0575302i
$841$	794.312			0.944485
$842$		−	934.465i		−	1.10982i
$843$	−135.553	−	38.1166i	−0.160799	−	0.0452155i
$844$	176.866			0.209557
$845$		−	395.253i		−	0.467755i
$846$	490.171	+	299.333i	0.579398	+	0.353822i
$847$	714.396			0.843443
$848$			296.530i			0.349681i
$849$	26.2651	−	93.4059i	0.0309365	−	0.110019i
$850$	93.9719			0.110555
$851$			354.358i			0.416401i
$852$	584.791	+	164.439i	0.686375	+	0.193004i
$853$	274.418			0.321710			0.160855	−	0.986978i	$-0.448575\pi$
$853$	274.418			0.321710			0.160855	+	0.986978i	$0.448575\pi$
$854$			268.513i			0.314418i
$855$	57.4163	−	94.0215i	0.0671536	−	0.109967i
$856$	−255.340			−0.298295
$857$		−	1272.83i		−	1.48521i	−0.669729	−	0.742606i	$-0.733590\pi$
$857$		−	1272.83i		−	1.48521i	0.669729	−	0.742606i	$-0.266410\pi$
$858$	422.282	−	1501.75i	0.492170	−	1.75029i
$859$	1092.97			1.27237			0.636185	−	0.771537i	$-0.280512\pi$
$859$	1092.97			1.27237			0.636185	+	0.771537i	$0.280512\pi$
$860$		−	85.4700i		−	0.0993837i
$861$	220.917	+	62.1204i	0.256582	+	0.0721491i
$862$	257.813			0.299086
$863$		−	782.875i		−	0.907155i	−0.891217	−	0.453577i	$-0.850148\pi$
$863$		−	782.875i		−	0.907155i	0.891217	−	0.453577i	$-0.149852\pi$
$864$	−103.937	−	111.916i	−0.120297	−	0.129532i
$865$	−366.884			−0.424144
$866$		−	164.788i		−	0.190286i
$867$	−91.2665	+	324.569i	−0.105267	+	0.374359i
$868$	−166.599			−0.191934
$869$			2784.37i			3.20411i
$870$	62.4021	+	17.5471i	0.0717266	+	0.0201690i
$871$	1238.89			1.42238
$872$		−	260.688i		−	0.298954i
$873$	−787.279	−	480.769i	−0.901809	−	0.550709i
$874$	269.459			0.308306
$875$		−	29.5804i		−	0.0338062i
$876$	74.7018	−	265.660i	0.0852760	−	0.303265i
$877$	240.309			0.274012			0.137006	−	0.990570i	$-0.456252\pi$
$877$	240.309			0.274012			0.137006	+	0.990570i	$0.456252\pi$
$878$		−	534.221i		−	0.608452i
$879$	−105.528	−	29.6737i	−0.120055	−	0.0337585i
$880$	−176.865			−0.200983
$881$			402.445i			0.456805i	0.973567	+	0.228403i	$0.0733502\pi$
$881$			402.445i			0.456805i	−0.973567	+	0.228403i	$0.926650\pi$
$882$	−46.4345	+	76.0384i	−0.0526468	+	0.0862113i
$883$	99.2223			0.112370			0.0561848	−	0.998420i	$-0.482106\pi$
$883$	99.2223			0.112370			0.0561848	+	0.998420i	$0.482106\pi$
$884$			494.234i			0.559088i
$885$	59.1304	−	210.284i	0.0668141	−	0.237609i
$886$	−216.074			−0.243876
$887$			197.974i			0.223195i	0.993754	+	0.111597i	$0.0355967\pi$
$887$			197.974i			0.223195i	−0.993754	+	0.111597i	$0.964403\pi$
$888$	83.1624	+	23.3847i	0.0936514	+	0.0263341i
$889$	−205.791			−0.231486
$890$			35.4285i			0.0398074i
$891$	1424.87	−	731.577i	1.59918	−	0.821074i
$892$	−660.466			−0.740433
$893$			247.021i			0.276620i
$894$	134.979	−	480.021i	0.150983	−	0.536936i
$895$	−598.134			−0.668306
$896$		−	29.9333i		−	0.0334077i
$897$	1869.14	+	525.589i	2.08377	+	0.585941i
$898$	−284.501			−0.316817
$899$		−	215.127i		−	0.239296i
$900$	−76.8104	−	46.9059i	−0.0853449	−	0.0521177i
$901$	985.193			1.09344
$902$		−	808.530i		−	0.896375i
$903$	−41.0628	+	146.031i	−0.0454738	+	0.161717i
$904$	421.234			0.465967
$905$		−	421.174i		−	0.465386i
$906$	1025.37	+	288.328i	1.13176	+	0.318243i
$907$	−1429.61			−1.57620			−0.788098	−	0.615550i	$-0.788934\pi$
$907$	−1429.61			−1.57620			−0.788098	+	0.615550i	$0.788934\pi$
$908$		−	566.049i		−	0.623402i
$909$	−661.402	+	1083.07i	−0.727615	+	1.19150i
$910$	155.574			0.170961
$911$		−	291.143i		−	0.319587i	−0.987150	−	0.159793i	$-0.948917\pi$
$911$		−	291.143i		−	0.319587i	0.987150	−	0.159793i	$-0.0510828\pi$
$912$	17.7821	−	63.2381i	0.0194979	−	0.0693400i
$913$	−1989.70			−2.17930
$914$			1015.49i			1.11103i
$915$	463.428	+	130.313i	0.506479	+	0.142418i
$916$	34.1956			0.0373314
$917$		−	607.941i		−	0.662968i
$918$	−371.829	+	345.321i	−0.405043	+	0.376167i
$919$	1118.26			1.21682			0.608412	−	0.793621i	$-0.291807\pi$
$919$	1118.26			1.21682			0.608412	+	0.793621i	$0.291807\pi$
$920$		−	220.133i		−	0.239275i
$921$	46.6939	−	166.056i	0.0506991	−	0.180300i
$922$	−487.740			−0.529002
$923$			1882.62i			2.03968i
$924$	302.185	+	84.9724i	0.327040	+	0.0919614i
$925$	50.9044			0.0550318
$926$			793.842i			0.857281i
$927$	−453.459	−	276.914i	−0.489168	−	0.298721i
$928$	38.6525			0.0416514
$929$			1182.23i			1.27258i	0.771449	+	0.636292i	$0.219532\pi$
$929$			1182.23i			1.27258i	−0.771449	+	0.636292i	$0.780468\pi$
$930$	−80.8526	+	287.534i	−0.0869383	+	0.309176i
$931$	−38.3195			−0.0411596
$932$		−	447.886i		−	0.480564i
$933$	665.749	+	187.204i	0.713557	+	0.200647i
$934$	206.498			0.221089
$935$			587.619i			0.628469i
$936$	246.696	−	403.974i	0.263564	−	0.431597i
$937$	1442.28			1.53925			0.769627	−	0.638494i	$-0.220442\pi$
$937$	1442.28			1.53925			0.769627	+	0.638494i	$0.220442\pi$
$938$			249.292i			0.265770i
$939$	−365.183	+	1298.69i	−0.388906	+	1.38306i
$940$	201.803			0.214684
$941$			617.890i			0.656631i	0.944568	+	0.328315i	$0.106481\pi$
$941$			617.890i			0.656631i	−0.944568	+	0.328315i	$0.893519\pi$
$942$	76.1380	+	21.4095i	0.0808259	+	0.0227277i
$943$	1006.33			1.06716
$944$		−	130.252i		−	0.137979i
$945$	108.700	+	117.044i	0.115026	+	0.123856i
$946$	534.455			0.564963
$947$			850.033i			0.897606i	0.893631	+	0.448803i	$0.148149\pi$
$947$			850.033i			0.897606i	−0.893631	+	0.448803i	$0.851851\pi$
$948$	−228.697	+	813.311i	−0.241242	+	0.857922i
$949$	855.242			0.901203
$950$		−	38.7086i		−	0.0407459i
$951$	−1068.88	−	300.563i	−1.12396	−	0.316050i
$952$	−99.4505			−0.104465
$953$			774.098i			0.812275i	0.913812	+	0.406138i	$0.133125\pi$
$953$			774.098i			0.812275i	−0.913812	+	0.406138i	$0.866875\pi$
$954$	−805.273	−	491.757i	−0.844101	−	0.515469i
$955$	−671.676			−0.703326
$956$		−	21.8608i		−	0.0228670i
$957$	−109.724	+	390.209i	−0.114654	+	0.407742i
$958$	−68.9533			−0.0719763
$959$		−	379.824i		−	0.396062i
$960$	−51.6620	−	14.5270i	−0.0538146	−	0.0151323i
$961$	30.2557			0.0314835
$962$			267.725i			0.278301i
$963$	423.450	−	693.417i	0.439720	−	0.720059i
$964$	−354.612			−0.367855
$965$		−	467.857i		−	0.484826i
$966$	−105.760	+	376.111i	−0.109482	+	0.389349i
$967$	−1167.79			−1.20764			−0.603819	−	0.797122i	$-0.706355\pi$
$967$	−1167.79			−1.20764			−0.603819	+	0.797122i	$0.706355\pi$
$968$		−	763.721i		−	0.788968i
$969$	−210.103	−	59.0795i	−0.216824	−	0.0609695i
$970$	−324.122			−0.334147
$971$		−	624.999i		−	0.643665i	−0.946797	−	0.321833i	$-0.895701\pi$
$971$		−	624.999i		−	0.643665i	0.946797	−	0.321833i	$-0.104299\pi$
$972$	476.291	−	96.6593i	0.490011	−	0.0994437i
$973$	682.492			0.701431
$974$		−	795.239i		−	0.816467i
$975$	75.5023	−	268.507i	0.0774383	−	0.275392i
$976$	287.052			0.294111
$977$		−	258.970i		−	0.265066i	−0.991179	−	0.132533i	$-0.957689\pi$
$977$		−	258.970i		−	0.265066i	0.991179	−	0.132533i	$-0.0423111\pi$
$978$	−57.9539	−	16.2962i	−0.0592575	−	0.0166628i
$979$	−221.539			−0.226291
$980$			31.3050i			0.0319438i
$981$	707.939	+	432.319i	0.721651	+	0.440692i
$982$	−175.693			−0.178913
$983$		−	1153.22i		−	1.17316i	−0.809890	−	0.586582i	$-0.800473\pi$
$983$		−	1153.22i		−	1.17316i	0.809890	−	0.586582i	$-0.199527\pi$
$984$	66.4095	−	236.170i	0.0674893	−	0.240010i
$985$	−217.051			−0.220357
$986$		−	128.420i		−	0.130243i
$987$	−344.793	−	96.9533i	−0.349334	−	0.0982303i
$988$	203.583			0.206056
$989$			665.204i			0.672603i
$990$	293.309	−	480.305i	0.296272	−	0.485157i
$991$	−977.180			−0.986054			−0.493027	−	0.870014i	$-0.664110\pi$
$991$	−977.180			−0.986054			−0.493027	+	0.870014i	$0.664110\pi$
$992$			178.102i			0.179538i
$993$	101.716	−	361.731i	0.102433	−	0.364281i
$994$	−378.825			−0.381111
$995$		−	653.089i		−	0.656371i
$996$	−581.189	−	163.426i	−0.583523	−	0.164083i
$997$	−1274.45			−1.27829			−0.639144	−	0.769087i	$-0.720711\pi$
$997$	−1274.45			−1.27829			−0.639144	+	0.769087i	$0.720711\pi$
$998$			1063.02i			1.06515i
$999$	−201.419	+	187.060i	−0.201621	+	0.187247i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.e.a.71.5	✓	16
3.2	odd	2	inner	210.3.e.a.71.13	yes	16
4.3	odd	2		1680.3.l.c.1121.7		16
5.2	odd	4		1050.3.c.c.449.30		32
5.3	odd	4		1050.3.c.c.449.3		32
5.4	even	2		1050.3.e.d.701.12		16
12.11	even	2		1680.3.l.c.1121.8		16
15.2	even	4		1050.3.c.c.449.4		32
15.8	even	4		1050.3.c.c.449.29		32
15.14	odd	2		1050.3.e.d.701.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.e.a.71.5	✓	16	1.1	even	1	trivial
210.3.e.a.71.13	yes	16	3.2	odd	2	inner
1050.3.c.c.449.3		32	5.3	odd	4
1050.3.c.c.449.4		32	15.2	even	4
1050.3.c.c.449.29		32	15.8	even	4
1050.3.c.c.449.30		32	5.2	odd	4
1050.3.e.d.701.4		16	15.14	odd	2
1050.3.e.d.701.12		16	5.4	even	2
1680.3.l.c.1121.7		16	4.3	odd	2
1680.3.l.c.1121.8		16	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(-0.812085 + 2.88800i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(4.08424 + 1.14846i) q^{6} -2.64575 q^{7} +2.82843i q^{8} +(-7.68104 - 4.69059i) q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +(-0.812085 + 2.88800i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(4.08424 + 1.14846i) q^{6} -2.64575 q^{7} +2.82843i q^{8} +(-7.68104 - 4.69059i) q^{9} -3.16228 q^{10} -19.7741i q^{11} +(1.62417 - 5.77599i) q^{12} +18.5947 q^{13} +3.74166i q^{14} +(6.45775 + 1.81588i) q^{15} +4.00000 q^{16} -13.2896i q^{17} +(-6.63350 + 10.8626i) q^{18} -5.47422 q^{19} +4.47214i q^{20} +(2.14857 - 7.64092i) q^{21} -27.9648 q^{22} -34.8062i q^{23} +(-8.16849 - 2.29692i) q^{24} -5.00000 q^{25} -26.2969i q^{26} +(19.7841 - 18.3736i) q^{27} +5.29150 q^{28} +6.83287i q^{29} +(2.56804 - 9.13264i) q^{30} -31.4842 q^{31} -5.65685i q^{32} +(57.1076 + 16.0583i) q^{33} -18.7944 q^{34} +5.91608i q^{35} +(15.3621 + 9.38119i) q^{36} -10.1809 q^{37} +7.74172i q^{38} +(-15.1005 + 53.7014i) q^{39} +6.32456 q^{40} +28.9124i q^{41} +(-10.8059 - 3.03854i) q^{42} -19.1117 q^{43} +39.5483i q^{44} +(-10.4885 + 17.1753i) q^{45} -49.2233 q^{46} -45.1245i q^{47} +(-3.24834 + 11.5520i) q^{48} +7.00000 q^{49} +7.07107i q^{50} +(38.3804 + 10.7923i) q^{51} -37.1894 q^{52} +74.1324i q^{53} +(-25.9843 - 27.9789i) q^{54} -44.2163 q^{55} -7.48331i q^{56} +(4.44553 - 15.8095i) q^{57} +9.66313 q^{58} -32.5630i q^{59} +(-12.9155 - 3.63175i) q^{60} +71.7631 q^{61} +44.5254i q^{62} +(20.3221 + 12.4101i) q^{63} -8.00000 q^{64} -41.5790i q^{65} +(22.7098 - 80.7624i) q^{66} +66.6261 q^{67} +26.5793i q^{68} +(100.520 + 28.2655i) q^{69} +8.36660 q^{70} +101.245i q^{71} +(13.2670 - 21.7253i) q^{72} +45.9939 q^{73} +14.3979i q^{74} +(4.06042 - 14.4400i) q^{75} +10.9484 q^{76} +52.3174i q^{77} +(75.9452 + 21.3553i) q^{78} -140.809 q^{79} -8.94427i q^{80} +(36.9967 + 72.0572i) q^{81} +40.8883 q^{82} -100.622i q^{83} +(-4.29715 + 15.2818i) q^{84} -29.7165 q^{85} +27.0280i q^{86} +(-19.7333 - 5.54887i) q^{87} +55.9297 q^{88} -11.2035i q^{89} +(24.2896 + 14.8330i) q^{90} -49.1969 q^{91} +69.6123i q^{92} +(25.5678 - 90.9263i) q^{93} -63.8157 q^{94} +12.2407i q^{95} +(16.3370 + 4.59384i) q^{96} +102.496 q^{97} -9.89949i q^{98} +(-92.7524 + 151.886i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} - 32 q^{4} + 16 q^{6} - 4 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 - 32 * q^4 + 16 * q^6 - 4 * q^9	\( 16 q - 8 q^{3} - 32 q^{4} + 16 q^{6} - 4 q^{9} + 16 q^{12} - 20 q^{15} + 64 q^{16} - 32 q^{18} + 48 q^{19} + 28 q^{21} - 96 q^{22} - 32 q^{24} - 80 q^{25} + 64 q^{27} - 88 q^{33} + 160 q^{34} + 8 q^{36} + 80 q^{37} + 156 q^{39} - 336 q^{43} - 80 q^{45} + 32 q^{46} - 32 q^{48} + 112 q^{49} + 84 q^{51} - 32 q^{54} - 80 q^{55} - 264 q^{57} + 96 q^{58} + 40 q^{60} + 112 q^{61} + 112 q^{63} - 128 q^{64} + 240 q^{67} + 8 q^{69} + 64 q^{72} + 48 q^{73} + 40 q^{75} - 96 q^{76} + 208 q^{78} + 8 q^{79} - 124 q^{81} - 608 q^{82} - 56 q^{84} + 120 q^{85} - 120 q^{87} + 192 q^{88} + 160 q^{90} - 56 q^{91} + 104 q^{93} + 32 q^{94} + 64 q^{96} - 192 q^{97} - 52 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 - 32 * q^4 + 16 * q^6 - 4 * q^9 + 16 * q^12 - 20 * q^15 + 64 * q^16 - 32 * q^18 + 48 * q^19 + 28 * q^21 - 96 * q^22 - 32 * q^24 - 80 * q^25 + 64 * q^27 - 88 * q^33 + 160 * q^34 + 8 * q^36 + 80 * q^37 + 156 * q^39 - 336 * q^43 - 80 * q^45 + 32 * q^46 - 32 * q^48 + 112 * q^49 + 84 * q^51 - 32 * q^54 - 80 * q^55 - 264 * q^57 + 96 * q^58 + 40 * q^60 + 112 * q^61 + 112 * q^63 - 128 * q^64 + 240 * q^67 + 8 * q^69 + 64 * q^72 + 48 * q^73 + 40 * q^75 - 96 * q^76 + 208 * q^78 + 8 * q^79 - 124 * q^81 - 608 * q^82 - 56 * q^84 + 120 * q^85 - 120 * q^87 + 192 * q^88 + 160 * q^90 - 56 * q^91 + 104 * q^93 + 32 * q^94 + 64 * q^96 - 192 * q^97 - 52 * q^99

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